id	sid	tid	token	lemma	pos
m-1112	1	1	ijo	ijo	PROPN
m-1112	1	2	international	international	PROPN
m-1112	1	3	journal	journal	PROPN
m-1112	1	4	of	of	ADP
m-1112	1	5	mathematics	mathematics	PROPN
m-1112	1	6	(	(	PUNCT
m-1112	1	7	issn	issn	PROPN
m-1112	1	8	:	:	PUNCT
m-1112	1	9	2992	2992	NUM
m-1112	1	10	-	-	SYM
m-1112	1	11	4421	4421	NUM
m-1112	1	12	)	)	PUNCT
m-1112	1	13	volume	volume	NOUN
m-1112	1	14	08	08	NUM
m-1112	2	1	|	|	ADV
m-1112	2	2	issue	issue	NOUN
m-1112	2	3	08	08	NUM
m-1112	3	1	|	|	ADV
m-1112	3	2	august	august	PROPN
m-1112	3	3	2025	2025	NUM
m-1112	3	4	|	|	ADV
m-1112	3	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3	6	ijo	ijo	NOUN
m-1112	3	7	journals	journal	NOUN
m-1112	3	8	the	the	DET
m-1112	3	9	polynomials	polynomial	NOUN
m-1112	3	10	[	[	PUNCT
m-1112	3	11	n	n	CCONJ
m-1112	3	12	..	..	PUNCT
m-1112	3	13	knots	knot	NOUN
m-1112	3	14	–	–	PUNCT
m-1112	3	15	figures	figure	NOUN
m-1112	3	16	]	]	PUNCT
m-1112	3	17	edge	edge	NOUN
m-1112	3	18	points	point	NOUN
m-1112	3	19	vibration	vibration	NOUN
m-1112	3	20	&	&	CCONJ
m-1112	3	21	m	m	NOUN
m-1112	3	22	-	-	NOUN
m-1112	3	23	geometry	geometry	NOUN
m-1112	3	24	by	by	ADP
m-1112	3	25	markos	markos	PROPN
m-1112	3	26	georgallides	georgallide	NOUN
m-1112	3	27	1larnaca	1larnaca	PROPN
m-1112	3	28	–	–	PUNCT
m-1112	3	29	cyprus	cyprus	PROPN
m-1112	3	30	(	(	PUNCT
m-1112	3	31	expelled	expel	VERB
m-1112	3	32	from	from	ADP
m-1112	3	33	varosha	varosha	PROPN
m-1112	3	34	-	-	PUNCT
m-1112	3	35	famagusta	famagusta	PROPN
m-1112	3	36	town	town	NOUN
m-1112	3	37	occupied	occupy	VERB
m-1112	3	38	by	by	ADP
m-1112	3	39	the	the	DET
m-1112	3	40	barbaric	barbaric	ADJ
m-1112	3	41	turks	turks	PROPN
m-1112	3	42	,	,	PUNCT
m-1112	3	43	in	in	ADP
m-1112	3	44	aug	aug	PROPN
m-1112	3	45	1974	1974	NUM
m-1112	3	46	)	)	PUNCT
m-1112	3	47	cyprus	cyprus	PROPN
m-1112	3	48	,	,	PUNCT
m-1112	3	49	civil	civil	ADJ
m-1112	3	50	structural	structural	ADJ
m-1112	3	51	o	o	NOUN
m-1112	3	52	engineer	engineer	NOUN
m-1112	3	53	(	(	PUNCT
m-1112	3	54	natua	natua	PROPN
m-1112	3	55	)	)	PUNCT
m-1112	3	56	,	,	PUNCT
m-1112	3	57	athens	athens	PROPN
m-1112	3	58	.	.	PUNCT
m-1112	4	1	abstract	abstract	ADJ
m-1112	4	2	the	the	DET
m-1112	4	3	interactions	interaction	NOUN
m-1112	4	4	:	:	PUNCT
m-1112	4	5	one	one	NUM
m-1112	4	6	of	of	ADP
m-1112	4	7	the	the	DET
m-1112	4	8	most	most	ADV
m-1112	4	9	important	important	ADJ
m-1112	4	10	concept	concept	NOUN
m-1112	4	11	in	in	ADP
m-1112	4	12	geometry	geometry	NOUN
m-1112	4	13	is	be	AUX
m-1112	4	14	,	,	PUNCT
m-1112	4	15	distance	distance	NOUN
m-1112	4	16	,	,	PUNCT
m-1112	4	17	which	which	PRON
m-1112	4	18	is	be	AUX
m-1112	4	19	the	the	DET
m-1112	4	20	quanta	quanta	PROPN
m-1112	4	21	in	in	ADP
m-1112	4	22	egeometry	egeometry	NOUN
m-1112	4	23	,	,	PUNCT
m-1112	4	24	while	while	SCONJ
m-1112	4	25	in	in	ADP
m-1112	4	26	material	material	NOUN
m-1112	4	27	-	-	PUNCT
m-1112	4	28	geometry	geometry	NOUN
m-1112	4	29	the	the	DET
m-1112	4	30	composition	composition	NOUN
m-1112	4	31	of	of	ADP
m-1112	4	32	opposite	opposite	ADJ
m-1112	4	33	,	,	PUNCT
m-1112	4	34	where	where	SCONJ
m-1112	4	35	the	the	DET
m-1112	4	36	material	material	NOUN
m-1112	4	37	point	point	NOUN
m-1112	4	38	is	be	AUX
m-1112	4	39	the	the	DET
m-1112	4	40	quanta	quanta	PROPN
m-1112	4	41	in	in	ADP
m-1112	4	42	chemistry	chemistry	NOUN
m-1112	4	43	and	and	CCONJ
m-1112	4	44	physics	physics	NOUN
m-1112	4	45	.	.	PUNCT
m-1112	5	1	as	as	ADP
m-1112	5	2	in	in	ADP
m-1112	5	3	algebra	algebra	NOUN
m-1112	5	4	zero	zero	NUM
m-1112	5	5	,	,	PUNCT
m-1112	5	6	0	0	NUM
m-1112	5	7	,	,	PUNCT
m-1112	5	8	is	be	AUX
m-1112	5	9	the	the	DET
m-1112	5	10	master	master	NOUN
m-1112	5	11	-	-	PUNCT
m-1112	5	12	key	key	NOUN
m-1112	5	13	number	number	NOUN
m-1112	5	14	for	for	ADP
m-1112	5	15	all	all	DET
m-1112	5	16	positive	positive	ADJ
m-1112	5	17	and	and	CCONJ
m-1112	5	18	negative	negative	ADJ
m-1112	5	19	numbers	number	NOUN
m-1112	5	20	and	and	CCONJ
m-1112	5	21	this	this	PRON
m-1112	5	22	because	because	SCONJ
m-1112	5	23	their	their	PRON
m-1112	5	24	sum	sum	NOUN
m-1112	5	25	and	and	CCONJ
m-1112	5	26	multiplication	multiplication	NOUN
m-1112	5	27	becomes	become	VERB
m-1112	5	28	zero	zero	NUM
m-1112	5	29	,	,	PUNCT
m-1112	5	30	and	and	CCONJ
m-1112	5	31	the	the	DET
m-1112	5	32	same	same	ADJ
m-1112	5	33	on	on	ADP
m-1112	5	34	any	any	DET
m-1112	5	35	coordinate	coordinate	NOUN
m-1112	5	36	-	-	PUNCT
m-1112	5	37	system	system	NOUN
m-1112	5	38	where	where	SCONJ
m-1112	5	39	±	±	NUM
m-1112	5	40	axes	axis	NOUN
m-1112	5	41	pass	pass	VERB
m-1112	5	42	from	from	ADP
m-1112	5	43	zero	zero	NUM
m-1112	5	44	.	.	PUNCT
m-1112	6	1	in	in	ADP
m-1112	6	2	pns	pns	PROPN
m-1112	6	3	space	space	NOUN
m-1112	6	4	,	,	PUNCT
m-1112	6	5	the	the	DET
m-1112	6	6	rolling	rolling	NOUN
m-1112	6	7	of	of	ADP
m-1112	6	8	the	the	DET
m-1112	6	9	positive	positive	ADJ
m-1112	6	10	⊕	⊕	PROPN
m-1112	6	11	constituent	constituent	NOUN
m-1112	6	12	on	on	ADP
m-1112	6	13	the	the	DET
m-1112	6	14	negative	negative	ADJ
m-1112	6	15	⊝	⊝	NOUN
m-1112	6	16	constituent	constituent	NOUN
m-1112	6	17	,	,	PUNCT
m-1112	6	18	creates	create	VERB
m-1112	6	19	the	the	DET
m-1112	6	20	neutral	neutral	ADJ
m-1112	6	21	material	material	NOUN
m-1112	6	22	point	point	NOUN
m-1112	6	23	which	which	DET
m-1112	6	24	equilibrium	equilibrium	NOUN
m-1112	6	25	.	.	PUNCT
m-1112	7	1	angular	angular	ADJ
m-1112	7	2	-	-	PUNCT
m-1112	7	3	momentum	momentum	NOUN
m-1112	7	4	is	be	AUX
m-1112	7	5	identical	identical	ADJ
m-1112	7	6	with	with	ADP
m-1112	7	7	spin	spin	NOUN
m-1112	7	8	and	and	CCONJ
m-1112	7	9	consists	consist	VERB
m-1112	7	10	the	the	DET
m-1112	7	11	first	first	ADJ
m-1112	7	12	-	-	PUNCT
m-1112	7	13	discrete	discrete	NOUN
m-1112	7	14	-	-	PUNCT
m-1112	7	15	energy	energy	NOUN
m-1112	7	16	-	-	PUNCT
m-1112	7	17	monad	monad	PROPN
m-1112	7	18	which	which	PRON
m-1112	7	19	occupies	occupy	VERB
m-1112	7	20	,	,	PUNCT
m-1112	7	21	discrete	discrete	ADJ
m-1112	7	22	value	value	NOUN
m-1112	7	23	and	and	CCONJ
m-1112	7	24	direction	direction	NOUN
m-1112	7	25	,	,	PUNCT
m-1112	7	26	in	in	ADP
m-1112	7	27	contradiction	contradiction	NOUN
m-1112	7	28	to	to	ADP
m-1112	7	29	the	the	DET
m-1112	7	30	point	point	NOUN
m-1112	7	31	which	which	PRON
m-1112	7	32	is	be	AUX
m-1112	7	33	nothing	nothing	PRON
m-1112	7	34	,	,	PUNCT
m-1112	7	35	dimensionless	dimensionless	NOUN
m-1112	7	36	and	and	CCONJ
m-1112	7	37	without	without	ADP
m-1112	7	38	any	any	DET
m-1112	7	39	direction	direction	NOUN
m-1112	7	40	.	.	PUNCT
m-1112	8	1	quaternions	quaternion	NOUN
m-1112	8	2	[	[	X
m-1112	8	3	(	(	PUNCT
m-1112	8	4	+	+	ADJ
m-1112	8	5	)	)	PUNCT
m-1112	8	6	↻	↻	NOUN
m-1112	8	7	↺	↺	NOUN
m-1112	8	8	(	(	PUNCT
m-1112	8	9	-	-	PUNCT
m-1112	8	10	)	)	PUNCT
m-1112	8	11	]	]	PUNCT
m-1112	8	12	≡	≡	PROPN
m-1112	8	13	box	box	PROPN
m-1112	8	14	𝐁	𝐁	PROPN
m-1112	8	15	𝐑	𝐑	PROPN
m-1112	8	16	=	=	PUNCT
m-1112	8	17	𝐀𝐁	𝐀𝐁	PROPN
m-1112	8	18	carries	carry	VERB
m-1112	8	19	the	the	DET
m-1112	8	20	principal	principal	ADJ
m-1112	8	21	stress	stress	NOUN
m-1112	9	1	𝛔	𝛔	PROPN
m-1112	9	2	𝐀	𝐀	PROPN
m-1112	9	3	,	,	PUNCT
m-1112	9	4	𝛔	𝛔	PROPN
m-1112	9	5	𝐁	𝐁	NOUN
m-1112	9	6	between	between	ADP
m-1112	9	7	points	point	NOUN
m-1112	9	8	a(+	a(+	NOUN
m-1112	9	9	)	)	PUNCT
m-1112	9	10	,	,	PUNCT
m-1112	9	11	b(-	b(-	PROPN
m-1112	9	12	)	)	PUNCT
m-1112	9	13	which	which	PRON
m-1112	9	14	σ	σ	NOUN
m-1112	9	15	,	,	PUNCT
m-1112	9	16	as	as	SCONJ
m-1112	9	17	centripetal	centripetal	NOUN
m-1112	9	18	-	-	PUNCT
m-1112	9	19	acceleration	acceleration	NOUN
m-1112	9	20	is	be	AUX
m-1112	9	21	the	the	DET
m-1112	9	22	minimum	minimum	ADJ
m-1112	9	23	energy	energy	NOUN
m-1112	9	24	becoming	become	VERB
m-1112	9	25	from	from	ADP
m-1112	9	26	the	the	DET
m-1112	9	27	in	in	ADP
m-1112	9	28	-	-	PUNCT
m-1112	9	29	storage	storage	NOUN
m-1112	9	30	ab	ab	NOUN
m-1112	9	31	acceleration	acceleration	NOUN
m-1112	9	32	and	and	CCONJ
m-1112	9	33	is	be	AUX
m-1112	9	34	equal	equal	ADJ
m-1112	9	35	to	to	ADP
m-1112	9	36	the	the	DET
m-1112	9	37	gravity	gravity	NOUN
m-1112	9	38	force	force	NOUN
m-1112	9	39	g	g	NOUN
m-1112	9	40	.	.	PUNCT
m-1112	10	1	[	[	X
m-1112	10	2	108	108	NUM
m-1112	10	3	–	–	PUNCT
m-1112	10	4	110	110	NUM
m-1112	10	5	]	]	PUNCT
m-1112	10	6	.	.	PUNCT
m-1112	11	1	because	because	SCONJ
m-1112	11	2	of	of	ADP
m-1112	11	3	the	the	DET
m-1112	11	4	revolving	revolve	VERB
m-1112	11	5	and	and	CCONJ
m-1112	11	6	periodic	periodic	ADJ
m-1112	11	7	acceleration	acceleration	NOUN
m-1112	11	8	of	of	ADP
m-1112	11	9	gravity	gravity	NOUN
m-1112	11	10	g	g	PROPN
m-1112	11	11	≡	≡	PROPN
m-1112	11	12			PROPN
m-1112	11	13	σ	σ	PROPN
m-1112	11	14	exists	exist	VERB
m-1112	11	15	as	as	ADP
m-1112	11	16	the	the	DET
m-1112	11	17	first	first	ADJ
m-1112	11	18	energy	energy	NOUN
m-1112	11	19	-	-	PUNCT
m-1112	11	20	box-𝐁	box-𝐁	NOUN
m-1112	11	21	𝐑	𝐑	PROPN
m-1112	11	22	,	,	PUNCT
m-1112	11	23	while	while	SCONJ
m-1112	11	24	in	in	ADP
m-1112	11	25	the	the	DET
m-1112	11	26	second	second	ADJ
m-1112	11	27	box	box	NOUN
m-1112	11	28	𝐁𝐏	𝐁𝐏	PROPN
m-1112	11	29	is	be	AUX
m-1112	11	30	followed	follow	VERB
m-1112	11	31	the	the	DET
m-1112	11	32	local	local	ADJ
m-1112	11	33	-	-	PUNCT
m-1112	11	34	extreme	extreme	ADJ
m-1112	11	35	-	-	PUNCT
m-1112	11	36	case	case	NOUN
m-1112	11	37	where	where	SCONJ
m-1112	11	38	gravity	gravity	NOUN
m-1112	11	39	g	g	PROPN
m-1112	11	40	≡	≡	PROPN
m-1112	11	41			PROPN
m-1112	11	42	σ	σ	PROPN
m-1112	11	43	,	,	PUNCT
m-1112	11	44	and	and	CCONJ
m-1112	11	45	is	be	AUX
m-1112	11	46	altered	alter	VERB
m-1112	11	47	locally	locally	ADV
m-1112	11	48	by	by	ADP
m-1112	11	49	changing	change	VERB
m-1112	11	50	the	the	DET
m-1112	11	51	principal	principal	ADJ
m-1112	11	52	-	-	PUNCT
m-1112	11	53	stress	stress	NOUN
m-1112	11	54	σ	σ	NOUN
m-1112	11	55	with	with	ADP
m-1112	11	56	an	an	DET
m-1112	11	57	local	local	ADJ
m-1112	11	58	-	-	PUNCT
m-1112	11	59	uniform	uniform	NOUN
m-1112	11	60	-	-	PUNCT
m-1112	11	61	pressure	pressure	NOUN
m-1112	11	62	→	→	PUNCT
m-1112	11	63	𝐠𝐋	𝐠𝐋	ADJ
m-1112	11	64	≡	≡	PROPN
m-1112	12	1	g	g	PROPN
m-1112	12	2	k	k	PROPN
m-1112	12	3	=	=	PUNCT
m-1112	12	4	g	g	PROPN
m-1112	12	5	.	.	PUNCT
m-1112	13	1	[	[	PUNCT
m-1112	13	2	force	force	NOUN
m-1112	13	3	/	/	SYM
m-1112	13	4	area	area	NOUN
m-1112	13	5	]	]	PUNCT
m-1112	14	1	=	=	PUNCT
m-1112	14	2	g	g	PROPN
m-1112	14	3	←	←	PROPN
m-1112	14	4	i.e.	i.e.	X
m-1112	14	5	the	the	DET
m-1112	14	6	minimum	minimum	ADJ
m-1112	14	7	local	local	ADJ
m-1112	14	8	energy	energy	NOUN
m-1112	14	9	acceleration	acceleration	NOUN
m-1112	14	10	is	be	AUX
m-1112	14	11	the	the	DET
m-1112	14	12	known	known	ADJ
m-1112	14	13	,	,	PUNCT
m-1112	14	14	universal	universal	ADJ
m-1112	14	15	gravitational	gravitational	ADJ
m-1112	14	16	-	-	PUNCT
m-1112	14	17	constant	constant	ADJ
m-1112	14	18	g	g	NOUN
m-1112	14	19	=	=	SYM
m-1112	14	20	g	g	NOUN
m-1112	14	21	k	k	PROPN
m-1112	14	22	=	=	PUNCT
m-1112	14	23	𝐤𝐄	𝐤𝐄	NOUN
m-1112	14	24	g	g	NOUN
m-1112	14	25	=	=	SYM
m-1112	14	26	𝐤𝐋	𝐤𝐋	PROPN
m-1112	14	27	σ	σ	NOUN
m-1112	14	28	,	,	PUNCT
m-1112	14	29	such	such	ADJ
m-1112	14	30	for	for	ADP
m-1112	14	31	macrocosm	macrocosm	PROPN
m-1112	14	32	and	and	CCONJ
m-1112	14	33	for	for	ADP
m-1112	14	34	microcosm	microcosm	NOUN
m-1112	14	35	,	,	PUNCT
m-1112	14	36	obeying	obey	VERB
m-1112	14	37	the	the	DET
m-1112	14	38	newton`s	newton`s	NOUN
m-1112	14	39	laws	law	NOUN
m-1112	14	40	of	of	ADP
m-1112	14	41	motion	motion	NOUN
m-1112	14	42	.	.	PUNCT
m-1112	15	1	g	g	PROPN
m-1112	15	2	⏊	⏊	PROPN
m-1112	15	3	σ	σ	PROPN
m-1112	15	4	this	this	DET
m-1112	15	5	energy	energy	NOUN
m-1112	15	6	in	in	ADP
m-1112	15	7	hydrogen	hydrogen	NOUN
m-1112	15	8	-	-	PUNCT
m-1112	15	9	cave	cave	NOUN
m-1112	15	10	as	as	ADP
m-1112	15	11	e	e	NOUN
m-1112	15	12	-	-	NOUN
m-1112	15	13	m	m	NOUN
m-1112	15	14	,	,	PUNCT
m-1112	15	15	conductor	conductor	NOUN
m-1112	15	16	≡	≡	PROPN
m-1112	15	17	edge	edge	NOUN
m-1112	15	18	points	point	NOUN
m-1112	15	19	vibration	vibration	NOUN
m-1112	15	20	≡	≡	PROPN
m-1112	15	21	the	the	DET
m-1112	15	22	pin	pin	NOUN
m-1112	15	23	of	of	ADP
m-1112	15	24	atom	atom	NOUN
m-1112	15	25	→	→	PUNCT
m-1112	15	26	plug	plug	NOUN
m-1112	15	27	into	into	ADP
m-1112	15	28	their	their	PRON
m-1112	15	29	sockets	socket	NOUN
m-1112	15	30	,	,	PUNCT
m-1112	15	31	which	which	PRON
m-1112	15	32	are	be	AUX
m-1112	15	33	the	the	DET
m-1112	15	34	orbit	orbit	NOUN
m-1112	15	35	–	–	PUNCT
m-1112	15	36	bracket	bracket	NOUN
m-1112	15	37	–	–	PUNCT
m-1112	15	38	hooks	hook	NOUN
m-1112	15	39	≡	≡	PROPN
m-1112	15	40	the	the	DET
m-1112	15	41	hands	hand	NOUN
m-1112	15	42	of	of	ADP
m-1112	15	43	atoms	atom	NOUN
m-1112	15	44	←	←	PROPN
m-1112	15	45	i.e.	i.e.	X
m-1112	15	46	the	the	DET
m-1112	15	47	atoms	atom	NOUN
m-1112	15	48	plug	plug	VERB
m-1112	15	49	with	with	ADP
m-1112	15	50	their	their	PRON
m-1112	15	51	pins	pin	NOUN
m-1112	15	52	into	into	ADP
m-1112	15	53	the	the	DET
m-1112	15	54	other	other	ADJ
m-1112	15	55	atoms	atom	NOUN
m-1112	15	56	-	-	PUNCT
m-1112	15	57	drains	drain	NOUN
m-1112	15	58	=	=	NOUN
m-1112	15	59	holes	hole	NOUN
m-1112	15	60	,	,	PUNCT
m-1112	15	61	and	and	CCONJ
m-1112	15	62	so	so	ADV
m-1112	15	63	bond	bond	NOUN
m-1112	15	64	and	and	CCONJ
m-1112	15	65	carry	carry	VERB
m-1112	15	66	informations	information	NOUN
m-1112	15	67	.	.	PUNCT
m-1112	16	1	1	1	NUM
m-1112	16	2	https://doi.org/10.5281/zenodo.16737369	https://doi.org/10.5281/zenodo.16737369	NOUN
m-1112	16	3	mailto:georgallides.marcos@cytanet.com.cy	mailto:georgallides.marcos@cytanet.com.cy	NOUN
m-1112	16	4	2	2	NUM
m-1112	16	5	the	the	DET
m-1112	16	6	fundamental	fundamental	ADJ
m-1112	16	7	particles	particle	NOUN
m-1112	16	8	origination	origination	NOUN
m-1112	16	9	mechanism	mechanism	NOUN
m-1112	16	10	in	in	ADP
m-1112	16	11	mfmf	mfmf	PROPN
m-1112	16	12	pns	pns	PROPN
m-1112	16	13	caves	cave	NOUN
m-1112	16	14	.	.	PUNCT
m-1112	17	1	this	this	DET
m-1112	17	2	resonance	resonance	NOUN
m-1112	17	3	frequency	frequency	NOUN
m-1112	17	4	of	of	ADP
m-1112	17	5	hydrogen	hydrogen	NOUN
m-1112	17	6	is	be	AUX
m-1112	17	7	common	common	ADJ
m-1112	17	8	to	to	ADP
m-1112	17	9	all	all	DET
m-1112	17	10	atoms	atom	NOUN
m-1112	17	11	and	and	CCONJ
m-1112	17	12	to	to	ADP
m-1112	17	13	all	all	DET
m-1112	17	14	compounds	compound	NOUN
m-1112	17	15	in	in	ADP
m-1112	17	16	this	this	DET
m-1112	17	17	cosmos	cosmos	NOUN
m-1112	17	18	.	.	PUNCT
m-1112	18	1	the	the	DET
m-1112	18	2	energy	energy	NOUN
m-1112	18	3	-	-	PUNCT
m-1112	18	4	quaternion	quaternion	NOUN
m-1112	18	5	w	w	PROPN
m-1112	18	6	̅̅	̅̅	PROPN
m-1112	18	7	̅	̅	NOUN
m-1112	18	8	,	,	PUNCT
m-1112	18	9	b̅	b̅	PROPN
m-1112	18	10	,	,	PUNCT
m-1112	18	11	monad	monad	PROPN
m-1112	18	12	-	-	PUNCT
m-1112	18	13	magnitudes	magnitude	NOUN
m-1112	18	14	exist	exist	VERB
m-1112	18	15	as	as	ADP
m-1112	18	16	dualnature	dualnature	NOUN
m-1112	18	17	for	for	ADP
m-1112	18	18	any	any	DET
m-1112	18	19	{	{	PUNCT
m-1112	18	20	⊕	⊕	NOUN
m-1112	18	21	,	,	PUNCT
m-1112	18	22	⊝	⊝	PROPN
m-1112	18	23	}	}	PUNCT
m-1112	18	24	,	,	PUNCT
m-1112	18	25	{	{	PUNCT
m-1112	18	26	position	position	NOUN
m-1112	18	27	,	,	PUNCT
m-1112	18	28	motion	motion	NOUN
m-1112	18	29	}	}	PUNCT
m-1112	18	30	,	,	PUNCT
m-1112	18	31	{	{	PUNCT
m-1112	18	32	universe	universe	NOUN
m-1112	18	33	,	,	PUNCT
m-1112	18	34	black	black	NOUN
m-1112	18	35	-	-	PUNCT
m-1112	18	36	holes	hole	NOUN
m-1112	18	37	}	}	PUNCT
m-1112	18	38	,	,	PUNCT
m-1112	18	39	{	{	PUNCT
m-1112	18	40	gravity	gravity	NOUN
m-1112	18	41	,	,	PUNCT
m-1112	18	42	antigravity	antigravity	NOUN
m-1112	18	43	}	}	PUNCT
m-1112	18	44	,	,	PUNCT
m-1112	18	45	{	{	PUNCT
m-1112	18	46	action	action	NOUN
m-1112	18	47	→	→	PUNCT
m-1112	18	48	.	.	PUNCT
m-1112	19	1	←	←	PROPN
m-1112	19	2	reaction	reaction	NOUN
m-1112	19	3	}	}	PUNCT
m-1112	19	4	,	,	PUNCT
m-1112	19	5	edge	edge	NOUN
m-1112	19	6	points	point	NOUN
m-1112	19	7	vibration	vibration	NOUN
m-1112	19	8	creating	create	VERB
m-1112	19	9	electric	electric	ADJ
m-1112	19	10	=	=	PUNCT
m-1112	20	1	[	[	X
m-1112	20	2	⊕	⊕	NOUN
m-1112	20	3	]	]	PUNCT
m-1112	20	4	and	and	CCONJ
m-1112	20	5	magnetic	magnetic	ADJ
m-1112	20	6	=	=	PUNCT
m-1112	21	1	[	[	X
m-1112	21	2	⊝	⊝	X
m-1112	21	3	]	]	X
m-1112	21	4	forces	force	NOUN
m-1112	21	5	as	as	ADP
m-1112	21	6	[	[	X
m-1112	21	7	⊕↔⊝	⊕↔⊝	X
m-1112	21	8	]	]	X
m-1112	21	9	,	,	PUNCT
m-1112	21	10	the	the	DET
m-1112	21	11	light	light	NOUN
m-1112	21	12	and	and	CCONJ
m-1112	21	13	others	other	NOUN
m-1112	21	14	.the	.the	PRON
m-1112	22	1	stplline	stplline	PROPN
m-1112	22	2	conductors	conductor	NOUN
m-1112	22	3	on	on	ADP
m-1112	22	4	the	the	DET
m-1112	22	5	[	[	X
m-1112	22	6	stpl]mechanism	stpl]mechanism	PROPN
m-1112	22	7	,	,	PUNCT
m-1112	22	8	are	be	AUX
m-1112	22	9	the	the	DET
m-1112	22	10	physical	physical	ADJ
m-1112	22	11	-	-	PUNCT
m-1112	22	12	rotors	rotor	NOUN
m-1112	22	13	for	for	ADP
m-1112	22	14	the	the	DET
m-1112	22	15	origination	origination	NOUN
m-1112	22	16	of	of	ADP
m-1112	22	17	the	the	DET
m-1112	22	18	cosmic	cosmic	ADJ
m-1112	22	19	–	–	PUNCT
m-1112	22	20	particles	particle	NOUN
m-1112	22	21	which	which	PRON
m-1112	22	22	transfer	transfer	VERB
m-1112	22	23	informations	information	NOUN
m-1112	22	24	as	as	SCONJ
m-1112	22	25	the	the	DET
m-1112	22	26	signals	signal	NOUN
m-1112	22	27	spectrum	spectrum	VERB
m-1112	22	28	.[110	.[110	PROPN
m-1112	22	29	]	]	PUNCT
m-1112	22	30	from	from	ADP
m-1112	22	31	mechanics	mechanic	NOUN
m-1112	22	32	-	-	PUNCT
m-1112	22	33	physics	physics	NOUN
m-1112	22	34	,	,	PUNCT
m-1112	22	35	all	all	DET
m-1112	22	36	systems	system	NOUN
m-1112	22	37	possessing	possess	VERB
m-1112	22	38	elasticity	elasticity	NOUN
m-1112	22	39	≡	≡	PROPN
m-1112	22	40	motion	motion	NOUN
m-1112	22	41	and	and	CCONJ
m-1112	22	42	reaction	reaction	NOUN
m-1112	22	43	to	to	ADP
m-1112	22	44	the	the	DET
m-1112	22	45	motion	motion	NOUN
m-1112	22	46	,	,	PUNCT
m-1112	22	47	the	the	DET
m-1112	22	48	called	call	VERB
m-1112	22	49	mass	mass	NOUN
m-1112	22	50	,	,	PUNCT
m-1112	22	51	are	be	AUX
m-1112	22	52	capable	capable	ADJ
m-1112	22	53	of	of	ADP
m-1112	22	54	free	free	ADJ
m-1112	22	55	vibration	vibration	NOUN
m-1112	22	56	or	or	CCONJ
m-1112	22	57	vibration	vibration	NOUN
m-1112	22	58	≡	≡	PROPN
m-1112	23	1	periodic	periodic	ADJ
m-1112	23	2	motion	motion	NOUN
m-1112	23	3	taking	take	VERB
m-1112	23	4	place	place	NOUN
m-1112	23	5	in	in	ADP
m-1112	23	6	the	the	DET
m-1112	23	7	absence	absence	NOUN
m-1112	23	8	of	of	ADP
m-1112	23	9	external	external	ADJ
m-1112	23	10	excitation	excitation	NOUN
m-1112	23	11	.this	.this	PRON
m-1112	23	12	principle	principle	ADJ
m-1112	23	13	issues	issue	NOUN
m-1112	23	14	for	for	ADP
m-1112	23	15	both	both	DET
m-1112	23	16	systems	system	NOUN
m-1112	23	17	closed	close	VERB
m-1112	23	18	{	{	PUNCT
m-1112	23	19	the	the	DET
m-1112	23	20	atoms	atom	NOUN
m-1112	23	21	nucleus	nucleus	NOUN
m-1112	23	22	}	}	PUNCT
m-1112	23	23	or	or	CCONJ
m-1112	23	24	open	open	ADJ
m-1112	23	25	systems	system	NOUN
m-1112	23	26	{	{	PUNCT
m-1112	23	27	the	the	DET
m-1112	23	28	orbitals	orbital	NOUN
m-1112	23	29	}	}	PUNCT
m-1112	23	30	.	.	PUNCT
m-1112	24	1	for	for	ADP
m-1112	24	2	instance	instance	NOUN
m-1112	24	3	,	,	PUNCT
m-1112	24	4	in	in	ADP
m-1112	24	5	order	order	NOUN
m-1112	24	6	that	that	SCONJ
m-1112	24	7	shifting	shift	VERB
m-1112	24	8	of	of	ADP
m-1112	24	9	an	an	DET
m-1112	24	10	u	u	ADJ
m-1112	24	11	-	-	PROPN
m-1112	24	12	d	d	NOUN
m-1112	24	13	-	-	NOUN
m-1112	24	14	quarks	quarks	NOUN
m-1112	24	15	from	from	ADP
m-1112	24	16	an	an	DET
m-1112	24	17	anti	anti	ADJ
m-1112	24	18	-	-	NOUN
m-1112	24	19	proton	proton	NOUN
m-1112	24	20	into	into	ADP
m-1112	24	21	a	a	DET
m-1112	24	22	proton	proton	NOUN
m-1112	24	23	,	,	PUNCT
m-1112	24	24	the	the	DET
m-1112	24	25	spin	spin	NOUN
m-1112	24	26	-	-	PUNCT
m-1112	24	27	pair	pair	NOUN
m-1112	24	28	requires	require	VERB
m-1112	24	29	extra	extra	ADJ
m-1112	24	30	input	input	NOUN
m-1112	24	31	of	of	ADP
m-1112	24	32	energy	energy	NOUN
m-1112	24	33	in	in	ADP
m-1112	24	34	(	(	PUNCT
m-1112	24	35	mev	mev	PROPN
m-1112	24	36	)	)	PUNCT
m-1112	24	37	,	,	PUNCT
m-1112	24	38	so	so	SCONJ
m-1112	24	39	that	that	PRON
m-1112	24	40	would	would	AUX
m-1112	24	41	the	the	DET
m-1112	24	42	proton	proton	NOUN
m-1112	24	43	paired	pair	VERB
m-1112	24	44	with	with	ADP
m-1112	24	45	a	a	DET
m-1112	24	46	neutron	neutron	NOUN
m-1112	24	47	and	and	CCONJ
m-1112	24	48	be	be	AUX
m-1112	24	49	stable	stable	ADJ
m-1112	24	50	.	.	PUNCT
m-1112	25	1	transfer	transfer	NOUN
m-1112	25	2	informations	information	NOUN
m-1112	25	3	as	as	ADP
m-1112	25	4	the	the	DET
m-1112	25	5	signals	signal	NOUN
m-1112	25	6	.	.	PUNCT
m-1112	26	1	vibration	vibration	NOUN
m-1112	26	2	in	in	ADP
m-1112	26	3	a	a	DET
m-1112	26	4	cave	cave	NOUN
m-1112	26	5	∆	∆	PROPN
m-1112	26	6	,	,	PUNCT
m-1112	26	7	means	mean	VERB
m-1112	26	8	the	the	DET
m-1112	26	9	wave	wave	NOUN
m-1112	26	10	pattern	pattern	NOUN
m-1112	26	11	.	.	PUNCT
m-1112	27	1	cave	cave	NOUN
m-1112	27	2	–	–	PUNCT
m-1112	27	3	spin-	spin-	X
m-1112	27	4	�	�	SYM
m-1112	27	5	̅	̅	NOUN
m-1112	27	6	�	�	PROPN
m-1112	27	7	of	of	ADP
m-1112	27	8	pns	pns	PROPN
m-1112	27	9	space	space	NOUN
m-1112	27	10	is	be	AUX
m-1112	27	11	�	�	NOUN
m-1112	27	12	̅	̅	NOUN
m-1112	27	13	�	�	NOUN
m-1112	27	14	=	=	SYM
m-1112	28	1	r	r	NOUN
m-1112	28	2	m	m	NOUN
m-1112	28	3	v	v	NOUN
m-1112	29	1	and	and	CCONJ
m-1112	29	2	is	be	AUX
m-1112	29	3	the	the	DET
m-1112	29	4	first	first	ADJ
m-1112	29	5	monad	monad	PROPN
m-1112	29	6	occupying	occupy	VERB
m-1112	29	7	4	4	NUM
m-1112	29	8	-	-	PUNCT
m-1112	29	9	spaces	space	NOUN
m-1112	29	10	,	,	PUNCT
m-1112	29	11	i.e.	i.e.	X
m-1112	29	12	from	from	ADP
m-1112	29	13	number	number	NOUN
m-1112	29	14	n	n	NOUN
m-1112	29	15	,	,	PUNCT
m-1112	29	16	of	of	ADP
m-1112	29	17	the	the	DET
m-1112	29	18	equilibrium	equilibrium	NOUN
m-1112	29	19	number	number	NOUN
m-1112	29	20	of	of	ADP
m-1112	29	21	masses	masse	NOUN
m-1112	29	22	m	m	VERB
m-1112	29	23	𝐧	𝐧	NOUN
m-1112	29	24	in	in	ADP
m-1112	29	25	a	a	DET
m-1112	29	26	system	system	NOUN
m-1112	29	27	.	.	PUNCT
m-1112	30	1	a	a	DET
m-1112	30	2	..	..	PUNCT
m-1112	30	3	the	the	DET
m-1112	30	4	n	n	NUM
m-1112	30	5	spaces	space	NOUN
m-1112	30	6	of	of	ADP
m-1112	30	7	monad	monad	PROPN
m-1112	30	8	�	�	PROPN
m-1112	30	9	̅	̅	NOUN
m-1112	30	10	�	�	NOUN
m-1112	30	11	are	be	AUX
m-1112	30	12	the	the	DET
m-1112	30	13	polygons	polygon	NOUN
m-1112	30	14	𝐒	𝐒	PROPN
m-1112	30	15	𝐧	𝐧	NOUN
m-1112	30	16	with	with	ADP
m-1112	30	17	n	n	NOUN
m-1112	30	18	=	=	SYM
m-1112	30	19	1	1	NUM
m-1112	30	20	≈	≈	NUM
m-1112	30	21	∞	∞	PROPN
m-1112	30	22	knots	knot	NOUN
m-1112	30	23	,	,	PUNCT
m-1112	30	24	b	b	X
m-1112	30	25	..	..	PUNCT
m-1112	30	26	the	the	DET
m-1112	30	27	n	n	ADV
m-1112	30	28	anti	anti	NOUN
m-1112	30	29	-	-	ADJ
m-1112	30	30	spaces	space	NOUN
m-1112	30	31	of	of	ADP
m-1112	30	32	monad	monad	PROPN
m-1112	30	33	�	�	PROPN
m-1112	30	34	̅	̅	NOUN
m-1112	30	35	�	�	NOUN
m-1112	30	36	are	be	AUX
m-1112	30	37	the	the	DET
m-1112	30	38	polygons	polygon	NOUN
m-1112	30	39	𝐒	𝐒	PROPN
m-1112	30	40	𝐧	𝐧	NOUN
m-1112	30	41	with	with	ADP
m-1112	30	42	n	n	PRON
m-1112	30	43	=	=	SYM
m-1112	30	44	1≈	1≈	NUM
m-1112	30	45	∞	∞	NUM
m-1112	30	46	knots	knot	NOUN
m-1112	30	47	,	,	PUNCT
m-1112	30	48	c	c	X
m-1112	30	49	..	..	PUNCT
m-1112	30	50	sub	sub	NOUN
m-1112	30	51	-	-	NOUN
m-1112	30	52	spaces	space	NOUN
m-1112	30	53	of	of	ADP
m-1112	30	54	monad	monad	PROPN
m-1112	30	55	≡	≡	PROPN
m-1112	30	56	±	±	PROPN
m-1112	31	1	√	√	PROPN
m-1112	31	2	�	�	NOUN
m-1112	31	3	̅	̅	NOUN
m-1112	31	4	�	�	NOUN
m-1112	31	5	𝒏=𝟏−∞	𝒏=𝟏−∞	PROPN
m-1112	31	6	are	be	AUX
m-1112	31	7	the	the	DET
m-1112	31	8	polygons	polygon	NOUN
m-1112	31	9	with	with	ADP
m-1112	31	10	n	n	NOUN
m-1112	31	11	=	=	SYM
m-1112	31	12	1	1	NUM
m-1112	31	13	≈	≈	NUM
m-1112	31	14	∞	∞	PROPN
m-1112	31	15	knots	knot	NOUN
m-1112	31	16	all	all	DET
m-1112	31	17	n	n	CCONJ
m-1112	31	18	-	-	PUNCT
m-1112	31	19	regular	regular	ADJ
m-1112	31	20	polygons	polygon	NOUN
m-1112	31	21	end	end	VERB
m-1112	31	22	to	to	ADP
m-1112	31	23	equations	equation	NOUN
m-1112	31	24	of	of	ADP
m-1112	31	25	n	n	CCONJ
m-1112	31	26	-	-	PUNCT
m-1112	31	27	degree	degree	NOUN
m-1112	31	28	segment	segment	NOUN
m-1112	31	29	,	,	PUNCT
m-1112	31	30	by	by	ADP
m-1112	31	31	finding	find	VERB
m-1112	31	32	a	a	DET
m-1112	31	33	suitable	suitable	ADJ
m-1112	31	34	value	value	NOUN
m-1112	31	35	of	of	ADP
m-1112	31	36	the	the	DET
m-1112	31	37	segment	segment	NOUN
m-1112	31	38	,	,	PUNCT
m-1112	31	39	x	x	INTJ
m-1112	31	40	,	,	PUNCT
m-1112	31	41	that	that	PRON
m-1112	31	42	is	is	ADV
m-1112	31	43	we	we	PRON
m-1112	31	44	have	have	VERB
m-1112	31	45	in	in	ADP
m-1112	31	46	the	the	DET
m-1112	31	47	general	general	ADJ
m-1112	31	48	case	case	NOUN
m-1112	31	49	to	to	PART
m-1112	31	50	solve	solve	VERB
m-1112	31	51	one	one	NUM
m-1112	31	52	or	or	CCONJ
m-1112	31	53	two	two	NUM
m-1112	31	54	equations	equation	NOUN
m-1112	31	55	of	of	ADP
m-1112	31	56	the	the	DET
m-1112	31	57	form	form	NOUN
m-1112	31	58	:	:	PUNCT
m-1112	31	59	a	a	DET
m-1112	31	60	.r0	.r0	NOUN
m-1112	31	61	.	.	PUNCT
m-1112	32	1	xn	xn	PROPN
m-1112	33	1	b	b	X
m-1112	33	2	.r2	.r2	PROPN
m-1112	33	3	.	.	PUNCT
m-1112	34	1	xn−2	xn−2	PROPN
m-1112	35	1	+	+	NUM
m-1112	35	2	c	c	NOUN
m-1112	35	3	.rn−6	.rn−6	PUNCT
m-1112	35	4	.	.	PUNCT
m-1112	36	1	x³	x³	PROPN
m-1112	36	2	–	–	PUNCT
m-1112	37	1	d	d	X
m-1112	37	2	.rn−4	.rn−4	NOUN
m-1112	37	3	.	.	PUNCT
m-1112	38	1	x²	x²	PROPN
m-1112	38	2	+	+	CCONJ
m-1112	38	3	e	e	PROPN
m-1112	38	4	.rn−2.x1	.rn−2.x1	PROPN
m-1112	38	5	–	–	PUNCT
m-1112	38	6	f.	f.	PROPN
m-1112	38	7	rn	rn	PROPN
m-1112	38	8	.	.	PUNCT
m-1112	39	1	x0	x0	PROPN
m-1112	39	2	=	=	PUNCT
m-1112	39	3	0	0	NUM
m-1112	39	4	for	for	ADP
m-1112	39	5	the	the	DET
m-1112	39	6	even	even	ADJ
m-1112	39	7	polygons	polygon	NOUN
m-1112	39	8	,	,	PUNCT
m-1112	39	9	and	and	CCONJ
m-1112	39	10	a	a	DET
m-1112	39	11	.r	.r	NOUN
m-1112	39	12	2	2	NUM
m-1112	39	13	.	.	PUNCT
m-1112	40	1	xn−2	xn−2	PROPN
m-1112	40	2	b.rn−2	b.rn−2	PROPN
m-1112	40	3	.	.	PUNCT
m-1112	41	1	xn−3	xn−3	PROPN
m-1112	41	2	+	+	NUM
m-1112	41	3	c.r2(n−4	c.r2(n−4	NOUN
m-1112	41	4	)	)	PUNCT
m-1112	41	5	.	.	PUNCT
m-1112	42	1	x³	x³	PROPN
m-1112	42	2	-d.r2(n−3	-d.r2(n−3	PUNCT
m-1112	42	3	)	)	PUNCT
m-1112	42	4	.	.	PUNCT
m-1112	43	1	x²	x²	PROPN
m-1112	43	2	+	+	PROPN
m-1112	43	3	e.r2(n−2	e.r2(n−2	PROPN
m-1112	43	4	)	)	PUNCT
m-1112	43	5	.	.	PUNCT
m-1112	44	1	x1	x1	X
m-1112	44	2	–	–	PUNCT
m-1112	44	3	f.r2(n−1).x0	f.r2(n−1).x0	NOUN
m-1112	44	4	=	=	NOUN
m-1112	44	5	0	0	NUM
m-1112	44	6	for	for	ADP
m-1112	44	7	the	the	DET
m-1112	44	8	odd	odd	ADJ
m-1112	44	9	polygons	polygon	NOUN
m-1112	44	10	,	,	PUNCT
m-1112	44	11	where	where	SCONJ
m-1112	44	12	a	a	DET
m-1112	44	13	,	,	PUNCT
m-1112	44	14	b	b	NOUN
m-1112	44	15	,	,	PUNCT
m-1112	44	16	c	c	NOUN
m-1112	44	17	,	,	PUNCT
m-1112	44	18	d	d	X
m-1112	44	19	are	be	AUX
m-1112	44	20	constants	constant	NOUN
m-1112	44	21	.	.	PUNCT
m-1112	45	1	the	the	DET
m-1112	45	2	presented	present	VERB
m-1112	45	3	geometrical	geometrical	ADJ
m-1112	45	4	method	method	NOUN
m-1112	45	5	is	be	AUX
m-1112	45	6	the	the	DET
m-1112	45	7	solution	solution	NOUN
m-1112	45	8	of	of	ADP
m-1112	45	9	the	the	DET
m-1112	45	10	above	above	ADJ
m-1112	45	11	equation	equation	NOUN
m-1112	45	12	in	in	ADP
m-1112	45	13	the	the	DET
m-1112	45	14	general	general	ADJ
m-1112	45	15	case	case	NOUN
m-1112	45	16	.	.	PUNCT
m-1112	46	1	because	because	SCONJ
m-1112	46	2	,	,	PUNCT
m-1112	46	3	the	the	DET
m-1112	46	4	nth	nth	NOUN
m-1112	46	5	degree	degree	NOUN
m-1112	46	6	equations	equation	NOUN
m-1112	46	7	are	be	AUX
m-1112	46	8	→	→	SYM
m-1112	46	9	the	the	DET
m-1112	46	10	vertices	vertex	NOUN
m-1112	46	11	(	(	PUNCT
m-1112	46	12	n	n	CCONJ
m-1112	46	13	)	)	PUNCT
m-1112	46	14	and	and	CCONJ
m-1112	46	15	the	the	DET
m-1112	46	16	sides	side	NOUN
m-1112	46	17	(	(	PUNCT
m-1112	46	18	𝐚𝐧=	𝐚𝐧=	PROPN
m-1112	46	19	𝛌𝐧	𝛌𝐧	PROPN
m-1112	46	20	)	)	PUNCT
m-1112	46	21	of	of	ADP
m-1112	46	22	the	the	DET
m-1112	46	23	n	n	CCONJ
m-1112	46	24	-	-	PUNCT
m-1112	46	25	polygon	polygon	NOUN
m-1112	46	26	in	in	ADP
m-1112	46	27	circle	circle	NOUN
m-1112	46	28	←	←	PROPN
m-1112	46	29	number	number	NOUN
m-1112	46	30	,	,	PUNCT
m-1112	46	31	π	π	PROPN
m-1112	46	32	,	,	PUNCT
m-1112	46	33	is	be	AUX
m-1112	46	34	their	their	PRON
m-1112	46	35	common	common	ADJ
m-1112	46	36	mould	mould	NOUN
m-1112	46	37	.	.	PUNCT
m-1112	47	1	[	[	PUNCT
m-1112	47	2	62	62	NUM
m-1112	47	3	]	]	PUNCT
m-1112	47	4	.	.	PUNCT
m-1112	48	1	the	the	DET
m-1112	48	2	natural	natural	ADJ
m-1112	48	3	mechanism	mechanism	NOUN
m-1112	48	4	continuously	continuously	ADV
m-1112	48	5	originates	originate	VERB
m-1112	48	6	the	the	DET
m-1112	48	7	elementary	elementary	ADJ
m-1112	48	8	particles	particle	NOUN
m-1112	48	9	and	and	CCONJ
m-1112	48	10	compounds	compound	NOUN
m-1112	48	11	,	,	PUNCT
m-1112	48	12	atoms	atom	NOUN
m-1112	48	13	and	and	CCONJ
m-1112	48	14	molecules	molecule	NOUN
m-1112	48	15	with	with	ADP
m-1112	48	16	the	the	DET
m-1112	48	17	one	one	NUM
m-1112	48	18	action	action	NOUN
m-1112	48	19	from	from	ADP
m-1112	48	20	opposite	opposite	ADJ
m-1112	48	21	.	.	PUNCT
m-1112	49	1	article	article	NOUN
m-1112	49	2	[	[	X
m-1112	49	3	111	111	NUM
m-1112	49	4	]	]	PUNCT
m-1112	49	5	encloses	enclose	VERB
m-1112	49	6	many	many	ADJ
m-1112	49	7	paragraphs	paragraph	NOUN
m-1112	49	8	of	of	ADP
m-1112	49	9	[	[	X
m-1112	49	10	110	110	NUM
m-1112	49	11	]	]	PUNCT
m-1112	49	12	,	,	PUNCT
m-1112	49	13	in	in	ADP
m-1112	49	14	order	order	NOUN
m-1112	49	15	to	to	PART
m-1112	49	16	distinguish	distinguish	VERB
m-1112	49	17	and	and	CCONJ
m-1112	49	18	prove	prove	VERB
m-1112	49	19	the	the	DET
m-1112	49	20	way	way	NOUN
m-1112	49	21	of	of	ADP
m-1112	49	22	energy	energy	NOUN
m-1112	49	23	and	and	CCONJ
m-1112	49	24	the	the	DET
m-1112	49	25	stressespaths	stressespath	NOUN
m-1112	49	26	in	in	ADP
m-1112	49	27	the	the	DET
m-1112	49	28	spaces	space	NOUN
m-1112	49	29	.	.	PUNCT
m-1112	50	1	for	for	ADP
m-1112	50	2	the	the	DET
m-1112	50	3	regular	regular	ADJ
m-1112	50	4	polygons	polygon	NOUN
m-1112	50	5	is	be	AUX
m-1112	50	6	given	give	VERB
m-1112	50	7	such	such	DET
m-1112	50	8	the	the	DET
m-1112	50	9	geometrical	geometrical	ADJ
m-1112	50	10	solution	solution	NOUN
m-1112	50	11	as	as	ADV
m-1112	50	12	well	well	ADV
m-1112	50	13	the	the	DET
m-1112	50	14	algebraic	algebraic	NOUN
m-1112	50	15	.	.	PUNCT
m-1112	51	1	[	[	X
m-1112	51	2	106	106	X
m-1112	51	3	]	]	X
m-1112	51	4	=	=	PUNCT
m-1112	51	5	programming	program	VERB
m-1112	51	6	the	the	DET
m-1112	51	7	atoms	atom	NOUN
m-1112	51	8	and	and	CCONJ
m-1112	51	9	compounds	compound	NOUN
m-1112	51	10	,	,	PUNCT
m-1112	51	11	is	be	AUX
m-1112	51	12	an	an	DET
m-1112	51	13	program	program	NOUN
m-1112	51	14	which	which	PRON
m-1112	51	15	solves	solve	VERB
m-1112	51	16	the	the	DET
m-1112	51	17	problem	problem	NOUN
m-1112	51	18	of	of	ADP
m-1112	51	19	the	the	DET
m-1112	51	20	n	n	CCONJ
m-1112	51	21	-	-	PUNCT
m-1112	51	22	knots	knot	NOUN
m-1112	51	23	figures	figure	NOUN
m-1112	51	24	and	and	CCONJ
m-1112	51	25	gives	give	VERB
m-1112	51	26	the	the	DET
m-1112	51	27	energy	energy	NOUN
m-1112	51	28	spectrum	spectrum	NOUN
m-1112	51	29	of	of	ADP
m-1112	51	30	any	any	DET
m-1112	51	31	complex	complex	ADJ
m-1112	51	32	-	-	PUNCT
m-1112	51	33	forced	force	VERB
m-1112	51	34	-	-	PUNCT
m-1112	51	35	vector	vector	NOUN
m-1112	51	36	.	.	PUNCT
m-1112	52	1	article	article	NOUN
m-1112	52	2	[	[	X
m-1112	52	3	114	114	NUM
m-1112	52	4	]	]	PUNCT
m-1112	52	5	an	an	DET
m-1112	52	6	way	way	NOUN
m-1112	52	7	of	of	ADP
m-1112	52	8	deceptioning	deceptione	VERB
m-1112	52	9	the	the	DET
m-1112	52	10	cells	cell	NOUN
m-1112	52	11	is	be	AUX
m-1112	52	12	prepared	prepare	VERB
m-1112	52	13	.	.	PUNCT
m-1112	53	1	keywords	keyword	NOUN
m-1112	53	2	:	:	PUNCT
m-1112	53	3	the	the	DET
m-1112	53	4	figure	figure	NOUN
m-1112	53	5	n	n	CCONJ
m-1112	53	6	-	-	PUNCT
m-1112	53	7	knots	knot	NOUN
m-1112	53	8	,	,	PUNCT
m-1112	53	9	the	the	DET
m-1112	53	10	polynomials	polynomial	NOUN
m-1112	53	11	n	n	CCONJ
m-1112	53	12	-	-	PUNCT
m-1112	53	13	knots	knot	NOUN
m-1112	53	14	,	,	PUNCT
m-1112	53	15	spaces	space	NOUN
m-1112	53	16	and	and	CCONJ
m-1112	53	17	figure	figure	VERB
m-1112	53	18	n	n	CCONJ
m-1112	53	19	-	-	PUNCT
m-1112	53	20	knots	knot	NOUN
m-1112	53	21	,	,	PUNCT
m-1112	53	22	the	the	DET
m-1112	53	23	waves	wave	NOUN
m-1112	53	24	of	of	ADP
m-1112	53	25	spaces	space	NOUN
m-1112	53	26	.	.	PUNCT
m-1112	54	1	ijo	ijo	PROPN
m-1112	54	2	international	international	PROPN
m-1112	54	3	journal	journal	PROPN
m-1112	54	4	of	of	ADP
m-1112	54	5	mathematics	mathematics	PROPN
m-1112	54	6	(	(	PUNCT
m-1112	54	7	issn	issn	PROPN
m-1112	54	8	:	:	PUNCT
m-1112	54	9	2992	2992	NUM
m-1112	54	10	-	-	SYM
m-1112	54	11	4421	4421	NUM
m-1112	54	12	)	)	PUNCT
m-1112	54	13	volume	volume	NOUN
m-1112	54	14	08	08	NUM
m-1112	55	1	|	|	ADV
m-1112	55	2	issue	issue	NOUN
m-1112	55	3	08	08	NUM
m-1112	56	1	|	|	ADV
m-1112	56	2	august	august	PROPN
m-1112	56	3	2025	2025	NUM
m-1112	56	4	|	|	ADV
m-1112	56	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	56	6	ijo	ijo	PROPN
m-1112	56	7	journals	journal	NOUN
m-1112	56	8	3	3	NUM
m-1112	56	9	the	the	DET
m-1112	56	10	fundamental	fundamental	ADJ
m-1112	56	11	particles	particle	NOUN
m-1112	56	12	origination	origination	NOUN
m-1112	56	13	mechanism	mechanism	NOUN
m-1112	56	14	in	in	ADP
m-1112	56	15	mfmf	mfmf	PROPN
m-1112	56	16	pns	pns	PROPN
m-1112	56	17	caves	cave	NOUN
m-1112	56	18	.	.	PUNCT
m-1112	57	1	content	content	NOUN
m-1112	57	2	abstract	abstract	ADJ
m-1112	57	3	page	page	NOUN
m-1112	57	4	…	…	PUNCT
m-1112	57	5	.................	.................	SYM
m-1112	57	6	1	1	NUM
m-1112	57	7	,	,	PUNCT
m-1112	57	8	a	a	PRON
m-1112	57	9	…	…	PUNCT
m-1112	57	10	the	the	DET
m-1112	57	11	structure	structure	NOUN
m-1112	57	12	of	of	ADP
m-1112	57	13	the	the	DET
m-1112	57	14	euclidean	euclidean	ADJ
m-1112	57	15	geometry	geometry	NOUN
m-1112	57	16	1a	1a	NOUN
m-1112	57	17	..	..	PUNCT
m-1112	57	18	:	:	PUNCT
m-1112	57	19	the	the	DET
m-1112	57	20	points	point	NOUN
m-1112	57	21	,	,	PUNCT
m-1112	57	22	vectors	vector	NOUN
m-1112	57	23	,	,	PUNCT
m-1112	57	24	lines	line	NOUN
m-1112	57	25	,	,	PUNCT
m-1112	57	26	planes	plane	NOUN
m-1112	57	27	,	,	PUNCT
m-1112	57	28	volumes	volume	NOUN
m-1112	57	29	,	,	PUNCT
m-1112	57	30	n	n	CCONJ
m-1112	57	31	-	-	PUNCT
m-1112	57	32	spces	spce	NOUN
m-1112	57	33	page	page	NOUN
m-1112	57	34	…	…	PUNCT
m-1112	57	35	.................	.................	SYM
m-1112	57	36	4	4	NUM
m-1112	57	37	,	,	PUNCT
m-1112	57	38	2a	2a	NUM
m-1112	57	39	..	..	PUNCT
m-1112	57	40	:	:	PUNCT
m-1112	58	1	the	the	DET
m-1112	58	2	fundamental	fundamental	ADJ
m-1112	58	3	principles	principle	NOUN
m-1112	58	4	of	of	ADP
m-1112	58	5	e	e	NOUN
m-1112	58	6	-	-	NOUN
m-1112	58	7	geometry	geometry	NOUN
m-1112	58	8	page	page	NOUN
m-1112	58	9	…	…	PUNCT
m-1112	58	10	…	…	PUNCT
m-1112	58	11	…	…	SYM
m-1112	58	12	.4.fig-1	.4.fig-1	PROPN
m-1112	58	13	,	,	PUNCT
m-1112	58	14	3a	3a	NUM
m-1112	58	15	..	..	PUNCT
m-1112	58	16	:	:	PUNCT
m-1112	58	17	the	the	DET
m-1112	58	18	quantization	quantization	NOUN
m-1112	58	19	of	of	ADP
m-1112	58	20	the	the	DET
m-1112	58	21	energy	energy	NOUN
m-1112	58	22	–	–	PUNCT
m-1112	58	23	space	space	NOUN
m-1112	58	24	–	–	PUNCT
m-1112	58	25	universe	universe	NOUN
m-1112	58	26	page	page	NOUN
m-1112	58	27	…	…	PUNCT
m-1112	58	28	…	…	PUNCT
m-1112	58	29	…	…	PUNCT
m-1112	58	30	…	…	PUNCT
m-1112	58	31	....	....	SYM
m-1112	58	32	7	7	NUM
m-1112	58	33	,	,	PUNCT
m-1112	58	34	4a	4a	NUM
m-1112	58	35	..	..	PUNCT
m-1112	58	36	:	:	PUNCT
m-1112	58	37	the	the	DET
m-1112	58	38	correlation	correlation	NOUN
m-1112	58	39	of	of	ADP
m-1112	58	40	spaces	space	NOUN
m-1112	58	41	and	and	CCONJ
m-1112	58	42	the	the	DET
m-1112	58	43	primary	primary	ADJ
m-1112	58	44	motion	motion	NOUN
m-1112	58	45	page	page	NOUN
m-1112	58	46	…	…	PUNCT
m-1112	58	47	…	…	PUNCT
m-1112	58	48	…	…	SYM
m-1112	58	49	11.fig-2	11.fig-2	NUM
m-1112	58	50	,	,	PUNCT
m-1112	58	51	5a	5a	NUM
m-1112	58	52	..	..	PUNCT
m-1112	58	53	:	:	PUNCT
m-1112	58	54	the	the	DET
m-1112	58	55	figure	figure	NOUN
m-1112	58	56	-	-	PUNCT
m-1112	58	57	eight	eight	NUM
m-1112	58	58	knot	knot	NOUN
m-1112	58	59	&	&	CCONJ
m-1112	58	60	the	the	DET
m-1112	58	61	figure	figure	NOUN
m-1112	58	62	n	n	NOUN
m-1112	58	63	=	=	SYM
m-1112	58	64	1	1	NUM
m-1112	58	65	≈	≈	NUM
m-1112	58	66	∞	∞	PROPN
m-1112	58	67	knots	knot	NOUN
m-1112	58	68	page	page	NOUN
m-1112	58	69	…	…	PUNCT
m-1112	58	70	…	…	PUNCT
m-1112	58	71	…	…	SYM
m-1112	58	72	13.fig-3	13.fig-3	NUM
m-1112	58	73	,	,	PUNCT
m-1112	58	74	6a	6a	NOUN
m-1112	58	75	..	..	PUNCT
m-1112	58	76	:	:	PUNCT
m-1112	58	77	the	the	DET
m-1112	58	78	origination	origination	NOUN
m-1112	58	79	of	of	ADP
m-1112	58	80	the	the	DET
m-1112	58	81	primary	primary	ADJ
m-1112	58	82	motion	motion	NOUN
m-1112	58	83	in	in	ADP
m-1112	58	84	spaces	space	NOUN
m-1112	58	85	page	page	NOUN
m-1112	58	86	…	…	PUNCT
m-1112	58	87	…	…	PUNCT
m-1112	58	88	..	..	PUNCT
m-1112	58	89	21.fig-4	21.fig-4	NUM
m-1112	58	90	,	,	PUNCT
m-1112	58	91	7a	7a	NUM
m-1112	58	92	..	..	PUNCT
m-1112	58	93	:	:	PUNCT
m-1112	58	94	the	the	DET
m-1112	58	95	mechanism	mechanism	NOUN
m-1112	58	96	and	and	CCONJ
m-1112	58	97	charges	charge	NOUN
m-1112	58	98	for	for	ADP
m-1112	58	99	the	the	DET
m-1112	58	100	dual	dual	ADJ
m-1112	58	101	originations	origination	NOUN
m-1112	58	102	page	page	NOUN
m-1112	58	103	…	…	PUNCT
m-1112	58	104	...............	...............	SYM
m-1112	58	105	23	23	NUM
m-1112	58	106	,	,	PUNCT
m-1112	58	107	8a	8a	NUM
m-1112	58	108	..	..	PUNCT
m-1112	58	109	:	:	PUNCT
m-1112	58	110	the	the	DET
m-1112	58	111	material	material	NOUN
m-1112	58	112	geometry	geometry	NOUN
m-1112	58	113	e	e	NOUN
m-1112	58	114	-	-	NOUN
m-1112	58	115	geometry	geometry	NOUN
m-1112	58	116	physicks	physick	NOUN
m-1112	58	117	and	and	CCONJ
m-1112	58	118	chemistry	chemistry	NOUN
m-1112	58	119	page	page	NOUN
m-1112	58	120	…	…	PUNCT
m-1112	58	121	…	…	PUNCT
m-1112	58	122	....	....	PUNCT
m-1112	58	123	24.fig-5	24.fig-5	NUM
m-1112	58	124	,	,	PUNCT
m-1112	59	1	[	[	X
m-1112	59	2	a	a	X
m-1112	59	3	]	]	X
m-1112	59	4	..	..	PUNCT
m-1112	59	5	the	the	DET
m-1112	59	6	{	{	PUNCT
m-1112	59	7	s	s	PROPN
m-1112	59	8	tp	tp	ADP
m-1112	59	9	l	l	NOUN
m-1112	59	10	}	}	PUNCT
m-1112	59	11	natural	natural	ADJ
m-1112	59	12	mechanisms	mechanism	NOUN
m-1112	59	13	page	page	NOUN
m-1112	59	14	…	…	PUNCT
m-1112	59	15	..	..	PUNCT
m-1112	59	16	26.fig-6,7.7a,7b,7c	26.fig-6,7.7a,7b,7c	NUM
m-1112	59	17	,	,	PUNCT
m-1112	60	1	[	[	X
m-1112	60	2	b	b	X
m-1112	60	3	]	]	X
m-1112	60	4	..	..	PUNCT
m-1112	60	5	the	the	DET
m-1112	60	6	{	{	PUNCT
m-1112	60	7	tvpm	tvpm	NOUN
m-1112	60	8	}	}	PUNCT
m-1112	60	9	natural	natural	ADJ
m-1112	60	10	mechanisms	mechanism	NOUN
m-1112	60	11	page	page	NOUN
m-1112	60	12	...	...	PUNCT
m-1112	60	13	32.fig-8a	32.fig-8a	NUM
m-1112	60	14	,	,	PUNCT
m-1112	60	15	8b	8b	NUM
m-1112	60	16	,	,	PUNCT
m-1112	61	1	[	[	X
m-1112	61	2	c	c	X
m-1112	61	3	]	]	X
m-1112	61	4	..	..	PUNCT
m-1112	62	1	the	the	DET
m-1112	62	2	{	{	PUNCT
m-1112	62	3	tc	tc	NOUN
m-1112	62	4	i	i	NOUN
m-1112	62	5	c	c	NOUN
m-1112	62	6	}	}	PUNCT
m-1112	62	7	natural	natural	ADJ
m-1112	62	8	mechanisms	mechanism	NOUN
m-1112	62	9	page	page	NOUN
m-1112	62	10	..	..	PUNCT
m-1112	62	11	35.fig-9,9a	35.fig-9,9a	NUM
m-1112	62	12	,	,	PUNCT
m-1112	62	13	b,9c,9d,9e	b,9c,9d,9e	NOUN
m-1112	62	14	,	,	PUNCT
m-1112	63	1	[	[	X
m-1112	63	2	d	d	X
m-1112	63	3	]	]	X
m-1112	63	4	..	..	PUNCT
m-1112	63	5	the	the	DET
m-1112	63	6	{	{	PUNCT
m-1112	63	7	tobm	tobm	PROPN
m-1112	63	8	}	}	PUNCT
m-1112	63	9	natural	natural	ADJ
m-1112	63	10	mechanisms	mechanism	NOUN
m-1112	63	11	page	page	NOUN
m-1112	63	12	.........	.........	PUNCT
m-1112	64	1	43.fig-10	43.fig-10	NUM
m-1112	64	2	,	,	PUNCT
m-1112	64	3	9a	9a	NOUN
m-1112	64	4	..	..	PUNCT
m-1112	64	5	:	:	PUNCT
m-1112	64	6	the	the	DET
m-1112	64	7	flow	flow	NOUN
m-1112	64	8	plan	plan	NOUN
m-1112	64	9	of	of	ADP
m-1112	64	10	the	the	DET
m-1112	64	11	space	space	NOUN
m-1112	64	12	energy	energy	NOUN
m-1112	64	13	universe	universe	NOUN
m-1112	64	14	page	page	NOUN
m-1112	64	15	…	…	PUNCT
m-1112	64	16	…	…	PUNCT
m-1112	64	17	..	..	PUNCT
m-1112	64	18	45.fig-11	45.fig-11	NUM
m-1112	64	19	,	,	PUNCT
m-1112	64	20	10a	10a	NOUN
m-1112	64	21	..	..	PUNCT
m-1112	64	22	:the	:the	DET
m-1112	64	23	e	e	NOUN
m-1112	64	24	-	-	NOUN
m-1112	64	25	spaces	space	NOUN
m-1112	64	26	and	and	CCONJ
m-1112	64	27	the	the	DET
m-1112	64	28	energy	energy	NOUN
m-1112	64	29	regular	regular	ADJ
m-1112	64	30	-	-	PUNCT
m-1112	64	31	polygons	polygon	NOUN
m-1112	64	32	page.49.fig-12a,12b,12c,12d	page.49.fig-12a,12b,12c,12d	PROPN
m-1112	64	33	,	,	PUNCT
m-1112	64	34	b	b	PROPN
m-1112	64	35	…	…	PUNCT
m-1112	64	36	:	:	PUNCT
m-1112	64	37	general	general	ADJ
m-1112	64	38	:	:	PUNCT
m-1112	64	39	1b	1b	NUM
m-1112	64	40	..	..	PUNCT
m-1112	64	41	:	:	PUNCT
m-1112	64	42	the	the	DET
m-1112	64	43	spaces	space	NOUN
m-1112	64	44	and	and	CCONJ
m-1112	64	45	the	the	DET
m-1112	64	46	energy	energy	NOUN
m-1112	64	47	states	state	NOUN
m-1112	64	48	page	page	NOUN
m-1112	64	49	…	…	PUNCT
m-1112	64	50	...	...	PUNCT
m-1112	64	51	54.fig-12	54.fig-12	NOUN
m-1112	64	52	,	,	PUNCT
m-1112	64	53	2b	2b	NOUN
m-1112	64	54	..	..	PUNCT
m-1112	64	55	:	:	PUNCT
m-1112	64	56	the	the	DET
m-1112	64	57	complex	complex	ADJ
m-1112	64	58	numbers	number	NOUN
m-1112	64	59	and	and	CCONJ
m-1112	64	60	quaternion	quaternion	NOUN
m-1112	64	61	.	.	PUNCT
m-1112	65	1	page	page	NOUN
m-1112	65	2	…	…	PUNCT
m-1112	65	3	.............	.............	PUNCT
m-1112	65	4	56	56	NUM
m-1112	65	5	,	,	PUNCT
m-1112	65	6	3b	3b	NUM
m-1112	65	7	..	..	PUNCT
m-1112	65	8	:	:	PUNCT
m-1112	65	9	the	the	DET
m-1112	65	10	stability	stability	NOUN
m-1112	65	11	of	of	ADP
m-1112	65	12	space	space	NOUN
m-1112	65	13	anti	anti	NOUN
m-1112	65	14	-	-	NOUN
m-1112	65	15	space	space	NOUN
m-1112	65	16	,	,	PUNCT
m-1112	65	17	in	in	ADP
m-1112	65	18	the	the	DET
m-1112	65	19	neutral	neutral	ADJ
m-1112	65	20	-	-	PUNCT
m-1112	65	21	space	space	NOUN
m-1112	65	22	page	page	NOUN
m-1112	65	23	…	…	PUNCT
m-1112	65	24	…	…	PUNCT
m-1112	65	25	.59.fig-13	.59.fig-13	PUNCT
m-1112	65	26	,	,	PUNCT
m-1112	65	27	4b	4b	X
m-1112	65	28	..	..	PUNCT
m-1112	65	29	:	:	PUNCT
m-1112	65	30	the	the	DET
m-1112	65	31	quantum	quantum	ADJ
m-1112	65	32	interference	interference	NOUN
m-1112	65	33	of	of	ADP
m-1112	65	34	the	the	DET
m-1112	65	35	duality	duality	NOUN
m-1112	65	36	-	-	PUNCT
m-1112	65	37	photon	photon	NOUN
m-1112	65	38	page	page	NOUN
m-1112	65	39	…	…	PUNCT
m-1112	65	40	…	…	PUNCT
m-1112	65	41	.59.fig-14	.59.fig-14	NUM
m-1112	65	42	,	,	PUNCT
m-1112	65	43	c	c	X
m-1112	65	44	..	..	PUNCT
m-1112	65	45	:	:	PUNCT
m-1112	65	46	the	the	DET
m-1112	65	47	origination	origination	NOUN
m-1112	65	48	of	of	ADP
m-1112	65	49	the	the	DET
m-1112	65	50	physical	physical	ADJ
m-1112	65	51	loops	loop	NOUN
m-1112	65	52	≡	≡	PROPN
m-1112	65	53	caves	cave	VERB
m-1112	65	54	1c	1c	NOUN
m-1112	65	55	..	..	PUNCT
m-1112	65	56	:	:	PUNCT
m-1112	65	57	the	the	DET
m-1112	65	58	gravitation	gravitation	NOUN
m-1112	65	59	force	force	NOUN
m-1112	65	60	g	g	PROPN
m-1112	65	61	,	,	PUNCT
m-1112	65	62	and	and	CCONJ
m-1112	65	63	the	the	DET
m-1112	65	64	kick	kick	NOUN
m-1112	65	65	-	-	PUNCT
m-1112	65	66	start	start	NOUN
m-1112	65	67	page	page	NOUN
m-1112	65	68	…	…	PUNCT
m-1112	65	69	..............	..............	PROPN
m-1112	65	70	62	62	NUM
m-1112	65	71	,	,	PUNCT
m-1112	65	72	2c	2c	NUM
m-1112	65	73	..	..	PUNCT
m-1112	65	74	:	:	PUNCT
m-1112	65	75	the	the	DET
m-1112	65	76	united	united	PROPN
m-1112	65	77	-	-	PUNCT
m-1112	65	78	coulomb	coulomb	PROPN
m-1112	65	79	-	-	PUNCT
m-1112	65	80	newton	newton	PROPN
m-1112	65	81	law	law	NOUN
m-1112	65	82	for	for	ADP
m-1112	65	83	interactions	interaction	NOUN
m-1112	65	84	page	page	NOUN
m-1112	65	85	…	…	PUNCT
m-1112	65	86	..............	..............	PROPN
m-1112	65	87	69	69	NUM
m-1112	65	88	,	,	PUNCT
m-1112	65	89	3c	3c	NUM
m-1112	65	90	...	...	PUNCT
m-1112	65	91	:	:	PUNCT
m-1112	65	92	the	the	DET
m-1112	65	93	origination	origination	NOUN
m-1112	65	94	of	of	ADP
m-1112	65	95	photon`s	photon`s	NOUN
m-1112	65	96	light	light	ADJ
m-1112	65	97	velocity	velocity	NOUN
m-1112	65	98	c	c	NOUN
m-1112	65	99	page	page	NOUN
m-1112	65	100	…	…	PUNCT
m-1112	65	101	…	…	PUNCT
m-1112	65	102	..........	..........	SYM
m-1112	65	103	69	69	NUM
m-1112	65	104	,	,	PUNCT
m-1112	65	105	4c	4c	NOUN
m-1112	65	106	...	...	PUNCT
m-1112	65	107	:	:	PUNCT
m-1112	65	108	the	the	DET
m-1112	65	109	origination	origination	NOUN
m-1112	65	110	of	of	ADP
m-1112	65	111	electron	electron	NOUN
m-1112	65	112	-	-	PUNCT
m-1112	65	113	charge	charge	NOUN
m-1112	65	114	e̅	e̅	DET
m-1112	65	115	≡	≡	PROPN
m-1112	65	116	q̅	q̅	PROPN
m-1112	65	117	page	page	NOUN
m-1112	65	118	…	…	PUNCT
m-1112	65	119	…	…	PUNCT
m-1112	65	120	..........	..........	SYM
m-1112	65	121	72	72	NUM
m-1112	65	122	,	,	PUNCT
m-1112	65	123	5c	5c	NUM
m-1112	65	124	...	...	PUNCT
m-1112	65	125	:	:	PUNCT
m-1112	65	126	the	the	DET
m-1112	65	127	origination	origination	NOUN
m-1112	65	128	of	of	ADP
m-1112	65	129	the	the	DET
m-1112	65	130	hydrogen	hydrogen	NOUN
m-1112	65	131	cave	cave	PROPN
m-1112	65	132	h	h	PROPN
m-1112	65	133	&	&	CCONJ
m-1112	65	134	explanations	explanation	NOUN
m-1112	65	135	page	page	NOUN
m-1112	65	136	…	…	PUNCT
m-1112	65	137	…	…	PUNCT
m-1112	65	138	..........	..........	PROPN
m-1112	65	139	73	73	NUM
m-1112	65	140	,	,	PUNCT
m-1112	65	141	6c	6c	NOUN
m-1112	65	142	.	.	PUNCT
m-1112	65	143	:	:	PUNCT
m-1112	66	1	the	the	DET
m-1112	66	2	epilogues	epilogue	NOUN
m-1112	66	3	of	of	ADP
m-1112	66	4	prior	prior	ADJ
m-1112	66	5	page	page	NOUN
m-1112	66	6	…	…	PUNCT
m-1112	66	7	78.fig-17a,17b,17c,17d,17e	78.fig-17a,17b,17c,17d,17e	NUM
m-1112	66	8	,	,	PUNCT
m-1112	66	9	d	d	X
m-1112	66	10	...	...	PUNCT
m-1112	66	11	the	the	DET
m-1112	66	12	origination	origination	NOUN
m-1112	66	13	of	of	ADP
m-1112	66	14	the	the	DET
m-1112	66	15	fundamental	fundamental	ADJ
m-1112	66	16	particles	particle	NOUN
m-1112	66	17	1d	1d	NUM
m-1112	66	18	…	…	PUNCT
m-1112	66	19	:	:	PUNCT
m-1112	66	20	the	the	DET
m-1112	66	21	balancing	balancing	NOUN
m-1112	66	22	of	of	ADP
m-1112	66	23	the	the	DET
m-1112	66	24	space	space	NOUN
m-1112	66	25	and	and	CCONJ
m-1112	66	26	anti	anti	ADJ
m-1112	66	27	-	-	ADJ
m-1112	66	28	space	space	ADJ
m-1112	66	29	page	page	NOUN
m-1112	66	30	…	…	PUNCT
m-1112	66	31	…	…	PUNCT
m-1112	66	32	..	..	PUNCT
m-1112	66	33	99.fig-18	99.fig-18	NUM
m-1112	66	34	2d	2d	NOUN
m-1112	66	35	…	…	PUNCT
m-1112	66	36	:	:	PUNCT
m-1112	66	37	the	the	DET
m-1112	66	38	vibration	vibration	NOUN
m-1112	66	39	of	of	ADP
m-1112	66	40	particles	particle	NOUN
m-1112	66	41	in	in	ADP
m-1112	66	42	all	all	DET
m-1112	66	43	levels	level	NOUN
m-1112	66	44	page	page	NOUN
m-1112	66	45	…	…	PUNCT
m-1112	66	46	…	…	SYM
m-1112	66	47	100.fig-19	100.fig-19	NOUN
m-1112	66	48	5d	5d	NUM
m-1112	66	49	…	…	PUNCT
m-1112	66	50	:	:	PUNCT
m-1112	66	51	the	the	DET
m-1112	66	52	natural	natural	ADJ
m-1112	66	53	electromagnetic	electromagnetic	ADJ
m-1112	66	54	e	e	NOUN
m-1112	66	55	-	-	NOUN
m-1112	66	56	tetrahedron	tetrahedron	NOUN
m-1112	66	57	,	,	PUNCT
m-1112	66	58	cube	cube	NOUN
m-1112	66	59	,	,	PUNCT
m-1112	66	60	spheres	sphere	NOUN
m-1112	66	61	page	page	NOUN
m-1112	66	62	…	…	PUNCT
m-1112	66	63	..	..	SYM
m-1112	66	64	102.fig20.b	102.fig20.b	NUM
m-1112	66	65	8d	8d	NUM
m-1112	66	66	..	..	PUNCT
m-1112	66	67	:	:	PUNCT
m-1112	66	68	the	the	DET
m-1112	66	69	stability	stability	NOUN
m-1112	66	70	of	of	ADP
m-1112	66	71	fundamental	fundamental	ADJ
m-1112	66	72	particles	particle	NOUN
m-1112	66	73	conductors	conductor	NOUN
m-1112	66	74	&	&	CCONJ
m-1112	66	75	atoms	atom	NOUN
m-1112	66	76	page	page	NOUN
m-1112	66	77	…	…	PUNCT
m-1112	66	78	…	…	SYM
m-1112	66	79	108.fig26	108.fig26	NUM
m-1112	66	80	9d	9d	NOUN
m-1112	66	81	..	..	PUNCT
m-1112	66	82	:	:	PUNCT
m-1112	66	83	the	the	DET
m-1112	66	84	origination	origination	NOUN
m-1112	66	85	of	of	ADP
m-1112	66	86	proton	proton	NOUN
m-1112	66	87	-	-	PUNCT
m-1112	66	88	neutron	neutron	NOUN
m-1112	66	89	funta	funta	NOUN
m-1112	66	90	-	-	PUNCT
m-1112	66	91	particles	particle	NOUN
m-1112	66	92	,	,	PUNCT
m-1112	66	93	objectivity	objectivity	NOUN
m-1112	66	94	page	page	NOUN
m-1112	66	95	…	…	PUNCT
m-1112	66	96	…	…	PUNCT
m-1112	66	97	110.fig28	110.fig28	NUM
m-1112	66	98	e	e	NOUN
m-1112	66	99	..	..	PUNCT
m-1112	66	100	:	:	PUNCT
m-1112	66	101	references	reference	NOUN
m-1112	66	102	page	page	NOUN
m-1112	66	103	…	…	PUNCT
m-1112	66	104	…	…	SYM
m-1112	66	105	.	.	NUM
m-1112	66	106	…	…	PUNCT
m-1112	66	107	…	…	SYM
m-1112	66	108	113	113	NUM
m-1112	66	109	,	,	PUNCT
m-1112	66	110	ijo	ijo	PROPN
m-1112	66	111	international	international	PROPN
m-1112	66	112	journal	journal	PROPN
m-1112	66	113	of	of	ADP
m-1112	66	114	mathematics	mathematics	PROPN
m-1112	66	115	(	(	PUNCT
m-1112	66	116	issn	issn	PROPN
m-1112	66	117	:	:	PUNCT
m-1112	66	118	2992	2992	NUM
m-1112	66	119	-	-	SYM
m-1112	66	120	4421	4421	NUM
m-1112	66	121	)	)	PUNCT
m-1112	66	122	volume	volume	NOUN
m-1112	66	123	08	08	NUM
m-1112	67	1	|	|	ADV
m-1112	67	2	issue	issue	NOUN
m-1112	67	3	08	08	NUM
m-1112	68	1	|	|	ADV
m-1112	68	2	august	august	PROPN
m-1112	68	3	2025	2025	NUM
m-1112	68	4	|	|	ADV
m-1112	68	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	68	6	ijo	ijo	PROPN
m-1112	68	7	journals	journal	NOUN
m-1112	68	8	4	4	NUM
m-1112	68	9	the	the	DET
m-1112	68	10	fundamental	fundamental	ADJ
m-1112	68	11	particles	particle	NOUN
m-1112	68	12	origination	origination	NOUN
m-1112	68	13	mechanism	mechanism	NOUN
m-1112	68	14	in	in	ADP
m-1112	68	15	mfmf	mfmf	PROPN
m-1112	68	16	pns	pns	PROPN
m-1112	68	17	caves	cave	NOUN
m-1112	68	18	.	.	PUNCT
m-1112	69	1	a	a	DET
m-1112	69	2	…	…	PUNCT
m-1112	69	3	the	the	DET
m-1112	69	4	structure	structure	NOUN
m-1112	69	5	of	of	ADP
m-1112	69	6	the	the	DET
m-1112	69	7	euclidean	euclidean	ADJ
m-1112	69	8	geometry	geometry	NOUN
m-1112	69	9	.	.	PUNCT
m-1112	70	1	[	[	X
m-1112	70	2	6	6	NUM
m-1112	70	3	-12	-12	SYM
m-1112	70	4	]	]	PUNCT
m-1112	70	5	a1	a1	PROPN
m-1112	70	6	..	..	PUNCT
m-1112	70	7	point	point	NOUN
m-1112	70	8	is	be	AUX
m-1112	70	9	nothing	nothing	PRON
m-1112	70	10	,	,	PUNCT
m-1112	70	11	has	have	AUX
m-1112	70	12	not	not	PART
m-1112	70	13	any	any	DET
m-1112	70	14	position	position	NOUN
m-1112	70	15	and	and	CCONJ
m-1112	70	16	dimension	dimension	NOUN
m-1112	70	17	,	,	PUNCT
m-1112	70	18	and	and	CCONJ
m-1112	70	19	may	may	AUX
m-1112	70	20	be	be	AUX
m-1112	70	21	anywhere	anywhere	ADV
m-1112	70	22	in	in	ADP
m-1112	70	23	the	the	DET
m-1112	70	24	known	know	VERB
m-1112	70	25	space	space	NOUN
m-1112	70	26	therefore	therefore	ADV
m-1112	70	27	,	,	PUNCT
m-1112	70	28	the	the	DET
m-1112	70	29	primary	primary	ADJ
m-1112	70	30	point	point	NOUN
m-1112	70	31	a	a	PRON
m-1112	70	32	,	,	PUNCT
m-1112	70	33	being	be	AUX
m-1112	70	34	nothing	nothing	PRON
m-1112	70	35	also	also	ADV
m-1112	70	36	in	in	ADP
m-1112	70	37	no	no	DET
m-1112	70	38	space	space	NOUN
m-1112	70	39	,	,	PUNCT
m-1112	70	40	it	it	PRON
m-1112	70	41	is	be	AUX
m-1112	70	42	the	the	DET
m-1112	70	43	only	only	ADJ
m-1112	70	44	point	point	NOUN
m-1112	70	45	and	and	CCONJ
m-1112	70	46	no	no	ADV
m-1112	70	47	-	-	PUNCT
m-1112	70	48	where	where	SCONJ
m-1112	70	49	(	(	PUNCT
m-1112	70	50	i.e.	i.e.	X
m-1112	70	51	primary	primary	ADJ
m-1112	70	52	point	point	NOUN
m-1112	70	53	is	be	AUX
m-1112	70	54	the	the	DET
m-1112	70	55	only	only	ADJ
m-1112	70	56	space	space	NOUN
m-1112	70	57	and	and	CCONJ
m-1112	70	58	from	from	ADP
m-1112	70	59	this	this	PRON
m-1112	70	60	all	all	DET
m-1112	70	61	the	the	DET
m-1112	70	62	others	other	NOUN
m-1112	70	63	)	)	PUNCT
m-1112	70	64	.	.	PUNCT
m-1112	71	1	[	[	PUNCT
m-1112	71	2	6	6	NUM
m-1112	71	3	]	]	SYM
m-1112	71	4	a2	a2	PROPN
m-1112	71	5	..	..	PUNCT
m-1112	71	6	straight	straight	ADJ
m-1112	71	7	line	line	NOUN
m-1112	71	8	is	be	AUX
m-1112	71	9	0	0	NUM
m-1112	71	10	,	,	PUNCT
m-1112	71	11	positive	positive	ADJ
m-1112	71	12	,	,	PUNCT
m-1112	71	13	negative	negative	ADJ
m-1112	71	14	,	,	PUNCT
m-1112	71	15	consisted	consist	VERB
m-1112	71	16	of	of	ADP
m-1112	71	17	±	±	NUM
m-1112	71	18	∞	∞	NUM
m-1112	71	19	points	point	NOUN
m-1112	71	20	which	which	PRON
m-1112	71	21	are	be	AUX
m-1112	71	22	nothing	nothing	PRON
m-1112	71	23	,	,	PUNCT
m-1112	71	24	and	and	CCONJ
m-1112	71	25	since	since	SCONJ
m-1112	71	26	it	it	PRON
m-1112	71	27	is	be	AUX
m-1112	71	28	composed	compose	VERB
m-1112	71	29	of	of	ADP
m-1112	71	30	infinite	infinite	ADJ
m-1112	71	31	points	point	NOUN
m-1112	71	32	which	which	PRON
m-1112	71	33	are	be	AUX
m-1112	71	34	filling	fill	VERB
m-1112	71	35	the	the	DET
m-1112	71	36	line	line	NOUN
m-1112	71	37	,	,	PUNCT
m-1112	71	38	then	then	ADV
m-1112	71	39	nature	nature	NOUN
m-1112	71	40	of	of	ADP
m-1112	71	41	line	line	NOUN
m-1112	71	42	is	be	AUX
m-1112	71	43	that	that	PRON
m-1112	71	44	of	of	ADP
m-1112	71	45	point	point	NOUN
m-1112	71	46	i.e.	i.e.	X
m-1112	71	47	(	(	PUNCT
m-1112	71	48	the	the	DET
m-1112	71	49	all	all	PRON
m-1112	71	50	is	be	AUX
m-1112	71	51	one	one	NUM
m-1112	71	52	for	for	ADP
m-1112	71	53	lines	line	NOUN
m-1112	71	54	and	and	CCONJ
m-1112	71	55	for	for	ADP
m-1112	71	56	points	point	NOUN
m-1112	71	57	)	)	PUNCT
m-1112	71	58	.	.	PUNCT
m-1112	72	1	a3	a3	PROPN
m-1112	72	2	..	..	PUNCT
m-1112	72	3	plane	plane	NOUN
m-1112	72	4	is	be	AUX
m-1112	72	5	positive	positive	ADJ
m-1112	72	6	,	,	PUNCT
m-1112	72	7	negative	negative	ADJ
m-1112	72	8	,	,	PUNCT
m-1112	72	9	±	±	NUM
m-1112	72	10	neutral	neutral	ADJ
m-1112	72	11	lines	line	NOUN
m-1112	72	12	and	and	CCONJ
m-1112	72	13	since	since	SCONJ
m-1112	72	14	points	point	NOUN
m-1112	72	15	are	be	AUX
m-1112	72	16	imaginary	imaginary	ADJ
m-1112	72	17	lines	line	NOUN
m-1112	72	18	it	it	PRON
m-1112	72	19	is	be	AUX
m-1112	72	20	composed	compose	VERB
m-1112	72	21	of	of	ADP
m-1112	72	22	infinite	infinite	ADJ
m-1112	72	23	straight	straight	ADJ
m-1112	72	24	lines	line	NOUN
m-1112	72	25	which	which	PRON
m-1112	72	26	are	be	AUX
m-1112	72	27	filling	fill	VERB
m-1112	72	28	plane	plane	NOUN
m-1112	72	29	,	,	PUNCT
m-1112	72	30	so	so	CCONJ
m-1112	72	31	then	then	ADV
m-1112	72	32	,	,	PUNCT
m-1112	72	33	nature	nature	NOUN
m-1112	72	34	of	of	ADP
m-1112	72	35	plane	plane	NOUN
m-1112	72	36	is	be	AUX
m-1112	72	37	that	that	PRON
m-1112	72	38	of	of	ADP
m-1112	72	39	line	line	NOUN
m-1112	72	40	and	and	CCONJ
m-1112	72	41	that	that	PRON
m-1112	72	42	of	of	ADP
m-1112	72	43	points	point	NOUN
m-1112	72	44	(	(	PUNCT
m-1112	72	45	i.e.	i.e.	X
m-1112	72	46	the	the	DET
m-1112	72	47	all	all	PRON
m-1112	72	48	is	be	AUX
m-1112	72	49	one	one	NUM
m-1112	72	50	for	for	ADP
m-1112	72	51	planes	plane	NOUN
m-1112	72	52	,	,	PUNCT
m-1112	72	53	lines	line	NOUN
m-1112	72	54	and	and	CCONJ
m-1112	72	55	points	point	NOUN
m-1112	72	56	)	)	PUNCT
m-1112	72	57	.	.	PUNCT
m-1112	73	1	a4	a4	X
m-1112	73	2	..	..	PUNCT
m-1112	73	3	space	space	NOUN
m-1112	73	4	is	be	AUX
m-1112	73	5	+	+	ADV
m-1112	73	6	positive	positive	ADJ
m-1112	73	7	,	,	PUNCT
m-1112	73	8	negative	negative	ADJ
m-1112	73	9	,	,	PUNCT
m-1112	73	10	±	±	NUM
m-1112	73	11	neutral	neutral	ADJ
m-1112	73	12	planes	plane	NOUN
m-1112	73	13	and	and	CCONJ
m-1112	73	14	since	since	SCONJ
m-1112	73	15	points	point	NOUN
m-1112	73	16	are	be	AUX
m-1112	73	17	imaginary	imaginary	ADJ
m-1112	73	18	planes	plane	NOUN
m-1112	73	19	it	it	PRON
m-1112	73	20	is	be	AUX
m-1112	73	21	composed	compose	VERB
m-1112	73	22	of	of	ADP
m-1112	73	23	infinite	infinite	ADJ
m-1112	73	24	planes	plane	NOUN
m-1112	73	25	which	which	PRON
m-1112	73	26	are	be	AUX
m-1112	73	27	filling	fill	VERB
m-1112	73	28	space	space	NOUN
m-1112	73	29	,	,	PUNCT
m-1112	73	30	so	so	CCONJ
m-1112	73	31	then	then	ADV
m-1112	73	32	,	,	PUNCT
m-1112	73	33	nature	nature	NOUN
m-1112	73	34	of	of	ADP
m-1112	73	35	space	space	NOUN
m-1112	73	36	is	be	AUX
m-1112	73	37	that	that	PRON
m-1112	73	38	of	of	ADP
m-1112	73	39	plane	plane	NOUN
m-1112	73	40	and	and	CCONJ
m-1112	73	41	that	that	PRON
m-1112	73	42	of	of	ADP
m-1112	73	43	points	point	NOUN
m-1112	73	44	(	(	PUNCT
m-1112	73	45	i.e.	i.e.	X
m-1112	73	46	the	the	DET
m-1112	73	47	all	all	PRON
m-1112	73	48	is	be	AUX
m-1112	73	49	one	one	NUM
m-1112	73	50	for	for	ADP
m-1112	73	51	spaces	space	NOUN
m-1112	73	52	,	,	PUNCT
m-1112	73	53	planes	plane	NOUN
m-1112	73	54	,	,	PUNCT
m-1112	73	55	lines	line	NOUN
m-1112	73	56	and	and	CCONJ
m-1112	73	57	points	point	NOUN
m-1112	73	58	)	)	PUNCT
m-1112	73	59	.	.	PUNCT
m-1112	74	1	2a	2a	NUM
m-1112	74	2	…	…	PUNCT
m-1112	74	3	the	the	DET
m-1112	74	4	fundamental	fundamental	ADJ
m-1112	74	5	principles	principle	NOUN
m-1112	74	6	of	of	ADP
m-1112	74	7	e	e	NOUN
m-1112	74	8	-	-	NOUN
m-1112	74	9	geometry	geometry	NOUN
m-1112	74	10	.	.	PUNCT
m-1112	75	1	2a1	2a1	X
m-1112	75	2	..	..	PUNCT
m-1112	75	3	the	the	DET
m-1112	75	4	first	first	ADJ
m-1112	75	5	dimensional	dimensional	ADJ
m-1112	75	6	unit	unit	NOUN
m-1112	75	7	ab	ab	PROPN
m-1112	75	8	is	be	AUX
m-1112	75	9	of	of	ADP
m-1112	75	10	two	two	NUM
m-1112	75	11	points	point	NOUN
m-1112	75	12	a	a	DET
m-1112	75	13	,	,	PUNCT
m-1112	75	14	b	b	X
m-1112	75	15	not	not	PART
m-1112	75	16	coinciding	coincide	VERB
m-1112	75	17	which	which	PRON
m-1112	75	18	is	be	AUX
m-1112	75	19	the	the	DET
m-1112	75	20	geometrical	geometrical	ADJ
m-1112	75	21	shape	shape	NOUN
m-1112	75	22	that	that	PRON
m-1112	75	23	has	have	AUX
m-1112	75	24	as	as	ADP
m-1112	75	25	position	position	NOUN
m-1112	75	26	the	the	DET
m-1112	75	27	point	point	NOUN
m-1112	75	28	of	of	ADP
m-1112	75	29	direction	direction	NOUN
m-1112	75	30	ab⃗⃗⃗⃗	ab⃗⃗⃗⃗	PROPN
m-1112	75	31	⃗	⃗	PROPN
m-1112	75	32	,	,	PUNCT
m-1112	75	33	ba⃖⃗⃗⃗⃗⃗	ba⃖⃗⃗⃗⃗⃗	PROPN
m-1112	75	34	,	,	PUNCT
m-1112	75	35	and	and	CCONJ
m-1112	75	36	as	as	ADP
m-1112	75	37	magnitude	magnitude	NOUN
m-1112	75	38	(	(	PUNCT
m-1112	75	39	the	the	DET
m-1112	75	40	length	length	NOUN
m-1112	75	41	|ab|	|ab|	PROPN
m-1112	75	42	=	=	SYM
m-1112	75	43	0	0	PUNCT
m-1112	75	44	→	→	SYM
m-1112	75	45	n	n	PROPN
m-1112	75	46	→	→	SYM
m-1112	75	47	∞	∞	NUM
m-1112	75	48	)	)	PUNCT
m-1112	75	49	.	.	PUNCT
m-1112	76	1	|ab|	|ab|	NOUN
m-1112	76	2	is	be	AUX
m-1112	76	3	a	a	DET
m-1112	76	4	straight	straight	ADJ
m-1112	76	5	line	line	NOUN
m-1112	76	6	through	through	ADP
m-1112	76	7	points	point	NOUN
m-1112	76	8	a	a	DET
m-1112	76	9	,	,	PUNCT
m-1112	76	10	b	b	NOUN
m-1112	76	11	.	.	PUNCT
m-1112	77	1	(	(	PUNCT
m-1112	77	2	f.1b	f.1b	NOUN
m-1112	77	3	)	)	PUNCT
m-1112	77	4	,	,	PUNCT
m-1112	77	5	[	[	PUNCT
m-1112	77	6	6	6	NUM
m-1112	77	7	]	]	PUNCT
m-1112	77	8	↓	↓	NOUN
m-1112	78	1	a	a	DET
m-1112	78	2	c	c	PROPN
m-1112	78	3	b	b	PROPN
m-1112	78	4	a	a	DET
m-1112	78	5	c	c	NOUN
m-1112	78	6	b	b	PROPN
m-1112	78	7	ca	ca	NOUN
m-1112	78	8	+	+	CCONJ
m-1112	78	9	cb	cb	PROPN
m-1112	78	10	=	=	SYM
m-1112	78	11	ab	ab	PROPN
m-1112	78	12	,	,	PUNCT
m-1112	78	13	where	where	SCONJ
m-1112	78	14	,	,	PUNCT
m-1112	78	15	▫	▫	PROPN
m-1112	78	16	▫	▫	PROPN
m-1112	78	17	▫	▫	PROPN
m-1112	78	18	—	—	PUNCT
m-1112	78	19	▫	▫	PROPN
m-1112	78	20	—	—	PUNCT
m-1112	78	21	—	—	PUNCT
m-1112	78	22	▫	▫	PROPN
m-1112	78	23	—	—	PUNCT
m-1112	78	24	—	—	PUNCT
m-1112	78	25	—	—	PUNCT
m-1112	78	26	—	—	PUNCT
m-1112	78	27	▫	▫	ADJ
m-1112	78	28	—	—	PUNCT
m-1112	78	29	f.1(a	f.1(a	ADJ
m-1112	78	30	)	)	PUNCT
m-1112	78	31	f.1(b	f.1(b	ADJ
m-1112	78	32	)	)	PUNCT
m-1112	78	33	ds	ds	NOUN
m-1112	78	34	=	=	PUNCT
m-1112	78	35	an	an	DET
m-1112	78	36	infinitely	infinitely	ADV
m-1112	78	37	small	small	ADJ
m-1112	78	38	increment	increment	NOUN
m-1112	78	39	of	of	ADP
m-1112	78	40	length	length	NOUN
m-1112	78	41	ab	ab	PROPN
m-1112	78	42	in	in	ADP
m-1112	78	43	the	the	DET
m-1112	78	44	direction	direction	NOUN
m-1112	78	45	ab⃗⃗⃗⃗	ab⃗⃗⃗⃗	PROPN
m-1112	78	46	⃗	⃗	PROPN
m-1112	78	47	or	or	CCONJ
m-1112	78	48	ba⃖⃗⃗⃗⃗⃗	ba⃖⃗⃗⃗⃗⃗	PROPN
m-1112	78	49	.	.	PUNCT
m-1112	79	1	∞	∞	PROPN
m-1112	79	2	=	=	PUNCT
m-1112	79	3	an	an	DET
m-1112	79	4	infinitely	infinitely	ADV
m-1112	79	5	great	great	ADJ
m-1112	79	6	magnitude	magnitude	NOUN
m-1112	79	7	|ab|	|ab|	NOUN
m-1112	79	8	in	in	ADP
m-1112	79	9	the	the	DET
m-1112	79	10	directions	direction	NOUN
m-1112	79	11	ab⃗⃗⃗⃗	ab⃗⃗⃗⃗	PROPN
m-1112	79	12	⃗	⃗	PROPN
m-1112	79	13	,	,	PUNCT
m-1112	79	14	ba⃖⃗⃗⃗⃗⃗	ba⃖⃗⃗⃗⃗⃗	PROPN
m-1112	79	15	)	)	PUNCT
m-1112	79	16	.	.	PUNCT
m-1112	80	1	any	any	DET
m-1112	80	2	point	point	NOUN
m-1112	80	3	c	c	NOUN
m-1112	80	4	is	be	AUX
m-1112	80	5	on	on	ADP
m-1112	80	6	straight	straight	ADJ
m-1112	80	7	line	line	NOUN
m-1112	80	8	ab	ab	PROPN
m-1112	80	9	,	,	PUNCT
m-1112	80	10	only	only	ADV
m-1112	80	11	when	when	SCONJ
m-1112	80	12	exists	exist	VERB
m-1112	80	13	the	the	DET
m-1112	80	14	equation	equation	NOUN
m-1112	80	15	ca	can	AUX
m-1112	80	16	+	+	CCONJ
m-1112	80	17	cb	cb	PROPN
m-1112	80	18	=	=	SYM
m-1112	80	19	ab	ab	PROPN
m-1112	80	20	,	,	PUNCT
m-1112	80	21	i.e.	i.e.	X
m-1112	80	22	the	the	DET
m-1112	80	23	whole	whole	ADJ
m-1112	80	24	ab	ab	PROPN
m-1112	80	25	is	be	AUX
m-1112	80	26	equal	equal	ADJ
m-1112	80	27	to	to	ADP
m-1112	80	28	the	the	DET
m-1112	80	29	parts	part	NOUN
m-1112	80	30	ca	ca	NOUN
m-1112	80	31	and	and	CCONJ
m-1112	80	32	cb	cb	PROPN
m-1112	80	33	.	.	PUNCT
m-1112	81	1	(	(	PUNCT
m-1112	81	2	as	as	ADP
m-1112	81	3	equation	equation	NOUN
m-1112	81	4	f	f	PROPN
m-1112	81	5	1.b	1.b	NUM
m-1112	81	6	)	)	PUNCT
m-1112	81	7	.	.	PUNCT
m-1112	82	1	in	in	ADP
m-1112	82	2	case	case	NOUN
m-1112	82	3	that	that	SCONJ
m-1112	82	4	ca	can	AUX
m-1112	82	5	+	+	CCONJ
m-1112	82	6	cb	cb	PROPN
m-1112	82	7	>	>	X
m-1112	82	8	ab	ab	PROPN
m-1112	82	9	then	then	ADV
m-1112	82	10	point	point	VERB
m-1112	82	11	c	c	PROPN
m-1112	82	12	is	be	AUX
m-1112	82	13	not	not	PART
m-1112	82	14	on	on	ADP
m-1112	82	15	line	line	NOUN
m-1112	82	16	ab	ab	PROPN
m-1112	82	17	,	,	PUNCT
m-1112	82	18	and	and	CCONJ
m-1112	82	19	this	this	PRON
m-1112	82	20	is	be	AUX
m-1112	82	21	the	the	DET
m-1112	82	22	main	main	ADJ
m-1112	82	23	difference	difference	NOUN
m-1112	82	24	between	between	ADP
m-1112	82	25	euclidean	euclidean	ADJ
m-1112	82	26	and	and	CCONJ
m-1112	82	27	non	non	ADJ
m-1112	82	28	-	-	ADJ
m-1112	82	29	euclidean	euclidean	ADJ
m-1112	82	30	geometries	geometry	NOUN
m-1112	82	31	.	.	PUNCT
m-1112	83	1	in	in	ADP
m-1112	83	2	definition	definition	NOUN
m-1112	83	3	2	2	NUM
m-1112	83	4	(	(	PUNCT
m-1112	83	5	a	a	DET
m-1112	83	6	line	line	NOUN
m-1112	83	7	ab	ab	PROPN
m-1112	83	8	is	be	AUX
m-1112	83	9	breathless	breathless	ADJ
m-1112	83	10	length	length	NOUN
m-1112	83	11	)	)	PUNCT
m-1112	83	12	is	be	AUX
m-1112	83	13	altered	alter	VERB
m-1112	83	14	as	as	ADP
m-1112	83	15	for	for	ADP
m-1112	83	16	any	any	DET
m-1112	83	17	point	point	NOUN
m-1112	83	18	c	c	NOUN
m-1112	83	19	on	on	ADP
m-1112	83	20	line	line	NOUN
m-1112	83	21	ab	ab	PROPN
m-1112	83	22	exists	exist	VERB
m-1112	83	23	ca	can	AUX
m-1112	83	24	+	+	CCONJ
m-1112	83	25	cb	cb	PROPN
m-1112	83	26	=	=	PROPN
m-1112	83	27	ab	ab	PROPN
m-1112	83	28	.	.	PUNCT
m-1112	83	29	edge	edge	PROPN
m-1112	83	30	points	point	NOUN
m-1112	83	31	a	a	DET
m-1112	83	32	,	,	PUNCT
m-1112	83	33	b	b	X
m-1112	83	34	not	not	PART
m-1112	83	35	coinciding	coincide	VERB
m-1112	83	36	on	on	ADP
m-1112	83	37	monad	monad	PROPN
m-1112	83	38	ab	ab	PROPN
m-1112	83	39	,	,	PUNCT
m-1112	83	40	keep	keep	VERB
m-1112	83	41	the	the	DET
m-1112	83	42	properties	property	NOUN
m-1112	83	43	of	of	ADP
m-1112	83	44	complex	complex	ADJ
m-1112	83	45	numbers	number	NOUN
m-1112	83	46	with	with	ADP
m-1112	83	47	imaginary	imaginary	ADJ
m-1112	83	48	part	part	NOUN
m-1112	83	49	which	which	PRON
m-1112	83	50	differs	differ	VERB
m-1112	83	51	between	between	ADP
m-1112	83	52	the	the	DET
m-1112	83	53	infinite	infinite	ADJ
m-1112	83	54	point	point	NOUN
m-1112	83	55	[	[	X
m-1112	83	56	11	11	NUM
m-1112	83	57	]	]	PUNCT
m-1112	83	58	–	–	PUNCT
m-1112	83	59	[	[	X
m-1112	83	60	13	13	NUM
m-1112	83	61	]	]	PUNCT
m-1112	83	62	unit	unit	NOUN
m-1112	83	63	ab	ab	PROPN
m-1112	83	64	creates	create	VERB
m-1112	83	65	spaces	space	NOUN
m-1112	83	66	with	with	ADP
m-1112	83	67	two	two	NUM
m-1112	83	68	basic	basic	ADJ
m-1112	83	69	elements	element	NOUN
m-1112	83	70	,	,	PUNCT
m-1112	83	71	the	the	DET
m-1112	83	72	position	position	NOUN
m-1112	83	73	(	(	PUNCT
m-1112	83	74	which	which	PRON
m-1112	83	75	are	be	AUX
m-1112	83	76	the	the	DET
m-1112	83	77	three	three	NUM
m-1112	83	78	directions	direction	NOUN
m-1112	83	79	ab⃗⃗⃗⃗	ab⃗⃗⃗⃗	PROPN
m-1112	83	80	⃗	⃗	PROPN
m-1112	83	81	,	,	PUNCT
m-1112	83	82	ba⃖⃗⃗⃗⃗⃗	ba⃖⃗⃗⃗⃗⃗	PROPN
m-1112	83	83	,	,	PUNCT
m-1112	83	84	ab⃖⃗⃗⃗	ab⃖⃗⃗⃗	NOUN
m-1112	83	85	⃗	⃗	PROPN
m-1112	83	86	)	)	PUNCT
m-1112	83	87	and	and	CCONJ
m-1112	83	88	the	the	DET
m-1112	83	89	dimension	dimension	NOUN
m-1112	83	90	(	(	PUNCT
m-1112	83	91	which	which	PRON
m-1112	83	92	is	be	AUX
m-1112	83	93	the	the	DET
m-1112	83	94	magnitude	magnitude	NOUN
m-1112	83	95	n	n	CCONJ
m-1112	83	96	such	such	ADJ
m-1112	83	97	that	that	SCONJ
m-1112	83	98	n	n	NOUN
m-1112	83	99	=	=	SYM
m-1112	83	100	0	0	PUNCT
m-1112	83	101	→	→	SYM
m-1112	83	102	|ab|	|ab|	PROPN
m-1112	83	103	→	→	SYM
m-1112	83	104	∞	∞	NUM
m-1112	83	105	)	)	PUNCT
m-1112	83	106	,	,	PUNCT
m-1112	83	107	and	and	CCONJ
m-1112	83	108	when	when	SCONJ
m-1112	83	109	exists	exist	VERB
m-1112	83	110	,	,	PUNCT
m-1112	83	111	a	a	DET
m-1112	83	112	=	=	SYM
m-1112	83	113	b	b	NOUN
m-1112	83	114	=	=	PUNCT
m-1112	83	115	the	the	DET
m-1112	83	116	principle	principle	NOUN
m-1112	83	117	of	of	ADP
m-1112	83	118	the	the	DET
m-1112	83	119	equality	equality	NOUN
m-1112	83	120	.	.	PUNCT
m-1112	84	1	a	a	DET
m-1112	84	2	≠	≠	PROPN
m-1112	84	3	b	b	NOUN
m-1112	84	4	=	=	PUNCT
m-1112	84	5	the	the	DET
m-1112	84	6	principle	principle	NOUN
m-1112	84	7	of	of	ADP
m-1112	84	8	the	the	DET
m-1112	84	9	inequality	inequality	NOUN
m-1112	84	10	.	.	PUNCT
m-1112	85	1	a→↔←	a→↔←	PROPN
m-1112	85	2	b	b	PROPN
m-1112	85	3	=	=	SYM
m-1112	85	4	∞	∞	PROPN
m-1112	85	5	the	the	DET
m-1112	85	6	principle	principle	NOUN
m-1112	85	7	of	of	ADP
m-1112	85	8	virtual	virtual	ADJ
m-1112	85	9	displacements	displacement	NOUN
m-1112	85	10	.	.	PUNCT
m-1112	86	1	w	w	X
m-1112	86	2	=	=	SYM
m-1112	86	3	∫	∫	PROPN
m-1112	86	4	p.ds	p.ds	PROPN
m-1112	86	5	=	=	NOUN
m-1112	86	6	0	0	NUM
m-1112	86	7	,	,	PUNCT
m-1112	86	8	ds	ds	NOUN
m-1112	86	9	=	=	SYM
m-1112	86	10	∂w	∂w	PROPN
m-1112	86	11	/	/	SYM
m-1112	86	12	∂p	∂p	PROPN
m-1112	86	13	ijo	ijo	PROPN
m-1112	86	14	international	international	PROPN
m-1112	86	15	journal	journal	PROPN
m-1112	86	16	of	of	ADP
m-1112	86	17	mathematics	mathematics	PROPN
m-1112	86	18	(	(	PUNCT
m-1112	86	19	issn	issn	PROPN
m-1112	86	20	:	:	PUNCT
m-1112	86	21	2992	2992	NUM
m-1112	86	22	-	-	SYM
m-1112	86	23	4421	4421	NUM
m-1112	86	24	)	)	PUNCT
m-1112	86	25	volume	volume	NOUN
m-1112	86	26	08	08	NUM
m-1112	87	1	|	|	ADV
m-1112	87	2	issue	issue	NOUN
m-1112	87	3	08	08	NUM
m-1112	88	1	|	|	ADV
m-1112	88	2	august	august	PROPN
m-1112	88	3	2025	2025	NUM
m-1112	88	4	|	|	ADV
m-1112	88	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	88	6	ijo	ijo	PROPN
m-1112	88	7	journals	journal	NOUN
m-1112	88	8	5	5	NUM
m-1112	88	9	the	the	DET
m-1112	88	10	fundamental	fundamental	ADJ
m-1112	88	11	particles	particle	NOUN
m-1112	88	12	origination	origination	NOUN
m-1112	88	13	mechanism	mechanism	NOUN
m-1112	88	14	in	in	ADP
m-1112	88	15	mfmf	mfmf	PROPN
m-1112	88	16	pns	pns	PROPN
m-1112	88	17	caves	cave	NOUN
m-1112	88	18	.	.	PUNCT
m-1112	89	1	pa⃗⃗⃗⃗	pa⃗⃗⃗⃗	PROPN
m-1112	89	2	⃗	⃗	PROPN
m-1112	89	3	+	+	NUM
m-1112	89	4	pb⃖⃗⃗⃗⃗⃗	pb⃖⃗⃗⃗⃗⃗	ADJ
m-1112	89	5	=	=	NOUN
m-1112	89	6	0	0	PROPN
m-1112	90	1	the	the	DET
m-1112	90	2	principle	principle	NOUN
m-1112	90	3	of	of	ADP
m-1112	90	4	stability	stability	NOUN
m-1112	90	5	pa⃗⃗⃗⃗	pa⃗⃗⃗⃗	PROPN
m-1112	90	6	⃗	⃗	PROPN
m-1112	90	7	+	+	X
m-1112	90	8	pb⃖⃗⃗⃗⃗⃗	pb⃖⃗⃗⃗⃗⃗	X
m-1112	90	9	>	>	X
m-1112	90	10	<	<	X
m-1112	90	11	0	0	PUNCT
m-1112	91	1	the	the	DET
m-1112	91	2	principle	principle	NOUN
m-1112	91	3	of	of	ADP
m-1112	91	4	motion	motion	NOUN
m-1112	91	5	.	.	PUNCT
m-1112	92	1	2a2	2a2	NUM
m-1112	92	2	..	..	PUNCT
m-1112	92	3	the	the	DET
m-1112	92	4	monads	monad	NOUN
m-1112	92	5	=	=	SYM
m-1112	92	6	quantum	quantum	NOUN
m-1112	92	7	=	=	SYM
m-1112	92	8	𝐝𝐬⃗⃗⃗⃗	𝐝𝐬⃗⃗⃗⃗	PUNCT
m-1112	92	9	=	=	SYM
m-1112	92	10	ab	ab	PROPN
m-1112	92	11	/	/	PUNCT
m-1112	92	12	(	(	PUNCT
m-1112	92	13	n	n	NOUN
m-1112	92	14	=	=	SYM
m-1112	92	15	∞	∞	NUM
m-1112	92	16	→	→	SYM
m-1112	92	17	0	0	NUM
m-1112	92	18	)	)	PUNCT
m-1112	93	1	=	=	PUNCT
m-1112	93	2	[	[	PUNCT
m-1112	93	3	a	a	PRON
m-1112	93	4	±	±	NOUN
m-1112	93	5	b	b	NOUN
m-1112	94	1	i	i	NOUN
m-1112	94	2	]	]	PUNCT
m-1112	95	1	=	=	PUNCT
m-1112	95	2	0	0	PUNCT
m-1112	95	3	→	→	SYM
m-1112	95	4	∞	∞	NUM
m-1112	95	5	,	,	PUNCT
m-1112	95	6	are	be	AUX
m-1112	95	7	simultaneously	simultaneously	ADV
m-1112	95	8	(	(	PUNCT
m-1112	95	9	actual	actual	ADJ
m-1112	95	10	infinity	infinity	NOUN
m-1112	95	11	)	)	PUNCT
m-1112	95	12	and	and	CCONJ
m-1112	95	13	also	also	ADV
m-1112	95	14	(	(	PUNCT
m-1112	95	15	potential	potential	ADJ
m-1112	95	16	infinity	infinity	NOUN
m-1112	95	17	)	)	PUNCT
m-1112	95	18	in	in	ADP
m-1112	95	19	complex	complex	ADJ
m-1112	95	20	number	number	NOUN
m-1112	95	21	form	form	NOUN
m-1112	95	22	and	and	CCONJ
m-1112	95	23	this	this	DET
m-1112	95	24	defines	define	NOUN
m-1112	95	25	,	,	PUNCT
m-1112	95	26	infinity	infinity	NOUN
m-1112	95	27	which	which	PRON
m-1112	95	28	exists	exist	VERB
m-1112	95	29	between	between	ADP
m-1112	95	30	all	all	DET
m-1112	95	31	points	point	NOUN
m-1112	95	32	which	which	PRON
m-1112	95	33	are	be	AUX
m-1112	95	34	not	not	PART
m-1112	95	35	coinciding	coincide	VERB
m-1112	95	36	and	and	CCONJ
m-1112	95	37	where	where	SCONJ
m-1112	95	38	(	(	PUNCT
m-1112	95	39	ds	ds	X
m-1112	95	40	>	>	X
m-1112	95	41	0	0	NUM
m-1112	95	42	)	)	PUNCT
m-1112	95	43	,	,	PUNCT
m-1112	95	44	and	and	CCONJ
m-1112	95	45	because	because	SCONJ
m-1112	95	46	ds	ds	ADJ
m-1112	95	47	comprises	comprise	VERB
m-1112	95	48	any	any	DET
m-1112	95	49	two	two	NUM
m-1112	95	50	edge	edge	NOUN
m-1112	95	51	points	point	NOUN
m-1112	95	52	with	with	ADP
m-1112	95	53	imaginary	imaginary	ADJ
m-1112	95	54	part	part	NOUN
m-1112	95	55	then	then	ADV
m-1112	95	56	this	this	DET
m-1112	95	57	property	property	NOUN
m-1112	95	58	differs	differ	VERB
m-1112	95	59	between	between	ADP
m-1112	95	60	the	the	DET
m-1112	95	61	infinite	infinite	ADJ
m-1112	95	62	points	point	NOUN
m-1112	95	63	.	.	PUNCT
m-1112	96	1	the	the	DET
m-1112	96	2	plank	plank	NOUN
m-1112	96	3	length	length	NOUN
m-1112	96	4	is	be	AUX
m-1112	96	5	a	a	DET
m-1112	96	6	monad	monad	PROPN
m-1112	96	7	ds	ds	NOUN
m-1112	96	8	=	=	SYM
m-1112	96	9	1,62	1,62	NUM
m-1112	96	10	x	x	SYM
m-1112	96	11	𝟏𝟎−𝟑𝟓	𝟏𝟎−𝟑𝟓	NOUN
m-1112	96	12	m	m	VERB
m-1112	96	13	,	,	PUNCT
m-1112	96	14	for	for	ADP
m-1112	96	15	the	the	DET
m-1112	96	16	two	two	NUM
m-1112	96	17	points	point	NOUN
m-1112	96	18	a	a	DET
m-1112	96	19	,	,	PUNCT
m-1112	96	20	b	b	NOUN
m-1112	96	21	,	,	PUNCT
m-1112	96	22	and	and	CCONJ
m-1112	96	23	for	for	ADP
m-1112	96	24	the	the	DET
m-1112	96	25	moment	moment	NOUN
m-1112	96	26	is	be	AUX
m-1112	96	27	accepted	accept	VERB
m-1112	96	28	as	as	ADP
m-1112	96	29	the	the	DET
m-1112	96	30	smallest	small	ADJ
m-1112	96	31	possible	possible	ADJ
m-1112	96	32	size	size	NOUN
m-1112	96	33	.	.	PUNCT
m-1112	97	1	monad	monad	PROPN
m-1112	97	2	is	be	AUX
m-1112	97	3	also	also	ADV
m-1112	97	4	infinitely	infinitely	ADV
m-1112	97	5	divided	divide	VERB
m-1112	97	6	because	because	SCONJ
m-1112	97	7	edge	edge	NOUN
m-1112	97	8	points	point	NOUN
m-1112	97	9	a	a	PRON
m-1112	97	10	,	,	PUNCT
m-1112	97	11	b	b	NOUN
m-1112	97	12	are	be	AUX
m-1112	97	13	not	not	PART
m-1112	97	14	coinciding	coincide	VERB
m-1112	98	1	i.e.	i.e.	X
m-1112	98	2	...	...	PUNCT
m-1112	98	3	ds	ds	VERB
m-1112	98	4	=	=	SYM
m-1112	98	5	1x𝟏𝟎−𝑵	1x𝟏𝟎−𝑵	PROPN
m-1112	98	6	<	<	X
m-1112	98	7	∞	∞	PROPN
m-1112	98	8	,	,	PUNCT
m-1112	98	9	where	where	SCONJ
m-1112	98	10	n	n	PRON
m-1112	98	11	is	be	AUX
m-1112	98	12	any	any	DET
m-1112	98	13	number	number	NOUN
m-1112	98	14	.	.	PUNCT
m-1112	99	1	1	1	X
m-1112	99	2	..	..	NUM
m-1112	99	3	spaces	space	NOUN
m-1112	99	4	of	of	ADP
m-1112	99	5	unit	unit	NOUN
m-1112	99	6	-	-	PUNCT
m-1112	99	7	ab	ab	PROPN
m-1112	99	8	are	be	AUX
m-1112	99	9	(	(	PUNCT
m-1112	99	10	in	in	ADP
m-1112	99	11	plane	plane	NOUN
m-1112	99	12	)	)	PUNCT
m-1112	99	13	the	the	DET
m-1112	99	14	infinite	infinite	ADJ
m-1112	99	15	(	(	PUNCT
m-1112	99	16	+	+	ADJ
m-1112	99	17	)	)	PUNCT
m-1112	99	18	circumscribed	circumscribed	ADJ
m-1112	99	19	-	-	PUNCT
m-1112	99	20	regular	regular	ADJ
m-1112	99	21	-	-	PUNCT
m-1112	99	22	polygons	polygon	NOUN
m-1112	99	23	on	on	ADP
m-1112	99	24	the	the	DET
m-1112	99	25	circles	circle	NOUN
m-1112	99	26	with	with	ADP
m-1112	99	27	ab	ab	PROPN
m-1112	99	28	as	as	ADP
m-1112	99	29	side	side	NOUN
m-1112	99	30	(	(	PUNCT
m-1112	99	31	repetition	repetition	NOUN
m-1112	99	32	of	of	ADP
m-1112	99	33	unit	unit	NOUN
m-1112	99	34	ab	ab	PROPN
m-1112	99	35	)	)	PUNCT
m-1112	99	36	the	the	DET
m-1112	99	37	nth	nth	NOUN
m-1112	99	38	space	space	NOUN
m-1112	99	39	,	,	PUNCT
m-1112	99	40	the	the	DET
m-1112	99	41	nth	nth	NOUN
m-1112	99	42	unit	unit	NOUN
m-1112	99	43	tensor	tensor	NOUN
m-1112	99	44	of	of	ADP
m-1112	99	45	the	the	DET
m-1112	99	46	n	n	ADV
m-1112	99	47	equal	equal	ADJ
m-1112	99	48	finite	finite	ADJ
m-1112	99	49	elements	element	NOUN
m-1112	99	50	ds	ds	VERB
m-1112	99	51	,	,	PUNCT
m-1112	99	52	and	and	CCONJ
m-1112	99	53	for	for	ADP
m-1112	99	54	the	the	DET
m-1112	99	55	∞	∞	PROPN
m-1112	99	56	spaces	space	NOUN
m-1112	99	57	,	,	PUNCT
m-1112	99	58	the	the	DET
m-1112	99	59	line	line	NOUN
m-1112	99	60	ab	ab	PROPN
m-1112	99	61	↔	↔	PROPN
m-1112	99	62	.	.	PUNCT
m-1112	100	1	(	(	PUNCT
m-1112	100	2	fig-1	fig-1	X
m-1112	100	3	)	)	PUNCT
m-1112	100	4	the	the	DET
m-1112	100	5	diameter	diameter	NOUN
m-1112	100	6	of	of	ADP
m-1112	100	7	this	this	DET
m-1112	100	8	circles	circle	NOUN
m-1112	100	9	extends	extend	VERB
m-1112	100	10	to	to	PART
m-1112	100	11	infinity	infinity	NOUN
m-1112	100	12	(	(	PUNCT
m-1112	100	13	it	it	PRON
m-1112	100	14	is	be	AUX
m-1112	100	15	of	of	ADP
m-1112	100	16	potential	potential	ADJ
m-1112	100	17	nature	nature	NOUN
m-1112	100	18	)	)	PUNCT
m-1112	100	19	.	.	PUNCT
m-1112	101	1	[	[	X
m-1112	101	2	11	11	NUM
m-1112	101	3	]	]	SYM
m-1112	101	4	2	2	NUM
m-1112	101	5	..	..	PUNCT
m-1112	101	6	anti	anti	ADJ
m-1112	101	7	spaces	space	NOUN
m-1112	101	8	of	of	ADP
m-1112	101	9	unit	unit	NOUN
m-1112	101	10	ab	ab	PROPN
m-1112	101	11	are	be	AUX
m-1112	101	12	(	(	PUNCT
m-1112	101	13	in	in	ADP
m-1112	101	14	the	the	DET
m-1112	101	15	three	three	NUM
m-1112	101	16	dimensional	dimensional	ADJ
m-1112	101	17	space	space	NOUN
m-1112	101	18	)	)	PUNCT
m-1112	101	19	the	the	DET
m-1112	101	20	symmetrically	symmetrically	ADV
m-1112	101	21	infinite	infinite	ADJ
m-1112	101	22	(	(	PUNCT
m-1112	101	23	-	-	PUNCT
m-1112	101	24	)	)	PUNCT
m-1112	101	25	circumscribedregular	circumscribedregular	ADJ
m-1112	101	26	-	-	PUNCT
m-1112	101	27	polygons	polygon	NOUN
m-1112	101	28	on	on	ADP
m-1112	101	29	the	the	DET
m-1112	101	30	circles	circle	NOUN
m-1112	101	31	or	or	CCONJ
m-1112	101	32	(	(	PUNCT
m-1112	101	33	a	a	DET
m-1112	101	34	solid	solid	ADJ
m-1112	101	35	in	in	ADP
m-1112	101	36	cube	cube	NOUN
m-1112	101	37	in	in	ADP
m-1112	101	38	sphere	sphere	NOUN
m-1112	101	39	with	with	ADP
m-1112	101	40	ab	ab	PROPN
m-1112	101	41	as	as	ADP
m-1112	101	42	side	side	NOUN
m-1112	101	43	of	of	ADP
m-1112	101	44	the	the	DET
m-1112	101	45	solid	solid	ADJ
m-1112	101	46	)	)	PUNCT
m-1112	101	47	.	.	PUNCT
m-1112	102	1	the	the	DET
m-1112	102	2	harmonic	harmonic	ADJ
m-1112	102	3	repetition	repetition	NOUN
m-1112	102	4	of	of	ADP
m-1112	102	5	unit	unit	NOUN
m-1112	102	6	ba	ba	PROPN
m-1112	102	7	,	,	PUNCT
m-1112	102	8	symmetrical	symmetrical	ADJ
m-1112	102	9	to	to	ADP
m-1112	102	10	ab	ab	PROPN
m-1112	102	11	)	)	PUNCT
m-1112	102	12	is	be	AUX
m-1112	102	13	the	the	DET
m-1112	102	14	nth	nth	NOUN
m-1112	102	15	anti	anti	ADJ
m-1112	102	16	-	-	NOUN
m-1112	102	17	space	space	NOUN
m-1112	102	18	,	,	PUNCT
m-1112	102	19	the	the	DET
m-1112	102	20	nth	nth	NOUN
m-1112	102	21	unit	unit	NOUN
m-1112	102	22	tensor	tensor	NOUN
m-1112	102	23	of	of	ADP
m-1112	102	24	the	the	DET
m-1112	102	25	n	n	ADV
m-1112	102	26	equal	equal	ADJ
m-1112	102	27	finite	finite	ADJ
m-1112	102	28	anti	anti	ADJ
m-1112	102	29	elements	element	NOUN
m-1112	102	30	,	,	PUNCT
m-1112	102	31	and	and	CCONJ
m-1112	102	32	for	for	ADP
m-1112	102	33	the	the	DET
m-1112	102	34	∞	∞	PROPN
m-1112	102	35	spaces	space	NOUN
m-1112	102	36	,	,	PUNCT
m-1112	102	37	the	the	DET
m-1112	102	38	sphere	sphere	NOUN
m-1112	102	39	through	through	ADP
m-1112	102	40	line	line	NOUN
m-1112	102	41	ba	ba	PROPN
m-1112	102	42	.the	.the	DET
m-1112	102	43	diameter	diameter	NOUN
m-1112	102	44	of	of	ADP
m-1112	102	45	this	this	DET
m-1112	102	46	spheres	sphere	NOUN
m-1112	102	47	extends	extend	VERB
m-1112	102	48	to	to	ADP
m-1112	102	49	the	the	DET
m-1112	102	50	infinity	infinity	NOUN
m-1112	102	51	(	(	PUNCT
m-1112	102	52	it	it	PRON
m-1112	102	53	is	be	AUX
m-1112	102	54	of	of	ADP
m-1112	102	55	potential	potential	ADJ
m-1112	102	56	nature	nature	NOUN
m-1112	102	57	)	)	PUNCT
m-1112	102	58	.	.	PUNCT
m-1112	103	1	[	[	X
m-1112	103	2	11	11	NUM
m-1112	103	3	]	]	SYM
m-1112	103	4	3	3	NUM
m-1112	103	5	..	..	SYM
m-1112	103	6	subspaces	subspace	NOUN
m-1112	103	7	of	of	ADP
m-1112	103	8	unit	unit	NOUN
m-1112	103	9	ab	ab	PROPN
m-1112	103	10	are	be	AUX
m-1112	103	11	(	(	PUNCT
m-1112	103	12	in	in	ADP
m-1112	103	13	plane	plane	NOUN
m-1112	103	14	)	)	PUNCT
m-1112	103	15	the	the	DET
m-1112	103	16	infinite	infinite	ADJ
m-1112	103	17	inscribed	inscribe	VERB
m-1112	103	18	-	-	PUNCT
m-1112	103	19	regular	regular	ADJ
m-1112	103	20	-	-	PUNCT
m-1112	103	21	polygons	polygon	NOUN
m-1112	103	22	in	in	ADP
m-1112	103	23	the	the	DET
m-1112	103	24	circle	circle	NOUN
m-1112	103	25	with	with	ADP
m-1112	103	26	ab	ab	PROPN
m-1112	103	27	as	as	ADP
m-1112	103	28	diameter	diameter	NOUN
m-1112	103	29	(	(	PUNCT
m-1112	103	30	are	be	AUX
m-1112	103	31	the	the	DET
m-1112	103	32	harmonic	harmonic	ADJ
m-1112	103	33	repetition	repetition	NOUN
m-1112	103	34	of	of	ADP
m-1112	103	35	the	the	DET
m-1112	103	36	roots	root	NOUN
m-1112	103	37	in	in	ADP
m-1112	103	38	unit	unit	NOUN
m-1112	103	39	ab	ab	PROPN
m-1112	103	40	)	)	PUNCT
m-1112	103	41	and	and	CCONJ
m-1112	103	42	in	in	ADP
m-1112	103	43	nth	nth	PROPN
m-1112	103	44	sub	sub	NOUN
m-1112	103	45	-	-	NOUN
m-1112	103	46	space	space	NOUN
m-1112	103	47	,	,	PUNCT
m-1112	103	48	the	the	DET
m-1112	103	49	nth	nth	NOUN
m-1112	103	50	unit	unit	NOUN
m-1112	103	51	tensor	tensor	NOUN
m-1112	103	52	of	of	ADP
m-1112	103	53	the	the	DET
m-1112	103	54	n	n	NOUN
m-1112	103	55	finite	finite	ADJ
m-1112	103	56	roots	root	NOUN
m-1112	103	57	and	and	CCONJ
m-1112	103	58	in	in	ADP
m-1112	103	59	case	case	NOUN
m-1112	103	60	of	of	ADP
m-1112	103	61	the	the	DET
m-1112	103	62	∞	∞	PROPN
m-1112	103	63	elements	element	NOUN
m-1112	103	64	are	be	AUX
m-1112	103	65	the	the	DET
m-1112	103	66	points	point	NOUN
m-1112	103	67	on	on	ADP
m-1112	103	68	the	the	DET
m-1112	103	69	circle	circle	NOUN
m-1112	103	70	,	,	PUNCT
m-1112	103	71	and	and	CCONJ
m-1112	103	72	for	for	ADP
m-1112	103	73	3d	3d	NOUN
m-1112	103	74	-	-	PUNCT
m-1112	103	75	space	space	NOUN
m-1112	103	76	,	,	PUNCT
m-1112	103	77	the	the	DET
m-1112	103	78	points	point	NOUN
m-1112	103	79	on	on	ADP
m-1112	103	80	sphere	sphere	NOUN
m-1112	103	81	n.ab	n.ab	PROPN
m-1112	103	82	)	)	PUNCT
m-1112	103	83	.	.	PUNCT
m-1112	104	1	the	the	DET
m-1112	104	2	superposition	superposition	NOUN
m-1112	104	3	of	of	ADP
m-1112	104	4	spaces	space	NOUN
m-1112	104	5	,	,	PUNCT
m-1112	104	6	anti	anti	ADJ
m-1112	104	7	-	-	ADJ
m-1112	104	8	spaces	space	NOUN
m-1112	104	9	and	and	CCONJ
m-1112	104	10	sub	sub	ADJ
m-1112	104	11	-	-	ADJ
m-1112	104	12	space	space	ADJ
m-1112	104	13	layers	layer	NOUN
m-1112	104	14	of	of	ADP
m-1112	104	15	unit	unit	NOUN
m-1112	104	16	ab	ab	PROPN
m-1112	104	17	is	be	AUX
m-1112	104	18	shown	show	VERB
m-1112	104	19	in	in	ADP
m-1112	104	20	figure	figure	NOUN
m-1112	104	21	.	.	PUNCT
m-1112	105	1	remark	remark	VERB
m-1112	105	2	:	:	PUNCT
m-1112	105	3	(	(	PUNCT
m-1112	105	4	+	+	NOUN
m-1112	105	5	)	)	PUNCT
m-1112	105	6	spaces	space	NOUN
m-1112	105	7	,	,	PUNCT
m-1112	105	8	(	(	PUNCT
m-1112	105	9	-	-	PUNCT
m-1112	105	10	)	)	PUNCT
m-1112	105	11	anti	anti	ADJ
m-1112	105	12	-spaces	-space	NOUN
m-1112	105	13	,	,	PUNCT
m-1112	105	14	(	(	PUNCT
m-1112	105	15	±	±	NOUN
m-1112	105	16	)	)	PUNCT
m-1112	105	17	sub	sub	NOUN
m-1112	105	18	-	-	NOUN
m-1112	105	19	spaces	space	NOUN
m-1112	105	20	,	,	PUNCT
m-1112	105	21	of	of	ADP
m-1112	105	22	a	a	DET
m-1112	105	23	unit	unit	NOUN
m-1112	105	24	ab	ab	PROPN
m-1112	105	25	are	be	AUX
m-1112	105	26	between	between	ADP
m-1112	105	27	magnitude	magnitude	NOUN
m-1112	105	28	(	(	PUNCT
m-1112	105	29	point	point	NOUN
m-1112	105	30	=	=	SYM
m-1112	105	31	0	0	NUM
m-1112	105	32	=	=	SYM
m-1112	105	33	nothing	nothing	PRON
m-1112	105	34	)	)	PUNCT
m-1112	105	35	and	and	CCONJ
m-1112	105	36	the	the	DET
m-1112	105	37	infinite	infinite	ADJ
m-1112	105	38	magnitude	magnitude	NOUN
m-1112	105	39	(	(	PUNCT
m-1112	105	40	↔	↔	PROPN
m-1112	105	41	=	=	SYM
m-1112	105	42	ab	ab	PROPN
m-1112	105	43	=	=	SYM
m-1112	105	44	±	±	PROPN
m-1112	105	45	∞	∞	NOUN
m-1112	105	46	=	=	SYM
m-1112	105	47	infinite	infinite	NOUN
m-1112	105	48	)	)	PUNCT
m-1112	105	49	which	which	PRON
m-1112	105	50	means	mean	VERB
m-1112	105	51	that	that	SCONJ
m-1112	105	52	all	all	DET
m-1112	105	53	spaces	space	NOUN
m-1112	105	54	exist	exist	VERB
m-1112	105	55	in	in	ADP
m-1112	105	56	one	one	NUM
m-1112	105	57	space	space	NOUN
m-1112	105	58	only	only	ADV
m-1112	105	59	.	.	PUNCT
m-1112	106	1	because	because	SCONJ
m-1112	106	2	in	in	ADP
m-1112	106	3	spaces	space	NOUN
m-1112	106	4	and	and	CCONJ
m-1112	106	5	anti	anti	NOUN
m-1112	106	6	-	-	ADJ
m-1112	106	7	spaces	space	NOUN
m-1112	106	8	,	,	PUNCT
m-1112	106	9	the	the	DET
m-1112	106	10	∞	∞	NUM
m-1112	106	11	spaces	space	NOUN
m-1112	106	12	of	of	ADP
m-1112	106	13	unit	unit	NOUN
m-1112	106	14	ab	ab	PROPN
m-1112	106	15	is	be	AUX
m-1112	106	16	sector	sector	NOUN
m-1112	106	17	ab	ab	PROPN
m-1112	106	18	↔	↔	PROPN
m-1112	106	19	,	,	PUNCT
m-1112	106	20	and	and	CCONJ
m-1112	106	21	in	in	ADP
m-1112	106	22	sub	sub	NOUN
m-1112	106	23	-	-	NOUN
m-1112	106	24	spaces	space	NOUN
m-1112	106	25	the	the	DET
m-1112	106	26	∞	∞	NUM
m-1112	106	27	sub	sub	NOUN
m-1112	106	28	-	-	NOUN
m-1112	106	29	spaces	space	NOUN
m-1112	106	30	of	of	ADP
m-1112	106	31	unit	unit	NOUN
m-1112	106	32	ab	ab	PROPN
m-1112	106	33	are	be	AUX
m-1112	106	34	the	the	DET
m-1112	106	35	points	point	NOUN
m-1112	106	36	on	on	ADP
m-1112	106	37	the	the	DET
m-1112	106	38	circle	circle	NOUN
m-1112	106	39	with	with	ADP
m-1112	106	40	ab	ab	PROPN
m-1112	106	41	as	as	ADP
m-1112	106	42	diameter	diameter	NOUN
m-1112	106	43	,	,	PUNCT
m-1112	106	44	then	then	ADV
m-1112	106	45	this	this	PRON
m-1112	106	46	ordered	order	VERB
m-1112	106	47	continuum	continuum	ADJ
m-1112	106	48	for	for	ADP
m-1112	106	49	points	point	NOUN
m-1112	106	50	on	on	ADP
m-1112	106	51	the	the	DET
m-1112	106	52	circle	circle	NOUN
m-1112	106	53	of	of	ADP
m-1112	106	54	unit	unit	NOUN
m-1112	106	55	ab	ab	PROPN
m-1112	106	56	and	and	CCONJ
m-1112	106	57	on	on	ADP
m-1112	106	58	line	line	NOUN
m-1112	106	59	ab	ab	PROPN
m-1112	106	60	shows	show	VERB
m-1112	106	61	the	the	DET
m-1112	106	62	correlation	correlation	NOUN
m-1112	106	63	of	of	ADP
m-1112	106	64	spaces	space	NOUN
m-1112	106	65	in	in	ADP
m-1112	106	66	unit	unit	NOUN
m-1112	106	67	ab	ab	PROPN
m-1112	106	68	.	.	PUNCT
m-1112	107	1	i.e.	i.e.	X
m-1112	107	2	monads	monad	NOUN
m-1112	107	3	ds	ds	ADJ
m-1112	107	4	=	=	SYM
m-1112	107	5	0	0	PUNCT
m-1112	108	1	→	→	SYM
m-1112	108	2	∞	∞	PROPN
m-1112	108	3	are	be	AUX
m-1112	108	4	simultaneously	simultaneously	ADV
m-1112	108	5	,	,	PUNCT
m-1112	108	6	actual	actual	ADJ
m-1112	108	7	infinity	infinity	NOUN
m-1112	108	8	(	(	PUNCT
m-1112	108	9	because	because	SCONJ
m-1112	108	10	for	for	ADP
m-1112	108	11	n	n	NOUN
m-1112	108	12	=	=	SYM
m-1112	108	13	∞	∞	NUM
m-1112	108	14	then	then	ADV
m-1112	108	15	ds	ds	ADJ
m-1112	108	16	=	=	SYM
m-1112	108	17	[	[	PUNCT
m-1112	108	18	ab	ab	PROPN
m-1112	108	19	/	/	SYM
m-1112	108	20	n	n	PROPN
m-1112	108	21	=	=	SYM
m-1112	108	22	∞	∞	NOUN
m-1112	108	23	]	]	PUNCT
m-1112	109	1	=	=	SYM
m-1112	109	2	0	0	NUM
m-1112	109	3	,	,	PUNCT
m-1112	109	4	or	or	CCONJ
m-1112	109	5	a	a	DET
m-1112	109	6	point	point	NOUN
m-1112	109	7	)	)	PUNCT
m-1112	109	8	and	and	CCONJ
m-1112	109	9	,	,	PUNCT
m-1112	109	10	potential	potential	ADJ
m-1112	109	11	infinity	infinity	NOUN
m-1112	109	12	,	,	PUNCT
m-1112	109	13	(	(	PUNCT
m-1112	109	14	because	because	SCONJ
m-1112	109	15	for	for	ADP
m-1112	109	16	n	n	NOUN
m-1112	109	17	=	=	SYM
m-1112	109	18	0	0	PUNCT
m-1112	109	19	then	then	ADV
m-1112	109	20	ds	ds	VERB
m-1112	109	21	=	=	SYM
m-1112	109	22	[	[	PUNCT
m-1112	109	23	ab	ab	PROPN
m-1112	109	24	/	/	SYM
m-1112	109	25	n	n	PROPN
m-1112	109	26	=	=	SYM
m-1112	109	27	0	0	NUM
m-1112	109	28	]	]	PUNCT
m-1112	110	1	=	=	PUNCT
m-1112	110	2	∞	∞	PROPN
m-1112	110	3	is	be	AUX
m-1112	110	4	the	the	DET
m-1112	110	5	straight	straight	ADJ
m-1112	110	6	line	line	NOUN
m-1112	110	7	through	through	ADP
m-1112	110	8	ab	ab	PROPN
m-1112	110	9	.	.	PUNCT
m-1112	111	1	infinity	infinity	NOUN
m-1112	111	2	exists	exist	VERB
m-1112	111	3	between	between	ADP
m-1112	111	4	all	all	DET
m-1112	111	5	points	point	NOUN
m-1112	111	6	ijo	ijo	PROPN
m-1112	111	7	international	international	PROPN
m-1112	111	8	journal	journal	PROPN
m-1112	111	9	of	of	ADP
m-1112	111	10	mathematics	mathematics	PROPN
m-1112	111	11	(	(	PUNCT
m-1112	111	12	issn	issn	PROPN
m-1112	111	13	:	:	PUNCT
m-1112	111	14	2992	2992	NUM
m-1112	111	15	-	-	SYM
m-1112	111	16	4421	4421	NUM
m-1112	111	17	)	)	PUNCT
m-1112	112	1	volume	volume	NOUN
m-1112	112	2	08	08	NUM
m-1112	113	1	|	|	ADV
m-1112	113	2	issue	issue	NOUN
m-1112	113	3	08	08	NUM
m-1112	114	1	|	|	ADV
m-1112	114	2	august	august	PROPN
m-1112	114	3	2025	2025	NUM
m-1112	114	4	|	|	ADV
m-1112	114	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	114	6	ijo	ijo	PROPN
m-1112	114	7	journals	journal	NOUN
m-1112	114	8	6	6	NUM
m-1112	114	9	the	the	DET
m-1112	114	10	fundamental	fundamental	ADJ
m-1112	114	11	particles	particle	NOUN
m-1112	114	12	origination	origination	NOUN
m-1112	114	13	mechanism	mechanism	NOUN
m-1112	114	14	in	in	ADP
m-1112	114	15	mfmf	mfmf	PROPN
m-1112	114	16	pns	pns	PROPN
m-1112	114	17	caves	cave	NOUN
m-1112	114	18	.	.	PUNCT
m-1112	115	1	which	which	PRON
m-1112	115	2	are	be	AUX
m-1112	115	3	not	not	PART
m-1112	115	4	coinciding	coincide	VERB
m-1112	115	5	,	,	PUNCT
m-1112	115	6	and	and	CCONJ
m-1112	115	7	because	because	SCONJ
m-1112	115	8	monads	monad	NOUN
m-1112	115	9	ds	ds	NOUN
m-1112	115	10	comprises	comprise	VERB
m-1112	115	11	any	any	DET
m-1112	115	12	two	two	NUM
m-1112	115	13	edge	edge	NOUN
m-1112	115	14	-	-	PUNCT
m-1112	115	15	points	point	NOUN
m-1112	115	16	with	with	ADP
m-1112	115	17	imaginary	imaginary	ADJ
m-1112	115	18	part	part	NOUN
m-1112	115	19	,	,	PUNCT
m-1112	115	20	then	then	ADV
m-1112	115	21	this	this	DET
m-1112	115	22	property	property	NOUN
m-1112	115	23	is	be	AUX
m-1112	115	24	the	the	DET
m-1112	115	25	difference	difference	NOUN
m-1112	115	26	between	between	ADP
m-1112	115	27	the	the	DET
m-1112	115	28	infinite	infinite	ADJ
m-1112	115	29	points	point	NOUN
m-1112	115	30	.	.	PUNCT
m-1112	116	1	[	[	X
m-1112	116	2	11	11	NUM
m-1112	116	3	]	]	SYM
m-1112	116	4	4	4	NUM
m-1112	116	5	..	..	PUNCT
m-1112	116	6	neutral	neutral	ADJ
m-1112	116	7	-	-	PUNCT
m-1112	116	8	spaces	space	NOUN
m-1112	116	9	of	of	ADP
m-1112	116	10	unit	unit	NOUN
m-1112	116	11	-	-	PUNCT
m-1112	116	12	ab	ab	PROPN
m-1112	116	13	are	be	AUX
m-1112	116	14	(	(	PUNCT
m-1112	116	15	in	in	ADP
m-1112	116	16	plane	plane	NOUN
m-1112	116	17	)	)	PUNCT
m-1112	116	18	the	the	DET
m-1112	116	19	infinite	infinite	ADJ
m-1112	116	20	circles	circle	NOUN
m-1112	116	21	with	with	ADP
m-1112	116	22	ab	ab	PROPN
m-1112	116	23	as	as	ADP
m-1112	116	24	diameter	diameter	NOUN
m-1112	116	25	(	(	PUNCT
m-1112	116	26	the	the	DET
m-1112	116	27	harmonic	harmonic	ADJ
m-1112	116	28	repetition	repetition	NOUN
m-1112	116	29	of	of	ADP
m-1112	116	30	the	the	DET
m-1112	116	31	roots	root	NOUN
m-1112	116	32	in	in	ADP
m-1112	116	33	unit	unit	NOUN
m-1112	116	34	ab	ab	PROPN
m-1112	116	35	)	)	PUNCT
m-1112	116	36	and	and	CCONJ
m-1112	116	37	in	in	ADP
m-1112	116	38	nth	nth	PROPN
m-1112	116	39	sub	sub	NOUN
m-1112	116	40	-	-	NOUN
m-1112	116	41	space	space	NOUN
m-1112	116	42	,	,	PUNCT
m-1112	116	43	the	the	DET
m-1112	116	44	nth	nth	NOUN
m-1112	116	45	unit	unit	NOUN
m-1112	116	46	tensor	tensor	NOUN
m-1112	116	47	of	of	ADP
m-1112	116	48	the	the	DET
m-1112	116	49	n	n	NOUN
m-1112	116	50	finite	finite	ADJ
m-1112	116	51	roots	root	NOUN
m-1112	116	52	,	,	PUNCT
m-1112	116	53	and	and	CCONJ
m-1112	116	54	in	in	ADP
m-1112	116	55	case	case	NOUN
m-1112	116	56	of	of	ADP
m-1112	116	57	the	the	DET
m-1112	116	58	∞	∞	PROPN
m-1112	116	59	elements	element	NOUN
m-1112	116	60	are	be	AUX
m-1112	116	61	the	the	DET
m-1112	116	62	points	point	NOUN
m-1112	116	63	on	on	ADP
m-1112	116	64	the	the	DET
m-1112	116	65	circle	circle	NOUN
m-1112	116	66	,	,	PUNCT
m-1112	116	67	and	and	CCONJ
m-1112	116	68	for	for	ADP
m-1112	116	69	the	the	DET
m-1112	116	70	3d	3d	NOUN
m-1112	116	71	-	-	PUNCT
m-1112	116	72	space	space	NOUN
m-1112	116	73	,	,	PUNCT
m-1112	116	74	the	the	DET
m-1112	116	75	points	point	NOUN
m-1112	116	76	on	on	ADP
m-1112	116	77	the	the	DET
m-1112	116	78	unit	unit	NOUN
m-1112	116	79	sphere	sphere	NOUN
m-1112	116	80	ab	ab	PROPN
m-1112	116	81	)	)	PUNCT
m-1112	116	82	.	.	PUNCT
m-1112	117	1	since	since	SCONJ
m-1112	117	2	spaces	space	NOUN
m-1112	117	3	,	,	PUNCT
m-1112	117	4	anti	anti	ADJ
m-1112	117	5	–	–	PUNCT
m-1112	117	6	spaces	space	NOUN
m-1112	117	7	and	and	CCONJ
m-1112	117	8	sub	sub	NOUN
m-1112	117	9	-	-	NOUN
m-1112	117	10	spaces	space	NOUN
m-1112	117	11	are	be	AUX
m-1112	117	12	created	create	VERB
m-1112	117	13	from	from	ADP
m-1112	117	14	unit	unit	NOUN
m-1112	117	15	ab	ab	PROPN
m-1112	117	16	,	,	PUNCT
m-1112	117	17	and	and	CCONJ
m-1112	117	18	are	be	AUX
m-1112	117	19	property	property	NOUN
m-1112	117	20	of	of	ADP
m-1112	117	21	this	this	DET
m-1112	117	22	unit	unit	NOUN
m-1112	117	23	only	only	ADV
m-1112	117	24	,	,	PUNCT
m-1112	117	25	therefore	therefore	ADV
m-1112	117	26	these	these	PRON
m-1112	117	27	are	be	AUX
m-1112	117	28	a	a	DET
m-1112	117	29	restrained	restrained	ADJ
m-1112	117	30	system	system	NOUN
m-1112	117	31	(	(	PUNCT
m-1112	117	32	s	s	NOUN
m-1112	117	33	)	)	PUNCT
m-1112	117	34	presupposition	presupposition	NOUN
m-1112	117	35	for	for	ADP
m-1112	117	36	unit	unit	NOUN
m-1112	117	37	|ab|	|ab|	NOUN
m-1112	117	38	=	=	SYM
m-1112	117	39	ds	ds	ADJ
m-1112	117	40	(	(	PUNCT
m-1112	117	41	displacement	displacement	NOUN
m-1112	117	42	ds	ds	NOUN
m-1112	117	43	)	)	PUNCT
m-1112	117	44	is	be	AUX
m-1112	117	45	point	point	NOUN
m-1112	117	46	a	a	PRON
m-1112	117	47	to	to	PART
m-1112	117	48	move	move	VERB
m-1112	117	49	at	at	ADP
m-1112	117	50	the	the	DET
m-1112	117	51	new	new	ADJ
m-1112	117	52	position	position	NOUN
m-1112	117	53	b	b	PROPN
m-1112	117	54	(	(	PUNCT
m-1112	117	55	a	a	DET
m-1112	117	56	≡	≡	PROPN
m-1112	117	57	b	b	PROPN
m-1112	117	58	)	)	PUNCT
m-1112	117	59	which	which	PRON
m-1112	117	60	means	mean	VERB
m-1112	117	61	an	an	DET
m-1112	117	62	impulse	impulse	ADJ
m-1112	117	63	(	(	PUNCT
m-1112	117	64	p	p	NOUN
m-1112	117	65	)	)	PUNCT
m-1112	117	66	transfers	transfer	NOUN
m-1112	117	67	point	point	VERB
m-1112	117	68	a	a	PRON
m-1112	117	69	to	to	ADP
m-1112	117	70	b	b	NOUN
m-1112	117	71	.	.	PUNCT
m-1112	118	1	since	since	SCONJ
m-1112	118	2	in	in	ADP
m-1112	118	3	each	each	DET
m-1112	118	4	restrained	restrained	ADJ
m-1112	118	5	system	system	NOUN
m-1112	118	6	(	(	PUNCT
m-1112	118	7	s	s	NOUN
m-1112	118	8	)	)	PUNCT
m-1112	118	9	the	the	DET
m-1112	118	10	work	work	NOUN
m-1112	118	11	done	do	VERB
m-1112	118	12	(	(	PUNCT
m-1112	118	13	w	w	NOUN
m-1112	118	14	)	)	PUNCT
m-1112	118	15	by	by	ADP
m-1112	118	16	impulse	impulse	ADJ
m-1112	118	17	(	(	PUNCT
m-1112	118	18	p	p	NOUN
m-1112	118	19	)	)	PUNCT
m-1112	118	20	on	on	ADP
m-1112	118	21	a	a	DET
m-1112	118	22	virtual	virtual	ADJ
m-1112	118	23	displacement	displacement	NOUN
m-1112	118	24	(	(	PUNCT
m-1112	118	25	ds	ds	INTJ
m-1112	118	26	>	>	X
m-1112	118	27	0	0	NUM
m-1112	118	28	)	)	PUNCT
m-1112	118	29	is	be	AUX
m-1112	118	30	zero	zero	NUM
m-1112	118	31	,	,	PUNCT
m-1112	118	32	or	or	CCONJ
m-1112	118	33	w	w	NOUN
m-1112	118	34	=	=	SYM
m-1112	118	35	∫	∫	PROPN
m-1112	118	36	𝑃𝑑𝑠	𝑃𝑑𝑠	NOUN
m-1112	118	37	𝐵	𝐵	NOUN
m-1112	118	38	𝐴	𝐴	NOUN
m-1112	118	39	=	=	SYM
m-1112	118	40	0	0	PUNCT
m-1112	119	1	therefore	therefore	ADV
m-1112	119	2	,	,	PUNCT
m-1112	119	3	each	each	DET
m-1112	119	4	unit	unit	NOUN
m-1112	119	5	|ab|	|ab|	VERB
m-1112	120	1	=	=	SYM
m-1112	120	2	|ds|	|ds|	X
m-1112	120	3	>	>	X
m-1112	120	4	0	0	NUM
m-1112	120	5	exists	exist	VERB
m-1112	120	6	,	,	PUNCT
m-1112	120	7	by	by	ADP
m-1112	120	8	this	this	DET
m-1112	120	9	inner	inner	ADJ
m-1112	120	10	impulse	impulse	NOUN
m-1112	120	11	(	(	PUNCT
m-1112	120	12	p	p	NOUN
m-1112	120	13	)	)	PUNCT
m-1112	120	14	which	which	PRON
m-1112	120	15	means	mean	VERB
m-1112	120	16	that	that	SCONJ
m-1112	120	17	,	,	PUNCT
m-1112	120	18	the	the	DET
m-1112	120	19	position	position	NOUN
m-1112	120	20	and	and	CCONJ
m-1112	120	21	dimension	dimension	NOUN
m-1112	120	22	of	of	ADP
m-1112	120	23	all	all	DET
m-1112	120	24	points	point	NOUN
m-1112	120	25	which	which	PRON
m-1112	120	26	are	be	AUX
m-1112	120	27	connected	connect	VERB
m-1112	120	28	across	across	ADP
m-1112	120	29	the	the	DET
m-1112	120	30	universe	universe	NOUN
m-1112	120	31	and	and	CCONJ
m-1112	120	32	that	that	PRON
m-1112	120	33	of	of	ADP
m-1112	120	34	spaces	space	NOUN
m-1112	120	35	,	,	PUNCT
m-1112	120	36	exist	exist	VERB
m-1112	120	37	because	because	SCONJ
m-1112	120	38	of	of	ADP
m-1112	120	39	this	this	DET
m-1112	120	40	static	static	ADJ
m-1112	120	41	inner	inner	ADJ
m-1112	120	42	impulse	impulse	ADJ
m-1112	120	43	p	p	NOUN
m-1112	120	44	between	between	ADP
m-1112	120	45	a	a	PRON
m-1112	120	46	and	and	CCONJ
m-1112	120	47	b	b	NOUN
m-1112	120	48	,	,	PUNCT
m-1112	120	49	on	on	ADP
m-1112	120	50	the	the	DET
m-1112	120	51	contrary	contrary	NOUN
m-1112	120	52	,	,	PUNCT
m-1112	120	53	should	should	AUX
m-1112	120	54	be	be	AUX
m-1112	120	55	one	one	NUM
m-1112	120	56	point	point	NOUN
m-1112	120	57	only	only	ADV
m-1112	120	58	(	(	PUNCT
m-1112	120	59	primary	primary	ADJ
m-1112	120	60	-	-	PUNCT
m-1112	120	61	point	point	NOUN
m-1112	120	62	=	=	NOUN
m-1112	120	63	black	black	ADJ
m-1112	120	64	-	-	PUNCT
m-1112	120	65	hole	hole	NOUN
m-1112	120	66	→	→	SYM
m-1112	120	67	ds	ds	ADJ
m-1112	120	68	=	=	SYM
m-1112	120	69	0	0	PUNCT
m-1112	120	70	→	→	SYM
m-1112	120	71	p	p	X
m-1112	120	72	=	=	SYM
m-1112	120	73	∞	∞	PROPN
m-1112	120	74	)	)	PUNCT
m-1112	120	75	impulse	impulse	ADJ
m-1112	120	76	p	p	NOUN
m-1112	120	77	=	=	NOUN
m-1112	120	78	∞	∞	PROPN
m-1112	120	79	,	,	PUNCT
m-1112	120	80	and	and	CCONJ
m-1112	120	81	may	may	AUX
m-1112	120	82	be	be	AUX
m-1112	120	83	vacuum	vacuum	NOUN
m-1112	120	84	,	,	PUNCT
m-1112	120	85	momentum	momentum	NOUN
m-1112	120	86	or	or	CCONJ
m-1112	120	87	potential	potential	ADJ
m-1112	120	88	or	or	CCONJ
m-1112	120	89	induced	induced	ADJ
m-1112	120	90	potential	potential	NOUN
m-1112	120	91	and	and	CCONJ
m-1112	120	92	it	it	PRON
m-1112	120	93	is	be	AUX
m-1112	120	94	a	a	DET
m-1112	120	95	type	type	NOUN
m-1112	120	96	of	of	ADP
m-1112	120	97	effect	effect	NOUN
m-1112	120	98	of	of	ADP
m-1112	120	99	push	push	NOUN
m-1112	120	100	nature	nature	NOUN
m-1112	120	101	.	.	PUNCT
m-1112	121	1	2a3	2a3	NUM
m-1112	121	2	..	..	PUNCT
m-1112	121	3	the	the	DET
m-1112	121	4	superposition	superposition	NOUN
m-1112	121	5	of	of	ADP
m-1112	121	6	plane	plane	NOUN
m-1112	121	7	space	space	NOUN
m-1112	121	8	,	,	PUNCT
m-1112	121	9	anti	anti	ADJ
m-1112	121	10	-	-	ADJ
m-1112	121	11	space	space	ADJ
m-1112	121	12	layers	layer	NOUN
m-1112	121	13	and	and	CCONJ
m-1112	121	14	sub	sub	ADJ
m-1112	121	15	-	-	ADJ
m-1112	121	16	space	space	ADJ
m-1112	121	17	layers	layer	NOUN
m-1112	121	18	the	the	DET
m-1112	121	19	simultaneously	simultaneously	ADV
m-1112	121	20	co	co	NOUN
m-1112	121	21	-	-	NOUN
m-1112	121	22	existence	existence	NOUN
m-1112	121	23	of	of	ADP
m-1112	121	24	spaces	space	NOUN
m-1112	121	25	,	,	PUNCT
m-1112	121	26	anti	anti	ADJ
m-1112	121	27	-	-	ADJ
m-1112	121	28	spaces	space	NOUN
m-1112	121	29	and	and	CCONJ
m-1112	121	30	sub	sub	NOUN
m-1112	121	31	-	-	NOUN
m-1112	121	32	spaces	space	NOUN
m-1112	121	33	of	of	ADP
m-1112	121	34	any	any	DET
m-1112	121	35	unit	unit	NOUN
m-1112	121	36	|ab|	|ab|	PROPN
m-1112	121	37	,	,	PUNCT
m-1112	121	38	unit	unit	NOUN
m-1112	121	39	ab	ab	NOUN
m-1112	121	40	=	=	NOUN
m-1112	121	41	0	0	PUNCT
m-1112	121	42	→	→	SYM
m-1112	121	43	∞	∞	NUM
m-1112	121	44	,	,	PUNCT
m-1112	121	45	(	(	PUNCT
m-1112	121	46	a	a	DET
m-1112	121	47	≡	≡	PROPN
m-1112	121	48	b	b	PROPN
m-1112	121	49	)	)	PUNCT
m-1112	121	50	i.e.	i.e.	X
m-1112	121	51	,	,	PUNCT
m-1112	121	52	euclidean	euclidean	ADJ
m-1112	121	53	,	,	PUNCT
m-1112	121	54	elliptic	elliptic	ADJ
m-1112	121	55	,	,	PUNCT
m-1112	121	56	spherical	spherical	ADJ
m-1112	121	57	,	,	PUNCT
m-1112	121	58	parabolic	parabolic	ADJ
m-1112	121	59	,	,	PUNCT
m-1112	121	60	hyperbolic	hyperbolic	ADJ
m-1112	121	61	,	,	PUNCT
m-1112	121	62	geodesics	geodesic	NOUN
m-1112	121	63	,	,	PUNCT
m-1112	121	64	metric	metric	ADJ
m-1112	121	65	and	and	CCONJ
m-1112	121	66	non	non	ADJ
m-1112	121	67	-	-	ADJ
m-1112	121	68	metric	metric	ADJ
m-1112	121	69	geometries	geometry	NOUN
m-1112	121	70	,	,	PUNCT
m-1112	121	71	exist	exist	VERB
m-1112	121	72	in	in	ADP
m-1112	121	73	euclidean	euclidean	ADJ
m-1112	121	74	model	model	NOUN
m-1112	121	75	as	as	ADP
m-1112	121	76	an	an	DET
m-1112	121	77	sub	sub	NOUN
m-1112	121	78	-	-	NOUN
m-1112	121	79	case	case	NOUN
m-1112	121	80	within	within	ADP
m-1112	121	81	.	.	PUNCT
m-1112	122	1	the	the	DET
m-1112	122	2	interconnection	interconnection	NOUN
m-1112	122	3	of	of	ADP
m-1112	122	4	homogeneous	homogeneous	ADJ
m-1112	122	5	and	and	CCONJ
m-1112	122	6	heterogeneous	heterogeneous	ADJ
m-1112	122	7	bounded	bounded	ADJ
m-1112	122	8	spaces	space	NOUN
m-1112	122	9	anti	anti	ADJ
m-1112	122	10	-	-	ADJ
m-1112	122	11	spaces	space	NOUN
m-1112	122	12	and	and	CCONJ
m-1112	122	13	subspaces	subspace	NOUN
m-1112	122	14	of	of	ADP
m-1112	122	15	the	the	DET
m-1112	122	16	universe	universe	NOUN
m-1112	122	17	.	.	PUNCT
m-1112	123	1	the	the	DET
m-1112	123	2	unity	unity	NOUN
m-1112	123	3	of	of	ADP
m-1112	123	4	opposites	opposite	NOUN
m-1112	123	5	is	be	AUX
m-1112	123	6	also	also	ADV
m-1112	123	7	the	the	DET
m-1112	123	8	quantized	quantize	VERB
m-1112	123	9	property	property	NOUN
m-1112	123	10	of	of	ADP
m-1112	123	11	euclidean	euclidean	ADJ
m-1112	123	12	geometry	geometry	NOUN
m-1112	123	13	<	<	X
m-1112	123	14	all	all	PRON
m-1112	123	15	is	be	AUX
m-1112	123	16	one	one	NUM
m-1112	123	17	>	>	PUNCT
m-1112	123	18	as	as	SCONJ
m-1112	123	19	it	it	PRON
m-1112	123	20	is	be	AUX
m-1112	123	21	discrete	discrete	ADJ
m-1112	123	22	(	(	PUNCT
m-1112	123	23	for	for	ADP
m-1112	123	24	monads	monad	NOUN
m-1112	123	25	ab	ab	PROPN
m-1112	123	26	)	)	PUNCT
m-1112	123	27	and	and	CCONJ
m-1112	123	28	continuous	continuous	ADJ
m-1112	123	29	(	(	PUNCT
m-1112	123	30	for	for	ADP
m-1112	123	31	points	point	NOUN
m-1112	123	32	a	a	DET
m-1112	123	33	,	,	PUNCT
m-1112	123	34	b	b	NOUN
m-1112	123	35	)	)	PUNCT
m-1112	123	36	.	.	PUNCT
m-1112	124	1	for	for	ADP
m-1112	124	2	primary	primary	ADJ
m-1112	124	3	point	point	NOUN
m-1112	124	4	a	a	PRON
m-1112	124	5	it	it	PRON
m-1112	124	6	is	be	AUX
m-1112	124	7	the	the	DET
m-1112	124	8	only	only	ADJ
m-1112	124	9	space	space	NOUN
m-1112	124	10	[	[	X
m-1112	124	11	17	17	NUM
m-1112	124	12	]	]	PUNCT
m-1112	124	13	the	the	DET
m-1112	124	14	unique	unique	ADJ
m-1112	124	15	case	case	NOUN
m-1112	124	16	where	where	SCONJ
m-1112	124	17	p	p	NOUN
m-1112	124	18	=	=	NOUN
m-1112	124	19	0	0	NUM
m-1112	124	20	and	and	CCONJ
m-1112	124	21	δs	δs	VERB
m-1112	124	22	>	>	X
m-1112	124	23	0	0	PUNCT
m-1112	125	1	=	=	SYM
m-1112	125	2	ab	ab	PROPN
m-1112	125	3	→	→	PUNCT
m-1112	125	4	∞	∞	PROPN
m-1112	125	5	is	be	AUX
m-1112	125	6	the	the	DET
m-1112	125	7	primary	primary	ADJ
m-1112	125	8	planck`s	planck`s	NOUN
m-1112	125	9	space	space	NOUN
m-1112	125	10	[	[	PUNCT
m-1112	125	11	ps	ps	X
m-1112	125	12	]	]	PUNCT
m-1112	125	13	the	the	DET
m-1112	125	14	spherical	spherical	ADJ
m-1112	125	15	connection	connection	NOUN
m-1112	125	16	of	of	ADP
m-1112	125	17	the	the	DET
m-1112	125	18	same	same	ADJ
m-1112	125	19	points	point	NOUN
m-1112	125	20	in	in	ADP
m-1112	125	21	ps	ps	PROPN
m-1112	125	22	,	,	PUNCT
m-1112	125	23	is	be	AUX
m-1112	125	24	related	relate	VERB
m-1112	125	25	on	on	ADP
m-1112	125	26	the	the	DET
m-1112	125	27	influence	influence	NOUN
m-1112	125	28	(	(	PUNCT
m-1112	125	29	p	p	X
m-1112	125	30	=	=	NOUN
m-1112	125	31	0	0	PUNCT
m-1112	125	32	→	→	SYM
m-1112	125	33	ab⃗⃗⃗⃗	ab⃗⃗⃗⃗	PROPN
m-1112	125	34	⃗	⃗	PROPN
m-1112	125	35	→	→	SYM
m-1112	125	36	∞	∞	NUM
m-1112	125	37	)	)	PUNCT
m-1112	125	38	of	of	ADP
m-1112	125	39	the	the	DET
m-1112	125	40	infinite	infinite	NOUN
m-1112	125	41	(	(	PUNCT
m-1112	125	42	∞	∞	PROPN
m-1112	125	43	)	)	PUNCT
m-1112	125	44	equilibrium	equilibrium	NOUN
m-1112	125	45	primary	primary	ADJ
m-1112	125	46	-	-	PUNCT
m-1112	125	47	spaces	space	NOUN
m-1112	125	48	and	and	CCONJ
m-1112	125	49	anti	anti	NOUN
m-1112	125	50	-	-	ADJ
m-1112	125	51	spaces	space	NOUN
m-1112	125	52	.	.	PUNCT
m-1112	126	1	for	for	ADP
m-1112	126	2	every	every	DET
m-1112	126	3	point	point	NOUN
m-1112	126	4	in	in	ADP
m-1112	126	5	[	[	PUNCT
m-1112	126	6	ps	ps	NOUN
m-1112	126	7	]	]	PUNCT
m-1112	126	8	exist	exist	VERB
m-1112	126	9	the	the	DET
m-1112	126	10	three	three	NUM
m-1112	126	11	spatial	spatial	ADJ
m-1112	126	12	dimensions	dimension	NOUN
m-1112	126	13	(	(	PUNCT
m-1112	126	14	x	x	X
m-1112	126	15	,	,	PUNCT
m-1112	126	16	y	y	PROPN
m-1112	126	17	,	,	PUNCT
m-1112	126	18	z	z	PROPN
m-1112	126	19	)	)	PUNCT
m-1112	126	20	and	and	CCONJ
m-1112	126	21	the	the	DET
m-1112	126	22	infinite	infinite	ADJ
m-1112	126	23	dimensions	dimension	NOUN
m-1112	126	24	of	of	ADP
m-1112	126	25	the	the	DET
m-1112	126	26	(	(	PUNCT
m-1112	126	27	i	i	NOUN
m-1112	126	28	)	)	PUNCT
m-1112	126	29	layers	layer	NOUN
m-1112	126	30	at	at	ADP
m-1112	126	31	this	this	DET
m-1112	126	32	point	point	NOUN
m-1112	126	33	existing	exist	VERB
m-1112	126	34	from	from	ADP
m-1112	126	35	the	the	DET
m-1112	126	36	other	other	ADJ
m-1112	126	37	layers	layer	NOUN
m-1112	126	38	(	(	PUNCT
m-1112	126	39	at	at	ADP
m-1112	126	40	small	small	ADJ
m-1112	126	41	scale	scale	NOUN
m-1112	126	42	using	use	VERB
m-1112	126	43	coordinate	coordinate	NOUN
m-1112	126	44	system	system	NOUN
m-1112	126	45	)	)	PUNCT
m-1112	126	46	of	of	ADP
m-1112	126	47	primary	primary	ADJ
m-1112	126	48	anti	anti	ADJ
m-1112	126	49	-	-	ADJ
m-1112	126	50	space	space	ADJ
m-1112	126	51	and	and	CCONJ
m-1112	126	52	sub	sub	NOUN
m-1112	126	53	-	-	NOUN
m-1112	126	54	space	space	NOUN
m-1112	126	55	where	where	SCONJ
m-1112	126	56	i	i	PRON
m-1112	126	57	=	=	NOUN
m-1112	126	58	1	1	NUM
m-1112	126	59	→	→	SYM
m-1112	126	60	∞	∞	NUM
m-1112	126	61	.	.	PUNCT
m-1112	127	1	it	it	PRON
m-1112	127	2	has	have	AUX
m-1112	127	3	been	be	AUX
m-1112	127	4	also	also	ADV
m-1112	127	5	shown	show	VERB
m-1112	127	6	that	that	SCONJ
m-1112	127	7	,	,	PUNCT
m-1112	127	8	every	every	DET
m-1112	127	9	point	point	NOUN
m-1112	127	10	m	m	VERB
m-1112	127	11	of	of	ADP
m-1112	127	12	primary	primary	ADJ
m-1112	127	13	planck`s	planck`s	NOUN
m-1112	127	14	space	space	NOUN
m-1112	127	15	[	[	PUNCT
m-1112	127	16	ps	ps	X
m-1112	127	17	]	]	PUNCT
m-1112	127	18	exists	exist	VERB
m-1112	127	19	in	in	ADP
m-1112	127	20	this	this	DET
m-1112	127	21	space	space	NOUN
m-1112	127	22	with	with	ADP
m-1112	127	23	a	a	DET
m-1112	127	24	deficit	deficit	NOUN
m-1112	127	25	of	of	ADP
m-1112	127	26	impulse	impulse	ADJ
m-1112	127	27	p	p	NOUN
m-1112	127	28	=	=	NOUN
m-1112	127	29	0	0	PUNCT
m-1112	127	30	→	→	SYM
m-1112	127	31	∞	∞	NUM
m-1112	127	32	,	,	PUNCT
m-1112	127	33	due	due	ADP
m-1112	127	34	to	to	ADP
m-1112	127	35	the	the	DET
m-1112	127	36	influence	influence	NOUN
m-1112	127	37	of	of	ADP
m-1112	127	38	the	the	DET
m-1112	127	39	other	other	ADJ
m-1112	127	40	equilibrium	equilibrium	NOUN
m-1112	127	41	primary	primary	ADJ
m-1112	127	42	spaces	space	NOUN
m-1112	127	43	.	.	PUNCT
m-1112	128	1	ijo	ijo	PROPN
m-1112	128	2	international	international	PROPN
m-1112	128	3	journal	journal	PROPN
m-1112	128	4	of	of	ADP
m-1112	128	5	mathematics	mathematics	PROPN
m-1112	128	6	(	(	PUNCT
m-1112	128	7	issn	issn	PROPN
m-1112	128	8	:	:	PUNCT
m-1112	128	9	2992	2992	NUM
m-1112	128	10	-	-	SYM
m-1112	128	11	4421	4421	NUM
m-1112	128	12	)	)	PUNCT
m-1112	128	13	volume	volume	NOUN
m-1112	128	14	08	08	NUM
m-1112	129	1	|	|	ADV
m-1112	129	2	issue	issue	NOUN
m-1112	129	3	08	08	NUM
m-1112	130	1	|	|	ADV
m-1112	130	2	august	august	PROPN
m-1112	130	3	2025	2025	NUM
m-1112	130	4	|	|	ADV
m-1112	130	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	130	6	ijo	ijo	PROPN
m-1112	130	7	journals	journal	NOUN
m-1112	130	8	7	7	NUM
m-1112	130	9	the	the	DET
m-1112	130	10	fundamental	fundamental	ADJ
m-1112	130	11	particles	particle	NOUN
m-1112	130	12	origination	origination	NOUN
m-1112	130	13	mechanism	mechanism	NOUN
m-1112	130	14	in	in	ADP
m-1112	130	15	mfmf	mfmf	PROPN
m-1112	130	16	pns	pns	PROPN
m-1112	130	17	caves	cave	NOUN
m-1112	130	18	.	.	PUNCT
m-1112	131	1	the	the	DET
m-1112	131	2	unique	unique	ADJ
m-1112	131	3	case	case	NOUN
m-1112	131	4	where	where	SCONJ
m-1112	131	5	p	p	NOUN
m-1112	131	6	=	=	NOUN
m-1112	131	7	0	0	NUM
m-1112	131	8	and	and	CCONJ
m-1112	131	9	δs	δs	NOUN
m-1112	131	10	=	=	SYM
m-1112	131	11	0	0	NUM
m-1112	131	12	→	→	SYM
m-1112	131	13	0	0	NUM
m-1112	131	14	is	be	AUX
m-1112	131	15	the	the	DET
m-1112	131	16	primary	primary	ADJ
m-1112	131	17	neutral	neutral	ADJ
m-1112	131	18	space	space	NOUN
m-1112	131	19	[	[	PUNCT
m-1112	131	20	pns	pns	NOUN
m-1112	131	21	]	]	PUNCT
m-1112	131	22	the	the	DET
m-1112	131	23	⊕	⊕	PROPN
m-1112	131	24	material	material	NOUN
m-1112	131	25	point	point	NOUN
m-1112	131	26	≡	≡	PROPN
m-1112	131	27	the	the	DET
m-1112	131	28	space	space	NOUN
m-1112	131	29	,	,	PUNCT
m-1112	131	30	continually	continually	ADV
m-1112	131	31	rotates	rotate	VERB
m-1112	131	32	around	around	ADP
m-1112	131	33	the	the	DET
m-1112	131	34	⊝	⊝	NUM
m-1112	131	35	material	material	NOUN
m-1112	131	36	point	point	NOUN
m-1112	131	37	≡	≡	PROPN
m-1112	131	38	the	the	DET
m-1112	131	39	anti	anti	ADJ
m-1112	131	40	-	-	NOUN
m-1112	131	41	space	space	NOUN
m-1112	131	42	,	,	PUNCT
m-1112	131	43	on	on	ADP
m-1112	131	44	2r	2r	NUM
m-1112	131	45	circle	circle	NOUN
m-1112	131	46	.	.	PUNCT
m-1112	132	1	[	[	X
m-1112	132	2	pns	pns	X
m-1112	132	3	]	]	X
m-1112	132	4	space	space	NOUN
m-1112	132	5	is	be	AUX
m-1112	132	6	a	a	DET
m-1112	132	7	this	this	DET
m-1112	132	8	property	property	NOUN
m-1112	132	9	of	of	ADP
m-1112	132	10	points	point	NOUN
m-1112	132	11	in	in	ADP
m-1112	132	12	neutral	neutral	ADJ
m-1112	132	13	space	space	NOUN
m-1112	132	14	is	be	AUX
m-1112	132	15	the	the	DET
m-1112	132	16	cause	cause	NOUN
m-1112	132	17	of	of	ADP
m-1112	132	18	their	their	PRON
m-1112	132	19	continuously	continuously	ADV
m-1112	132	20	survive	survive	VERB
m-1112	132	21	.	.	PUNCT
m-1112	133	1	the	the	DET
m-1112	133	2	quantization	quantization	NOUN
m-1112	133	3	of	of	ADP
m-1112	133	4	points	point	NOUN
m-1112	133	5	becomes	become	VERB
m-1112	133	6	through	through	ADP
m-1112	133	7	vector	vector	NOUN
m-1112	133	8	unit	unit	NOUN
m-1112	133	9	d	d	PROPN
m-1112	133	10	�	�	PROPN
m-1112	133	11	̆	̆	NOUN
m-1112	133	12	�	�	PROPN
m-1112	133	13	=	=	SYM
m-1112	133	14	|ab|	|ab|	PROPN
m-1112	133	15	,	,	PUNCT
m-1112	133	16	and	and	CCONJ
m-1112	133	17	for	for	ADP
m-1112	133	18	energy	energy	NOUN
m-1112	133	19	is	be	AUX
m-1112	133	20	done	do	VERB
m-1112	133	21	in	in	ADP
m-1112	133	22	bound	bind	VERB
m-1112	133	23	states	state	NOUN
m-1112	133	24	(	(	PUNCT
m-1112	133	25	loops	loop	NOUN
m-1112	133	26	)	)	PUNCT
m-1112	133	27	which	which	PRON
m-1112	133	28	withhold	withhold	VERB
m-1112	133	29	the	the	DET
m-1112	133	30	diffusion	diffusion	NOUN
m-1112	133	31	(	(	PUNCT
m-1112	133	32	flow	flow	NOUN
m-1112	133	33	)	)	PUNCT
m-1112	133	34	.the	.the	PUNCT
m-1112	134	1	two	two	NUM
m-1112	134	2	fundamental	fundamental	ADJ
m-1112	134	3	dimensions	dimension	NOUN
m-1112	134	4	(	(	PUNCT
m-1112	134	5	quanta	quanta	PROPN
m-1112	134	6	of	of	ADP
m-1112	134	7	points	point	NOUN
m-1112	134	8	(	(	PUNCT
m-1112	134	9	ds	ds	NOUN
m-1112	134	10	)	)	PUNCT
m-1112	134	11	and	and	CCONJ
m-1112	134	12	quanta	quanta	PROPN
m-1112	134	13	of	of	ADP
m-1112	134	14	energy	energy	NOUN
m-1112	134	15	(	(	PUNCT
m-1112	134	16	d	d	NOUN
m-1112	134	17	p	p	NOUN
m-1112	134	18	)	)	PUNCT
m-1112	134	19	,	,	PUNCT
m-1112	134	20	are	be	AUX
m-1112	134	21	connected	connect	VERB
m-1112	134	22	on|	on|	NOUN
m-1112	134	23	ab|	ab|	NOUN
m-1112	134	24	,	,	PUNCT
m-1112	134	25	so	so	SCONJ
m-1112	134	26	at	at	ADP
m-1112	134	27	any	any	DET
m-1112	134	28	point	point	NOUN
m-1112	134	29	m	m	VERB
m-1112	134	30	exist	exist	VERB
m-1112	134	31	the	the	DET
m-1112	134	32	centripetal	centripetal	ADJ
m-1112	134	33	force	force	NOUN
m-1112	134	34	of	of	ADP
m-1112	134	35	two	two	NUM
m-1112	134	36	opposite	opposite	ADJ
m-1112	134	37	[	[	NOUN
m-1112	134	38	⊕	⊕	NOUN
m-1112	134	39	↻	↻	NOUN
m-1112	134	40	↺	↺	NOUN
m-1112	134	41	⊝	⊝	NOUN
m-1112	134	42	]	]	PUNCT
m-1112	134	43	.all	.all	ADP
m-1112	134	44	points	point	NOUN
m-1112	134	45	of	of	ADP
m-1112	134	46	[	[	X
m-1112	134	47	pns	pns	X
m-1112	134	48	]	]	PUNCT
m-1112	134	49	are	be	AUX
m-1112	134	50	homogenous	homogenous	ADJ
m-1112	134	51	(	(	PUNCT
m-1112	134	52	i.e.	i.e.	X
m-1112	134	53	all	all	DET
m-1112	134	54	points	point	NOUN
m-1112	134	55	of	of	ADP
m-1112	134	56	pns	pns	PROPN
m-1112	134	57	space	space	NOUN
m-1112	134	58	are	be	AUX
m-1112	134	59	equivalent	equivalent	ADJ
m-1112	134	60	≡	≡	PROPN
m-1112	134	61	)	)	PUNCT
m-1112	134	62	and	and	CCONJ
m-1112	134	63	isotropic	isotropic	NOUN
m-1112	134	64	(	(	PUNCT
m-1112	134	65	i.e.	i.e.	X
m-1112	134	66	all	all	DET
m-1112	134	67	directions	direction	NOUN
m-1112	134	68	,	,	PUNCT
m-1112	134	69	⇉	⇉	X
m-1112	134	70	,	,	PUNCT
m-1112	134	71	of	of	ADP
m-1112	134	72	ab	ab	PROPN
m-1112	134	73	are	be	AUX
m-1112	134	74	equivalent	equivalent	ADJ
m-1112	134	75	)	)	PUNCT
m-1112	135	1	→	→	PUNCT
m-1112	135	2	[	[	PUNCT
m-1112	135	3	a	a	DET
m-1112	135	4	≡	≡	PROPN
m-1112	135	5	a	a	X
m-1112	135	6	]	]	X
m-1112	135	7	,	,	PUNCT
m-1112	135	8	for	for	ADP
m-1112	135	9	the	the	DET
m-1112	135	10	primary	primary	ADJ
m-1112	135	11	dipole	dipole	NOUN
m-1112	135	12	and	and	CCONJ
m-1112	135	13	for	for	ADP
m-1112	135	14	any	any	DET
m-1112	135	15	dipole	dipole	NOUN
m-1112	135	16	ai	ai	ADJ
m-1112	135	17	-	-	PUNCT
m-1112	135	18	bi	bi	ADJ
m-1112	135	19	issues	issue	NOUN
m-1112	135	20	,	,	PUNCT
m-1112	135	21	the	the	DET
m-1112	135	22	position	position	NOUN
m-1112	135	23	of	of	ADP
m-1112	135	24	dipole	dipole	NOUN
m-1112	135	25	in	in	ADP
m-1112	135	26	the	the	DET
m-1112	135	27	equilibrium	equilibrium	NOUN
m-1112	135	28	space	space	NOUN
m-1112	135	29	antispace	antispace	NOUN
m-1112	135	30	creates	create	VERB
m-1112	135	31	charge	charge	NOUN
m-1112	135	32	=	=	NOUN
m-1112	135	33	momentum	momentum	NOUN
m-1112	135	34	and	and	CCONJ
m-1112	135	35	angular	angular	ADJ
m-1112	135	36	momentum	momentum	NOUN
m-1112	135	37	(	(	PUNCT
m-1112	135	38	spin	spin	VERB
m-1112	135	39	=	=	PUNCT
m-1112	135	40	the	the	DET
m-1112	135	41	intrinsic	intrinsic	ADJ
m-1112	135	42	twist	twist	NOUN
m-1112	135	43	of	of	ADP
m-1112	135	44	space	space	NOUN
m-1112	135	45	,	,	PUNCT
m-1112	135	46	anti	anti	ADJ
m-1112	135	47	-	-	NOUN
m-1112	135	48	space	space	NOUN
m-1112	135	49	)	)	PUNCT
m-1112	135	50	which	which	PRON
m-1112	135	51	inextricably	inextricably	ADV
m-1112	135	52	unify	unify	VERB
m-1112	135	53	geometry	geometry	NOUN
m-1112	135	54	of	of	ADP
m-1112	135	55	space	space	NOUN
m-1112	135	56	and	and	CCONJ
m-1112	135	57	motion	motion	NOUN
m-1112	135	58	.	.	PUNCT
m-1112	136	1	[	[	X
m-1112	136	2	10	10	NUM
m-1112	136	3	]	]	PUNCT
m-1112	136	4	figure	figure	NOUN
m-1112	136	5	–	–	PUNCT
m-1112	136	6	1	1	NUM
m-1112	136	7	.	.	PUNCT
m-1112	137	1	the	the	DET
m-1112	137	2	4	4	NUM
m-1112	137	3	-	-	PUNCT
m-1112	137	4	primary	primary	ADJ
m-1112	137	5	-	-	PUNCT
m-1112	137	6	spaces	space	NOUN
m-1112	137	7	of	of	ADP
m-1112	137	8	euclidean	euclidean	ADJ
m-1112	137	9	-	-	PUNCT
m-1112	137	10	geometry	geometry	NOUN
m-1112	137	11	and	and	CCONJ
m-1112	137	12	the	the	DET
m-1112	137	13	primary	primary	ADJ
m-1112	137	14	rotational	rotational	ADJ
m-1112	137	15	quantized	quantize	VERB
m-1112	137	16	motion	motion	NOUN
m-1112	137	17	≡	≡	PROPN
m-1112	137	18	the	the	DET
m-1112	137	19	unit	unit	NOUN
m-1112	137	20	-	-	PUNCT
m-1112	137	21	angular	angular	ADJ
m-1112	137	22	-	-	PUNCT
m-1112	137	23	momentum	momentum	NOUN
m-1112	137	24	-	-	PUNCT
m-1112	137	25	energy	energy	NOUN
m-1112	137	26	in	in	ADP
m-1112	137	27	pns	pns	PROPN
m-1112	137	28	spaces	space	NOUN
m-1112	137	29	.	.	PUNCT
m-1112	138	1	3a	3a	NUM
m-1112	138	2	…	…	PUNCT
m-1112	138	3	the	the	DET
m-1112	138	4	quantization	quantization	NOUN
m-1112	138	5	of	of	ADP
m-1112	138	6	the	the	DET
m-1112	138	7	→	→	NOUN
m-1112	138	8	{	{	PUNCT
m-1112	138	9	energy	energy	NOUN
m-1112	138	10	–	–	PUNCT
m-1112	138	11	space	space	NOUN
m-1112	138	12	universe	universe	NOUN
m-1112	138	13	}	}	PUNCT
m-1112	138	14	←	←	PROPN
m-1112	138	15	in	in	ADP
m-1112	138	16	a	a	DET
m-1112	138	17	conservative	conservative	ADJ
m-1112	138	18	system	system	NOUN
m-1112	138	19	the	the	DET
m-1112	138	20	total	total	ADJ
m-1112	138	21	energy	energy	NOUN
m-1112	138	22	≡	≡	PROPN
m-1112	138	23	motion	motion	NOUN
m-1112	138	24	is	be	AUX
m-1112	138	25	constant	constant	ADJ
m-1112	138	26	and	and	CCONJ
m-1112	138	27	the	the	DET
m-1112	138	28	differential	differential	ADJ
m-1112	138	29	equation	equation	NOUN
m-1112	138	30	of	of	ADP
m-1112	138	31	motion	motion	NOUN
m-1112	138	32	can	can	AUX
m-1112	138	33	be	be	AUX
m-1112	138	34	established	establish	VERB
m-1112	138	35	by	by	ADP
m-1112	138	36	the	the	DET
m-1112	138	37	principle	principle	NOUN
m-1112	138	38	of	of	ADP
m-1112	138	39	conservation	conservation	NOUN
m-1112	138	40	of	of	ADP
m-1112	138	41	energy	energy	NOUN
m-1112	138	42	.	.	PUNCT
m-1112	139	1	for	for	ADP
m-1112	139	2	the	the	DET
m-1112	139	3	free	free	ADJ
m-1112	139	4	vibration	vibration	NOUN
m-1112	139	5	of	of	ADP
m-1112	139	6	an	an	DET
m-1112	139	7	undamped	undampe	VERB
m-1112	139	8	system	system	NOUN
m-1112	139	9	,	,	PUNCT
m-1112	139	10	the	the	DET
m-1112	139	11	energy	energy	NOUN
m-1112	139	12	is	be	AUX
m-1112	139	13	party	party	NOUN
m-1112	139	14	kinetic	kinetic	NOUN
m-1112	139	15	=	=	PUNCT
m-1112	139	16	𝐄	𝐄	PROPN
m-1112	139	17	𝐊	𝐊	NOUN
m-1112	139	18	which	which	PRON
m-1112	139	19	is	be	AUX
m-1112	139	20	stored	store	VERB
m-1112	139	21	in	in	ADP
m-1112	139	22	ijo	ijo	PROPN
m-1112	139	23	international	international	PROPN
m-1112	139	24	journal	journal	PROPN
m-1112	139	25	of	of	ADP
m-1112	139	26	mathematics	mathematics	PROPN
m-1112	139	27	(	(	PUNCT
m-1112	139	28	issn	issn	PROPN
m-1112	139	29	:	:	PUNCT
m-1112	139	30	2992	2992	NUM
m-1112	139	31	-	-	SYM
m-1112	139	32	4421	4421	NUM
m-1112	139	33	)	)	PUNCT
m-1112	140	1	volume	volume	NOUN
m-1112	140	2	08	08	NUM
m-1112	141	1	|	|	ADV
m-1112	141	2	issue	issue	NOUN
m-1112	141	3	08	08	NUM
m-1112	142	1	|	|	ADV
m-1112	142	2	august	august	PROPN
m-1112	142	3	2025	2025	NUM
m-1112	142	4	|	|	ADV
m-1112	142	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	142	6	ijo	ijo	PROPN
m-1112	142	7	journals	journal	NOUN
m-1112	142	8	8	8	NUM
m-1112	142	9	the	the	DET
m-1112	142	10	fundamental	fundamental	ADJ
m-1112	142	11	particles	particle	NOUN
m-1112	142	12	origination	origination	NOUN
m-1112	142	13	mechanism	mechanism	NOUN
m-1112	142	14	in	in	ADP
m-1112	142	15	mfmf	mfmf	PROPN
m-1112	142	16	pns	pns	PROPN
m-1112	142	17	caves	cave	NOUN
m-1112	142	18	.	.	PUNCT
m-1112	143	1	the	the	DET
m-1112	143	2	mass	mass	NOUN
m-1112	143	3	by	by	ADP
m-1112	143	4	virtue	virtue	NOUN
m-1112	143	5	of	of	ADP
m-1112	143	6	its	its	PRON
m-1112	143	7	velocity	velocity	NOUN
m-1112	143	8	and	and	CCONJ
m-1112	143	9	party	party	NOUN
m-1112	143	10	potential	potential	NOUN
m-1112	143	11	=	=	PUNCT
m-1112	143	12	𝐄	𝐄	PROPN
m-1112	143	13	𝐏	𝐏	PROPN
m-1112	143	14	which	which	PRON
m-1112	143	15	is	be	AUX
m-1112	143	16	stored	store	VERB
m-1112	143	17	in	in	ADP
m-1112	143	18	the	the	DET
m-1112	143	19	form	form	NOUN
m-1112	143	20	of	of	ADP
m-1112	143	21	strain	strain	ADJ
m-1112	143	22	energy	energy	NOUN
m-1112	143	23	in	in	ADP
m-1112	143	24	elastic	elastic	ADJ
m-1112	143	25	deformation	deformation	NOUN
m-1112	143	26	,	,	PUNCT
m-1112	143	27	or	or	CCONJ
m-1112	143	28	the	the	DET
m-1112	143	29	work	work	NOUN
m-1112	143	30	done	do	VERB
m-1112	143	31	in	in	ADP
m-1112	143	32	a	a	DET
m-1112	143	33	forced	force	VERB
m-1112	143	34	-	-	PUNCT
m-1112	143	35	field	field	NOUN
m-1112	143	36	such	such	ADJ
m-1112	143	37	as	as	ADP
m-1112	143	38	gravity	gravity	NOUN
m-1112	143	39	.	.	PUNCT
m-1112	144	1	newton`s	newton`s	PROPN
m-1112	144	2	second	second	ADJ
m-1112	144	3	law	law	NOUN
m-1112	144	4	is	be	AUX
m-1112	144	5	the	the	DET
m-1112	144	6	first	first	ADJ
m-1112	144	7	basis	basis	NOUN
m-1112	144	8	for	for	ADP
m-1112	144	9	examining	examine	VERB
m-1112	144	10	the	the	DET
m-1112	144	11	motion	motion	NOUN
m-1112	144	12	of	of	ADP
m-1112	144	13	a	a	DET
m-1112	144	14	free	free	ADJ
m-1112	144	15	–	–	PUNCT
m-1112	144	16	vibration	vibration	NOUN
m-1112	144	17	in	in	ADP
m-1112	144	18	a	a	DET
m-1112	144	19	system	system	NOUN
m-1112	144	20	.	.	PUNCT
m-1112	145	1	when	when	SCONJ
m-1112	145	2	the	the	DET
m-1112	145	3	deformation	deformation	NOUN
m-1112	145	4	of	of	ADP
m-1112	145	5	a	a	DET
m-1112	145	6	spring	spring	NOUN
m-1112	145	7	in	in	ADP
m-1112	145	8	the	the	DET
m-1112	145	9	static	static	ADJ
m-1112	145	10	equilibrium	equilibrium	NOUN
m-1112	145	11	position	position	NOUN
m-1112	145	12	is	be	AUX
m-1112	145	13	δ	δ	PROPN
m-1112	145	14	and	and	CCONJ
m-1112	145	15	the	the	DET
m-1112	145	16	spring	spring	NOUN
m-1112	145	17	force	force	NOUN
m-1112	145	18	k.δ	k.δ	PROPN
m-1112	145	19	equal	equal	ADJ
m-1112	145	20	to	to	ADP
m-1112	145	21	the	the	DET
m-1112	145	22	gravitation	gravitation	NOUN
m-1112	145	23	al	al	PROPN
m-1112	145	24	force	force	PROPN
m-1112	145	25	mg	mg	PROPN
m-1112	145	26	,	,	PUNCT
m-1112	145	27	then	then	ADV
m-1112	145	28	issues	issue	VERB
m-1112	145	29	k.δ	k.δ	PROPN
m-1112	145	30	=	=	X
m-1112	145	31	mg	mg	PROPN
m-1112	145	32	…	…	PUNCT
m-1112	145	33	.	.	PUNCT
m-1112	146	1	(	(	PUNCT
m-1112	146	2	a	a	X
m-1112	146	3	)	)	PUNCT
m-1112	146	4	applying	apply	VERB
m-1112	146	5	newton`s	newton`s	PROPN
m-1112	146	6	second	second	ADJ
m-1112	146	7	law	law	NOUN
m-1112	146	8	to	to	ADP
m-1112	146	9	the	the	DET
m-1112	146	10	mass	mass	NOUN
m-1112	146	11	m	m	PROPN
m-1112	146	12	,	,	PUNCT
m-1112	146	13	or	or	CCONJ
m-1112	146	14	mass	mass	NOUN
m-1112	146	15	can	can	AUX
m-1112	146	16	be	be	AUX
m-1112	146	17	replaced	replace	VERB
m-1112	146	18	by	by	ADP
m-1112	146	19	a	a	DET
m-1112	146	20	mass	mass	ADJ
m-1112	146	21	moment	moment	NOUN
m-1112	146	22	of	of	ADP
m-1112	146	23	inertia	inertia	NOUN
m-1112	146	24	denoting	denote	VERB
m-1112	146	25	the	the	DET
m-1112	146	26	resistance	resistance	NOUN
m-1112	146	27	to	to	ADP
m-1112	146	28	motion	motion	NOUN
m-1112	146	29	δ	δ	PROPN
m-1112	146	30	,	,	PUNCT
m-1112	146	31	and	and	CCONJ
m-1112	146	32	then	then	ADV
m-1112	146	33	m	m	PROPN
m-1112	146	34	�	�	PROPN
m-1112	146	35	̈	̈	X
m-1112	146	36	�	�	NOUN
m-1112	146	37	=	=	SYM
m-1112	146	38	k	k	PROPN
m-1112	146	39	x	x	PUNCT
m-1112	146	40	for	for	ADP
m-1112	146	41	an	an	DET
m-1112	146	42	x	x	X
m-1112	146	43	–	–	PUNCT
m-1112	146	44	x	x	VERB
m-1112	146	45	axis	axis	NOUN
m-1112	146	46	.	.	PUNCT
m-1112	147	1	the	the	DET
m-1112	147	2	natural	natural	ADJ
m-1112	147	3	–	–	PUNCT
m-1112	147	4	period	period	NOUN
m-1112	147	5	of	of	ADP
m-1112	147	6	the	the	DET
m-1112	147	7	oscillation	oscillation	NOUN
m-1112	147	8	is	be	AUX
m-1112	147	9	established	establish	VERB
m-1112	147	10	from	from	ADP
m-1112	147	11	relation	relation	NOUN
m-1112	147	12	wn	wn	PROPN
m-1112	147	13	t	t	PROPN
m-1112	147	14	=	=	PUNCT
m-1112	147	15	2	2	NUM
m-1112	147	16	π	π	NOUN
m-1112	147	17	where	where	SCONJ
m-1112	147	18	issues	issue	NOUN
m-1112	147	19	[	[	X
m-1112	147	20	7	7	X
m-1112	147	21	]	]	X
m-1112	147	22	t	t	NOUN
m-1112	147	23	=	=	SYM
m-1112	147	24	2	2	NUM
m-1112	147	25	π	π	NOUN
m-1112	147	26	√	√	VERB
m-1112	147	27	m	m	VERB
m-1112	147	28	𝐤	𝐤	NOUN
m-1112	147	29	,	,	PUNCT
m-1112	147	30	𝐟	𝐟	PROPN
m-1112	147	31	𝐧	𝐧	NOUN
m-1112	147	32	=	=	SYM
m-1112	147	33	1	1	NUM
m-1112	147	34	/	/	SYM
m-1112	147	35	t	t	NOUN
m-1112	147	36	=	=	SYM
m-1112	147	37	1	1	NUM
m-1112	147	38	2π	2π	NOUN
m-1112	147	39	√	√	NOUN
m-1112	147	40	k	k	NOUN
m-1112	147	41	𝐦	𝐦	PROPN
m-1112	147	42	,	,	PUNCT
m-1112	147	43	𝐟	𝐟	PROPN
m-1112	147	44	𝐧	𝐧	NOUN
m-1112	147	45	=	=	SYM
m-1112	147	46	1	1	NUM
m-1112	147	47	/	/	SYM
m-1112	147	48	t	t	NOUN
m-1112	147	49	=	=	SYM
m-1112	147	50	1	1	NUM
m-1112	147	51	2π	2π	NUM
m-1112	147	52	√	√	NOUN
m-1112	147	53	g	g	PROPN
m-1112	147	54	δ	δ	PROPN
m-1112	147	55	…	…	PUNCT
m-1112	147	56	.	.	PUNCT
m-1112	147	57	…	…	PUNCT
m-1112	147	58	(b	(b	NOUN
m-1112	147	59	)	)	PUNCT
m-1112	147	60	i.e.	i.e.	X
m-1112	147	61	the	the	DET
m-1112	147	62	kinetic	kinetic	ADJ
m-1112	147	63	energy	energy	NOUN
m-1112	147	64	𝐄	𝐄	PROPN
m-1112	147	65	𝐊	𝐊	PROPN
m-1112	147	66	is	be	AUX
m-1112	147	67	applicable	applicable	ADJ
m-1112	147	68	in	in	ADP
m-1112	147	69	a	a	DET
m-1112	147	70	single	single	ADJ
m-1112	147	71	dof	dof	NOUN
m-1112	147	72	system	system	NOUN
m-1112	147	73	including	include	VERB
m-1112	147	74	rotation	rotation	NOUN
m-1112	147	75	.	.	PUNCT
m-1112	148	1	since	since	SCONJ
m-1112	148	2	issues	issue	NOUN
m-1112	148	3	e	e	X
m-1112	148	4	k	k	NOUN
m-1112	148	5	=	=	PUNCT
m-1112	148	6	e	e	X
m-1112	148	7	p	p	NOUN
m-1112	148	8	so	so	ADV
m-1112	148	9	and	and	CCONJ
m-1112	148	10	e	e	X
m-1112	148	11	k	k	PROPN
m-1112	149	1	+	+	CCONJ
m-1112	149	2	e	e	X
m-1112	149	3	p	p	NOUN
m-1112	149	4	=	=	NOUN
m-1112	149	5	constant	constant	ADJ
m-1112	149	6	.	.	PUNCT
m-1112	150	1	from	from	ADP
m-1112	150	2	the	the	DET
m-1112	150	3	theory	theory	NOUN
m-1112	150	4	of	of	ADP
m-1112	150	5	vibrations	vibration	NOUN
m-1112	150	6	,	,	PUNCT
m-1112	150	7	{	{	PUNCT
m-1112	150	8	all	all	DET
m-1112	150	9	systems	system	NOUN
m-1112	150	10	possessing	possess	VERB
m-1112	150	11	mass=	mass=	PROPN
m-1112	150	12	m	m	NOUN
m-1112	150	13	and	and	CCONJ
m-1112	150	14	elasticity	elasticity	NOUN
m-1112	150	15	=	=	SYM
m-1112	150	16	e	e	NOUN
m-1112	150	17	=	=	SYM
m-1112	150	18	1	1	NUM
m-1112	150	19	/	/	SYM
m-1112	150	20	k	k	NOUN
m-1112	150	21	are	be	AUX
m-1112	150	22	capable	capable	ADJ
m-1112	150	23	of	of	ADP
m-1112	150	24	free	free	ADJ
m-1112	150	25	vibration	vibration	NOUN
m-1112	150	26	in	in	ADP
m-1112	150	27	the	the	DET
m-1112	150	28	absence	absence	NOUN
m-1112	150	29	of	of	ADP
m-1112	150	30	external	external	ADJ
m-1112	150	31	excitation	excitation	NOUN
m-1112	150	32	which	which	PRON
m-1112	150	33	is	be	AUX
m-1112	150	34	its	its	PRON
m-1112	150	35	natural	natural	ADJ
m-1112	150	36	frequency	frequency	NOUN
m-1112	150	37	of	of	ADP
m-1112	150	38	vibration	vibration	NOUN
m-1112	150	39	=	=	PUNCT
m-1112	150	40	𝐰	𝐰	PART
m-1112	150	41	𝐧	𝐧	NOUN
m-1112	150	42	and	and	CCONJ
m-1112	150	43	the	the	DET
m-1112	150	44	equation	equation	NOUN
m-1112	150	45	of	of	ADP
m-1112	150	46	motion	motion	NOUN
m-1112	150	47	is	be	AUX
m-1112	150	48	→	→	SYM
m-1112	150	49	�	�	PROPN
m-1112	150	50	̈	̈	X
m-1112	150	51	�	�	NOUN
m-1112	150	52	+	+	CCONJ
m-1112	150	53	𝐰	𝐰	X
m-1112	150	54	²𝐧	²𝐧	NOUN
m-1112	150	55	x	x	X
m-1112	151	1	=	=	SYM
m-1112	151	2	0	0	NUM
m-1112	151	3	←where	←where	NUM
m-1112	151	4	w	w	PROPN
m-1112	151	5	²n=	²n=	PROPN
m-1112	151	6	k	k	NOUN
m-1112	151	7	m	m	ADJ
m-1112	151	8	,	,	PUNCT
m-1112	151	9	gravitational	gravitational	ADJ
m-1112	151	10	force	force	NOUN
m-1112	151	11	g	g	PROPN
m-1112	151	12	=	=	PROPN
m-1112	151	13	m	m	PROPN
m-1112	151	14	g	g	NOUN
m-1112	151	15	}	}	PUNCT
m-1112	151	16	i.e.	i.e.	X
m-1112	151	17	since	since	SCONJ
m-1112	151	18	the	the	DET
m-1112	151	19	hydrogen	hydrogen	NOUN
m-1112	151	20	-	-	PUNCT
m-1112	151	21	cave	cave	NOUN
m-1112	151	22	system	system	NOUN
m-1112	151	23	h	h	NOUN
m-1112	151	24	,	,	PUNCT
m-1112	151	25	as	as	ADP
m-1112	151	26	e	e	NOUN
m-1112	151	27	-	-	NOUN
m-1112	151	28	m	m	NOUN
m-1112	151	29	conductor	conductor	NOUN
m-1112	151	30	,	,	PUNCT
m-1112	151	31	possesses	possess	VERB
m-1112	151	32	mass	mass	NOUN
m-1112	151	33	𝐦	𝐦	PROPN
m-1112	151	34	𝐇	𝐇	PROPN
m-1112	151	35	,	,	PUNCT
m-1112	151	36	and	and	CCONJ
m-1112	151	37	light	light	ADJ
m-1112	151	38	-	-	PUNCT
m-1112	151	39	velocity	velocity	NOUN
m-1112	151	40	c	c	NOUN
m-1112	151	41	,	,	PUNCT
m-1112	151	42	then	then	ADV
m-1112	151	43	vibrates	vibrate	VERB
m-1112	151	44	in	in	ADP
m-1112	151	45	–	–	PUNCT
m-1112	151	46	out	out	ADP
m-1112	151	47	the	the	DET
m-1112	151	48	space	space	NOUN
m-1112	151	49	-	-	PUNCT
m-1112	151	50	positions	position	NOUN
m-1112	151	51	(	(	PUNCT
m-1112	151	52	x	x	X
m-1112	151	53	,	,	PUNCT
m-1112	151	54	y	y	PROPN
m-1112	151	55	,	,	PUNCT
m-1112	151	56	z	z	NOUN
m-1112	151	57	)	)	PUNCT
m-1112	151	58	of	of	ADP
m-1112	151	59	all	all	DET
m-1112	151	60	universe	universe	NOUN
m-1112	151	61	with	with	ADP
m-1112	151	62	its	its	PRON
m-1112	151	63	natural	natural	ADJ
m-1112	151	64	frequency	frequency	NOUN
m-1112	151	65	𝐰𝐇	𝐰𝐇	PROPN
m-1112	152	1	=	=	NOUN
m-1112	152	2	√	√	NOUN
m-1112	152	3	k	k	NOUN
m-1112	152	4	𝐦	𝐦	X
m-1112	152	5	𝐇	𝐇	PROPN
m-1112	152	6	.	.	PUNCT
m-1112	153	1	or	or	CCONJ
m-1112	153	2	and	and	CCONJ
m-1112	153	3	frequency	frequency	NOUN
m-1112	153	4	𝐟	𝐟	NOUN
m-1112	153	5	𝐇	𝐇	PROPN
m-1112	154	1	=	=	SYM
m-1112	154	2	𝐰	𝐰	PROPN
m-1112	154	3	𝐇	𝐇	PROPN
m-1112	154	4	𝟐𝛑	𝟐𝛑	VERB
m-1112	154	5	,	,	PUNCT
m-1112	154	6	and	and	CCONJ
m-1112	154	7	is	be	AUX
m-1112	154	8	a	a	DET
m-1112	154	9	wave	wave	NOUN
m-1112	154	10	–	–	PUNCT
m-1112	154	11	function	function	NOUN
m-1112	154	12	providing	provide	VERB
m-1112	154	13	the	the	DET
m-1112	154	14	complete	complete	ADJ
m-1112	154	15	description	description	NOUN
m-1112	154	16	of	of	ADP
m-1112	154	17	the	the	DET
m-1112	154	18	physical	physical	ADJ
m-1112	154	19	reality	reality	NOUN
m-1112	154	20	.	.	PUNCT
m-1112	155	1	from	from	ADP
m-1112	155	2	,	,	PUNCT
m-1112	155	3	work	work	NOUN
m-1112	155	4	=	=	SYM
m-1112	155	5	w	w	NOUN
m-1112	155	6	=	=	VERB
m-1112	155	7	force	force	NOUN
m-1112	155	8	𝐅	𝐅	NOUN
m-1112	155	9	𝐢,𝐣,𝐤	𝐢,𝐣,𝐤	NOUN
m-1112	155	10	x	x	SYM
m-1112	155	11	displacement	displacement	NOUN
m-1112	155	12	𝐝𝐬	𝐝𝐬	ADP
m-1112	155	13	𝐢,𝐣,𝐤	𝐢,𝐣,𝐤	NOUN
m-1112	155	14	=	=	SYM
m-1112	155	15	(	(	PUNCT
m-1112	155	16	𝐅	𝐅	PROPN
m-1112	155	17	𝐢,𝐣,𝐤	𝐢,𝐣,𝐤	NOUN
m-1112	155	18	x	x	PUNCT
m-1112	155	19	𝐝𝐬	𝐝𝐬	ADP
m-1112	155	20	𝐢,𝐣,𝐤	𝐢,𝐣,𝐤	NOUN
m-1112	155	21	)	)	PUNCT
m-1112	155	22	=	=	SYM
m-1112	156	1	(	(	PUNCT
m-1112	156	2	f	f	NOUN
m-1112	156	3	x	x	X
m-1112	156	4	ds	ds	PROPN
m-1112	156	5	)	)	PUNCT
m-1112	156	6	,	,	PUNCT
m-1112	156	7	and	and	CCONJ
m-1112	156	8	for	for	ADP
m-1112	156	9	the	the	DET
m-1112	156	10	unit	unit	NOUN
m-1112	156	11	of	of	ADP
m-1112	156	12	time	time	NOUN
m-1112	156	13	dt	dt	X
m-1112	156	14	,	,	PUNCT
m-1112	156	15	→	→	SYM
m-1112	156	16	w	w	X
m-1112	156	17	/	/	SYM
m-1112	156	18	dt	dt	NOUN
m-1112	156	19	=	=	SYM
m-1112	157	1	f	f	PROPN
m-1112	157	2	x	x	INTJ
m-1112	157	3	(	(	PUNCT
m-1112	157	4	ds	ds	PROPN
m-1112	157	5	/	/	SYM
m-1112	157	6	dt	dt	NOUN
m-1112	157	7	)	)	PUNCT
m-1112	158	1	=	=	PUNCT
m-1112	158	2	(	(	PUNCT
m-1112	158	3	f	f	PROPN
m-1112	158	4	x	x	SYM
m-1112	158	5	�	�	PROPN
m-1112	158	6	⃡	⃡	NOUN
m-1112	158	7	�	�	PROPN
m-1112	159	1	i	i	PRON
m-1112	159	2	,	,	PUNCT
m-1112	159	3	j	j	PROPN
m-1112	159	4	,	,	PUNCT
m-1112	159	5	k	k	PROPN
m-1112	159	6	)	)	PUNCT
m-1112	160	1	=	=	NOUN
m-1112	160	2	power	power	NOUN
m-1112	160	3	=	=	SYM
m-1112	160	4	p	p	NOUN
m-1112	160	5	.	.	PUNCT
m-1112	161	1	i.e.	i.e.	X
m-1112	161	2	power	power	NOUN
m-1112	161	3	≡	≡	PROPN
m-1112	161	4	force	force	NOUN
m-1112	161	5	x	x	VERB
m-1112	161	6	velocity	velocity	NOUN
m-1112	161	7	or	or	CCONJ
m-1112	161	8	(	(	PUNCT
m-1112	161	9	p	p	X
m-1112	161	10	=	=	X
m-1112	161	11	f	f	PROPN
m-1112	161	12	x	x	SYM
m-1112	161	13	�	�	PROPN
m-1112	161	14	⃡	⃡	NOUN
m-1112	161	15	�	�	PROPN
m-1112	161	16	)	)	PUNCT
m-1112	161	17	remarks	remark	NOUN
m-1112	161	18	,	,	PUNCT
m-1112	161	19	from	from	ADP
m-1112	161	20	mechanics	mechanic	NOUN
m-1112	161	21	physics	physics	NOUN
m-1112	161	22	:	:	PUNCT
m-1112	161	23	1	1	NUM
m-1112	161	24	…	…	SYM
m-1112	161	25	energy	energy	NOUN
m-1112	161	26	e	e	NOUN
m-1112	161	27	=	=	SYM
m-1112	161	28	1	1	NUM
m-1112	161	29	2	2	NUM
m-1112	161	30	m	m	NOUN
m-1112	161	31	h	h	NOUN
m-1112	161	32	.	.	PUNCT
m-1112	162	1	c	c	NOUN
m-1112	162	2	²	²	NUM
m-1112	162	3	,	,	PUNCT
m-1112	162	4	or	or	CCONJ
m-1112	162	5	→	→	ADP
m-1112	162	6	2e	2e	NUM
m-1112	162	7	=	=	PUNCT
m-1112	162	8	𝐦	𝐦	PROPN
m-1112	162	9	𝐇	𝐇	PROPN
m-1112	162	10	.	.	PUNCT
m-1112	163	1	c	c	PROPN
m-1112	163	2	²	²	NUM
m-1112	163	3	←	←	PROPN
m-1112	163	4	and	and	CCONJ
m-1112	163	5	velocity	velocity	NOUN
m-1112	163	6	=	=	PUNCT
m-1112	164	1	the	the	DET
m-1112	164	2	light	light	ADJ
m-1112	164	3	-	-	PUNCT
m-1112	164	4	velocity	velocity	NOUN
m-1112	164	5	c	c	NOUN
m-1112	164	6	,	,	PUNCT
m-1112	164	7	2	2	NUM
m-1112	164	8	…	…	SYM
m-1112	164	9	wave	wave	NOUN
m-1112	164	10	length	length	NOUN
m-1112	164	11	λ	λ	PROPN
m-1112	164	12	h	h	NOUN
m-1112	164	13	=	=	PUNCT
m-1112	164	14	𝟐𝛑	𝟐𝛑	VERB
m-1112	164	15	𝐜	𝐜	NOUN
m-1112	164	16	𝐰	𝐰	PROPN
m-1112	164	17	𝐇	𝐇	PROPN
m-1112	164	18	,	,	PUNCT
m-1112	164	19	and	and	CCONJ
m-1112	164	20	wave	wave	NOUN
m-1112	164	21	amplitude	amplitude	NOUN
m-1112	164	22	𝐀	𝐀	PROPN
m-1112	164	23	𝐇	𝐇	NOUN
m-1112	164	24	=	=	SYM
m-1112	164	25	λ	λ	PROPN
m-1112	164	26	h	h	NOUN
m-1112	164	27	𝟐𝛑	𝟐𝛑	NOUN
m-1112	164	28	,	,	PUNCT
m-1112	164	29	3	3	NUM
m-1112	164	30	…	…	SYM
m-1112	164	31	hydrogen	hydrogen	NOUN
m-1112	164	32	power	power	NOUN
m-1112	164	33	𝐏	𝐏	PROPN
m-1112	164	34	𝐇	𝐇	PROPN
m-1112	164	35	=	=	NOUN
m-1112	164	36	0,5	0,5	NUM
m-1112	164	37	.	.	PUNCT
m-1112	165	1	𝐦	𝐦	PROPN
m-1112	165	2	𝐇	𝐇	PROPN
m-1112	165	3	.	.	PUNCT
m-1112	166	1	[	[	PUNCT
m-1112	166	2	𝐀	𝐀	NOUN
m-1112	166	3	𝐇	𝐇	PROPN
m-1112	166	4	]	]	PUNCT
m-1112	166	5	²	²	X
m-1112	166	6	.	.	PUNCT
m-1112	167	1	[	[	PUNCT
m-1112	167	2	c	c	X
m-1112	167	3	]	]	PUNCT
m-1112	167	4	²	²	NUM
m-1112	167	5	4	4	NUM
m-1112	167	6	…	…	PUNCT
m-1112	167	7	the	the	DET
m-1112	167	8	hydrogen	hydrogen	NOUN
m-1112	167	9	stress	stress	NOUN
m-1112	167	10	-	-	PUNCT
m-1112	167	11	vector	vector	NOUN
m-1112	167	12	𝛔	𝛔	PROPN
m-1112	167	13	𝐇	𝐇	PROPN
m-1112	167	14	is	be	AUX
m-1112	167	15	related	relate	VERB
m-1112	167	16	to	to	ADP
m-1112	167	17	c	c	NOUN
m-1112	167	18	as	as	ADP
m-1112	167	19	,	,	PUNCT
m-1112	167	20	c	c	PROPN
m-1112	167	21	=	=	SYM
m-1112	167	22	𝚽	𝚽	PROPN
m-1112	167	23	.	.	PUNCT
m-1112	168	1	𝛔	𝛔	PROPN
m-1112	168	2	𝐇	𝐇	PROPN
m-1112	168	3	5	5	NUM
m-1112	168	4	…	…	PUNCT
m-1112	168	5	since	since	SCONJ
m-1112	168	6	hydrogen	hydrogen	NOUN
m-1112	168	7	cave	cave	NOUN
m-1112	168	8	is	be	AUX
m-1112	168	9	an	an	DET
m-1112	168	10	e	e	NOUN
m-1112	168	11	-	-	NOUN
m-1112	168	12	m	m	NOUN
m-1112	168	13	conductor	conductor	NOUN
m-1112	168	14	then	then	ADV
m-1112	168	15	it	it	PRON
m-1112	168	16	is	be	AUX
m-1112	168	17	a	a	DET
m-1112	168	18	wave	wave	NOUN
m-1112	168	19	with	with	ADP
m-1112	168	20	natural	natural	ADJ
m-1112	168	21	frequency	frequency	NOUN
m-1112	168	22	,	,	PUNCT
m-1112	168	23	and	and	CCONJ
m-1112	168	24	since	since	SCONJ
m-1112	168	25	occupies	occupy	VERB
m-1112	168	26	the	the	DET
m-1112	168	27	property	property	NOUN
m-1112	168	28	of	of	ADP
m-1112	168	29	→atoms	→atom	NOUN
m-1112	168	30	-	-	PUNCT
m-1112	168	31	plug	plug	ADJ
m-1112	168	32	≡	≡	PROPN
m-1112	168	33	pin	pin	NOUN
m-1112	168	34	and	and	CCONJ
m-1112	168	35	atoms	atom	NOUN
m-1112	168	36	-	-	PUNCT
m-1112	168	37	drain	drain	NOUN
m-1112	168	38	=	=	NOUN
m-1112	168	39	hole	hole	NOUN
m-1112	168	40	so	so	ADV
m-1112	168	41	are	be	AUX
m-1112	168	42	bonded	bond	VERB
m-1112	168	43	←	←	PROPN
m-1112	168	44	in	in	ADP
m-1112	168	45	a	a	DET
m-1112	168	46	multi	multi	ADJ
m-1112	168	47	-	-	ADJ
m-1112	168	48	dof	dof	ADJ
m-1112	168	49	system	system	NOUN
m-1112	168	50	at	at	ADP
m-1112	168	51	the	the	DET
m-1112	168	52	stationary	stationary	ADJ
m-1112	168	53	conditions	condition	NOUN
m-1112	168	54	.	.	PUNCT
m-1112	169	1	6	6	NUM
m-1112	169	2	…	…	PUNCT
m-1112	169	3	to	to	PART
m-1112	169	4	find	find	VERB
m-1112	169	5	the	the	DET
m-1112	169	6	eigenvalues	eigenvalue	NOUN
m-1112	169	7	and	and	CCONJ
m-1112	169	8	eigenvectors	eigenvector	NOUN
m-1112	169	9	of	of	ADP
m-1112	169	10	a	a	DET
m-1112	169	11	multi	multi	ADJ
m-1112	169	12	-	-	ADJ
m-1112	169	13	dof	dof	ADJ
m-1112	169	14	system	system	NOUN
m-1112	169	15	,	,	PUNCT
m-1112	169	16	iteration	iteration	NOUN
m-1112	169	17	method	method	NOUN
m-1112	169	18	of	of	ADP
m-1112	169	19	motion	motion	NOUN
m-1112	169	20	is	be	AUX
m-1112	169	21	formulated	formulate	VERB
m-1112	169	22	by	by	ADP
m-1112	169	23	either	either	CCONJ
m-1112	169	24	the	the	DET
m-1112	169	25	flexibility	flexibility	NOUN
m-1112	169	26	matrix	matrix	NOUN
m-1112	169	27	[	[	X
m-1112	169	28	a	a	X
m-1112	169	29	]	]	X
m-1112	169	30	or	or	CCONJ
m-1112	169	31	the	the	DET
m-1112	169	32	stiffness	stiffness	ADJ
m-1112	169	33	matrix	matrix	NOUN
m-1112	169	34	.	.	PUNCT
m-1112	170	1	7	7	NUM
m-1112	170	2	…	…	SYM
m-1112	170	3	momentum	momentum	NOUN
m-1112	170	4	≡	≡	PROPN
m-1112	170	5	±	±	PROPN
m-1112	170	6	spin	spin	NOUN
m-1112	170	7	≡	≡	PROPN
m-1112	171	1	[	[	X
m-1112	171	2	gravity	gravity	NOUN
m-1112	171	3	and	and	CCONJ
m-1112	171	4	antigravity	antigravity	NOUN
m-1112	171	5	]	]	PUNCT
m-1112	171	6	because	because	SCONJ
m-1112	171	7	the	the	DET
m-1112	171	8	light	light	ADJ
m-1112	171	9	velocity	velocity	NOUN
m-1112	171	10	�	�	NOUN
m-1112	171	11	̅	̅	NOUN
m-1112	171	12	�	�	NOUN
m-1112	171	13	=	=	SYM
m-1112	171	14	[	[	PUNCT
m-1112	171	15	𝐆	𝐆	PROPN
m-1112	171	16	𝚽	𝚽	PROPN
m-1112	171	17	𝐀	𝐀	PROPN
m-1112	171	18	]	]	PUNCT
m-1112	171	19	,	,	PUNCT
m-1112	171	20	ijo	ijo	PROPN
m-1112	171	21	international	international	PROPN
m-1112	171	22	journal	journal	PROPN
m-1112	171	23	of	of	ADP
m-1112	171	24	mathematics	mathematics	PROPN
m-1112	171	25	(	(	PUNCT
m-1112	171	26	issn	issn	PROPN
m-1112	171	27	:	:	PUNCT
m-1112	171	28	2992	2992	NUM
m-1112	171	29	-	-	SYM
m-1112	171	30	4421	4421	NUM
m-1112	171	31	)	)	PUNCT
m-1112	171	32	volume	volume	NOUN
m-1112	171	33	08	08	NUM
m-1112	172	1	|	|	ADV
m-1112	172	2	issue	issue	NOUN
m-1112	172	3	08	08	NUM
m-1112	173	1	|	|	ADV
m-1112	173	2	august	august	PROPN
m-1112	173	3	2025	2025	NUM
m-1112	173	4	|	|	ADV
m-1112	173	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	173	6	ijo	ijo	NOUN
m-1112	173	7	journals	journal	NOUN
m-1112	173	8	9	9	NUM
m-1112	173	9	the	the	DET
m-1112	173	10	fundamental	fundamental	ADJ
m-1112	173	11	particles	particle	NOUN
m-1112	173	12	origination	origination	NOUN
m-1112	173	13	mechanism	mechanism	NOUN
m-1112	173	14	in	in	ADP
m-1112	173	15	mfmf	mfmf	PROPN
m-1112	173	16	pns	pns	PROPN
m-1112	173	17	caves	cave	NOUN
m-1112	173	18	.	.	PUNCT
m-1112	174	1	and	and	CCONJ
m-1112	174	2	precedes	precede	VERB
m-1112	174	3	that	that	PRON
m-1112	174	4	of	of	ADP
m-1112	174	5	a	a	DET
m-1112	174	6	-	-	PUNCT
m-1112	174	7	momentum	momentum	NOUN
m-1112	174	8			NOUN
m-1112	174	9	�	�	PROPN
m-1112	174	10	̅	̅	NOUN
m-1112	174	11	�	�	NOUN
m-1112	174	12	=	=	SYM
m-1112	174	13	r	r	NOUN
m-1112	174	14	m	m	NOUN
m-1112	174	15	�	�	NOUN
m-1112	174	16	̅	̅	NOUN
m-1112	174	17	�	�	PROPN
m-1112	174	18	.	.	PUNCT
m-1112	174	19	exists	exist	VERB
m-1112	174	20	vector	vector	NOUN
m-1112	174	21	b	b	PROPN
m-1112	174	22	⊥	⊥	PROPN
m-1112	174	23	r	r	X
m-1112	174	24	-	-	PUNCT
m-1112	174	25	c	c	NOUN
m-1112	174	26	plane	plane	NOUN
m-1112	174	27	.	.	PUNCT
m-1112	175	1	8	8	NUM
m-1112	175	2	…	…	PUNCT
m-1112	175	3	since	since	SCONJ
m-1112	175	4	angular	angular	ADJ
m-1112	175	5	-	-	PUNCT
m-1112	175	6	velocity	velocity	NOUN
m-1112	175	7	|w̅|	|w̅|	NOUN
m-1112	175	8	,	,	PUNCT
m-1112	175	9	a	a	DET
m-1112	175	10	vector	vector	NOUN
m-1112	175	11	,	,	PUNCT
m-1112	175	12	rotates	rotate	VERB
m-1112	175	13	in	in	ADP
m-1112	175	14	one	one	NUM
m-1112	175	15	axis	axis	NOUN
m-1112	175	16	k	k	NOUN
m-1112	175	17	with	with	ADP
m-1112	175	18	respect	respect	NOUN
m-1112	175	19	to	to	ADP
m-1112	175	20	one	one	NUM
m-1112	175	21	variable	variable	NOUN
m-1112	175	22	only	only	ADV
m-1112	175	23	and	and	CCONJ
m-1112	175	24	this	this	PRON
m-1112	175	25	happens	happen	VERB
m-1112	175	26	in	in	ADP
m-1112	175	27	{	{	PUNCT
m-1112	175	28	pns	pns	NOUN
m-1112	175	29	-	-	NOUN
m-1112	175	30	space	space	NOUN
m-1112	175	31	,	,	PUNCT
m-1112	175	32	atoms	atom	NOUN
m-1112	175	33	-	-	PUNCT
m-1112	175	34	space	space	NOUN
m-1112	175	35	,	,	PUNCT
m-1112	175	36	objective	objective	NOUN
m-1112	175	37	-	-	PUNCT
m-1112	175	38	reality	reality	NOUN
m-1112	175	39	and	and	CCONJ
m-1112	175	40	in	in	ADP
m-1112	175	41	universe	universe	NOUN
m-1112	175	42	}	}	PUNCT
m-1112	175	43	then	then	ADV
m-1112	175	44	quaternion	quaternion	NOUN
m-1112	175	45	momentum	momentum	NOUN
m-1112	175	46	,	,	PUNCT
m-1112	175	47	b̅	b̅	PROPN
m-1112	175	48	&	&	CCONJ
m-1112	175	49	w̅	w̅	PROPN
m-1112	175	50	,	,	PUNCT
m-1112	175	51	and	and	CCONJ
m-1112	175	52	w	w	PROPN
m-1112	175	53	≡	≡	PROPN
m-1112	175	54	motion	motion	NOUN
m-1112	175	55	are	be	AUX
m-1112	175	56	stabilized	stabilize	VERB
m-1112	175	57	in	in	ADP
m-1112	175	58	the	the	DET
m-1112	175	59	dual	dual	ADJ
m-1112	175	60	–	–	PUNCT
m-1112	175	61	type	type	NOUN
m-1112	175	62	,	,	PUNCT
m-1112	175	63	such	such	ADJ
m-1112	175	64	in	in	ADP
m-1112	175	65	microcosm	microcosm	NOUN
m-1112	175	66	,	,	PUNCT
m-1112	175	67	as	as	ADP
m-1112	175	68	in	in	ADP
m-1112	175	69	macrocosm	macrocosm	PROPN
m-1112	175	70	,	,	PUNCT
m-1112	175	71	or	or	CCONJ
m-1112	175	72	both	both	PRON
m-1112	175	73	as	as	ADP
m-1112	175	74	omnipresent	omnipresent	NOUN
m-1112	175	75	.	.	PUNCT
m-1112	176	1	1	1	NUM
m-1112	176	2	…	…	PUNCT
m-1112	176	3	the	the	DET
m-1112	176	4	dual	dual	ADJ
m-1112	176	5	-	-	PUNCT
m-1112	176	6	momentum	momentum	NOUN
m-1112	176	7	b̅	b̅	PROPN
m-1112	176	8	&	&	CCONJ
m-1112	176	9	w̅	w̅	PROPN
m-1112	176	10	,	,	PUNCT
m-1112	176	11	as	as	ADP
m-1112	176	12	real	real	ADJ
m-1112	176	13	≡	≡	ADJ
m-1112	176	14	existing	exist	VERB
m-1112	176	15	-	-	PUNCT
m-1112	176	16	universe	universe	NOUN
m-1112	176	17	,	,	PUNCT
m-1112	176	18	imaginary≡	imaginary≡	PROPN
m-1112	176	19	black	black	NOUN
m-1112	176	20	-	-	PUNCT
m-1112	176	21	holes	hole	NOUN
m-1112	176	22	2	2	NUM
m-1112	176	23	…	…	PUNCT
m-1112	176	24	the	the	DET
m-1112	176	25	dual	dual	ADJ
m-1112	176	26	photon	photon	NOUN
m-1112	176	27	,	,	PUNCT
m-1112	176	28	as	as	ADP
m-1112	176	29	real	real	ADJ
m-1112	176	30	≡	≡	PROPN
m-1112	176	31	space	space	NOUN
m-1112	176	32	≡	≡	PROPN
m-1112	176	33	particle	particle	NOUN
m-1112	176	34	and	and	CCONJ
m-1112	176	35	,	,	PUNCT
m-1112	176	36	imaginary	imaginary	ADJ
m-1112	176	37	≡	≡	PROPN
m-1112	176	38	{	{	PUNCT
m-1112	176	39	e	e	PROPN
m-1112	176	40	m	m	NOUN
m-1112	176	41	wave	wave	NOUN
m-1112	176	42	}	}	PUNCT
m-1112	176	43	.	.	PUNCT
m-1112	177	1	3	3	NUM
m-1112	177	2	…	…	PUNCT
m-1112	177	3	the	the	DET
m-1112	177	4	dual	dual	ADJ
m-1112	177	5	spin	spin	NOUN
m-1112	177	6	b̅	b̅	NOUN
m-1112	177	7	,	,	PUNCT
m-1112	177	8	as	as	ADP
m-1112	177	9	real	real	ADJ
m-1112	177	10	≡	≡	PROPN
m-1112	177	11	space	space	NOUN
m-1112	177	12	≡	≡	PROPN
m-1112	177	13	gravity	gravity	NOUN
m-1112	177	14	and	and	CCONJ
m-1112	177	15	,	,	PUNCT
m-1112	177	16	imaginary	imaginary	ADJ
m-1112	177	17	≡	≡	PROPN
m-1112	177	18	{	{	PUNCT
m-1112	177	19	anti	anti	X
m-1112	177	20	gravity	gravity	NOUN
m-1112	177	21	}	}	PUNCT
m-1112	177	22	.	.	PUNCT
m-1112	178	1	4	4	NUM
m-1112	178	2	…	…	PUNCT
m-1112	178	3	the	the	DET
m-1112	178	4	dual	dual	ADJ
m-1112	178	5	–	–	PUNCT
m-1112	178	6	matter	matter	NOUN
m-1112	178	7	b̅	b̅	NOUN
m-1112	178	8	,	,	PUNCT
m-1112	178	9	as	as	ADP
m-1112	178	10	real	real	ADJ
m-1112	178	11	≡	≡	PROPN
m-1112	178	12	space	space	NOUN
m-1112	178	13	≡	≡	PROPN
m-1112	178	14	atoms	atom	NOUN
m-1112	178	15	and	and	CCONJ
m-1112	178	16	,	,	PUNCT
m-1112	178	17	imaginary	imaginary	ADJ
m-1112	178	18	≡	≡	PROPN
m-1112	178	19	{	{	PUNCT
m-1112	178	20	e	e	NOUN
m-1112	178	21	m	m	NOUN
m-1112	178	22	-wave	-wave	NOUN
m-1112	178	23	}	}	PUNCT
m-1112	178	24	.	.	PUNCT
m-1112	179	1	5	5	NUM
m-1112	179	2	…	…	NUM
m-1112	179	3	the	the	DET
m-1112	179	4	dual	dual	ADJ
m-1112	179	5	-	-	PUNCT
m-1112	179	6	refraction	refraction	NOUN
m-1112	179	7	of	of	ADP
m-1112	179	8	energy	energy	NOUN
m-1112	179	9	as	as	ADP
m-1112	179	10	real	real	ADJ
m-1112	179	11	≡	≡	PROPN
m-1112	179	12	the	the	DET
m-1112	179	13	space	space	NOUN
m-1112	179	14	angle	angle	NOUN
m-1112	179	15	φ	φ	PROPN
m-1112	179	16	,	,	PUNCT
m-1112	179	17	imaginary	imaginary	PROPN
m-1112	179	18	≡	≡	PROPN
m-1112	179	19	�	�	PROPN
m-1112	179	20	̅	̅	NOUN
m-1112	179	21	�	�	PROPN
m-1112	179	22	1	1	NUM
m-1112	179	23	,	,	PUNCT
m-1112	179	24	�	�	NOUN
m-1112	179	25	̅	̅	NOUN
m-1112	179	26	�	�	X
m-1112	179	27	2	2	NUM
m-1112	179	28	{	{	PUNCT
m-1112	179	29	the	the	DET
m-1112	179	30	energy	energy	NOUN
m-1112	179	31	≡	≡	PROPN
m-1112	179	32	w	w	PROPN
m-1112	179	33	from	from	ADP
m-1112	179	34	the	the	DET
m-1112	179	35	different	different	ADJ
m-1112	179	36	velocities	velocity	NOUN
m-1112	179	37	,	,	PUNCT
m-1112	179	38	�	�	PROPN
m-1112	179	39	̅	̅	NOUN
m-1112	179	40	�	�	PROPN
m-1112	179	41	1	1	NUM
m-1112	179	42	,	,	PUNCT
m-1112	179	43	�	�	NOUN
m-1112	179	44	̅	̅	NOUN
m-1112	179	45	�	�	NOUN
m-1112	179	46	2	2	NUM
m-1112	179	47	}	}	PUNCT
m-1112	179	48	.	.	PUNCT
m-1112	180	1	the	the	DET
m-1112	180	2	results	result	NOUN
m-1112	180	3	in	in	ADP
m-1112	180	4	hydrogen	hydrogen	NOUN
m-1112	180	5	cave	cave	NOUN
m-1112	180	6	:	:	PUNCT
m-1112	180	7	1	1	NUM
m-1112	180	8	…	…	SYM
m-1112	180	9	hydrogen	hydrogen	NOUN
m-1112	180	10	-	-	PUNCT
m-1112	180	11	cave	cave	NOUN
m-1112	180	12	,	,	PUNCT
m-1112	180	13	in	in	ADP
m-1112	180	14	–	–	PUNCT
m-1112	180	15	out	out	ADP
m-1112	180	16	universe	universe	NOUN
m-1112	180	17	occupies	occupy	VERB
m-1112	180	18	mass	mass	NOUN
m-1112	180	19	𝐦	𝐦	PROPN
m-1112	180	20	𝐇	𝐇	PROPN
m-1112	180	21	,	,	PUNCT
m-1112	180	22	velocity	velocity	PROPN
m-1112	180	23	�	�	PROPN
m-1112	180	24	⃡	⃡	NOUN
m-1112	180	25	�	�	PROPN
m-1112	180	26	,	,	PUNCT
m-1112	180	27	and	and	CCONJ
m-1112	180	28	power	power	NOUN
m-1112	180	29	𝐏	𝐏	PROPN
m-1112	180	30	𝐇	𝐇	PROPN
m-1112	180	31	2	2	NUM
m-1112	180	32	…	…	PUNCT
m-1112	180	33	electron	electron	NOUN
m-1112	180	34	in	in	ADP
m-1112	180	35	hydrogen	hydrogen	NOUN
m-1112	180	36	-	-	PUNCT
m-1112	180	37	cave	cave	NOUN
m-1112	180	38	precesses	precesse	NOUN
m-1112	180	39	and	and	CCONJ
m-1112	180	40	nutates	nutate	NOUN
m-1112	180	41	due	due	ADP
m-1112	180	42	to	to	ADP
m-1112	180	43	the	the	DET
m-1112	180	44	gravitational	gravitational	ADJ
m-1112	180	45	constant	constant	ADJ
m-1112	180	46	g.	g.	NOUN
m-1112	180	47	the	the	DET
m-1112	180	48	produced	produce	VERB
m-1112	180	49	work	work	NOUN
m-1112	180	50	is	be	AUX
m-1112	180	51	stored	store	VERB
m-1112	180	52	in	in	ADP
m-1112	180	53	form	form	NOUN
m-1112	180	54	of→	of→	NOUN
m-1112	180	55	stress	stress	NOUN
m-1112	180	56	energy	energy	NOUN
m-1112	180	57	as	as	ADP
m-1112	180	58	hydrogen	hydrogen	NOUN
m-1112	180	59	-	-	PUNCT
m-1112	180	60	bracket	bracket	NOUN
m-1112	180	61	-	-	PUNCT
m-1112	180	62	hook←	hook←	NOUN
m-1112	180	63	the	the	DET
m-1112	180	64	electron	electron	NOUN
m-1112	180	65	precesses	precesse	NOUN
m-1112	180	66	from	from	ADP
m-1112	180	67	the	the	DET
m-1112	180	68	continuous	continuous	ADJ
m-1112	180	69	and	and	CCONJ
m-1112	180	70	immense	immense	ADJ
m-1112	180	71	-	-	PUNCT
m-1112	180	72	communication	communication	NOUN
m-1112	180	73	to	to	ADP
m-1112	180	74	gravity	gravity	NOUN
m-1112	180	75	,	,	PUNCT
m-1112	180	76	g	g	PROPN
m-1112	180	77	.	.	PUNCT
m-1112	180	78	electron	electron	NOUN
m-1112	180	79	-	-	PUNCT
m-1112	180	80	spin	spin	NOUN
m-1112	180	81	is	be	AUX
m-1112	180	82	the	the	DET
m-1112	180	83	angular	angular	ADJ
m-1112	180	84	-	-	PUNCT
m-1112	180	85	momentum	momentum	NOUN
m-1112	180	86	-	-	PUNCT
m-1112	180	87	vector	vector	NOUN
m-1112	180	88	�	�	PROPN
m-1112	180	89	̅	̅	NOUN
m-1112	180	90	�	�	NOUN
m-1112	180	91	and	and	CCONJ
m-1112	180	92	rotates	rotate	NOUN
m-1112	180	93	according	accord	VERB
m-1112	180	94	to	to	ADP
m-1112	180	95	equation	equation	NOUN
m-1112	180	96	db	db	PROPN
m-1112	180	97	dt	dt	NOUN
m-1112	180	98	3	3	NUM
m-1112	180	99	…	…	PUNCT
m-1112	180	100	the	the	DET
m-1112	180	101	stationary	stationary	ADJ
m-1112	180	102	→	→	SYM
m-1112	180	103	tetrahedron	tetrahedron	NOUN
m-1112	180	104	,	,	PUNCT
m-1112	180	105	in	in	ADP
m-1112	180	106	-	-	PUNCT
m-1112	180	107	sphere	sphere	NOUN
m-1112	180	108	,	,	PUNCT
m-1112	180	109	cube	cube	NOUN
m-1112	180	110	,	,	PUNCT
m-1112	180	111	ex	ex	NOUN
m-1112	180	112	-	-	NOUN
m-1112	180	113	sphere	sphere	ADJ
m-1112	180	114	←construction	←construction	NUM
m-1112	180	115	of	of	ADP
m-1112	180	116	atoms	atom	NOUN
m-1112	180	117	permits	permit	VERB
m-1112	180	118	the	the	DET
m-1112	180	119	space	space	NOUN
m-1112	180	120	–	–	PUNCT
m-1112	180	121	coordinate	coordinate	NOUN
m-1112	180	122	structure	structure	NOUN
m-1112	180	123	of	of	ADP
m-1112	180	124	atoms	atom	NOUN
m-1112	180	125	,	,	PUNCT
m-1112	180	126	the	the	DET
m-1112	180	127	wave	wave	NOUN
m-1112	180	128	-	-	PUNCT
m-1112	180	129	eigenfunctions	eigenfunction	NOUN
m-1112	180	130	of	of	ADP
m-1112	180	131	many	many	ADJ
m-1112	180	132	non	non	ADJ
m-1112	180	133	-	-	ADJ
m-1112	180	134	commuting	commuting	ADJ
m-1112	180	135	physical	physical	ADJ
m-1112	180	136	operators	operator	NOUN
m-1112	180	137	as	as	ADP
m-1112	180	138	momentum	momentum	NOUN
m-1112	180	139	power	power	NOUN
m-1112	180	140	,	,	PUNCT
m-1112	180	141	from	from	ADP
m-1112	180	142	the	the	DET
m-1112	180	143	quantum	quantum	ADJ
m-1112	180	144	-	-	ADJ
m-1112	180	145	mechanical	mechanical	ADJ
m-1112	180	146	description	description	NOUN
m-1112	180	147	of	of	ADP
m-1112	180	148	the	the	DET
m-1112	180	149	physical	physical	ADJ
m-1112	180	150	-	-	PUNCT
m-1112	180	151	reality	reality	NOUN
m-1112	180	152	is	be	AUX
m-1112	180	153	complete	complete	ADJ
m-1112	180	154	i.e.	i.e.	X
m-1112	180	155	if	if	ADV
m-1112	180	156	-	-	PUNCT
m-1112	180	157	known	know	VERB
m-1112	180	158	the	the	DET
m-1112	180	159	physical	physical	ADJ
m-1112	180	160	operators	operator	NOUN
m-1112	180	161	,	,	PUNCT
m-1112	180	162	their	their	PRON
m-1112	180	163	coordinates	coordinate	NOUN
m-1112	180	164	are	be	AUX
m-1112	180	165	simultaneous	simultaneous	ADJ
m-1112	180	166	physical	physical	ADJ
m-1112	180	167	reality	reality	NOUN
m-1112	180	168	.	.	PUNCT
m-1112	181	1	4	4	NUM
m-1112	181	2	…	…	PUNCT
m-1112	181	3	the	the	DET
m-1112	181	4	interactions	interaction	NOUN
m-1112	181	5	of	of	ADP
m-1112	181	6	two	two	NUM
m-1112	181	7	or	or	CCONJ
m-1112	181	8	more	more	ADJ
m-1112	181	9	systems	system	NOUN
m-1112	181	10	with	with	ADP
m-1112	181	11	known	know	VERB
m-1112	181	12	status	status	NOUN
m-1112	181	13	can	can	AUX
m-1112	181	14	be	be	AUX
m-1112	181	15	calculated	calculate	VERB
m-1112	181	16	any	any	DET
m-1112	181	17	time	time	NOUN
m-1112	181	18	by	by	ADP
m-1112	181	19	the	the	DET
m-1112	181	20	bioelectronic	bioelectronic	NOUN
m-1112	181	21	-	-	PUNCT
m-1112	181	22	spectrum	spectrum	NOUN
m-1112	181	23	of	of	ADP
m-1112	181	24	→	→	NOUN
m-1112	181	25	{	{	PUNCT
m-1112	181	26	carrier	carrier	NOUN
m-1112	181	27	-	-	PUNCT
m-1112	181	28	modulating	modulate	VERB
m-1112	181	29	-	-	PUNCT
m-1112	181	30	modulated	modulate	VERB
m-1112	181	31	,	,	PUNCT
m-1112	181	32	demodulation	demodulation	NOUN
m-1112	181	33	process	process	NOUN
m-1112	181	34	mechanism	mechanism	NOUN
m-1112	181	35	}	}	PUNCT
m-1112	181	36	←	←	PROPN
m-1112	181	37	using	use	VERB
m-1112	181	38	markos	markos	PROPN
m-1112	181	39	program	program	NOUN
m-1112	181	40	<	<	X
m-1112	181	41	programming	programming	NOUN
m-1112	181	42	atoms	atom	NOUN
m-1112	181	43	-	-	PUNCT
m-1112	181	44	bonding	bonding	NOUN
m-1112	181	45	and	and	CCONJ
m-1112	181	46	their	their	PRON
m-1112	181	47	compounds	compound	NOUN
m-1112	181	48	>	>	X
m-1112	182	1	so	so	ADV
m-1112	182	2	,	,	PUNCT
m-1112	182	3	energy	energy	NOUN
m-1112	182	4	≡	≡	PROPN
m-1112	182	5	motion	motion	NOUN
m-1112	182	6	is	be	AUX
m-1112	182	7	of	of	ADP
m-1112	182	8	wave	wave	NOUN
m-1112	182	9	nature	nature	NOUN
m-1112	182	10	which	which	PRON
m-1112	182	11	enters	enter	VERB
m-1112	182	12	the	the	DET
m-1112	182	13	energy	energy	NOUN
m-1112	182	14	caves	cave	NOUN
m-1112	182	15	and	and	CCONJ
m-1112	182	16	becomes	become	VERB
m-1112	182	17	a	a	DET
m-1112	182	18	particle	particle	NOUN
m-1112	182	19	or	or	CCONJ
m-1112	182	20	wave	wave	NOUN
m-1112	182	21	or	or	CCONJ
m-1112	182	22	both	both	PRON
m-1112	182	23	.	.	PUNCT
m-1112	183	1	in	in	ADP
m-1112	183	2	case	case	NOUN
m-1112	183	3	of	of	ADP
m-1112	183	4	photons	photon	NOUN
m-1112	183	5	exists	exist	VERB
m-1112	183	6	this	this	DET
m-1112	183	7	dual	dual	ADJ
m-1112	183	8	property	property	NOUN
m-1112	183	9	,	,	PUNCT
m-1112	183	10	wave	wave	NOUN
m-1112	183	11	–	–	PUNCT
m-1112	183	12	particle	particle	NOUN
m-1112	183	13	.	.	PUNCT
m-1112	184	1	thus	thus	ADV
m-1112	184	2	the	the	DET
m-1112	184	3	historical	historical	ADJ
m-1112	184	4	doubt	doubt	NOUN
m-1112	184	5	of	of	ADP
m-1112	184	6	einstein	einstein	PROPN
m-1112	184	7	podolsky	podolsky	PROPN
m-1112	184	8	rosen	rosen	PROPN
m-1112	184	9	for	for	ADP
m-1112	184	10	the	the	DET
m-1112	184	11	q	q	ADJ
m-1112	184	12	-	-	PUNCT
m-1112	184	13	mechanics	mechanic	NOUN
m-1112	184	14	completion	completion	NOUN
m-1112	184	15	vanishes	vanish	VERB
m-1112	184	16	.	.	PUNCT
m-1112	185	1	[	[	X
m-1112	185	2	100,104	100,104	X
m-1112	185	3	]	]	PUNCT
m-1112	185	4	.	.	PUNCT
m-1112	186	1	5	5	NUM
m-1112	186	2	…	…	PUNCT
m-1112	186	3	the	the	DET
m-1112	186	4	programming	programming	NOUN
m-1112	186	5	of	of	ADP
m-1112	186	6	atoms	atom	NOUN
m-1112	186	7	bonding	bonding	NOUN
m-1112	186	8	is	be	AUX
m-1112	186	9	the	the	DET
m-1112	186	10	quantization	quantization	NOUN
m-1112	186	11	of	of	ADP
m-1112	186	12	atoms	atom	NOUN
m-1112	186	13	-wave	-wave	NOUN
m-1112	186	14	-energy	-energy	NOUN
m-1112	186	15	to	to	ADP
m-1112	186	16	all	all	DET
m-1112	186	17	possible	possible	ADJ
m-1112	186	18	equilibrium	equilibrium	NOUN
m-1112	186	19	positions	position	NOUN
m-1112	186	20	of	of	ADP
m-1112	186	21	the	the	DET
m-1112	186	22	[	[	X
m-1112	186	23	⊕↔⊝	⊕↔⊝	NOUN
m-1112	186	24	]	]	PUNCT
m-1112	186	25	constitutes	constitute	VERB
m-1112	186	26	reactions	reaction	NOUN
m-1112	186	27	.	.	PUNCT
m-1112	187	1	the	the	DET
m-1112	187	2	wave	wave	NOUN
m-1112	187	3	-	-	PUNCT
m-1112	187	4	energy	energy	NOUN
m-1112	187	5	as	as	SCONJ
m-1112	187	6	vibration	vibration	NOUN
m-1112	187	7	travels	travel	VERB
m-1112	187	8	at	at	ADP
m-1112	187	9	75	75	NUM
m-1112	187	10	-	-	SYM
m-1112	187	11	90	90	NUM
m-1112	187	12	%	%	NOUN
m-1112	187	13	of	of	ADP
m-1112	187	14	the	the	DET
m-1112	187	15	light	light	ADJ
m-1112	187	16	speed	speed	NOUN
m-1112	187	17	c	c	NOUN
m-1112	187	18	,	,	PUNCT
m-1112	187	19	while	while	SCONJ
m-1112	187	20	the	the	DET
m-1112	187	21	wave	wave	NOUN
m-1112	187	22	-	-	PUNCT
m-1112	187	23	energy	energy	NOUN
m-1112	187	24	in	in	ADP
m-1112	187	25	black	black	ADJ
m-1112	187	26	holes	hole	NOUN
m-1112	187	27	is	be	AUX
m-1112	187	28	n	n	PRON
m-1112	187	29	π	π	PROPN
m-1112	187	30	c	c	PROPN
m-1112	187	31	times	time	NOUN
m-1112	187	32	of	of	ADP
m-1112	187	33	the	the	DET
m-1112	187	34	light	light	ADJ
m-1112	187	35	speed	speed	NOUN
m-1112	187	36	.	.	PUNCT
m-1112	188	1	[	[	X
m-1112	188	2	100	100	NUM
m-1112	188	3	-	-	SYM
m-1112	188	4	101	101	NUM
m-1112	188	5	]	]	SYM
m-1112	188	6	6	6	NUM
m-1112	188	7	…	…	PUNCT
m-1112	188	8	from	from	ADP
m-1112	188	9	all	all	DET
m-1112	188	10	the	the	DET
m-1112	188	11	possible	possible	ADJ
m-1112	188	12	reactions	reaction	NOUN
m-1112	188	13	in	in	ADP
m-1112	188	14	compounds	compound	NOUN
m-1112	188	15	,	,	PUNCT
m-1112	188	16	the	the	DET
m-1112	188	17	bonding	bonding	NOUN
m-1112	188	18	or	or	CCONJ
m-1112	188	19	the	the	DET
m-1112	188	20	releasing	releasing	NOUN
m-1112	188	21	of	of	ADP
m-1112	188	22	energy	energy	NOUN
m-1112	188	23	is	be	AUX
m-1112	188	24	the	the	DET
m-1112	188	25	vital	vital	ADJ
m-1112	188	26	rule	rule	NOUN
m-1112	188	27	of	of	ADP
m-1112	188	28	the	the	DET
m-1112	188	29	theory	theory	NOUN
m-1112	188	30	of	of	ADP
m-1112	188	31	vibrations	vibration	NOUN
m-1112	188	32	.the	.the	PRON
m-1112	188	33	program	program	NOUN
m-1112	188	34	programming	program	VERB
m-1112	188	35	the	the	DET
m-1112	188	36	atoms	atom	NOUN
m-1112	188	37	and	and	CCONJ
m-1112	188	38	their	their	PRON
m-1112	188	39	compounds	compound	NOUN
m-1112	188	40	,	,	PUNCT
m-1112	188	41	analyses	analyse	VERB
m-1112	188	42	the	the	DET
m-1112	188	43	interactions	interaction	NOUN
m-1112	188	44	of	of	ADP
m-1112	188	45	two	two	NUM
m-1112	188	46	or	or	CCONJ
m-1112	188	47	more	more	ADJ
m-1112	188	48	energy	energy	NOUN
m-1112	188	49	systems	system	NOUN
m-1112	188	50	with	with	ADP
m-1112	188	51	known	known	ADJ
m-1112	188	52	ijo	ijo	PROPN
m-1112	188	53	international	international	PROPN
m-1112	188	54	journal	journal	PROPN
m-1112	188	55	of	of	ADP
m-1112	188	56	mathematics	mathematics	PROPN
m-1112	188	57	(	(	PUNCT
m-1112	188	58	issn	issn	PROPN
m-1112	188	59	:	:	PUNCT
m-1112	188	60	2992	2992	NUM
m-1112	188	61	-	-	SYM
m-1112	188	62	4421	4421	NUM
m-1112	188	63	)	)	PUNCT
m-1112	188	64	volume	volume	NOUN
m-1112	188	65	08	08	NUM
m-1112	189	1	|	|	ADV
m-1112	189	2	issue	issue	NOUN
m-1112	189	3	08	08	NUM
m-1112	190	1	|	|	ADV
m-1112	190	2	august	august	PROPN
m-1112	190	3	2025	2025	NUM
m-1112	190	4	|	|	ADV
m-1112	190	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	190	6	ijo	ijo	PROPN
m-1112	190	7	journals	journal	NOUN
m-1112	190	8	10	10	NUM
m-1112	190	9	the	the	DET
m-1112	190	10	fundamental	fundamental	ADJ
m-1112	190	11	particles	particle	NOUN
m-1112	190	12	origination	origination	NOUN
m-1112	190	13	mechanism	mechanism	NOUN
m-1112	190	14	in	in	ADP
m-1112	190	15	mfmf	mfmf	PROPN
m-1112	190	16	pns	pns	PROPN
m-1112	190	17	caves	cave	NOUN
m-1112	190	18	.	.	PUNCT
m-1112	191	1	status	status	NOUN
m-1112	191	2	using	use	VERB
m-1112	191	3	the	the	DET
m-1112	191	4	→	→	SYM
m-1112	191	5	carrier	carrier	NOUN
m-1112	191	6	–	–	PUNCT
m-1112	191	7	modulating	modulating	ADJ
m-1112	191	8	–	–	PUNCT
m-1112	191	9	modulated	modulate	VERB
m-1112	191	10	–	–	PUNCT
m-1112	191	11	demodulation	demodulation	NOUN
m-1112	191	12	waves	wave	NOUN
m-1112	191	13	process	process	NOUN
m-1112	191	14	←	←	PROPN
m-1112	191	15	some	some	DET
m-1112	191	16	following	follow	VERB
m-1112	191	17	wave	wave	NOUN
m-1112	191	18	properties	property	NOUN
m-1112	191	19	that	that	PRON
m-1112	191	20	are	be	AUX
m-1112	191	21	defined	define	VERB
m-1112	191	22	:	:	PUNCT
m-1112	191	23	6a	6a	NUM
m-1112	191	24	...	...	PUNCT
m-1112	191	25	the	the	DET
m-1112	191	26	equilibrium	equilibrium	NOUN
m-1112	191	27	mode	mode	NOUN
m-1112	191	28	–	–	PUNCT
m-1112	191	29	shapes	shape	NOUN
m-1112	191	30	,	,	PUNCT
m-1112	191	31	φ	φ	PROPN
m-1112	191	32	,	,	PUNCT
m-1112	191	33	diagrams	diagram	NOUN
m-1112	191	34	.	.	PUNCT
m-1112	192	1	6b1	6b1	NUM
m-1112	192	2	..	..	PUNCT
m-1112	192	3	the	the	DET
m-1112	192	4	circular	circular	ADJ
m-1112	192	5	–	–	PUNCT
m-1112	192	6	frequencies	frequency	NOUN
m-1112	192	7	,	,	PUNCT
m-1112	192	8	𝐖	𝐖	PROPN
m-1112	192	9	𝐑	𝐑	PROPN
m-1112	192	10	,	,	PUNCT
m-1112	192	11	in	in	ADP
m-1112	192	12	1015	1015	NUM
m-1112	192	13	hz	hz	VERB
m-1112	192	14	,	,	PUNCT
m-1112	192	15	6b2	6b2	NUM
m-1112	192	16	..	..	PUNCT
m-1112	192	17	the	the	DET
m-1112	192	18	natural	natural	ADJ
m-1112	192	19	–	–	PUNCT
m-1112	192	20	frequencies	frequency	NOUN
m-1112	192	21	,	,	PUNCT
m-1112	192	22	𝐟	𝐟	PROPN
m-1112	192	23	𝐑	𝐑	PROPN
m-1112	192	24	,	,	PUNCT
m-1112	192	25	in	in	ADP
m-1112	192	26	1015	1015	NUM
m-1112	192	27	hz	hz	VERB
m-1112	192	28	,	,	PUNCT
m-1112	192	29	6c	6c	PROPN
m-1112	192	30	..	..	PUNCT
m-1112	193	1	the	the	DET
m-1112	193	2	resultant	resultant	NOUN
m-1112	193	3	energy	energy	NOUN
m-1112	193	4	–	–	PUNCT
m-1112	193	5	state	state	NOUN
m-1112	193	6	,	,	PUNCT
m-1112	193	7	𝐄	𝐄	PROPN
m-1112	193	8	𝐑	𝐑	PROPN
m-1112	193	9	,	,	PUNCT
m-1112	193	10	in	in	ADP
m-1112	193	11	e	e	NOUN
m-1112	193	12	-	-	NOUN
m-1112	193	13	volt	volt	NOUN
m-1112	193	14	,	,	PUNCT
m-1112	193	15	6d	6d	NUM
m-1112	193	16	...	...	PUNCT
m-1112	193	17	the	the	DET
m-1112	193	18	electric	electric	ADJ
m-1112	193	19	–	–	PUNCT
m-1112	193	20	magnetic	magnetic	ADJ
m-1112	193	21	field	field	NOUN
m-1112	193	22	,	,	PUNCT
m-1112	193	23	𝐄	𝐄	PROPN
m-1112	193	24	𝐑	𝐑	PROPN
m-1112	193	25	𝐌	𝐌	PROPN
m-1112	193	26	𝐑	𝐑	PROPN
m-1112	193	27	,	,	PUNCT
m-1112	193	28	in	in	ADP
m-1112	193	29	10−12	10−12	NOUN
m-1112	193	30	ampere	ampere	ADV
m-1112	193	31	-10−6	-10−6	PROPN
m-1112	193	32	tesla	tesla	PROPN
m-1112	193	33	,	,	PUNCT
m-1112	193	34	6e	6e	NOUN
m-1112	193	35	..	..	PUNCT
m-1112	193	36	the	the	DET
m-1112	193	37	intensity	intensity	NOUN
m-1112	193	38	of	of	ADP
m-1112	193	39	the	the	DET
m-1112	193	40	λ	λ	NOUN
m-1112	193	41	-	-	ADJ
m-1112	193	42	electric	electric	ADJ
m-1112	193	43	–	–	PUNCT
m-1112	193	44	field	field	NOUN
m-1112	193	45	,	,	PUNCT
m-1112	193	46	𝐈	𝐈	VERB
m-1112	193	47	𝝀	𝝀	NOUN
m-1112	193	48	,	,	PUNCT
m-1112	193	49	in	in	ADP
m-1112	193	50	10−12	10−12	NOUN
m-1112	193	51	ampere	ampere	NOUN
m-1112	193	52	,	,	PUNCT
m-1112	193	53	6f	6f	NUM
m-1112	193	54	..	..	PUNCT
m-1112	193	55	the	the	DET
m-1112	193	56	intensity	intensity	NOUN
m-1112	193	57	of	of	ADP
m-1112	193	58	magnetic	magnetic	ADJ
m-1112	193	59	–	–	PUNCT
m-1112	193	60	field	field	NOUN
m-1112	193	61	,	,	PUNCT
m-1112	193	62	𝐌	𝐌	PROPN
m-1112	193	63	𝝀	𝝀	NOUN
m-1112	193	64	,	,	PUNCT
m-1112	193	65	in	in	ADP
m-1112	193	66	10−6	10−6	NUM
m-1112	193	67	tesla	tesla	NOUN
m-1112	193	68	,	,	PUNCT
m-1112	193	69	6	6	NUM
m-1112	193	70	g	g	NOUN
m-1112	193	71	..	..	PUNCT
m-1112	193	72	the	the	DET
m-1112	193	73	wavelength	wavelength	NOUN
m-1112	193	74	,	,	PUNCT
m-1112	193	75	λ	λ	INTJ
m-1112	193	76	,	,	PUNCT
m-1112	193	77	in	in	ADP
m-1112	193	78	.10−10	.10−10	NUM
m-1112	193	79	meters	meter	NOUN
m-1112	193	80	,	,	PUNCT
m-1112	193	81	6h	6h	NUM
m-1112	193	82	..	..	PUNCT
m-1112	193	83	the	the	DET
m-1112	193	84	wave	wave	NOUN
m-1112	193	85	velocity	velocity	NOUN
m-1112	193	86	,	,	PUNCT
m-1112	193	87	�	�	PROPN
m-1112	193	88	̅	̅	NOUN
m-1112	193	89	�	�	PROPN
m-1112	193	90	,	,	PUNCT
m-1112	193	91	in	in	ADP
m-1112	193	92	105	105	NUM
m-1112	193	93	meters	meter	NOUN
m-1112	193	94	/	/	SYM
m-1112	193	95	s	s	X
m-1112	193	96	,	,	PUNCT
m-1112	193	97	6i1	6i1	NUM
m-1112	193	98	..	..	PUNCT
m-1112	193	99	the	the	DET
m-1112	193	100	resultant	resultant	NOUN
m-1112	193	101	voltage	voltage	NOUN
m-1112	193	102	at	at	ADP
m-1112	193	103	wavelength	wavelength	NOUN
m-1112	193	104	-	-	PUNCT
m-1112	193	105	sides	side	NOUN
m-1112	193	106	,	,	PUNCT
m-1112	193	107	𝐕	𝐕	PROPN
m-1112	193	108	𝝀	𝝀	NOUN
m-1112	193	109	,	,	PUNCT
m-1112	193	110	in	in	ADP
m-1112	193	111	volt	volt	NOUN
m-1112	193	112	,	,	PUNCT
m-1112	193	113	6i2	6i2	NUM
m-1112	193	114	..	..	PUNCT
m-1112	193	115	the	the	DET
m-1112	193	116	s	s	NOUN
m-1112	193	117	-	-	PUNCT
m-1112	193	118	bands	band	NOUN
m-1112	193	119	voltages	voltage	NOUN
m-1112	193	120	at	at	ADP
m-1112	193	121	wavelength	wavelength	NOUN
m-1112	193	122	-	-	PUNCT
m-1112	193	123	sides	side	NOUN
m-1112	193	124	,	,	PUNCT
m-1112	193	125	𝐕	𝐕	PROPN
m-1112	193	126	𝝀	𝝀	NOUN
m-1112	193	127	,	,	PUNCT
m-1112	193	128	in	in	ADP
m-1112	193	129	volt	volt	NOUN
m-1112	193	130	,	,	PUNCT
m-1112	193	131	6j	6j	NUM
m-1112	193	132	..	..	PUNCT
m-1112	193	133	the	the	DET
m-1112	193	134	radius	radius	NOUN
m-1112	193	135	of	of	ADP
m-1112	193	136	the	the	DET
m-1112	193	137	helical	helical	ADJ
m-1112	193	138	motion	motion	NOUN
m-1112	193	139	,	,	PUNCT
m-1112	193	140	r	r	NOUN
m-1112	193	141	=	=	SYM
m-1112	193	142	𝐀	𝐀	NOUN
m-1112	193	143	𝐑	𝐑	PROPN
m-1112	193	144	in	in	ADP
m-1112	193	145	.10−10	.10−10	PUNCT
m-1112	193	146	meter	meter	NOUN
m-1112	193	147	,	,	PUNCT
m-1112	193	148	6k	6k	PROPN
m-1112	193	149	..	..	PUNCT
m-1112	193	150	the	the	DET
m-1112	193	151	total	total	ADJ
m-1112	193	152	carrier	carrier	NOUN
m-1112	193	153	power	power	NOUN
m-1112	193	154	,	,	PUNCT
m-1112	193	155	𝐏	𝐏	PROPN
m-1112	193	156	𝐂𝐓	𝐂𝐓	PROPN
m-1112	193	157	,	,	PUNCT
m-1112	193	158	in	in	ADP
m-1112	193	159	10−20	10−20	PROPN
m-1112	193	160	watt	watt	NOUN
m-1112	193	161	,	,	PUNCT
m-1112	193	162	6l	6l	NUM
m-1112	193	163	..	..	PUNCT
m-1112	193	164	the	the	DET
m-1112	193	165	total	total	ADJ
m-1112	193	166	side	side	NOUN
m-1112	193	167	-	-	PUNCT
m-1112	193	168	bands	band	NOUN
m-1112	193	169	power	power	NOUN
m-1112	193	170	,	,	PUNCT
m-1112	193	171	𝐏	𝐏	PROPN
m-1112	193	172	𝐓	𝐓	PROPN
m-1112	193	173	,	,	PUNCT
m-1112	193	174	in	in	ADP
m-1112	193	175	10−20	10−20	PROPN
m-1112	193	176	watt	watt	NOUN
m-1112	193	177	,	,	PUNCT
m-1112	193	178	6	6	NUM
m-1112	193	179	m	m	NOUN
m-1112	193	180	..	..	PUNCT
m-1112	193	181	the	the	DET
m-1112	193	182	side	side	NOUN
m-1112	193	183	-	-	PUNCT
m-1112	193	184	bands	band	NOUN
m-1112	193	185	amplitude	amplitude	NOUN
m-1112	193	186	,	,	PUNCT
m-1112	193	187	𝐀	𝐀	PROPN
m-1112	193	188	𝐁	𝐁	PROPN
m-1112	193	189	,	,	PUNCT
m-1112	193	190	in	in	ADP
m-1112	193	191	10−10	10−10	NUM
m-1112	193	192	meter	meter	NOUN
m-1112	193	193	,	,	PUNCT
m-1112	193	194	6n	6n	PROPN
m-1112	193	195	..	..	PUNCT
m-1112	193	196	the	the	DET
m-1112	193	197	side	side	NOUN
m-1112	193	198	-	-	PUNCT
m-1112	193	199	bands	band	NOUN
m-1112	193	200	coefficients	coefficient	NOUN
m-1112	193	201	,	,	PUNCT
m-1112	193	202	a	a	DET
m-1112	193	203	m	m	NOUN
m-1112	193	204	,	,	PUNCT
m-1112	193	205	in	in	ADP
m-1112	193	206	n	n	CCONJ
m-1112	193	207	-	-	PUNCT
m-1112	193	208	n	n	NOUN
m-1112	193	209	,	,	PUNCT
m-1112	193	210	6o	6o	NOUN
m-1112	193	211	..	..	PUNCT
m-1112	193	212	the	the	DET
m-1112	193	213	modulating	modulating	ADJ
m-1112	193	214	phase	phase	NOUN
m-1112	193	215	shift	shift	NOUN
m-1112	193	216	,	,	PUNCT
m-1112	193	217	𝛗	𝛗	X
m-1112	193	218	,	,	PUNCT
m-1112	193	219	in	in	ADP
m-1112	193	220	rad	rad	PROPN
m-1112	193	221	/2π	/2π	PRON
m-1112	193	222	,	,	PUNCT
m-1112	193	223	6p	6p	NUM
m-1112	193	224	..	..	PUNCT
m-1112	193	225	the	the	DET
m-1112	193	226	modulating	modulating	ADJ
m-1112	193	227	factor	factor	NOUN
m-1112	193	228	,	,	PUNCT
m-1112	193	229	𝒎	𝒎	PROPN
m-1112	193	230	,	,	PUNCT
m-1112	193	231	in	in	ADP
m-1112	193	232	n	n	CCONJ
m-1112	193	233	-	-	PUNCT
m-1112	193	234	n	n	NOUN
m-1112	193	235	,	,	PUNCT
m-1112	193	236	6q	6q	NUM
m-1112	193	237	..	..	PUNCT
m-1112	193	238	the	the	DET
m-1112	193	239	total	total	ADJ
m-1112	193	240	energy	energy	NOUN
m-1112	193	241	-	-	PUNCT
m-1112	193	242	status	status	NOUN
m-1112	193	243	,	,	PUNCT
m-1112	193	244	a	a	DET
m-1112	193	245	m	m	NOUN
m-1112	193	246	,	,	PUNCT
m-1112	193	247	in	in	ADP
m-1112	193	248	h	h	NOUN
m-1112	193	249	-	-	PUNCT
m-1112	193	250	w	w	NOUN
m-1112	193	251	,	,	PUNCT
m-1112	193	252	figure-2	figure-2	PROPN
m-1112	193	253	..	..	PUNCT
m-1112	193	254	the	the	DET
m-1112	193	255	±	±	NOUN
m-1112	193	256	energy	energy	NOUN
m-1112	193	257	in	in	ADP
m-1112	193	258	hydrogen	hydrogen	NOUN
m-1112	193	259	and	and	CCONJ
m-1112	193	260	atoms	atom	NOUN
m-1112	193	261	exists	exist	VERB
m-1112	193	262	from	from	ADP
m-1112	193	263	hydrogen	hydrogen	NOUN
m-1112	193	264	common	common	ADJ
m-1112	193	265	-	-	PUNCT
m-1112	193	266	atom	atom	NOUN
m-1112	193	267	.	.	PUNCT
m-1112	194	1	ijo	ijo	PROPN
m-1112	194	2	international	international	PROPN
m-1112	194	3	journal	journal	PROPN
m-1112	194	4	of	of	ADP
m-1112	194	5	mathematics	mathematics	PROPN
m-1112	194	6	(	(	PUNCT
m-1112	194	7	issn	issn	PROPN
m-1112	194	8	:	:	PUNCT
m-1112	194	9	2992	2992	NUM
m-1112	194	10	-	-	SYM
m-1112	194	11	4421	4421	NUM
m-1112	194	12	)	)	PUNCT
m-1112	194	13	volume	volume	NOUN
m-1112	194	14	08	08	NUM
m-1112	195	1	|	|	ADV
m-1112	195	2	issue	issue	NOUN
m-1112	195	3	08	08	NUM
m-1112	196	1	|	|	ADV
m-1112	196	2	august	august	PROPN
m-1112	196	3	2025	2025	NUM
m-1112	196	4	|	|	ADV
m-1112	196	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	196	6	ijo	ijo	PROPN
m-1112	196	7	journals	journal	NOUN
m-1112	196	8	11	11	NUM
m-1112	196	9	the	the	DET
m-1112	196	10	fundamental	fundamental	ADJ
m-1112	196	11	particles	particle	NOUN
m-1112	196	12	origination	origination	NOUN
m-1112	196	13	mechanism	mechanism	NOUN
m-1112	196	14	in	in	ADP
m-1112	196	15	mfmf	mfmf	PROPN
m-1112	196	16	pns	pns	PROPN
m-1112	196	17	caves	cave	NOUN
m-1112	196	18	.	.	PUNCT
m-1112	197	1	the	the	DET
m-1112	197	2	two	two	NUM
m-1112	197	3	hydrogen	hydrogen	NOUN
m-1112	197	4	bonding	bonding	NOUN
m-1112	197	5	→	→	PUNCT
m-1112	197	6	h	h	NOUN
m-1112	197	7	+	+	CCONJ
m-1112	197	8	h	h	NOUN
m-1112	197	9	=	=	NOUN
m-1112	197	10	h1	h1	VERB
m-1112	197	11	1	1	NUM
m-1112	197	12	+	+	CCONJ
m-1112	197	13	h1	h1	ADJ
m-1112	197	14	1	1	NUM
m-1112	197	15	=	=	SYM
m-1112	197	16	h1	h1	PROPN
m-1112	197	17	1−1	1−1	NUM
m-1112	197	18	h1−1	h1−1	NUM
m-1112	197	19	1	1	NUM
m-1112	197	20	=	=	SYM
m-1112	197	21	h1	h1	NOUN
m-1112	197	22	0	0	NUM
m-1112	197	23	+	+	CCONJ
m-1112	197	24	h0	h0	NOUN
m-1112	197	25	1	1	NUM
m-1112	197	26	=	=	SYM
m-1112	197	27	h2	h2	NOUN
m-1112	197	28	water	water	NOUN
m-1112	197	29	h2o	h2o	PROPN
m-1112	197	30	=	=	SYM
m-1112	197	31	o1	o1	PROPN
m-1112	197	32	h2=	h2=	PROPN
m-1112	197	33	o2	o2	ADJ
m-1112	197	34	2	2	NUM
m-1112	197	35	h2	h2	NOUN
m-1112	197	36	2	2	NUM
m-1112	197	37	=	=	SYM
m-1112	197	38	t	t	PROPN
m-1112	197	39	4	4	NUM
m-1112	197	40	4	4	NUM
m-1112	197	41	=	=	SYM
m-1112	197	42	o2	o2	PROPN
m-1112	197	43	2−2h2−2	2−2h2−2	NUM
m-1112	197	44	2	2	NUM
m-1112	197	45	=	=	SYM
m-1112	197	46	o2	o2	PROPN
m-1112	197	47	0	0	NUM
m-1112	197	48	h0	h0	NOUN
m-1112	197	49	2	2	NUM
m-1112	197	50	=	=	SYM
m-1112	197	51	es	es	ADP
m-1112	197	52	2	2	NUM
m-1112	197	53	=	=	NOUN
m-1112	197	54	t/2	t/2	NUM
m-1112	197	55	2	2	NUM
m-1112	197	56	=	=	NOUN
m-1112	197	57	t/2	t/2	NUM
m-1112	197	58	,	,	PUNCT
m-1112	197	59	still	still	ADV
m-1112	197	60	.	.	PUNCT
m-1112	198	1	[	[	X
m-1112	198	2	102	102	NUM
m-1112	198	3	]	]	SYM
m-1112	198	4	4a	4a	NOUN
m-1112	198	5	..	..	PUNCT
m-1112	198	6	the	the	DET
m-1112	198	7	corelations	corelation	NOUN
m-1112	198	8	of	of	ADP
m-1112	198	9	spaces	space	NOUN
m-1112	198	10	and	and	CCONJ
m-1112	198	11	the	the	DET
m-1112	198	12	primary	primary	ADJ
m-1112	198	13	motion	motion	NOUN
m-1112	198	14	.	.	PUNCT
m-1112	199	1	euclidean	euclidean	ADJ
m-1112	199	2	geometry	geometry	NOUN
m-1112	199	3	spaces	space	NOUN
m-1112	199	4	occupy	occupy	VERB
m-1112	199	5	position	position	NOUN
m-1112	199	6	(	(	PUNCT
m-1112	199	7	x	x	INTJ
m-1112	199	8	,	,	PUNCT
m-1112	199	9	y	y	PROPN
m-1112	199	10	,	,	PUNCT
m-1112	199	11	z	z	PROPN
m-1112	199	12	)	)	PUNCT
m-1112	199	13	and	and	CCONJ
m-1112	199	14	dimension	dimension	NOUN
m-1112	199	15	|	|	ADV
m-1112	199	16	⇅	⇅	NOUN
m-1112	199	17	|	|	ADV
m-1112	199	18	at	at	ADP
m-1112	199	19	any	any	DET
m-1112	199	20	point	point	NOUN
m-1112	199	21	p	p	X
m-1112	199	22	,	,	PUNCT
m-1112	199	23	cauchy	cauchy	PROPN
m-1112	199	24	stress	stress	NOUN
m-1112	199	25	tensor	tensor	NOUN
m-1112	199	26	defines	define	VERB
m-1112	199	27	the	the	DET
m-1112	199	28	state	state	NOUN
m-1112	199	29	of	of	ADP
m-1112	199	30	stress	stress	NOUN
m-1112	199	31	(	(	PUNCT
m-1112	199	32	σ	σ	PROPN
m-1112	199	33	,	,	PUNCT
m-1112	199	34	τ	τ	PROPN
m-1112	199	35	)	)	PUNCT
m-1112	199	36	to	to	ADP
m-1112	199	37	the	the	DET
m-1112	199	38	traction	traction	NOUN
m-1112	199	39	-	-	PUNCT
m-1112	199	40	vector	vector	NOUN
m-1112	199	41	(	(	PUNCT
m-1112	199	42	te=	te=	PROPN
m-1112	199	43	e.	e.	PROPN
m-1112	199	44	σ	σ	PROPN
m-1112	199	45	)	)	PUNCT
m-1112	199	46	the	the	DET
m-1112	199	47	position	position	NOUN
m-1112	199	48	of	of	ADP
m-1112	199	49	spaces	space	NOUN
m-1112	199	50	is	be	AUX
m-1112	199	51	defined	define	VERB
m-1112	199	52	from	from	ADP
m-1112	199	53	any	any	DET
m-1112	199	54	3	3	NUM
m-1112	199	55	-	-	PUNCT
m-1112	199	56	dimension	dimension	NOUN
m-1112	199	57	coordinate	coordinate	NOUN
m-1112	199	58	(	(	PUNCT
m-1112	199	59	x	x	INTJ
m-1112	199	60	,	,	PUNCT
m-1112	199	61	y	y	PROPN
m-1112	199	62	,	,	PUNCT
m-1112	199	63	z	z	PROPN
m-1112	199	64	)	)	PUNCT
m-1112	199	65	or	or	CCONJ
m-1112	199	66	from	from	ADP
m-1112	199	67	angular	angular	ADJ
m-1112	199	68	-	-	PUNCT
m-1112	199	69	system	system	NOUN
m-1112	199	70	(	(	PUNCT
m-1112	199	71	φ	φ	PROPN
m-1112	199	72	,	,	PUNCT
m-1112	199	73	θ	θ	PROPN
m-1112	199	74	,	,	PUNCT
m-1112	199	75	ω	ω	PROPN
m-1112	199	76	)	)	PUNCT
m-1112	199	77	or	or	CCONJ
m-1112	199	78	any	any	DET
m-1112	199	79	other	other	ADJ
m-1112	199	80	system	system	NOUN
m-1112	199	81	with	with	ADP
m-1112	199	82	axis	axis	NOUN
m-1112	199	83	from	from	ADP
m-1112	199	84	any	any	DET
m-1112	199	85	fixed	fixed	ADJ
m-1112	199	86	point	point	NOUN
m-1112	199	87	o	o	INTJ
m-1112	199	88	.	.	PUNCT
m-1112	200	1	the	the	DET
m-1112	200	2	dimension	dimension	NOUN
m-1112	200	3	of	of	ADP
m-1112	200	4	spaces	space	NOUN
m-1112	200	5	is	be	AUX
m-1112	200	6	defined	define	VERB
m-1112	200	7	as	as	ADP
m-1112	200	8	the	the	DET
m-1112	200	9	distance	distance	NOUN
m-1112	200	10	between	between	ADP
m-1112	200	11	any	any	DET
m-1112	200	12	two	two	NUM
m-1112	200	13	points	point	NOUN
m-1112	200	14	o	o	NOUN
m-1112	200	15	,	,	PUNCT
m-1112	200	16	p	p	X
m-1112	200	17	,	,	PUNCT
m-1112	200	18	and	and	CCONJ
m-1112	200	19	from	from	ADP
m-1112	200	20	any	any	DET
m-1112	200	21	fixed	fixed	ADJ
m-1112	200	22	point	point	NOUN
m-1112	200	23	o	o	NOUN
m-1112	200	24	the	the	DET
m-1112	200	25	magnitude	magnitude	NOUN
m-1112	200	26	|op|	|op|	NUM
m-1112	200	27	=	=	PUNCT
m-1112	200	28	𝐧	𝐧	DET
m-1112	200	29	|op|	|op|	NOUN
m-1112	200	30	,	,	PUNCT
m-1112	200	31	where	where	SCONJ
m-1112	200	32	n⃡	n⃡	NOUN
m-1112	200	33	is	be	AUX
m-1112	200	34	the	the	DET
m-1112	200	35	unit	unit	NOUN
m-1112	200	36	line	line	NOUN
m-1112	200	37	length	length	NOUN
m-1112	200	38	direction	direction	NOUN
m-1112	200	39	and	and	CCONJ
m-1112	200	40	is	be	AUX
m-1112	200	41	identified	identify	VERB
m-1112	200	42	by	by	ADP
m-1112	200	43	vector	vector	NOUN
m-1112	200	44	n⃡	n⃡	X
m-1112	200	45	≡	≡	PROPN
m-1112	200	46	|ab|	|ab|	PROPN
m-1112	200	47	=	=	PUNCT
m-1112	200	48	the	the	DET
m-1112	200	49	unity	unity	NOUN
m-1112	200	50	monad	monad	PROPN
m-1112	200	51	.	.	PUNCT
m-1112	201	1	in	in	ADP
m-1112	201	2	fig-1	fig-1	NOUN
m-1112	201	3	-	-	SYM
m-1112	201	4	1	1	NUM
m-1112	201	5	,	,	PUNCT
m-1112	201	6	on	on	ADP
m-1112	201	7	ab	ab	PROPN
m-1112	201	8	diameter	diameter	NOUN
m-1112	201	9	=	=	SYM
m-1112	201	10	2r	2r	NUM
m-1112	201	11	=	=	PUNCT
m-1112	202	1	the	the	DET
m-1112	202	2	monad	monad	PROPN
m-1112	202	3	of	of	ADP
m-1112	202	4	neutral	neutral	ADJ
m-1112	202	5	-	-	PUNCT
m-1112	202	6	circle	circle	NOUN
m-1112	202	7	exist	exist	VERB
m-1112	202	8	the	the	DET
m-1112	202	9	spaces	space	NOUN
m-1112	202	10	with	with	ADP
m-1112	202	11	their	their	PRON
m-1112	202	12	sides	side	NOUN
m-1112	203	1	𝛌𝐧=	𝛌𝐧=	ADJ
m-1112	203	2	2,√r2	2,√r2	PROPN
m-1112	204	1	−	−	PROPN
m-1112	204	2	a²n	a²n	PROPN
m-1112	204	3	,	,	PUNCT
m-1112	204	4	and	and	CCONJ
m-1112	204	5	their	their	PRON
m-1112	204	6	critical	critical	ADJ
m-1112	204	7	-	-	PUNCT
m-1112	204	8	sides	side	NOUN
m-1112	204	9	𝐚𝐧	𝐚𝐧	NOUN
m-1112	204	10	=	=	SYM
m-1112	204	11	1	1	NUM
m-1112	204	12	2	2	NUM
m-1112	204	13	√4r2	√4r2	PROPN
m-1112	204	14	−	−	PROPN
m-1112	204	15	λ²n	λ²n	X
m-1112	204	16	,	,	PUNCT
m-1112	204	17	as	as	ADP
m-1112	204	18	below	below	ADP
m-1112	204	19	1	1	NUM
m-1112	204	20	…	…	PUNCT
m-1112	204	21	for	for	ADP
m-1112	204	22	spaces	space	NOUN
m-1112	204	23	,	,	PUNCT
m-1112	204	24	the	the	DET
m-1112	204	25	polygon	polygon	NOUN
m-1112	204	26	side	side	NOUN
m-1112	204	27	is	be	AUX
m-1112	204	28	λ	λ	NOUN
m-1112	204	29	n(s	n(s	PROPN
m-1112	204	30	)	)	PUNCT
m-1112	204	31	=	=	SYM
m-1112	205	1	2	2	NUM
m-1112	205	2	.√r2	.√r2	NOUN
m-1112	205	3	−	−	PROPN
m-1112	205	4	a²n(s	a²n(s	PROPN
m-1112	205	5	)	)	PUNCT
m-1112	205	6	,	,	PUNCT
m-1112	205	7	2	2	NUM
m-1112	205	8	…	…	PUNCT
m-1112	205	9	for	for	ADP
m-1112	205	10	anti	anti	NOUN
m-1112	205	11	-	-	ADJ
m-1112	205	12	spaces	space	NOUN
m-1112	205	13	,	,	PUNCT
m-1112	205	14	the	the	DET
m-1112	205	15	polygon	polygon	NOUN
m-1112	205	16	side	side	NOUN
m-1112	205	17	is	be	AUX
m-1112	205	18	λ	λ	X
m-1112	205	19	n(as	n(as	ADJ
m-1112	205	20	)	)	PUNCT
m-1112	205	21	=	=	SYM
m-1112	206	1	2	2	NUM
m-1112	206	2	.√r2	.√r2	NOUN
m-1112	206	3	−	−	PROPN
m-1112	206	4	a²n(as	a²n(as	PROPN
m-1112	206	5	)	)	PUNCT
m-1112	206	6	,	,	PUNCT
m-1112	206	7	3	3	NUM
m-1112	206	8	…	…	PUNCT
m-1112	206	9	for	for	ADP
m-1112	206	10	sub	sub	NOUN
m-1112	206	11	-	-	NOUN
m-1112	206	12	spaces	space	NOUN
m-1112	206	13	,	,	PUNCT
m-1112	206	14	the	the	DET
m-1112	206	15	polygon	polygon	NOUN
m-1112	206	16	side	side	NOUN
m-1112	206	17	is	be	AUX
m-1112	206	18	λ	λ	X
m-1112	206	19	n(ss	n(s	NOUN
m-1112	206	20	)	)	PUNCT
m-1112	206	21	=	=	SYM
m-1112	207	1	2	2	NUM
m-1112	207	2	.√r2	.√r2	NOUN
m-1112	207	3	−	−	PROPN
m-1112	207	4	a²n(ss	a²n(ss	NUM
m-1112	207	5	)	)	PUNCT
m-1112	207	6	,	,	PUNCT
m-1112	207	7	4	4	NUM
m-1112	207	8	…	…	PUNCT
m-1112	207	9	for	for	ADP
m-1112	207	10	neutral	neutral	ADJ
m-1112	207	11	spaces	space	NOUN
m-1112	207	12	,	,	PUNCT
m-1112	207	13	the	the	DET
m-1112	207	14	polygon	polygon	NOUN
m-1112	207	15	side	side	NOUN
m-1112	207	16	is	be	AUX
m-1112	207	17	λ	λ	X
m-1112	207	18	n(ns	n(ns	PROPN
m-1112	207	19	)	)	PUNCT
m-1112	207	20	=	=	SYM
m-1112	207	21	0	0	NUM
m-1112	207	22	,	,	PUNCT
m-1112	207	23	while	while	SCONJ
m-1112	207	24	in	in	ADP
m-1112	207	25	material	material	NOUN
m-1112	207	26	-	-	PUNCT
m-1112	207	27	geometry	geometry	NOUN
m-1112	207	28	becomes	become	VERB
m-1112	207	29	from	from	ADP
m-1112	207	30	the	the	DET
m-1112	207	31	centripetal	centripetal	ADJ
m-1112	207	32	force	force	NOUN
m-1112	208	1	fc	fc	PROPN
m-1112	208	2	=	=	PUNCT
m-1112	208	3	σ	σ	PROPN
m-1112	208	4	=	=	PUNCT
m-1112	208	5	m.v³	m.v³	NOUN
m-1112	208	6	r	r	NOUN
m-1112	208	7	=	=	SYM
m-1112	208	8	j	j	PROPN
m-1112	208	9	w²	w²	PROPN
m-1112	208	10	r	r	NOUN
m-1112	208	11	,	,	PUNCT
m-1112	208	12	where	where	SCONJ
m-1112	208	13	the	the	DET
m-1112	208	14	unity	unity	NOUN
m-1112	208	15	monad	monad	PROPN
m-1112	208	16	r	r	NOUN
m-1112	208	17	≡	≡	PROPN
m-1112	208	18	monad	monad	PROPN
m-1112	208	19	r	r	NOUN
m-1112	208	20	=	=	SYM
m-1112	208	21	σ	σ	X
m-1112	208	22	j.w²	j.w²	NOUN
m-1112	208	23	=	=	SYM
m-1112	208	24	𝛔	𝛔	PART
m-1112	208	25	�	�	PROPN
m-1112	208	26	̅	̅	NOUN
m-1112	208	27	�	�	NOUN
m-1112	208	28	=	=	SYM
m-1112	208	29	stress	stress	NOUN
m-1112	208	30	angular−momentum̅̅	angular−momentum̅̅	PROPN
m-1112	208	31	̅̅	̅̅	PROPN
m-1112	208	32	̅̅	̅̅	PROPN
m-1112	208	33	̅̅	̅̅	PROPN
m-1112	208	34	̅̅	̅̅	PROPN
m-1112	208	35	̅̅	̅̅	PROPN
m-1112	208	36	̅̅	̅̅	PROPN
m-1112	208	37	̅̅	̅̅	PROPN
m-1112	208	38	̅̅	̅̅	PROPN
m-1112	208	39	̅̅	̅̅	PROPN
m-1112	208	40	̅̅	̅̅	PROPN
m-1112	208	41	̅̅	̅̅	PROPN
m-1112	208	42	̅̅	̅̅	PROPN
m-1112	208	43	̅̅	̅̅	PROPN
m-1112	208	44	̅̅	̅̅	PROPN
m-1112	208	45	̅	̅	PROPN
m-1112	208	46	,	,	PUNCT
m-1112	208	47	and	and	CCONJ
m-1112	208	48	polygon	polygon	PROPN
m-1112	208	49	side	side	NOUN
m-1112	208	50	𝛌	𝛌	PROPN
m-1112	208	51	𝐧(𝐍𝐒	𝐧(𝐍𝐒	PROPN
m-1112	208	52	)	)	PUNCT
m-1112	208	53	=	=	SYM
m-1112	209	1	2	2	NUM
m-1112	209	2	√r2	√r2	SYM
m-1112	209	3	−	−	PROPN
m-1112	209	4	a²n	a²n	PROPN
m-1112	209	5	,	,	PUNCT
m-1112	209	6	all	all	PRON
m-1112	209	7	becoming	become	VERB
m-1112	209	8	from	from	ADP
m-1112	209	9	pythagorean	pythagorean	PROPN
m-1112	209	10	relation	relation	NOUN
m-1112	209	11	[	[	PUNCT
m-1112	209	12	r	r	NOUN
m-1112	209	13	]	]	PUNCT
m-1112	209	14	²	²	NUM
m-1112	209	15	=	=	SYM
m-1112	209	16	[	[	PUNCT
m-1112	209	17	an	an	X
m-1112	209	18	]	]	X
m-1112	209	19	²	²	NUM
m-1112	210	1	+	+	CCONJ
m-1112	210	2	[	[	PUNCT
m-1112	210	3	λn	λn	NOUN
m-1112	210	4	2	2	NUM
m-1112	210	5	]	]	PUNCT
m-1112	210	6	²	²	NUM
m-1112	210	7	.	.	PUNCT
m-1112	211	1	in	in	ADP
m-1112	211	2	fig-3	fig-3	X
m-1112	211	3	,	,	PUNCT
m-1112	211	4	is	be	AUX
m-1112	211	5	shown	show	VERB
m-1112	211	6	the	the	DET
m-1112	211	7	geometrical	geometrical	ADJ
m-1112	211	8	construction	construction	NOUN
m-1112	211	9	of	of	ADP
m-1112	211	10	the	the	DET
m-1112	211	11	inscribed	inscribe	VERB
m-1112	211	12	and	and	CCONJ
m-1112	211	13	the	the	DET
m-1112	211	14	circumscribed	circumscribed	ADJ
m-1112	211	15	n	n	CCONJ
m-1112	211	16	-	-	PUNCT
m-1112	211	17	regular	regular	ADJ
m-1112	211	18	polygons	polygon	NOUN
m-1112	211	19	.	.	PUNCT
m-1112	212	1	with	with	ADP
m-1112	212	2	4	4	NUM
m-1112	212	3	,	,	PUNCT
m-1112	212	4	5	5	NUM
m-1112	212	5	,	,	PUNCT
m-1112	212	6	6	6	NUM
m-1112	212	7	,	,	PUNCT
m-1112	212	8	different	different	ADJ
m-1112	212	9	vibrating	vibrate	VERB
m-1112	212	10	masses	masse	NOUN
m-1112	212	11	for	for	ADP
m-1112	212	12	each	each	DET
m-1112	212	13	space	space	NOUN
m-1112	212	14	and	and	CCONJ
m-1112	212	15	by	by	ADP
m-1112	212	16	using	use	VERB
m-1112	212	17	the	the	DET
m-1112	212	18	argand	argand	NOUN
m-1112	212	19	diagram	diagram	NOUN
m-1112	212	20	for	for	ADP
m-1112	212	21	a	a	DET
m-1112	212	22	vector	vector	NOUN
m-1112	212	23	of	of	ADP
m-1112	212	24	amplitude	amplitude	NOUN
m-1112	212	25	ab	ab	NOUN
m-1112	212	26	=	=	SYM
m-1112	212	27	2r	2r	NUM
m-1112	213	1	=	=	PUNCT
m-1112	214	1	the	the	DET
m-1112	214	2	monad	monad	PROPN
m-1112	214	3	,	,	PUNCT
m-1112	214	4	then	then	ADV
m-1112	214	5	the	the	DET
m-1112	214	6	4	4	NUM
m-1112	214	7	spaces	space	NOUN
m-1112	214	8	are	be	AUX
m-1112	214	9	measured	measure	VERB
m-1112	214	10	using	use	VERB
m-1112	214	11	the	the	DET
m-1112	214	12	euler	euler	NOUN
m-1112	214	13	equation	equation	NOUN
m-1112	214	14	for	for	ADP
m-1112	214	15	exponential	exponential	ADJ
m-1112	214	16	functions	function	NOUN
m-1112	214	17	as	as	SCONJ
m-1112	214	18	follows	follow	VERB
m-1112	214	19	,	,	PUNCT
m-1112	214	20	on	on	ADP
m-1112	214	21	the	the	DET
m-1112	214	22	spaces	space	NOUN
m-1112	214	23	,	,	PUNCT
m-1112	214	24	the	the	DET
m-1112	214	25	vector	vector	NOUN
m-1112	214	26	of	of	ADP
m-1112	214	27	amplitude	amplitude	NOUN
m-1112	214	28	can	can	AUX
m-1112	214	29	be	be	AUX
m-1112	214	30	represented	represent	VERB
m-1112	214	31	as	as	ADP
m-1112	214	32	the	the	DET
m-1112	214	33	complex	complex	ADJ
m-1112	214	34	quantity	quantity	NOUN
m-1112	214	35	on	on	ADP
m-1112	214	36	→	→	SYM
m-1112	214	37	s	s	PART
m-1112	214	38			NOUN
m-1112	214	39	z	z	NOUN
m-1112	214	40	+	+	CCONJ
m-1112	214	41	n	n	PROPN
m-1112	214	42	=	=	SYM
m-1112	214	43	+	+	NUM
m-1112	214	44	2r.𝑒𝑖.𝑛𝜔𝑡	2r.𝑒𝑖.𝑛𝜔𝑡	NUM
m-1112	214	45	=	=	SYM
m-1112	215	1	+	+	NUM
m-1112	215	2	2rn	2rn	NOUN
m-1112	215	3	.	.	PUNCT
m-1112	216	1	[	[	PUNCT
m-1112	216	2	cosw	cosw	NOUN
m-1112	216	3	.	.	PUNCT
m-1112	217	1	t	t	PROPN
m-1112	217	2	+	+	NUM
m-1112	217	3	i.	i.	NOUN
m-1112	217	4	sinw	sinw	NOUN
m-1112	217	5	.	.	PUNCT
m-1112	218	1	t	t	X
m-1112	218	2	]	]	PUNCT
m-1112	219	1	=	=	PUNCT
m-1112	219	2	x	x	PUNCT
m-1112	220	1	+	+	CCONJ
m-1112	220	2	i	i	PRON
m-1112	220	3	.y	.y	NOUN
m-1112	220	4	on	on	ADP
m-1112	220	5	→	→	PUNCT
m-1112	220	6	as	as	ADP
m-1112	220	7			PROPN
m-1112	220	8	z	z	NOUN
m-1112	220	9	−	−	PROPN
m-1112	220	10	n	n	PROPN
m-1112	220	11	=	=	SYM
m-1112	220	12	2r.𝑒𝑖.𝑛𝜔𝑡	2r.𝑒𝑖.𝑛𝜔𝑡	NUM
m-1112	220	13	=	=	SYM
m-1112	220	14	2rn	2rn	NOUN
m-1112	220	15	.	.	PUNCT
m-1112	221	1	[	[	PUNCT
m-1112	221	2	cosw	cosw	NOUN
m-1112	221	3	.	.	PUNCT
m-1112	222	1	t	t	PROPN
m-1112	222	2	+	+	NUM
m-1112	222	3	i.	i.	NOUN
m-1112	222	4	sinw	sinw	NOUN
m-1112	222	5	.	.	PUNCT
m-1112	223	1	t	t	X
m-1112	223	2	]	]	PUNCT
m-1112	224	1	=	=	PUNCT
m-1112	224	2	x	x	PUNCT
m-1112	225	1	+	+	CCONJ
m-1112	225	2	i	i	PRON
m-1112	225	3	.y	.y	NOUN
m-1112	225	4	on	on	ADP
m-1112	225	5	→	→	SYM
m-1112	225	6	ss	ss	PROPN
m-1112	225	7			NOUN
m-1112	225	8	z	z	PROPN
m-1112	225	9	±	±	PROPN
m-1112	225	10	1/𝑛	1/𝑛	NUM
m-1112	225	11	=	=	SYM
m-1112	225	12	±2r	±2r	ADP
m-1112	225	13	1	1	NUM
m-1112	225	14	/	/	SYM
m-1112	225	15	n.	n.	NOUN
m-1112	225	16	ei.θ	ei.θ	NOUN
m-1112	225	17	/	/	SYM
m-1112	225	18	n	n	NOUN
m-1112	225	19	=	=	SYM
m-1112	225	20	±	±	NOUN
m-1112	225	21	√2r	√2r	NUM
m-1112	225	22	n	n	NOUN
m-1112	225	23	.	.	PUNCT
m-1112	226	1	√	√	NUM
m-1112	226	2	[	[	PUNCT
m-1112	226	3	cosw	cosw	NOUN
m-1112	226	4	.	.	PUNCT
m-1112	227	1	t	t	PROPN
m-1112	227	2	+	+	CCONJ
m-1112	227	3	𝐢.	𝐢.	ADJ
m-1112	227	4	sinw	sinw	NOUN
m-1112	227	5	.	.	PUNCT
m-1112	228	1	t	t	NOUN
m-1112	228	2	]	]	PUNCT
m-1112	229	1	n	n	NOUN
m-1112	229	2	=	=	SYM
m-1112	229	3	x	x	PROPN
m-1112	230	1	+	+	CCONJ
m-1112	230	2	i	i	PROPN
m-1112	230	3	.y	.y	NOUN
m-1112	230	4	where	where	SCONJ
m-1112	230	5	the	the	DET
m-1112	230	6	space	space	NOUN
m-1112	230	7	vector	vector	NOUN
m-1112	230	8	–	–	PUNCT
m-1112	230	9	amplitude	amplitude	NOUN
m-1112	230	10	2r	2r	NUM
m-1112	230	11	=	=	SYM
m-1112	230	12	√	√	ADP
m-1112	230	13	λ	λ	SYM
m-1112	230	14	n(s	n(s	PROPN
m-1112	230	15	)	)	PUNCT
m-1112	230	16	2	2	NUM
m-1112	230	17	−	−	NOUN
m-1112	230	18	a²n(s	a²n(s	PROPN
m-1112	230	19	)	)	PUNCT
m-1112	230	20	,	,	PUNCT
m-1112	230	21	for	for	ADP
m-1112	230	22	the	the	DET
m-1112	230	23	n	n	NOUN
m-1112	230	24	-	-	PUNCT
m-1112	230	25	masses	masse	NOUN
m-1112	230	26	.	.	PUNCT
m-1112	231	1	the	the	DET
m-1112	231	2	anti	anti	ADJ
m-1112	231	3	-	-	ADJ
m-1112	231	4	space	space	ADJ
m-1112	231	5	vector	vector	NOUN
m-1112	231	6	–	–	PUNCT
m-1112	231	7	amplitude	amplitude	NOUN
m-1112	231	8	2r	2r	NUM
m-1112	231	9	=	=	SYM
m-1112	231	10	√	√	PROPN
m-1112	231	11	λ	λ	X
m-1112	231	12	n(as	n(as	PROPN
m-1112	231	13	)	)	PUNCT
m-1112	231	14	2	2	NUM
m-1112	231	15	−	−	PROPN
m-1112	231	16	a²n(as	a²n(as	PROPN
m-1112	231	17	)	)	PUNCT
m-1112	231	18	,	,	PUNCT
m-1112	231	19	for	for	ADP
m-1112	231	20	the	the	DET
m-1112	231	21	n	n	NOUN
m-1112	231	22	-	-	PUNCT
m-1112	231	23	masses	masse	NOUN
m-1112	231	24	.	.	PUNCT
m-1112	232	1	the	the	DET
m-1112	232	2	sub	sub	NOUN
m-1112	232	3	space	space	NOUN
m-1112	232	4	vector	vector	NOUN
m-1112	232	5	–	–	PUNCT
m-1112	232	6	amplitude	amplitude	NOUN
m-1112	232	7	2r	2r	NUM
m-1112	232	8	=	=	SYM
m-1112	232	9	√	√	PROPN
m-1112	232	10	λ	λ	SYM
m-1112	232	11	n(ss	n(s	NOUN
m-1112	232	12	)	)	PUNCT
m-1112	232	13	2	2	NUM
m-1112	232	14	−	−	PROPN
m-1112	232	15	a²n(ss	a²n(ss	NUM
m-1112	232	16	)	)	PUNCT
m-1112	232	17	,	,	PUNCT
m-1112	232	18	for	for	ADP
m-1112	232	19	the	the	DET
m-1112	232	20	n	n	NOUN
m-1112	232	21	-	-	PUNCT
m-1112	232	22	masses	masse	NOUN
m-1112	232	23	.	.	PUNCT
m-1112	233	1	ijo	ijo	PROPN
m-1112	233	2	international	international	PROPN
m-1112	233	3	journal	journal	PROPN
m-1112	233	4	of	of	ADP
m-1112	233	5	mathematics	mathematics	PROPN
m-1112	233	6	(	(	PUNCT
m-1112	233	7	issn	issn	PROPN
m-1112	233	8	:	:	PUNCT
m-1112	233	9	2992	2992	NUM
m-1112	233	10	-	-	SYM
m-1112	233	11	4421	4421	NUM
m-1112	233	12	)	)	PUNCT
m-1112	233	13	volume	volume	NOUN
m-1112	233	14	08	08	NUM
m-1112	234	1	|	|	ADV
m-1112	234	2	issue	issue	NOUN
m-1112	234	3	08	08	NUM
m-1112	235	1	|	|	ADV
m-1112	235	2	august	august	PROPN
m-1112	235	3	2025	2025	NUM
m-1112	235	4	|	|	ADV
m-1112	235	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	235	6	ijo	ijo	PROPN
m-1112	235	7	journals	journal	NOUN
m-1112	235	8	12	12	NUM
m-1112	235	9	the	the	DET
m-1112	235	10	fundamental	fundamental	ADJ
m-1112	235	11	particles	particle	NOUN
m-1112	235	12	origination	origination	NOUN
m-1112	235	13	mechanism	mechanism	NOUN
m-1112	235	14	in	in	ADP
m-1112	235	15	mfmf	mfmf	PROPN
m-1112	235	16	pns	pns	PROPN
m-1112	235	17	caves	cave	NOUN
m-1112	235	18	.	.	PUNCT
m-1112	236	1	remarks	remark	NOUN
m-1112	236	2	:	:	PUNCT
m-1112	236	3	a	a	DET
m-1112	236	4	…	…	PUNCT
m-1112	236	5	from	from	ADP
m-1112	236	6	argand	argand	NOUN
m-1112	236	7	diagram	diagram	NOUN
m-1112	236	8	the	the	DET
m-1112	236	9	vector	vector	NOUN
m-1112	236	10	z	z	PROPN
m-1112	236	11	+	+	CCONJ
m-1112	236	12	n	n	PROPN
m-1112	236	13	=	=	NOUN
m-1112	236	14	2r.𝑒𝑖.𝑛𝜔𝑡=+2rn.[cosw	2r.𝑒𝑖.𝑛𝜔𝑡=+2rn.[cosw	NUM
m-1112	236	15	.	.	PUNCT
m-1112	237	1	t	t	PROPN
m-1112	237	2	+	+	NUM
m-1112	237	3	i.	i.	NOUN
m-1112	237	4	sinw	sinw	PROPN
m-1112	237	5	.	.	PUNCT
m-1112	238	1	t	t	X
m-1112	238	2	]	]	X
m-1112	239	1	=	=	PUNCT
m-1112	239	2	x	x	PUNCT
m-1112	240	1	+	+	CCONJ
m-1112	240	2	i	i	PRON
m-1112	240	3	.y	.y	NOUN
m-1112	240	4	meaning	mean	VERB
m-1112	240	5	the	the	DET
m-1112	240	6	wave	wave	NOUN
m-1112	240	7	pattern	pattern	NOUN
m-1112	240	8	of	of	ADP
m-1112	240	9	spaces	space	NOUN
m-1112	240	10	in	in	ADP
m-1112	240	11	planck`s	planck`s	NOUN
m-1112	240	12	cave	cave	NOUN
m-1112	240	13	10−35	10−35	PROPN
m-1112	240	14	m	m	NOUN
m-1112	240	15	.the	.the	PRON
m-1112	240	16	vector	vector	NOUN
m-1112	240	17	amplitude	amplitude	NOUN
m-1112	240	18	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	240	19	̅̅	̅̅	PROPN
m-1112	240	20	=	=	SYM
m-1112	241	1	2r	2r	NUM
m-1112	242	1	=	=	PUNCT
m-1112	243	1	the	the	DET
m-1112	243	2	monad	monad	PROPN
m-1112	243	3	,	,	PUNCT
m-1112	243	4	is	be	AUX
m-1112	243	5	the	the	DET
m-1112	243	6	complex	complex	ADJ
m-1112	243	7	quantity	quantity	NOUN
m-1112	243	8	𝐀𝐁̅̅	𝐀𝐁̅̅	NUM
m-1112	243	9	̅̅	̅̅	PROPN
m-1112	243	10	≡	≡	PROPN
m-1112	243	11	�	�	PROPN
m-1112	243	12	̅	̅	NOUN
m-1112	243	13	�	�	NOUN
m-1112	243	14	≡	≡	PROPN
m-1112	243	15	x	x	PUNCT
m-1112	244	1	+	+	CCONJ
m-1112	244	2	i	i	PRON
m-1112	244	3	.y	.y	NOUN
m-1112	244	4	,	,	PUNCT
m-1112	245	1	where	where	SCONJ
m-1112	245	2	x	x	X
m-1112	245	3	=	=	SYM
m-1112	245	4	2r	2r	NUM
m-1112	245	5	→	→	PUNCT
m-1112	245	6	the	the	DET
m-1112	245	7	geometry	geometry	NOUN
m-1112	245	8	of	of	ADP
m-1112	245	9	pns	pns	PROPN
m-1112	245	10	space	space	NOUN
m-1112	245	11	and	and	CCONJ
m-1112	245	12	y	y	PROPN
m-1112	245	13	=	=	SYM
m-1112	245	14	𝑒𝑖.𝑛𝜔𝑡→	𝑒𝑖.𝑛𝜔𝑡→	PROPN
m-1112	245	15	the	the	DET
m-1112	245	16	motion	motion	NOUN
m-1112	245	17	in	in	ADP
m-1112	245	18	planck`s	planck`s	NOUN
m-1112	245	19	space	space	NOUN
m-1112	245	20	.	.	PUNCT
m-1112	246	1	b	b	X
m-1112	246	2	…	…	PUNCT
m-1112	246	3	since	since	SCONJ
m-1112	246	4	anti	anti	ADJ
m-1112	246	5	-	-	ADJ
m-1112	246	6	space	space	ADJ
m-1112	246	7	z	z	NOUN
m-1112	246	8	−	−	PROPN
m-1112	246	9	n	n	CCONJ
m-1112	246	10	≡	≡	PROPN
m-1112	246	11	z	z	PROPN
m-1112	247	1	+	+	CCONJ
m-1112	247	2	n	n	CCONJ
m-1112	247	3	,	,	PUNCT
m-1112	247	4	means	mean	VERB
m-1112	247	5	the	the	DET
m-1112	247	6	conjugate	conjugate	ADJ
m-1112	247	7	space	space	NOUN
m-1112	247	8	to	to	ADP
m-1112	247	9	the	the	DET
m-1112	247	10	space	space	NOUN
m-1112	247	11	z	z	NOUN
m-1112	247	12	+	+	NOUN
m-1112	247	13	n	n	CCONJ
m-1112	247	14	.	.	PUNCT
m-1112	248	1	c	c	X
m-1112	248	2	…	…	PUNCT
m-1112	248	3	since	since	SCONJ
m-1112	248	4	from	from	ADP
m-1112	248	5	wave	wave	NOUN
m-1112	248	6	-	-	PUNCT
m-1112	248	7	action	action	NOUN
m-1112	248	8	of	of	ADP
m-1112	248	9	spaces	space	NOUN
m-1112	248	10	issues	issue	NOUN
m-1112	248	11	z	z	NOUN
m-1112	248	12	−	−	PROPN
m-1112	248	13	n	n	NOUN
m-1112	248	14	x	x	NOUN
m-1112	248	15	z	z	PROPN
m-1112	248	16	+	+	CCONJ
m-1112	248	17	n	n	NOUN
m-1112	248	18	=	=	SYM
m-1112	249	1	[	[	X
m-1112	249	2	2r	2r	NUM
m-1112	249	3	]	]	X
m-1112	249	4	2n	2n	NUM
m-1112	249	5	.	.	PUNCT
m-1112	250	1	e	e	X
m-1112	250	2	i.2nθ	i.2nθ	PROPN
m-1112	250	3	,	,	PUNCT
m-1112	250	4	this	this	PRON
m-1112	250	5	means	mean	VERB
m-1112	250	6	that	that	SCONJ
m-1112	250	7	,	,	PUNCT
m-1112	250	8	the	the	DET
m-1112	250	9	conservation	conservation	NOUN
m-1112	250	10	of	of	ADP
m-1112	250	11	energy	energy	NOUN
m-1112	250	12	=	=	NOUN
m-1112	250	13	work	work	NOUN
m-1112	250	14	,	,	PUNCT
m-1112	250	15	between	between	ADP
m-1112	250	16	the	the	DET
m-1112	250	17	spaces	space	NOUN
m-1112	250	18	and	and	CCONJ
m-1112	250	19	the	the	DET
m-1112	250	20	anti	anti	NOUN
m-1112	250	21	-	-	ADJ
m-1112	250	22	spaces	space	NOUN
m-1112	250	23	happens	happen	VERB
m-1112	250	24	by	by	ADP
m-1112	250	25	doubling	double	VERB
m-1112	250	26	the	the	DET
m-1112	250	27	number	number	NOUN
m-1112	250	28	,	,	PUNCT
m-1112	250	29	n	n	CCONJ
m-1112	250	30	,	,	PUNCT
m-1112	250	31	of	of	ADP
m-1112	250	32	the	the	DET
m-1112	250	33	vertices	vertex	NOUN
m-1112	250	34	of	of	ADP
m-1112	250	35	the	the	DET
m-1112	250	36	regular	regular	ADJ
m-1112	250	37	polygon	polygon	NOUN
m-1112	250	38	.	.	PUNCT
m-1112	251	1	d	d	X
m-1112	251	2	...	...	PUNCT
m-1112	251	3	the	the	DET
m-1112	251	4	natural	natural	ADJ
m-1112	251	5	frequency	frequency	NOUN
m-1112	251	6	of	of	ADP
m-1112	251	7	an	an	DET
m-1112	251	8	x	x	ADJ
m-1112	251	9	-	-	ADJ
m-1112	251	10	x	x	ADJ
m-1112	251	11	linear	linear	ADJ
m-1112	251	12	vibration	vibration	NOUN
m-1112	251	13	,	,	PUNCT
m-1112	252	1	[	[	X
m-1112	252	2	⊕↔⊝	⊕↔⊝	NOUN
m-1112	252	3	]	]	X
m-1112	252	4	,	,	PUNCT
m-1112	252	5	becomes	become	VERB
m-1112	252	6	from	from	ADP
m-1112	252	7	𝐰𝐧=	𝐰𝐧=	NOUN
m-1112	252	8	2π.f	2π.f	NUM
m-1112	252	9	n	n	PRON
m-1112	252	10	meaning	mean	VERB
m-1112	252	11	that	that	SCONJ
m-1112	252	12	the	the	DET
m-1112	252	13	infinite	infinite	ADJ
m-1112	252	14	frequencies	frequency	NOUN
m-1112	252	15	f	f	PROPN
m-1112	252	16	n	n	VERB
m-1112	252	17	are	be	AUX
m-1112	252	18	stored	store	VERB
m-1112	252	19	in	in	ADP
m-1112	252	20	subspaces	subspace	NOUN
m-1112	252	21	by	by	ADP
m-1112	252	22	doubling	double	VERB
m-1112	252	23	the	the	DET
m-1112	252	24	number	number	NOUN
m-1112	252	25	,	,	PUNCT
m-1112	252	26	n	n	CCONJ
m-1112	252	27	,	,	PUNCT
m-1112	252	28	of	of	ADP
m-1112	252	29	the	the	DET
m-1112	252	30	vertices	vertex	NOUN
m-1112	252	31	with	with	ADP
m-1112	252	32	2n	2n	NOUN
m-1112	252	33	-	-	PUNCT
m-1112	252	34	sides	side	NOUN
m-1112	252	35	to	to	ADP
m-1112	252	36	a	a	DET
m-1112	252	37	regular	regular	ADJ
m-1112	252	38	polygon	polygon	NOUN
m-1112	252	39	of	of	ADP
m-1112	252	40	initial	initial	ADJ
m-1112	252	41	n.sides	n.side	NOUN
m-1112	252	42	.	.	PUNCT
m-1112	253	1	e	e	X
m-1112	253	2	...	...	PUNCT
m-1112	253	3	the	the	DET
m-1112	253	4	natural	natural	ADJ
m-1112	253	5	frequency	frequency	NOUN
m-1112	253	6	of	of	ADP
m-1112	253	7	an	an	DET
m-1112	253	8	rotational	rotational	ADJ
m-1112	253	9	↻	↻	NOUN
m-1112	253	10	r	r	NOUN
m-1112	253	11	↺	↺	NUM
m-1112	253	12	dof	dof	ADJ
m-1112	253	13	vibration	vibration	NOUN
m-1112	253	14	system	system	NOUN
m-1112	253	15	becomes	become	VERB
m-1112	253	16	from	from	ADP
m-1112	253	17	�	�	NOUN
m-1112	253	18	̅	̅	NOUN
m-1112	253	19	�	�	NOUN
m-1112	253	20	=	=	SYM
m-1112	253	21	r.m.v	r.m.v	PROPN
m-1112	253	22	n=	n=	PROPN
m-1112	253	23	r.m.v	r.m.v	PROPN
m-1112	253	24	n=	n=	PROPN
m-1112	253	25	r.m.w	r.m.w	PROPN
m-1112	253	26	n.r	n.r	PROPN
m-1112	253	27	=	=	PROPN
m-1112	253	28	m.w	m.w	PROPN
m-1112	253	29	n.r	n.r	PROPN
m-1112	253	30	²	²	PROPN
m-1112	253	31	=	=	SYM
m-1112	253	32	m.r².w	m.r².w	PROPN
m-1112	253	33	n	n	NOUN
m-1112	253	34	,	,	PUNCT
m-1112	253	35	meaning	mean	VERB
m-1112	253	36	the	the	DET
m-1112	253	37	natural	natural	ADJ
m-1112	253	38	identities	identity	NOUN
m-1112	253	39	of	of	ADP
m-1112	253	40	the	the	DET
m-1112	253	41	∞	∞	ADJ
m-1112	253	42	monads	monad	NOUN
m-1112	253	43	in	in	ADP
m-1112	253	44	our	our	PRON
m-1112	253	45	universe	universe	NOUN
m-1112	253	46	.	.	PUNCT
m-1112	254	1	the	the	DET
m-1112	254	2	equations	equation	NOUN
m-1112	254	3	of	of	ADP
m-1112	254	4	motion	motion	NOUN
m-1112	254	5	in	in	ADP
m-1112	254	6	a	a	DET
m-1112	254	7	material	material	NOUN
m-1112	254	8	point	point	NOUN
m-1112	254	9	related	relate	VERB
m-1112	254	10	to	to	ADP
m-1112	254	11	the	the	DET
m-1112	254	12	inner	inner	ADJ
m-1112	254	13	motion	motion	NOUN
m-1112	254	14	was	be	AUX
m-1112	254	15	referred	refer	VERB
m-1112	254	16	before	before	ADP
m-1112	254	17	where	where	SCONJ
m-1112	254	18	the	the	PRON
m-1112	254	19	in	in	NOUN
m-1112	254	20	-	-	PUNCT
m-1112	254	21	between	between	ADP
m-1112	254	22	-	-	PUNCT
m-1112	254	23	magnitude	magnitude	NOUN
m-1112	254	24	circumscribed	circumscribed	ADJ
m-1112	254	25	–	–	PUNCT
m-1112	254	26	inscribed	inscribe	VERB
m-1112	254	27	polygon	polygon	NOUN
m-1112	254	28	,	,	PUNCT
m-1112	254	29	the	the	DET
m-1112	254	30	part	part	NOUN
m-1112	254	31	,	,	PUNCT
m-1112	254	32	becomes	become	VERB
m-1112	254	33	the	the	DET
m-1112	254	34	outer	outer	ADJ
m-1112	254	35	ab	ab	NOUN
m-1112	254	36	as	as	ADP
m-1112	254	37	the	the	DET
m-1112	254	38	,	,	PUNCT
m-1112	254	39	whole	whole	NOUN
m-1112	254	40	or	or	CCONJ
m-1112	254	41	the	the	DET
m-1112	254	42	self	self	NOUN
m-1112	254	43	-	-	PUNCT
m-1112	254	44	growth	growth	NOUN
m-1112	254	45	.this	.this	PRON
m-1112	254	46	augmentation	augmentation	NOUN
m-1112	254	47	-	-	PUNCT
m-1112	254	48	property	property	NOUN
m-1112	254	49	,	,	PUNCT
m-1112	254	50	of	of	ADP
m-1112	254	51	these	these	DET
m-1112	254	52	two	two	NUM
m-1112	254	53	golden	golden	ADJ
m-1112	254	54	-	-	PUNCT
m-1112	254	55	ratios	ratio	NOUN
m-1112	254	56	,	,	PUNCT
m-1112	254	57	exists	exist	VERB
m-1112	254	58	in	in	ADP
m-1112	254	59	the	the	DET
m-1112	254	60	material	material	NOUN
m-1112	254	61	-	-	PUNCT
m-1112	254	62	point	point	NOUN
m-1112	254	63	and	and	CCONJ
m-1112	254	64	on	on	ADP
m-1112	254	65	frequency	frequency	NOUN
m-1112	254	66	fn	fn	NOUN
m-1112	254	67	,	,	PUNCT
m-1112	254	68	which	which	DET
m-1112	254	69	motion	motion	NOUN
m-1112	254	70	≡	≡	PROPN
m-1112	254	71	growth	growth	NOUN
m-1112	254	72	,	,	PUNCT
m-1112	254	73	and	and	CCONJ
m-1112	254	74	spread	spread	VERB
m-1112	254	75	in	in	ADP
m-1112	254	76	two	two	NUM
m-1112	254	77	-	-	PUNCT
m-1112	254	78	closed	closed	ADJ
m-1112	254	79	-	-	PUNCT
m-1112	254	80	transverse	transverse	NOUN
m-1112	254	81	planes	plane	NOUN
m-1112	254	82	as	as	SCONJ
m-1112	254	83	is	be	AUX
m-1112	254	84	in	in	ADP
m-1112	254	85	the	the	DET
m-1112	254	86	propagating	propagate	VERB
m-1112	254	87	electromagnetic	electromagnetic	ADJ
m-1112	254	88	wave	wave	NOUN
m-1112	254	89	where	where	SCONJ
m-1112	254	90	e	e	NOUN
m-1112	254	91	⊥	⊥	NUM
m-1112	254	92	h	h	NOUN
m-1112	254	93	.	.	PUNCT
m-1112	255	1	from	from	ADP
m-1112	255	2	planck	planck	NOUN
m-1112	255	3	e	e	NOUN
m-1112	255	4	=	=	PUNCT
m-1112	255	5	h.fn	h.fn	PROPN
m-1112	255	6	≡	≡	PROPN
m-1112	255	7	[	[	PUNCT
m-1112	255	8	1+√5	1+√5	NUM
m-1112	255	9	2	2	NUM
m-1112	255	10	]	]	PUNCT
m-1112	255	11	hσ	hσ	NOUN
m-1112	255	12	2πr	2πr	NOUN
m-1112	256	1	=	=	PUNCT
m-1112	256	2	[	[	PUNCT
m-1112	256	3	nσ	nσ	NOUN
m-1112	256	4	8	8	NUM
m-1112	256	5	r²	r²	VERB
m-1112	256	6	]	]	PUNCT
m-1112	256	7	.b̅	.b̅	PROPN
m-1112	256	8	,	,	PUNCT
m-1112	256	9	𝐟𝐑	𝐟𝐑	PROPN
m-1112	256	10	≡	≡	PROPN
m-1112	256	11	[	[	PUNCT
m-1112	256	12	f1	f1	NOUN
m-1112	256	13	=	=	SYM
m-1112	256	14	n	n	NOUN
m-1112	256	15	,	,	PUNCT
m-1112	256	16	f2	f2	PROPN
m-1112	256	17	,	,	PUNCT
m-1112	256	18	f3	f3	PROPN
m-1112	256	19	,	,	PUNCT
m-1112	256	20	f	f	PROPN
m-1112	256	21	r	r	NOUN
m-1112	256	22	=	=	SYM
m-1112	256	23	w²n	w²n	PROPN
m-1112	256	24	]	]	PUNCT
m-1112	256	25	,	,	PUNCT
m-1112	256	26	euler`s	euler`s	PROPN
m-1112	256	27	𝐞−𝐢.𝐀	𝐞−𝐢.𝐀	PROPN
m-1112	256	28	(	(	PUNCT
m-1112	256	29	𝛑	𝛑	ADP
m-1112	256	30	𝟐	𝟐	NUM
m-1112	256	31	+	+	NOUN
m-1112	256	32	𝟐𝐤𝛑).𝐛	𝟐𝐤𝛑).𝐛	PROPN
m-1112	256	33	=	=	SYM
m-1112	256	34	e−i.a	e−i.a	NOUN
m-1112	256	35	(	(	PUNCT
m-1112	256	36	π+4kπ	π+4kπ	NOUN
m-1112	256	37	2	2	NUM
m-1112	256	38	)	)	PUNCT
m-1112	256	39	.b	.b	PUNCT
m-1112	257	1	=	=	PUNCT
m-1112	257	2	a.cos	a.cos	PROPN
m-1112	257	3	[	[	PUNCT
m-1112	257	4	π+4kπ	π+4kπ	NOUN
m-1112	257	5	2	2	NUM
m-1112	257	6	]	]	PUNCT
m-1112	257	7	.	.	PUNCT
m-1112	258	1	b	b	X
m-1112	258	2	–	–	PUNCT
m-1112	258	3	i	i	PROPN
m-1112	258	4	.	.	PUNCT
m-1112	259	1	asin	asin	PROPN
m-1112	259	2	[	[	PUNCT
m-1112	259	3	π+4kπ	π+4kπ	NOUN
m-1112	259	4	2	2	NUM
m-1112	259	5	]	]	PUNCT
m-1112	259	6	.b	.b	PROPN
m-1112	259	7	,	,	PUNCT
m-1112	259	8	l	l	X
m-1112	259	9	=	=	PUNCT
m-1112	260	1	[	[	PUNCT
m-1112	260	2	b̅/2].w	b̅/2].w	PROPN
m-1112	260	3	,	,	PUNCT
m-1112	260	4	so	so	CCONJ
m-1112	260	5	then	then	ADV
m-1112	260	6	w	w	PROPN
m-1112	260	7	=	=	PUNCT
m-1112	260	8	√2π	√2π	PROPN
m-1112	260	9	.	.	PUNCT
m-1112	261	1	fr	fr	NOUN
m-1112	262	1	=	=	PUNCT
m-1112	262	2	2l	2l	NUM
m-1112	262	3	/	/	SYM
m-1112	262	4	b̅	b̅	NOUN
m-1112	262	5	,	,	PUNCT
m-1112	262	6	and	and	CCONJ
m-1112	262	7	the	the	DET
m-1112	262	8	wave	wave	NOUN
m-1112	262	9	equation	equation	NOUN
m-1112	262	10	is	be	AUX
m-1112	262	11	y	y	PROPN
m-1112	262	12	=	=	SYM
m-1112	262	13	2a.sin	2a.sin	PROPN
m-1112	262	14	(	(	PUNCT
m-1112	262	15	2π.x	2π.x	NUM
m-1112	262	16	λ	λ	NOUN
m-1112	262	17	)	)	PUNCT
m-1112	262	18	.cos	.cos	PUNCT
m-1112	262	19	.	.	PUNCT
m-1112	263	1	wt	wt	X
m-1112	264	1	....	....	PUNCT
m-1112	264	2	(	(	PUNCT
m-1112	264	3	a	a	X
m-1112	264	4	)	)	PUNCT
m-1112	264	5	f	f	X
m-1112	264	6	...	...	PUNCT
m-1112	265	1	the	the	DET
m-1112	265	2	natural	natural	ADJ
m-1112	265	3	frequency	frequency	NOUN
m-1112	265	4	of	of	ADP
m-1112	265	5	the	the	DET
m-1112	265	6	unit	unit	NOUN
m-1112	265	7	-	-	PUNCT
m-1112	265	8	energy	energy	NOUN
m-1112	265	9	-	-	PUNCT
m-1112	265	10	vectors	vector	NOUN
m-1112	265	11	,	,	PUNCT
m-1112	265	12	�	�	NOUN
m-1112	265	13	̅	̅	NOUN
m-1112	265	14	�	�	PROPN
m-1112	265	15	.	.	PUNCT
m-1112	265	16	�	�	PROPN
m-1112	265	17	̅	̅	NOUN
m-1112	265	18	�	�	NOUN
m-1112	265	19	=	=	SYM
m-1112	265	20	m.r².w	m.r².w	NOUN
m-1112	265	21	²n	²n	NOUN
m-1112	265	22	=	=	SYM
m-1112	265	23	m.v²n=	m.v²n=	NOUN
m-1112	265	24	ke	ke	NOUN
m-1112	265	25	.	.	PUNCT
m-1112	266	1	from	from	ADP
m-1112	266	2	momentum	momentum	NOUN
m-1112	266	3	�	�	NOUN
m-1112	266	4	̅	̅	NOUN
m-1112	266	5	�	�	NOUN
m-1112	266	6	=	=	SYM
m-1112	266	7	r	r	NOUN
m-1112	266	8	m	m	NOUN
m-1112	266	9	v	v	NOUN
m-1112	266	10	=	=	PUNCT
m-1112	266	11	m	m	NOUN
m-1112	266	12	�	�	PROPN
m-1112	266	13	̆	̆	NOUN
m-1112	266	14	�	�	PROPN
m-1112	266	15	r²	r²	NOUN
m-1112	266	16	=	=	SYM
m-1112	266	17	±	±	NOUN
m-1112	266	18	[	[	PUNCT
m-1112	266	19	𝛑.𝐫𝟐	𝛑.𝐫𝟐	X
m-1112	266	20	𝟐	𝟐	NUM
m-1112	266	21	]	]	PUNCT
m-1112	266	22	.	.	PUNCT
m-1112	266	23	�	�	PROPN
m-1112	266	24	̅	̅	NOUN
m-1112	266	25	�	�	PROPN
m-1112	266	26	x	x	SYM
m-1112	266	27	�	�	PROPN
m-1112	266	28	̅	̅	NOUN
m-1112	266	29	�	�	PROPN
m-1112	266	30	,	,	PUNCT
m-1112	266	31	�	�	PROPN
m-1112	266	32	̅	̅	NOUN
m-1112	266	33	�	�	PROPN
m-1112	266	34	.	.	PUNCT
m-1112	266	35	�	�	PROPN
m-1112	266	36	̆	̆	NOUN
m-1112	266	37	�	�	PROPN
m-1112	266	38	=	=	SYM
m-1112	266	39	±	±	PROPN
m-1112	266	40	[	[	PUNCT
m-1112	266	41	π.r2	π.r2	NOUN
m-1112	266	42	2	2	NUM
m-1112	266	43	]	]	PUNCT
m-1112	266	44	.c̅	.c̅	NUM
m-1112	266	45	²	²	NUM
m-1112	266	46	,	,	PUNCT
m-1112	266	47	c̅	c̅	PROPN
m-1112	266	48	=	=	SYM
m-1112	266	49	σ	σ	PROPN
m-1112	266	50	φ	φ	PROPN
m-1112	266	51	,	,	PUNCT
m-1112	266	52	i.e.	i.e.	X
m-1112	266	53	the	the	DET
m-1112	266	54	primary	primary	ADJ
m-1112	266	55	space	space	NOUN
m-1112	266	56	is	be	AUX
m-1112	266	57	originated	originate	VERB
m-1112	266	58	from	from	ADP
m-1112	266	59	the	the	DET
m-1112	266	60	stress	stress	NOUN
m-1112	266	61			PROPN
m-1112	266	62	σ	σ	NOUN
m-1112	266	63	,	,	PUNCT
m-1112	266	64	and	and	CCONJ
m-1112	266	65	from	from	ADP
m-1112	266	66	the	the	DET
m-1112	266	67	angular	angular	ADJ
m-1112	266	68	momentum	momentum	NOUN
m-1112	266	69			NOUN
m-1112	266	70	�	�	PROPN
m-1112	266	71	̅	̅	NOUN
m-1112	266	72	�	�	PROPN
m-1112	266	73	,	,	PUNCT
m-1112	266	74	�	�	PROPN
m-1112	266	75	̅	̅	NOUN
m-1112	266	76	�	�	PROPN
m-1112	266	77	,	,	PUNCT
m-1112	266	78	produced	produce	VERB
m-1112	266	79	from	from	ADP
m-1112	266	80	the	the	DET
m-1112	266	81	two	two	NUM
m-1112	266	82	opposite	opposite	ADJ
m-1112	266	83	[	[	X
m-1112	266	84	⊕↔⊝	⊕↔⊝	X
m-1112	266	85	]	]	X
m-1112	266	86	components	component	NOUN
m-1112	266	87	.	.	PUNCT
m-1112	267	1	g	g	ADP
m-1112	267	2	...	...	PUNCT
m-1112	267	3	since	since	SCONJ
m-1112	267	4	monads	monad	NOUN
m-1112	267	5	are	be	AUX
m-1112	267	6	complex	complex	ADJ
m-1112	267	7	quantities	quantity	NOUN
m-1112	267	8	as	as	ADP
m-1112	267	9	ab	ab	PROPN
m-1112	267	10	≡	≡	PROPN
m-1112	267	11	�	�	PROPN
m-1112	267	12	̅	̅	PROPN
m-1112	267	13	�	�	NOUN
m-1112	267	14	≡	≡	PROPN
m-1112	267	15	x	x	PUNCT
m-1112	268	1	+	+	NUM
m-1112	268	2	i.	i.	PROPN
m-1112	268	3	y	y	PROPN
m-1112	268	4	,	,	PUNCT
m-1112	268	5	then	then	ADV
m-1112	268	6	are	be	AUX
m-1112	268	7	quaternions	quaternion	NOUN
m-1112	268	8	where	where	SCONJ
m-1112	268	9	material	material	NOUN
m-1112	268	10	-	-	PUNCT
m-1112	268	11	points	point	NOUN
m-1112	268	12	≡	≡	PROPN
m-1112	268	13	quaternions	quaternion	NOUN
m-1112	268	14	,	,	PUNCT
m-1112	268	15	which	which	PRON
m-1112	268	16	carry	carry	VERB
m-1112	268	17	the	the	DET
m-1112	268	18	→	→	SYM
m-1112	268	19	motion	motion	NOUN
m-1112	268	20	≡	≡	PROPN
m-1112	268	21	energy	energy	NOUN
m-1112	268	22	←	←	PROPN
m-1112	268	23	from	from	ADP
m-1112	268	24	the	the	DET
m-1112	268	25	two	two	NUM
m-1112	268	26	edge	edge	NOUN
m-1112	268	27	-	-	PUNCT
m-1112	268	28	poinds	poind	NOUN
m-1112	268	29	[	[	PUNCT
m-1112	268	30	�	�	NOUN
m-1112	268	31	̅	̅	NOUN
m-1112	268	32	�	�	NOUN
m-1112	268	33	↔	↔	NOUN
m-1112	268	34	�	�	NOUN
m-1112	268	35	̅	̅	NOUN
m-1112	268	36	�	�	PROPN
m-1112	268	37	]	]	PUNCT
m-1112	268	38	,	,	PUNCT
m-1112	268	39	as	as	SCONJ
m-1112	268	40	this	this	PRON
m-1112	268	41	is	be	AUX
m-1112	268	42	from	from	ADP
m-1112	268	43	point	point	NOUN
m-1112	268	44	a	a	PRON
m-1112	268	45	,	,	PUNCT
m-1112	268	46	to	to	PART
m-1112	268	47	point	point	VERB
m-1112	268	48	b	b	PUNCT
m-1112	268	49	circularly	circularly	ADV
m-1112	268	50	.	.	PUNCT
m-1112	269	1	simultaneousley	simultaneousley	PROPN
m-1112	269	2	on	on	ADP
m-1112	269	3	ab	ab	PROPN
m-1112	269	4	conductor	conductor	NOUN
m-1112	269	5	is	be	AUX
m-1112	269	6	created	create	VERB
m-1112	269	7	an	an	DET
m-1112	269	8	electric	electric	ADJ
m-1112	269	9	field	field	NOUN
m-1112	269	10	𝐄	𝐄	NOUN
m-1112	269	11	𝐅	𝐅	NOUN
m-1112	269	12	between	between	ADP
m-1112	269	13	a	a	DET
m-1112	269	14	–	–	PUNCT
m-1112	269	15	b	b	NOUN
m-1112	269	16	points	point	NOUN
m-1112	269	17	and	and	CCONJ
m-1112	269	18	⊥	⊥	NOUN
m-1112	269	19	on	on	ADP
m-1112	269	20	ab	ab	PROPN
m-1112	269	21	axis	axis	NOUN
m-1112	269	22	directed	direct	VERB
m-1112	269	23	to	to	ADP
m-1112	269	24	the	the	DET
m-1112	269	25	motion	motion	NOUN
m-1112	269	26	,	,	PUNCT
m-1112	269	27	and	and	CCONJ
m-1112	269	28	an	an	DET
m-1112	269	29	transverse	transverse	NOUN
m-1112	269	30	(	(	PUNCT
m-1112	269	31	⊥ab	⊥ab	ADJ
m-1112	269	32	)	)	PUNCT
m-1112	269	33	magnetic	magnetic	ADJ
m-1112	269	34	field	field	NOUN
m-1112	269	35	as	as	ADP
m-1112	269	36	,	,	PUNCT
m-1112	269	37	𝐌	𝐌	PROPN
m-1112	269	38	𝐅	𝐅	PROPN
m-1112	269	39	⊥	⊥	NOUN
m-1112	269	40	𝐀𝐁̅̅	𝐀𝐁̅̅	PUNCT
m-1112	269	41	̅̅	̅̅	PROPN
m-1112	269	42	⊥	⊥	PROPN
m-1112	269	43	𝐄	𝐄	PROPN
m-1112	269	44	𝐅	𝐅	PROPN
m-1112	269	45	.	.	PUNCT
m-1112	270	1	ijo	ijo	PROPN
m-1112	270	2	international	international	PROPN
m-1112	270	3	journal	journal	PROPN
m-1112	270	4	of	of	ADP
m-1112	270	5	mathematics	mathematics	PROPN
m-1112	270	6	(	(	PUNCT
m-1112	270	7	issn	issn	PROPN
m-1112	270	8	:	:	PUNCT
m-1112	270	9	2992	2992	NUM
m-1112	270	10	-	-	SYM
m-1112	270	11	4421	4421	NUM
m-1112	270	12	)	)	PUNCT
m-1112	270	13	volume	volume	NOUN
m-1112	270	14	08	08	NUM
m-1112	271	1	|	|	ADV
m-1112	271	2	issue	issue	NOUN
m-1112	271	3	08	08	NUM
m-1112	272	1	|	|	ADV
m-1112	272	2	august	august	PROPN
m-1112	272	3	2025	2025	NUM
m-1112	272	4	|	|	ADV
m-1112	272	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	272	6	ijo	ijo	PROPN
m-1112	272	7	journals	journal	NOUN
m-1112	272	8	13	13	NUM
m-1112	272	9	the	the	DET
m-1112	272	10	fundamental	fundamental	ADJ
m-1112	272	11	particles	particle	NOUN
m-1112	272	12	origination	origination	NOUN
m-1112	272	13	mechanism	mechanism	NOUN
m-1112	272	14	in	in	ADP
m-1112	272	15	mfmf	mfmf	PROPN
m-1112	272	16	pns	pns	PROPN
m-1112	272	17	caves	cave	NOUN
m-1112	272	18	.	.	PUNCT
m-1112	273	1	5a	5a	NUM
m-1112	273	2	..	..	PUNCT
m-1112	273	3	the	the	DET
m-1112	273	4	figure	figure	NOUN
m-1112	273	5	-	-	PUNCT
m-1112	273	6	eight	eight	NUM
m-1112	273	7	knot	knot	NOUN
m-1112	273	8	&	&	CCONJ
m-1112	273	9	the	the	DET
m-1112	273	10	figure	figure	NOUN
m-1112	273	11	n	n	NOUN
m-1112	273	12	=	=	SYM
m-1112	273	13	1	1	NUM
m-1112	273	14	≈	≈	NUM
m-1112	273	15	∞	∞	PROPN
m-1112	273	16	knots	knot	NOUN
m-1112	273	17	:	:	PUNCT
m-1112	273	18	figure	figure	VERB
m-1112	273	19	-3	-3	PUNCT
m-1112	273	20	:	:	PUNCT
m-1112	273	21	the	the	DET
m-1112	273	22	geometrical	geometrical	ADJ
m-1112	273	23	construction	construction	NOUN
m-1112	273	24	of	of	ADP
m-1112	273	25	the	the	DET
m-1112	273	26	4	4	NUM
m-1112	273	27	-	-	PUNCT
m-1112	273	28	spaces	space	NOUN
m-1112	273	29	and	and	CCONJ
m-1112	273	30	the	the	PRON
m-1112	273	31	,	,	PUNCT
m-1112	273	32	spaces	space	VERB
m-1112	273	33	waves	wave	NOUN
m-1112	273	34	of	of	ADP
m-1112	273	35	pns	pns	PROPN
m-1112	273	36	.	.	PUNCT
m-1112	274	1	in	in	ADP
m-1112	274	2	argand	argand	PROPN
m-1112	274	3	diagram	diagram	PROPN
m-1112	274	4	ab	ab	PROPN
m-1112	274	5	=	=	PUNCT
m-1112	274	6	2r	2r	NUM
m-1112	274	7	→	→	PUNCT
m-1112	274	8	x	x	SYM
m-1112	274	9	=	=	SYM
m-1112	274	10	-1	-1	NOUN
m-1112	274	11	,	,	PUNCT
m-1112	274	12	o	o	INTJ
m-1112	274	13	,	,	PUNCT
m-1112	274	14	+1	+1	INTJ
m-1112	274	15	,	,	PUNCT
m-1112	274	16	y	y	PROPN
m-1112	274	17	=	=	PUNCT
m-1112	274	18	i	i	PROPN
m-1112	274	19	,	,	PUNCT
m-1112	274	20	exist	exist	VERB
m-1112	274	21	the	the	DET
m-1112	274	22	vector	vector	NOUN
m-1112	274	23	of	of	ADP
m-1112	274	24	amplitude	amplitude	NOUN
m-1112	274	25	�	�	NOUN
m-1112	274	26	̅	̅	NOUN
m-1112	274	27	�	�	NOUN
m-1112	274	28	≡	≡	PROPN
m-1112	274	29	x	x	PUNCT
m-1112	275	1	+	+	CCONJ
m-1112	275	2	i	i	PRON
m-1112	275	3	.	.	PUNCT
m-1112	276	1	y	y	PROPN
m-1112	276	2	,	,	PUNCT
m-1112	276	3	with	with	ADP
m-1112	276	4	angle	angle	NOUN
m-1112	276	5	θ	θ	PROPN
m-1112	276	6	ᶱ	ᶱ	NOUN
m-1112	276	7	=	=	X
m-1112	276	8	[	[	PUNCT
m-1112	276	9	z	z	X
m-1112	276	10	–	–	PUNCT
m-1112	276	11	oc	oc	X
m-1112	276	12	]	]	X
m-1112	276	13	ᶱ	ᶱ	NOUN
m-1112	276	14	,	,	PUNCT
m-1112	277	1	[	[	X
m-1112	277	2	i	i	NOUN
m-1112	277	3	=	=	SYM
m-1112	277	4	√−1	√−1	PROPN
m-1112	277	5	]	]	X
m-1112	277	6	.x	.x	NOUN
m-1112	277	7	.	.	PUNCT
m-1112	278	1	the	the	DET
m-1112	278	2	wave	wave	NOUN
m-1112	278	3	's	's	PART
m-1112	278	4	"	"	PUNCT
m-1112	278	5	strength	strength	NOUN
m-1112	278	6	"	"	PUNCT
m-1112	278	7	and	and	CCONJ
m-1112	278	8	"	"	PUNCT
m-1112	278	9	direction	direction	NOUN
m-1112	278	10	"	"	PUNCT
m-1112	278	11	,	,	PUNCT
m-1112	278	12	where	where	SCONJ
m-1112	278	13	x	x	PRON
m-1112	278	14	is	be	AUX
m-1112	278	15	a	a	DET
m-1112	278	16	number	number	NOUN
m-1112	278	17	that	that	PRON
m-1112	278	18	represents	represent	VERB
m-1112	278	19	the	the	DET
m-1112	278	20	magnitude	magnitude	NOUN
m-1112	278	21	or	or	CCONJ
m-1112	278	22	length	length	NOUN
m-1112	278	23	of	of	ADP
m-1112	278	24	the	the	DET
m-1112	278	25	vector	vector	NOUN
m-1112	278	26	z	z	NOUN
m-1112	278	27	,	,	PUNCT
m-1112	278	28	and	and	CCONJ
m-1112	278	29	from	from	ADP
m-1112	278	30	definition	definition	NOUN
m-1112	278	31	of	of	ADP
m-1112	278	32	the	the	DET
m-1112	278	33	complex	complex	ADJ
m-1112	278	34	vector	vector	NOUN
m-1112	278	35	space	space	NOUN
m-1112	278	36	,	,	PUNCT
m-1112	278	37	is	be	AUX
m-1112	278	38	the	the	DET
m-1112	278	39	set	set	NOUN
m-1112	278	40	of	of	ADP
m-1112	278	41	vectors	vector	NOUN
m-1112	278	42	of	of	ADP
m-1112	278	43	length	length	NOUN
m-1112	278	44	(	(	PUNCT
m-1112	278	45	the	the	DET
m-1112	278	46	n	n	NOUN
m-1112	278	47	vertices	vertex	NOUN
m-1112	278	48	which	which	PRON
m-1112	278	49	form	form	VERB
m-1112	278	50	the	the	DET
m-1112	278	51	n	n	NUM
m-1112	278	52	polygon	polygon	NOUN
m-1112	278	53	sides	side	NOUN
m-1112	278	54	,	,	PUNCT
m-1112	278	55	or	or	CCONJ
m-1112	278	56	the	the	DET
m-1112	278	57	norm	norm	NOUN
m-1112	278	58	of	of	ADP
m-1112	278	59	the	the	DET
m-1112	278	60	complex	complex	ADJ
m-1112	278	61	-	-	PUNCT
m-1112	278	62	vectors	vector	NOUN
m-1112	278	63	)	)	PUNCT
m-1112	278	64	in	in	ADP
m-1112	278	65	(	(	PUNCT
m-1112	278	66	1	1	NUM
m-1112	278	67	)	)	PUNCT
m-1112	278	68	,	,	PUNCT
m-1112	278	69	(	(	PUNCT
m-1112	278	70	2	2	X
m-1112	278	71	)	)	PUNCT
m-1112	278	72	,	,	PUNCT
m-1112	278	73	are	be	AUX
m-1112	278	74	the	the	DET
m-1112	278	75	4	4	NUM
m-1112	278	76	-	-	PUNCT
m-1112	278	77	geometrical	geometrical	ADJ
m-1112	278	78	spaces	space	NOUN
m-1112	278	79	consisting	consist	VERB
m-1112	278	80	the	the	DET
m-1112	278	81	geometrical	geometrical	ADJ
m-1112	278	82	mould	mould	NOUN
m-1112	278	83	.	.	PUNCT
m-1112	279	1	in	in	ADP
m-1112	279	2	(	(	PUNCT
m-1112	279	3	2	2	NUM
m-1112	279	4	)	)	PUNCT
m-1112	279	5	,	,	PUNCT
m-1112	279	6	are	be	AUX
m-1112	279	7	the	the	DET
m-1112	279	8	vectors	vector	NOUN
m-1112	279	9	of	of	ADP
m-1112	279	10	amplitude	amplitude	NOUN
m-1112	279	11	on	on	ADP
m-1112	279	12	the	the	DET
m-1112	279	13	4	4	NUM
m-1112	279	14	-spaces	-space	NOUN
m-1112	279	15	consisting	consist	VERB
m-1112	279	16	the	the	DET
m-1112	279	17	e	e	NOUN
m-1112	279	18	-	-	NOUN
m-1112	279	19	form	form	NOUN
m-1112	279	20	-	-	PUNCT
m-1112	279	21	mould	mould	NOUN
m-1112	279	22	.	.	PUNCT
m-1112	280	1	it	it	PRON
m-1112	280	2	is	be	AUX
m-1112	280	3	constructed	construct	VERB
m-1112	280	4	in	in	ADP
m-1112	280	5	space	space	NOUN
m-1112	280	6	→	→	PUNCT
m-1112	280	7	the	the	DET
m-1112	280	8	inscribed	inscribe	VERB
m-1112	280	9	and	and	CCONJ
m-1112	280	10	the	the	DET
m-1112	280	11	circumscribed	circumscribed	ADJ
m-1112	280	12	to	to	ADP
m-1112	280	13	the	the	DET
m-1112	280	14	circle	circle	NOUN
m-1112	280	15	of	of	ADP
m-1112	280	16	diameter	diameter	PROPN
m-1112	280	17	ab	ab	PROPN
m-1112	280	18	,	,	PUNCT
m-1112	280	19	the	the	DET
m-1112	280	20	→	→	NOUN
m-1112	280	21	regular	regular	ADJ
m-1112	280	22	tetra	tetra	NOUN
m-1112	280	23	pleuron	pleuron	PROPN
m-1112	280	24	←	←	PROPN
m-1112	280	25	it	it	PRON
m-1112	280	26	is	be	AUX
m-1112	280	27	constructed	construct	VERB
m-1112	280	28	in	in	ADP
m-1112	280	29	anti	anti	ADJ
m-1112	280	30	-	-	NOUN
m-1112	280	31	space	space	NOUN
m-1112	280	32	→	→	PUNCT
m-1112	280	33	the	the	DET
m-1112	280	34	inscribed	inscribe	VERB
m-1112	280	35	and	and	CCONJ
m-1112	280	36	the	the	DET
m-1112	280	37	circumscribed	circumscribed	ADJ
m-1112	280	38	to	to	ADP
m-1112	280	39	the	the	DET
m-1112	280	40	circle	circle	NOUN
m-1112	280	41	of	of	ADP
m-1112	280	42	diameter	diameter	PROPN
m-1112	280	43	ab	ab	PROPN
m-1112	280	44	,	,	PUNCT
m-1112	280	45	the	the	DET
m-1112	280	46	→	→	SYM
m-1112	280	47	regular	regular	ADJ
m-1112	280	48	penta	penta	ADJ
m-1112	280	49	pleuron	pleuron	NOUN
m-1112	280	50	←	←	PROPN
m-1112	280	51	it	it	PRON
m-1112	280	52	is	be	AUX
m-1112	280	53	constructed	construct	VERB
m-1112	280	54	in	in	ADP
m-1112	280	55	sub	sub	NOUN
m-1112	280	56	-	-	NOUN
m-1112	280	57	space	space	NOUN
m-1112	280	58	→	→	PUNCT
m-1112	280	59	the	the	DET
m-1112	280	60	inscribed	inscribe	VERB
m-1112	280	61	and	and	CCONJ
m-1112	280	62	the	the	DET
m-1112	280	63	circumscribed	circumscribed	ADJ
m-1112	280	64	to	to	ADP
m-1112	280	65	the	the	DET
m-1112	280	66	circle	circle	NOUN
m-1112	280	67	of	of	ADP
m-1112	280	68	diameter	diameter	PROPN
m-1112	280	69	ab	ab	PROPN
m-1112	280	70	,	,	PUNCT
m-1112	280	71	the	the	DET
m-1112	280	72	→	→	NOUN
m-1112	280	73	regular	regular	ADJ
m-1112	280	74	hexa	hexa	ADJ
m-1112	280	75	pleuron	pleuron	NOUN
m-1112	280	76	←	←	PROPN
m-1112	280	77	in	in	ADP
m-1112	280	78	(	(	PUNCT
m-1112	280	79	3	3	NUM
m-1112	280	80	)	)	PUNCT
m-1112	280	81	,	,	PUNCT
m-1112	280	82	are	be	AUX
m-1112	280	83	the	the	DET
m-1112	280	84	norm	norm	NOUN
m-1112	280	85	(	(	PUNCT
m-1112	280	86	magnitudes	magnitude	NOUN
m-1112	280	87	)	)	PUNCT
m-1112	280	88	of	of	ADP
m-1112	280	89	the	the	DET
m-1112	280	90	4	4	NUM
m-1112	280	91	-vectors	-vector	NOUN
m-1112	280	92	consisting	consist	VERB
m-1112	280	93	the	the	DET
m-1112	280	94	strength	strength	NOUN
m-1112	280	95	-mould	-mould	NOUN
m-1112	280	96	.	.	PUNCT
m-1112	281	1	in	in	ADP
m-1112	281	2	fig-3	fig-3	PUNCT
m-1112	281	3	the	the	DET
m-1112	281	4	time	time	NOUN
m-1112	281	5	-	-	PUNCT
m-1112	281	6	harmonic	harmonic	ADJ
m-1112	281	7	function	function	NOUN
m-1112	281	8	�	�	NOUN
m-1112	281	9	̅	̅	NOUN
m-1112	281	10	�	�	PROPN
m-1112	281	11	(	(	PUNCT
m-1112	281	12	t)≡wave	t)≡wave	X
m-1112	281	13	,	,	PUNCT
m-1112	281	14	x	x	X
m-1112	281	15	is	be	AUX
m-1112	281	16	the	the	DET
m-1112	281	17	amplitude	amplitude	NOUN
m-1112	281	18	,	,	PUNCT
m-1112	281	19	w	w	ADP
m-1112	281	20	the	the	DET
m-1112	281	21	angular	angular	ADJ
m-1112	281	22	frequency	frequency	NOUN
m-1112	281	23	,	,	PUNCT
m-1112	281	24	and	and	CCONJ
m-1112	281	25	phase	phase	NOUN
m-1112	281	26	of	of	ADP
m-1112	281	27	�	�	NOUN
m-1112	281	28	̅	̅	NOUN
m-1112	281	29	�	�	PROPN
m-1112	281	30	(	(	PUNCT
m-1112	281	31	t	t	PROPN
m-1112	281	32	)	)	PUNCT
m-1112	281	33	to	to	PART
m-1112	281	34	be	be	AUX
m-1112	281	35	determined	determine	VERB
m-1112	281	36	by	by	ADP
m-1112	281	37	the	the	DET
m-1112	281	38	number	number	NOUN
m-1112	281	39	n	n	NOUN
m-1112	281	40	,	,	PUNCT
m-1112	281	41	n+1	n+1	ADV
m-1112	281	42	of	of	ADP
m-1112	281	43	vertices	vertex	NOUN
m-1112	281	44	.	.	PUNCT
m-1112	282	1	the	the	DET
m-1112	282	2	complex	complex	ADJ
m-1112	282	3	–	–	PUNCT
m-1112	282	4	vector	vector	NOUN
m-1112	282	5	±	±	NUM
m-1112	282	6	�	�	PROPN
m-1112	282	7	̅	̅	NOUN
m-1112	282	8	�	�	PROPN
m-1112	282	9	(	(	PUNCT
m-1112	282	10	t	t	PROPN
m-1112	282	11	)	)	PUNCT
m-1112	282	12	uses	use	VERB
m-1112	282	13	the	the	DET
m-1112	282	14	norm	norm	NOUN
m-1112	282	15	iz̅i	iz̅i	VERB
m-1112	282	16	=	=	SYM
m-1112	282	17	2.r	2.r	NUM
m-1112	282	18	,	,	PUNCT
m-1112	282	19	and	and	CCONJ
m-1112	282	20	the	the	DET
m-1112	282	21	number	number	NOUN
m-1112	282	22	n	n	NOUN
m-1112	282	23	,	,	PUNCT
m-1112	282	24	of	of	ADP
m-1112	282	25	the	the	DET
m-1112	282	26	space	space	NOUN
m-1112	282	27	which	which	PRON
m-1112	282	28	determines	determine	VERB
m-1112	282	29	the	the	DET
m-1112	282	30	number	number	NOUN
m-1112	282	31	of	of	ADP
m-1112	282	32	knots	knot	NOUN
m-1112	282	33	and	and	CCONJ
m-1112	282	34	sides	side	NOUN
m-1112	282	35	of	of	ADP
m-1112	282	36	regular	regular	ADJ
m-1112	282	37	polygons	polygon	NOUN
m-1112	282	38	as	as	ADP
m-1112	282	39	,	,	PUNCT
m-1112	282	40	ijo	ijo	PROPN
m-1112	282	41	international	international	PROPN
m-1112	282	42	journal	journal	PROPN
m-1112	282	43	of	of	ADP
m-1112	282	44	mathematics	mathematics	PROPN
m-1112	282	45	(	(	PUNCT
m-1112	282	46	issn	issn	PROPN
m-1112	282	47	:	:	PUNCT
m-1112	282	48	2992	2992	NUM
m-1112	282	49	-	-	SYM
m-1112	282	50	4421	4421	NUM
m-1112	282	51	)	)	PUNCT
m-1112	282	52	volume	volume	NOUN
m-1112	282	53	08	08	NUM
m-1112	283	1	|	|	ADV
m-1112	283	2	issue	issue	NOUN
m-1112	283	3	08	08	NUM
m-1112	284	1	|	|	ADV
m-1112	284	2	august	august	PROPN
m-1112	284	3	2025	2025	NUM
m-1112	284	4	|	|	ADV
m-1112	284	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	284	6	ijo	ijo	PROPN
m-1112	284	7	journals	journal	NOUN
m-1112	284	8	14	14	NUM
m-1112	284	9	the	the	DET
m-1112	284	10	fundamental	fundamental	ADJ
m-1112	284	11	particles	particle	NOUN
m-1112	284	12	origination	origination	NOUN
m-1112	284	13	mechanism	mechanism	NOUN
m-1112	284	14	in	in	ADP
m-1112	284	15	mfmf	mfmf	PROPN
m-1112	284	16	pns	pns	PROPN
m-1112	284	17	caves	cave	NOUN
m-1112	284	18	.	.	PUNCT
m-1112	285	1	1	1	NUM
m-1112	285	2	…	…	PUNCT
m-1112	285	3	the	the	DET
m-1112	285	4	space	space	NOUN
m-1112	285	5	is	be	AUX
m-1112	285	6	consisted	consist	VERB
m-1112	285	7	of	of	ADP
m-1112	285	8	4	4	NUM
m-1112	285	9	masses	masse	NOUN
m-1112	285	10	[	[	X
m-1112	285	11	99	99	NUM
m-1112	285	12	]	]	PUNCT
m-1112	285	13	which	which	PRON
m-1112	285	14	produce	produce	VERB
m-1112	285	15	the	the	DET
m-1112	285	16	space	space	NOUN
m-1112	285	17	wave	wave	NOUN
m-1112	285	18	=	=	SYM
m-1112	285	19	2r.𝑒𝑖.𝑛𝜔𝑡	2r.𝑒𝑖.𝑛𝜔𝑡	NUM
m-1112	285	20	,	,	PUNCT
m-1112	285	21	2	2	NUM
m-1112	285	22	…	…	PUNCT
m-1112	285	23	the	the	DET
m-1112	285	24	anti	anti	ADJ
m-1112	285	25	-	-	ADJ
m-1112	285	26	space	space	NOUN
m-1112	285	27	is	be	AUX
m-1112	285	28	consisted	consist	VERB
m-1112	285	29	of	of	ADP
m-1112	285	30	5	5	NUM
m-1112	285	31	masses	masse	NOUN
m-1112	285	32	producing	produce	VERB
m-1112	285	33	the	the	DET
m-1112	285	34	anti	anti	ADJ
m-1112	285	35	-	-	NOUN
m-1112	285	36	space	space	ADJ
m-1112	285	37	–	–	PUNCT
m-1112	285	38	wave=	wave=	NUM
m-1112	285	39	2r.𝑒𝑖.𝑛𝜔𝑡	2r.𝑒𝑖.𝑛𝜔𝑡	NUM
m-1112	285	40	3	3	NUM
m-1112	285	41	…	…	SYM
m-1112	285	42	sub	sub	NOUN
m-1112	285	43	-	-	NOUN
m-1112	285	44	space	space	NOUN
m-1112	285	45	is	be	AUX
m-1112	285	46	consisted	consist	VERB
m-1112	285	47	of	of	ADP
m-1112	285	48	6	6	NUM
m-1112	285	49	masses	masse	NOUN
m-1112	285	50	producing	produce	VERB
m-1112	285	51	the	the	DET
m-1112	285	52	sub	sub	NOUN
m-1112	285	53	-	-	NOUN
m-1112	285	54	space	space	ADJ
m-1112	285	55	–	–	PUNCT
m-1112	285	56	wave	wave	NOUN
m-1112	285	57	=	=	SYM
m-1112	285	58	±	±	NUM
m-1112	285	59	2r	2r	NUM
m-1112	285	60	1	1	NUM
m-1112	285	61	/	/	SYM
m-1112	285	62	n.	n.	NOUN
m-1112	285	63	ei.θ	ei.θ	NOUN
m-1112	285	64	/	/	SYM
m-1112	285	65	n	n	PRON
m-1112	285	66	5a1	5a1	NUM
m-1112	285	67	..	..	PUNCT
m-1112	286	1	the	the	DET
m-1112	286	2	physical	physical	ADJ
m-1112	286	3	notion	notion	NOUN
m-1112	286	4	of	of	ADP
m-1112	286	5	the	the	DET
m-1112	286	6	regular	regular	ADJ
m-1112	286	7	polygones	polygone	NOUN
m-1112	286	8	:	:	PUNCT
m-1112	286	9	[	[	PUNCT
m-1112	286	10	62	62	NUM
m-1112	286	11	]	]	PUNCT
m-1112	286	12	according	accord	VERB
m-1112	286	13	to	to	ADP
m-1112	286	14	archimedes	archimede	NOUN
m-1112	286	15	,	,	PUNCT
m-1112	286	16	geometric	geometric	ADJ
m-1112	286	17	means	mean	NOUN
m-1112	286	18	,	,	PUNCT
m-1112	286	19	speaking	speak	VERB
m-1112	286	20	of	of	ADP
m-1112	286	21	numbers	number	NOUN
m-1112	286	22	,	,	PUNCT
m-1112	286	23	whether	whether	SCONJ
m-1112	286	24	solid	solid	ADJ
m-1112	286	25	or	or	CCONJ
m-1112	286	26	square	square	ADJ
m-1112	286	27	,	,	PUNCT
m-1112	286	28	observes	observe	VERB
m-1112	286	29	that	that	SCONJ
m-1112	286	30	,	,	PUNCT
m-1112	286	31	between	between	ADP
m-1112	286	32	plane	plane	NOUN
m-1112	286	33	one	one	NUM
m-1112	286	34	mean	mean	NOUN
m-1112	286	35	suffices	suffice	VERB
m-1112	286	36	,	,	PUNCT
m-1112	286	37	but	but	CCONJ
m-1112	286	38	to	to	PART
m-1112	286	39	connect	connect	VERB
m-1112	286	40	two	two	NUM
m-1112	286	41	solids	solid	NOUN
m-1112	286	42	two	two	NUM
m-1112	286	43	–	–	PUNCT
m-1112	286	44	means	mean	NOUN
m-1112	286	45	are	be	AUX
m-1112	286	46	necessary	necessary	ADJ
m-1112	286	47	.this	.this	PRON
m-1112	286	48	denotes	denote	NOUN
m-1112	286	49	that	that	SCONJ
m-1112	286	50	between	between	ADP
m-1112	286	51	two	two	NUM
m-1112	286	52	square	square	ADJ
m-1112	286	53	numbers	number	NOUN
m-1112	286	54	there	there	PRON
m-1112	286	55	is	be	VERB
m-1112	286	56	one	one	NUM
m-1112	286	57	mean	mean	NOUN
m-1112	286	58	proportional	proportional	ADJ
m-1112	286	59	number	number	NOUN
m-1112	286	60	and	and	CCONJ
m-1112	286	61	between	between	ADP
m-1112	286	62	two	two	NUM
m-1112	286	63	cubes	cube	NOUN
m-1112	286	64	there	there	ADV
m-1112	286	65	are	be	VERB
m-1112	286	66	two	two	NUM
m-1112	286	67	means	mean	VERB
m-1112	286	68	proportional	proportional	ADJ
m-1112	286	69	numbers	number	NOUN
m-1112	286	70	.	.	PUNCT
m-1112	287	1	it	it	PRON
m-1112	287	2	was	be	AUX
m-1112	287	3	proved	prove	VERB
m-1112	287	4	that	that	SCONJ
m-1112	287	5	odd	odd	ADJ
m-1112	287	6	numbers	number	NOUN
m-1112	287	7	become	become	VERB
m-1112	287	8	from	from	ADP
m-1112	287	9	any	any	DET
m-1112	287	10	two	two	NUM
m-1112	287	11	consequent	consequent	ADJ
m-1112	287	12	even	even	ADJ
m-1112	287	13	numbers	number	NOUN
m-1112	287	14	,	,	PUNCT
m-1112	287	15	so	so	CCONJ
m-1112	287	16	the	the	DET
m-1112	287	17	sum	sum	NOUN
m-1112	287	18	of	of	ADP
m-1112	287	19	two	two	NUM
m-1112	287	20	irrationals	irrational	NOUN
m-1112	287	21	may	may	AUX
m-1112	287	22	be	be	AUX
m-1112	287	23	either	either	CCONJ
m-1112	287	24	rational	rational	ADJ
m-1112	287	25	or	or	CCONJ
m-1112	287	26	irrational	irrational	ADJ
m-1112	287	27	.	.	PUNCT
m-1112	288	1	the	the	DET
m-1112	288	2	cattle	cattle	NOUN
m-1112	288	3	–	–	PUNCT
m-1112	288	4	problem	problem	NOUN
m-1112	288	5	of	of	ADP
m-1112	288	6	archimedes	archimede	NOUN
m-1112	288	7	may	may	AUX
m-1112	288	8	be	be	AUX
m-1112	288	9	further	far	ADV
m-1112	288	10	analyzed	analyze	VERB
m-1112	288	11	reaching	reach	VERB
m-1112	288	12	to	to	ADP
m-1112	288	13	equations	equation	NOUN
m-1112	288	14	of	of	ADP
m-1112	288	15	any	any	DET
m-1112	288	16	degree	degree	NOUN
m-1112	288	17	.	.	PUNCT
m-1112	289	1	it	it	PRON
m-1112	289	2	was	be	AUX
m-1112	289	3	shown	show	VERB
m-1112	289	4	before	before	ADP
m-1112	289	5	that	that	PRON
m-1112	289	6	,	,	PUNCT
m-1112	289	7	all	all	PRON
m-1112	289	8	n	n	CCONJ
m-1112	289	9	-	-	PUNCT
m-1112	289	10	regular	regular	ADJ
m-1112	289	11	polygons	polygon	NOUN
m-1112	289	12	end	end	VERB
m-1112	289	13	to	to	ADP
m-1112	289	14	equations	equation	NOUN
m-1112	289	15	of	of	ADP
m-1112	289	16	n	n	CCONJ
m-1112	289	17	-	-	PUNCT
m-1112	289	18	degree	degree	NOUN
m-1112	289	19	segment	segment	NOUN
m-1112	289	20	,	,	PUNCT
m-1112	289	21	by	by	ADP
m-1112	289	22	finding	find	VERB
m-1112	289	23	a	a	DET
m-1112	289	24	suitable	suitable	ADJ
m-1112	289	25	value	value	NOUN
m-1112	289	26	of	of	ADP
m-1112	289	27	the	the	DET
m-1112	289	28	segment	segment	NOUN
m-1112	289	29	,	,	PUNCT
m-1112	289	30	x	x	INTJ
m-1112	289	31	,	,	PUNCT
m-1112	289	32	that	that	PRON
m-1112	289	33	is	is	ADV
m-1112	289	34	we	we	PRON
m-1112	289	35	have	have	VERB
m-1112	289	36	in	in	ADP
m-1112	289	37	the	the	DET
m-1112	289	38	general	general	ADJ
m-1112	289	39	case	case	NOUN
m-1112	289	40	to	to	PART
m-1112	289	41	solve	solve	VERB
m-1112	289	42	one	one	NUM
m-1112	289	43	or	or	CCONJ
m-1112	289	44	two	two	NUM
m-1112	289	45	equations	equation	NOUN
m-1112	289	46	of	of	ADP
m-1112	289	47	the	the	DET
m-1112	289	48	form	form	NOUN
m-1112	289	49	:	:	PUNCT
m-1112	289	50	a	a	X
m-1112	289	51	.	.	PUNCT
m-1112	290	1	r	r	NOUN
m-1112	290	2	0	0	NUM
m-1112	290	3	.	.	PUNCT
m-1112	290	4	x	x	PROPN
m-1112	291	1	n	n	NUM
m-1112	291	2	b	b	NOUN
m-1112	291	3	.	.	PUNCT
m-1112	292	1	r	r	NOUN
m-1112	292	2	2	2	NUM
m-1112	292	3	.	.	PUNCT
m-1112	292	4	x	x	X
m-1112	293	1	n−2	n−2	PROPN
m-1112	293	2	+	+	CCONJ
m-1112	293	3	c	c	NOUN
m-1112	293	4	.	.	PUNCT
m-1112	294	1	r	r	NOUN
m-1112	294	2	n−6	n−6	PROPN
m-1112	294	3	.	.	PUNCT
m-1112	294	4	x	x	X
m-1112	294	5	³	³	X
m-1112	294	6	–	–	PUNCT
m-1112	294	7	d	d	NOUN
m-1112	294	8	.	.	PUNCT
m-1112	295	1	r	r	NOUN
m-1112	295	2	n−4	n−4	PROPN
m-1112	295	3	.	.	PUNCT
m-1112	295	4	x	x	X
m-1112	295	5	²	²	PROPN
m-1112	295	6	+	+	NUM
m-1112	295	7	e	e	NOUN
m-1112	295	8	.	.	PUNCT
m-1112	296	1	r	r	PROPN
m-1112	296	2	n−2	n−2	PROPN
m-1112	296	3	.	.	PUNCT
m-1112	297	1	x1	x1	PROPN
m-1112	297	2	–	–	PUNCT
m-1112	297	3	f	f	X
m-1112	297	4	.	.	PUNCT
m-1112	298	1	r	r	NOUN
m-1112	298	2	n.	n.	NOUN
m-1112	298	3	x0	x0	PROPN
m-1112	299	1	=	=	PUNCT
m-1112	299	2	0	0	NUM
m-1112	300	1	for	for	ADP
m-1112	300	2	the	the	DET
m-1112	300	3	even	even	ADJ
m-1112	300	4	polygons	polygon	NOUN
m-1112	300	5	,	,	PUNCT
m-1112	300	6	and	and	CCONJ
m-1112	300	7	a	a	DET
m-1112	300	8	.r	.r	NOUN
m-1112	300	9	2	2	NUM
m-1112	300	10	.	.	PUNCT
m-1112	300	11	x	x	X
m-1112	300	12	n−2	n−2	PROPN
m-1112	300	13	b	b	PROPN
m-1112	300	14	.r	.r	NOUN
m-1112	300	15	n−2	n−2	PROPN
m-1112	300	16	.	.	PUNCT
m-1112	301	1	x	x	X
m-1112	302	1	n−3	n−3	PROPN
m-1112	302	2	+	+	NUM
m-1112	302	3	c	c	NOUN
m-1112	302	4	.r2(n−4	.r2(n−4	PROPN
m-1112	302	5	)	)	PUNCT
m-1112	302	6	.	.	PUNCT
m-1112	303	1	x	x	X
m-1112	303	2	³	³	X
m-1112	303	3	d	d	X
m-1112	303	4	.r	.r	PROPN
m-1112	303	5	2(n−3	2(n−3	ADJ
m-1112	303	6	)	)	PUNCT
m-1112	303	7	.	.	PUNCT
m-1112	304	1	x	x	X
m-1112	304	2	²	²	PROPN
m-1112	304	3	+	+	NUM
m-1112	304	4	e	e	NOUN
m-1112	304	5	.r	.r	PROPN
m-1112	304	6	2(n−2	2(n−2	PROPN
m-1112	304	7	)	)	PUNCT
m-1112	304	8	.	.	PUNCT
m-1112	305	1	x1	x1	NUM
m-1112	305	2	–	–	PUNCT
m-1112	305	3	f	f	X
m-1112	305	4	.r	.r	PROPN
m-1112	305	5	2(n−1	2(n−1	NUM
m-1112	305	6	)	)	PUNCT
m-1112	305	7	.	.	PUNCT
m-1112	306	1	x0	x0	PROPN
m-1112	307	1	=	=	PUNCT
m-1112	308	1	0	0	NUM
m-1112	309	1	for	for	ADP
m-1112	309	2	the	the	DET
m-1112	309	3	odd	odd	ADJ
m-1112	309	4	polygons	polygon	NOUN
m-1112	309	5	,	,	PUNCT
m-1112	309	6	where	where	SCONJ
m-1112	309	7	a	a	DET
m-1112	309	8	,	,	PUNCT
m-1112	309	9	b	b	NOUN
m-1112	309	10	,	,	PUNCT
m-1112	309	11	c	c	NOUN
m-1112	309	12	,	,	PUNCT
m-1112	309	13	d	d	X
m-1112	309	14	are	be	AUX
m-1112	309	15	constants	constant	NOUN
m-1112	309	16	.	.	PUNCT
m-1112	310	1	the	the	DET
m-1112	310	2	presented	present	VERB
m-1112	310	3	geometrical	geometrical	ADJ
m-1112	310	4	method	method	NOUN
m-1112	310	5	is	be	AUX
m-1112	310	6	the	the	DET
m-1112	310	7	solution	solution	NOUN
m-1112	310	8	of	of	ADP
m-1112	310	9	the	the	DET
m-1112	310	10	above	above	ADJ
m-1112	310	11	equation	equation	NOUN
m-1112	310	12	in	in	ADP
m-1112	310	13	the	the	DET
m-1112	310	14	general	general	ADJ
m-1112	310	15	case	case	NOUN
m-1112	310	16	.	.	PUNCT
m-1112	311	1	because	because	SCONJ
m-1112	311	2	,	,	PUNCT
m-1112	311	3	the	the	DET
m-1112	311	4	nth	nth	NOUN
m-1112	311	5	degree	degree	NOUN
m-1112	311	6	equations	equation	NOUN
m-1112	311	7	are	be	AUX
m-1112	311	8	→	→	SYM
m-1112	311	9	the	the	DET
m-1112	311	10	vertices	vertex	NOUN
m-1112	311	11	(	(	PUNCT
m-1112	311	12	n	n	CCONJ
m-1112	311	13	)	)	PUNCT
m-1112	311	14	and	and	CCONJ
m-1112	311	15	the	the	DET
m-1112	311	16	sides	side	NOUN
m-1112	311	17	(	(	PUNCT
m-1112	311	18	𝐚𝐧	𝐚𝐧	NOUN
m-1112	311	19	)	)	PUNCT
m-1112	311	20	of	of	ADP
m-1112	311	21	the	the	DET
m-1112	311	22	npolygon	npolygon	NOUN
m-1112	311	23	in	in	ADP
m-1112	311	24	circle	circle	PROPN
m-1112	311	25	←	←	PROPN
m-1112	311	26	so	so	ADV
m-1112	311	27	number	number	NOUN
m-1112	311	28	,	,	PUNCT
m-1112	311	29	π	π	PROPN
m-1112	311	30	,	,	PUNCT
m-1112	311	31	is	be	AUX
m-1112	311	32	their	their	PRON
m-1112	311	33	mould	mould	NOUN
m-1112	311	34	.	.	PUNCT
m-1112	312	1	the	the	DET
m-1112	312	2	knot	knot	NOUN
m-1112	312	3	is	be	AUX
m-1112	312	4	a	a	DET
m-1112	312	5	closed	closed	ADJ
m-1112	312	6	–	–	PUNCT
m-1112	312	7	curve	curve	NOUN
m-1112	312	8	in	in	ADP
m-1112	312	9	space	space	NOUN
m-1112	312	10	(	(	PUNCT
m-1112	312	11	x	x	X
m-1112	312	12	,	,	PUNCT
m-1112	312	13	y	y	PROPN
m-1112	312	14	,	,	PUNCT
m-1112	312	15	z	z	PROPN
m-1112	312	16	)	)	PUNCT
m-1112	312	17	,	,	PUNCT
m-1112	312	18	that	that	PRON
m-1112	312	19	does	do	AUX
m-1112	312	20	not	not	PART
m-1112	312	21	intersect	intersect	VERB
m-1112	312	22	itself	itself	PRON
m-1112	312	23	.	.	PUNCT
m-1112	313	1	a	a	DET
m-1112	313	2	simple	simple	ADJ
m-1112	313	3	parametric	parametric	ADJ
m-1112	313	4	representation	representation	NOUN
m-1112	313	5	of	of	ADP
m-1112	313	6	the	the	DET
m-1112	313	7	figure	figure	NOUN
m-1112	313	8	-	-	PUNCT
m-1112	313	9	eight	eight	NUM
m-1112	313	10	knot	knot	NOUN
m-1112	313	11	is	be	AUX
m-1112	313	12	as	as	ADP
m-1112	313	13	the	the	DET
m-1112	313	14	set	set	NOUN
m-1112	313	15	of	of	ADP
m-1112	313	16	all	all	PRON
m-1112	313	17	(	(	PUNCT
m-1112	313	18	x	x	X
m-1112	313	19	,	,	PUNCT
m-1112	313	20	y	y	PROPN
m-1112	313	21	,	,	PUNCT
m-1112	313	22	z	z	NOUN
m-1112	313	23	)	)	PUNCT
m-1112	313	24	points	point	NOUN
m-1112	313	25	where	where	SCONJ
m-1112	313	26	,	,	PUNCT
m-1112	313	27	x	x	SYM
m-1112	313	28	=	=	PUNCT
m-1112	313	29	(	(	PUNCT
m-1112	313	30	2	2	NUM
m-1112	313	31	+	+	CCONJ
m-1112	313	32	cos	cos	ADJ
m-1112	313	33	2𝑡	2𝑡	NOUN
m-1112	313	34	)	)	PUNCT
m-1112	313	35	.	.	PUNCT
m-1112	314	1	cos(3𝑡	cos(3𝑡	PROPN
m-1112	314	2	)	)	PUNCT
m-1112	314	3	,	,	PUNCT
m-1112	314	4	y	y	PROPN
m-1112	314	5	=	=	PUNCT
m-1112	314	6	(	(	PUNCT
m-1112	314	7	2	2	NUM
m-1112	314	8	+	+	CCONJ
m-1112	314	9	cos	cos	ADJ
m-1112	314	10	2𝑡	2𝑡	NOUN
m-1112	314	11	)	)	PUNCT
m-1112	314	12	.	.	PUNCT
m-1112	315	1	sin(3𝑡	sin(3𝑡	NOUN
m-1112	315	2	)	)	PUNCT
m-1112	315	3	,	,	PUNCT
m-1112	315	4	z	z	NOUN
m-1112	315	5	=	=	SYM
m-1112	315	6	sin(3𝑡	sin(3𝑡	NOUN
m-1112	315	7	)	)	PUNCT
m-1112	315	8	,	,	PUNCT
m-1112	315	9	for	for	ADP
m-1112	315	10	the	the	DET
m-1112	315	11	cave	cave	NOUN
m-1112	315	12	-	-	PUNCT
m-1112	315	13	spin	spin	NOUN
m-1112	315	14	,	,	PUNCT
m-1112	315	15	�	�	NOUN
m-1112	315	16	̅	̅	NOUN
m-1112	315	17	�	�	NOUN
m-1112	315	18	=	=	SYM
m-1112	315	19	r	r	NOUN
m-1112	315	20	m	m	VERB
m-1112	315	21	v	v	NOUN
m-1112	315	22	,	,	PUNCT
m-1112	315	23	which	which	PRON
m-1112	315	24	is	be	AUX
m-1112	315	25	a	a	DET
m-1112	315	26	monad	monad	PROPN
m-1112	315	27	and	and	CCONJ
m-1112	315	28	is	be	AUX
m-1112	315	29	consisted	consist	VERB
m-1112	315	30	of	of	ADP
m-1112	315	31	4	4	NUM
m-1112	315	32	-	-	PUNCT
m-1112	315	33	spaces	space	NOUN
m-1112	315	34	exists	exist	VERB
m-1112	315	35	→	→	PUNCT
m-1112	315	36	(	(	PUNCT
m-1112	315	37	(	(	PUNCT
m-1112	315	38	the	the	DET
m-1112	315	39	spaces	space	NOUN
m-1112	315	40	n.	n.	PROPN
m-1112	315	41	�	�	PROPN
m-1112	315	42	̅	̅	NOUN
m-1112	315	43	�	�	NOUN
m-1112	315	44	polygons	polygon	NOUN
m-1112	315	45	,	,	PUNCT
m-1112	315	46	the	the	DET
m-1112	315	47	anti	anti	ADJ
m-1112	315	48	-	-	ADJ
m-1112	315	49	spaces	spaces	ADJ
m-1112	315	50	n.	n.	PROPN
m-1112	315	51	�	�	PROPN
m-1112	315	52	̅	̅	NOUN
m-1112	315	53	�	�	NOUN
m-1112	315	54	polygons	polygon	NOUN
m-1112	315	55	,	,	PUNCT
m-1112	315	56	the	the	DET
m-1112	315	57	sub	sub	ADJ
m-1112	315	58	-	-	ADJ
m-1112	315	59	spaces	spaces	ADJ
m-1112	315	60	±	±	NOUN
m-1112	315	61	√𝐧.	√𝐧.	ADP
m-1112	315	62	�	�	PROPN
m-1112	315	63	̅	̅	NOUN
m-1112	315	64	�	�	PROPN
m-1112	315	65	𝒏=𝟏−∞	𝒏=𝟏−∞	ADJ
m-1112	315	66	polygons	polygon	NOUN
m-1112	315	67	)	)	PUNCT
m-1112	315	68	)	)	PUNCT
m-1112	315	69	←	←	PROPN
m-1112	315	70	,	,	PUNCT
m-1112	315	71	with	with	ADP
m-1112	315	72	n	n	NOUN
m-1112	315	73	=	=	SYM
m-1112	315	74	1	1	NUM
m-1112	315	75	≈	≈	NUM
m-1112	315	76	∞	∞	PROPN
m-1112	315	77	knots	knot	NOUN
m-1112	315	78	it	it	PRON
m-1112	315	79	has	have	AUX
m-1112	315	80	been	be	AUX
m-1112	315	81	proved	prove	VERB
m-1112	315	82	[	[	X
m-1112	315	83	62	62	NUM
m-1112	315	84	]	]	PUNCT
m-1112	315	85	that	that	SCONJ
m-1112	315	86	,	,	PUNCT
m-1112	315	87	projecting	project	VERB
m-1112	315	88	the	the	DET
m-1112	315	89	vertices	vertex	NOUN
m-1112	315	90	of	of	ADP
m-1112	315	91	the	the	DET
m-1112	315	92	regular	regular	ADJ
m-1112	315	93	n	n	CCONJ
m-1112	315	94	-	-	PUNCT
m-1112	315	95	polygon	polygon	NOUN
m-1112	315	96	on	on	ADP
m-1112	315	97	any	any	DET
m-1112	315	98	tangent	tangent	NOUN
m-1112	315	99	of	of	ADP
m-1112	315	100	the	the	DET
m-1112	315	101	circle	circle	NOUN
m-1112	315	102	,	,	PUNCT
m-1112	315	103	then	then	ADV
m-1112	315	104	the	the	DET
m-1112	315	105	sum	sum	NOUN
m-1112	315	106	of	of	ADP
m-1112	315	107	the	the	DET
m-1112	315	108	heights	height	NOUN
m-1112	315	109	𝐲	𝐲	ADP
m-1112	315	110	𝐧	𝐧	NOUN
m-1112	315	111	is	be	AUX
m-1112	315	112	equal	equal	ADJ
m-1112	315	113	to	to	ADP
m-1112	315	114	,	,	PUNCT
m-1112	315	115	n	n	PROPN
m-1112	315	116			PROPN
m-1112	315	117	r	r	NOUN
m-1112	315	118	.	.	PUNCT
m-1112	316	1	this	this	PRON
m-1112	316	2	is	be	AUX
m-1112	316	3	a	a	DET
m-1112	316	4	linear	linear	ADJ
m-1112	316	5	relation	relation	NOUN
m-1112	316	6	between	between	ADP
m-1112	316	7	heights	height	NOUN
m-1112	316	8	,	,	PUNCT
m-1112	316	9	h	h	NOUN
m-1112	316	10	,	,	PUNCT
m-1112	316	11	and	and	CCONJ
m-1112	316	12	the	the	DET
m-1112	316	13	radius	radius	NOUN
m-1112	316	14	of	of	ADP
m-1112	316	15	the	the	DET
m-1112	316	16	circle	circle	NOUN
m-1112	316	17	,	,	PUNCT
m-1112	316	18	the	the	DET
m-1112	316	19	monad	monad	PROPN
m-1112	316	20	.	.	PUNCT
m-1112	317	1	this	this	DET
m-1112	317	2	property	property	NOUN
m-1112	317	3	on	on	ADP
m-1112	317	4	the	the	DET
m-1112	317	5	circle	circle	NOUN
m-1112	317	6	yields	yield	NOUN
m-1112	317	7	to	to	ADP
m-1112	317	8	the	the	DET
m-1112	317	9	geometrical	geometrical	ADJ
m-1112	317	10	construction	construction	NOUN
m-1112	317	11	(	(	PUNCT
m-1112	317	12	as	as	ADP
m-1112	317	13	resemblance	resemblance	ADJ
m-1112	317	14	ratio	ratio	NOUN
m-1112	317	15	of	of	ADP
m-1112	317	16	areas	area	NOUN
m-1112	317	17	which	which	PRON
m-1112	317	18	is	be	AUX
m-1112	317	19	controlled	control	VERB
m-1112	317	20	)	)	PUNCT
m-1112	317	21	and	and	CCONJ
m-1112	317	22	the	the	DET
m-1112	317	23	algebraic	algebraic	ADJ
m-1112	317	24	measuring	measuring	NOUN
m-1112	317	25	of	of	ADP
m-1112	317	26	the	the	DET
m-1112	317	27	regular	regular	ADJ
m-1112	317	28	polygons	polygon	NOUN
m-1112	317	29	as	as	SCONJ
m-1112	317	30	follows	follow	VERB
m-1112	317	31	,	,	PUNCT
m-1112	317	32	when	when	SCONJ
m-1112	317	33	:	:	PUNCT
m-1112	317	34	r	r	X
m-1112	317	35	=	=	PUNCT
m-1112	317	36	the	the	DET
m-1112	317	37	radius	radius	NOUN
m-1112	317	38	of	of	ADP
m-1112	317	39	the	the	DET
m-1112	317	40	circle	circle	NOUN
m-1112	317	41	,	,	PUNCT
m-1112	317	42	with	with	ADP
m-1112	317	43	a	a	DET
m-1112	317	44	random	random	ADJ
m-1112	317	45	diameter	diameter	NOUN
m-1112	317	46	iab	iab	NOUN
m-1112	317	47	i	i	PROPN
m-1112	317	48	.	.	PUNCT
m-1112	318	1	𝐚𝐧	𝐚𝐧	X
m-1112	318	2	=	=	PUNCT
m-1112	318	3	the	the	DET
m-1112	318	4	side	side	NOUN
m-1112	318	5	of	of	ADP
m-1112	318	6	the	the	DET
m-1112	318	7	regular	regular	ADJ
m-1112	318	8	n	n	PRON
m-1112	318	9	-polygon	-polygon	NOUN
m-1112	318	10	inscribed	inscribe	VERB
m-1112	318	11	in	in	ADP
m-1112	318	12	the	the	DET
m-1112	318	13	circle	circle	NOUN
m-1112	318	14	n	n	NOUN
m-1112	318	15	=	=	NOUN
m-1112	318	16	number	number	NOUN
m-1112	318	17	of	of	ADP
m-1112	318	18	sides	side	NOUN
m-1112	318	19	,	,	PUNCT
m-1112	318	20	a	a	PRON
m-1112	318	21	,	,	PUNCT
m-1112	318	22	and	and	CCONJ
m-1112	318	23	knots	knot	NOUN
m-1112	318	24	of	of	ADP
m-1112	318	25	the	the	DET
m-1112	318	26	n	n	ADV
m-1112	318	27	-polygon	-polygon	NOUN
m-1112	318	28	,	,	PUNCT
m-1112	318	29	then	then	ADV
m-1112	318	30	exists	exist	VERB
m-1112	318	31	:	:	PUNCT
m-1112	318	32	ijo	ijo	PROPN
m-1112	318	33	international	international	PROPN
m-1112	318	34	journal	journal	PROPN
m-1112	318	35	of	of	ADP
m-1112	318	36	mathematics	mathematics	PROPN
m-1112	318	37	(	(	PUNCT
m-1112	318	38	issn	issn	PROPN
m-1112	318	39	:	:	PUNCT
m-1112	318	40	2992	2992	NUM
m-1112	318	41	-	-	SYM
m-1112	318	42	4421	4421	NUM
m-1112	318	43	)	)	PUNCT
m-1112	318	44	volume	volume	NOUN
m-1112	318	45	08	08	NUM
m-1112	319	1	|	|	ADV
m-1112	319	2	issue	issue	NOUN
m-1112	319	3	08	08	NUM
m-1112	320	1	|	|	ADV
m-1112	320	2	august	august	PROPN
m-1112	320	3	2025	2025	NUM
m-1112	320	4	|	|	ADV
m-1112	320	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	320	6	ijo	ijo	PROPN
m-1112	320	7	journals	journal	NOUN
m-1112	320	8	15	15	NUM
m-1112	320	9	the	the	DET
m-1112	320	10	fundamental	fundamental	ADJ
m-1112	320	11	particles	particle	NOUN
m-1112	320	12	origination	origination	NOUN
m-1112	320	13	mechanism	mechanism	NOUN
m-1112	320	14	in	in	ADP
m-1112	320	15	mfmf	mfmf	PROPN
m-1112	320	16	pns	pns	PROPN
m-1112	320	17	caves	cave	NOUN
m-1112	320	18	.	.	PUNCT
m-1112	321	1	n	n	X
m-1112	321	2	.	.	PUNCT
m-1112	322	1	r	r	NOUN
m-1112	322	2	=	=	SYM
m-1112	322	3	2	2	NUM
m-1112	322	4	.	.	PUNCT
m-1112	323	1	r	r	NOUN
m-1112	323	2	+	+	NOUN
m-1112	323	3	2	2	NUM
m-1112	323	4	.	.	PUNCT
m-1112	324	1	y1	y1	NOUN
m-1112	325	1	+	+	CCONJ
m-1112	325	2	2	2	NUM
m-1112	325	3	.	.	PUNCT
m-1112	326	1	y2	y2	NOUN
m-1112	327	1	+	+	CCONJ
m-1112	327	2	2	2	NUM
m-1112	327	3	.	.	PUNCT
m-1112	328	1	y3	y3	NOUN
m-1112	328	2	+	+	NOUN
m-1112	328	3	…	…	SYM
m-1112	328	4	……	……	X
m-1112	328	5	2	2	NUM
m-1112	328	6	.	.	PUNCT
m-1112	328	7	𝐲𝐧	𝐲𝐧	ADP
m-1112	328	8	…	…	PUNCT
m-1112	328	9	…	…	SYM
m-1112	328	10	……	……	NOUN
m-1112	328	11	.	.	PUNCT
m-1112	329	1	(	(	PUNCT
m-1112	329	2	n	n	CCONJ
m-1112	329	3	)	)	PUNCT
m-1112	329	4	the	the	DET
m-1112	329	5	heights	height	NOUN
m-1112	329	6	yn	yn	PRON
m-1112	329	7	are	be	AUX
m-1112	329	8	as	as	SCONJ
m-1112	329	9	follows	follow	VERB
m-1112	329	10	yb	yb	X
m-1112	329	11	=	=	PUNCT
m-1112	330	1	[	[	PUNCT
m-1112	330	2	2	2	NUM
m-1112	330	3	.	.	PUNCT
m-1112	331	1	r	r	NOUN
m-1112	331	2	]	]	PUNCT
m-1112	331	3	,	,	PUNCT
m-1112	331	4	y1	y1	INTJ
m-1112	331	5	=	=	PUNCT
m-1112	331	6	[	[	PUNCT
m-1112	331	7	4.r	4.r	NUM
m-1112	331	8	²	²	NUM
m-1112	331	9	a	a	DET
m-1112	331	10	²	²	NUM
m-1112	331	11	]	]	PUNCT
m-1112	331	12	/.	/.	PUNCT
m-1112	332	1	(	(	PUNCT
m-1112	332	2	2	2	NUM
m-1112	332	3	r	r	NOUN
m-1112	332	4	)	)	PUNCT
m-1112	332	5	…	…	PUNCT
m-1112	332	6	(	(	PUNCT
m-1112	332	7	y	y	NOUN
m-1112	332	8	)	)	PUNCT
m-1112	332	9	equation	equation	NOUN
m-1112	332	10	(	(	PUNCT
m-1112	332	11	y	y	NOUN
m-1112	332	12	)	)	PUNCT
m-1112	332	13	is	be	AUX
m-1112	332	14	a	a	DET
m-1112	332	15	space	space	NOUN
m-1112	332	16	-	-	PUNCT
m-1112	332	17	wave	wave	NOUN
m-1112	332	18	depended	depend	VERB
m-1112	332	19	on	on	ADP
m-1112	332	20	𝐚𝐧	𝐚𝐧	PRON
m-1112	332	21	,	,	PUNCT
m-1112	332	22	meaning	mean	VERB
m-1112	332	23	n	n	ADP
m-1112	332	24	informations	information	NOUN
m-1112	332	25	on	on	ADP
m-1112	332	26	𝐲𝐁	𝐲𝐁	ADJ
m-1112	332	27	height	height	NOUN
m-1112	332	28	.	.	PUNCT
m-1112	333	1	y2	y2	X
m-1112	334	1	=	=	PUNCT
m-1112	335	1	[	[	PUNCT
m-1112	335	2	4.r4	4.r4	NUM
m-1112	335	3	–	–	PUNCT
m-1112	335	4	4	4	NUM
m-1112	335	5	.	.	PUNCT
m-1112	336	1	r2	r2	NOUN
m-1112	336	2	.	.	PUNCT
m-1112	337	1	a2	a2	PROPN
m-1112	337	2	+	+	CCONJ
m-1112	337	3	a4	a4	NOUN
m-1112	337	4	]	]	PUNCT
m-1112	337	5	/(2	/(2	PROPN
m-1112	337	6	.	.	PUNCT
m-1112	338	1	r3	r3	PROPN
m-1112	338	2	)	)	PUNCT
m-1112	338	3	y3	y3	NOUN
m-1112	338	4	=	=	PUNCT
m-1112	338	5	[	[	PUNCT
m-1112	338	6	8	8	X
m-1112	338	7	.	.	X
m-1112	339	1	r6	r6	NOUN
m-1112	339	2	–	–	PUNCT
m-1112	339	3	10	10	NUM
m-1112	339	4	.	.	PUNCT
m-1112	340	1	r4	r4	NOUN
m-1112	340	2	.	.	PUNCT
m-1112	341	1	a2	a2	PROPN
m-1112	341	2	+	+	CCONJ
m-1112	342	1	6	6	NUM
m-1112	342	2	.	.	PUNCT
m-1112	343	1	r2	r2	NOUN
m-1112	343	2	.	.	PUNCT
m-1112	344	1	a4	a4	NUM
m-1112	344	2	–	–	PUNCT
m-1112	344	3	a6	a6	NOUN
m-1112	344	4	]	]	PUNCT
m-1112	344	5	–	–	PUNCT
m-1112	344	6	a2	a2	X
m-1112	344	7	.	.	PROPN
m-1112	345	1	64	64	NUM
m-1112	345	2	.	.	PUNCT
m-1112	346	1	r	r	NOUN
m-1112	346	2	896	896	NUM
m-1112	346	3	.	.	PUNCT
m-1112	347	1	r6.a²+52	r6.a²+52	PROPN
m-1112	347	2	.	.	PUNCT
m-1112	348	1	r4	r4	NOUN
m-1112	348	2	.	.	PUNCT
m-1112	349	1	a4	a4	NOUN
m-1112	349	2	–	–	PUNCT
m-1112	349	3	12.r²	12.r²	NUM
m-1112	349	4	.	.	PUNCT
m-1112	350	1	a6	a6	NOUN
m-1112	350	2	+	+	PROPN
m-1112	350	3	a8	a8	PROPN
m-1112	350	4	¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯	¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯	PROPN
m-1112	350	5	2	2	NUM
m-1112	350	6	.	.	PUNCT
m-1112	351	1	r5	r5	PROPN
m-1112	351	2	¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯	¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯	VERB
m-1112	351	3	yn	yn	NOUN
m-1112	351	4	=	=	PUNCT
m-1112	351	5	[	[	PUNCT
m-1112	351	6	…	…	PUNCT
m-1112	351	7	…	…	PUNCT
m-1112	351	8	…	…	SYM
m-1112	351	9	……	……	NOUN
m-1112	351	10	..	..	PUNCT
m-1112	351	11	]	]	PUNCT
m-1112	351	12	/	/	SYM
m-1112	351	13	2	2	X
m-1112	351	14	.	.	X
m-1112	351	15	rn	rn	PROPN
m-1112	351	16	figure	figure	VERB
m-1112	351	17	–	–	PUNCT
m-1112	351	18	3a	3a	NUM
m-1112	351	19	in	in	ADP
m-1112	351	20	fig-1	fig-1	NOUN
m-1112	351	21	-	-	SYM
m-1112	351	22	1	1	NUM
m-1112	351	23	,	,	PUNCT
m-1112	351	24	on	on	ADP
m-1112	351	25	ab	ab	PROPN
m-1112	351	26	diameter	diameter	NOUN
m-1112	351	27	=	=	SYM
m-1112	351	28	2r	2r	NUM
m-1112	352	1	=	=	PUNCT
m-1112	352	2	the	the	DET
m-1112	352	3	monad	monad	PROPN
m-1112	352	4	of	of	ADP
m-1112	352	5	neutral	neutral	ADJ
m-1112	352	6	-	-	PUNCT
m-1112	352	7	circle	circle	NOUN
m-1112	352	8	exist	exist	VERB
m-1112	352	9	the	the	DET
m-1112	352	10	spaces	space	NOUN
m-1112	352	11	with	with	ADP
m-1112	352	12	their	their	PRON
m-1112	352	13	sides	side	NOUN
m-1112	352	14	𝛌𝐧	𝛌𝐧	ADP
m-1112	352	15	=	=	SYM
m-1112	352	16	2,√r2	2,√r2	PROPN
m-1112	353	1	−	−	PROPN
m-1112	353	2	a²n	a²n	PROPN
m-1112	353	3	,	,	PUNCT
m-1112	353	4	and	and	CCONJ
m-1112	353	5	their	their	PRON
m-1112	353	6	critical	critical	ADJ
m-1112	353	7	-	-	PUNCT
m-1112	353	8	sides	side	NOUN
m-1112	353	9	𝐚𝐧	𝐚𝐧	NOUN
m-1112	353	10	=	=	SYM
m-1112	353	11	1	1	NUM
m-1112	353	12	2	2	NUM
m-1112	353	13	√4r2	√4r2	PROPN
m-1112	353	14	−	−	PROPN
m-1112	353	15	λ²n	λ²n	X
m-1112	353	16	,	,	PUNCT
m-1112	353	17	as	as	ADP
m-1112	353	18	below	below	ADP
m-1112	353	19	1	1	NUM
m-1112	353	20	…	…	PUNCT
m-1112	353	21	for	for	ADP
m-1112	353	22	spaces	space	NOUN
m-1112	353	23	,	,	PUNCT
m-1112	353	24	the	the	DET
m-1112	353	25	polygon	polygon	NOUN
m-1112	353	26	side	side	NOUN
m-1112	353	27	is	be	AUX
m-1112	353	28	λ	λ	NOUN
m-1112	353	29	n(s	n(s	PROPN
m-1112	353	30	)	)	PUNCT
m-1112	353	31	=	=	SYM
m-1112	354	1	2	2	NUM
m-1112	354	2	.√r2	.√r2	NOUN
m-1112	354	3	−	−	PROPN
m-1112	354	4	a²n(s	a²n(s	PROPN
m-1112	354	5	)	)	PUNCT
m-1112	354	6	,	,	PUNCT
m-1112	354	7	2	2	NUM
m-1112	354	8	…	…	PUNCT
m-1112	354	9	for	for	ADP
m-1112	354	10	anti	anti	NOUN
m-1112	354	11	-	-	ADJ
m-1112	354	12	spaces	space	NOUN
m-1112	354	13	,	,	PUNCT
m-1112	354	14	the	the	DET
m-1112	354	15	polygon	polygon	NOUN
m-1112	354	16	side	side	NOUN
m-1112	354	17	is	be	AUX
m-1112	354	18	λ	λ	X
m-1112	354	19	n(as	n(as	ADJ
m-1112	354	20	)	)	PUNCT
m-1112	354	21	=	=	SYM
m-1112	355	1	2	2	NUM
m-1112	355	2	.√r2	.√r2	NOUN
m-1112	355	3	−	−	PROPN
m-1112	355	4	a²n(as	a²n(as	PROPN
m-1112	355	5	)	)	PUNCT
m-1112	355	6	,	,	PUNCT
m-1112	355	7	3	3	NUM
m-1112	355	8	…	…	PUNCT
m-1112	355	9	for	for	ADP
m-1112	355	10	sub	sub	NOUN
m-1112	355	11	-	-	NOUN
m-1112	355	12	spaces	space	NOUN
m-1112	355	13	,	,	PUNCT
m-1112	355	14	the	the	DET
m-1112	355	15	polygon	polygon	NOUN
m-1112	355	16	side	side	NOUN
m-1112	355	17	is	be	AUX
m-1112	355	18	λ	λ	X
m-1112	355	19	n(ss	n(s	NOUN
m-1112	355	20	)	)	PUNCT
m-1112	355	21	=	=	SYM
m-1112	356	1	2	2	NUM
m-1112	356	2	.√r2	.√r2	NOUN
m-1112	356	3	−	−	PROPN
m-1112	356	4	a²n(ss	a²n(ss	NUM
m-1112	356	5	)	)	PUNCT
m-1112	356	6	,	,	PUNCT
m-1112	356	7	4	4	NUM
m-1112	356	8	…	…	PUNCT
m-1112	356	9	for	for	ADP
m-1112	356	10	neutral	neutral	ADJ
m-1112	356	11	spaces	space	NOUN
m-1112	356	12	,	,	PUNCT
m-1112	356	13	the	the	DET
m-1112	356	14	polygon	polygon	NOUN
m-1112	356	15	side	side	NOUN
m-1112	356	16	is	be	AUX
m-1112	356	17	λ	λ	X
m-1112	356	18	n(ns	n(ns	PROPN
m-1112	356	19	)	)	PUNCT
m-1112	356	20	=	=	SYM
m-1112	356	21	0	0	NUM
m-1112	356	22	,	,	PUNCT
m-1112	356	23	while	while	SCONJ
m-1112	356	24	in	in	ADP
m-1112	356	25	material	material	NOUN
m-1112	356	26	-	-	PUNCT
m-1112	356	27	geometry	geometry	NOUN
m-1112	356	28	becomes	become	VERB
m-1112	356	29	from	from	ADP
m-1112	356	30	the	the	DET
m-1112	356	31	centripetal	centripetal	ADJ
m-1112	356	32	force	force	NOUN
m-1112	357	1	fc	fc	PROPN
m-1112	357	2	=	=	PUNCT
m-1112	357	3	σ	σ	PROPN
m-1112	357	4	=	=	PUNCT
m-1112	357	5	m.v³	m.v³	NOUN
m-1112	357	6	r	r	NOUN
m-1112	357	7	=	=	SYM
m-1112	357	8	j	j	PROPN
m-1112	357	9	w²	w²	PROPN
m-1112	357	10	r	r	NOUN
m-1112	357	11	,	,	PUNCT
m-1112	357	12	where	where	SCONJ
m-1112	357	13	the	the	DET
m-1112	357	14	unity	unity	NOUN
m-1112	357	15	monad	monad	PROPN
m-1112	357	16	r	r	NOUN
m-1112	357	17	≡	≡	PROPN
m-1112	357	18	monad	monad	PROPN
m-1112	357	19	r	r	NOUN
m-1112	357	20	=	=	SYM
m-1112	357	21	σ	σ	X
m-1112	357	22	j.w²	j.w²	NOUN
m-1112	357	23	=	=	SYM
m-1112	357	24	𝛔	𝛔	PART
m-1112	357	25	�	�	PROPN
m-1112	357	26	̅	̅	NOUN
m-1112	357	27	�	�	NOUN
m-1112	357	28	=	=	SYM
m-1112	357	29	stress	stress	NOUN
m-1112	357	30	angular−momentum̅̅	angular−momentum̅̅	PROPN
m-1112	357	31	̅̅	̅̅	PROPN
m-1112	357	32	̅̅	̅̅	PROPN
m-1112	357	33	̅̅	̅̅	PROPN
m-1112	357	34	̅̅	̅̅	PROPN
m-1112	357	35	̅̅	̅̅	PROPN
m-1112	357	36	̅̅	̅̅	PROPN
m-1112	357	37	̅̅	̅̅	PROPN
m-1112	357	38	̅̅	̅̅	PROPN
m-1112	357	39	̅̅	̅̅	PROPN
m-1112	357	40	̅̅	̅̅	PROPN
m-1112	357	41	̅̅	̅̅	PROPN
m-1112	357	42	̅̅	̅̅	PROPN
m-1112	357	43	̅̅	̅̅	PROPN
m-1112	357	44	̅̅	̅̅	PROPN
m-1112	357	45	̅	̅	PROPN
m-1112	357	46	,	,	PUNCT
m-1112	357	47	and	and	CCONJ
m-1112	357	48	polygon	polygon	PROPN
m-1112	357	49	side	side	NOUN
m-1112	357	50	𝛌	𝛌	PROPN
m-1112	357	51	𝐧(𝐍𝐒	𝐧(𝐍𝐒	PROPN
m-1112	357	52	)	)	PUNCT
m-1112	357	53	=	=	SYM
m-1112	358	1	2	2	NUM
m-1112	358	2	√r2	√r2	SYM
m-1112	358	3	−	−	PROPN
m-1112	358	4	a²n	a²n	PROPN
m-1112	358	5	,	,	PUNCT
m-1112	358	6	all	all	PRON
m-1112	358	7	becoming	become	VERB
m-1112	358	8	from	from	ADP
m-1112	358	9	pythagorean	pythagorean	PROPN
m-1112	358	10	relation	relation	NOUN
m-1112	358	11	[	[	PUNCT
m-1112	358	12	r	r	NOUN
m-1112	358	13	]	]	PUNCT
m-1112	358	14	²	²	NUM
m-1112	358	15	=	=	SYM
m-1112	358	16	[	[	PUNCT
m-1112	358	17	an	an	X
m-1112	358	18	]	]	X
m-1112	358	19	²	²	NUM
m-1112	359	1	+	+	CCONJ
m-1112	359	2	[	[	PUNCT
m-1112	359	3	λn	λn	NOUN
m-1112	359	4	2	2	NUM
m-1112	359	5	]	]	PUNCT
m-1112	359	6	²	²	NUM
m-1112	359	7	.	.	PUNCT
m-1112	360	1	5a2	5a2	NUM
m-1112	360	2	..	..	PUNCT
m-1112	361	1	the	the	DET
m-1112	361	2	general	general	ADJ
m-1112	361	3	equations	equation	NOUN
m-1112	361	4	of	of	ADP
m-1112	361	5	motion	motion	NOUN
m-1112	361	6	in	in	ADP
m-1112	361	7	a	a	DET
m-1112	361	8	polygon	polygon	NOUN
m-1112	361	9	-	-	PUNCT
m-1112	361	10	vector	vector	NOUN
m-1112	361	11	–	–	PUNCT
m-1112	361	12	conductor	conductor	NOUN
m-1112	361	13	d	d	NOUN
m-1112	361	14	=	=	PUNCT
m-1112	361	15	side	side	NOUN
m-1112	361	16	𝛌	𝛌	PROPN
m-1112	361	17	𝐧(𝐍𝐒	𝐧(𝐍𝐒	PROPN
m-1112	361	18	)	)	PUNCT
m-1112	361	19	the	the	DET
m-1112	361	20	displacement	displacement	NOUN
m-1112	361	21	at	at	ADP
m-1112	361	22	point	point	NOUN
m-1112	361	23	x	x	PUNCT
m-1112	361	24	of	of	ADP
m-1112	361	25	a	a	DET
m-1112	361	26	conductor	conductor	NOUN
m-1112	361	27	d	d	NOUN
m-1112	361	28	,	,	PUNCT
m-1112	361	29	is	be	AUX
m-1112	361	30	x	x	PUNCT
m-1112	361	31	+	+	NUM
m-1112	361	32	dx	dx	PROPN
m-1112	361	33	and	and	CCONJ
m-1112	361	34	strain	strain	NOUN
m-1112	361	35	will	will	AUX
m-1112	361	36	be	be	AUX
m-1112	361	37	u	u	NOUN
m-1112	361	38	+	+	CCONJ
m-1112	361	39	(	(	PUNCT
m-1112	361	40	∂u	∂u	PROPN
m-1112	361	41	∂t	∂t	PROPN
m-1112	361	42	)	)	PUNCT
m-1112	361	43	.dx	.dx	PUNCT
m-1112	361	44	,	,	PUNCT
m-1112	361	45	and	and	CCONJ
m-1112	361	46	the	the	DET
m-1112	361	47	unit	unit	NOUN
m-1112	361	48	strain	strain	NOUN
m-1112	361	49	is	be	AUX
m-1112	361	50	(	(	PUNCT
m-1112	361	51	∂u	∂u	PROPN
m-1112	361	52	∂x	∂x	PROPN
m-1112	361	53	)	)	PUNCT
m-1112	361	54	.	.	PUNCT
m-1112	362	1	from	from	ADP
m-1112	362	2	hook`s	hook`s	PROPN
m-1112	362	3	law	law	NOUN
m-1112	362	4	,	,	PUNCT
m-1112	362	5	σ	σ	X
m-1112	362	6	=	=	PUNCT
m-1112	362	7	e	e	PROPN
m-1112	362	8	u	u	PROPN
m-1112	362	9	,	,	PUNCT
m-1112	362	10	the	the	DET
m-1112	362	11	ratio	ratio	NOUN
m-1112	362	12	of	of	ADP
m-1112	362	13	unit	unit	NOUN
m-1112	362	14	-	-	PUNCT
m-1112	362	15	stress	stress	NOUN
m-1112	362	16	to	to	ADP
m-1112	362	17	unit	unit	NOUN
m-1112	362	18	-	-	PUNCT
m-1112	362	19	strain	strain	NOUN
m-1112	362	20	is	be	AUX
m-1112	362	21	equal	equal	ADJ
m-1112	362	22	to	to	ADP
m-1112	362	23	the	the	DET
m-1112	362	24	`	`	PUNCT
m-1112	362	25	modulus	modulus	NOUN
m-1112	362	26	of	of	ADP
m-1112	362	27	elasticity	elasticity	NOUN
m-1112	362	28	e	e	NOUN
m-1112	362	29	and	and	CCONJ
m-1112	362	30	a	a	DET
m-1112	362	31	=	=	X
m-1112	362	32	the	the	DET
m-1112	362	33	cross	cross	PROPN
m-1112	362	34	section	section	PROPN
m-1112	362	35	area	area	NOUN
m-1112	362	36	of	of	ADP
m-1112	362	37	the	the	DET
m-1112	362	38	conductor	conductor	NOUN
m-1112	362	39	,	,	PUNCT
m-1112	362	40	then	then	ADV
m-1112	362	41	issues	issue	VERB
m-1112	362	42	∂u	∂u	PROPN
m-1112	362	43	∂t	∂t	PROPN
m-1112	362	44	=	=	PUNCT
m-1112	362	45	force	force	VERB
m-1112	362	46	a	a	DET
m-1112	362	47	.e	.e	NOUN
m-1112	363	1	=	=	X
m-1112	363	2	f	f	X
m-1112	363	3	a	a	DET
m-1112	363	4	.e	.e	NOUN
m-1112	363	5	and	and	CCONJ
m-1112	363	6	by	by	ADP
m-1112	363	7	differentiation	differentiation	NOUN
m-1112	363	8	becomes	become	VERB
m-1112	363	9	→	→	PUNCT
m-1112	363	10	a	a	DET
m-1112	363	11	.e	.e	NOUN
m-1112	363	12	.	.	PUNCT
m-1112	364	1	𝛛²𝐮	𝛛²𝐮	X
m-1112	364	2	𝛛𝐱²	𝛛𝐱²	X
m-1112	365	1	=	=	PUNCT
m-1112	365	2	𝛛𝐄	𝛛𝐄	NOUN
m-1112	365	3	𝛛𝐱	𝛛𝐱	NUM
m-1112	365	4	…	…	PUNCT
m-1112	365	5	…	…	PUNCT
m-1112	365	6	.(1	.(1	NUM
m-1112	365	7	)	)	PUNCT
m-1112	365	8	applying	apply	VERB
m-1112	365	9	newton`s	newton`s	NOUN
m-1112	365	10	law	law	NOUN
m-1112	365	11	of	of	ADP
m-1112	365	12	motion	motion	NOUN
m-1112	365	13	for	for	ADP
m-1112	365	14	the	the	DET
m-1112	365	15	element	element	NOUN
m-1112	365	16	dx	dx	PROPN
m-1112	365	17	and	and	CCONJ
m-1112	365	18	equate	equate	VERB
m-1112	365	19	the	the	DET
m-1112	365	20	unbalance	unbalance	NOUN
m-1112	365	21	-	-	PUNCT
m-1112	365	22	force	force	NOUN
m-1112	365	23	∂p	∂p	PROPN
m-1112	365	24	∂x	∂x	PROPN
m-1112	365	25	,	,	PUNCT
m-1112	365	26	to	to	ADP
m-1112	365	27	the	the	DET
m-1112	365	28	product	product	NOUN
m-1112	365	29	of	of	ADP
m-1112	365	30	the	the	DET
m-1112	365	31	mass	mass	NOUN
m-1112	365	32	and	and	CCONJ
m-1112	365	33	acceleration	acceleration	NOUN
m-1112	365	34	of	of	ADP
m-1112	365	35	the	the	DET
m-1112	365	36	elements	element	NOUN
m-1112	365	37	,	,	PUNCT
m-1112	365	38	and	and	CCONJ
m-1112	365	39	then	then	ADV
m-1112	365	40	∂e	∂e	PROPN
m-1112	365	41	∂x	∂x	PROPN
m-1112	365	42	dx	dx	PROPN
m-1112	366	1	=	=	SYM
m-1112	366	2	ρ	ρ	PROPN
m-1112	366	3	a	a	DET
m-1112	366	4	dx	dx	PROPN
m-1112	366	5	∂²u	∂²u	PROPN
m-1112	366	6	∂t²	∂t²	NOUN
m-1112	366	7	…	…	PUNCT
m-1112	366	8	.(2	.(2	NOUN
m-1112	366	9	)	)	PUNCT
m-1112	366	10	eliminating	eliminate	VERB
m-1112	366	11	∂u	∂u	PROPN
m-1112	366	12	∂x	∂x	PROPN
m-1112	366	13	then	then	ADV
m-1112	366	14	we	we	PRON
m-1112	366	15	have	have	VERB
m-1112	366	16	the	the	DET
m-1112	366	17	partial	partial	ADJ
m-1112	366	18	differential	differential	NOUN
m-1112	366	19	equation	equation	NOUN
m-1112	366	20	∂²u	∂²u	NOUN
m-1112	366	21	∂t²	∂t²	NOUN
m-1112	366	22	=	=	PUNCT
m-1112	366	23	[	[	PUNCT
m-1112	366	24	e	e	X
m-1112	366	25	ρ	ρ	X
m-1112	366	26	]	]	PUNCT
m-1112	366	27	∂²u	∂²u	PROPN
m-1112	366	28	∂	∂	NOUN
m-1112	366	29	x²	x²	PROPN
m-1112	366	30	.	.	PUNCT
m-1112	367	1	…	…	PUNCT
m-1112	367	2	(3	(3	X
m-1112	367	3	)	)	PUNCT
m-1112	367	4	and	and	CCONJ
m-1112	367	5	𝛛²𝐮	𝛛²𝐮	ADJ
m-1112	367	6	𝛛	𝛛	ADJ
m-1112	367	7	𝐱²	𝐱²	NOUN
m-1112	367	8	=	=	PUNCT
m-1112	367	9	[	[	PUNCT
m-1112	367	10	𝛒	𝛒	SYM
m-1112	367	11	𝐄	𝐄	PROPN
m-1112	367	12	]	]	PUNCT
m-1112	367	13	.	.	PUNCT
m-1112	368	1	𝛛²𝐮	𝛛²𝐮	PUNCT
m-1112	369	1	𝛛𝐭²	𝛛𝐭²	NOUN
m-1112	369	2	≡	≡	PROPN
m-1112	369	3	[	[	PUNCT
m-1112	369	4	𝟏	𝟏	NUM
m-1112	369	5	𝐜²	𝐜²	PROPN
m-1112	369	6	]	]	PUNCT
m-1112	369	7	.	.	PUNCT
m-1112	370	1	𝛛²𝐮	𝛛²𝐮	VERB
m-1112	371	1	𝛛	𝛛	ADJ
m-1112	371	2	𝐱²	𝐱²	NOUN
m-1112	371	3	…	…	PUNCT
m-1112	371	4	(	(	PUNCT
m-1112	371	5	4	4	NUM
m-1112	371	6	)	)	PUNCT
m-1112	371	7	where	where	SCONJ
m-1112	371	8	�	�	NOUN
m-1112	371	9	̅	̅	NOUN
m-1112	371	10	�	�	NOUN
m-1112	371	11	=	=	NOUN
m-1112	371	12	√	√	SYM
m-1112	371	13	e	e	NOUN
m-1112	371	14	ρ	ρ	PROPN
m-1112	371	15	,	,	PUNCT
m-1112	371	16	and	and	CCONJ
m-1112	371	17	it	it	PRON
m-1112	371	18	is	be	AUX
m-1112	371	19	the	the	DET
m-1112	371	20	velocity	velocity	NOUN
m-1112	371	21	of	of	ADP
m-1112	371	22	propagation	propagation	NOUN
m-1112	371	23	of	of	ADP
m-1112	371	24	the	the	DET
m-1112	371	25	displacement	displacement	NOUN
m-1112	371	26	dx	dx	PROPN
m-1112	371	27	,	,	PUNCT
m-1112	371	28	along	along	ADP
m-1112	371	29	the	the	DET
m-1112	371	30	conductor	conductor	NOUN
m-1112	371	31	or	or	CCONJ
m-1112	371	32	→	→	PUNCT
m-1112	371	33	is	be	AUX
m-1112	371	34	the	the	DET
m-1112	371	35	stress	stress	NOUN
m-1112	371	36	–	–	PUNCT
m-1112	371	37	wave	wave	NOUN
m-1112	371	38	←	←	NOUN
m-1112	371	39	applying	apply	VERB
m-1112	371	40	equation	equation	NOUN
m-1112	371	41	(	(	PUNCT
m-1112	371	42	4	4	NUM
m-1112	371	43	)	)	PUNCT
m-1112	371	44	in	in	ADP
m-1112	371	45	an	an	DET
m-1112	371	46	conductor	conductor	NOUN
m-1112	371	47	[	[	PUNCT
m-1112	371	48	d	d	PROPN
m-1112	371	49	≡	≡	PROPN
m-1112	371	50	𝛌	𝛌	PROPN
m-1112	371	51	𝐧(𝐍𝐒	𝐧(𝐍𝐒	PROPN
m-1112	371	52	)	)	PUNCT
m-1112	371	53	]	]	PUNCT
m-1112	371	54	of	of	ADP
m-1112	371	55	space	space	NOUN
m-1112	371	56	anti	anti	ADJ
m-1112	371	57	-	-	ADJ
m-1112	371	58	space	space	ADJ
m-1112	371	59	equilibrium	equilibrium	NOUN
m-1112	371	60	formation	formation	NOUN
m-1112	371	61	of	of	ADP
m-1112	371	62	polygon	polygon	PROPN
m-1112	371	63	stpl	stpl	PROPN
m-1112	371	64	line	line	NOUN
m-1112	371	65	with	with	ADP
m-1112	371	66	both	both	DET
m-1112	371	67	ends	end	VERB
m-1112	371	68	free	free	ADJ
m-1112	371	69	,	,	PUNCT
m-1112	371	70	then	then	ADV
m-1112	371	71	the	the	DET
m-1112	371	72	natural	natural	ADJ
m-1112	371	73	frequencies	frequency	NOUN
m-1112	371	74	must	must	AUX
m-1112	371	75	ijo	ijo	PROPN
m-1112	371	76	international	international	ADJ
m-1112	371	77	journal	journal	PROPN
m-1112	371	78	of	of	ADP
m-1112	371	79	mathematics	mathematics	PROPN
m-1112	371	80	(	(	PUNCT
m-1112	371	81	issn	issn	PROPN
m-1112	371	82	:	:	PUNCT
m-1112	371	83	2992	2992	NUM
m-1112	371	84	-	-	SYM
m-1112	371	85	4421	4421	NUM
m-1112	371	86	)	)	PUNCT
m-1112	372	1	volume	volume	NOUN
m-1112	372	2	08	08	NUM
m-1112	373	1	|	|	ADV
m-1112	373	2	issue	issue	NOUN
m-1112	373	3	08	08	NUM
m-1112	374	1	|	|	ADV
m-1112	374	2	august	august	PROPN
m-1112	374	3	2025	2025	NUM
m-1112	374	4	|	|	ADV
m-1112	374	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	374	6	ijo	ijo	PROPN
m-1112	374	7	journals	journal	NOUN
m-1112	374	8	16	16	NUM
m-1112	374	9	the	the	DET
m-1112	374	10	fundamental	fundamental	ADJ
m-1112	374	11	particles	particle	NOUN
m-1112	374	12	origination	origination	NOUN
m-1112	374	13	mechanism	mechanism	NOUN
m-1112	374	14	in	in	ADP
m-1112	374	15	mfmf	mfmf	PROPN
m-1112	374	16	pns	pns	PROPN
m-1112	374	17	caves	cave	NOUN
m-1112	374	18	.	.	PUNCT
m-1112	375	1	be	be	AUX
m-1112	375	2	zero	zero	NUM
m-1112	375	3	because	because	SCONJ
m-1112	375	4	charges	charge	NOUN
m-1112	375	5	⊕	⊕	PROPN
m-1112	375	6	,	,	PUNCT
m-1112	375	7	⊝	⊝	CCONJ
m-1112	375	8	interchange	interchange	NOUN
m-1112	375	9	at	at	ADP
m-1112	375	10	both	both	DET
m-1112	375	11	ends	end	NOUN
m-1112	375	12	,	,	PUNCT
m-1112	375	13	a	a	DET
m-1112	375	14	,	,	PUNCT
m-1112	375	15	ka	ka	PROPN
m-1112	375	16	,	,	PUNCT
m-1112	375	17	and	and	CCONJ
m-1112	375	18	issues	issue	NOUN
m-1112	375	19	∂u	∂u	PROPN
m-1112	376	1	∂t	∂t	PROPN
m-1112	376	2	=	=	PUNCT
m-1112	376	3	0	0	NUM
m-1112	376	4	such	such	ADJ
m-1112	376	5	at	at	ADP
m-1112	376	6	x	x	X
m-1112	376	7	=	=	NOUN
m-1112	376	8	0	0	NUM
m-1112	376	9	,	,	PUNCT
m-1112	376	10	and	and	CCONJ
m-1112	376	11	as	as	ADP
m-1112	376	12	at	at	ADP
m-1112	376	13	,	,	PUNCT
m-1112	376	14	x	x	PUNCT
m-1112	377	1	=	=	PUNCT
m-1112	377	2	d	d	NOUN
m-1112	377	3	=	=	SYM
m-1112	377	4	λ	λ	X
m-1112	377	5	n(ns	n(ns	ADV
m-1112	377	6	)	)	PUNCT
m-1112	377	7	=	=	PUNCT
m-1112	377	8	aka	aka	ADV
m-1112	377	9	.	.	PUNCT
m-1112	378	1	the	the	DET
m-1112	378	2	two	two	NUM
m-1112	378	3	equations	equation	NOUN
m-1112	378	4	of	of	ADP
m-1112	378	5	the	the	DET
m-1112	378	6	below	below	ADV
m-1112	378	7	(	(	PUNCT
m-1112	378	8	5	5	NUM
m-1112	378	9	)	)	PUNCT
m-1112	378	10	correspond	correspond	VERB
m-1112	378	11	to	to	ADP
m-1112	378	12	these	these	PRON
m-1112	378	13	,	,	PUNCT
m-1112	378	14	stretched	stretch	VERB
m-1112	378	15	≡	≡	PROPN
m-1112	378	16	linear	linear	PROPN
m-1112	378	17	,	,	PUNCT
m-1112	378	18	boundary	boundary	ADJ
m-1112	378	19	conditions	condition	NOUN
m-1112	378	20	which	which	PRON
m-1112	378	21	are	be	AUX
m-1112	378	22	as	as	SCONJ
m-1112	378	23	follows	follow	VERB
m-1112	378	24	,	,	PUNCT
m-1112	378	25	{	{	PUNCT
m-1112	378	26	∂u	∂u	PROPN
m-1112	378	27	∂x	∂x	PROPN
m-1112	378	28	}	}	PUNCT
m-1112	378	29	𝑥	𝑥	X
m-1112	379	1	=	=	NOUN
m-1112	379	2	0	0	X
m-1112	379	3	=	=	PUNCT
m-1112	379	4	a	a	DET
m-1112	379	5	𝟏	𝟏	NUM
m-1112	379	6	𝐜	𝐜	NOUN
m-1112	379	7	[	[	X
m-1112	379	8	c	c	X
m-1112	379	9	sin	sin	NOUN
m-1112	379	10	wt	wt	PROPN
m-1112	380	1	+	+	CCONJ
m-1112	380	2	d	d	X
m-1112	380	3	cos	cos	ADP
m-1112	380	4	wt	wt	PROPN
m-1112	380	5	]	]	PUNCT
m-1112	380	6	=	=	SYM
m-1112	380	7	0	0	PUNCT
m-1112	380	8	{	{	PUNCT
m-1112	380	9	∂u	∂u	PROPN
m-1112	380	10	∂x	∂x	PROPN
m-1112	380	11	}	}	PUNCT
m-1112	380	12	𝑥	𝑥	X
m-1112	381	1	=	=	SYM
m-1112	381	2	0	0	NUM
m-1112	381	3	=	=	SYM
m-1112	381	4	𝐰	𝐰	NOUN
m-1112	381	5	𝐜	𝐜	NOUN
m-1112	381	6	.	.	PUNCT
m-1112	382	1	[	[	PUNCT
m-1112	382	2	a	a	DET
m-1112	382	3	cos	cos	NOUN
m-1112	382	4	|	|	ADV
m-1112	382	5	𝐰	𝐰	NOUN
m-1112	382	6	.𝐀𝐊𝐀	.𝐀𝐊𝐀	NOUN
m-1112	383	1	𝐜	𝐜	PROPN
m-1112	383	2	|	|	ADV
m-1112	383	3	b	b	PROPN
m-1112	383	4	sin|	sin|	NOUN
m-1112	383	5	𝐰	𝐰	X
m-1112	383	6	.𝐀𝐊𝐀	.𝐀𝐊𝐀	NOUN
m-1112	383	7	𝐜	𝐜	NOUN
m-1112	384	1	|	|	ADV
m-1112	384	2	]	]	PUNCT
m-1112	384	3	.	.	PUNCT
m-1112	385	1	[	[	PUNCT
m-1112	385	2	c	c	X
m-1112	385	3	sin	sin	VERB
m-1112	385	4	wt	wt	PROPN
m-1112	386	1	+	+	CCONJ
m-1112	386	2	d	d	X
m-1112	386	3	cos	cos	ADP
m-1112	386	4	wt	wt	PROPN
m-1112	386	5	]	]	PUNCT
m-1112	386	6	…	…	PUNCT
m-1112	386	7	..	..	PUNCT
m-1112	386	8	(	(	PUNCT
m-1112	386	9	5	5	X
m-1112	386	10	)	)	PUNCT
m-1112	386	11	equation	equation	NOUN
m-1112	386	12	(	(	PUNCT
m-1112	386	13	5	5	NUM
m-1112	386	14	)	)	PUNCT
m-1112	386	15	must	must	AUX
m-1112	386	16	be	be	AUX
m-1112	386	17	true	true	ADJ
m-1112	386	18	for	for	ADP
m-1112	386	19	any	any	DET
m-1112	386	20	time	time	NOUN
m-1112	386	21	t	t	NOUN
m-1112	386	22	,	,	PUNCT
m-1112	386	23	therefore	therefore	ADV
m-1112	386	24	from	from	ADP
m-1112	386	25	the	the	DET
m-1112	386	26	first	first	ADJ
m-1112	386	27	equation	equation	NOUN
m-1112	386	28	a	a	DET
m-1112	386	29	=	=	NOUN
m-1112	386	30	0	0	NUM
m-1112	386	31	.	.	PUNCT
m-1112	387	1	from	from	ADP
m-1112	387	2	the	the	DET
m-1112	387	3	second	second	ADJ
m-1112	387	4	equation	equation	NOUN
m-1112	387	5	b	b	NOUN
m-1112	387	6	must	must	AUX
m-1112	387	7	be	be	AUX
m-1112	387	8	finite	finite	ADJ
m-1112	387	9	in	in	ADP
m-1112	387	10	order	order	NOUN
m-1112	387	11	to	to	PART
m-1112	387	12	have	have	AUX
m-1112	387	13	vibration	vibration	NOUN
m-1112	387	14	and	and	CCONJ
m-1112	387	15	is	be	AUX
m-1112	387	16	satisfied	satisfied	ADJ
m-1112	387	17	when	when	SCONJ
m-1112	387	18	,	,	PUNCT
m-1112	387	19	sin	sin	VERB
m-1112	388	1	|	|	ADV
m-1112	388	2	w	w	NOUN
m-1112	388	3	.	.	PUNCT
m-1112	389	1	aka	aka	ADV
m-1112	389	2	c	c	PROPN
m-1112	389	3	|	|	NOUN
m-1112	389	4	=	=	NOUN
m-1112	389	5	0	0	NUM
m-1112	389	6	,	,	PUNCT
m-1112	389	7	or	or	CCONJ
m-1112	389	8	,	,	PUNCT
m-1112	389	9	|	|	ADV
m-1112	389	10	w.n	w.n	PROPN
m-1112	389	11	.	.	PUNCT
m-1112	390	1	aka	aka	ADV
m-1112	390	2	c	c	PROPN
m-1112	390	3	|	|	NOUN
m-1112	391	1	=	=	PUNCT
m-1112	392	1	|	|	ADV
m-1112	392	2	𝐰	𝐰	ADV
m-1112	392	3	𝐧	𝐧	NOUN
m-1112	392	4	𝐝	𝐝	NOUN
m-1112	392	5	𝐜	𝐜	NOUN
m-1112	393	1	|	|	ADV
m-1112	393	2	=	=	NOUN
m-1112	393	3	𝟐.𝐧	𝟐.𝐧	PROPN
m-1112	393	4	�	�	PROPN
m-1112	393	5	̅	̅	NOUN
m-1112	393	6	�	�	NOUN
m-1112	393	7	𝐜	𝐜	NOUN
m-1112	393	8	=	=	PROPN
m-1112	393	9	π	π	PROPN
m-1112	393	10	,	,	PUNCT
m-1112	393	11	2π	2π	PROPN
m-1112	393	12	,	,	PUNCT
m-1112	393	13	3π	3π	NOUN
m-1112	393	14	,	,	PUNCT
m-1112	393	15	...	...	PUNCT
m-1112	393	16	nπ	nπ	NOUN
m-1112	393	17	,	,	PUNCT
m-1112	393	18	.	.	PUNCT
m-1112	394	1	…	…	PUNCT
m-1112	394	2	(6	(6	PROPN
m-1112	394	3	)	)	PUNCT
m-1112	394	4	where	where	SCONJ
m-1112	394	5	,	,	PUNCT
m-1112	394	6	n	n	PRON
m-1112	394	7	=	=	NOUN
m-1112	394	8	the	the	DET
m-1112	394	9	order	order	NOUN
m-1112	394	10	of	of	ADP
m-1112	394	11	the	the	DET
m-1112	394	12	mode	mode	NOUN
m-1112	394	13	and	and	CCONJ
m-1112	394	14	the	the	DET
m-1112	394	15	equation	equation	NOUN
m-1112	394	16	of	of	ADP
m-1112	394	17	motion	motion	NOUN
m-1112	394	18	in	in	ADP
m-1112	394	19	conductor	conductor	NOUN
m-1112	394	20	becomes	become	VERB
m-1112	394	21	d	d	NOUN
m-1112	394	22	=	=	SYM
m-1112	394	23	λ	λ	X
m-1112	394	24	n(ns	n(ns	ADV
m-1112	394	25	)	)	PUNCT
m-1112	394	26	=	=	VERB
m-1112	394	27	aka	aka	ADV
m-1112	394	28	which	which	PRON
m-1112	394	29	is	be	AUX
m-1112	394	30	an	an	DET
m-1112	394	31	longitudinal	longitudinal	ADJ
m-1112	394	32	-	-	PUNCT
m-1112	394	33	vibration	vibration	NOUN
m-1112	394	34	u	u	NOUN
m-1112	395	1	=	=	PROPN
m-1112	395	2	𝐮𝟎	𝐮𝟎	PROPN
m-1112	395	3	cos	cos	ADP
m-1112	395	4	[	[	PUNCT
m-1112	395	5	𝐧	𝐧	NOUN
m-1112	395	6	𝛑	𝛑	ADP
m-1112	395	7	𝐝	𝐝	X
m-1112	395	8	]	]	X
m-1112	395	9	x	x	SYM
m-1112	395	10	sin	sin	NOUN
m-1112	395	11	[	[	PUNCT
m-1112	395	12	𝐧	𝐧	NOUN
m-1112	395	13	𝛑	𝛑	ADP
m-1112	395	14	𝐝	𝐝	X
m-1112	395	15	]	]	X
m-1112	395	16	.c	.c	NOUN
m-1112	395	17	..	..	PUNCT
m-1112	395	18	(	(	PUNCT
m-1112	395	19	7	7	X
m-1112	395	20	)	)	PUNCT
m-1112	395	21	a	a	DET
m-1112	395	22	cosine	cosine	NOUN
m-1112	395	23	-	-	PUNCT
m-1112	395	24	wave	wave	NOUN
m-1112	395	25	having	have	VERB
m-1112	395	26	n	n	PRON
m-1112	395	27	nodes	node	NOUN
m-1112	395	28	in	in	ADP
m-1112	395	29	pipe	pipe	NOUN
m-1112	395	30	d	d	NOUN
m-1112	395	31	.	.	PUNCT
m-1112	396	1	the	the	DET
m-1112	396	2	equation	equation	NOUN
m-1112	396	3	of	of	ADP
m-1112	396	4	motion	motion	NOUN
m-1112	396	5	for	for	ADP
m-1112	396	6	an	an	DET
m-1112	396	7	longitudinal	longitudinal	ADJ
m-1112	396	8	wave	wave	NOUN
m-1112	396	9	in	in	ADP
m-1112	396	10	a	a	DET
m-1112	396	11	conductor	conductor	NOUN
m-1112	396	12	d	d	NOUN
m-1112	396	13	=	=	SYM
m-1112	396	14	λ	λ	X
m-1112	396	15	n(ns	n(ns	ADV
m-1112	396	16	)	)	PUNCT
m-1112	396	17	=	=	SYM
m-1112	396	18	aka	aka	ADV
m-1112	396	19	is	be	AUX
m-1112	396	20	→	→	SYM
m-1112	396	21	y(x	y(x	PROPN
m-1112	396	22	,	,	PUNCT
m-1112	396	23	t	t	PROPN
m-1112	396	24	)	)	PUNCT
m-1112	396	25	=	=	SYM
m-1112	396	26	n.	n.	NOUN
m-1112	396	27	sin	sin	NOUN
m-1112	396	28	[	[	PUNCT
m-1112	396	29	kx	kx	X
m-1112	396	30	wt	wt	PROPN
m-1112	396	31	+	+	PROPN
m-1112	396	32	φ	φ	PROPN
m-1112	396	33	]	]	X
m-1112	396	34	←	←	PROPN
m-1112	396	35	…	…	PUNCT
m-1112	396	36	(	(	PUNCT
m-1112	396	37	8)	8)	NUM
m-1112	396	38	where	where	SCONJ
m-1112	396	39	,	,	PUNCT
m-1112	396	40	c	c	PROPN
m-1112	396	41	=	=	PUNCT
m-1112	397	1	the	the	DET
m-1112	397	2	light	light	ADJ
m-1112	397	3	velocity	velocity	NOUN
m-1112	397	4	-	-	PUNCT
m-1112	397	5	vector	vector	NOUN
m-1112	397	6	,	,	PUNCT
m-1112	397	7	n	n	NOUN
m-1112	397	8	=	=	PUNCT
m-1112	397	9	the	the	DET
m-1112	397	10	amplitude	amplitude	NOUN
m-1112	397	11	,	,	PUNCT
m-1112	397	12	w	w	NOUN
m-1112	397	13	=	=	PUNCT
m-1112	397	14	the	the	DET
m-1112	397	15	angular	angular	ADJ
m-1112	397	16	velocity	velocity	NOUN
m-1112	397	17	-	-	PUNCT
m-1112	397	18	vector	vector	NOUN
m-1112	397	19	,	,	PUNCT
m-1112	397	20	φ	φ	PROPN
m-1112	397	21	=	=	SYM
m-1112	397	22	the	the	DET
m-1112	397	23	phase	phase	NOUN
m-1112	397	24	angle	angle	NOUN
m-1112	397	25	,	,	PUNCT
m-1112	397	26	and	and	CCONJ
m-1112	397	27	k	k	X
m-1112	398	1	=	=	PUNCT
m-1112	398	2	2π	2π	NOUN
m-1112	398	3	λ	λ	NOUN
m-1112	398	4	=	=	SYM
m-1112	398	5	π	π	X
m-1112	398	6	rl	rl	ADP
m-1112	398	7	=	=	PUNCT
m-1112	398	8	propagating	propagate	VERB
m-1112	398	9	-	-	PUNCT
m-1112	398	10	energy	energy	NOUN
m-1112	398	11	constant	constant	ADJ
m-1112	398	12	=	=	ADJ
m-1112	398	13	wave	wave	NOUN
m-1112	398	14	-	-	PUNCT
m-1112	398	15	number	number	NOUN
m-1112	398	16	,	,	PUNCT
m-1112	398	17	λ	λ	X
m-1112	398	18	=	=	VERB
m-1112	398	19	the	the	DET
m-1112	398	20	wave	wave	NOUN
m-1112	398	21	length	length	NOUN
m-1112	398	22	,	,	PUNCT
m-1112	398	23	�	�	NOUN
m-1112	398	24	̅	̅	NOUN
m-1112	398	25	�	�	NOUN
m-1112	398	26	=	=	SYM
m-1112	398	27	w	w	PROPN
m-1112	398	28	k	k	NOUN
m-1112	398	29	=	=	PUNCT
m-1112	398	30	λ	λ	X
m-1112	398	31	t	t	NOUN
m-1112	398	32	=	=	SYM
m-1112	398	33	√	√	PROPN
m-1112	398	34	t	t	PROPN
m-1112	398	35	m	m	NOUN
m-1112	398	36	=	=	NOUN
m-1112	398	37	√	√	PROPN
m-1112	398	38	e	e	NOUN
m-1112	398	39	ρ	ρ	PROPN
m-1112	398	40	=	=	PUNCT
m-1112	398	41	the	the	DET
m-1112	398	42	light	light	NOUN
m-1112	398	43	-	-	PUNCT
m-1112	398	44	velocity	velocity	NOUN
m-1112	398	45	in	in	ADP
m-1112	398	46	conductors	conductor	NOUN
m-1112	398	47	.	.	PUNCT
m-1112	399	1	the	the	DET
m-1112	399	2	frequency	frequency	NOUN
m-1112	399	3	of	of	ADP
m-1112	399	4	the	the	DET
m-1112	399	5	longitudinal	longitudinal	ADJ
m-1112	399	6	wave	wave	NOUN
m-1112	399	7	is	be	AUX
m-1112	399	8	→	→	SYM
m-1112	399	9	f	f	X
m-1112	399	10	l	l	NOUN
m-1112	400	1	=	=	PUNCT
m-1112	401	1	[	[	PUNCT
m-1112	401	2	n	n	X
m-1112	401	3	]	]	PUNCT
m-1112	401	4	�	�	PROPN
m-1112	401	5	̅	̅	NOUN
m-1112	401	6	�	�	PROPN
m-1112	401	7	2λ	2λ	X
m-1112	401	8	=	=	SYM
m-1112	401	9	0	0	NUM
m-1112	401	10	,	,	PUNCT
m-1112	401	11	1.c	1.c	NUM
m-1112	401	12	2λ	2λ	NOUN
m-1112	401	13	,	,	PUNCT
m-1112	401	14	𝟐.c	𝟐.c	PROPN
m-1112	401	15	2λ	2λ	NUM
m-1112	401	16	,	,	PUNCT
m-1112	401	17	𝟑.c	𝟑.c	PROPN
m-1112	401	18	2λ	2λ	NUM
m-1112	401	19	…	…	PUNCT
m-1112	401	20	.	.	PUNCT
m-1112	401	21	.	.	PUNCT
m-1112	401	22	.	.	PUNCT
m-1112	402	1	𝐧.c	𝐧.c	PROPN
m-1112	402	2	2λ	2λ	PROPN
m-1112	402	3	,	,	PUNCT
m-1112	402	4	the	the	DET
m-1112	402	5	equation	equation	NOUN
m-1112	402	6	of	of	ADP
m-1112	402	7	motion	motion	NOUN
m-1112	402	8	of	of	ADP
m-1112	402	9	a	a	DET
m-1112	402	10	standing	standing	NOUN
m-1112	402	11	-	-	PUNCT
m-1112	402	12	wave	wave	NOUN
m-1112	402	13	in	in	ADP
m-1112	402	14	conductor	conductor	NOUN
m-1112	403	1	d	d	NOUN
m-1112	403	2	=	=	SYM
m-1112	403	3	λ	λ	X
m-1112	403	4	n(ns	n(ns	ADV
m-1112	403	5	)	)	PUNCT
m-1112	403	6	=	=	SYM
m-1112	403	7	aka	aka	ADV
m-1112	403	8	≡	≡	PROPN
m-1112	403	9	2	2	NUM
m-1112	403	10	|ra−k𝐴|	|ra−k𝐴|	PROPN
m-1112	403	11	≡	≡	PROPN
m-1112	403	12	r	r	NOUN
m-1112	403	13	l	l	PROPN
m-1112	403	14	≡	≡	PROPN
m-1112	403	15	λ	λ	PROPN
m-1112	403	16	is	be	AUX
m-1112	403	17	as	as	ADP
m-1112	403	18	,	,	PUNCT
m-1112	403	19	y(x	y(x	PROPN
m-1112	403	20	,	,	PUNCT
m-1112	403	21	t	t	PROPN
m-1112	403	22	)	)	PUNCT
m-1112	403	23	=	=	SYM
m-1112	403	24	2n	2n	NUM
m-1112	404	1	sin[k	sin[k	PROPN
m-1112	404	2	x].cos	x].cos	X
m-1112	405	1	[	[	X
m-1112	405	2	(	(	PUNCT
m-1112	405	3	w	w	NOUN
m-1112	405	4	=	=	NOUN
m-1112	405	5	2πc	2πc	ADJ
m-1112	405	6	/	/	SYM
m-1112	405	7	λ	λ	NOUN
m-1112	405	8	)	)	PUNCT
m-1112	405	9	t	t	PROPN
m-1112	405	10	]	]	PUNCT
m-1112	405	11	...	...	PUNCT
m-1112	405	12	(	(	PUNCT
m-1112	405	13	9	9	X
m-1112	405	14	)	)	PUNCT
m-1112	405	15	where	where	SCONJ
m-1112	405	16	longitudinal	longitudinal	ADJ
m-1112	405	17	frequency	frequency	NOUN
m-1112	405	18	f	f	PROPN
m-1112	405	19	l	l	NOUN
m-1112	405	20	=	=	PUNCT
m-1112	405	21	(	(	PUNCT
m-1112	405	22	n	n	PROPN
m-1112	405	23	+	+	CCONJ
m-1112	405	24	1	1	NUM
m-1112	405	25	2	2	NUM
m-1112	405	26	)	)	PUNCT
m-1112	405	27	�	�	PROPN
m-1112	405	28	̅	̅	NOUN
m-1112	405	29	�	�	PROPN
m-1112	405	30	2λ	2λ	NUM
m-1112	405	31	.	.	PUNCT
m-1112	406	1	the	the	DET
m-1112	406	2	amplitudes	amplitude	NOUN
m-1112	406	3	become	become	VERB
m-1112	406	4	zero	zero	NUM
m-1112	406	5	at	at	ADP
m-1112	406	6	y	y	PROPN
m-1112	406	7	=	=	NOUN
m-1112	406	8	0	0	PROPN
m-1112	406	9	when	when	SCONJ
m-1112	406	10	k	k	X
m-1112	406	11	x	x	X
m-1112	406	12	=	=	SYM
m-1112	406	13	0	0	NUM
m-1112	406	14	,	,	PUNCT
m-1112	406	15	which	which	PRON
m-1112	406	16	implies	imply	VERB
m-1112	406	17	k	k	PROPN
m-1112	406	18	x	x	SYM
m-1112	406	19	=	=	SYM
m-1112	406	20	n	n	PROPN
m-1112	406	21	π	π	NOUN
m-1112	406	22	,	,	PUNCT
m-1112	406	23	n	n	NOUN
m-1112	406	24	=	=	SYM
m-1112	406	25	0	0	NUM
m-1112	406	26	,	,	PUNCT
m-1112	406	27	1	1	NUM
m-1112	406	28	,	,	PUNCT
m-1112	406	29	2	2	NUM
m-1112	406	30	,	,	PUNCT
m-1112	406	31	3	3	NUM
m-1112	406	32	,	,	PUNCT
m-1112	406	33	…	…	PUNCT
m-1112	406	34	n	n	X
m-1112	406	35	.	.	PUNCT
m-1112	407	1	and	and	CCONJ
m-1112	407	2	since	since	SCONJ
m-1112	407	3	the	the	DET
m-1112	407	4	sine	sine	NOUN
m-1112	407	5	-	-	PUNCT
m-1112	407	6	function	function	NOUN
m-1112	407	7	repeats	repeat	NOUN
m-1112	407	8	itself	itself	PRON
m-1112	407	9	after	after	SCONJ
m-1112	407	10	every	every	DET
m-1112	407	11	2π	2π	PROPN
m-1112	407	12	change	change	VERB
m-1112	407	13	in	in	ADP
m-1112	407	14	angle	angle	NOUN
m-1112	407	15	which	which	PRON
m-1112	407	16	is	be	AUX
m-1112	407	17	the	the	DET
m-1112	407	18	wavelength	wavelength	NOUN
m-1112	407	19	λ	λ	PROPN
m-1112	407	20	,	,	PUNCT
m-1112	407	21	of	of	ADP
m-1112	407	22	the	the	DET
m-1112	407	23	wave	wave	NOUN
m-1112	407	24	,	,	PUNCT
m-1112	407	25	and	and	CCONJ
m-1112	407	26	from	from	ADP
m-1112	407	27	equation	equation	NOUN
m-1112	407	28	→	→	SYM
m-1112	407	29	sin[k	sin[k	PROPN
m-1112	407	30	x	x	X
m-1112	407	31	]	]	X
m-1112	407	32	≡	≡	PROPN
m-1112	407	33	sin[k	sin[k	PROPN
m-1112	407	34	x	x	PROPN
m-1112	408	1	+2nπ	+2nπ	X
m-1112	408	2	]	]	X
m-1112	408	3	≡	≡	PROPN
m-1112	408	4	sink.[x+	sink.[x+	PROPN
m-1112	408	5	2n.π	2n.π	NUM
m-1112	409	1	k	k	X
m-1112	409	2	]	]	PUNCT
m-1112	409	3	←	←	PROPN
m-1112	409	4	then	then	ADV
m-1112	409	5	for	for	ADP
m-1112	409	6	n	n	PRON
m-1112	409	7	=	=	SYM
m-1112	409	8	1	1	NUM
m-1112	409	9	,	,	PUNCT
m-1112	409	10	the	the	DET
m-1112	409	11	wavelength	wavelength	NOUN
m-1112	409	12	λ	λ	PROPN
m-1112	409	13	=	=	PUNCT
m-1112	410	1	[	[	PUNCT
m-1112	410	2	2.1.π	2.1.π	X
m-1112	410	3	k	k	X
m-1112	410	4	]	]	X
m-1112	411	1	=	=	PUNCT
m-1112	411	2	2π	2π	NOUN
m-1112	411	3	k	k	X
m-1112	411	4	,	,	PUNCT
m-1112	411	5	and	and	CCONJ
m-1112	411	6	is	be	AUX
m-1112	411	7	the	the	DET
m-1112	411	8	-	-	PUNCT
m-1112	411	9	unit	unit	NOUN
m-1112	411	10	-	-	PUNCT
m-1112	411	11	energy	energy	NOUN
m-1112	411	12	,	,	PUNCT
m-1112	411	13	the	the	DET
m-1112	411	14	quantum	quantum	NOUN
m-1112	411	15	,	,	PUNCT
m-1112	411	16	k	k	NOUN
m-1112	411	17	=	=	PUNCT
m-1112	411	18	𝟐𝛑	𝟐𝛑	X
m-1112	412	1	𝛌	𝛌	X
m-1112	412	2	.....	.....	PUNCT
m-1112	412	3	(	(	PUNCT
m-1112	412	4	10	10	NUM
m-1112	412	5	)	)	PUNCT
m-1112	412	6	and	and	CCONJ
m-1112	412	7	wave	wave	NOUN
m-1112	412	8	-	-	PUNCT
m-1112	412	9	equation	equation	NOUN
m-1112	412	10	→	→	SYM
m-1112	412	11	sin[k	sin[k	PROPN
m-1112	412	12	x	x	X
m-1112	412	13	]	]	X
m-1112	412	14	≡	≡	PROPN
m-1112	412	15	sin[k	sin[k	PROPN
m-1112	412	16	x	x	PROPN
m-1112	413	1	+2nπ	+2nπ	X
m-1112	413	2	]	]	X
m-1112	413	3	≡	≡	PROPN
m-1112	413	4	sink.[x+	sink.[x+	PROPN
m-1112	414	1	2n.π	2n.π	NUM
m-1112	414	2	k	k	X
m-1112	414	3	]	]	PUNCT
m-1112	414	4	≡	≡	PROPN
m-1112	414	5	sin	sin	PROPN
m-1112	414	6	[	[	PUNCT
m-1112	414	7	𝟐𝛑	𝟐𝛑	X
m-1112	414	8	𝛌	𝛌	X
m-1112	414	9	]	]	X
m-1112	414	10	.	.	PUNCT
m-1112	415	1	[	[	PUNCT
m-1112	415	2	x	x	X
m-1112	415	3	+	+	NUM
m-1112	415	4	λπ	λπ	X
m-1112	415	5	]	]	PUNCT
m-1112	415	6	....	....	PUNCT
m-1112	415	7	(	(	PUNCT
m-1112	415	8	10a	10a	NOUN
m-1112	415	9	)	)	PUNCT
m-1112	415	10	since	since	SCONJ
m-1112	415	11	,	,	PUNCT
m-1112	415	12	k	k	PROPN
m-1112	415	13	λ	λ	PROPN
m-1112	415	14	=	=	SYM
m-1112	415	15	2π	2π	NOUN
m-1112	415	16	constant	constant	ADJ
m-1112	415	17	and	and	CCONJ
m-1112	415	18	λ	λ	PROPN
m-1112	415	19	,	,	PUNCT
m-1112	415	20	is	be	AUX
m-1112	415	21	the	the	DET
m-1112	415	22	displacement	displacement	NOUN
m-1112	415	23	for	for	ADP
m-1112	415	24	n	n	NOUN
m-1112	415	25	=	=	SYM
m-1112	415	26	1	1	NUM
m-1112	415	27	,	,	PUNCT
m-1112	415	28	then	then	ADV
m-1112	415	29	implies	imply	VERB
m-1112	415	30	that	that	SCONJ
m-1112	415	31	k	k	PROPN
m-1112	415	32	,	,	PUNCT
m-1112	415	33	is	be	AUX
m-1112	415	34	force	force	NOUN
m-1112	415	35	and	and	CCONJ
m-1112	415	36	because	because	SCONJ
m-1112	415	37	force	force	NOUN
m-1112	415	38	x	x	SYM
m-1112	415	39	displacement	displacement	NOUN
m-1112	415	40	=	=	PUNCT
m-1112	415	41	work	work	NOUN
m-1112	415	42	≡	≡	PROPN
m-1112	415	43	energy	energy	NOUN
m-1112	415	44	≡	≡	PROPN
m-1112	415	45	motion	motion	NOUN
m-1112	415	46	,	,	PUNCT
m-1112	415	47	therefore	therefore	ADV
m-1112	415	48	k	k	PROPN
m-1112	415	49	λ	λ	PROPN
m-1112	415	50	≡	≡	PROPN
m-1112	415	51	e	e	PROPN
m-1112	415	52	≡	≡	PROPN
m-1112	415	53	constant	constant	ADJ
m-1112	415	54	≡	≡	PROPN
m-1112	415	55	the	the	DET
m-1112	415	56	unit	unit	NOUN
m-1112	415	57	-	-	PUNCT
m-1112	415	58	energy	energy	NOUN
m-1112	415	59	≡	≡	PROPN
m-1112	415	60	energyquantum	energyquantum	PROPN
m-1112	415	61	.	.	PUNCT
m-1112	416	1	in	in	ADP
m-1112	416	2	case	case	NOUN
m-1112	416	3	of	of	ADP
m-1112	416	4	energy	energy	NOUN
m-1112	416	5	equilibrium	equilibrium	NOUN
m-1112	416	6	,	,	PUNCT
m-1112	416	7	then	then	ADV
m-1112	416	8	frequency	frequency	NOUN
m-1112	416	9	in	in	ADP
m-1112	416	10	conductor	conductor	NOUN
m-1112	416	11	d	d	NOUN
m-1112	416	12	=	=	PUNCT
m-1112	416	13	aka=	aka=	PROPN
m-1112	416	14	λ	λ	PROPN
m-1112	416	15	/	/	SYM
m-1112	416	16	2	2	NUM
m-1112	416	17	and	and	CCONJ
m-1112	416	18	,	,	PUNCT
m-1112	416	19	f	f	PROPN
m-1112	416	20	l	l	NOUN
m-1112	416	21	=	=	PUNCT
m-1112	416	22	(	(	PUNCT
m-1112	416	23	n	n	PROPN
m-1112	416	24	+	+	CCONJ
m-1112	416	25	1	1	NUM
m-1112	416	26	2	2	NUM
m-1112	416	27	)	)	PUNCT
m-1112	416	28	�	�	PROPN
m-1112	416	29	̅	̅	NOUN
m-1112	416	30	�	�	PROPN
m-1112	416	31	2λ	2λ	PROPN
m-1112	416	32	≡	≡	PROPN
m-1112	416	33	0,5	0,5	PROPN
m-1112	416	34	c	c	PROPN
m-1112	416	35	2λ	2λ	NOUN
m-1112	416	36	,	,	PUNCT
m-1112	416	37	1,5.c	1,5.c	PROPN
m-1112	416	38	2λ	2λ	NOUN
m-1112	416	39	,	,	PUNCT
m-1112	416	40	2,5.c	2,5.c	PROPN
m-1112	416	41	2λ	2λ	NOUN
m-1112	416	42	,	,	PUNCT
m-1112	416	43	3,5.c	3,5.c	PROPN
m-1112	416	44	2λ	2λ	NOUN
m-1112	416	45	,	,	PUNCT
m-1112	416	46	,	,	PUNCT
m-1112	416	47	,	,	PUNCT
m-1112	416	48	,	,	PUNCT
m-1112	416	49	,	,	PUNCT
m-1112	416	50	(	(	PUNCT
m-1112	416	51	2n+1	2n+1	NOUN
m-1112	416	52	)	)	PUNCT
m-1112	416	53	.c	.c	NOUN
m-1112	417	1	2	2	NUM
m-1112	417	2	2λ	2λ	NOUN
m-1112	417	3	=	=	SYM
m-1112	417	4	1	1	NUM
m-1112	417	5	2	2	NUM
m-1112	417	6	[	[	PUNCT
m-1112	417	7	c	c	NOUN
m-1112	417	8	2λ	2λ	PROPN
m-1112	417	9	]	]	PUNCT
m-1112	417	10	,	,	PUNCT
m-1112	417	11	3	3	NUM
m-1112	417	12	2	2	NUM
m-1112	417	13	[	[	PUNCT
m-1112	417	14	c	c	NOUN
m-1112	417	15	2λ	2λ	PROPN
m-1112	417	16	]	]	PUNCT
m-1112	417	17	,	,	PUNCT
m-1112	417	18	5	5	NUM
m-1112	417	19	2	2	NUM
m-1112	417	20	|	|	NOUN
m-1112	417	21	c	c	NOUN
m-1112	417	22	2λ	2λ	NOUN
m-1112	418	1	|	|	ADV
m-1112	418	2	,	,	PUNCT
m-1112	418	3	,	,	PUNCT
m-1112	418	4	,	,	PUNCT
m-1112	418	5	,	,	PUNCT
m-1112	418	6	,	,	PUNCT
m-1112	418	7	,	,	PUNCT
m-1112	418	8	2n+1	2n+1	PROPN
m-1112	418	9	2	2	NUM
m-1112	419	1	|	|	ADV
m-1112	419	2	c	c	PROPN
m-1112	419	3	2λ	2λ	NOUN
m-1112	419	4	|	|	ADV
m-1112	419	5	the	the	DET
m-1112	419	6	wave	wave	NOUN
m-1112	419	7	is	be	AUX
m-1112	419	8	a	a	DET
m-1112	419	9	force	force	NOUN
m-1112	419	10	𝐐	𝐐	PROPN
m-1112	419	11	aka⃗⃗	aka⃗⃗	PROPN
m-1112	419	12	⃗⃗	⃗⃗	PROPN
m-1112	419	13	⃗⃗	⃗⃗	PROPN
m-1112	419	14	⃗⃗	⃗⃗	PROPN
m-1112	420	1	⃗	⃗	PROPN
m-1112	420	2	=	=	SYM
m-1112	420	3	f	f	X
m-1112	420	4	=	=	PUNCT
m-1112	420	5	|⊕	|⊕	PROPN
m-1112	421	1	=	=	SYM
m-1112	421	2	>	>	X
m-1112	421	3	aka|	aka|	PROPN
m-1112	421	4	,	,	PUNCT
m-1112	421	5	an	an	DET
m-1112	421	6	energy	energy	NOUN
m-1112	421	7	-	-	PUNCT
m-1112	421	8	vector	vector	NOUN
m-1112	421	9	|	|	NOUN
m-1112	421	10	⊕	⊕	NOUN
m-1112	421	11	𝐐	𝐐	PROPN
m-1112	421	12	⇉	⇉	PROPN
m-1112	422	1	aka⃗⃗	aka⃗⃗	PROPN
m-1112	422	2	⃗⃗	⃗⃗	PROPN
m-1112	422	3	⃗⃗	⃗⃗	PROPN
m-1112	422	4	⃗⃗	⃗⃗	PROPN
m-1112	422	5	⃗	⃗	PROPN
m-1112	422	6	|≡|	|≡|	ADP
m-1112	422	7	↔	↔	PROPN
m-1112	422	8	|	|	ADV
m-1112	422	9	that	that	PRON
m-1112	422	10	propagates	propagate	VERB
m-1112	422	11	from	from	ADP
m-1112	422	12	the	the	DET
m-1112	422	13	place	place	NOUN
m-1112	422	14	where	where	SCONJ
m-1112	422	15	it	it	PRON
m-1112	422	16	was	be	AUX
m-1112	422	17	created	create	VERB
m-1112	422	18	,	,	PUNCT
m-1112	422	19	the	the	DET
m-1112	422	20	point	point	NOUN
m-1112	422	21	a	a	PRON
m-1112	422	22	,	,	PUNCT
m-1112	422	23	so	so	CCONJ
m-1112	422	24	when	when	SCONJ
m-1112	422	25	is	be	AUX
m-1112	422	26	found	find	VERB
m-1112	422	27	an	an	DET
m-1112	422	28	obstacle	obstacle	NOUN
m-1112	422	29	at	at	ADP
m-1112	422	30	end	end	NOUN
m-1112	422	31	-	-	PUNCT
m-1112	422	32	point	point	NOUN
m-1112	422	33	𝐊𝐀	𝐊𝐀	NOUN
m-1112	422	34	then	then	ADV
m-1112	422	35	the	the	DET
m-1112	422	36	particles	particle	NOUN
m-1112	422	37	of	of	ADP
m-1112	422	38	the	the	DET
m-1112	422	39	conductor	conductor	NOUN
m-1112	422	40	medium	medium	NOUN
m-1112	422	41	oscillate	oscillate	NOUN
m-1112	422	42	perpendicular	perpendicular	ADJ
m-1112	422	43	|	|	NOUN
m-1112	422	44	↕	↕	PROPN
m-1112	422	45	||	||	NOUN
m-1112	422	46	,	,	PUNCT
m-1112	422	47	because	because	SCONJ
m-1112	422	48	it	it	PRON
m-1112	422	49	is	be	AUX
m-1112	422	50	the	the	DET
m-1112	422	51	only	only	ADJ
m-1112	422	52	exit	exit	NOUN
m-1112	422	53	,	,	PUNCT
m-1112	422	54	to	to	ADP
m-1112	422	55	the	the	DET
m-1112	422	56	direction	direction	NOUN
m-1112	422	57	of	of	ADP
m-1112	422	58	the	the	DET
m-1112	422	59	wave	wave	NOUN
m-1112	422	60	propagation	propagation	NOUN
m-1112	422	61	,	,	PUNCT
m-1112	422	62	and	and	CCONJ
m-1112	422	63	by	by	ADP
m-1112	422	64	this	this	DET
m-1112	422	65	way	way	NOUN
m-1112	422	66	the	the	DET
m-1112	422	67	motion	motion	NOUN
m-1112	422	68	continues	continue	VERB
m-1112	422	69	transverse	transverse	ADV
m-1112	422	70	as	as	ADP
m-1112	422	71	longitudinal	longitudinal	ADJ
m-1112	422	72	wave	wave	NOUN
m-1112	422	73	in	in	ADP
m-1112	422	74	conductor	conductor	NOUN
m-1112	422	75	d	d	NOUN
m-1112	422	76	=	=	PUNCT
m-1112	422	77	aka	aka	ADV
m-1112	422	78	as	as	ADP
m-1112	422	79	,	,	PUNCT
m-1112	422	80	|	|	ADV
m-1112	422	81	⇉	⇉	PUNCT
m-1112	422	82	⇈	⇈	ADJ
m-1112	422	83	|	|	ADV
m-1112	422	84	≡	≡	ADJ
m-1112	422	85	®	®	NOUN
m-1112	422	86	,	,	PUNCT
m-1112	422	87	or	or	CCONJ
m-1112	422	88	in	in	ADP
m-1112	422	89	conductor	conductor	NOUN
m-1112	422	90	d	d	NOUN
m-1112	422	91	=	=	SYM
m-1112	422	92	λ	λ	X
m-1112	422	93	n(ns	n(ns	ADV
m-1112	422	94	)	)	PUNCT
m-1112	423	1	=	=	VERB
m-1112	423	2	aka	aka	ADV
m-1112	423	3	,	,	PUNCT
m-1112	423	4	the	the	DET
m-1112	423	5	two	two	NUM
m-1112	423	6	perpendicular	perpendicular	ADJ
m-1112	423	7	energy	energy	NOUN
m-1112	423	8	-	-	PUNCT
m-1112	423	9	vectors	vector	NOUN
m-1112	423	10	,	,	PUNCT
m-1112	423	11	|k	|k	NOUN
m-1112	423	12	1	1	NUM
m-1112	423	13	x	x	SYM
m-1112	423	14	k	k	NOUN
m-1112	423	15	2|	2|	NUM
m-1112	424	1	=	=	PUNCT
m-1112	424	2	k	k	PROPN
m-1112	424	3	1	1	NUM
m-1112	424	4	┴	┴	NOUN
m-1112	424	5	2	2	NUM
m-1112	424	6	=	=	SYM
m-1112	424	7	k	k	X
m-1112	424	8	=	=	PUNCT
m-1112	424	9	𝟐𝛑	𝟐𝛑	VERB
m-1112	424	10	𝛌	𝛌	X
m-1112	424	11	=	=	PUNCT
m-1112	424	12	𝟐𝛑𝐟=𝐰	𝟐𝛑𝐟=𝐰	NOUN
m-1112	424	13	𝐜	𝐜	NOUN
m-1112	424	14	and	and	CCONJ
m-1112	424	15	longitudinal	longitudinal	ADJ
m-1112	424	16	wave	wave	NOUN
m-1112	424	17	-energy	-energy	PROPN
m-1112	424	18	→	→	SYM
m-1112	424	19	c	c	X
m-1112	424	20	{	{	PUNCT
m-1112	424	21	k	k	NOUN
m-1112	424	22	1	1	NUM
m-1112	424	23	x	x	SYM
m-1112	424	24	k	k	NOUN
m-1112	424	25	2	2	X
m-1112	424	26	}	}	PUNCT
m-1112	424	27	=	=	SYM
m-1112	424	28	2π.f	2π.f	NUM
m-1112	424	29	,	,	PUNCT
m-1112	424	30	or	or	CCONJ
m-1112	424	31	|	|	ADV
m-1112	424	32	𝐤	𝐤	NOUN
m-1112	424	33	𝟏	𝟏	PROPN
m-1112	425	1	𝐱	𝐱	PROPN
m-1112	425	2	𝐤	𝐤	X
m-1112	425	3	𝟐	𝟐	NUM
m-1112	425	4	𝟐𝝅	𝟐𝝅	NOUN
m-1112	425	5	|.c	|.c	NOUN
m-1112	425	6	=	=	SYM
m-1112	425	7	𝐜	𝐜	PART
m-1112	425	8	𝛌	𝛌	NOUN
m-1112	425	9	=	=	SYM
m-1112	425	10	f	f	PROPN
m-1112	425	11	.	.	PUNCT
m-1112	426	1	in	in	ADP
m-1112	426	2	figure	figure	NOUN
m-1112	426	3	-3	-3	PUNCT
m-1112	426	4	and	and	CCONJ
m-1112	426	5	-9	-9	PROPN
m-1112	426	6	ijo	ijo	PROPN
m-1112	426	7	international	international	PROPN
m-1112	426	8	journal	journal	PROPN
m-1112	426	9	of	of	ADP
m-1112	426	10	mathematics	mathematics	PROPN
m-1112	426	11	(	(	PUNCT
m-1112	426	12	issn	issn	PROPN
m-1112	426	13	:	:	PUNCT
m-1112	426	14	2992	2992	NUM
m-1112	426	15	-	-	SYM
m-1112	426	16	4421	4421	NUM
m-1112	426	17	)	)	PUNCT
m-1112	426	18	volume	volume	NOUN
m-1112	426	19	08	08	NUM
m-1112	427	1	|	|	ADV
m-1112	427	2	issue	issue	NOUN
m-1112	427	3	08	08	NUM
m-1112	428	1	|	|	ADV
m-1112	428	2	august	august	PROPN
m-1112	428	3	2025	2025	NUM
m-1112	428	4	|	|	ADV
m-1112	428	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	428	6	ijo	ijo	PROPN
m-1112	428	7	journals	journal	NOUN
m-1112	428	8	17	17	NUM
m-1112	428	9	the	the	DET
m-1112	428	10	fundamental	fundamental	ADJ
m-1112	428	11	particles	particle	NOUN
m-1112	428	12	origination	origination	NOUN
m-1112	428	13	mechanism	mechanism	NOUN
m-1112	428	14	in	in	ADP
m-1112	428	15	mfmf	mfmf	PROPN
m-1112	428	16	pns	pns	PROPN
m-1112	428	17	caves	cave	NOUN
m-1112	428	18	.	.	PUNCT
m-1112	429	1	the	the	DET
m-1112	429	2	obstacle	obstacle	NOUN
m-1112	429	3	at	at	ADP
m-1112	429	4	edge	edge	NOUN
m-1112	429	5	𝐊𝐀	𝐊𝐀	PROPN
m-1112	429	6	point	point	NOUN
m-1112	429	7	,	,	PUNCT
m-1112	429	8	is	be	AUX
m-1112	429	9	the	the	DET
m-1112	429	10	presentation	presentation	NOUN
m-1112	429	11	of	of	ADP
m-1112	429	12	the	the	DET
m-1112	429	13	,	,	PUNCT
m-1112	429	14	⊕	⊕	NOUN
m-1112	429	15	constituent	constituent	NOUN
m-1112	429	16	and	and	CCONJ
m-1112	429	17	the	the	DET
m-1112	429	18	lack	lack	NOUN
m-1112	429	19	of	of	ADP
m-1112	429	20	⊝	⊝	NUM
m-1112	429	21	constituent	constituent	NOUN
m-1112	429	22	.	.	PUNCT
m-1112	430	1	the	the	DET
m-1112	430	2	transverse	transverse	NOUN
m-1112	430	3	propagating	propagating	NOUN
m-1112	430	4	-	-	PUNCT
m-1112	430	5	wave	wave	NOUN
m-1112	430	6	,	,	PUNCT
m-1112	430	7	or	or	CCONJ
m-1112	430	8	the	the	DET
m-1112	430	9	moving	move	VERB
m-1112	430	10	energy	energy	NOUN
m-1112	430	11	-vector	-vector	NOUN
m-1112	430	12	|⊕	|⊕	PROPN
m-1112	430	13	𝐐	𝐐	PROPN
m-1112	430	14	⇈	⇈	PROPN
m-1112	430	15	aka⃗⃗	aka⃗⃗	PROPN
m-1112	430	16	⃗⃗	⃗⃗	PROPN
m-1112	430	17	⃗⃗	⃗⃗	PROPN
m-1112	430	18	⃗⃗	⃗⃗	PROPN
m-1112	430	19	⃗	⃗	PROPN
m-1112	430	20	|	|	NOUN
m-1112	430	21	=	=	PUNCT
m-1112	430	22	|	|	NOUN
m-1112	430	23	↕	↕	PROPN
m-1112	430	24	|	|	PROPN
m-1112	430	25	at	at	ADP
m-1112	430	26	node	node	PROPN
m-1112	430	27	ka	ka	PROPN
m-1112	430	28	,	,	PUNCT
m-1112	430	29	and	and	CCONJ
m-1112	430	30	with	with	ADP
m-1112	430	31	the	the	DET
m-1112	430	32	energy	energy	NOUN
m-1112	430	33	-	-	PUNCT
m-1112	430	34	vector	vector	NOUN
m-1112	430	35	|	|	NOUN
m-1112	430	36	⊕	⊕	NOUN
m-1112	430	37	𝐐	𝐐	PROPN
m-1112	430	38	⇉	⇉	PROPN
m-1112	431	1	aka⃗⃗	aka⃗⃗	PROPN
m-1112	431	2	⃗⃗	⃗⃗	PROPN
m-1112	431	3	⃗⃗	⃗⃗	PROPN
m-1112	431	4	⃗⃗	⃗⃗	PROPN
m-1112	431	5	⃗	⃗	PROPN
m-1112	431	6	|	|	ADV
m-1112	431	7	≡	≡	PROPN
m-1112	431	8	|↔|	|↔|	PROPN
m-1112	431	9	at	at	ADP
m-1112	431	10	node	node	PROPN
m-1112	431	11	a	a	PRON
m-1112	431	12	,	,	PUNCT
m-1112	431	13	consist	consist	VERB
m-1112	431	14	the	the	DET
m-1112	431	15	electromagnetic	electromagnetic	ADJ
m-1112	431	16	wave	wave	NOUN
m-1112	431	17	in	in	ADP
m-1112	431	18	d	d	PROPN
m-1112	431	19	=	=	SYM
m-1112	431	20	aka=	aka=	PROPN
m-1112	431	21	2r	2r	NUM
m-1112	431	22	conductor	conductor	NOUN
m-1112	431	23	.	.	PUNCT
m-1112	432	1	the	the	DET
m-1112	432	2	energy	energy	NOUN
m-1112	432	3	in	in	ADP
m-1112	432	4	this	this	DET
m-1112	432	5	stationary	stationary	ADJ
m-1112	432	6	wave	wave	NOUN
m-1112	432	7	of	of	ADP
m-1112	432	8	wavelength	wavelength	NOUN
m-1112	432	9	λ	λ	PROPN
m-1112	432	10	=	=	SYM
m-1112	432	11	2d	2d	PROPN
m-1112	432	12	is	be	AUX
m-1112	432	13	,	,	PUNCT
m-1112	432	14	e	e	X
m-1112	432	15	=	=	SYM
m-1112	432	16	h	h	NOUN
m-1112	433	1	f	f	NOUN
m-1112	433	2	l	l	NOUN
m-1112	434	1	=	=	PUNCT
m-1112	434	2	h	h	NOUN
m-1112	434	3	2n+1	2n+1	NOUN
m-1112	434	4	2	2	NUM
m-1112	435	1	|	|	ADV
m-1112	435	2	c	c	NOUN
m-1112	435	3	2λ	2λ	NOUN
m-1112	436	1	|	|	ADV
m-1112	436	2	=	=	SYM
m-1112	436	3	2n+1	2n+1	PROPN
m-1112	436	4	2	2	NUM
m-1112	436	5	|	|	ADV
m-1112	436	6	hc	hc	ADP
m-1112	436	7	2λ	2λ	NOUN
m-1112	437	1	|	|	ADV
m-1112	437	2	=	=	SYM
m-1112	438	1	|	|	NOUN
m-1112	438	2	3.h.c	3.h.c	NUM
m-1112	438	3	4λ	4λ	NOUN
m-1112	438	4	|	|	ADV
m-1112	438	5	…	…	PUNCT
m-1112	438	6	……	……	NOUN
m-1112	438	7	(	(	PUNCT
m-1112	438	8	11	11	NUM
m-1112	438	9	)	)	PUNCT
m-1112	438	10	and	and	CCONJ
m-1112	438	11	from	from	ADP
m-1112	438	12	relation	relation	NOUN
m-1112	438	13	λ	λ	NOUN
m-1112	438	14	=	=	PUNCT
m-1112	438	15	c	c	NOUN
m-1112	438	16	t	t	NOUN
m-1112	439	1	=	=	PUNCT
m-1112	439	2	c	c	NOUN
m-1112	439	3	f	f	X
m-1112	440	1	=	=	SYM
m-1112	440	2	2π	2π	PROPN
m-1112	441	1	k	k	NOUN
m-1112	441	2	,	,	PUNCT
m-1112	441	3	then	then	ADV
m-1112	441	4	k	k	X
m-1112	441	5	=	=	PUNCT
m-1112	441	6	2π	2π	NOUN
m-1112	441	7	λ	λ	NOUN
m-1112	441	8	=	=	PUNCT
m-1112	441	9	2πf	2πf	NOUN
m-1112	441	10	c	c	NOUN
m-1112	441	11	=	=	PUNCT
m-1112	441	12	w	w	PROPN
m-1112	441	13	c	c	NOUN
m-1112	441	14	=	=	SYM
m-1112	441	15	|	|	ADV
m-1112	441	16	v̅	v̅	NOUN
m-1112	441	17	c	c	NOUN
m-1112	441	18	|.|	|.|	NOUN
m-1112	441	19	1	1	NUM
m-1112	441	20	r	r	NOUN
m-1112	441	21	|	|	NOUN
m-1112	441	22	=	=	PUNCT
m-1112	442	1	|	|	ADV
m-1112	442	2	v̅	v̅	NOUN
m-1112	442	3	c	c	NOUN
m-1112	442	4	|.|	|.|	NOUN
m-1112	442	5	2	2	NUM
m-1112	442	6	λ	λ	NOUN
m-1112	442	7	|	|	ADV
m-1112	442	8	,	,	PUNCT
m-1112	442	9	or	or	CCONJ
m-1112	442	10	the	the	DET
m-1112	442	11	propagating	propagate	VERB
m-1112	442	12	-	-	PUNCT
m-1112	442	13	transverse	transverse	NOUN
m-1112	442	14	-	-	PUNCT
m-1112	442	15	wave	wave	NOUN
m-1112	442	16	carries	carry	VERB
m-1112	442	17	the	the	DET
m-1112	442	18	standing	standing	NOUN
m-1112	442	19	-	-	PUNCT
m-1112	442	20	wave	wave	NOUN
m-1112	442	21	-	-	PUNCT
m-1112	442	22	energy	energy	NOUN
m-1112	442	23	-	-	PUNCT
m-1112	442	24	constant	constant	ADJ
m-1112	442	25	-	-	PUNCT
m-1112	442	26	magnitude	magnitude	NOUN
m-1112	442	27	constant	constant	ADJ
m-1112	442	28	-	-	PUNCT
m-1112	442	29	motion	motion	NOUN
m-1112	442	30	k	k	NOUN
m-1112	442	31	=	=	PUNCT
m-1112	442	32	2π	2π	NOUN
m-1112	442	33	λ	λ	NOUN
m-1112	442	34	=	=	PUNCT
m-1112	442	35	2πf	2πf	NOUN
m-1112	442	36	c	c	NOUN
m-1112	443	1	=	=	PUNCT
m-1112	443	2	w	w	PROPN
m-1112	443	3	c	c	NOUN
m-1112	443	4	=	=	SYM
m-1112	444	1	|	|	ADV
m-1112	444	2	v̅	v̅	NOUN
m-1112	444	3	c	c	NOUN
m-1112	445	1	|	|	NOUN
m-1112	445	2	.	.	PUNCT
m-1112	446	1	[	[	PUNCT
m-1112	446	2	2	2	NUM
m-1112	446	3	r[a−ka	r[a−ka	NOUN
m-1112	446	4	]	]	PUNCT
m-1112	446	5	]	]	PUNCT
m-1112	446	6	.	.	PUNCT
m-1112	447	1	…	…	PUNCT
m-1112	447	2	...	...	PUNCT
m-1112	447	3	(12	(12	SYM
m-1112	447	4	)	)	PUNCT
m-1112	447	5	the	the	DET
m-1112	447	6	two	two	NUM
m-1112	447	7	perpendicular	perpendicular	ADJ
m-1112	447	8	energy	energy	NOUN
m-1112	447	9	-	-	PUNCT
m-1112	447	10	vectors	vector	NOUN
m-1112	447	11	,	,	PUNCT
m-1112	447	12	|𝐐	|𝐐	VERB
m-1112	447	13	⇉	⇉	PROPN
m-1112	447	14	aka⃗⃗	aka⃗⃗	PROPN
m-1112	447	15	⃗⃗	⃗⃗	PROPN
m-1112	447	16	⃗⃗	⃗⃗	PROPN
m-1112	447	17	⃗⃗	⃗⃗	PROPN
m-1112	448	1	⃗	⃗	PROPN
m-1112	448	2	=	=	SYM
m-1112	448	3	↔	↔	PROPN
m-1112	448	4	|	|	ADV
m-1112	448	5	and	and	CCONJ
m-1112	448	6	|𝐐	|𝐐	VERB
m-1112	448	7	⇈	⇈	PROPN
m-1112	448	8	aka⃗⃗	aka⃗⃗	PROPN
m-1112	448	9	⃗⃗	⃗⃗	PROPN
m-1112	448	10	⃗⃗	⃗⃗	PROPN
m-1112	448	11	⃗⃗	⃗⃗	PROPN
m-1112	448	12	⃗	⃗	PROPN
m-1112	448	13	=	=	SYM
m-1112	448	14	↕	↕	PROPN
m-1112	448	15	|	|	ADV
m-1112	448	16	,	,	PUNCT
m-1112	448	17	in	in	ADP
m-1112	448	18	conductor	conductor	NOUN
m-1112	448	19	d	d	NOUN
m-1112	448	20	,	,	PUNCT
m-1112	448	21	of	of	ADP
m-1112	448	22	this	this	DET
m-1112	448	23	moving	move	VERB
m-1112	448	24	energy	energy	NOUN
m-1112	448	25	form	form	NOUN
m-1112	448	26	the	the	DET
m-1112	448	27	energy	energy	NOUN
m-1112	448	28	-	-	PUNCT
m-1112	448	29	square	square	NOUN
m-1112	448	30	,	,	PUNCT
m-1112	448	31	{	{	PUNCT
m-1112	448	32	|	|	ADV
m-1112	448	33	↔	↔	PROPN
m-1112	448	34	|.|	|.|	NOUN
m-1112	448	35	↕	↕	PROPN
m-1112	448	36	|≡|𝐐	|≡|𝐐	NUM
m-1112	448	37	⇉	⇉	PROPN
m-1112	448	38	|}.{|	|}.{|	X
m-1112	449	1	𝐐	𝐐	PROPN
m-1112	449	2	⇈	⇈	NOUN
m-1112	449	3	|	|	PRON
m-1112	449	4	}	}	PUNCT
m-1112	449	5	≡	≡	PROPN
m-1112	449	6	u0	u0	NOUN
m-1112	449	7	,	,	PUNCT
m-1112	449	8	on	on	ADP
m-1112	449	9	conductors	conductor	NOUN
m-1112	449	10	aka	aka	ADV
m-1112	449	11	.	.	PUNCT
m-1112	450	1	with	with	ADP
m-1112	450	2	conductors	conductor	NOUN
m-1112	450	3	pivot	pivot	NOUN
m-1112	450	4	-	-	PUNCT
m-1112	450	5	axis	axis	NOUN
m-1112	450	6	propelled	propel	VERB
m-1112	450	7	on	on	ADP
m-1112	450	8	their	their	PRON
m-1112	450	9	merging	merge	VERB
m-1112	450	10	-resultant	-resultant	ADJ
m-1112	450	11	-axis	-axis	NOUN
m-1112	450	12	of	of	ADP
m-1112	450	13	direction	direction	NOUN
m-1112	450	14	|	|	ADV
m-1112	450	15	⇉	⇉	PROPN
m-1112	451	1	⇈	⇈	NUM
m-1112	451	2	≡	≡	PROPN
m-1112	451	3	⤱|	⤱|	PROPN
m-1112	451	4	.	.	PUNCT
m-1112	452	1	in	in	ADP
m-1112	452	2	case	case	NOUN
m-1112	452	3	of	of	ADP
m-1112	452	4	an	an	DET
m-1112	452	5	closed	closed	ADJ
m-1112	452	6	conductor	conductor	NOUN
m-1112	452	7	above	above	ADP
m-1112	452	8	motion	motion	NOUN
m-1112	452	9	with	with	ADP
m-1112	452	10	energy	energy	NOUN
m-1112	452	11	=	=	SYM
m-1112	452	12	k	k	NOUN
m-1112	452	13	=	=	PUNCT
m-1112	452	14	2π	2π	NOUN
m-1112	452	15	λ	λ	NOUN
m-1112	452	16	=	=	PUNCT
m-1112	452	17	2πf	2πf	NOUN
m-1112	452	18	c	c	X
m-1112	452	19	=	=	PUNCT
m-1112	452	20	w	w	PROPN
m-1112	452	21	c	c	NOUN
m-1112	452	22	,	,	PUNCT
m-1112	452	23	and	and	CCONJ
m-1112	452	24	with	with	ADP
m-1112	452	25	velocity	velocity	NOUN
m-1112	452	26	�	�	NOUN
m-1112	452	27	̅	̅	NOUN
m-1112	452	28	�	�	NOUN
m-1112	452	29	=	=	SYM
m-1112	452	30	w	w	PROPN
m-1112	452	31	k	k	NOUN
m-1112	452	32	=	=	PUNCT
m-1112	452	33	λ	λ	X
m-1112	452	34	t	t	NOUN
m-1112	452	35	=	=	SYM
m-1112	452	36	√	√	PROPN
m-1112	452	37	t	t	PROPN
m-1112	452	38	m	m	NOUN
m-1112	452	39	=	=	NOUN
m-1112	452	40	√	√	PROPN
m-1112	452	41	e	e	PROPN
m-1112	452	42	ρ	ρ	PROPN
m-1112	452	43	,	,	PUNCT
m-1112	452	44	consists	consist	VERB
m-1112	452	45	the	the	DET
m-1112	452	46	stationary	stationary	ADJ
m-1112	452	47	–	–	PUNCT
m-1112	452	48	energy	energy	NOUN
m-1112	452	49	-	-	PUNCT
m-1112	452	50	storage	storage	NOUN
m-1112	452	51	with	with	ADP
m-1112	452	52	fundamental	fundamental	ADJ
m-1112	452	53	frequency	frequency	NOUN
m-1112	452	54	f	f	NOUN
m-1112	452	55	1	1	NUM
m-1112	452	56	=	=	SYM
m-1112	452	57	(	(	PUNCT
m-1112	452	58	n	n	PROPN
m-1112	452	59	+	+	CCONJ
m-1112	452	60	1	1	NUM
m-1112	452	61	2	2	NUM
m-1112	452	62	)	)	PUNCT
m-1112	452	63	�	�	PROPN
m-1112	452	64	̅	̅	NOUN
m-1112	452	65	�	�	PROPN
m-1112	452	66	2λ	2λ	PROPN
m-1112	452	67	≡	≡	PROPN
m-1112	452	68	3.	3.	NUM
m-1112	452	69	�	�	PROPN
m-1112	452	70	̅	̅	NOUN
m-1112	452	71	�	�	NOUN
m-1112	452	72	4	4	NUM
m-1112	452	73	λ	λ	SYM
m-1112	452	74	≡	≡	PROPN
m-1112	452	75	3.𝛔	3.𝛔	NUM
m-1112	452	76	𝚽	𝚽	NOUN
m-1112	452	77	4	4	NUM
m-1112	452	78	λ	λ	NOUN
m-1112	452	79	…	…	PUNCT
m-1112	452	80	.	.	PUNCT
m-1112	452	81	…	…	PUNCT
m-1112	452	82	(13	(13	X
m-1112	452	83	)	)	PUNCT
m-1112	452	84	.	.	PUNCT
m-1112	453	1	the	the	DET
m-1112	453	2	obstacle	obstacle	NOUN
m-1112	453	3	at	at	ADP
m-1112	453	4	ka	ka	PROPN
m-1112	453	5	point	point	PROPN
m-1112	453	6	is	be	AUX
m-1112	453	7	the	the	DET
m-1112	453	8	⊕	⊕	PROPN
m-1112	453	9	constituent	constituent	NOUN
m-1112	453	10	which	which	PRON
m-1112	453	11	executes	execute	VERB
m-1112	453	12	an	an	DET
m-1112	453	13	coulomb	coulomb	NOUN
m-1112	453	14	force	force	NOUN
m-1112	453	15	f	f	PROPN
m-1112	454	1	[	[	X
m-1112	454	2	+	+	X
m-1112	454	3	↔	↔	PROPN
m-1112	454	4	+	+	NOUN
m-1112	454	5	]	]	X
m-1112	454	6	=	=	PUNCT
m-1112	455	1	[	[	X
m-1112	455	2	⊕↔⊕	⊕↔⊕	X
m-1112	455	3	]	]	X
m-1112	455	4	r²	r²	NOUN
m-1112	455	5	=	=	PUNCT
m-1112	456	1	[	[	X
m-1112	456	2	σ.σ	σ.σ	X
m-1112	456	3	]	]	X
m-1112	456	4	r²	r²	NOUN
m-1112	456	5	=	=	PUNCT
m-1112	456	6	|	|	NOUN
m-1112	456	7	σ	σ	PROPN
m-1112	456	8	.	.	PUNCT
m-1112	457	1	r	r	NOUN
m-1112	457	2	|	|	NOUN
m-1112	457	3	2	2	NUM
m-1112	457	4	=|	=|	NOUN
m-1112	457	5	e.	e.	PROPN
m-1112	457	6	r	r	NOUN
m-1112	458	1	|	|	ADV
m-1112	458	2	2	2	NUM
m-1112	458	3	=	=	SYM
m-1112	459	1	|	|	ADV
m-1112	459	2	2πf	2πf	NOUN
m-1112	459	3	φ	φ	NUM
m-1112	459	4	|	|	NOUN
m-1112	459	5	2	2	NUM
m-1112	459	6	=	=	SYM
m-1112	460	1	|	|	ADV
m-1112	460	2	w	w	NOUN
m-1112	460	3	φ	φ	NOUN
m-1112	460	4	|	|	ADV
m-1112	460	5	2	2	NUM
m-1112	460	6	.	.	PUNCT
m-1112	461	1	the	the	DET
m-1112	461	2	energy	energy	NOUN
m-1112	461	3	k	k	PROPN
m-1112	461	4	at	at	ADP
m-1112	461	5	point	point	NOUN
m-1112	461	6	ka	ka	PROPN
m-1112	461	7	is	be	AUX
m-1112	461	8	the	the	DET
m-1112	461	9	total	total	ADJ
m-1112	461	10	mass	mass	PROPN
m-1112	461	11	mt	mt	PROPN
m-1112	461	12	of	of	ADP
m-1112	461	13	conductor	conductor	PROPN
m-1112	462	1	d	d	NOUN
m-1112	462	2	=	=	PUNCT
m-1112	462	3	aka	aka	ADV
m-1112	462	4	=	=	NOUN
m-1112	462	5	r	r	NOUN
m-1112	462	6	=	=	PUNCT
m-1112	462	7	λ	λ	X
m-1112	462	8	n(ns	n(ns	ADV
m-1112	462	9	)	)	PUNCT
m-1112	462	10	equal	equal	ADJ
m-1112	462	11	to	to	ADP
m-1112	462	12	the	the	DET
m-1112	462	13	moment	moment	NOUN
m-1112	462	14	of	of	ADP
m-1112	462	15	inertia	inertia	NOUN
m-1112	462	16	jt	jt	PROPN
m-1112	462	17	=	=	PROPN
m-1112	462	18	m.r²	m.r²	NUM
m-1112	462	19	3	3	NUM
m-1112	462	20	,	,	PUNCT
m-1112	462	21	where	where	SCONJ
m-1112	462	22	m	m	NOUN
m-1112	462	23	is	be	AUX
m-1112	462	24	the	the	DET
m-1112	462	25	stiffness	stiffness	NOUN
m-1112	462	26	per	per	ADP
m-1112	462	27	meter	meter	NOUN
m-1112	462	28	of	of	ADP
m-1112	462	29	conductor	conductor	NOUN
m-1112	462	30	r	r	NOUN
m-1112	462	31	.	.	PUNCT
m-1112	463	1	the	the	DET
m-1112	463	2	impact	impact	NOUN
m-1112	463	3	of	of	ADP
m-1112	463	4	this	this	DET
m-1112	463	5	mass	mass	NOUN
m-1112	463	6	at	at	ADP
m-1112	463	7	the	the	DET
m-1112	463	8	end	end	NOUN
m-1112	463	9	-	-	PUNCT
m-1112	463	10	point	point	NOUN
m-1112	463	11	is	be	AUX
m-1112	463	12	the	the	DET
m-1112	463	13	energy	energy	NOUN
m-1112	463	14	=	=	PUNCT
m-1112	463	15	j	j	PROPN
m-1112	463	16	w	w	NOUN
m-1112	463	17	and	and	CCONJ
m-1112	463	18	impact	impact	NOUN
m-1112	463	19	→	→	SYM
m-1112	463	20	m	m	NOUN
m-1112	463	21	v	v	NOUN
m-1112	463	22	=	=	SYM
m-1112	463	23	j	j	PROPN
m-1112	463	24	w	w	PROPN
m-1112	463	25	r	r	NOUN
m-1112	463	26	=	=	PUNCT
m-1112	463	27	[	[	PUNCT
m-1112	463	28	m.r²	m.r²	X
m-1112	463	29	3	3	NUM
m-1112	463	30	]	]	PUNCT
m-1112	463	31	.	.	PUNCT
m-1112	464	1	wr	wr	NOUN
m-1112	464	2	,	,	PUNCT
m-1112	464	3	or	or	CCONJ
m-1112	464	4	velocity	velocity	NOUN
m-1112	464	5	after	after	ADP
m-1112	464	6	impact	impact	NOUN
m-1112	464	7	velocity	velocity	NOUN
m-1112	464	8	→	→	SYM
m-1112	464	9	v	v	NOUN
m-1112	464	10	=	=	SYM
m-1112	464	11	[	[	PUNCT
m-1112	464	12	r³	r³	PROPN
m-1112	464	13	3	3	NUM
m-1112	464	14	]	]	PUNCT
m-1112	464	15	.2πf	.2πf	PUNCT
m-1112	465	1	=	=	PUNCT
m-1112	465	2	[	[	PUNCT
m-1112	465	3	2πf.r³	2πf.r³	NUM
m-1112	465	4	3	3	NUM
m-1112	465	5	]	]	PUNCT
m-1112	465	6	.......	.......	PUNCT
m-1112	465	7	(	(	PUNCT
m-1112	465	8	14	14	NUM
m-1112	465	9	)	)	PUNCT
m-1112	465	10	coulomb	coulomb	NOUN
m-1112	465	11	force	force	NOUN
m-1112	465	12	with	with	ADP
m-1112	465	13	fundamental	fundamental	ADJ
m-1112	465	14	frequency	frequency	NOUN
m-1112	465	15	becomes	become	VERB
m-1112	465	16	f	f	NOUN
m-1112	466	1	[	[	X
m-1112	466	2	+	+	NOUN
m-1112	466	3	↔+	↔+	NOUN
m-1112	466	4	]	]	X
m-1112	466	5	=	=	PUNCT
m-1112	466	6	|	|	ADV
m-1112	466	7	2πf	2πf	NOUN
m-1112	466	8	.	.	PUNCT
m-1112	467	1	φ	φ	PROPN
m-1112	467	2	|	|	ADJ
m-1112	467	3	2	2	NUM
m-1112	467	4	=	=	PUNCT
m-1112	467	5	[	[	PUNCT
m-1112	467	6	2π	2π	PROPN
m-1112	467	7	φ	φ	NUM
m-1112	467	8	|	|	PROPN
m-1112	467	9	3.	3.	NUM
m-1112	467	10	�	�	NOUN
m-1112	467	11	̅	̅	NOUN
m-1112	467	12	�	�	NOUN
m-1112	467	13	4	4	NUM
m-1112	467	14	λ	λ	NOUN
m-1112	467	15	|	|	NOUN
m-1112	467	16	]	]	X
m-1112	467	17	²	²	PROPN
m-1112	467	18	=	=	SYM
m-1112	467	19	|	|	ADP
m-1112	467	20	3πv	3πv	ADJ
m-1112	467	21	2λφ	2λφ	NOUN
m-1112	468	1	|	|	CCONJ
m-1112	468	2	2	2	NUM
m-1112	468	3	…	…	SYM
m-1112	468	4	…	…	SYM
m-1112	468	5	.(15	.(15	X
m-1112	468	6	)	)	PUNCT
m-1112	469	1	placing	place	VERB
m-1112	469	2	velocity	velocity	NOUN
m-1112	469	3	after	after	ADP
m-1112	469	4	impact	impact	NOUN
m-1112	469	5	(	(	PUNCT
m-1112	469	6	14	14	NUM
m-1112	469	7	)	)	PUNCT
m-1112	469	8	in	in	ADP
m-1112	469	9	equation	equation	NOUN
m-1112	469	10	(	(	PUNCT
m-1112	469	11	15	15	NUM
m-1112	469	12	)	)	PUNCT
m-1112	469	13	then	then	ADV
m-1112	469	14	the	the	DET
m-1112	469	15	concentrated	concentrated	ADJ
m-1112	469	16	energy	energy	NOUN
m-1112	469	17	at	at	ADP
m-1112	469	18	point	point	NOUN
m-1112	469	19	ka	ka	PROPN
m-1112	469	20	is	be	AUX
m-1112	469	21	f	f	PROPN
m-1112	470	1	[	[	X
m-1112	470	2	+	+	NOUN
m-1112	470	3	↔+	↔+	NOUN
m-1112	470	4	]	]	X
m-1112	470	5	=	=	SYM
m-1112	470	6	{	{	PUNCT
m-1112	470	7	3π	3π	NUM
m-1112	470	8	2λφ	2λφ	NOUN
m-1112	471	1	[	[	PUNCT
m-1112	471	2	2πf.r³	2πf.r³	NUM
m-1112	471	3	3	3	NUM
m-1112	471	4	]	]	PUNCT
m-1112	471	5	}	}	PUNCT
m-1112	471	6	²	²	PROPN
m-1112	471	7	=	=	SYM
m-1112	471	8	|	|	NOUN
m-1112	471	9	π2r4f	π2r4f	PUNCT
m-1112	471	10	λr.φ	λr.φ	NOUN
m-1112	471	11	|	|	CCONJ
m-1112	471	12	2	2	NUM
m-1112	471	13	=|	=|	NOUN
m-1112	471	14	b=(π2r4f	b=(π2r4f	PROPN
m-1112	471	15	)	)	PUNCT
m-1112	471	16	λr.φ	λr.φ	NOUN
m-1112	471	17	|	|	ADV
m-1112	471	18	2	2	NUM
m-1112	471	19	=|	=|	NOUN
m-1112	471	20	�	�	NOUN
m-1112	471	21	̅	̅	NOUN
m-1112	471	22	�	�	NOUN
m-1112	471	23	λr.φ	λr.φ	NOUN
m-1112	471	24	|	|	ADV
m-1112	471	25	2	2	NUM
m-1112	471	26	≡	≡	ADJ
m-1112	471	27	angular	angular	ADJ
m-1112	471	28	-	-	PUNCT
m-1112	471	29	momentum	momentum	NOUN
m-1112	471	30	≡	≡	PROPN
m-1112	471	31	spin	spin	NOUN
m-1112	471	32	…	…	PUNCT
m-1112	471	33	...	...	PUNCT
m-1112	471	34	(	(	PUNCT
m-1112	471	35	16	16	NUM
m-1112	471	36	)	)	PUNCT
m-1112	471	37	in	in	ADP
m-1112	471	38	short	short	ADJ
m-1112	471	39	-	-	PUNCT
m-1112	471	40	distance	distance	NOUN
m-1112	471	41	conductor	conductor	NOUN
m-1112	472	1	d	d	NOUN
m-1112	472	2	=	=	PUNCT
m-1112	472	3	6,195543.10−7	6,195543.10−7	NUM
m-1112	472	4	m	m	PRON
m-1112	472	5	,	,	PUNCT
m-1112	472	6	the	the	DET
m-1112	472	7	magnetic	magnetic	ADJ
m-1112	472	8	-	-	PUNCT
m-1112	472	9	field	field	NOUN
m-1112	472	10	b̅	b̅	NOUN
m-1112	472	11	=	=	PUNCT
m-1112	472	12	m.v	m.v	PROPN
m-1112	472	13	q̅	q̅	PROPN
m-1112	472	14	r	r	NOUN
m-1112	472	15	=	=	SYM
m-1112	472	16	9.10−31kg.2,9979.108	9.10−31kg.2,9979.108	PROPN
m-1112	472	17	𝑚/𝑠	𝑚/𝑠	NOUN
m-1112	472	18	1,6.10−19c.[6,195543.10−7	1,6.10−19c.[6,195543.10−7	NUM
m-1112	472	19	]	]	PUNCT
m-1112	472	20	=	=	SYM
m-1112	472	21	2,718088.1013	2,718088.1013	NUM
m-1112	472	22	telsa	telsa	NOUN
m-1112	472	23	,	,	PUNCT
m-1112	472	24	which	which	PRON
m-1112	472	25	is	be	AUX
m-1112	472	26	perpendicular	perpendicular	ADJ
m-1112	472	27	,	,	PUNCT
m-1112	472	28	normal	normal	ADJ
m-1112	472	29	,	,	PUNCT
m-1112	472	30	to	to	ADP
m-1112	472	31	the	the	DET
m-1112	472	32	conductor`s	conductor`s	ADJ
m-1112	472	33	axis	axis	NOUN
m-1112	472	34	.	.	PUNCT
m-1112	473	1	⇉	⇉	PROPN
m-1112	474	1	i.e.	i.e.	X
m-1112	474	2	in	in	ADP
m-1112	474	3	a	a	DET
m-1112	474	4	closed	closed	ADJ
m-1112	474	5	energy	energy	NOUN
m-1112	474	6	-	-	PUNCT
m-1112	474	7	conductor	conductor	NOUN
m-1112	474	8	𝐫	𝐫	ADP
m-1112	475	1	[	[	X
m-1112	475	2	+	+	NOUN
m-1112	475	3	↔+	↔+	NOUN
m-1112	475	4	]	]	PUNCT
m-1112	475	5	,	,	PUNCT
m-1112	475	6	the	the	DET
m-1112	475	7	fundamental	fundamental	ADJ
m-1112	475	8	frequency	frequency	NOUN
m-1112	475	9	𝐟	𝐟	NOUN
m-1112	475	10	𝟏	𝟏	NUM
m-1112	475	11	becomes	become	VERB
m-1112	475	12	the	the	DET
m-1112	475	13	spin	spin	NOUN
m-1112	475	14	.	.	PUNCT
m-1112	476	1	the	the	DET
m-1112	476	2	energysquare	energysquare	PROPN
m-1112	476	3	prism	prism	NOUN
m-1112	476	4	,	,	PUNCT
m-1112	476	5	|aka|	|aka|	PROPN
m-1112	476	6	.{𝐐	.{𝐐	PUNCT
m-1112	476	7	⇉	⇉	X
m-1112	477	1	aka⃗⃗	aka⃗⃗	PROPN
m-1112	477	2	⃗⃗	⃗⃗	PROPN
m-1112	477	3	⃗⃗	⃗⃗	PROPN
m-1112	477	4	⃗⃗	⃗⃗	PROPN
m-1112	477	5	⃗	⃗	PROPN
m-1112	477	6	}	}	PUNCT
m-1112	477	7	.{𝐐	.{𝐐	PUNCT
m-1112	478	1	⇈	⇈	NUM
m-1112	478	2	aka⃗⃗	aka⃗⃗	X
m-1112	478	3	⃗⃗	⃗⃗	PROPN
m-1112	478	4	⃗⃗	⃗⃗	PROPN
m-1112	478	5	⃗⃗	⃗⃗	PROPN
m-1112	478	6	⃗	⃗	PROPN
m-1112	478	7	}	}	PUNCT
m-1112	478	8	=	=	SYM
m-1112	478	9	|qx.qy|.|aka|=kx.ky|.|aka|	|qx.qy|.|aka|=kx.ky|.|aka|	PROPN
m-1112	478	10	=	=	SYM
m-1112	478	11	|↔|.|	|↔|.|	NUM
m-1112	478	12	↕	↕	PROPN
m-1112	478	13	|.|aka|	|.|aka|	PROPN
m-1112	478	14	…	…	PUNCT
m-1112	478	15	..	..	PUNCT
m-1112	478	16	(	(	PUNCT
m-1112	478	17	17	17	NUM
m-1112	478	18	)	)	PUNCT
m-1112	478	19	,	,	PUNCT
m-1112	478	20	where	where	SCONJ
m-1112	478	21	|↔|	|↔|	PROPN
m-1112	478	22	=	=	PROPN
m-1112	478	23	|kx|	|kx|	PROPN
m-1112	478	24	the	the	DET
m-1112	478	25	conductor`s	conductor`s	ADJ
m-1112	478	26	axial	axial	ADJ
m-1112	478	27	-	-	PUNCT
m-1112	478	28	energy	energy	NOUN
m-1112	478	29	,	,	PUNCT
m-1112	478	30	|	|	ADV
m-1112	478	31	↕	↕	PROPN
m-1112	478	32	|	|	NOUN
m-1112	478	33	=|	=|	NOUN
m-1112	478	34	↺	↺	NOUN
m-1112	478	35	|	|	ADV
m-1112	478	36	the	the	DET
m-1112	478	37	conductor`s	conductor`s	ADJ
m-1112	478	38	rotation	rotation	NOUN
m-1112	478	39	-	-	PUNCT
m-1112	478	40	energy	energy	NOUN
m-1112	478	41	=	=	NOUN
m-1112	478	42	spin	spin	NOUN
m-1112	478	43	,	,	PUNCT
m-1112	478	44	and	and	CCONJ
m-1112	478	45	|↔|.|	|↔|.|	NUM
m-1112	478	46	↕	↕	PROPN
m-1112	478	47	|	|	ADV
m-1112	478	48	the	the	DET
m-1112	478	49	conductor`s	conductor`s	NOUN
m-1112	478	50	resultant	resultant	NOUN
m-1112	478	51	-	-	PUNCT
m-1112	478	52	energy	energy	NOUN
m-1112	478	53	-	-	PUNCT
m-1112	478	54	vector	vector	NOUN
m-1112	478	55	is	be	AUX
m-1112	478	56	an	an	DET
m-1112	478	57	cruise	cruise	NOUN
m-1112	478	58	-	-	PUNCT
m-1112	478	59	missile	missile	NOUN
m-1112	478	60	.	.	PUNCT
m-1112	479	1	when	when	SCONJ
m-1112	479	2	a	a	DET
m-1112	479	3	conductor	conductor	NOUN
m-1112	479	4	d	d	NOUN
m-1112	479	5	=	=	PUNCT
m-1112	479	6	aka	aka	ADV
m-1112	479	7	=	=	NOUN
m-1112	479	8	r	r	NOUN
m-1112	479	9	=	=	SYM
m-1112	479	10	λ	λ	X
m-1112	479	11	n(ns	n(ns	ADV
m-1112	479	12	)	)	PUNCT
m-1112	479	13	has	have	VERB
m-1112	479	14	a	a	DET
m-1112	479	15	hole	hole	NOUN
m-1112	479	16	at	at	ADP
m-1112	479	17	an	an	DET
m-1112	479	18	point	point	NOUN
m-1112	479	19	𝐀𝐄	𝐀𝐄	NOUN
m-1112	479	20	such	such	ADJ
m-1112	479	21	that	that	SCONJ
m-1112	479	22	aae=	aae=	NOUN
m-1112	479	23	2	2	NUM
m-1112	479	24	r	r	NOUN
m-1112	479	25	,	,	PUNCT
m-1112	479	26	{	{	PUNCT
m-1112	479	27	a	a	PRON
m-1112	479	28	-2r	-2r	PROPN
m-1112	479	29	𝐀e	𝐀e	PROPN
m-1112	479	30	-r𝐊a}=	-r𝐊a}=	NOUN
m-1112	480	1	d	d	X
m-1112	480	2	then	then	ADV
m-1112	480	3	the	the	DET
m-1112	480	4	energy	energy	NOUN
m-1112	480	5	k	k	PROPN
m-1112	480	6	at	at	ADP
m-1112	480	7	point	point	NOUN
m-1112	480	8	a	a	DET
m-1112	480	9	e	e	NOUN
m-1112	480	10	is	be	AUX
m-1112	480	11	the	the	DET
m-1112	480	12	total	total	ADJ
m-1112	480	13	mass	mass	PROPN
m-1112	480	14	mt	mt	PROPN
m-1112	480	15	of	of	ADP
m-1112	480	16	conductor	conductor	PROPN
m-1112	480	17	aae	aae	PROPN
m-1112	480	18	=	=	SYM
m-1112	480	19	2	2	NUM
m-1112	480	20	r	r	NOUN
m-1112	480	21	equal	equal	ADJ
m-1112	480	22	to	to	ADP
m-1112	480	23	the	the	DET
m-1112	480	24	moment	moment	NOUN
m-1112	480	25	of	of	ADP
m-1112	480	26	inertia	inertia	NOUN
m-1112	480	27	jt	jt	PROPN
m-1112	481	1	=	=	PROPN
m-1112	482	1	|	|	ADV
m-1112	483	1	m.4r²	m.4r²	PROPN
m-1112	484	1	3	3	NUM
m-1112	485	1	|	|	ADV
m-1112	485	2	,	,	PUNCT
m-1112	485	3	where	where	SCONJ
m-1112	485	4	m	m	NOUN
m-1112	485	5	is	be	AUX
m-1112	485	6	ijo	ijo	PROPN
m-1112	485	7	international	international	ADJ
m-1112	485	8	journal	journal	PROPN
m-1112	485	9	of	of	ADP
m-1112	485	10	mathematics	mathematics	PROPN
m-1112	485	11	(	(	PUNCT
m-1112	485	12	issn	issn	PROPN
m-1112	485	13	:	:	PUNCT
m-1112	485	14	2992	2992	NUM
m-1112	485	15	-	-	SYM
m-1112	485	16	4421	4421	NUM
m-1112	485	17	)	)	PUNCT
m-1112	486	1	volume	volume	NOUN
m-1112	486	2	08	08	NUM
m-1112	487	1	|	|	ADV
m-1112	487	2	issue	issue	NOUN
m-1112	487	3	08	08	NUM
m-1112	488	1	|	|	ADV
m-1112	488	2	august	august	PROPN
m-1112	488	3	2025	2025	NUM
m-1112	488	4	|	|	ADV
m-1112	488	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	488	6	ijo	ijo	PROPN
m-1112	488	7	journals	journal	NOUN
m-1112	488	8	18	18	NUM
m-1112	488	9	the	the	DET
m-1112	488	10	fundamental	fundamental	ADJ
m-1112	488	11	particles	particle	NOUN
m-1112	488	12	origination	origination	NOUN
m-1112	488	13	mechanism	mechanism	NOUN
m-1112	488	14	in	in	ADP
m-1112	488	15	mfmf	mfmf	PROPN
m-1112	488	16	pns	pns	PROPN
m-1112	488	17	caves	cave	NOUN
m-1112	488	18	.	.	PUNCT
m-1112	489	1	the	the	DET
m-1112	489	2	stiffness	stiffness	NOUN
m-1112	489	3	per	per	ADP
m-1112	489	4	meter	meter	NOUN
m-1112	489	5	of	of	ADP
m-1112	489	6	conductor	conductor	NOUN
m-1112	489	7	2r	2r	NUM
m-1112	489	8	.	.	PUNCT
m-1112	490	1	from	from	ADP
m-1112	490	2	equation	equation	NOUN
m-1112	490	3	(	(	PUNCT
m-1112	490	4	15	15	NUM
m-1112	490	5	)	)	PUNCT
m-1112	490	6	coulomb	coulomb	NOUN
m-1112	490	7	force	force	NOUN
m-1112	490	8	f	f	PROPN
m-1112	491	1	[	[	X
m-1112	491	2	+	+	ADJ
m-1112	491	3	↔+	↔+	NOUN
m-1112	491	4	]	]	X
m-1112	491	5	=|	=|	NOUN
m-1112	491	6	2πf	2πf	NOUN
m-1112	491	7	.	.	PUNCT
m-1112	492	1	φ	φ	PROPN
m-1112	492	2	|	|	ADJ
m-1112	492	3	2	2	NUM
m-1112	492	4	=	=	PUNCT
m-1112	492	5	[	[	PUNCT
m-1112	492	6	2π	2π	PROPN
m-1112	492	7	φ	φ	NUM
m-1112	492	8	|	|	PROPN
m-1112	492	9	3.	3.	NUM
m-1112	492	10	�	�	NOUN
m-1112	492	11	̅	̅	NOUN
m-1112	492	12	�	�	NOUN
m-1112	492	13	4	4	NUM
m-1112	492	14	λ	λ	NOUN
m-1112	492	15	|]²	|]²	NOUN
m-1112	492	16	=|	=|	NOUN
m-1112	492	17	3πv	3πv	ADJ
m-1112	492	18	2λφ	2λφ	NOUN
m-1112	493	1	|	|	ADV
m-1112	493	2	2	2	NUM
m-1112	493	3	becomes	become	VERB
m-1112	493	4	as	as	ADP
m-1112	493	5	f[+	f[+	NOUN
m-1112	493	6	⇅	⇅	NOUN
m-1112	493	7	⇵+	⇵+	NOUN
m-1112	493	8	]	]	X
m-1112	493	9	≡	≡	PROPN
m-1112	493	10	f[+↔+	f[+↔+	PROPN
m-1112	493	11	]	]	PUNCT
m-1112	493	12	,	,	PUNCT
m-1112	493	13	equal	equal	ADJ
m-1112	493	14	and	and	CCONJ
m-1112	493	15	perpendicular	perpendicular	ADJ
m-1112	493	16	and	and	CCONJ
m-1112	493	17	{	{	PUNCT
m-1112	493	18	𝐐	𝐐	NOUN
m-1112	493	19	⇉	⇉	PROPN
m-1112	493	20	aae⃗⃗	aae⃗⃗	NUM
m-1112	493	21	⃗⃗	⃗⃗	PROPN
m-1112	493	22	⃗⃗	⃗⃗	PROPN
m-1112	493	23	⃗⃗	⃗⃗	PROPN
m-1112	493	24	⃗	⃗	PROPN
m-1112	493	25	}	}	PUNCT
m-1112	493	26	=	=	SYM
m-1112	493	27	{	{	PUNCT
m-1112	493	28	𝐐	𝐐	PROPN
m-1112	493	29	⇈	⇈	PROPN
m-1112	493	30	aae⃗⃗	aae⃗⃗	NUM
m-1112	493	31	⃗⃗	⃗⃗	PROPN
m-1112	493	32	⃗⃗	⃗⃗	PROPN
m-1112	493	33	⃗⃗	⃗⃗	PROPN
m-1112	493	34	⃗	⃗	PROPN
m-1112	493	35	}	}	PUNCT
m-1112	493	36	,	,	PUNCT
m-1112	493	37	|qx|	|qx|	ADP
m-1112	493	38	=	=	SYM
m-1112	493	39	|qy|	|qy|	NOUN
m-1112	493	40	,	,	PUNCT
m-1112	493	41	|kx|	|kx|	NOUN
m-1112	493	42	=	=	SYM
m-1112	493	43	|ky|	|ky|	PROPN
m-1112	493	44	,	,	PUNCT
m-1112	493	45	|↔|	|↔|	PROPN
m-1112	493	46	=	=	PUNCT
m-1112	493	47	|	|	NOUN
m-1112	493	48	↕	↕	PROPN
m-1112	493	49	|	|	PROPN
m-1112	493	50	…	…	PUNCT
m-1112	493	51	....	....	PUNCT
m-1112	493	52	(	(	PUNCT
m-1112	493	53	17a	17a	X
m-1112	493	54	)	)	PUNCT
m-1112	493	55	transverse	transverse	NOUN
m-1112	493	56	motion	motion	NOUN
m-1112	493	57	|	|	PROPN
m-1112	493	58	↕	↕	PROPN
m-1112	493	59	|	|	PROPN
m-1112	493	60	,	,	PUNCT
m-1112	493	61	presupposes	presuppose	VERB
m-1112	493	62	an	an	DET
m-1112	493	63	|←|	|←|	PROPN
m-1112	493	64	impact	impact	NOUN
m-1112	493	65	of	of	ADP
m-1112	493	66	the	the	DET
m-1112	493	67	mass	mass	NOUN
m-1112	493	68	at	at	ADP
m-1112	493	69	end	end	NOUN
m-1112	493	70	-	-	PUNCT
m-1112	493	71	point	point	NOUN
m-1112	493	72	a	a	DET
m-1112	493	73	e	e	NOUN
m-1112	493	74	and	and	CCONJ
m-1112	493	75	is	be	AUX
m-1112	493	76	the	the	DET
m-1112	493	77	energy	energy	NOUN
m-1112	494	1	=	=	PUNCT
m-1112	494	2	j	j	PROPN
m-1112	494	3	w	w	NOUN
m-1112	494	4	and	and	CCONJ
m-1112	494	5	because	because	SCONJ
m-1112	494	6	lack	lack	NOUN
m-1112	494	7	of	of	ADP
m-1112	494	8	obstacle	obstacle	NOUN
m-1112	494	9	impact	impact	NOUN
m-1112	494	10	→	→	SYM
m-1112	494	11	mv	mv	PROPN
m-1112	494	12	=	=	PROPN
m-1112	494	13	jw²	jw²	PROPN
m-1112	494	14	=	=	PUNCT
m-1112	495	1	[	[	PUNCT
m-1112	495	2	m.r²	m.r²	X
m-1112	495	3	3	3	NUM
m-1112	495	4	]	]	PUNCT
m-1112	495	5	.w²	.w²	NOUN
m-1112	495	6	,	,	PUNCT
m-1112	495	7	or	or	CCONJ
m-1112	495	8	velocity	velocity	NOUN
m-1112	495	9	after	after	ADP
m-1112	495	10	impact	impact	NOUN
m-1112	495	11	→	→	SYM
m-1112	495	12	v	v	NOUN
m-1112	495	13	=	=	X
m-1112	495	14	[	[	PUNCT
m-1112	495	15	2πf.r³	2πf.r³	NUM
m-1112	495	16	3	3	NUM
m-1112	495	17	]	]	PUNCT
m-1112	495	18	=	=	PUNCT
m-1112	495	19	[	[	PUNCT
m-1112	495	20	v.r²	v.r²	X
m-1112	495	21	3	3	NUM
m-1112	495	22	]	]	PUNCT
m-1112	495	23	..	..	PUNCT
m-1112	495	24	(	(	PUNCT
m-1112	495	25	14a	14a	NOUN
m-1112	495	26	)	)	PUNCT
m-1112	495	27	.	.	PUNCT
m-1112	496	1	placing	place	VERB
m-1112	496	2	velocity	velocity	NOUN
m-1112	496	3	after	after	ADP
m-1112	496	4	impact	impact	NOUN
m-1112	496	5	(	(	PUNCT
m-1112	496	6	14a	14a	NOUN
m-1112	496	7	)	)	PUNCT
m-1112	496	8	in	in	ADP
m-1112	496	9	equation	equation	NOUN
m-1112	496	10	(	(	PUNCT
m-1112	496	11	15a	15a	NOUN
m-1112	496	12	)	)	PUNCT
m-1112	496	13	then	then	ADV
m-1112	496	14	the	the	DET
m-1112	496	15	concentrated	concentrated	ADJ
m-1112	496	16	energy	energy	NOUN
m-1112	496	17	at	at	ADP
m-1112	496	18	edge	edge	NOUN
m-1112	496	19	point	point	NOUN
m-1112	496	20	ka	ka	PROPN
m-1112	496	21	is	be	AUX
m-1112	496	22	f[+↔+	f[+↔+	NOUN
m-1112	496	23	]	]	X
m-1112	496	24	=	=	X
m-1112	496	25	{	{	PUNCT
m-1112	496	26	3πw	3πw	NUM
m-1112	496	27	2λφ	2λφ	NOUN
m-1112	496	28	[	[	PUNCT
m-1112	496	29	−2πf.r²	−2πf.r²	NOUN
m-1112	496	30	3	3	NUM
m-1112	496	31	]	]	PUNCT
m-1112	496	32	}	}	PUNCT
m-1112	496	33	²	²	NUM
m-1112	496	34	=	=	PUNCT
m-1112	497	1	|	|	NOUN
m-1112	497	2	𝑤[π2r4f	𝑤[π2r4f	NOUN
m-1112	497	3	]	]	PUNCT
m-1112	497	4	rλφ	rλφ	ADV
m-1112	498	1	|	|	ADV
m-1112	498	2	2	2	X
m-1112	498	3	=	=	NOUN
m-1112	498	4	|	|	NOUN
m-1112	498	5	w.b=(π2r4f	w.b=(π2r4f	NOUN
m-1112	498	6	)	)	PUNCT
m-1112	499	1	r.λφ	r.λφ	NOUN
m-1112	499	2	|	|	ADV
m-1112	499	3	2	2	NUM
m-1112	499	4	=	=	NOUN
m-1112	499	5	w².|	w².|	ADJ
m-1112	499	6	�	�	PROPN
m-1112	499	7	̅	̅	NOUN
m-1112	499	8	�	�	PROPN
m-1112	499	9	rλφ	rλφ	ADV
m-1112	499	10	|	|	ADV
m-1112	499	11	2	2	NUM
m-1112	499	12	≡	≡	NOUN
m-1112	500	1	|	|	ADV
m-1112	500	2	2l=	2l=	NUM
m-1112	500	3	w.	w.	NOUN
m-1112	500	4	�	�	PROPN
m-1112	500	5	̅	̅	NOUN
m-1112	500	6	�	�	PROPN
m-1112	500	7	rλφ	rλφ	ADV
m-1112	500	8	|	|	ADV
m-1112	500	9	2	2	NUM
m-1112	500	10	≡	≡	PROPN
m-1112	500	11	the	the	DET
m-1112	500	12	total	total	ADJ
m-1112	500	13	energy	energy	NOUN
m-1112	500	14	2l	2l	NOUN
m-1112	500	15	to	to	ADP
m-1112	500	16	the	the	DET
m-1112	500	17	twin	twin	ADJ
m-1112	500	18	circles	circle	NOUN
m-1112	500	19	squared	square	VERB
m-1112	500	20	,	,	PUNCT
m-1112	500	21	or	or	CCONJ
m-1112	500	22	to	to	ADP
m-1112	500	23	angularmomentum	angularmomentum	PROPN
m-1112	500	24	≡	≡	PROPN
m-1112	500	25	spin	spin	NOUN
m-1112	500	26	squared	square	VERB
m-1112	500	27	…	…	PUNCT
m-1112	500	28	…	…	PUNCT
m-1112	500	29	.(16	.(16	NUM
m-1112	500	30	)	)	PUNCT
m-1112	500	31	⇉	⇉	PUNCT
m-1112	501	1	i.e.	i.e.	X
m-1112	501	2	in	in	ADP
m-1112	501	3	an	an	DET
m-1112	501	4	energy	energy	NOUN
m-1112	501	5	–	–	PUNCT
m-1112	501	6	slit	slit	NOUN
m-1112	501	7	conductor	conductor	NOUN
m-1112	501	8	𝐫	𝐫	ADP
m-1112	501	9	+	+	PROPN
m-1112	501	10	{	{	PUNCT
m-1112	501	11	𝐀	𝐀	PROPN
m-1112	501	12	−2r−	−2r−	NOUN
m-1112	501	13	𝐀e	𝐀e	PROPN
m-1112	501	14	−r−	−r−	NOUN
m-1112	501	15	𝐊a}=	𝐊a}=	PROPN
m-1112	501	16	𝐝	𝐝	X
m-1112	501	17	+	+	X
m-1112	501	18	,	,	PUNCT
m-1112	501	19	the	the	DET
m-1112	501	20	fundamental	fundamental	ADJ
m-1112	501	21	frequency	frequency	NOUN
m-1112	501	22	𝐟	𝐟	NOUN
m-1112	501	23	𝟏	𝟏	NUM
m-1112	501	24	becomes	become	VERB
m-1112	501	25	the	the	DET
m-1112	501	26	spin	spin	NOUN
m-1112	501	27	,	,	PUNCT
m-1112	501	28	or	or	CCONJ
m-1112	501	29	,	,	PUNCT
m-1112	501	30	the	the	DET
m-1112	501	31	carrier	carrier	NOUN
m-1112	501	32	of	of	ADP
m-1112	501	33	the	the	DET
m-1112	501	34	total	total	ADJ
m-1112	501	35	-	-	PUNCT
m-1112	501	36	energy	energy	NOUN
m-1112	501	37	2l	2l	NOUN
m-1112	501	38	of	of	ADP
m-1112	501	39	the	the	DET
m-1112	501	40	moving	move	VERB
m-1112	501	41	system	system	NOUN
m-1112	501	42	.	.	PUNCT
m-1112	502	1	at	at	ADP
m-1112	502	2	ae	ae	PROPN
m-1112	502	3	point	point	VERB
m-1112	502	4	energy	energy	NOUN
m-1112	502	5	square	square	ADJ
m-1112	502	6	-	-	PUNCT
m-1112	502	7	prism	prism	NOUN
m-1112	502	8	is	be	AUX
m-1112	502	9	→	→	SYM
m-1112	502	10	|aae|.{𝐐	|aae|.{𝐐	NUM
m-1112	502	11	⇉	⇉	PROPN
m-1112	503	1	aae⃗⃗	aae⃗⃗	NUM
m-1112	503	2	⃗⃗	⃗⃗	PROPN
m-1112	503	3	⃗⃗	⃗⃗	PROPN
m-1112	503	4	⃗⃗	⃗⃗	PROPN
m-1112	503	5	⃗	⃗	PROPN
m-1112	503	6	}	}	PUNCT
m-1112	503	7	.{𝐐	.{𝐐	PUNCT
m-1112	504	1	⇈	⇈	NUM
m-1112	504	2	aae⃗⃗	aae⃗⃗	NUM
m-1112	504	3	⃗⃗	⃗⃗	PROPN
m-1112	504	4	⃗⃗	⃗⃗	PROPN
m-1112	504	5	⃗⃗	⃗⃗	PROPN
m-1112	504	6	⃗	⃗	PROPN
m-1112	504	7	}	}	PUNCT
m-1112	504	8	=	=	SYM
m-1112	504	9	|qx.qy|.|ae	|qx.qy|.|ae	NUM
m-1112	504	10	ka	ka	NOUN
m-1112	505	1	|	|	ADV
m-1112	505	2	=	=	SYM
m-1112	505	3	|kx.ky|.|ae	|kx.ky|.|ae	PROPN
m-1112	505	4	ka	ka	PROPN
m-1112	506	1	|	|	ADV
m-1112	506	2	=	=	SYM
m-1112	506	3	≡	≡	PROPN
m-1112	506	4	|↔|.|	|↔|.|	PROPN
m-1112	506	5	↕	↕	PROPN
m-1112	506	6	|.|ae	|.|ae	PROPN
m-1112	506	7	ka	ka	PROPN
m-1112	507	1	|	|	ADV
m-1112	507	2	.........	.........	PUNCT
m-1112	507	3	(	(	PUNCT
m-1112	507	4	18	18	NUM
m-1112	507	5	)	)	PUNCT
m-1112	507	6	,	,	PUNCT
m-1112	507	7	where	where	SCONJ
m-1112	507	8	|↔|	|↔|	PROPN
m-1112	507	9	=	=	PROPN
m-1112	507	10	|kx|	|kx|	PROPN
m-1112	507	11	the	the	DET
m-1112	507	12	conductor`s	conductor`s	ADJ
m-1112	507	13	axial	axial	ADJ
m-1112	507	14	-	-	PUNCT
m-1112	507	15	energy	energy	NOUN
m-1112	507	16	,	,	PUNCT
m-1112	507	17	|	|	ADV
m-1112	507	18	↕	↕	PROPN
m-1112	507	19	|	|	ADV
m-1112	507	20	=	=	PRON
m-1112	507	21	|ky|	|ky|	ADP
m-1112	507	22	the	the	DET
m-1112	507	23	conductor`s	conductor`s	NOUN
m-1112	507	24	.	.	PUNCT
m-1112	508	1	transverse	transverse	NOUN
m-1112	508	2	energy	energy	NOUN
m-1112	508	3	,	,	PUNCT
m-1112	508	4	|	|	ADV
m-1112	508	5	↺	↺	NOUN
m-1112	508	6	|	|	ADV
m-1112	508	7	the	the	DET
m-1112	508	8	conductor`s	conductor`s	ADJ
m-1112	508	9	rotational	rotational	ADJ
m-1112	508	10	-	-	PUNCT
m-1112	508	11	energy	energy	NOUN
m-1112	508	12	=	=	NOUN
m-1112	508	13	spin	spin	NOUN
m-1112	508	14	,	,	PUNCT
m-1112	508	15	where	where	SCONJ
m-1112	508	16	|kx.ky|	|kx.ky|	NOUN
m-1112	508	17	=	=	SYM
m-1112	508	18	|↔|.|	|↔|.|	NUM
m-1112	508	19	↕	↕	PROPN
m-1112	508	20	|	|	ADV
m-1112	508	21	≡	≡	PROPN
m-1112	508	22	⤱	⤱	NOUN
m-1112	508	23	=	=	X
m-1112	508	24	the	the	DET
m-1112	508	25	dot	dot	NOUN
m-1112	508	26	-	-	PUNCT
m-1112	508	27	product	product	NOUN
m-1112	508	28	=	=	SYM
m-1112	508	29	area	area	NOUN
m-1112	508	30	of	of	ADP
m-1112	508	31	vectors	vector	NOUN
m-1112	508	32	,	,	PUNCT
m-1112	508	33	which	which	PRON
m-1112	508	34	is	be	AUX
m-1112	508	35	a	a	DET
m-1112	508	36	scalar	scalar	ADJ
m-1112	508	37	magnitude	magnitude	NOUN
m-1112	508	38	𝐀	𝐀	PROPN
m-1112	508	39	𝐱.𝐲	𝐱.𝐲	X
m-1112	508	40	=	=	NOUN
m-1112	508	41	|𝐤𝐱|.|𝐤𝐲|.𝐜𝐨𝐬	|𝐤𝐱|.|𝐤𝐲|.𝐜𝐨𝐬	PROPN
m-1112	508	42	𝛉	𝛉	NOUN
m-1112	508	43	,	,	PUNCT
m-1112	508	44	where	where	SCONJ
m-1112	508	45	θ	θ	PROPN
m-1112	508	46	,	,	PUNCT
m-1112	508	47	is	be	AUX
m-1112	508	48	the	the	DET
m-1112	508	49	angle	angle	NOUN
m-1112	508	50	between	between	ADP
m-1112	508	51	the	the	DET
m-1112	508	52	two	two	NUM
m-1112	508	53	vectors	vector	NOUN
m-1112	508	54	,	,	PUNCT
m-1112	508	55	kx	kx	PROPN
m-1112	508	56	,	,	PUNCT
m-1112	508	57	ky	ky	PROPN
m-1112	508	58	and	and	CCONJ
m-1112	508	59	,	,	PUNCT
m-1112	508	60	the	the	DET
m-1112	508	61	cross	cross	NOUN
m-1112	508	62	-	-	NOUN
m-1112	508	63	product	product	NOUN
m-1112	508	64	=	=	NOUN
m-1112	508	65	the	the	DET
m-1112	508	66	resultant	resultant	NOUN
m-1112	508	67	-	-	PUNCT
m-1112	508	68	vector	vector	NOUN
m-1112	508	69	=	=	NOUN
m-1112	508	70	®	®	NOUN
m-1112	508	71	=	=	SYM
m-1112	508	72	�	�	PROPN
m-1112	508	73	̅	̅	NOUN
m-1112	508	74	�	�	NOUN
m-1112	508	75	=	=	SYM
m-1112	508	76	𝐤𝐱	𝐤𝐱	NOUN
m-1112	508	77	x	x	X
m-1112	508	78	𝐤𝐲	𝐤𝐲	ADP
m-1112	508	79	which	which	PRON
m-1112	508	80	is	be	AUX
m-1112	508	81	perpendicular	perpendicular	ADJ
m-1112	508	82	to	to	ADP
m-1112	508	83	kx	kx	PROPN
m-1112	508	84	,	,	PUNCT
m-1112	508	85	kyvectors	kyvector	VERB
m-1112	508	86	where	where	SCONJ
m-1112	508	87	,	,	PUNCT
m-1112	508	88	r	r	NOUN
m-1112	508	89	=	=	ADJ
m-1112	508	90	√k²x	√k²x	NOUN
m-1112	508	91	+	+	CCONJ
m-1112	508	92	k²y	k²y	ADJ
m-1112	508	93	,	,	PUNCT
m-1112	508	94	x	x	PUNCT
m-1112	508	95	=	=	SYM
m-1112	508	96	r.cos	r.cos	X
m-1112	508	97	θ	θ	PROPN
m-1112	508	98	,	,	PUNCT
m-1112	508	99	y	y	PROPN
m-1112	508	100	=	=	PUNCT
m-1112	508	101	r.sin	r.sin	NOUN
m-1112	508	102	θ	θ	PROPN
m-1112	508	103	,	,	PUNCT
m-1112	508	104	θ	θ	X
m-1112	508	105	=	=	SYM
m-1112	509	1	tan−1	tan−1	PROPN
m-1112	509	2	(	(	PUNCT
m-1112	509	3	y	y	NOUN
m-1112	509	4	x	x	PROPN
m-1112	509	5	)	)	PUNCT
m-1112	509	6	,	,	PUNCT
m-1112	509	7	and	and	CCONJ
m-1112	509	8	�	�	PROPN
m-1112	509	9	̅	̅	NOUN
m-1112	509	10	�	�	NOUN
m-1112	509	11	=	=	SYM
m-1112	509	12	𝐤𝐱	𝐤𝐱	NOUN
m-1112	509	13	x	x	X
m-1112	509	14	𝐤𝐲	𝐤𝐲	ADP
m-1112	509	15	=	=	NOUN
m-1112	509	16	𝐰	𝐰	NOUN
m-1112	509	17	𝐜	𝐜	NOUN
m-1112	509	18	=	=	SYM
m-1112	509	19	𝟐	𝟐	PROPN
m-1112	509	20	𝛑	𝛑	ADP
m-1112	509	21	𝛌	𝛌	X
m-1112	509	22	the	the	DET
m-1112	509	23	conductor`s	conductor`s	ADJ
m-1112	509	24	resultant	resultant	NOUN
m-1112	509	25	-	-	PUNCT
m-1112	509	26	energy	energy	NOUN
m-1112	509	27	-	-	PUNCT
m-1112	509	28	vector	vector	NOUN
m-1112	509	29	,	,	PUNCT
m-1112	509	30	®	®	NOUN
m-1112	509	31	=	=	SYM
m-1112	509	32	�	�	PROPN
m-1112	509	33	̅	̅	NOUN
m-1112	509	34	�	�	PROPN
m-1112	509	35	,	,	PUNCT
m-1112	509	36	is	be	AUX
m-1112	509	37	as	as	ADP
m-1112	509	38	an	an	DET
m-1112	509	39	non	non	ADJ
m-1112	509	40	-	-	ADJ
m-1112	509	41	guided	guide	VERB
m-1112	509	42	cruise	cruise	NOUN
m-1112	509	43	–	–	PUNCT
m-1112	509	44	missile	missile	NOUN
m-1112	509	45	.	.	PUNCT
m-1112	510	1	from	from	ADP
m-1112	510	2	total	total	ADJ
m-1112	510	3	energy	energy	NOUN
m-1112	510	4	relation	relation	NOUN
m-1112	510	5	2l	2l	NUM
m-1112	510	6	=	=	SYM
m-1112	510	7	b	b	PROPN
m-1112	510	8	w	w	PROPN
m-1112	510	9	≡	≡	PROPN
m-1112	510	10	e	e	PROPN
m-1112	510	11	k	k	PROPN
m-1112	511	1	+	+	CCONJ
m-1112	511	2	e	e	X
m-1112	511	3	u	u	NOUN
m-1112	511	4	≡	≡	PROPN
m-1112	511	5	|kx|+	|kx|+	ADV
m-1112	511	6	|ky|	|ky|	ADJ
m-1112	511	7	is	be	AUX
m-1112	511	8	seen	see	VERB
m-1112	511	9	that	that	SCONJ
m-1112	511	10	,	,	PUNCT
m-1112	511	11	kx	kx	PROPN
m-1112	511	12	,	,	PUNCT
m-1112	511	13	ky	ky	PROPN
m-1112	511	14	,	,	PUNCT
m-1112	511	15	consist	consist	VERB
m-1112	511	16	the	the	DET
m-1112	511	17	2	2	NUM
m-1112	511	18	-	-	PUNCT
m-1112	511	19	line	line	NOUN
m-1112	511	20	,	,	PUNCT
m-1112	511	21	plane	plane	NOUN
m-1112	511	22	-	-	PUNCT
m-1112	511	23	launcher	launcher	NOUN
m-1112	511	24	of	of	ADP
m-1112	511	25	{	{	PUNCT
m-1112	511	26	energy	energy	NOUN
m-1112	511	27	≡	≡	PROPN
m-1112	511	28	motionmissile	motionmissile	NOUN
m-1112	511	29	}	}	PUNCT
m-1112	511	30	into	into	ADP
m-1112	511	31	→	→	SYM
m-1112	511	32	two	two	NUM
m-1112	511	33	perpendicular	perpendicular	ADJ
m-1112	511	34	and	and	CCONJ
m-1112	511	35	equal	equal	ADJ
m-1112	511	36	conductors	conductor	NOUN
m-1112	511	37	,	,	PUNCT
m-1112	511	38	with	with	SCONJ
m-1112	511	39	conductors	conductor	NOUN
m-1112	511	40	-	-	PUNCT
m-1112	511	41	pivot	pivot	NOUN
m-1112	511	42	-	-	PUNCT
m-1112	511	43	axis	axis	NOUN
m-1112	511	44	propelled	propel	VERB
m-1112	511	45	on	on	ADP
m-1112	511	46	their	their	PRON
m-1112	511	47	merging	merge	VERB
m-1112	511	48	-	-	PUNCT
m-1112	511	49	resultant	resultant	NOUN
m-1112	511	50	axis	axis	NOUN
m-1112	511	51	of	of	ADP
m-1112	511	52	the	the	DET
m-1112	511	53	two	two	NUM
m-1112	511	54	directions	direction	NOUN
m-1112	511	55	⇉	⇉	PUNCT
m-1112	512	1	⇈	⇈	NUM
m-1112	512	2	≡	≡	PROPN
m-1112	512	3	⤱	⤱	NOUN
m-1112	512	4	.	.	PUNCT
m-1112	513	1	in	in	ADP
m-1112	513	2	one	one	NUM
m-1112	513	3	-	-	PUNCT
m-1112	513	4	conductor	conductor	NOUN
m-1112	513	5	,	,	PUNCT
m-1112	513	6	kx=	kx=	PROPN
m-1112	513	7	za̅̅̅̅	za̅̅̅̅	NUM
m-1112	513	8	,	,	PUNCT
m-1112	513	9	k	k	PROPN
m-1112	513	10	y=	y=	PROPN
m-1112	513	11	1,mm̅̅	1,mm̅̅	NUM
m-1112	513	12	̅̅	̅̅	PROPN
m-1112	513	13	̅̅	̅̅	PROPN
m-1112	513	14	̅̅	̅̅	PROPN
m-1112	513	15	,	,	PUNCT
m-1112	513	16	resultant	resultant	VERB
m-1112	513	17	r̅	r̅	ADP
m-1112	513	18	=	=	SYM
m-1112	513	19	z1mo̅̅	z1mo̅̅	PROPN
m-1112	513	20	̅̅	̅̅	PROPN
m-1112	513	21	̅̅	̅̅	PROPN
m-1112	513	22	̅̅	̅̅	PROPN
m-1112	513	23	,	,	PUNCT
m-1112	513	24	while	while	SCONJ
m-1112	513	25	for	for	ADP
m-1112	513	26	(	(	PUNCT
m-1112	513	27	2	2	NUM
m-1112	513	28	)	)	PUNCT
m-1112	513	29	→	→	PUNCT
m-1112	513	30	in	in	ADP
m-1112	513	31	two	two	NUM
m-1112	513	32	-	-	PUNCT
m-1112	513	33	conductors	conductor	NOUN
m-1112	513	34	,	,	PUNCT
m-1112	513	35	kx=	kx=	PROPN
m-1112	513	36	zb̅̅̅̅	zb̅̅̅̅	PROPN
m-1112	513	37	,	,	PUNCT
m-1112	513	38	k	k	PROPN
m-1112	513	39	y=	y=	NUM
m-1112	513	40	za̅̅̅̅	za̅̅̅̅	NUM
m-1112	513	41	,	,	PUNCT
m-1112	514	1	r̅	r̅	PROPN
m-1112	514	2	=	=	PUNCT
m-1112	514	3	z	z	PROPN
m-1112	514	4	,	,	PUNCT
m-1112	514	5	1_2_3	1_2_3	NUM
m-1112	514	6	,	,	PUNCT
m-1112	514	7	mo̅̅	mo̅̅	NOUN
m-1112	514	8	̅̅	̅̅	PROPN
m-1112	514	9	̅̅	̅̅	PROPN
m-1112	514	10	̅̅	̅̅	PROPN
m-1112	514	11	̅̅	̅̅	PROPN
m-1112	514	12	̅̅	̅̅	PROPN
m-1112	514	13	̅̅	̅̅	PROPN
m-1112	514	14	̅̅	̅̅	PROPN
m-1112	514	15	̅	̅	PROPN
m-1112	514	16	≡	≡	PROPN
m-1112	514	17	⤱	⤱	VERB
m-1112	514	18	the	the	DET
m-1112	514	19	total	total	ADJ
m-1112	514	20	energy	energy	NOUN
m-1112	514	21	2l	2l	NUM
m-1112	514	22	=	=	SYM
m-1112	514	23	b	b	PROPN
m-1112	514	24	w	w	PROPN
m-1112	514	25	≡	≡	PROPN
m-1112	515	1	e	e	PROPN
m-1112	515	2	k	k	PROPN
m-1112	515	3	+	+	CCONJ
m-1112	515	4	e	e	X
m-1112	515	5	u	u	PROPN
m-1112	515	6	≡	≡	PROPN
m-1112	515	7	|kx|x|ky|x|aka|	|kx|x|ky|x|aka|	PROPN
m-1112	515	8	≡	≡	PROPN
m-1112	515	9	|kx|x|ky|x|λ|	|kx|x|ky|x|λ|	ADP
m-1112	515	10	≡	≡	PROPN
m-1112	515	11	an	an	DET
m-1112	515	12	propagatingwave	propagatingwave	NOUN
m-1112	515	13	in	in	ADP
m-1112	515	14	λ	λ	PROPN
m-1112	515	15	,	,	PUNCT
m-1112	515	16	i.e.	i.e.	X
m-1112	515	17	energy	energy	NOUN
m-1112	515	18	-	-	PUNCT
m-1112	515	19	square	square	ADJ
m-1112	515	20	-	-	PUNCT
m-1112	515	21	prism	prism	NOUN
m-1112	515	22	is	be	AUX
m-1112	515	23	a	a	DET
m-1112	515	24	moving	move	VERB
m-1112	515	25	-	-	PUNCT
m-1112	515	26	energy	energy	NOUN
m-1112	515	27	-	-	PUNCT
m-1112	515	28	volume	volume	NOUN
m-1112	515	29	and	and	CCONJ
m-1112	515	30	because	because	SCONJ
m-1112	515	31	from	from	ADP
m-1112	515	32	cauchy	cauchy	PROPN
m-1112	515	33	equations	equation	NOUN
m-1112	515	34	of	of	ADP
m-1112	515	35	stresses	stress	NOUN
m-1112	515	36	in	in	ADP
m-1112	515	37	three	three	NUM
m-1112	515	38	dimensions	dimension	NOUN
m-1112	515	39	,	,	PUNCT
m-1112	515	40	the	the	DET
m-1112	515	41	energy	energy	NOUN
m-1112	515	42	stress	stress	NOUN
m-1112	515	43	remains	remain	VERB
m-1112	515	44	flat	flat	ADJ
m-1112	515	45	only	only	ADV
m-1112	515	46	when	when	SCONJ
m-1112	515	47	the	the	DET
m-1112	515	48	plane	plane	NOUN
m-1112	515	49	section	section	NOUN
m-1112	515	50	becomes	become	VERB
m-1112	515	51	a	a	DET
m-1112	515	52	circle	circle	NOUN
m-1112	515	53	,	,	PUNCT
m-1112	515	54	and	and	CCONJ
m-1112	515	55	because	because	SCONJ
m-1112	515	56	from	from	ADP
m-1112	515	57	mechanics	mechanic	NOUN
m-1112	515	58	the	the	DET
m-1112	515	59	sphere	sphere	NOUN
m-1112	515	60	occupies	occupy	VERB
m-1112	515	61	the	the	DET
m-1112	515	62	least	least	ADJ
m-1112	515	63	resistance	resistance	NOUN
m-1112	515	64	to	to	ADP
m-1112	515	65	the	the	DET
m-1112	515	66	motion	motion	NOUN
m-1112	515	67	,	,	PUNCT
m-1112	515	68	then	then	ADV
m-1112	515	69	the	the	DET
m-1112	515	70	square	square	ADJ
m-1112	515	71	prism	prism	NOUN
m-1112	515	72	is	be	AUX
m-1112	515	73	altered	alter	VERB
m-1112	515	74	to	to	ADP
m-1112	515	75	the	the	DET
m-1112	515	76	equivalent	equivalent	NOUN
m-1112	515	77	,	,	PUNCT
m-1112	515	78	energy	energy	NOUN
m-1112	515	79	-	-	PUNCT
m-1112	515	80	sphere	sphere	NOUN
m-1112	515	81	cone	cone	NOUN
m-1112	515	82	→	→	SYM
m-1112	515	83	⸿	⸿	PROPN
m-1112	515	84	=	=	SYM
m-1112	515	85	k	k	PROPN
m-1112	515	86	πr	πr	PROPN
m-1112	515	87	³	³	NUM
m-1112	515	88	←	←	PROPN
m-1112	515	89	fig-9a	fig-9a	PROPN
m-1112	515	90	,	,	PUNCT
m-1112	515	91	9b	9b	NOUN
m-1112	515	92	,	,	PUNCT
m-1112	515	93	9c	9c	NUM
m-1112	515	94	.	.	PUNCT
m-1112	516	1	where	where	SCONJ
m-1112	516	2	the	the	DET
m-1112	516	3	cube	cube	NOUN
m-1112	516	4	[	[	X
m-1112	516	5	|	|	NOUN
m-1112	516	6	↔	↔	PROPN
m-1112	516	7	|.|	|.|	NOUN
m-1112	516	8	↕	↕	PROPN
m-1112	516	9	|.|𝐀𝐊𝐀|	|.|𝐀𝐊𝐀|	PROPN
m-1112	516	10	]	]	X
m-1112	516	11	=	=	SYM
m-1112	516	12	x	x	SYM
m-1112	516	13	³	³	X
m-1112	516	14	becomes	become	VERB
m-1112	516	15	an	an	DET
m-1112	516	16	sphere	sphere	NOUN
m-1112	516	17	–	–	PUNCT
m-1112	516	18	cone	cone	PROPN
m-1112	516	19	≡	≡	PROPN
m-1112	516	20	𝐐.𝐀𝐊𝐀	𝐐.𝐀𝐊𝐀	PROPN
m-1112	516	21	⃗⃗	⃗⃗	PROPN
m-1112	516	22	⃗⃗	⃗⃗	PROPN
m-1112	516	23	⃗⃗	⃗⃗	PROPN
m-1112	516	24	⃗⃗	⃗⃗	PROPN
m-1112	516	25	⃗⃗	⃗⃗	PROPN
m-1112	517	1	|	|	ADV
m-1112	517	2	⇉	⇉	PROPN
m-1112	518	1	|	|	ADV
m-1112	518	2	↑↓	↑↓	X
m-1112	519	1	𝛌	𝛌	NOUN
m-1112	519	2	|	|	ADV
m-1112	519	3	→	→	SYM
m-1112	519	4	k	k	PROPN
m-1112	519	5	π	π	PROPN
m-1112	519	6	r³	r³	PROPN
m-1112	519	7	=	=	SYM
m-1112	519	8	x	x	SYM
m-1112	519	9	³	³	PROPN
m-1112	519	10	.	.	PUNCT
m-1112	520	1	from	from	ADP
m-1112	520	2	the	the	DET
m-1112	520	3	max	max	PROPN
m-1112	520	4	-	-	PUNCT
m-1112	520	5	sin	sin	NOUN
m-1112	520	6	|	|	NOUN
m-1112	520	7	w	w	PROPN
m-1112	520	8	.aka	.aka	PUNCT
m-1112	520	9	c	c	NOUN
m-1112	521	1	|	|	ADV
m-1112	521	2	=	=	NOUN
m-1112	521	3	1	1	NUM
m-1112	521	4	,	,	PUNCT
m-1112	521	5	of	of	ADP
m-1112	521	6	equation	equation	NOUN
m-1112	521	7	(	(	PUNCT
m-1112	521	8	6	6	NUM
m-1112	521	9	)	)	PUNCT
m-1112	521	10	then	then	ADV
m-1112	521	11	u	u	X
m-1112	522	1	=	=	PUNCT
m-1112	522	2	[	[	PUNCT
m-1112	522	3	c	c	X
m-1112	522	4	sin	sin	NOUN
m-1112	522	5	wt	wt	PROPN
m-1112	523	1	+	+	CCONJ
m-1112	523	2	d	d	PROPN
m-1112	523	3	cos	cos	ADP
m-1112	523	4	wt	wt	PROPN
m-1112	523	5	]	]	PUNCT
m-1112	523	6	.sin|	.sin|	PUNCT
m-1112	523	7	.	.	PUNCT
m-1112	524	1	𝐰	𝐰	PART
m-1112	524	2	.𝐀𝐊𝐀	.𝐀𝐊𝐀	PUNCT
m-1112	525	1	𝐜	𝐜	NOUN
m-1112	525	2	|	|	ADV
m-1112	525	3	…	…	PUNCT
m-1112	525	4	…	…	PUNCT
m-1112	525	5	..	..	PUNCT
m-1112	525	6	…	…	PUNCT
m-1112	525	7	(	(	PUNCT
m-1112	525	8	14a	14a	NOUN
m-1112	525	9	)	)	PUNCT
m-1112	525	10	the	the	DET
m-1112	525	11	condition	condition	NOUN
m-1112	525	12	u	u	NOUN
m-1112	525	13	=	=	PROPN
m-1112	525	14	y	y	PROPN
m-1112	525	15	(	(	PUNCT
m-1112	525	16	aka	aka	ADV
m-1112	525	17	,	,	PUNCT
m-1112	525	18	t	t	PROPN
m-1112	525	19	)	)	PUNCT
m-1112	526	1	=	=	SYM
m-1112	526	2	0	0	NUM
m-1112	526	3	,	,	PUNCT
m-1112	526	4	leads	lead	VERB
m-1112	526	5	to	to	ADP
m-1112	526	6	the	the	DET
m-1112	526	7	equation	equation	NOUN
m-1112	526	8	→	→	PUNCT
m-1112	526	9	sin	sin	NOUN
m-1112	526	10	|	|	ADV
m-1112	526	11	𝐰	𝐰	ADJ
m-1112	526	12	.𝐀𝐊𝐀	.𝐀𝐊𝐀	NOUN
m-1112	527	1	𝐜	𝐜	NOUN
m-1112	527	2	|	|	ADV
m-1112	527	3	=	=	SYM
m-1112	527	4	0	0	NUM
m-1112	527	5	,	,	PUNCT
m-1112	527	6	or	or	CCONJ
m-1112	527	7	to	to	ADP
m-1112	527	8	…	…	PUNCT
m-1112	527	9	(	(	PUNCT
m-1112	527	10	14	14	NUM
m-1112	527	11	)	)	PUNCT
m-1112	527	12	for	for	ADP
m-1112	527	13	the	the	DET
m-1112	527	14	duality	duality	NOUN
m-1112	527	15	-	-	PUNCT
m-1112	527	16	photons	photon	NOUN
m-1112	527	17	issues	issue	NOUN
m-1112	527	18	,	,	PUNCT
m-1112	527	19	v̅	v̅	PROPN
m-1112	527	20	.	.	PUNCT
m-1112	528	1	[	[	PUNCT
m-1112	528	2	fn̅	fn̅	PROPN
m-1112	528	3	+	+	NUM
m-1112	528	4	fn	fn	NOUN
m-1112	528	5	]	]	PUNCT
m-1112	528	6	≡	≡	PROPN
m-1112	528	7	|	|	CCONJ
m-1112	528	8	𝐯	𝐯	X
m-1112	528	9	𝛑²	𝛑²	ADV
m-1112	528	10	.	.	PUNCT
m-1112	529	1	𝐫⁴𝐧	𝐫⁴𝐧	PROPN
m-1112	529	2	|	|	NOUN
m-1112	529	3	.	.	PUNCT
m-1112	530	1	b̅n	b̅n	PROPN
m-1112	530	2	+	+	CCONJ
m-1112	531	1	|	|	ADV
m-1112	531	2	c̅	c̅	ADP
m-1112	531	3	|	|	ADV
m-1112	531	4	fn	fn	PROPN
m-1112	531	5	..	..	PUNCT
m-1112	531	6	…	…	PUNCT
m-1112	531	7	…	…	PUNCT
m-1112	531	8	...	...	PUNCT
m-1112	531	9	(	(	PUNCT
m-1112	531	10	15a	15a	NOUN
m-1112	531	11	)	)	PUNCT
m-1112	531	12	or	or	CCONJ
m-1112	531	13	v̅.	v̅.	NOUN
m-1112	531	14	[	[	PUNCT
m-1112	531	15	fn̅	fn̅	PROPN
m-1112	531	16	≡	≡	PROPN
m-1112	531	17	(	(	PUNCT
m-1112	531	18	n	n	PROPN
m-1112	531	19	+	+	CCONJ
m-1112	531	20	1	1	NUM
m-1112	531	21	2	2	NUM
m-1112	531	22	)	)	PUNCT
m-1112	531	23	�	�	PROPN
m-1112	531	24	̅	̅	NOUN
m-1112	531	25	�	�	PROPN
m-1112	531	26	2.|aka|	2.|aka|	NUM
m-1112	531	27	]	]	PUNCT
m-1112	532	1	+	+	CCONJ
m-1112	532	2	[	[	X
m-1112	532	3	f	f	X
m-1112	532	4	n	n	CCONJ
m-1112	532	5	≡	≡	PROPN
m-1112	532	6	n	n	PRON
m-1112	532	7	�	�	PROPN
m-1112	532	8	̅	̅	NOUN
m-1112	532	9	�	�	PROPN
m-1112	532	10	2λ	2λ	PROPN
m-1112	532	11	]	]	X
m-1112	532	12	≡	≡	PROPN
m-1112	532	13	→	→	SYM
m-1112	532	14	�	�	PROPN
m-1112	532	15	̅	̅	NOUN
m-1112	532	16	�	�	PROPN
m-1112	532	17	{	{	PUNCT
m-1112	532	18	|	|	NOUN
m-1112	532	19	�	�	NOUN
m-1112	532	20	̅	̅	NOUN
m-1112	532	21	�	�	NOUN
m-1112	532	22	𝟐.𝛌	𝟐.𝛌	NOUN
m-1112	532	23	|	|	ADV
m-1112	532	24	(	(	PUNCT
m-1112	532	25	n	n	PROPN
m-1112	532	26	+	+	CCONJ
m-1112	532	27	𝟏	𝟏	NUM
m-1112	532	28	𝟐	𝟐	NUM
m-1112	532	29	)	)	PUNCT
m-1112	532	30	+	+	CCONJ
m-1112	532	31	𝐧	𝐧	DET
m-1112	532	32	𝟐𝛌	𝟐𝛌	NOUN
m-1112	532	33	}	}	PUNCT
m-1112	532	34	..........	..........	PUNCT
m-1112	532	35	(	(	PUNCT
m-1112	532	36	15	15	NUM
m-1112	532	37	)	)	PUNCT
m-1112	532	38	ijo	ijo	PROPN
m-1112	532	39	international	international	PROPN
m-1112	532	40	journal	journal	PROPN
m-1112	532	41	of	of	ADP
m-1112	532	42	mathematics	mathematics	PROPN
m-1112	532	43	(	(	PUNCT
m-1112	532	44	issn	issn	PROPN
m-1112	532	45	:	:	PUNCT
m-1112	532	46	2992	2992	NUM
m-1112	532	47	-	-	SYM
m-1112	532	48	4421	4421	NUM
m-1112	532	49	)	)	PUNCT
m-1112	532	50	volume	volume	NOUN
m-1112	532	51	08	08	NUM
m-1112	533	1	|	|	ADV
m-1112	533	2	issue	issue	NOUN
m-1112	533	3	08	08	NUM
m-1112	534	1	|	|	ADV
m-1112	534	2	august	august	PROPN
m-1112	534	3	2025	2025	NUM
m-1112	534	4	|	|	ADV
m-1112	534	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	534	6	ijo	ijo	PROPN
m-1112	534	7	journals	journal	NOUN
m-1112	534	8	19	19	NUM
m-1112	534	9	the	the	DET
m-1112	534	10	fundamental	fundamental	ADJ
m-1112	534	11	particles	particle	NOUN
m-1112	534	12	origination	origination	NOUN
m-1112	534	13	mechanism	mechanism	NOUN
m-1112	534	14	in	in	ADP
m-1112	534	15	mfmf	mfmf	PROPN
m-1112	534	16	pns	pns	PROPN
m-1112	534	17	caves	cave	NOUN
m-1112	534	18	.	.	PUNCT
m-1112	535	1	e	e	X
m-1112	535	2	-	-	NOUN
m-1112	535	3	vectors	vector	NOUN
m-1112	535	4	|𝐐	|𝐐	VERB
m-1112	535	5	⇉	⇉	PROPN
m-1112	535	6	aka⃗⃗	aka⃗⃗	PROPN
m-1112	535	7	⃗⃗	⃗⃗	PROPN
m-1112	535	8	⃗⃗	⃗⃗	PROPN
m-1112	535	9	⃗⃗	⃗⃗	PROPN
m-1112	535	10	⃗	⃗	PROPN
m-1112	535	11	=	=	SYM
m-1112	535	12	↔|	↔|	PROPN
m-1112	535	13	x	x	SYM
m-1112	535	14	|𝐐	|𝐐	PROPN
m-1112	535	15	⇈	⇈	NUM
m-1112	535	16	aka⃗⃗	aka⃗⃗	PROPN
m-1112	535	17	⃗⃗	⃗⃗	PROPN
m-1112	535	18	⃗⃗	⃗⃗	PROPN
m-1112	535	19	⃗⃗	⃗⃗	PROPN
m-1112	535	20	⃗	⃗	PROPN
m-1112	535	21	=	=	SYM
m-1112	535	22	↕	↕	PROPN
m-1112	535	23	|x|aka|	|x|aka|	PROPN
m-1112	535	24	≡	≡	PROPN
m-1112	535	25	|qx.qy|.|aka|	|qx.qy|.|aka|	PROPN
m-1112	535	26	≡	≡	PROPN
m-1112	536	1	|	|	ADV
m-1112	536	2	↔	↔	PROPN
m-1112	536	3	|x|	|x|	PROPN
m-1112	536	4	↕	↕	PROPN
m-1112	536	5	|y|	|y|	PROPN
m-1112	536	6	λ	λ	PROPN
m-1112	536	7	|	|	ADV
m-1112	537	1	≡	≡	PROPN
m-1112	537	2	k	k	PROPN
m-1112	537	3	π	π	PROPN
m-1112	537	4	r³.	r³.	NOUN
m-1112	537	5	from	from	ADP
m-1112	537	6	wave	wave	NOUN
m-1112	537	7	-	-	PUNCT
m-1112	537	8	energy	energy	NOUN
m-1112	537	9	-	-	PUNCT
m-1112	537	10	constant	constant	ADJ
m-1112	537	11	k	k	NOUN
m-1112	537	12	=	=	PUNCT
m-1112	537	13	2π	2π	NOUN
m-1112	537	14	λ	λ	NOUN
m-1112	537	15	=	=	PUNCT
m-1112	537	16	2πf	2πf	NOUN
m-1112	537	17	c	c	NOUN
m-1112	538	1	=	=	PUNCT
m-1112	538	2	w	w	PROPN
m-1112	538	3	c	c	NOUN
m-1112	538	4	=	=	SYM
m-1112	539	1	|	|	ADV
m-1112	539	2	v̅	v̅	NOUN
m-1112	539	3	c	c	NOUN
m-1112	539	4	|	|	ADV
m-1112	539	5	.	.	PUNCT
m-1112	539	6	{	{	PUNCT
m-1112	540	1	1	1	NUM
m-1112	540	2	r	r	NOUN
m-1112	540	3	=	=	SYM
m-1112	540	4	2	2	NUM
m-1112	540	5	r|a−k𝐴|	r|a−k𝐴|	ADJ
m-1112	540	6	}	}	PUNCT
m-1112	540	7	so	so	ADV
m-1112	540	8	c=	c=	NOUN
m-1112	540	9	w	w	NOUN
m-1112	540	10	k	k	NOUN
m-1112	540	11	=	=	PUNCT
m-1112	540	12	λ	λ	X
m-1112	540	13	f	f	PROPN
m-1112	540	14	,	,	PUNCT
m-1112	540	15	or	or	CCONJ
m-1112	540	16	|	|	ADV
m-1112	540	17	�	�	NOUN
m-1112	540	18	̅	̅	NOUN
m-1112	540	19	�	�	NOUN
m-1112	540	20	𝟐.|𝐀𝐊𝐀|	𝟐.|𝐀𝐊𝐀|	PUNCT
m-1112	540	21	|≡	|≡	ADP
m-1112	540	22	f	f	PROPN
m-1112	540	23	i.e.	i.e.	X
m-1112	540	24	frequency	frequency	NOUN
m-1112	540	25	f	f	PROPN
m-1112	540	26	aka	aka	ADV
m-1112	540	27	of	of	ADP
m-1112	540	28	pipe	pipe	NOUN
m-1112	540	29	|aka|	|aka|	NOUN
m-1112	540	30	is	be	AUX
m-1112	540	31	the	the	DET
m-1112	540	32	stationary	stationary	ADJ
m-1112	540	33	-	-	PUNCT
m-1112	540	34	photon	photon	NOUN
m-1112	540	35	energy	energy	NOUN
m-1112	540	36	-	-	PUNCT
m-1112	540	37	storage	storage	NOUN
m-1112	540	38	fn̅	fn̅	PROPN
m-1112	540	39	≡	≡	PROPN
m-1112	540	40	|	|	PROPN
m-1112	540	41	�	�	PROPN
m-1112	540	42	̅	̅	NOUN
m-1112	540	43	�	�	PROPN
m-1112	540	44	𝟐.|𝐀𝐊𝐀|	𝟐.|𝐀𝐊𝐀|	PUNCT
m-1112	540	45	|	|	ADV
m-1112	540	46	≡	≡	PROPN
m-1112	541	1	|	|	PROPN
m-1112	541	2	�	�	PROPN
m-1112	541	3	̅	̅	NOUN
m-1112	541	4	�	�	NOUN
m-1112	541	5	𝛌	𝛌	X
m-1112	541	6	|	|	NOUN
m-1112	541	7	...	...	PUNCT
m-1112	541	8	(	(	PUNCT
m-1112	541	9	16	16	NUM
m-1112	541	10	)	)	PUNCT
m-1112	541	11	and	and	CCONJ
m-1112	541	12	photon	photon	NOUN
m-1112	541	13	v̅.	v̅.	NOUN
m-1112	541	14	[	[	PUNCT
m-1112	541	15	fn̅	fn̅	PROPN
m-1112	541	16	+	+	CCONJ
m-1112	541	17	fn	fn	NOUN
m-1112	541	18	]	]	PUNCT
m-1112	541	19	≡	≡	PROPN
m-1112	541	20	�	�	PROPN
m-1112	541	21	̅	̅	NOUN
m-1112	541	22	�	�	PROPN
m-1112	541	23	.	.	PUNCT
m-1112	541	24	{	{	PUNCT
m-1112	542	1	|	|	ADV
m-1112	542	2	�	�	NOUN
m-1112	542	3	̅	̅	NOUN
m-1112	542	4	�	�	NOUN
m-1112	543	1	𝛌	𝛌	ADP
m-1112	543	2	|	|	ADV
m-1112	543	3	+	+	CCONJ
m-1112	543	4	𝐟𝐧	𝐟𝐧	ADJ
m-1112	543	5	}	}	PUNCT
m-1112	543	6	i.e.	i.e.	X
m-1112	543	7	,	,	PUNCT
m-1112	543	8	as	as	SCONJ
m-1112	543	9	particle	particle	NOUN
m-1112	543	10	≡	≡	PROPN
m-1112	543	11	v̅.	v̅.	PROPN
m-1112	543	12	|	|	NOUN
m-1112	543	13	�	�	NOUN
m-1112	543	14	̅	̅	NOUN
m-1112	543	15	�	�	PROPN
m-1112	543	16	𝛌	𝛌	ADP
m-1112	543	17	|	|	ADV
m-1112	543	18	≡	≡	PROPN
m-1112	543	19	e	e	PROPN
m-1112	543	20	u	u	PROPN
m-1112	543	21	≡	≡	ADJ
m-1112	543	22	potential	potential	ADJ
m-1112	543	23	energy	energy	NOUN
m-1112	543	24	,	,	PUNCT
m-1112	543	25	and	and	CCONJ
m-1112	543	26	as	as	ADP
m-1112	543	27	wave	wave	NOUN
m-1112	543	28	≡	≡	PROPN
m-1112	543	29	v̅.	v̅.	PROPN
m-1112	543	30	fn	fn	PROPN
m-1112	543	31	≡	≡	PROPN
m-1112	543	32	e	e	PROPN
m-1112	543	33	k	k	PROPN
m-1112	543	34	≡	≡	PROPN
m-1112	543	35	kinetic	kinetic	ADJ
m-1112	543	36	energy	energy	NOUN
m-1112	543	37	.	.	PUNCT
m-1112	544	1	since	since	SCONJ
m-1112	544	2	energyconstant	energyconstant	NOUN
m-1112	544	3	-	-	PUNCT
m-1112	544	4	magnitude	magnitude	NOUN
m-1112	544	5	,	,	PUNCT
m-1112	544	6	k	k	PROPN
m-1112	544	7	,	,	PUNCT
m-1112	544	8	denotes	denote	VERB
m-1112	544	9	the	the	DET
m-1112	544	10	total	total	ADJ
m-1112	544	11	motion	motion	NOUN
m-1112	544	12	then	then	ADV
m-1112	544	13	needs	need	VERB
m-1112	544	14	a	a	DET
m-1112	544	15	scalar	scalar	ADJ
m-1112	544	16	-magnitude	-magnitude	NOUN
m-1112	544	17	for	for	ADP
m-1112	544	18	measurements	measurement	NOUN
m-1112	544	19	and	and	CCONJ
m-1112	544	20	a	a	DET
m-1112	544	21	vectormagnitude	vectormagnitude	NOUN
m-1112	544	22	for	for	ADP
m-1112	544	23	directions	direction	NOUN
m-1112	544	24	.	.	PUNCT
m-1112	545	1	in	in	ADP
m-1112	545	2	conductor	conductor	NOUN
m-1112	545	3	d	d	NOUN
m-1112	545	4	=	=	PUNCT
m-1112	545	5	|aka|	|aka|	NOUN
m-1112	545	6	,	,	PUNCT
m-1112	546	1	|	|	ADV
m-1112	547	1	d	d	NOUN
m-1112	548	1	|	|	ADV
m-1112	548	2	≡	≡	PROPN
m-1112	548	3	the	the	DET
m-1112	548	4	scalar	scalar	ADJ
m-1112	548	5	magnitude	magnitude	NOUN
m-1112	548	6	between	between	ADP
m-1112	548	7	points	point	NOUN
m-1112	548	8	,	,	PUNCT
m-1112	548	9	which	which	PRON
m-1112	548	10	gives	give	VERB
m-1112	548	11	also	also	ADV
m-1112	548	12	the	the	DET
m-1112	548	13	direction	direction	NOUN
m-1112	548	14	of	of	ADP
m-1112	548	15	motion	motion	NOUN
m-1112	548	16	with	with	ADP
m-1112	548	17	points	point	NOUN
m-1112	548	18	,	,	PUNCT
m-1112	548	19	a	a	DET
m-1112	548	20	,	,	PUNCT
m-1112	548	21	ka	ka	PROPN
m-1112	548	22	,	,	PUNCT
m-1112	548	23	and	and	CCONJ
m-1112	548	24	aka	aka	ADV
m-1112	548	25	⃗⃗	⃗⃗	PROPN
m-1112	548	26	⃗⃗	⃗⃗	PROPN
m-1112	548	27	⃗⃗	⃗⃗	PROPN
m-1112	548	28	⃗⃗	⃗⃗	PROPN
m-1112	548	29	vector	vector	NOUN
m-1112	548	30	the	the	DET
m-1112	548	31	direction	direction	NOUN
m-1112	548	32	which	which	PRON
m-1112	548	33	defines	define	VERB
m-1112	548	34	the	the	DET
m-1112	548	35	vector	vector	NOUN
m-1112	548	36	aka	aka	ADP
m-1112	548	37	⃗⃗	⃗⃗	PROPN
m-1112	548	38	⃗⃗	⃗⃗	PROPN
m-1112	548	39	⃗⃗	⃗⃗	PROPN
m-1112	548	40	⃗⃗	⃗⃗	PROPN
m-1112	548	41	.	.	PUNCT
m-1112	549	1	the	the	DET
m-1112	549	2	total	total	ADJ
m-1112	549	3	energy	energy	NOUN
m-1112	549	4	k	k	NOUN
m-1112	550	1	=	=	PUNCT
m-1112	550	2	|	|	ADV
m-1112	550	3	v̅	v̅	NOUN
m-1112	550	4	c	c	NOUN
m-1112	550	5	|	|	NOUN
m-1112	550	6	.	.	PUNCT
m-1112	551	1	[	[	PUNCT
m-1112	551	2	2	2	NUM
m-1112	551	3	r[a−ka	r[a−ka	NOUN
m-1112	551	4	]	]	PUNCT
m-1112	551	5	]	]	PUNCT
m-1112	551	6	of	of	ADP
m-1112	551	7	photon	photon	NOUN
m-1112	551	8	-	-	PUNCT
m-1112	551	9	wave	wave	NOUN
m-1112	551	10	is	be	AUX
m-1112	551	11	split	split	VERB
m-1112	551	12	as	as	ADP
m-1112	551	13	,	,	PUNCT
m-1112	551	14	e	e	NOUN
m-1112	551	15	u+	u+	NOUN
m-1112	551	16	e	e	PROPN
m-1112	551	17	k=	k=	X
m-1112	551	18	k	k	PROPN
m-1112	551	19	≡	≡	PROPN
m-1112	551	20	potential	potential	NOUN
m-1112	551	21	+	+	CCONJ
m-1112	551	22	kinetic	kinetic	ADJ
m-1112	551	23	energy	energy	NOUN
m-1112	551	24	where	where	SCONJ
m-1112	551	25	e	e	PROPN
m-1112	551	26	u	u	NOUN
m-1112	551	27	≡	≡	PROPN
m-1112	551	28	v̅.	v̅.	PROPN
m-1112	551	29	|	|	NOUN
m-1112	551	30	�	�	NOUN
m-1112	551	31	̅	̅	NOUN
m-1112	551	32	�	�	PROPN
m-1112	551	33	𝛌	𝛌	ADP
m-1112	551	34	|	|	ADV
m-1112	551	35	≡	≡	PROPN
m-1112	551	36	particle	particle	NOUN
m-1112	551	37	≡	≡	PROPN
m-1112	551	38	�	�	PROPN
m-1112	551	39	̅	̅	PROPN
m-1112	551	40	�	�	PROPN
m-1112	551	41	{	{	PUNCT
m-1112	551	42	|	|	NOUN
m-1112	551	43	�	�	NOUN
m-1112	551	44	̅	̅	NOUN
m-1112	551	45	�	�	NOUN
m-1112	551	46	𝟐.𝛌	𝟐.𝛌	NOUN
m-1112	551	47	|	|	ADV
m-1112	551	48	(	(	PUNCT
m-1112	551	49	n	n	PROPN
m-1112	551	50	+	+	CCONJ
m-1112	551	51	𝟏	𝟏	NUM
m-1112	551	52	𝟐	𝟐	NUM
m-1112	551	53	)	)	PUNCT
m-1112	551	54	}	}	PUNCT
m-1112	551	55	≡	≡	PROPN
m-1112	551	56	|	|	ADV
m-1112	551	57	𝐯	𝐯	X
m-1112	551	58	𝛑²	𝛑²	ADV
m-1112	551	59	.	.	PUNCT
m-1112	552	1	𝐫⁴𝐧	𝐫⁴𝐧	PROPN
m-1112	552	2	|	|	NOUN
m-1112	552	3	.	.	PUNCT
m-1112	553	1	b̅n	b̅n	PROPN
m-1112	553	2	=	=	PUNCT
m-1112	554	1	|	|	ADV
m-1112	554	2	𝐯	𝐯	X
m-1112	554	3	𝛑²	𝛑²	NOUN
m-1112	554	4	.	.	PUNCT
m-1112	555	1	𝐫⁴𝐧	𝐫⁴𝐧	PRON
m-1112	555	2	|	|	ADV
m-1112	555	3	r².q.b̅m	r².q.b̅m	VERB
m-1112	555	4	≡	≡	PROPN
m-1112	556	1	|	|	ADV
m-1112	556	2	𝐪.𝐯	𝐪.𝐯	PROPN
m-1112	556	3	𝛑²	𝛑²	PROPN
m-1112	556	4	.	.	PUNCT
m-1112	557	1	𝐫⁴𝐧	𝐫⁴𝐧	PRON
m-1112	557	2	|	|	ADV
m-1112	557	3	x	x	X
m-1112	557	4	b̅m	b̅m	NOUN
m-1112	557	5	is	be	AUX
m-1112	557	6	the	the	DET
m-1112	557	7	stationary	stationary	ADJ
m-1112	557	8	-	-	PUNCT
m-1112	557	9	storage	storage	NOUN
m-1112	557	10	≡	≡	PROPN
m-1112	557	11	particle	particle	NOUN
m-1112	557	12	≡	≡	PROPN
m-1112	557	13	magnetic	magnetic	ADJ
m-1112	557	14	-	-	PUNCT
m-1112	557	15	field	field	NOUN
m-1112	557	16	with	with	ADP
m-1112	557	17	velocity	velocity	NOUN
m-1112	557	18	,	,	PUNCT
m-1112	557	19	v	v	INTJ
m-1112	557	20	,	,	PUNCT
m-1112	557	21	in	in	ADP
m-1112	557	22	cave	cave	NOUN
m-1112	557	23	λ	λ	PROPN
m-1112	557	24	=	=	SYM
m-1112	557	25	2r	2r	NUM
m-1112	558	1	=	=	PUNCT
m-1112	558	2	2π	2π	PROPN
m-1112	558	3	/	/	SYM
m-1112	558	4	k	k	PROPN
m-1112	558	5	and	and	CCONJ
m-1112	558	6	e	e	PROPN
m-1112	558	7	k	k	PROPN
m-1112	558	8	≡	≡	PROPN
m-1112	558	9	v̅.fn	v̅.fn	PROPN
m-1112	558	10	≡	≡	PROPN
m-1112	558	11	wave	wave	NOUN
m-1112	558	12	≡	≡	PROPN
m-1112	558	13	kinetic	kinetic	ADJ
m-1112	558	14	energy	energy	NOUN
m-1112	558	15	=	=	PUNCT
m-1112	558	16	2π	2π	NOUN
m-1112	558	17	λ	λ	NOUN
m-1112	558	18	=	=	SYM
m-1112	558	19	q	q	PROPN
m-1112	558	20	k.a	k.a	PROPN
m-1112	558	21	=	=	SYM
m-1112	558	22	q	q	PROPN
m-1112	558	23	k.πr	k.πr	PROPN
m-1112	558	24	²	²	PROPN
m-1112	558	25	=	=	PUNCT
m-1112	558	26	σ.φ	σ.φ	PROPN
m-1112	558	27	k.3rb̅m	k.3rb̅m	NOUN
m-1112	558	28	=	=	PUNCT
m-1112	558	29	{	{	PUNCT
m-1112	558	30	σ.φ	σ.φ	PROPN
m-1112	558	31	k.3r	k.3r	PROPN
m-1112	558	32	}	}	PUNCT
m-1112	558	33	𝟏	𝟏	NUM
m-1112	559	1	b̅m	b̅m	NOUN
m-1112	559	2	=	=	SYM
m-1112	559	3	𝐜/𝐄	𝐜/𝐄	PROPN
m-1112	559	4	b̅m	b̅m	NOUN
m-1112	559	5	,	,	PUNCT
m-1112	559	6	and	and	CCONJ
m-1112	559	7	�	�	NOUN
m-1112	559	8	̅	̅	NOUN
m-1112	559	9	�	�	NOUN
m-1112	559	10	𝐄	𝐄	NOUN
m-1112	559	11	≡	≡	PROPN
m-1112	559	12	c	c	PROPN
m-1112	559	13	�	�	PROPN
m-1112	559	14	̅	̅	NOUN
m-1112	559	15	�	�	NOUN
m-1112	559	16	𝐌	𝐌	NOUN
m-1112	559	17	,	,	PUNCT
m-1112	559	18	and	and	CCONJ
m-1112	559	19	the	the	DET
m-1112	559	20	moving	move	VERB
m-1112	559	21	electromagnetic	electromagnetic	ADJ
m-1112	559	22	-	-	PUNCT
m-1112	559	23	wave	wave	NOUN
m-1112	559	24	is	be	AUX
m-1112	559	25	,	,	PUNCT
m-1112	559	26	e̅e	e̅e	PROPN
m-1112	559	27	=	=	PUNCT
m-1112	559	28	|e̅0|.sine	|e̅0|.sine	PROPN
m-1112	560	1	[	[	X
m-1112	560	2	kz	kz	PROPN
m-1112	560	3	wt	wt	PROPN
m-1112	560	4	]	]	PUNCT
m-1112	560	5	,	,	PUNCT
m-1112	560	6	b̅m	b̅m	X
m-1112	560	7	=	=	SYM
m-1112	560	8	|b̅0|.sine	|b̅0|.sine	PROPN
m-1112	561	1	[	[	X
m-1112	561	2	kz	kz	PROPN
m-1112	561	3	wt	wt	PROPN
m-1112	561	4	]	]	PUNCT
m-1112	561	5	,	,	PUNCT
m-1112	561	6	k	k	X
m-1112	561	7	=	=	PUNCT
m-1112	561	8	2π	2π	PROPN
m-1112	561	9	λ	λ	NOUN
m-1112	561	10	,	,	PUNCT
m-1112	561	11	motion	motion	NOUN
m-1112	561	12	is	be	AUX
m-1112	561	13	kept	keep	VERB
m-1112	561	14	in	in	ADP
m-1112	561	15	caves	cave	NOUN
m-1112	561	16	as	as	ADP
m-1112	561	17	electric	electric	ADJ
m-1112	561	18	,	,	PUNCT
m-1112	561	19	magnetic	magnetic	ADJ
m-1112	561	20	fields	field	NOUN
m-1112	561	21	and	and	CCONJ
m-1112	561	22	as	as	ADP
m-1112	561	23	frequencies	frequency	NOUN
m-1112	561	24	and	and	CCONJ
m-1112	561	25	conserved	conserve	VERB
m-1112	561	26	in	in	ADP
m-1112	561	27	them	they	PRON
m-1112	561	28	when	when	SCONJ
m-1112	561	29	the	the	DET
m-1112	561	30	space	space	NOUN
m-1112	561	31	-	-	PUNCT
m-1112	561	32	points	point	NOUN
m-1112	561	33	become	become	VERB
m-1112	561	34	energy	energy	NOUN
m-1112	561	35	-	-	PUNCT
m-1112	561	36	conductors	conductor	NOUN
m-1112	561	37	.	.	PUNCT
m-1112	562	1	the	the	PRON
m-1112	562	2	in	in	ADP
m-1112	562	3	caves	cave	NOUN
m-1112	562	4	energy	energy	NOUN
m-1112	562	5	-	-	PUNCT
m-1112	562	6	import	import	NOUN
m-1112	562	7	is	be	AUX
m-1112	562	8	shown	show	VERB
m-1112	562	9	in	in	ADP
m-1112	562	10	figures	figure	NOUN
m-1112	562	11	.	.	PUNCT
m-1112	563	1	examples	example	NOUN
m-1112	563	2	:	:	PUNCT
m-1112	563	3	1	1	X
m-1112	563	4	..	..	PUNCT
m-1112	563	5	in	in	ADP
m-1112	563	6	an	an	DET
m-1112	563	7	conductor	conductor	NOUN
m-1112	564	1	d	d	NOUN
m-1112	564	2	=	=	SYM
m-1112	564	3	aka=	aka=	PROPN
m-1112	564	4	2r	2r	NUM
m-1112	564	5	,	,	PUNCT
m-1112	564	6	with	with	ADP
m-1112	564	7	⊕	⊕	PROPN
m-1112	564	8	obstacle	obstacle	NOUN
m-1112	564	9	at	at	ADP
m-1112	564	10	ka	ka	PROPN
m-1112	564	11	point	point	PROPN
m-1112	564	12	occupies	occupy	VERB
m-1112	564	13	zero	zero	NUM
m-1112	564	14	velocity	velocity	NOUN
m-1112	564	15	and	and	CCONJ
m-1112	564	16	⊕	⊕	PROPN
m-1112	564	17	charge	charge	NOUN
m-1112	564	18	is	be	AUX
m-1112	564	19	accelerated	accelerate	VERB
m-1112	564	20	.	.	PUNCT
m-1112	565	1	the	the	DET
m-1112	565	2	initial	initial	ADJ
m-1112	565	3	light	light	ADJ
m-1112	565	4	-	-	PUNCT
m-1112	565	5	velocity	velocity	NOUN
m-1112	565	6	is	be	AUX
m-1112	565	7	accelerated	accelerate	VERB
m-1112	565	8	as	as	ADP
m-1112	565	9	v²	v²	PROPN
m-1112	565	10	=	=	PROPN
m-1112	565	11	v̅o²+2a.r	v̅o²+2a.r	X
m-1112	565	12	,	,	PUNCT
m-1112	565	13	or	or	CCONJ
m-1112	565	14	a	a	DET
m-1112	565	15	=	=	NOUN
m-1112	565	16	−v̅o²	−v̅o²	X
m-1112	565	17	2.r	2.r	NUM
m-1112	565	18	=	=	PUNCT
m-1112	566	1	[	[	X
m-1112	566	2	2,9979.108]²	2,9979.108]²	NUM
m-1112	566	3	2.r	2.r	NUM
m-1112	566	4	=	=	SYM
m-1112	566	5	8,9874044.1016	8,9874044.1016	NUM
m-1112	566	6	2.r	2.r	NUM
m-1112	566	7	m	m	PROPN
m-1112	566	8	/	/	SYM
m-1112	566	9	s²	s²	PROPN
m-1112	566	10	.	.	PUNCT
m-1112	567	1	for	for	ADP
m-1112	567	2	conductors	conductor	NOUN
m-1112	567	3	,	,	PUNCT
m-1112	567	4	r	r	NOUN
m-1112	567	5	=	=	NOUN
m-1112	567	6	10−16,100,1016	10−16,100,1016	NOUN
m-1112	567	7	then	then	ADV
m-1112	567	8	,	,	PUNCT
m-1112	567	9	a1	a1	NOUN
m-1112	567	10	=	=	PUNCT
m-1112	567	11	−v̅o²	−v̅o²	PROPN
m-1112	567	12	2.r	2.r	NUM
m-1112	567	13	=	=	SYM
m-1112	567	14	8,9874.1016	8,9874.1016	NUM
m-1112	567	15	2.10−16	2.10−16	NUM
m-1112	567	16	=	=	SYM
m-1112	567	17	4,4937.1032	4,4937.1032	NUM
m-1112	567	18	m	m	VERB
m-1112	567	19	s²	s²	PROPN
m-1112	567	20	,	,	PUNCT
m-1112	567	21	a2	a2	PROPN
m-1112	567	22	=	=	PUNCT
m-1112	567	23	−v̅o²	−v̅o²	PROPN
m-1112	567	24	2.r	2.r	NUM
m-1112	567	25	=	=	SYM
m-1112	567	26	8,9874044.1016	8,9874044.1016	NUM
m-1112	567	27	2.100	2.100	NUM
m-1112	567	28	=	=	SYM
m-1112	568	1	4,4937022.1016	4,4937022.1016	NUM
m-1112	568	2	m	m	NOUN
m-1112	568	3	/	/	SYM
m-1112	568	4	s²	s²	PROPN
m-1112	568	5	,	,	PUNCT
m-1112	568	6	a3	a3	NOUN
m-1112	568	7	=	=	SYM
m-1112	568	8	−v̅o²	−v̅o²	PROPN
m-1112	568	9	2.r	2.r	NUM
m-1112	568	10	=	=	SYM
m-1112	568	11	8,9874044.1016	8,9874044.1016	NUM
m-1112	569	1	2.1016	2.1016	NUM
m-1112	569	2	=	=	NUM
m-1112	569	3	4,4937022.100	4,4937022.100	NUM
m-1112	569	4	m	m	NOUN
m-1112	569	5	/	/	SYM
m-1112	569	6	s²	s²	PROPN
m-1112	569	7	.	.	PUNCT
m-1112	570	1	force	force	NOUN
m-1112	570	2	on	on	ADP
m-1112	570	3	charge	charge	NOUN
m-1112	570	4	becomes	become	VERB
m-1112	570	5	from	from	ADP
m-1112	570	6	the	the	DET
m-1112	570	7	electric	electric	ADJ
m-1112	570	8	field	field	NOUN
m-1112	570	9	as	as	ADP
m-1112	570	10	f̅k	f̅k	PROPN
m-1112	570	11	=	=	PUNCT
m-1112	570	12	m.a̅x=	m.a̅x=	PART
m-1112	570	13	q.e̅f	q.e̅f	NOUN
m-1112	570	14	=	=	ADJ
m-1112	570	15	+	+	PROPN
m-1112	570	16	e.	e.	PROPN
m-1112	570	17	e̅f	e̅f	PROPN
m-1112	570	18	and	and	CCONJ
m-1112	570	19	e̅f=	e̅f=	PROPN
m-1112	570	20	m.a	m.a	NOUN
m-1112	570	21	q	q	NOUN
m-1112	570	22	=	=	SYM
m-1112	570	23	e	e	NOUN
m-1112	570	24	,	,	PUNCT
m-1112	570	25	or	or	CCONJ
m-1112	570	26	e̅f	e̅f	NOUN
m-1112	570	27	=	=	SYM
m-1112	570	28	m.a	m.a	NOUN
m-1112	570	29	e	e	NOUN
m-1112	570	30	=	=	NOUN
m-1112	570	31	m	m	PUNCT
m-1112	570	32	e	e	NOUN
m-1112	571	1	[	[	X
m-1112	571	2	a	a	X
m-1112	571	3	]	]	X
m-1112	571	4	=	=	PUNCT
m-1112	571	5	9.10−31	9.10−31	NUM
m-1112	571	6	1,6022.10−19	1,6022.10−19	NUM
m-1112	571	7	[	[	X
m-1112	571	8	4,4937022.1032	4,4937022.1032	X
m-1112	571	9	]	]	X
m-1112	571	10	=	=	SYM
m-1112	571	11	25,242366	25,242366	NUM
m-1112	571	12	.	.	PUNCT
m-1112	572	1	1020	1020	NUM
m-1112	573	1	n	n	DET
m-1112	573	2	c	c	NOUN
m-1112	573	3	e̅f	e̅f	NOUN
m-1112	573	4	=	=	SYM
m-1112	573	5	m.a	m.a	NOUN
m-1112	573	6	e	e	NOUN
m-1112	573	7	=	=	NOUN
m-1112	573	8	m	m	PUNCT
m-1112	573	9	e	e	NOUN
m-1112	574	1	[	[	X
m-1112	574	2	a	a	X
m-1112	574	3	]	]	X
m-1112	574	4	=	=	PUNCT
m-1112	574	5	9.10−31	9.10−31	NUM
m-1112	574	6	1,6022.10−19	1,6022.10−19	NUM
m-1112	575	1	[	[	X
m-1112	575	2	4,4937022.1016	4,4937022.1016	X
m-1112	575	3	]	]	X
m-1112	575	4	=	=	SYM
m-1112	575	5	25,242366	25,242366	NUM
m-1112	575	6	.	.	PUNCT
m-1112	576	1	10	10	NUM
m-1112	576	2	4	4	NUM
m-1112	576	3	n	n	ADP
m-1112	576	4	c	c	NOUN
m-1112	576	5	e̅f	e̅f	NOUN
m-1112	576	6	=	=	SYM
m-1112	576	7	m.a	m.a	NOUN
m-1112	576	8	e	e	NOUN
m-1112	576	9	=	=	NOUN
m-1112	576	10	m	m	PUNCT
m-1112	576	11	e	e	NOUN
m-1112	577	1	[	[	X
m-1112	577	2	a	a	X
m-1112	577	3	]	]	X
m-1112	577	4	=	=	PUNCT
m-1112	577	5	9.10−31	9.10−31	NUM
m-1112	577	6	1,6022.10−19	1,6022.10−19	NUM
m-1112	577	7	[	[	X
m-1112	577	8	4,4937022.100	4,4937022.100	NUM
m-1112	577	9	]	]	X
m-1112	577	10	=	=	SYM
m-1112	577	11	25,242366	25,242366	NUM
m-1112	577	12	.	.	PUNCT
m-1112	578	1	10−12	10−12	NOUN
m-1112	578	2	n	n	ADP
m-1112	578	3	c	c	NOUN
m-1112	578	4	i.e.	i.e.	X
m-1112	578	5	the	the	DET
m-1112	578	6	⊕	⊕	PROPN
m-1112	578	7	charge	charge	NOUN
m-1112	578	8	is	be	AUX
m-1112	578	9	accelerated	accelerate	VERB
m-1112	578	10	opposite	opposite	ADV
m-1112	578	11	to	to	ADP
m-1112	578	12	initial	initial	ADJ
m-1112	578	13	direction	direction	NOUN
m-1112	578	14	of	of	ADP
m-1112	578	15	⊝	⊝	NUM
m-1112	578	16	charge	charge	NOUN
m-1112	578	17	in	in	ADP
m-1112	578	18	an	an	DET
m-1112	578	19	electric	electric	ADJ
m-1112	578	20	-	-	PUNCT
m-1112	578	21	field	field	NOUN
m-1112	578	22	e̅f	e̅f	NOUN
m-1112	578	23	.	.	PUNCT
m-1112	579	1	this	this	DET
m-1112	579	2	property	property	NOUN
m-1112	579	3	of	of	ADP
m-1112	579	4	acceleration	acceleration	NOUN
m-1112	579	5	,	,	PUNCT
m-1112	579	6	creates	create	VERB
m-1112	579	7	the	the	DET
m-1112	579	8	magnetic	magnetic	NOUN
m-1112	579	9	-	-	PUNCT
m-1112	579	10	fields	field	NOUN
m-1112	579	11	in	in	ADP
m-1112	579	12	electric	electric	ADJ
m-1112	579	13	conductors	conductor	NOUN
m-1112	579	14	as	as	SCONJ
m-1112	579	15	atoms	atom	NOUN
m-1112	579	16	are	be	AUX
m-1112	579	17	.	.	PUNCT
m-1112	580	1	2	2	X
m-1112	580	2	..	..	PUNCT
m-1112	580	3	uniform	uniform	ADJ
m-1112	580	4	circular	circular	ADJ
m-1112	580	5	motion	motion	NOUN
m-1112	580	6	of	of	ADP
m-1112	580	7	electron	electron	NOUN
m-1112	580	8	in	in	ADP
m-1112	580	9	caves	cave	NOUN
m-1112	580	10	constitutes	constitute	VERB
m-1112	580	11	a	a	DET
m-1112	580	12	current	current	ADJ
m-1112	580	13	i	i	NOUN
m-1112	580	14	=	=	PUNCT
m-1112	580	15	e	e	NOUN
m-1112	580	16	t	t	NOUN
m-1112	580	17	=	=	SYM
m-1112	580	18	e.f	e.f	PROPN
m-1112	580	19	,	,	PUNCT
m-1112	580	20	and	and	CCONJ
m-1112	580	21	t=	t=	ADJ
m-1112	581	1	2πr	2πr	NOUN
m-1112	581	2	c	c	NOUN
m-1112	581	3	,	,	PUNCT
m-1112	581	4	i	i	PRON
m-1112	581	5	=	=	NOUN
m-1112	582	1	e.c	e.c	PROPN
m-1112	582	2	2πr	2πr	NOUN
m-1112	582	3	=	=	SYM
m-1112	582	4	1,6022.10−19.2,9979108	1,6022.10−19.2,9979108	NUM
m-1112	582	5	.	.	PUNCT
m-1112	582	6	2π.r	2π.r	NUM
m-1112	582	7	=	=	SYM
m-1112	582	8	7	7	NUM
m-1112	582	9	,	,	PUNCT
m-1112	582	10	644811.10−12	644811.10−12	NOUN
m-1112	582	11	.	.	PUNCT
m-1112	583	1	[	[	PUNCT
m-1112	583	2	1	1	NUM
m-1112	583	3	r	r	NOUN
m-1112	583	4	]	]	PUNCT
m-1112	583	5	,	,	PUNCT
m-1112	583	6	and	and	CCONJ
m-1112	583	7	for	for	ADP
m-1112	583	8	r	r	NOUN
m-1112	583	9	=	=	SYM
m-1112	583	10	𝟏𝟎−𝟏𝟔	𝟏𝟎−𝟏𝟔	NOUN
m-1112	583	11	,	,	PUNCT
m-1112	583	12	𝟏𝟎𝟎	𝟏𝟎𝟎	NUM
m-1112	583	13	,	,	PUNCT
m-1112	583	14	𝟏𝟎𝟏𝟔	𝟏𝟎𝟏𝟔	NUM
m-1112	583	15	m	m	VERB
m-1112	583	16	then	then	ADV
m-1112	584	1	i	i	PRON
m-1112	584	2	=	=	PUNCT
m-1112	585	1	e.c	e.c	PROPN
m-1112	585	2	2πr	2πr	NOUN
m-1112	586	1	=	=	NOUN
m-1112	586	2	7	7	NUM
m-1112	586	3	,	,	PUNCT
m-1112	586	4	644811.10−12	644811.10−12	NOUN
m-1112	586	5	.	.	PUNCT
m-1112	587	1	[	[	PUNCT
m-1112	587	2	1	1	NUM
m-1112	587	3	r	r	NOUN
m-1112	587	4	=	=	NOUN
m-1112	587	5	10−16	10−16	PROPN
m-1112	587	6	,	,	PUNCT
m-1112	587	7	]	]	PUNCT
m-1112	587	8	=	=	SYM
m-1112	587	9	7	7	NUM
m-1112	587	10	,	,	PUNCT
m-1112	587	11	644811.104	644811.104	PROPN
m-1112	587	12	7	7	NUM
m-1112	587	13	,	,	PUNCT
m-1112	587	14	644811.10−12	644811.10−12	NUM
m-1112	587	15	–	–	PUNCT
m-1112	587	16	and	and	CCONJ
m-1112	587	17	7	7	NUM
m-1112	587	18	,	,	PUNCT
m-1112	587	19	644811.10−28	644811.10−28	NUM
m-1112	587	20	ampere	ampere	NOUN
m-1112	587	21	.	.	PUNCT
m-1112	588	1	ijo	ijo	PROPN
m-1112	588	2	international	international	PROPN
m-1112	588	3	journal	journal	PROPN
m-1112	588	4	of	of	ADP
m-1112	588	5	mathematics	mathematics	PROPN
m-1112	588	6	(	(	PUNCT
m-1112	588	7	issn	issn	PROPN
m-1112	588	8	:	:	PUNCT
m-1112	588	9	2992	2992	NUM
m-1112	588	10	-	-	SYM
m-1112	588	11	4421	4421	NUM
m-1112	588	12	)	)	PUNCT
m-1112	588	13	volume	volume	NOUN
m-1112	588	14	08	08	NUM
m-1112	589	1	|	|	ADV
m-1112	589	2	issue	issue	NOUN
m-1112	589	3	08	08	NUM
m-1112	590	1	|	|	ADV
m-1112	590	2	august	august	PROPN
m-1112	590	3	2025	2025	NUM
m-1112	590	4	|	|	ADV
m-1112	590	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	590	6	ijo	ijo	PROPN
m-1112	590	7	journals	journal	NOUN
m-1112	590	8	20	20	NUM
m-1112	590	9	the	the	DET
m-1112	590	10	fundamental	fundamental	ADJ
m-1112	590	11	particles	particle	NOUN
m-1112	590	12	origination	origination	NOUN
m-1112	590	13	mechanism	mechanism	NOUN
m-1112	590	14	in	in	ADP
m-1112	590	15	mfmf	mfmf	PROPN
m-1112	590	16	pns	pns	PROPN
m-1112	590	17	caves	cave	NOUN
m-1112	590	18	.	.	PUNCT
m-1112	591	1	3	3	X
m-1112	591	2	..	..	PUNCT
m-1112	591	3	the	the	DET
m-1112	591	4	electric	electric	NOUN
m-1112	591	5	-	-	PUNCT
m-1112	591	6	potential	potential	NOUN
m-1112	591	7	v	v	NOUN
m-1112	591	8	=	=	SYM
m-1112	591	9	𝐪	𝐪	PROPN
m-1112	591	10	𝐫	𝐫	PROPN
m-1112	591	11	=	=	SYM
m-1112	591	12	8,99.109	8,99.109	NUM
m-1112	591	13	nm²	nm²	ADV
m-1112	591	14	c²	c²	PROPN
m-1112	591	15	[	[	PUNCT
m-1112	591	16	1,602.10−19	1,602.10−19	NUM
m-1112	591	17	.	.	PUNCT
m-1112	592	1	r	r	NOUN
m-1112	592	2	=	=	PUNCT
m-1112	592	3	10−16	10−16	PROPN
m-1112	592	4	]=	]=	NOUN
m-1112	592	5	14,4038.106	14,4038.106	NUM
m-1112	592	6	=	=	NUM
m-1112	592	7	1,44038.107volt	1,44038.107volt	NUM
m-1112	592	8	v	v	NOUN
m-1112	592	9	=	=	SYM
m-1112	592	10	𝐪	𝐪	PROPN
m-1112	592	11	𝐫	𝐫	X
m-1112	592	12	=	=	SYM
m-1112	592	13	8,99.109	8,99.109	NUM
m-1112	592	14	nm²	nm²	ADV
m-1112	592	15	c²	c²	NOUN
m-1112	592	16	[	[	PUNCT
m-1112	592	17	1,6022.10−19	1,6022.10−19	NUM
m-1112	592	18	.	.	PUNCT
m-1112	593	1	r	r	NOUN
m-1112	593	2	=	=	SYM
m-1112	593	3	100,10	100,10	NUM
m-1112	593	4	16	16	NUM
m-1112	593	5	]	]	PUNCT
m-1112	593	6	=	=	SYM
m-1112	593	7	14	14	NUM
m-1112	593	8	,	,	PUNCT
m-1112	593	9	403778.10−10	403778.10−10	NUM
m-1112	593	10	v	v	NOUN
m-1112	593	11	,	,	PUNCT
m-1112	593	12	14,403778.10−26	14,403778.10−26	NUM
m-1112	593	13	v	v	NOUN
m-1112	593	14	,	,	PUNCT
m-1112	593	15	4	4	NUM
m-1112	593	16	..	..	PUNCT
m-1112	593	17	electric	electric	ADJ
m-1112	593	18	-	-	PUNCT
m-1112	593	19	field	field	NOUN
m-1112	593	20	�	�	NOUN
m-1112	593	21	̅	̅	NOUN
m-1112	593	22	�	�	NOUN
m-1112	593	23	𝐅	𝐅	NOUN
m-1112	593	24	=	=	SYM
m-1112	593	25	𝚫𝐕	𝚫𝐕	NOUN
m-1112	593	26	𝐝	𝐝	X
m-1112	594	1	=	=	PUNCT
m-1112	594	2	[	[	PUNCT
m-1112	594	3	14,403778.106	14,403778.106	NUM
m-1112	594	4	.	.	PUNCT
m-1112	595	1	r	r	NOUN
m-1112	595	2	=	=	NOUN
m-1112	595	3	10−16,100,,10	10−16,100,,10	NUM
m-1112	595	4	16	16	NUM
m-1112	595	5	]	]	PUNCT
m-1112	595	6	=	=	SYM
m-1112	595	7	14,403778.1022	14,403778.1022	NUM
m-1112	595	8	,	,	PUNCT
m-1112	595	9	14,403778.10−10	14,403778.10−10	PROPN
m-1112	595	10	v	v	ADP
m-1112	595	11	5	5	NUM
m-1112	595	12	..	..	PUNCT
m-1112	595	13	force	force	NOUN
m-1112	595	14	on	on	ADP
m-1112	595	15	electron	electron	NOUN
m-1112	595	16	is	be	AUX
m-1112	595	17	f	f	X
m-1112	595	18	=	=	PUNCT
m-1112	595	19	q	q	PROPN
m-1112	595	20	.	.	PUNCT
m-1112	595	21	�	�	NOUN
m-1112	595	22	̅	̅	NOUN
m-1112	595	23	�	�	NOUN
m-1112	595	24	𝐅	𝐅	NOUN
m-1112	595	25	=	=	NUM
m-1112	595	26	1,6022.10−19.{14	1,6022.10−19.{14	NUM
m-1112	595	27	,	,	PUNCT
m-1112	595	28	403778.1022}=	403778.1022}=	NUM
m-1112	595	29	23,077733.103	23,077733.103	NUM
m-1112	595	30	n	n	NOUN
m-1112	595	31	and	and	CCONJ
m-1112	595	32	f	f	PROPN
m-1112	596	1	=	=	SYM
m-1112	596	2	q	q	PROPN
m-1112	596	3	.	.	PUNCT
m-1112	596	4	�	�	NOUN
m-1112	596	5	̅	̅	NOUN
m-1112	596	6	�	�	NOUN
m-1112	596	7	𝐅	𝐅	NOUN
m-1112	596	8	=	=	NUM
m-1112	596	9	1,6022.10−19.{14	1,6022.10−19.{14	NUM
m-1112	596	10	,	,	PUNCT
m-1112	596	11	403778.10	403778.10	NUM
m-1112	596	12	6−16}=23,07.10−13	6−16}=23,07.10−13	NOUN
m-1112	596	13	n,23	n,23	NOUN
m-1112	596	14	,	,	PUNCT
m-1112	596	15	077733.10−35	077733.10−35	NUM
m-1112	596	16	n	n	NOUN
m-1112	596	17	,	,	PUNCT
m-1112	596	18	and	and	CCONJ
m-1112	596	19	6	6	NUM
m-1112	596	20	..	..	PUNCT
m-1112	596	21	the	the	DET
m-1112	596	22	produced	produce	VERB
m-1112	596	23	work	work	NOUN
m-1112	596	24	is	be	AUX
m-1112	596	25	w	w	PROPN
m-1112	596	26	=	=	PUNCT
m-1112	596	27	f.ds	f.ds	PROPN
m-1112	597	1	=	=	SYM
m-1112	597	2	f	f	PROPN
m-1112	597	3	r	r	NOUN
m-1112	597	4	=	=	SYM
m-1112	597	5	23	23	NUM
m-1112	597	6	,	,	PUNCT
m-1112	597	7	077733.103.{10−16	077733.103.{10−16	NUM
m-1112	597	8	}	}	PUNCT
m-1112	598	1	=	=	SYM
m-1112	598	2	23	23	NUM
m-1112	598	3	,	,	PUNCT
m-1112	598	4	077733.10−13	077733.10−13	NUM
m-1112	598	5	j	j	PROPN
m-1112	598	6	.	.	PUNCT
m-1112	599	1	w	w	PROPN
m-1112	599	2	=	=	PUNCT
m-1112	599	3	f.ds	f.ds	PROPN
m-1112	599	4	=	=	SYM
m-1112	600	1	f	f	PROPN
m-1112	600	2	r	r	NOUN
m-1112	600	3	=	=	SYM
m-1112	600	4	23	23	NUM
m-1112	600	5	,	,	PUNCT
m-1112	600	6	077733.103.{100,1016	077733.103.{100,1016	NUM
m-1112	600	7	}	}	PUNCT
m-1112	600	8	=	=	SYM
m-1112	600	9	23	23	NUM
m-1112	600	10	,	,	PUNCT
m-1112	600	11	077733.103	077733.103	NUM
m-1112	600	12	,	,	PUNCT
m-1112	600	13	23	23	NUM
m-1112	600	14	,	,	PUNCT
m-1112	600	15	077733.1019	077733.1019	NUM
m-1112	601	1	j	j	PROPN
m-1112	601	2	.	.	PUNCT
m-1112	602	1	𝑒	𝑒	PROPN
m-1112	602	2	0	0	NUM
m-1112	602	3	7	7	NUM
m-1112	602	4	..	..	PUNCT
m-1112	602	5	intensity	intensity	NOUN
m-1112	602	6	i	i	PRON
m-1112	602	7	e−r	e−r	VERB
m-1112	602	8	is	be	AUX
m-1112	602	9	,	,	PUNCT
m-1112	602	10	𝐈	𝐈	VERB
m-1112	602	11	𝐄−𝐫=	𝐄−𝐫=	NOUN
m-1112	602	12	c.e²	c.e²	NOUN
m-1112	602	13	2	2	NUM
m-1112	602	14	=	=	SYM
m-1112	602	15	[	[	PUNCT
m-1112	602	16	2,998.108.1,602210−19(14	2,998.108.1,602210−19(14	NUM
m-1112	602	17	,	,	PUNCT
m-1112	602	18	4038.1022)²	4038.1022)²	PROPN
m-1112	602	19	2	2	NUM
m-1112	602	20	]=	]=	NOUN
m-1112	602	21	498,26077.1033w	498,26077.1033w	NUM
m-1112	602	22	/	/	SYM
m-1112	602	23	m2	m2	PROPN
m-1112	602	24	𝐈	𝐈	PROPN
m-1112	602	25	𝐄−𝟐=	𝐄−𝟐=	X
m-1112	602	26	c.e²	c.e²	NOUN
m-1112	602	27	2	2	NUM
m-1112	602	28	=	=	SYM
m-1112	602	29	498	498	NUM
m-1112	602	30	,	,	PUNCT
m-1112	602	31	261.101w=	261.101w=	NUM
m-1112	602	32	4,9826077.103w	4,9826077.103w	NOUN
m-1112	602	33	and	and	CCONJ
m-1112	602	34	𝐈	𝐈	VERB
m-1112	602	35	𝐄−𝟑=	𝐄−𝟑=	NUM
m-1112	602	36	c.e²	c.e²	NOUN
m-1112	602	37	2	2	NUM
m-1112	602	38	=	=	SYM
m-1112	602	39	4,9826077.10−29	4,9826077.10−29	NUM
m-1112	602	40	w	w	NOUN
m-1112	602	41	/	/	SYM
m-1112	602	42	m²	m²	PROPN
m-1112	602	43	8	8	NUM
m-1112	602	44	..	..	PUNCT
m-1112	602	45	the	the	DET
m-1112	602	46	power	power	NOUN
m-1112	602	47	𝐏	𝐏	PROPN
m-1112	602	48	𝐄−𝐫=	𝐄−𝐫=	NOUN
m-1112	602	49	e²	e²	NOUN
m-1112	602	50	z	z	X
m-1112	602	51	=	=	NOUN
m-1112	602	52	πr²	πr²	NOUN
m-1112	602	53	=	=	SYM
m-1112	602	54	(	(	PUNCT
m-1112	602	55	14,403778.1022)²	14,403778.1022)²	NUM
m-1112	602	56	π.(10−16)²	π.(10−16)²	NOUN
m-1112	602	57	=	=	SYM
m-1112	602	58	6,60394.1077w	6,60394.1077w	NUM
m-1112	602	59	,	,	PUNCT
m-1112	602	60	6,60394.1057	6,60394.1057	NUM
m-1112	602	61	,	,	PUNCT
m-1112	602	62	6,604.1013w	6,604.1013w	NUM
m-1112	602	63	9	9	NUM
m-1112	602	64	..	..	SYM
m-1112	602	65	two	two	NUM
m-1112	602	66	-	-	PUNCT
m-1112	602	67	capacitors	capacitor	NOUN
m-1112	602	68	conductor	conductor	NOUN
m-1112	602	69	of	of	ADP
m-1112	602	70	area	area	NOUN
m-1112	602	71	a	a	DET
m-1112	602	72	and	and	CCONJ
m-1112	602	73	charge	charge	VERB
m-1112	602	74	q	q	NOUN
m-1112	602	75	charge	charge	NOUN
m-1112	602	76	density	density	NOUN
m-1112	602	77	is	be	AUX
m-1112	602	78	on	on	ADP
m-1112	602	79	plates	plate	NOUN
m-1112	602	80	σ	σ	NOUN
m-1112	602	81	=	=	PUNCT
m-1112	602	82	q	q	PROPN
m-1112	602	83	a	a	DET
m-1112	602	84	and	and	CCONJ
m-1112	602	85	electric	electric	ADJ
m-1112	602	86	field	field	NOUN
m-1112	602	87	e	e	NOUN
m-1112	602	88	=	=	PUNCT
m-1112	602	89	σ	σ	PROPN
m-1112	602	90	𝑒	𝑒	PROPN
m-1112	602	91	0	0	NUM
m-1112	603	1	=	=	PUNCT
m-1112	604	1	q	q	PROPN
m-1112	605	1	a	a	DET
m-1112	605	2	𝑒	𝑒	PROPN
m-1112	605	3	0	0	NUM
m-1112	605	4	and	and	CCONJ
m-1112	605	5	from	from	ADP
m-1112	605	6	potential	potential	ADJ
m-1112	605	7	difference	difference	NOUN
m-1112	605	8	v=	v=	NOUN
m-1112	605	9	e	e	NOUN
m-1112	605	10	d	d	NOUN
m-1112	605	11	then	then	ADV
m-1112	605	12	e	e	PROPN
m-1112	605	13	=	=	PUNCT
m-1112	605	14	v	v	PROPN
m-1112	605	15	𝑒	𝑒	PROPN
m-1112	605	16	0	0	NUM
m-1112	605	17	and	and	CCONJ
m-1112	605	18	v	v	NOUN
m-1112	605	19	d	d	PROPN
m-1112	605	20	=	=	PUNCT
m-1112	605	21	q	q	X
m-1112	605	22	a	a	DET
m-1112	605	23	𝑒	𝑒	PROPN
m-1112	605	24	0	0	NUM
m-1112	605	25	or	or	CCONJ
m-1112	605	26	v	v	NOUN
m-1112	605	27	=	=	SYM
m-1112	605	28	q.	q.	NOUN
m-1112	605	29	[	[	X
m-1112	605	30	d	d	X
m-1112	605	31	a	a	DET
m-1112	605	32	.e	.e	NOUN
m-1112	605	33	0	0	NUM
m-1112	605	34	.	.	PUNCT
m-1112	605	35	]	]	PUNCT
m-1112	606	1	=	=	PUNCT
m-1112	606	2	q	q	X
m-1112	606	3	a	a	X
m-1112	606	4	=	=	SYM
m-1112	606	5	e	e	NOUN
m-1112	606	6	d	d	PROPN
m-1112	606	7	.	.	PUNCT
m-1112	607	1	from	from	ADP
m-1112	607	2	above	above	ADV
m-1112	607	3	→	→	SYM
m-1112	607	4	a	a	PRON
m-1112	607	5	=	=	X
m-1112	607	6	q.d	q.d	NOUN
m-1112	607	7	v	v	NOUN
m-1112	607	8	=	=	SYM
m-1112	607	9	[	[	PUNCT
m-1112	607	10	1,602210−19(10−16	1,602210−19(10−16	NUM
m-1112	607	11	)	)	PUNCT
m-1112	607	12	14,403778.(r=106	14,403778.(r=106	NUM
m-1112	607	13	)	)	PUNCT
m-1112	607	14	]	]	PUNCT
m-1112	608	1	=	=	PUNCT
m-1112	608	2	m2	m2	PROPN
m-1112	608	3	1,11235.10−42	1,11235.10−42	NUM
m-1112	608	4	,	,	PUNCT
m-1112	608	5	1,11235.10−26,1,11235.10−10	1,11235.10−26,1,11235.10−10	NUM
m-1112	608	6	m2	m2	PROPN
m-1112	608	7	,	,	PUNCT
m-1112	608	8	stress	stress	NOUN
m-1112	608	9	σ	σ	NOUN
m-1112	608	10	=	=	PUNCT
m-1112	608	11	q	q	PROPN
m-1112	608	12	a	a	NOUN
m-1112	608	13	=	=	SYM
m-1112	608	14	1,44038.1023	1,44038.1023	NUM
m-1112	608	15	,	,	PUNCT
m-1112	608	16	7	7	NUM
m-1112	608	17	,	,	PUNCT
m-1112	608	18	−9	−9	NOUN
m-1112	608	19	t	t	NOUN
m-1112	608	20	m²	m²	NOUN
m-1112	608	21	remarks	remark	VERB
m-1112	608	22	:	:	PUNCT
m-1112	608	23	1	1	X
m-1112	608	24	..	..	PUNCT
m-1112	608	25	the	the	DET
m-1112	608	26	stress	stress	NOUN
m-1112	608	27	-	-	PUNCT
m-1112	608	28	strain	strain	NOUN
m-1112	608	29	relationship	relationship	NOUN
m-1112	608	30	,	,	PUNCT
m-1112	608	31	from	from	ADP
m-1112	608	32	static	static	ADJ
m-1112	608	33	theory	theory	NOUN
m-1112	608	34	of	of	ADP
m-1112	608	35	elasticity	elasticity	NOUN
m-1112	608	36	solves	solve	VERB
m-1112	608	37	the	the	DET
m-1112	608	38	problem	problem	NOUN
m-1112	608	39	of	of	ADP
m-1112	608	40	static	static	ADJ
m-1112	608	41	indeterminacy	indeterminacy	NOUN
m-1112	608	42	.	.	PUNCT
m-1112	609	1	that	that	ADV
m-1112	609	2	is	is	ADV
m-1112	609	3	,	,	PUNCT
m-1112	609	4	the	the	DET
m-1112	609	5	stress	stress	NOUN
m-1112	609	6	parameters	parameter	NOUN
m-1112	609	7	σ	σ	PROPN
m-1112	609	8	x	x	PROPN
m-1112	609	9	,	,	PUNCT
m-1112	609	10	σ	σ	PROPN
m-1112	609	11	y	y	PROPN
m-1112	609	12	,	,	PUNCT
m-1112	609	13	are	be	AUX
m-1112	609	14	bound	bind	VERB
m-1112	609	15	in	in	ADP
m-1112	609	16	,	,	PUNCT
m-1112	609	17	(	(	PUNCT
m-1112	609	18	1	1	X
m-1112	609	19	)	)	PUNCT
m-1112	609	20	by	by	ADP
m-1112	609	21	the	the	DET
m-1112	609	22	stereo	stereo	ADJ
m-1112	609	23	static	static	ADJ
m-1112	609	24	conditions	condition	NOUN
m-1112	609	25	(	(	PUNCT
m-1112	609	26	2	2	NUM
m-1112	609	27	)	)	PUNCT
m-1112	609	28	and	and	CCONJ
m-1112	609	29	by	by	ADP
m-1112	609	30	the	the	DET
m-1112	609	31	constraint	constraint	NOUN
m-1112	609	32	that	that	SCONJ
m-1112	609	33	the	the	DET
m-1112	609	34	strain	strain	NOUN
m-1112	609	35	accompanying	accompany	VERB
m-1112	609	36	the	the	DET
m-1112	609	37	stress	stress	NOUN
m-1112	609	38	s	s	NOUN
m-1112	609	39	x	x	X
m-1112	609	40	,	,	PUNCT
m-1112	609	41	s	s	PROPN
m-1112	609	42	y	y	PROPN
m-1112	609	43	,	,	PUNCT
m-1112	609	44	remains	remain	VERB
m-1112	609	45	geometrically	geometrically	ADV
m-1112	609	46	continuous	continuous	ADJ
m-1112	609	47	.	.	PUNCT
m-1112	610	1	this	this	DET
m-1112	610	2	property	property	NOUN
m-1112	610	3	of	of	ADP
m-1112	610	4	the	the	DET
m-1112	610	5	stresses	stress	NOUN
m-1112	610	6	allows	allow	VERB
m-1112	610	7	.the	.the	DET
m-1112	610	8	transportation	transportation	NOUN
m-1112	610	9	of	of	ADP
m-1112	610	10	the	the	DET
m-1112	610	11	informations	information	NOUN
m-1112	610	12	on	on	ADP
m-1112	610	13	knots	knot	NOUN
m-1112	610	14	to	to	ADP
m-1112	610	15	the	the	DET
m-1112	610	16	polygon	polygon	NOUN
m-1112	610	17	-	-	PUNCT
m-1112	610	18	sides	side	NOUN
m-1112	610	19	.	.	PUNCT
m-1112	611	1	2	2	NUM
m-1112	611	2	..	..	PUNCT
m-1112	611	3	when	when	SCONJ
m-1112	611	4	a	a	DET
m-1112	611	5	body	body	NOUN
m-1112	611	6	contains	contain	VERB
m-1112	611	7	potential	potential	ADJ
m-1112	611	8	energy	energy	NOUN
m-1112	611	9	,	,	PUNCT
m-1112	611	10	during	during	ADP
m-1112	611	11	any	any	DET
m-1112	611	12	unloading	unloading	NOUN
m-1112	611	13	it	it	PRON
m-1112	611	14	gives	give	VERB
m-1112	611	15	off	off	ADP
m-1112	611	16	mechanical	mechanical	ADJ
m-1112	611	17	work	work	NOUN
m-1112	611	18	,	,	PUNCT
m-1112	611	19	since	since	SCONJ
m-1112	611	20	the	the	DET
m-1112	611	21	points	point	NOUN
m-1112	611	22	of	of	ADP
m-1112	611	23	application	application	NOUN
m-1112	611	24	of	of	ADP
m-1112	611	25	the	the	DET
m-1112	611	26	gradually	gradually	ADV
m-1112	611	27	withdrawn	withdraw	VERB
m-1112	611	28	loads	load	NOUN
m-1112	611	29	are	be	AUX
m-1112	611	30	displaced	displace	VERB
m-1112	611	31	.	.	PUNCT
m-1112	612	1	if	if	SCONJ
m-1112	612	2	the	the	DET
m-1112	612	3	unloading	unloading	NOUN
m-1112	612	4	is	be	AUX
m-1112	612	5	abrupt	abrupt	ADJ
m-1112	612	6	,	,	PUNCT
m-1112	612	7	then	then	ADV
m-1112	612	8	kinetic	kinetic	ADJ
m-1112	612	9	energy	energy	NOUN
m-1112	612	10	is	be	AUX
m-1112	612	11	converted	convert	VERB
m-1112	612	12	into	into	ADP
m-1112	612	13	potential	potential	ADJ
m-1112	612	14	and	and	CCONJ
m-1112	612	15	after	after	SCONJ
m-1112	612	16	is	be	AUX
m-1112	612	17	kinetic	kinetic	ADJ
m-1112	612	18	,	,	PUNCT
m-1112	612	19	converted	convert	VERB
m-1112	612	20	back	back	ADV
m-1112	612	21	into	into	ADP
m-1112	612	22	kinetic	kinetic	NOUN
m-1112	612	23	and	and	CCONJ
m-1112	612	24	so	so	ADV
m-1112	612	25	on	on	ADV
m-1112	612	26	.	.	PUNCT
m-1112	613	1	that	that	PRON
m-1112	613	2	is	is	ADV
m-1112	613	3	,	,	PUNCT
m-1112	613	4	the	the	DET
m-1112	613	5	body	body	NOUN
m-1112	613	6	performs	perform	VERB
m-1112	613	7	an	an	DET
m-1112	613	8	oscillating	oscillating	NOUN
m-1112	613	9	motion	motion	NOUN
m-1112	613	10	until	until	SCONJ
m-1112	613	11	the	the	DET
m-1112	613	12	mechanical	mechanical	ADJ
m-1112	613	13	energy	energy	NOUN
m-1112	613	14	is	be	AUX
m-1112	613	15	extinguished	extinguish	VERB
m-1112	613	16	due	due	ADP
m-1112	613	17	to	to	ADP
m-1112	613	18	a	a	DET
m-1112	613	19	state	state	NOUN
m-1112	613	20	of	of	ADP
m-1112	613	21	equilibrium	equilibrium	NOUN
m-1112	613	22	or	or	CCONJ
m-1112	613	23	alters	alter	VERB
m-1112	613	24	.	.	PUNCT
m-1112	614	1	3	3	X
m-1112	614	2	..	..	PUNCT
m-1112	614	3	the	the	DET
m-1112	614	4	action	action	NOUN
m-1112	614	5	of	of	ADP
m-1112	614	6	the	the	DET
m-1112	614	7	complex	complex	ADJ
m-1112	614	8	–	–	PUNCT
m-1112	614	9	vectors	vector	NOUN
m-1112	614	10	create	create	VERB
m-1112	614	11	the	the	DET
m-1112	614	12	waves	wave	NOUN
m-1112	614	13	of	of	ADP
m-1112	614	14	motion	motion	NOUN
m-1112	614	15	≡	≡	PROPN
m-1112	614	16	energy	energy	NOUN
m-1112	614	17	waves	wave	NOUN
m-1112	614	18	,	,	PUNCT
m-1112	614	19	which	which	PRON
m-1112	614	20	are	be	AUX
m-1112	614	21	closed	close	VERB
m-1112	614	22	curves	curve	NOUN
m-1112	614	23	and	and	CCONJ
m-1112	614	24	transported	transport	VERB
m-1112	614	25	.	.	PUNCT
m-1112	615	1	the	the	DET
m-1112	615	2	pattern	pattern	NOUN
m-1112	615	3	of	of	ADP
m-1112	615	4	disturbances	disturbance	NOUN
m-1112	615	5	with	with	ADP
m-1112	615	6	the	the	DET
m-1112	615	7	informations	information	NOUN
m-1112	615	8	,	,	PUNCT
m-1112	615	9	propagates	propagate	VERB
m-1112	615	10	from	from	ADP
m-1112	615	11	the	the	DET
m-1112	615	12	one	one	NUM
m-1112	615	13	-	-	PUNCT
m-1112	615	14	edge	edge	NOUN
m-1112	615	15	-	-	PUNCT
m-1112	615	16	point	point	NOUN
m-1112	615	17	to	to	ADP
m-1112	615	18	the	the	DET
m-1112	615	19	other	other	ADJ
m-1112	615	20	edge	edge	NOUN
m-1112	615	21	-	-	PUNCT
m-1112	615	22	point	point	NOUN
m-1112	615	23	of	of	ADP
m-1112	615	24	conductors	conductor	NOUN
m-1112	615	25	,	,	PUNCT
m-1112	615	26	or	or	CCONJ
m-1112	615	27	is	be	AUX
m-1112	615	28	on	on	ADP
m-1112	615	29	the	the	DET
m-1112	615	30	[	[	X
m-1112	615	31	sub	sub	NOUN
m-1112	615	32	-	-	NOUN
m-1112	615	33	units	unit	NOUN
m-1112	615	34	]	]	PUNCT
m-1112	615	35	.	.	PUNCT
m-1112	616	1	action	action	NOUN
m-1112	616	2	of	of	ADP
m-1112	616	3	vectors	vector	NOUN
m-1112	616	4	exist	exist	VERB
m-1112	616	5	on	on	ADP
m-1112	616	6	polygon	polygon	NOUN
m-1112	616	7	–	–	PUNCT
m-1112	616	8	conductor`s	conductor`s	ADJ
m-1112	616	9	d	d	NOUN
m-1112	616	10	=	=	PUNCT
m-1112	616	11	side	side	NOUN
m-1112	616	12	λ	λ	NOUN
m-1112	616	13	n(ns	n(ns	PROPN
m-1112	616	14	)	)	PUNCT
m-1112	616	15	of	of	ADP
m-1112	616	16	polygons	polygon	NOUN
m-1112	616	17	.	.	PUNCT
m-1112	617	1	4	4	NUM
m-1112	617	2	..	..	PUNCT
m-1112	617	3	action	action	NOUN
m-1112	617	4	of	of	ADP
m-1112	617	5	a	a	DET
m-1112	617	6	signal	signal	NOUN
m-1112	617	7	which	which	PRON
m-1112	617	8	strikes	strike	VERB
m-1112	617	9	the	the	DET
m-1112	617	10	tetrahedron	tetrahedron	NOUN
m-1112	617	11	–	–	PUNCT
m-1112	617	12	cube	cube	NOUN
m-1112	617	13	-	-	PUNCT
m-1112	617	14	spheres	sphere	NOUN
m-1112	617	15	mechanism	mechanism	NOUN
m-1112	617	16	.	.	PUNCT
m-1112	618	1	unloading	unloading	NOUN
m-1112	618	2	happens	happen	VERB
m-1112	618	3	on	on	ADP
m-1112	618	4	the	the	DET
m-1112	618	5	three	three	NUM
m-1112	618	6	tetrahedron	tetrahedron	NOUN
m-1112	618	7	sides	side	NOUN
m-1112	618	8	which	which	DET
m-1112	618	9	withdrawn	withdraw	VERB
m-1112	618	10	loads	load	NOUN
m-1112	618	11	are	be	AUX
m-1112	618	12	displaced	displace	VERB
m-1112	618	13	on	on	ADP
m-1112	618	14	the	the	DET
m-1112	618	15	anti	anti	ADJ
m-1112	618	16	-	-	ADJ
m-1112	618	17	parallel	parallel	ADJ
m-1112	618	18	-	-	PUNCT
m-1112	618	19	strand	strand	NOUN
m-1112	618	20	.	.	PUNCT
m-1112	619	1	if	if	SCONJ
m-1112	619	2	the	the	DET
m-1112	619	3	unloading	unloading	NOUN
m-1112	619	4	is	be	AUX
m-1112	619	5	abrupt	abrupt	ADJ
m-1112	619	6	,	,	PUNCT
m-1112	619	7	then	then	ADV
m-1112	619	8	kinetic	kinetic	ADJ
m-1112	619	9	energy	energy	NOUN
m-1112	619	10	of	of	ADP
m-1112	619	11	1	1	NUM
m-1112	619	12	-	-	PUNCT
m-1112	619	13	strand	strand	NOUN
m-1112	619	14	is	be	AUX
m-1112	619	15	converted	convert	VERB
m-1112	619	16	in	in	ADP
m-1112	619	17	the	the	DET
m-1112	619	18	2	2	NUM
m-1112	619	19	-	-	PUNCT
m-1112	619	20	strand	strand	NOUN
m-1112	619	21	as	as	ADP
m-1112	619	22	potential	potential	ADJ
m-1112	619	23	and	and	CCONJ
m-1112	619	24	so	so	ADV
m-1112	619	25	on	on	ADV
m-1112	619	26	.	.	PUNCT
m-1112	620	1	that	that	ADV
m-1112	620	2	is	is	ADV
m-1112	620	3	,	,	PUNCT
m-1112	620	4	cubes	cube	NOUN
m-1112	620	5	perform	perform	VERB
m-1112	620	6	an	an	DET
m-1112	620	7	oscillating	oscillating	NOUN
m-1112	620	8	motion	motion	NOUN
m-1112	620	9	until	until	SCONJ
m-1112	620	10	the	the	DET
m-1112	620	11	mechanical	mechanical	ADJ
m-1112	620	12	energy	energy	NOUN
m-1112	620	13	is	be	AUX
m-1112	620	14	extinguished	extinguish	VERB
m-1112	620	15	to	to	ADP
m-1112	620	16	their	their	PRON
m-1112	620	17	vertices	vertex	NOUN
m-1112	620	18	,	,	PUNCT
m-1112	620	19	which	which	PRON
m-1112	620	20	are	be	AUX
m-1112	620	21	the	the	DET
m-1112	620	22	stores	store	NOUN
m-1112	620	23	of	of	ADP
m-1112	620	24	information	information	NOUN
m-1112	620	25	.	.	PUNCT
m-1112	621	1	5	5	X
m-1112	621	2	..	..	PUNCT
m-1112	621	3	the	the	DET
m-1112	621	4	harmonic	harmonic	ADJ
m-1112	621	5	displacement	displacement	NOUN
m-1112	621	6	of	of	ADP
m-1112	621	7	support	support	NOUN
m-1112	621	8	-	-	PUNCT
m-1112	621	9	points	point	NOUN
m-1112	621	10	on	on	ADP
m-1112	621	11	a	a	DET
m-1112	621	12	regular	regular	ADJ
m-1112	621	13	polygon	polygon	NOUN
m-1112	621	14	vertices	vertex	NOUN
m-1112	621	15	.	.	PUNCT
m-1112	622	1	the	the	DET
m-1112	622	2	projections	projection	NOUN
m-1112	622	3	of	of	ADP
m-1112	622	4	heights	height	NOUN
m-1112	622	5	y	y	PROPN
m-1112	622	6	n	n	PROPN
m-1112	622	7	of	of	ADP
m-1112	622	8	a	a	DET
m-1112	622	9	regular	regular	ADJ
m-1112	622	10	polygon	polygon	NOUN
m-1112	622	11	are	be	AUX
m-1112	622	12	as	as	ADP
m-1112	622	13	2.y	2.y	NUM
m-1112	622	14	n=	n=	ADJ
m-1112	622	15	n	n	PRON
m-1112	622	16	r	r	NOUN
m-1112	622	17	,	,	PUNCT
m-1112	622	18	which	which	PRON
m-1112	622	19	allows	allow	VERB
m-1112	622	20	to	to	ADP
m-1112	622	21	the	the	DET
m-1112	622	22	vectorforce	vectorforce	NOUN
m-1112	622	23	polygon	polygon	NOUN
m-1112	622	24	to	to	PART
m-1112	622	25	follow	follow	VERB
m-1112	622	26	the	the	DET
m-1112	622	27	space	space	NOUN
m-1112	622	28	-	-	PUNCT
m-1112	622	29	vector	vector	NOUN
m-1112	622	30	-	-	PUNCT
m-1112	622	31	wave	wave	NOUN
m-1112	622	32	=	=	SYM
m-1112	622	33	2r.𝑒𝑖.𝑛𝑤𝑡	2r.𝑒𝑖.𝑛𝑤𝑡	NUM
m-1112	623	1	=	=	SYM
m-1112	623	2	2r.[cos	2r.[cos	PROPN
m-1112	623	3	w	w	NOUN
m-1112	623	4	t	t	PROPN
m-1112	624	1	+	+	CCONJ
m-1112	624	2	i	i	PRON
m-1112	624	3	.sin	.sin	PROPN
m-1112	624	4	wt	wt	X
m-1112	624	5	]	]	PUNCT
m-1112	624	6	.	.	PUNCT
m-1112	625	1	i.e.	i.e.	X
m-1112	625	2	complex	complex	ADJ
m-1112	625	3	frequency	frequency	NOUN
m-1112	625	4	response	response	NOUN
m-1112	625	5	,	,	PUNCT
m-1112	625	6	happens	happen	VERB
m-1112	625	7	on	on	ADP
m-1112	625	8	the	the	DET
m-1112	625	9	regular	regular	ADJ
m-1112	625	10	polygon	polygon	NOUN
m-1112	625	11	vertices	vertex	NOUN
m-1112	625	12	only	only	ADV
m-1112	625	13	.	.	PUNCT
m-1112	626	1	6a	6a	NOUN
m-1112	626	2	..	..	PUNCT
m-1112	626	3	the	the	DET
m-1112	626	4	origination	origination	NOUN
m-1112	626	5	of	of	ADP
m-1112	626	6	primary	primary	ADJ
m-1112	626	7	motion	motion	NOUN
m-1112	626	8	in	in	ADP
m-1112	626	9	e	e	NOUN
m-1112	626	10	spaces	space	NOUN
m-1112	626	11	.	.	PUNCT
m-1112	627	1	ijo	ijo	PROPN
m-1112	627	2	international	international	PROPN
m-1112	627	3	journal	journal	PROPN
m-1112	627	4	of	of	ADP
m-1112	627	5	mathematics	mathematics	PROPN
m-1112	627	6	(	(	PUNCT
m-1112	627	7	issn	issn	PROPN
m-1112	627	8	:	:	PUNCT
m-1112	627	9	2992	2992	NUM
m-1112	627	10	-	-	SYM
m-1112	627	11	4421	4421	NUM
m-1112	627	12	)	)	PUNCT
m-1112	627	13	volume	volume	NOUN
m-1112	627	14	08	08	NUM
m-1112	628	1	|	|	ADV
m-1112	628	2	issue	issue	NOUN
m-1112	628	3	08	08	NUM
m-1112	629	1	|	|	ADV
m-1112	629	2	august	august	PROPN
m-1112	629	3	2025	2025	NUM
m-1112	629	4	|	|	ADV
m-1112	629	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	629	6	ijo	ijo	PROPN
m-1112	629	7	journals	journal	NOUN
m-1112	629	8	21	21	NUM
m-1112	629	9	the	the	DET
m-1112	629	10	fundamental	fundamental	ADJ
m-1112	629	11	particles	particle	NOUN
m-1112	629	12	origination	origination	NOUN
m-1112	629	13	mechanism	mechanism	NOUN
m-1112	629	14	in	in	ADP
m-1112	629	15	mfmf	mfmf	PROPN
m-1112	629	16	pns	pns	PROPN
m-1112	629	17	caves	cave	NOUN
m-1112	629	18	.	.	PUNCT
m-1112	630	1	the	the	DET
m-1112	630	2	stress	stress	NOUN
m-1112	630	3	state	state	NOUN
m-1112	630	4	(	(	PUNCT
m-1112	630	5	σ	σ	PROPN
m-1112	630	6	,	,	PUNCT
m-1112	630	7	τ	τ	PROPN
m-1112	630	8	)	)	PUNCT
m-1112	630	9	in	in	ADP
m-1112	630	10	spaces	space	NOUN
m-1112	630	11	is	be	AUX
m-1112	630	12	defined	define	VERB
m-1112	630	13	from	from	ADP
m-1112	630	14	the	the	DET
m-1112	630	15	cauchy	cauchy	PROPN
m-1112	630	16	stress	stress	NOUN
m-1112	630	17	tensor	tensor	NOUN
m-1112	630	18	where	where	SCONJ
m-1112	630	19	,	,	PUNCT
m-1112	630	20	exists	exist	VERB
m-1112	630	21	at	at	ADP
m-1112	630	22	any	any	DET
m-1112	630	23	point	point	NOUN
m-1112	630	24	inside	inside	ADP
m-1112	630	25	a	a	DET
m-1112	630	26	material	material	NOUN
m-1112	630	27	in	in	ADP
m-1112	630	28	the	the	DET
m-1112	630	29	deformed	deform	VERB
m-1112	630	30	state	state	NOUN
m-1112	630	31	placement	placement	NOUN
m-1112	630	32	or	or	CCONJ
m-1112	630	33	configuration	configuration	NOUN
m-1112	630	34	.	.	PUNCT
m-1112	631	1	the	the	DET
m-1112	631	2	second	second	ADJ
m-1112	631	3	order	order	NOUN
m-1112	631	4	tensor	tensor	NOUN
m-1112	631	5	consists	consist	VERB
m-1112	631	6	of	of	ADP
m-1112	631	7	nine	nine	NUM
m-1112	631	8	components	component	NOUN
m-1112	631	9	and	and	CCONJ
m-1112	631	10	relates	relate	VERB
m-1112	631	11	a	a	DET
m-1112	631	12	unit	unit	NOUN
m-1112	631	13	length	length	NOUN
m-1112	631	14	direction	direction	NOUN
m-1112	631	15	vector	vector	NOUN
m-1112	631	16	𝐧	𝐧	NOUN
m-1112	631	17	to	to	ADP
m-1112	631	18	the	the	DET
m-1112	631	19	traction	traction	NOUN
m-1112	631	20	-	-	PUNCT
m-1112	631	21	vector	vector	NOUN
m-1112	631	22	𝐓𝐧	𝐓𝐧	PROPN
m-1112	631	23	across	across	ADP
m-1112	631	24	an	an	DET
m-1112	631	25	imaginary	imaginary	ADJ
m-1112	631	26	surface	surface	NOUN
m-1112	631	27	(	(	PUNCT
m-1112	631	28	in	in	ADP
m-1112	631	29	m	m	NOUN
m-1112	631	30	-	-	NOUN
m-1112	631	31	geometry	geometry	NOUN
m-1112	631	32	is	be	AUX
m-1112	631	33	φ	φ	NOUN
m-1112	631	34	)	)	PUNCT
m-1112	631	35	perpendicular	perpendicular	NOUN
m-1112	631	36	to	to	ADP
m-1112	631	37	n⃡	n⃡	NOUN
m-1112	631	38	,	,	PUNCT
m-1112	631	39	tn⃖	tn⃖	NOUN
m-1112	631	40	=	=	SYM
m-1112	631	41	n⃡	n⃡	X
m-1112	631	42	σ	σ	NOUN
m-1112	631	43	,	,	PUNCT
m-1112	631	44	or	or	CCONJ
m-1112	631	45	tj	tj	NOUN
m-1112	631	46	n⃖	n⃖	NOUN
m-1112	631	47	=	=	PUNCT
m-1112	632	1	∑σ	∑σ	PROPN
m-1112	632	2	i	i	PRON
m-1112	632	3	j	j	PROPN
m-1112	632	4	n	n	CCONJ
m-1112	632	5	i	i	PRON
m-1112	632	6	,	,	PUNCT
m-1112	632	7	obeying	obey	VERB
m-1112	632	8	to	to	ADP
m-1112	632	9	the	the	DET
m-1112	632	10	tensor	tensor	NOUN
m-1112	632	11	transformation	transformation	NOUN
m-1112	632	12	law	law	NOUN
m-1112	632	13	for	for	ADP
m-1112	632	14	stress	stress	NOUN
m-1112	632	15	analysis	analysis	NOUN
m-1112	632	16	.	.	PUNCT
m-1112	633	1	a	a	DET
m-1112	633	2	contact	contact	NOUN
m-1112	633	3	force	force	NOUN
m-1112	633	4	∆f	∆f	PROPN
m-1112	633	5	exerted	exert	VERB
m-1112	633	6	at	at	ADP
m-1112	633	7	point	point	NOUN
m-1112	633	8	p	p	NOUN
m-1112	633	9	of	of	ADP
m-1112	633	10	element	element	NOUN
m-1112	633	11	area	area	NOUN
m-1112	633	12	∆a	∆a	PROPN
m-1112	633	13	,	,	PUNCT
m-1112	633	14	the	the	DET
m-1112	633	15	ratio	ratio	NOUN
m-1112	633	16	∆f/∆a	∆f/∆a	PROPN
m-1112	633	17	becomes	become	VERB
m-1112	633	18	df	df	PROPN
m-1112	633	19	/	/	SYM
m-1112	633	20	da	da	PROPN
m-1112	633	21	and	and	CCONJ
m-1112	633	22	the	the	DET
m-1112	633	23	couple	couple	NOUN
m-1112	633	24	stress	stress	NOUN
m-1112	633	25	vector	vector	NOUN
m-1112	633	26	∆m	∆m	PROPN
m-1112	633	27	vanishes	vanish	VERB
m-1112	633	28	and	and	CCONJ
m-1112	633	29	prior	prior	ADJ
m-1112	633	30	tensor	tensor	NOUN
m-1112	633	31	becomes	become	VERB
m-1112	633	32	tj	tj	NOUN
m-1112	633	33	n⃖	n⃖	PROPN
m-1112	633	34	=	=	PROPN
m-1112	633	35	lim	lim	PROPN
m-1112	633	36	∆s=0	∆s=0	PROPN
m-1112	633	37	∆fi/∆s	∆fi/∆s	PROPN
m-1112	634	1	=	=	SYM
m-1112	634	2	dfi	dfi	PROPN
m-1112	634	3	𝑑𝑆	𝑑𝑆	PROPN
m-1112	634	4	.	.	PUNCT
m-1112	635	1	equation	equation	NOUN
m-1112	635	2	means	mean	VERB
m-1112	635	3	that	that	SCONJ
m-1112	635	4	the	the	DET
m-1112	635	5	stress	stress	NOUN
m-1112	635	6	-	-	PUNCT
m-1112	635	7	tensor	tensor	NOUN
m-1112	635	8	depends	depend	VERB
m-1112	635	9	on	on	ADP
m-1112	635	10	the	the	DET
m-1112	635	11	position	position	NOUN
m-1112	635	12	(	(	PUNCT
m-1112	635	13	location	location	NOUN
m-1112	635	14	)	)	PUNCT
m-1112	635	15	in	in	ADP
m-1112	635	16	body	body	NOUN
m-1112	635	17	and	and	CCONJ
m-1112	635	18	the	the	DET
m-1112	635	19	orientation	orientation	NOUN
m-1112	635	20	of	of	ADP
m-1112	635	21	the	the	DET
m-1112	635	22	plane	plane	NOUN
m-1112	635	23	on	on	ADP
m-1112	635	24	which	which	PRON
m-1112	635	25	it	it	PRON
m-1112	635	26	is	be	AUX
m-1112	635	27	acting	act	VERB
m-1112	635	28	.	.	PUNCT
m-1112	636	1	from	from	ADP
m-1112	636	2	spaces	space	NOUN
m-1112	636	3	(	(	PUNCT
m-1112	636	4	4	4	NUM
m-1112	636	5	)	)	PUNCT
m-1112	636	6	in	in	ADP
m-1112	636	7	material	material	NOUN
m-1112	636	8	-	-	PUNCT
m-1112	636	9	geometry	geometry	NOUN
m-1112	636	10	of	of	ADP
m-1112	636	11	pns	pns	PROPN
m-1112	636	12	-space	-space	PROPN
m-1112	636	13	(	(	PUNCT
m-1112	636	14	fig-1	fig-1	NOUN
m-1112	636	15	-	-	SYM
m-1112	636	16	3	3	NUM
m-1112	636	17	)	)	PUNCT
m-1112	636	18	the	the	DET
m-1112	636	19	eternal	eternal	ADJ
m-1112	636	20	rotation	rotation	NOUN
m-1112	636	21	of	of	ADP
m-1112	636	22	the	the	DET
m-1112	636	23	two	two	NUM
m-1112	636	24	opposite	opposite	ADJ
m-1112	636	25	[	[	NOUN
m-1112	636	26	⊕	⊕	NOUN
m-1112	636	27	↻	↻	NOUN
m-1112	636	28	↺	↺	NOUN
m-1112	636	29	⊝	⊝	NOUN
m-1112	636	30	]	]	PUNCT
m-1112	636	31	constitutes	constitute	VERB
m-1112	636	32	,	,	PUNCT
m-1112	636	33	and	and	CCONJ
m-1112	636	34	because	because	SCONJ
m-1112	636	35	of	of	ADP
m-1112	636	36	their	their	PRON
m-1112	636	37	in	in	ADP
m-1112	636	38	between	between	ADP
m-1112	636	39	stress	stress	NOUN
m-1112	636	40	σ	σ	NOUN
m-1112	636	41	which	which	PRON
m-1112	636	42	is	be	AUX
m-1112	636	43	equal	equal	ADJ
m-1112	636	44	to	to	ADP
m-1112	636	45	the	the	DET
m-1112	636	46	centripetal	centripetal	NOUN
m-1112	636	47	-	-	PUNCT
m-1112	636	48	force	force	NOUN
m-1112	636	49	then	then	ADV
m-1112	636	50	issues	issue	VERB
m-1112	636	51	fc	fc	PROPN
m-1112	637	1	=	=	SYM
m-1112	637	2	σ	σ	PROPN
m-1112	637	3	=	=	NOUN
m-1112	637	4	𝐦.𝐯³	𝐦.𝐯³	NOUN
m-1112	637	5	𝐫	𝐫	X
m-1112	637	6	=	=	SYM
m-1112	637	7	j	j	PROPN
m-1112	637	8	w²	w²	PROPN
m-1112	637	9	r	r	NOUN
m-1112	637	10	=	=	SYM
m-1112	637	11	�	�	NOUN
m-1112	637	12	̅	̅	NOUN
m-1112	637	13	�	�	NOUN
m-1112	637	14	r	r	NOUN
m-1112	637	15	,	,	PUNCT
m-1112	637	16	where	where	SCONJ
m-1112	637	17	the	the	DET
m-1112	637	18	monad	monad	PROPN
m-1112	637	19	r	r	PROPN
m-1112	637	20	≡	≡	PROPN
m-1112	637	21	monad	monad	PROPN
m-1112	637	22	r	r	NOUN
m-1112	637	23	=	=	SYM
m-1112	637	24	σ	σ	X
m-1112	637	25	j.w²	j.w²	NOUN
m-1112	637	26	=	=	SYM
m-1112	637	27	𝛔	𝛔	PART
m-1112	637	28	�	�	PROPN
m-1112	637	29	̅	̅	NOUN
m-1112	637	30	�	�	NOUN
m-1112	637	31	i.e.	i.e.	X
m-1112	637	32	the	the	DET
m-1112	637	33	stress	stress	NOUN
m-1112	637	34	σ	σ	PROPN
m-1112	637	35	,	,	PUNCT
m-1112	637	36	which	which	PRON
m-1112	637	37	is	be	AUX
m-1112	637	38	created	create	VERB
m-1112	637	39	between	between	ADP
m-1112	637	40	the	the	DET
m-1112	637	41	opposite	opposite	ADJ
m-1112	637	42	[	[	X
m-1112	637	43	⊕↔⊝	⊕↔⊝	X
m-1112	637	44	]	]	PUNCT
m-1112	637	45	,	,	PUNCT
m-1112	637	46	and	and	CCONJ
m-1112	637	47	through	through	ADP
m-1112	637	48	the	the	DET
m-1112	637	49	only	only	ADJ
m-1112	637	50	possible	possible	ADJ
m-1112	637	51	rotational	rotational	ADJ
m-1112	637	52	-	-	PUNCT
m-1112	637	53	motion	motion	NOUN
m-1112	637	54	,	,	PUNCT
m-1112	637	55	originates	originate	VERB
m-1112	637	56	the	the	DET
m-1112	637	57	angular	angular	ADJ
m-1112	637	58	-	-	PUNCT
m-1112	637	59	velocity	velocity	NOUN
m-1112	637	60	�	�	NOUN
m-1112	637	61	̆	̆	NOUN
m-1112	637	62	�	�	PROPN
m-1112	637	63	=	=	PUNCT
m-1112	637	64	𝛔.𝚽	𝛔.𝚽	PUNCT
m-1112	637	65	𝐫	𝐫	X
m-1112	637	66	=	=	SYM
m-1112	637	67	2πr.f	2πr.f	PROPN
m-1112	637	68	and	and	CCONJ
m-1112	637	69	the	the	DET
m-1112	637	70	angular	angular	ADJ
m-1112	637	71	momentum	momentum	NOUN
m-1112	637	72	�	�	NOUN
m-1112	637	73	̅	̅	NOUN
m-1112	637	74	�	�	NOUN
m-1112	637	75	=	=	PUNCT
m-1112	637	76	𝛔.	𝛔.	NOUN
m-1112	637	77	𝐫	𝐫	X
m-1112	637	78	=	=	SYM
m-1112	637	79	𝛔.	𝛔.	PROPN
m-1112	637	80	𝐑	𝐑	PROPN
m-1112	637	81	,	,	PUNCT
m-1112	637	82	which	which	PRON
m-1112	637	83	when	when	SCONJ
m-1112	637	84	placed	place	VERB
m-1112	637	85	on	on	ADP
m-1112	637	86	ab	ab	NOUN
m-1112	637	87	diameter	diameter	NOUN
m-1112	637	88	=	=	SYM
m-1112	637	89	2r	2r	NUM
m-1112	638	1	=	=	PUNCT
m-1112	638	2	the	the	DET
m-1112	638	3	monad	monad	PROPN
m-1112	638	4	consist	consist	VERB
m-1112	638	5	the	the	DET
m-1112	638	6	neutral	neutral	ADJ
m-1112	638	7	–	–	PUNCT
m-1112	638	8	spaces	space	NOUN
m-1112	638	9	energy	energy	NOUN
m-1112	638	10	.	.	PUNCT
m-1112	639	1	the	the	DET
m-1112	639	2	planck`s	planck`s	NOUN
m-1112	639	3	cave	cave	NOUN
m-1112	639	4	,	,	PUNCT
m-1112	639	5	10−35	10−35	NOUN
m-1112	639	6	m	m	NOUN
m-1112	639	7	,	,	PUNCT
m-1112	639	8	is	be	AUX
m-1112	639	9	the	the	DET
m-1112	639	10	safety	safety	NOUN
m-1112	639	11	-	-	PUNCT
m-1112	639	12	valve	valve	NOUN
m-1112	639	13	≡	≡	NOUN
m-1112	639	14	the	the	DET
m-1112	639	15	critical	critical	ADJ
m-1112	639	16	state	state	NOUN
m-1112	639	17	for	for	ADP
m-1112	639	18	the	the	DET
m-1112	639	19	stress	stress	NOUN
m-1112	639	20	ellipsoids	ellipsoid	NOUN
m-1112	639	21	,	,	PUNCT
m-1112	639	22	b̅	b̅	PROPN
m-1112	639	23	w̅	w̅	PROPN
m-1112	639	24	,	,	PUNCT
m-1112	639	25	vectors	vector	NOUN
m-1112	639	26	in	in	ADP
m-1112	639	27	order	order	NOUN
m-1112	639	28	that	that	SCONJ
m-1112	639	29	this	this	DET
m-1112	639	30	total	total	ADJ
m-1112	639	31	-	-	PUNCT
m-1112	639	32	energy	energy	NOUN
m-1112	639	33	to	to	PART
m-1112	639	34	superflow	superflow	VERB
m-1112	639	35	and	and	CCONJ
m-1112	639	36	be	be	AUX
m-1112	639	37	still	still	ADV
m-1112	639	38	into	into	ADP
m-1112	639	39	vacuum	vacuum	PROPN
m-1112	639	40	≡	≡	PROPN
m-1112	640	1	[	[	X
m-1112	640	2	10−62	10−62	NUM
m-1112	640	3	-	-	PUNCT
m-1112	640	4	10−35	10−35	NUM
m-1112	640	5	m	m	NOUN
m-1112	640	6	]	]	PUNCT
m-1112	640	7	.	.	PUNCT
m-1112	641	1	this	this	DET
m-1112	641	2	vacuum	vacuum	NOUN
m-1112	641	3	between	between	ADP
m-1112	641	4	the	the	DET
m-1112	641	5	|gravity	|gravity	NOUN
m-1112	641	6	cave	cave	NOUN
m-1112	641	7	planck`s	planck`s	NOUN
m-1112	641	8	cave|	cave|	PROPN
m-1112	641	9	consists	consist	VERB
m-1112	641	10	the	the	DET
m-1112	641	11	black	black	ADJ
m-1112	641	12	holes	hole	NOUN
m-1112	641	13	chaos	chaos	NOUN
m-1112	641	14	,	,	PUNCT
m-1112	641	15	as	as	ADP
m-1112	641	16	the	the	DET
m-1112	641	17	recycling	recycling	NOUN
m-1112	641	18	–	–	PUNCT
m-1112	641	19	energy	energy	NOUN
m-1112	641	20	into	into	ADP
m-1112	641	21	which	which	PRON
m-1112	641	22	→	→	PUNCT
m-1112	641	23	the	the	DET
m-1112	641	24	{	{	PUNCT
m-1112	641	25	energy	energy	NOUN
m-1112	641	26	–	–	PUNCT
m-1112	641	27	space	space	NOUN
m-1112	642	1	monad	monad	PROPN
m-1112	642	2	|	|	NOUN
m-1112	642	3	�	�	PROPN
m-1112	642	4	̅	̅	NOUN
m-1112	642	5	�	�	PROPN
m-1112	642	6	|	|	ADV
m-1112	642	7	≡	≡	PROPN
m-1112	642	8	|ab|	|ab|	PROPN
m-1112	642	9	}	}	PUNCT
m-1112	642	10	,	,	PUNCT
m-1112	642	11	decomposes	decompose	VERB
m-1112	642	12	←	←	PROPN
m-1112	642	13	{	{	PUNCT
m-1112	642	14	fig-14	fig-14	PROPN
m-1112	642	15	}	}	PUNCT
m-1112	642	16	the	the	DET
m-1112	642	17	rolling	rolling	NOUN
m-1112	642	18	of	of	ADP
m-1112	642	19	polhode	polhode	NOUN
m-1112	642	20	unit	unit	NOUN
m-1112	642	21	-	-	PUNCT
m-1112	642	22	space	space	NOUN
m-1112	642	23	into	into	ADP
m-1112	642	24	the	the	DET
m-1112	642	25	herpolhode	herpolhode	ADJ
m-1112	642	26	space	space	NOUN
m-1112	642	27	-	-	PUNCT
m-1112	642	28	monad	monad	PROPN
m-1112	642	29	cone	cone	NOUN
m-1112	642	30	.	.	PUNCT
m-1112	643	1	figure	figure	VERB
m-1112	643	2	-4the	-4the	DET
m-1112	643	3	central	central	ADJ
m-1112	643	4	axial	axial	ADJ
m-1112	643	5	-	-	PUNCT
m-1112	643	6	ellipsoid	ellipsoid	NOUN
m-1112	643	7	of	of	ADP
m-1112	643	8	⊕	⊕	PROPN
m-1112	643	9	constituent	constituent	NOUN
m-1112	643	10	rotating	rotate	VERB
m-1112	643	11	through	through	ADP
m-1112	643	12	constant	constant	ADJ
m-1112	643	13	point	point	NOUN
m-1112	643	14	o	o	INTJ
m-1112	643	15	.	.	PUNCT
m-1112	644	1	in	in	ADP
m-1112	644	2	(	(	PUNCT
m-1112	644	3	1	1	NUM
m-1112	644	4	-	-	SYM
m-1112	644	5	2	2	NUM
m-1112	644	6	)	)	PUNCT
m-1112	644	7	the	the	DET
m-1112	644	8	⊕	⊕	PROPN
m-1112	644	9	material	material	NOUN
m-1112	644	10	point	point	NOUN
m-1112	644	11	ok	ok	INTJ
m-1112	644	12	,	,	PUNCT
m-1112	644	13	{	{	PUNCT
m-1112	644	14	⊕	⊕	PROPN
m-1112	644	15	≡	≡	PROPN
m-1112	644	16	o,[ok	o,[ok	PROPN
m-1112	644	17	=	=	SYM
m-1112	644	18	r	r	X
m-1112	644	19	]	]	PUNCT
m-1112	644	20	≡	≡	PROPN
m-1112	644	21	the	the	DET
m-1112	644	22	space	space	NOUN
m-1112	644	23	}	}	PUNCT
m-1112	644	24	,	,	PUNCT
m-1112	644	25	continually	continually	ADV
m-1112	644	26	rotates	rotate	VERB
m-1112	644	27	around	around	ADP
m-1112	644	28	the	the	DET
m-1112	644	29	⊝	⊝	NUM
m-1112	644	30	material	material	NOUN
m-1112	644	31	point	point	NOUN
m-1112	644	32	ok	ok	ADJ
m-1112	644	33	,	,	PUNCT
m-1112	644	34	{	{	PUNCT
m-1112	644	35	⊝	⊝	NUM
m-1112	644	36	≡	≡	PROPN
m-1112	644	37	o	o	X
m-1112	644	38	,	,	PUNCT
m-1112	644	39	[	[	X
m-1112	644	40	ok	ok	X
m-1112	644	41	]	]	X
m-1112	644	42	≡	≡	PROPN
m-1112	644	43	the	the	DET
m-1112	644	44	anti	anti	ADJ
m-1112	644	45	-	-	NOUN
m-1112	644	46	space	space	NOUN
m-1112	644	47	}	}	PUNCT
m-1112	644	48	,	,	PUNCT
m-1112	644	49	on	on	ADP
m-1112	644	50	2r	2r	NUM
m-1112	644	51	circle	circle	NOUN
m-1112	644	52	.	.	PUNCT
m-1112	645	1	their	their	PRON
m-1112	645	2	common	common	ADJ
m-1112	645	3	circle	circle	NOUN
m-1112	645	4	center	center	NOUN
m-1112	645	5	,	,	PUNCT
m-1112	645	6	forms	form	VERB
m-1112	645	7	the	the	DET
m-1112	645	8	material	material	NOUN
m-1112	645	9	angle	angle	NOUN
m-1112	645	10	φ	φ	NOUN
m-1112	645	11	=	=	SYM
m-1112	645	12	φp.t	φp.t	NOUN
m-1112	645	13	=	=	SYM
m-1112	645	14	(	(	PUNCT
m-1112	645	15	vp	vp	PROPN
m-1112	645	16	√c²−r²	√c²−r²	NUM
m-1112	645	17	)	)	PUNCT
m-1112	645	18	.t	.t	PROPN
m-1112	645	19	,	,	PUNCT
m-1112	645	20	which	which	PRON
m-1112	645	21	then	then	ADV
m-1112	645	22	ijo	ijo	PROPN
m-1112	645	23	international	international	PROPN
m-1112	645	24	journal	journal	PROPN
m-1112	645	25	of	of	ADP
m-1112	645	26	mathematics	mathematics	PROPN
m-1112	645	27	(	(	PUNCT
m-1112	645	28	issn	issn	PROPN
m-1112	645	29	:	:	PUNCT
m-1112	645	30	2992	2992	NUM
m-1112	645	31	-	-	SYM
m-1112	645	32	4421	4421	NUM
m-1112	645	33	)	)	PUNCT
m-1112	645	34	volume	volume	NOUN
m-1112	645	35	08	08	NUM
m-1112	646	1	|	|	ADV
m-1112	646	2	issue	issue	NOUN
m-1112	646	3	08	08	NUM
m-1112	647	1	|	|	ADV
m-1112	647	2	august	august	PROPN
m-1112	647	3	2025	2025	NUM
m-1112	647	4	|	|	ADV
m-1112	647	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	647	6	ijo	ijo	PROPN
m-1112	647	7	journals	journal	NOUN
m-1112	647	8	22	22	NUM
m-1112	647	9	the	the	DET
m-1112	647	10	fundamental	fundamental	ADJ
m-1112	647	11	particles	particle	NOUN
m-1112	647	12	origination	origination	NOUN
m-1112	647	13	mechanism	mechanism	NOUN
m-1112	647	14	in	in	ADP
m-1112	647	15	mfmf	mfmf	PROPN
m-1112	647	16	pns	pns	PROPN
m-1112	647	17	caves	cave	NOUN
m-1112	647	18	.	.	PUNCT
m-1112	648	1	creates	create	VERB
m-1112	648	2	at	at	ADP
m-1112	648	3	any	any	DET
m-1112	648	4	contact	contact	NOUN
m-1112	648	5	point	point	NOUN
m-1112	648	6	p	p	NOUN
m-1112	648	7	the	the	DET
m-1112	648	8	centripetal	centripetal	ADJ
m-1112	648	9	force	force	NOUN
m-1112	648	10	𝐅𝐂	𝐅𝐂	PROPN
m-1112	648	11	=	=	PUNCT
m-1112	648	12	mv²	mv²	ADJ
m-1112	648	13	r	r	NOUN
m-1112	648	14	=	=	SYM
m-1112	648	15	𝜋r²	𝜋r²	NOUN
m-1112	649	1	2r	2r	NUM
m-1112	650	1	[	[	X
m-1112	650	2	w²	w²	NOUN
m-1112	650	3	.	.	PUNCT
m-1112	651	1	r²	r²	VERB
m-1112	651	2	]	]	PUNCT
m-1112	651	3	=	=	SYM
m-1112	651	4	𝝅.𝐫³	𝝅.𝐫³	NOUN
m-1112	651	5	𝟐	𝟐	NUM
m-1112	652	1	[	[	X
m-1112	652	2	w	w	ADP
m-1112	652	3	²	²	NUM
m-1112	652	4	]	]	PUNCT
m-1112	652	5	.	.	PUNCT
m-1112	653	1	the	the	DET
m-1112	653	2	vector	vector	PROPN
m-1112	653	3	�	�	PROPN
m-1112	653	4	̆	̆	NOUN
m-1112	653	5	�	�	PROPN
m-1112	653	6	of	of	ADP
m-1112	653	7	angular	angular	ADJ
m-1112	653	8	velocity	velocity	NOUN
m-1112	653	9	w	w	NOUN
m-1112	653	10	,	,	PUNCT
m-1112	653	11	formulates	formulate	VERB
m-1112	653	12	the	the	DET
m-1112	653	13	polhode	polhode	NOUN
m-1112	653	14	cone	cone	NOUN
m-1112	653	15	of	of	ADP
m-1112	653	16	base	base	NOUN
m-1112	653	17	-	-	PUNCT
m-1112	653	18	radius	radius	NOUN
m-1112	653	19	a	a	PRON
m-1112	653	20	,	,	PUNCT
m-1112	653	21	and	and	CCONJ
m-1112	653	22	of	of	ADP
m-1112	653	23	op	op	NOUN
m-1112	653	24	=	=	SYM
m-1112	653	25	s	s	PART
m-1112	653	26	side	side	NOUN
m-1112	653	27	forming	form	VERB
m-1112	653	28	the	the	DET
m-1112	653	29	𝐰-angle	𝐰-angle	NOUN
m-1112	653	30	with	with	ADP
m-1112	653	31	z	z	NOUN
m-1112	653	32	axis	axis	NOUN
m-1112	653	33	,	,	PUNCT
m-1112	653	34	while	while	SCONJ
m-1112	653	35	the	the	DET
m-1112	653	36	vector	vector	PROPN
m-1112	653	37	�	�	PROPN
m-1112	653	38	̆	̆	NOUN
m-1112	653	39	�	�	PROPN
m-1112	653	40	of	of	ADP
m-1112	653	41	angular	angular	ADJ
m-1112	653	42	momentum	momentum	NOUN
m-1112	653	43	b	b	NOUN
m-1112	653	44	,	,	PUNCT
m-1112	653	45	formulates	formulate	VERB
m-1112	653	46	the	the	DET
m-1112	653	47	herpolhode	herpolhode	ADJ
m-1112	653	48	cone	cone	NOUN
m-1112	653	49	of	of	ADP
m-1112	653	50	base	base	NOUN
m-1112	653	51	-	-	PUNCT
m-1112	653	52	radius	radius	NOUN
m-1112	653	53	r	r	NOUN
m-1112	653	54	,	,	PUNCT
m-1112	653	55	of	of	ADP
m-1112	653	56	op	op	NOUN
m-1112	653	57	=	=	SYM
m-1112	653	58	s	s	PART
m-1112	653	59	side	side	NOUN
m-1112	653	60	and	and	CCONJ
m-1112	653	61	𝛉-angle	𝛉-angle	NOUN
m-1112	653	62	with	with	ADP
m-1112	653	63	z	z	NOUN
m-1112	653	64	axis	axis	NOUN
m-1112	653	65	in	in	ADP
m-1112	653	66	(	(	PUNCT
m-1112	653	67	3	3	NUM
m-1112	653	68	)	)	PUNCT
m-1112	653	69	,	,	PUNCT
m-1112	653	70	is	be	AUX
m-1112	653	71	the	the	DET
m-1112	653	72	mpmp	mpmp	ADJ
m-1112	653	73	space	space	NOUN
m-1112	653	74	where	where	SCONJ
m-1112	653	75	time	time	NOUN
m-1112	653	76	is	be	AUX
m-1112	653	77	not	not	PART
m-1112	653	78	existing	exist	VERB
m-1112	653	79	t	t	NOUN
m-1112	653	80	=	=	SYM
m-1112	653	81	0	0	NUM
m-1112	653	82	,	,	PUNCT
m-1112	653	83	and	and	CCONJ
m-1112	653	84	the	the	DET
m-1112	653	85	same	same	ADJ
m-1112	653	86	for	for	ADP
m-1112	653	87	motion	motion	NOUN
m-1112	653	88	also	also	ADV
m-1112	653	89	.	.	PUNCT
m-1112	654	1	in	in	ADP
m-1112	654	2	pns	pns	NOUN
m-1112	654	3	-	-	NOUN
m-1112	654	4	space	space	NOUN
m-1112	654	5	the	the	DET
m-1112	654	6	3	3	NUM
m-1112	654	7	-	-	PUNCT
m-1112	654	8	dimension	dimension	NOUN
m-1112	654	9	motion	motion	NOUN
m-1112	654	10	of	of	ADP
m-1112	654	11	the	the	DET
m-1112	654	12	primary	primary	ADJ
m-1112	654	13	constituents	constituent	NOUN
m-1112	654	14	[	[	X
m-1112	654	15	⊕	⊕	NOUN
m-1112	654	16	↻	↻	NOUN
m-1112	654	17	↺	↺	NOUN
m-1112	654	18	⊝	⊝	NOUN
m-1112	654	19	]	]	PUNCT
m-1112	654	20	the	the	DET
m-1112	654	21	time	time	NOUN
m-1112	654	22	is	be	AUX
m-1112	654	23	as	as	ADP
m-1112	654	24	period	period	NOUN
m-1112	654	25	t	t	NOUN
m-1112	654	26	,	,	PUNCT
m-1112	654	27	and	and	CCONJ
m-1112	654	28	momentum	momentum	NOUN
m-1112	654	29	is	be	AUX
m-1112	654	30	the	the	DET
m-1112	654	31	angular	angular	ADJ
m-1112	654	32	-	-	PUNCT
m-1112	654	33	velocity	velocity	NOUN
m-1112	654	34	�	�	PROPN
m-1112	654	35	̆	̆	NOUN
m-1112	654	36	�	�	PROPN
m-1112	654	37	and	and	CCONJ
m-1112	654	38	angular	angular	ADJ
m-1112	654	39	momentum	momentum	NOUN
m-1112	654	40	�	�	NOUN
m-1112	654	41	̅	̅	NOUN
m-1112	654	42	�	�	PROPN
m-1112	654	43	,	,	PUNCT
m-1112	654	44	where	where	SCONJ
m-1112	654	45	the	the	DET
m-1112	654	46	momentum	momentum	NOUN
m-1112	654	47	�	�	NOUN
m-1112	654	48	̅	̅	NOUN
m-1112	654	49	�	�	NOUN
m-1112	654	50	=	=	SYM
m-1112	654	51	r	r	NOUN
m-1112	654	52	m	m	NOUN
m-1112	654	53	v	v	NOUN
m-1112	654	54	=	=	PUNCT
m-1112	654	55	m	m	NOUN
m-1112	654	56	�	�	PROPN
m-1112	654	57	̆	̆	NOUN
m-1112	654	58	�	�	PROPN
m-1112	654	59	r²	r²	NOUN
m-1112	654	60	=	=	SYM
m-1112	654	61	±	±	NOUN
m-1112	654	62	[	[	PUNCT
m-1112	654	63	𝛑.𝐫𝟐	𝛑.𝐫𝟐	X
m-1112	654	64	𝟐	𝟐	NUM
m-1112	654	65	]	]	PUNCT
m-1112	654	66	.	.	PUNCT
m-1112	654	67	�	�	PROPN
m-1112	654	68	̅	̅	NOUN
m-1112	654	69	�	�	PROPN
m-1112	654	70	x	x	SYM
m-1112	654	71	�	�	PROPN
m-1112	654	72	̅	̅	NOUN
m-1112	654	73	�	�	PROPN
m-1112	654	74	and	and	CCONJ
m-1112	654	75	±	±	NUM
m-1112	654	76	[	[	PUNCT
m-1112	654	77	𝛑.𝐫𝟐	𝛑.𝐫𝟐	X
m-1112	654	78	𝟐	𝟐	PROPN
m-1112	654	79	]	]	PUNCT
m-1112	654	80	≡	≡	PROPN
m-1112	654	81	the	the	DET
m-1112	654	82	hemi	hemi	PROPN
m-1112	654	83	circle	circle	PROPN
m-1112	654	84	area	area	NOUN
m-1112	654	85	.	.	PUNCT
m-1112	655	1	the	the	DET
m-1112	655	2	polhode	polhode	NOUN
m-1112	655	3	is	be	AUX
m-1112	655	4	of	of	ADP
m-1112	655	5	radius	radius	NOUN
m-1112	655	6	a	a	PRON
m-1112	655	7	,	,	PUNCT
m-1112	655	8	and	and	CCONJ
m-1112	655	9	rotates	rotate	VERB
m-1112	655	10	with	with	ADP
m-1112	655	11	an	an	DET
m-1112	655	12	angular	angular	ADJ
m-1112	655	13	velocity	velocity	NOUN
m-1112	655	14	w̆	w̆	NOUN
m-1112	656	1	=	=	NOUN
m-1112	656	2	2π.fp	2π.fp	NUM
m-1112	656	3	in	in	ADP
m-1112	656	4	the	the	DET
m-1112	656	5	cone	cone	NOUN
m-1112	656	6	πa².s	πa².s	PROPN
m-1112	656	7	.	.	PUNCT
m-1112	657	1	the	the	DET
m-1112	657	2	herpolhode	herpolhode	PROPN
m-1112	657	3	is	be	AUX
m-1112	657	4	of	of	ADP
m-1112	657	5	radius	radius	NOUN
m-1112	657	6	r	r	NOUN
m-1112	657	7	,	,	PUNCT
m-1112	657	8	and	and	CCONJ
m-1112	657	9	is	be	AUX
m-1112	657	10	the	the	DET
m-1112	657	11	stationary	stationary	ADJ
m-1112	657	12	cone	cone	NOUN
m-1112	657	13	πr².s	πr².s	X
m-1112	657	14	.	.	PUNCT
m-1112	658	1	with	with	ADP
m-1112	658	2	an	an	DET
m-1112	658	3	angular	angular	ADJ
m-1112	658	4	momentum	momentum	NOUN
m-1112	658	5	b̆	b̆	NOUN
m-1112	659	1	=	=	SYM
m-1112	659	2	r	r	NOUN
m-1112	659	3	m	m	VERB
m-1112	659	4	v	v	AUX
m-1112	659	5	=	=	SYM
m-1112	659	6	r	r	NOUN
m-1112	659	7	m	m	VERB
m-1112	659	8	(	(	PUNCT
m-1112	659	9	w	w	NOUN
m-1112	659	10	r	r	NOUN
m-1112	659	11	)	)	PUNCT
m-1112	659	12	=	=	SYM
m-1112	659	13	m	m	PROPN
m-1112	659	14	�	�	PROPN
m-1112	659	15	̆	̆	NOUN
m-1112	659	16	�	�	PROPN
m-1112	659	17	r²	r²	NOUN
m-1112	659	18	.	.	PUNCT
m-1112	660	1	the	the	DET
m-1112	660	2	polhode	polhode	NOUN
m-1112	660	3	cone	cone	NOUN
m-1112	660	4	is	be	AUX
m-1112	660	5	rolling	roll	VERB
m-1112	660	6	on	on	ADP
m-1112	660	7	op	op	NOUN
m-1112	660	8	and	and	CCONJ
m-1112	660	9	contact	contact	VERB
m-1112	660	10	common	common	ADJ
m-1112	660	11	line	line	NOUN
m-1112	660	12	,	,	PUNCT
m-1112	660	13	into	into	ADP
m-1112	660	14	the	the	DET
m-1112	660	15	herpolhode	herpolhode	ADJ
m-1112	660	16	cone	cone	NOUN
m-1112	660	17	without	without	ADP
m-1112	660	18	friction	friction	NOUN
m-1112	660	19	.	.	PUNCT
m-1112	661	1	i.e.	i.e.	X
m-1112	661	2	the	the	DET
m-1112	661	3	motion	motion	NOUN
m-1112	661	4	in	in	ADP
m-1112	661	5	pns	pns	NOUN
m-1112	661	6	-	-	PUNCT
m-1112	661	7	space	space	NOUN
m-1112	661	8	exists	exist	VERB
m-1112	661	9	as	as	ADP
m-1112	661	10	the	the	DET
m-1112	661	11	rotation	rotation	NOUN
m-1112	661	12	of	of	ADP
m-1112	661	13	space	space	NOUN
m-1112	661	14	point	point	NOUN
m-1112	661	15	p	p	X
m-1112	661	16	(	(	PUNCT
m-1112	661	17	+	+	NOUN
m-1112	661	18	)	)	PUNCT
m-1112	661	19	on	on	ADP
m-1112	661	20	[	[	PUNCT
m-1112	661	21	o	o	NOUN
m-1112	661	22	,	,	PUNCT
m-1112	661	23	ok	ok	INTJ
m-1112	661	24	]	]	PUNCT
m-1112	661	25	circle	circle	NOUN
m-1112	661	26	anti	anti	NOUN
m-1112	661	27	-	-	NOUN
m-1112	661	28	point	point	ADJ
m-1112	661	29	p	p	X
m-1112	661	30	`	`	PUNCT
m-1112	661	31	(	(	PUNCT
m-1112	661	32	-	-	INTJ
m-1112	661	33	)	)	PUNCT
m-1112	661	34	on	on	ADP
m-1112	661	35	[	[	PUNCT
m-1112	661	36	o	o	NOUN
m-1112	661	37	,	,	PUNCT
m-1112	661	38	ok	ok	INTJ
m-1112	661	39	]	]	PUNCT
m-1112	661	40	of	of	ADP
m-1112	661	41	anti	anti	ADJ
m-1112	661	42	-	-	ADJ
m-1112	661	43	circle	circle	ADJ
m-1112	661	44	and	and	CCONJ
m-1112	661	45	defines	define	VERB
m-1112	661	46	the	the	DET
m-1112	661	47	angular	angular	ADJ
m-1112	661	48	-	-	PUNCT
m-1112	661	49	momentum	momentum	NOUN
m-1112	661	50	�	�	NOUN
m-1112	661	51	̅	̅	NOUN
m-1112	661	52	�	�	PROPN
m-1112	661	53	,	,	PUNCT
m-1112	661	54	so	so	ADV
m-1112	661	55	the	the	DET
m-1112	661	56	position	position	NOUN
m-1112	661	57	of	of	ADP
m-1112	661	58	spaces	space	NOUN
m-1112	661	59	points	point	NOUN
m-1112	661	60	p	p	X
m-1112	661	61	(	(	PUNCT
m-1112	661	62	+	+	NOUN
m-1112	661	63	)	)	PUNCT
m-1112	661	64	and	and	CCONJ
m-1112	661	65	points	point	VERB
m-1112	661	66	p	p	X
m-1112	661	67	(	(	PUNCT
m-1112	661	68	-	-	PUNCT
m-1112	661	69	)	)	PUNCT
m-1112	661	70	and	and	CCONJ
m-1112	661	71	momentum	momentum	NOUN
m-1112	661	72	are	be	AUX
m-1112	661	73	simultaneously	simultaneously	ADV
m-1112	661	74	determined	determine	VERB
m-1112	661	75	and	and	CCONJ
m-1112	661	76	measured	measure	VERB
m-1112	661	77	,	,	PUNCT
m-1112	661	78	consisting	consist	VERB
m-1112	661	79	a	a	DET
m-1112	661	80	direct	direct	ADJ
m-1112	661	81	violation	violation	NOUN
m-1112	661	82	of	of	ADP
m-1112	661	83	the	the	DET
m-1112	661	84	uncertainty	uncertainty	NOUN
m-1112	661	85	principle	principle	NOUN
m-1112	661	86	.	.	PUNCT
m-1112	662	1	the	the	DET
m-1112	662	2	primary	primary	ADJ
m-1112	662	3	rigid	rigid	ADJ
m-1112	662	4	-body	-body	ADJ
m-1112	662	5	analysis	analysis	NOUN
m-1112	662	6	:	:	PUNCT
m-1112	662	7	a	a	X
m-1112	662	8	..	..	PUNCT
m-1112	662	9	the	the	DET
m-1112	662	10	position	position	NOUN
m-1112	662	11	of	of	ADP
m-1112	662	12	the	the	DET
m-1112	662	13	herpolhode	herpolhode	ADJ
m-1112	662	14	cone	cone	NOUN
m-1112	662	15	is	be	AUX
m-1112	662	16	,	,	PUNCT
m-1112	662	17	fig-4	fig-4	X
m-1112	662	18	.	.	PUNCT
m-1112	663	1	x	x	PUNCT
m-1112	663	2	=	=	PUNCT
m-1112	663	3	a.sin	a.sin	PROPN
m-1112	663	4	θ	θ	PROPN
m-1112	663	5	.	.	PUNCT
m-1112	664	1	coswt	coswt	PROPN
m-1112	664	2	,	,	PUNCT
m-1112	664	3	y	y	PROPN
m-1112	664	4	=	=	SYM
m-1112	664	5	a.sin	a.sin	PROPN
m-1112	664	6	θ	θ	PROPN
m-1112	664	7	.	.	PUNCT
m-1112	664	8	sinwt	sinwt	PROPN
m-1112	664	9	,	,	PUNCT
m-1112	664	10	z	z	NOUN
m-1112	664	11	=	=	PUNCT
m-1112	664	12	a	a	DET
m-1112	664	13	a.cos	a.cos	ADJ
m-1112	664	14	θ	θ	NOUN
m-1112	664	15	=	=	PUNCT
m-1112	664	16	a.	a.	NOUN
m-1112	664	17	[	[	PUNCT
m-1112	664	18	1	1	NUM
m-1112	664	19	cos	cos	ADP
m-1112	664	20	θ	θ	PROPN
m-1112	664	21	]	]	PUNCT
m-1112	664	22	where	where	SCONJ
m-1112	664	23	exists	exist	VERB
m-1112	664	24	,	,	PUNCT
m-1112	664	25	a	a	PRON
m-1112	664	26	=	=	X
m-1112	664	27	the	the	DET
m-1112	664	28	polhode	polhode	NOUN
m-1112	664	29	cone	cone	NOUN
m-1112	664	30	base	base	NOUN
m-1112	664	31	-	-	PUNCT
m-1112	664	32	radius	radius	NOUN
m-1112	664	33	,	,	PUNCT
m-1112	665	1	r	r	NOUN
m-1112	665	2	=	=	PUNCT
m-1112	665	3	the	the	DET
m-1112	665	4	herpolhode	herpolhode	ADJ
m-1112	665	5	cone	cone	NOUN
m-1112	665	6	base	base	NOUN
m-1112	665	7	-	-	PUNCT
m-1112	665	8	radius	radius	NOUN
m-1112	665	9	[	[	PUNCT
m-1112	665	10	x	x	X
m-1112	665	11	,	,	PUNCT
m-1112	665	12	y	y	PROPN
m-1112	665	13	.	.	PUNCT
m-1112	666	1	z	z	X
m-1112	666	2	]	]	PUNCT
m-1112	667	1	=	=	SYM
m-1112	667	2	coordinate	coordinate	NOUN
m-1112	667	3	system	system	NOUN
m-1112	667	4	such	such	ADJ
m-1112	667	5	that	that	SCONJ
m-1112	667	6	z	z	NOUN
m-1112	667	7	-	-	PUNCT
m-1112	667	8	axis	axis	NOUN
m-1112	668	1	⊥	⊥	PROPN
m-1112	668	2	[	[	X
m-1112	668	3	kok	kok	X
m-1112	668	4	]	]	X
m-1112	668	5	line	line	NOUN
m-1112	668	6	,	,	PUNCT
m-1112	668	7	and	and	CCONJ
m-1112	668	8	angle	angle	NOUN
m-1112	668	9	𝛉	𝛉	PRON
m-1112	668	10	between	between	ADP
m-1112	668	11	op	op	NOUN
m-1112	668	12	,	,	PUNCT
m-1112	668	13	oz	oz	ADP
m-1112	668	14	axis	axis	NOUN
m-1112	668	15	.	.	PUNCT
m-1112	669	1	b	b	X
m-1112	669	2	..	..	PUNCT
m-1112	669	3	the	the	DET
m-1112	669	4	energies	energy	NOUN
m-1112	669	5	of	of	ADP
m-1112	669	6	the	the	DET
m-1112	669	7	polhode	polhode	NOUN
m-1112	669	8	herpolhode	herpolhode	ADJ
m-1112	669	9	cones	cone	NOUN
m-1112	669	10	are	be	AUX
m-1112	669	11	from	from	ADP
m-1112	669	12	lagrange`s	lagrange`s	PROPN
m-1112	669	13	principle	principle	NOUN
m-1112	669	14	where	where	SCONJ
m-1112	669	15	for	for	ADP
m-1112	669	16	any	any	DET
m-1112	669	17	particle	particle	NOUN
m-1112	669	18	,	,	PUNCT
m-1112	669	19	the	the	DET
m-1112	669	20	kinetic	kinetic	ADJ
m-1112	669	21	𝐄	𝐄	PROPN
m-1112	669	22	𝐊	𝐊	NOUN
m-1112	669	23	and	and	CCONJ
m-1112	669	24	potential	potential	ADJ
m-1112	669	25	𝐄	𝐄	PROPN
m-1112	669	26	𝐔	𝐔	PROPN
m-1112	669	27	energy	energy	NOUN
m-1112	669	28	are	be	AUX
m-1112	669	29	measured	measure	VERB
m-1112	669	30	as	as	ADP
m-1112	669	31	below	below	ADV
m-1112	669	32	,	,	PUNCT
m-1112	669	33	𝐄	𝐄	PROPN
m-1112	669	34	𝐊	𝐊	NOUN
m-1112	669	35	=	=	SYM
m-1112	669	36	1	1	NUM
m-1112	669	37	2	2	NUM
m-1112	669	38	m.	m.	NOUN
m-1112	669	39	[	[	PUNCT
m-1112	669	40	ẋ	ẋ	PROPN
m-1112	669	41	²	²	PROPN
m-1112	670	1	+	+	NOUN
m-1112	670	2	ẏ	ẏ	PROPN
m-1112	670	3	²	²	PROPN
m-1112	671	1	+	+	CCONJ
m-1112	671	2	ż	ż	NOUN
m-1112	671	3	²	²	X
m-1112	671	4	]	]	PUNCT
m-1112	671	5	=	=	SYM
m-1112	671	6	1	1	NUM
m-1112	671	7	2	2	NUM
m-1112	671	8	m	m	NOUN
m-1112	671	9	a²	a²	NOUN
m-1112	671	10	.	.	PUNCT
m-1112	672	1	[	[	PUNCT
m-1112	672	2	θ̇	θ̇	SYM
m-1112	672	3	²	²	NUM
m-1112	672	4	+	+	CCONJ
m-1112	672	5	w².sin	w².sin	X
m-1112	672	6	²	²	NUM
m-1112	672	7	θ	θ	PROPN
m-1112	672	8	]	]	PUNCT
m-1112	672	9	,	,	PUNCT
m-1112	672	10	and	and	CCONJ
m-1112	672	11	𝐄	𝐄	PROPN
m-1112	672	12	𝐔	𝐔	NOUN
m-1112	672	13	=	=	NOUN
m-1112	672	14	m	m	VERB
m-1112	672	15	g	g	NOUN
m-1112	672	16	z	z	PROPN
m-1112	672	17	=	=	PUNCT
m-1112	672	18	m	m	VERB
m-1112	672	19	g	g	NOUN
m-1112	672	20	a.cos	a.co	NOUN
m-1112	672	21	θ	θ	PROPN
m-1112	672	22	the	the	DET
m-1112	672	23	lagrangian	lagrangian	ADJ
m-1112	672	24	𝐋	𝐋	ADJ
m-1112	672	25	𝐊𝐔	𝐊𝐔	NOUN
m-1112	672	26	=	=	NOUN
m-1112	672	27	m.a²	m.a²	NOUN
m-1112	672	28	.	.	PUNCT
m-1112	673	1	[	[	PUNCT
m-1112	673	2	θ̇	θ̇	NOUN
m-1112	673	3	²	²	NUM
m-1112	673	4	2	2	NUM
m-1112	673	5	v	v	NOUN
m-1112	673	6	effective	effective	ADJ
m-1112	673	7	]	]	PUNCT
m-1112	673	8	,	,	PUNCT
m-1112	673	9	where	where	SCONJ
m-1112	673	10	the	the	DET
m-1112	673	11	effective	effective	ADJ
m-1112	673	12	potential	potential	NOUN
m-1112	673	13	v	v	ADP
m-1112	673	14	effe	effe	ADV
m-1112	673	15	is	be	AUX
m-1112	673	16	v	v	ADP
m-1112	673	17	effe	effe	ADJ
m-1112	673	18	=	=	SYM
m-1112	673	19	1	1	NUM
m-1112	673	20	𝑚,𝑎²	𝑚,𝑎²	PROPN
m-1112	673	21	[	[	PUNCT
m-1112	673	22	m	m	VERB
m-1112	673	23	g	g	NOUN
m-1112	673	24	a.cos	a.co	NOUN
m-1112	673	25	θ	θ	PROPN
m-1112	674	1	+	+	CCONJ
m-1112	674	2	1	1	NUM
m-1112	674	3	2	2	NUM
m-1112	674	4	m	m	NOUN
m-1112	674	5	a².w².sin	a².w².sin	PROPN
m-1112	674	6	²	²	NUM
m-1112	674	7	θ	θ	NOUN
m-1112	674	8	]	]	PUNCT
m-1112	675	1	=	=	PUNCT
m-1112	675	2	[	[	PUNCT
m-1112	675	3	g	g	NOUN
m-1112	675	4	.cosθ	.cosθ	ADP
m-1112	675	5	𝑎	𝑎	PROPN
m-1112	675	6	+	+	X
m-1112	675	7	w².sin	w².sin	X
m-1112	675	8	²θ	²θ	ADV
m-1112	675	9	𝑎	𝑎	X
m-1112	675	10	]	]	X
m-1112	675	11	…	…	PUNCT
m-1112	675	12	..	..	PUNCT
m-1112	675	13	(	(	PUNCT
m-1112	675	14	e	e	X
m-1112	675	15	)	)	PUNCT
m-1112	675	16	the	the	DET
m-1112	675	17	equation	equation	NOUN
m-1112	675	18	of	of	ADP
m-1112	675	19	motion	motion	NOUN
m-1112	675	20	for	for	ADP
m-1112	675	21	the	the	DET
m-1112	675	22	bead	bead	NOUN
m-1112	675	23	becomes	become	VERB
m-1112	675	24	from	from	ADP
m-1112	675	25	lagrangian	lagrangian	ADJ
m-1112	675	26	which	which	PRON
m-1112	675	27	is	be	AUX
m-1112	675	28	�	�	NOUN
m-1112	675	29	̈	̈	X
m-1112	675	30	�	�	NOUN
m-1112	675	31	=	=	PUNCT
m-1112	676	1	[	[	PUNCT
m-1112	676	2	∂v	∂v	X
m-1112	676	3	effe	effe	PROPN
m-1112	676	4	∂θ	∂θ	X
m-1112	676	5	]	]	PUNCT
m-1112	676	6	..	..	PUNCT
m-1112	676	7	(	(	PUNCT
m-1112	676	8	b	b	X
m-1112	676	9	)	)	PUNCT
m-1112	676	10	since	since	SCONJ
m-1112	676	11	θ	θ	PROPN
m-1112	676	12	is	be	AUX
m-1112	676	13	constant	constant	ADJ
m-1112	676	14	then	then	ADV
m-1112	676	15	issues	issue	VERB
m-1112	676	16	θ̇	θ̇	PRON
m-1112	676	17	=	=	SYM
m-1112	676	18	θ	θ	NOUN
m-1112	676	19	̈	̈	PUNCT
m-1112	676	20	=	=	NOUN
m-1112	676	21	0	0	NUM
m-1112	676	22	,	,	PUNCT
m-1112	676	23	and	and	CCONJ
m-1112	676	24	for	for	ADP
m-1112	676	25	the	the	DET
m-1112	676	26	bead	bead	ADJ
m-1112	676	27	-	-	PUNCT
m-1112	676	28	herpolhode	herpolhode	NOUN
m-1112	676	29	motion	motion	NOUN
m-1112	676	30	∂v	∂v	PROPN
m-1112	676	31	eff	eff	PROPN
m-1112	676	32	∂θ	∂θ	PUNCT
m-1112	677	1	=	=	PUNCT
m-1112	677	2	0	0	PUNCT
m-1112	677	3	..	..	PUNCT
m-1112	677	4	(	(	PUNCT
m-1112	677	5	c	c	X
m-1112	677	6	)	)	PUNCT
m-1112	677	7	equation	equation	NOUN
m-1112	677	8	(	(	PUNCT
m-1112	677	9	c	c	NOUN
m-1112	677	10	)	)	PUNCT
m-1112	677	11	is	be	AUX
m-1112	677	12	stationary	stationary	ADJ
m-1112	677	13	at	at	ADP
m-1112	677	14	positions	position	NOUN
m-1112	677	15	which	which	PRON
m-1112	677	16	satisfy	satisfy	VERB
m-1112	677	17	relation	relation	NOUN
m-1112	677	18	g.𝐬𝐢𝐧𝛉	g.𝐬𝐢𝐧𝛉	NOUN
m-1112	677	19	=	=	VERB
m-1112	677	20	a.w².𝐬𝐢𝐧𝛉.𝐜𝐨𝐬	a.w².𝐬𝐢𝐧𝛉.𝐜𝐨𝐬	NOUN
m-1112	677	21	𝛉	𝛉	X
m-1112	677	22	..	..	PUNCT
m-1112	677	23	(c1	(c1	NUM
m-1112	677	24	)	)	PUNCT
m-1112	677	25	1	1	NUM
m-1112	677	26	…	…	PUNCT
m-1112	677	27	the	the	DET
m-1112	677	28	solutions	solution	NOUN
m-1112	677	29	of	of	ADP
m-1112	677	30	(	(	PUNCT
m-1112	677	31	c1	c1	PROPN
m-1112	677	32	)	)	PUNCT
m-1112	677	33	are	be	AUX
m-1112	677	34	at	at	ADP
m-1112	677	35	position	position	NOUN
m-1112	677	36	sin	sin	NOUN
m-1112	677	37	θ	θ	NOUN
m-1112	677	38	=	=	SYM
m-1112	677	39	0	0	NUM
m-1112	677	40	where	where	SCONJ
m-1112	677	41	issues	issue	NOUN
m-1112	677	42	𝛉	𝛉	NOUN
m-1112	677	43	=	=	SYM
m-1112	677	44	0	0	NUM
m-1112	677	45	2	2	NUM
m-1112	677	46	…	…	PUNCT
m-1112	677	47	the	the	DET
m-1112	677	48	solutions	solution	NOUN
m-1112	677	49	of	of	ADP
m-1112	677	50	(	(	PUNCT
m-1112	677	51	c1	c1	PROPN
m-1112	677	52	)	)	PUNCT
m-1112	677	53	are	be	AUX
m-1112	677	54	at	at	ADP
m-1112	677	55	position	position	NOUN
m-1112	677	56	sin	sin	NOUN
m-1112	677	57	θ.cos	θ.cos	X
m-1112	677	58	θ	θ	NOUN
m-1112	678	1	=	=	PUNCT
m-1112	678	2	sin	sin	VERB
m-1112	678	3	2θ	2θ	NUM
m-1112	678	4	=	=	SYM
m-1112	678	5	0	0	PUNCT
m-1112	678	6	and	and	CCONJ
m-1112	678	7	is	be	AUX
m-1112	678	8	𝛉	𝛉	X
m-1112	678	9	=	=	PROPN
m-1112	678	10	π	π	PROPN
m-1112	678	11	&	&	CCONJ
m-1112	678	12	2𝛉	2𝛉	NUM
m-1112	679	1	=	=	SYM
m-1112	679	2	2π	2π	PROPN
m-1112	679	3	3	3	NUM
m-1112	679	4	…	…	PUNCT
m-1112	679	5	the	the	DET
m-1112	679	6	solutions	solution	NOUN
m-1112	679	7	of	of	ADP
m-1112	679	8	(	(	PUNCT
m-1112	679	9	c1	c1	PROPN
m-1112	679	10	)	)	PUNCT
m-1112	679	11	are	be	AUX
m-1112	679	12	at	at	ADP
m-1112	679	13	position	position	NOUN
m-1112	679	14	cos	cos	PROPN
m-1112	679	15	θ	θ	PROPN
m-1112	680	1	=	=	PUNCT
m-1112	681	1	g	g	PROPN
m-1112	681	2	a	a	X
m-1112	681	3	,	,	PUNCT
m-1112	681	4	w	w	NOUN
m-1112	681	5	²	²	NUM
m-1112	681	6	and	and	CCONJ
m-1112	681	7	for	for	ADP
m-1112	681	8	θ	θ	PROPN
m-1112	681	9	=	=	SYM
m-1112	681	10	0	0	PUNCT
m-1112	682	1	then	then	ADV
m-1112	682	2	w	w	PROPN
m-1112	682	3	²	²	PROPN
m-1112	682	4	=	=	SYM
m-1112	682	5	𝐠	𝐠	PRON
m-1112	682	6	𝐚	𝐚	PRON
m-1112	682	7	remarks	remark	NOUN
m-1112	682	8	:	:	PUNCT
m-1112	682	9	1	1	NUM
m-1112	682	10	…	…	PUNCT
m-1112	682	11	solution	solution	NOUN
m-1112	682	12	(	(	PUNCT
m-1112	682	13	1	1	NUM
m-1112	682	14	)	)	PUNCT
m-1112	682	15	for	for	ADP
m-1112	682	16	θ	θ	PROPN
m-1112	682	17	=	=	SYM
m-1112	682	18	0	0	NUM
m-1112	682	19	exists	exist	VERB
m-1112	682	20	always	always	ADV
m-1112	682	21	and	and	CCONJ
m-1112	682	22	from	from	ADP
m-1112	682	23	figure-4-(2	figure-4-(2	ADV
m-1112	682	24	)	)	PUNCT
m-1112	682	25	the	the	DET
m-1112	682	26	velocity	velocity	NOUN
m-1112	682	27	vector	vector	NOUN
m-1112	682	28	�	�	PROPN
m-1112	682	29	̆	̆	PROPN
m-1112	682	30	�	�	PROPN
m-1112	682	31	is	be	AUX
m-1112	682	32	applied	apply	VERB
m-1112	682	33	at	at	ADP
m-1112	682	34	the	the	DET
m-1112	682	35	center	center	NOUN
m-1112	682	36	of	of	ADP
m-1112	682	37	mass	mass	PROPN
m-1112	682	38	𝐊	𝐊	PROPN
m-1112	682	39	𝟎	𝟎	NUM
m-1112	682	40	,	,	PUNCT
m-1112	682	41	anti	anti	ADJ
m-1112	682	42	-	-	ADJ
m-1112	682	43	clockwise	clockwise	ADJ
m-1112	682	44	spinning	spinning	NOUN
m-1112	682	45	.	.	PUNCT
m-1112	683	1	fig-4-(3	fig-4-(3	PROPN
m-1112	683	2	)	)	PUNCT
m-1112	683	3	2	2	NUM
m-1112	683	4	…	…	SYM
m-1112	683	5	solution	solution	NOUN
m-1112	683	6	(	(	PUNCT
m-1112	683	7	2	2	NUM
m-1112	683	8	)	)	PUNCT
m-1112	683	9	for	for	ADP
m-1112	683	10	θ	θ	PROPN
m-1112	683	11	=	=	PUNCT
m-1112	684	1	π	π	NOUN
m-1112	684	2	exists	exist	VERB
m-1112	684	3	always	always	ADV
m-1112	684	4	and	and	CCONJ
m-1112	684	5	from	from	ADP
m-1112	684	6	figure-4-(2	figure-4-(2	ADV
m-1112	684	7	)	)	PUNCT
m-1112	684	8	the	the	DET
m-1112	684	9	velocity	velocity	NOUN
m-1112	684	10	vector	vector	NOUN
m-1112	684	11	�	�	PROPN
m-1112	684	12	̆	̆	PROPN
m-1112	684	13	�	�	PROPN
m-1112	684	14	is	be	AUX
m-1112	684	15	ijo	ijo	PROPN
m-1112	684	16	international	international	ADJ
m-1112	684	17	journal	journal	PROPN
m-1112	684	18	of	of	ADP
m-1112	684	19	mathematics	mathematics	PROPN
m-1112	684	20	(	(	PUNCT
m-1112	684	21	issn	issn	PROPN
m-1112	684	22	:	:	PUNCT
m-1112	684	23	2992	2992	NUM
m-1112	684	24	-	-	SYM
m-1112	684	25	4421	4421	NUM
m-1112	684	26	)	)	PUNCT
m-1112	684	27	volume	volume	NOUN
m-1112	684	28	08	08	NUM
m-1112	685	1	|	|	ADV
m-1112	685	2	issue	issue	NOUN
m-1112	685	3	08	08	NUM
m-1112	686	1	|	|	ADV
m-1112	686	2	august	august	PROPN
m-1112	686	3	2025	2025	NUM
m-1112	686	4	|	|	ADV
m-1112	686	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	686	6	ijo	ijo	PROPN
m-1112	686	7	journals	journal	NOUN
m-1112	686	8	23	23	NUM
m-1112	686	9	the	the	DET
m-1112	686	10	fundamental	fundamental	ADJ
m-1112	686	11	particles	particle	NOUN
m-1112	686	12	origination	origination	NOUN
m-1112	686	13	mechanism	mechanism	NOUN
m-1112	686	14	in	in	ADP
m-1112	686	15	mfmf	mfmf	PROPN
m-1112	686	16	pns	pns	PROPN
m-1112	686	17	caves	cave	NOUN
m-1112	686	18	.	.	PUNCT
m-1112	687	1	applied	apply	VERB
m-1112	687	2	at	at	ADP
m-1112	687	3	the	the	DET
m-1112	687	4	center	center	NOUN
m-1112	687	5	of	of	ADP
m-1112	687	6	mass	mass	PROPN
m-1112	687	7	𝐊	𝐊	PROPN
m-1112	687	8	𝟎	𝟎	PROPN
m-1112	687	9	,	,	PUNCT
m-1112	687	10	clockwise	clockwise	NOUN
m-1112	687	11	spinning	spinning	NOUN
m-1112	687	12	.	.	PUNCT
m-1112	688	1	fig-4-(3	fig-4-(3	PROPN
m-1112	688	2	)	)	PUNCT
m-1112	688	3	3	3	NUM
m-1112	688	4	…	…	SYM
m-1112	688	5	solution	solution	NOUN
m-1112	688	6	(	(	PUNCT
m-1112	688	7	3	3	NUM
m-1112	688	8	)	)	PUNCT
m-1112	688	9	where	where	SCONJ
m-1112	688	10	since	since	SCONJ
m-1112	688	11	θ	θ	PROPN
m-1112	688	12	=	=	SYM
m-1112	688	13	0	0	NUM
m-1112	688	14	exist	exist	VERB
m-1112	688	15	the	the	DET
m-1112	688	16	prior	prior	ADJ
m-1112	688	17	and	and	CCONJ
m-1112	688	18	from	from	ADP
m-1112	688	19	figure-4-(2	figure-4-(2	ADJ
m-1112	688	20	)	)	PUNCT
m-1112	688	21	velocity	velocity	NOUN
m-1112	688	22	vector	vector	NOUN
m-1112	688	23	�	�	PROPN
m-1112	688	24	̆	̆	PROPN
m-1112	688	25	�	�	PROPN
m-1112	688	26	is	be	AUX
m-1112	688	27	applied	apply	VERB
m-1112	688	28	at	at	ADP
m-1112	688	29	the	the	DET
m-1112	688	30	center	center	NOUN
m-1112	688	31	of	of	ADP
m-1112	688	32	mass	mass	NOUN
m-1112	688	33	𝐊	𝐊	PROPN
m-1112	688	34	𝟎	𝟎	NUM
m-1112	688	35	,	,	PUNCT
m-1112	688	36	and	and	CCONJ
m-1112	688	37	the	the	DET
m-1112	688	38	±	±	NOUN
m-1112	688	39	spinning	spinning	NOUN
m-1112	688	40	is	be	AUX
m-1112	688	41	very	very	ADV
m-1112	688	42	fast	fast	ADV
m-1112	688	43	from	from	ADP
m-1112	688	44	the	the	DET
m-1112	688	45	center	center	NOUN
m-1112	688	46	and	and	CCONJ
m-1112	688	47	is	be	AUX
m-1112	688	48	such	such	ADJ
m-1112	688	49	that	that	SCONJ
m-1112	688	50	w	w	PROPN
m-1112	688	51	²	²	NUM
m-1112	688	52	≥	≥	NOUN
m-1112	688	53	0	0	NUM
m-1112	688	54	,	,	PUNCT
m-1112	688	55	and	and	CCONJ
m-1112	688	56	happening	happen	VERB
m-1112	688	57	when	when	SCONJ
m-1112	688	58	{	{	PUNCT
m-1112	688	59	from	from	ADP
m-1112	688	60	relation	relation	NOUN
m-1112	688	61	g	g	PROPN
m-1112	688	62	a	a	DET
m-1112	688	63	}	}	PUNCT
m-1112	688	64	the	the	DET
m-1112	688	65	radius	radius	NOUN
m-1112	688	66	a	a	DET
m-1112	688	67			NOUN
m-1112	688	68	0	0	NUM
m-1112	688	69	.	.	PUNCT
m-1112	689	1	4	4	NUM
m-1112	689	2	…	…	PUNCT
m-1112	689	3	the	the	DET
m-1112	689	4	solution	solution	NOUN
m-1112	689	5	w	w	PROPN
m-1112	689	6	²	²	NUM
m-1112	689	7	≥	≥	NOUN
m-1112	689	8	𝐠	𝐠	PRON
m-1112	689	9	𝐚	𝐚	X
m-1112	689	10	,	,	PUNCT
m-1112	689	11	determines	determine	VERB
m-1112	689	12	the	the	DET
m-1112	689	13	stability	stability	NOUN
m-1112	689	14	of	of	ADP
m-1112	689	15	the	the	DET
m-1112	689	16	polhode	polhode	NOUN
m-1112	689	17	system	system	NOUN
m-1112	689	18	.	.	PUNCT
m-1112	690	1	the	the	DET
m-1112	690	2	solution	solution	NOUN
m-1112	690	3	w	w	ADP
m-1112	690	4	²	²	NUM
m-1112	690	5	<	<	X
m-1112	690	6	𝐠	𝐠	PRON
m-1112	690	7	𝐚	𝐚	NOUN
m-1112	690	8	and	and	CCONJ
m-1112	690	9	θ	θ	PROPN
m-1112	690	10	=	=	SYM
m-1112	690	11	0	0	NUM
m-1112	690	12	,	,	PUNCT
m-1112	690	13	determines	determine	VERB
m-1112	690	14	stability	stability	NOUN
m-1112	690	15	at	at	ADP
m-1112	690	16	point	point	NOUN
m-1112	690	17	o	o	NOUN
m-1112	690	18	position	position	NOUN
m-1112	690	19	and−v	and−v	ADV
m-1112	690	20	effe	effe	ADJ
m-1112	690	21	.	.	PUNCT
m-1112	691	1	the	the	DET
m-1112	691	2	solution	solution	NOUN
m-1112	691	3	w	w	ADP
m-1112	691	4	²	²	NUM
m-1112	691	5	<	<	X
m-1112	691	6	𝐠	𝐠	PRON
m-1112	691	7	𝐚	𝐚	NOUN
m-1112	691	8	and	and	CCONJ
m-1112	691	9	θ	θ	PROPN
m-1112	691	10	=	=	SYM
m-1112	691	11	π	π	PROPN
m-1112	691	12	,	,	PUNCT
m-1112	691	13	determines	determine	VERB
m-1112	691	14	stability	stability	NOUN
m-1112	691	15	at	at	ADP
m-1112	691	16	point	point	NOUN
m-1112	691	17	o	o	NOUN
m-1112	691	18	position	position	NOUN
m-1112	691	19	and+v	and+v	VERB
m-1112	691	20	effe	effe	ADJ
m-1112	691	21	.	.	PUNCT
m-1112	692	1	for	for	ADP
m-1112	692	2	solution	solution	NOUN
m-1112	692	3	w	w	ADP
m-1112	692	4	²	²	NUM
m-1112	692	5	>	>	X
m-1112	692	6	𝐠	𝐠	DET
m-1112	692	7	𝐚	𝐚	NOUN
m-1112	692	8	and	and	CCONJ
m-1112	692	9	θ	θ	PROPN
m-1112	692	10	=	=	SYM
m-1112	692	11	0	0	NUM
m-1112	692	12	,	,	PUNCT
m-1112	692	13	the	the	DET
m-1112	692	14	position	position	NOUN
m-1112	692	15	is	be	AUX
m-1112	692	16	unstable	unstable	ADJ
m-1112	692	17	at	at	ADP
m-1112	692	18	point	point	NOUN
m-1112	692	19	o	o	NOUN
m-1112	692	20	with	with	ADP
m-1112	692	21	−v	−v	NOUN
m-1112	692	22	effe	effe	ADJ
m-1112	692	23	.	.	PUNCT
m-1112	693	1	for	for	ADP
m-1112	693	2	solution	solution	NOUN
m-1112	693	3	w	w	ADP
m-1112	693	4	²	²	NUM
m-1112	693	5	>	>	X
m-1112	693	6	𝐠	𝐠	DET
m-1112	693	7	𝐚	𝐚	NOUN
m-1112	693	8	and	and	CCONJ
m-1112	693	9	θ	θ	PROPN
m-1112	693	10	=	=	SYM
m-1112	693	11	π	π	PROPN
m-1112	693	12	,	,	PUNCT
m-1112	693	13	the	the	DET
m-1112	693	14	position	position	NOUN
m-1112	693	15	is	be	AUX
m-1112	693	16	unstable	unstable	ADJ
m-1112	693	17	at	at	ADP
m-1112	693	18	point	point	NOUN
m-1112	693	19	o	o	NOUN
m-1112	693	20	with	with	ADP
m-1112	693	21	+	+	NOUN
m-1112	693	22	v	v	NOUN
m-1112	693	23	effe	effe	ADJ
m-1112	693	24	.	.	PUNCT
m-1112	694	1	meaning	mean	VERB
m-1112	694	2	the	the	DET
m-1112	694	3	black	black	ADJ
m-1112	694	4	–	–	PUNCT
m-1112	694	5	holes	hole	NOUN
m-1112	694	6	origination	origination	NOUN
m-1112	694	7	.	.	PUNCT
m-1112	695	1	from	from	ADP
m-1112	695	2	solutions	solution	NOUN
m-1112	695	3	w	w	ADP
m-1112	695	4	²	²	NUM
m-1112	695	5	=	=	SYM
m-1112	695	6	𝐠	𝐠	PRON
m-1112	695	7	𝐚	𝐚	X
m-1112	695	8	,	,	PUNCT
m-1112	695	9	the	the	DET
m-1112	695	10	θ	θ	NOUN
m-1112	695	11	=	=	SYM
m-1112	695	12	0	0	PUNCT
m-1112	696	1	=	=	PUNCT
m-1112	696	2	π	π	X
m-1112	696	3	=	=	NOUN
m-1112	696	4	2π	2π	NOUN
m-1112	696	5	positions	position	NOUN
m-1112	696	6	are	be	AUX
m-1112	696	7	unstable	unstable	ADJ
m-1112	696	8	and	and	CCONJ
m-1112	696	9	below	below	ADP
m-1112	696	10	point	point	NOUN
m-1112	696	11	o	o	PROPN
m-1112	696	12	with+v	with+v	X
m-1112	696	13	effe	effe	ADJ
m-1112	696	14	.	.	PUNCT
m-1112	697	1	meaning	mean	VERB
m-1112	697	2	an	an	DET
m-1112	697	3	evolving	evolve	VERB
m-1112	697	4	and	and	CCONJ
m-1112	697	5	operational	operational	ADJ
m-1112	697	6	black	black	ADJ
m-1112	697	7	-	-	PUNCT
m-1112	697	8	hole	hole	NOUN
m-1112	697	9	stable	stable	ADJ
m-1112	697	10	origination	origination	NOUN
m-1112	697	11	.	.	PUNCT
m-1112	698	1	5	5	NUM
m-1112	698	2	…	…	NUM
m-1112	698	3	all	all	PRON
m-1112	698	4	above	above	ADP
m-1112	698	5	stable	stable	ADJ
m-1112	698	6	solutions	solution	NOUN
m-1112	698	7	result	result	VERB
m-1112	698	8	to	to	ADP
m-1112	698	9	the	the	DET
m-1112	698	10	determination	determination	NOUN
m-1112	698	11	of	of	ADP
m-1112	698	12	the	the	DET
m-1112	698	13	two	two	NUM
m-1112	698	14	vector	vector	NOUN
m-1112	698	15	magnitudes	magnitude	NOUN
m-1112	698	16	that	that	PRON
m-1112	698	17	of	of	ADP
m-1112	698	18	angular	angular	ADJ
m-1112	698	19	-	-	PUNCT
m-1112	698	20	velocity	velocity	NOUN
m-1112	698	21	�	�	PROPN
m-1112	698	22	̆	̆	NOUN
m-1112	698	23	�	�	PROPN
m-1112	698	24	and	and	CCONJ
m-1112	698	25	that	that	PRON
m-1112	698	26	of	of	ADP
m-1112	698	27	angular	angular	ADJ
m-1112	698	28	momentum	momentum	NOUN
m-1112	698	29	�	�	NOUN
m-1112	698	30	̅	̅	NOUN
m-1112	698	31	�	�	PROPN
m-1112	698	32	,	,	PUNCT
m-1112	698	33	differently	differently	ADV
m-1112	698	34	black	black	ADJ
m-1112	698	35	-	-	PUNCT
m-1112	698	36	hole	hole	NOUN
m-1112	698	37	.	.	PUNCT
m-1112	699	1	----------------------------------------------------------------------------------------------------------	----------------------------------------------------------------------------------------------------------	PUNCT
m-1112	700	1	both	both	DET
m-1112	700	2	magnitudes	magnitude	VERB
m-1112	700	3	define	define	VERB
m-1112	700	4	the	the	DET
m-1112	700	5	unit	unit	NOUN
m-1112	700	6	-	-	PUNCT
m-1112	700	7	energy	energy	NOUN
m-1112	700	8	vectors	vector	NOUN
m-1112	700	9	→	→	SYM
m-1112	700	10	{	{	PUNCT
m-1112	700	11	unit	unit	NOUN
m-1112	700	12	-	-	PUNCT
m-1112	700	13	e	e	NOUN
m-1112	700	14	vector	vector	NOUN
m-1112	700	15	r	r	NOUN
m-1112	700	16	=	=	SYM
m-1112	700	17	σ	σ	X
m-1112	700	18	j.w²	j.w²	NOUN
m-1112	700	19	=	=	SYM
m-1112	700	20	𝛔	𝛔	PART
m-1112	700	21	�	�	PROPN
m-1112	700	22	̅	̅	NOUN
m-1112	700	23	�	�	PROPN
m-1112	700	24	}	}	PUNCT
m-1112	700	25	←	←	PROPN
m-1112	700	26	when	when	SCONJ
m-1112	700	27	the	the	DET
m-1112	700	28	unit-e.vector	unit-e.vector	PROPN
m-1112	700	29	r	r	NOUN
m-1112	700	30	is	be	AUX
m-1112	700	31	placed	place	VERB
m-1112	700	32	on	on	ADP
m-1112	700	33	[	[	X
m-1112	700	34	ab≡2r	ab≡2r	ADP
m-1112	700	35	s.diameter	s.diameter	NOUN
m-1112	700	36	of	of	ADP
m-1112	700	37	spaces	space	NOUN
m-1112	700	38	-	-	PUNCT
m-1112	700	39	neutral	neutral	ADJ
m-1112	700	40	-	-	PUNCT
m-1112	700	41	circle	circle	NOUN
m-1112	700	42	]	]	PUNCT
m-1112	700	43	then	then	ADV
m-1112	700	44	the	the	DET
m-1112	700	45	energy	energy	NOUN
m-1112	700	46	-	-	PUNCT
m-1112	700	47	monad	monad	PROPN
m-1112	700	48	|	|	NOUN
m-1112	700	49	�	�	NOUN
m-1112	700	50	̅	̅	NOUN
m-1112	700	51	�	�	NOUN
m-1112	700	52	|	|	NOUN
m-1112	700	53	exists	exist	VERB
m-1112	700	54	on	on	ADP
m-1112	700	55	space	space	NOUN
m-1112	700	56	-	-	PUNCT
m-1112	700	57	monad	monad	PROPN
m-1112	700	58	|ab|	|ab|	NUM
m-1112	700	59	≡	≡	PROPN
m-1112	700	60	|	|	NOUN
m-1112	700	61	�	�	PROPN
m-1112	700	62	̅	̅	NOUN
m-1112	700	63	�	�	NOUN
m-1112	700	64	|	|	ADV
m-1112	700	65	as	as	ADP
m-1112	700	66	{	{	PUNCT
m-1112	700	67	e+s	e+s	NUM
m-1112	700	68	-monad	-monad	PROPN
m-1112	700	69	|	|	NOUN
m-1112	700	70	�	�	NOUN
m-1112	700	71	̅	̅	NOUN
m-1112	700	72	�	�	NOUN
m-1112	700	73	|	|	NOUN
m-1112	700	74	}	}	PUNCT
m-1112	700	75	,	,	PUNCT
m-1112	700	76	i.e.	i.e.	X
m-1112	700	77	is	be	AUX
m-1112	700	78	the	the	DET
m-1112	700	79	{	{	PUNCT
m-1112	700	80	energy	energy	NOUN
m-1112	700	81	space	space	NOUN
m-1112	701	1	monad	monad	PROPN
m-1112	701	2	|	|	NOUN
m-1112	701	3	�	�	PROPN
m-1112	701	4	̅	̅	NOUN
m-1112	701	5	�	�	NOUN
m-1112	701	6	|	|	NOUN
m-1112	701	7	}	}	PUNCT
m-1112	701	8	,	,	PUNCT
m-1112	701	9	with	with	ADP
m-1112	701	10	the	the	DET
m-1112	701	11	magnitudes	magnitude	NOUN
m-1112	701	12	,	,	PUNCT
m-1112	701	13	spaces	space	VERB
m-1112	701	14	sides	side	NOUN
m-1112	701	15	𝛌𝐧=	𝛌𝐧=	ADJ
m-1112	701	16	2,√r2	2,√r2	PROPN
m-1112	702	1	−	−	PROPN
m-1112	703	1	a²n	a²n	PROPN
m-1112	703	2	,	,	PUNCT
m-1112	703	3	&	&	CCONJ
m-1112	703	4	,	,	PUNCT
m-1112	703	5	quantum	quantum	ADJ
m-1112	703	6	critical	critical	ADJ
m-1112	703	7	-	-	PUNCT
m-1112	703	8	side	side	NOUN
m-1112	703	9	𝐚𝐧	𝐚𝐧	NOUN
m-1112	703	10	=	=	SYM
m-1112	703	11	1	1	NUM
m-1112	703	12	2	2	NUM
m-1112	703	13	√4r2	√4r2	PROPN
m-1112	703	14	−	−	PROPN
m-1112	703	15	λ²n	λ²n	X
m-1112	703	16	,	,	PUNCT
m-1112	703	17	----------------------------------------------------------------------------------------------------------	----------------------------------------------------------------------------------------------------------	PUNCT
m-1112	703	18	the	the	DET
m-1112	703	19	quantization	quantization	NOUN
m-1112	703	20	of	of	ADP
m-1112	703	21	energy	energy	NOUN
m-1112	703	22	in	in	ADP
m-1112	703	23	spaces	space	NOUN
m-1112	703	24	,	,	PUNCT
m-1112	703	25	happens	happen	VERB
m-1112	703	26	when	when	SCONJ
m-1112	703	27	follow	follow	VERB
m-1112	703	28	the	the	DET
m-1112	703	29	archimedes	archimedes	PROPN
m-1112	703	30	formula	formula	NOUN
m-1112	703	31	for	for	ADP
m-1112	703	32	doubling	double	VERB
m-1112	703	33	the	the	DET
m-1112	703	34	vertices	vertex	NOUN
m-1112	703	35	n	n	X
m-1112	703	36	,	,	PUNCT
m-1112	703	37	𝛌𝟐𝐧=√2r2	𝛌𝟐𝐧=√2r2	VERB
m-1112	703	38	−	−	PROPN
m-1112	703	39	r√4r2	r√4r2	PROPN
m-1112	703	40	−	−	PROPN
m-1112	703	41	λ²n	λ²n	X
m-1112	703	42	&	&	CCONJ
m-1112	703	43	critical	critical	ADJ
m-1112	703	44	-	-	PUNCT
m-1112	703	45	sides	side	NOUN
m-1112	703	46	𝐚𝟐𝐧=	𝐚𝟐𝐧=	VERB
m-1112	703	47	1	1	NUM
m-1112	703	48	2	2	NUM
m-1112	703	49	√4r2	√4r2	NOUN
m-1112	704	1	−	−	PROPN
m-1112	704	2	λ²2n	λ²2n	PUNCT
m-1112	705	1	where	where	SCONJ
m-1112	705	2	then	then	ADV
m-1112	705	3	energy	energy	NOUN
m-1112	705	4	is	be	AUX
m-1112	705	5	divided	divide	VERB
m-1112	705	6	and	and	CCONJ
m-1112	705	7	spread	spread	VERB
m-1112	705	8	on	on	ADP
m-1112	705	9	the	the	DET
m-1112	705	10	double	double	ADJ
m-1112	705	11	number	number	NOUN
m-1112	705	12	of	of	ADP
m-1112	705	13	the	the	DET
m-1112	705	14	polygon	polygon	NOUN
m-1112	705	15	sides	side	NOUN
m-1112	705	16	.	.	PUNCT
m-1112	706	1	monad	monad	PROPN
m-1112	706	2	r	r	NOUN
m-1112	706	3	=	=	SYM
m-1112	706	4	σ	σ	X
m-1112	706	5	j.w²	j.w²	NOUN
m-1112	706	6	=	=	SYM
m-1112	706	7	𝛔	𝛔	PART
m-1112	706	8	�	�	PROPN
m-1112	706	9	̅	̅	NOUN
m-1112	706	10	�	�	NOUN
m-1112	706	11	remains	remain	VERB
m-1112	706	12	the	the	DET
m-1112	706	13	same	same	ADJ
m-1112	706	14	,	,	PUNCT
m-1112	706	15	while	while	SCONJ
m-1112	706	16	spaces	space	NOUN
m-1112	706	17	sides	side	NOUN
m-1112	706	18	change	change	VERB
m-1112	706	19	as	as	ADP
m-1112	706	20	above	above	ADV
m-1112	706	21	𝛌𝟐𝐧	𝛌𝟐𝐧	PRON
m-1112	706	22	,	,	PUNCT
m-1112	706	23	𝐚𝟐𝐧	𝐚𝟐𝐧	PROPN
m-1112	706	24	.	.	PUNCT
m-1112	707	1	7a	7a	NUM
m-1112	707	2	..	..	PUNCT
m-1112	707	3	the	the	DET
m-1112	707	4	mechanisms	mechanism	NOUN
m-1112	707	5	&	&	CCONJ
m-1112	707	6	charges	charge	NOUN
m-1112	707	7	,	,	PUNCT
m-1112	707	8	for	for	ADP
m-1112	707	9	dual	dual	ADJ
m-1112	707	10	originations	origination	NOUN
m-1112	707	11	,	,	PUNCT
m-1112	707	12	the	the	DET
m-1112	707	13	natural	natural	ADJ
m-1112	707	14	spaces	space	NOUN
m-1112	707	15	of	of	ADP
m-1112	707	16	ab	ab	PROPN
m-1112	707	17	diameter	diameter	NOUN
m-1112	707	18	is	be	AUX
m-1112	707	19	the	the	DET
m-1112	707	20	{	{	PUNCT
m-1112	707	21	ab̅̅	ab̅̅	NOUN
m-1112	707	22	̅̅	̅̅	PROPN
m-1112	707	23	unit	unit	NOUN
m-1112	707	24	complex	complex	ADJ
m-1112	707	25	vector	vector	NOUN
m-1112	707	26	}	}	PUNCT
m-1112	707	27	.	.	PUNCT
m-1112	708	1	1	1	X
m-1112	708	2	…	…	NUM
m-1112	708	3	spaces	space	VERB
m-1112	708	4	≡	≡	PROPN
m-1112	708	5	the	the	DET
m-1112	708	6	infinite	infinite	ADJ
m-1112	708	7	(	(	PUNCT
m-1112	708	8	+	+	ADJ
m-1112	708	9	)	)	PUNCT
m-1112	708	10	circumscribed	circumscribed	ADJ
m-1112	708	11	-	-	PUNCT
m-1112	708	12	regular	regular	ADJ
m-1112	708	13	-	-	PUNCT
m-1112	708	14	polygons	polygon	NOUN
m-1112	708	15	in	in	ADP
m-1112	708	16	ab̅̅	ab̅̅	PROPN
m-1112	708	17	̅̅	̅̅	PROPN
m-1112	708	18	.	.	PUNCT
m-1112	709	1	[	[	X
m-1112	709	2	fig-1,3	fig-1,3	X
m-1112	709	3	]	]	PUNCT
m-1112	709	4	.	.	PUNCT
m-1112	710	1	2	2	NUM
m-1112	710	2	…	…	SYM
m-1112	710	3	anti	anti	X
m-1112	710	4	spaces	space	NOUN
m-1112	710	5	≡	≡	PROPN
m-1112	710	6	the	the	DET
m-1112	710	7	infinite	infinite	ADJ
m-1112	710	8	(	(	PUNCT
m-1112	710	9	-	-	PUNCT
m-1112	710	10	)	)	PUNCT
m-1112	710	11	circumscribed	circumscribe	VERB
m-1112	710	12	-	-	PUNCT
m-1112	710	13	regular	regular	ADJ
m-1112	710	14	-	-	PUNCT
m-1112	710	15	polygons	polygon	NOUN
m-1112	710	16	in	in	ADP
m-1112	710	17	ab̅̅	ab̅̅	PROPN
m-1112	710	18	̅̅	̅̅	PROPN
m-1112	710	19	.[fig-1,3	.[fig-1,3	PROPN
m-1112	710	20	]	]	X
m-1112	710	21	.	.	PUNCT
m-1112	711	1	3	3	NUM
m-1112	711	2	…	…	SYM
m-1112	711	3	sub	sub	NOUN
m-1112	711	4	.	.	NOUN
m-1112	711	5	spaces	space	NOUN
m-1112	711	6	≡	≡	PROPN
m-1112	711	7	the	the	DET
m-1112	711	8	infinite	infinite	ADJ
m-1112	711	9	(	(	PUNCT
m-1112	711	10	+	+	ADJ
m-1112	711	11	)	)	PUNCT
m-1112	711	12	inscribed	inscribe	VERB
m-1112	711	13	-	-	PUNCT
m-1112	711	14	regular	regular	ADJ
m-1112	711	15	-	-	PUNCT
m-1112	711	16	polygons	polygon	NOUN
m-1112	711	17	on	on	ADP
m-1112	711	18	diameter	diameter	NOUN
m-1112	711	19	ab̅̅	ab̅̅	PROPN
m-1112	711	20	̅̅	̅̅	PROPN
m-1112	711	21	.[f-1,3	.[f-1,3	PROPN
m-1112	711	22	]	]	PUNCT
m-1112	711	23	.	.	PUNCT
m-1112	712	1	4	4	NUM
m-1112	712	2	…	…	SYM
m-1112	712	3	neutral	neutral	ADJ
m-1112	712	4	-	-	PUNCT
m-1112	712	5	spaces	space	NOUN
m-1112	712	6	≡	≡	PROPN
m-1112	712	7	the	the	DET
m-1112	712	8	infinite	infinite	ADJ
m-1112	712	9	circles	circle	NOUN
m-1112	712	10	on	on	ADP
m-1112	712	11	diameter	diameter	PROPN
m-1112	712	12	ab̅̅	ab̅̅	PROPN
m-1112	712	13	̅̅	̅̅	PROPN
m-1112	713	1	.(the	.(the	PROPN
m-1112	713	2	sphere	sphere	ADV
m-1112	713	3	on	on	ADP
m-1112	713	4	ab	ab	PROPN
m-1112	713	5	)	)	PUNCT
m-1112	713	6	,	,	PUNCT
m-1112	714	1	[	[	X
m-1112	714	2	fig-1,3	fig-1,3	X
m-1112	714	3	]	]	PUNCT
m-1112	714	4	.	.	PUNCT
m-1112	715	1	5	5	NUM
m-1112	715	2	…	…	SYM
m-1112	715	3	{mfmf	{mfmf	PUNCT
m-1112	715	4	}	}	PUNCT
m-1112	715	5	≡	≡	PROPN
m-1112	715	6	the	the	DET
m-1112	715	7	gravity	gravity	NOUN
m-1112	715	8	cave	cave	NOUN
m-1112	715	9	=	=	PUNCT
m-1112	716	1	10−62	10−62	NUM
m-1112	716	2	m	m	NOUN
m-1112	716	3	.	.	PUNCT
m-1112	717	1	6	6	NUM
m-1112	717	2	…	…	NUM
m-1112	717	3	{	{	PUNCT
m-1112	717	4	pns	pns	PROPN
m-1112	717	5	}	}	PUNCT
m-1112	717	6	≡	≡	PROPN
m-1112	717	7	the	the	DET
m-1112	717	8	planck`s	planck`s	NOUN
m-1112	717	9	cave	cave	NOUN
m-1112	717	10	length	length	NOUN
m-1112	718	1	=	=	SYM
m-1112	718	2	10−35	10−35	NOUN
m-1112	718	3	m	m	NOUN
m-1112	718	4	.	.	PUNCT
m-1112	719	1	7	7	NUM
m-1112	719	2	…	…	SYM
m-1112	719	3	vacuum	vacuum	PROPN
m-1112	719	4	≡	≡	PROPN
m-1112	719	5	[	[	PUNCT
m-1112	719	6	10−62	10−62	NUM
m-1112	719	7	-10−35	-10−35	NOUN
m-1112	719	8	m	m	NOUN
m-1112	719	9	]	]	PUNCT
m-1112	720	1	=	=	PUNCT
m-1112	720	2	the	the	DET
m-1112	720	3	in	in	ADP
m-1112	720	4	-	-	PUNCT
m-1112	720	5	between	between	NOUN
m-1112	720	6	distance	distance	NOUN
m-1112	720	7			NOUN
m-1112	720	8	the	the	DET
m-1112	720	9	origination	origination	NOUN
m-1112	720	10	-	-	PUNCT
m-1112	720	11	mechanisms	mechanism	NOUN
m-1112	720	12	in	in	ADP
m-1112	720	13	spaces	space	NOUN
m-1112	720	14	&	&	CCONJ
m-1112	720	15	the	the	DET
m-1112	720	16	origin	origin	NOUN
m-1112	720	17	of	of	ADP
m-1112	720	18	charges	charge	NOUN
m-1112	720	19	.	.	PUNCT
m-1112	721	1	8	8	NUM
m-1112	721	2	…	…	SYM
m-1112	721	3	action	action	NOUN
m-1112	721	4	-	-	PUNCT
m-1112	721	5	spaces	space	NOUN
m-1112	721	6	≡	≡	PROPN
m-1112	721	7	the	the	DET
m-1112	721	8	infinite	infinite	ADJ
m-1112	721	9	quaternion	quaternion	NOUN
m-1112	721	10	monads	monad	NOUN
m-1112	721	11	→	→	SYM
m-1112	721	12	�	�	NOUN
m-1112	721	13	̅	̅	NOUN
m-1112	721	14	�	�	PROPN
m-1112	721	15	≡	≡	PROPN
m-1112	721	16	(	(	PUNCT
m-1112	721	17	s	s	NOUN
m-1112	721	18	+	+	NUM
m-1112	721	19	v̅.i	v̅.i	X
m-1112	721	20	)	)	PUNCT
m-1112	721	21	≡	≡	PROPN
m-1112	721	22	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	721	23	̅̅	̅̅	PROPN
m-1112	721	24	≡	≡	PROPN
m-1112	721	25	≡	≡	PROPN
m-1112	721	26	√s2	√s2	PROPN
m-1112	722	1	+	+	PUNCT
m-1112	722	2	[	[	PUNCT
m-1112	722	3	v̅.	v̅.	NOUN
m-1112	722	4	i	i	X
m-1112	722	5	]	]	X
m-1112	722	6	²	²	X
m-1112	722	7	]	]	PUNCT
m-1112	722	8	,	,	PUNCT
m-1112	722	9	or	or	CCONJ
m-1112	722	10	�	�	PROPN
m-1112	722	11	̅	̅	NOUN
m-1112	722	12	�	�	NOUN
m-1112	722	13	≡	≡	PROPN
m-1112	722	14	x	x	PUNCT
m-1112	723	1	+	+	CCONJ
m-1112	723	2	i	i	PRON
m-1112	723	3	.	.	PUNCT
m-1112	724	1	y	y	PROPN
m-1112	724	2	≡	≡	PROPN
m-1112	724	3	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	724	4	̅̅	̅̅	PROPN
m-1112	724	5	≡	≡	PROPN
m-1112	724	6	moduli	modulus	NOUN
m-1112	724	7	,	,	PUNCT
m-1112	724	8	r	r	NOUN
m-1112	724	9	,	,	PUNCT
m-1112	724	10	is	be	AUX
m-1112	724	11	their	their	PRON
m-1112	724	12	magnitude	magnitude	NOUN
m-1112	724	13	[	[	PUNCT
m-1112	724	14	r	r	NOUN
m-1112	724	15	=	=	NOUN
m-1112	724	16	|	|	ADV
m-1112	724	17	r	r	NOUN
m-1112	724	18	|	|	NOUN
m-1112	724	19	=	=	PUNCT
m-1112	725	1	√	√	PROPN
m-1112	726	1	x2	x2	NOUN
m-1112	727	1	+	+	CCONJ
m-1112	728	1	y2	y2	NOUN
m-1112	728	2	]	]	PUNCT
m-1112	728	3	,	,	PUNCT
m-1112	728	4	on	on	ADP
m-1112	728	5	unit	unit	NOUN
m-1112	728	6	-	-	PUNCT
m-1112	728	7	diameter	diameter	NOUN
m-1112	728	8	ab̅̅	ab̅̅	PROPN
m-1112	728	9	̅̅	̅̅	PROPN
m-1112	728	10	.	.	PUNCT
m-1112	729	1	the	the	DET
m-1112	729	2	[	[	X
m-1112	729	3	qmas	qmas	NOUN
m-1112	729	4	]	]	PUNCT
m-1112	729	5	.	.	PUNCT
m-1112	730	1	for	for	ADP
m-1112	730	2	quaternion	quaternion	NOUN
m-1112	730	3	v	v	ADP
m-1112	730	4	=	=	SYM
m-1112	730	5	s	s	VERB
m-1112	730	6	𝐳	𝐳	X
m-1112	730	7	*	*	PUNCT
m-1112	730	8	𝐳	𝐳	X
m-1112	730	9	=	=	X
m-1112	730	10	(	(	PUNCT
m-1112	730	11	s	s	NOUN
m-1112	730	12	+	+	NUM
m-1112	730	13	v̅.i	v̅.i	X
m-1112	730	14	)	)	PUNCT
m-1112	730	15	²	²	PROPN
m-1112	730	16	=	=	PUNCT
m-1112	730	17	s²	s²	NOUN
m-1112	731	1	+	+	PROPN
m-1112	731	2	[	[	X
m-1112	731	3	v̅]²	v̅]²	X
m-1112	731	4	+2.sv̅.i	+2.sv̅.i	ADJ
m-1112	731	5	=	=	SYM
m-1112	731	6	s²	s²	PROPN
m-1112	731	7	–	–	PUNCT
m-1112	731	8	v̅	v̅	NOUN
m-1112	731	9	²	²	NUM
m-1112	731	10	±	±	NUM
m-1112	731	11	2.s	2.s	NUM
m-1112	731	12	v̅	v̅	NOUN
m-1112	732	1	=	=	NOUN
m-1112	732	2	|s|²	|s|²	PROPN
m-1112	732	3	-|s̅|²	-|s̅|²	NOUN
m-1112	732	4	±	±	NOUN
m-1112	732	5	2.|s|.|s̅|	2.|s|.|s̅|	NUM
m-1112	732	6	,	,	PUNCT
m-1112	732	7	for	for	ADP
m-1112	732	8	|v̅|	|v̅|	X
m-1112	732	9	=	=	SYM
m-1112	732	10	s	s	PROPN
m-1112	732	11	.	.	PUNCT
m-1112	733	1	8a	8a	NUM
m-1112	733	2	..	..	PUNCT
m-1112	733	3	the	the	DET
m-1112	733	4	material	material	NOUN
m-1112	733	5	geometry	geometry	NOUN
m-1112	733	6	,	,	PUNCT
m-1112	733	7	e	e	NOUN
m-1112	733	8	-	-	NOUN
m-1112	733	9	geometry	geometry	NOUN
m-1112	733	10	,	,	PUNCT
m-1112	733	11	physics	physics	NOUN
m-1112	733	12	and	and	CCONJ
m-1112	733	13	chemistry	chemistry	NOUN
m-1112	733	14	.	.	PUNCT
m-1112	734	1	ijo	ijo	PROPN
m-1112	734	2	international	international	PROPN
m-1112	734	3	journal	journal	PROPN
m-1112	734	4	of	of	ADP
m-1112	734	5	mathematics	mathematics	PROPN
m-1112	734	6	(	(	PUNCT
m-1112	734	7	issn	issn	PROPN
m-1112	734	8	:	:	PUNCT
m-1112	734	9	2992	2992	NUM
m-1112	734	10	-	-	SYM
m-1112	734	11	4421	4421	NUM
m-1112	734	12	)	)	PUNCT
m-1112	734	13	volume	volume	NOUN
m-1112	734	14	08	08	NUM
m-1112	735	1	|	|	ADV
m-1112	735	2	issue	issue	NOUN
m-1112	735	3	08	08	NUM
m-1112	736	1	|	|	ADV
m-1112	736	2	august	august	PROPN
m-1112	736	3	2025	2025	NUM
m-1112	737	1	|	|	ADV
m-1112	737	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	737	3	ijo	ijo	PROPN
m-1112	737	4	journals	journal	NOUN
m-1112	737	5	24	24	NUM
m-1112	737	6	the	the	DET
m-1112	737	7	fundamental	fundamental	ADJ
m-1112	737	8	particles	particle	NOUN
m-1112	737	9	origination	origination	NOUN
m-1112	737	10	mechanism	mechanism	NOUN
m-1112	737	11	in	in	ADP
m-1112	737	12	mfmf	mfmf	PROPN
m-1112	737	13	pns	pns	PROPN
m-1112	737	14	caves	cave	NOUN
m-1112	737	15	.	.	PUNCT
m-1112	738	1	8	8	X
m-1112	738	2	..	..	PUNCT
m-1112	738	3	[a	[a	X
m-1112	738	4	]	]	X
m-1112	738	5	..	..	PUNCT
m-1112	738	6	the	the	DET
m-1112	738	7	{	{	PUNCT
m-1112	738	8	stpl	stpl	PROPN
m-1112	738	9	}	}	PUNCT
m-1112	738	10	mechanisms	mechanism	NOUN
m-1112	738	11	in	in	ADP
m-1112	738	12	spaces	space	NOUN
m-1112	738	13	,	,	PUNCT
m-1112	738	14	from	from	ADP
m-1112	738	15	charges	charge	NOUN
m-1112	738	16	in	in	ADP
m-1112	738	17	under	under	ADP
m-1112	738	18	-	-	PUNCT
m-1112	738	19	planck`s	planck`s	NOUN
m-1112	738	20	-	-	PUNCT
m-1112	738	21	length	length	NOUN
m-1112	738	22	≡	≡	PROPN
m-1112	738	23	the	the	DET
m-1112	738	24	six	six	NUM
m-1112	738	25	triple	triple	ADJ
m-1112	738	26	points	point	NOUN
m-1112	738	27	line	line	NOUN
m-1112	738	28	mechanism	mechanism	NOUN
m-1112	738	29	≡	≡	PROPN
m-1112	738	30	the	the	DET
m-1112	738	31	complex	complex	ADJ
m-1112	738	32	vector	vector	NOUN
m-1112	738	33	-	-	PUNCT
m-1112	738	34	spaces	space	NOUN
m-1112	738	35	rotor	rotor	NOUN
m-1112	738	36	,	,	PUNCT
m-1112	738	37	it	it	PRON
m-1112	738	38	is	be	AUX
m-1112	738	39	a	a	DET
m-1112	738	40	mechanism	mechanism	NOUN
m-1112	738	41	on	on	ADP
m-1112	738	42	where	where	SCONJ
m-1112	738	43	the	the	DET
m-1112	738	44	charges	charge	NOUN
m-1112	738	45	of	of	ADP
m-1112	738	46	opposites	opposite	NOUN
m-1112	738	47	,	,	PUNCT
m-1112	738	48	[	[	X
m-1112	738	49	⊕↔⊝	⊕↔⊝	X
m-1112	738	50	]	]	X
m-1112	738	51	,	,	PUNCT
m-1112	738	52	react	react	VERB
m-1112	738	53	as	as	ADP
m-1112	738	54	centrifugal	centrifugal	ADJ
m-1112	738	55	force	force	NOUN
m-1112	738	56	fc	fc	INTJ
m-1112	738	57	which	which	PRON
m-1112	738	58	in	in	ADP
m-1112	738	59	turn	turn	NOUN
m-1112	738	60	changes	change	NOUN
m-1112	738	61	→	→	SYM
m-1112	738	62	(	(	PUNCT
m-1112	738	63	action	action	NOUN
m-1112	738	64	-	-	PUNCT
m-1112	738	65	reaction	reaction	NOUN
m-1112	738	66	≡	≡	PROPN
m-1112	738	67	+	+	CCONJ
m-1112	738	68	spin	spin	NOUN
m-1112	738	69	–	–	PUNCT
m-1112	738	70	anti	anti	ADJ
m-1112	738	71	spin	spin	NOUN
m-1112	738	72	)	)	PUNCT
m-1112	738	73	←of	←of	PROPN
m-1112	738	74	[	[	X
m-1112	738	75	mfmf	mfmf	X
m-1112	738	76	]	]	X
m-1112	738	77	space	space	NOUN
m-1112	738	78	to	to	PART
m-1112	738	79	rotational	rotational	ADJ
m-1112	738	80	motion	motion	NOUN
m-1112	738	81	angular	angular	ADJ
m-1112	738	82	-	-	PUNCT
m-1112	738	83	velocity	velocity	NOUN
m-1112	738	84	=	=	SYM
m-1112	738	85	�	�	PROPN
m-1112	738	86	̅	̅	NOUN
m-1112	738	87	�	�	PROPN
m-1112	738	88	&	&	CCONJ
m-1112	738	89	angular	angular	ADJ
m-1112	738	90	-	-	PUNCT
m-1112	738	91	momentum	momentum	NOUN
m-1112	738	92	=	=	SYM
m-1112	738	93	�	�	PROPN
m-1112	738	94	̅	̅	NOUN
m-1112	738	95	�	�	NOUN
m-1112	738	96	.	.	PUNCT
m-1112	739	1	[	[	X
m-1112	739	2	fig-6	fig-6	SYM
m-1112	739	3	]	]	PUNCT
m-1112	739	4	.	.	PUNCT
m-1112	739	5	8	8	NUM
m-1112	739	6	..	..	PUNCT
m-1112	739	7	[b	[b	X
m-1112	739	8	]	]	X
m-1112	739	9	..	..	PUNCT
m-1112	739	10	the	the	DET
m-1112	739	11	{	{	PUNCT
m-1112	739	12	tvpm	tvpm	NOUN
m-1112	739	13	}	}	PUNCT
m-1112	739	14	mechanisms	mechanism	NOUN
m-1112	739	15	,	,	PUNCT
m-1112	739	16	from	from	ADP
m-1112	739	17	charges	charge	NOUN
m-1112	739	18	on	on	ADP
m-1112	739	19	two	two	NUM
m-1112	739	20	-	-	PUNCT
m-1112	739	21	perpendicular	perpendicular	ADJ
m-1112	739	22	-	-	PUNCT
m-1112	739	23	vectors	vector	NOUN
m-1112	739	24	-	-	PUNCT
m-1112	739	25	edges	edge	NOUN
m-1112	739	26	≡	≡	PROPN
m-1112	739	27	markos	markos	PROPN
m-1112	739	28	two	two	NUM
m-1112	739	29	vectors	vector	NOUN
m-1112	739	30	three	three	NUM
m-1112	739	31	poles	pole	NOUN
m-1112	739	32	mechanism	mechanism	NOUN
m-1112	739	33	.	.	PUNCT
m-1112	740	1	[	[	X
m-1112	740	2	fig-8a	fig-8a	NOUN
m-1112	740	3	,	,	PUNCT
m-1112	740	4	8b	8b	PROPN
m-1112	740	5	]	]	PUNCT
m-1112	740	6	.	.	PUNCT
m-1112	741	1	in	in	ADP
m-1112	741	2	fig-8|4|	fig-8|4|	PROPN
m-1112	741	3	,	,	PUNCT
m-1112	741	4	vector	vector	NOUN
m-1112	741	5	cp̅̅̅̅	cp̅̅̅̅	VERB
m-1112	741	6	⏊	⏊	PROPN
m-1112	741	7	ca̅̅̅̅	ca̅̅̅̅	PROPN
m-1112	741	8	vector	vector	NOUN
m-1112	741	9	,	,	PUNCT
m-1112	741	10	which	which	PRON
m-1112	741	11	changes	change	VERB
m-1112	741	12	the	the	DET
m-1112	741	13	energy	energy	NOUN
m-1112	741	14	≡	≡	PROPN
m-1112	741	15	the	the	DET
m-1112	741	16	stress	stress	PROPN
m-1112	741	17	σ	σ	NOUN
m-1112	741	18	of	of	ADP
m-1112	741	19	the	the	DET
m-1112	741	20	|	|	ADV
m-1112	741	21	cp̅̅̅̅	cp̅̅̅̅	PROPN
m-1112	741	22	x	x	PUNCT
m-1112	741	23	ca̅̅̅̅	ca̅̅̅̅	PROPN
m-1112	741	24	|	|	ADV
m-1112	741	25	square	square	ADJ
m-1112	741	26	,	,	PUNCT
m-1112	741	27	to	to	ADP
m-1112	741	28	2	2	NUM
m-1112	741	29	halve	halve	NOUN
m-1112	741	30	±	±	NUM
m-1112	741	31	squares	square	NOUN
m-1112	741	32	on	on	ADP
m-1112	741	33	vectors	vector	NOUN
m-1112	741	34	-	-	PUNCT
m-1112	741	35	axis	axis	NOUN
m-1112	741	36	for	for	ADP
m-1112	741	37	equilibrium	equilibrium	NOUN
m-1112	741	38	.	.	PUNCT
m-1112	742	1	8	8	NUM
m-1112	742	2	..	..	PUNCT
m-1112	742	3	[c	[c	X
m-1112	742	4	]	]	X
m-1112	742	5	..	..	PUNCT
m-1112	742	6	the	the	DET
m-1112	742	7	{	{	PUNCT
m-1112	742	8	tcic	tcic	NOUN
m-1112	742	9	}	}	PUNCT
m-1112	742	10	mechanisms	mechanism	NOUN
m-1112	742	11	,	,	PUNCT
m-1112	742	12	from	from	ADP
m-1112	742	13	charges	charge	NOUN
m-1112	742	14	in	in	ADP
m-1112	742	15	three	three	NUM
m-1112	742	16	-	-	PUNCT
m-1112	742	17	vectors	vector	NOUN
m-1112	742	18	-	-	PUNCT
m-1112	742	19	conductors	conductor	NOUN
m-1112	742	20	-	-	PUNCT
m-1112	742	21	edges	edge	NOUN
m-1112	742	22	≡	≡	PROPN
m-1112	742	23	markos	markos	PROPN
m-1112	742	24	tetrahedron	tetrahedron	NOUN
m-1112	742	25	cube	cube	NOUN
m-1112	742	26	inscribed	inscribe	VERB
m-1112	742	27	-	-	PUNCT
m-1112	742	28	circumscribed	circumscribe	VERB
m-1112	742	29	circles	circle	NOUN
m-1112	742	30	mechanism	mechanism	NOUN
m-1112	742	31	.	.	PUNCT
m-1112	743	1	[	[	X
m-1112	743	2	fig-27	fig-27	NOUN
m-1112	743	3	-	-	SYM
m-1112	743	4	29	29	NUM
m-1112	743	5	]	]	PUNCT
m-1112	743	6	.	.	PUNCT
m-1112	744	1	in	in	ADP
m-1112	744	2	fig-6	fig-6	NUM
m-1112	744	3	,	,	PUNCT
m-1112	744	4	the	the	DET
m-1112	744	5	tetrahedron	tetrahedron	NOUN
m-1112	744	6	conductors	conductor	NOUN
m-1112	744	7	-vectors	-vector	NOUN
m-1112	744	8	da̅̅	da̅̅	PROPN
m-1112	744	9	̅̅	̅̅	PROPN
m-1112	744	10	⏊	⏊	PROPN
m-1112	744	11	db̅̅	db̅̅	PROPN
m-1112	744	12	̅̅	̅̅	PROPN
m-1112	744	13	⏊	⏊	PROPN
m-1112	744	14	dc̅̅	dc̅̅	PROPN
m-1112	744	15	̅̅	̅̅	PROPN
m-1112	744	16	,	,	PUNCT
m-1112	744	17	carry	carry	VERB
m-1112	744	18	energy	energy	NOUN
m-1112	744	19	as	as	ADP
m-1112	744	20	electromagnetic	electromagnetic	NOUN
m-1112	744	21	-	-	PUNCT
m-1112	744	22	fields	field	NOUN
m-1112	744	23	(	(	PUNCT
m-1112	744	24	forces	force	NOUN
m-1112	744	25	-	-	PUNCT
m-1112	744	26	frequencies	frequency	NOUN
m-1112	744	27	-	-	PUNCT
m-1112	744	28	stresses	stress	NOUN
m-1112	744	29	-	-	PUNCT
m-1112	744	30	any	any	DET
m-1112	744	31	motion	motion	NOUN
m-1112	744	32	)	)	PUNCT
m-1112	744	33	to	to	PART
m-1112	744	34	inscribed	inscribe	VERB
m-1112	744	35	sphere	sphere	ADV
m-1112	744	36	(	(	PUNCT
m-1112	744	37	nucleus	nucleus	NOUN
m-1112	744	38	of	of	ADP
m-1112	744	39	atoms	atom	NOUN
m-1112	744	40	)	)	PUNCT
m-1112	744	41	,	,	PUNCT
m-1112	744	42	to	to	ADP
m-1112	744	43	cube	cube	NOUN
m-1112	744	44	vertices	vertex	NOUN
m-1112	744	45	(	(	PUNCT
m-1112	744	46	electrons	electron	NOUN
m-1112	744	47	-	-	PUNCT
m-1112	744	48	position	position	NOUN
m-1112	744	49	)	)	PUNCT
m-1112	744	50	,	,	PUNCT
m-1112	744	51	to	to	ADP
m-1112	744	52	circumscribed	circumscribed	ADJ
m-1112	744	53	sphere	sphere	NOUN
m-1112	744	54	(	(	PUNCT
m-1112	744	55	the	the	DET
m-1112	744	56	electrons	electron	NOUN
m-1112	744	57	orbits	orbit	NOUN
m-1112	744	58	)	)	PUNCT
m-1112	744	59	for	for	ADP
m-1112	744	60	equilibrium	equilibrium	NOUN
m-1112	744	61	and	and	CCONJ
m-1112	744	62	for	for	ADP
m-1112	744	63	transferring	transfer	VERB
m-1112	744	64	information	information	NOUN
m-1112	744	65	and	and	CCONJ
m-1112	744	66	signals	signal	NOUN
m-1112	744	67	.	.	PUNCT
m-1112	745	1	8	8	X
m-1112	745	2	..	..	PUNCT
m-1112	745	3	[d	[d	X
m-1112	745	4	]	]	X
m-1112	745	5	..	..	PUNCT
m-1112	745	6	the	the	DET
m-1112	745	7	{	{	PUNCT
m-1112	745	8	tobh	tobh	NOUN
m-1112	745	9	}	}	PUNCT
m-1112	745	10	mechanisms	mechanism	NOUN
m-1112	745	11	,	,	PUNCT
m-1112	745	12	from	from	ADP
m-1112	745	13	charges	charge	NOUN
m-1112	745	14	in	in	ADP
m-1112	745	15	two	two	NUM
m-1112	745	16	-	-	PUNCT
m-1112	745	17	orbits	orbit	NOUN
m-1112	745	18	-	-	PUNCT
m-1112	745	19	pins	pin	NOUN
m-1112	745	20	&	&	CCONJ
m-1112	745	21	drain	drain	NOUN
m-1112	745	22	.	.	PUNCT
m-1112	746	1	markos	markos	PROPN
m-1112	746	2	atoms	atom	NOUN
m-1112	746	3	bonding	bond	VERB
m-1112	746	4	bracket	bracket	NOUN
m-1112	746	5	hook	hook	NOUN
m-1112	746	6	mechanism	mechanism	NOUN
m-1112	746	7	.	.	PUNCT
m-1112	747	1	[	[	X
m-1112	747	2	fig-2	fig-2	X
m-1112	747	3	]	]	X
m-1112	747	4	.	.	PUNCT
m-1112	748	1	in	in	ADP
m-1112	748	2	fig-9	fig-9	NUM
m-1112	748	3	,	,	PUNCT
m-1112	748	4	the	the	DET
m-1112	748	5	⊝	⊝	NUM
m-1112	748	6	electron	electron	NOUN
m-1112	748	7	precesses	precesse	NOUN
m-1112	748	8	due	due	ADP
m-1112	748	9	to	to	ADP
m-1112	748	10	the	the	DET
m-1112	748	11	gravity	gravity	NOUN
m-1112	748	12	and	and	CCONJ
m-1112	748	13	produces	produce	VERB
m-1112	748	14	work	work	NOUN
m-1112	748	15	which	which	PRON
m-1112	748	16	is	be	AUX
m-1112	748	17	stored	store	VERB
m-1112	748	18	in	in	ADP
m-1112	748	19	a	a	DET
m-1112	748	20	second	second	ADJ
m-1112	748	21	orbit	orbit	NOUN
m-1112	748	22	.	.	PUNCT
m-1112	749	1	this	this	DET
m-1112	749	2	2	2	NUM
m-1112	749	3	-	-	PUNCT
m-1112	749	4	orbit	orbit	NOUN
m-1112	749	5	equilibrium	equilibrium	NOUN
m-1112	749	6	exists	exist	VERB
m-1112	749	7	from	from	ADP
m-1112	749	8	the	the	DET
m-1112	749	9	existing	exist	VERB
m-1112	749	10	⊝	⊝	NUM
m-1112	749	11	-electron	-electron	PROPN
m-1112	749	12	≡	≡	PROPN
m-1112	749	13	drain	drain	NOUN
m-1112	749	14	and	and	CCONJ
m-1112	749	15	from	from	ADP
m-1112	749	16	the	the	DET
m-1112	749	17	new	new	PROPN
m-1112	749	18	⊕	⊕	PROPN
m-1112	749	19	-nucleus	-nucleus	PROPN
m-1112	749	20	≡	≡	PROPN
m-1112	749	21	the	the	DET
m-1112	749	22	pin	pin	PROPN
m-1112	749	23	.	.	PUNCT
m-1112	750	1	the	the	DET
m-1112	750	2	second	second	ADJ
m-1112	750	3	-orbit	-orbit	NOUN
m-1112	750	4	called	call	VERB
m-1112	750	5	as	as	ADP
m-1112	750	6	the	the	DET
m-1112	750	7	bracket	bracket	NOUN
m-1112	750	8	–	–	PUNCT
m-1112	750	9	hook	hook	NOUN
m-1112	750	10	-mechanism	-mechanism	NOUN
m-1112	750	11	,	,	PUNCT
m-1112	750	12	with	with	ADP
m-1112	750	13	which	which	PRON
m-1112	750	14	atoms	atom	NOUN
m-1112	750	15	and	and	CCONJ
m-1112	750	16	compounds	compound	NOUN
m-1112	750	17	are	be	AUX
m-1112	750	18	bonded	bond	VERB
m-1112	750	19	.[99	.[99	NOUN
m-1112	750	20	-	-	SYM
m-1112	750	21	104	104	NUM
m-1112	750	22	]	]	PUNCT
m-1112	750	23	the	the	DET
m-1112	750	24	{	{	PUNCT
m-1112	750	25	lncs	lncs	PROPN
m-1112	750	26	}	}	PUNCT
m-1112	750	27	mechanisms	mechanism	NOUN
m-1112	750	28	,	,	PUNCT
m-1112	750	29	from	from	ADP
m-1112	750	30	spaces	space	NOUN
m-1112	750	31	action	action	NOUN
m-1112	750	32	on	on	ADP
m-1112	750	33	quaternion	quaternion	ADJ
m-1112	750	34	monads	monad	NOUN
m-1112	750	35	𝐀𝐁̅̅	𝐀𝐁̅̅	NUM
m-1112	751	1	̅̅	̅̅	PROPN
m-1112	751	2	is	be	AUX
m-1112	751	3	the	the	DET
m-1112	751	4	lagrange`s	lagrange`s	PROPN
m-1112	751	5	non	non	ADJ
m-1112	751	6	conservative	conservative	ADJ
m-1112	751	7	systems	system	NOUN
m-1112	751	8	for	for	ADP
m-1112	751	9	generalized	generalized	ADJ
m-1112	751	10	coordinates	coordinate	NOUN
m-1112	751	11	,	,	PUNCT
m-1112	751	12	where	where	SCONJ
m-1112	751	13	the	the	DET
m-1112	751	14	system	system	NOUN
m-1112	751	15	is	be	AUX
m-1112	751	16	subjected	subject	VERB
m-1112	751	17	to	to	ADP
m-1112	751	18	forces	force	NOUN
m-1112	751	19	that	that	PRON
m-1112	751	20	do	do	AUX
m-1112	751	21	not	not	PART
m-1112	751	22	have	have	VERB
m-1112	751	23	potential	potential	ADJ
m-1112	751	24	or	or	CCONJ
m-1112	751	25	,	,	PUNCT
m-1112	751	26	d	d	X
m-1112	751	27	(	(	PUNCT
m-1112	751	28	t	t	PROPN
m-1112	751	29	+	+	CCONJ
m-1112	751	30	u	u	NOUN
m-1112	751	31	)	)	PUNCT
m-1112	751	32	≡	≡	PROPN
m-1112	751	33	δw𝐍𝐏𝐅	δw𝐍𝐏𝐅	ADP
m-1112	751	34	=	=	SYM
m-1112	751	35	0	0	NUM
m-1112	751	36	,	,	PUNCT
m-1112	751	37	as	as	SCONJ
m-1112	751	38	exists	exist	NOUN
m-1112	751	39	in	in	ADP
m-1112	751	40	the	the	DET
m-1112	751	41	gravitational	gravitational	ADJ
m-1112	751	42	force	force	NOUN
m-1112	751	43	g	g	PROPN
m-1112	751	44	and	and	CCONJ
m-1112	751	45	from	from	ADP
m-1112	751	46	which	which	PRON
m-1112	751	47	are	be	AUX
m-1112	751	48	created	create	VERB
m-1112	751	49	→	→	PUNCT
m-1112	751	50	the	the	DET
m-1112	751	51	elementary	elementary	ADJ
m-1112	751	52	particles	particle	NOUN
m-1112	751	53	using	use	VERB
m-1112	751	54	the	the	DET
m-1112	751	55	stpl	stpl	ADJ
m-1112	751	56	–	–	PUNCT
m-1112	751	57	mechanism	mechanism	NOUN
m-1112	751	58	,	,	PUNCT
m-1112	751	59	and	and	CCONJ
m-1112	751	60	all	all	DET
m-1112	751	61	universe	universe	NOUN
m-1112	751	62	using	use	VERB
m-1112	751	63	the	the	DET
m-1112	751	64	istccs	istccs	NOUN
m-1112	751	65	–	–	PUNCT
m-1112	751	66	mechanism	mechanism	NOUN
m-1112	751	67	←	←	PROPN
m-1112	751	68	and	and	CCONJ
m-1112	751	69	the	the	DET
m-1112	751	70	dual	dual	ADJ
m-1112	751	71	→	→	ADP
m-1112	751	72	the	the	DET
m-1112	751	73	black	black	ADJ
m-1112	751	74	holes	hole	NOUN
m-1112	751	75	←	←	PROPN
m-1112	751	76	as	as	ADP
m-1112	751	77	equation	equation	NOUN
m-1112	751	78	δw𝐍𝐏𝐅	δw𝐍𝐏𝐅	ADP
m-1112	751	79	=	=	SYM
m-1112	751	80	∑	∑	PROPN
m-1112	751	81	qi	qi	PROPN
m-1112	751	82	.	.	PROPN
m-1112	751	83	δqin	δqin	PROPN
m-1112	751	84	i=1	i=1	X
m-1112	751	85	,	,	PUNCT
m-1112	752	1	[	[	X
m-1112	752	2	fig-3	fig-3	X
m-1112	752	3	,	,	PUNCT
m-1112	752	4	21	21	NUM
m-1112	752	5	,	,	PUNCT
m-1112	752	6	22	22	NUM
m-1112	752	7	]	]	PUNCT
m-1112	752	8	.	.	PUNCT
m-1112	753	1	8	8	NUM
m-1112	753	2	..	..	PUNCT
m-1112	753	3	[e	[e	X
m-1112	753	4	]	]	X
m-1112	753	5	..	..	PUNCT
m-1112	753	6	material	material	NOUN
m-1112	753	7	-	-	PUNCT
m-1112	753	8	geometry	geometry	NOUN
m-1112	753	9	&	&	CCONJ
m-1112	753	10	e	e	NOUN
m-1112	753	11	-	-	NOUN
m-1112	753	12	geometry	geometry	NOUN
m-1112	753	13	in	in	ADP
m-1112	753	14	physics	physics	NOUN
m-1112	753	15	and	and	CCONJ
m-1112	753	16	chemistry	chemistry	NOUN
m-1112	753	17	figure	figure	NOUN
m-1112	753	18	–	–	PUNCT
m-1112	753	19	5	5	NUM
m-1112	753	20	:	:	PUNCT
m-1112	753	21	the	the	DET
m-1112	753	22	relation	relation	NOUN
m-1112	753	23	between	between	ADP
m-1112	753	24	the	the	DET
m-1112	753	25	[	[	X
m-1112	753	26	+	+	NOUN
m-1112	753	27	]	]	X
m-1112	753	28	spaces	space	NOUN
m-1112	753	29	,	,	PUNCT
m-1112	753	30	[	[	X
m-1112	753	31	-	-	PUNCT
m-1112	753	32	]	]	X
m-1112	753	33	anti	anti	ADJ
m-1112	753	34	-	-	ADJ
m-1112	753	35	spaces	space	NOUN
m-1112	753	36	,	,	PUNCT
m-1112	754	1	[	[	X
m-1112	754	2	+	+	X
m-1112	754	3	-	-	PUNCT
m-1112	754	4	]	]	X
m-1112	754	5	sub	sub	ADJ
m-1112	754	6	-	-	ADJ
m-1112	754	7	spaces	spaces	ADJ
m-1112	754	8	ijo	ijo	PROPN
m-1112	754	9	international	international	PROPN
m-1112	754	10	journal	journal	PROPN
m-1112	754	11	of	of	ADP
m-1112	754	12	mathematics	mathematics	PROPN
m-1112	754	13	(	(	PUNCT
m-1112	754	14	issn	issn	PROPN
m-1112	754	15	:	:	PUNCT
m-1112	754	16	2992	2992	NUM
m-1112	754	17	-	-	SYM
m-1112	754	18	4421	4421	NUM
m-1112	754	19	)	)	PUNCT
m-1112	754	20	volume	volume	NOUN
m-1112	754	21	08	08	NUM
m-1112	755	1	|	|	ADV
m-1112	755	2	issue	issue	NOUN
m-1112	755	3	08	08	NUM
m-1112	756	1	|	|	ADV
m-1112	756	2	august	august	PROPN
m-1112	756	3	2025	2025	NUM
m-1112	756	4	|	|	ADV
m-1112	756	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	756	6	ijo	ijo	PROPN
m-1112	756	7	journals	journal	NOUN
m-1112	756	8	25	25	NUM
m-1112	756	9	the	the	DET
m-1112	756	10	fundamental	fundamental	ADJ
m-1112	756	11	particles	particle	NOUN
m-1112	756	12	origination	origination	NOUN
m-1112	756	13	mechanism	mechanism	NOUN
m-1112	756	14	in	in	ADP
m-1112	756	15	mfmf	mfmf	PROPN
m-1112	756	16	pns	pns	PROPN
m-1112	756	17	caves	cave	NOUN
m-1112	756	18	.	.	PUNCT
m-1112	757	1	of	of	ADP
m-1112	757	2	euclidean	euclidean	PROPN
m-1112	757	3	&	&	CCONJ
m-1112	757	4	material	material	NOUN
m-1112	757	5	-	-	PUNCT
m-1112	757	6	geometry	geometry	NOUN
m-1112	757	7	in	in	ADP
m-1112	757	8	a	a	DET
m-1112	757	9	circle	circle	NOUN
m-1112	757	10	(	(	PUNCT
m-1112	757	11	r	r	NOUN
m-1112	757	12	,	,	PUNCT
m-1112	757	13	oa	oa	INTJ
m-1112	757	14	)	)	PUNCT
m-1112	757	15	of	of	ADP
m-1112	757	16	three	three	NUM
m-1112	757	17	-	-	PUNCT
m-1112	757	18	dimensions	dimension	NOUN
m-1112	757	19	.	.	PUNCT
m-1112	758	1	in	in	ADP
m-1112	758	2	(	(	PUNCT
m-1112	758	3	1	1	NUM
m-1112	758	4	)	)	PUNCT
m-1112	758	5	,	,	PUNCT
m-1112	758	6	the	the	DET
m-1112	758	7	euclidean	euclidean	ADJ
m-1112	758	8	geometry	geometry	NOUN
m-1112	758	9	,	,	PUNCT
m-1112	758	10	e	e	NOUN
m-1112	758	11	-	-	NOUN
m-1112	758	12	g	g	NOUN
m-1112	758	13	,	,	PUNCT
m-1112	758	14	is	be	AUX
m-1112	758	15	defined	define	VERB
m-1112	758	16	upon	upon	SCONJ
m-1112	758	17	the	the	DET
m-1112	758	18	number	number	NOUN
m-1112	758	19	of	of	ADP
m-1112	758	20	points	point	NOUN
m-1112	758	21	which	which	PRON
m-1112	758	22	can	can	AUX
m-1112	758	23	define	define	VERB
m-1112	758	24	the	the	DET
m-1112	758	25	specific	specific	ADJ
m-1112	758	26	space	space	NOUN
m-1112	758	27	i.e.	i.e.	X
m-1112	758	28	the	the	DET
m-1112	758	29	→	→	SYM
m-1112	758	30	one	one	NUM
m-1112	758	31	-	-	PUNCT
m-1112	758	32	point	point	NOUN
m-1112	758	33	in	in	ADP
m-1112	758	34	e	e	NOUN
m-1112	758	35	-	-	NOUN
m-1112	758	36	g	g	PROPN
m-1112	758	37	is	be	AUX
m-1112	758	38	defining	define	VERB
m-1112	758	39	one	one	NUM
m-1112	758	40	-	-	PUNCT
m-1112	758	41	material	material	NOUN
m-1112	758	42	-	-	PUNCT
m-1112	758	43	point	point	NOUN
m-1112	758	44	-	-	PUNCT
m-1112	758	45	space	space	NOUN
m-1112	758	46	,	,	PUNCT
m-1112	758	47	the	the	DET
m-1112	758	48	m	m	PROPN
m-1112	758	49	-	-	PUNCT
m-1112	758	50	p	p	PROPN
m-1112	758	51	-	-	PUNCT
m-1112	758	52	s	s	NOUN
m-1112	758	53	.	.	PUNCT
m-1112	759	1	the	the	DET
m-1112	759	2	→	→	SYM
m-1112	759	3	two	two	NUM
m-1112	759	4	-	-	PUNCT
m-1112	759	5	points	point	NOUN
m-1112	759	6	are	be	AUX
m-1112	759	7	defining	define	VERB
m-1112	759	8	the	the	DET
m-1112	759	9	line	line	NOUN
m-1112	759	10	-	-	PUNCT
m-1112	759	11	segment	segment	NOUN
m-1112	759	12	-	-	PUNCT
m-1112	759	13	space	space	NOUN
m-1112	759	14	,	,	PUNCT
m-1112	759	15	the	the	DET
m-1112	759	16	line	line	NOUN
m-1112	759	17	-	-	PUNCT
m-1112	759	18	m	m	NOUN
m-1112	759	19	-	-	PUNCT
m-1112	759	20	p	p	NOUN
m-1112	759	21	-	-	PUNCT
m-1112	759	22	s	s	NOUN
m-1112	759	23	.	.	PUNCT
m-1112	760	1	the	the	DET
m-1112	760	2	→	→	SYM
m-1112	760	3	three	three	NUM
m-1112	760	4	-	-	PUNCT
m-1112	760	5	points	point	NOUN
m-1112	760	6	are	be	AUX
m-1112	760	7	defining	define	VERB
m-1112	760	8	the	the	DET
m-1112	760	9	plane	plane	NOUN
m-1112	760	10	-	-	PUNCT
m-1112	760	11	triangle	triangle	NOUN
m-1112	760	12	-	-	PUNCT
m-1112	760	13	space	space	NOUN
m-1112	760	14	,	,	PUNCT
m-1112	760	15	the	the	DET
m-1112	760	16	plane	plane	NOUN
m-1112	760	17	-	-	PUNCT
m-1112	760	18	m	m	NOUN
m-1112	760	19	-	-	PUNCT
m-1112	760	20	p	p	X
m-1112	760	21	-	-	PUNCT
m-1112	760	22	s	s	X
m-1112	760	23	..	..	PUNCT
m-1112	760	24	the	the	DET
m-1112	760	25	→	→	SYM
m-1112	760	26	four	four	NUM
m-1112	760	27	-	-	PUNCT
m-1112	760	28	points	point	NOUN
m-1112	760	29	are	be	AUX
m-1112	760	30	defining	define	VERB
m-1112	760	31	the	the	DET
m-1112	760	32	volume	volume	NOUN
m-1112	760	33	tetrahedron	tetrahedron	NOUN
m-1112	760	34	-	-	PUNCT
m-1112	760	35	space	space	NOUN
m-1112	760	36	,	,	PUNCT
m-1112	760	37	the	the	DET
m-1112	760	38	volume	volume	NOUN
m-1112	760	39	-	-	PUNCT
m-1112	760	40	m	m	NOUN
m-1112	760	41	-	-	PUNCT
m-1112	760	42	p	p	X
m-1112	760	43	-	-	PUNCT
m-1112	760	44	s	s	NOUN
m-1112	760	45	.	.	PUNCT
m-1112	761	1	the	the	DET
m-1112	761	2	→	→	SYM
m-1112	761	3	five	five	NUM
m-1112	761	4	-	-	PUNCT
m-1112	761	5	points	point	NOUN
m-1112	761	6	are	be	AUX
m-1112	761	7	defining	define	VERB
m-1112	761	8	the	the	DET
m-1112	761	9	volume	volume	NOUN
m-1112	761	10	regular	regular	ADJ
m-1112	761	11	pentahedron	pentahedron	NOUN
m-1112	761	12	-	-	PUNCT
m-1112	761	13	space	space	NOUN
m-1112	761	14	the	the	DET
m-1112	761	15	sv	sv	PROPN
m-1112	761	16	-	-	PUNCT
m-1112	761	17	m	m	NOUN
m-1112	761	18	-	-	PUNCT
m-1112	761	19	p	p	NOUN
m-1112	761	20	-	-	PUNCT
m-1112	761	21	s.	s.	PROPN
m-1112	761	22	and	and	CCONJ
m-1112	761	23	so	so	ADV
m-1112	761	24	on	on	ADV
m-1112	761	25	,	,	PUNCT
m-1112	761	26	representing	represent	VERB
m-1112	761	27	the	the	DET
m-1112	761	28	steady	steady	ADJ
m-1112	761	29	-	-	PUNCT
m-1112	761	30	stable	stable	ADJ
m-1112	761	31	-	-	PUNCT
m-1112	761	32	regular	regular	ADJ
m-1112	761	33	geometrical	geometrical	ADJ
m-1112	761	34	-	-	PUNCT
m-1112	761	35	formations	formation	NOUN
m-1112	761	36	.	.	PUNCT
m-1112	762	1	the	the	DET
m-1112	762	2	corresponding	corresponding	NOUN
m-1112	762	3	to	to	ADP
m-1112	762	4	the	the	DET
m-1112	762	5	material	material	NOUN
m-1112	762	6	-	-	PUNCT
m-1112	762	7	geometry	geometry	NOUN
m-1112	762	8	-	-	PUNCT
m-1112	762	9	units	unit	NOUN
m-1112	762	10	are	be	AUX
m-1112	762	11	for	for	ADP
m-1112	762	12	:	:	PUNCT
m-1112	762	13	1	1	X
m-1112	762	14	..	..	SYM
m-1112	762	15	one	one	NUM
m-1112	762	16	-	-	PUNCT
m-1112	762	17	point	point	NOUN
m-1112	762	18	→	→	SYM
m-1112	762	19	two	two	NUM
m-1112	762	20	-	-	PUNCT
m-1112	762	21	units	unit	NOUN
m-1112	762	22	,	,	PUNCT
m-1112	762	23	[	[	X
m-1112	762	24	⊕],[⊝	⊕],[⊝	X
m-1112	762	25	]	]	X
m-1112	762	26	with	with	ADP
m-1112	762	27	dimension	dimension	NOUN
m-1112	762	28	as	as	ADP
m-1112	762	29	,	,	PUNCT
m-1112	762	30	the	the	DET
m-1112	762	31	material	material	NOUN
m-1112	762	32	-	-	PUNCT
m-1112	762	33	vector	vector	NOUN
m-1112	762	34	[	[	X
m-1112	762	35	⊕→	⊕→	NOUN
m-1112	762	36	⊝	⊝	VERB
m-1112	762	37	]	]	PUNCT
m-1112	762	38	2	2	NUM
m-1112	762	39	..	..	SYM
m-1112	762	40	two	two	NUM
m-1112	762	41	-	-	PUNCT
m-1112	762	42	points	point	NOUN
m-1112	762	43	→	→	SYM
m-1112	762	44	four	four	NUM
m-1112	762	45	-	-	PUNCT
m-1112	762	46	units	unit	NOUN
m-1112	762	47	,	,	PUNCT
m-1112	762	48	[	[	X
m-1112	762	49	⊕],[⊝	⊕],[⊝	X
m-1112	762	50	]	]	X
m-1112	762	51	with	with	ADP
m-1112	762	52	one	one	NUM
m-1112	762	53	dimension	dimension	NOUN
m-1112	762	54	as	as	ADP
m-1112	762	55	,	,	PUNCT
m-1112	762	56	the	the	DET
m-1112	762	57	material	material	NOUN
m-1112	762	58	-	-	PUNCT
m-1112	762	59	line	line	NOUN
m-1112	762	60	3	3	NUM
m-1112	762	61	..	..	SYM
m-1112	762	62	three	three	NUM
m-1112	762	63	-	-	PUNCT
m-1112	762	64	points	point	NOUN
m-1112	762	65	→	→	SYM
m-1112	762	66	six	six	NUM
m-1112	762	67	-	-	PUNCT
m-1112	762	68	units	unit	NOUN
m-1112	762	69	,	,	PUNCT
m-1112	762	70	[	[	X
m-1112	762	71	⊕],[⊝	⊕],[⊝	X
m-1112	762	72	]	]	X
m-1112	762	73	with	with	ADP
m-1112	762	74	two	two	NUM
m-1112	762	75	dimension	dimension	NOUN
m-1112	762	76	as	as	ADP
m-1112	762	77	,	,	PUNCT
m-1112	762	78	the	the	DET
m-1112	762	79	material	material	NOUN
m-1112	762	80	-	-	PUNCT
m-1112	762	81	plane	plane	NOUN
m-1112	762	82	4	4	NUM
m-1112	762	83	..	..	SYM
m-1112	762	84	four	four	NUM
m-1112	762	85	-	-	PUNCT
m-1112	762	86	points	point	NOUN
m-1112	762	87	→	→	SYM
m-1112	762	88	eight	eight	NUM
m-1112	762	89	-	-	PUNCT
m-1112	762	90	units	unit	NOUN
m-1112	762	91	,	,	PUNCT
m-1112	762	92	[	[	X
m-1112	762	93	⊕],[⊝	⊕],[⊝	X
m-1112	762	94	]	]	X
m-1112	762	95	with	with	ADP
m-1112	762	96	three	three	NUM
m-1112	762	97	dimension	dimension	NOUN
m-1112	762	98	as	as	ADP
m-1112	762	99	the	the	DET
m-1112	762	100	material	material	NOUN
m-1112	762	101	-	-	PUNCT
m-1112	762	102	volume	volume	NOUN
m-1112	762	103	keeping	keep	VERB
m-1112	762	104	the	the	DET
m-1112	762	105	property	property	NOUN
m-1112	762	106	of	of	ADP
m-1112	762	107	edge	edge	NOUN
m-1112	762	108	-	-	PUNCT
m-1112	762	109	points	point	NOUN
m-1112	762	110	to	to	PART
m-1112	762	111	be	be	AUX
m-1112	762	112	the	the	DET
m-1112	762	113	vector	vector	NOUN
m-1112	762	114	⊕	⊕	PROPN
m-1112	762	115	→	→	PUNCT
m-1112	762	116	⊝	⊝	NUM
m-1112	762	117	then	then	ADV
m-1112	762	118	bond	bond	NOUN
m-1112	762	119	is	be	AUX
m-1112	762	120	the	the	DET
m-1112	762	121	potential	potential	NOUN
m-1112	762	122	to	to	ADP
m-1112	762	123	the	the	DET
m-1112	762	124	unique	unique	ADJ
m-1112	762	125	-	-	PUNCT
m-1112	762	126	steady	steady	ADJ
m-1112	762	127	-	-	PUNCT
m-1112	762	128	stable	stable	ADJ
m-1112	762	129	-	-	PUNCT
m-1112	762	130	regular	regular	ADJ
m-1112	762	131	material	material	NOUN
m-1112	762	132	-	-	PUNCT
m-1112	762	133	geometry	geometry	NOUN
m-1112	762	134	-	-	PUNCT
m-1112	762	135	formations	formation	NOUN
m-1112	762	136	.	.	PUNCT
m-1112	763	1	in	in	ADP
m-1112	763	2	(	(	PUNCT
m-1112	763	3	2	2	NUM
m-1112	763	4	-	-	SYM
m-1112	763	5	3	3	NUM
m-1112	763	6	-	-	PUNCT
m-1112	763	7	4	4	NUM
m-1112	763	8	-	-	SYM
m-1112	763	9	5	5	NUM
m-1112	763	10	)	)	PUNCT
m-1112	763	11	.	.	PUNCT
m-1112	764	1	all	all	DET
m-1112	764	2	units	unit	NOUN
m-1112	764	3	in	in	ADP
m-1112	764	4	vectors	vector	NOUN
m-1112	764	5	follow	follow	VERB
m-1112	764	6	quaternion	quaternion	NOUN
m-1112	764	7	q	q	NOUN
m-1112	765	1	=	=	PUNCT
m-1112	765	2	[	[	X
m-1112	765	3	s+v̅.i	s+v̅.i	X
m-1112	765	4	]	]	X
m-1112	765	5	=	=	SYM
m-1112	765	6	ab̅̅	ab̅̅	NOUN
m-1112	765	7	̅̅	̅̅	PROPN
m-1112	765	8	properties	property	NOUN
m-1112	765	9	i.e.	i.e.	X
m-1112	765	10	[	[	X
m-1112	765	11	⊕	⊕	NOUN
m-1112	765	12	]	]	X
m-1112	765	13	→	→	X
m-1112	765	14	the	the	DET
m-1112	765	15	positive	positive	ADJ
m-1112	765	16	constituent	constituent	NOUN
m-1112	765	17	of	of	ADP
m-1112	765	18	quaternion	quaternion	NOUN
m-1112	765	19	at	at	ADP
m-1112	765	20	,	,	PUNCT
m-1112	765	21	point	point	VERB
m-1112	765	22	a	a	PRON
m-1112	765	23	.	.	PUNCT
m-1112	766	1	[	[	X
m-1112	766	2	⊝	⊝	X
m-1112	766	3	]	]	PUNCT
m-1112	766	4	→	→	PUNCT
m-1112	766	5	the	the	DET
m-1112	766	6	negative	negative	ADJ
m-1112	766	7	constituent	constituent	NOUN
m-1112	766	8	of	of	ADP
m-1112	766	9	quaternion	quaternion	NOUN
m-1112	766	10	at	at	ADP
m-1112	766	11	,	,	PUNCT
m-1112	766	12	point	point	NOUN
m-1112	766	13	b	b	PROPN
m-1112	766	14	.	.	PUNCT
m-1112	767	1	pythagorean	pythagorean	PROPN
m-1112	767	2	relation	relation	NOUN
m-1112	767	3	[	[	PUNCT
m-1112	767	4	r	r	NOUN
m-1112	767	5	]	]	PUNCT
m-1112	767	6	²	²	NUM
m-1112	767	7	=	=	SYM
m-1112	767	8	[	[	PUNCT
m-1112	767	9	an	an	X
m-1112	767	10	]	]	X
m-1112	767	11	²	²	NUM
m-1112	767	12	+	+	CCONJ
m-1112	767	13	[	[	PUNCT
m-1112	767	14	λn	λn	NOUN
m-1112	767	15	2	2	NUM
m-1112	767	16	]	]	PUNCT
m-1112	767	17	²	²	NUM
m-1112	767	18	.	.	PUNCT
m-1112	768	1	in	in	ADP
m-1112	768	2	euclidean	euclidean	ADJ
m-1112	768	3	-	-	PUNCT
m-1112	768	4	geometry	geometry	NOUN
m-1112	768	5	e	e	NOUN
m-1112	768	6	-	-	NOUN
m-1112	768	7	vector	vector	ADJ
m-1112	768	8	ab̅̅	ab̅̅	NOUN
m-1112	768	9	̅̅	̅̅	PROPN
m-1112	768	10	carries	carry	VERB
m-1112	768	11	point	point	NOUN
m-1112	768	12	a	a	PRON
m-1112	768	13	to	to	PART
m-1112	768	14	point	point	VERB
m-1112	768	15	b	b	PROPN
m-1112	768	16	as	as	ADP
m-1112	768	17	,	,	PUNCT
m-1112	768	18	vector	vector	NOUN
m-1112	768	19	a	a	DET
m-1112	768	20	→	→	SYM
m-1112	768	21	b	b	NOUN
m-1112	768	22	in	in	ADP
m-1112	768	23	material	material	NOUN
m-1112	768	24	-	-	PUNCT
m-1112	768	25	geometry	geometry	NOUN
m-1112	768	26	m	m	NOUN
m-1112	768	27	-	-	PUNCT
m-1112	768	28	vector	vector	PROPN
m-1112	768	29	ab̅̅	ab̅̅	NOUN
m-1112	768	30	̅̅	̅̅	PROPN
m-1112	768	31	carries	carry	VERB
m-1112	768	32	energy	energy	NOUN
m-1112	768	33	,	,	PUNCT
m-1112	768	34	⊕	⊕	PROPN
m-1112	768	35	,	,	PUNCT
m-1112	768	36	from	from	ADP
m-1112	768	37	point	point	NOUN
m-1112	768	38	a	a	PRON
m-1112	768	39	to	to	ADP
m-1112	768	40	⊝	⊝	NUM
m-1112	768	41	,	,	PUNCT
m-1112	768	42	energy	energy	NOUN
m-1112	768	43	of	of	ADP
m-1112	768	44	point	point	NOUN
m-1112	768	45	b	b	PROPN
m-1112	768	46	as	as	ADP
m-1112	768	47	,	,	PUNCT
m-1112	768	48	⊕	⊕	PROPN
m-1112	768	49	moves	move	VERB
m-1112	768	50	to	to	ADP
m-1112	768	51	⊝	⊝	NUM
m-1112	768	52	,	,	PUNCT
m-1112	768	53	which	which	PRON
m-1112	768	54	is	be	AUX
m-1112	768	55	as	as	ADP
m-1112	768	56	the	the	DET
m-1112	768	57	periodic	periodic	ADJ
m-1112	768	58	pattern	pattern	NOUN
m-1112	768	59	.	.	PUNCT
m-1112	769	1	velocity	velocity	NOUN
m-1112	769	2	�	�	PROPN
m-1112	769	3	̅	̅	NOUN
m-1112	769	4	�	�	NOUN
m-1112	769	5	=	=	PUNCT
m-1112	769	6	the	the	DET
m-1112	769	7	rate	rate	NOUN
m-1112	769	8	of	of	ADP
m-1112	769	9	change	change	NOUN
m-1112	769	10	(	(	PUNCT
m-1112	769	11	m	m	PROPN
m-1112	769	12	/	/	SYM
m-1112	769	13	s	s	NOUN
m-1112	769	14	)	)	PUNCT
m-1112	769	15	in	in	ADP
m-1112	769	16	ab	ab	PROPN
m-1112	769	17	,	,	PUNCT
m-1112	769	18	therefore	therefore	ADV
m-1112	769	19	units	unit	NOUN
m-1112	769	20	are	be	AUX
m-1112	769	21	formatted	format	VERB
m-1112	769	22	according	accord	VERB
m-1112	769	23	to	to	ADP
m-1112	769	24	the	the	DET
m-1112	769	25	steady	steady	ADJ
m-1112	769	26	-	-	PUNCT
m-1112	769	27	material	material	NOUN
m-1112	769	28	-	-	PUNCT
m-1112	769	29	geometry	geometry	NOUN
m-1112	769	30	-	-	PUNCT
m-1112	769	31	formations	formation	NOUN
m-1112	769	32	which	which	PRON
m-1112	769	33	are	be	AUX
m-1112	769	34	:	:	PUNCT
m-1112	769	35	the	the	DET
m-1112	769	36	line	line	NOUN
m-1112	769	37	-	-	PUNCT
m-1112	769	38	vector	vector	NOUN
m-1112	769	39	in	in	ADP
m-1112	769	40	cave	cave	NOUN
m-1112	769	41	,	,	PUNCT
m-1112	769	42	r	r	NOUN
m-1112	769	43	,	,	PUNCT
m-1112	769	44	which	which	PRON
m-1112	769	45	is	be	AUX
m-1112	769	46	the	the	DET
m-1112	769	47	simplest	simple	ADJ
m-1112	769	48	with	with	ADP
m-1112	769	49	double	double	ADJ
m-1112	769	50	number	number	NOUN
m-1112	769	51	of	of	ADP
m-1112	769	52	4	4	NUM
m-1112	769	53	-	-	PUNCT
m-1112	769	54	units	unit	NOUN
m-1112	769	55	the	the	DET
m-1112	769	56	plane	plane	NOUN
m-1112	769	57	-	-	PUNCT
m-1112	769	58	regular	regular	ADJ
m-1112	769	59	-	-	PUNCT
m-1112	769	60	triangle	triangle	NOUN
m-1112	769	61	in	in	ADP
m-1112	769	62	orbits	orbit	NOUN
m-1112	769	63	,	,	PUNCT
m-1112	769	64	is	be	AUX
m-1112	769	65	the	the	DET
m-1112	769	66	most	most	ADV
m-1112	769	67	stable	stable	ADJ
m-1112	769	68	shape	shape	NOUN
m-1112	769	69	of	of	ADP
m-1112	769	70	6	6	NUM
m-1112	769	71	-	-	PUNCT
m-1112	769	72	plane	plane	NOUN
m-1112	769	73	-	-	PUNCT
m-1112	769	74	units	unit	NOUN
m-1112	769	75	the	the	DET
m-1112	769	76	volume	volume	NOUN
m-1112	769	77	-	-	PUNCT
m-1112	769	78	regular	regular	ADJ
m-1112	769	79	-	-	PUNCT
m-1112	769	80	tetrahedron	tetrahedron	NOUN
m-1112	769	81	in	in	ADP
m-1112	769	82	space	space	NOUN
m-1112	769	83	is	be	AUX
m-1112	769	84	the	the	DET
m-1112	769	85	most	most	ADV
m-1112	769	86	stable	stable	ADJ
m-1112	769	87	shape	shape	NOUN
m-1112	769	88	of	of	ADP
m-1112	769	89	8	8	NUM
m-1112	769	90	-	-	PUNCT
m-1112	769	91	volume	volume	NOUN
m-1112	769	92	units	unit	NOUN
m-1112	769	93	,	,	PUNCT
m-1112	769	94	the	the	DET
m-1112	769	95	cube	cube	NOUN
m-1112	769	96	,	,	PUNCT
m-1112	769	97	which	which	PRON
m-1112	769	98	are	be	AUX
m-1112	769	99	the	the	DET
m-1112	769	100	crystals	crystal	NOUN
m-1112	769	101	.	.	PUNCT
m-1112	770	1	the	the	DET
m-1112	770	2	regular	regular	ADJ
m-1112	770	3	n	n	CCONJ
m-1112	770	4	-	-	PUNCT
m-1112	770	5	hedron	hedron	NOUN
m-1112	770	6	are	be	AUX
m-1112	770	7	for	for	ADP
m-1112	770	8	all	all	DET
m-1112	770	9	others	other	NOUN
m-1112	770	10	.	.	PUNCT
m-1112	771	1	this	this	PRON
m-1112	771	2	is	be	AUX
m-1112	771	3	the	the	PRON
m-1112	771	4	why	why	SCONJ
m-1112	771	5	the	the	DET
m-1112	771	6	glue	glue	NOUN
m-1112	771	7	-	-	PUNCT
m-1112	771	8	bond	bond	NOUN
m-1112	771	9	,	,	PUNCT
m-1112	771	10	bond	bond	NOUN
m-1112	771	11	is	be	AUX
m-1112	771	12	the	the	DET
m-1112	771	13	potential	potential	NOUN
m-1112	771	14	,	,	PUNCT
m-1112	771	15	between	between	SCONJ
m-1112	771	16	the	the	DET
m-1112	771	17	6	6	NUM
m-1112	771	18	-	-	PUNCT
m-1112	771	19	units	unit	NOUN
m-1112	771	20	formulates	formulate	VERB
m-1112	771	21	the	the	DET
m-1112	771	22	regular	regular	ADJ
m-1112	771	23	-	-	PUNCT
m-1112	771	24	hexagon	hexagon	NOUN
m-1112	771	25	as	as	ADP
m-1112	771	26	the	the	DET
m-1112	771	27	first	first	ADJ
m-1112	771	28	steady	steady	ADJ
m-1112	771	29	plane	plane	NOUN
m-1112	771	30	formulation	formulation	NOUN
m-1112	771	31	in	in	ADP
m-1112	771	32	nature	nature	NOUN
m-1112	771	33	as	as	ADP
m-1112	771	34	in	in	ADP
m-1112	771	35	fig-18	fig-18	NUM
m-1112	771	36	remark	remark	NOUN
m-1112	771	37	:	:	PUNCT
m-1112	771	38	the	the	DET
m-1112	771	39	constraint	constraint	NOUN
m-1112	771	40	,	,	PUNCT
m-1112	771	41	that	that	PRON
m-1112	771	42	strain	strain	VERB
m-1112	771	43	accompanying	accompany	VERB
m-1112	771	44	the	the	DET
m-1112	771	45	stresses	stress	NOUN
m-1112	771	46	s	s	PART
m-1112	771	47	x	x	X
m-1112	771	48	,	,	PUNCT
m-1112	771	49	s	s	PART
m-1112	771	50	y	y	PROPN
m-1112	771	51	remains	remain	VERB
m-1112	771	52	geometrically	geometrically	ADV
m-1112	771	53	continuous	continuous	ADJ
m-1112	771	54	is	be	AUX
m-1112	771	55	,	,	PUNCT
m-1112	771	56	because	because	SCONJ
m-1112	771	57	the	the	DET
m-1112	771	58	material	material	NOUN
m-1112	771	59	point	point	NOUN
m-1112	771	60	is	be	AUX
m-1112	771	61	consisted	consist	VERB
m-1112	771	62	of	of	ADP
m-1112	771	63	the	the	DET
m-1112	771	64	two	two	NUM
m-1112	771	65	units	unit	NOUN
m-1112	771	66	⊕	⊕	PROPN
m-1112	771	67	,	,	PUNCT
m-1112	771	68	⊝	⊝	NUM
m-1112	771	69	.only	.only	ADV
m-1112	771	70	ijo	ijo	PROPN
m-1112	771	71	international	international	PROPN
m-1112	771	72	journal	journal	PROPN
m-1112	771	73	of	of	ADP
m-1112	771	74	mathematics	mathematics	PROPN
m-1112	771	75	(	(	PUNCT
m-1112	771	76	issn	issn	PROPN
m-1112	771	77	:	:	PUNCT
m-1112	771	78	2992	2992	NUM
m-1112	771	79	-	-	SYM
m-1112	771	80	4421	4421	NUM
m-1112	771	81	)	)	PUNCT
m-1112	772	1	volume	volume	NOUN
m-1112	772	2	08	08	NUM
m-1112	773	1	|	|	ADV
m-1112	773	2	issue	issue	NOUN
m-1112	773	3	08	08	NUM
m-1112	774	1	|	|	ADV
m-1112	774	2	august	august	PROPN
m-1112	774	3	2025	2025	NUM
m-1112	774	4	|	|	ADV
m-1112	774	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	774	6	ijo	ijo	PROPN
m-1112	774	7	journals	journal	NOUN
m-1112	774	8	26	26	NUM
m-1112	774	9	the	the	DET
m-1112	774	10	fundamental	fundamental	ADJ
m-1112	774	11	particles	particle	NOUN
m-1112	774	12	origination	origination	NOUN
m-1112	774	13	mechanism	mechanism	NOUN
m-1112	774	14	in	in	ADP
m-1112	774	15	mfmf	mfmf	PROPN
m-1112	774	16	pns	pns	PROPN
m-1112	774	17	caves	cave	NOUN
m-1112	774	18	.	.	PUNCT
m-1112	775	1	8	8	X
m-1112	775	2	..	..	PUNCT
m-1112	775	3	[a	[a	X
m-1112	775	4	]	]	X
m-1112	775	5	..	..	PUNCT
m-1112	775	6	the	the	DET
m-1112	775	7	{	{	PUNCT
m-1112	775	8	stpl	stpl	PROPN
m-1112	775	9	}	}	PUNCT
m-1112	775	10	physical	physical	ADJ
m-1112	775	11	mechanisms	mechanism	NOUN
m-1112	775	12	:	:	PUNCT
m-1112	775	13	the	the	DET
m-1112	775	14	six	six	NUM
m-1112	775	15	triple	triple	ADJ
m-1112	775	16	points	point	NOUN
m-1112	775	17	line	line	NOUN
m-1112	775	18	mechanism	mechanism	NOUN
m-1112	775	19	.	.	PUNCT
m-1112	776	1	figure	figure	VERB
m-1112	777	1	-6	-6	PROPN
m-1112	777	2	:	:	PUNCT
m-1112	778	1	the	the	DET
m-1112	778	2	physical	physical	ADJ
m-1112	778	3	three	three	NUM
m-1112	778	4	–	–	PUNCT
m-1112	778	5	phase	phase	NOUN
m-1112	778	6	mechanism	mechanism	NOUN
m-1112	778	7	,	,	PUNCT
m-1112	778	8	producing	produce	VERB
m-1112	778	9	the	the	DET
m-1112	778	10	fundamental	fundamental	ADJ
m-1112	778	11	particles	particle	NOUN
m-1112	778	12	and	and	CCONJ
m-1112	778	13	the	the	DET
m-1112	778	14	primary	primary	ADJ
m-1112	778	15	forces	force	NOUN
m-1112	778	16	in	in	ADP
m-1112	778	17	absolute	absolute	ADJ
m-1112	778	18	system	system	NOUN
m-1112	778	19	a	a	DET
m-1112	778	20	≡	≡	PROPN
m-1112	778	21	r	r	NOUN
m-1112	778	22	.	.	PUNCT
m-1112	779	1	γ	γ	X
m-1112	779	2	=	=	SYM
m-1112	779	3	r.	r.	PROPN
m-1112	779	4	𝐬𝐞𝐜𝛗.	𝐬𝐞𝐜𝛗.	NOUN
m-1112	780	1	[	[	X
m-1112	780	2	97	97	NUM
m-1112	780	3	]	]	X
m-1112	780	4	in	in	ADP
m-1112	780	5	–	–	PUNCT
m-1112	780	6	fig	fig	NOUN
m-1112	780	7	.	.	PUNCT
m-1112	781	1	abc	abc	PROPN
m-1112	781	2	is	be	AUX
m-1112	781	3	any	any	DET
m-1112	781	4	right	right	ADJ
m-1112	781	5	-	-	PUNCT
m-1112	781	6	angled	angle	VERB
m-1112	781	7	triangle	triangle	NOUN
m-1112	781	8	at	at	ADP
m-1112	781	9	,	,	PUNCT
m-1112	781	10	a	a	DET
m-1112	781	11	=	=	X
m-1112	781	12	(	(	PUNCT
m-1112	781	13	the	the	DET
m-1112	781	14	-	-	PUNCT
m-1112	781	15	space	space	NOUN
m-1112	781	16	)	)	PUNCT
m-1112	781	17	,	,	PUNCT
m-1112	781	18	kakbkc	kakbkc	NOUN
m-1112	781	19	=	=	PUNCT
m-1112	781	20	triangle	triangle	NOUN
m-1112	781	21	is	be	AUX
m-1112	781	22	the	the	DET
m-1112	781	23	(	(	PUNCT
m-1112	781	24	anti	anti	ADJ
m-1112	781	25	-	-	NOUN
m-1112	781	26	space	space	NOUN
m-1112	781	27	)	)	PUNCT
m-1112	781	28	,	,	PUNCT
m-1112	781	29	,	,	PUNCT
m-1112	781	30	aebece	aebece	NOUN
m-1112	781	31	=	=	NOUN
m-1112	781	32	triangle	triangle	NOUN
m-1112	781	33	is	be	AUX
m-1112	781	34	the	the	DET
m-1112	781	35	(	(	PUNCT
m-1112	781	36	sub	sub	NOUN
m-1112	781	37	-	-	NOUN
m-1112	781	38	space	space	NOUN
m-1112	781	39	)	)	PUNCT
m-1112	781	40	respectively.the	respectively.the	DET
m-1112	781	41	instaneous	instaneous	ADJ
m-1112	781	42	pole	pole	NOUN
m-1112	781	43	p	p	NOUN
m-1112	781	44	of	of	ADP
m-1112	781	45	rotation	rotation	NOUN
m-1112	781	46	is	be	AUX
m-1112	781	47	off	off	ADP
m-1112	781	48	the	the	DET
m-1112	781	49	circle	circle	NOUN
m-1112	781	50	of	of	ADP
m-1112	781	51	diameter	diameter	NOUN
m-1112	781	52	|bc|	|bc|	PROPN
m-1112	781	53	.	.	PUNCT
m-1112	782	1	the	the	DET
m-1112	782	2	poles	pole	NOUN
m-1112	782	3	of	of	ADP
m-1112	782	4	rotation	rotation	NOUN
m-1112	782	5	lie	lie	NOUN
m-1112	782	6	on{dapa	on{dapa	NOUN
m-1112	782	7	}	}	PUNCT
m-1112	782	8	reference	reference	NOUN
m-1112	782	9	system	system	NOUN
m-1112	782	10	.the	.the	PRON
m-1112	782	11	reference	reference	NOUN
m-1112	782	12	system	system	NOUN
m-1112	782	13	{	{	PUNCT
m-1112	782	14	𝐃𝐀𝐏𝐀}≡	𝐃𝐀𝐏𝐀}≡	ADV
m-1112	782	15	[	[	X
m-1112	782	16	r	r	X
m-1112	782	17	]	]	X
m-1112	782	18	(	(	PUNCT
m-1112	782	19	x	x	X
m-1112	782	20	'	'	PUNCT
m-1112	782	21	,	,	PUNCT
m-1112	782	22	y	y	PROPN
m-1112	782	23	'	'	PUNCT
m-1112	782	24	,	,	PUNCT
m-1112	782	25	z	z	X
m-1112	782	26	'	'	PROPN
m-1112	782	27	,	,	PUNCT
m-1112	782	28	t	t	PROPN
m-1112	782	29	'	'	PUNCT
m-1112	782	30	)	)	PUNCT
m-1112	782	31	moves	move	NOUN
m-1112	782	32	with	with	ADP
m-1112	782	33	velocity	velocity	NOUN
m-1112	782	34	�	�	NOUN
m-1112	782	35	̅	̅	NOUN
m-1112	782	36	�	�	NOUN
m-1112	782	37	,	,	PUNCT
m-1112	782	38	parallel	parallel	ADJ
m-1112	782	39	to	to	ADP
m-1112	782	40	,	,	PUNCT
m-1112	782	41	x	x	PUNCT
m-1112	782	42	x	x	X
m-1112	782	43	'	'	NUM
m-1112	782	44	,	,	PUNCT
m-1112	782	45	axis	axis	VERB
m-1112	782	46	with	with	ADP
m-1112	782	47	respect	respect	NOUN
m-1112	782	48	to	to	ADP
m-1112	782	49	the	the	DET
m-1112	782	50	fixed	fix	VERB
m-1112	782	51	and	and	CCONJ
m-1112	782	52	absolute	absolute	ADJ
m-1112	782	53	system	system	NOUN
m-1112	782	54	{	{	PUNCT
m-1112	782	55	𝐃𝐀o	𝐃𝐀o	NOUN
m-1112	782	56	}	}	PUNCT
m-1112	782	57	≡	≡	PROPN
m-1112	783	1	[	[	X
m-1112	783	2	s]-(x	s]-(x	PROPN
m-1112	783	3	,	,	PUNCT
m-1112	783	4	y	y	PROPN
m-1112	783	5	,	,	PUNCT
m-1112	783	6	z	z	PROPN
m-1112	783	7	,	,	PUNCT
m-1112	783	8	t	t	PROPN
m-1112	783	9	)	)	PUNCT
m-1112	783	10	.	.	PUNCT
m-1112	784	1	the	the	DET
m-1112	784	2	geometrical	geometrical	ADJ
m-1112	784	3	expression	expression	NOUN
m-1112	784	4	of	of	ADP
m-1112	784	5	lorentz	lorentz	PROPN
m-1112	784	6	factor	factor	NOUN
m-1112	784	7	γ	γ	NOUN
m-1112	784	8	=	=	SYM
m-1112	784	9	𝒄	𝒄	PROPN
m-1112	784	10	𝒗	𝒗	PROPN
m-1112	784	11	,	,	PUNCT
m-1112	784	12	is	be	AUX
m-1112	784	13	the	the	DET
m-1112	784	14	𝐬𝐞𝐜𝛗	𝐬𝐞𝐜𝛗	NOUN
m-1112	784	15	=	=	PUNCT
m-1112	784	16	γ	γ	X
m-1112	784	17	=	=	SYM
m-1112	784	18	o𝐃𝐀	o𝐃𝐀	NOUN
m-1112	784	19	:	:	PUNCT
m-1112	784	20	a𝐃𝐀	a𝐃𝐀	PROPN
m-1112	784	21	=	=	SYM
m-1112	784	22	±	±	NOUN
m-1112	784	23	1	1	NUM
m-1112	784	24	/	/	SYM
m-1112	784	25	[	[	PUNCT
m-1112	784	26	√1	√1	PROPN
m-1112	784	27	–	–	PUNCT
m-1112	784	28	(	(	PUNCT
m-1112	784	29	v	v	NOUN
m-1112	784	30	/	/	SYM
m-1112	784	31	c	c	NOUN
m-1112	784	32	)	)	PUNCT
m-1112	784	33	²	²	NOUN
m-1112	784	34	]	]	PUNCT
m-1112	785	1	=	=	PUNCT
m-1112	785	2	c	c	NOUN
m-1112	785	3	/	/	SYM
m-1112	786	1	[	[	X
m-1112	786	2	√c²	√c²	X
m-1112	786	3	–	–	PUNCT
m-1112	786	4	v²	v²	PROPN
m-1112	786	5	]	]	PUNCT
m-1112	786	6	,	,	PUNCT
m-1112	786	7	which	which	PRON
m-1112	786	8	is	be	AUX
m-1112	786	9	the	the	DET
m-1112	786	10	conchoidal	conchoidal	NOUN
m-1112	786	11	of	of	ADP
m-1112	786	12	nicomedes	nicomede	NOUN
m-1112	786	13	{	{	PUNCT
m-1112	786	14	s	s	X
m-1112	786	15	=	=	PUNCT
m-1112	786	16	a	a	DET
m-1112	786	17	+	+	PROPN
m-1112	786	18	b.	b.	PROPN
m-1112	786	19	secφ	secφ	PROPN
m-1112	786	20	}	}	PUNCT
m-1112	786	21	and	and	CCONJ
m-1112	786	22	which	which	PRON
m-1112	786	23	acquires	acquire	VERB
m-1112	786	24	the	the	DET
m-1112	786	25	material	material	NOUN
m-1112	786	26	angle	angle	NOUN
m-1112	786	27	,	,	PUNCT
m-1112	786	28	φ	φ	PROPN
m-1112	786	29	=	=	SYM
m-1112	786	30	𝐯	𝐯	X
m-1112	786	31	√c²−r²	√c²−r²	ADV
m-1112	786	32	,	,	PUNCT
m-1112	786	33	i.e.	i.e.	X
m-1112	786	34	issues	issue	NOUN
m-1112	786	35	|a|	|a|	PROPN
m-1112	786	36	≡	≡	PROPN
m-1112	786	37	|r|	|r|	PROPN
m-1112	786	38	.	.	PUNCT
m-1112	787	1	γ	γ	X
m-1112	787	2	[	[	X
m-1112	787	3	a]-1	a]-1	PROPN
m-1112	787	4	…	…	SYM
m-1112	787	5	the	the	DET
m-1112	787	6	[	[	X
m-1112	787	7	stpl	stpl	X
m-1112	787	8	]	]	X
m-1112	787	9	line	line	NOUN
m-1112	787	10	is	be	AUX
m-1112	787	11	an	an	DET
m-1112	787	12	extreme	extreme	ADJ
m-1112	787	13	spaces	space	NOUN
m-1112	787	14	–	–	PUNCT
m-1112	787	15	physical	physical	ADJ
m-1112	787	16	-originating	-originating	ADJ
m-1112	787	17	-	-	PUNCT
m-1112	787	18	wave	wave	NOUN
m-1112	787	19	pattern	pattern	NOUN
m-1112	787	20	.	.	PUNCT
m-1112	788	1	extreme	extreme	ADJ
m-1112	788	2	-	-	PUNCT
m-1112	788	3	spaces	space	NOUN
m-1112	788	4	(	(	PUNCT
m-1112	788	5	are	be	AUX
m-1112	788	6	the	the	DET
m-1112	788	7	extreme	extreme	ADJ
m-1112	788	8	space	space	NOUN
m-1112	788	9	-	-	PUNCT
m-1112	788	10	triangles	triangle	NOUN
m-1112	788	11	abc≡	abc≡	NOUN
m-1112	788	12	⊕	⊕	PROPN
m-1112	788	13	)	)	PUNCT
m-1112	788	14	meet	meet	VERB
m-1112	788	15	anti	anti	ADJ
m-1112	788	16	-	-	ADJ
m-1112	788	17	spaces	space	NOUN
m-1112	788	18	(	(	PUNCT
m-1112	788	19	extreme	extreme	ADJ
m-1112	788	20	anti	anti	ADJ
m-1112	788	21	-	-	ADJ
m-1112	788	22	space	space	NOUN
m-1112	788	23	-	-	PUNCT
m-1112	788	24	triangles	triangle	NOUN
m-1112	788	25	,	,	PUNCT
m-1112	788	26	kakb	kakb	NOUN
m-1112	788	27	kc≡	kc≡	PROPN
m-1112	788	28	⊝	⊝	NUM
m-1112	788	29	)	)	PUNCT
m-1112	788	30	through	through	ADP
m-1112	788	31	the	the	DET
m-1112	788	32	only	only	ADJ
m-1112	788	33	-	-	PUNCT
m-1112	788	34	gateway	gateway	NOUN
m-1112	788	35	which	which	PRON
m-1112	788	36	is	be	AUX
m-1112	788	37	the	the	DET
m-1112	788	38	circularly	circularly	ADV
m-1112	788	39	charged	charge	VERB
m-1112	788	40	+	+	CCONJ
m-1112	788	41	,	,	PUNCT
m-1112	788	42	0	0	NUM
m-1112	788	43	,	,	PUNCT
m-1112	788	44	,	,	PUNCT
m-1112	788	45	or	or	CCONJ
m-1112	788	46	[	[	PUNCT
m-1112	788	47	⊕	⊕	PROPN
m-1112	788	48			PROPN
m-1112	788	49	⊝	⊝	NUM
m-1112	788	50	]	]	PUNCT
m-1112	788	51	,	,	PUNCT
m-1112	788	52	[	[	PUNCT
m-1112	788	53	⊝	⊝	CCONJ
m-1112	788	54			PROPN
m-1112	788	55	⊕	⊕	PROPN
m-1112	788	56	]	]	PUNCT
m-1112	788	57	,	,	PUNCT
m-1112	788	58	[	[	PUNCT
m-1112	788	59	⊕	⊕	NOUN
m-1112	788	60	⊝	⊝	PUNCT
m-1112	788	61			PROPN
m-1112	788	62	]	]	PUNCT
m-1112	788	63	formulation	formulation	NOUN
m-1112	788	64	which	which	PRON
m-1112	788	65	is	be	AUX
m-1112	788	66	a	a	DET
m-1112	788	67	physical	physical	ADJ
m-1112	788	68	geometrical	geometrical	ADJ
m-1112	788	69	formation	formation	NOUN
m-1112	788	70	mechanism	mechanism	NOUN
m-1112	788	71	called	call	VERB
m-1112	788	72	the	the	DET
m-1112	788	73	[	[	X
m-1112	788	74	stpl	stpl	X
m-1112	788	75	]	]	X
m-1112	788	76	line	line	NOUN
m-1112	788	77	.	.	PUNCT
m-1112	789	1	figures-	figures-	X
m-1112	790	1	[	[	PUNCT
m-1112	790	2	6	6	NUM
m-1112	790	3	,	,	PUNCT
m-1112	790	4	7	7	NUM
m-1112	790	5	]	]	PUNCT
m-1112	790	6	→	→	PUNCT
m-1112	790	7	the	the	DET
m-1112	790	8	[	[	X
m-1112	790	9	stpl	stpl	X
m-1112	790	10	]	]	X
m-1112	790	11	line	line	NOUN
m-1112	790	12	is	be	AUX
m-1112	790	13	a	a	DET
m-1112	790	14	physical	physical	ADJ
m-1112	790	15	–	–	PUNCT
m-1112	790	16	mechanism	mechanism	NOUN
m-1112	790	17	as	as	ADP
m-1112	790	18	,	,	PUNCT
m-1112	790	19	in	in	ADP
m-1112	790	20	-	-	PUNCT
m-1112	790	21	circle	circle	NOUN
m-1112	790	22			NOUN
m-1112	790	23	triangle	triangle	NOUN
m-1112	790	24			NOUN
m-1112	791	1	ex	ex	NOUN
m-1112	791	2	-	-	NOUN
m-1112	791	3	circle	circle	ADJ
m-1112	791	4			NOUN
m-1112	791	5	ex	ex	NOUN
m-1112	791	6	triangle	triangle	NOUN
m-1112	791	7	consisted	consist	VERB
m-1112	791	8	from	from	ADP
m-1112	791	9	the	the	DET
m-1112	791	10	three	three	NUM
m-1112	791	11	spaces	space	NOUN
m-1112	791	12	,	,	PUNCT
m-1112	791	13	on	on	ADP
m-1112	791	14	which	which	PRON
m-1112	791	15	the	the	DET
m-1112	791	16	three	three	NUM
m-1112	791	17	breakages	breakage	NOUN
m-1112	791	18	[	[	PUNCT
m-1112	791	19	s²	s²	NOUN
m-1112	791	20	=	=	SYM
m-1112	791	21	⊕	⊕	PROPN
m-1112	791	22	,	,	PUNCT
m-1112	791	23	2s	2s	PROPN
m-1112	791	24	²	²	NUM
m-1112	791	25	=	=	SYM
m-1112	791	26			ADJ
m-1112	791	27	,	,	PUNCT
m-1112	791	28	s	s	NOUN
m-1112	791	29	²	²	NUM
m-1112	791	30	=	=	PUNCT
m-1112	791	31	⊝	⊝	PROPN
m-1112	791	32	]	]	PUNCT
m-1112	791	33	are	be	AUX
m-1112	791	34	circularlycharged	circularlycharge	VERB
m-1112	791	35	on	on	ADP
m-1112	791	36	the	the	DET
m-1112	791	37	three	three	NUM
m-1112	791	38	–	–	PUNCT
m-1112	791	39	extreme	extreme	ADJ
m-1112	791	40	triangles	triangle	NOUN
m-1112	791	41	{	{	PUNCT
m-1112	791	42	a	a	DET
m-1112	791	43	b	b	NOUN
m-1112	791	44	c	c	NOUN
m-1112	791	45	}	}	PUNCT
m-1112	791	46	,	,	PUNCT
m-1112	791	47	{	{	PUNCT
m-1112	791	48	ka	ka	PROPN
m-1112	791	49	kb	kb	PROPN
m-1112	791	50	kc	kc	PROPN
m-1112	791	51	}	}	PUNCT
m-1112	791	52	,	,	PUNCT
m-1112	791	53	{	{	PUNCT
m-1112	791	54	ae	ae	PROPN
m-1112	791	55	be	be	VERB
m-1112	791	56	ce	ce	PROPN
m-1112	791	57	}	}	PUNCT
m-1112	791	58	←	←	PROPN
m-1112	791	59	producing	produce	VERB
m-1112	791	60	the	the	DET
m-1112	791	61	energy	energy	NOUN
m-1112	791	62	-	-	PUNCT
m-1112	791	63	quantities	quantity	NOUN
m-1112	791	64	±	±	NOUN
m-1112	791	65	𝐐𝐩−𝐩	𝐐𝐩−𝐩	NOUN
m-1112	791	66	.	.	PUNCT
m-1112	792	1	this	this	DET
m-1112	792	2	circular	circular	ADJ
m-1112	792	3	-	-	PUNCT
m-1112	792	4	charge	charge	NOUN
m-1112	792	5	from	from	ADP
m-1112	792	6	breakages	breakages	PROPN
m-1112	792	7	ijo	ijo	PROPN
m-1112	792	8	international	international	PROPN
m-1112	792	9	journal	journal	PROPN
m-1112	792	10	of	of	ADP
m-1112	792	11	mathematics	mathematics	PROPN
m-1112	792	12	(	(	PUNCT
m-1112	792	13	issn	issn	PROPN
m-1112	792	14	:	:	PUNCT
m-1112	792	15	2992	2992	NUM
m-1112	792	16	-	-	SYM
m-1112	792	17	4421	4421	NUM
m-1112	792	18	)	)	PUNCT
m-1112	792	19	volume	volume	NOUN
m-1112	792	20	08	08	NUM
m-1112	793	1	|	|	ADV
m-1112	793	2	issue	issue	NOUN
m-1112	793	3	08	08	NUM
m-1112	794	1	|	|	ADV
m-1112	794	2	august	august	PROPN
m-1112	794	3	2025	2025	NUM
m-1112	794	4	|	|	ADV
m-1112	794	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	794	6	ijo	ijo	PROPN
m-1112	794	7	journals	journal	NOUN
m-1112	794	8	27	27	NUM
m-1112	794	9	the	the	DET
m-1112	794	10	fundamental	fundamental	ADJ
m-1112	794	11	particles	particle	NOUN
m-1112	794	12	origination	origination	NOUN
m-1112	794	13	mechanism	mechanism	NOUN
m-1112	794	14	in	in	ADP
m-1112	794	15	mfmf	mfmf	PROPN
m-1112	794	16	pns	pns	PROPN
m-1112	794	17	caves	cave	NOUN
m-1112	794	18	.	.	PUNCT
m-1112	795	1	on	on	ADP
m-1112	795	2	the	the	PRON
m-1112	795	3	-	-	PUNCT
m-1112	795	4	three	three	NUM
m-1112	795	5	-triangles	-triangle	NOUN
m-1112	795	6	is	be	AUX
m-1112	795	7	the	the	DET
m-1112	795	8	thrust	thrust	NOUN
m-1112	795	9	upon	upon	SCONJ
m-1112	795	10	the	the	DET
m-1112	795	11	energy	energy	NOUN
m-1112	795	12	-	-	PUNCT
m-1112	795	13	quantity	quantity	NOUN
m-1112	795	14	produced	produce	VERB
m-1112	795	15	,	,	PUNCT
m-1112	795	16	for	for	ADP
m-1112	795	17	each	each	DET
m-1112	795	18	needed	need	VERB
m-1112	795	19	circular	circular	ADJ
m-1112	795	20	charge	charge	NOUN
m-1112	795	21	,	,	PUNCT
m-1112	795	22	to	to	PART
m-1112	795	23	shake	shake	VERB
m-1112	795	24	off	off	ADP
m-1112	795	25	quantity	quantity	NOUN
m-1112	795	26	𝐐𝐩−𝐩	𝐐𝐩−𝐩	NOUN
m-1112	795	27	.	.	PUNCT
m-1112	796	1	the	the	DET
m-1112	796	2	3	3	NUM
m-1112	796	3	-	-	PUNCT
m-1112	796	4	circular	circular	ADJ
m-1112	796	5	charges	charge	NOUN
m-1112	796	6	correspond	correspond	VERB
m-1112	796	7	to	to	ADP
m-1112	796	8	the	the	DET
m-1112	796	9	3	3	NUM
m-1112	796	10	-	-	PUNCT
m-1112	796	11	phase	phase	NOUN
m-1112	796	12	rotors	rotor	NOUN
m-1112	796	13	produce	produce	VERB
m-1112	796	14	the	the	DET
m-1112	796	15	3	3	NUM
m-1112	796	16	-	-	PUNCT
m-1112	796	17	phase	phase	NOUN
m-1112	796	18	physical	physical	NOUN
m-1112	796	19	-	-	PUNCT
m-1112	796	20	current	current	NOUN
m-1112	796	21	,	,	PUNCT
m-1112	796	22	since	since	SCONJ
m-1112	796	23	common	common	ADJ
m-1112	796	24	circle	circle	NOUN
m-1112	796	25	exists	exist	VERB
m-1112	796	26	on	on	ADP
m-1112	796	27	their	their	PRON
m-1112	796	28	common	common	ADJ
m-1112	796	29	sphere	sphere	NOUN
m-1112	796	30	,	,	PUNCT
m-1112	796	31	then	then	ADV
m-1112	796	32	the	the	DET
m-1112	796	33	infinite	infinite	ADJ
m-1112	796	34	straightlines	straightline	NOUN
m-1112	796	35	,	,	PUNCT
m-1112	796	36	launch	launch	VERB
m-1112	796	37	the	the	DET
m-1112	796	38	e	e	NOUN
m-1112	796	39	quantity	quantity	NOUN
m-1112	796	40	𝐐	𝐐	PROPN
m-1112	796	41	𝐩−𝐩	𝐩−𝐩	NOUN
m-1112	796	42	off	off	ADP
m-1112	796	43	the	the	DET
m-1112	796	44	fundamental	fundamental	ADJ
m-1112	796	45	particles	particle	NOUN
m-1112	796	46	to	to	ADP
m-1112	796	47	all	all	DET
m-1112	796	48	universe	universe	NOUN
m-1112	796	49	and	and	CCONJ
m-1112	796	50	into	into	ADP
m-1112	796	51	the	the	DET
m-1112	796	52	planck`s	planck`s	NOUN
m-1112	796	53	confinement	confinement	NOUN
m-1112	796	54	only	only	ADV
m-1112	796	55	.	.	PUNCT
m-1112	797	1	i.e.	i.e.	X
m-1112	797	2	the	the	DET
m-1112	797	3	physical	physical	ADJ
m-1112	797	4	-	-	PUNCT
m-1112	797	5	three	three	NUM
m-1112	797	6	-	-	PUNCT
m-1112	797	7	phasestpl	phasestpl	NOUN
m-1112	797	8	mechanism	mechanism	NOUN
m-1112	797	9	is	be	AUX
m-1112	797	10	the	the	DET
m-1112	797	11	only	only	ADJ
m-1112	797	12	absolute	absolute	ADJ
m-1112	797	13	-	-	PUNCT
m-1112	797	14	system	system	NOUN
m-1112	797	15	[	[	X
m-1112	797	16	a	a	X
m-1112	797	17	]	]	X
m-1112	797	18	on	on	ADP
m-1112	797	19	which	which	PRON
m-1112	797	20	circularly	circularly	ADV
m-1112	797	21	exist	exist	VERB
m-1112	797	22	the	the	DET
m-1112	797	23	relative	relative	ADJ
m-1112	797	24	-	-	PUNCT
m-1112	797	25	system	system	NOUN
m-1112	797	26	[	[	X
m-1112	797	27	r	r	X
m-1112	797	28	]	]	X
m-1112	797	29	≡	≡	PROPN
m-1112	797	30	[	[	PUNCT
m-1112	797	31	⊕	⊕	PROPN
m-1112	797	32			PROPN
m-1112	797	33	⊝	⊝	X
m-1112	797	34	]	]	PUNCT
m-1112	797	35	↻	↻	NOUN
m-1112	797	36	[	[	PUNCT
m-1112	797	37	⊝	⊝	X
m-1112	797	38			PROPN
m-1112	797	39	⊕	⊕	PROPN
m-1112	797	40	]	]	PUNCT
m-1112	797	41	↻	↻	PROPN
m-1112	797	42	[	[	PUNCT
m-1112	797	43	⊕	⊕	PROPN
m-1112	797	44	⊝	⊝	PUNCT
m-1112	797	45			PROPN
m-1112	797	46	]	]	PUNCT
m-1112	797	47	of	of	ADP
m-1112	797	48	the	the	DET
m-1112	797	49	three	three	NUM
m-1112	797	50	constituents	constituent	NOUN
m-1112	797	51	[	[	PUNCT
m-1112	797	52	⊕	⊕	PROPN
m-1112	797	53			PROPN
m-1112	797	54	⊝	⊝	NUM
m-1112	797	55	]	]	PUNCT
m-1112	797	56	,	,	PUNCT
m-1112	797	57	which	which	PRON
m-1112	797	58	produces	produce	VERB
m-1112	797	59	the	the	DET
m-1112	797	60	fundamental	fundamental	ADJ
m-1112	797	61	particles	particle	NOUN
m-1112	797	62	and	and	CCONJ
m-1112	797	63	the	the	DET
m-1112	797	64	existing	exist	VERB
m-1112	797	65	objectivity	objectivity	NOUN
m-1112	797	66	as	as	ADP
m-1112	797	67	[	[	X
m-1112	797	68	a	a	X
m-1112	797	69	]	]	X
m-1112	797	70	≡	≡	PROPN
m-1112	798	1	[	[	X
m-1112	798	2	r].γ	r].γ	X
m-1112	798	3	,	,	PUNCT
m-1112	798	4	where	where	SCONJ
m-1112	798	5	γ	γ	PROPN
m-1112	798	6	=	=	PROPN
m-1112	798	7	sec	sec	PROPN
m-1112	798	8	φ	φ	PROPN
m-1112	798	9	=	=	X
m-1112	798	10	[	[	PUNCT
m-1112	798	11	𝐎da	𝐎da	PROPN
m-1112	798	12	𝐀da	𝐀da	PROPN
m-1112	798	13	]	]	PUNCT
m-1112	798	14	=	=	SYM
m-1112	798	15	±	±	NOUN
m-1112	798	16	[	[	PUNCT
m-1112	798	17	𝟏	𝟏	NUM
m-1112	798	18	√1−(v	√1−(v	NOUN
m-1112	798	19	/	/	SYM
m-1112	798	20	c)²	c)²	NOUN
m-1112	798	21	]	]	PUNCT
m-1112	799	1	=	=	PUNCT
m-1112	799	2	[	[	PUNCT
m-1112	799	3	𝐜	𝐜	X
m-1112	799	4	√c²−v²	√c²−v²	VERB
m-1112	799	5	]	]	PUNCT
m-1112	799	6	the	the	DET
m-1112	799	7	material	material	NOUN
m-1112	799	8	angle	angle	NOUN
m-1112	799	9	φ	φ	PROPN
m-1112	799	10	=	=	SYM
m-1112	799	11	𝐯	𝐯	X
m-1112	799	12	√c²−r²	√c²−r²	NOUN
m-1112	799	13	,	,	PUNCT
m-1112	799	14	and	and	CCONJ
m-1112	799	15	{	{	PUNCT
m-1112	799	16	a	a	DET
m-1112	799	17	≡	≡	PROPN
m-1112	799	18	dao}≡{r≡	dao}≡{r≡	PRON
m-1112	799	19	da	da	PROPN
m-1112	799	20	-	-	PUNCT
m-1112	799	21	pa	pa	NOUN
m-1112	799	22	}	}	PUNCT
m-1112	799	23	.	.	PUNCT
m-1112	800	1	γ	γ	NOUN
m-1112	800	2	,	,	PUNCT
m-1112	800	3	or	or	CCONJ
m-1112	800	4	|a|	|a|	PROPN
m-1112	800	5	≡	≡	PROPN
m-1112	800	6	|r|	|r|	PROPN
m-1112	800	7	.	.	PUNCT
m-1112	801	1	γ	γ	X
m-1112	801	2	the	the	DET
m-1112	801	3	euclidean	euclidean	ADJ
m-1112	801	4	geometry	geometry	NOUN
m-1112	801	5	is	be	AUX
m-1112	801	6	the	the	DET
m-1112	801	7	spring	spring	NOUN
m-1112	801	8	,	,	PUNCT
m-1112	801	9	for	for	ADP
m-1112	801	10	the	the	DET
m-1112	801	11	geometrical	geometrical	ADJ
m-1112	801	12	relative	relative	ADJ
m-1112	801	13	-velocities	-velocitie	NOUN
m-1112	801	14	.	.	PUNCT
m-1112	802	1	when	when	SCONJ
m-1112	802	2	the	the	DET
m-1112	802	3	points	point	NOUN
m-1112	802	4	[	[	PUNCT
m-1112	802	5	a	a	DET
m-1112	802	6	,	,	PUNCT
m-1112	802	7	b	b	NOUN
m-1112	802	8	,	,	PUNCT
m-1112	802	9	c	c	NOUN
m-1112	802	10	]	]	PUNCT
m-1112	802	11	,	,	PUNCT
m-1112	802	12	[	[	X
m-1112	802	13	𝐀𝐄	𝐀𝐄	PROPN
m-1112	802	14	,	,	PUNCT
m-1112	802	15	𝐁𝐄	𝐁𝐄	PROPN
m-1112	802	16	,	,	PUNCT
m-1112	802	17	𝐂𝐄	𝐂𝐄	PROPN
m-1112	802	18	]	]	PUNCT
m-1112	802	19	,	,	PUNCT
m-1112	802	20	[	[	PUNCT
m-1112	802	21	𝐊𝐀	𝐊𝐀	PROPN
m-1112	802	22	,	,	PUNCT
m-1112	802	23	𝐊𝐁	𝐊𝐁	PROPN
m-1112	802	24	,	,	PUNCT
m-1112	802	25	𝐊𝐂	𝐊𝐂	PROPN
m-1112	802	26	]	]	PUNCT
m-1112	802	27	are	be	AUX
m-1112	802	28	applied	apply	VERB
m-1112	802	29	on	on	ADP
m-1112	802	30	the	the	DET
m-1112	802	31	three	three	NUM
m-1112	802	32	lines	line	NOUN
m-1112	802	33	(	(	PUNCT
m-1112	802	34	𝐊𝐀𝐊𝐁	𝐊𝐀𝐊𝐁	PROPN
m-1112	802	35	,	,	PUNCT
m-1112	802	36	𝐊𝐁	𝐊𝐁	PROPN
m-1112	802	37	𝐊𝐂	𝐊𝐂	PROPN
m-1112	802	38	,	,	PUNCT
m-1112	802	39	𝐊𝐂𝐊𝐀	𝐊𝐂𝐊𝐀	PROPN
m-1112	802	40	)	)	PUNCT
m-1112	802	41	,	,	PUNCT
m-1112	802	42	then	then	ADV
m-1112	802	43	the	the	DET
m-1112	802	44	six	six	NUM
m-1112	802	45	pairs	pair	NOUN
m-1112	802	46	of	of	ADP
m-1112	802	47	the	the	DET
m-1112	802	48	corresponding	corresponding	ADJ
m-1112	802	49	lines	line	NOUN
m-1112	802	50	,	,	PUNCT
m-1112	802	51	extended	extend	VERB
m-1112	802	52	are	be	AUX
m-1112	802	53	concurrent	concurrent	ADJ
m-1112	802	54	at	at	ADP
m-1112	802	55	points	point	NOUN
m-1112	802	56	pa	pa	PROPN
m-1112	802	57	,	,	PUNCT
m-1112	802	58	pb	pb	INTJ
m-1112	802	59	,	,	PUNCT
m-1112	802	60	pc	pc	NOUN
m-1112	802	61	for	for	ADP
m-1112	802	62	the	the	DET
m-1112	802	63	triple	triple	ADJ
m-1112	802	64	pairs	pair	NOUN
m-1112	802	65	of	of	ADP
m-1112	802	66	lines	line	NOUN
m-1112	802	67	(	(	PUNCT
m-1112	802	68	the	the	DET
m-1112	802	69	pascal`s	pascal`s	ADJ
m-1112	802	70	perspectivity	perspectivity	NOUN
m-1112	802	71	of	of	ADP
m-1112	802	72	points	point	NOUN
m-1112	802	73	in	in	ADP
m-1112	802	74	euclidean	euclidean	ADJ
m-1112	802	75	geometry	geometry	NOUN
m-1112	802	76	)	)	PUNCT
m-1112	802	77	,	,	PUNCT
m-1112	802	78	[	[	PUNCT
m-1112	802	79	a𝐀𝐄	a𝐀𝐄	NOUN
m-1112	802	80	,	,	PUNCT
m-1112	802	81	𝐁𝐂𝐄	𝐁𝐂𝐄	PROPN
m-1112	802	82	,	,	PUNCT
m-1112	802	83	𝐂𝐁𝐄	𝐂𝐁𝐄	NOUN
m-1112	802	84	]	]	PUNCT
m-1112	802	85	,	,	PUNCT
m-1112	803	1	[	[	X
m-1112	803	2	b𝐁𝐄	b𝐁𝐄	X
m-1112	803	3	,	,	PUNCT
m-1112	803	4	𝐂𝐀𝐄	𝐂𝐀𝐄	ADJ
m-1112	803	5	,	,	PUNCT
m-1112	803	6	𝐀𝐂𝐄	𝐀𝐂𝐄	PROPN
m-1112	803	7	]	]	PUNCT
m-1112	803	8	,	,	PUNCT
m-1112	804	1	[	[	X
m-1112	804	2	c𝐂𝐄	c𝐂𝐄	NOUN
m-1112	804	3	,	,	PUNCT
m-1112	804	4	𝐀𝐁𝐄	𝐀𝐁𝐄	PROPN
m-1112	804	5	,	,	PUNCT
m-1112	804	6	𝐁𝐀𝐄	𝐁𝐀𝐄	PROPN
m-1112	804	7	]	]	PUNCT
m-1112	804	8	and	and	CCONJ
m-1112	804	9	at	at	ADP
m-1112	804	10	points	point	NOUN
m-1112	804	11	da	da	INTJ
m-1112	804	12	,	,	PUNCT
m-1112	804	13	db	db	PROPN
m-1112	804	14	,	,	PUNCT
m-1112	804	15	dc	dc	PROPN
m-1112	804	16	for	for	ADP
m-1112	804	17	the	the	DET
m-1112	804	18	triple	triple	ADJ
m-1112	804	19	pairs	pair	NOUN
m-1112	804	20	of	of	ADP
m-1112	804	21	lines	line	NOUN
m-1112	804	22	[	[	X
m-1112	804	23	𝐊𝐁	𝐊𝐁	PROPN
m-1112	804	24	𝐊𝐂	𝐊𝐂	PROPN
m-1112	804	25	,	,	PUNCT
m-1112	804	26	bc	bc	PROPN
m-1112	804	27	,	,	PUNCT
m-1112	804	28	𝐁𝐄𝐂𝐄	𝐁𝐄𝐂𝐄	PROPN
m-1112	804	29	]	]	PUNCT
m-1112	804	30	,	,	PUNCT
m-1112	804	31	[	[	X
m-1112	804	32	𝐊𝐀𝐊𝐂	𝐊𝐀𝐊𝐂	PROPN
m-1112	804	33	,	,	PUNCT
m-1112	804	34	ac	ac	PROPN
m-1112	804	35	,	,	PUNCT
m-1112	804	36	𝐀𝐄𝐂𝐄	𝐀𝐄𝐂𝐄	PROPN
m-1112	804	37	]	]	PUNCT
m-1112	804	38	and	and	CCONJ
m-1112	804	39	[	[	X
m-1112	804	40	𝐊𝐀𝐊𝐁	𝐊𝐀𝐊𝐁	PROPN
m-1112	804	41	,	,	PUNCT
m-1112	804	42	ab	ab	INTJ
m-1112	804	43	,	,	PUNCT
m-1112	804	44	𝐀𝐄𝐁𝐄	𝐀𝐄𝐁𝐄	PROPN
m-1112	804	45	]	]	PUNCT
m-1112	804	46	,	,	PUNCT
m-1112	804	47	(	(	PUNCT
m-1112	804	48	desargues`s	desargues`s	NOUN
m-1112	804	49	perspectivity	perspectivity	NOUN
m-1112	804	50	of	of	ADP
m-1112	804	51	points	point	NOUN
m-1112	804	52	in	in	ADP
m-1112	804	53	euclidean	euclidean	ADJ
m-1112	804	54	geometry	geometry	NOUN
m-1112	804	55	)	)	PUNCT
m-1112	804	56	and	and	CCONJ
m-1112	804	57	all	all	DET
m-1112	804	58	the	the	DET
m-1112	804	59	18	18	NUM
m-1112	804	60	common	common	ADJ
m-1112	804	61	points	point	NOUN
m-1112	804	62	lie	lie	VERB
m-1112	804	63	on	on	ADP
m-1112	804	64	a	a	DET
m-1112	804	65	straight	straight	ADJ
m-1112	804	66	line	line	NOUN
m-1112	804	67	the	the	DET
m-1112	804	68			NOUN
m-1112	804	69	stpl	stpl	PROPN
m-1112	804	70	mechanism	mechanism	NOUN
m-1112	804	71	this	this	DET
m-1112	804	72	mechanism	mechanism	NOUN
m-1112	804	73	stabilizes	stabilize	VERB
m-1112	804	74	the	the	DET
m-1112	804	75	nucleus	nucleus	ADJ
m-1112	804	76	forces	force	NOUN
m-1112	804	77	for	for	ADP
m-1112	804	78	the	the	DET
m-1112	804	79	{	{	PUNCT
m-1112	804	80	⊕	⊕	PROPN
m-1112	804	81	space	space	NOUN
m-1112	804	82	[	[	PUNCT
m-1112	804	83	a	a	DET
m-1112	804	84	b	b	X
m-1112	804	85	c	c	NOUN
m-1112	804	86	]	]	PUNCT
m-1112	804	87	}	}	PUNCT
m-1112	804	88	and	and	CCONJ
m-1112	804	89	for	for	ADP
m-1112	804	90	the	the	DET
m-1112	804	91	{	{	PUNCT
m-1112	804	92	⊝	⊝	NOUN
m-1112	804	93	anti	anti	ADJ
m-1112	804	94	-	-	NOUN
m-1112	804	95	space	space	ADJ
m-1112	804	96	[	[	PUNCT
m-1112	804	97	ka	ka	X
m-1112	804	98	kb	kb	PROPN
m-1112	804	99	kc	kc	PROPN
m-1112	804	100	]	]	X
m-1112	804	101	}	}	PUNCT
m-1112	804	102	and	and	CCONJ
m-1112	804	103	this	this	PRON
m-1112	804	104	succeeded	succeed	VERB
m-1112	804	105	by	by	ADP
m-1112	804	106	the	the	DET
m-1112	804	107	pascal`s	pascal`s	NUM
m-1112	804	108	–	–	PUNCT
m-1112	804	109	launched	launch	VERB
m-1112	804	110	caves	cave	NOUN
m-1112	804	111	r	r	NOUN
m-1112	804	112	through	through	ADP
m-1112	804	113	the	the	DET
m-1112	804	114	stpl	stpl	PROPN
m-1112	804	115	circuit	circuit	NOUN
m-1112	804	116	of	of	ADP
m-1112	804	117	the	the	DET
m-1112	804	118	ptolemy`s	ptolemy`	NOUN
m-1112	804	119	and	and	CCONJ
m-1112	804	120	the	the	DET
m-1112	804	121	ceba`s	ceba`s	NOUN
m-1112	804	122	geometry	geometry	NOUN
m-1112	804	123	theorem	theorem	NOUN
m-1112	804	124	for	for	ADP
m-1112	804	125	the	the	DET
m-1112	804	126	complex	complex	ADJ
m-1112	804	127	vector	vector	NOUN
m-1112	804	128	forces	force	NOUN
m-1112	804	129	which	which	PRON
m-1112	804	130	are	be	AUX
m-1112	804	131	,	,	PUNCT
m-1112	804	132	circularly	circularly	ADJ
m-1112	804	133	and	and	CCONJ
m-1112	804	134	diagonally	diagonally	ADV
m-1112	804	135	equilibrium	equilibrium	NOUN
m-1112	804	136	.i.e	.i.e	PUNCT
m-1112	804	137	.	.	PUNCT
m-1112	805	1	→	→	PUNCT
m-1112	805	2	stpl	stpl	PROPN
m-1112	805	3	is	be	AUX
m-1112	805	4	the	the	DET
m-1112	805	5	in	in	ADP
m-1112	805	6	-	-	PUNCT
m-1112	805	7	sphere	sphere	NOUN
m-1112	805	8	,	,	PUNCT
m-1112	805	9	tetrahedron	tetrahedron	NOUN
m-1112	805	10	-	-	PUNCT
m-1112	805	11	cube	cube	NOUN
m-1112	805	12	,	,	PUNCT
m-1112	805	13	out	out	ADP
m-1112	805	14	-	-	PUNCT
m-1112	805	15	sphere	sphere	NOUN
m-1112	805	16	physical	physical	ADJ
m-1112	805	17	mechanism	mechanism	NOUN
m-1112	805	18	←	←	PROPN
m-1112	805	19	for	for	ADP
m-1112	805	20	its	its	PRON
m-1112	805	21	27	27	NUM
m-1112	805	22	-	-	PUNCT
m-1112	805	23	conductors	conductor	NOUN
m-1112	805	24	≡	≡	PROPN
m-1112	805	25	electric	electric	PROPN
m-1112	805	26	magnetic	magnetic	PROPN
m-1112	805	27	fields	field	NOUN
m-1112	805	28	,	,	PUNCT
m-1112	805	29	space	space	NOUN
m-1112	805	30	-	-	PUNCT
m-1112	805	31	energy	energy	NOUN
m-1112	805	32	cpt	cpt	NOUN
m-1112	805	33	is	be	AUX
m-1112	805	34	invariant	invariant	ADJ
m-1112	805	35	.	.	PUNCT
m-1112	806	1	8	8	NUM
m-1112	806	2	..	..	PUNCT
m-1112	806	3	[a]-2	[a]-2	X
m-1112	806	4	…	…	PUNCT
m-1112	806	5	the	the	DET
m-1112	806	6	explanation	explanation	NOUN
m-1112	806	7	of	of	ADP
m-1112	806	8	the	the	DET
m-1112	806	9	absolute	absolute	ADJ
m-1112	806	10	and	and	CCONJ
m-1112	806	11	relative	relative	ADJ
m-1112	806	12	motion	motion	NOUN
m-1112	806	13	.	.	PUNCT
m-1112	806	14	.	.	PUNCT
m-1112	807	1	fig	fig	NOUN
m-1112	807	2	–	–	PUNCT
m-1112	807	3	6	6	NUM
m-1112	807	4	because	because	SCONJ
m-1112	807	5	properties	property	NOUN
m-1112	807	6	in	in	ADP
m-1112	807	7	and	and	CCONJ
m-1112	807	8	on	on	ADP
m-1112	807	9	[	[	X
m-1112	807	10	stpl	stpl	X
m-1112	807	11	]	]	X
m-1112	807	12	line	line	NOUN
m-1112	807	13	,	,	PUNCT
m-1112	807	14	are	be	AUX
m-1112	807	15	relative	relative	ADJ
m-1112	807	16	to	to	ADP
m-1112	807	17	the	the	DET
m-1112	807	18	only	only	ADJ
m-1112	807	19	one	one	NUM
m-1112	807	20	equilibrium	equilibrium	NOUN
m-1112	807	21	and	and	CCONJ
m-1112	807	22	also	also	ADV
m-1112	807	23	absolute	absolute	ADJ
m-1112	807	24	system	system	NOUN
m-1112	807	25	±	±	NUM
m-1112	807	26	λ	λ	NOUN
m-1112	807	27	=	=	PUNCT
m-1112	807	28	r.mv̅	r.mv̅	NOUN
m-1112	807	29	=	=	PUNCT
m-1112	808	1	r.m.w̅.r	r.m.w̅.r	X
m-1112	808	2	=	=	NOUN
m-1112	808	3	mr².w̅	mr².w̅	NOUN
m-1112	808	4	,	,	PUNCT
m-1112	808	5	so	so	ADV
m-1112	808	6	exists	exist	VERB
m-1112	808	7	that	that	SCONJ
m-1112	808	8	what	what	PRON
m-1112	808	9	is	be	AUX
m-1112	808	10	called	call	VERB
m-1112	808	11	relativity	relativity	NOUN
m-1112	808	12	.	.	PUNCT
m-1112	809	1	absolute	absolute	ADJ
m-1112	809	2	system	system	NOUN
m-1112	809	3	let	let	VERB
m-1112	809	4	it	it	PRON
m-1112	809	5	be	be	AUX
m-1112	809	6	the	the	DET
m-1112	809	7	[	[	X
m-1112	809	8	a	a	X
m-1112	809	9	]	]	X
m-1112	809	10	≡	≡	PROPN
m-1112	809	11	{	{	PUNCT
m-1112	809	12	dao	dao	PROPN
m-1112	809	13	}	}	PUNCT
m-1112	809	14	≡	≡	PROPN
m-1112	809	15	the	the	DET
m-1112	809	16	stpl	stpl	PROPN
m-1112	809	17	mechanism	mechanism	NOUN
m-1112	809	18	,	,	PUNCT
m-1112	809	19	and	and	CCONJ
m-1112	809	20	as	as	ADP
m-1112	809	21	relative	relative	ADJ
m-1112	809	22	system	system	NOUN
m-1112	809	23	(	(	PUNCT
m-1112	809	24	reference	reference	NOUN
m-1112	809	25	,	,	PUNCT
m-1112	809	26	affine	affine	NOUN
m-1112	809	27	)	)	PUNCT
m-1112	810	1	[	[	X
m-1112	810	2	r	r	X
m-1112	810	3	]	]	X
m-1112	810	4	≡	≡	PROPN
m-1112	810	5	{	{	PUNCT
m-1112	810	6	dao	dao	VERB
m-1112	810	7	}	}	PUNCT
m-1112	810	8	the	the	DET
m-1112	810	9	absolute	absolute	ADJ
m-1112	810	10	motion	motion	NOUN
m-1112	810	11	happens	happen	VERB
m-1112	810	12	on	on	ADP
m-1112	810	13	[	[	X
m-1112	810	14	a	a	X
m-1112	810	15	]	]	X
m-1112	810	16	≡	≡	PROPN
m-1112	810	17	{	{	PUNCT
m-1112	810	18	dao	dao	VERB
m-1112	810	19	}	}	PUNCT
m-1112	810	20	and	and	CCONJ
m-1112	810	21	on	on	ADP
m-1112	810	22	[	[	X
m-1112	810	23	r	r	X
m-1112	810	24	]	]	PUNCT
m-1112	810	25	≡{da	≡{da	NOUN
m-1112	810	26	-	-	NOUN
m-1112	810	27	pa	pa	NOUN
m-1112	810	28	}	}	PUNCT
m-1112	810	29	of	of	ADP
m-1112	810	30	the	the	DET
m-1112	810	31	two	two	NUM
m-1112	810	32	systems	system	NOUN
m-1112	810	33	.	.	PUNCT
m-1112	811	1	it	it	PRON
m-1112	811	2	was	be	AUX
m-1112	811	3	shown	show	VERB
m-1112	811	4	,	,	PUNCT
m-1112	811	5	that	that	SCONJ
m-1112	811	6	in	in	ADP
m-1112	811	7	{	{	PUNCT
m-1112	811	8	dao	dao	NOUN
m-1112	811	9	}	}	PUNCT
m-1112	811	10	,	,	PUNCT
m-1112	811	11	(	(	PUNCT
m-1112	811	12	x	x	X
m-1112	811	13	,	,	PUNCT
m-1112	811	14	y	y	PROPN
m-1112	811	15	,	,	PUNCT
m-1112	811	16	z	z	PROPN
m-1112	811	17	,	,	PUNCT
m-1112	811	18	t	t	PROPN
m-1112	811	19	)	)	PUNCT
m-1112	811	20	,	,	PUNCT
m-1112	811	21	system	system	NOUN
m-1112	811	22	�	�	PROPN
m-1112	811	23	̅	̅	NOUN
m-1112	811	24	�	�	PROPN
m-1112	811	25	,	,	PUNCT
m-1112	811	26	�	�	PROPN
m-1112	811	27	̅	̅	NOUN
m-1112	811	28	�	�	PROPN
m-1112	811	29	,	,	PUNCT
m-1112	811	30	vectors	vector	NOUN
m-1112	811	31	are	be	AUX
m-1112	811	32	isochrones	isochrone	NOUN
m-1112	811	33	i.e.	i.e.	X
m-1112	811	34	period	period	NOUN
m-1112	811	35	t	t	NOUN
m-1112	811	36	=	=	SYM
m-1112	811	37	l	l	NOUN
m-1112	811	38	/	/	SYM
m-1112	811	39	v	v	NOUN
m-1112	812	1	=	=	PUNCT
m-1112	812	2	2πr	2πr	NOUN
m-1112	812	3	/	/	SYM
m-1112	812	4	v	v	NOUN
m-1112	812	5	=	=	PUNCT
m-1112	812	6	2π	2π	NOUN
m-1112	812	7	/	/	SYM
m-1112	813	1	[	[	X
m-1112	813	2	c/𝑟𝑐	c/𝑟𝑐	NOUN
m-1112	813	3	]	]	X
m-1112	813	4	=	=	SYM
m-1112	813	5	2π/[v/𝑟𝑐	2π/[v/𝑟𝑐	NUM
m-1112	813	6	]	]	PUNCT
m-1112	813	7	→	→	SYM
m-1112	813	8	c	c	X
m-1112	813	9	/	/	SYM
m-1112	813	10	rc	rc	PROPN
m-1112	813	11	=	=	PROPN
m-1112	813	12	v	v	PROPN
m-1112	813	13	/	/	SYM
m-1112	813	14	rv	rv	PROPN
m-1112	813	15	→	→	SYM
m-1112	813	16	c.rv=	c.rv=	PROPN
m-1112	813	17	v.	v.	PROPN
m-1112	813	18	rc	rc	PROPN
m-1112	813	19	,	,	PUNCT
m-1112	813	20	where	where	SCONJ
m-1112	813	21	rv	rv	PROPN
m-1112	813	22	,	,	PUNCT
m-1112	813	23	rc	rc	PROPN
m-1112	813	24	are	be	AUX
m-1112	813	25	the	the	DET
m-1112	813	26	radius	radius	NOUN
m-1112	813	27	of	of	ADP
m-1112	813	28	their	their	PRON
m-1112	813	29	intrinsic	intrinsic	ADJ
m-1112	813	30	rolling	rolling	ADJ
m-1112	813	31	circles	circle	NOUN
m-1112	813	32	.	.	PUNCT
m-1112	814	1	this	this	DET
m-1112	814	2	relation	relation	NOUN
m-1112	814	3	is	be	AUX
m-1112	814	4	geometrically	geometrically	ADV
m-1112	814	5	expressed	express	VERB
m-1112	814	6	as	as	ADP
m-1112	814	7	,	,	PUNCT
m-1112	814	8	𝐬𝐞𝐜𝛗	𝐬𝐞𝐜𝛗	NOUN
m-1112	814	9	=	=	PUNCT
m-1112	815	1	o	o	NOUN
m-1112	816	1	da	da	NOUN
m-1112	816	2	:	:	PUNCT
m-1112	816	3	a	a	DET
m-1112	816	4	da	da	NOUN
m-1112	816	5	=	=	PUNCT
m-1112	816	6	γ	γ	X
m-1112	816	7	=	=	SYM
m-1112	816	8	𝒄	𝒄	PROPN
m-1112	816	9	𝒗	𝒗	PROPN
m-1112	816	10	=	=	SYM
m-1112	816	11	±	±	PROPN
m-1112	816	12	1	1	NUM
m-1112	816	13	/	/	SYM
m-1112	816	14	[	[	PUNCT
m-1112	816	15	√1–(v	√1–(v	NUM
m-1112	816	16	/	/	SYM
m-1112	816	17	c	c	NOUN
m-1112	816	18	)	)	PUNCT
m-1112	816	19	²	²	NUM
m-1112	816	20	]	]	PUNCT
m-1112	816	21	=	=	PUNCT
m-1112	816	22	c	c	NOUN
m-1112	816	23	/	/	SYM
m-1112	817	1	[	[	X
m-1112	817	2	√	√	X
m-1112	817	3	c²	c²	NOUN
m-1112	817	4	–	–	PUNCT
m-1112	817	5	v²	v²	PROPN
m-1112	817	6	]	]	PUNCT
m-1112	817	7	,	,	PUNCT
m-1112	817	8	and	and	CCONJ
m-1112	817	9	it	it	PRON
m-1112	817	10	is	be	AUX
m-1112	817	11	a	a	DET
m-1112	817	12	ijo	ijo	PROPN
m-1112	817	13	international	international	ADJ
m-1112	817	14	journal	journal	PROPN
m-1112	817	15	of	of	ADP
m-1112	817	16	mathematics	mathematics	PROPN
m-1112	817	17	(	(	PUNCT
m-1112	817	18	issn	issn	PROPN
m-1112	817	19	:	:	PUNCT
m-1112	817	20	2992	2992	NUM
m-1112	817	21	-	-	SYM
m-1112	817	22	4421	4421	NUM
m-1112	817	23	)	)	PUNCT
m-1112	818	1	volume	volume	NOUN
m-1112	818	2	08	08	NUM
m-1112	819	1	|	|	ADV
m-1112	819	2	issue	issue	NOUN
m-1112	819	3	08	08	NUM
m-1112	820	1	|	|	ADV
m-1112	820	2	august	august	PROPN
m-1112	820	3	2025	2025	NUM
m-1112	820	4	|	|	ADV
m-1112	820	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	820	6	ijo	ijo	PROPN
m-1112	820	7	journals	journal	NOUN
m-1112	820	8	28	28	NUM
m-1112	820	9	the	the	DET
m-1112	820	10	fundamental	fundamental	ADJ
m-1112	820	11	particles	particle	NOUN
m-1112	820	12	origination	origination	NOUN
m-1112	820	13	mechanism	mechanism	NOUN
m-1112	820	14	in	in	ADP
m-1112	820	15	mfmf	mfmf	PROPN
m-1112	820	16	pns	pns	PROPN
m-1112	820	17	caves	cave	NOUN
m-1112	820	18	.	.	PUNCT
m-1112	821	1	geometrical	geometrical	ADJ
m-1112	821	2	cycloid	cycloid	NOUN
m-1112	821	3	property	property	NOUN
m-1112	821	4	equal	equal	ADJ
m-1112	821	5	to	to	ADP
m-1112	821	6	lorentz`s	lorentz`s	PROPN
m-1112	821	7	,	,	PUNCT
m-1112	821	8	γ	γ	X
m-1112	821	9	,	,	PUNCT
m-1112	821	10	factor	factor	NOUN
m-1112	821	11	.	.	PUNCT
m-1112	822	1	the	the	DET
m-1112	822	2	newton`s	newton`s	NOUN
m-1112	822	3	laws	law	NOUN
m-1112	822	4	are	be	AUX
m-1112	822	5	true	true	ADJ
m-1112	822	6	into	into	ADP
m-1112	822	7	the	the	DET
m-1112	822	8	reference	reference	NOUN
m-1112	822	9	system	system	NOUN
m-1112	822	10	[	[	X
m-1112	822	11	r	r	X
m-1112	822	12	]	]	X
m-1112	822	13	≡	≡	PROPN
m-1112	822	14	{	{	PUNCT
m-1112	822	15	dapa	dapa	PROPN
m-1112	822	16	}	}	PUNCT
m-1112	822	17	as	as	SCONJ
m-1112	822	18	follows	follow	VERB
m-1112	822	19	proof	proof	NOUN
m-1112	822	20	,	,	PUNCT
m-1112	822	21	considering	consider	VERB
m-1112	822	22	{	{	PUNCT
m-1112	822	23	dao},(x	dao},(x	PROPN
m-1112	822	24	,	,	PUNCT
m-1112	822	25	y	y	PROPN
m-1112	822	26	,	,	PUNCT
m-1112	822	27	z	z	PROPN
m-1112	822	28	,	,	PUNCT
m-1112	822	29	t	t	PROPN
m-1112	822	30	)	)	PUNCT
m-1112	822	31	,	,	PUNCT
m-1112	822	32	as	as	ADP
m-1112	822	33	the	the	DET
m-1112	822	34	fixed	fix	VERB
m-1112	822	35	frame	frame	NOUN
m-1112	822	36	[	[	X
m-1112	822	37	a	a	X
m-1112	822	38	]	]	X
m-1112	822	39	of	of	ADP
m-1112	822	40	the	the	DET
m-1112	822	41	coordinate	coordinate	NOUN
m-1112	822	42	system	system	NOUN
m-1112	822	43	in	in	ADP
m-1112	822	44	the	the	DET
m-1112	822	45	gravity	gravity	NOUN
m-1112	822	46	cave	cave	NOUN
m-1112	822	47	(	(	PUNCT
m-1112	822	48	d	d	NOUN
m-1112	822	49	=	=	SYM
m-1112	822	50	2r	2r	NUM
m-1112	822	51	)	)	PUNCT
m-1112	822	52	,	,	PUNCT
m-1112	822	53	and	and	CCONJ
m-1112	822	54	point	point	VERB
m-1112	822	55	a=	a=	VERB
m-1112	822	56	(	(	PUNCT
m-1112	822	57	x	x	X
m-1112	822	58	,	,	PUNCT
m-1112	822	59	y	y	PROPN
m-1112	822	60	,	,	PUNCT
m-1112	822	61	z	z	PROPN
m-1112	822	62	)	)	PUNCT
m-1112	822	63	is	be	AUX
m-1112	822	64	fixed	fix	VERB
m-1112	822	65	on	on	ADP
m-1112	822	66	circle	circle	NOUN
m-1112	822	67	(	(	PUNCT
m-1112	822	68	o	o	NOUN
m-1112	822	69	,	,	PUNCT
m-1112	822	70	oa	oa	PROPN
m-1112	822	71	)	)	PUNCT
m-1112	822	72	which	which	PRON
m-1112	822	73	is	be	AUX
m-1112	822	74	rotating	rotate	VERB
m-1112	822	75	with	with	ADP
m-1112	822	76	a	a	DET
m-1112	822	77	velocity	velocity	NOUN
m-1112	822	78	v̅	v̅	NOUN
m-1112	822	79	=	=	SYM
m-1112	822	80	w	w	PROPN
m-1112	822	81	̅̅	̅̅	PROPN
m-1112	822	82	̅r	̅r	NOUN
m-1112	822	83	,	,	PUNCT
m-1112	822	84	of	of	ADP
m-1112	822	85	angular	angular	ADJ
m-1112	822	86	velocity	velocity	NOUN
m-1112	822	87	w̅	w̅	PUNCT
m-1112	823	1	=	=	PUNCT
m-1112	823	2	2π	2π	NOUN
m-1112	823	3	/t	/t	PUNCT
m-1112	824	1	=	=	SYM
m-1112	824	2	2πf	2πf	NOUN
m-1112	824	3	,	,	PUNCT
m-1112	824	4	in	in	ADP
m-1112	824	5	where	where	SCONJ
m-1112	824	6	period	period	NOUN
m-1112	824	7	of	of	ADP
m-1112	824	8	rotation	rotation	NOUN
m-1112	824	9	t	t	PROPN
m-1112	824	10	,	,	PUNCT
m-1112	824	11	is	be	AUX
m-1112	824	12	then	then	ADV
m-1112	824	13	also	also	ADV
m-1112	824	14	constant	constant	ADJ
m-1112	824	15	.	.	PUNCT
m-1112	825	1	since	since	SCONJ
m-1112	825	2	the	the	DET
m-1112	825	3	acceleration	acceleration	NOUN
m-1112	825	4	,	,	PUNCT
m-1112	825	5	a	a	PRON
m-1112	825	6	,	,	PUNCT
m-1112	825	7	for	for	ADP
m-1112	825	8	a	a	DET
m-1112	825	9	quaternion	quaternion	NOUN
m-1112	825	10	z	z	NOUN
m-1112	825	11	=	=	PUNCT
m-1112	825	12	(	(	PUNCT
m-1112	825	13	s	s	NUM
m-1112	825	14	+	+	NUM
m-1112	825	15	v̅.	v̅.	NOUN
m-1112	825	16	i	i	NOUN
m-1112	825	17	)	)	PUNCT
m-1112	825	18	is	be	AUX
m-1112	825	19	a	a	DET
m-1112	825	20	=	=	NOUN
m-1112	825	21	[	[	X
m-1112	825	22	d²z	d²z	NOUN
m-1112	825	23	/	/	SYM
m-1112	825	24	dt²	dt²	NOUN
m-1112	825	25	]	]	X
m-1112	825	26	=	=	SYM
m-1112	825	27	(	(	PUNCT
m-1112	825	28	ds	ds	ADJ
m-1112	825	29	/	/	SYM
m-1112	825	30	dt.v̅.	dt.v̅.	NOUN
m-1112	825	31	i	i	NOUN
m-1112	825	32	)	)	PUNCT
m-1112	826	1	+	+	CCONJ
m-1112	826	2	s.	s.	PROPN
m-1112	826	3	d(v̅.	d(v̅.	PROPN
m-1112	827	1	i)/dt	i)/dt	NOUN
m-1112	827	2	=	=	PROPN
m-1112	827	3	0	0	PUNCT
m-1112	827	4	+	+	NUM
m-1112	827	5	s.	s.	PROPN
m-1112	827	6	d(w	d(w	PROPN
m-1112	827	7	r)/dt	r)/dt	PROPN
m-1112	827	8	=	=	NOUN
m-1112	827	9	0	0	PUNCT
m-1112	828	1	+	+	CCONJ
m-1112	828	2	0	0	NUM
m-1112	828	3	,	,	PUNCT
m-1112	828	4	and	and	CCONJ
m-1112	828	5	this	this	PRON
m-1112	828	6	because	because	SCONJ
m-1112	828	7	w̅	w̅	PROPN
m-1112	828	8	is	be	AUX
m-1112	828	9	constant	constant	ADJ
m-1112	828	10	for	for	SCONJ
m-1112	828	11	both	both	DET
m-1112	828	12	therefore	therefore	ADV
m-1112	828	13	velocity	velocity	NOUN
m-1112	828	14	�	�	NOUN
m-1112	828	15	̅	̅	NOUN
m-1112	828	16	�	�	NOUN
m-1112	828	17	=	=	SYM
m-1112	828	18	constant	constant	ADJ
m-1112	828	19	also	also	ADV
m-1112	828	20	,	,	PUNCT
m-1112	828	21	i.e.	i.e.	X
m-1112	828	22	→	→	PUNCT
m-1112	828	23	the	the	DET
m-1112	828	24	centrifugal	centrifugal	ADJ
m-1112	828	25	velocity	velocity	NOUN
m-1112	828	26	of	of	ADP
m-1112	828	27	the	the	DET
m-1112	828	28	absolute	absolute	ADJ
m-1112	828	29	system	system	NOUN
m-1112	828	30	[	[	PUNCT
m-1112	828	31	a	a	X
m-1112	828	32	]	]	X
m-1112	828	33	is	be	AUX
m-1112	828	34	any	any	DET
m-1112	828	35	constant	constant	ADJ
m-1112	828	36	,	,	PUNCT
m-1112	828	37	�	�	PROPN
m-1112	828	38	̅	̅	NOUN
m-1112	828	39	�	�	PROPN
m-1112	828	40	,	,	PUNCT
m-1112	828	41	and	and	CCONJ
m-1112	828	42	this	this	PRON
m-1112	828	43	because	because	SCONJ
m-1112	828	44	angular	angular	ADJ
m-1112	828	45	velocity	velocity	NOUN
m-1112	828	46	,	,	PUNCT
m-1112	828	47	�	�	PROPN
m-1112	828	48	̅	̅	NOUN
m-1112	828	49	�	�	PROPN
m-1112	828	50	,	,	PUNCT
m-1112	828	51	is	be	AUX
m-1112	828	52	constant	constant	ADJ
m-1112	828	53	also	also	ADV
m-1112	828	54	and	and	CCONJ
m-1112	828	55	thus	thus	ADV
m-1112	828	56	,	,	PUNCT
m-1112	828	57	is	be	AUX
m-1112	828	58	not	not	PART
m-1112	828	59	needed	need	VERB
m-1112	828	60	to	to	PART
m-1112	828	61	accept	accept	VERB
m-1112	828	62	a	a	DET
m-1112	828	63	priori	priori	NOUN
m-1112	828	64	this	this	DET
m-1112	828	65	constancy	constancy	NOUN
m-1112	828	66	of	of	ADP
m-1112	828	67	velocity	velocity	NOUN
m-1112	828	68	�	�	NOUN
m-1112	828	69	̅	̅	NOUN
m-1112	828	70	�	�	NOUN
m-1112	828	71	=	=	SYM
m-1112	828	72	0	0	NUM
m-1112	828	73	→	→	SYM
m-1112	828	74	�	�	NOUN
m-1112	828	75	̅	̅	NOUN
m-1112	828	76	�	�	PROPN
m-1112	828	77	→	→	SYM
m-1112	828	78	∞	∞	PROPN
m-1112	828	79	on	on	ADP
m-1112	828	80	circle	circle	NOUN
m-1112	828	81	(	(	PUNCT
m-1112	828	82	o	o	NOUN
m-1112	828	83	,	,	PUNCT
m-1112	828	84	oa	oa	INTJ
m-1112	828	85	)	)	PUNCT
m-1112	828	86	and	and	CCONJ
m-1112	828	87	to	to	PART
m-1112	828	88	exist	exist	VERB
m-1112	828	89	in	in	ADP
m-1112	828	90	frame	frame	NOUN
m-1112	828	91	,	,	PUNCT
m-1112	828	92	(	(	PUNCT
m-1112	828	93	it	it	PRON
m-1112	828	94	has	have	AUX
m-1112	828	95	been	be	AUX
m-1112	828	96	proved	prove	VERB
m-1112	828	97	that	that	SCONJ
m-1112	828	98	this	this	DET
m-1112	828	99	velocity	velocity	NOUN
m-1112	828	100	�	�	NOUN
m-1112	828	101	̅	̅	NOUN
m-1112	828	102	�	�	PROPN
m-1112	828	103	≡	≡	PROPN
m-1112	828	104			PROPN
m-1112	828	105	σ	σ	PROPN
m-1112	828	106	φ	φ	PROPN
m-1112	828	107	)	)	PUNCT
m-1112	829	1	so	so	ADV
m-1112	829	2	,	,	PUNCT
m-1112	829	3	automatically	automatically	ADV
m-1112	829	4	is	be	AUX
m-1112	829	5	defined	define	VERB
m-1112	829	6	the	the	DET
m-1112	829	7	conversion	conversion	NOUN
m-1112	829	8	factor	factor	NOUN
m-1112	829	9	t	t	NOUN
m-1112	829	10	=	=	PUNCT
m-1112	829	11	time	time	NOUN
m-1112	829	12	,	,	PUNCT
m-1112	829	13	between	between	ADP
m-1112	829	14	the	the	DET
m-1112	829	15	conventional	conventional	ADJ
m-1112	829	16	time	time	NOUN
m-1112	829	17	units	unit	NOUN
m-1112	829	18	(	(	PUNCT
m-1112	829	19	second	second	ADJ
m-1112	829	20	)	)	PUNCT
m-1112	829	21	and	and	CCONJ
m-1112	829	22	the	the	DET
m-1112	829	23	length	length	NOUN
m-1112	829	24	units	unit	NOUN
m-1112	829	25	(	(	PUNCT
m-1112	829	26	meter	meter	NOUN
m-1112	829	27	=	=	SYM
m-1112	829	28	a.da	a.da	NOUN
m-1112	829	29	)	)	PUNCT
m-1112	829	30	or	or	CCONJ
m-1112	829	31	as	as	ADP
m-1112	829	32	c̅.	c̅.	NOUN
m-1112	829	33	rv	rv	NOUN
m-1112	829	34	=	=	SYM
m-1112	829	35	v̅.	v̅.	PROPN
m-1112	829	36	rc	rc	PROPN
m-1112	829	37	,	,	PUNCT
m-1112	829	38	→	→	SYM
m-1112	829	39	c̅	c̅	PROPN
m-1112	829	40	(	(	PUNCT
m-1112	829	41	v)(t/2π	v)(t/2π	PROPN
m-1112	829	42	)	)	PUNCT
m-1112	829	43	=	=	SYM
m-1112	829	44	v̅(c).(t/2π	v̅(c).(t/2π	PROPN
m-1112	829	45	)	)	PUNCT
m-1112	829	46	→	→	PUNCT
m-1112	829	47	c̅(v)/w	c̅(v)/w	PROPN
m-1112	829	48	=	=	SYM
m-1112	829	49	v̅(c	v̅(c	X
m-1112	829	50	)	)	PUNCT
m-1112	829	51	/	/	SYM
m-1112	830	1	w	w	NOUN
m-1112	830	2	,	,	PUNCT
m-1112	830	3	which	which	PRON
m-1112	830	4	is	be	AUX
m-1112	830	5	happening	happen	VERB
m-1112	830	6	with	with	ADP
m-1112	830	7	the	the	DET
m-1112	830	8	same	same	ADJ
m-1112	830	9	w	w	NOUN
m-1112	830	10	,	,	PUNCT
m-1112	830	11	without	without	ADP
m-1112	830	12	setting	set	VERB
m-1112	830	13	any	any	DET
m-1112	830	14	restrictions	restriction	NOUN
m-1112	830	15	,	,	PUNCT
m-1112	830	16	in	in	ADP
m-1112	830	17	contradiction	contradiction	NOUN
m-1112	830	18	to	to	ADP
m-1112	830	19	the	the	DET
m-1112	830	20	general	general	ADJ
m-1112	830	21	relativity	relativity	NOUN
m-1112	830	22	which	which	PRON
m-1112	830	23	is	be	AUX
m-1112	830	24	an	an	DET
m-1112	830	25	axiom	axiom	NOUN
m-1112	830	26	a	a	PRON
m-1112	830	27	priori	priori	ADV
m-1112	830	28	.	.	PUNCT
m-1112	831	1	additional	additional	ADJ
m-1112	831	2	,	,	PUNCT
m-1112	831	3	this	this	PRON
m-1112	831	4	is	be	AUX
m-1112	831	5	the	the	PRON
m-1112	831	6	why	why	SCONJ
m-1112	831	7	that	that	SCONJ
m-1112	831	8	the	the	DET
m-1112	831	9	conversion	conversion	NOUN
m-1112	831	10	factor	factor	NOUN
m-1112	831	11	,	,	PUNCT
m-1112	831	12	t	t	NOUN
m-1112	831	13	=	=	PUNCT
m-1112	831	14	time	time	NOUN
m-1112	831	15	,	,	PUNCT
m-1112	831	16	has	have	VERB
m-1112	831	17	not	not	PART
m-1112	831	18	any	any	DET
m-1112	831	19	essence	essence	NOUN
m-1112	831	20	in	in	ADP
m-1112	831	21	all	all	DET
m-1112	831	22	universe	universe	NOUN
m-1112	832	1	but	but	CCONJ
m-1112	832	2	it	it	PRON
m-1112	832	3	is	be	AUX
m-1112	832	4	only	only	ADV
m-1112	832	5	a	a	DET
m-1112	832	6	meter	meter	NOUN
m-1112	832	7	of	of	ADP
m-1112	832	8	changes	change	NOUN
m-1112	832	9	in	in	ADP
m-1112	832	10	all	all	DET
m-1112	832	11	relative	relative	ADJ
m-1112	832	12	systems	system	NOUN
m-1112	832	13	.	.	PUNCT
m-1112	833	1	stpl	stpl	ADJ
m-1112	833	2	mechanism	mechanism	NOUN
m-1112	833	3	is	be	AUX
m-1112	833	4	the	the	DET
m-1112	833	5	only	only	ADJ
m-1112	833	6	absolute	absolute	ADJ
m-1112	833	7	system	system	NOUN
m-1112	833	8	on	on	ADP
m-1112	833	9	which	which	PRON
m-1112	833	10	circularly	circularly	ADV
m-1112	833	11	exist	exist	VERB
m-1112	833	12	[	[	PUNCT
m-1112	833	13	⊕	⊕	PROPN
m-1112	833	14			PROPN
m-1112	833	15	⊝	⊝	NUM
m-1112	833	16	]	]	PUNCT
m-1112	833	17	,	,	PUNCT
m-1112	833	18	[	[	PUNCT
m-1112	833	19	⊝	⊝	CCONJ
m-1112	833	20			PROPN
m-1112	833	21	⊕	⊕	PROPN
m-1112	833	22	]	]	PUNCT
m-1112	833	23	,	,	PUNCT
m-1112	833	24	[	[	PUNCT
m-1112	833	25	⊕	⊕	NOUN
m-1112	833	26	⊝	⊝	PUNCT
m-1112	833	27			PROPN
m-1112	833	28	]	]	PUNCT
m-1112	833	29	,	,	PUNCT
m-1112	833	30	the	the	DET
m-1112	833	31	three	three	NUM
m-1112	833	32	constituents	constituent	NOUN
m-1112	833	33	,	,	PUNCT
m-1112	833	34	[	[	PUNCT
m-1112	833	35	⊕	⊕	NOUN
m-1112	833	36			PROPN
m-1112	833	37	⊝	⊝	NUM
m-1112	833	38	]	]	PUNCT
m-1112	833	39	,	,	PUNCT
m-1112	833	40	and	and	CCONJ
m-1112	833	41	originates	originate	VERB
m-1112	833	42	this	this	DET
m-1112	833	43	existing	exist	VERB
m-1112	833	44	objective	objective	ADJ
m-1112	833	45	cosmos	cosmos	NOUN
m-1112	833	46	.	.	PUNCT
m-1112	834	1	this	this	DET
m-1112	834	2	circularity	circularity	NOUN
m-1112	834	3	of	of	ADP
m-1112	834	4	the	the	DET
m-1112	834	5	constitutes	constitute	NOUN
m-1112	834	6	exist	exist	VERB
m-1112	834	7	because	because	SCONJ
m-1112	834	8	of	of	ADP
m-1112	834	9	their	their	PRON
m-1112	834	10	natural	natural	ADJ
m-1112	834	11	frequency	frequency	NOUN
m-1112	834	12	of	of	ADP
m-1112	834	13	vibrations	vibration	NOUN
m-1112	834	14	.	.	PUNCT
m-1112	835	1	because	because	SCONJ
m-1112	835	2	[	[	X
m-1112	835	3	stpl	stpl	X
m-1112	835	4	]	]	X
m-1112	835	5	line	line	NOUN
m-1112	835	6	of	of	ADP
m-1112	835	7	the	the	DET
m-1112	835	8	fixed	fix	VERB
m-1112	835	9	frame	frame	NOUN
m-1112	835	10	becomes	become	VERB
m-1112	835	11	from	from	ADP
m-1112	835	12	this	this	DET
m-1112	835	13	system	system	NOUN
m-1112	835	14	[	[	X
m-1112	835	15	a	a	X
m-1112	835	16	]	]	X
m-1112	835	17	,	,	PUNCT
m-1112	835	18	then	then	ADV
m-1112	835	19	this	this	DET
m-1112	835	20	relative	relative	ADJ
m-1112	835	21	frame	frame	NOUN
m-1112	835	22	[	[	X
m-1112	835	23	r	r	X
m-1112	835	24	}	}	PUNCT
m-1112	835	25	is	be	AUX
m-1112	835	26	common	common	ADJ
m-1112	835	27	to	to	ADP
m-1112	835	28	the	the	DET
m-1112	835	29	fixed	fix	VERB
m-1112	835	30	one	one	NOUN
m-1112	835	31	(	(	PUNCT
m-1112	835	32	common	common	ADJ
m-1112	835	33	da	da	NOUN
m-1112	835	34	)	)	PUNCT
m-1112	835	35	and	and	CCONJ
m-1112	835	36	let	let	VERB
m-1112	835	37	it	it	PRON
m-1112	835	38	be	be	AUX
m-1112	835	39	[	[	X
m-1112	835	40	r	r	X
m-1112	835	41	]	]	X
m-1112	835	42	≡	≡	PROPN
m-1112	835	43	(	(	PUNCT
m-1112	835	44	x	x	X
m-1112	835	45	'	'	PUNCT
m-1112	835	46	,	,	PUNCT
m-1112	835	47	y	y	PROPN
m-1112	835	48	'	'	PUNCT
m-1112	835	49	,	,	PUNCT
m-1112	835	50	z	z	X
m-1112	835	51	'	'	PUNCT
m-1112	835	52	,	,	PUNCT
m-1112	835	53	t	t	PROPN
m-1112	835	54	'	'	PUNCT
m-1112	835	55	)	)	PUNCT
m-1112	835	56	.	.	PUNCT
m-1112	836	1	from	from	ADP
m-1112	836	2	figure	figure	NOUN
m-1112	836	3	,	,	PUNCT
m-1112	836	4	sin	sin	NOUN
m-1112	836	5	φ	φ	PROPN
m-1112	836	6	=	=	SYM
m-1112	836	7	(	(	PUNCT
m-1112	836	8	�	�	NOUN
m-1112	836	9	̅	̅	NOUN
m-1112	836	10	�	�	PROPN
m-1112	836	11	/	/	SYM
m-1112	836	12	�	�	PROPN
m-1112	836	13	̅	̅	NOUN
m-1112	836	14	�	�	NOUN
m-1112	836	15	)	)	PUNCT
m-1112	836	16	,	,	PUNCT
m-1112	836	17	meaning	mean	VERB
m-1112	836	18	that	that	SCONJ
m-1112	836	19	the	the	DET
m-1112	836	20	relative	relative	ADJ
m-1112	836	21	system	system	NOUN
m-1112	836	22	,	,	PUNCT
m-1112	836	23	[	[	X
m-1112	836	24	r	r	X
m-1112	836	25	]	]	X
m-1112	836	26	≡	≡	PROPN
m-1112	836	27	(	(	PUNCT
m-1112	836	28	x	x	X
m-1112	836	29	'	'	PUNCT
m-1112	836	30	,	,	PUNCT
m-1112	836	31	y	y	PROPN
m-1112	836	32	'	'	PUNCT
m-1112	836	33	,	,	PUNCT
m-1112	836	34	z	z	X
m-1112	836	35	'	'	X
m-1112	836	36	,	,	PUNCT
m-1112	836	37	t	t	PROPN
m-1112	836	38	'	'	PUNCT
m-1112	836	39	)	)	PUNCT
m-1112	836	40	,	,	PUNCT
m-1112	836	41	(	(	PUNCT
m-1112	836	42	the	the	DET
m-1112	836	43	affine	affine	NOUN
m-1112	836	44	frame	frame	NOUN
m-1112	836	45	)	)	PUNCT
m-1112	836	46	is	be	AUX
m-1112	836	47	the	the	DET
m-1112	836	48	projection	projection	NOUN
m-1112	836	49	of	of	ADP
m-1112	836	50	absolute	absolute	ADJ
m-1112	836	51	frame	frame	NOUN
m-1112	837	1	[	[	X
m-1112	837	2	a	a	X
m-1112	837	3	]	]	X
m-1112	837	4	≡	≡	PROPN
m-1112	837	5	{	{	PUNCT
m-1112	837	6	da	da	PROPN
m-1112	837	7	-	-	ADJ
m-1112	837	8	o	o	NOUN
m-1112	837	9	}	}	PUNCT
m-1112	837	10	(	(	PUNCT
m-1112	837	11	x	x	X
m-1112	837	12	,	,	PUNCT
m-1112	837	13	y	y	PROPN
m-1112	837	14	,	,	PUNCT
m-1112	837	15	z	z	PROPN
m-1112	837	16	,	,	PUNCT
m-1112	837	17	t	t	PROPN
m-1112	837	18	)	)	PUNCT
m-1112	837	19	where	where	SCONJ
m-1112	837	20	exists	exist	VERB
m-1112	837	21	as	as	ADP
m-1112	837	22	the	the	DET
m-1112	837	23	simultaneity	simultaneity	NOUN
m-1112	837	24	for	for	ADP
m-1112	837	25	all	all	DET
m-1112	837	26	motions	motion	NOUN
m-1112	837	27	where	where	SCONJ
m-1112	837	28	issues	issue	NOUN
m-1112	837	29	,	,	PUNCT
m-1112	837	30	[	[	X
m-1112	837	31	r	r	X
m-1112	837	32	]	]	X
m-1112	837	33	≡	≡	PROPN
m-1112	837	34	{	{	PUNCT
m-1112	837	35	daa	daa	PROPN
m-1112	837	36	}	}	PUNCT
m-1112	837	37	≡	≡	PROPN
m-1112	837	38	[	[	PUNCT
m-1112	837	39	(	(	PUNCT
m-1112	837	40	x	x	X
m-1112	837	41	'	'	PUNCT
m-1112	837	42	,	,	PUNCT
m-1112	837	43	y	y	PROPN
m-1112	837	44	'	'	PUNCT
m-1112	837	45	,	,	PUNCT
m-1112	837	46	z	z	X
m-1112	837	47	'	'	PUNCT
m-1112	837	48	,	,	PUNCT
m-1112	837	49	t	t	PROPN
m-1112	837	50	'	'	PUNCT
m-1112	837	51	)	)	PUNCT
m-1112	837	52	]	]	PUNCT
m-1112	837	53	,	,	PUNCT
m-1112	838	1	[	[	X
m-1112	838	2	a	a	X
m-1112	838	3	]	]	X
m-1112	838	4	≡	≡	PROPN
m-1112	838	5	{	{	PUNCT
m-1112	838	6	dao	dao	PROPN
m-1112	838	7	}	}	PUNCT
m-1112	838	8	≡	≡	PROPN
m-1112	838	9	(	(	PUNCT
m-1112	838	10	x	x	INTJ
m-1112	838	11	,	,	PUNCT
m-1112	838	12	y	y	PROPN
m-1112	838	13	,	,	PUNCT
m-1112	838	14	z	z	PROPN
m-1112	838	15	,	,	PUNCT
m-1112	838	16	t	t	PROPN
m-1112	838	17	)	)	PUNCT
m-1112	838	18	=	=	PUNCT
m-1112	839	1	[	[	X
m-1112	839	2	r	r	X
m-1112	839	3	]	]	PUNCT
m-1112	839	4	.γ	.γ	PUNCT
m-1112	839	5	≡	≡	PROPN
m-1112	839	6	(	(	PUNCT
m-1112	839	7	x	x	X
m-1112	839	8	'	'	PUNCT
m-1112	839	9	,	,	PUNCT
m-1112	839	10	y	y	PROPN
m-1112	839	11	'	'	PUNCT
m-1112	839	12	,	,	PUNCT
m-1112	839	13	z	z	X
m-1112	839	14	'	'	X
m-1112	839	15	,	,	PUNCT
m-1112	839	16	t	t	PROPN
m-1112	839	17	'	'	PUNCT
m-1112	839	18	)	)	PUNCT
m-1112	839	19	.	.	PUNCT
m-1112	840	1	γ	γ	X
m-1112	840	2	considering	consider	VERB
m-1112	840	3	point	point	NOUN
m-1112	840	4	da	da	NOUN
m-1112	840	5	as	as	ADP
m-1112	840	6	the	the	DET
m-1112	840	7	common	common	ADJ
m-1112	840	8	center	center	NOUN
m-1112	840	9	and	and	CCONJ
m-1112	840	10	[	[	X
m-1112	840	11	stpl	stpl	X
m-1112	840	12	]	]	X
m-1112	840	13	as	as	ADP
m-1112	840	14	the	the	DET
m-1112	840	15	x	x	ADJ
m-1112	840	16	-	-	PUNCT
m-1112	840	17	x	x	ADJ
m-1112	840	18	axis	axis	NOUN
m-1112	840	19	of	of	ADP
m-1112	840	20	the	the	DET
m-1112	840	21	two	two	NUM
m-1112	840	22	systems	system	NOUN
m-1112	840	23	,	,	PUNCT
m-1112	840	24	then	then	ADV
m-1112	840	25	becomes	become	VERB
m-1112	840	26	da	da	NOUN
m-1112	840	27	(	(	PUNCT
m-1112	840	28	x	x	X
m-1112	840	29	,	,	PUNCT
m-1112	840	30	y	y	PROPN
m-1112	840	31	=	=	PROPN
m-1112	840	32	y	y	PROPN
m-1112	840	33	'	'	PUNCT
m-1112	840	34	,	,	PUNCT
m-1112	840	35	z	z	PROPN
m-1112	840	36	=	=	PUNCT
m-1112	840	37	z	z	NOUN
m-1112	840	38	'	'	NUM
m-1112	840	39	,	,	PUNCT
m-1112	840	40	t	t	PROPN
m-1112	840	41	)	)	PUNCT
m-1112	840	42	and	and	CCONJ
m-1112	840	43	for	for	ADP
m-1112	840	44	all	all	DET
m-1112	840	45	linear	linear	PROPN
m-1112	840	46	systems	system	NOUN
m-1112	840	47	da	da	X
m-1112	840	48	(	(	PUNCT
m-1112	840	49	x	x	X
m-1112	840	50	'	'	NUM
m-1112	840	51	,	,	PUNCT
m-1112	840	52	y'=	y'=	NUM
m-1112	840	53	y	y	PROPN
m-1112	840	54	,	,	PUNCT
m-1112	840	55	z	z	NOUN
m-1112	840	56	'	'	NOUN
m-1112	840	57	=	=	SYM
m-1112	840	58	z	z	PROPN
m-1112	840	59	,	,	PUNCT
m-1112	840	60	t	t	PROPN
m-1112	840	61	'	'	PUNCT
m-1112	840	62	)	)	PUNCT
m-1112	840	63	this	this	DET
m-1112	840	64	specific	specific	ADJ
m-1112	840	65	state	state	NOUN
m-1112	840	66	of	of	ADP
m-1112	840	67	constancy	constancy	NOUN
m-1112	840	68	,	,	PUNCT
m-1112	840	69	i.e.	i.e.	X
m-1112	840	70	,	,	PUNCT
m-1112	840	71	the	the	DET
m-1112	840	72	centrifugal	centrifugal	ADJ
m-1112	840	73	velocity	velocity	NOUN
m-1112	840	74	of	of	ADP
m-1112	840	75	absolute	absolute	ADJ
m-1112	840	76	system	system	NOUN
m-1112	840	77	[	[	X
m-1112	840	78	a	a	X
m-1112	840	79	]	]	X
m-1112	840	80	to	to	PART
m-1112	840	81	be	be	AUX
m-1112	840	82	a	a	DET
m-1112	840	83	constant	constant	ADJ
m-1112	840	84	c̅	c̅	NOUN
m-1112	840	85	,	,	PUNCT
m-1112	840	86	and	and	CCONJ
m-1112	840	87	the	the	DET
m-1112	840	88	rectilinear	rectilinear	ADJ
m-1112	840	89	motion	motion	NOUN
m-1112	840	90	with	with	ADP
m-1112	840	91	respect	respect	NOUN
m-1112	840	92	to	to	ADP
m-1112	840	93	one	one	NUM
m-1112	840	94	another	another	DET
m-1112	840	95	defines	define	VERB
m-1112	840	96	the	the	DET
m-1112	840	97	natural	natural	ADJ
m-1112	840	98	inertial	inertial	NOUN
m-1112	840	99	frames	frame	NOUN
m-1112	840	100	,	,	PUNCT
m-1112	840	101	and	and	CCONJ
m-1112	840	102	because	because	SCONJ
m-1112	840	103	of	of	ADP
m-1112	840	104	uniformity	uniformity	NOUN
m-1112	840	105	of	of	ADP
m-1112	840	106	space	space	NOUN
m-1112	840	107	and	and	CCONJ
m-1112	840	108	motion	motion	NOUN
m-1112	840	109	,	,	PUNCT
m-1112	840	110	therefore	therefore	ADV
m-1112	840	111	occupies	occupy	VERB
m-1112	840	112	the	the	DET
m-1112	840	113	same	same	ADJ
m-1112	840	114	meter	meter	NOUN
m-1112	840	115	for	for	ADP
m-1112	840	116	their	their	PRON
m-1112	840	117	changes	change	NOUN
m-1112	840	118	,	,	PUNCT
m-1112	840	119	(	(	PUNCT
m-1112	840	120	i.e.	i.e.	X
m-1112	840	121	the	the	DET
m-1112	840	122	time	time	NOUN
m-1112	840	123	)	)	PUNCT
m-1112	840	124	.	.	PUNCT
m-1112	841	1	since	since	SCONJ
m-1112	841	2	also	also	ADV
m-1112	841	3	points	point	VERB
m-1112	841	4	o	o	NOUN
m-1112	841	5	,	,	PUNCT
m-1112	841	6	a	a	DET
m-1112	841	7	remove	remove	NOUN
m-1112	841	8	to	to	PART
m-1112	841	9	point	point	VERB
m-1112	841	10	da	da	PROPN
m-1112	841	11	isochrones	isochrone	NOUN
m-1112	841	12	by	by	ADP
m-1112	841	13	their	their	PRON
m-1112	841	14	intrinsic	intrinsic	ADJ
m-1112	841	15	property	property	NOUN
m-1112	841	16	motion	motion	NOUN
m-1112	841	17	which	which	PRON
m-1112	841	18	are	be	AUX
m-1112	841	19	→	→	PUNCT
m-1112	841	20	their	their	PRON
m-1112	841	21	wavelengths	wavelength	NOUN
m-1112	841	22	are	be	AUX
m-1112	841	23	a	a	DET
m-1112	841	24	stationary	stationary	ADJ
m-1112	841	25	wave	wave	NOUN
m-1112	841	26	in	in	ADP
m-1112	841	27	cycloid	cycloid	PROPN
m-1112	841	28	←	←	PROPN
m-1112	841	29	following	follow	VERB
m-1112	841	30	lorentz`s	lorentz`s	DET
m-1112	841	31	factor	factor	NOUN
m-1112	841	32	γ	γ	PROPN
m-1112	841	33	,	,	PUNCT
m-1112	841	34	then	then	ADV
m-1112	841	35	this	this	DET
m-1112	841	36	following	follow	VERB
m-1112	841	37	happens	happen	VERB
m-1112	841	38	also	also	ADV
m-1112	841	39	to	to	ADP
m-1112	841	40	all	all	DET
m-1112	841	41	frames	frame	NOUN
m-1112	841	42	which	which	PRON
m-1112	841	43	make	make	VERB
m-1112	841	44	this	this	DET
m-1112	841	45	motion	motion	NOUN
m-1112	841	46	,	,	PUNCT
m-1112	841	47	and	and	CCONJ
m-1112	841	48	so	so	ADV
m-1112	841	49	issues	issue	NOUN
m-1112	841	50	for	for	ADP
m-1112	841	51	all	all	DET
m-1112	841	52	the	the	DET
m-1112	841	53	system	system	NOUN
m-1112	841	54	relations	relation	NOUN
m-1112	841	55	{	{	PUNCT
m-1112	841	56	da	da	X
m-1112	841	57	–	–	PUNCT
m-1112	841	58	o	o	NOUN
m-1112	841	59	}	}	PUNCT
m-1112	841	60	=	=	SYM
m-1112	841	61	γ	γ	X
m-1112	841	62	.	.	PUNCT
m-1112	841	63	{	{	PUNCT
m-1112	842	1	da	da	INTJ
m-1112	842	2	–	–	PUNCT
m-1112	842	3	a	a	PRON
m-1112	842	4	}	}	PUNCT
m-1112	842	5	.	.	PUNCT
m-1112	843	1	fig-6	fig-6	NOUN
m-1112	843	2	on	on	ADP
m-1112	843	3	this	this	DET
m-1112	843	4	relative	relative	ADJ
m-1112	843	5	system	system	NOUN
m-1112	843	6	da	da	X
m-1112	843	7	(	(	PUNCT
m-1112	843	8	x	x	NOUN
m-1112	843	9	'	'	X
m-1112	843	10	,	,	PUNCT
m-1112	843	11	y	y	PROPN
m-1112	843	12	'	'	PUNCT
m-1112	843	13	=	=	SYM
m-1112	843	14	y	y	PROPN
m-1112	843	15	,	,	PUNCT
m-1112	843	16	z	z	NOUN
m-1112	843	17	'	'	PUNCT
m-1112	843	18	=	=	ADJ
m-1112	843	19	z	z	PROPN
m-1112	843	20	,	,	PUNCT
m-1112	843	21	t	t	PROPN
m-1112	843	22	`	`	PUNCT
m-1112	843	23	)	)	PUNCT
m-1112	843	24	are	be	AUX
m-1112	843	25	conveyed	convey	VERB
m-1112	843	26	,	,	PUNCT
m-1112	843	27	the	the	DET
m-1112	843	28	breakages	breakage	NOUN
m-1112	843	29	[	[	PUNCT
m-1112	843	30	±	±	NOUN
m-1112	843	31	(	(	PUNCT
m-1112	843	32	wr)²	wr)²	PROPN
m-1112	843	33	,	,	PUNCT
m-1112	843	34	2(wr)²	2(wr)²	NOUN
m-1112	843	35	]	]	PUNCT
m-1112	843	36	of	of	ADP
m-1112	843	37	(	(	PUNCT
m-1112	843	38	o	o	NOUN
m-1112	843	39	,	,	PUNCT
m-1112	843	40	oa	oa	PROPN
m-1112	843	41	)	)	PUNCT
m-1112	843	42	circle	circle	NOUN
m-1112	843	43	after	after	ADP
m-1112	843	44	the	the	DET
m-1112	843	45	colliding	colliding	NOUN
m-1112	843	46	with	with	ADP
m-1112	843	47	the	the	DET
m-1112	843	48	rotating	rotate	VERB
m-1112	843	49	velocity	velocity	NOUN
m-1112	843	50	v̅	v̅	NOUN
m-1112	844	1	=	=	SYM
m-1112	844	2	w̅.r	w̅.r	PRON
m-1112	844	3	of	of	ADP
m-1112	844	4	the	the	DET
m-1112	844	5	[	[	X
m-1112	844	6	a	a	X
m-1112	844	7	]	]	X
m-1112	844	8	system	system	NOUN
m-1112	844	9	,	,	PUNCT
m-1112	844	10	and	and	CCONJ
m-1112	844	11	are	be	AUX
m-1112	844	12	the	the	DET
m-1112	844	13	fundamental	fundamental	ADJ
m-1112	844	14	particles	particle	NOUN
m-1112	844	15	,	,	PUNCT
m-1112	844	16	fermions	fermion	NOUN
m-1112	844	17	and	and	CCONJ
m-1112	844	18	bosons	boson	NOUN
m-1112	844	19	,	,	PUNCT
m-1112	844	20	or	or	CCONJ
m-1112	844	21	by	by	ADP
m-1112	844	22	escaping	escape	VERB
m-1112	844	23	consisting	consist	VERB
m-1112	844	24	the	the	DET
m-1112	844	25	rest	rest	NOUN
m-1112	844	26	field	field	NOUN
m-1112	844	27	and	and	CCONJ
m-1112	844	28	gravity	gravity	NOUN
m-1112	844	29	,	,	PUNCT
m-1112	844	30	or	or	CCONJ
m-1112	844	31	dark	dark	ADJ
m-1112	844	32	matter	matter	NOUN
m-1112	844	33	and	and	CCONJ
m-1112	844	34	dark	dark	ADJ
m-1112	844	35	energy	energy	NOUN
m-1112	844	36	as	as	ADP
m-1112	844	37	analytically	analytically	ADV
m-1112	844	38	was	be	AUX
m-1112	844	39	shown	show	VERB
m-1112	844	40	.[39	.[39	NOUN
m-1112	844	41	]	]	X
m-1112	844	42	ijo	ijo	PROPN
m-1112	844	43	international	international	PROPN
m-1112	844	44	journal	journal	PROPN
m-1112	844	45	of	of	ADP
m-1112	844	46	mathematics	mathematics	PROPN
m-1112	844	47	(	(	PUNCT
m-1112	844	48	issn	issn	PROPN
m-1112	844	49	:	:	PUNCT
m-1112	844	50	2992	2992	NUM
m-1112	844	51	-	-	SYM
m-1112	844	52	4421	4421	NUM
m-1112	844	53	)	)	PUNCT
m-1112	845	1	volume	volume	NOUN
m-1112	845	2	08	08	NUM
m-1112	846	1	|	|	ADV
m-1112	846	2	issue	issue	NOUN
m-1112	846	3	08	08	NUM
m-1112	847	1	|	|	ADV
m-1112	847	2	august	august	PROPN
m-1112	847	3	2025	2025	NUM
m-1112	847	4	|	|	ADV
m-1112	847	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	847	6	ijo	ijo	PROPN
m-1112	847	7	journals	journal	NOUN
m-1112	847	8	29	29	NUM
m-1112	847	9	the	the	DET
m-1112	847	10	fundamental	fundamental	ADJ
m-1112	847	11	particles	particle	NOUN
m-1112	847	12	origination	origination	NOUN
m-1112	847	13	mechanism	mechanism	NOUN
m-1112	847	14	in	in	ADP
m-1112	847	15	mfmf	mfmf	PROPN
m-1112	847	16	pns	pns	PROPN
m-1112	847	17	caves	cave	NOUN
m-1112	847	18	.	.	PUNCT
m-1112	848	1	the	the	DET
m-1112	848	2	angular	angular	ADJ
m-1112	848	3	-	-	PUNCT
m-1112	848	4	momentum	momentum	NOUN
m-1112	848	5	ellipsoid	ellipsoid	NOUN
m-1112	848	6	nibs	nibs	NOUN
m-1112	848	7	on	on	ADP
m-1112	848	8	→	→	NOUN
m-1112	848	9	{	{	PUNCT
m-1112	848	10	herpolhode	herpolhode	ADJ
m-1112	848	11	and	and	CCONJ
m-1112	848	12	polhode	polhode	NOUN
m-1112	848	13	ellipsoids	ellipsoid	NOUN
m-1112	848	14	}	}	PUNCT
m-1112	848	15	.	.	PUNCT
m-1112	849	1	in	in	ADP
m-1112	849	2	any	any	DET
m-1112	849	3	rotational	rotational	ADJ
m-1112	849	4	motion	motion	NOUN
m-1112	849	5	,	,	PUNCT
m-1112	849	6	b̅xw̅	b̅xw̅	NOUN
m-1112	849	7	are	be	AUX
m-1112	849	8	constants	constant	NOUN
m-1112	849	9	and	and	CCONJ
m-1112	849	10	the	the	DET
m-1112	849	11	angular	angular	ADJ
m-1112	849	12	-	-	PUNCT
m-1112	849	13	velocity	velocity	NOUN
m-1112	849	14	-	-	PUNCT
m-1112	849	15	vector	vector	NOUN
m-1112	849	16	�	�	PROPN
m-1112	849	17	̅	̅	NOUN
m-1112	849	18	�	�	PROPN
m-1112	849	19	,	,	PUNCT
m-1112	849	20	describes	describe	VERB
m-1112	849	21	the	the	DET
m-1112	849	22	ellipsoid	ellipsoid	NOUN
m-1112	849	23	of	of	ADP
m-1112	849	24	angular	angular	ADJ
m-1112	849	25	velocity	velocity	NOUN
m-1112	849	26	and	and	CCONJ
m-1112	849	27	its	its	PRON
m-1112	849	28	nib	nib	NOUN
m-1112	849	29	describes	describe	VERB
m-1112	849	30	a	a	DET
m-1112	849	31	cone	cone	NOUN
m-1112	849	32	of	of	ADP
m-1112	849	33	which	which	DET
m-1112	849	34	plane	plane	NOUN
m-1112	849	35	-	-	PUNCT
m-1112	849	36	base	base	NOUN
m-1112	849	37	is	be	AUX
m-1112	849	38	fixed	fix	VERB
m-1112	849	39	.	.	PUNCT
m-1112	850	1	simultaneously	simultaneously	ADV
m-1112	850	2	.the	.the	PRON
m-1112	850	3	angular	angular	ADJ
m-1112	850	4	-	-	PUNCT
m-1112	850	5	momentum	momentum	NOUN
m-1112	850	6	�	�	NOUN
m-1112	850	7	̅	̅	NOUN
m-1112	850	8	�	�	NOUN
m-1112	850	9	describes	describe	VERB
m-1112	850	10	the	the	DET
m-1112	850	11	ellipsoid	ellipsoid	NOUN
m-1112	850	12	of	of	ADP
m-1112	850	13	angular	angular	ADJ
m-1112	850	14	momentum	momentum	NOUN
m-1112	850	15	and	and	CCONJ
m-1112	850	16	its	its	PRON
m-1112	850	17	nib	nib	NOUN
m-1112	850	18	describes	describe	VERB
m-1112	850	19	a	a	DET
m-1112	850	20	cone	cone	NOUN
m-1112	850	21	also	also	ADV
m-1112	850	22	of	of	ADP
m-1112	850	23	which	which	DET
m-1112	850	24	plane	plane	NOUN
m-1112	850	25	-	-	PUNCT
m-1112	850	26	base	base	NOUN
m-1112	850	27	is	be	AUX
m-1112	850	28	also	also	ADV
m-1112	850	29	fixed	fix	VERB
m-1112	850	30	.	.	PUNCT
m-1112	851	1	the	the	DET
m-1112	851	2	nib	nib	NOUN
m-1112	851	3	of	of	ADP
m-1112	851	4	angular	angular	ADJ
m-1112	851	5	velocity	velocity	NOUN
m-1112	851	6	-	-	PUNCT
m-1112	851	7	vector	vector	NOUN
m-1112	851	8	,	,	PUNCT
m-1112	851	9	�	�	PROPN
m-1112	851	10	̅	̅	NOUN
m-1112	851	11	�	�	PROPN
m-1112	851	12	,	,	PUNCT
m-1112	851	13	describes	describe	VERB
m-1112	851	14	on	on	ADP
m-1112	851	15	the	the	DET
m-1112	851	16	tangential	tangential	ADJ
m-1112	851	17	-	-	PUNCT
m-1112	851	18	plane	plane	NOUN
m-1112	851	19	of	of	ADP
m-1112	851	20	the	the	DET
m-1112	851	21	angular	angular	ADJ
m-1112	851	22	-	-	PUNCT
m-1112	851	23	momentum	momentum	NOUN
m-1112	851	24	ellipsoid	ellipsoid	NOUN
m-1112	851	25	,	,	PUNCT
m-1112	851	26	the	the	DET
m-1112	851	27	polhode	polhode	NOUN
m-1112	851	28	,	,	PUNCT
m-1112	851	29	while	while	SCONJ
m-1112	851	30	the	the	DET
m-1112	851	31	nib	nib	NOUN
m-1112	851	32	of	of	ADP
m-1112	851	33	angular	angular	ADJ
m-1112	851	34	-	-	PUNCT
m-1112	851	35	momentum	momentum	NOUN
m-1112	851	36	�	�	NOUN
m-1112	851	37	̅	̅	NOUN
m-1112	851	38	�	�	PROPN
m-1112	851	39	,	,	PUNCT
m-1112	851	40	describes	describe	VERB
m-1112	851	41	on	on	ADP
m-1112	851	42	the	the	DET
m-1112	851	43	tangential	tangential	ADJ
m-1112	851	44	-	-	PUNCT
m-1112	851	45	plane	plane	NOUN
m-1112	851	46	,	,	PUNCT
m-1112	851	47	of	of	ADP
m-1112	851	48	the	the	DET
m-1112	851	49	angular	angular	ADJ
m-1112	851	50	–	–	PUNCT
m-1112	851	51	velocity	velocity	NOUN
m-1112	851	52	ellipsoid	ellipsoid	NOUN
m-1112	851	53	,	,	PUNCT
m-1112	851	54	the	the	DET
m-1112	851	55	herpolhode	herpolhode	ADJ
m-1112	851	56	.	.	PUNCT
m-1112	852	1	or	or	CCONJ
m-1112	852	2	the	the	DET
m-1112	852	3	fixed	fix	VERB
m-1112	852	4	tangential	tangential	ADJ
m-1112	852	5	-	-	PUNCT
m-1112	852	6	planes	plane	NOUN
m-1112	852	7	on	on	ADP
m-1112	852	8	�	�	NOUN
m-1112	852	9	̅	̅	NOUN
m-1112	852	10	�	�	PROPN
m-1112	852	11	,	,	PUNCT
m-1112	852	12	�	�	NOUN
m-1112	852	13	̅	̅	NOUN
m-1112	852	14	�	�	NOUN
m-1112	852	15	nibs	nib	NOUN
m-1112	852	16	which	which	PRON
m-1112	852	17	are	be	AUX
m-1112	852	18	alternately	alternately	ADV
m-1112	852	19	perpendicular	perpendicular	ADJ
m-1112	852	20	to	to	ADP
m-1112	852	21	b̅	b̅	VERB
m-1112	852	22	,	,	PUNCT
m-1112	852	23	and	and	CCONJ
m-1112	852	24	w̅	w̅	PROPN
m-1112	852	25	,	,	PUNCT
m-1112	852	26	common	common	ADJ
m-1112	852	27	central	central	ADJ
m-1112	852	28	axes	axis	NOUN
m-1112	852	29	of	of	ADP
m-1112	852	30	rotation	rotation	NOUN
m-1112	852	31	,	,	PUNCT
m-1112	852	32	or	or	CCONJ
m-1112	852	33	the	the	DET
m-1112	852	34	angular	angular	ADJ
m-1112	852	35	-	-	PUNCT
m-1112	852	36	momentum	momentum	NOUN
m-1112	852	37	ellipsoid	ellipsoid	NOUN
m-1112	852	38	nibs	nibs	NOUN
m-1112	852	39	,	,	PUNCT
m-1112	852	40	in	in	ADP
m-1112	852	41	herpolhode	herpolhode	PROPN
m-1112	852	42	and	and	CCONJ
m-1112	852	43	on	on	ADP
m-1112	852	44	polhode	polhode	NOUN
m-1112	852	45	ellipsoids	ellipsoid	NOUN
m-1112	852	46	as	as	ADP
m-1112	852	47	→	→	SYM
m-1112	852	48	electro	electro	VERB
m-1112	852	49	magnetic	magnetic	ADJ
m-1112	852	50	fields	field	NOUN
m-1112	852	51	←	←	PROPN
m-1112	852	52	and	and	CCONJ
m-1112	852	53	which	which	PRON
m-1112	852	54	are	be	AUX
m-1112	852	55	space	space	NOUN
m-1112	852	56	-	-	PUNCT
m-1112	852	57	energy	energy	NOUN
m-1112	852	58	cpt	cpt	NOUN
m-1112	852	59	invariants	invariant	NOUN
m-1112	852	60	.	.	PUNCT
m-1112	853	1	the	the	DET
m-1112	853	2	moving	move	VERB
m-1112	853	3	energy	energy	NOUN
m-1112	853	4	-	-	PUNCT
m-1112	853	5	vector	vector	NOUN
m-1112	853	6	is	be	AUX
m-1112	853	7	|⊕	|⊕	NUM
m-1112	853	8	𝐐	𝐐	PROPN
m-1112	853	9	⇈	⇈	PROPN
m-1112	853	10	aka⃗⃗	aka⃗⃗	PROPN
m-1112	853	11	⃗⃗	⃗⃗	PROPN
m-1112	853	12	⃗⃗	⃗⃗	PROPN
m-1112	853	13	⃗⃗	⃗⃗	PROPN
m-1112	853	14	⃗	⃗	PROPN
m-1112	854	1	|	|	NOUN
m-1112	854	2	=	=	PUNCT
m-1112	854	3	|	|	NOUN
m-1112	854	4	↕	↕	PROPN
m-1112	854	5	|	|	PROPN
m-1112	854	6	→	→	PUNCT
m-1112	854	7	{	{	PUNCT
m-1112	854	8	the	the	DET
m-1112	854	9	electron	electron	NOUN
m-1112	854	10	-	-	PUNCT
m-1112	854	11	unit	unit	NOUN
m-1112	854	12	-	-	PUNCT
m-1112	854	13	charge	charge	NOUN
m-1112	854	14	}	}	PUNCT
m-1112	854	15	,	,	PUNCT
m-1112	854	16	and	and	CCONJ
m-1112	854	17	since	since	SCONJ
m-1112	854	18	charges	charge	NOUN
m-1112	854	19	correspond	correspond	VERB
m-1112	854	20	to	to	ADP
m-1112	854	21	the	the	DET
m-1112	854	22	3	3	NUM
m-1112	854	23	-	-	PUNCT
m-1112	854	24	phase	phase	NOUN
m-1112	854	25	rotors	rotor	NOUN
m-1112	854	26	is	be	AUX
m-1112	854	27	,	,	PUNCT
m-1112	854	28	the	the	DET
m-1112	854	29	unit	unit	NOUN
m-1112	854	30	-	-	PUNCT
m-1112	854	31	charge	charge	NOUN
m-1112	854	32	complex	complex	ADJ
m-1112	854	33	-	-	PUNCT
m-1112	854	34	vector	vector	NOUN
m-1112	854	35	.	.	PUNCT
m-1112	855	1	remarks	remark	NOUN
m-1112	855	2	:	:	PUNCT
m-1112	855	3	material	material	NOUN
m-1112	855	4	point	point	NOUN
m-1112	855	5	a	a	DET
m-1112	855	6	≡	≡	PROPN
m-1112	855	7	±	±	NOUN
m-1112	855	8	|(w̅.r)²|	|(w̅.r)²|	NOUN
m-1112	855	9	of	of	ADP
m-1112	855	10	the	the	DET
m-1112	855	11	fixed	fix	VERB
m-1112	855	12	system	system	NOUN
m-1112	855	13	{	{	PUNCT
m-1112	855	14	dao	dao	AUX
m-1112	855	15	}	}	PUNCT
m-1112	855	16	travels	travel	VERB
m-1112	855	17	with	with	ADP
m-1112	855	18	velocity	velocity	NOUN
m-1112	855	19	v̅	v̅	NOUN
m-1112	855	20	at	at	ADP
m-1112	855	21	point	point	NOUN
m-1112	855	22	da	da	INTJ
m-1112	855	23	,	,	PUNCT
m-1112	855	24	so	so	ADV
m-1112	855	25	geometrical	geometrical	ADJ
m-1112	855	26	distance	distance	NOUN
m-1112	855	27	a.da	a.da	VERB
m-1112	855	28	in	in	ADP
m-1112	855	29	the	the	DET
m-1112	855	30	relative	relative	ADJ
m-1112	855	31	system	system	NOUN
m-1112	856	1	[	[	X
m-1112	856	2	r	r	X
m-1112	856	3	]	]	X
m-1112	856	4	≡	≡	PROPN
m-1112	856	5	{	{	PUNCT
m-1112	856	6	dapa	dapa	PROPN
m-1112	856	7	}	}	PUNCT
m-1112	856	8	is	be	AUX
m-1112	856	9	a.da	a.da	ADJ
m-1112	856	10	=	=	SYM
m-1112	857	1	x'+	x'+	PROPN
m-1112	857	2	v̅	v̅	PROPN
m-1112	857	3	t	t	PROPN
m-1112	857	4	'	'	PUNCT
m-1112	857	5	,	,	PUNCT
m-1112	857	6	and	and	CCONJ
m-1112	857	7	because	because	SCONJ
m-1112	857	8	of	of	ADP
m-1112	857	9	the	the	DET
m-1112	857	10	isochrones	isochrone	NOUN
m-1112	857	11	motion	motion	NOUN
m-1112	857	12	in	in	ADP
m-1112	857	13	the	the	DET
m-1112	857	14	fixed	fix	VERB
m-1112	857	15	system	system	NOUN
m-1112	858	1	[	[	X
m-1112	858	2	a	a	X
m-1112	858	3	]	]	X
m-1112	858	4	≡	≡	PROPN
m-1112	858	5	{	{	PUNCT
m-1112	858	6	dao	dao	PROPN
m-1112	858	7	}	}	PUNCT
m-1112	858	8	,	,	PUNCT
m-1112	858	9	then	then	ADV
m-1112	858	10	holds	hold	VERB
m-1112	858	11	,	,	PUNCT
m-1112	858	12	x	x	PUNCT
m-1112	858	13	=	=	SYM
m-1112	858	14	(	(	PUNCT
m-1112	858	15	x'+	x'+	NOUN
m-1112	858	16	v̅.t	v̅.t	X
m-1112	858	17	'	'	NUM
m-1112	858	18	)	)	PUNCT
m-1112	858	19	.γ	.γ	NOUN
m-1112	859	1	or	or	CCONJ
m-1112	859	2	x	x	X
m-1112	859	3	=	=	SYM
m-1112	859	4	(	(	PUNCT
m-1112	859	5	x'+	x'+	PROPN
m-1112	859	6	v̅.t').γ	v̅.t').γ	PROPN
m-1112	859	7	≡	≡	PROPN
m-1112	859	8	[	[	PUNCT
m-1112	859	9	x'+	x'+	NOUN
m-1112	859	10	v̅.t	v̅.t	X
m-1112	859	11	'	'	NUM
m-1112	859	12	]	]	PUNCT
m-1112	859	13	/	/	PUNCT
m-1112	860	1	[	[	X
m-1112	860	2	√1-(v	√1-(v	NOUN
m-1112	860	3	/	/	SYM
m-1112	860	4	c	c	NOUN
m-1112	860	5	)	)	PUNCT
m-1112	860	6	²	²	NUM
m-1112	860	7	]	]	PUNCT
m-1112	860	8	…	…	PUNCT
m-1112	860	9	…	…	PUNCT
m-1112	860	10	.	.	PUNCT
m-1112	861	1	(	(	PUNCT
m-1112	861	2	a	a	X
m-1112	861	3	)	)	PUNCT
m-1112	861	4	inversely	inversely	ADV
m-1112	861	5	,	,	PUNCT
m-1112	861	6	by	by	ADP
m-1112	861	7	using	use	VERB
m-1112	861	8	(	(	PUNCT
m-1112	861	9	a	a	NOUN
m-1112	861	10	)	)	PUNCT
m-1112	861	11	,	,	PUNCT
m-1112	861	12	where	where	SCONJ
m-1112	861	13	[	[	X
m-1112	861	14	a	a	X
m-1112	861	15	]	]	X
m-1112	861	16	≡	≡	PROPN
m-1112	861	17	{	{	PUNCT
m-1112	861	18	da	da	VERB
m-1112	861	19	-	-	PUNCT
m-1112	861	20	a	a	DET
m-1112	861	21	}	}	PUNCT
m-1112	861	22	≡	≡	PROPN
m-1112	861	23	{	{	PUNCT
m-1112	861	24	dao}/	dao}/	PROPN
m-1112	861	25	γ	γ	PROPN
m-1112	861	26	,	,	PUNCT
m-1112	861	27	then	then	ADV
m-1112	861	28	if	if	SCONJ
m-1112	861	29	material	material	NOUN
m-1112	861	30	point	point	VERB
m-1112	861	31	a	a	PRON
m-1112	861	32	of	of	ADP
m-1112	861	33	the	the	DET
m-1112	861	34	fixed	fix	VERB
m-1112	861	35	system	system	NOUN
m-1112	861	36	{	{	PUNCT
m-1112	861	37	dao	dao	AUX
m-1112	861	38	}	}	PUNCT
m-1112	861	39	travels	travel	VERB
m-1112	861	40	with	with	ADP
m-1112	861	41	velocity	velocity	NOUN
m-1112	861	42	v̅	v̅	NOUN
m-1112	861	43	at	at	ADP
m-1112	861	44	point	point	NOUN
m-1112	861	45	da	da	INTJ
m-1112	861	46	,	,	PUNCT
m-1112	861	47	where	where	SCONJ
m-1112	861	48	then	then	ADV
m-1112	861	49	the	the	DET
m-1112	861	50	geometrical	geometrical	ADJ
m-1112	861	51	distance	distance	NOUN
m-1112	861	52	ada	ada	PROPN
m-1112	861	53	in	in	ADP
m-1112	861	54	the	the	DET
m-1112	861	55	fixed	fix	VERB
m-1112	861	56	system	system	NOUN
m-1112	861	57	is	be	AUX
m-1112	861	58	,	,	PUNCT
m-1112	861	59	[	[	X
m-1112	861	60	a	a	X
m-1112	861	61	]	]	X
m-1112	861	62	≡	≡	PROPN
m-1112	861	63	{	{	PUNCT
m-1112	861	64	da	da	PROPN
m-1112	861	65	o	o	PROPN
m-1112	861	66	}	}	PUNCT
m-1112	861	67	is	be	AUX
m-1112	861	68	→	→	PUNCT
m-1112	861	69	a.da	a.da	VERB
m-1112	861	70	=	=	SYM
m-1112	861	71	x	x	SYM
m-1112	861	72	v̅.t	v̅.t	NOUN
m-1112	861	73	and	and	CCONJ
m-1112	861	74	in	in	ADP
m-1112	861	75	the	the	DET
m-1112	861	76	relative	relative	ADJ
m-1112	861	77	system	system	NOUN
m-1112	861	78	,	,	PUNCT
m-1112	861	79	[	[	X
m-1112	861	80	r	r	X
m-1112	861	81	]	]	X
m-1112	861	82	≡	≡	PROPN
m-1112	861	83	{	{	PUNCT
m-1112	861	84	dapa	dapa	PROPN
m-1112	861	85	}	}	PUNCT
m-1112	861	86	is	be	AUX
m-1112	861	87	→	→	SYM
m-1112	861	88	x	x	X
m-1112	861	89	'	'	PUNCT
m-1112	862	1	=	=	SYM
m-1112	862	2	(	(	PUNCT
m-1112	862	3	x	x	NOUN
m-1112	862	4	-	-	NOUN
m-1112	862	5	v	v	NOUN
m-1112	862	6	t).γ	t).γ	PROPN
m-1112	862	7	=	=	PUNCT
m-1112	863	1	[	[	X
m-1112	863	2	x	x	X
m-1112	863	3	-	-	NOUN
m-1112	863	4	v	v	ADP
m-1112	863	5	t	t	NOUN
m-1112	863	6	]	]	PUNCT
m-1112	863	7	:	:	PUNCT
m-1112	864	1	[	[	X
m-1112	864	2	√1	√1	PROPN
m-1112	864	3	(	(	PUNCT
m-1112	864	4	v	v	NOUN
m-1112	864	5	/	/	SYM
m-1112	864	6	c)²	c)²	NOUN
m-1112	864	7	]	]	X
m-1112	864	8	…	…	PUNCT
m-1112	864	9	...	...	PUNCT
m-1112	864	10	(	(	PUNCT
m-1112	864	11	b	b	NOUN
m-1112	864	12	)	)	PUNCT
m-1112	864	13	fig-6	fig-6	NOUN
m-1112	864	14	an	an	DET
m-1112	864	15	application	application	NOUN
m-1112	864	16	to	to	ADP
m-1112	864	17	gravity	gravity	NOUN
m-1112	864	18	[	[	X
m-1112	864	19	72	72	NUM
m-1112	864	20	]	]	PUNCT
m-1112	864	21	and	and	CCONJ
m-1112	864	22	photon	photon	VERB
m-1112	865	1	[	[	X
m-1112	865	2	95	95	NUM
m-1112	865	3	]	]	PUNCT
m-1112	865	4	,	,	PUNCT
m-1112	865	5	because	because	SCONJ
m-1112	865	6	gravitational	gravitational	ADJ
m-1112	865	7	force	force	NOUN
m-1112	865	8	is	be	AUX
m-1112	865	9	equal	equal	ADJ
m-1112	865	10	to	to	ADP
m-1112	865	11	→	→	SYM
m-1112	865	12	the	the	DET
m-1112	865	13	geometric	geometric	NOUN
m-1112	865	14	-	-	PUNCT
m-1112	865	15	resultant	resultant	NOUN
m-1112	865	16	of	of	ADP
m-1112	865	17	the	the	DET
m-1112	865	18	light	light	ADJ
m-1112	865	19	-	-	PUNCT
m-1112	865	20	velocity	velocity	NOUN
m-1112	865	21	c	c	NOUN
m-1112	865	22	,	,	PUNCT
m-1112	865	23	acting	act	VERB
m-1112	865	24	on	on	ADP
m-1112	865	25	electron	electron	NOUN
m-1112	865	26	-	-	PUNCT
m-1112	865	27	unit	unit	NOUN
m-1112	865	28	-	-	PUNCT
m-1112	865	29	charge	charge	NOUN
m-1112	865	30	�	�	PROPN
m-1112	865	31	̅	̅	NOUN
m-1112	865	32	�	�	PROPN
m-1112	865	33	←	←	PROPN
m-1112	865	34	or	or	CCONJ
m-1112	865	35	is	be	AUX
m-1112	865	36	,	,	PUNCT
m-1112	865	37	g	g	PROPN
m-1112	865	38	=	=	SYM
m-1112	865	39	c	c	PROPN
m-1112	865	40	√𝟐	√𝟐	PROPN
m-1112	865	41	�	�	PROPN
m-1112	865	42	̅	̅	NOUN
m-1112	865	43	�	�	PROPN
m-1112	865	44	,	,	PUNCT
m-1112	865	45	then	then	ADV
m-1112	865	46	electron	electron	NOUN
m-1112	865	47	charge	charge	NOUN
m-1112	865	48	is	be	AUX
m-1112	865	49	,	,	PUNCT
m-1112	865	50	q̅	q̅	PROPN
m-1112	865	51	=	=	PUNCT
m-1112	865	52	g	g	PROPN
m-1112	865	53	c	c	PROPN
m-1112	865	54	√2	√2	PROPN
m-1112	865	55	=	=	SYM
m-1112	865	56	6,680561	6,680561	PROPN
m-1112	865	57	.10−11	.10−11	PUNCT
m-1112	865	58	1,41429.[2,9979346.10	1,41429.[2,9979346.10	NUM
m-1112	865	59	8	8	NUM
m-1112	865	60	]	]	PUNCT
m-1112	865	61	=	=	SYM
m-1112	865	62	1,58.10−19	1,58.10−19	NUM
m-1112	865	63	coulomb	coulomb	NOUN
m-1112	865	64	,	,	PUNCT
m-1112	865	65	which	which	PRON
m-1112	865	66	is	be	AUX
m-1112	865	67	the	the	DET
m-1112	865	68	known	know	VERB
m-1112	865	69	coulomb`s	coulomb`s	NUM
m-1112	865	70	charge	charge	NOUN
m-1112	865	71	quantity	quantity	NOUN
m-1112	865	72	.	.	PUNCT
m-1112	866	1	from	from	ADP
m-1112	866	2	gl	gl	PROPN
m-1112	866	3	,	,	PUNCT
m-1112	866	4	kl	kl	PROPN
m-1112	866	5	universal	universal	PROPN
m-1112	866	6	constants	constant	VERB
m-1112	866	7	the	the	DET
m-1112	866	8	newton`s	newton`s	PROPN
m-1112	866	9	gravitational	gravitational	ADJ
m-1112	866	10	constant	constant	ADJ
m-1112	866	11	force	force	NOUN
m-1112	866	12	g	g	PROPN
m-1112	866	13	≡	≡	PROPN
m-1112	866	14	g.ke	g.ke	PROPN
m-1112	866	15	≡	≡	PROPN
m-1112	866	16	g	g	PROPN
m-1112	866	17	.[gl	.[gl	PROPN
m-1112	866	18	kl	kl	X
m-1112	866	19	]	]	PUNCT
m-1112	867	1	≡	≡	PROPN
m-1112	867	2	[	[	PUNCT
m-1112	867	3	t²p	t²p	X
m-1112	867	4	𝐚³	𝐚³	ADJ
m-1112	867	5	]	]	PUNCT
m-1112	867	6	.[gl	.[gl	PUNCT
m-1112	868	1	kl	kl	X
m-1112	868	2	]	]	PUNCT
m-1112	868	3	≡	≡	PROPN
m-1112	868	4	9,808238	9,808238	PROPN
m-1112	868	5	*	*	SYM
m-1112	868	6	6,8116.10−12	6,8116.10−12	NUM
m-1112	868	7	≡	≡	PROPN
m-1112	868	8	6,68056.10−11	6,68056.10−11	NUM
m-1112	868	9	𝐦³	𝐦³	PROPN
m-1112	868	10	𝐍𝐬²	𝐍𝐬²	VERB
m-1112	868	11	the	the	DET
m-1112	868	12	in	in	ADP
m-1112	868	13	depth	depth	NOUN
m-1112	868	14	position	position	NOUN
m-1112	868	15	of	of	ADP
m-1112	868	16	electrons	electron	NOUN
m-1112	868	17	allows	allow	VERB
m-1112	868	18	to	to	ADP
m-1112	868	19	the	the	DET
m-1112	868	20	work	work	NOUN
m-1112	868	21	produced	produce	VERB
m-1112	868	22	in	in	ADP
m-1112	868	23	prior	prior	ADJ
m-1112	868	24	phase	phase	NOUN
m-1112	868	25	areas	area	NOUN
m-1112	868	26	as	as	ADP
m-1112	868	27	golden	golden	ADJ
m-1112	868	28	ratio	ratio	NOUN
m-1112	868	29	pattern	pattern	NOUN
m-1112	868	30	,	,	PUNCT
m-1112	868	31	to	to	PART
m-1112	868	32	be	be	AUX
m-1112	868	33	stored	store	VERB
m-1112	868	34	in	in	ADP
m-1112	868	35	the	the	DET
m-1112	868	36	next	next	ADJ
m-1112	868	37	.	.	PUNCT
m-1112	869	1	energy	energy	NOUN
m-1112	869	2	=	=	NOUN
m-1112	869	3	motion	motion	NOUN
m-1112	869	4	/	/	SYM
m-1112	869	5	t	t	PROPN
m-1112	869	6	≡	≡	PROPN
m-1112	869	7	(	(	PUNCT
m-1112	869	8	v	v	NUM
m-1112	869	9	2πr	2πr	NOUN
m-1112	869	10	)	)	PUNCT
m-1112	869	11	.	.	PUNCT
m-1112	870	1	[	[	X
m-1112	870	2	σ	σ	X
m-1112	870	3	+	+	X
m-1112	870	4	σ	σ	PROPN
m-1112	870	5	φ	φ	X
m-1112	870	6	]	]	X
m-1112	870	7	=	=	SYM
m-1112	870	8	�	�	PROPN
m-1112	870	9	̅	̅	NOUN
m-1112	870	10	�	�	PROPN
m-1112	870	11	.	.	PUNCT
m-1112	871	1	[	[	PUNCT
m-1112	871	2	𝛔	𝛔	X
m-1112	871	3	𝟐𝛑𝐫	𝟐𝛑𝐫	NOUN
m-1112	872	1	+	+	X
m-1112	873	1	𝛔𝚽	𝛔𝚽	ADJ
m-1112	873	2	𝟐𝛑𝐫	𝟐𝛑𝐫	NOUN
m-1112	873	3	]	]	PUNCT
m-1112	873	4	≡	≡	PROPN
m-1112	873	5	�	�	PROPN
m-1112	873	6	̅	̅	NOUN
m-1112	873	7	�	�	PROPN
m-1112	873	8	.	.	PUNCT
m-1112	874	1	[	[	X
m-1112	874	2	.	.	PUNCT
m-1112	875	1	fn̅	fn̅	PROPN
m-1112	876	1	+	+	NUM
m-1112	876	2	𝐟𝐧	𝐟𝐧	NOUN
m-1112	876	3	]	]	PUNCT
m-1112	876	4	≡	≡	PROPN
m-1112	876	5	moving	move	VERB
m-1112	876	6	storage	storage	NOUN
m-1112	876	7	→	→	NOUN
m-1112	876	8	[	[	PUNCT
m-1112	876	9	�	�	NOUN
m-1112	876	10	̅	̅	NOUN
m-1112	876	11	�	�	PROPN
m-1112	876	12	.	.	PUNCT
m-1112	877	1	fn̅	fn̅	PROPN
m-1112	877	2	]	]	PUNCT
m-1112	877	3	←	←	PROPN
m-1112	877	4	+	+	CCONJ
m-1112	877	5	moving	move	VERB
m-1112	877	6	-	-	PUNCT
m-1112	877	7	frequency	frequency	NOUN
m-1112	877	8	→	→	SYM
m-1112	877	9	[	[	PUNCT
m-1112	877	10	�	�	NOUN
m-1112	877	11	̅	̅	NOUN
m-1112	877	12	�	�	NOUN
m-1112	877	13	.𝐟𝐧	.𝐟𝐧	PUNCT
m-1112	877	14	]	]	PUNCT
m-1112	877	15	←	←	PROPN
m-1112	877	16	≡	≡	PROPN
m-1112	877	17	the	the	DET
m-1112	877	18	material	material	NOUN
m-1112	877	19	-	-	PUNCT
m-1112	877	20	point	point	NOUN
m-1112	877	21	.	.	PUNCT
m-1112	878	1	i.e.	i.e.	X
m-1112	878	2	the	the	DET
m-1112	878	3	energy	energy	NOUN
m-1112	878	4	produced	produce	VERB
m-1112	878	5	in	in	ADP
m-1112	878	6	photon	photon	NOUN
m-1112	878	7	-	-	PUNCT
m-1112	878	8	cave	cave	NOUN
m-1112	878	9	is	be	AUX
m-1112	878	10	consisted	consist	VERB
m-1112	878	11	of	of	ADP
m-1112	878	12	two	two	NUM
m-1112	878	13	-	-	PUNCT
m-1112	878	14	moving	move	VERB
m-1112	878	15	-	-	PUNCT
m-1112	878	16	storages	storage	NOUN
m-1112	878	17	,	,	PUNCT
m-1112	878	18	that	that	PRON
m-1112	878	19	travel	travel	VERB
m-1112	878	20	as	as	ADP
m-1112	878	21	wave	wave	NOUN
m-1112	878	22	[	[	X
m-1112	878	23	�	�	NOUN
m-1112	878	24	̅	̅	NOUN
m-1112	878	25	�	�	NOUN
m-1112	878	26	.𝐟𝐧	.𝐟𝐧	PRON
m-1112	878	27	]	]	PUNCT
m-1112	879	1	→	→	ADP
m-1112	879	2	[	[	PUNCT
m-1112	879	3	�	�	NOUN
m-1112	879	4	̅	̅	NOUN
m-1112	879	5	�	�	PROPN
m-1112	879	6	.	.	PUNCT
m-1112	880	1	fn̅	fn̅	PROPN
m-1112	880	2	]	]	PUNCT
m-1112	881	1	→	→	X
m-1112	881	2	[	[	PUNCT
m-1112	881	3	�	�	NOUN
m-1112	881	4	̅	̅	NOUN
m-1112	881	5	�	�	PROPN
m-1112	881	6	=	=	SYM
m-1112	881	7	�	�	PROPN
m-1112	881	8	̅	̅	NOUN
m-1112	881	9	�	�	NOUN
m-1112	881	10	=	=	SYM
m-1112	881	11	λ	λ	X
m-1112	881	12	f	f	PROPN
m-1112	881	13	φ	φ	X
m-1112	881	14	]	]	PUNCT
m-1112	881	15	→	→	X
m-1112	881	16	[	[	PUNCT
m-1112	881	17	s	s	X
m-1112	881	18	≡	≡	PROPN
m-1112	881	19	em	em	PROPN
m-1112	881	20	-	-	PUNCT
m-1112	881	21	r	r	NOUN
m-1112	881	22	≡	≡	PROPN
m-1112	881	23	f1	f1	NOUN
m-1112	881	24	=	=	SYM
m-1112	881	25	n	n	NOUN
m-1112	881	26	,	,	PUNCT
m-1112	881	27	f2	f2	ADV
m-1112	881	28	,	,	PUNCT
m-1112	881	29	f3	f3	PROPN
m-1112	881	30	,	,	PUNCT
m-1112	881	31	fd	fd	X
m-1112	881	32	,	,	PUNCT
m-1112	881	33	,	,	PUNCT
m-1112	881	34	f	f	PROPN
m-1112	881	35	n=	n=	ADJ
m-1112	881	36	w²	w²	PROPN
m-1112	881	37	]	]	PUNCT
m-1112	881	38	,	,	PUNCT
m-1112	881	39	and	and	CCONJ
m-1112	881	40	as	as	ADP
m-1112	881	41	particle	particle	NOUN
m-1112	881	42	→	→	PROPN
m-1112	881	43	[	[	PUNCT
m-1112	881	44	f1=	f1=	PROPN
m-1112	881	45	(	(	PUNCT
m-1112	881	46	e²+h²	e²+h²	PROPN
m-1112	881	47	)	)	PUNCT
m-1112	881	48	=	=	SYM
m-1112	881	49	n	n	CCONJ
m-1112	881	50	(	(	PUNCT
m-1112	881	51	1+√5)σ	1+√5)σ	NUM
m-1112	881	52	2πr	2πr	NOUN
m-1112	881	53	=	=	PUNCT
m-1112	881	54	nb̅	nb̅	PROPN
m-1112	881	55	π²	π²	NOUN
m-1112	881	56	r⁴	r⁴	NOUN
m-1112	881	57	]	]	PUNCT
m-1112	881	58	→{w≡em	→{w≡em	NOUN
m-1112	881	59	-	-	PUNCT
m-1112	881	60	r≡	r≡	NOUN
m-1112	881	61	[	[	X
m-1112	881	62	εe²	εe²	NOUN
m-1112	881	63	+	+	CCONJ
m-1112	881	64	μb²	μb²	NOUN
m-1112	881	65	]	]	X
m-1112	881	66	=	=	PUNCT
m-1112	882	1	2.λc.sin.2φ	2.λc.sin.2φ	NUM
m-1112	882	2	}	}	PUNCT
m-1112	882	3	and	and	CCONJ
m-1112	882	4	is	be	AUX
m-1112	882	5	the	the	DET
m-1112	882	6	duality	duality	NOUN
m-1112	882	7	of	of	ADP
m-1112	882	8	the	the	DET
m-1112	882	9	energy	energy	NOUN
m-1112	882	10	-	-	PUNCT
m-1112	882	11	storage	storage	NOUN
m-1112	882	12	s	s	PART
m-1112	882	13	≡	≡	PROPN
m-1112	882	14	{	{	PUNCT
m-1112	883	1	[	[	X
m-1112	883	2	⊕←	⊕←	X
m-1112	883	3	𝐫	𝐫	PART
m-1112	883	4	→⊝	→⊝	NOUN
m-1112	883	5	]	]	X
m-1112	883	6	+	+	NUM
m-1112	883	7	motion	motion	NOUN
m-1112	883	8	m	m	VERB
m-1112	883	9	.	.	PUNCT
m-1112	884	1	[	[	X
m-1112	884	2	87	87	NUM
m-1112	884	3	-	-	SYM
m-1112	884	4	89	89	NUM
m-1112	884	5	]	]	PUNCT
m-1112	884	6	.the	.the	PRON
m-1112	884	7	three	three	NUM
m-1112	884	8	elements	element	NOUN
m-1112	884	9	[	[	X
m-1112	884	10	σ	σ	X
m-1112	884	11	=	=	SYM
m-1112	884	12	n	n	PROPN
m-1112	884	13	.	.	PUNCT
m-1112	885	1	h	h	X
m-1112	885	2	]	]	X
m-1112	885	3			NOUN
m-1112	886	1	[	[	X
m-1112	886	2	s²	s²	NOUN
m-1112	886	3	=	=	SYM
m-1112	886	4	⊕	⊕	PROPN
m-1112	886	5	,	,	PUNCT
m-1112	886	6	2s²=	2s²=	NUM
m-1112	886	7	,	,	PUNCT
m-1112	886	8	s²	s²	NOUN
m-1112	886	9	=	=	SYM
m-1112	886	10	⊝	⊝	X
m-1112	886	11	]	]	PUNCT
m-1112	886	12	of	of	ADP
m-1112	886	13	this	this	PRON
m-1112	886	14	{	{	PUNCT
m-1112	886	15	stpl}-mechanism	stpl}-mechanism	NOUN
m-1112	886	16	formulate	formulate	VERB
m-1112	886	17	the	the	DET
m-1112	886	18	3	3	NUM
m-1112	886	19	-	-	PUNCT
m-1112	886	20	knots	knot	NOUN
m-1112	886	21	figures	figure	NOUN
m-1112	886	22	(	(	PUNCT
m-1112	886	23	n	n	NOUN
m-1112	886	24	=	=	SYM
m-1112	886	25	3	3	NUM
m-1112	886	26	)	)	PUNCT
m-1112	886	27	and	and	CCONJ
m-1112	886	28	determinates	determinate	VERB
m-1112	886	29	the	the	DET
m-1112	886	30	elementary	elementary	ADJ
m-1112	886	31	-	-	PUNCT
m-1112	886	32	particles	particle	NOUN
m-1112	886	33	vector	vector	NOUN
m-1112	886	34	mould	mould	NOUN
m-1112	886	35	.	.	PUNCT
m-1112	887	1	ijo	ijo	PROPN
m-1112	887	2	international	international	PROPN
m-1112	887	3	journal	journal	PROPN
m-1112	887	4	of	of	ADP
m-1112	887	5	mathematics	mathematics	PROPN
m-1112	887	6	(	(	PUNCT
m-1112	887	7	issn	issn	PROPN
m-1112	887	8	:	:	PUNCT
m-1112	887	9	2992	2992	NUM
m-1112	887	10	-	-	SYM
m-1112	887	11	4421	4421	NUM
m-1112	887	12	)	)	PUNCT
m-1112	887	13	volume	volume	NOUN
m-1112	887	14	08	08	NUM
m-1112	888	1	|	|	ADV
m-1112	888	2	issue	issue	NOUN
m-1112	888	3	08	08	NUM
m-1112	889	1	|	|	ADV
m-1112	889	2	august	august	PROPN
m-1112	889	3	2025	2025	NUM
m-1112	889	4	|	|	ADV
m-1112	889	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	889	6	ijo	ijo	PROPN
m-1112	889	7	journals	journal	NOUN
m-1112	889	8	30	30	NUM
m-1112	889	9	the	the	DET
m-1112	889	10	fundamental	fundamental	ADJ
m-1112	889	11	particles	particle	NOUN
m-1112	889	12	origination	origination	NOUN
m-1112	889	13	mechanism	mechanism	NOUN
m-1112	889	14	in	in	ADP
m-1112	889	15	mfmf	mfmf	PROPN
m-1112	889	16	pns	pns	PROPN
m-1112	889	17	caves	cave	NOUN
m-1112	889	18	.	.	PUNCT
m-1112	890	1	8.[a]-3	8.[a]-3	X
m-1112	890	2	..	..	PUNCT
m-1112	890	3	the	the	DET
m-1112	890	4	circularly	circularly	ADJ
m-1112	890	5	existing	exist	VERB
m-1112	890	6	unit	unit	NOUN
m-1112	890	7	-	-	PUNCT
m-1112	890	8	charge	charge	NOUN
m-1112	890	9	complex	complex	ADJ
m-1112	890	10	-	-	PUNCT
m-1112	890	11	vector	vector	NOUN
m-1112	890	12	[	[	X
m-1112	890	13	⊕	⊕	PROPN
m-1112	890	14			PROPN
m-1112	890	15	⊝],[⊝	⊝],[⊝	PUNCT
m-1112	890	16			PROPN
m-1112	890	17	⊕],[⊕	⊕],[⊕	CCONJ
m-1112	890	18	⊝	⊝	ADJ
m-1112	890	19			PROPN
m-1112	890	20	]	]	PUNCT
m-1112	890	21	,	,	PUNCT
m-1112	890	22	figure	figure	VERB
m-1112	890	23	7	7	NUM
m-1112	890	24	:	:	PUNCT
m-1112	890	25	the	the	DET
m-1112	890	26	,	,	PUNCT
m-1112	890	27	stpl	stpl	PROPN
m-1112	890	28	,	,	PUNCT
m-1112	890	29	mechanism	mechanism	NOUN
m-1112	890	30	is	be	AUX
m-1112	890	31	the	the	DET
m-1112	890	32	generator	generator	NOUN
m-1112	890	33	of	of	ADP
m-1112	890	34	the	the	DET
m-1112	890	35	cosmic	cosmic	ADJ
m-1112	890	36	-	-	PUNCT
m-1112	890	37	particles	particle	NOUN
m-1112	890	38	.	.	PUNCT
m-1112	891	1	the	the	DET
m-1112	891	2	unit	unit	NOUN
m-1112	891	3	-	-	PUNCT
m-1112	891	4	charge	charge	NOUN
m-1112	891	5	is	be	AUX
m-1112	891	6	as	as	ADP
m-1112	891	7	complex	complex	ADJ
m-1112	891	8	-	-	PUNCT
m-1112	891	9	vector	vector	NOUN
m-1112	891	10	velocity	velocity	NOUN
m-1112	891	11	thrust	thrust	NOUN
m-1112	891	12	(	(	PUNCT
m-1112	891	13	v̅	v̅	X
m-1112	891	14	=	=	SYM
m-1112	891	15	w̅.r	w̅.r	X
m-1112	891	16	)	)	PUNCT
m-1112	891	17	,	,	PUNCT
m-1112	891	18	with	with	ADP
m-1112	891	19	and	and	CCONJ
m-1112	891	20	from	from	ADP
m-1112	891	21	the	the	DET
m-1112	891	22	breakages	breakage	NOUN
m-1112	891	23	→	→	SYM
m-1112	891	24	𝐳	𝐳	X
m-1112	891	25	*	*	PUNCT
m-1112	891	26	𝐳	𝐳	X
m-1112	891	27	=	=	X
m-1112	891	28	(	(	PUNCT
m-1112	891	29	s	s	NOUN
m-1112	891	30	+	+	NUM
m-1112	891	31	v̅.i	v̅.i	X
m-1112	891	32	)	)	PUNCT
m-1112	891	33	²	²	PROPN
m-1112	891	34	=	=	SYM
m-1112	891	35	s²	s²	PROPN
m-1112	891	36	+	+	CCONJ
m-1112	891	37	[	[	X
m-1112	891	38	v̅]²	v̅]²	X
m-1112	891	39	+2.sv̅.i	+2.sv̅.i	X
m-1112	891	40	.	.	PUNCT
m-1112	892	1	7	7	NUM
m-1112	892	2	-	-	SYM
m-1112	892	3	a	a	PRON
m-1112	892	4	=	=	NOUN
m-1112	892	5	the	the	DET
m-1112	892	6	positive	positive	ADJ
m-1112	892	7	breakage	breakage	NOUN
m-1112	892	8	quantity	quantity	NOUN
m-1112	892	9	q	q	PROPN
m-1112	892	10	≡	≡	PROPN
m-1112	892	11	[	[	PUNCT
m-1112	892	12	⊕	⊕	PROPN
m-1112	892	13			PROPN
m-1112	892	14	⊝	⊝	NUM
m-1112	892	15	]	]	PUNCT
m-1112	892	16	,	,	PUNCT
m-1112	892	17	for	for	ADP
m-1112	892	18	leptons	lepton	NOUN
m-1112	892	19	and	and	CCONJ
m-1112	892	20	quarks	quark	NOUN
m-1112	892	21	.	.	PUNCT
m-1112	893	1	figure	figure	NOUN
m-1112	893	2	–	–	PUNCT
m-1112	893	3	7a	7a	NUM
m-1112	893	4	:	:	PUNCT
m-1112	893	5	the	the	DET
m-1112	893	6	,	,	PUNCT
m-1112	893	7	stpl	stpl	PROPN
m-1112	893	8	,	,	PUNCT
m-1112	893	9	mechanism	mechanism	NOUN
m-1112	893	10	is	be	AUX
m-1112	893	11	the	the	DET
m-1112	893	12	generator	generator	NOUN
m-1112	893	13	of	of	ADP
m-1112	893	14	the	the	DET
m-1112	893	15	cosmic	cosmic	ADJ
m-1112	893	16	-	-	PUNCT
m-1112	893	17	particles	particle	NOUN
m-1112	893	18	.	.	PUNCT
m-1112	894	1	the	the	DET
m-1112	894	2	unit	unit	NOUN
m-1112	894	3	-	-	PUNCT
m-1112	894	4	charge	charge	NOUN
m-1112	894	5	is	be	AUX
m-1112	894	6	as	as	ADP
m-1112	894	7	complex	complex	ADJ
m-1112	894	8	-	-	PUNCT
m-1112	894	9	vector	vector	NOUN
m-1112	894	10	velocity	velocity	NOUN
m-1112	894	11	thrust	thrust	NOUN
m-1112	894	12	(	(	PUNCT
m-1112	894	13	v̅	v̅	X
m-1112	894	14	=	=	SYM
m-1112	894	15	w̅.r	w̅.r	X
m-1112	894	16	)	)	PUNCT
m-1112	894	17	,	,	PUNCT
m-1112	894	18	with	with	ADP
m-1112	894	19	and	and	CCONJ
m-1112	894	20	from	from	ADP
m-1112	894	21	the	the	DET
m-1112	894	22	breakages	breakage	NOUN
m-1112	894	23	→	→	SYM
m-1112	894	24	𝐳	𝐳	X
m-1112	894	25	*	*	PUNCT
m-1112	894	26	𝐳	𝐳	X
m-1112	894	27	=	=	X
m-1112	894	28	(	(	PUNCT
m-1112	894	29	s	s	NOUN
m-1112	894	30	+	+	NUM
m-1112	894	31	v̅.i	v̅.i	X
m-1112	894	32	)	)	PUNCT
m-1112	894	33	²	²	PROPN
m-1112	894	34	=	=	SYM
m-1112	894	35	s²	s²	PROPN
m-1112	894	36	+	+	CCONJ
m-1112	894	37	[	[	X
m-1112	894	38	v̅]²	v̅]²	X
m-1112	894	39	+2.sv̅.i	+2.sv̅.i	NUM
m-1112	894	40	.	.	PUNCT
m-1112	895	1	v	v	X
m-1112	895	2	-	-	PUNCT
m-1112	895	3	trust	trust	NOUN
m-1112	895	4	≡	≡	PROPN
m-1112	895	5	[	[	PUNCT
m-1112	895	6	⊕	⊕	PROPN
m-1112	895	7			PROPN
m-1112	895	8	⊝	⊝	PUNCT
m-1112	895	9	]	]	PUNCT
m-1112	895	10	ijo	ijo	PROPN
m-1112	895	11	international	international	PROPN
m-1112	895	12	journal	journal	PROPN
m-1112	895	13	of	of	ADP
m-1112	895	14	mathematics	mathematics	PROPN
m-1112	895	15	(	(	PUNCT
m-1112	895	16	issn	issn	PROPN
m-1112	895	17	:	:	PUNCT
m-1112	895	18	2992	2992	NUM
m-1112	895	19	-	-	SYM
m-1112	895	20	4421	4421	NUM
m-1112	895	21	)	)	PUNCT
m-1112	895	22	volume	volume	NOUN
m-1112	895	23	08	08	NUM
m-1112	896	1	|	|	ADV
m-1112	896	2	issue	issue	NOUN
m-1112	896	3	08	08	NUM
m-1112	897	1	|	|	ADV
m-1112	897	2	august	august	PROPN
m-1112	897	3	2025	2025	NUM
m-1112	897	4	|	|	ADV
m-1112	897	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	897	6	ijo	ijo	PROPN
m-1112	897	7	journals	journal	NOUN
m-1112	897	8	31	31	NUM
m-1112	897	9	the	the	DET
m-1112	897	10	fundamental	fundamental	ADJ
m-1112	897	11	particles	particle	NOUN
m-1112	897	12	origination	origination	NOUN
m-1112	897	13	mechanism	mechanism	NOUN
m-1112	897	14	in	in	ADP
m-1112	897	15	mfmf	mfmf	PROPN
m-1112	897	16	pns	pns	PROPN
m-1112	897	17	caves	cave	NOUN
m-1112	897	18	.	.	PUNCT
m-1112	898	1	7	7	NUM
m-1112	898	2	-	-	SYM
m-1112	898	3	b	b	NOUN
m-1112	898	4	=	=	NOUN
m-1112	898	5	the	the	DET
m-1112	898	6	positive	positive	ADJ
m-1112	898	7	breakage	breakage	NOUN
m-1112	898	8	quantity	quantity	NOUN
m-1112	898	9	q	q	PROPN
m-1112	898	10	≡	≡	PROPN
m-1112	899	1	[	[	X
m-1112	899	2	⊝	⊝	ADP
m-1112	899	3			PROPN
m-1112	899	4	⊕	⊕	PROPN
m-1112	899	5	]	]	PUNCT
m-1112	899	6	,	,	PUNCT
m-1112	899	7	for	for	ADP
m-1112	899	8	anti	anti	ADJ
m-1112	899	9	-	-	ADJ
m-1112	899	10	leptons	leptons	ADJ
m-1112	899	11	,	,	PUNCT
m-1112	899	12	anti	anti	ADJ
m-1112	899	13	-	-	NOUN
m-1112	899	14	quarks	quarks	NOUN
m-1112	899	15	.	.	PUNCT
m-1112	900	1	figure	figure	NOUN
m-1112	900	2	-7b	-7b	NOUN
m-1112	900	3	:	:	PUNCT
m-1112	900	4	the	the	DET
m-1112	900	5	,	,	PUNCT
m-1112	900	6	stpl	stpl	PROPN
m-1112	900	7	,	,	PUNCT
m-1112	900	8	mechanism	mechanism	NOUN
m-1112	900	9	is	be	AUX
m-1112	900	10	the	the	DET
m-1112	900	11	generator	generator	NOUN
m-1112	900	12	of	of	ADP
m-1112	900	13	the	the	DET
m-1112	900	14	cosmic	cosmic	ADJ
m-1112	900	15	-	-	PUNCT
m-1112	900	16	particles	particle	NOUN
m-1112	900	17	.	.	PUNCT
m-1112	901	1	the	the	DET
m-1112	901	2	unit	unit	NOUN
m-1112	901	3	-	-	PUNCT
m-1112	901	4	charge	charge	NOUN
m-1112	901	5	is	be	AUX
m-1112	901	6	as	as	ADP
m-1112	901	7	complex	complex	ADJ
m-1112	901	8	-	-	PUNCT
m-1112	901	9	vector	vector	NOUN
m-1112	901	10	velocity	velocity	NOUN
m-1112	901	11	thrust	thrust	NOUN
m-1112	901	12	(	(	PUNCT
m-1112	901	13	v̅	v̅	X
m-1112	901	14	=	=	SYM
m-1112	901	15	w̅.r	w̅.r	X
m-1112	901	16	)	)	PUNCT
m-1112	901	17	,	,	PUNCT
m-1112	901	18	with	with	ADP
m-1112	901	19	and	and	CCONJ
m-1112	901	20	from	from	ADP
m-1112	901	21	the	the	DET
m-1112	901	22	breakages	breakage	NOUN
m-1112	901	23	→	→	SYM
m-1112	901	24	𝐳	𝐳	X
m-1112	901	25	*	*	PUNCT
m-1112	901	26	𝐳	𝐳	X
m-1112	901	27	=	=	X
m-1112	901	28	(	(	PUNCT
m-1112	901	29	s	s	NOUN
m-1112	901	30	+	+	NUM
m-1112	901	31	v̅.i	v̅.i	X
m-1112	901	32	)	)	PUNCT
m-1112	901	33	²	²	PROPN
m-1112	901	34	=	=	SYM
m-1112	901	35	s²	s²	PROPN
m-1112	901	36	+	+	CCONJ
m-1112	902	1	[	[	X
m-1112	902	2	v̅]²	v̅]²	X
m-1112	902	3	+2.sv̅.i	+2.sv̅.i	X
m-1112	902	4	.	.	PUNCT
m-1112	903	1	v	v	X
m-1112	903	2	trust	trust	NOUN
m-1112	903	3	≡	≡	PROPN
m-1112	904	1	[	[	X
m-1112	904	2	⊝	⊝	ADP
m-1112	904	3			PROPN
m-1112	904	4	⊕	⊕	NOUN
m-1112	904	5	]	]	X
m-1112	904	6	7	7	NUM
m-1112	904	7	-	-	SYM
m-1112	904	8	c	c	NOUN
m-1112	904	9	=	=	PUNCT
m-1112	904	10	the	the	DET
m-1112	904	11	positive	positive	ADJ
m-1112	904	12	breakage	breakage	NOUN
m-1112	904	13	quantity	quantity	NOUN
m-1112	904	14	q	q	PROPN
m-1112	904	15	≡	≡	PROPN
m-1112	905	1	[	[	X
m-1112	905	2	⊕	⊕	PROPN
m-1112	905	3	⊝	⊝	PUNCT
m-1112	905	4			PROPN
m-1112	905	5	]	]	PUNCT
m-1112	905	6	,	,	PUNCT
m-1112	905	7	for	for	ADP
m-1112	905	8	bosons	bosons	NOUN
m-1112	905	9	origination	origination	NOUN
m-1112	905	10	.	.	PUNCT
m-1112	906	1	figure	figure	NOUN
m-1112	906	2	-7c	-7c	PROPN
m-1112	906	3	:	:	PUNCT
m-1112	906	4	the	the	DET
m-1112	906	5	,	,	PUNCT
m-1112	906	6	stpl	stpl	PROPN
m-1112	906	7	,	,	PUNCT
m-1112	906	8	mechanism	mechanism	NOUN
m-1112	906	9	is	be	AUX
m-1112	906	10	the	the	DET
m-1112	906	11	generator	generator	NOUN
m-1112	906	12	of	of	ADP
m-1112	906	13	the	the	DET
m-1112	906	14	cosmic	cosmic	ADJ
m-1112	906	15	-	-	PUNCT
m-1112	906	16	particles	particle	NOUN
m-1112	906	17	.	.	PUNCT
m-1112	907	1	the	the	DET
m-1112	907	2	unit	unit	NOUN
m-1112	907	3	-	-	PUNCT
m-1112	907	4	charge	charge	NOUN
m-1112	907	5	is	be	AUX
m-1112	907	6	as	as	ADP
m-1112	907	7	complex	complex	ADJ
m-1112	907	8	-	-	PUNCT
m-1112	907	9	vector	vector	NOUN
m-1112	907	10	velocity	velocity	NOUN
m-1112	907	11	thrust	thrust	NOUN
m-1112	907	12	(	(	PUNCT
m-1112	907	13	v̅	v̅	X
m-1112	907	14	=	=	SYM
m-1112	907	15	w̅.r	w̅.r	X
m-1112	907	16	)	)	PUNCT
m-1112	907	17	,	,	PUNCT
m-1112	907	18	with	with	ADP
m-1112	907	19	and	and	CCONJ
m-1112	907	20	from	from	ADP
m-1112	907	21	the	the	DET
m-1112	907	22	breakages	breakage	NOUN
m-1112	907	23	→	→	SYM
m-1112	907	24	𝐳	𝐳	X
m-1112	907	25	*	*	PUNCT
m-1112	907	26	𝐳	𝐳	X
m-1112	907	27	=	=	X
m-1112	907	28	(	(	PUNCT
m-1112	907	29	s	s	NOUN
m-1112	907	30	+	+	NUM
m-1112	907	31	v̅.i	v̅.i	X
m-1112	907	32	)	)	PUNCT
m-1112	907	33	²	²	PROPN
m-1112	907	34	=	=	SYM
m-1112	907	35	s²	s²	PROPN
m-1112	907	36	+	+	CCONJ
m-1112	908	1	[	[	X
m-1112	908	2	v̅]²	v̅]²	X
m-1112	908	3	+2.sv̅.i	+2.sv̅.i	X
m-1112	908	4	.	.	PUNCT
m-1112	909	1	v	v	X
m-1112	909	2	trust	trust	NOUN
m-1112	909	3	≡	≡	PROPN
m-1112	910	1	[	[	X
m-1112	910	2	⊕	⊕	PROPN
m-1112	910	3	⊝	⊝	PUNCT
m-1112	910	4			PROPN
m-1112	910	5	]	]	PUNCT
m-1112	910	6	,	,	PUNCT
m-1112	910	7	since	since	SCONJ
m-1112	910	8	the	the	DET
m-1112	910	9	primary	primary	ADJ
m-1112	910	10	motion	motion	NOUN
m-1112	910	11	≡	≡	PROPN
m-1112	910	12	[	[	X
m-1112	910	13	pm	pm	X
m-1112	910	14	]	]	PUNCT
m-1112	910	15	exist	exist	VERB
m-1112	910	16	from	from	ADP
m-1112	910	17	the	the	DET
m-1112	910	18	three	three	NUM
m-1112	910	19	breakages	breakage	NOUN
m-1112	910	20	only	only	ADV
m-1112	910	21	,	,	PUNCT
m-1112	910	22	and	and	CCONJ
m-1112	910	23	stpl	stpl	PROPN
m-1112	910	24	is	be	AUX
m-1112	910	25	the	the	DET
m-1112	910	26	n	n	ADV
m-1112	910	27	=3	=3	VERB
m-1112	910	28	mechanism	mechanism	NOUN
m-1112	910	29	creating	create	VERB
m-1112	910	30	elementary	elementary	ADJ
m-1112	910	31	particles	particle	NOUN
m-1112	910	32			PUNCT
m-1112	911	1	[	[	X
m-1112	911	2	n	n	X
m-1112	911	3	-	-	PUNCT
m-1112	911	4	knots=3	knots=3	X
m-1112	911	5	]	]	X
m-1112	911	6	in	in	ADP
m-1112	911	7	𝐕	𝐕	PROPN
m-1112	911	8	gra	gra	NOUN
m-1112	911	9	=	=	PROPN
m-1112	911	10	7,593.1035	7,593.1035	PROPN
m-1112	911	11	v.	v.	ADP
m-1112	911	12	ijo	ijo	PROPN
m-1112	911	13	international	international	PROPN
m-1112	911	14	journal	journal	PROPN
m-1112	911	15	of	of	ADP
m-1112	911	16	mathematics	mathematics	PROPN
m-1112	911	17	(	(	PUNCT
m-1112	911	18	issn	issn	PROPN
m-1112	911	19	:	:	PUNCT
m-1112	911	20	2992	2992	NUM
m-1112	911	21	-	-	SYM
m-1112	911	22	4421	4421	NUM
m-1112	911	23	)	)	PUNCT
m-1112	911	24	volume	volume	NOUN
m-1112	911	25	08	08	NUM
m-1112	912	1	|	|	ADV
m-1112	912	2	issue	issue	NOUN
m-1112	912	3	08	08	NUM
m-1112	913	1	|	|	ADV
m-1112	913	2	august	august	PROPN
m-1112	913	3	2025	2025	NUM
m-1112	913	4	|	|	ADV
m-1112	913	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	913	6	ijo	ijo	PROPN
m-1112	913	7	journals	journal	NOUN
m-1112	913	8	32	32	NUM
m-1112	913	9	the	the	DET
m-1112	913	10	fundamental	fundamental	ADJ
m-1112	913	11	particles	particle	NOUN
m-1112	913	12	origination	origination	NOUN
m-1112	913	13	mechanism	mechanism	NOUN
m-1112	913	14	in	in	ADP
m-1112	913	15	mfmf	mfmf	PROPN
m-1112	913	16	pns	pns	PROPN
m-1112	913	17	caves	cave	NOUN
m-1112	913	18	.	.	PUNCT
m-1112	914	1	8	8	X
m-1112	914	2	..	..	PUNCT
m-1112	914	3	[b	[b	X
m-1112	914	4	]	]	X
m-1112	914	5	..	..	PUNCT
m-1112	914	6	the	the	DET
m-1112	914	7	{	{	PUNCT
m-1112	914	8	tvpm	tvpm	NOUN
m-1112	914	9	}	}	PUNCT
m-1112	914	10	physical	physical	ADJ
m-1112	914	11	mechanisms	mechanism	NOUN
m-1112	914	12	:	:	PUNCT
m-1112	914	13	two	two	NUM
m-1112	914	14	vectors	vector	NOUN
m-1112	914	15	three	three	NUM
m-1112	914	16	poles	pole	NOUN
m-1112	914	17	mechanism	mechanism	NOUN
m-1112	914	18	.	.	PUNCT
m-1112	915	1	figure	figure	NOUN
m-1112	915	2	-8a	-8a	PROPN
m-1112	915	3	:	:	PUNCT
m-1112	915	4	the	the	DET
m-1112	915	5	two	two	NUM
m-1112	915	6	-	-	PUNCT
m-1112	915	7	perpendicular	perpendicular	ADJ
m-1112	915	8	complex	complex	ADJ
m-1112	915	9	-	-	PUNCT
m-1112	915	10	vectors	vector	NOUN
m-1112	915	11	,	,	PUNCT
m-1112	915	12	ca	can	AUX
m-1112	915	13	⊥	⊥	PROPN
m-1112	915	14	cp	cp	INTJ
m-1112	915	15	,	,	PUNCT
m-1112	915	16	slide	slide	VERB
m-1112	915	17	on	on	ADP
m-1112	915	18	(	(	PUNCT
m-1112	915	19	o	o	NOUN
m-1112	915	20	,	,	PUNCT
m-1112	915	21	oa	oa	PROPN
m-1112	915	22	)	)	PUNCT
m-1112	915	23	circle	circle	NOUN
m-1112	915	24	,	,	PUNCT
m-1112	915	25	and	and	CCONJ
m-1112	915	26	through	through	ADP
m-1112	915	27	the	the	DET
m-1112	915	28	three	three	NUM
m-1112	915	29	poles	pole	NOUN
m-1112	915	30	,	,	PUNCT
m-1112	915	31	a	a	PRON
m-1112	915	32	,	,	PUNCT
m-1112	915	33	c	c	NOUN
m-1112	915	34	,	,	PUNCT
m-1112	915	35	p	p	X
m-1112	915	36	,	,	PUNCT
m-1112	915	37	carry	carry	VERB
m-1112	915	38	the	the	DET
m-1112	915	39	stress	stress	NOUN
m-1112	915	40	σ	σ	NOUN
m-1112	915	41	,	,	PUNCT
m-1112	915	42	of	of	ADP
m-1112	915	43	square	square	ADJ
m-1112	915	44	,	,	PUNCT
m-1112	915	45	acpc	acpc	NOUN
m-1112	915	46	’	'	PUNCT
m-1112	915	47	,	,	PUNCT
m-1112	915	48	to	to	ADP
m-1112	915	49	the	the	DET
m-1112	915	50	two	two	NUM
m-1112	915	51	equal	equal	ADJ
m-1112	915	52	and	and	CCONJ
m-1112	915	53	opposite	opposite	ADJ
m-1112	915	54	squares	square	NOUN
m-1112	915	55	|coab|	|coab|	NUM
m-1112	915	56	,	,	PUNCT
m-1112	915	57	|copb’|	|copb’|	NOUN
m-1112	915	58	for	for	ADP
m-1112	915	59	halve	halve	NOUN
m-1112	915	60	area	area	NOUN
m-1112	915	61	stress	stress	NOUN
m-1112	915	62	conservation	conservation	NOUN
m-1112	915	63	b-1	b-1	PROPN
m-1112	915	64	...	...	PUNCT
m-1112	916	1	the	the	DET
m-1112	916	2	conservation	conservation	NOUN
m-1112	916	3	of	of	ADP
m-1112	916	4	energy	energy	NOUN
m-1112	916	5	in	in	ADP
m-1112	916	6	geometry	geometry	NOUN
m-1112	916	7	mechanism	mechanism	NOUN
m-1112	916	8	:	:	PUNCT
m-1112	916	9	[	[	X
m-1112	916	10	62	62	NUM
m-1112	916	11	]	]	PUNCT
m-1112	916	12	in(1)	in(1)	NOUN
m-1112	916	13	…	…	PUNCT
m-1112	916	14	on	on	ADP
m-1112	916	15	aa	aa	PROPN
m-1112	916	16	`	`	PUNCT
m-1112	916	17	diameter	diameter	NOUN
m-1112	916	18	circle	circle	NOUN
m-1112	916	19	(	(	PUNCT
m-1112	916	20	o	o	NOUN
m-1112	916	21	,	,	PUNCT
m-1112	916	22	oa	oa	NOUN
m-1112	916	23	)	)	PUNCT
m-1112	916	24	exists	exist	VERB
m-1112	916	25	the	the	DET
m-1112	916	26	inscribed	inscribe	VERB
m-1112	916	27	-square	-square	PROPN
m-1112	916	28	oa	oa	INTJ
m-1112	916	29	x	x	X
m-1112	916	30	oa	oa	PROPN
m-1112	916	31	=	=	PUNCT
m-1112	916	32	oa²	oa²	ADJ
m-1112	916	33	,	,	PUNCT
m-1112	916	34	and	and	CCONJ
m-1112	916	35	the	the	DET
m-1112	916	36	circumscribed	circumscribed	ADJ
m-1112	916	37	square	square	ADJ
m-1112	917	1	cp	cp	INTJ
m-1112	917	2	x	x	SYM
m-1112	917	3	cp	cp	PROPN
m-1112	917	4	=	=	PUNCT
m-1112	917	5	cp²	cp²	PROPN
m-1112	917	6	.	.	PUNCT
m-1112	918	1	since	since	SCONJ
m-1112	918	2	vector	vector	NOUN
m-1112	918	3	cp	cp	NOUN
m-1112	918	4	=	=	PUNCT
m-1112	919	1	[	[	X
m-1112	919	2	oc=	oc=	ADJ
m-1112	919	3	oa].√𝟐	oa].√𝟐	NOUN
m-1112	919	4	,	,	PUNCT
m-1112	919	5	therefore	therefore	ADV
m-1112	919	6	the	the	DET
m-1112	919	7	inscribed	inscribe	VERB
m-1112	919	8	square	square	NOUN
m-1112	919	9	is	be	AUX
m-1112	919	10	halve	halve	NOUN
m-1112	919	11	the	the	DET
m-1112	919	12	circumscribed	circumscribed	ADJ
m-1112	919	13	.	.	PUNCT
m-1112	920	1	the	the	DET
m-1112	920	2	same	same	ADJ
m-1112	920	3	to	to	ADP
m-1112	920	4	the	the	DET
m-1112	920	5	circles	circle	NOUN
m-1112	921	1	π	π	NOUN
m-1112	921	2	[	[	PUNCT
m-1112	921	3	𝐂𝐏	𝐂𝐏	PROPN
m-1112	921	4	√𝟐	√𝟐	PROPN
m-1112	921	5	]	]	PUNCT
m-1112	921	6	²	²	PROPN
m-1112	921	7	=	=	SYM
m-1112	921	8	π	π	PROPN
m-1112	921	9	[	[	X
m-1112	921	10	cp	cp	X
m-1112	921	11	]	]	X
m-1112	921	12	²	²	PROPN
m-1112	921	13	=	=	SYM
m-1112	921	14	π	π	PROPN
m-1112	922	1	[	[	X
m-1112	922	2	oa.√𝟐	oa.√𝟐	X
m-1112	922	3	]	]	X
m-1112	922	4	²	²	PROPN
m-1112	922	5	=	=	SYM
m-1112	922	6	2.π	2.π	NUM
m-1112	923	1	[	[	X
m-1112	923	2	oa]²	oa]²	X
m-1112	923	3	.	.	PUNCT
m-1112	924	1	this	this	DET
m-1112	924	2	linear	linear	ADJ
m-1112	924	3	expansion	expansion	NOUN
m-1112	924	4	of	of	ADP
m-1112	924	5	archimedes	archimede	NOUN
m-1112	924	6	-	-	PUNCT
m-1112	924	7	circles	circle	NOUN
m-1112	924	8	and	and	CCONJ
m-1112	924	9	squares	square	NOUN
m-1112	924	10	passes	pass	VERB
m-1112	924	11	from	from	ADP
m-1112	924	12	a	a	DET
m-1112	924	13	point	point	NOUN
m-1112	924	14	m	m	VERB
m-1112	924	15	,	,	PUNCT
m-1112	924	16	such	such	ADJ
m-1112	924	17	that	that	SCONJ
m-1112	924	18	π	π	PROPN
m-1112	924	19	r	r	NOUN
m-1112	924	20	²	²	NUM
m-1112	924	21	=	=	SYM
m-1112	924	22	cmnh	cmnh	NOUN
m-1112	924	23	square	square	NOUN
m-1112	924	24	.	.	PUNCT
m-1112	925	1	[	[	PUNCT
m-1112	925	2	47	47	NUM
m-1112	925	3	51	51	NUM
m-1112	925	4	]	]	PUNCT
m-1112	925	5	in(2	in(2	NOUN
m-1112	925	6	)	)	PUNCT
m-1112	925	7	...	...	PUNCT
m-1112	925	8	on	on	ADP
m-1112	925	9	two	two	NUM
m-1112	925	10	-	-	PUNCT
m-1112	925	11	perpendicular	perpendicular	ADJ
m-1112	925	12	vectors	vector	NOUN
m-1112	925	13	,	,	PUNCT
m-1112	925	14	ca	can	AUX
m-1112	925	15	⊥	⊥	PROPN
m-1112	925	16	cp	cp	INTJ
m-1112	925	17	,	,	PUNCT
m-1112	925	18	point	point	VERB
m-1112	925	19	c	c	NOUN
m-1112	925	20	`	`	PUNCT
m-1112	925	21	slides	slide	VERB
m-1112	925	22	on	on	ADP
m-1112	925	23	(	(	PUNCT
m-1112	925	24	o	o	NOUN
m-1112	925	25	,	,	PUNCT
m-1112	925	26	oa	oa	PROPN
m-1112	925	27	=	=	PUNCT
m-1112	925	28	op	op	NOUN
m-1112	925	29	)	)	PUNCT
m-1112	925	30	circle	circle	NOUN
m-1112	925	31	forming	form	VERB
m-1112	925	32	the	the	DET
m-1112	925	33	cac`p	cac`p	NOUN
m-1112	925	34	to	to	PART
m-1112	925	35	cmnh	cmnh	VERB
m-1112	925	36	to	to	ADP
m-1112	925	37	cbao	cbao	NOUN
m-1112	925	38	squares	square	NOUN
m-1112	925	39	with	with	ADP
m-1112	925	40	prior	prior	ADV
m-1112	925	41	of	of	ADP
m-1112	925	42	(	(	PUNCT
m-1112	925	43	1	1	X
m-1112	925	44	)	)	PUNCT
m-1112	925	45	properties	property	NOUN
m-1112	925	46	.this	.this	PRON
m-1112	925	47	sliding	slide	VERB
m-1112	925	48	-	-	PUNCT
m-1112	925	49	rotating	rotate	VERB
m-1112	925	50	method	method	NOUN
m-1112	925	51	is	be	AUX
m-1112	925	52	the	the	DET
m-1112	925	53	markos	markos	PROPN
m-1112	925	54	{	{	PUNCT
m-1112	925	55	2	2	NUM
m-1112	925	56	-vectors	-vector	NOUN
m-1112	925	57	3	3	NUM
m-1112	925	58	-poles	-pole	NOUN
m-1112	925	59	mechanism	mechanism	NOUN
m-1112	925	60	}	}	PUNCT
m-1112	925	61	which	which	DET
m-1112	925	62	circles	circle	NOUN
m-1112	925	63	and	and	CCONJ
m-1112	925	64	squares	square	NOUN
m-1112	925	65	as	as	SCONJ
m-1112	925	66	areas	area	NOUN
m-1112	925	67	pass	pass	VERB
m-1112	925	68	from	from	ADP
m-1112	925	69	the	the	DET
m-1112	925	70	point	point	NOUN
m-1112	925	71	m	m	AUX
m-1112	925	72	determined	determine	VERB
m-1112	925	73	by	by	ADP
m-1112	925	74	the	the	DET
m-1112	925	75	position	position	NOUN
m-1112	925	76	𝐀	𝐀	PROPN
m-1112	925	77	𝐞	𝐞	NOUN
m-1112	925	78	,	,	PUNCT
m-1112	925	79	such	such	ADJ
m-1112	925	80	that	that	SCONJ
m-1112	925	81	π	π	PROPN
m-1112	925	82	r	r	NOUN
m-1112	925	83	²	²	NUM
m-1112	925	84	=	=	SYM
m-1112	925	85	cmnh	cmnh	NOUN
m-1112	925	86	square	square	NOUN
m-1112	925	87	.	.	PUNCT
m-1112	926	1	the	the	DET
m-1112	926	2	squaring	squaring	NOUN
m-1112	926	3	of	of	ADP
m-1112	926	4	the	the	DET
m-1112	926	5	circle	circle	NOUN
m-1112	926	6	π	π	PROPN
m-1112	926	7	[	[	PUNCT
m-1112	926	8	𝐂𝐀	𝐂𝐀	PROPN
m-1112	926	9	√𝟐	√𝟐	PROPN
m-1112	926	10	]	]	PUNCT
m-1112	926	11	²	²	NUM
m-1112	926	12	=	=	NOUN
m-1112	926	13	cm²	cm²	PROPN
m-1112	926	14	.	.	PUNCT
m-1112	927	1	[	[	PUNCT
m-1112	927	2	47	47	NUM
m-1112	927	3	51	51	NUM
m-1112	927	4	–	–	PUNCT
m-1112	927	5	98a	98a	NUM
m-1112	927	6	]	]	PUNCT
m-1112	927	7	in(3	in(3	PROPN
m-1112	927	8	)	)	PUNCT
m-1112	927	9	..	..	PUNCT
m-1112	928	1	if	if	SCONJ
m-1112	928	2	the	the	DET
m-1112	928	3	two	two	NUM
m-1112	928	4	-	-	PUNCT
m-1112	928	5	perpendicular	perpendicular	ADJ
m-1112	928	6	vectors	vector	NOUN
m-1112	928	7	are	be	AUX
m-1112	928	8	conductors	conductor	NOUN
m-1112	928	9	with	with	ADP
m-1112	928	10	prior	prior	ADJ
m-1112	928	11	properties	property	NOUN
m-1112	928	12	then	then	ADV
m-1112	928	13	square	square	VERB
m-1112	928	14	cac`p	cac`p	PROPN
m-1112	928	15	to	to	PART
m-1112	928	16	cmnh	cmnh	VERB
m-1112	928	17	to	to	ADP
m-1112	928	18	cbao	cbao	NOUN
m-1112	928	19	square	square	ADJ
m-1112	928	20	,	,	PUNCT
m-1112	928	21	are	be	AUX
m-1112	928	22	a	a	DET
m-1112	928	23	rotating	rotate	VERB
m-1112	928	24	and	and	CCONJ
m-1112	928	25	changing	change	VERB
m-1112	928	26	-	-	PUNCT
m-1112	928	27	squares	square	NOUN
m-1112	928	28	-	-	PUNCT
m-1112	928	29	system	system	NOUN
m-1112	928	30	,	,	PUNCT
m-1112	928	31	cp	cp	INTJ
m-1112	928	32	²	²	NUM
m-1112	928	33	↑	↑	NOUN
m-1112	928	34	=	=	PROPN
m-1112	928	35	|∷|	|∷|	PROPN
m-1112	928	36	,	,	PUNCT
m-1112	928	37	↻	↻	PROPN
m-1112	928	38	,	,	PUNCT
m-1112	928	39	→	→	SYM
m-1112	928	40	to	to	ADP
m-1112	928	41	2	2	NUM
m-1112	928	42	-	-	PUNCT
m-1112	928	43	half	half	NOUN
m-1112	928	44	and	and	CCONJ
m-1112	928	45	equal	equal	ADJ
m-1112	928	46	area	area	NOUN
m-1112	928	47	squares	square	NOUN
m-1112	928	48	cb	cb	PROPN
m-1112	928	49	²	²	PROPN
m-1112	928	50	=	=	NOUN
m-1112	928	51	⤭	⤭	NOUN
m-1112	928	52	=[	=[	NOUN
m-1112	928	53	⊕	⊕	NOUN
m-1112	928	54	∷	∷	NOUN
m-1112	928	55	2	2	NUM
m-1112	929	1	+	+	NOUN
m-1112	929	2	⊝	⊝	NOUN
m-1112	929	3	∷	∷	NOUN
m-1112	929	4	2	2	NUM
m-1112	929	5	]	]	PUNCT
m-1112	929	6	cb`²	cb`²	NOUN
m-1112	929	7	,	,	PUNCT
m-1112	929	8	by	by	ADP
m-1112	929	9	turns	turn	NOUN
m-1112	929	10	in	in	ADP
m-1112	929	11	oabc	oabc	NOUN
m-1112	929	12	⊥	⊥	PROPN
m-1112	929	13	opb`c	opb`c	X
m-1112	929	14	planes	plane	NOUN
m-1112	929	15	,	,	PUNCT
m-1112	929	16	which	which	DET
m-1112	929	17	equilibrium	equilibrium	NOUN
m-1112	929	18	and	and	CCONJ
m-1112	929	19	consist	consist	VERB
m-1112	929	20	,	,	PUNCT
m-1112	929	21	the	the	DET
m-1112	929	22	neutral	neutral	ADJ
m-1112	929	23	-	-	PUNCT
m-1112	929	24	space	space	NOUN
m-1112	929	25	.	.	PUNCT
m-1112	930	1	placing	place	VERB
m-1112	930	2	stress	stress	NOUN
m-1112	930	3	in	in	ADP
m-1112	930	4	squares	square	NOUN
m-1112	930	5	becomes	become	VERB
m-1112	930	6	the	the	DET
m-1112	930	7	physical	physical	ADJ
m-1112	930	8	world	world	NOUN
m-1112	930	9	as	as	ADP
m-1112	930	10	,	,	PUNCT
m-1112	930	11	physics	physics	NOUN
m-1112	930	12	mechanics	mechanic	NOUN
m-1112	930	13	and	and	CCONJ
m-1112	930	14	chemistry	chemistry	NOUN
m-1112	930	15	,	,	PUNCT
m-1112	930	16	by	by	ADP
m-1112	930	17	conservation	conservation	NOUN
m-1112	930	18	of	of	ADP
m-1112	930	19	energy	energy	NOUN
m-1112	930	20	as	as	ADP
m-1112	930	21	stresses	stress	NOUN
m-1112	930	22	in	in	ADP
m-1112	930	23	areas	area	NOUN
m-1112	930	24	.	.	PUNCT
m-1112	931	1	as	as	ADP
m-1112	931	2	in	in	ADP
m-1112	931	3	electricity	electricity	NOUN
m-1112	931	4	,	,	PUNCT
m-1112	931	5	the	the	DET
m-1112	931	6	flow	flow	NOUN
m-1112	931	7	of	of	ADP
m-1112	931	8	a	a	DET
m-1112	931	9	current	current	NOUN
m-1112	931	10	in	in	ADP
m-1112	931	11	an	an	DET
m-1112	931	12	conductor	conductor	NOUN
m-1112	931	13	,	,	PUNCT
m-1112	931	14	ca	ca	NOUN
m-1112	931	15	=	=	SYM
m-1112	931	16	d	d	PROPN
m-1112	931	17	,	,	PUNCT
m-1112	931	18	represents	represent	VERB
m-1112	931	19	the	the	DET
m-1112	931	20	created	create	VERB
m-1112	931	21	around	around	ADP
m-1112	931	22	the	the	DET
m-1112	931	23	conductor	conductor	NOUN
m-1112	931	24	by	by	ADP
m-1112	931	25	the	the	DET
m-1112	931	26	circular	circular	ADJ
m-1112	931	27	-	-	PUNCT
m-1112	931	28	lines	line	NOUN
m-1112	931	29	of	of	ADP
m-1112	931	30	forces	force	NOUN
m-1112	931	31	,	,	PUNCT
m-1112	931	32	magnetic	magnetic	ADJ
m-1112	931	33	field	field	NOUN
m-1112	931	34	,	,	PUNCT
m-1112	931	35	the	the	DET
m-1112	931	36	flow	flow	NOUN
m-1112	931	37	of	of	ADP
m-1112	931	38	⊕→⊝-charge	⊕→⊝-charge	PROPN
m-1112	931	39	in	in	ADP
m-1112	931	40	d	d	PROPN
m-1112	931	41	ijo	ijo	PROPN
m-1112	931	42	international	international	PROPN
m-1112	931	43	journal	journal	PROPN
m-1112	931	44	of	of	ADP
m-1112	931	45	mathematics	mathematics	PROPN
m-1112	931	46	(	(	PUNCT
m-1112	931	47	issn	issn	PROPN
m-1112	931	48	:	:	PUNCT
m-1112	931	49	2992	2992	NUM
m-1112	931	50	-	-	SYM
m-1112	931	51	4421	4421	NUM
m-1112	931	52	)	)	PUNCT
m-1112	931	53	volume	volume	NOUN
m-1112	931	54	08	08	NUM
m-1112	932	1	|	|	ADV
m-1112	932	2	issue	issue	NOUN
m-1112	932	3	08	08	NUM
m-1112	933	1	|	|	ADV
m-1112	933	2	august	august	PROPN
m-1112	933	3	2025	2025	NUM
m-1112	933	4	|	|	ADV
m-1112	933	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	933	6	ijo	ijo	PROPN
m-1112	933	7	journals	journal	NOUN
m-1112	933	8	33	33	NUM
m-1112	933	9	the	the	DET
m-1112	933	10	fundamental	fundamental	ADJ
m-1112	933	11	particles	particle	NOUN
m-1112	933	12	origination	origination	NOUN
m-1112	933	13	mechanism	mechanism	NOUN
m-1112	933	14	in	in	ADP
m-1112	933	15	mfmf	mfmf	PROPN
m-1112	933	16	pns	pns	PROPN
m-1112	933	17	caves	cave	NOUN
m-1112	933	18	.	.	PUNCT
m-1112	934	1	conductor	conductor	NOUN
m-1112	934	2	,	,	PUNCT
m-1112	934	3	is	be	AUX
m-1112	934	4	the	the	DET
m-1112	934	5	torsional	torsional	ADJ
m-1112	934	6	force	force	NOUN
m-1112	934	7	�	�	NOUN
m-1112	934	8	̅	̅	NOUN
m-1112	934	9	�	�	NOUN
m-1112	934	10	𝐅	𝐅	NOUN
m-1112	934	11	=	=	SYM
m-1112	934	12	v⃗	v⃗	NOUN
m-1112	934	13	.r	.r	NOUN
m-1112	935	1	=	=	X
m-1112	935	2	w⃗⃗⃗	w⃗⃗⃗	NOUN
m-1112	935	3	.r	.r	NOUN
m-1112	935	4	²	²	NUM
m-1112	935	5	=	=	SYM
m-1112	935	6	2πf	2πf	NOUN
m-1112	935	7	.	.	PUNCT
m-1112	936	1	r	r	NOUN
m-1112	936	2	²	²	NUM
m-1112	936	3	=	=	SYM
m-1112	936	4	σ	σ	PROPN
m-1112	936	5	φ	φ	PROPN
m-1112	936	6	r	r	NOUN
m-1112	936	7	…	…	PUNCT
m-1112	936	8	....	....	PUNCT
m-1112	936	9	(	(	PUNCT
m-1112	936	10	1	1	NUM
m-1112	936	11	)	)	PUNCT
m-1112	936	12	.	.	PUNCT
m-1112	937	1	since	since	SCONJ
m-1112	937	2	edge	edge	NOUN
m-1112	937	3	-	-	PUNCT
m-1112	937	4	velocities	velocity	NOUN
m-1112	937	5	v̅c	v̅c	NOUN
m-1112	937	6	=	=	PUNCT
m-1112	937	7	v̅a=	v̅a=	NOUN
m-1112	937	8	0	0	NUM
m-1112	937	9	,	,	PUNCT
m-1112	937	10	therefore	therefore	ADV
m-1112	937	11	ca	can	AUX
m-1112	937	12	=	=	NOUN
m-1112	937	13	d=	d=	NOUN
m-1112	937	14	½	½	NOUN
m-1112	937	15	(	(	PUNCT
m-1112	937	16	at²	at²	NOUN
m-1112	937	17	)	)	PUNCT
m-1112	937	18	and	and	CCONJ
m-1112	937	19	acceleration	acceleration	NOUN
m-1112	937	20	,	,	PUNCT
m-1112	937	21	a	a	DET
m-1112	937	22	=	=	NOUN
m-1112	937	23	2d	2d	X
m-1112	937	24	/t²	/t²	PUNCT
m-1112	938	1	=	=	NOUN
m-1112	938	2	2d.f²	2d.f²	PROPN
m-1112	938	3	,	,	PUNCT
m-1112	938	4	and	and	CCONJ
m-1112	938	5	then	then	ADV
m-1112	938	6	the	the	DET
m-1112	938	7	velocities	velocity	NOUN
m-1112	938	8	diagram	diagram	NOUN
m-1112	938	9	is	be	AUX
m-1112	938	10	energy	energy	NOUN
m-1112	938	11	-	-	PUNCT
m-1112	938	12	triangle	triangle	NOUN
m-1112	938	13	→	→	SYM
m-1112	938	14	v.[δ	v.[δ	NOUN
m-1112	938	15	-	-	PUNCT
m-1112	938	16	cap	cap	NOUN
m-1112	938	17	]	]	PUNCT
m-1112	939	1	=	=	PUNCT
m-1112	939	2	v.[½	v.[½	PROPN
m-1112	939	3	(	(	PUNCT
m-1112	939	4	2d	2d	NOUN
m-1112	939	5	.	.	PUNCT
m-1112	939	6	|v⃗	|v⃗	PROPN
m-1112	939	7	|	|	ADV
m-1112	939	8	)	)	PUNCT
m-1112	939	9	]	]	PUNCT
m-1112	940	1	=	=	PUNCT
m-1112	940	2	v.[d	v.[d	PROPN
m-1112	940	3	w	w	NOUN
m-1112	940	4	r	r	NOUN
m-1112	940	5	]	]	PUNCT
m-1112	940	6	=	=	SYM
m-1112	940	7	v	v	X
m-1112	940	8	d.2πf.r	d.2πf.r	PROPN
m-1112	940	9	=	=	SYM
m-1112	940	10	v.[σ	v.[σ	PROPN
m-1112	940	11	φ	φ	PROPN
m-1112	940	12	d	d	X
m-1112	940	13	]	]	X
m-1112	940	14	..	..	PUNCT
m-1112	940	15	(	(	PUNCT
m-1112	940	16	2	2	X
m-1112	940	17	)	)	PUNCT
m-1112	940	18	the	the	DET
m-1112	940	19	current	current	ADJ
m-1112	940	20	flow	flow	NOUN
m-1112	940	21	in	in	ADP
m-1112	940	22	electric	electric	ADJ
m-1112	940	23	-	-	PUNCT
m-1112	940	24	field	field	NOUN
m-1112	940	25	�	�	NOUN
m-1112	940	26	̅	̅	NOUN
m-1112	940	27	�	�	NOUN
m-1112	940	28	𝐂𝐀𝐏	𝐂𝐀𝐏	PROPN
m-1112	940	29	of	of	ADP
m-1112	940	30	cap	cap	NOUN
m-1112	940	31	plane	plane	NOUN
m-1112	940	32	is	be	AUX
m-1112	940	33	transported	transport	VERB
m-1112	940	34	into	into	ADP
m-1112	940	35	the	the	DET
m-1112	940	36	perpendicular	perpendicular	NOUN
m-1112	940	37	to	to	PART
m-1112	940	38	ca	can	AUX
m-1112	940	39	axis	axis	VERB
m-1112	940	40	opposite	opposite	ADJ
m-1112	940	41	magnetic	magnetic	ADJ
m-1112	940	42	-	-	PUNCT
m-1112	940	43	field	field	NOUN
m-1112	940	44	�	�	NOUN
m-1112	940	45	̅	̅	NOUN
m-1112	940	46	�	�	NOUN
m-1112	940	47	𝐏𝐀	𝐏𝐀	PROPN
m-1112	940	48	in	in	ADP
m-1112	940	49	pa	pa	PROPN
m-1112	940	50	-	-	NOUN
m-1112	940	51	plane	plane	NOUN
m-1112	940	52	due	due	ADP
m-1112	940	53	to	to	ADP
m-1112	940	54	the	the	DET
m-1112	940	55	force	force	NOUN
m-1112	940	56	�	�	PROPN
m-1112	940	57	̅	̅	NOUN
m-1112	940	58	�	�	PROPN
m-1112	940	59	𝐅=	𝐅=	PROPN
m-1112	940	60	�	�	PROPN
m-1112	940	61	⃗	⃗	NOUN
m-1112	940	62	�	�	NOUN
m-1112	940	63	.r	.r	NOUN
m-1112	941	1	=	=	PUNCT
m-1112	941	2	i	i	NOUN
m-1112	941	3	=	=	PUNCT
m-1112	941	4	𝟐𝛑𝐫	𝟐𝛑𝐫	NOUN
m-1112	941	5	𝛍	𝛍	ADP
m-1112	941	6	�	�	PROPN
m-1112	941	7	̅	̅	NOUN
m-1112	941	8	�	�	PROPN
m-1112	941	9	𝐏𝐀=	𝐏𝐀=	NOUN
m-1112	941	10	σ	σ	PROPN
m-1112	941	11	φ	φ	PROPN
m-1112	941	12	r	r	PROPN
m-1112	941	13	.(3	.(3	NOUN
m-1112	941	14	)	)	PUNCT
m-1112	941	15	stress	stress	NOUN
m-1112	941	16	σ	σ	NOUN
m-1112	942	1	=	=	PUNCT
m-1112	942	2	𝐅𝐨𝐫𝐜𝐞	𝐅𝐨𝐫𝐜𝐞	PROPN
m-1112	942	3	𝐀𝐫𝐞𝐚	𝐀𝐫𝐞𝐚	PROPN
m-1112	942	4	=	=	SYM
m-1112	942	5	𝐆	𝐆	PROPN
m-1112	942	6	𝐯.𝐯	𝐯.𝐯	PROPN
m-1112	943	1	=	=	SYM
m-1112	943	2	g	g	PROPN
m-1112	943	3	√2	√2	PROPN
m-1112	943	4	.c	.c	PROPN
m-1112	944	1	=	=	PRON
m-1112	944	2	the	the	DET
m-1112	944	3	�	�	PROPN
m-1112	944	4	̅	̅	NOUN
m-1112	944	5	�	�	PROPN
m-1112	944	6	electron	electron	NOUN
m-1112	944	7	charge	charge	NOUN
m-1112	944	8	=	=	SYM
m-1112	944	9	g	g	PROPN
m-1112	944	10	√2	√2	PROPN
m-1112	944	11	.c	.c	PROPN
m-1112	945	1	=	=	PUNCT
m-1112	946	1	6,6736923	6,6736923	NUM
m-1112	946	2	.10−11	.10−11	SYM
m-1112	946	3	1,41429.2,9979346.108	1,41429.2,9979346.108	NUM
m-1112	947	1	=	=	NUM
m-1112	947	2	1,574.10−19	1,574.10−19	NUM
m-1112	947	3	c	c	NOUN
m-1112	947	4	the	the	DET
m-1112	947	5	spin	spin	NOUN
m-1112	947	6	of	of	ADP
m-1112	947	7	cave	cave	NOUN
m-1112	947	8	,	,	PUNCT
m-1112	947	9	r	r	NOUN
m-1112	947	10	,	,	PUNCT
m-1112	947	11	is	be	AUX
m-1112	947	12	equal	equal	ADJ
m-1112	947	13	to	to	ADP
m-1112	947	14	the	the	DET
m-1112	947	15	angular	angular	ADJ
m-1112	947	16	-	-	PUNCT
m-1112	947	17	momentum	momentum	NOUN
m-1112	947	18	-	-	PUNCT
m-1112	947	19	vector	vector	NOUN
m-1112	947	20	→	→	SYM
m-1112	947	21	spin	spin	NOUN
m-1112	947	22	≡	≡	PROPN
m-1112	947	23	|	|	NOUN
m-1112	947	24	�	�	PROPN
m-1112	947	25	̅	̅	NOUN
m-1112	947	26	�	�	NOUN
m-1112	947	27	|	|	CCONJ
m-1112	947	28	≡	≡	PROPN
m-1112	947	29	r	r	PROPN
m-1112	947	30	σ	σ	PROPN
m-1112	947	31	φ	φ	PROPN
m-1112	947	32	←	←	PROPN
m-1112	947	33	which	which	PRON
m-1112	947	34	contains	contain	VERB
m-1112	947	35	and	and	CCONJ
m-1112	947	36	it	it	PRON
m-1112	947	37	is	be	AUX
m-1112	947	38	the	the	DET
m-1112	947	39	golden	golden	ADJ
m-1112	947	40	-	-	PUNCT
m-1112	947	41	radio	radio	NOUN
m-1112	947	42	-	-	PUNCT
m-1112	947	43	frequency	frequency	NOUN
m-1112	947	44	φ	φ	NOUN
m-1112	947	45	as	as	ADP
m-1112	947	46	pressure	pressure	NOUN
m-1112	947	47	,	,	PUNCT
m-1112	947	48	σ	σ	PROPN
m-1112	947	49	,	,	PUNCT
m-1112	947	50	in	in	ADP
m-1112	947	51	cave	cave	NOUN
m-1112	947	52	r	r	NOUN
m-1112	947	53	.	.	PUNCT
m-1112	948	1	i.e.	i.e.	X
m-1112	948	2	[	[	X
m-1112	948	3	a	a	X
m-1112	948	4	]	]	X
m-1112	948	5	the	the	DET
m-1112	948	6	forces	force	NOUN
m-1112	948	7	are	be	AUX
m-1112	948	8	spread	spread	VERB
m-1112	948	9	on	on	ADP
m-1112	948	10	surfaces	surface	NOUN
m-1112	948	11	as	as	ADP
m-1112	948	12	stresses	stress	NOUN
m-1112	948	13	σ	σ	NOUN
m-1112	948	14	,	,	PUNCT
m-1112	948	15	and	and	CCONJ
m-1112	948	16	in	in	ADP
m-1112	948	17	case	case	NOUN
m-1112	948	18	of	of	ADP
m-1112	948	19	area	area	NOUN
m-1112	948	20	=	=	SYM
m-1112	948	21	0	0	NUM
m-1112	948	22	then	then	ADV
m-1112	948	23	are	be	AUX
m-1112	948	24	spread	spread	VERB
m-1112	948	25	on	on	ADP
m-1112	948	26	the	the	DET
m-1112	948	27	velocity	velocity	NOUN
m-1112	948	28	–	–	PUNCT
m-1112	948	29	square	square	ADJ
m-1112	948	30	–	–	PUNCT
m-1112	948	31	surfaces	surface	NOUN
m-1112	948	32	,	,	PUNCT
m-1112	948	33	and	and	CCONJ
m-1112	948	34	for	for	ADP
m-1112	948	35	the	the	DET
m-1112	948	36	light	light	NOUN
m-1112	948	37	c	c	PROPN
m-1112	948	38	,	,	PUNCT
m-1112	948	39	on	on	ADP
m-1112	948	40	resultant	resultant	NOUN
m-1112	948	41	√𝟐.c	√𝟐.c	NOUN
m-1112	948	42	.	.	PUNCT
m-1112	949	1	b-2	b-2	PROPN
m-1112	949	2	...	...	PUNCT
m-1112	949	3	for	for	ADP
m-1112	949	4	conductor	conductor	NOUN
m-1112	949	5	-	-	PUNCT
m-1112	949	6	case	case	NOUN
m-1112	949	7	which	which	PRON
m-1112	949	8	is	be	AUX
m-1112	949	9	an	an	DET
m-1112	949	10	screw	screw	NOUN
m-1112	949	11	-	-	PUNCT
m-1112	949	12	motion	motion	NOUN
m-1112	949	13	where	where	SCONJ
m-1112	949	14	a	a	DET
m-1112	949	15	torque	torque	NOUN
m-1112	949	16	is	be	AUX
m-1112	949	17	created	create	VERB
m-1112	949	18	in	in	ADP
m-1112	949	19	perpendicular	perpendicular	ADJ
m-1112	949	20	plane	plane	NOUN
m-1112	949	21	of	of	ADP
m-1112	949	22	con	con	NOUN
m-1112	949	23	-	-	PUNCT
m-1112	949	24	axis	axis	NOUN
m-1112	949	25	.	.	PUNCT
m-1112	950	1	markos	markos	PROPN
m-1112	950	2	{	{	PUNCT
m-1112	950	3	2	2	NUM
m-1112	950	4	-	-	NUM
m-1112	950	5	vector	vector	NOUN
m-1112	950	6	3	3	NUM
m-1112	950	7	-	-	PUNCT
m-1112	950	8	poles	poles	NOUN
m-1112	950	9	rotating	rotate	VERB
m-1112	950	10	mechanism	mechanism	NOUN
m-1112	950	11	}	}	PUNCT
m-1112	950	12	,	,	PUNCT
m-1112	950	13	{	{	PUNCT
m-1112	950	14	−a	−a	ADV
m-1112	950	15	∷	∷	NOUN
m-1112	950	16	↻	↻	PROPN
m-1112	951	1	+	+	PROPN
m-1112	951	2	𝐂	𝐂	PROPN
m-1112	951	3	↑	↑	NOUN
m-1112	952	1	[	[	X
m-1112	952	2	⊕	⊕	NOUN
m-1112	952	3	∷	∷	NOUN
m-1112	952	4	2	2	NUM
m-1112	952	5	+	+	NOUN
m-1112	952	6	⊝	⊝	NOUN
m-1112	952	7	∷	∷	NOUN
m-1112	952	8	2	2	NUM
m-1112	952	9	]	]	PUNCT
m-1112	952	10	𝐏	𝐏	PROPN
m-1112	952	11	}	}	PUNCT
m-1112	952	12	carries	carry	VERB
m-1112	952	13	motion	motion	NOUN
m-1112	952	14	(	(	PUNCT
m-1112	952	15	+	+	NOUN
m-1112	952	16	)	)	PUNCT
m-1112	952	17	→	→	SYM
m-1112	952	18	(	(	PUNCT
m-1112	952	19	-	-	INTJ
m-1112	952	20	)	)	PUNCT
m-1112	952	21	from	from	ADP
m-1112	952	22	point	point	NOUN
m-1112	952	23	a	a	PRON
m-1112	952	24	through	through	ADP
m-1112	952	25	an	an	DET
m-1112	952	26	perpendicular	perpendicular	ADJ
m-1112	952	27	-	-	PUNCT
m-1112	952	28	conductor	conductor	NOUN
m-1112	952	29	ca	ca	NOUN
m-1112	952	30	,	,	PUNCT
m-1112	952	31	to	to	PART
m-1112	952	32	point	point	VERB
m-1112	952	33	b	b	PROPN
m-1112	952	34	,	,	PUNCT
m-1112	952	35	into	into	ADP
m-1112	952	36	an	an	DET
m-1112	952	37	changeable	changeable	ADJ
m-1112	952	38	and	and	CCONJ
m-1112	952	39	rotating	rotate	VERB
m-1112	952	40	-	-	PUNCT
m-1112	952	41	squares	square	NOUN
m-1112	952	42	-	-	PUNCT
m-1112	952	43	system	system	NOUN
m-1112	952	44	,	,	PUNCT
m-1112	952	45	pa	pa	PROPN
m-1112	952	46	↑	↑	PROPN
m-1112	953	1	=	=	PROPN
m-1112	953	2	|∷|	|∷|	PROPN
m-1112	953	3	,	,	PUNCT
m-1112	953	4	↻	↻	PROPN
m-1112	953	5	,	,	PUNCT
m-1112	953	6	→	→	SYM
m-1112	953	7	to	to	ADP
m-1112	953	8	2	2	NUM
m-1112	953	9	-	-	PUNCT
m-1112	953	10	half	half	NOUN
m-1112	953	11	and	and	CCONJ
m-1112	953	12	equal	equal	ADJ
m-1112	953	13	area	area	NOUN
m-1112	953	14	squares	square	NOUN
m-1112	953	15	cb	cb	NOUN
m-1112	953	16	=	=	PUNCT
m-1112	953	17	⤭	⤭	X
m-1112	953	18	=	=	PUNCT
m-1112	954	1	[	[	X
m-1112	954	2	⊕	⊕	NOUN
m-1112	954	3	∷	∷	NOUN
m-1112	954	4	2	2	NUM
m-1112	955	1	+	+	NOUN
m-1112	955	2	⊝	⊝	NOUN
m-1112	955	3	∷	∷	NOUN
m-1112	955	4	2	2	NUM
m-1112	955	5	]	]	PUNCT
m-1112	955	6	cb	cb	PROPN
m-1112	955	7	`	`	PUNCT
m-1112	955	8	,	,	PUNCT
m-1112	955	9	by	by	ADP
m-1112	955	10	turns	turn	NOUN
m-1112	955	11	in	in	ADP
m-1112	955	12	oabc	oabc	NOUN
m-1112	955	13	⊥	⊥	NOUN
m-1112	955	14	opb`c	opb`c	X
m-1112	955	15	planes	plane	NOUN
m-1112	955	16	which	which	DET
m-1112	955	17	equilibrium	equilibrium	NOUN
m-1112	956	1	[	[	X
m-1112	956	2	⊕	⊕	NOUN
m-1112	956	3	∷	∷	NOUN
m-1112	956	4	2	2	NUM
m-1112	956	5	+	+	NOUN
m-1112	956	6	⊝	⊝	NOUN
m-1112	956	7	∷	∷	NOUN
m-1112	956	8	2	2	NUM
m-1112	956	9	]=	]=	NOUN
m-1112	956	10	0	0	NUM
m-1112	956	11	(	(	PUNCT
m-1112	956	12	the	the	DET
m-1112	956	13	neutral	neutral	ADJ
m-1112	956	14	-	-	PUNCT
m-1112	956	15	space	space	NOUN
m-1112	956	16	)	)	PUNCT
m-1112	956	17	.	.	PUNCT
m-1112	957	1	b-3	b-3	PROPN
m-1112	957	2	..	..	PUNCT
m-1112	957	3	for	for	ADP
m-1112	957	4	the	the	DET
m-1112	957	5	motion	motion	NOUN
m-1112	957	6	of	of	ADP
m-1112	957	7	the	the	DET
m-1112	957	8	⊕→⊝-charge	⊕→⊝-charge	PROPN
m-1112	957	9	of	of	ADP
m-1112	957	10	any	any	DET
m-1112	957	11	conductor	conductor	NOUN
m-1112	958	1	d	d	NOUN
m-1112	958	2	=	=	PRON
m-1112	958	3	ca	can	AUX
m-1112	958	4	becomes	become	VERB
m-1112	958	5	stress	stress	NOUN
m-1112	958	6	σ	σ	NOUN
m-1112	958	7	in	in	ADP
m-1112	958	8	length	length	NOUN
m-1112	958	9	d	d	X
m-1112	958	10	motion	motion	NOUN
m-1112	958	11	is	be	AUX
m-1112	958	12	created	create	VERB
m-1112	958	13	in	in	ADP
m-1112	958	14	conductors	conductor	NOUN
m-1112	958	15	d	d	X
m-1112	958	16	≡	≡	PROPN
m-1112	959	1	[	[	X
m-1112	959	2	⊕←	⊕←	X
m-1112	959	3	2𝐫	2𝐫	ADJ
m-1112	959	4	→⊝	→⊝	NOUN
m-1112	959	5	]	]	PUNCT
m-1112	959	6	following	follow	VERB
m-1112	959	7	the	the	DET
m-1112	959	8	[	[	X
m-1112	959	9	⊕↔⊝	⊕↔⊝	NOUN
m-1112	959	10	]	]	X
m-1112	959	11	interactions	interaction	NOUN
m-1112	959	12	.this	.this	PRON
m-1112	959	13	motion	motion	NOUN
m-1112	959	14	is	be	AUX
m-1112	959	15	conserved	conserve	VERB
m-1112	959	16	and	and	CCONJ
m-1112	959	17	kept	keep	VERB
m-1112	959	18	in	in	ADP
m-1112	959	19	caves	cave	NOUN
m-1112	959	20	as	as	ADP
m-1112	959	21	electric	electric	ADJ
m-1112	959	22	and	and	CCONJ
m-1112	959	23	magnetic	magnetic	ADJ
m-1112	959	24	fields	field	NOUN
m-1112	959	25	and	and	CCONJ
m-1112	959	26	as	as	ADP
m-1112	959	27	frequencies	frequency	NOUN
m-1112	959	28	which	which	PRON
m-1112	959	29	are	be	AUX
m-1112	959	30	conserved	conserve	VERB
m-1112	959	31	in	in	ADP
m-1112	959	32	them	they	PRON
m-1112	959	33	when	when	SCONJ
m-1112	959	34	the	the	DET
m-1112	959	35	space	space	NOUN
m-1112	959	36	-	-	PUNCT
m-1112	959	37	points	point	NOUN
m-1112	959	38	become	become	VERB
m-1112	959	39	energy	energy	NOUN
m-1112	959	40	-	-	PUNCT
m-1112	959	41	conductors	conductor	NOUN
m-1112	959	42	and	and	CCONJ
m-1112	959	43	energy	energy	NOUN
m-1112	959	44	k	k	X
m-1112	960	1	=	=	PUNCT
m-1112	960	2	2π	2π	NOUN
m-1112	960	3	λ	λ	X
m-1112	960	4	=	=	SYM
m-1112	960	5	2π	2π	PROPN
m-1112	960	6	d	d	X
m-1112	960	7	.	.	PUNCT
m-1112	961	1	b-4	b-4	NOUN
m-1112	961	2	...	...	PUNCT
m-1112	961	3	the	the	DET
m-1112	961	4	in	in	ADP
m-1112	961	5	caves	cave	NOUN
m-1112	961	6	energy	energy	NOUN
m-1112	961	7	imports	import	NOUN
m-1112	961	8	are	be	AUX
m-1112	961	9	in	in	ADP
m-1112	961	10	squares	square	NOUN
m-1112	961	11	which	which	DET
m-1112	961	12	equilibrium	equilibrium	NOUN
m-1112	961	13	through	through	ADP
m-1112	961	14	mpm	mpm	NOUN
m-1112	961	15	≡	≡	PROPN
m-1112	961	16	markos	markos	PROPN
m-1112	961	17	of	of	ADP
m-1112	961	18	⊝	⊝	NUM
m-1112	961	19	charge	charge	NOUN
m-1112	961	20	in	in	ADP
m-1112	961	21	an	an	DET
m-1112	961	22	electric	electric	ADJ
m-1112	961	23	–	–	PUNCT
m-1112	961	24	field	field	NOUN
m-1112	961	25	e̅f	e̅f	NOUN
m-1112	961	26	.	.	PUNCT
m-1112	962	1	for	for	ADP
m-1112	962	2	velocity	velocity	NOUN
m-1112	962	3	-	-	PUNCT
m-1112	962	4	vectors	vector	NOUN
m-1112	962	5	at	at	ADP
m-1112	962	6	point	point	NOUN
m-1112	962	7	c	c	NOUN
m-1112	962	8	issues	issue	NOUN
m-1112	962	9	,	,	PUNCT
m-1112	962	10	cp⃖⃗⃗⃗	cp⃖⃗⃗⃗	NOUN
m-1112	962	11	=	=	NOUN
m-1112	962	12	ca⃖⃗⃗⃗	ca⃖⃗⃗⃗	PROPN
m-1112	962	13	and	and	CCONJ
m-1112	962	14	cp⃖⃗⃗⃗	cp⃖⃗⃗⃗	NOUN
m-1112	962	15	⊥	⊥	NOUN
m-1112	962	16	ca⃖⃗⃗⃗	ca⃖⃗⃗⃗	PROPN
m-1112	962	17	and	and	CCONJ
m-1112	962	18	the	the	DET
m-1112	962	19	resultant	resultant	NOUN
m-1112	962	20	is	be	AUX
m-1112	962	21	the	the	DET
m-1112	962	22	velocity	velocity	NOUN
m-1112	962	23	-	-	PUNCT
m-1112	962	24	vector	vector	NOUN
m-1112	962	25	c⃡c`ap	c⃡c`ap	NOUN
m-1112	962	26	,	,	PUNCT
m-1112	962	27	electric	electric	NOUN
m-1112	962	28	-	-	PUNCT
m-1112	962	29	vector	vector	NOUN
m-1112	962	30	=	=	SYM
m-1112	962	31	πσφ	πσφ	NOUN
m-1112	963	1	4	4	NUM
m-1112	963	2	[	[	X
m-1112	963	3	d]²	d]²	PROPN
m-1112	963	4	,	,	PUNCT
m-1112	963	5	magnetic	magnetic	ADJ
m-1112	963	6	-	-	PUNCT
m-1112	963	7	vector	vector	NOUN
m-1112	963	8	=	=	SYM
m-1112	963	9	πσφ	πσφ	NOUN
m-1112	963	10	4	4	NUM
m-1112	964	1	[	[	X
m-1112	964	2	d]²	d]²	PROPN
m-1112	964	3	.	.	PUNCT
m-1112	965	1	similarly	similarly	ADV
m-1112	965	2	on	on	ADP
m-1112	965	3	material	material	NOUN
m-1112	965	4	vector	vector	NOUN
m-1112	965	5	cp⃖⃗⃗⃗	cp⃖⃗⃗⃗	NOUN
m-1112	965	6	carries	carry	VERB
m-1112	965	7	the	the	DET
m-1112	965	8	maximum	maximum	ADJ
m-1112	965	9	conjugate	conjugate	ADJ
m-1112	965	10	-	-	PUNCT
m-1112	965	11	force	force	NOUN
m-1112	965	12	cc`=	cc`=	NUM
m-1112	965	13	c⃡ka	c⃡ka	NOUN
m-1112	965	14	from	from	ADP
m-1112	965	15	e	e	NOUN
m-1112	965	16	-	-	ADJ
m-1112	965	17	square	square	ADJ
m-1112	965	18	cp²	cp²	VERB
m-1112	965	19	to	to	ADP
m-1112	965	20	two	two	NUM
m-1112	965	21	equal	equal	ADJ
m-1112	965	22	and	and	CCONJ
m-1112	965	23	opposite	opposite	ADJ
m-1112	965	24	squares	square	NOUN
m-1112	965	25	–	–	PUNCT
m-1112	965	26	cb`po	cb`po	VERB
m-1112	965	27	,	,	PUNCT
m-1112	965	28	+	+	CCONJ
m-1112	965	29	cbao	cbao	VERB
m-1112	965	30	from	from	ADP
m-1112	965	31	cac`p	cac`p	PROPN
m-1112	965	32	≡	≡	PROPN
m-1112	965	33	+	+	PROPN
m-1112	965	34	𝐂𝐎𝐀𝐁	𝐂𝐎𝐀𝐁	PROPN
m-1112	965	35	−𝐂𝐎𝐏𝐁	−𝐂𝐎𝐏𝐁	NOUN
m-1112	965	36	`	`	PUNCT
m-1112	965	37	[	[	X
m-1112	965	38	⤭	⤭	X
m-1112	965	39	]	]	PUNCT
m-1112	965	40	which	which	PRON
m-1112	965	41	rest	rest	VERB
m-1112	965	42	in	in	ADP
m-1112	965	43	the	the	DET
m-1112	965	44	circumscribed	circumscribed	ADJ
m-1112	965	45	circle	circle	NOUN
m-1112	965	46	π.oa²	π.oa²	PUNCT
m-1112	966	1	=	=	PUNCT
m-1112	966	2	2π	2π	NOUN
m-1112	966	3	(	(	PUNCT
m-1112	966	4	𝐎𝐀	𝐎𝐀	PROPN
m-1112	966	5	√𝟐	√𝟐	PROPN
m-1112	966	6	)	)	PUNCT
m-1112	966	7	²	²	PROPN
m-1112	966	8	,	,	PUNCT
m-1112	966	9	to	to	ADP
m-1112	966	10	the	the	DET
m-1112	966	11	screwdriver	screwdriver	NOUN
m-1112	966	12	inscribed	inscribe	VERB
m-1112	966	13	to	to	ADP
m-1112	966	14	,	,	PUNCT
m-1112	966	15	ca⃖⃗⃗⃗	ca⃖⃗⃗⃗	PROPN
m-1112	966	16	,	,	PUNCT
m-1112	966	17	cd⃖⃗	cd⃖⃗	PROPN
m-1112	966	18	⃗⃗	⃗⃗	PROPN
m-1112	966	19	circles	circle	NOUN
m-1112	966	20	,	,	PUNCT
m-1112	966	21	π	π	PROPN
m-1112	966	22	[	[	PUNCT
m-1112	966	23	𝐂𝐀²	𝐂𝐀²	NOUN
m-1112	966	24	𝟒	𝟒	NUM
m-1112	966	25	]	]	PUNCT
m-1112	966	26	,	,	PUNCT
m-1112	966	27	π	π	X
m-1112	966	28	[	[	PUNCT
m-1112	966	29	𝐂𝐏²	𝐂𝐏²	NOUN
m-1112	966	30	𝟒	𝟒	PROPN
m-1112	966	31	]	]	PUNCT
m-1112	966	32	.	.	PUNCT
m-1112	967	1	motion	motion	NOUN
m-1112	967	2	to	to	PART
m-1112	967	3	rest	rest	VERB
m-1112	967	4	,	,	PUNCT
m-1112	967	5	before	before	ADP
m-1112	967	6	the	the	DET
m-1112	967	7	halve	halve	NOUN
m-1112	967	8	areas	area	NOUN
m-1112	967	9	,	,	PUNCT
m-1112	967	10	circles	circle	NOUN
m-1112	967	11	pass	pass	VERB
m-1112	967	12	through	through	ADP
m-1112	967	13	the	the	DET
m-1112	967	14	equal	equal	ADJ
m-1112	967	15	to	to	ADP
m-1112	967	16	cmnh	cmnh	PROPN
m-1112	967	17	square	square	PROPN
m-1112	967	18	where	where	SCONJ
m-1112	967	19	exist	exist	VERB
m-1112	967	20	quadrature	quadrature	NOUN
m-1112	967	21	at	at	ADP
m-1112	967	22	position	position	NOUN
m-1112	967	23	m	m	VERB
m-1112	967	24	and	and	CCONJ
m-1112	967	25	to	to	ADP
m-1112	967	26	half	half	ADJ
m-1112	967	27	-	-	PUNCT
m-1112	967	28	area	area	NOUN
m-1112	967	29	circle	circle	NOUN
m-1112	967	30	π	π	PROPN
m-1112	967	31	[	[	PUNCT
m-1112	967	32	𝐎𝐁	𝐎𝐁	PROPN
m-1112	967	33	√𝟐	√𝟐	PROPN
m-1112	967	34	]	]	PUNCT
m-1112	967	35	²	²	PROPN
m-1112	967	36	=	=	SYM
m-1112	967	37	π	π	PROPN
m-1112	967	38	[	[	PUNCT
m-1112	967	39	𝐎𝐁	𝐎𝐁	PROPN
m-1112	967	40	²	²	PROPN
m-1112	967	41	𝟐	𝟐	NUM
m-1112	967	42	]	]	PUNCT
m-1112	967	43	at	at	ADP
m-1112	967	44	position	position	NOUN
m-1112	967	45	m	m	NOUN
m-1112	967	46	b-5	b-5	NUM
m-1112	967	47	..	..	PUNCT
m-1112	967	48	this	this	DET
m-1112	967	49	property	property	NOUN
m-1112	967	50	of	of	ADP
m-1112	967	51	any	any	DET
m-1112	967	52	two	two	NUM
m-1112	967	53	equal	equal	ADJ
m-1112	967	54	and	and	CCONJ
m-1112	967	55	perpendicular	perpendicular	ADJ
m-1112	967	56	vectors	vector	NOUN
m-1112	967	57	at	at	ADP
m-1112	967	58	point	point	NOUN
m-1112	967	59	c	c	NOUN
m-1112	967	60	,	,	PUNCT
m-1112	967	61	issues	issue	NOUN
m-1112	967	62	for	for	ADP
m-1112	967	63	any	any	DET
m-1112	967	64	point	point	NOUN
m-1112	967	65	n	n	NOUN
m-1112	967	66	,	,	PUNCT
m-1112	967	67	which	which	PRON
m-1112	967	68	has	have	VERB
m-1112	967	69	a	a	DET
m-1112	967	70	screwdriver	screwdriver	NOUN
m-1112	967	71	–	–	PUNCT
m-1112	967	72	material	material	NOUN
m-1112	967	73	vectorcn	vectorcn	PROPN
m-1112	967	74	.	.	PUNCT
m-1112	968	1	the	the	DET
m-1112	968	2	quantization	quantization	NOUN
m-1112	968	3	of	of	ADP
m-1112	968	4	e	e	NOUN
m-1112	968	5	-	-	NOUN
m-1112	968	6	geometry	geometry	NOUN
m-1112	968	7	to	to	ADP
m-1112	968	8	its	its	PRON
m-1112	968	9	dimensional	dimensional	ADJ
m-1112	968	10	-	-	PUNCT
m-1112	968	11	moulds	mould	NOUN
m-1112	968	12	:	:	PUNCT
m-1112	968	13	theone	theone	NOUN
m-1112	968	14	,	,	PUNCT
m-1112	968	15	two	two	NUM
m-1112	968	16	,	,	PUNCT
m-1112	968	17	three	three	NUM
m-1112	968	18	vectors	vector	NOUN
m-1112	968	19	and	and	CCONJ
m-1112	968	20	three	three	NUM
m-1112	968	21	poles	pole	NOUN
m-1112	968	22	mechanism	mechanism	NOUN
m-1112	968	23	.	.	PUNCT
m-1112	969	1	ijo	ijo	PROPN
m-1112	969	2	international	international	PROPN
m-1112	969	3	journal	journal	PROPN
m-1112	969	4	of	of	ADP
m-1112	969	5	mathematics	mathematics	PROPN
m-1112	969	6	(	(	PUNCT
m-1112	969	7	issn	issn	PROPN
m-1112	969	8	:	:	PUNCT
m-1112	969	9	2992	2992	NUM
m-1112	969	10	-	-	SYM
m-1112	969	11	4421	4421	NUM
m-1112	969	12	)	)	PUNCT
m-1112	969	13	volume	volume	NOUN
m-1112	969	14	08	08	NUM
m-1112	970	1	|	|	ADV
m-1112	970	2	issue	issue	NOUN
m-1112	970	3	08	08	NUM
m-1112	971	1	|	|	ADV
m-1112	971	2	august	august	PROPN
m-1112	971	3	2025	2025	NUM
m-1112	971	4	|	|	ADV
m-1112	971	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	971	6	ijo	ijo	PROPN
m-1112	971	7	journals	journal	NOUN
m-1112	971	8	34	34	NUM
m-1112	971	9	the	the	DET
m-1112	971	10	fundamental	fundamental	ADJ
m-1112	971	11	particles	particle	NOUN
m-1112	971	12	origination	origination	NOUN
m-1112	971	13	mechanism	mechanism	NOUN
m-1112	971	14	in	in	ADP
m-1112	971	15	mfmf	mfmf	PROPN
m-1112	971	16	pns	pns	PROPN
m-1112	971	17	caves	cave	NOUN
m-1112	971	18	.	.	PUNCT
m-1112	972	1	figure	figure	VERB
m-1112	972	2	-8	-8	NOUN
m-1112	972	3	b	b	NOUN
m-1112	972	4	:	:	PUNCT
m-1112	972	5	the	the	DET
m-1112	972	6	quantization	quantization	NOUN
m-1112	972	7	of	of	ADP
m-1112	972	8	e	e	NOUN
m-1112	972	9	-	-	NOUN
m-1112	972	10	geometry	geometry	NOUN
m-1112	972	11	to	to	ADP
m-1112	972	12	its	its	PRON
m-1112	972	13	moulds	mould	NOUN
m-1112	972	14	,	,	PUNCT
m-1112	972	15	the	the	DET
m-1112	972	16	point	point	NOUN
m-1112	972	17	,	,	PUNCT
m-1112	972	18	the	the	DET
m-1112	972	19	linear	linear	NOUN
m-1112	972	20	,	,	PUNCT
m-1112	972	21	the	the	DET
m-1112	972	22	plane	plane	NOUN
m-1112	972	23	,	,	PUNCT
m-1112	972	24	the	the	DET
m-1112	972	25	space	space	NOUN
m-1112	972	26	(	(	PUNCT
m-1112	972	27	volume	volume	NOUN
m-1112	972	28	)	)	PUNCT
m-1112	972	29	mould	mould	NOUN
m-1112	972	30	for	for	ADP
m-1112	972	31	e	e	NOUN
m-1112	972	32	-	-	NOUN
m-1112	972	33	geometry	geometry	NOUN
m-1112	972	34	quantization	quantization	NOUN
m-1112	972	35	,	,	PUNCT
m-1112	972	36	to	to	ADP
m-1112	972	37	opposite	opposite	ADJ
m-1112	972	38	.	.	PUNCT
m-1112	973	1	b-6	b-6	PROPN
m-1112	973	2	…	…	PUNCT
m-1112	973	3	for	for	ADP
m-1112	973	4	(	(	PUNCT
m-1112	973	5	1	1	X
m-1112	973	6	)	)	PUNCT
m-1112	973	7	monad	monad	PROPN
m-1112	973	8	ea	ea	PROPN
m-1112	973	9	,	,	PUNCT
m-1112	973	10	to	to	PART
m-1112	973	11	antimonad	antimonad	VERB
m-1112	973	12	ec	ec	PROPN
m-1112	973	13	–	–	PUNCT
m-1112	973	14	for	for	ADP
m-1112	973	15	(	(	PUNCT
m-1112	973	16	2	2	NUM
m-1112	973	17	)	)	PUNCT
m-1112	973	18	ab	ab	NOUN
m-1112	973	19	line	line	NOUN
m-1112	973	20	to	to	PART
m-1112	973	21	parallel	parallel	VERB
m-1112	973	22	line	line	NOUN
m-1112	973	23	mm	mm	INTJ
m-1112	973	24	`	`	PUNCT
m-1112	973	25	for	for	ADP
m-1112	973	26	(	(	PUNCT
m-1112	973	27	3	3	NUM
m-1112	973	28	)	)	PUNCT
m-1112	973	29	ce	ce	PROPN
m-1112	973	30	radius	radius	NOUN
m-1112	973	31	to	to	ADP
m-1112	973	32	the	the	DET
m-1112	973	33	cm	cm	PROPN
m-1112	973	34	square	square	ADJ
m-1112	973	35	segment	segment	NOUN
m-1112	973	36	for	for	ADP
m-1112	973	37	(	(	PUNCT
m-1112	973	38	4	4	NUM
m-1112	973	39	)	)	PUNCT
m-1112	973	40	ka	ka	PROPN
m-1112	973	41	segment	segment	NOUN
m-1112	973	42	to	to	ADP
m-1112	973	43	the	the	DET
m-1112	973	44	kd	kd	PROPN
m-1112	973	45	cube	cube	NOUN
m-1112	973	46	segment	segment	NOUN
m-1112	973	47	.	.	PUNCT
m-1112	974	1	from	from	ADP
m-1112	974	2	(	(	PUNCT
m-1112	974	3	3	3	X
m-1112	974	4	)	)	PUNCT
m-1112	974	5	the	the	DET
m-1112	974	6	two	two	NUM
m-1112	974	7	-	-	PUNCT
m-1112	974	8	perpendicular	perpendicular	ADJ
m-1112	974	9	vectors	vector	NOUN
m-1112	974	10	,	,	PUNCT
m-1112	974	11	ca	can	AUX
m-1112	974	12	⊥	⊥	PROPN
m-1112	974	13	cp	cp	INTJ
m-1112	974	14	,	,	PUNCT
m-1112	974	15	slide	slide	VERB
m-1112	974	16	on	on	ADP
m-1112	974	17	(	(	PUNCT
m-1112	974	18	o	o	NOUN
m-1112	974	19	,	,	PUNCT
m-1112	974	20	oa	oa	PROPN
m-1112	974	21	)	)	PUNCT
m-1112	974	22	circle	circle	NOUN
m-1112	974	23	and	and	CCONJ
m-1112	974	24	through	through	ADP
m-1112	974	25	the	the	DET
m-1112	974	26	three	three	NUM
m-1112	974	27	poles	pole	NOUN
m-1112	974	28	,	,	PUNCT
m-1112	974	29	a	a	DET
m-1112	974	30	,	,	PUNCT
m-1112	974	31	c	c	NOUN
m-1112	974	32	,	,	PUNCT
m-1112	974	33	p	p	X
m-1112	974	34	,	,	PUNCT
m-1112	974	35	carry	carry	VERB
m-1112	974	36	the	the	DET
m-1112	974	37	stress	stress	NOUN
m-1112	974	38	σ	σ	NOUN
m-1112	974	39	,	,	PUNCT
m-1112	974	40	of	of	ADP
m-1112	974	41	square	square	ADJ
m-1112	974	42	acpc	acpc	NOUN
m-1112	974	43	,	,	PUNCT
m-1112	974	44	to	to	ADP
m-1112	974	45	the	the	DET
m-1112	974	46	two	two	NUM
m-1112	974	47	equal	equal	ADJ
m-1112	974	48	and	and	CCONJ
m-1112	974	49	opposite	opposite	ADJ
m-1112	974	50	squares	square	NOUN
m-1112	974	51	|coab|	|coab|	NUM
m-1112	974	52	,	,	PUNCT
m-1112	974	53	|copb’|	|copb’|	NOUN
m-1112	974	54	for	for	ADP
m-1112	974	55	still	still	ADV
m-1112	974	56	to	to	ADP
m-1112	974	57	the	the	DET
m-1112	974	58	halve	halve	NOUN
m-1112	974	59	area	area	NOUN
m-1112	974	60	stress	stress	NOUN
m-1112	974	61	conservation	conservation	NOUN
m-1112	974	62	.	.	PUNCT
m-1112	975	1	for	for	ADP
m-1112	975	2	the	the	DET
m-1112	975	3	rotating	rotate	VERB
m-1112	975	4	square	square	ADJ
m-1112	975	5	cmnh	cmnh	NOUN
m-1112	975	6	exist	exist	VERB
m-1112	975	7	as	as	ADP
m-1112	975	8	upper	upper	ADJ
m-1112	975	9	-	-	PUNCT
m-1112	975	10	still	still	ADV
m-1112	975	11	-	-	PUNCT
m-1112	975	12	state	state	NOUN
m-1112	975	13	the	the	DET
m-1112	975	14	square	square	ADJ
m-1112	975	15	cac`p	cac`p	NOUN
m-1112	976	1	and	and	CCONJ
m-1112	976	2	as	as	ADP
m-1112	976	3	lower	low	ADJ
m-1112	976	4	still	still	ADJ
m-1112	976	5	-	-	PUNCT
m-1112	976	6	state	state	NOUN
m-1112	976	7	the	the	DET
m-1112	976	8	square	square	ADJ
m-1112	976	9	cbao	cbao	NOUN
m-1112	976	10	,	,	PUNCT
m-1112	976	11	related	relate	VERB
m-1112	976	12	[	[	PUNCT
m-1112	976	13	cac`p	cac`p	NOUN
m-1112	976	14	]	]	PUNCT
m-1112	976	15	=	=	SYM
m-1112	976	16	2	2	X
m-1112	976	17	.	.	PUNCT
m-1112	976	18	[	[	PUNCT
m-1112	976	19	cbao	cbao	X
m-1112	976	20	]	]	PUNCT
m-1112	976	21	.	.	PUNCT
m-1112	977	1	in(3)	in(3)	PROPN
m-1112	977	2	..	..	PUNCT
m-1112	977	3	on	on	ADP
m-1112	977	4	two	two	NUM
m-1112	977	5	-	-	PUNCT
m-1112	977	6	perpendicular	perpendicular	ADJ
m-1112	977	7	vectors	vector	NOUN
m-1112	977	8	,	,	PUNCT
m-1112	977	9	ca	can	AUX
m-1112	977	10	⊥	⊥	PROPN
m-1112	977	11	cp	cp	INTJ
m-1112	977	12	,	,	PUNCT
m-1112	977	13	point	point	VERB
m-1112	977	14	c	c	NOUN
m-1112	977	15	`	`	PUNCT
m-1112	977	16	slides	slide	VERB
m-1112	977	17	on	on	ADP
m-1112	977	18	(	(	PUNCT
m-1112	977	19	o	o	NOUN
m-1112	977	20	,	,	PUNCT
m-1112	977	21	oa	oa	PROPN
m-1112	977	22	=	=	PUNCT
m-1112	977	23	op	op	NOUN
m-1112	977	24	)	)	PUNCT
m-1112	977	25	circle	circle	NOUN
m-1112	977	26	forming	form	VERB
m-1112	977	27	the	the	DET
m-1112	977	28	cac`p	cac`p	NOUN
m-1112	977	29	to	to	PART
m-1112	977	30	cmnh	cmnh	VERB
m-1112	977	31	to	to	ADP
m-1112	977	32	cbao	cbao	NOUN
m-1112	977	33	squares	square	NOUN
m-1112	977	34	with	with	ADP
m-1112	977	35	prior	prior	ADV
m-1112	977	36	of	of	ADP
m-1112	977	37	(	(	PUNCT
m-1112	977	38	1	1	X
m-1112	977	39	)	)	PUNCT
m-1112	977	40	properties	property	NOUN
m-1112	977	41	.this	.this	PRON
m-1112	977	42	sliding	slide	VERB
m-1112	977	43	rotating	rotate	VERB
m-1112	977	44	method	method	NOUN
m-1112	977	45	is	be	AUX
m-1112	977	46	markos	markos	PROPN
m-1112	977	47	{	{	PUNCT
m-1112	977	48	2	2	NUM
m-1112	977	49	-	-	PUNCT
m-1112	977	50	vectors	vector	NOUN
m-1112	977	51	3	3	NUM
m-1112	977	52	-	-	PUNCT
m-1112	977	53	poles	pole	NOUN
m-1112	977	54	mechanism	mechanism	NOUN
m-1112	977	55	}	}	PUNCT
m-1112	977	56	which	which	DET
m-1112	977	57	circles	circle	NOUN
m-1112	977	58	and	and	CCONJ
m-1112	977	59	squares	square	NOUN
m-1112	977	60	as	as	SCONJ
m-1112	977	61	areas	area	NOUN
m-1112	977	62	pass	pass	VERB
m-1112	977	63	from	from	ADP
m-1112	977	64	the	the	DET
m-1112	977	65	point	point	NOUN
m-1112	977	66	m	m	AUX
m-1112	977	67	determined	determine	VERB
m-1112	977	68	by	by	ADP
m-1112	977	69	position	position	NOUN
m-1112	977	70	𝐀	𝐀	PROPN
m-1112	977	71	𝐞	𝐞	PROPN
m-1112	977	72	,	,	PUNCT
m-1112	977	73	such	such	ADJ
m-1112	977	74	that	that	SCONJ
m-1112	977	75	issues	issue	NOUN
m-1112	977	76	π	π	NOUN
m-1112	977	77	r	r	NOUN
m-1112	977	78	²	²	NUM
m-1112	977	79	=	=	SYM
m-1112	977	80	cmnh	cmnh	NOUN
m-1112	977	81	square	square	NOUN
m-1112	977	82	.the	.the	PUNCT
m-1112	977	83	squaring	squaring	NOUN
m-1112	977	84	of	of	ADP
m-1112	977	85	the	the	DET
m-1112	977	86	circle	circle	NOUN
m-1112	977	87	is	be	AUX
m-1112	977	88	π	π	PROPN
m-1112	977	89	[	[	PUNCT
m-1112	977	90	𝐂𝐀	𝐂𝐀	PROPN
m-1112	977	91	√𝟐	√𝟐	PROPN
m-1112	977	92	]	]	PUNCT
m-1112	977	93	²	²	NUM
m-1112	977	94	=	=	NOUN
m-1112	977	95	cm²	cm²	ADP
m-1112	977	96	=	=	SYM
m-1112	977	97	|cm`|²	|cm`|²	PUNCT
m-1112	977	98	,	,	PUNCT
m-1112	977	99	fig-15	fig-15	NOUN
m-1112	977	100	,	,	PUNCT
m-1112	977	101	[	[	PUNCT
m-1112	977	102	47	47	NUM
m-1112	977	103	-	-	SYM
m-1112	977	104	51	51	NUM
m-1112	977	105	]	]	PUNCT
m-1112	977	106	,	,	PUNCT
m-1112	978	1	[	[	X
m-1112	978	2	62	62	NUM
m-1112	978	3	]	]	PUNCT
m-1112	978	4	remarks	remark	VERB
m-1112	978	5	:	:	PUNCT
m-1112	978	6	1	1	X
m-1112	978	7	…	…	PUNCT
m-1112	978	8	the	the	DET
m-1112	978	9	two	two	NUM
m-1112	978	10	vectors	vector	NOUN
m-1112	978	11	three	three	NUM
m-1112	978	12	poles	pole	NOUN
m-1112	978	13	mechanism	mechanism	NOUN
m-1112	978	14	is	be	AUX
m-1112	978	15	a	a	DET
m-1112	978	16	mechanism	mechanism	NOUN
m-1112	978	17	from	from	ADP
m-1112	978	18	two	two	NUM
m-1112	978	19	⊥	⊥	ADJ
m-1112	978	20	vectors	vector	NOUN
m-1112	978	21	in	in	ADP
m-1112	978	22	geometry	geometry	NOUN
m-1112	978	23	,	,	PUNCT
m-1112	978	24	where	where	SCONJ
m-1112	978	25	the	the	DET
m-1112	978	26	action	action	NOUN
m-1112	978	27	of	of	ADP
m-1112	978	28	energy	energy	NOUN
m-1112	978	29	on	on	ADP
m-1112	978	30	their	their	PRON
m-1112	978	31	vectors	vector	NOUN
m-1112	978	32	square	square	ADJ
m-1112	978	33	and	and	CCONJ
m-1112	978	34	is	be	AUX
m-1112	978	35	conservated	conservate	VERB
m-1112	978	36	.	.	PUNCT
m-1112	979	1	2	2	X
m-1112	979	2	…	…	PUNCT
m-1112	979	3	the	the	DET
m-1112	979	4	mechanism	mechanism	NOUN
m-1112	979	5	is	be	AUX
m-1112	979	6	a	a	DET
m-1112	979	7	rotating	rotate	VERB
m-1112	979	8	and	and	CCONJ
m-1112	979	9	changing	change	VERB
m-1112	979	10	-	-	PUNCT
m-1112	979	11	squares	square	NOUN
m-1112	979	12	system	system	NOUN
m-1112	979	13	,	,	PUNCT
m-1112	979	14	on	on	ADP
m-1112	979	15	a	a	DET
m-1112	979	16	circle	circle	NOUN
m-1112	979	17	which	which	PRON
m-1112	979	18	changes	change	VERB
m-1112	979	19	the	the	DET
m-1112	979	20	inscribed	inscribe	VERB
m-1112	979	21	to	to	ADP
m-1112	979	22	the	the	DET
m-1112	979	23	circle	circle	NOUN
m-1112	979	24	square	square	NOUN
m-1112	979	25	,	,	PUNCT
m-1112	979	26	changes	change	NOUN
m-1112	979	27	to	to	ADP
m-1112	979	28	2	2	NUM
m-1112	979	29	–	–	PUNCT
m-1112	979	30	halve	halve	NOUN
m-1112	979	31	opposite	opposite	ADJ
m-1112	979	32	and	and	CCONJ
m-1112	979	33	equal	equal	ADJ
m-1112	979	34	squares	square	NOUN
m-1112	979	35	.the	.the	DET
m-1112	979	36	same	same	ADJ
m-1112	979	37	procedure	procedure	NOUN
m-1112	979	38	issues	issue	NOUN
m-1112	979	39	for	for	ADP
m-1112	979	40	the	the	DET
m-1112	979	41	inscribed	inscribe	VERB
m-1112	979	42	and	and	CCONJ
m-1112	979	43	circumscribed	circumscribed	ADJ
m-1112	979	44	circles	circle	NOUN
m-1112	979	45	to	to	ADP
m-1112	979	46	the	the	DET
m-1112	979	47	circle	circle	NOUN
m-1112	979	48	.	.	PUNCT
m-1112	980	1	3	3	X
m-1112	980	2	…	…	PUNCT
m-1112	980	3	since	since	SCONJ
m-1112	980	4	from	from	ADP
m-1112	980	5	wave	wave	NOUN
m-1112	980	6	-	-	PUNCT
m-1112	980	7	action	action	NOUN
m-1112	980	8	of	of	ADP
m-1112	980	9	spaces	space	NOUN
m-1112	980	10	issues	issue	NOUN
m-1112	980	11	z	z	NOUN
m-1112	980	12	−	−	PROPN
m-1112	980	13	n	n	NOUN
m-1112	980	14	x	x	NOUN
m-1112	980	15	z	z	PROPN
m-1112	980	16	+	+	CCONJ
m-1112	980	17	n	n	NOUN
m-1112	980	18	=	=	SYM
m-1112	981	1	[	[	X
m-1112	981	2	2r	2r	NUM
m-1112	981	3	]	]	X
m-1112	981	4	2n	2n	NUM
m-1112	981	5	.	.	PUNCT
m-1112	982	1	e	e	X
m-1112	982	2	i.2nθ	i.2nθ	PROPN
m-1112	982	3	,	,	PUNCT
m-1112	982	4	this	this	PRON
m-1112	982	5	means	mean	VERB
m-1112	982	6	that	that	SCONJ
m-1112	982	7	,	,	PUNCT
m-1112	982	8	the	the	DET
m-1112	982	9	conservation	conservation	NOUN
m-1112	982	10	of	of	ADP
m-1112	982	11	energy	energy	NOUN
m-1112	982	12	=	=	NOUN
m-1112	982	13	work	work	NOUN
m-1112	982	14	,	,	PUNCT
m-1112	982	15	between	between	ADP
m-1112	982	16	the	the	DET
m-1112	982	17	spaces	space	NOUN
m-1112	982	18	and	and	CCONJ
m-1112	982	19	the	the	DET
m-1112	982	20	anti	anti	NOUN
m-1112	982	21	-	-	ADJ
m-1112	982	22	spaces	space	NOUN
m-1112	982	23	happens	happen	VERB
m-1112	982	24	by	by	ADP
m-1112	982	25	doubling	double	VERB
m-1112	982	26	the	the	DET
m-1112	982	27	number	number	NOUN
m-1112	982	28	n	n	NOUN
m-1112	982	29	,	,	PUNCT
m-1112	982	30	of	of	ADP
m-1112	982	31	the	the	DET
m-1112	982	32	vertices	vertex	NOUN
m-1112	982	33	of	of	ADP
m-1112	982	34	the	the	DET
m-1112	982	35	regular	regular	ADJ
m-1112	982	36	polygon	polygon	NOUN
m-1112	982	37	.	.	PUNCT
m-1112	983	1	i.e.	i.e.	X
m-1112	983	2	the	the	DET
m-1112	983	3	surplus	surplus	ADJ
m-1112	983	4	energy	energy	NOUN
m-1112	983	5	is	be	AUX
m-1112	983	6	stored	store	VERB
m-1112	983	7	in	in	ADP
m-1112	983	8	2.n	2.n	NUM
m-1112	983	9	vertices	vertex	NOUN
m-1112	983	10	,	,	PUNCT
m-1112	983	11	and	and	CCONJ
m-1112	983	12	on	on	ADP
m-1112	983	13	𝛌𝟐𝐧=√2r2	𝛌𝟐𝐧=√2r2	NOUN
m-1112	983	14	−	−	PROPN
m-1112	983	15	r√4r2	r√4r2	NOUN
m-1112	983	16	−	−	NOUN
m-1112	983	17	λ²n	λ²n	PROPN
m-1112	983	18	sides	side	NOUN
m-1112	983	19	,	,	PUNCT
m-1112	983	20	where	where	SCONJ
m-1112	983	21	then	then	ADV
m-1112	983	22	energy	energy	NOUN
m-1112	983	23	is	be	AUX
m-1112	983	24	divided	divide	VERB
m-1112	983	25	and	and	CCONJ
m-1112	983	26	spread	spread	VERB
m-1112	983	27	on	on	ADP
m-1112	983	28	the	the	DET
m-1112	983	29	double	double	ADJ
m-1112	983	30	number	number	NOUN
m-1112	983	31	of	of	ADP
m-1112	983	32	the	the	DET
m-1112	983	33	polygon	polygon	NOUN
m-1112	983	34	sides	side	NOUN
m-1112	983	35	.	.	PUNCT
m-1112	984	1	ijo	ijo	PROPN
m-1112	984	2	international	international	PROPN
m-1112	984	3	journal	journal	PROPN
m-1112	984	4	of	of	ADP
m-1112	984	5	mathematics	mathematics	PROPN
m-1112	984	6	(	(	PUNCT
m-1112	984	7	issn	issn	PROPN
m-1112	984	8	:	:	PUNCT
m-1112	984	9	2992	2992	NUM
m-1112	984	10	-	-	SYM
m-1112	984	11	4421	4421	NUM
m-1112	984	12	)	)	PUNCT
m-1112	984	13	volume	volume	NOUN
m-1112	984	14	08	08	NUM
m-1112	985	1	|	|	ADV
m-1112	985	2	issue	issue	NOUN
m-1112	985	3	08	08	NUM
m-1112	986	1	|	|	ADV
m-1112	986	2	august	august	PROPN
m-1112	986	3	2025	2025	NUM
m-1112	986	4	|	|	ADV
m-1112	986	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	986	6	ijo	ijo	PROPN
m-1112	986	7	journals	journal	NOUN
m-1112	986	8	35	35	NUM
m-1112	986	9	the	the	DET
m-1112	986	10	fundamental	fundamental	ADJ
m-1112	986	11	particles	particle	NOUN
m-1112	986	12	origination	origination	NOUN
m-1112	986	13	mechanism	mechanism	NOUN
m-1112	986	14	in	in	ADP
m-1112	986	15	mfmf	mfmf	PROPN
m-1112	986	16	pns	pns	PROPN
m-1112	986	17	caves	cave	NOUN
m-1112	986	18	.	.	PUNCT
m-1112	987	1	8	8	NUM
m-1112	987	2	..	..	PUNCT
m-1112	987	3	[c	[c	X
m-1112	987	4	]	]	X
m-1112	987	5	..	..	PUNCT
m-1112	988	1	the	the	DET
m-1112	988	2	{	{	PUNCT
m-1112	988	3	tcic	tcic	NOUN
m-1112	988	4	}	}	PUNCT
m-1112	988	5	mechanism	mechanism	NOUN
m-1112	988	6	:	:	PUNCT
m-1112	988	7	the	the	DET
m-1112	988	8	tetrahedron	tetrahedron	NOUN
m-1112	988	9	,	,	PUNCT
m-1112	988	10	the	the	DET
m-1112	988	11	cube	cube	NOUN
m-1112	988	12	,	,	PUNCT
m-1112	988	13	and	and	CCONJ
m-1112	988	14	the	the	DET
m-1112	988	15	inscribed	inscribe	VERB
m-1112	988	16	–	–	PUNCT
m-1112	988	17	circumscribed	circumscribe	VERB
m-1112	988	18	to	to	ADP
m-1112	988	19	the	the	DET
m-1112	988	20	circle	circle	NOUN
m-1112	988	21	mechanism	mechanism	NOUN
m-1112	988	22	.	.	PUNCT
m-1112	989	1	figure	figure	VERB
m-1112	989	2	9	9	NUM
m-1112	989	3	:	:	PUNCT
m-1112	989	4	the	the	DET
m-1112	989	5	active	active	ADJ
m-1112	989	6	-	-	PUNCT
m-1112	989	7	conductors	conductor	NOUN
m-1112	989	8	of	of	ADP
m-1112	989	9	elements	element	NOUN
m-1112	989	10	and	and	CCONJ
m-1112	989	11	the	the	DET
m-1112	989	12	space	space	NOUN
m-1112	989	13	,	,	PUNCT
m-1112	989	14	anti	anti	ADJ
m-1112	989	15	-	-	ADJ
m-1112	989	16	space	space	ADJ
m-1112	989	17	formation	formation	NOUN
m-1112	989	18	.	.	PUNCT
m-1112	990	1	in	in	ADP
m-1112	990	2	figure	figure	NOUN
m-1112	990	3	za	za	PROPN
m-1112	990	4	,	,	PUNCT
m-1112	990	5	zb	zb	PROPN
m-1112	990	6	,	,	PUNCT
m-1112	990	7	zc	zc	PROPN
m-1112	990	8	,	,	PUNCT
m-1112	990	9	are	be	AUX
m-1112	990	10	the	the	DET
m-1112	990	11	three	three	NUM
m-1112	990	12	conductors	conductor	NOUN
m-1112	990	13	on	on	ADP
m-1112	990	14	the	the	DET
m-1112	990	15	three	three	NUM
m-1112	990	16	diagonals	diagonal	NOUN
m-1112	990	17	of	of	ADP
m-1112	990	18	cube	cube	NOUN
m-1112	990	19	with	with	ADP
m-1112	990	20	1	1	NUM
m-1112	990	21	,	,	PUNCT
m-1112	990	22	2	2	NUM
m-1112	990	23	,	,	PUNCT
m-1112	990	24	3	3	NUM
m-1112	990	25	,	,	PUNCT
m-1112	990	26	4	4	NUM
m-1112	990	27	,	,	PUNCT
m-1112	990	28	5	5	NUM
m-1112	990	29	,	,	PUNCT
m-1112	990	30	6	6	NUM
m-1112	990	31	,	,	PUNCT
m-1112	990	32	7	7	NUM
m-1112	990	33	,	,	PUNCT
m-1112	990	34	8	8	NUM
m-1112	990	35	,	,	PUNCT
m-1112	990	36	vertices	vertex	NOUN
m-1112	990	37	.	.	PUNCT
m-1112	991	1	at	at	ADP
m-1112	991	2	point	point	NOUN
m-1112	991	3	z	z	PROPN
m-1112	991	4	is	be	AUX
m-1112	991	5	acting	act	VERB
m-1112	991	6	a	a	DET
m-1112	991	7	complex	complex	ADJ
m-1112	991	8	-	-	PUNCT
m-1112	991	9	vector	vector	NOUN
m-1112	991	10	z̅	z̅	NOUN
m-1112	991	11	and	and	CCONJ
m-1112	991	12	which	which	PRON
m-1112	991	13	transform	transform	VERB
m-1112	991	14	the	the	DET
m-1112	991	15	vibration	vibration	NOUN
m-1112	991	16	to	to	ADP
m-1112	991	17	the	the	DET
m-1112	991	18	three	three	NUM
m-1112	991	19	conductors	conductor	NOUN
m-1112	991	20	in	in	ADP
m-1112	991	21	space	space	NOUN
m-1112	991	22	pattern	pattern	NOUN
m-1112	991	23	.	.	PUNCT
m-1112	992	1	it	it	PRON
m-1112	992	2	was	be	AUX
m-1112	992	3	shown	show	VERB
m-1112	992	4	[	[	PUNCT
m-1112	992	5	61	61	NUM
m-1112	992	6	]	]	PUNCT
m-1112	992	7	that	that	SCONJ
m-1112	992	8	the	the	DET
m-1112	992	9	stresses	stress	NOUN
m-1112	992	10	of	of	ADP
m-1112	992	11	complex	complex	ADJ
m-1112	992	12	-	-	PUNCT
m-1112	992	13	vectors	vector	NOUN
m-1112	992	14	are	be	AUX
m-1112	992	15	spread	spread	VERB
m-1112	992	16	in	in	ADP
m-1112	992	17	surfaces	surface	NOUN
m-1112	992	18	only	only	ADV
m-1112	992	19	for	for	ADP
m-1112	992	20	still	still	ADV
m-1112	992	21	states	state	NOUN
m-1112	992	22	.	.	PUNCT
m-1112	993	1	the	the	DET
m-1112	993	2	number	number	NOUN
m-1112	993	3	of	of	ADP
m-1112	993	4	moulds	mould	NOUN
m-1112	993	5	of	of	ADP
m-1112	993	6	stationary	stationary	ADJ
m-1112	993	7	-	-	PUNCT
m-1112	993	8	states	state	NOUN
m-1112	993	9	are	be	AUX
m-1112	993	10	→	→	SYM
m-1112	993	11	𝟐n=1−4	𝟐n=1−4	NOUN
m-1112	993	12	points	point	NOUN
m-1112	993	13	≡	≡	PROPN
m-1112	993	14	2	2	NUM
m-1112	993	15	,	,	PUNCT
m-1112	993	16	4	4	NUM
m-1112	993	17	,	,	PUNCT
m-1112	993	18	8	8	NUM
m-1112	993	19	,	,	PUNCT
m-1112	993	20	16	16	NUM
m-1112	993	21	≡	≡	PROPN
m-1112	993	22	4	4	NUM
m-1112	993	23	–	–	PUNCT
m-1112	993	24	types←	types←	PROPN
m-1112	993	25	(	(	PUNCT
m-1112	993	26	2	2	NUM
m-1112	993	27	)	)	PUNCT
m-1112	993	28	=	=	PUNCT
m-1112	993	29	for	for	ADP
m-1112	993	30	the	the	DET
m-1112	993	31	proton	proton	NOUN
m-1112	993	32	=	=	PUNCT
m-1112	993	33	nucleus	nucleus	NOUN
m-1112	993	34	,	,	PUNCT
m-1112	993	35	(	(	PUNCT
m-1112	993	36	4	4	X
m-1112	993	37	)	)	PUNCT
m-1112	994	1	=	=	NOUN
m-1112	994	2	tetrahedron	tetrahedron	NOUN
m-1112	994	3	,	,	PUNCT
m-1112	994	4	(	(	PUNCT
m-1112	994	5	8)	8)	NUM
m-1112	994	6	=	=	NOUN
m-1112	994	7	cube	cube	NOUN
m-1112	994	8	=	=	PUNCT
m-1112	994	9	the	the	DET
m-1112	994	10	neutral	neutral	ADJ
m-1112	994	11	-	-	PUNCT
m-1112	994	12	caves	cave	NOUN
m-1112	994	13	,	,	PUNCT
m-1112	994	14	(	(	PUNCT
m-1112	994	15	16	16	NUM
m-1112	994	16	)	)	PUNCT
m-1112	994	17	=	=	NOUN
m-1112	995	1	the	the	DET
m-1112	995	2	double	double	ADJ
m-1112	995	3	number	number	NOUN
m-1112	995	4	of	of	ADP
m-1112	995	5	vertices	vertex	NOUN
m-1112	995	6	for	for	ADP
m-1112	995	7	the	the	DET
m-1112	995	8	8	8	NUM
m-1112	995	9	-	-	PUNCT
m-1112	995	10	stationary	stationary	ADJ
m-1112	995	11	neutral	neutral	ADJ
m-1112	995	12	-	-	PUNCT
m-1112	995	13	caves	cave	NOUN
m-1112	995	14	and	and	CCONJ
m-1112	995	15	called	call	VERB
m-1112	995	16	tcic	tcic	NOUN
m-1112	995	17	-	-	PUNCT
m-1112	995	18	pattern	pattern	NOUN
m-1112	995	19	→	→	PUNCT
m-1112	995	20	{	{	PUNCT
m-1112	995	21	the	the	DET
m-1112	995	22	sphere	sphere	NOUN
m-1112	995	23	–	–	PUNCT
m-1112	995	24	in	in	ADP
m-1112	995	25	tetrahedron	tetrahedron	NOUN
m-1112	995	26	–	–	PUNCT
m-1112	995	27	in	in	ADP
m-1112	995	28	cube	cube	NOUN
m-1112	995	29	,	,	PUNCT
m-1112	995	30	in	in	ADP
m-1112	995	31	external	external	ADJ
m-1112	995	32	sphere	sphere	NOUN
m-1112	995	33	}	}	PUNCT
m-1112	995	34	←	←	PROPN
m-1112	995	35	the	the	DET
m-1112	995	36	active	active	ADJ
m-1112	995	37	-	-	PUNCT
m-1112	995	38	conductors	conductor	NOUN
m-1112	995	39	of	of	ADP
m-1112	995	40	elements	element	NOUN
m-1112	995	41	and	and	CCONJ
m-1112	995	42	the	the	DET
m-1112	995	43	space	space	NOUN
m-1112	995	44	,	,	PUNCT
m-1112	995	45	anti	anti	ADJ
m-1112	995	46	-	-	ADJ
m-1112	995	47	space	space	ADJ
m-1112	995	48	formation	formation	NOUN
m-1112	995	49	.	.	PUNCT
m-1112	996	1	point	point	NOUN
m-1112	996	2	,	,	PUNCT
m-1112	996	3	in	in	ADP
m-1112	996	4	e	e	NOUN
m-1112	996	5	-	-	NOUN
m-1112	996	6	geometry	geometry	NOUN
m-1112	996	7	is	be	AUX
m-1112	996	8	considered	consider	VERB
m-1112	996	9	nothing	nothing	PRON
m-1112	996	10	,	,	PUNCT
m-1112	996	11	without	without	ADP
m-1112	996	12	position	position	NOUN
m-1112	996	13	and	and	CCONJ
m-1112	996	14	direction	direction	NOUN
m-1112	996	15	while	while	SCONJ
m-1112	996	16	in	in	ADV
m-1112	996	17	,	,	PUNCT
m-1112	996	18	mg	mg	PROPN
m-1112	996	19	≡	≡	PROPN
m-1112	996	20	material	material	NOUN
m-1112	996	21	geometry	geometry	NOUN
m-1112	997	1	[	[	X
m-1112	997	2	1	1	NUM
m-1112	997	3	positive	positive	ADJ
m-1112	997	4	⊕	⊕	NOUN
m-1112	997	5	and	and	CCONJ
m-1112	997	6	1	1	NUM
m-1112	997	7	negative	negative	ADJ
m-1112	997	8	⊝	⊝	NUM
m-1112	997	9	]	]	PUNCT
m-1112	997	10	.	.	PUNCT
m-1112	998	1	from	from	ADP
m-1112	998	2	nothing	nothing	PRON
m-1112	998	3	(	(	PUNCT
m-1112	998	4	i.e.	i.e.	X
m-1112	998	5	the	the	DET
m-1112	998	6	point	point	NOUN
m-1112	998	7	z	z	NOUN
m-1112	998	8	)	)	PUNCT
m-1112	998	9	to	to	ADP
m-1112	998	10	existence	existence	NOUN
m-1112	998	11	(	(	PUNCT
m-1112	998	12	i.e.	i.e.	X
m-1112	998	13	to	to	PART
m-1112	998	14	be	be	AUX
m-1112	998	15	another	another	DET
m-1112	998	16	spherical	spherical	ADJ
m-1112	998	17	point	point	NOUN
m-1112	998	18	p	p	NOUN
m-1112	998	19	)	)	PUNCT
m-1112	998	20	issues	issue	NOUN
m-1112	998	21	the	the	DET
m-1112	998	22	zero	zero	NUM
m-1112	998	23	virtual	virtual	ADJ
m-1112	998	24	work	work	NOUN
m-1112	998	25	law	law	NOUN
m-1112	998	26	,	,	PUNCT
m-1112	998	27	where	where	SCONJ
m-1112	998	28	zero	zero	NUM
m-1112	998	29	work	work	NOUN
m-1112	998	30	is	be	AUX
m-1112	998	31	the	the	DET
m-1112	998	32	equilibrium	equilibrium	NOUN
m-1112	998	33	of	of	ADP
m-1112	998	34	two	two	NUM
m-1112	998	35	equal	equal	ADJ
m-1112	998	36	and	and	CCONJ
m-1112	998	37	opposite	opposite	ADJ
m-1112	998	38	forces	force	NOUN
m-1112	998	39	on	on	ADP
m-1112	998	40	points	point	NOUN
m-1112	998	41	and	and	CCONJ
m-1112	998	42	is	be	AUX
m-1112	998	43	[	[	PUNCT
m-1112	998	44	⊕	⊕	PROPN
m-1112	998	45	d	d	NOUN
m-1112	998	46	⊝	⊝	NOUN
m-1112	998	47	]	]	PUNCT
m-1112	998	48	.	.	PUNCT
m-1112	999	1	thus	thus	ADV
m-1112	999	2	space	space	NOUN
m-1112	999	3	[	[	X
m-1112	999	4	s	s	X
m-1112	999	5	]	]	X
m-1112	999	6	is	be	AUX
m-1112	999	7	z	z	NOUN
m-1112	999	8	-	-	PUNCT
m-1112	999	9	point	point	NOUN
m-1112	999	10	⊕	⊕	PROPN
m-1112	999	11	,	,	PUNCT
m-1112	999	12	anti	anti	ADJ
m-1112	999	13	-	-	ADJ
m-1112	999	14	space	space	ADJ
m-1112	999	15	p	p	NOUN
m-1112	999	16	-	-	PUNCT
m-1112	999	17	point	point	NOUN
m-1112	999	18	⊝	⊝	NOUN
m-1112	999	19	,	,	PUNCT
m-1112	999	20	and	and	CCONJ
m-1112	999	21	d	d	X
m-1112	999	22	=	=	SYM
m-1112	1000	1	zp	zp	PROPN
m-1112	1000	2	=	=	PUNCT
m-1112	1000	3	the	the	DET
m-1112	1000	4	conductor	conductor	NOUN
m-1112	1000	5	of	of	ADP
m-1112	1000	6	points	point	NOUN
m-1112	1000	7	since	since	ADV
m-1112	1000	8	,	,	PUNCT
m-1112	1000	9	the	the	DET
m-1112	1000	10	position	position	NOUN
m-1112	1000	11	and	and	CCONJ
m-1112	1000	12	the	the	DET
m-1112	1000	13	number	number	NOUN
m-1112	1000	14	of	of	ADP
m-1112	1000	15	points	point	NOUN
m-1112	1000	16	,	,	PUNCT
m-1112	1000	17	create	create	VERB
m-1112	1000	18	the	the	DET
m-1112	1000	19	spaces	space	NOUN
m-1112	1000	20	so	so	SCONJ
m-1112	1000	21	the	the	DET
m-1112	1000	22	only	only	ADV
m-1112	1000	23	three	three	NUM
m-1112	1000	24	elements	element	NOUN
m-1112	1000	25	are	be	AUX
m-1112	1000	26	→	→	PUNCT
m-1112	1000	27	{	{	PUNCT
m-1112	1000	28	⊕	⊕	NOUN
m-1112	1000	29	,	,	PUNCT
m-1112	1001	1	[	[	X
m-1112	1001	2	⊕↔⊝	⊕↔⊝	X
m-1112	1001	3	]	]	X
m-1112	1001	4	,	,	PUNCT
m-1112	1001	5	⊝	⊝	PUNCT
m-1112	1001	6	}	}	PUNCT
m-1112	1001	7	≡	≡	PROPN
m-1112	1002	1	[	[	X
m-1112	1002	2	+	+	ADJ
m-1112	1002	3	,	,	PUNCT
m-1112	1002	4	0	0	NUM
m-1112	1002	5	,	,	PUNCT
m-1112	1002	6	-	-	PUNCT
m-1112	1002	7	]	]	X
m-1112	1002	8	←	←	PROPN
m-1112	1002	9	for	for	ADP
m-1112	1002	10	material	material	NOUN
m-1112	1002	11	geometry	geometry	NOUN
m-1112	1002	12	exist	exist	VERB
m-1112	1002	13	linearly	linearly	ADV
m-1112	1002	14	in	in	ADP
m-1112	1002	15	moulds	mould	NOUN
m-1112	1002	16	.	.	PUNCT
m-1112	1003	1	the	the	DET
m-1112	1003	2	stresses	stress	NOUN
m-1112	1003	3	of	of	ADP
m-1112	1003	4	complex	complex	ADJ
m-1112	1003	5	-	-	PUNCT
m-1112	1003	6	vectors	vector	NOUN
m-1112	1003	7	act	act	VERB
m-1112	1003	8	on	on	ADP
m-1112	1003	9	a	a	DET
m-1112	1003	10	surface	surface	NOUN
m-1112	1003	11	,	,	PUNCT
m-1112	1003	12	a	a	DET
m-1112	1003	13	circle	circle	NOUN
m-1112	1003	14	of	of	ADP
m-1112	1003	15	sphere	sphere	NOUN
m-1112	1003	16	,	,	PUNCT
m-1112	1003	17	between	between	ADP
m-1112	1003	18	the	the	DET
m-1112	1003	19	sub	sub	NOUN
m-1112	1003	20	units	unit	NOUN
m-1112	1003	21	axially	axially	ADV
m-1112	1003	22	and	and	CCONJ
m-1112	1003	23	rotationally	rotationally	ADV
m-1112	1003	24	following	follow	VERB
m-1112	1003	25	ptolemy`s	ptolemy`	NOUN
m-1112	1003	26	and	and	CCONJ
m-1112	1003	27	cebas	cebas	PROPN
m-1112	1003	28	theorem	theorem	NOUN
m-1112	1003	29	of	of	ADP
m-1112	1003	30	equilibrium	equilibrium	NOUN
m-1112	1003	31	.	.	PUNCT
m-1112	1004	1	the	the	DET
m-1112	1004	2	space	space	NOUN
m-1112	1004	3	anti	anti	NOUN
m-1112	1004	4	-	-	NOUN
m-1112	1004	5	space	space	ADJ
m-1112	1004	6	and	and	CCONJ
m-1112	1004	7	,	,	PUNCT
m-1112	1004	8	neutral	neutral	ADJ
m-1112	1004	9	-	-	PUNCT
m-1112	1004	10	space	space	NOUN
m-1112	1004	11	conductors	conductor	NOUN
m-1112	1004	12	are	be	AUX
m-1112	1004	13	self	self	NOUN
m-1112	1004	14	-	-	PUNCT
m-1112	1004	15	sustaining	sustain	VERB
m-1112	1004	16	.	.	PUNCT
m-1112	1005	1	stability	stability	NOUN
m-1112	1005	2	:	:	PUNCT
m-1112	1005	3	ijo	ijo	PROPN
m-1112	1005	4	international	international	PROPN
m-1112	1005	5	journal	journal	PROPN
m-1112	1005	6	of	of	ADP
m-1112	1005	7	mathematics	mathematics	PROPN
m-1112	1005	8	(	(	PUNCT
m-1112	1005	9	issn	issn	PROPN
m-1112	1005	10	:	:	PUNCT
m-1112	1005	11	2992	2992	NUM
m-1112	1005	12	-	-	SYM
m-1112	1005	13	4421	4421	NUM
m-1112	1005	14	)	)	PUNCT
m-1112	1005	15	volume	volume	NOUN
m-1112	1005	16	08	08	NUM
m-1112	1006	1	|	|	ADV
m-1112	1006	2	issue	issue	NOUN
m-1112	1006	3	08	08	NUM
m-1112	1007	1	|	|	ADV
m-1112	1007	2	august	august	PROPN
m-1112	1007	3	2025	2025	NUM
m-1112	1007	4	|	|	ADV
m-1112	1007	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1007	6	ijo	ijo	PROPN
m-1112	1007	7	journals	journal	NOUN
m-1112	1007	8	36	36	NUM
m-1112	1007	9	the	the	DET
m-1112	1007	10	fundamental	fundamental	ADJ
m-1112	1007	11	particles	particle	NOUN
m-1112	1007	12	origination	origination	NOUN
m-1112	1007	13	mechanism	mechanism	NOUN
m-1112	1007	14	in	in	ADP
m-1112	1007	15	mfmf	mfmf	PROPN
m-1112	1007	16	pns	pns	PROPN
m-1112	1007	17	caves	cave	NOUN
m-1112	1007	18	.	.	PUNCT
m-1112	1008	1	the	the	DET
m-1112	1008	2	number	number	NOUN
m-1112	1008	3	of	of	ADP
m-1112	1008	4	moulds	mould	NOUN
m-1112	1008	5	of	of	ADP
m-1112	1008	6	stationary	stationary	ADJ
m-1112	1008	7	-	-	PUNCT
m-1112	1008	8	states	state	NOUN
m-1112	1008	9	are	be	AUX
m-1112	1008	10	as→	as→	ADV
m-1112	1008	11	2n=1−4	2n=1−4	NUM
m-1112	1008	12	points	point	NOUN
m-1112	1008	13	≡	≡	PROPN
m-1112	1008	14	2	2	NUM
m-1112	1008	15	,	,	PUNCT
m-1112	1008	16	4	4	NUM
m-1112	1008	17	,	,	PUNCT
m-1112	1008	18	8	8	NUM
m-1112	1008	19	,	,	PUNCT
m-1112	1008	20	16	16	NUM
m-1112	1008	21	≡	≡	PROPN
m-1112	1008	22	4	4	NUM
m-1112	1008	23	–	–	PUNCT
m-1112	1008	24	types←	types←	NOUN
m-1112	1008	25	i.e.	i.e.	X
m-1112	1008	26	monads	monad	NOUN
m-1112	1008	27	are	be	AUX
m-1112	1008	28	formed	form	VERB
m-1112	1008	29	from	from	ADP
m-1112	1008	30	the	the	DET
m-1112	1008	31	first	first	ADJ
m-1112	1008	32	4moulds	4moulds	NUM
m-1112	1008	33	as	as	ADP
m-1112	1008	34	→	→	SYM
m-1112	1008	35	the	the	DET
m-1112	1008	36	1	1	NUM
m-1112	1008	37	-	-	PUNCT
m-1112	1008	38	point	point	NOUN
m-1112	1008	39	which	which	PRON
m-1112	1008	40	is	be	AUX
m-1112	1008	41	everywhere	everywhere	ADV
m-1112	1008	42	,	,	PUNCT
m-1112	1008	43	the	the	DET
m-1112	1008	44	2points	2points	NUM
m-1112	1008	45	which	which	PRON
m-1112	1008	46	form	form	VERB
m-1112	1008	47	vectors	vector	NOUN
m-1112	1008	48	,	,	PUNCT
m-1112	1008	49	the	the	DET
m-1112	1008	50	3points	3point	NOUN
m-1112	1008	51	which	which	PRON
m-1112	1008	52	form	form	VERB
m-1112	1008	53	the	the	DET
m-1112	1008	54	planes	plane	NOUN
m-1112	1008	55	,	,	PUNCT
m-1112	1008	56	the	the	DET
m-1112	1008	57	4	4	NUM
m-1112	1008	58	points	point	NOUN
m-1112	1008	59	which	which	PRON
m-1112	1008	60	form	form	VERB
m-1112	1008	61	the	the	DET
m-1112	1008	62	volumes	volume	NOUN
m-1112	1008	63	.	.	PUNCT
m-1112	1009	1	for	for	ADP
m-1112	1009	2	n	n	X
m-1112	1009	3	>	>	X
m-1112	1009	4	4	4	NUM
m-1112	1009	5	as	as	SCONJ
m-1112	1009	6	this	this	PRON
m-1112	1009	7	is	be	AUX
m-1112	1009	8	the	the	DET
m-1112	1009	9	atoms	atom	NOUN
m-1112	1009	10	structure	structure	NOUN
m-1112	1009	11	,	,	PUNCT
m-1112	1009	12	follows	follow	VERB
m-1112	1009	13	the	the	DET
m-1112	1009	14	sustainability	sustainability	NOUN
m-1112	1009	15	of	of	ADP
m-1112	1009	16	the	the	DET
m-1112	1009	17	spaces	space	NOUN
m-1112	1009	18	and	and	CCONJ
m-1112	1009	19	anti	anti	NOUN
m-1112	1009	20	-	-	ADJ
m-1112	1009	21	spaces	space	NOUN
m-1112	1009	22	.	.	PUNCT
m-1112	1010	1	since	since	SCONJ
m-1112	1010	2	space	space	NOUN
m-1112	1010	3	-	-	PUNCT
m-1112	1010	4	energy	energy	NOUN
m-1112	1010	5	structures	structure	NOUN
m-1112	1010	6	follow	follow	VERB
m-1112	1010	7	the	the	DET
m-1112	1010	8	m	m	NOUN
m-1112	1010	9	-	-	PUNCT
m-1112	1010	10	geometry	geometry	NOUN
m-1112	1010	11	stability	stability	NOUN
m-1112	1010	12	these	these	PRON
m-1112	1010	13	follow	follow	VERB
m-1112	1010	14	the	the	DET
m-1112	1010	15	mould	mould	NOUN
m-1112	1010	16	of	of	ADP
m-1112	1010	17	spaces	space	NOUN
m-1112	1010	18	2	2	NUM
m-1112	1010	19	n	n	NOUN
m-1112	1010	20	=	=	SYM
m-1112	1010	21	3	3	NUM
m-1112	1010	22	=	=	SYM
m-1112	1010	23	8	8	NUM
m-1112	1010	24	elements	element	NOUN
m-1112	1010	25	which	which	PRON
m-1112	1010	26	is	be	AUX
m-1112	1010	27	the	the	DET
m-1112	1010	28	-	-	PUNCT
m-1112	1010	29	cube	cube	NOUN
m-1112	1010	30	as	as	SCONJ
m-1112	1010	31	shown	show	VERB
m-1112	1010	32	before	before	ADV
m-1112	1010	33	.	.	PUNCT
m-1112	1011	1	instances	instance	NOUN
m-1112	1011	2	,	,	PUNCT
m-1112	1011	3	1	1	X
m-1112	1011	4	..	..	PUNCT
m-1112	1011	5	in	in	ADP
m-1112	1011	6	the	the	DET
m-1112	1011	7	constant	constant	ADJ
m-1112	1011	8	,	,	PUNCT
m-1112	1011	9	hydrogen	hydrogen	NOUN
m-1112	1011	10	conservative	conservative	ADJ
m-1112	1011	11	-	-	PUNCT
m-1112	1011	12	cave	cave	NOUN
m-1112	1011	13	-	-	PUNCT
m-1112	1011	14	system	system	NOUN
m-1112	1011	15	,	,	PUNCT
m-1112	1011	16	which	which	PRON
m-1112	1011	17	creates	create	VERB
m-1112	1011	18	only	only	ADV
m-1112	1011	19	closed	close	VERB
m-1112	1011	20	orbit	orbit	NOUN
m-1112	1011	21	shapes	shape	NOUN
m-1112	1011	22	as	as	ADP
m-1112	1011	23	circles	circle	NOUN
m-1112	1011	24	,	,	PUNCT
m-1112	1011	25	ellipses	ellipsis	NOUN
m-1112	1011	26	and	and	CCONJ
m-1112	1011	27	eight	eight	NUM
m-1112	1011	28	-	-	PUNCT
m-1112	1011	29	shape	shape	NOUN
m-1112	1011	30	,	,	PUNCT
m-1112	1011	31	∞	∞	PROPN
m-1112	1011	32	,	,	PUNCT
m-1112	1011	33	are	be	AUX
m-1112	1011	34	placed	place	VERB
m-1112	1011	35	the	the	DET
m-1112	1011	36	above	above	ADJ
m-1112	1011	37	elements	element	NOUN
m-1112	1011	38	,	,	PUNCT
m-1112	1011	39	π	π	PROPN
m-1112	1011	40	g	g	PROPN
m-1112	1011	41	≡	≡	PROPN
m-1112	1011	42	energy	energy	NOUN
m-1112	1011	43	≡	≡	PROPN
m-1112	1012	1	[	[	X
m-1112	1012	2	meter	meter	NOUN
m-1112	1012	3	of	of	ADP
m-1112	1012	4	area	area	NOUN
m-1112	1012	5	*	*	PUNCT
m-1112	1012	6	meter	meter	NOUN
m-1112	1012	7	of	of	ADP
m-1112	1012	8	force	force	NOUN
m-1112	1012	9	]	]	PUNCT
m-1112	1012	10	≡	≡	ADJ
m-1112	1012	11	electrons	electron	NOUN
m-1112	1012	12	on	on	ADP
m-1112	1012	13	orbits	orbit	NOUN
m-1112	1012	14	,	,	PUNCT
m-1112	1012	15	and	and	CCONJ
m-1112	1012	16	also	also	ADV
m-1112	1012	17	the	the	DET
m-1112	1012	18	unit	unit	NOUN
m-1112	1012	19	-	-	PUNCT
m-1112	1012	20	space	space	NOUN
m-1112	1012	21	≡	≡	PROPN
m-1112	1012	22	massive	massive	ADJ
m-1112	1012	23	-	-	PUNCT
m-1112	1012	24	complex	complex	ADJ
m-1112	1012	25	-	-	PUNCT
m-1112	1012	26	unit	unit	NOUN
m-1112	1012	27	-	-	PUNCT
m-1112	1012	28	space	space	NOUN
m-1112	1012	29	≡	≡	PROPN
m-1112	1012	30	→[+	→[+	NUM
m-1112	1012	31	�	�	PROPN
m-1112	1012	32	̅	̅	NOUN
m-1112	1012	33	�	�	NOUN
m-1112	1012	34	.s²]←	.s²]←	NOUN
m-1112	1012	35	jointed	joint	VERB
m-1112	1012	36	through	through	ADP
m-1112	1012	37	the	the	DET
m-1112	1012	38	neutral	neutral	ADJ
m-1112	1012	39	material	material	NOUN
m-1112	1012	40	-	-	PUNCT
m-1112	1012	41	points	point	NOUN
m-1112	1012	42	[	[	PUNCT
m-1112	1012	43	(	(	PUNCT
m-1112	1012	44	+	+	NOUN
m-1112	1012	45	)	)	PUNCT
m-1112	1013	1	[	[	X
m-1112	1013	2	↔	↔	X
m-1112	1013	3	]	]	X
m-1112	1013	4	(	(	PUNCT
m-1112	1013	5	-	-	PUNCT
m-1112	1013	6	)	)	PUNCT
m-1112	1013	7	]	]	PUNCT
m-1112	1013	8	with	with	ADP
m-1112	1013	9	the	the	DET
m-1112	1013	10	strong	strong	ADJ
m-1112	1013	11	-	-	PUNCT
m-1112	1013	12	force	force	NOUN
m-1112	1013	13	→	→	SYM
m-1112	1013	14	s	s	PART
m-1112	1013	15	f	f	X
m-1112	1013	16	=	=	SYM
m-1112	1013	17	h	h	PROPN
m-1112	1013	18	.fn	.fn	PUNCT
m-1112	1013	19	≡	≡	PROPN
m-1112	1013	20	h	h	PROPN
m-1112	1013	21	.	.	PUNCT
m-1112	1013	22	{	{	PUNCT
m-1112	1014	1	[	[	X
m-1112	1014	2	s	s	X
m-1112	1014	3	≡	≡	PROPN
m-1112	1014	4	bp	bp	PROPN
m-1112	1014	5	≡	≡	PROPN
m-1112	1014	6	em	em	PROPN
m-1112	1014	7	-	-	PUNCT
m-1112	1014	8	r	r	NOUN
m-1112	1014	9	≡	≡	PROPN
m-1112	1014	10	f1	f1	NOUN
m-1112	1014	11	=	=	SYM
m-1112	1014	12	n	n	NOUN
m-1112	1014	13	,	,	PUNCT
m-1112	1014	14	f2	f2	ADV
m-1112	1014	15	,	,	PUNCT
m-1112	1014	16	f3	f3	PROPN
m-1112	1014	17	,	,	PUNCT
m-1112	1014	18	fd	fd	X
m-1112	1014	19	,	,	PUNCT
m-1112	1014	20	,	,	PUNCT
m-1112	1014	21	f	f	PROPN
m-1112	1014	22	n	n	X
m-1112	1014	23	]	]	PUNCT
m-1112	1014	24	≡	≡	PROPN
m-1112	1014	25	h.n	h.n	PROPN
m-1112	1014	26	(	(	PUNCT
m-1112	1014	27	1+√5	1+√5	NUM
m-1112	1014	28	)	)	PUNCT
m-1112	1014	29	σ	σ	PROPN
m-1112	1014	30	2πr	2πr	NOUN
m-1112	1014	31	≡	≡	PROPN
m-1112	1014	32	h	h	NOUN
m-1112	1014	33	[	[	PUNCT
m-1112	1014	34	n.b̅	n.b̅	PROPN
m-1112	1014	35	4𝜋2	4𝜋2	NUM
m-1112	1014	36	.	.	PUNCT
m-1112	1015	1	r4	r4	VERB
m-1112	1015	2	]	]	PUNCT
m-1112	1015	3	…	…	PUNCT
m-1112	1015	4	.(mg	.(mg	ADJ
m-1112	1015	5	)	)	PUNCT
m-1112	1015	6	equations	equation	NOUN
m-1112	1015	7	(	(	PUNCT
m-1112	1015	8	m	m	NOUN
m-1112	1015	9	)	)	PUNCT
m-1112	1015	10	,	,	PUNCT
m-1112	1015	11	(	(	PUNCT
m-1112	1015	12	mg	mg	X
m-1112	1015	13	)	)	PUNCT
m-1112	1015	14	are	be	AUX
m-1112	1015	15	the	the	DET
m-1112	1015	16	energy	energy	NOUN
m-1112	1015	17	-	-	PUNCT
m-1112	1015	18	space	space	NOUN
m-1112	1015	19	-	-	PUNCT
m-1112	1015	20	constituents	constituent	NOUN
m-1112	1015	21	in	in	ADP
m-1112	1015	22	hydrogen	hydrogen	NOUN
m-1112	1015	23	-	-	PUNCT
m-1112	1015	24	system	system	NOUN
m-1112	1015	25	.	.	PUNCT
m-1112	1016	1	c-1	c-1	NOUN
m-1112	1016	2	..	..	PUNCT
m-1112	1017	1	the	the	DET
m-1112	1017	2	protons	proton	NOUN
m-1112	1017	3	and	and	CCONJ
m-1112	1017	4	the	the	DET
m-1112	1017	5	nucleus	nucleus	ADJ
m-1112	1017	6	structure	structure	NOUN
m-1112	1017	7	:	:	PUNCT
m-1112	1017	8	from	from	ADP
m-1112	1017	9	above	above	ADP
m-1112	1017	10	mp	mp	PROPN
m-1112	1017	11	≡	≡	PROPN
m-1112	1018	1	[	[	X
m-1112	1018	2	(	(	PUNCT
m-1112	1018	3	+	+	NOUN
m-1112	1018	4	)	)	PUNCT
m-1112	1018	5	[	[	X
m-1112	1018	6	↔](-	↔](-	NOUN
m-1112	1018	7	)	)	PUNCT
m-1112	1018	8	]	]	PUNCT
m-1112	1019	1	≡	≡	PROPN
m-1112	1019	2	neutral	neutral	ADJ
m-1112	1019	3	=	=	SYM
m-1112	1019	4	n	n	NOUN
m-1112	1019	5	,	,	PUNCT
m-1112	1019	6	then	then	ADV
m-1112	1019	7	a	a	X
m-1112	1019	8	..	..	PUNCT
m-1112	1019	9	for	for	ADP
m-1112	1019	10	1	1	NUM
m-1112	1019	11	proton	proton	NOUN
m-1112	1019	12	[	[	X
m-1112	1019	13	(	(	PUNCT
m-1112	1019	14	+	+	NOUN
m-1112	1019	15	)	)	PUNCT
m-1112	1019	16	[	[	X
m-1112	1019	17	↔](-)]↔(+	↔](-)]↔(+	NOUN
m-1112	1019	18	)	)	PUNCT
m-1112	1019	19	≡	≡	PROPN
m-1112	1019	20	neutral	neutral	ADJ
m-1112	1019	21	→	→	SYM
m-1112	1019	22	n	n	NOUN
m-1112	1019	23	=	=	SYM
m-1112	1019	24	1	1	NUM
m-1112	1019	25	p	p	NOUN
m-1112	1019	26	=	=	SYM
m-1112	1019	27	1	1	NUM
m-1112	1019	28	b	b	PROPN
m-1112	1019	29	..	..	PUNCT
m-1112	1019	30	for	for	ADP
m-1112	1019	31	2	2	NUM
m-1112	1019	32	proton	proton	NOUN
m-1112	1019	33	(	(	PUNCT
m-1112	1019	34	+	+	NOUN
m-1112	1019	35	)	)	PUNCT
m-1112	1019	36	↔[(-)↔(+)][(+)↔(-)]↔(+	↔[(-)↔(+)][(+)↔(-)]↔(+	NOUN
m-1112	1019	37	)	)	PUNCT
m-1112	1020	1	≡	≡	PROPN
m-1112	1020	2	neutral	neutral	ADJ
m-1112	1020	3	→	→	SYM
m-1112	1020	4	p	p	NOUN
m-1112	1020	5	n	n	CCONJ
m-1112	1020	6	n	n	NOUN
m-1112	1020	7	p	p	NOUN
m-1112	1020	8	c	c	PROPN
m-1112	1020	9	..	..	PUNCT
m-1112	1020	10	for	for	ADP
m-1112	1020	11	3	3	NUM
m-1112	1020	12	proton	proton	NOUN
m-1112	1020	13	(	(	PUNCT
m-1112	1020	14	+	+	NOUN
m-1112	1020	15	)	)	PUNCT
m-1112	1020	16	↔[(-)(+)](+)[(-)(+)](+)[(-)(+	↔[(-)(+)](+)[(-)(+)](+)[(-)(+	NOUN
m-1112	1020	17	)	)	PUNCT
m-1112	1020	18	]	]	PUNCT
m-1112	1021	1	≡	≡	PROPN
m-1112	1021	2	neutral	neutral	ADJ
m-1112	1021	3	→	→	SYM
m-1112	1021	4	[	[	PUNCT
m-1112	1021	5	0	0	NUM
m-1112	1021	6	0	0	NUM
m-1112	1021	7	0	0	NUM
m-1112	1021	8	0	0	NUM
m-1112	1021	9	2⃡	2⃡	NOUN
m-1112	1021	10	0	0	NUM
m-1112	1022	1	1e	1e	NOUN
m-1112	1022	2	0	0	NUM
m-1112	1022	3	0	0	NUM
m-1112	1022	4	]	]	PUNCT
m-1112	1023	1	d	d	X
m-1112	1023	2	..	..	PUNCT
m-1112	1023	3	for	for	ADP
m-1112	1023	4	4	4	NUM
m-1112	1023	5	proton	proton	NOUN
m-1112	1023	6	(	(	PUNCT
m-1112	1023	7	+	+	NOUN
m-1112	1023	8	)	)	PUNCT
m-1112	1023	9	↔[(-)(+)](+)[(-)(+)](+)[(-)(+)](+)[(-)(+	↔[(-)(+)](+)[(-)(+)](+)[(-)(+)](+)[(-)(+	NOUN
m-1112	1023	10	)	)	PUNCT
m-1112	1023	11	]	]	PUNCT
m-1112	1024	1	→	→	PUNCT
m-1112	1024	2	[	[	PUNCT
m-1112	1024	3	0	0	NUM
m-1112	1024	4	0	0	NUM
m-1112	1024	5	0	0	NUM
m-1112	1024	6	0	0	NUM
m-1112	1024	7	2⃡	2⃡	NOUN
m-1112	1024	8	0	0	NUM
m-1112	1025	1	1e	1e	NOUN
m-1112	1025	2	1e	1e	NOUN
m-1112	1025	3	0	0	NUM
m-1112	1025	4	]	]	PUNCT
m-1112	1026	1	e	e	X
m-1112	1026	2	..	..	PUNCT
m-1112	1026	3	for	for	ADP
m-1112	1026	4	k	k	PROPN
m-1112	1026	5	proton	proton	NOUN
m-1112	1026	6	(	(	PUNCT
m-1112	1026	7	k1)↔[(-)(+)](k2)[(-)(+)](+)[(-)(+)](+)[(-)(𝐡𝐤	k1)↔[(-)(+)](k2)[(-)(+)](+)[(-)(+)](+)[(-)(𝐡𝐤	PROPN
m-1112	1026	8	)	)	PUNCT
m-1112	1026	9	]	]	PUNCT
m-1112	1027	1	→	→	PUNCT
m-1112	1027	2	[	[	PUNCT
m-1112	1027	3	ke	ke	NOUN
m-1112	1027	4	ke	ke	NOUN
m-1112	1027	5	ke	ke	PROPN
m-1112	1027	6	ke	ke	PROPN
m-1112	1027	7	𝑘	𝑘	PROPN
m-1112	1027	8	∶	∶	NOUN
m-1112	1027	9	8	8	NUM
m-1112	1027	10	−	−	PROPN
m-1112	1027	11	18⃖⃗	18⃖⃗	NUM
m-1112	1027	12	⃗⃗	⃗⃗	PROPN
m-1112	1027	13	⃗⃗	⃗⃗	PROPN
m-1112	1027	14	⃗⃗	⃗⃗	PROPN
m-1112	1027	15	⃗⃗	⃗⃗	PROPN
m-1112	1027	16	⃗⃗	⃗⃗	PROPN
m-1112	1027	17	⃗⃗	⃗⃗	PROPN
m-1112	1027	18	⃗⃗	⃗⃗	PROPN
m-1112	1027	19	⃗⃗	⃗⃗	PROPN
m-1112	1027	20	⃗⃗	⃗⃗	PROPN
m-1112	1027	21	ke	ke	PROPN
m-1112	1027	22	ke	ke	PROPN
m-1112	1027	23	ke	ke	PROPN
m-1112	1027	24	ke	ke	PROPN
m-1112	1027	25	]	]	PUNCT
m-1112	1028	1	f	f	X
m-1112	1028	2	..	..	PUNCT
m-1112	1028	3	the	the	DET
m-1112	1028	4	inscribed	inscribe	VERB
m-1112	1028	5	to	to	ADP
m-1112	1028	6	the	the	DET
m-1112	1028	7	tetrahedron	tetrahedron	NOUN
m-1112	1028	8	-	-	PUNCT
m-1112	1028	9	sphere	sphere	NOUN
m-1112	1028	10	consists	consist	VERB
m-1112	1028	11	the	the	DET
m-1112	1028	12	nucleus	nucleus	PROPN
m-1112	1028	13	≡	≡	PROPN
m-1112	1028	14	the	the	DET
m-1112	1028	15	⊕	⊕	PROPN
m-1112	1028	16	space	space	NOUN
m-1112	1028	17	,	,	PUNCT
m-1112	1028	18	and	and	CCONJ
m-1112	1028	19	in	in	ADP
m-1112	1028	20	circumscribed	circumscribe	VERB
m-1112	1028	21	to	to	ADP
m-1112	1028	22	the	the	DET
m-1112	1028	23	tetrahedron	tetrahedron	NOUN
m-1112	1028	24	-	-	PUNCT
m-1112	1028	25	cube	cube	NOUN
m-1112	1028	26	sphere	sphere	NOUN
m-1112	1028	27	consists	consist	VERB
m-1112	1028	28	the	the	DET
m-1112	1028	29	orbitals	orbital	NOUN
m-1112	1028	30	≡	≡	VERB
m-1112	1028	31	the	the	DET
m-1112	1028	32	⊝	⊝	VERB
m-1112	1028	33	space	space	NOUN
m-1112	1028	34	.	.	PUNCT
m-1112	1029	1	c-2	c-2	NOUN
m-1112	1029	2	..	..	PUNCT
m-1112	1030	1	the	the	DET
m-1112	1030	2	annihilation	annihilation	NOUN
m-1112	1030	3	of	of	ADP
m-1112	1030	4	the	the	DET
m-1112	1030	5	fundamental	fundamental	ADJ
m-1112	1030	6	particles	particle	NOUN
m-1112	1030	7	.	.	PUNCT
m-1112	1031	1	considering	consider	VERB
m-1112	1031	2	the	the	DET
m-1112	1031	3	,	,	PUNCT
m-1112	1031	4	matter	matter	NOUN
m-1112	1031	5	antimatter	antimatter	NOUN
m-1112	1031	6	,	,	PUNCT
m-1112	1031	7	with	with	ADP
m-1112	1031	8	the	the	DET
m-1112	1031	9	classical	classical	ADJ
m-1112	1031	10	known	know	VERB
m-1112	1031	11	theory	theory	NOUN
m-1112	1031	12	of	of	ADP
m-1112	1031	13	annihilation	annihilation	NOUN
m-1112	1031	14	as	as	ADP
m-1112	1031	15	the	the	DET
m-1112	1031	16	common	common	ADJ
m-1112	1031	17	constant	constant	ADJ
m-1112	1031	18	energy	energy	NOUN
m-1112	1031	19	then	then	ADV
m-1112	1031	20	issue	issue	VERB
m-1112	1031	21	for	for	ADP
m-1112	1031	22	a	a	DET
m-1112	1031	23	force	force	NOUN
m-1112	1031	24	↔anti	↔anti	PROPN
m-1112	1031	25	force	force	NOUN
m-1112	1031	26	,	,	PUNCT
m-1112	1031	27	action	action	NOUN
m-1112	1031	28	↔reaction	↔reaction	NOUN
m-1112	1031	29	electron	electron	NOUN
m-1112	1031	30	=	=	PUNCT
m-1112	1031	31	e−=	e−=	PROPN
m-1112	1031	32	⊝→	⊝→	PROPN
m-1112	1031	33	mass	mass	PROPN
m-1112	1031	34	𝐦𝐞	𝐦𝐞	PROPN
m-1112	1031	35	=	=	SYM
m-1112	1031	36	9,11.10−31	9,11.10−31	NUM
m-1112	1031	37	kg	kg	NOUN
m-1112	1031	38	→	→	PUNCT
m-1112	1031	39	charge	charge	NOUN
m-1112	1031	40	𝐂𝐞	𝐂𝐞	PROPN
m-1112	1031	41	=	=	SYM
m-1112	1031	42	1,602.10−19	1,602.10−19	NUM
m-1112	1031	43	ev	ev	PROPN
m-1112	1031	44	→	→	X
m-1112	1031	45	cave	cave	NOUN
m-1112	1031	46	a	a	DET
m-1112	1031	47	=	=	SYM
m-1112	1031	48	5,0.10−17	5,0.10−17	PROPN
m-1112	1031	49	m	m	NOUN
m-1112	1031	50	1	1	NUM
m-1112	1031	51	..	..	PUNCT
m-1112	1031	52	electron	electron	NOUN
m-1112	1031	53	positron	positron	NOUN
m-1112	1031	54			NOUN
m-1112	1032	1	e−→	e−→	NOUN
m-1112	1032	2	e+	e+	PUNCT
m-1112	1032	3	≡	≡	PROPN
m-1112	1032	4	2	2	NUM
m-1112	1032	5	γ	γ	X
m-1112	1032	6	≠	≠	PROPN
m-1112	1032	7	0	0	NUM
m-1112	1032	8	the	the	DET
m-1112	1032	9	common	common	ADJ
m-1112	1032	10	me→p	me→p	NOUN
m-1112	1032	11	is	be	AUX
m-1112	1032	12	from	from	ADP
m-1112	1032	13	relation	relation	NOUN
m-1112	1032	14	1	1	NUM
m-1112	1032	15	mt	mt	NOUN
m-1112	1033	1	=	=	NOUN
m-1112	1033	2	1	1	NUM
m-1112	1033	3	me	i	PRON
m-1112	1033	4	+	+	CCONJ
m-1112	1033	5	1	1	NUM
m-1112	1033	6	mp	mp	NOUN
m-1112	1033	7	=	=	SYM
m-1112	1033	8	1	1	NUM
m-1112	1033	9	me	i	PRON
m-1112	1033	10	+	+	CCONJ
m-1112	1033	11	1	1	NUM
m-1112	1033	12	me	me	NOUN
m-1112	1033	13	=	=	SYM
m-1112	1033	14	2	2	NUM
m-1112	1033	15	me	me	NOUN
m-1112	1033	16	=	=	SYM
m-1112	1033	17	2	2	NUM
m-1112	1033	18	9,11.10−31	9,11.10−31	NUM
m-1112	1033	19	=	=	SYM
m-1112	1033	20	1	1	NUM
m-1112	1033	21	4,555.10−31	4,555.10−31	NUM
m-1112	1033	22	from	from	ADP
m-1112	1033	23	energy	energy	NOUN
m-1112	1033	24	equation	equation	NOUN
m-1112	1033	25	e	e	NOUN
m-1112	1033	26	=	=	SYM
m-1112	1033	27	1	1	NUM
m-1112	1033	28	2	2	NUM
m-1112	1033	29	me→p	me→p	NOUN
m-1112	1033	30	c²	c²	NOUN
m-1112	1033	31	=	=	NOUN
m-1112	1033	32	1	1	NUM
m-1112	1033	33	2	2	NUM
m-1112	1033	34	[	[	SYM
m-1112	1033	35	4,555	4,555	NUM
m-1112	1033	36	.	.	PUNCT
m-1112	1034	1	10−31].[2,998	10−31].[2,998	NUM
m-1112	1034	2	.	.	PUNCT
m-1112	1035	1	108]²	108]²	NUM
m-1112	1035	2	=	=	PUNCT
m-1112	1036	1	6,827945	6,827945	NOUN
m-1112	1036	2	.	.	PUNCT
m-1112	1036	3	10−15	10−15	PROPN
m-1112	1036	4	j	j	PROPN
m-1112	1036	5	=	=	SYM
m-1112	1036	6	j	j	PROPN
m-1112	1036	7	/	/	SYM
m-1112	1036	8	(	(	PUNCT
m-1112	1036	9	1,6022.10−19	1,6022.10−19	NUM
m-1112	1036	10	ev	ev	X
m-1112	1036	11	)	)	PUNCT
m-1112	1036	12	=	=	SYM
m-1112	1037	1	4,2616059	4,2616059	NUM
m-1112	1037	2	.	.	PUNCT
m-1112	1038	1	10	10	NUM
m-1112	1038	2	4	4	NUM
m-1112	1038	3	ev	ev	NOUN
m-1112	1038	4	=	=	SYM
m-1112	1038	5	42,616059	42,616059	NUM
m-1112	1038	6	.kev	.kev	PUNCT
m-1112	1038	7	the	the	DET
m-1112	1038	8	common	common	ADJ
m-1112	1038	9	frequency	frequency	NOUN
m-1112	1038	10	is	be	AUX
m-1112	1038	11	f	f	PROPN
m-1112	1038	12	e→p	e→p	PROPN
m-1112	1038	13	=	=	SYM
m-1112	1038	14	e	e	NOUN
m-1112	1038	15	h	h	NOUN
m-1112	1038	16	=	=	SYM
m-1112	1038	17	6,827945.10−15	6,827945.10−15	NUM
m-1112	1038	18	j	j	NOUN
m-1112	1038	19	6.62607.10−34	6.62607.10−34	NUM
m-1112	1038	20	js	js	ADJ
m-1112	1038	21	.	.	PUNCT
m-1112	1039	1	=	=	PUNCT
m-1112	1039	2	1,0304667	1,0304667	PROPN
m-1112	1039	3	.	.	PROPN
m-1112	1040	1	10	10	NUM
m-1112	1040	2	19	19	NUM
m-1112	1040	3	h	h	NOUN
m-1112	1040	4			NOUN
m-1112	1040	5	i.e.	i.e.	X
m-1112	1040	6	𝐟	𝐟	X
m-1112	1040	7	𝛄	𝛄	PROPN
m-1112	1040	8	ijo	ijo	PROPN
m-1112	1040	9	international	international	PROPN
m-1112	1040	10	journal	journal	PROPN
m-1112	1040	11	of	of	ADP
m-1112	1040	12	mathematics	mathematics	PROPN
m-1112	1040	13	(	(	PUNCT
m-1112	1040	14	issn	issn	PROPN
m-1112	1040	15	:	:	PUNCT
m-1112	1040	16	2992	2992	NUM
m-1112	1040	17	-	-	SYM
m-1112	1040	18	4421	4421	NUM
m-1112	1040	19	)	)	PUNCT
m-1112	1040	20	volume	volume	NOUN
m-1112	1040	21	08	08	NUM
m-1112	1041	1	|	|	ADV
m-1112	1041	2	issue	issue	NOUN
m-1112	1041	3	08	08	NUM
m-1112	1042	1	|	|	ADV
m-1112	1042	2	august	august	PROPN
m-1112	1042	3	2025	2025	NUM
m-1112	1042	4	|	|	ADV
m-1112	1042	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1042	6	ijo	ijo	PROPN
m-1112	1042	7	journals	journal	NOUN
m-1112	1042	8	37	37	NUM
m-1112	1042	9	the	the	DET
m-1112	1042	10	fundamental	fundamental	ADJ
m-1112	1042	11	particles	particle	NOUN
m-1112	1042	12	origination	origination	NOUN
m-1112	1042	13	mechanism	mechanism	NOUN
m-1112	1042	14	in	in	ADP
m-1112	1042	15	mfmf	mfmf	PROPN
m-1112	1042	16	pns	pns	PROPN
m-1112	1042	17	caves	cave	NOUN
m-1112	1042	18	.	.	PUNCT
m-1112	1043	1	c-3	c-3	PROPN
m-1112	1043	2	..	..	PUNCT
m-1112	1044	1	the	the	DET
m-1112	1044	2	equilibrium	equilibrium	NOUN
m-1112	1044	3	of	of	ADP
m-1112	1044	4	the	the	DET
m-1112	1044	5	three	three	NUM
m-1112	1044	6	-	-	PUNCT
m-1112	1044	7	spaces	space	NOUN
m-1112	1044	8	,	,	PUNCT
m-1112	1044	9	the	the	DET
m-1112	1044	10	space	space	NOUN
m-1112	1044	11	anti	anti	NOUN
m-1112	1044	12	-	-	ADJ
m-1112	1044	13	space	space	ADJ
m-1112	1044	14	,	,	PUNCT
m-1112	1044	15	neutral	neutral	ADJ
m-1112	1044	16	-	-	PUNCT
m-1112	1044	17	space	space	NOUN
m-1112	1044	18	the	the	DET
m-1112	1044	19	stability	stability	NOUN
m-1112	1044	20	of	of	ADP
m-1112	1044	21	elementary	elementary	ADJ
m-1112	1044	22	particles	particle	NOUN
m-1112	1044	23	,	,	PUNCT
m-1112	1044	24	conductors	conductor	NOUN
m-1112	1044	25	and	and	CCONJ
m-1112	1044	26	the	the	DET
m-1112	1044	27	atoms	atom	NOUN
m-1112	1044	28	-nucleus	-nucleus	NOUN
m-1112	1044	29	:	:	PUNCT
m-1112	1045	1	[	[	X
m-1112	1045	2	60	60	NUM
m-1112	1045	3	]	]	PUNCT
m-1112	1045	4	figure	figure	NOUN
m-1112	1045	5	–	–	PUNCT
m-1112	1045	6	9a	9a	NOUN
m-1112	1045	7	:	:	PUNCT
m-1112	1045	8	the	the	DET
m-1112	1045	9	electric	electric	ADJ
m-1112	1045	10	and	and	CCONJ
m-1112	1045	11	magnetic	magnetic	ADJ
m-1112	1045	12	field	field	NOUN
m-1112	1045	13	of	of	ADP
m-1112	1045	14	3	3	NUM
m-1112	1045	15	conductors	conductor	NOUN
m-1112	1045	16	on	on	ADP
m-1112	1045	17	2	2	NUM
m-1112	1045	18	anti	anti	ADJ
m-1112	1045	19	-	-	ADJ
m-1112	1045	20	parallel	parallel	ADJ
m-1112	1045	21	-	-	PUNCT
m-1112	1045	22	strands	strand	NOUN
m-1112	1045	23	the	the	DET
m-1112	1045	24	waves	wave	NOUN
m-1112	1045	25	motion	motion	NOUN
m-1112	1045	26	≡	≡	PROPN
m-1112	1045	27	energy	energy	NOUN
m-1112	1045	28	,	,	PUNCT
m-1112	1045	29	is	be	AUX
m-1112	1045	30	transported	transport	VERB
m-1112	1045	31	and	and	CCONJ
m-1112	1045	32	,	,	PUNCT
m-1112	1045	33	the	the	DET
m-1112	1045	34	pattern	pattern	NOUN
m-1112	1045	35	of	of	ADP
m-1112	1045	36	disturbances	disturbance	NOUN
m-1112	1045	37	with	with	ADP
m-1112	1045	38	informations	information	NOUN
m-1112	1045	39	,	,	PUNCT
m-1112	1045	40	propagates	propagate	VERB
m-1112	1045	41	from	from	ADP
m-1112	1045	42	the	the	DET
m-1112	1045	43	one	one	NUM
m-1112	1045	44	-	-	PUNCT
m-1112	1045	45	edge	edge	NOUN
m-1112	1045	46	-	-	PUNCT
m-1112	1045	47	point	point	NOUN
m-1112	1045	48	to	to	ADP
m-1112	1045	49	the	the	DET
m-1112	1045	50	other	other	ADJ
m-1112	1045	51	edge	edge	NOUN
m-1112	1045	52	-	-	PUNCT
m-1112	1045	53	point	point	NOUN
m-1112	1045	54	of	of	ADP
m-1112	1045	55	conductors	conductor	NOUN
m-1112	1045	56	,	,	PUNCT
m-1112	1045	57	or	or	CCONJ
m-1112	1045	58	is	be	AUX
m-1112	1045	59	on	on	ADP
m-1112	1045	60	[	[	PUNCT
m-1112	1045	61	sub	sub	NOUN
m-1112	1045	62	-	-	NOUN
m-1112	1045	63	units	unit	NOUN
m-1112	1045	64	]	]	PUNCT
m-1112	1045	65	.	.	PUNCT
m-1112	1046	1	to	to	PART
m-1112	1046	2	prove	prove	VERB
m-1112	1046	3	the	the	DET
m-1112	1046	4	stability	stability	NOUN
m-1112	1046	5	of	of	ADP
m-1112	1046	6	the	the	DET
m-1112	1046	7	system	system	NOUN
m-1112	1046	8	,	,	PUNCT
m-1112	1046	9	the	the	DET
m-1112	1046	10	equations	equation	NOUN
m-1112	1046	11	of	of	ADP
m-1112	1046	12	motion	motion	NOUN
m-1112	1046	13	become	become	VERB
m-1112	1046	14	everywhere	everywhere	ADV
m-1112	1046	15	from	from	ADP
m-1112	1046	16	any	any	DET
m-1112	1046	17	opposite	opposite	ADJ
m-1112	1046	18	space	space	NOUN
m-1112	1046	19	≡	≡	PROPN
m-1112	1046	20	⊕	⊕	PROPN
m-1112	1046	21	,	,	PUNCT
m-1112	1046	22	anti	anti	ADJ
m-1112	1046	23	space	space	NOUN
m-1112	1046	24	≡	≡	PROPN
m-1112	1046	25	⊝	⊝	PROPN
m-1112	1046	26	.	.	PUNCT
m-1112	1047	1	during	during	ADP
m-1112	1047	2	these	these	DET
m-1112	1047	3	motions	motion	NOUN
m-1112	1047	4	as	as	ADP
m-1112	1047	5	,	,	PUNCT
m-1112	1047	6	ds	ds	INTJ
m-1112	1047	7	.	.	PUNCT
m-1112	1047	8	is	be	AUX
m-1112	1047	9	done	do	VERB
m-1112	1047	10	a	a	DET
m-1112	1047	11	constant	constant	ADJ
m-1112	1047	12	-	-	PUNCT
m-1112	1047	13	work	work	NOUN
m-1112	1047	14	,	,	PUNCT
m-1112	1047	15	k	k	NOUN
m-1112	1047	16	,	,	PUNCT
m-1112	1047	17	or	or	CCONJ
m-1112	1047	18	and	and	CCONJ
m-1112	1047	19	from	from	ADP
m-1112	1047	20	their	their	PRON
m-1112	1047	21	velocities	velocity	NOUN
m-1112	1047	22	�	�	NOUN
m-1112	1047	23	̅	̅	NOUN
m-1112	1047	24	�	�	NOUN
m-1112	1047	25	and	and	CCONJ
m-1112	1047	26	this	this	DET
m-1112	1047	27	work	work	NOUN
m-1112	1047	28	may	may	AUX
m-1112	1047	29	be	be	AUX
m-1112	1047	30	positive	positive	ADJ
m-1112	1047	31	or	or	CCONJ
m-1112	1047	32	negative	negative	ADJ
m-1112	1047	33	for	for	ADP
m-1112	1047	34	equilibrium	equilibrium	NOUN
m-1112	1047	35	.	.	PUNCT
m-1112	1048	1	in	in	ADP
m-1112	1048	2	f-23	f-23	PROPN
m-1112	1048	3	cycloid	cycloid	NOUN
m-1112	1048	4	anti	anti	ADJ
m-1112	1048	5	-	-	ADJ
m-1112	1048	6	cycloid	cycloid	ADJ
m-1112	1048	7	motion	motion	NOUN
m-1112	1048	8	is	be	AUX
m-1112	1048	9	as	as	ADP
m-1112	1048	10	,	,	PUNCT
m-1112	1048	11	d.	d.	PROPN
m-1112	1048	12	the	the	DET
m-1112	1048	13	origination	origination	NOUN
m-1112	1048	14	of	of	ADP
m-1112	1048	15	gravity	gravity	NOUN
m-1112	1048	16	g	g	NOUN
m-1112	1048	17	,	,	PUNCT
m-1112	1048	18	antigravity	antigravity	NOUN
m-1112	1049	1	[	[	X
m-1112	1049	2	g	g	X
m-1112	1049	3	]	]	PUNCT
m-1112	1049	4	in	in	ADP
m-1112	1049	5	fig-9a	fig-9a	PROPN
m-1112	1049	6	,	,	PUNCT
m-1112	1049	7	conductor	conductor	NOUN
m-1112	1050	1	d	d	NOUN
m-1112	1050	2	=	=	SYM
m-1112	1050	3	d	d	NOUN
m-1112	1050	4	=	=	PUNCT
m-1112	1050	5	aka	aka	ADV
m-1112	1050	6	where	where	SCONJ
m-1112	1050	7	⊕	⊕	PROPN
m-1112	1050	8	constituent	constituent	NOUN
m-1112	1050	9	attacks	attack	NOUN
m-1112	1050	10	⊝	⊝	VERB
m-1112	1050	11	by	by	ADP
m-1112	1050	12	a	a	DET
m-1112	1050	13	hook`s	hook`	NOUN
m-1112	1050	14	law	law	NOUN
m-1112	1050	15	force	force	NOUN
m-1112	1050	16	as	as	ADP
m-1112	1050	17	stress	stress	NOUN
m-1112	1050	18	σ	σ	NOUN
m-1112	1050	19	=	=	PUNCT
m-1112	1050	20	e	e	PROPN
m-1112	1050	21	u	u	PROPN
m-1112	1050	22	,	,	PUNCT
m-1112	1050	23	and	and	CCONJ
m-1112	1050	24	an	an	DET
m-1112	1050	25	coulomb	coulomb	NOUN
m-1112	1050	26	force	force	NOUN
m-1112	1050	27	f	f	PROPN
m-1112	1051	1	[	[	X
m-1112	1051	2	+	+	X
m-1112	1051	3	↔	↔	PROPN
m-1112	1051	4	−	−	NOUN
m-1112	1051	5	]	]	X
m-1112	1052	1	=	=	PUNCT
m-1112	1053	1	[	[	X
m-1112	1053	2	⊕↔⊝	⊕↔⊝	X
m-1112	1053	3	]	]	X
m-1112	1053	4	r²	r²	NOUN
m-1112	1053	5	=	=	PUNCT
m-1112	1054	1	[	[	X
m-1112	1054	2	2	2	NUM
m-1112	1054	3	σ	σ	NOUN
m-1112	1054	4	]	]	X
m-1112	1054	5	r²	r²	NOUN
m-1112	1054	6	,	,	PUNCT
m-1112	1054	7	creating	create	VERB
m-1112	1054	8	work	work	NOUN
m-1112	1054	9	≡	≡	PROPN
m-1112	1054	10	motion	motion	NOUN
m-1112	1054	11	ijo	ijo	PROPN
m-1112	1054	12	international	international	PROPN
m-1112	1054	13	journal	journal	PROPN
m-1112	1054	14	of	of	ADP
m-1112	1054	15	mathematics	mathematics	PROPN
m-1112	1054	16	(	(	PUNCT
m-1112	1054	17	issn	issn	PROPN
m-1112	1054	18	:	:	PUNCT
m-1112	1054	19	2992	2992	NUM
m-1112	1054	20	-	-	SYM
m-1112	1054	21	4421	4421	NUM
m-1112	1054	22	)	)	PUNCT
m-1112	1054	23	volume	volume	NOUN
m-1112	1054	24	08	08	NUM
m-1112	1055	1	|	|	ADV
m-1112	1055	2	issue	issue	NOUN
m-1112	1055	3	08	08	NUM
m-1112	1056	1	|	|	ADV
m-1112	1056	2	august	august	PROPN
m-1112	1056	3	2025	2025	NUM
m-1112	1056	4	|	|	ADV
m-1112	1056	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1056	6	ijo	ijo	PROPN
m-1112	1056	7	journals	journal	NOUN
m-1112	1056	8	38	38	NUM
m-1112	1056	9	the	the	DET
m-1112	1056	10	fundamental	fundamental	ADJ
m-1112	1056	11	particles	particle	NOUN
m-1112	1056	12	origination	origination	NOUN
m-1112	1056	13	mechanism	mechanism	NOUN
m-1112	1056	14	in	in	ADP
m-1112	1056	15	mfmf	mfmf	PROPN
m-1112	1056	16	pns	pns	PROPN
m-1112	1056	17	caves	cave	NOUN
m-1112	1056	18	.	.	PUNCT
m-1112	1057	1	as	as	SCONJ
m-1112	1057	2	was	be	AUX
m-1112	1057	3	shown	show	VERB
m-1112	1057	4	it	it	PRON
m-1112	1057	5	was	be	AUX
m-1112	1057	6	shown	show	VERB
m-1112	1057	7	that	that	SCONJ
m-1112	1057	8	,	,	PUNCT
m-1112	1057	9	the	the	DET
m-1112	1057	10	stability	stability	NOUN
m-1112	1057	11	of	of	ADP
m-1112	1057	12	nucleus	nucleus	ADJ
m-1112	1057	13	forces	force	NOUN
m-1112	1057	14	,	,	PUNCT
m-1112	1057	15	is	be	AUX
m-1112	1057	16	succeeded	succeed	VERB
m-1112	1057	17	through	through	ADP
m-1112	1057	18	the	the	DET
m-1112	1057	19	pascal`s	pascal`s	ADJ
m-1112	1057	20	ceba`s	ceba`s	NOUN
m-1112	1057	21	triangle	triangle	NOUN
m-1112	1057	22	launched	launch	VERB
m-1112	1057	23	caves	cave	NOUN
m-1112	1057	24	r	r	NOUN
m-1112	1057	25	,	,	PUNCT
m-1112	1057	26	while	while	SCONJ
m-1112	1057	27	leptons	lepton	NOUN
m-1112	1057	28	from	from	ADP
m-1112	1057	29	their	their	PRON
m-1112	1057	30	anti	anti	ADJ
m-1112	1057	31	leptons	lepton	NOUN
m-1112	1057	32	existence	existence	NOUN
m-1112	1057	33	in	in	ADP
m-1112	1057	34	the	the	DET
m-1112	1057	35	same	same	ADJ
m-1112	1057	36	launched	launch	VERB
m-1112	1057	37	pascal`s	pascal`s	NUM
m-1112	1057	38	caves	cave	NOUN
m-1112	1057	39	r	r	NOUN
m-1112	1057	40	.	.	PUNCT
m-1112	1058	1	[	[	X
m-1112	1058	2	58	58	NUM
m-1112	1058	3	]	]	PUNCT
m-1112	1058	4	the	the	DET
m-1112	1058	5	equilibrium	equilibrium	NOUN
m-1112	1058	6	of	of	ADP
m-1112	1058	7	the	the	DET
m-1112	1058	8	three	three	NUM
m-1112	1058	9	-	-	PUNCT
m-1112	1058	10	spaces	space	NOUN
m-1112	1058	11	is	be	AUX
m-1112	1058	12	done	do	VERB
m-1112	1058	13	on	on	ADP
m-1112	1058	14	the	the	DET
m-1112	1058	15	three	three	NUM
m-1112	1058	16	cyclic	cyclic	ADJ
m-1112	1058	17	-	-	PUNCT
m-1112	1058	18	quadrilaterals	quadrilateral	NOUN
m-1112	1058	19	(	(	PUNCT
m-1112	1058	20	abeaece	abeaece	NOUN
m-1112	1058	21	)	)	PUNCT
m-1112	1058	22	,	,	PUNCT
m-1112	1058	23	(	(	PUNCT
m-1112	1058	24	bcebeae	bcebeae	PROPN
m-1112	1058	25	)	)	PUNCT
m-1112	1058	26	,	,	PUNCT
m-1112	1058	27	(	(	PUNCT
m-1112	1058	28	caecebe	caecebe	NOUN
m-1112	1058	29	)	)	PUNCT
m-1112	1058	30	,	,	PUNCT
m-1112	1058	31	of	of	ADP
m-1112	1058	32	the	the	DET
m-1112	1058	33	6	6	NUM
m-1112	1058	34	conductors	conductor	NOUN
m-1112	1058	35	each	each	PRON
m-1112	1058	36	for	for	ADP
m-1112	1058	37	,	,	PUNCT
m-1112	1058	38	[	[	X
m-1112	1058	39	a	a	DET
m-1112	1058	40	,	,	PUNCT
m-1112	1058	41	b	b	NOUN
m-1112	1058	42	,	,	PUNCT
m-1112	1058	43	c	c	NOUN
m-1112	1058	44	,	,	PUNCT
m-1112	1058	45	d	d	PROPN
m-1112	1058	46	,	,	PUNCT
m-1112	1058	47	p	p	X
m-1112	1058	48	,	,	PUNCT
m-1112	1058	49	q	q	X
m-1112	1058	50	]	]	X
m-1112	1058	51	x	x	PUNCT
m-1112	1059	1	[	[	X
m-1112	1059	2	3	3	NUM
m-1112	1059	3	-	-	PUNCT
m-1112	1059	4	abc	abc	X
m-1112	1059	5	]	]	X
m-1112	1059	6	=	=	SYM
m-1112	1059	7	18	18	NUM
m-1112	1059	8	conductors	conductor	NOUN
m-1112	1059	9	.	.	PUNCT
m-1112	1060	1	the	the	DET
m-1112	1060	2	stability	stability	NOUN
m-1112	1060	3	is	be	AUX
m-1112	1060	4	1	1	NUM
m-1112	1060	5	..	..	PUNCT
m-1112	1060	6	linearly	linearly	ADV
m-1112	1060	7	through	through	ADP
m-1112	1060	8	the	the	DET
m-1112	1060	9	products	product	NOUN
m-1112	1060	10	of	of	ADP
m-1112	1060	11	the	the	DET
m-1112	1060	12	diagonal	diagonal	ADJ
m-1112	1060	13	connectors	connector	NOUN
m-1112	1060	14	as	as	ADP
m-1112	1060	15	,	,	PUNCT
m-1112	1060	16	→	→	SYM
m-1112	1060	17	→	→	SYM
m-1112	1060	18	→	→	SYM
m-1112	1060	19	[	[	X
m-1112	1060	20	aae].[bece	aae].[bece	X
m-1112	1060	21	]	]	X
m-1112	1060	22	=	=	PUNCT
m-1112	1061	1	[	[	X
m-1112	1061	2	ace].[aebe]+[abe].[aece	ace].[aebe]+[abe].[aece	NOUN
m-1112	1061	3	]	]	PUNCT
m-1112	1061	4	,	,	PUNCT
m-1112	1061	5	[	[	X
m-1112	1061	6	bbe].[ceae	bbe].[ceae	X
m-1112	1061	7	]	]	X
m-1112	1061	8	=	=	PUNCT
m-1112	1062	1	[	[	X
m-1112	1062	2	bae].[bece]+[bce].[beae	bae].[bece]+[bce].[beae	X
m-1112	1062	3	]	]	PUNCT
m-1112	1062	4	,	,	PUNCT
m-1112	1062	5	[	[	X
m-1112	1062	6	cce].[aebe	cce].[aebe	X
m-1112	1062	7	]	]	PUNCT
m-1112	1062	8	=	=	PUNCT
m-1112	1063	1	[	[	X
m-1112	1063	2	cae].[bece]+[cbe].[ceae	cae].[bece]+[cbe].[ceae	X
m-1112	1063	3	]	]	X
m-1112	1063	4	and	and	CCONJ
m-1112	1063	5	,	,	PUNCT
m-1112	1063	6	2	2	X
m-1112	1063	7	..	..	PUNCT
m-1112	1063	8	rotationally	rotationally	ADV
m-1112	1063	9	through	through	ADP
m-1112	1063	10	the	the	DET
m-1112	1063	11	ratio	ratio	NOUN
m-1112	1063	12	of	of	ADP
m-1112	1063	13	the	the	DET
m-1112	1063	14	diagonals	diagonal	NOUN
m-1112	1063	15	≡	≡	PROPN
m-1112	1063	16	the	the	DET
m-1112	1063	17	conductors	conductor	NOUN
m-1112	1064	1	|	|	ADV
m-1112	1064	2	akb	akb	PROPN
m-1112	1064	3	akc	akc	PROPN
m-1112	1064	4	|x|	|x|	PROPN
m-1112	1064	5	bkc	bkc	PROPN
m-1112	1064	6	bka	bka	PROPN
m-1112	1064	7	|x|	|x|	PROPN
m-1112	1064	8	cka	cka	PROPN
m-1112	1064	9	ckb	ckb	PROPN
m-1112	1064	10	|	|	ADV
m-1112	1064	11	=	=	SYM
m-1112	1064	12	1	1	NUM
m-1112	1064	13	or	or	CCONJ
m-1112	1064	14			PROPN
m-1112	1064	15	rotational	rotational	ADJ
m-1112	1064	16	-	-	PUNCT
m-1112	1064	17	equilibrium	equilibrium	NOUN
m-1112	1064	18	as	as	ADP
m-1112	1064	19	,	,	PUNCT
m-1112	1064	20	[	[	X
m-1112	1064	21	akb].[cka].[bkc]=[akc].[bka].[ckb	akb].[cka].[bkc]=[akc].[bka].[ckb	X
m-1112	1064	22	]	]	X
m-1112	1064	23	,	,	PUNCT
m-1112	1064	24	of	of	ADP
m-1112	1064	25	all	all	DET
m-1112	1064	26	opposites	opposite	NOUN
m-1112	1064	27			VERB
m-1112	1064	28	tangential	tangential	ADJ
m-1112	1064	29	-	-	PUNCT
m-1112	1064	30	electromotive	electromotive	ADJ
m-1112	1064	31	forces	force	NOUN
m-1112	1064	32	.	.	PUNCT
m-1112	1065	1	3	3	X
m-1112	1065	2	..	..	PUNCT
m-1112	1065	3	from	from	ADP
m-1112	1065	4	mechanics	mechanic	NOUN
m-1112	1065	5	-	-	PUNCT
m-1112	1065	6	physics	physics	NOUN
m-1112	1065	7	,	,	PUNCT
m-1112	1065	8	all	all	DET
m-1112	1065	9	systems	system	NOUN
m-1112	1065	10	possessing	possess	VERB
m-1112	1065	11	elasticity	elasticity	NOUN
m-1112	1065	12	≡	≡	PROPN
m-1112	1065	13	motion	motion	NOUN
m-1112	1065	14	and	and	CCONJ
m-1112	1065	15	reaction	reaction	NOUN
m-1112	1065	16	to	to	ADP
m-1112	1065	17	motion	motion	NOUN
m-1112	1065	18	,	,	PUNCT
m-1112	1065	19	the	the	DET
m-1112	1065	20	called	call	VERB
m-1112	1065	21	mass	mass	NOUN
m-1112	1065	22	,	,	PUNCT
m-1112	1065	23	are	be	AUX
m-1112	1065	24	capable	capable	ADJ
m-1112	1065	25	of	of	ADP
m-1112	1065	26	free	free	ADJ
m-1112	1065	27	vibration	vibration	NOUN
m-1112	1065	28	or	or	CCONJ
m-1112	1065	29	vibration	vibration	NOUN
m-1112	1065	30	taking	take	VERB
m-1112	1065	31	place	place	NOUN
m-1112	1065	32	in	in	ADP
m-1112	1065	33	the	the	DET
m-1112	1065	34	absence	absence	NOUN
m-1112	1065	35	of	of	ADP
m-1112	1065	36	external	external	ADJ
m-1112	1065	37	excitation	excitation	NOUN
m-1112	1065	38	[	[	X
m-1112	1065	39	7	7	X
m-1112	1065	40	]	]	PUNCT
m-1112	1065	41	.this	.this	PRON
m-1112	1065	42	principle	principle	ADJ
m-1112	1065	43	issues	issue	NOUN
m-1112	1065	44	for	for	ADP
m-1112	1065	45	both	both	PRON
m-1112	1065	46	closed	closed	ADJ
m-1112	1065	47	or	or	CCONJ
m-1112	1065	48	open	open	ADJ
m-1112	1065	49	systems	system	NOUN
m-1112	1065	50	.	.	PUNCT
m-1112	1066	1	i.e.	i.e.	X
m-1112	1066	2	either	either	CCONJ
m-1112	1066	3	for	for	ADP
m-1112	1066	4	the	the	DET
m-1112	1066	5	nucleus	nucleus	NOUN
m-1112	1066	6	where	where	SCONJ
m-1112	1066	7	issues	issue	VERB
m-1112	1066	8	the	the	DET
m-1112	1066	9	pascal`s	pascal`s	ADJ
m-1112	1066	10	ceba`s	ceba`s	NOUN
m-1112	1066	11	triangle	triangle	VERB
m-1112	1066	12	stability	stability	NOUN
m-1112	1066	13	,	,	PUNCT
m-1112	1066	14	or	or	CCONJ
m-1112	1066	15	for	for	ADP
m-1112	1066	16	the	the	DET
m-1112	1066	17	orbitals	orbital	NOUN
m-1112	1066	18	where	where	SCONJ
m-1112	1066	19	issues	issue	VERB
m-1112	1066	20	the	the	DET
m-1112	1066	21	tetrahedron	tetrahedron	NOUN
m-1112	1066	22	-	-	PUNCT
m-1112	1066	23	cube	cube	NOUN
m-1112	1066	24	-sphere	-sphere	NOUN
m-1112	1066	25	-	-	PUNCT
m-1112	1066	26	mould	mould	NOUN
m-1112	1066	27	.a	.a	ADJ
m-1112	1066	28	signal	signal	NOUN
m-1112	1066	29	as	as	SCONJ
m-1112	1066	30	the	the	DET
m-1112	1066	31	electric	electric	ADJ
m-1112	1066	32	and	and	CCONJ
m-1112	1066	33	magnetic	magnetic	ADJ
m-1112	1066	34	field	field	NOUN
m-1112	1066	35	in	in	ADP
m-1112	1066	36	3	3	NUM
m-1112	1066	37	-	-	PUNCT
m-1112	1066	38	conductors	conductor	NOUN
m-1112	1066	39	is	be	AUX
m-1112	1066	40	transformed	transform	VERB
m-1112	1066	41	on	on	ADP
m-1112	1066	42	the	the	DET
m-1112	1066	43	2	2	NUM
m-1112	1066	44	anti	anti	ADJ
m-1112	1066	45	-	-	ADJ
m-1112	1066	46	parallel	parallel	ADJ
m-1112	1066	47	–	–	PUNCT
m-1112	1066	48	strands	strand	NOUN
m-1112	1066	49	.	.	PUNCT
m-1112	1067	1	c-4	c-4	NOUN
m-1112	1067	2	...	...	PUNCT
m-1112	1068	1	the	the	DET
m-1112	1068	2	natural	natural	ADJ
m-1112	1068	3	electromagnetic	electromagnetic	ADJ
m-1112	1068	4	energy	energy	NOUN
m-1112	1068	5	-	-	PUNCT
m-1112	1068	6	tetrahedron	tetrahedron	NOUN
m-1112	1068	7	and	and	CCONJ
m-1112	1068	8	,	,	PUNCT
m-1112	1068	9	the	the	DET
m-1112	1068	10	3conductors	3conductor	NOUN
m-1112	1068	11	into	into	ADP
m-1112	1068	12	the	the	DET
m-1112	1068	13	energy	energy	NOUN
m-1112	1068	14	cube	cube	NOUN
m-1112	1068	15	and	and	CCONJ
m-1112	1068	16	spheres	sphere	NOUN
m-1112	1068	17	:	:	PUNCT
m-1112	1068	18	[	[	X
m-1112	1068	19	102	102	NUM
m-1112	1068	20	]	]	X
m-1112	1068	21	in	in	ADP
m-1112	1068	22	fig9c	fig9c	PROPN
m-1112	1068	23	the	the	DET
m-1112	1068	24	electric	electric	PROPN
m-1112	1068	25	magnetic	magnetic	ADJ
m-1112	1068	26	field	field	NOUN
m-1112	1068	27	of	of	ADP
m-1112	1068	28	3	3	NUM
m-1112	1068	29	-	-	PUNCT
m-1112	1068	30	conductors	conductor	NOUN
m-1112	1068	31	which	which	PRON
m-1112	1068	32	lie	lie	VERB
m-1112	1068	33	on	on	ADP
m-1112	1068	34	the	the	DET
m-1112	1068	35	dabc	dabc	PROPN
m-1112	1068	36	occurs	occur	VERB
m-1112	1068	37	into	into	ADP
m-1112	1068	38	the	the	DET
m-1112	1068	39	{	{	PUNCT
m-1112	1068	40	⊝	⊝	NOUN
m-1112	1068	41	8	8	NUM
m-1112	1068	42	-	-	PUNCT
m-1112	1068	43	anti	anti	ADJ
m-1112	1068	44	-	-	ADJ
m-1112	1068	45	space	space	ADJ
m-1112	1068	46	cube	cube	NOUN
m-1112	1068	47	,	,	PUNCT
m-1112	1068	48	[	[	X
m-1112	1068	49	da1a	da1a	ADP
m-1112	1068	50	d1	d1	PROPN
m-1112	1068	51	,	,	PUNCT
m-1112	1068	52	b	b	NOUN
m-1112	1068	53	b1cc1	b1cc1	NOUN
m-1112	1068	54	]	]	PUNCT
m-1112	1068	55	}	}	PUNCT
m-1112	1068	56	,	,	PUNCT
m-1112	1068	57	and	and	CCONJ
m-1112	1068	58	the	the	DET
m-1112	1068	59	positive	positive	ADJ
m-1112	1068	60	→	→	PUNCT
m-1112	1068	61	{	{	PUNCT
m-1112	1068	62	⊕	⊕	NOUN
m-1112	1068	63	8	8	NUM
m-1112	1068	64	space	space	NOUN
m-1112	1068	65	–	–	PUNCT
m-1112	1068	66	cube	cube	NOUN
m-1112	1068	67	,	,	PUNCT
m-1112	1069	1	[	[	X
m-1112	1069	2	da1a	da1a	ADP
m-1112	1069	3	d1	d1	PROPN
m-1112	1069	4	,	,	PUNCT
m-1112	1069	5	b	b	X
m-1112	1069	6	b1cc1	b1cc1	NOUN
m-1112	1069	7	]	]	PUNCT
m-1112	1069	8	}	}	PUNCT
m-1112	1069	9	,	,	PUNCT
m-1112	1069	10	into	into	ADP
m-1112	1069	11	the	the	DET
m-1112	1069	12	{	{	PUNCT
m-1112	1069	13	⊝	⊝	NUM
m-1112	1069	14	16	16	NUM
m-1112	1069	15	-	-	PUNCT
m-1112	1069	16	anti	anti	NOUN
m-1112	1069	17	-	-	NOUN
m-1112	1069	18	space	space	ADJ
m-1112	1069	19	[	[	PUNCT
m-1112	1069	20	1	1	NUM
m-1112	1069	21	,	,	PUNCT
m-1112	1069	22	2	2	NUM
m-1112	1069	23	,	,	PUNCT
m-1112	1069	24	3	3	NUM
m-1112	1069	25	,	,	PUNCT
m-1112	1069	26	4	4	NUM
m-1112	1069	27	5	5	NUM
m-1112	1069	28	,	,	PUNCT
m-1112	1069	29	6	6	NUM
m-1112	1069	30	,	,	PUNCT
m-1112	1069	31	7	7	NUM
m-1112	1069	32	,	,	PUNCT
m-1112	1069	33	8	8	NUM
m-1112	1069	34	9	9	NUM
m-1112	1069	35	,	,	PUNCT
m-1112	1069	36	10	10	NUM
m-1112	1069	37	,	,	PUNCT
m-1112	1069	38	11	11	NUM
m-1112	1069	39	,	,	PUNCT
m-1112	1069	40	12	12	NUM
m-1112	1069	41	,	,	PUNCT
m-1112	1069	42	13	13	NUM
m-1112	1069	43	,	,	PUNCT
m-1112	1069	44	14	14	NUM
m-1112	1069	45	,	,	PUNCT
m-1112	1069	46	15	15	NUM
m-1112	1069	47	,	,	PUNCT
m-1112	1069	48	16	16	NUM
m-1112	1069	49	]	]	PUNCT
m-1112	1069	50	}	}	PUNCT
m-1112	1069	51	sphere	sphere	NOUN
m-1112	1069	52	cube	cube	NOUN
m-1112	1069	53	on	on	ADP
m-1112	1069	54	vertices.=	vertices.=	PROPN
m-1112	1069	55	point	point	NOUN
m-1112	1069	56	[	[	X
m-1112	1069	57	the	the	DET
m-1112	1069	58	point	point	NOUN
m-1112	1069	59	16	16	NUM
m-1112	1069	60	≡	≡	PROPN
m-1112	1069	61	|	|	ADV
m-1112	1069	62	⇉	⇉	NOUN
m-1112	1069	63	|z|	|z|	NOUN
m-1112	1069	64	]	]	PUNCT
m-1112	1069	65	consists	consist	VERB
m-1112	1069	66	the	the	DET
m-1112	1069	67	navel	navel	NOUN
m-1112	1069	68	-	-	PUNCT
m-1112	1069	69	string	string	NOUN
m-1112	1069	70	gate	gate	NOUN
m-1112	1069	71	into	into	ADP
m-1112	1069	72	the	the	DET
m-1112	1069	73	triangle	triangle	NOUN
m-1112	1069	74	-	-	PUNCT
m-1112	1069	75	circle	circle	NOUN
m-1112	1069	76	-	-	PUNCT
m-1112	1069	77	system	system	NOUN
m-1112	1069	78	{	{	PUNCT
m-1112	1069	79	z-(∆d	z-(∆d	NOUN
m-1112	1069	80	,	,	PUNCT
m-1112	1069	81	abc	abc	PROPN
m-1112	1069	82	)	)	PUNCT
m-1112	1069	83	,	,	PUNCT
m-1112	1069	84	∆[t1t2	∆[t1t2	PROPN
m-1112	1069	85	t3	t3	PROPN
m-1112	1069	86	]	]	X
m-1112	1069	87	}	}	PUNCT
m-1112	1069	88	of	of	ADP
m-1112	1069	89	the	the	DET
m-1112	1069	90	stationary	stationary	ADJ
m-1112	1069	91	bases	basis	NOUN
m-1112	1069	92	which	which	PRON
m-1112	1069	93	results	result	VERB
m-1112	1069	94	on	on	ADP
m-1112	1069	95	the	the	DET
m-1112	1069	96	2	2	NUM
m-1112	1069	97	-anti	-anti	NOUN
m-1112	1069	98	-	-	PUNCT
m-1112	1069	99	parallel	parallel	ADJ
m-1112	1069	100	-	-	PUNCT
m-1112	1069	101	strands	strand	NOUN
m-1112	1069	102	.	.	PUNCT
m-1112	1070	1	the	the	DET
m-1112	1070	2	dual	dual	ADJ
m-1112	1070	3	photon	photon	NOUN
m-1112	1070	4	v̅	v̅	PROPN
m-1112	1070	5	[	[	PUNCT
m-1112	1070	6	σφ	σφ	NOUN
m-1112	1070	7	2πr	2πr	NOUN
m-1112	1071	1	+	+	CCONJ
m-1112	1071	2	σ	σ	NUM
m-1112	1071	3	2πr	2πr	NOUN
m-1112	1071	4	]	]	PUNCT
m-1112	1072	1	≡	≡	PROPN
m-1112	1072	2	v̅.	v̅.	PROPN
m-1112	1072	3	[	[	PUNCT
m-1112	1072	4	fn̅	fn̅	PROPN
m-1112	1072	5	+	+	NUM
m-1112	1072	6	fn	fn	NOUN
m-1112	1072	7	]	]	PUNCT
m-1112	1072	8	,	,	PUNCT
m-1112	1072	9	occupies	occupy	VERB
m-1112	1072	10	stresses	stress	NOUN
m-1112	1072	11	=	=	SYM
m-1112	1072	12	σ	σ	PROPN
m-1112	1072	13	and	and	CCONJ
m-1112	1072	14	velocities	velocity	NOUN
m-1112	1072	15	v̅	v̅	VERB
m-1112	1072	16	,	,	PUNCT
m-1112	1072	17	in	in	ADP
m-1112	1072	18	the	the	DET
m-1112	1072	19	tiny	tiny	ADJ
m-1112	1072	20	-	-	PUNCT
m-1112	1072	21	caves	cave	NOUN
m-1112	1072	22	r	r	NOUN
m-1112	1072	23	.	.	PUNCT
m-1112	1073	1	the	the	DET
m-1112	1073	2	colours	colour	NOUN
m-1112	1073	3	in	in	ADP
m-1112	1073	4	light	light	NOUN
m-1112	1073	5	,	,	PUNCT
m-1112	1073	6	are	be	AUX
m-1112	1073	7	the	the	DET
m-1112	1073	8	still	still	ADV
m-1112	1073	9	-	-	PUNCT
m-1112	1073	10	sub	sub	NOUN
m-1112	1073	11	-	-	NOUN
m-1112	1073	12	units	unit	NOUN
m-1112	1073	13	in	in	ADP
m-1112	1073	14	storage	storage	NOUN
m-1112	1073	15	→[v̅	→[v̅	PROPN
m-1112	1073	16	.	.	PUNCT
m-1112	1074	1	fn̅	fn̅	PROPN
m-1112	1074	2	]	]	PUNCT
m-1112	1074	3	←	←	PROPN
m-1112	1075	1	and	and	CCONJ
m-1112	1075	2	exist	exist	VERB
m-1112	1075	3	as	as	ADP
m-1112	1075	4	frequencies	frequency	NOUN
m-1112	1075	5	of	of	ADP
m-1112	1075	6	→	→	SYM
m-1112	1075	7	violet	violet	NOUN
m-1112	1075	8	,	,	PUNCT
m-1112	1075	9	blue	blue	ADJ
m-1112	1075	10	,	,	PUNCT
m-1112	1075	11	green	green	ADJ
m-1112	1075	12	,	,	PUNCT
m-1112	1075	13	with	with	ADP
m-1112	1075	14	their	their	PRON
m-1112	1075	15	complementary	complementary	ADJ
m-1112	1075	16	colours	colour	NOUN
m-1112	1075	17	yellow	yellow	ADJ
m-1112	1075	18	,	,	PUNCT
m-1112	1075	19	orange	orange	PROPN
m-1112	1075	20	,	,	PUNCT
m-1112	1075	21	red	red	ADJ
m-1112	1075	22	←	←	PROPN
m-1112	1076	1	every	every	DET
m-1112	1076	2	8	8	NUM
m-1112	1076	3	-	-	PUNCT
m-1112	1076	4	electrons	electron	NOUN
m-1112	1076	5	are	be	AUX
m-1112	1076	6	vibrations	vibration	NOUN
m-1112	1076	7	on	on	ADP
m-1112	1076	8	atoms	atom	NOUN
m-1112	1076	9	-	-	PUNCT
m-1112	1076	10	cube	cube	NOUN
m-1112	1076	11	-	-	PUNCT
m-1112	1076	12	structure	structure	NOUN
m-1112	1076	13	{	{	PUNCT
m-1112	1076	14	a	a	DET
m-1112	1076	15	tetrahedron	tetrahedron	NOUN
m-1112	1076	16	in	in	ADP
m-1112	1076	17	cube	cube	NOUN
m-1112	1076	18	in	in	ADP
m-1112	1076	19	a	a	DET
m-1112	1076	20	sphere	sphere	NOUN
m-1112	1076	21	}	}	PUNCT
m-1112	1076	22	whether	whether	SCONJ
m-1112	1076	23	it	it	PRON
m-1112	1076	24	be	be	AUX
m-1112	1076	25	sound	sound	ADJ
m-1112	1076	26	or	or	CCONJ
m-1112	1076	27	light	light	NOUN
m-1112	1076	28	.	.	PUNCT
m-1112	1077	1	above	above	ADP
m-1112	1077	2	structure	structure	NOUN
m-1112	1077	3	is	be	AUX
m-1112	1077	4	followed	follow	VERB
m-1112	1077	5	by	by	ADP
m-1112	1077	6	all	all	DET
m-1112	1077	7	compounds	compound	NOUN
m-1112	1077	8	.	.	PUNCT
m-1112	1078	1	the	the	DET
m-1112	1078	2	molecules	molecule	NOUN
m-1112	1078	3	are	be	AUX
m-1112	1078	4	systems	system	NOUN
m-1112	1078	5	consisted	consist	VERB
m-1112	1078	6	of	of	ADP
m-1112	1078	7	the	the	DET
m-1112	1078	8	periferal	periferal	PROPN
m-1112	1078	9	≡	≡	PROPN
m-1112	1078	10	skeleton	skeleton	PROPN
m-1112	1078	11	𝐌	𝐌	PROPN
m-1112	1078	12	𝟏𝟔	𝟏𝟔	NUM
m-1112	1078	13	and	and	CCONJ
m-1112	1078	14	the	the	DET
m-1112	1078	15	central	central	ADJ
m-1112	1078	16	≡	≡	PROPN
m-1112	1078	17	fittings	fitting	NOUN
m-1112	1078	18	𝐌	𝐌	PROPN
m-1112	1078	19	𝟖	𝟖	NUM
m-1112	1078	20	,	,	PUNCT
m-1112	1078	21	and	and	CCONJ
m-1112	1078	22	the	the	DET
m-1112	1078	23	accessories	accessory	NOUN
m-1112	1078	24	≡	≡	PROPN
m-1112	1078	25	𝐌	𝐌	ADP
m-1112	1078	26	𝟒	𝟒	PROPN
m-1112	1078	27	or	or	CCONJ
m-1112	1078	28	𝐌	𝐌	PROPN
m-1112	1078	29	𝟐	𝟐	NUM
m-1112	1078	30	,	,	PUNCT
m-1112	1078	31	𝐌	𝐌	PROPN
m-1112	1078	32	𝟏	𝟏	NUM
m-1112	1078	33	.	.	PUNCT
m-1112	1079	1	this	this	DET
m-1112	1079	2	property	property	NOUN
m-1112	1079	3	of	of	ADP
m-1112	1079	4	atoms	atom	NOUN
m-1112	1079	5	and	and	CCONJ
m-1112	1079	6	of	of	ADP
m-1112	1079	7	the	the	DET
m-1112	1079	8	compounds	compound	NOUN
m-1112	1079	9	is	be	AUX
m-1112	1079	10	the	the	DET
m-1112	1079	11	critical	critical	ADJ
m-1112	1079	12	valve	valve	NOUN
m-1112	1079	13	of	of	ADP
m-1112	1079	14	switching	switch	VERB
m-1112	1079	15	the	the	DET
m-1112	1079	16	motion	motion	NOUN
m-1112	1079	17	as	as	SCONJ
m-1112	1079	18	this	this	PRON
m-1112	1079	19	happens	happen	VERB
m-1112	1079	20	in	in	ADP
m-1112	1079	21	the	the	DET
m-1112	1079	22	electro	electro	ADJ
m-1112	1079	23	-	-	PUNCT
m-1112	1079	24	magnetic	magnetic	ADJ
m-1112	1079	25	solenoid	solenoid	NOUN
m-1112	1079	26	valves	valve	NOUN
m-1112	1079	27	with	with	ADP
m-1112	1079	28	high	high	ADJ
m-1112	1079	29	or	or	CCONJ
m-1112	1079	30	low	low	ADJ
m-1112	1079	31	pressure	pressure	NOUN
m-1112	1079	32	and	and	CCONJ
m-1112	1079	33	flow	flow	NOUN
m-1112	1079	34	rates	rate	NOUN
m-1112	1079	35	directly	directly	ADV
m-1112	1079	36	or	or	CCONJ
m-1112	1079	37	not	not	PART
m-1112	1079	38	.	.	PUNCT
m-1112	1080	1	remarks	remark	NOUN
m-1112	1080	2	:	:	PUNCT
m-1112	1080	3	work	work	NOUN
m-1112	1080	4	of	of	ADP
m-1112	1080	5	elastic	elastic	ADJ
m-1112	1080	6	deformation	deformation	NOUN
m-1112	1080	7	.	.	PUNCT
m-1112	1081	1	elastic	elastic	ADJ
m-1112	1081	2	deformation	deformation	NOUN
m-1112	1081	3	requires	require	VERB
m-1112	1081	4	(	(	PUNCT
m-1112	1081	5	1	1	X
m-1112	1081	6	)	)	PUNCT
m-1112	1081	7	that	that	SCONJ
m-1112	1081	8	every	every	DET
m-1112	1081	9	new	new	ADJ
m-1112	1081	10	stress	stress	NOUN
m-1112	1081	11	that	that	PRON
m-1112	1081	12	is	be	AUX
m-1112	1081	13	applied	apply	VERB
m-1112	1081	14	to	to	ADP
m-1112	1081	15	a	a	DET
m-1112	1081	16	new	new	ADJ
m-1112	1081	17	infinite	infinite	ADJ
m-1112	1081	18	element	element	NOUN
m-1112	1081	19	is	be	AUX
m-1112	1081	20	always	always	ADV
m-1112	1081	21	added	add	VERB
m-1112	1081	22	to	to	ADP
m-1112	1081	23	the	the	DET
m-1112	1081	24	existing	exist	VERB
m-1112	1081	25	one	one	NUM
m-1112	1081	26	.(2	.(2	PUNCT
m-1112	1081	27	)	)	PUNCT
m-1112	1081	28	be	be	AUX
m-1112	1081	29	always	always	ADV
m-1112	1081	30	unity	unity	NOUN
m-1112	1081	31	work	work	NOUN
m-1112	1081	32	of	of	ADP
m-1112	1081	33	deformation	deformation	NOUN
m-1112	1081	34	.	.	PUNCT
m-1112	1082	1	when	when	SCONJ
m-1112	1082	2	a	a	DET
m-1112	1082	3	body	body	NOUN
m-1112	1082	4	contains	contain	VERB
m-1112	1082	5	potential	potential	ADJ
m-1112	1082	6	energy	energy	NOUN
m-1112	1082	7	,	,	PUNCT
m-1112	1082	8	during	during	ADP
m-1112	1082	9	any	any	DET
m-1112	1082	10	unloading	unloading	NOUN
m-1112	1082	11	it	it	PRON
m-1112	1082	12	gives	give	VERB
m-1112	1082	13	off	off	ADP
m-1112	1082	14	mechanical	mechanical	ADJ
m-1112	1082	15	work	work	NOUN
m-1112	1082	16	,	,	PUNCT
m-1112	1082	17	since	since	SCONJ
m-1112	1082	18	the	the	DET
m-1112	1082	19	points	point	NOUN
m-1112	1082	20	of	of	ADP
m-1112	1082	21	application	application	NOUN
m-1112	1082	22	of	of	ADP
m-1112	1082	23	the	the	DET
m-1112	1082	24	gradually	gradually	ADV
m-1112	1082	25	withdrawn	withdraw	VERB
m-1112	1082	26	loads	load	NOUN
m-1112	1082	27	are	be	AUX
m-1112	1082	28	displaced	displace	VERB
m-1112	1082	29	.	.	PUNCT
m-1112	1083	1	ijo	ijo	PROPN
m-1112	1083	2	international	international	PROPN
m-1112	1083	3	journal	journal	PROPN
m-1112	1083	4	of	of	ADP
m-1112	1083	5	mathematics	mathematics	PROPN
m-1112	1083	6	(	(	PUNCT
m-1112	1083	7	issn	issn	PROPN
m-1112	1083	8	:	:	PUNCT
m-1112	1083	9	2992	2992	NUM
m-1112	1083	10	-	-	SYM
m-1112	1083	11	4421	4421	NUM
m-1112	1083	12	)	)	PUNCT
m-1112	1083	13	volume	volume	NOUN
m-1112	1083	14	08	08	NUM
m-1112	1084	1	|	|	ADV
m-1112	1084	2	issue	issue	NOUN
m-1112	1084	3	08	08	NUM
m-1112	1085	1	|	|	ADV
m-1112	1085	2	august	august	PROPN
m-1112	1085	3	2025	2025	NUM
m-1112	1085	4	|	|	ADV
m-1112	1085	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1085	6	ijo	ijo	PROPN
m-1112	1085	7	journals	journal	NOUN
m-1112	1085	8	39	39	NUM
m-1112	1085	9	the	the	DET
m-1112	1085	10	fundamental	fundamental	ADJ
m-1112	1085	11	particles	particle	NOUN
m-1112	1085	12	origination	origination	NOUN
m-1112	1085	13	mechanism	mechanism	NOUN
m-1112	1085	14	in	in	ADP
m-1112	1085	15	mfmf	mfmf	PROPN
m-1112	1085	16	pns	pns	PROPN
m-1112	1085	17	caves	cave	NOUN
m-1112	1085	18	.	.	PUNCT
m-1112	1086	1	if	if	SCONJ
m-1112	1086	2	the	the	DET
m-1112	1086	3	unloading	unloading	NOUN
m-1112	1086	4	is	be	AUX
m-1112	1086	5	abrupt	abrupt	ADJ
m-1112	1086	6	,	,	PUNCT
m-1112	1086	7	then	then	ADV
m-1112	1086	8	kinetic	kinetic	ADJ
m-1112	1086	9	energy	energy	NOUN
m-1112	1086	10	is	be	AUX
m-1112	1086	11	converted	convert	VERB
m-1112	1086	12	into	into	ADP
m-1112	1086	13	potential	potential	ADJ
m-1112	1086	14	and	and	CCONJ
m-1112	1086	15	after	after	SCONJ
m-1112	1086	16	is	be	AUX
m-1112	1086	17	kinetic	kinetic	ADJ
m-1112	1086	18	,	,	PUNCT
m-1112	1086	19	converted	convert	VERB
m-1112	1086	20	back	back	ADV
m-1112	1086	21	into	into	ADP
m-1112	1086	22	kinetic	kinetic	NOUN
m-1112	1086	23	and	and	CCONJ
m-1112	1086	24	so	so	ADV
m-1112	1086	25	on	on	ADV
m-1112	1086	26	.	.	PUNCT
m-1112	1087	1	that	that	PRON
m-1112	1087	2	is	is	ADV
m-1112	1087	3	,	,	PUNCT
m-1112	1087	4	the	the	DET
m-1112	1087	5	body	body	NOUN
m-1112	1087	6	performs	perform	VERB
m-1112	1087	7	an	an	DET
m-1112	1087	8	oscillating	oscillating	NOUN
m-1112	1087	9	motion	motion	NOUN
m-1112	1087	10	until	until	SCONJ
m-1112	1087	11	the	the	DET
m-1112	1087	12	mechanical	mechanical	ADJ
m-1112	1087	13	energy	energy	NOUN
m-1112	1087	14	is	be	AUX
m-1112	1087	15	extinguished	extinguish	VERB
m-1112	1087	16	due	due	ADP
m-1112	1087	17	to	to	ADP
m-1112	1087	18	a	a	DET
m-1112	1087	19	state	state	NOUN
m-1112	1087	20	of	of	ADP
m-1112	1087	21	equilibrium	equilibrium	NOUN
m-1112	1087	22	or	or	CCONJ
m-1112	1087	23	alters	alter	VERB
m-1112	1087	24	.	.	PUNCT
m-1112	1088	1	figure	figure	VERB
m-1112	1088	2	–	–	PUNCT
m-1112	1088	3	9b	9b	NUM
m-1112	1088	4	:	:	PUNCT
m-1112	1088	5	the	the	DET
m-1112	1088	6	electric	electric	PROPN
m-1112	1088	7	magnetic	magnetic	ADJ
m-1112	1088	8	field	field	NOUN
m-1112	1088	9	of	of	ADP
m-1112	1088	10	3	3	NUM
m-1112	1088	11	conductors	conductor	NOUN
m-1112	1088	12	results	result	NOUN
m-1112	1088	13	on	on	ADP
m-1112	1088	14	2	2	NUM
m-1112	1088	15	-anti	-anti	NOUN
m-1112	1088	16	-	-	ADJ
m-1112	1088	17	parallel	parallel	ADJ
m-1112	1088	18	strands	strand	NOUN
m-1112	1088	19	.the	.the	PUNCT
m-1112	1088	20	stability	stability	NOUN
m-1112	1088	21	of	of	ADP
m-1112	1088	22	→	→	NOUN
m-1112	1088	23	{	{	PUNCT
m-1112	1088	24	⊕	⊕	PROPN
m-1112	1088	25	4	4	NUM
m-1112	1088	26	-	-	PUNCT
m-1112	1088	27	space	space	NOUN
m-1112	1089	1	[	[	X
m-1112	1089	2	d	d	X
m-1112	1089	3	a	a	DET
m-1112	1089	4	b	b	X
m-1112	1089	5	c	c	NOUN
m-1112	1089	6	]	]	X
m-1112	1089	7	}	}	PUNCT
m-1112	1089	8	regular	regular	ADJ
m-1112	1089	9	tetrahedron	tetrahedron	NOUN
m-1112	1089	10	,	,	PUNCT
m-1112	1089	11	in	in	ADP
m-1112	1089	12	{	{	PUNCT
m-1112	1089	13	⊝	⊝	NUM
m-1112	1089	14	8anti	8anti	NUM
m-1112	1089	15	-	-	ADJ
m-1112	1089	16	space	space	NOUN
m-1112	1089	17	cube	cube	NOUN
m-1112	1089	18	,	,	PUNCT
m-1112	1089	19	[	[	PUNCT
m-1112	1089	20	da1b	da1b	VERB
m-1112	1089	21	d1	d1	PROPN
m-1112	1089	22	,	,	PUNCT
m-1112	1089	23	c	c	PROPN
m-1112	1089	24	c1ab1	c1ab1	NOUN
m-1112	1089	25	]	]	PUNCT
m-1112	1089	26	}	}	PUNCT
m-1112	1089	27	,	,	PUNCT
m-1112	1089	28	and	and	CCONJ
m-1112	1089	29	the	the	DET
m-1112	1089	30	→	→	NOUN
m-1112	1089	31	{	{	PUNCT
m-1112	1089	32	⊕	⊕	PROPN
m-1112	1089	33	8space	8space	PROPN
m-1112	1089	34	[	[	PUNCT
m-1112	1089	35	da1bd1	da1bd1	NOUN
m-1112	1089	36	,	,	PUNCT
m-1112	1089	37	cc1ab1	cc1ab1	X
m-1112	1089	38	]	]	PUNCT
m-1112	1089	39	}	}	PUNCT
m-1112	1089	40	cube	cube	NOUN
m-1112	1089	41	,	,	PUNCT
m-1112	1089	42	into	into	ADP
m-1112	1089	43	the	the	DET
m-1112	1089	44	{	{	PUNCT
m-1112	1089	45	⊝	⊝	NUM
m-1112	1089	46	16	16	NUM
m-1112	1089	47	-	-	PUNCT
m-1112	1089	48	anti	anti	NOUN
m-1112	1089	49	-	-	NOUN
m-1112	1089	50	space	space	ADJ
m-1112	1089	51	[	[	PUNCT
m-1112	1089	52	1	1	NUM
m-1112	1089	53	,	,	PUNCT
m-1112	1089	54	2	2	NUM
m-1112	1089	55	,	,	PUNCT
m-1112	1089	56	3	3	NUM
m-1112	1089	57	,	,	PUNCT
m-1112	1089	58	4	4	NUM
m-1112	1089	59	,	,	PUNCT
m-1112	1089	60	5	5	NUM
m-1112	1089	61	,	,	PUNCT
m-1112	1089	62	6	6	NUM
m-1112	1089	63	,	,	PUNCT
m-1112	1089	64	7	7	NUM
m-1112	1089	65	,	,	PUNCT
m-1112	1089	66	8	8	NUM
m-1112	1089	67	9	9	NUM
m-1112	1089	68	,	,	PUNCT
m-1112	1089	69	10	10	NUM
m-1112	1089	70	,	,	PUNCT
m-1112	1089	71	11	11	NUM
m-1112	1089	72	,	,	PUNCT
m-1112	1089	73	12	12	NUM
m-1112	1089	74	,	,	PUNCT
m-1112	1089	75	13	13	NUM
m-1112	1089	76	,	,	PUNCT
m-1112	1089	77	14	14	NUM
m-1112	1089	78	,	,	PUNCT
m-1112	1089	79	15	15	NUM
m-1112	1089	80	,	,	PUNCT
m-1112	1089	81	16	16	NUM
m-1112	1089	82	]	]	PUNCT
m-1112	1089	83	}	}	PUNCT
m-1112	1089	84	sphere	sphere	NOUN
m-1112	1089	85	cube	cube	NOUN
m-1112	1089	86	vertices	vertex	NOUN
m-1112	1089	87	.	.	PUNCT
m-1112	1090	1	the	the	DET
m-1112	1090	2	point	point	NOUN
m-1112	1090	3	[	[	X
m-1112	1090	4	16	16	NUM
m-1112	1090	5	≡	≡	PROPN
m-1112	1090	6	|	|	ADV
m-1112	1090	7	⇉	⇉	PROPN
m-1112	1090	8	|z|	|z|	NOUN
m-1112	1090	9	]	]	PUNCT
m-1112	1090	10	consists	consist	VERB
m-1112	1090	11	the	the	DET
m-1112	1090	12	navel	navel	PROPN
m-1112	1090	13	string	string	NOUN
m-1112	1090	14	gate	gate	NOUN
m-1112	1090	15	in	in	ADP
m-1112	1090	16	system	system	NOUN
m-1112	1090	17	.	.	PUNCT
m-1112	1091	1	and	and	CCONJ
m-1112	1091	2	are	be	AUX
m-1112	1091	3	{	{	PUNCT
m-1112	1091	4	z	z	NOUN
m-1112	1091	5	(	(	PUNCT
m-1112	1091	6	∆d	∆d	PROPN
m-1112	1091	7	,	,	PUNCT
m-1112	1091	8	abc	abc	PROPN
m-1112	1091	9	)	)	PUNCT
m-1112	1091	10	,	,	PUNCT
m-1112	1091	11	∆	∆	PROPN
m-1112	1092	1	[	[	PUNCT
m-1112	1092	2	t1	t1	NOUN
m-1112	1092	3	t2	t2	PROPN
m-1112	1092	4	t3	t3	PROPN
m-1112	1092	5	]	]	PUNCT
m-1112	1092	6	}	}	PUNCT
m-1112	1092	7	stationary	stationary	ADJ
m-1112	1092	8	bases	basis	NOUN
m-1112	1092	9	.	.	PUNCT
m-1112	1093	1	the	the	DET
m-1112	1093	2	stability	stability	NOUN
m-1112	1093	3	analysis	analysis	NOUN
m-1112	1093	4	in	in	ADP
m-1112	1093	5	[	[	X
m-1112	1093	6	88	88	NUM
m-1112	1093	7	]	]	PUNCT
m-1112	1093	8	c-5	c-5	NOUN
m-1112	1093	9	..	..	PUNCT
m-1112	1093	10	:	:	PUNCT
m-1112	1093	11	the	the	DET
m-1112	1093	12	mater	mater	NOUN
m-1112	1093	13	antimatter	antimatter	NOUN
m-1112	1093	14	3	3	NUM
m-1112	1093	15	-	-	PUNCT
m-1112	1093	16	d	d	NOUN
m-1112	1093	17	origination	origination	NOUN
m-1112	1093	18	mechanism	mechanism	NOUN
m-1112	1093	19	[	[	X
m-1112	1093	20	⊕↔⊝	⊕↔⊝	NOUN
m-1112	1093	21	]	]	X
m-1112	1093	22	figure	figure	NOUN
m-1112	1093	23	–	–	PUNCT
m-1112	1093	24	9c	9c	NUM
m-1112	1093	25	:	:	PUNCT
m-1112	1093	26	the	the	DET
m-1112	1093	27	4	4	NUM
m-1112	1093	28	-	-	PUNCT
m-1112	1093	29	dimentional	dimentional	ADJ
m-1112	1093	30	spinning	spinning	NOUN
m-1112	1093	31	,	,	PUNCT
m-1112	1093	32	tetrahedron	tetrahedron	NOUN
m-1112	1093	33	cube	cube	NOUN
m-1112	1093	34	–	–	PUNCT
m-1112	1093	35	spheres	sphere	NOUN
m-1112	1093	36	mould	mould	NOUN
m-1112	1093	37	.	.	PUNCT
m-1112	1094	1	the	the	DET
m-1112	1094	2	stationary	stationary	ADJ
m-1112	1094	3	-	-	PUNCT
m-1112	1094	4	states	state	NOUN
m-1112	1094	5	are	be	AUX
m-1112	1094	6	→	→	SYM
m-1112	1094	7	2n=1−4	2n=1−4	NUM
m-1112	1094	8	points	point	NOUN
m-1112	1094	9	≡	≡	PROPN
m-1112	1094	10	2	2	NUM
m-1112	1094	11	,	,	PUNCT
m-1112	1094	12	4	4	NUM
m-1112	1094	13	,	,	PUNCT
m-1112	1094	14	8	8	NUM
m-1112	1094	15	,	,	PUNCT
m-1112	1094	16	16	16	NUM
m-1112	1094	17	≡	≡	PROPN
m-1112	1094	18	4	4	NUM
m-1112	1094	19	–	–	PUNCT
m-1112	1094	20	types	type	NOUN
m-1112	1094	21	←	←	PROPN
m-1112	1094	22	ijo	ijo	PROPN
m-1112	1094	23	international	international	PROPN
m-1112	1094	24	journal	journal	PROPN
m-1112	1094	25	of	of	ADP
m-1112	1094	26	mathematics	mathematics	PROPN
m-1112	1094	27	(	(	PUNCT
m-1112	1094	28	issn	issn	PROPN
m-1112	1094	29	:	:	PUNCT
m-1112	1094	30	2992	2992	NUM
m-1112	1094	31	-	-	SYM
m-1112	1094	32	4421	4421	NUM
m-1112	1094	33	)	)	PUNCT
m-1112	1095	1	volume	volume	NOUN
m-1112	1095	2	08	08	NUM
m-1112	1096	1	|	|	ADV
m-1112	1096	2	issue	issue	NOUN
m-1112	1096	3	08	08	NUM
m-1112	1097	1	|	|	ADV
m-1112	1097	2	august	august	PROPN
m-1112	1097	3	2025	2025	NUM
m-1112	1097	4	|	|	ADV
m-1112	1097	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1097	6	ijo	ijo	PROPN
m-1112	1097	7	journals	journal	NOUN
m-1112	1097	8	40	40	NUM
m-1112	1097	9	the	the	DET
m-1112	1097	10	fundamental	fundamental	ADJ
m-1112	1097	11	particles	particle	NOUN
m-1112	1097	12	origination	origination	NOUN
m-1112	1097	13	mechanism	mechanism	NOUN
m-1112	1097	14	in	in	ADP
m-1112	1097	15	mfmf	mfmf	PROPN
m-1112	1097	16	pns	pns	PROPN
m-1112	1097	17	caves	cave	NOUN
m-1112	1097	18	.	.	PUNCT
m-1112	1098	1	figure	figure	NOUN
m-1112	1098	2	–	–	PUNCT
m-1112	1098	3	9d	9d	NUM
m-1112	1098	4	..	..	PUNCT
m-1112	1098	5	:	:	PUNCT
m-1112	1098	6	the	the	DET
m-1112	1098	7	hydrogen	hydrogen	NOUN
m-1112	1098	8	,	,	PUNCT
m-1112	1098	9	carbon	carbon	NOUN
m-1112	1098	10	,	,	PUNCT
m-1112	1098	11	oxygen	oxygen	NOUN
m-1112	1098	12	,	,	PUNCT
m-1112	1098	13	atoms	atom	NOUN
m-1112	1098	14	-	-	PUNCT
m-1112	1098	15	conductors	conductor	NOUN
m-1112	1098	16	into	into	ADP
m-1112	1098	17	the	the	DET
m-1112	1098	18	sphere	sphere	NOUN
m-1112	1098	19	-	-	PUNCT
m-1112	1098	20	cube	cube	NOUN
m-1112	1098	21	mould	mould	NOUN
m-1112	1098	22	.	.	PUNCT
m-1112	1099	1	deka	deka	PROPN
m-1112	1099	2	hexahedron	hexahedron	NOUN
m-1112	1099	3	,	,	PUNCT
m-1112	1099	4	octahedron	octahedron	NOUN
m-1112	1099	5	≡	≡	PROPN
m-1112	1099	6	cube	cube	NOUN
m-1112	1099	7	,	,	PUNCT
m-1112	1099	8	tetrahedron	tetrahedron	NOUN
m-1112	1099	9	≡	≡	PROPN
m-1112	1099	10	4	4	NUM
m-1112	1099	11	-	-	PUNCT
m-1112	1099	12	points	point	NOUN
m-1112	1099	13	,	,	PUNCT
m-1112	1099	14	triangle	triangle	NOUN
m-1112	1099	15	.	.	PUNCT
m-1112	1100	1	the	the	DET
m-1112	1100	2	nucleus	nucleus	PROPN
m-1112	1100	3	≡	≡	PROPN
m-1112	1100	4	(	(	PUNCT
m-1112	1100	5	in	in	ADP
m-1112	1100	6	-	-	PUNCT
m-1112	1100	7	sphere	sphere	NOUN
m-1112	1100	8	)	)	PUNCT
m-1112	1100	9	,	,	PUNCT
m-1112	1100	10	tetrahedron	tetrahedron	NOUN
m-1112	1100	11	≡	≡	PROPN
m-1112	1100	12	(	(	PUNCT
m-1112	1100	13	d	d	NOUN
m-1112	1100	14	a.b.c	a.b.c	ADV
m-1112	1100	15	)	)	PUNCT
m-1112	1100	16	,	,	PUNCT
m-1112	1100	17	cube	cube	NOUN
m-1112	1100	18	≡	≡	PROPN
m-1112	1100	19	(	(	PUNCT
m-1112	1100	20	o,2,a,4,b,6,c,8	o,2,a,4,b,6,c,8	PROPN
m-1112	1100	21	)	)	PUNCT
m-1112	1100	22	,	,	PUNCT
m-1112	1100	23	orbitals	orbital	NOUN
m-1112	1100	24	≡	≡	PROPN
m-1112	1100	25	(	(	PUNCT
m-1112	1100	26	ex	ex	NOUN
m-1112	1100	27	-	-	NOUN
m-1112	1100	28	sphere	sphere	ADV
m-1112	1100	29	)	)	PUNCT
m-1112	1100	30	,	,	PUNCT
m-1112	1100	31	mould	mould	AUX
m-1112	1100	32	.	.	PUNCT
m-1112	1101	1	when	when	SCONJ
m-1112	1101	2	vector	vector	PROPN
m-1112	1101	3	≡	≡	PROPN
m-1112	1101	4	2	2	NUM
m-1112	1101	5	-	-	PUNCT
m-1112	1101	6	points	point	NOUN
m-1112	1101	7	≡	≡	PROPN
m-1112	1101	8	the	the	DET
m-1112	1101	9	closed	close	VERB
m-1112	1101	10	-	-	PUNCT
m-1112	1101	11	conductor	conductor	NOUN
m-1112	1101	12	,	,	PUNCT
m-1112	1101	13	1	1	NUM
m-1112	1101	14	-	-	PUNCT
m-1112	1101	15	point	point	NOUN
m-1112	1101	16	≡	≡	PROPN
m-1112	1101	17	the	the	DET
m-1112	1101	18	opened	open	VERB
m-1112	1101	19	-conductor	-conductor	NOUN
m-1112	1101	20	≡	≡	PROPN
m-1112	1101	21	the	the	DET
m-1112	1101	22	bracket	bracket	NOUN
m-1112	1101	23	-	-	PUNCT
m-1112	1101	24	hook	hook	NOUN
m-1112	1101	25	.	.	PUNCT
m-1112	1102	1	oxygen	oxygen	NOUN
m-1112	1102	2	is	be	AUX
m-1112	1102	3	the	the	DET
m-1112	1102	4	element	element	NOUN
m-1112	1102	5	which	which	PRON
m-1112	1102	6	fills	fill	VERB
m-1112	1102	7	8	8	NUM
m-1112	1102	8	2	2	NUM
m-1112	1102	9	=	=	SYM
m-1112	1102	10	6	6	NUM
m-1112	1102	11	vertices	vertex	NOUN
m-1112	1102	12	of	of	ADP
m-1112	1102	13	cube	cube	NOUN
m-1112	1102	14	as	as	ADP
m-1112	1102	15	el	el	PROPN
m-1112	1102	16	→	→	PUNCT
m-1112	1102	17	{	{	PUNCT
m-1112	1102	18	1𝑒	1𝑒	NUM
m-1112	1102	19	0𝑒	0𝑒	VERB
m-1112	1102	20	1𝑒	1𝑒	PROPN
m-1112	1102	21	1	1	NUM
m-1112	1102	22	𝑒	𝑒	PROPN
m-1112	1102	23	2⃡	2⃡	NUM
m-1112	1102	24	0	0	PUNCT
m-1112	1102	25	𝑒	𝑒	PROPN
m-1112	1102	26	1𝑒	1𝑒	NUM
m-1112	1102	27	1𝑒	1𝑒	PROPN
m-1112	1102	28	1𝑒	1𝑒	PROPN
m-1112	1102	29	}	}	PUNCT
m-1112	1102	30	≡	≡	PROPN
m-1112	1102	31	(	(	PUNCT
m-1112	1102	32	±	±	NOUN
m-1112	1102	33	2	2	NUM
m-1112	1102	34	2	2	NUM
m-1112	1102	35	)	)	PUNCT
m-1112	1102	36	,	,	PUNCT
m-1112	1102	37	where	where	SCONJ
m-1112	1102	38	⓪	⓪	X
m-1112	1102	39	is	be	AUX
m-1112	1102	40	the	the	DET
m-1112	1102	41	first	first	ADJ
m-1112	1102	42	,	,	PUNCT
m-1112	1102	43	zero	zero	NUM
m-1112	1102	44	-	-	PUNCT
m-1112	1102	45	acting	act	VERB
m-1112	1102	46	cube	cube	NOUN
m-1112	1102	47	filled	fill	VERB
m-1112	1102	48	with	with	ADP
m-1112	1102	49	1e	1e	PROPN
m-1112	1102	50	,	,	PUNCT
m-1112	1102	51	therefore	therefore	ADV
m-1112	1102	52	is	be	AUX
m-1112	1102	53	the	the	DET
m-1112	1102	54	only	only	ADJ
m-1112	1102	55	steady	steady	ADJ
m-1112	1102	56	element	element	NOUN
m-1112	1102	57	which	which	PRON
m-1112	1102	58	occupies	occupy	VERB
m-1112	1102	59	the	the	DET
m-1112	1102	60	first	first	ADJ
m-1112	1102	61	energy	energy	NOUN
m-1112	1102	62	-	-	PUNCT
m-1112	1102	63	level	level	NOUN
m-1112	1102	64	①	①	NOUN
m-1112	1102	65	with	with	ADP
m-1112	1102	66	2	2	NUM
m-1112	1102	67	electron	electron	NOUN
m-1112	1102	68	-	-	PUNCT
m-1112	1102	69	positions	position	NOUN
m-1112	1102	70	as	as	ADP
m-1112	1102	71	①	①	X
m-1112	1102	72	=	=	SYM
m-1112	1102	73	2e	2e	NOUN
m-1112	1102	74	=	=	SYM
m-1112	1102	75	2⃡	2⃡	NOUN
m-1112	1102	76	positions	position	NOUN
m-1112	1102	77	at	at	ADP
m-1112	1102	78	1⃗	1⃗	NUM
m-1112	1102	79	,	,	PUNCT
m-1112	1102	80	1⃗⃖	1⃗⃖	NUM
m-1112	1102	81	the	the	DET
m-1112	1102	82	electron	electron	NOUN
m-1112	1102	83	being	be	AUX
m-1112	1102	84	in	in	ADP
m-1112	1102	85	the	the	DET
m-1112	1102	86	hydrogen	hydrogen	NOUN
m-1112	1102	87	precesses	precesse	NOUN
m-1112	1102	88	because	because	SCONJ
m-1112	1102	89	of	of	ADP
m-1112	1102	90	the	the	DET
m-1112	1102	91	different	different	ADJ
m-1112	1102	92	axis	axis	NOUN
m-1112	1102	93	of	of	ADP
m-1112	1102	94	rotation	rotation	NOUN
m-1112	1102	95	and	and	CCONJ
m-1112	1102	96	nutation`s	nutation`s	ADP
m-1112	1102	97	,	,	PUNCT
m-1112	1102	98	from	from	ADP
m-1112	1102	99	the	the	DET
m-1112	1102	100	continuous	continuous	ADJ
m-1112	1102	101	and	and	CCONJ
m-1112	1102	102	immense	immense	ADJ
m-1112	1102	103	-	-	PUNCT
m-1112	1102	104	communication	communication	NOUN
m-1112	1102	105	to	to	ADP
m-1112	1102	106	the	the	DET
m-1112	1102	107	effect	effect	NOUN
m-1112	1102	108	of	of	ADP
m-1112	1102	109	gravity	gravity	NOUN
m-1112	1102	110	g	g	NOUN
m-1112	1102	111	.	.	PUNCT
m-1112	1103	1	since	since	SCONJ
m-1112	1103	2	electron	electron	NOUN
m-1112	1103	3	is	be	AUX
m-1112	1103	4	continually	continually	ADV
m-1112	1103	5	oscillating	oscillate	VERB
m-1112	1103	6	,	,	PUNCT
m-1112	1103	7	with	with	ADP
m-1112	1103	8	the	the	DET
m-1112	1103	9	nutation	nutation	NOUN
m-1112	1103	10	-	-	PUNCT
m-1112	1103	11	frequency	frequency	NOUN
m-1112	1103	12	𝐟	𝐟	NOUN
m-1112	1103	13	𝐍	𝐍	NOUN
m-1112	1103	14	,	,	PUNCT
m-1112	1103	15	so	so	ADV
m-1112	1103	16	produces	produce	VERB
m-1112	1103	17	a	a	DET
m-1112	1103	18	continuous	continuous	ADJ
m-1112	1103	19	and	and	CCONJ
m-1112	1103	20	oscillating	oscillate	VERB
m-1112	1103	21	magnetic	magnetic	ADJ
m-1112	1103	22	-	-	PUNCT
m-1112	1103	23	field	field	NOUN
m-1112	1103	24	–	–	PUNCT
m-1112	1103	25	mwhich	mwhich	NOUN
m-1112	1103	26	in	in	ADP
m-1112	1103	27	turn	turn	NOUN
m-1112	1103	28	is	be	AUX
m-1112	1103	29	the	the	DET
m-1112	1103	30	source	source	NOUN
m-1112	1103	31	of	of	ADP
m-1112	1103	32	an	an	DET
m-1112	1103	33	oscillating	oscillate	VERB
m-1112	1103	34	electric	electric	NOUN
m-1112	1103	35	-	-	PUNCT
m-1112	1103	36	field	field	NOUN
m-1112	1103	37	–	–	PUNCT
m-1112	1103	38	e	e	NOUN
m-1112	1103	39	which	which	PRON
m-1112	1103	40	implies	imply	VERB
m-1112	1103	41	the	the	DET
m-1112	1103	42	regeneration	regeneration	NOUN
m-1112	1103	43	of	of	ADP
m-1112	1103	44	each	each	DET
m-1112	1103	45	other	other	ADJ
m-1112	1103	46	,	,	PUNCT
m-1112	1103	47	i.e.	i.e.	X
m-1112	1103	48	it	it	PRON
m-1112	1103	49	is	be	AUX
m-1112	1103	50	a	a	DET
m-1112	1103	51	propagating	propagate	VERB
m-1112	1103	52	electromagnetic	electromagnetic	ADJ
m-1112	1103	53	-	-	PUNCT
m-1112	1103	54	wave	wave	NOUN
m-1112	1104	1	where	where	SCONJ
m-1112	1104	2	e	e	NOUN
m-1112	1104	3	=	=	SYM
m-1112	1104	4	b	b	PROPN
m-1112	1104	5	c	c	NOUN
m-1112	1104	6	,	,	PUNCT
m-1112	1104	7	and	and	CCONJ
m-1112	1104	8	with	with	ADP
m-1112	1104	9	a	a	DET
m-1112	1104	10	quantum	quantum	NOUN
m-1112	1104	11	-	-	PUNCT
m-1112	1104	12	energy	energy	NOUN
m-1112	1104	13	e	e	NOUN
m-1112	1104	14	=	=	NOUN
m-1112	1104	15	h	h	PROPN
m-1112	1104	16	fn	fn	NOUN
m-1112	1104	17	or	or	CCONJ
m-1112	1104	18	e	e	X
m-1112	1104	19	=	=	SYM
m-1112	1104	20	2μ.b	2μ.b	NUM
m-1112	1104	21	,	,	PUNCT
m-1112	1104	22	this	this	DET
m-1112	1104	23	energy	energy	NOUN
m-1112	1104	24	e	e	NOUN
m-1112	1104	25	consists	consist	VERB
m-1112	1104	26	the	the	DET
m-1112	1104	27	hydrogen	hydrogen	NOUN
m-1112	1104	28	bracket	bracket	NOUN
m-1112	1104	29	hook	hook	NOUN
m-1112	1105	1	[	[	X
m-1112	1105	2	hbh	hbh	X
m-1112	1105	3	]	]	PUNCT
m-1112	1105	4	,	,	PUNCT
m-1112	1105	5	or	or	CCONJ
m-1112	1105	6	[	[	X
m-1112	1105	7	bh⃗⃗⃗⃗	bh⃗⃗⃗⃗	NOUN
m-1112	1105	8	⃗	⃗	NOUN
m-1112	1105	9	]	]	X
m-1112	1105	10	and	and	CCONJ
m-1112	1105	11	it	it	PRON
m-1112	1105	12	is	be	AUX
m-1112	1105	13	the	the	DET
m-1112	1105	14	only	only	ADJ
m-1112	1105	15	free	free	ADJ
m-1112	1105	16	monad	monad	PROPN
m-1112	1105	17	which	which	PRON
m-1112	1105	18	can	can	AUX
m-1112	1105	19	bond	bond	VERB
m-1112	1105	20	to	to	ADP
m-1112	1105	21	all	all	DET
m-1112	1105	22	energy	energy	NOUN
m-1112	1105	23	structures	structure	NOUN
m-1112	1105	24	.	.	PUNCT
m-1112	1106	1	ijo	ijo	PROPN
m-1112	1106	2	international	international	PROPN
m-1112	1106	3	journal	journal	PROPN
m-1112	1106	4	of	of	ADP
m-1112	1106	5	mathematics	mathematics	PROPN
m-1112	1106	6	(	(	PUNCT
m-1112	1106	7	issn	issn	PROPN
m-1112	1106	8	:	:	PUNCT
m-1112	1106	9	2992	2992	NUM
m-1112	1106	10	-	-	SYM
m-1112	1106	11	4421	4421	NUM
m-1112	1106	12	)	)	PUNCT
m-1112	1106	13	volume	volume	NOUN
m-1112	1106	14	08	08	NUM
m-1112	1107	1	|	|	ADV
m-1112	1107	2	issue	issue	NOUN
m-1112	1107	3	08	08	NUM
m-1112	1108	1	|	|	ADV
m-1112	1108	2	august	august	PROPN
m-1112	1108	3	2025	2025	NUM
m-1112	1108	4	|	|	ADV
m-1112	1108	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1108	6	ijo	ijo	PROPN
m-1112	1108	7	journals	journal	NOUN
m-1112	1108	8	41	41	NUM
m-1112	1108	9	the	the	DET
m-1112	1108	10	fundamental	fundamental	ADJ
m-1112	1108	11	particles	particle	NOUN
m-1112	1108	12	origination	origination	NOUN
m-1112	1108	13	mechanism	mechanism	NOUN
m-1112	1108	14	in	in	ADP
m-1112	1108	15	mfmf	mfmf	PROPN
m-1112	1108	16	pns	pns	PROPN
m-1112	1108	17	caves	cave	NOUN
m-1112	1108	18	.	.	PUNCT
m-1112	1109	1	the	the	DET
m-1112	1109	2	spheres	sphere	NOUN
m-1112	1109	3	-	-	PUNCT
m-1112	1109	4	cube	cube	NOUN
m-1112	1109	5	-	-	PUNCT
m-1112	1109	6	structure	structure	NOUN
m-1112	1109	7	of	of	ADP
m-1112	1109	8	atoms	atom	NOUN
m-1112	1109	9	in	in	ADP
m-1112	1109	10	sphere	sphere	NOUN
m-1112	1109	11	center	center	NOUN
m-1112	1109	12	–	–	PUNCT
m-1112	1109	13	oallows	oallow	VERB
m-1112	1109	14	the	the	DET
m-1112	1109	15	stability	stability	NOUN
m-1112	1109	16	of	of	ADP
m-1112	1109	17	the	the	DET
m-1112	1109	18	system	system	NOUN
m-1112	1109	19	,	,	PUNCT
m-1112	1109	20	per	per	ADP
m-1112	1109	21	–	–	PUNCT
m-1112	1109	22	two	two	NUM
m-1112	1109	23	electrons	electron	NOUN
m-1112	1109	24	in	in	ADP
m-1112	1109	25	dipole	dipole	NOUN
m-1112	1109	26	positions	position	NOUN
m-1112	1109	27	,	,	PUNCT
m-1112	1109	28	1	1	NUM
m-1112	1109	29	↔	↔	PROPN
m-1112	1109	30	6	6	NUM
m-1112	1109	31	,	,	PUNCT
m-1112	1109	32	2	2	NUM
m-1112	1109	33	↔	↔	PROPN
m-1112	1109	34	5	5	NUM
m-1112	1109	35	,	,	PUNCT
m-1112	1109	36	3	3	NUM
m-1112	1109	37	↔	↔	PROPN
m-1112	1109	38	8	8	NUM
m-1112	1109	39	,	,	PUNCT
m-1112	1109	40	4	4	NUM
m-1112	1109	41	↔7	↔7	NUM
m-1112	1109	42	,	,	PUNCT
m-1112	1109	43	consisting	consist	VERB
m-1112	1109	44	the	the	PRON
m-1112	1109	45	-	-	PUNCT
m-1112	1109	46	positive	positive	ADJ
m-1112	1109	47	dipole-[bh⃗⃗⃗⃗	dipole-[bh⃗⃗⃗⃗	X
m-1112	1109	48	⃗	⃗	PROPN
m-1112	1109	49	]	]	PUNCT
m-1112	1109	50	,	,	PUNCT
m-1112	1109	51	to	to	PART
m-1112	1109	52	be	be	AUX
m-1112	1109	53	able	able	ADJ
m-1112	1109	54	to	to	PART
m-1112	1109	55	move	move	VERB
m-1112	1109	56	→	→	SYM
m-1112	1109	57	into	into	AUX
m-1112	1109	58	-	-	PUNCT
m-1112	1109	59	inoutside	inoutside	NOUN
m-1112	1109	60	it	it	PRON
m-1112	1109	61	←	←	PROPN
m-1112	1109	62	and	and	CCONJ
m-1112	1109	63	allow	allow	VERB
m-1112	1109	64	the	the	DET
m-1112	1109	65	atoms	atom	NOUN
m-1112	1109	66	bonding	bonding	NOUN
m-1112	1109	67	as	as	ADP
m-1112	1109	68	this	this	PRON
m-1112	1109	69	in	in	ADP
m-1112	1109	70	energy	energy	NOUN
m-1112	1109	71	levels	level	NOUN
m-1112	1109	72	.	.	PUNCT
m-1112	1110	1	the	the	DET
m-1112	1110	2	cube	cube	NOUN
m-1112	1110	3	-	-	PUNCT
m-1112	1110	4	structure	structure	NOUN
m-1112	1110	5	of	of	ADP
m-1112	1110	6	atoms	atom	NOUN
m-1112	1110	7	and	and	CCONJ
m-1112	1110	8	orbits	orbit	NOUN
m-1112	1110	9	in	in	ADP
m-1112	1110	10	the	the	DET
m-1112	1110	11	outsphere	outsphere	NOUN
m-1112	1110	12	formulates	formulate	VERB
m-1112	1110	13	+	+	PROPN
m-1112	1110	14	[	[	X
m-1112	1110	15	bh⃗⃗⃗⃗	bh⃗⃗⃗⃗	NOUN
m-1112	1110	16	⃗	⃗	ADJ
m-1112	1110	17	]	]	X
m-1112	1110	18	to	to	ADP
m-1112	1110	19	those	those	DET
m-1112	1110	20	dipole	dipole	NOUN
m-1112	1110	21	positions	position	NOUN
m-1112	1110	22	which	which	PRON
m-1112	1110	23	lack	lack	NOUN
m-1112	1110	24	of	of	ADP
m-1112	1110	25	one	one	NUM
m-1112	1110	26	electron	electron	NOUN
m-1112	1110	27	and	and	CCONJ
m-1112	1110	28	so	so	ADV
m-1112	1110	29	can	can	AUX
m-1112	1110	30	plug	plug	VERB
m-1112	1110	31	-	-	PUNCT
m-1112	1110	32	in	in	ADP
m-1112	1110	33	the	the	DET
m-1112	1110	34	loop	loop	NOUN
m-1112	1110	35	of	of	ADP
m-1112	1110	36	the	the	DET
m-1112	1110	37	others	other	NOUN
m-1112	1110	38	.	.	PUNCT
m-1112	1111	1	the	the	DET
m-1112	1111	2	atoms	atom	NOUN
m-1112	1111	3	with	with	ADP
m-1112	1111	4	zero	zero	NUM
m-1112	1111	5	stable	stable	ADJ
m-1112	1111	6	state	state	NOUN
m-1112	1111	7	are	be	AUX
m-1112	1111	8	,	,	PUNCT
m-1112	1111	9	the	the	DET
m-1112	1111	10	hydrogen	hydrogen	NOUN
m-1112	1111	11	bracket	bracket	NOUN
m-1112	1111	12	-	-	PUNCT
m-1112	1111	13	hook	hook	NOUN
m-1112	1111	14	into	into	ADP
m-1112	1111	15	the	the	DET
m-1112	1111	16	carbon	carbon	NOUN
m-1112	1111	17	encloses	enclose	VERB
m-1112	1111	18	the	the	DET
m-1112	1111	19	inscribed	inscribe	VERB
m-1112	1111	20	sphere	sphere	NOUN
m-1112	1111	21	for	for	ADP
m-1112	1111	22	the	the	DET
m-1112	1111	23	nucleus	nucleus	NOUN
m-1112	1111	24	,	,	PUNCT
m-1112	1111	25	into	into	ADP
m-1112	1111	26	the	the	DET
m-1112	1111	27	oxygen	oxygen	NOUN
m-1112	1111	28	for	for	ADP
m-1112	1111	29	the	the	DET
m-1112	1111	30	orbitals	orbital	NOUN
m-1112	1111	31	,	,	PUNCT
m-1112	1111	32	into	into	ADP
m-1112	1111	33	the	the	DET
m-1112	1111	34	sulfur	sulfur	NOUN
m-1112	1111	35	enclosed	enclose	VERB
m-1112	1111	36	into	into	ADP
m-1112	1111	37	the	the	DET
m-1112	1111	38	circumscribed	circumscribed	ADJ
m-1112	1111	39	sphere	sphere	NOUN
m-1112	1111	40	for	for	SCONJ
m-1112	1111	41	the	the	DET
m-1112	1111	42	atoms	atom	NOUN
m-1112	1111	43	-	-	PUNCT
m-1112	1111	44	conductors	conductor	NOUN
m-1112	1111	45	sustains	sustain	VERB
m-1112	1111	46	.	.	PUNCT
m-1112	1112	1	the	the	DET
m-1112	1112	2	first	first	ADJ
m-1112	1112	3	4	4	NUM
m-1112	1112	4	-	-	PUNCT
m-1112	1112	5	dimentional	dimentional	ADJ
m-1112	1112	6	spinning	spinning	NOUN
m-1112	1112	7	,	,	PUNCT
m-1112	1112	8	tetrahedron	tetrahedron	NOUN
m-1112	1112	9	-	-	PUNCT
m-1112	1112	10	cube	cube	NOUN
m-1112	1112	11	–	–	PUNCT
m-1112	1112	12	sphere	sphere	NOUN
m-1112	1112	13	-	-	PUNCT
m-1112	1112	14	mould	mould	NOUN
m-1112	1112	15	are	be	AUX
m-1112	1112	16	,	,	PUNCT
m-1112	1112	17	9c--2	9c--2	NUM
m-1112	1112	18	1	1	NUM
m-1112	1112	19	…	…	PUNCT
m-1112	1112	20	o-1	o-1	NOUN
m-1112	1112	21	-	-	PUNCT
m-1112	1112	22	3	3	NUM
m-1112	1112	23	-	-	SYM
m-1112	1112	24	5	5	NUM
m-1112	1112	25	-	-	SYM
m-1112	1112	26	7	7	NUM
m-1112	1112	27	→	→	PUNCT
m-1112	1112	28	the	the	DET
m-1112	1112	29	first	first	ADJ
m-1112	1112	30	solid	solid	ADJ
m-1112	1112	31	tetrahedron	tetrahedron	NOUN
m-1112	1112	32	structure	structure	NOUN
m-1112	1112	33	in	in	ADP
m-1112	1112	34	nature	nature	NOUN
m-1112	1112	35	,	,	PUNCT
m-1112	1112	36	2	2	NUM
m-1112	1112	37	…	…	SYM
m-1112	1112	38	o-1	o-1	NOUN
m-1112	1112	39	-	-	PUNCT
m-1112	1112	40	2	2	NUM
m-1112	1112	41	-	-	PUNCT
m-1112	1112	42	3	3	NUM
m-1112	1112	43	-	-	PUNCT
m-1112	1112	44	4	4	NUM
m-1112	1112	45	-	-	SYM
m-1112	1112	46	5	5	NUM
m-1112	1112	47	-	-	PUNCT
m-1112	1112	48	6	6	NUM
m-1112	1112	49	-	-	PUNCT
m-1112	1112	50	7	7	NUM
m-1112	1112	51	-	-	SYM
m-1112	1112	52	8	8	NUM
m-1112	1112	53	→	→	PUNCT
m-1112	1112	54	the	the	DET
m-1112	1112	55	first	first	ADJ
m-1112	1112	56	cube	cube	NOUN
m-1112	1112	57	with	with	ADP
m-1112	1112	58	max	max	PROPN
m-1112	1112	59	.	.	PUNCT
m-1112	1113	1	positions	position	NOUN
m-1112	1113	2	e	e	X
m-1112	1113	3	=	=	SYM
m-1112	1113	4	2.n²	2.n²	NUM
m-1112	1113	5	=	=	SYM
m-1112	1113	6	8	8	NUM
m-1112	1113	7	,	,	PUNCT
m-1112	1113	8	3	3	NUM
m-1112	1113	9	…	…	SYM
m-1112	1113	10	r	r	NOUN
m-1112	1113	11	[	[	PUNCT
m-1112	1113	12	o	o	X
m-1112	1113	13	,	,	PUNCT
m-1112	1113	14	a	a	DET
m-1112	1113	15	,	,	PUNCT
m-1112	1113	16	b	b	NOUN
m-1112	1113	17	,	,	PUNCT
m-1112	1113	18	c	c	NOUN
m-1112	1113	19	]	]	PUNCT
m-1112	1113	20	→	→	SYM
m-1112	1113	21	nucleus	nucleus	NOUN
m-1112	1113	22	is	be	AUX
m-1112	1113	23	in	in	ADP
m-1112	1113	24	the	the	DET
m-1112	1113	25	first	first	ADJ
m-1112	1113	26	inscribed	inscribe	VERB
m-1112	1113	27	sphere	sphere	ADV
m-1112	1113	28	into	into	ADP
m-1112	1113	29	tetrahedron	tetrahedron	NOUN
m-1112	1113	30	.	.	PUNCT
m-1112	1114	1	4	4	NUM
m-1112	1114	2	…	…	SYM
m-1112	1114	3	r	r	X
m-1112	1114	4	-	-	PUNCT
m-1112	1114	5	o-1	o-1	NOUN
m-1112	1114	6	,	,	PUNCT
m-1112	1114	7	2	2	NUM
m-1112	1114	8	,	,	PUNCT
m-1112	1114	9	3	3	NUM
m-1112	1114	10	,	,	PUNCT
m-1112	1114	11	4	4	NUM
m-1112	1114	12	,	,	PUNCT
m-1112	1114	13	5	5	NUM
m-1112	1114	14	,	,	PUNCT
m-1112	1114	15	6	6	NUM
m-1112	1114	16	,	,	PUNCT
m-1112	1114	17	7	7	NUM
m-1112	1114	18	,	,	PUNCT
m-1112	1114	19	8	8	NUM
m-1112	1114	20	→	→	SYM
m-1112	1114	21	orbits	orbit	NOUN
m-1112	1114	22	are	be	AUX
m-1112	1114	23	in	in	ADP
m-1112	1114	24	enveloped	envelop	VERB
m-1112	1114	25	cube	cube	NOUN
m-1112	1114	26	-	-	PUNCT
m-1112	1114	27	sphere	sphere	NOUN
m-1112	1114	28	of	of	ADP
m-1112	1114	29	tetrahedron	tetrahedron	NOUN
m-1112	1114	30	.	.	PUNCT
m-1112	1115	1	deka	deka	PROPN
m-1112	1115	2	hexahedron	hexahedron	NOUN
m-1112	1115	3	,	,	PUNCT
m-1112	1115	4	octahedron	octahedron	NOUN
m-1112	1115	5	≡	≡	PROPN
m-1112	1115	6	cubes	cube	NOUN
m-1112	1115	7	,	,	PUNCT
m-1112	1115	8	tetrahedron	tetrahedron	NOUN
m-1112	1115	9	≡	≡	PROPN
m-1112	1115	10	4	4	NUM
m-1112	1115	11	-	-	PUNCT
m-1112	1115	12	points	point	NOUN
m-1112	1115	13	,	,	PUNCT
m-1112	1115	14	triangle	triangle	NOUN
m-1112	1115	15	≡	≡	PROPN
m-1112	1115	16	3	3	NUM
m-1112	1115	17	-	-	PUNCT
m-1112	1115	18	points	point	NOUN
m-1112	1115	19	,	,	PUNCT
m-1112	1115	20	vector	vector	NOUN
m-1112	1115	21	≡	≡	PROPN
m-1112	1115	22	2	2	NUM
m-1112	1115	23	-	-	PUNCT
m-1112	1115	24	points	point	NOUN
m-1112	1115	25	≡	≡	PROPN
m-1112	1115	26	the	the	DET
m-1112	1115	27	closed	close	VERB
m-1112	1115	28	-	-	PUNCT
m-1112	1115	29	conductor	conductor	NOUN
m-1112	1115	30	,	,	PUNCT
m-1112	1115	31	1	1	NUM
m-1112	1115	32	-	-	PUNCT
m-1112	1115	33	point	point	NOUN
m-1112	1115	34	≡	≡	PROPN
m-1112	1115	35	the	the	DET
m-1112	1115	36	opened	open	VERB
m-1112	1115	37	-conductor	-conductor	NOUN
m-1112	1115	38	≡the	≡the	DET
m-1112	1115	39	bracket	bracket	NOUN
m-1112	1115	40	-	-	PUNCT
m-1112	1115	41	hook	hook	NOUN
m-1112	1115	42	.	.	PUNCT
m-1112	1116	1	the	the	DET
m-1112	1116	2	hydrogen	hydrogen	PROPN
m-1112	1116	3	nucleus	nucleus	PROPN
m-1112	1116	4	is	be	AUX
m-1112	1116	5	kept	keep	VERB
m-1112	1116	6	in	in	ADP
m-1112	1116	7	the	the	DET
m-1112	1116	8	inscribed	inscribe	VERB
m-1112	1116	9	to	to	ADP
m-1112	1116	10	the	the	DET
m-1112	1116	11	tetrahedron	tetrahedron	NOUN
m-1112	1116	12	-	-	PUNCT
m-1112	1116	13	cube	cube	NOUN
m-1112	1116	14	-	-	PUNCT
m-1112	1116	15	system	system	NOUN
m-1112	1116	16	where	where	SCONJ
m-1112	1116	17	exist	exist	VERB
m-1112	1116	18	the	the	DET
m-1112	1116	19	protons	proton	NOUN
m-1112	1116	20	and	and	CCONJ
m-1112	1116	21	neutrons	neutron	NOUN
m-1112	1116	22	,	,	PUNCT
m-1112	1116	23	while	while	SCONJ
m-1112	1116	24	the	the	DET
m-1112	1116	25	electrons	electron	NOUN
m-1112	1116	26	of	of	ADP
m-1112	1116	27	hydrogen	hydrogen	NOUN
m-1112	1116	28	orbits	orbit	NOUN
m-1112	1116	29	are	be	AUX
m-1112	1116	30	kept	keep	VERB
m-1112	1116	31	into	into	ADP
m-1112	1116	32	the	the	DET
m-1112	1116	33	circumscribed	circumscribed	ADJ
m-1112	1116	34	,	,	PUNCT
m-1112	1116	35	to	to	ADP
m-1112	1116	36	the	the	DET
m-1112	1116	37	tetrahedron	tetrahedron	NOUN
m-1112	1116	38	-	-	PUNCT
m-1112	1116	39	cube	cube	NOUN
m-1112	1116	40	-	-	PUNCT
m-1112	1116	41	system	system	NOUN
m-1112	1116	42	.	.	PUNCT
m-1112	1117	1	both	both	DET
m-1112	1117	2	equilibrium	equilibrium	NOUN
m-1112	1117	3	by	by	ADP
m-1112	1117	4	following	follow	VERB
m-1112	1117	5	the	the	DET
m-1112	1117	6	menelaus	menelaus	PROPN
m-1112	1117	7	ceba`s	ceba`s	NOUN
m-1112	1117	8	principles	principle	NOUN
m-1112	1117	9	.	.	PUNCT
m-1112	1118	1	[	[	X
m-1112	1118	2	70	70	NUM
m-1112	1118	3	]	]	PUNCT
m-1112	1118	4	any	any	DET
m-1112	1118	5	two	two	NUM
m-1112	1118	6	perpendicular	perpendicular	ADJ
m-1112	1118	7	energy	energy	NOUN
m-1112	1118	8	-	-	PUNCT
m-1112	1118	9	vectors	vector	NOUN
m-1112	1118	10	,	,	PUNCT
m-1112	1118	11	|𝐐	|𝐐	VERB
m-1112	1118	12	⇉	⇉	PROPN
m-1112	1118	13	aka⃗⃗	aka⃗⃗	PROPN
m-1112	1118	14	⃗⃗	⃗⃗	PROPN
m-1112	1118	15	⃗⃗	⃗⃗	PROPN
m-1112	1118	16	⃗⃗	⃗⃗	PROPN
m-1112	1118	17	⃗	⃗	PROPN
m-1112	1118	18	=	=	SYM
m-1112	1118	19	↔	↔	PROPN
m-1112	1118	20	|	|	ADV
m-1112	1118	21	,	,	PUNCT
m-1112	1118	22	|𝐐	|𝐐	PROPN
m-1112	1118	23	⇈	⇈	NUM
m-1112	1118	24	aka⃗⃗	aka⃗⃗	PROPN
m-1112	1118	25	⃗⃗	⃗⃗	PROPN
m-1112	1118	26	⃗⃗	⃗⃗	PROPN
m-1112	1118	27	⃗⃗	⃗⃗	PROPN
m-1112	1118	28	⃗	⃗	PROPN
m-1112	1118	29	=	=	SYM
m-1112	1118	30	↕	↕	PROPN
m-1112	1118	31	|	|	ADV
m-1112	1118	32	of	of	ADP
m-1112	1118	33	this	this	DET
m-1112	1118	34	propagating	propagate	VERB
m-1112	1118	35	energy	energy	NOUN
m-1112	1118	36	,	,	PUNCT
m-1112	1118	37	form	form	VERB
m-1112	1118	38	the	the	DET
m-1112	1118	39	energy	energy	NOUN
m-1112	1118	40	-	-	PUNCT
m-1112	1118	41	square	square	NOUN
m-1112	1118	42	,	,	PUNCT
m-1112	1118	43	|↔|.|	|↔|.|	NUM
m-1112	1118	44	↕	↕	PROPN
m-1112	1118	45	|≡|𝐐	|≡|𝐐	NUM
m-1112	1118	46	⇉	⇉	PROPN
m-1112	1118	47	|.|	|.|	NOUN
m-1112	1118	48	𝐐	𝐐	PROPN
m-1112	1118	49	⇈	⇈	PROPN
m-1112	1118	50	|	|	ADV
m-1112	1118	51	≡	≡	PROPN
m-1112	1118	52	q0	q0	PROPN
m-1112	1118	53	,	,	PUNCT
m-1112	1118	54	on	on	ADP
m-1112	1118	55	conductor	conductor	NOUN
m-1112	1118	56	aka	aka	ADV
m-1112	1118	57	and	and	CCONJ
m-1112	1118	58	then	then	ADV
m-1112	1118	59	energy	energy	NOUN
m-1112	1118	60	-	-	PUNCT
m-1112	1118	61	circular	circular	ADJ
m-1112	1118	62	-	-	PUNCT
m-1112	1118	63	prism	prism	NOUN
m-1112	1118	64	=	=	PROPN
m-1112	1118	65	|aka|	|aka|	PROPN
m-1112	1118	66	.{𝐐	.{𝐐	PUNCT
m-1112	1119	1	⇉	⇉	X
m-1112	1119	2	aka⃗⃗	aka⃗⃗	PROPN
m-1112	1119	3	⃗⃗	⃗⃗	PROPN
m-1112	1119	4	⃗⃗	⃗⃗	PROPN
m-1112	1119	5	⃗⃗	⃗⃗	PROPN
m-1112	1119	6	⃗	⃗	PROPN
m-1112	1119	7	}	}	PUNCT
m-1112	1119	8	.	.	PUNCT
m-1112	1119	9	{	{	PUNCT
m-1112	1120	1	𝐐	𝐐	PROPN
m-1112	1120	2	⇈	⇈	PROPN
m-1112	1120	3	aka⃗⃗	aka⃗⃗	PROPN
m-1112	1120	4	⃗⃗	⃗⃗	PROPN
m-1112	1120	5	⃗⃗	⃗⃗	PROPN
m-1112	1120	6	⃗⃗	⃗⃗	PROPN
m-1112	1120	7	⃗	⃗	PROPN
m-1112	1120	8	}	}	PUNCT
m-1112	1120	9	≡	≡	PROPN
m-1112	1120	10	[	[	X
m-1112	1120	11	�	�	NOUN
m-1112	1120	12	̅	̅	VERB
m-1112	1120	13	�	�	PROPN
m-1112	1120	14	𝐱	𝐱	PROPN
m-1112	1120	15	�	�	PROPN
m-1112	1120	16	̅	̅	NOUN
m-1112	1120	17	�	�	NOUN
m-1112	1120	18	𝐲].|aka|	𝐲].|aka|	X
m-1112	1121	1	=	=	PUNCT
m-1112	1121	2	|	|	ADV
m-1112	1121	3	↔	↔	PROPN
m-1112	1121	4	|.|	|.|	NOUN
m-1112	1121	5	↕	↕	NOUN
m-1112	1121	6	|.|aka|	|.|aka|	NOUN
m-1112	1121	7	,	,	PUNCT
m-1112	1121	8	i.e.	i.e.	X
m-1112	1121	9	an	an	DET
m-1112	1121	10	energy	energy	NOUN
m-1112	1121	11	-	-	PUNCT
m-1112	1121	12	circular	circular	ADJ
m-1112	1121	13	-	-	PUNCT
m-1112	1121	14	cone	cone	NOUN
m-1112	1121	15	which	which	PRON
m-1112	1121	16	is	be	AUX
m-1112	1121	17	a	a	DET
m-1112	1121	18	moving	move	VERB
m-1112	1121	19	energy	energy	NOUN
m-1112	1121	20	-volume	-volume	NOUN
m-1112	1121	21	,	,	PUNCT
m-1112	1121	22	and	and	CCONJ
m-1112	1121	23	because	because	SCONJ
m-1112	1121	24	from	from	ADP
m-1112	1121	25	cauchy	cauchy	PROPN
m-1112	1121	26	equations	equation	NOUN
m-1112	1121	27	of	of	ADP
m-1112	1121	28	stresses	stress	NOUN
m-1112	1121	29	are	be	AUX
m-1112	1121	30	of	of	ADP
m-1112	1121	31	three	three	NUM
m-1112	1121	32	dimensions	dimension	NOUN
m-1112	1121	33	,	,	PUNCT
m-1112	1121	34	then	then	ADV
m-1112	1121	35	the	the	DET
m-1112	1121	36	energy	energy	NOUN
m-1112	1121	37	stresses	stress	NOUN
m-1112	1121	38	remains	remain	VERB
m-1112	1121	39	flat	flat	ADJ
m-1112	1121	40	onlywhen	onlywhen	NOUN
m-1112	1121	41	the	the	DET
m-1112	1121	42	plane	plane	NOUN
m-1112	1121	43	-	-	PUNCT
m-1112	1121	44	section	section	NOUN
m-1112	1121	45	is	be	AUX
m-1112	1121	46	a	a	DET
m-1112	1121	47	circle	circle	NOUN
m-1112	1122	1	[	[	X
m-1112	1122	2	𝐄𝟐	𝐄𝟐	X
m-1112	1122	3	]	]	PUNCT
m-1112	1122	4	and	and	CCONJ
m-1112	1122	5	the	the	DET
m-1112	1122	6	square	square	NOUN
m-1112	1122	7	becomes	become	VERB
m-1112	1122	8	circle	circle	NOUN
m-1112	1122	9	,	,	PUNCT
m-1112	1122	10	anti	anti	ADJ
m-1112	1122	11	-	-	ADJ
m-1112	1122	12	quadrature	quadrature	ADJ
m-1112	1122	13	..	..	PUNCT
m-1112	1123	1	because	because	SCONJ
m-1112	1123	2	from	from	ADP
m-1112	1123	3	mechanics	mechanic	NOUN
m-1112	1123	4	,	,	PUNCT
m-1112	1123	5	the	the	DET
m-1112	1123	6	hydrogen	hydrogen	NOUN
m-1112	1123	7	nucleus	nucleus	PROPN
m-1112	1123	8	is	be	AUX
m-1112	1123	9	kept	keep	VERB
m-1112	1123	10	in	in	ADP
m-1112	1123	11	the	the	DET
m-1112	1123	12	inscribed	inscribe	VERB
m-1112	1123	13	to	to	ADP
m-1112	1123	14	the	the	DET
m-1112	1123	15	tetrahedron	tetrahedron	NOUN
m-1112	1123	16	-	-	PUNCT
m-1112	1123	17	cube	cube	NOUN
m-1112	1123	18	-	-	PUNCT
m-1112	1123	19	system	system	NOUN
m-1112	1123	20	where	where	SCONJ
m-1112	1123	21	exist	exist	VERB
m-1112	1123	22	the	the	DET
m-1112	1123	23	protons	proton	NOUN
m-1112	1123	24	and	and	CCONJ
m-1112	1123	25	neutrons	neutron	NOUN
m-1112	1123	26	,	,	PUNCT
m-1112	1123	27	while	while	SCONJ
m-1112	1123	28	the	the	DET
m-1112	1123	29	electrons	electron	NOUN
m-1112	1123	30	of	of	ADP
m-1112	1123	31	hydrogen	hydrogen	NOUN
m-1112	1123	32	orbits	orbit	NOUN
m-1112	1123	33	are	be	AUX
m-1112	1123	34	kept	keep	VERB
m-1112	1123	35	into	into	ADP
m-1112	1123	36	the	the	DET
m-1112	1123	37	circumscribed	circumscribed	ADJ
m-1112	1123	38	,	,	PUNCT
m-1112	1123	39	to	to	ADP
m-1112	1123	40	the	the	DET
m-1112	1123	41	tetrahedron	tetrahedron	NOUN
m-1112	1123	42	–	–	PUNCT
m-1112	1123	43	cube	cube	NOUN
m-1112	1123	44	-	-	PUNCT
m-1112	1123	45	system	system	NOUN
m-1112	1123	46	.	.	PUNCT
m-1112	1124	1	both	both	DET
m-1112	1124	2	equilibrium	equilibrium	NOUN
m-1112	1124	3	by	by	ADP
m-1112	1124	4	following	follow	VERB
m-1112	1124	5	the	the	DET
m-1112	1124	6	menelaus	menelaus	PROPN
m-1112	1124	7	-	-	PUNCT
m-1112	1124	8	cebas	cebas	NOUN
m-1112	1124	9	principles	principle	NOUN
m-1112	1124	10	.	.	PUNCT
m-1112	1125	1	oxygen	oxygen	NOUN
m-1112	1125	2	is	be	AUX
m-1112	1125	3	the	the	DET
m-1112	1125	4	element	element	NOUN
m-1112	1125	5	which	which	PRON
m-1112	1125	6	fills	fill	VERB
m-1112	1125	7	8	8	NUM
m-1112	1125	8	2	2	NUM
m-1112	1125	9	=	=	SYM
m-1112	1125	10	6	6	NUM
m-1112	1125	11	vertices	vertex	NOUN
m-1112	1125	12	of	of	ADP
m-1112	1125	13	cube	cube	NOUN
m-1112	1125	14	and	and	CCONJ
m-1112	1125	15	for	for	ADP
m-1112	1125	16	neon	neon	NOUN
m-1112	1125	17	10	10	NUM
m-1112	1125	18	-2	-2	NOUN
m-1112	1125	19	=	=	NOUN
m-1112	1125	20	8	8	NUM
m-1112	1125	21	,	,	PUNCT
m-1112	1125	22	as	as	ADP
m-1112	1125	23	ox	ox	NOUN
m-1112	1125	24	→	→	PUNCT
m-1112	1125	25	{	{	PUNCT
m-1112	1125	26	1𝑒	1𝑒	NUM
m-1112	1125	27	0|	0|	NUM
m-1112	1126	1	0/	0/	NUM
m-1112	1126	2	1	1	NUM
m-1112	1126	3	𝑒	𝑒	ADP
m-1112	1126	4	2|⃖⃗	2|⃖⃗	NUM
m-1112	1126	5	⃗/	⃗/	NOUN
m-1112	1126	6	1	1	NUM
m-1112	1126	7	𝑒	𝑒	PROPN
m-1112	1126	8	1𝑒/	1𝑒/	NUM
m-1112	1126	9	1𝑒|	1𝑒|	NUM
m-1112	1126	10	1𝑒	1𝑒	NUM
m-1112	1126	11	}	}	PUNCT
m-1112	1126	12	≡	≡	PROPN
m-1112	1126	13	(	(	PUNCT
m-1112	1126	14	−2	−2	PROPN
m-1112	1126	15	+2	+2	PROPN
m-1112	1126	16	)	)	PUNCT
m-1112	1126	17	,	,	PUNCT
m-1112	1126	18	②	②	NUM
m-1112	1126	19	≡	≡	PROPN
m-1112	1126	20	𝐍𝐞	𝐍𝐞	ADP
m-1112	1126	21	1x8	1x8	NUM
m-1112	1126	22	2⃡	2⃡	NOUN
m-1112	1126	23	=	=	SYM
m-1112	1126	24	2⃡	2⃡	NOUN
m-1112	1126	25	+	+	CCONJ
m-1112	1126	26	8	8	NUM
m-1112	1126	27	=	=	SYM
m-1112	1126	28	10	10	NUM
m-1112	1126	29	→	→	SYM
m-1112	1126	30	{	{	PUNCT
m-1112	1126	31	1	1	NUM
m-1112	1126	32	1	1	NUM
m-1112	1126	33	1	1	NUM
m-1112	1126	34	1	1	NUM
m-1112	1126	35	2⃡	2⃡	NUM
m-1112	1126	36	1	1	NUM
m-1112	1126	37	1	1	NUM
m-1112	1126	38	1	1	NUM
m-1112	1126	39	1	1	NUM
m-1112	1126	40	}	}	PUNCT
m-1112	1126	41	,	,	PUNCT
m-1112	1126	42	the	the	DET
m-1112	1126	43	possible	possible	ADJ
m-1112	1126	44	orbits	orbit	NOUN
m-1112	1126	45	of	of	ADP
m-1112	1126	46	oxygen	oxygen	NOUN
m-1112	1126	47	are	be	AUX
m-1112	1126	48	two	two	NUM
m-1112	1126	49	as	as	ADP
m-1112	1126	50	,	,	PUNCT
m-1112	1126	51	→	→	X
m-1112	1126	52	1e	1e	NUM
m-1112	1126	53	/-2⃡/-/	/-2⃡/-/	SYM
m-1112	1126	54	0	0	NUM
m-1112	1126	55	←	←	PROPN
m-1112	1126	56	and	and	CCONJ
m-1112	1127	1	→	→	SYM
m-1112	1127	2	1e	1e	NUM
m-1112	1127	3	|-2|⃖⃗	|-2|⃖⃗	X
m-1112	1127	4	⃗-	⃗-	NOUN
m-1112	1127	5	0	0	NUM
m-1112	1128	1	|	|	ADV
m-1112	1128	2	←	←	PROPN
m-1112	1128	3	for	for	ADP
m-1112	1128	4	all	all	DET
m-1112	1128	5	the	the	DET
m-1112	1128	6	8	8	NUM
m-1112	1128	7	-	-	PUNCT
m-1112	1128	8	cube	cube	NOUN
m-1112	1128	9	positions	position	NOUN
m-1112	1128	10	.	.	PUNCT
m-1112	1129	1	⓪	⓪	X
m-1112	1129	2	is	be	AUX
m-1112	1129	3	the	the	DET
m-1112	1129	4	first	first	ADJ
m-1112	1129	5	,	,	PUNCT
m-1112	1129	6	zero	zero	NUM
m-1112	1129	7	-	-	PUNCT
m-1112	1129	8	acting	act	VERB
m-1112	1129	9	cube	cube	NOUN
m-1112	1129	10	and	and	CCONJ
m-1112	1129	11	is	be	AUX
m-1112	1129	12	filled	fill	VERB
m-1112	1129	13	with	with	ADP
m-1112	1129	14	1e	1e	PROPN
m-1112	1129	15	,	,	PUNCT
m-1112	1129	16	therefore	therefore	ADV
m-1112	1129	17	is	be	AUX
m-1112	1129	18	the	the	DET
m-1112	1129	19	only	only	ADJ
m-1112	1129	20	steady	steady	ADJ
m-1112	1129	21	element	element	NOUN
m-1112	1129	22	which	which	PRON
m-1112	1129	23	occupies	occupy	VERB
m-1112	1129	24	the	the	DET
m-1112	1129	25	first	first	ADJ
m-1112	1129	26	energy	energy	NOUN
m-1112	1129	27	-	-	PUNCT
m-1112	1129	28	level	level	NOUN
m-1112	1129	29	①	①	NOUN
m-1112	1129	30	with	with	ADP
m-1112	1129	31	2	2	NUM
m-1112	1129	32	electron	electron	NOUN
m-1112	1129	33	-	-	PUNCT
m-1112	1129	34	positions	position	NOUN
m-1112	1129	35	as	as	ADP
m-1112	1129	36	①	①	PROPN
m-1112	1129	37	=	=	SYM
m-1112	1129	38	2e	2e	NOUN
m-1112	1129	39	positions	position	NOUN
m-1112	1129	40	at	at	ADP
m-1112	1129	41	1⃗	1⃗	NUM
m-1112	1129	42	,	,	PUNCT
m-1112	1129	43	1⃗⃖	1⃗⃖	NUM
m-1112	1129	44	.	.	PUNCT
m-1112	1130	1	in	in	ADP
m-1112	1130	2	the	the	DET
m-1112	1130	3	same	same	ADJ
m-1112	1130	4	way	way	NOUN
m-1112	1130	5	①	①	NUM
m-1112	1130	6	is	be	AUX
m-1112	1130	7	the	the	DET
m-1112	1130	8	first	first	ADJ
m-1112	1130	9	one	one	NUM
m-1112	1130	10	-	-	PUNCT
m-1112	1130	11	acting	act	VERB
m-1112	1130	12	cube	cube	NOUN
m-1112	1130	13	and	and	CCONJ
m-1112	1130	14	is	be	AUX
m-1112	1130	15	filled	fill	VERB
m-1112	1130	16	ijo	ijo	PROPN
m-1112	1130	17	international	international	PROPN
m-1112	1130	18	journal	journal	PROPN
m-1112	1130	19	of	of	ADP
m-1112	1130	20	mathematics	mathematics	PROPN
m-1112	1130	21	(	(	PUNCT
m-1112	1130	22	issn	issn	PROPN
m-1112	1130	23	:	:	PUNCT
m-1112	1130	24	2992	2992	NUM
m-1112	1130	25	-	-	SYM
m-1112	1130	26	4421	4421	NUM
m-1112	1130	27	)	)	PUNCT
m-1112	1131	1	volume	volume	NOUN
m-1112	1131	2	08	08	NUM
m-1112	1132	1	|	|	ADV
m-1112	1132	2	issue	issue	NOUN
m-1112	1132	3	08	08	NUM
m-1112	1133	1	|	|	ADV
m-1112	1133	2	august	august	PROPN
m-1112	1133	3	2025	2025	NUM
m-1112	1133	4	|	|	ADV
m-1112	1133	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1133	6	ijo	ijo	PROPN
m-1112	1133	7	journals	journal	NOUN
m-1112	1133	8	42	42	NUM
m-1112	1133	9	the	the	DET
m-1112	1133	10	fundamental	fundamental	ADJ
m-1112	1133	11	particles	particle	NOUN
m-1112	1133	12	origination	origination	NOUN
m-1112	1133	13	mechanism	mechanism	NOUN
m-1112	1133	14	in	in	ADP
m-1112	1133	15	mfmf	mfmf	PROPN
m-1112	1133	16	pns	pns	PROPN
m-1112	1133	17	caves	cave	NOUN
m-1112	1133	18	.	.	PUNCT
m-1112	1134	1	with	with	ADP
m-1112	1134	2	2e	2e	NUM
m-1112	1134	3	,	,	PUNCT
m-1112	1134	4	and	and	CCONJ
m-1112	1134	5	so	so	ADV
m-1112	1134	6	on	on	ADV
m-1112	1134	7	,	,	PUNCT
m-1112	1134	8	the	the	DET
m-1112	1134	9	electron	electron	NOUN
m-1112	1134	10	being	be	AUX
m-1112	1134	11	in	in	ADP
m-1112	1134	12	the	the	DET
m-1112	1134	13	hydrogen	hydrogen	NOUN
m-1112	1134	14	-cave	-cave	PROPN
m-1112	1134	15	precesses	precesse	NOUN
m-1112	1134	16	because	because	SCONJ
m-1112	1134	17	of	of	ADP
m-1112	1134	18	the	the	DET
m-1112	1134	19	different	different	ADJ
m-1112	1134	20	axis	axis	NOUN
m-1112	1134	21	of	of	ADP
m-1112	1134	22	rotation	rotation	NOUN
m-1112	1134	23	and	and	CCONJ
m-1112	1134	24	nutation`s	nutation`s	ADP
m-1112	1134	25	,	,	PUNCT
m-1112	1134	26	from	from	ADP
m-1112	1134	27	the	the	DET
m-1112	1134	28	continuous	continuous	ADJ
m-1112	1134	29	and	and	CCONJ
m-1112	1134	30	immense	immense	ADJ
m-1112	1134	31	-	-	PUNCT
m-1112	1134	32	communication	communication	NOUN
m-1112	1134	33	to	to	ADP
m-1112	1134	34	the	the	DET
m-1112	1134	35	gravity	gravity	NOUN
m-1112	1134	36	g	g	NOUN
m-1112	1134	37	.	.	PUNCT
m-1112	1135	1	since	since	SCONJ
m-1112	1135	2	electron	electron	NOUN
m-1112	1135	3	is	be	AUX
m-1112	1135	4	continually	continually	ADV
m-1112	1135	5	oscillating	oscillate	VERB
m-1112	1135	6	with	with	ADP
m-1112	1135	7	the	the	DET
m-1112	1135	8	nutation	nutation	NOUN
m-1112	1135	9	-	-	PUNCT
m-1112	1135	10	frequency	frequency	NOUN
m-1112	1135	11	𝐟	𝐟	NOUN
m-1112	1135	12	𝐍	𝐍	NOUN
m-1112	1135	13	so	so	ADV
m-1112	1135	14	produces	produce	VERB
m-1112	1135	15	a	a	DET
m-1112	1135	16	continuous	continuous	ADJ
m-1112	1135	17	and	and	CCONJ
m-1112	1135	18	oscillating	oscillate	VERB
m-1112	1135	19	magnetic	magnetic	ADJ
m-1112	1135	20	-	-	PUNCT
m-1112	1135	21	field	field	NOUN
m-1112	1135	22	–	–	PUNCT
m-1112	1135	23	mwhich	mwhich	NOUN
m-1112	1135	24	in	in	ADP
m-1112	1135	25	turn	turn	NOUN
m-1112	1135	26	is	be	AUX
m-1112	1135	27	the	the	DET
m-1112	1135	28	source	source	NOUN
m-1112	1135	29	of	of	ADP
m-1112	1135	30	an	an	DET
m-1112	1135	31	oscillating	oscillate	VERB
m-1112	1135	32	electric	electric	NOUN
m-1112	1135	33	-	-	PUNCT
m-1112	1135	34	field	field	NOUN
m-1112	1135	35	–	–	PUNCT
m-1112	1135	36	e	e	NOUN
m-1112	1135	37	which	which	PRON
m-1112	1135	38	implies	imply	VERB
m-1112	1135	39	the	the	DET
m-1112	1135	40	regeneration	regeneration	NOUN
m-1112	1135	41	of	of	ADP
m-1112	1135	42	each	each	DET
m-1112	1135	43	other	other	ADJ
m-1112	1135	44	,	,	PUNCT
m-1112	1135	45	i.e.	i.e.	X
m-1112	1135	46	it	it	PRON
m-1112	1135	47	is	be	AUX
m-1112	1135	48	a	a	DET
m-1112	1135	49	propagating	propagate	VERB
m-1112	1135	50	electromagnetic	electromagnetic	ADJ
m-1112	1135	51	-	-	PUNCT
m-1112	1135	52	wave	wave	NOUN
m-1112	1135	53	where	where	SCONJ
m-1112	1135	54	e	e	NOUN
m-1112	1135	55	=	=	SYM
m-1112	1135	56	b	b	PROPN
m-1112	1135	57	c	c	NOUN
m-1112	1135	58	and	and	CCONJ
m-1112	1135	59	with	with	ADP
m-1112	1135	60	a	a	DET
m-1112	1135	61	quantum	quantum	NOUN
m-1112	1135	62	-	-	PUNCT
m-1112	1135	63	energy	energy	NOUN
m-1112	1135	64	e	e	NOUN
m-1112	1135	65	=	=	NOUN
m-1112	1135	66	h	h	PROPN
m-1112	1135	67	fn	fn	NOUN
m-1112	1135	68	or	or	CCONJ
m-1112	1135	69	e	e	X
m-1112	1135	70	=	=	SYM
m-1112	1135	71	2μ.b	2μ.b	NUM
m-1112	1135	72	,	,	PUNCT
m-1112	1135	73	this	this	DET
m-1112	1135	74	energy	energy	NOUN
m-1112	1135	75	e	e	NOUN
m-1112	1135	76	consists	consist	VERB
m-1112	1135	77	the	the	DET
m-1112	1135	78	hydrogen	hydrogen	NOUN
m-1112	1135	79	bracket	bracket	NOUN
m-1112	1135	80	hook	hook	NOUN
m-1112	1135	81	hbh	hbh	PROPN
m-1112	1135	82	,	,	PUNCT
m-1112	1135	83	or	or	CCONJ
m-1112	1135	84	[	[	X
m-1112	1135	85	bh⃗⃗⃗⃗	bh⃗⃗⃗⃗	NOUN
m-1112	1135	86	⃗	⃗	NOUN
m-1112	1135	87	]	]	X
m-1112	1135	88	and	and	CCONJ
m-1112	1135	89	it	it	PRON
m-1112	1135	90	is	be	AUX
m-1112	1135	91	the	the	DET
m-1112	1135	92	only	only	ADJ
m-1112	1135	93	free	free	ADJ
m-1112	1135	94	monad	monad	PROPN
m-1112	1135	95	which	which	PRON
m-1112	1135	96	can	can	AUX
m-1112	1135	97	bond	bond	VERB
m-1112	1135	98	to	to	ADP
m-1112	1135	99	all	all	DET
m-1112	1135	100	energy	energy	NOUN
m-1112	1135	101	structures	structure	NOUN
m-1112	1135	102	.	.	PUNCT
m-1112	1136	1	the	the	DET
m-1112	1136	2	sphere	sphere	NOUN
m-1112	1136	3	-	-	PUNCT
m-1112	1136	4	cube	cube	NOUN
m-1112	1136	5	-	-	PUNCT
m-1112	1136	6	tetrahedron	tetrahedron	NOUN
m-1112	1136	7	structure	structure	NOUN
m-1112	1136	8	of	of	ADP
m-1112	1136	9	atoms	atom	NOUN
m-1112	1136	10	in	in	ADP
m-1112	1136	11	sphere	sphere	NOUN
m-1112	1136	12	center	center	NOUN
m-1112	1136	13	–	–	PUNCT
m-1112	1136	14	oallows	oallow	VERB
m-1112	1136	15	to	to	PART
m-1112	1136	16	issue	issue	VERB
m-1112	1136	17	the	the	DET
m-1112	1136	18	ceba`s	ceba`	NOUN
m-1112	1136	19	theorem	theorem	VERB
m-1112	1136	20	for	for	ADP
m-1112	1136	21	6	6	NUM
m-1112	1136	22	-	-	PUNCT
m-1112	1136	23	stresses	stress	NOUN
m-1112	1136	24	on	on	ADP
m-1112	1136	25	the	the	DET
m-1112	1136	26	inscribed	inscribe	VERB
m-1112	1136	27	tetrahedron	tetrahedron	NOUN
m-1112	1136	28	which	which	PRON
m-1112	1136	29	secure	secure	VERB
m-1112	1136	30	the	the	DET
m-1112	1136	31	stability	stability	NOUN
m-1112	1136	32	for	for	ADP
m-1112	1136	33	the	the	DET
m-1112	1136	34	nucleus	nucleus	NOUN
m-1112	1136	35	-	-	PUNCT
m-1112	1136	36	system	system	NOUN
m-1112	1136	37	,	,	PUNCT
m-1112	1136	38	and	and	CCONJ
m-1112	1136	39	for	for	ADP
m-1112	1136	40	the	the	DET
m-1112	1136	41	outer	outer	ADJ
m-1112	1136	42	electron	electron	NOUN
m-1112	1136	43	-	-	PUNCT
m-1112	1136	44	system	system	NOUN
m-1112	1136	45	the	the	DET
m-1112	1136	46	stability	stability	NOUN
m-1112	1136	47	is	be	AUX
m-1112	1136	48	obtained	obtain	VERB
m-1112	1136	49	per	per	ADP
m-1112	1136	50	–	–	PUNCT
m-1112	1136	51	two	two	NUM
m-1112	1136	52	electrons	electron	NOUN
m-1112	1136	53	the	the	DET
m-1112	1136	54	dipole	dipole	NOUN
m-1112	1136	55	positions	position	NOUN
m-1112	1136	56	1	1	NUM
m-1112	1136	57	↔	↔	PROPN
m-1112	1136	58	6	6	NUM
m-1112	1136	59	,	,	PUNCT
m-1112	1136	60	2	2	NUM
m-1112	1136	61	↔	↔	PROPN
m-1112	1136	62	5	5	NUM
m-1112	1136	63	,	,	PUNCT
m-1112	1136	64	3	3	NUM
m-1112	1136	65	↔	↔	PROPN
m-1112	1136	66	8	8	NUM
m-1112	1136	67	,	,	PUNCT
m-1112	1136	68	4	4	NUM
m-1112	1136	69	↔7	↔7	NUM
m-1112	1136	70	,	,	PUNCT
m-1112	1136	71	consisting	consist	VERB
m-1112	1136	72	thepositive	thepositive	ADJ
m-1112	1136	73	dipole-[bh⃗⃗⃗⃗	dipole-[bh⃗⃗⃗⃗	X
m-1112	1136	74	⃗	⃗	PROPN
m-1112	1136	75	]	]	PUNCT
m-1112	1136	76	,	,	PUNCT
m-1112	1136	77	to	to	PART
m-1112	1136	78	be	be	AUX
m-1112	1136	79	able	able	ADJ
m-1112	1136	80	to	to	PART
m-1112	1136	81	move	move	VERB
m-1112	1136	82	→	→	SYM
m-1112	1136	83	into	into	AUX
m-1112	1136	84	-	-	PUNCT
m-1112	1136	85	inoutside	inoutside	NOUN
m-1112	1136	86	it	it	PRON
m-1112	1136	87	←	←	PROPN
m-1112	1136	88	and	and	CCONJ
m-1112	1136	89	allow	allow	VERB
m-1112	1136	90	the	the	DET
m-1112	1136	91	atomsbonding	atomsbonding	NOUN
m-1112	1136	92	as	as	ADP
m-1112	1136	93	this	this	PRON
m-1112	1136	94	in	in	ADP
m-1112	1136	95	energy	energy	NOUN
m-1112	1136	96	levels	level	NOUN
m-1112	1136	97	.	.	PUNCT
m-1112	1137	1	the	the	DET
m-1112	1137	2	cube	cube	NOUN
m-1112	1137	3	-	-	PUNCT
m-1112	1137	4	structure	structure	NOUN
m-1112	1137	5	of	of	ADP
m-1112	1137	6	atoms	atom	NOUN
m-1112	1137	7	and	and	CCONJ
m-1112	1137	8	orbits	orbit	NOUN
m-1112	1137	9	in	in	ADP
m-1112	1137	10	the	the	DET
m-1112	1137	11	out	out	ADJ
m-1112	1137	12	-	-	PUNCT
m-1112	1137	13	sphere	sphere	NOUN
m-1112	1137	14	formulates	formulate	VERB
m-1112	1137	15	the	the	DET
m-1112	1137	16	+	+	PROPN
m-1112	1137	17	[	[	X
m-1112	1137	18	bh⃗⃗⃗⃗	bh⃗⃗⃗⃗	NOUN
m-1112	1137	19	⃗	⃗	ADJ
m-1112	1137	20	]	]	X
m-1112	1137	21	to	to	ADP
m-1112	1137	22	those	those	DET
m-1112	1137	23	dipole	dipole	NOUN
m-1112	1137	24	positions	position	NOUN
m-1112	1137	25	which	which	PRON
m-1112	1137	26	lack	lack	NOUN
m-1112	1137	27	of	of	ADP
m-1112	1137	28	one	one	NUM
m-1112	1137	29	electron	electron	NOUN
m-1112	1137	30	and	and	CCONJ
m-1112	1137	31	so	so	ADV
m-1112	1137	32	can	can	AUX
m-1112	1137	33	plug	plug	VERB
m-1112	1137	34	-	-	PUNCT
m-1112	1137	35	in	in	ADP
m-1112	1137	36	the	the	DET
m-1112	1137	37	loop	loop	NOUN
m-1112	1137	38	of	of	ADP
m-1112	1137	39	the	the	DET
m-1112	1137	40	others	other	NOUN
m-1112	1137	41	.	.	PUNCT
m-1112	1138	1	conclusion	conclusion	NOUN
m-1112	1138	2	:	:	PUNCT
m-1112	1138	3	1	1	X
m-1112	1138	4	…	…	PUNCT
m-1112	1138	5	the	the	DET
m-1112	1138	6	forces	force	NOUN
m-1112	1138	7	of	of	ADP
m-1112	1138	8	atom`s	atom`s	PROPN
m-1112	1138	9	nucleus	nucleus	PROPN
m-1112	1138	10	,	,	PUNCT
m-1112	1138	11	are	be	AUX
m-1112	1138	12	holded	hold	VERB
m-1112	1138	13	from	from	ADP
m-1112	1138	14	→	→	PUNCT
m-1112	1138	15	the	the	DET
m-1112	1138	16	inscribed	inscribe	VERB
m-1112	1138	17	sphere	sphere	NOUN
m-1112	1138	18	in	in	ADP
m-1112	1138	19	the	the	DET
m-1112	1138	20	tetrahedron	tetrahedron	NOUN
m-1112	1138	21	,	,	PUNCT
m-1112	1138	22	which	which	PRON
m-1112	1138	23	follows	follow	VERB
m-1112	1138	24	the	the	DET
m-1112	1138	25	ptolemy`s	ptolemy`	NOUN
m-1112	1138	26	and	and	CCONJ
m-1112	1138	27	ceba`s	ceba`s	NOUN
m-1112	1138	28	vectors	vector	NOUN
m-1112	1138	29	structure	structure	NOUN
m-1112	1138	30	.	.	PUNCT
m-1112	1139	1	2	2	X
m-1112	1139	2	…	…	PUNCT
m-1112	1139	3	the	the	DET
m-1112	1139	4	forces	force	NOUN
m-1112	1139	5	of	of	ADP
m-1112	1139	6	atom`s	atom`s	X
m-1112	1139	7	orbitals	orbital	NOUN
m-1112	1139	8	,	,	PUNCT
m-1112	1139	9	are	be	AUX
m-1112	1139	10	holded	hold	VERB
m-1112	1139	11	from	from	ADP
m-1112	1139	12	→	→	SYM
m-1112	1139	13	the	the	PRON
m-1112	1139	14	into	into	ADP
m-1112	1139	15	the	the	DET
m-1112	1139	16	cube	cube	NOUN
m-1112	1139	17	,	,	PUNCT
m-1112	1139	18	circumscribed	circumscribed	ADJ
m-1112	1139	19	–	–	PUNCT
m-1112	1139	20	sphere	sphere	NOUN
m-1112	1139	21	complex	complex	ADJ
m-1112	1139	22	vectors	vector	NOUN
m-1112	1139	23	structure	structure	NOUN
m-1112	1139	24	.	.	PUNCT
m-1112	1140	1	3	3	X
m-1112	1140	2	…	…	PUNCT
m-1112	1140	3	the	the	DET
m-1112	1140	4	forces	force	NOUN
m-1112	1140	5	of	of	ADP
m-1112	1140	6	atom`s	atom`s	PROPN
m-1112	1140	7	positions	position	NOUN
m-1112	1140	8	,	,	PUNCT
m-1112	1140	9	are	be	AUX
m-1112	1140	10	holded	hold	VERB
m-1112	1140	11	from	from	ADP
m-1112	1140	12	→	→	SYM
m-1112	1140	13	the	the	PRON
m-1112	1140	14	on	on	ADP
m-1112	1140	15	cube	cube	NOUN
m-1112	1140	16	inscribed	inscribe	VERB
m-1112	1140	17	tetrahedron	tetrahedron	NOUN
m-1112	1140	18	complex	complex	NOUN
m-1112	1140	19	vectors	vector	NOUN
m-1112	1140	20	structure	structure	NOUN
m-1112	1140	21	.	.	PUNCT
m-1112	1141	1	4	4	X
m-1112	1141	2	…	…	PUNCT
m-1112	1141	3	the	the	DET
m-1112	1141	4	stability	stability	NOUN
m-1112	1141	5	of	of	ADP
m-1112	1141	6	the	the	DET
m-1112	1141	7	{	{	PUNCT
m-1112	1141	8	tcic	tcic	NOUN
m-1112	1141	9	}	}	PUNCT
m-1112	1141	10	mechanism	mechanism	NOUN
m-1112	1141	11	follows	follow	VERB
m-1112	1141	12	the	the	DET
m-1112	1141	13	ptolemy`s	ptolemy`s	PROPN
m-1112	1141	14	&	&	CCONJ
m-1112	1141	15	ceba`s	ceba`s	PROPN
m-1112	1141	16	complex	complex	ADJ
m-1112	1141	17	vectors	vector	NOUN
m-1112	1141	18	structure	structure	NOUN
m-1112	1141	19	[	[	X
m-1112	1141	20	62	62	NUM
m-1112	1141	21	]	]	PUNCT
m-1112	1141	22	the	the	DET
m-1112	1141	23	action	action	NOUN
m-1112	1141	24	of	of	ADP
m-1112	1141	25	the	the	DET
m-1112	1141	26	complex	complex	ADJ
m-1112	1141	27	–	–	PUNCT
m-1112	1141	28	vectors	vector	NOUN
m-1112	1141	29	create	create	VERB
m-1112	1141	30	the	the	DET
m-1112	1141	31	waves	wave	NOUN
m-1112	1141	32	of	of	ADP
m-1112	1141	33	motion	motion	NOUN
m-1112	1141	34	≡	≡	PROPN
m-1112	1141	35	energy	energy	NOUN
m-1112	1141	36	waves	wave	NOUN
m-1112	1141	37	which	which	PRON
m-1112	1141	38	are	be	AUX
m-1112	1141	39	closed	closed	ADJ
m-1112	1141	40	curves	curve	NOUN
m-1112	1141	41	and	and	CCONJ
m-1112	1141	42	transported	transport	VERB
m-1112	1141	43	.	.	PUNCT
m-1112	1142	1	the	the	DET
m-1112	1142	2	pattern	pattern	NOUN
m-1112	1142	3	of	of	ADP
m-1112	1142	4	disturbances	disturbance	NOUN
m-1112	1142	5	with	with	ADP
m-1112	1142	6	the	the	DET
m-1112	1142	7	informations	information	NOUN
m-1112	1142	8	propagates	propagate	VERB
m-1112	1142	9	from	from	ADP
m-1112	1142	10	the	the	DET
m-1112	1142	11	one	one	NUM
m-1112	1142	12	-	-	PUNCT
m-1112	1142	13	edge	edge	NOUN
m-1112	1142	14	-	-	PUNCT
m-1112	1142	15	point	point	NOUN
m-1112	1142	16	to	to	ADP
m-1112	1142	17	the	the	DET
m-1112	1142	18	other	other	ADJ
m-1112	1142	19	edge	edge	NOUN
m-1112	1142	20	-	-	PUNCT
m-1112	1142	21	point	point	NOUN
m-1112	1142	22	of	of	ADP
m-1112	1142	23	conductors	conductor	NOUN
m-1112	1142	24	,	,	PUNCT
m-1112	1142	25	or	or	CCONJ
m-1112	1142	26	is	be	AUX
m-1112	1142	27	on	on	ADP
m-1112	1142	28	the	the	DET
m-1112	1142	29	[	[	PUNCT
m-1112	1142	30	sub	sub	NOUN
m-1112	1142	31	-	-	NOUN
m-1112	1142	32	units	unit	NOUN
m-1112	1142	33	]	]	PUNCT
m-1112	1142	34	.	.	PUNCT
m-1112	1143	1	coulomb	coulomb	NOUN
m-1112	1143	2	force	force	NOUN
m-1112	1144	1	[	[	X
m-1112	1144	2	⊕→⊝	⊕→⊝	PROPN
m-1112	1144	3	]	]	X
m-1112	1144	4	=	=	SYM
m-1112	1144	5	f	f	X
m-1112	1145	1	[	[	X
m-1112	1145	2	+	+	X
m-1112	1145	3	↔	↔	PROPN
m-1112	1145	4	−	−	NOUN
m-1112	1145	5	]	]	X
m-1112	1145	6	=	=	PUNCT
m-1112	1146	1	[	[	X
m-1112	1146	2	⊕↔⊝	⊕↔⊝	X
m-1112	1146	3	]	]	X
m-1112	1146	4	r²	r²	NOUN
m-1112	1146	5	=	=	SYM
m-1112	1146	6	[	[	PUNCT
m-1112	1146	7	𝟐	𝟐	NUM
m-1112	1146	8	𝛔	𝛔	NOUN
m-1112	1146	9	]	]	PUNCT
m-1112	1146	10	𝐫²	𝐫²	NOUN
m-1112	1146	11	=	=	SYM
m-1112	1146	12	f	f	PROPN
m-1112	1146	13	=	=	SYM
m-1112	1146	14	σ	σ	PROPN
m-1112	1146	15	.a	.a	NOUN
m-1112	1147	1	=	=	PUNCT
m-1112	1147	2	[	[	PUNCT
m-1112	1147	3	2πrf	2πrf	NUM
m-1112	1147	4	φ	φ	NOUN
m-1112	1147	5	]	]	X
m-1112	1147	6	.a	.a	NOUN
m-1112	1148	1	=	=	PUNCT
m-1112	1148	2	w	w	PROPN
m-1112	1148	3	r.	r.	PROPN
m-1112	1148	4	[	[	PUNCT
m-1112	1148	5	𝐀	𝐀	PROPN
m-1112	1148	6	𝚽	𝚽	NOUN
m-1112	1148	7	]	]	PUNCT
m-1112	1148	8	=	=	SYM
m-1112	1148	9	v	v	NOUN
m-1112	1148	10	.	.	PUNCT
m-1112	1149	1	[	[	PUNCT
m-1112	1149	2	𝐀	𝐀	PROPN
m-1112	1149	3	𝚽	𝚽	PROPN
m-1112	1149	4	]	]	PUNCT
m-1112	1149	5	,	,	PUNCT
m-1112	1149	6	and	and	CCONJ
m-1112	1149	7	acts	act	VERB
m-1112	1149	8	on	on	ADP
m-1112	1149	9	a	a	DET
m-1112	1149	10	surface	surface	NOUN
m-1112	1149	11	,	,	PUNCT
m-1112	1149	12	a	a	PRON
m-1112	1149	13	,	,	PUNCT
m-1112	1149	14	between	between	ADP
m-1112	1149	15	the	the	DET
m-1112	1149	16	sub	sub	NOUN
m-1112	1149	17	-	-	NOUN
m-1112	1149	18	units	unit	NOUN
m-1112	1149	19	axially	axially	ADV
m-1112	1149	20	and	and	CCONJ
m-1112	1149	21	rotationally	rotationally	ADV
m-1112	1149	22	following	follow	VERB
m-1112	1149	23	ptolemy`s	ptolemy`	NOUN
m-1112	1149	24	and	and	CCONJ
m-1112	1149	25	cebas	cebas	PROPN
m-1112	1149	26	theorem	theorem	NOUN
m-1112	1149	27	of	of	ADP
m-1112	1149	28	equilibrium	equilibrium	NOUN
m-1112	1149	29	.	.	PUNCT
m-1112	1150	1	figure	figure	NOUN
m-1112	1150	2	–	–	PUNCT
m-1112	1150	3	9e	9e	NUM
m-1112	1150	4	remarks	remark	NOUN
m-1112	1150	5	:	:	PUNCT
m-1112	1150	6	the	the	DET
m-1112	1150	7	work	work	NOUN
m-1112	1150	8	of	of	ADP
m-1112	1150	9	elastic	elastic	ADJ
m-1112	1150	10	deformation	deformation	NOUN
m-1112	1150	11	on	on	ADP
m-1112	1150	12	the	the	DET
m-1112	1150	13	{	{	PUNCT
m-1112	1150	14	tcic	tcic	NOUN
m-1112	1150	15	}	}	PUNCT
m-1112	1150	16	mechanism	mechanism	NOUN
m-1112	1150	17	:	:	PUNCT
m-1112	1150	18	every	every	DET
m-1112	1150	19	new	new	ADJ
m-1112	1150	20	stress	stress	NOUN
m-1112	1150	21	that	that	PRON
m-1112	1150	22	is	be	AUX
m-1112	1150	23	applied	apply	VERB
m-1112	1150	24	to	to	ADP
m-1112	1150	25	d	d	PROPN
m-1112	1150	26	element	element	NOUN
m-1112	1150	27	is	be	AUX
m-1112	1150	28	always	always	ADV
m-1112	1150	29	added	add	VERB
m-1112	1150	30	to	to	ADP
m-1112	1150	31	the	the	DET
m-1112	1150	32	existing	exist	VERB
m-1112	1150	33	and	and	CCONJ
m-1112	1150	34	the	the	DET
m-1112	1150	35	unity	unity	NOUN
m-1112	1150	36	work	work	NOUN
m-1112	1150	37	of	of	ADP
m-1112	1150	38	deformation	deformation	NOUN
m-1112	1150	39	is	be	AUX
m-1112	1150	40	transformed	transform	VERB
m-1112	1150	41	to	to	ADP
m-1112	1150	42	three	three	NUM
m-1112	1150	43	tetrahedron	tetrahedron	NOUN
m-1112	1150	44	sides	side	NOUN
m-1112	1150	45	.	.	PUNCT
m-1112	1151	1	when	when	SCONJ
m-1112	1151	2	a	a	DET
m-1112	1151	3	signal	signal	NOUN
m-1112	1151	4	strikes	strike	VERB
m-1112	1151	5	the	the	DET
m-1112	1151	6	tcic	tcic	NOUN
m-1112	1151	7	–	–	PUNCT
m-1112	1151	8	cube`s	cube`s	NUM
m-1112	1151	9	mechanism	mechanism	NOUN
m-1112	1151	10	.	.	PUNCT
m-1112	1152	1	the	the	DET
m-1112	1152	2	signal	signal	NOUN
m-1112	1152	3	is	be	AUX
m-1112	1152	4	energy	energy	NOUN
m-1112	1152	5	-	-	PUNCT
m-1112	1152	6	wave	wave	NOUN
m-1112	1152	7	carrying	carry	VERB
m-1112	1152	8	motion	motion	NOUN
m-1112	1152	9	.	.	PUNCT
m-1112	1153	1	unloading	unloading	NOUN
m-1112	1153	2	happens	happen	VERB
m-1112	1153	3	on	on	ADP
m-1112	1153	4	the	the	DET
m-1112	1153	5	three	three	NUM
m-1112	1153	6	still	still	ADV
m-1112	1153	7	-	-	PUNCT
m-1112	1153	8	spaces	space	NOUN
m-1112	1153	9	in	in	ADP
m-1112	1153	10	tetrahedron	tetrahedron	NOUN
m-1112	1153	11	sides	side	NOUN
m-1112	1153	12	which	which	DET
m-1112	1153	13	withdrawn	withdraw	VERB
m-1112	1153	14	loads	load	NOUN
m-1112	1153	15	are	be	AUX
m-1112	1153	16	displaced	displace	VERB
m-1112	1153	17	on	on	ADP
m-1112	1153	18	the	the	DET
m-1112	1153	19	anti	anti	ADJ
m-1112	1153	20	-	-	ADJ
m-1112	1153	21	parallel	parallel	ADJ
m-1112	1153	22	-	-	PUNCT
m-1112	1153	23	strand	strand	NOUN
m-1112	1153	24	.	.	PUNCT
m-1112	1154	1	if	if	SCONJ
m-1112	1154	2	the	the	DET
m-1112	1154	3	unloading	unloading	NOUN
m-1112	1154	4	is	be	AUX
m-1112	1154	5	abrupt	abrupt	ADJ
m-1112	1154	6	,	,	PUNCT
m-1112	1154	7	then	then	ADV
m-1112	1154	8	kinetic	kinetic	ADJ
m-1112	1154	9	energy	energy	NOUN
m-1112	1154	10	of	of	ADP
m-1112	1154	11	1	1	NUM
m-1112	1154	12	-	-	PUNCT
m-1112	1154	13	strand	strand	NOUN
m-1112	1154	14	is	be	AUX
m-1112	1154	15	converted	convert	VERB
m-1112	1154	16	in	in	ADP
m-1112	1154	17	the	the	DET
m-1112	1154	18	2	2	NUM
m-1112	1154	19	-	-	PUNCT
m-1112	1154	20	strand	strand	NOUN
m-1112	1154	21	as	as	ADP
m-1112	1154	22	potential	potential	ADJ
m-1112	1154	23	and	and	CCONJ
m-1112	1154	24	so	so	ADV
m-1112	1154	25	on	on	ADV
m-1112	1154	26	.	.	PUNCT
m-1112	1155	1	that	that	ADV
m-1112	1155	2	is	is	ADV
m-1112	1155	3	,	,	PUNCT
m-1112	1155	4	cubes	cube	NOUN
m-1112	1155	5	perform	perform	VERB
m-1112	1155	6	an	an	DET
m-1112	1155	7	oscillating	oscillating	NOUN
m-1112	1155	8	motion	motion	NOUN
m-1112	1155	9	until	until	SCONJ
m-1112	1155	10	the	the	DET
m-1112	1155	11	mechanical	mechanical	ADJ
m-1112	1155	12	energy	energy	NOUN
m-1112	1155	13	is	be	AUX
m-1112	1155	14	extinguished	extinguish	VERB
m-1112	1155	15	to	to	ADP
m-1112	1155	16	their	their	PRON
m-1112	1155	17	vertices	vertex	NOUN
m-1112	1155	18	,	,	PUNCT
m-1112	1155	19	which	which	PRON
m-1112	1155	20	are	be	AUX
m-1112	1155	21	the	the	DET
m-1112	1155	22	stores	store	NOUN
m-1112	1155	23	of	of	ADP
m-1112	1155	24	information	information	NOUN
m-1112	1155	25	.	.	PUNCT
m-1112	1156	1	anti	anti	ADJ
m-1112	1156	2	-	-	ADJ
m-1112	1156	3	parallel	parallel	ADJ
m-1112	1156	4	-	-	PUNCT
m-1112	1156	5	strand	strand	NOUN
m-1112	1156	6	is	be	AUX
m-1112	1156	7	the	the	DET
m-1112	1156	8	body	body	NOUN
m-1112	1156	9	containing	contain	VERB
m-1112	1156	10	the	the	DET
m-1112	1156	11	potential	potential	ADJ
m-1112	1156	12	energy	energy	NOUN
m-1112	1156	13	,	,	PUNCT
m-1112	1156	14	during	during	ADP
m-1112	1156	15	any	any	DET
m-1112	1156	16	unloading	unloading	NOUN
m-1112	1156	17	on	on	ADP
m-1112	1156	18	cubes	cube	NOUN
m-1112	1156	19	,	,	PUNCT
m-1112	1156	20	it	it	PRON
m-1112	1156	21	gives	give	VERB
m-1112	1156	22	off	off	ADP
m-1112	1156	23	mechanical	mechanical	ADJ
m-1112	1156	24	-	-	PUNCT
m-1112	1156	25	work	work	NOUN
m-1112	1156	26	,	,	PUNCT
m-1112	1156	27	since	since	SCONJ
m-1112	1156	28	the	the	DET
m-1112	1156	29	points	point	NOUN
m-1112	1156	30	of	of	ADP
m-1112	1156	31	application	application	NOUN
m-1112	1156	32	of	of	ADP
m-1112	1156	33	the	the	DET
m-1112	1156	34	gradually	gradually	ADV
m-1112	1156	35	withdrawn	withdraw	VERB
m-1112	1156	36	loads	load	NOUN
m-1112	1156	37	are	be	AUX
m-1112	1156	38	displaced	displace	VERB
m-1112	1156	39	.	.	PUNCT
m-1112	1157	1	the	the	DET
m-1112	1157	2	stability	stability	NOUN
m-1112	1157	3	of	of	ADP
m-1112	1157	4	kinetic	kinetic	ADJ
m-1112	1157	5	–	–	PUNCT
m-1112	1157	6	potential	potential	ADJ
m-1112	1157	7	energy	energy	NOUN
m-1112	1157	8	is	be	AUX
m-1112	1157	9	continues	continue	VERB
m-1112	1157	10	.	.	PUNCT
m-1112	1158	1	ijo	ijo	PROPN
m-1112	1158	2	international	international	PROPN
m-1112	1158	3	journal	journal	PROPN
m-1112	1158	4	of	of	ADP
m-1112	1158	5	mathematics	mathematics	PROPN
m-1112	1158	6	(	(	PUNCT
m-1112	1158	7	issn	issn	PROPN
m-1112	1158	8	:	:	PUNCT
m-1112	1158	9	2992	2992	NUM
m-1112	1158	10	-	-	SYM
m-1112	1158	11	4421	4421	NUM
m-1112	1158	12	)	)	PUNCT
m-1112	1158	13	volume	volume	NOUN
m-1112	1158	14	08	08	NUM
m-1112	1159	1	|	|	ADV
m-1112	1159	2	issue	issue	NOUN
m-1112	1159	3	08	08	NUM
m-1112	1160	1	|	|	ADV
m-1112	1160	2	august	august	PROPN
m-1112	1160	3	2025	2025	NUM
m-1112	1160	4	|	|	ADV
m-1112	1160	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1160	6	ijo	ijo	PROPN
m-1112	1160	7	journals	journal	NOUN
m-1112	1160	8	43	43	NUM
m-1112	1160	9	the	the	DET
m-1112	1160	10	fundamental	fundamental	ADJ
m-1112	1160	11	particles	particle	NOUN
m-1112	1160	12	origination	origination	NOUN
m-1112	1160	13	mechanism	mechanism	NOUN
m-1112	1160	14	in	in	ADP
m-1112	1160	15	mfmf	mfmf	PROPN
m-1112	1160	16	pns	pns	PROPN
m-1112	1160	17	caves	cave	NOUN
m-1112	1160	18	.	.	PUNCT
m-1112	1161	1	figure	figure	NOUN
m-1112	1161	2	–	–	PUNCT
m-1112	1161	3	10the	10the	DET
m-1112	1161	4	hydrogen	hydrogen	NOUN
m-1112	1161	5	bracket	bracket	NOUN
m-1112	1161	6	–	–	PUNCT
m-1112	1161	7	hook	hook	NOUN
m-1112	1161	8	of	of	ADP
m-1112	1161	9	2	2	NUM
m-1112	1161	10	=	=	SYM
m-1112	1161	11	orbitals	orbital	NOUN
m-1112	1161	12			NOUN
m-1112	1161	13	[	[	PUNCT
m-1112	1161	14	(	(	PUNCT
m-1112	1161	15	+	+	NOUN
m-1112	1161	16	)	)	PUNCT
m-1112	1162	1	[	[	X
m-1112	1162	2	↔	↔	X
m-1112	1162	3	]	]	X
m-1112	1162	4	(	(	PUNCT
m-1112	1162	5	-	-	INTJ
m-1112	1162	6	)	)	PUNCT
m-1112	1162	7	]	]	PUNCT
m-1112	1162	8	stationary	stationary	ADJ
m-1112	1162	9	-	-	PUNCT
m-1112	1162	10	state	state	NOUN
m-1112	1162	11	happens	happen	VERB
m-1112	1162	12	as	as	ADP
m-1112	1162	13	→	→	SYM
m-1112	1162	14	[	[	X
m-1112	1162	15	⊝	⊝	X
m-1112	1162	16	]	]	X
m-1112	1162	17	≡	≡	PROPN
m-1112	1162	18	orbit-1	orbit-1	PROPN
m-1112	1162	19	↔	↔	PROPN
m-1112	1162	20	[	[	X
m-1112	1162	21	⊕	⊕	X
m-1112	1162	22	]	]	X
m-1112	1162	23	≡	≡	PROPN
m-1112	1162	24	orbit-2	orbit-2	PRON
m-1112	1162	25	←	←	PROPN
m-1112	1162	26	8	8	NUM
m-1112	1162	27	..	..	PUNCT
m-1112	1162	28	[d	[d	X
m-1112	1162	29	]	]	X
m-1112	1162	30	..	..	PUNCT
m-1112	1162	31	the	the	DET
m-1112	1162	32	{	{	PUNCT
m-1112	1162	33	tobh	tobh	NOUN
m-1112	1162	34	}	}	PUNCT
m-1112	1162	35	mechanisms	mechanism	VERB
m-1112	1162	36	atoms	atom	NOUN
m-1112	1162	37	bonding	bond	VERB
m-1112	1162	38	bracket	bracket	NOUN
m-1112	1162	39	hook	hook	NOUN
m-1112	1162	40	mechanism	mechanism	NOUN
m-1112	1162	41	.	.	PUNCT
m-1112	1163	1	d-1	d-1	PROPN
m-1112	1163	2	..	..	PUNCT
m-1112	1163	3	:	:	PUNCT
m-1112	1163	4	the	the	DET
m-1112	1163	5	precession	precession	NOUN
m-1112	1163	6	and	and	CCONJ
m-1112	1163	7	nutation	nutation	NOUN
m-1112	1163	8	of	of	ADP
m-1112	1163	9	electron	electron	NOUN
m-1112	1163	10	:	:	PUNCT
m-1112	1163	11	gravitational	gravitational	ADJ
m-1112	1163	12	constant	constant	ADJ
m-1112	1163	13	g	g	NOUN
m-1112	1163	14	,	,	PUNCT
m-1112	1163	15	is	be	AUX
m-1112	1163	16	the	the	DET
m-1112	1163	17	pulling	pulling	NOUN
m-1112	1163	18	and	and	CCONJ
m-1112	1163	19	the	the	DET
m-1112	1163	20	cohesive	cohesive	ADJ
m-1112	1163	21	force	force	NOUN
m-1112	1163	22	on	on	ADP
m-1112	1163	23	all	all	DET
m-1112	1163	24	the	the	DET
m-1112	1163	25	quantized	quantize	VERB
m-1112	1163	26	energy	energy	NOUN
m-1112	1163	27	structures	structure	NOUN
m-1112	1163	28	which	which	PRON
m-1112	1163	29	communicates	communicate	VERB
m-1112	1163	30	with	with	ADP
m-1112	1163	31	everything	everything	PRON
m-1112	1163	32	due	due	ADJ
m-1112	1163	33	to	to	ADP
m-1112	1163	34	the	the	DET
m-1112	1163	35	periodic	periodic	ADJ
m-1112	1163	36	excitation	excitation	NOUN
m-1112	1163	37	on	on	ADP
m-1112	1163	38	all	all	DET
m-1112	1163	39	spaces.[84	spaces.[84	NOUN
m-1112	1163	40	]	]	PUNCT
m-1112	1163	41	the	the	DET
m-1112	1163	42	newton`s	newton`s	NOUN
m-1112	1163	43	laws	law	NOUN
m-1112	1163	44	issues	issue	NOUN
m-1112	1163	45	for	for	ADP
m-1112	1163	46	the	the	DET
m-1112	1163	47	masses	masse	NOUN
m-1112	1163	48	and	and	CCONJ
m-1112	1163	49	also	also	ADV
m-1112	1163	50	the	the	DET
m-1112	1163	51	same	same	ADJ
m-1112	1163	52	to	to	ADP
m-1112	1163	53	electrons	electron	NOUN
m-1112	1163	54	in	in	ADP
m-1112	1163	55	caves	cave	NOUN
m-1112	1163	56	as	as	ADP
m-1112	1163	57	below	below	ADV
m-1112	1163	58	,	,	PUNCT
m-1112	1163	59	g	g	PROPN
m-1112	1163	60	≡	≡	PROPN
m-1112	1163	61	g.ke	g.ke	PROPN
m-1112	1163	62	≡	≡	PROPN
m-1112	1163	63	g	g	PROPN
m-1112	1164	1	.[gl	.[gl	PROPN
m-1112	1164	2	kl	kl	X
m-1112	1164	3	]	]	PUNCT
m-1112	1165	1	≡	≡	PROPN
m-1112	1165	2	[	[	PUNCT
m-1112	1165	3	t²p	t²p	X
m-1112	1165	4	𝐚³	𝐚³	ADJ
m-1112	1165	5	]	]	PUNCT
m-1112	1165	6	.[gl	.[gl	PUNCT
m-1112	1165	7	kl	kl	X
m-1112	1165	8	]	]	PUNCT
m-1112	1165	9	≡	≡	PROPN
m-1112	1165	10	9,8078925	9,8078925	PROPN
m-1112	1165	11	*	*	SYM
m-1112	1165	12	6,8116.10−12	6,8116.10−12	NUM
m-1112	1165	13	≡	≡	PROPN
m-1112	1165	14	6,68056.10−11	6,68056.10−11	NUM
m-1112	1165	15	𝐦³	𝐦³	PROPN
m-1112	1165	16	𝐍𝐬²	𝐍𝐬²	VERB
m-1112	1165	17	the	the	DET
m-1112	1165	18	electron	electron	NOUN
m-1112	1165	19	being	be	AUX
m-1112	1165	20	in	in	ADP
m-1112	1165	21	hydrogen	hydrogen	NOUN
m-1112	1165	22	-	-	PUNCT
m-1112	1165	23	cave	cave	NOUN
m-1112	1165	24	precesses	precesse	NOUN
m-1112	1165	25	because	because	SCONJ
m-1112	1165	26	of	of	ADP
m-1112	1165	27	the	the	DET
m-1112	1165	28	different	different	ADJ
m-1112	1165	29	axis	axis	NOUN
m-1112	1165	30	of	of	ADP
m-1112	1165	31	rotation	rotation	NOUN
m-1112	1165	32	and	and	CCONJ
m-1112	1165	33	nutation`s	nutation`s	ADP
m-1112	1165	34	,	,	PUNCT
m-1112	1165	35	from	from	ADP
m-1112	1165	36	the	the	DET
m-1112	1165	37	continuous	continuous	ADJ
m-1112	1165	38	and	and	CCONJ
m-1112	1165	39	immense	immense	ADJ
m-1112	1165	40	-	-	PUNCT
m-1112	1165	41	communication	communication	NOUN
m-1112	1165	42	to	to	ADP
m-1112	1165	43	the	the	DET
m-1112	1165	44	gravity	gravity	NOUN
m-1112	1165	45	,	,	PUNCT
m-1112	1165	46	g	g	PROPN
m-1112	1165	47	.	.	PUNCT
m-1112	1165	48	electron	electron	NOUN
m-1112	1165	49	-	-	PUNCT
m-1112	1165	50	spin	spin	NOUN
m-1112	1165	51	is	be	AUX
m-1112	1165	52	the	the	DET
m-1112	1165	53	angular	angular	ADJ
m-1112	1165	54	-	-	PUNCT
m-1112	1165	55	momentum	momentum	NOUN
m-1112	1165	56	-	-	PUNCT
m-1112	1165	57	vector	vector	NOUN
m-1112	1165	58	b̅	b̅	NOUN
m-1112	1165	59	and	and	CCONJ
m-1112	1165	60	rotates	rotate	NOUN
m-1112	1165	61	according	accord	VERB
m-1112	1165	62	to	to	ADP
m-1112	1165	63	equation	equation	NOUN
m-1112	1165	64	db	db	NOUN
m-1112	1165	65	dt	dt	NOUN
m-1112	1166	1	=	=	PUNCT
m-1112	1167	1	[	[	X
m-1112	1167	2	u̅b̅	u̅b̅	X
m-1112	1167	3	]	]	X
m-1112	1167	4	=	=	SYM
m-1112	1167	5	u	u	NOUN
m-1112	1167	6	b.[k̅k̅	b.[k̅k̅	NOUN
m-1112	1167	7	`	`	PUNCT
m-1112	1167	8	]	]	PUNCT
m-1112	1167	9	in	in	ADP
m-1112	1167	10	gravitational	gravitational	ADJ
m-1112	1167	11	potential	potential	NOUN
m-1112	1167	12	ug	ug	ADP
m-1112	1167	13	=	=	X
m-1112	1167	14	[	[	PUNCT
m-1112	1167	15	mg	mg	PROPN
m-1112	1167	16	]	]	PUNCT
m-1112	1167	17	.s.cos	.s.cos	PUNCT
m-1112	1168	1	θ	θ	X
m-1112	1168	2	=	=	PUNCT
m-1112	1168	3	s	s	X
m-1112	1168	4	q	q	X
m-1112	1168	5	.	.	PUNCT
m-1112	1169	1	[	[	X
m-1112	1169	2	k̅k̅	k̅k̅	X
m-1112	1169	3	`	`	PUNCT
m-1112	1169	4	]	]	PUNCT
m-1112	1169	5	so	so	CCONJ
m-1112	1169	6	the	the	DET
m-1112	1169	7	change	change	NOUN
m-1112	1169	8	of	of	ADP
m-1112	1169	9	angular	angular	ADJ
m-1112	1169	10	momentum	momentum	NOUN
m-1112	1169	11	b̅	b̅	NOUN
m-1112	1169	12	is	be	AUX
m-1112	1169	13	→	→	SYM
m-1112	1169	14	db	db	ADJ
m-1112	1169	15	dt	dt	NOUN
m-1112	1169	16	=	=	SYM
m-1112	1169	17	u	u	PROPN
m-1112	1169	18	=	=	PROPN
m-1112	1169	19	s.q	s.q	PROPN
m-1112	1169	20	b	b	PROPN
m-1112	1169	21	=	=	PROPN
m-1112	1169	22	s.q	s.q	PROPN
m-1112	1169	23	j3.w3	j3.w3	PROPN
m-1112	1169	24	.	.	PUNCT
m-1112	1170	1	←	←	PROPN
m-1112	1170	2	and	and	CCONJ
m-1112	1170	3	from	from	ADP
m-1112	1170	4	the	the	DET
m-1112	1170	5	1	1	NUM
m-1112	1170	6	-	-	PUNCT
m-1112	1170	7	degree	degree	NOUN
m-1112	1170	8	equation	equation	NOUN
m-1112	1170	9	of	of	ADP
m-1112	1170	10	motion	motion	NOUN
m-1112	1170	11	u	u	PROPN
m-1112	1170	12	,	,	PUNCT
m-1112	1170	13	become	become	VERB
m-1112	1170	14	�	�	NOUN
m-1112	1170	15	̈	̈	X
m-1112	1170	16	�	�	NOUN
m-1112	1170	17	+	+	CCONJ
m-1112	1170	18	w	w	PROPN
m-1112	1170	19	²	²	NUM
m-1112	1170	20	u	u	NOUN
m-1112	1170	21	=	=	NOUN
m-1112	1170	22	0	0	NUM
m-1112	1170	23	,	,	PUNCT
m-1112	1170	24	with	with	ADP
m-1112	1170	25	solution	solution	NOUN
m-1112	1170	26	a	a	DET
m-1112	1170	27	period	period	NOUN
m-1112	1170	28	of	of	ADP
m-1112	1170	29	nutation	nutation	NOUN
m-1112	1170	30	t	t	NOUN
m-1112	1170	31	=	=	PUNCT
m-1112	1170	32	2π	2π	NUM
m-1112	1170	33	u	u	NOUN
m-1112	1170	34	=	=	X
m-1112	1170	35	2π.j3w	2π.j3w	NUM
m-1112	1170	36	sq	sq	PROPN
m-1112	1170	37	,	,	PUNCT
m-1112	1170	38	and	and	CCONJ
m-1112	1170	39	its	its	PRON
m-1112	1170	40	natural	natural	ADJ
m-1112	1170	41	frequency	frequency	NOUN
m-1112	1170	42	f	f	PROPN
m-1112	1170	43	n	n	NOUN
m-1112	1170	44	=	=	SYM
m-1112	1170	45	sq	sq	PROPN
m-1112	1170	46	2π.j3w	2π.j3w	NOUN
m-1112	1170	47	…	…	PUNCT
m-1112	1170	48	.(1	.(1	NUM
m-1112	1170	49	)	)	PUNCT
m-1112	1170	50	with	with	ADP
m-1112	1170	51	total	total	ADJ
m-1112	1170	52	energy	energy	NOUN
m-1112	1170	53	of	of	ADP
m-1112	1170	54	nutation	nutation	NOUN
m-1112	1170	55	e	e	NOUN
m-1112	1170	56	n	n	NOUN
m-1112	1170	57	=	=	SYM
m-1112	1170	58	j1	j1	PROPN
m-1112	1170	59	2	2	NUM
m-1112	1170	60	[	[	X
m-1112	1170	61	w1²	w1²	NOUN
m-1112	1170	62	+	+	CCONJ
m-1112	1170	63	w2²	w2²	NOUN
m-1112	1170	64	]	]	X
m-1112	1171	1	+	+	CCONJ
m-1112	1171	2	j3	j3	PROPN
m-1112	1171	3	2	2	NUM
m-1112	1171	4	w3²	w3²	ADV
m-1112	1171	5	…	…	PUNCT
m-1112	1171	6	.(2	.(2	PUNCT
m-1112	1171	7	)	)	PUNCT
m-1112	1172	1	[	[	X
m-1112	1172	2	70	70	NUM
m-1112	1172	3	]	]	PUNCT
m-1112	1172	4	.	.	PUNCT
m-1112	1173	1	for	for	ADP
m-1112	1173	2	material	material	NOUN
m-1112	1173	3	-	-	PUNCT
m-1112	1173	4	points	point	NOUN
m-1112	1173	5	,	,	PUNCT
m-1112	1173	6	the	the	DET
m-1112	1173	7	chains	chain	NOUN
m-1112	1173	8	of	of	ADP
m-1112	1173	9	spins	spin	NOUN
m-1112	1173	10	due	due	ADP
m-1112	1173	11	to	to	ADP
m-1112	1173	12	periodic	periodic	ADJ
m-1112	1173	13	excitation	excitation	NOUN
m-1112	1173	14	[	[	X
m-1112	1173	15	↔	↔	X
m-1112	1173	16	]	]	PUNCT
m-1112	1173	17	is	be	AUX
m-1112	1173	18	created	create	VERB
m-1112	1173	19	in	in	ADP
m-1112	1173	20	orbit	orbit	NOUN
m-1112	1173	21	a	a	DET
m-1112	1173	22	magnetic	magnetic	ADJ
m-1112	1173	23	field	field	NOUN
m-1112	1173	24	due	due	ADP
m-1112	1173	25	to	to	ADP
m-1112	1173	26	lrc	lrc	PROPN
m-1112	1173	27	-	-	PUNCT
m-1112	1173	28	circuit	circuit	PROPN
m-1112	1173	29	and	and	CCONJ
m-1112	1173	30	which	which	PRON
m-1112	1173	31	is	be	AUX
m-1112	1173	32	tuning	tune	VERB
m-1112	1173	33	to	to	ADP
m-1112	1173	34	the	the	DET
m-1112	1173	35	critical	critical	ADJ
m-1112	1173	36	quantum	quantum	ADJ
m-1112	1173	37	critical	critical	ADJ
m-1112	1173	38	-	-	PUNCT
m-1112	1173	39	state	state	NOUN
m-1112	1173	40	𝐠𝐆	𝐠𝐆	NOUN
m-1112	1173	41	.	.	PUNCT
m-1112	1174	1	the	the	DET
m-1112	1174	2	light	light	ADJ
m-1112	1174	3	velocity	velocity	NOUN
m-1112	1174	4	vector	vector	NOUN
m-1112	1174	5	�	�	PROPN
m-1112	1174	6	̅	̅	NOUN
m-1112	1174	7	�	�	PROPN
m-1112	1174	8	=	=	SYM
m-1112	1174	9	�	�	PROPN
m-1112	1174	10	̅	̅	NOUN
m-1112	1174	11	�	�	PROPN
m-1112	1174	12	,	,	PUNCT
m-1112	1174	13	by	by	ADP
m-1112	1174	14	acting	act	VERB
m-1112	1174	15	on	on	ADP
m-1112	1174	16	cave	cave	NOUN
m-1112	1174	17	,	,	PUNCT
m-1112	1174	18	r	r	NOUN
m-1112	1174	19	=	=	SYM
m-1112	1174	20	𝐋	𝐋	PROPN
m-1112	1174	21	𝐏	𝐏	PROPN
m-1112	1174	22	,	,	PUNCT
m-1112	1174	23	finds	find	VERB
m-1112	1174	24	the	the	DET
m-1112	1174	25	impedance	impedance	NOUN
m-1112	1174	26	m	m	VERB
m-1112	1174	27	g	g	NOUN
m-1112	1174	28	,	,	PUNCT
m-1112	1174	29	and	and	CCONJ
m-1112	1174	30	becomes	become	VERB
m-1112	1174	31	the	the	DET
m-1112	1174	32	centrifugal	centrifugal	ADJ
m-1112	1174	33	-	-	PUNCT
m-1112	1174	34	force	force	NOUN
m-1112	1174	35	𝐅𝐠	𝐅𝐠	PROPN
m-1112	1174	36	of	of	ADP
m-1112	1174	37	cave	cave	NOUN
m-1112	1174	38	equal	equal	ADJ
m-1112	1174	39	to	to	ADP
m-1112	1174	40	gravity	gravity	NOUN
m-1112	1174	41	g	g	NOUN
m-1112	1174	42	.	.	PUNCT
m-1112	1175	1	the	the	DET
m-1112	1175	2	chains	chain	NOUN
m-1112	1175	3	of	of	ADP
m-1112	1175	4	spins	spin	NOUN
m-1112	1175	5	for	for	ADP
m-1112	1175	6	the	the	DET
m-1112	1175	7	,	,	PUNCT
m-1112	1175	8	one	one	NUM
m-1112	1175	9	-	-	PUNCT
m-1112	1175	10	way	way	NOUN
m-1112	1175	11	pointy	pointy	NOUN
m-1112	1175	12	vibrating	vibrating	NOUN
m-1112	1175	13	,	,	PUNCT
m-1112	1175	14	is	be	AUX
m-1112	1175	15	the	the	DET
m-1112	1175	16	resonance	resonance	NOUN
m-1112	1175	17	–	–	PUNCT
m-1112	1175	18	frequency	frequency	NOUN
m-1112	1175	19	fr	fr	NOUN
m-1112	1175	20	=	=	PUNCT
m-1112	1175	21	(	(	PUNCT
m-1112	1175	22	1	1	NUM
m-1112	1175	23	+	+	NUM
m-1112	1175	24	√5	√5	NOUN
m-1112	1175	25	]	]	PUNCT
m-1112	1175	26	)	)	PUNCT
m-1112	1175	27	.σ	.σ	PROPN
m-1112	1176	1	4πr	4πr	NOUN
m-1112	1177	1	=	=	PUNCT
m-1112	1177	2	σ	σ	PROPN
m-1112	1177	3	𝛷	𝛷	PROPN
m-1112	1177	4	2πr	2πr	NOUN
m-1112	1177	5	of	of	ADP
m-1112	1177	6	vectors	vector	NOUN
m-1112	1177	7	v̅	v̅	PROPN
m-1112	1177	8	and	and	CCONJ
m-1112	1177	9	b̅	b̅	PROPN
m-1112	1177	10	,	,	PUNCT
m-1112	1177	11	of	of	ADP
m-1112	1177	12	the	the	DET
m-1112	1177	13	-	-	PUNCT
m-1112	1177	14	stationary	stationary	ADJ
m-1112	1177	15	-	-	PUNCT
m-1112	1177	16	photon	photon	NOUN
m-1112	1177	17	-	-	PUNCT
m-1112	1177	18	cave	cave	NOUN
m-1112	1177	19	,	,	PUNCT
m-1112	1177	20	where	where	SCONJ
m-1112	1177	21	b̅	b̅	PROPN
m-1112	1177	22	≡	≡	PROPN
m-1112	1177	23	s̅	s̅	PUNCT
m-1112	1177	24	≡	≡	PROPN
m-1112	1177	25	spin	spin	NOUN
m-1112	1177	26	,	,	PUNCT
m-1112	1177	27	i.e.	i.e.	X
m-1112	1177	28	the	the	DET
m-1112	1177	29	fr	fr	NOUN
m-1112	1177	30	is	be	AUX
m-1112	1177	31	common	common	ADJ
m-1112	1177	32	to	to	ADP
m-1112	1177	33	both	both	PRON
m-1112	1177	34	.	.	PUNCT
m-1112	1178	1	the	the	DET
m-1112	1178	2	moving	move	VERB
m-1112	1178	3	electron	electron	NOUN
m-1112	1178	4	in	in	ADP
m-1112	1178	5	orbit	orbit	NOUN
m-1112	1178	6	of	of	ADP
m-1112	1178	7	charge	charge	NOUN
m-1112	1178	8	�	�	PROPN
m-1112	1178	9	̅	̅	NOUN
m-1112	1178	10	�	�	PROPN
m-1112	1178	11	≡	≡	PROPN
m-1112	1178	12	⊝	⊝	NUM
m-1112	1178	13	,	,	PUNCT
m-1112	1178	14	energy	energy	NOUN
m-1112	1178	15	e	e	NOUN
m-1112	1178	16	with	with	ADP
m-1112	1178	17	the	the	DET
m-1112	1178	18	orbit	orbit	NOUN
m-1112	1178	19	-velocity	-velocity	PROPN
m-1112	1178	20	vector	vector	NOUN
m-1112	1178	21	�	�	PROPN
m-1112	1178	22	̅	̅	NOUN
m-1112	1178	23	�	�	NOUN
m-1112	1178	24	=	=	NOUN
m-1112	1178	25	√	√	ADP
m-1112	1178	26	2	2	NUM
m-1112	1178	27	𝑚	𝑚	NOUN
m-1112	1178	28	[	[	X
m-1112	1178	29	e	e	X
m-1112	1178	30	−	−	PROPN
m-1112	1178	31	{	{	PUNCT
m-1112	1178	32	𝐤	𝐤	X
m-1112	1178	33	𝐫	𝐫	PROPN
m-1112	1178	34	+	+	CCONJ
m-1112	1178	35	𝐋	𝐋	PROPN
m-1112	1178	36	𝟐	𝟐	NUM
m-1112	1178	37	𝟐𝒎	𝟐𝒎	NOUN
m-1112	1178	38	𝒓𝟐	𝒓𝟐	PROPN
m-1112	1178	39	}	}	PUNCT
m-1112	1178	40	]	]	PUNCT
m-1112	1178	41	which	which	PRON
m-1112	1178	42	creates	create	VERB
m-1112	1178	43	in	in	ADP
m-1112	1178	44	orbit	orbit	NOUN
m-1112	1178	45	,	,	PUNCT
m-1112	1178	46	r	r	NOUN
m-1112	1178	47	,	,	PUNCT
m-1112	1178	48	the	the	DET
m-1112	1178	49	varying	vary	VERB
m-1112	1178	50	and	and	CCONJ
m-1112	1178	51	perpendicular	perpendicular	ADJ
m-1112	1178	52	magnetic	magnetic	ADJ
m-1112	1178	53	ijo	ijo	PROPN
m-1112	1178	54	international	international	PROPN
m-1112	1178	55	journal	journal	PROPN
m-1112	1178	56	of	of	ADP
m-1112	1178	57	mathematics	mathematics	PROPN
m-1112	1178	58	(	(	PUNCT
m-1112	1178	59	issn	issn	PROPN
m-1112	1178	60	:	:	PUNCT
m-1112	1178	61	2992	2992	NUM
m-1112	1178	62	-	-	SYM
m-1112	1178	63	4421	4421	NUM
m-1112	1178	64	)	)	PUNCT
m-1112	1178	65	volume	volume	NOUN
m-1112	1178	66	08	08	NUM
m-1112	1179	1	|	|	ADV
m-1112	1179	2	issue	issue	NOUN
m-1112	1179	3	08	08	NUM
m-1112	1180	1	|	|	ADV
m-1112	1180	2	august	august	PROPN
m-1112	1180	3	2025	2025	NUM
m-1112	1180	4	|	|	ADV
m-1112	1180	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1180	6	ijo	ijo	PROPN
m-1112	1180	7	journals	journal	NOUN
m-1112	1180	8	44	44	NUM
m-1112	1180	9	the	the	DET
m-1112	1180	10	fundamental	fundamental	ADJ
m-1112	1180	11	particles	particle	NOUN
m-1112	1180	12	origination	origination	NOUN
m-1112	1180	13	mechanism	mechanism	NOUN
m-1112	1180	14	in	in	ADP
m-1112	1180	15	mfmf	mfmf	PROPN
m-1112	1180	16	pns	pns	PROPN
m-1112	1180	17	caves	cave	NOUN
m-1112	1180	18	.	.	PUNCT
m-1112	1181	1	field	field	NOUN
m-1112	1181	2	�	�	PROPN
m-1112	1181	3	̅	̅	NOUN
m-1112	1181	4	�	�	PROPN
m-1112	1181	5	,	,	PUNCT
m-1112	1181	6	which	which	PRON
m-1112	1181	7	in	in	ADP
m-1112	1181	8	time	time	NOUN
m-1112	1181	9	-	-	PUNCT
m-1112	1181	10	turn	turn	NOUN
m-1112	1181	11	creates	create	VERB
m-1112	1181	12	an	an	DET
m-1112	1181	13	electric	electric	ADJ
m-1112	1181	14	-	-	PUNCT
m-1112	1181	15	field	field	NOUN
m-1112	1181	16	�	�	NOUN
m-1112	1181	17	̅	̅	NOUN
m-1112	1181	18	�	�	PROPN
m-1112	1181	19	⊥	⊥	NUM
m-1112	1181	20	�	�	PROPN
m-1112	1181	21	̅	̅	NOUN
m-1112	1181	22	�	�	PROPN
m-1112	1181	23	,	,	PUNCT
m-1112	1181	24	with	with	ADP
m-1112	1181	25	the	the	DET
m-1112	1181	26	resultant	resultant	NOUN
m-1112	1181	27	force	force	NOUN
m-1112	1181	28	f	f	PROPN
m-1112	1181	29	acting	act	VERB
m-1112	1181	30	on	on	ADP
m-1112	1181	31	electron	electron	NOUN
m-1112	1181	32	velocity	velocity	NOUN
m-1112	1181	33	�	�	NOUN
m-1112	1181	34	̅	̅	NOUN
m-1112	1181	35	�	�	PROPN
m-1112	1181	36	and	and	CCONJ
m-1112	1181	37	which	which	PRON
m-1112	1181	38	is	be	AUX
m-1112	1181	39	composed	compose	VERB
m-1112	1181	40	of	of	ADP
m-1112	1181	41	the	the	DET
m-1112	1181	42	𝐕𝐩	𝐕𝐩	PROPN
m-1112	1181	43	,	,	PUNCT
m-1112	1181	44	perpendicular	perpendicular	ADJ
m-1112	1181	45	to	to	ADP
m-1112	1181	46	the	the	DET
m-1112	1181	47	magnetic	magnetic	ADJ
m-1112	1181	48	-	-	PUNCT
m-1112	1181	49	circles	circle	NOUN
m-1112	1181	50	o	o	NOUN
m-1112	1181	51	⊥	⊥	PROPN
m-1112	1181	52	b	b	PROPN
m-1112	1181	53	,	,	PUNCT
m-1112	1181	54	and	and	CCONJ
m-1112	1181	55	𝐕	𝐕	PROPN
m-1112	1181	56	𝐯	𝐯	NOUN
m-1112	1181	57	,	,	PUNCT
m-1112	1181	58	parallel	parallel	ADJ
m-1112	1181	59	to	to	ADP
m-1112	1181	60	the	the	DET
m-1112	1181	61	magnetic	magnetic	ADJ
m-1112	1181	62	-	-	PUNCT
m-1112	1181	63	field	field	NOUN
m-1112	1181	64	-	-	PUNCT
m-1112	1181	65	vector	vector	NOUN
m-1112	1181	66	|	|	NOUN
m-1112	1181	67	�	�	NOUN
m-1112	1181	68	̅	̅	NOUN
m-1112	1181	69	�	�	NOUN
m-1112	1181	70	|	|	NOUN
m-1112	1181	71	,	,	PUNCT
m-1112	1181	72	is	be	AUX
m-1112	1181	73	tending	tend	VERB
m-1112	1181	74	in	in	ADP
m-1112	1181	75	such	such	ADJ
m-1112	1181	76	way	way	NOUN
m-1112	1181	77	that	that	PRON
m-1112	1181	78	l	l	PROPN
m-1112	1181	79	≡	≡	PROPN
m-1112	1181	80	s	s	PART
m-1112	1181	81	≡	≡	PROPN
m-1112	1181	82	spin	spin	NOUN
m-1112	1181	83	.	.	PUNCT
m-1112	1182	1	the	the	DET
m-1112	1182	2	resulting	result	VERB
m-1112	1182	3	motion	motion	NOUN
m-1112	1182	4	of	of	ADP
m-1112	1182	5	electron	electron	NOUN
m-1112	1182	6	in	in	ADP
m-1112	1182	7	trajectory	trajectory	NOUN
m-1112	1182	8	is	be	AUX
m-1112	1182	9	the	the	DET
m-1112	1182	10	helical	helical	ADJ
m-1112	1182	11	motion	motion	NOUN
m-1112	1182	12	and	and	CCONJ
m-1112	1182	13	work	work	NOUN
m-1112	1182	14	produced	produce	VERB
m-1112	1182	15	during	during	ADP
m-1112	1182	16	this	this	DET
m-1112	1182	17	motion	motion	NOUN
m-1112	1182	18	.	.	PUNCT
m-1112	1183	1	the	the	DET
m-1112	1183	2	conservation	conservation	NOUN
m-1112	1183	3	of	of	ADP
m-1112	1183	4	energy	energy	NOUN
m-1112	1183	5	exist	exist	VERB
m-1112	1183	6	in	in	ADP
m-1112	1183	7	orbit	orbit	NOUN
m-1112	1183	8	between	between	ADP
m-1112	1183	9	protons	proton	NOUN
m-1112	1183	10	and	and	CCONJ
m-1112	1183	11	electrons	electron	NOUN
m-1112	1183	12	[	[	X
m-1112	1183	13	p↔	p↔	NOUN
m-1112	1183	14	e	e	NOUN
m-1112	1183	15	]	]	X
m-1112	1183	16	therefore	therefore	ADV
m-1112	1183	17	energy	energy	NOUN
m-1112	1183	18	as	as	ADP
m-1112	1183	19	frequency	frequency	NOUN
m-1112	1183	20	exists	exist	VERB
m-1112	1183	21	in	in	ADP
m-1112	1183	22	orbit	orbit	NOUN
m-1112	1183	23	only	only	ADV
m-1112	1183	24	,	,	PUNCT
m-1112	1183	25	and	and	CCONJ
m-1112	1183	26	differs	differ	VERB
m-1112	1183	27	of	of	ADP
m-1112	1183	28	those	those	PRON
m-1112	1183	29	of	of	ADP
m-1112	1183	30	energylevels	energylevel	NOUN
m-1112	1183	31	.	.	PUNCT
m-1112	1184	1	since	since	SCONJ
m-1112	1184	2	frequency	frequency	NOUN
m-1112	1184	3	𝐟	𝐟	NOUN
m-1112	1184	4	𝐍	𝐍	NOUN
m-1112	1184	5	=	=	PUNCT
m-1112	1184	6	𝐟𝐑	𝐟𝐑	NOUN
m-1112	1184	7	=	=	SYM
m-1112	1184	8	2	2	NUM
m-1112	1184	9	,	,	PUNCT
m-1112	1184	10	839845.𝟏𝟎𝟏𝟎	839845.𝟏𝟎𝟏𝟎	NUM
m-1112	1184	11	s−1	s−1	NOUN
m-1112	1184	12	and	and	CCONJ
m-1112	1184	13	exists	exist	VERB
m-1112	1184	14	in	in	ADP
m-1112	1184	15	all	all	DET
m-1112	1184	16	atoms	atom	NOUN
m-1112	1184	17	,	,	PUNCT
m-1112	1184	18	due	due	ADP
m-1112	1184	19	to	to	ADP
m-1112	1184	20	the	the	DET
m-1112	1184	21	hydrogen	hydrogen	NOUN
m-1112	1184	22	first	first	ADJ
m-1112	1184	23	cave	cave	NOUN
m-1112	1184	24	,	,	PUNCT
m-1112	1184	25	then	then	ADV
m-1112	1184	26	this	this	DET
m-1112	1184	27	𝐟𝐍	𝐟𝐍	NOUN
m-1112	1184	28	is	be	AUX
m-1112	1184	29	the	the	DET
m-1112	1184	30	resonance	resonance	NOUN
m-1112	1184	31	frequency	frequency	NOUN
m-1112	1184	32	𝐟𝐑	𝐟𝐑	ADV
m-1112	1184	33	between	between	ADP
m-1112	1184	34	all	all	DET
m-1112	1184	35	atoms	atom	NOUN
m-1112	1184	36	and	and	CCONJ
m-1112	1184	37	molecules	molecule	NOUN
m-1112	1184	38	.	.	PUNCT
m-1112	1185	1	it	it	PRON
m-1112	1185	2	was	be	AUX
m-1112	1185	3	proved	prove	VERB
m-1112	1185	4	that	that	SCONJ
m-1112	1185	5	→	→	PUNCT
m-1112	1185	6	since	since	SCONJ
m-1112	1185	7	fr	fr	PROPN
m-1112	1185	8	=	=	SYM
m-1112	1185	9	σ	σ	PROPN
m-1112	1185	10	𝛷	𝛷	PROPN
m-1112	1185	11	2πr	2πr	NOUN
m-1112	1185	12	and	and	CCONJ
m-1112	1185	13	related	relate	VERB
m-1112	1185	14	to	to	ADP
m-1112	1185	15	hydrogen	hydrogen	NOUN
m-1112	1185	16	cave	cave	NOUN
m-1112	1185	17	r	r	NOUN
m-1112	1185	18	and	and	CCONJ
m-1112	1185	19	stress	stress	NOUN
m-1112	1185	20	σ	σ	PROPN
m-1112	1185	21	only	only	ADJ
m-1112	1185	22	←	←	PROPN
m-1112	1185	23	it	it	PRON
m-1112	1185	24	is	be	AUX
m-1112	1185	25	the	the	DET
m-1112	1185	26	unique	unique	ADJ
m-1112	1185	27	common	common	ADJ
m-1112	1185	28	and	and	CCONJ
m-1112	1185	29	neutral	neutral	ADJ
m-1112	1185	30	-	-	PUNCT
m-1112	1185	31	monad	monad	PROPN
m-1112	1185	32	,	,	PUNCT
m-1112	1185	33	in	in	ADP
m-1112	1185	34	all	all	DET
m-1112	1185	35	chemistry	chemistry	NOUN
m-1112	1185	36	structures	structure	NOUN
m-1112	1185	37	and	and	CCONJ
m-1112	1185	38	composites	composite	NOUN
m-1112	1185	39	.	.	PUNCT
m-1112	1186	1	d-2	d-2	NOUN
m-1112	1186	2	..	..	PUNCT
m-1112	1186	3	energy	energy	NOUN
m-1112	1186	4	from	from	ADP
m-1112	1186	5	equation	equation	NOUN
m-1112	1186	6	e=	e=	NOUN
m-1112	1186	7	h.𝐟	h.𝐟	VERB
m-1112	1186	8	𝐍	𝐍	NOUN
m-1112	1186	9	=	=	NOUN
m-1112	1186	10	6.62607.10−34	6.62607.10−34	NUM
m-1112	1186	11	.	.	PUNCT
m-1112	1187	1	2,8398447.1010	2,8398447.1010	NUM
m-1112	1187	2	=	=	SYM
m-1112	1188	1	18,817009.10−24	18,817009.10−24	NUM
m-1112	1188	2	j	j	PROPN
m-1112	1188	3	/	/	SYM
m-1112	1188	4	(	(	PUNCT
m-1112	1188	5	1,6022	1,6022	PROPN
m-1112	1188	6	.	.	PUNCT
m-1112	1189	1	10−19	10−19	ADJ
m-1112	1189	2	)	)	PUNCT
m-1112	1190	1	=	=	SYM
m-1112	1190	2	1,174463	1,174463	NUM
m-1112	1190	3	.10−4	.10−4	NOUN
m-1112	1190	4	ev	ev	X
m-1112	1190	5	,	,	PUNCT
m-1112	1190	6	and	and	CCONJ
m-1112	1190	7	conserved	conserve	VERB
m-1112	1190	8	as	as	ADP
m-1112	1190	9	thermal	thermal	ADJ
m-1112	1190	10	-	-	PUNCT
m-1112	1190	11	energy	energy	NOUN
m-1112	1190	12	𝐄	𝐄	NOUN
m-1112	1190	13	𝐓	𝐓	PROPN
m-1112	1190	14	in	in	ADP
m-1112	1190	15	kilo	kilo	PROPN
m-1112	1190	16	cal	cal	PROPN
m-1112	1190	17	and	and	CCONJ
m-1112	1190	18	which	which	PRON
m-1112	1190	19	is	be	AUX
m-1112	1190	20	continually	continually	ADV
m-1112	1190	21	increasing	increase	VERB
m-1112	1190	22	as	as	ADP
m-1112	1190	23	,	,	PUNCT
m-1112	1190	24	e	e	PROPN
m-1112	1190	25	t	t	NOUN
m-1112	1190	26	=	=	PUNCT
m-1112	1190	27	18,817009	18,817009	NUM
m-1112	1190	28	.	.	PUNCT
m-1112	1191	1	10−24	10−24	NUM
m-1112	1191	2	j	j	PROPN
m-1112	1191	3	/	/	PUNCT
m-1112	1192	1	[	[	X
m-1112	1192	2	(	(	PUNCT
m-1112	1192	3	4,19	4,19	NUM
m-1112	1192	4	.	.	NOUN
m-1112	1192	5	103	103	NUM
m-1112	1192	6	)	)	PUNCT
m-1112	1192	7	=	=	SYM
m-1112	1192	8	kcal	kcal	X
m-1112	1192	9	]	]	PUNCT
m-1112	1192	10	=	=	SYM
m-1112	1192	11	4,49093	4,49093	NUM
m-1112	1192	12	.	.	PUNCT
m-1112	1193	1	10−27	10−27	PROPN
m-1112	1193	2	kcal	kcal	NOUN
m-1112	1193	3	.	.	PUNCT
m-1112	1194	1	since	since	SCONJ
m-1112	1194	2	1ev	1ev	PROPN
m-1112	1194	3	=	=	SYM
m-1112	1194	4	96,363636	96,363636	NUM
m-1112	1194	5	kj	kj	PROPN
m-1112	1194	6	/	/	SYM
m-1112	1194	7	mol	mol	ADP
m-1112	1194	8	thermal	thermal	ADJ
m-1112	1194	9	energy	energy	NOUN
m-1112	1194	10	e	e	NOUN
m-1112	1194	11	t	t	NOUN
m-1112	1194	12	=	=	SYM
m-1112	1194	13	4,49093	4,49093	NUM
m-1112	1194	14	.	.	PUNCT
m-1112	1195	1	10−27	10−27	NUM
m-1112	1195	2	kcal	kcal	NOUN
m-1112	1195	3	/	/	SYM
m-1112	1196	1	[	[	X
m-1112	1196	2	96,363636.kcal	96,363636.kcal	NOUN
m-1112	1196	3	/	/	SYM
m-1112	1196	4	mol=1ev	mol=1ev	PROPN
m-1112	1196	5	]	]	PUNCT
m-1112	1196	6	=	=	SYM
m-1112	1196	7	e	e	X
m-1112	1196	8	t	t	NOUN
m-1112	1196	9	=	=	SYM
m-1112	1196	10	4,660399.10−29	4,660399.10−29	NUM
m-1112	1196	11	ev	ev	PROPN
m-1112	1196	12	.	.	PUNCT
m-1112	1197	1	this	this	PRON
m-1112	1197	2	happens	happen	VERB
m-1112	1197	3	because	because	SCONJ
m-1112	1197	4	of	of	ADP
m-1112	1197	5	the	the	DET
m-1112	1197	6	closed	closed	ADJ
m-1112	1197	7	energy	energy	NOUN
m-1112	1197	8	orbit	orbit	NOUN
m-1112	1197	9	-	-	PUNCT
m-1112	1197	10	rims	rim	NOUN
m-1112	1197	11	r	r	NOUN
m-1112	1197	12	,	,	PUNCT
m-1112	1197	13	constant	constant	ADJ
m-1112	1197	14	light	light	ADJ
m-1112	1197	15	velocity	velocity	NOUN
m-1112	1197	16	c	c	NOUN
m-1112	1197	17	,	,	PUNCT
m-1112	1197	18	and	and	CCONJ
m-1112	1197	19	from	from	ADP
m-1112	1197	20	spin	spin	NOUN
m-1112	1197	21	equation	equation	NOUN
m-1112	1197	22	s	s	PART
m-1112	1197	23	=	=	NOUN
m-1112	1197	24	r	r	NOUN
m-1112	1197	25	m	m	NOUN
m-1112	1197	26	c	c	NOUN
m-1112	1197	27	.	.	PUNCT
m-1112	1198	1	taking	take	VERB
m-1112	1198	2	into	into	ADP
m-1112	1198	3	consideration	consideration	NOUN
m-1112	1198	4	the	the	DET
m-1112	1198	5	thermal	thermal	ADJ
m-1112	1198	6	energy	energy	NOUN
m-1112	1198	7	of	of	ADP
m-1112	1198	8	a	a	DET
m-1112	1198	9	photon	photon	NOUN
m-1112	1198	10	when	when	SCONJ
m-1112	1198	11	it	it	PRON
m-1112	1198	12	is	be	AUX
m-1112	1198	13	pressing	press	VERB
m-1112	1198	14	the	the	DET
m-1112	1198	15	surface	surface	NOUN
m-1112	1198	16	of	of	ADP
m-1112	1198	17	1	1	NUM
m-1112	1198	18	m2	m2	PROPN
m-1112	1198	19	for	for	ADP
m-1112	1198	20	60s	60	NOUN
m-1112	1198	21	then	then	ADV
m-1112	1198	22	,	,	PUNCT
m-1112	1198	23	𝐄	𝐄	PROPN
m-1112	1198	24	𝐏	𝐏	PROPN
m-1112	1198	25	=	=	PUNCT
m-1112	1198	26	20	20	NUM
m-1112	1198	27	kcal	kcal	NOUN
m-1112	1198	28	=	=	SYM
m-1112	1198	29	20.(4,19	20.(4,19	NUM
m-1112	1198	30	.	.	NOUN
m-1112	1198	31	103	103	NUM
m-1112	1198	32	)	)	PUNCT
m-1112	1199	1	=	=	SYM
m-1112	1200	1	8,3777.104	8,3777.104	NUM
m-1112	1201	1	j	j	NOUN
m-1112	1201	2	,	,	PUNCT
m-1112	1201	3	and	and	CCONJ
m-1112	1201	4	the	the	DET
m-1112	1201	5	ratio	ratio	NOUN
m-1112	1201	6	,	,	PUNCT
m-1112	1201	7	[	[	PUNCT
m-1112	1201	8	e	e	PROPN
m-1112	1201	9	t	t	PROPN
m-1112	1201	10	/	/	SYM
m-1112	1201	11	e	e	X
m-1112	1201	12	p	p	X
m-1112	1201	13	]	]	X
m-1112	1201	14	=	=	SYM
m-1112	1201	15	4,49093	4,49093	NUM
m-1112	1201	16	.	.	PUNCT
m-1112	1202	1	10−27/20	10−27/20	NUM
m-1112	1202	2	=	=	SYM
m-1112	1202	3	2,24546.10−28	2,24546.10−28	NUM
m-1112	1202	4	,	,	PUNCT
m-1112	1202	5	which	which	PRON
m-1112	1202	6	is	be	AUX
m-1112	1202	7	a	a	DET
m-1112	1202	8	quantity	quantity	NOUN
m-1112	1202	9	not	not	PART
m-1112	1202	10	detected	detect	VERB
m-1112	1202	11	.	.	PUNCT
m-1112	1203	1	the	the	DET
m-1112	1203	2	hydrogen	hydrogen	NOUN
m-1112	1203	3	caves	cave	NOUN
m-1112	1203	4	created	create	VERB
m-1112	1203	5	in	in	ADP
m-1112	1203	6	the	the	DET
m-1112	1203	7	sun	sun	NOUN
m-1112	1203	8	1	1	NUM
m-1112	1203	9	million	million	NUM
m-1112	1203	10	years	year	NOUN
m-1112	1203	11	-	-	PUNCT
m-1112	1203	12	ago	ago	ADV
m-1112	1203	13	=	=	SYM
m-1112	1203	14	106.365.24.3600	106.365.24.3600	NUM
m-1112	1203	15	=	=	SYM
m-1112	1203	16	3,1536.1013	3,1536.1013	NUM
m-1112	1203	17	sec	sec	PROPN
m-1112	1203	18	,	,	PUNCT
m-1112	1203	19	is	be	AUX
m-1112	1203	20	accumulated	accumulate	VERB
m-1112	1203	21	a	a	DET
m-1112	1203	22	thermal	thermal	ADJ
m-1112	1203	23	-	-	PUNCT
m-1112	1203	24	energy	energy	NOUN
m-1112	1203	25	of	of	ADP
m-1112	1203	26	a	a	DET
m-1112	1203	27	magnitude	magnitude	NOUN
m-1112	1203	28	e	e	X
m-1112	1203	29	therm=	therm=	NOUN
m-1112	1203	30	3,1536.1013.4,49093.10−27	3,1536.1013.4,49093.10−27	NUM
m-1112	1203	31	=	=	SYM
m-1112	1203	32	1,41626.𝟏𝟎−𝟏𝟑	1,41626.𝟏𝟎−𝟏𝟑	NUM
m-1112	1203	33	kcal	kcal	NOUN
m-1112	1203	34	,	,	PUNCT
m-1112	1203	35	i.e.	i.e.	X
m-1112	1203	36	the	the	DET
m-1112	1203	37	stationary	stationary	ADJ
m-1112	1203	38	hydrogen	hydrogen	NOUN
m-1112	1203	39	-	-	PUNCT
m-1112	1203	40	wave	wave	NOUN
m-1112	1203	41	–	–	PUNCT
m-1112	1203	42	cave	cave	NOUN
m-1112	1203	43	needs	need	VERB
m-1112	1203	44	1quadrillion	1quadrillion	NUM
m-1112	1203	45	years	year	NOUN
m-1112	1203	46	to	to	PART
m-1112	1203	47	conserve	conserve	VERB
m-1112	1203	48	1	1	NUM
m-1112	1203	49	-	-	PUNCT
m-1112	1203	50	kcal	kcal	ADJ
m-1112	1203	51	thermal	thermal	ADJ
m-1112	1203	52	-	-	PUNCT
m-1112	1203	53	energy	energy	NOUN
m-1112	1203	54	.	.	PUNCT
m-1112	1204	1	for	for	ADP
m-1112	1204	2	half	half	ADJ
m-1112	1204	3	-	-	PUNCT
m-1112	1204	4	frequency	frequency	NOUN
m-1112	1204	5	fr	fr	NOUN
m-1112	1204	6	/	/	SYM
m-1112	1204	7	2	2	NUM
m-1112	1204	8	=	=	SYM
m-1112	1204	9	1,4199223.1010	1,4199223.1010	NUM
m-1112	1204	10	s−1	s−1	PROPN
m-1112	1204	11	,	,	PUNCT
m-1112	1204	12	the	the	DET
m-1112	1204	13	kinetic	kinetic	ADJ
m-1112	1204	14	energy	energy	NOUN
m-1112	1204	15	is	be	AUX
m-1112	1204	16	zero	zero	NUM
m-1112	1204	17	and	and	CCONJ
m-1112	1204	18	the	the	DET
m-1112	1204	19	potential	potential	ADJ
m-1112	1204	20	-	-	PUNCT
m-1112	1204	21	energy	energy	NOUN
m-1112	1204	22	is	be	AUX
m-1112	1204	23	u	u	NOUN
m-1112	1204	24	=	=	SYM
m-1112	1204	25	e	e	NOUN
m-1112	1204	26	=	=	SYM
m-1112	1205	1	h	h	NOUN
m-1112	1205	2	f	f	NOUN
m-1112	1205	3	=	=	SYM
m-1112	1205	4	6,62606957.10−34	6,62606957.10−34	NUM
m-1112	1205	5	.	.	PUNCT
m-1112	1206	1	1,4199223.1010	1,4199223.1010	NUM
m-1112	1206	2	=	=	SYM
m-1112	1207	1	9,4085039.10−24	9,4085039.10−24	NUM
m-1112	1207	2	j	j	NOUN
m-1112	1207	3	/	/	SYM
m-1112	1207	4	(	(	PUNCT
m-1112	1207	5	1,6022.10−19	1,6022.10−19	NUM
m-1112	1207	6	ev	ev	X
m-1112	1207	7	)	)	PUNCT
m-1112	1207	8	=	=	SYM
m-1112	1207	9	5,8722405.10−6	5,8722405.10−6	NUM
m-1112	1207	10	ev	ev	NOUN
m-1112	1207	11	,	,	PUNCT
m-1112	1207	12	which	which	PRON
m-1112	1207	13	agree	agree	VERB
m-1112	1207	14	with	with	ADP
m-1112	1207	15	the	the	DET
m-1112	1207	16	bohr	bohr	NOUN
m-1112	1207	17	-	-	PUNCT
m-1112	1207	18	magneton	magneton	PROPN
m-1112	1207	19	.	.	PUNCT
m-1112	1208	1	remarks	remark	NOUN
m-1112	1208	2	:	:	PUNCT
m-1112	1209	1	1	1	X
m-1112	1209	2	..	..	PUNCT
m-1112	1209	3	the	the	DET
m-1112	1209	4	real	real	ADJ
m-1112	1209	5	shear	shear	NOUN
m-1112	1209	6	stress	stress	NOUN
m-1112	1209	7	that	that	PRON
m-1112	1209	8	exists	exist	VERB
m-1112	1209	9	in	in	ADP
m-1112	1209	10	the	the	DET
m-1112	1209	11	force	force	NOUN
m-1112	1209	12	–	–	PUNCT
m-1112	1209	13	carriers	carrier	NOUN
m-1112	1209	14	.	.	PUNCT
m-1112	1210	1	from	from	ADP
m-1112	1210	2	the	the	DET
m-1112	1210	3	static	static	ADJ
m-1112	1210	4	theory	theory	NOUN
m-1112	1210	5	of	of	ADP
m-1112	1210	6	equivalent	equivalent	ADJ
m-1112	1210	7	tension	tension	NOUN
m-1112	1210	8	(	(	PUNCT
m-1112	1210	9	moore	moore	PROPN
m-1112	1210	10	's	's	PART
m-1112	1210	11	cycle	cycle	NOUN
m-1112	1210	12	)	)	PUNCT
m-1112	1210	13	is	be	AUX
m-1112	1210	14	(	(	PUNCT
m-1112	1210	15	1	1	NUM
m-1112	1210	16	)	)	PUNCT
m-1112	1211	1	=	=	SYM
m-1112	1211	2	σ	σ	NOUN
m-1112	1211	3	=	=	PUNCT
m-1112	1211	4	√(𝛔𝟏	√(𝛔𝟏	PROPN
m-1112	1211	5	−	−	PROPN
m-1112	1211	6	𝛔𝟐)²	𝛔𝟐)²	SYM
m-1112	1212	1	+	+	NUM
m-1112	1212	2	𝟒	𝟒	NUM
m-1112	1212	3	𝛕𝟏𝟐	𝛕𝟏𝟐	NOUN
m-1112	1212	4	,	,	PUNCT
m-1112	1212	5	and	and	CCONJ
m-1112	1212	6	σ1,2	σ1,2	PROPN
m-1112	1212	7	=	=	SYM
m-1112	1212	8	(	(	PUNCT
m-1112	1212	9	σ1+σ2	σ1+σ2	PROPN
m-1112	1212	10	)	)	PUNCT
m-1112	1212	11	/2	/2	PROPN
m-1112	1212	12	±	±	NOUN
m-1112	1212	13	(	(	PUNCT
m-1112	1212	14	½)√(σ1	½)√(σ1	NOUN
m-1112	1212	15	−	−	NOUN
m-1112	1212	16	σ2)²	σ2)²	PUNCT
m-1112	1212	17	+	+	NOUN
m-1112	1212	18	4	4	NUM
m-1112	1212	19	τyz²	τyz²	NOUN
m-1112	1212	20	,	,	PUNCT
m-1112	1212	21	instead	instead	ADV
m-1112	1212	22	of	of	ADP
m-1112	1212	23	the	the	DET
m-1112	1212	24	classical	classical	ADJ
m-1112	1212	25	case	case	NOUN
m-1112	1212	26	which	which	PRON
m-1112	1212	27	is	be	AUX
m-1112	1212	28	σ	σ	NOUN
m-1112	1212	29	=	=	NUM
m-1112	1212	30	2.τ	2.τ	NUM
m-1112	1212	31	max	max	NOUN
m-1112	1212	32	=	=	SYM
m-1112	1212	33	√σ1	√σ1	PROPN
m-1112	1212	34	2	2	NUM
m-1112	1212	35	+	+	NUM
m-1112	1212	36	4	4	NUM
m-1112	1212	37	.	.	PUNCT
m-1112	1212	38	τ	τ	PROPN
m-1112	1212	39	²	²	NUM
m-1112	1212	40	,	,	PUNCT
m-1112	1212	41	.	.	PUNCT
m-1112	1213	1	(	(	PUNCT
m-1112	1213	2	2	2	NUM
m-1112	1213	3	)	)	PUNCT
m-1112	1213	4	.	.	PUNCT
m-1112	1214	1	because	because	SCONJ
m-1112	1214	2	nature	nature	NOUN
m-1112	1214	3	always	always	ADV
m-1112	1214	4	follows	follow	VERB
m-1112	1214	5	the	the	DET
m-1112	1214	6	uniform	uniform	ADJ
m-1112	1214	7	tension	tension	NOUN
m-1112	1214	8	so	so	SCONJ
m-1112	1214	9	it	it	PRON
m-1112	1214	10	follows	follow	VERB
m-1112	1214	11	the	the	DET
m-1112	1214	12	(	(	PUNCT
m-1112	1214	13	1	1	NUM
m-1112	1214	14	)	)	PUNCT
m-1112	1214	15	case	case	NOUN
m-1112	1214	16	.	.	PUNCT
m-1112	1215	1	where	where	SCONJ
m-1112	1215	2	exist	exist	VERB
m-1112	1215	3	the	the	DET
m-1112	1215	4	equation	equation	NOUN
m-1112	1215	5	σ	σ	NOUN
m-1112	1215	6	=	=	PUNCT
m-1112	1215	7	√(𝛔𝟏	√(𝛔𝟏	PROPN
m-1112	1215	8	−	−	PROPN
m-1112	1215	9	𝛔𝟐)²	𝛔𝟐)²	SYM
m-1112	1215	10	+	+	NUM
m-1112	1215	11	𝟒𝛕𝟏𝟐	𝟒𝛕𝟏𝟐	NOUN
m-1112	1215	12	,	,	PUNCT
m-1112	1215	13	and	and	CCONJ
m-1112	1215	14	σ	σ	NUM
m-1112	1215	15	1,2	1,2	NUM
m-1112	1215	16	=	=	SYM
m-1112	1215	17	(	(	PUNCT
m-1112	1215	18	σ1+σ2	σ1+σ2	PROPN
m-1112	1215	19	)	)	PUNCT
m-1112	1215	20	/2	/2	PROPN
m-1112	1216	1	±	±	NOUN
m-1112	1216	2	(	(	PUNCT
m-1112	1216	3	½)√(σ1	½)√(σ1	NOUN
m-1112	1216	4	−	−	ADP
m-1112	1216	5	σ2)²	σ2)²	SYM
m-1112	1216	6	+	+	NUM
m-1112	1216	7	4τyz²	4τyz²	NUM
m-1112	1216	8	=	=	SYM
m-1112	1216	9	σ	σ	X
m-1112	1216	10	2	2	NUM
m-1112	1217	1	[	[	X
m-1112	1217	2	√5	√5	X
m-1112	1217	3	+	+	NOUN
m-1112	1217	4	1	1	NUM
m-1112	1217	5	]	]	PUNCT
m-1112	1217	6	=	=	PROPN
m-1112	1217	7	σ	σ	PROPN
m-1112	1217	8	.	.	PUNCT
m-1112	1218	1	[	[	PUNCT
m-1112	1218	2	√𝟓+𝟏	√𝟓+𝟏	NOUN
m-1112	1218	3	𝟐	𝟐	NUM
m-1112	1218	4	]	]	PUNCT
m-1112	1218	5	,	,	PUNCT
m-1112	1218	6	which	which	PRON
m-1112	1218	7	is	be	AUX
m-1112	1218	8	the	the	DET
m-1112	1218	9	golden	golden	ADJ
m-1112	1218	10	ratio	ratio	NOUN
m-1112	1218	11	for	for	ADP
m-1112	1218	12	stresses	stress	NOUN
m-1112	1218	13	.	.	PUNCT
m-1112	1219	1	2	2	X
m-1112	1219	2	..	..	PUNCT
m-1112	1219	3	the	the	DET
m-1112	1219	4	bernoulli	bernoulli	NOUN
m-1112	1219	5	astute	astute	ADJ
m-1112	1219	6	about	about	ADP
m-1112	1219	7	stresses	stress	NOUN
m-1112	1219	8	-	-	PUNCT
m-1112	1219	9	linear	linear	NOUN
m-1112	1219	10	-	-	PUNCT
m-1112	1219	11	distribution	distribution	NOUN
m-1112	1219	12	is	be	AUX
m-1112	1219	13	equallytrue	equallytrue	VERB
m-1112	1219	14	for	for	ADP
m-1112	1219	15	bending	bend	VERB
m-1112	1219	16	too	too	ADV
m-1112	1219	17	.	.	PUNCT
m-1112	1220	1	3	3	X
m-1112	1220	2	..	..	PUNCT
m-1112	1220	3	in	in	ADP
m-1112	1220	4	the	the	DET
m-1112	1220	5	case	case	NOUN
m-1112	1220	6	of	of	ADP
m-1112	1220	7	concentrated	concentrated	ADJ
m-1112	1220	8	stresses	stress	NOUN
m-1112	1220	9	(	(	PUNCT
m-1112	1220	10	such	such	ADJ
m-1112	1220	11	as	as	ADP
m-1112	1220	12	closed	closed	ADJ
m-1112	1220	13	or	or	CCONJ
m-1112	1220	14	open	open	ADJ
m-1112	1220	15	conductors	conductor	NOUN
m-1112	1220	16	)	)	PUNCT
m-1112	1220	17	,	,	PUNCT
m-1112	1220	18	the	the	DET
m-1112	1220	19	doubling	doubling	NOUN
m-1112	1220	20	of	of	ADP
m-1112	1220	21	the	the	DET
m-1112	1220	22	main	main	ADJ
m-1112	1220	23	stresses	stress	NOUN
m-1112	1220	24	observation	observation	NOUN
m-1112	1220	25	is	be	AUX
m-1112	1220	26	true	true	ADJ
m-1112	1220	27	,	,	PUNCT
m-1112	1220	28	and	and	CCONJ
m-1112	1220	29	this	this	PRON
m-1112	1220	30	because	because	SCONJ
m-1112	1220	31	of	of	ADP
m-1112	1220	32	the	the	DET
m-1112	1220	33	golden	golden	ADJ
m-1112	1220	34	ratio	ratio	NOUN
m-1112	1220	35	pattern	pattern	NOUN
m-1112	1220	36	.	.	PUNCT
m-1112	1221	1	ijo	ijo	PROPN
m-1112	1221	2	international	international	PROPN
m-1112	1221	3	journal	journal	PROPN
m-1112	1221	4	of	of	ADP
m-1112	1221	5	mathematics	mathematics	PROPN
m-1112	1221	6	(	(	PUNCT
m-1112	1221	7	issn	issn	PROPN
m-1112	1221	8	:	:	PUNCT
m-1112	1221	9	2992	2992	NUM
m-1112	1221	10	-	-	SYM
m-1112	1221	11	4421	4421	NUM
m-1112	1221	12	)	)	PUNCT
m-1112	1221	13	volume	volume	NOUN
m-1112	1221	14	08	08	NUM
m-1112	1222	1	|	|	ADV
m-1112	1222	2	issue	issue	NOUN
m-1112	1222	3	08	08	NUM
m-1112	1223	1	|	|	ADV
m-1112	1223	2	august	august	PROPN
m-1112	1223	3	2025	2025	NUM
m-1112	1223	4	|	|	ADV
m-1112	1223	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1223	6	ijo	ijo	PROPN
m-1112	1223	7	journals	journal	NOUN
m-1112	1223	8	45	45	NUM
m-1112	1223	9	the	the	DET
m-1112	1223	10	fundamental	fundamental	ADJ
m-1112	1223	11	particles	particle	NOUN
m-1112	1223	12	origination	origination	NOUN
m-1112	1223	13	mechanism	mechanism	NOUN
m-1112	1223	14	in	in	ADP
m-1112	1223	15	mfmf	mfmf	PROPN
m-1112	1223	16	pns	pns	PROPN
m-1112	1223	17	caves	cave	NOUN
m-1112	1223	18	.	.	PUNCT
m-1112	1224	1	1d	1d	NUM
m-1112	1224	2	..	..	PUNCT
m-1112	1225	1	the	the	DET
m-1112	1225	2	spaces	space	NOUN
m-1112	1225	3	and	and	CCONJ
m-1112	1225	4	the	the	DET
m-1112	1225	5	energy	energy	NOUN
m-1112	1225	6	states	state	NOUN
m-1112	1225	7	:	:	PUNCT
m-1112	1225	8	in	in	ADP
m-1112	1225	9	articles	article	NOUN
m-1112	1225	10	[	[	X
m-1112	1225	11	87	87	NUM
m-1112	1225	12	-	-	SYM
m-1112	1225	13	89	89	NUM
m-1112	1225	14	]	]	PUNCT
m-1112	1225	15	is	be	AUX
m-1112	1225	16	elucidated	elucidate	VERB
m-1112	1225	17	the	the	DET
m-1112	1225	18	duality	duality	NOUN
m-1112	1225	19	-	-	PUNCT
m-1112	1225	20	photon	photon	NOUN
m-1112	1225	21	as	as	ADP
m-1112	1225	22	particle	particle	NOUN
m-1112	1225	23	and	and	CCONJ
m-1112	1225	24	as	as	ADP
m-1112	1225	25	wave	wave	NOUN
m-1112	1225	26	.	.	PUNCT
m-1112	1226	1	the	the	DET
m-1112	1226	2	photon`s	photon`s	PROPN
m-1112	1226	3	charge	charge	NOUN
m-1112	1226	4	�	�	PROPN
m-1112	1226	5	̅	̅	NOUN
m-1112	1226	6	�	�	NOUN
m-1112	1226	7	photon	photon	NOUN
m-1112	1226	8	=	=	PUNCT
m-1112	1226	9	v.σφ	v.σφ	PROPN
m-1112	1226	10	2πr	2πr	NOUN
m-1112	1226	11	,	,	PUNCT
m-1112	1226	12	transfers	transfer	NOUN
m-1112	1226	13	information`s	information`s	NOUN
m-1112	1226	14	and	and	CCONJ
m-1112	1226	15	energy	energy	NOUN
m-1112	1226	16	-	-	PUNCT
m-1112	1226	17	storage	storage	NOUN
m-1112	1226	18	in	in	ADP
m-1112	1226	19	nature	nature	NOUN
m-1112	1226	20	.	.	PUNCT
m-1112	1227	1	in	in	ADP
m-1112	1227	2	articles	article	NOUN
m-1112	1227	3	[	[	X
m-1112	1227	4	87	87	NUM
m-1112	1227	5	-	-	SYM
m-1112	1227	6	88	88	NUM
m-1112	1227	7	-	-	PUNCT
m-1112	1227	8	89	89	NUM
m-1112	1227	9	-	-	SYM
m-1112	1227	10	90	90	NUM
m-1112	1227	11	]	]	PUNCT
m-1112	1227	12	are	be	AUX
m-1112	1227	13	elucidated	elucidate	VERB
m-1112	1227	14	the	the	DET
m-1112	1227	15	gravitational	gravitational	ADJ
m-1112	1227	16	constant	constant	ADJ
m-1112	1227	17	g	g	NOUN
m-1112	1227	18	,	,	PUNCT
m-1112	1227	19	the	the	DET
m-1112	1227	20	stresses	stress	NOUN
m-1112	1227	21	σ	σ	PROPN
m-1112	1227	22	,	,	PUNCT
m-1112	1227	23	the	the	DET
m-1112	1227	24	light	light	ADJ
m-1112	1227	25	-	-	PUNCT
m-1112	1227	26	velocity	velocity	NOUN
m-1112	1227	27	�	�	NOUN
m-1112	1227	28	̅	̅	NOUN
m-1112	1227	29	�	�	PROPN
m-1112	1227	30	,	,	PUNCT
m-1112	1227	31	the	the	DET
m-1112	1227	32	gravity	gravity	NOUN
m-1112	1227	33	�	�	NOUN
m-1112	1227	34	̅	̅	NOUN
m-1112	1227	35	�	�	PROPN
m-1112	1227	36	,	,	PUNCT
m-1112	1227	37	the	the	DET
m-1112	1227	38	hydrogen	hydrogen	NOUN
m-1112	1227	39	cave	cave	NOUN
m-1112	1227	40	h	h	PROPN
m-1112	1227	41	,	,	PUNCT
m-1112	1227	42	the	the	DET
m-1112	1227	43	electron	electron	NOUN
m-1112	1227	44	�	�	PROPN
m-1112	1227	45	̅	̅	NOUN
m-1112	1227	46	�	�	PROPN
m-1112	1227	47	,	,	PUNCT
m-1112	1227	48	the	the	DET
m-1112	1227	49	electron	electron	NOUN
m-1112	1227	50	-	-	PUNCT
m-1112	1227	51	charge	charge	NOUN
m-1112	1227	52	�	�	PROPN
m-1112	1227	53	̅	̅	NOUN
m-1112	1227	54	�	�	PROPN
m-1112	1227	55	𝐞	𝐞	PROPN
m-1112	1227	56	,	,	PUNCT
m-1112	1227	57	the	the	DET
m-1112	1227	58	weak	weak	ADJ
m-1112	1227	59	-	-	PUNCT
m-1112	1227	60	forces	force	NOUN
m-1112	1227	61	�	�	NOUN
m-1112	1227	62	̅	̅	NOUN
m-1112	1227	63	�	�	PROPN
m-1112	1227	64	𝐅	𝐅	PROPN
m-1112	1227	65	,	,	PUNCT
m-1112	1227	66	the	the	DET
m-1112	1227	67	strong	strong	ADJ
m-1112	1227	68	–	–	PUNCT
m-1112	1227	69	forces	force	NOUN
m-1112	1227	70	𝐐𝐓	𝐐𝐓	VERB
m-1112	1227	71	,	,	PUNCT
m-1112	1227	72	and	and	CCONJ
m-1112	1227	73	the	the	DET
m-1112	1227	74	uniform	uniform	ADJ
m-1112	1227	75	-	-	PUNCT
m-1112	1227	76	resonance	resonance	NOUN
m-1112	1227	77	frequencies	frequency	NOUN
m-1112	1227	78	𝐟	𝐟	PROPN
m-1112	1227	79	𝐑	𝐑	PROPN
m-1112	1227	80	,	,	PUNCT
m-1112	1227	81	for	for	ADP
m-1112	1227	82	atoms	atom	NOUN
m-1112	1227	83	structure	structure	NOUN
m-1112	1227	84	.	.	PUNCT
m-1112	1228	1	in	in	ADP
m-1112	1228	2	articles	article	NOUN
m-1112	1228	3	[	[	X
m-1112	1228	4	91	91	NUM
m-1112	1228	5	]	]	PUNCT
m-1112	1228	6	is	be	AUX
m-1112	1228	7	shown	show	VERB
m-1112	1228	8	how	how	SCONJ
m-1112	1228	9	,	,	PUNCT
m-1112	1228	10	the	the	DET
m-1112	1228	11	three	three	NUM
m-1112	1228	12	circularly	circularly	ADV
m-1112	1228	13	-	-	PUNCT
m-1112	1228	14	placed	place	VERB
m-1112	1228	15	physical	physical	NOUN
m-1112	1228	16	-	-	PUNCT
m-1112	1228	17	charged	charge	VERB
m-1112	1228	18	breakages	breakage	NOUN
m-1112	1228	19	on	on	ADP
m-1112	1228	20	the	the	DET
m-1112	1228	21	-	-	PUNCT
m-1112	1228	22	three	three	NUM
m-1112	1228	23	spaces	space	NOUN
m-1112	1228	24	[	[	X
m-1112	1228	25	⊕	⊕	X
m-1112	1228	26			PROPN
m-1112	1228	27	⊝	⊝	NUM
m-1112	1228	28	]	]	PUNCT
m-1112	1228	29	,	,	PUNCT
m-1112	1228	30	or	or	CCONJ
m-1112	1228	31	on	on	ADP
m-1112	1228	32	the	the	DET
m-1112	1228	33	3	3	NUM
m-1112	1228	34	-	-	PUNCT
m-1112	1228	35	extreme	extreme	ADJ
m-1112	1228	36	-triangles	-triangle	NOUN
m-1112	1228	37	of	of	ADP
m-1112	1228	38	stplmechanism	stplmechanism	NOUN
m-1112	1228	39	which	which	PRON
m-1112	1228	40	is	be	AUX
m-1112	1228	41	the	the	DET
m-1112	1228	42	-thrust	-thrust	NOUN
m-1112	1228	43	for	for	ADP
m-1112	1228	44	the	the	DET
m-1112	1228	45	-	-	PUNCT
m-1112	1228	46	origination	origination	NOUN
m-1112	1228	47	of	of	ADP
m-1112	1228	48	all	all	DET
m-1112	1228	49	the	the	DET
m-1112	1228	50	cosmic	cosmic	ADJ
m-1112	1228	51	particles	particle	NOUN
m-1112	1228	52	in	in	ADP
m-1112	1228	53	linear	linear	PROPN
m-1112	1228	54	&	&	CCONJ
m-1112	1228	55	rotational	rotational	ADJ
m-1112	1228	56	conductors	conductor	NOUN
m-1112	1228	57	frequencies	frequency	NOUN
m-1112	1228	58	,	,	PUNCT
m-1112	1228	59	either	either	CCONJ
m-1112	1228	60	into	into	ADP
m-1112	1228	61	the	the	DET
m-1112	1228	62	atoms	atom	NOUN
m-1112	1228	63	or	or	CCONJ
m-1112	1228	64	to	to	ADP
m-1112	1228	65	their	their	PRON
m-1112	1228	66	compounds	compound	NOUN
m-1112	1228	67	[	[	X
m-1112	1228	68	91	91	NUM
m-1112	1228	69	]	]	PUNCT
m-1112	1228	70	.	.	PUNCT
m-1112	1229	1	9a	9a	NOUN
m-1112	1229	2	..	..	PUNCT
m-1112	1230	1	the	the	DET
m-1112	1230	2	flow	flow	NOUN
m-1112	1230	3	plan	plan	NOUN
m-1112	1230	4	of	of	ADP
m-1112	1230	5	the	the	DET
m-1112	1230	6	→	→	SYM
m-1112	1230	7	space	space	NOUN
m-1112	1230	8	energy	energy	NOUN
m-1112	1230	9	←	←	PROPN
m-1112	1230	10	universe	universe	NOUN
m-1112	1230	11	.	.	PUNCT
m-1112	1231	1	1	1	X
m-1112	1231	2	..	..	PUNCT
m-1112	1231	3	it	it	PRON
m-1112	1231	4	was	be	AUX
m-1112	1231	5	shown	show	VERB
m-1112	1231	6	in	in	ADP
m-1112	1231	7	[	[	PUNCT
m-1112	1231	8	9	9	NUM
m-1112	1231	9	-	-	SYM
m-1112	1231	10	18	18	NUM
m-1112	1231	11	]	]	X
m-1112	1231	12	what	what	PRON
m-1112	1231	13	is	be	AUX
m-1112	1231	14	primary	primary	ADJ
m-1112	1231	15	-	-	PUNCT
m-1112	1231	16	neutral	neutral	ADJ
m-1112	1231	17	-	-	PUNCT
m-1112	1231	18	space	space	NOUN
m-1112	1232	1	[	[	X
m-1112	1232	2	pns	pns	X
m-1112	1232	3	]	]	PUNCT
m-1112	1232	4	as	as	ADV
m-1112	1232	5	well	well	ADV
m-1112	1232	6	as	as	ADP
m-1112	1232	7	what	what	PRON
m-1112	1232	8	is	be	AUX
m-1112	1232	9	infinity	infinity	NOUN
m-1112	1232	10	[	[	X
m-1112	1232	11	15	15	NUM
m-1112	1232	12	]	]	PUNCT
m-1112	1232	13	,	,	PUNCT
m-1112	1232	14	and	and	CCONJ
m-1112	1232	15	rotational	rotational	ADJ
m-1112	1232	16	energy	energy	NOUN
m-1112	1232	17	≡	≡	PROPN
m-1112	1232	18	λ	λ	PROPN
m-1112	1232	19	≡	≡	PROPN
m-1112	1232	20	torque	torque	NOUN
m-1112	1232	21	≡	≡	PROPN
m-1112	1232	22	momentum	momentum	NOUN
m-1112	1233	1	[	[	X
m-1112	1233	2	22	22	NUM
m-1112	1233	3	]	]	PUNCT
m-1112	1233	4	so	so	CCONJ
m-1112	1233	5	[	[	X
m-1112	1233	6	pns	pns	X
m-1112	1233	7	]	]	X
m-1112	1233	8	→	→	PUNCT
m-1112	1233	9	[	[	X
m-1112	1233	10	a𝐏𝐀	a𝐏𝐀	X
m-1112	1233	11	↔	↔	PROPN
m-1112	1233	12	𝐏𝐁	𝐏𝐁	PROPN
m-1112	1233	13	b	b	NOUN
m-1112	1233	14	]	]	X
m-1112	1233	15	≡	≡	PROPN
m-1112	1233	16	work	work	NOUN
m-1112	1233	17	w	w	ADP
m-1112	1233	18	=	=	NOUN
m-1112	1233	19	|ep	|ep	X
m-1112	1233	20	|=	|=	X
m-1112	1233	21	[	[	PUNCT
m-1112	1233	22	|λ|	|λ|	NOUN
m-1112	1233	23	.	.	PUNCT
m-1112	1234	1	+	+	NUM
m-1112	1234	2	λ	λ	X
m-1112	1234	3	x	x	X
m-1112	1234	4	]	]	X
m-1112	1234	5	→	→	PUNCT
m-1112	1234	6	w	w	X
m-1112	1234	7	=	=	SYM
m-1112	1234	8	∫	∫	PROPN
m-1112	1234	9	p.ds	p.ds	PROPN
m-1112	1234	10	=	=	NOUN
m-1112	1234	11	0	0	PUNCT
m-1112	1234	12	→	→	PUNCT
m-1112	1234	13	and	and	CCONJ
m-1112	1234	14	so	so	ADV
m-1112	1234	15	exists	exist	VERB
m-1112	1234	16	time	time	NOUN
m-1112	1234	17	t	t	NOUN
m-1112	1234	18	=	=	SYM
m-1112	1234	19	ds	ds	PROPN
m-1112	1234	20	/	/	SYM
m-1112	1234	21	v	v	NOUN
m-1112	1234	22	=	=	SYM
m-1112	1234	23	0	0	NUM
m-1112	1234	24	.	.	PUNCT
m-1112	1235	1	the	the	DET
m-1112	1235	2	cause	cause	NOUN
m-1112	1235	3	is	be	AUX
m-1112	1235	4	,	,	PUNCT
m-1112	1235	5	because	because	SCONJ
m-1112	1235	6	primary	primary	ADJ
m-1112	1235	7	point	point	NOUN
m-1112	1235	8	,	,	PUNCT
m-1112	1235	9	a	a	PRON
m-1112	1235	10	,	,	PUNCT
m-1112	1235	11	is	be	AUX
m-1112	1235	12	nothing	nothing	PRON
m-1112	1235	13	and	and	CCONJ
m-1112	1235	14	then	then	ADV
m-1112	1235	15	is	be	AUX
m-1112	1235	16	quantized	quantize	VERB
m-1112	1235	17	as	as	ADP
m-1112	1235	18	→	→	SYM
m-1112	1235	19	an	an	DET
m-1112	1235	20	point	point	NOUN
m-1112	1235	21	b	b	X
m-1112	1235	22	(	(	PUNCT
m-1112	1235	23	which	which	PRON
m-1112	1235	24	is	be	AUX
m-1112	1235	25	following	follow	VERB
m-1112	1235	26	the	the	DET
m-1112	1235	27	principle	principle	NOUN
m-1112	1235	28	of	of	ADP
m-1112	1235	29	virtual	virtual	ADJ
m-1112	1235	30	displacements	displacement	NOUN
m-1112	1236	1	w	w	PROPN
m-1112	1236	2	=	=	SYM
m-1112	1236	3	∫	∫	PROPN
m-1112	1236	4	p.ds	p.ds	PROPN
m-1112	1236	5	=	=	NOUN
m-1112	1236	6	0	0	PUNCT
m-1112	1236	7	=	=	SYM
m-1112	1236	8	force	force	NOUN
m-1112	1236	9	x	x	NOUN
m-1112	1236	10	displacement	displacement	NOUN
m-1112	1236	11	=	=	PUNCT
m-1112	1236	12	energy	energy	NOUN
m-1112	1236	13	x	x	NOUN
m-1112	1236	14	space	space	NOUN
m-1112	1236	15	,	,	PUNCT
m-1112	1236	16	and	and	CCONJ
m-1112	1236	17	according	accord	VERB
m-1112	1236	18	to	to	ADP
m-1112	1236	19	the	the	DET
m-1112	1236	20	ancient	ancient	ADJ
m-1112	1236	21	greek	greek	ADJ
m-1112	1236	22	philosopher	philosopher	NOUN
m-1112	1236	23	anaximander	anaximander	NOUN
m-1112	1236	24	[	[	PUNCT
m-1112	1236	25	the	the	DET
m-1112	1236	26	non	non	ADJ
m-1112	1236	27	-	-	ADJ
m-1112	1236	28	existent	existent	ADJ
m-1112	1236	29	(	(	PUNCT
m-1112	1236	30	i.e.	i.e.	X
m-1112	1236	31	the	the	DET
m-1112	1236	32	point	point	NOUN
m-1112	1236	33	a	a	PRON
m-1112	1236	34	)	)	PUNCT
m-1112	1236	35	,	,	PUNCT
m-1112	1236	36	exist	exist	VERB
m-1112	1236	37	when	when	SCONJ
m-1112	1236	38	is	be	AUX
m-1112	1236	39	done	do	VERB
m-1112	1236	40	,	,	PUNCT
m-1112	1236	41	it	it	PRON
m-1112	1236	42	occurs	occur	VERB
m-1112	1236	43	as	as	ADP
m-1112	1236	44	(	(	PUNCT
m-1112	1236	45	point	point	NOUN
m-1112	1236	46	b	b	NOUN
m-1112	1236	47	)	)	PUNCT
m-1112	1236	48	i.e.	i.e.	X
m-1112	1236	49	≡	≡	PROPN
m-1112	1237	1	[	[	PUNCT
m-1112	1237	2	το	το	ADP
m-1112	1237	3	μη	μη	INTJ
m-1112	1237	4	ον	ον	INTJ
m-1112	1237	5	,	,	PUNCT
m-1112	1237	6	ον	ον	PROPN
m-1112	1237	7	γίγνεσθαι	γίγνεσθαι	NOUN
m-1112	1237	8	]	]	PUNCT
m-1112	1238	1	=	=	PUNCT
m-1112	1238	2	[	[	PUNCT
m-1112	1238	3	το	το	ADP
m-1112	1238	4	τίποτα	τίποτα	NOUN
m-1112	1238	5	υπάρχει	υπάρχει	VERB
m-1112	1238	6	όταν	όταν	VERB
m-1112	1238	7	αυτό	αυτό	DET
m-1112	1238	8	γίνεται	γίνεται	NOUN
m-1112	1238	9	]	]	PUNCT
m-1112	1238	10	time	time	NOUN
m-1112	1238	11	is	be	AUX
m-1112	1238	12	not	not	PART
m-1112	1238	13	existing	exist	VERB
m-1112	1238	14	because	because	SCONJ
m-1112	1238	15	ds	ds	ADJ
m-1112	1238	16	=	=	SYM
m-1112	1238	17	∞	∞	NUM
m-1112	1238	18	.	.	PUNCT
m-1112	1238	19	0	0	NUM
m-1112	1239	1	=	=	PUNCT
m-1112	1239	2	constant	constant	ADJ
m-1112	1240	1	[	[	PUNCT
m-1112	1240	2	21	21	NUM
m-1112	1240	3	-	-	SYM
m-1112	1240	4	22	22	NUM
m-1112	1240	5	]	]	PUNCT
m-1112	1240	6	.	.	PUNCT
m-1112	1241	1	the	the	DET
m-1112	1241	2	relative	relative	ADJ
m-1112	1241	3	range	range	NOUN
m-1112	1241	4	is	be	AUX
m-1112	1241	5	the	the	DET
m-1112	1241	6	displacement	displacement	NOUN
m-1112	1241	7	ab	ab	PROPN
m-1112	1241	8	→	→	PUNCT
m-1112	1241	9	which	which	PRON
m-1112	1241	10	is	be	AUX
m-1112	1241	11	the	the	DET
m-1112	1241	12	monad	monad	PROPN
m-1112	1241	13	-	-	PUNCT
m-1112	1241	14	space	space	NOUN
m-1112	1241	15	as	as	ADP
m-1112	1241	16	ab	ab	PROPN
m-1112	1241	17	=	=	PROPN
m-1112	1241	18	0	0	PUNCT
m-1112	1242	1	→	→	SYM
m-1112	1242	2	k	k	X
m-1112	1242	3	→	→	PUNCT
m-1112	1242	4	the	the	DET
m-1112	1242	5	infinity	infinity	NOUN
m-1112	1242	6	anti	anti	ADJ
m-1112	1242	7	-	-	NOUN
m-1112	1242	8	space	space	NOUN
m-1112	1242	9	.	.	PUNCT
m-1112	1243	1	2	2	NUM
m-1112	1243	2	..	..	PUNCT
m-1112	1243	3	[	[	X
m-1112	1243	4	pns	pns	X
m-1112	1243	5	]	]	PUNCT
m-1112	1243	6	the	the	DET
m-1112	1243	7	energy	energy	NOUN
m-1112	1243	8	-	-	PUNCT
m-1112	1243	9	quaternion	quaternion	NOUN
m-1112	1243	10	[	[	PUNCT
m-1112	1243	11	|λ|	|λ|	NOUN
m-1112	1243	12	.	.	PUNCT
m-1112	1244	1	+	+	NUM
m-1112	1244	2	λ	λ	X
m-1112	1244	3	x	x	SYM
m-1112	1244	4	]	]	X
m-1112	1244	5	≡	≡	PROPN
m-1112	1244	6	�	�	PROPN
m-1112	1244	7	̅	̅	PROPN
m-1112	1244	8	�	�	PROPN
m-1112	1244	9	≡	≡	PROPN
m-1112	1244	10	[	[	PUNCT
m-1112	1244	11	λ	λ	X
m-1112	1244	12	±	±	NUM
m-1112	1244	13	λ	λ	X
m-1112	1244	14	x	x	X
m-1112	1244	15	]	]	X
m-1112	1244	16	≡	≡	PROPN
m-1112	1244	17	|	|	PROPN
m-1112	1244	18	�	�	PROPN
m-1112	1244	19	⃡	⃡	NOUN
m-1112	1244	20	�	�	PROPN
m-1112	1244	21	𝐨|	𝐨|	PROPN
m-1112	1244	22	𝐰.	𝐰.	NOUN
m-1112	1244	23	𝐞^	𝐞^	PROPN
m-1112	1244	24	{	{	PUNCT
m-1112	1244	25	[	[	PUNCT
m-1112	1244	26	�	�	PROPN
m-1112	1244	27	⃗⃖	⃗⃖	NOUN
m-1112	1244	28	�	�	PROPN
m-1112	1244	29	i	i	PROPN
m-1112	1244	30	/	/	SYM
m-1112	1244	31	√	√	NUM
m-1112	1244	32	λ	λ	NOUN
m-1112	1244	33	'	'	PART
m-1112	1244	34	�	�	PROPN
m-1112	1244	35	⃗⃖	⃗⃖	NOUN
m-1112	1244	36	�	�	PROPN
m-1112	1244	37	]	]	PUNCT
m-1112	1244	38	.	.	PUNCT
m-1112	1245	1	[	[	X
m-1112	1245	2	arc	arc	NOUN
m-1112	1245	3	cos	cos	PROPN
m-1112	1245	4	(	(	PUNCT
m-1112	1245	5	w|λ|/2	w|λ|/2	PROPN
m-1112	1245	6	.	.	PUNCT
m-1112	1245	7	|√	|√	PROPN
m-1112	1245	8	�	�	PROPN
m-1112	1245	9	⃡	⃡	NOUN
m-1112	1245	10	�	�	PROPN
m-1112	1245	11	`	`	PUNCT
m-1112	1245	12	𝐨.	𝐨.	NOUN
m-1112	1245	13	�	�	PROPN
m-1112	1245	14	⃡	⃡	PROPN
m-1112	1245	15	�	�	PROPN
m-1112	1245	16	𝐨|	𝐨|	PROPN
m-1112	1245	17	]	]	X
m-1112	1245	18	}	}	PUNCT
m-1112	1245	19	which	which	PRON
m-1112	1245	20	is	be	AUX
m-1112	1245	21	the	the	DET
m-1112	1245	22	beyond	beyond	ADP
m-1112	1245	23	-	-	PUNCT
m-1112	1245	24	gravity	gravity	NOUN
m-1112	1245	25	forced	force	VERB
m-1112	1245	26	field	field	NOUN
m-1112	1245	27	.	.	PUNCT
m-1112	1246	1	[	[	X
m-1112	1246	2	25	25	NUM
m-1112	1246	3	]	]	PUNCT
m-1112	1246	4	.	.	PUNCT
m-1112	1247	1	as	as	ADP
m-1112	1247	2	in	in	ADP
m-1112	1247	3	case	case	NOUN
m-1112	1247	4	(	(	PUNCT
m-1112	1247	5	1	1	NUM
m-1112	1247	6	)	)	PUNCT
m-1112	1247	7	→	→	PUNCT
m-1112	1247	8	there	there	PRON
m-1112	1247	9	is	be	VERB
m-1112	1247	10	no	no	DET
m-1112	1247	11	change	change	NOUN
m-1112	1247	12	of	of	ADP
m-1112	1247	13	ds	ds	ADJ
m-1112	1247	14	→	→	PUNCT
m-1112	1247	15	so	so	SCONJ
m-1112	1247	16	time	time	NOUN
m-1112	1247	17	t	t	NOUN
m-1112	1247	18	=	=	SYM
m-1112	1247	19	ds	ds	PROPN
m-1112	1247	20	/	/	SYM
m-1112	1247	21	v	v	NOUN
m-1112	1247	22	=	=	SYM
m-1112	1247	23	0	0	NUM
m-1112	1247	24	.	.	PUNCT
m-1112	1248	1	the	the	DET
m-1112	1248	2	cause	cause	NOUN
m-1112	1248	3	is	be	AUX
m-1112	1248	4	the	the	DET
m-1112	1248	5	lever	lever	ADJ
m-1112	1248	6	arm	arm	NOUN
m-1112	1248	7	moment	moment	NOUN
m-1112	1248	8	of	of	ADP
m-1112	1248	9	the	the	DET
m-1112	1248	10	primary	primary	ADJ
m-1112	1248	11	forces	force	NOUN
m-1112	1248	12	and	and	CCONJ
m-1112	1248	13	is	be	AUX
m-1112	1248	14	quantised	quantise	VERB
m-1112	1248	15	as	as	ADP
m-1112	1248	16	the	the	DET
m-1112	1248	17	torque	torque	NOUN
m-1112	1248	18	,	,	PUNCT
m-1112	1248	19	<	<	X
m-1112	1248	20	the	the	DET
m-1112	1248	21	torque	torque	NOUN
m-1112	1248	22	modelling	modelling	NOUN
m-1112	1248	23	of	of	ADP
m-1112	1248	24	microscopic	microscopic	ADJ
m-1112	1248	25	description	description	NOUN
m-1112	1248	26	>	>	X
m-1112	1248	27	,	,	PUNCT
m-1112	1248	28	and	and	CCONJ
m-1112	1248	29	later	later	ADV
m-1112	1248	30	the	the	DET
m-1112	1248	31	momentum	momentum	NOUN
m-1112	1248	32	[	[	X
m-1112	1248	33	19	19	NUM
m-1112	1248	34	]	]	PUNCT
m-1112	1248	35	.	.	PUNCT
m-1112	1249	1	the	the	DET
m-1112	1249	2	relative	relative	ADJ
m-1112	1249	3	range	range	NOUN
m-1112	1249	4	of	of	ADP
m-1112	1249	5	the	the	DET
m-1112	1249	6	infinite	infinite	ADJ
m-1112	1249	7	points	point	NOUN
m-1112	1249	8	is	be	AUX
m-1112	1249	9	the	the	DET
m-1112	1249	10	displacement	displacement	NOUN
m-1112	1249	11	ab	ab	PROPN
m-1112	1249	12	=	=	PROPN
m-1112	1249	13	�	�	PROPN
m-1112	1249	14	⃡	⃡	NOUN
m-1112	1249	15	�	�	PROPN
m-1112	1249	16	to	to	PART
m-1112	1249	17	infinity	infinity	VERB
m-1112	1249	18	∞	∞	PROPN
m-1112	1249	19	.	.	PUNCT
m-1112	1250	1	3	3	X
m-1112	1250	2	..	..	PUNCT
m-1112	1250	3	[	[	X
m-1112	1250	4	pns	pns	X
m-1112	1250	5	]	]	X
m-1112	1250	6	→	→	PUNCT
m-1112	1250	7	the	the	DET
m-1112	1250	8	temperature	temperature	NOUN
m-1112	1250	9	-	-	PUNCT
m-1112	1250	10	quaternion	quaternion	NOUN
m-1112	1250	11	[	[	PUNCT
m-1112	1250	12	λ	λ	PROPN
m-1112	1250	13	,	,	PUNCT
m-1112	1250	14	±	±	NUM
m-1112	1250	15	λ	λ	NOUN
m-1112	1250	16	x	x	X
m-1112	1250	17	]	]	PUNCT
m-1112	1250	18	=	=	PUNCT
m-1112	1251	1	z	z	NOUN
m-1112	1251	2	o	o	NOUN
m-1112	1252	1	=	=	PUNCT
m-1112	1252	2	λ	λ	NOUN
m-1112	1252	3	=	=	PUNCT
m-1112	1252	4	n.r.t	n.r.t	PROPN
m-1112	1252	5	/	/	SYM
m-1112	1252	6	v	v	PROPN
m-1112	1252	7	(	(	PUNCT
m-1112	1252	8	λ	λ	X
m-1112	1252	9	=	=	SYM
m-1112	1252	10	c	c	NOUN
m-1112	1252	11	)	)	PUNCT
m-1112	1252	12	→	→	PUNCT
m-1112	1252	13	the	the	DET
m-1112	1252	14	gas	gas	NOUN
m-1112	1252	15	equation	equation	NOUN
m-1112	1252	16	→	→	PUNCT
m-1112	1252	17	no	no	DET
m-1112	1252	18	change	change	NOUN
m-1112	1252	19	of	of	ADP
m-1112	1252	20	ds	ds	ADJ
m-1112	1252	21	→	→	PUNCT
m-1112	1252	22	so	so	SCONJ
m-1112	1252	23	time	time	NOUN
m-1112	1252	24	t	t	PROPN
m-1112	1252	25	=	=	SYM
m-1112	1252	26	0	0	PROPN
m-1112	1252	27	.	.	PUNCT
m-1112	1253	1	the	the	DET
m-1112	1253	2	cause	cause	NOUN
m-1112	1253	3	is	be	AUX
m-1112	1253	4	the	the	DET
m-1112	1253	5	heat	heat	NOUN
m-1112	1253	6	causing	cause	VERB
m-1112	1253	7	vibration	vibration	NOUN
m-1112	1253	8	on	on	ADP
m-1112	1253	9	molecules	molecule	NOUN
m-1112	1253	10	and	and	CCONJ
m-1112	1253	11	is	be	AUX
m-1112	1253	12	quantised	quantise	VERB
m-1112	1253	13	as	as	ADP
m-1112	1253	14	→	→	SYM
m-1112	1253	15	intensity	intensity	NOUN
m-1112	1253	16	(	(	PUNCT
m-1112	1253	17	pressure	pressure	NOUN
m-1112	1253	18	σ	σ	NOUN
m-1112	1254	1	=	=	PUNCT
m-1112	1254	2	𝟐𝛑𝐫.𝐟	𝟐𝛑𝐫.𝐟	PROPN
m-1112	1255	1	𝚽	𝚽	NOUN
m-1112	1255	2	=	=	SYM
m-1112	1255	3	𝟐𝛑𝐫.𝐜	𝟐𝛑𝐫.𝐜	PUNCT
m-1112	1255	4	𝚽.𝛌	𝚽.𝛌	NOUN
m-1112	1255	5	=	=	SYM
m-1112	1255	6	ijo	ijo	PROPN
m-1112	1255	7	international	international	PROPN
m-1112	1255	8	journal	journal	PROPN
m-1112	1255	9	of	of	ADP
m-1112	1255	10	mathematics	mathematics	PROPN
m-1112	1255	11	(	(	PUNCT
m-1112	1255	12	issn	issn	PROPN
m-1112	1255	13	:	:	PUNCT
m-1112	1255	14	2992	2992	NUM
m-1112	1255	15	-	-	SYM
m-1112	1255	16	4421	4421	NUM
m-1112	1255	17	)	)	PUNCT
m-1112	1255	18	volume	volume	NOUN
m-1112	1255	19	08	08	NUM
m-1112	1256	1	|	|	ADV
m-1112	1256	2	issue	issue	NOUN
m-1112	1256	3	08	08	NUM
m-1112	1257	1	|	|	ADV
m-1112	1257	2	august	august	PROPN
m-1112	1257	3	2025	2025	NUM
m-1112	1257	4	|	|	ADV
m-1112	1257	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1257	6	ijo	ijo	PROPN
m-1112	1257	7	journals	journal	NOUN
m-1112	1257	8	46	46	NUM
m-1112	1257	9	the	the	DET
m-1112	1257	10	fundamental	fundamental	ADJ
m-1112	1257	11	particles	particle	NOUN
m-1112	1257	12	origination	origination	NOUN
m-1112	1257	13	mechanism	mechanism	NOUN
m-1112	1257	14	in	in	ADP
m-1112	1257	15	mfmf	mfmf	PROPN
m-1112	1257	16	pns	pns	PROPN
m-1112	1257	17	caves	cave	NOUN
m-1112	1257	18	.	.	PUNCT
m-1112	1258	1	𝟐𝛑𝐫.𝛔	𝟐𝛑𝐫.𝛔	PUNCT
m-1112	1259	1	𝛌	𝛌	NOUN
m-1112	1259	2	)	)	PUNCT
m-1112	1259	3	between	between	ADP
m-1112	1259	4	them	they	PRON
m-1112	1259	5	.	.	PUNCT
m-1112	1260	1	the	the	DET
m-1112	1260	2	relative	relative	ADJ
m-1112	1260	3	range	range	NOUN
m-1112	1260	4	of	of	ADP
m-1112	1260	5	the	the	DET
m-1112	1260	6	infinite	infinite	ADJ
m-1112	1260	7	points	point	NOUN
m-1112	1260	8	in	in	ADP
m-1112	1260	9	displacement	displacement	NOUN
m-1112	1260	10	is	be	AUX
m-1112	1260	11	ab	ab	PROPN
m-1112	1260	12	=	=	PUNCT
m-1112	1260	13	λ	λ	PROPN
m-1112	1260	14	=	=	PUNCT
m-1112	1260	15	𝟐𝛑𝐫	𝟐𝛑𝐫	NOUN
m-1112	1260	16	which	which	PRON
m-1112	1260	17	is	be	AUX
m-1112	1260	18	the	the	DET
m-1112	1260	19	wavelength	wavelength	NOUN
m-1112	1260	20	λ	λ	PROPN
m-1112	1260	21	.	.	PROPN
m-1112	1261	1	3.a	3.a	NUM
m-1112	1261	2	→	→	SYM
m-1112	1261	3	k1	k1	PROPN
m-1112	1261	4	≡	≡	PROPN
m-1112	1261	5	z	z	PROPN
m-1112	1261	6	=	=	SYM
m-1112	1261	7	|𝑧	|𝑧	NOUN
m-1112	1261	8	0|	0|	X
m-1112	1261	9	.	.	PUNCT
m-1112	1262	1	e	e	PROPN
m-1112	1262	2	i.	i.	PROPN
m-1112	1262	3	(	(	PUNCT
m-1112	1262	4	9.π	9.π	NUM
m-1112	1262	5	/2	/2	NUM
m-1112	1262	6	)	)	PUNCT
m-1112	1262	7	.10	.10	NUM
m-1112	1263	1	=	=	PUNCT
m-1112	1263	2	the	the	DET
m-1112	1263	3	energy	energy	NOUN
m-1112	1263	4	under	under	ADP
m-1112	1263	5	planck	planck	NOUN
m-1112	1263	6	length	length	NOUN
m-1112	1263	7	,	,	PUNCT
m-1112	1263	8	the	the	DET
m-1112	1263	9	tank	tank	NOUN
m-1112	1263	10	cavity	cavity	NOUN
m-1112	1263	11	of	of	ADP
m-1112	1263	12	gravity	gravity	NOUN
m-1112	1263	13	where	where	SCONJ
m-1112	1263	14	�	�	NOUN
m-1112	1263	15	̅	̅	NOUN
m-1112	1263	16	�	�	NOUN
m-1112	1263	17	𝐄	𝐄	NOUN
m-1112	1263	18	=	=	PUNCT
m-1112	1263	19	0	0	NUM
m-1112	1263	20	and	and	CCONJ
m-1112	1263	21	et	et	NOUN
m-1112	1263	22	=	=	PUNCT
m-1112	1264	1	λ.v	λ.v	PROPN
m-1112	1264	2	b	b	NOUN
m-1112	1264	3	+	+	CCONJ
m-1112	1264	4	λ	λ	PROPN
m-1112	1264	5	x	x	PROPN
m-1112	1264	6	v.	v.	PROPN
m-1112	1264	7	�	�	PROPN
m-1112	1264	8	̅	̅	NOUN
m-1112	1264	9	�	�	PROPN
m-1112	1264	10	and	and	CCONJ
m-1112	1264	11	is	be	AUX
m-1112	1264	12	the	the	DET
m-1112	1264	13	accelerating	accelerate	VERB
m-1112	1264	14	removing	remove	VERB
m-1112	1264	15	,	,	PUNCT
m-1112	1264	16	rotating	rotate	VERB
m-1112	1264	17	energy	energy	NOUN
m-1112	1264	18	λ	λ	NOUN
m-1112	1264	19	to	to	ADP
m-1112	1264	20	v	v	NOUN
m-1112	1264	21	�	�	NOUN
m-1112	1264	22	̅	̅	NOUN
m-1112	1264	23	�	�	PROPN
m-1112	1264	24	,	,	PUNCT
m-1112	1264	25	m	m	VERB
m-1112	1264	26	=	=	SYM
m-1112	1264	27	0	0	NUM
m-1112	1264	28	and	and	CCONJ
m-1112	1264	29	et	et	NOUN
m-1112	1264	30	=	=	PUNCT
m-1112	1265	1	λ.v.b	λ.v.b	PROPN
m-1112	1266	1	+	+	CCONJ
m-1112	1266	2	λ	λ	X
m-1112	1266	3	x	x	PROPN
m-1112	1266	4	v.	v.	PROPN
m-1112	1266	5	�	�	PROPN
m-1112	1266	6	̅	̅	NOUN
m-1112	1266	7	�	�	PROPN
m-1112	1267	1	and	and	CCONJ
m-1112	1267	2	it	it	PRON
m-1112	1267	3	is	be	AUX
m-1112	1267	4	the	the	DET
m-1112	1267	5	linearly	linearly	ADV
m-1112	1267	6	removing	remove	VERB
m-1112	1267	7	,	,	PUNCT
m-1112	1267	8	energy	energy	NOUN
m-1112	1267	9	λ	λ	NOUN
m-1112	1267	10	towards	towards	ADP
m-1112	1267	11	v	v	NUM
m-1112	1267	12	b	b	NOUN
m-1112	1267	13	,	,	PUNCT
m-1112	1267	14	so	so	CCONJ
m-1112	1267	15	no	no	DET
m-1112	1267	16	change	change	NOUN
m-1112	1267	17	of	of	ADP
m-1112	1267	18	ds	ds	NOUN
m-1112	1267	19	→	→	PUNCT
m-1112	1267	20	therefore	therefore	ADV
m-1112	1267	21	time	time	NOUN
m-1112	1267	22	t	t	PROPN
m-1112	1267	23	=	=	SYM
m-1112	1267	24	0	0	PROPN
m-1112	1267	25	.	.	PUNCT
m-1112	1268	1	the	the	DET
m-1112	1268	2	cause	cause	NOUN
m-1112	1268	3	is	be	AUX
m-1112	1268	4	the	the	DET
m-1112	1268	5	high	high	ADJ
m-1112	1268	6	heat	heat	NOUN
m-1112	1268	7	conservational	conservational	ADJ
m-1112	1268	8	balanced	balanced	ADJ
m-1112	1268	9	tank	tank	NOUN
m-1112	1268	10	of	of	ADP
m-1112	1268	11	gravity	gravity	NOUN
m-1112	1268	12	and	and	CCONJ
m-1112	1268	13	is	be	AUX
m-1112	1268	14	quantised	quantise	VERB
m-1112	1268	15	as	as	ADP
m-1112	1268	16	the	the	DET
m-1112	1268	17	fundamental	fundamental	ADJ
m-1112	1268	18	particles	particle	NOUN
m-1112	1268	19	(	(	PUNCT
m-1112	1268	20	bosons	boson	NOUN
m-1112	1268	21	and	and	CCONJ
m-1112	1268	22	fermions	fermion	NOUN
m-1112	1268	23	)	)	PUNCT
m-1112	1268	24	.	.	PUNCT
m-1112	1269	1	[	[	X
m-1112	1269	2	30	30	NUM
m-1112	1269	3	]	]	X
m-1112	1269	4	the	the	DET
m-1112	1269	5	relative	relative	ADJ
m-1112	1269	6	range	range	NOUN
m-1112	1269	7	is	be	AUX
m-1112	1269	8	of	of	ADP
m-1112	1269	9	the	the	DET
m-1112	1269	10	infinite	infinite	ADJ
m-1112	1269	11	points	point	NOUN
m-1112	1269	12	in	in	ADP
m-1112	1269	13	displacement	displacement	ADJ
m-1112	1269	14	|ab|	|ab|	NOUN
m-1112	1269	15	to	to	PART
m-1112	1269	16	infinity	infinity	NOUN
m-1112	1269	17	.	.	PUNCT
m-1112	1270	1	3.b	3.b	NUM
m-1112	1270	2	→	→	SYM
m-1112	1270	3	k2	k2	PROPN
m-1112	1270	4	≡	≡	PROPN
m-1112	1270	5	z	z	NOUN
m-1112	1270	6	=	=	PRON
m-1112	1270	7	|𝑧	|𝑧	NOUN
m-1112	1270	8	0|.𝐞−	0|.𝐞−	PRON
m-1112	1270	9	𝐢	𝐢	X
m-1112	1270	10	(	(	PUNCT
m-1112	1270	11	𝟓𝛑	𝟓𝛑	NOUN
m-1112	1270	12	𝟐	𝟐	NUM
m-1112	1270	13	)	)	PUNCT
m-1112	1270	14	𝟏𝟎	𝟏𝟎	PROPN
m-1112	1270	15	=	=	PRON
m-1112	1270	16	the	the	DET
m-1112	1270	17	energy	energy	NOUN
m-1112	1270	18	in	in	ADP
m-1112	1270	19	planck	planck	NOUN
m-1112	1270	20	length	length	NOUN
m-1112	1270	21	→	→	SYM
m-1112	1270	22	∞	∞	NUM
m-1112	1270	23	changes	change	NOUN
m-1112	1270	24	of	of	ADP
m-1112	1270	25	ds	ds	NOUN
m-1112	1270	26	→	→	PUNCT
m-1112	1270	27	so	so	SCONJ
m-1112	1270	28	time	time	NOUN
m-1112	1270	29	t	t	PROPN
m-1112	1270	30	=	=	SYM
m-1112	1270	31	t	t	PROPN
m-1112	1270	32	.	.	PUNCT
m-1112	1271	1	cause	cause	NOUN
m-1112	1271	2	are	be	AUX
m-1112	1271	3	the	the	DET
m-1112	1271	4	infinite	infinite	ADJ
m-1112	1271	5	changes	change	NOUN
m-1112	1271	6	of	of	ADP
m-1112	1271	7	space	space	NOUN
m-1112	1271	8	and	and	CCONJ
m-1112	1271	9	is	be	AUX
m-1112	1271	10	quantised	quantise	VERB
m-1112	1271	11	as	as	ADP
m-1112	1271	12	→	→	SYM
m-1112	1271	13	matter	matter	NOUN
m-1112	1271	14	,	,	PUNCT
m-1112	1271	15	energy	energy	NOUN
m-1112	1271	16	and	and	CCONJ
m-1112	1271	17	the	the	DET
m-1112	1271	18	existent	existent	ADJ
m-1112	1271	19	as	as	ADP
m-1112	1271	20	caves	cave	NOUN
m-1112	1271	21	.	.	PUNCT
m-1112	1272	1	the	the	DET
m-1112	1272	2	material	material	NOUN
m-1112	1272	3	-	-	PUNCT
m-1112	1272	4	points	point	NOUN
m-1112	1272	5	occupy	occupy	VERB
m-1112	1272	6	a	a	DET
m-1112	1272	7	relative	relative	ADJ
m-1112	1272	8	range	range	NOUN
m-1112	1272	9	in	in	ADP
m-1112	1272	10	planck`s	planck`s	NOUN
m-1112	1272	11	length	length	NOUN
m-1112	1272	12	as	as	ADP
m-1112	1272	13	in	in	ADP
m-1112	1272	14	fig-1	fig-1	NUM
m-1112	1272	15	3.c	3.c	NUM
m-1112	1272	16	.	.	PUNCT
m-1112	1273	1	→	→	SYM
m-1112	1273	2	k3	k3	X
m-1112	1273	3	≡	≡	PROPN
m-1112	1273	4	z	z	NOUN
m-1112	1273	5	=	=	PUNCT
m-1112	1273	6	|𝑧	|𝑧	NOUN
m-1112	1273	7	0	0	PUNCT
m-1112	1273	8	=	=	SYM
m-1112	1273	9	λ|	λ|	PROPN
m-1112	1273	10	.	.	PUNCT
m-1112	1274	1	e	e	PROPN
m-1112	1274	2	i.	i.	PROPN
m-1112	1274	3	(	(	PUNCT
m-1112	1274	4	π	π	PROPN
m-1112	1274	5	/	/	SYM
m-1112	1274	6	2	2	NUM
m-1112	1274	7	)	)	PUNCT
m-1112	1274	8	.	.	PUNCT
m-1112	1275	1	10	10	NUM
m-1112	1275	2	=	=	NOUN
m-1112	1275	3	the	the	DET
m-1112	1275	4	black	black	ADJ
m-1112	1275	5	hole	hole	NOUN
m-1112	1275	6	temperature	temperature	NOUN
m-1112	1275	7	,	,	PUNCT
m-1112	1275	8	balanced	balanced	ADJ
m-1112	1275	9	tank	tank	NOUN
m-1112	1275	10	energy	energy	NOUN
m-1112	1275	11	length	length	NOUN
m-1112	1275	12	,	,	PUNCT
m-1112	1275	13	where	where	SCONJ
m-1112	1275	14	pv	pv	NOUN
m-1112	1275	15	=	=	PUNCT
m-1112	1275	16	n.r.t	n.r.t	ADJ
m-1112	1275	17	and	and	CCONJ
m-1112	1275	18	(	(	PUNCT
m-1112	1275	19	pa	pa	PROPN
m-1112	1275	20	=	=	SYM
m-1112	1275	21	wd	wd	PROPN
m-1112	1275	22	=	=	SYM
m-1112	1275	23	σ.t	σ.t	PROPN
m-1112	1275	24	4	4	NUM
m-1112	1275	25	)	)	PUNCT
m-1112	1275	26	→	→	PUNCT
m-1112	1275	27	no	no	DET
m-1112	1275	28	change	change	NOUN
m-1112	1275	29	of	of	ADP
m-1112	1275	30	ds	ds	NOUN
m-1112	1275	31	→	→	PUNCT
m-1112	1275	32	so	so	CCONJ
m-1112	1275	33	time	time	NOUN
m-1112	1275	34	is	be	AUX
m-1112	1275	35	t	t	NOUN
m-1112	1275	36	=	=	SYM
m-1112	1275	37	constant	constant	ADJ
m-1112	1275	38	.	.	PUNCT
m-1112	1276	1	cause	cause	NOUN
m-1112	1276	2	is	be	AUX
m-1112	1276	3	the	the	DET
m-1112	1276	4	very	very	ADV
m-1112	1276	5	high	high	ADJ
m-1112	1276	6	heat	heat	NOUN
m-1112	1276	7	causing	cause	VERB
m-1112	1276	8	vibration	vibration	NOUN
m-1112	1276	9	on	on	ADP
m-1112	1276	10	molecules	molecule	NOUN
m-1112	1276	11	and	and	CCONJ
m-1112	1276	12	is	be	AUX
m-1112	1276	13	quantized	quantize	VERB
m-1112	1276	14	as	as	ADP
m-1112	1276	15	→	→	SYM
m-1112	1276	16	intensity	intensity	NOUN
m-1112	1276	17	=	=	NOUN
m-1112	1276	18	(	(	PUNCT
m-1112	1276	19	pressure	pressure	NOUN
m-1112	1276	20	=	=	PUNCT
m-1112	1276	21	fd	fd	PROPN
m-1112	1276	22	=	=	SYM
m-1112	1276	23	c.	c.	PROPN
m-1112	1276	24	�	�	PROPN
m-1112	1276	25	̅	̅	NOUN
m-1112	1276	26	�	�	PROPN
m-1112	1276	27	=	=	SYM
m-1112	1276	28	±	±	NUM
m-1112	1277	1	co	co	X
m-1112	1277	2	.w.[√	.w.[√	PROPN
m-1112	1277	3	a²	a²	PROPN
m-1112	1277	4	x²	x²	PROPN
m-1112	1277	5	]	]	PUNCT
m-1112	1277	6	)	)	PUNCT
m-1112	1277	7	i.e.	i.e.	X
m-1112	1277	8	cause	cause	NOUN
m-1112	1277	9	→	→	SYM
m-1112	1277	10	(	(	PUNCT
m-1112	1277	11	constant	constant	ADJ
m-1112	1277	12	co	co	NOUN
m-1112	1277	13	)	)	PUNCT
m-1112	1277	14	→	→	PUNCT
m-1112	1277	15	quantized	quantize	VERB
m-1112	1277	16	as	as	ADP
m-1112	1277	17	new	new	ADJ
m-1112	1277	18	monad	monad	PROPN
m-1112	1277	19	and	and	CCONJ
m-1112	1277	20	relative	relative	ADJ
m-1112	1277	21	range	range	NOUN
m-1112	1277	22	is	be	AUX
m-1112	1277	23	infinity	infinity	NOUN
m-1112	1277	24	,	,	PUNCT
m-1112	1277	25	or	or	CCONJ
m-1112	1277	26	the	the	DET
m-1112	1277	27	meter	meter	NOUN
m-1112	1277	28	of	of	ADP
m-1112	1277	29	space	space	NOUN
m-1112	1277	30	-	-	PUNCT
m-1112	1277	31	energychanges	energychange	NOUN
m-1112	1277	32	is	be	AUX
m-1112	1277	33	time	time	NOUN
m-1112	1277	34	t	t	PROPN
m-1112	1277	35	,	,	PUNCT
m-1112	1277	36	which	which	PRON
m-1112	1277	37	exists	exist	VERB
m-1112	1277	38	in	in	ADP
m-1112	1277	39	k2	k2	PROPN
m-1112	1277	40	quantized	quantize	VERB
m-1112	1277	41	-	-	PUNCT
m-1112	1277	42	region	region	NOUN
m-1112	1277	43	only	only	ADV
m-1112	1277	44	.	.	PUNCT
m-1112	1278	1	from	from	ADP
m-1112	1278	2	quaternion	quaternion	NOUN
m-1112	1278	3	equation	equation	NOUN
m-1112	1278	4	�	�	NOUN
m-1112	1278	5	̅	̅	NOUN
m-1112	1278	6	�	�	NOUN
m-1112	1278	7	=	=	PUNCT
m-1112	1279	1	[	[	X
m-1112	1279	2	s	s	X
m-1112	1279	3			PROPN
m-1112	1279	4	�	�	PROPN
m-1112	1279	5	̅	̅	NOUN
m-1112	1279	6	�	�	NOUN
m-1112	1279	7	.	.	PUNCT
m-1112	1280	1	i	i	PRON
m-1112	1280	2	]	]	PUNCT
m-1112	1280	3	=	=	PUNCT
m-1112	1281	1	[	[	X
m-1112	1281	2	s²	s²	ADJ
m-1112	1281	3	±	±	NUM
m-1112	1281	4	�	�	PROPN
m-1112	1281	5	̅	̅	NOUN
m-1112	1281	6	�	�	NOUN
m-1112	1281	7	.s²	.s²	ADJ
m-1112	1281	8	]	]	PUNCT
m-1112	1282	1	=	=	SYM
m-1112	1282	2	[	[	PUNCT
m-1112	1282	3	�	�	NOUN
m-1112	1282	4	̅	̅	NOUN
m-1112	1282	5	�	�	NOUN
m-1112	1282	6	↔	↔	NOUN
m-1112	1282	7	�	�	NOUN
m-1112	1282	8	̅	̅	NOUN
m-1112	1282	9	�	�	NOUN
m-1112	1282	10	]	]	PUNCT
m-1112	1282	11	=	=	PUNCT
m-1112	1283	1	[	[	PUNCT
m-1112	1283	2	+	+	ADJ
m-1112	1283	3	|	|	ADJ
m-1112	1283	4	�	�	SYM
m-1112	1283	5	̅	̅	NOUN
m-1112	1283	6	�	�	PROPN
m-1112	1283	7	|²	|²	VERB
m-1112	1283	8	↔	↔	PROPN
m-1112	1283	9	|	|	NOUN
m-1112	1283	10	�	�	PROPN
m-1112	1283	11	̅	̅	NOUN
m-1112	1283	12	�	�	NOUN
m-1112	1283	13	|²	|²	NUM
m-1112	1283	14	]	]	PUNCT
m-1112	1283	15	is	be	AUX
m-1112	1283	16	seen	see	VERB
m-1112	1283	17	that	that	PRON
m-1112	1283	18	motion	motion	NOUN
m-1112	1283	19	,	,	PUNCT
m-1112	1283	20	+	+	PROPN
m-1112	1283	21	|	|	ADJ
m-1112	1283	22	�	�	SYM
m-1112	1283	23	̅	̅	NOUN
m-1112	1283	24	�	�	NOUN
m-1112	1283	25	|²	|²	NUM
m-1112	1283	26	at	at	ADP
m-1112	1283	27	point	point	NOUN
m-1112	1283	28	a	a	PRON
m-1112	1283	29	,	,	PUNCT
m-1112	1283	30	is	be	AUX
m-1112	1283	31	transferred	transfer	VERB
m-1112	1283	32	as	as	ADP
m-1112	1283	33	motion	motion	NOUN
m-1112	1283	34	|	|	NOUN
m-1112	1283	35	�	�	NOUN
m-1112	1283	36	̅	̅	NOUN
m-1112	1283	37	�	�	NOUN
m-1112	1283	38	|²	|²	NUM
m-1112	1283	39	at	at	ADP
m-1112	1283	40	point	point	NOUN
m-1112	1283	41	b	b	PROPN
m-1112	1283	42	.	.	PUNCT
m-1112	1284	1	this	this	DET
m-1112	1284	2	issues	issue	NOUN
m-1112	1284	3	from	from	ADP
m-1112	1284	4	quaternion	quaternion	NOUN
m-1112	1284	5	equation	equation	NOUN
m-1112	1284	6	�	�	NOUN
m-1112	1284	7	̅	̅	NOUN
m-1112	1284	8	�	�	NOUN
m-1112	1284	9	=	=	PUNCT
m-1112	1285	1	[	[	X
m-1112	1285	2	s	s	X
m-1112	1285	3			PROPN
m-1112	1285	4	�	�	PROPN
m-1112	1285	5	̅	̅	NOUN
m-1112	1285	6	�	�	NOUN
m-1112	1285	7	.	.	PUNCT
m-1112	1286	1	i	i	PRON
m-1112	1286	2	]	]	PUNCT
m-1112	1286	3	=	=	PUNCT
m-1112	1287	1	[	[	X
m-1112	1287	2	s²	s²	ADJ
m-1112	1287	3	±	±	NUM
m-1112	1287	4	�	�	PROPN
m-1112	1287	5	̅	̅	NOUN
m-1112	1287	6	�	�	NOUN
m-1112	1287	7	.s²	.s²	ADJ
m-1112	1287	8	]	]	PUNCT
m-1112	1288	1	=	=	PUNCT
m-1112	1288	2	[	[	PUNCT
m-1112	1288	3	�	�	NOUN
m-1112	1288	4	̅	̅	NOUN
m-1112	1288	5	�	�	NOUN
m-1112	1288	6	↔	↔	NOUN
m-1112	1288	7	�	�	NOUN
m-1112	1288	8	̅	̅	NOUN
m-1112	1288	9	�	�	NOUN
m-1112	1288	10	]	]	X
m-1112	1288	11	=	=	PUNCT
m-1112	1289	1	[	[	PUNCT
m-1112	1289	2	+	+	ADJ
m-1112	1289	3	|	|	ADJ
m-1112	1289	4	�	�	SYM
m-1112	1289	5	̅	̅	NOUN
m-1112	1289	6	�	�	PROPN
m-1112	1289	7	|²	|²	VERB
m-1112	1289	8	↔	↔	PROPN
m-1112	1289	9	|	|	NOUN
m-1112	1289	10	�	�	PROPN
m-1112	1289	11	̅	̅	NOUN
m-1112	1289	12	�	�	NOUN
m-1112	1289	13	|²	|²	NUM
m-1112	1289	14	]	]	PUNCT
m-1112	1289	15	.	.	PUNCT
m-1112	1290	1	fig	fig	NOUN
m-1112	1290	2	-1	-1	PUNCT
m-1112	1290	3	i.e.	i.e.	X
m-1112	1290	4	the	the	DET
m-1112	1290	5	vectors	vector	NOUN
m-1112	1290	6	-	-	PUNCT
m-1112	1290	7	sum	sum	NOUN
m-1112	1290	8	of	of	ADP
m-1112	1290	9	,	,	PUNCT
m-1112	1290	10	n	n	CCONJ
m-1112	1290	11	,	,	PUNCT
m-1112	1290	12	vectors	vector	NOUN
m-1112	1290	13	,	,	PUNCT
m-1112	1290	14	either	either	CCONJ
m-1112	1290	15	on	on	ADP
m-1112	1290	16	the	the	DET
m-1112	1290	17	same	same	ADJ
m-1112	1290	18	linear	linear	NOUN
m-1112	1290	19	-	-	PUNCT
m-1112	1290	20	direction	direction	NOUN
m-1112	1290	21	or	or	CCONJ
m-1112	1290	22	,	,	PUNCT
m-1112	1290	23	on	on	ADP
m-1112	1290	24	non	non	ADJ
m-1112	1290	25	linear	linear	ADJ
m-1112	1290	26	-	-	PUNCT
m-1112	1290	27	directions	direction	NOUN
m-1112	1290	28	results	result	NOUN
m-1112	1290	29	on	on	ADP
m-1112	1290	30	the	the	DET
m-1112	1290	31	–	–	PUNCT
m-1112	1290	32	resultant	resultant	NOUN
m-1112	1290	33	vector	vector	PROPN
m-1112	1290	34	�	�	PROPN
m-1112	1290	35	⃗⃖	⃗⃖	PROPN
m-1112	1290	36	�	�	PROPN
m-1112	1290	37	of	of	ADP
m-1112	1290	38	the	the	DET
m-1112	1290	39	linear	linear	ADJ
m-1112	1290	40	-	-	PUNCT
m-1112	1290	41	vibration	vibration	NOUN
m-1112	1290	42	and	and	CCONJ
m-1112	1290	43	between	between	ADP
m-1112	1290	44	the	the	DET
m-1112	1290	45	quaternion	quaternion	NOUN
m-1112	1290	46	edge	edge	NOUN
m-1112	1290	47	-	-	PUNCT
m-1112	1290	48	poinds	poind	NOUN
m-1112	1290	49	[	[	PUNCT
m-1112	1290	50	�	�	NOUN
m-1112	1290	51	̅	̅	NOUN
m-1112	1290	52	�	�	NOUN
m-1112	1290	53	↔	↔	NOUN
m-1112	1290	54	�	�	NOUN
m-1112	1290	55	̅	̅	NOUN
m-1112	1290	56	�	�	NOUN
m-1112	1290	57	]	]	PUNCT
m-1112	1290	58	.	.	PUNCT
m-1112	1291	1	conclusions	conclusion	NOUN
m-1112	1291	2	–	–	PUNCT
m-1112	1291	3	1	1	NUM
m-1112	1291	4	:	:	PUNCT
m-1112	1291	5	energy	energy	NOUN
m-1112	1291	6	in	in	ADP
m-1112	1291	7	primary	primary	ADJ
m-1112	1291	8	-	-	PUNCT
m-1112	1291	9	neutral	neutral	ADJ
m-1112	1291	10	-	-	PUNCT
m-1112	1291	11	space	space	NOUN
m-1112	1291	12	[	[	X
m-1112	1291	13	pns	pns	X
m-1112	1291	14	]	]	PUNCT
m-1112	1291	15	and	and	CCONJ
m-1112	1291	16	,	,	PUNCT
m-1112	1291	17	in	in	ADP
m-1112	1291	18	under	under	ADP
m-1112	1291	19	planck1s	planck1s	PROPN
m-1112	1291	20	length	length	NOUN
m-1112	1291	21	≡	≡	PROPN
m-1112	1291	22	the	the	DET
m-1112	1291	23	tank	tank	NOUN
m-1112	1291	24	cavity	cavity	NOUN
m-1112	1291	25	of	of	ADP
m-1112	1291	26	gravity	gravity	NOUN
m-1112	1291	27	is	be	AUX
m-1112	1291	28	an	an	DET
m-1112	1291	29	standing	standing	ADJ
m-1112	1291	30	wave	wave	NOUN
m-1112	1291	31	with	with	ADP
m-1112	1291	32	no	no	DET
m-1112	1291	33	-	-	PUNCT
m-1112	1291	34	time	time	NOUN
m-1112	1291	35	existing	exist	VERB
m-1112	1291	36	as	as	ADP
m-1112	1291	37	t	t	NOUN
m-1112	1291	38	=	=	SYM
m-1112	1291	39	ds	ds	PROPN
m-1112	1291	40	/	/	SYM
m-1112	1291	41	v	v	NOUN
m-1112	1291	42	=	=	SYM
m-1112	1291	43	0	0	NUM
m-1112	1291	44	.	.	PUNCT
m-1112	1292	1	conclusions	conclusion	NOUN
m-1112	1292	2	–	–	PUNCT
m-1112	1292	3	2	2	NUM
m-1112	1292	4	:	:	PUNCT
m-1112	1292	5	since	since	SCONJ
m-1112	1292	6	in	in	ADP
m-1112	1292	7	primary	primary	ADJ
m-1112	1292	8	-	-	PUNCT
m-1112	1292	9	neutral	neutral	ADJ
m-1112	1292	10	-	-	PUNCT
m-1112	1292	11	space	space	NOUN
m-1112	1292	12	[	[	X
m-1112	1292	13	pns	pns	X
m-1112	1292	14	]	]	PUNCT
m-1112	1292	15	and	and	CCONJ
m-1112	1292	16	,	,	PUNCT
m-1112	1292	17	in	in	ADP
m-1112	1292	18	under	under	ADP
m-1112	1292	19	planck1s	planck1s	PROPN
m-1112	1292	20	length	length	NOUN
m-1112	1292	21	≡	≡	PROPN
m-1112	1292	22	the	the	DET
m-1112	1292	23	tank	tank	NOUN
m-1112	1292	24	cavity	cavity	NOUN
m-1112	1292	25	of	of	ADP
m-1112	1292	26	gravity	gravity	NOUN
m-1112	1292	27	existing	exist	VERB
m-1112	1292	28	as	as	ADP
m-1112	1292	29	t	t	NOUN
m-1112	1292	30	=	=	SYM
m-1112	1292	31	ds	ds	PROPN
m-1112	1292	32	/	/	SYM
m-1112	1292	33	v	v	NOUN
m-1112	1292	34	=	=	SYM
m-1112	1292	35	0	0	NUM
m-1112	1292	36	.	.	PUNCT
m-1112	1293	1	the	the	DET
m-1112	1293	2	only	only	ADJ
m-1112	1293	3	meter	meter	NOUN
m-1112	1293	4	of	of	ADP
m-1112	1293	5	changes	change	NOUN
m-1112	1293	6	is	be	AUX
m-1112	1293	7	the	the	DET
m-1112	1293	8	period	period	NOUN
m-1112	1293	9	of	of	ADP
m-1112	1293	10	rotation	rotation	NOUN
m-1112	1293	11	of	of	ADP
m-1112	1293	12	the	the	DET
m-1112	1293	13	[	[	NOUN
m-1112	1293	14	⊝	⊝	SYM
m-1112	1293	15	↻	↻	PROPN
m-1112	1293	16	⊕	⊕	PROPN
m-1112	1293	17	]	]	PUNCT
m-1112	1293	18	as	as	ADP
m-1112	1293	19	in	in	ADP
m-1112	1293	20	the	the	DET
m-1112	1293	21	next	next	ADJ
m-1112	1293	22	figure-11	figure-11	PROPN
m-1112	1293	23	.	.	PUNCT
m-1112	1294	1	ijo	ijo	PROPN
m-1112	1294	2	international	international	PROPN
m-1112	1294	3	journal	journal	PROPN
m-1112	1294	4	of	of	ADP
m-1112	1294	5	mathematics	mathematics	PROPN
m-1112	1294	6	(	(	PUNCT
m-1112	1294	7	issn	issn	PROPN
m-1112	1294	8	:	:	PUNCT
m-1112	1294	9	2992	2992	NUM
m-1112	1294	10	-	-	SYM
m-1112	1294	11	4421	4421	NUM
m-1112	1294	12	)	)	PUNCT
m-1112	1294	13	volume	volume	NOUN
m-1112	1294	14	08	08	NUM
m-1112	1295	1	|	|	ADV
m-1112	1295	2	issue	issue	NOUN
m-1112	1295	3	08	08	NUM
m-1112	1296	1	|	|	ADV
m-1112	1296	2	august	august	PROPN
m-1112	1296	3	2025	2025	NUM
m-1112	1297	1	|	|	ADV
m-1112	1297	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1297	3	ijo	ijo	PROPN
m-1112	1297	4	journals	journal	NOUN
m-1112	1297	5	47	47	NUM
m-1112	1297	6	the	the	DET
m-1112	1297	7	fundamental	fundamental	ADJ
m-1112	1297	8	particles	particle	NOUN
m-1112	1297	9	origination	origination	NOUN
m-1112	1297	10	mechanism	mechanism	NOUN
m-1112	1297	11	in	in	ADP
m-1112	1297	12	mfmf	mfmf	PROPN
m-1112	1297	13	pns	pns	PROPN
m-1112	1297	14	caves	cave	NOUN
m-1112	1297	15	.	.	PUNCT
m-1112	1298	1	figure	figure	NOUN
m-1112	1298	2	–	–	PUNCT
m-1112	1298	3	11	11	NUM
m-1112	1298	4	-	-	PUNCT
m-1112	1298	5	the	the	DET
m-1112	1298	6	rotation	rotation	NOUN
m-1112	1298	7	of	of	ADP
m-1112	1298	8	opposites	opposite	NOUN
m-1112	1298	9	[	[	X
m-1112	1298	10	⊝	⊝	NUM
m-1112	1298	11	↻	↻	PROPN
m-1112	1298	12	⊕	⊕	PROPN
m-1112	1298	13	]	]	PUNCT
m-1112	1298	14	and	and	CCONJ
m-1112	1298	15	the	the	DET
m-1112	1298	16	how	how	SCONJ
m-1112	1298	17	and	and	CCONJ
m-1112	1298	18	why	why	SCONJ
m-1112	1298	19	spin	spin	NOUN
m-1112	1298	20	is	be	AUX
m-1112	1298	21	equal	equal	ADJ
m-1112	1298	22	to	to	ADP
m-1112	1298	23	1	1	NUM
m-1112	1298	24	,	,	PUNCT
m-1112	1298	25	𝟏	𝟏	NUM
m-1112	1298	26	𝟐	𝟐	NUM
m-1112	1298	27	in	in	ADP
m-1112	1298	28	(	(	PUNCT
m-1112	1298	29	1	1	NUM
m-1112	1298	30	)	)	PUNCT
m-1112	1298	31	.	.	PUNCT
m-1112	1299	1	the	the	DET
m-1112	1299	2	glue	glue	NOUN
m-1112	1299	3	-	-	PUNCT
m-1112	1299	4	bond	bond	NOUN
m-1112	1299	5	-	-	PUNCT
m-1112	1299	6	pair	pair	NOUN
m-1112	1299	7	of	of	ADP
m-1112	1299	8	opposites	opposite	NOUN
m-1112	1299	9	[	[	X
m-1112	1299	10	⊝	⊝	X
m-1112	1299	11	σ	σ	PROPN
m-1112	1299	12	⊕	⊕	PROPN
m-1112	1299	13	]	]	PUNCT
m-1112	1299	14	of	of	ADP
m-1112	1299	15	the	the	DET
m-1112	1299	16	rectilinear	rectilinear	ADJ
m-1112	1299	17	motion	motion	NOUN
m-1112	1299	18	for	for	ADP
m-1112	1299	19	both	both	DET
m-1112	1299	20	→	→	SYM
m-1112	1299	21	great	great	ADJ
m-1112	1299	22	circles	circle	NOUN
m-1112	1299	23	and	and	CCONJ
m-1112	1299	24	the	the	DET
m-1112	1299	25	small	small	ADJ
m-1112	1299	26	circles	circle	NOUN
m-1112	1299	27	,	,	PUNCT
m-1112	1299	28	creates	create	VERB
m-1112	1299	29	on	on	ADP
m-1112	1299	30	the	the	DET
m-1112	1299	31	stress	stress	NOUN
m-1112	1299	32	-	-	PUNCT
m-1112	1299	33	common	common	ADJ
m-1112	1299	34	-	-	PUNCT
m-1112	1299	35	curve	curve	NOUN
m-1112	1299	36	rotation	rotation	NOUN
m-1112	1299	37	of	of	ADP
m-1112	1299	38	circle	circle	NOUN
m-1112	1299	39	of	of	ADP
m-1112	1299	40	radius	radius	NOUN
m-1112	1299	41	r	r	NOUN
m-1112	1299	42	,	,	PUNCT
m-1112	1299	43	the	the	DET
m-1112	1299	44	velocity	velocity	NOUN
m-1112	1299	45	v̅	v̅	X
m-1112	1300	1	=	=	PUNCT
m-1112	1300	2	w.r	w.r	NOUN
m-1112	1300	3	=	=	SYM
m-1112	1300	4	2π	2π	PROPN
m-1112	1300	5	t	t	NOUN
m-1112	1300	6	.r	.r	NOUN
m-1112	1301	1	=	=	PUNCT
m-1112	1301	2	2πr	2πr	NOUN
m-1112	1301	3	.	.	PUNCT
m-1112	1302	1	f	f	X
m-1112	1303	1	=	=	PUNCT
m-1112	1303	2	[	[	PUNCT
m-1112	1303	3	σ	σ	PROPN
m-1112	1303	4	2	2	NUM
m-1112	1303	5	]	]	PUNCT
m-1112	1303	6	.(1+√5	.(1+√5	PUNCT
m-1112	1303	7	)	)	PUNCT
m-1112	1304	1	=	=	SYM
m-1112	1304	2	±	±	NUM
m-1112	1304	3	σ.φ	σ.φ	PROPN
m-1112	1304	4	,	,	PUNCT
m-1112	1304	5	and	and	CCONJ
m-1112	1304	6	the	the	DET
m-1112	1304	7	frequency	frequency	NOUN
m-1112	1304	8	f	f	X
m-1112	1304	9	=	=	PUNCT
m-1112	1304	10	(	(	PUNCT
m-1112	1304	11	1	1	NUM
m-1112	1304	12	+	+	NUM
m-1112	1304	13	√5	√5	NOUN
m-1112	1304	14	]	]	PUNCT
m-1112	1304	15	)	)	PUNCT
m-1112	1304	16	.	.	PUNCT
m-1112	1305	1	σ	σ	NOUN
m-1112	1305	2	4πr	4πr	NOUN
m-1112	1306	1	=	=	PUNCT
m-1112	1306	2	σ	σ	PROPN
m-1112	1306	3	φ	φ	PROPN
m-1112	1306	4	2πr	2πr	NOUN
m-1112	1306	5	,	,	PUNCT
m-1112	1306	6	of	of	ADP
m-1112	1306	7	a	a	DET
m-1112	1306	8	period	period	NOUN
m-1112	1306	9	t	t	NOUN
m-1112	1306	10	=	=	SYM
m-1112	1306	11	4πr	4πr	PROPN
m-1112	1306	12	σ(1+√5	σ(1+√5	PROPN
m-1112	1306	13	)	)	PUNCT
m-1112	1306	14	=	=	PUNCT
m-1112	1307	1	2πr	2πr	NOUN
m-1112	1307	2	σ.φ	σ.φ	NOUN
m-1112	1307	3	and	and	CCONJ
m-1112	1307	4	,	,	PUNCT
m-1112	1307	5	±	±	NUM
m-1112	1307	6	σ	σ	NOUN
m-1112	1307	7	,	,	PUNCT
m-1112	1307	8	where	where	SCONJ
m-1112	1307	9	then	then	ADV
m-1112	1307	10	exist	exist	VERB
m-1112	1307	11	two	two	NUM
m-1112	1307	12	equal	equal	ADJ
m-1112	1307	13	and	and	CCONJ
m-1112	1307	14	opposite	opposite	ADJ
m-1112	1307	15	forces	force	NOUN
m-1112	1307	16	,	,	PUNCT
m-1112	1307	17	→	→	PUNCT
m-1112	1307	18	the	the	DET
m-1112	1307	19	centripetal	centripetal	NOUN
m-1112	1307	20	,	,	PUNCT
m-1112	1307	21	fp	fp	INTJ
m-1112	1307	22	,	,	PUNCT
m-1112	1307	23	and	and	CCONJ
m-1112	1307	24	the	the	DET
m-1112	1307	25	centrifugal	centrifugal	ADJ
m-1112	1307	26	,	,	PUNCT
m-1112	1307	27	ff	ff	NOUN
m-1112	1307	28	force	force	NOUN
m-1112	1307	29	.	.	PUNCT
m-1112	1308	1	the	the	DET
m-1112	1308	2	produced	produce	VERB
m-1112	1308	3	work	work	NOUN
m-1112	1308	4	as	as	ADP
m-1112	1308	5	energy	energy	NOUN
m-1112	1308	6	is	be	AUX
m-1112	1308	7	→	→	SYM
m-1112	1308	8	e	e	X
m-1112	1308	9	=	=	SYM
m-1112	1308	10	h	h	PROPN
m-1112	1308	11	f	f	NOUN
m-1112	1308	12	=	=	SYM
m-1112	1308	13	�	�	PROPN
m-1112	1308	14	̅	̅	NOUN
m-1112	1308	15	�	�	NOUN
m-1112	1308	16	=	=	PUNCT
m-1112	1308	17	momentum	momentum	NOUN
m-1112	1309	1	=	=	NOUN
m-1112	1309	2	r	r	NOUN
m-1112	1309	3	m	m	VERB
m-1112	1309	4	v	v	NOUN
m-1112	1309	5	=	=	SYM
m-1112	1309	6	r	r	NOUN
m-1112	1309	7	[	[	PUNCT
m-1112	1309	8	𝜋	𝜋	NOUN
m-1112	1309	9	𝑟²	𝑟²	NOUN
m-1112	1309	10	2	2	NUM
m-1112	1309	11	]	]	PUNCT
m-1112	1309	12	w	w	NOUN
m-1112	1309	13	r	r	NOUN
m-1112	1309	14	=	=	PUNCT
m-1112	1310	1	[	[	PUNCT
m-1112	1310	2	𝜋	𝜋	NOUN
m-1112	1310	3	r4	r4	NOUN
m-1112	1310	4	2	2	NUM
m-1112	1310	5	]	]	PUNCT
m-1112	1310	6	w	w	NOUN
m-1112	1311	1	=	=	PUNCT
m-1112	1312	1	[	[	PUNCT
m-1112	1312	2	𝜋	𝜋	NOUN
m-1112	1312	3	r4	r4	NOUN
m-1112	1312	4	2	2	NUM
m-1112	1312	5	]	]	SYM
m-1112	1312	6	2πf	2πf	ADJ
m-1112	1312	7	=	=	SYM
m-1112	1312	8	π²	π²	NOUN
m-1112	1312	9	.	.	PUNCT
m-1112	1313	1	r4.f	r4.f	NOUN
m-1112	1313	2	=	=	SYM
m-1112	1313	3	�	�	PROPN
m-1112	1313	4	̅	̅	NOUN
m-1112	1313	5	�	�	PROPN
m-1112	1313	6	,	,	PUNCT
m-1112	1313	7	where	where	SCONJ
m-1112	1313	8	f	f	AUX
m-1112	1313	9	=	=	PRON
m-1112	1313	10	(	(	PUNCT
m-1112	1313	11	1	1	NUM
m-1112	1313	12	+	+	NUM
m-1112	1313	13	√5	√5	ADJ
m-1112	1313	14	)	)	PUNCT
m-1112	1313	15	.σ	.σ	NOUN
m-1112	1313	16	4πr	4πr	NOUN
m-1112	1314	1	=	=	PUNCT
m-1112	1314	2	σ.φ	σ.φ	PROPN
m-1112	1314	3	2πr	2πr	NOUN
m-1112	1314	4	,	,	PUNCT
m-1112	1314	5	meaning	mean	VERB
m-1112	1314	6	that	that	SCONJ
m-1112	1314	7	the	the	DET
m-1112	1314	8	stress	stress	ADJ
m-1112	1314	9	pointy	pointy	ADJ
m-1112	1314	10	rotation	rotation	NOUN
m-1112	1314	11	creates	create	VERB
m-1112	1314	12	the	the	DET
m-1112	1314	13	angular	angular	ADJ
m-1112	1314	14	–	–	PUNCT
m-1112	1314	15	momentum	momentum	NOUN
m-1112	1314	16	and	and	CCONJ
m-1112	1314	17	momentum	momentum	NOUN
m-1112	1314	18	as	as	ADP
m-1112	1314	19	,	,	PUNCT
m-1112	1314	20	�	�	PROPN
m-1112	1314	21	̅	̅	NOUN
m-1112	1314	22	�	�	PROPN
m-1112	1314	23	,	,	PUNCT
m-1112	1314	24	�	�	PROPN
m-1112	1314	25	̅	̅	NOUN
m-1112	1314	26	�	�	PROPN
m-1112	1314	27	,	,	PUNCT
m-1112	1314	28	in	in	ADP
m-1112	1314	29	the	the	DET
m-1112	1314	30	zero	zero	NUM
m-1112	1314	31	wave	wave	NOUN
m-1112	1314	32	-	-	PUNCT
m-1112	1314	33	note	note	NOUN
m-1112	1314	34	.	.	PUNCT
m-1112	1315	1	[	[	X
m-1112	1315	2	70	70	NUM
m-1112	1315	3	]	]	PUNCT
m-1112	1315	4	the	the	DET
m-1112	1315	5	glue	glue	NOUN
m-1112	1315	6	-	-	PUNCT
m-1112	1315	7	bond	bond	NOUN
m-1112	1315	8	pair	pair	NOUN
m-1112	1315	9	of	of	ADP
m-1112	1315	10	opposites	opposite	NOUN
m-1112	1315	11	[	[	X
m-1112	1315	12	⊝	⊝	X
m-1112	1315	13	⊕	⊕	NOUN
m-1112	1315	14	]	]	PUNCT
m-1112	1315	15	in	in	ADP
m-1112	1315	16	the	the	DET
m-1112	1315	17	→	→	PUNCT
m-1112	1315	18	left	left	ADJ
m-1112	1315	19	direction	direction	NOUN
m-1112	1315	20	of	of	ADP
m-1112	1315	21	small	small	ADJ
m-1112	1315	22	circles	circle	NOUN
m-1112	1315	23	creates	create	VERB
m-1112	1315	24	a	a	DET
m-1112	1315	25	rotation	rotation	NOUN
m-1112	1315	26	on	on	ADP
m-1112	1315	27	circle	circle	NOUN
m-1112	1315	28	of	of	ADP
m-1112	1315	29	radius	radius	NOUN
m-1112	1315	30	,	,	PUNCT
m-1112	1315	31	r	r	NOUN
m-1112	1315	32	,	,	PUNCT
m-1112	1315	33	with	with	ADP
m-1112	1315	34	velocity	velocity	NOUN
m-1112	1315	35	v	v	X
m-1112	1315	36	=	=	PUNCT
m-1112	1315	37	w.2r	w.2r	NOUN
m-1112	1315	38	=	=	SYM
m-1112	1315	39	2π	2π	NOUN
m-1112	1315	40	t	t	NOUN
m-1112	1315	41	.2r	.2r	PUNCT
m-1112	1316	1	=	=	PUNCT
m-1112	1316	2	4πr	4πr	PROPN
m-1112	1316	3	.	.	PUNCT
m-1112	1317	1	f	f	X
m-1112	1318	1	=	=	PUNCT
m-1112	1318	2	[	[	PUNCT
m-1112	1318	3	σ	σ	PROPN
m-1112	1318	4	2	2	NUM
m-1112	1318	5	]	]	PUNCT
m-1112	1318	6	.(1+√5	.(1+√5	PROPN
m-1112	1318	7	)	)	PUNCT
m-1112	1318	8	,	,	PUNCT
m-1112	1318	9	where	where	SCONJ
m-1112	1318	10	frequency	frequency	NOUN
m-1112	1318	11	f	f	X
m-1112	1318	12	=	=	PUNCT
m-1112	1318	13	(	(	PUNCT
m-1112	1318	14	1	1	NUM
m-1112	1318	15	+	+	NUM
m-1112	1318	16	√5	√5	NOUN
m-1112	1318	17	]	]	PUNCT
m-1112	1318	18	)	)	PUNCT
m-1112	1318	19	.σ	.σ	PROPN
m-1112	1318	20	8πr	8πr	NOUN
m-1112	1318	21	=	=	SYM
m-1112	1319	1	σ	σ	PROPN
m-1112	1319	2	φ	φ	PROPN
m-1112	1319	3	2πr	2πr	NOUN
m-1112	1319	4	,	,	PUNCT
m-1112	1319	5	period	period	NOUN
m-1112	1319	6	t	t	NOUN
m-1112	1319	7	=	=	SYM
m-1112	1319	8	8πr	8πr	PROPN
m-1112	1319	9	σ(1+√5	σ(1+√5	PROPN
m-1112	1319	10	)	)	PUNCT
m-1112	1319	11	=	=	SYM
m-1112	1320	1	2π(2r	2π(2r	X
m-1112	1320	2	)	)	PUNCT
m-1112	1320	3	σ.φ	σ.φ	PROPN
m-1112	1320	4	,	,	PUNCT
m-1112	1320	5	where	where	SCONJ
m-1112	1320	6	±	±	NOUN
m-1112	1320	7	σ	σ	NOUN
m-1112	1320	8	are	be	AUX
m-1112	1320	9	the	the	DET
m-1112	1320	10	two	two	NUM
m-1112	1320	11	equal	equal	ADJ
m-1112	1320	12	and	and	CCONJ
m-1112	1320	13	opposite	opposite	ADJ
m-1112	1320	14	centripetal	centripetal	ADJ
m-1112	1320	15	,	,	PUNCT
m-1112	1320	16	fp	fp	INTJ
m-1112	1320	17	,	,	PUNCT
m-1112	1320	18	centrifugal	centrifugal	PROPN
m-1112	1320	19	,	,	PUNCT
m-1112	1320	20	ff	ff	NOUN
m-1112	1320	21	force	force	NOUN
m-1112	1320	22	,	,	PUNCT
m-1112	1320	23	with	with	ADP
m-1112	1320	24	energy	energy	NOUN
m-1112	1320	25	→	→	SYM
m-1112	1320	26	e	e	X
m-1112	1320	27	=	=	SYM
m-1112	1320	28	h.f	h.f	PROPN
m-1112	1320	29	=	=	PUNCT
m-1112	1320	30	h.σφ	h.σφ	PROPN
m-1112	1320	31	2πr	2πr	NOUN
m-1112	1320	32	,	,	PUNCT
m-1112	1320	33	in	in	ADP
m-1112	1320	34	one	one	NUM
m-1112	1320	35	wavenote	wavenote	NOUN
m-1112	1320	36	.	.	PUNCT
m-1112	1321	1	the	the	DET
m-1112	1321	2	glue	glue	NOUN
m-1112	1321	3	-	-	PUNCT
m-1112	1321	4	bond	bond	NOUN
m-1112	1321	5	pair	pair	NOUN
m-1112	1321	6	of	of	ADP
m-1112	1321	7	opposites	opposite	NOUN
m-1112	1321	8	[	[	X
m-1112	1321	9	⊝	⊝	X
m-1112	1321	10	⊕	⊕	NOUN
m-1112	1321	11	]	]	PUNCT
m-1112	1321	12	in	in	ADP
m-1112	1321	13	the	the	DET
m-1112	1321	14	→	→	NOUN
m-1112	1321	15	right	right	ADJ
m-1112	1321	16	direction	direction	NOUN
m-1112	1321	17	of	of	ADP
m-1112	1321	18	small	small	ADJ
m-1112	1321	19	circles	circle	NOUN
m-1112	1321	20	creates	create	VERB
m-1112	1321	21	a	a	DET
m-1112	1321	22	rotation	rotation	NOUN
m-1112	1321	23	on	on	ADP
m-1112	1321	24	circle	circle	NOUN
m-1112	1321	25	of	of	ADP
m-1112	1321	26	radius	radius	NOUN
m-1112	1321	27	,	,	PUNCT
m-1112	1321	28	r	r	NOUN
m-1112	1321	29	=	=	SYM
m-1112	1321	30	2	2	NUM
m-1112	1321	31	r	r	NOUN
m-1112	1321	32	,	,	PUNCT
m-1112	1321	33	with	with	ADP
m-1112	1321	34	velocity	velocity	NOUN
m-1112	1321	35	v	v	X
m-1112	1321	36	=	=	PUNCT
m-1112	1321	37	w.2r	w.2r	NOUN
m-1112	1321	38	=	=	SYM
m-1112	1321	39	2π	2π	NOUN
m-1112	1321	40	t	t	NOUN
m-1112	1321	41	.2r	.2r	NUM
m-1112	1321	42	=	=	PUNCT
m-1112	1322	1	4πr	4πr	PROPN
m-1112	1322	2	.f	.f	PROPN
m-1112	1323	1	=	=	PUNCT
m-1112	1323	2	[	[	PUNCT
m-1112	1323	3	σ	σ	PROPN
m-1112	1323	4	2	2	NUM
m-1112	1323	5	]	]	PUNCT
m-1112	1323	6	.(1+√5	.(1+√5	PROPN
m-1112	1323	7	)	)	PUNCT
m-1112	1323	8	,	,	PUNCT
m-1112	1323	9	where	where	SCONJ
m-1112	1323	10	frequency	frequency	NOUN
m-1112	1323	11	f	f	X
m-1112	1323	12	=	=	PUNCT
m-1112	1323	13	(	(	PUNCT
m-1112	1323	14	1	1	NUM
m-1112	1323	15	+	+	NUM
m-1112	1323	16	√5	√5	NOUN
m-1112	1323	17	]	]	PUNCT
m-1112	1323	18	)	)	PUNCT
m-1112	1323	19	.	.	PUNCT
m-1112	1324	1	σ	σ	NOUN
m-1112	1324	2	8πr	8πr	NOUN
m-1112	1324	3	,	,	PUNCT
m-1112	1324	4	period	period	NOUN
m-1112	1324	5	t	t	NOUN
m-1112	1324	6	=	=	SYM
m-1112	1324	7	8πr	8πr	PROPN
m-1112	1324	8	σ(1+√5	σ(1+√5	PROPN
m-1112	1324	9	)	)	PUNCT
m-1112	1324	10	=	=	PUNCT
m-1112	1325	1	4πr	4πr	PROPN
m-1112	1325	2	σ.φ	σ.φ	PROPN
m-1112	1325	3	and	and	CCONJ
m-1112	1325	4	the	the	DET
m-1112	1325	5	±	±	PROPN
m-1112	1325	6	σ	σ	NOUN
m-1112	1325	7	are	be	AUX
m-1112	1325	8	the	the	DET
m-1112	1325	9	two	two	NUM
m-1112	1325	10	equal	equal	ADJ
m-1112	1325	11	and	and	CCONJ
m-1112	1325	12	opposite	opposite	ADJ
m-1112	1325	13	stresses	stress	NOUN
m-1112	1325	14	,	,	PUNCT
m-1112	1325	15	or	or	CCONJ
m-1112	1325	16	centripetal	centripetal	ADJ
m-1112	1325	17	,	,	PUNCT
m-1112	1325	18	fp	fp	NOUN
m-1112	1325	19	,	,	PUNCT
m-1112	1325	20	centrifugal	centrifugal	ADJ
m-1112	1325	21	,	,	PUNCT
m-1112	1325	22	ff	ff	NOUN
m-1112	1325	23	force	force	NOUN
m-1112	1325	24	.	.	PUNCT
m-1112	1326	1	energy	energy	NOUN
m-1112	1326	2	is	be	AUX
m-1112	1326	3	→	→	SYM
m-1112	1326	4	e	e	X
m-1112	1326	5	=	=	SYM
m-1112	1327	1	h	h	NOUN
m-1112	1327	2	f	f	NOUN
m-1112	1327	3	=	=	PUNCT
m-1112	1327	4	(	(	PUNCT
m-1112	1327	5	1	1	NUM
m-1112	1327	6	+	+	NUM
m-1112	1327	7	√5	√5	NOUN
m-1112	1327	8	]	]	PUNCT
m-1112	1327	9	)	)	PUNCT
m-1112	1327	10	.σh	.σh	PUNCT
m-1112	1328	1	8πr	8πr	NOUN
m-1112	1328	2	=	=	PUNCT
m-1112	1328	3	σφh	σφh	NOUN
m-1112	1328	4	4πr	4πr	NOUN
m-1112	1328	5	,	,	PUNCT
m-1112	1328	6	in	in	ADP
m-1112	1328	7	the	the	DET
m-1112	1328	8	one	one	NUM
m-1112	1328	9	wave	wave	NOUN
m-1112	1328	10	note	note	NOUN
m-1112	1328	11	.	.	PUNCT
m-1112	1329	1	in	in	ADP
m-1112	1329	2	(	(	PUNCT
m-1112	1329	3	2	2	X
m-1112	1329	4	)	)	PUNCT
m-1112	1329	5	the	the	DET
m-1112	1329	6	hollow	hollow	ADJ
m-1112	1329	7	-	-	PUNCT
m-1112	1329	8	cone	cone	NOUN
m-1112	1329	9	of	of	ADP
m-1112	1329	10	90ᵒ	90ᵒ	NOUN
m-1112	1329	11	,	,	PUNCT
m-1112	1329	12	between	between	ADP
m-1112	1329	13	angular	angular	ADJ
m-1112	1329	14	-	-	PUNCT
m-1112	1329	15	momentum	momentum	NOUN
m-1112	1329	16	-	-	PUNCT
m-1112	1329	17	vector	vector	NOUN
m-1112	1329	18	�	�	PROPN
m-1112	1329	19	̅	̅	NOUN
m-1112	1329	20	�	�	PROPN
m-1112	1329	21	and	and	CCONJ
m-1112	1329	22	angular	angular	ADJ
m-1112	1329	23	-	-	PUNCT
m-1112	1329	24	velocity	velocity	NOUN
m-1112	1329	25	vector	vector	NOUN
m-1112	1329	26	�	�	PROPN
m-1112	1329	27	̅	̅	NOUN
m-1112	1329	28	�	�	NOUN
m-1112	1329	29	when	when	SCONJ
m-1112	1329	30	illuminated	illuminate	VERB
m-1112	1329	31	by	by	ADP
m-1112	1329	32	a	a	DET
m-1112	1329	33	circularly	circularly	ADV
m-1112	1329	34	polarized	polarize	VERB
m-1112	1329	35	light	light	ADJ
m-1112	1329	36	beam	beam	NOUN
m-1112	1329	37	,	,	PUNCT
m-1112	1329	38	then	then	ADV
m-1112	1329	39	any	any	DET
m-1112	1329	40	changes	change	NOUN
m-1112	1329	41	in	in	ADP
m-1112	1329	42	spin	spin	NOUN
m-1112	1329	43	ijo	ijo	PROPN
m-1112	1329	44	international	international	PROPN
m-1112	1329	45	journal	journal	PROPN
m-1112	1329	46	of	of	ADP
m-1112	1329	47	mathematics	mathematics	PROPN
m-1112	1329	48	(	(	PUNCT
m-1112	1329	49	issn	issn	PROPN
m-1112	1329	50	:	:	PUNCT
m-1112	1329	51	2992	2992	NUM
m-1112	1329	52	-	-	SYM
m-1112	1329	53	4421	4421	NUM
m-1112	1329	54	)	)	PUNCT
m-1112	1329	55	volume	volume	NOUN
m-1112	1329	56	08	08	NUM
m-1112	1330	1	|	|	ADV
m-1112	1330	2	issue	issue	NOUN
m-1112	1330	3	08	08	NUM
m-1112	1331	1	|	|	ADV
m-1112	1331	2	august	august	PROPN
m-1112	1331	3	2025	2025	NUM
m-1112	1331	4	|	|	ADV
m-1112	1331	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1331	6	ijo	ijo	PROPN
m-1112	1331	7	journals	journal	NOUN
m-1112	1331	8	48	48	NUM
m-1112	1331	9	the	the	DET
m-1112	1331	10	fundamental	fundamental	ADJ
m-1112	1331	11	particles	particle	NOUN
m-1112	1331	12	origination	origination	NOUN
m-1112	1331	13	mechanism	mechanism	NOUN
m-1112	1331	14	in	in	ADP
m-1112	1331	15	mfmf	mfmf	PROPN
m-1112	1331	16	pns	pns	PROPN
m-1112	1331	17	caves	cave	NOUN
m-1112	1331	18	.	.	PUNCT
m-1112	1332	1	≡	≡	PROPN
m-1112	1332	2	�	�	PROPN
m-1112	1332	3	̅	̅	NOUN
m-1112	1332	4	�	�	PROPN
m-1112	1332	5	of	of	ADP
m-1112	1332	6	the	the	DET
m-1112	1332	7	polhode	polhode	NOUN
m-1112	1332	8	cone	cone	NOUN
m-1112	1332	9	pot	pot	NOUN
m-1112	1332	10	and	and	CCONJ
m-1112	1332	11	the	the	DET
m-1112	1332	12	exchange	exchange	NOUN
m-1112	1332	13	of	of	ADP
m-1112	1332	14	linear	linear	PROPN
m-1112	1332	15	and	and	CCONJ
m-1112	1332	16	angular	angular	ADJ
m-1112	1332	17	momentum	momentum	NOUN
m-1112	1332	18	between	between	ADP
m-1112	1332	19	electromagnetic	electromagnetic	ADJ
m-1112	1332	20	fields	field	NOUN
m-1112	1332	21	and	and	CCONJ
m-1112	1332	22	the	the	DET
m-1112	1332	23	material	material	NOUN
m-1112	1332	24	media	medium	NOUN
m-1112	1332	25	are	be	AUX
m-1112	1332	26	shown	show	VERB
m-1112	1332	27	as	as	ADP
m-1112	1332	28	the	the	DET
m-1112	1332	29	profiles	profile	NOUN
m-1112	1332	30	of	of	ADP
m-1112	1332	31	the	the	DET
m-1112	1332	32	phase	phase	NOUN
m-1112	1332	33	and	and	CCONJ
m-1112	1332	34	the	the	DET
m-1112	1332	35	angular	angular	ADJ
m-1112	1332	36	-	-	PUNCT
m-1112	1332	37	velocity	velocity	NOUN
m-1112	1332	38	-	-	PUNCT
m-1112	1332	39	vector	vector	NOUN
m-1112	1332	40	in	in	ADP
m-1112	1332	41	the	the	DET
m-1112	1332	42	potcone	potcone	NOUN
m-1112	1332	43	cross	cross	ADJ
m-1112	1332	44	-	-	ADJ
m-1112	1332	45	sectional	sectional	ADJ
m-1112	1332	46	plane	plane	NOUN
m-1112	1332	47	,	,	PUNCT
m-1112	1332	48	i.e.	i.e.	X
m-1112	1332	49	the	the	DET
m-1112	1332	50	space	space	NOUN
m-1112	1332	51	can	can	AUX
m-1112	1332	52	be	be	AUX
m-1112	1332	53	eternally	eternally	ADV
m-1112	1332	54	twisted	twist	VERB
m-1112	1332	55	but	but	CCONJ
m-1112	1332	56	can	can	AUX
m-1112	1332	57	not	not	PART
m-1112	1332	58	disappear	disappear	VERB
m-1112	1332	59	.	.	PUNCT
m-1112	1333	1	[	[	X
m-1112	1333	2	70	70	NUM
m-1112	1333	3	]	]	SYM
m-1112	1333	4	measurements	measurement	NOUN
m-1112	1333	5	of	of	ADP
m-1112	1333	6	physical	physical	ADJ
m-1112	1333	7	-	-	PUNCT
m-1112	1333	8	properties	property	NOUN
m-1112	1333	9	such	such	ADJ
m-1112	1333	10	as	as	ADP
m-1112	1333	11	position	position	NOUN
m-1112	1333	12	,	,	PUNCT
m-1112	1333	13	momentum	momentum	NOUN
m-1112	1333	14	,	,	PUNCT
m-1112	1333	15	spin	spin	NOUN
m-1112	1333	16	and	and	CCONJ
m-1112	1333	17	polarization	polarization	NOUN
m-1112	1333	18	,	,	PUNCT
m-1112	1333	19	performed	perform	VERB
m-1112	1333	20	on	on	ADP
m-1112	1333	21	entanglement	entanglement	NOUN
m-1112	1333	22	particles	particle	NOUN
m-1112	1333	23	gives	give	VERB
m-1112	1333	24	rise	rise	NOUN
m-1112	1333	25	to	to	ADP
m-1112	1333	26	seemingly	seemingly	ADV
m-1112	1333	27	paradoxical	paradoxical	ADJ
m-1112	1333	28	effects	effect	NOUN
m-1112	1333	29	considering	consider	VERB
m-1112	1333	30	systems	system	NOUN
m-1112	1333	31	as	as	ADP
m-1112	1333	32	a	a	DET
m-1112	1333	33	whole	whole	NOUN
m-1112	1333	34	and	and	CCONJ
m-1112	1333	35	the	the	DET
m-1112	1333	36	erp	erp	PROPN
m-1112	1333	37	paradox	paradox	NOUN
m-1112	1333	38	.	.	PUNCT
m-1112	1334	1	the	the	DET
m-1112	1334	2	answer	answer	NOUN
m-1112	1334	3	is	be	AUX
m-1112	1334	4	given	give	VERB
m-1112	1334	5	in	in	ADP
m-1112	1334	6	figure	figure	NOUN
m-1112	1334	7	1-(the	1-(the	DET
m-1112	1334	8	right-2	right-2	NOUN
m-1112	1334	9	)	)	PUNCT
m-1112	1334	10	where	where	SCONJ
m-1112	1334	11	is	be	AUX
m-1112	1334	12	shown	show	VERB
m-1112	1334	13	each	each	DET
m-1112	1334	14	property	property	NOUN
m-1112	1334	15	of	of	ADP
m-1112	1334	16	the	the	DET
m-1112	1334	17	material	material	NOUN
m-1112	1334	18	-	-	PUNCT
m-1112	1334	19	point	point	NOUN
m-1112	1334	20	.	.	PUNCT
m-1112	1335	1	the	the	DET
m-1112	1335	2	spins	spin	NOUN
m-1112	1335	3	[	[	X
m-1112	1335	4	⊝	⊝	NUM
m-1112	1335	5	↻	↻	PROPN
m-1112	1335	6	⊕	⊕	PROPN
m-1112	1335	7	]	]	X
m-1112	1335	8	presuppose	presuppose	VERB
m-1112	1335	9	[	[	X
m-1112	1335	10	⊝	⊝	X
m-1112	1335	11	,	,	PUNCT
m-1112	1335	12	⊕	⊕	PROPN
m-1112	1335	13	]	]	PUNCT
m-1112	1335	14	material	material	NOUN
m-1112	1335	15	-	-	PUNCT
m-1112	1335	16	points	point	NOUN
m-1112	1335	17	which	which	PRON
m-1112	1335	18	are	be	AUX
m-1112	1335	19	the	the	DET
m-1112	1335	20	caves	cave	NOUN
m-1112	1335	21	in	in	ADP
m-1112	1335	22	pns	pns	PROPN
m-1112	1335	23	space	space	NOUN
m-1112	1335	24	.	.	PUNCT
m-1112	1336	1	conclusions	conclusion	NOUN
m-1112	1336	2	the	the	DET
m-1112	1336	3	energy	energy	NOUN
m-1112	1336	4	in	in	ADP
m-1112	1336	5	spins	spin	NOUN
m-1112	1336	6	,	,	PUNCT
m-1112	1336	7	presuppose	presuppose	VERB
m-1112	1336	8	that	that	SCONJ
m-1112	1336	9	the	the	DET
m-1112	1336	10	caves	cave	NOUN
m-1112	1336	11	to	to	PART
m-1112	1336	12	be	be	AUX
m-1112	1336	13	in	in	ADP
m-1112	1336	14	[	[	X
m-1112	1336	15	pns	pns	NOUN
m-1112	1336	16	]	]	X
m-1112	1336	17	space	space	NOUN
m-1112	1336	18	and	and	CCONJ
m-1112	1336	19	in	in	ADP
m-1112	1336	20	the	the	PRON
m-1112	1336	21	under	under	ADP
m-1112	1336	22	planck1s	planck1s	PROPN
m-1112	1336	23	length	length	NOUN
m-1112	1336	24	.	.	PUNCT
m-1112	1337	1	the	the	DET
m-1112	1337	2	±	±	NOUN
m-1112	1337	3	spin	spin	NOUN
m-1112	1337	4	is	be	AUX
m-1112	1337	5	created	create	VERB
m-1112	1337	6	from	from	ADP
m-1112	1337	7	the	the	DET
m-1112	1337	8	opposite	opposite	ADJ
m-1112	1337	9	centripetal	centripetal	NOUN
m-1112	1337	10	,	,	PUNCT
m-1112	1338	1	𝐅𝐩	𝐅𝐩	PROPN
m-1112	1338	2	,	,	PUNCT
m-1112	1338	3	centrifugal	centrifugal	ADJ
m-1112	1338	4	,	,	PUNCT
m-1112	1339	1	𝐅𝐟	𝐅𝐟	PROPN
m-1112	1339	2	,	,	PUNCT
m-1112	1339	3	forces	force	NOUN
m-1112	1339	4	.	.	PUNCT
m-1112	1340	1	the	the	DET
m-1112	1340	2	energy	energy	NOUN
m-1112	1340	3	e	e	NOUN
m-1112	1340	4	is	be	AUX
m-1112	1340	5	initially	initially	ADV
m-1112	1340	6	absorbed	absorb	VERB
m-1112	1340	7	in	in	ADP
m-1112	1340	8	[	[	X
m-1112	1340	9	pns	pns	NOUN
m-1112	1340	10	]	]	PUNCT
m-1112	1340	11	and	and	CCONJ
m-1112	1340	12	in	in	ADP
m-1112	1340	13	all	all	DET
m-1112	1340	14	quantized	quantize	VERB
m-1112	1340	15	regions	region	NOUN
m-1112	1340	16	,	,	PUNCT
m-1112	1340	17	either	either	CCONJ
m-1112	1340	18	as	as	ADP
m-1112	1340	19	momentum	momentum	NOUN
m-1112	1340	20	(	(	PUNCT
m-1112	1340	21	mv	mv	NOUN
m-1112	1340	22	)	)	PUNCT
m-1112	1340	23	or	or	CCONJ
m-1112	1340	24	as	as	ADP
m-1112	1340	25	rotational	rotational	ADJ
m-1112	1340	26	momentum	momentum	NOUN
m-1112	1340	27	(	(	PUNCT
m-1112	1340	28	λ	λ	X
m-1112	1340	29	=	=	PROPN
m-1112	1340	30	r.	r.	PROPN
m-1112	1340	31	mv	mv	PROPN
m-1112	1340	32	)	)	PUNCT
m-1112	1340	33	.	.	PUNCT
m-1112	1341	1	from	from	ADP
m-1112	1341	2	momentum	momentum	NOUN
m-1112	1341	3	relation	relation	NOUN
m-1112	1341	4	�	�	PROPN
m-1112	1341	5	̅	̅	NOUN
m-1112	1341	6	�	�	NOUN
m-1112	1341	7	=	=	SYM
m-1112	1341	8	m	m	VERB
m-1112	1341	9	r	r	NOUN
m-1112	1341	10	v	v	NOUN
m-1112	1341	11	=	=	PUNCT
m-1112	1341	12	m	m	VERB
m-1112	1341	13	r²	r²	NOUN
m-1112	1341	14	w	w	PROPN
m-1112	1341	15	=	=	VERB
m-1112	1341	16	m	m	VERB
m-1112	1341	17	r²	r²	NOUN
m-1112	1341	18	(	(	PUNCT
m-1112	1341	19	2πf	2πf	ADJ
m-1112	1341	20	)	)	PUNCT
m-1112	1342	1	=	=	PUNCT
m-1112	1342	2	j.w	j.w	PROPN
m-1112	1342	3	2	2	NUM
m-1112	1342	4	=	=	PUNCT
m-1112	1342	5	[	[	PUNCT
m-1112	1342	6	πr⁴	πr⁴	PROPN
m-1112	1342	7	4	4	NUM
m-1112	1342	8	]	]	PUNCT
m-1112	1342	9	.[2πf	.[2πf	X
m-1112	1342	10	]	]	X
m-1112	1343	1	=	=	PUNCT
m-1112	1343	2	π	π	X
m-1112	1343	3	²𝐫⁴f	²𝐫⁴f	X
m-1112	1343	4	2	2	NUM
m-1112	1343	5	,	,	PUNCT
m-1112	1343	6	then	then	ADV
m-1112	1343	7	the	the	DET
m-1112	1343	8	mass	mass	NOUN
m-1112	1343	9	of	of	ADP
m-1112	1343	10	the	the	DET
m-1112	1343	11	elementary	elementary	ADJ
m-1112	1343	12	particles	particle	NOUN
m-1112	1343	13	is	be	AUX
m-1112	1343	14	→	→	SYM
m-1112	1343	15	m	m	NOUN
m-1112	1343	16	=	=	SYM
m-1112	1343	17	2π³𝐫⁴,f	2π³𝐫⁴,f	NUM
m-1112	1343	18	²	²	NUM
m-1112	1343	19	r²2πf	r²2πf	NUM
m-1112	1343	20	=	=	SYM
m-1112	1344	1	𝛑²𝐫²	𝛑²𝐫²	X
m-1112	1344	2	𝟏	𝟏	PUNCT
m-1112	1344	3	f	f	NOUN
m-1112	1344	4	=	=	PRON
m-1112	1345	1	[	[	PUNCT
m-1112	1345	2	𝛑𝐫.𝐯	𝛑𝐫.𝐯	NOUN
m-1112	1345	3	𝟐	𝟐	NUM
m-1112	1345	4	]	]	SYM
m-1112	1345	5	v	v	NOUN
m-1112	1345	6	,	,	PUNCT
m-1112	1345	7	or	or	CCONJ
m-1112	1345	8	𝐦	𝐦	DET
m-1112	1345	9	𝐄𝐏	𝐄𝐏	PROPN
m-1112	1345	10	=	=	PUNCT
m-1112	1345	11	𝛑.𝐫²	𝛑.𝐫²	X
m-1112	1345	12	𝟒	𝟒	NUM
m-1112	1345	13	=	=	SYM
m-1112	1345	14	π.(1,07.10−7)²	π.(1,07.10−7)²	NUM
m-1112	1345	15	4	4	NUM
m-1112	1345	16	=	=	SYM
m-1112	1345	17	8,992023.10−15	8,992023.10−15	NUM
m-1112	1345	18	kg	kg	NOUN
m-1112	1345	19	,	,	PUNCT
m-1112	1345	20	in	in	ADP
m-1112	1345	21	the	the	DET
m-1112	1345	22	min	min	NOUN
m-1112	1345	23	planck`s	planck`s	NOUN
m-1112	1345	24	cave	cave	NOUN
m-1112	1345	25	𝐝	𝐝	ADP
m-1112	1346	1	𝐏𝐜	𝐏𝐜	PROPN
m-1112	1346	2	=	=	SYM
m-1112	1346	3	1,07	1,07	NUM
m-1112	1346	4	.	.	PUNCT
m-1112	1347	1	10−7	10−7	NUM
m-1112	1347	2	m	m	NOUN
m-1112	1347	3	→	→	NOUN
m-1112	1347	4	which	which	PRON
m-1112	1347	5	agree	agree	VERB
m-1112	1347	6	with	with	ADP
m-1112	1347	7	the	the	DET
m-1112	1347	8	diffraction	diffraction	NOUN
m-1112	1347	9	energy	energy	NOUN
m-1112	1347	10	mechanism	mechanism	NOUN
m-1112	1347	11	for	for	ADP
m-1112	1347	12	all	all	DET
m-1112	1347	13	space	space	NOUN
m-1112	1347	14	levels	level	NOUN
m-1112	1347	15	of	of	ADP
m-1112	1347	16	quantization	quantization	NOUN
m-1112	1347	17	and	and	CCONJ
m-1112	1347	18	which	which	PRON
m-1112	1347	19	are	be	AUX
m-1112	1347	20	the	the	DET
m-1112	1347	21	energy	energy	NOUN
m-1112	1347	22	particles	particle	NOUN
m-1112	1347	23	only	only	ADV
m-1112	1347	24	,	,	PUNCT
m-1112	1347	25	where	where	SCONJ
m-1112	1347	26	for	for	ADP
m-1112	1347	27	base	base	NOUN
m-1112	1347	28	e	e	NOUN
m-1112	1347	29	=	=	PUNCT
m-1112	1347	30	2,71828	2,71828	PROPN
m-1112	1347	31	and	and	CCONJ
m-1112	1347	32	k	k	NOUN
m-1112	1347	33	=	=	NOUN
m-1112	1347	34	0	0	PUNCT
m-1112	1347	35	→	→	SYM
m-1112	1347	36	𝐋	𝐋	PROPN
m-1112	1347	37	𝐯=	𝐯=	NOUN
m-1112	1347	38	e^i	e^i	PROPN
m-1112	1347	39	.	.	PROPN
m-1112	1347	40	(	(	PUNCT
m-1112	1347	41	±	±	X
m-1112	1347	42	π/2).b	π/2).b	ADP
m-1112	1347	43	the	the	DET
m-1112	1347	44	space	space	NOUN
m-1112	1347	45	is	be	AUX
m-1112	1347	46	e^	e^	VERB
m-1112	1347	47	(	(	PUNCT
m-1112	1347	48	-15,7079	-15,7079	NOUN
m-1112	1347	49	)	)	PUNCT
m-1112	1347	50	=	=	PUNCT
m-1112	1348	1	1,78118	1,78118	NUM
m-1112	1348	2	.10	.10	NUM
m-1112	1348	3	̄	̄	NOUN
m-1112	1348	4	7	7	NUM
m-1112	1348	5	m	m	NOUN
m-1112	1348	6	since	since	SCONJ
m-1112	1348	7	velocity	velocity	NOUN
m-1112	1348	8	v	v	X
m-1112	1348	9	=	=	SYM
m-1112	1348	10	s	s	NOUN
m-1112	1348	11	/	/	SYM
m-1112	1348	12	t	t	NOUN
m-1112	1348	13	=	=	SYM
m-1112	1348	14	distance	distance	NOUN
m-1112	1348	15	/	/	SYM
m-1112	1348	16	time	time	NOUN
m-1112	1348	17	then	then	ADV
m-1112	1348	18	for	for	ADP
m-1112	1348	19	constant	constant	ADJ
m-1112	1348	20	s	s	NOUN
m-1112	1348	21	,	,	PUNCT
m-1112	1348	22	then	then	ADV
m-1112	1348	23	v	v	NOUN
m-1112	1348	24	is	be	AUX
m-1112	1348	25	also	also	ADV
m-1112	1348	26	constant	constant	ADJ
m-1112	1348	27	and	and	CCONJ
m-1112	1348	28	t	t	PROPN
m-1112	1348	29	=	=	SYM
m-1112	1348	30	t	t	PROPN
m-1112	1348	31	,	,	PUNCT
m-1112	1348	32	the	the	DET
m-1112	1348	33	period	period	NOUN
m-1112	1348	34	of	of	ADP
m-1112	1348	35	vibration	vibration	NOUN
m-1112	1348	36	and	and	CCONJ
m-1112	1348	37	for	for	ADP
m-1112	1348	38	any	any	DET
m-1112	1348	39	constant	constant	ADJ
m-1112	1348	40	momentum	momentum	NOUN
m-1112	1348	41	λ	λ	NOUN
m-1112	1348	42	=	=	SYM
m-1112	1348	43	λ2	λ2	PROPN
m-1112	1348	44	m2	m2	PROPN
m-1112	1348	45	v²2	v²2	PROPN
m-1112	1348	46	/	/	SYM
m-1112	1348	47	2	2	NUM
m-1112	1348	48	=	=	SYM
m-1112	1348	49	λ2	λ2	NOUN
m-1112	1348	50	m2	m2	PROPN
m-1112	1349	1	[	[	X
m-1112	1349	2	wλ2	wλ2	X
m-1112	1349	3	]	]	X
m-1112	1349	4	²	²	PROPN
m-1112	1349	5	=	=	SYM
m-1112	1349	6	4π²	4π²	NUM
m-1112	1349	7	.	.	PUNCT
m-1112	1350	1	m2	m2	PROPN
m-1112	1350	2	.	.	PUNCT
m-1112	1351	1	λ³2	λ³2	PROPN
m-1112	1351	2	.f	.f	NOUN
m-1112	1351	3	²	²	NUM
m-1112	1351	4	=	=	SYM
m-1112	1352	1	[	[	X
m-1112	1352	2	4π²	4π²	NUM
m-1112	1352	3	.	.	PUNCT
m-1112	1353	1	m2	m2	PROPN
m-1112	1353	2	.	.	PUNCT
m-1112	1354	1	λ³2	λ³2	PROPN
m-1112	1354	2	]	]	PUNCT
m-1112	1354	3	f	f	PROPN
m-1112	1354	4	²	²	PROPN
m-1112	1354	5	=	=	SYM
m-1112	1354	6	co.	co.	PROPN
m-1112	1354	7	f	f	PROPN
m-1112	1354	8	²	²	PROPN
m-1112	1354	9	=	=	SYM
m-1112	1354	10	λ	λ	PROPN
m-1112	1354	11	,	,	PUNCT
m-1112	1354	12	i.e.	i.e.	X
m-1112	1354	13	in	in	ADP
m-1112	1354	14	all	all	DET
m-1112	1354	15	rotational	rotational	ADJ
m-1112	1354	16	systems	system	NOUN
m-1112	1354	17	time	time	NOUN
m-1112	1354	18	t	t	PROPN
m-1112	1354	19	is	be	AUX
m-1112	1354	20	constant	constant	ADJ
m-1112	1354	21	and	and	CCONJ
m-1112	1354	22	equal	equal	ADJ
m-1112	1354	23	to	to	ADP
m-1112	1354	24	the	the	DET
m-1112	1354	25	period	period	NOUN
m-1112	1354	26	of	of	ADP
m-1112	1354	27	rotation	rotation	NOUN
m-1112	1354	28	which	which	PRON
m-1112	1354	29	is	be	AUX
m-1112	1354	30	the	the	DET
m-1112	1354	31	meter	meter	NOUN
m-1112	1354	32	of	of	ADP
m-1112	1354	33	changes	change	NOUN
m-1112	1354	34	.	.	PUNCT
m-1112	1355	1	for	for	ADP
m-1112	1355	2	monads	monad	NOUN
m-1112	1355	3	in	in	ADP
m-1112	1355	4	k2	k2	PROPN
m-1112	1355	5	≡	≡	PROPN
m-1112	1355	6	pns	pns	PROPN
m-1112	1355	7	region	region	PROPN
m-1112	1355	8	et	et	NOUN
m-1112	1355	9	=	=	PUNCT
m-1112	1356	1	[	[	X
m-1112	1356	2	λ	λ	X
m-1112	1356	3	+	+	NOUN
m-1112	1356	4	λ	λ	X
m-1112	1356	5	x	x	X
m-1112	1356	6	]	]	PUNCT
m-1112	1356	7	=	=	PUNCT
m-1112	1357	1	[	[	X
m-1112	1357	2	λ.m+λxm	λ.m+λxm	X
m-1112	1357	3	]	]	X
m-1112	1357	4	=	=	PUNCT
m-1112	1357	5	√	√	ADP
m-1112	1357	6	m.	m.	NOUN
m-1112	1357	7	v²e	v²e	NOUN
m-1112	1357	8	+	+	CCONJ
m-1112	1358	1	[	[	X
m-1112	1358	2	λ	λ	X
m-1112	1358	3	.	.	NOUN
m-1112	1358	4	vb	vb	PROPN
m-1112	1358	5	+	+	CCONJ
m-1112	1358	6	λ	λ	X
m-1112	1358	7	𝐱	𝐱	PROPN
m-1112	1358	8	vb	vb	NOUN
m-1112	1358	9	]	]	PUNCT
m-1112	1358	10	²	²	X
m-1112	1358	11	=	=	SYM
m-1112	1358	12	=	=	NOUN
m-1112	1358	13	√	√	PROPN
m-1112	1358	14	m.	m.	NOUN
m-1112	1358	15	v²e	v²e	NOUN
m-1112	1358	16	+	+	CCONJ
m-1112	1359	1	[	[	X
m-1112	1359	2	λ	λ	X
m-1112	1359	3	.	.	NOUN
m-1112	1359	4	vb	vb	PROPN
m-1112	1359	5	+	+	CCONJ
m-1112	1359	6	s	s	VERB
m-1112	1359	7	²	²	NUM
m-1112	1359	8	]	]	PUNCT
m-1112	1359	9	²	²	PROPN
m-1112	1359	10	=	=	SYM
m-1112	1359	11	h	h	NOUN
m-1112	1359	12	.	.	PUNCT
m-1112	1360	1	f	f	X
m-1112	1361	1	=	=	NOUN
m-1112	1361	2	h	h	PROPN
m-1112	1361	3	/	/	SYM
m-1112	1361	4	t	t	NOUN
m-1112	1361	5	=	=	SYM
m-1112	1361	6	h	h	NOUN
m-1112	1361	7	.v	.v	NOUN
m-1112	1361	8	/	/	PUNCT
m-1112	1362	1	λ	λ	INTJ
m-1112	1362	2	,	,	PUNCT
m-1112	1362	3	i.e.	i.e.	X
m-1112	1362	4	in	in	ADP
m-1112	1362	5	every	every	DET
m-1112	1362	6	monad	monad	PROPN
m-1112	1362	7	issues	issue	VERB
m-1112	1362	8	λ.mv/2	λ.mv/2	X
m-1112	1363	1	=	=	PUNCT
m-1112	1363	2	h	h	NOUN
m-1112	1363	3	f	f	NOUN
m-1112	1363	4	=	=	SYM
m-1112	1363	5	λ	λ	X
m-1112	1363	6	λ	λ	NOUN
m-1112	1363	7	and	and	CCONJ
m-1112	1363	8	kinetic	kinetic	NOUN
m-1112	1363	9	-	-	PUNCT
m-1112	1363	10	energy	energy	NOUN
m-1112	1363	11	λ	λ	NOUN
m-1112	1363	12	=	=	SYM
m-1112	1363	13	h	h	PROPN
m-1112	1363	14	f	f	PROPN
m-1112	1363	15	/	/	SYM
m-1112	1363	16	λ	λ	PROPN
m-1112	1363	17	=	=	NOUN
m-1112	1363	18	co.f	co.f	NOUN
m-1112	1363	19	where	where	SCONJ
m-1112	1363	20	the	the	DET
m-1112	1363	21	constant	constant	ADJ
m-1112	1363	22	𝐂𝐨	𝐂𝐨	PROPN
m-1112	1363	23	=	=	SYM
m-1112	1363	24	e/	e/	PROPN
m-1112	1363	25	f	f	PROPN
m-1112	1363	26	²	²	NUM
m-1112	1363	27	a	a	DET
m-1112	1363	28	gauge	gauge	ADJ
m-1112	1363	29	magnitude	magnitude	NOUN
m-1112	1363	30	depended	depend	VERB
m-1112	1363	31	on	on	ADP
m-1112	1363	32	the	the	DET
m-1112	1363	33	angular	angular	ADJ
m-1112	1363	34	velocity	velocity	NOUN
m-1112	1363	35	�	�	NOUN
m-1112	1363	36	̅	̅	NOUN
m-1112	1363	37	�	�	PROPN
m-1112	1363	38	,	,	PUNCT
m-1112	1363	39	the	the	DET
m-1112	1363	40	velocity	velocity	NOUN
m-1112	1363	41	�	�	NOUN
m-1112	1363	42	̅	̅	NOUN
m-1112	1363	43	�	�	PROPN
m-1112	1363	44	,	,	PUNCT
m-1112	1363	45	and	and	CCONJ
m-1112	1363	46	then	then	ADV
m-1112	1363	47	wavelength	wavelength	NOUN
m-1112	1363	48	λ	λ	PROPN
m-1112	1363	49	is	be	AUX
m-1112	1363	50	conserved	conserve	VERB
m-1112	1363	51	as	as	ADP
m-1112	1363	52	momentum	momentum	NOUN
m-1112	1363	53	(	(	PUNCT
m-1112	1363	54	mv	mv	NOUN
m-1112	1363	55	)	)	PUNCT
m-1112	1363	56	or	or	CCONJ
m-1112	1363	57	angular	angular	ADJ
m-1112	1363	58	momentum	momentum	NOUN
m-1112	1363	59	(	(	PUNCT
m-1112	1363	60	λ	λ	X
m-1112	1363	61	=	=	SYM
m-1112	1363	62	r.	r.	X
m-1112	1363	63	mv̅	mv̅	PROPN
m-1112	1363	64	=	=	PUNCT
m-1112	1363	65	m.	m.	PROPN
m-1112	1363	66	wλ²/4	wλ²/4	PROPN
m-1112	1363	67	)	)	PUNCT
m-1112	1363	68	or	or	CCONJ
m-1112	1363	69	both	both	PRON
m-1112	1363	70	.	.	PUNCT
m-1112	1364	1	considering	consider	VERB
m-1112	1364	2	oscillatory	oscillatory	ADJ
m-1112	1364	3	motion	motion	NOUN
m-1112	1364	4	as	as	ADP
m-1112	1364	5	the	the	DET
m-1112	1364	6	simplest	simple	ADJ
m-1112	1364	7	case	case	NOUN
m-1112	1364	8	of	of	ADP
m-1112	1364	9	energy	energy	NOUN
m-1112	1364	10	dissipation	dissipation	NOUN
m-1112	1364	11	,	,	PUNCT
m-1112	1364	12	and	and	CCONJ
m-1112	1364	13	this	this	PRON
m-1112	1364	14	because	because	SCONJ
m-1112	1364	15	any	any	DET
m-1112	1364	16	other	other	ADJ
m-1112	1364	17	motion	motion	NOUN
m-1112	1364	18	is	be	AUX
m-1112	1364	19	not	not	PART
m-1112	1364	20	differently	differently	ADV
m-1112	1364	21	conserved	conserve	VERB
m-1112	1364	22	,	,	PUNCT
m-1112	1364	23	then	then	ADV
m-1112	1364	24	the	the	DET
m-1112	1364	25	work	work	NOUN
m-1112	1364	26	embodied	embody	VERB
m-1112	1364	27	in	in	ADP
m-1112	1364	28	dipole	dipole	NOUN
m-1112	1364	29	is	be	AUX
m-1112	1364	30	an	an	DET
m-1112	1364	31	<	<	X
m-1112	1364	32	spring	spring	NOUN
m-1112	1364	33	-	-	PUNCT
m-1112	1364	34	mass	mass	NOUN
m-1112	1364	35	system	system	NOUN
m-1112	1364	36	with	with	ADP
m-1112	1364	37	viscous	viscous	ADJ
m-1112	1364	38	dumping	dumping	NOUN
m-1112	1364	39	>	>	X
m-1112	1364	40	with	with	ADP
m-1112	1364	41	co	co	NOUN
m-1112	1364	42	variants	variant	NOUN
m-1112	1364	43	,	,	PUNCT
m-1112	1364	44	energy	energy	NOUN
m-1112	1364	45	e	e	NOUN
m-1112	1364	46	,	,	PUNCT
m-1112	1364	47	mass	mass	PROPN
m-1112	1364	48	m	m	PROPN
m-1112	1364	49	,	,	PUNCT
m-1112	1364	50	velocity	velocity	NOUN
m-1112	1364	51	�	�	NOUN
m-1112	1364	52	̅	̅	NOUN
m-1112	1364	53	�	�	PROPN
m-1112	1364	54	=	=	SYM
m-1112	1364	55	�	�	PROPN
m-1112	1364	56	̅	̅	NOUN
m-1112	1364	57	�	�	NOUN
m-1112	1364	58	e	e	NOUN
m-1112	1364	59	=	=	SYM
m-1112	1364	60	ẋ	ẋ	PROPN
m-1112	1364	61	wavelength	wavelength	NOUN
m-1112	1364	62	λ	λ	PROPN
m-1112	1364	63	,	,	PUNCT
m-1112	1364	64	and	and	CCONJ
m-1112	1364	65	then	then	ADV
m-1112	1364	66	energy	energy	NOUN
m-1112	1364	67	dissipation	dissipation	NOUN
m-1112	1364	68	is	be	AUX
m-1112	1364	69	the	the	DET
m-1112	1364	70	damping	damp	VERB
m-1112	1364	71	force	force	NOUN
m-1112	1364	72	equal	equal	ADJ
m-1112	1365	1	f	f	NOUN
m-1112	1365	2	d	d	PROPN
m-1112	1365	3	=	=	PROPN
m-1112	1366	1	c	c	PROPN
m-1112	1366	2	ẋ	ẋ	PROPN
m-1112	1366	3	where	where	SCONJ
m-1112	1366	4	c	c	NOUN
m-1112	1366	5	is	be	AUX
m-1112	1366	6	a	a	DET
m-1112	1366	7	constant	constant	ADJ
m-1112	1366	8	and	and	CCONJ
m-1112	1366	9	ẋ	ẋ	PRON
m-1112	1367	1	the	the	DET
m-1112	1367	2	velocity	velocity	NOUN
m-1112	1367	3	.	.	PUNCT
m-1112	1368	1	ijo	ijo	PROPN
m-1112	1368	2	international	international	PROPN
m-1112	1368	3	journal	journal	PROPN
m-1112	1368	4	of	of	ADP
m-1112	1368	5	mathematics	mathematics	PROPN
m-1112	1368	6	(	(	PUNCT
m-1112	1368	7	issn	issn	PROPN
m-1112	1368	8	:	:	PUNCT
m-1112	1368	9	2992	2992	NUM
m-1112	1368	10	-	-	SYM
m-1112	1368	11	4421	4421	NUM
m-1112	1368	12	)	)	PUNCT
m-1112	1368	13	volume	volume	NOUN
m-1112	1368	14	08	08	NUM
m-1112	1369	1	|	|	ADV
m-1112	1369	2	issue	issue	NOUN
m-1112	1369	3	08	08	NUM
m-1112	1370	1	|	|	ADV
m-1112	1370	2	august	august	PROPN
m-1112	1370	3	2025	2025	NUM
m-1112	1370	4	|	|	ADV
m-1112	1370	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1370	6	ijo	ijo	PROPN
m-1112	1370	7	journals	journal	NOUN
m-1112	1370	8	49	49	NUM
m-1112	1370	9	the	the	DET
m-1112	1370	10	fundamental	fundamental	ADJ
m-1112	1370	11	particles	particle	NOUN
m-1112	1370	12	origination	origination	NOUN
m-1112	1370	13	mechanism	mechanism	NOUN
m-1112	1370	14	in	in	ADP
m-1112	1370	15	mfmf	mfmf	PROPN
m-1112	1370	16	pns	pns	PROPN
m-1112	1370	17	caves	cave	NOUN
m-1112	1370	18	.	.	PUNCT
m-1112	1371	1	following	follow	VERB
m-1112	1371	2	the	the	DET
m-1112	1371	3	steady	steady	ADJ
m-1112	1371	4	-	-	PUNCT
m-1112	1371	5	state	state	NOUN
m-1112	1371	6	of	of	ADP
m-1112	1371	7	displacement	displacement	NOUN
m-1112	1371	8	and	and	CCONJ
m-1112	1371	9	velocity	velocity	NOUN
m-1112	1371	10	then	then	ADV
m-1112	1371	11	→	→	SYM
m-1112	1371	12	x	x	SYM
m-1112	1371	13	=	=	PUNCT
m-1112	1371	14	a.	a.	NOUN
m-1112	1371	15	sin(wt	sin(wt	PROPN
m-1112	1371	16	θ	θ	PROPN
m-1112	1371	17	)	)	PUNCT
m-1112	1371	18	←	←	PROPN
m-1112	1371	19	and	and	CCONJ
m-1112	1371	20	ẋ	ẋ	PROPN
m-1112	1371	21	=	=	PROPN
m-1112	1371	22	w.a	w.a	PROPN
m-1112	1371	23	.cos(wt	.cos(wt	PROPN
m-1112	1371	24	-	-	PUNCT
m-1112	1371	25	θ	θ	PROPN
m-1112	1371	26	)	)	PUNCT
m-1112	1371	27	=	=	SYM
m-1112	1371	28	w	w	PROPN
m-1112	1371	29	x	x	X
m-1112	1371	30	,	,	PUNCT
m-1112	1371	31	where	where	SCONJ
m-1112	1371	32	the	the	DET
m-1112	1371	33	energy	energy	NOUN
m-1112	1371	34	dissipated	dissipate	VERB
m-1112	1371	35	per	per	ADP
m-1112	1371	36	cycle	cycle	NOUN
m-1112	1371	37	is	be	AUX
m-1112	1371	38	the	the	DET
m-1112	1371	39	executed	execute	VERB
m-1112	1371	40	work	work	NOUN
m-1112	1371	41	which	which	PRON
m-1112	1371	42	is	be	AUX
m-1112	1371	43	,	,	PUNCT
m-1112	1371	44	w	w	PROPN
m-1112	1371	45	d	d	PROPN
m-1112	1371	46	=	=	SYM
m-1112	1371	47	f	f	PROPN
m-1112	1371	48	d	d	X
m-1112	1371	49	.dx	.dx	PUNCT
m-1112	1372	1	=	=	NOUN
m-1112	1372	2	∲	∲	NUM
m-1112	1372	3	c	c	PROPN
m-1112	1372	4	x̅	x̅	PROPN
m-1112	1372	5	dx	dx	PROPN
m-1112	1372	6	=	=	PUNCT
m-1112	1372	7	∲	∲	NUM
m-1112	1372	8	c	c	NOUN
m-1112	1372	9	x̅	x̅	PROPN
m-1112	1372	10	²dt	²dt	NOUN
m-1112	1373	1	=	=	PUNCT
m-1112	1374	1	π	π	X
m-1112	1374	2	c	c	X
m-1112	1374	3	w	w	PROPN
m-1112	1374	4	a²	a²	NOUN
m-1112	1374	5	=	=	SYM
m-1112	1374	6	(	(	PUNCT
m-1112	1374	7	π/4	π/4	NOUN
m-1112	1374	8	)	)	PUNCT
m-1112	1374	9	c	c	NOUN
m-1112	1374	10	wλ²	wλ²	NOUN
m-1112	1375	1	=	=	PUNCT
m-1112	1376	1	[	[	X
m-1112	1376	2	π²/2	π²/2	X
m-1112	1376	3	]	]	X
m-1112	1376	4	c.	c.	PROPN
m-1112	1376	5	f	f	PROPN
m-1112	1376	6	.	.	PUNCT
m-1112	1377	1	λ²	λ²	PROPN
m-1112	1377	2	→	→	SYM
m-1112	1377	3	the	the	DET
m-1112	1377	4	energy	energy	NOUN
m-1112	1377	5	dissipated	dissipate	VERB
m-1112	1377	6	per	per	ADP
m-1112	1377	7	cycle	cycle	NOUN
m-1112	1377	8	wd	wd	PROPN
m-1112	1377	9	by	by	ADP
m-1112	1377	10	the	the	DET
m-1112	1377	11	damping	damp	VERB
m-1112	1377	12	force	force	NOUN
m-1112	1377	13	𝐅	𝐅	PROPN
m-1112	1377	14	𝐝	𝐝	PROPN
m-1112	1377	15	,	,	PUNCT
m-1112	1377	16	is	be	AUX
m-1112	1377	17	mapped	map	VERB
m-1112	1377	18	by	by	ADP
m-1112	1377	19	writing	write	VERB
m-1112	1377	20	velocity	velocity	NOUN
m-1112	1377	21	ẋ	ẋ	PROPN
m-1112	1377	22	in	in	ADP
m-1112	1377	23	the	the	DET
m-1112	1377	24	form	form	NOUN
m-1112	1377	25	ẋ	ẋ	PUNCT
m-1112	1378	1	=	=	SYM
m-1112	1378	2	wa.cos(wt	wa.cos(wt	PROPN
m-1112	1378	3	θ	θ	PROPN
m-1112	1378	4	)	)	PUNCT
m-1112	1378	5	=	=	PUNCT
m-1112	1379	1	±wa.[√1	±wa.[√1	PROPN
m-1112	1380	1	−	−	NOUN
m-1112	1380	2	sin²(wt	sin²(wt	NOUN
m-1112	1380	3	−	−	NOUN
m-1112	1380	4	θ	θ	NOUN
m-1112	1380	5	)	)	PUNCT
m-1112	1380	6	]	]	PUNCT
m-1112	1381	1	=	=	PUNCT
m-1112	1382	1			PROPN
m-1112	1382	2	w	w	NOUN
m-1112	1382	3	.	.	PUNCT
m-1112	1383	1	[	[	PUNCT
m-1112	1383	2	√a²	√a²	PROPN
m-1112	1383	3	−	−	PROPN
m-1112	1383	4	x²	x²	PROPN
m-1112	1383	5	]	]	PUNCT
m-1112	1383	6	where	where	SCONJ
m-1112	1383	7	then	then	ADV
m-1112	1383	8	the	the	DET
m-1112	1383	9	dumping	dump	VERB
m-1112	1383	10	force	force	NOUN
m-1112	1383	11	f	f	PROPN
m-1112	1384	1	d	d	PROPN
m-1112	1384	2	=	=	PROPN
m-1112	1384	3	c.	c.	PROPN
m-1112	1384	4	ẋ	ẋ	PROPN
m-1112	1385	1	=	=	SYM
m-1112	1385	2	±	±	PROPN
m-1112	1385	3	co	co	NOUN
m-1112	1385	4	.w	.w	PROPN
m-1112	1385	5	.	.	PUNCT
m-1112	1386	1	[	[	PUNCT
m-1112	1386	2	√a²	√a²	PROPN
m-1112	1386	3	−	−	PROPN
m-1112	1386	4	x²	x²	PROPN
m-1112	1386	5	]	]	PUNCT
m-1112	1386	6	and	and	CCONJ
m-1112	1386	7	by	by	ADP
m-1112	1386	8	rearranging	rearrange	VERB
m-1112	1386	9	[	[	PUNCT
m-1112	1386	10	cos²(wt	cos²(wt	PROPN
m-1112	1386	11	-	-	PUNCT
m-1112	1386	12	θ	θ	NOUN
m-1112	1386	13	)	)	PUNCT
m-1112	1386	14	+	+	NOUN
m-1112	1386	15	sin²(wt	sin²(wt	NOUN
m-1112	1386	16	-	-	PUNCT
m-1112	1386	17	θ	θ	NOUN
m-1112	1386	18	)	)	PUNCT
m-1112	1386	19	=	=	NOUN
m-1112	1386	20	1	1	NUM
m-1112	1386	21	]	]	PUNCT
m-1112	1386	22	then	then	ADV
m-1112	1386	23	is	be	AUX
m-1112	1386	24	fd	fd	PROPN
m-1112	1386	25	²	²	PROPN
m-1112	1386	26	/	/	SYM
m-1112	1386	27	[	[	PUNCT
m-1112	1386	28	co	co	X
m-1112	1386	29	.w	.w	PROPN
m-1112	1386	30	.	.	PUNCT
m-1112	1387	1	a	a	DET
m-1112	1387	2	]	]	X
m-1112	1387	3	²	²	PROPN
m-1112	1387	4	+	+	CCONJ
m-1112	1387	5	x²	x²	PROPN
m-1112	1387	6	/	/	SYM
m-1112	1387	7	a²	a²	NOUN
m-1112	1387	8	=	=	SYM
m-1112	1387	9	1	1	NUM
m-1112	1387	10	,	,	PUNCT
m-1112	1387	11	i.e.	i.e.	X
m-1112	1387	12	energy	energy	NOUN
m-1112	1387	13	=	=	NOUN
m-1112	1387	14	motion	motion	NOUN
m-1112	1387	15	is	be	AUX
m-1112	1387	16	mapped	map	VERB
m-1112	1387	17	as	as	ADP
m-1112	1387	18	an	an	DET
m-1112	1387	19	ellipse	ellipse	NOUN
m-1112	1387	20	with	with	ADP
m-1112	1387	21	𝐅	𝐅	PROPN
m-1112	1387	22	𝐝	𝐝	PROPN
m-1112	1387	23	,	,	PUNCT
m-1112	1387	24	x	x	PRON
m-1112	1387	25	mapped	map	VERB
m-1112	1387	26	along	along	ADP
m-1112	1387	27	the	the	DET
m-1112	1387	28	vertical	vertical	ADJ
m-1112	1387	29	and	and	CCONJ
m-1112	1387	30	horizontal	horizontal	ADJ
m-1112	1387	31	axes	axis	NOUN
m-1112	1387	32	respectively	respectively	ADV
m-1112	1387	33	and	and	CCONJ
m-1112	1387	34	the	the	DET
m-1112	1387	35	energy	energy	NOUN
m-1112	1387	36	dissipated	dissipate	VERB
m-1112	1387	37	per	per	ADP
m-1112	1387	38	cycle	cycle	NOUN
m-1112	1387	39	is	be	AUX
m-1112	1387	40	given	give	VERB
m-1112	1387	41	by	by	ADP
m-1112	1387	42	the	the	DET
m-1112	1387	43	area	area	NOUN
m-1112	1387	44	enclosed	enclose	VERB
m-1112	1387	45	by	by	ADP
m-1112	1387	46	the	the	DET
m-1112	1387	47	above	above	ADJ
m-1112	1387	48	ellipse	ellipse	NOUN
m-1112	1387	49	.	.	PUNCT
m-1112	1388	1	the	the	DET
m-1112	1388	2	total	total	ADJ
m-1112	1388	3	energy	energy	NOUN
m-1112	1388	4	e	e	NOUN
m-1112	1388	5	=	=	SYM
m-1112	1388	6	λ2	λ2	NOUN
m-1112	1388	7	.	.	PUNCT
m-1112	1389	1	λ	λ	NOUN
m-1112	1389	2	which	which	PRON
m-1112	1389	3	is	be	AUX
m-1112	1389	4	embodied	embody	VERB
m-1112	1389	5	in	in	ADP
m-1112	1389	6	monad	monad	PROPN
m-1112	1389	7	ab̅̅	ab̅̅	PROPN
m-1112	1389	8	̅̅	̅̅	PROPN
m-1112	1389	9	is	be	AUX
m-1112	1389	10	moving	move	VERB
m-1112	1389	11	as	as	ADP
m-1112	1389	12	an	an	DET
m-1112	1389	13	ellipsoid	ellipsoid	NOUN
m-1112	1389	14	in	in	ADP
m-1112	1389	15	the	the	DET
m-1112	1389	16	configuration	configuration	NOUN
m-1112	1389	17	of	of	ADP
m-1112	1389	18	co	co	PROPN
m-1112	1389	19	variants	variant	NOUN
m-1112	1389	20	λ	λ	PROPN
m-1112	1389	21	,	,	PUNCT
m-1112	1389	22	m	m	PROPN
m-1112	1389	23	,	,	PUNCT
m-1112	1389	24	v	v	NOUN
m-1112	1389	25	=	=	SYM
m-1112	1389	26	�	�	NOUN
m-1112	1389	27	̅	̅	NOUN
m-1112	1389	28	�	�	NOUN
m-1112	1389	29	e	e	NOUN
m-1112	1389	30	,	,	PUNCT
m-1112	1389	31	as	as	ADP
m-1112	1389	32	kinetic	kinetic	NOUN
m-1112	1389	33	(	(	PUNCT
m-1112	1389	34	energy	energy	NOUN
m-1112	1389	35	of	of	ADP
m-1112	1389	36	motion	motion	NOUN
m-1112	1389	37	ω̅	ω̅	ADP
m-1112	1389	38	)	)	PUNCT
m-1112	1389	39	and	and	CCONJ
m-1112	1389	40	potential	potential	ADJ
m-1112	1389	41	energy	energy	NOUN
m-1112	1389	42	(	(	PUNCT
m-1112	1389	43	the	the	DET
m-1112	1389	44	stored	store	VERB
m-1112	1389	45	energy	energy	NOUN
m-1112	1389	46	in	in	ADP
m-1112	1389	47	λ	λ	PROPN
m-1112	1389	48	,	,	PUNCT
m-1112	1389	49	m	m	PROPN
m-1112	1389	50	,	,	PUNCT
m-1112	1389	51	v	v	NOUN
m-1112	1389	52	)	)	PUNCT
m-1112	1389	53	by	by	ADP
m-1112	1389	54	rotation	rotation	NOUN
m-1112	1389	55	and	and	CCONJ
m-1112	1389	56	displacement	displacement	NOUN
m-1112	1389	57	,	,	PUNCT
m-1112	1389	58	on	on	ADP
m-1112	1389	59	the	the	DET
m-1112	1389	60	principal	principal	ADJ
m-1112	1389	61	axis	axis	NOUN
m-1112	1389	62	(	(	PUNCT
m-1112	1389	63	through	through	ADP
m-1112	1389	64	the	the	DET
m-1112	1389	65	centre	centre	NOUN
m-1112	1389	66	of	of	ADP
m-1112	1389	67	monad	monad	PROPN
m-1112	1389	68	)	)	PUNCT
m-1112	1389	69	,	,	PUNCT
m-1112	1389	70	which	which	PRON
m-1112	1389	71	is	be	AUX
m-1112	1389	72	mapped	map	VERB
m-1112	1389	73	out	out	ADP
m-1112	1389	74	,	,	PUNCT
m-1112	1389	75	as	as	ADP
m-1112	1389	76	in	in	ADP
m-1112	1389	77	solid	solid	ADJ
m-1112	1389	78	material	material	NOUN
m-1112	1389	79	configuration	configuration	NOUN
m-1112	1389	80	by	by	ADP
m-1112	1389	81	the	the	DET
m-1112	1389	82	nib	nib	NOUN
m-1112	1389	83	of	of	ADP
m-1112	1389	84	the	the	DET
m-1112	1389	85	rotational	rotational	ADJ
m-1112	1389	86	-	-	NOUN
m-1112	1389	87	vector	vector	NOUN
m-1112	1389	88	(	(	PUNCT
m-1112	1389	89	ω̅	ω̅	X
m-1112	1389	90	)	)	PUNCT
m-1112	1390	1	=	=	SYM
m-1112	1390	2	δ	δ	X
m-1112	1390	3	r̅	r̅	NUM
m-1112	1390	4	c	c	NOUN
m-1112	1390	5	)	)	PUNCT
m-1112	1390	6	=	=	NOUN
m-1112	1391	1	[	[	PUNCT
m-1112	1391	2	v̅	v̅	PUNCT
m-1112	1391	3	c	c	PROPN
m-1112	1391	4	+	+	CCONJ
m-1112	1391	5	w̅	w̅	PROPN
m-1112	1391	6	.	.	PUNCT
m-1112	1392	1	r̅	r̅	NOUN
m-1112	1392	2	n	n	CCONJ
m-1112	1392	3	]	]	PUNCT
m-1112	1392	4	.	.	PUNCT
m-1112	1393	1	δt	δt	NOUN
m-1112	1393	2	,	,	PUNCT
m-1112	1393	3	as	as	ADP
m-1112	1393	4	the	the	DET
m-1112	1393	5	inertia	inertia	NOUN
m-1112	1393	6	-	-	PUNCT
m-1112	1393	7	ellipsoid	ellipsoid	NOUN
m-1112	1393	8	[	[	PUNCT
m-1112	1393	9	the	the	DET
m-1112	1393	10	poinsot	poinsot	NOUN
m-1112	1393	11	's	's	PART
m-1112	1393	12	ellipsoid	ellipsoid	NOUN
m-1112	1393	13	of	of	ADP
m-1112	1393	14	construction	construction	NOUN
m-1112	1393	15	]	]	PUNCT
m-1112	1393	16	in	in	ADP
m-1112	1393	17	an	an	DET
m-1112	1393	18	absolute	absolute	ADJ
m-1112	1393	19	frame	frame	NOUN
m-1112	1393	20	which	which	PRON
m-1112	1393	21	instantaneously	instantaneously	ADV
m-1112	1393	22	rotates	rotate	VERB
m-1112	1393	23	around	around	ADP
m-1112	1393	24	vector	vector	NOUN
m-1112	1393	25	axis	axis	NOUN
m-1112	1393	26	w̅	w̅	PROPN
m-1112	1393	27	,	,	PUNCT
m-1112	1393	28	θ	θ	PROPN
m-1112	1393	29	,	,	PUNCT
m-1112	1393	30	with	with	ADP
m-1112	1393	31	the	the	DET
m-1112	1393	32	constant	constant	ADJ
m-1112	1393	33	polar	polar	ADJ
m-1112	1393	34	distance	distance	NOUN
m-1112	1393	35	w̅.fd/|fd|	w̅.fd/|fd|	NOUN
m-1112	1393	36	and	and	CCONJ
m-1112	1393	37	the	the	DET
m-1112	1393	38	constant	constant	ADJ
m-1112	1393	39	angles	angle	NOUN
m-1112	1393	40	ϑs	ϑs	X
m-1112	1393	41	,	,	PUNCT
m-1112	1393	42	ϑb	ϑb	VERB
m-1112	1393	43	,	,	PUNCT
m-1112	1393	44	traced	trace	VERB
m-1112	1393	45	on	on	ADP
m-1112	1393	46	reference	reference	NOUN
m-1112	1393	47	cone	cone	NOUN
m-1112	1394	1	[	[	X
m-1112	1394	2	body	body	NOUN
m-1112	1394	3	frame	frame	NOUN
m-1112	1394	4	]	]	PUNCT
m-1112	1394	5	and	and	CCONJ
m-1112	1394	6	on	on	ADP
m-1112	1394	7	[	[	PUNCT
m-1112	1394	8	absolute	absolute	ADJ
m-1112	1394	9	frame	frame	NOUN
m-1112	1394	10	]	]	PUNCT
m-1112	1394	11	cone	cone	NOUN
m-1112	1394	12	,	,	PUNCT
m-1112	1394	13	which	which	PRON
m-1112	1394	14	are	be	AUX
m-1112	1394	15	rolling	roll	VERB
m-1112	1394	16	around	around	ADP
m-1112	1394	17	the	the	DET
m-1112	1394	18	common	common	ADJ
m-1112	1394	19	axis	axis	NOUN
m-1112	1394	20	of	of	ADP
m-1112	1394	21	,	,	PUNCT
m-1112	1394	22	w̅	w̅	PROPN
m-1112	1394	23	vector	vector	NOUN
m-1112	1394	24	,	,	PUNCT
m-1112	1394	25	without	without	ADP
m-1112	1394	26	slipping	slip	VERB
m-1112	1394	27	,	,	PUNCT
m-1112	1394	28	and	and	CCONJ
m-1112	1394	29	if	if	SCONJ
m-1112	1394	30	(	(	PUNCT
m-1112	1394	31	ω̅	ω̅	X
m-1112	1394	32	)	)	PUNCT
m-1112	1394	33	=	=	SYM
m-1112	1394	34	fe	fe	X
m-1112	1394	35	,	,	PUNCT
m-1112	1394	36	is	be	AUX
m-1112	1394	37	the	the	DET
m-1112	1394	38	diagonal	diagonal	ADJ
m-1112	1394	39	of	of	ADP
m-1112	1394	40	the	the	DET
m-1112	1394	41	energy	energy	NOUN
m-1112	1394	42	cuboid	cuboid	NOUN
m-1112	1394	43	with	with	ADP
m-1112	1394	44	the	the	DET
m-1112	1394	45	three	three	NUM
m-1112	1394	46	dimensions	dimension	NOUN
m-1112	1394	47	a̅	a̅	PROPN
m-1112	1394	48	,	,	PUNCT
m-1112	1394	49	b̅	b̅	PROPN
m-1112	1394	50	,	,	PUNCT
m-1112	1394	51	c̅	c̅	AUX
m-1112	1394	52	then	then	ADV
m-1112	1394	53	follow	follow	VERB
m-1112	1394	54	pythagoras	pythagoras	PROPN
m-1112	1394	55	conservation	conservation	NOUN
m-1112	1394	56	law	law	NOUN
m-1112	1394	57	,	,	PUNCT
m-1112	1394	58	with	with	ADP
m-1112	1394	59	the	the	DET
m-1112	1394	60	three	three	NUM
m-1112	1394	61	magnitudes	magnitude	NOUN
m-1112	1394	62	[	[	X
m-1112	1394	63	j	j	PROPN
m-1112	1394	64	,	,	PUNCT
m-1112	1394	65	e	e	PROPN
m-1112	1394	66	,	,	PUNCT
m-1112	1394	67	b	b	NOUN
m-1112	1394	68	]	]	PUNCT
m-1112	1394	69	of	of	ADP
m-1112	1394	70	energy	energy	NOUN
m-1112	1394	71	state	state	NOUN
m-1112	1394	72	following	follow	VERB
m-1112	1394	73	→	→	SYM
m-1112	1394	74	cuboidal	cuboidal	NOUN
m-1112	1394	75	,	,	PUNCT
m-1112	1394	76	plane	plane	NOUN
m-1112	1394	77	,	,	PUNCT
m-1112	1394	78	or	or	CCONJ
m-1112	1394	79	the	the	DET
m-1112	1394	80	linear	linear	ADJ
m-1112	1394	81	diagonal	diagonal	ADJ
m-1112	1394	82	direction	direction	NOUN
m-1112	1394	83	.	.	PUNCT
m-1112	1395	1	[	[	PUNCT
m-1112	1395	2	25	25	NUM
m-1112	1395	3	26	26	NUM
m-1112	1395	4	]	]	PUNCT
m-1112	1395	5	.	.	PUNCT
m-1112	1396	1	the	the	DET
m-1112	1396	2	transportation	transportation	NOUN
m-1112	1396	3	of	of	ADP
m-1112	1396	4	energy	energy	NOUN
m-1112	1396	5	on	on	ADP
m-1112	1396	6	edge	edge	NOUN
m-1112	1396	7	points	point	NOUN
m-1112	1396	8	happens	happen	VERB
m-1112	1396	9	in	in	ADP
m-1112	1396	10	material	material	NOUN
m-1112	1396	11	geometry	geometry	NOUN
m-1112	1396	12	,	,	PUNCT
m-1112	1396	13	while	while	SCONJ
m-1112	1396	14	the	the	DET
m-1112	1396	15	transportation	transportation	NOUN
m-1112	1396	16	of	of	ADP
m-1112	1396	17	the	the	DET
m-1112	1396	18	edge	edge	NOUN
m-1112	1396	19	-	-	PUNCT
m-1112	1396	20	points	point	NOUN
m-1112	1396	21	as	as	ADP
m-1112	1396	22	,	,	PUNCT
m-1112	1396	23	positions	position	NOUN
m-1112	1396	24	,	,	PUNCT
m-1112	1396	25	exists	exist	VERB
m-1112	1396	26	in	in	ADP
m-1112	1396	27	vector	vector	NOUN
m-1112	1396	28	geometry	geometry	NOUN
m-1112	1396	29	only	only	ADV
m-1112	1396	30	.	.	PUNCT
m-1112	1397	1	since	since	SCONJ
m-1112	1397	2	in	in	ADP
m-1112	1397	3	vibrations	vibration	NOUN
m-1112	1397	4	the	the	DET
m-1112	1397	5	deformation	deformation	NOUN
m-1112	1397	6	of	of	ADP
m-1112	1397	7	the	the	DET
m-1112	1397	8	spring	spring	NOUN
m-1112	1397	9	is	be	AUX
m-1112	1397	10	an	an	DET
m-1112	1397	11	equilibrium	equilibrium	NOUN
m-1112	1397	12	position	position	NOUN
m-1112	1397	13	in	in	ADP
m-1112	1397	14	∆	∆	PROPN
m-1112	1397	15	,	,	PUNCT
m-1112	1397	16	and	and	CCONJ
m-1112	1397	17	the	the	DET
m-1112	1397	18	spring	spring	NOUN
m-1112	1397	19	-	-	PUNCT
m-1112	1397	20	forse	forse	PROPN
m-1112	1397	21	k	k	PROPN
m-1112	1397	22	∆	∆	PROPN
m-1112	1398	1	=	=	PUNCT
m-1112	1398	2	w	w	PROPN
m-1112	1398	3	=	=	VERB
m-1112	1398	4	m	m	PROPN
m-1112	1398	5	g	g	NOUN
m-1112	1398	6	=	=	SYM
m-1112	1398	7	gravitational	gravitational	ADJ
m-1112	1398	8	force	force	NOUN
m-1112	1398	9	w	w	VERB
m-1112	1398	10	acting	act	VERB
m-1112	1398	11	on	on	ADP
m-1112	1398	12	mass	mass	PROPN
m-1112	1398	13	m	m	PROPN
m-1112	1398	14	,	,	PUNCT
m-1112	1398	15	then	then	ADV
m-1112	1398	16	exists	exist	VERB
m-1112	1398	17	→	→	PUNCT
m-1112	1398	18	m	m	VERB
m-1112	1398	19	�	�	PROPN
m-1112	1398	20	̈	̈	X
m-1112	1398	21	�	�	NOUN
m-1112	1398	22	=	=	SYM
m-1112	1398	23	σf	σf	NOUN
m-1112	1398	24	=	=	PUNCT
m-1112	1398	25	w	w	PROPN
m-1112	1398	26	=	=	SYM
m-1112	1398	27	k	k	PROPN
m-1112	1398	28	[	[	PUNCT
m-1112	1398	29	∆	∆	X
m-1112	1398	30	+	+	CCONJ
m-1112	1398	31	x	x	X
m-1112	1398	32	]	]	X
m-1112	1398	33	…	…	PUNCT
m-1112	1398	34	.(1	.(1	NUM
m-1112	1398	35	)	)	PUNCT
m-1112	1398	36	,	,	PUNCT
m-1112	1398	37	and	and	CCONJ
m-1112	1398	38	because	because	SCONJ
m-1112	1398	39	k	k	PROPN
m-1112	1398	40	∆	∆	PROPN
m-1112	1398	41	=	=	PUNCT
m-1112	1398	42	w	w	NOUN
m-1112	1398	43	we	we	PRON
m-1112	1398	44	obtain	obtain	VERB
m-1112	1398	45	w	w	ADJ
m-1112	1398	46	²n	²n	NOUN
m-1112	1398	47	=	=	SYM
m-1112	1399	1	k	k	X
m-1112	1399	2	/	/	SYM
m-1112	1399	3	m	m	PROPN
m-1112	1399	4	..	..	PUNCT
m-1112	1399	5	(	(	PUNCT
m-1112	1399	6	2	2	X
m-1112	1399	7	)	)	PUNCT
m-1112	1399	8	and	and	CCONJ
m-1112	1399	9	(	(	PUNCT
m-1112	1399	10	1	1	X
m-1112	1399	11	)	)	PUNCT
m-1112	1399	12	becomes	become	VERB
m-1112	1399	13	→	→	SYM
m-1112	1399	14	�	�	NOUN
m-1112	1399	15	̈	̈	X
m-1112	1399	16	�	�	NOUN
m-1112	1399	17	+	+	CCONJ
m-1112	1399	18	𝐰	𝐰	ADJ
m-1112	1399	19	²𝐧	²𝐧	NOUN
m-1112	1399	20	=	=	SYM
m-1112	1399	21	0	0	NUM
m-1112	1399	22	,	,	PUNCT
m-1112	1399	23	…	…	PUNCT
m-1112	1399	24	(	(	PUNCT
m-1112	1399	25	3	3	NUM
m-1112	1399	26	)	)	PUNCT
m-1112	1399	27	←	←	PROPN
m-1112	1399	28	i.e.	i.e.	X
m-1112	1399	29	the	the	DET
m-1112	1399	30	transportation	transportation	NOUN
m-1112	1399	31	of	of	ADP
m-1112	1399	32	energy	energy	NOUN
m-1112	1399	33	is	be	AUX
m-1112	1399	34	a	a	DET
m-1112	1399	35	harmonic	harmonic	ADJ
m-1112	1399	36	vibration	vibration	NOUN
m-1112	1399	37	in	in	ADP
m-1112	1399	38	cave	cave	NOUN
m-1112	1399	39	∆	∆	PROPN
m-1112	1399	40	,	,	PUNCT
m-1112	1399	41	means	mean	VERB
m-1112	1399	42	the	the	DET
m-1112	1399	43	wave	wave	NOUN
m-1112	1399	44	pattern	pattern	NOUN
m-1112	1399	45	.	.	PUNCT
m-1112	1400	1	it	it	PRON
m-1112	1400	2	is	be	AUX
m-1112	1400	3	shown	show	VERB
m-1112	1400	4	[	[	PUNCT
m-1112	1400	5	92	92	NUM
m-1112	1400	6	]	]	PUNCT
m-1112	1400	7	that	that	SCONJ
m-1112	1400	8	in	in	ADP
m-1112	1400	9	pns	pns	NOUN
m-1112	1400	10	-	-	NOUN
m-1112	1400	11	space	space	NOUN
m-1112	1400	12	the	the	DET
m-1112	1400	13	two	two	NUM
m-1112	1400	14	equal	equal	ADJ
m-1112	1400	15	and	and	CCONJ
m-1112	1400	16	opposite	opposite	ADJ
m-1112	1400	17	stresses	stress	NOUN
m-1112	1400	18	±	±	PROPN
m-1112	1400	19	σ	σ	NOUN
m-1112	1400	20	,	,	PUNCT
m-1112	1400	21	are	be	AUX
m-1112	1400	22	the	the	DET
m-1112	1400	23	two	two	NUM
m-1112	1400	24	centripetal	centripetal	NOUN
m-1112	1400	25	,	,	PUNCT
m-1112	1401	1	𝐅𝐩	𝐅𝐩	PROPN
m-1112	1401	2	,	,	PUNCT
m-1112	1401	3	centrifugal	centrifugal	ADJ
m-1112	1401	4	,	,	PUNCT
m-1112	1401	5	𝐅𝐟	𝐅𝐟	PROPN
m-1112	1401	6	force	force	NOUN
m-1112	1401	7	where	where	SCONJ
m-1112	1401	8	energy	energy	NOUN
m-1112	1401	9	is	be	AUX
m-1112	1401	10	→	→	SYM
m-1112	1401	11	e	e	X
m-1112	1401	12	=	=	SYM
m-1112	1401	13	h	h	NOUN
m-1112	1401	14	f	f	NOUN
m-1112	1401	15	=	=	PUNCT
m-1112	1401	16	(	(	PUNCT
m-1112	1401	17	1	1	NUM
m-1112	1401	18	+	+	NUM
m-1112	1401	19	√5	√5	NOUN
m-1112	1401	20	]	]	PUNCT
m-1112	1401	21	)	)	PUNCT
m-1112	1401	22	.σh	.σh	PUNCT
m-1112	1402	1	8πr	8πr	NOUN
m-1112	1402	2	=	=	PUNCT
m-1112	1402	3	σφh	σφh	NOUN
m-1112	1402	4	4πr	4πr	NOUN
m-1112	1402	5	,	,	PUNCT
m-1112	1402	6	in	in	ADP
m-1112	1402	7	the	the	DET
m-1112	1402	8	one	one	NUM
m-1112	1402	9	wave	wave	NOUN
m-1112	1402	10	note	note	NOUN
m-1112	1402	11	.and	.and	PUNCT
m-1112	1403	1	the	the	DET
m-1112	1403	2	frequency	frequency	NOUN
m-1112	1403	3	f	f	X
m-1112	1403	4	=	=	PUNCT
m-1112	1403	5	(	(	PUNCT
m-1112	1403	6	1	1	NUM
m-1112	1403	7	+	+	NUM
m-1112	1403	8	√5	√5	NOUN
m-1112	1403	9	]	]	PUNCT
m-1112	1403	10	)	)	PUNCT
m-1112	1403	11	.	.	PUNCT
m-1112	1404	1	σ	σ	NOUN
m-1112	1404	2	8πr	8πr	NOUN
m-1112	1404	3	,	,	PUNCT
m-1112	1404	4	period	period	NOUN
m-1112	1404	5	t	t	NOUN
m-1112	1404	6	=	=	SYM
m-1112	1404	7	8πr	8πr	PROPN
m-1112	1404	8	σ(1+√5	σ(1+√5	PROPN
m-1112	1404	9	)	)	PUNCT
m-1112	1404	10	=	=	SYM
m-1112	1405	1	4πr	4πr	PROPN
m-1112	1405	2	σ.φ	σ.φ	PROPN
m-1112	1405	3	.	.	PUNCT
m-1112	1406	1	10.a	10.a	NUM
m-1112	1406	2	..	..	PUNCT
m-1112	1407	1	the	the	DET
m-1112	1407	2	e	e	NOUN
m-1112	1407	3	-	-	NOUN
m-1112	1407	4	spaces	space	NOUN
m-1112	1407	5	and	and	CCONJ
m-1112	1407	6	the	the	DET
m-1112	1407	7	energy	energy	NOUN
m-1112	1407	8	regular	regular	ADJ
m-1112	1407	9	polygons	polygon	NOUN
m-1112	1407	10	.	.	PUNCT
m-1112	1408	1	a.	a.	NOUN
m-1112	1409	1	the	the	DET
m-1112	1409	2	geometrical	geometrical	ADJ
m-1112	1409	3	solution	solution	NOUN
m-1112	1409	4	:	:	PUNCT
m-1112	1409	5	a	a	X
m-1112	1409	6	..	..	PUNCT
m-1112	1409	7	the	the	DET
m-1112	1409	8	even	even	ADJ
m-1112	1409	9	and	and	CCONJ
m-1112	1409	10	odd	odd	ADJ
m-1112	1409	11	n	n	CCONJ
m-1112	1409	12	-	-	PUNCT
m-1112	1409	13	polygons	polygon	NOUN
m-1112	1409	14	[	[	PUNCT
m-1112	1409	15	80	80	NUM
m-1112	1409	16	]	]	PUNCT
m-1112	1409	17	:	:	PUNCT
m-1112	1409	18	ijo	ijo	PROPN
m-1112	1409	19	international	international	PROPN
m-1112	1409	20	journal	journal	PROPN
m-1112	1409	21	of	of	ADP
m-1112	1409	22	mathematics	mathematics	PROPN
m-1112	1409	23	(	(	PUNCT
m-1112	1409	24	issn	issn	PROPN
m-1112	1409	25	:	:	PUNCT
m-1112	1409	26	2992	2992	NUM
m-1112	1409	27	-	-	SYM
m-1112	1409	28	4421	4421	NUM
m-1112	1409	29	)	)	PUNCT
m-1112	1409	30	volume	volume	NOUN
m-1112	1409	31	08	08	NUM
m-1112	1410	1	|	|	ADV
m-1112	1410	2	issue	issue	NOUN
m-1112	1410	3	08	08	NUM
m-1112	1411	1	|	|	ADV
m-1112	1411	2	august	august	PROPN
m-1112	1411	3	2025	2025	NUM
m-1112	1411	4	|	|	ADV
m-1112	1411	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1411	6	ijo	ijo	PROPN
m-1112	1411	7	journals	journal	NOUN
m-1112	1411	8	50	50	NUM
m-1112	1411	9	the	the	DET
m-1112	1411	10	fundamental	fundamental	ADJ
m-1112	1411	11	particles	particle	NOUN
m-1112	1411	12	origination	origination	NOUN
m-1112	1411	13	mechanism	mechanism	NOUN
m-1112	1411	14	in	in	ADP
m-1112	1411	15	mfmf	mfmf	PROPN
m-1112	1411	16	pns	pns	PROPN
m-1112	1411	17	caves	cave	NOUN
m-1112	1411	18	.	.	PUNCT
m-1112	1412	1	figure	figure	NOUN
m-1112	1412	2	–	–	PUNCT
m-1112	1412	3	12aan	12aan	NOUN
m-1112	1412	4	even	even	ADV
m-1112	1412	5	and	and	CCONJ
m-1112	1412	6	an	an	DET
m-1112	1412	7	odd	odd	ADJ
m-1112	1412	8	n	n	CCONJ
m-1112	1412	9	-	-	PUNCT
m-1112	1412	10	polygon	polygon	NOUN
m-1112	1412	11	in	in	ADP
m-1112	1412	12	circle	circle	NOUN
m-1112	1412	13	o	o	PROPN
m-1112	1412	14	,	,	PUNCT
m-1112	1412	15	oa	oa	PROPN
m-1112	1412	16	with	with	ADP
m-1112	1412	17	diameters	diameter	NOUN
m-1112	1412	18	,	,	PUNCT
m-1112	1412	19	ak	ak	PROPN
m-1112	1412	20	a2k	a2k	PROPN
m-1112	1412	21	,	,	PUNCT
m-1112	1412	22	passing	pass	VERB
m-1112	1412	23	from	from	ADP
m-1112	1412	24	point	point	NOUN
m-1112	1412	25	a2k	a2k	PROPN
m-1112	1412	26	,	,	PUNCT
m-1112	1412	27	as	as	SCONJ
m-1112	1412	28	vertex	vertex	NOUN
m-1112	1412	29	(	(	PUNCT
m-1112	1412	30	apex	apex	NOUN
m-1112	1412	31	)	)	PUNCT
m-1112	1412	32	of	of	ADP
m-1112	1412	33	the	the	DET
m-1112	1412	34	polygone	polygone	NOUN
m-1112	1412	35	,	,	PUNCT
m-1112	1412	36	and	and	CCONJ
m-1112	1412	37	diameters	diameter	NOUN
m-1112	1412	38	,	,	PUNCT
m-1112	1412	39	ak+2	ak+2	NUM
m-1112	1412	40	m1	m1	PROPN
m-1112	1412	41	to	to	PART
m-1112	1412	42	be	be	AUX
m-1112	1412	43	perpendicular	perpendicular	ADJ
m-1112	1412	44	to	to	PART
m-1112	1412	45	side	side	VERB
m-1112	1413	1	a1a2	a1a2	INTJ
m-1112	1413	2	.	.	PUNCT
m-1112	1414	1	the	the	DET
m-1112	1414	2	projections	projection	NOUN
m-1112	1414	3	of	of	ADP
m-1112	1414	4	the	the	DET
m-1112	1414	5	heights	height	NOUN
m-1112	1414	6	𝒉	𝒉	PROPN
m-1112	1414	7	𝒏	𝒏	PROPN
m-1112	1414	8	.	.	PUNCT
m-1112	1415	1	let	let	AUX
m-1112	1415	2	be	be	AUX
m-1112	1415	3	the	the	DET
m-1112	1415	4	n	n	CCONJ
m-1112	1415	5	-	-	PUNCT
m-1112	1415	6	polygon	polygon	NOUN
m-1112	1415	7	a1	a1	NOUN
m-1112	1415	8	,	,	PUNCT
m-1112	1415	9	a2	a2	PROPN
m-1112	1415	10	,	,	PUNCT
m-1112	1415	11	a3	a3	NOUN
m-1112	1415	12	,	,	PUNCT
m-1112	1415	13	ak	ak	PROPN
m-1112	1415	14	,	,	PUNCT
m-1112	1415	15	ak+1	ak+1	VERB
m-1112	1415	16	,	,	PUNCT
m-1112	1415	17	ak+2	ak+2	NUM
m-1112	1415	18	,	,	PUNCT
m-1112	1415	19	a2k	a2k	X
m-1112	1415	20	,	,	PUNCT
m-1112	1415	21	in	in	ADP
m-1112	1415	22	circle	circle	NOUN
m-1112	1415	23	(	(	PUNCT
m-1112	1415	24	o	o	NOUN
m-1112	1415	25	,	,	PUNCT
m-1112	1415	26	oa1	oa1	NOUN
m-1112	1415	27	)	)	PUNCT
m-1112	1415	28	,	,	PUNCT
m-1112	1415	29	(	(	PUNCT
m-1112	1415	30	e	e	X
m-1112	1415	31	)	)	PUNCT
m-1112	1415	32	a	a	DET
m-1112	1415	33	straight	straight	ADJ
m-1112	1415	34	line	line	NOUN
m-1112	1415	35	not	not	PART
m-1112	1415	36	intersecting	intersect	VERB
m-1112	1415	37	the	the	DET
m-1112	1415	38	circle	circle	NOUN
m-1112	1415	39	d1	d1	PROPN
m-1112	1415	40	,	,	PUNCT
m-1112	1415	41	d2	d2	PROPN
m-1112	1415	42	,	,	PUNCT
m-1112	1415	43	d2k	d2k	PROPN
m-1112	1415	44	,	,	PUNCT
m-1112	1415	45	the	the	DET
m-1112	1415	46	heights	height	NOUN
m-1112	1415	47	of	of	ADP
m-1112	1415	48	the	the	DET
m-1112	1415	49	vertices	vertex	NOUN
m-1112	1415	50	to	to	ADP
m-1112	1415	51	(	(	PUNCT
m-1112	1415	52	e	e	NOUN
m-1112	1415	53	)	)	PUNCT
m-1112	1415	54	line	line	NOUN
m-1112	1415	55	,	,	PUNCT
m-1112	1415	56	h1	h1	NOUN
m-1112	1415	57	,	,	PUNCT
m-1112	1415	58	h2	h2	PROPN
m-1112	1415	59	,	,	PUNCT
m-1112	1415	60	h2k+1	h2k+1	NOUN
m-1112	1415	61	,	,	PUNCT
m-1112	1415	62	the	the	DET
m-1112	1415	63	heights	height	NOUN
m-1112	1415	64	of	of	ADP
m-1112	1415	65	the	the	DET
m-1112	1415	66	midpoints	midpoint	NOUN
m-1112	1415	67	mk	mk	NOUN
m-1112	1415	68	mk+1	mk+1	NUM
m-1112	1415	69	of	of	ADP
m-1112	1415	70	the	the	DET
m-1112	1415	71	sides	side	NOUN
m-1112	1415	72	to	to	ADP
m-1112	1415	73	(	(	PUNCT
m-1112	1415	74	e	e	NOUN
m-1112	1415	75	)	)	PUNCT
m-1112	1415	76	line	line	NOUN
m-1112	1415	77	φ	φ	NOUN
m-1112	1415	78	h−λ	h−λ	PROPN
m-1112	1415	79	,	,	PUNCT
m-1112	1415	80	,	,	PUNCT
m-1112	1415	81	the	the	DET
m-1112	1415	82	angle	angle	NOUN
m-1112	1415	83	of	of	ADP
m-1112	1415	84	the	the	DET
m-1112	1415	85	vertices	vertex	NOUN
m-1112	1415	86	and	and	CCONJ
m-1112	1415	87	the	the	DET
m-1112	1415	88	(	(	PUNCT
m-1112	1415	89	⏊	⏊	PROPN
m-1112	1415	90	)	)	PUNCT
m-1112	1415	91	semi	semi	ADV
m-1112	1415	92	-sides	-side	NOUN
m-1112	1415	93	,	,	PUNCT
m-1112	1415	94	and	and	CCONJ
m-1112	1415	95	ok	ok	INTJ
m-1112	1415	96	=	=	ADJ
m-1112	1415	97	h	h	NOUN
m-1112	1415	98	,	,	PUNCT
m-1112	1415	99	the	the	DET
m-1112	1415	100	height	height	NOUN
m-1112	1415	101	from	from	ADP
m-1112	1415	102	the	the	DET
m-1112	1415	103	center	center	NOUN
m-1112	1415	104	o	o	NOUN
m-1112	1415	105	to	to	ADP
m-1112	1415	106	(	(	PUNCT
m-1112	1415	107	e	e	NOUN
m-1112	1415	108	)	)	PUNCT
m-1112	1415	109	line	line	NOUN
m-1112	1415	110	.	.	PUNCT
m-1112	1416	1	to	to	ADP
m-1112	1416	2	proof	proof	NOUN
m-1112	1416	3	:	:	PUNCT
m-1112	1416	4	in	in	ADP
m-1112	1416	5	any	any	DET
m-1112	1416	6	n	n	X
m-1112	1416	7	polygon	polygon	NOUN
m-1112	1416	8	,	,	PUNCT
m-1112	1416	9	the	the	DET
m-1112	1416	10	sum	sum	NOUN
m-1112	1416	11	,	,	PUNCT
m-1112	1416	12	σ	σ	PROPN
m-1112	1416	13	=	=	SYM
m-1112	1416	14	σ	σ	PROPN
m-1112	1416	15	(	(	PUNCT
m-1112	1416	16	h	h	NOUN
m-1112	1416	17	)	)	PUNCT
m-1112	1416	18	,	,	PUNCT
m-1112	1416	19	of	of	ADP
m-1112	1416	20	the	the	DET
m-1112	1416	21	heights	height	NOUN
m-1112	1416	22	,	,	PUNCT
m-1112	1416	23	d1	d1	PROPN
m-1112	1416	24	,	,	PUNCT
m-1112	1416	25	d2	d2	PROPN
m-1112	1416	26	,	,	PUNCT
m-1112	1416	27	d2k	d2k	NOUN
m-1112	1416	28	,	,	PUNCT
m-1112	1416	29	of	of	ADP
m-1112	1416	30	the	the	DET
m-1112	1416	31	vertices	vertex	NOUN
m-1112	1416	32	a1	a1	NOUN
m-1112	1416	33	,	,	PUNCT
m-1112	1416	34	a2	a2	PROPN
m-1112	1416	35	,	,	PUNCT
m-1112	1416	36	a3	a3	NOUN
m-1112	1416	37	,	,	PUNCT
m-1112	1416	38	ak	ak	PROPN
m-1112	1416	39	,	,	PUNCT
m-1112	1416	40	ak+1	ak+1	VERB
m-1112	1416	41	,	,	PUNCT
m-1112	1416	42	ak+2	ak+2	NUM
m-1112	1416	43	,	,	PUNCT
m-1112	1416	44	a2k	a2k	PROPN
m-1112	1416	45	,	,	PUNCT
m-1112	1416	46	where	where	SCONJ
m-1112	1416	47	n	n	NOUN
m-1112	1416	48	=	=	SYM
m-1112	1416	49	2k	2k	PROPN
m-1112	1416	50	,	,	PUNCT
m-1112	1416	51	from	from	ADP
m-1112	1416	52	any	any	DET
m-1112	1416	53	straight	straight	ADJ
m-1112	1416	54	line	line	NOUN
m-1112	1416	55	(	(	PUNCT
m-1112	1416	56	e	e	NOUN
m-1112	1416	57	)	)	PUNCT
m-1112	1416	58	is	be	AUX
m-1112	1416	59	equal	equal	ADJ
m-1112	1416	60	to	to	ADP
m-1112	1416	61	σ	σ	X
m-1112	1416	62	=	=	SYM
m-1112	1416	63	σ	σ	PROPN
m-1112	1416	64	(	(	PUNCT
m-1112	1416	65	h	h	NOUN
m-1112	1416	66	)	)	PUNCT
m-1112	1416	67	=	=	SYM
m-1112	1417	1	n	n	PROPN
m-1112	1417	2	.	.	PUNCT
m-1112	1418	1	ok	ok	INTJ
m-1112	1418	2	=	=	NOUN
m-1112	1418	3	n	n	PROPN
m-1112	1418	4	.	.	PUNCT
m-1112	1419	1	h	h	NOUN
m-1112	1419	2	.	.	PUNCT
m-1112	1420	1	the	the	DET
m-1112	1420	2	geometrical	geometrical	ADJ
m-1112	1420	3	proof	proof	NOUN
m-1112	1420	4	in	in	ADP
m-1112	1420	5	[	[	PUNCT
m-1112	1420	6	80	80	NUM
m-1112	1420	7	]	]	PUNCT
m-1112	1420	8	remarks	remark	NOUN
m-1112	1420	9	:	:	PUNCT
m-1112	1420	10	1	1	X
m-1112	1420	11	..	..	PUNCT
m-1112	1420	12	in	in	ADP
m-1112	1420	13	the	the	DET
m-1112	1420	14	system	system	NOUN
m-1112	1420	15	of	of	ADP
m-1112	1420	16	regular	regular	ADJ
m-1112	1420	17	polygons	polygon	NOUN
m-1112	1420	18	the	the	PRON
m-1112	1420	19	,	,	PUNCT
m-1112	1420	20	interior	interior	ADJ
m-1112	1420	21	angles	angle	NOUN
m-1112	1420	22	(	(	PUNCT
m-1112	1420	23	w	w	NOUN
m-1112	1420	24	)	)	PUNCT
m-1112	1420	25	and	and	CCONJ
m-1112	1420	26	gradient	gradient	NOUN
m-1112	1420	27	(	(	PUNCT
m-1112	1420	28	φ	φ	PROPN
m-1112	1420	29	)	)	PUNCT
m-1112	1420	30	,	,	PUNCT
m-1112	1420	31	heights	height	NOUN
m-1112	1420	32	(	(	PUNCT
m-1112	1420	33	h	h	NOUN
m-1112	1420	34	)	)	PUNCT
m-1112	1420	35	and	and	CCONJ
m-1112	1420	36	their	their	PRON
m-1112	1420	37	differences	difference	NOUN
m-1112	1420	38	,	,	PUNCT
m-1112	1420	39	δh	δh	INTJ
m-1112	1420	40	,	,	PUNCT
m-1112	1420	41	–	–	PUNCT
m-1112	1420	42	summation	summation	NOUN
m-1112	1420	43	and	and	CCONJ
m-1112	1420	44	subtraction	subtraction	NOUN
m-1112	1420	45	of	of	ADP
m-1112	1420	46	heights	height	NOUN
m-1112	1420	47	are	be	AUX
m-1112	1420	48	interconnected	interconnect	VERB
m-1112	1420	49	and	and	CCONJ
m-1112	1420	50	intertwined	intertwine	VERB
m-1112	1420	51	at	at	ADP
m-1112	1420	52	the	the	DET
m-1112	1420	53	common	common	ADJ
m-1112	1420	54	circle	circle	NOUN
m-1112	1420	55	[	[	PUNCT
m-1112	1420	56	a	a	X
m-1112	1420	57	,	,	PUNCT
m-1112	1421	1	δh	δh	ADP
m-1112	1421	2	=	=	SYM
m-1112	1421	3	𝐡	𝐡	PROPN
m-1112	1422	1	𝐀𝐡	𝐀𝐡	PROPN
m-1112	1422	2	𝐁	𝐁	PROPN
m-1112	1422	3	]	]	PUNCT
m-1112	1422	4	producing	produce	VERB
m-1112	1422	5	the	the	DET
m-1112	1422	6	common	common	ADJ
m-1112	1422	7	(	(	PUNCT
m-1112	1422	8	n+1	n+1	PROPN
m-1112	1422	9	)	)	PUNCT
m-1112	1422	10	,	,	PUNCT
m-1112	1422	11	odd	odd	ADJ
m-1112	1422	12	–	–	PUNCT
m-1112	1422	13	regular	regular	ADJ
m-1112	1422	14	polygon	polygon	NOUN
m-1112	1422	15	.	.	PUNCT
m-1112	1423	1	this	this	DET
m-1112	1423	2	property	property	NOUN
m-1112	1423	3	allows	allow	VERB
m-1112	1423	4	to	to	PART
m-1112	1423	5	refer	refer	VERB
m-1112	1423	6	the	the	DET
m-1112	1423	7	regular	regular	ADJ
m-1112	1423	8	polygons	polygon	NOUN
m-1112	1423	9	to	to	ADP
m-1112	1423	10	the	the	DET
m-1112	1423	11	tangents	tangent	NOUN
m-1112	1423	12	of	of	ADP
m-1112	1423	13	any	any	DET
m-1112	1423	14	triangle	triangle	NOUN
m-1112	1423	15	a	a	DET
m-1112	1423	16	,	,	PUNCT
m-1112	1423	17	b	b	NOUN
m-1112	1423	18	,	,	PUNCT
m-1112	1423	19	c	c	NOUN
m-1112	1423	20	,	,	PUNCT
m-1112	1423	21	as	as	SCONJ
m-1112	1423	22	it	it	PRON
m-1112	1423	23	is	be	AUX
m-1112	1423	24	the	the	DET
m-1112	1423	25	8	8	NUM
m-1112	1423	26	..	..	PUNCT
m-1112	1423	27	[a	[a	X
m-1112	1423	28	]	]	X
m-1112	1423	29			NOUN
m-1112	1423	30	{	{	PUNCT
m-1112	1423	31	stpl	stpl	PROPN
m-1112	1423	32	}	}	PUNCT
m-1112	1423	33	mechanisms	mechanism	NOUN
m-1112	1423	34	:	:	PUNCT
m-1112	1423	35	the	the	DET
m-1112	1423	36	six	six	NUM
m-1112	1423	37	triple	triple	ADJ
m-1112	1423	38	points	point	NOUN
m-1112	1423	39	line	line	NOUN
m-1112	1423	40	mechanism	mechanism	NOUN
m-1112	1423	41	.	.	PUNCT
m-1112	1424	1	i.e.	i.e.	X
m-1112	1424	2	the	the	DET
m-1112	1424	3	fundamental	fundamental	ADJ
m-1112	1424	4	particles	particle	NOUN
m-1112	1424	5	origination	origination	NOUN
m-1112	1424	6	happens	happen	VERB
m-1112	1424	7	from	from	ADP
m-1112	1424	8	the	the	DET
m-1112	1424	9	electric	electric	ADJ
m-1112	1424	10	and	and	CCONJ
m-1112	1424	11	magnetic	magnetic	ADJ
m-1112	1424	12	field	field	NOUN
m-1112	1424	13	of	of	ADP
m-1112	1424	14	the	the	DET
m-1112	1424	15	3	3	NUM
m-1112	1424	16	conductors	conductor	NOUN
m-1112	1424	17	on	on	ADP
m-1112	1424	18	2	2	NUM
m-1112	1424	19	anti	anti	ADJ
m-1112	1424	20	-	-	ADJ
m-1112	1424	21	parallel	parallel	ADJ
m-1112	1424	22	-	-	PUNCT
m-1112	1424	23	strands	strand	NOUN
m-1112	1424	24	,	,	PUNCT
m-1112	1424	25	fig	fig	NOUN
m-1112	1424	26	–	–	PUNCT
m-1112	1424	27	9a	9a	NUM
m-1112	1424	28	2	2	NUM
m-1112	1424	29	..	..	PUNCT
m-1112	1424	30	𝐬𝐢𝐧	𝐬𝐢𝐧	ADP
m-1112	1424	31	𝛗	𝛗	X
m-1112	1424	32	=	=	SYM
m-1112	1424	33	(	(	PUNCT
m-1112	1424	34	𝐡	𝐡	NOUN
m-1112	1424	35	𝛗	𝛗	X
m-1112	1424	36	𝛌	𝛌	X
m-1112	1424	37	𝛗	𝛗	X
m-1112	1424	38	)	)	PUNCT
m-1112	1424	39	,	,	PUNCT
m-1112	1424	40	is	be	AUX
m-1112	1424	41	the	the	DET
m-1112	1424	42	harmonic	harmonic	ADJ
m-1112	1424	43	mean	mean	NOUN
m-1112	1424	44	between	between	ADP
m-1112	1424	45	[	[	PUNCT
m-1112	1424	46	𝐡	𝐡	NOUN
m-1112	1424	47	𝐀	𝐀	PROPN
m-1112	1424	48	𝐡	𝐡	PROPN
m-1112	1424	49	𝐁	𝐁	PROPN
m-1112	1424	50	]	]	PUNCT
m-1112	1424	51	,	,	PUNCT
m-1112	1424	52	[	[	PUNCT
m-1112	1424	53	𝟏	𝟏	NUM
m-1112	1424	54	𝟐	𝟐	NUM
m-1112	1424	55	(	(	PUNCT
m-1112	1424	56	𝐫	𝐫	PROPN
m-1112	1424	57	𝐚	𝐚	ADP
m-1112	1424	58	−	−	PROPN
m-1112	1424	59	𝐫	𝐫	PROPN
m-1112	1424	60	𝐛	𝐛	PROPN
m-1112	1424	61	)	)	PUNCT
m-1112	1424	62	]	]	PUNCT
m-1112	1425	1	ijo	ijo	PROPN
m-1112	1425	2	international	international	PROPN
m-1112	1425	3	journal	journal	PROPN
m-1112	1425	4	of	of	ADP
m-1112	1425	5	mathematics	mathematics	PROPN
m-1112	1425	6	(	(	PUNCT
m-1112	1425	7	issn	issn	PROPN
m-1112	1425	8	:	:	PUNCT
m-1112	1425	9	2992	2992	NUM
m-1112	1425	10	-	-	SYM
m-1112	1425	11	4421	4421	NUM
m-1112	1425	12	)	)	PUNCT
m-1112	1425	13	volume	volume	NOUN
m-1112	1425	14	08	08	NUM
m-1112	1426	1	|	|	ADV
m-1112	1426	2	issue	issue	NOUN
m-1112	1426	3	08	08	NUM
m-1112	1427	1	|	|	ADV
m-1112	1427	2	august	august	PROPN
m-1112	1427	3	2025	2025	NUM
m-1112	1427	4	|	|	ADV
m-1112	1427	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1427	6	ijo	ijo	PROPN
m-1112	1427	7	journals	journal	NOUN
m-1112	1427	8	51	51	NUM
m-1112	1427	9	the	the	DET
m-1112	1427	10	fundamental	fundamental	ADJ
m-1112	1427	11	particles	particle	NOUN
m-1112	1427	12	origination	origination	NOUN
m-1112	1427	13	mechanism	mechanism	NOUN
m-1112	1427	14	in	in	ADP
m-1112	1427	15	mfmf	mfmf	PROPN
m-1112	1427	16	pns	pns	PROPN
m-1112	1427	17	caves	cave	NOUN
m-1112	1427	18	.	.	PUNCT
m-1112	1428	1	the	the	DET
m-1112	1428	2	force	force	NOUN
m-1112	1428	3	harmonic	harmonic	VERB
m-1112	1428	4	vibration	vibration	NOUN
m-1112	1428	5	&	&	CCONJ
m-1112	1428	6	the	the	DET
m-1112	1428	7	unbalance	unbalance	NOUN
m-1112	1428	8	vibration	vibration	NOUN
m-1112	1428	9	system	system	NOUN
m-1112	1428	10	:	:	PUNCT
m-1112	1428	11	figure	figure	VERB
m-1112	1428	12	–	–	PUNCT
m-1112	1428	13	12bthe	12bthe	DET
m-1112	1428	14	complex	complex	ADJ
m-1112	1428	15	frequency	frequency	NOUN
m-1112	1428	16	response	response	NOUN
m-1112	1428	17	from	from	ADP
m-1112	1428	18	the	the	DET
m-1112	1428	19	vector	vector	NOUN
m-1112	1428	20	-	-	PUNCT
m-1112	1428	21	force	force	NOUN
m-1112	1428	22	-	-	PUNCT
m-1112	1428	23	polygon	polygon	NOUN
m-1112	1428	24	is	be	AUX
m-1112	1428	25	seen	see	VERB
m-1112	1428	26	that	that	SCONJ
m-1112	1428	27	the	the	DET
m-1112	1428	28	terms	term	NOUN
m-1112	1428	29	of	of	ADP
m-1112	1428	30	the	the	DET
m-1112	1428	31	forced	force	VERB
m-1112	1428	32	harmonic	harmonic	ADJ
m-1112	1428	33	vibration	vibration	NOUN
m-1112	1428	34	,	,	PUNCT
m-1112	1428	35	(	(	PUNCT
m-1112	1428	36	m	m	X
m-1112	1428	37	ẍ	ẍ	X
m-1112	1429	1	+	+	PUNCT
m-1112	1429	2	cẋ	cẋ	NOUN
m-1112	1430	1	+	+	CCONJ
m-1112	1431	1	k	k	X
m-1112	1431	2	x	x	X
m-1112	1431	3	)	)	PUNCT
m-1112	1431	4	=	=	SYM
m-1112	1431	5	𝐅	𝐅	PROPN
m-1112	1431	6	𝟎	𝟎	NUM
m-1112	1431	7	.sin(w	.sin(w	ADP
m-1112	1431	8	t	t	PROPN
m-1112	1431	9	)	)	PUNCT
m-1112	1431	10	,	,	PUNCT
m-1112	1431	11	are	be	AUX
m-1112	1431	12	perpendicular	perpendicular	ADJ
m-1112	1431	13	to	to	ADP
m-1112	1431	14	the	the	DET
m-1112	1431	15	y	y	PROPN
m-1112	1431	16	-	-	PUNCT
m-1112	1431	17	y	y	PROPN
m-1112	1431	18	axis	axis	NOUN
m-1112	1431	19	.when	.when	SCONJ
m-1112	1431	20	the	the	DET
m-1112	1431	21	force	force	NOUN
m-1112	1431	22	changes	change	VERB
m-1112	1431	23	to	to	ADP
m-1112	1431	24	=	=	PUNCT
m-1112	1431	25	𝐅	𝐅	PROPN
m-1112	1431	26	𝟎	𝟎	NUM
m-1112	1431	27	.cos(w	.cos(w	NUM
m-1112	1431	28	t	t	PROPN
m-1112	1431	29	)	)	PUNCT
m-1112	1431	30	,	,	PUNCT
m-1112	1431	31	then	then	ADV
m-1112	1431	32	the	the	DET
m-1112	1431	33	terms	term	NOUN
m-1112	1431	34	are	be	AUX
m-1112	1431	35	perpendicular	perpendicular	ADJ
m-1112	1431	36	to	to	ADP
m-1112	1431	37	the	the	DET
m-1112	1431	38	x	x	ADJ
m-1112	1431	39	-	-	PUNCT
m-1112	1431	40	x	x	ADJ
m-1112	1431	41	axis	axis	NOUN
m-1112	1431	42	,	,	PUNCT
m-1112	1431	43	i.e.	i.e.	X
m-1112	1431	44	vector	vector	NOUN
m-1112	1431	45	-	-	PUNCT
m-1112	1431	46	force	force	NOUN
m-1112	1431	47	is	be	AUX
m-1112	1431	48	𝐅	𝐅	PROPN
m-1112	1431	49	𝟎	𝟎	NUM
m-1112	1431	50	.	.	PUNCT
m-1112	1432	1	[	[	PUNCT
m-1112	1432	2	cos(w	cos(w	PROPN
m-1112	1432	3	t	t	PROPN
m-1112	1432	4	)	)	PUNCT
m-1112	1433	1	+	+	CCONJ
m-1112	1433	2	sin(w	sin(w	PROPN
m-1112	1433	3	t	t	PROPN
m-1112	1433	4	)	)	PUNCT
m-1112	1433	5	]	]	PUNCT
m-1112	1434	1	=	=	PUNCT
m-1112	1434	2	𝐅	𝐅	PROPN
m-1112	1434	3	𝟎	𝟎	NUM
m-1112	1434	4	.e	.e	PUNCT
m-1112	1435	1	i.[w	i.[w	PROPN
m-1112	1435	2	t	t	PROPN
m-1112	1435	3	]	]	X
m-1112	1435	4	the	the	DET
m-1112	1435	5	rotation	rotation	NOUN
m-1112	1435	6	unbalance	unbalance	NOUN
m-1112	1435	7	vibration	vibration	NOUN
m-1112	1435	8	system	system	NOUN
m-1112	1435	9	:	:	PUNCT
m-1112	1435	10	for	for	ADP
m-1112	1435	11	an	an	DET
m-1112	1435	12	unbalance	unbalance	NOUN
m-1112	1435	13	-	-	PUNCT
m-1112	1435	14	rotational	rotational	ADJ
m-1112	1435	15	system	system	NOUN
m-1112	1435	16	,	,	PUNCT
m-1112	1435	17	the	the	DET
m-1112	1435	18	source	source	NOUN
m-1112	1435	19	of	of	ADP
m-1112	1435	20	vibration	vibration	NOUN
m-1112	1435	21	excitation	excitation	NOUN
m-1112	1435	22	is	be	AUX
m-1112	1435	23	considered	consider	VERB
m-1112	1435	24	an	an	DET
m-1112	1435	25	spring	spring	NOUN
m-1112	1435	26	mass	mass	NOUN
m-1112	1435	27	system	system	NOUN
m-1112	1435	28	constrained	constrain	VERB
m-1112	1435	29	to	to	PART
m-1112	1435	30	move	move	VERB
m-1112	1435	31	in	in	ADP
m-1112	1435	32	the	the	DET
m-1112	1435	33	vertical	vertical	ADJ
m-1112	1435	34	dirtection	dirtection	NOUN
m-1112	1435	35	and	and	CCONJ
m-1112	1435	36	is	be	AUX
m-1112	1435	37	excited	excite	VERB
m-1112	1435	38	by	by	ADP
m-1112	1435	39	an	an	DET
m-1112	1435	40	unbalanced	unbalanced	ADJ
m-1112	1435	41	rotation	rotation	NOUN
m-1112	1435	42	.	.	PUNCT
m-1112	1436	1	the	the	DET
m-1112	1436	2	unbalance	unbalance	NOUN
m-1112	1436	3	is	be	AUX
m-1112	1436	4	represented	represent	VERB
m-1112	1436	5	by	by	ADP
m-1112	1436	6	an	an	DET
m-1112	1436	7	eccentric	eccentric	ADJ
m-1112	1436	8	mass	mass	NOUN
m-1112	1436	9	m	m	VERB
m-1112	1436	10	,	,	PUNCT
m-1112	1436	11	with	with	ADP
m-1112	1436	12	eccentricity	eccentricity	NOUN
m-1112	1436	13	e	e	NOUN
m-1112	1436	14	,	,	PUNCT
m-1112	1436	15	and	and	CCONJ
m-1112	1436	16	rotates	rotate	VERB
m-1112	1436	17	with	with	ADP
m-1112	1436	18	angular	angular	ADJ
m-1112	1436	19	velocity	velocity	NOUN
m-1112	1436	20	w	w	NOUN
m-1112	1436	21	,	,	PUNCT
m-1112	1436	22	on	on	ADP
m-1112	1436	23	the	the	DET
m-1112	1436	24	nonrotating	nonrotating	NOUN
m-1112	1436	25	mass	mass	PROPN
m-1112	1436	26	m	m	VERB
m-1112	1436	27	m	m	VERB
m-1112	1436	28	,	,	PUNCT
m-1112	1436	29	with	with	ADP
m-1112	1436	30	displacement	displacement	NOUN
m-1112	1436	31	x	x	X
m-1112	1437	1	+	+	CCONJ
m-1112	1437	2	|	|	ADV
m-1112	1437	3	𝐞	𝐞	ADJ
m-1112	1437	4	√𝟐(𝐧	√𝟐(𝐧	NOUN
m-1112	1437	5	)	)	PUNCT
m-1112	1437	6	|	|	ADV
m-1112	1437	7	,	,	PUNCT
m-1112	1437	8	the	the	DET
m-1112	1437	9	equation	equation	NOUN
m-1112	1437	10	of	of	ADP
m-1112	1437	11	motion	motion	NOUN
m-1112	1437	12	is	be	AUX
m-1112	1437	13	,	,	PUNCT
m-1112	1437	14	[	[	PUNCT
m-1112	1437	15	m	m	NOUN
m-1112	1437	16	-	-	NOUN
m-1112	1437	17	m	m	X
m-1112	1437	18	]	]	PUNCT
m-1112	1437	19	ẍ	ẍ	X
m-1112	1438	1	+	+	NUM
m-1112	1438	2	m	m	VERB
m-1112	1438	3	d²	d²	PROPN
m-1112	1438	4	dt²	dt²	NOUN
m-1112	1438	5	[	[	X
m-1112	1438	6	x	x	X
m-1112	1438	7	+	+	ADJ
m-1112	1438	8	|	|	NOUN
m-1112	1438	9	e	e	NOUN
m-1112	1438	10	√2(n	√2(n	ADJ
m-1112	1438	11	)	)	PUNCT
m-1112	1438	12	|	|	ADV
m-1112	1438	13	]	]	PUNCT
m-1112	1439	1	+	+	CCONJ
m-1112	1439	2	c	c	X
m-1112	1439	3	ẋ	ẋ	PROPN
m-1112	1440	1	+	+	CCONJ
m-1112	1440	2	kx	kx	X
m-1112	1440	3	=	=	NOUN
m-1112	1440	4	0	0	PROPN
m-1112	1440	5	,	,	PUNCT
m-1112	1440	6	which	which	PRON
m-1112	1440	7	can	can	AUX
m-1112	1440	8	be	be	AUX
m-1112	1440	9	rearranged	rearrange	VERB
m-1112	1440	10	to	to	ADP
m-1112	1440	11	→	→	X
m-1112	1440	12	m	m	X
m-1112	1440	13	ẍ	ẍ	X
m-1112	1441	1	+	+	CCONJ
m-1112	1441	2	c	c	PROPN
m-1112	1441	3	ẋ	ẋ	PROPN
m-1112	1442	1	+	+	CCONJ
m-1112	1443	1	k	k	X
m-1112	1443	2	x	x	X
m-1112	1443	3	=	=	VERB
m-1112	1443	4	m	m	VERB
m-1112	1443	5	|	|	ADV
m-1112	1443	6	𝐞	𝐞	NOUN
m-1112	1443	7	√𝟐(𝐧	√𝟐(𝐧	NOUN
m-1112	1443	8	)	)	PUNCT
m-1112	1444	1	|	|	ADV
m-1112	1444	2	←	←	PROPN
m-1112	1444	3	…	…	PUNCT
m-1112	1444	4	...	...	PUNCT
m-1112	1444	5	(	(	PUNCT
m-1112	1444	6	c-2	c-2	NOUN
m-1112	1444	7	)	)	PUNCT
m-1112	1444	8	.	.	PUNCT
m-1112	1445	1	as	as	ADP
m-1112	1445	2	in	in	ADP
m-1112	1445	3	fig-12b-2	fig-12b-2	PRON
m-1112	1445	4	.	.	PUNCT
m-1112	1446	1	by	by	ADP
m-1112	1446	2	tuning	tune	VERB
m-1112	1446	3	the	the	DET
m-1112	1446	4	system	system	NOUN
m-1112	1446	5	to	to	ADP
m-1112	1446	6	the	the	DET
m-1112	1446	7	frequency	frequency	NOUN
m-1112	1446	8	of	of	ADP
m-1112	1446	9	the	the	DET
m-1112	1446	10	exciting	exciting	ADJ
m-1112	1446	11	force	force	NOUN
m-1112	1446	12	fo=	fo=	PROPN
m-1112	1446	13	1	1	NUM
m-1112	1446	14	such	such	ADJ
m-1112	1446	15	that	that	SCONJ
m-1112	1446	16	w	w	PROPN
m-1112	1446	17	²	²	PROPN
m-1112	1446	18	=	=	SYM
m-1112	1446	19	k	k	PROPN
m-1112	1446	20	2	2	NUM
m-1112	1446	21	m	m	NOUN
m-1112	1446	22	2	2	NUM
m-1112	1446	23	,	,	PUNCT
m-1112	1446	24	then	then	ADV
m-1112	1446	25	system	system	NOUN
m-1112	1446	26	acts	act	VERB
m-1112	1446	27	as	as	ADP
m-1112	1446	28	an	an	DET
m-1112	1446	29	vibrator	vibrator	NOUN
m-1112	1446	30	-	-	PUNCT
m-1112	1446	31	absorber	absorber	NOUN
m-1112	1446	32	and	and	CCONJ
m-1112	1446	33	reduces	reduce	VERB
m-1112	1446	34	the	the	DET
m-1112	1446	35	motion	motion	NOUN
m-1112	1446	36	of	of	ADP
m-1112	1446	37	the	the	DET
m-1112	1446	38	main	main	ADJ
m-1112	1446	39	mass	mass	NOUN
m-1112	1446	40	m	m	PROPN
m-1112	1446	41	≡	≡	PROPN
m-1112	1446	42	m16	m16	PROPN
m-1112	1446	43	≡	≡	PROPN
m-1112	1446	44	m1	m1	PROPN
m-1112	1446	45	and	and	CCONJ
m-1112	1446	46	m	m	PROPN
m-1112	1446	47	8	8	NUM
m-1112	1446	48	,	,	PUNCT
m-1112	1446	49	4	4	NUM
m-1112	1446	50	,	,	PUNCT
m-1112	1446	51	2	2	NUM
m-1112	1446	52	≡	≡	PROPN
m-1112	1446	53	m2	m2	PROPN
m-1112	1446	54	≡	≡	PROPN
m-1112	1446	55	m	m	PROPN
m-1112	1446	56	,	,	PUNCT
m-1112	1446	57	to	to	ADP
m-1112	1446	58	zero	zero	NUM
m-1112	1446	59	.	.	PUNCT
m-1112	1447	1	making	make	VERB
m-1112	1447	2	the	the	DET
m-1112	1447	3	substitution	substitution	NOUN
m-1112	1447	4	,	,	PUNCT
m-1112	1447	5	w11²	w11²	PROPN
m-1112	1447	6	=	=	SYM
m-1112	1447	7	k	k	PROPN
m-1112	1447	8	1	1	NUM
m-1112	1447	9	m1	m1	PROPN
m-1112	1447	10	,	,	PUNCT
m-1112	1447	11	w22²	w22²	PROPN
m-1112	1447	12	=	=	SYM
m-1112	1447	13	k	k	PROPN
m-1112	1447	14	2	2	NUM
m-1112	1447	15	m	m	NOUN
m-1112	1447	16	2	2	NUM
m-1112	1447	17	,	,	PUNCT
m-1112	1447	18	and	and	CCONJ
m-1112	1447	19	assuming	assume	VERB
m-1112	1447	20	the	the	DET
m-1112	1447	21	motion	motion	NOUN
m-1112	1447	22	to	to	PART
m-1112	1447	23	be	be	AUX
m-1112	1447	24	harmonic	harmonic	ADJ
m-1112	1447	25	,	,	PUNCT
m-1112	1447	26	then	then	ADV
m-1112	1447	27	the	the	DET
m-1112	1447	28	steady	steady	ADJ
m-1112	1447	29	-	-	PUNCT
m-1112	1447	30	state	state	NOUN
m-1112	1447	31	solution	solution	NOUN
m-1112	1447	32	is	be	AUX
m-1112	1447	33	,	,	PUNCT
m-1112	1447	34	xs	xs	PROPN
m-1112	1448	1	=	=	PUNCT
m-1112	1448	2	m	m	VERB
m-1112	1448	3	|	|	ADV
m-1112	1448	4	e	e	NOUN
m-1112	1448	5	√2(n	√2(n	ADJ
m-1112	1448	6	)	)	PUNCT
m-1112	1449	1	|	|	ADV
m-1112	1449	2	w	w	NOUN
m-1112	1449	3	²	²	NUM
m-1112	1449	4	√(k−mw2)2	√(k−mw2)2	ADP
m-1112	1449	5	+	+	NOUN
m-1112	1449	6	[	[	X
m-1112	1449	7	cw]2	cw]2	X
m-1112	1449	8	,	,	PUNCT
m-1112	1449	9	and	and	CCONJ
m-1112	1449	10	tanφ	tanφ	X
m-1112	1449	11	=	=	SYM
m-1112	1449	12	c	c	PROPN
m-1112	1449	13	w	w	PROPN
m-1112	1449	14	k−mw	k−mw	PROPN
m-1112	1449	15	²	²	NUM
m-1112	1449	16	and	and	CCONJ
m-1112	1449	17	so	so	ADV
m-1112	1449	18	the	the	DET
m-1112	1449	19	reduced	reduce	VERB
m-1112	1449	20	to	to	ADP
m-1112	1449	21	non	non	ADJ
m-1112	1449	22	-	-	ADJ
m-1112	1449	23	dimensional	dimensional	ADJ
m-1112	1449	24	form	form	NOUN
m-1112	1449	25	equation	equation	NOUN
m-1112	1449	26	for	for	ADP
m-1112	1449	27	amplitudes	amplitude	NOUN
m-1112	1449	28	is	be	AUX
m-1112	1449	29	,	,	PUNCT
m-1112	1449	30	x	x	SYM
m-1112	1449	31	s	s	X
m-1112	1449	32	=	=	X
m-1112	1450	1	|	|	ADV
m-1112	1450	2	m	m	VERB
m-1112	1450	3	e	e	NOUN
m-1112	1450	4	m√2(n	m√2(n	ADJ
m-1112	1450	5	)	)	PUNCT
m-1112	1450	6	|.|	|.|	NOUN
m-1112	1450	7	[	[	PUNCT
m-1112	1450	8	𝐰	𝐰	NOUN
m-1112	1450	9	w	w	NOUN
m-1112	1450	10	n.	n.	NOUN
m-1112	1450	11	]	]	PUNCT
m-1112	1450	12	²	²	NUM
m-1112	1450	13	√(1−	√(1−	PROPN
m-1112	1450	14	[	[	PUNCT
m-1112	1450	15	𝐰	𝐰	NOUN
m-1112	1450	16	w	w	NOUN
m-1112	1450	17	n.	n.	NOUN
m-1112	1450	18	]	]	PUNCT
m-1112	1450	19	2	2	NUM
m-1112	1450	20	)	)	PUNCT
m-1112	1450	21	2	2	NUM
m-1112	1451	1	+	+	CCONJ
m-1112	1451	2	[	[	X
m-1112	1451	3	2𝜁	2𝜁	NUM
m-1112	1451	4	𝐰	𝐰	NOUN
m-1112	1451	5	w	w	NOUN
m-1112	1451	6	n.	n.	NOUN
m-1112	1451	7	]	]	PUNCT
m-1112	1452	1	2|	2|	NUM
m-1112	1452	2	,	,	PUNCT
m-1112	1452	3	and	and	CCONJ
m-1112	1452	4	tanφ	tanφ	X
m-1112	1452	5	=	=	SYM
m-1112	1452	6	2	2	NUM
m-1112	1452	7	ζ	ζ	NOUN
m-1112	1452	8	.	.	PUNCT
m-1112	1453	1	[	[	PUNCT
m-1112	1453	2	𝑤	𝑤	X
m-1112	1453	3	w	w	NOUN
m-1112	1453	4	n	n	X
m-1112	1453	5	]	]	PUNCT
m-1112	1453	6	1−	1−	NUM
m-1112	1453	7	(	(	PUNCT
m-1112	1453	8	𝐰	𝐰	PROPN
m-1112	1453	9	wn	wn	X
m-1112	1453	10	)	)	PUNCT
m-1112	1453	11	²	²	PROPN
m-1112	1453	12	…	…	PUNCT
m-1112	1453	13	...	...	PUNCT
m-1112	1453	14	(	(	PUNCT
m-1112	1453	15	c-3	c-3	NOUN
m-1112	1453	16	)	)	PUNCT
m-1112	1453	17	which	which	PRON
m-1112	1453	18	is	be	AUX
m-1112	1453	19	identical	identical	ADJ
m-1112	1453	20	with	with	ADP
m-1112	1453	21	,	,	PUNCT
m-1112	1453	22	m	m	VERB
m-1112	1453	23	ẍ	ẍ	X
m-1112	1454	1	+	+	PUNCT
m-1112	1454	2	c	c	PROPN
m-1112	1454	3	ẋ	ẋ	PROPN
m-1112	1455	1	+	+	CCONJ
m-1112	1455	2	k	k	X
m-1112	1455	3	x	x	X
m-1112	1455	4	=	=	PUNCT
m-1112	1455	5	fo.sin	fo.sin	NOUN
m-1112	1455	6	wt	wt	ADP
m-1112	1455	7	…	…	PROPN
m-1112	1455	8	..	..	PUNCT
m-1112	1455	9	(	(	PUNCT
m-1112	1455	10	b-4	b-4	NOUN
m-1112	1455	11	)	)	PUNCT
m-1112	1455	12	for	for	ADP
m-1112	1455	13	steadystate	steadystate	ADJ
m-1112	1455	14	solution	solution	NOUN
m-1112	1455	15	.	.	PUNCT
m-1112	1456	1	the	the	DET
m-1112	1456	2	resonance	resonance	NOUN
m-1112	1456	3	frequency	frequency	NOUN
m-1112	1456	4	𝐟	𝐟	PRON
m-1112	1456	5	𝟏	𝟏	X
m-1112	1456	6	=	=	SYM
m-1112	1456	7	w1	w1	NOUN
m-1112	1456	8	2π	2π	NOUN
m-1112	1456	9	.	.	PUNCT
m-1112	1457	1	=	=	NOUN
m-1112	1457	2	1	1	NUM
m-1112	1457	3	2π	2π	NOUN
m-1112	1457	4	.	.	PUNCT
m-1112	1458	1	√	√	VERB
m-1112	1458	2	𝑘	𝑘	PRON
m-1112	1458	3	𝑚	𝑚	NOUN
m-1112	1458	4	−	−	PROPN
m-1112	1458	5	𝑥²1	𝑥²1	NOUN
m-1112	1458	6	2	2	NUM
m-1112	1458	7	m²	m²	NOUN
m-1112	1458	8	.	.	PUNCT
m-1112	1458	9	,	,	PUNCT
m-1112	1458	10	from	from	ADP
m-1112	1458	11	(	(	PUNCT
m-1112	1458	12	c-3	c-3	PROPN
m-1112	1458	13	)	)	PUNCT
m-1112	1458	14	,	,	PUNCT
m-1112	1458	15	a	a	PRON
m-1112	1458	16	)	)	PUNCT
m-1112	1458	17	.	.	PUNCT
m-1112	1459	1	choosing	choose	VERB
m-1112	1459	2	the	the	DET
m-1112	1459	3	damping	damp	VERB
m-1112	1459	4	factor	factor	NOUN
m-1112	1459	5	-	-	PUNCT
m-1112	1459	6	values	value	NOUN
m-1112	1459	7	ζ	ζ	NOUN
m-1112	1459	8	and	and	CCONJ
m-1112	1459	9	the	the	DET
m-1112	1459	10	eccentric	eccentric	ADJ
m-1112	1459	11	weight	weight	NOUN
m-1112	1459	12	exciter	exciter	NOUN
m-1112	1459	13	e	e	NOUN
m-1112	1459	14	,	,	PUNCT
m-1112	1459	15	is	be	AUX
m-1112	1459	16	possible	possible	ADJ
m-1112	1459	17	to	to	PART
m-1112	1459	18	define	define	VERB
m-1112	1459	19	the	the	DET
m-1112	1459	20	resonant	resonant	ADJ
m-1112	1459	21	amplitude	amplitude	NOUN
m-1112	1459	22	x	x	PUNCT
m-1112	1459	23	=	=	SYM
m-1112	1459	24	1	1	NUM
m-1112	1459	25	2	2	NUM
m-1112	1459	26	ζ	ζ	NOUN
m-1112	1459	27	.	.	PUNCT
m-1112	1460	1	[	[	PUNCT
m-1112	1460	2	m	m	X
m-1112	1460	3	e	e	NOUN
m-1112	1460	4	m	m	NOUN
m-1112	1460	5	]	]	PUNCT
m-1112	1460	6	,	,	PUNCT
m-1112	1460	7	and	and	CCONJ
m-1112	1460	8	by	by	ADP
m-1112	1460	9	altering	alter	VERB
m-1112	1460	10	the	the	DET
m-1112	1460	11	eccentric	eccentric	ADJ
m-1112	1460	12	mass	mass	NOUN
m-1112	1460	13	-	-	PUNCT
m-1112	1460	14	m	m	VERB
m-1112	1460	15	the	the	DET
m-1112	1460	16	prober	prober	NOUN
m-1112	1460	17	x	x	PUNCT
m-1112	1461	1	=	=	PUNCT
m-1112	1461	2	m	m	VERB
m-1112	1461	3	e	e	NOUN
m-1112	1461	4	m	m	NOUN
m-1112	1461	5	.	.	PUNCT
m-1112	1462	1	ijo	ijo	PROPN
m-1112	1462	2	international	international	PROPN
m-1112	1462	3	journal	journal	PROPN
m-1112	1462	4	of	of	ADP
m-1112	1462	5	mathematics	mathematics	PROPN
m-1112	1462	6	(	(	PUNCT
m-1112	1462	7	issn	issn	PROPN
m-1112	1462	8	:	:	PUNCT
m-1112	1462	9	2992	2992	NUM
m-1112	1462	10	-	-	SYM
m-1112	1462	11	4421	4421	NUM
m-1112	1462	12	)	)	PUNCT
m-1112	1462	13	volume	volume	NOUN
m-1112	1462	14	08	08	NUM
m-1112	1463	1	|	|	ADV
m-1112	1463	2	issue	issue	NOUN
m-1112	1463	3	08	08	NUM
m-1112	1464	1	|	|	ADV
m-1112	1464	2	august	august	PROPN
m-1112	1464	3	2025	2025	NUM
m-1112	1464	4	|	|	ADV
m-1112	1464	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1464	6	ijo	ijo	PROPN
m-1112	1464	7	journals	journal	NOUN
m-1112	1464	8	52	52	NUM
m-1112	1464	9	the	the	DET
m-1112	1464	10	fundamental	fundamental	ADJ
m-1112	1464	11	particles	particle	NOUN
m-1112	1464	12	origination	origination	NOUN
m-1112	1464	13	mechanism	mechanism	NOUN
m-1112	1464	14	in	in	ADP
m-1112	1464	15	mfmf	mfmf	PROPN
m-1112	1464	16	pns	pns	PROPN
m-1112	1464	17	caves	cave	NOUN
m-1112	1464	18	.	.	PUNCT
m-1112	1465	1	b	b	X
m-1112	1465	2	)	)	PUNCT
m-1112	1465	3	.	.	PUNCT
m-1112	1466	1	above	above	ADP
m-1112	1466	2	un	un	PROPN
m-1112	1466	3	balance	balance	NOUN
m-1112	1466	4	happens	happen	VERB
m-1112	1466	5	in	in	ADP
m-1112	1466	6	rotating	rotate	VERB
m-1112	1466	7	machines	machine	NOUN
m-1112	1466	8	or	or	CCONJ
m-1112	1466	9	wheels	wheel	NOUN
m-1112	1466	10	,	,	PUNCT
m-1112	1466	11	which	which	PRON
m-1112	1466	12	can	can	AUX
m-1112	1466	13	be	be	AUX
m-1112	1466	14	repaired	repair	VERB
m-1112	1466	15	by	by	ADP
m-1112	1466	16	adding	add	VERB
m-1112	1466	17	or	or	CCONJ
m-1112	1466	18	detaching	detach	VERB
m-1112	1466	19	±	±	NOUN
m-1112	1466	20	masses	masse	NOUN
m-1112	1466	21	,	,	PUNCT
m-1112	1466	22	or	or	CCONJ
m-1112	1466	23	the	the	DET
m-1112	1466	24	opposite	opposite	ADJ
m-1112	1466	25	∓	∓	PROPN
m-1112	1466	26	detaching	detaching	NOUN
m-1112	1466	27	–	–	PUNCT
m-1112	1466	28	adding	add	VERB
m-1112	1466	29	masses	masse	NOUN
m-1112	1466	30	.	.	PUNCT
m-1112	1467	1	1	1	NUM
m-1112	1467	2	)	)	PUNCT
m-1112	1467	3	.	.	PUNCT
m-1112	1468	1	for	for	ADP
m-1112	1468	2	small	small	ADJ
m-1112	1468	3	values	value	NOUN
m-1112	1468	4	of	of	ADP
m-1112	1468	5	,	,	PUNCT
m-1112	1468	6	𝐰	𝐰	PROPN
m-1112	1468	7	wn	wn	AUX
m-1112	1468	8	<	<	X
m-1112	1468	9	<	<	X
m-1112	1468	10	1	1	NUM
m-1112	1468	11	,	,	PUNCT
m-1112	1468	12	both	both	CCONJ
m-1112	1468	13	the	the	DET
m-1112	1468	14	inertia	inertia	NOUN
m-1112	1468	15	m.w².x	m.w².x	PROPN
m-1112	1468	16	,	,	PUNCT
m-1112	1468	17	and	and	CCONJ
m-1112	1468	18	damping	damp	VERB
m-1112	1468	19	forces	force	NOUN
m-1112	1468	20	c	c	NOUN
m-1112	1468	21	w	w	NOUN
m-1112	1468	22	x	x	PUNCT
m-1112	1468	23	,	,	PUNCT
m-1112	1468	24	are	be	AUX
m-1112	1468	25	small	small	ADJ
m-1112	1468	26	which	which	PRON
m-1112	1468	27	results	result	VERB
m-1112	1468	28	in	in	ADP
m-1112	1468	29	a	a	DET
m-1112	1468	30	small	small	ADJ
m-1112	1468	31	phase	phase	NOUN
m-1112	1468	32	angle	angle	NOUN
m-1112	1468	33	φ	φ	PROPN
m-1112	1468	34	.	.	PUNCT
m-1112	1469	1	the	the	DET
m-1112	1469	2	magnitude	magnitude	NOUN
m-1112	1469	3	of	of	ADP
m-1112	1469	4	the	the	DET
m-1112	1469	5	impressed	impressed	ADJ
m-1112	1469	6	force	force	NOUN
m-1112	1469	7	f0	f0	PROPN
m-1112	1469	8	,	,	PUNCT
m-1112	1469	9	is	be	AUX
m-1112	1469	10	then	then	ADV
m-1112	1469	11	nearly	nearly	ADV
m-1112	1469	12	equal	equal	ADJ
m-1112	1469	13	to	to	ADP
m-1112	1469	14	the	the	DET
m-1112	1469	15	spring	spring	NOUN
m-1112	1469	16	-	-	PUNCT
m-1112	1469	17	force	force	NOUN
m-1112	1469	18	,	,	PUNCT
m-1112	1469	19	k	k	PROPN
m-1112	1469	20	x	x	X
m-1112	1469	21	,	,	PUNCT
m-1112	1469	22	as	as	ADP
m-1112	1469	23	in	in	ADP
m-1112	1469	24	fig.12.b-2	fig.12.b-2	NOUN
m-1112	1469	25	2	2	NUM
m-1112	1469	26	)	)	PUNCT
m-1112	1469	27	.	.	PUNCT
m-1112	1470	1	for	for	ADP
m-1112	1470	2	value	value	NOUN
m-1112	1470	3	,	,	PUNCT
m-1112	1470	4	𝐰	𝐰	PROPN
m-1112	1470	5	wn	wn	X
m-1112	1470	6	=	=	SYM
m-1112	1470	7	1	1	NUM
m-1112	1470	8	,	,	PUNCT
m-1112	1470	9	the	the	DET
m-1112	1470	10	phase	phase	NOUN
m-1112	1470	11	angle	angle	NOUN
m-1112	1470	12	φ	φ	PROPN
m-1112	1470	13	=	=	PROPN
m-1112	1470	14	90	90	NUM
m-1112	1470	15	°	°	NOUN
m-1112	1470	16	,	,	PUNCT
m-1112	1470	17	as	as	ADP
m-1112	1470	18	in	in	ADP
m-1112	1470	19	diagram	diagram	NOUN
m-1112	1470	20	.the	.the	PRON
m-1112	1470	21	inertia	inertia	PROPN
m-1112	1470	22	force	force	PROPN
m-1112	1470	23	mw²x	mw²x	PROPN
m-1112	1470	24	,	,	PUNCT
m-1112	1470	25	is	be	AUX
m-1112	1470	26	larger	large	ADJ
m-1112	1470	27	and	and	CCONJ
m-1112	1470	28	balanced	balance	VERB
m-1112	1470	29	by	by	ADP
m-1112	1470	30	the	the	DET
m-1112	1470	31	spring	spring	NOUN
m-1112	1470	32	force	force	NOUN
m-1112	1470	33	k	k	PROPN
m-1112	1470	34	x	x	X
m-1112	1470	35	.	.	PUNCT
m-1112	1471	1	whereas	whereas	SCONJ
m-1112	1471	2	the	the	DET
m-1112	1471	3	impressed	impressed	ADJ
m-1112	1471	4	force	force	NOUN
m-1112	1471	5	f0	f0	PROPN
m-1112	1471	6	is	be	AUX
m-1112	1471	7	>	>	X
m-1112	1471	8	>	>	X
m-1112	1471	9	the	the	DET
m-1112	1471	10	damping	damp	VERB
m-1112	1471	11	force	force	NOUN
m-1112	1471	12	.	.	PUNCT
m-1112	1472	1	the	the	DET
m-1112	1472	2	amplitude	amplitude	NOUN
m-1112	1472	3	at	at	ADP
m-1112	1472	4	resonance	resonance	NOUN
m-1112	1472	5	is	be	AUX
m-1112	1472	6	x	x	X
m-1112	1472	7	=	=	SYM
m-1112	1472	8	f	f	PROPN
m-1112	1472	9	0	0	PUNCT
m-1112	1472	10	𝒄.wn	𝒄.wn	PROPN
m-1112	1472	11	=	=	SYM
m-1112	1472	12	f	f	PROPN
m-1112	1472	13	0	0	NUM
m-1112	1472	14	𝟐𝛇	𝟐𝛇	PROPN
m-1112	1472	15	𝐤	𝐤	NOUN
m-1112	1472	16	,	,	PUNCT
m-1112	1472	17	or	or	CCONJ
m-1112	1472	18	from	from	ADP
m-1112	1472	19	diagram	diagram	NOUN
m-1112	1472	20	.	.	PUNCT
m-1112	1473	1	3	3	NUM
m-1112	1473	2	)	)	PUNCT
m-1112	1473	3	.	.	PUNCT
m-1112	1474	1	for	for	ADP
m-1112	1474	2	large	large	ADJ
m-1112	1474	3	values	value	NOUN
m-1112	1474	4	,	,	PUNCT
m-1112	1474	5	𝐰	𝐰	PROPN
m-1112	1474	6	wn	wn	INTJ
m-1112	1474	7	>	>	X
m-1112	1474	8	>	>	X
m-1112	1474	9	1	1	NUM
m-1112	1474	10	,	,	PUNCT
m-1112	1474	11	the	the	DET
m-1112	1474	12	phase	phase	NOUN
m-1112	1474	13	angle	angle	NOUN
m-1112	1474	14	approaches	approach	VERB
m-1112	1474	15	φ	φ	NOUN
m-1112	1474	16	=	=	PROPN
m-1112	1474	17	180	180	NUM
m-1112	1474	18	°	°	NOUN
m-1112	1474	19	,	,	PUNCT
m-1112	1474	20	and	and	CCONJ
m-1112	1474	21	the	the	DET
m-1112	1474	22	impressed	impressed	ADJ
m-1112	1474	23	force	force	NOUN
m-1112	1474	24	f0	f0	PROPN
m-1112	1474	25	,	,	PUNCT
m-1112	1474	26	is	be	AUX
m-1112	1474	27	expended	expend	VERB
m-1112	1474	28	almost	almost	ADV
m-1112	1474	29	in	in	ADP
m-1112	1474	30	overcoming	overcome	VERB
m-1112	1474	31	the	the	DET
m-1112	1474	32	large	large	ADJ
m-1112	1474	33	inertia	inertia	NOUN
m-1112	1474	34	force	force	NOUN
m-1112	1474	35	,	,	PUNCT
m-1112	1474	36	mw²x	mw²x	PROPN
m-1112	1474	37	.	.	PUNCT
m-1112	1475	1	a.	a.	NOUN
m-1112	1476	1	the	the	DET
m-1112	1476	2	natural	natural	ADJ
m-1112	1476	3	analogous	analogous	NOUN
m-1112	1476	4	of	of	ADP
m-1112	1476	5	the	the	DET
m-1112	1476	6	energy	energy	NOUN
m-1112	1476	7	motion	motion	NOUN
m-1112	1476	8	through	through	ADP
m-1112	1476	9	the	the	DET
m-1112	1476	10	paths	path	NOUN
m-1112	1476	11	.	.	PUNCT
m-1112	1477	1	the	the	DET
m-1112	1477	2	propagation	propagation	NOUN
m-1112	1477	3	path	path	NOUN
m-1112	1477	4	of	of	ADP
m-1112	1477	5	vibrations	vibration	NOUN
m-1112	1477	6	&	&	CCONJ
m-1112	1477	7	the	the	DET
m-1112	1477	8	vibration	vibration	NOUN
m-1112	1477	9	-	-	PUNCT
m-1112	1477	10	absorber	absorber	NOUN
m-1112	1477	11	.	.	PUNCT
m-1112	1478	1	figure	figure	NOUN
m-1112	1478	2	–	–	PUNCT
m-1112	1478	3	12c	12c	NUM
m-1112	1478	4	the	the	DET
m-1112	1478	5	electromagnetic	electromagnetic	ADJ
m-1112	1478	6	-	-	PUNCT
m-1112	1478	7	wave	wave	NOUN
m-1112	1478	8	{	{	PUNCT
m-1112	1478	9	�	�	NOUN
m-1112	1478	10	̅	̅	NOUN
m-1112	1478	11	�	�	PROPN
m-1112	1478	12	.	.	PUNCT
m-1112	1479	1	fn̅	fn̅	PROPN
m-1112	1479	2	+	+	NUM
m-1112	1479	3	�	�	PROPN
m-1112	1479	4	̅	̅	NOUN
m-1112	1479	5	�	�	NOUN
m-1112	1479	6	.𝐟𝐧	.𝐟𝐧	PUNCT
m-1112	1479	7	}	}	PUNCT
m-1112	1479	8	into	into	ADP
m-1112	1479	9	the	the	DET
m-1112	1479	10	atoms	atom	NOUN
m-1112	1479	11	-	-	PUNCT
m-1112	1479	12	bracket	bracket	NOUN
m-1112	1479	13	-	-	PUNCT
m-1112	1479	14	axes	axis	NOUN
m-1112	1479	15	-	-	PUNCT
m-1112	1479	16	hook	hook	NOUN
m-1112	1479	17	.	.	PUNCT
m-1112	1480	1	the	the	DET
m-1112	1480	2	process	process	NOUN
m-1112	1480	3	of	of	ADP
m-1112	1480	4	the	the	DET
m-1112	1480	5	photo	photo	NOUN
m-1112	1480	6	elastic	elastic	ADJ
m-1112	1480	7	fringe	fringe	NOUN
m-1112	1480	8	–	–	PUNCT
m-1112	1480	9	pattern	pattern	NOUN
m-1112	1480	10	[	[	X
m-1112	1480	11	96a	96a	NOUN
m-1112	1480	12	]	]	X
m-1112	1480	13	in-1	in-1	NOUN
m-1112	1480	14	the	the	DET
m-1112	1480	15	unloaded	unload	VERB
m-1112	1480	16	beam	beam	NOUN
m-1112	1480	17	(	(	PUNCT
m-1112	1480	18	f	f	NOUN
m-1112	1480	19	=	=	SYM
m-1112	1480	20	0	0	NUM
m-1112	1480	21	)	)	PUNCT
m-1112	1480	22	is	be	AUX
m-1112	1480	23	the	the	DET
m-1112	1480	24	length	length	NOUN
m-1112	1480	25	ab̅̅	ab̅̅	PROPN
m-1112	1480	26	̅̅	̅̅	PROPN
m-1112	1480	27	.	.	PUNCT
m-1112	1481	1	in-2	in-2	AUX
m-1112	1481	2	the	the	DET
m-1112	1481	3	loaded	load	VERB
m-1112	1481	4	beam	beam	NOUN
m-1112	1481	5	(	(	PUNCT
m-1112	1481	6	f	f	PROPN
m-1112	1481	7	=	=	SYM
m-1112	1481	8	f	f	PROPN
m-1112	1481	9	)	)	PUNCT
m-1112	1481	10	is	be	AUX
m-1112	1481	11	the	the	DET
m-1112	1481	12	deflection	deflection	NOUN
m-1112	1481	13	-	-	PUNCT
m-1112	1481	14	curve	curve	NOUN
m-1112	1481	15	ab⏟	ab⏟	NOUN
m-1112	1481	16	dh	dh	PROPN
m-1112	1481	17	,	,	PUNCT
m-1112	1481	18	the	the	DET
m-1112	1481	19	strain	strain	NOUN
m-1112	1481	20	,	,	PUNCT
m-1112	1481	21	where	where	SCONJ
m-1112	1481	22	exist	exist	VERB
m-1112	1481	23	,	,	PUNCT
m-1112	1481	24	a	a	PRON
m-1112	1481	25	..	..	PUNCT
m-1112	1481	26	the	the	DET
m-1112	1481	27	shape	shape	NOUN
m-1112	1481	28	of	of	ADP
m-1112	1481	29	the	the	DET
m-1112	1481	30	beam	beam	NOUN
m-1112	1481	31	is	be	AUX
m-1112	1481	32	the	the	DET
m-1112	1481	33	space	space	NOUN
m-1112	1481	34	,	,	PUNCT
m-1112	1481	35	the	the	DET
m-1112	1481	36	strain	strain	NOUN
m-1112	1481	37	,	,	PUNCT
m-1112	1481	38	the	the	DET
m-1112	1481	39	figure	figure	NOUN
m-1112	1481	40	of	of	ADP
m-1112	1481	41	the	the	DET
m-1112	1481	42	system	system	NOUN
m-1112	1481	43	,	,	PUNCT
m-1112	1481	44	b	b	X
m-1112	1481	45	..	..	PUNCT
m-1112	1481	46	the	the	DET
m-1112	1481	47	shape	shape	NOUN
m-1112	1481	48	of	of	ADP
m-1112	1481	49	the	the	DET
m-1112	1481	50	line	line	NOUN
m-1112	1481	51	-	-	PUNCT
m-1112	1481	52	stresses	stress	NOUN
m-1112	1481	53	is	be	AUX
m-1112	1481	54	the	the	DET
m-1112	1481	55	figure	figure	NOUN
m-1112	1481	56	-	-	PUNCT
m-1112	1481	57	fringe	fringe	NOUN
m-1112	1481	58	the	the	DET
m-1112	1481	59	path	path	NOUN
m-1112	1481	60	of	of	ADP
m-1112	1481	61	energy	energy	NOUN
m-1112	1481	62	.	.	PUNCT
m-1112	1482	1	c	c	X
m-1112	1482	2	..	..	PUNCT
m-1112	1482	3	the	the	DET
m-1112	1482	4	colure	colure	NOUN
m-1112	1482	5	of	of	ADP
m-1112	1482	6	the	the	DET
m-1112	1482	7	figure	figure	NOUN
m-1112	1482	8	-	-	PUNCT
m-1112	1482	9	fringe	fringe	NOUN
m-1112	1482	10	.	.	PUNCT
m-1112	1483	1	is	be	AUX
m-1112	1483	2	the	the	DET
m-1112	1483	3	motion	motion	NOUN
m-1112	1483	4	=	=	PUNCT
m-1112	1483	5	the	the	DET
m-1112	1483	6	energy	energy	NOUN
m-1112	1483	7	the	the	DET
m-1112	1483	8	forced	force	VERB
m-1112	1483	9	vector	vector	NOUN
m-1112	1483	10	.	.	PUNCT
m-1112	1484	1	in-3	in-3	ADP
m-1112	1484	2	the	the	DET
m-1112	1484	3	loaded	load	VERB
m-1112	1484	4	and	and	CCONJ
m-1112	1484	5	deflected	deflected	ADJ
m-1112	1484	6	-	-	PUNCT
m-1112	1484	7	beam	beam	NOUN
m-1112	1484	8	are	be	AUX
m-1112	1484	9	the	the	DET
m-1112	1484	10	spaces	space	NOUN
m-1112	1484	11	=	=	PRON
m-1112	1484	12	the	the	DET
m-1112	1484	13	figures	figure	NOUN
m-1112	1484	14	of	of	ADP
m-1112	1484	15	system	system	NOUN
m-1112	1484	16	.	.	PUNCT
m-1112	1485	1	the	the	DET
m-1112	1485	2	loaded	loaded	ADJ
m-1112	1485	3	and	and	CCONJ
m-1112	1485	4	deflected	deflected	ADJ
m-1112	1485	5	-	-	PUNCT
m-1112	1485	6	beam	beam	NOUN
m-1112	1485	7	strain	strain	NOUN
m-1112	1485	8	-	-	PUNCT
m-1112	1485	9	lines	line	NOUN
m-1112	1485	10	-	-	PUNCT
m-1112	1485	11	fringes	fringe	NOUN
m-1112	1485	12	,	,	PUNCT
m-1112	1485	13	are	be	AUX
m-1112	1485	14	the	the	DET
m-1112	1485	15	path	path	NOUN
m-1112	1485	16	of	of	ADP
m-1112	1485	17	motion	motion	NOUN
m-1112	1485	18	,	,	PUNCT
m-1112	1485	19	the	the	DET
m-1112	1485	20	loaded	load	VERB
m-1112	1485	21	and	and	CCONJ
m-1112	1485	22	deflected	deflected	ADJ
m-1112	1485	23	-	-	PUNCT
m-1112	1485	24	beam	beam	NOUN
m-1112	1485	25	colure	colure	NOUN
m-1112	1485	26	fringes	fringe	NOUN
m-1112	1485	27	,	,	PUNCT
m-1112	1485	28	are	be	AUX
m-1112	1485	29	the	the	DET
m-1112	1485	30	kind	kind	NOUN
m-1112	1485	31	of	of	ADP
m-1112	1485	32	forced	force	VERB
m-1112	1485	33	vector	vector	NOUN
m-1112	1485	34	,	,	PUNCT
m-1112	1485	35	ijo	ijo	PROPN
m-1112	1485	36	international	international	PROPN
m-1112	1485	37	journal	journal	PROPN
m-1112	1485	38	of	of	ADP
m-1112	1485	39	mathematics	mathematics	PROPN
m-1112	1485	40	(	(	PUNCT
m-1112	1485	41	issn	issn	PROPN
m-1112	1485	42	:	:	PUNCT
m-1112	1485	43	2992	2992	NUM
m-1112	1485	44	-	-	SYM
m-1112	1485	45	4421	4421	NUM
m-1112	1485	46	)	)	PUNCT
m-1112	1486	1	volume	volume	NOUN
m-1112	1486	2	08	08	NUM
m-1112	1487	1	|	|	ADV
m-1112	1487	2	issue	issue	NOUN
m-1112	1487	3	08	08	NUM
m-1112	1488	1	|	|	ADV
m-1112	1488	2	august	august	PROPN
m-1112	1488	3	2025	2025	NUM
m-1112	1488	4	|	|	ADV
m-1112	1488	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1488	6	ijo	ijo	PROPN
m-1112	1488	7	journals	journal	NOUN
m-1112	1488	8	53	53	NUM
m-1112	1488	9	the	the	DET
m-1112	1488	10	fundamental	fundamental	ADJ
m-1112	1488	11	particles	particle	NOUN
m-1112	1488	12	origination	origination	NOUN
m-1112	1488	13	mechanism	mechanism	NOUN
m-1112	1488	14	in	in	ADP
m-1112	1488	15	mfmf	mfmf	PROPN
m-1112	1488	16	pns	pns	PROPN
m-1112	1488	17	caves	cave	NOUN
m-1112	1488	18	.	.	PUNCT
m-1112	1489	1	the	the	DET
m-1112	1489	2	complex	complex	ADJ
m-1112	1489	3	force	force	NOUN
m-1112	1489	4	–	–	PUNCT
m-1112	1489	5	vector	vector	NOUN
m-1112	1489	6	harmonic	harmonic	ADJ
m-1112	1489	7	vibration	vibration	NOUN
m-1112	1489	8	&	&	CCONJ
m-1112	1489	9	the	the	DET
m-1112	1489	10	vibration	vibration	NOUN
m-1112	1489	11	-	-	PUNCT
m-1112	1489	12	absorber	absorber	NOUN
m-1112	1489	13	.	.	PUNCT
m-1112	1490	1	figure	figure	VERB
m-1112	1490	2	–	–	PUNCT
m-1112	1490	3	12dthe	12dthe	DET
m-1112	1490	4	complex	complex	ADJ
m-1112	1490	5	-force	-force	NOUN
m-1112	1490	6	-vector	-vector	NOUN
m-1112	1490	7	is	be	AUX
m-1112	1490	8	𝐅	𝐅	PROPN
m-1112	1490	9	𝟎	𝟎	NUM
m-1112	1490	10	.	.	PUNCT
m-1112	1491	1	[	[	PUNCT
m-1112	1491	2	cos(w	cos(w	PROPN
m-1112	1491	3	t	t	PROPN
m-1112	1491	4	)	)	PUNCT
m-1112	1492	1	+	+	CCONJ
m-1112	1492	2	sin(w	sin(w	PROPN
m-1112	1492	3	t	t	PROPN
m-1112	1492	4	)	)	PUNCT
m-1112	1492	5	]	]	PUNCT
m-1112	1493	1	=	=	PUNCT
m-1112	1493	2	𝐅	𝐅	PROPN
m-1112	1493	3	𝟎	𝟎	NUM
m-1112	1493	4	.e	.e	PUNCT
m-1112	1494	1	i.[w	i.[w	PROPN
m-1112	1494	2	t	t	PROPN
m-1112	1494	3	]	]	PUNCT
m-1112	1494	4	.	.	PUNCT
m-1112	1495	1	in-1	in-1	VERB
m-1112	1495	2	the	the	DET
m-1112	1495	3	terms	term	NOUN
m-1112	1495	4	=	=	PUNCT
m-1112	1495	5	(	(	PUNCT
m-1112	1495	6	m	m	PROPN
m-1112	1495	7	ẍ	ẍ	X
m-1112	1495	8	,	,	PUNCT
m-1112	1495	9	cẋ	cẋ	PUNCT
m-1112	1495	10	,	,	PUNCT
m-1112	1495	11	k	k	PROPN
m-1112	1495	12	x	x	PROPN
m-1112	1495	13	)	)	PUNCT
m-1112	1495	14	,	,	PUNCT
m-1112	1495	15	of	of	ADP
m-1112	1495	16	vector	vector	NOUN
m-1112	1495	17	force	force	NOUN
m-1112	1495	18	polygon	polygon	NOUN
m-1112	1495	19	are	be	AUX
m-1112	1495	20	perpendicular	perpendicular	ADJ
m-1112	1495	21	to	to	ADP
m-1112	1495	22	y	y	PROPN
m-1112	1495	23	-	-	PUNCT
m-1112	1495	24	y	y	PROPN
m-1112	1495	25	axis	axis	NOUN
m-1112	1495	26	.	.	PUNCT
m-1112	1496	1	in	in	ADP
m-1112	1496	2	case	case	NOUN
m-1112	1496	3	of	of	ADP
m-1112	1496	4	complex	complex	ADJ
m-1112	1496	5	-force	-force	ADJ
m-1112	1496	6	-vector	-vector	NOUN
m-1112	1496	7	the	the	DET
m-1112	1496	8	polygon	polygon	NOUN
m-1112	1496	9	becomes	become	VERB
m-1112	1496	10	an	an	DET
m-1112	1496	11	absorber	absorber	NOUN
m-1112	1496	12	which	which	PRON
m-1112	1496	13	reduces	reduce	VERB
m-1112	1496	14	the	the	DET
m-1112	1496	15	motion	motion	NOUN
m-1112	1496	16	from	from	ADP
m-1112	1496	17	kinetic	kinetic	ADJ
m-1112	1496	18	energy	energy	NOUN
m-1112	1496	19	to	to	ADP
m-1112	1496	20	potential	potential	ADJ
m-1112	1496	21	energy	energy	NOUN
m-1112	1496	22	(	(	PUNCT
m-1112	1496	23	a	a	DET
m-1112	1496	24	magnetic	magnetic	ADJ
m-1112	1496	25	field	field	NOUN
m-1112	1496	26	)	)	PUNCT
m-1112	1496	27	.	.	PUNCT
m-1112	1497	1	in-2	in-2	PRON
m-1112	1497	2	the	the	DET
m-1112	1497	3	2	2	NUM
m-1112	1497	4	-	-	PUNCT
m-1112	1497	5	dof	dof	NOUN
m-1112	1497	6	system	system	NOUN
m-1112	1497	7	with	with	ADP
m-1112	1497	8	vector	vector	NOUN
m-1112	1497	9	force	force	NOUN
m-1112	1497	10	such	such	ADJ
m-1112	1497	11	that	that	PRON
m-1112	1497	12	,	,	PUNCT
m-1112	1497	13	w	w	PROPN
m-1112	1497	14	²11	²11	PROPN
m-1112	1497	15	=	=	SYM
m-1112	1497	16	k	k	PROPN
m-1112	1497	17	1	1	NUM
m-1112	1497	18	m1	m1	PROPN
m-1112	1497	19	,	,	PUNCT
m-1112	1497	20	w	w	PROPN
m-1112	1497	21	²22	²22	NUM
m-1112	1497	22	=	=	SYM
m-1112	1497	23	k	k	PROPN
m-1112	1497	24	2	2	NUM
m-1112	1497	25	m2	m2	PROPN
m-1112	1497	26	,	,	PUNCT
m-1112	1497	27	acts	act	VERB
m-1112	1497	28	as	as	ADP
m-1112	1497	29	an	an	DET
m-1112	1497	30	vibrator	vibrator	NOUN
m-1112	1497	31	absorber	absorber	NOUN
m-1112	1497	32	,	,	PUNCT
m-1112	1497	33	and	and	CCONJ
m-1112	1497	34	reduces	reduce	VERB
m-1112	1497	35	the	the	DET
m-1112	1497	36	motion	motion	NOUN
m-1112	1497	37	of	of	ADP
m-1112	1497	38	the	the	DET
m-1112	1497	39	mass	mass	NOUN
m-1112	1497	40	m	m	NOUN
m-1112	1497	41	1	1	NUM
m-1112	1497	42	to	to	ADP
m-1112	1497	43	zero	zero	NUM
m-1112	1497	44	.the	.the	PUNCT
m-1112	1497	45	two	two	NUM
m-1112	1497	46	natural	natural	ADJ
m-1112	1497	47	frequencies	frequency	NOUN
m-1112	1497	48	,	,	PUNCT
m-1112	1497	49	f	f	PROPN
m-1112	1497	50	1	1	NUM
m-1112	1497	51	,	,	PUNCT
m-1112	1497	52	f	f	PROPN
m-1112	1497	53	2	2	NUM
m-1112	1497	54	,	,	PUNCT
m-1112	1497	55	are	be	AUX
m-1112	1497	56	perpendicular	perpendicular	ADJ
m-1112	1497	57	[	[	PUNCT
m-1112	1497	58	⏊	⏊	X
m-1112	1497	59	]	]	PUNCT
m-1112	1497	60	each	each	DET
m-1112	1497	61	other	other	ADJ
m-1112	1497	62	as	as	ADP
m-1112	1497	63	the	the	DET
m-1112	1497	64	diagrams	diagram	NOUN
m-1112	1497	65	.	.	PUNCT
m-1112	1498	1	this	this	PRON
m-1112	1498	2	happens	happen	VERB
m-1112	1498	3	for	for	ADP
m-1112	1498	4	every	every	DET
m-1112	1498	5	action	action	NOUN
m-1112	1498	6	on	on	ADP
m-1112	1498	7	the	the	DET
m-1112	1498	8	8	8	NUM
m-1112	1498	9	.	.	PUNCT
m-1112	1499	1	[	[	PUNCT
m-1112	1499	2	a	a	PRON
m-1112	1499	3	,	,	PUNCT
m-1112	1499	4	b	b	NOUN
m-1112	1499	5	,	,	PUNCT
m-1112	1499	6	c	c	NOUN
m-1112	1499	7	,	,	PUNCT
m-1112	1499	8	d	d	X
m-1112	1499	9	]	]	X
m-1112	1499	10	physical	physical	ADJ
m-1112	1499	11	mechanisms	mechanism	NOUN
m-1112	1499	12	.	.	PUNCT
m-1112	1500	1	in-3	in-3	SCONJ
m-1112	1500	2	the	the	DET
m-1112	1500	3	{	{	PUNCT
m-1112	1500	4	stpl	stpl	PROPN
m-1112	1500	5	}	}	PUNCT
m-1112	1500	6	six	six	NUM
m-1112	1500	7	triple	triple	ADJ
m-1112	1500	8	points	point	NOUN
m-1112	1500	9	line	line	NOUN
m-1112	1500	10	mechanism	mechanism	NOUN
m-1112	1500	11	is	be	AUX
m-1112	1500	12	formed	form	VERB
m-1112	1500	13	from	from	ADP
m-1112	1500	14	three	three	NUM
m-1112	1500	15	tangents	tangent	NOUN
m-1112	1500	16	from	from	ADP
m-1112	1500	17	a	a	DET
m-1112	1500	18	,	,	PUNCT
m-1112	1500	19	b	b	NOUN
m-1112	1500	20	,	,	PUNCT
m-1112	1500	21	c	c	PROPN
m-1112	1500	22	spaces	space	NOUN
m-1112	1500	23	on	on	ADP
m-1112	1500	24	2r	2r	NUM
m-1112	1500	25	circle	circle	NOUN
m-1112	1500	26	.	.	PUNCT
m-1112	1501	1	since	since	SCONJ
m-1112	1501	2	pascal	pascal	NOUN
m-1112	1501	3	-	-	PUNCT
m-1112	1501	4	desargues	desargue	NOUN
m-1112	1501	5	lines	line	NOUN
m-1112	1501	6	meet	meet	VERB
m-1112	1501	7	on	on	ADP
m-1112	1501	8	markos	markos	PROPN
m-1112	1501	9	stpl	stpl	PROPN
m-1112	1501	10	mechanism	mechanism	NOUN
m-1112	1501	11	lines	line	NOUN
m-1112	1501	12	,	,	PUNCT
m-1112	1501	13	then	then	ADV
m-1112	1501	14	transfer	transfer	VERB
m-1112	1501	15	the	the	DET
m-1112	1501	16	properties	property	NOUN
m-1112	1501	17	&	&	CCONJ
m-1112	1501	18	information	information	NOUN
m-1112	1501	19	(	(	PUNCT
m-1112	1501	20	f	f	PROPN
m-1112	1501	21	1	1	NUM
m-1112	1501	22	,	,	PUNCT
m-1112	1501	23	f	f	PROPN
m-1112	1501	24	2	2	NUM
m-1112	1501	25	,	,	PUNCT
m-1112	1501	26	,	,	PUNCT
m-1112	1501	27	,	,	PUNCT
m-1112	1501	28	f	f	PROPN
m-1112	1501	29	n	n	ADV
m-1112	1501	30	)	)	PUNCT
m-1112	1501	31	from	from	ADP
m-1112	1501	32	the	the	DET
m-1112	1501	33	complex	complex	ADJ
m-1112	1501	34	-	-	PUNCT
m-1112	1501	35	vector	vector	NOUN
m-1112	1501	36	-	-	PUNCT
m-1112	1501	37	absorber	absorber	NOUN
m-1112	1501	38	=	=	SYM
m-1112	1501	39	𝟐𝐑̅̅	𝟐𝐑̅̅	PROPN
m-1112	1501	40	̅̅	̅̅	PROPN
m-1112	1501	41	,	,	PUNCT
m-1112	1501	42	to	to	ADP
m-1112	1501	43	the	the	DET
m-1112	1501	44	vector	vector	NOUN
m-1112	1501	45	-	-	PUNCT
m-1112	1501	46	force	force	NOUN
m-1112	1501	47	-	-	PUNCT
m-1112	1501	48	polygons	polygon	NOUN
m-1112	1501	49	remarks	remark	NOUN
m-1112	1501	50	:	:	PUNCT
m-1112	1501	51	1	1	X
m-1112	1501	52	..	..	PUNCT
m-1112	1501	53	the	the	DET
m-1112	1501	54	n	n	CCONJ
m-1112	1501	55	-	-	PUNCT
m-1112	1501	56	knots	knot	NOUN
m-1112	1501	57	figures	figure	NOUN
m-1112	1501	58	is	be	AUX
m-1112	1501	59	any	any	DET
m-1112	1501	60	n	n	CCONJ
m-1112	1501	61	-	-	PUNCT
m-1112	1501	62	dof	dof	NOUN
m-1112	1501	63	system	system	NOUN
m-1112	1501	64	,	,	PUNCT
m-1112	1501	65	which	which	DET
m-1112	1501	66	characteristic	characteristic	ADJ
m-1112	1501	67	equation	equation	NOUN
m-1112	1501	68	results	result	VERB
m-1112	1501	69	to	to	ADP
m-1112	1501	70	an	an	DET
m-1112	1501	71	algebraic	algebraic	ADJ
m-1112	1501	72	equation	equation	NOUN
m-1112	1501	73	of	of	ADP
m-1112	1501	74	3	3	NUM
m-1112	1501	75	-	-	PUNCT
m-1112	1501	76	n	n	PRON
m-1112	1501	77	degree	degree	NOUN
m-1112	1501	78	,	,	PUNCT
m-1112	1501	79	with	with	ADP
m-1112	1501	80	main	main	ADJ
m-1112	1501	81	equation	equation	NOUN
m-1112	1501	82	of	of	ADP
m-1112	1501	83	motion	motion	NOUN
m-1112	1501	84	[	[	PUNCT
m-1112	1501	85	λ.m	λ.m	X
m-1112	1501	86	+	+	X
m-1112	1501	87	k	k	X
m-1112	1501	88	]	]	X
m-1112	1501	89	x	x	PUNCT
m-1112	1501	90	=	=	SYM
m-1112	1501	91	0	0	NUM
m-1112	1501	92	2	2	NUM
m-1112	1501	93	..	..	PUNCT
m-1112	1501	94	the	the	DET
m-1112	1501	95	n	n	CCONJ
m-1112	1501	96	-	-	PUNCT
m-1112	1501	97	knots	knot	NOUN
m-1112	1501	98	figures	figure	NOUN
m-1112	1501	99	exist	exist	VERB
m-1112	1501	100	in	in	ADP
m-1112	1501	101	figures	figure	NOUN
m-1112	1501	102	where	where	SCONJ
m-1112	1501	103	the	the	DET
m-1112	1501	104	vector	vector	NOUN
m-1112	1501	105	-force	-force	NOUN
m-1112	1501	106	polygons	polygon	NOUN
m-1112	1501	107	have	have	VERB
m-1112	1501	108	the	the	DET
m-1112	1501	109	same	same	ADJ
m-1112	1501	110	number	number	NOUN
m-1112	1501	111	n	n	NOUN
m-1112	1501	112	,	,	PUNCT
m-1112	1501	113	as	as	SCONJ
m-1112	1501	114	the	the	DET
m-1112	1501	115	in	in	ADP
m-1112	1501	116	figures	figure	NOUN
m-1112	1501	117	.	.	PUNCT
m-1112	1502	1	in	in	ADP
m-1112	1502	2	(	(	PUNCT
m-1112	1502	3	3	3	X
m-1112	1502	4	)	)	PUNCT
m-1112	1502	5	the	the	DET
m-1112	1502	6	circularlycharged	circularlycharged	ADJ
m-1112	1502	7	breakages	breakage	NOUN
m-1112	1502	8	are	be	AUX
m-1112	1502	9	the	the	DET
m-1112	1502	10	three3	three3	NOUN
m-1112	1502	11	elements	element	NOUN
m-1112	1502	12	[	[	X
m-1112	1502	13	σ	σ	X
m-1112	1502	14	=	=	SYM
m-1112	1502	15	n	n	PROPN
m-1112	1502	16	.	.	PUNCT
m-1112	1503	1	h	h	X
m-1112	1503	2	]	]	X
m-1112	1503	3			NOUN
m-1112	1504	1	[	[	X
m-1112	1504	2	s²	s²	NOUN
m-1112	1504	3	=	=	SYM
m-1112	1504	4	⊕	⊕	PROPN
m-1112	1504	5	,	,	PUNCT
m-1112	1504	6	2s²=	2s²=	NUM
m-1112	1504	7	,	,	PUNCT
m-1112	1504	8	s²	s²	NOUN
m-1112	1504	9	=	=	SYM
m-1112	1504	10	⊝	⊝	X
m-1112	1504	11	]	]	PUNCT
m-1112	1504	12	which	which	PRON
m-1112	1504	13	formulate	formulate	VERB
m-1112	1504	14	the	the	DET
m-1112	1504	15	3	3	NUM
m-1112	1504	16	-	-	PUNCT
m-1112	1504	17	knots	knot	NOUN
m-1112	1504	18	figures	figure	NOUN
m-1112	1504	19	.	.	PUNCT
m-1112	1505	1	this	this	DET
m-1112	1505	2	{	{	PUNCT
m-1112	1505	3	stpl}-mechanism	stpl}-mechanism	NOUN
m-1112	1505	4	of	of	ADP
m-1112	1505	5	3	3	NUM
m-1112	1505	6	elements	element	NOUN
m-1112	1505	7	(	(	PUNCT
m-1112	1505	8	n=3	n=3	PUNCT
m-1112	1505	9	)	)	PUNCT
m-1112	1505	10	determinates	determinate	VERB
m-1112	1505	11	the	the	DET
m-1112	1505	12	mould	mould	NOUN
m-1112	1505	13	which	which	PRON
m-1112	1505	14	denotes	denote	VERB
m-1112	1505	15	the	the	DET
m-1112	1505	16	number	number	NOUN
m-1112	1505	17	n	n	NOUN
m-1112	1505	18	,	,	PUNCT
m-1112	1505	19	of	of	ADP
m-1112	1505	20	the	the	DET
m-1112	1505	21	spaces	space	NOUN
m-1112	1505	22	for	for	ADP
m-1112	1505	23	elementary	elementary	ADJ
m-1112	1505	24	-	-	PUNCT
m-1112	1505	25	particles	particle	NOUN
m-1112	1505	26	vector	vector	NOUN
m-1112	1505	27	.	.	PUNCT
m-1112	1506	1	3	3	NUM
m-1112	1506	2	..	..	PUNCT
m-1112	1506	3	the	the	DET
m-1112	1506	4	case	case	NOUN
m-1112	1506	5	of	of	ADP
m-1112	1506	6	{	{	PUNCT
m-1112	1506	7	tcic}≡	tcic}≡	PROPN
m-1112	1506	8	[	[	PUNCT
m-1112	1506	9	σ	σ	X
m-1112	1506	10	=	=	SYM
m-1112	1506	11	n	n	PROPN
m-1112	1506	12	.	.	PUNCT
m-1112	1507	1	h	h	NOUN
m-1112	1507	2	]	]	PUNCT
m-1112	1508	1			NOUN
m-1112	1508	2	8	8	NUM
m-1112	1508	3	x	x	SYM
m-1112	1508	4	①	①	PROPN
m-1112	1508	5	which	which	PRON
m-1112	1508	6	is	be	AUX
m-1112	1508	7	the	the	DET
m-1112	1508	8	physical	physical	ADJ
m-1112	1508	9	mechanism	mechanism	NOUN
m-1112	1508	10	,	,	PUNCT
m-1112	1508	11	gives	give	VERB
m-1112	1508	12	the	the	DET
m-1112	1508	13	n	n	NOUN
m-1112	1508	14	-	-	PUNCT
m-1112	1508	15	masses	masse	NOUN
m-1112	1508	16	of	of	ADP
m-1112	1508	17	atom`s	atom`s	PROPN
m-1112	1508	18	&	&	CCONJ
m-1112	1508	19	compounds	compound	NOUN
m-1112	1508	20	determining	determine	VERB
m-1112	1508	21	the	the	DET
m-1112	1508	22	atoms	atom	NOUN
m-1112	1508	23	complex	complex	ADJ
m-1112	1508	24	-	-	PUNCT
m-1112	1508	25	vector	vector	NOUN
m-1112	1508	26	-	-	PUNCT
m-1112	1508	27	response	response	NOUN
m-1112	1508	28	.	.	PUNCT
m-1112	1509	1	ijo	ijo	PROPN
m-1112	1509	2	international	international	PROPN
m-1112	1509	3	journal	journal	PROPN
m-1112	1509	4	of	of	ADP
m-1112	1509	5	mathematics	mathematics	PROPN
m-1112	1509	6	(	(	PUNCT
m-1112	1509	7	issn	issn	PROPN
m-1112	1509	8	:	:	PUNCT
m-1112	1509	9	2992	2992	NUM
m-1112	1509	10	-	-	SYM
m-1112	1509	11	4421	4421	NUM
m-1112	1509	12	)	)	PUNCT
m-1112	1509	13	volume	volume	NOUN
m-1112	1509	14	08	08	NUM
m-1112	1510	1	|	|	ADV
m-1112	1510	2	issue	issue	NOUN
m-1112	1510	3	08	08	NUM
m-1112	1511	1	|	|	ADV
m-1112	1511	2	august	august	PROPN
m-1112	1511	3	2025	2025	NUM
m-1112	1511	4	|	|	ADV
m-1112	1511	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1511	6	ijo	ijo	PROPN
m-1112	1511	7	journals	journal	NOUN
m-1112	1511	8	54	54	NUM
m-1112	1511	9	the	the	DET
m-1112	1511	10	fundamental	fundamental	ADJ
m-1112	1511	11	particles	particle	NOUN
m-1112	1511	12	origination	origination	NOUN
m-1112	1511	13	mechanism	mechanism	NOUN
m-1112	1511	14	in	in	ADP
m-1112	1511	15	mfmf	mfmf	PROPN
m-1112	1511	16	pns	pns	PROPN
m-1112	1511	17	caves	cave	NOUN
m-1112	1511	18	.	.	PUNCT
m-1112	1512	1	b	b	X
m-1112	1512	2	…	…	PUNCT
m-1112	1512	3	general	general	ADJ
m-1112	1512	4	:	:	PUNCT
m-1112	1512	5	1.b	1.b	NUM
m-1112	1512	6	.	.	PUNCT
m-1112	1513	1	the	the	DET
m-1112	1513	2	spaces	space	NOUN
m-1112	1513	3	and	and	CCONJ
m-1112	1513	4	the	the	DET
m-1112	1513	5	energy	energy	NOUN
m-1112	1513	6	states	state	NOUN
m-1112	1513	7	.	.	PUNCT
m-1112	1514	1	1	1	NUM
m-1112	1514	2	…	…	PUNCT
m-1112	1514	3	the	the	DET
m-1112	1514	4	objective	objective	ADJ
m-1112	1514	5	reality	reality	NOUN
m-1112	1514	6	is	be	AUX
m-1112	1514	7	composed	compose	VERB
m-1112	1514	8	of	of	ADP
m-1112	1514	9	two	two	NUM
m-1112	1514	10	elements	element	NOUN
m-1112	1514	11	,	,	PUNCT
m-1112	1514	12	that	that	PRON
m-1112	1514	13	of	of	ADP
m-1112	1514	14	distance	distance	NOUN
m-1112	1514	15	.	.	PUNCT
m-1112	1515	1	the	the	DET
m-1112	1515	2	space	space	NOUN
m-1112	1515	3	ds	ds	NOUN
m-1112	1515	4	,	,	PUNCT
m-1112	1515	5	and	and	CCONJ
m-1112	1515	6	that	that	PRON
m-1112	1515	7	of	of	ADP
m-1112	1515	8	motion	motion	NOUN
m-1112	1515	9	,	,	PUNCT
m-1112	1515	10	or	or	CCONJ
m-1112	1515	11	else	else	ADV
m-1112	1515	12	the	the	DET
m-1112	1515	13	called	call	VERB
m-1112	1515	14	energy	energy	NOUN
m-1112	1515	15	,	,	PUNCT
m-1112	1515	16	and	and	CCONJ
m-1112	1515	17	it	it	PRON
m-1112	1515	18	is	be	AUX
m-1112	1515	19	the	the	DET
m-1112	1515	20	content	content	NOUN
m-1112	1515	21	of	of	ADP
m-1112	1515	22	all	all	DET
m-1112	1515	23	sciences	science	NOUN
m-1112	1516	1	[	[	X
m-1112	1516	2	32	32	NUM
m-1112	1516	3	]	]	SYM
m-1112	1516	4	2	2	NUM
m-1112	1516	5	…	…	PUNCT
m-1112	1516	6	the	the	DET
m-1112	1516	7	euclidean	euclidean	ADJ
m-1112	1516	8	-	-	PUNCT
m-1112	1516	9	geometry	geometry	NOUN
m-1112	1516	10	describes	describe	VERB
m-1112	1516	11	the	the	DET
m-1112	1516	12	space	space	NOUN
m-1112	1516	13	only	only	ADV
m-1112	1516	14	but	but	CCONJ
m-1112	1516	15	not	not	PART
m-1112	1516	16	the	the	DET
m-1112	1516	17	energy	energy	NOUN
m-1112	1516	18	as	as	SCONJ
m-1112	1516	19	is	be	AUX
m-1112	1516	20	motion	motion	NOUN
m-1112	1516	21	[	[	X
m-1112	1516	22	48	48	NUM
m-1112	1516	23	]	]	SYM
m-1112	1516	24	3	3	NUM
m-1112	1516	25	...	...	PUNCT
m-1112	1516	26	the	the	DET
m-1112	1516	27	solution	solution	NOUN
m-1112	1516	28	of	of	ADP
m-1112	1516	29	all	all	DET
m-1112	1516	30	the	the	DET
m-1112	1516	31	unsolved	unsolved	ADJ
m-1112	1516	32	-	-	PUNCT
m-1112	1516	33	ancient	ancient	ADJ
m-1112	1516	34	-	-	PUNCT
m-1112	1516	35	greek	greek	NOUN
m-1112	1516	36	-	-	PUNCT
m-1112	1516	37	problems	problem	NOUN
m-1112	1516	38	[	[	X
m-1112	1516	39	50	50	NUM
m-1112	1516	40	]	]	PUNCT
m-1112	1516	41	opened	open	VERB
m-1112	1516	42	the	the	DET
m-1112	1516	43	way	way	NOUN
m-1112	1516	44	to	to	ADP
m-1112	1516	45	the	the	DET
m-1112	1516	46	material	material	NOUN
m-1112	1516	47	-	-	PUNCT
m-1112	1516	48	geometry	geometry	NOUN
m-1112	1516	49	[	[	X
m-1112	1516	50	54	54	NUM
m-1112	1516	51	]	]	PUNCT
m-1112	1516	52	which	which	PRON
m-1112	1516	53	incorporates	incorporate	VERB
m-1112	1516	54	the	the	DET
m-1112	1516	55	motion	motion	NOUN
m-1112	1516	56	→	→	SYM
m-1112	1516	57	in	in	ADP
m-1112	1516	58	-	-	PUNCT
m-1112	1516	59	space	space	NOUN
m-1112	1516	60	as	as	ADP
m-1112	1516	61	(	(	PUNCT
m-1112	1516	62	⊕↔⊝	⊕↔⊝	NOUN
m-1112	1516	63	)	)	PUNCT
m-1112	1516	64	≡	≡	PROPN
m-1112	1516	65	0,[61	0,[61	PROPN
m-1112	1516	66	]	]	X
m-1112	1516	67	the	the	DET
m-1112	1516	68	space	space	NOUN
m-1112	1516	69	exists	exist	VERB
m-1112	1516	70	in	in	ADP
m-1112	1516	71	energy	energy	NOUN
m-1112	1516	72	caves	cave	NOUN
m-1112	1516	73	as	as	ADP
m-1112	1516	74	energy	energy	NOUN
m-1112	1516	75	-	-	PUNCT
m-1112	1516	76	quantum	quantum	NOUN
m-1112	1516	77	-	-	PUNCT
m-1112	1516	78	quantities	quantity	NOUN
m-1112	1516	79	[	[	X
m-1112	1516	80	39	39	NUM
m-1112	1516	81	]	]	PUNCT
m-1112	1516	82	,	,	PUNCT
m-1112	1516	83	while	while	SCONJ
m-1112	1516	84	motion	motion	NOUN
m-1112	1516	85	or	or	CCONJ
m-1112	1516	86	energy	energy	NOUN
m-1112	1516	87	exist	exist	VERB
m-1112	1516	88	in	in	ADP
m-1112	1516	89	caves	cave	NOUN
m-1112	1516	90	as	as	ADP
m-1112	1516	91	an	an	DET
m-1112	1516	92	confined	confine	VERB
m-1112	1516	93	stationary	stationary	ADJ
m-1112	1516	94	-	-	PUNCT
m-1112	1516	95	wave	wave	NOUN
m-1112	1516	96	which	which	PRON
m-1112	1516	97	is	be	AUX
m-1112	1516	98	either	either	CCONJ
m-1112	1516	99	static	static	ADJ
m-1112	1516	100	or	or	CCONJ
m-1112	1516	101	an	an	DET
m-1112	1516	102	moving	move	VERB
m-1112	1516	103	energy	energy	NOUN
m-1112	1516	104	-	-	PUNCT
m-1112	1516	105	storage	storage	NOUN
m-1112	1516	106	or	or	CCONJ
m-1112	1516	107	an	an	DET
m-1112	1516	108	energy	energy	NOUN
m-1112	1516	109	-	-	PUNCT
m-1112	1516	110	box	box	NOUN
m-1112	1516	111	[	[	X
m-1112	1516	112	68	68	NUM
m-1112	1516	113	]	]	PUNCT
m-1112	1516	114	.	.	PUNCT
m-1112	1517	1	the	the	DET
m-1112	1517	2	any	any	PRON
m-1112	1517	3	-	-	PUNCT
m-1112	1517	4	two	two	NUM
m-1112	1517	5	opposites	opposite	NOUN
m-1112	1517	6	(	(	PUNCT
m-1112	1517	7	+	+	NOUN
m-1112	1517	8	)	)	PUNCT
m-1112	1517	9	,	,	PUNCT
m-1112	1517	10	(	(	PUNCT
m-1112	1517	11	-	-	SYM
m-1112	1517	12	)	)	PUNCT
m-1112	1517	13	exist	exist	VERB
m-1112	1517	14	in	in	ADP
m-1112	1517	15	nature	nature	NOUN
m-1112	1517	16	and	and	CCONJ
m-1112	1517	17	are	be	AUX
m-1112	1517	18	found	find	VERB
m-1112	1517	19	everywhere	everywhere	ADV
m-1112	1517	20	from	from	ADP
m-1112	1517	21	→	→	PUNCT
m-1112	1517	22	zero	zero	NUM
m-1112	1517	23	-	-	PUNCT
m-1112	1517	24	point	point	NOUN
m-1112	1517	25	(	(	PUNCT
m-1112	1517	26	0	0	NUM
m-1112	1517	27	)	)	PUNCT
m-1112	1517	28	≡	≡	PROPN
m-1112	1518	1	[	[	X
m-1112	1518	2	+	+	X
m-1112	1518	3	=	=	SYM
m-1112	1518	4	-	-	PUNCT
m-1112	1518	5	]	]	X
m-1112	1518	6	or	or	CCONJ
m-1112	1518	7	as	as	ADP
m-1112	1518	8	(	(	PUNCT
m-1112	1518	9	+	+	X
m-1112	1518	10	a	a	X
m-1112	1518	11	)	)	PUNCT
m-1112	1518	12	+	+	CCONJ
m-1112	1518	13	(	(	PUNCT
m-1112	1518	14	a	a	X
m-1112	1518	15	)	)	PUNCT
m-1112	1518	16	=	=	SYM
m-1112	1518	17	0	0	NUM
m-1112	1518	18	in	in	ADP
m-1112	1518	19	e	e	NOUN
m-1112	1518	20	-	-	NOUN
m-1112	1518	21	geometry	geometry	NOUN
m-1112	1518	22	and	and	CCONJ
m-1112	1518	23	→	→	SYM
m-1112	1518	24	[	[	X
m-1112	1518	25	0	0	X
m-1112	1518	26	]	]	X
m-1112	1518	27	=	=	PUNCT
m-1112	1519	1	[	[	X
m-1112	1519	2	⊕↔⊝	⊕↔⊝	X
m-1112	1519	3	]	]	X
m-1112	1519	4	≡	≡	PROPN
m-1112	1519	5	f	f	PROPN
m-1112	1519	6	n	n	PROPN
m-1112	1519	7	,	,	PUNCT
m-1112	1519	8	[	[	X
m-1112	1519	9	⊕←ds→⊝	⊕←ds→⊝	X
m-1112	1519	10	]	]	X
m-1112	1519	11	≡	≡	X
m-1112	1519	12	ds	ds	NOUN
m-1112	1519	13	in	in	ADP
m-1112	1519	14	material	material	NOUN
m-1112	1519	15	-	-	PUNCT
m-1112	1519	16	geometry	geometry	NOUN
m-1112	1519	17	,	,	PUNCT
m-1112	1519	18	to	to	ADP
m-1112	1519	19	the	the	DET
m-1112	1519	20	aperon	aperon	NOUN
m-1112	1519	21	,	,	PUNCT
m-1112	1519	22	±	±	NUM
m-1112	1519	23	∞	∞	NUM
m-1112	1519	24	where	where	SCONJ
m-1112	1519	25	→	→	PUNCT
m-1112	1519	26	the	the	DET
m-1112	1519	27	space	space	NOUN
m-1112	1519	28	≡	≡	PROPN
m-1112	1519	29	ds	ds	X
m-1112	1519	30	,	,	PUNCT
m-1112	1519	31	is	be	AUX
m-1112	1519	32	the	the	DET
m-1112	1519	33	nodes	node	NOUN
m-1112	1519	34	distance	distance	NOUN
m-1112	1519	35	,	,	PUNCT
m-1112	1519	36	and	and	CCONJ
m-1112	1519	37	motion	motion	NOUN
m-1112	1519	38	exist	exist	VERB
m-1112	1519	39	as	as	ADP
m-1112	1519	40	the	the	DET
m-1112	1519	41	vibration	vibration	NOUN
m-1112	1519	42	type	type	NOUN
m-1112	1519	43	←	←	PROPN
m-1112	1519	44	[	[	X
m-1112	1519	45	52	52	NUM
m-1112	1519	46	]	]	SYM
m-1112	1519	47	4	4	NUM
m-1112	1519	48	..	..	PUNCT
m-1112	1519	49	the	the	DET
m-1112	1519	50	electron	electron	NOUN
m-1112	1519	51	-	-	PUNCT
m-1112	1519	52	nutation	nutation	NOUN
m-1112	1519	53	in	in	ADP
m-1112	1519	54	hydrogen	hydrogen	NOUN
m-1112	1519	55	cave	cave	NOUN
m-1112	1519	56	produces	produce	VERB
m-1112	1519	57	energy	energy	NOUN
m-1112	1519	58	due	due	ADP
m-1112	1519	59	to	to	ADP
m-1112	1519	60	g	g	NOUN
m-1112	1519	61	effect	effect	NOUN
m-1112	1519	62	,	,	PUNCT
m-1112	1519	63	as	as	ADP
m-1112	1519	64	an	an	DET
m-1112	1519	65	minimum	minimum	ADJ
m-1112	1519	66	frequency	frequency	NOUN
m-1112	1519	67	fn	fn	X
m-1112	1519	68	≡	≡	PROPN
m-1112	1519	69	2,8398447	2,8398447	NUM
m-1112	1519	70	.	.	PUNCT
m-1112	1520	1	1010	1010	NUM
m-1112	1520	2	h	h	NOUN
m-1112	1520	3	and	and	CCONJ
m-1112	1520	4	thus	thus	ADV
m-1112	1520	5	exists	exist	VERB
m-1112	1520	6	in	in	ADP
m-1112	1520	7	all	all	DET
m-1112	1520	8	atoms	atom	NOUN
m-1112	1520	9	.	.	PUNCT
m-1112	1521	1	this	this	DET
m-1112	1521	2	energy	energy	NOUN
m-1112	1521	3	in	in	ADP
m-1112	1521	4	hydrogen	hydrogen	NOUN
m-1112	1521	5	cave	cave	NOUN
m-1112	1521	6	is	be	AUX
m-1112	1521	7	an	an	DET
m-1112	1521	8	electrical	electrical	ADJ
m-1112	1521	9	-magnetic	-magnetic	ADJ
m-1112	1521	10	conductor	conductor	NOUN
m-1112	1521	11	,	,	PUNCT
m-1112	1521	12	which	which	PRON
m-1112	1521	13	is	be	AUX
m-1112	1521	14	the	the	DET
m-1112	1521	15	pin	pin	NOUN
m-1112	1521	16	of	of	ADP
m-1112	1521	17	atom	atom	NOUN
m-1112	1521	18	-	-	PUNCT
m-1112	1521	19	plug	plug	NOUN
m-1112	1521	20	and	and	CCONJ
m-1112	1521	21	enters	enter	VERB
m-1112	1521	22	into	into	ADP
m-1112	1521	23	the	the	DET
m-1112	1521	24	other	other	ADJ
m-1112	1521	25	atom	atom	NOUN
m-1112	1521	26	-	-	PUNCT
m-1112	1521	27	sockets	socket	NOUN
m-1112	1521	28	,	,	PUNCT
m-1112	1521	29	which	which	PRON
m-1112	1521	30	are	be	AUX
m-1112	1521	31	the	the	DET
m-1112	1521	32	orbit	orbit	NOUN
m-1112	1521	33	-	-	PUNCT
m-1112	1521	34	bracket	bracket	NOUN
m-1112	1521	35	–	–	PUNCT
m-1112	1521	36	hooks	hook	NOUN
m-1112	1521	37	.	.	PUNCT
m-1112	1522	1	these	these	PRON
m-1112	1522	2	are	be	AUX
m-1112	1522	3	the	the	DET
m-1112	1522	4	hands	hand	NOUN
m-1112	1522	5	of	of	ADP
m-1112	1522	6	atoms	atom	NOUN
m-1112	1522	7	,	,	PUNCT
m-1112	1522	8	i.e.	i.e.	X
m-1112	1522	9	→	→	ADP
m-1112	1522	10	the	the	DET
m-1112	1522	11	atoms	atoms	NOUN
m-1112	1522	12	-	-	PUNCT
m-1112	1522	13	plug	plug	NOUN
m-1112	1522	14	,	,	PUNCT
m-1112	1522	15	placing	place	VERB
m-1112	1522	16	their	their	PRON
m-1112	1522	17	pins	pin	NOUN
m-1112	1522	18	into	into	ADP
m-1112	1522	19	the	the	DET
m-1112	1522	20	other	other	ADJ
m-1112	1522	21	atoms	atom	NOUN
m-1112	1522	22	drains	drain	VERB
m-1112	1522	23	≡	≡	PROPN
m-1112	1522	24	holes	hole	NOUN
m-1112	1522	25	,	,	PUNCT
m-1112	1522	26	and	and	CCONJ
m-1112	1522	27	so	so	ADV
m-1112	1522	28	is	be	AUX
m-1112	1522	29	done	do	VERB
m-1112	1522	30	that	that	SCONJ
m-1112	1522	31	what	what	PRON
m-1112	1522	32	we	we	PRON
m-1112	1522	33	say	say	VERB
m-1112	1522	34	the	the	DET
m-1112	1522	35	bonding	bonding	NOUN
m-1112	1522	36	of	of	ADP
m-1112	1522	37	atoms	atom	NOUN
m-1112	1522	38	.	.	PUNCT
m-1112	1523	1	5	5	X
m-1112	1523	2	..	..	PUNCT
m-1112	1523	3	because	because	SCONJ
m-1112	1523	4	of	of	ADP
m-1112	1523	5	the	the	DET
m-1112	1523	6	resonance	resonance	NOUN
m-1112	1523	7	frequency	frequency	NOUN
m-1112	1523	8	between	between	ADP
m-1112	1523	9	all	all	DET
m-1112	1523	10	atoms	atom	NOUN
m-1112	1523	11	,	,	PUNCT
m-1112	1523	12	and	and	CCONJ
m-1112	1523	13	because	because	SCONJ
m-1112	1523	14	of	of	ADP
m-1112	1523	15	the	the	DET
m-1112	1523	16	common	common	ADJ
m-1112	1523	17	hydrogen	hydrogen	NOUN
m-1112	1523	18	,	,	PUNCT
m-1112	1523	19	so	so	CCONJ
m-1112	1523	20	atoms	atom	NOUN
m-1112	1523	21	bond	bond	NOUN
m-1112	1523	22	by	by	ADP
m-1112	1523	23	pinning	pin	VERB
m-1112	1523	24	and	and	CCONJ
m-1112	1523	25	form	form	NOUN
m-1112	1523	26	molecules	molecule	NOUN
m-1112	1523	27	and	and	CCONJ
m-1112	1523	28	all	all	DET
m-1112	1523	29	compounds	compound	NOUN
m-1112	1523	30	in	in	ADP
m-1112	1523	31	this	this	DET
m-1112	1523	32	cosmos	cosmos	NOUN
m-1112	1523	33	.	.	PUNCT
m-1112	1524	1	this	this	PRON
m-1112	1524	2	is	be	AUX
m-1112	1524	3	possible	possible	ADJ
m-1112	1524	4	because	because	SCONJ
m-1112	1524	5	the	the	DET
m-1112	1524	6	periodic	periodic	ADJ
m-1112	1524	7	-	-	PUNCT
m-1112	1524	8	system	system	NOUN
m-1112	1524	9	of	of	ADP
m-1112	1524	10	atoms	atom	NOUN
m-1112	1524	11	is	be	AUX
m-1112	1524	12	now	now	ADV
m-1112	1524	13	modulated	modulate	VERB
m-1112	1524	14	into	into	ADP
m-1112	1524	15	4	4	NUM
m-1112	1524	16	new	new	ADJ
m-1112	1524	17	categories	category	NOUN
m-1112	1524	18	with	with	ADP
m-1112	1524	19	only	only	ADV
m-1112	1524	20	-	-	PUNCT
m-1112	1524	21	one	one	NUM
m-1112	1524	22	newcriterion	newcriterion	NOUN
m-1112	1524	23	which	which	PRON
m-1112	1524	24	is	be	AUX
m-1112	1524	25	the	the	DET
m-1112	1524	26	number	number	NOUN
m-1112	1524	27	of	of	ADP
m-1112	1524	28	(	(	PUNCT
m-1112	1524	29	±	±	PROPN
m-1112	1524	30	)	)	PUNCT
m-1112	1524	31	energy	energy	NOUN
m-1112	1524	32	conductors	conductor	NOUN
m-1112	1524	33	in	in	ADP
m-1112	1524	34	atoms	atom	NOUN
m-1112	1524	35	,	,	PUNCT
m-1112	1524	36	related	relate	VERB
m-1112	1524	37	to	to	ADP
m-1112	1524	38	their	their	PRON
m-1112	1524	39	stability	stability	NOUN
m-1112	1524	40	.	.	PUNCT
m-1112	1525	1	6	6	X
m-1112	1525	2	..	..	PUNCT
m-1112	1525	3	the	the	DET
m-1112	1525	4	first	first	ADJ
m-1112	1525	5	solid	solid	ADJ
m-1112	1525	6	(	(	PUNCT
m-1112	1525	7	4	4	NUM
m-1112	1525	8	points	point	NOUN
m-1112	1525	9	not	not	PART
m-1112	1525	10	coinciding	coincide	VERB
m-1112	1525	11	)	)	PUNCT
m-1112	1525	12	is	be	AUX
m-1112	1525	13	the	the	DET
m-1112	1525	14	tetrahedron	tetrahedron	NOUN
m-1112	1525	15	,	,	PUNCT
m-1112	1525	16	and	and	CCONJ
m-1112	1525	17	the	the	DET
m-1112	1525	18	first	first	ADJ
m-1112	1525	19	material	material	NOUN
m-1112	1525	20	space	space	NOUN
m-1112	1525	21	for	for	ADP
m-1112	1525	22	the	the	DET
m-1112	1525	23	two	two	NUM
m-1112	1525	24	elements	element	NOUN
m-1112	1525	25	(	(	PUNCT
m-1112	1525	26	+	+	NOUN
m-1112	1525	27	)	)	PUNCT
m-1112	1525	28	,	,	PUNCT
m-1112	1525	29	(	(	PUNCT
m-1112	1525	30	-	-	PUNCT
m-1112	1525	31	)	)	PUNCT
m-1112	1525	32	,	,	PUNCT
m-1112	1525	33	are	be	AUX
m-1112	1525	34	(	(	PUNCT
m-1112	1525	35	4	4	NUM
m-1112	1525	36	x	x	SYM
m-1112	1525	37	2	2	NUM
m-1112	1525	38	=	=	SYM
m-1112	1525	39	8	8	NUM
m-1112	1525	40	positions	position	NOUN
m-1112	1525	41	for	for	ADP
m-1112	1525	42	electrons	electron	NOUN
m-1112	1525	43	)	)	PUNCT
m-1112	1525	44	the	the	DET
m-1112	1525	45	-	-	PUNCT
m-1112	1525	46	cube	cube	NOUN
m-1112	1525	47	,	,	PUNCT
m-1112	1525	48	i.e.	i.e.	X
m-1112	1525	49	the	the	DET
m-1112	1525	50	tetrahedron	tetrahedron	NOUN
m-1112	1525	51	is	be	AUX
m-1112	1525	52	into	into	ADP
m-1112	1525	53	the	the	DET
m-1112	1525	54	cube	cube	NOUN
m-1112	1525	55	and	and	CCONJ
m-1112	1525	56	into	into	ADP
m-1112	1525	57	its	its	PRON
m-1112	1525	58	ex	ex	PRON
m-1112	1525	59	sphere	sphere	NOUN
m-1112	1525	60	,	,	PUNCT
m-1112	1525	61	and	and	CCONJ
m-1112	1525	62	this	this	PRON
m-1112	1525	63	because	because	SCONJ
m-1112	1525	64	all	all	DET
m-1112	1525	65	the	the	DET
m-1112	1525	66	circles	circle	NOUN
m-1112	1525	67	on	on	ADP
m-1112	1525	68	tetrahedron	tetrahedron	NOUN
m-1112	1525	69	exist	exist	VERB
m-1112	1525	70	on	on	ADP
m-1112	1525	71	sphere	sphere	NOUN
m-1112	1525	72	.	.	PUNCT
m-1112	1526	1	7	7	X
m-1112	1526	2	..	..	PUNCT
m-1112	1526	3	when	when	SCONJ
m-1112	1526	4	1	1	NUM
m-1112	1526	5	-	-	SYM
m-1112	1526	6	8	8	NUM
m-1112	1526	7	electrons	electron	NOUN
m-1112	1526	8	⊝	⊝	NUM
m-1112	1526	9	are	be	AUX
m-1112	1526	10	placed	place	VERB
m-1112	1526	11	on	on	ADP
m-1112	1526	12	the	the	DET
m-1112	1526	13	cube	cube	NOUN
m-1112	1526	14	's	's	PART
m-1112	1526	15	vertices	vertex	NOUN
m-1112	1526	16	and	and	CCONJ
m-1112	1526	17	into	into	ADP
m-1112	1526	18	this	this	DET
m-1112	1526	19	onion	onion	NOUN
m-1112	1526	20	system	system	NOUN
m-1112	1526	21	,	,	PUNCT
m-1112	1526	22	then	then	ADV
m-1112	1526	23	automatically	automatically	ADV
m-1112	1526	24	are	be	AUX
m-1112	1526	25	formed	form	VERB
m-1112	1526	26	the	the	DET
m-1112	1526	27	14	14	NUM
m-1112	1526	28	,	,	PUNCT
m-1112	1526	29	energy	energy	NOUN
m-1112	1526	30	-	-	PUNCT
m-1112	1526	31	conductors	conductor	NOUN
m-1112	1526	32	,	,	PUNCT
m-1112	1526	33	where	where	SCONJ
m-1112	1526	34	issues	issue	NOUN
m-1112	1526	35	[	[	X
m-1112	1526	36	⊕	⊕	NOUN
m-1112	1526	37	↔	↔	PROPN
m-1112	1526	38	⊝	⊝	X
m-1112	1526	39	]	]	PUNCT
m-1112	1527	1	=	=	PUNCT
m-1112	1527	2	[	[	PUNCT
m-1112	1527	3	p	p	X
m-1112	1527	4	↔	↔	PROPN
m-1112	1527	5	e	e	NOUN
m-1112	1527	6	]	]	PUNCT
m-1112	1527	7	=	=	PUNCT
m-1112	1528	1	[	[	PUNCT
m-1112	1528	2	atom	atom	NOUN
m-1112	1528	3	-	-	PUNCT
m-1112	1528	4	plug	plug	NOUN
m-1112	1528	5	=	=	SYM
m-1112	1528	6	+	+	NUM
m-1112	1528	7	electric	electric	ADJ
m-1112	1528	8	vector	vector	NOUN
m-1112	1528	9	↔	↔	PROPN
m-1112	1528	10	magnetic	magnetic	ADJ
m-1112	1528	11	vector	vector	NOUN
m-1112	1528	12	≡	≡	PROPN
m-1112	1528	13	drain	drain	NOUN
m-1112	1528	14	≡	≡	PROPN
m-1112	1528	15	hole	hole	PROPN
m-1112	1528	16	]	]	PUNCT
m-1112	1528	17	,	,	PUNCT
m-1112	1528	18	and	and	CCONJ
m-1112	1528	19	are	be	AUX
m-1112	1528	20	the	the	DET
m-1112	1528	21	actions	action	NOUN
m-1112	1528	22	between	between	ADP
m-1112	1528	23	opposite	opposite	ADJ
m-1112	1528	24	.	.	PUNCT
m-1112	1529	1	with	with	ADP
m-1112	1529	2	this	this	DET
m-1112	1529	3	new	new	ADJ
m-1112	1529	4	modulation	modulation	NOUN
m-1112	1529	5	[	[	PUNCT
m-1112	1529	6	the	the	DET
m-1112	1529	7	,	,	PUNCT
m-1112	1529	8	1	1	NUM
m-1112	1529	9	,	,	PUNCT
m-1112	1529	10	2	2	NUM
m-1112	1529	11	,	,	PUNCT
m-1112	1529	12	3	3	NUM
m-1112	1529	13	,	,	PUNCT
m-1112	1529	14	4	4	NUM
m-1112	1529	15	,	,	PUNCT
m-1112	1529	16	energyconductors	energyconductor	NOUN
m-1112	1529	17	≡	≡	PROPN
m-1112	1529	18	atoms	atom	NOUN
m-1112	1529	19	-	-	PUNCT
m-1112	1529	20	four	four	NUM
m-1112	1529	21	fundamental	fundamental	ADJ
m-1112	1529	22	frequencies	frequency	NOUN
m-1112	1529	23	]	]	PUNCT
m-1112	1529	24	,	,	PUNCT
m-1112	1529	25	conductors	conductor	NOUN
m-1112	1529	26	exist	exist	VERB
m-1112	1529	27	on	on	ADP
m-1112	1529	28	system	system	NOUN
m-1112	1529	29	and	and	CCONJ
m-1112	1529	30	are	be	AUX
m-1112	1529	31	active	active	ADJ
m-1112	1529	32	+	+	CCONJ
m-1112	1529	33	as	as	SCONJ
m-1112	1529	34	→	→	SYM
m-1112	1529	35	the	the	DET
m-1112	1529	36	-	-	PUNCT
m-1112	1529	37	electric	electric	ADJ
m-1112	1529	38	-	-	PUNCT
m-1112	1529	39	vectors	vector	NOUN
m-1112	1529	40	←	←	NOUN
m-1112	1529	41	and	and	CCONJ
m-1112	1529	42	simultaneously	simultaneously	ADV
m-1112	1529	43	passive	passive	ADJ
m-1112	1529	44	≡	≡	PROPN
m-1112	1529	45	drains	drain	NOUN
m-1112	1529	46	(	(	PUNCT
m-1112	1529	47	-	-	INTJ
m-1112	1529	48	)	)	PUNCT
m-1112	1529	49	as	as	SCONJ
m-1112	1529	50	→	→	SYM
m-1112	1529	51	the	the	PRON
m-1112	1529	52	-	-	PUNCT
m-1112	1529	53	magnetic	magnetic	ADJ
m-1112	1529	54	vectors	vector	NOUN
m-1112	1529	55	≡	≡	PROPN
m-1112	1529	56	holes	hole	VERB
m-1112	1529	57	←	←	PROPN
m-1112	1529	58	.	.	PUNCT
m-1112	1530	1	the	the	DET
m-1112	1530	2	zero	zero	NUM
m-1112	1530	3	-	-	PUNCT
m-1112	1530	4	state	state	NOUN
m-1112	1530	5	conductors	conductor	NOUN
m-1112	1530	6	are	be	AUX
m-1112	1530	7	those	those	PRON
m-1112	1530	8	whose	whose	DET
m-1112	1530	9	8	8	NUM
m-1112	1530	10	cube	cube	NOUN
m-1112	1530	11	positions	position	NOUN
m-1112	1530	12	are	be	AUX
m-1112	1530	13	all	all	PRON
m-1112	1530	14	filled	fill	VERB
m-1112	1530	15	with	with	ADP
m-1112	1530	16	electrons	electron	NOUN
m-1112	1530	17	.	.	PUNCT
m-1112	1531	1	the	the	DET
m-1112	1531	2	multiple	multiple	ADJ
m-1112	1531	3	–	–	PUNCT
m-1112	1531	4	plug	plug	NOUN
m-1112	1531	5	-	-	PUNCT
m-1112	1531	6	pins	pin	NOUN
m-1112	1531	7	atoms	atom	NOUN
m-1112	1531	8	can	can	AUX
m-1112	1531	9	plug	plug	VERB
m-1112	1531	10	all	all	DET
m-1112	1531	11	the	the	DET
m-1112	1531	12	less	less	ADJ
m-1112	1531	13	number	number	NOUN
m-1112	1531	14	electrons	electron	NOUN
m-1112	1531	15	atoms	atom	NOUN
m-1112	1531	16	and	and	CCONJ
m-1112	1531	17	can	can	AUX
m-1112	1531	18	be	be	AUX
m-1112	1531	19	-	-	PUNCT
m-1112	1531	20	plugged	plug	VERB
m-1112	1531	21	from	from	ADP
m-1112	1531	22	all	all	DET
m-1112	1531	23	the	the	DET
m-1112	1531	24	greater	great	ADJ
m-1112	1531	25	number	number	NOUN
m-1112	1531	26	electronsatoms	electronsatom	NOUN
m-1112	1531	27	.with	.with	ADP
m-1112	1531	28	these	these	DET
m-1112	1531	29	four	four	NUM
m-1112	1531	30	modulations	modulation	NOUN
m-1112	1531	31	are	be	AUX
m-1112	1531	32	formed	form	VERB
m-1112	1531	33	all	all	DET
m-1112	1531	34	atoms	atom	NOUN
m-1112	1531	35	and	and	CCONJ
m-1112	1531	36	their	their	PRON
m-1112	1531	37	compounds	compound	NOUN
m-1112	1531	38	these	these	PRON
m-1112	1531	39	are	be	AUX
m-1112	1531	40	the	the	DET
m-1112	1531	41	mechanisms	mechanism	NOUN
m-1112	1531	42	of	of	ADP
m-1112	1531	43	,	,	PUNCT
m-1112	1531	44	water	water	NOUN
m-1112	1531	45	,	,	PUNCT
m-1112	1531	46	the	the	DET
m-1112	1531	47	cells	cell	NOUN
m-1112	1531	48	,	,	PUNCT
m-1112	1531	49	rna	rna	NOUN
m-1112	1531	50	,	,	PUNCT
m-1112	1531	51	dna	dna	PROPN
m-1112	1531	52	,	,	PUNCT
m-1112	1531	53	cancer	cancer	NOUN
m-1112	1531	54	,	,	PUNCT
m-1112	1531	55	and	and	CCONJ
m-1112	1531	56	everything	everything	PRON
m-1112	1531	57	in	in	ADP
m-1112	1531	58	this	this	DET
m-1112	1531	59	energy	energy	NOUN
m-1112	1531	60	space	space	NOUN
m-1112	1531	61	universe	universe	NOUN
m-1112	1531	62	.	.	PUNCT
m-1112	1532	1	8	8	X
m-1112	1532	2	..	..	PUNCT
m-1112	1532	3	in	in	ADP
m-1112	1532	4	the	the	DET
m-1112	1532	5	same	same	ADJ
m-1112	1532	6	way	way	NOUN
m-1112	1532	7	,	,	PUNCT
m-1112	1532	8	is	be	AUX
m-1112	1532	9	that	that	SCONJ
m-1112	1532	10	where	where	SCONJ
m-1112	1532	11	an	an	DET
m-1112	1532	12	110	110	NUM
m-1112	1532	13	volt	volt	NOUN
m-1112	1532	14	refrigerator	refrigerator	NOUN
m-1112	1532	15	can’t	can’t	NOUN
m-1112	1532	16	-	-	PUNCT
m-1112	1532	17	plug	plug	NOUN
m-1112	1532	18	into	into	ADP
m-1112	1532	19	220	220	NUM
m-1112	1532	20	volt	volt	NOUN
m-1112	1532	21	socket	socket	NOUN
m-1112	1532	22	and	and	CCONJ
m-1112	1532	23	this	this	PRON
m-1112	1532	24	because	because	SCONJ
m-1112	1532	25	are	be	AUX
m-1112	1532	26	different	different	ADJ
m-1112	1532	27	in	in	ADP
m-1112	1532	28	construction	construction	NOUN
m-1112	1532	29	,	,	PUNCT
m-1112	1532	30	the	the	DET
m-1112	1532	31	same	same	ADJ
m-1112	1532	32	to	to	ADP
m-1112	1532	33	atoms	atom	NOUN
m-1112	1532	34	-	-	PUNCT
m-1112	1532	35	plug	plug	NOUN
m-1112	1532	36	which	which	PRON
m-1112	1532	37	differ	differ	VERB
m-1112	1532	38	to	to	ADP
m-1112	1532	39	the	the	DET
m-1112	1532	40	ijo	ijo	PROPN
m-1112	1532	41	international	international	PROPN
m-1112	1532	42	journal	journal	PROPN
m-1112	1532	43	of	of	ADP
m-1112	1532	44	mathematics	mathematics	PROPN
m-1112	1532	45	(	(	PUNCT
m-1112	1532	46	issn	issn	PROPN
m-1112	1532	47	:	:	PUNCT
m-1112	1532	48	2992	2992	NUM
m-1112	1532	49	-	-	SYM
m-1112	1532	50	4421	4421	NUM
m-1112	1532	51	)	)	PUNCT
m-1112	1532	52	volume	volume	NOUN
m-1112	1532	53	08	08	NUM
m-1112	1533	1	|	|	ADV
m-1112	1533	2	issue	issue	NOUN
m-1112	1533	3	08	08	NUM
m-1112	1534	1	|	|	ADV
m-1112	1534	2	august	august	PROPN
m-1112	1534	3	2025	2025	NUM
m-1112	1534	4	|	|	ADV
m-1112	1534	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1534	6	ijo	ijo	PROPN
m-1112	1534	7	journals	journal	NOUN
m-1112	1534	8	55	55	NUM
m-1112	1534	9	the	the	DET
m-1112	1534	10	fundamental	fundamental	ADJ
m-1112	1534	11	particles	particle	NOUN
m-1112	1534	12	origination	origination	NOUN
m-1112	1534	13	mechanism	mechanism	NOUN
m-1112	1534	14	in	in	ADP
m-1112	1534	15	mfmf	mfmf	PROPN
m-1112	1534	16	pns	pns	PROPN
m-1112	1534	17	caves	cave	NOUN
m-1112	1534	18	.	.	PUNCT
m-1112	1535	1	number	number	NOUN
m-1112	1535	2	and	and	CCONJ
m-1112	1535	3	the	the	DET
m-1112	1535	4	length	length	NOUN
m-1112	1535	5	of	of	ADP
m-1112	1535	6	their	their	PRON
m-1112	1535	7	pins	pin	NOUN
m-1112	1535	8	.	.	PUNCT
m-1112	1536	1	hydrogen	hydrogen	NOUN
m-1112	1536	2	is	be	AUX
m-1112	1536	3	the	the	DET
m-1112	1536	4	multiple	multiple	ADJ
m-1112	1536	5	-	-	PUNCT
m-1112	1536	6	plug	plug	NOUN
m-1112	1536	7	-	-	PUNCT
m-1112	1536	8	pins	pin	NOUN
m-1112	1536	9	atom	atom	NOUN
m-1112	1536	10	which	which	PRON
m-1112	1536	11	can	can	AUX
m-1112	1536	12	plug	plug	VERB
m-1112	1536	13	all	all	DET
m-1112	1536	14	atoms	atom	NOUN
m-1112	1536	15	and	and	CCONJ
m-1112	1536	16	itself	itself	PRON
m-1112	1536	17	.	.	PUNCT
m-1112	1537	1	9	9	X
m-1112	1537	2	..	..	PUNCT
m-1112	1537	3	the	the	DET
m-1112	1537	4	new	new	ADJ
m-1112	1537	5	-	-	PUNCT
m-1112	1537	6	atom	atom	NOUN
m-1112	1537	7	-	-	PUNCT
m-1112	1537	8	structure	structure	NOUN
m-1112	1537	9	is	be	AUX
m-1112	1537	10	consisted	consist	VERB
m-1112	1537	11	of	of	ADP
m-1112	1537	12	→	→	SYM
m-1112	1537	13	a	a	X
m-1112	1537	14	)	)	PUNCT
m-1112	1537	15	the	the	DET
m-1112	1537	16	nucleus	nucleus	NOUN
m-1112	1537	17	in	in	ADP
m-1112	1537	18	-	-	PUNCT
m-1112	1537	19	sphere	sphere	NOUN
m-1112	1537	20	b	b	NOUN
m-1112	1537	21	)	)	PUNCT
m-1112	1537	22	the	the	DET
m-1112	1537	23	dynamic	dynamic	ADJ
m-1112	1537	24	electro	electro	NOUN
m-1112	1537	25	-	-	PUNCT
m-1112	1537	26	magnetic	magnetic	ADJ
m-1112	1537	27	-tetrahedron	-tetrahedron	NOUN
m-1112	1537	28	,	,	PUNCT
m-1112	1537	29	c	c	NOUN
m-1112	1537	30	)	)	PUNCT
m-1112	1537	31	the	the	DET
m-1112	1537	32	n	n	ADV
m-1112	1537	33	-	-	PUNCT
m-1112	1537	34	outercube	outercube	NOUN
m-1112	1537	35	,	,	PUNCT
m-1112	1537	36	d	d	X
m-1112	1537	37	)	)	PUNCT
m-1112	1537	38	the	the	DET
m-1112	1537	39	orbitals	orbital	NOUN
m-1112	1537	40	in	in	ADP
m-1112	1537	41	ex	ex	NOUN
m-1112	1537	42	-	-	NOUN
m-1112	1537	43	sphere	sphere	NOUN
m-1112	1537	44	.	.	PUNCT
m-1112	1538	1	10	10	NUM
m-1112	1538	2	..	..	PUNCT
m-1112	1538	3	in	in	ADP
m-1112	1538	4	the	the	DET
m-1112	1538	5	new	new	ADJ
m-1112	1538	6	-	-	PUNCT
m-1112	1538	7	atom	atom	NOUN
m-1112	1538	8	-	-	PUNCT
m-1112	1538	9	structure	structure	NOUN
m-1112	1538	10	,	,	PUNCT
m-1112	1538	11	the	the	DET
m-1112	1538	12	master	master	NOUN
m-1112	1538	13	-	-	PUNCT
m-1112	1538	14	keys	key	NOUN
m-1112	1538	15	resonances	resonance	NOUN
m-1112	1538	16	are	be	AUX
m-1112	1538	17	the	the	DET
m-1112	1538	18	communications	communication	NOUN
m-1112	1538	19	11	11	NUM
m-1112	1538	20	..	..	PUNCT
m-1112	1538	21	article	article	NOUN
m-1112	1538	22	[	[	X
m-1112	1538	23	110	110	NUM
m-1112	1538	24	]	]	PUNCT
m-1112	1538	25	is	be	AUX
m-1112	1538	26	the	the	DET
m-1112	1538	27	completion	completion	NOUN
m-1112	1538	28	of	of	ADP
m-1112	1538	29	[	[	X
m-1112	1538	30	72	72	NUM
m-1112	1538	31	-	-	SYM
m-1112	1538	32	82	82	NUM
m-1112	1538	33	]	]	PUNCT
m-1112	1538	34	and	and	CCONJ
m-1112	1538	35	of	of	ADP
m-1112	1538	36	physical	physical	ADJ
m-1112	1538	37	interpretation	interpretation	NOUN
m-1112	1538	38	of	of	ADP
m-1112	1538	39	the	the	DET
m-1112	1538	40	three	three	NUM
m-1112	1538	41	constants	constant	NOUN
m-1112	1538	42	of	of	ADP
m-1112	1538	43	nature	nature	NOUN
m-1112	1538	44	,	,	PUNCT
m-1112	1538	45	that	that	PRON
m-1112	1538	46	of	of	ADP
m-1112	1538	47	planck	planck	NOUN
m-1112	1538	48	constant	constant	ADJ
m-1112	1538	49	𝐋	𝐋	PROPN
m-1112	1538	50	𝐏	𝐏	PROPN
m-1112	1538	51	,	,	PUNCT
m-1112	1538	52	newton`s	newton`s	PROPN
m-1112	1538	53	gravitational	gravitational	ADJ
m-1112	1538	54	constant	constant	ADJ
m-1112	1538	55	g	g	NOUN
m-1112	1538	56	,	,	PUNCT
m-1112	1538	57	and	and	CCONJ
m-1112	1538	58	the	the	DET
m-1112	1538	59	gravity	gravity	NOUN
m-1112	1538	60	constant	constant	ADJ
m-1112	1538	61	g	g	NOUN
m-1112	1538	62	,	,	PUNCT
m-1112	1538	63	with	with	ADP
m-1112	1538	64	a	a	DET
m-1112	1538	65	rigorous	rigorous	ADJ
m-1112	1538	66	geometrical	geometrical	ADJ
m-1112	1538	67	and	and	CCONJ
m-1112	1538	68	mechanical	mechanical	ADJ
m-1112	1538	69	logic	logic	NOUN
m-1112	1538	70	.	.	PUNCT
m-1112	1539	1	it	it	PRON
m-1112	1539	2	was	be	AUX
m-1112	1539	3	shown	show	VERB
m-1112	1539	4	[	[	PUNCT
m-1112	1539	5	33	33	NUM
m-1112	1539	6	-	-	SYM
m-1112	1539	7	36	36	NUM
m-1112	1539	8	]	]	PUNCT
m-1112	1539	9	that	that	SCONJ
m-1112	1539	10	un	un	PROPN
m-1112	1539	11	-	-	ADJ
m-1112	1539	12	clashed	clash	VERB
m-1112	1539	13	fragments	fragment	NOUN
m-1112	1539	14	through	through	ADP
m-1112	1539	15	the	the	DET
m-1112	1539	16	center	center	NOUN
m-1112	1539	17	,	,	PUNCT
m-1112	1539	18	o	o	INTJ
m-1112	1539	19	,	,	PUNCT
m-1112	1539	20	consist	consist	VERB
m-1112	1539	21	the	the	DET
m-1112	1539	22	mediumfield	mediumfield	NOUN
m-1112	1539	23	material	material	NOUN
m-1112	1539	24	-	-	PUNCT
m-1112	1539	25	fragment	fragment	NOUN
m-1112	1539	26	→	→	PUNCT
m-1112	1539	27	[	[	PUNCT
m-1112	1539	28	±	±	NUM
m-1112	1539	29	s²	s²	NOUN
m-1112	1539	30	]	]	PUNCT
m-1112	1539	31	=	=	PUNCT
m-1112	1540	1	[	[	X
m-1112	1540	2	mfmf	mfmf	X
m-1112	1540	3	]	]	PUNCT
m-1112	1540	4	≡	≡	PROPN
m-1112	1540	5	the	the	DET
m-1112	1540	6	chaos	chaos	NOUN
m-1112	1540	7	,	,	PUNCT
m-1112	1540	8	the	the	DET
m-1112	1540	9	base	base	NOUN
m-1112	1540	10	for	for	ADP
m-1112	1540	11	all	all	DET
m-1112	1540	12	motions	motion	NOUN
m-1112	1540	13	←	←	PROPN
m-1112	1540	14	and	and	CCONJ
m-1112	1540	15	gravity	gravity	NOUN
m-1112	1540	16	which	which	PRON
m-1112	1540	17	is	be	AUX
m-1112	1540	18	a	a	DET
m-1112	1540	19	force	force	NOUN
m-1112	1540	20	[	[	PUNCT
m-1112	1540	21	i	i	X
m-1112	1540	22	]	]	PUNCT
m-1112	1540	23	while	while	SCONJ
m-1112	1540	24	the	the	PRON
m-1112	1540	25	clashed	clash	VERB
m-1112	1540	26	with	with	ADP
m-1112	1540	27	the	the	DET
m-1112	1540	28	constant	constant	ADJ
m-1112	1540	29	velocity	velocity	NOUN
m-1112	1540	30	,	,	PUNCT
m-1112	1540	31	c̅	c̅	PROPN
m-1112	1540	32	,	,	PUNCT
m-1112	1540	33	consist	consist	VERB
m-1112	1540	34	the	the	DET
m-1112	1540	35	dark	dark	ADJ
m-1112	1540	36	matter	matter	NOUN
m-1112	1540	37	[	[	PUNCT
m-1112	1540	38	±	±	X
m-1112	1540	39	.c̅.s	.c̅.s	X
m-1112	1540	40	]	]	PUNCT
m-1112	1540	41	and	and	CCONJ
m-1112	1540	42	the	the	DET
m-1112	1540	43	dark	dark	ADJ
m-1112	1540	44	energy	energy	NOUN
m-1112	1541	1	[	[	X
m-1112	1541	2	c̅.	c̅.	X
m-1112	1541	3	i	i	X
m-1112	1541	4	]	]	PUNCT
m-1112	1541	5	,	,	PUNCT
m-1112	1541	6	so	so	CCONJ
m-1112	1541	7	declaring	declare	VERB
m-1112	1541	8	that	that	SCONJ
m-1112	1541	9	→	→	NOUN
m-1112	1541	10	antimatter	antimatter	NOUN
m-1112	1541	11	-	-	PUNCT
m-1112	1541	12	galaxies	galaxy	NOUN
m-1112	1541	13	and	and	CCONJ
m-1112	1541	14	antimatter	antimatter	NOUN
m-1112	1541	15	-	-	PUNCT
m-1112	1541	16	asteroids	asteroid	NOUN
m-1112	1541	17	can	can	AUX
m-1112	1541	18	exist	exist	VERB
m-1112	1541	19	only	only	ADV
m-1112	1541	20	as	as	ADP
m-1112	1541	21	dark	dark	ADJ
m-1112	1541	22	-	-	PUNCT
m-1112	1541	23	matter	matter	NOUN
m-1112	1541	24	or	or	CCONJ
m-1112	1541	25	and	and	CCONJ
m-1112	1541	26	dark	dark	ADJ
m-1112	1541	27	-	-	PUNCT
m-1112	1541	28	energy	energy	NOUN
m-1112	1541	29	and	and	CCONJ
m-1112	1541	30	not	not	PART
m-1112	1541	31	as	as	ADP
m-1112	1541	32	antimatter	antimatter	NOUN
m-1112	1541	33	light	light	NOUN
m-1112	1541	34	,	,	PUNCT
m-1112	1541	35	c	c	NOUN
m-1112	1541	36	.	.	PUNCT
m-1112	1542	1	from	from	ADP
m-1112	1542	2	the	the	DET
m-1112	1542	3	velocity	velocity	NOUN
m-1112	1542	4	breakages	breakage	NOUN
m-1112	1542	5	[	[	PUNCT
m-1112	1542	6	±	±	NOUN
m-1112	1542	7	s²	s²	NOUN
m-1112	1542	8	=	=	SYM
m-1112	1542	9	±	±	NOUN
m-1112	1542	10	(	(	PUNCT
m-1112	1542	11	w	w	NOUN
m-1112	1542	12	r)²	r)²	NOUN
m-1112	1542	13	]	]	PUNCT
m-1112	1542	14	,	,	PUNCT
m-1112	1542	15	[	[	PUNCT
m-1112	1542	16	i	i	NOUN
m-1112	1542	17	=	=	NOUN
m-1112	1542	18	2(w	2(w	NUM
m-1112	1542	19	r)²	r)²	NOUN
m-1112	1542	20	]	]	PUNCT
m-1112	1542	21	and	and	CCONJ
m-1112	1542	22	the	the	PRON
m-1112	1542	23	between	between	ADP
m-1112	1542	24	instress	instress	PROPN
m-1112	1542	25	σ	σ	PROPN
m-1112	1542	26	,	,	PUNCT
m-1112	1542	27	become	become	VERB
m-1112	1542	28	the	the	DET
m-1112	1542	29	waves	wave	NOUN
m-1112	1542	30	{	{	PUNCT
m-1112	1542	31	the	the	DET
m-1112	1542	32	distance	distance	NOUN
m-1112	1542	33	ds	ds	NOUN
m-1112	1542	34	=	=	SYM
m-1112	1542	35	r	r	NOUN
m-1112	1542	36	=	=	SYM
m-1112	1542	37	|aae|	|aae|	PROPN
m-1112	1542	38	which	which	PRON
m-1112	1542	39	is	be	AUX
m-1112	1542	40	the	the	DET
m-1112	1542	41	work	work	NOUN
m-1112	1542	42	embedded	embed	VERB
m-1112	1542	43	in	in	ADP
m-1112	1542	44	monads	monad	NOUN
m-1112	1542	45	and	and	CCONJ
m-1112	1542	46	it	it	PRON
m-1112	1542	47	is	be	AUX
m-1112	1542	48	what	what	PRON
m-1112	1542	49	is	be	AUX
m-1112	1542	50	vibrated	vibrate	VERB
m-1112	1542	51	as	as	ADP
m-1112	1542	52	frequency	frequency	NOUN
m-1112	1542	53	f	f	PROPN
m-1112	1542	54	}	}	PUNCT
m-1112	1542	55	of	of	ADP
m-1112	1542	56	the	the	DET
m-1112	1542	57	material	material	NOUN
m-1112	1542	58	-	-	PUNCT
m-1112	1542	59	point	point	NOUN
m-1112	1542	60	with	with	ADP
m-1112	1542	61	their	their	PRON
m-1112	1542	62	vibrating	vibrate	VERB
m-1112	1542	63	equations	equation	NOUN
m-1112	1542	64	of	of	ADP
m-1112	1542	65	motion	motion	NOUN
m-1112	1542	66	and	and	CCONJ
m-1112	1542	67	after	after	ADP
m-1112	1542	68	to	to	PART
m-1112	1542	69	become	become	VERB
m-1112	1542	70	the	the	DET
m-1112	1542	71	waves	wave	NOUN
m-1112	1542	72	.	.	PUNCT
m-1112	1543	1	a	a	DET
m-1112	1543	2	→	→	X
m-1112	1543	3	the	the	DET
m-1112	1543	4	particles	particle	NOUN
m-1112	1543	5	with	with	ADP
m-1112	1543	6	inherent	inherent	ADJ
m-1112	1543	7	vibration	vibration	NOUN
m-1112	1543	8	occupying	occupy	VERB
m-1112	1543	9	the	the	DET
m-1112	1543	10	distances	distance	NOUN
m-1112	1543	11	r	r	NOUN
m-1112	1543	12	=	=	PUNCT
m-1112	1543	13	ds	ds	ADJ
m-1112	1543	14	=	=	NOUN
m-1112	1543	15	positions	position	NOUN
m-1112	1543	16	|aae|	|aae|	PROPN
m-1112	1543	17	the	the	DET
m-1112	1543	18	{	{	PUNCT
m-1112	1543	19	monad	monad	PROPN
m-1112	1543	20	=	=	SYM
m-1112	1543	21	𝐎𝐊𝟎	𝐎𝐊𝟎	PROPN
m-1112	1543	22	=	=	SYM
m-1112	1543	23	r	r	NOUN
m-1112	1543	24	}	}	PUNCT
m-1112	1543	25	≡	≡	PROPN
m-1112	1543	26	energy	energy	NOUN
m-1112	1543	27	in	in	ADP
m-1112	1543	28	vacuum	vacuum	PROPN
m-1112	1543	29	spaces	space	NOUN
m-1112	1543	30	are	be	AUX
m-1112	1543	31	the	the	DET
m-1112	1543	32	fundamental	fundamental	ADJ
m-1112	1543	33	particles	particle	NOUN
m-1112	1543	34	,	,	PUNCT
m-1112	1543	35	as	as	ADP
m-1112	1543	36	[	[	PUNCT
m-1112	1543	37	±	±	NUM
m-1112	1543	38	v̅.s²	v̅.s²	NOUN
m-1112	1543	39	]	]	PUNCT
m-1112	1543	40	→	→	SYM
m-1112	1543	41	fermions	fermion	NOUN
m-1112	1543	42	,	,	PUNCT
m-1112	1543	43	quarks	quark	NOUN
m-1112	1543	44	and	and	CCONJ
m-1112	1543	45	leptons	lepton	NOUN
m-1112	1543	46	,	,	PUNCT
m-1112	1543	47	and	and	CCONJ
m-1112	1543	48	→	→	PUNCT
m-1112	1543	49	[	[	PUNCT
m-1112	1543	50			PROPN
m-1112	1543	51	v̅.	v̅.	NOUN
m-1112	1543	52	i	i	PRON
m-1112	1543	53	]	]	X
m-1112	1543	54	→	→	PUNCT
m-1112	1543	55	the	the	DET
m-1112	1543	56	bosons	boson	NOUN
m-1112	1543	57	,	,	PUNCT
m-1112	1543	58	b	b	X
m-1112	1543	59	→	→	SYM
m-1112	1543	60	the	the	DET
m-1112	1543	61	gravity	gravity	NOUN
m-1112	1543	62	-	-	PUNCT
m-1112	1543	63	antigravity	antigravity	NOUN
m-1112	1543	64	field	field	NOUN
m-1112	1543	65	-	-	PUNCT
m-1112	1543	66	energy	energy	NOUN
m-1112	1543	67	g	g	NOUN
m-1112	1543	68	without	without	ADP
m-1112	1543	69	vibration	vibration	NOUN
m-1112	1543	70	being	be	AUX
m-1112	1543	71	a	a	DET
m-1112	1543	72	stationary	stationary	ADJ
m-1112	1543	73	-	-	PUNCT
m-1112	1543	74	rotating	rotate	VERB
m-1112	1543	75	spinning	spinning	NOUN
m-1112	1543	76	material	material	NOUN
m-1112	1543	77	point	point	NOUN
m-1112	1543	78	m	m	NOUN
m-1112	1543	79	-	-	PROPN
m-1112	1543	80	p.	p.	NOUN
m-1112	1543	81	[	[	PUNCT
m-1112	1543	82	±	±	NOUN
m-1112	1543	83	s²	s²	NOUN
m-1112	1543	84	]	]	PUNCT
m-1112	1543	85	→	→	PUNCT
m-1112	1543	86	the	the	DET
m-1112	1543	87	[	[	X
m-1112	1543	88	mfmf	mfmf	X
m-1112	1543	89	]	]	X
m-1112	1543	90	neutral	neutral	ADJ
m-1112	1543	91	field	field	NOUN
m-1112	1543	92	≡	≡	PROPN
m-1112	1543	93	the	the	DET
m-1112	1543	94	energy	energy	NOUN
m-1112	1543	95	chaos	chaos	NOUN
m-1112	1543	96	,	,	PUNCT
m-1112	1543	97	and	and	CCONJ
m-1112	1543	98	their	their	PRON
m-1112	1543	99	negative	negative	ADJ
m-1112	1543	100	energy	energy	NOUN
m-1112	1543	101	binder	binder	NOUN
m-1112	1543	102	field	field	NOUN
m-1112	1543	103	[	[	PUNCT
m-1112	1543	104	i	i	NOUN
m-1112	1543	105	]	]	X
m-1112	1543	106	→	→	PUNCT
m-1112	1543	107	as	as	ADP
m-1112	1543	108	±	±	NOUN
m-1112	1543	109	positions	position	NOUN
m-1112	1543	110	,	,	PUNCT
m-1112	1543	111	for	for	ADP
m-1112	1543	112	�	�	NOUN
m-1112	1543	113	̅	̅	NOUN
m-1112	1543	114	�	�	NOUN
m-1112	1543	115	=	=	SYM
m-1112	1543	116	±	±	NUM
m-1112	1543	117	�	�	PROPN
m-1112	1543	118	̅	̅	NOUN
m-1112	1543	119	�	�	PROPN
m-1112	1543	120	,	,	PUNCT
m-1112	1543	121	then	then	ADV
m-1112	1543	122	+	+	CCONJ
m-1112	1543	123	�	�	NOUN
m-1112	1543	124	̅	̅	NOUN
m-1112	1543	125	�	�	NOUN
m-1112	1543	126	=	=	SYM
m-1112	1543	127	+	+	NUM
m-1112	1543	128	gravity	gravity	NOUN
m-1112	1543	129	–	–	PUNCT
m-1112	1543	130	spin	spin	NOUN
m-1112	1543	131	=	=	SYM
m-1112	1544	1	+	+	NUM
m-1112	1544	2	𝛑.𝐫𝟑𝛔.𝚽	𝛑.𝐫𝟑𝛔.𝚽	X
m-1112	1544	3	𝟐	𝟐	NUM
m-1112	1544	4			NOUN
m-1112	1544	5	the	the	DET
m-1112	1544	6	gravity	gravity	NOUN
m-1112	1544	7	spin	spin	NOUN
m-1112	1544	8	�	�	NOUN
m-1112	1544	9	̅	̅	NOUN
m-1112	1544	10	�	�	NOUN
m-1112	1544	11	=	=	SYM
m-1112	1544	12	gravity	gravity	NOUN
m-1112	1544	13	–	–	PUNCT
m-1112	1544	14	spin	spin	NOUN
m-1112	1544	15	=	=	SYM
m-1112	1544	16	𝛑𝐫𝟑𝛔.𝚽	𝛑𝐫𝟑𝛔.𝚽	X
m-1112	1544	17	𝟐	𝟐	NUM
m-1112	1544	18			NOUN
m-1112	1544	19	the	the	DET
m-1112	1544	20	antigravity	antigravity	NOUN
m-1112	1544	21	spin	spin	VERB
m-1112	1544	22	c	c	PROPN
m-1112	1544	23	→	→	PUNCT
m-1112	1544	24	the	the	DET
m-1112	1544	25	dark	dark	ADJ
m-1112	1544	26	-	-	PUNCT
m-1112	1544	27	matter	matter	NOUN
m-1112	1544	28	and	and	CCONJ
m-1112	1544	29	the	the	DET
m-1112	1544	30	dark	dark	ADJ
m-1112	1544	31	-	-	PUNCT
m-1112	1544	32	energy	energy	NOUN
m-1112	1544	33	constituents	constituent	NOUN
m-1112	1544	34	are	be	AUX
m-1112	1544	35	as	as	ADP
m-1112	1544	36	below	below	ADV
m-1112	1544	37	,	,	PUNCT
m-1112	1544	38	[	[	PUNCT
m-1112	1544	39	±c̅.s²	±c̅.s²	X
m-1112	1544	40	]	]	X
m-1112	1544	41	→	→	PUNCT
m-1112	1544	42	the	the	DET
m-1112	1544	43	dark	dark	ADJ
m-1112	1544	44	-	-	PUNCT
m-1112	1544	45	matter	matter	NOUN
m-1112	1544	46	,	,	PUNCT
m-1112	1544	47	and	and	CCONJ
m-1112	1544	48	the	the	DET
m-1112	1544	49	binder	binder	NOUN
m-1112	1544	50	gravity	gravity	NOUN
m-1112	1544	51	-	-	PUNCT
m-1112	1544	52	force	force	NOUN
m-1112	1544	53	g̅	g̅	PROPN
m-1112	1544	54	≡	≡	PROPN
m-1112	1545	1	[	[	PUNCT
m-1112	1545	2	i	i	X
m-1112	1545	3	]	]	PUNCT
m-1112	1545	4	,	,	PUNCT
m-1112	1545	5	[	[	PUNCT
m-1112	1545	6	c̅.	c̅.	X
m-1112	1545	7	i	i	PRON
m-1112	1545	8	]	]	PUNCT
m-1112	1545	9	→	→	PUNCT
m-1112	1545	10	the	the	DET
m-1112	1545	11	expanding	expand	VERB
m-1112	1545	12	dark	dark	ADJ
m-1112	1545	13	-energy	-energy	NOUN
m-1112	1545	14	,	,	PUNCT
m-1112	1545	15	positive	positive	ADJ
m-1112	1545	16	-	-	PUNCT
m-1112	1545	17	energy	energy	NOUN
m-1112	1545	18	,	,	PUNCT
m-1112	1545	19	which	which	PRON
m-1112	1545	20	both	both	PRON
m-1112	1545	21	are	be	AUX
m-1112	1545	22	moving	move	VERB
m-1112	1545	23	with	with	ADP
m-1112	1545	24	light	light	ADJ
m-1112	1545	25	velocity	velocity	NOUN
m-1112	1545	26	,	,	PUNCT
m-1112	1545	27	c̅	c̅	PROPN
m-1112	1545	28	,	,	PUNCT
m-1112	1545	29	causing	cause	VERB
m-1112	1545	30	the	the	DET
m-1112	1545	31	universe	universe	NOUN
m-1112	1545	32	to	to	PART
m-1112	1545	33	grow	grow	VERB
m-1112	1545	34	.	.	PUNCT
m-1112	1546	1	from	from	ADP
m-1112	1546	2	above	above	ADP
m-1112	1546	3	in	in	ADP
m-1112	1546	4	,	,	PUNCT
m-1112	1546	5	a	a	PRON
m-1112	1546	6	,	,	PUNCT
m-1112	1546	7	and	and	CCONJ
m-1112	1546	8	,	,	PUNCT
m-1112	1546	9	c	c	X
m-1112	1546	10	,	,	PUNCT
m-1112	1546	11	case	case	NOUN
m-1112	1546	12	→	→	SYM
m-1112	1546	13	energy	energy	NOUN
m-1112	1546	14	as	as	ADP
m-1112	1546	15	velocity	velocity	NOUN
m-1112	1546	16	,	,	PUNCT
m-1112	1546	17	v̅	v̅	PROPN
m-1112	1546	18	,	,	PUNCT
m-1112	1546	19	and	and	CCONJ
m-1112	1546	20	,	,	PUNCT
m-1112	1546	21	c̅	c̅	PROPN
m-1112	1546	22	,	,	PUNCT
m-1112	1546	23	exists	exist	VERB
m-1112	1546	24	in	in	ADP
m-1112	1546	25	the	the	DET
m-1112	1546	26	discrete	discrete	ADJ
m-1112	1546	27	monads	monad	NOUN
m-1112	1546	28	,	,	PUNCT
m-1112	1546	29	±	±	NUM
m-1112	1546	30	v̅.s²	v̅.s²	PROPN
m-1112	1546	31	,	,	PUNCT
m-1112	1546	32	and	and	CCONJ
m-1112	1546	33	,	,	PUNCT
m-1112	1546	34	±	±	NOUN
m-1112	1546	35	c̅.s²	c̅.s²	PROPN
m-1112	1546	36	only	only	ADV
m-1112	1546	37	.	.	PUNCT
m-1112	1547	1	2	2	NUM
m-1112	1547	2	,	,	PUNCT
m-1112	1547	3	the	the	DET
m-1112	1547	4	case	case	NOUN
m-1112	1547	5	of	of	ADP
m-1112	1547	6	transportation	transportation	NOUN
m-1112	1547	7	of	of	ADP
m-1112	1547	8	energy	energy	NOUN
m-1112	1547	9	,	,	PUNCT
m-1112	1547	10	from	from	ADP
m-1112	1547	11	chaos	chaos	NOUN
m-1112	1547	12	to	to	ADP
m-1112	1547	13	stationary	stationary	ADJ
m-1112	1547	14	-	-	PUNCT
m-1112	1547	15	material	material	NOUN
m-1112	1547	16	-	-	PUNCT
m-1112	1547	17	points	point	NOUN
m-1112	1547	18	.	.	PUNCT
m-1112	1548	1	dark	dark	ADJ
m-1112	1548	2	energy	energy	PROPN
m-1112	1548	3	de	de	X
m-1112	1548	4	≡	≡	PROPN
m-1112	1548	5	[	[	PUNCT
m-1112	1548	6	�	�	PROPN
m-1112	1548	7	̅	̅	NOUN
m-1112	1548	8	�	�	PROPN
m-1112	1548	9	.	.	PUNCT
m-1112	1549	1	i	i	PRON
m-1112	1549	2	]	]	X
m-1112	1549	3	(	(	PUNCT
m-1112	1549	4	©	©	PROPN
m-1112	1549	5	)	)	PUNCT
m-1112	1549	6	,	,	PUNCT
m-1112	1549	7	acting	act	VERB
m-1112	1549	8			NOUN
m-1112	1549	9	positive	positive	ADJ
m-1112	1549	10	-	-	PUNCT
m-1112	1549	11	energy	energy	NOUN
m-1112	1549	12	,	,	PUNCT
m-1112	1549	13	on	on	ADP
m-1112	1549	14	the	the	DET
m-1112	1549	15	five	five	NUM
m-1112	1549	16	constituents	constituent	NOUN
m-1112	1549	17	{	{	PUNCT
m-1112	1549	18	[	[	PUNCT
m-1112	1549	19	(	(	PUNCT
m-1112	1549	20	i	i	NOUN
m-1112	1549	21	)	)	PUNCT
m-1112	1549	22	,	,	PUNCT
m-1112	1549	23	(	(	PUNCT
m-1112	1549	24	+	+	NOUN
m-1112	1549	25	s²	s²	NOUN
m-1112	1549	26	)	)	PUNCT
m-1112	1549	27	,	,	PUNCT
m-1112	1549	28	(	(	PUNCT
m-1112	1549	29	-s²	-s²	INTJ
m-1112	1549	30	)	)	PUNCT
m-1112	1549	31	,	,	PUNCT
m-1112	1549	32	(	(	PUNCT
m-1112	1549	33	+	+	NOUN
m-1112	1549	34	cs²	cs²	NOUN
m-1112	1549	35	)	)	PUNCT
m-1112	1549	36	,	,	PUNCT
m-1112	1549	37	(	(	PUNCT
m-1112	1549	38	-cs²	-cs²	X
m-1112	1549	39	)	)	PUNCT
m-1112	1549	40	]	]	PUNCT
m-1112	1549	41	}	}	PUNCT
m-1112	1549	42	then	then	ADV
m-1112	1549	43	produces	produce	VERB
m-1112	1549	44	,	,	PUNCT
m-1112	1549	45	[	[	PUNCT
m-1112	1549	46	±	±	NOUN
m-1112	1549	47	s²	s²	NOUN
m-1112	1549	48	]	]	PUNCT
m-1112	1549	49	→	→	PUNCT
m-1112	1549	50	the	the	DET
m-1112	1549	51	[	[	X
m-1112	1549	52	mfmf	mfmf	NOUN
m-1112	1549	53	]	]	X
m-1112	1549	54	field	field	NOUN
m-1112	1549	55	[	[	PUNCT
m-1112	1549	56	±	±	X
m-1112	1549	57	c̅.s²	c̅.s²	PROPN
m-1112	1549	58	]	]	PUNCT
m-1112	1549	59	→	→	PUNCT
m-1112	1549	60	dm	dm	NOUN
m-1112	1549	61	-	-	PUNCT
m-1112	1549	62	de	de	NOUN
m-1112	1549	63	field	field	NOUN
m-1112	1549	64	of	of	ADP
m-1112	1549	65	,	,	PUNCT
m-1112	1549	66	dm	dm	PROPN
m-1112	1549	67	=	=	PUNCT
m-1112	1549	68	dark	dark	ADJ
m-1112	1549	69	matter	matter	NOUN
m-1112	1549	70	,	,	PUNCT
m-1112	1549	71	and	and	CCONJ
m-1112	1549	72	df	df	PROPN
m-1112	1549	73	=	=	ADJ
m-1112	1549	74	anti	anti	ADJ
m-1112	1549	75	matter	matter	NOUN
m-1112	1549	76	=	=	SYM
m-1112	1549	77	dark	dark	ADJ
m-1112	1549	78	energy	energy	NOUN
m-1112	1549	79	.	.	PUNCT
m-1112	1550	1	[	[	PUNCT
m-1112	1550	2	±v̅.s²	±v̅.s²	X
m-1112	1550	3	]	]	PUNCT
m-1112	1550	4	→	→	PUNCT
m-1112	1550	5	the	the	DET
m-1112	1550	6	pns	pns	PROPN
m-1112	1550	7	space	space	NOUN
m-1112	1550	8	,	,	PUNCT
m-1112	1550	9	particles	particle	NOUN
m-1112	1550	10	fermions	fermion	NOUN
m-1112	1550	11	,	,	PUNCT
m-1112	1550	12	and	and	CCONJ
m-1112	1550	13	[	[	PUNCT
m-1112	1550	14	i	i	X
m-1112	1550	15	]	]	X
m-1112	1550	16	→	→	PUNCT
m-1112	1550	17	gf	gf	PROPN
m-1112	1550	18	≡	≡	PROPN
m-1112	1550	19	gravity	gravity	NOUN
m-1112	1550	20	-	-	PUNCT
m-1112	1550	21	force	force	NOUN
m-1112	1550	22	in	in	ADP
m-1112	1550	23	dm	dm	PROPN
m-1112	1550	24	-	-	PUNCT
m-1112	1550	25	de	de	X
m-1112	1550	26	stationary	stationary	ADJ
m-1112	1550	27	rotating	rotate	VERB
m-1112	1550	28	=	=	NOUN
m-1112	1550	29	field	field	NOUN
m-1112	1550	30	.	.	PUNCT
m-1112	1551	1	[	[	PUNCT
m-1112	1551	2	v̅.	v̅.	NOUN
m-1112	1551	3	i	i	PRON
m-1112	1551	4	]	]	PUNCT
m-1112	1551	5	→	→	PUNCT
m-1112	1551	6	the	the	DET
m-1112	1551	7	bosons	boson	NOUN
m-1112	1551	8	,	,	PUNCT
m-1112	1551	9	[	[	PUNCT
m-1112	1551	10	c̅.	c̅.	X
m-1112	1551	11	i	i	PRON
m-1112	1551	12	]	]	PUNCT
m-1112	1551	13	≡	≡	PROPN
m-1112	1551	14	the	the	DET
m-1112	1551	15	de	de	PROPN
m-1112	1551	16	→	→	SYM
m-1112	1551	17	dark	dark	ADJ
m-1112	1551	18	energy	energy	NOUN
m-1112	1551	19	→	→	PUNCT
m-1112	1551	20	the	the	DET
m-1112	1551	21	travelling	travel	VERB
m-1112	1551	22	-	-	PUNCT
m-1112	1551	23	energy	energy	NOUN
m-1112	1551	24	with	with	ADP
m-1112	1551	25	,	,	PUNCT
m-1112	1551	26	�	�	PROPN
m-1112	1551	27	̅	̅	NOUN
m-1112	1551	28	�	�	PROPN
m-1112	1551	29	,	,	PUNCT
m-1112	1551	30	velocity	velocity	NOUN
m-1112	1551	31	.	.	PUNCT
m-1112	1552	1	𝐜	𝐜	NOUN
m-1112	1552	2	x	x	SYM
m-1112	1552	3	(	(	PUNCT
m-1112	1552	4	©	©	NOUN
m-1112	1552	5	)	)	PUNCT
m-1112	1552	6	[	[	PUNCT
m-1112	1552	7	i	i	PRON
m-1112	1552	8	]	]	PUNCT
m-1112	1552	9	≡	≡	PROPN
m-1112	1552	10	gf	gf	PROPN
m-1112	1552	11	→	→	PUNCT
m-1112	1552	12	the	the	DET
m-1112	1552	13	gravity	gravity	NOUN
m-1112	1552	14	force	force	NOUN
m-1112	1552	15	.	.	PUNCT
m-1112	1553	1	ijo	ijo	PROPN
m-1112	1553	2	international	international	PROPN
m-1112	1553	3	journal	journal	PROPN
m-1112	1553	4	of	of	ADP
m-1112	1553	5	mathematics	mathematics	PROPN
m-1112	1553	6	(	(	PUNCT
m-1112	1553	7	issn	issn	PROPN
m-1112	1553	8	:	:	PUNCT
m-1112	1553	9	2992	2992	NUM
m-1112	1553	10	-	-	SYM
m-1112	1553	11	4421	4421	NUM
m-1112	1553	12	)	)	PUNCT
m-1112	1553	13	volume	volume	NOUN
m-1112	1553	14	08	08	NUM
m-1112	1554	1	|	|	ADV
m-1112	1554	2	issue	issue	NOUN
m-1112	1554	3	08	08	NUM
m-1112	1555	1	|	|	ADV
m-1112	1555	2	august	august	PROPN
m-1112	1555	3	2025	2025	NUM
m-1112	1555	4	|	|	ADV
m-1112	1555	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1555	6	ijo	ijo	PROPN
m-1112	1555	7	journals	journal	NOUN
m-1112	1555	8	56	56	NUM
m-1112	1555	9	the	the	DET
m-1112	1555	10	fundamental	fundamental	ADJ
m-1112	1555	11	particles	particle	NOUN
m-1112	1555	12	origination	origination	NOUN
m-1112	1555	13	mechanism	mechanism	NOUN
m-1112	1555	14	in	in	ADP
m-1112	1555	15	mfmf	mfmf	PROPN
m-1112	1555	16	pns	pns	PROPN
m-1112	1555	17	caves	cave	NOUN
m-1112	1555	18	.	.	PUNCT
m-1112	1556	1	in	in	ADP
m-1112	1556	2	all	all	PRON
m-1112	1556	3	above	above	ADP
m-1112	1556	4	issue	issue	NOUN
m-1112	1556	5	kepler	kepler	NOUN
m-1112	1556	6	laws	law	NOUN
m-1112	1556	7	,	,	PUNCT
m-1112	1556	8	denoting	denote	VERB
m-1112	1556	9	that	that	DET
m-1112	1556	10	macrocosm	macrocosm	PROPN
m-1112	1556	11	and	and	CCONJ
m-1112	1556	12	microcosm	microcosm	PROPN
m-1112	1556	13	obey	obey	VERB
m-1112	1556	14	the	the	DET
m-1112	1556	15	newton`s	newton`s	NOUN
m-1112	1556	16	laws	law	NOUN
m-1112	1556	17	of	of	ADP
m-1112	1556	18	motion	motion	NOUN
m-1112	1556	19	,	,	PUNCT
m-1112	1556	20	in	in	ADP
m-1112	1556	21	all	all	DET
m-1112	1556	22	scales	scale	NOUN
m-1112	1556	23	,	,	PUNCT
m-1112	1556	24	as	as	SCONJ
m-1112	1556	25	was	be	AUX
m-1112	1556	26	proofed	proof	VERB
m-1112	1556	27	.	.	PUNCT
m-1112	1557	1	figure	figure	VERB
m-1112	1557	2	13	13	NUM
m-1112	1557	3	vector	vector	NOUN
m-1112	1557	4	-	-	PUNCT
m-1112	1557	5	geometry	geometry	NOUN
m-1112	1557	6	follows	follow	VERB
m-1112	1557	7	the	the	DET
m-1112	1557	8	geometry	geometry	NOUN
m-1112	1557	9	rules	rule	NOUN
m-1112	1557	10	as	as	ADP
m-1112	1557	11	the	the	DET
m-1112	1557	12	left	left	ADJ
m-1112	1557	13	figure	figure	NOUN
m-1112	1557	14	.	.	PUNCT
m-1112	1558	1	euclideanvector	euclideanvector	NOUN
m-1112	1558	2	carry	carry	VERB
m-1112	1558	3	point	point	NOUN
m-1112	1558	4	a	a	PRON
m-1112	1558	5	to	to	PART
m-1112	1558	6	point	point	VERB
m-1112	1558	7	b	b	PROPN
m-1112	1558	8	as	as	ADP
m-1112	1558	9	,	,	PUNCT
m-1112	1558	10	ab	ab	PROPN
m-1112	1558	11	,	,	PUNCT
m-1112	1558	12	following	follow	VERB
m-1112	1558	13	the	the	DET
m-1112	1558	14	geometry	geometry	NOUN
m-1112	1558	15	rules	rule	NOUN
m-1112	1558	16	,	,	PUNCT
m-1112	1558	17	while	while	SCONJ
m-1112	1558	18	the	the	DET
m-1112	1558	19	material	material	NOUN
m-1112	1558	20	–	–	PUNCT
m-1112	1558	21	points	point	NOUN
m-1112	1558	22	≡	≡	PROPN
m-1112	1558	23	quaternions	quaternion	NOUN
m-1112	1558	24	,	,	PUNCT
m-1112	1558	25	carry	carry	VERB
m-1112	1558	26	the	the	DET
m-1112	1558	27	motion	motion	NOUN
m-1112	1558	28	≡	≡	PROPN
m-1112	1558	29	energy	energy	NOUN
m-1112	1558	30	,	,	PUNCT
m-1112	1558	31	from	from	ADP
m-1112	1558	32	point	point	NOUN
m-1112	1558	33	a	a	PRON
m-1112	1558	34	,	,	PUNCT
m-1112	1558	35	to	to	ADP
m-1112	1558	36	the	the	DET
m-1112	1558	37	point	point	NOUN
m-1112	1558	38	,	,	PUNCT
m-1112	1558	39	b	b	NOUN
m-1112	1558	40	,	,	PUNCT
m-1112	1558	41	linearly	linearly	ADV
m-1112	1558	42	.	.	PUNCT
m-1112	1559	1	in	in	ADP
m-1112	1559	2	both	both	DET
m-1112	1559	3	cases	case	NOUN
m-1112	1559	4	the	the	DET
m-1112	1559	5	points	point	NOUN
m-1112	1559	6	are	be	AUX
m-1112	1559	7	nothing	nothing	PRON
m-1112	1559	8	possessing	possess	VERB
m-1112	1559	9	zero	zero	NUM
m-1112	1559	10	-	-	PUNCT
m-1112	1559	11	magnitude	magnitude	NOUN
m-1112	1559	12	and	and	CCONJ
m-1112	1559	13	infinite	infinite	ADJ
m-1112	1559	14	directions	direction	NOUN
m-1112	1559	15	.	.	PUNCT
m-1112	1560	1	the	the	DET
m-1112	1560	2	two	two	NUM
m-1112	1560	3	points	point	NOUN
m-1112	1560	4	in	in	ADP
m-1112	1560	5	e	e	NOUN
m-1112	1560	6	-	-	NOUN
m-1112	1560	7	geometry	geometry	NOUN
m-1112	1560	8	consist	consist	VERB
m-1112	1560	9	the	the	DET
m-1112	1560	10	straight	straight	ADJ
m-1112	1560	11	-	-	PUNCT
m-1112	1560	12	line	line	NOUN
m-1112	1560	13	-	-	PUNCT
m-1112	1560	14	segment	segment	NOUN
m-1112	1560	15	possessing	possess	VERB
m-1112	1560	16	|ab|	|ab|	NOUN
m-1112	1560	17	magnitude	magnitude	NOUN
m-1112	1560	18	and	and	CCONJ
m-1112	1560	19	the	the	DET
m-1112	1560	20	|a→b|	|a→b|	PROPN
m-1112	1560	21	directions	direction	NOUN
m-1112	1560	22	while	while	SCONJ
m-1112	1560	23	the	the	DET
m-1112	1560	24	two	two	NUM
m-1112	1560	25	-	-	PUNCT
m-1112	1560	26	points	point	NOUN
m-1112	1560	27	in	in	ADP
m-1112	1560	28	material	material	NOUN
m-1112	1560	29	-	-	PUNCT
m-1112	1560	30	geometry	geometry	NOUN
m-1112	1560	31	denote	denote	NOUN
m-1112	1560	32	two	two	NUM
m-1112	1560	33	-	-	PUNCT
m-1112	1560	34	elements	element	NOUN
m-1112	1560	35	as	as	ADP
m-1112	1560	36	one	one	NUM
m-1112	1560	37	(	(	PUNCT
m-1112	1560	38	+	+	NOUN
m-1112	1560	39	)	)	PUNCT
m-1112	1560	40	and	and	CCONJ
m-1112	1560	41	one	one	NUM
m-1112	1560	42	(	(	PUNCT
m-1112	1560	43	-	-	PUNCT
m-1112	1560	44	)	)	PUNCT
m-1112	1560	45	performing	perform	VERB
m-1112	1560	46	the	the	DET
m-1112	1560	47	space	space	NOUN
m-1112	1560	48	≡	≡	PROPN
m-1112	1560	49	|ab|	|ab|	NOUN
m-1112	1560	50	of	of	ADP
m-1112	1560	51	motion	motion	NOUN
m-1112	1560	52	=	=	SYM
m-1112	1560	53	energy	energy	NOUN
m-1112	1560	54	≡	≡	PROPN
m-1112	1561	1	[	[	X
m-1112	1561	2	a	a	DET
m-1112	1561	3	↔	↔	PROPN
m-1112	1561	4	b	b	NOUN
m-1112	1561	5	]	]	X
m-1112	1561	6	in	in	ADP
m-1112	1561	7	|ab|	|ab|	NUM
m-1112	1561	8	space	space	NOUN
m-1112	1561	9	.the	.the	NOUN
m-1112	1561	10	above	above	ADP
m-1112	1561	11	comparison	comparison	NOUN
m-1112	1561	12	can	can	AUX
m-1112	1561	13	bee	bee	NOUN
m-1112	1561	14	seen	see	VERB
m-1112	1561	15	in	in	ADP
m-1112	1561	16	figure-1also	figure-1also	ADV
m-1112	1561	17	.	.	PUNCT
m-1112	1562	1	conclusions	conclusion	NOUN
m-1112	1562	2	–	–	PUNCT
m-1112	1562	3	3	3	NUM
m-1112	1562	4	:	:	PUNCT
m-1112	1562	5	from	from	ADP
m-1112	1562	6	above	above	ADP
m-1112	1562	7	analysis	analysis	NOUN
m-1112	1562	8	is	be	AUX
m-1112	1562	9	seen	see	VERB
m-1112	1562	10	the	the	DET
m-1112	1562	11	path	path	NOUN
m-1112	1562	12	which	which	DET
m-1112	1562	13	energy	energy	NOUN
m-1112	1562	14	as	as	ADP
m-1112	1562	15	motion	motion	NOUN
m-1112	1562	16	follows	follow	VERB
m-1112	1562	17	to	to	PART
m-1112	1562	18	propagate	propagate	VERB
m-1112	1562	19	.	.	PUNCT
m-1112	1563	1	this	this	DET
m-1112	1563	2	path	path	NOUN
m-1112	1563	3	is	be	AUX
m-1112	1563	4	the	the	DET
m-1112	1563	5	resultant	resultant	NOUN
m-1112	1563	6	of	of	ADP
m-1112	1563	7	the	the	DET
m-1112	1563	8	vector	vector	NOUN
m-1112	1563	9	-	-	NOUN
m-1112	1563	10	sum	sum	NOUN
m-1112	1563	11	,	,	PUNCT
m-1112	1563	12	or	or	CCONJ
m-1112	1563	13	the	the	DET
m-1112	1563	14	quaternion	quaternion	NOUN
m-1112	1563	15	as	as	ADP
m-1112	1563	16	material	material	NOUN
m-1112	1563	17	–	–	PUNCT
m-1112	1563	18	point	point	NOUN
m-1112	1563	19	.	.	PUNCT
m-1112	1564	1	the	the	DET
m-1112	1564	2	vector	vector	NOUN
m-1112	1564	3	-	-	PUNCT
m-1112	1564	4	sum	sum	NOUN
m-1112	1564	5	-	-	PUNCT
m-1112	1564	6	length	length	NOUN
m-1112	1564	7	as	as	ADP
m-1112	1564	8	a	a	DET
m-1112	1564	9	geometrical	geometrical	ADJ
m-1112	1564	10	-	-	PUNCT
m-1112	1564	11	resultant	resultant	NOUN
m-1112	1564	12	-	-	PUNCT
m-1112	1564	13	vector	vector	NOUN
m-1112	1564	14	is	be	AUX
m-1112	1564	15	the	the	DET
m-1112	1564	16	quaternion`s	quaternion`s	NOUN
m-1112	1564	17	edge	edge	NOUN
m-1112	1564	18	points	point	NOUN
m-1112	1564	19	energy	energy	NOUN
m-1112	1564	20	-	-	PUNCT
m-1112	1564	21	vibration	vibration	NOUN
m-1112	1564	22	which	which	PRON
m-1112	1564	23	transfers	transfer	VERB
m-1112	1564	24	the	the	DET
m-1112	1564	25	motion	motion	NOUN
m-1112	1564	26	from	from	ADP
m-1112	1564	27	the	the	DET
m-1112	1564	28	vibrating	vibrating	NOUN
m-1112	1564	29	-	-	PUNCT
m-1112	1564	30	edge	edge	NOUN
m-1112	1564	31	-	-	PUNCT
m-1112	1564	32	points	point	NOUN
m-1112	1564	33	.	.	PUNCT
m-1112	1565	1	thus	thus	ADV
m-1112	1565	2	stress	stress	NOUN
m-1112	1565	3	→	→	SYM
m-1112	1565	4	σ	σ	NOUN
m-1112	1565	5	=	=	PUNCT
m-1112	1566	1	[	[	PUNCT
m-1112	1566	2	2πr	2πr	NOUN
m-1112	1566	3	φ	φ	X
m-1112	1566	4	²	²	NUM
m-1112	1566	5	]	]	PUNCT
m-1112	1566	6	.	.	PUNCT
m-1112	1567	1	f	f	PROPN
m-1112	1567	2	n	n	PRON
m-1112	1567	3	←	←	PROPN
m-1112	1567	4	is	be	AUX
m-1112	1567	5	the	the	DET
m-1112	1567	6	way	way	NOUN
m-1112	1567	7	of	of	ADP
m-1112	1567	8	information	information	NOUN
m-1112	1567	9	and	and	CCONJ
m-1112	1567	10	storage	storage	NOUN
m-1112	1567	11	in	in	ADP
m-1112	1567	12	nature	nature	NOUN
m-1112	1567	13	.	.	PUNCT
m-1112	1568	1	extending	extend	VERB
m-1112	1568	2	above	above	ADV
m-1112	1568	3	to	to	ADP
m-1112	1568	4	all	all	DET
m-1112	1568	5	planetary	planetary	ADJ
m-1112	1568	6	systems	system	NOUN
m-1112	1568	7	and	and	CCONJ
m-1112	1568	8	to	to	PART
m-1112	1568	9	universe	universe	NOUN
m-1112	1568	10	is	be	AUX
m-1112	1568	11	seen	see	VERB
m-1112	1568	12	that	that	SCONJ
m-1112	1568	13	big	big	ADJ
m-1112	1568	14	bang	bang	NOUN
m-1112	1568	15	.	.	PUNCT
m-1112	1569	1	has	have	AUX
m-1112	1569	2	never	never	ADV
m-1112	1569	3	been	be	AUX
m-1112	1569	4	existed	exist	VERB
m-1112	1569	5	,	,	PUNCT
m-1112	1569	6	inversely	inversely	ADV
m-1112	1569	7	energy	energy	NOUN
m-1112	1569	8	≡	≡	PROPN
m-1112	1569	9	motion	motion	NOUN
m-1112	1569	10	≡	≡	PROPN
m-1112	1569	11	matter	matter	NOUN
m-1112	1569	12	followed	follow	VERB
m-1112	1569	13	the	the	DET
m-1112	1569	14	(	(	PUNCT
m-1112	1569	15	+	+	NOUN
m-1112	1569	16	)	)	PUNCT
m-1112	1569	17	stress	stress	NOUN
m-1112	1569	18	-	-	PUNCT
m-1112	1569	19	storage	storage	NOUN
m-1112	1569	20	,	,	PUNCT
m-1112	1569	21	±	±	NUM
m-1112	1569	22	σ	σ	NOUN
m-1112	1569	23	=	=	PUNCT
m-1112	1570	1	[	[	PUNCT
m-1112	1570	2	2πr	2πr	NOUN
m-1112	1570	3	φ	φ	X
m-1112	1570	4	²	²	NUM
m-1112	1570	5	]	]	PUNCT
m-1112	1570	6	.	.	PUNCT
m-1112	1571	1	f	f	PROPN
m-1112	1571	2	n	n	CCONJ
m-1112	1571	3	,	,	PUNCT
m-1112	1571	4	and	and	CCONJ
m-1112	1571	5	anti	anti	ADJ
m-1112	1571	6	-	-	ADJ
m-1112	1571	7	matter	matter	NOUN
m-1112	1571	8	followed	follow	VERB
m-1112	1571	9	the	the	DET
m-1112	1571	10	(	(	PUNCT
m-1112	1571	11	-	-	PUNCT
m-1112	1571	12	)	)	PUNCT
m-1112	1571	13	stress	stress	NOUN
m-1112	1571	14	-	-	PUNCT
m-1112	1571	15	storage	storage	NOUN
m-1112	1571	16	and	and	CCONJ
m-1112	1571	17	material	material	NOUN
m-1112	1571	18	-	-	PUNCT
m-1112	1571	19	geometry	geometry	NOUN
m-1112	1571	20	.	.	PUNCT
m-1112	1572	1	2.b	2.b	NUM
m-1112	1572	2	.	.	PUNCT
m-1112	1573	1	the	the	DET
m-1112	1573	2	complex	complex	ADJ
m-1112	1573	3	numbers	number	NOUN
m-1112	1573	4	&	&	CCONJ
m-1112	1573	5	quaternion	quaternion	NOUN
m-1112	1573	6	.	.	PUNCT
m-1112	1574	1	1	1	NUM
m-1112	1574	2	…	…	PUNCT
m-1112	1574	3	de	de	X
m-1112	1574	4	moivre´s	moivre´s	PROPN
m-1112	1574	5	formula	formula	NOUN
m-1112	1574	6	for	for	ADP
m-1112	1574	7	complex	complex	ADJ
m-1112	1574	8	numbers	number	NOUN
m-1112	1574	9	states	state	VERB
m-1112	1574	10	that	that	SCONJ
m-1112	1574	11	the	the	DET
m-1112	1574	12	multiplication	multiplication	NOUN
m-1112	1574	13	of	of	ADP
m-1112	1574	14	any	any	DET
m-1112	1574	15	two	two	NUM
m-1112	1574	16	complex	complex	ADJ
m-1112	1574	17	numbers	number	NOUN
m-1112	1574	18	say	say	VERB
m-1112	1574	19	z1	z1	NOUN
m-1112	1574	20	,	,	PUNCT
m-1112	1574	21	z2	z2	PROPN
m-1112	1574	22	,	,	PUNCT
m-1112	1574	23	or	or	CCONJ
m-1112	1575	1	[	[	X
m-1112	1575	2	z1	z1	X
m-1112	1575	3	=	=	SYM
m-1112	1575	4	x1	x1	PROPN
m-1112	1575	5	+	+	NUM
m-1112	1575	6	i.	i.	PROPN
m-1112	1575	7	y1	y1	PROPN
m-1112	1575	8	,	,	PUNCT
m-1112	1575	9	z2	z2	PROPN
m-1112	1575	10	=	=	SYM
m-1112	1575	11	x2	x2	PROPN
m-1112	1576	1	+	+	NUM
m-1112	1576	2	i.	i.	PROPN
m-1112	1576	3	y2	y2	PROPN
m-1112	1576	4	]	]	PUNCT
m-1112	1577	1	where	where	SCONJ
m-1112	1577	2	x	x	X
m-1112	1577	3	=	=	PUNCT
m-1112	1577	4	real	real	ADJ
m-1112	1577	5	[	[	X
m-1112	1577	6	z	z	X
m-1112	1577	7	]	]	X
m-1112	1577	8	ijo	ijo	PROPN
m-1112	1577	9	international	international	PROPN
m-1112	1577	10	journal	journal	PROPN
m-1112	1577	11	of	of	ADP
m-1112	1577	12	mathematics	mathematics	PROPN
m-1112	1577	13	(	(	PUNCT
m-1112	1577	14	issn	issn	PROPN
m-1112	1577	15	:	:	PUNCT
m-1112	1577	16	2992	2992	NUM
m-1112	1577	17	-	-	SYM
m-1112	1577	18	4421	4421	NUM
m-1112	1577	19	)	)	PUNCT
m-1112	1577	20	volume	volume	NOUN
m-1112	1577	21	08	08	NUM
m-1112	1578	1	|	|	ADV
m-1112	1578	2	issue	issue	NOUN
m-1112	1578	3	08	08	NUM
m-1112	1579	1	|	|	ADV
m-1112	1579	2	august	august	PROPN
m-1112	1579	3	2025	2025	NUM
m-1112	1579	4	|	|	ADV
m-1112	1579	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1579	6	ijo	ijo	PROPN
m-1112	1579	7	journals	journal	NOUN
m-1112	1579	8	57	57	NUM
m-1112	1579	9	the	the	DET
m-1112	1579	10	fundamental	fundamental	ADJ
m-1112	1579	11	particles	particle	NOUN
m-1112	1579	12	origination	origination	NOUN
m-1112	1579	13	mechanism	mechanism	NOUN
m-1112	1579	14	in	in	ADP
m-1112	1579	15	mfmf	mfmf	PROPN
m-1112	1579	16	pns	pns	PROPN
m-1112	1579	17	caves	cave	NOUN
m-1112	1579	18	.	.	PUNCT
m-1112	1580	1	the	the	DET
m-1112	1580	2	real	real	ADJ
m-1112	1580	3	-	-	PUNCT
m-1112	1580	4	part	part	NOUN
m-1112	1580	5	and	and	CCONJ
m-1112	1580	6	y	y	NOUN
m-1112	1580	7	=	=	PUNCT
m-1112	1580	8	imaginary[z	imaginary[z	PROPN
m-1112	1580	9	]	]	PUNCT
m-1112	1580	10	.	.	PUNCT
m-1112	1581	1	the	the	DET
m-1112	1581	2	imaginary	imaginary	ADJ
m-1112	1581	3	part	part	NOUN
m-1112	1581	4	of	of	ADP
m-1112	1581	5	,	,	PUNCT
m-1112	1581	6	z	z	PROPN
m-1112	1581	7	,	,	PUNCT
m-1112	1581	8	is	be	AUX
m-1112	1581	9	the	the	DET
m-1112	1581	10	multiplication	multiplication	NOUN
m-1112	1581	11	of	of	ADP
m-1112	1581	12	their	their	PRON
m-1112	1581	13	moduli	moduli	NOUN
m-1112	1581	14	r1	r1	NOUN
m-1112	1581	15	,	,	PUNCT
m-1112	1581	16	r2	r2	PROPN
m-1112	1581	17	,	,	PUNCT
m-1112	1581	18	where	where	SCONJ
m-1112	1581	19	the	the	DET
m-1112	1581	20	moduli	modulus	NOUN
m-1112	1581	21	,	,	PUNCT
m-1112	1581	22	r	r	NOUN
m-1112	1581	23	,	,	PUNCT
m-1112	1581	24	is	be	AUX
m-1112	1581	25	the	the	DET
m-1112	1581	26	magnitude	magnitude	NOUN
m-1112	1581	27	[	[	PUNCT
m-1112	1581	28	r	r	NOUN
m-1112	1581	29	=	=	NOUN
m-1112	1581	30	|	|	ADV
m-1112	1581	31	r	r	NOUN
m-1112	1581	32	|	|	NOUN
m-1112	1581	33	=	=	SYM
m-1112	1581	34	√x²	√x²	PROPN
m-1112	1582	1	+	+	CCONJ
m-1112	1582	2	y²	y²	NOUN
m-1112	1582	3	]	]	PUNCT
m-1112	1582	4	and	and	CCONJ
m-1112	1582	5	the	the	DET
m-1112	1582	6	addition	addition	NOUN
m-1112	1582	7	of	of	ADP
m-1112	1582	8	their	their	PRON
m-1112	1582	9	angles	angle	NOUN
m-1112	1582	10	,	,	PUNCT
m-1112	1582	11	φ1	φ1	NOUN
m-1112	1582	12	,	,	PUNCT
m-1112	1582	13	φ2	φ2	PROPN
m-1112	1582	14	,	,	PUNCT
m-1112	1582	15	where	where	SCONJ
m-1112	1582	16	φ	φ	PROPN
m-1112	1582	17	=	=	SYM
m-1112	1582	18	arg.(z	arg.(z	PROPN
m-1112	1582	19	)	)	PUNCT
m-1112	1582	20	=	=	PUNCT
m-1112	1583	1	atan2.(y	atan2.(y	NOUN
m-1112	1583	2	,	,	PUNCT
m-1112	1583	3	x	x	X
m-1112	1583	4	)	)	PUNCT
m-1112	1583	5	and	and	CCONJ
m-1112	1583	6	so	so	ADV
m-1112	1583	7	,	,	PUNCT
m-1112	1583	8	z1	z1	PROPN
m-1112	1583	9	*	*	PUNCT
m-1112	1583	10	z2	z2	PROPN
m-1112	1583	11	=	=	SYM
m-1112	1583	12	(	(	PUNCT
m-1112	1583	13	x1	x1	PROPN
m-1112	1583	14	+	+	NUM
m-1112	1583	15	i.	i.	PROPN
m-1112	1583	16	y1	y1	PROPN
m-1112	1583	17	)	)	PUNCT
m-1112	1583	18	.	.	PUNCT
m-1112	1584	1	(	(	PUNCT
m-1112	1584	2	x2	x2	NOUN
m-1112	1584	3	+	+	NUM
m-1112	1584	4	i.	i.	PROPN
m-1112	1584	5	y2	y2	PROPN
m-1112	1584	6	)	)	PUNCT
m-1112	1584	7	=	=	SYM
m-1112	1585	1	r1	r1	PROPN
m-1112	1585	2	.	.	PUNCT
m-1112	1586	1	r2	r2	PROPN
m-1112	1587	1	[	[	X
m-1112	1587	2	cos(φ1	cos(φ1	PROPN
m-1112	1587	3	+	+	SYM
m-1112	1587	4	φ2	φ2	PROPN
m-1112	1587	5	)	)	PUNCT
m-1112	1588	1	+	+	CCONJ
m-1112	1588	2	i	i	PRON
m-1112	1588	3	.	.	PUNCT
m-1112	1589	1	sin(φ1	sin(φ1	PROPN
m-1112	1589	2	+	+	PROPN
m-1112	1589	3	φ2	φ2	PROPN
m-1112	1589	4	)	)	PUNCT
m-1112	1589	5	and	and	CCONJ
m-1112	1589	6	when	when	SCONJ
m-1112	1589	7	z1	z1	ADJ
m-1112	1589	8	=	=	SYM
m-1112	1589	9	z2	z2	PROPN
m-1112	1589	10	=	=	SYM
m-1112	1589	11	z	z	PROPN
m-1112	1589	12	,	,	PUNCT
m-1112	1589	13	and	and	CCONJ
m-1112	1589	14	φ1	φ1	PROPN
m-1112	1589	15	=	=	SYM
m-1112	1589	16	φ2	φ2	PROPN
m-1112	1589	17	=	=	PROPN
m-1112	1589	18	φ	φ	PROPN
m-1112	1589	19	,	,	PUNCT
m-1112	1589	20	then	then	ADV
m-1112	1589	21	z	z	NOUN
m-1112	1589	22	=	=	PUNCT
m-1112	1590	1	x	x	PUNCT
m-1112	1591	1	+	+	CCONJ
m-1112	1591	2	i	i	PRON
m-1112	1591	3	y	y	PROPN
m-1112	1591	4	and	and	CCONJ
m-1112	1591	5	z	z	NOUN
m-1112	1591	6	.	.	PUNCT
m-1112	1592	1	z	z	NOUN
m-1112	1592	2	=	=	PUNCT
m-1112	1592	3	z²	z²	NOUN
m-1112	1592	4	=	=	SYM
m-1112	1592	5	r².[cos2φ+i.sin2φ	r².[cos2φ+i.sin2φ	NOUN
m-1112	1592	6	)	)	PUNCT
m-1112	1592	7	and	and	CCONJ
m-1112	1592	8	for	for	ADP
m-1112	1592	9	,	,	PUNCT
m-1112	1592	10	w	w	NOUN
m-1112	1592	11	,	,	PUNCT
m-1112	1592	12	complex	complex	ADJ
m-1112	1592	13	numbers	number	NOUN
m-1112	1592	14	becomes	become	VERB
m-1112	1592	15	the	the	DET
m-1112	1592	16	euler`s	euler`s	PROPN
m-1112	1592	17	,	,	PUNCT
m-1112	1592	18	zw	zw	PROPN
m-1112	1592	19	=	=	PUNCT
m-1112	1592	20	rw	rw	PROPN
m-1112	1592	21	.	.	PUNCT
m-1112	1593	1	[	[	PUNCT
m-1112	1593	2	cos(wφ	cos(wφ	PROPN
m-1112	1593	3	)	)	PUNCT
m-1112	1593	4	+	+	CCONJ
m-1112	1593	5	i.	i.	NOUN
m-1112	1593	6	sin(wφ	sin(wφ	NOUN
m-1112	1593	7	)	)	PUNCT
m-1112	1593	8	]	]	PUNCT
m-1112	1593	9	and	and	CCONJ
m-1112	1593	10	so	so	ADV
m-1112	1593	11	for	for	ADP
m-1112	1593	12	r	r	NOUN
m-1112	1593	13	=	=	SYM
m-1112	1593	14	1	1	NUM
m-1112	1593	15	then	then	ADV
m-1112	1593	16	→	→	SYM
m-1112	1593	17	zw	zw	PROPN
m-1112	1593	18	=	=	PUNCT
m-1112	1593	19	1w	1w	NUM
m-1112	1593	20	.	.	PUNCT
m-1112	1594	1	[	[	PUNCT
m-1112	1594	2	cos	cos	X
m-1112	1594	3	φ+i	φ+i	PROPN
m-1112	1594	4	.	.	PUNCT
m-1112	1594	5	sin	sin	PROPN
m-1112	1594	6	φ	φ	X
m-1112	1594	7	]	]	X
m-1112	1594	8	w	w	PROPN
m-1112	1594	9	=	=	PUNCT
m-1112	1594	10	[	[	PUNCT
m-1112	1594	11	cos.(wφ	cos.(wφ	PROPN
m-1112	1594	12	)	)	PUNCT
m-1112	1594	13	+	+	CCONJ
m-1112	1594	14	i	i	PROPN
m-1112	1594	15	sin.(wφ	sin.(wφ	NOUN
m-1112	1594	16	)	)	PUNCT
m-1112	1594	17	]	]	PUNCT
m-1112	1594	18	.	.	PUNCT
m-1112	1595	1	the	the	DET
m-1112	1595	2	n.th	n.th	PROPN
m-1112	1595	3	root	root	NOUN
m-1112	1595	4	of	of	ADP
m-1112	1595	5	any	any	DET
m-1112	1595	6	number	number	NOUN
m-1112	1595	7	z	z	NOUN
m-1112	1595	8	,	,	PUNCT
m-1112	1595	9	is	be	AUX
m-1112	1595	10	a	a	DET
m-1112	1595	11	number	number	NOUN
m-1112	1595	12	b	b	NOUN
m-1112	1595	13	[	[	PUNCT
m-1112	1595	14	√z	√z	X
m-1112	1595	15	n	n	PROPN
m-1112	1595	16	=	=	SYM
m-1112	1595	17	b	b	NOUN
m-1112	1595	18	]	]	X
m-1112	1595	19	such	such	ADJ
m-1112	1595	20	that	that	DET
m-1112	1595	21	bn	bn	NOUN
m-1112	1595	22	=	=	SYM
m-1112	1595	23	z	z	NOUN
m-1112	1596	1	and	and	CCONJ
m-1112	1596	2	when	when	SCONJ
m-1112	1596	3	z	z	NOUN
m-1112	1596	4	is	be	AUX
m-1112	1596	5	a	a	DET
m-1112	1596	6	point	point	NOUN
m-1112	1596	7	on	on	ADP
m-1112	1596	8	the	the	DET
m-1112	1596	9	unit	unit	NOUN
m-1112	1596	10	circle	circle	NOUN
m-1112	1596	11	r	r	NOUN
m-1112	1596	12	=	=	NOUN
m-1112	1596	13	1	1	NUM
m-1112	1596	14	,	,	PUNCT
m-1112	1596	15	the	the	DET
m-1112	1596	16	first	first	ADJ
m-1112	1596	17	vertex	vertex	NOUN
m-1112	1596	18	of	of	ADP
m-1112	1596	19	the	the	DET
m-1112	1596	20	polygon	polygon	NOUN
m-1112	1596	21	where	where	SCONJ
m-1112	1596	22	φ	φ	PROPN
m-1112	1596	23	=	=	SYM
m-1112	1596	24	0	0	PROPN
m-1112	1596	25	is	be	AUX
m-1112	1596	26	[	[	PUNCT
m-1112	1596	27	b	b	NOUN
m-1112	1596	28	=	=	PUNCT
m-1112	1596	29	(	(	PUNCT
m-1112	1596	30	cosφ	cosφ	NOUN
m-1112	1596	31	+	+	CCONJ
m-1112	1596	32	i	i	PRON
m-1112	1596	33	sinφ	sinφ	VERB
m-1112	1596	34	)	)	PUNCT
m-1112	1596	35	]	]	PUNCT
m-1112	1597	1	ⁿ	ⁿ	PROPN
m-1112	1597	2	=	=	SYM
m-1112	1597	3	b	b	PROPN
m-1112	1597	4	ⁿ	ⁿ	X
m-1112	1597	5	=	=	SYM
m-1112	1597	6	z	z	NOUN
m-1112	1597	7	=	=	SYM
m-1112	1597	8	cos(nφ	cos(nφ	NOUN
m-1112	1597	9	)	)	PUNCT
m-1112	1598	1	+	+	CCONJ
m-1112	1598	2	i	i	PRON
m-1112	1598	3	.sin(nφ)=	.sin(nφ)=	PUNCT
m-1112	1599	1	[	[	X
m-1112	1599	2	cos(360	cos(360	PROPN
m-1112	1599	3	/	/	SYM
m-1112	1599	4	n	n	CCONJ
m-1112	1599	5	)	)	PUNCT
m-1112	1599	6	+	+	CCONJ
m-1112	1599	7	i.	i.	PROPN
m-1112	1599	8	sin(360	sin(360	PROPN
m-1112	1599	9	/	/	SYM
m-1112	1599	10	n	n	CCONJ
m-1112	1599	11	)	)	PUNCT
m-1112	1599	12	]	]	PUNCT
m-1112	1600	1	ⁿ	ⁿ	PROPN
m-1112	1600	2	=	=	SYM
m-1112	1600	3	cos	cos	ADP
m-1112	1600	4	360	360	NUM
m-1112	1600	5	+	+	CCONJ
m-1112	1600	6	i.sin360	i.sin360	ADJ
m-1112	1600	7	=	=	SYM
m-1112	1600	8	1	1	NUM
m-1112	1600	9	+	+	NUM
m-1112	1600	10	0.i	0.i	NUM
m-1112	1600	11	=	=	NOUN
m-1112	1600	12	1	1	NUM
m-1112	1600	13	i.e.	i.e.	X
m-1112	1600	14	the	the	DET
m-1112	1600	15	w	w	NOUN
m-1112	1600	16	-	-	PUNCT
m-1112	1600	17	spaces	space	NOUN
m-1112	1600	18	which	which	PRON
m-1112	1600	19	are	be	AUX
m-1112	1600	20	the	the	DET
m-1112	1600	21	repetition	repetition	NOUN
m-1112	1600	22	of	of	ADP
m-1112	1600	23	any	any	DET
m-1112	1600	24	unit	unit	NOUN
m-1112	1600	25	complex	complex	ADJ
m-1112	1600	26	number	number	NOUN
m-1112	1600	27	z	z	NOUN
m-1112	1600	28	(	(	PUNCT
m-1112	1600	29	multiplication	multiplication	NOUN
m-1112	1600	30	by	by	ADP
m-1112	1600	31	itself	itself	PRON
m-1112	1600	32	)	)	PUNCT
m-1112	1600	33	is	be	AUX
m-1112	1600	34	equivalent	equivalent	ADJ
m-1112	1600	35	to	to	ADP
m-1112	1600	36	the	the	DET
m-1112	1600	37	addition	addition	NOUN
m-1112	1600	38	of	of	ADP
m-1112	1600	39	their	their	PRON
m-1112	1600	40	angle	angle	NOUN
m-1112	1600	41	and	and	CCONJ
m-1112	1600	42	the	the	DET
m-1112	1600	43	mapping	mapping	NOUN
m-1112	1600	44	of	of	ADP
m-1112	1600	45	the	the	DET
m-1112	1600	46	regular	regular	ADJ
m-1112	1600	47	polygons	polygon	NOUN
m-1112	1600	48	on	on	ADP
m-1112	1600	49	circles	circle	NOUN
m-1112	1600	50	with	with	ADP
m-1112	1600	51	unit	unit	NOUN
m-1112	1600	52	sides	side	NOUN
m-1112	1600	53	,	,	PUNCT
m-1112	1600	54	while	while	SCONJ
m-1112	1600	55	the	the	DET
m-1112	1600	56	n	n	PRON
m-1112	1600	57	spaces	space	NOUN
m-1112	1600	58	which	which	PRON
m-1112	1600	59	are	be	AUX
m-1112	1600	60	the	the	DET
m-1112	1600	61	different	different	ADJ
m-1112	1600	62	roots	root	NOUN
m-1112	1600	63	of	of	ADP
m-1112	1600	64	unit	unit	NOUN
m-1112	1600	65	1	1	NUM
m-1112	1600	66	and	and	CCONJ
m-1112	1600	67	are	be	AUX
m-1112	1600	68	represented	represent	VERB
m-1112	1600	69	by	by	ADP
m-1112	1600	70	the	the	DET
m-1112	1600	71	unit	unit	NOUN
m-1112	1600	72	circle	circle	NOUN
m-1112	1600	73	and	and	CCONJ
m-1112	1600	74	have	have	VERB
m-1112	1600	75	points	point	NOUN
m-1112	1600	76	z	z	NOUN
m-1112	1600	77	=	=	SYM
m-1112	1600	78	1	1	NUM
m-1112	1600	79	as	as	ADP
m-1112	1600	80	one	one	NUM
m-1112	1600	81	of	of	ADP
m-1112	1600	82	their	their	PRON
m-1112	1600	83	vertices	vertex	NOUN
m-1112	1600	84	,	,	PUNCT
m-1112	1600	85	are	be	AUX
m-1112	1600	86	mapped	map	VERB
m-1112	1600	87	as	as	SCONJ
m-1112	1600	88	these	these	DET
m-1112	1600	89	regular	regular	ADJ
m-1112	1600	90	polygons	polygon	NOUN
m-1112	1600	91	inscribed	inscribe	VERB
m-1112	1600	92	the	the	DET
m-1112	1600	93	unit	unit	NOUN
m-1112	1600	94	circle	circle	NOUN
m-1112	1600	95	,	,	PUNCT
m-1112	1600	96	figure-1(1	figure-1(1	NOUN
m-1112	1600	97	)	)	PUNCT
m-1112	1600	98	since	since	SCONJ
m-1112	1600	99	also	also	ADV
m-1112	1600	100	𝐳𝐰	𝐳𝐰	PROPN
m-1112	1600	101	=	=	SYM
m-1112	1600	102	𝐳−	𝐳−	PROPN
m-1112	1600	103	𝐧	𝐧	PROPN
m-1112	1600	104	and	and	CCONJ
m-1112	1600	105	𝐳−	𝐳−	PROPN
m-1112	1601	1	𝐧	𝐧	NOUN
m-1112	1601	2	=	=	PUNCT
m-1112	1601	3	𝐳−𝟏/	𝐳−𝟏/	PROPN
m-1112	1601	4	𝐧	𝐧	PROPN
m-1112	1601	5	=	=	SYM
m-1112	1601	6	𝐳+	𝐳+	PROPN
m-1112	1601	7	𝐧	𝐧	INTJ
m-1112	1601	8	therefore	therefore	ADV
m-1112	1601	9	complex	complex	ADJ
m-1112	1601	10	numbers	number	NOUN
m-1112	1601	11	are	be	AUX
m-1112	1601	12	even	even	ADV
m-1112	1601	13	and	and	CCONJ
m-1112	1601	14	odd	odd	ADJ
m-1112	1601	15	functions	function	NOUN
m-1112	1601	16	,	,	PUNCT
m-1112	1601	17	i.e.	i.e.	X
m-1112	1601	18	are	be	AUX
m-1112	1601	19	symmetrical	symmetrical	ADJ
m-1112	1601	20	about	about	ADP
m-1112	1601	21	y	y	PROPN
m-1112	1601	22	,	,	PUNCT
m-1112	1601	23	axis	axis	NOUN
m-1112	1601	24	(	(	PUNCT
m-1112	1601	25	mirror	mirror	NOUN
m-1112	1601	26	)	)	PUNCT
m-1112	1601	27	and	and	CCONJ
m-1112	1601	28	also	also	ADV
m-1112	1601	29	about	about	ADP
m-1112	1601	30	the	the	DET
m-1112	1601	31	origin	origin	NOUN
m-1112	1601	32	.	.	PUNCT
m-1112	1602	1	euler`s	euler`s	PROPN
m-1112	1602	2	rotation	rotation	PROPN
m-1112	1602	3	in	in	ADP
m-1112	1602	4	3d	3d	PROPN
m-1112	1602	5	space	space	NOUN
m-1112	1602	6	is	be	AUX
m-1112	1602	7	represented	represent	VERB
m-1112	1602	8	by	by	ADP
m-1112	1602	9	an	an	DET
m-1112	1602	10	axis	axis	NOUN
m-1112	1602	11	(	(	PUNCT
m-1112	1602	12	vector	vector	NOUN
m-1112	1602	13	)	)	PUNCT
m-1112	1602	14	and	and	CCONJ
m-1112	1602	15	an	an	DET
m-1112	1602	16	angle	angle	NOUN
m-1112	1602	17	of	of	ADP
m-1112	1602	18	rotation	rotation	NOUN
m-1112	1602	19	which	which	PRON
m-1112	1602	20	is	be	AUX
m-1112	1602	21	a	a	DET
m-1112	1602	22	property	property	NOUN
m-1112	1602	23	of	of	ADP
m-1112	1602	24	complex	complex	ADJ
m-1112	1602	25	number	number	NOUN
m-1112	1602	26	and	and	CCONJ
m-1112	1602	27	defined	define	VERB
m-1112	1602	28	as	as	ADP
m-1112	1602	29	�	�	NOUN
m-1112	1602	30	̅	̅	NOUN
m-1112	1602	31	�	�	NOUN
m-1112	1602	32	=	=	PUNCT
m-1112	1602	33	[	[	PUNCT
m-1112	1602	34	s	s	NOUN
m-1112	1602	35	±	±	NUM
m-1112	1602	36	�	�	PROPN
m-1112	1602	37	̅	̅	NOUN
m-1112	1602	38	�	�	NOUN
m-1112	1602	39	.i	.i	NOUN
m-1112	1602	40	]	]	PUNCT
m-1112	1602	41	where	where	SCONJ
m-1112	1602	42	s	s	X
m-1112	1602	43	,	,	PUNCT
m-1112	1602	44	�	�	PROPN
m-1112	1602	45	̅	̅	NOUN
m-1112	1602	46	�	�	NOUN
m-1112	1602	47	are	be	AUX
m-1112	1602	48	real	real	ADJ
m-1112	1602	49	numbers	number	NOUN
m-1112	1602	50	and	and	CCONJ
m-1112	1602	51	i	i	PRON
m-1112	1602	52	the	the	DET
m-1112	1602	53	imaginary	imaginary	ADJ
m-1112	1602	54	part	part	NOUN
m-1112	1602	55	such	such	ADJ
m-1112	1602	56	that	that	SCONJ
m-1112	1602	57	i	i	PRON
m-1112	1602	58	²	²	NUM
m-1112	1602	59	=	=	SYM
m-1112	1602	60	1	1	NUM
m-1112	1602	61	.	.	PUNCT
m-1112	1603	1	extending	extend	VERB
m-1112	1603	2	imaginary	imaginary	ADJ
m-1112	1603	3	part	part	NOUN
m-1112	1603	4	to	to	ADP
m-1112	1603	5	three	three	NUM
m-1112	1603	6	dimensions	dimension	NOUN
m-1112	1603	7	,	,	PUNCT
m-1112	1603	8	𝐯𝟏	𝐯𝟏	PROPN
m-1112	1603	9	,	,	PUNCT
m-1112	1603	10	i	i	PRON
m-1112	1603	11	,	,	PUNCT
m-1112	1603	12	𝐯𝟐	𝐯𝟐	PROPN
m-1112	1603	13	,	,	PUNCT
m-1112	1603	14	j	j	PROPN
m-1112	1603	15	,	,	PUNCT
m-1112	1603	16	𝐯𝟑	𝐯𝟑	PROPN
m-1112	1603	17	,	,	PUNCT
m-1112	1603	18	k	k	PROPN
m-1112	1603	19	→	→	SYM
m-1112	1603	20	�	�	PROPN
m-1112	1603	21	̅	̅	NOUN
m-1112	1603	22	�	�	NOUN
m-1112	1603	23	.	.	PUNCT
m-1112	1604	1	i	i	PRON
m-1112	1604	2	becomes	become	VERB
m-1112	1604	3	quaternion	quaternion	NOUN
m-1112	1604	4	which	which	PRON
m-1112	1604	5	has	have	VERB
m-1112	1604	6	1	1	NUM
m-1112	1604	7	+	+	SYM
m-1112	1604	8	3	3	NUM
m-1112	1604	9	=	=	SYM
m-1112	1604	10	4	4	NUM
m-1112	1604	11	degrees	degree	NOUN
m-1112	1604	12	of	of	ADP
m-1112	1604	13	freedom	freedom	NOUN
m-1112	1604	14	i.e.	i.e.	X
m-1112	1604	15	[	[	PUNCT
m-1112	1604	16	dx	dx	X
m-1112	1604	17	–	–	PUNCT
m-1112	1604	18	dy	dy	X
m-1112	1604	19	–	–	PUNCT
m-1112	1604	20	dz	dz	PROPN
m-1112	1604	21	–	–	PUNCT
m-1112	1604	22	df	df	NOUN
m-1112	1604	23	]	]	PUNCT
m-1112	1604	24	≡	≡	PROPN
m-1112	1604	25	the	the	DET
m-1112	1604	26	space	space	NOUN
m-1112	1604	27	energymode	energymode	NOUN
m-1112	1604	28	.	.	PUNCT
m-1112	1605	1	2	2	X
m-1112	1605	2	…	…	PUNCT
m-1112	1605	3	de	de	X
m-1112	1605	4	moivre´s	moivre´s	NOUN
m-1112	1605	5	formula	formula	NOUN
m-1112	1605	6	for	for	ADP
m-1112	1605	7	the	the	DET
m-1112	1605	8	n	n	ADV
m-1112	1605	9	-	-	PUNCT
m-1112	1605	10	th	th	VERB
m-1112	1605	11	roots	root	NOUN
m-1112	1605	12	of	of	ADP
m-1112	1605	13	quaternion	quaternion	NOUN
m-1112	1605	14	,	,	PUNCT
m-1112	1605	15	where	where	SCONJ
m-1112	1605	16	q	q	PROPN
m-1112	1605	17	=	=	SYM
m-1112	1605	18	k.	k.	PROPN
m-1112	1605	19	[	[	PUNCT
m-1112	1605	20	cos.φ+	cos.φ+	X
m-1112	1605	21	[	[	PUNCT
m-1112	1605	22	i].sin.φ	i].sin.φ	PROPN
m-1112	1605	23	]	]	X
m-1112	1605	24	is	be	AUX
m-1112	1605	25	for	for	ADP
m-1112	1605	26	w	w	NOUN
m-1112	1605	27	=	=	SYM
m-1112	1605	28	1	1	NUM
m-1112	1605	29	/	/	SYM
m-1112	1605	30	n	n	NOUN
m-1112	1605	31	,	,	PUNCT
m-1112	1605	32	𝐪𝐰	𝐪𝐰	NOUN
m-1112	1605	33	=	=	SYM
m-1112	1605	34	𝐤𝐰.	𝐤𝐰.	NUM
m-1112	1605	35	cos.wφ	cos.wφ	PROPN
m-1112	1605	36	+	+	CCONJ
m-1112	1605	37	ε	ε	PROPN
m-1112	1605	38	.	.	PUNCT
m-1112	1606	1	sin.wφ	sin.wφ	NOUN
m-1112	1606	2	]	]	PUNCT
m-1112	1606	3	where	where	SCONJ
m-1112	1606	4	,	,	PUNCT
m-1112	1606	5	q	q	X
m-1112	1606	6	=	=	PUNCT
m-1112	1606	7	z	z	NOUN
m-1112	1606	8	=	=	SYM
m-1112	1606	9	±	±	NOUN
m-1112	1606	10	(	(	PUNCT
m-1112	1606	11	x+y.i	x+y.i	PROPN
m-1112	1606	12	)	)	PUNCT
m-1112	1606	13	decomposed	decompose	VERB
m-1112	1606	14	into	into	ADP
m-1112	1606	15	its	its	PRON
m-1112	1606	16	scalar	scalar	ADJ
m-1112	1606	17	(	(	PUNCT
m-1112	1606	18	x	x	NOUN
m-1112	1606	19	)	)	PUNCT
m-1112	1606	20	and	and	CCONJ
m-1112	1606	21	vector	vector	NOUN
m-1112	1606	22	part	part	NOUN
m-1112	1606	23	[	[	X
m-1112	1606	24	y.i	y.i	X
m-1112	1606	25	]	]	X
m-1112	1606	26	and	and	CCONJ
m-1112	1606	27	this	this	PRON
m-1112	1606	28	because	because	SCONJ
m-1112	1606	29	all	all	DET
m-1112	1606	30	the	the	DET
m-1112	1606	31	inscribed	inscribe	VERB
m-1112	1606	32	regular	regular	ADJ
m-1112	1606	33	polygons	polygon	NOUN
m-1112	1606	34	in	in	ADP
m-1112	1606	35	the	the	DET
m-1112	1606	36	unit	unit	NOUN
m-1112	1606	37	circle	circle	NOUN
m-1112	1606	38	have	have	VERB
m-1112	1606	39	this	this	DET
m-1112	1606	40	first	first	ADJ
m-1112	1606	41	vertex	vertex	NOUN
m-1112	1606	42	at	at	ADP
m-1112	1606	43	points	point	NOUN
m-1112	1606	44	,	,	PUNCT
m-1112	1606	45	1	1	NUM
m-1112	1606	46	,	,	PUNCT
m-1112	1606	47	or	or	CCONJ
m-1112	1606	48	at	at	ADP
m-1112	1606	49	,	,	PUNCT
m-1112	1606	50	1	1	NUM
m-1112	1606	51	,	,	PUNCT
m-1112	1606	52	(	(	PUNCT
m-1112	1606	53	for	for	ADP
m-1112	1606	54	real	real	ADJ
m-1112	1606	55	part	part	NOUN
m-1112	1606	56	φ	φ	NOUN
m-1112	1606	57	=	=	SYM
m-1112	1606	58	0	0	PROPN
m-1112	1606	59	,	,	PUNCT
m-1112	1606	60	φ	φ	NOUN
m-1112	1606	61	=	=	SYM
m-1112	1606	62	2π	2π	PROPN
m-1112	1606	63	)	)	PUNCT
m-1112	1606	64	and	and	CCONJ
m-1112	1606	65	all	all	DET
m-1112	1606	66	others	other	NOUN
m-1112	1606	67	at	at	ADP
m-1112	1606	68	imaginary	imaginary	ADJ
m-1112	1606	69	part	part	NOUN
m-1112	1606	70	where	where	SCONJ
m-1112	1606	71	,	,	PUNCT
m-1112	1606	72	k	k	PROPN
m-1112	1606	73	=	=	PUNCT
m-1112	1606	74	𝐓	𝐓	PROPN
m-1112	1606	75	𝐳	𝐳	NOUN
m-1112	1606	76	=	=	X
m-1112	1606	77	tensor	tensor	NOUN
m-1112	1606	78	(	(	PUNCT
m-1112	1606	79	the	the	DET
m-1112	1606	80	length	length	NOUN
m-1112	1606	81	)	)	PUNCT
m-1112	1606	82	of	of	ADP
m-1112	1606	83	vector	vector	NOUN
m-1112	1606	84	,	,	PUNCT
m-1112	1606	85	z	z	X
m-1112	1606	86	,	,	PUNCT
m-1112	1606	87	in	in	ADP
m-1112	1606	88	euclidean	euclidean	ADJ
m-1112	1606	89	coordinates	coordinate	NOUN
m-1112	1606	90	which	which	PRON
m-1112	1606	91	is	be	AUX
m-1112	1606	92	k	k	PROPN
m-1112	1606	93	=	=	SYM
m-1112	1606	94	𝐓	𝐓	PROPN
m-1112	1606	95	𝐳=√𝐱	𝐳=√𝐱	PROPN
m-1112	1606	96	²	²	PROPN
m-1112	1607	1	+	+	CCONJ
m-1112	1607	2	𝐲²𝟏	𝐲²𝟏	NOUN
m-1112	1607	3	+	+	CCONJ
m-1112	1607	4	𝐲²𝟐	𝐲²𝟐	NOUN
m-1112	1607	5	+	+	CCONJ
m-1112	1607	6	𝐲²𝐧	𝐲²𝐧	PROPN
m-1112	1607	7	and	and	CCONJ
m-1112	1607	8	for	for	ADP
m-1112	1607	9	imaginary	imaginary	ADJ
m-1112	1607	10	unit	unit	NOUN
m-1112	1607	11	vector	vector	NOUN
m-1112	1607	12	�	�	PROPN
m-1112	1607	13	̅	̅	NOUN
m-1112	1607	14	�	�	PROPN
m-1112	1607	15	(	(	PUNCT
m-1112	1607	16	𝐚𝟏	𝐚𝟏	PROPN
m-1112	1607	17	,	,	PUNCT
m-1112	1607	18	𝐚𝟐	𝐚𝟐	NOUN
m-1112	1607	19	,	,	PUNCT
m-1112	1607	20	𝐚𝟑	𝐚𝟑	PROPN
m-1112	1607	21	,	,	PUNCT
m-1112	1607	22	𝐚𝐧,w	𝐚𝐧,w	NOUN
m-1112	1607	23	)	)	PUNCT
m-1112	1607	24	the	the	DET
m-1112	1607	25	unit	unit	NOUN
m-1112	1607	26	vector	vector	NOUN
m-1112	1607	27	,	,	PUNCT
m-1112	1607	28	ε	ε	PROPN
m-1112	1607	29	,	,	PUNCT
m-1112	1607	30	of	of	ADP
m-1112	1607	31	imaginary	imaginary	ADJ
m-1112	1607	32	part	part	NOUN
m-1112	1607	33	is	be	AUX
m-1112	1607	34	→	→	SYM
m-1112	1607	35	ε	ε	PROPN
m-1112	1607	36	=	=	PUNCT
m-1112	1607	37	(	(	PUNCT
m-1112	1607	38	y.i	y.i	PROPN
m-1112	1607	39	/	/	SYM
m-1112	1607	40	𝐓𝐲	𝐓𝐲	PROPN
m-1112	1607	41	)	)	PUNCT
m-1112	1607	42	=	=	PUNCT
m-1112	1608	1	[	[	X
m-1112	1608	2	y.	y.	NOUN
m-1112	1608	3	i	i	X
m-1112	1608	4	]	]	PUNCT
m-1112	1608	5	/	/	PUNCT
m-1112	1609	1	[	[	X
m-1112	1609	2	𝐓𝐲	𝐓𝐲	NOUN
m-1112	1609	3	]	]	X
m-1112	1609	4	=	=	SYM
m-1112	1609	5	±	±	PROPN
m-1112	1609	6	(	(	PUNCT
m-1112	1609	7	𝐲𝟏	𝐲𝟏	PROPN
m-1112	1609	8	.	.	PUNCT
m-1112	1609	9	𝐚𝟏+	𝐚𝟏+	PUNCT
m-1112	1610	1	𝐲𝟐	𝐲𝟐	NOUN
m-1112	1610	2	.	.	PUNCT
m-1112	1611	1	𝐚𝟐	𝐚𝟐	NOUN
m-1112	1611	2	)	)	PUNCT
m-1112	1611	3	/	/	SYM
m-1112	1612	1	√	√	NUM
m-1112	1612	2	𝐲²𝟏	𝐲²𝟏	NOUN
m-1112	1612	3	+	+	CCONJ
m-1112	1612	4	𝐲²𝟐	𝐲²𝟐	NOUN
m-1112	1612	5	+	+	CCONJ
m-1112	1612	6	𝐲²𝐧	𝐲²𝐧	NOUN
m-1112	1612	7	,	,	PUNCT
m-1112	1612	8	the	the	DET
m-1112	1612	9	rotation	rotation	NOUN
m-1112	1612	10	angle	angle	NOUN
m-1112	1612	11	0	0	PUNCT
m-1112	1612	12	<	<	X
m-1112	1612	13	=	=	X
m-1112	1612	14	φ	φ	X
m-1112	1612	15	<	<	X
m-1112	1612	16	2π	2π	PROPN
m-1112	1612	17	,	,	PUNCT
m-1112	1612	18	φ	φ	PROPN
m-1112	1612	19	=	=	SYM
m-1112	1612	20	±	±	NUM
m-1112	1612	21	sin	sin	NOUN
m-1112	1612	22	1	1	NUM
m-1112	1612	23	(	(	PUNCT
m-1112	1612	24	𝐓𝐲	𝐓𝐲	PROPN
m-1112	1612	25	/	/	SYM
m-1112	1612	26	𝐓𝐳	𝐓𝐳	PROPN
m-1112	1612	27	)	)	PUNCT
m-1112	1612	28	,	,	PUNCT
m-1112	1612	29	cosφ	cosφ	NOUN
m-1112	1613	1	=	=	SYM
m-1112	1613	2	x	x	PUNCT
m-1112	1613	3	/	/	SYM
m-1112	1613	4	𝐓	𝐓	PROPN
m-1112	1613	5	𝐳	𝐳	NOUN
m-1112	1613	6	,	,	PUNCT
m-1112	1613	7	which	which	PRON
m-1112	1613	8	follow	follow	VERB
m-1112	1613	9	pythagoras	pythagoras	PROPN
m-1112	1613	10	theorem	theorem	VERB
m-1112	1613	11	for	for	ADP
m-1112	1613	12	them	they	PRON
m-1112	1613	13	and	and	CCONJ
m-1112	1613	14	for	for	ADP
m-1112	1613	15	their	their	PRON
m-1112	1613	16	reciprocal	reciprocal	ADJ
m-1112	1613	17	quaternions	quaternion	NOUN
m-1112	1613	18	�	�	PROPN
m-1112	1613	19	̅	̅	NOUN
m-1112	1613	20	�	�	NOUN
m-1112	1613	21	`	`	PUNCT
m-1112	1613	22	[	[	X
m-1112	1613	23	�	�	NOUN
m-1112	1613	24	̅	̅	NOUN
m-1112	1613	25	�	�	PROPN
m-1112	1613	26	.	.	PUNCT
m-1112	1614	1	�	�	PROPN
m-1112	1614	2	̅	̅	NOUN
m-1112	1614	3	�	�	NOUN
m-1112	1614	4	`	`	PUNCT
m-1112	1614	5	=	=	NOUN
m-1112	1614	6	1	1	NUM
m-1112	1614	7	]	]	PUNCT
m-1112	1614	8	.	.	PUNCT
m-1112	1615	1	since	since	SCONJ
m-1112	1615	2	also	also	ADV
m-1112	1615	3	the	the	DET
m-1112	1615	4	directional	directional	ADJ
m-1112	1615	5	derivative	derivative	NOUN
m-1112	1615	6	of	of	ADP
m-1112	1615	7	the	the	DET
m-1112	1615	8	scalar	scalar	ADJ
m-1112	1615	9	field	field	NOUN
m-1112	1615	10	relation	relation	NOUN
m-1112	1615	11	y.	y.	PROPN
m-1112	1615	12	(	(	PUNCT
m-1112	1615	13	𝐲𝟏	𝐲𝟏	PROPN
m-1112	1615	14	,	,	PUNCT
m-1112	1615	15	𝐲𝟐	𝐲𝟐	PROPN
m-1112	1615	16	,	,	PUNCT
m-1112	1615	17	…	…	PUNCT
m-1112	1615	18	.	.	PUNCT
m-1112	1615	19	𝐲𝐧	𝐲𝐧	INTJ
m-1112	1615	20	,	,	PUNCT
m-1112	1615	21	,	,	PUNCT
m-1112	1615	22	,	,	PUNCT
m-1112	1615	23	)	)	PUNCT
m-1112	1615	24	in	in	ADP
m-1112	1615	25	the	the	DET
m-1112	1615	26	direction	direction	NOUN
m-1112	1615	27	,	,	PUNCT
m-1112	1615	28	i	i	PRON
m-1112	1615	29	,	,	PUNCT
m-1112	1615	30	is	be	AUX
m-1112	1615	31	→	→	PUNCT
m-1112	1615	32	i	i	PROPN
m-1112	1615	33	(	(	PUNCT
m-1112	1615	34	𝐲𝟏	𝐲𝟏	PROPN
m-1112	1615	35	,	,	PUNCT
m-1112	1615	36	𝐲𝟐	𝐲𝟐	PROPN
m-1112	1615	37	…	…	PUNCT
m-1112	1615	38	.	.	PUNCT
m-1112	1616	1	𝐲𝐧	𝐲𝐧	X
m-1112	1616	2	)	)	PUNCT
m-1112	1617	1	=	=	SYM
m-1112	1617	2	𝐢	𝐢	PROPN
m-1112	1617	3	𝟏.	𝟏.	X
m-1112	1617	4	𝐲𝟏	𝐲𝟏	PROPN
m-1112	1618	1	+	+	CCONJ
m-1112	1619	1	𝐢	𝐢	PROPN
m-1112	1619	2	𝟐.	𝟐.	X
m-1112	1619	3	𝐲𝟐	𝐲𝟐	NOUN
m-1112	1619	4	+	+	CCONJ
m-1112	1619	5	i.n.𝐲𝐧	i.n.𝐲𝐧	PUNCT
m-1112	1619	6	and	and	CCONJ
m-1112	1619	7	is	be	AUX
m-1112	1619	8	defined	define	VERB
m-1112	1619	9	as	as	ADP
m-1112	1619	10	→	→	SYM
m-1112	1619	11	i.	i.	PROPN
m-1112	1619	12	grad	grad	PROPN
m-1112	1620	1	y	y	PROPN
m-1112	1621	1	=	=	PUNCT
m-1112	1621	2	𝐢	𝐢	PROPN
m-1112	1621	3	𝟏.	𝟏.	X
m-1112	1621	4	(	(	PUNCT
m-1112	1621	5	𝝏𝒚	𝝏𝒚	PROPN
m-1112	1621	6	𝝏𝟏	𝝏𝟏	X
m-1112	1621	7	)	)	PUNCT
m-1112	1622	1	+	+	CCONJ
m-1112	1622	2	𝐢	𝐢	X
m-1112	1622	3	𝟐.	𝟐.	NOUN
m-1112	1622	4	(	(	PUNCT
m-1112	1622	5	𝝏𝒚	𝝏𝒚	PROPN
m-1112	1622	6	𝝏𝟐	𝝏𝟐	PROPN
m-1112	1622	7	)	)	PUNCT
m-1112	1623	1	+	+	X
m-1112	1623	2	…	…	PUNCT
m-1112	1623	3	=	=	SYM
m-1112	1623	4	[	[	PUNCT
m-1112	1623	5	i.	i.	NOUN
m-1112	1623	6	]	]	X
m-1112	1623	7	.y	.y	PROPN
m-1112	1623	8	,	,	PUNCT
m-1112	1623	9	which	which	PRON
m-1112	1623	10	gives	give	VERB
m-1112	1623	11	the	the	DET
m-1112	1623	12	change	change	NOUN
m-1112	1623	13	of	of	ADP
m-1112	1623	14	field	field	NOUN
m-1112	1623	15	y	y	PROPN
m-1112	1623	16	,	,	PUNCT
m-1112	1623	17	in	in	ADP
m-1112	1623	18	the	the	DET
m-1112	1623	19	direction	direction	NOUN
m-1112	1623	20	→	→	PUNCT
m-1112	1623	21	i	i	PRON
m-1112	1623	22	,	,	PUNCT
m-1112	1623	23	ijo	ijo	PROPN
m-1112	1623	24	international	international	PROPN
m-1112	1623	25	journal	journal	PROPN
m-1112	1623	26	of	of	ADP
m-1112	1623	27	mathematics	mathematics	PROPN
m-1112	1623	28	(	(	PUNCT
m-1112	1623	29	issn	issn	PROPN
m-1112	1623	30	:	:	PUNCT
m-1112	1623	31	2992	2992	NUM
m-1112	1623	32	-	-	SYM
m-1112	1623	33	4421	4421	NUM
m-1112	1623	34	)	)	PUNCT
m-1112	1623	35	volume	volume	NOUN
m-1112	1623	36	08	08	NUM
m-1112	1624	1	|	|	ADV
m-1112	1624	2	issue	issue	NOUN
m-1112	1624	3	08	08	NUM
m-1112	1625	1	|	|	ADV
m-1112	1625	2	august	august	PROPN
m-1112	1625	3	2025	2025	NUM
m-1112	1625	4	|	|	ADV
m-1112	1625	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1625	6	ijo	ijo	PROPN
m-1112	1625	7	journals	journal	NOUN
m-1112	1625	8	58	58	NUM
m-1112	1625	9	the	the	DET
m-1112	1625	10	fundamental	fundamental	ADJ
m-1112	1625	11	particles	particle	NOUN
m-1112	1625	12	origination	origination	NOUN
m-1112	1625	13	mechanism	mechanism	NOUN
m-1112	1625	14	in	in	ADP
m-1112	1625	15	mfmf	mfmf	PROPN
m-1112	1625	16	pns	pns	PROPN
m-1112	1625	17	caves	cave	NOUN
m-1112	1625	18	.	.	PUNCT
m-1112	1626	1	and	and	CCONJ
m-1112	1626	2	[	[	X
m-1112	1626	3	i.	i.	NOUN
m-1112	1626	4	]	]	PUNCT
m-1112	1626	5	is	be	AUX
m-1112	1626	6	the	the	DET
m-1112	1626	7	single	single	ADJ
m-1112	1626	8	coherent	coherent	ADJ
m-1112	1626	9	unit	unit	NOUN
m-1112	1626	10	,	,	PUNCT
m-1112	1626	11	therefore	therefore	ADV
m-1112	1626	12	coexistance	coexistance	NOUN
m-1112	1626	13	between	between	ADP
m-1112	1626	14	spaces	space	NOUN
m-1112	1626	15	,	,	PUNCT
m-1112	1626	16	antispaces	antispace	NOUN
m-1112	1626	17	and	and	CCONJ
m-1112	1626	18	sub	sub	NOUN
m-1112	1626	19	-	-	NOUN
m-1112	1626	20	spaces	space	NOUN
m-1112	1626	21	of	of	ADP
m-1112	1626	22	any	any	DET
m-1112	1626	23	monad	monad	PROPN
m-1112	1626	24	→	→	SYM
m-1112	1626	25	𝐳	𝐳	X
m-1112	1626	26	=	=	PUNCT
m-1112	1626	27	x	x	PROPN
m-1112	1627	1	+	+	CCONJ
m-1112	1627	2	y	y	PROPN
m-1112	1627	3	.i	.i	PUNCT
m-1112	1628	1	=	=	SYM
m-1112	1628	2	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	1628	3	̅̅	̅̅	PROPN
m-1112	1628	4	,	,	PUNCT
m-1112	1628	5	is	be	AUX
m-1112	1628	6	happening	happen	VERB
m-1112	1628	7	through	through	ADP
m-1112	1628	8	the	the	DET
m-1112	1628	9	general	general	ADJ
m-1112	1628	10	equation	equation	NOUN
m-1112	1628	11	which	which	PRON
m-1112	1628	12	follows	follow	VERB
m-1112	1628	13	𝐦	𝐦	PROPN
m-1112	1628	14	[𝐬+𝐯	[𝐬+𝐯	PROPN
m-1112	1628	15	𝐢	𝐢	X
m-1112	1628	16	]	]	X
m-1112	1628	17	=	=	PUNCT
m-1112	1628	18	𝐪𝐰	𝐪𝐰	NOUN
m-1112	1628	19	=	=	SYM
m-1112	1628	20	(	(	PUNCT
m-1112	1628	21	𝐓𝐪	𝐓𝐪	PROPN
m-1112	1628	22	)	)	PUNCT
m-1112	1628	23	.	.	PUNCT
m-1112	1629	1	[	[	X
m-1112	1629	2	cos.wφ	cos.wφ	PRON
m-1112	1629	3	+	+	CCONJ
m-1112	1629	4	ε	ε	PROPN
m-1112	1629	5	.sin.wφ	.sin.wφ	PROPN
m-1112	1629	6	]	]	PUNCT
m-1112	1629	7	,	,	PUNCT
m-1112	1629	8	where	where	SCONJ
m-1112	1629	9	,	,	PUNCT
m-1112	1629	10	m	m	VERB
m-1112	1629	11	=	=	NOUN
m-1112	1629	12	𝐥𝐢𝐦(𝟏	𝐥𝐢𝐦(𝟏	PROPN
m-1112	1629	13	+	+	CCONJ
m-1112	1629	14	𝟏/𝐰)𝐰	𝟏/𝐰)𝐰	NOUN
m-1112	1629	15	for	for	ADP
m-1112	1629	16	w	w	NOUN
m-1112	1629	17	=	=	SYM
m-1112	1629	18	1	1	NUM
m-1112	1629	19	→	→	SYM
m-1112	1629	20	∞	∞	NUM
m-1112	1629	21	,	,	PUNCT
m-1112	1629	22	q	q	X
m-1112	1629	23	=	=	PUNCT
m-1112	1629	24	z	z	NOUN
m-1112	1629	25	=	=	SYM
m-1112	1629	26	±	±	NOUN
m-1112	1629	27	(	(	PUNCT
m-1112	1629	28	x+y.i	x+y.i	PROPN
m-1112	1629	29	)	)	PUNCT
m-1112	1629	30	sinφ	sinφ	NOUN
m-1112	1629	31	=	=	PUNCT
m-1112	1629	32	y	y	PROPN
m-1112	1629	33	/	/	SYM
m-1112	1629	34	√𝐱²	√𝐱²	PROPN
m-1112	1630	1	+	+	CCONJ
m-1112	1630	2	𝐲²	𝐲²	NOUN
m-1112	1630	3	𝟐	𝟐	NUM
m-1112	1630	4	,	,	PUNCT
m-1112	1630	5	cos.φ	cos.φ	PROPN
m-1112	1630	6	=	=	SYM
m-1112	1630	7	x	x	PUNCT
m-1112	1630	8	/	/	SYM
m-1112	1630	9	√𝐱	√𝐱	NOUN
m-1112	1630	10	²	²	NUM
m-1112	1630	11	+	+	X
m-1112	1630	12	𝐲	𝐲	ADP
m-1112	1630	13	²	²	NUM
m-1112	1630	14	𝟐	𝟐	NUM
m-1112	1630	15	,	,	PUNCT
m-1112	1630	16	|z|	|z|	NOUN
m-1112	1630	17	=	=	SYM
m-1112	1630	18	√𝐱²	√𝐱²	PROPN
m-1112	1630	19	+	+	CCONJ
m-1112	1630	20	𝐲²	𝐲²	NOUN
m-1112	1630	21	𝟐	𝟐	NUM
m-1112	1630	22	𝐓𝐪	𝐓𝐪	PROPN
m-1112	1630	23	=	=	PUNCT
m-1112	1630	24	√𝐱	√𝐱	NOUN
m-1112	1630	25	²	²	NUM
m-1112	1630	26	+	+	CCONJ
m-1112	1630	27	𝐲²𝟏	𝐲²𝟏	NOUN
m-1112	1630	28	+	+	CCONJ
m-1112	1630	29	𝐲²𝟐	𝐲²𝟐	NOUN
m-1112	1630	30	+	+	CCONJ
m-1112	1630	31	⋯	⋯	PROPN
m-1112	1630	32	.	.	PUNCT
m-1112	1630	33	.	.	PUNCT
m-1112	1631	1	𝐲²𝐧	𝐲²𝐧	NOUN
m-1112	1631	2	,	,	PUNCT
m-1112	1631	3	ty	ty	INTJ
m-1112	1631	4	=	=	NOUN
m-1112	1631	5	√	√	ADP
m-1112	1631	6	𝐲²𝟏	𝐲²𝟏	NOUN
m-1112	1631	7	+	+	CCONJ
m-1112	1631	8	𝐲²𝟐	𝐲²𝟐	NOUN
m-1112	1631	9	+	+	NOUN
m-1112	1631	10	.	.	PUNCT
m-1112	1631	11	.	.	PUNCT
m-1112	1632	1	…	…	PUNCT
m-1112	1632	2	𝐲²𝐧	𝐲²𝐧	NOUN
m-1112	1632	3	,	,	PUNCT
m-1112	1632	4	ε	ε	PROPN
m-1112	1632	5	=	=	PUNCT
m-1112	1632	6	(	(	PUNCT
m-1112	1632	7	y.i	y.i	PROPN
m-1112	1632	8	/	/	SYM
m-1112	1632	9	𝐓𝐲	𝐓𝐲	PROPN
m-1112	1632	10	)	)	PUNCT
m-1112	1632	11	=	=	PUNCT
m-1112	1633	1	[	[	X
m-1112	1633	2	y.	y.	NOUN
m-1112	1633	3	i	i	X
m-1112	1633	4	]	]	PUNCT
m-1112	1633	5	/	/	PUNCT
m-1112	1634	1	[	[	X
m-1112	1634	2	𝐓𝐲	𝐓𝐲	NOUN
m-1112	1634	3	]	]	X
m-1112	1634	4	=	=	SYM
m-1112	1634	5	±	±	NOUN
m-1112	1634	6	(	(	PUNCT
m-1112	1634	7	𝐲𝟏.𝐚𝟏+	𝐲𝟏.𝐚𝟏+	PROPN
m-1112	1634	8	𝐲𝟐.𝐚𝟐	𝐲𝟐.𝐚𝟐	PROPN
m-1112	1634	9	)	)	PUNCT
m-1112	1634	10	/	/	SYM
m-1112	1635	1	√	√	NUM
m-1112	1635	2	𝐲²𝟏	𝐲²𝟏	NOUN
m-1112	1635	3	+	+	CCONJ
m-1112	1635	4	𝐲²𝟐	𝐲²𝟐	NOUN
m-1112	1635	5	+	+	CCONJ
m-1112	1635	6	⋯	⋯	NOUN
m-1112	1635	7	𝐲²𝐧	𝐲²𝐧	NOUN
m-1112	1635	8	i.e.	i.e.	X
m-1112	1635	9	the	the	DET
m-1112	1635	10	spaces	space	NOUN
m-1112	1635	11	,	,	PUNCT
m-1112	1635	12	antispaces	antispace	NOUN
m-1112	1635	13	and	and	CCONJ
m-1112	1635	14	sub	sub	NOUN
m-1112	1635	15	-	-	NOUN
m-1112	1635	16	spaces	space	NOUN
m-1112	1635	17	of	of	ADP
m-1112	1635	18	any	any	DET
m-1112	1635	19	monad	monad	PROPN
m-1112	1635	20	→	→	SYM
m-1112	1635	21	𝐳	𝐳	X
m-1112	1635	22	=	=	PUNCT
m-1112	1635	23	x	x	PROPN
m-1112	1636	1	+	+	NUM
m-1112	1636	2	y.i	y.i	PROPN
m-1112	1636	3	=	=	SYM
m-1112	1636	4	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	1636	5	̅̅	̅̅	PROPN
m-1112	1636	6	follows	follow	VERB
m-1112	1636	7	the	the	DET
m-1112	1636	8	euclidean	euclidean	ADJ
m-1112	1636	9	geometry	geometry	NOUN
m-1112	1636	10	(	(	PUNCT
m-1112	1636	11	2a	2a	NUM
m-1112	1636	12	)	)	PUNCT
m-1112	1636	13	and	and	CCONJ
m-1112	1636	14	the	the	DET
m-1112	1636	15	energy	energy	NOUN
m-1112	1636	16	flow	flow	NOUN
m-1112	1636	17	(	(	PUNCT
m-1112	1636	18	2b	2b	NOUN
m-1112	1636	19	)	)	PUNCT
m-1112	1636	20	,	,	PUNCT
m-1112	1636	21	as	as	ADP
m-1112	1636	22	in	in	ADP
m-1112	1636	23	figure	figure	NOUN
m-1112	1636	24	-1	-1	ADJ
m-1112	1636	25	-	-	PUNCT
m-1112	1636	26	3	3	NUM
m-1112	1636	27	-	-	SYM
m-1112	1636	28	21	21	NUM
m-1112	1636	29	.	.	PUNCT
m-1112	1637	1	the	the	DET
m-1112	1637	2	vectors	vector	NOUN
m-1112	1637	3	-	-	PUNCT
m-1112	1637	4	sum	sum	NOUN
m-1112	1637	5	of	of	ADP
m-1112	1637	6	vectors	vector	NOUN
m-1112	1637	7	,	,	PUNCT
m-1112	1637	8	either	either	CCONJ
m-1112	1637	9	on	on	ADP
m-1112	1637	10	points	point	NOUN
m-1112	1637	11	on	on	ADP
m-1112	1637	12	the	the	DET
m-1112	1637	13	same	same	ADJ
m-1112	1637	14	linear	linear	NOUN
m-1112	1637	15	-	-	PUNCT
m-1112	1637	16	direction	direction	NOUN
m-1112	1637	17	of	of	ADP
m-1112	1637	18	vectors	vector	NOUN
m-1112	1637	19	,	,	PUNCT
m-1112	1637	20	or	or	CCONJ
m-1112	1637	21	on	on	ADP
m-1112	1637	22	non	non	ADJ
m-1112	1637	23	-	-	ADJ
m-1112	1637	24	linear	linear	ADJ
m-1112	1637	25	-	-	PUNCT
m-1112	1637	26	directions	direction	NOUN
m-1112	1637	27	,	,	PUNCT
m-1112	1637	28	results	result	NOUN
m-1112	1637	29	onto	onto	ADP
m-1112	1637	30	the	the	DET
m-1112	1637	31	-	-	PUNCT
m-1112	1637	32	resultant	resultant	NOUN
m-1112	1637	33	-	-	PUNCT
m-1112	1637	34	vector	vector	NOUN
m-1112	1637	35	�	�	PROPN
m-1112	1637	36	⃗⃖	⃗⃖	NOUN
m-1112	1637	37	�	�	PROPN
m-1112	1637	38	,	,	PUNCT
m-1112	1637	39	of	of	ADP
m-1112	1637	40	all	all	DET
m-1112	1637	41	system	system	NOUN
m-1112	1637	42	-	-	PUNCT
m-1112	1637	43	vectors	vector	NOUN
m-1112	1637	44	and	and	CCONJ
m-1112	1637	45	becomes	become	VERB
m-1112	1637	46	a	a	DET
m-1112	1637	47	linear	linear	NOUN
m-1112	1637	48	-	-	PUNCT
m-1112	1637	49	vibration	vibration	NOUN
m-1112	1637	50	between	between	ADP
m-1112	1637	51	quaternion	quaternion	NOUN
m-1112	1637	52	-	-	PUNCT
m-1112	1637	53	edge	edge	NOUN
m-1112	1637	54	-	-	PUNCT
m-1112	1637	55	points	point	NOUN
m-1112	1637	56	.	.	PUNCT
m-1112	1638	1	this	this	DET
m-1112	1638	2	remark	remark	NOUN
m-1112	1638	3	denotes	denote	VERB
m-1112	1638	4	that	that	PRON
m-1112	1638	5	quaternions	quaternion	NOUN
m-1112	1638	6	which	which	PRON
m-1112	1638	7	are	be	AUX
m-1112	1638	8	composed	compose	VERB
m-1112	1638	9	of	of	ADP
m-1112	1638	10	real	real	ADJ
m-1112	1638	11	(	(	PUNCT
m-1112	1638	12	+	+	NOUN
m-1112	1638	13	charge	charge	NOUN
m-1112	1638	14	)	)	PUNCT
m-1112	1638	15	and	and	CCONJ
m-1112	1638	16	of	of	ADP
m-1112	1638	17	imaginary	imaginary	ADJ
m-1112	1638	18	part	part	NOUN
m-1112	1638	19	(	(	PUNCT
m-1112	1638	20	charge	charge	NOUN
m-1112	1638	21	)	)	PUNCT
m-1112	1638	22	act	act	NOUN
m-1112	1638	23	only	only	ADV
m-1112	1638	24	on	on	ADP
m-1112	1638	25	the	the	DET
m-1112	1638	26	resultant	resultant	NOUN
m-1112	1638	27	-	-	PUNCT
m-1112	1638	28	direction	direction	NOUN
m-1112	1638	29	end	end	NOUN
m-1112	1638	30	-	-	PUNCT
m-1112	1638	31	points	point	NOUN
m-1112	1638	32	carry	carry	VERB
m-1112	1638	33	energy	energy	NOUN
m-1112	1638	34	from	from	ADP
m-1112	1638	35	one	one	NUM
m-1112	1638	36	edge	edge	NOUN
m-1112	1638	37	to	to	PART
m-1112	1638	38	anotheredge	anotheredge	VERB
m-1112	1638	39	as	as	ADP
m-1112	1638	40	in	in	ADP
m-1112	1638	41	fig	fig	NOUN
m-1112	1638	42	–	–	PUNCT
m-1112	1638	43	6	6	NUM
m-1112	1638	44	the	the	DET
m-1112	1638	45	above	above	ADJ
m-1112	1638	46	property	property	NOUN
m-1112	1638	47	of	of	ADP
m-1112	1638	48	imaginary	imaginary	ADJ
m-1112	1638	49	-	-	PUNCT
m-1112	1638	50	part	part	NOUN
m-1112	1638	51	≡	≡	PROPN
m-1112	1638	52	energy	energy	NOUN
m-1112	1638	53	shows	show	VERB
m-1112	1638	54	the	the	PRON
m-1112	1638	55	how	how	SCONJ
m-1112	1638	56	elementary	elementary	ADJ
m-1112	1638	57	particles	particle	NOUN
m-1112	1638	58	are	be	AUX
m-1112	1638	59	originated	originate	VERB
m-1112	1638	60	from	from	ADP
m-1112	1638	61	the	the	DET
m-1112	1638	62	three	three	NUM
m-1112	1638	63	charges	charge	NOUN
m-1112	1638	64	(	(	PUNCT
m-1112	1638	65	of	of	ADP
m-1112	1638	66	the	the	DET
m-1112	1638	67	spaces	space	NOUN
m-1112	1638	68	[	[	X
m-1112	1638	69	⊕	⊕	PROPN
m-1112	1638	70			PROPN
m-1112	1638	71	⊝	⊝	PROPN
m-1112	1638	72	]	]	PUNCT
m-1112	1638	73	)	)	PUNCT
m-1112	1638	74	,	,	PUNCT
m-1112	1638	75	circularly	circularly	ADV
m-1112	1638	76	-	-	PUNCT
m-1112	1638	77	placed	place	VERB
m-1112	1638	78	on	on	ADP
m-1112	1638	79	the	the	DET
m-1112	1638	80	-	-	PUNCT
m-1112	1638	81	three	three	NUM
m-1112	1638	82	-	-	PUNCT
m-1112	1638	83	triangles	triangle	NOUN
m-1112	1638	84	of	of	ADP
m-1112	1638	85	stplmechanism	stplmechanism	NOUN
m-1112	1638	86	.	.	PUNCT
m-1112	1639	1	[	[	X
m-1112	1639	2	93	93	NUM
m-1112	1639	3	]	]	PUNCT
m-1112	1639	4	from	from	ADP
m-1112	1639	5	planck`s	planck`s	NOUN
m-1112	1639	6	energy	energy	NOUN
m-1112	1639	7	e	e	NOUN
m-1112	1639	8	=	=	SYM
m-1112	1639	9	h.fp	h.fp	PROPN
m-1112	1639	10	=	=	PUNCT
m-1112	1639	11	[	[	PUNCT
m-1112	1639	12	6,6262.10−34	6,6262.10−34	NUM
m-1112	1639	13	j.s	j.s	X
m-1112	1639	14	]	]	PUNCT
m-1112	1639	15	x	x	PUNCT
m-1112	1639	16	[	[	PUNCT
m-1112	1639	17	[	[	PUNCT
m-1112	1639	18	3,28393.1015	3,28393.1015	NUM
m-1112	1639	19	/	/	SYM
m-1112	1639	20	s	s	X
m-1112	1639	21	]	]	X
m-1112	1639	22	=	=	SYM
m-1112	1639	23	2	2	NUM
m-1112	1639	24	,	,	PUNCT
m-1112	1639	25	176.10−18	176.10−18	NUM
m-1112	1639	26	j	j	NOUN
m-1112	1639	27	,	,	PUNCT
m-1112	1639	28	and	and	CCONJ
m-1112	1639	29	in	in	ADP
m-1112	1639	30	ev	ev	X
m-1112	1639	31	becomes	become	VERB
m-1112	1639	32	→	→	SYM
m-1112	1639	33	[	[	PUNCT
m-1112	1639	34	2	2	NUM
m-1112	1639	35	,	,	PUNCT
m-1112	1639	36	176.10−18	176.10−18	NUM
m-1112	1639	37	]	]	PUNCT
m-1112	1639	38	/	/	PUNCT
m-1112	1640	1	[	[	X
m-1112	1640	2	1,6.10−19	1,6.10−19	NUM
m-1112	1640	3	]	]	X
m-1112	1640	4	=	=	SYM
m-1112	1640	5	13,6	13,6	NUM
m-1112	1640	6	ev	ev	X
m-1112	1640	7	or	or	CCONJ
m-1112	1640	8	,	,	PUNCT
m-1112	1640	9	energy	energy	NOUN
m-1112	1640	10	in	in	ADP
m-1112	1640	11	gravity	gravity	NOUN
m-1112	1640	12	-	-	PUNCT
m-1112	1640	13	layer	layer	NOUN
m-1112	1640	14	g	g	PROPN
m-1112	1640	15			NOUN
m-1112	1641	1	13,6	13,6	NUM
m-1112	1641	2	ev	ev	X
m-1112	1641	3	=	=	SYM
m-1112	1641	4	h	h	NOUN
m-1112	1641	5	f	f	NOUN
m-1112	1641	6	=	=	SYM
m-1112	1641	7	h	h	PROPN
m-1112	1641	8	/	/	SYM
m-1112	1641	9	t	t	NOUN
m-1112	1641	10	=	=	SYM
m-1112	1641	11	h	h	NOUN
m-1112	1641	12	/√𝐠.	/√𝐠.	NOUN
m-1112	1642	1	𝐚³.	𝐚³.	PROPN
m-1112	1642	2	\figure	\figure	NOUN
m-1112	1642	3	14	14	NUM
m-1112	1642	4	:	:	PUNCT
m-1112	1642	5	the	the	DET
m-1112	1642	6	action	action	NOUN
m-1112	1642	7	of	of	ADP
m-1112	1642	8	quaternion	quaternion	NOUN
m-1112	1642	9	�	�	NOUN
m-1112	1642	10	̅	̅	NOUN
m-1112	1642	11	�	�	PROPN
m-1112	1642	12	.	.	PUNCT
m-1112	1643	1	�	�	PROPN
m-1112	1643	2	̅	̅	NOUN
m-1112	1643	3	�	�	NOUN
m-1112	1643	4	=	=	PUNCT
m-1112	1644	1	[	[	X
m-1112	1644	2	s	s	X
m-1112	1644	3	+	+	NUM
m-1112	1644	4	�	�	NOUN
m-1112	1644	5	̅	̅	NOUN
m-1112	1644	6	�	�	NOUN
m-1112	1644	7	.	.	PUNCT
m-1112	1645	1	i	i	PRON
m-1112	1645	2	]	]	PUNCT
m-1112	1645	3	²	²	NUM
m-1112	1645	4	≡	≡	PROPN
m-1112	1645	5	s²	s²	PROPN
m-1112	1645	6	|	|	NOUN
m-1112	1645	7	�	�	NOUN
m-1112	1645	8	̅	̅	NOUN
m-1112	1645	9	�	�	NOUN
m-1112	1645	10	|	|	ADV
m-1112	1645	11	²	²	NUM
m-1112	1646	1	+	+	CCONJ
m-1112	1646	2	[	[	X
m-1112	1646	3	2.	2.	NOUN
m-1112	1646	4	�	�	NOUN
m-1112	1646	5	̅	̅	NOUN
m-1112	1646	6	�	�	NOUN
m-1112	1646	7	].|s	].|s	SYM
m-1112	1646	8	r|	r|	NOUN
m-1112	1646	9	.	.	PUNCT
m-1112	1647	1	i	i	PRON
m-1112	1647	2	≡	≡	PROPN
m-1112	1647	3	≡	≡	PROPN
m-1112	1647	4	s²	s²	ADJ
m-1112	1647	5	s²	s²	PROPN
m-1112	1647	6	+	+	CCONJ
m-1112	1647	7	2.𝐬²	2.𝐬²	NUM
m-1112	1648	1	and	and	CCONJ
m-1112	1648	2	follows	follow	VERB
m-1112	1648	3	pythagoras	pythagoras	PROPN
m-1112	1648	4	theorem	theorem	PROPN
m-1112	1648	5	of	of	ADP
m-1112	1648	6	the	the	DET
m-1112	1648	7	euclidean	euclidean	ADJ
m-1112	1648	8	geometry	geometry	NOUN
m-1112	1648	9	.	.	PUNCT
m-1112	1649	1	3b	3b	NUM
m-1112	1649	2	…	…	PUNCT
m-1112	1649	3	:	:	PUNCT
m-1112	1649	4	the	the	DET
m-1112	1649	5	stability	stability	NOUN
m-1112	1649	6	of	of	ADP
m-1112	1649	7	space	space	NOUN
m-1112	1649	8	anti	anti	NOUN
m-1112	1649	9	-	-	NOUN
m-1112	1649	10	space	space	NOUN
m-1112	1649	11	,	,	PUNCT
m-1112	1649	12	in	in	ADP
m-1112	1649	13	the	the	DET
m-1112	1649	14	neutral	neutral	ADJ
m-1112	1649	15	-	-	PUNCT
m-1112	1649	16	space	space	NOUN
m-1112	1649	17	the	the	DET
m-1112	1649	18	number	number	NOUN
m-1112	1649	19	of	of	ADP
m-1112	1649	20	moulds	mould	NOUN
m-1112	1649	21	of	of	ADP
m-1112	1649	22	stationary	stationary	ADJ
m-1112	1649	23	-	-	PUNCT
m-1112	1649	24	states	state	NOUN
m-1112	1649	25	are	be	AUX
m-1112	1649	26	as	as	SCONJ
m-1112	1649	27	,	,	PUNCT
m-1112	1649	28	2n=1−4	2n=1−4	NUM
m-1112	1649	29	points	point	NOUN
m-1112	1649	30	≡	≡	PROPN
m-1112	1649	31	2	2	NUM
m-1112	1649	32	,	,	PUNCT
m-1112	1649	33	4	4	NUM
m-1112	1649	34	,	,	PUNCT
m-1112	1649	35	8	8	NUM
m-1112	1649	36	,	,	PUNCT
m-1112	1649	37	16	16	NUM
m-1112	1649	38	≡	≡	PROPN
m-1112	1649	39	4	4	NUM
m-1112	1649	40	–	–	PUNCT
m-1112	1649	41	types	type	NOUN
m-1112	1649	42	i.e.	i.e.	X
m-1112	1649	43	monads	monad	NOUN
m-1112	1649	44	are	be	AUX
m-1112	1649	45	formed	form	VERB
m-1112	1649	46	from	from	ADP
m-1112	1649	47	the	the	DET
m-1112	1649	48	first	first	ADJ
m-1112	1649	49	4moulds	4moulds	NUM
m-1112	1649	50	as	as	ADP
m-1112	1649	51	→	→	SYM
m-1112	1649	52	the	the	DET
m-1112	1649	53	1	1	NUM
m-1112	1649	54	-	-	PUNCT
m-1112	1649	55	point	point	NOUN
m-1112	1649	56	which	which	PRON
m-1112	1649	57	is	be	AUX
m-1112	1649	58	everywhere	everywhere	ADV
m-1112	1649	59	,	,	PUNCT
m-1112	1649	60	ijo	ijo	PROPN
m-1112	1649	61	international	international	PROPN
m-1112	1649	62	journal	journal	PROPN
m-1112	1649	63	of	of	ADP
m-1112	1649	64	mathematics	mathematics	PROPN
m-1112	1649	65	(	(	PUNCT
m-1112	1649	66	issn	issn	PROPN
m-1112	1649	67	:	:	PUNCT
m-1112	1649	68	2992	2992	NUM
m-1112	1649	69	-	-	SYM
m-1112	1649	70	4421	4421	NUM
m-1112	1649	71	)	)	PUNCT
m-1112	1650	1	volume	volume	NOUN
m-1112	1650	2	08	08	NUM
m-1112	1651	1	|	|	ADV
m-1112	1651	2	issue	issue	NOUN
m-1112	1651	3	08	08	NUM
m-1112	1652	1	|	|	ADV
m-1112	1652	2	august	august	PROPN
m-1112	1652	3	2025	2025	NUM
m-1112	1652	4	|	|	ADV
m-1112	1652	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1652	6	ijo	ijo	PROPN
m-1112	1652	7	journals	journal	NOUN
m-1112	1652	8	59	59	NUM
m-1112	1652	9	the	the	DET
m-1112	1652	10	fundamental	fundamental	ADJ
m-1112	1652	11	particles	particle	NOUN
m-1112	1652	12	origination	origination	NOUN
m-1112	1652	13	mechanism	mechanism	NOUN
m-1112	1652	14	in	in	ADP
m-1112	1652	15	mfmf	mfmf	PROPN
m-1112	1652	16	pns	pns	PROPN
m-1112	1652	17	caves	cave	NOUN
m-1112	1652	18	.	.	PUNCT
m-1112	1653	1	the	the	DET
m-1112	1653	2	2points	2points	NUM
m-1112	1653	3	which	which	PRON
m-1112	1653	4	form	form	VERB
m-1112	1653	5	vectors	vector	NOUN
m-1112	1653	6	,	,	PUNCT
m-1112	1653	7	the	the	DET
m-1112	1653	8	3points	3point	NOUN
m-1112	1653	9	which	which	PRON
m-1112	1653	10	form	form	VERB
m-1112	1653	11	the	the	DET
m-1112	1653	12	planes	plane	NOUN
m-1112	1653	13	,	,	PUNCT
m-1112	1653	14	the	the	DET
m-1112	1653	15	4points	4point	NOUN
m-1112	1653	16	which	which	PRON
m-1112	1653	17	form	form	VERB
m-1112	1653	18	the	the	DET
m-1112	1653	19	volumes	volume	NOUN
m-1112	1653	20	.	.	PUNCT
m-1112	1654	1	for	for	ADP
m-1112	1654	2	n	n	X
m-1112	1654	3	>	>	X
m-1112	1654	4	4	4	NUM
m-1112	1654	5	as	as	SCONJ
m-1112	1654	6	this	this	PRON
m-1112	1654	7	is	be	AUX
m-1112	1654	8	the	the	DET
m-1112	1654	9	atom	atom	NOUN
m-1112	1654	10	structure	structure	NOUN
m-1112	1654	11	,	,	PUNCT
m-1112	1654	12	follows	follow	VERB
m-1112	1654	13	the	the	DET
m-1112	1654	14	sustainability	sustainability	NOUN
m-1112	1654	15	of	of	ADP
m-1112	1654	16	the	the	DET
m-1112	1654	17	spaces	space	NOUN
m-1112	1654	18	and	and	CCONJ
m-1112	1654	19	anti	anti	NOUN
m-1112	1654	20	-	-	ADJ
m-1112	1654	21	spaces	space	NOUN
m-1112	1654	22	.	.	PUNCT
m-1112	1655	1	since	since	SCONJ
m-1112	1655	2	space	space	NOUN
m-1112	1655	3	-	-	PUNCT
m-1112	1655	4	energy	energy	NOUN
m-1112	1655	5	structures	structure	NOUN
m-1112	1655	6	follow	follow	VERB
m-1112	1655	7	the	the	DET
m-1112	1655	8	m	m	NOUN
m-1112	1655	9	-	-	PUNCT
m-1112	1655	10	geometry	geometry	NOUN
m-1112	1655	11	stability	stability	NOUN
m-1112	1655	12	these	these	PRON
m-1112	1655	13	follow	follow	VERB
m-1112	1655	14	the	the	DET
m-1112	1655	15	mould	mould	NOUN
m-1112	1655	16	of	of	ADP
m-1112	1655	17	spaces	space	NOUN
m-1112	1655	18	2	2	NUM
m-1112	1655	19	n	n	NOUN
m-1112	1655	20	=	=	SYM
m-1112	1655	21	3	3	NUM
m-1112	1655	22	=	=	SYM
m-1112	1655	23	8	8	NUM
m-1112	1655	24	elements	element	NOUN
m-1112	1655	25	which	which	PRON
m-1112	1655	26	is	be	AUX
m-1112	1655	27	the	the	DET
m-1112	1655	28	-	-	PUNCT
m-1112	1655	29	cube	cube	NOUN
m-1112	1655	30	as	as	SCONJ
m-1112	1655	31	was	be	AUX
m-1112	1655	32	shown	show	VERB
m-1112	1655	33	before	before	ADV
m-1112	1655	34	for	for	ADP
m-1112	1655	35	the	the	DET
m-1112	1655	36	atoms	atom	NOUN
m-1112	1655	37	structure	structure	NOUN
m-1112	1655	38	fig-5	fig-5	NOUN
m-1112	1655	39	-	-	SYM
m-1112	1655	40	28	28	NUM
m-1112	1655	41	.	.	PUNCT
m-1112	1656	1	the	the	DET
m-1112	1656	2	atoms	atoms	NOUN
m-1112	1656	3	-	-	PUNCT
m-1112	1656	4	bonding	bonding	NOUN
m-1112	1656	5	follows	follow	VERB
m-1112	1656	6	→	→	SYM
m-1112	1656	7	space	space	NOUN
m-1112	1656	8	≡	≡	PROPN
m-1112	1656	9	electric	electric	NOUN
m-1112	1656	10	-	-	PUNCT
m-1112	1656	11	field	field	NOUN
m-1112	1656	12	&	&	CCONJ
m-1112	1656	13	anti	anti	ADJ
m-1112	1656	14	-	-	ADJ
m-1112	1656	15	space	space	ADJ
m-1112	1656	16	≡	≡	PROPN
m-1112	1656	17	magnetic	magnetic	ADJ
m-1112	1656	18	-	-	PUNCT
m-1112	1656	19	field	field	NOUN
m-1112	1656	20	←	←	PROPN
m-1112	1656	21	4b	4b	X
m-1112	1656	22	…	…	PUNCT
m-1112	1656	23	the	the	DET
m-1112	1656	24	quantum	quantum	ADJ
m-1112	1656	25	interference	interference	NOUN
m-1112	1656	26	of	of	ADP
m-1112	1656	27	the	the	DET
m-1112	1656	28	duality	duality	NOUN
m-1112	1656	29	-	-	PUNCT
m-1112	1656	30	photon	photon	NOUN
m-1112	1656	31	:	:	PUNCT
m-1112	1656	32	quantum	quantum	ADJ
m-1112	1656	33	interference	interference	NOUN
m-1112	1656	34	is	be	AUX
m-1112	1656	35	the	the	DET
m-1112	1656	36	phenomenon	phenomenon	NOUN
m-1112	1656	37	when	when	SCONJ
m-1112	1656	38	,	,	PUNCT
m-1112	1656	39	a	a	DET
m-1112	1656	40	photon	photon	NOUN
m-1112	1656	41	interferes	interfere	VERB
m-1112	1656	42	with	with	ADP
m-1112	1656	43	itself	itself	PRON
m-1112	1656	44	.[92e	.[92e	NUM
m-1112	1656	45	]	]	PUNCT
m-1112	1656	46	.	.	PUNCT
m-1112	1657	1	this	this	DET
m-1112	1657	2	proposition	proposition	NOUN
m-1112	1657	3	is	be	AUX
m-1112	1657	4	right	right	ADJ
m-1112	1657	5	when	when	SCONJ
m-1112	1657	6	photon	photon	NOUN
m-1112	1657	7	is	be	AUX
m-1112	1657	8	considered	consider	VERB
m-1112	1657	9	having	have	VERB
m-1112	1657	10	a	a	DET
m-1112	1657	11	twin	twin	ADJ
m-1112	1657	12	-	-	PUNCT
m-1112	1657	13	existance	existance	NOUN
m-1112	1657	14	,	,	PUNCT
m-1112	1658	1	[	[	X
m-1112	1658	2	101]-3c.p-21	101]-3c.p-21	NUM
m-1112	1658	3	.	.	PUNCT
m-1112	1659	1	the	the	DET
m-1112	1659	2	problem	problem	NOUN
m-1112	1659	3	is	be	AUX
m-1112	1659	4	to	to	PART
m-1112	1659	5	determine	determine	VERB
m-1112	1659	6	the	the	DET
m-1112	1659	7	expression	expression	NOUN
m-1112	1659	8	of	of	ADP
m-1112	1659	9	the	the	DET
m-1112	1659	10	power	power	NOUN
m-1112	1659	11	developed	develop	VERB
m-1112	1659	12	by	by	ADP
m-1112	1659	13	gravitational	gravitational	ADJ
m-1112	1659	14	force	force	NOUN
m-1112	1659	15	.	.	PUNCT
m-1112	1660	1	from	from	ADP
m-1112	1660	2	dual	dual	ADJ
m-1112	1660	3	-	-	PUNCT
m-1112	1660	4	photon	photon	NOUN
m-1112	1660	5	-	-	PUNCT
m-1112	1660	6	equation	equation	NOUN
m-1112	1660	7	,	,	PUNCT
m-1112	1660	8	v̅.	v̅.	PROPN
m-1112	1660	9	[	[	PUNCT
m-1112	1660	10	fn̅	fn̅	PROPN
m-1112	1660	11	+	+	NUM
m-1112	1660	12	fn	fn	NOUN
m-1112	1660	13	]	]	PUNCT
m-1112	1660	14	≡	≡	PROPN
m-1112	1660	15	|	|	ADV
m-1112	1660	16	𝐯	𝐯	X
m-1112	1660	17	𝛑².𝐫⁴𝐧	𝛑².𝐫⁴𝐧	NOUN
m-1112	1660	18	|	|	NOUN
m-1112	1660	19	.	.	PUNCT
m-1112	1661	1	b̅n	b̅n	PROPN
m-1112	1662	1	+	+	CCONJ
m-1112	1662	2	|	|	ADV
m-1112	1662	3	c	c	NOUN
m-1112	1663	1	̅|	̅|	INTJ
m-1112	1663	2	fn	fn	INTJ
m-1112	1663	3	,	,	PUNCT
m-1112	1663	4	when	when	SCONJ
m-1112	1663	5	c	c	NOUN
m-1112	1663	6	=	=	SYM
m-1112	1663	7	0	0	NUM
m-1112	1663	8	or	or	CCONJ
m-1112	1663	9	c	c	NOUN
m-1112	1663	10	=	=	SYM
m-1112	1663	11	c⃖	c⃖	ADJ
m-1112	1663	12	,	,	PUNCT
m-1112	1663	13	then	then	ADV
m-1112	1663	14	photon	photon	NOUN
m-1112	1663	15	motion	motion	NOUN
m-1112	1663	16	becomes	become	VERB
m-1112	1663	17	→	→	PUNCT
m-1112	1663	18	|	|	ADV
m-1112	1663	19	𝐯	𝐯	ADP
m-1112	1663	20	𝛑².𝐫⁴𝐧	𝛑².𝐫⁴𝐧	NOUN
m-1112	1663	21	|	|	ADV
m-1112	1663	22	.	.	PUNCT
m-1112	1664	1	b̅n	b̅n	PROPN
m-1112	1664	2	←	←	PROPN
m-1112	1664	3	≡	≡	PROPN
m-1112	1664	4	spin	spin	NOUN
m-1112	1664	5	.	.	PUNCT
m-1112	1665	1	i.e.	i.e.	X
m-1112	1665	2	the	the	DET
m-1112	1665	3	stationary	stationary	ADJ
m-1112	1665	4	photons	photon	NOUN
m-1112	1665	5	exist	exist	VERB
m-1112	1665	6	as	as	ADP
m-1112	1665	7	their	their	PRON
m-1112	1665	8	spin	spin	NOUN
m-1112	1665	9	only	only	ADV
m-1112	1665	10	.	.	PUNCT
m-1112	1666	1	this	this	DET
m-1112	1666	2	rest	rest	NOUN
m-1112	1666	3	-	-	PUNCT
m-1112	1666	4	space	space	NOUN
m-1112	1666	5	is	be	AUX
m-1112	1666	6	the	the	DET
m-1112	1666	7	part	part	NOUN
m-1112	1666	8	|	|	ADV
m-1112	1666	9	𝐯	𝐯	X
m-1112	1666	10	𝛑².𝐫⁴𝐧	𝛑².𝐫⁴𝐧	NOUN
m-1112	1666	11	|	|	NOUN
m-1112	1666	12	.	.	PUNCT
m-1112	1667	1	b̅n	b̅n	PROPN
m-1112	1667	2	and	and	CCONJ
m-1112	1667	3	its	its	PRON
m-1112	1667	4	communication	communication	NOUN
m-1112	1667	5	code	code	NOUN
m-1112	1667	6	to	to	PART
m-1112	1667	7	be	be	AUX
m-1112	1667	8	the	the	DET
m-1112	1667	9	term	term	NOUN
m-1112	1667	10	|	|	ADV
m-1112	1667	11	𝐯	𝐯	AUX
m-1112	1667	12	𝛑².𝐫⁴𝐧	𝛑².𝐫⁴𝐧	VERB
m-1112	1667	13	|=|	|=|	PROPN
m-1112	1667	14	𝐰	𝐰	X
m-1112	1667	15	𝐫	𝐫	X
m-1112	1667	16	𝛑𝟐.𝐫⁴	𝛑𝟐.𝐫⁴	PROPN
m-1112	1668	1	|	|	ADV
m-1112	1668	2	=	=	PUNCT
m-1112	1669	1	|	|	ADV
m-1112	1669	2	𝟐	𝟐	NUM
m-1112	1669	3	𝐯	𝐯	NOUN
m-1112	1669	4	𝟐𝛑	𝟐𝛑	NOUN
m-1112	1669	5	𝟑𝐫	𝟑𝐫	PROPN
m-1112	1669	6	⁴	⁴	NUM
m-1112	1669	7	|	|	ADV
m-1112	1669	8	,	,	PUNCT
m-1112	1669	9	the	the	DET
m-1112	1669	10	rest	rest	NOUN
m-1112	1669	11	space	space	NOUN
m-1112	1669	12	is	be	AUX
m-1112	1669	13	a	a	DET
m-1112	1669	14	stationary	stationary	ADJ
m-1112	1669	15	wave	wave	NOUN
m-1112	1669	16	with	with	ADP
m-1112	1669	17	fundamental	fundamental	ADJ
m-1112	1669	18	frequency	frequency	NOUN
m-1112	1669	19	f	f	PROPN
m-1112	1669	20	1=	1=	NUM
m-1112	1669	21	1	1	NUM
m-1112	1669	22	t	t	PROPN
m-1112	1669	23	1	1	NUM
m-1112	1669	24	=	=	SYM
m-1112	1669	25	λ̅	λ̅	PROPN
m-1112	1669	26	c	c	NOUN
m-1112	1669	27	,	,	PUNCT
m-1112	1669	28	with	with	ADP
m-1112	1669	29	an	an	DET
m-1112	1669	30	electric	electric	ADJ
m-1112	1669	31	wave	wave	NOUN
m-1112	1669	32	,	,	PUNCT
m-1112	1669	33	that	that	PRON
m-1112	1669	34	is	be	AUX
m-1112	1669	35	acting	act	VERB
m-1112	1669	36	on	on	ADP
m-1112	1669	37	vector	vector	NOUN
m-1112	1669	38	c	c	NOUN
m-1112	1669	39	̅	̅	NOUN
m-1112	1669	40	=	=	SYM
m-1112	1669	41	(	(	PUNCT
m-1112	1669	42	i.	i.	PROPN
m-1112	1669	43	cx	cx	PROPN
m-1112	1670	1	+	+	CCONJ
m-1112	1670	2	j.	j.	PROPN
m-1112	1670	3	cy	cy	PROPN
m-1112	1670	4	)	)	PUNCT
m-1112	1670	5	.	.	PUNCT
m-1112	1671	1	it	it	PRON
m-1112	1671	2	was	be	AUX
m-1112	1671	3	proved	prove	VERB
m-1112	1671	4	[	[	X
m-1112	1671	5	78	78	NUM
m-1112	1671	6	]	]	PUNCT
m-1112	1671	7	that	that	SCONJ
m-1112	1671	8	the	the	DET
m-1112	1671	9	newton`s	newton`s	PROPN
m-1112	1671	10	gravitational	gravitational	ADJ
m-1112	1671	11	constant	constant	ADJ
m-1112	1671	12	g	g	NOUN
m-1112	1671	13	does	do	AUX
m-1112	1671	14	not	not	PART
m-1112	1671	15	effect	effect	VERB
m-1112	1671	16	on	on	ADP
m-1112	1671	17	plane	plane	NOUN
m-1112	1671	18	surfaces	surface	NOUN
m-1112	1671	19	,	,	PUNCT
m-1112	1671	20	but	but	CCONJ
m-1112	1671	21	on	on	ADP
m-1112	1671	22	volume	volume	NOUN
m-1112	1671	23	surfaces	surface	NOUN
m-1112	1671	24	only	only	ADV
m-1112	1671	25	.	.	PUNCT
m-1112	1672	1	this	this	DET
m-1112	1672	2	property	property	NOUN
m-1112	1672	3	of	of	ADP
m-1112	1672	4	,	,	PUNCT
m-1112	1672	5	g	g	PROPN
m-1112	1672	6	,	,	PUNCT
m-1112	1672	7	means	mean	VERB
m-1112	1672	8	that	that	SCONJ
m-1112	1672	9	the	the	DET
m-1112	1672	10	only	only	ADJ
m-1112	1672	11	one	one	NUM
m-1112	1672	12	force	force	NOUN
m-1112	1672	13	which	which	PRON
m-1112	1672	14	effects	effect	NOUN
m-1112	1672	15	on	on	ADP
m-1112	1672	16	the	the	DET
m-1112	1672	17	rest	rest	NOUN
m-1112	1672	18	-	-	PUNCT
m-1112	1672	19	space	space	NOUN
m-1112	1672	20	in	in	ADP
m-1112	1672	21	torsional	torsional	ADJ
m-1112	1672	22	motion	motion	NOUN
m-1112	1672	23	,	,	PUNCT
m-1112	1672	24	and	and	CCONJ
m-1112	1672	25	onto	onto	ADP
m-1112	1672	26	the	the	DET
m-1112	1672	27	light	light	ADJ
m-1112	1672	28	velocity	velocity	NOUN
m-1112	1672	29	vector	vector	NOUN
m-1112	1672	30	c	c	NOUN
m-1112	1672	31	̅	̅	NOUN
m-1112	1672	32	,	,	PUNCT
m-1112	1672	33	is	be	AUX
m-1112	1672	34	the	the	DET
m-1112	1672	35	gravity	gravity	NOUN
m-1112	1672	36	force	force	NOUN
m-1112	1672	37	g	g	NOUN
m-1112	1672	38	only	only	ADV
m-1112	1672	39	.	.	PUNCT
m-1112	1673	1	figure	figure	VERB
m-1112	1673	2	15	15	NUM
m-1112	1673	3	-	-	NUM
m-1112	1673	4	the	the	DET
m-1112	1673	5	stability	stability	NOUN
m-1112	1673	6	of	of	ADP
m-1112	1673	7	{	{	PUNCT
m-1112	1673	8	⊕space	⊕space	NOUN
m-1112	1673	9	[	[	X
m-1112	1673	10	electric	electric	ADJ
m-1112	1673	11	wave},{⊝-anti	wave},{⊝-anti	NOUN
m-1112	1673	12	-	-	NOUN
m-1112	1673	13	space	space	NOUN
m-1112	1673	14	[	[	X
m-1112	1673	15	magnetic	magnetic	ADJ
m-1112	1673	16	wave	wave	NOUN
m-1112	1673	17	]	]	PUNCT
m-1112	1673	18	of	of	ADP
m-1112	1673	19	sub	sub	NOUN
m-1112	1673	20	-	-	NOUN
m-1112	1673	21	space	space	ADJ
m-1112	1673	22	{	{	PUNCT
m-1112	1673	23	[	[	X
m-1112	1673	24	⊕↔⊝	⊕↔⊝	X
m-1112	1673	25	]	]	X
m-1112	1673	26	≡	≡	PROPN
m-1112	1673	27	ds	ds	PROPN
m-1112	1673	28	≡	≡	PROPN
m-1112	1674	1	[	[	X
m-1112	1674	2	⊕←ds→⊝	⊕←ds→⊝	X
m-1112	1674	3	]	]	X
m-1112	1674	4	–	–	PUNCT
m-1112	1674	5	or	or	CCONJ
m-1112	1674	6	–	–	PUNCT
m-1112	1674	7	the	the	DET
m-1112	1674	8	neutral	neutral	ADJ
m-1112	1674	9	-	-	PUNCT
m-1112	1674	10	space	space	NOUN
m-1112	1674	11	[	[	X
m-1112	1674	12	a	a	X
m-1112	1674	13	e	e	NOUN
m-1112	1674	14	,	,	PUNCT
m-1112	1674	15	b	b	PROPN
m-1112	1674	16	e	e	NOUN
m-1112	1674	17	,	,	PUNCT
m-1112	1674	18	c	c	PROPN
m-1112	1674	19	e	e	NOUN
m-1112	1674	20	]	]	PUNCT
m-1112	1674	21	}	}	PUNCT
m-1112	1674	22	:	:	PUNCT
m-1112	1674	23	ijo	ijo	PROPN
m-1112	1674	24	international	international	PROPN
m-1112	1674	25	journal	journal	PROPN
m-1112	1674	26	of	of	ADP
m-1112	1674	27	mathematics	mathematics	PROPN
m-1112	1674	28	(	(	PUNCT
m-1112	1674	29	issn	issn	PROPN
m-1112	1674	30	:	:	PUNCT
m-1112	1674	31	2992	2992	NUM
m-1112	1674	32	-	-	SYM
m-1112	1674	33	4421	4421	NUM
m-1112	1674	34	)	)	PUNCT
m-1112	1674	35	volume	volume	NOUN
m-1112	1674	36	08	08	NUM
m-1112	1675	1	|	|	ADV
m-1112	1675	2	issue	issue	NOUN
m-1112	1675	3	08	08	NUM
m-1112	1676	1	|	|	ADV
m-1112	1676	2	august	august	PROPN
m-1112	1676	3	2025	2025	NUM
m-1112	1676	4	|	|	ADV
m-1112	1676	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1676	6	ijo	ijo	NOUN
m-1112	1676	7	journals	journal	NOUN
m-1112	1676	8	60	60	NUM
m-1112	1676	9	the	the	DET
m-1112	1676	10	fundamental	fundamental	ADJ
m-1112	1676	11	particles	particle	NOUN
m-1112	1676	12	origination	origination	NOUN
m-1112	1676	13	mechanism	mechanism	NOUN
m-1112	1676	14	in	in	ADP
m-1112	1676	15	mfmf	mfmf	PROPN
m-1112	1676	16	pns	pns	PROPN
m-1112	1676	17	caves	cave	NOUN
m-1112	1676	18	.	.	PUNCT
m-1112	1677	1	since	since	SCONJ
m-1112	1677	2	c	c	PROPN
m-1112	1677	3	is	be	AUX
m-1112	1677	4	constant	constant	ADJ
m-1112	1677	5	,	,	PUNCT
m-1112	1677	6	it	it	PRON
m-1112	1677	7	is	be	AUX
m-1112	1677	8	analyzed	analyze	VERB
m-1112	1677	9	to	to	ADP
m-1112	1677	10	,	,	PUNCT
m-1112	1677	11	(	(	PUNCT
m-1112	1677	12	cx	cx	INTJ
m-1112	1677	13	,	,	PUNCT
m-1112	1677	14	cy	cy	PROPN
m-1112	1677	15	)	)	PUNCT
m-1112	1677	16	in	in	ADP
m-1112	1677	17	any	any	DET
m-1112	1677	18	two	two	NUM
m-1112	1677	19	directions	direction	NOUN
m-1112	1677	20	x	x	X
m-1112	1677	21	,	,	PUNCT
m-1112	1677	22	y	y	PROPN
m-1112	1677	23	where	where	SCONJ
m-1112	1677	24	x	x	PUNCT
m-1112	1677	25	⏊	⏊	VERB
m-1112	1677	26	y	y	PROPN
m-1112	1677	27	and	and	CCONJ
m-1112	1677	28	y	y	PROPN
m-1112	1677	29	to	to	PART
m-1112	1677	30	be	be	AUX
m-1112	1677	31	the	the	DET
m-1112	1677	32	gravity	gravity	NOUN
m-1112	1677	33	direction	direction	NOUN
m-1112	1677	34	on	on	ADP
m-1112	1677	35	where	where	SCONJ
m-1112	1677	36	gravity	gravity	NOUN
m-1112	1677	37	is	be	AUX
m-1112	1677	38	acting	act	VERB
m-1112	1677	39	.	.	PUNCT
m-1112	1678	1	the	the	DET
m-1112	1678	2	produced	produce	VERB
m-1112	1678	3	work	work	NOUN
m-1112	1678	4	is	be	AUX
m-1112	1678	5	in	in	ADP
m-1112	1678	6	y	y	PROPN
m-1112	1678	7	range	range	NOUN
m-1112	1678	8	,	,	PUNCT
m-1112	1678	9	s	s	VERB
m-1112	1678	10	y	y	NOUN
m-1112	1678	11	=	=	SYM
m-1112	1678	12	cy	cy	PROPN
m-1112	1678	13	t	t	PROPN
m-1112	1678	14	1	1	NUM
m-1112	1678	15	2	2	NUM
m-1112	1678	16	g	g	NOUN
m-1112	1678	17	𝑡2	𝑡2	NOUN
m-1112	1678	18	=	=	PUNCT
m-1112	1678	19	c	c	PROPN
m-1112	1678	20	sin	sin	NOUN
m-1112	1678	21	𝑎𝑡	𝑎𝑡	ADP
m-1112	1678	22	1	1	NUM
m-1112	1678	23	2	2	NUM
m-1112	1678	24	g	g	NOUN
m-1112	1678	25	𝑡2	𝑡2	NOUN
m-1112	1678	26	,	,	PUNCT
m-1112	1678	27	where	where	SCONJ
m-1112	1678	28	maximum	maximum	ADJ
m-1112	1678	29	range	range	NOUN
m-1112	1678	30	is	be	AUX
m-1112	1678	31	s	s	NOUN
m-1112	1678	32	max−y	max−y	NOUN
m-1112	1678	33	=	=	SYM
m-1112	1678	34	cy	cy	PROPN
m-1112	1678	35	2/	2/	NUM
m-1112	1678	36	2	2	NUM
m-1112	1678	37	g	g	NOUN
m-1112	1678	38	=	=	PUNCT
m-1112	1678	39	(	(	PUNCT
m-1112	1678	40	c	c	NOUN
m-1112	1678	41	sin𝑎𝑡	sin𝑎𝑡	ADJ
m-1112	1678	42	)	)	PUNCT
m-1112	1678	43	²	²	NUM
m-1112	1678	44	2	2	NUM
m-1112	1678	45	g	g	NOUN
m-1112	1678	46	=	=	PUNCT
m-1112	1678	47	[	[	PUNCT
m-1112	1678	48	c	c	NOUN
m-1112	1678	49	²	²	NUM
m-1112	1678	50	2	2	NUM
m-1112	1678	51	g	g	NOUN
m-1112	1678	52	]	]	PUNCT
m-1112	1678	53	sin²	sin²	PROPN
m-1112	1678	54	𝑎	𝑎	X
m-1112	1678	55	,	,	PUNCT
m-1112	1678	56	happening	happen	VERB
m-1112	1678	57	at	at	ADP
m-1112	1678	58	angle	angle	NOUN
m-1112	1678	59	a	a	DET
m-1112	1678	60	=	=	SYM
m-1112	1678	61	90	90	NUM
m-1112	1678	62	°	°	NUM
m-1112	1679	1	and	and	CCONJ
m-1112	1680	1	where	where	SCONJ
m-1112	1680	2	sin²	sin²	PROPN
m-1112	1680	3	𝑎	𝑎	PROPN
m-1112	1680	4	=	=	SYM
m-1112	1680	5	1	1	NUM
m-1112	1680	6	.	.	PUNCT
m-1112	1681	1	since	since	SCONJ
m-1112	1681	2	at	at	ADP
m-1112	1681	3	point	point	NOUN
m-1112	1681	4	(	(	PUNCT
m-1112	1681	5	1	1	X
m-1112	1681	6	)	)	PUNCT
m-1112	1681	7	the	the	DET
m-1112	1681	8	velocity	velocity	NOUN
m-1112	1681	9	v	v	ADP
m-1112	1681	10	y	y	PROPN
m-1112	1681	11	=	=	SYM
m-1112	1681	12	0	0	PROPN
m-1112	1681	13	,	,	PUNCT
m-1112	1681	14	the	the	DET
m-1112	1681	15	motion	motion	NOUN
m-1112	1681	16	in	in	ADP
m-1112	1681	17	0	0	NUM
m-1112	1681	18	-1	-1	CCONJ
m-1112	1681	19	,	,	PUNCT
m-1112	1681	20	may	may	AUX
m-1112	1681	21	be	be	AUX
m-1112	1681	22	considered	consider	VERB
m-1112	1681	23	as	as	ADP
m-1112	1681	24	falling	fall	VERB
m-1112	1681	25	in	in	ADP
m-1112	1681	26	linear	linear	ADJ
m-1112	1681	27	motion	motion	NOUN
m-1112	1681	28	and	and	CCONJ
m-1112	1681	29	so	so	ADV
m-1112	1681	30	issues	issue	NOUN
m-1112	1681	31	v	v	ADP
m-1112	1681	32	y	y	PROPN
m-1112	1681	33	=	=	PUNCT
m-1112	1681	34	g	g	PROPN
m-1112	1681	35	t	t	NOUN
m-1112	1681	36	or	or	CCONJ
m-1112	1681	37	time	time	NOUN
m-1112	1681	38	t	t	PROPN
m-1112	1681	39	=	=	PUNCT
m-1112	1681	40	v	v	PROPN
m-1112	1681	41	y	y	PROPN
m-1112	1681	42	g	g	PROPN
m-1112	1681	43	=	=	PUNCT
m-1112	1681	44	(	(	PUNCT
m-1112	1681	45	c	c	NOUN
m-1112	1681	46	sin𝑎𝑡	sin𝑎𝑡	ADJ
m-1112	1681	47	)	)	PUNCT
m-1112	1681	48	g	g	NOUN
m-1112	1681	49	,	,	PUNCT
m-1112	1681	50	as	as	ADP
m-1112	1681	51	halve	halve	NOUN
m-1112	1681	52	period	period	NOUN
m-1112	1681	53	with	with	ADP
m-1112	1681	54	total	total	ADJ
m-1112	1681	55	period	period	NOUN
m-1112	1681	56	→	→	SYM
m-1112	1681	57	t	t	NOUN
m-1112	1681	58	=	=	SYM
m-1112	1681	59	2	2	NUM
m-1112	1681	60	(	(	PUNCT
m-1112	1681	61	c	c	NOUN
m-1112	1681	62	sin𝑎𝑡	sin𝑎𝑡	ADJ
m-1112	1681	63	)	)	PUNCT
m-1112	1681	64	g	g	NOUN
m-1112	1681	65	.	.	PUNCT
m-1112	1682	1	in	in	ADP
m-1112	1682	2	figure	figure	NOUN
m-1112	1682	3	are	be	AUX
m-1112	1682	4	seen	see	VERB
m-1112	1682	5	the	the	DET
m-1112	1682	6	4	4	NUM
m-1112	1682	7	-	-	PUNCT
m-1112	1682	8	point	point	NOUN
m-1112	1682	9	positions	position	NOUN
m-1112	1682	10	,	,	PUNCT
m-1112	1682	11	at	at	ADP
m-1112	1682	12	where	where	SCONJ
m-1112	1682	13	change	change	VERB
m-1112	1682	14	the	the	DET
m-1112	1682	15	phase	phase	NOUN
m-1112	1682	16	and	and	CCONJ
m-1112	1682	17	the	the	DET
m-1112	1682	18	work	work	NOUN
m-1112	1682	19	done	do	VERB
m-1112	1682	20	in	in	ADP
m-1112	1682	21	each	each	DET
m-1112	1682	22	phase	phase	NOUN
m-1112	1682	23	of	of	ADP
m-1112	1682	24	photon`s	photon`s	NOUN
m-1112	1682	25	inner	inner	ADJ
m-1112	1682	26	motion	motion	NOUN
m-1112	1682	27	.	.	PUNCT
m-1112	1683	1	the	the	DET
m-1112	1683	2	4	4	NUM
m-1112	1683	3	phases	phase	NOUN
m-1112	1683	4	correspond	correspond	VERB
m-1112	1683	5	to	to	ADP
m-1112	1683	6	the	the	DET
m-1112	1683	7	wavelength	wavelength	NOUN
m-1112	1683	8	.	.	PUNCT
m-1112	1684	1	λ	λ	INTJ
m-1112	1684	2	,	,	PUNCT
m-1112	1684	3	as	as	ADP
m-1112	1684	4	λ	λ	PROPN
m-1112	1684	5	/	/	SYM
m-1112	1684	6	4	4	NUM
m-1112	1684	7	.	.	PUNCT
m-1112	1685	1	distance	distance	NOUN
m-1112	1685	2	with	with	ADP
m-1112	1685	3	90	90	NUM
m-1112	1685	4	°	°	NOUN
m-1112	1685	5	=	=	PUNCT
m-1112	1685	6	𝜋	𝜋	ADP
m-1112	1685	7	2	2	NUM
m-1112	1685	8	to	to	PART
m-1112	1685	9	be	be	AUX
m-1112	1685	10	the	the	DET
m-1112	1685	11	change	change	NOUN
m-1112	1685	12	of	of	ADP
m-1112	1685	13	phase	phase	NOUN
m-1112	1685	14	.	.	PUNCT
m-1112	1686	1	this	this	PRON
m-1112	1686	2	means	mean	VERB
m-1112	1686	3	that	that	SCONJ
m-1112	1686	4	the	the	DET
m-1112	1686	5	produced	produce	VERB
m-1112	1686	6	work	work	NOUN
m-1112	1686	7	in	in	ADP
m-1112	1686	8	prior	prior	ADJ
m-1112	1686	9	phase	phase	NOUN
m-1112	1686	10	area	area	NOUN
m-1112	1686	11	as	as	ADP
m-1112	1686	12	the	the	DET
m-1112	1686	13	golden	golden	ADJ
m-1112	1686	14	–	–	PUNCT
m-1112	1686	15	ratio	ratio	NOUN
m-1112	1686	16	pattern	pattern	NOUN
m-1112	1686	17	is	be	AUX
m-1112	1686	18	stored	store	VERB
m-1112	1686	19	in	in	ADP
m-1112	1686	20	the	the	DET
m-1112	1686	21	next	next	ADJ
m-1112	1686	22	and	and	CCONJ
m-1112	1686	23	perpendicular	perpendicular	ADJ
m-1112	1686	24	phase	phase	NOUN
m-1112	1686	25	-	-	PUNCT
m-1112	1686	26	area	area	NOUN
m-1112	1686	27	.	.	PUNCT
m-1112	1687	1	the	the	DET
m-1112	1687	2	total	total	ADJ
m-1112	1687	3	distance	distance	NOUN
m-1112	1687	4	for	for	ADP
m-1112	1687	5	doing	do	VERB
m-1112	1687	6	work	work	NOUN
m-1112	1687	7	is	be	AUX
m-1112	1687	8	the	the	DET
m-1112	1687	9	wavelength	wavelength	NOUN
m-1112	1687	10	λ	λ	PROPN
m-1112	1687	11	,	,	PUNCT
m-1112	1687	12	in	in	ADP
m-1112	1687	13	total	total	ADJ
m-1112	1687	14	period	period	NOUN
m-1112	1687	15	t	t	PROPN
m-1112	1687	16	as	as	ADP
m-1112	1687	17	λ	λ	PROPN
m-1112	1687	18	=	=	SYM
m-1112	1687	19	cx	cx	PROPN
m-1112	1687	20	t	t	PROPN
m-1112	1687	21	=	=	PUNCT
m-1112	1687	22	c	c	X
m-1112	1687	23	.cos	.cos	PUNCT
m-1112	1687	24	𝑎	𝑎	X
m-1112	1687	25	.t	.t	NOUN
m-1112	1687	26	or	or	CCONJ
m-1112	1687	27	λ	λ	X
m-1112	1687	28	=	=	SYM
m-1112	1687	29	c	c	PROPN
m-1112	1687	30	.	.	PUNCT
m-1112	1688	1	cos	cos	PROPN
m-1112	1689	1	𝑎	𝑎	X
m-1112	1689	2	.	.	NOUN
m-1112	1689	3	2	2	NUM
m-1112	1689	4	(	(	PUNCT
m-1112	1689	5	c	c	NOUN
m-1112	1689	6	sin𝑎𝑡	sin𝑎𝑡	ADJ
m-1112	1689	7	)	)	PUNCT
m-1112	1689	8	g	g	NOUN
m-1112	1689	9	=	=	PUNCT
m-1112	1690	1	[	[	PUNCT
m-1112	1690	2	2	2	NUM
m-1112	1690	3	c	c	NOUN
m-1112	1690	4	²	²	NUM
m-1112	1690	5	g	g	NOUN
m-1112	1690	6	]	]	PUNCT
m-1112	1690	7	sin	sin	NOUN
m-1112	1690	8	𝑎	𝑎	X
m-1112	1690	9	,	,	PUNCT
m-1112	1690	10	cos	cos	X
m-1112	1690	11	𝑎	𝑎	NOUN
m-1112	1690	12	=	=	X
m-1112	1690	13	[	[	PUNCT
m-1112	1690	14	𝐜	𝐜	NOUN
m-1112	1690	15	²	²	NUM
m-1112	1690	16	𝐠	𝐠	X
m-1112	1690	17	]	]	PUNCT
m-1112	1690	18	𝐬𝐢𝐧	𝐬𝐢𝐧	ADP
m-1112	1690	19	𝟐𝒂	𝟐𝒂	NOUN
m-1112	1690	20	,	,	PUNCT
m-1112	1690	21	…	…	PUNCT
m-1112	1690	22	…	…	PUNCT
m-1112	1690	23	(	(	PUNCT
m-1112	1690	24	1	1	NUM
m-1112	1690	25	)	)	PUNCT
m-1112	1690	26	since	since	SCONJ
m-1112	1690	27	from	from	ADP
m-1112	1690	28	trigonometry	trigonometry	NOUN
m-1112	1690	29	exists	exist	VERB
m-1112	1690	30	,	,	PUNCT
m-1112	1690	31	sin	sin	VERB
m-1112	1690	32	2𝑎	2𝑎	NUM
m-1112	1690	33	=	=	SYM
m-1112	1690	34	2	2	NUM
m-1112	1690	35	sin	sin	NOUN
m-1112	1690	36	𝑎	𝑎	NOUN
m-1112	1690	37	.	.	PUNCT
m-1112	1691	1	cos	cos	PROPN
m-1112	1691	2	𝑎	𝑎	X
m-1112	1691	3	.	.	PUNCT
m-1112	1692	1	the	the	DET
m-1112	1692	2	maximum	maximum	ADJ
m-1112	1692	3	wavelength	wavelength	NOUN
m-1112	1692	4	λ	λ	PROPN
m-1112	1692	5	happens	happen	VERB
m-1112	1692	6	when	when	SCONJ
m-1112	1692	7	𝐬𝐢𝐧𝟐𝒂	𝐬𝐢𝐧𝟐𝒂	PUNCT
m-1112	1693	1	=	=	NOUN
m-1112	1693	2	1	1	NUM
m-1112	1693	3	or	or	CCONJ
m-1112	1693	4	2a	2a	NUM
m-1112	1693	5	=	=	SYM
m-1112	1693	6	90	90	NUM
m-1112	1693	7	°	°	NUM
m-1112	1693	8	and	and	CCONJ
m-1112	1693	9	a	a	DET
m-1112	1693	10	=	=	SYM
m-1112	1693	11	45	45	NUM
m-1112	1693	12	°	°	NOUN
m-1112	1693	13	,	,	PUNCT
m-1112	1693	14	i.e.	i.e.	X
m-1112	1693	15	→the	→the	DET
m-1112	1693	16	total	total	ADJ
m-1112	1693	17	motion	motion	NOUN
m-1112	1693	18	in	in	ADP
m-1112	1693	19	the	the	DET
m-1112	1693	20	wavelength	wavelength	NOUN
m-1112	1693	21	,	,	PUNCT
m-1112	1693	22	λ	λ	INTJ
m-1112	1693	23	,	,	PUNCT
m-1112	1693	24	corresponds	correspond	VERB
m-1112	1693	25	to	to	ADP
m-1112	1693	26	the	the	DET
m-1112	1693	27	angle	angle	NOUN
m-1112	1693	28	a	a	DET
m-1112	1693	29	=	=	SYM
m-1112	1693	30	45	45	NUM
m-1112	1693	31	°	°	NOUN
m-1112	1693	32	,	,	PUNCT
m-1112	1693	33	meaning	mean	VERB
m-1112	1693	34	that	that	SCONJ
m-1112	1693	35	the	the	DET
m-1112	1693	36	motion	motion	NOUN
m-1112	1693	37	of	of	ADP
m-1112	1693	38	space	space	NOUN
m-1112	1693	39	,	,	PUNCT
m-1112	1693	40	the	the	DET
m-1112	1693	41	electric	electric	NOUN
m-1112	1693	42	-	-	PUNCT
m-1112	1693	43	field	field	NOUN
m-1112	1693	44	,	,	PUNCT
m-1112	1693	45	and	and	CCONJ
m-1112	1693	46	anti	anti	ADJ
m-1112	1693	47	-	-	NOUN
m-1112	1693	48	space	space	NOUN
m-1112	1693	49	,	,	PUNCT
m-1112	1693	50	the	the	DET
m-1112	1693	51	magnetic	magnetic	ADJ
m-1112	1693	52	-	-	PUNCT
m-1112	1693	53	field	field	NOUN
m-1112	1693	54	,	,	PUNCT
m-1112	1693	55	equilibrium	equilibrium	NOUN
m-1112	1693	56	as	as	ADP
m-1112	1693	57	an	an	DET
m-1112	1693	58	bellow	bellow	NOUN
m-1112	1693	59	.	.	PUNCT
m-1112	1694	1	the	the	DET
m-1112	1694	2	two	two	NUM
m-1112	1694	3	wings	wing	NOUN
m-1112	1694	4	in	in	ADP
m-1112	1694	5	90	90	NUM
m-1112	1694	6	°	°	NOUN
m-1112	1694	7	type	type	NOUN
m-1112	1694	8	simultaneously	simultaneously	ADV
m-1112	1694	9	oscillate	oscillate	ADJ
m-1112	1694	10	to	to	ADP
m-1112	1694	11	its	its	PRON
m-1112	1694	12	45	45	NUM
m-1112	1694	13	°	°	NUM
m-1112	1694	14	bisector	bisector	NOUN
m-1112	1694	15	-axis	-axis	NOUN
m-1112	1694	16	,	,	PUNCT
m-1112	1694	17	and	and	CCONJ
m-1112	1694	18	the	the	DET
m-1112	1694	19	produced	produce	VERB
m-1112	1694	20	work	work	NOUN
m-1112	1694	21	from	from	ADP
m-1112	1694	22	the	the	DET
m-1112	1694	23	electric	electric	ADJ
m-1112	1694	24	-	-	PUNCT
m-1112	1694	25	field	field	NOUN
m-1112	1694	26	-	-	PUNCT
m-1112	1694	27	area	area	NOUN
m-1112	1694	28	is	be	AUX
m-1112	1694	29	stored	store	VERB
m-1112	1694	30	into	into	ADP
m-1112	1694	31	the	the	DET
m-1112	1694	32	magnetic	magnetic	ADJ
m-1112	1694	33	-	-	PUNCT
m-1112	1694	34	field	field	NOUN
m-1112	1694	35	area	area	NOUN
m-1112	1694	36	.	.	PUNCT
m-1112	1695	1	the	the	DET
m-1112	1695	2	common	common	ADJ
m-1112	1695	3	axis	axis	NOUN
m-1112	1695	4	of	of	ADP
m-1112	1695	5	the	the	DET
m-1112	1695	6	two	two	NUM
m-1112	1695	7	perpendicular	perpendicular	ADJ
m-1112	1695	8	fields	field	NOUN
m-1112	1695	9	,	,	PUNCT
m-1112	1695	10	carry	carry	VERB
m-1112	1695	11	the	the	DET
m-1112	1695	12	g	g	NOUN
m-1112	1695	13	-	-	PUNCT
m-1112	1695	14	ratio	ratio	NOUN
m-1112	1695	15	surfaces	surface	NOUN
m-1112	1695	16	,	,	PUNCT
m-1112	1695	17	runs	run	VERB
m-1112	1695	18	with	with	ADP
m-1112	1695	19	the	the	DET
m-1112	1695	20	same	same	ADJ
m-1112	1695	21	velocity	velocity	NOUN
m-1112	1695	22	c	c	NOUN
m-1112	1695	23	̅	̅	NOUN
m-1112	1695	24	to	to	ADP
m-1112	1695	25	the	the	DET
m-1112	1695	26	direction	direction	NOUN
m-1112	1695	27	of	of	ADP
m-1112	1695	28	the	the	DET
m-1112	1695	29	inner	inner	ADJ
m-1112	1695	30	motion	motion	NOUN
m-1112	1695	31	or	or	CCONJ
m-1112	1695	32	,	,	PUNCT
m-1112	1695	33	from	from	ADP
m-1112	1695	34	90	90	NUM
m-1112	1695	35	°	°	NOUN
m-1112	1695	36	→	→	SYM
m-1112	1695	37	45	45	NUM
m-1112	1695	38	°	°	NOUN
m-1112	1695	39	,	,	PUNCT
m-1112	1695	40	the	the	DET
m-1112	1695	41	created	create	VERB
m-1112	1695	42	work	work	NOUN
m-1112	1695	43	w	w	NOUN
m-1112	1696	1	=	=	PUNCT
m-1112	1696	2	c	c	PROPN
m-1112	1696	3	y	y	PROPN
m-1112	1696	4	g	g	PROPN
m-1112	1696	5	,	,	PUNCT
m-1112	1696	6	is	be	AUX
m-1112	1696	7	symmetrically	symmetrically	ADV
m-1112	1696	8	stored	store	VERB
m-1112	1696	9	from	from	ADP
m-1112	1696	10	0	0	NUM
m-1112	1696	11	°	°	NOUN
m-1112	1696	12	→	→	SYM
m-1112	1696	13	45	45	NUM
m-1112	1696	14	°	°	PROPN
m-1112	1696	15	.	.	PUNCT
m-1112	1697	1	the	the	DET
m-1112	1697	2	created	create	VERB
m-1112	1697	3	work	work	NOUN
m-1112	1697	4	in	in	ADP
m-1112	1697	5	[	[	PUNCT
m-1112	1697	6	0	0	NUM
m-1112	1697	7	-	-	SYM
m-1112	1697	8	1	1	NUM
m-1112	1697	9	]	]	PUNCT
m-1112	1697	10	is	be	AUX
m-1112	1697	11	in	in	ADP
m-1112	1697	12	→	→	SYM
m-1112	1697	13	λ	λ	X
m-1112	1697	14	/	/	SYM
m-1112	1697	15	4	4	NUM
m-1112	1697	16	of	of	ADP
m-1112	1697	17	transverse	transverse	NOUN
m-1112	1697	18	surface	surface	NOUN
m-1112	1697	19	and	and	CCONJ
m-1112	1697	20	is	be	AUX
m-1112	1697	21	stored	store	VERB
m-1112	1697	22	in	in	ADP
m-1112	1697	23	the	the	DET
m-1112	1697	24	horizontal	horizontal	ADJ
m-1112	1697	25	and	and	CCONJ
m-1112	1697	26	perpendicular	perpendicular	ADJ
m-1112	1697	27	surface	surface	NOUN
m-1112	1697	28	[	[	PUNCT
m-1112	1697	29	1`-2	1`-2	NOUN
m-1112	1697	30	]	]	PUNCT
m-1112	1697	31	=	=	PUNCT
m-1112	1697	32	λ	λ	X
m-1112	1697	33	/	/	SYM
m-1112	1697	34	4	4	NUM
m-1112	1697	35	.	.	PUNCT
m-1112	1698	1	surface	surface	NOUN
m-1112	1698	2	[	[	PUNCT
m-1112	1698	3	0	0	NUM
m-1112	1698	4	-1	-1	CCONJ
m-1112	1698	5	-1	-1	NOUN
m-1112	1698	6	`	`	PUNCT
m-1112	1698	7	]	]	PUNCT
m-1112	1698	8	=	=	PUNCT
m-1112	1698	9	⏊	⏊	PROPN
m-1112	1698	10	surface	surface	NOUN
m-1112	1698	11	[	[	PUNCT
m-1112	1698	12	1	1	NUM
m-1112	1698	13	`	`	NUM
m-1112	1698	14	-2	-2	NOUN
m-1112	1698	15	`	`	PUNCT
m-1112	1698	16	-2	-2	INTJ
m-1112	1698	17	]	]	PUNCT
m-1112	1698	18	.	.	PUNCT
m-1112	1699	1	the	the	DET
m-1112	1699	2	created	create	VERB
m-1112	1699	3	work	work	NOUN
m-1112	1699	4	in	in	ADP
m-1112	1699	5	[	[	PUNCT
m-1112	1699	6	1	1	NUM
m-1112	1699	7	-	-	SYM
m-1112	1699	8	2	2	NUM
m-1112	1699	9	]	]	PUNCT
m-1112	1699	10	is	be	AUX
m-1112	1699	11	in	in	ADP
m-1112	1699	12	→	→	SYM
m-1112	1699	13	λ	λ	X
m-1112	1699	14	/	/	SYM
m-1112	1699	15	4	4	NUM
m-1112	1699	16	of	of	ADP
m-1112	1699	17	transverse	transverse	NOUN
m-1112	1699	18	surface	surface	NOUN
m-1112	1699	19	and	and	CCONJ
m-1112	1699	20	is	be	AUX
m-1112	1699	21	stored	store	VERB
m-1112	1699	22	in	in	ADP
m-1112	1699	23	the	the	DET
m-1112	1699	24	horizontal	horizontal	ADJ
m-1112	1699	25	and	and	CCONJ
m-1112	1699	26	perpendicular	perpendicular	ADJ
m-1112	1699	27	surface	surface	NOUN
m-1112	1699	28	[	[	PUNCT
m-1112	1699	29	2	2	NUM
m-1112	1699	30	-	-	SYM
m-1112	1699	31	3	3	NUM
m-1112	1699	32	`	`	PUNCT
m-1112	1699	33	]	]	PUNCT
m-1112	1700	1	=	=	PUNCT
m-1112	1700	2	λ	λ	X
m-1112	1700	3	/	/	SYM
m-1112	1700	4	4	4	NUM
m-1112	1700	5	.	.	PUNCT
m-1112	1701	1	surface	surface	NOUN
m-1112	1701	2	[	[	PUNCT
m-1112	1701	3	1	1	NUM
m-1112	1701	4	-2	-2	INTJ
m-1112	1701	5	-1	-1	NOUN
m-1112	1701	6	`	`	PUNCT
m-1112	1701	7	]	]	PUNCT
m-1112	1701	8	=	=	PUNCT
m-1112	1701	9	⏊	⏊	PROPN
m-1112	1701	10	surface	surface	NOUN
m-1112	1701	11	[	[	PUNCT
m-1112	1701	12	2	2	NUM
m-1112	1701	13	`	`	PUNCT
m-1112	1701	14	-3	-3	INTJ
m-1112	1701	15	`	`	PUNCT
m-1112	1701	16	-2	-2	INTJ
m-1112	1701	17	]	]	PUNCT
m-1112	1701	18	.	.	PUNCT
m-1112	1702	1	the	the	DET
m-1112	1702	2	created	create	VERB
m-1112	1702	3	work	work	NOUN
m-1112	1702	4	in	in	ADP
m-1112	1702	5	[	[	PUNCT
m-1112	1702	6	2	2	NUM
m-1112	1702	7	-	-	SYM
m-1112	1702	8	3	3	NUM
m-1112	1702	9	]	]	PUNCT
m-1112	1702	10	is	be	AUX
m-1112	1702	11	in	in	ADP
m-1112	1702	12	→	→	SYM
m-1112	1702	13	λ	λ	X
m-1112	1702	14	/	/	SYM
m-1112	1702	15	4	4	NUM
m-1112	1702	16	of	of	ADP
m-1112	1702	17	transverse	transverse	NOUN
m-1112	1702	18	surface	surface	NOUN
m-1112	1702	19	and	and	CCONJ
m-1112	1702	20	is	be	AUX
m-1112	1702	21	stored	store	VERB
m-1112	1702	22	in	in	ADP
m-1112	1702	23	the	the	DET
m-1112	1702	24	horizontal	horizontal	ADJ
m-1112	1702	25	and	and	CCONJ
m-1112	1702	26	perpendicular	perpendicular	ADJ
m-1112	1702	27	surface	surface	NOUN
m-1112	1702	28	[	[	PUNCT
m-1112	1702	29	3	3	NUM
m-1112	1702	30	`	`	PUNCT
m-1112	1702	31	-4	-4	PUNCT
m-1112	1702	32	]	]	PUNCT
m-1112	1703	1	=	=	PUNCT
m-1112	1703	2	λ	λ	X
m-1112	1703	3	/	/	SYM
m-1112	1703	4	4	4	NUM
m-1112	1703	5	.	.	PUNCT
m-1112	1704	1	surface	surface	NOUN
m-1112	1704	2	[	[	PUNCT
m-1112	1704	3	2	2	NUM
m-1112	1704	4	-3	-3	INTJ
m-1112	1704	5	-3	-3	INTJ
m-1112	1704	6	`	`	PUNCT
m-1112	1704	7	]	]	PUNCT
m-1112	1705	1	=	=	PUNCT
m-1112	1705	2	⏊	⏊	PROPN
m-1112	1705	3	surface	surface	NOUN
m-1112	1705	4	[	[	PUNCT
m-1112	1705	5	3	3	NUM
m-1112	1705	6	`	`	PUNCT
m-1112	1705	7	-4	-4	INTJ
m-1112	1705	8	`	`	PUNCT
m-1112	1705	9	-4	-4	INTJ
m-1112	1705	10	`	`	PUNCT
m-1112	1705	11	]	]	PUNCT
m-1112	1705	12	.	.	PUNCT
m-1112	1706	1	the	the	DET
m-1112	1706	2	created	create	VERB
m-1112	1706	3	work	work	NOUN
m-1112	1706	4	in	in	ADP
m-1112	1706	5	[	[	PUNCT
m-1112	1706	6	3	3	NUM
m-1112	1706	7	-	-	SYM
m-1112	1706	8	4	4	NUM
m-1112	1706	9	]	]	PUNCT
m-1112	1706	10	is	be	AUX
m-1112	1706	11	in	in	ADP
m-1112	1706	12	→	→	SYM
m-1112	1706	13	λ	λ	X
m-1112	1706	14	/	/	SYM
m-1112	1706	15	4	4	NUM
m-1112	1706	16	of	of	ADP
m-1112	1706	17	transverse	transverse	NOUN
m-1112	1706	18	surface	surface	NOUN
m-1112	1706	19	and	and	CCONJ
m-1112	1706	20	is	be	AUX
m-1112	1706	21	stored	store	VERB
m-1112	1706	22	in	in	ADP
m-1112	1706	23	the	the	DET
m-1112	1706	24	horizontal	horizontal	ADJ
m-1112	1706	25	and	and	CCONJ
m-1112	1706	26	perpendicular	perpendicular	ADJ
m-1112	1706	27	surface	surface	NOUN
m-1112	1706	28	[	[	PUNCT
m-1112	1706	29	3	3	NUM
m-1112	1706	30	`	`	PUNCT
m-1112	1706	31	-4	-4	PUNCT
m-1112	1706	32	]	]	PUNCT
m-1112	1707	1	=	=	PUNCT
m-1112	1707	2	λ	λ	X
m-1112	1707	3	/	/	SYM
m-1112	1707	4	4	4	NUM
m-1112	1707	5	.	.	PUNCT
m-1112	1708	1	surface	surface	NOUN
m-1112	1708	2	[	[	PUNCT
m-1112	1708	3	3	3	NUM
m-1112	1708	4	-4	-4	INTJ
m-1112	1708	5	-2	-2	NOUN
m-1112	1708	6	]	]	PUNCT
m-1112	1708	7	=	=	PUNCT
m-1112	1708	8	⏊	⏊	NUM
m-1112	1708	9	surface	surface	NOUN
m-1112	1708	10	[	[	PUNCT
m-1112	1708	11	4	4	NUM
m-1112	1708	12	`	`	PUNCT
m-1112	1708	13	-5	-5	ADJ
m-1112	1708	14	`	`	PUNCT
m-1112	1708	15	-4	-4	PUNCT
m-1112	1708	16	]	]	PUNCT
m-1112	1708	17	.	.	PUNCT
m-1112	1709	1	since	since	SCONJ
m-1112	1709	2	from	from	ADP
m-1112	1709	3	trigonometry	trigonometry	NOUN
m-1112	1709	4	issues	issue	NOUN
m-1112	1709	5	sin	sin	VERB
m-1112	1709	6	2𝜋=	2𝜋=	NUM
m-1112	1709	7	sin(180	sin(180	PROPN
m-1112	1709	8	−	−	NUM
m-1112	1709	9	2𝑎	2𝑎	NUM
m-1112	1709	10	)	)	PUNCT
m-1112	1710	1	=	=	SYM
m-1112	1710	2	sιn	sιn	NOUN
m-1112	1710	3	2(90	2(90	NUM
m-1112	1710	4	−	−	NOUN
m-1112	1711	1	𝑎	𝑎	X
m-1112	1711	2	)	)	PUNCT
m-1112	1711	3	then	then	ADV
m-1112	1711	4	(	(	PUNCT
m-1112	1711	5	1	1	X
m-1112	1711	6	)	)	PUNCT
m-1112	1711	7	becomes	become	VERB
m-1112	1711	8	.	.	PUNCT
m-1112	1712	1	λ	λ	X
m-1112	1712	2	=	=	PUNCT
m-1112	1712	3	c	c	X
m-1112	1712	4	cos	cos	PROPN
m-1112	1712	5	𝑎	𝑎	PROPN
m-1112	1712	6	2	2	NUM
m-1112	1712	7	(	(	PUNCT
m-1112	1712	8	c	c	NOUN
m-1112	1712	9	sin𝑎𝑡	sin𝑎𝑡	ADJ
m-1112	1712	10	)	)	PUNCT
m-1112	1712	11	g	g	NOUN
m-1112	1713	1	=	=	PUNCT
m-1112	1713	2	[	[	PUNCT
m-1112	1713	3	2	2	NUM
m-1112	1713	4	c	c	NOUN
m-1112	1713	5	²	²	NUM
m-1112	1713	6	g	g	NOUN
m-1112	1713	7	]	]	PUNCT
m-1112	1713	8	sin	sin	NOUN
m-1112	1713	9	𝑎	𝑎	X
m-1112	1713	10	,	,	PUNCT
m-1112	1713	11	cos	cos	X
m-1112	1713	12	𝑎	𝑎	NOUN
m-1112	1713	13	=	=	X
m-1112	1713	14	[	[	PUNCT
m-1112	1713	15	𝐜	𝐜	NOUN
m-1112	1713	16	²	²	NUM
m-1112	1713	17	𝐠	𝐠	X
m-1112	1713	18	]	]	PUNCT
m-1112	1713	19	𝐬𝐢𝐧	𝐬𝐢𝐧	ADP
m-1112	1713	20	𝟐𝒂	𝟐𝒂	X
m-1112	1713	21	=	=	PUNCT
m-1112	1714	1	[	[	PUNCT
m-1112	1714	2	𝐜	𝐜	NOUN
m-1112	1714	3	²	²	NUM
m-1112	1714	4	𝐠	𝐠	X
m-1112	1714	5	]	]	X
m-1112	1714	6	.sin(𝜋	.sin(𝜋	PUNCT
m-1112	1715	1	−	−	NOUN
m-1112	1715	2	2𝑎	2𝑎	NUM
m-1112	1715	3	)	)	PUNCT
m-1112	1716	1	=	=	PUNCT
m-1112	1716	2	[	[	PUNCT
m-1112	1716	3	𝐜	𝐜	NOUN
m-1112	1716	4	²	²	NUM
m-1112	1716	5	𝐠	𝐠	X
m-1112	1716	6	]	]	X
m-1112	1716	7	.sin	.sin	NOUN
m-1112	1716	8	(	(	PUNCT
m-1112	1716	9	𝜋	𝜋	NOUN
m-1112	1716	10	2	2	NUM
m-1112	1716	11	−	−	NUM
m-1112	1716	12	𝑎	𝑎	NOUN
m-1112	1716	13	)	)	PUNCT
m-1112	1716	14	…	…	PUNCT
m-1112	1716	15	(	(	PUNCT
m-1112	1716	16	2	2	NUM
m-1112	1716	17	)	)	PUNCT
m-1112	1716	18	since	since	SCONJ
m-1112	1716	19	𝐬𝐢𝐧	𝐬𝐢𝐧	ADP
m-1112	1716	20	𝟐𝒂	𝟐𝒂	X
m-1112	1716	21	=	=	SYM
m-1112	1716	22	sin(180	sin(180	PROPN
m-1112	1716	23	−	−	NUM
m-1112	1716	24	2𝑎	2𝑎	NUM
m-1112	1716	25	)	)	PUNCT
m-1112	1716	26	=	=	PRON
m-1112	1716	27	sin(𝜋	sin(𝜋	VERB
m-1112	1716	28	−	−	NOUN
m-1112	1716	29	2𝑎	2𝑎	NUM
m-1112	1716	30	)	)	PUNCT
m-1112	1716	31	,	,	PUNCT
m-1112	1716	32	and	and	CCONJ
m-1112	1716	33	also	also	ADV
m-1112	1716	34	𝐬𝐢𝐧	𝐬𝐢𝐧	ADP
m-1112	1716	35	𝟐𝒂	𝟐𝒂	X
m-1112	1716	36	=	=	SYM
m-1112	1716	37	sin(180	sin(180	PROPN
m-1112	1716	38	−	−	NUM
m-1112	1716	39	2𝑎	2𝑎	NUM
m-1112	1716	40	)	)	PUNCT
m-1112	1716	41	=	=	SYM
m-1112	1716	42	sin	sin	NOUN
m-1112	1716	43	(	(	PUNCT
m-1112	1716	44	𝜋	𝜋	NOUN
m-1112	1716	45	2	2	NUM
m-1112	1716	46	−	−	NUM
m-1112	1716	47	𝑎	𝑎	NOUN
m-1112	1716	48	)	)	PUNCT
m-1112	1716	49	…	…	PUNCT
m-1112	1716	50	…	…	PUNCT
m-1112	1716	51	(	(	PUNCT
m-1112	1716	52	1a	1a	NUM
m-1112	1716	53	)	)	PUNCT
m-1112	1716	54	ijo	ijo	PROPN
m-1112	1716	55	international	international	PROPN
m-1112	1716	56	journal	journal	PROPN
m-1112	1716	57	of	of	ADP
m-1112	1716	58	mathematics	mathematics	PROPN
m-1112	1716	59	(	(	PUNCT
m-1112	1716	60	issn	issn	PROPN
m-1112	1716	61	:	:	PUNCT
m-1112	1716	62	2992	2992	NUM
m-1112	1716	63	-	-	SYM
m-1112	1716	64	4421	4421	NUM
m-1112	1716	65	)	)	PUNCT
m-1112	1717	1	volume	volume	NOUN
m-1112	1717	2	08	08	NUM
m-1112	1718	1	|	|	ADV
m-1112	1718	2	issue	issue	NOUN
m-1112	1718	3	08	08	NUM
m-1112	1719	1	|	|	ADV
m-1112	1719	2	august	august	PROPN
m-1112	1719	3	2025	2025	NUM
m-1112	1719	4	|	|	ADV
m-1112	1719	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1719	6	ijo	ijo	PROPN
m-1112	1719	7	journals	journal	NOUN
m-1112	1719	8	61	61	NUM
m-1112	1719	9	the	the	DET
m-1112	1719	10	fundamental	fundamental	ADJ
m-1112	1719	11	particles	particle	NOUN
m-1112	1719	12	origination	origination	NOUN
m-1112	1719	13	mechanism	mechanism	NOUN
m-1112	1719	14	in	in	ADP
m-1112	1719	15	mfmf	mfmf	PROPN
m-1112	1719	16	pns	pns	PROPN
m-1112	1719	17	caves	cave	NOUN
m-1112	1719	18	.	.	PUNCT
m-1112	1720	1	from	from	ADP
m-1112	1720	2	dual	dual	ADJ
m-1112	1720	3	-	-	PUNCT
m-1112	1720	4	photon	photon	NOUN
m-1112	1720	5	-	-	PUNCT
m-1112	1720	6	equation	equation	NOUN
m-1112	1720	7	,	,	PUNCT
m-1112	1720	8	v̅.	v̅.	PROPN
m-1112	1720	9	[	[	PUNCT
m-1112	1720	10	fn̅	fn̅	PROPN
m-1112	1720	11	+	+	NUM
m-1112	1720	12	fn	fn	NOUN
m-1112	1720	13	]	]	PUNCT
m-1112	1720	14	≡	≡	PROPN
m-1112	1720	15	|	|	ADV
m-1112	1720	16	𝐯	𝐯	X
m-1112	1720	17	𝛑².𝐫⁴𝐧	𝛑².𝐫⁴𝐧	NOUN
m-1112	1720	18	|	|	NOUN
m-1112	1720	19	.	.	PUNCT
m-1112	1721	1	b̅n	b̅n	PROPN
m-1112	1722	1	+	+	CCONJ
m-1112	1722	2	|	|	ADV
m-1112	1722	3	c	c	NOUN
m-1112	1723	1	̅|	̅|	INTJ
m-1112	1723	2	fn	fn	INTJ
m-1112	1723	3	,	,	PUNCT
m-1112	1723	4	when	when	SCONJ
m-1112	1723	5	c	c	NOUN
m-1112	1723	6	=	=	SYM
m-1112	1723	7	0	0	NUM
m-1112	1723	8	or	or	CCONJ
m-1112	1723	9	c	c	NOUN
m-1112	1723	10	=	=	SYM
m-1112	1723	11	c⃖	c⃖	ADJ
m-1112	1723	12	,	,	PUNCT
m-1112	1723	13	then	then	ADV
m-1112	1723	14	photon	photon	NOUN
m-1112	1723	15	motion	motion	NOUN
m-1112	1723	16	becomes	become	VERB
m-1112	1723	17	→	→	PUNCT
m-1112	1723	18	|	|	ADV
m-1112	1723	19	𝐯	𝐯	ADP
m-1112	1723	20	𝛑².𝐫⁴𝐧	𝛑².𝐫⁴𝐧	NOUN
m-1112	1723	21	|	|	ADV
m-1112	1723	22	.	.	PUNCT
m-1112	1724	1	b̅n	b̅n	PROPN
m-1112	1724	2	←	←	PROPN
m-1112	1724	3	≡	≡	PROPN
m-1112	1724	4	spin	spin	NOUN
m-1112	1724	5	.	.	PUNCT
m-1112	1725	1	i.e.	i.e.	X
m-1112	1725	2	the	the	DET
m-1112	1725	3	stationary	stationary	ADJ
m-1112	1725	4	photons	photon	NOUN
m-1112	1725	5	exist	exist	VERB
m-1112	1725	6	as	as	ADP
m-1112	1725	7	their	their	PRON
m-1112	1725	8	spin	spin	NOUN
m-1112	1725	9	only	only	ADV
m-1112	1725	10	.	.	PUNCT
m-1112	1726	1	the	the	DET
m-1112	1726	2	rest	rest	NOUN
m-1112	1726	3	-	-	PUNCT
m-1112	1726	4	space	space	NOUN
m-1112	1726	5	is	be	AUX
m-1112	1726	6	the	the	DET
m-1112	1726	7	part	part	NOUN
m-1112	1726	8	|	|	ADV
m-1112	1726	9	𝐯	𝐯	X
m-1112	1726	10	𝛑².𝐫⁴𝐧	𝛑².𝐫⁴𝐧	NOUN
m-1112	1726	11	|	|	NOUN
m-1112	1726	12	.	.	PUNCT
m-1112	1727	1	b̅n	b̅n	PROPN
m-1112	1727	2	where	where	SCONJ
m-1112	1727	3	v	v	NOUN
m-1112	1727	4	=	=	SYM
m-1112	1727	5	n.π.c	n.π.c	NOUN
m-1112	1727	6	,	,	PUNCT
m-1112	1727	7	and	and	CCONJ
m-1112	1727	8	communication	communication	NOUN
m-1112	1727	9	code	code	NOUN
m-1112	1727	10	to	to	PART
m-1112	1727	11	be	be	AUX
m-1112	1727	12	the	the	DET
m-1112	1727	13	term	term	NOUN
m-1112	1727	14	|	|	INTJ
m-1112	1727	15	𝐯	𝐯	X
m-1112	1727	16	𝛑².𝐫⁴𝐧	𝛑².𝐫⁴𝐧	PROPN
m-1112	1727	17	|=	|=	PUNCT
m-1112	1727	18	|	|	ADV
m-1112	1727	19	n.𝜋𝑐	n.𝜋𝑐	PROPN
m-1112	1727	20	𝛑².𝐫⁴𝐧	𝛑².𝐫⁴𝐧	NOUN
m-1112	1727	21	|	|	ADV
m-1112	1727	22	=	=	PUNCT
m-1112	1728	1	|	|	NOUN
m-1112	1728	2	𝑛.𝑐	𝑛.𝑐	VERB
m-1112	1728	3	𝝅.𝒓⁴	𝝅.𝒓⁴	VERB
m-1112	1728	4	|=|	|=|	PROPN
m-1112	1728	5	𝐰	𝐰	X
m-1112	1728	6	𝐫	𝐫	X
m-1112	1728	7	𝛑𝟐.𝐫⁴	𝛑𝟐.𝐫⁴	PROPN
m-1112	1729	1	|	|	ADV
m-1112	1729	2	=	=	PUNCT
m-1112	1730	1	|	|	ADV
m-1112	1730	2	𝟐	𝟐	NUM
m-1112	1730	3	𝛑.𝐟	𝛑.𝐟	X
m-1112	1730	4	𝛑	𝛑	PROPN
m-1112	1730	5	𝟐𝐫³	𝟐𝐫³	PUNCT
m-1112	1731	1	|	|	ADV
m-1112	1731	2	=	=	SYM
m-1112	1731	3	|	|	ADJ
m-1112	1731	4	𝟐	𝟐	X
m-1112	1731	5	.𝐟	.𝐟	X
m-1112	1731	6	(	(	PUNCT
m-1112	1731	7	𝛑	𝛑	PROPN
m-1112	1731	8	𝐫	𝐫	ADP
m-1112	1731	9	³	³	X
m-1112	1731	10	)	)	PUNCT
m-1112	1731	11	|	|	ADV
m-1112	1731	12	with	with	ADP
m-1112	1731	13	electromagnetic	electromagnetic	ADJ
m-1112	1731	14	radiation	radiation	NOUN
m-1112	1731	15	the	the	DET
m-1112	1731	16	in	in	ADP
m-1112	1731	17	monads	monad	NOUN
m-1112	1731	18	frequency	frequency	NOUN
m-1112	1731	19	-	-	PUNCT
m-1112	1731	20	f	f	NOUN
m-1112	1731	21	,	,	PUNCT
m-1112	1731	22	which	which	PRON
m-1112	1731	23	is	be	AUX
m-1112	1731	24	satisfied	satisfied	ADJ
m-1112	1731	25	by	by	ADP
m-1112	1731	26	the	the	DET
m-1112	1731	27	relation	relation	NOUN
m-1112	1731	28	|	|	ADV
m-1112	1731	29	2rw	2rw	ADJ
m-1112	1731	30	2	2	NUM
m-1112	1731	31	v	v	NOUN
m-1112	1731	32	|=	|=	NOUN
m-1112	1731	33	π	π	NOUN
m-1112	1731	34	/2	/2	PUNCT
m-1112	1731	35	,	,	PUNCT
m-1112	1731	36	π	π	PROPN
m-1112	1731	37	,	,	PUNCT
m-1112	1731	38	3π	3π	PROPN
m-1112	1731	39	/2	/2	PUNCT
m-1112	1731	40	.	.	PUNCT
m-1112	1732	1	,	,	PUNCT
m-1112	1732	2	,	,	PUNCT
m-1112	1732	3	,	,	PUNCT
m-1112	1732	4	n.[π/2	n.[π/2	PROPN
m-1112	1732	5	]	]	PUNCT
m-1112	1732	6	,	,	PUNCT
m-1112	1732	7	and	and	CCONJ
m-1112	1732	8	w	w	PROPN
m-1112	1732	9	=	=	NOUN
m-1112	1732	10	n.	n.	PROPN
m-1112	1732	11	[	[	PUNCT
m-1112	1732	12	�	�	NOUN
m-1112	1732	13	̅	̅	NOUN
m-1112	1732	14	�	�	NOUN
m-1112	1732	15	2r	2r	NUM
m-1112	1732	16	]	]	X
m-1112	1732	17	x	x	X
m-1112	1732	18	[	[	PUNCT
m-1112	1732	19	π	π	PROPN
m-1112	1732	20	2	2	NUM
m-1112	1732	21	]	]	PUNCT
m-1112	1732	22	,	,	PUNCT
m-1112	1732	23	where	where	SCONJ
m-1112	1732	24	n	n	X
m-1112	1732	25	=	=	SYM
m-1112	1732	26	1	1	NUM
m-1112	1732	27	→	→	SYM
m-1112	1732	28	∞	∞	NUM
m-1112	1732	29	.	.	PUNCT
m-1112	1733	1	when	when	SCONJ
m-1112	1733	2	two	two	NUM
m-1112	1733	3	photons	photon	NOUN
m-1112	1733	4	strike	strike	VERB
m-1112	1733	5	each	each	DET
m-1112	1733	6	other	other	ADJ
m-1112	1733	7	c	c	NOUN
m-1112	1733	8	=	=	SYM
m-1112	1733	9	c⃖	c⃖	ADJ
m-1112	1733	10	,	,	PUNCT
m-1112	1733	11	or	or	CCONJ
m-1112	1733	12	reflect	reflect	VERB
m-1112	1733	13	on	on	ADP
m-1112	1733	14	a	a	DET
m-1112	1733	15	wall	wall	NOUN
m-1112	1733	16	,	,	PUNCT
m-1112	1733	17	then	then	ADV
m-1112	1733	18	c	c	NOUN
m-1112	1733	19	=	=	SYM
m-1112	1733	20	0	0	NUM
m-1112	1733	21	,	,	PUNCT
m-1112	1733	22	and	and	CCONJ
m-1112	1733	23	from	from	ADP
m-1112	1733	24	spin	spin	NOUN
m-1112	1733	25	�	�	NOUN
m-1112	1733	26	̅	̅	NOUN
m-1112	1733	27	�	�	NOUN
m-1112	1733	28	=	=	SYM
m-1112	1733	29	b̅	b̅	PROPN
m-1112	1733	30	=	=	PUNCT
m-1112	1733	31	π	π	PROPN
m-1112	1733	32	²	²	NUM
m-1112	1733	33	.	.	PUNCT
m-1112	1734	1	r	r	NOUN
m-1112	1734	2	⁴.	⁴.	PUNCT
m-1112	1734	3	f1	f1	NOUN
m-1112	1734	4	its	its	PRON
m-1112	1734	5	angular	angular	ADJ
m-1112	1734	6	velocity	velocity	NOUN
m-1112	1734	7	w	w	PROPN
m-1112	1734	8	=	=	NOUN
m-1112	1734	9	n.	n.	PROPN
m-1112	1734	10	[	[	PUNCT
m-1112	1734	11	�	�	NOUN
m-1112	1734	12	̅	̅	NOUN
m-1112	1734	13	�	�	NOUN
m-1112	1734	14	2r	2r	NUM
m-1112	1734	15	]	]	PUNCT
m-1112	1735	1	x	x	PUNCT
m-1112	1736	1	[	[	PUNCT
m-1112	1736	2	π	π	NOUN
m-1112	1736	3	2	2	NUM
m-1112	1736	4	]	]	PUNCT
m-1112	1736	5	=	=	SYM
m-1112	1736	6	2π.𝐟𝟏	2π.𝐟𝟏	NUM
m-1112	1736	7	,	,	PUNCT
m-1112	1736	8	where	where	SCONJ
m-1112	1736	9	then	then	ADV
m-1112	1736	10	its	its	PRON
m-1112	1736	11	fundamental	fundamental	ADJ
m-1112	1736	12	frequency	frequency	NOUN
m-1112	1736	13	𝐟𝟏	𝐟𝟏	NOUN
m-1112	1736	14	=	=	PUNCT
m-1112	1736	15	n.	n.	NOUN
m-1112	1736	16	[	[	PUNCT
m-1112	1736	17	�	�	NOUN
m-1112	1736	18	̅	̅	NOUN
m-1112	1736	19	�	�	NOUN
m-1112	1736	20	𝟐𝐫	𝟐𝐫	NOUN
m-1112	1736	21	]	]	X
m-1112	1736	22	x	x	X
m-1112	1736	23	[	[	PUNCT
m-1112	1736	24	𝟏	𝟏	NUM
m-1112	1736	25	𝟒	𝟒	NUM
m-1112	1736	26	]	]	PUNCT
m-1112	1736	27	=	=	PUNCT
m-1112	1736	28	n.	n.	NOUN
m-1112	1736	29	[	[	PUNCT
m-1112	1736	30	�	�	NOUN
m-1112	1736	31	̅	̅	NOUN
m-1112	1736	32	�	�	PROPN
m-1112	1736	33	𝟖.𝐫	𝟖.𝐫	NOUN
m-1112	1736	34	]	]	PUNCT
m-1112	1736	35	which	which	PRON
m-1112	1736	36	for	for	ADP
m-1112	1736	37	n	n	NOUN
m-1112	1736	38	=	=	PUNCT
m-1112	1736	39	[	[	PUNCT
m-1112	1736	40	16.𝑟²	16.𝑟²	NUM
m-1112	1736	41	v.c	v.c	PROPN
m-1112	1736	42	]	]	PUNCT
m-1112	1736	43	increases	increase	VERB
m-1112	1736	44	to	to	ADP
m-1112	1736	45	λ	λ	PROPN
m-1112	1736	46	c	c	PROPN
m-1112	1736	47	.	.	PUNCT
m-1112	1737	1	r3	r3	PROPN
m-1112	1737	2	and	and	CCONJ
m-1112	1737	3	photon	photon	NOUN
m-1112	1737	4	-	-	PUNCT
m-1112	1737	5	motion	motion	NOUN
m-1112	1737	6	becomes	become	VERB
m-1112	1737	7	→	→	PUNCT
m-1112	1737	8	|	|	ADV
m-1112	1737	9	𝐯	𝐯	ADP
m-1112	1737	10	𝛑².𝐫⁴𝐧	𝛑².𝐫⁴𝐧	NOUN
m-1112	1737	11	|	|	ADV
m-1112	1737	12	.	.	PUNCT
m-1112	1738	1	b̅n	b̅n	PROPN
m-1112	1738	2	←	←	PROPN
m-1112	1738	3	≡	≡	PROPN
m-1112	1738	4	spin	spin	NOUN
m-1112	1738	5	,	,	PUNCT
m-1112	1738	6	i.e.	i.e.	X
m-1112	1738	7	the	the	DET
m-1112	1738	8	stationary	stationary	ADJ
m-1112	1738	9	photons	photon	NOUN
m-1112	1738	10	are	be	AUX
m-1112	1738	11	spin	spin	NOUN
m-1112	1738	12	only	only	ADV
m-1112	1738	13	and	and	CCONJ
m-1112	1738	14	consist	consist	VERB
m-1112	1738	15	an	an	DET
m-1112	1738	16	stationary	stationary	ADJ
m-1112	1738	17	harmonic	harmonic	ADJ
m-1112	1738	18	vibration	vibration	NOUN
m-1112	1738	19	,	,	PUNCT
m-1112	1738	20	(	(	PUNCT
m-1112	1738	21	1	1	NUM
m-1112	1738	22	)	)	PUNCT
m-1112	1738	23	–	–	PUNCT
m-1112	1738	24	(	(	PUNCT
m-1112	1738	25	1a	1a	X
m-1112	1738	26	)	)	PUNCT
m-1112	1738	27	,	,	PUNCT
m-1112	1738	28	with	with	ADP
m-1112	1738	29	the	the	DET
m-1112	1738	30	same	same	ADJ
m-1112	1738	31	period	period	NOUN
m-1112	1738	32	t	t	NOUN
m-1112	1738	33	of	of	ADP
m-1112	1738	34	the	the	DET
m-1112	1738	35	two	two	NUM
m-1112	1738	36	waves	wave	NOUN
m-1112	1738	37	[	[	X
m-1112	1738	38	92	92	NUM
m-1112	1738	39	-	-	PUNCT
m-1112	1738	40	e	e	NOUN
m-1112	1738	41	}	}	PUNCT
m-1112	1738	42	.	.	PUNCT
m-1112	1739	1	the	the	DET
m-1112	1739	2	effective	effective	ADJ
m-1112	1739	3	-	-	PUNCT
m-1112	1739	4	range	range	NOUN
m-1112	1739	5	of	of	ADP
m-1112	1739	6	the	the	DET
m-1112	1739	7	wavelength	wavelength	NOUN
m-1112	1739	8	λ	λ	PROPN
m-1112	1739	9	,	,	PUNCT
m-1112	1739	10	for	for	SCONJ
m-1112	1739	11	the	the	DET
m-1112	1739	12	dual	dual	ADJ
m-1112	1739	13	-	-	PUNCT
m-1112	1739	14	photon	photon	NOUN
m-1112	1739	15	is	be	AUX
m-1112	1739	16	related	relate	VERB
m-1112	1739	17	to	to	ADP
m-1112	1739	18	the	the	DET
m-1112	1739	19	consistence	consistence	NOUN
m-1112	1739	20	v	v	NOUN
m-1112	1739	21	x	x	X
m-1112	1739	22	,	,	PUNCT
m-1112	1739	23	v	v	PROPN
m-1112	1739	24	y	y	PROPN
m-1112	1739	25	,	,	PUNCT
m-1112	1739	26	velocities	velocity	NOUN
m-1112	1739	27	to	to	ADP
m-1112	1739	28	any	any	DET
m-1112	1739	29	two	two	NUM
m-1112	1739	30	perpendicular	perpendicular	ADJ
m-1112	1739	31	directions	direction	NOUN
m-1112	1739	32	of	of	ADP
m-1112	1739	33	electromagnetic	electromagnetic	ADJ
m-1112	1739	34	fields	field	NOUN
m-1112	1739	35	e	e	NOUN
m-1112	1739	36	x	x	PUNCT
m-1112	1739	37	,	,	PUNCT
m-1112	1739	38	e	e	X
m-1112	1739	39	y	y	PROPN
m-1112	1739	40	.	.	PUNCT
m-1112	1740	1	the	the	DET
m-1112	1740	2	maximum	maximum	ADJ
m-1112	1740	3	displacement	displacement	NOUN
m-1112	1740	4	in	in	ADP
m-1112	1740	5	y	y	PROPN
m-1112	1740	6	,	,	PUNCT
m-1112	1740	7	direction	direction	NOUN
m-1112	1740	8	is	be	AUX
m-1112	1740	9	the	the	DET
m-1112	1740	10	centrifugal	centrifugal	ADJ
m-1112	1740	11	λ	λ	NOUN
m-1112	1740	12	x	x	SYM
m-1112	1740	13	=	=	SYM
m-1112	1740	14	v²	v²	NOUN
m-1112	1740	15	y	y	NOUN
m-1112	1740	16	2	2	NUM
m-1112	1740	17	e	e	X
m-1112	1740	18	y	y	PROPN
m-1112	1740	19	and	and	CCONJ
m-1112	1740	20	sisin(φ	sisin(φ	ADV
m-1112	1740	21	)	)	PUNCT
m-1112	1740	22	λ	λ	PROPN
m-1112	1740	23	y	y	NOUN
m-1112	1740	24	=	=	PUNCT
m-1112	1740	25	=	=	SYM
m-1112	1740	26	c2	c2	PROPN
m-1112	1740	27	.	.	PUNCT
m-1112	1741	1	sin	sin	PROPN
m-1112	1741	2	²(φ	²(φ	NOUN
m-1112	1741	3	)	)	PUNCT
m-1112	1741	4	2	2	NUM
m-1112	1741	5	e	e	PART
m-1112	1741	6	y	y	PROPN
m-1112	1741	7	,	,	PUNCT
m-1112	1741	8	where	where	SCONJ
m-1112	1741	9	φ	φ	PROPN
m-1112	1741	10	=	=	PUNCT
m-1112	1741	11	the	the	DET
m-1112	1741	12	phase	phase	NOUN
m-1112	1741	13	difference	difference	NOUN
m-1112	1741	14	between	between	ADP
m-1112	1741	15	the	the	DET
m-1112	1741	16	two	two	NUM
m-1112	1741	17	vibrations	vibration	NOUN
m-1112	1741	18	.	.	PUNCT
m-1112	1742	1	since	since	SCONJ
m-1112	1742	2	time	time	NOUN
m-1112	1742	3	t	t	PROPN
m-1112	1742	4	,	,	PUNCT
m-1112	1742	5	is	be	AUX
m-1112	1742	6	the	the	DET
m-1112	1742	7	same	same	ADJ
m-1112	1742	8	between	between	ADP
m-1112	1742	9	the	the	DET
m-1112	1742	10	two	two	NUM
m-1112	1742	11	vibrations	vibration	NOUN
m-1112	1742	12	where	where	SCONJ
m-1112	1742	13	then	then	ADV
m-1112	1742	14	t	t	PROPN
m-1112	1742	15	=	=	PUNCT
m-1112	1742	16	v	v	PROPN
m-1112	1742	17	y	y	PROPN
m-1112	1742	18	e	e	X
m-1112	1742	19	y	y	PROPN
m-1112	1742	20	=	=	PUNCT
m-1112	1742	21	c.sin(φ	c.sin(φ	PROPN
m-1112	1742	22	)	)	PUNCT
m-1112	1742	23	.	.	PUNCT
m-1112	1743	1	e	e	NOUN
m-1112	1743	2	x	x	PUNCT
m-1112	1743	3	and	and	CCONJ
m-1112	1743	4	since	since	SCONJ
m-1112	1743	5	the	the	DET
m-1112	1743	6	period	period	NOUN
m-1112	1743	7	=	=	SYM
m-1112	1743	8	2.t	2.t	NUM
m-1112	1743	9	then	then	ADV
m-1112	1743	10	t	t	PROPN
m-1112	1743	11	=	=	SYM
m-1112	1743	12	2c.sin(φ	2c.sin(φ	NUM
m-1112	1743	13	)	)	PUNCT
m-1112	1743	14	.	.	PUNCT
m-1112	1744	1	e	e	X
m-1112	1744	2	x	x	PUNCT
m-1112	1744	3	…	…	PUNCT
m-1112	1744	4	...	...	PUNCT
m-1112	1744	5	(	(	PUNCT
m-1112	1744	6	2	2	NUM
m-1112	1744	7	)	)	PUNCT
m-1112	1744	8	from	from	ADP
m-1112	1744	9	the	the	DET
m-1112	1744	10	in	in	NOUN
m-1112	1744	11	x	x	SYM
m-1112	1744	12	→	→	SYM
m-1112	1744	13	direction	direction	NOUN
m-1112	1744	14	velocity	velocity	NOUN
m-1112	1744	15	v	v	NOUN
m-1112	1744	16	x	x	X
m-1112	1744	17	=	=	SYM
m-1112	1744	18	c	c	NOUN
m-1112	1744	19	.	.	PUNCT
m-1112	1745	1	cos(φ	cos(φ	NOUN
m-1112	1745	2	)	)	PUNCT
m-1112	1745	3	,	,	PUNCT
m-1112	1745	4	and	and	CCONJ
m-1112	1745	5	displacements	displacement	NOUN
m-1112	1745	6	,	,	PUNCT
m-1112	1745	7	λ	λ	X
m-1112	1745	8	x	x	X
m-1112	1745	9	,	,	PUNCT
m-1112	1745	10	λ	λ	X
m-1112	1745	11	y	y	PROPN
m-1112	1745	12	,	,	PUNCT
m-1112	1745	13	become	become	VERB
m-1112	1745	14	,	,	PUNCT
m-1112	1745	15	λ	λ	X
m-1112	1745	16	x	x	SYM
m-1112	1745	17	=	=	SYM
m-1112	1745	18	v	v	NUM
m-1112	1745	19	x	x	X
m-1112	1745	20	t	t	NOUN
m-1112	1745	21	=	=	PROPN
m-1112	1745	22	c.	c.	PROPN
m-1112	1745	23	cos(φ	cos(φ	PROPN
m-1112	1745	24	)	)	PUNCT
m-1112	1745	25	{	{	PUNCT
m-1112	1745	26	2c.sin(φ	2c.sin(φ	NUM
m-1112	1745	27	)	)	PUNCT
m-1112	1745	28	.	.	PUNCT
m-1112	1746	1	e	e	X
m-1112	1746	2	x	x	PUNCT
m-1112	1746	3	}	}	PUNCT
m-1112	1746	4	=	=	PUNCT
m-1112	1746	5	λ	λ	NOUN
m-1112	1746	6	x	x	SYM
m-1112	1746	7	=	=	NOUN
m-1112	1746	8	{	{	PUNCT
m-1112	1746	9	2.𝑐²	2.𝑐²	NUM
m-1112	1746	10	𝐸	𝐸	NOUN
m-1112	1746	11	𝑥	𝑥	X
m-1112	1746	12	}	}	PUNCT
m-1112	1746	13	.	.	PUNCT
m-1112	1747	1	sin(φ).cos(φ	sin(φ).cos(φ	NOUN
m-1112	1747	2	)	)	PUNCT
m-1112	1747	3	=	=	PRON
m-1112	1747	4	{	{	PUNCT
m-1112	1747	5	c	c	NOUN
m-1112	1747	6	²	²	NUM
m-1112	1747	7	e	e	NOUN
m-1112	1747	8	x	x	PUNCT
m-1112	1747	9	}	}	PUNCT
m-1112	1747	10	.	.	PUNCT
m-1112	1748	1	sin(2	sin(2	ADJ
m-1112	1748	2	.	.	PUNCT
m-1112	1749	1	φ	φ	NUM
m-1112	1749	2	)	)	PUNCT
m-1112	1749	3	(	(	PUNCT
m-1112	1749	4	3	3	X
m-1112	1749	5	)	)	PUNCT
m-1112	1749	6	since	since	SCONJ
m-1112	1749	7	in	in	ADP
m-1112	1749	8	trigonometry	trigonometry	NOUN
m-1112	1749	9	issues	issue	NOUN
m-1112	1749	10	,	,	PUNCT
m-1112	1749	11	sin(2φ	sin(2φ	NOUN
m-1112	1749	12	)	)	PUNCT
m-1112	1750	1	=	=	PUNCT
m-1112	1750	2	sin(𝜋	sin(𝜋	NOUN
m-1112	1750	3	−	−	NOUN
m-1112	1750	4	2φ	2φ	NUM
m-1112	1750	5	)	)	PUNCT
m-1112	1751	1	=	=	VERB
m-1112	1751	2	sin	sin	NOUN
m-1112	1751	3	(	(	PUNCT
m-1112	1751	4	𝜋	𝜋	NOUN
m-1112	1751	5	2	2	NUM
m-1112	1751	6	−	−	NUM
m-1112	1751	7	φ	φ	NUM
m-1112	1751	8	)	)	PUNCT
m-1112	1751	9	and	and	CCONJ
m-1112	1751	10	in	in	ADP
m-1112	1751	11	physics	physics	NOUN
m-1112	1751	12	e	e	NOUN
m-1112	1751	13	x	x	X
m-1112	1751	14	=	=	SYM
m-1112	1751	15	g	g	PROPN
m-1112	1751	16	,	,	PUNCT
m-1112	1751	17	ijo	ijo	PROPN
m-1112	1751	18	international	international	PROPN
m-1112	1751	19	journal	journal	PROPN
m-1112	1751	20	of	of	ADP
m-1112	1751	21	mathematics	mathematics	PROPN
m-1112	1751	22	(	(	PUNCT
m-1112	1751	23	issn	issn	PROPN
m-1112	1751	24	:	:	PUNCT
m-1112	1751	25	2992	2992	NUM
m-1112	1751	26	-	-	SYM
m-1112	1751	27	4421	4421	NUM
m-1112	1751	28	)	)	PUNCT
m-1112	1751	29	volume	volume	NOUN
m-1112	1751	30	08	08	NUM
m-1112	1752	1	|	|	ADV
m-1112	1752	2	issue	issue	NOUN
m-1112	1752	3	08	08	NUM
m-1112	1753	1	|	|	ADV
m-1112	1753	2	august	august	PROPN
m-1112	1753	3	2025	2025	NUM
m-1112	1753	4	|	|	ADV
m-1112	1753	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1753	6	ijo	ijo	PROPN
m-1112	1753	7	journals	journal	NOUN
m-1112	1753	8	62	62	NUM
m-1112	1753	9	the	the	DET
m-1112	1753	10	fundamental	fundamental	ADJ
m-1112	1753	11	particles	particle	NOUN
m-1112	1753	12	origination	origination	NOUN
m-1112	1753	13	mechanism	mechanism	NOUN
m-1112	1753	14	in	in	ADP
m-1112	1753	15	mfmf	mfmf	PROPN
m-1112	1753	16	pns	pns	PROPN
m-1112	1753	17	caves	cave	NOUN
m-1112	1753	18	.	.	PUNCT
m-1112	1754	1	then	then	ADV
m-1112	1754	2	→	→	SYM
m-1112	1754	3	𝛌	𝛌	PROPN
m-1112	1754	4	𝐱	𝐱	NOUN
m-1112	1754	5	=	=	PUNCT
m-1112	1754	6	{	{	PUNCT
m-1112	1754	7	𝐜	𝐜	PROPN
m-1112	1754	8	²	²	NUM
m-1112	1754	9	𝐠	𝐠	PROPN
m-1112	1754	10	}	}	PUNCT
m-1112	1754	11	.	.	PUNCT
m-1112	1755	1	𝐬𝐢𝐧(𝝅	𝐬𝐢𝐧(𝝅	PRON
m-1112	1755	2	−	−	PROPN
m-1112	1755	3	𝟐𝛗	𝟐𝛗	PROPN
m-1112	1755	4	)	)	PUNCT
m-1112	1755	5	,	,	PUNCT
m-1112	1755	6	𝛌	𝛌	PROPN
m-1112	1756	1	𝐲	𝐲	ADV
m-1112	1756	2	=	=	PUNCT
m-1112	1756	3	{	{	PUNCT
m-1112	1756	4	𝐜	𝐜	PROPN
m-1112	1756	5	²	²	NUM
m-1112	1756	6	𝐠	𝐠	PROPN
m-1112	1756	7	}	}	PUNCT
m-1112	1756	8	.	.	PUNCT
m-1112	1757	1	𝐬𝐢𝐧	𝐬𝐢𝐧	ADP
m-1112	1757	2	(	(	PUNCT
m-1112	1757	3	𝝅	𝝅	PROPN
m-1112	1757	4	𝟐	𝟐	NUM
m-1112	1757	5	−	−	NUM
m-1112	1757	6	𝛗	𝛗	NOUN
m-1112	1757	7	)	)	PUNCT
m-1112	1757	8	←	←	PROPN
m-1112	1757	9	…	…	PUNCT
m-1112	1757	10	…	…	PUNCT
m-1112	1757	11	.(4	.(4	NUM
m-1112	1757	12	)	)	PUNCT
m-1112	1757	13	since	since	SCONJ
m-1112	1757	14	monads	monad	NOUN
m-1112	1757	15	are	be	AUX
m-1112	1757	16	complex	complex	ADJ
m-1112	1757	17	quantities	quantity	NOUN
m-1112	1757	18	as	as	ADP
m-1112	1757	19	ab	ab	PROPN
m-1112	1757	20	≡	≡	PROPN
m-1112	1757	21	�	�	PROPN
m-1112	1757	22	̅	̅	PROPN
m-1112	1757	23	�	�	NOUN
m-1112	1757	24	≡	≡	PROPN
m-1112	1757	25	x	x	PUNCT
m-1112	1758	1	+	+	NUM
m-1112	1758	2	i.	i.	PROPN
m-1112	1758	3	y	y	PROPN
m-1112	1758	4	,	,	PUNCT
m-1112	1758	5	then	then	ADV
m-1112	1758	6	are	be	AUX
m-1112	1758	7	quaternions	quaternion	NOUN
m-1112	1758	8	where	where	SCONJ
m-1112	1758	9	material	material	NOUN
m-1112	1758	10	-	-	PUNCT
m-1112	1758	11	points	point	NOUN
m-1112	1758	12	≡	≡	PROPN
m-1112	1758	13	quaternions	quaternion	NOUN
m-1112	1758	14	,	,	PUNCT
m-1112	1758	15	which	which	PRON
m-1112	1758	16	carry	carry	VERB
m-1112	1758	17	the	the	DET
m-1112	1758	18	→	→	SYM
m-1112	1758	19	motion	motion	NOUN
m-1112	1758	20	≡	≡	PROPN
m-1112	1758	21	energy	energy	NOUN
m-1112	1758	22	←	←	PROPN
m-1112	1758	23	from	from	ADP
m-1112	1758	24	the	the	DET
m-1112	1758	25	two	two	NUM
m-1112	1758	26	edge	edge	NOUN
m-1112	1758	27	-	-	PUNCT
m-1112	1758	28	poinds	poind	NOUN
m-1112	1758	29	[	[	PUNCT
m-1112	1758	30	�	�	NOUN
m-1112	1758	31	̅	̅	NOUN
m-1112	1758	32	�	�	NOUN
m-1112	1758	33	↔	↔	NOUN
m-1112	1758	34	�	�	NOUN
m-1112	1758	35	̅	̅	NOUN
m-1112	1758	36	�	�	PROPN
m-1112	1758	37	]	]	PUNCT
m-1112	1758	38	,	,	PUNCT
m-1112	1758	39	as	as	SCONJ
m-1112	1758	40	this	this	PRON
m-1112	1758	41	is	be	AUX
m-1112	1758	42	from	from	ADP
m-1112	1758	43	point	point	NOUN
m-1112	1758	44	a	a	PRON
m-1112	1758	45	,	,	PUNCT
m-1112	1758	46	to	to	PART
m-1112	1758	47	point	point	VERB
m-1112	1758	48	b	b	PRON
m-1112	1758	49	circularly	circularly	ADV
m-1112	1758	50	.	.	PUNCT
m-1112	1759	1	since	since	SCONJ
m-1112	1759	2	λ	λ	X
m-1112	1759	3	x	x	X
m-1112	1759	4	⏊	⏊	PUNCT
m-1112	1759	5	λ	λ	X
m-1112	1759	6	y	y	PROPN
m-1112	1759	7	,	,	PUNCT
m-1112	1759	8	then	then	ADV
m-1112	1759	9	issues	issue	VERB
m-1112	1759	10	λ	λ	NOUN
m-1112	1759	11	y	y	NOUN
m-1112	1760	1	=	=	PUNCT
m-1112	1761	1	[	[	PUNCT
m-1112	1761	2	i	i	NOUN
m-1112	1761	3	=	=	NOUN
m-1112	1761	4	√−1	√−1	NOUN
m-1112	1761	5	]	]	PUNCT
m-1112	1761	6	*	*	PUNCT
m-1112	1761	7	λ	λ	NOUN
m-1112	1761	8	x	x	PUNCT
m-1112	1761	9	,	,	PUNCT
m-1112	1761	10	or	or	CCONJ
m-1112	1761	11	equivalent	equivalent	ADJ
m-1112	1761	12	to	to	ADP
m-1112	1761	13	multiplying	multiply	VERB
m-1112	1761	14	the	the	DET
m-1112	1761	15	quantities	quantity	NOUN
m-1112	1761	16	along	along	ADP
m-1112	1761	17	the	the	DET
m-1112	1761	18	x	x	X
m-1112	1761	19	–	–	PUNCT
m-1112	1761	20	x	x	VERB
m-1112	1761	21	axis	axis	NOUN
m-1112	1761	22	,	,	PUNCT
m-1112	1761	23	by	by	ADP
m-1112	1761	24	i	i	NOUN
m-1112	1761	25	=	=	SYM
m-1112	1761	26	√−1	√−1	NOUN
m-1112	1761	27	.	.	PUNCT
m-1112	1762	1	i.e.	i.e.	X
m-1112	1762	2	photons	photon	NOUN
m-1112	1762	3	occupy	occupy	VERB
m-1112	1762	4	1	1	NUM
m-1112	1762	5	..	..	PUNCT
m-1112	1762	6	the	the	DET
m-1112	1762	7	dual	dual	ADJ
m-1112	1762	8	-	-	PUNCT
m-1112	1762	9	property	property	NOUN
m-1112	1762	10	of	of	ADP
m-1112	1762	11	particles	particle	NOUN
m-1112	1762	12	and	and	CCONJ
m-1112	1762	13	waves	wave	NOUN
m-1112	1762	14	,	,	PUNCT
m-1112	1762	15	2	2	X
m-1112	1762	16	..	..	PUNCT
m-1112	1762	17	the	the	DET
m-1112	1762	18	dual	dual	ADJ
m-1112	1762	19	-	-	PUNCT
m-1112	1762	20	property	property	NOUN
m-1112	1762	21	of	of	ADP
m-1112	1762	22	stationary	stationary	ADJ
m-1112	1762	23	and	and	CCONJ
m-1112	1762	24	spin	spin	NOUN
m-1112	1762	25	,	,	PUNCT
m-1112	1762	26	3	3	X
m-1112	1762	27	..	..	PUNCT
m-1112	1762	28	the	the	DET
m-1112	1762	29	dual	dual	ADJ
m-1112	1762	30	-	-	PUNCT
m-1112	1762	31	property	property	NOUN
m-1112	1762	32	of	of	ADP
m-1112	1762	33	simultaneous	simultaneous	ADJ
m-1112	1762	34	existence	existence	NOUN
m-1112	1762	35	,	,	PUNCT
m-1112	1762	36	4	4	NUM
m-1112	1762	37	..	..	PUNCT
m-1112	1762	38	as	as	ADP
m-1112	1762	39	electric	electric	ADJ
m-1112	1762	40	and	and	CCONJ
m-1112	1762	41	magnetic	magnetic	ADJ
m-1112	1762	42	fields	field	NOUN
m-1112	1762	43	in	in	ADP
m-1112	1762	44	,	,	PUNCT
m-1112	1762	45	𝛌	𝛌	PROPN
m-1112	1762	46	𝐱	𝐱	PROPN
m-1112	1762	47	,	,	PUNCT
m-1112	1762	48	𝛌	𝛌	AUX
m-1112	1762	49	𝐲	𝐲	PROPN
m-1112	1762	50	,	,	PUNCT
m-1112	1762	51	5	5	NUM
m-1112	1762	52	..	..	PUNCT
m-1112	1762	53	the	the	DET
m-1112	1762	54	bellow	bellow	ADJ
m-1112	1762	55	motion	motion	NOUN
m-1112	1762	56	in	in	ADP
m-1112	1762	57	transverse	transverse	NOUN
m-1112	1762	58	e	e	NOUN
m-1112	1762	59	-	-	NOUN
m-1112	1762	60	mwaves	mwave	NOUN
m-1112	1762	61	as	as	SCONJ
m-1112	1762	62	is	be	AUX
m-1112	1762	63	the	the	DET
m-1112	1762	64	way	way	NOUN
m-1112	1762	65	to	to	PART
m-1112	1762	66	fly	fly	VERB
m-1112	1762	67	,	,	PUNCT
m-1112	1762	68	6	6	NUM
m-1112	1762	69	..	..	PUNCT
m-1112	1762	70	the	the	DET
m-1112	1762	71	transverse	transverse	NOUN
m-1112	1762	72	e	e	NOUN
m-1112	1762	73	-	-	NOUN
m-1112	1762	74	m	m	NOUN
m-1112	1762	75	waves	wave	NOUN
m-1112	1762	76	are	be	AUX
m-1112	1762	77	⏊	⏊	PROPN
m-1112	1762	78	to	to	ADP
m-1112	1762	79	the	the	DET
m-1112	1762	80	propagation	propagation	NOUN
m-1112	1762	81	-	-	PUNCT
m-1112	1762	82	direction	direction	NOUN
m-1112	1762	83	,	,	PUNCT
m-1112	1762	84	7	7	NUM
m-1112	1762	85	..	..	PUNCT
m-1112	1762	86	the	the	DET
m-1112	1762	87	electric	electric	ADJ
m-1112	1762	88	effective	effective	ADJ
m-1112	1762	89	range	range	NOUN
m-1112	1762	90	is	be	AUX
m-1112	1762	91	thrusted	thrust	VERB
m-1112	1762	92	through	through	ADP
m-1112	1762	93	g	g	NOUN
m-1112	1762	94	only	only	ADV
m-1112	1762	95	.	.	PUNCT
m-1112	1763	1	[	[	PUNCT
m-1112	1763	2	fig-5	fig-5	NUM
m-1112	1763	3	]	]	PUNCT
m-1112	1763	4	.	.	PUNCT
m-1112	1764	1	8	8	NUM
m-1112	1764	2	..	..	PUNCT
m-1112	1764	3	with	with	ADP
m-1112	1764	4	the	the	DET
m-1112	1764	5	same	same	ADJ
m-1112	1764	6	initial	initial	ADJ
m-1112	1764	7	velocity	velocity	NOUN
m-1112	1764	8	is	be	AUX
m-1112	1764	9	succeeded	succeed	VERB
m-1112	1764	10	the	the	DET
m-1112	1764	11	same	same	ADJ
m-1112	1764	12	length	length	NOUN
m-1112	1764	13	-	-	PUNCT
m-1112	1764	14	range	range	NOUN
m-1112	1764	15	with	with	ADP
m-1112	1764	16	two	two	NUM
m-1112	1764	17	complementary	complementary	ADJ
m-1112	1764	18	angles	angle	NOUN
m-1112	1764	19	.	.	PUNCT
m-1112	1765	1	since	since	SCONJ
m-1112	1765	2	v	v	NUM
m-1112	1765	3	y	y	PROPN
m-1112	1765	4	=	=	PROPN
m-1112	1765	5	c.	c.	PROPN
m-1112	1765	6	,	,	PUNCT
m-1112	1765	7	c	c	X
m-1112	1765	8	..	..	PUNCT
m-1112	1765	9	:	:	PUNCT
m-1112	1765	10	the	the	DET
m-1112	1765	11	origination	origination	NOUN
m-1112	1765	12	of	of	ADP
m-1112	1765	13	the	the	DET
m-1112	1765	14	physical	physical	ADJ
m-1112	1765	15	loops	loop	NOUN
m-1112	1765	16	≡	≡	PROPN
m-1112	1765	17	caves	cave	VERB
m-1112	1765	18	1c	1c	NOUN
m-1112	1765	19	..	..	PUNCT
m-1112	1765	20	the	the	DET
m-1112	1765	21	gravitation	gravitation	NOUN
m-1112	1765	22	force	force	NOUN
m-1112	1765	23	g	g	PROPN
m-1112	1765	24	,	,	PUNCT
m-1112	1765	25	and	and	CCONJ
m-1112	1765	26	the	the	DET
m-1112	1765	27	kick	kick	NOUN
m-1112	1765	28	start	start	VERB
m-1112	1765	29	:	:	PUNCT
m-1112	1766	1	[	[	X
m-1112	1766	2	78	78	NUM
m-1112	1766	3	-	-	SYM
m-1112	1766	4	79	79	NUM
m-1112	1766	5	]	]	PUNCT
m-1112	1766	6	figure	figure	NOUN
m-1112	1766	7	–	–	PUNCT
m-1112	1766	8	16	16	NUM
m-1112	1766	9	.	.	PUNCT
m-1112	1767	1	the	the	DET
m-1112	1767	2	newton`s	newton`s	ADJ
m-1112	1767	3	universal	universal	ADJ
m-1112	1767	4	laws	law	NOUN
m-1112	1767	5	in	in	ADP
m-1112	1767	6	primary	primary	ADJ
m-1112	1767	7	-	-	PUNCT
m-1112	1767	8	material	material	NOUN
m-1112	1767	9	-	-	PUNCT
m-1112	1767	10	point	point	NOUN
m-1112	1767	11	,	,	PUNCT
m-1112	1767	12	above	above	ADV
m-1112	1767	13	,	,	PUNCT
m-1112	1767	14	is	be	AUX
m-1112	1767	15	consisted	consist	VERB
m-1112	1767	16	of	of	ADP
m-1112	1767	17	the	the	DET
m-1112	1767	18	two	two	NUM
m-1112	1767	19	-	-	PUNCT
m-1112	1767	20	primary	primary	ADJ
m-1112	1767	21	-	-	PUNCT
m-1112	1767	22	opposite	opposite	NOUN
m-1112	1767	23	-	-	PUNCT
m-1112	1767	24	spaces	space	NOUN
m-1112	1767	25	,	,	PUNCT
m-1112	1767	26	{	{	PUNCT
m-1112	1767	27	+	+	NOUN
m-1112	1767	28	}	}	PUNCT
m-1112	1767	29	{	{	PUNCT
m-1112	1767	30	-	-	PUNCT
m-1112	1767	31	}	}	PUNCT
m-1112	1767	32	,	,	PUNCT
m-1112	1767	33	poles	pole	NOUN
m-1112	1767	34	,	,	PUNCT
m-1112	1767	35	with	with	ADP
m-1112	1767	36	infinite	infinite	ADJ
m-1112	1767	37	points	point	NOUN
m-1112	1767	38	and	and	CCONJ
m-1112	1767	39	parallel	parallel	NOUN
m-1112	1767	40	-	-	PUNCT
m-1112	1767	41	lines	line	NOUN
m-1112	1767	42	such	such	ADJ
m-1112	1767	43	that	that	SCONJ
m-1112	1767	44	g	g	PROPN
m-1112	1767	45	is	be	AUX
m-1112	1767	46	a	a	DET
m-1112	1767	47	uniform	uniform	ADJ
m-1112	1767	48	-	-	PUNCT
m-1112	1767	49	pointy	pointy	NOUN
m-1112	1767	50	–	–	PUNCT
m-1112	1767	51	force	force	NOUN
m-1112	1767	52	.	.	PUNCT
m-1112	1768	1	from	from	ADP
m-1112	1768	2	where	where	SCONJ
m-1112	1768	3	g	g	NOUN
m-1112	1768	4	,	,	PUNCT
m-1112	1768	5	is	be	AUX
m-1112	1768	6	produced	produce	VERB
m-1112	1768	7	?	?	PUNCT
m-1112	1769	1	→	→	PUNCT
m-1112	1769	2	it	it	PRON
m-1112	1769	3	was	be	AUX
m-1112	1769	4	prior	prior	ADV
m-1112	1769	5	referred	refer	VERB
m-1112	1769	6	that	that	SCONJ
m-1112	1769	7	,	,	PUNCT
m-1112	1769	8	periodic	periodic	ADJ
m-1112	1769	9	excitation	excitation	NOUN
m-1112	1769	10	between	between	ADP
m-1112	1769	11	primary	primary	ADJ
m-1112	1769	12	space	space	NOUN
m-1112	1769	13	(	(	PUNCT
m-1112	1769	14	+	+	NOUN
m-1112	1769	15	)	)	PUNCT
m-1112	1769	16	and	and	CCONJ
m-1112	1769	17	anti	anti	ADJ
m-1112	1769	18	-	-	ADJ
m-1112	1769	19	space	space	ADJ
m-1112	1769	20	(	(	PUNCT
m-1112	1769	21	-	-	PUNCT
m-1112	1769	22	)	)	PUNCT
m-1112	1769	23	may	may	AUX
m-1112	1769	24	exist	exist	VERB
m-1112	1769	25	only	only	ADV
m-1112	1769	26	as	as	ADP
m-1112	1769	27	collision	collision	NOUN
m-1112	1769	28	of	of	ADP
m-1112	1769	29	opposite	opposite	ADJ
m-1112	1769	30	,	,	PUNCT
m-1112	1769	31	so	so	CCONJ
m-1112	1769	32	energy	energy	NOUN
m-1112	1769	33	captured	capture	VERB
m-1112	1769	34	in	in	ADP
m-1112	1769	35	box-𝐁𝐏	box-𝐁𝐏	PROPN
m-1112	1769	36	,	,	PUNCT
m-1112	1769	37	planck`s	planck`s	NOUN
m-1112	1769	38	loop	loop	NOUN
m-1112	1769	39	,	,	PUNCT
m-1112	1769	40	contains	contain	VERB
m-1112	1769	41	these	these	DET
m-1112	1769	42	ijo	ijo	PROPN
m-1112	1769	43	international	international	PROPN
m-1112	1769	44	journal	journal	PROPN
m-1112	1769	45	of	of	ADP
m-1112	1769	46	mathematics	mathematics	PROPN
m-1112	1769	47	(	(	PUNCT
m-1112	1769	48	issn	issn	PROPN
m-1112	1769	49	:	:	PUNCT
m-1112	1769	50	2992	2992	NUM
m-1112	1769	51	-	-	SYM
m-1112	1769	52	4421	4421	NUM
m-1112	1769	53	)	)	PUNCT
m-1112	1770	1	volume	volume	NOUN
m-1112	1770	2	08	08	NUM
m-1112	1771	1	|	|	ADV
m-1112	1771	2	issue	issue	NOUN
m-1112	1771	3	08	08	NUM
m-1112	1772	1	|	|	ADV
m-1112	1772	2	august	august	PROPN
m-1112	1772	3	2025	2025	NUM
m-1112	1772	4	|	|	ADV
m-1112	1772	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1772	6	ijo	ijo	PROPN
m-1112	1772	7	journals	journal	NOUN
m-1112	1772	8	63	63	NUM
m-1112	1772	9	the	the	DET
m-1112	1772	10	fundamental	fundamental	ADJ
m-1112	1772	11	particles	particle	NOUN
m-1112	1772	12	origination	origination	NOUN
m-1112	1772	13	mechanism	mechanism	NOUN
m-1112	1772	14	in	in	ADP
m-1112	1772	15	mfmf	mfmf	PROPN
m-1112	1772	16	pns	pns	PROPN
m-1112	1772	17	caves	cave	NOUN
m-1112	1772	18	.	.	PUNCT
m-1112	1773	1	three	three	NUM
m-1112	1773	2	constitute	constitute	VERB
m-1112	1773	3	elements	element	NOUN
m-1112	1773	4	[	[	X
m-1112	1773	5	(	(	PUNCT
m-1112	1773	6	+	+	NOUN
m-1112	1773	7	)	)	PUNCT
m-1112	1773	8	,	,	PUNCT
m-1112	1774	1	[	[	X
m-1112	1774	2	↔	↔	X
m-1112	1774	3	]	]	PUNCT
m-1112	1774	4	,	,	PUNCT
m-1112	1774	5	(	(	PUNCT
m-1112	1774	6	-	-	PUNCT
m-1112	1774	7	)	)	PUNCT
m-1112	1774	8	]	]	PUNCT
m-1112	1774	9	without	without	ADP
m-1112	1774	10	the	the	DET
m-1112	1774	11	inner	inner	ADJ
m-1112	1774	12	acceleration	acceleration	NOUN
m-1112	1774	13	but	but	CCONJ
m-1112	1774	14	the	the	DET
m-1112	1774	15	material	material	NOUN
m-1112	1774	16	–	–	PUNCT
m-1112	1774	17	extreme	extreme	ADJ
m-1112	1774	18	case	case	NOUN
m-1112	1774	19	of	of	ADP
m-1112	1774	20	periodic	periodic	ADJ
m-1112	1774	21	acceleration	acceleration	NOUN
m-1112	1774	22	[	[	X
m-1112	1774	23	→	→	X
m-1112	1774	24	←	←	PROPN
m-1112	1774	25	]	]	X
m-1112	1774	26	=	=	SYM
m-1112	1774	27	0	0	PUNCT
m-1112	1774	28	and	and	CCONJ
m-1112	1774	29	which	which	PRON
m-1112	1774	30	is	be	AUX
m-1112	1774	31	the	the	DET
m-1112	1774	32	reciprocating	reciprocate	VERB
m-1112	1774	33	motion	motion	NOUN
m-1112	1774	34	so	so	ADV
m-1112	1774	35	,	,	PUNCT
m-1112	1774	36	above	above	ADP
m-1112	1774	37	property	property	NOUN
m-1112	1774	38	of	of	ADP
m-1112	1774	39	primary	primary	ADJ
m-1112	1774	40	space	space	NOUN
m-1112	1774	41	exists	exist	VERB
m-1112	1774	42	also	also	ADV
m-1112	1774	43	and	and	CCONJ
m-1112	1774	44	for	for	ADP
m-1112	1774	45	all	all	DET
m-1112	1774	46	primary	primary	ADJ
m-1112	1774	47	complexspaces	complexspace	NOUN
m-1112	1774	48	.	.	PUNCT
m-1112	1775	1	complex	complex	ADJ
m-1112	1775	2	spaces	space	NOUN
m-1112	1775	3	either	either	CCONJ
m-1112	1775	4	at	at	ADP
m-1112	1775	5	,	,	PUNCT
m-1112	1775	6	[	[	X
m-1112	1775	7	(	(	PUNCT
m-1112	1775	8	+	+	NOUN
m-1112	1775	9	)	)	PUNCT
m-1112	1775	10	]	]	PUNCT
m-1112	1776	1	or	or	CCONJ
m-1112	1776	2	[	[	X
m-1112	1776	3	(	(	PUNCT
m-1112	1776	4	-	-	INTJ
m-1112	1776	5	)	)	PUNCT
m-1112	1776	6	]	]	PUNCT
m-1112	1776	7	,	,	PUNCT
m-1112	1776	8	constitutes	constitute	VERB
m-1112	1776	9	may	may	AUX
m-1112	1776	10	be	be	AUX
m-1112	1776	11	realized	realize	VERB
m-1112	1776	12	,	,	PUNCT
m-1112	1776	13	exist	exist	VERB
m-1112	1776	14	,	,	PUNCT
m-1112	1776	15	separately	separately	ADV
m-1112	1776	16	because	because	SCONJ
m-1112	1776	17	of	of	ADP
m-1112	1776	18	the	the	DET
m-1112	1776	19	→	→	SYM
m-1112	1776	20	primary	primary	NOUN
m-1112	1776	21	-	-	PUNCT
m-1112	1776	22	opposites	opposite	NOUN
m-1112	1776	23	which	which	PRON
m-1112	1776	24	pull	pull	VERB
m-1112	1776	25	each	each	DET
m-1112	1776	26	other	other	ADJ
m-1112	1776	27	←	←	PROPN
m-1112	1776	28	therefore	therefore	ADV
m-1112	1776	29	the	the	DET
m-1112	1776	30	initial	initial	ADJ
m-1112	1776	31	property	property	NOUN
m-1112	1776	32	of	of	ADP
m-1112	1776	33	attraction	attraction	NOUN
m-1112	1776	34	,	,	PUNCT
m-1112	1776	35	g	g	PROPN
m-1112	1776	36	,	,	PUNCT
m-1112	1776	37	between	between	ADP
m-1112	1776	38	primary	primary	ADJ
m-1112	1776	39	-	-	PUNCT
m-1112	1776	40	opposites	opposite	NOUN
m-1112	1776	41	continue	continue	VERB
m-1112	1776	42	issues	issue	NOUN
m-1112	1776	43	and	and	CCONJ
m-1112	1776	44	for	for	ADP
m-1112	1776	45	all	all	DET
m-1112	1776	46	the	the	DET
m-1112	1776	47	other	other	ADJ
m-1112	1776	48	infinite	infinite	ADJ
m-1112	1776	49	composite	composite	ADJ
m-1112	1776	50	and	and	CCONJ
m-1112	1776	51	complex	complex	ADJ
m-1112	1776	52	structures	structure	NOUN
m-1112	1776	53	as	as	ADV
m-1112	1776	54	well	well	ADV
m-1112	1776	55	as	as	ADP
m-1112	1776	56	in	in	ADP
m-1112	1776	57	all	all	DET
m-1112	1776	58	groups	group	NOUN
m-1112	1776	59	of	of	ADP
m-1112	1776	60	them	they	PRON
m-1112	1776	61	.	.	PUNCT
m-1112	1777	1	since	since	SCONJ
m-1112	1777	2	force	force	NOUN
m-1112	1777	3	g	g	PROPN
m-1112	1777	4	is	be	AUX
m-1112	1777	5	a	a	DET
m-1112	1777	6	uniform	uniform	ADJ
m-1112	1777	7	-	-	PUNCT
m-1112	1777	8	pointy	pointy	NOUN
m-1112	1777	9	–	–	PUNCT
m-1112	1777	10	force	force	NOUN
m-1112	1777	11	,	,	PUNCT
m-1112	1777	12	therefore	therefore	ADV
m-1112	1777	13	needs	need	VERB
m-1112	1777	14	a	a	DET
m-1112	1777	15	conductor	conductor	NOUN
m-1112	1777	16	,	,	PUNCT
m-1112	1777	17	a	a	DET
m-1112	1777	18	layer	layer	NOUN
m-1112	1777	19	,	,	PUNCT
m-1112	1777	20	a	a	DET
m-1112	1777	21	kind	kind	NOUN
m-1112	1777	22	of	of	ADP
m-1112	1777	23	mass	mass	NOUN
m-1112	1777	24	,	,	PUNCT
m-1112	1777	25	to	to	PART
m-1112	1777	26	be	be	AUX
m-1112	1777	27	spread	spread	VERB
m-1112	1777	28	and	and	CCONJ
m-1112	1777	29	act	act	VERB
m-1112	1777	30	on	on	ADP
m-1112	1777	31	it	it	PRON
m-1112	1777	32	as	as	ADP
m-1112	1777	33	surface	surface	NOUN
m-1112	1777	34	-	-	PUNCT
m-1112	1777	35	force	force	NOUN
m-1112	1777	36	,	,	PUNCT
m-1112	1777	37	a	a	DET
m-1112	1777	38	layer	layer	NOUN
m-1112	1777	39	which	which	PRON
m-1112	1777	40	is	be	AUX
m-1112	1777	41	the	the	DET
m-1112	1777	42	base	base	NOUN
m-1112	1777	43	or	or	CCONJ
m-1112	1777	44	the	the	DET
m-1112	1777	45	conductor	conductor	NOUN
m-1112	1777	46	spin	spin	NOUN
m-1112	1777	47	s	s	X
m-1112	1777	48	,	,	PUNCT
m-1112	1777	49	or	or	CCONJ
m-1112	1777	50	the	the	DET
m-1112	1777	51	stress	stress	NOUN
m-1112	1777	52	g	g	NOUN
m-1112	1777	53	,	,	PUNCT
m-1112	1777	54	as	as	SCONJ
m-1112	1777	55	this	this	PRON
m-1112	1777	56	is	be	AUX
m-1112	1777	57	the	the	DET
m-1112	1777	58	growing	grow	VERB
m-1112	1777	59	-	-	PUNCT
m-1112	1777	60	golden	golden	ADJ
m-1112	1777	61	-	-	PUNCT
m-1112	1777	62	ratio	ratio	NOUN
m-1112	1777	63	-	-	PUNCT
m-1112	1777	64	pattern	pattern	NOUN
m-1112	1777	65	φ	φ	NOUN
m-1112	1777	66	.	.	PUNCT
m-1112	1778	1	because	because	SCONJ
m-1112	1778	2	of	of	ADP
m-1112	1778	3	this	this	DET
m-1112	1778	4	stress	stress	NOUN
m-1112	1778	5	-	-	PUNCT
m-1112	1778	6	layer	layer	NOUN
m-1112	1778	7	g	g	NOUN
m-1112	1778	8	,	,	PUNCT
m-1112	1778	9	all	all	DET
m-1112	1778	10	the	the	DET
m-1112	1778	11	energy	energy	NOUN
m-1112	1778	12	-	-	PUNCT
m-1112	1778	13	structures	structure	NOUN
m-1112	1778	14	present	present	ADJ
m-1112	1778	15	→	→	PUNCT
m-1112	1778	16	reaction	reaction	NOUN
m-1112	1778	17	to	to	ADP
m-1112	1778	18	any	any	DET
m-1112	1778	19	motion	motion	NOUN
m-1112	1778	20	←	←	PROPN
m-1112	1778	21	i.e.	i.e.	X
m-1112	1778	22	mass	mass	PROPN
m-1112	1778	23	.	.	PUNCT
m-1112	1779	1	the	the	DET
m-1112	1779	2	gravity	gravity	NOUN
m-1112	1779	3	acceleration	acceleration	NOUN
m-1112	1779	4	g	g	NOUN
m-1112	1779	5	,	,	PUNCT
m-1112	1779	6	produced	produce	VERB
m-1112	1779	7	from	from	ADP
m-1112	1779	8	the	the	DET
m-1112	1779	9	in	in	ADP
m-1112	1779	10	material	material	NOUN
m-1112	1779	11	-	-	PUNCT
m-1112	1779	12	points	point	NOUN
m-1112	1779	13	acceleration	acceleration	NOUN
m-1112	1779	14	is	be	AUX
m-1112	1779	15	equal	equal	ADJ
m-1112	1779	16	to	to	ADP
m-1112	1779	17	the	the	DET
m-1112	1779	18	pressure	pressure	NOUN
m-1112	1779	19	σ	σ	NOUN
m-1112	1779	20	,	,	PUNCT
m-1112	1779	21	and	and	CCONJ
m-1112	1779	22	is	be	AUX
m-1112	1779	23	the	the	DET
m-1112	1779	24	conductor	conductor	NOUN
m-1112	1779	25	to	to	ADP
m-1112	1779	26	all	all	DET
m-1112	1779	27	waves	wave	NOUN
m-1112	1779	28	as	as	ADP
m-1112	1779	29	,	,	PUNCT
m-1112	1779	30	force	force	VERB
m-1112	1779	31	g	g	NOUN
m-1112	1779	32	over	over	ADP
m-1112	1779	33	-	-	PUNCT
m-1112	1779	34	layer	layer	NOUN
m-1112	1779	35	a	a	PRON
m-1112	1779	36	→	→	X
m-1112	1779	37	[	[	X
m-1112	1779	38	a	a	DET
m-1112	1779	39	≡	≡	PROPN
m-1112	1779	40	mass	mass	NOUN
m-1112	1779	41	*	*	PUNCT
m-1112	1779	42	g	g	NOUN
m-1112	1779	43	]	]	X
m-1112	1779	44	→	→	PUNCT
m-1112	1779	45	gσ	gσ	NUM
m-1112	1779	46	≡	≡	PROPN
m-1112	1779	47	g	g	NOUN
m-1112	1779	48	,	,	PUNCT
m-1112	1779	49	and	and	CCONJ
m-1112	1779	50	stress	stress	NOUN
m-1112	1779	51	=	=	SYM
m-1112	1779	52	g	g	NOUN
m-1112	1779	53	=	=	NOUN
m-1112	1779	54	σ²	σ²	NOUN
m-1112	1779	55	r².φ²	r².φ²	PROPN
m-1112	1779	56	8	8	NUM
m-1112	1779	57	from	from	ADP
m-1112	1779	58	figure	figure	NOUN
m-1112	1779	59	-15(3	-15(3	NUM
m-1112	1779	60	)	)	PUNCT
m-1112	1779	61	is	be	AUX
m-1112	1779	62	seen	see	VERB
m-1112	1779	63	that	that	SCONJ
m-1112	1779	64	gravitational	gravitational	ADJ
m-1112	1779	65	force	force	NOUN
m-1112	1779	66	is	be	AUX
m-1112	1779	67	attractive	attractive	ADJ
m-1112	1779	68	following	follow	VERB
m-1112	1779	69	newton	newton	PROPN
m-1112	1779	70	inverse	inverse	PROPN
m-1112	1779	71	square	square	PROPN
m-1112	1779	72	law	law	NOUN
m-1112	1779	73	,	,	PUNCT
m-1112	1779	74	and	and	CCONJ
m-1112	1779	75	it	it	PRON
m-1112	1779	76	is	be	AUX
m-1112	1779	77	an	an	DET
m-1112	1779	78	attractive	attractive	ADJ
m-1112	1779	79	-	-	PUNCT
m-1112	1779	80	force	force	NOUN
m-1112	1779	81	[	[	X
m-1112	1779	82	↔	↔	X
m-1112	1779	83	]	]	PUNCT
m-1112	1779	84	,	,	PUNCT
m-1112	1779	85	on	on	ADP
m-1112	1779	86	any	any	DET
m-1112	1779	87	two	two	NUM
m-1112	1779	88	opposite	opposite	ADJ
m-1112	1779	89	-	-	PUNCT
m-1112	1779	90	elements	element	NOUN
m-1112	1779	91	[	[	PUNCT
m-1112	1779	92	(	(	PUNCT
m-1112	1779	93	+	+	NOUN
m-1112	1779	94	)	)	PUNCT
m-1112	1779	95	,	,	PUNCT
m-1112	1779	96	(	(	PUNCT
m-1112	1779	97	-	-	PUNCT
m-1112	1779	98	)	)	PUNCT
m-1112	1779	99	]	]	PUNCT
m-1112	1779	100	realized	realize	VERB
m-1112	1779	101	through	through	ADP
m-1112	1779	102	a	a	DET
m-1112	1779	103	layer	layer	NOUN
m-1112	1779	104	of	of	ADP
m-1112	1779	105	unit	unit	NOUN
m-1112	1779	106	-	-	PUNCT
m-1112	1779	107	stresses	stress	NOUN
m-1112	1779	108	[	[	X
m-1112	1779	109	σ	σ	X
m-1112	1779	110	=	=	SYM
m-1112	1779	111	g	g	NOUN
m-1112	1779	112	]	]	PUNCT
m-1112	1779	113	,	,	PUNCT
m-1112	1779	114	and	and	CCONJ
m-1112	1779	115	becomes	become	VERB
m-1112	1779	116	from	from	ADP
m-1112	1779	117	an	an	DET
m-1112	1779	118	huge	huge	ADJ
m-1112	1779	119	magnet	magnet	NOUN
m-1112	1779	120	in	in	ADP
m-1112	1779	121	planck`s	planck`s	NOUN
m-1112	1779	122	loop	loop	NOUN
m-1112	1779	123	containing	contain	VERB
m-1112	1779	124	the	the	DET
m-1112	1779	125	whole	whole	ADJ
m-1112	1779	126	universe	universe	NOUN
m-1112	1779	127	[	[	X
m-1112	1779	128	89	89	NUM
m-1112	1779	129	]	]	PUNCT
m-1112	1779	130	.	.	PUNCT
m-1112	1780	1	g	g	NOUN
m-1112	1780	2	kick	kick	NOUN
m-1112	1780	3	-	-	PUNCT
m-1112	1780	4	start	start	NOUN
m-1112	1780	5	,	,	PUNCT
m-1112	1780	6	is	be	AUX
m-1112	1780	7	planck`s	planck`s	NOUN
m-1112	1780	8	frequency	frequency	NOUN
m-1112	1780	9	→	→	SYM
m-1112	1780	10	fp	fp	NOUN
m-1112	1780	11	=	=	SYM
m-1112	1780	12	1	1	NUM
m-1112	1780	13	/	/	SYM
m-1112	1780	14	tp	tp	NOUN
m-1112	1780	15	=	=	PUNCT
m-1112	1780	16	w	w	NUM
m-1112	1780	17	2π	2π	PROPN
m-1112	1780	18	=	=	SYM
m-1112	1780	19	√	√	NUM
m-1112	1780	20	1	1	NUM
m-1112	1780	21	g.a	g.a	NOUN
m-1112	1780	22	³	³	NUM
m-1112	1780	23	2	2	NUM
m-1112	1780	24	and	and	CCONJ
m-1112	1780	25	in	in	ADP
m-1112	1780	26	this	this	DET
m-1112	1780	27	world	world	NOUN
m-1112	1781	1	the	the	PRON
m-1112	1781	2	how	how	SCONJ
m-1112	1781	3	this	this	DET
m-1112	1781	4	frequency	frequency	NOUN
m-1112	1781	5	can	can	AUX
m-1112	1781	6	→	→	PART
m-1112	1781	7	enter	enter	VERB
m-1112	1781	8	,	,	PUNCT
m-1112	1781	9	format	format	NOUN
m-1112	1781	10	and	and	CCONJ
m-1112	1781	11	cohesive	cohesive	ADJ
m-1112	1781	12	,	,	PUNCT
m-1112	1781	13	to	to	ADP
m-1112	1781	14	the	the	DET
m-1112	1781	15	first	first	ADJ
m-1112	1781	16	or	or	CCONJ
m-1112	1781	17	any	any	DET
m-1112	1781	18	other	other	ADJ
m-1112	1781	19	energy	energy	NOUN
m-1112	1781	20	-	-	PUNCT
m-1112	1781	21	cave	cave	NOUN
m-1112	1781	22	in	in	ADP
m-1112	1781	23	planck`s	planck`s	NOUN
m-1112	1781	24	length	length	NOUN
m-1112	1781	25	,	,	PUNCT
m-1112	1781	26	e	e	NOUN
m-1112	1781	27	-	-	NOUN
m-1112	1781	28	unit	unit	NOUN
m-1112	1781	29	monad	monad	PROPN
m-1112	1781	30	,	,	PUNCT
m-1112	1781	31	1	1	NUM
m-1112	1781	32	=	=	SYM
m-1112	1781	33	g	g	PROPN
m-1112	1781	34	.𝐟	.𝐟	X
m-1112	1781	35	²𝐧	²𝐧	VERB
m-1112	1781	36	.	.	PUNCT
m-1112	1782	1	𝐚	𝐚	PRON
m-1112	1782	2	𝟑	𝟑	X
m-1112	1782	3	=	=	SYM
m-1112	1782	4	[	[	PUNCT
m-1112	1782	5	𝟒𝛑²	𝟒𝛑²	INTJ
m-1112	1782	6	𝐆𝐌	𝐆𝐌	PROPN
m-1112	1782	7	]	]	PUNCT
m-1112	1782	8	.	.	PUNCT
m-1112	1783	1	𝐟	𝐟	PRON
m-1112	1783	2	²𝐧	²𝐧	NOUN
m-1112	1783	3	.	.	PUNCT
m-1112	1784	1	𝐚𝟑	𝐚𝟑	PROPN
m-1112	1784	2	,	,	PUNCT
m-1112	1784	3	where	where	SCONJ
m-1112	1784	4	g	g	NOUN
m-1112	1784	5	=	=	PUNCT
m-1112	1784	6	[	[	PUNCT
m-1112	1784	7	𝟒𝛑²	𝟒𝛑²	INTJ
m-1112	1784	8	𝐆𝐌	𝐆𝐌	PROPN
m-1112	1784	9	]	]	PUNCT
m-1112	1784	10	as	as	SCONJ
m-1112	1784	11	this	this	PRON
m-1112	1784	12	was	be	AUX
m-1112	1784	13	shown	show	VERB
m-1112	1784	14	in	in	ADP
m-1112	1784	15	[	[	X
m-1112	1784	16	79	79	NUM
m-1112	1784	17	]	]	PUNCT
m-1112	1784	18	for	for	ADP
m-1112	1784	19	unit	unit	NOUN
m-1112	1784	20	-	-	PUNCT
m-1112	1784	21	monad	monad	PROPN
m-1112	1784	22	-	-	PUNCT
m-1112	1784	23	relation	relation	NOUN
m-1112	1784	24	.	.	PUNCT
m-1112	1785	1	an	an	DET
m-1112	1785	2	energy	energy	NOUN
m-1112	1785	3	-	-	PUNCT
m-1112	1785	4	rim	rim	NOUN
m-1112	1785	5	=	=	NOUN
m-1112	1785	6	cave	cave	NOUN
m-1112	1785	7	is	be	AUX
m-1112	1785	8	a	a	DET
m-1112	1785	9	plane	plane	NOUN
m-1112	1785	10	surface	surface	NOUN
m-1112	1785	11	,	,	PUNCT
m-1112	1785	12	an	an	DET
m-1112	1785	13	orbit	orbit	NOUN
m-1112	1785	14	,	,	PUNCT
m-1112	1785	15	representing	represent	VERB
m-1112	1785	16	an	an	DET
m-1112	1785	17	constant	constant	ADJ
m-1112	1785	18	energy	energy	NOUN
m-1112	1785	19	becoming	become	VERB
m-1112	1785	20	from	from	ADP
m-1112	1785	21	the	the	DET
m-1112	1785	22	squared	square	VERB
m-1112	1785	23	frequency	frequency	NOUN
m-1112	1785	24	𝐟𝐧²	𝐟𝐧²	VERB
m-1112	1785	25	,	,	PUNCT
m-1112	1785	26	representing	represent	VERB
m-1112	1785	27	the	the	DET
m-1112	1785	28	imaginary	imaginary	ADJ
m-1112	1785	29	part	part	NOUN
m-1112	1785	30	,	,	PUNCT
m-1112	1785	31	and	and	CCONJ
m-1112	1785	32	r	r	NOUN
m-1112	1785	33	p³	p³	PROPN
m-1112	1785	34	,	,	PUNCT
m-1112	1785	35	representing	represent	VERB
m-1112	1785	36	the	the	DET
m-1112	1785	37	real	real	ADJ
m-1112	1785	38	–	–	PUNCT
m-1112	1785	39	space	space	NOUN
m-1112	1785	40	part	part	NOUN
m-1112	1785	41	of	of	ADP
m-1112	1785	42	monad	monad	PROPN
m-1112	1785	43	as	as	ADP
m-1112	1785	44	equation	equation	NOUN
m-1112	1785	45	1	1	NUM
m-1112	1785	46	=	=	SYM
m-1112	1785	47	k.𝐟𝐧².𝐫𝐏³	k.𝐟𝐧².𝐫𝐏³	NOUN
m-1112	1785	48	.	.	PUNCT
m-1112	1786	1	the	the	DET
m-1112	1786	2	stationary	stationary	ADJ
m-1112	1786	3	energy	energy	NOUN
m-1112	1786	4	is	be	AUX
m-1112	1786	5	spread	spread	VERB
m-1112	1786	6	in	in	ADP
m-1112	1786	7	one	one	NUM
m-1112	1786	8	plane	plane	NOUN
m-1112	1786	9	as	as	SCONJ
m-1112	1786	10	this	this	PRON
m-1112	1786	11	happens	happen	VERB
m-1112	1786	12	for	for	ADP
m-1112	1786	13	the	the	DET
m-1112	1786	14	stationary	stationary	ADJ
m-1112	1786	15	-	-	PUNCT
m-1112	1786	16	waves	wave	NOUN
m-1112	1786	17	in	in	ADP
m-1112	1786	18	caves	cave	NOUN
m-1112	1786	19	,	,	PUNCT
m-1112	1786	20	while	while	SCONJ
m-1112	1786	21	in	in	ADP
m-1112	1786	22	propagating	propagate	VERB
m-1112	1786	23	energy	energy	NOUN
m-1112	1786	24	in	in	ADP
m-1112	1786	25	two	two	NUM
m-1112	1786	26	,	,	PUNCT
m-1112	1786	27	as	as	SCONJ
m-1112	1786	28	are	be	AUX
m-1112	1786	29	the	the	DET
m-1112	1786	30	electromagnetic	electromagnetic	ADJ
m-1112	1786	31	transverse	transverse	NOUN
m-1112	1786	32	waves	wave	NOUN
m-1112	1786	33	.	.	PUNCT
m-1112	1787	1	all	all	DET
m-1112	1787	2	these	these	DET
m-1112	1787	3	energy	energy	NOUN
m-1112	1787	4	-	-	PUNCT
m-1112	1787	5	rims	rim	NOUN
m-1112	1787	6	consist	consist	VERB
m-1112	1787	7	the	the	DET
m-1112	1787	8	quantized	quantize	VERB
m-1112	1787	9	-	-	PUNCT
m-1112	1787	10	plane	plane	NOUN
m-1112	1787	11	-	-	PUNCT
m-1112	1787	12	curves	curve	NOUN
m-1112	1787	13	as	as	ADP
m-1112	1787	14	fig-15	fig-15	NUM
m-1112	1787	15	.	.	PUNCT
m-1112	1788	1	the	the	DET
m-1112	1788	2	two	two	NUM
m-1112	1788	3	different	different	ADJ
m-1112	1788	4	motions	motion	NOUN
m-1112	1788	5	of	of	ADP
m-1112	1788	6	⊕	⊕	PROPN
m-1112	1788	7	space	space	NOUN
m-1112	1788	8	,	,	PUNCT
m-1112	1788	9	⊝	⊝	VERB
m-1112	1788	10	anti	anti	ADJ
m-1112	1788	11	-	-	ADJ
m-1112	1788	12	space	space	NOUN
m-1112	1788	13	,	,	PUNCT
m-1112	1788	14	in	in	ADP
m-1112	1788	15	any	any	DET
m-1112	1788	16	cave	cave	NOUN
m-1112	1788	17	r	r	NOUN
m-1112	1788	18	and	and	CCONJ
m-1112	1788	19	in	in	ADP
m-1112	1788	20	a	a	DET
m-1112	1788	21	finite	finite	ADJ
m-1112	1788	22	space	space	NOUN
m-1112	1788	23	,	,	PUNCT
m-1112	1788	24	the	the	DET
m-1112	1788	25	revolving	revolving	NOUN
m-1112	1788	26	and	and	CCONJ
m-1112	1788	27	periodic	periodic	ADJ
m-1112	1788	28	excitation	excitation	NOUN
m-1112	1788	29	create	create	VERB
m-1112	1788	30	an	an	DET
m-1112	1788	31	eternal	eternal	ADJ
m-1112	1788	32	frequency	frequency	NOUN
m-1112	1788	33	which	which	PRON
m-1112	1788	34	influence	influence	VERB
m-1112	1788	35	all	all	DET
m-1112	1788	36	other	other	ADJ
m-1112	1788	37	spaces	space	NOUN
m-1112	1788	38	,	,	PUNCT
m-1112	1788	39	the	the	DET
m-1112	1788	40	caves	cave	NOUN
m-1112	1788	41	.	.	PUNCT
m-1112	1789	1	the	the	DET
m-1112	1789	2	minimum	minimum	ADJ
m-1112	1789	3	quantized	quantize	VERB
m-1112	1789	4	-	-	PUNCT
m-1112	1789	5	energy	energy	NOUN
m-1112	1789	6	is	be	AUX
m-1112	1789	7	stored	store	VERB
m-1112	1789	8	in	in	ADP
m-1112	1789	9	the	the	DET
m-1112	1789	10	gravity	gravity	NOUN
m-1112	1789	11	-	-	PUNCT
m-1112	1789	12	layer	layer	NOUN
m-1112	1789	13	,	,	PUNCT
m-1112	1789	14	g	g	NOUN
m-1112	1789	15	,	,	PUNCT
m-1112	1789	16	becoming	become	VERB
m-1112	1789	17	from	from	ADP
m-1112	1789	18	the	the	DET
m-1112	1789	19	unit	unit	NOUN
m-1112	1789	20	energy	energy	NOUN
m-1112	1789	21	of	of	ADP
m-1112	1789	22	the	the	DET
m-1112	1789	23	sinus	sinus	NOUN
m-1112	1789	24	orbit	orbit	NOUN
m-1112	1789	25	.	.	PUNCT
m-1112	1790	1	from	from	ADP
m-1112	1790	2	equation	equation	NOUN
m-1112	1790	3	,	,	PUNCT
m-1112	1790	4	g	g	PROPN
m-1112	1790	5	=	=	SYM
m-1112	1790	6	t	t	PROPN
m-1112	1790	7	²	²	NUM
m-1112	1790	8	/	/	SYM
m-1112	1790	9	a³	a³	PROPN
m-1112	1790	10	,	,	PUNCT
m-1112	1790	11	and	and	CCONJ
m-1112	1790	12	minimum	minimum	NOUN
m-1112	1790	13	a	a	DET
m-1112	1790	14	then	then	ADJ
m-1112	1790	15	period	period	NOUN
m-1112	1790	16	is	be	AUX
m-1112	1790	17	t	t	NOUN
m-1112	1790	18	=	=	PUNCT
m-1112	1790	19	√g	√g	NOUN
m-1112	1790	20	.	.	PUNCT
m-1112	1791	1	a³	a³	PROPN
m-1112	1791	2	=	=	PROPN
m-1112	1791	3	√9,8076925	√9,8076925	PROPN
m-1112	1791	4	.	.	PUNCT
m-1112	1792	1	(	(	PUNCT
m-1112	1792	2	2,1145016	2,1145016	PROPN
m-1112	1792	3	.	.	NOUN
m-1112	1792	4	10−11)³	10−11)³	NUM
m-1112	1792	5	=	=	SYM
m-1112	1792	6	3,04513.10−16	3,04513.10−16	NUM
m-1112	1792	7	s	s	PART
m-1112	1792	8	,	,	PUNCT
m-1112	1792	9	since	since	SCONJ
m-1112	1792	10	the	the	DET
m-1112	1792	11	unit	unit	NOUN
m-1112	1792	12	-	-	PUNCT
m-1112	1792	13	work	work	NOUN
m-1112	1792	14	=	=	NOUN
m-1112	1792	15	sine	sine	ADJ
m-1112	1792	16	integral	integral	ADJ
m-1112	1792	17	=	=	ADJ
m-1112	1792	18	∫	∫	PROPN
m-1112	1792	19	sin	sin	PROPN
m-1112	1792	20	t	t	PROPN
m-1112	1792	21	t	t	PROPN
m-1112	1792	22	𝑡	𝑡	PROPN
m-1112	1792	23	0	0	PUNCT
m-1112	1792	24	dt	dt	NOUN
m-1112	1792	25	=	=	NOUN
m-1112	1792	26	1	1	NUM
m-1112	1792	27	,	,	PUNCT
m-1112	1792	28	the	the	DET
m-1112	1792	29	semi	semi	ADJ
m-1112	1792	30	-	-	ADJ
m-1112	1792	31	major	major	ADJ
m-1112	1792	32	axis	axis	NOUN
m-1112	1792	33	,	,	PUNCT
m-1112	1792	34	a	a	PRON
m-1112	1792	35	,	,	PUNCT
m-1112	1792	36	is	be	AUX
m-1112	1792	37	a	a	DET
m-1112	1792	38	=	=	SYM
m-1112	1792	39	2,1145016.10−16	2,1145016.10−16	NUM
m-1112	1792	40	m	m	PROPN
m-1112	1792	41	,	,	PUNCT
m-1112	1792	42	where	where	SCONJ
m-1112	1792	43	frequency	frequency	NOUN
m-1112	1792	44	t	t	NOUN
m-1112	1792	45	−1	−1	NOUN
m-1112	1793	1	=	=	SYM
m-1112	1793	2	fp	fp	PROPN
m-1112	1793	3	=	=	SYM
m-1112	1793	4	3,28393	3,28393	PROPN
m-1112	1793	5	..	..	SYM
m-1112	1793	6	1015	1015	NUM
m-1112	1793	7	/s	/s	PUNCT
m-1112	1793	8	,	,	PUNCT
m-1112	1793	9	corresponds	correspond	VERB
m-1112	1793	10	to	to	ADP
m-1112	1793	11	a	a	DET
m-1112	1793	12	sphere	sphere	NOUN
m-1112	1793	13	-	-	PUNCT
m-1112	1793	14	loop	loop	NOUN
m-1112	1793	15	in	in	ADP
m-1112	1793	16	planck`s	planck`s	NOUN
m-1112	1793	17	scale	scale	NOUN
m-1112	1793	18	as	as	ADP
m-1112	1793	19	(	(	PUNCT
m-1112	1793	20	4	4	NUM
m-1112	1793	21	/	/	SYM
m-1112	1793	22	3).π.r³	3).π.r³	NUM
m-1112	1793	23	=	=	NOUN
m-1112	1793	24	3,96	3,96	NUM
m-1112	1793	25	.	.	PUNCT
m-1112	1794	1	10−32	10−32	NUM
m-1112	1794	2	m³	m³	PROPN
m-1112	1794	3	,	,	PUNCT
m-1112	1794	4	and	and	CCONJ
m-1112	1794	5	then	then	ADV
m-1112	1794	6	the	the	DET
m-1112	1794	7	energy	energy	NOUN
m-1112	1794	8	in	in	ADP
m-1112	1794	9	this	this	DET
m-1112	1794	10	planck`s	planck`s	NOUN
m-1112	1794	11	loop	loop	NOUN
m-1112	1794	12	is	be	AUX
m-1112	1794	13	the	the	DET
m-1112	1794	14	minimum	minimum	NOUN
m-1112	1794	15	quantized	quantize	VERB
m-1112	1794	16	.	.	PUNCT
m-1112	1795	1	from	from	ADP
m-1112	1795	2	planck`s	planck`s	NOUN
m-1112	1795	3	energy	energy	NOUN
m-1112	1795	4	e	e	NOUN
m-1112	1795	5	=	=	SYM
m-1112	1795	6	h.fp	h.fp	PROPN
m-1112	1795	7	=	=	PUNCT
m-1112	1795	8	[	[	PUNCT
m-1112	1795	9	6,6262.10−34	6,6262.10−34	NUM
m-1112	1795	10	j.s	j.s	X
m-1112	1795	11	]	]	PUNCT
m-1112	1795	12	x	x	PUNCT
m-1112	1795	13	[	[	PUNCT
m-1112	1795	14	[	[	PUNCT
m-1112	1795	15	3,28393.1015	3,28393.1015	NUM
m-1112	1795	16	/	/	SYM
m-1112	1795	17	s	s	X
m-1112	1795	18	]	]	X
m-1112	1795	19	=	=	SYM
m-1112	1795	20	ijo	ijo	PROPN
m-1112	1795	21	international	international	PROPN
m-1112	1795	22	journal	journal	PROPN
m-1112	1795	23	of	of	ADP
m-1112	1795	24	mathematics	mathematics	PROPN
m-1112	1795	25	(	(	PUNCT
m-1112	1795	26	issn	issn	PROPN
m-1112	1795	27	:	:	PUNCT
m-1112	1795	28	2992	2992	NUM
m-1112	1795	29	-	-	SYM
m-1112	1795	30	4421	4421	NUM
m-1112	1795	31	)	)	PUNCT
m-1112	1795	32	volume	volume	NOUN
m-1112	1795	33	08	08	NUM
m-1112	1796	1	|	|	ADV
m-1112	1796	2	issue	issue	NOUN
m-1112	1796	3	08	08	NUM
m-1112	1797	1	|	|	ADV
m-1112	1797	2	august	august	PROPN
m-1112	1797	3	2025	2025	NUM
m-1112	1797	4	|	|	ADV
m-1112	1797	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1797	6	ijo	ijo	PROPN
m-1112	1797	7	journals	journal	NOUN
m-1112	1797	8	64	64	NUM
m-1112	1797	9	the	the	DET
m-1112	1797	10	fundamental	fundamental	ADJ
m-1112	1797	11	particles	particle	NOUN
m-1112	1797	12	origination	origination	NOUN
m-1112	1797	13	mechanism	mechanism	NOUN
m-1112	1797	14	in	in	ADP
m-1112	1797	15	mfmf	mfmf	PROPN
m-1112	1797	16	pns	pns	PROPN
m-1112	1797	17	caves	cave	NOUN
m-1112	1797	18	.	.	PUNCT
m-1112	1798	1	2	2	NUM
m-1112	1798	2	,	,	PUNCT
m-1112	1798	3	176.10−18	176.10−18	NUM
m-1112	1798	4	j	j	NOUN
m-1112	1798	5	,	,	PUNCT
m-1112	1798	6	and	and	CCONJ
m-1112	1798	7	in	in	ADP
m-1112	1798	8	ev	ev	X
m-1112	1798	9	becomes	become	VERB
m-1112	1798	10	→	→	SYM
m-1112	1798	11	[	[	PUNCT
m-1112	1798	12	2	2	NUM
m-1112	1798	13	,	,	PUNCT
m-1112	1798	14	176.10−18	176.10−18	NUM
m-1112	1798	15	]	]	PUNCT
m-1112	1798	16	/	/	PUNCT
m-1112	1799	1	[	[	X
m-1112	1799	2	1,6.10−19	1,6.10−19	NUM
m-1112	1799	3	]	]	X
m-1112	1799	4	=	=	SYM
m-1112	1799	5	13,6	13,6	NUM
m-1112	1799	6	ev	ev	X
m-1112	1799	7	or	or	CCONJ
m-1112	1799	8	,	,	PUNCT
m-1112	1799	9	energy	energy	NOUN
m-1112	1799	10	in	in	ADP
m-1112	1799	11	gravity	gravity	NOUN
m-1112	1799	12	-	-	PUNCT
m-1112	1799	13	layer	layer	NOUN
m-1112	1799	14	g	g	PROPN
m-1112	1799	15			NOUN
m-1112	1800	1	13,6	13,6	NUM
m-1112	1800	2	ev	ev	X
m-1112	1800	3	=	=	SYM
m-1112	1800	4	h	h	NOUN
m-1112	1800	5	f	f	NOUN
m-1112	1800	6	=	=	SYM
m-1112	1800	7	h	h	PROPN
m-1112	1800	8	/	/	SYM
m-1112	1800	9	t	t	NOUN
m-1112	1800	10	=	=	SYM
m-1112	1800	11	h	h	NOUN
m-1112	1800	12	/√𝐠.	/√𝐠.	NOUN
m-1112	1801	1	𝐚³.	𝐚³.	NOUN
m-1112	1801	2	the	the	DET
m-1112	1801	3	above	above	ADJ
m-1112	1801	4	quantity	quantity	NOUN
m-1112	1801	5	of	of	ADP
m-1112	1801	6	energy	energy	NOUN
m-1112	1801	7	consist	consist	VERB
m-1112	1801	8	the	the	DET
m-1112	1801	9	hydrogen	hydrogen	NOUN
m-1112	1801	10	minimum	minimum	NOUN
m-1112	1801	11	energy	energy	NOUN
m-1112	1801	12	-	-	PUNCT
m-1112	1801	13	rim	rim	NOUN
m-1112	1801	14	,	,	PUNCT
m-1112	1801	15	which	which	PRON
m-1112	1801	16	becomes	become	VERB
m-1112	1801	17	from	from	ADP
m-1112	1801	18	loop	loop	NOUN
m-1112	1801	19	-	-	PUNCT
m-1112	1801	20	equation	equation	NOUN
m-1112	1802	1	a	a	DET
m-1112	1802	2	=	=	X
m-1112	1802	3	√𝐓𝟐/𝐠	√𝐓𝟐/𝐠	NOUN
m-1112	1802	4	𝟑	𝟑	X
m-1112	1802	5	=	=	SYM
m-1112	1802	6	√	√	PROPN
m-1112	1803	1	[	[	X
m-1112	1803	2	3,04513.10−16]²	3,04513.10−16]²	NUM
m-1112	1803	3	9,80769251	9,80769251	NUM
m-1112	1803	4	3	3	NUM
m-1112	1803	5	=	=	SYM
m-1112	1803	6	2,1145016.10−16	2,1145016.10−16	NUM
m-1112	1803	7	m	m	NOUN
m-1112	1803	8	,	,	PUNCT
m-1112	1803	9	and	and	CCONJ
m-1112	1803	10	it	it	PRON
m-1112	1803	11	is	be	AUX
m-1112	1803	12	the	the	DET
m-1112	1803	13	energy	energy	NOUN
m-1112	1803	14	-	-	PUNCT
m-1112	1803	15	cave	cave	NOUN
m-1112	1803	16	for	for	ADP
m-1112	1803	17	the	the	DET
m-1112	1803	18	unit	unit	NOUN
m-1112	1803	19	energy	energy	NOUN
m-1112	1803	20	quantity	quantity	NOUN
m-1112	1803	21	.	.	PUNCT
m-1112	1804	1	from	from	ADP
m-1112	1804	2	newtonian	newtonian	ADJ
m-1112	1804	3	constant	constant	ADJ
m-1112	1804	4	of	of	ADP
m-1112	1804	5	gravitation	gravitation	NOUN
m-1112	1804	6	relation	relation	NOUN
m-1112	1804	7	issues	issue	NOUN
m-1112	1804	8	,	,	PUNCT
m-1112	1804	9	g	g	PROPN
m-1112	1804	10	=	=	SYM
m-1112	1804	11	e	e	NOUN
m-1112	1804	12	=	=	NOUN
m-1112	1804	13	h	h	PROPN
m-1112	1804	14	.	.	PUNCT
m-1112	1805	1	fn	fn	NOUN
m-1112	1806	1	=	=	PUNCT
m-1112	1806	2	[	[	PUNCT
m-1112	1806	3	𝐜.𝐫³	𝐜.𝐫³	NOUN
m-1112	1806	4	𝐚³	𝐚³	NOUN
m-1112	1806	5	]	]	PUNCT
m-1112	1806	6	.	.	PUNCT
m-1112	1807	1	[	[	PUNCT
m-1112	1807	2	gl	gl	X
m-1112	1807	3	kl	kl	X
m-1112	1807	4	]	]	PUNCT
m-1112	1807	5	=	=	PUNCT
m-1112	1807	6	g	g	NOUN
m-1112	1807	7	.k	.k	NOUN
m-1112	1808	1	e	e	X
m-1112	1808	2	=	=	NOUN
m-1112	1808	3	g	g	PROPN
m-1112	1808	4	.	.	PUNCT
m-1112	1809	1	[	[	PUNCT
m-1112	1809	2	gl	gl	X
m-1112	1809	3	kl	kl	X
m-1112	1809	4	]	]	PUNCT
m-1112	1809	5	,	,	PUNCT
m-1112	1809	6	and	and	CCONJ
m-1112	1809	7	since	since	SCONJ
m-1112	1809	8	for	for	ADP
m-1112	1809	9	the	the	DET
m-1112	1809	10	first	first	ADJ
m-1112	1809	11	chemical	chemical	NOUN
m-1112	1809	12	-	-	PUNCT
m-1112	1809	13	neutral	neutral	ADJ
m-1112	1809	14	-	-	PUNCT
m-1112	1809	15	material	material	NOUN
m-1112	1809	16	-	-	PUNCT
m-1112	1809	17	cave	cave	NOUN
m-1112	1809	18	,	,	PUNCT
m-1112	1809	19	r	r	NOUN
m-1112	1809	20	,	,	PUNCT
m-1112	1809	21	constants	constant	NOUN
m-1112	1809	22	gl	gl	INTJ
m-1112	1809	23	,	,	PUNCT
m-1112	1809	24	kl	kl	PROPN
m-1112	1809	25	are	be	AUX
m-1112	1809	26	equal	equal	ADJ
m-1112	1809	27	to	to	ADP
m-1112	1809	28	unity	unity	NOUN
m-1112	1809	29	i.e.	i.e.	X
m-1112	1809	30	𝐠𝐋	𝐠𝐋	ADV
m-1112	1809	31	=	=	SYM
m-1112	1809	32	𝐤𝐋	𝐤𝐋	NOUN
m-1112	1809	33	=	=	SYM
m-1112	1809	34	1	1	NUM
m-1112	1809	35	,	,	PUNCT
m-1112	1809	36	then	then	ADV
m-1112	1809	37	above	above	ADP
m-1112	1809	38	energy	energy	NOUN
m-1112	1809	39	of	of	ADP
m-1112	1809	40	e	e	NOUN
m-1112	1809	41	=	=	SYM
m-1112	1809	42	13,6	13,6	NUM
m-1112	1809	43	ev	ev	INTJ
m-1112	1809	44	,	,	PUNCT
m-1112	1809	45	in	in	ADP
m-1112	1809	46	hydrogen	hydrogen	NOUN
m-1112	1809	47	-	-	PUNCT
m-1112	1809	48	plane	plane	NOUN
m-1112	1809	49	-	-	PUNCT
m-1112	1809	50	orbit	orbit	NOUN
m-1112	1809	51	corresponds	correspond	NOUN
m-1112	1809	52	to	to	ADP
m-1112	1809	53	the	the	DET
m-1112	1809	54	minimum	minimum	ADJ
m-1112	1809	55	-	-	PUNCT
m-1112	1809	56	energy	energy	NOUN
m-1112	1809	57	-	-	PUNCT
m-1112	1809	58	cave	cave	NOUN
m-1112	1809	59	,	,	PUNCT
m-1112	1809	60	or	or	CCONJ
m-1112	1809	61	→	→	PUNCT
m-1112	1809	62	the	the	DET
m-1112	1809	63	phys	phy	NOUN
m-1112	1809	64	-	-	PUNCT
m-1112	1809	65	quantized	quantize	VERB
m-1112	1809	66	-	-	PUNCT
m-1112	1809	67	energy	energy	NOUN
m-1112	1809	68	-	-	PUNCT
m-1112	1809	69	structure	structure	NOUN
m-1112	1809	70	←	←	NOUN
m-1112	1809	71	since	since	SCONJ
m-1112	1809	72	g	g	PROPN
m-1112	1809	73	pushes	push	VERB
m-1112	1809	74	→	→	SYM
m-1112	1809	75	g	g	PROPN
m-1112	1809	76	,	,	PUNCT
m-1112	1809	77	on	on	ADP
m-1112	1809	78	the	the	DET
m-1112	1809	79	earth	earth	NOUN
m-1112	1809	80	-	-	PUNCT
m-1112	1809	81	unit	unit	NOUN
m-1112	1809	82	-	-	NOUN
m-1112	1809	83	coefficient	coefficient	NOUN
m-1112	1809	84	,	,	PUNCT
m-1112	1809	85	k	k	PROPN
m-1112	1809	86	e	e	NOUN
m-1112	1809	87	,	,	PUNCT
m-1112	1809	88	and	and	CCONJ
m-1112	1809	89	because	because	SCONJ
m-1112	1809	90	is	be	AUX
m-1112	1809	91	the	the	DET
m-1112	1809	92	starting	starting	NOUN
m-1112	1809	93	for	for	ADP
m-1112	1809	94	the	the	DET
m-1112	1809	95	first	first	ADJ
m-1112	1809	96	time	time	NOUN
m-1112	1809	97	beginning	begin	VERB
m-1112	1809	98	,	,	PUNCT
m-1112	1809	99	of	of	ADP
m-1112	1809	100	this	this	DET
m-1112	1809	101	mechanism	mechanism	NOUN
m-1112	1809	102	then	then	ADV
m-1112	1809	103	from	from	ADP
m-1112	1809	104	g	g	PROPN
m-1112	1809	105	=	=	PUNCT
m-1112	1809	106	g.[gl	g.[gl	PROPN
m-1112	1809	107	kl	kl	X
m-1112	1809	108	]	]	X
m-1112	1809	109	≡	≡	PROPN
m-1112	1809	110	g.[1	g.[1	AUX
m-1112	1809	111	*	*	SYM
m-1112	1809	112	1	1	NUM
m-1112	1809	113	]	]	X
m-1112	1809	114	≡	≡	PROPN
m-1112	1809	115	→	→	SYM
m-1112	1809	116	g	g	PROPN
m-1112	1809	117	←	←	PROPN
m-1112	1809	118	or	or	CCONJ
m-1112	1809	119	g	g	PROPN
m-1112	1809	120	=	=	SYM
m-1112	1809	121	g	g	PROPN
m-1112	1809	122	,	,	PUNCT
m-1112	1809	123	meaning	mean	VERB
m-1112	1809	124	that	that	SCONJ
m-1112	1809	125	in	in	ADP
m-1112	1809	126	earth	earth	NOUN
m-1112	1809	127	system	system	NOUN
m-1112	1809	128	of	of	ADP
m-1112	1809	129	gravity	gravity	NOUN
m-1112	1809	130	,	,	PUNCT
m-1112	1809	131	the	the	DET
m-1112	1809	132	newton`s	newton`s	PROPN
m-1112	1809	133	gravitational	gravitational	ADJ
m-1112	1809	134	constant	constant	ADJ
m-1112	1809	135	g	g	NOUN
m-1112	1809	136	,	,	PUNCT
m-1112	1809	137	and	and	CCONJ
m-1112	1809	138	gravity	gravity	NOUN
m-1112	1809	139	g	g	NOUN
m-1112	1809	140	are	be	AUX
m-1112	1809	141	equal	equal	ADJ
m-1112	1809	142	,	,	PUNCT
m-1112	1809	143	while	while	SCONJ
m-1112	1809	144	in	in	ADP
m-1112	1809	145	all	all	DET
m-1112	1809	146	other	other	ADJ
m-1112	1809	147	relative	relative	ADJ
m-1112	1809	148	systems	system	NOUN
m-1112	1809	149	are	be	AUX
m-1112	1809	150	equal	equal	ADJ
m-1112	1809	151	to	to	ADP
m-1112	1809	152	the	the	DET
m-1112	1809	153	proportionality	proportionality	NOUN
m-1112	1809	154	of	of	ADP
m-1112	1809	155	their	their	PRON
m-1112	1809	156	local	local	ADJ
m-1112	1809	157	-	-	PUNCT
m-1112	1809	158	constant	constant	ADJ
m-1112	1809	159	𝐤	𝐤	X
m-1112	1809	160	𝐋	𝐋	PROPN
m-1112	1809	161	.	.	PUNCT
m-1112	1810	1	gravity	gravity	NOUN
m-1112	1810	2	,	,	PUNCT
m-1112	1810	3	g	g	PROPN
m-1112	1810	4	,	,	PUNCT
m-1112	1810	5	is	be	AUX
m-1112	1810	6	the	the	DET
m-1112	1810	7	minimum	minimum	ADJ
m-1112	1810	8	energy	energy	NOUN
m-1112	1810	9	becoming	become	VERB
m-1112	1810	10	from	from	ADP
m-1112	1810	11	the	the	DET
m-1112	1810	12	in	in	ADP
m-1112	1810	13	-	-	PUNCT
m-1112	1810	14	storages	storage	NOUN
m-1112	1810	15	angular	angular	ADJ
m-1112	1810	16	velocity	velocity	NOUN
m-1112	1810	17	acceleration	acceleration	NOUN
m-1112	1810	18	a	a	DET
m-1112	1810	19	=	=	SYM
m-1112	1810	20	v²/	v²/	NOUN
m-1112	1810	21	r	r	NOUN
m-1112	1810	22	≡	≡	PROPN
m-1112	1810	23	9	9	NUM
m-1112	1810	24	,	,	PUNCT
m-1112	1810	25	8076941	8076941	NUM
m-1112	1810	26	.	.	PUNCT
m-1112	1811	1	in	in	ADP
m-1112	1811	2	the	the	DET
m-1112	1811	3	material	material	NOUN
m-1112	1811	4	-	-	PUNCT
m-1112	1811	5	point	point	NOUN
m-1112	1811	6	.	.	PUNCT
m-1112	1812	1	[	[	X
m-1112	1812	2	72	72	NUM
m-1112	1812	3	]	]	X
m-1112	1812	4	photon	photon	NOUN
m-1112	1812	5	is	be	AUX
m-1112	1812	6	a	a	DET
m-1112	1812	7	material	material	NOUN
m-1112	1812	8	-	-	PUNCT
m-1112	1812	9	point	point	NOUN
m-1112	1812	10	,	,	PUNCT
m-1112	1812	11	box	box	NOUN
m-1112	1812	12	br	br	PROPN
m-1112	1812	13	,	,	PUNCT
m-1112	1812	14	with	with	ADP
m-1112	1812	15	fix	fix	NOUN
m-1112	1812	16	-	-	PUNCT
m-1112	1812	17	ends	end	NOUN
m-1112	1812	18	inward	inward	ADV
m-1112	1812	19	-	-	PUNCT
m-1112	1812	20	cave	cave	NOUN
m-1112	1812	21	r	r	NOUN
m-1112	1812	22	,	,	PUNCT
m-1112	1812	23	and	and	CCONJ
m-1112	1812	24	which	which	PRON
m-1112	1812	25	is	be	AUX
m-1112	1812	26	the	the	DET
m-1112	1812	27	energy	energy	NOUN
m-1112	1812	28	storage	storage	NOUN
m-1112	1812	29	𝐁𝐑	𝐁𝐑	PROPN
m-1112	1812	30	,	,	PUNCT
m-1112	1812	31	outward	outward	ADJ
m-1112	1812	32	-	-	PUNCT
m-1112	1812	33	cave	cave	NOUN
m-1112	1812	34	-	-	PUNCT
m-1112	1812	35	r	r	NOUN
m-1112	1812	36	is	be	AUX
m-1112	1812	37	an	an	DET
m-1112	1812	38	electromagnetic	electromagnetic	ADJ
m-1112	1812	39	-	-	PUNCT
m-1112	1812	40	radiation	radiation	NOUN
m-1112	1812	41	on	on	ADP
m-1112	1812	42	wavelength	wavelength	NOUN
m-1112	1812	43	λ	λ	PROPN
m-1112	1812	44	=	=	SYM
m-1112	1812	45	c	c	NOUN
m-1112	1812	46	t	t	NOUN
m-1112	1813	1	=	=	PUNCT
m-1112	1813	2	c	c	PROPN
m-1112	1813	3	/	/	SYM
m-1112	1813	4	fp	fp	X
m-1112	1813	5	which	which	PRON
m-1112	1813	6	em	em	NOUN
m-1112	1813	7	-	-	NOUN
m-1112	1813	8	radiation	radiation	NOUN
m-1112	1813	9	,	,	PUNCT
m-1112	1813	10	carries	carry	VERB
m-1112	1813	11	the	the	DET
m-1112	1813	12	box	box	NOUN
m-1112	1813	13	br	br	NOUN
m-1112	1813	14	.	.	PUNCT
m-1112	1814	1	universal	universal	ADJ
m-1112	1814	2	gravitational	gravitational	ADJ
m-1112	1814	3	constant	constant	ADJ
m-1112	1814	4	g	g	PROPN
m-1112	1814	5	=	=	SYM
m-1112	1814	6	g	g	PROPN
m-1112	1814	7	k	k	PROPN
m-1112	1814	8	related	relate	VERB
m-1112	1814	9	to	to	ADP
m-1112	1814	10	g	g	PROPN
m-1112	1814	11	,	,	PUNCT
m-1112	1814	12	kr	kr	PROPN
m-1112	1814	13	,	,	PUNCT
m-1112	1814	14	is	be	AUX
m-1112	1814	15	a	a	DET
m-1112	1814	16	force	force	NOUN
m-1112	1814	17	and	and	CCONJ
m-1112	1814	18	through	through	ADP
m-1112	1814	19	the	the	DET
m-1112	1814	20	static	static	ADJ
m-1112	1814	21	g	g	PROPN
m-1112	1814	22	becomes	become	VERB
m-1112	1814	23	the	the	DET
m-1112	1814	24	principal	principal	ADJ
m-1112	1814	25	stress	stress	NOUN
m-1112	1814	26			PROPN
m-1112	1814	27	σ	σ	PROPN
m-1112	1814	28	,	,	PUNCT
m-1112	1814	29	or	or	CCONJ
m-1112	1814	30	frequency	frequency	NOUN
m-1112	1814	31	f	f	NOUN
m-1112	1814	32	r	r	NOUN
m-1112	1814	33	which	which	PRON
m-1112	1814	34	exists	exist	VERB
m-1112	1814	35	in	in	ADP
m-1112	1814	36	nature	nature	NOUN
m-1112	1814	37	as	as	ADP
m-1112	1814	38	motion	motion	NOUN
m-1112	1814	39	in	in	ADP
m-1112	1814	40	the	the	DET
m-1112	1814	41	minimum	minimum	ADJ
m-1112	1814	42	resonance	resonance	NOUN
m-1112	1814	43	golden	golden	ADJ
m-1112	1814	44	-	-	PUNCT
m-1112	1814	45	ratio	ratio	NOUN
m-1112	1814	46	-	-	PUNCT
m-1112	1814	47	frequencies	frequency	NOUN
m-1112	1815	1	fr	fr	NOUN
m-1112	1815	2	=	=	PUNCT
m-1112	1815	3	fn	fn	NOUN
m-1112	1815	4	=	=	NOUN
m-1112	1815	5	1	1	NUM
m-1112	1815	6	,	,	PUNCT
m-1112	1815	7	and	and	CCONJ
m-1112	1815	8	this	this	PRON
m-1112	1815	9	because	because	SCONJ
m-1112	1815	10	of	of	ADP
m-1112	1815	11	the	the	DET
m-1112	1815	12	periodic	periodic	ADJ
m-1112	1815	13	motion	motion	NOUN
m-1112	1815	14	,	,	PUNCT
m-1112	1815	15	in	in	ADP
m-1112	1815	16	excitation	excitation	NOUN
m-1112	1815	17	,	,	PUNCT
m-1112	1815	18	where	where	SCONJ
m-1112	1815	19	issues	issue	NOUN
m-1112	1815	20	the	the	DET
m-1112	1815	21	coulomb	coulomb	NOUN
m-1112	1815	22	-	-	PUNCT
m-1112	1815	23	dipole	dipole	NOUN
m-1112	1815	24	law	law	NOUN
m-1112	1815	25	and	and	CCONJ
m-1112	1815	26	which	which	DET
m-1112	1815	27	coulomb	coulomb	NOUN
m-1112	1815	28	inverse	inverse	NOUN
m-1112	1815	29	law	law	NOUN
m-1112	1815	30	is	be	AUX
m-1112	1815	31	as	as	ADP
m-1112	1815	32	,	,	PUNCT
m-1112	1815	33	f	f	PROPN
m-1112	1816	1	=	=	PUNCT
m-1112	1816	2	kc	kc	PROPN
m-1112	1817	1	[	[	X
m-1112	1817	2	q1.q2	q1.q2	PROPN
m-1112	1817	3	/	/	SYM
m-1112	1817	4	r²	r²	NOUN
m-1112	1817	5	]	]	PUNCT
m-1112	1818	1	=	=	PUNCT
m-1112	1818	2	kc	kc	PROPN
m-1112	1819	1	[	[	X
m-1112	1819	2	⊕→←⊝	⊕→←⊝	X
m-1112	1819	3	]	]	X
m-1112	1819	4	/r²	/r²	X
m-1112	1820	1	=	=	NOUN
m-1112	1820	2	8	8	NUM
m-1112	1820	3	πr(1+√5	πr(1+√5	NUM
m-1112	1820	4	)	)	PUNCT
m-1112	1820	5	[	[	PUNCT
m-1112	1820	6	b	b	X
m-1112	1820	7	r²	r²	NOUN
m-1112	1820	8	]	]	PUNCT
m-1112	1820	9	,	,	PUNCT
m-1112	1820	10	and	and	CCONJ
m-1112	1820	11	coulomb	coulomb	NOUN
m-1112	1820	12	constant	constant	ADJ
m-1112	1820	13	kc	kc	PROPN
m-1112	1820	14	=	=	PUNCT
m-1112	1820	15	9.109	9.109	NUM
m-1112	1820	16	nm2	nm2	ADJ
m-1112	1820	17	/	/	SYM
m-1112	1820	18	c²	c²	NOUN
m-1112	1820	19	,	,	PUNCT
m-1112	1820	20	i.e.	i.e.	X
m-1112	1820	21	because	because	SCONJ
m-1112	1820	22	of	of	ADP
m-1112	1820	23	the	the	DET
m-1112	1820	24	periodic	periodic	ADJ
m-1112	1820	25	excitation	excitation	NOUN
m-1112	1820	26	between	between	ADP
m-1112	1820	27	the	the	DET
m-1112	1820	28	,	,	PUNCT
m-1112	1820	29	space	space	NOUN
m-1112	1820	30	(	(	PUNCT
m-1112	1820	31	+	+	NOUN
m-1112	1820	32	)	)	PUNCT
m-1112	1820	33	and	and	CCONJ
m-1112	1820	34	anti	anti	ADJ
m-1112	1820	35	-	-	ADJ
m-1112	1820	36	space	space	ADJ
m-1112	1820	37	(	(	PUNCT
m-1112	1820	38	-	-	PUNCT
m-1112	1820	39	)	)	PUNCT
m-1112	1820	40	,	,	PUNCT
m-1112	1820	41	[	[	X
m-1112	1820	42	⊕→←⊝	⊕→←⊝	X
m-1112	1820	43	]	]	PUNCT
m-1112	1820	44	exists	exist	VERB
m-1112	1820	45	only	only	ADV
m-1112	1820	46	collision	collision	NOUN
m-1112	1820	47	of	of	ADP
m-1112	1820	48	opposite	opposite	NOUN
m-1112	1820	49	where	where	SCONJ
m-1112	1820	50	the	the	DET
m-1112	1820	51	inner	inner	ADJ
m-1112	1820	52	acceleration	acceleration	NOUN
m-1112	1820	53	is	be	AUX
m-1112	1820	54	equal	equal	ADJ
m-1112	1820	55	to	to	ADP
m-1112	1820	56	zero	zero	NUM
m-1112	1820	57	gravity	gravity	NOUN
m-1112	1820	58	g	g	NOUN
m-1112	1820	59	,	,	PUNCT
m-1112	1820	60	and	and	CCONJ
m-1112	1820	61	this	this	PRON
m-1112	1820	62	because	because	SCONJ
m-1112	1820	63	of	of	ADP
m-1112	1820	64	the	the	DET
m-1112	1820	65	material	material	ADJ
m-1112	1820	66	extreme	extreme	ADJ
m-1112	1820	67	-	-	PUNCT
m-1112	1820	68	case	case	NOUN
m-1112	1820	69	of	of	ADP
m-1112	1820	70	the	the	DET
m-1112	1820	71	periodic	periodic	ADJ
m-1112	1820	72	acceleration	acceleration	NOUN
m-1112	1820	73	{	{	PUNCT
m-1112	1821	1	[	[	X
m-1112	1821	2	→←]=0	→←]=0	NOUN
m-1112	1821	3	}	}	PUNCT
m-1112	1821	4	which	which	PRON
m-1112	1821	5	is	be	AUX
m-1112	1821	6	zero	zero	NUM
m-1112	1821	7	,	,	PUNCT
m-1112	1821	8	the	the	DET
m-1112	1821	9	net	net	ADJ
m-1112	1821	10	force	force	NOUN
m-1112	1821	11	vanishes	vanish	VERB
m-1112	1821	12	,	,	PUNCT
m-1112	1821	13	issues	issue	VERB
m-1112	1821	14	the	the	DET
m-1112	1821	15	coulomb	coulomb	NOUN
m-1112	1821	16	dipole	dipole	NOUN
m-1112	1821	17	-	-	PUNCT
m-1112	1821	18	law	law	NOUN
m-1112	1821	19	where	where	SCONJ
m-1112	1821	20	static	static	ADJ
m-1112	1821	21	stress	stress	NOUN
m-1112	1821	22	g	g	NOUN
m-1112	1821	23	,	,	PUNCT
m-1112	1821	24	becomes	become	VERB
m-1112	1821	25	from	from	ADP
m-1112	1821	26	the	the	DET
m-1112	1821	27	stationary	stationary	ADJ
m-1112	1821	28	constant	constant	ADJ
m-1112	1821	29	dipole	dipole	NOUN
m-1112	1821	30	moment	moment	NOUN
m-1112	1821	31	�	�	NOUN
m-1112	1821	32	̅	̅	NOUN
m-1112	1821	33	�	�	PROPN
m-1112	1821	34	≡	≡	PROPN
m-1112	1821	35	�	�	PROPN
m-1112	1821	36	̅	̅	PROPN
m-1112	1821	37	�	�	NOUN
m-1112	1821	38	≡	≡	PROPN
m-1112	1821	39	as	as	ADP
m-1112	1821	40	momentum	momentum	NOUN
m-1112	1821	41	which	which	PRON
m-1112	1821	42	is	be	AUX
m-1112	1821	43	the	the	DET
m-1112	1821	44	analogous	analogous	ADJ
m-1112	1821	45	in	in	ADP
m-1112	1821	46	the	the	DET
m-1112	1821	47	revolving	revolve	VERB
m-1112	1821	48	motion	motion	NOUN
m-1112	1821	49	where	where	SCONJ
m-1112	1821	50	then	then	ADV
m-1112	1821	51	issues	issue	VERB
m-1112	1821	52	→	→	SYM
m-1112	1821	53	g	g	PROPN
m-1112	1821	54	=	=	SYM
m-1112	1821	55	g	g	NOUN
m-1112	1821	56	k	k	PROPN
m-1112	1821	57	=	=	PUNCT
m-1112	1821	58	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1821	59	g	g	NOUN
m-1112	1821	60	=	=	SYM
m-1112	1821	61	g.𝐤𝐑	g.𝐤𝐑	NUM
m-1112	1821	62	𝐠𝐑	𝐠𝐑	NOUN
m-1112	1821	63	=	=	SYM
m-1112	1821	64	�	�	PROPN
m-1112	1821	65	̅	̅	NOUN
m-1112	1821	66	�	�	NOUN
m-1112	1821	67	,	,	PUNCT
m-1112	1821	68	𝐠𝐜	𝐠𝐜	PROPN
m-1112	1821	69	=	=	SYM
m-1112	1821	70	σ	σ	NOUN
m-1112	1821	71	=	=	PUNCT
m-1112	1821	72	𝐅𝐨𝐫𝐜𝐞	𝐅𝐨𝐫𝐜𝐞	PROPN
m-1112	1821	73	𝐀𝐫𝐞𝐚	𝐀𝐫𝐞𝐚	PROPN
m-1112	1821	74	=	=	SYM
m-1112	1821	75	𝐠.𝐌𝐚𝐬𝐬	𝐠.𝐌𝐚𝐬𝐬	PROPN
m-1112	1821	76	𝐀𝐫𝐞𝐚	𝐀𝐫𝐞𝐚	PROPN
m-1112	1821	77	for	for	ADP
m-1112	1821	78	earth	earth	NOUN
m-1112	1821	79	-	-	PUNCT
m-1112	1821	80	system	system	NOUN
m-1112	1821	81	mass	mass	NOUN
m-1112	1821	82	me	i	PRON
m-1112	1821	83	=	=	SYM
m-1112	1821	84	5,9723.1024	5,9723.1024	NUM
m-1112	1821	85	kg	kg	NOUN
m-1112	1821	86	and	and	CCONJ
m-1112	1821	87	radius	radius	NOUN
m-1112	1821	88	re	re	NOUN
m-1112	1821	89	=	=	NOUN
m-1112	1821	90	6378,137	6378,137	NUM
m-1112	1821	91	km	km	NOUN
m-1112	1821	92	=	=	SYM
m-1112	1822	1	6,378.106	6,378.106	NUM
m-1112	1822	2	m	m	VERB
m-1112	1822	3	,	,	PUNCT
m-1112	1822	4	then	then	ADV
m-1112	1822	5	earth	earth	NOUN
m-1112	1822	6	-	-	PUNCT
m-1112	1822	7	constant	constant	ADJ
m-1112	1822	8	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1822	9	=	=	PUNCT
m-1112	1822	10	r²e	r²e	ADP
m-1112	1822	11	me	i	PRON
m-1112	1823	1	=	=	PUNCT
m-1112	1824	1	[	[	X
m-1112	1824	2	6,378.106]²	6,378.106]²	NUM
m-1112	1824	3	5,98.1024	5,98.1024	NUM
m-1112	1824	4	=	=	SYM
m-1112	1824	5	6,811551810−12	6,811551810−12	NUM
m-1112	1824	6	and	and	CCONJ
m-1112	1824	7	g	g	NOUN
m-1112	1824	8	=	=	SYM
m-1112	1824	9	g	g	PROPN
m-1112	1824	10	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1824	11	=	=	SYM
m-1112	1824	12	[	[	PUNCT
m-1112	1824	13	9,8076941	9,8076941	NUM
m-1112	1824	14	]	]	PUNCT
m-1112	1824	15	.	.	PUNCT
m-1112	1825	1	6,8116.10−12	6,8116.10−12	NUM
m-1112	1825	2	=	=	SYM
m-1112	1825	3	6	6	NUM
m-1112	1825	4	,	,	PUNCT
m-1112	1825	5	68056.𝟏𝟎−𝟏𝟏	68056.𝟏𝟎−𝟏𝟏	NUM
m-1112	1825	6	m3/	m3/	NOUN
m-1112	1825	7	n.s²	n.s²	ADV
m-1112	1825	8	becoming	become	VERB
m-1112	1825	9	from	from	ADP
m-1112	1825	10	g	g	PROPN
m-1112	1825	11	,	,	PUNCT
m-1112	1825	12	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1825	13	only	only	ADV
m-1112	1825	14	,	,	PUNCT
m-1112	1825	15	i.e.	i.e.	X
m-1112	1825	16	g	g	NOUN
m-1112	1825	17	as	as	SCONJ
m-1112	1825	18	force	force	NOUN
m-1112	1825	19	pushes	push	VERB
m-1112	1825	20	→	→	SYM
m-1112	1825	21	g	g	NOUN
m-1112	1825	22	as	as	SCONJ
m-1112	1825	23	stress	stress	NOUN
m-1112	1825	24	energy	energy	NOUN
m-1112	1825	25	in	in	ADP
m-1112	1825	26	→	→	SYM
m-1112	1825	27	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1825	28	constant	constant	ADJ
m-1112	1825	29	.	.	PUNCT
m-1112	1826	1	now	now	ADV
m-1112	1826	2	is	be	AUX
m-1112	1826	3	proved	prove	VERB
m-1112	1826	4	that	that	SCONJ
m-1112	1826	5	,	,	PUNCT
m-1112	1826	6	the	the	DET
m-1112	1826	7	gravitational	gravitational	ADJ
m-1112	1826	8	constant	constant	ADJ
m-1112	1826	9	g	g	PROPN
m-1112	1826	10	is	be	AUX
m-1112	1826	11	the	the	DET
m-1112	1826	12	mechanism	mechanism	NOUN
m-1112	1826	13	or	or	CCONJ
m-1112	1826	14	the	the	DET
m-1112	1826	15	mould	mould	NOUN
m-1112	1826	16	,	,	PUNCT
m-1112	1826	17	for	for	ADP
m-1112	1826	18	the	the	DET
m-1112	1826	19	first	first	ADJ
m-1112	1826	20	-	-	PUNCT
m-1112	1826	21	kick	kick	NOUN
m-1112	1826	22	-	-	PUNCT
m-1112	1826	23	start	start	NOUN
m-1112	1826	24	upon	upon	SCONJ
m-1112	1826	25	this	this	DET
m-1112	1826	26	unit	unit	NOUN
m-1112	1826	27	-	-	PUNCT
m-1112	1826	28	granular	granular	ADJ
m-1112	1826	29	-	-	PUNCT
m-1112	1826	30	energy	energy	NOUN
m-1112	1826	31	-	-	PUNCT
m-1112	1826	32	stress	stress	NOUN
m-1112	1826	33	-	-	PUNCT
m-1112	1826	34	layer	layer	NOUN
m-1112	1826	35	,	,	PUNCT
m-1112	1826	36	g	g	PROPN
m-1112	1826	37	,	,	PUNCT
m-1112	1826	38	to	to	ADP
m-1112	1826	39	ijo	ijo	PROPN
m-1112	1826	40	international	international	PROPN
m-1112	1826	41	journal	journal	PROPN
m-1112	1826	42	of	of	ADP
m-1112	1826	43	mathematics	mathematics	PROPN
m-1112	1826	44	(	(	PUNCT
m-1112	1826	45	issn	issn	PROPN
m-1112	1826	46	:	:	PUNCT
m-1112	1826	47	2992	2992	NUM
m-1112	1826	48	-	-	SYM
m-1112	1826	49	4421	4421	NUM
m-1112	1826	50	)	)	PUNCT
m-1112	1827	1	volume	volume	NOUN
m-1112	1827	2	08	08	NUM
m-1112	1828	1	|	|	ADV
m-1112	1828	2	issue	issue	NOUN
m-1112	1828	3	08	08	NUM
m-1112	1829	1	|	|	ADV
m-1112	1829	2	august	august	PROPN
m-1112	1829	3	2025	2025	NUM
m-1112	1829	4	|	|	ADV
m-1112	1829	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1829	6	ijo	ijo	PROPN
m-1112	1829	7	journals	journal	NOUN
m-1112	1829	8	65	65	NUM
m-1112	1829	9	the	the	DET
m-1112	1829	10	fundamental	fundamental	ADJ
m-1112	1829	11	particles	particle	NOUN
m-1112	1829	12	origination	origination	NOUN
m-1112	1829	13	mechanism	mechanism	NOUN
m-1112	1829	14	in	in	ADP
m-1112	1829	15	mfmf	mfmf	PROPN
m-1112	1829	16	pns	pns	PROPN
m-1112	1829	17	caves	cave	NOUN
m-1112	1829	18	.	.	PUNCT
m-1112	1830	1	formulate	formulate	VERB
m-1112	1830	2	in	in	ADP
m-1112	1830	3	that	that	DET
m-1112	1830	4	orbit	orbit	NOUN
m-1112	1830	5	a	a	PRON
m-1112	1830	6	,	,	PUNCT
m-1112	1830	7	into	into	ADP
m-1112	1830	8	planck`s	planck`s	NOUN
m-1112	1830	9	cave	cave	NOUN
m-1112	1830	10	the	the	DET
m-1112	1830	11	lightest	light	ADJ
m-1112	1830	12	and	and	CCONJ
m-1112	1830	13	the	the	DET
m-1112	1830	14	less	less	ADJ
m-1112	1830	15	-	-	PUNCT
m-1112	1830	16	energy	energy	NOUN
m-1112	1830	17	mass	mass	NOUN
m-1112	1830	18	particle	particle	NOUN
m-1112	1830	19	of	of	ADP
m-1112	1830	20	this	this	DET
m-1112	1830	21	universe	universe	NOUN
m-1112	1830	22	,	,	PUNCT
m-1112	1830	23	which	which	PRON
m-1112	1830	24	is	be	AUX
m-1112	1830	25	the	the	DET
m-1112	1830	26	hydrogen	hydrogen	NOUN
m-1112	1830	27	with	with	ADP
m-1112	1830	28	the	the	DET
m-1112	1830	29	minimum	minimum	ADJ
m-1112	1830	30	quantized	quantize	VERB
m-1112	1830	31	-	-	PUNCT
m-1112	1830	32	energy	energy	NOUN
m-1112	1830	33	of	of	ADP
m-1112	1830	34	13,6	13,6	NUM
m-1112	1830	35	ev	ev	NOUN
m-1112	1830	36	.	.	PUNCT
m-1112	1831	1	the	the	DET
m-1112	1831	2	centripetal	centripetal	ADJ
m-1112	1831	3	acceleration	acceleration	NOUN
m-1112	1831	4	in	in	ADP
m-1112	1831	5	photon	photon	NOUN
m-1112	1831	6	cave	cave	NOUN
m-1112	1831	7	due	due	ADP
m-1112	1831	8	to	to	ADP
m-1112	1831	9	pressure	pressure	NOUN
m-1112	1831	10	σ	σ	NOUN
m-1112	1831	11	,	,	PUNCT
m-1112	1831	12	where	where	SCONJ
m-1112	1831	13	issues	issue	NOUN
m-1112	1831	14	only	only	ADV
m-1112	1831	15	rotational	rotational	ADJ
m-1112	1831	16	energy	energy	NOUN
m-1112	1831	17	e	e	NOUN
m-1112	1831	18	r	r	NOUN
m-1112	1831	19	=	=	SYM
m-1112	1831	20	b̅	b̅	PROPN
m-1112	1831	21	.	.	PUNCT
m-1112	1831	22	w̅	w̅	X
m-1112	1832	1	=	=	PUNCT
m-1112	1832	2	2l=	2l=	NUM
m-1112	1832	3	j.w²	j.w²	NOUN
m-1112	1832	4	,	,	PUNCT
m-1112	1832	5	and	and	CCONJ
m-1112	1832	6	2e	2e	NUM
m-1112	1832	7	=	=	SYM
m-1112	1832	8	b	b	PROPN
m-1112	1832	9	f	f	PROPN
m-1112	1832	10	,	,	PUNCT
m-1112	1832	11	or	or	CCONJ
m-1112	1832	12	→	→	SYM
m-1112	1832	13	2.(0,5.m.c²	2.(0,5.m.c²	NUM
m-1112	1832	14	)	)	PUNCT
m-1112	1832	15	=	=	NOUN
m-1112	1832	16	m.c²	m.c²	X
m-1112	1832	17	=	=	SYM
m-1112	1832	18	0,5.π.𝑟4.𝑐2/4	0,5.π.𝑟4.𝑐2/4	PRON
m-1112	1832	19	,	,	PUNCT
m-1112	1832	20	then	then	ADV
m-1112	1832	21	4	4	X
m-1112	1832	22	.	.	X
m-1112	1832	23	�	�	NOUN
m-1112	1832	24	̅	̅	NOUN
m-1112	1832	25	�	�	PROPN
m-1112	1832	26	.	.	PUNCT
m-1112	1833	1	f	f	X
m-1112	1833	2	=	=	PUNCT
m-1112	1833	3	𝐜𝟐.	𝐜𝟐.	PROPN
m-1112	1833	4	𝐫𝟒	𝐫𝟒	PROPN
m-1112	1833	5	,	,	PUNCT
m-1112	1833	6	where	where	SCONJ
m-1112	1833	7	the	the	DET
m-1112	1833	8	golden	golden	ADJ
m-1112	1833	9	ratio	ratio	NOUN
m-1112	1833	10	frequencies	frequency	NOUN
m-1112	1833	11	→	→	SYM
m-1112	1833	12	fn	fn	NOUN
m-1112	1833	13	=	=	PUNCT
m-1112	1833	14	[	[	PUNCT
m-1112	1833	15	n.σ.φ	n.σ.φ	X
m-1112	1833	16	2.π.r	2.π.r	NUM
m-1112	1833	17	]	]	PUNCT
m-1112	1833	18	≡	≡	PROPN
m-1112	1833	19	n.(1+√5	n.(1+√5	PUNCT
m-1112	1833	20	)	)	PUNCT
m-1112	1833	21	.σ	.σ	NOUN
m-1112	1833	22	2.𝜋.𝑟	2.𝜋.𝑟	NUM
m-1112	1834	1	=	=	SYM
m-1112	1834	2	=	=	SYM
m-1112	1834	3	𝐜𝟐.	𝐜𝟐.	PROPN
m-1112	1834	4	𝐫𝟒	𝐫𝟒	PROPN
m-1112	1834	5	/	/	SYM
m-1112	1834	6	4.	4.	NUM
m-1112	1834	7	�	�	NOUN
m-1112	1834	8	̅	̅	NOUN
m-1112	1834	9	�	�	NOUN
m-1112	1834	10	=	=	SYM
m-1112	1834	11	e	e	PROPN
m-1112	1834	12	h	h	NOUN
m-1112	1834	13	←	←	PROPN
m-1112	1834	14	i.e.	i.e.	X
m-1112	1834	15	the	the	DET
m-1112	1834	16	box	box	PROPN
m-1112	1834	17	𝐁	𝐁	PROPN
m-1112	1834	18	𝐏	𝐏	PROPN
m-1112	1834	19	,	,	PUNCT
m-1112	1834	20	or	or	CCONJ
m-1112	1834	21	the	the	DET
m-1112	1834	22	planck`s	planck`s	NOUN
m-1112	1834	23	cave	cave	NOUN
m-1112	1834	24	,	,	PUNCT
m-1112	1834	25	carried	carry	VERB
m-1112	1834	26	with	with	ADP
m-1112	1834	27	light	light	ADJ
m-1112	1834	28	velocity	velocity	NOUN
m-1112	1834	29	c	c	NOUN
m-1112	1834	30	and	and	CCONJ
m-1112	1834	31	pressed	press	VERB
m-1112	1834	32	into	into	ADP
m-1112	1834	33	the	the	DET
m-1112	1834	34	planck`s	planck`s	NOUN
m-1112	1834	35	loop	loop	NOUN
m-1112	1834	36	,	,	PUNCT
m-1112	1834	37	as	as	ADP
m-1112	1834	38	n	n	PRON
m-1112	1834	39	𝐜𝟐	𝐜𝟐	NOUN
m-1112	1834	40	=	=	PROPN
m-1112	1834	41	n.	n.	NOUN
m-1112	1834	42	c	c	PROPN
m-1112	1834	43	c	c	NOUN
m-1112	1834	44	,	,	PUNCT
m-1112	1834	45	becomes	become	VERB
m-1112	1834	46	the	the	DET
m-1112	1834	47	gravity	gravity	NOUN
m-1112	1834	48	g	g	NOUN
m-1112	1834	49	,	,	PUNCT
m-1112	1834	50	which	which	PRON
m-1112	1834	51	is	be	AUX
m-1112	1834	52	a	a	DET
m-1112	1834	53	stress	stress	NOUN
m-1112	1834	54	by	by	ADP
m-1112	1834	55	which	which	PRON
m-1112	1834	56	gravitational	gravitational	ADJ
m-1112	1834	57	-	-	PUNCT
m-1112	1834	58	force	force	NOUN
m-1112	1834	59	g	g	PROPN
m-1112	1834	60	is	be	AUX
m-1112	1834	61	communicating	communicate	VERB
m-1112	1834	62	as	as	ADP
m-1112	1834	63	,	,	PUNCT
m-1112	1834	64	g	g	PROPN
m-1112	1834	65	g	g	NOUN
m-1112	1834	66	=	=	PUNCT
m-1112	1834	67	[	[	PUNCT
m-1112	1834	68	π	π	X
m-1112	1834	69	r	r	NOUN
m-1112	1834	70	v4	v4	NOUN
m-1112	1834	71	2	2	NUM
m-1112	1834	72	]	]	PUNCT
m-1112	1834	73	.𝑒3	.𝑒3	PUNCT
m-1112	1835	1	=	=	PUNCT
m-1112	1836	1	9,808238	9,808238	NUM
m-1112	1836	2	m	m	NOUN
m-1112	1836	3	/	/	SYM
m-1112	1836	4	s	s	PART
m-1112	1836	5	.	.	PUNCT
m-1112	1837	1	gravity	gravity	NOUN
m-1112	1837	2	is	be	AUX
m-1112	1837	3	the	the	DET
m-1112	1837	4	minimum	minimum	ADJ
m-1112	1837	5	unit	unit	NOUN
m-1112	1837	6	-	-	PUNCT
m-1112	1837	7	stress	stress	NOUN
m-1112	1837	8	-	-	PUNCT
m-1112	1837	9	monad	monad	PROPN
m-1112	1837	10	in	in	ADP
m-1112	1837	11	planck`s	planck`s	NOUN
m-1112	1837	12	scale	scale	NOUN
m-1112	1837	13	becoming	become	VERB
m-1112	1837	14	from	from	ADP
m-1112	1837	15	a	a	DET
m-1112	1837	16	m	m	NOUN
m-1112	1837	17	-	-	PUNCT
m-1112	1837	18	point	point	NOUN
m-1112	1837	19	and	and	CCONJ
m-1112	1837	20	which	which	PRON
m-1112	1837	21	is	be	AUX
m-1112	1837	22	under	under	ADP
m-1112	1837	23	-planck`s	-planck`s	PUNCT
m-1112	1837	24	length	length	NOUN
m-1112	1837	25	region	region	NOUN
m-1112	1837	26	.	.	PUNCT
m-1112	1838	1	since	since	SCONJ
m-1112	1838	2	also	also	ADV
m-1112	1838	3	acceleration	acceleration	NOUN
m-1112	1838	4	in	in	ADP
m-1112	1838	5	a	a	DET
m-1112	1838	6	material	material	NOUN
m-1112	1838	7	-	-	PUNCT
m-1112	1838	8	point	point	NOUN
m-1112	1838	9	(	(	PUNCT
m-1112	1838	10	centrifugal	centrifugal	ADJ
m-1112	1838	11	-	-	PUNCT
m-1112	1838	12	centripetal	centripetal	NOUN
m-1112	1838	13	)	)	PUNCT
m-1112	1838	14	becomes	become	VERB
m-1112	1838	15	from	from	ADP
m-1112	1838	16	the	the	DET
m-1112	1838	17	principal	principal	NOUN
m-1112	1838	18	stresses	stress	VERB
m-1112	1838	19			PROPN
m-1112	1838	20	σ	σ	PROPN
m-1112	1838	21	,	,	PUNCT
m-1112	1838	22	therefore	therefore	ADV
m-1112	1838	23	constant	constant	ADJ
m-1112	1838	24	g	g	PROPN
m-1112	1838	25	g	g	PROPN
m-1112	1838	26	≅	≅	PROPN
m-1112	1838	27	±	±	PROPN
m-1112	1838	28	σ	σ	PROPN
m-1112	1838	29	=	=	PROPN
m-1112	1838	30	force	force	NOUN
m-1112	1838	31	area	area	NOUN
m-1112	1838	32	=	=	NOUN
m-1112	1838	33	g.mass	g.mass	NOUN
m-1112	1838	34	area	area	NOUN
m-1112	1838	35	=	=	PUNCT
m-1112	1838	36	g	g	PROPN
m-1112	1838	37	k	k	PROPN
m-1112	1838	38	,	,	PUNCT
m-1112	1838	39	and	and	CCONJ
m-1112	1838	40	for	for	ADP
m-1112	1838	41	unit	unit	NOUN
m-1112	1838	42	-	-	PUNCT
m-1112	1838	43	g	g	PROPN
m-1112	1838	44	constant	constant	ADJ
m-1112	1838	45	k	k	NOUN
m-1112	1838	46	becomes	become	VERB
m-1112	1838	47	,	,	PUNCT
m-1112	1838	48	k	k	NOUN
m-1112	1838	49	=	=	SYM
m-1112	1838	50	system	system	NOUN
m-1112	1838	51	area	area	NOUN
m-1112	1838	52	system	system	NOUN
m-1112	1838	53	mass	mass	NOUN
m-1112	1838	54	g	g	NOUN
m-1112	1838	55	where	where	SCONJ
m-1112	1838	56	→	→	SYM
m-1112	1838	57	1	1	NUM
m-1112	1838	58	𝐠	𝐠	NOUN
m-1112	1838	59	=	=	SYM
m-1112	1838	60	k	k	PROPN
m-1112	1838	61	g	g	PROPN
m-1112	1838	62	=	=	NOUN
m-1112	1838	63	system	system	NOUN
m-1112	1838	64	area	area	NOUN
m-1112	1838	65	system	system	NOUN
m-1112	1838	66	mass	mass	NOUN
m-1112	1838	67	and	and	CCONJ
m-1112	1838	68	g	g	NOUN
m-1112	1838	69	=	=	SYM
m-1112	1838	70	k	k	PROPN
m-1112	1838	71	g	g	PROPN
m-1112	1838	72	g	g	PROPN
m-1112	1838	73	,	,	PUNCT
m-1112	1838	74	and	and	CCONJ
m-1112	1838	75	for	for	ADP
m-1112	1838	76	the	the	DET
m-1112	1838	77	earth	earth	NOUN
m-1112	1838	78	g	g	PROPN
m-1112	1838	79	≡	≡	PROPN
m-1112	1838	80	g.ke	g.ke	PROPN
m-1112	1838	81	≡	≡	PROPN
m-1112	1838	82	g	g	PROPN
m-1112	1838	83	.[gl	.[gl	PROPN
m-1112	1838	84	kl	kl	X
m-1112	1838	85	]	]	PUNCT
m-1112	1839	1	≡	≡	PROPN
m-1112	1839	2	[	[	PUNCT
m-1112	1839	3	t²p	t²p	X
m-1112	1839	4	𝐚³	𝐚³	PROPN
m-1112	1839	5	]	]	PUNCT
m-1112	1839	6	.	.	PUNCT
m-1112	1840	1	[	[	PUNCT
m-1112	1840	2	gl	gl	X
m-1112	1840	3	kl	kl	X
m-1112	1840	4	]	]	PUNCT
m-1112	1840	5	≡	≡	PROPN
m-1112	1840	6	9,808238	9,808238	PROPN
m-1112	1840	7	*	*	SYM
m-1112	1840	8	6,8116.10−12	6,8116.10−12	NUM
m-1112	1840	9	≡	≡	PROPN
m-1112	1840	10	6,68056.10−11	6,68056.10−11	NUM
m-1112	1840	11	𝐦³	𝐦³	PROPN
m-1112	1840	12	𝐍𝐬²	𝐍𝐬²	NOUN
m-1112	1840	13	so	so	SCONJ
m-1112	1840	14	g	g	PROPN
m-1112	1840	15	,	,	PUNCT
m-1112	1840	16	is	be	AUX
m-1112	1840	17	the	the	DET
m-1112	1840	18	pulling	pull	VERB
m-1112	1840	19	and	and	CCONJ
m-1112	1840	20	cohesive	cohesive	ADJ
m-1112	1840	21	force	force	NOUN
m-1112	1840	22	on	on	ADP
m-1112	1840	23	all	all	DET
m-1112	1840	24	the	the	DET
m-1112	1840	25	quantized	quantize	VERB
m-1112	1840	26	-	-	PUNCT
m-1112	1840	27	energy	energy	NOUN
m-1112	1840	28	-	-	PUNCT
m-1112	1840	29	structures	structure	NOUN
m-1112	1840	30	which	which	PRON
m-1112	1840	31	communicates	communicate	VERB
m-1112	1840	32	with	with	ADP
m-1112	1840	33	everything	everything	PRON
m-1112	1840	34	due	due	ADJ
m-1112	1840	35	to	to	ADP
m-1112	1840	36	periodic	periodic	ADJ
m-1112	1840	37	excitation	excitation	NOUN
m-1112	1840	38	on	on	ADP
m-1112	1840	39	all	all	DET
m-1112	1840	40	spaces	space	NOUN
m-1112	1840	41	.	.	PUNCT
m-1112	1841	1	from	from	ADP
m-1112	1841	2	equation	equation	NOUN
m-1112	1841	3	g	g	NOUN
m-1112	1841	4	=	=	SYM
m-1112	1841	5	g	g	PROPN
m-1112	1841	6	/	/	SYM
m-1112	1841	7	[	[	X
m-1112	1841	8	gl	gl	X
m-1112	1841	9	kl	kl	X
m-1112	1841	10	]	]	PUNCT
m-1112	1841	11	,	,	PUNCT
m-1112	1841	12	is	be	AUX
m-1112	1841	13	seen	see	VERB
m-1112	1841	14	that	that	SCONJ
m-1112	1841	15	g	g	PROPN
m-1112	1841	16	becomes	become	VERB
m-1112	1841	17	from	from	ADP
m-1112	1841	18	g	g	NOUN
m-1112	1841	19	under	under	ADP
m-1112	1841	20	local	local	ADJ
m-1112	1841	21	-	-	PUNCT
m-1112	1841	22	laws	law	NOUN
m-1112	1841	23	,	,	PUNCT
m-1112	1841	24	and	and	CCONJ
m-1112	1841	25	also	also	ADV
m-1112	1841	26	,	,	PUNCT
m-1112	1841	27	gravity	gravity	NOUN
m-1112	1841	28	g	g	NOUN
m-1112	1841	29	,	,	PUNCT
m-1112	1841	30	is	be	AUX
m-1112	1841	31	the	the	DET
m-1112	1841	32	unit	unit	NOUN
m-1112	1841	33	-	-	PUNCT
m-1112	1841	34	energy	energy	NOUN
m-1112	1841	35	-	-	PUNCT
m-1112	1841	36	path	path	NOUN
m-1112	1841	37	,	,	PUNCT
m-1112	1841	38	quanta	quanta	PROPN
m-1112	1841	39	of	of	ADP
m-1112	1841	40	gravitation	gravitation	NOUN
m-1112	1841	41	,	,	PUNCT
m-1112	1841	42	due	due	ADP
m-1112	1841	43	to	to	ADP
m-1112	1841	44	m	m	NOUN
m-1112	1841	45	-	-	PUNCT
m-1112	1841	46	point	point	NOUN
m-1112	1841	47	frequency	frequency	NOUN
m-1112	1841	48	fg	fg	PROPN
m-1112	1841	49	≅	≅	PROPN
m-1112	1841	50	±	±	PROPN
m-1112	1841	51	𝜎	𝜎	PROPN
m-1112	1841	52	from	from	ADP
m-1112	1841	53	the	the	DET
m-1112	1841	54	revolving	revolve	VERB
m-1112	1841	55	motion	motion	NOUN
m-1112	1841	56	,	,	PUNCT
m-1112	1841	57	and	and	CCONJ
m-1112	1841	58	also	also	ADV
m-1112	1841	59	the	the	DET
m-1112	1841	60	unit	unit	NOUN
m-1112	1841	61	-	-	PUNCT
m-1112	1841	62	energy	energy	NOUN
m-1112	1841	63	-	-	PUNCT
m-1112	1841	64	stress	stress	NOUN
m-1112	1841	65	per	per	ADP
m-1112	1841	66	surface	surface	NOUN
m-1112	1841	67	and	and	CCONJ
m-1112	1841	68	for	for	ADP
m-1112	1841	69	the	the	DET
m-1112	1841	70	force	force	NOUN
m-1112	1841	71	g	g	NOUN
m-1112	1841	72	,	,	PUNCT
m-1112	1841	73	is	be	AUX
m-1112	1841	74	the	the	DET
m-1112	1841	75	permitted	permit	VERB
m-1112	1841	76	path	path	NOUN
m-1112	1841	77	,	,	PUNCT
m-1112	1841	78	or	or	CCONJ
m-1112	1841	79	the	the	DET
m-1112	1841	80	communication	communication	NOUN
m-1112	1841	81	conductor	conductor	NOUN
m-1112	1841	82	on	on	ADP
m-1112	1841	83	all	all	DET
m-1112	1841	84	energy	energy	NOUN
m-1112	1841	85	wave	wave	NOUN
m-1112	1841	86	structures	structure	NOUN
m-1112	1841	87	,	,	PUNCT
m-1112	1841	88	in	in	ADP
m-1112	1841	89	and	and	CCONJ
m-1112	1841	90	out	out	ADP
m-1112	1841	91	planck`s	planck`s	NOUN
m-1112	1841	92	length	length	NOUN
m-1112	1841	93	.	.	PUNCT
m-1112	1842	1	remarks	remark	NOUN
m-1112	1842	2	:	:	PUNCT
m-1112	1842	3	gravitational	gravitational	ADJ
m-1112	1842	4	force	force	NOUN
m-1112	1842	5	,	,	PUNCT
m-1112	1842	6	g	g	PROPN
m-1112	1842	7	,	,	PUNCT
m-1112	1842	8	is	be	AUX
m-1112	1842	9	the	the	DET
m-1112	1842	10	pressure	pressure	NOUN
m-1112	1842	11	which	which	PRON
m-1112	1842	12	every	every	DET
m-1112	1842	13	object	object	NOUN
m-1112	1842	14	in	in	ADP
m-1112	1842	15	the	the	DET
m-1112	1842	16	universe	universe	NOUN
m-1112	1842	17	exerts	exert	VERB
m-1112	1842	18	on	on	ADP
m-1112	1842	19	every	every	DET
m-1112	1842	20	other	other	ADJ
m-1112	1842	21	,	,	PUNCT
m-1112	1842	22	whether	whether	SCONJ
m-1112	1842	23	small	small	ADJ
m-1112	1842	24	or	or	CCONJ
m-1112	1842	25	big	big	ADJ
m-1112	1842	26	and	and	CCONJ
m-1112	1842	27	is	be	AUX
m-1112	1842	28	equal	equal	ADJ
m-1112	1842	29	to	to	ADP
m-1112	1842	30	fgrav	fgrav	ADJ
m-1112	1842	31	=	=	PUNCT
m-1112	1842	32	g.m.m	g.m.m	NOUN
m-1112	1842	33	d²	d²	NOUN
m-1112	1842	34	=	=	PUNCT
m-1112	1842	35	g.𝐑²𝐄	g.𝐑²𝐄	PROPN
m-1112	1842	36	m.m	m.m	PROPN
m-1112	1842	37	md²	md²	NOUN
m-1112	1842	38	=	=	PUNCT
m-1112	1842	39	g.𝐑²𝐄	g.𝐑²𝐄	VERB
m-1112	1842	40	.m	.m	PUNCT
m-1112	1843	1	d²	d²	NOUN
m-1112	1843	2	=	=	PUNCT
m-1112	1843	3	mg.𝐑²𝐄	mg.𝐑²𝐄	NOUN
m-1112	1843	4	d²	d²	NOUN
m-1112	1843	5	,	,	PUNCT
m-1112	1843	6	and	and	CCONJ
m-1112	1843	7	g	g	NOUN
m-1112	1843	8	=	=	PUNCT
m-1112	1843	9	g.𝐑²𝐄	g.𝐑²𝐄	VERB
m-1112	1843	10	m.m.d²	m.m.d²	NUM
m-1112	1843	11	md²	md²	NOUN
m-1112	1843	12	=	=	SYM
m-1112	1843	13	g.	g.	PROPN
m-1112	1843	14	[	[	PUNCT
m-1112	1843	15	𝐑²𝐄	𝐑²𝐄	X
m-1112	1843	16	]	]	PUNCT
m-1112	1844	1	m	m	VERB
m-1112	1844	2	=	=	SYM
m-1112	1844	3	g	g	PROPN
m-1112	1844	4	.	.	PUNCT
m-1112	1845	1	ke	ke	NOUN
m-1112	1845	2	,	,	PUNCT
m-1112	1845	3	where	where	SCONJ
m-1112	1845	4	ke	ke	NOUN
m-1112	1846	1	=	=	PUNCT
m-1112	1847	1	[	[	PUNCT
m-1112	1847	2	𝐑²𝐄	𝐑²𝐄	X
m-1112	1847	3	]	]	PUNCT
m-1112	1848	1	m	m	VERB
m-1112	1848	2	,	,	PUNCT
m-1112	1848	3	and	and	CCONJ
m-1112	1848	4	g	g	PROPN
m-1112	1848	5	=	=	PUNCT
m-1112	1848	6	the	the	DET
m-1112	1848	7	minimum	minimum	ADJ
m-1112	1848	8	quantized	quantize	VERB
m-1112	1848	9	work	work	NOUN
m-1112	1848	10	as	as	ADP
m-1112	1848	11	acceleration	acceleration	NOUN
m-1112	1848	12	≡	≡	PROPN
m-1112	1848	13	9	9	NUM
m-1112	1848	14	,	,	PUNCT
m-1112	1848	15	8076941	8076941	NUM
m-1112	1848	16	m	m	NOUN
m-1112	1848	17	/	/	SYM
m-1112	1848	18	s²	s²	PROPN
m-1112	1848	19	ke	ke	NOUN
m-1112	1848	20	=	=	PUNCT
m-1112	1848	21	the	the	DET
m-1112	1848	22	earth	earth	NOUN
m-1112	1848	23	local	local	ADJ
m-1112	1848	24	-	-	PUNCT
m-1112	1848	25	coefficient	coefficient	NOUN
m-1112	1848	26	between	between	ADP
m-1112	1848	27	the	the	DET
m-1112	1848	28	two	two	NUM
m-1112	1848	29	constants	constant	NOUN
m-1112	1848	30	g	g	NOUN
m-1112	1848	31	,	,	PUNCT
m-1112	1848	32	g	g	PROPN
m-1112	1848	33	.	.	PUNCT
m-1112	1849	1	for	for	ADP
m-1112	1849	2	earth	earth	NOUN
m-1112	1849	3	(	(	PUNCT
m-1112	1849	4	e	e	NOUN
m-1112	1849	5	)	)	PUNCT
m-1112	1849	6	→	→	PUNCT
m-1112	1849	7	k	k	X
m-1112	1849	8	e	e	X
m-1112	1849	9	=	=	PUNCT
m-1112	1849	10	r	r	NOUN
m-1112	1849	11	²e	²e	X
m-1112	1849	12	/	/	SYM
m-1112	1849	13	m	m	VERB
m-1112	1849	14	e	e	NOUN
m-1112	1849	15	,	,	PUNCT
m-1112	1849	16	for	for	ADP
m-1112	1849	17	bodies	body	NOUN
m-1112	1849	18	(	(	PUNCT
m-1112	1849	19	b	b	NOUN
m-1112	1849	20	)	)	PUNCT
m-1112	1849	21	→	→	PUNCT
m-1112	1849	22	k	k	PROPN
m-1112	1849	23	b	b	X
m-1112	1849	24	=	=	SYM
m-1112	1849	25	r	r	NOUN
m-1112	1849	26	²b	²b	NOUN
m-1112	1849	27	/	/	SYM
m-1112	1849	28	m	m	PROPN
m-1112	1849	29	b	b	NOUN
m-1112	1849	30	,	,	PUNCT
m-1112	1849	31	for	for	ADP
m-1112	1849	32	any	any	DET
m-1112	1849	33	body	body	NOUN
m-1112	1849	34	→	→	SYM
m-1112	1849	35	local	local	ADJ
m-1112	1849	36	gravity	gravity	NOUN
m-1112	1849	37	g	g	PROPN
m-1112	1849	38	l	l	NOUN
m-1112	1849	39	=	=	PUNCT
m-1112	1849	40	ke	ke	NOUN
m-1112	1849	41	/	/	PUNCT
m-1112	1849	42	kl	kl	NOUN
m-1112	1849	43	from	from	ADP
m-1112	1849	44	relation	relation	NOUN
m-1112	1849	45	g	g	PROPN
m-1112	1849	46	=	=	SYM
m-1112	1849	47	g	g	PROPN
m-1112	1849	48	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1849	49	=	=	SYM
m-1112	1849	50	9,8076941.6,8116.10−12	9,8076941.6,8116.10−12	NUM
m-1112	1849	51	=	=	SYM
m-1112	1849	52	6,68056.𝟏𝟎−𝟏𝟏	6,68056.𝟏𝟎−𝟏𝟏	PROPN
m-1112	1849	53	m3/	m3/	X
m-1112	1849	54	n.s²	n.s²	ADJ
m-1112	1849	55	and	and	CCONJ
m-1112	1849	56	from	from	ADP
m-1112	1849	57	relation	relation	NOUN
m-1112	1849	58	1	1	NUM
m-1112	1849	59	=	=	SYM
m-1112	1849	60	c.	c.	PROPN
m-1112	1849	61	r³.	r³.	NOUN
m-1112	1849	62	𝐟𝐏²	𝐟𝐏²	PROPN
m-1112	1849	63	→	→	SYM
m-1112	1849	64	fp	fp	PROPN
m-1112	1849	65	=	=	PUNCT
m-1112	1849	66	√1	√1	PROPN
m-1112	1849	67	/	/	SYM
m-1112	1849	68	cr³	cr³	ADJ
m-1112	1849	69	and	and	CCONJ
m-1112	1849	70	from	from	ADP
m-1112	1849	71	f	f	PROPN
m-1112	1849	72	=	=	SYM
m-1112	1849	73	e	e	X
m-1112	1849	74	/	/	SYM
m-1112	1849	75	h	h	NOUN
m-1112	1849	76	then	then	ADV
m-1112	1849	77	𝐄	𝐄	VERB
m-1112	1849	78	𝐡	𝐡	NOUN
m-1112	1849	79	=	=	PUNCT
m-1112	1849	80	√1	√1	PROPN
m-1112	1849	81	/	/	SYM
m-1112	1849	82	cr³	cr³	ADJ
m-1112	1849	83	or	or	CCONJ
m-1112	1849	84	→	→	SYM
m-1112	1849	85	e	e	NOUN
m-1112	1849	86	=	=	SYM
m-1112	1849	87	h	h	PROPN
m-1112	1849	88	.	.	PUNCT
m-1112	1850	1	√1	√1	PROPN
m-1112	1850	2	/	/	SYM
m-1112	1850	3	c.	c.	PROPN
m-1112	1850	4	r³	r³	PROPN
m-1112	1850	5	,	,	PUNCT
m-1112	1850	6	e²	e²	VERB
m-1112	1850	7	h²	h²	PROPN
m-1112	1850	8	=	=	SYM
m-1112	1850	9	1	1	NUM
m-1112	1850	10	cr³	cr³	NOUN
m-1112	1850	11	→	→	PUNCT
m-1112	1850	12	and	and	CCONJ
m-1112	1850	13	,	,	PUNCT
m-1112	1850	14	e	e	X
m-1112	1850	15	²	²	NUM
m-1112	1850	16	=	=	SYM
m-1112	1850	17	𝐡²	𝐡²	PROPN
m-1112	1850	18	𝐜	𝐜	PROPN
m-1112	1850	19	𝐫³	𝐫³	NOUN
m-1112	1850	20	,	,	PUNCT
m-1112	1850	21	is	be	AUX
m-1112	1850	22	an	an	DET
m-1112	1850	23	energy	energy	NOUN
m-1112	1850	24	relation	relation	NOUN
m-1112	1850	25	between	between	ADP
m-1112	1850	26	c	c	PROPN
m-1112	1850	27	,	,	PUNCT
m-1112	1850	28	r	r	NOUN
m-1112	1850	29	.	.	PUNCT
m-1112	1851	1	instances	instance	NOUN
m-1112	1851	2	:	:	PUNCT
m-1112	1852	1	[	[	X
m-1112	1852	2	77	77	NUM
m-1112	1852	3	]	]	SYM
m-1112	1852	4	1	1	NUM
m-1112	1852	5	..	..	PUNCT
m-1112	1852	6	for	for	ADP
m-1112	1852	7	earth	earth	NOUN
m-1112	1852	8	-	-	PUNCT
m-1112	1852	9	system	system	NOUN
m-1112	1852	10	mass	mass	NOUN
m-1112	1852	11	me	i	PRON
m-1112	1853	1	=	=	SYM
m-1112	1853	2	5,9723.1024	5,9723.1024	NUM
m-1112	1853	3	kg	kg	NOUN
m-1112	1853	4	and	and	CCONJ
m-1112	1853	5	for	for	ADP
m-1112	1853	6	area	area	NOUN
m-1112	1853	7	→	→	SYM
m-1112	1853	8	radius	radius	NOUN
m-1112	1853	9	6378,137	6378,137	NUM
m-1112	1853	10	km	km	NOUN
m-1112	1854	1	=	=	SYM
m-1112	1855	1	6,378.106	6,378.106	NUM
m-1112	1855	2	m	m	VERB
m-1112	1855	3	then	then	ADV
m-1112	1855	4	the	the	DET
m-1112	1855	5	earth	earth	NOUN
m-1112	1855	6	-	-	PUNCT
m-1112	1855	7	constant	constant	ADJ
m-1112	1855	8	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1855	9	=	=	PUNCT
m-1112	1856	1	[	[	X
m-1112	1856	2	6,378.106]²	6,378.106]²	NUM
m-1112	1856	3	5,9723.1024	5,9723.1024	NUM
m-1112	1856	4	=	=	SYM
m-1112	1856	5	6,811551810−12	6,811551810−12	NUM
m-1112	1856	6	and	and	CCONJ
m-1112	1856	7	g	g	PROPN
m-1112	1856	8	≡	≡	PROPN
m-1112	1856	9	σ.𝚽³	σ.𝚽³	NOUN
m-1112	1856	10	=	=	SYM
m-1112	1856	11	g	g	PROPN
m-1112	1856	12	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1856	13	=	=	SYM
m-1112	1857	1	9,8076941	9,8076941	NUM
m-1112	1857	2	*	*	SYM
m-1112	1857	3	6,8115518.10−12	6,8115518.10−12	NUM
m-1112	1857	4	=	=	SYM
m-1112	1857	5	6,6805616*𝟏𝟎−𝟏𝟏	6,6805616*𝟏𝟎−𝟏𝟏	PROPN
m-1112	1857	6	m³/kg	m³/kg	NOUN
m-1112	1857	7	.s²	.s²	PUNCT
m-1112	1858	1	i.e.	i.e.	X
m-1112	1858	2	gravitational	gravitational	ADJ
m-1112	1858	3	-	-	PUNCT
m-1112	1858	4	constant	constant	ADJ
m-1112	1858	5	g	g	NOUN
m-1112	1858	6	becomes	become	VERB
m-1112	1858	7	from	from	ADP
m-1112	1858	8	g	g	NOUN
m-1112	1858	9	,	,	PUNCT
m-1112	1858	10	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1858	11	,	,	PUNCT
m-1112	1858	12	and	and	CCONJ
m-1112	1858	13	issues	issue	NOUN
m-1112	1858	14	g	g	NOUN
m-1112	1858	15	=	=	SYM
m-1112	1858	16	6,6805616.10−11	6,6805616.10−11	NUM
m-1112	1858	17	m3	m3	PROPN
m-1112	1858	18	/	/	SYM
m-1112	1858	19	n.s²	n.s²	NOUN
m-1112	1858	20	…	…	PUNCT
m-1112	1858	21	…	…	PUNCT
m-1112	1858	22	..	..	PUNCT
m-1112	1858	23	…	…	PUNCT
m-1112	1858	24	.(7	.(7	NUM
m-1112	1858	25	)	)	PUNCT
m-1112	1858	26	for	for	ADP
m-1112	1858	27	black	black	ADJ
m-1112	1858	28	-	-	PUNCT
m-1112	1858	29	holes	hole	NOUN
m-1112	1858	30	-	-	PUNCT
m-1112	1858	31	system	system	NOUN
m-1112	1858	32	mass	mass	NOUN
m-1112	1858	33	m	m	NOUN
m-1112	1858	34	bh	bh	NOUN
m-1112	1859	1	=	=	PUNCT
m-1112	1859	2	4,0.10	4,0.10	NUM
m-1112	1859	3	52	52	NUM
m-1112	1859	4	kg	kg	NOUN
m-1112	1859	5	and	and	CCONJ
m-1112	1859	6	for	for	ADP
m-1112	1859	7	the	the	DET
m-1112	1859	8	area	area	NOUN
m-1112	1859	9	ijo	ijo	PROPN
m-1112	1859	10	international	international	PROPN
m-1112	1859	11	journal	journal	PROPN
m-1112	1859	12	of	of	ADP
m-1112	1859	13	mathematics	mathematics	PROPN
m-1112	1859	14	(	(	PUNCT
m-1112	1859	15	issn	issn	PROPN
m-1112	1859	16	:	:	PUNCT
m-1112	1859	17	2992	2992	NUM
m-1112	1859	18	-	-	SYM
m-1112	1859	19	4421	4421	NUM
m-1112	1859	20	)	)	PUNCT
m-1112	1859	21	volume	volume	NOUN
m-1112	1859	22	08	08	NUM
m-1112	1860	1	|	|	ADV
m-1112	1860	2	issue	issue	NOUN
m-1112	1860	3	08	08	NUM
m-1112	1861	1	|	|	ADV
m-1112	1861	2	august	august	PROPN
m-1112	1861	3	2025	2025	NUM
m-1112	1861	4	|	|	ADV
m-1112	1861	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1861	6	ijo	ijo	PROPN
m-1112	1861	7	journals	journal	NOUN
m-1112	1861	8	66	66	NUM
m-1112	1861	9	the	the	DET
m-1112	1861	10	fundamental	fundamental	ADJ
m-1112	1861	11	particles	particle	NOUN
m-1112	1861	12	origination	origination	NOUN
m-1112	1861	13	mechanism	mechanism	NOUN
m-1112	1861	14	in	in	ADP
m-1112	1861	15	mfmf	mfmf	PROPN
m-1112	1861	16	pns	pns	PROPN
m-1112	1861	17	caves	cave	NOUN
m-1112	1861	18	.	.	PUNCT
m-1112	1862	1	radius	radius	VERB
m-1112	1862	2	3,08.1025	3,08.1025	NUM
m-1112	1862	3	m	m	NOUN
m-1112	1862	4	,	,	PUNCT
m-1112	1862	5	then	then	ADV
m-1112	1862	6	black	black	ADJ
m-1112	1862	7	-	-	PUNCT
m-1112	1862	8	hole	hole	NOUN
m-1112	1862	9	-	-	PUNCT
m-1112	1862	10	constant	constant	ADJ
m-1112	1862	11	kbh	kbh	NOUN
m-1112	1862	12	=	=	PUNCT
m-1112	1863	1	[	[	X
m-1112	1863	2	3,08.1025]²	3,08.1025]²	NUM
m-1112	1863	3	4,0.1052	4,0.1052	NUM
m-1112	1864	1	=	=	SYM
m-1112	1865	1	2,3716.10−2	2,3716.10−2	NUM
m-1112	1865	2	𝐠𝐁𝐇	𝐠𝐁𝐇	NOUN
m-1112	1865	3	=	=	SYM
m-1112	1865	4	k	k	NOUN
m-1112	1865	5	e	e	X
m-1112	1865	6	k	k	PROPN
m-1112	1865	7	bh	bh	PROPN
m-1112	1865	8	=	=	VERB
m-1112	1865	9	6,81155.10−12	6,81155.10−12	NUM
m-1112	1865	10	/	/	SYM
m-1112	1865	11	2,3716.10−2	2,3716.10−2	NUM
m-1112	1865	12	=	=	SYM
m-1112	1865	13	2	2	NUM
m-1112	1865	14	,	,	PUNCT
m-1112	1865	15	872.10−10	872.10−10	PROPN
m-1112	1865	16	.	.	PUNCT
m-1112	1866	1	ge	ge	PROPN
m-1112	1866	2	→	→	PUNCT
m-1112	1866	3	i.e.	i.e.	X
m-1112	1866	4	for	for	ADP
m-1112	1866	5	earth	earth	NOUN
m-1112	1866	6	-	-	PUNCT
m-1112	1866	7	unit	unit	NOUN
m-1112	1866	8	-	-	PUNCT
m-1112	1866	9	coefficient	coefficient	NOUN
m-1112	1866	10	ke	ke	NOUN
m-1112	1866	11	=	=	NOUN
m-1112	1866	12	6,81155.10−12	6,81155.10−12	NUM
m-1112	1866	13	→	→	PUNCT
m-1112	1866	14	black	black	ADJ
m-1112	1866	15	-	-	PUNCT
m-1112	1866	16	hole	hole	NOUN
m-1112	1866	17	–	–	PUNCT
m-1112	1866	18	unit	unit	NOUN
m-1112	1866	19	-	-	PUNCT
m-1112	1866	20	coefficient	coefficient	NOUN
m-1112	1866	21	kbh	kbh	PROPN
m-1112	1866	22	=	=	PROPN
m-1112	1866	23	2,3716.10−2	2,3716.10−2	NUM
m-1112	1866	24	m2	m2	PROPN
m-1112	1866	25	/	/	SYM
m-1112	1866	26	kg	kg	X
m-1112	1866	27	,	,	PUNCT
m-1112	1866	28	and	and	CCONJ
m-1112	1866	29	gravity	gravity	NOUN
m-1112	1866	30	acceleration	acceleration	NOUN
m-1112	1866	31	of	of	ADP
m-1112	1866	32	a	a	DET
m-1112	1866	33	black	black	ADJ
m-1112	1866	34	-	-	PUNCT
m-1112	1866	35	hole	hole	NOUN
m-1112	1866	36	is	be	AUX
m-1112	1866	37	,	,	PUNCT
m-1112	1866	38	𝐠𝐁𝐇	𝐠𝐁𝐇	PROPN
m-1112	1866	39	=	=	SYM
m-1112	1866	40	2,872.10−10	2,872.10−10	PROPN
m-1112	1866	41	.	.	PUNCT
m-1112	1867	1	ge	ge	PROPN
m-1112	1867	2	,	,	PUNCT
m-1112	1867	3	an	an	DET
m-1112	1867	4	expected	expect	VERB
m-1112	1867	5	explanation	explanation	NOUN
m-1112	1867	6	.	.	PUNCT
m-1112	1868	1	for	for	ADP
m-1112	1868	2	all	all	DET
m-1112	1868	3	planes	plane	NOUN
m-1112	1868	4	issues	issue	NOUN
m-1112	1868	5	g	g	NOUN
m-1112	1868	6	=	=	PUNCT
m-1112	1868	7	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1868	8	g	g	NOUN
m-1112	1868	9	=	=	SYM
m-1112	1868	10	𝐠	𝐠	PROPN
m-1112	1868	11	.	.	PUNCT
m-1112	1868	12	𝐤𝐋	𝐤𝐋	PUNCT
m-1112	1868	13	𝐠𝐋	𝐠𝐋	ADJ
m-1112	1868	14	,	,	PUNCT
m-1112	1868	15	and	and	CCONJ
m-1112	1868	16	for	for	ADP
m-1112	1868	17	black	black	ADJ
m-1112	1868	18	-	-	PUNCT
m-1112	1868	19	holes	hole	NOUN
m-1112	1868	20	also	also	ADV
m-1112	1868	21	where	where	SCONJ
m-1112	1868	22	,	,	PUNCT
m-1112	1868	23	g	g	PROPN
m-1112	1868	24	=	=	SYM
m-1112	1868	25	g	g	PROPN
m-1112	1868	26	.	.	PUNCT
m-1112	1869	1	𝐤𝐁𝐇	𝐤𝐁𝐇	NOUN
m-1112	1869	2	.	.	PUNCT
m-1112	1870	1	𝐠𝐁𝐇	𝐠𝐁𝐇	NUM
m-1112	1871	1	=	=	SYM
m-1112	1871	2	9,8076941	9,8076941	NUM
m-1112	1871	3	*	*	SYM
m-1112	1871	4	2,3716.10−2	2,3716.10−2	NUM
m-1112	1871	5	*	*	PUNCT
m-1112	1871	6	2,872.10−10	2,872.10−10	NUM
m-1112	1871	7	=	=	SYM
m-1112	1871	8	6,6805616*𝟏𝟎−𝟏𝟏	6,6805616*𝟏𝟎−𝟏𝟏	PROPN
m-1112	1871	9	meaning	mean	VERB
m-1112	1871	10	that	that	SCONJ
m-1112	1871	11	gravitational	gravitational	ADJ
m-1112	1871	12	constant	constant	NOUN
m-1112	1871	13	is	be	AUX
m-1112	1871	14	the	the	DET
m-1112	1871	15	same	same	ADJ
m-1112	1871	16	for	for	ADP
m-1112	1871	17	all	all	DET
m-1112	1871	18	systems	system	NOUN
m-1112	1871	19	.	.	PUNCT
m-1112	1872	1	the	the	DET
m-1112	1872	2	gravitational	gravitational	ADJ
m-1112	1872	3	force	force	NOUN
m-1112	1872	4	,	,	PUNCT
m-1112	1872	5	g	g	PROPN
m-1112	1872	6	,	,	PUNCT
m-1112	1872	7	is	be	AUX
m-1112	1872	8	the	the	DET
m-1112	1872	9	pressure	pressure	NOUN
m-1112	1872	10	which	which	PRON
m-1112	1872	11	every	every	DET
m-1112	1872	12	object	object	NOUN
m-1112	1872	13	in	in	ADP
m-1112	1872	14	the	the	DET
m-1112	1872	15	universe	universe	NOUN
m-1112	1872	16	exerts	exert	VERB
m-1112	1872	17	on	on	ADP
m-1112	1872	18	every	every	DET
m-1112	1872	19	other	other	ADJ
m-1112	1872	20	,	,	PUNCT
m-1112	1872	21	whether	whether	SCONJ
m-1112	1872	22	small	small	ADJ
m-1112	1872	23	or	or	CCONJ
m-1112	1872	24	big	big	ADJ
m-1112	1872	25	and	and	CCONJ
m-1112	1872	26	from	from	ADP
m-1112	1872	27	newton	newton	PROPN
m-1112	1872	28	are	be	AUX
m-1112	1872	29	equal	equal	ADJ
m-1112	1872	30	to	to	ADP
m-1112	1872	31	→	→	SYM
m-1112	1872	32	𝐅𝐠𝐫𝐚𝐯	𝐅𝐠𝐫𝐚𝐯	PROPN
m-1112	1872	33	=	=	PUNCT
m-1112	1872	34	𝐆.𝐌.𝐦	𝐆.𝐌.𝐦	PROPN
m-1112	1872	35	𝐝²	𝐝²	NOUN
m-1112	1872	36	=	=	PUNCT
m-1112	1872	37	𝐠.𝐑²𝐄	𝐠.𝐑²𝐄	VERB
m-1112	1872	38	𝐌.𝐦	𝐌.𝐦	NOUN
m-1112	1872	39	𝐌𝐝²	𝐌𝐝²	ADJ
m-1112	1872	40	=	=	PUNCT
m-1112	1872	41	𝐠.𝐑²𝐄	𝐠.𝐑²𝐄	VERB
m-1112	1872	42	.𝐦	.𝐦	PROPN
m-1112	1873	1	𝐝²	𝐝²	NOUN
m-1112	1873	2	=	=	PUNCT
m-1112	1873	3	𝐦𝐠.𝐑²𝐄	𝐦𝐠.𝐑²𝐄	PROPN
m-1112	1873	4	𝐝²	𝐝²	NOUN
m-1112	1873	5	,	,	PUNCT
m-1112	1873	6	g	g	PROPN
m-1112	1873	7	=	=	PUNCT
m-1112	1873	8	𝐠.𝐑²𝐄	𝐠.𝐑²𝐄	VERB
m-1112	1873	9	𝐌.𝐦.𝐝²	𝐌.𝐦.𝐝²	NOUN
m-1112	1873	10	𝐌𝐝²	𝐌𝐝²	ADJ
m-1112	1873	11	=	=	PUNCT
m-1112	1873	12	𝐠.	𝐠.	NOUN
m-1112	1873	13	[	[	X
m-1112	1873	14	𝐑²𝐄	𝐑²𝐄	X
m-1112	1873	15	]	]	PUNCT
m-1112	1874	1	𝐌	𝐌	PROPN
m-1112	1874	2	=	=	SYM
m-1112	1874	3	g	g	PROPN
m-1112	1874	4	.	.	PUNCT
m-1112	1875	1	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1875	2	where	where	SCONJ
m-1112	1875	3	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1875	4	=	=	PRON
m-1112	1875	5	𝐠.	𝐠.	VERB
m-1112	1875	6	[	[	X
m-1112	1875	7	𝐑²𝐄	𝐑²𝐄	X
m-1112	1875	8	]	]	PUNCT
m-1112	1876	1	𝐌	𝐌	PROPN
m-1112	1876	2	=	=	PUNCT
m-1112	1876	3	𝐠.𝐌	𝐠.𝐌	X
m-1112	1877	1	𝐆	𝐆	PROPN
m-1112	1877	2	g	g	PROPN
m-1112	1878	1	=	=	PRON
m-1112	1878	2	the	the	DET
m-1112	1878	3	minimum	minimum	ADJ
m-1112	1878	4	quantized	quantize	VERB
m-1112	1878	5	work	work	NOUN
m-1112	1878	6	as	as	ADP
m-1112	1878	7	change	change	NOUN
m-1112	1878	8	of	of	ADP
m-1112	1878	9	velocity	velocity	NOUN
m-1112	1878	10	→	→	SYM
m-1112	1878	11	acceleration	acceleration	NOUN
m-1112	1878	12	≡	≡	PROPN
m-1112	1878	13	9,807694	9,807694	PROPN
m-1112	1878	14	m	m	PROPN
m-1112	1878	15	/	/	SYM
m-1112	1878	16	s²	s²	ADJ
m-1112	1878	17	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1878	18	=	=	SYM
m-1112	1878	19	the	the	DET
m-1112	1878	20	earth	earth	NOUN
m-1112	1878	21	local	local	ADJ
m-1112	1878	22	-	-	PUNCT
m-1112	1878	23	coefficient	coefficient	NOUN
m-1112	1878	24	between	between	ADP
m-1112	1878	25	the	the	DET
m-1112	1878	26	two	two	NUM
m-1112	1878	27	constants	constant	NOUN
m-1112	1878	28	,	,	PUNCT
m-1112	1878	29	g	g	NOUN
m-1112	1878	30	,	,	PUNCT
m-1112	1878	31	g	g	NOUN
m-1112	1878	32	,	,	PUNCT
m-1112	1878	33	and	and	CCONJ
m-1112	1878	34	𝐤𝐄.g	𝐤𝐄.g	PROPN
m-1112	1878	35	=	=	SYM
m-1112	1878	36	g	g	NOUN
m-1112	1878	37	.m	.m	NOUN
m-1112	1878	38	for	for	ADP
m-1112	1878	39	earth	earth	NOUN
m-1112	1878	40	(	(	PUNCT
m-1112	1878	41	e	e	NOUN
m-1112	1878	42	)	)	PUNCT
m-1112	1878	43	→	→	SYM
m-1112	1878	44	𝐤	𝐤	X
m-1112	1878	45	𝐄	𝐄	PROPN
m-1112	1878	46	=	=	SYM
m-1112	1878	47	𝐫	𝐫	PROPN
m-1112	1878	48	²𝐄	²𝐄	NOUN
m-1112	1878	49	/	/	SYM
m-1112	1878	50	𝐦	𝐦	PROPN
m-1112	1878	51	𝐄	𝐄	PROPN
m-1112	1878	52	,	,	PUNCT
m-1112	1878	53	for	for	ADP
m-1112	1878	54	bodies	body	NOUN
m-1112	1878	55	(	(	PUNCT
m-1112	1878	56	b	b	NOUN
m-1112	1878	57	)	)	PUNCT
m-1112	1878	58	→	→	SYM
m-1112	1878	59	𝐤	𝐤	X
m-1112	1878	60	𝐁	𝐁	PROPN
m-1112	1878	61	=	=	SYM
m-1112	1878	62	𝐫	𝐫	PROPN
m-1112	1878	63	²𝐁	²𝐁	NOUN
m-1112	1878	64	/	/	SYM
m-1112	1878	65	𝐦	𝐦	PROPN
m-1112	1878	66	𝐁	𝐁	PROPN
m-1112	1878	67	,	,	PUNCT
m-1112	1878	68	for	for	ADP
m-1112	1878	69	any	any	DET
m-1112	1878	70	body	body	NOUN
m-1112	1878	71	→	→	SYM
m-1112	1878	72	local	local	ADJ
m-1112	1878	73	gravity	gravity	NOUN
m-1112	1878	74	𝐠	𝐠	PROPN
m-1112	1878	75	𝐋	𝐋	PROPN
m-1112	1878	76	=	=	PUNCT
m-1112	1878	77	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1878	78	/	/	SYM
m-1112	1878	79	𝐤𝐋	𝐤𝐋	ADJ
m-1112	1878	80	2	2	NUM
m-1112	1878	81	..	..	SYM
m-1112	1878	82	coulomb	coulomb	NOUN
m-1112	1878	83	electrical	electrical	ADJ
m-1112	1878	84	force	force	NOUN
m-1112	1878	85	,	,	PUNCT
m-1112	1879	1	𝐅𝐞𝐥𝐞𝐜𝐭𝐫𝐨𝐧	𝐅𝐞𝐥𝐞𝐜𝐭𝐫𝐨𝐧	PROPN
m-1112	1879	2	=	=	PUNCT
m-1112	1879	3	𝐤𝐜	𝐤𝐜	NUM
m-1112	1879	4	𝐐𝟏.𝐐𝟐	𝐐𝟏.𝐐𝟐	NUM
m-1112	1880	1	𝐝²	𝐝²	NOUN
m-1112	1880	2	=	=	PUNCT
m-1112	1881	1	[	[	X
m-1112	1881	2	⊕→←⊝	⊕→←⊝	X
m-1112	1881	3	]	]	X
m-1112	1881	4	𝐝²	𝐝²	NOUN
m-1112	1881	5	=	=	SYM
m-1112	1881	6	𝟖	𝟖	NUM
m-1112	1881	7	𝛑𝐫(𝟏+√𝟓	𝛑𝐫(𝟏+√𝟓	NOUN
m-1112	1881	8	)	)	PUNCT
m-1112	1881	9	[	[	PUNCT
m-1112	1881	10	𝐁	𝐁	NOUN
m-1112	1881	11	𝐫²	𝐫²	NOUN
m-1112	1881	12	]	]	PUNCT
m-1112	1881	13	,	,	PUNCT
m-1112	1881	14	where	where	SCONJ
m-1112	1881	15	coulomb	coulomb	NOUN
m-1112	1881	16	constant	constant	ADJ
m-1112	1881	17	𝐤𝐂	𝐤𝐂	NOUN
m-1112	1881	18	=	=	SYM
m-1112	1881	19	9.𝟏𝟎𝟗	9.𝟏𝟎𝟗	NUM
m-1112	1881	20	nm²/c²	nm²/c²	PROPN
m-1112	1881	21	3	3	NUM
m-1112	1881	22	..	..	PUNCT
m-1112	1881	23	the	the	DET
m-1112	1881	24	work	work	NOUN
m-1112	1881	25	done	do	VERB
m-1112	1881	26	by	by	ADP
m-1112	1881	27	the	the	DET
m-1112	1881	28	electric	electric	ADJ
m-1112	1881	29	field	field	NOUN
m-1112	1881	30	to	to	PART
m-1112	1881	31	rotate	rotate	VERB
m-1112	1881	32	the	the	DET
m-1112	1881	33	dipole	dipole	NOUN
m-1112	1881	34	is	be	AUX
m-1112	1881	35	w	w	NOUN
m-1112	1881	36	=	=	SYM
m-1112	1881	37	𝐅𝐞𝐥𝐞𝐜𝐭𝐫𝐨𝐧	𝐅𝐞𝐥𝐞𝐜𝐭𝐫𝐨𝐧	PROPN
m-1112	1881	38	.	.	PUNCT
m-1112	1882	1	𝐄	𝐄	PROPN
m-1112	1882	2	𝐅𝐢𝐞𝐥𝐝	𝐅𝐢𝐞𝐥𝐝	PROPN
m-1112	1882	3	.	.	PUNCT
m-1112	1883	1	4	4	X
m-1112	1883	2	..	..	PUNCT
m-1112	1883	3	the	the	DET
m-1112	1883	4	work	work	NOUN
m-1112	1883	5	done	do	VERB
m-1112	1883	6	in	in	ADP
m-1112	1883	7	material	material	NOUN
m-1112	1883	8	point	point	NOUN
m-1112	1883	9	needs	need	VERB
m-1112	1883	10	a	a	DET
m-1112	1883	11	path	path	NOUN
m-1112	1883	12	to	to	PART
m-1112	1883	13	exit	exit	VERB
m-1112	1883	14	from	from	ADP
m-1112	1883	15	the	the	DET
m-1112	1883	16	box	box	NOUN
m-1112	1883	17	𝐟𝐑	𝐟𝐑	PROPN
m-1112	1883	18	=	=	PUNCT
m-1112	1884	1	[	[	PUNCT
m-1112	1884	2	𝐁𝐏𝐇	𝐁𝐏𝐇	PROPN
m-1112	1884	3	]	]	PUNCT
m-1112	1884	4	≡	≡	PROPN
m-1112	1884	5	[	[	PUNCT
m-1112	1884	6	𝐟𝟏=𝐍	𝐟𝟏=𝐍	PROPN
m-1112	1884	7	,	,	PUNCT
m-1112	1884	8	𝐟𝟐	𝐟𝟐	PROPN
m-1112	1884	9	,	,	PUNCT
m-1112	1884	10	𝐟𝟑	𝐟𝟑	NOUN
m-1112	1884	11	,	,	PUNCT
m-1112	1884	12	𝐟	𝐟	PROPN
m-1112	1884	13	𝐑	𝐑	NOUN
m-1112	1884	14	=	=	SYM
m-1112	1884	15	𝐰²𝐍	𝐰²𝐍	X
m-1112	1884	16	]	]	X
m-1112	1884	17	≡	≡	PROPN
m-1112	1885	1	[	[	X
m-1112	1885	2	e²	e²	X
m-1112	1885	3	+	+	CCONJ
m-1112	1885	4	h²	h²	PROPN
m-1112	1885	5	]	]	PUNCT
m-1112	1885	6	,	,	PUNCT
m-1112	1885	7	and	and	CCONJ
m-1112	1885	8	from	from	ADP
m-1112	1885	9	where	where	SCONJ
m-1112	1885	10	is	be	AUX
m-1112	1885	11	propagated	propagate	VERB
m-1112	1885	12	.	.	PUNCT
m-1112	1886	1	resonance	resonance	NOUN
m-1112	1886	2	-	-	PUNCT
m-1112	1886	3	path	path	NOUN
m-1112	1886	4	happens	happen	VERB
m-1112	1886	5	as	as	ADP
m-1112	1886	6	the	the	DET
m-1112	1886	7	force	force	NOUN
m-1112	1886	8	,	,	PUNCT
m-1112	1886	9	em	em	NOUN
m-1112	1886	10	-	-	NOUN
m-1112	1886	11	radiation	radiation	NOUN
m-1112	1886	12	in	in	ADP
m-1112	1886	13	two	two	NUM
m-1112	1886	14	directions	direction	NOUN
m-1112	1886	15	,	,	PUNCT
m-1112	1886	16	which	which	PRON
m-1112	1886	17	can	can	AUX
m-1112	1886	18	travel	travel	VERB
m-1112	1886	19	in	in	ADP
m-1112	1886	20	any	any	DET
m-1112	1886	21	closed	closed	ADJ
m-1112	1886	22	system	system	NOUN
m-1112	1886	23	,	,	PUNCT
m-1112	1886	24	and	and	CCONJ
m-1112	1886	25	for	for	ADP
m-1112	1886	26	solids	solid	NOUN
m-1112	1886	27	through	through	ADP
m-1112	1886	28	cauchy	cauchy	NOUN
m-1112	1886	29	-	-	PUNCT
m-1112	1886	30	stress	stress	NOUN
m-1112	1886	31	-	-	PUNCT
m-1112	1886	32	tensor	tensor	NOUN
m-1112	1886	33	where	where	SCONJ
m-1112	1886	34	the	the	DET
m-1112	1886	35	two	two	NUM
m-1112	1886	36	conveyers	conveyer	NOUN
m-1112	1886	37	e	e	X
m-1112	1886	38	⊥	⊥	PROPN
m-1112	1886	39	b	b	PROPN
m-1112	1886	40	⊥	⊥	NUM
m-1112	1886	41	r	r	NOUN
m-1112	1886	42	≡	≡	PROPN
m-1112	1886	43	𝛔𝟏	𝛔𝟏	NOUN
m-1112	1886	44	⊥	⊥	PROPN
m-1112	1886	45	𝛔𝟐	𝛔𝟐	VERB
m-1112	1886	46	⊥	⊥	PROPN
m-1112	1886	47	𝛔𝟑	𝛔𝟑	NOUN
m-1112	1886	48	,	,	PUNCT
m-1112	1886	49	can	can	AUX
m-1112	1886	50	carry	carry	VERB
m-1112	1886	51	the	the	DET
m-1112	1886	52	energy	energy	NOUN
m-1112	1886	53	storage	storage	NOUN
m-1112	1886	54	r	r	NOUN
m-1112	1886	55	in	in	ADP
m-1112	1886	56	system	system	NOUN
m-1112	1886	57	[	[	PUNCT
m-1112	1886	58	+	+	X
m-1112	1886	59	0	0	NUM
m-1112	1886	60	]	]	PUNCT
m-1112	1886	61	and	and	CCONJ
m-1112	1886	62	change	change	VERB
m-1112	1886	63	the	the	DET
m-1112	1886	64	inner	inner	ADJ
m-1112	1886	65	-	-	PUNCT
m-1112	1886	66	structure	structure	NOUN
m-1112	1886	67	of	of	ADP
m-1112	1886	68	this	this	DET
m-1112	1886	69	system	system	NOUN
m-1112	1886	70	to	to	ADP
m-1112	1886	71	another	another	PRON
m-1112	1886	72	or	or	CCONJ
m-1112	1886	73	destroy	destroy	VERB
m-1112	1886	74	it	it	PRON
m-1112	1886	75	.	.	PUNCT
m-1112	1887	1	in	in	ADP
m-1112	1887	2	[	[	X
m-1112	1887	3	70	70	NUM
m-1112	1887	4	]	]	PUNCT
m-1112	1887	5	,	,	PUNCT
m-1112	1887	6	the	the	DET
m-1112	1887	7	work	work	NOUN
m-1112	1887	8	produced	produce	VERB
m-1112	1887	9	in	in	ADP
m-1112	1887	10	material	material	NOUN
m-1112	1887	11	-	-	PUNCT
m-1112	1887	12	point	point	NOUN
m-1112	1887	13	𝐀𝐁⃖⃗⃗⃗	𝐀𝐁⃖⃗⃗⃗	NOUN
m-1112	1887	14	⃗	⃗	PROPN
m-1112	1887	15	is	be	AUX
m-1112	1887	16	equal	equal	ADJ
m-1112	1887	17	to	to	ADP
m-1112	1887	18	→	→	SYM
m-1112	1887	19	w	w	NOUN
m-1112	1887	20	=	=	VERB
m-1112	1887	21	2l	2l	NUM
m-1112	1887	22	=	=	SYM
m-1112	1887	23	�	�	NOUN
m-1112	1887	24	̅	̅	NOUN
m-1112	1887	25	�	�	PROPN
m-1112	1887	26	.	.	PUNCT
m-1112	1888	1	�	�	PROPN
m-1112	1888	2	̅	̅	NOUN
m-1112	1888	3	�	�	NOUN
m-1112	1888	4	=	=	SYM
m-1112	1888	5	j.w²	j.w²	PROPN
m-1112	1888	6	←	←	PROPN
m-1112	1888	7	consisting	consist	VERB
m-1112	1888	8	the	the	DET
m-1112	1888	9	first	first	ADJ
m-1112	1888	10	-	-	PUNCT
m-1112	1888	11	energy	energy	NOUN
m-1112	1888	12	-	-	PUNCT
m-1112	1888	13	store	store	NOUN
m-1112	1888	14	which	which	PRON
m-1112	1888	15	is	be	AUX
m-1112	1888	16	a	a	DET
m-1112	1888	17	stationary	stationary	ADJ
m-1112	1888	18	wave	wave	NOUN
m-1112	1888	19	with	with	ADP
m-1112	1888	20	,	,	PUNCT
m-1112	1888	21	n	n	PRON
m-1112	1888	22	lobes	lobe	NOUN
m-1112	1888	23	as	as	ADP
m-1112	1888	24	,	,	PUNCT
m-1112	1888	25	𝐖𝐧(𝐧+𝟏	𝐖𝐧(𝐧+𝟏	NOUN
m-1112	1888	26	)	)	PUNCT
m-1112	1889	1	=	=	PRON
m-1112	1889	2	[	[	PUNCT
m-1112	1889	3	𝟒𝝅𝐫²𝐟𝟏	𝟒𝝅𝐫²𝐟𝟏	VERB
m-1112	1889	4	𝟑	𝟑	NUM
m-1112	1889	5	]	]	X
m-1112	1889	6	.n.(n+1	.n.(n+1	X
m-1112	1889	7	)	)	PUNCT
m-1112	1889	8	and	and	CCONJ
m-1112	1889	9	wavelength	wavelength	VERB
m-1112	1889	10	𝛌𝐍	𝛌𝐍	NOUN
m-1112	1889	11	=	=	PUNCT
m-1112	1889	12	𝛔.(𝟏+√𝟓	𝛔.(𝟏+√𝟓	NUM
m-1112	1889	13	)	)	PUNCT
m-1112	1889	14	𝟒𝛑𝐫	𝟒𝛑𝐫	NOUN
m-1112	1889	15	=	=	PUNCT
m-1112	1889	16	𝒏	𝒏	PROPN
m-1112	1889	17	.	.	PUNCT
m-1112	1889	18	�	�	PROPN
m-1112	1889	19	̅	̅	NOUN
m-1112	1889	20	�	�	X
m-1112	1889	21	𝟒𝛑𝐫²	𝟒𝛑𝐫²	NOUN
m-1112	1889	22	=	=	SYM
m-1112	1889	23	𝟐𝒏	𝟐𝒏	PROPN
m-1112	1889	24	.	.	PUNCT
m-1112	1890	1	�	�	PROPN
m-1112	1890	2	̅	̅	NOUN
m-1112	1890	3	�	�	NOUN
m-1112	1890	4	𝐰	𝐰	NOUN
m-1112	1890	5	of	of	ADP
m-1112	1890	6	r	r	NOUN
m-1112	1890	7	=	=	SYM
m-1112	1890	8	𝒎	𝒎	PROPN
m-1112	1890	9	.	.	PUNCT
m-1112	1890	10	�	�	PROPN
m-1112	1890	11	̅	̅	NOUN
m-1112	1890	12	�	�	PROPN
m-1112	1890	13	𝐪.𝐁	𝐪.𝐁	VERB
m-1112	1890	14	related	related	ADJ
m-1112	1890	15	to	to	ADP
m-1112	1890	16	m	m	NOUN
m-1112	1890	17	-	-	PUNCT
m-1112	1890	18	field	field	NOUN
m-1112	1890	19	b	b	NOUN
m-1112	1890	20	in	in	ADP
m-1112	1890	21	[	[	PUNCT
m-1112	1890	22	75	75	NUM
m-1112	1890	23	-	-	PUNCT
m-1112	1890	24	b	b	NOUN
m-1112	1890	25	]	]	PUNCT
m-1112	1890	26	,	,	PUNCT
m-1112	1890	27	the	the	DET
m-1112	1890	28	permeable	permeable	ADJ
m-1112	1890	29	-	-	PUNCT
m-1112	1890	30	resonance	resonance	NOUN
m-1112	1890	31	-	-	PUNCT
m-1112	1890	32	path	path	NOUN
m-1112	1890	33	for	for	ADP
m-1112	1890	34	m	m	NOUN
m-1112	1890	35	-	-	PUNCT
m-1112	1890	36	point	point	NOUN
m-1112	1890	37	is	be	AUX
m-1112	1890	38	→	→	PUNCT
m-1112	1890	39	the	the	DET
m-1112	1890	40	resonance	resonance	NOUN
m-1112	1890	41	-	-	PUNCT
m-1112	1890	42	frequencies	frequency	NOUN
m-1112	1890	43	𝐟𝐑	𝐟𝐑	NOUN
m-1112	1891	1	[	[	X
m-1112	1891	2	s≡	s≡	NOUN
m-1112	1891	3	𝐟𝟏=𝐧	𝐟𝟏=𝐧	NOUN
m-1112	1891	4	,	,	PUNCT
m-1112	1891	5	𝐟𝟐	𝐟𝟐	PROPN
m-1112	1891	6	,	,	PUNCT
m-1112	1891	7	𝐟𝐑	𝐟𝐑	NOUN
m-1112	1891	8	=	=	SYM
m-1112	1891	9	𝐰²	𝐰²	NOUN
m-1112	1891	10	]	]	PUNCT
m-1112	1891	11	with	with	ADP
m-1112	1891	12	𝐟𝐧=	𝐟𝐧=	NOUN
m-1112	1892	1	[	[	X
m-1112	1892	2	n	n	X
m-1112	1892	3	(	(	PUNCT
m-1112	1892	4	𝟏+√𝟓)𝛔	𝟏+√𝟓)𝛔	VERB
m-1112	1892	5	𝟒𝛑𝐫	𝟒𝛑𝐫	ADJ
m-1112	1892	6	=	=	SYM
m-1112	1892	7	𝐧𝛔.	𝐧𝛔.	NOUN
m-1112	1892	8	�	�	NOUN
m-1112	1892	9	̅	̅	NOUN
m-1112	1892	10	�	�	NOUN
m-1112	1892	11	𝟖	𝟖	NUM
m-1112	1892	12	𝐫²	𝐫²	NOUN
m-1112	1892	13	]	]	PUNCT
m-1112	1892	14	related	relate	VERB
m-1112	1892	15	to	to	PART
m-1112	1892	16	spin	spin	VERB
m-1112	1892	17	�	�	PROPN
m-1112	1892	18	̅	̅	NOUN
m-1112	1892	19	�	�	NOUN
m-1112	1892	20	,	,	PUNCT
m-1112	1892	21	stress	stress	NOUN
m-1112	1892	22	𝛔	𝛔	NOUN
m-1112	1892	23	and	and	CCONJ
m-1112	1892	24	cave	cave	PROPN
m-1112	1892	25	r	r	NOUN
m-1112	1892	26	.	.	PUNCT
m-1112	1893	1	since	since	SCONJ
m-1112	1893	2	the	the	DET
m-1112	1893	3	frequency	frequency	NOUN
m-1112	1893	4	in	in	ADP
m-1112	1893	5	material	material	NOUN
m-1112	1893	6	-	-	PUNCT
m-1112	1893	7	point	point	NOUN
m-1112	1893	8	is	be	AUX
m-1112	1893	9	→	→	SYM
m-1112	1893	10	ijo	ijo	PROPN
m-1112	1893	11	international	international	ADJ
m-1112	1893	12	journal	journal	PROPN
m-1112	1893	13	of	of	ADP
m-1112	1893	14	mathematics	mathematics	PROPN
m-1112	1893	15	(	(	PUNCT
m-1112	1893	16	issn	issn	PROPN
m-1112	1893	17	:	:	PUNCT
m-1112	1893	18	2992	2992	NUM
m-1112	1893	19	-	-	SYM
m-1112	1893	20	4421	4421	NUM
m-1112	1893	21	)	)	PUNCT
m-1112	1894	1	volume	volume	NOUN
m-1112	1894	2	08	08	NUM
m-1112	1895	1	|	|	ADV
m-1112	1895	2	issue	issue	NOUN
m-1112	1895	3	08	08	NUM
m-1112	1896	1	|	|	ADV
m-1112	1896	2	august	august	PROPN
m-1112	1896	3	2025	2025	NUM
m-1112	1896	4	|	|	ADV
m-1112	1896	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1896	6	ijo	ijo	PROPN
m-1112	1896	7	journals	journal	NOUN
m-1112	1896	8	67	67	NUM
m-1112	1896	9	the	the	DET
m-1112	1896	10	fundamental	fundamental	ADJ
m-1112	1896	11	particles	particle	NOUN
m-1112	1896	12	origination	origination	NOUN
m-1112	1896	13	mechanism	mechanism	NOUN
m-1112	1896	14	in	in	ADP
m-1112	1896	15	mfmf	mfmf	PROPN
m-1112	1896	16	pns	pns	PROPN
m-1112	1896	17	caves	cave	NOUN
m-1112	1896	18	.	.	PUNCT
m-1112	1897	1	𝐟𝐧	𝐟𝐧	NOUN
m-1112	1897	2	=	=	PUNCT
m-1112	1897	3	(	(	PUNCT
m-1112	1897	4	𝐧𝛔	𝐧𝛔	X
m-1112	1897	5	𝟖	𝟖	PROPN
m-1112	1897	6	𝐫	𝐫	SYM
m-1112	1897	7	²	²	NUM
m-1112	1897	8	)	)	PUNCT
m-1112	1897	9	.	.	PUNCT
m-1112	1898	1	�	�	PROPN
m-1112	1898	2	̅	̅	NOUN
m-1112	1898	3	�	�	PROPN
m-1112	1898	4	≡	≡	PROPN
m-1112	1898	5	[	[	PUNCT
m-1112	1898	6	1+√5	1+√5	NUM
m-1112	1898	7	2	2	NUM
m-1112	1898	8	]	]	PUNCT
m-1112	1898	9	𝛔	𝛔	PROPN
m-1112	1898	10	𝟐𝛑𝐫	𝟐𝛑𝐫	NOUN
m-1112	1898	11	≡	≡	PROPN
m-1112	1898	12	[	[	PUNCT
m-1112	1898	13	nσ	nσ	NOUN
m-1112	1898	14	8	8	NUM
m-1112	1898	15	r	r	NOUN
m-1112	1898	16	²	²	NUM
m-1112	1898	17	]	]	PUNCT
m-1112	1898	18	.b̅	.b̅	PROPN
m-1112	1898	19	≡	≡	PROPN
m-1112	1898	20	[	[	PUNCT
m-1112	1898	21	1+√5	1+√5	NUM
m-1112	1898	22	2	2	NUM
m-1112	1898	23	]	]	PUNCT
m-1112	1898	24	stress	stress	NOUN
m-1112	1898	25	perimeter	perimeter	PROPN
m-1112	1898	26	≡	≡	PROPN
m-1112	1898	27	[	[	PUNCT
m-1112	1898	28	1+√5	1+√5	NUM
m-1112	1898	29	2	2	NUM
m-1112	1898	30	]	]	PUNCT
m-1112	1898	31	force	force	NOUN
m-1112	1898	32	[	[	X
m-1112	1898	33	n	n	CCONJ
m-1112	1898	34	]	]	X
m-1112	1898	35	area∗l[m3	area∗l[m3	PROPN
m-1112	1898	36	]	]	PUNCT
m-1112	1898	37	≡	≡	PROPN
m-1112	1898	38	𝐄	𝐄	PROPN
m-1112	1898	39	𝐡	𝐡	NOUN
m-1112	1898	40	,	,	PUNCT
m-1112	1898	41	then	then	ADV
m-1112	1898	42	it	it	PRON
m-1112	1898	43	occupies	occupy	VERB
m-1112	1898	44	the	the	DET
m-1112	1898	45	property	property	NOUN
m-1112	1898	46	of	of	ADP
m-1112	1898	47	the	the	DET
m-1112	1898	48	golden	golden	ADJ
m-1112	1898	49	-	-	PUNCT
m-1112	1898	50	ratio	ratio	NOUN
m-1112	1898	51	pattern	pattern	NOUN
m-1112	1898	52	φ	φ	PROPN
m-1112	1898	53	,	,	PUNCT
m-1112	1898	54	and	and	CCONJ
m-1112	1898	55	equation	equation	NOUN
m-1112	1898	56	defines	define	VERB
m-1112	1898	57	that	that	SCONJ
m-1112	1898	58	the	the	DET
m-1112	1898	59	material	material	NOUN
m-1112	1898	60	point	point	NOUN
m-1112	1898	61	of	of	ADP
m-1112	1898	62	frequency	frequency	NOUN
m-1112	1898	63	𝐟𝐧	𝐟𝐧	ADP
m-1112	1898	64	,	,	PUNCT
m-1112	1898	65	when	when	SCONJ
m-1112	1898	66	collide	collide	VERB
m-1112	1898	67	with	with	ADP
m-1112	1898	68	another	another	DET
m-1112	1898	69	material	material	NOUN
m-1112	1898	70	point	point	NOUN
m-1112	1898	71	,	,	PUNCT
m-1112	1898	72	or	or	CCONJ
m-1112	1898	73	with	with	ADP
m-1112	1898	74	any	any	DET
m-1112	1898	75	other	other	ADJ
m-1112	1898	76	particle	particle	NOUN
m-1112	1898	77	or	or	CCONJ
m-1112	1898	78	particles	particle	NOUN
m-1112	1898	79	then	then	ADV
m-1112	1898	80	produces	produce	VERB
m-1112	1898	81	another	another	DET
m-1112	1898	82	monad	monad	PROPN
m-1112	1898	83	as	as	ADP
m-1112	1898	84	→	→	SYM
m-1112	1898	85	1	1	NUM
m-1112	1898	86	≡	≡	PROPN
m-1112	1898	87	a	a	DET
m-1112	1898	88	new	new	ADJ
m-1112	1898	89	quaternion	quaternion	NOUN
m-1112	1898	90	and	and	CCONJ
m-1112	1898	91	the	the	DET
m-1112	1898	92	first	first	ADJ
m-1112	1898	93	continuous	continuous	ADJ
m-1112	1898	94	to	to	PART
m-1112	1898	95	be	be	AUX
m-1112	1898	96	of	of	ADP
m-1112	1898	97	the	the	DET
m-1112	1898	98	same	same	ADJ
m-1112	1898	99	identity	identity	NOUN
m-1112	1898	100	,	,	PUNCT
m-1112	1898	101	frequency	frequency	NOUN
m-1112	1898	102	𝐟𝐧	𝐟𝐧	NOUN
m-1112	1898	103	,	,	PUNCT
m-1112	1898	104	as	as	ADP
m-1112	1898	105	before	before	ADV
m-1112	1898	106	and	and	CCONJ
m-1112	1898	107	from	from	ADP
m-1112	1898	108	euler`s	euler`s	PROPN
m-1112	1898	109	,	,	PUNCT
m-1112	1898	110	rigid	rigid	ADJ
m-1112	1898	111	body	body	NOUN
m-1112	1898	112	dynamics	dynamic	NOUN
m-1112	1898	113	work	work	NOUN
m-1112	1898	114	→	→	SYM
m-1112	1899	1	w	w	NOUN
m-1112	1899	2	=	=	VERB
m-1112	1899	3	2l	2l	NUM
m-1112	1899	4	=	=	SYM
m-1112	1899	5	b̅	b̅	PROPN
m-1112	1899	6	.	.	PUNCT
m-1112	1899	7	w̅	w̅	X
m-1112	1900	1	=	=	SYM
m-1112	1900	2	j	j	PROPN
m-1112	1900	3	.	.	PUNCT
m-1112	1901	1	w²	w²	PROPN
m-1112	1901	2	≡	≡	PROPN
m-1112	1901	3	h.	h.	PROPN
m-1112	1901	4	𝐟𝐧	𝐟𝐧	PROPN
m-1112	1901	5	←	←	PROPN
m-1112	1901	6	i.e.	i.e.	X
m-1112	1901	7	the	the	DET
m-1112	1901	8	frequency	frequency	NOUN
m-1112	1901	9	of	of	ADP
m-1112	1901	10	photon	photon	NOUN
m-1112	1901	11	,	,	PUNCT
m-1112	1901	12	is	be	AUX
m-1112	1901	13	embodied	embody	VERB
m-1112	1901	14	with	with	ADP
m-1112	1901	15	the	the	DET
m-1112	1901	16	→	→	SYM
m-1112	1901	17	growing	grow	VERB
m-1112	1901	18	-	-	PUNCT
m-1112	1901	19	golden	golden	ADJ
m-1112	1901	20	-	-	PUNCT
m-1112	1901	21	ratio	ratio	NOUN
m-1112	1901	22	-	-	PUNCT
m-1112	1901	23	pattern	pattern	NOUN
m-1112	1901	24	φ	φ	NOUN
m-1112	1901	25	and	and	CCONJ
m-1112	1901	26	it	it	PRON
m-1112	1901	27	uses	use	VERB
m-1112	1901	28	the	the	DET
m-1112	1901	29	vibrating	vibrate	VERB
m-1112	1901	30	physical	physical	ADJ
m-1112	1901	31	structures	structure	NOUN
m-1112	1901	32	,	,	PUNCT
m-1112	1901	33	or	or	CCONJ
m-1112	1901	34	the	the	DET
m-1112	1901	35	same	same	ADJ
m-1112	1901	36	the	the	DET
m-1112	1901	37	granular	granular	ADJ
m-1112	1901	38	material	material	NOUN
m-1112	1901	39	-	-	PUNCT
m-1112	1901	40	instruments	instrument	NOUN
m-1112	1901	41	,	,	PUNCT
m-1112	1901	42	to	to	PART
m-1112	1901	43	kick	kick	VERB
m-1112	1901	44	start	start	VERB
m-1112	1901	45	all	all	PRON
m-1112	1901	46	of	of	ADP
m-1112	1901	47	them	they	PRON
m-1112	1901	48	and	and	CCONJ
m-1112	1901	49	everything	everything	PRON
m-1112	1901	50	in	in	ADP
m-1112	1901	51	this	this	DET
m-1112	1901	52	world	world	NOUN
m-1112	1901	53	.	.	PUNCT
m-1112	1902	1	the	the	DET
m-1112	1902	2	how	how	SCONJ
m-1112	1902	3	in	in	ADP
m-1112	1902	4	[	[	PUNCT
m-1112	1902	5	75	75	NUM
m-1112	1902	6	-	-	PUNCT
m-1112	1902	7	b	b	NOUN
m-1112	1902	8	]	]	PUNCT
m-1112	1902	9	page	page	NOUN
m-1112	1902	10	34	34	NUM
m-1112	1902	11	.	.	PUNCT
m-1112	1903	1	because	because	SCONJ
m-1112	1903	2	of	of	ADP
m-1112	1903	3	the	the	DET
m-1112	1903	4	periodic	periodic	ADJ
m-1112	1903	5	excitation	excitation	NOUN
m-1112	1903	6	between	between	ADP
m-1112	1903	7	,	,	PUNCT
m-1112	1903	8	space	space	NOUN
m-1112	1903	9	(	(	PUNCT
m-1112	1903	10	+	+	NOUN
m-1112	1903	11	)	)	PUNCT
m-1112	1903	12	and	and	CCONJ
m-1112	1903	13	anti	anti	ADJ
m-1112	1903	14	-	-	ADJ
m-1112	1903	15	space	space	ADJ
m-1112	1903	16	(	(	PUNCT
m-1112	1903	17	-	-	PUNCT
m-1112	1903	18	)	)	PUNCT
m-1112	1903	19	,	,	PUNCT
m-1112	1903	20	[	[	X
m-1112	1903	21	⊕→←⊝	⊕→←⊝	X
m-1112	1903	22	]	]	PUNCT
m-1112	1903	23	exists	exist	VERB
m-1112	1903	24	only	only	ADV
m-1112	1903	25	collision	collision	NOUN
m-1112	1903	26	of	of	ADP
m-1112	1903	27	opposite	opposite	ADJ
m-1112	1903	28	,	,	PUNCT
m-1112	1903	29	where	where	SCONJ
m-1112	1903	30	the	the	DET
m-1112	1903	31	inner	inner	ADJ
m-1112	1903	32	acceleration	acceleration	NOUN
m-1112	1903	33	is	be	AUX
m-1112	1903	34	equal	equal	ADJ
m-1112	1903	35	to	to	ADP
m-1112	1903	36	zero	zero	NUM
m-1112	1903	37	gravity	gravity	NOUN
m-1112	1903	38	g	g	NOUN
m-1112	1903	39	and	and	CCONJ
m-1112	1903	40	this	this	PRON
m-1112	1903	41	because	because	SCONJ
m-1112	1903	42	of	of	ADP
m-1112	1903	43	material	material	ADJ
m-1112	1903	44	extreme	extreme	ADJ
m-1112	1903	45	-	-	PUNCT
m-1112	1903	46	case	case	NOUN
m-1112	1903	47	of	of	ADP
m-1112	1903	48	the	the	DET
m-1112	1903	49	periodic	periodic	ADJ
m-1112	1903	50	acceleration	acceleration	NOUN
m-1112	1903	51	{	{	PUNCT
m-1112	1904	1	[	[	X
m-1112	1904	2	→←	→←	X
m-1112	1904	3	]	]	X
m-1112	1904	4	=	=	SYM
m-1112	1904	5	0	0	NUM
m-1112	1904	6	}	}	PUNCT
m-1112	1904	7	,	,	PUNCT
m-1112	1904	8	and	and	CCONJ
m-1112	1904	9	which	which	PRON
m-1112	1904	10	is	be	AUX
m-1112	1904	11	zero	zero	NUM
m-1112	1904	12	and	and	CCONJ
m-1112	1904	13	the	the	DET
m-1112	1904	14	net	net	ADJ
m-1112	1904	15	force	force	NOUN
m-1112	1904	16	vanishes	vanish	VERB
m-1112	1904	17	,	,	PUNCT
m-1112	1904	18	and	and	CCONJ
m-1112	1905	1	in	in	ADP
m-1112	1905	2	where	where	SCONJ
m-1112	1905	3	issues	issue	NOUN
m-1112	1905	4	the	the	DET
m-1112	1905	5	coulomb	coulomb	NOUN
m-1112	1905	6	dipole	dipole	NOUN
m-1112	1905	7	-	-	PUNCT
m-1112	1905	8	law	law	NOUN
m-1112	1905	9	and	and	CCONJ
m-1112	1905	10	where	where	SCONJ
m-1112	1905	11	acceleration	acceleration	NOUN
m-1112	1905	12	g	g	PROPN
m-1112	1905	13	becomes	become	VERB
m-1112	1905	14	from	from	ADP
m-1112	1905	15	the	the	DET
m-1112	1905	16	stationary	stationary	ADJ
m-1112	1905	17	constant	constant	ADJ
m-1112	1905	18	dipole	dipole	NOUN
m-1112	1905	19	moment	moment	NOUN
m-1112	1905	20	�	�	NOUN
m-1112	1905	21	̅	̅	NOUN
m-1112	1905	22	�	�	PROPN
m-1112	1905	23	≡	≡	PROPN
m-1112	1905	24	�	�	PROPN
m-1112	1905	25	̅	̅	PROPN
m-1112	1905	26	�	�	PROPN
m-1112	1905	27	≡	≡	ADJ
m-1112	1905	28	momentum	momentum	NOUN
m-1112	1905	29	and	and	CCONJ
m-1112	1905	30	which	which	PRON
m-1112	1905	31	is	be	AUX
m-1112	1905	32	the	the	DET
m-1112	1905	33	analogous	analogous	ADJ
m-1112	1905	34	in	in	ADP
m-1112	1905	35	the	the	DET
m-1112	1905	36	revolving	revolve	VERB
m-1112	1905	37	motion	motion	NOUN
m-1112	1905	38	in	in	ADP
m-1112	1905	39	where	where	SCONJ
m-1112	1905	40	then	then	ADV
m-1112	1905	41	issues	issue	NOUN
m-1112	1905	42	→	→	SYM
m-1112	1905	43	gravitational	gravitational	ADJ
m-1112	1905	44	force	force	NOUN
m-1112	1905	45			NOUN
m-1112	1905	46	g	g	NOUN
m-1112	1905	47	=	=	SYM
m-1112	1905	48	g	g	PROPN
m-1112	1906	1	k	k	PROPN
m-1112	1906	2	=	=	PUNCT
m-1112	1906	3	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1906	4	g	g	NOUN
m-1112	1906	5	=	=	SYM
m-1112	1906	6	g	g	PROPN
m-1112	1906	7	.	.	PUNCT
m-1112	1907	1	𝐤𝐑	𝐤𝐑	PUNCT
m-1112	1907	2	𝐠𝐑	𝐠𝐑	X
m-1112	1907	3	=	=	SYM
m-1112	1907	4	�	�	PROPN
m-1112	1907	5	̅	̅	NOUN
m-1112	1907	6	�	�	PROPN
m-1112	1907	7	.	.	PUNCT
m-1112	1908	1	𝐠𝐜	𝐠𝐜	PROPN
m-1112	1908	2	=	=	SYM
m-1112	1908	3	σ	σ	NOUN
m-1112	1908	4	=	=	PUNCT
m-1112	1908	5	𝐅𝐨𝐫𝐜𝐞	𝐅𝐨𝐫𝐜𝐞	PROPN
m-1112	1908	6	𝐀𝐫𝐞𝐚	𝐀𝐫𝐞𝐚	PROPN
m-1112	1908	7	=	=	SYM
m-1112	1908	8	𝐌𝐚𝐬𝐬	𝐌𝐚𝐬𝐬	PROPN
m-1112	1908	9	𝐀𝐫𝐞𝐚	𝐀𝐫𝐞𝐚	PROPN
m-1112	1908	10	g	g	NOUN
m-1112	1908	11	in	in	ADP
m-1112	1908	12	page-33	page-33	PROPN
m-1112	1908	13	[	[	X
m-1112	1908	14	77	77	NUM
m-1112	1908	15	]	]	PUNCT
m-1112	1908	16	,	,	PUNCT
m-1112	1908	17	the	the	DET
m-1112	1908	18	earth	earth	NOUN
m-1112	1908	19	-	-	PUNCT
m-1112	1908	20	constant	constant	ADJ
m-1112	1908	21	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1908	22	=	=	PUNCT
m-1112	1908	23	r²e	r²e	ADP
m-1112	1908	24	me	i	PRON
m-1112	1908	25	=	=	PUNCT
m-1112	1909	1	[	[	X
m-1112	1909	2	6,378.106]²	6,378.106]²	NUM
m-1112	1909	3	5,98.1024	5,98.1024	NUM
m-1112	1909	4	=	=	SYM
m-1112	1909	5	6,811551810−12	6,811551810−12	NUM
m-1112	1909	6	and	and	CCONJ
m-1112	1909	7	the	the	DET
m-1112	1909	8	gravitational	gravitational	ADJ
m-1112	1909	9	force	force	NOUN
m-1112	1909	10	g	g	PROPN
m-1112	1909	11	=	=	SYM
m-1112	1909	12	g	g	PROPN
m-1112	1909	13	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1909	14	=	=	SYM
m-1112	1909	15	[	[	PUNCT
m-1112	1909	16	9,8076941	9,8076941	NUM
m-1112	1909	17	]	]	PUNCT
m-1112	1909	18	.	.	PUNCT
m-1112	1910	1	6,8116.10−12	6,8116.10−12	NUM
m-1112	1910	2	=	=	SYM
m-1112	1910	3	6,68056.𝟏𝟎−𝟏𝟏	6,68056.𝟏𝟎−𝟏𝟏	NUM
m-1112	1910	4	m3	m3	PROPN
m-1112	1910	5	/	/	SYM
m-1112	1910	6	n.s²	n.s²	ADV
m-1112	1910	7	becoming	become	VERB
m-1112	1910	8	from	from	ADP
m-1112	1910	9	g	g	PROPN
m-1112	1910	10	,	,	PUNCT
m-1112	1910	11	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1910	12	only	only	ADV
m-1112	1910	13	,	,	PUNCT
m-1112	1910	14	i.e.	i.e.	X
m-1112	1910	15	g	g	PROPN
m-1112	1910	16	is	be	AUX
m-1112	1910	17	a	a	DET
m-1112	1910	18	force	force	NOUN
m-1112	1910	19	which	which	PRON
m-1112	1910	20	pushes	push	VERB
m-1112	1910	21	→	→	SYM
m-1112	1910	22	g	g	NOUN
m-1112	1910	23	as	as	ADP
m-1112	1910	24	energy	energy	NOUN
m-1112	1910	25	in	in	ADP
m-1112	1910	26	→	→	SYM
m-1112	1910	27	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1910	28	from	from	ADP
m-1112	1910	29	gravity	gravity	NOUN
m-1112	1910	30	relation	relation	NOUN
m-1112	1910	31	g	g	PROPN
m-1112	1910	32	=	=	SYM
m-1112	1910	33	g	g	PROPN
m-1112	1910	34	𝐤𝐄	𝐤𝐄	NOUN
m-1112	1910	35	=	=	NOUN
m-1112	1910	36	9,8076941.6,8116.10−12=	9,8076941.6,8116.10−12=	PROPN
m-1112	1910	37	6,68056.𝟏𝟎−𝟏𝟏	6,68056.𝟏𝟎−𝟏𝟏	NUM
m-1112	1910	38	m3/	m3/	X
m-1112	1910	39	n.s²	n.s²	ADJ
m-1112	1910	40	and	and	CCONJ
m-1112	1910	41	from	from	ADP
m-1112	1910	42	energy	energy	NOUN
m-1112	1910	43	-	-	PUNCT
m-1112	1910	44	loop	loop	NOUN
m-1112	1910	45	relation	relation	NOUN
m-1112	1910	46	1=	1=	PROPN
m-1112	1910	47	c.	c.	PROPN
m-1112	1910	48	r³.	r³.	NOUN
m-1112	1910	49	𝐟𝐏²	𝐟𝐏²	PROPN
m-1112	1910	50	→	→	SYM
m-1112	1910	51	fp=√1	fp=√1	PROPN
m-1112	1910	52	/	/	SYM
m-1112	1910	53	cr³	cr³	NOUN
m-1112	1910	54	,	,	PUNCT
m-1112	1910	55	from	from	ADP
m-1112	1910	56	f	f	X
m-1112	1910	57	=	=	SYM
m-1112	1910	58	e	e	PROPN
m-1112	1910	59	/	/	SYM
m-1112	1910	60	h	h	NOUN
m-1112	1911	1	then	then	ADV
m-1112	1911	2	f	f	PROPN
m-1112	1911	3	=	=	SYM
m-1112	1911	4	𝐄	𝐄	PROPN
m-1112	1911	5	𝐡	𝐡	NOUN
m-1112	1911	6	=	=	PUNCT
m-1112	1911	7	√1	√1	PROPN
m-1112	1911	8	/	/	SYM
m-1112	1911	9	cr³	cr³	ADJ
m-1112	1911	10	or	or	CCONJ
m-1112	1911	11	→	→	SYM
m-1112	1911	12	e	e	NOUN
m-1112	1911	13	=	=	SYM
m-1112	1911	14	h.√1	h.√1	PROPN
m-1112	1911	15	/	/	SYM
m-1112	1911	16	c.	c.	PROPN
m-1112	1911	17	r³	r³	PROPN
m-1112	1911	18	,	,	PUNCT
m-1112	1911	19	and	and	CCONJ
m-1112	1911	20	e²	e²	VERB
m-1112	1911	21	h²	h²	PROPN
m-1112	1911	22	=	=	SYM
m-1112	1911	23	1	1	NUM
m-1112	1911	24	cr³	cr³	NOUN
m-1112	1911	25	→	→	SYM
m-1112	1911	26	e	e	NOUN
m-1112	1911	27	²	²	PROPN
m-1112	1911	28	=	=	SYM
m-1112	1911	29	h²	h²	PROPN
m-1112	1911	30	c	c	PROPN
m-1112	1911	31	r³	r³	PROPN
m-1112	1911	32	,	,	PUNCT
m-1112	1911	33	an	an	DET
m-1112	1911	34	energy	energy	NOUN
m-1112	1911	35	relation	relation	NOUN
m-1112	1911	36	between	between	ADP
m-1112	1911	37	the	the	PRON
m-1112	1911	38	,	,	PUNCT
m-1112	1911	39	c	c	NOUN
m-1112	1911	40	,	,	PUNCT
m-1112	1911	41	r	r	NOUN
m-1112	1911	42	.	.	PUNCT
m-1112	1912	1	this	this	DET
m-1112	1912	2	relation	relation	NOUN
m-1112	1912	3	is	be	AUX
m-1112	1912	4	used	use	VERB
m-1112	1912	5	for	for	ADP
m-1112	1912	6	blackholes	blackhole	NOUN
m-1112	1912	7	energy	energy	NOUN
m-1112	1912	8	where	where	SCONJ
m-1112	1912	9	r	r	NOUN
m-1112	1912	10	,	,	PUNCT
m-1112	1912	11	result	result	VERB
m-1112	1912	12	to	to	ADP
m-1112	1912	13	zero	zero	NUM
m-1112	1912	14	,	,	PUNCT
m-1112	1912	15	[	[	X
m-1112	1912	16	71	71	NUM
m-1112	1912	17	]	]	PUNCT
m-1112	1912	18	the	the	DET
m-1112	1912	19	permissible	permissible	ADJ
m-1112	1912	20	permeable	permeable	ADJ
m-1112	1912	21	resonance	resonance	NOUN
m-1112	1912	22	paths	path	NOUN
m-1112	1912	23	for	for	ADP
m-1112	1912	24	the	the	DET
m-1112	1912	25	means	mean	NOUN
m-1112	1912	26	,	,	PUNCT
m-1112	1912	27	is	be	AUX
m-1112	1912	28	as	as	ADP
m-1112	1912	29	below	below	ADV
m-1112	1912	30	.	.	PUNCT
m-1112	1913	1	1	1	X
m-1112	1913	2	)	)	PUNCT
m-1112	1913	3	solids	solid	NOUN
m-1112	1913	4	→	→	PUNCT
m-1112	1913	5	the	the	DET
m-1112	1913	6	normal	normal	ADJ
m-1112	1913	7	-	-	PUNCT
m-1112	1913	8	mode	mode	NOUN
m-1112	1913	9	-	-	PUNCT
m-1112	1913	10	vibration	vibration	NOUN
m-1112	1913	11	system	system	NOUN
m-1112	1913	12	{	{	PUNCT
m-1112	1913	13	w²	w²	PROPN
m-1112	1913	14	[	[	X
m-1112	1913	15	m	m	X
m-1112	1913	16	]	]	X
m-1112	1914	1	+	+	CCONJ
m-1112	1914	2	[	[	X
m-1112	1914	3	k	k	X
m-1112	1914	4	]	]	X
m-1112	1914	5	(	(	PUNCT
m-1112	1914	6	x	x	NOUN
m-1112	1914	7	)	)	PUNCT
m-1112	1914	8	}	}	PUNCT
m-1112	1914	9	=	=	SYM
m-1112	1914	10	0	0	NUM
m-1112	1914	11	2	2	NUM
m-1112	1914	12	)	)	PUNCT
m-1112	1914	13	liquids	liquid	NOUN
m-1112	1914	14	→	→	PUNCT
m-1112	1914	15	the	the	DET
m-1112	1914	16	cauchy	cauchy	ADJ
m-1112	1914	17	stress	stress	NOUN
m-1112	1914	18	-	-	PUNCT
m-1112	1914	19	tensor	tensor	NOUN
m-1112	1914	20	as	as	ADP
m-1112	1914	21	momentum	momentum	NOUN
m-1112	1914	22	equation	equation	NOUN
m-1112	1914	23	{	{	PUNCT
m-1112	1914	24	∇.σ	∇.σ	PROPN
m-1112	1914	25	=	=	SYM
m-1112	1914	26	-∇p	-∇p	PUNCT
m-1112	1914	27	+	+	NOUN
m-1112	1914	28	∇.τ	∇.τ	NUM
m-1112	1914	29	}	}	PUNCT
m-1112	1914	30	3	3	NUM
m-1112	1914	31	)	)	PUNCT
m-1112	1914	32	gazes	gaze	VERB
m-1112	1914	33	→	→	PUNCT
m-1112	1914	34	the	the	DET
m-1112	1914	35	combined	combined	ADJ
m-1112	1914	36	avogadro`s	avogadro`s	ADJ
m-1112	1914	37	pressure	pressure	NOUN
m-1112	1914	38	law	law	NOUN
m-1112	1914	39	{	{	PUNCT
m-1112	1914	40	pv	pv	NOUN
m-1112	1914	41	=	=	SYM
m-1112	1914	42	n	n	CCONJ
m-1112	1914	43	rt	rt	PROPN
m-1112	1914	44	=	=	SYM
m-1112	1914	45	n.mv²/3	n.mv²/3	PROPN
m-1112	1914	46	}	}	PUNCT
m-1112	1914	47	4	4	NUM
m-1112	1914	48	)	)	PUNCT
m-1112	1914	49	crystals	crystal	NOUN
m-1112	1914	50	→	→	PUNCT
m-1112	1914	51	the	the	DET
m-1112	1914	52	cauchy	cauchy	ADJ
m-1112	1914	53	ellipsoid	ellipsoid	NOUN
m-1112	1914	54	-	-	PUNCT
m-1112	1914	55	stress	stress	NOUN
m-1112	1914	56	-	-	PUNCT
m-1112	1914	57	tensor	tensor	NOUN
m-1112	1914	58	where	where	SCONJ
m-1112	1914	59	{	{	PUNCT
m-1112	1914	60	e⊥b⊥r	e⊥b⊥r	PROPN
m-1112	1914	61	≡	≡	PROPN
m-1112	1914	62	σ1⊥	σ1⊥	NOUN
m-1112	1914	63	σ2⊥σ3	σ2⊥σ3	PUNCT
m-1112	1915	1	}	}	PUNCT
m-1112	1915	2	5	5	NUM
m-1112	1915	3	)	)	PUNCT
m-1112	1915	4	molecules	molecule	NOUN
m-1112	1915	5	→	→	PUNCT
m-1112	1915	6	the	the	DET
m-1112	1915	7	lattice	lattice	NOUN
m-1112	1915	8	-	-	PUNCT
m-1112	1915	9	crystal	crystal	NOUN
m-1112	1915	10	-	-	PUNCT
m-1112	1915	11	arrangement	arrangement	NOUN
m-1112	1915	12	with	with	ADP
m-1112	1915	13	their	their	PRON
m-1112	1915	14	chemical	chemical	NOUN
m-1112	1915	15	bonds	bond	NOUN
m-1112	1915	16	relation	relation	NOUN
m-1112	1915	17	6	6	NUM
m-1112	1915	18	)	)	PUNCT
m-1112	1915	19	atoms	atom	NOUN
m-1112	1915	20	→	→	PUNCT
m-1112	1915	21	the	the	DET
m-1112	1915	22	energy	energy	NOUN
m-1112	1915	23	-	-	PUNCT
m-1112	1915	24	rims	rim	NOUN
m-1112	1915	25	with	with	ADP
m-1112	1915	26	chemical	chemical	ADJ
m-1112	1915	27	bonds	bond	NOUN
m-1112	1915	28	,	,	PUNCT
m-1112	1915	29	ionic	ionic	ADJ
m-1112	1915	30	,	,	PUNCT
m-1112	1915	31	covalent	covalent	NOUN
m-1112	1915	32	,	,	PUNCT
m-1112	1915	33	relation	relation	NOUN
m-1112	1915	34	7	7	NUM
m-1112	1915	35	)	)	PUNCT
m-1112	1915	36	particles	particle	NOUN
m-1112	1915	37	→	→	PUNCT
m-1112	1915	38	the	the	DET
m-1112	1915	39	resultance	resultance	NOUN
m-1112	1915	40	of	of	ADP
m-1112	1915	41	the	the	DET
m-1112	1915	42	one	one	NUM
m-1112	1915	43	-	-	PUNCT
m-1112	1915	44	dimensional	dimensional	ADJ
m-1112	1915	45	-	-	PUNCT
m-1112	1915	46	collision	collision	NOUN
m-1112	1915	47	v̅ij=	v̅ij=	NOUN
m-1112	1916	1	v̅j	v̅j	PROPN
m-1112	1916	2	v̅i	v̅i	PUNCT
m-1112	1916	3	=	=	PUNCT
m-1112	1916	4	w̅ij	w̅ij	PROPN
m-1112	1916	5	.	.	PUNCT
m-1112	1917	1	r̅ij	r̅ij	PROPN
m-1112	1917	2	ijo	ijo	PROPN
m-1112	1917	3	international	international	PROPN
m-1112	1917	4	journal	journal	PROPN
m-1112	1917	5	of	of	ADP
m-1112	1917	6	mathematics	mathematics	PROPN
m-1112	1917	7	(	(	PUNCT
m-1112	1917	8	issn	issn	PROPN
m-1112	1917	9	:	:	PUNCT
m-1112	1917	10	2992	2992	NUM
m-1112	1917	11	-	-	SYM
m-1112	1917	12	4421	4421	NUM
m-1112	1917	13	)	)	PUNCT
m-1112	1917	14	volume	volume	NOUN
m-1112	1917	15	08	08	NUM
m-1112	1918	1	|	|	ADV
m-1112	1918	2	issue	issue	NOUN
m-1112	1918	3	08	08	NUM
m-1112	1919	1	|	|	ADV
m-1112	1919	2	august	august	PROPN
m-1112	1919	3	2025	2025	NUM
m-1112	1919	4	|	|	ADV
m-1112	1919	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1919	6	ijo	ijo	PROPN
m-1112	1919	7	journals	journal	NOUN
m-1112	1919	8	68	68	NUM
m-1112	1919	9	the	the	DET
m-1112	1919	10	fundamental	fundamental	ADJ
m-1112	1919	11	particles	particle	NOUN
m-1112	1919	12	origination	origination	NOUN
m-1112	1919	13	mechanism	mechanism	NOUN
m-1112	1919	14	in	in	ADP
m-1112	1919	15	mfmf	mfmf	PROPN
m-1112	1919	16	pns	pns	PROPN
m-1112	1919	17	caves	cave	NOUN
m-1112	1919	18	.	.	PUNCT
m-1112	1920	1	8)	8)	NUM
m-1112	1920	2	m	m	NOUN
m-1112	1920	3	-	-	PUNCT
m-1112	1920	4	points	point	NOUN
m-1112	1920	5	→	→	PUNCT
m-1112	1920	6	the	the	DET
m-1112	1920	7	resonance	resonance	NOUN
m-1112	1920	8	-	-	PUNCT
m-1112	1920	9	frequencies	frequency	NOUN
m-1112	1920	10	𝐟𝐑	𝐟𝐑	NOUN
m-1112	1921	1	[	[	X
m-1112	1921	2	s	s	X
m-1112	1921	3	≡	≡	PROPN
m-1112	1921	4	f1=	f1=	PROPN
m-1112	1921	5	n	n	PROPN
m-1112	1921	6	,	,	PUNCT
m-1112	1921	7	f2	f2	PROPN
m-1112	1921	8	,	,	PUNCT
m-1112	1921	9	f3,fr	f3,fr	NOUN
m-1112	1921	10	=	=	NOUN
m-1112	1921	11	w²	w²	PROPN
m-1112	1921	12	]	]	PUNCT
m-1112	1921	13	=	=	PUNCT
m-1112	1921	14	𝐟𝐧	𝐟𝐧	NOUN
m-1112	1921	15	=	=	PUNCT
m-1112	1922	1	[	[	X
m-1112	1922	2	⊕	⊕	NOUN
m-1112	1922	3	↔	↔	PROPN
m-1112	1922	4	⊝	⊝	X
m-1112	1922	5	]	]	PUNCT
m-1112	1922	6	=	=	SYM
m-1112	1922	7	n	n	X
m-1112	1922	8	(	(	PUNCT
m-1112	1922	9	1+√5)σ	1+√5)σ	NUM
m-1112	1922	10	4πr	4πr	NOUN
m-1112	1922	11	=	=	PUNCT
m-1112	1922	12	n.σ.b̅	n.σ.b̅	ADJ
m-1112	1922	13	8	8	NUM
m-1112	1922	14	r²	r²	NOUN
m-1112	1922	15	→	→	SYM
m-1112	1922	16	i.e.	i.e.	X
m-1112	1922	17	the	the	DET
m-1112	1922	18	golden	golden	ADJ
m-1112	1922	19	-	-	PUNCT
m-1112	1922	20	ratio	ratio	NOUN
m-1112	1922	21	-	-	PUNCT
m-1112	1922	22	pattern	pattern	NOUN
m-1112	1922	23	,	,	PUNCT
m-1112	1922	24	which	which	PRON
m-1112	1922	25	is	be	AUX
m-1112	1922	26	related	relate	VERB
m-1112	1922	27	to	to	PART
m-1112	1922	28	spin	spin	VERB
m-1112	1922	29	.	.	PUNCT
m-1112	1923	1	9	9	X
m-1112	1923	2	)	)	PUNCT
m-1112	1923	3	cave	cave	NOUN
m-1112	1923	4	-	-	PUNCT
m-1112	1923	5	orbit→	orbit→	PROPN
m-1112	1923	6	the	the	DET
m-1112	1923	7	relation	relation	NOUN
m-1112	1923	8	c.l	c.l	PROPN
m-1112	1923	9	s	s	PROPN
m-1112	1923	10	=	=	X
m-1112	1923	11	lv	lv	PROPN
m-1112	1923	12	,	,	PUNCT
m-1112	1923	13	light	light	NOUN
m-1112	1923	14	-	-	PUNCT
m-1112	1923	15	velocity	velocity	NOUN
m-1112	1923	16	3.108	3.108	NUM
m-1112	1923	17	m	m	NOUN
m-1112	1923	18	/	/	SYM
m-1112	1923	19	s*1.10−42	s*1.10−42	PROPN
m-1112	1923	20	m	m	NOUN
m-1112	1923	21	cave	cave	NOUN
m-1112	1923	22	=	=	NOUN
m-1112	1923	23	3.10−34	3.10−34	NUM
m-1112	1923	24	m²/s	m²/s	ADV
m-1112	1923	25	are	be	AUX
m-1112	1923	26	the	the	DET
m-1112	1923	27	cave	cave	NOUN
m-1112	1923	28	-	-	PUNCT
m-1112	1923	29	energy	energy	NOUN
m-1112	1923	30	-	-	PUNCT
m-1112	1923	31	plane	plane	NOUN
m-1112	1923	32	-	-	PUNCT
m-1112	1923	33	rims	rim	NOUN
m-1112	1923	34	in	in	ADP
m-1112	1923	35	atom`s	atom`s	PROPN
m-1112	1923	36	,	,	PUNCT
m-1112	1923	37	planet	planet	NOUN
m-1112	1923	38	orbits	orbit	NOUN
m-1112	1923	39	.	.	PUNCT
m-1112	1924	1	in	in	ADP
m-1112	1924	2	vibrations	vibration	NOUN
m-1112	1924	3	of	of	ADP
m-1112	1924	4	systems	system	NOUN
m-1112	1924	5	,	,	PUNCT
m-1112	1924	6	for	for	ADP
m-1112	1924	7	orbits	orbit	NOUN
m-1112	1924	8	issues	issue	NOUN
m-1112	1924	9	→	→	SYM
m-1112	1924	10	w	w	X
m-1112	1924	11	=	=	SYM
m-1112	1924	12	4π²	4π²	NUM
m-1112	1924	13	.	.	PUNCT
m-1112	1925	1	𝐫³	𝐫³	PROPN
m-1112	1925	2	𝐓²	𝐓²	PROPN
m-1112	1925	3	.	.	PUNCT
m-1112	1926	1	�	�	PROPN
m-1112	1926	2	̅	̅	NOUN
m-1112	1926	3	�	�	NOUN
m-1112	1926	4	=	=	SYM
m-1112	1926	5	4π².r	4π².r	NUM
m-1112	1926	6	³.	³.	X
m-1112	1926	7	𝐟²𝐩	𝐟²𝐩	PROPN
m-1112	1926	8	.	.	PUNCT
m-1112	1927	1	�	�	PROPN
m-1112	1927	2	̅	̅	NOUN
m-1112	1927	3	�	�	PROPN
m-1112	1927	4	←	←	PROPN
m-1112	1927	5	which	which	PRON
m-1112	1927	6	is	be	AUX
m-1112	1927	7	the	the	DET
m-1112	1927	8	energy	energy	NOUN
m-1112	1927	9	in	in	ADP
m-1112	1927	10	the	the	DET
m-1112	1927	11	conic	conic	ADJ
m-1112	1927	12	-	-	PUNCT
m-1112	1927	13	sections	section	NOUN
m-1112	1927	14	of	of	ADP
m-1112	1927	15	kepler`s	kepler`s	NOUN
m-1112	1927	16	unit	unit	NOUN
m-1112	1927	17	orbits	orbit	NOUN
m-1112	1927	18	.	.	PUNCT
m-1112	1928	1	the	the	DET
m-1112	1928	2	energy	energy	NOUN
m-1112	1928	3	-	-	PUNCT
m-1112	1928	4	storages	storage	NOUN
m-1112	1928	5	r	r	NOUN
m-1112	1928	6	=	=	SYM
m-1112	1928	7	n.	n.	NOUN
m-1112	1928	8	[	[	PUNCT
m-1112	1928	9	λ	λ	X
m-1112	1928	10	2	2	NUM
m-1112	1928	11	]	]	PUNCT
m-1112	1928	12	≡	≡	PROPN
m-1112	1928	13	wn(n+1)=	wn(n+1)=	PROPN
m-1112	1928	14	[	[	PUNCT
m-1112	1928	15	4𝜋r²f1	4𝜋r²f1	NUM
m-1112	1928	16	3	3	NUM
m-1112	1928	17	]	]	PUNCT
m-1112	1928	18	.n.(n+1	.n.(n+1	NUM
m-1112	1928	19	)	)	PUNCT
m-1112	1928	20	,	,	PUNCT
m-1112	1928	21	are	be	AUX
m-1112	1928	22	travelling	travel	VERB
m-1112	1928	23	through	through	ADP
m-1112	1928	24	bodies	body	NOUN
m-1112	1928	25	and	and	CCONJ
m-1112	1928	26	follow	follow	VERB
m-1112	1928	27	,	,	PUNCT
m-1112	1928	28	lame	lame	VERB
m-1112	1928	29	stress	stress	NOUN
m-1112	1928	30	ellipsoid	ellipsoid	PROPN
m-1112	1928	31	n1²	n1²	NOUN
m-1112	1928	32	+	+	CCONJ
m-1112	1928	33	n2²	n2²	X
m-1112	1928	34	+	+	CCONJ
m-1112	1928	35	n3²	n3²	NOUN
m-1112	1928	36	=	=	SYM
m-1112	1928	37	t1²	t1²	NUM
m-1112	1928	38	σ1²	σ1²	PROPN
m-1112	1928	39	+	+	CCONJ
m-1112	1928	40	t2²	t2²	PRON
m-1112	1928	41	σ2²	σ2²	NOUN
m-1112	1928	42	+	+	CCONJ
m-1112	1928	43	t3²	t3²	NOUN
m-1112	1928	44	σ3²	σ3²	NOUN
m-1112	1928	45	=	=	NOUN
m-1112	1928	46	1	1	NUM
m-1112	1928	47	on	on	ADP
m-1112	1928	48	principal	principal	NOUN
m-1112	1928	49	stresses	stress	NOUN
m-1112	1928	50	σ1	σ1	PROPN
m-1112	1928	51	,	,	PUNCT
m-1112	1928	52	σ2	σ2	ADJ
m-1112	1928	53	,	,	PUNCT
m-1112	1928	54	σ3	σ3	NOUN
m-1112	1928	55	,	,	PUNCT
m-1112	1928	56	which	which	PRON
m-1112	1928	57	is	be	AUX
m-1112	1928	58	the	the	DET
m-1112	1928	59	passage	passage	NOUN
m-1112	1928	60	through	through	ADP
m-1112	1928	61	which	which	PRON
m-1112	1928	62	forces	force	NOUN
m-1112	1928	63	(	(	PUNCT
m-1112	1928	64	the	the	DET
m-1112	1928	65	em	em	NOUN
m-1112	1928	66	-	-	PUNCT
m-1112	1928	67	radiation	radiation	NOUN
m-1112	1928	68	)	)	PUNCT
m-1112	1928	69	travel	travel	NOUN
m-1112	1928	70	in	in	ADP
m-1112	1928	71	any	any	DET
m-1112	1928	72	solid	solid	ADJ
m-1112	1928	73	either	either	CCONJ
m-1112	1928	74	it	it	PRON
m-1112	1928	75	is	be	AUX
m-1112	1928	76	in	in	ADP
m-1112	1928	77	motion	motion	NOUN
m-1112	1928	78	or	or	CCONJ
m-1112	1928	79	is	be	AUX
m-1112	1928	80	at	at	ADP
m-1112	1928	81	rest	rest	NOUN
m-1112	1928	82	.	.	PUNCT
m-1112	1929	1	laplace`s	laplace`s	PROPN
m-1112	1929	2	orbital	orbital	ADJ
m-1112	1929	3	angular	angular	ADJ
m-1112	1929	4	-	-	PUNCT
m-1112	1929	5	momentum	momentum	NOUN
m-1112	1929	6	ei.2πn	ei.2πn	NOUN
m-1112	1929	7	=	=	SYM
m-1112	1929	8	1	1	NUM
m-1112	1929	9	and	and	CCONJ
m-1112	1929	10	for	for	ADP
m-1112	1929	11	n	n	NOUN
m-1112	1929	12	=	=	SYM
m-1112	1929	13	0	0	NUM
m-1112	1929	14	,	,	PUNCT
m-1112	1929	15	1,2	1,2	ADJ
m-1112	1929	16	,	,	PUNCT
m-1112	1929	17	3,.	3,.	PROPN
m-1112	1929	18	n	n	PROPN
m-1112	1929	19	,	,	PUNCT
m-1112	1929	20	consist	consist	VERB
m-1112	1929	21	the	the	DET
m-1112	1929	22	eigenvalues	eigenvalue	NOUN
m-1112	1929	23	operator	operator	NOUN
m-1112	1929	24	lz	lz	ADP
m-1112	1929	25	which	which	PRON
m-1112	1929	26	agree	agree	VERB
m-1112	1929	27	with	with	ADP
m-1112	1929	28	prior	prior	ADJ
m-1112	1929	29	resonance	resonance	NOUN
m-1112	1929	30	-	-	PUNCT
m-1112	1929	31	frequencies	frequency	NOUN
m-1112	1929	32	𝐟𝐑	𝐟𝐑	NOUN
m-1112	1930	1	[	[	X
m-1112	1930	2	s≡	s≡	NOUN
m-1112	1930	3	f1	f1	NOUN
m-1112	1930	4	=	=	SYM
m-1112	1930	5	n	n	NOUN
m-1112	1930	6	,	,	PUNCT
m-1112	1930	7	f2	f2	PROPN
m-1112	1930	8	,	,	PUNCT
m-1112	1930	9	f3,f	f3,f	PROPN
m-1112	1930	10	r	r	NOUN
m-1112	1930	11	=	=	SYM
m-1112	1930	12	w²	w²	NOUN
m-1112	1930	13	]	]	PUNCT
m-1112	1930	14	as	as	ADP
m-1112	1930	15	wavelengths	wavelength	NOUN
m-1112	1930	16	λ	λ	PROPN
m-1112	1930	17	≡	≡	PROPN
m-1112	1930	18	[	[	X
m-1112	1930	19	f1	f1	PROPN
m-1112	1930	20	,	,	PUNCT
m-1112	1930	21	f2	f2	PROPN
m-1112	1930	22	…	…	NUM
m-1112	1930	23	fn=	fn=	NOUN
m-1112	1930	24	w²	w²	PROPN
m-1112	1930	25	]	]	PUNCT
m-1112	1930	26	≡	≡	PROPN
m-1112	1930	27	the	the	DET
m-1112	1930	28	n	n	PROPN
m-1112	1930	29	lobes	lobe	NOUN
m-1112	1930	30	,	,	PUNCT
m-1112	1930	31	or	or	CCONJ
m-1112	1930	32	→	→	ADP
m-1112	1930	33	fn	fn	NOUN
m-1112	1930	34	=	=	SYM
m-1112	1930	35	n	n	PROPN
m-1112	1930	36	(	(	PUNCT
m-1112	1930	37	1+√5)σ	1+√5)σ	NUM
m-1112	1930	38	4πr	4πr	NOUN
m-1112	1930	39	=	=	PUNCT
m-1112	1930	40	nσ.b̅	nσ.b̅	ADJ
m-1112	1930	41	8	8	NUM
m-1112	1930	42	r²	r²	NOUN
m-1112	1930	43	,	,	PUNCT
m-1112	1930	44	as	as	SCONJ
m-1112	1930	45	the	the	DET
m-1112	1930	46	principal	principal	NOUN
m-1112	1930	47	-	-	PUNCT
m-1112	1930	48	stresses	stress	NOUN
m-1112	1930	49	σ	σ	NOUN
m-1112	1930	50	,	,	PUNCT
m-1112	1930	51	and	and	CCONJ
m-1112	1930	52	resonance	resonance	NOUN
m-1112	1930	53	frequencies	frequency	NOUN
m-1112	1930	54	𝐟𝐑	𝐟𝐑	PROPN
m-1112	1930	55	relation	relation	NOUN
m-1112	1930	56	,	,	PUNCT
m-1112	1930	57	which	which	PRON
m-1112	1930	58	is	be	AUX
m-1112	1930	59	energy	energy	NOUN
m-1112	1930	60	stored	store	VERB
m-1112	1930	61	in	in	ADP
m-1112	1930	62	the	the	DET
m-1112	1930	63	mp	mp	NOUN
m-1112	1930	64	-	-	PUNCT
m-1112	1930	65	lobes	lobe	NOUN
m-1112	1930	66	.	.	PUNCT
m-1112	1931	1	[	[	X
m-1112	1931	2	70	70	NUM
m-1112	1931	3	]	]	PUNCT
m-1112	1931	4	type	type	NOUN
m-1112	1931	5	particles	particle	NOUN
m-1112	1931	6	at	at	ADP
m-1112	1931	7	sites	site	NOUN
m-1112	1931	8	type	type	NOUN
m-1112	1931	9	of	of	ADP
m-1112	1931	10	bounding	bounding	NOUN
m-1112	1931	11	-	-	PUNCT
m-1112	1931	12	force	force	NOUN
m-1112	1931	13	properties	property	NOUN
m-1112	1931	14	em	em	NOUN
m-1112	1931	15	-	-	PUNCT
m-1112	1931	16	radiation	radiation	NOUN
m-1112	1931	17	ionic	ionic	NOUN
m-1112	1931	18	:	:	PUNCT
m-1112	1931	19	⊕	⊕	PROPN
m-1112	1931	20	,	,	PUNCT
m-1112	1931	21	⊝	⊝	VERB
m-1112	1931	22	ions	ion	NOUN
m-1112	1931	23	electrostatic	electrostatic	ADJ
m-1112	1931	24	⊕	⊕	PROPN
m-1112	1931	25	↔⊝	↔⊝	PROPN
m-1112	1931	26	non	non	ADJ
m-1112	1931	27	-	-	ADJ
m-1112	1931	28	conductors	conductor	NOUN
m-1112	1931	29	infrared	infrare	VERB
m-1112	1931	30	molecular	molecular	ADJ
m-1112	1931	31	:	:	PUNCT
m-1112	1931	32	atoms	atom	NOUN
m-1112	1931	33	or	or	CCONJ
m-1112	1931	34	molecules	molecule	NOUN
m-1112	1931	35	dipole	dipole	NOUN
m-1112	1931	36	attraction	attraction	NOUN
m-1112	1931	37	repulsion	repulsion	NOUN
m-1112	1931	38	non	non	ADJ
m-1112	1931	39	-	-	ADJ
m-1112	1931	40	conductors	conductors	ADJ
m-1112	1931	41	chemical	chemical	NOUN
m-1112	1931	42	-	-	PUNCT
m-1112	1931	43	bonds	bond	NOUN
m-1112	1931	44	.	.	PUNCT
m-1112	1932	1	covalent	covalent	NOUN
m-1112	1932	2	:	:	PUNCT
m-1112	1932	3	atoms	atom	NOUN
m-1112	1932	4	networkbonds	networkbond	VERB
m-1112	1932	5	between	between	ADP
m-1112	1932	6	atoms	atom	NOUN
m-1112	1932	7	-non	-non	X
m-1112	1932	8	-	-	PUNCT
m-1112	1932	9	conductors	conductor	NOUN
m-1112	1932	10	em	em	NOUN
m-1112	1932	11	-	-	PUNCT
m-1112	1932	12	spectrum	spectrum	ADJ
m-1112	1932	13	metallic	metallic	NOUN
m-1112	1932	14	:	:	PUNCT
m-1112	1932	15	atoms	atom	NOUN
m-1112	1932	16	ions	ion	NOUN
m-1112	1932	17	and	and	CCONJ
m-1112	1932	18	electrons	electron	NOUN
m-1112	1932	19	attraction	attraction	NOUN
m-1112	1932	20	conductors	conductor	NOUN
m-1112	1932	21	e	e	NOUN
m-1112	1932	22	-	-	NOUN
m-1112	1932	23	conduction	conduction	NOUN
m-1112	1932	24	.	.	PUNCT
m-1112	1933	1	the	the	DET
m-1112	1933	2	kinetic	kinetic	NOUN
m-1112	1933	3	-	-	PUNCT
m-1112	1933	4	energy	energy	NOUN
m-1112	1933	5	e	e	NOUN
m-1112	1933	6	k	k	PROPN
m-1112	1933	7	of	of	ADP
m-1112	1933	8	a	a	DET
m-1112	1933	9	moving	move	VERB
m-1112	1933	10	material	material	NOUN
m-1112	1933	11	-	-	PUNCT
m-1112	1933	12	point	point	NOUN
m-1112	1933	13	,	,	PUNCT
m-1112	1933	14	as	as	SCONJ
m-1112	1933	15	this	this	PRON
m-1112	1933	16	is	be	AUX
m-1112	1933	17	the	the	DET
m-1112	1933	18	photon	photon	NOUN
m-1112	1933	19	,	,	PUNCT
m-1112	1933	20	is	be	AUX
m-1112	1933	21	stored	store	VERB
m-1112	1933	22	as	as	ADP
m-1112	1933	23	motion	motion	NOUN
m-1112	1933	24	in	in	ADP
m-1112	1933	25	its	its	PRON
m-1112	1933	26	storage	storage	NOUN
m-1112	1933	27	,	,	PUNCT
m-1112	1933	28	r	r	NOUN
m-1112	1933	29	=	=	PUNCT
m-1112	1933	30	[	[	PUNCT
m-1112	1933	31	n.	n.	NOUN
m-1112	1933	32	λ/2	λ/2	NUM
m-1112	1933	33	]	]	PUNCT
m-1112	1933	34	,	,	PUNCT
m-1112	1933	35	with	with	ADP
m-1112	1933	36	the	the	DET
m-1112	1933	37	n	n	DET
m-1112	1933	38	frequencies	frequency	NOUN
m-1112	1933	39	f	f	PROPN
m-1112	1933	40	n	n	NOUN
m-1112	1933	41	=	=	PUNCT
m-1112	1933	42	n.f	n.f	PROPN
m-1112	1933	43	1	1	NUM
m-1112	1933	44	,	,	PUNCT
m-1112	1933	45	with	with	ADP
m-1112	1933	46	the	the	DET
m-1112	1933	47	n	n	DET
m-1112	1933	48	lobes	lobe	NOUN
m-1112	1933	49	,	,	PUNCT
m-1112	1933	50	and	and	CCONJ
m-1112	1933	51	with	with	ADP
m-1112	1933	52	an	an	DET
m-1112	1933	53	fundamental	fundamental	ADJ
m-1112	1933	54	frequency	frequency	NOUN
m-1112	1933	55	f	f	NOUN
m-1112	1933	56	1	1	NUM
m-1112	1933	57	.	.	PUNCT
m-1112	1934	1	from	from	ADP
m-1112	1934	2	above	above	ADV
m-1112	1934	3	is	be	AUX
m-1112	1934	4	seen	see	VERB
m-1112	1934	5	the	the	DET
m-1112	1934	6	passage	passage	NOUN
m-1112	1934	7	and	and	CCONJ
m-1112	1934	8	the	the	DET
m-1112	1934	9	-	-	PUNCT
m-1112	1934	10	how	how	SCONJ
m-1112	1934	11	emradiation	emradiation	NOUN
m-1112	1934	12	can	can	AUX
m-1112	1934	13	travel	travel	VERB
m-1112	1934	14	in	in	ADP
m-1112	1934	15	crystals	crystal	NOUN
m-1112	1934	16	and	and	CCONJ
m-1112	1934	17	which	which	PRON
m-1112	1934	18	are	be	AUX
m-1112	1934	19	the	the	DET
m-1112	1934	20	cauchy	cauchy	NOUN
m-1112	1934	21	-	-	PUNCT
m-1112	1934	22	stress	stress	NOUN
m-1112	1934	23	-	-	PUNCT
m-1112	1934	24	tensor	tensor	NOUN
m-1112	1934	25	,	,	PUNCT
m-1112	1934	26	where	where	SCONJ
m-1112	1934	27	exists	exist	VERB
m-1112	1934	28	e	e	NOUN
m-1112	1934	29	⊥	⊥	PROPN
m-1112	1934	30	b	b	PROPN
m-1112	1934	31	⊥	⊥	NUM
m-1112	1934	32	r	r	NOUN
m-1112	1934	33	≡	≡	PROPN
m-1112	1934	34	σ1	σ1	PROPN
m-1112	1934	35	⊥	⊥	PROPN
m-1112	1934	36	σ2	σ2	PROPN
m-1112	1934	37	⊥	⊥	PROPN
m-1112	1934	38	σ3	σ3	PROPN
m-1112	1934	39	,	,	PUNCT
m-1112	1934	40	in	in	ADP
m-1112	1934	41	-	-	PUNCT
m-1112	1934	42	where	where	SCONJ
m-1112	1934	43	energy	energy	NOUN
m-1112	1934	44	propagates	propagate	VERB
m-1112	1934	45	along	along	ADP
m-1112	1934	46	directions	direction	NOUN
m-1112	1934	47	without	without	ADP
m-1112	1934	48	any	any	DET
m-1112	1934	49	birefringence	birefringence	NOUN
m-1112	1934	50	,	,	PUNCT
m-1112	1934	51	and	and	CCONJ
m-1112	1934	52	carries	carry	VERB
m-1112	1934	53	the	the	DET
m-1112	1934	54	energy	energy	NOUN
m-1112	1934	55	-	-	PUNCT
m-1112	1934	56	storage	storage	NOUN
m-1112	1934	57	r	r	NOUN
m-1112	1934	58	,	,	PUNCT
m-1112	1934	59	which	which	DET
m-1112	1934	60	radiation	radiation	NOUN
m-1112	1934	61	is	be	AUX
m-1112	1934	62	the	the	DET
m-1112	1934	63	conveyer	conveyer	NOUN
m-1112	1934	64	.	.	PUNCT
m-1112	1935	1	above	above	ADP
m-1112	1935	2	procedure	procedure	NOUN
m-1112	1935	3	can	can	AUX
m-1112	1935	4	be	be	AUX
m-1112	1935	5	used	use	VERB
m-1112	1935	6	in	in	ADP
m-1112	1935	7	cells	cell	NOUN
m-1112	1935	8	,	,	PUNCT
m-1112	1935	9	where	where	SCONJ
m-1112	1935	10	cells	cell	NOUN
m-1112	1935	11	are	be	AUX
m-1112	1935	12	cases	case	NOUN
m-1112	1935	13	of	of	ADP
m-1112	1935	14	an	an	DET
m-1112	1935	15	birefringence	birefringence	NOUN
m-1112	1935	16	material	material	NOUN
m-1112	1935	17	and	and	CCONJ
m-1112	1935	18	the	the	DET
m-1112	1935	19	resonance	resonance	NOUN
m-1112	1935	20	-	-	PUNCT
m-1112	1935	21	passage	passage	NOUN
m-1112	1935	22	happens	happen	VERB
m-1112	1935	23	as	as	SCONJ
m-1112	1935	24	the	the	DET
m-1112	1935	25	force	force	NOUN
m-1112	1935	26	,	,	PUNCT
m-1112	1935	27	an	an	DET
m-1112	1935	28	em	em	NOUN
m-1112	1935	29	-	-	NOUN
m-1112	1935	30	radiation	radiation	NOUN
m-1112	1935	31	in	in	ADP
m-1112	1935	32	two	two	NUM
m-1112	1935	33	directions	direction	NOUN
m-1112	1935	34	,	,	PUNCT
m-1112	1935	35	can	can	AUX
m-1112	1935	36	travel	travel	VERB
m-1112	1935	37	in	in	ADP
m-1112	1935	38	cell	cell	NOUN
m-1112	1935	39	through	through	ADP
m-1112	1935	40	cauchy	cauchy	NOUN
m-1112	1935	41	-	-	PUNCT
m-1112	1935	42	stress	stress	NOUN
m-1112	1935	43	-	-	PUNCT
m-1112	1935	44	tensor	tensor	NOUN
m-1112	1935	45	where	where	SCONJ
m-1112	1935	46	the	the	DET
m-1112	1935	47	two	two	NUM
m-1112	1935	48	conveyers	conveyer	NOUN
m-1112	1935	49	e	e	X
m-1112	1935	50	⊥	⊥	PROPN
m-1112	1935	51	b	b	PROPN
m-1112	1935	52	⊥	⊥	NUM
m-1112	1935	53	r	r	NOUN
m-1112	1935	54	≡	≡	PROPN
m-1112	1935	55	σ1	σ1	PROPN
m-1112	1935	56	⊥	⊥	PROPN
m-1112	1935	57	σ2	σ2	PROPN
m-1112	1935	58	⊥	⊥	PROPN
m-1112	1935	59	σ3	σ3	PROPN
m-1112	1935	60	,	,	PUNCT
m-1112	1935	61	and	and	CCONJ
m-1112	1935	62	can	can	AUX
m-1112	1935	63	carry	carry	VERB
m-1112	1935	64	the	the	DET
m-1112	1935	65	energy	energy	NOUN
m-1112	1935	66	-	-	PUNCT
m-1112	1935	67	storage	storage	NOUN
m-1112	1935	68	,	,	PUNCT
m-1112	1935	69	r	r	NOUN
m-1112	1935	70	,	,	PUNCT
m-1112	1935	71	in	in	ADP
m-1112	1935	72	cell	cell	NOUN
m-1112	1935	73	,	,	PUNCT
m-1112	1935	74	and	and	CCONJ
m-1112	1935	75	alter	alter	VERB
m-1112	1935	76	the	the	DET
m-1112	1935	77	inner	inner	ADJ
m-1112	1935	78	-	-	PUNCT
m-1112	1935	79	structure	structure	NOUN
m-1112	1935	80	of	of	ADP
m-1112	1935	81	cell	cell	NOUN
m-1112	1935	82	to	to	ADP
m-1112	1935	83	another	another	DET
m-1112	1935	84	desirable	desirable	ADJ
m-1112	1935	85	property	property	NOUN
m-1112	1935	86	.	.	PUNCT
m-1112	1936	1	from	from	ADP
m-1112	1936	2	inner	inner	ADJ
m-1112	1936	3	-	-	PUNCT
m-1112	1936	4	velocity	velocity	NOUN
m-1112	1936	5	equation	equation	NOUN
m-1112	1936	6	v	v	ADP
m-1112	1936	7	=	=	SYM
m-1112	1936	8	w	w	NOUN
m-1112	1936	9	r	r	NOUN
m-1112	1936	10	=	=	PUNCT
m-1112	1936	11	(	(	PUNCT
m-1112	1936	12	2π	2π	NOUN
m-1112	1936	13	/	/	SYM
m-1112	1936	14	t).r	t).r	X
m-1112	1936	15	=	=	NOUN
m-1112	1936	16	2π.f1	2π.f1	NUM
m-1112	1936	17	r	r	NOUN
m-1112	1936	18	,	,	PUNCT
m-1112	1936	19	wavelength	wavelength	NOUN
m-1112	1936	20	λ	λ	PROPN
m-1112	1936	21	=	=	SYM
m-1112	1936	22	ijo	ijo	PROPN
m-1112	1936	23	international	international	PROPN
m-1112	1936	24	journal	journal	PROPN
m-1112	1936	25	of	of	ADP
m-1112	1936	26	mathematics	mathematics	PROPN
m-1112	1936	27	(	(	PUNCT
m-1112	1936	28	issn	issn	PROPN
m-1112	1936	29	:	:	PUNCT
m-1112	1936	30	2992	2992	NUM
m-1112	1936	31	-	-	SYM
m-1112	1936	32	4421	4421	NUM
m-1112	1936	33	)	)	PUNCT
m-1112	1936	34	volume	volume	NOUN
m-1112	1936	35	08	08	NUM
m-1112	1937	1	|	|	ADV
m-1112	1937	2	issue	issue	NOUN
m-1112	1937	3	08	08	NUM
m-1112	1938	1	|	|	ADV
m-1112	1938	2	august	august	PROPN
m-1112	1938	3	2025	2025	NUM
m-1112	1938	4	|	|	ADV
m-1112	1938	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1938	6	ijo	ijo	PROPN
m-1112	1938	7	journals	journal	NOUN
m-1112	1938	8	69	69	NUM
m-1112	1938	9	the	the	DET
m-1112	1938	10	fundamental	fundamental	ADJ
m-1112	1938	11	particles	particle	NOUN
m-1112	1938	12	origination	origination	NOUN
m-1112	1938	13	mechanism	mechanism	NOUN
m-1112	1938	14	in	in	ADP
m-1112	1938	15	mfmf	mfmf	PROPN
m-1112	1938	16	pns	pns	PROPN
m-1112	1938	17	caves	cave	NOUN
m-1112	1938	18	.	.	PUNCT
m-1112	1939	1	ct	ct	X
m-1112	1940	1	=	=	SYM
m-1112	1940	2	c	c	NOUN
m-1112	1940	3	/f	/f	NOUN
m-1112	1940	4	1	1	NUM
m-1112	1940	5	,	,	PUNCT
m-1112	1940	6	cave	cave	NOUN
m-1112	1940	7	r	r	NOUN
m-1112	1940	8	=	=	SYM
m-1112	1940	9	n.[λ/2	n.[λ/2	PROPN
m-1112	1940	10	]	]	PUNCT
m-1112	1940	11	,	,	PUNCT
m-1112	1940	12	then	then	ADV
m-1112	1940	13	r	r	NOUN
m-1112	1940	14	=	=	SYM
m-1112	1940	15	n.(c/2f1	n.(c/2f1	NOUN
m-1112	1940	16	)	)	PUNCT
m-1112	1940	17	and	and	CCONJ
m-1112	1940	18	v	v	ADP
m-1112	1940	19	=	=	NOUN
m-1112	1940	20	2π.f	2π.f	NUM
m-1112	1940	21	1[n.c/2f1	1[n.c/2f1	NUM
m-1112	1940	22	]	]	PUNCT
m-1112	1940	23	=	=	PUNCT
m-1112	1940	24	n.π.c	n.π.c	ADJ
m-1112	1940	25	or	or	CCONJ
m-1112	1940	26	v=	v=	VERB
m-1112	1940	27	n.π.c	n.π.c	ADJ
m-1112	1940	28	....	....	PUNCT
m-1112	1940	29	(	(	PUNCT
m-1112	1940	30	4	4	X
m-1112	1940	31	)	)	PUNCT
m-1112	1940	32	showing	show	VERB
m-1112	1940	33	that	that	SCONJ
m-1112	1940	34	velocities	velocity	NOUN
m-1112	1940	35	in	in	ADP
m-1112	1940	36	lobes	lobe	NOUN
m-1112	1940	37	are	be	AUX
m-1112	1940	38	,	,	PUNCT
m-1112	1940	39	n.π	n.π	PROPN
m-1112	1940	40	,	,	PUNCT
m-1112	1940	41	times	time	NOUN
m-1112	1940	42	that	that	PRON
m-1112	1940	43	of	of	ADP
m-1112	1940	44	light	light	NOUN
m-1112	1940	45	and	and	CCONJ
m-1112	1940	46	for	for	ADP
m-1112	1940	47	n	n	NOUN
m-1112	1940	48	=	=	SYM
m-1112	1940	49	1	1	NUM
m-1112	1940	50	then	then	ADV
m-1112	1940	51	v	v	NOUN
m-1112	1940	52	=	=	SYM
m-1112	1940	53	π.c	π.c	NOUN
m-1112	1940	54	,	,	PUNCT
m-1112	1940	55	more	more	ADJ
m-1112	1940	56	than	than	ADP
m-1112	1940	57	three	three	NUM
m-1112	1940	58	times	time	NOUN
m-1112	1940	59	faster	fast	ADV
m-1112	1940	60	of	of	ADP
m-1112	1940	61	light	light	ADJ
m-1112	1940	62	velocity	velocity	NOUN
m-1112	1940	63	.	.	PUNCT
m-1112	1941	1	because	because	SCONJ
m-1112	1941	2	of	of	ADP
m-1112	1941	3	the	the	DET
m-1112	1941	4	above	above	ADJ
m-1112	1941	5	velocity	velocity	NOUN
m-1112	1941	6	v	v	NOUN
m-1112	1941	7	,	,	PUNCT
m-1112	1941	8	an	an	DET
m-1112	1941	9	e	e	NOUN
m-1112	1941	10	field	field	NOUN
m-1112	1941	11	is	be	AUX
m-1112	1941	12	produced	produce	VERB
m-1112	1941	13	,	,	PUNCT
m-1112	1941	14	which	which	PRON
m-1112	1941	15	produces	produce	VERB
m-1112	1941	16	the	the	DET
m-1112	1941	17	𝛛𝐃/𝛛𝐭	𝛛𝐃/𝛛𝐭	NOUN
m-1112	1941	18	field	field	NOUN
m-1112	1941	19	,	,	PUNCT
m-1112	1941	20	which	which	PRON
m-1112	1941	21	in	in	ADP
m-1112	1941	22	turn	turn	NOUN
m-1112	1941	23	produces	produce	VERB
m-1112	1941	24	the	the	DET
m-1112	1941	25	h	h	NOUN
m-1112	1941	26	field	field	NOUN
m-1112	1941	27	which	which	PRON
m-1112	1941	28	produces	produce	VERB
m-1112	1941	29	the	the	DET
m-1112	1941	30	𝛛𝐁/𝛛𝐭	𝛛𝐁/𝛛𝐭	NOUN
m-1112	1941	31	field	field	NOUN
m-1112	1941	32	and	and	CCONJ
m-1112	1941	33	which	which	PRON
m-1112	1941	34	again	again	ADV
m-1112	1941	35	produces	produce	VERB
m-1112	1941	36	the	the	DET
m-1112	1941	37	e	e	NOUN
m-1112	1941	38	field	field	NOUN
m-1112	1941	39	,	,	PUNCT
m-1112	1941	40	i.e.	i.e.	X
m-1112	1941	41	the	the	DET
m-1112	1941	42	total	total	ADJ
m-1112	1941	43	em	em	NOUN
m-1112	1941	44	-	-	PUNCT
m-1112	1941	45	field	field	NOUN
m-1112	1941	46	regenerates	regenerate	VERB
m-1112	1941	47	itself	itself	PRON
m-1112	1941	48	as	as	SCONJ
m-1112	1941	49	it	it	PRON
m-1112	1941	50	rotates	rotate	VERB
m-1112	1941	51	,	,	PUNCT
m-1112	1941	52	and	and	CCONJ
m-1112	1941	53	is	be	AUX
m-1112	1941	54	a	a	DET
m-1112	1941	55	phenomenon	phenomenon	NOUN
m-1112	1941	56	happening	happen	VERB
m-1112	1941	57	in	in	ADP
m-1112	1941	58	a	a	DET
m-1112	1941	59	propagating	propagate	VERB
m-1112	1941	60	plane	plane	NOUN
m-1112	1941	61	-	-	PUNCT
m-1112	1941	62	wave	wave	NOUN
m-1112	1941	63	.	.	PUNCT
m-1112	1942	1	its	its	PRON
m-1112	1942	2	permeable	permeable	ADJ
m-1112	1942	3	resonance	resonance	NOUN
m-1112	1942	4	path	path	NOUN
m-1112	1942	5	is	be	AUX
m-1112	1942	6	impossible	impossible	ADJ
m-1112	1942	7	in	in	ADP
m-1112	1942	8	an	an	DET
m-1112	1942	9	three	three	NUM
m-1112	1942	10	-	-	PUNCT
m-1112	1942	11	times	time	NOUN
m-1112	1942	12	stronger	strong	ADJ
m-1112	1942	13	em	em	NOUN
m-1112	1942	14	-	-	NOUN
m-1112	1942	15	field	field	NOUN
m-1112	1942	16	because	because	SCONJ
m-1112	1942	17	issues	issue	NOUN
m-1112	1942	18	…	…	PUNCT
m-1112	1942	19	(	(	PUNCT
m-1112	1942	20	4	4	X
m-1112	1942	21	)	)	PUNCT
m-1112	1942	22	2c	2c	NOUN
m-1112	1942	23	..	..	PUNCT
m-1112	1942	24	the	the	DET
m-1112	1942	25	united	united	PROPN
m-1112	1942	26	-	-	PUNCT
m-1112	1942	27	coulomb	coulomb	PROPN
m-1112	1942	28	-	-	PUNCT
m-1112	1942	29	newton	newton	PROPN
m-1112	1942	30	law	law	NOUN
m-1112	1942	31	for	for	ADP
m-1112	1942	32	interactions	interaction	NOUN
m-1112	1942	33	:	:	PUNCT
m-1112	1942	34	for	for	ADP
m-1112	1942	35	a	a	DET
m-1112	1942	36	stationary	stationary	ADJ
m-1112	1942	37	interaction	interaction	NOUN
m-1112	1942	38	the	the	DET
m-1112	1942	39	coulomb	coulomb	NOUN
m-1112	1942	40	-	-	PUNCT
m-1112	1942	41	law	law	NOUN
m-1112	1942	42	-	-	PUNCT
m-1112	1942	43	force	force	NOUN
m-1112	1942	44	is	be	AUX
m-1112	1942	45	𝐅𝐂	𝐅𝐂	NOUN
m-1112	1942	46	=	=	PUNCT
m-1112	1942	47	𝐤[𝐪𝟏𝐪𝟐	𝐤[𝐪𝟏𝐪𝟐	NOUN
m-1112	1942	48	]	]	X
m-1112	1942	49	𝐫²	𝐫²	NOUN
m-1112	1942	50	,	,	PUNCT
m-1112	1942	51	and	and	CCONJ
m-1112	1942	52	for	for	ADP
m-1112	1942	53	charges	charge	NOUN
m-1112	1942	54	𝐪𝟏	𝐪𝟏	ADJ
m-1112	1942	55	,	,	PUNCT
m-1112	1942	56	𝐪𝟐	𝐪𝟐	VERB
m-1112	1942	57	where	where	SCONJ
m-1112	1942	58	constant	constant	ADJ
m-1112	1942	59	k	k	NOUN
m-1112	1942	60	=	=	PROPN
m-1112	1942	61	9,0.109	9,0.109	NUM
m-1112	1942	62	n.m²/c²	n.m²/c²	PROPN
m-1112	1942	63	,	,	PUNCT
m-1112	1942	64	and	and	CCONJ
m-1112	1942	65	r	r	NOUN
m-1112	1942	66	,	,	PUNCT
m-1112	1942	67	is	be	AUX
m-1112	1942	68	the	the	DET
m-1112	1942	69	distance	distance	NOUN
m-1112	1942	70	between	between	ADP
m-1112	1942	71	the	the	DET
m-1112	1942	72	charges	charge	NOUN
m-1112	1942	73	.	.	PUNCT
m-1112	1943	1	for	for	ADP
m-1112	1943	2	a	a	DET
m-1112	1943	3	stationary	stationary	ADJ
m-1112	1943	4	interaction	interaction	NOUN
m-1112	1943	5	newton	newton	PROPN
m-1112	1943	6	law	law	PROPN
m-1112	1943	7	for	for	ADP
m-1112	1943	8	masses	masse	NOUN
m-1112	1943	9	m1	m1	NOUN
m-1112	1943	10	,	,	PUNCT
m-1112	1943	11	m2	m2	PROPN
m-1112	1943	12	is	be	AUX
m-1112	1943	13	𝐅𝐍	𝐅𝐍	PROPN
m-1112	1943	14	=	=	SYM
m-1112	1943	15	𝐆[𝐦𝟏𝐦𝟐	𝐆[𝐦𝟏𝐦𝟐	ADJ
m-1112	1943	16	]	]	X
m-1112	1943	17	𝐫²	𝐫²	NOUN
m-1112	1943	18	,	,	PUNCT
m-1112	1943	19	and	and	CCONJ
m-1112	1943	20	for	for	ADP
m-1112	1943	21	v̅=r̅	v̅=r̅	PROPN
m-1112	1943	22	conjugating	conjugate	VERB
m-1112	1943	23	interaction	interaction	NOUN
m-1112	1943	24	,	,	PUNCT
m-1112	1943	25	energy	energy	NOUN
m-1112	1943	26	e	e	NOUN
m-1112	1943	27	=	=	SYM
m-1112	1943	28	𝐯²	𝐯²	ADJ
m-1112	1943	29	𝟐	𝟐	NUM
m-1112	1943	30	[	[	X
m-1112	1943	31	m1	m1	PROPN
m-1112	1943	32	+	+	CCONJ
m-1112	1943	33	m2	m2	PROPN
m-1112	1943	34	]	]	X
m-1112	1943	35	=	=	SYM
m-1112	1943	36	𝐫²	𝐫²	NOUN
m-1112	1943	37	𝟐	𝟐	NUM
m-1112	1943	38	[	[	PUNCT
m-1112	1943	39	f1	f1	NOUN
m-1112	1943	40	g	g	PROPN
m-1112	1943	41	+	+	CCONJ
m-1112	1943	42	f2	f2	PROPN
m-1112	1943	43	g	g	NOUN
m-1112	1943	44	]	]	PUNCT
m-1112	1944	1	=	=	SYM
m-1112	1944	2	𝐅.𝐫²	𝐅.𝐫²	NOUN
m-1112	1944	3	𝟐	𝟐	NUM
m-1112	1944	4	[	[	PUNCT
m-1112	1944	5	1	1	NUM
m-1112	1944	6	g	g	NOUN
m-1112	1944	7	+	+	NOUN
m-1112	1944	8	1	1	NUM
m-1112	1944	9	g	g	NOUN
m-1112	1944	10	]	]	PUNCT
m-1112	1944	11	=	=	SYM
m-1112	1944	12	𝐅.𝐫²	𝐅.𝐫²	NOUN
m-1112	1944	13	𝟐	𝟐	NUM
m-1112	1944	14	=	=	SYM
m-1112	1944	15	=	=	SYM
m-1112	1944	16	𝐅.𝐫²	𝐅.𝐫²	NOUN
m-1112	1944	17	𝟐	𝟐	NUM
m-1112	1944	18	[	[	PUNCT
m-1112	1944	19	2.g	2.g	NUM
m-1112	1944	20	g	g	NOUN
m-1112	1944	21	²	²	NUM
m-1112	1944	22	]	]	PUNCT
m-1112	1944	23	=	=	SYM
m-1112	1944	24	𝐅𝐍	𝐅𝐍	X
m-1112	1944	25	.𝐫²	.𝐫²	NOUN
m-1112	1945	1	𝐠	𝐠	X
m-1112	1945	2	,	,	PUNCT
m-1112	1945	3	where	where	SCONJ
m-1112	1945	4	𝐅𝐍	𝐅𝐍	PROPN
m-1112	1945	5	is	be	AUX
m-1112	1945	6	newton	newton	PROPN
m-1112	1945	7	force	force	NOUN
m-1112	1945	8	,	,	PUNCT
m-1112	1945	9	and	and	CCONJ
m-1112	1945	10	e	e	NOUN
m-1112	1945	11	is	be	AUX
m-1112	1945	12	the	the	DET
m-1112	1945	13	energy	energy	NOUN
m-1112	1945	14	of	of	ADP
m-1112	1945	15	the	the	DET
m-1112	1945	16	field	field	NOUN
m-1112	1945	17	-	-	PUNCT
m-1112	1945	18	system	system	NOUN
m-1112	1945	19	.	.	PUNCT
m-1112	1946	1	[	[	PUNCT
m-1112	1946	2	g+g	g+g	X
m-1112	1946	3	g∗g	g∗g	NOUN
m-1112	1946	4	}	}	PUNCT
m-1112	1946	5	equating	equate	VERB
m-1112	1946	6	the	the	DET
m-1112	1946	7	two	two	NUM
m-1112	1946	8	forces	force	NOUN
m-1112	1946	9	then	then	ADV
m-1112	1946	10	k	k	PROPN
m-1112	1947	1	[	[	X
m-1112	1947	2	q1q2	q1q2	X
m-1112	1947	3	]	]	X
m-1112	1947	4	r²	r²	NOUN
m-1112	1947	5	=	=	PUNCT
m-1112	1947	6	ge	ge	PROPN
m-1112	1947	7	r	r	NOUN
m-1112	1947	8	²	²	NUM
m-1112	1947	9	,	,	PUNCT
m-1112	1947	10	or	or	CCONJ
m-1112	1947	11			NOUN
m-1112	1947	12	k	k	PROPN
m-1112	1948	1	[	[	X
m-1112	1948	2	𝐪𝟏	𝐪𝟏	ADJ
m-1112	1948	3	,	,	PUNCT
m-1112	1948	4	𝐪𝟐	𝐪𝟐	VERB
m-1112	1948	5	]	]	X
m-1112	1948	6	=	=	SYM
m-1112	1948	7	g	g	NOUN
m-1112	1948	8	.	.	PUNCT
m-1112	1949	1	e	e	X
m-1112	1949	2	…	…	PUNCT
m-1112	1949	3	…	…	PUNCT
m-1112	1949	4	..	..	PUNCT
m-1112	1949	5	(	(	PUNCT
m-1112	1949	6	1	1	X
m-1112	1949	7	)	)	PUNCT
m-1112	1949	8	equation	equation	NOUN
m-1112	1949	9	(	(	PUNCT
m-1112	1949	10	1	1	X
m-1112	1949	11	)	)	PUNCT
m-1112	1949	12	relates	relate	VERB
m-1112	1949	13	any	any	DET
m-1112	1949	14	two	two	NUM
m-1112	1949	15	charges	charge	NOUN
m-1112	1949	16	q1	q1	PROPN
m-1112	1949	17	,	,	PUNCT
m-1112	1949	18	q2	q2	NOUN
m-1112	1949	19	,	,	PUNCT
m-1112	1949	20	with	with	ADP
m-1112	1949	21	field	field	NOUN
m-1112	1949	22	-	-	PUNCT
m-1112	1949	23	energy	energy	NOUN
m-1112	1949	24	e	e	NOUN
m-1112	1949	25	,	,	PUNCT
m-1112	1949	26	under	under	ADP
m-1112	1949	27	vector	vector	NOUN
m-1112	1949	28	�	�	PROPN
m-1112	1949	29	̅	̅	NOUN
m-1112	1949	30	�	�	PROPN
m-1112	1949	31	=	=	SYM
m-1112	1949	32	�	�	PROPN
m-1112	1949	33	̅	̅	NOUN
m-1112	1949	34	�	�	PROPN
m-1112	1949	35	=	=	SYM
m-1112	1949	36	�	�	PROPN
m-1112	1949	37	̅	̅	NOUN
m-1112	1949	38	�	�	PROPN
m-1112	1949	39	3c	3c	NUM
m-1112	1949	40	..	..	PUNCT
m-1112	1949	41	the	the	DET
m-1112	1949	42	origination	origination	NOUN
m-1112	1949	43	of	of	ADP
m-1112	1949	44	light	light	ADJ
m-1112	1949	45	velocity	velocity	NOUN
m-1112	1949	46	c	c	NOUN
m-1112	1949	47	:	:	PUNCT
m-1112	1949	48	gravity	gravity	NOUN
m-1112	1949	49	g	g	PROPN
m-1112	1949	50	≡	≡	PROPN
m-1112	1949	51	𝐓²	𝐓²	VERB
m-1112	1949	52	𝐚³	𝐚³	PROPN
m-1112	1949	53	≡	≡	PROPN
m-1112	1949	54	𝟏	𝟏	PROPN
m-1112	1949	55	f	f	PROPN
m-1112	1949	56	²n.𝐚³	²n.𝐚³	NOUN
m-1112	1949	57	≡	≡	PROPN
m-1112	1949	58	9	9	NUM
m-1112	1949	59	,	,	PUNCT
m-1112	1949	60	8076941	8076941	NUM
m-1112	1949	61	→	→	PUNCT
m-1112	1949	62	the	the	DET
m-1112	1949	63	minimum	minimum	ADJ
m-1112	1949	64	granular	granular	ADJ
m-1112	1949	65	quantized	quantize	VERB
m-1112	1949	66	energy	energy	NOUN
m-1112	1949	67	,	,	PUNCT
m-1112	1949	68	the	the	DET
m-1112	1949	69	forces	force	NOUN
m-1112	1949	70	beyond	beyond	ADP
m-1112	1949	71	-	-	PUNCT
m-1112	1949	72	planck	planck	NOUN
m-1112	1949	73	-	-	PUNCT
m-1112	1949	74	length	length	NOUN
m-1112	1949	75	are	be	AUX
m-1112	1949	76	→	→	SYM
m-1112	1950	1	f	f	X
m-1112	1950	2	=	=	SYM
m-1112	1950	3	φ³.	φ³.	PROPN
m-1112	1951	1	[	[	X
m-1112	1951	2	⊕	⊕	PROPN
m-1112	1951	3	𝛔	𝛔	ADP
m-1112	1951	4	⊝	⊝	NOUN
m-1112	1951	5	]	]	PUNCT
m-1112	1951	6	=	=	SYM
m-1112	1951	7	σ	σ	PUNCT
m-1112	1951	8	x	x	PUNCT
m-1112	1951	9	𝚽	𝚽	PROPN
m-1112	1951	10	³	³	X
m-1112	1951	11	←	←	PROPN
m-1112	1951	12	(	(	PUNCT
m-1112	1951	13	1)-[87	1)-[87	PROPN
m-1112	1951	14	]	]	PUNCT
m-1112	1951	15	force	force	NOUN
m-1112	1951	16	g	g	NOUN
m-1112	1951	17	acts	act	NOUN
m-1112	1951	18	→	→	PUNCT
m-1112	1951	19	on	on	ADP
m-1112	1951	20	spinning	spin	VERB
m-1112	1951	21	m	m	NOUN
m-1112	1951	22	-	-	PUNCT
m-1112	1951	23	points	point	NOUN
m-1112	1951	24	on	on	ADP
m-1112	1951	25	�	�	NOUN
m-1112	1951	26	̅	̅	NOUN
m-1112	1951	27	�	�	NOUN
m-1112	1951	28	through	through	ADP
m-1112	1951	29	g̅	g̅	PROPN
m-1112	1951	30	→	→	PUNCT
m-1112	1951	31	on	on	ADP
m-1112	1951	32	planck`s	planck`s	NOUN
m-1112	1951	33	b̅	b̅	NOUN
m-1112	1951	34	→	→	PUNCT
m-1112	1951	35	on	on	ADP
m-1112	1951	36	𝐠𝐆	𝐠𝐆	NOUN
m-1112	1951	37	,	,	PUNCT
m-1112	1951	38	through	through	ADP
m-1112	1951	39	the	the	DET
m-1112	1951	40	resonance	resonance	NOUN
m-1112	1951	41	frequency	frequency	NOUN
m-1112	1951	42	𝐟	𝐟	PROPN
m-1112	1951	43	𝐑.	𝐑.	PROPN
m-1112	1951	44	it	it	PRON
m-1112	1951	45	was	be	AUX
m-1112	1951	46	proved	prove	VERB
m-1112	1951	47	that	that	SCONJ
m-1112	1951	48	g	g	PROPN
m-1112	1951	49	=	=	SYM
m-1112	1951	50	σ	σ	NUM
m-1112	1951	51	φ³	φ³	NOUN
m-1112	1951	52	,	,	PUNCT
m-1112	1951	53	and	and	CCONJ
m-1112	1951	54	σ	σ	X
m-1112	1951	55	=	=	PUNCT
m-1112	1951	56	𝐆	𝐆	PROPN
m-1112	1951	57	φ³	φ³	VERB
m-1112	1951	58	=	=	SYM
m-1112	1951	59	𝐆.𝛔³	𝐆.𝛔³	X
m-1112	1951	60	c	c	PROPN
m-1112	1951	61	³	³	X
m-1112	1951	62	,	,	PUNCT
m-1112	1951	63	or	or	CCONJ
m-1112	1951	64	→	→	SYM
m-1112	1951	65	σ	σ	NOUN
m-1112	1951	66	²	²	NUM
m-1112	1951	67	g	g	NOUN
m-1112	1951	68	=	=	SYM
m-1112	1951	69	c	c	NOUN
m-1112	1951	70	³	³	X
m-1112	1951	71	…	…	PUNCT
m-1112	1951	72	(2	(2	NUM
m-1112	1951	73	)	)	PUNCT
m-1112	1951	74	,	,	PUNCT
m-1112	1951	75	where	where	SCONJ
m-1112	1951	76	σ	σ	PROPN
m-1112	1951	77	is	be	AUX
m-1112	1951	78	a	a	DET
m-1112	1951	79	stress	stress	NOUN
m-1112	1951	80	between	between	ADP
m-1112	1951	81	the	the	DET
m-1112	1951	82	frequencies	frequency	NOUN
m-1112	1951	83	.	.	PUNCT
m-1112	1952	1	from	from	ADP
m-1112	1952	2	force	force	NOUN
m-1112	1952	3	-	-	PUNCT
m-1112	1952	4	relation	relation	NOUN
m-1112	1952	5	f	f	NOUN
m-1112	1952	6	=	=	SYM
m-1112	1952	7	σ	σ	PROPN
m-1112	1952	8	a	a	X
m-1112	1952	9	=	=	X
m-1112	1952	10	(	(	PUNCT
m-1112	1952	11	2πf	2πf	ADJ
m-1112	1952	12	r	r	NOUN
m-1112	1952	13	)	)	PUNCT
m-1112	1952	14	a	a	DET
m-1112	1952	15	φ	φ	NOUN
m-1112	1952	16	=	=	SYM
m-1112	1952	17	w	w	PROPN
m-1112	1952	18	r	r	NOUN
m-1112	1952	19	a	a	DET
m-1112	1952	20	φ	φ	PROPN
m-1112	1952	21	=	=	SYM
m-1112	1952	22	�	�	PROPN
m-1112	1952	23	̅	̅	NOUN
m-1112	1952	24	�	�	PROPN
m-1112	1952	25	a	a	DET
m-1112	1952	26	φ	φ	PROPN
m-1112	1952	27	,	,	PUNCT
m-1112	1952	28	is	be	AUX
m-1112	1952	29	seen	see	VERB
m-1112	1952	30	that	that	SCONJ
m-1112	1952	31	force	force	NOUN
m-1112	1952	32	g	g	NOUN
m-1112	1952	33	becomes	become	VERB
m-1112	1952	34	a	a	DET
m-1112	1952	35	velocity	velocity	NOUN
m-1112	1952	36	�	�	NOUN
m-1112	1952	37	̅	̅	NOUN
m-1112	1952	38	�	�	PROPN
m-1112	1952	39	.	.	PUNCT
m-1112	1953	1	in	in	ADP
m-1112	1953	2	the	the	DET
m-1112	1953	3	case	case	NOUN
m-1112	1953	4	of	of	ADP
m-1112	1953	5	planck`s	planck`s	NOUN
m-1112	1953	6	length	length	NOUN
m-1112	1953	7	this	this	DET
m-1112	1953	8	velocity	velocity	NOUN
m-1112	1953	9	is	be	AUX
m-1112	1953	10	�	�	NOUN
m-1112	1953	11	̅	̅	NOUN
m-1112	1953	12	�	�	NOUN
m-1112	1953	13	=	=	SYM
m-1112	1953	14	w	w	NOUN
m-1112	1953	15	r	r	NOUN
m-1112	1953	16	=	=	PUNCT
m-1112	1953	17	𝛔.𝚽	𝛔.𝚽	PUNCT
m-1112	1953	18	𝐫	𝐫	PRON
m-1112	1953	19	𝐫𝐩	𝐫𝐩	NOUN
m-1112	1953	20	=	=	SYM
m-1112	1953	21	σ	σ	PROPN
m-1112	1953	22	x	x	SYM
m-1112	1953	23	φ	φ	PROPN
m-1112	1953	24	=	=	SYM
m-1112	1954	1	|	|	ADV
m-1112	1954	2	𝐆	𝐆	PROPN
m-1112	1954	3	𝐋𝐏	𝐋𝐏	PROPN
m-1112	1954	4	.	.	PUNCT
m-1112	1955	1	r	r	NOUN
m-1112	1955	2	φ³	φ³	NOUN
m-1112	1955	3	|φ	|φ	NOUN
m-1112	1955	4	=	=	PUNCT
m-1112	1955	5	[	[	PUNCT
m-1112	1955	6	𝐆.𝐋𝐏	𝐆.𝐋𝐏	NUM
m-1112	1955	7	𝐫.𝚽²	𝐫.𝚽²	NUM
m-1112	1955	8	]	]	PUNCT
m-1112	1955	9	and	and	CCONJ
m-1112	1955	10	from	from	ADP
m-1112	1955	11	gravity	gravity	NOUN
m-1112	1955	12	relation	relation	NOUN
m-1112	1955	13	g	g	PROPN
m-1112	1955	14	≡	≡	PROPN
m-1112	1955	15	σ	σ	PROPN
m-1112	1955	16	x	x	PROPN
m-1112	1955	17	𝚽³	𝚽³	NOUN
m-1112	1955	18	,	,	PUNCT
m-1112	1955	19	then	then	ADV
m-1112	1955	20	issues	issue	NOUN
m-1112	1955	21	→	→	SYM
m-1112	1955	22	[	[	PUNCT
m-1112	1955	23	�	�	NOUN
m-1112	1955	24	̅	̅	NOUN
m-1112	1955	25	�	�	NOUN
m-1112	1955	26	=	=	SYM
m-1112	1955	27	𝐆	𝐆	PROPN
m-1112	1955	28	𝐋	𝐋	PROPN
m-1112	1955	29	𝐏	𝐏	PROPN
m-1112	1955	30	𝐫.𝚽²	𝐫.𝚽²	ADV
m-1112	1955	31	]	]	PUNCT
m-1112	1955	32	=	=	SYM
m-1112	1955	33	[	[	PUNCT
m-1112	1955	34	�	�	NOUN
m-1112	1955	35	̅	̅	NOUN
m-1112	1955	36	�	�	NOUN
m-1112	1955	37	=	=	SYM
m-1112	1955	38	𝟐.𝐆	𝟐.𝐆	NOUN
m-1112	1955	39	𝐋	𝐋	PROPN
m-1112	1955	40	𝐏	𝐏	PROPN
m-1112	1955	41	𝝀.𝚽²	𝝀.𝚽²	NOUN
m-1112	1955	42	]	]	PUNCT
m-1112	1955	43	which	which	PRON
m-1112	1955	44	is	be	AUX
m-1112	1955	45	the	the	DET
m-1112	1955	46	light	light	ADJ
m-1112	1955	47	-	-	PUNCT
m-1112	1955	48	velocity	velocity	NOUN
m-1112	1955	49	vector	vector	NOUN
m-1112	1955	50	.	.	PUNCT
m-1112	1956	1	since	since	SCONJ
m-1112	1956	2	r	r	NOUN
m-1112	1956	3	,	,	PUNCT
m-1112	1956	4	becomes	become	VERB
m-1112	1956	5	from	from	ADP
m-1112	1956	6	the	the	DET
m-1112	1956	7	beyond	beyond	ADP
m-1112	1956	8	-	-	PUNCT
m-1112	1956	9	planck`s	planck`s	NOUN
m-1112	1956	10	-	-	PUNCT
m-1112	1956	11	region	region	NOUN
m-1112	1956	12	then	then	ADV
m-1112	1956	13			NOUN
m-1112	1956	14	�	�	PROPN
m-1112	1956	15	̅	̅	NOUN
m-1112	1956	16	�	�	NOUN
m-1112	1956	17	=	=	SYM
m-1112	1956	18	f.φ	f.φ	PROPN
m-1112	1956	19	a	a	NOUN
m-1112	1956	20	=	=	PUNCT
m-1112	1957	1	[	[	PUNCT
m-1112	1957	2	g	g	X
m-1112	1957	3	φ	φ	PROPN
m-1112	1957	4	a	a	X
m-1112	1957	5	]	]	X
m-1112	1957	6	…	…	PUNCT
m-1112	1957	7	...	...	PUNCT
m-1112	1957	8	(	(	PUNCT
m-1112	1957	9	f	f	X
m-1112	1957	10	)	)	PUNCT
m-1112	1957	11	equation	equation	NOUN
m-1112	1957	12	(	(	PUNCT
m-1112	1957	13	f	f	X
m-1112	1957	14	)	)	PUNCT
m-1112	1957	15	may	may	AUX
m-1112	1957	16	be	be	AUX
m-1112	1957	17	written	write	VERB
m-1112	1957	18	as	as	ADP
m-1112	1957	19	force	force	NOUN
m-1112	1957	20	g	g	PROPN
m-1112	1957	21	=	=	SYM
m-1112	1957	22	�	�	PROPN
m-1112	1957	23	̅	̅	NOUN
m-1112	1957	24	�	�	PROPN
m-1112	1957	25	𝐀	𝐀	PROPN
m-1112	1957	26	𝚽	𝚽	PROPN
m-1112	1957	27	,	,	PUNCT
m-1112	1957	28	which	which	PRON
m-1112	1957	29	is	be	AUX
m-1112	1957	30	a	a	DET
m-1112	1957	31	viscusdampingforce	viscusdampingforce	NOUN
m-1112	1957	32	where	where	SCONJ
m-1112	1957	33	a	a	DET
m-1112	1957	34	φ	φ	NOUN
m-1112	1957	35	is	be	AUX
m-1112	1957	36	a	a	DET
m-1112	1957	37	constant	constant	NOUN
m-1112	1957	38	of	of	ADP
m-1112	1957	39	proportionality	proportionality	NOUN
m-1112	1957	40	and	and	CCONJ
m-1112	1957	41	the	the	DET
m-1112	1957	42	equation	equation	NOUN
m-1112	1957	43	of	of	ADP
m-1112	1957	44	motion	motion	NOUN
m-1112	1957	45	is	be	AUX
m-1112	1957	46	𝐅𝐆	𝐅𝐆	NOUN
m-1112	1957	47	=	=	PUNCT
m-1112	1957	48	[	[	PUNCT
m-1112	1957	49	𝐀	𝐀	PROPN
m-1112	1957	50	𝚽	𝚽	PROPN
m-1112	1957	51	]	]	PUNCT
m-1112	1957	52	.	.	PUNCT
m-1112	1958	1	�	�	PROPN
m-1112	1958	2	̇	̇	PROPN
m-1112	1958	3	�	�	PROPN
m-1112	1958	4	force	force	NOUN
m-1112	1958	5	g	g	PROPN
m-1112	1958	6	is	be	AUX
m-1112	1958	7	applied	apply	VERB
m-1112	1958	8	in	in	ADP
m-1112	1958	9	all	all	PRON
m-1112	1958	10	quantized	quantize	VERB
m-1112	1958	11	-	-	PUNCT
m-1112	1958	12	universe	universe	NOUN
m-1112	1958	13	a	a	DET
m-1112	1958	14	as	as	ADP
m-1112	1958	15	velocity	velocity	NOUN
m-1112	1958	16	�	�	NOUN
m-1112	1958	17	̅	̅	NOUN
m-1112	1958	18	�	�	PROPN
m-1112	1958	19	and	and	CCONJ
m-1112	1958	20	as	as	ADP
m-1112	1958	21	stress	stress	NOUN
m-1112	1958	22	σ	σ	NOUN
m-1112	1958	23	on	on	ADP
m-1112	1958	24	spaces	space	NOUN
m-1112	1958	25	anti	anti	ADJ
m-1112	1958	26	-	-	ADJ
m-1112	1958	27	spaces	space	NOUN
m-1112	1958	28	as	as	ADP
m-1112	1958	29	spaces	space	NOUN
m-1112	1958	30	-	-	PUNCT
m-1112	1958	31	relation	relation	NOUN
m-1112	1958	32	𝐋𝐩	𝐋𝐩	NOUN
m-1112	1958	33	=	=	SYM
m-1112	1958	34	ei	ei	PROPN
m-1112	1958	35	.	.	PUNCT
m-1112	1959	1	(	(	PUNCT
m-1112	1959	2	π	π	PROPN
m-1112	1959	3	2	2	NUM
m-1112	1959	4	+2kπ).b	+2kπ).b	NOUN
m-1112	1959	5	,	,	PUNCT
m-1112	1959	6	where	where	SCONJ
m-1112	1959	7	from	from	ADP
m-1112	1959	8	material	material	NOUN
m-1112	1959	9	-	-	PUNCT
m-1112	1959	10	geometry	geometry	NOUN
m-1112	1959	11	[	[	X
m-1112	1959	12	24	24	NUM
m-1112	1959	13	-	-	SYM
m-1112	1959	14	58	58	NUM
m-1112	1959	15	]	]	PUNCT
m-1112	1959	16	,	,	PUNCT
m-1112	1959	17	space	space	NOUN
m-1112	1959	18	≡	≡	PROPN
m-1112	1959	19	1	1	NUM
m-1112	1959	20	and	and	CCONJ
m-1112	1959	21	anti	anti	ADJ
m-1112	1959	22	-	-	ADJ
m-1112	1959	23	space	space	ADJ
m-1112	1959	24	≡	≡	PROPN
m-1112	1959	25	√1	√1	PROPN
m-1112	1959	26	=	=	PUNCT
m-1112	1960	1	+	+	CCONJ
m-1112	1960	2	1	1	NUM
m-1112	1960	3	,	,	PUNCT
m-1112	1960	4	1	1	NUM
m-1112	1960	5	,	,	PUNCT
m-1112	1960	6	and	and	CCONJ
m-1112	1961	1	√−1	√−1	PROPN
m-1112	1961	2	=	=	SYM
m-1112	1961	3	i	i	NOUN
m-1112	1961	4	=	=	PUNCT
m-1112	1961	5	the	the	DET
m-1112	1961	6	imaginary	imaginary	ADJ
m-1112	1961	7	part	part	NOUN
m-1112	1961	8	into	into	ADP
m-1112	1961	9	the	the	DET
m-1112	1961	10	→	→	NOUN
m-1112	1961	11	anti	anti	ADJ
m-1112	1961	12	-	-	ADJ
m-1112	1961	13	space	space	ADJ
m-1112	1961	14	+	+	CCONJ
m-1112	1961	15	space	space	NOUN
m-1112	1961	16	≡	≡	PROPN
m-1112	1961	17	motion	motion	NOUN
m-1112	1961	18	≡	≡	PROPN
m-1112	1961	19	i	i	PROPN
m-1112	1961	20	≡	≡	PROPN
m-1112	1961	21	√−1	√−1	PUNCT
m-1112	1961	22	2	2	NUM
m-1112	1961	23	≡	≡	ADJ
m-1112	1961	24	√−1	√−1	PUNCT
m-1112	1961	25	4	4	NUM
m-1112	1961	26	≡	≡	PROPN
m-1112	1961	27	e−i	e−i	NOUN
m-1112	1961	28	.	.	PUNCT
m-1112	1962	1	(	(	PUNCT
m-1112	1962	2	π	π	NOUN
m-1112	1962	3	4	4	NUM
m-1112	1962	4	)	)	PUNCT
m-1112	1962	5	.b	.b	PUNCT
m-1112	1963	1	=	=	PUNCT
m-1112	1963	2	0,707106781	0,707106781	NUM
m-1112	1963	3	.	.	PUNCT
m-1112	1964	1	b	b	X
m-1112	1964	2	.	.	PUNCT
m-1112	1965	1	the	the	DET
m-1112	1965	2	base	base	PROPN
m-1112	1965	3	b	b	PROPN
m-1112	1965	4	,	,	PUNCT
m-1112	1965	5	which	which	PRON
m-1112	1965	6	for	for	ADP
m-1112	1965	7	natural	natural	ADJ
m-1112	1965	8	logarithms	logarithm	NOUN
m-1112	1965	9	issues	issue	NOUN
m-1112	1965	10	<	<	X
m-1112	1965	11	<	<	X
m-1112	1965	12	the	the	DET
m-1112	1965	13	natural	natural	ADJ
m-1112	1965	14	logarithm	logarithm	NOUN
m-1112	1965	15	ln(x	ln(x	X
m-1112	1965	16	)	)	PUNCT
m-1112	1965	17	of	of	ADP
m-1112	1965	18	a	a	DET
m-1112	1965	19	magnitude	magnitude	NOUN
m-1112	1965	20	x	x	X
m-1112	1965	21	,	,	PUNCT
m-1112	1965	22	is	be	AUX
m-1112	1965	23	the	the	DET
m-1112	1965	24	power	power	NOUN
m-1112	1965	25	to	to	PART
m-1112	1965	26	which	which	PRON
m-1112	1965	27	,	,	PUNCT
m-1112	1965	28	e	e	X
m-1112	1965	29	,	,	PUNCT
m-1112	1965	30	would	would	AUX
m-1112	1965	31	have	have	VERB
m-1112	1965	32	to	to	PART
m-1112	1965	33	be	be	AUX
m-1112	1965	34	raised	raise	VERB
m-1112	1965	35	to	to	PART
m-1112	1965	36	equal	equal	VERB
m-1112	1965	37	x	x	X
m-1112	1965	38	>	>	PUNCT
m-1112	1965	39	>	>	X
m-1112	1965	40	and	and	CCONJ
m-1112	1965	41	is	be	AUX
m-1112	1965	42	defining	define	VERB
m-1112	1965	43	that	that	SCONJ
m-1112	1965	44	→	→	SYM
m-1112	1965	45	ln(x	ln(x	X
m-1112	1965	46	)	)	PUNCT
m-1112	1965	47	is	be	AUX
m-1112	1965	48	the	the	DET
m-1112	1965	49	period	period	NOUN
m-1112	1965	50	-	-	PUNCT
m-1112	1965	51	needed	need	VERB
m-1112	1965	52	to	to	PART
m-1112	1965	53	grow	grow	VERB
m-1112	1965	54	x	x	PUNCT
m-1112	1965	55	,	,	PUNCT
m-1112	1965	56	as	as	SCONJ
m-1112	1965	57	this	this	PRON
m-1112	1965	58	is	be	AUX
m-1112	1965	59	in	in	ADP
m-1112	1965	60	integration	integration	NOUN
m-1112	1965	61	∫	∫	PROPN
m-1112	1966	1	x	x	INTJ
m-1112	1966	2	,	,	PUNCT
m-1112	1966	3	so	so	ADV
m-1112	1966	4	ex	ex	PROPN
m-1112	1966	5	ijo	ijo	PROPN
m-1112	1966	6	international	international	PROPN
m-1112	1966	7	journal	journal	PROPN
m-1112	1966	8	of	of	ADP
m-1112	1966	9	mathematics	mathematics	PROPN
m-1112	1966	10	(	(	PUNCT
m-1112	1966	11	issn	issn	PROPN
m-1112	1966	12	:	:	PUNCT
m-1112	1966	13	2992	2992	NUM
m-1112	1966	14	-	-	SYM
m-1112	1966	15	4421	4421	NUM
m-1112	1966	16	)	)	PUNCT
m-1112	1966	17	volume	volume	NOUN
m-1112	1966	18	08	08	NUM
m-1112	1967	1	|	|	ADV
m-1112	1967	2	issue	issue	NOUN
m-1112	1967	3	08	08	NUM
m-1112	1968	1	|	|	ADV
m-1112	1968	2	august	august	PROPN
m-1112	1968	3	2025	2025	NUM
m-1112	1968	4	|	|	ADV
m-1112	1968	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1968	6	ijo	ijo	PROPN
m-1112	1968	7	journals	journal	NOUN
m-1112	1968	8	70	70	NUM
m-1112	1968	9	the	the	DET
m-1112	1968	10	fundamental	fundamental	ADJ
m-1112	1968	11	particles	particle	NOUN
m-1112	1968	12	origination	origination	NOUN
m-1112	1968	13	mechanism	mechanism	NOUN
m-1112	1968	14	in	in	ADP
m-1112	1968	15	mfmf	mfmf	PROPN
m-1112	1968	16	pns	pns	PROPN
m-1112	1968	17	caves	cave	NOUN
m-1112	1968	18	.	.	PUNCT
m-1112	1969	1	is	be	AUX
m-1112	1969	2	the	the	DET
m-1112	1969	3	amount	amount	NOUN
m-1112	1969	4	of	of	ADP
m-1112	1969	5	growth	growth	NOUN
m-1112	1969	6	after	after	ADP
m-1112	1969	7	period	period	NOUN
m-1112	1969	8	x	x	PUNCT
m-1112	1969	9	,	,	PUNCT
m-1112	1969	10	and	and	CCONJ
m-1112	1969	11	the	the	DET
m-1112	1969	12	possible	possible	ADJ
m-1112	1969	13	-	-	PUNCT
m-1112	1969	14	repetitive	repetitive	ADJ
m-1112	1969	15	-	-	PUNCT
m-1112	1969	16	permutations	permutation	NOUN
m-1112	1969	17	for	for	ADP
m-1112	1969	18	moulds	mould	NOUN
m-1112	1969	19	and	and	CCONJ
m-1112	1969	20	elements	element	NOUN
m-1112	1969	21	in	in	ADP
m-1112	1969	22	which	which	PRON
m-1112	1969	23	issues	issue	NOUN
m-1112	1969	24	𝐌𝐨𝐮𝐥𝐝	𝐌𝐨𝐮𝐥𝐝	PROPN
m-1112	1969	25	𝐄𝐥𝐞𝐦𝐞𝐧𝐭𝐬	𝐄𝐥𝐞𝐦𝐞𝐧𝐭𝐬	PROPN
m-1112	1969	26	=	=	PUNCT
m-1112	1969	27	the	the	DET
m-1112	1969	28	growth	growth	NOUN
m-1112	1969	29	-	-	PUNCT
m-1112	1969	30	periods	period	NOUN
m-1112	1969	31	i.e.	i.e.	X
m-1112	1969	32	when	when	SCONJ
m-1112	1969	33	mould	mould	AUX
m-1112	1969	34	=	=	NOUN
m-1112	1969	35	elements	element	NOUN
m-1112	1969	36	then	then	ADV
m-1112	1969	37	is	be	AUX
m-1112	1969	38	succeeded	succeed	VERB
m-1112	1969	39	maximum	maximum	ADV
m-1112	1969	40	and	and	CCONJ
m-1112	1969	41	for	for	SCONJ
m-1112	1969	42	e	e	PROPN
m-1112	1969	43	is	be	AUX
m-1112	1969	44	ee	ee	ADP
m-1112	1969	45	,	,	PUNCT
m-1112	1969	46	and	and	CCONJ
m-1112	1969	47	any	any	DET
m-1112	1969	48	logx	logx	NOUN
m-1112	1969	49	x	x	X
m-1112	1969	50	.	.	PUNCT
m-1112	1970	1	for	for	ADP
m-1112	1970	2	logx	logx	PROPN
m-1112	1970	3	x	x	PUNCT
m-1112	1970	4	and	and	CCONJ
m-1112	1970	5	base	base	NOUN
m-1112	1970	6	x	x	PUNCT
m-1112	1970	7	=	=	SYM
m-1112	1970	8	10	10	NUM
m-1112	1970	9	then	then	ADV
m-1112	1970	10	log10	log10	PROPN
m-1112	1970	11	10	10	NUM
m-1112	1970	12	=	=	SYM
m-1112	1970	13	1010	1010	NUM
m-1112	1970	14	and	and	CCONJ
m-1112	1970	15	for	for	ADP
m-1112	1970	16	the	the	DET
m-1112	1970	17	two	two	NUM
m-1112	1970	18	elements	element	NOUN
m-1112	1970	19	[	[	X
m-1112	1970	20	⊕	⊕	NOUN
m-1112	1970	21	,	,	PUNCT
m-1112	1970	22	⊝	⊝	PROPN
m-1112	1970	23	]	]	PUNCT
m-1112	1970	24	is	be	AUX
m-1112	1970	25	10[10]²	10[10]²	NUM
m-1112	1970	26	=	=	SYM
m-1112	1970	27	1020	1020	NUM
m-1112	1970	28	positions	position	NOUN
m-1112	1970	29	≡	≡	PROPN
m-1112	1970	30	distances	distance	NOUN
m-1112	1970	31	≡	≡	PROPN
m-1112	1970	32	r	r	NOUN
m-1112	1970	33	and	and	CCONJ
m-1112	1970	34	since	since	SCONJ
m-1112	1970	35	10−x	10−x	NUM
m-1112	1970	36	=	=	SYM
m-1112	1970	37	1	1	NUM
m-1112	1970	38	10x	10x	X
m-1112	1970	39	then	then	ADV
m-1112	1970	40	b	b	PROPN
m-1112	1970	41	=	=	SYM
m-1112	1970	42	10−20	10−20	PROPN
m-1112	1970	43	,	,	PUNCT
m-1112	1970	44	and	and	CCONJ
m-1112	1970	45	the	the	DET
m-1112	1970	46	anti	anti	ADJ
m-1112	1970	47	-	-	ADJ
m-1112	1970	48	space	space	ADJ
m-1112	1970	49	+	+	CCONJ
m-1112	1970	50	space	space	NOUN
m-1112	1970	51	-	-	PUNCT
m-1112	1970	52	positions	position	NOUN
m-1112	1970	53	are	be	AUX
m-1112	1970	54	,	,	PUNCT
m-1112	1970	55	0,707106781.10−20	0,707106781.10−20	PUNCT
m-1112	1971	1	=	=	SYM
m-1112	1971	2	1	1	NUM
m-1112	1971	3	,	,	PUNCT
m-1112	1971	4	0707106781.10−19	0707106781.10−19	NUM
m-1112	1971	5	.	.	PUNCT
m-1112	1972	1	in	in	ADP
m-1112	1972	2	this	this	DET
m-1112	1972	3	way	way	NOUN
m-1112	1972	4	the	the	DET
m-1112	1972	5	non	non	ADJ
m-1112	1972	6	-	-	ADJ
m-1112	1972	7	dimensional	dimensional	ADJ
m-1112	1972	8	-	-	PUNCT
m-1112	1972	9	number	number	NOUN
m-1112	1972	10	[	[	PUNCT
m-1112	1972	11	0,707106781	0,707106781	PROPN
m-1112	1972	12	*	*	SYM
m-1112	1972	13	10−1	10−1	NUM
m-1112	1972	14	=	=	SYM
m-1112	1972	15	0	0	NUM
m-1112	1972	16	,	,	PUNCT
m-1112	1972	17	0707106781	0707106781	NUM
m-1112	1972	18	]	]	PUNCT
m-1112	1972	19	,	,	PUNCT
m-1112	1972	20	is	be	AUX
m-1112	1972	21	quantized	quantize	VERB
m-1112	1972	22	in	in	ADP
m-1112	1972	23	cave	cave	NOUN
m-1112	1972	24	,	,	PUNCT
m-1112	1972	25	r	r	NOUN
m-1112	1972	26	,	,	PUNCT
m-1112	1972	27	as	as	ADP
m-1112	1972	28	distance	distance	NOUN
m-1112	1972	29	and	and	CCONJ
m-1112	1972	30	becomes	become	VERB
m-1112	1972	31	the	the	PRON
m-1112	1972	32	-	-	PUNCT
m-1112	1972	33	dimensional	dimensional	ADJ
m-1112	1972	34	-	-	PUNCT
m-1112	1972	35	space	space	NOUN
m-1112	1972	36	in	in	ADP
m-1112	1972	37	the	the	DET
m-1112	1972	38	decimal	decimal	ADJ
m-1112	1972	39	system	system	NOUN
m-1112	1972	40	b	b	NOUN
m-1112	1973	1	=	=	NOUN
m-1112	1973	2	10	10	NUM
m-1112	1973	3	as	as	ADP
m-1112	1973	4	cave	cave	NOUN
m-1112	1973	5	r	r	NOUN
m-1112	1973	6	,	,	PUNCT
m-1112	1973	7	and	and	CCONJ
m-1112	1973	8	which	which	DET
m-1112	1973	9	cave	cave	NOUN
m-1112	1973	10	is	be	AUX
m-1112	1973	11	monad	monad	PROPN
m-1112	1973	12	r	r	NOUN
m-1112	1973	13	=	=	SYM
m-1112	1973	14	1	1	NUM
m-1112	1973	15	,	,	PUNCT
m-1112	1973	16	0707106781	0707106781	NUM
m-1112	1973	17	or	or	CCONJ
m-1112	1973	18	,	,	PUNCT
m-1112	1973	19	r	r	NOUN
m-1112	1973	20	=	=	SYM
m-1112	1973	21	1	1	NUM
m-1112	1973	22	,	,	PUNCT
m-1112	1973	23	0707106781	0707106781	NUM
m-1112	1973	24	m	m	VERB
m-1112	1973	25	,	,	PUNCT
m-1112	1973	26	having	have	VERB
m-1112	1973	27	unit	unit	NOUN
m-1112	1973	28	-	-	PUNCT
m-1112	1973	29	area	area	NOUN
m-1112	1973	30	π.r²	π.r²	X
m-1112	1973	31	=	=	NOUN
m-1112	1973	32	3.601588	3.601588	NUM
m-1112	1973	33	m2	m2	NOUN
m-1112	1973	34	,	,	PUNCT
m-1112	1973	35	and	and	CCONJ
m-1112	1973	36	the	the	DET
m-1112	1973	37	qua	qua	NOUN
m-1112	1973	38	-	-	PUNCT
m-1112	1973	39	universe	universe	NOUN
m-1112	1973	40	is	be	AUX
m-1112	1973	41	a	a	DET
m-1112	1973	42	=	=	PROPN
m-1112	1973	43	3.601588	3.601588	NUM
m-1112	1973	44	.	.	PUNCT
m-1112	1974	1	𝟏𝟎−𝟏𝟗	𝟏𝟎−𝟏𝟗	PROPN
m-1112	1974	2	m2	m2	PROPN
m-1112	1974	3	/	/	SYM
m-1112	1974	4	s	s	PROPN
m-1112	1974	5	,	,	PUNCT
m-1112	1974	6	which	which	PRON
m-1112	1974	7	are	be	AUX
m-1112	1974	8	the	the	DET
m-1112	1974	9	space	space	NOUN
m-1112	1975	1	+	+	NOUN
m-1112	1976	1	anti	anti	ADJ
m-1112	1976	2	-	-	ADJ
m-1112	1976	3	space	space	ADJ
m-1112	1976	4	positions	position	NOUN
m-1112	1976	5	in	in	ADP
m-1112	1976	6	universe	universe	NOUN
m-1112	1976	7	...	...	PUNCT
m-1112	1976	8	(	(	PUNCT
m-1112	1976	9	i	i	NOUN
m-1112	1976	10	)	)	PUNCT
m-1112	1976	11	from	from	ADP
m-1112	1976	12	(	(	PUNCT
m-1112	1976	13	h	h	NOUN
m-1112	1976	14	)	)	PUNCT
m-1112	1976	15	,	,	PUNCT
m-1112	1976	16	light	light	ADJ
m-1112	1976	17	-	-	PUNCT
m-1112	1976	18	velocity	velocity	NOUN
m-1112	1976	19	�	�	NOUN
m-1112	1976	20	̅	̅	NOUN
m-1112	1976	21	�	�	NOUN
m-1112	1977	1	=	=	SYM
m-1112	1977	2	[	[	PUNCT
m-1112	1977	3	𝐆	𝐆	PROPN
m-1112	1977	4	𝚽	𝚽	PROPN
m-1112	1977	5	𝐀	𝐀	PROPN
m-1112	1977	6	]	]	X
m-1112	1977	7	=	=	PUNCT
m-1112	1977	8	𝟔,𝟔𝟕𝟑𝟔𝟗𝟐.𝟏𝟎−𝟏𝟏𝟏,𝟔𝟏𝟖𝟎𝟑𝟑𝟗𝟖𝟖𝟕	𝟔,𝟔𝟕𝟑𝟔𝟗𝟐.𝟏𝟎−𝟏𝟏𝟏,𝟔𝟏𝟖𝟎𝟑𝟑𝟗𝟖𝟖𝟕	PROPN
m-1112	1977	9	𝟑,𝟔𝟎𝟏𝟓𝟖𝟖	𝟑,𝟔𝟎𝟏𝟓𝟖𝟖	ADJ
m-1112	1977	10	.𝟏𝟎−𝟏𝟗	.𝟏𝟎−𝟏𝟗	PUNCT
m-1112	1977	11	.	.	PUNCT
m-1112	1978	1	=	=	PUNCT
m-1112	1978	2	2.99819938	2.99819938	NUM
m-1112	1978	3	.𝟏𝟎𝟖	.𝟏𝟎𝟖	NUM
m-1112	1978	4	m	m	PROPN
m-1112	1978	5	/	/	SYM
m-1112	1978	6	s	s	PART
m-1112	1978	7	i.e.	i.e.	X
m-1112	1978	8	gravity	gravity	NOUN
m-1112	1978	9	force	force	NOUN
m-1112	1978	10	g	g	PROPN
m-1112	1978	11	≡	≡	PROPN
m-1112	1978	12	motion	motion	NOUN
m-1112	1978	13	,	,	PUNCT
m-1112	1978	14	exists	exist	VERB
m-1112	1978	15	without	without	ADP
m-1112	1978	16	mass	mass	NOUN
m-1112	1978	17	and	and	CCONJ
m-1112	1978	18	is	be	AUX
m-1112	1978	19	quantized	quantize	VERB
m-1112	1978	20	→	→	PUNCT
m-1112	1978	21	spread	spread	VERB
m-1112	1978	22	in	in	ADP
m-1112	1978	23	{	{	PUNCT
m-1112	1978	24	space	space	NOUN
m-1112	1978	25	and	and	CCONJ
m-1112	1978	26	anti	anti	ADJ
m-1112	1978	27	-	-	NOUN
m-1112	1978	28	space	space	ADJ
m-1112	1978	29	}	}	PUNCT
m-1112	1978	30	or	or	CCONJ
m-1112	1978	31	≡	≡	PROPN
m-1112	1978	32	qua	qua	PROPN
m-1112	1978	33	≡	≡	PROPN
m-1112	1978	34	{	{	PUNCT
m-1112	1978	35	is	be	AUX
m-1112	1978	36	the	the	DET
m-1112	1978	37	quantized	quantize	VERB
m-1112	1978	38	-	-	PUNCT
m-1112	1978	39	units	unit	NOUN
m-1112	1978	40	in	in	ADP
m-1112	1978	41	-	-	PUNCT
m-1112	1978	42	area	area	NOUN
m-1112	1978	43	of	of	ADP
m-1112	1978	44	space	space	NOUN
m-1112	1978	45	and	and	CCONJ
m-1112	1978	46	anti	anti	ADJ
m-1112	1978	47	-	-	NOUN
m-1112	1978	48	space	space	NOUN
m-1112	1978	49	}	}	PUNCT
m-1112	1978	50	,	,	PUNCT
m-1112	1978	51	and	and	CCONJ
m-1112	1978	52	as	as	ADP
m-1112	1978	53	a	a	DET
m-1112	1978	54	mould	mould	NOUN
m-1112	1978	55	𝚽	𝚽	PRON
m-1112	1978	56	golden	golden	ADJ
m-1112	1978	57	-	-	PUNCT
m-1112	1978	58	ratio	ratio	NOUN
m-1112	1978	59	,	,	PUNCT
m-1112	1978	60	exists	exist	VERB
m-1112	1978	61	in	in	ADP
m-1112	1978	62	the	the	DET
m-1112	1978	63	impedance	impedance	NOUN
m-1112	1978	64	b	b	PROPN
m-1112	1978	65	.	.	PUNCT
m-1112	1979	1	impedance	impedance	NOUN
m-1112	1979	2	in	in	ADP
m-1112	1979	3	mechanics	mechanic	NOUN
m-1112	1979	4	is	be	AUX
m-1112	1979	5	the	the	DET
m-1112	1979	6	friction	friction	NOUN
m-1112	1979	7	coefficient	coefficient	NOUN
m-1112	1979	8	,	,	PUNCT
m-1112	1979	9	where	where	SCONJ
m-1112	1979	10	for	for	ADP
m-1112	1979	11	force	force	NOUN
m-1112	1979	12	g	g	PROPN
m-1112	1979	13	to	to	PART
m-1112	1979	14	be	be	AUX
m-1112	1979	15	proportional	proportional	ADJ
m-1112	1979	16	to	to	ADP
m-1112	1979	17	the	the	DET
m-1112	1979	18	light	light	ADJ
m-1112	1979	19	-	-	PUNCT
m-1112	1979	20	velocity	velocity	NOUN
m-1112	1979	21	c	c	NOUN
m-1112	1979	22	=	=	SYM
m-1112	1979	23	�	�	PROPN
m-1112	1979	24	̅	̅	NOUN
m-1112	1979	25	�	�	PROPN
m-1112	1979	26	,	,	PUNCT
m-1112	1979	27	then	then	ADV
m-1112	1979	28	the	the	DET
m-1112	1979	29	harmonic	harmonic	ADJ
m-1112	1979	30	–	–	PUNCT
m-1112	1979	31	oscillation	oscillation	NOUN
m-1112	1979	32	is	be	AUX
m-1112	1979	33	an	an	DET
m-1112	1979	34	dumped	dump	VERB
m-1112	1979	35	-	-	PUNCT
m-1112	1979	36	oscillator	oscillator	NOUN
m-1112	1979	37	,	,	PUNCT
m-1112	1979	38	and	and	CCONJ
m-1112	1979	39	can	can	AUX
m-1112	1979	40	oscillate	oscillate	VERB
m-1112	1979	41	due	due	ADP
m-1112	1979	42	to	to	ADP
m-1112	1979	43	the	the	DET
m-1112	1979	44	excitation	excitation	NOUN
m-1112	1979	45	as	as	ADP
m-1112	1979	46	,	,	PUNCT
m-1112	1979	47	a	a	X
m-1112	1979	48	..	..	PUNCT
m-1112	1979	49	with	with	ADP
m-1112	1979	50	a	a	DET
m-1112	1979	51	frequency	frequency	NOUN
m-1112	1979	52	lower	low	ADJ
m-1112	1979	53	than	than	ADP
m-1112	1979	54	in	in	ADP
m-1112	1979	55	the	the	DET
m-1112	1979	56	undamped	undampe	VERB
m-1112	1979	57	case	case	NOUN
m-1112	1979	58	and	and	CCONJ
m-1112	1979	59	an	an	DET
m-1112	1979	60	amplitude	amplitude	NOUN
m-1112	1979	61	decreasing	decrease	VERB
m-1112	1979	62	with	with	ADP
m-1112	1979	63	time	time	NOUN
m-1112	1979	64	,	,	PUNCT
m-1112	1979	65	the	the	DET
m-1112	1979	66	under	under	ADV
m-1112	1979	67	-	-	PUNCT
m-1112	1979	68	damped	damp	VERB
m-1112	1979	69	-	-	PUNCT
m-1112	1979	70	oscillator	oscillator	NOUN
m-1112	1979	71	which	which	PRON
m-1112	1979	72	originates	originate	VERB
m-1112	1979	73	the	the	DET
m-1112	1979	74	quantum	quantum	NOUN
m-1112	1979	75	of	of	ADP
m-1112	1979	76	motion	motion	NOUN
m-1112	1979	77	which	which	PRON
m-1112	1979	78	is	be	AUX
m-1112	1979	79	a	a	DET
m-1112	1979	80	limiting	limit	VERB
m-1112	1979	81	case	case	NOUN
m-1112	1979	82	between	between	ADP
m-1112	1979	83	the	the	DET
m-1112	1979	84	oscillatory	oscillatory	ADJ
m-1112	1979	85	and	and	CCONJ
m-1112	1979	86	non	non	ADJ
m-1112	1979	87	-	-	ADJ
m-1112	1979	88	oscillatory	oscillatory	ADJ
m-1112	1979	89	motion	motion	NOUN
m-1112	1979	90	the	the	DET
m-1112	1979	91	critical	critical	ADJ
m-1112	1979	92	damping	damping	NOUN
m-1112	1979	93	,	,	PUNCT
m-1112	1979	94	and	and	CCONJ
m-1112	1979	95	which	which	PRON
m-1112	1979	96	originates	originate	VERB
m-1112	1979	97	the	the	DET
m-1112	1979	98	light	light	ADJ
m-1112	1979	99	-	-	PUNCT
m-1112	1979	100	velocity	velocity	NOUN
m-1112	1979	101	�	�	NOUN
m-1112	1979	102	̅	̅	NOUN
m-1112	1979	103	�	�	NOUN
m-1112	1979	104	,	,	PUNCT
m-1112	1979	105	[	[	X
m-1112	1979	106	49	49	NUM
m-1112	1979	107	]	]	SYM
m-1112	1979	108	b	b	X
m-1112	1979	109	..	..	PUNCT
m-1112	1979	110	with	with	ADP
m-1112	1979	111	undamped	undampe	VERB
m-1112	1979	112	case	case	NOUN
m-1112	1979	113	frequency	frequency	NOUN
m-1112	1979	114	and	and	CCONJ
m-1112	1979	115	decay	decay	NOUN
m-1112	1979	116	to	to	ADP
m-1112	1979	117	the	the	DET
m-1112	1979	118	equilibrium	equilibrium	NOUN
m-1112	1979	119	-	-	PUNCT
m-1112	1979	120	position	position	NOUN
m-1112	1979	121	without	without	ADP
m-1112	1979	122	oscillation	oscillation	NOUN
m-1112	1979	123	and	and	CCONJ
m-1112	1979	124	the	the	DET
m-1112	1979	125	over	over	ADV
m-1112	1979	126	-	-	PUNCT
m-1112	1979	127	damped	damp	VERB
m-1112	1979	128	-	-	PUNCT
m-1112	1979	129	oscillator	oscillator	NOUN
m-1112	1979	130	originating	originate	VERB
m-1112	1979	131	the	the	DET
m-1112	1979	132	n	n	NUM
m-1112	1979	133	-	-	PUNCT
m-1112	1979	134	times	times	NOUN
m-1112	1979	135	velocity	velocity	NOUN
m-1112	1979	136	c	c	NOUN
m-1112	1979	137	.	.	PUNCT
m-1112	1980	1	what	what	PRON
m-1112	1980	2	is	be	AUX
m-1112	1980	3	quantization	quantization	NOUN
m-1112	1980	4	of	of	ADP
m-1112	1980	5	motion	motion	NOUN
m-1112	1980	6	and	and	CCONJ
m-1112	1980	7	impedance	impedance	NOUN
m-1112	1980	8	is	be	AUX
m-1112	1980	9	analytically	analytically	ADV
m-1112	1980	10	referred	refer	VERB
m-1112	1980	11	in	in	ADP
m-1112	1980	12	[	[	X
m-1112	1980	13	83	83	NUM
m-1112	1980	14	]	]	PUNCT
m-1112	1980	15	a	a	DET
m-1112	1980	16	parallel	parallel	ADJ
m-1112	1980	17	solution	solution	NOUN
m-1112	1980	18	becomes	become	VERB
m-1112	1980	19	also	also	ADV
m-1112	1980	20	from	from	ADP
m-1112	1980	21	the	the	DET
m-1112	1980	22	attendant	attendant	ADJ
m-1112	1980	23	geometry	geometry	NOUN
m-1112	1980	24	logic	logic	NOUN
m-1112	1980	25	,	,	PUNCT
m-1112	1980	26	the	the	DET
m-1112	1980	27	three	three	NUM
m-1112	1980	28	elements	element	NOUN
m-1112	1980	29	≡	≡	ADJ
m-1112	1980	30	digits	digit	NOUN
m-1112	1980	31	of	of	ADP
m-1112	1980	32	material	material	NOUN
m-1112	1980	33	-	-	PUNCT
m-1112	1980	34	geometry	geometry	NOUN
m-1112	1980	35	are	be	AUX
m-1112	1980	36	→{⊕	→{⊕	ADJ
m-1112	1980	37	,	,	PUNCT
m-1112	1980	38	[	[	X
m-1112	1980	39	⊕↔⊝	⊕↔⊝	X
m-1112	1980	40	]	]	X
m-1112	1980	41	,	,	PUNCT
m-1112	1980	42	⊝	⊝	PUNCT
m-1112	1980	43	}	}	PUNCT
m-1112	1980	44	≡	≡	PROPN
m-1112	1981	1	[	[	X
m-1112	1981	2	+	+	X
m-1112	1981	3	,	,	PUNCT
m-1112	1981	4	0	0	NUM
m-1112	1981	5	,	,	PUNCT
m-1112	1981	6	-]←	-]←	ADJ
m-1112	1982	1	the	the	DET
m-1112	1982	2	permutation	permutation	NOUN
m-1112	1982	3	,	,	PUNCT
m-1112	1982	4	arrangement	arrangement	NOUN
m-1112	1982	5	of	of	ADP
m-1112	1982	6	the	the	DET
m-1112	1982	7	two	two	NUM
m-1112	1982	8	-	-	PUNCT
m-1112	1982	9	elements	element	NOUN
m-1112	1982	10	p1	p1	NOUN
m-1112	1982	11	2	2	NUM
m-1112	1982	12	=	=	SYM
m-1112	1982	13	2	2	NUM
m-1112	1982	14	,	,	PUNCT
m-1112	1982	15	i.e.	i.e.	X
m-1112	1982	16	are→	are→	NOUN
m-1112	1983	1	[	[	X
m-1112	1983	2	⊕,⊝	⊕,⊝	NOUN
m-1112	1983	3	]	]	X
m-1112	1984	1	[	[	X
m-1112	1984	2	⊝,⊕]←	⊝,⊕]←	X
m-1112	1984	3	the	the	DET
m-1112	1984	4	three	three	NUM
m-1112	1984	5	-	-	PUNCT
m-1112	1984	6	elements	element	NOUN
m-1112	1984	7	in	in	ADP
m-1112	1984	8	space	space	NOUN
m-1112	1984	9	need	need	VERB
m-1112	1984	10	p	p	NOUN
m-1112	1984	11	1	1	NUM
m-1112	1984	12	3	3	NUM
m-1112	1984	13	=	=	SYM
m-1112	1984	14	3.(3	3.(3	NUM
m-1112	1984	15	-	-	PROPN
m-1112	1984	16	1).(3	1).(3	NUM
m-1112	1984	17	-	-	PUNCT
m-1112	1984	18	2	2	NUM
m-1112	1984	19	)	)	PUNCT
m-1112	1984	20	=	=	SYM
m-1112	1984	21	6	6	NUM
m-1112	1984	22	positions	position	NOUN
m-1112	1984	23	and	and	CCONJ
m-1112	1984	24	the	the	DET
m-1112	1984	25	same	same	ADJ
m-1112	1984	26	for	for	ADP
m-1112	1984	27	three	three	NUM
m-1112	1984	28	-	-	PUNCT
m-1112	1984	29	elements	element	NOUN
m-1112	1984	30	in	in	ADP
m-1112	1984	31	anti	anti	ADJ
m-1112	1984	32	-	-	ADJ
m-1112	1984	33	space	space	ADJ
m-1112	1984	34	need	need	NOUN
m-1112	1984	35	p	p	NOUN
m-1112	1984	36	1	1	NUM
m-1112	1984	37	3	3	NUM
m-1112	1984	38	=	=	SYM
m-1112	1984	39	3.(3	3.(3	NUM
m-1112	1984	40	-	-	PROPN
m-1112	1984	41	1).(3	1).(3	NUM
m-1112	1984	42	-	-	PUNCT
m-1112	1984	43	2	2	NUM
m-1112	1984	44	)	)	PUNCT
m-1112	1984	45	=	=	SYM
m-1112	1984	46	6	6	NUM
m-1112	1984	47	positions	position	NOUN
m-1112	1984	48	,	,	PUNCT
m-1112	1984	49	and	and	CCONJ
m-1112	1984	50	total	total	ADJ
m-1112	1984	51	places	place	NOUN
m-1112	1984	52	→	→	SYM
m-1112	1984	53	p1	p1	NOUN
m-1112	1984	54	3	3	NUM
m-1112	1984	55	.	.	PUNCT
m-1112	1985	1	p1	p1	NOUN
m-1112	1985	2	3	3	NUM
m-1112	1985	3	=	=	SYM
m-1112	1985	4	6	6	NUM
m-1112	1985	5	x	x	SYM
m-1112	1985	6	6	6	NUM
m-1112	1985	7	=	=	SYM
m-1112	1985	8	36	36	NUM
m-1112	1985	9	positions	position	NOUN
m-1112	1985	10	=	=	PUNCT
m-1112	1985	11	a	a	PRON
m-1112	1985	12	,	,	PUNCT
m-1112	1985	13	for	for	ADP
m-1112	1985	14	spaces	space	NOUN
m-1112	1985	15	and	and	CCONJ
m-1112	1985	16	anti	anti	NOUN
m-1112	1985	17	-	-	ADJ
m-1112	1985	18	spaces	space	NOUN
m-1112	1985	19	as	as	ADP
m-1112	1985	20	impedance	impedance	NOUN
m-1112	1985	21	and	and	CCONJ
m-1112	1985	22	as	as	ADP
m-1112	1985	23	before	before	ADV
m-1112	1985	24	for	for	ADP
m-1112	1985	25	logx	logx	NOUN
m-1112	1985	26	x	x	PUNCT
m-1112	1985	27	and	and	CCONJ
m-1112	1985	28	base	base	NOUN
m-1112	1985	29	x	x	PUNCT
m-1112	1986	1	=	=	SYM
m-1112	1986	2	10	10	NUM
m-1112	1986	3	then	then	ADV
m-1112	1986	4	log10	log10	PROPN
m-1112	1986	5	10	10	NUM
m-1112	1986	6	=	=	SYM
m-1112	1986	7	1010	1010	NUM
m-1112	1986	8	and	and	CCONJ
m-1112	1986	9	for	for	ADP
m-1112	1986	10	the	the	DET
m-1112	1986	11	two	two	NUM
m-1112	1986	12	elements	element	NOUN
m-1112	1986	13	[	[	X
m-1112	1986	14	⊕	⊕	NOUN
m-1112	1986	15	,	,	PUNCT
m-1112	1986	16	⊝	⊝	PROPN
m-1112	1986	17	]	]	PUNCT
m-1112	1987	1	the	the	DET
m-1112	1987	2	growth	growth	NOUN
m-1112	1987	3	is	be	AUX
m-1112	1987	4	10	10	NUM
m-1112	1987	5	[	[	X
m-1112	1987	6	10	10	NUM
m-1112	1987	7	]	]	SYM
m-1112	1987	8	²	²	PROPN
m-1112	1987	9	=	=	SYM
m-1112	1987	10	1020	1020	NUM
m-1112	1987	11	positions	position	NOUN
m-1112	1987	12	≡	≡	PROPN
m-1112	1987	13	distances	distance	NOUN
m-1112	1987	14	≡	≡	PROPN
m-1112	1987	15	r	r	NOUN
m-1112	1987	16	,	,	PUNCT
m-1112	1987	17	and	and	CCONJ
m-1112	1987	18	since	since	SCONJ
m-1112	1987	19	issues	issue	NOUN
m-1112	1987	20	10−x	10−x	NUM
m-1112	1987	21	=	=	SYM
m-1112	1987	22	1	1	NUM
m-1112	1987	23	10x	10x	X
m-1112	1987	24	then	then	ADV
m-1112	1987	25	b	b	X
m-1112	1987	26	=	=	SYM
m-1112	1987	27	36.10−20	36.10−20	PROPN
m-1112	1987	28	,	,	PUNCT
m-1112	1987	29	and	and	CCONJ
m-1112	1987	30			NOUN
m-1112	1987	31	�	�	PROPN
m-1112	1987	32	̅	̅	NOUN
m-1112	1987	33	�	�	NOUN
m-1112	1987	34	=	=	SYM
m-1112	1987	35	f	f	PROPN
m-1112	1987	36	φ	φ	PROPN
m-1112	1987	37	a	a	PROPN
m-1112	1987	38	=	=	X
m-1112	1988	1	[	[	PUNCT
m-1112	1988	2	g	g	X
m-1112	1988	3	φ	φ	PROPN
m-1112	1988	4	a	a	X
m-1112	1988	5	]	]	X
m-1112	1988	6	=	=	PUNCT
m-1112	1988	7	[	[	PUNCT
m-1112	1988	8	6,673692	6,673692	NUM
m-1112	1988	9	.10−11.1,6180339887	.10−11.1,6180339887	PROPN
m-1112	1988	10	36	36	NUM
m-1112	1988	11	.10	.10	NUM
m-1112	1988	12	−20	−20	NOUN
m-1112	1988	13	.	.	PUNCT
m-1112	1988	14	]	]	PUNCT
m-1112	1989	1	=	=	PUNCT
m-1112	1989	2	2.9795163	2.9795163	NUM
m-1112	1989	3	.	.	PUNCT
m-1112	1989	4	108	108	NUM
m-1112	1989	5	m	m	NOUN
m-1112	1989	6	/	/	SYM
m-1112	1989	7	s	s	VERB
m-1112	1989	8	i.e.	i.e.	X
m-1112	1989	9	the	the	DET
m-1112	1989	10	ubiquity	ubiquity	NOUN
m-1112	1989	11	of	of	ADP
m-1112	1989	12	material	material	NOUN
m-1112	1989	13	geometry	geometry	NOUN
m-1112	1989	14	in	in	ADP
m-1112	1989	15	electromagnetism	electromagnetism	NOUN
m-1112	1989	16	is	be	AUX
m-1112	1989	17	everywhere	everywhere	ADV
m-1112	1989	18	.	.	PUNCT
m-1112	1990	1	the	the	DET
m-1112	1990	2	gravity	gravity	NOUN
m-1112	1990	3	constant	constant	ADJ
m-1112	1990	4	g	g	NOUN
m-1112	1990	5	,	,	PUNCT
m-1112	1990	6	is	be	AUX
m-1112	1990	7	the	the	DET
m-1112	1990	8	permeable	permeable	ADJ
m-1112	1990	9	path	path	NOUN
m-1112	1990	10	for	for	ADP
m-1112	1990	11	inner	inner	ADJ
m-1112	1990	12	stress	stress	NOUN
m-1112	1990	13	σ	σ	NOUN
m-1112	1990	14	,	,	PUNCT
m-1112	1990	15	to	to	PART
m-1112	1990	16	pass	pass	VERB
m-1112	1990	17	the	the	DET
m-1112	1990	18	material`s	material`s	NOUN
m-1112	1990	19	point	point	NOUN
m-1112	1990	20	a	a	DET
m-1112	1990	21	surface	surface	NOUN
m-1112	1990	22	4πr³/3	4πr³/3	NOUN
m-1112	1990	23	and	and	CCONJ
m-1112	1990	24	to	to	PART
m-1112	1990	25	expenditure	expenditure	VERB
m-1112	1990	26	its	its	PRON
m-1112	1990	27	energy	energy	NOUN
m-1112	1990	28	.the	.the	DET
m-1112	1990	29	same	same	ADJ
m-1112	1990	30	exists	exist	VERB
m-1112	1990	31	also	also	ADV
m-1112	1990	32	to	to	ADP
m-1112	1990	33	the	the	DET
m-1112	1990	34	electromagnetic	electromagnetic	ADJ
m-1112	1990	35	force	force	NOUN
m-1112	1990	36	which	which	PRON
m-1112	1990	37	is	be	AUX
m-1112	1990	38	associated	associate	VERB
m-1112	1990	39	with	with	ADP
m-1112	1990	40	a	a	DET
m-1112	1990	41	fundamental	fundamental	ADJ
m-1112	1990	42	property	property	NOUN
m-1112	1990	43	of	of	ADP
m-1112	1990	44	matter	matter	NOUN
m-1112	1990	45	which	which	PRON
m-1112	1990	46	is	be	AUX
m-1112	1990	47	the	the	DET
m-1112	1990	48	electric	electric	ADJ
m-1112	1990	49	charge	charge	NOUN
m-1112	1990	50	and	and	CCONJ
m-1112	1990	51	which	which	PRON
m-1112	1990	52	is	be	AUX
m-1112	1990	53	a	a	DET
m-1112	1990	54	clue	clue	NOUN
m-1112	1990	55	to	to	ADP
m-1112	1990	56	the	the	DET
m-1112	1990	57	ubiquity	ubiquity	NOUN
m-1112	1990	58	of	of	ADP
m-1112	1990	59	electromagnetism	electromagnetism	NOUN
m-1112	1990	60	.	.	PUNCT
m-1112	1991	1	from	from	ADP
m-1112	1991	2	equation	equation	NOUN
m-1112	1991	3	of	of	ADP
m-1112	1991	4	gravitation	gravitation	NOUN
m-1112	1991	5	g	g	PROPN
m-1112	1991	6	=	=	PROPN
m-1112	1991	7	ke	ke	PROPN
m-1112	1991	8	g	g	PROPN
m-1112	1991	9	=	=	PROPN
m-1112	1991	10	g.	g.	PROPN
m-1112	1992	1	[	[	PUNCT
m-1112	1992	2	kr	kr	PROPN
m-1112	1992	3	gr	gr	X
m-1112	1992	4	]	]	X
m-1112	1992	5	seems	seem	VERB
m-1112	1992	6	that	that	SCONJ
m-1112	1992	7	the	the	DET
m-1112	1992	8	two	two	NUM
m-1112	1992	9	constants	constant	NOUN
m-1112	1992	10	are	be	AUX
m-1112	1992	11	related	relate	VERB
m-1112	1992	12	i.e.	i.e.	X
m-1112	1992	13	act	act	NOUN
m-1112	1992	14	each	each	DET
m-1112	1992	15	other	other	ADJ
m-1112	1992	16	through	through	ADP
m-1112	1992	17	local	local	ADJ
m-1112	1992	18	-	-	PUNCT
m-1112	1992	19	coefficients	coefficient	NOUN
m-1112	1992	20	or	or	CCONJ
m-1112	1992	21	through	through	ADP
m-1112	1992	22	field	field	NOUN
m-1112	1992	23	-	-	PUNCT
m-1112	1992	24	lines	line	NOUN
m-1112	1992	25	,	,	PUNCT
m-1112	1992	26	called	call	VERB
m-1112	1992	27	the	the	DET
m-1112	1992	28	medium	medium	ADJ
m-1112	1992	29	or	or	CCONJ
m-1112	1992	30	permissible	permissible	ADJ
m-1112	1992	31	path	path	NOUN
m-1112	1992	32	which	which	PRON
m-1112	1992	33	are	be	AUX
m-1112	1992	34	as	as	ADP
m-1112	1992	35	σ	σ	NOUN
m-1112	1992	36	=	=	SYM
m-1112	1992	37	𝐅	𝐅	PROPN
m-1112	1992	38	𝐀	𝐀	NOUN
m-1112	1992	39	=	=	SYM
m-1112	1992	40	2πrf	2πrf	PROPN
m-1112	1992	41	φ	φ	NOUN
m-1112	1992	42	=	=	SYM
m-1112	1992	43	w	w	PROPN
m-1112	1992	44	r	r	NOUN
m-1112	1992	45	φ	φ	PROPN
m-1112	1992	46	=	=	SYM
m-1112	1992	47	𝐯	𝐯	PROPN
m-1112	1992	48	𝚽	𝚽	NOUN
m-1112	1992	49	,	,	PUNCT
m-1112	1992	50	velocity	velocity	NOUN
m-1112	1992	51	vector	vector	NOUN
m-1112	1992	52	in	in	ADP
m-1112	1992	53	a	a	DET
m-1112	1992	54	unit	unit	NOUN
m-1112	1992	55	-	-	PUNCT
m-1112	1992	56	space	space	NOUN
m-1112	1992	57	𝚽.	𝚽.	PROPN
m-1112	1992	58	ijo	ijo	PROPN
m-1112	1992	59	international	international	PROPN
m-1112	1992	60	journal	journal	PROPN
m-1112	1992	61	of	of	ADP
m-1112	1992	62	mathematics	mathematics	PROPN
m-1112	1992	63	(	(	PUNCT
m-1112	1992	64	issn	issn	PROPN
m-1112	1992	65	:	:	PUNCT
m-1112	1992	66	2992	2992	NUM
m-1112	1992	67	-	-	SYM
m-1112	1992	68	4421	4421	NUM
m-1112	1992	69	)	)	PUNCT
m-1112	1992	70	volume	volume	NOUN
m-1112	1992	71	08	08	NUM
m-1112	1993	1	|	|	ADV
m-1112	1993	2	issue	issue	NOUN
m-1112	1993	3	08	08	NUM
m-1112	1994	1	|	|	ADV
m-1112	1994	2	august	august	PROPN
m-1112	1994	3	2025	2025	NUM
m-1112	1994	4	|	|	ADV
m-1112	1994	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	1994	6	ijo	ijo	PROPN
m-1112	1994	7	journals	journal	NOUN
m-1112	1994	8	71	71	NUM
m-1112	1994	9	the	the	DET
m-1112	1994	10	fundamental	fundamental	ADJ
m-1112	1994	11	particles	particle	NOUN
m-1112	1994	12	origination	origination	NOUN
m-1112	1994	13	mechanism	mechanism	NOUN
m-1112	1994	14	in	in	ADP
m-1112	1994	15	mfmf	mfmf	PROPN
m-1112	1994	16	pns	pns	PROPN
m-1112	1994	17	caves	cave	NOUN
m-1112	1994	18	.	.	PUNCT
m-1112	1995	1	it	it	PRON
m-1112	1995	2	was	be	AUX
m-1112	1995	3	shown	show	VERB
m-1112	1995	4	that	that	SCONJ
m-1112	1995	5	the	the	DET
m-1112	1995	6	first	first	ADJ
m-1112	1995	7	path	path	NOUN
m-1112	1995	8	is	be	AUX
m-1112	1995	9	gravity	gravity	NOUN
m-1112	1995	10	,	,	PUNCT
m-1112	1995	11	g	g	NOUN
m-1112	1995	12	,	,	PUNCT
m-1112	1995	13	and	and	CCONJ
m-1112	1995	14	original	original	ADJ
m-1112	1995	15	field	field	NOUN
m-1112	1995	16	-	-	PUNCT
m-1112	1995	17	lines	line	NOUN
m-1112	1995	18	of	of	ADP
m-1112	1995	19	force	force	NOUN
m-1112	1995	20	,	,	PUNCT
m-1112	1995	21	g	g	PROPN
m-1112	1995	22	,	,	PUNCT
m-1112	1995	23	are	be	AUX
m-1112	1995	24	distorted	distort	VERB
m-1112	1995	25	by	by	ADP
m-1112	1995	26	these	these	DET
m-1112	1995	27	charges	charge	NOUN
m-1112	1995	28	,	,	PUNCT
m-1112	1995	29	local	local	ADJ
m-1112	1995	30	-	-	PUNCT
m-1112	1995	31	coefficients	coefficient	NOUN
m-1112	1995	32	,	,	PUNCT
m-1112	1995	33	the	the	DET
m-1112	1995	34	layers	layer	NOUN
m-1112	1995	35	following	follow	VERB
m-1112	1995	36	newton`s	newton`s	NOUN
m-1112	1995	37	laws	law	NOUN
m-1112	1995	38	.	.	PUNCT
m-1112	1996	1	the	the	DET
m-1112	1996	2	original	original	ADJ
m-1112	1996	3	field	field	NOUN
m-1112	1996	4	-	-	PUNCT
m-1112	1996	5	lines	line	NOUN
m-1112	1996	6	terminate	terminate	NOUN
m-1112	1996	7	at	at	ADP
m-1112	1996	8	the	the	DET
m-1112	1996	9	surface	surface	NOUN
m-1112	1996	10	on	on	ADP
m-1112	1996	11	one	one	NUM
m-1112	1996	12	side	side	NOUN
m-1112	1996	13	of	of	ADP
m-1112	1996	14	the	the	DET
m-1112	1996	15	medium	medium	NOUN
m-1112	1996	16	,	,	PUNCT
m-1112	1996	17	and	and	CCONJ
m-1112	1996	18	new	new	ADJ
m-1112	1996	19	field	field	NOUN
m-1112	1996	20	lines	line	NOUN
m-1112	1996	21	originate	originate	VERB
m-1112	1996	22	from	from	ADP
m-1112	1996	23	the	the	DET
m-1112	1996	24	other	other	ADJ
m-1112	1996	25	side	side	NOUN
m-1112	1996	26	of	of	ADP
m-1112	1996	27	it	it	PRON
m-1112	1996	28	.	.	PUNCT
m-1112	1997	1	it	it	PRON
m-1112	1997	2	was	be	AUX
m-1112	1997	3	shown	show	VERB
m-1112	1997	4	that	that	SCONJ
m-1112	1997	5	the	the	DET
m-1112	1997	6	momentum	momentum	NOUN
m-1112	1997	7	vector	vector	NOUN
m-1112	1997	8	,	,	PUNCT
m-1112	1997	9	�	�	PROPN
m-1112	1997	10	̅	̅	NOUN
m-1112	1997	11	�	�	PROPN
m-1112	1997	12	,	,	PUNCT
m-1112	1997	13	is	be	AUX
m-1112	1997	14	equal	equal	ADJ
m-1112	1997	15	to	to	PART
m-1112	1997	16	spin	spin	VERB
m-1112	1997	17	s	s	PRON
m-1112	1997	18	,	,	PUNCT
m-1112	1997	19	because	because	SCONJ
m-1112	1997	20	it	it	PRON
m-1112	1997	21	is	be	AUX
m-1112	1997	22	following	follow	VERB
m-1112	1997	23	the	the	DET
m-1112	1997	24	stationary	stationary	ADJ
m-1112	1997	25	wave	wave	NOUN
m-1112	1997	26	nodes	nod	VERB
m-1112	1997	27	principle	principle	NOUN
m-1112	1997	28	in	in	ADP
m-1112	1997	29	the	the	DET
m-1112	1997	30	material	material	NOUN
m-1112	1997	31	-	-	PUNCT
m-1112	1997	32	points	point	NOUN
m-1112	1997	33	creating	create	VERB
m-1112	1997	34	the	the	DET
m-1112	1997	35	minimum	minimum	ADJ
m-1112	1997	36	quantized	quantize	VERB
m-1112	1997	37	energy	energy	NOUN
m-1112	1997	38	which	which	PRON
m-1112	1997	39	is	be	AUX
m-1112	1997	40	conserved	conserve	VERB
m-1112	1997	41	in	in	ADP
m-1112	1997	42	lobes	lobe	NOUN
m-1112	1997	43	.	.	PUNCT
m-1112	1998	1	this	this	DET
m-1112	1998	2	property	property	NOUN
m-1112	1998	3	is	be	AUX
m-1112	1998	4	extended	extend	VERB
m-1112	1998	5	also	also	ADV
m-1112	1998	6	to	to	ADP
m-1112	1998	7	the	the	DET
m-1112	1998	8	number	number	NOUN
m-1112	1998	9	of	of	ADP
m-1112	1998	10	lobes	lobe	NOUN
m-1112	1998	11	as	as	ADV
m-1112	1998	12	well	well	ADV
m-1112	1998	13	as	as	ADP
m-1112	1998	14	to	to	ADP
m-1112	1998	15	,	,	PUNCT
m-1112	1998	16	π	π	INTJ
m-1112	1998	17	,	,	PUNCT
m-1112	1998	18	number	number	NOUN
m-1112	1998	19	as	as	ADP
m-1112	1998	20	velocity	velocity	NOUN
m-1112	1998	21	{	{	PUNCT
m-1112	1998	22	v	v	NOUN
m-1112	1998	23	=	=	SYM
m-1112	1998	24	n.π.c	n.π.c	NOUN
m-1112	1998	25	}	}	PUNCT
m-1112	1998	26	which	which	PRON
m-1112	1998	27	is	be	AUX
m-1112	1998	28	the	the	DET
m-1112	1998	29	minimum	minimum	ADJ
m-1112	1998	30	number	number	NOUN
m-1112	1998	31	relating	relate	VERB
m-1112	1998	32	lines	line	NOUN
m-1112	1998	33	and	and	CCONJ
m-1112	1998	34	surfaces	surface	NOUN
m-1112	1998	35	.	.	PUNCT
m-1112	1999	1	analogous	analogous	ADJ
m-1112	1999	2	happens	happen	VERB
m-1112	1999	3	in	in	ADP
m-1112	1999	4	equation	equation	NOUN
m-1112	1999	5	when	when	SCONJ
m-1112	1999	6	v	v	X
m-1112	1999	7	=	=	SYM
m-1112	1999	8	c	c	NOUN
m-1112	1999	9	,	,	PUNCT
m-1112	1999	10	and	and	CCONJ
m-1112	1999	11	→	→	SYM
m-1112	1999	12	r	r	NOUN
m-1112	1999	13	=	=	SYM
m-1112	1999	14	c	c	NOUN
m-1112	1999	15	.	.	PUNCT
m-1112	2000	1	from	from	ADP
m-1112	2000	2	inner	inner	ADJ
m-1112	2000	3	-	-	PUNCT
m-1112	2000	4	velocity	velocity	NOUN
m-1112	2000	5	equation	equation	NOUN
m-1112	2000	6	v	v	NOUN
m-1112	2000	7	=	=	PUNCT
m-1112	2000	8	w.r	w.r	PROPN
m-1112	2000	9	=	=	SYM
m-1112	2000	10	(	(	PUNCT
m-1112	2000	11	2π	2π	PROPN
m-1112	2000	12	/	/	PUNCT
m-1112	2000	13	t).r	t).r	NUM
m-1112	2000	14	=	=	SYM
m-1112	2000	15	2π.f1	2π.f1	NUM
m-1112	2000	16	.	.	PUNCT
m-1112	2001	1	r	r	NOUN
m-1112	2001	2	,	,	PUNCT
m-1112	2001	3	of	of	ADP
m-1112	2001	4	fundamental	fundamental	ADJ
m-1112	2001	5	frequency	frequency	NOUN
m-1112	2001	6	f1	f1	NOUN
m-1112	2001	7	,	,	PUNCT
m-1112	2001	8	of	of	ADP
m-1112	2001	9	wavelength	wavelength	NOUN
m-1112	2001	10	λ	λ	PROPN
m-1112	2001	11	=	=	SYM
m-1112	2001	12	c.t	c.t	PROPN
m-1112	2001	13	=	=	SYM
m-1112	2001	14	c	c	PROPN
m-1112	2001	15	/	/	SYM
m-1112	2001	16	f1	f1	NOUN
m-1112	2001	17	,	,	PUNCT
m-1112	2001	18	and	and	CCONJ
m-1112	2001	19	cave	cave	PROPN
m-1112	2001	20	r	r	NOUN
m-1112	2001	21	=	=	SYM
m-1112	2001	22	n.[λ/2	n.[λ/2	PROPN
m-1112	2001	23	]	]	PUNCT
m-1112	2001	24	,	,	PUNCT
m-1112	2001	25	then	then	ADV
m-1112	2001	26	r	r	NOUN
m-1112	2001	27	=	=	SYM
m-1112	2001	28	n.(c	n.(c	PROPN
m-1112	2001	29	/2f1	/2f1	PUNCT
m-1112	2001	30	)	)	PUNCT
m-1112	2001	31	and	and	CCONJ
m-1112	2001	32	v	v	X
m-1112	2001	33	=	=	SYM
m-1112	2001	34	2π.f1	2π.f1	NUM
m-1112	2001	35	.	.	PUNCT
m-1112	2002	1	[	[	X
m-1112	2002	2	n.	n.	NOUN
m-1112	2002	3	c	c	PROPN
m-1112	2002	4	/	/	SYM
m-1112	2002	5	2f1	2f1	PROPN
m-1112	2002	6	]	]	X
m-1112	2002	7	=	=	PUNCT
m-1112	2002	8	n.π.c	n.π.c	ADJ
m-1112	2002	9	or	or	CCONJ
m-1112	2002	10	v	v	NOUN
m-1112	2002	11	=	=	SYM
m-1112	2002	12	n	n	NOUN
m-1112	2002	13	.	.	PUNCT
m-1112	2003	1	π	π	X
m-1112	2003	2	.	.	PUNCT
m-1112	2004	1	c	c	X
m-1112	2004	2	…	…	PUNCT
m-1112	2004	3	…	…	PUNCT
m-1112	2004	4	..	..	PUNCT
m-1112	2004	5	(	(	PUNCT
m-1112	2004	6	π	π	X
m-1112	2004	7	)	)	PUNCT
m-1112	2004	8	equation	equation	NOUN
m-1112	2004	9	(	(	PUNCT
m-1112	2004	10	π	π	NOUN
m-1112	2004	11	)	)	PUNCT
m-1112	2004	12	shows	show	VERB
m-1112	2004	13	that	that	SCONJ
m-1112	2004	14	velocities	velocity	NOUN
m-1112	2004	15	in	in	ADP
m-1112	2004	16	lobes	lobe	NOUN
m-1112	2004	17	are	be	AUX
m-1112	2004	18	,	,	PUNCT
m-1112	2004	19	n.π	n.π	PROPN
m-1112	2004	20	times	time	NOUN
m-1112	2004	21	that	that	PRON
m-1112	2004	22	of	of	ADP
m-1112	2004	23	light	light	NOUN
m-1112	2004	24	,	,	PUNCT
m-1112	2004	25	following	follow	VERB
m-1112	2004	26	,	,	PUNCT
m-1112	2004	27	π	π	PROPN
m-1112	2004	28	,	,	PUNCT
m-1112	2004	29	number	number	NOUN
m-1112	2004	30	in	in	ADP
m-1112	2004	31	circle	circle	NOUN
m-1112	2004	32	,	,	PUNCT
m-1112	2004	33	i.e.	i.e.	X
m-1112	2004	34	in	in	ADP
m-1112	2004	35	material	material	NOUN
m-1112	2004	36	-	-	PUNCT
m-1112	2004	37	points	point	NOUN
m-1112	2004	38	exist	exist	VERB
m-1112	2004	39	velocities	velocity	NOUN
m-1112	2004	40	multi	multi	NOUN
m-1112	2004	41	-	-	NOUN
m-1112	2004	42	times	times	ADJ
m-1112	2004	43	that	that	PRON
m-1112	2004	44	of	of	ADP
m-1112	2004	45	light	light	NOUN
m-1112	2004	46	and	and	CCONJ
m-1112	2004	47	the	the	DET
m-1112	2004	48	minimum	minimum	ADJ
m-1112	2004	49	surface	surface	NOUN
m-1112	2004	50	-	-	PUNCT
m-1112	2004	51	constant	constant	ADJ
m-1112	2004	52	,	,	PUNCT
m-1112	2004	53	unit	unit	NOUN
m-1112	2004	54	π	π	NOUN
m-1112	2004	55	,	,	PUNCT
m-1112	2004	56	or	or	CCONJ
m-1112	2004	57	the	the	DET
m-1112	2004	58	growth	growth	NOUN
m-1112	2004	59	of	of	ADP
m-1112	2004	60	the	the	DET
m-1112	2004	61	velocity	velocity	NOUN
m-1112	2004	62	-	-	PUNCT
m-1112	2004	63	vectors	vector	NOUN
m-1112	2004	64	occurs	occur	VERB
m-1112	2004	65	in	in	ADP
m-1112	2004	66	lobes	lobe	NOUN
m-1112	2004	67	by	by	ADP
m-1112	2004	68	following	follow	VERB
m-1112	2004	69	the	the	DET
m-1112	2004	70	logarithm	logarithm	NOUN
m-1112	2004	71	laws	law	NOUN
m-1112	2004	72	of	of	ADP
m-1112	2004	73	energy	energy	NOUN
m-1112	2004	74	-	-	PUNCT
m-1112	2004	75	constant	constant	ADJ
m-1112	2004	76	c	c	NOUN
m-1112	2004	77	which	which	PRON
m-1112	2004	78	acts	act	VERB
m-1112	2004	79	on	on	ADP
m-1112	2004	80	space	space	NOUN
m-1112	2004	81	constant	constant	ADJ
m-1112	2004	82	π	π	PROPN
m-1112	2004	83	.	.	PUNCT
m-1112	2005	1	from	from	ADP
m-1112	2005	2	velocity	velocity	NOUN
m-1112	2005	3	,	,	PUNCT
m-1112	2005	4	v	v	NOUN
m-1112	2005	5	=	=	SYM
m-1112	2005	6	n.π.c	n.π.c	NOUN
m-1112	2005	7	,	,	PUNCT
m-1112	2005	8	is	be	AUX
m-1112	2005	9	seen	see	VERB
m-1112	2005	10	that	that	SCONJ
m-1112	2005	11	light	light	ADJ
m-1112	2005	12	-	-	PUNCT
m-1112	2005	13	velocity	velocity	NOUN
m-1112	2005	14	is	be	AUX
m-1112	2005	15	the	the	DET
m-1112	2005	16	quantum	quantum	NOUN
m-1112	2005	17	of	of	ADP
m-1112	2005	18	unit	unit	NOUN
m-1112	2005	19	-	-	PUNCT
m-1112	2005	20	velocity	velocity	NOUN
m-1112	2005	21	in	in	ADP
m-1112	2005	22	planck`s	planck`s	NOUN
m-1112	2005	23	length	length	NOUN
m-1112	2005	24	.	.	PUNCT
m-1112	2006	1	the	the	DET
m-1112	2006	2	why	why	SCONJ
m-1112	2006	3	velocity	velocity	NOUN
m-1112	2006	4	c	c	PROPN
m-1112	2006	5	and	and	CCONJ
m-1112	2006	6	π	π	PROPN
m-1112	2006	7	,	,	PUNCT
m-1112	2006	8	is	be	AUX
m-1112	2006	9	such	such	ADJ
m-1112	2006	10	in	in	ADP
m-1112	2006	11	[	[	PUNCT
m-1112	2006	12	42	42	NUM
m-1112	2006	13	-	-	SYM
m-1112	2006	14	51	51	NUM
m-1112	2006	15	-	-	SYM
m-1112	2006	16	63	63	NUM
m-1112	2006	17	]	]	PUNCT
m-1112	2006	18	kepler`s	kepler`s	NOUN
m-1112	2006	19	laws	law	NOUN
m-1112	2006	20	→	→	PUNCT
m-1112	2006	21	explain	explain	VERB
m-1112	2006	22	how	how	SCONJ
m-1112	2006	23	the	the	DET
m-1112	2006	24	planets	planet	NOUN
m-1112	2006	25	move	move	VERB
m-1112	2006	26	around	around	ADP
m-1112	2006	27	the	the	DET
m-1112	2006	28	sun	sun	NOUN
m-1112	2006	29	but	but	CCONJ
m-1112	2006	30	not	not	PART
m-1112	2006	31	the	the	DET
m-1112	2006	32	why	why	SCONJ
m-1112	2006	33	.	.	PUNCT
m-1112	2007	1	newton`s	newton`s	NOUN
m-1112	2007	2	laws	law	NOUN
m-1112	2007	3	→	→	PUNCT
m-1112	2007	4	explain	explain	VERB
m-1112	2007	5	the	the	DET
m-1112	2007	6	why	why	SCONJ
m-1112	2007	7	by	by	ADP
m-1112	2007	8	filling	fill	VERB
m-1112	2007	9	this	this	DET
m-1112	2007	10	gap	gap	NOUN
m-1112	2007	11	by	by	ADP
m-1112	2007	12	a	a	DET
m-1112	2007	13	force	force	NOUN
m-1112	2007	14	f	f	PROPN
m-1112	2007	15	=	=	SYM
m-1112	2007	16	g.m	g.m	PROPN
m-1112	2007	17	1.m	1.m	PROPN
m-1112	2007	18	2/	2/	NUM
m-1112	2007	19	r²	r²	NOUN
m-1112	2007	20	.	.	PUNCT
m-1112	2008	1	acting	act	VERB
m-1112	2008	2	instantly	instantly	ADV
m-1112	2008	3	between	between	ADP
m-1112	2008	4	the	the	DET
m-1112	2008	5	bodies	body	NOUN
m-1112	2008	6	that	that	PRON
m-1112	2008	7	are	be	AUX
m-1112	2008	8	moving	move	VERB
m-1112	2008	9	around	around	ADP
m-1112	2008	10	each	each	DET
m-1112	2008	11	other	other	ADJ
m-1112	2008	12	but	but	CCONJ
m-1112	2008	13	not	not	PART
m-1112	2008	14	their	their	PRON
m-1112	2008	15	nature	nature	NOUN
m-1112	2008	16	and	and	CCONJ
m-1112	2008	17	not	not	PART
m-1112	2008	18	the	the	DET
m-1112	2008	19	how	how	SCONJ
m-1112	2008	20	force	force	NOUN
m-1112	2008	21	is	be	AUX
m-1112	2008	22	acting	act	VERB
m-1112	2008	23	.	.	PUNCT
m-1112	2009	1	markos	markos	ADJ
m-1112	2009	2	-	-	PUNCT
m-1112	2009	3	spaces	space	NOUN
m-1112	2009	4	→	→	PUNCT
m-1112	2009	5	explain	explain	VERB
m-1112	2009	6	the	the	DET
m-1112	2009	7	why	why	SCONJ
m-1112	2009	8	by	by	ADP
m-1112	2009	9	filling	fill	VERB
m-1112	2009	10	the	the	DET
m-1112	2009	11	gap	gap	NOUN
m-1112	2009	12	with	with	ADP
m-1112	2009	13	a	a	DET
m-1112	2009	14	double	double	ADJ
m-1112	2009	15	ocean	ocean	NOUN
m-1112	2009	16	of	of	ADP
m-1112	2009	17	the	the	DET
m-1112	2009	18	pointy	pointy	NOUN
m-1112	2009	19	-	-	PUNCT
m-1112	2009	20	spinningmaterial	spinningmaterial	ADJ
m-1112	2009	21	-	-	PUNCT
m-1112	2009	22	points	point	NOUN
m-1112	2009	23	,	,	PUNCT
m-1112	2009	24	becoming	become	VERB
m-1112	2009	25	from	from	ADP
m-1112	2009	26	the	the	DET
m-1112	2009	27	stationarymaterial	stationarymaterial	ADJ
m-1112	2009	28	-	-	PUNCT
m-1112	2009	29	points	point	NOUN
m-1112	2009	30	,	,	PUNCT
m-1112	2009	31	photons	photon	NOUN
m-1112	2009	32	or	or	CCONJ
m-1112	2009	33	electrons	electron	NOUN
m-1112	2009	34	,	,	PUNCT
m-1112	2009	35	and	and	CCONJ
m-1112	2009	36	from	from	ADP
m-1112	2009	37	the	the	DET
m-1112	2009	38	moving	move	VERB
m-1112	2009	39	-	-	PUNCT
m-1112	2009	40	energystorages	energystorage	NOUN
m-1112	2009	41	,	,	PUNCT
m-1112	2009	42	the	the	DET
m-1112	2009	43	photons	photon	NOUN
m-1112	2009	44	,	,	PUNCT
m-1112	2009	45	which	which	PRON
m-1112	2009	46	orientate	orientate	VERB
m-1112	2009	47	and	and	CCONJ
m-1112	2009	48	re	re	VERB
m-1112	2009	49	-	-	VERB
m-1112	2009	50	orientate	orientate	VERB
m-1112	2009	51	the	the	DET
m-1112	2009	52	stationary	stationary	NOUN
m-1112	2009	53	-	-	PUNCT
m-1112	2009	54	spins	spin	NOUN
m-1112	2009	55	,	,	PUNCT
m-1112	2009	56	and	and	CCONJ
m-1112	2009	57	explain	explain	VERB
m-1112	2009	58	the	the	DET
m-1112	2009	59	how	how	SCONJ
m-1112	2009	60	and	and	CCONJ
m-1112	2009	61	the	the	PRON
m-1112	2009	62	why	why	SCONJ
m-1112	2009	63	all	all	DET
m-1112	2009	64	motions	motion	NOUN
m-1112	2009	65	follow	follow	VERB
m-1112	2009	66	the	the	DET
m-1112	2009	67	ubiquity	ubiquity	NOUN
m-1112	2009	68	of	of	ADP
m-1112	2009	69	the	the	DET
m-1112	2009	70	electromagnetism	electromagnetism	NOUN
m-1112	2009	71	,	,	PUNCT
m-1112	2009	72	starting	start	VERB
m-1112	2009	73	from	from	ADP
m-1112	2009	74	the	the	DET
m-1112	2009	75	primary	primary	ADJ
m-1112	2009	76	material	material	NOUN
m-1112	2009	77	-	-	PUNCT
m-1112	2009	78	points	point	NOUN
m-1112	2009	79	,	,	PUNCT
m-1112	2009	80	photons	photon	NOUN
m-1112	2009	81	,	,	PUNCT
m-1112	2009	82	which	which	PRON
m-1112	2009	83	through	through	ADP
m-1112	2009	84	the	the	DET
m-1112	2009	85	golden	golden	ADJ
m-1112	2009	86	-	-	PUNCT
m-1112	2009	87	ratio	ratio	NOUN
m-1112	2009	88	-	-	PUNCT
m-1112	2009	89	frequency	frequency	NOUN
m-1112	2009	90	-	-	PUNCT
m-1112	2009	91	growth	growth	NOUN
m-1112	2009	92	effect	effect	NOUN
m-1112	2009	93	and	and	CCONJ
m-1112	2009	94	conserve	conserve	VERB
m-1112	2009	95	the	the	DET
m-1112	2009	96	whole	whole	ADJ
m-1112	2009	97	natural	natural	ADJ
m-1112	2009	98	-	-	PUNCT
m-1112	2009	99	world	world	NOUN
m-1112	2009	100	from	from	ADP
m-1112	2009	101	microcosm	microcosm	PROPN
m-1112	2009	102	to	to	ADP
m-1112	2009	103	macrocosm	macrocosm	PROPN
m-1112	2009	104	.	.	PUNCT
m-1112	2010	1	a	a	X
m-1112	2010	2	)	)	PUNCT
m-1112	2010	3	in	in	ADP
m-1112	2010	4	vacuum	vacuum	PROPN
m-1112	2010	5	≡	≡	PROPN
m-1112	2011	1	[	[	X
m-1112	2011	2	10−62	10−62	NUM
m-1112	2011	3	-	-	PUNCT
m-1112	2011	4	10−35	10−35	NOUN
m-1112	2011	5	m	m	NOUN
m-1112	2011	6	]	]	X
m-1112	2011	7	,	,	PUNCT
m-1112	2011	8	the	the	DET
m-1112	2011	9	{	{	PUNCT
m-1112	2011	10	energy	energy	NOUN
m-1112	2011	11	-	-	PUNCT
m-1112	2011	12	space	space	NOUN
m-1112	2011	13	-	-	PUNCT
m-1112	2011	14	monad	monad	PROPN
m-1112	2011	15	|	|	NOUN
m-1112	2011	16	�	�	NOUN
m-1112	2011	17	̅	̅	NOUN
m-1112	2011	18	�	�	PROPN
m-1112	2011	19	|	|	ADV
m-1112	2011	20	≡	≡	PROPN
m-1112	2011	21	|ab|},vanishes	|ab|},vanishes	PROPN
m-1112	2011	22	.	.	PUNCT
m-1112	2011	23	b	b	X
m-1112	2011	24	)	)	PUNCT
m-1112	2011	25	in	in	ADP
m-1112	2011	26	vacuum	vacuum	NOUN
m-1112	2011	27	exists	exist	VERB
m-1112	2011	28	only	only	ADV
m-1112	2011	29	pointy	pointy	ADJ
m-1112	2011	30	vibrating	vibrate	VERB
m-1112	2011	31	(	(	PUNCT
m-1112	2011	32	the	the	DET
m-1112	2011	33	circular	circular	ADJ
m-1112	2011	34	motion	motion	NOUN
m-1112	2011	35	only	only	ADV
m-1112	2011	36	)	)	PUNCT
m-1112	2011	37	between	between	ADP
m-1112	2011	38	the	the	DET
m-1112	2011	39	opposite	opposite	ADJ
m-1112	2011	40	dipole	dipole	NOUN
m-1112	2011	41	[	[	X
m-1112	2011	42	⊕	⊕	NOUN
m-1112	2011	43	↻	↻	NOUN
m-1112	2011	44	↺	↺	NOUN
m-1112	2011	45	⊝	⊝	X
m-1112	2011	46	]	]	PUNCT
m-1112	2011	47	generating	generate	VERB
m-1112	2011	48	the	the	DET
m-1112	2011	49	,	,	PUNCT
m-1112	2011	50	w	w	PROPN
m-1112	2011	51	,	,	PUNCT
m-1112	2011	52	b	b	PROPN
m-1112	2011	53	,	,	PUNCT
m-1112	2011	54	momentum	momentum	NOUN
m-1112	2011	55	.	.	PUNCT
m-1112	2012	1	c	c	X
m-1112	2012	2	)	)	PUNCT
m-1112	2012	3	as	as	SCONJ
m-1112	2012	4	unit	unit	NOUN
m-1112	2012	5	-	-	PUNCT
m-1112	2012	6	energy	energy	NOUN
m-1112	2012	7	vectors	vector	NOUN
m-1112	2012	8	�	�	NOUN
m-1112	2012	9	̅	̅	NOUN
m-1112	2012	10	�	�	NOUN
m-1112	2012	11	=	=	SYM
m-1112	2012	12	σ	σ	PROPN
m-1112	2012	13	/	/	SYM
m-1112	2012	14	b̅	b̅	PROPN
m-1112	2012	15	→	→	PUNCT
m-1112	2012	16	exists	exist	VERB
m-1112	2012	17	on	on	ADP
m-1112	2012	18	{	{	PUNCT
m-1112	2012	19	unit	unit	NOUN
m-1112	2012	20	-	-	PUNCT
m-1112	2012	21	space	space	NOUN
m-1112	2012	22	-	-	PUNCT
m-1112	2012	23	monad	monad	PROPN
m-1112	2012	24	|ab|	|ab|	NUM
m-1112	2012	25	≡	≡	PROPN
m-1112	2012	26	|r̅|←	|r̅|←	PROPN
m-1112	2012	27	and	and	CCONJ
m-1112	2012	28	then	then	ADV
m-1112	2012	29	→	→	PUNCT
m-1112	2012	30	{	{	PUNCT
m-1112	2012	31	the	the	DET
m-1112	2012	32	energy	energy	NOUN
m-1112	2012	33	–	–	PUNCT
m-1112	2012	34	space	space	NOUN
m-1112	2013	1	monad	monad	PROPN
m-1112	2013	2	|	|	NOUN
m-1112	2013	3	�	�	PROPN
m-1112	2013	4	̅	̅	NOUN
m-1112	2013	5	�	�	NOUN
m-1112	2013	6	|	|	ADV
m-1112	2013	7	≡	≡	PROPN
m-1112	2013	8	|ab|	|ab|	PROPN
m-1112	2013	9	≡	≡	PROPN
m-1112	2013	10	the	the	DET
m-1112	2013	11	existing	exist	VERB
m-1112	2013	12	universe	universe	NOUN
m-1112	2013	13	}	}	PUNCT
m-1112	2013	14	d	d	X
m-1112	2013	15	)	)	PUNCT
m-1112	2013	16	stpl	stpl	ADJ
m-1112	2013	17	-	-	PUNCT
m-1112	2013	18	line	line	NOUN
m-1112	2013	19	-	-	PUNCT
m-1112	2013	20	machine	machine	NOUN
m-1112	2013	21	is	be	AUX
m-1112	2013	22	the	the	DET
m-1112	2013	23	physical	physical	ADJ
m-1112	2013	24	rotor	rotor	NOUN
m-1112	2013	25	for	for	ADP
m-1112	2013	26	the	the	DET
m-1112	2013	27	cosmic	cosmic	ADJ
m-1112	2013	28	-	-	PUNCT
m-1112	2013	29	particles	particle	NOUN
m-1112	2013	30	origination	origination	NOUN
m-1112	2013	31	.	.	PUNCT
m-1112	2014	1	the	the	DET
m-1112	2014	2	gravitational	gravitational	ADJ
m-1112	2014	3	-	-	PUNCT
m-1112	2014	4	force	force	NOUN
m-1112	2014	5	g	g	NOUN
m-1112	2014	6	,	,	PUNCT
m-1112	2014	7	acting	act	VERB
m-1112	2014	8	in	in	ADP
m-1112	2014	9	the	the	DET
m-1112	2014	10	beyond	beyond	NOUN
m-1112	2014	11	-	-	PUNCT
m-1112	2014	12	planckcave	planckcave	NOUN
m-1112	2014	13	,	,	PUNCT
m-1112	2014	14	and	and	CCONJ
m-1112	2014	15	on	on	ADP
m-1112	2014	16	the	the	DET
m-1112	2014	17	light	light	ADJ
m-1112	2014	18	velocity	velocity	NOUN
m-1112	2014	19	vector	vector	NOUN
m-1112	2014	20	�	�	PROPN
m-1112	2014	21	̅	̅	NOUN
m-1112	2014	22	�	�	PROPN
m-1112	2014	23	,	,	PUNCT
m-1112	2014	24	creates	create	VERB
m-1112	2014	25	electron	electron	NOUN
m-1112	2014	26	-	-	PUNCT
m-1112	2014	27	charge	charge	NOUN
m-1112	2014	28	�	�	PROPN
m-1112	2014	29	̅	̅	NOUN
m-1112	2014	30	�	�	PROPN
m-1112	2014	31	electron	electron	NOUN
m-1112	2014	32	=	=	PUNCT
m-1112	2014	33	g	g	PROPN
m-1112	2014	34	c	c	PROPN
m-1112	2014	35	√2	√2	NOUN
m-1112	2014	36	=	=	PUNCT
m-1112	2014	37	1,574.10−19	1,574.10−19	NUM
m-1112	2014	38	c	c	NOUN
m-1112	2014	39	.	.	PUNCT
m-1112	2015	1	which	which	PRON
m-1112	2015	2	agrees	agree	VERB
m-1112	2015	3	with	with	ADP
m-1112	2015	4	that	that	PRON
m-1112	2015	5	of	of	ADP
m-1112	2015	6	coulomb`s	coulomb`	NOUN
m-1112	2015	7	charge	charge	NOUN
m-1112	2015	8	q̅	q̅	PROPN
m-1112	2015	9	,	,	PUNCT
m-1112	2015	10	and	and	CCONJ
m-1112	2015	11	the	the	DET
m-1112	2015	12	material	material	NOUN
m-1112	2015	13	-	-	PUNCT
m-1112	2015	14	points	point	NOUN
m-1112	2015	15	�	�	NOUN
m-1112	2015	16	̅	̅	NOUN
m-1112	2015	17	�	�	NOUN
m-1112	2015	18	photon=	photon=	NUM
m-1112	2015	19	g	g	PROPN
m-1112	2015	20	√2.f	√2.f	PROPN
m-1112	2015	21	,	,	PUNCT
m-1112	2015	22	while	while	SCONJ
m-1112	2015	23	by	by	ADP
m-1112	2015	24	effecting	effect	VERB
m-1112	2015	25	on	on	ADP
m-1112	2015	26	the	the	DET
m-1112	2015	27	whole	whole	ADJ
m-1112	2015	28	-	-	PUNCT
m-1112	2015	29	planck	planck	NOUN
m-1112	2015	30	-	-	PUNCT
m-1112	2015	31	cave	cave	NOUN
m-1112	2015	32	𝐋	𝐋	PROPN
m-1112	2015	33	𝐏	𝐏	PROPN
m-1112	2015	34	≡	≡	PROPN
m-1112	2015	35	e	e	PROPN
m-1112	2015	36	i	i	PROPN
m-1112	2015	37	.	.	PUNCT
m-1112	2016	1	(	(	PUNCT
m-1112	2016	2	5π/2	5π/2	NUM
m-1112	2016	3	)	)	PUNCT
m-1112	2016	4	.10	.10	NUM
m-1112	2016	5	,	,	PUNCT
m-1112	2016	6	creates	create	VERB
m-1112	2016	7	the	the	DET
m-1112	2016	8	pointy	pointy	ADJ
m-1112	2016	9	-	-	PUNCT
m-1112	2016	10	gravity	gravity	NOUN
m-1112	2016	11	force	force	NOUN
m-1112	2016	12	as	as	SCONJ
m-1112	2016	13	this	this	PRON
m-1112	2016	14	is	be	AUX
m-1112	2016	15	the	the	DET
m-1112	2016	16	ocean	ocean	NOUN
m-1112	2016	17	of	of	ADP
m-1112	2016	18	spins	spin	NOUN
m-1112	2016	19	g̅	g̅	PROPN
m-1112	2016	20	,	,	PUNCT
m-1112	2016	21	and	and	CCONJ
m-1112	2016	22	which	which	DET
m-1112	2016	23	oriented	orient	VERB
m-1112	2016	24	-	-	PUNCT
m-1112	2016	25	spins	spin	NOUN
m-1112	2016	26	,	,	PUNCT
m-1112	2016	27	originate	originate	VERB
m-1112	2016	28	gravity	gravity	NOUN
m-1112	2016	29	�	�	NOUN
m-1112	2016	30	̅	̅	NOUN
m-1112	2016	31	�	�	NOUN
m-1112	2016	32	=	=	PUNCT
m-1112	2017	1	[	[	X
m-1112	2017	2	↓=	↓=	X
m-1112	2017	3	↻	↻	NOUN
m-1112	2017	4	]	]	PUNCT
m-1112	2017	5	,	,	PUNCT
m-1112	2017	6	and	and	CCONJ
m-1112	2017	7	antigravity	antigravity	NOUN
m-1112	2017	8	g	g	NOUN
m-1112	2017	9	=	=	PUNCT
m-1112	2018	1	[	[	X
m-1112	2018	2	↑=	↑=	ADP
m-1112	2018	3	↺	↺	NOUN
m-1112	2018	4	]	]	PUNCT
m-1112	2018	5	as	as	ADP
m-1112	2018	6	electron	electron	NOUN
m-1112	2018	7	e̅	e̅	PRON
m-1112	2018	8	[	[	X
m-1112	2018	9	72	72	NUM
m-1112	2018	10	]	]	PUNCT
m-1112	2018	11	.	.	PUNCT
m-1112	2019	1	the	the	DET
m-1112	2019	2	light	light	ADJ
m-1112	2019	3	-	-	PUNCT
m-1112	2019	4	velocity	velocity	NOUN
m-1112	2019	5	c̅	c̅	PROPN
m-1112	2019	6	of	of	ADP
m-1112	2019	7	photons	photon	NOUN
m-1112	2019	8	becoming	become	VERB
m-1112	2019	9	from	from	ADP
m-1112	2019	10	the	the	DET
m-1112	2019	11	action	action	NOUN
m-1112	2019	12	of	of	ADP
m-1112	2019	13	g	g	NOUN
m-1112	2019	14	on	on	ADP
m-1112	2019	15	planck`s	planck`s	NOUN
m-1112	2019	16	length	length	NOUN
m-1112	2019	17	,	,	PUNCT
m-1112	2019	18	when	when	SCONJ
m-1112	2019	19	act	act	VERB
m-1112	2019	20	on	on	ADP
m-1112	2019	21	a	a	DET
m-1112	2019	22	-	-	PUNCT
m-1112	2019	23	cave	cave	NOUN
m-1112	2019	24	,	,	PUNCT
m-1112	2019	25	r	r	NOUN
m-1112	2019	26	=	=	SYM
m-1112	2019	27	𝐡	𝐡	NOUN
m-1112	2019	28	𝐜.𝐙𝐜	𝐜.𝐙𝐜	NOUN
m-1112	2019	29	≠	≠	PROPN
m-1112	2019	30	𝐋	𝐋	PROPN
m-1112	2019	31	𝐏	𝐏	PROPN
m-1112	2019	32	then	then	ADV
m-1112	2019	33	originates	originate	VERB
m-1112	2019	34	the	the	DET
m-1112	2019	35	hydrogen	hydrogen	NOUN
m-1112	2019	36	-	-	PUNCT
m-1112	2019	37	cave	cave	NOUN
m-1112	2019	38	e	e	NOUN
m-1112	2020	1	=	=	SYM
m-1112	2020	2	h	h	PROPN
m-1112	2020	3	fm	fm	NOUN
m-1112	2020	4	,	,	PUNCT
m-1112	2020	5	because	because	SCONJ
m-1112	2020	6	angular	angular	ADJ
m-1112	2020	7	-	-	PUNCT
m-1112	2020	8	momentum	momentum	NOUN
m-1112	2020	9	�	�	NOUN
m-1112	2020	10	̅	̅	NOUN
m-1112	2020	11	�	�	NOUN
m-1112	2020	12	=	=	SYM
m-1112	2020	13	2l	2l	NOUN
m-1112	2020	14	w̅	w̅	PUNCT
m-1112	2021	1	=	=	SYM
m-1112	2021	2	2l	2l	NUM
m-1112	2021	3	2πf	2πf	NOUN
m-1112	2022	1	=	=	PUNCT
m-1112	2023	1	[	[	PUNCT
m-1112	2023	2	2l	2l	NUM
m-1112	2023	3	2π	2π	NOUN
m-1112	2023	4	]	]	PUNCT
m-1112	2023	5	.	.	PUNCT
m-1112	2024	1	[	[	PUNCT
m-1112	2024	2	1	1	NUM
m-1112	2024	3	f	f	NOUN
m-1112	2024	4	]	]	X
m-1112	2024	5	=	=	PUNCT
m-1112	2024	6	constant	constant	ADJ
m-1112	2024	7	2π	2π	NOUN
m-1112	2024	8	[	[	PUNCT
m-1112	2024	9	1	1	NUM
m-1112	2024	10	fm	fm	NOUN
m-1112	2024	11	]	]	PUNCT
m-1112	2024	12	=	=	PUNCT
m-1112	2025	1	spin	spin	NOUN
m-1112	2026	1	[	[	X
m-1112	2026	2	70	70	NUM
m-1112	2026	3	]	]	PUNCT
m-1112	2026	4	.	.	PUNCT
m-1112	2027	1	ijo	ijo	PROPN
m-1112	2027	2	international	international	PROPN
m-1112	2027	3	journal	journal	PROPN
m-1112	2027	4	of	of	ADP
m-1112	2027	5	mathematics	mathematics	PROPN
m-1112	2027	6	(	(	PUNCT
m-1112	2027	7	issn	issn	PROPN
m-1112	2027	8	:	:	PUNCT
m-1112	2027	9	2992	2992	NUM
m-1112	2027	10	-	-	SYM
m-1112	2027	11	4421	4421	NUM
m-1112	2027	12	)	)	PUNCT
m-1112	2027	13	volume	volume	NOUN
m-1112	2027	14	08	08	NUM
m-1112	2028	1	|	|	ADV
m-1112	2028	2	issue	issue	NOUN
m-1112	2028	3	08	08	NUM
m-1112	2029	1	|	|	ADV
m-1112	2029	2	august	august	PROPN
m-1112	2029	3	2025	2025	NUM
m-1112	2029	4	|	|	ADV
m-1112	2029	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2029	6	ijo	ijo	PROPN
m-1112	2029	7	journals	journal	NOUN
m-1112	2029	8	72	72	NUM
m-1112	2029	9	the	the	DET
m-1112	2029	10	fundamental	fundamental	ADJ
m-1112	2029	11	particles	particle	NOUN
m-1112	2029	12	origination	origination	NOUN
m-1112	2029	13	mechanism	mechanism	NOUN
m-1112	2029	14	in	in	ADP
m-1112	2029	15	mfmf	mfmf	PROPN
m-1112	2029	16	pns	pns	PROPN
m-1112	2029	17	caves	cave	NOUN
m-1112	2029	18	.	.	PUNCT
m-1112	2030	1	the	the	DET
m-1112	2030	2	four	four	NUM
m-1112	2030	3	energy	energy	NOUN
m-1112	2030	4	-	-	PUNCT
m-1112	2030	5	space	space	NOUN
m-1112	2030	6	constants	constant	NOUN
m-1112	2030	7	in	in	ADP
m-1112	2030	8	nature	nature	NOUN
m-1112	2030	9	are	be	AUX
m-1112	2030	10	,	,	PUNCT
m-1112	2030	11	[	[	X
m-1112	2030	12	99	99	NUM
m-1112	2030	13	]	]	X
m-1112	2030	14	𝐋	𝐋	PROPN
m-1112	2030	15	𝐏	𝐏	PROPN
m-1112	2030	16	≡	≡	PROPN
m-1112	2030	17	𝐞−i	𝐞−i	PROPN
m-1112	2030	18	.	.	PUNCT
m-1112	2031	1	(	(	PUNCT
m-1112	2031	2	π	π	PROPN
m-1112	2031	3	2	2	NUM
m-1112	2031	4	+2kπ).b	+2kπ).b	ADP
m-1112	2031	5	≡	≡	PROPN
m-1112	2031	6	ei	ei	PROPN
m-1112	2031	7	.(5π/2	.(5π/2	PROPN
m-1112	2031	8	)	)	PUNCT
m-1112	2031	9	.10	.10	NUM
m-1112	2031	10	≡	≡	PROPN
m-1112	2031	11	ei	ei	X
m-1112	2031	12	.(-5π/2	.(-5π/2	PROPN
m-1112	2031	13	)	)	PUNCT
m-1112	2031	14	.10	.10	NUM
m-1112	2031	15	≡	≡	PROPN
m-1112	2031	16	{	{	PUNCT
m-1112	2031	17	√3.π	√3.π	PROPN
m-1112	2031	18	.	.	PUNCT
m-1112	2032	1	1,616199.10−35	1,616199.10−35	NUM
m-1112	2032	2	m	m	VERB
m-1112	2032	3	}	}	PUNCT
m-1112	2032	4	→	→	PUNCT
m-1112	2032	5	and	and	CCONJ
m-1112	2032	6	is	be	AUX
m-1112	2032	7	the	the	DET
m-1112	2032	8	planck`s	planck`s	NOUN
m-1112	2032	9	length	length	NOUN
m-1112	2032	10	cave	cave	NOUN
m-1112	2032	11	,	,	PUNCT
m-1112	2032	12	g	g	PROPN
m-1112	2032	13	≡	≡	PROPN
m-1112	2032	14	𝐓²	𝐓²	VERB
m-1112	2032	15	𝐚³	𝐚³	PROPN
m-1112	2032	16	≡	≡	PROPN
m-1112	2032	17	𝟏	𝟏	PROPN
m-1112	2033	1	f	f	PROPN
m-1112	2033	2	²n.𝐚³	²n.𝐚³	NOUN
m-1112	2033	3	≡	≡	PROPN
m-1112	2033	4	9	9	NUM
m-1112	2033	5	,	,	PUNCT
m-1112	2033	6	8076941	8076941	NUM
m-1112	2033	7	→	→	PUNCT
m-1112	2033	8	the	the	DET
m-1112	2033	9	minimum	minimum	ADJ
m-1112	2033	10	granular	granular	ADJ
m-1112	2033	11	quantized	quantize	VERB
m-1112	2033	12	energy	energy	NOUN
m-1112	2033	13	,	,	PUNCT
m-1112	2033	14	from	from	ADP
m-1112	2033	15	the	the	DET
m-1112	2033	16	gravity	gravity	NOUN
m-1112	2033	17	frequency	frequency	NOUN
m-1112	2033	18	fg	fg	NOUN
m-1112	2033	19	,	,	PUNCT
m-1112	2033	20	representing	represent	VERB
m-1112	2033	21	the	the	DET
m-1112	2033	22	bedding	bed	VERB
m-1112	2033	23	-	-	PUNCT
m-1112	2033	24	quantum	quantum	NOUN
m-1112	2033	25	-	-	PUNCT
m-1112	2033	26	raw	raw	ADJ
m-1112	2033	27	-	-	PUNCT
m-1112	2033	28	material	material	NOUN
m-1112	2033	29	of	of	ADP
m-1112	2033	30	force	force	NOUN
m-1112	2033	31	g	g	PROPN
m-1112	2033	32	,	,	PUNCT
m-1112	2033	33	on	on	ADP
m-1112	2033	34	all	all	DET
m-1112	2033	35	energy	energy	NOUN
m-1112	2033	36	structures	structure	NOUN
m-1112	2033	37	.	.	PUNCT
m-1112	2034	1	g	g	PROPN
m-1112	2034	2	≡	≡	PROPN
m-1112	2034	3	σ.𝚽³	σ.𝚽³	X
m-1112	2034	4	≡	≡	PROPN
m-1112	2034	5	g.	g.	PROPN
m-1112	2034	6	ke	ke	PROPN
m-1112	2034	7	≡	≡	PROPN
m-1112	2034	8	g	g	PROPN
m-1112	2034	9	.[gl	.[gl	PROPN
m-1112	2034	10	kl	kl	X
m-1112	2034	11	]	]	PUNCT
m-1112	2034	12	≡	≡	PROPN
m-1112	2034	13	[	[	PUNCT
m-1112	2034	14	t²p	t²p	X
m-1112	2034	15	𝐚³	𝐚³	ADJ
m-1112	2034	16	]	]	PUNCT
m-1112	2034	17	.[gl	.[gl	PUNCT
m-1112	2035	1	kl	kl	X
m-1112	2035	2	]	]	PUNCT
m-1112	2035	3	≡	≡	PROPN
m-1112	2035	4	9,8076941	9,8076941	PROPN
m-1112	2035	5	*	*	SYM
m-1112	2035	6	6,8116.10−12	6,8116.10−12	NUM
m-1112	2035	7	≡	≡	PROPN
m-1112	2035	8	6,68056.𝟏𝟎−𝟏𝟏	6,68056.𝟏𝟎−𝟏𝟏	NUM
m-1112	2035	9	m3/	m3/	PROPN
m-1112	2035	10	n.s²	n.s²	ADV
m-1112	2035	11	the	the	DET
m-1112	2035	12	pulling	pull	VERB
m-1112	2035	13	and	and	CCONJ
m-1112	2035	14	cohesive	cohesive	ADJ
m-1112	2035	15	bond	bond	NOUN
m-1112	2035	16	,	,	PUNCT
m-1112	2035	17	of	of	ADP
m-1112	2035	18	all	all	DET
m-1112	2035	19	the	the	DET
m-1112	2035	20	quantized	quantize	VERB
m-1112	2035	21	-	-	PUNCT
m-1112	2035	22	energy	energy	NOUN
m-1112	2035	23	-	-	PUNCT
m-1112	2035	24	structures	structure	NOUN
m-1112	2035	25	in	in	ADP
m-1112	2035	26	all	all	DET
m-1112	2035	27	spaces	space	NOUN
m-1112	2035	28	.	.	PUNCT
m-1112	2036	1	𝐟𝐧	𝐟𝐧	ADP
m-1112	2036	2	≡	≡	PROPN
m-1112	2036	3	{	{	PUNCT
m-1112	2037	1	[	[	X
m-1112	2037	2	s	s	X
m-1112	2037	3	≡	≡	PROPN
m-1112	2037	4	bp	bp	PROPN
m-1112	2037	5	≡	≡	PROPN
m-1112	2037	6	em	em	PROPN
m-1112	2037	7	-	-	PUNCT
m-1112	2037	8	r	r	NOUN
m-1112	2037	9	≡	≡	PROPN
m-1112	2037	10	f1	f1	NOUN
m-1112	2037	11	=	=	SYM
m-1112	2037	12	n	n	NOUN
m-1112	2037	13	,	,	PUNCT
m-1112	2037	14	f2	f2	ADV
m-1112	2037	15	,	,	PUNCT
m-1112	2037	16	f3	f3	PROPN
m-1112	2037	17	,	,	PUNCT
m-1112	2037	18	fd	fd	X
m-1112	2037	19	,	,	PUNCT
m-1112	2037	20	,	,	PUNCT
m-1112	2037	21	f	f	PROPN
m-1112	2037	22	n	n	CCONJ
m-1112	2037	23	]	]	X
m-1112	2037	24	≡	≡	PROPN
m-1112	2037	25	n	n	PROPN
m-1112	2037	26	(	(	PUNCT
m-1112	2037	27	1+√5)σ	1+√5)σ	NUM
m-1112	2037	28	4πr	4πr	NOUN
m-1112	2037	29	=	=	PUNCT
m-1112	2037	30	nσ.b̅	nσ.b̅	ADJ
m-1112	2037	31	2	2	NUM
m-1112	2037	32	r²	r²	NOUN
m-1112	2037	33	and	and	CCONJ
m-1112	2037	34	from	from	ADP
m-1112	2037	35	cave	cave	PROPN
m-1112	2037	36	𝛌𝐍	𝛌𝐍	NOUN
m-1112	2037	37	=	=	PUNCT
m-1112	2038	1	4𝜋.r	4𝜋.r	PROPN
m-1112	2038	2	c	c	NOUN
m-1112	2038	3	nσ.(1+√5	nσ.(1+√5	PROPN
m-1112	2038	4	)	)	PUNCT
m-1112	2038	5	=	=	SYM
m-1112	2038	6	𝜋2.𝑟	𝜋2.𝑟	NOUN
m-1112	2038	7	4	4	NUM
m-1112	2038	8	c	c	NOUN
m-1112	2038	9	n.b̅	n.b̅	PROPN
m-1112	2038	10	]	]	PUNCT
m-1112	2038	11	}	}	PUNCT
m-1112	2038	12	,	,	PUNCT
m-1112	2038	13	the	the	DET
m-1112	2038	14	amount	amount	NOUN
m-1112	2038	15	of	of	ADP
m-1112	2038	16	energy	energy	NOUN
m-1112	2038	17	,	,	PUNCT
m-1112	2038	18	the	the	DET
m-1112	2038	19	unit	unit	NOUN
m-1112	2038	20	meter	meter	NOUN
m-1112	2038	21	of	of	ADP
m-1112	2038	22	motion	motion	NOUN
m-1112	2038	23	,	,	PUNCT
m-1112	2038	24	in	in	ADP
m-1112	2038	25	the	the	DET
m-1112	2038	26	torsional	torsional	ADJ
m-1112	2038	27	and	and	CCONJ
m-1112	2038	28	resonance	resonance	NOUN
m-1112	2038	29	-	-	PUNCT
m-1112	2038	30	augmented	augment	VERB
m-1112	2038	31	-	-	PUNCT
m-1112	2038	32	golden	golden	ADJ
m-1112	2038	33	-	-	PUNCT
m-1112	2038	34	ratio	ratio	NOUN
m-1112	2038	35	-	-	PUNCT
m-1112	2038	36	pattern	pattern	NOUN
m-1112	2038	37	φ	φ	NOUN
m-1112	2038	38	,	,	PUNCT
m-1112	2038	39	and	and	CCONJ
m-1112	2038	40	�	�	PROPN
m-1112	2038	41	̅	̅	NOUN
m-1112	2038	42	�	�	PROPN
m-1112	2038	43	=	=	SYM
m-1112	2038	44	�	�	PROPN
m-1112	2038	45	̅	̅	NOUN
m-1112	2038	46	�	�	NOUN
m-1112	2038	47	=	=	SYM
m-1112	2038	48	σ	σ	PROPN
m-1112	2038	49	.	.	PUNCT
m-1112	2039	1	φ	φ	PROPN
m-1112	2039	2	=	=	X
m-1112	2040	1	f	f	PROPN
m-1112	2040	2	a	a	DET
m-1112	2040	3	φ	φ	PROPN
m-1112	2040	4	=	=	PRON
m-1112	2041	1	[	[	PUNCT
m-1112	2041	2	g	g	X
m-1112	2041	3	φ	φ	PROPN
m-1112	2041	4	a	a	X
m-1112	2041	5	]	]	X
m-1112	2041	6	=	=	PUNCT
m-1112	2041	7	[	[	PUNCT
m-1112	2041	8	6,673692	6,673692	NUM
m-1112	2041	9	.10−11.1,6180339887	.10−11.1,6180339887	PROPN
m-1112	2041	10	36	36	NUM
m-1112	2041	11	.10	.10	NUM
m-1112	2041	12	−20	−20	NOUN
m-1112	2041	13	.	.	PUNCT
m-1112	2041	14	]	]	PUNCT
m-1112	2042	1	=	=	PUNCT
m-1112	2043	1	2.9985163	2.9985163	NUM
m-1112	2043	2	.	.	PUNCT
m-1112	2043	3	108	108	NUM
m-1112	2043	4	m	m	NOUN
m-1112	2043	5	.	.	PUNCT
m-1112	2044	1	4c	4c	NOUN
m-1112	2044	2	..	..	PUNCT
m-1112	2044	3	the	the	DET
m-1112	2044	4	origination	origination	NOUN
m-1112	2044	5	of	of	ADP
m-1112	2044	6	electron	electron	NOUN
m-1112	2044	7	-	-	PUNCT
m-1112	2044	8	charge	charge	NOUN
m-1112	2044	9	�	�	PROPN
m-1112	2044	10	̅	̅	NOUN
m-1112	2044	11	�	�	PROPN
m-1112	2044	12	≡	≡	PROPN
m-1112	2044	13	�	�	PROPN
m-1112	2044	14	̅	̅	PROPN
m-1112	2044	15	�	�	PROPN
m-1112	2044	16	:	:	PUNCT
m-1112	2044	17	from	from	ADP
m-1112	2044	18	relation	relation	NOUN
m-1112	2044	19	g	g	PROPN
m-1112	2044	20	≡	≡	PROPN
m-1112	2044	21	g.ke	g.ke	PROPN
m-1112	2044	22	≡	≡	PROPN
m-1112	2044	23	g	g	PROPN
m-1112	2044	24	.[gl	.[gl	PROPN
m-1112	2044	25	kl	kl	X
m-1112	2044	26	]	]	PUNCT
m-1112	2045	1	≡	≡	PROPN
m-1112	2045	2	[	[	PUNCT
m-1112	2045	3	t²p	t²p	X
m-1112	2045	4	𝐚³	𝐚³	ADJ
m-1112	2045	5	]	]	PUNCT
m-1112	2045	6	.[gl	.[gl	PUNCT
m-1112	2046	1	kl	kl	X
m-1112	2046	2	]	]	PUNCT
m-1112	2047	1	=	=	PUNCT
m-1112	2047	2	g	g	PROPN
m-1112	2047	3	k	k	PROPN
m-1112	2047	4	,	,	PUNCT
m-1112	2047	5	is	be	AUX
m-1112	2047	6	seen	see	VERB
m-1112	2047	7	that	that	SCONJ
m-1112	2047	8	gravitational	gravitational	ADJ
m-1112	2047	9	-	-	PUNCT
m-1112	2047	10	force	force	NOUN
m-1112	2047	11	g	g	NOUN
m-1112	2047	12	,	,	PUNCT
m-1112	2047	13	is	be	AUX
m-1112	2047	14	the	the	DET
m-1112	2047	15	spring	spring	NOUN
m-1112	2047	16	-	-	PUNCT
m-1112	2047	17	like	like	ADJ
m-1112	2047	18	central	central	ADJ
m-1112	2047	19	-	-	PUNCT
m-1112	2047	20	force	force	NOUN
m-1112	2047	21	from	from	ADP
m-1112	2047	22	a	a	DET
m-1112	2047	23	fix	fix	NOUN
m-1112	2047	24	point	point	NOUN
m-1112	2047	25	,	,	PUNCT
m-1112	2047	26	the	the	DET
m-1112	2047	27	source	source	NOUN
m-1112	2047	28	,	,	PUNCT
m-1112	2047	29	on	on	ADP
m-1112	2047	30	an	an	DET
m-1112	2047	31	attached	attached	ADJ
m-1112	2047	32	,	,	PUNCT
m-1112	2047	33	probe	probe	NOUN
m-1112	2047	34	,	,	PUNCT
m-1112	2047	35	mass	mass	NOUN
m-1112	2047	36	as	as	ADP
m-1112	2047	37	→	→	SYM
m-1112	2047	38	f	f	NOUN
m-1112	2047	39	=	=	SYM
m-1112	2047	40	k	k	PROPN
m-1112	2047	41	r	r	NOUN
m-1112	2047	42	=	=	SYM
m-1112	2047	43	k	k	PROPN
m-1112	2047	44	r.r̅	r.r̅	PROPN
m-1112	2047	45	,	,	PUNCT
m-1112	2047	46	as	as	ADP
m-1112	2047	47	the	the	DET
m-1112	2047	48	1	1	NUM
m-1112	2047	49	-	-	PUNCT
m-1112	2047	50	dof	dof	NOUN
m-1112	2047	51	equation	equation	NOUN
m-1112	2047	52	,	,	PUNCT
m-1112	2047	53	r̈	r̈	VERB
m-1112	2047	54	+	+	CCONJ
m-1112	2047	55	w	w	PROPN
m-1112	2047	56	²	²	NUM
m-1112	2047	57	r	r	NOUN
m-1112	2047	58	=	=	SYM
m-1112	2047	59	0	0	NUM
m-1112	2047	60	,	,	PUNCT
m-1112	2047	61	where	where	SCONJ
m-1112	2048	1	k	k	NOUN
m-1112	2048	2	=	=	PUNCT
m-1112	2048	3	the	the	DET
m-1112	2048	4	unit	unit	NOUN
m-1112	2048	5	-	-	PUNCT
m-1112	2048	6	spring	spring	NOUN
m-1112	2048	7	-	-	PUNCT
m-1112	2048	8	force	force	NOUN
m-1112	2048	9	≡	≡	PROPN
m-1112	2048	10	[	[	X
m-1112	2048	11	meter	meter	NOUN
m-1112	2048	12	of	of	ADP
m-1112	2048	13	area].[meter	area].[meter	PRON
m-1112	2048	14	of	of	ADP
m-1112	2048	15	force	force	NOUN
m-1112	2048	16	≡	≡	PROPN
m-1112	2048	17	stress	stress	NOUN
m-1112	2048	18	]	]	PUNCT
m-1112	2048	19	≡	≡	PROPN
m-1112	2048	20	π	π	PROPN
m-1112	2048	21	g	g	PROPN
m-1112	2048	22	≡	≡	PROPN
m-1112	2048	23	with	with	ADP
m-1112	2048	24	a	a	DET
m-1112	2048	25	general	general	ADJ
m-1112	2048	26	solution	solution	NOUN
m-1112	2049	1	r	r	NOUN
m-1112	2049	2	=	=	PUNCT
m-1112	2049	3	a	a	DET
m-1112	2049	4	sinwnt	sinwnt	NOUN
m-1112	2049	5	+	+	CCONJ
m-1112	2049	6	b	b	X
m-1112	2049	7	coswnt	coswnt	NOUN
m-1112	2049	8	,	,	PUNCT
m-1112	2049	9	where	where	SCONJ
m-1112	2049	10	a	a	DET
m-1112	2049	11	,	,	PUNCT
m-1112	2049	12	b	b	NOUN
m-1112	2049	13	are	be	AUX
m-1112	2049	14	constants	constant	NOUN
m-1112	2049	15	and	and	CCONJ
m-1112	2049	16	evaluated	evaluate	VERB
m-1112	2049	17	from	from	ADP
m-1112	2049	18	the	the	DET
m-1112	2049	19	initial	initial	ADJ
m-1112	2049	20	velocity	velocity	NOUN
m-1112	2049	21	-	-	PUNCT
m-1112	2049	22	conditions	condition	NOUN
m-1112	2049	23	which	which	PRON
m-1112	2049	24	become	become	VERB
m-1112	2049	25	r	r	NOUN
m-1112	2049	26	=	=	PUNCT
m-1112	2049	27	[	[	X
m-1112	2049	28	x́(0	x́(0	NOUN
m-1112	2049	29	)	)	PUNCT
m-1112	2049	30	/	/	SYM
m-1112	2049	31	wn	wn	PROPN
m-1112	2049	32	]	]	PUNCT
m-1112	2049	33	.	.	PUNCT
m-1112	2050	1	sinwnt	sinwnt	NOUN
m-1112	2050	2	+	+	PRON
m-1112	2050	3	x(0).coswnt	x(0).coswnt	PROPN
m-1112	2050	4	.	.	PUNCT
m-1112	2051	1	above	above	ADP
m-1112	2051	2	equation	equation	NOUN
m-1112	2051	3	represents	represent	VERB
m-1112	2051	4	the	the	DET
m-1112	2051	5	natural	natural	ADJ
m-1112	2051	6	-	-	PUNCT
m-1112	2051	7	frequency	frequency	NOUN
m-1112	2051	8	of	of	ADP
m-1112	2051	9	the	the	DET
m-1112	2051	10	celestial	celestial	ADJ
m-1112	2051	11	-	-	PUNCT
m-1112	2051	12	structures	structure	NOUN
m-1112	2051	13	,	,	PUNCT
m-1112	2051	14	and	and	CCONJ
m-1112	2051	15	for	for	ADP
m-1112	2051	16	planck`s	planck`s	NOUN
m-1112	2051	17	length	length	NOUN
m-1112	2051	18	the	the	DET
m-1112	2051	19	only	only	ADJ
m-1112	2051	20	one	one	NUM
m-1112	2051	21	primary	primary	ADJ
m-1112	2051	22	-	-	PUNCT
m-1112	2051	23	particle	particle	NOUN
m-1112	2051	24	occupying	occupy	VERB
m-1112	2051	25	the	the	DET
m-1112	2051	26	less	less	ADV
m-1112	2051	27	frequency	frequency	NOUN
m-1112	2051	28	and	and	CCONJ
m-1112	2051	29	negative	negative	ADJ
m-1112	2051	30	-	-	PUNCT
m-1112	2051	31	charge	charge	NOUN
m-1112	2051	32	,	,	PUNCT
m-1112	2051	33	which	which	PRON
m-1112	2051	34	is	be	AUX
m-1112	2051	35	the	the	DET
m-1112	2051	36	electron	electron	NOUN
m-1112	2051	37	equation	equation	NOUN
m-1112	2051	38	and	and	CCONJ
m-1112	2051	39	with	with	ADP
m-1112	2051	40	the	the	DET
m-1112	2051	41	solution	solution	NOUN
m-1112	2051	42	as	as	ADP
m-1112	2051	43	,	,	PUNCT
m-1112	2051	44	𝐰𝐧	𝐰𝐧	ADP
m-1112	2051	45	𝟐𝛑	𝟐𝛑	NOUN
m-1112	2051	46	=	=	PUNCT
m-1112	2051	47	𝐟𝐞	𝐟𝐞	NOUN
m-1112	2051	48	=	=	SYM
m-1112	2051	49	1	1	NUM
m-1112	2051	50	2𝜋	2𝜋	NUM
m-1112	2051	51	√	√	NOUN
m-1112	2051	52	k	k	NOUN
m-1112	2051	53	m	m	VERB
m-1112	2051	54	,	,	PUNCT
m-1112	2051	55	or	or	CCONJ
m-1112	2051	56	4	4	NUM
m-1112	2051	57	π²	π²	NOUN
m-1112	2051	58	f	f	X
m-1112	2051	59	²e	²e	ADJ
m-1112	2051	60	.	.	PUNCT
m-1112	2052	1	me	i	PRON
m-1112	2053	1	=	=	PUNCT
m-1112	2053	2	k	k	X
m-1112	2053	3	=	=	PUNCT
m-1112	2054	1	π	π	X
m-1112	2054	2	g	g	NOUN
m-1112	2054	3	and	and	CCONJ
m-1112	2054	4	or	or	CCONJ
m-1112	2054	5	→	→	ADP
m-1112	2054	6	𝐦𝐞	𝐦𝐞	X
m-1112	2054	7	=	=	X
m-1112	2054	8	𝐠	𝐠	PRON
m-1112	2054	9	𝟒	𝟒	PROPN
m-1112	2054	10	𝛑	𝛑	ADP
m-1112	2054	11	𝐟	𝐟	PROPN
m-1112	2054	12	²𝐞	²𝐞	NOUN
m-1112	2054	13	from	from	ADP
m-1112	2054	14	planck`s	planck`s	NOUN
m-1112	2054	15	min	min	NOUN
m-1112	2054	16	-	-	NOUN
m-1112	2054	17	equation	equation	NOUN
m-1112	2054	18	f	f	NOUN
m-1112	2054	19	e	e	PROPN
m-1112	2054	20	=	=	SYM
m-1112	2054	21	e	e	PROPN
m-1112	2054	22	/	/	SYM
m-1112	2054	23	h	h	NOUN
m-1112	2054	24	=	=	PUNCT
m-1112	2055	1	[	[	X
m-1112	2055	2	-13,6	-13,6	X
m-1112	2055	3	x	x	SYM
m-1112	2055	4	1,6.10−19	1,6.10−19	NUM
m-1112	2055	5	=	=	SYM
m-1112	2055	6	2,176.10−16	2,176.10−16	NUM
m-1112	2055	7	joule	joule	NOUN
m-1112	2055	8	]	]	PUNCT
m-1112	2055	9	/	/	PUNCT
m-1112	2056	1	[	[	PUNCT
m-1112	2056	2	6,6262.10−34	6,6262.10−34	NUM
m-1112	2056	3	j.s	j.s	X
m-1112	2056	4	]	]	PUNCT
m-1112	2056	5	=	=	SYM
m-1112	2056	6	3	3	NUM
m-1112	2056	7	,	,	PUNCT
m-1112	2056	8	283998.𝟏𝟎𝟏𝟔	283998.𝟏𝟎𝟏𝟔	NUM
m-1112	2056	9	/s	/s	NOUN
m-1112	2056	10	,	,	PUNCT
m-1112	2056	11	where	where	SCONJ
m-1112	2056	12	in	in	ADP
m-1112	2056	13	hydrogen	hydrogen	NOUN
m-1112	2056	14	atom	atom	NOUN
m-1112	2056	15	energy	energy	NOUN
m-1112	2056	16	e	e	NOUN
m-1112	2056	17	=	=	SYM
m-1112	2056	18	h	h	NOUN
m-1112	2056	19	f	f	NOUN
m-1112	2056	20	=	=	NOUN
m-1112	2056	21	-13,6	-13,6	PUNCT
m-1112	2056	22	ev	ev	PROPN
m-1112	2056	23	substituting	substitute	VERB
m-1112	2056	24	all	all	DET
m-1112	2056	25	the	the	DET
m-1112	2056	26	minimum	minimum	ADJ
m-1112	2056	27	-	-	PUNCT
m-1112	2056	28	meters	meter	NOUN
m-1112	2056	29	of	of	ADP
m-1112	2056	30	planck`s	planck`s	NOUN
m-1112	2056	31	scale	scale	NOUN
m-1112	2056	32	then	then	ADV
m-1112	2056	33	,	,	PUNCT
m-1112	2056	34	electron	electron	NOUN
m-1112	2056	35	mass	mass	NOUN
m-1112	2056	36	is	be	AUX
m-1112	2056	37	,	,	PUNCT
m-1112	2056	38	𝐦𝐞	𝐦𝐞	VERB
m-1112	2056	39	=	=	VERB
m-1112	2056	40	g	g	PROPN
m-1112	2056	41	4	4	NUM
m-1112	2056	42	π	π	NOUN
m-1112	2056	43	f	f	PROPN
m-1112	2056	44	²e	²e	ADV
m-1112	2056	45	=	=	PUNCT
m-1112	2057	1	9,808238	9,808238	NUM
m-1112	2057	2	4.π.[3,28399.1016	4.π.[3,28399.1016	NUM
m-1112	2057	3	]	]	PUNCT
m-1112	2057	4	²	²	X
m-1112	2057	5	=	=	SYM
m-1112	2057	6	7	7	NUM
m-1112	2057	7	,	,	PUNCT
m-1112	2057	8	2373149	2373149	NUM
m-1112	2057	9	.	.	PUNCT
m-1112	2058	1	𝟏𝟎−𝟑𝟎	𝟏𝟎−𝟑𝟎	NOUN
m-1112	2058	2	kg	kg	PROPN
m-1112	2058	3	…	…	PUNCT
m-1112	2058	4	……	……	X
m-1112	2058	5	(	(	PUNCT
m-1112	2058	6	4b	4b	NUM
m-1112	2058	7	)	)	PUNCT
m-1112	2059	1	𝐟	𝐟	PRON
m-1112	2060	1	𝐞	𝐞	X
m-1112	2060	2	=	=	SYM
m-1112	2060	3	3	3	NUM
m-1112	2060	4	,	,	PUNCT
m-1112	2060	5	283998.𝟏𝟎𝟏𝟔	283998.𝟏𝟎𝟏𝟔	NUM
m-1112	2060	6	/s	/s	NOUN
m-1112	2060	7	,	,	PUNCT
m-1112	2060	8	and	and	CCONJ
m-1112	2060	9	loop	loop	VERB
m-1112	2060	10	𝐋	𝐋	PROPN
m-1112	2060	11	𝐞	𝐞	NOUN
m-1112	2060	12	=	=	SYM
m-1112	2060	13	2	2	NUM
m-1112	2060	14	,	,	PUNCT
m-1112	2060	15	3762992.𝟏𝟎−𝟏𝟔	3762992.𝟏𝟎−𝟏𝟔	NUM
m-1112	2060	16	m	m	NOUN
m-1112	2060	17	…	…	PUNCT
m-1112	2060	18	..	..	PUNCT
m-1112	2060	19	(	(	PUNCT
m-1112	2060	20	4c	4c	NOUN
m-1112	2060	21	)	)	PUNCT
m-1112	2060	22	relation	relation	NOUN
m-1112	2060	23	4π²f²e	4π²f²e	NOUN
m-1112	2060	24	.me	.me	PUNCT
m-1112	2061	1	=	=	PUNCT
m-1112	2061	2	k	k	X
m-1112	2062	1	=	=	PUNCT
m-1112	2062	2	π	π	X
m-1112	2062	3	g	g	NOUN
m-1112	2062	4	,	,	PUNCT
m-1112	2062	5	denotes	denote	VERB
m-1112	2062	6	that	that	SCONJ
m-1112	2062	7	electric	electric	NOUN
m-1112	2062	8	-	-	PUNCT
m-1112	2062	9	field	field	NOUN
m-1112	2062	10	generated	generate	VERB
m-1112	2062	11	by	by	ADP
m-1112	2062	12	an	an	DET
m-1112	2062	13	electron	electron	NOUN
m-1112	2062	14	has	have	VERB
m-1112	2062	15	both	both	PRON
m-1112	2062	16	,	,	PUNCT
m-1112	2062	17	a	a	DET
m-1112	2062	18	component	component	NOUN
m-1112	2062	19	oscillating	oscillate	VERB
m-1112	2062	20	at	at	ADP
m-1112	2062	21	the	the	DET
m-1112	2062	22	electron`s	electron`s	NOUN
m-1112	2062	23	compton	compton	PROPN
m-1112	2062	24	frequency	frequency	PROPN
m-1112	2063	1	𝐟	𝐟	PROPN
m-1112	2063	2	𝐞	𝐞	PROPN
m-1112	2063	3	,	,	PUNCT
m-1112	2063	4	which	which	PRON
m-1112	2063	5	is	be	AUX
m-1112	2063	6	ijo	ijo	PROPN
m-1112	2063	7	international	international	ADJ
m-1112	2063	8	journal	journal	PROPN
m-1112	2063	9	of	of	ADP
m-1112	2063	10	mathematics	mathematics	PROPN
m-1112	2063	11	(	(	PUNCT
m-1112	2063	12	issn	issn	PROPN
m-1112	2063	13	:	:	PUNCT
m-1112	2063	14	2992	2992	NUM
m-1112	2063	15	-	-	SYM
m-1112	2063	16	4421	4421	NUM
m-1112	2063	17	)	)	PUNCT
m-1112	2063	18	volume	volume	NOUN
m-1112	2063	19	08	08	NUM
m-1112	2064	1	|	|	ADV
m-1112	2064	2	issue	issue	NOUN
m-1112	2064	3	08	08	NUM
m-1112	2065	1	|	|	ADV
m-1112	2065	2	august	august	PROPN
m-1112	2065	3	2025	2025	NUM
m-1112	2065	4	|	|	ADV
m-1112	2065	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2065	6	ijo	ijo	PROPN
m-1112	2065	7	journals	journal	NOUN
m-1112	2065	8	73	73	NUM
m-1112	2065	9	the	the	DET
m-1112	2065	10	fundamental	fundamental	ADJ
m-1112	2065	11	particles	particle	NOUN
m-1112	2065	12	origination	origination	NOUN
m-1112	2065	13	mechanism	mechanism	NOUN
m-1112	2065	14	in	in	ADP
m-1112	2065	15	mfmf	mfmf	PROPN
m-1112	2065	16	pns	pns	PROPN
m-1112	2065	17	caves	cave	NOUN
m-1112	2065	18	.	.	PUNCT
m-1112	2066	1	the	the	DET
m-1112	2066	2	energy	energy	NOUN
m-1112	2066	3	-	-	PUNCT
m-1112	2066	4	part	part	NOUN
m-1112	2066	5	,	,	PUNCT
m-1112	2066	6	and	and	CCONJ
m-1112	2066	7	the	the	DET
m-1112	2066	8	non	non	ADJ
m-1112	2066	9	-	-	ADJ
m-1112	2066	10	oscillating	oscillating	ADJ
m-1112	2066	11	component	component	NOUN
m-1112	2066	12	,	,	PUNCT
m-1112	2066	13	the	the	DET
m-1112	2066	14	electric	electric	ADJ
m-1112	2066	15	-	-	PUNCT
m-1112	2066	16	field	field	NOUN
m-1112	2066	17	-	-	PUNCT
m-1112	2066	18	lines	line	NOUN
m-1112	2066	19	as	as	ADP
m-1112	2066	20	the	the	DET
m-1112	2066	21	energy	energy	NOUN
m-1112	2066	22	-	-	PUNCT
m-1112	2066	23	conductor	conductor	NOUN
m-1112	2066	24	,	,	PUNCT
m-1112	2066	25	the	the	DET
m-1112	2066	26	space	space	NOUN
m-1112	2066	27	-	-	PUNCT
m-1112	2066	28	part	part	NOUN
m-1112	2066	29	,	,	PUNCT
m-1112	2066	30	which	which	PRON
m-1112	2066	31	is	be	AUX
m-1112	2066	32	connecting	connect	VERB
m-1112	2066	33	gravity	gravity	NOUN
m-1112	2066	34	with	with	ADP
m-1112	2066	35	electric	electric	NOUN
m-1112	2066	36	-	-	PUNCT
m-1112	2066	37	field	field	NOUN
m-1112	2066	38	.	.	PUNCT
m-1112	2067	1	so	so	ADV
m-1112	2067	2	,	,	PUNCT
m-1112	2067	3	electron	electron	NOUN
m-1112	2067	4	,	,	PUNCT
m-1112	2067	5	is	be	AUX
m-1112	2067	6	the	the	DET
m-1112	2067	7	minimum	minimum	ADJ
m-1112	2067	8	-	-	PUNCT
m-1112	2067	9	energy	energy	NOUN
m-1112	2067	10	massive	massive	ADJ
m-1112	2067	11	particle	particle	NOUN
m-1112	2067	12	in	in	ADP
m-1112	2067	13	hydrogen	hydrogen	NOUN
m-1112	2067	14	-	-	PUNCT
m-1112	2067	15	cave	cave	NOUN
m-1112	2067	16	{	{	PUNCT
m-1112	2067	17	-13,6	-13,6	PUNCT
m-1112	2067	18	ev	ev	INTJ
m-1112	2067	19	}	}	PUNCT
m-1112	2067	20	,	,	PUNCT
m-1112	2067	21	becoming	become	VERB
m-1112	2067	22	from	from	ADP
m-1112	2067	23	material	material	NOUN
m-1112	2067	24	-	-	PUNCT
m-1112	2067	25	point	point	NOUN
m-1112	2067	26	in	in	ADP
m-1112	2067	27	planck`s	planck`s	NOUN
m-1112	2067	28	-	-	PUNCT
m-1112	2067	29	length	length	NOUN
m-1112	2067	30	,	,	PUNCT
m-1112	2067	31	minimum	minimum	NOUN
m-1112	2067	32	-	-	PUNCT
m-1112	2067	33	cave	cave	NOUN
m-1112	2067	34	,	,	PUNCT
m-1112	2067	35	occupying	occupy	VERB
m-1112	2067	36	the	the	DET
m-1112	2067	37	less	less	ADJ
m-1112	2067	38	unit	unit	NOUN
m-1112	2067	39	frequency	frequency	NOUN
m-1112	2067	40	in	in	ADP
m-1112	2067	41	planck`s	planck`s	NOUN
m-1112	2067	42	–	–	PUNCT
m-1112	2067	43	length	length	NOUN
m-1112	2067	44	,	,	PUNCT
m-1112	2067	45	with	with	ADP
m-1112	2067	46	negative	negative	ADJ
m-1112	2067	47	-	-	PUNCT
m-1112	2067	48	charge	charge	NOUN
m-1112	2067	49	{	{	PUNCT
m-1112	2067	50	𝐟𝐞=	𝐟𝐞=	ADP
m-1112	2067	51	3,283998.1016	3,283998.1016	NUM
m-1112	2067	52	/s	/s	PUNCT
m-1112	2067	53	}	}	PUNCT
m-1112	2067	54	.	.	PUNCT
m-1112	2068	1	because	because	SCONJ
m-1112	2068	2	of	of	ADP
m-1112	2068	3	the	the	DET
m-1112	2068	4	negative	negative	ADJ
m-1112	2068	5	-	-	PUNCT
m-1112	2068	6	energy	energy	NOUN
m-1112	2068	7	in	in	ADP
m-1112	2068	8	hydrogen	hydrogen	NOUN
m-1112	2068	9	-	-	PUNCT
m-1112	2068	10	cave	cave	NOUN
m-1112	2068	11	,	,	PUNCT
m-1112	2068	12	and	and	CCONJ
m-1112	2068	13	the	the	DET
m-1112	2068	14	less	less	ADV
m-1112	2068	15	-	-	PUNCT
m-1112	2068	16	negative	negative	ADJ
m-1112	2068	17	energy	energy	NOUN
m-1112	2068	18	of	of	ADP
m-1112	2068	19	rims	rim	NOUN
m-1112	2068	20	which	which	PRON
m-1112	2068	21	consist	consist	VERB
m-1112	2068	22	the	the	DET
m-1112	2068	23	plane	plane	NOUN
m-1112	2068	24	-	-	PUNCT
m-1112	2068	25	traces	trace	NOUN
m-1112	2068	26	-	-	PUNCT
m-1112	2068	27	conductors	conductor	NOUN
m-1112	2068	28	or	or	CCONJ
m-1112	2068	29	the	the	DET
m-1112	2068	30	paths	path	NOUN
m-1112	2068	31	in	in	ADP
m-1112	2068	32	-	-	PUNCT
m-1112	2068	33	where	where	SCONJ
m-1112	2068	34	electrons	electron	NOUN
m-1112	2068	35	roll	roll	VERB
m-1112	2068	36	so	so	SCONJ
m-1112	2068	37	energy	energy	NOUN
m-1112	2068	38	rims	rim	NOUN
m-1112	2068	39	consist	consist	VERB
m-1112	2068	40	the	the	DET
m-1112	2068	41	energy	energy	NOUN
m-1112	2068	42	-	-	PUNCT
m-1112	2068	43	minimum	minimum	NOUN
m-1112	2068	44	-	-	PUNCT
m-1112	2068	45	paths	path	NOUN
m-1112	2068	46	in	in	ADP
m-1112	2068	47	hydrogen	hydrogen	NOUN
m-1112	2068	48	-	-	PUNCT
m-1112	2068	49	cave	cave	NOUN
m-1112	2068	50	-	-	PUNCT
m-1112	2068	51	potentials	potential	NOUN
m-1112	2068	52	,	,	PUNCT
m-1112	2068	53	as	as	ADP
m-1112	2068	54	en	en	ADP
m-1112	2068	55	en−1	en−1	PROPN
m-1112	2068	56	=	=	PUNCT
m-1112	2069	1	[	[	X
m-1112	2069	2	me.v²	me.v²	X
m-1112	2069	3	]	]	X
m-1112	2069	4	.[2n-1	.[2n-1	PROPN
m-1112	2069	5	]	]	PUNCT
m-1112	2069	6	,	,	PUNCT
m-1112	2069	7	where	where	SCONJ
m-1112	2069	8	the	the	DET
m-1112	2069	9	electrons	electron	NOUN
m-1112	2069	10	,	,	PUNCT
m-1112	2069	11	the	the	DET
m-1112	2069	12	electric	electric	ADJ
m-1112	2069	13	–	–	PUNCT
m-1112	2069	14	charges	charge	NOUN
m-1112	2069	15	,	,	PUNCT
m-1112	2069	16	roll	roll	NOUN
m-1112	2069	17	.	.	PUNCT
m-1112	2070	1	electron	electron	PROPN
m-1112	2070	2	charge	charge	NOUN
m-1112	2070	3	�	�	PROPN
m-1112	2070	4	̅	̅	NOUN
m-1112	2070	5	�	�	NOUN
m-1112	2070	6	becomes	become	VERB
m-1112	2070	7	from	from	ADP
m-1112	2070	8	magnetic	magnetic	ADJ
m-1112	2070	9	field	field	NOUN
m-1112	2070	10	m	m	VERB
m-1112	2070	11	which	which	PRON
m-1112	2070	12	creates	create	VERB
m-1112	2070	13	the	the	DET
m-1112	2070	14	electric	electric	NOUN
m-1112	2070	15	-	-	PUNCT
m-1112	2070	16	field	field	NOUN
m-1112	2070	17	e	e	NOUN
m-1112	2070	18	,	,	PUNCT
m-1112	2070	19	which	which	PRON
m-1112	2070	20	is	be	AUX
m-1112	2070	21	acting	act	VERB
m-1112	2070	22	on	on	ADP
m-1112	2070	23	charge	charge	NOUN
m-1112	2070	24	q	q	PROPN
m-1112	2070	25	,	,	PUNCT
m-1112	2070	26	and	and	CCONJ
m-1112	2070	27	the	the	DET
m-1112	2070	28	acting	act	VERB
m-1112	2070	29	force	force	NOUN
m-1112	2070	30	per	per	ADP
m-1112	2070	31	second	second	ADJ
m-1112	2070	32	creates	create	VERB
m-1112	2070	33	work	work	NOUN
m-1112	2070	34	which	which	PRON
m-1112	2070	35	is	be	AUX
m-1112	2070	36	conserved	conserve	VERB
m-1112	2070	37	and	and	CCONJ
m-1112	2070	38	coincide	coincide	VERB
m-1112	2070	39	with	with	ADP
m-1112	2070	40	the	the	DET
m-1112	2070	41	planck`s	planck`s	NOUN
m-1112	2070	42	constant	constant	ADJ
m-1112	2070	43	h	h	NOUN
m-1112	2070	44	.	.	PUNCT
m-1112	2071	1	this	this	PRON
m-1112	2071	2	is	be	AUX
m-1112	2071	3	because	because	SCONJ
m-1112	2071	4	h	h	PROPN
m-1112	2071	5	→	→	SYM
m-1112	2071	6	j	j	PROPN
m-1112	2071	7	s	s	PART
m-1112	2071	8	=	=	PUNCT
m-1112	2071	9	n	n	PROPN
m-1112	2071	10	m	m	NOUN
m-1112	2071	11	s	s	NOUN
m-1112	2071	12	=	=	X
m-1112	2071	13	power	power	NOUN
m-1112	2071	14	,	,	PUNCT
m-1112	2071	15	where	where	SCONJ
m-1112	2071	16	from	from	ADP
m-1112	2071	17	,	,	PUNCT
m-1112	2071	18	energy	energy	NOUN
m-1112	2071	19	=	=	NOUN
m-1112	2071	20	power	power	NOUN
m-1112	2071	21	x	x	NOUN
m-1112	2071	22	time	time	NOUN
m-1112	2071	23	,	,	PUNCT
m-1112	2071	24	issues	issue	VERB
m-1112	2071	25	the	the	DET
m-1112	2071	26	beyond	beyond	ADP
m-1112	2071	27	planck`s	planck`s	NOUN
m-1112	2071	28	length	length	NOUN
m-1112	2071	29	𝐋𝐏	𝐋𝐏	PROPN
m-1112	2071	30	,	,	PUNCT
m-1112	2071	31	and	and	CCONJ
m-1112	2071	32	the	the	DET
m-1112	2071	33	voltage	voltage	NOUN
m-1112	2071	34	v	v	NOUN
m-1112	2071	35	is	be	AUX
m-1112	2071	36	→	→	SYM
m-1112	2071	37	q̅	q̅	PROPN
m-1112	2071	38	≡	≡	PROPN
m-1112	2071	39	ke	ke	PROPN
m-1112	2071	40	vp	vp	PROPN
m-1112	2072	1	=	=	NOUN
m-1112	2072	2	1	1	X
m-1112	2072	3	=	=	PRON
m-1112	2072	4	me	i	PRON
m-1112	2072	5	𝑐	𝑐	PROPN
m-1112	2072	6	²	²	NUM
m-1112	2072	7	2	2	NUM
m-1112	2072	8	=	=	SYM
m-1112	2072	9	g	g	NOUN
m-1112	2072	10	c	c	NOUN
m-1112	2072	11	²	²	NUM
m-1112	2072	12	8πf	8πf	NOUN
m-1112	2072	13	².1	².1	NUM
m-1112	2072	14	,	,	PUNCT
m-1112	2072	15	and	and	CCONJ
m-1112	2072	16	v̅	v̅	PROPN
m-1112	2072	17	≡	≡	PROPN
m-1112	2072	18	vp	vp	PROPN
m-1112	2072	19	≡	≡	PROPN
m-1112	2072	20	c	c	PROPN
m-1112	2072	21	.charge	.charge	VERB
m-1112	2072	22	total−energy=	total−energy=	ADV
m-1112	2072	23	h	h	NOUN
m-1112	2073	1	=	=	SYM
m-1112	2073	2	c	c	PROPN
m-1112	2073	3	.q̅	.q̅	PROPN
m-1112	2073	4	h	h	PROPN
m-1112	2073	5	...	...	PUNCT
m-1112	2073	6	(	(	PUNCT
m-1112	2073	7	1	1	X
m-1112	2073	8	)	)	PUNCT
m-1112	2073	9	using	use	VERB
m-1112	2073	10	the	the	DET
m-1112	2073	11	two	two	NUM
m-1112	2073	12	energy	energy	NOUN
m-1112	2073	13	-	-	PUNCT
m-1112	2073	14	equations	equation	NOUN
m-1112	2073	15	for	for	ADP
m-1112	2073	16	linear	linear	NOUN
m-1112	2073	17	-	-	PUNCT
m-1112	2073	18	motion	motion	NOUN
m-1112	2073	19	→	→	SYM
m-1112	2073	20	fn	fn	NOUN
m-1112	2073	21	=	=	SYM
m-1112	2073	22	1	1	NUM
m-1112	2073	23	2π	2π	NUM
m-1112	2073	24	√	√	NOUN
m-1112	2074	1	k	k	NOUN
m-1112	2074	2	m	m	VERB
m-1112	2074	3	2	2	NUM
m-1112	2074	4	and	and	CCONJ
m-1112	2074	5	orbital	orbital	ADJ
m-1112	2074	6	-	-	PUNCT
m-1112	2074	7	motion	motion	NOUN
m-1112	2074	8	a	a	DET
m-1112	2074	9	=	=	NOUN
m-1112	2074	10	√	√	ADP
m-1112	2074	11	1	1	NUM
m-1112	2074	12	k	k	PROPN
m-1112	2074	13	.f	.f	PROPN
m-1112	2074	14	²	²	NUM
m-1112	2074	15	3	3	NUM
m-1112	2074	16	,	,	PUNCT
m-1112	2074	17	for	for	ADP
m-1112	2074	18	unit	unit	NOUN
m-1112	2074	19	-	-	PUNCT
m-1112	2074	20	energy	energy	NOUN
m-1112	2074	21	-	-	PUNCT
m-1112	2074	22	space	space	NOUN
m-1112	2074	23	-	-	PUNCT
m-1112	2074	24	frequency	frequency	NOUN
m-1112	2074	25	k	k	NOUN
m-1112	2074	26	=	=	PUNCT
m-1112	2074	27	g	g	PROPN
m-1112	2074	28	,	,	PUNCT
m-1112	2074	29	a	a	DET
m-1112	2074	30	=	=	SYM
m-1112	2074	31	π	π	PROPN
m-1112	2074	32	,	,	PUNCT
m-1112	2074	33	then	then	ADV
m-1112	2074	34	→	→	SYM
m-1112	2074	35	g	g	NOUN
m-1112	2074	36	.f	.f	PROPN
m-1112	2074	37	²	²	X
m-1112	2074	38	.	.	PUNCT
m-1112	2075	1	π	π	PROPN
m-1112	2075	2	³	³	X
m-1112	2075	3	=	=	SYM
m-1112	2075	4	1	1	NUM
m-1112	2075	5	...	...	PUNCT
m-1112	2075	6	(	(	PUNCT
m-1112	2075	7	2	2	X
m-1112	2075	8	)	)	PUNCT
m-1112	2075	9	frequency	frequency	NOUN
m-1112	2075	10	fn	fn	NOUN
m-1112	2076	1	=	=	NOUN
m-1112	2076	2	√	√	ADJ
m-1112	2076	3	1	1	NUM
m-1112	2076	4	g.π	g.π	PROPN
m-1112	2076	5	³	³	NUM
m-1112	2076	6	2	2	NUM
m-1112	2076	7	=	=	NOUN
m-1112	2076	8	√	√	ADJ
m-1112	2076	9	1	1	NUM
m-1112	2076	10	9,808238.π	9,808238.π	NUM
m-1112	2076	11	³	³	NUM
m-1112	2076	12	2	2	NUM
m-1112	2076	13	=	=	NOUN
m-1112	2076	14	1,8133418.10−3	1,8133418.10−3	NUM
m-1112	2076	15	,	,	PUNCT
m-1112	2076	16	i.e.	i.e.	X
m-1112	2076	17	the	the	DET
m-1112	2076	18	unit	unit	NOUN
m-1112	2076	19	-	-	PUNCT
m-1112	2076	20	charge	charge	NOUN
m-1112	2076	21	-	-	PUNCT
m-1112	2076	22	cave	cave	NOUN
m-1112	2076	23	,	,	PUNCT
m-1112	2076	24	q̅	q̅	PROPN
m-1112	2076	25	into	into	ADP
m-1112	2076	26	hydrogen	hydrogen	NOUN
m-1112	2076	27	cave	cave	NOUN
m-1112	2076	28	[	[	X
m-1112	2076	29	a	a	DET
m-1112	2076	30	=	=	NOUN
m-1112	2076	31	1,82043047.10−12m].[1,813342.10−3	1,82043047.10−12m].[1,813342.10−3	NUM
m-1112	2076	32	/	/	SYM
m-1112	2076	33	s	s	NOUN
m-1112	2076	34	]	]	X
m-1112	2076	35	=	=	SYM
m-1112	2076	36	3,3010625.𝟏𝟎−𝟏𝟓	3,3010625.𝟏𝟎−𝟏𝟓	NUM
m-1112	2076	37	c	c	NOUN
m-1112	2076	38	from	from	ADP
m-1112	2076	39	equations	equation	NOUN
m-1112	2076	40	charge	charge	NOUN
m-1112	2076	41	and	and	CCONJ
m-1112	2076	42	voltage	voltage	NOUN
m-1112	2076	43	is	be	AUX
m-1112	2076	44	the	the	DET
m-1112	2076	45	self	self	NOUN
m-1112	2076	46	-	-	PUNCT
m-1112	2076	47	growing	grow	VERB
m-1112	2076	48	property	property	NOUN
m-1112	2076	49	of	of	ADP
m-1112	2076	50	frequency	frequency	NOUN
m-1112	2076	51	𝐟𝐧	𝐟𝐧	NOUN
m-1112	2076	52	in	in	ADP
m-1112	2076	53	material	material	NOUN
m-1112	2076	54	-	-	PUNCT
m-1112	2076	55	point	point	NOUN
m-1112	2076	56	,	,	PUNCT
m-1112	2076	57	therefore	therefore	ADV
m-1112	2076	58	and	and	CCONJ
m-1112	2076	59	for	for	ADP
m-1112	2076	60	hydrogen	hydrogen	NOUN
m-1112	2076	61	-	-	PUNCT
m-1112	2076	62	cave	cave	NOUN
m-1112	2076	63	is	be	AUX
m-1112	2076	64	equal	equal	ADJ
m-1112	2076	65	to	to	ADP
m-1112	2076	66	→	→	SYM
m-1112	2076	67	q̅.φ	q̅.φ	X
m-1112	2076	68	,	,	PUNCT
m-1112	2076	69	because	because	SCONJ
m-1112	2076	70	gravitational	gravitational	ADJ
m-1112	2076	71	force	force	NOUN
m-1112	2076	72	is	be	AUX
m-1112	2076	73	equal	equal	ADJ
m-1112	2076	74	to	to	ADP
m-1112	2076	75	→	→	SYM
m-1112	2076	76	the	the	DET
m-1112	2076	77	geometric	geometric	NOUN
m-1112	2076	78	-	-	PUNCT
m-1112	2076	79	resultant	resultant	NOUN
m-1112	2076	80	of	of	ADP
m-1112	2076	81	light	light	ADJ
m-1112	2076	82	-	-	PUNCT
m-1112	2076	83	velocity	velocity	NOUN
m-1112	2076	84	c	c	NOUN
m-1112	2076	85	,	,	PUNCT
m-1112	2076	86	acting	act	VERB
m-1112	2076	87	on	on	ADP
m-1112	2076	88	electron	electron	NOUN
m-1112	2076	89	-	-	PUNCT
m-1112	2076	90	unit	unit	NOUN
m-1112	2076	91	-	-	PUNCT
m-1112	2076	92	charge	charge	NOUN
m-1112	2076	93	�	�	PROPN
m-1112	2076	94	̅	̅	NOUN
m-1112	2076	95	�	�	PROPN
m-1112	2076	96	←	←	PROPN
m-1112	2076	97	or	or	CCONJ
m-1112	2076	98	,	,	PUNCT
m-1112	2076	99	g	g	PROPN
m-1112	2076	100	=	=	SYM
m-1112	2076	101	c	c	PROPN
m-1112	2076	102	√𝟐	√𝟐	PROPN
m-1112	2076	103	�	�	PROPN
m-1112	2076	104	̅	̅	NOUN
m-1112	2076	105	�	�	PROPN
m-1112	2076	106	,	,	PUNCT
m-1112	2076	107	then	then	ADV
m-1112	2076	108	electron	electron	NOUN
m-1112	2076	109	-	-	PUNCT
m-1112	2076	110	charge	charge	NOUN
m-1112	2076	111	is	be	AUX
m-1112	2076	112	,	,	PUNCT
m-1112	2076	113	q̅	q̅	PROPN
m-1112	2076	114	=	=	PUNCT
m-1112	2076	115	g	g	PROPN
m-1112	2076	116	c	c	PROPN
m-1112	2076	117	√2	√2	PROPN
m-1112	2076	118	=	=	SYM
m-1112	2076	119	6,680561	6,680561	PROPN
m-1112	2076	120	.10−11	.10−11	PUNCT
m-1112	2076	121	1,41429.[2,9979346.10	1,41429.[2,9979346.10	NUM
m-1112	2076	122	8	8	NUM
m-1112	2076	123	]	]	PUNCT
m-1112	2076	124	=	=	SYM
m-1112	2076	125	1,58.10−19	1,58.10−19	NUM
m-1112	2076	126	coulomb	coulomb	NOUN
m-1112	2076	127	,	,	PUNCT
m-1112	2076	128	the	the	DET
m-1112	2076	129	known	know	VERB
m-1112	2076	130	coulomb`s	coulomb`s	NUM
m-1112	2076	131	charge	charge	NOUN
m-1112	2076	132	quantity	quantity	NOUN
m-1112	2076	133	,	,	PUNCT
m-1112	2076	134	from	from	ADP
m-1112	2076	135	gl	gl	PROPN
m-1112	2076	136	,	,	PUNCT
m-1112	2076	137	kl	kl	PROPN
m-1112	2076	138	universal	universal	PROPN
m-1112	2076	139	constants	constant	VERB
m-1112	2076	140	the	the	DET
m-1112	2076	141	newton`s	newton`s	PROPN
m-1112	2076	142	gravitational	gravitational	ADJ
m-1112	2076	143	constant	constant	ADJ
m-1112	2076	144	force	force	NOUN
m-1112	2076	145	is	be	AUX
m-1112	2076	146	,	,	PUNCT
m-1112	2076	147	g	g	PROPN
m-1112	2076	148	≡	≡	PROPN
m-1112	2077	1	g.ke	g.ke	PROPN
m-1112	2077	2	≡	≡	PROPN
m-1112	2077	3	g	g	PROPN
m-1112	2078	1	.[gl	.[gl	PROPN
m-1112	2078	2	kl	kl	X
m-1112	2078	3	]	]	PUNCT
m-1112	2079	1	≡	≡	PROPN
m-1112	2079	2	[	[	PUNCT
m-1112	2079	3	t²p	t²p	X
m-1112	2079	4	𝐚³	𝐚³	ADJ
m-1112	2079	5	]	]	PUNCT
m-1112	2079	6	.[gl	.[gl	PUNCT
m-1112	2080	1	kl	kl	X
m-1112	2080	2	]	]	PUNCT
m-1112	2080	3	≡	≡	PROPN
m-1112	2080	4	9,808238	9,808238	PROPN
m-1112	2080	5	*	*	SYM
m-1112	2080	6	6,8116.10−12	6,8116.10−12	NUM
m-1112	2080	7	≡	≡	PROPN
m-1112	2080	8	6,68056.10−11	6,68056.10−11	NUM
m-1112	2080	9	𝐦³	𝐦³	PROPN
m-1112	2080	10	𝐍𝐬²	𝐍𝐬²	VERB
m-1112	2080	11	the	the	DET
m-1112	2080	12	in	in	ADP
m-1112	2080	13	depth	depth	NOUN
m-1112	2080	14	position	position	NOUN
m-1112	2080	15	of	of	ADP
m-1112	2080	16	electrons	electron	NOUN
m-1112	2080	17	allows	allow	VERB
m-1112	2080	18	to	to	ADP
m-1112	2080	19	the	the	DET
m-1112	2080	20	work	work	NOUN
m-1112	2080	21	produced	produce	VERB
m-1112	2080	22	in	in	ADP
m-1112	2080	23	prior	prior	ADJ
m-1112	2080	24	phase	phase	NOUN
m-1112	2080	25	-	-	PUNCT
m-1112	2080	26	areas	area	NOUN
m-1112	2080	27	as	as	ADP
m-1112	2080	28	golden	golden	ADJ
m-1112	2080	29	ratio	ratio	NOUN
m-1112	2080	30	pattern	pattern	NOUN
m-1112	2080	31	,	,	PUNCT
m-1112	2080	32	to	to	PART
m-1112	2080	33	be	be	AUX
m-1112	2080	34	stored	store	VERB
m-1112	2080	35	in	in	ADP
m-1112	2080	36	the	the	DET
m-1112	2080	37	next	next	ADJ
m-1112	2080	38	.	.	PUNCT
m-1112	2081	1	energy	energy	NOUN
m-1112	2081	2	=	=	NOUN
m-1112	2081	3	motion	motion	NOUN
m-1112	2081	4	/	/	SYM
m-1112	2081	5	t	t	PROPN
m-1112	2081	6	≡	≡	PROPN
m-1112	2081	7	(	(	PUNCT
m-1112	2081	8	v	v	NUM
m-1112	2081	9	2πr	2πr	NOUN
m-1112	2081	10	)	)	PUNCT
m-1112	2081	11	.	.	PUNCT
m-1112	2082	1	[	[	X
m-1112	2082	2	σ	σ	X
m-1112	2082	3	+	+	X
m-1112	2082	4	σ	σ	PROPN
m-1112	2082	5	φ	φ	X
m-1112	2082	6	]	]	X
m-1112	2082	7	=	=	SYM
m-1112	2082	8	�	�	PROPN
m-1112	2082	9	̅	̅	NOUN
m-1112	2082	10	�	�	PROPN
m-1112	2082	11	.	.	PUNCT
m-1112	2083	1	[	[	PUNCT
m-1112	2083	2	𝛔	𝛔	X
m-1112	2083	3	𝟐𝛑𝐫	𝟐𝛑𝐫	NOUN
m-1112	2084	1	+	+	X
m-1112	2085	1	𝛔𝚽	𝛔𝚽	ADJ
m-1112	2085	2	𝟐𝛑𝐫	𝟐𝛑𝐫	NOUN
m-1112	2085	3	]	]	PUNCT
m-1112	2085	4	≡	≡	PROPN
m-1112	2085	5	�	�	PROPN
m-1112	2085	6	̅	̅	NOUN
m-1112	2085	7	�	�	PROPN
m-1112	2085	8	.	.	PUNCT
m-1112	2086	1	[	[	X
m-1112	2086	2	.	.	PUNCT
m-1112	2087	1	fn̅	fn̅	PROPN
m-1112	2088	1	+	+	NUM
m-1112	2088	2	𝐟𝐧	𝐟𝐧	NOUN
m-1112	2088	3	]	]	PUNCT
m-1112	2088	4	≡	≡	PROPN
m-1112	2088	5	moving	move	VERB
m-1112	2088	6	storage	storage	NOUN
m-1112	2088	7	→	→	NOUN
m-1112	2088	8	[	[	PUNCT
m-1112	2088	9	�	�	NOUN
m-1112	2088	10	̅	̅	NOUN
m-1112	2088	11	�	�	PROPN
m-1112	2088	12	.	.	PUNCT
m-1112	2089	1	fn̅	fn̅	PROPN
m-1112	2089	2	]	]	PUNCT
m-1112	2089	3	←	←	PROPN
m-1112	2089	4	+	+	CCONJ
m-1112	2089	5	moving	move	VERB
m-1112	2089	6	-	-	PUNCT
m-1112	2089	7	frequency	frequency	NOUN
m-1112	2089	8	→	→	SYM
m-1112	2089	9	[	[	PUNCT
m-1112	2089	10	�	�	NOUN
m-1112	2089	11	̅	̅	NOUN
m-1112	2089	12	�	�	NOUN
m-1112	2089	13	.𝐟𝐧	.𝐟𝐧	PRON
m-1112	2089	14	]	]	PUNCT
m-1112	2089	15	←	←	PROPN
m-1112	2089	16	≡	≡	PROPN
m-1112	2089	17	material	material	NOUN
m-1112	2089	18	-	-	PUNCT
m-1112	2089	19	point	point	NOUN
m-1112	2089	20	i.e.	i.e.	X
m-1112	2089	21	the	the	DET
m-1112	2089	22	energy	energy	NOUN
m-1112	2089	23	produced	produce	VERB
m-1112	2089	24	in	in	ADP
m-1112	2089	25	photon	photon	NOUN
m-1112	2089	26	-	-	PUNCT
m-1112	2089	27	cave	cave	NOUN
m-1112	2089	28	is	be	AUX
m-1112	2089	29	consisted	consist	VERB
m-1112	2089	30	of	of	ADP
m-1112	2089	31	two	two	NUM
m-1112	2089	32	-	-	PUNCT
m-1112	2089	33	moving	move	VERB
m-1112	2089	34	-	-	PUNCT
m-1112	2089	35	storages	storage	NOUN
m-1112	2089	36	,	,	PUNCT
m-1112	2089	37	that	that	PRON
m-1112	2089	38	travel	travel	VERB
m-1112	2089	39	as	as	ADP
m-1112	2089	40	wave	wave	NOUN
m-1112	2089	41	[	[	X
m-1112	2089	42	�	�	NOUN
m-1112	2089	43	̅	̅	NOUN
m-1112	2089	44	�	�	NOUN
m-1112	2089	45	.𝐟𝐧	.𝐟𝐧	PRON
m-1112	2089	46	]	]	PUNCT
m-1112	2090	1	→	→	ADP
m-1112	2090	2	[	[	PUNCT
m-1112	2090	3	�	�	NOUN
m-1112	2090	4	̅	̅	NOUN
m-1112	2090	5	�	�	PROPN
m-1112	2090	6	.	.	PUNCT
m-1112	2091	1	fn̅	fn̅	PROPN
m-1112	2091	2	]	]	PUNCT
m-1112	2092	1	→	→	X
m-1112	2092	2	[	[	PUNCT
m-1112	2092	3	�	�	NOUN
m-1112	2092	4	̅	̅	NOUN
m-1112	2092	5	�	�	PROPN
m-1112	2092	6	=	=	SYM
m-1112	2092	7	�	�	PROPN
m-1112	2092	8	̅	̅	NOUN
m-1112	2092	9	�	�	NOUN
m-1112	2092	10	=	=	SYM
m-1112	2092	11	λ	λ	X
m-1112	2092	12	f	f	PROPN
m-1112	2092	13	φ	φ	X
m-1112	2092	14	]	]	PUNCT
m-1112	2092	15	→	→	X
m-1112	2092	16	[	[	PUNCT
m-1112	2092	17	s	s	X
m-1112	2092	18	≡	≡	PROPN
m-1112	2092	19	em	em	PROPN
m-1112	2092	20	-	-	PUNCT
m-1112	2092	21	r	r	NOUN
m-1112	2092	22	≡	≡	PROPN
m-1112	2092	23	f1	f1	NOUN
m-1112	2092	24	=	=	SYM
m-1112	2092	25	n	n	NOUN
m-1112	2092	26	,	,	PUNCT
m-1112	2092	27	f2	f2	ADV
m-1112	2092	28	,	,	PUNCT
m-1112	2092	29	f3	f3	PROPN
m-1112	2092	30	,	,	PUNCT
m-1112	2092	31	fd	fd	X
m-1112	2092	32	,	,	PUNCT
m-1112	2092	33	,	,	PUNCT
m-1112	2092	34	f	f	PROPN
m-1112	2092	35	n=	n=	ADJ
m-1112	2092	36	w²	w²	PROPN
m-1112	2092	37	]	]	PUNCT
m-1112	2092	38	,	,	PUNCT
m-1112	2092	39	and	and	CCONJ
m-1112	2092	40	as	as	ADP
m-1112	2092	41	particle	particle	NOUN
m-1112	2092	42	→	→	PROPN
m-1112	2092	43	[	[	PUNCT
m-1112	2092	44	f1=	f1=	PROPN
m-1112	2092	45	(	(	PUNCT
m-1112	2092	46	e²+h²	e²+h²	PROPN
m-1112	2092	47	)	)	PUNCT
m-1112	2092	48	=	=	SYM
m-1112	2092	49	n	n	CCONJ
m-1112	2092	50	(	(	PUNCT
m-1112	2092	51	1+√5)σ	1+√5)σ	NUM
m-1112	2092	52	2πr	2πr	NOUN
m-1112	2092	53	=	=	PUNCT
m-1112	2092	54	nb̅	nb̅	PROPN
m-1112	2092	55	π²	π²	NOUN
m-1112	2092	56	r⁴	r⁴	NOUN
m-1112	2092	57	]	]	PUNCT
m-1112	2092	58	→{w≡em	→{w≡em	NOUN
m-1112	2092	59	-	-	PUNCT
m-1112	2092	60	r≡	r≡	NOUN
m-1112	2092	61	[	[	X
m-1112	2092	62	εe²	εe²	NOUN
m-1112	2092	63	+	+	CCONJ
m-1112	2092	64	μb²	μb²	NOUN
m-1112	2092	65	]	]	X
m-1112	2092	66	=	=	PUNCT
m-1112	2093	1	2.λc.sin.2φ	2.λc.sin.2φ	NUM
m-1112	2093	2	}	}	PUNCT
m-1112	2093	3	and	and	CCONJ
m-1112	2093	4	is	be	AUX
m-1112	2093	5	the	the	DET
m-1112	2093	6	duality	duality	NOUN
m-1112	2093	7	of	of	ADP
m-1112	2093	8	an	an	DET
m-1112	2093	9	energy	energy	NOUN
m-1112	2093	10	-	-	PUNCT
m-1112	2093	11	storage	storage	NOUN
m-1112	2093	12	s	s	PART
m-1112	2093	13	≡	≡	PROPN
m-1112	2093	14	{	{	PUNCT
m-1112	2094	1	[	[	X
m-1112	2094	2	⊕←	⊕←	X
m-1112	2094	3	𝐫	𝐫	PART
m-1112	2094	4	→⊝	→⊝	NOUN
m-1112	2094	5	]	]	X
m-1112	2094	6	+	+	NUM
m-1112	2094	7	motion	motion	NOUN
m-1112	2094	8	m	m	VERB
m-1112	2094	9	.	.	PUNCT
m-1112	2095	1	[	[	X
m-1112	2095	2	87	87	NUM
m-1112	2095	3	-	-	SYM
m-1112	2095	4	89	89	NUM
m-1112	2095	5	]	]	PUNCT
m-1112	2095	6	5c	5c	NUM
m-1112	2095	7	..	..	PUNCT
m-1112	2095	8	the	the	DET
m-1112	2095	9	origination	origination	NOUN
m-1112	2095	10	of	of	ADP
m-1112	2095	11	hydrogen	hydrogen	NOUN
m-1112	2095	12	cave	cave	NOUN
m-1112	2095	13	h	h	NOUN
m-1112	2095	14	:	:	PUNCT
m-1112	2096	1	[	[	X
m-1112	2096	2	99	99	NUM
m-1112	2096	3	]	]	PUNCT
m-1112	2096	4	from	from	ADP
m-1112	2096	5	kepler	kepler	PROPN
m-1112	2096	6	third	third	ADJ
m-1112	2096	7	law	law	NOUN
m-1112	2096	8	,	,	PUNCT
m-1112	2096	9	the	the	DET
m-1112	2096	10	energy	energy	NOUN
m-1112	2096	11	-	-	PUNCT
m-1112	2096	12	closed	close	VERB
m-1112	2096	13	-	-	PUNCT
m-1112	2096	14	space	space	NOUN
m-1112	2096	15	equation	equation	NOUN
m-1112	2096	16	and	and	CCONJ
m-1112	2096	17	newton`s	newton`s	NOUN
m-1112	2096	18	laws	law	NOUN
m-1112	2096	19	of	of	ADP
m-1112	2096	20	motion	motion	NOUN
m-1112	2096	21	constant	constant	ADJ
m-1112	2096	22	k	k	X
m-1112	2096	23	=	=	SYM
m-1112	2096	24	v²	v²	PROPN
m-1112	2096	25	.	.	PUNCT
m-1112	2097	1	r	r	NOUN
m-1112	2097	2	=	=	PUNCT
m-1112	2097	3	(	(	PUNCT
m-1112	2097	4	w	w	NOUN
m-1112	2097	5	r	r	NOUN
m-1112	2097	6	)	)	PUNCT
m-1112	2097	7	².r	².r	PROPN
m-1112	2097	8	=	=	PUNCT
m-1112	2098	1	[	[	PUNCT
m-1112	2098	2	𝟐𝛑	𝟐𝛑	X
m-1112	2098	3	𝐓	𝐓	PROPN
m-1112	2098	4	𝐫	𝐫	PROPN
m-1112	2098	5	]	]	PUNCT
m-1112	2098	6	²	²	NUM
m-1112	2098	7	.	.	PUNCT
m-1112	2099	1	r	r	NOUN
m-1112	2099	2	=	=	PUNCT
m-1112	2099	3	𝟒𝛑²	𝟒𝛑²	PRON
m-1112	2099	4	𝐫²	𝐫²	NOUN
m-1112	2099	5	𝐓²	𝐓²	VERB
m-1112	2099	6	.	.	PUNCT
m-1112	2100	1	r	r	NOUN
m-1112	2100	2	=	=	PUNCT
m-1112	2100	3	𝟒𝛑²	𝟒𝛑²	NOUN
m-1112	2100	4	𝐫	𝐫	PROPN
m-1112	2100	5	³	³	PROPN
m-1112	2100	6	𝐓²	𝐓²	PROPN
m-1112	2100	7	=	=	SYM
m-1112	2100	8	4π²	4π²	NUM
m-1112	2100	9	.	.	PUNCT
m-1112	2101	1	𝐫³	𝐫³	PROPN
m-1112	2101	2	𝐓²	𝐓²	PROPN
m-1112	2101	3	=	=	SYM
m-1112	2101	4	4π².r³.𝐟²𝐩	4π².r³.𝐟²𝐩	NUM
m-1112	2101	5	…	…	PUNCT
m-1112	2101	6	…	…	PUNCT
m-1112	2101	7	..	..	PUNCT
m-1112	2101	8	(	(	PUNCT
m-1112	2101	9	k	k	X
m-1112	2101	10	)	)	PUNCT
m-1112	2101	11	ijo	ijo	PROPN
m-1112	2101	12	international	international	PROPN
m-1112	2101	13	journal	journal	PROPN
m-1112	2101	14	of	of	ADP
m-1112	2101	15	mathematics	mathematics	PROPN
m-1112	2101	16	(	(	PUNCT
m-1112	2101	17	issn	issn	PROPN
m-1112	2101	18	:	:	PUNCT
m-1112	2101	19	2992	2992	NUM
m-1112	2101	20	-	-	SYM
m-1112	2101	21	4421	4421	NUM
m-1112	2101	22	)	)	PUNCT
m-1112	2102	1	volume	volume	NOUN
m-1112	2102	2	08	08	NUM
m-1112	2103	1	|	|	ADV
m-1112	2103	2	issue	issue	NOUN
m-1112	2103	3	08	08	NUM
m-1112	2104	1	|	|	ADV
m-1112	2104	2	august	august	PROPN
m-1112	2104	3	2025	2025	NUM
m-1112	2104	4	|	|	ADV
m-1112	2104	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2104	6	ijo	ijo	PROPN
m-1112	2104	7	journals	journal	NOUN
m-1112	2104	8	74	74	NUM
m-1112	2104	9	the	the	DET
m-1112	2104	10	fundamental	fundamental	ADJ
m-1112	2104	11	particles	particle	NOUN
m-1112	2104	12	origination	origination	NOUN
m-1112	2104	13	mechanism	mechanism	NOUN
m-1112	2104	14	in	in	ADP
m-1112	2104	15	mfmf	mfmf	PROPN
m-1112	2104	16	pns	pns	PROPN
m-1112	2104	17	caves	cave	NOUN
m-1112	2104	18	.	.	PUNCT
m-1112	2105	1	because	because	SCONJ
m-1112	2105	2	(	(	PUNCT
m-1112	2105	3	k	k	X
m-1112	2105	4	)	)	PUNCT
m-1112	2105	5	is	be	AUX
m-1112	2105	6	constant	constant	ADJ
m-1112	2105	7	,	,	PUNCT
m-1112	2105	8	r	r	NOUN
m-1112	2105	9	³.f	³.f	VERB
m-1112	2105	10	²p	²p	NOUN
m-1112	2105	11	,	,	PUNCT
m-1112	2105	12	is	be	AUX
m-1112	2105	13	also	also	ADV
m-1112	2105	14	a	a	DET
m-1112	2105	15	constant	constant	ADJ
m-1112	2105	16	multiplication	multiplication	NOUN
m-1112	2105	17	of	of	ADP
m-1112	2105	18	cave	cave	NOUN
m-1112	2105	19	,	,	PUNCT
m-1112	2105	20	r	r	NOUN
m-1112	2105	21	,	,	PUNCT
m-1112	2105	22	and	and	CCONJ
m-1112	2105	23	the	the	DET
m-1112	2105	24	frequency	frequency	NOUN
m-1112	2105	25	f	f	NOUN
m-1112	2105	26	,	,	PUNCT
m-1112	2105	27	and	and	CCONJ
m-1112	2105	28	the	the	DET
m-1112	2105	29	work	work	NOUN
m-1112	2105	30	≡	≡	PROPN
m-1112	2105	31	motion	motion	NOUN
m-1112	2105	32	are	be	AUX
m-1112	2105	33	conserved	conserve	VERB
m-1112	2105	34	in	in	ADP
m-1112	2105	35	cave	cave	NOUN
m-1112	2105	36	,	,	PUNCT
m-1112	2105	37	r	r	NOUN
m-1112	2105	38	,	,	PUNCT
m-1112	2105	39	as	as	ADP
m-1112	2105	40	the	the	DET
m-1112	2105	41	,	,	PUNCT
m-1112	2105	42	n	n	NOUN
m-1112	2105	43	,	,	PUNCT
m-1112	2105	44	frequencies	frequency	NOUN
m-1112	2105	45	fn	fn	NOUN
m-1112	2105	46	=	=	SYM
m-1112	2105	47	n	n	PROPN
m-1112	2105	48	(	(	PUNCT
m-1112	2105	49	1+√5)σ	1+√5)σ	NUM
m-1112	2105	50	2πr	2πr	NOUN
m-1112	2105	51	=	=	PUNCT
m-1112	2105	52	nb	nb	INTJ
m-1112	2105	53	𝜋2r4	𝜋2r4	PROPN
m-1112	2105	54	,	,	PUNCT
m-1112	2105	55	and	and	CCONJ
m-1112	2105	56	for	for	ADP
m-1112	2105	57	a	a	DET
m-1112	2105	58	damping	damp	VERB
m-1112	2105	59	-	-	PUNCT
m-1112	2105	60	cave	cave	NOUN
m-1112	2105	61	→	→	SYM
m-1112	2105	62	r(t	r(t	NOUN
m-1112	2105	63	)	)	PUNCT
m-1112	2105	64	=	=	PUNCT
m-1112	2106	1	r(t	r(t	NOUN
m-1112	2106	2	+	+	CCONJ
m-1112	2106	3	w	w	X
m-1112	2106	4	)	)	PUNCT
m-1112	2106	5	←	←	PROPN
m-1112	2106	6	as	as	SCONJ
m-1112	2106	7	planck`s	planck`s	NOUN
m-1112	2106	8	scale	scale	NOUN
m-1112	2106	9	is	be	AUX
m-1112	2106	10	with	with	ADP
m-1112	2106	11	min	min	NOUN
m-1112	2106	12	-	-	ADJ
m-1112	2106	13	damping	damp	VERB
m-1112	2106	14	=	=	NOUN
m-1112	2106	15	1	1	NUM
m-1112	2106	16	and	and	CCONJ
m-1112	2106	17	unit	unit	NOUN
m-1112	2106	18	-	-	PUNCT
m-1112	2106	19	energy	energy	NOUN
m-1112	2106	20	-	-	PUNCT
m-1112	2106	21	quantity	quantity	NOUN
m-1112	2106	22	𝐖𝐮	𝐖𝐮	PROPN
m-1112	2106	23	,	,	PUNCT
m-1112	2106	24	(	(	PUNCT
m-1112	2106	25	the	the	DET
m-1112	2106	26	critical	critical	ADJ
m-1112	2106	27	-	-	PUNCT
m-1112	2106	28	energy	energy	NOUN
m-1112	2106	29	-	-	PUNCT
m-1112	2106	30	unit	unit	NOUN
m-1112	2106	31	in	in	ADP
m-1112	2106	32	min	min	PROPN
m-1112	2106	33	,	,	PUNCT
m-1112	2106	34	r	r	NOUN
m-1112	2106	35	)	)	PUNCT
m-1112	2106	36	,	,	PUNCT
m-1112	2106	37	is	be	AUX
m-1112	2106	38	this	this	DET
m-1112	2106	39	unit	unit	NOUN
m-1112	2106	40	-	-	PUNCT
m-1112	2106	41	stress	stress	NOUN
m-1112	2106	42	-	-	PUNCT
m-1112	2106	43	gravity	gravity	NOUN
m-1112	2106	44	g	g	NOUN
m-1112	2106	45	,	,	PUNCT
m-1112	2106	46	as	as	SCONJ
m-1112	2106	47	k	k	PROPN
m-1112	2106	48	=	=	SYM
m-1112	2106	49	e	e	X
m-1112	2106	50	=	=	NOUN
m-1112	2106	51	t²	t²	NOUN
m-1112	2106	52	a³	a³	ADV
m-1112	2106	53	=	=	SYM
m-1112	2106	54	g	g	NOUN
m-1112	2106	55	=	=	SYM
m-1112	2106	56	1	1	NUM
m-1112	2106	57	f	f	PROPN
m-1112	2106	58	².a³	².a³	NOUN
m-1112	2106	59	,	,	PUNCT
m-1112	2106	60	i.e.	i.e.	X
m-1112	2106	61	→	→	SYM
m-1112	2106	62	stress	stress	ADJ
m-1112	2106	63	�	�	PROPN
m-1112	2106	64	̅	̅	NOUN
m-1112	2106	65	�	�	PROPN
m-1112	2106	66	,	,	PUNCT
m-1112	2106	67	when	when	SCONJ
m-1112	2106	68	is	be	AUX
m-1112	2106	69	entering	enter	VERB
m-1112	2106	70	into	into	ADP
m-1112	2106	71	the	the	DET
m-1112	2106	72	minimum	minimum	ADJ
m-1112	2106	73	cave	cave	NOUN
m-1112	2106	74	,	,	PUNCT
m-1112	2106	75	a	a	PRON
m-1112	2106	76	,	,	PUNCT
m-1112	2106	77	of	of	ADP
m-1112	2106	78	a	a	DET
m-1112	2106	79	minimum	minimum	ADJ
m-1112	2106	80	surface	surface	NOUN
m-1112	2106	81	,	,	PUNCT
m-1112	2106	82	then	then	ADV
m-1112	2106	83	from	from	ADP
m-1112	2106	84	the	the	DET
m-1112	2106	85	period	period	NOUN
m-1112	2106	86	of	of	ADP
m-1112	2106	87	rotation	rotation	NOUN
m-1112	2106	88	t	t	PROPN
m-1112	2106	89	on	on	ADP
m-1112	2106	90	the	the	DET
m-1112	2106	91	perimeter	perimeter	NOUN
m-1112	2106	92	,	,	PUNCT
m-1112	2106	93	is	be	AUX
m-1112	2106	94	created	create	VERB
m-1112	2106	95	in	in	ADP
m-1112	2106	96	surface	surface	NOUN
m-1112	2106	97	the	the	DET
m-1112	2106	98	minimum	minimum	ADJ
m-1112	2106	99	quantity	quantity	NOUN
m-1112	2106	100	of	of	ADP
m-1112	2106	101	energy	energy	NOUN
m-1112	2106	102	-	-	PUNCT
m-1112	2106	103	cave	cave	NOUN
m-1112	2106	104	and	and	CCONJ
m-1112	2106	105	is	be	AUX
m-1112	2106	106	the	the	DET
m-1112	2106	107	hydrogen	hydrogen	NOUN
m-1112	2106	108	-	-	PUNCT
m-1112	2106	109	atom	atom	NOUN
m-1112	2106	110	,	,	PUNCT
m-1112	2106	111	where	where	SCONJ
m-1112	2106	112	gf	gf	PROPN
m-1112	2106	113	²	²	NUM
m-1112	2106	114	≡	≡	PROPN
m-1112	2106	115	the	the	DET
m-1112	2106	116	energy	energy	NOUN
m-1112	2106	117	-	-	PUNCT
m-1112	2106	118	part	part	NOUN
m-1112	2106	119	embodied	embody	VERB
m-1112	2106	120	with	with	ADP
m-1112	2106	121	stress	stress	NOUN
m-1112	2106	122	�	�	PROPN
m-1112	2106	123	̅	̅	NOUN
m-1112	2106	124	�	�	PROPN
m-1112	2106	125	,	,	PUNCT
m-1112	2106	126	and	and	CCONJ
m-1112	2106	127	the	the	DET
m-1112	2106	128	cave	cave	NOUN
m-1112	2106	129	a³	a³	PROPN
m-1112	2106	130	,	,	PUNCT
m-1112	2106	131	is	be	AUX
m-1112	2106	132	the	the	DET
m-1112	2106	133	space	space	NOUN
m-1112	2106	134	-	-	PUNCT
m-1112	2106	135	part	part	NOUN
m-1112	2106	136	,	,	PUNCT
m-1112	2106	137	in	in	ADP
m-1112	2106	138	3	3	NUM
m-1112	2106	139	-	-	PUNCT
m-1112	2106	140	dof	dof	NOUN
m-1112	2106	141	space	space	NOUN
m-1112	2106	142	as	as	ADP
m-1112	2106	143	→	→	SYM
m-1112	2106	144	t	t	NOUN
m-1112	2106	145	²	²	NUM
m-1112	2106	146	=	=	SYM
m-1112	2106	147	g	g	NOUN
m-1112	2106	148	a³	a³	NOUN
m-1112	2106	149	=	=	SYM
m-1112	2106	150	9,808238	9,808238	NUM
m-1112	2106	151	.	.	PUNCT
m-1112	2107	1	[	[	PUNCT
m-1112	2107	2	2	2	NUM
m-1112	2107	3	,	,	PUNCT
m-1112	2107	4	1145016.10−11	1145016.10−11	NUM
m-1112	2107	5	]	]	PUNCT
m-1112	2107	6	³	³	PROPN
m-1112	2107	7	=	=	SYM
m-1112	2107	8	9	9	NUM
m-1112	2107	9	,	,	PUNCT
m-1112	2107	10	2728158.10−32	2728158.10−32	NUM
m-1112	2107	11	s	s	NOUN
m-1112	2107	12	,	,	PUNCT
m-1112	2107	13	and	and	CCONJ
m-1112	2107	14	period	period	NOUN
m-1112	2107	15	t	t	NOUN
m-1112	2107	16	=	=	PUNCT
m-1112	2108	1	3,04513.10−16	3,04513.10−16	NUM
m-1112	2108	2	s	s	PART
m-1112	2108	3	,	,	PUNCT
m-1112	2108	4	or	or	CCONJ
m-1112	2108	5	frequency	frequency	NOUN
m-1112	2108	6	f	f	NOUN
m-1112	2108	7	=	=	SYM
m-1112	2108	8	3,2839982.1015	3,2839982.1015	NUM
m-1112	2108	9	/	/	SYM
m-1112	2108	10	s	s	PROPN
m-1112	2108	11	.	.	PUNCT
m-1112	2109	1	from	from	ADP
m-1112	2109	2	equation	equation	NOUN
m-1112	2109	3	e	e	NOUN
m-1112	2109	4	=	=	NOUN
m-1112	2109	5	h	h	NOUN
m-1112	2109	6	f	f	NOUN
m-1112	2109	7	=	=	NOUN
m-1112	2109	8	6.62607.10−34	6.62607.10−34	NUM
m-1112	2109	9	.	.	PUNCT
m-1112	2110	1	3,2839982.1015	3,2839982.1015	NUM
m-1112	2110	2	=	=	SYM
m-1112	2110	3	2,175999	2,175999	NOUN
m-1112	2110	4	.	.	PUNCT
m-1112	2111	1	10−18	10−18	NUM
m-1112	2111	2	j	j	PROPN
m-1112	2111	3	/	/	SYM
m-1112	2111	4	(	(	PUNCT
m-1112	2111	5	1,6022	1,6022	PROPN
m-1112	2111	6	.	.	PUNCT
m-1112	2112	1	10−19	10−19	ADJ
m-1112	2112	2	)	)	PUNCT
m-1112	2112	3	=	=	SYM
m-1112	2112	4	13,59999	13,59999	NUM
m-1112	2112	5	ev	ev	NOUN
m-1112	2112	6	above	above	ADP
m-1112	2112	7	quantized	quantize	VERB
m-1112	2112	8	energy	energy	NOUN
m-1112	2112	9	of	of	ADP
m-1112	2112	10	13,6	13,6	NUM
m-1112	2112	11	ev	ev	NOUN
m-1112	2112	12	,	,	PUNCT
m-1112	2112	13	corresponds	correspond	VERB
m-1112	2112	14	to	to	ADP
m-1112	2112	15	the	the	DET
m-1112	2112	16	hydrogen	hydrogen	NOUN
m-1112	2112	17	-	-	PUNCT
m-1112	2112	18	atom	atom	NOUN
m-1112	2112	19	-	-	PUNCT
m-1112	2112	20	cave	cave	NOUN
m-1112	2112	21	.	.	PUNCT
m-1112	2113	1	it	it	PRON
m-1112	2113	2	was	be	AUX
m-1112	2113	3	shown	show	VERB
m-1112	2113	4	that	that	SCONJ
m-1112	2113	5	in	in	ADP
m-1112	2113	6	conservative	conservative	ADJ
m-1112	2113	7	systems	system	NOUN
m-1112	2113	8	of	of	ADP
m-1112	2113	9	a	a	DET
m-1112	2113	10	central	central	ADJ
m-1112	2113	11	-	-	PUNCT
m-1112	2113	12	force	force	NOUN
m-1112	2113	13	,	,	PUNCT
m-1112	2113	14	the	the	DET
m-1112	2113	15	total	total	ADJ
m-1112	2113	16	energy	energy	NOUN
m-1112	2113	17	e	e	NOUN
m-1112	2113	18	is	be	AUX
m-1112	2113	19	conserved	conserve	VERB
m-1112	2113	20	and	and	CCONJ
m-1112	2113	21	at	at	ADP
m-1112	2113	22	periapsis	periapsis	NOUN
m-1112	2113	23	,	,	PUNCT
m-1112	2113	24	energy	energy	NOUN
m-1112	2113	25	e	e	NOUN
m-1112	2113	26	=	=	SYM
m-1112	2113	27	𝐆.𝐌𝐦	𝐆.𝐌𝐦	PROPN
m-1112	2113	28	𝟐	𝟐	NUM
m-1112	2113	29	𝐚	𝐚	NOUN
m-1112	2113	30	and	and	CCONJ
m-1112	2113	31	e	e	X
m-1112	2114	1	=	=	PUNCT
m-1112	2114	2	√1	√1	PROPN
m-1112	2114	3	+	+	CCONJ
m-1112	2114	4	2el2	2el2	NUM
m-1112	2114	5	/	/	SYM
m-1112	2114	6	g²m²m³	g²m²m³	NOUN
m-1112	2114	7	and	and	CCONJ
m-1112	2114	8	for	for	ADP
m-1112	2114	9	e	e	NOUN
m-1112	2114	10	=	=	SYM
m-1112	2114	11	0	0	PROPN
m-1112	2114	12	then	then	ADV
m-1112	2114	13	→	→	SYM
m-1112	2114	14	e	e	X
m-1112	2114	15	=	=	SYM
m-1112	2114	16	g²m²	g²m²	X
m-1112	2115	1	m³	m³	VERB
m-1112	2115	2	2	2	NUM
m-1112	2115	3	l²	l²	NOUN
m-1112	2115	4	,	,	PUNCT
m-1112	2115	5	i.e.	i.e.	X
m-1112	2115	6	energy	energy	NOUN
m-1112	2115	7	is	be	AUX
m-1112	2115	8	always	always	ADV
m-1112	2115	9	negative	negative	ADJ
m-1112	2115	10	.	.	PUNCT
m-1112	2116	1	hydrogen	hydrogen	NOUN
m-1112	2116	2	cave	cave	PROPN
m-1112	2116	3	constant	constant	ADJ
m-1112	2116	4	is	be	AUX
m-1112	2116	5	k	k	NOUN
m-1112	2116	6	=	=	PUNCT
m-1112	2116	7	e	e	NOUN
m-1112	2116	8	=	=	NOUN
m-1112	2116	9	t²	t²	NOUN
m-1112	2116	10	a³	a³	ADV
m-1112	2116	11	=	=	SYM
m-1112	2116	12	g	g	NOUN
m-1112	2116	13	=	=	PUNCT
m-1112	2117	1	[	[	PUNCT
m-1112	2117	2	4π²	4π²	NUM
m-1112	2117	3	gm	gm	X
m-1112	2117	4	]	]	PUNCT
m-1112	2117	5	therefore	therefore	ADV
m-1112	2117	6	gm	gm	PROPN
m-1112	2118	1	=	=	PUNCT
m-1112	2118	2	4π²a	4π²a	NUM
m-1112	2118	3	g	g	NOUN
m-1112	2118	4	and	and	CCONJ
m-1112	2118	5	from	from	ADP
m-1112	2118	6	newton	newton	PROPN
m-1112	2118	7	total	total	ADJ
m-1112	2118	8	-	-	PUNCT
m-1112	2118	9	energy	energy	NOUN
m-1112	2118	10	e	e	NOUN
m-1112	2118	11	=	=	SYM
m-1112	2118	12	gm	gm	PROPN
m-1112	2118	13	m	m	PROPN
m-1112	2118	14	2	2	NUM
m-1112	2118	15	a	a	PRON
m-1112	2118	16	,	,	PUNCT
m-1112	2118	17	rotational	rotational	ADJ
m-1112	2118	18	-	-	PUNCT
m-1112	2118	19	momentum	momentum	NOUN
m-1112	2118	20	l	l	NOUN
m-1112	2118	21	=	=	PUNCT
m-1112	2118	22	√(1	√(1	NOUN
m-1112	2118	23	−	−	PROPN
m-1112	2118	24	e2	e2	PROPN
m-1112	2118	25	)	)	PUNCT
m-1112	2118	26	.	.	PUNCT
m-1112	2119	1	gmm²	gmm²	PROPN
m-1112	2119	2	.	.	PUNCT
m-1112	2120	1	a	a	DET
m-1112	2120	2	eccentricity	eccentricity	NOUN
m-1112	2120	3	e	e	X
m-1112	2120	4	=	=	SYM
m-1112	2120	5	0	0	NUM
m-1112	2120	6	,	,	PUNCT
m-1112	2120	7	g	g	PROPN
m-1112	2120	8	mm	mm	PROPN
m-1112	2120	9	=	=	SYM
m-1112	2120	10	2a.e	2a.e	NUM
m-1112	2120	11	,	,	PUNCT
m-1112	2120	12	and	and	CCONJ
m-1112	2120	13	then	then	ADV
m-1112	2120	14	→	→	SYM
m-1112	2120	15	l²	l²	NOUN
m-1112	2120	16	=	=	SYM
m-1112	2120	17	gmm².a	gmm².a	PROPN
m-1112	2120	18	=	=	PUNCT
m-1112	2120	19	2ae[a	2ae[a	NUM
m-1112	2120	20	]	]	X
m-1112	2120	21	=	=	PUNCT
m-1112	2120	22	2a²e	2a²e	NOUN
m-1112	2120	23	.	.	PUNCT
m-1112	2121	1	i.e.	i.e.	X
m-1112	2121	2	equation	equation	NOUN
m-1112	2121	3	l²	l²	PROPN
m-1112	2121	4	=	=	SYM
m-1112	2121	5	2a².e	2a².e	PROPN
m-1112	2121	6	,	,	PUNCT
m-1112	2121	7	denotes	denote	VERB
m-1112	2121	8	that	that	SCONJ
m-1112	2121	9	angular	angular	ADJ
m-1112	2121	10	-momentum	-momentum	PROPN
m-1112	2121	11	l	l	NOUN
m-1112	2121	12	,	,	PUNCT
m-1112	2121	13	in	in	ADP
m-1112	2121	14	orbit	orbit	NOUN
m-1112	2121	15	rims	rim	NOUN
m-1112	2121	16	is	be	AUX
m-1112	2121	17	always	always	ADV
m-1112	2121	18	negative	negative	ADJ
m-1112	2121	19	and	and	CCONJ
m-1112	2121	20	equal	equal	ADJ
m-1112	2121	21	to	to	ADP
m-1112	2121	22	,	,	PUNCT
m-1112	2121	23	l	l	PROPN
m-1112	2121	24	=	=	PUNCT
m-1112	2121	25	a	a	DET
m-1112	2121	26	√𝟐.	√𝟐.	VERB
m-1112	2121	27	𝐚𝐄	𝐚𝐄	NOUN
m-1112	2121	28	.	.	PUNCT
m-1112	2122	1	so	so	ADV
m-1112	2122	2	,	,	PUNCT
m-1112	2122	3	hydrogen	hydrogen	NOUN
m-1112	2122	4	-	-	PUNCT
m-1112	2122	5	atom	atom	NOUN
m-1112	2122	6	,	,	PUNCT
m-1112	2122	7	is	be	AUX
m-1112	2122	8	the	the	DET
m-1112	2122	9	minimum	minimum	ADJ
m-1112	2122	10	-	-	PUNCT
m-1112	2122	11	energy	energy	NOUN
m-1112	2122	12	-	-	PUNCT
m-1112	2122	13	cave	cave	NOUN
m-1112	2122	14	in	in	ADP
m-1112	2122	15	planck`s	planck`s	NOUN
m-1112	2122	16	-	-	PUNCT
m-1112	2122	17	length	length	NOUN
m-1112	2122	18	,	,	PUNCT
m-1112	2122	19	occupying	occupy	VERB
m-1112	2122	20	the	the	DET
m-1112	2122	21	minimum	minimum	ADJ
m-1112	2122	22	negative	negative	ADJ
m-1112	2122	23	-	-	PUNCT
m-1112	2122	24	energy	energy	NOUN
m-1112	2122	25	in	in	ADP
m-1112	2122	26	rims	rims	PROPN
m-1112	2122	27	≡	≡	PROPN
m-1112	2122	28	caves	cave	NOUN
m-1112	2122	29	,	,	PUNCT
m-1112	2122	30	the	the	DET
m-1112	2122	31	space	space	NOUN
m-1112	2122	32	,	,	PUNCT
m-1112	2122	33	where	where	SCONJ
m-1112	2122	34	quantum	quantum	NOUN
m-1112	2122	35	-	-	PUNCT
m-1112	2122	36	energy	energy	NOUN
m-1112	2122	37	-	-	PUNCT
m-1112	2122	38	rims	rim	NOUN
m-1112	2122	39	are	be	AUX
m-1112	2122	40	the	the	DET
m-1112	2122	41	plane	plane	NOUN
m-1112	2122	42	traces	trace	NOUN
m-1112	2122	43	-	-	PUNCT
m-1112	2122	44	conductors	conductor	NOUN
m-1112	2122	45	in	in	ADP
m-1112	2122	46	where	where	SCONJ
m-1112	2122	47	can	can	AUX
m-1112	2122	48	roll	roll	VERB
m-1112	2122	49	the	the	DET
m-1112	2122	50	⊝	⊝	NUM
m-1112	2122	51	charged	charge	VERB
m-1112	2122	52	electrons	electron	NOUN
m-1112	2122	53	.	.	PUNCT
m-1112	2123	1	in	in	ADP
m-1112	2123	2	hydrogen	hydrogen	NOUN
m-1112	2123	3	-	-	PUNCT
m-1112	2123	4	cave	cave	NOUN
m-1112	2123	5	,	,	PUNCT
m-1112	2123	6	the	the	DET
m-1112	2123	7	resonance	resonance	NOUN
m-1112	2123	8	frequency	frequency	NOUN
m-1112	2123	9	of	of	ADP
m-1112	2123	10	an	an	DET
m-1112	2123	11	electron	electron	NOUN
m-1112	2123	12	⊝	⊝	NUM
m-1112	2123	13	,	,	PUNCT
m-1112	2123	14	and	and	CCONJ
m-1112	2123	15	a	a	DET
m-1112	2123	16	proton	proton	NOUN
m-1112	2123	17	⊕	⊕	PROPN
m-1112	2123	18	,	,	PUNCT
m-1112	2123	19	happens	happen	VERB
m-1112	2123	20	from	from	ADP
m-1112	2123	21	the	the	DET
m-1112	2123	22	stationary	stationary	ADJ
m-1112	2123	23	unit	unit	NOUN
m-1112	2123	24	-	-	PUNCT
m-1112	2123	25	cave	cave	NOUN
m-1112	2123	26	of	of	ADP
m-1112	2123	27	a	a	DET
m-1112	2123	28	system	system	NOUN
m-1112	2123	29	of	of	ADP
m-1112	2123	30	kepler	kepler	PROPN
m-1112	2123	31	second	second	ADJ
m-1112	2123	32	planetary	planetary	NOUN
m-1112	2123	33	-	-	PUNCT
m-1112	2123	34	law	law	NOUN
m-1112	2123	35	as	as	ADP
m-1112	2123	36	equation	equation	NOUN
m-1112	2123	37	,	,	PUNCT
m-1112	2123	38	4	4	NUM
m-1112	2123	39	π²	π²	NOUN
m-1112	2123	40	m	m	NOUN
m-1112	2123	41	f	f	NOUN
m-1112	2123	42	²o	²o	NOUN
m-1112	2124	1	=	=	SYM
m-1112	2124	2	k	k	PROPN
m-1112	2124	3	,	,	PUNCT
m-1112	2124	4	and	and	CCONJ
m-1112	2124	5	from	from	ADP
m-1112	2124	6	constant	constant	ADJ
m-1112	2124	7	law	law	NOUN
m-1112	2124	8	of	of	ADP
m-1112	2124	9	areas	area	NOUN
m-1112	2124	10	1	1	NUM
m-1112	2124	11	=	=	SYM
m-1112	2124	12	k	k	X
m-1112	2124	13	.𝐟	.𝐟	X
m-1112	2124	14	²𝐨	²𝐨	VERB
m-1112	2124	15	𝐚	𝐚	ADP
m-1112	2124	16	𝟑	𝟑	INTJ
m-1112	2124	17	.their	.their	PRON
m-1112	2124	18	common	common	ADJ
m-1112	2124	19	constant	constant	ADJ
m-1112	2124	20	-	-	PUNCT
m-1112	2124	21	energy	energy	NOUN
m-1112	2124	22	k	k	NOUN
m-1112	2124	23	,	,	PUNCT
m-1112	2124	24	is	be	AUX
m-1112	2124	25	→	→	SYM
m-1112	2124	26	k	k	X
m-1112	2124	27	=	=	SYM
m-1112	2124	28	4	4	NUM
m-1112	2124	29	π²	π²	NOUN
m-1112	2124	30	m	m	PROPN
m-1112	2124	31	f	f	NOUN
m-1112	2124	32	²p	²p	NOUN
m-1112	2124	33	=	=	SYM
m-1112	2124	34	1	1	NUM
m-1112	2124	35	𝐟	𝐟	NUM
m-1112	2124	36	²𝐩	²𝐩	PROPN
m-1112	2124	37	𝐚𝟑	𝐚𝟑	PROPN
m-1112	2124	38	or	or	CCONJ
m-1112	2124	39	,	,	PUNCT
m-1112	2124	40	f	f	PROPN
m-1112	2124	41	⁴p	⁴p	NOUN
m-1112	2124	42	=	=	SYM
m-1112	2124	43	1	1	NUM
m-1112	2124	44	4π²ma3	4π²ma3	NUM
m-1112	2124	45	and	and	CCONJ
m-1112	2124	46	fp	fp	NOUN
m-1112	2124	47	=	=	NOUN
m-1112	2124	48	√	√	NUM
m-1112	2124	49	1	1	NUM
m-1112	2124	50	4π²m.a3	4π²m.a3	NUM
m-1112	2124	51	4	4	NUM
m-1112	2124	52	.	.	PUNCT
m-1112	2125	1	a	a	DET
m-1112	2125	2	loop	loop	NOUN
m-1112	2125	3	in	in	ADP
m-1112	2125	4	planck`s	planck`s	NOUN
m-1112	2125	5	length	length	NOUN
m-1112	2125	6	2a	2a	NUM
m-1112	2125	7	=	=	PUNCT
m-1112	2126	1	l	l	NOUN
m-1112	2126	2	p	p	X
m-1112	2126	3	=	=	PROPN
m-1112	2126	4	π.1,616199.10−35	π.1,616199.10−35	PROPN
m-1112	2126	5	m	m	NOUN
m-1112	2126	6	with	with	ADP
m-1112	2126	7	frequency	frequency	NOUN
m-1112	2126	8	f	f	NOUN
m-1112	2126	9	=	=	PUNCT
m-1112	2126	10	c	c	PROPN
m-1112	2126	11	𝜆	𝜆	NOUN
m-1112	2126	12	,	,	PUNCT
m-1112	2126	13	where	where	SCONJ
m-1112	2126	14	then	then	ADV
m-1112	2126	15	issues	issue	VERB
m-1112	2126	16	f	f	PROPN
m-1112	2126	17	⁴p	⁴p	NOUN
m-1112	2126	18	=	=	SYM
m-1112	2126	19	1	1	NUM
m-1112	2126	20	4π²ma3	4π²ma3	NUM
m-1112	2126	21	=	=	PUNCT
m-1112	2127	1	[	[	PUNCT
m-1112	2127	2	c	c	NOUN
m-1112	2127	3	𝜆	𝜆	X
m-1112	2127	4	]	]	PUNCT
m-1112	2127	5	⁴	⁴	PROPN
m-1112	2127	6	=	=	SYM
m-1112	2127	7	[	[	PUNCT
m-1112	2127	8	1	1	NUM
m-1112	2127	9	𝜆	𝜆	NOUN
m-1112	2127	10	]	]	PUNCT
m-1112	2127	11	⁴.{𝑐4	⁴.{𝑐4	NOUN
m-1112	2127	12	=	=	SYM
m-1112	2127	13	1	1	NUM
m-1112	2128	1	[	[	X
m-1112	2128	2	4πa3]mπa	4πa3]mπa	NUM
m-1112	2128	3	}	}	PUNCT
m-1112	2128	4	,	,	PUNCT
m-1112	2128	5	and	and	CCONJ
m-1112	2128	6	for	for	ADP
m-1112	2128	7	the	the	DET
m-1112	2128	8	unit	unit	NOUN
m-1112	2128	9	intensity	intensity	NOUN
m-1112	2129	1	i	i	NOUN
m-1112	2129	2	=	=	NOUN
m-1112	2129	3	energy	energy	NOUN
m-1112	2129	4	area	area	NOUN
m-1112	2129	5	=	=	SYM
m-1112	2129	6	e	e	X
m-1112	2129	7	=	=	PRON
m-1112	2129	8	hf	hf	ADP
m-1112	2129	9	a	a	PRON
m-1112	2129	10	=	=	SYM
m-1112	2129	11	4πa3	4πa3	NUM
m-1112	2129	12	=	=	NOUN
m-1112	2129	13	1kw	1kw	NOUN
m-1112	2129	14	a	a	PRON
m-1112	2129	15	=	=	SYM
m-1112	2129	16	1	1	NUM
m-1112	2130	1	[	[	X
m-1112	2130	2	4πa3	4πa3	X
m-1112	2130	3	]	]	X
m-1112	2130	4	=	=	SYM
m-1112	2130	5	1	1	NUM
m-1112	2130	6	𝜆⁴	𝜆⁴	PROPN
m-1112	2130	7	{	{	PUNCT
m-1112	2130	8	mc4	mc4	PROPN
m-1112	2130	9	.	.	PUNCT
m-1112	2131	1	πa}=	πa}=	ADJ
m-1112	2131	2	1	1	NUM
m-1112	2131	3	𝜆⁴	𝜆⁴	PROPN
m-1112	2131	4	{	{	PUNCT
m-1112	2131	5	1}.80,760865.1032	1}.80,760865.1032	NUM
m-1112	2131	6	.	.	PUNCT
m-1112	2132	1	(	(	PUNCT
m-1112	2132	2	3,14).0,8081.10−35	3,14).0,8081.10−35	NUM
m-1112	2132	3	=	=	NUM
m-1112	2132	4	0,5865	0,5865	PROPN
m-1112	2132	5	.	.	PUNCT
m-1112	2132	6	{	{	PUNCT
m-1112	2132	7	1	1	NUM
m-1112	2132	8	𝜆⁴	𝜆⁴	NOUN
m-1112	2132	9	}	}	PUNCT
m-1112	2132	10	,	,	PUNCT
m-1112	2132	11	and	and	CCONJ
m-1112	2132	12	e	e	X
m-1112	2132	13	-	-	NOUN
m-1112	2132	14	intension	intension	NOUN
m-1112	2132	15	is	be	AUX
m-1112	2132	16	→	→	SYM
m-1112	2132	17	i	i	PRON
m-1112	2132	18	=	=	PUNCT
m-1112	2132	19	0,5865	0,5865	ADJ
m-1112	2132	20	.	.	PUNCT
m-1112	2133	1	{	{	PUNCT
m-1112	2133	2	𝟏	𝟏	NUM
m-1112	2133	3	𝝀⁴	𝝀⁴	NOUN
m-1112	2133	4	}	}	PUNCT
m-1112	2133	5	←	←	PROPN
m-1112	2133	6	or	or	CCONJ
m-1112	2133	7	,	,	PUNCT
m-1112	2133	8	is	be	AUX
m-1112	2133	9	the	the	DET
m-1112	2133	10	rayleigh	rayleigh	NOUN
m-1112	2133	11	scattering	scattering	NOUN
m-1112	2133	12	,	,	PUNCT
m-1112	2133	13	i.e.	i.e.	X
m-1112	2133	14	ijo	ijo	PROPN
m-1112	2133	15	international	international	PROPN
m-1112	2133	16	journal	journal	PROPN
m-1112	2133	17	of	of	ADP
m-1112	2133	18	mathematics	mathematics	PROPN
m-1112	2133	19	(	(	PUNCT
m-1112	2133	20	issn	issn	PROPN
m-1112	2133	21	:	:	PUNCT
m-1112	2133	22	2992	2992	NUM
m-1112	2133	23	-	-	SYM
m-1112	2133	24	4421	4421	NUM
m-1112	2133	25	)	)	PUNCT
m-1112	2134	1	volume	volume	NOUN
m-1112	2134	2	08	08	NUM
m-1112	2135	1	|	|	ADV
m-1112	2135	2	issue	issue	NOUN
m-1112	2135	3	08	08	NUM
m-1112	2136	1	|	|	ADV
m-1112	2136	2	august	august	PROPN
m-1112	2136	3	2025	2025	NUM
m-1112	2136	4	|	|	ADV
m-1112	2136	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2136	6	ijo	ijo	PROPN
m-1112	2136	7	journals	journal	NOUN
m-1112	2136	8	75	75	NUM
m-1112	2136	9	the	the	DET
m-1112	2136	10	fundamental	fundamental	ADJ
m-1112	2136	11	particles	particle	NOUN
m-1112	2136	12	origination	origination	NOUN
m-1112	2136	13	mechanism	mechanism	NOUN
m-1112	2136	14	in	in	ADP
m-1112	2136	15	mfmf	mfmf	PROPN
m-1112	2136	16	pns	pns	PROPN
m-1112	2136	17	caves	cave	NOUN
m-1112	2136	18	.	.	PUNCT
m-1112	2137	1	the	the	DET
m-1112	2137	2	quanta	quanta	PROPN
m-1112	2137	3	of	of	ADP
m-1112	2137	4	energy	energy	NOUN
m-1112	2137	5	,	,	PUNCT
m-1112	2137	6	passing	pass	VERB
m-1112	2137	7	through	through	ADP
m-1112	2137	8	a	a	DET
m-1112	2137	9	unit	unit	NOUN
m-1112	2137	10	-	-	PUNCT
m-1112	2137	11	surface	surface	NOUN
m-1112	2137	12	or	or	CCONJ
m-1112	2137	13	volume	volume	NOUN
m-1112	2137	14	,	,	PUNCT
m-1112	2137	15	which	which	PRON
m-1112	2137	16	becomes	become	VERB
m-1112	2137	17	from	from	ADP
m-1112	2137	18	the	the	DET
m-1112	2137	19	kepler`s	kepler`s	NOUN
m-1112	2137	20	second	second	ADJ
m-1112	2137	21	and	and	CCONJ
m-1112	2137	22	third	third	ADJ
m-1112	2137	23	law	law	NOUN
m-1112	2137	24	mechanism	mechanism	NOUN
m-1112	2137	25	,	,	PUNCT
m-1112	2137	26	is	be	AUX
m-1112	2137	27	inversely	inversely	ADV
m-1112	2137	28	proportional	proportional	ADJ
m-1112	2137	29	to	to	ADP
m-1112	2137	30	the	the	DET
m-1112	2137	31	fourth	fourth	ADJ
m-1112	2137	32	power	power	NOUN
m-1112	2137	33	of	of	ADP
m-1112	2137	34	the	the	DET
m-1112	2137	35	wavelength	wavelength	NOUN
m-1112	2137	36	𝝀	𝝀	PROPN
m-1112	2137	37	.	.	PUNCT
m-1112	2138	1	in	in	ADP
m-1112	2138	2	outer	outer	ADJ
m-1112	2138	3	electromagnetic	electromagnetic	ADJ
m-1112	2138	4	fields	field	NOUN
m-1112	2138	5	,	,	PUNCT
m-1112	2138	6	frequency	frequency	NOUN
m-1112	2138	7	,	,	PUNCT
m-1112	2138	8	w	w	PROPN
m-1112	2138	9	,	,	PUNCT
m-1112	2138	10	is	be	AUX
m-1112	2138	11	that	that	PRON
m-1112	2138	12	of	of	ADP
m-1112	2138	13	inner	inner	ADJ
m-1112	2138	14	motion	motion	NOUN
m-1112	2138	15	→	→	SYM
m-1112	2138	16	w	w	NOUN
m-1112	2138	17	=	=	SYM
m-1112	2138	18	2π	2π	NOUN
m-1112	2138	19	t	t	NOUN
m-1112	2138	20	=	=	SYM
m-1112	2138	21	2π.fn	2π.fn	NUM
m-1112	2138	22	≡	≡	PROPN
m-1112	2138	23	[	[	PUNCT
m-1112	2138	24	1+√5	1+√5	NUM
m-1112	2138	25	2	2	NUM
m-1112	2138	26	]	]	PUNCT
m-1112	2138	27	σ	σ	NUM
m-1112	2138	28	2πr	2πr	NOUN
m-1112	2138	29	=	=	X
m-1112	2138	30	𝛔.𝚽	𝛔.𝚽	PUNCT
m-1112	2139	1	𝐫	𝐫	X
m-1112	2139	2	,	,	PUNCT
m-1112	2139	3	which	which	PRON
m-1112	2139	4	continuous	continuous	ADJ
m-1112	2139	5	to	to	PART
m-1112	2139	6	follow	follow	VERB
m-1112	2139	7	the	the	DET
m-1112	2139	8	growth	growth	NOUN
m-1112	2139	9	-	-	PUNCT
m-1112	2139	10	golden	golden	ADJ
m-1112	2139	11	-	-	PUNCT
m-1112	2139	12	ratio	ratio	NOUN
m-1112	2139	13	-	-	PUNCT
m-1112	2139	14	pattern	pattern	NOUN
m-1112	2139	15	.	.	PUNCT
m-1112	2140	1	photon	photon	NOUN
m-1112	2140	2	occupies	occupy	VERB
m-1112	2140	3	such	such	DET
m-1112	2140	4	the	the	DET
m-1112	2140	5	property	property	NOUN
m-1112	2140	6	of	of	ADP
m-1112	2140	7	material	material	ADJ
m-1112	2140	8	point	point	NOUN
m-1112	2140	9	as	as	ADP
m-1112	2140	10	the	the	DET
m-1112	2140	11	growth	growth	NOUN
m-1112	2140	12	-	-	PUNCT
m-1112	2140	13	pattern	pattern	NOUN
m-1112	2140	14	.with	.with	ADP
m-1112	2140	15	this	this	DET
m-1112	2140	16	way	way	NOUN
m-1112	2140	17	photon`s	photon`s	NOUN
m-1112	2140	18	frequency	frequency	NOUN
m-1112	2140	19	→	→	SYM
m-1112	2140	20	fp	fp	NOUN
m-1112	2140	21	=	=	SYM
m-1112	2140	22	1	1	NUM
m-1112	2140	23	/	/	SYM
m-1112	2140	24	tp	tp	NOUN
m-1112	2140	25	,	,	PUNCT
m-1112	2140	26	kicks	kick	NOUN
m-1112	2140	27	-	-	PUNCT
m-1112	2140	28	start	start	VERB
m-1112	2140	29	everything	everything	PRON
m-1112	2140	30	found	find	VERB
m-1112	2140	31	on	on	ADP
m-1112	2140	32	its	its	PRON
m-1112	2140	33	-	-	PUNCT
m-1112	2140	34	way	way	NOUN
m-1112	2140	35	.	.	PUNCT
m-1112	2141	1	from	from	ADP
m-1112	2141	2	the	the	DET
m-1112	2141	3	resonance	resonance	NOUN
m-1112	2141	4	constant	constant	ADJ
m-1112	2141	5	k	k	X
m-1112	2141	6	=	=	SYM
m-1112	2141	7	1	1	NUM
m-1112	2141	8	f	f	PROPN
m-1112	2141	9	²n.a	²n.a	X
m-1112	2141	10	³	³	X
m-1112	2141	11	→	→	SYM
m-1112	2141	12	or	or	CCONJ
m-1112	2141	13	1	1	NUM
m-1112	2141	14	=	=	SYM
m-1112	2141	15	k	k	PROPN
m-1112	2141	16	.f	.f	PROPN
m-1112	2141	17	²n	²n	PROPN
m-1112	2141	18	.	.	PUNCT
m-1112	2142	1	a3	a3	PROPN
m-1112	2142	2	←	←	PROPN
m-1112	2142	3	and	and	CCONJ
m-1112	2142	4	from	from	ADP
m-1112	2142	5	kepler`s	kepler`s	NOUN
m-1112	2142	6	laws	law	NOUN
m-1112	2142	7	and	and	CCONJ
m-1112	2142	8	newton`s	newton`s	PROPN
m-1112	2142	9	lagrange	lagrange	NOUN
m-1112	2142	10	laws	law	NOUN
m-1112	2142	11	for	for	ADP
m-1112	2142	12	orbits	orbit	NOUN
m-1112	2142	13	,	,	PUNCT
m-1112	2142	14	the	the	DET
m-1112	2142	15	cave	cave	NOUN
m-1112	2142	16	-	-	PUNCT
m-1112	2142	17	semi	semi	ADJ
m-1112	2142	18	-	-	ADJ
m-1112	2142	19	major	major	ADJ
m-1112	2142	20	-	-	PUNCT
m-1112	2142	21	axis	axis	NOUN
m-1112	2142	22	is	be	AUX
m-1112	2142	23	as	as	SCONJ
m-1112	2142	24	,	,	PUNCT
m-1112	2142	25	a	a	PRON
m-1112	2142	26	=	=	PUNCT
m-1112	2142	27	√t2/	√t2/	VERB
m-1112	2142	28	k	k	NOUN
m-1112	2142	29	3	3	NUM
m-1112	2142	30	=	=	SYM
m-1112	2142	31	√	√	PROPN
m-1112	2142	32	1	1	NUM
m-1112	2142	33	g.f	g.f	NOUN
m-1112	2142	34	²	²	NUM
m-1112	2142	35	3	3	NUM
m-1112	2142	36	=	=	NOUN
m-1112	2142	37	√	√	NUM
m-1112	2142	38	4.π².r²	4.π².r²	NUM
m-1112	2142	39	g.σ².φ²	g.σ².φ²	NOUN
m-1112	2142	40	3	3	NUM
m-1112	2142	41	=	=	SYM
m-1112	2142	42	√	√	NUM
m-1112	2143	1	[	[	X
m-1112	2143	2	4π2].x	4π2].x	NUM
m-1112	2143	3	r²	r²	NOUN
m-1112	2143	4	[	[	X
m-1112	2143	5	g.φ2].x	g.φ2].x	X
m-1112	2143	6	σ²	σ²	NOUN
m-1112	2143	7	3	3	NUM
m-1112	2143	8	,	,	PUNCT
m-1112	2143	9	and	and	CCONJ
m-1112	2143	10	𝐟	𝐟	PRON
m-1112	2143	11	𝐑	𝐑	NOUN
m-1112	2143	12	=	=	PUNCT
m-1112	2143	13	wr	wr	NOUN
m-1112	2143	14	2π	2π	NOUN
m-1112	2143	15	=	=	PUNCT
m-1112	2144	1	√	√	PUNCT
m-1112	2144	2	k=1	k=1	PUNCT
m-1112	2144	3	g.a	g.a	PROPN
m-1112	2144	4	³	³	NUM
m-1112	2144	5	2	2	NUM
m-1112	2144	6	=	=	SYM
m-1112	2144	7	√	√	PROPN
m-1112	2144	8	𝛔	𝛔	ADP
m-1112	2144	9	g	g	NOUN
m-1112	2144	10	.φ2.a³	.φ2.a³	NOUN
m-1112	2144	11	2	2	NUM
m-1112	2144	12	≡	≡	PROPN
m-1112	2144	13	√	√	PROPN
m-1112	2144	14	k	k	PROPN
m-1112	2144	15	md	md	PROPN
m-1112	2144	16	ev	ev	X
m-1112	2144	17	…	…	PUNCT
m-1112	2144	18	(	(	PUNCT
m-1112	2144	19	a	a	X
m-1112	2144	20	)	)	PUNCT
m-1112	2144	21	i.e.	i.e.	X
m-1112	2144	22	it	it	PRON
m-1112	2144	23	is	be	AUX
m-1112	2144	24	the	the	DET
m-1112	2144	25	resonance	resonance	NOUN
m-1112	2144	26	-	-	PUNCT
m-1112	2144	27	frequency	frequency	NOUN
m-1112	2144	28	fr	fr	NOUN
m-1112	2144	29	,	,	PUNCT
m-1112	2144	30	in	in	ADP
m-1112	2144	31	photons	photon	NOUN
m-1112	2144	32	loop	loop	NOUN
m-1112	2144	33	,	,	PUNCT
m-1112	2144	34	and	and	CCONJ
m-1112	2144	35	which	which	PRON
m-1112	2144	36	is	be	AUX
m-1112	2144	37	the	the	DET
m-1112	2144	38	energy	energy	NOUN
m-1112	2144	39	-	-	PUNCT
m-1112	2144	40	space	space	NOUN
m-1112	2144	41	quanta	quanta	NOUN
m-1112	2144	42	,	,	PUNCT
m-1112	2144	43	following	follow	VERB
m-1112	2144	44	the	the	DET
m-1112	2144	45	growth	growth	NOUN
m-1112	2144	46	-	-	PUNCT
m-1112	2144	47	golden	golden	ADJ
m-1112	2144	48	ratio	ratio	NOUN
m-1112	2144	49	-	-	PUNCT
m-1112	2144	50	pattern	pattern	NOUN
m-1112	2144	51	,	,	PUNCT
m-1112	2144	52	which	which	PRON
m-1112	2144	53	travels	travel	VERB
m-1112	2144	54	in	in	ADP
m-1112	2144	55	all	all	DET
m-1112	2144	56	cosmos	cosmos	PROPN
m-1112	2144	57	.	.	PUNCT
m-1112	2145	1	a	a	X
m-1112	2145	2	)	)	PUNCT
m-1112	2145	3	...	...	PUNCT
m-1112	2146	1	it	it	PRON
m-1112	2146	2	was	be	AUX
m-1112	2146	3	shown	show	VERB
m-1112	2146	4	that	that	SCONJ
m-1112	2146	5	when	when	SCONJ
m-1112	2146	6	two	two	NUM
m-1112	2146	7	photons	photon	NOUN
m-1112	2146	8	strike	strike	VERB
m-1112	2146	9	each	each	DET
m-1112	2146	10	other	other	ADJ
m-1112	2146	11	,	,	PUNCT
m-1112	2146	12	c	c	NOUN
m-1112	2146	13	=	=	SYM
m-1112	2146	14	c⃖	c⃖	ADJ
m-1112	2146	15	,	,	PUNCT
m-1112	2146	16	or	or	CCONJ
m-1112	2146	17	reflect	reflect	VERB
m-1112	2146	18	on	on	ADP
m-1112	2146	19	a	a	DET
m-1112	2146	20	wall	wall	NOUN
m-1112	2146	21	,	,	PUNCT
m-1112	2146	22	then	then	ADV
m-1112	2146	23	c	c	NOUN
m-1112	2146	24	=	=	SYM
m-1112	2146	25	0	0	PUNCT
m-1112	2147	1	and	and	CCONJ
m-1112	2147	2	so	so	ADV
m-1112	2147	3	their	their	PRON
m-1112	2147	4	fundamental	fundamental	ADJ
m-1112	2147	5	frequency	frequency	NOUN
m-1112	2147	6	f1	f1	NOUN
m-1112	2147	7	=	=	SYM
m-1112	2147	8	n.	n.	PROPN
m-1112	2147	9	[	[	PUNCT
m-1112	2147	10	�	�	NOUN
m-1112	2147	11	̅	̅	NOUN
m-1112	2147	12	�	�	NOUN
m-1112	2147	13	2r	2r	NUM
m-1112	2147	14	]	]	X
m-1112	2147	15	x	x	X
m-1112	2147	16	[	[	PUNCT
m-1112	2147	17	1	1	NUM
m-1112	2147	18	4	4	NUM
m-1112	2147	19	]	]	PUNCT
m-1112	2147	20	=	=	PUNCT
m-1112	2147	21	n.	n.	NOUN
m-1112	2147	22	[	[	PUNCT
m-1112	2147	23	�	�	NOUN
m-1112	2147	24	̅	̅	NOUN
m-1112	2147	25	�	�	PROPN
m-1112	2147	26	8.r	8.r	NUM
m-1112	2147	27	]	]	PUNCT
m-1112	2147	28	which	which	PRON
m-1112	2147	29	for	for	ADP
m-1112	2147	30	n	n	NOUN
m-1112	2147	31	=	=	PRON
m-1112	2147	32	[	[	PUNCT
m-1112	2147	33	8.𝜋𝑟𝑐	8.𝜋𝑟𝑐	NUM
m-1112	2147	34	v.λ	v.λ	X
m-1112	2147	35	]	]	PUNCT
m-1112	2147	36	increases	increase	NOUN
m-1112	2147	37	to	to	ADP
m-1112	2147	38	λ	λ	PROPN
m-1112	2147	39	c	c	PROPN
m-1112	2147	40	,	,	PUNCT
m-1112	2147	41	therefore	therefore	ADV
m-1112	2147	42	for	for	ADP
m-1112	2147	43	n	n	NOUN
m-1112	2147	44	=	=	SYM
m-1112	2147	45	n.	n.	NOUN
m-1112	2147	46	[	[	PUNCT
m-1112	2148	1	8.𝜋𝑟𝑐	8.𝜋𝑟𝑐	NOUN
m-1112	2148	2	v.λ	v.λ	X
m-1112	2148	3	]	]	X
m-1112	2148	4	=	=	PUNCT
m-1112	2148	5	n.|	n.|	PROPN
m-1112	2148	6	c	c	NOUN
m-1112	2149	1	𝜆	𝜆	PROPN
m-1112	2150	1	|	|	ADV
m-1112	2150	2	and	and	CCONJ
m-1112	2150	3	for	for	ADP
m-1112	2150	4	n	n	NOUN
m-1112	2150	5	→	→	SYM
m-1112	2150	6	∞	∞	PROPN
m-1112	2150	7	then	then	ADV
m-1112	2150	8	f1	f1	NOUN
m-1112	2150	9	=	=	SYM
m-1112	2150	10	e	e	PROPN
m-1112	2150	11	/	/	SYM
m-1112	2150	12	h	h	PROPN
m-1112	2151	1	=	=	NOUN
m-1112	2151	2	∞	∞	NUM
m-1112	2151	3	...	...	PUNCT
m-1112	2151	4	(	(	PUNCT
m-1112	2151	5	b	b	NOUN
m-1112	2151	6	)	)	PUNCT
m-1112	2151	7	in	in	ADP
m-1112	2151	8	dual	dual	ADJ
m-1112	2151	9	photon	photon	NOUN
m-1112	2151	10	v̅	v̅	PROPN
m-1112	2151	11	[	[	PUNCT
m-1112	2151	12	σφ	σφ	NOUN
m-1112	2151	13	2πr	2πr	NOUN
m-1112	2152	1	+	+	CCONJ
m-1112	2152	2	σ	σ	NUM
m-1112	2152	3	2πr	2πr	NOUN
m-1112	2152	4	]	]	PUNCT
m-1112	2153	1	≡	≡	ADJ
m-1112	2153	2	v̅	v̅	PROPN
m-1112	2153	3	.	.	PUNCT
m-1112	2154	1	[	[	PUNCT
m-1112	2154	2	fn̅	fn̅	PROPN
m-1112	2154	3	+	+	CCONJ
m-1112	2154	4	fn	fn	NOUN
m-1112	2154	5	]	]	PUNCT
m-1112	2154	6	,	,	PUNCT
m-1112	2154	7	colours	colour	NOUN
m-1112	2154	8	are	be	AUX
m-1112	2154	9	the	the	DET
m-1112	2154	10	still	still	ADV
m-1112	2154	11	-	-	PUNCT
m-1112	2154	12	sub	sub	NOUN
m-1112	2154	13	-	-	NOUN
m-1112	2154	14	units	unit	NOUN
m-1112	2154	15	of	of	ADP
m-1112	2154	16	storage	storage	NOUN
m-1112	2154	17	[	[	PUNCT
m-1112	2154	18	v̅	v̅	NOUN
m-1112	2154	19	.	.	PUNCT
m-1112	2155	1	fn̅	fn̅	PROPN
m-1112	2155	2	]	]	PUNCT
m-1112	2155	3	,	,	PUNCT
m-1112	2155	4	and	and	CCONJ
m-1112	2155	5	exist	exist	VERB
m-1112	2155	6	as	as	ADP
m-1112	2155	7	frequencies	frequency	NOUN
m-1112	2155	8	,	,	PUNCT
m-1112	2155	9	violet	violet	NOUN
m-1112	2155	10	,	,	PUNCT
m-1112	2155	11	blue	blue	ADJ
m-1112	2155	12	,	,	PUNCT
m-1112	2155	13	green	green	ADJ
m-1112	2155	14	,	,	PUNCT
m-1112	2155	15	which	which	PRON
m-1112	2155	16	stabilize	stabilize	VERB
m-1112	2155	17	with	with	ADP
m-1112	2155	18	their	their	PRON
m-1112	2155	19	complementary	complementary	ADJ
m-1112	2155	20	colors	color	NOUN
m-1112	2155	21	yellow	yellow	VERB
m-1112	2155	22	,	,	PUNCT
m-1112	2155	23	orange	orange	PROPN
m-1112	2155	24	,	,	PUNCT
m-1112	2155	25	red	red	NOUN
m-1112	2155	26	,	,	PUNCT
m-1112	2155	27	of	of	ADP
m-1112	2155	28	wavelength	wavelength	NOUN
m-1112	2155	29	d	d	NOUN
m-1112	2155	30	=	=	SYM
m-1112	2155	31	λ	λ	PROPN
m-1112	2155	32	→	→	SYM
m-1112	2155	33	𝝀	𝝀	X
m-1112	2155	34	𝐦𝐢𝐧	𝐦𝐢𝐧	NOUN
m-1112	2155	35			X
m-1112	2155	36	𝝀	𝝀	PROPN
m-1112	2155	37	𝐦𝐚𝐱	𝐦𝐚𝐱	NOUN
m-1112	2155	38	=	=	SYM
m-1112	2155	39	3.10−7	3.10−7	NUM
m-1112	2155	40	m	m	NOUN
m-1112	2155	41			NOUN
m-1112	2155	42	3.√3.10−7	3.√3.10−7	NUM
m-1112	2155	43	m	m	NOUN
m-1112	2155	44	.	.	PUNCT
m-1112	2156	1	b	b	X
m-1112	2156	2	)	)	PUNCT
m-1112	2156	3	..	..	PUNCT
m-1112	2157	1	the	the	DET
m-1112	2157	2	quanta	quanta	PROPN
m-1112	2157	3	of	of	ADP
m-1112	2157	4	energy	energy	NOUN
m-1112	2157	5	,	,	PUNCT
m-1112	2157	6	passing	pass	VERB
m-1112	2157	7	through	through	ADP
m-1112	2157	8	a	a	DET
m-1112	2157	9	unit	unit	NOUN
m-1112	2157	10	-	-	PUNCT
m-1112	2157	11	surface	surface	NOUN
m-1112	2157	12	or	or	CCONJ
m-1112	2157	13	volume	volume	NOUN
m-1112	2157	14	is	be	AUX
m-1112	2157	15	inversely	inversely	ADV
m-1112	2157	16	proportional	proportional	ADJ
m-1112	2157	17	to	to	ADP
m-1112	2157	18	the	the	DET
m-1112	2157	19	fourth	fourth	ADJ
m-1112	2157	20	power	power	NOUN
m-1112	2157	21	of	of	ADP
m-1112	2157	22	the	the	DET
m-1112	2157	23	wavelength	wavelength	NOUN
m-1112	2157	24	𝜆	𝜆	ADP
m-1112	2157	25	as	as	SCONJ
m-1112	2157	26	i	i	PRON
m-1112	2157	27	=	=	PUNCT
m-1112	2157	28	0,5865	0,5865	ADJ
m-1112	2157	29	.	.	PUNCT
m-1112	2158	1	{	{	PUNCT
m-1112	2158	2	1	1	NUM
m-1112	2158	3	𝜆⁴	𝜆⁴	NOUN
m-1112	2158	4	}	}	PUNCT
m-1112	2158	5	.	.	PUNCT
m-1112	2159	1	when	when	SCONJ
m-1112	2159	2	fbe	fbe	NOUN
m-1112	2159	3	=	=	SYM
m-1112	2159	4	e	e	NOUN
m-1112	2159	5	/	/	SYM
m-1112	2159	6	h	h	NOUN
m-1112	2159	7	=	=	SYM
m-1112	2159	8	∞	∞	NUM
m-1112	2159	9	then	then	ADV
m-1112	2159	10	the	the	DET
m-1112	2159	11	energy	energy	NOUN
m-1112	2159	12	-	-	PUNCT
m-1112	2159	13	intension	intension	NOUN
m-1112	2159	14	increases	increase	NOUN
m-1112	2159	15	and	and	CCONJ
m-1112	2159	16	the	the	DET
m-1112	2159	17	wavelength	wavelength	NOUN
m-1112	2159	18	𝝀	𝝀	NOUN
m-1112	2159	19	decreases	decrease	NOUN
m-1112	2159	20	and	and	CCONJ
m-1112	2159	21	for	for	ADP
m-1112	2159	22	fbe	fbe	NOUN
m-1112	2159	23	=	=	SYM
m-1112	2159	24	∞	∞	NUM
m-1112	2159	25	then	then	ADV
m-1112	2159	26	𝝀	𝝀	VERB
m-1112	2159	27	=	=	X
m-1112	2159	28	0	0	PROPN
m-1112	2159	29	.	.	PUNCT
m-1112	2160	1	this	this	PRON
m-1112	2160	2	is	be	AUX
m-1112	2160	3	what	what	PRON
m-1112	2160	4	happens	happen	VERB
m-1112	2160	5	in	in	ADP
m-1112	2160	6	black	black	ADJ
m-1112	2160	7	-	-	PUNCT
m-1112	2160	8	holes	hole	NOUN
m-1112	2160	9	where	where	SCONJ
m-1112	2160	10	d	d	NOUN
m-1112	2160	11	=	=	SYM
m-1112	2160	12	𝜆	𝜆	PROPN
m-1112	2160	13	=	=	SYM
m-1112	2160	14	0	0	NUM
m-1112	2160	15	,	,	PUNCT
m-1112	2160	16	and	and	CCONJ
m-1112	2160	17	in	in	ADP
m-1112	2160	18	where	where	SCONJ
m-1112	2160	19	e	e	NOUN
m-1112	2160	20	=	=	SYM
m-1112	2160	21	fbe	fbe	PROPN
m-1112	2160	22	=	=	SYM
m-1112	2160	23	∞	∞	PROPN
m-1112	2160	24	.	.	PUNCT
m-1112	2161	1	hydrogen	hydrogen	NOUN
m-1112	2161	2	-	-	PUNCT
m-1112	2161	3	energy	energy	NOUN
m-1112	2161	4	e	e	NOUN
m-1112	2161	5	=	=	SYM
m-1112	2161	6	h.fp	h.fp	PROPN
m-1112	2161	7	=	=	PUNCT
m-1112	2162	1	[	[	PUNCT
m-1112	2162	2	6,6262.10−34	6,6262.10−34	NUM
m-1112	2162	3	j.s	j.s	PROPN
m-1112	2162	4	]	]	PUNCT
m-1112	2162	5	.	.	PUNCT
m-1112	2163	1	[	[	PUNCT
m-1112	2163	2	3,28393.1015	3,28393.1015	NUM
m-1112	2163	3	/	/	SYM
m-1112	2163	4	s	s	X
m-1112	2163	5	]	]	X
m-1112	2163	6	=	=	PUNCT
m-1112	2163	7	2,176.10−18	2,176.10−18	NUM
m-1112	2163	8	j	j	PROPN
m-1112	2163	9	and	and	CCONJ
m-1112	2163	10	in	in	ADP
m-1112	2163	11	ev	ev	X
m-1112	2163	12	→	→	X
m-1112	2163	13	[	[	X
m-1112	2163	14	2	2	NUM
m-1112	2163	15	,	,	PUNCT
m-1112	2163	16	176.10−18	176.10−18	NUM
m-1112	2163	17	]	]	PUNCT
m-1112	2163	18	/	/	PUNCT
m-1112	2164	1	[	[	X
m-1112	2164	2	1,6.10−19	1,6.10−19	NUM
m-1112	2164	3	]	]	X
m-1112	2164	4	=	=	SYM
m-1112	2164	5	13,6	13,6	NUM
m-1112	2164	6	ev	ev	INTJ
m-1112	2164	7	,	,	PUNCT
m-1112	2164	8	above	above	ADP
m-1112	2164	9	quantity	quantity	NOUN
m-1112	2164	10	of	of	ADP
m-1112	2164	11	energy	energy	NOUN
m-1112	2164	12	consist	consist	VERB
m-1112	2164	13	the	the	DET
m-1112	2164	14	hydrogen	hydrogen	NOUN
m-1112	2164	15	minimum	minimum	NOUN
m-1112	2164	16	energy	energy	NOUN
m-1112	2164	17	-	-	PUNCT
m-1112	2164	18	rim	rim	NOUN
m-1112	2164	19	,	,	PUNCT
m-1112	2164	20	becoming	become	VERB
m-1112	2164	21	from	from	ADP
m-1112	2164	22	equation	equation	NOUN
m-1112	2165	1	a	a	DET
m-1112	2165	2	=	=	X
m-1112	2165	3	√𝐓𝟐/𝐠	√𝐓𝟐/𝐠	NOUN
m-1112	2165	4	𝟑	𝟑	X
m-1112	2165	5	=	=	SYM
m-1112	2165	6	√	√	PROPN
m-1112	2166	1	[	[	X
m-1112	2166	2	3,04513.10−16]²	3,04513.10−16]²	NUM
m-1112	2166	3	9,80769411	9,80769411	NOUN
m-1112	2166	4	3	3	NUM
m-1112	2166	5	=	=	SYM
m-1112	2166	6	2,1145016.10−11	2,1145016.10−11	NUM
m-1112	2166	7	m	m	VERB
m-1112	2166	8	,	,	PUNCT
m-1112	2166	9	for	for	ADP
m-1112	2166	10	unit	unit	NOUN
m-1112	2166	11	energy	energy	NOUN
m-1112	2166	12	cave	cave	NOUN
m-1112	2166	13	.	.	PUNCT
m-1112	2167	1	from	from	ADP
m-1112	2167	2	angular	angular	ADJ
m-1112	2167	3	-	-	PUNCT
m-1112	2167	4	momentum	momentum	NOUN
m-1112	2167	5	b	b	NOUN
m-1112	2167	6	=	=	SYM
m-1112	2167	7	r.mv	r.mv	PROPN
m-1112	2167	8	=	=	SYM
m-1112	2167	9	r	r	NOUN
m-1112	2167	10	[	[	PUNCT
m-1112	2167	11	πrv	πrv	VERB
m-1112	2167	12	2	2	NUM
m-1112	2167	13	]	]	PUNCT
m-1112	2167	14	v	v	NOUN
m-1112	2167	15	=	=	SYM
m-1112	2167	16	𝛑	𝛑	ADP
m-1112	2167	17	𝐫²	𝐫²	NOUN
m-1112	2167	18	𝟐	𝟐	NUM
m-1112	2167	19	v²	v²	NOUN
m-1112	2167	20	=	=	PUNCT
m-1112	2167	21	𝛑	𝛑	ADP
m-1112	2167	22	𝐫²	𝐫²	NOUN
m-1112	2167	23	𝟐	𝟐	NUM
m-1112	2167	24	v²	v²	NOUN
m-1112	2167	25	=	=	PUNCT
m-1112	2167	26	πr³	πr³	X
m-1112	2167	27	2	2	NUM
m-1112	2168	1	[	[	X
m-1112	2168	2	n.π.c]²	n.π.c]²	NOUN
m-1112	2168	3	=	=	SYM
m-1112	2168	4	𝛑³	𝛑³	PROPN
m-1112	2168	5	𝐫³	𝐫³	NOUN
m-1112	2168	6	𝟐	𝟐	NUM
m-1112	2168	7	c²	c²	NOUN
m-1112	2168	8	,	,	PUNCT
m-1112	2168	9	or	or	CCONJ
m-1112	2168	10	black	black	ADJ
m-1112	2168	11	-	-	PUNCT
m-1112	2168	12	hole	hole	NOUN
m-1112	2168	13	-	-	PUNCT
m-1112	2168	14	energy	energy	NOUN
m-1112	2168	15	→	→	SYM
m-1112	2168	16	𝐁𝐄	𝐁𝐄	NOUN
m-1112	2168	17	=	=	SYM
m-1112	2168	18	2.π⁵.r³.f	2.π⁵.r³.f	NUM
m-1112	2168	19	²	²	NUM
m-1112	2168	20	=	=	SYM
m-1112	2168	21	(	(	PUNCT
m-1112	2168	22	𝛑𝐫)³.w²	𝛑𝐫)³.w²	PROPN
m-1112	2168	23	←	←	PROPN
m-1112	2168	24	i.e.	i.e.	X
m-1112	2168	25	velocity	velocity	NOUN
m-1112	2168	26	in	in	ADP
m-1112	2168	27	black	black	ADJ
m-1112	2168	28	-	-	PUNCT
m-1112	2168	29	holes	hole	NOUN
m-1112	2168	30	is	be	AUX
m-1112	2168	31	related	relate	VERB
m-1112	2168	32	to	to	PART
m-1112	2168	33	cave	cave	VERB
m-1112	2168	34	,	,	PUNCT
m-1112	2168	35	r	r	NOUN
m-1112	2168	36	³	³	NOUN
m-1112	2168	37	,	,	PUNCT
m-1112	2168	38	and	and	CCONJ
m-1112	2168	39	energy	energy	NOUN
m-1112	2168	40	w²	w²	NOUN
m-1112	2168	41	times	time	NOUN
m-1112	2168	42	of	of	ADP
m-1112	2168	43	light	light	ADJ
m-1112	2168	44	velocity	velocity	NOUN
m-1112	2168	45	.	.	PUNCT
m-1112	2169	1	c	c	X
m-1112	2169	2	)	)	PUNCT
m-1112	2169	3	..	..	PUNCT
m-1112	2169	4	since	since	SCONJ
m-1112	2169	5	the	the	DET
m-1112	2169	6	primary	primary	ADJ
m-1112	2169	7	motion	motion	NOUN
m-1112	2169	8	≡	≡	PROPN
m-1112	2169	9	[	[	X
m-1112	2169	10	pm	pm	X
m-1112	2169	11	]	]	PUNCT
m-1112	2169	12	exist	exist	VERB
m-1112	2169	13	from	from	ADP
m-1112	2169	14	the	the	DET
m-1112	2169	15	three	three	NUM
m-1112	2169	16	breakages	breakage	NOUN
m-1112	2169	17	only	only	ADV
m-1112	2169	18	,	,	PUNCT
m-1112	2169	19	and	and	CCONJ
m-1112	2169	20	stpl	stpl	PROPN
m-1112	2169	21	is	be	AUX
m-1112	2169	22	the	the	PRON
m-1112	2169	23	n	n	ADV
m-1112	2170	1	=3	=3	VERB
m-1112	2170	2	mechanism	mechanism	NOUN
m-1112	2170	3	creating	create	VERB
m-1112	2170	4	elementary	elementary	ADJ
m-1112	2170	5	particles	particle	NOUN
m-1112	2170	6			PUNCT
m-1112	2171	1	[	[	X
m-1112	2171	2	n	n	X
m-1112	2171	3	-	-	PUNCT
m-1112	2171	4	knots=3	knots=3	X
m-1112	2171	5	]	]	X
m-1112	2171	6	in	in	ADP
m-1112	2171	7	𝐕	𝐕	PROPN
m-1112	2171	8	gra	gra	NOUN
m-1112	2171	9	=	=	PUNCT
m-1112	2171	10	7,593.1035	7,593.1035	NUM
m-1112	2171	11	v.	v.	ADP
m-1112	2171	12	explanations	explanation	NOUN
m-1112	2171	13	:	:	PUNCT
m-1112	2171	14	ijo	ijo	PROPN
m-1112	2171	15	international	international	PROPN
m-1112	2171	16	journal	journal	PROPN
m-1112	2171	17	of	of	ADP
m-1112	2171	18	mathematics	mathematics	PROPN
m-1112	2171	19	(	(	PUNCT
m-1112	2171	20	issn	issn	PROPN
m-1112	2171	21	:	:	PUNCT
m-1112	2171	22	2992	2992	NUM
m-1112	2171	23	-	-	SYM
m-1112	2171	24	4421	4421	NUM
m-1112	2171	25	)	)	PUNCT
m-1112	2171	26	volume	volume	NOUN
m-1112	2171	27	08	08	NUM
m-1112	2172	1	|	|	ADV
m-1112	2172	2	issue	issue	NOUN
m-1112	2172	3	08	08	NUM
m-1112	2173	1	|	|	ADV
m-1112	2173	2	august	august	PROPN
m-1112	2173	3	2025	2025	NUM
m-1112	2173	4	|	|	ADV
m-1112	2173	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2173	6	ijo	ijo	PROPN
m-1112	2173	7	journals	journal	NOUN
m-1112	2173	8	76	76	NUM
m-1112	2173	9	the	the	DET
m-1112	2173	10	fundamental	fundamental	ADJ
m-1112	2173	11	particles	particle	NOUN
m-1112	2173	12	origination	origination	NOUN
m-1112	2173	13	mechanism	mechanism	NOUN
m-1112	2173	14	in	in	ADP
m-1112	2173	15	mfmf	mfmf	PROPN
m-1112	2173	16	pns	pns	PROPN
m-1112	2173	17	caves	cave	NOUN
m-1112	2173	18	.	.	PUNCT
m-1112	2174	1	the	the	DET
m-1112	2174	2	action	action	NOUN
m-1112	2174	3	-	-	PUNCT
m-1112	2174	4	spaces	space	NOUN
m-1112	2174	5	≡	≡	PROPN
m-1112	2174	6	the	the	DET
m-1112	2174	7	infinite	infinite	ADJ
m-1112	2174	8	quaternion	quaternion	NOUN
m-1112	2174	9	monads	monad	NOUN
m-1112	2174	10	→	→	SYM
m-1112	2174	11	�	�	NOUN
m-1112	2174	12	̅	̅	NOUN
m-1112	2174	13	�	�	PROPN
m-1112	2174	14	≡	≡	PROPN
m-1112	2174	15	(	(	PUNCT
m-1112	2174	16	s	s	NOUN
m-1112	2174	17	+	+	NUM
m-1112	2174	18	v̅.i	v̅.i	X
m-1112	2174	19	)	)	PUNCT
m-1112	2174	20	≡	≡	PROPN
m-1112	2174	21	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	2174	22	̅̅	̅̅	PROPN
m-1112	2174	23	≡	≡	PROPN
m-1112	2174	24	≡	≡	PROPN
m-1112	2174	25	√s2	√s2	PROPN
m-1112	2175	1	+	+	PUNCT
m-1112	2175	2	[	[	PUNCT
m-1112	2175	3	v̅.	v̅.	NOUN
m-1112	2175	4	i	i	X
m-1112	2175	5	]	]	X
m-1112	2175	6	²	²	X
m-1112	2175	7	]	]	PUNCT
m-1112	2175	8	,	,	PUNCT
m-1112	2175	9	or	or	CCONJ
m-1112	2175	10	�	�	PROPN
m-1112	2175	11	̅	̅	NOUN
m-1112	2175	12	�	�	NOUN
m-1112	2175	13	≡	≡	PROPN
m-1112	2175	14	x	x	PUNCT
m-1112	2176	1	+	+	CCONJ
m-1112	2176	2	i	i	PRON
m-1112	2176	3	.	.	PUNCT
m-1112	2177	1	y	y	PROPN
m-1112	2177	2	≡	≡	PROPN
m-1112	2177	3	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	2177	4	̅̅	̅̅	PROPN
m-1112	2177	5	≡	≡	PROPN
m-1112	2177	6	moduli	modulus	NOUN
m-1112	2177	7	,	,	PUNCT
m-1112	2177	8	r	r	NOUN
m-1112	2177	9	,	,	PUNCT
m-1112	2177	10	is	be	AUX
m-1112	2177	11	their	their	PRON
m-1112	2177	12	magnitude	magnitude	NOUN
m-1112	2177	13	[	[	PUNCT
m-1112	2177	14	r	r	NOUN
m-1112	2177	15	=	=	NOUN
m-1112	2177	16	|	|	ADV
m-1112	2177	17	r	r	NOUN
m-1112	2177	18	|	|	NOUN
m-1112	2177	19	=	=	PUNCT
m-1112	2178	1	√	√	PROPN
m-1112	2179	1	x2	x2	NOUN
m-1112	2180	1	+	+	CCONJ
m-1112	2181	1	y2	y2	NOUN
m-1112	2181	2	]	]	PUNCT
m-1112	2181	3	,	,	PUNCT
m-1112	2181	4	on	on	ADP
m-1112	2181	5	unit	unit	NOUN
m-1112	2181	6	-	-	PUNCT
m-1112	2181	7	diameter	diameter	NOUN
m-1112	2181	8	ab̅̅	ab̅̅	PROPN
m-1112	2181	9	̅̅	̅̅	PROPN
m-1112	2181	10	.	.	PUNCT
m-1112	2182	1	the	the	DET
m-1112	2182	2	[	[	X
m-1112	2182	3	qmas	qmas	NOUN
m-1112	2182	4	]	]	PUNCT
m-1112	2182	5	.	.	PUNCT
m-1112	2183	1	for	for	ADP
m-1112	2183	2	quaternion	quaternion	NOUN
m-1112	2183	3	|v̅|	|v̅|	NOUN
m-1112	2183	4	=	=	SYM
m-1112	2183	5	s	s	VERB
m-1112	2183	6	breakages	breakage	VERB
m-1112	2183	7	𝐳	𝐳	X
m-1112	2183	8	*	*	PUNCT
m-1112	2183	9	𝐳	𝐳	X
m-1112	2183	10	=	=	X
m-1112	2183	11	(	(	PUNCT
m-1112	2183	12	s	s	NOUN
m-1112	2183	13	+	+	NUM
m-1112	2183	14	v̅.i	v̅.i	X
m-1112	2183	15	)	)	PUNCT
m-1112	2183	16	²	²	PROPN
m-1112	2183	17	=	=	PUNCT
m-1112	2183	18	s²	s²	NOUN
m-1112	2184	1	+	+	PROPN
m-1112	2184	2	[	[	X
m-1112	2184	3	v̅]²	v̅]²	X
m-1112	2184	4	+2.sv̅.i	+2.sv̅.i	ADJ
m-1112	2184	5	=	=	SYM
m-1112	2184	6	s²	s²	PROPN
m-1112	2184	7	–	–	PUNCT
m-1112	2184	8	v̅	v̅	NOUN
m-1112	2184	9	²	²	NUM
m-1112	2184	10	±	±	NUM
m-1112	2184	11	2.s	2.s	NUM
m-1112	2184	12	v̅	v̅	NOUN
m-1112	2185	1	=	=	NOUN
m-1112	2185	2	|s|²	|s|²	PROPN
m-1112	2185	3	|	|	NOUN
m-1112	2185	4	�	�	NOUN
m-1112	2185	5	̅	̅	NOUN
m-1112	2185	6	�	�	PROPN
m-1112	2185	7	|²	|²	NUM
m-1112	2185	8	±	±	NUM
m-1112	2185	9	2.|s|.|s̅|	2.|s|.|s̅|	NUM
m-1112	2185	10	,	,	PUNCT
m-1112	2185	11	i.e.	i.e.	X
m-1112	2185	12	in	in	ADP
m-1112	2185	13	figure	figure	NOUN
m-1112	2185	14	-3	-3	PUNCT
m-1112	2185	15	the	the	DET
m-1112	2185	16	vector	vector	NOUN
m-1112	2185	17	of	of	ADP
m-1112	2185	18	amplitude	amplitude	NOUN
m-1112	2185	19	is	be	AUX
m-1112	2185	20	quaternion	quaternion	ADJ
m-1112	2185	21	�	�	NOUN
m-1112	2185	22	̅	̅	NOUN
m-1112	2185	23	�	�	NOUN
m-1112	2185	24	≡	≡	PROPN
m-1112	2185	25	x	x	PUNCT
m-1112	2186	1	+	+	CCONJ
m-1112	2186	2	i	i	PRON
m-1112	2186	3	.	.	PUNCT
m-1112	2187	1	y	y	PROPN
m-1112	2187	2	,	,	PUNCT
m-1112	2187	3	with	with	ADP
m-1112	2187	4	vector	vector	NOUN
m-1112	2187	5	�	�	PROPN
m-1112	2187	6	̅	̅	NOUN
m-1112	2187	7	�	�	PROPN
m-1112	2187	8	,	,	PUNCT
m-1112	2187	9	to	to	PART
m-1112	2187	10	be	be	AUX
m-1112	2187	11	from	from	ADP
m-1112	2187	12	definition	definition	NOUN
m-1112	2187	13	of	of	ADP
m-1112	2187	14	the	the	DET
m-1112	2187	15	complex	complex	ADJ
m-1112	2187	16	vector	vector	NOUN
m-1112	2187	17	space	space	NOUN
m-1112	2187	18	,	,	PUNCT
m-1112	2187	19	the	the	DET
m-1112	2187	20	set	set	NOUN
m-1112	2187	21	of	of	ADP
m-1112	2187	22	vectors	vector	NOUN
m-1112	2187	23	of	of	ADP
m-1112	2187	24	length	length	NOUN
m-1112	2187	25	(	(	PUNCT
m-1112	2187	26	the	the	DET
m-1112	2187	27	n	n	NOUN
m-1112	2187	28	vertices	vertex	NOUN
m-1112	2187	29	which	which	PRON
m-1112	2187	30	form	form	VERB
m-1112	2187	31	the	the	DET
m-1112	2187	32	n	n	NUM
m-1112	2187	33	polygon	polygon	NOUN
m-1112	2187	34	sides	side	NOUN
m-1112	2187	35	,	,	PUNCT
m-1112	2187	36	or	or	CCONJ
m-1112	2187	37	the	the	DET
m-1112	2187	38	norm	norm	NOUN
m-1112	2187	39	of	of	ADP
m-1112	2187	40	the	the	DET
m-1112	2187	41	complex	complex	ADJ
m-1112	2187	42	vectors	vector	NOUN
m-1112	2187	43	)	)	PUNCT
m-1112	2188	1	a	a	X
m-1112	2188	2	...	...	PUNCT
m-1112	2188	3	the	the	DET
m-1112	2188	4	4	4	NUM
m-1112	2188	5	-	-	PUNCT
m-1112	2188	6	geometrical	geometrical	ADJ
m-1112	2188	7	spaces	space	NOUN
m-1112	2188	8	,	,	PUNCT
m-1112	2188	9	[	[	PUNCT
m-1112	2188	10	space	space	NOUN
m-1112	2188	11	,	,	PUNCT
m-1112	2188	12	anti	anti	ADJ
m-1112	2188	13	-	-	ADJ
m-1112	2188	14	space	space	ADJ
m-1112	2188	15	,	,	PUNCT
m-1112	2188	16	neutral	neutral	ADJ
m-1112	2188	17	-	-	PUNCT
m-1112	2188	18	space	space	NOUN
m-1112	2188	19	,	,	PUNCT
m-1112	2188	20	sub	sub	NOUN
m-1112	2188	21	-	-	NOUN
m-1112	2188	22	space	space	NOUN
m-1112	2188	23	]	]	PUNCT
m-1112	2188	24	consist	consist	NOUN
m-1112	2188	25	→	→	PUNCT
m-1112	2188	26	the	the	DET
m-1112	2188	27	geometrical	geometrical	ADJ
m-1112	2188	28	mould	mould	NOUN
m-1112	2188	29	of	of	ADP
m-1112	2188	30	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	2188	31	̅̅	̅̅	PROPN
m-1112	2188	32	monad	monad	PROPN
m-1112	2188	33	≡	≡	PROPN
m-1112	2189	1	[	[	X
m-1112	2189	2	pm-2r	pm-2r	NOUN
m-1112	2189	3	-	-	PUNCT
m-1112	2189	4	m	m	NOUN
m-1112	2189	5	]	]	X
m-1112	2189	6	←	←	PROPN
m-1112	2189	7	b	b	X
m-1112	2189	8	...	...	PUNCT
m-1112	2189	9	the	the	DET
m-1112	2189	10	vectors	vector	NOUN
m-1112	2189	11	of	of	ADP
m-1112	2189	12	amplitude	amplitude	NOUN
m-1112	2189	13	z	z	NOUN
m-1112	2189	14	=	=	SYM
m-1112	2189	15	2r	2r	NUM
m-1112	2189	16	,	,	PUNCT
m-1112	2189	17	on	on	ADP
m-1112	2189	18	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	2189	19	̅̅	̅̅	PROPN
m-1112	2189	20	monad	monad	PROPN
m-1112	2189	21	,	,	PUNCT
m-1112	2189	22	consist	consist	VERB
m-1112	2189	23	the	the	DET
m-1112	2189	24	energy	energy	NOUN
m-1112	2189	25	-	-	PUNCT
m-1112	2189	26	mould	mould	NOUN
m-1112	2189	27	.	.	PUNCT
m-1112	2190	1	of	of	ADP
m-1112	2190	2	2r	2r	NUM
m-1112	2190	3	-	-	PUNCT
m-1112	2190	4	form	form	NOUN
m-1112	2190	5	.the	.the	DET
m-1112	2190	6	physical	physical	ADJ
m-1112	2190	7	-mechanisms	-mechanism	NOUN
m-1112	2190	8	→	→	PUNCT
m-1112	2190	9	[	[	PUNCT
m-1112	2190	10	physical	physical	ADJ
m-1112	2190	11	mould	mould	NOUN
m-1112	2190	12	of	of	ADP
m-1112	2190	13	2rmonad	2rmonad	NUM
m-1112	2190	14	]	]	PUNCT
m-1112	2190	15	≡	≡	PROPN
m-1112	2191	1	[	[	X
m-1112	2191	2	gm	gm	PROPN
m-1112	2191	3	-	-	PUNCT
m-1112	2191	4	ab	ab	PROPN
m-1112	2191	5	-	-	PUNCT
m-1112	2191	6	m	m	PROPN
m-1112	2191	7	]	]	X
m-1112	2191	8	←	←	PROPN
m-1112	2191	9	are	be	AUX
m-1112	2191	10	such	such	ADJ
m-1112	2191	11	and	and	CCONJ
m-1112	2191	12	dependent	dependent	ADJ
m-1112	2191	13	on	on	ADP
m-1112	2191	14	the	the	DET
m-1112	2191	15	n	n	ADJ
m-1112	2191	16	number	number	NOUN
m-1112	2191	17	of	of	ADP
m-1112	2191	18	accessories	accessory	NOUN
m-1112	2191	19	they	they	PRON
m-1112	2191	20	use	use	VERB
m-1112	2191	21	.	.	PUNCT
m-1112	2192	1	a	a	PRON
m-1112	2192	2	…	…	PUNCT
m-1112	2192	3	the	the	DET
m-1112	2192	4	gravity	gravity	NOUN
m-1112	2192	5	force	force	NOUN
m-1112	2192	6	g	g	PROPN
m-1112	2192	7	≡	≡	PROPN
m-1112	2192	8	motion	motion	NOUN
m-1112	2192	9	≡	≡	PROPN
m-1112	2192	10	σ.𝚽³	σ.𝚽³	NOUN
m-1112	2192	11	,	,	PUNCT
m-1112	2192	12	exists	exist	VERB
m-1112	2192	13	without	without	ADP
m-1112	2192	14	mass	mass	NOUN
m-1112	2192	15	and	and	CCONJ
m-1112	2192	16	is	be	AUX
m-1112	2192	17	quantized	quantize	VERB
m-1112	2192	18	spread	spread	VERB
m-1112	2192	19	in{space	in{space	NOUN
m-1112	2192	20	and	and	CCONJ
m-1112	2192	21	anti	anti	ADJ
m-1112	2192	22	-	-	ADJ
m-1112	2192	23	space	space	NOUN
m-1112	2192	24	or	or	CCONJ
m-1112	2192	25	≡	≡	PROPN
m-1112	2192	26	qua	qua	PROPN
m-1112	2192	27	≡	≡	PROPN
m-1112	2192	28	{	{	PUNCT
m-1112	2192	29	is	be	AUX
m-1112	2192	30	the	the	DET
m-1112	2192	31	quantized	quantize	VERB
m-1112	2192	32	-	-	PUNCT
m-1112	2192	33	units	unit	NOUN
m-1112	2192	34	in	in	ADP
m-1112	2192	35	-	-	PUNCT
m-1112	2192	36	area	area	NOUN
m-1112	2192	37	of	of	ADP
m-1112	2192	38	space	space	NOUN
m-1112	2192	39	and	and	CCONJ
m-1112	2192	40	anti	anti	ADJ
m-1112	2192	41	-	-	NOUN
m-1112	2192	42	space	space	NOUN
m-1112	2192	43	}	}	PUNCT
m-1112	2192	44	,	,	PUNCT
m-1112	2192	45	and	and	CCONJ
m-1112	2192	46	as	as	ADP
m-1112	2192	47	a	a	DET
m-1112	2192	48	mould	mould	NOUN
m-1112	2192	49	𝚽	𝚽	PRON
m-1112	2192	50	golden	golden	ADJ
m-1112	2192	51	-	-	PUNCT
m-1112	2192	52	ratio	ratio	NOUN
m-1112	2192	53	,	,	PUNCT
m-1112	2192	54	exists	exist	VERB
m-1112	2192	55	as	as	ADP
m-1112	2192	56	impedance	impedance	NOUN
m-1112	2192	57	b.	b.	NOUN
m-1112	2192	58	placing	placing	NOUN
m-1112	2192	59	[	[	PUNCT
m-1112	2192	60	physical	physical	ADJ
m-1112	2192	61	mould	mould	NOUN
m-1112	2192	62	of	of	ADP
m-1112	2192	63	2rmonad	2rmonad	NUM
m-1112	2192	64	]	]	PUNCT
m-1112	2192	65	on	on	ADP
m-1112	2192	66	[	[	PUNCT
m-1112	2192	67	geometrical	geometrical	ADJ
m-1112	2192	68	mould	mould	NOUN
m-1112	2192	69	of	of	ADP
m-1112	2192	70	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	2192	71	̅̅	̅̅	PROPN
m-1112	2192	72	monad	monad	PROPN
m-1112	2192	73	]	]	X
m-1112	2192	74	[	[	PUNCT
m-1112	2192	75	pm-2r	pm-2r	NOUN
m-1112	2192	76	-	-	PUNCT
m-1112	2192	77	m	m	NOUN
m-1112	2192	78	]	]	PUNCT
m-1112	2193	1	→	→	SYM
m-1112	2193	2	⇅	⇅	PROPN
m-1112	2193	3	←	←	PROPN
m-1112	2193	4	[	[	PUNCT
m-1112	2193	5	gm	gm	PROPN
m-1112	2193	6	-	-	PUNCT
m-1112	2193	7	ab	ab	PROPN
m-1112	2193	8	-	-	PROPN
m-1112	2193	9	m	m	VERB
m-1112	2193	10	]	]	PUNCT
m-1112	2193	11	then	then	ADV
m-1112	2193	12	→	→	PUNCT
m-1112	2193	13	gravitational	gravitational	ADJ
m-1112	2193	14	-	-	PUNCT
m-1112	2193	15	force	force	NOUN
m-1112	2193	16	g	g	PROPN
m-1112	2193	17	≡	≡	PROPN
m-1112	2193	18	[	[	PUNCT
m-1112	2193	19	σ	σ	X
m-1112	2193	20	=	=	SYM
m-1112	2193	21	n	n	PROPN
m-1112	2193	22	.	.	PUNCT
m-1112	2194	1	h	h	NOUN
m-1112	2194	2	]	]	PUNCT
m-1112	2194	3	,	,	PUNCT
m-1112	2194	4	and	and	CCONJ
m-1112	2194	5	n	n	CCONJ
m-1112	2194	6	-	-	PUNCT
m-1112	2194	7	na	na	NOUN
m-1112	2194	8	=	=	SYM
m-1112	2194	9	1	1	NUM
m-1112	2194	10			NOUN
m-1112	2194	11	creates	create	VERB
m-1112	2194	12	&	&	CCONJ
m-1112	2194	13	constructs	construct	NOUN
m-1112	2194	14	,	,	PUNCT
m-1112	2194	15	for	for	ADP
m-1112	2194	16	n	n	PRON
m-1112	2194	17	=	=	SYM
m-1112	2194	18	1	1	NUM
m-1112	2194	19	abm	abm	NOUN
m-1112	2194	20	=	=	PUNCT
m-1112	2195	1	[	[	X
m-1112	2195	2	σ	σ	X
m-1112	2195	3	=	=	SYM
m-1112	2195	4	n	n	PRON
m-1112	2195	5	h	h	NOUN
m-1112	2195	6	]	]	X
m-1112	2195	7			NOUN
m-1112	2195	8	g	g	PROPN
m-1112	2195	9	/	/	SYM
m-1112	2195	10	c	c	NOUN
m-1112	2195	11	=	=	NOUN
m-1112	2195	12	charge	charge	NOUN
m-1112	2195	13	�	�	PROPN
m-1112	2195	14	̅	̅	NOUN
m-1112	2195	15	�	�	NOUN
m-1112	2195	16	=	=	SYM
m-1112	2195	17	𝐆	𝐆	PROPN
m-1112	2195	18	𝐜	𝐜	NOUN
m-1112	2195	19	√𝟐	√𝟐	PROPN
m-1112	2195	20	=	=	SYM
m-1112	2195	21	1,58.10−19	1,58.10−19	NUM
m-1112	2195	22	coulomb	coulomb	NOUN
m-1112	2195	23	.	.	PUNCT
m-1112	2196	1	1)	1)	NUM
m-1112	2196	2	..	..	PUNCT
m-1112	2196	3	→	→	SYM
m-1112	2196	4	g	g	PROPN
m-1112	2196	5	←	←	PROPN
m-1112	2196	6	g	g	PROPN
m-1112	2196	7	≡	≡	PROPN
m-1112	2196	8	σ.𝚽³	σ.𝚽³	NOUN
m-1112	2196	9	≡	≡	PROPN
m-1112	2196	10	g.	g.	PROPN
m-1112	2196	11	ke	ke	PROPN
m-1112	2196	12	≡	≡	PROPN
m-1112	2196	13	g	g	PROPN
m-1112	2196	14	.[gl	.[gl	PROPN
m-1112	2196	15	kl	kl	X
m-1112	2196	16	]	]	PUNCT
m-1112	2196	17	≡	≡	PROPN
m-1112	2197	1	[	[	PUNCT
m-1112	2197	2	t²p	t²p	X
m-1112	2197	3	𝐚³	𝐚³	ADJ
m-1112	2197	4	]	]	PUNCT
m-1112	2197	5	.[gl	.[gl	PUNCT
m-1112	2198	1	kl	kl	X
m-1112	2198	2	]	]	PUNCT
m-1112	2198	3	,	,	PUNCT
m-1112	2198	4	and	and	CCONJ
m-1112	2198	5	g	g	PROPN
m-1112	2198	6	=	=	SYM
m-1112	2198	7	𝐆	𝐆	PROPN
m-1112	2198	8	ke	ke	NOUN
m-1112	2198	9	=	=	PUNCT
m-1112	2199	1	[	[	PUNCT
m-1112	2199	2	6,673692	6,673692	NUM
m-1112	2199	3	.10−11	.10−11	PUNCT
m-1112	2199	4	6,8116	6,8116	NUM
m-1112	2199	5	.10	.10	NUM
m-1112	2199	6	−12	−12	NOUN
m-1112	2199	7	.	.	PUNCT
m-1112	2199	8	]	]	PUNCT
m-1112	2200	1	≡	≡	PROPN
m-1112	2200	2	9,8076941	9,8076941	PROPN
m-1112	2200	3	.	.	PUNCT
m-1112	2201	1	gravity	gravity	NOUN
m-1112	2201	2	-	-	PUNCT
m-1112	2201	3	acceleration	acceleration	NOUN
m-1112	2201	4	in	in	ADP
m-1112	2201	5	black	black	ADJ
m-1112	2201	6	-	-	PUNCT
m-1112	2201	7	holes	hole	NOUN
m-1112	2201	8	g	g	NOUN
m-1112	2201	9	g	g	NOUN
m-1112	2201	10	=	=	PUNCT
m-1112	2202	1	[	[	PUNCT
m-1112	2202	2	π	π	X
m-1112	2202	3	r	r	NOUN
m-1112	2202	4	v4	v4	NOUN
m-1112	2202	5	2	2	NUM
m-1112	2202	6	]	]	PUNCT
m-1112	2202	7	.𝑒3	.𝑒3	PUNCT
m-1112	2203	1	=	=	PUNCT
m-1112	2204	1	9,808238	9,808238	NUM
m-1112	2204	2	m	m	NOUN
m-1112	2204	3	/	/	SYM
m-1112	2204	4	s	s	PART
m-1112	2204	5	.	.	PUNCT
m-1112	2205	1	for	for	ADP
m-1112	2205	2	b	b	NOUN
m-1112	2205	3	=	=	SYM
m-1112	2205	4	36.10−20	36.10−20	PROPN
m-1112	2205	5	,	,	PUNCT
m-1112	2205	6	�	�	NOUN
m-1112	2205	7	̅	̅	NOUN
m-1112	2205	8	�	�	NOUN
m-1112	2205	9	=	=	SYM
m-1112	2205	10	f	f	PROPN
m-1112	2205	11	φ	φ	PROPN
m-1112	2205	12	a	a	PROPN
m-1112	2205	13	=	=	X
m-1112	2205	14	[	[	PUNCT
m-1112	2205	15	g	g	X
m-1112	2205	16	φ	φ	PROPN
m-1112	2205	17	a	a	X
m-1112	2205	18	]	]	X
m-1112	2205	19	=	=	PUNCT
m-1112	2205	20	[	[	PUNCT
m-1112	2205	21	6,673692	6,673692	NUM
m-1112	2205	22	.10−11.1,6180339887	.10−11.1,6180339887	PROPN
m-1112	2205	23	36	36	NUM
m-1112	2205	24	.10	.10	NUM
m-1112	2205	25	−20	−20	NOUN
m-1112	2205	26	.	.	PUNCT
m-1112	2205	27	]	]	PUNCT
m-1112	2206	1	=	=	PUNCT
m-1112	2206	2	2.9895163.108	2.9895163.108	NUM
m-1112	2206	3	m	m	PROPN
m-1112	2206	4	/	/	SYM
m-1112	2206	5	s	s	PART
m-1112	2206	6	2	2	NUM
m-1112	2206	7	)	)	PUNCT
m-1112	2206	8	..	..	PUNCT
m-1112	2207	1	→	→	PUNCT
m-1112	2207	2	c̅	c̅	PROPN
m-1112	2207	3	←	←	PROPN
m-1112	2207	4	�	�	PROPN
m-1112	2207	5	̅	̅	NOUN
m-1112	2207	6	�	�	PROPN
m-1112	2207	7	=	=	SYM
m-1112	2207	8	�	�	PROPN
m-1112	2207	9	̅	̅	NOUN
m-1112	2207	10	�	�	NOUN
m-1112	2207	11	=	=	SYM
m-1112	2207	12	σ	σ	PROPN
m-1112	2207	13	.	.	PUNCT
m-1112	2208	1	φ	φ	PROPN
m-1112	2208	2	=	=	X
m-1112	2209	1	f	f	PROPN
m-1112	2209	2	a	a	DET
m-1112	2209	3	φ	φ	PROPN
m-1112	2209	4	=	=	PRON
m-1112	2210	1	[	[	PUNCT
m-1112	2210	2	g	g	X
m-1112	2210	3	φ	φ	PROPN
m-1112	2210	4	a	a	X
m-1112	2210	5	]	]	X
m-1112	2210	6	=	=	PUNCT
m-1112	2210	7	[	[	PUNCT
m-1112	2210	8	6,673692	6,673692	NUM
m-1112	2210	9	.10−11.1,6180339887	.10−11.1,6180339887	PROPN
m-1112	2210	10	36	36	NUM
m-1112	2210	11	.10	.10	NUM
m-1112	2210	12	−20	−20	NOUN
m-1112	2210	13	.	.	PUNCT
m-1112	2210	14	]	]	PUNCT
m-1112	2211	1	=	=	PUNCT
m-1112	2211	2	2.9985163.108	2.9985163.108	NUM
m-1112	2211	3	m	m	NOUN
m-1112	2211	4	.	.	PUNCT
m-1112	2212	1	3	3	X
m-1112	2212	2	)	)	PUNCT
m-1112	2212	3	..	..	PUNCT
m-1112	2212	4	→	→	PUNCT
m-1112	2212	5	q̅	q̅	PROPN
m-1112	2212	6	←	←	PROPN
m-1112	2212	7	from	from	ADP
m-1112	2212	8	g	g	PROPN
m-1112	2212	9	=	=	SYM
m-1112	2212	10	c	c	PROPN
m-1112	2212	11	√𝟐	√𝟐	PROPN
m-1112	2212	12	�	�	PROPN
m-1112	2212	13	̅	̅	NOUN
m-1112	2212	14	�	�	PROPN
m-1112	2212	15	,	,	PUNCT
m-1112	2212	16	electron	electron	NOUN
m-1112	2212	17	-	-	PUNCT
m-1112	2212	18	charge	charge	NOUN
m-1112	2212	19	is	be	AUX
m-1112	2212	20	,	,	PUNCT
m-1112	2212	21	q̅	q̅	PROPN
m-1112	2212	22	=	=	PUNCT
m-1112	2212	23	g	g	PROPN
m-1112	2212	24	c	c	PROPN
m-1112	2212	25	√2	√2	PROPN
m-1112	2212	26	=	=	SYM
m-1112	2212	27	1,58.𝟏𝟎−𝟏𝟗	1,58.𝟏𝟎−𝟏𝟗	NUM
m-1112	2212	28	coulomb	coulomb	NOUN
m-1112	2212	29	,	,	PUNCT
m-1112	2212	30	b	b	X
m-1112	2212	31	…	…	PUNCT
m-1112	2212	32	the{tvpm	the{tvpm	NOUN
m-1112	2212	33	}	}	PUNCT
m-1112	2212	34	mechanisms	mechanism	NOUN
m-1112	2212	35	,	,	PUNCT
m-1112	2212	36	from	from	ADP
m-1112	2212	37	charges	charge	NOUN
m-1112	2212	38	on	on	ADP
m-1112	2212	39	two	two	NUM
m-1112	2212	40	-	-	PUNCT
m-1112	2212	41	perpendicular	perpendicular	ADJ
m-1112	2212	42	-	-	PUNCT
m-1112	2212	43	vectors	vector	NOUN
m-1112	2212	44	-	-	PUNCT
m-1112	2212	45	edges	edge	NOUN
m-1112	2212	46	≡	≡	PROPN
m-1112	2212	47	markos	markos	PROPN
m-1112	2212	48	two	two	NUM
m-1112	2212	49	-	-	PUNCT
m-1112	2212	50	vectors	vector	NOUN
m-1112	2212	51	three	three	NUM
m-1112	2212	52	-	-	PUNCT
m-1112	2212	53	poles	pole	NOUN
m-1112	2212	54	mechanism	mechanism	NOUN
m-1112	2212	55	is	be	AUX
m-1112	2212	56	case	case	NOUN
m-1112	2212	57	{	{	PUNCT
m-1112	2212	58	qua	qua	NOUN
m-1112	2212	59	}	}	PUNCT
m-1112	2212	60	≡	≡	PROPN
m-1112	2212	61	[	[	PUNCT
m-1112	2212	62	σ	σ	PROPN
m-1112	2212	63	=	=	SYM
m-1112	2212	64	n	n	PROPN
m-1112	2212	65	.	.	PUNCT
m-1112	2213	1	h	h	NOUN
m-1112	2213	2	]	]	PUNCT
m-1112	2214	1			NOUN
m-1112	2215	1	∞	∞	NUM
m-1112	2215	2	x	x	PUNCT
m-1112	2215	3	𝚽	𝚽	NOUN
m-1112	2215	4	which	which	PRON
m-1112	2215	5	is	be	AUX
m-1112	2215	6	the	the	DET
m-1112	2215	7	physical	physical	ADJ
m-1112	2215	8	mechanism	mechanism	NOUN
m-1112	2215	9	,	,	PUNCT
m-1112	2215	10	and	and	CCONJ
m-1112	2215	11	gives	give	VERB
m-1112	2215	12	the	the	DET
m-1112	2215	13	∞	∞	PROPN
m-1112	2215	14	impedance	impedance	NOUN
m-1112	2215	15	b	b	NOUN
m-1112	2215	16	,	,	PUNCT
m-1112	2215	17	determining	determine	VERB
m-1112	2215	18	the	the	DET
m-1112	2215	19	objective	objective	ADJ
m-1112	2215	20	reality	reality	NOUN
m-1112	2215	21	which	which	PRON
m-1112	2215	22	is	be	AUX
m-1112	2215	23	the	the	DET
m-1112	2215	24	existing	exist	VERB
m-1112	2215	25	universe	universe	NOUN
m-1112	2215	26	.	.	PUNCT
m-1112	2216	1	the	the	DET
m-1112	2216	2	two	two	NUM
m-1112	2216	3	⏊	⏊	PROPN
m-1112	2216	4	vectors	vector	NOUN
m-1112	2216	5	produce	produce	VERB
m-1112	2216	6	the	the	DET
m-1112	2216	7	∞	∞	NUM
m-1112	2216	8	squares	square	NOUN
m-1112	2216	9	∞	∞	PROPN
m-1112	2216	10	,	,	PUNCT
m-1112	2216	11	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	2216	12	̅̅	̅̅	PROPN
m-1112	2216	13	monad	monad	PROPN
m-1112	2216	14	≡	≡	PROPN
m-1112	2216	15	∞	∞	PROPN
m-1112	2217	1	[	[	PUNCT
m-1112	2217	2	gm	gm	PROPN
m-1112	2217	3	-	-	PUNCT
m-1112	2217	4	ab	ab	PROPN
m-1112	2217	5	-	-	NOUN
m-1112	2217	6	m	m	PROPN
m-1112	2217	7	]	]	PUNCT
m-1112	2217	8	with	with	ADP
m-1112	2217	9	∞	∞	PROPN
m-1112	2217	10	,	,	PUNCT
m-1112	2217	11	2r	2r	NUM
m-1112	2217	12	-	-	PUNCT
m-1112	2217	13	form	form	NOUN
m-1112	2217	14	[	[	PUNCT
m-1112	2217	15	pm-2r	pm-2r	NOUN
m-1112	2217	16	-	-	PUNCT
m-1112	2217	17	m	m	NOUN
m-1112	2217	18	]	]	PUNCT
m-1112	2217	19	and	and	CCONJ
m-1112	2217	20	n	n	CCONJ
m-1112	2217	21	≡	≡	ADJ
m-1112	2217	22	∞	∞	NUM
m-1112	2217	23	number	number	NOUN
m-1112	2217	24	of	of	ADP
m-1112	2217	25	accessories	accessory	NOUN
m-1112	2217	26	,	,	PUNCT
m-1112	2217	27	as	as	ADP
m-1112	2217	28	from	from	ADP
m-1112	2217	29	monad	monad	PROPN
m-1112	2217	30	r	r	NOUN
m-1112	2217	31	=	=	SYM
m-1112	2217	32	σ	σ	X
m-1112	2217	33	j.w²	j.w²	NOUN
m-1112	2217	34	=	=	SYM
m-1112	2217	35	𝛔	𝛔	PART
m-1112	2217	36	�	�	PROPN
m-1112	2217	37	̅	̅	NOUN
m-1112	2217	38	�	�	PROPN
m-1112	2217	39	and	and	CCONJ
m-1112	2217	40	velocity	velocity	NOUN
m-1112	2217	41	�	�	NOUN
m-1112	2217	42	̅	̅	NOUN
m-1112	2217	43	�	�	PROPN
m-1112	2217	44	≡	≡	PROPN
m-1112	2217	45			PROPN
m-1112	2217	46	σ	σ	PROPN
m-1112	2217	47	φ	φ	PROPN
m-1112	2217	48	.	.	PUNCT
m-1112	2218	1	c	c	X
m-1112	2218	2	…	…	PUNCT
m-1112	2218	3	primary	primary	ADJ
m-1112	2218	4	motion	motion	NOUN
m-1112	2218	5	≡	≡	PROPN
m-1112	2218	6	[	[	X
m-1112	2218	7	pm	pm	X
m-1112	2218	8	]	]	PUNCT
m-1112	2218	9	exist	exist	VERB
m-1112	2218	10	from	from	ADP
m-1112	2218	11	the	the	DET
m-1112	2218	12	three	three	NUM
m-1112	2218	13	breakages	breakage	NOUN
m-1112	2218	14	only	only	ADV
m-1112	2218	15	[	[	X
m-1112	2218	16	s²	s²	PROPN
m-1112	2218	17	=	=	SYM
m-1112	2218	18	⊕	⊕	PROPN
m-1112	2218	19	,	,	PUNCT
m-1112	2218	20	2s²	2s²	NUM
m-1112	2218	21	=	=	SYM
m-1112	2219	1			X
m-1112	2219	2	,	,	PUNCT
m-1112	2219	3	s²	s²	NOUN
m-1112	2219	4	=	=	SYM
m-1112	2219	5	⊝	⊝	X
m-1112	2219	6	]	]	PUNCT
m-1112	2219	7	,	,	PUNCT
m-1112	2219	8	on	on	ADP
m-1112	2219	9	triangle	triangle	NOUN
m-1112	2219	10	3	3	NUM
m-1112	2219	11	-	-	PUNCT
m-1112	2219	12	knots	knot	NOUN
m-1112	2219	13	with	with	ADP
m-1112	2219	14	n	n	X
m-1112	2219	15	≡	≡	ADJ
m-1112	2219	16	3	3	NUM
m-1112	2219	17	number	number	NOUN
m-1112	2219	18	of	of	ADP
m-1112	2219	19	accessories	accessory	NOUN
m-1112	2219	20	,	,	PUNCT
m-1112	2219	21	therefore	therefore	ADV
m-1112	2219	22	[	[	X
m-1112	2219	23	stpl	stpl	X
m-1112	2219	24	]	]	X
m-1112	2219	25	mechanism	mechanism	NOUN
m-1112	2219	26	is	be	AUX
m-1112	2219	27	the	the	DET
m-1112	2219	28	n	n	NOUN
m-1112	2219	29	=	=	SYM
m-1112	2219	30	3	3	NUM
m-1112	2219	31	accessories	accessory	NOUN
m-1112	2219	32	-	-	PUNCT
m-1112	2219	33	mechanism	mechanism	NOUN
m-1112	2219	34	creating	create	VERB
m-1112	2219	35	the	the	DET
m-1112	2219	36	elementary	elementary	ADJ
m-1112	2219	37	particles	particle	NOUN
m-1112	2219	38	,	,	PUNCT
m-1112	2219	39	[	[	X
m-1112	2219	40	n	n	X
m-1112	2219	41	-	-	PUNCT
m-1112	2219	42	knots=3	knots=3	X
m-1112	2219	43	]	]	X
m-1112	2219	44	in	in	ADP
m-1112	2219	45	the	the	DET
m-1112	2219	46	gravity	gravity	NOUN
m-1112	2219	47	voltage	voltage	NOUN
m-1112	2219	48			NOUN
m-1112	2219	49	𝐕	𝐕	PROPN
m-1112	2219	50	gra	gra	NOUN
m-1112	2219	51	=	=	PUNCT
m-1112	2219	52	7,593.1035	7,593.1035	PROPN
m-1112	2219	53	v.	v.	ADP
m-1112	2219	54	this	this	DET
m-1112	2219	55	physical	physical	ADJ
m-1112	2219	56	mechanism	mechanism	NOUN
m-1112	2219	57	creates	create	VERB
m-1112	2219	58	the	the	DET
m-1112	2219	59	elementary	elementary	ADJ
m-1112	2219	60	particles	particle	NOUN
m-1112	2219	61	their	their	PRON
m-1112	2219	62	n	n	NOUN
m-1112	2219	63	=	=	SYM
m-1112	2219	64	1	1	NUM
m-1112	2219	65	∞	∞	NUM
m-1112	2219	66	,	,	PUNCT
m-1112	2219	67	masses	masse	NOUN
m-1112	2219	68	of	of	ADP
m-1112	2219	69	atom`s	atom`s	PROPN
m-1112	2219	70	&	&	CCONJ
m-1112	2219	71	compounds	compound	NOUN
m-1112	2219	72	determining	determine	VERB
m-1112	2219	73	their	their	PRON
m-1112	2219	74	atoms	atom	NOUN
m-1112	2219	75	complex	complex	ADJ
m-1112	2219	76	-	-	PUNCT
m-1112	2219	77	vector	vector	NOUN
m-1112	2219	78	-	-	PUNCT
m-1112	2219	79	response	response	NOUN
m-1112	2219	80	.these	.these	SCONJ
m-1112	2219	81	sparse	sparse	ADJ
m-1112	2219	82	particles	particle	NOUN
m-1112	2219	83	exist	exist	VERB
m-1112	2219	84	in	in	ADP
m-1112	2219	85	all	all	PRON
m-1112	2219	86	of	of	ADP
m-1112	2219	87	the	the	DET
m-1112	2219	88	ijo	ijo	PROPN
m-1112	2219	89	international	international	PROPN
m-1112	2219	90	journal	journal	PROPN
m-1112	2219	91	of	of	ADP
m-1112	2219	92	mathematics	mathematics	PROPN
m-1112	2219	93	(	(	PUNCT
m-1112	2219	94	issn	issn	PROPN
m-1112	2219	95	:	:	PUNCT
m-1112	2219	96	2992	2992	NUM
m-1112	2219	97	-	-	SYM
m-1112	2219	98	4421	4421	NUM
m-1112	2219	99	)	)	PUNCT
m-1112	2220	1	volume	volume	NOUN
m-1112	2220	2	08	08	NUM
m-1112	2221	1	|	|	ADV
m-1112	2221	2	issue	issue	NOUN
m-1112	2221	3	08	08	NUM
m-1112	2222	1	|	|	ADV
m-1112	2222	2	august	august	PROPN
m-1112	2222	3	2025	2025	NUM
m-1112	2222	4	|	|	ADV
m-1112	2222	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2222	6	ijo	ijo	PROPN
m-1112	2222	7	journals	journal	NOUN
m-1112	2222	8	77	77	NUM
m-1112	2222	9	the	the	DET
m-1112	2222	10	fundamental	fundamental	ADJ
m-1112	2222	11	particles	particle	NOUN
m-1112	2222	12	origination	origination	NOUN
m-1112	2222	13	mechanism	mechanism	NOUN
m-1112	2222	14	in	in	ADP
m-1112	2222	15	mfmf	mfmf	PROPN
m-1112	2222	16	pns	pns	PROPN
m-1112	2222	17	caves	cave	NOUN
m-1112	2222	18	.	.	PUNCT
m-1112	2223	1	universe	universe	NOUN
m-1112	2223	2	in	in	ADP
m-1112	2223	3	the	the	DET
m-1112	2223	4	sense	sense	NOUN
m-1112	2223	5	that	that	SCONJ
m-1112	2223	6	they	they	PRON
m-1112	2223	7	are	be	AUX
m-1112	2223	8	uniformly	uniformly	ADV
m-1112	2223	9	distributed	distribute	VERB
m-1112	2223	10	.	.	PUNCT
m-1112	2224	1	d	d	X
m-1112	2224	2	…	…	PUNCT
m-1112	2224	3	the	the	DET
m-1112	2224	4	{	{	PUNCT
m-1112	2224	5	tcic	tcic	NOUN
m-1112	2224	6	}	}	PUNCT
m-1112	2224	7	mechanisms	mechanism	VERB
m-1112	2224	8	≡	≡	PROPN
m-1112	2225	1	[	[	PUNCT
m-1112	2225	2	σ	σ	X
m-1112	2225	3	=	=	SYM
m-1112	2225	4	n	n	PROPN
m-1112	2225	5	.	.	PUNCT
m-1112	2226	1	h	h	NOUN
m-1112	2226	2	]	]	PUNCT
m-1112	2227	1			NOUN
m-1112	2227	2	8	8	NUM
m-1112	2227	3	x	x	SYM
m-1112	2227	4	①	①	PROPN
m-1112	2227	5	is	be	AUX
m-1112	2227	6	the	the	DET
m-1112	2227	7	physical	physical	ADJ
m-1112	2227	8	mechanism	mechanism	NOUN
m-1112	2227	9	,	,	PUNCT
m-1112	2227	10	from	from	ADP
m-1112	2227	11	charges	charge	NOUN
m-1112	2227	12	in	in	ADP
m-1112	2227	13	three	three	NUM
m-1112	2227	14	-	-	PUNCT
m-1112	2227	15	vectors	vector	NOUN
m-1112	2227	16	-	-	PUNCT
m-1112	2227	17	conductors	conductor	NOUN
m-1112	2227	18	-	-	PUNCT
m-1112	2227	19	edges	edge	NOUN
m-1112	2227	20	≡	≡	PROPN
m-1112	2227	21	markos	markos	PROPN
m-1112	2227	22	tetrahedron	tetrahedron	NOUN
m-1112	2227	23	cube	cube	NOUN
m-1112	2227	24	inscribed	inscribe	VERB
m-1112	2227	25	–	–	PUNCT
m-1112	2227	26	circumscribed	circumscribed	ADJ
m-1112	2227	27	circles	circle	NOUN
m-1112	2227	28	.the	.the	DET
m-1112	2227	29	tetrahedron	tetrahedron	PROPN
m-1112	2227	30	conductors	conductor	NOUN
m-1112	2227	31	-vectors	-vector	NOUN
m-1112	2227	32	da̅̅	da̅̅	PROPN
m-1112	2227	33	̅̅	̅̅	PROPN
m-1112	2227	34	⏊	⏊	PROPN
m-1112	2227	35	db̅̅	db̅̅	PROPN
m-1112	2227	36	̅̅	̅̅	PROPN
m-1112	2227	37	⏊	⏊	PROPN
m-1112	2227	38	dc̅̅	dc̅̅	PROPN
m-1112	2227	39	̅̅	̅̅	PROPN
m-1112	2227	40	curry	curry	VERB
m-1112	2227	41	energy	energy	NOUN
m-1112	2227	42	as	as	ADP
m-1112	2227	43	electromagnetic	electromagnetic	NOUN
m-1112	2227	44	-	-	PUNCT
m-1112	2227	45	fields	field	NOUN
m-1112	2227	46	(	(	PUNCT
m-1112	2227	47	forces	force	NOUN
m-1112	2227	48	-	-	PUNCT
m-1112	2227	49	frequencies	frequency	NOUN
m-1112	2227	50	-	-	PUNCT
m-1112	2227	51	stresses	stress	NOUN
m-1112	2227	52	-	-	PUNCT
m-1112	2227	53	any	any	DET
m-1112	2227	54	motion	motion	NOUN
m-1112	2227	55	)	)	PUNCT
m-1112	2227	56	to	to	ADP
m-1112	2227	57	the	the	DET
m-1112	2227	58	inscribed	inscribe	VERB
m-1112	2227	59	sphere	sphere	NOUN
m-1112	2227	60	(	(	PUNCT
m-1112	2227	61	nucleus	nucleus	NOUN
m-1112	2227	62	of	of	ADP
m-1112	2227	63	atoms	atom	NOUN
m-1112	2227	64	)	)	PUNCT
m-1112	2227	65	,	,	PUNCT
m-1112	2227	66	to	to	ADP
m-1112	2227	67	cube	cube	NOUN
m-1112	2227	68	vertices	vertex	NOUN
m-1112	2227	69	(	(	PUNCT
m-1112	2227	70	electrons	electron	NOUN
m-1112	2227	71	-	-	PUNCT
m-1112	2227	72	position	position	NOUN
m-1112	2227	73	)	)	PUNCT
m-1112	2227	74	,	,	PUNCT
m-1112	2227	75	to	to	ADP
m-1112	2227	76	the	the	DET
m-1112	2227	77	circumscribed	circumscribed	ADJ
m-1112	2227	78	sphere	sphere	NOUN
m-1112	2227	79	(	(	PUNCT
m-1112	2227	80	the	the	DET
m-1112	2227	81	electrons	electron	NOUN
m-1112	2227	82	orbits	orbit	NOUN
m-1112	2227	83	)	)	PUNCT
m-1112	2227	84	for	for	ADP
m-1112	2227	85	equilibrium	equilibrium	NOUN
m-1112	2227	86	and	and	CCONJ
m-1112	2227	87	for	for	ADP
m-1112	2227	88	transferring	transfer	VERB
m-1112	2227	89	information	information	NOUN
m-1112	2227	90	and	and	CCONJ
m-1112	2227	91	signals	signal	NOUN
m-1112	2227	92	.	.	PUNCT
m-1112	2228	1	a	a	DET
m-1112	2228	2	..	..	PUNCT
m-1112	2228	3	the	the	DET
m-1112	2228	4	protons	proton	NOUN
m-1112	2228	5	and	and	CCONJ
m-1112	2228	6	the	the	DET
m-1112	2228	7	nucleus	nucleus	ADJ
m-1112	2228	8	structure	structure	NOUN
m-1112	2228	9	:	:	PUNCT
m-1112	2228	10	from	from	ADP
m-1112	2228	11	above	above	ADP
m-1112	2228	12	[	[	PUNCT
m-1112	2228	13	gm	gm	PROPN
m-1112	2228	14	-	-	PUNCT
m-1112	2228	15	ab	ab	PROPN
m-1112	2228	16	-	-	PUNCT
m-1112	2228	17	m	m	PROPN
m-1112	2228	18	]	]	X
m-1112	2228	19	≡	≡	ADJ
m-1112	2228	20	8	8	NUM
m-1112	2228	21	x	x	SYM
m-1112	2229	1	[	[	X
m-1112	2229	2	(	(	PUNCT
m-1112	2229	3	+	+	NOUN
m-1112	2229	4	)	)	PUNCT
m-1112	2229	5	[	[	X
m-1112	2229	6	↔](-	↔](-	NOUN
m-1112	2229	7	)	)	PUNCT
m-1112	2229	8	]	]	PUNCT
m-1112	2230	1	≡	≡	PROPN
m-1112	2230	2	neutral	neutral	ADJ
m-1112	2230	3	=	=	SYM
m-1112	2230	4	n	n	NOUN
m-1112	2230	5	,	,	PUNCT
m-1112	2230	6	then	then	ADV
m-1112	2230	7	a	a	PRON
m-1112	2230	8	...	...	PUNCT
m-1112	2230	9	for	for	ADP
m-1112	2230	10	1	1	NUM
m-1112	2230	11	proton	proton	NOUN
m-1112	2230	12	[	[	X
m-1112	2230	13	(	(	PUNCT
m-1112	2230	14	+	+	NOUN
m-1112	2230	15	)	)	PUNCT
m-1112	2230	16	[	[	X
m-1112	2230	17	↔](-)]↔(+	↔](-)]↔(+	NOUN
m-1112	2230	18	)	)	PUNCT
m-1112	2230	19	≡	≡	PROPN
m-1112	2230	20	neutral	neutral	ADJ
m-1112	2230	21	→	→	SYM
m-1112	2230	22	n	n	NOUN
m-1112	2230	23	=	=	SYM
m-1112	2230	24	1	1	NUM
m-1112	2230	25	p	p	NOUN
m-1112	2230	26	=	=	SYM
m-1112	2230	27	1	1	NUM
m-1112	2230	28	b	b	NOUN
m-1112	2230	29	...	...	PUNCT
m-1112	2230	30	for	for	ADP
m-1112	2230	31	2	2	NUM
m-1112	2230	32	proton	proton	NOUN
m-1112	2230	33	(	(	PUNCT
m-1112	2230	34	+	+	NOUN
m-1112	2230	35	)	)	PUNCT
m-1112	2230	36	↔[(-)↔(+)][(+)↔(-)]↔(+	↔[(-)↔(+)][(+)↔(-)]↔(+	NOUN
m-1112	2230	37	)	)	PUNCT
m-1112	2231	1	≡	≡	PROPN
m-1112	2231	2	neutral	neutral	ADJ
m-1112	2231	3	→	→	SYM
m-1112	2231	4	p	p	NOUN
m-1112	2231	5	n	n	CCONJ
m-1112	2231	6	n	n	NOUN
m-1112	2231	7	p	p	NOUN
m-1112	2231	8	c	c	PROPN
m-1112	2231	9	...	...	PUNCT
m-1112	2231	10	for	for	ADP
m-1112	2231	11	3	3	NUM
m-1112	2231	12	proton	proton	NOUN
m-1112	2231	13	(	(	PUNCT
m-1112	2231	14	+	+	NOUN
m-1112	2231	15	)	)	PUNCT
m-1112	2231	16	↔[(-)(+)](+)[(-)(+)](+)[(-)(+	↔[(-)(+)](+)[(-)(+)](+)[(-)(+	NOUN
m-1112	2231	17	)	)	PUNCT
m-1112	2231	18	]	]	PUNCT
m-1112	2232	1	≡	≡	PROPN
m-1112	2232	2	neutral	neutral	ADJ
m-1112	2232	3	→	→	SYM
m-1112	2232	4	n	n	PROPN
m-1112	2232	5	p	p	NOUN
m-1112	2232	6	n	n	PROPN
m-1112	2232	7	p	p	NOUN
m-1112	2232	8	n	n	PRON
m-1112	2232	9	p	p	NOUN
m-1112	2232	10	d	d	PROPN
m-1112	2232	11	...	...	PUNCT
m-1112	2232	12	for	for	ADP
m-1112	2232	13	4	4	NUM
m-1112	2232	14	proton	proton	NOUN
m-1112	2232	15	(	(	PUNCT
m-1112	2232	16	+	+	NOUN
m-1112	2232	17	)	)	PUNCT
m-1112	2232	18	↔[(-)(+)](+)[(-)(+)](+)[(-)(+)](+)[(-)(+	↔[(-)(+)](+)[(-)(+)](+)[(-)(+)](+)[(-)(+	NOUN
m-1112	2232	19	)	)	PUNCT
m-1112	2232	20	]	]	PUNCT
m-1112	2233	1	→	→	PUNCT
m-1112	2233	2	p	p	X
m-1112	2233	3	n	n	CCONJ
m-1112	2233	4	p	p	NOUN
m-1112	2233	5	n	n	NOUN
m-1112	2233	6	0	0	NUM
m-1112	2233	7	n	n	PROPN
m-1112	2233	8	p	p	NOUN
m-1112	2233	9	n	n	PRON
m-1112	2233	10	p	p	PROPN
m-1112	2233	11	h	h	NOUN
m-1112	2233	12	...	...	PUNCT
m-1112	2233	13	for	for	ADP
m-1112	2233	14	k	k	PROPN
m-1112	2233	15	proton	proton	NOUN
m-1112	2233	16	(	(	PUNCT
m-1112	2233	17	k1)↔[(-)(+)](k2)[(-)(+)](+)[(-)(+)](+)[(-)(𝐡𝐤	k1)↔[(-)(+)](k2)[(-)(+)](+)[(-)(+)](+)[(-)(𝐡𝐤	PROPN
m-1112	2233	18	)	)	PUNCT
m-1112	2233	19	]	]	PUNCT
m-1112	2234	1	→	→	PUNCT
m-1112	2234	2	kp	kp	PROPN
m-1112	2234	3	kn	kn	PROPN
m-1112	2234	4	kp	kp	PROPN
m-1112	2235	1	kn	kn	PROPN
m-1112	2235	2	0	0	PUNCT
m-1112	2236	1	kn	kn	PROPN
m-1112	2236	2	kp	kp	PROPN
m-1112	2236	3	kn	kn	PROPN
m-1112	2236	4	kp	kp	PROPN
m-1112	2236	5	where	where	SCONJ
m-1112	2236	6	n	n	AUX
m-1112	2236	7	-	-	PUNCT
m-1112	2236	8	na	na	NOUN
m-1112	2236	9	≡	≡	PROPN
m-1112	2236	10	k	k	PROPN
m-1112	2236	11	≡	≡	PROPN
m-1112	2236	12	the	the	DET
m-1112	2236	13	number	number	NOUN
m-1112	2236	14	of	of	ADP
m-1112	2236	15	accessories	accessory	NOUN
m-1112	2236	16	of	of	ADP
m-1112	2236	17	{	{	PUNCT
m-1112	2236	18	tcic	tcic	NOUN
m-1112	2236	19	}	}	PUNCT
m-1112	2236	20	mechanisms	mechanism	NOUN
m-1112	2236	21	≡	≡	PROPN
m-1112	2236	22	[	[	PUNCT
m-1112	2236	23	σ	σ	X
m-1112	2236	24	=	=	SYM
m-1112	2236	25	n	n	PROPN
m-1112	2236	26	.	.	PUNCT
m-1112	2237	1	h	h	NOUN
m-1112	2237	2	]	]	PUNCT
m-1112	2238	1	on	on	ADP
m-1112	2238	2	→	→	PUNCT
m-1112	2238	3	kp	kp	PROPN
m-1112	2238	4	kn	kn	PROPN
m-1112	2238	5	kp	kp	PROPN
m-1112	2238	6	kn	kn	PROPN
m-1112	2238	7	0	0	PUNCT
m-1112	2239	1	kn	kn	PROPN
m-1112	2239	2	kp	kp	PROPN
m-1112	2239	3	kn	kn	PROPN
m-1112	2239	4	kp	kp	PROPN
m-1112	2239	5	k	k	PROPN
m-1112	2239	6	space	space	PROPN
m-1112	2239	7	[	[	PUNCT
m-1112	2239	8	gm	gm	PROPN
m-1112	2239	9	-	-	PUNCT
m-1112	2239	10	ab	ab	PROPN
m-1112	2239	11	-	-	NOUN
m-1112	2239	12	m	m	PROPN
m-1112	2239	13	]	]	PUNCT
m-1112	2239	14	.	.	PUNCT
m-1112	2240	1	from	from	ADP
m-1112	2240	2	above	above	ADV
m-1112	2240	3	is	be	AUX
m-1112	2240	4	seen	see	VERB
m-1112	2240	5	the	the	DET
m-1112	2240	6	way	way	NOUN
m-1112	2240	7	of	of	ADP
m-1112	2240	8	atoms	atom	NOUN
m-1112	2240	9	construction	construction	NOUN
m-1112	2240	10	.	.	PUNCT
m-1112	2241	1	(	(	PUNCT
m-1112	2241	2	geometrical	geometrical	ADJ
m-1112	2241	3	-	-	PUNCT
m-1112	2241	4	mould	mould	NOUN
m-1112	2241	5	of	of	ADP
m-1112	2241	6	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	2241	7	̅̅	̅̅	PROPN
m-1112	2241	8	-monad	-monad	PROPN
m-1112	2241	9	)	)	PUNCT
m-1112	2241	10	.	.	PUNCT
m-1112	2242	1	e	e	X
m-1112	2242	2	…	…	PUNCT
m-1112	2242	3	from	from	ADP
m-1112	2242	4	energy	energy	NOUN
m-1112	2242	5	=	=	NOUN
m-1112	2242	6	motion	motion	NOUN
m-1112	2242	7	/	/	SYM
m-1112	2242	8	t	t	PROPN
m-1112	2242	9	≡	≡	PROPN
m-1112	2242	10	(	(	PUNCT
m-1112	2242	11	v	v	NUM
m-1112	2242	12	2πr	2πr	NOUN
m-1112	2242	13	)	)	PUNCT
m-1112	2242	14	.[σ+σ	.[σ+σ	PUNCT
m-1112	2243	1	φ	φ	X
m-1112	2243	2	]	]	X
m-1112	2243	3	=	=	SYM
m-1112	2243	4	�	�	PROPN
m-1112	2243	5	̅	̅	NOUN
m-1112	2243	6	�	�	NOUN
m-1112	2243	7	.	.	PUNCT
m-1112	2244	1	[	[	PUNCT
m-1112	2244	2	𝛔	𝛔	X
m-1112	2244	3	𝟐𝛑𝐫	𝟐𝛑𝐫	NOUN
m-1112	2245	1	+	+	X
m-1112	2245	2	𝛔𝚽	𝛔𝚽	ADJ
m-1112	2245	3	𝟐𝛑𝐫	𝟐𝛑𝐫	NOUN
m-1112	2245	4	]	]	PUNCT
m-1112	2245	5	≡	≡	PROPN
m-1112	2245	6	�	�	PROPN
m-1112	2245	7	̅	̅	NOUN
m-1112	2245	8	�	�	PROPN
m-1112	2245	9	.	.	PUNCT
m-1112	2246	1	[	[	X
m-1112	2246	2	.	.	PUNCT
m-1112	2247	1	fn̅	fn̅	PROPN
m-1112	2248	1	+	+	NUM
m-1112	2248	2	𝐟𝐧	𝐟𝐧	NOUN
m-1112	2248	3	]	]	PUNCT
m-1112	2248	4	≡	≡	PROPN
m-1112	2248	5	moving	move	VERB
m-1112	2248	6	storage	storage	NOUN
m-1112	2248	7	→	→	NOUN
m-1112	2248	8	[	[	PUNCT
m-1112	2248	9	�	�	NOUN
m-1112	2248	10	̅	̅	NOUN
m-1112	2248	11	�	�	PROPN
m-1112	2248	12	.	.	PUNCT
m-1112	2249	1	fn̅	fn̅	PROPN
m-1112	2249	2	]	]	PUNCT
m-1112	2249	3	≡	≡	PROPN
m-1112	2250	1	[	[	X
m-1112	2250	2	gm	gm	PROPN
m-1112	2250	3	-	-	PUNCT
m-1112	2250	4	ab	ab	PROPN
m-1112	2250	5	-	-	PUNCT
m-1112	2250	6	m	m	PROPN
m-1112	2250	7	]	]	X
m-1112	2250	8	←	←	PROPN
m-1112	2250	9	+	+	CCONJ
m-1112	2250	10	moving	move	VERB
m-1112	2250	11	-	-	PUNCT
m-1112	2250	12	frequency	frequency	NOUN
m-1112	2250	13	→	→	SYM
m-1112	2250	14	[	[	X
m-1112	2250	15	�	�	NOUN
m-1112	2250	16	̅	̅	NOUN
m-1112	2250	17	�	�	NOUN
m-1112	2250	18	.𝐟𝐧	.𝐟𝐧	SYM
m-1112	2250	19	]	]	PUNCT
m-1112	2251	1	≡	≡	PROPN
m-1112	2252	1	[	[	X
m-1112	2252	2	pm-2r	pm-2r	NOUN
m-1112	2252	3	-	-	PUNCT
m-1112	2252	4	m	m	NOUN
m-1112	2252	5	]	]	X
m-1112	2252	6	←	←	PROPN
m-1112	2252	7	≡	≡	PROPN
m-1112	2252	8	[	[	PUNCT
m-1112	2252	9	σ	σ	PROPN
m-1112	2252	10	=	=	SYM
m-1112	2252	11	n	n	PROPN
m-1112	2252	12	.	.	PUNCT
m-1112	2253	1	h	h	NOUN
m-1112	2253	2	]	]	PUNCT
m-1112	2253	3	,	,	PUNCT
m-1112	2253	4	and	and	CCONJ
m-1112	2253	5	n	n	CCONJ
m-1112	2253	6	-	-	PUNCT
m-1112	2253	7	na	na	NOUN
m-1112	2253	8	=	=	SYM
m-1112	2253	9	1	1	NUM
m-1112	2253	10			NOUN
m-1112	2253	11	material	material	NOUN
m-1112	2253	12	-	-	PUNCT
m-1112	2253	13	point	point	NOUN
m-1112	2253	14	i.e.	i.e.	X
m-1112	2253	15	the	the	DET
m-1112	2253	16	energy	energy	NOUN
m-1112	2253	17	produced	produce	VERB
m-1112	2253	18	in	in	ADP
m-1112	2253	19	photon	photon	NOUN
m-1112	2253	20	-	-	PUNCT
m-1112	2253	21	cave	cave	NOUN
m-1112	2253	22	is	be	AUX
m-1112	2253	23	consisted	consist	VERB
m-1112	2253	24	of	of	ADP
m-1112	2253	25	two	two	NUM
m-1112	2253	26	-	-	PUNCT
m-1112	2253	27	moving	moving	NOUN
m-1112	2253	28	-	-	PUNCT
m-1112	2253	29	storages	storage	NOUN
m-1112	2253	30	that	that	PRON
m-1112	2253	31	travel	travel	VERB
m-1112	2253	32	as	as	ADP
m-1112	2253	33	wave	wave	NOUN
m-1112	2253	34	[	[	X
m-1112	2253	35	�	�	NOUN
m-1112	2253	36	̅	̅	NOUN
m-1112	2253	37	�	�	NOUN
m-1112	2253	38	.𝐟𝐧	.𝐟𝐧	PRON
m-1112	2253	39	]	]	PUNCT
m-1112	2254	1	→	→	ADP
m-1112	2254	2	[	[	PUNCT
m-1112	2254	3	�	�	NOUN
m-1112	2254	4	̅	̅	NOUN
m-1112	2254	5	�	�	PROPN
m-1112	2254	6	.	.	PUNCT
m-1112	2255	1	fn̅	fn̅	PROPN
m-1112	2255	2	]	]	PUNCT
m-1112	2256	1	→	→	X
m-1112	2256	2	[	[	PUNCT
m-1112	2256	3	�	�	NOUN
m-1112	2256	4	̅	̅	NOUN
m-1112	2256	5	�	�	PROPN
m-1112	2256	6	=	=	SYM
m-1112	2256	7	�	�	PROPN
m-1112	2256	8	̅	̅	NOUN
m-1112	2256	9	�	�	NOUN
m-1112	2256	10	=	=	SYM
m-1112	2256	11	λ	λ	X
m-1112	2256	12	f	f	PROPN
m-1112	2256	13	φ	φ	X
m-1112	2256	14	]	]	PUNCT
m-1112	2256	15	→	→	X
m-1112	2257	1	[	[	X
m-1112	2257	2	s≡	s≡	NOUN
m-1112	2257	3	em	em	NOUN
m-1112	2257	4	-	-	PUNCT
m-1112	2257	5	r	r	NOUN
m-1112	2257	6	≡	≡	PROPN
m-1112	2257	7	f1	f1	NOUN
m-1112	2257	8	=	=	SYM
m-1112	2257	9	n	n	CCONJ
m-1112	2257	10	]	]	PUNCT
m-1112	2257	11	&	&	CCONJ
m-1112	2257	12	as	as	ADP
m-1112	2257	13	particle→	particle→	PROPN
m-1112	2257	14	[	[	PUNCT
m-1112	2257	15	f1=	f1=	PROPN
m-1112	2257	16	(	(	PUNCT
m-1112	2257	17	e²+h²	e²+h²	PROPN
m-1112	2257	18	)	)	PUNCT
m-1112	2257	19	=	=	SYM
m-1112	2257	20	n	n	CCONJ
m-1112	2257	21	(	(	PUNCT
m-1112	2257	22	1+√5)σ	1+√5)σ	NUM
m-1112	2257	23	2πr	2πr	NOUN
m-1112	2257	24	=	=	PUNCT
m-1112	2257	25	nb̅	nb̅	PROPN
m-1112	2257	26	π²	π²	NOUN
m-1112	2257	27	r⁴	r⁴	NOUN
m-1112	2257	28	]	]	PUNCT
m-1112	2257	29	→{w≡em	→{w≡em	NOUN
m-1112	2257	30	-	-	PUNCT
m-1112	2257	31	r≡	r≡	NOUN
m-1112	2257	32	[	[	X
m-1112	2257	33	εe²+μb²	εe²+μb²	X
m-1112	2257	34	]	]	X
m-1112	2257	35	=	=	SYM
m-1112	2257	36	2.λc.sin.2φ	2.λc.sin.2φ	NUM
m-1112	2257	37	}	}	PUNCT
m-1112	2257	38	and	and	CCONJ
m-1112	2257	39	the	the	DET
m-1112	2257	40	duality	duality	NOUN
m-1112	2257	41	of	of	ADP
m-1112	2257	42	an	an	DET
m-1112	2257	43	energy	energy	NOUN
m-1112	2257	44	-	-	PUNCT
m-1112	2257	45	storage	storage	NOUN
m-1112	2257	46	≡{[gm	≡{[gm	PROPN
m-1112	2257	47	-	-	ADJ
m-1112	2257	48	ab	ab	NOUN
m-1112	2257	49	-	-	PUNCT
m-1112	2257	50	m	m	PROPN
m-1112	2257	51	]	]	X
m-1112	2257	52	≡	≡	PROPN
m-1112	2257	53	s	s	PART
m-1112	2258	1	=	=	PUNCT
m-1112	2258	2	[	[	X
m-1112	2258	3	⊕←	⊕←	X
m-1112	2258	4	𝐫	𝐫	PART
m-1112	2258	5	→⊝	→⊝	NOUN
m-1112	2258	6	]	]	X
m-1112	2258	7	+	+	NUM
m-1112	2258	8	motion	motion	NOUN
m-1112	2258	9	≡	≡	PROPN
m-1112	2259	1	[	[	PUNCT
m-1112	2259	2	pm-2r	pm-2r	NOUN
m-1112	2259	3	-	-	PUNCT
m-1112	2259	4	m	m	NOUN
m-1112	2259	5	]	]	X
m-1112	2259	6	≡m≡	≡m≡	PROPN
m-1112	2259	7	�	�	PROPN
m-1112	2259	8	̅	̅	NOUN
m-1112	2259	9	�	�	PROPN
m-1112	2259	10	−	−	PROPN
m-1112	2259	11	𝐕𝐞𝐜𝐭𝐨𝐫	𝐕𝐞𝐜𝐭𝐨𝐫	PROPN
m-1112	2259	12	}	}	PUNCT
m-1112	2259	13	,	,	PUNCT
m-1112	2259	14	issuing	issue	VERB
m-1112	2259	15	[	[	X
m-1112	2259	16	pm-2r	pm-2r	NOUN
m-1112	2259	17	-	-	PUNCT
m-1112	2259	18	m	m	NOUN
m-1112	2259	19	]	]	X
m-1112	2259	20	=	=	PUNCT
m-1112	2259	21	√−1	√−1	PROPN
m-1112	2259	22	.[gm	.[gm	PROPN
m-1112	2259	23	-	-	PUNCT
m-1112	2259	24	ab	ab	PROPN
m-1112	2259	25	-	-	PUNCT
m-1112	2259	26	m	m	PROPN
m-1112	2259	27	]	]	PUNCT
m-1112	2259	28	,	,	PUNCT
m-1112	2259	29	therefore	therefore	ADV
m-1112	2259	30	→	→	SYM
m-1112	2259	31	photon	photon	NOUN
m-1112	2259	32	-	-	PUNCT
m-1112	2259	33	mechanism	mechanism	NOUN
m-1112	2259	34	is	be	AUX
m-1112	2259	35	for	for	ADP
m-1112	2259	36	both	both	PRON
m-1112	2259	37	travelling	travel	VERB
m-1112	2259	38	as	as	ADP
m-1112	2259	39	particle	particle	NOUN
m-1112	2259	40	and	and	CCONJ
m-1112	2259	41	as	as	ADP
m-1112	2259	42	wave	wave	NOUN
m-1112	2259	43	,	,	PUNCT
m-1112	2259	44	ijo	ijo	PROPN
m-1112	2259	45	international	international	PROPN
m-1112	2259	46	journal	journal	PROPN
m-1112	2259	47	of	of	ADP
m-1112	2259	48	mathematics	mathematics	PROPN
m-1112	2259	49	(	(	PUNCT
m-1112	2259	50	issn	issn	PROPN
m-1112	2259	51	:	:	PUNCT
m-1112	2259	52	2992	2992	NUM
m-1112	2259	53	-	-	SYM
m-1112	2259	54	4421	4421	NUM
m-1112	2259	55	)	)	PUNCT
m-1112	2259	56	volume	volume	NOUN
m-1112	2259	57	08	08	NUM
m-1112	2260	1	|	|	ADV
m-1112	2260	2	issue	issue	NOUN
m-1112	2260	3	08	08	NUM
m-1112	2261	1	|	|	ADV
m-1112	2261	2	august	august	PROPN
m-1112	2261	3	2025	2025	NUM
m-1112	2261	4	|	|	ADV
m-1112	2261	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2261	6	ijo	ijo	PROPN
m-1112	2261	7	journals	journal	NOUN
m-1112	2261	8	78	78	NUM
m-1112	2261	9	the	the	DET
m-1112	2261	10	fundamental	fundamental	ADJ
m-1112	2261	11	particles	particle	NOUN
m-1112	2261	12	origination	origination	NOUN
m-1112	2261	13	mechanism	mechanism	NOUN
m-1112	2261	14	in	in	ADP
m-1112	2261	15	mfmf	mfmf	PROPN
m-1112	2261	16	pns	pns	PROPN
m-1112	2261	17	caves	cave	NOUN
m-1112	2261	18	.	.	PUNCT
m-1112	2262	1	6c	6c	NOUN
m-1112	2262	2	..	..	PUNCT
m-1112	2262	3	the	the	DET
m-1112	2262	4	epilogues	epilogue	NOUN
m-1112	2262	5	of	of	ADP
m-1112	2262	6	prior	prior	ADV
m-1112	2262	7	.	.	PUNCT
m-1112	2263	1	figure	figure	NOUN
m-1112	2263	2	–	–	PUNCT
m-1112	2263	3	17	17	NUM
m-1112	2263	4	:	:	PUNCT
m-1112	2263	5	the	the	DET
m-1112	2263	6	periodic	periodic	ADJ
m-1112	2263	7	motion	motion	NOUN
m-1112	2263	8	in	in	ADP
m-1112	2263	9	caves	cave	NOUN
m-1112	2263	10	follows	follow	VERB
m-1112	2263	11	material	material	NOUN
m-1112	2263	12	geometry	geometry	NOUN
m-1112	2263	13	rules	rule	NOUN
m-1112	2263	14	.	.	PUNCT
m-1112	2264	1	in	in	ADP
m-1112	2264	2	(	(	PUNCT
m-1112	2264	3	1	1	NUM
m-1112	2264	4	)	)	PUNCT
m-1112	2264	5	.	.	PUNCT
m-1112	2264	6	is	be	AUX
m-1112	2264	7	shown	show	VERB
m-1112	2264	8	the	the	DET
m-1112	2264	9	geometrical	geometrical	ADJ
m-1112	2264	10	expose	expose	NOUN
m-1112	2264	11	of	of	ADP
m-1112	2264	12	,	,	PUNCT
m-1112	2264	13	dynamic	dynamic	ADJ
m-1112	2264	14	-	-	PUNCT
m-1112	2264	15	space	space	NOUN
m-1112	2264	16	-	-	PUNCT
m-1112	2264	17	energy	energy	NOUN
m-1112	2264	18	relation	relation	NOUN
m-1112	2264	19	g	g	PROPN
m-1112	2264	20	.r	.r	NOUN
m-1112	2265	1	³.𝐟²𝐩=	³.𝐟²𝐩=	PROPN
m-1112	2265	2	1	1	NUM
m-1112	2265	3	in	in	ADP
m-1112	2265	4	(	(	PUNCT
m-1112	2265	5	2	2	NUM
m-1112	2265	6	)	)	PUNCT
m-1112	2265	7	.	.	PUNCT
m-1112	2266	1	is	be	AUX
m-1112	2266	2	shown	show	VERB
m-1112	2266	3	the	the	DET
m-1112	2266	4	mechanical	mechanical	ADJ
m-1112	2266	5	impress	impress	NOUN
m-1112	2266	6	of	of	ADP
m-1112	2266	7	the	the	DET
m-1112	2266	8	,	,	PUNCT
m-1112	2266	9	orbit	orbit	NOUN
m-1112	2266	10	-	-	PUNCT
m-1112	2266	11	space	space	NOUN
m-1112	2266	12	-	-	PUNCT
m-1112	2266	13	energy	energy	NOUN
m-1112	2266	14	relation	relation	NOUN
m-1112	2266	15	g	g	PROPN
m-1112	2266	16	.r	.r	NOUN
m-1112	2267	1	³.𝐟²𝐩=	³.𝐟²𝐩=	PROPN
m-1112	2267	2	1	1	NUM
m-1112	2267	3	in	in	ADP
m-1112	2267	4	(	(	PUNCT
m-1112	2267	5	3	3	NUM
m-1112	2267	6	)	)	PUNCT
m-1112	2267	7	.	.	PUNCT
m-1112	2268	1	is	be	AUX
m-1112	2268	2	shown	show	VERB
m-1112	2268	3	the	the	DET
m-1112	2268	4	extreme	extreme	ADJ
m-1112	2268	5	design	design	NOUN
m-1112	2268	6	of	of	ADP
m-1112	2268	7	the	the	DET
m-1112	2268	8	,	,	PUNCT
m-1112	2268	9	dynamic	dynamic	ADJ
m-1112	2268	10	-	-	PUNCT
m-1112	2268	11	space	space	NOUN
m-1112	2268	12	-	-	PUNCT
m-1112	2268	13	energy	energy	NOUN
m-1112	2268	14	relation	relation	NOUN
m-1112	2268	15	g	g	PROPN
m-1112	2268	16	.r	.r	NOUN
m-1112	2269	1	³.𝐟²𝐩=	³.𝐟²𝐩=	PROPN
m-1112	2269	2	1	1	NUM
m-1112	2269	3	in	in	ADP
m-1112	2269	4	(	(	PUNCT
m-1112	2269	5	4	4	NUM
m-1112	2269	6	)	)	PUNCT
m-1112	2269	7	.	.	PUNCT
m-1112	2270	1	is	be	AUX
m-1112	2270	2	shown	show	VERB
m-1112	2270	3	the	the	DET
m-1112	2270	4	geometrical	geometrical	ADJ
m-1112	2270	5	creation	creation	NOUN
m-1112	2270	6	of	of	ADP
m-1112	2270	7	the	the	DET
m-1112	2270	8	energy	energy	NOUN
m-1112	2270	9	-	-	PUNCT
m-1112	2270	10	monads	monad	NOUN
m-1112	2270	11	-	-	PUNCT
m-1112	2270	12	motion	motion	NOUN
m-1112	2270	13	&	&	CCONJ
m-1112	2270	14	the	the	DET
m-1112	2270	15	physical	physical	ADJ
m-1112	2270	16	monads	monad	NOUN
m-1112	2270	17	motion	motion	NOUN
m-1112	2270	18	from	from	ADP
m-1112	2270	19	their	their	PRON
m-1112	2270	20	unit	unit	NOUN
m-1112	2270	21	relation	relation	NOUN
m-1112	2270	22	g	g	PROPN
m-1112	2270	23	.r	.r	PROPN
m-1112	2271	1	³.𝐟²𝐩=	³.𝐟²𝐩=	PROPN
m-1112	2271	2	1	1	NUM
m-1112	2271	3	the	the	DET
m-1112	2271	4	origination	origination	NOUN
m-1112	2271	5	of	of	ADP
m-1112	2271	6	anti	anti	ADJ
m-1112	2271	7	–	–	PUNCT
m-1112	2271	8	gravity	gravity	NOUN
m-1112	2271	9	stress	stress	NOUN
m-1112	2271	10	g	g	NOUN
m-1112	2271	11	:	:	PUNCT
m-1112	2271	12	6c1	6c1	NUM
m-1112	2271	13	..	..	PUNCT
m-1112	2271	14	the	the	DET
m-1112	2271	15	origination	origination	NOUN
m-1112	2271	16	&	&	CCONJ
m-1112	2271	17	the	the	DET
m-1112	2271	18	nature	nature	NOUN
m-1112	2271	19	of	of	ADP
m-1112	2271	20	gravity	gravity	NOUN
m-1112	2271	21	g	g	NOUN
m-1112	2271	22	.	.	PUNCT
m-1112	2272	1	ijo	ijo	PROPN
m-1112	2272	2	international	international	PROPN
m-1112	2272	3	journal	journal	PROPN
m-1112	2272	4	of	of	ADP
m-1112	2272	5	mathematics	mathematics	PROPN
m-1112	2272	6	(	(	PUNCT
m-1112	2272	7	issn	issn	PROPN
m-1112	2272	8	:	:	PUNCT
m-1112	2272	9	2992	2992	NUM
m-1112	2272	10	-	-	SYM
m-1112	2272	11	4421	4421	NUM
m-1112	2272	12	)	)	PUNCT
m-1112	2272	13	volume	volume	NOUN
m-1112	2272	14	08	08	NUM
m-1112	2273	1	|	|	ADV
m-1112	2273	2	issue	issue	NOUN
m-1112	2273	3	08	08	NUM
m-1112	2274	1	|	|	ADV
m-1112	2274	2	august	august	PROPN
m-1112	2274	3	2025	2025	NUM
m-1112	2274	4	|	|	ADV
m-1112	2274	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2274	6	ijo	ijo	PROPN
m-1112	2274	7	journals	journal	NOUN
m-1112	2274	8	79	79	NUM
m-1112	2274	9	the	the	DET
m-1112	2274	10	fundamental	fundamental	ADJ
m-1112	2274	11	particles	particle	NOUN
m-1112	2274	12	origination	origination	NOUN
m-1112	2274	13	mechanism	mechanism	NOUN
m-1112	2274	14	in	in	ADP
m-1112	2274	15	mfmf	mfmf	PROPN
m-1112	2274	16	pns	pns	PROPN
m-1112	2274	17	caves	cave	NOUN
m-1112	2274	18	.	.	PUNCT
m-1112	2275	1	figure	figure	VERB
m-1112	2275	2	-17a-:the	-17a-:the	DET
m-1112	2275	3	stability	stability	NOUN
m-1112	2275	4	of	of	ADP
m-1112	2275	5	±spin	±spin	PROPN
m-1112	2275	6	as	as	ADP
m-1112	2275	7	an	an	DET
m-1112	2275	8	electromagnetic	electromagnetic	ADJ
m-1112	2275	9	wave	wave	NOUN
m-1112	2275	10	of	of	ADP
m-1112	2275	11	two	two	NUM
m-1112	2275	12	frequencies	frequency	NOUN
m-1112	2275	13	,	,	PUNCT
m-1112	2275	14	0	0	NUM
m-1112	2275	15	,	,	PUNCT
m-1112	2275	16	c	c	NOUN
m-1112	2275	17	from	from	ADP
m-1112	2275	18	relation	relation	NOUN
m-1112	2276	1	angular	angular	ADJ
m-1112	2276	2	velocity	velocity	NOUN
m-1112	2276	3	c	c	NOUN
m-1112	2277	1	=	=	PUNCT
m-1112	2277	2	w	w	NOUN
m-1112	2277	3	r	r	NOUN
m-1112	2277	4	=	=	SYM
m-1112	2277	5	2πfn.r	2πfn.r	NUM
m-1112	2277	6	=	=	SYM
m-1112	2277	7	2πr	2πr	NOUN
m-1112	2277	8	.fn	.fn	PUNCT
m-1112	2278	1	=	=	SYM
m-1112	2278	2	σ	σ	PROPN
m-1112	2278	3	φ	φ	PROPN
m-1112	2278	4	.	.	PUNCT
m-1112	2279	1	since	since	SCONJ
m-1112	2279	2	light	light	NOUN
m-1112	2279	3	-	-	PUNCT
m-1112	2279	4	velocity	velocity	NOUN
m-1112	2279	5	is	be	AUX
m-1112	2279	6	created	create	VERB
m-1112	2279	7	from	from	ADP
m-1112	2279	8	g	g	PROPN
m-1112	2279	9	beyond	beyond	ADP
m-1112	2279	10	the	the	DET
m-1112	2279	11	planck`s	planck`s	NOUN
m-1112	2280	1	length	length	NOUN
m-1112	2280	2	r	r	NOUN
m-1112	2280	3	p	p	NOUN
m-1112	2280	4	=	=	NOUN
m-1112	2280	5	1,61626.10−35	1,61626.10−35	NUM
m-1112	2280	6	m	m	NOUN
m-1112	2280	7	,	,	PUNCT
m-1112	2280	8	therefore	therefore	ADV
m-1112	2280	9	issues	issue	VERB
m-1112	2280	10	c	c	NOUN
m-1112	2281	1	=	=	SYM
m-1112	2281	2	w	w	NOUN
m-1112	2281	3	r	r	NOUN
m-1112	2281	4	=	=	PUNCT
m-1112	2281	5	w	w	NOUN
m-1112	2281	6	r	r	NOUN
m-1112	2281	7	p	p	NOUN
m-1112	2281	8	=	=	PUNCT
m-1112	2281	9	2π	2π	NOUN
m-1112	2281	10	rp	rp	NOUN
m-1112	2281	11	.fn	.fn	PUNCT
m-1112	2282	1	=	=	PROPN
m-1112	2282	2	σ	σ	PROPN
m-1112	2282	3	φ	φ	PROPN
m-1112	2282	4	,	,	PUNCT
m-1112	2282	5	and	and	CCONJ
m-1112	2282	6	from	from	ADP
m-1112	2282	7	the	the	DET
m-1112	2282	8	light	light	ADJ
m-1112	2282	9	-	-	PUNCT
m-1112	2282	10	velocity	velocity	NOUN
m-1112	2282	11	properties	property	NOUN
m-1112	2282	12	becomes	become	VERB
m-1112	2282	13	,	,	PUNCT
m-1112	2282	14	a	a	PRON
m-1112	2282	15	)	)	PUNCT
m-1112	2282	16	..	..	PUNCT
m-1112	2283	1	the	the	DET
m-1112	2283	2	light	light	ADJ
m-1112	2283	3	velocity	velocity	NOUN
m-1112	2283	4	c	c	NOUN
m-1112	2283	5	is	be	AUX
m-1112	2283	6	constant	constant	ADJ
m-1112	2283	7	.	.	PUNCT
m-1112	2284	1	since	since	SCONJ
m-1112	2284	2	c	c	PROPN
m-1112	2284	3	is	be	AUX
m-1112	2284	4	constant	constant	ADJ
m-1112	2284	5	then	then	ADV
m-1112	2284	6	is	be	AUX
m-1112	2284	7	analyzed	analyze	VERB
m-1112	2284	8	to	to	ADP
m-1112	2284	9	,	,	PUNCT
m-1112	2284	10	(	(	PUNCT
m-1112	2284	11	cx	cx	INTJ
m-1112	2284	12	,	,	PUNCT
m-1112	2284	13	cy	cy	PROPN
m-1112	2284	14	)	)	PUNCT
m-1112	2284	15	in	in	ADP
m-1112	2284	16	any	any	DET
m-1112	2284	17	two	two	NUM
m-1112	2284	18	directions	direction	NOUN
m-1112	2284	19	x	x	X
m-1112	2284	20	,	,	PUNCT
m-1112	2284	21	y	y	PROPN
m-1112	2284	22	where	where	SCONJ
m-1112	2284	23	x	x	PUNCT
m-1112	2284	24	⏊	⏊	VERB
m-1112	2284	25	y	y	PROPN
m-1112	2284	26	and	and	CCONJ
m-1112	2284	27	y	y	PROPN
m-1112	2284	28	to	to	PART
m-1112	2284	29	be	be	AUX
m-1112	2284	30	the	the	DET
m-1112	2284	31	gravity	gravity	NOUN
m-1112	2284	32	direction	direction	NOUN
m-1112	2284	33	on	on	ADP
m-1112	2284	34	where	where	SCONJ
m-1112	2284	35	gravity	gravity	NOUN
m-1112	2284	36	is	be	AUX
m-1112	2284	37	acting	act	VERB
m-1112	2284	38	.	.	PUNCT
m-1112	2285	1	in	in	ADP
m-1112	2285	2	figure	figure	NOUN
m-1112	2285	3	(	(	PUNCT
m-1112	2285	4	8)	8)	NUM
m-1112	2285	5	are	be	AUX
m-1112	2285	6	seen	see	VERB
m-1112	2285	7	the	the	DET
m-1112	2285	8	4	4	NUM
m-1112	2285	9	-	-	PUNCT
m-1112	2285	10	point	point	NOUN
m-1112	2285	11	positions	position	NOUN
m-1112	2285	12	,	,	PUNCT
m-1112	2285	13	at	at	ADP
m-1112	2285	14	where	where	SCONJ
m-1112	2285	15	velocity	velocity	NOUN
m-1112	2285	16	phase	phase	NOUN
m-1112	2285	17	changes	change	NOUN
m-1112	2285	18	and	and	CCONJ
m-1112	2285	19	the	the	DET
m-1112	2285	20	work	work	NOUN
m-1112	2285	21	done	do	VERB
m-1112	2285	22	in	in	ADP
m-1112	2285	23	each	each	DET
m-1112	2285	24	phase	phase	NOUN
m-1112	2285	25	of	of	ADP
m-1112	2285	26	photon`s	photon`s	NOUN
m-1112	2285	27	inner	inner	ADJ
m-1112	2285	28	motion	motion	NOUN
m-1112	2285	29	.	.	PUNCT
m-1112	2286	1	the	the	DET
m-1112	2286	2	4	4	NUM
m-1112	2286	3	-	-	PUNCT
m-1112	2286	4	phases	phase	NOUN
m-1112	2286	5	correspond	correspond	VERB
m-1112	2286	6	to	to	ADP
m-1112	2286	7	the	the	DET
m-1112	2286	8	wavelength	wavelength	NOUN
m-1112	2286	9	.	.	PUNCT
m-1112	2287	1	λ	λ	INTJ
m-1112	2287	2	,	,	PUNCT
m-1112	2287	3	as	as	ADP
m-1112	2287	4	λ	λ	PROPN
m-1112	2287	5	/	/	SYM
m-1112	2287	6	4	4	NUM
m-1112	2287	7	.	.	PUNCT
m-1112	2288	1	in	in	ADP
m-1112	2288	2	distance	distance	NOUN
m-1112	2288	3	with	with	ADP
m-1112	2288	4	90	90	NUM
m-1112	2288	5	°	°	NOUN
m-1112	2288	6	=	=	PUNCT
m-1112	2288	7	𝜋	𝜋	ADP
m-1112	2288	8	2	2	NUM
m-1112	2288	9	to	to	PART
m-1112	2288	10	be	be	AUX
m-1112	2288	11	the	the	DET
m-1112	2288	12	change	change	NOUN
m-1112	2288	13	of	of	ADP
m-1112	2288	14	phase	phase	NOUN
m-1112	2288	15	.	.	PUNCT
m-1112	2289	1	this	this	PRON
m-1112	2289	2	means	mean	VERB
m-1112	2289	3	that	that	SCONJ
m-1112	2289	4	the	the	DET
m-1112	2289	5	produced	produce	VERB
m-1112	2289	6	work	work	NOUN
m-1112	2289	7	in	in	ADP
m-1112	2289	8	the	the	DET
m-1112	2289	9	prior	prior	ADJ
m-1112	2289	10	phase	phase	NOUN
m-1112	2289	11	-	-	PUNCT
m-1112	2289	12	area	area	NOUN
m-1112	2289	13	is	be	AUX
m-1112	2289	14	as	as	ADP
m-1112	2289	15	the	the	DET
m-1112	2289	16	golden	golden	ADJ
m-1112	2289	17	-	-	PUNCT
m-1112	2289	18	ratio	ratio	NOUN
m-1112	2289	19	pattern	pattern	NOUN
m-1112	2289	20	which	which	PRON
m-1112	2289	21	is	be	AUX
m-1112	2289	22	stored	store	VERB
m-1112	2289	23	in	in	ADP
m-1112	2289	24	the	the	DET
m-1112	2289	25	next	next	ADJ
m-1112	2289	26	and	and	CCONJ
m-1112	2289	27	perpendicular	perpendicular	ADJ
m-1112	2289	28	phase	phase	NOUN
m-1112	2289	29	-	-	PUNCT
m-1112	2289	30	area	area	NOUN
m-1112	2289	31	.	.	PUNCT
m-1112	2290	1	the	the	DET
m-1112	2290	2	light	light	ADJ
m-1112	2290	3	velocity	velocity	NOUN
m-1112	2290	4	�	�	NOUN
m-1112	2290	5	̅	̅	NOUN
m-1112	2290	6	�	�	PROPN
m-1112	2290	7	,	,	PUNCT
m-1112	2290	8	changes	change	NOUN
m-1112	2290	9	phase	phase	NOUN
m-1112	2290	10	every	every	DET
m-1112	2290	11	90	90	NUM
m-1112	2290	12	°	°	NOUN
m-1112	2290	13	and	and	CCONJ
m-1112	2290	14	the	the	DET
m-1112	2290	15	created	create	VERB
m-1112	2290	16	work	work	NOUN
m-1112	2290	17	{	{	PUNCT
m-1112	2290	18	w	w	NOUN
m-1112	2290	19	=	=	PUNCT
m-1112	2290	20	c	c	NOUN
m-1112	2290	21	y	y	NOUN
m-1112	2290	22	x	x	PUNCT
m-1112	2291	1	[	[	X
m-1112	2291	2	quarter	quarter	NOUN
m-1112	2291	3	circle	circle	NOUN
m-1112	2291	4	1	1	NUM
m-1112	2291	5	-	-	PUNCT
m-1112	2291	6	o-4	o-4	NOUN
m-1112	2291	7	]	]	PUNCT
m-1112	2291	8	}	}	PUNCT
m-1112	2291	9	is	be	AUX
m-1112	2291	10	symmetrically	symmetrically	ADV
m-1112	2291	11	stored	store	VERB
m-1112	2291	12	from	from	ADP
m-1112	2291	13	0	0	NUM
m-1112	2291	14	°	°	NOUN
m-1112	2291	15	→	→	SYM
m-1112	2291	16	90	90	NUM
m-1112	2291	17	°	°	NOUN
m-1112	2291	18	alternately	alternately	ADV
m-1112	2291	19	+	+	CCONJ
m-1112	2291	20	,	,	PUNCT
m-1112	2291	21	,	,	PUNCT
m-1112	2291	22	,	,	PUNCT
m-1112	2291	23	+	+	CCONJ
m-1112	2291	24	,	,	PUNCT
m-1112	2291	25	in	in	ADP
m-1112	2291	26	[	[	PUNCT
m-1112	2291	27	quarter	quarter	NOUN
m-1112	2291	28	circle	circle	NOUN
m-1112	2291	29	1	1	NUM
m-1112	2291	30	-	-	PUNCT
m-1112	2291	31	o-4	o-4	NOUN
m-1112	2291	32	]	]	PUNCT
m-1112	2291	33	in	in	ADP
m-1112	2291	34	the	the	DET
m-1112	2291	35	[	[	NOUN
m-1112	2291	36	quarter	quarter	NOUN
m-1112	2291	37	circle	circle	NOUN
m-1112	2291	38	4	4	NUM
m-1112	2291	39	-	-	NUM
m-1112	2291	40	o-2	o-2	VERB
m-1112	2291	41	]	]	PUNCT
m-1112	2291	42	into	into	ADP
m-1112	2291	43	[	[	X
m-1112	2291	44	quarter	quarter	NOUN
m-1112	2291	45	circle	circle	NOUN
m-1112	2291	46	2	2	NUM
m-1112	2291	47	-	-	NUM
m-1112	2291	48	o-3	o-3	NOUN
m-1112	2291	49	]	]	PUNCT
m-1112	2291	50	into	into	ADP
m-1112	2291	51	[	[	X
m-1112	2291	52	quarter	quarter	NOUN
m-1112	2291	53	circle	circle	NOUN
m-1112	2291	54	3	3	NUM
m-1112	2291	55	-	-	SYM
m-1112	2291	56	o-1	o-1	NOUN
m-1112	2291	57	]	]	PUNCT
m-1112	2292	1	the	the	DET
m-1112	2292	2	momentum	momentum	NOUN
m-1112	2292	3	≡	≡	PROPN
m-1112	2292	4	spin	spin	VERB
m-1112	2292	5	≡	≡	PROPN
m-1112	2292	6	�	�	PROPN
m-1112	2292	7	̅	̅	NOUN
m-1112	2292	8	�	�	NOUN
m-1112	2292	9	≡	≡	ADJ
m-1112	2292	10	r	r	NOUN
m-1112	2292	11	m	m	VERB
m-1112	2292	12	v	v	NOUN
m-1112	2292	13	=	=	X
m-1112	2292	14	[	[	PUNCT
m-1112	2292	15	𝛑.𝐫𝟐	𝛑.𝐫𝟐	NUM
m-1112	2292	16	𝟒	𝟒	NUM
m-1112	2292	17	]	]	PUNCT
m-1112	2292	18	.	.	PUNCT
m-1112	2292	19	�	�	PROPN
m-1112	2292	20	̅	̅	NOUN
m-1112	2292	21	�	�	PROPN
m-1112	2292	22	x	x	SYM
m-1112	2292	23	�	�	PROPN
m-1112	2292	24	̅	̅	NOUN
m-1112	2292	25	�	�	NOUN
m-1112	2292	26	where	where	SCONJ
m-1112	2292	27	±	±	PROPN
m-1112	2292	28	[	[	PUNCT
m-1112	2292	29	𝛑.𝐫𝟐	𝛑.𝐫𝟐	X
m-1112	2292	30	𝟒	𝟒	NOUN
m-1112	2292	31	]	]	PUNCT
m-1112	2292	32	=	=	PUNCT
m-1112	2292	33	the	the	DET
m-1112	2292	34	quarter	quarter	NOUN
m-1112	2292	35	circle	circle	NOUN
m-1112	2292	36	.	.	PUNCT
m-1112	2293	1	the	the	DET
m-1112	2293	2	quarter	quarter	NOUN
m-1112	2293	3	circle	circle	NOUN
m-1112	2293	4	,	,	PUNCT
m-1112	2294	1	+	+	CCONJ
m-1112	2294	2	+	+	CCONJ
m-1112	2294	3	,	,	PUNCT
m-1112	2294	4	consist	consist	VERB
m-1112	2294	5	the	the	DET
m-1112	2294	6	+	+	NUM
m-1112	2294	7	spin	spin	ADJ
m-1112	2294	8	≡	≡	PROPN
m-1112	2294	9	�	�	PROPN
m-1112	2294	10	̅	̅	PROPN
m-1112	2294	11	�	�	NOUN
m-1112	2294	12	which	which	PRON
m-1112	2294	13	is	be	AUX
m-1112	2294	14	the	the	DET
m-1112	2294	15	gravity	gravity	NOUN
m-1112	2294	16	force	force	NOUN
m-1112	2294	17	,	,	PUNCT
m-1112	2294	18	and	and	CCONJ
m-1112	2294	19	the	the	DET
m-1112	2294	20	quarter	quarter	NOUN
m-1112	2294	21	circle	circle	NOUN
m-1112	2294	22	,	,	PUNCT
m-1112	2294	23	,	,	PUNCT
m-1112	2294	24	consist	consist	VERB
m-1112	2294	25	the	the	DET
m-1112	2294	26	-spin	-spin	PROPN
m-1112	2294	27	≡	≡	PROPN
m-1112	2294	28	�	�	PROPN
m-1112	2294	29	̅	̅	PROPN
m-1112	2294	30	�	�	NOUN
m-1112	2294	31	which	which	PRON
m-1112	2294	32	is	be	AUX
m-1112	2294	33	the	the	DET
m-1112	2294	34	gravity	gravity	NOUN
m-1112	2294	35	force	force	NOUN
m-1112	2294	36	from	from	ADP
m-1112	2294	37	total	total	ADJ
m-1112	2294	38	,	,	PUNCT
m-1112	2294	39	+	+	PROPN
m-1112	2294	40	,	,	PUNCT
m-1112	2294	41	-,-,+	-,-,+	INTJ
m-1112	2294	42	,	,	PUNCT
m-1112	2294	43	when	when	SCONJ
m-1112	2294	44	r	r	NOUN
m-1112	2294	45	→	→	SYM
m-1112	2294	46	0	0	NUM
m-1112	2294	47	or	or	CCONJ
m-1112	2294	48	when	when	SCONJ
m-1112	2294	49	�	�	NOUN
m-1112	2294	50	̅	̅	NOUN
m-1112	2294	51	�	�	PROPN
m-1112	2294	52	doesn`t	doesn`t	PROPN
m-1112	2294	53	act	act	NOUN
m-1112	2294	54	on	on	ADP
m-1112	2294	55	the	the	DET
m-1112	2294	56	quarter	quarter	NOUN
m-1112	2294	57	circle	circle	NOUN
m-1112	2294	58	then	then	ADV
m-1112	2294	59	happens	happen	VERB
m-1112	2294	60	black	black	ADJ
m-1112	2294	61	-	-	PUNCT
m-1112	2294	62	hole	hole	NOUN
m-1112	2294	63	.	.	PUNCT
m-1112	2295	1	in	in	ADP
m-1112	2295	2	[	[	X
m-1112	2295	3	108	108	NUM
m-1112	2295	4	]	]	PUNCT
m-1112	2295	5	is	be	AUX
m-1112	2295	6	determined	determine	VERB
m-1112	2295	7	the	the	DET
m-1112	2295	8	when	when	SCONJ
m-1112	2295	9	newton	newton	PROPN
m-1112	2295	10	’s	’s	PART
m-1112	2295	11	gravitational	gravitational	ADJ
m-1112	2295	12	force	force	NOUN
m-1112	2295	13	𝐆	𝐆	PROPN
m-1112	2295	14	,	,	PUNCT
m-1112	2295	15	stops	stop	VERB
m-1112	2295	16	acting	act	VERB
m-1112	2295	17	thrusting	thrusting	NOUN
m-1112	2295	18	,	,	PUNCT
m-1112	2295	19	on	on	ADP
m-1112	2295	20	the	the	DET
m-1112	2295	21	light	light	ADJ
m-1112	2295	22	velocity	velocity	NOUN
m-1112	2295	23	vector	vector	NOUN
m-1112	2295	24	�	�	PROPN
m-1112	2295	25	̅	̅	NOUN
m-1112	2295	26	�	�	PROPN
m-1112	2295	27	,	,	PUNCT
m-1112	2295	28	and	and	CCONJ
m-1112	2295	29	happen	happen	VERB
m-1112	2295	30	the	the	DET
m-1112	2295	31	black	black	NOUN
m-1112	2295	32	-	-	PUNCT
m-1112	2295	33	holes	hole	NOUN
m-1112	2295	34	.	.	PUNCT
m-1112	2296	1	b	b	X
m-1112	2296	2	)	)	PUNCT
m-1112	2296	3	..	..	PUNCT
m-1112	2297	1	the	the	DET
m-1112	2297	2	dual	dual	ADJ
m-1112	2297	3	property	property	NOUN
m-1112	2297	4	of	of	ADP
m-1112	2297	5	the	the	DET
m-1112	2297	6	simultaneously	simultaneously	ADV
m-1112	2297	7	existing	exist	VERB
m-1112	2297	8	spin	spin	NOUN
m-1112	2297	9	as	as	ADP
m-1112	2297	10	electric	electric	ADJ
m-1112	2297	11	and	and	CCONJ
m-1112	2297	12	as	as	ADP
m-1112	2297	13	magnetic	magnetic	ADJ
m-1112	2297	14	ijo	ijo	PROPN
m-1112	2297	15	international	international	PROPN
m-1112	2297	16	journal	journal	PROPN
m-1112	2297	17	of	of	ADP
m-1112	2297	18	mathematics	mathematics	PROPN
m-1112	2297	19	(	(	PUNCT
m-1112	2297	20	issn	issn	PROPN
m-1112	2297	21	:	:	PUNCT
m-1112	2297	22	2992	2992	NUM
m-1112	2297	23	-	-	SYM
m-1112	2297	24	4421	4421	NUM
m-1112	2297	25	)	)	PUNCT
m-1112	2297	26	volume	volume	NOUN
m-1112	2297	27	08	08	NUM
m-1112	2297	28	|	|	ADV
m-1112	2297	29	issue	issue	NOUN
m-1112	2297	30	08	08	NUM
m-1112	2298	1	|	|	ADV
m-1112	2298	2	august	august	PROPN
m-1112	2298	3	2025	2025	NUM
m-1112	2298	4	|	|	ADV
m-1112	2298	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2298	6	ijo	ijo	PROPN
m-1112	2298	7	journals	journal	NOUN
m-1112	2298	8	80	80	NUM
m-1112	2298	9	the	the	DET
m-1112	2298	10	fundamental	fundamental	ADJ
m-1112	2298	11	particles	particle	NOUN
m-1112	2298	12	origination	origination	NOUN
m-1112	2298	13	mechanism	mechanism	NOUN
m-1112	2298	14	in	in	ADP
m-1112	2298	15	mfmf	mfmf	PROPN
m-1112	2298	16	pns	pns	PROPN
m-1112	2298	17	caves	cave	NOUN
m-1112	2298	18	.	.	PUNCT
m-1112	2299	1	field	field	NOUN
m-1112	2299	2	in	in	ADP
m-1112	2299	3	wavelengths	wavelength	NOUN
m-1112	2299	4	,	,	PUNCT
m-1112	2299	5	λ	λ	X
m-1112	2299	6	x	x	X
m-1112	2299	7	,	,	PUNCT
m-1112	2299	8	λ	λ	X
m-1112	2299	9	y	y	PROPN
m-1112	2299	10	,	,	PUNCT
m-1112	2299	11	as	as	ADP
m-1112	2299	12	effective	effective	ADJ
m-1112	2299	13	range	range	NOUN
m-1112	2299	14	,	,	PUNCT
m-1112	2299	15	is	be	AUX
m-1112	2299	16	thrusted	thrust	VERB
m-1112	2299	17	through	through	ADP
m-1112	2299	18	the	the	DET
m-1112	2299	19	light	light	ADJ
m-1112	2299	20	velocity	velocity	NOUN
m-1112	2299	21	�	�	NOUN
m-1112	2299	22	̅	̅	NOUN
m-1112	2299	23	�	�	PROPN
m-1112	2299	24	,	,	PUNCT
m-1112	2299	25	and	and	CCONJ
m-1112	2299	26	finally	finally	ADV
m-1112	2299	27	is	be	AUX
m-1112	2299	28	from	from	ADP
m-1112	2299	29	the	the	DET
m-1112	2299	30	newton	newton	PROPN
m-1112	2299	31	’s	’s	PART
m-1112	2299	32	gravitational	gravitational	ADJ
m-1112	2299	33	force	force	NOUN
m-1112	2299	34	𝐆	𝐆	PROPN
m-1112	2299	35	.	.	PUNCT
m-1112	2300	1	in	in	ADP
m-1112	2300	2	planck`s	planck`s	NOUN
m-1112	2300	3	length	length	NOUN
m-1112	2300	4	r	r	NOUN
m-1112	2300	5	p	p	NOUN
m-1112	2300	6	=	=	NOUN
m-1112	2300	7	1,616255.10−35	1,616255.10−35	NUM
m-1112	2300	8	m	m	VERB
m-1112	2300	9	the	the	DET
m-1112	2300	10	created	create	VERB
m-1112	2300	11	work	work	NOUN
m-1112	2300	12	from	from	ADP
m-1112	2300	13	�	�	PROPN
m-1112	2300	14	̅	̅	NOUN
m-1112	2300	15	�	�	NOUN
m-1112	2300	16	,	,	PUNCT
m-1112	2300	17	on	on	ADP
m-1112	2300	18	1	1	NUM
m-1112	2300	19	-	-	SYM
m-1112	2300	20	4	4	NUM
m-1112	2300	21	position	position	NOUN
m-1112	2300	22	is	be	AUX
m-1112	2300	23	stored	store	VERB
m-1112	2300	24	in	in	ADP
m-1112	2300	25	the	the	DET
m-1112	2300	26	[	[	X
m-1112	2300	27	1	1	NUM
m-1112	2300	28	-	-	PUNCT
m-1112	2300	29	o-4	o-4	NOUN
m-1112	2300	30	]	]	PUNCT
m-1112	2300	31	quarter	quarter	NOUN
m-1112	2300	32	-	-	PUNCT
m-1112	2300	33	circle	circle	NOUN
m-1112	2300	34	surface	surface	NOUN
m-1112	2300	35	and	and	CCONJ
m-1112	2300	36	at	at	ADP
m-1112	2300	37	phase-4	phase-4	NUM
m-1112	2300	38	where	where	SCONJ
m-1112	2300	39	c	c	AUX
m-1112	2300	40	=	=	SYM
m-1112	2300	41	0	0	NUM
m-1112	2300	42	is	be	AUX
m-1112	2300	43	then	then	ADV
m-1112	2300	44	stored	store	VERB
m-1112	2300	45	in	in	ADP
m-1112	2300	46	the	the	DET
m-1112	2300	47	[	[	X
m-1112	2300	48	4	4	NUM
m-1112	2300	49	-	-	NUM
m-1112	2300	50	o-2	o-2	VERB
m-1112	2300	51	]	]	PUNCT
m-1112	2300	52	quarter	quarter	NOUN
m-1112	2300	53	circle	circle	NOUN
m-1112	2300	54	surface	surface	NOUN
m-1112	2300	55	.	.	PUNCT
m-1112	2301	1	at	at	ADP
m-1112	2301	2	phase-2	phase-2	PROPN
m-1112	2301	3	where	where	SCONJ
m-1112	2301	4	�	�	NOUN
m-1112	2301	5	̅	̅	NOUN
m-1112	2301	6	�	�	PROPN
m-1112	2301	7	=	=	SYM
m-1112	2301	8	�	�	PROPN
m-1112	2301	9	̅	̅	NOUN
m-1112	2301	10	�	�	NOUN
m-1112	2301	11	motion	motion	NOUN
m-1112	2301	12	is	be	AUX
m-1112	2301	13	stored	store	VERB
m-1112	2301	14	in	in	ADP
m-1112	2301	15	the	the	DET
m-1112	2301	16	[	[	X
m-1112	2301	17	2	2	NUM
m-1112	2301	18	-	-	NUM
m-1112	2301	19	o-3	o-3	NUM
m-1112	2301	20	]	]	PUNCT
m-1112	2301	21	quarter	quarter	NOUN
m-1112	2301	22	circle	circle	NOUN
m-1112	2301	23	surface	surface	NOUN
m-1112	2301	24	,	,	PUNCT
m-1112	2301	25	and	and	CCONJ
m-1112	2301	26	at	at	ADP
m-1112	2301	27	phase-3	phase-3	NUM
m-1112	2301	28	where	where	SCONJ
m-1112	2301	29	�	�	NOUN
m-1112	2301	30	̅	̅	NOUN
m-1112	2301	31	�	�	NOUN
m-1112	2301	32	=	=	SYM
m-1112	2301	33	0	0	NUM
m-1112	2301	34	motion	motion	NOUN
m-1112	2301	35	is	be	AUX
m-1112	2301	36	stored	store	VERB
m-1112	2301	37	in	in	ADP
m-1112	2301	38	the	the	DET
m-1112	2301	39	[	[	X
m-1112	2301	40	3	3	NUM
m-1112	2301	41	-	-	PUNCT
m-1112	2301	42	o-1	o-1	NOUN
m-1112	2301	43	]	]	PUNCT
m-1112	2301	44	quarter	quarter	NOUN
m-1112	2301	45	circle	circle	NOUN
m-1112	2301	46	surface	surface	NOUN
m-1112	2301	47	,	,	PUNCT
m-1112	2301	48	i.e.	i.e.	X
m-1112	2301	49	is	be	AUX
m-1112	2301	50	alternately	alternately	ADV
m-1112	2301	51	repeated	repeat	VERB
m-1112	2301	52	the	the	DET
m-1112	2301	53	+	+	NOUN
m-1112	2301	54	[	[	PUNCT
m-1112	2301	55	𝛑.𝐫𝟐	𝛑.𝐫𝟐	X
m-1112	2301	56	𝟒	𝟒	NOUN
m-1112	2301	57	]	]	PUNCT
m-1112	2301	58	=	=	NOUN
m-1112	2301	59	the	the	DET
m-1112	2301	60	+	+	ADJ
m-1112	2301	61	quarter	quarter	NOUN
m-1112	2301	62	circle	circle	NOUN
m-1112	2302	1	[	[	X
m-1112	2302	2	1	1	NUM
m-1112	2302	3	-	-	PUNCT
m-1112	2302	4	o-4	o-4	NOUN
m-1112	2302	5	]	]	PUNCT
m-1112	2302	6	,	,	PUNCT
m-1112	2302	7	and	and	CCONJ
m-1112	2302	8	the	the	DET
m-1112	2302	9	[	[	PUNCT
m-1112	2302	10	𝛑.𝐫𝟐	𝛑.𝐫𝟐	NUM
m-1112	2302	11	𝟒	𝟒	NOUN
m-1112	2302	12	]	]	PUNCT
m-1112	2302	13	=	=	NOUN
m-1112	2302	14	the	the	DET
m-1112	2302	15	quarter	quarter	NOUN
m-1112	2302	16	circle	circle	NOUN
m-1112	2302	17	[	[	X
m-1112	2302	18	4	4	NUM
m-1112	2302	19	-	-	NUM
m-1112	2302	20	o-2	o-2	ADJ
m-1112	2302	21	]	]	PUNCT
m-1112	2302	22	both	both	CCONJ
m-1112	2302	23	in	in	ADP
m-1112	2302	24	the	the	DET
m-1112	2302	25	same	same	ADJ
m-1112	2302	26	plane	plane	NOUN
m-1112	2302	27	-	-	PUNCT
m-1112	2302	28	surface	surface	NOUN
m-1112	2302	29	[	[	X
m-1112	2302	30	1	1	NUM
m-1112	2302	31	-	-	SYM
m-1112	2302	32	4	4	NUM
m-1112	2302	33	-	-	PUNCT
m-1112	2302	34	2	2	NUM
m-1112	2302	35	-	-	SYM
m-1112	2302	36	3	3	NUM
m-1112	2302	37	]	]	PUNCT
m-1112	2302	38	of	of	ADP
m-1112	2302	39	motion	motion	NOUN
m-1112	2302	40	.	.	PUNCT
m-1112	2303	1	the	the	DET
m-1112	2303	2	surface	surface	NOUN
m-1112	2303	3	[	[	PUNCT
m-1112	2303	4	1	1	NUM
m-1112	2303	5	–	–	SYM
m-1112	2303	6	4	4	NUM
m-1112	2303	7	–	–	SYM
m-1112	2303	8	2	2	NUM
m-1112	2303	9	–	–	PUNCT
m-1112	2303	10	3	3	NUM
m-1112	2303	11	]	]	PUNCT
m-1112	2303	12	is	be	AUX
m-1112	2303	13	⏊	⏊	PROPN
m-1112	2303	14	on	on	ADP
m-1112	2303	15	the	the	DET
m-1112	2303	16	spin	spin	NOUN
m-1112	2303	17	axis	axis	NOUN
m-1112	2303	18	→	→	SYM
m-1112	2303	19	u	u	NOUN
m-1112	2303	20	–	–	PUNCT
m-1112	2303	21	d	d	NOUN
m-1112	2303	22	.	.	PUNCT
m-1112	2304	1	from	from	ADP
m-1112	2304	2	fn	fn	NOUN
m-1112	2304	3	=	=	SYM
m-1112	2304	4	σ	σ	PROPN
m-1112	2304	5	2πr	2πr	PROPN
m-1112	2304	6	φ	φ	PROPN
m-1112	2304	7	and	and	CCONJ
m-1112	2304	8	c̅	c̅	PROPN
m-1112	2304	9	=	=	SYM
m-1112	2304	10	w̅.r	w̅.r	X
m-1112	2304	11	=	=	PUNCT
m-1112	2305	1	2πfn.r	2πfn.r	NUM
m-1112	2305	2	=	=	SYM
m-1112	2305	3	2πr	2πr	NOUN
m-1112	2305	4	.fn	.fn	PUNCT
m-1112	2306	1	=	=	SYM
m-1112	2306	2	σ	σ	PROPN
m-1112	2306	3	φ	φ	PROPN
m-1112	2306	4	,	,	PUNCT
m-1112	2306	5	are	be	AUX
m-1112	2306	6	frequencies	frequency	NOUN
m-1112	2306	7	,	,	PUNCT
m-1112	2306	8	0	0	NUM
m-1112	2306	9	,	,	PUNCT
m-1112	2306	10	c	c	NOUN
m-1112	2306	11	,	,	PUNCT
m-1112	2306	12	relation	relation	NOUN
m-1112	2306	13	.	.	PUNCT
m-1112	2307	1	at	at	ADP
m-1112	2307	2	c	c	NOUN
m-1112	2307	3	=	=	SYM
m-1112	2307	4	0	0	NUM
m-1112	2307	5	exist	exist	VERB
m-1112	2307	6	minima	minima	NOUN
m-1112	2307	7	or	or	CCONJ
m-1112	2307	8	maxima	maxima	NOUN
m-1112	2307	9	where	where	SCONJ
m-1112	2307	10	is	be	AUX
m-1112	2307	11	the	the	DET
m-1112	2307	12	change	change	NOUN
m-1112	2307	13	of	of	ADP
m-1112	2307	14	two	two	NUM
m-1112	2307	15	energy	energy	NOUN
m-1112	2307	16	-	-	PUNCT
m-1112	2307	17	semicircles	semicircle	NOUN
m-1112	2307	18	.	.	PUNCT
m-1112	2308	1	c	c	X
m-1112	2308	2	)	)	PUNCT
m-1112	2308	3	..	..	PUNCT
m-1112	2309	1	the	the	DET
m-1112	2309	2	origination	origination	NOUN
m-1112	2309	3	of	of	ADP
m-1112	2309	4	spin	spin	NOUN
m-1112	2309	5	in	in	ADP
m-1112	2309	6	cave	cave	PROPN
m-1112	2309	7	h	h	PROPN
m-1112	2309	8	.	.	PUNCT
m-1112	2310	1	from	from	ADP
m-1112	2310	2	orbit	orbit	NOUN
m-1112	2310	3	vibration	vibration	NOUN
m-1112	2310	4	fn	fn	NOUN
m-1112	2310	5	=	=	PUNCT
m-1112	2310	6	(	(	PUNCT
m-1112	2310	7	1+√5)σ	1+√5)σ	NUM
m-1112	2310	8	4πr	4πr	NOUN
m-1112	2310	9	=	=	PUNCT
m-1112	2311	1	σ	σ	PROPN
m-1112	2311	2	2πr	2πr	PROPN
m-1112	2311	3	φ	φ	PROPN
m-1112	2311	4	and	and	CCONJ
m-1112	2311	5	from	from	ADP
m-1112	2311	6	relation	relation	NOUN
m-1112	2311	7	g.a³.f	g.a³.f	VERB
m-1112	2311	8	²n	²n	NOUN
m-1112	2311	9	=	=	SYM
m-1112	2311	10	1	1	NUM
m-1112	2311	11	,	,	PUNCT
m-1112	2311	12	f	f	NOUN
m-1112	2311	13	²n	²n	NOUN
m-1112	2311	14	=	=	SYM
m-1112	2311	15	σ²	σ²	NOUN
m-1112	2311	16	4π²r²	4π²r²	NUM
m-1112	2311	17	φ²	φ²	NOUN
m-1112	2311	18	=	=	NOUN
m-1112	2311	19	=	=	SYM
m-1112	2311	20	1	1	NUM
m-1112	2311	21	g	g	NOUN
m-1112	2311	22	.a³	.a³	NOUN
m-1112	2311	23	then	then	ADV
m-1112	2311	24	g.a³.φ²	g.a³.φ²	PROPN
m-1112	2311	25	=	=	SYM
m-1112	2311	26	4𝜋²𝑎²	4𝜋²𝑎²	NUM
m-1112	2311	27	𝜎²	𝜎²	NOUN
m-1112	2311	28	,	,	PUNCT
m-1112	2311	29	or	or	CCONJ
m-1112	2311	30	1	1	NUM
m-1112	2311	31	)	)	PUNCT
m-1112	2311	32	.	.	PUNCT
m-1112	2312	1	a	a	DET
m-1112	2312	2	=	=	SYM
m-1112	2312	3	1	1	NUM
m-1112	2312	4	g	g	NOUN
m-1112	2312	5	[	[	PUNCT
m-1112	2312	6	2𝜋	2𝜋	PROPN
m-1112	2312	7	σ	σ	PROPN
m-1112	2312	8	φ	φ	X
m-1112	2312	9	]	]	PUNCT
m-1112	2312	10	²	²	NUM
m-1112	2312	11	,	,	PUNCT
m-1112	2312	12	and	and	CCONJ
m-1112	2312	13	from	from	ADP
m-1112	2312	14	work	work	NOUN
m-1112	2312	15	w	w	NOUN
m-1112	2312	16	=	=	X
m-1112	2312	17	2e	2e	PROPN
m-1112	2312	18	=	=	SYM
m-1112	2312	19	b	b	PROPN
m-1112	2312	20	w	w	NOUN
m-1112	2312	21	=	=	PUNCT
m-1112	2312	22	j.w²	j.w²	NOUN
m-1112	2312	23	,	,	PUNCT
m-1112	2312	24	or	or	CCONJ
m-1112	2312	25	2e	2e	NUM
m-1112	2312	26	=	=	SYM
m-1112	2312	27	2π.f	2π.f	NUM
m-1112	2312	28	and	and	CCONJ
m-1112	2312	29	�	�	NOUN
m-1112	2312	30	̅	̅	NOUN
m-1112	2312	31	�	�	NOUN
m-1112	2312	32	f	f	NOUN
m-1112	2312	33	=	=	SYM
m-1112	2312	34	e	e	PROPN
m-1112	2312	35	π	π	PROPN
m-1112	2312	36	then	then	ADV
m-1112	2312	37	2	2	NUM
m-1112	2312	38	)	)	PUNCT
m-1112	2312	39	.	.	PUNCT
m-1112	2313	1	the	the	DET
m-1112	2313	2	energy	energy	NOUN
m-1112	2313	3	in	in	ADP
m-1112	2313	4	planck	planck	NOUN
m-1112	2313	5	-	-	PUNCT
m-1112	2313	6	scale	scale	NOUN
m-1112	2313	7	-	-	PUNCT
m-1112	2313	8	cave	cave	NOUN
m-1112	2313	9	2e	2e	NOUN
m-1112	2313	10	=	=	PUNCT
m-1112	2313	11	b̅fn	b̅fn	NOUN
m-1112	2313	12	=	=	PUNCT
m-1112	2313	13	[	[	PUNCT
m-1112	2313	14	(	(	PUNCT
m-1112	2313	15	1+√5)σ	1+√5)σ	NUM
m-1112	2313	16	4πr	4πr	NOUN
m-1112	2313	17	]	]	PUNCT
m-1112	2313	18	.b̅	.b̅	PUNCT
m-1112	2313	19	=	=	PUNCT
m-1112	2314	1	[	[	PUNCT
m-1112	2314	2	σ	σ	NUM
m-1112	2314	3	2πr	2πr	NOUN
m-1112	2314	4	]	]	X
m-1112	2314	5	.b̅	.b̅	PROPN
m-1112	2314	6	φ	φ	PROPN
m-1112	2314	7	,	,	PUNCT
m-1112	2314	8	or	or	CCONJ
m-1112	2314	9	e	e	NOUN
m-1112	2314	10	=	=	PUNCT
m-1112	2315	1	[	[	X
m-1112	2315	2	𝚽	𝚽	NOUN
m-1112	2315	3	𝛔	𝛔	NOUN
m-1112	2315	4	𝟒𝛑𝐫	𝟒𝛑𝐫	ADJ
m-1112	2315	5	]	]	X
m-1112	2315	6	.	.	PUNCT
m-1112	2315	7	�	�	PROPN
m-1112	2315	8	̅	̅	NOUN
m-1112	2315	9	�	�	NOUN
m-1112	2315	10	i.e.	i.e.	X
m-1112	2315	11	the	the	DET
m-1112	2315	12	energy	energy	NOUN
m-1112	2315	13	in	in	ADP
m-1112	2315	14	planck	planck	NOUN
m-1112	2315	15	-	-	PUNCT
m-1112	2315	16	cave	cave	NOUN
m-1112	2315	17	-	-	PUNCT
m-1112	2315	18	particles	particle	NOUN
m-1112	2315	19	is	be	AUX
m-1112	2315	20	dependent	dependent	ADJ
m-1112	2315	21	on	on	ADP
m-1112	2315	22	their	their	PRON
m-1112	2315	23	spin	spin	NOUN
m-1112	2315	24	only	only	ADV
m-1112	2315	25	,	,	PUNCT
m-1112	2315	26	and	and	CCONJ
m-1112	2315	27	for	for	ADP
m-1112	2315	28	electron	electron	NOUN
m-1112	2315	29	r	r	NOUN
m-1112	2315	30	=	=	PUNCT
m-1112	2315	31	a	a	DET
m-1112	2315	32	e	e	NOUN
m-1112	2315	33	→	→	SYM
m-1112	2315	34	e	e	X
m-1112	2315	35	=	=	PUNCT
m-1112	2316	1	[	[	X
m-1112	2316	2	φ	φ	PROPN
m-1112	2316	3	σ	σ	PROPN
m-1112	2316	4	4π.r	4π.r	NUM
m-1112	2316	5	]	]	PUNCT
m-1112	2316	6	.b̅	.b̅	PUNCT
m-1112	2317	1	=	=	SYM
m-1112	2317	2	1,6180339	1,6180339	X
m-1112	2317	3	[	[	PUNCT
m-1112	2317	4	1	1	NUM
m-1112	2317	5	4𝜋.1,6840307.10−17	4𝜋.1,6840307.10−17	NUM
m-1112	2317	6	]	]	SYM
m-1112	2317	7	x	x	X
m-1112	2317	8	x	x	SYM
m-1112	2317	9	2,845976	2,845976	NUM
m-1112	2317	10	.	.	PUNCT
m-1112	2318	1	10−17=	10−17=	NUM
m-1112	2319	1	21,76.10−19	21,76.10−19	NUM
m-1112	2319	2	1,6.10	1,6.10	NUM
m-1112	2319	3	19	19	NUM
m-1112	2319	4	.	.	PUNCT
m-1112	2320	1	=	=	SYM
m-1112	2320	2	13,6	13,6	NUM
m-1112	2320	3	ev	ev	X
m-1112	2320	4	,	,	PUNCT
m-1112	2320	5	which	which	PRON
m-1112	2320	6	is	be	AUX
m-1112	2320	7	the	the	DET
m-1112	2320	8	min	min	NOUN
m-1112	2320	9	-	-	NOUN
m-1112	2320	10	voltage	voltage	NOUN
m-1112	2320	11	in	in	ADP
m-1112	2320	12	hydrogen	hydrogen	NOUN
m-1112	2320	13	cave	cave	NOUN
m-1112	2320	14	.	.	PUNCT
m-1112	2321	1	d	d	X
m-1112	2321	2	)	)	PUNCT
m-1112	2321	3	..	..	PUNCT
m-1112	2321	4	the	the	DET
m-1112	2321	5	angular	angular	ADJ
m-1112	2321	6	momentum	momentum	NOUN
m-1112	2321	7	in	in	ADP
m-1112	2321	8	cave	cave	NOUN
m-1112	2321	9	c̅	c̅	PROPN
m-1112	2321	10	r	r	NOUN
m-1112	2321	11	,	,	PUNCT
m-1112	2321	12	in	in	ADP
m-1112	2321	13	cave	cave	NOUN
m-1112	2321	14	,	,	PUNCT
m-1112	2321	15	r	r	NOUN
m-1112	2321	16	,	,	PUNCT
m-1112	2321	17	the	the	DET
m-1112	2321	18	energy	energy	NOUN
m-1112	2321	19	-	-	PUNCT
m-1112	2321	20	vector	vector	NOUN
m-1112	2321	21	�	�	NOUN
m-1112	2321	22	̅	̅	NOUN
m-1112	2321	23	�	�	NOUN
m-1112	2321	24	is	be	AUX
m-1112	2321	25	positive	positive	ADJ
m-1112	2321	26	for	for	ADP
m-1112	2321	27	o3⃗⃗⃗⃗	o3⃗⃗⃗⃗	NOUN
m-1112	2321	28	⃗	⃗	PROPN
m-1112	2321	29	,	,	PUNCT
m-1112	2321	30	o1⃗⃗⃗⃗	o1⃗⃗⃗⃗	ADV
m-1112	2321	31	⃗	⃗	PROPN
m-1112	2321	32	,	,	PUNCT
m-1112	2321	33	o4⃗⃗⃗⃗	o4⃗⃗⃗⃗	NOUN
m-1112	2321	34	⃗	⃗	PROPN
m-1112	2321	35	,	,	PUNCT
m-1112	2321	36	directions	direction	NOUN
m-1112	2321	37	while	while	SCONJ
m-1112	2321	38	,	,	PUNCT
m-1112	2321	39	the	the	DET
m-1112	2321	40	energy	energy	NOUN
m-1112	2321	41	-	-	PUNCT
m-1112	2321	42	vector	vector	NOUN
m-1112	2321	43	�	�	NOUN
m-1112	2321	44	̅	̅	NOUN
m-1112	2321	45	�	�	NOUN
m-1112	2321	46	is	be	AUX
m-1112	2321	47	negative	negative	ADJ
m-1112	2321	48	for	for	ADP
m-1112	2321	49	o3⃐⃗⃗⃗⃗⃗	o3⃐⃗⃗⃗⃗⃗	PROPN
m-1112	2321	50	,	,	PUNCT
m-1112	2321	51	o2⃐⃗⃗⃗⃗⃗	o2⃐⃗⃗⃗⃗⃗	ADV
m-1112	2321	52	,	,	PUNCT
m-1112	2321	53	o4⃐⃗⃗⃗⃗⃗	o4⃐⃗⃗⃗⃗⃗	ADV
m-1112	2321	54	,	,	PUNCT
m-1112	2321	55	directions	direction	NOUN
m-1112	2321	56	.	.	PUNCT
m-1112	2322	1	since	since	SCONJ
m-1112	2322	2	total	total	ADJ
m-1112	2322	3	-	-	PUNCT
m-1112	2322	4	energy	energy	NOUN
m-1112	2322	5	l	l	NOUN
m-1112	2322	6	=	=	SYM
m-1112	2322	7	b	b	X
m-1112	2322	8	w	w	PROPN
m-1112	2322	9	=	=	PUNCT
m-1112	2322	10	j.w	j.w	PROPN
m-1112	2322	11	2	2	NUM
m-1112	2322	12	w	w	NOUN
m-1112	2322	13	=	=	PUNCT
m-1112	2322	14	j.w²	j.w²	NOUN
m-1112	2322	15	2	2	NUM
m-1112	2322	16	then	then	ADV
m-1112	2322	17	2l	2l	NUM
m-1112	2322	18	=	=	SYM
m-1112	2322	19	j.w²	j.w²	NOUN
m-1112	2322	20	,	,	PUNCT
m-1112	2322	21	then	then	ADV
m-1112	2322	22	angular	angular	ADJ
m-1112	2322	23	momentum	momentum	NOUN
m-1112	2322	24	relation	relation	NOUN
m-1112	2322	25	b̅	b̅	PUNCT
m-1112	2322	26	=	=	PUNCT
m-1112	2322	27	r.mv	r.mv	NOUN
m-1112	2322	28	=	=	SYM
m-1112	2322	29	r	r	NOUN
m-1112	2322	30	[	[	PUNCT
m-1112	2322	31	π.r⁴	π.r⁴	NOUN
m-1112	2322	32	2	2	NUM
m-1112	2322	33	]	]	PUNCT
m-1112	2322	34	.	.	PUNCT
m-1112	2323	1	2πf	2πf	NOUN
m-1112	2323	2	r	r	NOUN
m-1112	2323	3	=	=	PUNCT
m-1112	2323	4	π	π	PROPN
m-1112	2323	5	².𝐫𝟔.f	².𝐫𝟔.f	ADV
m-1112	2323	6	.	.	PUNCT
m-1112	2324	1	and	and	CCONJ
m-1112	2324	2	b	b	X
m-1112	2324	3	=	=	SYM
m-1112	2324	4	j	j	PROPN
m-1112	2324	5	w	w	X
m-1112	2324	6	i.e.	i.e.	X
m-1112	2324	7	angular	angular	ADJ
m-1112	2324	8	momentum	momentum	NOUN
m-1112	2324	9	�	�	NOUN
m-1112	2324	10	̅	̅	NOUN
m-1112	2324	11	�	�	NOUN
m-1112	2324	12	=	=	SYM
m-1112	2325	1	r	r	NOUN
m-1112	2325	2	m	m	NOUN
m-1112	2325	3	v	v	NOUN
m-1112	2325	4	=	=	X
m-1112	2325	5	j.w	j.w	PROPN
m-1112	2325	6	2	2	NUM
m-1112	2325	7	=	=	PUNCT
m-1112	2325	8	[	[	PUNCT
m-1112	2325	9	π.𝐫𝟒	π.𝐫𝟒	X
m-1112	2325	10	4	4	NUM
m-1112	2325	11	]	]	PUNCT
m-1112	2325	12	c	c	NOUN
m-1112	2325	13	r	r	NOUN
m-1112	2325	14	=	=	SYM
m-1112	2325	15	[	[	PUNCT
m-1112	2325	16	𝛑.𝐫𝟑	𝛑.𝐫𝟑	NOUN
m-1112	2325	17	𝟒	𝟒	NUM
m-1112	2325	18	]	]	PUNCT
m-1112	2325	19	.	.	PUNCT
m-1112	2325	20	�	�	PROPN
m-1112	2325	21	̅	̅	NOUN
m-1112	2325	22	�	�	NOUN
m-1112	2325	23	=	=	SYM
m-1112	2325	24	[	[	PUNCT
m-1112	2325	25	𝛑.𝐫	𝛑.𝐫	X
m-1112	2325	26	𝟐	𝟐	NUM
m-1112	2325	27	𝟒	𝟒	NUM
m-1112	2325	28	]	]	PUNCT
m-1112	2325	29	.	.	PUNCT
m-1112	2325	30	�	�	PROPN
m-1112	2325	31	̅	̅	NOUN
m-1112	2325	32	�	�	PROPN
m-1112	2325	33	x	x	SYM
m-1112	2325	34	�	�	PROPN
m-1112	2325	35	̅	̅	NOUN
m-1112	2325	36	�	�	PROPN
m-1112	2325	37	......	......	PUNCT
m-1112	2325	38	(	(	PUNCT
m-1112	2325	39	a	a	X
m-1112	2325	40	)	)	PUNCT
m-1112	2325	41	ijo	ijo	PROPN
m-1112	2325	42	international	international	PROPN
m-1112	2325	43	journal	journal	PROPN
m-1112	2325	44	of	of	ADP
m-1112	2325	45	mathematics	mathematics	PROPN
m-1112	2325	46	(	(	PUNCT
m-1112	2325	47	issn	issn	PROPN
m-1112	2325	48	:	:	PUNCT
m-1112	2325	49	2992	2992	NUM
m-1112	2325	50	-	-	SYM
m-1112	2325	51	4421	4421	NUM
m-1112	2325	52	)	)	PUNCT
m-1112	2325	53	volume	volume	NOUN
m-1112	2325	54	08	08	NUM
m-1112	2326	1	|	|	ADV
m-1112	2326	2	issue	issue	NOUN
m-1112	2326	3	08	08	NUM
m-1112	2327	1	|	|	ADV
m-1112	2327	2	august	august	PROPN
m-1112	2327	3	2025	2025	NUM
m-1112	2328	1	|	|	ADV
m-1112	2328	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2328	3	ijo	ijo	PROPN
m-1112	2328	4	journals	journal	NOUN
m-1112	2328	5	81	81	NUM
m-1112	2328	6	the	the	DET
m-1112	2328	7	fundamental	fundamental	ADJ
m-1112	2328	8	particles	particle	NOUN
m-1112	2328	9	origination	origination	NOUN
m-1112	2328	10	mechanism	mechanism	NOUN
m-1112	2328	11	in	in	ADP
m-1112	2328	12	mfmf	mfmf	PROPN
m-1112	2328	13	pns	pns	PROPN
m-1112	2328	14	caves	cave	NOUN
m-1112	2328	15	.	.	PUNCT
m-1112	2329	1	for	for	ADP
m-1112	2329	2	�	�	PROPN
m-1112	2329	3	̅	̅	NOUN
m-1112	2329	4	�	�	NOUN
m-1112	2329	5	=	=	SYM
m-1112	2329	6	±	±	NUM
m-1112	2329	7	�	�	PROPN
m-1112	2329	8	̅	̅	NOUN
m-1112	2329	9	�	�	PROPN
m-1112	2329	10	,	,	PUNCT
m-1112	2329	11	then	then	ADV
m-1112	2329	12	+	+	CCONJ
m-1112	2329	13	�	�	NOUN
m-1112	2329	14	̅	̅	NOUN
m-1112	2329	15	�	�	NOUN
m-1112	2329	16	=	=	SYM
m-1112	2329	17	+	+	NUM
m-1112	2329	18	gravity	gravity	NOUN
m-1112	2329	19	–	–	PUNCT
m-1112	2329	20	spin	spin	NOUN
m-1112	2329	21	=	=	X
m-1112	2330	1	+	+	CCONJ
m-1112	2330	2	[	[	PUNCT
m-1112	2330	3	𝛑.𝐫𝟐	𝛑.𝐫𝟐	NUM
m-1112	2330	4	𝟒	𝟒	NUM
m-1112	2330	5	]	]	PUNCT
m-1112	2330	6	.	.	PUNCT
m-1112	2330	7	�	�	PROPN
m-1112	2330	8	̅	̅	NOUN
m-1112	2330	9	�	�	PROPN
m-1112	2330	10	x	x	SYM
m-1112	2330	11	�	�	PROPN
m-1112	2330	12	̅	̅	NOUN
m-1112	2330	13	�	�	PROPN
m-1112	2330	14	,	,	PUNCT
m-1112	2330	15	the	the	DET
m-1112	2330	16	+	+	NUM
m-1112	2330	17	gravity	gravity	NOUN
m-1112	2330	18	force	force	NOUN
m-1112	2330	19	�	�	NOUN
m-1112	2330	20	̅	̅	NOUN
m-1112	2330	21	�	�	NOUN
m-1112	2330	22	=	=	SYM
m-1112	2330	23	gravity	gravity	NOUN
m-1112	2330	24	–	–	PUNCT
m-1112	2330	25	spin	spin	NOUN
m-1112	2330	26	=	=	SYM
m-1112	2330	27	[	[	PUNCT
m-1112	2330	28	𝛑.𝐫𝟐	𝛑.𝐫𝟐	NUM
m-1112	2330	29	𝟒	𝟒	NUM
m-1112	2330	30	]	]	PUNCT
m-1112	2330	31	.	.	PUNCT
m-1112	2330	32	�	�	PROPN
m-1112	2330	33	̅	̅	NOUN
m-1112	2330	34	�	�	PROPN
m-1112	2330	35	x	x	SYM
m-1112	2330	36	�	�	PROPN
m-1112	2330	37	̅	̅	NOUN
m-1112	2330	38	�	�	PROPN
m-1112	2330	39	,	,	PUNCT
m-1112	2330	40	the	the	DET
m-1112	2330	41	-antigravity	-antigravity	NOUN
m-1112	2330	42	force	force	NOUN
m-1112	2330	43	from	from	ADP
m-1112	2330	44	momentum	momentum	NOUN
m-1112	2330	45	relation	relation	NOUN
m-1112	2330	46	b̅	b̅	PUNCT
m-1112	2331	1	=	=	PUNCT
m-1112	2331	2	m	m	VERB
m-1112	2331	3	r	r	NOUN
m-1112	2331	4	v	v	NOUN
m-1112	2331	5	=	=	PUNCT
m-1112	2331	6	m	m	VERB
m-1112	2331	7	r²	r²	NOUN
m-1112	2331	8	w	w	PROPN
m-1112	2331	9	=	=	VERB
m-1112	2331	10	m	m	VERB
m-1112	2331	11	r²	r²	NOUN
m-1112	2331	12	(	(	PUNCT
m-1112	2331	13	2πf	2πf	ADJ
m-1112	2331	14	)	)	PUNCT
m-1112	2332	1	=	=	PUNCT
m-1112	2332	2	j.w	j.w	PROPN
m-1112	2332	3	2	2	NUM
m-1112	2332	4	=	=	PUNCT
m-1112	2332	5	[	[	PUNCT
m-1112	2332	6	πr⁴	πr⁴	NOUN
m-1112	2332	7	2	2	NUM
m-1112	2332	8	]	]	PUNCT
m-1112	2332	9	.[2πf	.[2πf	NOUN
m-1112	2332	10	]	]	PUNCT
m-1112	2332	11	then	then	ADV
m-1112	2332	12	spin	spin	VERB
m-1112	2332	13	s	s	VERB
m-1112	2332	14	≡	≡	ADJ
m-1112	2332	15	angular	angular	ADJ
m-1112	2332	16	-	-	PUNCT
m-1112	2332	17	momentum	momentum	NOUN
m-1112	2332	18	�	�	NOUN
m-1112	2332	19	̅	̅	NOUN
m-1112	2332	20	�	�	PROPN
m-1112	2332	21	≡	≡	PROPN
m-1112	2332	22	�	�	PROPN
m-1112	2332	23	̅	̅	NOUN
m-1112	2332	24	�	�	NOUN
m-1112	2332	25	=	=	SYM
m-1112	2332	26	j.w	j.w	PROPN
m-1112	2332	27	2	2	NUM
m-1112	2332	28	=	=	SYM
m-1112	2332	29	πr⁴	πr⁴	NOUN
m-1112	2332	30	4	4	NUM
m-1112	2333	1	[	[	SYM
m-1112	2333	2	2πf]=	2πf]=	NUM
m-1112	2333	3	π².r⁴.[f	π².r⁴.[f	ADJ
m-1112	2333	4	]	]	X
m-1112	2333	5	=	=	SYM
m-1112	2333	6	𝛑.𝐫³𝚽.𝛔	𝛑.𝐫³𝚽.𝛔	X
m-1112	2333	7	𝟐	𝟐	NUM
m-1112	2333	8	≡	≡	PROPN
m-1112	2334	1	[	[	X
m-1112	2334	2	𝟏+√𝟓	𝟏+√𝟓	ADJ
m-1112	2334	3	]	]	X
m-1112	2334	4	.𝛔.𝛑.𝐫³	.𝛔.𝛑.𝐫³	SYM
m-1112	2334	5	𝟒	𝟒	NUM
m-1112	2334	6	=	=	SYM
m-1112	2334	7	𝛑𝐫𝟑𝛔.𝚽	𝛑𝐫𝟑𝛔.𝚽	X
m-1112	2334	8	𝟐	𝟐	NUM
m-1112	2334	9	..	..	PUNCT
m-1112	2334	10	(	(	PUNCT
m-1112	2334	11	b	b	NOUN
m-1112	2334	12	)	)	PUNCT
m-1112	2334	13	for	for	ADP
m-1112	2334	14	�	�	NOUN
m-1112	2334	15	̅	̅	NOUN
m-1112	2334	16	�	�	PROPN
m-1112	2334	17	=	=	SYM
m-1112	2334	18	±	±	NUM
m-1112	2334	19	�	�	PROPN
m-1112	2334	20	̅	̅	NOUN
m-1112	2334	21	�	�	PROPN
m-1112	2334	22	,	,	PUNCT
m-1112	2334	23	then	then	ADV
m-1112	2334	24	+	+	CCONJ
m-1112	2334	25	�	�	NOUN
m-1112	2334	26	̅	̅	NOUN
m-1112	2334	27	�	�	NOUN
m-1112	2334	28	=	=	SYM
m-1112	2334	29	+	+	NUM
m-1112	2334	30	gravity	gravity	NOUN
m-1112	2334	31	–	–	PUNCT
m-1112	2334	32	spin	spin	NOUN
m-1112	2334	33	=	=	SYM
m-1112	2335	1	+	+	NUM
m-1112	2335	2	𝛑.𝐫𝟑𝛔.𝚽	𝛑.𝐫𝟑𝛔.𝚽	X
m-1112	2335	3	𝟐	𝟐	NUM
m-1112	2335	4	,	,	PUNCT
m-1112	2335	5	the	the	DET
m-1112	2335	6	gravity	gravity	NOUN
m-1112	2335	7	spin	spin	NOUN
m-1112	2335	8	�	�	NOUN
m-1112	2335	9	̅	̅	NOUN
m-1112	2335	10	�	�	NOUN
m-1112	2335	11	=	=	SYM
m-1112	2335	12	gravity	gravity	NOUN
m-1112	2335	13	–	–	PUNCT
m-1112	2335	14	spin	spin	NOUN
m-1112	2335	15	=	=	SYM
m-1112	2335	16	𝛑𝐫𝟑𝛔.𝚽	𝛑𝐫𝟑𝛔.𝚽	X
m-1112	2335	17	𝟐	𝟐	NUM
m-1112	2335	18	,	,	PUNCT
m-1112	2335	19	the	the	DET
m-1112	2335	20	antigravity	antigravity	NOUN
m-1112	2335	21	spin	spin	NOUN
m-1112	2335	22	from	from	ADP
m-1112	2335	23	spin	spin	NOUN
m-1112	2335	24	-	-	PUNCT
m-1112	2335	25	momentum	momentum	NOUN
m-1112	2335	26	relation	relation	NOUN
m-1112	2335	27	s	s	PART
m-1112	2335	28	=	=	ADJ
m-1112	2335	29	�	�	PROPN
m-1112	2335	30	̅	̅	NOUN
m-1112	2335	31	�	�	NOUN
m-1112	2335	32	=	=	SYM
m-1112	2335	33	𝐄	𝐄	NOUN
m-1112	2335	34	𝐰	𝐰	NOUN
m-1112	2335	35	=	=	SYM
m-1112	2335	36	𝐄	𝐄	NOUN
m-1112	2335	37	𝟐𝛑𝐟	𝟐𝛑𝐟	NOUN
m-1112	2335	38	=	=	PUNCT
m-1112	2336	1	𝐄𝐫	𝐄𝐫	NOUN
m-1112	2336	2	𝛔𝚽	𝛔𝚽	NOUN
m-1112	2336	3	=	=	PUNCT
m-1112	2336	4	𝐫𝐆	𝐫𝐆	PROPN
m-1112	2336	5	𝛔𝚽	𝛔𝚽	ADV
m-1112	2336	6	,	,	PUNCT
m-1112	2336	7	and	and	CCONJ
m-1112	2336	8	�	�	PROPN
m-1112	2336	9	̅	̅	NOUN
m-1112	2336	10	�	�	NOUN
m-1112	2336	11	²	²	NUM
m-1112	2336	12	=	=	SYM
m-1112	2336	13	𝐉²𝛔²	𝐉²𝛔²	NOUN
m-1112	2336	14	𝐫²	𝐫²	NOUN
m-1112	2336	15	φ²	φ²	NOUN
m-1112	2336	16	,	,	PUNCT
m-1112	2336	17	so	so	SCONJ
m-1112	2336	18	→	→	SYM
m-1112	2336	19	[	[	X
m-1112	2336	20	�	�	NOUN
m-1112	2336	21	̅	̅	NOUN
m-1112	2336	22	�	�	NOUN
m-1112	2336	23	]²	]²	X
m-1112	2336	24	=	=	PUNCT
m-1112	2337	1	[	[	PUNCT
m-1112	2337	2	𝚽𝐉𝛔	𝚽𝐉𝛔	NOUN
m-1112	2337	3	𝐫	𝐫	X
m-1112	2337	4	]	]	PUNCT
m-1112	2337	5	²←	²←	NOUN
m-1112	2337	6	while	while	SCONJ
m-1112	2337	7	from	from	ADP
m-1112	2337	8	gravity	gravity	NOUN
m-1112	2337	9	-	-	PUNCT
m-1112	2337	10	force	force	NOUN
m-1112	2337	11	𝐅𝐆	𝐅𝐆	PROPN
m-1112	2337	12	≡	≡	PROPN
m-1112	2337	13	𝐦𝐆g=	𝐦𝐆g=	PROPN
m-1112	2337	14	g.	g.	PROPN
m-1112	2338	1	[	[	X
m-1112	2338	2	σ	σ	X
m-1112	2338	3	c].r	c].r	NOUN
m-1112	2338	4	=	=	PUNCT
m-1112	2338	5	𝐦𝐆	𝐦𝐆	NOUN
m-1112	2338	6	𝐜²	𝐜²	PROPN
m-1112	2338	7	𝐫	𝐫	X
m-1112	2338	8	=	=	SYM
m-1112	2338	9	jw².𝐠𝐆	jw².𝐠𝐆	PROPN
m-1112	2338	10	=	=	PUNCT
m-1112	2338	11	𝐯²	𝐯²	PROPN
m-1112	2338	12	𝐫	𝐫	NOUN
m-1112	2338	13	.	.	PUNCT
m-1112	2339	1	[	[	PUNCT
m-1112	2339	2	𝛑𝐫𝟒	𝛑𝐫𝟒	NOUN
m-1112	2339	3	𝟐	𝟐	NUM
m-1112	2339	4	]	]	PUNCT
m-1112	2339	5	𝐯²	𝐯²	ADJ
m-1112	2339	6	𝐫²	𝐫²	NOUN
m-1112	2339	7	=	=	PUNCT
m-1112	2339	8	𝛑𝐫𝐯𝟒	𝛑𝐫𝐯𝟒	PROPN
m-1112	2339	9	𝟐	𝟐	NUM
m-1112	2339	10	,	,	PUNCT
m-1112	2339	11	and	and	CCONJ
m-1112	2339	12	gravity	gravity	NOUN
m-1112	2339	13	-	-	PUNCT
m-1112	2339	14	acceleration	acceleration	NOUN
m-1112	2339	15	±	±	NUM
m-1112	2339	16	𝐠𝐆	𝐠𝐆	NOUN
m-1112	2339	17	=	=	PUNCT
m-1112	2339	18	[	[	PUNCT
m-1112	2339	19	𝛑𝐫𝐯𝟒	𝛑𝐫𝐯𝟒	NOUN
m-1112	2339	20	𝟐	𝟐	NUM
m-1112	2339	21	]	]	PUNCT
m-1112	2339	22	.	.	PUNCT
m-1112	2340	1	𝒆𝟑	𝒆𝟑	PROPN
m-1112	2340	2	,	,	PUNCT
m-1112	2340	3	geometry	geometry	NOUN
m-1112	2340	4	growth	growth	NOUN
m-1112	2340	5	[	[	PUNCT
m-1112	2340	6	𝛑𝐫𝐯𝟒	𝛑𝐫𝐯𝟒	NOUN
m-1112	2340	7	𝟐	𝟐	NUM
m-1112	2340	8	]	]	PUNCT
m-1112	2340	9	=[	=[	NOUN
m-1112	2340	10	𝟑,𝟏𝟒𝟏𝟓𝟗𝟐𝟔([√𝟓+𝟏	𝟑,𝟏𝟒𝟏𝟓𝟗𝟐𝟔([√𝟓+𝟏	NOUN
m-1112	2340	11	]	]	PUNCT
m-1112	2340	12	.	.	PUNCT
m-1112	2341	1	√𝟐	√𝟐	PROPN
m-1112	2341	2	𝟒	𝟒	PROPN
m-1112	2341	3	.𝟏𝟎−𝟑𝟓).(𝟐,𝟗𝟗𝟕𝟗𝟑𝟒𝟓𝟖.𝟏𝟎𝟖	.𝟏𝟎−𝟑𝟓).(𝟐,𝟗𝟗𝟕𝟗𝟑𝟒𝟓𝟖.𝟏𝟎𝟖	PUNCT
m-1112	2341	4	)	)	PUNCT
m-1112	2341	5	𝟒	𝟒	PROPN
m-1112	2341	6	𝟐	𝟐	NUM
m-1112	2341	7	]	]	PUNCT
m-1112	2341	8	.𝒆𝟑	.𝒆𝟑	PUNCT
m-1112	2341	9	=	=	PUNCT
m-1112	2342	1	=	=	PUNCT
m-1112	2343	1	6,044981.𝟏𝟎−𝟑𝟓.	6,044981.𝟏𝟎−𝟑𝟓.	NUM
m-1112	2343	2	80,773378.𝟏𝟎𝟑𝟐.	80,773378.𝟏𝟎𝟑𝟐.	NUM
m-1112	2343	3	20,085536	20,085536	NUM
m-1112	2343	4	=	=	SYM
m-1112	2343	5	𝐠𝐆	𝐠𝐆	X
m-1112	2343	6	=	=	SYM
m-1112	2343	7	±	±	NUM
m-1112	2343	8	9,8076925	9,8076925	NUM
m-1112	2343	9	.	.	PUNCT
m-1112	2344	1	i.e.	i.e.	X
m-1112	2344	2	gravity	gravity	NOUN
m-1112	2344	3	+	+	CCONJ
m-1112	2344	4	𝐠𝐆	𝐠𝐆	X
m-1112	2344	5	=	=	SYM
m-1112	2344	6	+	+	NUM
m-1112	2344	7	9,8076925	9,8076925	NUM
m-1112	2344	8	=	=	SYM
m-1112	2344	9	𝛝𝐫c̅	𝛝𝐫c̅	X
m-1112	2344	10	𝛝𝐭	𝛝𝐭	X
m-1112	2344	11	=	=	SYM
m-1112	2344	12	+	+	NUM
m-1112	2344	13	�	�	NOUN
m-1112	2344	14	̅	̅	NOUN
m-1112	2344	15	�	�	PROPN
m-1112	2344	16	,	,	PUNCT
m-1112	2344	17	and	and	CCONJ
m-1112	2344	18	antigravity=	antigravity=	NUM
m-1112	2344	19	𝐠𝐆	𝐠𝐆	NOUN
m-1112	2344	20	=	=	SYM
m-1112	2344	21	9,8076925	9,8076925	NUM
m-1112	2344	22	=	=	PUNCT
m-1112	2344	23	𝛝𝐫c̅	𝛝𝐫c̅	PRON
m-1112	2344	24	𝛝𝐭	𝛝𝐭	PROPN
m-1112	2344	25	=	=	VERB
m-1112	2344	26	�	�	NOUN
m-1112	2344	27	̅	̅	NOUN
m-1112	2344	28	�	�	NOUN
m-1112	2344	29	are	be	AUX
m-1112	2344	30	the	the	DET
m-1112	2344	31	two	two	NUM
m-1112	2344	32	opposite	opposite	ADJ
m-1112	2344	33	forces	force	NOUN
m-1112	2344	34	as	as	ADP
m-1112	2344	35	spin	spin	NOUN
m-1112	2344	36	and	and	CCONJ
m-1112	2344	37	for	for	ADP
m-1112	2344	38	the	the	DET
m-1112	2344	39	stability	stability	NOUN
m-1112	2344	40	of	of	ADP
m-1112	2344	41	the	the	DET
m-1112	2344	42	spin	spin	NOUN
m-1112	2344	43	�	�	PROPN
m-1112	2344	44	̅	̅	NOUN
m-1112	2344	45	�	�	PROPN
m-1112	2344	46	,	,	PUNCT
m-1112	2344	47	equilibrium	equilibrium	NOUN
m-1112	2344	48	.	.	PUNCT
m-1112	2345	1	for	for	ADP
m-1112	2345	2	c	c	NOUN
m-1112	2345	3	=	=	SYM
m-1112	2345	4	0	0	NUM
m-1112	2345	5	exist	exist	VERB
m-1112	2345	6	minima	minima	NOUN
m-1112	2345	7	or	or	CCONJ
m-1112	2345	8	maxima	maxima	NOUN
m-1112	2345	9	and	and	CCONJ
m-1112	2345	10	thus	thus	ADV
m-1112	2345	11	spin	spin	NOUN
m-1112	2345	12	is	be	AUX
m-1112	2345	13	equal	equal	ADJ
m-1112	2345	14	to	to	ADP
m-1112	2345	15	the	the	DET
m-1112	2345	16	negative	negative	ADJ
m-1112	2345	17	gradient	gradient	NOUN
m-1112	2345	18	of	of	ADP
m-1112	2345	19	the	the	DET
m-1112	2345	20	potential	potential	ADJ
m-1112	2345	21	energy	energy	NOUN
m-1112	2345	22	in	in	ADP
m-1112	2345	23	the	the	DET
m-1112	2345	24	two	two	NUM
m-1112	2345	25	interchange	interchange	NOUN
m-1112	2345	26	energy	energy	NOUN
m-1112	2345	27	semi	semi	ADJ
m-1112	2345	28	circles	circle	NOUN
m-1112	2345	29	.	.	PUNCT
m-1112	2346	1	centripetal	centripetal	ADJ
m-1112	2346	2	force	force	NOUN
m-1112	2346	3	originates	originate	VERB
m-1112	2346	4	the	the	DET
m-1112	2346	5	two	two	NUM
m-1112	2346	6	-	-	PUNCT
m-1112	2346	7	momentum	momentum	NOUN
m-1112	2346	8	±	±	NUM
m-1112	2346	9	�	�	PROPN
m-1112	2346	10	̅	̅	NOUN
m-1112	2346	11	�	�	PROPN
m-1112	2346	12	,	,	PUNCT
m-1112	2346	13	�	�	PROPN
m-1112	2346	14	̅	̅	NOUN
m-1112	2346	15	�	�	NOUN
m-1112	2346	16	=	=	SYM
m-1112	2347	1	r	r	NOUN
m-1112	2347	2	m	m	VERB
m-1112	2347	3	v	v	NOUN
m-1112	2347	4	=	=	X
m-1112	2347	5	[	[	PUNCT
m-1112	2347	6	𝛑𝐫𝟑𝛔.𝚽	𝛑𝐫𝟑𝛔.𝚽	X
m-1112	2347	7	𝟐	𝟐	NUM
m-1112	2347	8	]	]	PUNCT
m-1112	2347	9	≡	≡	PROPN
m-1112	2347	10	gravity	gravity	NOUN
m-1112	2347	11	–	–	PUNCT
m-1112	2347	12	antigravity	antigravity	NOUN
m-1112	2347	13	–	–	PUNCT
m-1112	2347	14	spin	spin	NOUN
m-1112	2347	15	.	.	PUNCT
m-1112	2348	1	6c2	6c2	X
m-1112	2348	2	..	..	PUNCT
m-1112	2348	3	the	the	DET
m-1112	2348	4	stability	stability	NOUN
m-1112	2348	5	of	of	ADP
m-1112	2348	6	equilibrium	equilibrium	NOUN
m-1112	2348	7	:	:	PUNCT
m-1112	2348	8	in	in	ADP
m-1112	2348	9	the	the	DET
m-1112	2348	10	conservative	conservative	ADJ
m-1112	2348	11	system	system	NOUN
m-1112	2348	12	,	,	PUNCT
m-1112	2348	13	of	of	ADP
m-1112	2348	14	cave	cave	PROPN
m-1112	2348	15	�	�	PROPN
m-1112	2348	16	̅	̅	NOUN
m-1112	2348	17	�	�	PROPN
m-1112	2348	18	r	r	NOUN
m-1112	2348	19	,	,	PUNCT
m-1112	2348	20	the	the	DET
m-1112	2348	21	total	total	ADJ
m-1112	2348	22	energy	energy	NOUN
m-1112	2348	23	𝐄	𝐄	PROPN
m-1112	2348	24	𝐓	𝐓	PROPN
m-1112	2348	25	remains	remain	VERB
m-1112	2348	26	constant	constant	ADJ
m-1112	2348	27	and	and	CCONJ
m-1112	2348	28	the	the	DET
m-1112	2348	29	total	total	ADJ
m-1112	2348	30	-	-	PUNCT
m-1112	2348	31	energy	energy	NOUN
m-1112	2348	32	is	be	AUX
m-1112	2348	33	𝐄	𝐄	PROPN
m-1112	2348	34	𝐓	𝐓	PROPN
m-1112	2348	35	=	=	PUNCT
m-1112	2348	36	𝐄	𝐄	PROPN
m-1112	2348	37	𝐊	𝐊	NOUN
m-1112	2348	38	+	+	CCONJ
m-1112	2348	39	𝐄	𝐄	PROPN
m-1112	2348	40	𝐔	𝐔	NOUN
m-1112	2349	1	=	=	NOUN
m-1112	2349	2	𝟏	𝟏	PROPN
m-1112	2349	3	𝟐	𝟐	NUM
m-1112	2349	4	[	[	PUNCT
m-1112	2349	5	�	�	PROPN
m-1112	2349	6	̇	̇	PROPN
m-1112	2349	7	�	�	PROPN
m-1112	2349	8	]	]	PUNCT
m-1112	2349	9	²	²	PROPN
m-1112	2349	10	+	+	NUM
m-1112	2349	11	u(x	u(x	NOUN
m-1112	2349	12	)	)	PUNCT
m-1112	2349	13	=	=	SYM
m-1112	2349	14	constant	constant	ADJ
m-1112	2349	15	…	…	PUNCT
m-1112	2349	16	..	..	PUNCT
m-1112	2349	17	(	(	PUNCT
m-1112	2349	18	1	1	X
m-1112	2349	19	)	)	PUNCT
m-1112	2349	20	where	where	SCONJ
m-1112	2349	21	𝐄	𝐄	PROPN
m-1112	2349	22	𝐊=	𝐊=	PROPN
m-1112	2349	23	the	the	DET
m-1112	2349	24	kinetic	kinetic	ADJ
m-1112	2349	25	energy	energy	NOUN
m-1112	2349	26	and	and	CCONJ
m-1112	2349	27	𝐄	𝐄	NOUN
m-1112	2349	28	𝐔	𝐔	NOUN
m-1112	2349	29	=	=	PUNCT
m-1112	2349	30	the	the	DET
m-1112	2349	31	potential	potential	ADJ
m-1112	2349	32	energy	energy	NOUN
m-1112	2349	33	.	.	PUNCT
m-1112	2350	1	for	for	ADP
m-1112	2350	2	y	y	PROPN
m-1112	2350	3	=	=	SYM
m-1112	2350	4	�	�	PROPN
m-1112	2350	5	̇	̇	PROPN
m-1112	2350	6	�	�	PROPN
m-1112	2350	7	then	then	ADV
m-1112	2350	8	,	,	PUNCT
m-1112	2350	9	y	y	PROPN
m-1112	2350	10	=	=	PUNCT
m-1112	2350	11	�	�	PROPN
m-1112	2350	12	̇	̇	PROPN
m-1112	2350	13	�	�	PROPN
m-1112	2350	14	=	=	PRON
m-1112	2350	15	±	±	NUM
m-1112	2350	16	√𝟐.	√𝟐.	VERB
m-1112	2351	1	[	[	X
m-1112	2351	2	𝐄	𝐄	NOUN
m-1112	2351	3	−	−	NOUN
m-1112	2351	4	𝐔(𝐱	𝐔(𝐱	NOUN
m-1112	2351	5	)	)	PUNCT
m-1112	2351	6	]	]	X
m-1112	2351	7	…	…	PUNCT
m-1112	2351	8	(	(	PUNCT
m-1112	2351	9	2	2	NUM
m-1112	2351	10	)	)	PUNCT
m-1112	2351	11	the	the	DET
m-1112	2351	12	differential	differential	ADJ
m-1112	2351	13	equation	equation	NOUN
m-1112	2351	14	of	of	ADP
m-1112	2351	15	motion	motion	NOUN
m-1112	2351	16	in	in	ADP
m-1112	2351	17	cave	cave	PROPN
m-1112	2351	18	�	�	PROPN
m-1112	2351	19	̅	̅	NOUN
m-1112	2351	20	�	�	NOUN
m-1112	2351	21	r	r	NOUN
m-1112	2351	22	,	,	PUNCT
m-1112	2351	23	for	for	ADP
m-1112	2351	24	conservative	conservative	ADJ
m-1112	2351	25	systems	system	NOUN
m-1112	2351	26	is	be	AUX
m-1112	2351	27	ẍ	ẍ	X
m-1112	2351	28	=	=	SYM
m-1112	2351	29	f(x	f(x	PROPN
m-1112	2351	30	)	)	PUNCT
m-1112	2351	31	and	and	CCONJ
m-1112	2351	32	because	because	SCONJ
m-1112	2351	33	ẍ	ẍ	PROPN
m-1112	2351	34	=	=	SYM
m-1112	2351	35	ẋ	ẋ	PROPN
m-1112	2351	36	(	(	PUNCT
m-1112	2351	37	d	d	X
m-1112	2351	38	�	�	PROPN
m-1112	2351	39	̇	̇	NOUN
m-1112	2351	40	�	�	PROPN
m-1112	2351	41	/dẋ	/dẋ	PUNCT
m-1112	2351	42	)	)	PUNCT
m-1112	2351	43	then	then	ADV
m-1112	2351	44	ẋ.	ẋ.	PROPN
m-1112	2351	45	dẋ	dẋ	PROPN
m-1112	2351	46	=	=	PRON
m-1112	2351	47	f(x)dx	f(x)dx	VERB
m-1112	2351	48	=	=	NOUN
m-1112	2351	49	0	0	NUM
m-1112	2351	50	..	..	PUNCT
m-1112	2351	51	(	(	PUNCT
m-1112	2351	52	3	3	X
m-1112	2351	53	)	)	PUNCT
m-1112	2351	54	by	by	ADP
m-1112	2351	55	integrating	integrate	VERB
m-1112	2351	56	then	then	ADV
m-1112	2352	1	ẋ²	ẋ²	PROPN
m-1112	2352	2	2	2	NUM
m-1112	2352	3	∫	∫	NOUN
m-1112	2352	4	𝑓(𝑥)𝑑𝑥	𝑓(𝑥)𝑑𝑥	NOUN
m-1112	2352	5	𝑥	𝑥	NOUN
m-1112	2352	6	0	0	NUM
m-1112	2352	7	=	=	SYM
m-1112	2352	8	ijo	ijo	PROPN
m-1112	2352	9	international	international	PROPN
m-1112	2352	10	journal	journal	PROPN
m-1112	2352	11	of	of	ADP
m-1112	2352	12	mathematics	mathematics	PROPN
m-1112	2352	13	(	(	PUNCT
m-1112	2352	14	issn	issn	PROPN
m-1112	2352	15	:	:	PUNCT
m-1112	2352	16	2992	2992	NUM
m-1112	2352	17	-	-	SYM
m-1112	2352	18	4421	4421	NUM
m-1112	2352	19	)	)	PUNCT
m-1112	2352	20	volume	volume	NOUN
m-1112	2352	21	08	08	NUM
m-1112	2353	1	|	|	ADV
m-1112	2353	2	issue	issue	NOUN
m-1112	2353	3	08	08	NUM
m-1112	2354	1	|	|	ADV
m-1112	2354	2	august	august	PROPN
m-1112	2354	3	2025	2025	NUM
m-1112	2354	4	|	|	ADV
m-1112	2354	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2354	6	ijo	ijo	PROPN
m-1112	2354	7	journals	journal	NOUN
m-1112	2354	8	82	82	NUM
m-1112	2354	9	the	the	DET
m-1112	2354	10	fundamental	fundamental	ADJ
m-1112	2354	11	particles	particle	NOUN
m-1112	2354	12	origination	origination	NOUN
m-1112	2354	13	mechanism	mechanism	NOUN
m-1112	2354	14	in	in	ADP
m-1112	2354	15	mfmf	mfmf	PROPN
m-1112	2354	16	pns	pns	PROPN
m-1112	2354	17	caves	cave	NOUN
m-1112	2354	18	.	.	PUNCT
m-1112	2355	1	e	e	NOUN
m-1112	2355	2	,	,	PUNCT
m-1112	2355	3	and	and	CCONJ
m-1112	2355	4	by	by	ADP
m-1112	2355	5	comparison	comparison	NOUN
m-1112	2355	6	to	to	ADP
m-1112	2355	7	priors	prior	NOUN
m-1112	2355	8	then	then	ADV
m-1112	2355	9	→	→	SYM
m-1112	2355	10	u(x	u(x	PROPN
m-1112	2355	11	)	)	PUNCT
m-1112	2355	12	=	=	SYM
m-1112	2355	13	∫	∫	PROPN
m-1112	2355	14	𝑓(𝑥)𝑑𝑥	𝑓(𝑥)𝑑𝑥	NUM
m-1112	2355	15	𝑥	𝑥	NOUN
m-1112	2355	16	0	0	NUM
m-1112	2355	17	or	or	CCONJ
m-1112	2355	18	f(x	f(x	PROPN
m-1112	2355	19	)	)	PUNCT
m-1112	2355	20	=	=	PUNCT
m-1112	2356	1	𝐝𝐔	𝐝𝐔	NOUN
m-1112	2356	2	𝐝𝐱	𝐝𝐱	NOUN
m-1112	2356	3	=	=	SYM
m-1112	2356	4	�	�	PROPN
m-1112	2356	5	̈	̈	X
m-1112	2356	6	�	�	NOUN
m-1112	2356	7	…	…	PUNCT
m-1112	2356	8	(	(	PUNCT
m-1112	2356	9	4	4	NUM
m-1112	2356	10	)	)	PUNCT
m-1112	2356	11	i.e.	i.e.	X
m-1112	2356	12	for	for	ADP
m-1112	2356	13	the	the	DET
m-1112	2356	14	conservative	conservative	ADJ
m-1112	2356	15	system	system	NOUN
m-1112	2356	16	,	,	PUNCT
m-1112	2356	17	of	of	ADP
m-1112	2356	18	cave	cave	PROPN
m-1112	2356	19	�	�	PROPN
m-1112	2356	20	̅	̅	NOUN
m-1112	2356	21	�	�	PROPN
m-1112	2356	22	r	r	NOUN
m-1112	2356	23	,	,	PUNCT
m-1112	2356	24	the	the	DET
m-1112	2356	25	force	force	NOUN
m-1112	2356	26	=	=	SYM
m-1112	2356	27	�	�	NOUN
m-1112	2356	28	̅	̅	NOUN
m-1112	2356	29	�	�	NOUN
m-1112	2356	30	=	=	SYM
m-1112	2356	31	r	r	NOUN
m-1112	2356	32	m	m	NOUN
m-1112	2356	33	�	�	NOUN
m-1112	2356	34	̅	̅	NOUN
m-1112	2356	35	�	�	NOUN
m-1112	2356	36	=	=	SYM
m-1112	2356	37	j.w²	j.w²	NOUN
m-1112	2356	38	2	2	NUM
m-1112	2356	39	=	=	SYM
m-1112	2356	40	[	[	PUNCT
m-1112	2356	41	𝛑.𝐫𝟐	𝛑.𝐫𝟐	X
m-1112	2356	42	𝟐	𝟐	NUM
m-1112	2356	43	]	]	PUNCT
m-1112	2356	44	.	.	PUNCT
m-1112	2356	45	�	�	PROPN
m-1112	2356	46	̅	̅	NOUN
m-1112	2356	47	�	�	PROPN
m-1112	2356	48	²	²	NUM
m-1112	2356	49	is	be	AUX
m-1112	2356	50	equal	equal	ADJ
m-1112	2356	51	to	to	ADP
m-1112	2356	52	the	the	DET
m-1112	2356	53	negative	negative	ADJ
m-1112	2356	54	gradient	gradient	NOUN
m-1112	2356	55	of	of	ADP
m-1112	2356	56	the	the	DET
m-1112	2356	57	potential	potential	ADJ
m-1112	2356	58	energy	energy	NOUN
m-1112	2356	59	into	into	ADP
m-1112	2356	60	2	2	NUM
m-1112	2356	61	-	-	PUNCT
m-1112	2356	62	energy	energy	NOUN
m-1112	2356	63	semi	semi	NOUN
m-1112	2356	64	-	-	NOUN
m-1112	2356	65	circles	circle	NOUN
m-1112	2356	66	.	.	PUNCT
m-1112	2357	1	for	for	ADP
m-1112	2357	2	y	y	PROPN
m-1112	2357	3	=	=	SYM
m-1112	2357	4	�	�	PROPN
m-1112	2357	5	̇	̇	PROPN
m-1112	2357	6	�	�	PROPN
m-1112	2357	7	then	then	ADV
m-1112	2357	8	(	(	PUNCT
m-1112	2357	9	3	3	X
m-1112	2357	10	)	)	PUNCT
m-1112	2357	11	becomes	become	VERB
m-1112	2357	12	dy	dy	NOUN
m-1112	2357	13	dx	dx	PROPN
m-1112	2357	14	=	=	SYM
m-1112	2357	15	f	f	PROPN
m-1112	2357	16	(	(	PUNCT
m-1112	2357	17	x	x	X
m-1112	2357	18	)	)	PUNCT
m-1112	2357	19	y	y	PROPN
m-1112	2357	20	=	=	SYM
m-1112	2357	21	φ	φ	PROPN
m-1112	2357	22	(	(	PUNCT
m-1112	2357	23	x	x	PROPN
m-1112	2357	24	,	,	PUNCT
m-1112	2357	25	y	y	PROPN
m-1112	2357	26	)	)	PUNCT
m-1112	2357	27	,	,	PUNCT
m-1112	2357	28	and	and	CCONJ
m-1112	2357	29	the	the	DET
m-1112	2357	30	singular	singular	PROPN
m-1112	2357	31	points	point	NOUN
m-1112	2357	32	correspond	correspond	VERB
m-1112	2357	33	to	to	ADP
m-1112	2357	34	f	f	PROPN
m-1112	2357	35	(	(	PUNCT
m-1112	2357	36	x	x	NOUN
m-1112	2357	37	)	)	PUNCT
m-1112	2357	38	=	=	SYM
m-1112	2357	39	0	0	NUM
m-1112	2357	40	,	,	PUNCT
m-1112	2357	41	and	and	CCONJ
m-1112	2358	1	y	y	PROPN
m-1112	2358	2	=	=	SYM
m-1112	2358	3	ẋ	ẋ	PROPN
m-1112	2359	1	=	=	PUNCT
m-1112	2359	2	0	0	PUNCT
m-1112	2360	1	and	and	CCONJ
m-1112	2360	2	hence	hence	ADV
m-1112	2360	3	are	be	AUX
m-1112	2360	4	the	the	DET
m-1112	2360	5	equilibrium	equilibrium	NOUN
m-1112	2360	6	points	point	NOUN
m-1112	2360	7	.	.	PUNCT
m-1112	2361	1	for	for	ADP
m-1112	2361	2	every	every	DET
m-1112	2361	3	point	point	NOUN
m-1112	2361	4	x	x	X
m-1112	2361	5	,	,	PUNCT
m-1112	2361	6	y	y	PROPN
m-1112	2361	7	in	in	ADP
m-1112	2361	8	the	the	DET
m-1112	2361	9	phase	phase	NOUN
m-1112	2361	10	-	-	PUNCT
m-1112	2361	11	plane	plane	NOUN
m-1112	2361	12	for	for	ADP
m-1112	2361	13	which	which	PRON
m-1112	2361	14	φ	φ	PROPN
m-1112	2361	15	(	(	PUNCT
m-1112	2361	16	x	x	PROPN
m-1112	2361	17	y	y	NOUN
m-1112	2361	18	)	)	PUNCT
m-1112	2361	19	is	be	AUX
m-1112	2361	20	not	not	PART
m-1112	2361	21	indeterminate	indeterminate	ADJ
m-1112	2361	22	exists	exist	VERB
m-1112	2361	23	a	a	DET
m-1112	2361	24	unique	unique	ADJ
m-1112	2361	25	slope	slope	NOUN
m-1112	2361	26	of	of	ADP
m-1112	2361	27	the	the	DET
m-1112	2361	28	trajectory	trajectory	NOUN
m-1112	2361	29	.	.	PUNCT
m-1112	2362	1	when	when	SCONJ
m-1112	2362	2	the	the	DET
m-1112	2362	3	velocity	velocity	NOUN
m-1112	2362	4	vector	vector	NOUN
m-1112	2362	5	is	be	AUX
m-1112	2362	6	at	at	ADP
m-1112	2362	7	points	point	NOUN
m-1112	2362	8	1,2	1,2	NUM
m-1112	2362	9	then	then	ADV
m-1112	2362	10	y	y	PROPN
m-1112	2362	11	=	=	SYM
m-1112	2362	12	0	0	PROPN
m-1112	2362	13	and	and	CCONJ
m-1112	2362	14	f(x	f(x	PROPN
m-1112	2362	15	,	,	PUNCT
m-1112	2362	16	y	y	PROPN
m-1112	2362	17	)	)	PUNCT
m-1112	2363	1	=	=	PUNCT
m-1112	2363	2	c	c	X
m-1112	2363	3	≠	≠	PROPN
m-1112	2363	4	0	0	NUM
m-1112	2363	5	then	then	ADV
m-1112	2363	6	the	the	DET
m-1112	2363	7	slope	slope	NOUN
m-1112	2363	8	of	of	ADP
m-1112	2363	9	the	the	DET
m-1112	2363	10	trajectory	trajectory	NOUN
m-1112	2363	11	is	be	AUX
m-1112	2363	12	infinite	infinite	ADJ
m-1112	2363	13	and	and	CCONJ
m-1112	2363	14	angle	angle	NOUN
m-1112	2363	15	φ	φ	PROPN
m-1112	2363	16	=	=	PROPN
m-1112	2363	17	90ᶱ	90ᶱ	PROPN
m-1112	2363	18	.	.	PUNCT
m-1112	2364	1	since	since	SCONJ
m-1112	2364	2	motion	motion	NOUN
m-1112	2364	3	in	in	ADP
m-1112	2364	4	cave	cave	PROPN
m-1112	2364	5	�	�	PROPN
m-1112	2364	6	̅	̅	NOUN
m-1112	2364	7	�	�	PROPN
m-1112	2364	8	r	r	NOUN
m-1112	2364	9	,	,	PUNCT
m-1112	2364	10	is	be	AUX
m-1112	2364	11	a	a	DET
m-1112	2364	12	single	single	ADJ
m-1112	2364	13	-	-	PUNCT
m-1112	2364	14	dof	dof	NOUN
m-1112	2364	15	oscillator	oscillator	NOUN
m-1112	2364	16	,	,	PUNCT
m-1112	2364	17	then	then	ADV
m-1112	2364	18	motion	motion	NOUN
m-1112	2364	19	equation	equation	NOUN
m-1112	2364	20	is	be	AUX
m-1112	2364	21	ẍ	ẍ	X
m-1112	2365	1	+	+	CCONJ
m-1112	2365	2	w²	w²	NOUN
m-1112	2365	3	x	x	SYM
m-1112	2365	4	=	=	SYM
m-1112	2365	5	0	0	NUM
m-1112	2365	6	.equation	.equation	NUM
m-1112	2365	7	indicates	indicate	VERB
m-1112	2365	8	that	that	SCONJ
m-1112	2365	9	at	at	ADP
m-1112	2365	10	the	the	DET
m-1112	2365	11	equilibrium	equilibrium	NOUN
m-1112	2365	12	singular	singular	ADJ
m-1112	2365	13	points	point	NOUN
m-1112	2365	14	,	,	PUNCT
m-1112	2365	15	3	3	NUM
m-1112	2365	16	,	,	PUNCT
m-1112	2365	17	4	4	NUM
m-1112	2365	18	,	,	PUNCT
m-1112	2365	19	the	the	DET
m-1112	2365	20	slope	slope	NOUN
m-1112	2365	21	of	of	ADP
m-1112	2365	22	the	the	DET
m-1112	2365	23	potential	potential	ADJ
m-1112	2365	24	energy	energy	NOUN
m-1112	2365	25	curve	curve	NOUN
m-1112	2365	26	u(x	u(x	NOUN
m-1112	2365	27	)	)	PUNCT
m-1112	2365	28	must	must	AUX
m-1112	2365	29	be	be	AUX
m-1112	2365	30	zero	zero	NUM
m-1112	2365	31	,	,	PUNCT
m-1112	2365	32	meaning	mean	VERB
m-1112	2365	33	minima	minima	NOUN
m-1112	2365	34	or	or	CCONJ
m-1112	2365	35	maxima	maxima	NOUN
m-1112	2365	36	,	,	PUNCT
m-1112	2365	37	and	and	CCONJ
m-1112	2365	38	which	which	PRON
m-1112	2365	39	is	be	AUX
m-1112	2365	40	the	the	DET
m-1112	2365	41	±	±	NUM
m-1112	2365	42	change	change	NOUN
m-1112	2365	43	of	of	ADP
m-1112	2365	44	direction	direction	NOUN
m-1112	2365	45	for	for	ADP
m-1112	2365	46	the	the	DET
m-1112	2365	47	four	four	NUM
m-1112	2365	48	energyquarter	energyquarter	ADJ
m-1112	2365	49	circles	circle	NOUN
m-1112	2365	50	[	[	X
m-1112	2365	51	1	1	NUM
m-1112	2365	52	-	-	PUNCT
m-1112	2365	53	o-4	o-4	NOUN
m-1112	2365	54	]	]	PUNCT
m-1112	2365	55	,	,	PUNCT
m-1112	2366	1	[	[	X
m-1112	2366	2	4	4	NUM
m-1112	2366	3	-	-	NUM
m-1112	2366	4	o-2	o-2	VERB
m-1112	2366	5	]	]	PUNCT
m-1112	2366	6	,	,	PUNCT
m-1112	2367	1	[	[	X
m-1112	2367	2	2	2	NUM
m-1112	2367	3	-	-	NUM
m-1112	2367	4	o-3	o-3	NOUN
m-1112	2367	5	]	]	PUNCT
m-1112	2367	6	,	,	PUNCT
m-1112	2368	1	[	[	X
m-1112	2368	2	3	3	NUM
m-1112	2368	3	-	-	SYM
m-1112	2368	4	o-1	o-1	NOUN
m-1112	2368	5	]	]	PUNCT
m-1112	2368	6	in	in	ADP
m-1112	2368	7	(	(	PUNCT
m-1112	2368	8	cx	cx	INTJ
m-1112	2368	9	,	,	PUNCT
m-1112	2368	10	cy	cy	PROPN
m-1112	2368	11	)	)	PUNCT
m-1112	2369	1	where	where	SCONJ
m-1112	2369	2	𝐜𝐲	𝐜𝐲	PRON
m-1112	2369	3	̅̅̅̅	̅̅̅̅	ADJ
m-1112	2369	4	=	=	PUNCT
m-1112	2369	5	�	�	PROPN
m-1112	2369	6	̅	̅	NOUN
m-1112	2369	7	�	�	NOUN
m-1112	2369	8	=	=	PUNCT
m-1112	2369	9	spin	spin	NOUN
m-1112	2369	10	direction	direction	NOUN
m-1112	2369	11	,	,	PUNCT
m-1112	2369	12	conclusions	conclusion	NOUN
m-1112	2369	13	:	:	PUNCT
m-1112	2369	14	1	1	NUM
m-1112	2369	15	…	…	PUNCT
m-1112	2369	16	from	from	ADP
m-1112	2369	17	a	a	DET
m-1112	2369	18	-	-	PUNCT
m-1112	2369	19	momentum	momentum	NOUN
m-1112	2369	20	�	�	NOUN
m-1112	2369	21	̅	̅	NOUN
m-1112	2369	22	�	�	NOUN
m-1112	2369	23	=	=	SYM
m-1112	2369	24	r	r	NOUN
m-1112	2369	25	m	m	NOUN
m-1112	2369	26	�	�	NOUN
m-1112	2369	27	̅	̅	NOUN
m-1112	2369	28	�	�	NOUN
m-1112	2369	29	=	=	SYM
m-1112	2369	30	j.w²	j.w²	NOUN
m-1112	2369	31	2	2	NUM
m-1112	2369	32	=	=	SYM
m-1112	2369	33	𝟏	𝟏	NUM
m-1112	2369	34	𝟐	𝟐	NUM
m-1112	2369	35	[	[	PUNCT
m-1112	2369	36	�	�	PROPN
m-1112	2369	37	̇	̇	NOUN
m-1112	2369	38	�	�	PROPN
m-1112	2369	39	]²	]²	X
m-1112	2369	40	+	+	NOUN
m-1112	2369	41	u(x	u(x	NOUN
m-1112	2369	42	)	)	PUNCT
m-1112	2369	43	=	=	SYM
m-1112	2369	44	𝟏	𝟏	NUM
m-1112	2369	45	𝟐	𝟐	NUM
m-1112	2369	46	[	[	PUNCT
m-1112	2369	47	y]²	y]²	X
m-1112	2369	48	+	+	CCONJ
m-1112	2369	49	𝟏	𝟏	NUM
m-1112	2369	50	𝟐	𝟐	NUM
m-1112	2369	51	k	k	PROPN
m-1112	2369	52	x²	x²	PROPN
m-1112	2369	53	=	=	PUNCT
m-1112	2369	54	constant	constant	ADJ
m-1112	2369	55	,	,	PUNCT
m-1112	2369	56	then	then	ADV
m-1112	2369	57	spin	spin	VERB
m-1112	2369	58	s	s	PROPN
m-1112	2369	59	≡	≡	PROPN
m-1112	2369	60	�	�	PROPN
m-1112	2369	61	̅	̅	NOUN
m-1112	2369	62	�	�	NOUN
m-1112	2369	63	=	=	SYM
m-1112	2369	64	1	1	NUM
m-1112	2369	65	2	2	NUM
m-1112	2369	66	[	[	X
m-1112	2369	67	y]²	y]²	X
m-1112	2369	68	+	+	CCONJ
m-1112	2369	69	1	1	NUM
m-1112	2369	70	2	2	NUM
m-1112	2369	71	k	k	NOUN
m-1112	2369	72	x²	x²	PROPN
m-1112	2369	73	=	=	PUNCT
m-1112	2370	1	[	[	X
m-1112	2370	2	y	y	X
m-1112	2370	3	]	]	X
m-1112	2370	4	²	²	PROPN
m-1112	2370	5	+	+	SYM
m-1112	2370	6	w	w	PROPN
m-1112	2370	7	²	²	NUM
m-1112	2370	8	x²	x²	NOUN
m-1112	2370	9	=	=	PUNCT
m-1112	2370	10	c	c	NOUN
m-1112	2370	11	=	=	PUNCT
m-1112	2370	12	constant	constant	ADJ
m-1112	2370	13	,	,	PUNCT
m-1112	2370	14	or	or	CCONJ
m-1112	2370	15	→	→	ADP
m-1112	2370	16	y²	y²	PROPN
m-1112	2370	17	+	+	CCONJ
m-1112	2370	18	w²	w²	PROPN
m-1112	2370	19	x²	x²	NOUN
m-1112	2370	20	=	=	SYM
m-1112	2370	21	c	c	PROPN
m-1112	2370	22	←	←	PROPN
m-1112	2370	23	…	…	PROPN
m-1112	2370	24	.(a	.(a	SYM
m-1112	2370	25	)	)	PUNCT
m-1112	2370	26	equation	equation	NOUN
m-1112	2370	27	(	(	PUNCT
m-1112	2370	28	a	a	X
m-1112	2370	29	)	)	PUNCT
m-1112	2370	30	is	be	AUX
m-1112	2370	31	a	a	DET
m-1112	2370	32	series	series	NOUN
m-1112	2370	33	of	of	ADP
m-1112	2370	34	ellipses	ellipsis	NOUN
m-1112	2370	35	determined	determine	VERB
m-1112	2370	36	by	by	ADP
m-1112	2370	37	c	c	PROPN
m-1112	2370	38	,	,	PUNCT
m-1112	2370	39	and	and	CCONJ
m-1112	2370	40	for	for	ADP
m-1112	2370	41	w	w	NOUN
m-1112	2370	42	=	=	SYM
m-1112	2370	43	1	1	NUM
m-1112	2370	44	y	y	PROPN
m-1112	2370	45	/	/	SYM
m-1112	2370	46	w	w	NOUN
m-1112	2370	47	=	=	SYM
m-1112	2370	48	y	y	PROPN
m-1112	2370	49	then	then	ADV
m-1112	2370	50	reduce	reduce	VERB
m-1112	2370	51	to	to	ADP
m-1112	2370	52	circles	circle	NOUN
m-1112	2370	53	y²	y²	PROPN
m-1112	2371	1	+	+	CCONJ
m-1112	2371	2	x²	x²	PROPN
m-1112	2371	3	=	=	PUNCT
m-1112	2371	4	c	c	PROPN
m-1112	2371	5	,	,	PUNCT
m-1112	2371	6	in	in	ADP
m-1112	2371	7	�	�	NOUN
m-1112	2371	8	̅	̅	NOUN
m-1112	2371	9	�	�	NOUN
m-1112	2371	10	r	r	NOUN
m-1112	2371	11	plane	plane	NOUN
m-1112	2371	12	and	and	CCONJ
m-1112	2371	13	perpendicular	perpendicular	NOUN
m-1112	2371	14	to	to	ADP
m-1112	2371	15	s	s	PRON
m-1112	2371	16	since	since	ADV
m-1112	2371	17	,	,	PUNCT
m-1112	2371	18	[	[	PUNCT
m-1112	2371	19	�	�	NOUN
m-1112	2371	20	̅	̅	NOUN
m-1112	2371	21	�	�	NOUN
m-1112	2371	22	r	r	NOUN
m-1112	2371	23	]	]	PUNCT
m-1112	2371	24	⊥	⊥	PROPN
m-1112	2371	25	�	�	PROPN
m-1112	2371	26	̅	̅	NOUN
m-1112	2371	27	�	�	PROPN
m-1112	2371	28	.	.	PUNCT
m-1112	2372	1	2	2	NUM
m-1112	2372	2	…	…	PUNCT
m-1112	2372	3	in	in	ADP
m-1112	2372	4	the	the	DET
m-1112	2372	5	conservative	conservative	ADJ
m-1112	2372	6	system	system	NOUN
m-1112	2372	7	of	of	ADP
m-1112	2372	8	cave	cave	PROPN
m-1112	2372	9	�	�	PROPN
m-1112	2372	10	̅	̅	NOUN
m-1112	2372	11	�	�	PROPN
m-1112	2372	12	r	r	NOUN
m-1112	2372	13	,	,	PUNCT
m-1112	2372	14	where	where	SCONJ
m-1112	2372	15	�	�	NOUN
m-1112	2372	16	̅	̅	NOUN
m-1112	2372	17	�	�	NOUN
m-1112	2372	18	=	=	PUNCT
m-1112	2372	19	light	light	ADJ
m-1112	2372	20	-	-	PUNCT
m-1112	2372	21	velocity	velocity	NOUN
m-1112	2372	22	=	=	SYM
m-1112	2372	23	2.9985163	2.9985163	NUM
m-1112	2372	24	.	.	NOUN
m-1112	2372	25	108	108	NUM
m-1112	2372	26	m	m	NOUN
m-1112	2372	27	/	/	SYM
m-1112	2372	28	s	s	PROPN
m-1112	2372	29	,	,	PUNCT
m-1112	2372	30	r	r	NOUN
m-1112	2372	31	=	=	SYM
m-1112	2372	32	planck`s	planck`s	NOUN
m-1112	2372	33	-length	-length	NOUN
m-1112	2372	34	=	=	SYM
m-1112	2372	35	√2	√2	NOUN
m-1112	2372	36	4	4	NUM
m-1112	2372	37	.	.	PUNCT
m-1112	2373	1	10−35	10−35	NUM
m-1112	2373	2	m	m	NOUN
m-1112	2373	3	,	,	PUNCT
m-1112	2373	4	motion	motion	NOUN
m-1112	2373	5	in	in	ADP
m-1112	2373	6	cave	cave	NOUN
m-1112	2373	7	is	be	AUX
m-1112	2373	8	an	an	DET
m-1112	2373	9	single	single	ADJ
m-1112	2373	10	-	-	PUNCT
m-1112	2373	11	dof	dof	NOUN
m-1112	2373	12	oscillator	oscillator	NOUN
m-1112	2373	13	as	as	ADP
m-1112	2373	14	equation	equation	NOUN
m-1112	2373	15	ẍ	ẍ	PUNCT
m-1112	2374	1	+	+	CCONJ
m-1112	2374	2	w²	w²	NOUN
m-1112	2374	3	x	x	X
m-1112	2374	4	=	=	SYM
m-1112	2374	5	0	0	NUM
m-1112	2374	6	.	.	PUNCT
m-1112	2375	1	equation	equation	NOUN
m-1112	2375	2	of	of	ADP
m-1112	2375	3	motion	motion	NOUN
m-1112	2375	4	is	be	AUX
m-1112	2375	5	a	a	DET
m-1112	2375	6	circle	circle	NOUN
m-1112	2375	7	on	on	ADP
m-1112	2375	8	where	where	SCONJ
m-1112	2375	9	exist	exist	VERB
m-1112	2375	10	the	the	DET
m-1112	2375	11	2	2	NUM
m-1112	2375	12	-	-	PUNCT
m-1112	2375	13	singular	singular	NOUN
m-1112	2375	14	points	point	NOUN
m-1112	2375	15	3	3	NUM
m-1112	2375	16	,	,	PUNCT
m-1112	2375	17	4	4	NUM
m-1112	2375	18	,	,	PUNCT
m-1112	2375	19	meaning	mean	VERB
m-1112	2375	20	minima	minima	NOUN
m-1112	2375	21	or	or	CCONJ
m-1112	2375	22	maxima	maxima	NOUN
m-1112	2375	23	,	,	PUNCT
m-1112	2375	24	where	where	SCONJ
m-1112	2375	25	issues	issue	NOUN
m-1112	2375	26	dy	dy	VERB
m-1112	2375	27	dx	dx	PROPN
m-1112	2375	28	=	=	SYM
m-1112	2375	29	f	f	PROPN
m-1112	2375	30	(	(	PUNCT
m-1112	2375	31	x	x	X
m-1112	2375	32	)	)	PUNCT
m-1112	2375	33	y	y	PROPN
m-1112	2375	34	=	=	SYM
m-1112	2375	35	φ	φ	PROPN
m-1112	2375	36	(	(	PUNCT
m-1112	2375	37	x	x	PROPN
m-1112	2375	38	,	,	PUNCT
m-1112	2375	39	y	y	PROPN
m-1112	2375	40	)	)	PUNCT
m-1112	2375	41	,	,	PUNCT
m-1112	2375	42	and	and	CCONJ
m-1112	2375	43	are	be	AUX
m-1112	2375	44	in	in	ADP
m-1112	2375	45	the	the	DET
m-1112	2375	46	mode	mode	NOUN
m-1112	2375	47	-	-	PUNCT
m-1112	2375	48	shapes	shape	NOUN
m-1112	2375	49	at	at	ADP
m-1112	2375	50	the	the	DET
m-1112	2375	51	points	point	NOUN
m-1112	2375	52	of	of	ADP
m-1112	2375	53	equilibrium	equilibrium	NOUN
m-1112	2375	54	.	.	PUNCT
m-1112	2376	1	at	at	ADP
m-1112	2376	2	singular	singular	PROPN
m-1112	2376	3	points	point	NOUN
m-1112	2376	4	3	3	NUM
m-1112	2376	5	,	,	PUNCT
m-1112	2376	6	4	4	NUM
m-1112	2376	7	,	,	PUNCT
m-1112	2376	8	velocity	velocity	NOUN
m-1112	2376	9	𝐜𝐲	𝐜𝐲	ADP
m-1112	2376	10	̅̅̅̅	̅̅̅̅	ADJ
m-1112	2376	11	=	=	PUNCT
m-1112	2376	12	�	�	PROPN
m-1112	2376	13	̅	̅	NOUN
m-1112	2376	14	�	�	NOUN
m-1112	2376	15	=	=	SYM
m-1112	2376	16	0	0	NUM
m-1112	2376	17	and	and	CCONJ
m-1112	2376	18	spin	spin	VERB
m-1112	2376	19	�	�	NOUN
m-1112	2376	20	̅	̅	NOUN
m-1112	2376	21	�	�	NOUN
m-1112	2376	22	=	=	SYM
m-1112	2376	23	gravity	gravity	NOUN
m-1112	2376	24	=	=	SYM
m-1112	2376	25	0	0	NUM
m-1112	2376	26	,	,	PUNCT
m-1112	2376	27	and	and	CCONJ
m-1112	2376	28	since	since	SCONJ
m-1112	2376	29	dy	dy	X
m-1112	2376	30	dx	dx	PROPN
m-1112	2376	31	<	<	X
m-1112	2376	32	0	0	PUNCT
m-1112	2376	33	,	,	PUNCT
m-1112	2376	34	then	then	ADV
m-1112	2376	35	spin	spin	VERB
m-1112	2376	36	�	�	PROPN
m-1112	2376	37	̅	̅	NOUN
m-1112	2376	38	�	�	NOUN
m-1112	2376	39	changes	change	NOUN
m-1112	2376	40	direction	direction	NOUN
m-1112	2376	41	becoming	become	VERB
m-1112	2376	42	�	�	NOUN
m-1112	2376	43	̅	̅	NOUN
m-1112	2376	44	�	�	NOUN
m-1112	2376	45	=	=	SYM
m-1112	2376	46	antigravity	antigravity	NOUN
m-1112	2376	47	=	=	SYM
m-1112	2376	48	0	0	PROPN
m-1112	2376	49	,	,	PUNCT
m-1112	2376	50	meaning	mean	VERB
m-1112	2376	51	that	that	SCONJ
m-1112	2376	52	at	at	ADP
m-1112	2376	53	singular	singular	ADJ
m-1112	2376	54	points	point	NOUN
m-1112	2376	55	gravity	gravity	NOUN
m-1112	2376	56	&	&	CCONJ
m-1112	2376	57	antigravity	antigravity	NOUN
m-1112	2376	58	are	be	AUX
m-1112	2376	59	zero	zero	NUM
m-1112	2376	60	.	.	PUNCT
m-1112	2377	1	3	3	NUM
m-1112	2377	2	…	…	PUNCT
m-1112	2377	3	at	at	ADP
m-1112	2377	4	point	point	NOUN
m-1112	2377	5	1	1	NUM
m-1112	2377	6	,	,	PUNCT
m-1112	2377	7	velocity	velocity	NOUN
m-1112	2377	8	𝐜𝐲	𝐜𝐲	PRON
m-1112	2377	9	̅̅̅̅	̅̅̅̅	NOUN
m-1112	2377	10	=	=	NOUN
m-1112	2377	11	+	+	NUM
m-1112	2377	12	�	�	NOUN
m-1112	2377	13	̅	̅	NOUN
m-1112	2377	14	�	�	NOUN
m-1112	2377	15	because	because	SCONJ
m-1112	2377	16	of	of	ADP
m-1112	2377	17	𝐜𝐲	𝐜𝐲	NUM
m-1112	2377	18	̅̅̅̅	̅̅̅̅	ADJ
m-1112	2377	19	,	,	PUNCT
m-1112	2377	20	+	+	ADJ
m-1112	2377	21	↓	↓	NOUN
m-1112	2377	22	direction	direction	NOUN
m-1112	2377	23	and	and	CCONJ
m-1112	2377	24	corresponds	correspond	VERB
m-1112	2377	25	the	the	DET
m-1112	2377	26	spin	spin	NOUN
m-1112	2377	27	�	�	NOUN
m-1112	2377	28	̅	̅	NOUN
m-1112	2377	29	�	�	NOUN
m-1112	2377	30	=	=	SYM
m-1112	2377	31	gravity	gravity	NOUN
m-1112	2377	32	=	=	SYM
m-1112	2377	33	�	�	PROPN
m-1112	2377	34	̅	̅	NOUN
m-1112	2377	35	�	�	NOUN
m-1112	2377	36	=	=	SYM
m-1112	2377	37	r	r	NOUN
m-1112	2377	38	m	m	NOUN
m-1112	2377	39	�	�	NOUN
m-1112	2377	40	̅	̅	NOUN
m-1112	2377	41	�	�	NOUN
m-1112	2377	42	which	which	PRON
m-1112	2377	43	is	be	AUX
m-1112	2377	44	constant	constant	ADJ
m-1112	2377	45	and	and	CCONJ
m-1112	2377	46	equal	equal	ADJ
m-1112	2377	47	to	to	ADP
m-1112	2377	48	work	work	NOUN
m-1112	2377	49	=	=	PUNCT
m-1112	2377	50	𝐜𝐲	𝐜𝐲	VERB
m-1112	2377	51	̅̅̅̅	̅̅̅̅	NOUN
m-1112	2377	52	x	x	PUNCT
m-1112	2378	1	[	[	X
m-1112	2378	2	quarter	quarter	NOUN
m-1112	2378	3	circle	circle	NOUN
m-1112	2378	4	1	1	NUM
m-1112	2378	5	-	-	PUNCT
m-1112	2378	6	o-4	o-4	NOUN
m-1112	2378	7	]	]	PUNCT
m-1112	2378	8	at	at	ADP
m-1112	2378	9	point	point	NOUN
m-1112	2378	10	2	2	NUM
m-1112	2378	11	,	,	PUNCT
m-1112	2378	12	velocity	velocity	NOUN
m-1112	2378	13	𝐜𝐲	𝐜𝐲	ADP
m-1112	2378	14	̅̅̅̅	̅̅̅̅	ADJ
m-1112	2378	15	=	=	X
m-1112	2378	16	�	�	PROPN
m-1112	2378	17	̅	̅	NOUN
m-1112	2378	18	�	�	PROPN
m-1112	2378	19	because	because	SCONJ
m-1112	2378	20	of	of	ADP
m-1112	2378	21	𝐜𝐲	𝐜𝐲	NUM
m-1112	2378	22	̅̅̅̅	̅̅̅̅	ADJ
m-1112	2378	23	,	,	PUNCT
m-1112	2378	24	-↑	-↑	PROPN
m-1112	2378	25	direction	direction	NOUN
m-1112	2378	26	and	and	CCONJ
m-1112	2378	27	corresponds	correspond	VERB
m-1112	2378	28	the	the	DET
m-1112	2378	29	spin	spin	NOUN
m-1112	2378	30	�	�	NOUN
m-1112	2378	31	̅	̅	NOUN
m-1112	2378	32	�	�	NOUN
m-1112	2378	33	=	=	SYM
m-1112	2378	34	gravity	gravity	NOUN
m-1112	2378	35	=	=	SYM
m-1112	2378	36	�	�	PROPN
m-1112	2378	37	̅	̅	NOUN
m-1112	2378	38	�	�	NOUN
m-1112	2378	39	=	=	SYM
m-1112	2378	40	r	r	NOUN
m-1112	2378	41	m	m	NOUN
m-1112	2378	42	�	�	NOUN
m-1112	2378	43	̅	̅	NOUN
m-1112	2378	44	�	�	NOUN
m-1112	2378	45	which	which	PRON
m-1112	2378	46	is	be	AUX
m-1112	2378	47	constant	constant	ADJ
m-1112	2378	48	and	and	CCONJ
m-1112	2378	49	equal	equal	ADJ
m-1112	2378	50	to	to	ADP
m-1112	2378	51	work	work	NOUN
m-1112	2378	52	=	=	PUNCT
m-1112	2378	53	𝐜𝐲	𝐜𝐲	VERB
m-1112	2378	54	̅̅̅̅	̅̅̅̅	NOUN
m-1112	2378	55	x	x	PUNCT
m-1112	2379	1	[	[	X
m-1112	2379	2	quarter	quarter	NOUN
m-1112	2379	3	circle	circle	NOUN
m-1112	2379	4	2	2	NUM
m-1112	2379	5	-	-	NUM
m-1112	2379	6	o-3	o-3	NOUN
m-1112	2379	7	]	]	PUNCT
m-1112	2379	8	where	where	SCONJ
m-1112	2379	9	the	the	DET
m-1112	2379	10	[	[	X
m-1112	2379	11	semicircle	semicircle	NOUN
m-1112	2379	12	4	4	NUM
m-1112	2379	13	-	-	SYM
m-1112	2379	14	1	1	NUM
m-1112	2379	15	-	-	SYM
m-1112	2379	16	3	3	NUM
m-1112	2379	17	]	]	PUNCT
m-1112	2379	18	=	=	SYM
m-1112	2379	19	+	+	NUM
m-1112	2379	20	�	�	NOUN
m-1112	2379	21	̅	̅	NOUN
m-1112	2379	22	�	�	NOUN
m-1112	2379	23	≡the	≡the	DET
m-1112	2379	24	gravity	gravity	NOUN
m-1112	2379	25	,	,	PUNCT
m-1112	2379	26	and	and	CCONJ
m-1112	2379	27	[	[	X
m-1112	2379	28	semicircle	semicircle	NOUN
m-1112	2379	29	4	4	NUM
m-1112	2379	30	-	-	SYM
m-1112	2379	31	2	2	NUM
m-1112	2379	32	-	-	SYM
m-1112	2379	33	3	3	NUM
m-1112	2379	34	]	]	PUNCT
m-1112	2379	35	≡	≡	PROPN
m-1112	2379	36	�	�	PROPN
m-1112	2379	37	̅	̅	NOUN
m-1112	2379	38	�	�	NOUN
m-1112	2379	39	=	=	SYM
m-1112	2379	40	the	the	DET
m-1112	2379	41	ijo	ijo	PROPN
m-1112	2379	42	international	international	PROPN
m-1112	2379	43	journal	journal	PROPN
m-1112	2379	44	of	of	ADP
m-1112	2379	45	mathematics	mathematics	PROPN
m-1112	2379	46	(	(	PUNCT
m-1112	2379	47	issn	issn	PROPN
m-1112	2379	48	:	:	PUNCT
m-1112	2379	49	2992	2992	NUM
m-1112	2379	50	-	-	SYM
m-1112	2379	51	4421	4421	NUM
m-1112	2379	52	)	)	PUNCT
m-1112	2379	53	volume	volume	NOUN
m-1112	2379	54	08	08	NUM
m-1112	2380	1	|	|	ADV
m-1112	2380	2	issue	issue	NOUN
m-1112	2380	3	08	08	NUM
m-1112	2381	1	|	|	ADV
m-1112	2381	2	august	august	PROPN
m-1112	2381	3	2025	2025	NUM
m-1112	2381	4	|	|	ADV
m-1112	2381	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2381	6	ijo	ijo	PROPN
m-1112	2381	7	journals	journal	NOUN
m-1112	2381	8	83	83	NUM
m-1112	2381	9	the	the	DET
m-1112	2381	10	fundamental	fundamental	ADJ
m-1112	2381	11	particles	particle	NOUN
m-1112	2381	12	origination	origination	NOUN
m-1112	2381	13	mechanism	mechanism	NOUN
m-1112	2381	14	in	in	ADP
m-1112	2381	15	mfmf	mfmf	PROPN
m-1112	2381	16	pns	pns	PROPN
m-1112	2381	17	caves	cave	NOUN
m-1112	2381	18	.	.	PUNCT
m-1112	2382	1	antigravity	antigravity	NOUN
m-1112	2382	2	.the	.the	PROPN
m-1112	2382	3	produced	produce	VERB
m-1112	2382	4	work	work	NOUN
m-1112	2382	5	from	from	ADP
m-1112	2382	6	the	the	DET
m-1112	2382	7	eternal	eternal	ADJ
m-1112	2382	8	rotation	rotation	NOUN
m-1112	2382	9	is	be	AUX
m-1112	2382	10	store	store	NOUN
m-1112	2382	11	in	in	ADP
m-1112	2382	12	the	the	DET
m-1112	2382	13	semicircles	semicircle	NOUN
m-1112	2382	14	as	as	ADP
m-1112	2382	15	,	,	PUNCT
m-1112	2382	16	(	(	PUNCT
m-1112	2382	17	+	+	ADJ
m-1112	2382	18	)	)	PUNCT
m-1112	2382	19	total	total	ADJ
m-1112	2382	20	work	work	NOUN
m-1112	2383	1	=	=	PUNCT
m-1112	2384	1	[	[	X
m-1112	2384	2	semicircle	semicircle	NOUN
m-1112	2384	3	4	4	NUM
m-1112	2384	4	-	-	SYM
m-1112	2384	5	1	1	NUM
m-1112	2384	6	-	-	SYM
m-1112	2384	7	3	3	NUM
m-1112	2384	8	]	]	PUNCT
m-1112	2384	9	=	=	SYM
m-1112	2384	10	+	+	NUM
m-1112	2384	11	�	�	PROPN
m-1112	2384	12	̅	̅	NOUN
m-1112	2384	13	�	�	PROPN
m-1112	2384	14	and	and	CCONJ
m-1112	2384	15	(	(	PUNCT
m-1112	2384	16	-	-	PUNCT
m-1112	2384	17	)	)	PUNCT
m-1112	2384	18	total	total	ADJ
m-1112	2384	19	work	work	NOUN
m-1112	2384	20	=[	=[	NOUN
m-1112	2384	21	semicircle	semicircle	NOUN
m-1112	2384	22	4	4	NUM
m-1112	2384	23	-	-	SYM
m-1112	2384	24	2	2	NUM
m-1112	2384	25	-	-	SYM
m-1112	2384	26	3	3	NUM
m-1112	2384	27	]	]	PUNCT
m-1112	2384	28	=	=	SYM
m-1112	2384	29	�	�	NOUN
m-1112	2384	30	̅	̅	NOUN
m-1112	2384	31	�	�	NOUN
m-1112	2384	32	4	4	NUM
m-1112	2384	33	…	…	PUNCT
m-1112	2384	34	from	from	ADP
m-1112	2384	35	newton`s	newton`s	PROPN
m-1112	2384	36	law	law	NOUN
m-1112	2384	37	of	of	ADP
m-1112	2384	38	universal	universal	ADJ
m-1112	2384	39	gravitation	gravitation	PROPN
m-1112	2384	40	m	m	PROPN
m-1112	2384	41	r.	r.	PROPN
m-1112	2384	42	�	�	PROPN
m-1112	2384	43	̅	̅	NOUN
m-1112	2384	44	�	�	PROPN
m-1112	2384	45	²	²	NUM
m-1112	2384	46	=	=	SYM
m-1112	2384	47	g	g	PROPN
m-1112	2384	48	𝐦.𝐌	𝐦.𝐌	PROPN
m-1112	2384	49	𝐫	𝐫	ADP
m-1112	2384	50	²	²	NUM
m-1112	2384	51	,	,	PUNCT
m-1112	2384	52	and	and	CCONJ
m-1112	2384	53	when	when	SCONJ
m-1112	2384	54	m	m	VERB
m-1112	2384	55	=	=	SYM
m-1112	2384	56	1	1	NUM
m-1112	2384	57	,	,	PUNCT
m-1112	2384	58	issues	issue	NOUN
m-1112	2384	59	�	�	NOUN
m-1112	2384	60	̅	̅	NOUN
m-1112	2384	61	�	�	PROPN
m-1112	2384	62	²	²	NUM
m-1112	2384	63	=	=	NOUN
m-1112	2384	64	𝐆.𝐌	𝐆.𝐌	X
m-1112	2384	65	𝐫	𝐫	X
m-1112	2384	66	³	³	X
m-1112	2384	67	,	,	PUNCT
m-1112	2384	68	and	and	CCONJ
m-1112	2384	69	b	b	X
m-1112	2384	70	=	=	SYM
m-1112	2384	71	j	j	PROPN
m-1112	2384	72	w	w	NOUN
m-1112	2384	73	,	,	PUNCT
m-1112	2384	74	therefore	therefore	ADV
m-1112	2384	75	angular	angular	ADJ
m-1112	2384	76	velocity	velocity	NOUN
m-1112	2384	77	�	�	NOUN
m-1112	2384	78	̅	̅	NOUN
m-1112	2384	79	�	�	NOUN
m-1112	2384	80	=	=	SYM
m-1112	2384	81	±	±	PROPN
m-1112	2384	82	√	√	PROPN
m-1112	2384	83	gm	gm	PROPN
m-1112	2384	84	r³	r³	PROPN
m-1112	2384	85	2	2	NUM
m-1112	2384	86	=	=	SYM
m-1112	2384	87	√	√	PROPN
m-1112	2384	88	gπ.r4	gπ.r4	NOUN
m-1112	2384	89	2.r³	2.r³	NOUN
m-1112	2384	90	2	2	NUM
m-1112	2384	91	=	=	SYM
m-1112	2384	92	√	√	PROPN
m-1112	2384	93	π.gr	π.gr	ADJ
m-1112	2384	94	2	2	NUM
m-1112	2384	95	2	2	NUM
m-1112	2384	96	.	.	PUNCT
m-1112	2385	1	this	this	DET
m-1112	2385	2	angular	angular	ADJ
m-1112	2385	3	-	-	PUNCT
m-1112	2385	4	momentum	momentum	NOUN
m-1112	2385	5	is	be	AUX
m-1112	2385	6	identical	identical	ADJ
m-1112	2385	7	with	with	ADP
m-1112	2385	8	spin	spin	NOUN
m-1112	2385	9	which	which	PRON
m-1112	2385	10	is	be	AUX
m-1112	2385	11	trapped	trap	VERB
m-1112	2385	12	in	in	ADP
m-1112	2385	13	caves`s	caves`s	PROPN
m-1112	2385	14	loops	loop	NOUN
m-1112	2385	15	which	which	PRON
m-1112	2385	16	are	be	AUX
m-1112	2385	17	in	in	ADP
m-1112	2385	18	phase	phase	NOUN
m-1112	2385	19	with	with	ADP
m-1112	2385	20	each	each	DET
m-1112	2385	21	other	other	ADJ
m-1112	2385	22	.	.	PUNCT
m-1112	2386	1	the	the	DET
m-1112	2386	2	amplitude	amplitude	NOUN
m-1112	2386	3	of	of	ADP
m-1112	2386	4	oscillation	oscillation	NOUN
m-1112	2386	5	varies	vary	VERB
m-1112	2386	6	from	from	ADP
m-1112	2386	7	zero	zero	NUM
m-1112	2386	8	at	at	ADP
m-1112	2386	9	nodes	node	NOUN
m-1112	2386	10	to	to	PART
m-1112	2386	11	maxima	maxima	VERB
m-1112	2386	12	at	at	ADP
m-1112	2386	13	antinodes	antinode	NOUN
m-1112	2386	14	.since	.since	PROPN
m-1112	2386	15	frequency	frequency	NOUN
m-1112	2386	16	≡	≡	PROPN
m-1112	2386	17	𝐟𝐧	𝐟𝐧	PROPN
m-1112	2386	18	=	=	PUNCT
m-1112	2386	19	(	(	PUNCT
m-1112	2386	20	nσ	nσ	NOUN
m-1112	2386	21	8	8	NUM
m-1112	2386	22	r	r	NOUN
m-1112	2386	23	²	²	NUM
m-1112	2386	24	)	)	PUNCT
m-1112	2386	25	.	.	PUNCT
m-1112	2387	1	�	�	PROPN
m-1112	2387	2	̅	̅	NOUN
m-1112	2387	3	�	�	PROPN
m-1112	2387	4	,	,	PUNCT
m-1112	2387	5	so	so	SCONJ
m-1112	2387	6	energy	energy	NOUN
m-1112	2387	7	-	-	PUNCT
m-1112	2387	8	caves	cave	NOUN
m-1112	2387	9	are	be	AUX
m-1112	2387	10	stationary	stationary	ADJ
m-1112	2387	11	wave	wave	NOUN
m-1112	2387	12	-	-	PUNCT
m-1112	2387	13	fringes	fringe	NOUN
m-1112	2387	14	5	5	NUM
m-1112	2387	15	…	…	PUNCT
m-1112	2387	16	the	the	DET
m-1112	2387	17	total	total	ADJ
m-1112	2387	18	-	-	PUNCT
m-1112	2387	19	energy	energy	NOUN
m-1112	2387	20	,	,	PUNCT
m-1112	2387	21	e	e	PROPN
m-1112	2387	22	t	t	NOUN
m-1112	2387	23	,	,	PUNCT
m-1112	2387	24	in	in	ADP
m-1112	2387	25	caves	cave	NOUN
m-1112	2387	26	,	,	PUNCT
m-1112	2387	27	[	[	X
m-1112	2387	28	70	70	NUM
m-1112	2387	29	]	]	X
m-1112	2387	30	a	a	X
m-1112	2387	31	…	…	PUNCT
m-1112	2387	32	→	→	SYM
m-1112	2387	33	in	in	ADP
m-1112	2387	34	any	any	DET
m-1112	2387	35	moving	move	VERB
m-1112	2387	36	system	system	NOUN
m-1112	2387	37	e	e	NOUN
m-1112	2387	38	t	t	NOUN
m-1112	2387	39	=	=	SYM
m-1112	2387	40	e	e	NOUN
m-1112	2387	41	r	r	NOUN
m-1112	2387	42	+	+	NOUN
m-1112	2387	43	e	e	X
m-1112	2387	44	k	k	X
m-1112	2387	45	=	=	PUNCT
m-1112	2387	46	πc²	πc²	PROPN
m-1112	2387	47	8	8	NUM
m-1112	2387	48	r³	r³	NOUN
m-1112	2387	49	+	+	NOUN
m-1112	2387	50	1	1	NUM
m-1112	2387	51	2	2	NUM
m-1112	2387	52	m.v²	m.v²	NOUN
m-1112	2387	53	=	=	SYM
m-1112	2387	54	3,535.1016	3,535.1016	NUM
m-1112	2387	55	.	.	PUNCT
m-1112	2388	1	r	r	NOUN
m-1112	2388	2	³	³	PROPN
m-1112	2388	3	+	+	CCONJ
m-1112	2388	4	1	1	NUM
m-1112	2388	5	2	2	NUM
m-1112	2388	6	m.v²	m.v²	NOUN
m-1112	2388	7	,	,	PUNCT
m-1112	2388	8	b	b	X
m-1112	2388	9	…	…	PUNCT
m-1112	2388	10	→	→	PUNCT
m-1112	2388	11	light	light	ADJ
m-1112	2388	12	-	-	PUNCT
m-1112	2388	13	velocity	velocity	NOUN
m-1112	2388	14	c̅	c̅	PROPN
m-1112	2388	15	of	of	ADP
m-1112	2388	16	photons	photon	NOUN
m-1112	2388	17	becomes	become	VERB
m-1112	2388	18	from	from	ADP
m-1112	2388	19	the	the	DET
m-1112	2388	20	action	action	NOUN
m-1112	2388	21	of	of	ADP
m-1112	2388	22	g	g	NOUN
m-1112	2388	23	on	on	ADP
m-1112	2388	24	plancks	planck	NOUN
m-1112	2388	25	length	length	NOUN
m-1112	2389	1	lp	lp	NOUN
m-1112	2389	2	=	=	PUNCT
m-1112	2389	3	r	r	NOUN
m-1112	2389	4	p	p	NOUN
m-1112	2389	5	=	=	NOUN
m-1112	2389	6	1,6162.10−35	1,6162.10−35	NUM
m-1112	2389	7	m	m	NOUN
m-1112	2389	8	cave	cave	NOUN
m-1112	2389	9	r	r	NOUN
m-1112	2389	10	,	,	PUNCT
m-1112	2389	11	and	and	CCONJ
m-1112	2389	12	when	when	SCONJ
m-1112	2389	13	cave	cave	NOUN
m-1112	2389	14	r	r	NOUN
m-1112	2389	15	=	=	SYM
m-1112	2389	16	𝐡	𝐡	NOUN
m-1112	2389	17	𝐜.𝐙𝐜	𝐜.𝐙𝐜	NOUN
m-1112	2389	18	≠	≠	PROPN
m-1112	2389	19	𝐋	𝐋	PROPN
m-1112	2389	20	𝐏	𝐏	PROPN
m-1112	2389	21	originates	originate	VERB
m-1112	2389	22	hydrogen	hydrogen	NOUN
m-1112	2389	23	-	-	PUNCT
m-1112	2389	24	cave	cave	NOUN
m-1112	2389	25	.	.	PUNCT
m-1112	2390	1	it	it	PRON
m-1112	2390	2	is	be	AUX
m-1112	2390	3	shown	show	VERB
m-1112	2390	4	later	later	ADV
m-1112	2390	5	that	that	SCONJ
m-1112	2390	6	when	when	SCONJ
m-1112	2390	7	the	the	DET
m-1112	2390	8	g	g	PROPN
m-1112	2390	9	action	action	NOUN
m-1112	2390	10	area	area	NOUN
m-1112	2390	11	resistance	resistance	NOUN
m-1112	2390	12	≡	≡	PROPN
m-1112	2390	13	gravitational	gravitational	ADJ
m-1112	2390	14	-	-	PUNCT
m-1112	2390	15	impedance	impedance	NOUN
m-1112	2390	16	z	z	NOUN
m-1112	2390	17	g−i	g−i	NOUN
m-1112	2390	18	=	=	SYM
m-1112	2390	19	6,344907.10−35	6,344907.10−35	NUM
m-1112	2390	20	kg	kg	NOUN
m-1112	2390	21	differs	differ	VERB
m-1112	2390	22	for	for	ADP
m-1112	2390	23	any	any	DET
m-1112	2390	24	reason	reason	NOUN
m-1112	2390	25	then	then	ADV
m-1112	2390	26	black	black	ADJ
m-1112	2390	27	-	-	PUNCT
m-1112	2390	28	holes	hole	NOUN
m-1112	2390	29	happen	happen	VERB
m-1112	2390	30	.	.	PUNCT
m-1112	2391	1	c	c	X
m-1112	2391	2	…	…	PUNCT
m-1112	2391	3	→	→	SYM
m-1112	2391	4	euler`s	euler`s	X
m-1112	2391	5	rotating	rotate	VERB
m-1112	2391	6	rigid	rigid	ADJ
m-1112	2391	7	body	body	NOUN
m-1112	2391	8	.the	.the	PUNCT
m-1112	2392	1	d	d	X
m-1112	2392	2	-	-	PUNCT
m-1112	2392	3	work	work	NOUN
m-1112	2392	4	is	be	AUX
m-1112	2392	5	w	w	NOUN
m-1112	2392	6	=	=	PUNCT
m-1112	2392	7	2l	2l	NOUN
m-1112	2392	8	=	=	SYM
m-1112	2392	9	b̅	b̅	PROPN
m-1112	2392	10	.	.	PUNCT
m-1112	2393	1	w̅	w̅	X
m-1112	2394	1	=	=	SYM
m-1112	2394	2	j	j	PROPN
m-1112	2394	3	.w²	.w²	PUNCT
m-1112	2394	4	≡	≡	PROPN
m-1112	2394	5	h.	h.	PROPN
m-1112	2394	6	𝐟𝐧	𝐟𝐧	PROPN
m-1112	2394	7	,	,	PUNCT
m-1112	2394	8	and	and	CCONJ
m-1112	2394	9	for	for	ADP
m-1112	2394	10	m	m	PROPN
m-1112	2394	11	mass	mass	PROPN
m-1112	2394	12	w	w	NOUN
m-1112	2394	13	=	=	PUNCT
m-1112	2394	14	h	h	NOUN
m-1112	2394	15	fm	fm	NOUN
m-1112	2394	16	,	,	PUNCT
m-1112	2394	17	angular	angular	ADJ
m-1112	2394	18	-	-	PUNCT
m-1112	2394	19	momentum	momentum	NOUN
m-1112	2394	20	�	�	NOUN
m-1112	2394	21	̅	̅	NOUN
m-1112	2394	22	�	�	NOUN
m-1112	2394	23	=	=	SYM
m-1112	2394	24	2l	2l	NOUN
m-1112	2394	25	w̅	w̅	PUNCT
m-1112	2395	1	=	=	SYM
m-1112	2395	2	2l	2l	NUM
m-1112	2395	3	2πf	2πf	NOUN
m-1112	2396	1	=	=	PUNCT
m-1112	2397	1	[	[	PUNCT
m-1112	2397	2	2l	2l	NUM
m-1112	2397	3	2π	2π	NOUN
m-1112	2397	4	]	]	PUNCT
m-1112	2397	5	.	.	PUNCT
m-1112	2398	1	[	[	PUNCT
m-1112	2398	2	1	1	NUM
m-1112	2398	3	f	f	NOUN
m-1112	2398	4	]	]	X
m-1112	2398	5	=	=	PUNCT
m-1112	2398	6	constant	constant	ADJ
m-1112	2398	7	2π	2π	NOUN
m-1112	2398	8	[	[	PUNCT
m-1112	2398	9	1	1	NUM
m-1112	2398	10	fm	fm	NOUN
m-1112	2398	11	]=	]=	NUM
m-1112	2398	12	spin	spin	NOUN
m-1112	2398	13	d	d	X
m-1112	2398	14	…	…	PUNCT
m-1112	2398	15	→	→	SYM
m-1112	2398	16	in	in	ADP
m-1112	2398	17	central	central	ADJ
m-1112	2398	18	-	-	PUNCT
m-1112	2398	19	motion	motion	NOUN
m-1112	2398	20	,	,	PUNCT
m-1112	2398	21	kepler	kepler	PROPN
m-1112	2398	22	constant	constant	ADJ
m-1112	2398	23	k	k	PROPN
m-1112	2398	24	=	=	SYM
m-1112	2398	25	4π²	4π²	PROPN
m-1112	2398	26	.	.	PUNCT
m-1112	2398	27	r³.	r³.	NOUN
m-1112	2398	28	fp²	fp²	PROPN
m-1112	2398	29	,	,	PUNCT
m-1112	2398	30	or	or	CCONJ
m-1112	2398	31	1	1	NUM
m-1112	2398	32	=	=	NOUN
m-1112	2398	33	[	[	PUNCT
m-1112	2398	34	4𝜋²	4𝜋²	NUM
m-1112	2398	35	𝑘	𝑘	X
m-1112	2398	36	]	]	PUNCT
m-1112	2398	37	r³.	r³.	NUM
m-1112	2398	38	fp²	fp²	PROPN
m-1112	2398	39	,	,	PUNCT
m-1112	2398	40	1	1	NUM
m-1112	2398	41	=	=	SYM
m-1112	2398	42	c	c	NOUN
m-1112	2398	43	.	.	PUNCT
m-1112	2399	1	r³.	r³.	NOUN
m-1112	2399	2	𝐟𝐏²	𝐟𝐏²	PROPN
m-1112	2399	3	where	where	SCONJ
m-1112	2399	4	for	for	ADP
m-1112	2399	5	→	→	SYM
m-1112	2399	6	r	r	NOUN
m-1112	2399	7	→	→	SYM
m-1112	2399	8	0	0	NUM
m-1112	2399	9	then	then	ADV
m-1112	2399	10	𝐟	𝐟	PROPN
m-1112	2399	11	𝐏	𝐏	PROPN
m-1112	2399	12	→	→	SYM
m-1112	2399	13	∞	∞	PROPN
m-1112	2399	14	←	←	PROPN
m-1112	2399	15	,	,	PUNCT
m-1112	2399	16	a	a	DET
m-1112	2399	17	case	case	NOUN
m-1112	2399	18	of	of	ADP
m-1112	2399	19	a	a	DET
m-1112	2399	20	black	black	ADJ
m-1112	2399	21	-	-	PUNCT
m-1112	2399	22	hole	hole	NOUN
m-1112	2399	23	in	in	ADP
m-1112	2399	24	any	any	DET
m-1112	2399	25	central	central	ADJ
m-1112	2399	26	motion	motion	NOUN
m-1112	2399	27	.	.	PUNCT
m-1112	2400	1	e	e	X
m-1112	2400	2	…	…	PUNCT
m-1112	2400	3	→the	→the	DET
m-1112	2400	4	vibrations	vibration	NOUN
m-1112	2400	5	in	in	ADP
m-1112	2400	6	orbit	orbit	NOUN
m-1112	2400	7	-	-	PUNCT
m-1112	2400	8	systems	system	NOUN
m-1112	2400	9	are	be	AUX
m-1112	2400	10	as	as	ADP
m-1112	2400	11	→	→	SYM
m-1112	2400	12	w	w	X
m-1112	2400	13	=	=	SYM
m-1112	2400	14	4π²	4π²	NUM
m-1112	2400	15	.	.	PUNCT
m-1112	2401	1	[	[	PUNCT
m-1112	2401	2	𝐫³	𝐫³	NOUN
m-1112	2401	3	𝐓²	𝐓²	VERB
m-1112	2401	4	]	]	PUNCT
m-1112	2401	5	.	.	PUNCT
m-1112	2402	1	�	�	NOUN
m-1112	2402	2	̅	̅	NOUN
m-1112	2402	3	�	�	PROPN
m-1112	2402	4	=	=	SYM
m-1112	2402	5	4π²	4π²	NUM
m-1112	2402	6	.	.	PUNCT
m-1112	2403	1	r	r	NOUN
m-1112	2403	2	³.	³.	X
m-1112	2403	3	𝐟²𝐩	𝐟²𝐩	PROPN
m-1112	2403	4	.	.	PUNCT
m-1112	2404	1	�	�	PROPN
m-1112	2404	2	̅	̅	NOUN
m-1112	2404	3	�	�	PROPN
m-1112	2404	4	←	←	PROPN
m-1112	2404	5	f	f	PROPN
m-1112	2404	6	…	…	PUNCT
m-1112	2404	7	→	→	SYM
m-1112	2404	8	in	in	ADP
m-1112	2404	9	[	[	X
m-1112	2404	10	pns	pns	X
m-1112	2404	11	]	]	X
m-1112	2404	12	neutral	neutral	ADJ
m-1112	2404	13	space	space	NOUN
m-1112	2404	14	,	,	PUNCT
m-1112	2404	15	dumping	dump	VERB
m-1112	2404	16	force	force	NOUN
m-1112	2404	17	is	be	AUX
m-1112	2404	18	fd	fd	ADJ
m-1112	2404	19	=	=	PUNCT
m-1112	2404	20	c	c	PROPN
m-1112	2404	21	.	.	PUNCT
m-1112	2405	1	ṙ	ṙ	NOUN
m-1112	2405	2	=	=	SYM
m-1112	2405	3	±	±	PROPN
m-1112	2405	4	co	co	NOUN
m-1112	2405	5	.w	.w	PROPN
m-1112	2405	6	.	.	PUNCT
m-1112	2406	1	[	[	X
m-1112	2406	2	√a2	√a2	X
m-1112	2406	3	−	−	NUM
m-1112	2406	4	r	r	NOUN
m-1112	2406	5	²	²	NUM
m-1112	2406	6	]	]	PUNCT
m-1112	2406	7	and	and	CCONJ
m-1112	2406	8	fd	fd	X
m-1112	2406	9	²	²	PROPN
m-1112	2406	10	/	/	SYM
m-1112	2406	11	[	[	PUNCT
m-1112	2406	12	co	co	X
m-1112	2406	13	.w	.w	PROPN
m-1112	2406	14	.	.	PUNCT
m-1112	2407	1	a	a	DET
m-1112	2407	2	]	]	SYM
m-1112	2407	3	²	²	PROPN
m-1112	2407	4	+	+	CCONJ
m-1112	2407	5	r	r	NOUN
m-1112	2407	6	²	²	NUM
m-1112	2407	7	/	/	SYM
m-1112	2407	8	a²	a²	NOUN
m-1112	2407	9	=	=	SYM
m-1112	2407	10	1	1	NUM
m-1112	2407	11	,	,	PUNCT
m-1112	2407	12	i.e.	i.e.	X
m-1112	2407	13	energy	energy	NOUN
m-1112	2407	14	≡	≡	PROPN
m-1112	2407	15	motion	motion	NOUN
m-1112	2407	16	is	be	AUX
m-1112	2407	17	mapped	map	VERB
m-1112	2407	18	as	as	ADP
m-1112	2407	19	an	an	DET
m-1112	2407	20	ellipse	ellipse	NOUN
m-1112	2407	21	with	with	ADP
m-1112	2407	22	axis	axis	NOUN
m-1112	2407	23	,	,	PUNCT
m-1112	2408	1	𝐅𝐝	𝐅𝐝	VERB
m-1112	2408	2	,	,	PUNCT
m-1112	2408	3	x	x	INTJ
m-1112	2408	4	,	,	PUNCT
m-1112	2408	5	and	and	CCONJ
m-1112	2408	6	energy	energy	NOUN
m-1112	2408	7	dissipated	dissipate	VERB
m-1112	2408	8	per	per	ADP
m-1112	2408	9	cycle	cycle	NOUN
m-1112	2408	10	,	,	PUNCT
m-1112	2408	11	the	the	DET
m-1112	2408	12	area	area	NOUN
m-1112	2408	13	enclosed	enclose	VERB
m-1112	2408	14	by	by	ADP
m-1112	2408	15	ellipse	ellipse	NOUN
m-1112	2408	16	.	.	PUNCT
m-1112	2409	1	g	g	ADP
m-1112	2409	2	…	…	PUNCT
m-1112	2409	3	→	→	SYM
m-1112	2409	4	the	the	DET
m-1112	2409	5	energy	energy	NOUN
m-1112	2409	6	in	in	ADP
m-1112	2409	7	[	[	X
m-1112	2409	8	pns	pns	NOUN
m-1112	2409	9	]	]	PUNCT
m-1112	2409	10	,	,	PUNCT
m-1112	2409	11	is	be	AUX
m-1112	2409	12	either	either	CCONJ
m-1112	2409	13	as	as	ADP
m-1112	2409	14	momentum	momentum	NOUN
m-1112	2409	15	(	(	PUNCT
m-1112	2409	16	mv	mv	NOUN
m-1112	2409	17	)	)	PUNCT
m-1112	2409	18	or	or	CCONJ
m-1112	2409	19	as	as	ADP
m-1112	2409	20	rotational	rotational	ADJ
m-1112	2409	21	momentum	momentum	NOUN
m-1112	2409	22	(	(	PUNCT
m-1112	2409	23	λ	λ	X
m-1112	2409	24	=	=	SYM
m-1112	2409	25	r.mv	r.mv	PROPN
m-1112	2409	26	)	)	PUNCT
m-1112	2409	27	.	.	PUNCT
m-1112	2410	1	velocity	velocity	PROPN
m-1112	2410	2	�	�	PROPN
m-1112	2410	3	̇	̇	PROPN
m-1112	2410	4	�	�	PROPN
m-1112	2410	5	,	,	PUNCT
m-1112	2410	6	in	in	ADP
m-1112	2410	7	form	form	NOUN
m-1112	2410	8	ẋ	ẋ	PROPN
m-1112	2411	1	=	=	PUNCT
m-1112	2411	2	w	w	ADP
m-1112	2411	3	a	a	DET
m-1112	2411	4	cos.(wt	cos.(wt	NOUN
m-1112	2411	5	θ	θ	NOUN
m-1112	2411	6	)	)	PUNCT
m-1112	2411	7	=	=	SYM
m-1112	2411	8	±	±	NUM
m-1112	2411	9	wa	wa	PROPN
m-1112	2411	10	.	.	PUNCT
m-1112	2411	11	[	[	PUNCT
m-1112	2411	12	√1	√1	ADP
m-1112	2411	13	−	−	PROPN
m-1112	2411	14	sin²(wt	sin²(wt	NOUN
m-1112	2411	15	−	−	NOUN
m-1112	2411	16	θ	θ	NOUN
m-1112	2411	17	)	)	PUNCT
m-1112	2411	18	]	]	PUNCT
m-1112	2412	1	=	=	PUNCT
m-1112	2413	1			PROPN
m-1112	2413	2	w	w	NOUN
m-1112	2413	3	.	.	PUNCT
m-1112	2414	1	[	[	PUNCT
m-1112	2414	2	√a²	√a²	PROPN
m-1112	2414	3	−	−	PROPN
m-1112	2414	4	x²	x²	PROPN
m-1112	2414	5	]	]	PUNCT
m-1112	2414	6	where	where	SCONJ
m-1112	2414	7	momentum	momentum	NOUN
m-1112	2414	8	relation	relation	NOUN
m-1112	2414	9	�	�	NOUN
m-1112	2414	10	̅	̅	NOUN
m-1112	2414	11	�	�	NOUN
m-1112	2414	12	=	=	SYM
m-1112	2414	13	m	m	VERB
m-1112	2414	14	r	r	NOUN
m-1112	2414	15	v	v	NOUN
m-1112	2414	16	=	=	PUNCT
m-1112	2414	17	m	m	VERB
m-1112	2414	18	r²	r²	NOUN
m-1112	2414	19	w	w	PROPN
m-1112	2414	20	=	=	VERB
m-1112	2414	21	m	m	VERB
m-1112	2414	22	r²	r²	NOUN
m-1112	2414	23	(	(	PUNCT
m-1112	2414	24	2πf	2πf	ADJ
m-1112	2414	25	)	)	PUNCT
m-1112	2415	1	=	=	PUNCT
m-1112	2415	2	j.w	j.w	PROPN
m-1112	2415	3	2	2	NUM
m-1112	2415	4	=	=	PUNCT
m-1112	2415	5	[	[	PUNCT
m-1112	2415	6	πr⁴	πr⁴	PROPN
m-1112	2415	7	4	4	NUM
m-1112	2415	8	]	]	PUNCT
m-1112	2415	9	.[2πf	.[2πf	X
m-1112	2415	10	]	]	X
m-1112	2416	1	=	=	X
m-1112	2416	2	π2r4f	π2r4f	PUNCT
m-1112	2416	3	2	2	NUM
m-1112	2416	4	,	,	PUNCT
m-1112	2416	5	and	and	CCONJ
m-1112	2416	6	mass	mass	NOUN
m-1112	2416	7	of	of	ADP
m-1112	2416	8	elementary	elementary	ADJ
m-1112	2416	9	-	-	PUNCT
m-1112	2416	10	particles	particle	NOUN
m-1112	2416	11	is	be	AUX
m-1112	2416	12	m	m	NOUN
m-1112	2416	13	=	=	PUNCT
m-1112	2416	14	π2r4f	π2r4f	NUM
m-1112	2416	15	2w.r²	2w.r²	NUM
m-1112	2416	16	=	=	SYM
m-1112	2417	1	π2r3	π2r3	PROPN
m-1112	2417	2	2v	2v	PROPN
m-1112	2417	3	f	f	PROPN
m-1112	2418	1	=	=	PUNCT
m-1112	2418	2	π1r2	π1r2	PUNCT
m-1112	2418	3	4	4	NUM
m-1112	2418	4	,	,	PUNCT
m-1112	2418	5	or	or	CCONJ
m-1112	2418	6	the	the	DET
m-1112	2418	7	repeated	repeat	VERB
m-1112	2418	8	quarter	quarter	NOUN
m-1112	2418	9	circle	circle	NOUN
m-1112	2418	10	[	[	PUNCT
m-1112	2418	11	𝛑.𝐫𝟐	𝛑.𝐫𝟐	X
m-1112	2418	12	𝟒	𝟒	PROPN
m-1112	2418	13	]	]	PUNCT
m-1112	2418	14	surface	surface	NOUN
m-1112	2418	15	of	of	ADP
m-1112	2418	16	the	the	DET
m-1112	2418	17	±	±	NUM
m-1112	2418	18	spin	spin	NOUN
m-1112	2418	19	dual	dual	ADJ
m-1112	2418	20	property	property	NOUN
m-1112	2418	21	in	in	ADP
m-1112	2418	22	planck`s	planck`s	NOUN
m-1112	2418	23	length	length	NOUN
m-1112	2418	24	and	and	CCONJ
m-1112	2418	25	area	area	NOUN
m-1112	2418	26	,	,	PUNCT
m-1112	2418	27	𝐀	𝐀	NOUN
m-1112	2418	28	𝐐𝐂	𝐐𝐂	NOUN
m-1112	2418	29	=	=	PUNCT
m-1112	2418	30	[	[	PUNCT
m-1112	2418	31	𝛑.𝐫²	𝛑.𝐫²	ADP
m-1112	2418	32	𝟒	𝟒	X
m-1112	2418	33	]	]	PUNCT
m-1112	2418	34	=	=	SYM
m-1112	2418	35	𝟑,𝟏𝟒𝟏𝟓𝟗𝟐𝟔.	𝟑,𝟏𝟒𝟏𝟓𝟗𝟐𝟔.	PROPN
m-1112	2418	36	(	(	PUNCT
m-1112	2418	37	√𝟐	√𝟐	PROPN
m-1112	2418	38	𝟒	𝟒	PROPN
m-1112	2418	39	.𝟏𝟎−𝟑𝟓)²	.𝟏𝟎−𝟑𝟓)²	SYM
m-1112	2418	40	𝟒	𝟒	NUM
m-1112	2418	41	=	=	SYM
m-1112	2418	42	1,1107206.10−70	1,1107206.10−70	NUM
m-1112	2418	43	m²	m²	PROPN
m-1112	2418	44	.	.	PUNCT
m-1112	2419	1	since	since	SCONJ
m-1112	2419	2	issues	issue	NOUN
m-1112	2419	3	the	the	DET
m-1112	2419	4	monad	monad	PROPN
m-1112	2419	5	of	of	ADP
m-1112	2419	6	mass	mass	NOUN
m-1112	2419	7	to	to	PART
m-1112	2419	8	be	be	AUX
m-1112	2419	9	[	[	PUNCT
m-1112	2419	10	ev	ev	ADP
m-1112	2419	11	c²	c²	NOUN
m-1112	2419	12	]	]	X
m-1112	2419	13	=	=	PUNCT
m-1112	2419	14	1,782662.10−36	1,782662.10−36	NUM
m-1112	2419	15	kg	kg	INTJ
m-1112	2419	16	,	,	PUNCT
m-1112	2419	17	then	then	ADV
m-1112	2419	18	energy	energy	NOUN
m-1112	2419	19	dissipated	dissipate	VERB
m-1112	2419	20	per	per	ADP
m-1112	2419	21	𝐴	𝐴	NOUN
m-1112	2419	22	𝑄𝐶	𝑄𝐶	PROPN
m-1112	2419	23	=	=	SYM
m-1112	2419	24	𝐄	𝐄	NOUN
m-1112	2419	25	𝐐𝐂	𝐐𝐂	NOUN
m-1112	2419	26	=	=	SYM
m-1112	2419	27	(	(	PUNCT
m-1112	2419	28	1,1107206.10−70	1,1107206.10−70	NUM
m-1112	2419	29	m²/	m²/	X
m-1112	2419	30	1,782662	1,782662	NUM
m-1112	2419	31	.	.	PUNCT
m-1112	2420	1	10−36	10−36	NOUN
m-1112	2420	2	=	=	SYM
m-1112	2420	3	6,230715	6,230715	X
m-1112	2420	4	.	.	PUNCT
m-1112	2421	1	10−35	10−35	NUM
m-1112	2421	2	kg	kg	NOUN
m-1112	2421	3	,	,	PUNCT
m-1112	2421	4	or	or	CCONJ
m-1112	2421	5	from	from	ADP
m-1112	2421	6	the	the	DET
m-1112	2421	7	g	g	PROPN
m-1112	2421	8	action	action	NOUN
m-1112	2421	9	area	area	NOUN
m-1112	2421	10	resistance	resistance	NOUN
m-1112	2421	11	≡	≡	PROPN
m-1112	2421	12	gravitational	gravitational	ADJ
m-1112	2421	13	-	-	PUNCT
m-1112	2421	14	impedance	impedance	NOUN
m-1112	2421	15	z	z	NOUN
m-1112	2421	16	iqc	iqc	NOUN
m-1112	2421	17	,	,	PUNCT
m-1112	2421	18	exists	exist	VERB
m-1112	2421	19	ziqc	ziqc	NOUN
m-1112	2421	20	=	=	SYM
m-1112	2421	21	√2𝑐3a	√2𝑐3a	X
m-1112	2421	22	qc	qc	PROPN
m-1112	2421	23	/	/	SYM
m-1112	2421	24	g	g	NOUN
m-1112	2421	25	,	,	PUNCT
m-1112	2421	26	and	and	CCONJ
m-1112	2421	27	𝐦	𝐦	PROPN
m-1112	2421	28	𝐏𝐍𝐒	𝐏𝐍𝐒	PROPN
m-1112	2421	29	≡	≡	PROPN
m-1112	2421	30	ziqc	ziqc	PROPN
m-1112	2421	31	=	=	SYM
m-1112	2421	32	√2.𝑐3a	√2.𝑐3a	PROPN
m-1112	2421	33	qc	qc	PROPN
m-1112	2421	34	/	/	SYM
m-1112	2421	35	g	g	NOUN
m-1112	2421	36	=	=	SYM
m-1112	2421	37	1,4143.(27.10"24)1,1107206.10−70	1,4143.(27.10"24)1,1107206.10−70	NUM
m-1112	2421	38	𝟔,680056.10−11	𝟔,680056.10−11	X
m-1112	2422	1	=	=	SYM
m-1112	2422	2	6,344907.10−35	6,344907.10−35	NUM
m-1112	2422	3	kg	kg	NOUN
m-1112	2422	4	.	.	PUNCT
m-1112	2423	1	the	the	DET
m-1112	2423	2	result	result	NOUN
m-1112	2423	3	agree	agree	VERB
m-1112	2423	4	with	with	ADP
m-1112	2423	5	prior	prior	ADV
m-1112	2423	6	because	because	SCONJ
m-1112	2423	7	in	in	ADP
m-1112	2423	8	[	[	X
m-1112	2423	9	pns	pns	NOUN
m-1112	2423	10	]	]	X
m-1112	2423	11	dipole	dipole	NOUN
m-1112	2423	12	of	of	ADP
m-1112	2423	13	space	space	NOUN
m-1112	2423	14	exists	exist	VERB
m-1112	2423	15	the	the	DET
m-1112	2423	16	impedance	impedance	NOUN
m-1112	2423	17	ziqc	ziqc	NOUN
m-1112	2423	18	,	,	PUNCT
m-1112	2423	19	which	which	PRON
m-1112	2423	20	doesn`t	doesn`t	VERB
m-1112	2423	21	exist	exist	VERB
m-1112	2423	22	in	in	ADP
m-1112	2423	23	[	[	X
m-1112	2423	24	mfmf	mfmf	NOUN
m-1112	2423	25	]	]	X
m-1112	2423	26	space	space	NOUN
m-1112	2423	27	.	.	PUNCT
m-1112	2424	1	[	[	X
m-1112	2424	2	22	22	NUM
m-1112	2424	3	-	-	SYM
m-1112	2424	4	26	26	NUM
m-1112	2424	5	]	]	PUNCT
m-1112	2424	6	ijo	ijo	PROPN
m-1112	2424	7	international	international	PROPN
m-1112	2424	8	journal	journal	PROPN
m-1112	2424	9	of	of	ADP
m-1112	2424	10	mathematics	mathematics	PROPN
m-1112	2424	11	(	(	PUNCT
m-1112	2424	12	issn	issn	PROPN
m-1112	2424	13	:	:	PUNCT
m-1112	2424	14	2992	2992	NUM
m-1112	2424	15	-	-	SYM
m-1112	2424	16	4421	4421	NUM
m-1112	2424	17	)	)	PUNCT
m-1112	2424	18	volume	volume	NOUN
m-1112	2424	19	08	08	NUM
m-1112	2424	20	|	|	ADV
m-1112	2424	21	issue	issue	NOUN
m-1112	2424	22	08	08	NUM
m-1112	2425	1	|	|	ADV
m-1112	2425	2	august	august	PROPN
m-1112	2425	3	2025	2025	NUM
m-1112	2425	4	|	|	ADV
m-1112	2425	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2425	6	ijo	ijo	PROPN
m-1112	2425	7	journals	journal	NOUN
m-1112	2425	8	84	84	NUM
m-1112	2425	9	the	the	DET
m-1112	2425	10	fundamental	fundamental	ADJ
m-1112	2425	11	particles	particle	NOUN
m-1112	2425	12	origination	origination	NOUN
m-1112	2425	13	mechanism	mechanism	NOUN
m-1112	2425	14	in	in	ADP
m-1112	2425	15	mfmf	mfmf	PROPN
m-1112	2425	16	pns	pns	PROPN
m-1112	2425	17	caves	cave	NOUN
m-1112	2425	18	.	.	PUNCT
m-1112	2426	1	h	h	X
m-1112	2426	2	…	…	PUNCT
m-1112	2426	3	→	→	SYM
m-1112	2426	4	in	in	ADP
m-1112	2426	5	[	[	X
m-1112	2426	6	mfmf	mfmf	NOUN
m-1112	2426	7	]	]	X
m-1112	2426	8	space	space	NOUN
m-1112	2426	9	,	,	PUNCT
m-1112	2426	10	work	work	NOUN
m-1112	2426	11	=	=	SYM
m-1112	2426	12	motion	motion	NOUN
m-1112	2426	13	=	=	NOUN
m-1112	2426	14	energy	energy	NOUN
m-1112	2426	15	is	be	AUX
m-1112	2426	16	zero	zero	NUM
m-1112	2426	17	as	as	ADP
m-1112	2426	18	w	w	PROPN
m-1112	2426	19	=	=	SYM
m-1112	2426	20	∫	∫	PROPN
m-1112	2427	1	p.	p.	NOUN
m-1112	2427	2	ds	ds	ADP
m-1112	2428	1	a	a	DET
m-1112	2428	2	b	b	NOUN
m-1112	2428	3	=	=	SYM
m-1112	2428	4	0	0	NUM
m-1112	2428	5	,	,	PUNCT
m-1112	2428	6	and	and	CCONJ
m-1112	2428	7	this	this	PRON
m-1112	2428	8	because	because	SCONJ
m-1112	2428	9	ds	ds	ADJ
m-1112	2428	10	=	=	SYM
m-1112	2428	11	v⃗	v⃗	NOUN
m-1112	2428	12	=	=	SYM
m-1112	2428	13	0	0	PUNCT
m-1112	2428	14	and	and	CCONJ
m-1112	2428	15	time	time	NOUN
m-1112	2428	16	is	be	AUX
m-1112	2428	17	not	not	PART
m-1112	2428	18	existing	exist	VERB
m-1112	2428	19	and	and	CCONJ
m-1112	2428	20	v⃗	v⃗	ADJ
m-1112	2428	21	=	=	SYM
m-1112	2428	22	0	0	PUNCT
m-1112	2428	23	as	as	ADP
m-1112	2428	24	relation	relation	NOUN
m-1112	2428	25	,	,	PUNCT
m-1112	2428	26	s	s	PART
m-1112	2428	27	=	=	SYM
m-1112	2428	28	�	�	PROPN
m-1112	2428	29	⃗	⃗	NOUN
m-1112	2428	30	�	�	PROPN
m-1112	2428	31	.t	.t	PROPN
m-1112	2428	32	.	.	PUNCT
m-1112	2429	1	each	each	DET
m-1112	2429	2	unit	unit	NOUN
m-1112	2429	3	ab⃗⃗⃗⃗	ab⃗⃗⃗⃗	PROPN
m-1112	2429	4	⃗	⃗	PROPN
m-1112	2429	5	=	=	SYM
m-1112	2429	6	ds	ds	NOUN
m-1112	2429	7	>	>	SYM
m-1112	2429	8	0	0	NUM
m-1112	2429	9	exists	exist	VERB
m-1112	2429	10	by	by	ADP
m-1112	2429	11	this	this	DET
m-1112	2429	12	inner	inner	ADJ
m-1112	2429	13	impulse	impulse	NOUN
m-1112	2429	14	(	(	PUNCT
m-1112	2429	15	p	p	NOUN
m-1112	2429	16	)	)	PUNCT
m-1112	2429	17	and	and	CCONJ
m-1112	2429	18	so	so	ADV
m-1112	2429	19	p	p	PRON
m-1112	2429	20	a+p	a+p	NUM
m-1112	2429	21	b	b	NOUN
m-1112	2429	22	=	=	SYM
m-1112	2429	23	0	0	PROPN
m-1112	2429	24	.	.	PUNCT
m-1112	2430	1	i.e.	i.e.	X
m-1112	2430	2	the	the	DET
m-1112	2430	3	position	position	NOUN
m-1112	2430	4	and	and	CCONJ
m-1112	2430	5	dimension	dimension	NOUN
m-1112	2430	6	of	of	ADP
m-1112	2430	7	all	all	DET
m-1112	2430	8	points	point	NOUN
m-1112	2430	9	which	which	PRON
m-1112	2430	10	are	be	AUX
m-1112	2430	11	connected	connect	VERB
m-1112	2430	12	across	across	ADP
m-1112	2430	13	universe	universe	NOUN
m-1112	2430	14	and	and	CCONJ
m-1112	2430	15	that	that	PRON
m-1112	2430	16	of	of	ADP
m-1112	2430	17	spaces	space	NOUN
m-1112	2430	18	exists	exist	VERB
m-1112	2430	19	because	because	SCONJ
m-1112	2430	20	of	of	ADP
m-1112	2430	21	this	this	DET
m-1112	2430	22	static	static	ADJ
m-1112	2430	23	inner	inner	ADJ
m-1112	2430	24	impulse	impulse	NOUN
m-1112	2430	25	,	,	PUNCT
m-1112	2430	26	on	on	ADP
m-1112	2430	27	the	the	DET
m-1112	2430	28	contrary	contrary	NOUN
m-1112	2430	29	should	should	AUX
m-1112	2430	30	be	be	AUX
m-1112	2430	31	one	one	NUM
m-1112	2430	32	point	point	NOUN
m-1112	2430	33	only	only	ADV
m-1112	2430	34	or	or	CCONJ
m-1112	2430	35	,	,	PUNCT
m-1112	2430	36	primary	primary	ADJ
m-1112	2430	37	point	point	NOUN
m-1112	2430	38	a	a	DET
m-1112	2430	39	=	=	X
m-1112	2430	40	black	black	ADJ
m-1112	2430	41	hole	hole	NOUN
m-1112	2430	42	→	→	X
m-1112	2430	43	ds	ds	ADJ
m-1112	2430	44	=	=	SYM
m-1112	2430	45	0	0	NUM
m-1112	2430	46	and	and	CCONJ
m-1112	2430	47	p	p	X
m-1112	2430	48	=	=	SYM
m-1112	2430	49	∞	∞	PROPN
m-1112	2430	50	.	.	PUNCT
m-1112	2431	1	since	since	SCONJ
m-1112	2431	2	impulse	impulse	ADJ
m-1112	2431	3	is	be	AUX
m-1112	2431	4	∞	∞	PROPN
m-1112	2431	5	then	then	ADV
m-1112	2431	6	may	may	AUX
m-1112	2431	7	be	be	AUX
m-1112	2431	8	→	→	SYM
m-1112	2431	9	vacuum	vacuum	NOUN
m-1112	2431	10	,	,	PUNCT
m-1112	2431	11	momentum	momentum	NOUN
m-1112	2431	12	or	or	CCONJ
m-1112	2431	13	potential	potential	ADJ
m-1112	2431	14	or	or	CCONJ
m-1112	2431	15	induced	induced	ADJ
m-1112	2431	16	potential	potential	NOUN
m-1112	2431	17	and	and	CCONJ
m-1112	2431	18	it	it	PRON
m-1112	2431	19	is	be	AUX
m-1112	2431	20	a	a	DET
m-1112	2431	21	type	type	NOUN
m-1112	2431	22	of	of	ADP
m-1112	2431	23	effect	effect	NOUN
m-1112	2431	24	,	,	PUNCT
m-1112	2431	25	to	to	PART
m-1112	2431	26	push	push	VERB
m-1112	2431	27	the	the	DET
m-1112	2431	28	nature	nature	NOUN
m-1112	2431	29	→	→	PUNCT
m-1112	2431	30	(	(	PUNCT
m-1112	2431	31	impulse	impulse	ADJ
m-1112	2431	32	≡	≡	PROPN
m-1112	2431	33	motion	motion	NOUN
m-1112	2431	34	≡	≡	PROPN
m-1112	2431	35	energy	energy	NOUN
m-1112	2431	36	)	)	PUNCT
m-1112	2431	37	←	←	PROPN
m-1112	2431	38	6c3	6c3	NUM
m-1112	2431	39	..	..	PUNCT
m-1112	2431	40	the	the	DET
m-1112	2431	41	nature	nature	NOUN
m-1112	2431	42	of	of	ADP
m-1112	2431	43	antigravity	antigravity	NOUN
m-1112	2431	44	(	(	PUNCT
m-1112	2431	45	g	g	PROPN
m-1112	2431	46	)	)	PUNCT
m-1112	2431	47	.	.	PUNCT
m-1112	2432	1	from	from	ADP
m-1112	2432	2	mechanics	mechanic	NOUN
m-1112	2432	3	in	in	ADP
m-1112	2432	4	case	case	NOUN
m-1112	2432	5	that	that	SCONJ
m-1112	2432	6	,	,	PUNCT
m-1112	2432	7	in	in	ADP
m-1112	2432	8	an	an	DET
m-1112	2432	9	axisymmetric	axisymmetric	ADJ
m-1112	2432	10	rotating	rotate	VERB
m-1112	2432	11	body	body	NOUN
m-1112	2432	12	,	,	PUNCT
m-1112	2432	13	with	with	ADP
m-1112	2432	14	constant	constant	ADJ
m-1112	2432	15	angular	angular	ADJ
m-1112	2432	16	-	-	PUNCT
m-1112	2432	17	velocity	velocity	NOUN
m-1112	2432	18	,	,	PUNCT
m-1112	2432	19	w	w	NOUN
m-1112	2432	20	,	,	PUNCT
m-1112	2432	21	the	the	DET
m-1112	2432	22	moment	moment	NOUN
m-1112	2432	23	of	of	ADP
m-1112	2432	24	inertia	inertia	NOUN
m-1112	2432	25	,	,	PUNCT
m-1112	2432	26	𝐉𝐱	𝐉𝐱	PROPN
m-1112	2432	27	=	=	SYM
m-1112	2432	28	𝐉𝐲	𝐉𝐲	NOUN
m-1112	2432	29	,	,	PUNCT
m-1112	2432	30	is	be	AUX
m-1112	2432	31	equal	equal	ADJ
m-1112	2432	32	about	about	ADP
m-1112	2432	33	the	the	DET
m-1112	2432	34	two	two	NUM
m-1112	2432	35	of	of	ADP
m-1112	2432	36	the	the	DET
m-1112	2432	37	three	three	NUM
m-1112	2432	38	principal	principal	ADJ
m-1112	2432	39	axis	axis	NOUN
m-1112	2432	40	,	,	PUNCT
m-1112	2432	41	and	and	CCONJ
m-1112	2432	42	then	then	ADV
m-1112	2432	43	,	,	PUNCT
m-1112	2432	44	1	1	X
m-1112	2432	45	..	..	PUNCT
m-1112	2432	46	the	the	DET
m-1112	2432	47	angular	angular	ADJ
m-1112	2432	48	–	–	PUNCT
m-1112	2432	49	velocity	velocity	NOUN
m-1112	2432	50	vector	vector	NOUN
m-1112	2432	51	,	,	PUNCT
m-1112	2432	52	�	�	PROPN
m-1112	2432	53	̅	̅	NOUN
m-1112	2432	54	�	�	PROPN
m-1112	2432	55	,	,	PUNCT
m-1112	2432	56	describes	describe	VERB
m-1112	2432	57	the	the	DET
m-1112	2432	58	ellipsoid	ellipsoid	NOUN
m-1112	2432	59	of	of	ADP
m-1112	2432	60	angular	angular	ADJ
m-1112	2432	61	velocity	velocity	NOUN
m-1112	2432	62	and	and	CCONJ
m-1112	2432	63	its	its	PRON
m-1112	2432	64	nib	nib	NOUN
m-1112	2432	65	describes	describe	VERB
m-1112	2432	66	a	a	DET
m-1112	2432	67	cone	cone	NOUN
m-1112	2432	68	of	of	ADP
m-1112	2432	69	which	which	DET
m-1112	2432	70	plane	plane	NOUN
m-1112	2432	71	-	-	PUNCT
m-1112	2432	72	base	base	NOUN
m-1112	2432	73	is	be	AUX
m-1112	2432	74	fixed	fix	VERB
m-1112	2432	75	simultaneously	simultaneously	ADV
m-1112	2432	76	,	,	PUNCT
m-1112	2432	77	2	2	X
m-1112	2432	78	..	..	PUNCT
m-1112	2432	79	the	the	DET
m-1112	2432	80	angular	angular	ADJ
m-1112	2432	81	-	-	PUNCT
m-1112	2432	82	momentum	momentum	NOUN
m-1112	2432	83	,	,	PUNCT
m-1112	2432	84	�	�	PROPN
m-1112	2432	85	̅	̅	NOUN
m-1112	2432	86	�	�	PROPN
m-1112	2432	87	,	,	PUNCT
m-1112	2432	88	describes	describe	VERB
m-1112	2432	89	the	the	DET
m-1112	2432	90	ellipsoid	ellipsoid	NOUN
m-1112	2432	91	of	of	ADP
m-1112	2432	92	angular	angular	ADJ
m-1112	2432	93	-	-	PUNCT
m-1112	2432	94	momentum	momentum	NOUN
m-1112	2432	95	and	and	CCONJ
m-1112	2432	96	its	its	PRON
m-1112	2432	97	nib	nib	NOUN
m-1112	2432	98	describes	describe	VERB
m-1112	2432	99	a	a	DET
m-1112	2432	100	cone	cone	NOUN
m-1112	2432	101	also	also	ADV
m-1112	2432	102	of	of	SCONJ
m-1112	2432	103	which	which	DET
m-1112	2432	104	plane	plane	NOUN
m-1112	2432	105	-	-	PUNCT
m-1112	2432	106	base	base	NOUN
m-1112	2432	107	is	be	AUX
m-1112	2432	108	also	also	ADV
m-1112	2432	109	fixed	fix	VERB
m-1112	2432	110	.	.	PUNCT
m-1112	2433	1	3	3	X
m-1112	2433	2	..	..	PUNCT
m-1112	2433	3	the	the	DET
m-1112	2433	4	nib	nib	NOUN
m-1112	2433	5	of	of	ADP
m-1112	2433	6	angular	angular	ADJ
m-1112	2433	7	velocity	velocity	NOUN
m-1112	2433	8	vector	vector	NOUN
m-1112	2433	9	,	,	PUNCT
m-1112	2433	10	�	�	PROPN
m-1112	2433	11	̅	̅	NOUN
m-1112	2433	12	�	�	PROPN
m-1112	2433	13	,	,	PUNCT
m-1112	2433	14	describes	describe	VERB
m-1112	2433	15	on	on	ADP
m-1112	2433	16	the	the	DET
m-1112	2433	17	tangential	tangential	ADJ
m-1112	2433	18	-	-	PUNCT
m-1112	2433	19	plane	plane	NOUN
m-1112	2433	20	of	of	ADP
m-1112	2433	21	the	the	DET
m-1112	2433	22	angular	angular	ADJ
m-1112	2433	23	-	-	PUNCT
m-1112	2433	24	momentum	momentum	NOUN
m-1112	2433	25	-	-	PUNCT
m-1112	2433	26	ellipsoid	ellipsoid	NOUN
m-1112	2433	27	,	,	PUNCT
m-1112	2433	28	the	the	DET
m-1112	2433	29	herpolhode	herpolhode	ADJ
m-1112	2433	30	,	,	PUNCT
m-1112	2433	31	while	while	SCONJ
m-1112	2433	32	,	,	PUNCT
m-1112	2433	33	4	4	NUM
m-1112	2433	34	..	..	PUNCT
m-1112	2433	35	the	the	DET
m-1112	2433	36	nib	nib	NOUN
m-1112	2433	37	of	of	ADP
m-1112	2433	38	angular	angular	ADJ
m-1112	2433	39	-	-	PUNCT
m-1112	2433	40	momentum	momentum	NOUN
m-1112	2433	41	,	,	PUNCT
m-1112	2433	42	�	�	PROPN
m-1112	2433	43	̅	̅	NOUN
m-1112	2433	44	�	�	PROPN
m-1112	2433	45	,	,	PUNCT
m-1112	2433	46	describes	describe	VERB
m-1112	2433	47	on	on	ADP
m-1112	2433	48	the	the	DET
m-1112	2433	49	tangential	tangential	ADJ
m-1112	2433	50	-	-	PUNCT
m-1112	2433	51	plane	plane	NOUN
m-1112	2433	52	,	,	PUNCT
m-1112	2433	53	of	of	ADP
m-1112	2433	54	the	the	DET
m-1112	2433	55	angular	angular	ADJ
m-1112	2433	56	-	-	PUNCT
m-1112	2433	57	velocity	velocity	NOUN
m-1112	2433	58	-	-	PUNCT
m-1112	2433	59	ellipsoid	ellipsoid	NOUN
m-1112	2433	60	,	,	PUNCT
m-1112	2433	61	the	the	DET
m-1112	2433	62	polhode	polhode	NOUN
m-1112	2433	63	.	.	PUNCT
m-1112	2434	1	5	5	X
m-1112	2434	2	..	..	PUNCT
m-1112	2434	3	the	the	DET
m-1112	2434	4	fixed	fix	VERB
m-1112	2434	5	-	-	PUNCT
m-1112	2434	6	tangential	tangential	ADJ
m-1112	2434	7	-	-	PUNCT
m-1112	2434	8	planes	plane	NOUN
m-1112	2434	9	on	on	ADP
m-1112	2434	10	,	,	PUNCT
m-1112	2434	11	�	�	PROPN
m-1112	2434	12	̅	̅	NOUN
m-1112	2434	13	�	�	PROPN
m-1112	2434	14	,	,	PUNCT
m-1112	2434	15	and	and	CCONJ
m-1112	2434	16	,	,	PUNCT
m-1112	2434	17	�	�	PROPN
m-1112	2434	18	̅	̅	NOUN
m-1112	2434	19	�	�	PROPN
m-1112	2434	20	,	,	PUNCT
m-1112	2434	21	nib	nib	NOUN
m-1112	2434	22	are	be	AUX
m-1112	2434	23	alternately	alternately	ADV
m-1112	2434	24	perpendicular	perpendicular	ADJ
m-1112	2434	25	to	to	ADP
m-1112	2434	26	,	,	PUNCT
m-1112	2434	27	b̅	b̅	PROPN
m-1112	2434	28	,	,	PUNCT
m-1112	2434	29	and	and	CCONJ
m-1112	2434	30	,	,	PUNCT
m-1112	2434	31	w̅	w̅	PROPN
m-1112	2434	32	,	,	PUNCT
m-1112	2434	33	common	common	ADJ
m-1112	2434	34	central	central	ADJ
m-1112	2434	35	axes	axis	NOUN
m-1112	2434	36	of	of	ADP
m-1112	2434	37	rotation	rotation	NOUN
m-1112	2434	38	.	.	PUNCT
m-1112	2435	1	6	6	X
m-1112	2435	2	..	..	PUNCT
m-1112	2435	3	the	the	DET
m-1112	2435	4	kinetic	kinetic	ADJ
m-1112	2435	5	rotational	rotational	ADJ
m-1112	2435	6	–	–	PUNCT
m-1112	2435	7	energy	energy	NOUN
m-1112	2435	8	of	of	ADP
m-1112	2435	9	monad	monad	PROPN
m-1112	2435	10	,	,	PUNCT
m-1112	2435	11	which	which	PRON
m-1112	2435	12	is	be	AUX
m-1112	2435	13	the	the	DET
m-1112	2435	14	work	work	NOUN
m-1112	2435	15	in	in	ADP
m-1112	2435	16	monad	monad	PROPN
m-1112	2435	17	,	,	PUNCT
m-1112	2435	18	is	be	AUX
m-1112	2435	19	the	the	DET
m-1112	2435	20	scalar	scalar	ADJ
m-1112	2435	21	quantity	quantity	NOUN
m-1112	2435	22	,	,	PUNCT
m-1112	2435	23	l	l	NOUN
m-1112	2435	24	,	,	PUNCT
m-1112	2435	25	the	the	DET
m-1112	2435	26	vector	vector	NOUN
m-1112	2435	27	angular	angular	ADJ
m-1112	2435	28	momentum	momentum	NOUN
m-1112	2435	29	quantity	quantity	NOUN
m-1112	2435	30	is	be	AUX
m-1112	2435	31	,	,	PUNCT
m-1112	2435	32	�	�	PROPN
m-1112	2435	33	̅	̅	NOUN
m-1112	2435	34	�	�	PROPN
m-1112	2435	35	,	,	PUNCT
m-1112	2435	36	and	and	CCONJ
m-1112	2435	37	the	the	DET
m-1112	2435	38	vector	vector	NOUN
m-1112	2435	39	of	of	ADP
m-1112	2435	40	angular	angular	ADJ
m-1112	2435	41	-	-	PUNCT
m-1112	2435	42	velocity	velocity	NOUN
m-1112	2435	43	quantity	quantity	NOUN
m-1112	2435	44	is	be	AUX
m-1112	2435	45	,	,	PUNCT
m-1112	2435	46	�	�	PROPN
m-1112	2435	47	̅	̅	NOUN
m-1112	2435	48	�	�	PROPN
m-1112	2435	49	,	,	PUNCT
m-1112	2435	50	which	which	PRON
m-1112	2435	51	three	three	NUM
m-1112	2435	52	monads	monad	NOUN
m-1112	2435	53	are	be	AUX
m-1112	2435	54	related	relate	VERB
m-1112	2435	55	as	as	ADP
m-1112	2435	56	�	�	NOUN
m-1112	2435	57	̅	̅	NOUN
m-1112	2435	58	�	�	PROPN
m-1112	2435	59	.	.	PUNCT
m-1112	2435	60	�	�	PROPN
m-1112	2435	61	̅	̅	NOUN
m-1112	2435	62	�	�	NOUN
m-1112	2435	63	=	=	SYM
m-1112	2435	64	2l	2l	NUM
m-1112	2435	65	=	=	NOUN
m-1112	2435	66	j.w²	j.w²	NOUN
m-1112	2436	1	where	where	SCONJ
m-1112	2436	2	j	j	PROPN
m-1112	2436	3	=	=	PUNCT
m-1112	2436	4	the	the	DET
m-1112	2436	5	moment	moment	NOUN
m-1112	2436	6	of	of	ADP
m-1112	2436	7	inertia	inertia	NOUN
m-1112	2436	8	around	around	ADP
m-1112	2436	9	the	the	DET
m-1112	2436	10	axis	axis	NOUN
m-1112	2436	11	of	of	ADP
m-1112	2436	12	rotation	rotation	NOUN
m-1112	2436	13	=	=	PUNCT
m-1112	2436	14	⇅	⇅	PROPN
m-1112	2436	15	7	7	NUM
m-1112	2436	16	..	..	PUNCT
m-1112	2436	17	all	all	PRON
m-1112	2436	18	above	above	ADV
m-1112	2436	19	happen	happen	VERB
m-1112	2436	20	in	in	ADV
m-1112	2436	21	,	,	PUNCT
m-1112	2436	22	material	material	NOUN
m-1112	2436	23	-	-	PUNCT
m-1112	2436	24	point	point	NOUN
m-1112	2436	25	,	,	PUNCT
m-1112	2436	26	where	where	SCONJ
m-1112	2436	27	the	the	DET
m-1112	2436	28	positive	positive	ADJ
m-1112	2436	29	⊕	⊕	PROPN
m-1112	2436	30	constituent	constituent	VERB
m-1112	2436	31	the	the	DET
m-1112	2436	32	+	+	NUM
m-1112	2436	33	�	�	NOUN
m-1112	2436	34	̅	̅	NOUN
m-1112	2436	35	�	�	PROPN
m-1112	2436	36	,	,	PUNCT
m-1112	2436	37	is	be	AUX
m-1112	2436	38	eternally	eternally	ADV
m-1112	2436	39	self	self	NOUN
m-1112	2436	40	rolling	roll	VERB
m-1112	2436	41	on	on	ADP
m-1112	2436	42	the	the	DET
m-1112	2436	43	negative	negative	ADJ
m-1112	2436	44	⊝	⊝	NOUN
m-1112	2436	45	constituent	constituent	NOUN
m-1112	2436	46	,	,	PUNCT
m-1112	2436	47	the	the	DET
m-1112	2436	48	�	�	PROPN
m-1112	2436	49	̅	̅	NOUN
m-1112	2436	50	�	�	PROPN
m-1112	2436	51	,	,	PUNCT
m-1112	2436	52	with	with	ADP
m-1112	2436	53	angular	angular	ADJ
m-1112	2436	54	-	-	PUNCT
m-1112	2436	55	velocity	velocity	NOUN
m-1112	2436	56	w	w	NOUN
m-1112	2436	57	,	,	PUNCT
m-1112	2436	58	in	in	ADP
m-1112	2436	59	infinite	infinite	ADJ
m-1112	2436	60	spherical	spherical	ADJ
m-1112	2436	61	traces	trace	NOUN
m-1112	2436	62	,	,	PUNCT
m-1112	2436	63	either	either	CCONJ
m-1112	2436	64	at	at	ADP
m-1112	2436	65	great	great	ADJ
m-1112	2436	66	-	-	PUNCT
m-1112	2436	67	circles	circle	NOUN
m-1112	2436	68	[	[	X
m-1112	2436	69	+	+	X
m-1112	2436	70	or	or	CCONJ
m-1112	2436	71	]	]	PUNCT
m-1112	2436	72	,	,	PUNCT
m-1112	2436	73	or	or	CCONJ
m-1112	2436	74	small	small	ADJ
m-1112	2436	75	-	-	PUNCT
m-1112	2436	76	circles	circle	NOUN
m-1112	2436	77	,	,	PUNCT
m-1112	2437	1	[	[	X
m-1112	2437	2	+	+	X
m-1112	2437	3	]	]	X
m-1112	2437	4	where	where	SCONJ
m-1112	2437	5	is	be	AUX
m-1112	2437	6	the	the	DET
m-1112	2437	7	clockwise	clockwise	NOUN
m-1112	2437	8	left	leave	VERB
m-1112	2437	9	direction	direction	NOUN
m-1112	2437	10	and	and	CCONJ
m-1112	2437	11	[	[	X
m-1112	2437	12	-	-	X
m-1112	2437	13	]	]	X
m-1112	2437	14	where	where	SCONJ
m-1112	2437	15	is	be	AUX
m-1112	2437	16	anti	anti	ADJ
m-1112	2437	17	-	-	ADJ
m-1112	2437	18	clockwise	clockwise	ADJ
m-1112	2437	19	right	right	ADJ
m-1112	2437	20	direction	direction	NOUN
m-1112	2437	21	or	or	CCONJ
m-1112	2437	22	any	any	DET
m-1112	2437	23	other	other	ADJ
m-1112	2437	24	close	close	ADJ
m-1112	2437	25	spherical	spherical	ADJ
m-1112	2437	26	-	-	PUNCT
m-1112	2437	27	curve	curve	NOUN
m-1112	2437	28	,	,	PUNCT
m-1112	2437	29	and	and	CCONJ
m-1112	2437	30	applying	apply	VERB
m-1112	2437	31	all	all	DET
m-1112	2437	32	laws	law	NOUN
m-1112	2437	33	of	of	ADP
m-1112	2437	34	mechanics	mechanic	NOUN
m-1112	2437	35	into	into	ADP
m-1112	2437	36	this	this	DET
m-1112	2437	37	energy	energy	NOUN
m-1112	2437	38	chaos	chaos	NOUN
m-1112	2437	39	,	,	PUNCT
m-1112	2437	40	is	be	AUX
m-1112	2437	41	thus	thus	ADV
m-1112	2437	42	created	create	VERB
m-1112	2437	43	the	the	DET
m-1112	2437	44	→	→	SYM
m-1112	2437	45	first	first	ADJ
m-1112	2437	46	–	–	PUNCT
m-1112	2437	47	discrete	discrete	ADJ
m-1112	2437	48	-	-	PUNCT
m-1112	2437	49	energy	energy	NOUN
m-1112	2437	50	–	–	PUNCT
m-1112	2437	51	monad	monad	PROPN
m-1112	2437	52	�	�	PROPN
m-1112	2437	53	̅	̅	NOUN
m-1112	2437	54	�	�	PROPN
m-1112	2437	55	,	,	PUNCT
m-1112	2437	56	the	the	DET
m-1112	2437	57	material	material	NOUN
m-1112	2437	58	point	point	NOUN
m-1112	2437	59	←	←	PROPN
m-1112	2437	60	i.e.	i.e.	X
m-1112	2437	61	the	the	DET
m-1112	2437	62	angular	angular	ADJ
m-1112	2437	63	momentum	momentum	NOUN
m-1112	2437	64	�	�	NOUN
m-1112	2437	65	̅	̅	NOUN
m-1112	2437	66	�	�	PROPN
m-1112	2437	67	,	,	PUNCT
m-1112	2437	68	is	be	AUX
m-1112	2437	69	the	the	DET
m-1112	2437	70	quantum	quantum	NOUN
m-1112	2437	71	of	of	ADP
m-1112	2437	72	physics	physics	NOUN
m-1112	2437	73	and	and	CCONJ
m-1112	2437	74	is	be	AUX
m-1112	2437	75	,	,	PUNCT
m-1112	2437	76	for	for	ADP
m-1112	2437	77	all	all	DET
m-1112	2437	78	the	the	DET
m-1112	2437	79	energy	energy	NOUN
m-1112	2437	80	–	–	PUNCT
m-1112	2437	81	space	space	NOUN
m-1112	2437	82	-	-	PUNCT
m-1112	2437	83	universe	universe	NOUN
m-1112	2438	1	.the	.the	DET
m-1112	2438	2	energy	energy	NOUN
m-1112	2438	3	=	=	PUNCT
m-1112	2438	4	e	e	NOUN
m-1112	2438	5	dissipated	dissipate	VERB
m-1112	2438	6	per	per	ADP
m-1112	2438	7	cycle	cycle	NOUN
m-1112	2438	8	is	be	AUX
m-1112	2438	9	equal	equal	ADJ
m-1112	2438	10	to	to	ADP
m-1112	2438	11	the	the	DET
m-1112	2438	12	work	work	NOUN
m-1112	2438	13	wd	wd	PROPN
m-1112	2439	1	=	=	SYM
m-1112	2439	2	e	e	X
m-1112	2439	3	=	=	SYM
m-1112	2439	4	h	h	NOUN
m-1112	2439	5	f	f	NOUN
m-1112	2439	6	=	=	SYM
m-1112	2439	7	h(1	h(1	PROPN
m-1112	2439	8	+	+	X
m-1112	2439	9	√5	√5	NOUN
m-1112	2439	10	]	]	PUNCT
m-1112	2439	11	)	)	PUNCT
m-1112	2440	1	4π	4π	NUM
m-1112	2440	2	.	.	PUNCT
m-1112	2441	1	[	[	PUNCT
m-1112	2441	2	𝜎	𝜎	SYM
m-1112	2441	3	𝑟	𝑟	X
m-1112	2441	4	]	]	X
m-1112	2441	5	=	=	SYM
m-1112	2441	6	8.kζ(πr²	8.kζ(πr²	NUM
m-1112	2441	7	)	)	PUNCT
m-1112	2441	8	and	and	CCONJ
m-1112	2441	9	is	be	AUX
m-1112	2441	10	stored	store	VERB
m-1112	2441	11	in	in	ADP
m-1112	2441	12	monad	monad	PROPN
m-1112	2441	13	,	,	PUNCT
m-1112	2441	14	which	which	PRON
m-1112	2441	15	is	be	AUX
m-1112	2441	16	a	a	DET
m-1112	2441	17	stationary	stationary	ADJ
m-1112	2441	18	wave	wave	NOUN
m-1112	2441	19	with	with	ADP
m-1112	2441	20	and	and	CCONJ
m-1112	2441	21	in	in	ADV
m-1112	2441	22	,	,	PUNCT
m-1112	2441	23	n	n	CCONJ
m-1112	2441	24	,	,	PUNCT
m-1112	2441	25	loops	loop	NOUN
m-1112	2441	26	as	as	ADP
m-1112	2441	27	𝐖𝐧	𝐖𝐧	PROPN
m-1112	2441	28	=	=	SYM
m-1112	2441	29	[	[	PUNCT
m-1112	2441	30	𝟒𝝅𝒓²	𝟒𝝅𝒓²	X
m-1112	2441	31	𝟑	𝟑	NUM
m-1112	2441	32	]	]	PUNCT
m-1112	2441	33	.𝐟𝐧	.𝐟𝐧	PUNCT
m-1112	2442	1	=	=	PUNCT
m-1112	2442	2	[	[	PUNCT
m-1112	2442	3	𝟒𝝅𝒓²	𝟒𝝅𝒓²	X
m-1112	2442	4	𝟑	𝟑	X
m-1112	2442	5	]	]	PUNCT
m-1112	2442	6	.𝐧𝐟𝟏	.𝐧𝐟𝟏	NOUN
m-1112	2442	7	=	=	SYM
m-1112	2442	8	n	n	PROPN
m-1112	2442	9	(	(	PUNCT
m-1112	2442	10	𝟏+√𝟓)𝛔𝐫	𝟏+√𝟓)𝛔𝐫	PROPN
m-1112	2442	11	𝟑	𝟑	X
m-1112	2442	12	=	=	SYM
m-1112	2442	13	n	n	PROPN
m-1112	2442	14	[	[	X
m-1112	2442	15	𝛔𝚽.𝐫	𝛔𝚽.𝐫	X
m-1112	2442	16	]	]	X
m-1112	2442	17	𝟏,𝟓	𝟏,𝟓	NOUN
m-1112	2442	18	.	.	PUNCT
m-1112	2443	1	8	8	NUM
m-1112	2443	2	..	..	PUNCT
m-1112	2443	3	geometry	geometry	NOUN
m-1112	2443	4	has	have	VERB
m-1112	2443	5	as	as	ADP
m-1112	2443	6	monad	monad	PROPN
m-1112	2443	7	,	,	PUNCT
m-1112	2443	8	the	the	DET
m-1112	2443	9	discrete	discrete	ADJ
m-1112	2443	10	continuity	continuity	NOUN
m-1112	2443	11	𝐀𝐁⃖⃗⃗⃗	𝐀𝐁⃖⃗⃗⃗	NOUN
m-1112	2444	1	⃗	⃗	PROPN
m-1112	2444	2	-length	-length	PROPN
m-1112	2444	3	becoming	become	VERB
m-1112	2444	4	from	from	ADP
m-1112	2444	5	the	the	DET
m-1112	2444	6	zero	zero	NUM
m-1112	2444	7	ijo	ijo	PROPN
m-1112	2444	8	international	international	ADJ
m-1112	2444	9	journal	journal	NOUN
m-1112	2444	10	of	of	ADP
m-1112	2444	11	mathematics	mathematics	PROPN
m-1112	2444	12	(	(	PUNCT
m-1112	2444	13	issn	issn	PROPN
m-1112	2444	14	:	:	PUNCT
m-1112	2444	15	2992	2992	NUM
m-1112	2444	16	-	-	SYM
m-1112	2444	17	4421	4421	NUM
m-1112	2444	18	)	)	PUNCT
m-1112	2444	19	volume	volume	NOUN
m-1112	2444	20	08	08	NUM
m-1112	2445	1	|	|	ADV
m-1112	2445	2	issue	issue	NOUN
m-1112	2445	3	08	08	NUM
m-1112	2446	1	|	|	ADV
m-1112	2446	2	august	august	PROPN
m-1112	2446	3	2025	2025	NUM
m-1112	2446	4	|	|	ADV
m-1112	2446	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2446	6	ijo	ijo	PROPN
m-1112	2446	7	journals	journal	NOUN
m-1112	2446	8	85	85	NUM
m-1112	2446	9	the	the	DET
m-1112	2446	10	fundamental	fundamental	ADJ
m-1112	2446	11	particles	particle	NOUN
m-1112	2446	12	origination	origination	NOUN
m-1112	2446	13	mechanism	mechanism	NOUN
m-1112	2446	14	in	in	ADP
m-1112	2446	15	mfmf	mfmf	PROPN
m-1112	2446	16	pns	pns	PROPN
m-1112	2446	17	caves	cave	NOUN
m-1112	2446	18	.	.	PUNCT
m-1112	2447	1	point	point	NOUN
m-1112	2447	2	≡	≡	PROPN
m-1112	2447	3	0	0	NUM
m-1112	2447	4	,	,	PUNCT
m-1112	2447	5	and	and	CCONJ
m-1112	2447	6	mechanics	mechanic	NOUN
m-1112	2447	7	-	-	PUNCT
m-1112	2447	8	physics	physics	NOUN
m-1112	2447	9	the	the	DET
m-1112	2447	10	recent	recent	ADJ
m-1112	2447	11	-	-	PUNCT
m-1112	2447	12	acquisition	acquisition	NOUN
m-1112	2447	13	of	of	ADP
m-1112	2447	14	the	the	DET
m-1112	2447	15	material	material	NOUN
m-1112	2447	16	geometry	geometry	NOUN
m-1112	2447	17	,	,	PUNCT
m-1112	2447	18	where	where	SCONJ
m-1112	2447	19	zero	zero	NUM
m-1112	2447	20	-	-	PUNCT
m-1112	2447	21	point	point	NOUN
m-1112	2447	22	,	,	PUNCT
m-1112	2447	23	0	0	NUM
m-1112	2447	24	=	=	SYM
m-1112	2448	1			VERB
m-1112	2448	2	=	=	SYM
m-1112	2448	3	{	{	PUNCT
m-1112	2448	4	⊕+⊝	⊕+⊝	NOUN
m-1112	2448	5	}	}	PUNCT
m-1112	2448	6	=	=	SYM
m-1112	2448	7	the	the	DET
m-1112	2448	8	material	material	NOUN
m-1112	2448	9	-	-	PUNCT
m-1112	2448	10	point	point	NOUN
m-1112	2448	11	=	=	PUNCT
m-1112	2448	12	the	the	DET
m-1112	2448	13	quantum	quantum	NOUN
m-1112	2448	14	of	of	ADP
m-1112	2448	15	space	space	NOUN
m-1112	2448	16	,	,	PUNCT
m-1112	2448	17	as	as	ADP
m-1112	2448	18	,	,	PUNCT
m-1112	2448	19	the	the	DET
m-1112	2448	20	positive	positive	ADJ
m-1112	2448	21	space	space	NOUN
m-1112	2448	22	and	and	CCONJ
m-1112	2448	23	the	the	DET
m-1112	2448	24	negative	negative	ADJ
m-1112	2448	25	anti	anti	ADJ
m-1112	2448	26	-	-	NOUN
m-1112	2448	27	space	space	NOUN
m-1112	2448	28	.	.	PUNCT
m-1112	2449	1	[	[	X
m-1112	2449	2	58	58	NUM
m-1112	2449	3	]	]	PUNCT
m-1112	2449	4	in	in	ADP
m-1112	2449	5	fig-8	fig-8	X
m-1112	2449	6	,	,	PUNCT
m-1112	2449	7	the	the	DET
m-1112	2449	8	light	light	ADJ
m-1112	2449	9	velocity	velocity	NOUN
m-1112	2449	10	vector	vector	NOUN
m-1112	2449	11	�	�	PROPN
m-1112	2449	12	̅	̅	NOUN
m-1112	2449	13	�	�	NOUN
m-1112	2449	14	=	=	PUNCT
m-1112	2449	15	2,9979	2,9979	NOUN
m-1112	2449	16	.	.	PUNCT
m-1112	2449	17	10	10	NUM
m-1112	2449	18	8	8	NUM
m-1112	2449	19	m	m	NUM
m-1112	2449	20	/	/	SYM
m-1112	2449	21	s	s	PART
m-1112	2449	22	rotates	rotate	NOUN
m-1112	2449	23	in	in	ADP
m-1112	2449	24	the	the	DET
m-1112	2449	25	planck`s	planck`s	NOUN
m-1112	2449	26	length	length	NOUN
m-1112	2449	27	perimeter	perimeter	NOUN
m-1112	2449	28	𝐫	𝐫	PROPN
m-1112	2449	29	𝐏	𝐏	PROPN
m-1112	2449	30	=	=	PUNCT
m-1112	2450	1	1,616255.10−35	1,616255.10−35	NUM
m-1112	2450	2	m	m	NOUN
m-1112	2450	3	,	,	PUNCT
m-1112	2451	1	and	and	CCONJ
m-1112	2451	2	is	be	AUX
m-1112	2451	3	thrusted	thrust	VERB
m-1112	2451	4	through	through	ADP
m-1112	2451	5	the	the	DET
m-1112	2451	6	newton	newton	PROPN
m-1112	2451	7	’s	’s	PART
m-1112	2451	8	–	–	PUNCT
m-1112	2451	9	gravitational	gravitational	ADJ
m-1112	2451	10	force	force	NOUN
m-1112	2451	11	𝐆	𝐆	PROPN
m-1112	2451	12	,	,	PUNCT
m-1112	2451	13	during	during	ADP
m-1112	2451	14	rotation	rotation	NOUN
m-1112	2451	15	is	be	AUX
m-1112	2451	16	created	create	VERB
m-1112	2451	17	work	work	NOUN
m-1112	2451	18	which	which	PRON
m-1112	2451	19	is	be	AUX
m-1112	2451	20	stored	store	VERB
m-1112	2451	21	in	in	ADP
m-1112	2451	22	the	the	DET
m-1112	2451	23	circle	circle	NOUN
m-1112	2451	24	surface	surface	NOUN
m-1112	2451	25	as	as	ADP
m-1112	2451	26	angular	angular	ADJ
m-1112	2451	27	momentum	momentum	NOUN
m-1112	2451	28	�	�	NOUN
m-1112	2451	29	̅	̅	NOUN
m-1112	2452	1	�	�	NOUN
m-1112	2452	2	=	=	SYM
m-1112	2453	1	r	r	NOUN
m-1112	2453	2	m	m	NOUN
m-1112	2453	3	v	v	NOUN
m-1112	2453	4	=	=	X
m-1112	2453	5	j.w	j.w	PROPN
m-1112	2453	6	2	2	NUM
m-1112	2453	7	=	=	PUNCT
m-1112	2453	8	[	[	PUNCT
m-1112	2453	9	π.𝐫𝟒	π.𝐫𝟒	X
m-1112	2453	10	4	4	NUM
m-1112	2453	11	]	]	PUNCT
m-1112	2453	12	c	c	NOUN
m-1112	2453	13	r	r	NOUN
m-1112	2453	14	=	=	SYM
m-1112	2453	15	[	[	PUNCT
m-1112	2453	16	𝛑.𝐫𝟑	𝛑.𝐫𝟑	NOUN
m-1112	2453	17	𝟒	𝟒	NUM
m-1112	2453	18	]	]	PUNCT
m-1112	2453	19	.	.	PUNCT
m-1112	2453	20	�	�	PROPN
m-1112	2453	21	̅	̅	NOUN
m-1112	2453	22	�	�	NOUN
m-1112	2453	23	=	=	SYM
m-1112	2453	24	[	[	PUNCT
m-1112	2453	25	𝛑.𝐫	𝛑.𝐫	X
m-1112	2453	26	𝟐	𝟐	NUM
m-1112	2453	27	𝟒	𝟒	NUM
m-1112	2453	28	]	]	PUNCT
m-1112	2453	29	.	.	PUNCT
m-1112	2453	30	�	�	PROPN
m-1112	2453	31	̅	̅	NOUN
m-1112	2453	32	�	�	PROPN
m-1112	2453	33	x	x	SYM
m-1112	2453	34	�	�	PROPN
m-1112	2453	35	̅	̅	NOUN
m-1112	2453	36	�	�	PROPN
m-1112	2453	37	,	,	PUNCT
m-1112	2453	38	in	in	ADP
m-1112	2453	39	semi	semi	ADJ
m-1112	2453	40	circle	circle	NOUN
m-1112	2453	41	{	{	PUNCT
m-1112	2453	42	+	+	NOUN
m-1112	2453	43	[	[	PUNCT
m-1112	2453	44	4	4	NUM
m-1112	2453	45	-1	-1	NOUN
m-1112	2453	46	-	-	PUNCT
m-1112	2453	47	3	3	NUM
m-1112	2453	48	]	]	PUNCT
m-1112	2453	49	}	}	PUNCT
m-1112	2453	50	,	,	PUNCT
m-1112	2453	51	and	and	CCONJ
m-1112	2453	52	semi	semi	ADV
m-1112	2453	53	circle	circle	NOUN
m-1112	2453	54	{	{	PUNCT
m-1112	2453	55	[	[	PUNCT
m-1112	2453	56	4	4	NUM
m-1112	2453	57	-	-	SYM
m-1112	2453	58	2	2	NUM
m-1112	2453	59	-	-	SYM
m-1112	2453	60	3	3	NUM
m-1112	2453	61	]	]	PUNCT
m-1112	2453	62	}	}	PUNCT
m-1112	2453	63	,	,	PUNCT
m-1112	2453	64	for	for	ADP
m-1112	2453	65	the	the	DET
m-1112	2453	66	stability	stability	NOUN
m-1112	2453	67	of	of	ADP
m-1112	2453	68	equilibrium	equilibrium	NOUN
m-1112	2453	69	.	.	PUNCT
m-1112	2454	1	i.e.	i.e.	X
m-1112	2454	2	gravity	gravity	NOUN
m-1112	2454	3	+	+	CCONJ
m-1112	2454	4	g	g	PROPN
m-1112	2454	5	≡	≡	PROPN
m-1112	2454	6	the	the	DET
m-1112	2454	7	vector	vector	NOUN
m-1112	2454	8	of	of	ADP
m-1112	2454	9	angular	angular	ADJ
m-1112	2454	10	-	-	PUNCT
m-1112	2454	11	momentum	momentum	NOUN
m-1112	2454	12	�	�	NOUN
m-1112	2454	13	̅	̅	NOUN
m-1112	2454	14	�	�	PROPN
m-1112	2454	15	≡	≡	PROPN
m-1112	2454	16	+	+	CCONJ
m-1112	2454	17	spin	spin	PROPN
m-1112	2454	18	≡	≡	PROPN
m-1112	2454	19	↓	↓	PROPN
m-1112	2454	20	↻	↻	PROPN
m-1112	2454	21	≡	≡	PROPN
m-1112	2454	22	the	the	DET
m-1112	2454	23	work	work	NOUN
m-1112	2454	24	stored	store	VERB
m-1112	2454	25	in	in	ADP
m-1112	2454	26	the	the	DET
m-1112	2454	27	[	[	X
m-1112	2454	28	4	4	NUM
m-1112	2454	29	-	-	SYM
m-1112	2454	30	1	1	NUM
m-1112	2454	31	-	-	SYM
m-1112	2454	32	3	3	NUM
m-1112	2454	33	]	]	PUNCT
m-1112	2454	34	semi	semi	ADJ
m-1112	2454	35	circle	circle	NOUN
m-1112	2454	36	of	of	ADP
m-1112	2454	37	the	the	DET
m-1112	2454	38	,	,	PUNCT
m-1112	2454	39	�	�	PROPN
m-1112	2454	40	̅	̅	NOUN
m-1112	2454	41	�	�	PROPN
m-1112	2454	42	�	�	NOUN
m-1112	2454	43	̅	̅	NOUN
m-1112	2454	44	�	�	PROPN
m-1112	2454	45	vectors	vector	NOUN
m-1112	2454	46	circle	circle	NOUN
m-1112	2454	47	surface	surface	PROPN
m-1112	2454	48	produced	produce	VERB
m-1112	2454	49	from	from	ADP
m-1112	2454	50	the	the	DET
m-1112	2454	51	gravitational	gravitational	ADJ
m-1112	2454	52	-	-	PUNCT
m-1112	2454	53	force	force	NOUN
m-1112	2454	54	,	,	PUNCT
m-1112	2454	55	g	g	PROPN
m-1112	2454	56	,	,	PUNCT
m-1112	2454	57	as	as	ADP
m-1112	2454	58	acting	act	VERB
m-1112	2454	59	into	into	ADP
m-1112	2454	60	the	the	DET
m-1112	2454	61	–	–	PUNCT
m-1112	2454	62	planckcave	planckcave	NOUN
m-1112	2454	63	,	,	PUNCT
m-1112	2454	64	and	and	CCONJ
m-1112	2454	65	on	on	ADP
m-1112	2454	66	the	the	DET
m-1112	2454	67	light	light	ADJ
m-1112	2454	68	velocity	velocity	NOUN
m-1112	2454	69	vector	vector	NOUN
m-1112	2454	70	in	in	ADP
m-1112	2454	71	,	,	PUNCT
m-1112	2454	72	+	+	CCONJ
m-1112	2454	73	↓	↓	PROPN
m-1112	2454	74	�	�	PROPN
m-1112	2454	75	̅	̅	NOUN
m-1112	2454	76	�	�	PROPN
m-1112	2454	77	direction	direction	NOUN
m-1112	2454	78	.	.	PUNCT
m-1112	2455	1	antigravity	antigravity	NOUN
m-1112	2455	2	g	g	PROPN
m-1112	2455	3	≡	≡	PROPN
m-1112	2455	4	the	the	DET
m-1112	2455	5	vector	vector	NOUN
m-1112	2455	6	of	of	ADP
m-1112	2455	7	angular	angular	ADJ
m-1112	2455	8	-momentum	-momentum	PROPN
m-1112	2455	9	�	�	PROPN
m-1112	2455	10	̅	̅	NOUN
m-1112	2455	11	�	�	PROPN
m-1112	2455	12	≡	≡	PROPN
m-1112	2455	13	spin	spin	PROPN
m-1112	2455	14	≡	≡	PROPN
m-1112	2455	15	↑	↑	PROPN
m-1112	2455	16	↺	↺	NOUN
m-1112	2455	17	≡	≡	PROPN
m-1112	2455	18	the	the	DET
m-1112	2455	19	work	work	NOUN
m-1112	2455	20	stored	store	VERB
m-1112	2455	21	in	in	ADP
m-1112	2455	22	the	the	DET
m-1112	2455	23	complementary	complementary	ADJ
m-1112	2456	1	[	[	X
m-1112	2456	2	4	4	NUM
m-1112	2456	3	-	-	SYM
m-1112	2456	4	2	2	NUM
m-1112	2456	5	-	-	SYM
m-1112	2456	6	3	3	NUM
m-1112	2456	7	]	]	PUNCT
m-1112	2456	8	semi	semi	ADJ
m-1112	2456	9	circle	circle	NOUN
m-1112	2456	10	of	of	ADP
m-1112	2456	11	the	the	DET
m-1112	2456	12	,	,	PUNCT
m-1112	2456	13	�	�	PROPN
m-1112	2456	14	̅	̅	NOUN
m-1112	2456	15	�	�	PROPN
m-1112	2456	16	�	�	NOUN
m-1112	2456	17	̅	̅	NOUN
m-1112	2456	18	�	�	PROPN
m-1112	2456	19	vectors	vector	NOUN
m-1112	2456	20	circle	circle	NOUN
m-1112	2456	21	-	-	PUNCT
m-1112	2456	22	surface	surface	NOUN
m-1112	2456	23	which	which	PRON
m-1112	2456	24	is	be	AUX
m-1112	2456	25	produced	produce	VERB
m-1112	2456	26	from	from	ADP
m-1112	2456	27	the	the	DET
m-1112	2456	28	gravitational	gravitational	ADJ
m-1112	2456	29	-	-	PUNCT
m-1112	2456	30	force	force	NOUN
m-1112	2456	31	,	,	PUNCT
m-1112	2456	32	g	g	PROPN
m-1112	2456	33	,	,	PUNCT
m-1112	2456	34	as	as	ADP
m-1112	2456	35	acting	act	VERB
m-1112	2456	36	into	into	ADP
m-1112	2456	37	the	the	DET
m-1112	2456	38	planckcave	planckcave	NOUN
m-1112	2456	39	,	,	PUNCT
m-1112	2456	40	and	and	CCONJ
m-1112	2456	41	on	on	ADP
m-1112	2456	42	the	the	DET
m-1112	2456	43	light	light	ADJ
m-1112	2456	44	velocity	velocity	NOUN
m-1112	2456	45	vector	vector	NOUN
m-1112	2456	46	in	in	ADP
m-1112	2456	47	the	the	DET
m-1112	2456	48	,	,	PUNCT
m-1112	2456	49	↑	↑	PROPN
m-1112	2456	50	�	�	PROPN
m-1112	2456	51	̅	̅	NOUN
m-1112	2456	52	�	�	PROPN
m-1112	2456	53	direction	direction	NOUN
m-1112	2456	54	.	.	PUNCT
m-1112	2457	1	figure	figure	NOUN
m-1112	2457	2	–	–	PUNCT
m-1112	2457	3	17b	17b	NUM
m-1112	2457	4	the	the	DET
m-1112	2457	5	material	material	NOUN
m-1112	2457	6	,	,	PUNCT
m-1112	2457	7	lrc	lrc	PROPN
m-1112	2457	8	circuit	circuit	PROPN
m-1112	2457	9	on	on	ADP
m-1112	2457	10	orbit	orbit	NOUN
m-1112	2457	11	,	,	PUNCT
m-1112	2457	12	on	on	ADP
m-1112	2457	13	focus	focus	NOUN
m-1112	2457	14	-	-	PUNCT
m-1112	2457	15	planet	planet	NOUN
m-1112	2457	16	-	-	PUNCT
m-1112	2457	17	sector	sector	NOUN
m-1112	2457	18	|f↔p|	|f↔p|	PROPN
m-1112	2457	19	in	in	ADP
m-1112	2457	20	(	(	PUNCT
m-1112	2457	21	1	1	NUM
m-1112	2457	22	)	)	PUNCT
m-1112	2457	23	.	.	PUNCT
m-1112	2458	1	force	force	PROPN
m-1112	2458	2	g	g	PROPN
m-1112	2458	3	,	,	PUNCT
m-1112	2458	4	as	as	ADP
m-1112	2458	5	wave	wave	NOUN
m-1112	2458	6	,	,	PUNCT
m-1112	2458	7	is	be	AUX
m-1112	2458	8	directed	direct	VERB
m-1112	2458	9	to	to	ADP
m-1112	2458	10	the	the	DET
m-1112	2458	11	center	center	NOUN
m-1112	2458	12	of	of	ADP
m-1112	2458	13	rotation	rotation	NOUN
m-1112	2458	14	f	f	PROPN
m-1112	2458	15	,	,	PUNCT
m-1112	2458	16	and	and	CCONJ
m-1112	2458	17	is	be	AUX
m-1112	2458	18	proportional	proportional	ADJ
m-1112	2458	19	to	to	ADP
m-1112	2458	20	the	the	DET
m-1112	2458	21	distance	distance	NOUN
m-1112	2458	22	pf	pf	PROPN
m-1112	2458	23	≡	≡	PROPN
m-1112	2458	24	focus	focus	NOUN
m-1112	2458	25	planet	planet	NOUN
m-1112	2459	1	.the	.the	PRON
m-1112	2459	2	gravitational	gravitational	ADJ
m-1112	2459	3	potential	potential	ADJ
m-1112	2459	4	-	-	PUNCT
m-1112	2459	5	energy	energy	NOUN
m-1112	2459	6	𝐠𝐆	𝐠𝐆	NOUN
m-1112	2459	7	=	=	SYM
m-1112	2459	8	9	9	NUM
m-1112	2459	9	,	,	PUNCT
m-1112	2459	10	8076925	8076925	NUM
m-1112	2459	11	is	be	AUX
m-1112	2459	12	stored	store	VERB
m-1112	2459	13	in	in	ADP
m-1112	2459	14	→	→	PUNCT
m-1112	2459	15	focus	focus	NOUN
m-1112	2459	16	-	-	PUNCT
m-1112	2459	17	planet	planet	NOUN
m-1112	2459	18	-	-	PUNCT
m-1112	2459	19	sector	sector	NOUN
m-1112	2459	20	≡	≡	PROPN
m-1112	2459	21	fp	fp	X
m-1112	2459	22	←	←	PROPN
m-1112	2459	23	which	which	PRON
m-1112	2459	24	is	be	AUX
m-1112	2459	25	the	the	DET
m-1112	2459	26	material	material	NOUN
m-1112	2459	27	capacitor	capacitor	NOUN
m-1112	2459	28	stores	store	NOUN
m-1112	2459	29	charge	charge	VERB
m-1112	2459	30	as	as	ADP
m-1112	2459	31	that	that	PRON
m-1112	2459	32	of	of	ADP
m-1112	2459	33	material	material	NOUN
m-1112	2459	34	-	-	PUNCT
m-1112	2459	35	lrc	lrc	NOUN
m-1112	2459	36	-	-	PUNCT
m-1112	2459	37	circuit	circuit	NOUN
m-1112	2459	38	,	,	PUNCT
m-1112	2459	39	and	and	CCONJ
m-1112	2459	40	inductors	inductor	NOUN
m-1112	2459	41	.	.	PUNCT
m-1112	2460	1	because	because	SCONJ
m-1112	2460	2	of	of	ADP
m-1112	2460	3	the	the	DET
m-1112	2460	4	chains	chain	NOUN
m-1112	2460	5	of	of	ADP
m-1112	2460	6	spins	spin	NOUN
m-1112	2460	7	and	and	CCONJ
m-1112	2460	8	of	of	ADP
m-1112	2460	9	their	their	PRON
m-1112	2460	10	periodic	periodic	ADJ
m-1112	2460	11	excitation	excitation	NOUN
m-1112	2460	12	[	[	X
m-1112	2460	13	↔	↔	X
m-1112	2460	14	]	]	PUNCT
m-1112	2460	15	,	,	PUNCT
m-1112	2460	16	is	be	AUX
m-1112	2460	17	thus	thus	ADV
m-1112	2460	18	created	create	VERB
m-1112	2460	19	a	a	DET
m-1112	2460	20	magnetic	magnetic	ADJ
m-1112	2460	21	field	field	NOUN
m-1112	2460	22	due	due	ADP
m-1112	2460	23	to	to	ADP
m-1112	2460	24	the	the	DET
m-1112	2460	25	lrc	lrc	NOUN
m-1112	2460	26	-	-	PUNCT
m-1112	2460	27	circuit	circuit	PROPN
m-1112	2460	28	and	and	CCONJ
m-1112	2460	29	which	which	PRON
m-1112	2460	30	is	be	AUX
m-1112	2460	31	tuning	tune	VERB
m-1112	2460	32	to	to	ADP
m-1112	2460	33	the	the	DET
m-1112	2460	34	critical	critical	ADJ
m-1112	2460	35	quantum	quantum	NOUN
m-1112	2460	36	and	and	CCONJ
m-1112	2460	37	critical	critical	ADJ
m-1112	2460	38	-	-	PUNCT
m-1112	2460	39	state	state	NOUN
m-1112	2460	40	𝐠𝐆	𝐠𝐆	NOUN
m-1112	2460	41	.	.	PUNCT
m-1112	2461	1	the	the	DET
m-1112	2461	2	chains	chain	NOUN
m-1112	2461	3	of	of	ADP
m-1112	2461	4	spins	spin	NOUN
m-1112	2461	5	are	be	AUX
m-1112	2461	6	pointy	pointy	ADV
m-1112	2461	7	vibrating	vibrate	VERB
m-1112	2461	8	with	with	ADP
m-1112	2461	9	their	their	PRON
m-1112	2461	10	characteristic	characteristic	ADJ
m-1112	2461	11	ijo	ijo	PROPN
m-1112	2461	12	international	international	PROPN
m-1112	2461	13	journal	journal	PROPN
m-1112	2461	14	of	of	ADP
m-1112	2461	15	mathematics	mathematics	PROPN
m-1112	2461	16	(	(	PUNCT
m-1112	2461	17	issn	issn	PROPN
m-1112	2461	18	:	:	PUNCT
m-1112	2461	19	2992	2992	NUM
m-1112	2461	20	-	-	SYM
m-1112	2461	21	4421	4421	NUM
m-1112	2461	22	)	)	PUNCT
m-1112	2461	23	volume	volume	NOUN
m-1112	2461	24	08	08	NUM
m-1112	2462	1	|	|	ADV
m-1112	2462	2	issue	issue	NOUN
m-1112	2462	3	08	08	NUM
m-1112	2463	1	|	|	ADV
m-1112	2463	2	august	august	PROPN
m-1112	2463	3	2025	2025	NUM
m-1112	2463	4	|	|	ADV
m-1112	2463	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2463	6	ijo	ijo	PROPN
m-1112	2463	7	journals	journal	NOUN
m-1112	2463	8	86	86	NUM
m-1112	2463	9	the	the	DET
m-1112	2463	10	fundamental	fundamental	ADJ
m-1112	2463	11	particles	particle	NOUN
m-1112	2463	12	origination	origination	NOUN
m-1112	2463	13	mechanism	mechanism	NOUN
m-1112	2463	14	in	in	ADP
m-1112	2463	15	mfmf	mfmf	PROPN
m-1112	2463	16	pns	pns	PROPN
m-1112	2463	17	caves	cave	NOUN
m-1112	2463	18	.	.	PUNCT
m-1112	2464	1	frequencies	frequency	NOUN
m-1112	2464	2	f	f	NOUN
m-1112	2465	1	=	=	PUNCT
m-1112	2465	2	(	(	PUNCT
m-1112	2465	3	1	1	NUM
m-1112	2465	4	+	+	NUM
m-1112	2465	5	√5	√5	NOUN
m-1112	2465	6	]	]	PUNCT
m-1112	2465	7	)	)	PUNCT
m-1112	2466	1	.σ	.σ	PROPN
m-1112	2466	2	4πr	4πr	ADJ
m-1112	2466	3	b̅	b̅	PROPN
m-1112	2466	4	,	,	PUNCT
m-1112	2466	5	and	and	CCONJ
m-1112	2466	6	filling	fill	VERB
m-1112	2466	7	up	up	ADP
m-1112	2466	8	the	the	DET
m-1112	2466	9	entire	entire	ADJ
m-1112	2466	10	universe	universe	NOUN
m-1112	2466	11	.	.	PUNCT
m-1112	2467	1	since	since	SCONJ
m-1112	2467	2	inner	inner	ADJ
m-1112	2467	3	-	-	PUNCT
m-1112	2467	4	stresses	stress	NOUN
m-1112	2467	5	𝛔𝟏,𝟐	𝛔𝟏,𝟐	X
m-1112	2467	6	=	=	SYM
m-1112	2467	7	σ1/2	σ1/2	PROPN
m-1112	2467	8	±	±	NOUN
m-1112	2467	9	(	(	PUNCT
m-1112	2467	10	½)√σ1²	½)√σ1²	PROPN
m-1112	2467	11	+	+	CCONJ
m-1112	2467	12	4	4	X
m-1112	2467	13	.	.	X
m-1112	2467	14	σ1²	σ1²	PROPN
m-1112	2467	15	=	=	SYM
m-1112	2467	16	σ1/2	σ1/2	PROPN
m-1112	2467	17	[	[	X
m-1112	2467	18	1±√5	1±√5	X
m-1112	2467	19	]	]	PUNCT
m-1112	2467	20	follow	follow	VERB
m-1112	2467	21	the	the	DET
m-1112	2467	22	golden	golden	ADJ
m-1112	2467	23	ratio	ratio	NOUN
m-1112	2467	24	on	on	ADP
m-1112	2467	25	stresses	stress	NOUN
m-1112	2467	26	then	then	ADV
m-1112	2467	27	this	this	DET
m-1112	2467	28	quantum	quantum	NOUN
m-1112	2467	29	-	-	PUNCT
m-1112	2467	30	energy	energy	NOUN
m-1112	2467	31	gg	gg	NOUN
m-1112	2467	32	produced	produce	VERB
m-1112	2467	33	,	,	PUNCT
m-1112	2467	34	is	be	AUX
m-1112	2467	35	the	the	DET
m-1112	2467	36	state	state	NOUN
m-1112	2467	37	causing	cause	VERB
m-1112	2467	38	them	they	PRON
m-1112	2467	39	to	to	PART
m-1112	2467	40	magneticallyresonate	magneticallyresonate	VERB
m-1112	2467	41	.	.	PUNCT
m-1112	2468	1	in	in	ADP
m-1112	2468	2	material	material	NOUN
m-1112	2468	3	-	-	PUNCT
m-1112	2468	4	point	point	NOUN
m-1112	2468	5	-	-	PUNCT
m-1112	2468	6	chain	chain	NOUN
m-1112	2468	7	of	of	ADP
m-1112	2468	8	caves	cave	NOUN
m-1112	2468	9	r	r	NOUN
m-1112	2468	10	=	=	SYM
m-1112	2468	11	λ/2	λ/2	PUNCT
m-1112	2468	12	,	,	PUNCT
m-1112	2468	13	and	and	CCONJ
m-1112	2468	14	since	since	SCONJ
m-1112	2468	15	ẋ	ẋ	PROPN
m-1112	2468	16	=	=	PUNCT
m-1112	2468	17	w.r	w.r	PROPN
m-1112	2468	18	→	→	SYM
m-1112	2468	19	w	w	NOUN
m-1112	2468	20	=	=	SYM
m-1112	2468	21	ẋ/r	ẋ/r	PROPN
m-1112	2468	22	then	then	ADV
m-1112	2468	23	golden	golden	ADJ
m-1112	2468	24	ratio	ratio	NOUN
m-1112	2468	25	damping	damp	VERB
m-1112	2468	26	-	-	PUNCT
m-1112	2468	27	force	force	NOUN
m-1112	2468	28	is	be	AUX
m-1112	2468	29	the	the	DET
m-1112	2468	30	work	work	NOUN
m-1112	2468	31	produced	produce	VERB
m-1112	2468	32	with	with	ADP
m-1112	2468	33	unit	unit	NOUN
m-1112	2468	34	damping	damp	VERB
m-1112	2468	35	-	-	PUNCT
m-1112	2468	36	ratio	ratio	NOUN
m-1112	2468	37	ζ=1	ζ=1	PUNCT
m-1112	2468	38	.since	.since	PROPN
m-1112	2468	39	also	also	ADV
m-1112	2468	40	ẋ	ẋ	PUNCT
m-1112	2469	1	=	=	SYM
m-1112	2469	2	v	v	PROPN
m-1112	2469	3	then	then	ADV
m-1112	2469	4	exists	exist	VERB
m-1112	2469	5	,	,	PUNCT
m-1112	2469	6	fd	fd	PROPN
m-1112	2469	7	=	=	PUNCT
m-1112	2469	8	c.	c.	PROPN
m-1112	2469	9	ẋ	ẋ	PROPN
m-1112	2470	1	=	=	SYM
m-1112	2470	2	1m.wn	1m.wn	NUM
m-1112	2470	3	.ẋ	.ẋ	PUNCT
m-1112	2471	1	=	=	SYM
m-1112	2471	2	1	1	NUM
m-1112	2471	3	.	.	PUNCT
m-1112	2471	4	[	[	PUNCT
m-1112	2471	5	(	(	PUNCT
m-1112	2471	6	π	π	NOUN
m-1112	2471	7	r²/2	r²/2	ADJ
m-1112	2471	8	)	)	PUNCT
m-1112	2471	9	v2	v2	PROPN
m-1112	2471	10	]	]	PUNCT
m-1112	2471	11	.	.	PUNCT
m-1112	2472	1	ẋ	ẋ	PROPN
m-1112	2473	1	²	²	NUM
m-1112	2473	2	𝑟	𝑟	NOUN
m-1112	2473	3	=	=	SYM
m-1112	2473	4	[	[	PUNCT
m-1112	2473	5	𝛑𝐫𝐯𝟒	𝛑𝐫𝐯𝟒	NOUN
m-1112	2473	6	𝟐	𝟐	NUM
m-1112	2473	7	]	]	PUNCT
m-1112	2473	8	=	=	PUNCT
m-1112	2473	9	g	g	NOUN
m-1112	2473	10	=	=	SYM
m-1112	2473	11	𝟐	𝟐	PROPN
m-1112	2473	12	𝒓	𝒓	PROPN
m-1112	2473	13	[	[	PUNCT
m-1112	2473	14	σ	σ	PROPN
m-1112	2473	15	(	(	PUNCT
m-1112	2473	16	1+√5	1+√5	NUM
m-1112	2473	17	)	)	PUNCT
m-1112	2473	18	]	]	PUNCT
m-1112	2473	19	²	²	X
m-1112	2473	20	=	=	NOUN
m-1112	2473	21	𝟒𝝈²	𝟒𝝈²	X
m-1112	2473	22	𝒓	𝒓	PROPN
m-1112	2473	23	[	[	PUNCT
m-1112	2473	24	3+√5	3+√5	NUM
m-1112	2473	25	]	]	PUNCT
m-1112	2473	26	.	.	PUNCT
m-1112	2474	1	this	this	DET
m-1112	2474	2	dissipation	dissipation	NOUN
m-1112	2474	3	of	of	ADP
m-1112	2474	4	energy	energy	NOUN
m-1112	2474	5	is	be	AUX
m-1112	2474	6	determined	determine	VERB
m-1112	2474	7	under	under	ADP
m-1112	2474	8	conditions	condition	NOUN
m-1112	2474	9	of	of	ADP
m-1112	2474	10	cyclic	cyclic	ADJ
m-1112	2474	11	oscillations	oscillation	NOUN
m-1112	2474	12	,	,	PUNCT
m-1112	2474	13	and	and	CCONJ
m-1112	2474	14	is	be	AUX
m-1112	2474	15	dependent	dependent	ADJ
m-1112	2474	16	on	on	ADP
m-1112	2474	17	glue	glue	NOUN
m-1112	2474	18	-	-	PUNCT
m-1112	2474	19	bond	bond	NOUN
m-1112	2474	20	σ	σ	NOUN
m-1112	2474	21	,	,	PUNCT
m-1112	2474	22	and	and	CCONJ
m-1112	2474	23	r	r	NOUN
m-1112	2474	24	,	,	PUNCT
m-1112	2474	25	cave	cave	NOUN
m-1112	2474	26	.	.	PUNCT
m-1112	2475	1	since	since	SCONJ
m-1112	2475	2	r	r	NOUN
m-1112	2475	3	is	be	AUX
m-1112	2475	4	in	in	ADP
m-1112	2475	5	denominator	denominator	NOUN
m-1112	2475	6	then	then	ADV
m-1112	2475	7	for	for	ADP
m-1112	2475	8	the	the	DET
m-1112	2475	9	very	very	ADV
m-1112	2475	10	small	small	ADJ
m-1112	2475	11	caves	cave	NOUN
m-1112	2475	12	,	,	PUNCT
m-1112	2475	13	the	the	DET
m-1112	2475	14	under	under	ADP
m-1112	2475	15	planck`s	planck`s	NOUN
m-1112	2475	16	caves	cave	NOUN
m-1112	2475	17	,	,	PUNCT
m-1112	2475	18	damping	damp	VERB
m-1112	2475	19	-	-	PUNCT
m-1112	2475	20	force	force	NOUN
m-1112	2475	21	becomes	become	VERB
m-1112	2475	22	infinite	infinite	ADJ
m-1112	2475	23	independently	independently	ADV
m-1112	2475	24	of	of	ADP
m-1112	2475	25	glue	glue	NOUN
m-1112	2475	26	-	-	PUNCT
m-1112	2475	27	bond	bond	NOUN
m-1112	2475	28	.	.	PUNCT
m-1112	2476	1	this	this	PRON
m-1112	2476	2	may	may	AUX
m-1112	2476	3	be	be	AUX
m-1112	2476	4	considered	consider	VERB
m-1112	2476	5	as	as	ADP
m-1112	2476	6	a	a	DET
m-1112	2476	7	type	type	NOUN
m-1112	2476	8	which	which	PRON
m-1112	2476	9	happens	happen	VERB
m-1112	2476	10	in	in	ADP
m-1112	2476	11	black	black	ADJ
m-1112	2476	12	holes	hole	NOUN
m-1112	2476	13	as	as	SCONJ
m-1112	2476	14	this	this	PRON
m-1112	2476	15	happens	happen	VERB
m-1112	2476	16	in	in	ADP
m-1112	2476	17	algebra	algebra	NOUN
m-1112	2476	18	inverse	inverse	NOUN
m-1112	2476	19	fractions	fraction	NOUN
m-1112	2476	20	also	also	ADV
m-1112	2476	21	.	.	PUNCT
m-1112	2477	1	in	in	ADP
m-1112	2477	2	(	(	PUNCT
m-1112	2477	3	2	2	X
m-1112	2477	4	)	)	PUNCT
m-1112	2477	5	is	be	AUX
m-1112	2477	6	presented	present	VERB
m-1112	2477	7	the	the	DET
m-1112	2477	8	back	back	VERB
m-1112	2477	9	-	-	PUNCT
m-1112	2477	10	up	up	ADP
m-1112	2477	11	electromagnetic	electromagnetic	ADJ
m-1112	2477	12	current	current	NOUN
m-1112	2477	13	flowing	flow	VERB
m-1112	2477	14	in	in	ADP
m-1112	2477	15	opposite	opposite	ADJ
m-1112	2477	16	direction	direction	NOUN
m-1112	2477	17	fp	fp	INTJ
m-1112	2477	18	,	,	PUNCT
m-1112	2477	19	by	by	ADP
m-1112	2477	20	changing	change	VERB
m-1112	2477	21	the	the	DET
m-1112	2477	22	spin	spin	NOUN
m-1112	2477	23	direction	direction	NOUN
m-1112	2477	24	of	of	ADP
m-1112	2477	25	the	the	DET
m-1112	2477	26	sector	sector	NOUN
m-1112	2477	27	-	-	PUNCT
m-1112	2477	28	material	material	NOUN
m-1112	2477	29	-	-	PUNCT
m-1112	2477	30	points	point	NOUN
m-1112	2477	31	such	such	ADJ
m-1112	2477	32	that	that	DET
m-1112	2477	33	work	work	NOUN
m-1112	2477	34	w	w	NOUN
m-1112	2477	35	=	=	NOUN
m-1112	2477	36	g	g	PROPN
m-1112	2477	37	.	.	PUNCT
m-1112	2478	1	from	from	ADP
m-1112	2478	2	kepler`s	kepler`s	PROPN
m-1112	2478	3	2nd	2nd	ADJ
m-1112	2478	4	law	law	NOUN
m-1112	2478	5	the	the	DET
m-1112	2478	6	,	,	PUNCT
m-1112	2478	7	area	area	NOUN
m-1112	2478	8	s	s	PART
m-1112	2478	9	,	,	PUNCT
m-1112	2478	10	swept	sweep	VERB
m-1112	2478	11	by	by	ADP
m-1112	2478	12	any	any	DET
m-1112	2478	13	focus	focus	NOUN
m-1112	2478	14	-	-	PUNCT
m-1112	2478	15	planet	planet	NOUN
m-1112	2478	16	-	-	PUNCT
m-1112	2478	17	sector	sector	NOUN
m-1112	2478	18	≡	≡	PROPN
m-1112	2478	19	fp	fp	PROPN
m-1112	2478	20	is	be	AUX
m-1112	2478	21	the	the	DET
m-1112	2478	22	constant	constant	ADJ
m-1112	2478	23	k	k	NOUN
m-1112	2478	24	,	,	PUNCT
m-1112	2478	25	and	and	CCONJ
m-1112	2478	26	equal	equal	ADJ
m-1112	2478	27	to	to	ADP
m-1112	2478	28	,	,	PUNCT
m-1112	2478	29	s²	s²	PROPN
m-1112	2478	30	=	=	SYM
m-1112	2478	31	l²	l²	NOUN
m-1112	2478	32	t²	t²	NOUN
m-1112	2478	33	4	4	NUM
m-1112	2478	34	m²	m²	NOUN
m-1112	2478	35	=	=	SYM
m-1112	2478	36	π²a²	π²a²	X
m-1112	2478	37	.	.	PUNCT
m-1112	2479	1	[	[	PUNCT
m-1112	2479	2	b	b	X
m-1112	2479	3	=	=	PRON
m-1112	2479	4	πa	πa	PROPN
m-1112	2479	5	(	(	PUNCT
m-1112	2479	6	l²	l²	PROPN
m-1112	2479	7	2me	2me	NOUN
m-1112	2479	8	)	)	PUNCT
m-1112	2479	9	]	]	PUNCT
m-1112	2479	10	,	,	PUNCT
m-1112	2479	11	or	or	CCONJ
m-1112	2479	12	t	t	X
m-1112	2479	13	²	²	NUM
m-1112	2479	14	a	a	DET
m-1112	2479	15	²	²	NUM
m-1112	2479	16	=	=	SYM
m-1112	2479	17	4π²m	4π²m	NOUN
m-1112	2479	18	2e	2e	NOUN
m-1112	2479	19	=	=	SYM
m-1112	2479	20	4π²	4π²	NUM
m-1112	2479	21	2e	2e	NUM
m-1112	2479	22	/	/	SYM
m-1112	2479	23	m	m	PROPN
m-1112	2479	24	=	=	NOUN
m-1112	2479	25	4π²	4π²	NUM
m-1112	2479	26	a	a	DET
m-1112	2479	27	gm	gm	PROPN
m-1112	2479	28	and	and	CCONJ
m-1112	2479	29	→	→	SYM
m-1112	2479	30	𝐓	𝐓	PROPN
m-1112	2479	31	²	²	PROPN
m-1112	2479	32	𝐚	𝐚	PROPN
m-1112	2479	33	³	³	X
m-1112	2479	34	=	=	X
m-1112	2479	35	𝟒𝛑²	𝟒𝛑²	NOUN
m-1112	2479	36	𝐆𝐌	𝐆𝐌	PROPN
m-1112	2479	37	=	=	PUNCT
m-1112	2480	1	k	k	PROPN
m-1112	2480	2	and	and	CCONJ
m-1112	2480	3	k	k	PROPN
m-1112	2481	1	=	=	NOUN
m-1112	2481	2	𝟏	𝟏	X
m-1112	2481	3	𝐟	𝐟	NOUN
m-1112	2481	4	²𝐧	²𝐧	VERB
m-1112	2481	5	.𝐚	.𝐚	PROPN
m-1112	2481	6	³	³	X
m-1112	2481	7	,	,	PUNCT
m-1112	2481	8	from	from	ADP
m-1112	2481	9	which	which	PRON
m-1112	2481	10	issues	issue	NOUN
m-1112	2481	11	→	→	SYM
m-1112	2481	12	1	1	NUM
m-1112	2481	13	=	=	SYM
m-1112	2481	14	k	k	X
m-1112	2481	15	.	.	PUNCT
m-1112	2482	1	𝐟²𝐧	𝐟²𝐧	PROPN
m-1112	2482	2	.	.	PUNCT
m-1112	2483	1	𝐚	𝐚	DET
m-1112	2483	2	𝟑	𝟑	X
m-1112	2483	3	and	and	CCONJ
m-1112	2483	4	,	,	PUNCT
m-1112	2483	5	k	k	PROPN
m-1112	2484	1	=	=	SYM
m-1112	2484	2	4π²	4π²	NUM
m-1112	2484	3	gm	gm	INTJ
m-1112	2484	4	where	where	SCONJ
m-1112	2484	5	is	be	AUX
m-1112	2484	6	seen	see	VERB
m-1112	2484	7	that	that	SCONJ
m-1112	2484	8	,	,	PUNCT
m-1112	2484	9	resonance	resonance	NOUN
m-1112	2484	10	between	between	ADP
m-1112	2484	11	focus	focus	NOUN
m-1112	2484	12	-	-	PUNCT
m-1112	2484	13	planet	planet	NOUN
m-1112	2484	14	exists	exist	VERB
m-1112	2484	15	through	through	ADP
m-1112	2484	16	space	space	NOUN
m-1112	2484	17	a	a	PRON
m-1112	2484	18	and	and	CCONJ
m-1112	2484	19	energy	energy	NOUN
m-1112	2484	20	f	f	NOUN
m-1112	2484	21	.	.	PUNCT
m-1112	2485	1	from	from	ADP
m-1112	2485	2	the	the	DET
m-1112	2485	3	second	second	ADJ
m-1112	2485	4	-	-	PUNCT
m-1112	2485	5	order	order	NOUN
m-1112	2485	6	differential	differential	ADJ
m-1112	2485	7	equation	equation	NOUN
m-1112	2485	8	excited	excite	VERB
m-1112	2485	9	by	by	ADP
m-1112	2485	10	a	a	DET
m-1112	2485	11	harmonic	harmonic	ADJ
m-1112	2485	12	external	external	ADJ
m-1112	2485	13	force	force	NOUN
m-1112	2485	14	,	,	PUNCT
m-1112	2485	15	ft	ft	NOUN
m-1112	2485	16	.sin	.sin	NOUN
m-1112	2485	17	wt	wt	INTJ
m-1112	2485	18	,	,	PUNCT
m-1112	2485	19	and	and	CCONJ
m-1112	2485	20	is	be	AUX
m-1112	2485	21	as	as	SCONJ
m-1112	2485	22	,	,	PUNCT
m-1112	2485	23	m	m	VERB
m-1112	2485	24	d²x	d²x	VERB
m-1112	2485	25	dt²	dt²	NOUN
m-1112	2485	26	+	+	CCONJ
m-1112	2485	27	c	c	X
m-1112	2485	28	dx	dx	PROPN
m-1112	2485	29	dt	dt	PROPN
m-1112	2486	1	+	+	CCONJ
m-1112	2486	2	k	k	X
m-1112	2486	3	.	.	PUNCT
m-1112	2487	1	x	x	X
m-1112	2487	2	=	=	NOUN
m-1112	2487	3	ft	ft	PROPN
m-1112	2487	4	.	.	PUNCT
m-1112	2487	5	sin	sin	PROPN
m-1112	2487	6	w	w	PROPN
m-1112	2487	7	t	t	PROPN
m-1112	2487	8	,	,	PUNCT
m-1112	2487	9	corresponds	correspond	VERB
m-1112	2487	10	physically	physically	ADV
m-1112	2487	11	to	to	ADP
m-1112	2487	12	the	the	DET
m-1112	2487	13	free	free	ADJ
m-1112	2487	14	damped	damped	NOUN
m-1112	2487	15	vibration	vibration	NOUN
m-1112	2487	16	,	,	PUNCT
m-1112	2487	17	where	where	SCONJ
m-1112	2487	18	x	x	X
m-1112	2487	19	=	=	PUNCT
m-1112	2487	20	the	the	DET
m-1112	2487	21	displacement	displacement	NOUN
m-1112	2487	22	,	,	PUNCT
m-1112	2487	23	dx	dx	PROPN
m-1112	2487	24	/	/	SYM
m-1112	2487	25	dt	dt	PROPN
m-1112	2488	1	=	=	PUNCT
m-1112	2488	2	the	the	DET
m-1112	2488	3	velocity	velocity	NOUN
m-1112	2488	4	and	and	CCONJ
m-1112	2488	5	,	,	PUNCT
m-1112	2488	6	d²x	d²x	PROPN
m-1112	2488	7	/	/	SYM
m-1112	2488	8	dt²	dt²	NOUN
m-1112	2488	9	=	=	PUNCT
m-1112	2488	10	the	the	DET
m-1112	2488	11	acceleration	acceleration	NOUN
m-1112	2488	12	of	of	ADP
m-1112	2488	13	monad	monad	PROPN
m-1112	2488	14	,	,	PUNCT
m-1112	2488	15	m	m	PROPN
m-1112	2488	16	,	,	PUNCT
m-1112	2488	17	c	c	NOUN
m-1112	2488	18	,	,	PUNCT
m-1112	2488	19	k	k	PROPN
m-1112	2488	20	constants	constant	NOUN
m-1112	2488	21	,	,	PUNCT
m-1112	2488	22	with	with	ADP
m-1112	2488	23	the	the	DET
m-1112	2488	24	general	general	ADJ
m-1112	2488	25	solution	solution	NOUN
m-1112	2488	26	given	give	VERB
m-1112	2488	27	by	by	ADP
m-1112	2488	28	the	the	DET
m-1112	2488	29	equation	equation	NOUN
m-1112	2488	30	x	x	PUNCT
m-1112	2488	31	=	=	PUNCT
m-1112	2488	32	a	a	PRON
m-1112	2488	33	.	.	PUNCT
m-1112	2488	34	𝑒𝑠1.𝑡+	𝑒𝑠1.𝑡+	ADV
m-1112	2488	35	b.𝑒𝑠2.𝑡	b.𝑒𝑠2.𝑡	ADJ
m-1112	2488	36	+	+	CCONJ
m-1112	2488	37	x	x	SYM
m-1112	2488	38	sin(wt	sin(wt	NOUN
m-1112	2488	39	-	-	PUNCT
m-1112	2488	40	φ	φ	NOUN
m-1112	2488	41	)	)	PUNCT
m-1112	2488	42	…	…	PUNCT
m-1112	2488	43	…	…	PUNCT
m-1112	2488	44	(	(	PUNCT
m-1112	2488	45	1	1	X
m-1112	2488	46	)	)	PUNCT
m-1112	2488	47	the	the	DET
m-1112	2488	48	equation	equation	NOUN
m-1112	2488	49	→	→	SYM
m-1112	2488	50	l	l	NOUN
m-1112	2488	51	d²q	d²q	NOUN
m-1112	2488	52	dt²	dt²	NOUN
m-1112	2488	53	+	+	CCONJ
m-1112	2488	54	r	r	NOUN
m-1112	2488	55	dq	dq	NOUN
m-1112	2488	56	dt	dt	NOUN
m-1112	2488	57	+	+	NOUN
m-1112	2488	58	1	1	NUM
m-1112	2488	59	𝐶	𝐶	PROPN
m-1112	2488	60	q	q	PROPN
m-1112	2489	1	=	=	PUNCT
m-1112	2489	2	e	e	PROPN
m-1112	2489	3	t	t	PROPN
m-1112	2489	4	.	.	PUNCT
m-1112	2490	1	sinwt	sinwt	PROPN
m-1112	2490	2	.corresponds	.correspond	VERB
m-1112	2490	3	physically	physically	ADV
m-1112	2490	4	to	to	ADP
m-1112	2490	5	the	the	DET
m-1112	2490	6	free	free	ADJ
m-1112	2490	7	damped	damped	NOUN
m-1112	2490	8	vibration	vibration	NOUN
m-1112	2490	9	,	,	PUNCT
m-1112	2490	10	where	where	SCONJ
m-1112	2490	11	charge	charge	NOUN
m-1112	2490	12	q	q	PROPN
m-1112	2490	13	=	=	PUNCT
m-1112	2490	14	is	be	AUX
m-1112	2490	15	the	the	DET
m-1112	2490	16	physical	physical	ADJ
m-1112	2490	17	property	property	NOUN
m-1112	2490	18	of	of	ADP
m-1112	2490	19	matter	matter	NOUN
m-1112	2490	20	that	that	PRON
m-1112	2490	21	causes	cause	VERB
m-1112	2490	22	it	it	PRON
m-1112	2490	23	to	to	PART
m-1112	2490	24	experience	experience	VERB
m-1112	2490	25	a	a	DET
m-1112	2490	26	force	force	NOUN
m-1112	2490	27	which	which	PRON
m-1112	2490	28	can	can	AUX
m-1112	2490	29	be	be	AUX
m-1112	2490	30	positive	positive	ADJ
m-1112	2490	31	or	or	CCONJ
m-1112	2490	32	negative	negative	ADJ
m-1112	2490	33	,	,	PUNCT
m-1112	2490	34	dq	dq	PROPN
m-1112	2490	35	/	/	SYM
m-1112	2490	36	dt	dt	NOUN
m-1112	2491	1	=	=	PUNCT
m-1112	2491	2	the	the	DET
m-1112	2491	3	least	least	ADV
m-1112	2491	4	quantized	quantize	VERB
m-1112	2491	5	amount	amount	NOUN
m-1112	2491	6	of	of	ADP
m-1112	2491	7	charge	charge	NOUN
m-1112	2491	8	,	,	PUNCT
m-1112	2491	9	and	and	CCONJ
m-1112	2491	10	d²q	d²q	NOUN
m-1112	2491	11	/	/	SYM
m-1112	2491	12	dt²	dt²	NOUN
m-1112	2491	13	=	=	PUNCT
m-1112	2491	14	the	the	DET
m-1112	2491	15	space	space	NOUN
m-1112	2491	16	distribution	distribution	NOUN
m-1112	2491	17	of	of	ADP
m-1112	2491	18	charge	charge	NOUN
m-1112	2491	19	,	,	PUNCT
m-1112	2491	20	and	and	CCONJ
m-1112	2491	21	l	l	NOUN
m-1112	2491	22	,	,	PUNCT
m-1112	2491	23	r	r	NOUN
m-1112	2491	24	,	,	PUNCT
m-1112	2491	25	c	c	NOUN
m-1112	2491	26	inductance	inductance	NOUN
m-1112	2491	27	,	,	PUNCT
m-1112	2491	28	resistance	resistance	NOUN
m-1112	2491	29	,	,	PUNCT
m-1112	2491	30	elasticity	elasticity	NOUN
m-1112	2491	31	constants	constant	NOUN
m-1112	2491	32	with	with	ADP
m-1112	2491	33	general	general	ADJ
m-1112	2491	34	solution	solution	NOUN
m-1112	2491	35	given	give	VERB
m-1112	2491	36	by	by	ADP
m-1112	2491	37	the	the	DET
m-1112	2491	38	equation	equation	NOUN
m-1112	2491	39	q	q	NOUN
m-1112	2492	1	=	=	PUNCT
m-1112	2492	2	a	a	DET
m-1112	2492	3	.	.	PUNCT
m-1112	2492	4	𝑒𝑠1.𝑡+	𝑒𝑠1.𝑡+	PROPN
m-1112	2492	5	b.	b.	PROPN
m-1112	2492	6	𝑒𝑠2.𝑡	𝑒𝑠2.𝑡	PROPN
m-1112	2493	1	+	+	CCONJ
m-1112	2493	2	x	x	SYM
m-1112	2493	3	sin(wt	sin(wt	NOUN
m-1112	2493	4	-	-	PUNCT
m-1112	2493	5	φ	φ	NOUN
m-1112	2493	6	)	)	PUNCT
m-1112	2493	7	…	…	PUNCT
m-1112	2493	8	...	...	PUNCT
m-1112	2493	9	(	(	PUNCT
m-1112	2493	10	2	2	X
m-1112	2493	11	)	)	PUNCT
m-1112	2493	12	equations	equation	NOUN
m-1112	2493	13	(	(	PUNCT
m-1112	2493	14	1	1	NUM
m-1112	2493	15	)	)	PUNCT
m-1112	2493	16	,	,	PUNCT
m-1112	2493	17	(	(	PUNCT
m-1112	2493	18	2	2	X
m-1112	2493	19	)	)	PUNCT
m-1112	2493	20	give	give	VERB
m-1112	2493	21	the	the	DET
m-1112	2493	22	analogic	analogic	ADJ
m-1112	2493	23	relation	relation	NOUN
m-1112	2493	24	of	of	ADP
m-1112	2493	25	the	the	DET
m-1112	2493	26	classical	classical	ADJ
m-1112	2493	27	mechanics	mechanic	NOUN
m-1112	2493	28	[	[	X
m-1112	2493	29	space	space	NOUN
m-1112	2493	30	position	position	NOUN
m-1112	2493	31	x	x	X
m-1112	2493	32	]	]	X
m-1112	2493	33	and	and	CCONJ
m-1112	2493	34	the	the	DET
m-1112	2493	35	electromagnetism	electromagnetism	NOUN
m-1112	2493	36	[	[	X
m-1112	2493	37	quanta	quanta	NOUN
m-1112	2493	38	of	of	ADP
m-1112	2493	39	energy	energy	NOUN
m-1112	2493	40	,	,	PUNCT
m-1112	2493	41	q	q	X
m-1112	2493	42	]	]	PUNCT
m-1112	2493	43	of	of	ADP
m-1112	2493	44	storing	store	VERB
m-1112	2493	45	and	and	CCONJ
m-1112	2493	46	removing	removing	NOUN
m-1112	2493	47	of	of	ADP
m-1112	2493	48	energy	energy	NOUN
m-1112	2493	49	in	in	ADP
m-1112	2493	50	energy	energy	NOUN
m-1112	2493	51	-	-	PUNCT
m-1112	2493	52	space	space	NOUN
m-1112	2493	53	cosmos	cosmos	PROPN
m-1112	2493	54	.distributed	.distribute	VERB
m-1112	2493	55	forces	force	NOUN
m-1112	2493	56	l1l2	l1l2	NOUN
m-1112	2493	57	=	=	NOUN
m-1112	2493	58	l	l	X
m-1112	2493	59	(	(	PUNCT
m-1112	2493	60	di	di	NOUN
m-1112	2493	61	/	/	SYM
m-1112	2493	62	dt	dt	PROPN
m-1112	2493	63	)	)	PUNCT
m-1112	2493	64	,	,	PUNCT
m-1112	2494	1	r1r2	r1r2	PROPN
m-1112	2494	2	=	=	NOUN
m-1112	2494	3	r	r	NOUN
m-1112	2494	4	.	.	PUNCT
m-1112	2495	1	i	i	PRON
m-1112	2495	2	,	,	PUNCT
m-1112	2495	3	c1c2	c1c2	X
m-1112	2495	4	=	=	PUNCT
m-1112	2495	5	q	q	PUNCT
m-1112	2495	6	/	/	SYM
m-1112	2495	7	c	c	NOUN
m-1112	2495	8	respectively	respectively	ADV
m-1112	2495	9	,	,	PUNCT
m-1112	2495	10	showing	show	VERB
m-1112	2495	11	the	the	DET
m-1112	2495	12	identification	identification	NOUN
m-1112	2495	13	of	of	ADP
m-1112	2495	14	the	the	DET
m-1112	2495	15	mechanical	mechanical	ADJ
m-1112	2495	16	and	and	CCONJ
m-1112	2495	17	physical	physical	ADJ
m-1112	2495	18	laws	law	NOUN
m-1112	2495	19	.	.	PUNCT
m-1112	2496	1	ijo	ijo	PROPN
m-1112	2496	2	international	international	PROPN
m-1112	2496	3	journal	journal	PROPN
m-1112	2496	4	of	of	ADP
m-1112	2496	5	mathematics	mathematics	PROPN
m-1112	2496	6	(	(	PUNCT
m-1112	2496	7	issn	issn	PROPN
m-1112	2496	8	:	:	PUNCT
m-1112	2496	9	2992	2992	NUM
m-1112	2496	10	-	-	SYM
m-1112	2496	11	4421	4421	NUM
m-1112	2496	12	)	)	PUNCT
m-1112	2496	13	volume	volume	NOUN
m-1112	2496	14	08	08	NUM
m-1112	2497	1	|	|	ADV
m-1112	2497	2	issue	issue	NOUN
m-1112	2497	3	08	08	NUM
m-1112	2498	1	|	|	ADV
m-1112	2498	2	august	august	PROPN
m-1112	2498	3	2025	2025	NUM
m-1112	2498	4	|	|	ADV
m-1112	2498	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2498	6	ijo	ijo	PROPN
m-1112	2498	7	journals	journal	NOUN
m-1112	2498	8	87	87	NUM
m-1112	2498	9	the	the	DET
m-1112	2498	10	fundamental	fundamental	ADJ
m-1112	2498	11	particles	particle	NOUN
m-1112	2498	12	origination	origination	NOUN
m-1112	2498	13	mechanism	mechanism	NOUN
m-1112	2498	14	in	in	ADP
m-1112	2498	15	mfmf	mfmf	PROPN
m-1112	2498	16	pns	pns	PROPN
m-1112	2498	17	caves	cave	NOUN
m-1112	2498	18	.	.	PUNCT
m-1112	2499	1	the	the	DET
m-1112	2499	2	way	way	NOUN
m-1112	2499	3	that	that	PRON
m-1112	2499	4	potential	potential	ADJ
m-1112	2499	5	-	-	PUNCT
m-1112	2499	6	energy	energy	NOUN
m-1112	2499	7	is	be	AUX
m-1112	2499	8	stored	store	VERB
m-1112	2499	9	,	,	PUNCT
m-1112	2499	10	is	be	AUX
m-1112	2499	11	that	that	PRON
m-1112	2499	12	of	of	ADP
m-1112	2499	13	material	material	ADJ
m-1112	2499	14	lrccircuit	lrccircuit	NOUN
m-1112	2499	15	,	,	PUNCT
m-1112	2499	16	which	which	PRON
m-1112	2499	17	is	be	AUX
m-1112	2499	18	for	for	ADP
m-1112	2499	19	the	the	DET
m-1112	2499	20	gravitational	gravitational	ADJ
m-1112	2499	21	-	-	PUNCT
m-1112	2499	22	potential	potential	ADJ
m-1112	2499	23	-	-	PUNCT
m-1112	2499	24	energy	energy	NOUN
m-1112	2499	25	the	the	DET
m-1112	2499	26	material	material	NOUN
m-1112	2499	27	-	-	PUNCT
m-1112	2499	28	capacitor	capacitor	NOUN
m-1112	2499	29	or	or	CCONJ
m-1112	2499	30	the	the	DET
m-1112	2499	31	→	→	PUNCT
m-1112	2499	32	focus	focus	NOUN
m-1112	2499	33	-	-	PUNCT
m-1112	2499	34	planet	planet	NOUN
m-1112	2499	35	–	–	PUNCT
m-1112	2499	36	sector	sector	NOUN
m-1112	2499	37	–	–	PUNCT
m-1112	2499	38	stores	store	NOUN
m-1112	2499	39	-	-	PUNCT
m-1112	2499	40	change	change	NOUN
m-1112	2499	41	←	←	NOUN
m-1112	2499	42	which	which	PRON
m-1112	2499	43	develop	develop	VERB
m-1112	2499	44	a	a	DET
m-1112	2499	45	voltage	voltage	NOUN
m-1112	2499	46	in	in	ADP
m-1112	2499	47	response	response	NOUN
m-1112	2499	48	to	to	ADP
m-1112	2499	49	that	that	DET
m-1112	2499	50	charge	charge	NOUN
m-1112	2499	51	.the	.the	DET
m-1112	2499	52	coil	coil	NOUN
m-1112	2499	53	of	of	ADP
m-1112	2499	54	wire	wire	NOUN
m-1112	2499	55	is	be	AUX
m-1112	2499	56	the	the	DET
m-1112	2499	57	infinite	infinite	ADJ
m-1112	2499	58	stationary	stationary	ADJ
m-1112	2499	59	-	-	PUNCT
m-1112	2499	60	dipole	dipole	NOUN
m-1112	2499	61	-	-	PUNCT
m-1112	2499	62	spinning	spin	VERB
m-1112	2499	63	material	material	NOUN
m-1112	2499	64	-	-	PUNCT
m-1112	2499	65	points	point	NOUN
m-1112	2499	66	of	of	ADP
m-1112	2499	67	this	this	PRON
m-1112	2499	68	→	→	SYM
m-1112	2499	69	focus	focus	NOUN
m-1112	2499	70	–	–	PUNCT
m-1112	2499	71	planet	planet	NOUN
m-1112	2499	72	sector	sector	NOUN
m-1112	2499	73	←	←	PROPN
m-1112	2499	74	which	which	PRON
m-1112	2499	75	develops	develop	VERB
m-1112	2499	76	the	the	DET
m-1112	2499	77	back	back	ADJ
m-1112	2499	78	-	-	PUNCT
m-1112	2499	79	electromagnetic	electromagnetic	NOUN
m-1112	2499	80	-	-	PUNCT
m-1112	2499	81	force	force	NOUN
m-1112	2499	82	,	,	PUNCT
m-1112	2499	83	when	when	SCONJ
m-1112	2499	84	current	current	ADJ
m-1112	2499	85	through	through	ADP
m-1112	2499	86	them	they	PRON
m-1112	2499	87	changes	change	NOUN
m-1112	2499	88	.	.	PUNCT
m-1112	2500	1	in	in	ADP
m-1112	2500	2	-	-	PUNCT
m-1112	2500	3	cave	cave	NOUN
m-1112	2500	4	-	-	PUNCT
m-1112	2500	5	box	box	NOUN
m-1112	2500	6	exist	exist	VERB
m-1112	2500	7	two	two	NUM
m-1112	2500	8	motions	motion	NOUN
m-1112	2500	9	,	,	PUNCT
m-1112	2500	10	revolving	revolving	NOUN
m-1112	2500	11	and	and	CCONJ
m-1112	2500	12	periodic	periodic	NOUN
m-1112	2500	13	,	,	PUNCT
m-1112	2500	14	the	the	DET
m-1112	2500	15	acceleration	acceleration	NOUN
m-1112	2500	16	of	of	ADP
m-1112	2500	17	gravity	gravity	NOUN
m-1112	2500	18	g	g	PROPN
m-1112	2500	19	≡	≡	PROPN
m-1112	2500	20			PROPN
m-1112	2500	21	σ	σ	PROPN
m-1112	2500	22	exists	exist	VERB
m-1112	2500	23	for	for	ADP
m-1112	2500	24	the	the	DET
m-1112	2500	25	first	first	ADJ
m-1112	2500	26	box-𝐁𝐑	box-𝐁𝐑	NOUN
m-1112	2500	27	,	,	PUNCT
m-1112	2500	28	while	while	SCONJ
m-1112	2500	29	local	local	ADJ
m-1112	2500	30	-	-	PUNCT
m-1112	2500	31	extreme	extreme	ADJ
m-1112	2500	32	-	-	PUNCT
m-1112	2500	33	case	case	NOUN
m-1112	2500	34	for	for	ADP
m-1112	2500	35	the	the	DET
m-1112	2500	36	second	second	ADJ
m-1112	2500	37	box-𝐁𝐏	box-𝐁𝐏	PROPN
m-1112	2500	38	.	.	PUNCT
m-1112	2501	1	in	in	ADP
m-1112	2501	2	this	this	DET
m-1112	2501	3	gravity	gravity	NOUN
m-1112	2501	4	g	g	PROPN
m-1112	2501	5	≡	≡	PROPN
m-1112	2501	6			PROPN
m-1112	2501	7	σ	σ	PROPN
m-1112	2501	8	,	,	PUNCT
m-1112	2501	9	is	be	AUX
m-1112	2501	10	locally	locally	ADV
m-1112	2501	11	altering	alter	VERB
m-1112	2501	12	s	s	PART
m-1112	2501	13	,	,	PUNCT
m-1112	2501	14	by	by	ADP
m-1112	2501	15	changing	change	VERB
m-1112	2501	16	the	the	DET
m-1112	2501	17	principal	principal	ADJ
m-1112	2501	18	-	-	PUNCT
m-1112	2501	19	stress	stress	NOUN
m-1112	2501	20	σ	σ	NOUN
m-1112	2501	21	with	with	ADP
m-1112	2501	22	local	local	ADJ
m-1112	2501	23	uniform	uniform	ADJ
m-1112	2501	24	pressure	pressure	NOUN
m-1112	2501	25	𝐠𝐋	𝐠𝐋	PROPN
m-1112	2501	26	≡	≡	PROPN
m-1112	2502	1	g	g	PROPN
m-1112	2502	2	ke	ke	PROPN
m-1112	2502	3	=	=	PUNCT
m-1112	2502	4	g	g	PROPN
m-1112	2502	5	*	*	PUNCT
m-1112	2503	1	[	[	X
m-1112	2503	2	force	force	NOUN
m-1112	2503	3	/	/	SYM
m-1112	2503	4	area	area	NOUN
m-1112	2503	5	]	]	X
m-1112	2504	1	=	=	PUNCT
m-1112	2504	2	g	g	PROPN
m-1112	2504	3	,	,	PUNCT
m-1112	2504	4	i.e.	i.e.	X
m-1112	2504	5	is	be	AUX
m-1112	2504	6	proved	prove	VERB
m-1112	2504	7	that	that	SCONJ
m-1112	2504	8	the	the	DET
m-1112	2504	9	minimum	minimum	ADJ
m-1112	2504	10	local	local	ADJ
m-1112	2504	11	-	-	PUNCT
m-1112	2504	12	energy	energy	NOUN
m-1112	2504	13	acceleration	acceleration	NOUN
m-1112	2504	14	is	be	AUX
m-1112	2504	15	the	the	DET
m-1112	2504	16	known	know	VERB
m-1112	2504	17	universal	universal	ADJ
m-1112	2504	18	gravitational	gravitational	ADJ
m-1112	2504	19	-	-	PUNCT
m-1112	2504	20	constant	constant	ADJ
m-1112	2504	21	g	g	NOUN
m-1112	2504	22	=	=	SYM
m-1112	2504	23	g	g	NOUN
m-1112	2504	24	k	k	PROPN
m-1112	2504	25	=	=	PUNCT
m-1112	2504	26	𝐤𝐄	𝐤𝐄	NOUN
m-1112	2504	27	g	g	NOUN
m-1112	2504	28	=	=	SYM
m-1112	2504	29	𝐤𝐋	𝐤𝐋	NOUN
m-1112	2504	30	σ	σ	NOUN
m-1112	2504	31	=	=	SYM
m-1112	2504	32	g	g	PROPN
m-1112	2504	33	gl	gl	PROPN
m-1112	2504	34	kl	kl	PROPN
m-1112	2504	35	such	such	ADJ
m-1112	2504	36	for	for	ADP
m-1112	2504	37	macrocosm	macrocosm	PROPN
m-1112	2504	38	as	as	ADP
m-1112	2504	39	for	for	ADP
m-1112	2504	40	microcosm	microcosm	NOUN
m-1112	2504	41	,	,	PUNCT
m-1112	2504	42	and	and	CCONJ
m-1112	2504	43	both	both	DET
m-1112	2504	44	cases	case	NOUN
m-1112	2504	45	obeying	obey	VERB
m-1112	2504	46	newton`s	newton`s	NOUN
m-1112	2504	47	laws	law	NOUN
m-1112	2504	48	of	of	ADP
m-1112	2504	49	motion	motion	NOUN
m-1112	2504	50	.	.	PUNCT
m-1112	2505	1	4	4	X
m-1112	2505	2	..	..	PUNCT
m-1112	2505	3	since	since	SCONJ
m-1112	2505	4	electron	electron	NOUN
m-1112	2505	5	is	be	AUX
m-1112	2505	6	rotating	rotate	VERB
m-1112	2505	7	in	in	ADP
m-1112	2505	8	orbits	orbit	NOUN
m-1112	2505	9	so	so	SCONJ
m-1112	2505	10	electromagnetic	electromagnetic	ADJ
m-1112	2505	11	wave	wave	NOUN
m-1112	2505	12	is	be	AUX
m-1112	2505	13	also	also	ADV
m-1112	2505	14	rotating	rotate	VERB
m-1112	2505	15	,	,	PUNCT
m-1112	2505	16	therefore	therefore	ADV
m-1112	2505	17	is	be	AUX
m-1112	2505	18	needed	need	VERB
m-1112	2505	19	a	a	DET
m-1112	2505	20	proper	proper	ADJ
m-1112	2505	21	-	-	PUNCT
m-1112	2505	22	stationary	stationary	ADJ
m-1112	2505	23	-	-	PUNCT
m-1112	2505	24	magnet	magnet	NOUN
m-1112	2505	25	on	on	ADP
m-1112	2505	26	which	which	PRON
m-1112	2505	27	rotation	rotation	NOUN
m-1112	2505	28	becomes	become	VERB
m-1112	2505	29	oscillation	oscillation	NOUN
m-1112	2505	30	in	in	ADP
m-1112	2505	31	order	order	NOUN
m-1112	2505	32	to	to	PART
m-1112	2505	33	succeed	succeed	VERB
m-1112	2505	34	a	a	DET
m-1112	2505	35	clear	clear	ADJ
m-1112	2505	36	3	3	NUM
m-1112	2505	37	-	-	PUNCT
m-1112	2505	38	dimensioned	dimension	VERB
m-1112	2505	39	,	,	PUNCT
m-1112	2505	40	φ	φ	PROPN
m-1112	2505	41	³	³	PROPN
m-1112	2505	42	,	,	PUNCT
m-1112	2505	43	magnetic	magnetic	ADJ
m-1112	2505	44	-	-	PUNCT
m-1112	2505	45	resonance	resonance	NOUN
m-1112	2505	46	-	-	PUNCT
m-1112	2505	47	imaging	imaging	NOUN
m-1112	2505	48	[	[	X
m-1112	2505	49	the	the	DET
m-1112	2505	50	mri	mri	NOUN
m-1112	2505	51	]	]	PUNCT
m-1112	2505	52	and	and	CCONJ
m-1112	2505	53	the	the	DET
m-1112	2505	54	other	other	ADJ
m-1112	2505	55	systems	system	NOUN
m-1112	2505	56	use	use	VERB
m-1112	2505	57	this	this	DET
m-1112	2505	58	property	property	NOUN
m-1112	2505	59	of	of	ADP
m-1112	2505	60	bottom	bottom	ADJ
m-1112	2505	61	-	-	PUNCT
m-1112	2505	62	information	information	NOUN
m-1112	2505	63	.	.	PUNCT
m-1112	2506	1	this	this	DET
m-1112	2506	2	property	property	NOUN
m-1112	2506	3	of	of	ADP
m-1112	2506	4	spin	spin	NOUN
m-1112	2506	5	in	in	ADP
m-1112	2506	6	all	all	DET
m-1112	2506	7	depths	depth	NOUN
m-1112	2506	8	of	of	ADP
m-1112	2506	9	energy	energy	NOUN
m-1112	2506	10	caves	cave	NOUN
m-1112	2506	11	allows	allow	VERB
m-1112	2506	12	the	the	DET
m-1112	2506	13	granularity	granularity	NOUN
m-1112	2506	14	of	of	ADP
m-1112	2506	15	energy	energy	NOUN
m-1112	2506	16	in	in	ADP
m-1112	2506	17	energyloops	energyloop	NOUN
m-1112	2506	18	,	,	PUNCT
m-1112	2506	19	and	and	CCONJ
m-1112	2506	20	after	after	SCONJ
m-1112	2506	21	to	to	PART
m-1112	2506	22	be	be	AUX
m-1112	2506	23	bonded	bond	VERB
m-1112	2506	24	.this	.this	PRON
m-1112	2506	25	property	property	NOUN
m-1112	2506	26	of	of	ADP
m-1112	2506	27	electron	electron	NOUN
m-1112	2506	28	may	may	AUX
m-1112	2506	29	be	be	AUX
m-1112	2506	30	used	use	VERB
m-1112	2506	31	for	for	ADP
m-1112	2506	32	cancer	cancer	NOUN
m-1112	2506	33	chromosomes	chromosome	NOUN
m-1112	2506	34	.	.	PUNCT
m-1112	2507	1	6c4	6c4	X
m-1112	2507	2	..	..	PUNCT
m-1112	2507	3	the	the	DET
m-1112	2507	4	conservation	conservation	NOUN
m-1112	2507	5	of	of	ADP
m-1112	2507	6	energy	energy	NOUN
m-1112	2507	7	in	in	ADP
m-1112	2507	8	→	→	PUNCT
m-1112	2507	9	velocity	velocity	NOUN
m-1112	2507	10	�	�	NOUN
m-1112	2507	11	̅	̅	NOUN
m-1112	2507	12	�	�	PROPN
m-1112	2507	13	and	and	CCONJ
m-1112	2507	14	in	in	ADP
m-1112	2507	15	gravity	gravity	NOUN
m-1112	2507	16	�	�	NOUN
m-1112	2507	17	̅	̅	NOUN
m-1112	2507	18	�	�	PROPN
m-1112	2507	19	caves	cave	VERB
m-1112	2507	20	←	←	PROPN
m-1112	2507	21	since	since	SCONJ
m-1112	2507	22	gravity	gravity	NOUN
m-1112	2507	23	�	�	NOUN
m-1112	2507	24	̅	̅	NOUN
m-1112	2507	25	�	�	NOUN
m-1112	2507	26	is	be	AUX
m-1112	2507	27	the	the	DET
m-1112	2507	28	energy	energy	NOUN
m-1112	2507	29	≡the	≡the	DET
m-1112	2507	30	angular	angular	ADJ
m-1112	2507	31	-	-	PUNCT
m-1112	2507	32	momentum	momentum	NOUN
m-1112	2507	33	{	{	PUNCT
m-1112	2507	34	�	�	NOUN
m-1112	2507	35	̅	̅	NOUN
m-1112	2507	36	�	�	NOUN
m-1112	2507	37	=	=	NOUN
m-1112	2507	38	r	r	NOUN
m-1112	2507	39	m	m	VERB
m-1112	2507	40	v}in	v}in	NUM
m-1112	2507	41	planck`s	planck`s	NOUN
m-1112	2507	42	length	length	NOUN
m-1112	2507	43	r	r	NOUN
m-1112	2507	44	p	p	NOUN
m-1112	2507	45	,	,	PUNCT
m-1112	2507	46	and	and	CCONJ
m-1112	2507	47	it	it	PRON
m-1112	2507	48	is	be	AUX
m-1112	2507	49	a	a	DET
m-1112	2507	50	stationary	stationary	ADJ
m-1112	2507	51	-	-	PUNCT
m-1112	2507	52	wave	wave	NOUN
m-1112	2507	53	or	or	CCONJ
m-1112	2507	54	an	an	DET
m-1112	2507	55	electromagnetic	electromagnetic	ADJ
m-1112	2507	56	wave	wave	NOUN
m-1112	2507	57	-	-	PUNCT
m-1112	2507	58	signal	signal	NOUN
m-1112	2507	59	which	which	PRON
m-1112	2507	60	transmits	transmit	VERB
m-1112	2507	61	informations	information	NOUN
m-1112	2507	62	then	then	ADV
m-1112	2507	63	follows	follow	VERB
m-1112	2507	64	the	the	DET
m-1112	2507	65	waves	wave	NOUN
m-1112	2507	66	-	-	PUNCT
m-1112	2507	67	frequency	frequency	NOUN
m-1112	2507	68	-	-	PUNCT
m-1112	2507	69	signal	signal	NOUN
m-1112	2507	70	-	-	PUNCT
m-1112	2507	71	spectrum	spectrum	NOUN
m-1112	2507	72	.the	.the	DET
m-1112	2507	73	gravitational	gravitational	ADJ
m-1112	2507	74	constant	constant	ADJ
m-1112	2507	75	g	g	PROPN
m-1112	2507	76	is	be	AUX
m-1112	2507	77	the	the	DET
m-1112	2507	78	active	active	ADJ
m-1112	2507	79	force	force	NOUN
m-1112	2507	80	on	on	ADP
m-1112	2507	81	light	light	ADJ
m-1112	2507	82	velocity	velocity	NOUN
m-1112	2507	83	�	�	NOUN
m-1112	2507	84	̅	̅	NOUN
m-1112	2507	85	�	�	PROPN
m-1112	2507	86	and	and	CCONJ
m-1112	2507	87	consequently	consequently	ADV
m-1112	2507	88	on	on	ADP
m-1112	2507	89	g̅	g̅	NOUN
m-1112	2507	90	also	also	ADV
m-1112	2507	91	.	.	PUNCT
m-1112	2508	1	from	from	ADP
m-1112	2508	2	waves	wave	NOUN
m-1112	2508	3	theory	theory	NOUN
m-1112	2508	4	→	→	SYM
m-1112	2508	5	position	position	NOUN
m-1112	2508	6	x	x	NOUN
m-1112	2508	7	=	=	SYM
m-1112	2508	8	a.sinwt	a.sinwt	NUM
m-1112	2508	9	and	and	CCONJ
m-1112	2508	10	acceleration	acceleration	NOUN
m-1112	2508	11	�	�	PROPN
m-1112	2508	12	̈	̈	SYM
m-1112	2508	13	�	�	PROPN
m-1112	2508	14	=	=	PUNCT
m-1112	2508	15	a	a	DET
m-1112	2508	16	w	w	PROPN
m-1112	2508	17	²	²	NUM
m-1112	2508	18	←	←	NOUN
m-1112	2508	19	where	where	SCONJ
m-1112	2508	20	the	the	DET
m-1112	2508	21	signal	signal	NOUN
m-1112	2508	22	-	-	PUNCT
m-1112	2508	23	spectrum	spectrum	NOUN
m-1112	2508	24	is	be	AUX
m-1112	2508	25	consisted	consist	VERB
m-1112	2508	26	of	of	ADP
m-1112	2508	27	the	the	DET
m-1112	2508	28	amplitude	amplitude	NOUN
m-1112	2508	29	𝐀	𝐀	PROPN
m-1112	2508	30	𝐂	𝐂	PROPN
m-1112	2508	31	and	and	CCONJ
m-1112	2508	32	of	of	ADP
m-1112	2508	33	the	the	DET
m-1112	2508	34	angular	angular	ADJ
m-1112	2508	35	frequency	frequency	NOUN
m-1112	2508	36	�	�	PROPN
m-1112	2508	37	̅	̅	NOUN
m-1112	2508	38	�	�	PROPN
m-1112	2508	39	,	,	PUNCT
m-1112	2508	40	from	from	ADP
m-1112	2508	41	where	where	SCONJ
m-1112	2508	42	all	all	DET
m-1112	2508	43	other	other	ADJ
m-1112	2508	44	properties	property	NOUN
m-1112	2508	45	follow	follow	VERB
m-1112	2508	46	.	.	PUNCT
m-1112	2509	1	since	since	SCONJ
m-1112	2509	2	�	�	PROPN
m-1112	2509	3	̈	̈	X
m-1112	2509	4	�	�	PROPN
m-1112	2509	5	ts	ts	ADP
m-1112	2509	6	the	the	DET
m-1112	2509	7	acceleration	acceleration	NOUN
m-1112	2509	8	force	force	NOUN
m-1112	2509	9	of	of	ADP
m-1112	2509	10	position	position	NOUN
m-1112	2509	11	x	x	INTJ
m-1112	2509	12	,	,	PUNCT
m-1112	2509	13	then	then	ADV
m-1112	2509	14	for	for	ADP
m-1112	2509	15	planck`s	planck`s	NOUN
m-1112	2509	16	length	length	NOUN
m-1112	2509	17	issues	issue	NOUN
m-1112	2509	18	ẍ	ẍ	PUNCT
m-1112	2510	1	=	=	SYM
m-1112	2510	2	g	g	PROPN
m-1112	2510	3	=	=	SYM
m-1112	2510	4	a²g.w	a²g.w	PROPN
m-1112	2510	5	²	²	NUM
m-1112	2510	6	,	,	PUNCT
m-1112	2510	7	or	or	CCONJ
m-1112	2510	8	�	�	PROPN
m-1112	2510	9	̅̅̅	̅̅̅	PROPN
m-1112	2510	10	�	�	PROPN
m-1112	2510	11	=	=	SYM
m-1112	2510	12	√g	√g	NOUN
m-1112	2510	13	/	/	SYM
m-1112	2510	14	a²	a²	NOUN
m-1112	2510	15	=	=	SYM
m-1112	2510	16	√6,68	√6,68	PROPN
m-1112	2510	17	.	.	NOUN
m-1112	2510	18	10−11/[2,6262	10−11/[2,6262	NUM
m-1112	2510	19	.	.	PUNCT
m-1112	2511	1	10−35]²	10−35]²	NUM
m-1112	2512	1	so	so	ADV
m-1112	2512	2	gravity	gravity	NOUN
m-1112	2512	3	-	-	PUNCT
m-1112	2512	4	frequency→	frequency→	PROPN
m-1112	2512	5	�	�	PROPN
m-1112	2512	6	̅̅̅	̅̅̅	PROPN
m-1112	2512	7	�	�	PROPN
m-1112	2512	8	=	=	SYM
m-1112	2512	9	0,5057.1030	0,5057.1030	NUM
m-1112	2512	10	h	h	NOUN
m-1112	2512	11	and	and	CCONJ
m-1112	2512	12	gravity	gravity	NOUN
m-1112	2512	13	-	-	PUNCT
m-1112	2512	14	wave	wave	NOUN
m-1112	2512	15	-	-	PUNCT
m-1112	2512	16	frequency	frequency	NOUN
m-1112	2512	17	𝐟	𝐟	NOUN
m-1112	2512	18	𝑮𝑾=8,05.1028	𝑮𝑾=8,05.1028	NOUN
m-1112	2512	19	h	h	NOUN
m-1112	2512	20	←	←	PROPN
m-1112	2512	21	the	the	DET
m-1112	2512	22	gravitational	gravitational	ADJ
m-1112	2512	23	force	force	NOUN
m-1112	2512	24	action	action	NOUN
m-1112	2512	25	:	:	PUNCT
m-1112	2513	1	[	[	X
m-1112	2513	2	[	[	X
m-1112	2513	3	g	g	X
m-1112	2513	4	]	]	X
m-1112	2513	5	]	]	X
m-1112	2513	6	→	→	PUNCT
m-1112	2513	7	{	{	PUNCT
m-1112	2513	8	[	[	PUNCT
m-1112	2513	9	�	�	NOUN
m-1112	2513	10	̅	̅	NOUN
m-1112	2513	11	�	�	PROPN
m-1112	2513	12	]	]	PUNCT
m-1112	2513	13	±	±	NUM
m-1112	2513	14	𝐄𝒏}≡	𝐄𝒏}≡	PROPN
m-1112	2513	15	�	�	NOUN
m-1112	2513	16	̅	̅	NOUN
m-1112	2513	17	�	�	PROPN
m-1112	2513	18	≡	≡	PROPN
m-1112	2513	19	𝐄𝒏+{[g	𝐄𝒏+{[g	PROPN
m-1112	2513	20	]	]	X
m-1112	2513	21	±	±	NUM
m-1112	2514	1	[	[	X
m-1112	2514	2	�	�	NOUN
m-1112	2514	3	̅	̅	NOUN
m-1112	2514	4	�	�	NOUN
m-1112	2514	5	]	]	PUNCT
m-1112	2514	6	}	}	PUNCT
m-1112	2514	7	and	and	CCONJ
m-1112	2514	8	→	→	SYM
m-1112	2514	9	𝐄	𝐄	NOUN
m-1112	2514	10	𝐑	𝐑	NOUN
m-1112	2514	11	=	=	SYM
m-1112	2514	12	𝐄	𝐄	PROPN
m-1112	2514	13	𝐆	𝐆	NOUN
m-1112	2514	14	+	+	CCONJ
m-1112	2514	15	𝐄	𝐄	PROPN
m-1112	2514	16	�	�	NOUN
m-1112	2514	17	̅	̅	NOUN
m-1112	2514	18	�	�	PROPN
m-1112	2514	19	←	←	PROPN
m-1112	2514	20	where	where	SCONJ
m-1112	2514	21	,	,	PUNCT
m-1112	2514	22	[	[	X
m-1112	2514	23	[	[	X
m-1112	2514	24	g	g	X
m-1112	2514	25	]	]	X
m-1112	2514	26	]	]	X
m-1112	2514	27	=	=	PUNCT
m-1112	2515	1	[	[	X
m-1112	2515	2	gravitational	gravitational	ADJ
m-1112	2515	3	constant	constant	ADJ
m-1112	2515	4	g	g	X
m-1112	2515	5	]	]	PUNCT
m-1112	2515	6	≡	≡	PROPN
m-1112	2515	7	the	the	DET
m-1112	2515	8	signalling.(w	signalling.(w	NOUN
m-1112	2515	9	c	c	NOUN
m-1112	2515	10	)	)	PUNCT
m-1112	2515	11	→	→	SYM
m-1112	2515	12	the	the	DET
m-1112	2515	13	carrier	carrier	NOUN
m-1112	2515	14	wave	wave	NOUN
m-1112	2516	1	[	[	X
m-1112	2516	2	[	[	X
m-1112	2516	3	�	�	NOUN
m-1112	2516	4	̅	̅	NOUN
m-1112	2516	5	�	�	NOUN
m-1112	2516	6	]	]	X
m-1112	2516	7	]	]	X
m-1112	2517	1	=	=	PUNCT
m-1112	2517	2	any	any	DET
m-1112	2517	3	action	action	NOUN
m-1112	2517	4	of	of	ADP
m-1112	2517	5	[	[	X
m-1112	2517	6	g	g	NOUN
m-1112	2517	7	on	on	ADP
m-1112	2517	8	�	�	NOUN
m-1112	2517	9	̅	̅	NOUN
m-1112	2517	10	�	�	NOUN
m-1112	2517	11	]	]	PUNCT
m-1112	2517	12	≡	≡	PROPN
m-1112	2517	13	any	any	DET
m-1112	2517	14	signalling.(	signalling.(	NUM
m-1112	2517	15	�	�	SYM
m-1112	2517	16	̅	̅	NOUN
m-1112	2517	17	�	�	NOUN
m-1112	2517	18	)	)	PUNCT
m-1112	2517	19	modulating	modulate	VERB
m-1112	2517	20	velocity	velocity	NOUN
m-1112	2517	21	-	-	PUNCT
m-1112	2517	22	wave	wave	NOUN
m-1112	2517	23	[	[	X
m-1112	2517	24	[	[	X
m-1112	2517	25	�	�	NOUN
m-1112	2517	26	̅	̅	NOUN
m-1112	2517	27	�	�	NOUN
m-1112	2517	28	]	]	X
m-1112	2517	29	]	]	X
m-1112	2517	30	=	=	PUNCT
m-1112	2517	31	the	the	DET
m-1112	2517	32	new	new	ADJ
m-1112	2517	33	modulated	modulate	VERB
m-1112	2517	34	[	[	X
m-1112	2517	35	g	g	X
m-1112	2517	36	↔	↔	PROPN
m-1112	2517	37	�	�	PROPN
m-1112	2517	38	̅	̅	NOUN
m-1112	2517	39	�	�	NOUN
m-1112	2517	40	]	]	PUNCT
m-1112	2517	41	signal	signal	NOUN
m-1112	2517	42	≡	≡	PROPN
m-1112	2517	43	f	f	PROPN
m-1112	2517	44	�	�	PROPN
m-1112	2517	45	̅	̅	NOUN
m-1112	2517	46	�	�	PROPN
m-1112	2517	47	m+wc	m+wc	NOUN
m-1112	2517	48	2	2	NUM
m-1112	2517	49	+	+	CCONJ
m-1112	2517	50	f	f	PROPN
m-1112	2517	51	�	�	PROPN
m-1112	2517	52	̅	̅	PROPN
m-1112	2517	53	�	�	PROPN
m-1112	2517	54	m−wc	m−wc	PROPN
m-1112	2517	55	2	2	NUM
m-1112	2517	56	≡	≡	PROPN
m-1112	2517	57	[	[	X
m-1112	2517	58	mas	mas	X
m-1112	2517	59	]	]	X
m-1112	2517	60	compound	compound	NOUN
m-1112	2517	61	=	=	PUNCT
m-1112	2517	62	the	the	DET
m-1112	2517	63	demodulated	demodulate	VERB
m-1112	2517	64	[	[	X
m-1112	2517	65	mas	mas	X
m-1112	2517	66	]	]	X
m-1112	2517	67	≡	≡	PROPN
m-1112	2517	68	f	f	PROPN
m-1112	2517	69	w+2wc	w+2wc	PROPN
m-1112	2517	70	2	2	NUM
m-1112	2517	71	+	+	CCONJ
m-1112	2517	72	f	f	PROPN
m-1112	2517	73	w−2wc	w−2wc	NOUN
m-1112	2517	74	2	2	NUM
m-1112	2517	75	≡	≡	PROPN
m-1112	2517	76	[	[	X
m-1112	2517	77	dmas	dmas	X
m-1112	2517	78	]	]	PUNCT
m-1112	2517	79	.	.	PUNCT
m-1112	2518	1	�	�	PROPN
m-1112	2518	2	̅	̅	NOUN
m-1112	2518	3	�	�	PROPN
m-1112	2518	4	,	,	PUNCT
m-1112	2518	5	since	since	SCONJ
m-1112	2518	6	[	[	PUNCT
m-1112	2518	7	g	g	NOUN
m-1112	2518	8	=	=	PUNCT
m-1112	2518	9	the	the	DET
m-1112	2518	10	carrier	carrier	NOUN
m-1112	2518	11	]	]	PUNCT
m-1112	2518	12	→	→	ADP
m-1112	2518	13	[	[	PUNCT
m-1112	2518	14	�	�	NOUN
m-1112	2518	15	̅	̅	NOUN
m-1112	2518	16	�	�	NOUN
m-1112	2518	17	=	=	PUNCT
m-1112	2518	18	the	the	DET
m-1112	2518	19	modulator	modulator	NOUN
m-1112	2518	20	]	]	X
m-1112	2518	21	→	→	ADP
m-1112	2518	22	[	[	PUNCT
m-1112	2518	23	g+	g+	X
m-1112	2518	24	�	�	PROPN
m-1112	2518	25	̅	̅	NOUN
m-1112	2518	26	�	�	NOUN
m-1112	2518	27	=	=	PUNCT
m-1112	2518	28	the	the	DET
m-1112	2518	29	modulated	modulate	VERB
m-1112	2518	30	]	]	PUNCT
m-1112	2518	31	and	and	CCONJ
m-1112	2518	32	[	[	PUNCT
m-1112	2518	33	g+	g+	NOUN
m-1112	2518	34	�	�	PROPN
m-1112	2518	35	̅	̅	NOUN
m-1112	2518	36	�	�	PROPN
m-1112	2518	37	]	]	PUNCT
m-1112	2519	1	+	+	NUM
m-1112	2519	2	�	�	NOUN
m-1112	2519	3	̅	̅	NOUN
m-1112	2519	4	�	�	NOUN
m-1112	2519	5	↔	↔	PROPN
m-1112	2519	6	[	[	PUNCT
m-1112	2519	7	dm	dm	NOUN
m-1112	2519	8	=	=	PUNCT
m-1112	2519	9	antidotes	antidote	NOUN
m-1112	2519	10	]	]	PUNCT
m-1112	2520	1	=	=	PUNCT
m-1112	2520	2	the	the	DET
m-1112	2520	3	demodulation	demodulation	NOUN
m-1112	2520	4	]	]	PUNCT
m-1112	2520	5	i.e.	i.e.	X
m-1112	2520	6	the	the	DET
m-1112	2520	7	communications	communication	NOUN
m-1112	2520	8	–	–	PUNCT
m-1112	2520	9	frequencies	frequency	NOUN
m-1112	2520	10	in	in	ADP
m-1112	2520	11	planck`s	planck`s	NOUN
m-1112	2520	12	cave	cave	NOUN
m-1112	2520	13	,	,	PUNCT
m-1112	2520	14	are	be	AUX
m-1112	2520	15	the	the	DET
m-1112	2520	16	wave	wave	NOUN
m-1112	2520	17	resonances	resonance	NOUN
m-1112	2520	18	which	which	PRON
m-1112	2520	19	consist	consist	VERB
m-1112	2520	20	the	the	DET
m-1112	2520	21	master	master	NOUN
m-1112	2520	22	-	-	PUNCT
m-1112	2520	23	keys	key	NOUN
m-1112	2520	24	of	of	ADP
m-1112	2520	25	these	these	DET
m-1112	2520	26	wave	wave	NOUN
m-1112	2520	27	caves	cave	NOUN
m-1112	2520	28	.	.	PUNCT
m-1112	2521	1	the	the	DET
m-1112	2521	2	conservation	conservation	NOUN
m-1112	2521	3	of	of	ADP
m-1112	2521	4	energy	energy	NOUN
m-1112	2521	5	in	in	ADP
m-1112	2521	6	caves	cave	NOUN
m-1112	2521	7	and	and	CCONJ
m-1112	2521	8	in	in	ADP
m-1112	2521	9	atoms	atom	NOUN
m-1112	2521	10	compounds	compound	NOUN
m-1112	2521	11	.	.	PUNCT
m-1112	2522	1	[	[	X
m-1112	2522	2	106	106	NUM
m-1112	2522	3	]	]	X
m-1112	2522	4	ijo	ijo	PROPN
m-1112	2522	5	international	international	PROPN
m-1112	2522	6	journal	journal	PROPN
m-1112	2522	7	of	of	ADP
m-1112	2522	8	mathematics	mathematics	PROPN
m-1112	2522	9	(	(	PUNCT
m-1112	2522	10	issn	issn	PROPN
m-1112	2522	11	:	:	PUNCT
m-1112	2522	12	2992	2992	NUM
m-1112	2522	13	-	-	SYM
m-1112	2522	14	4421	4421	NUM
m-1112	2522	15	)	)	PUNCT
m-1112	2522	16	volume	volume	NOUN
m-1112	2522	17	08	08	NUM
m-1112	2523	1	|	|	ADV
m-1112	2523	2	issue	issue	NOUN
m-1112	2523	3	08	08	NUM
m-1112	2524	1	|	|	ADV
m-1112	2524	2	august	august	PROPN
m-1112	2524	3	2025	2025	NUM
m-1112	2524	4	|	|	ADV
m-1112	2524	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2524	6	ijo	ijo	PROPN
m-1112	2524	7	journals	journal	NOUN
m-1112	2524	8	88	88	NUM
m-1112	2524	9	the	the	DET
m-1112	2524	10	fundamental	fundamental	ADJ
m-1112	2524	11	particles	particle	NOUN
m-1112	2524	12	origination	origination	NOUN
m-1112	2524	13	mechanism	mechanism	NOUN
m-1112	2524	14	in	in	ADP
m-1112	2524	15	mfmf	mfmf	PROPN
m-1112	2524	16	pns	pns	PROPN
m-1112	2524	17	caves	cave	NOUN
m-1112	2524	18	.	.	PUNCT
m-1112	2525	1	the	the	DET
m-1112	2525	2	atoms	atom	NOUN
m-1112	2525	3	–	–	PUNCT
m-1112	2525	4	actions	action	NOUN
m-1112	2525	5	:	:	PUNCT
m-1112	2526	1	[	[	X
m-1112	2526	2	[	[	X
m-1112	2526	3	a	a	X
m-1112	2526	4	]	]	X
m-1112	2526	5	]	]	X
m-1112	2526	6	→	→	PUNCT
m-1112	2526	7	{	{	PUNCT
m-1112	2526	8	[	[	X
m-1112	2526	9	b]±𝐄𝒏	b]±𝐄𝒏	NOUN
m-1112	2526	10	}	}	PUNCT
m-1112	2526	11	≡	≡	PROPN
m-1112	2526	12	c	c	PROPN
m-1112	2526	13	≡	≡	PROPN
m-1112	2526	14	𝐄𝒏+	𝐄𝒏+	PROPN
m-1112	2526	15	{	{	PUNCT
m-1112	2526	16	[	[	X
m-1112	2526	17	a	a	X
m-1112	2526	18	]	]	X
m-1112	2526	19	±	±	NOUN
m-1112	2526	20	[	[	X
m-1112	2526	21	b]},→	b]},→	NOUN
m-1112	2526	22	𝐄𝒏=	𝐄𝒏=	NOUN
m-1112	2526	23	𝐄𝐂	𝐄𝐂	NOUN
m-1112	2526	24	+	+	CCONJ
m-1112	2526	25	𝐄𝐀	𝐄𝐀	PROPN
m-1112	2526	26	←	←	PROPN
m-1112	2526	27	and	and	CCONJ
m-1112	2526	28	where	where	SCONJ
m-1112	2526	29	[	[	X
m-1112	2526	30	[	[	X
m-1112	2526	31	a	a	X
m-1112	2526	32	]	]	X
m-1112	2526	33	]	]	X
m-1112	2526	34	=	=	PUNCT
m-1112	2527	1	[	[	X
m-1112	2527	2	atom	atom	NOUN
m-1112	2527	3	or	or	CCONJ
m-1112	2527	4	compound	compound	NOUN
m-1112	2527	5	]	]	PUNCT
m-1112	2527	6	≡	≡	PROPN
m-1112	2527	7	the	the	DET
m-1112	2527	8	signalling.(wc	signalling.(wc	NOUN
m-1112	2527	9	)	)	PUNCT
m-1112	2527	10	→	→	PUNCT
m-1112	2527	11	the	the	DET
m-1112	2527	12	carrier	carrier	NOUN
m-1112	2527	13	wave	wave	NOUN
m-1112	2528	1	[	[	X
m-1112	2528	2	[	[	X
m-1112	2528	3	b	b	X
m-1112	2528	4	]	]	X
m-1112	2528	5	]	]	X
m-1112	2528	6	=	=	SYM
m-1112	2528	7	any[a	any[a	PROPN
m-1112	2528	8	-	-	PUNCT
m-1112	2528	9	or	or	CCONJ
m-1112	2528	10	-	-	PUNCT
m-1112	2528	11	c	c	NOUN
m-1112	2528	12	]	]	PUNCT
m-1112	2528	13	≡	≡	PROPN
m-1112	2528	14	any	any	DET
m-1112	2528	15	signalling.(w	signalling.(w	NOUN
m-1112	2528	16	)	)	PUNCT
m-1112	2528	17	wave	wave	NOUN
m-1112	2528	18	=	=	PUNCT
m-1112	2529	1	the	the	DET
m-1112	2529	2	modulating	modulate	VERB
m-1112	2529	3	wave	wave	NOUN
m-1112	2529	4	[	[	X
m-1112	2529	5	[	[	X
m-1112	2529	6	c	c	X
m-1112	2529	7	]	]	X
m-1112	2529	8	]	]	X
m-1112	2529	9	=	=	PUNCT
m-1112	2529	10	the	the	DET
m-1112	2529	11	new	new	ADJ
m-1112	2529	12	modulated	modulate	VERB
m-1112	2529	13	wave	wave	NOUN
m-1112	2530	1	[	[	X
m-1112	2530	2	a	a	X
m-1112	2530	3	]	]	X
m-1112	2530	4	signal	signal	NOUN
m-1112	2530	5	≡	≡	PROPN
m-1112	2530	6	f	f	PROPN
m-1112	2530	7	w+wc	w+wc	PROPN
m-1112	2530	8	2	2	NUM
m-1112	2530	9	+	+	CCONJ
m-1112	2530	10	f	f	PROPN
m-1112	2530	11	w−wc	w−wc	NOUN
m-1112	2530	12	2	2	NUM
m-1112	2530	13	≡	≡	PROPN
m-1112	2530	14	[	[	X
m-1112	2530	15	mas	mas	X
m-1112	2530	16	]	]	X
m-1112	2530	17	antidote	antidote	NOUN
m-1112	2530	18	=	=	PUNCT
m-1112	2530	19	the	the	DET
m-1112	2530	20	demodulated	demodulate	VERB
m-1112	2530	21	[	[	X
m-1112	2530	22	mas	mas	X
m-1112	2530	23	]	]	X
m-1112	2530	24	≡	≡	PROPN
m-1112	2530	25	f	f	PROPN
m-1112	2531	1	w+2wc	w+2wc	PROPN
m-1112	2531	2	2	2	NUM
m-1112	2531	3	+	+	CCONJ
m-1112	2531	4	f	f	PROPN
m-1112	2531	5	w−2wc	w−2wc	NOUN
m-1112	2531	6	2	2	NUM
m-1112	2531	7	≡	≡	PROPN
m-1112	2531	8	[	[	X
m-1112	2531	9	dmas	dmas	X
m-1112	2531	10	]	]	PUNCT
m-1112	2531	11	,	,	PUNCT
m-1112	2531	12	�	�	PROPN
m-1112	2531	13	̅	̅	NOUN
m-1112	2531	14	�	�	NOUN
m-1112	2531	15	,	,	PUNCT
m-1112	2531	16	as	as	ADP
m-1112	2531	17	the	the	DET
m-1112	2531	18	atoms	atom	NOUN
m-1112	2531	19	action	action	NOUN
m-1112	2531	20	(	(	PUNCT
m-1112	2531	21	1	1	NUM
m-1112	2531	22	)	)	PUNCT
m-1112	2531	23	...	...	PUNCT
m-1112	2532	1	[	[	X
m-1112	2532	2	a	a	X
m-1112	2532	3	]	]	X
m-1112	2532	4	→	→	PUNCT
m-1112	2532	5	{	{	PUNCT
m-1112	2532	6	[	[	X
m-1112	2532	7	b]±𝐄𝐍	b]±𝐄𝐍	NOUN
m-1112	2532	8	}	}	PUNCT
m-1112	2532	9	≡	≡	PROPN
m-1112	2532	10	[	[	X
m-1112	2532	11	c	c	X
m-1112	2532	12	]	]	X
m-1112	2532	13	≡	≡	PROPN
m-1112	2532	14	±	±	NUM
m-1112	2532	15	𝐄𝐍	𝐄𝐍	PROPN
m-1112	2532	16	+	+	CCONJ
m-1112	2532	17	{	{	PUNCT
m-1112	2533	1	[	[	X
m-1112	2533	2	b	b	X
m-1112	2533	3	]	]	X
m-1112	2533	4	+	+	CCONJ
m-1112	2533	5	[	[	X
m-1112	2533	6	a	a	X
m-1112	2533	7	]	]	X
m-1112	2533	8	}	}	PUNCT
m-1112	2533	9	,	,	PUNCT
m-1112	2533	10	,	,	PUNCT
m-1112	2533	11	[	[	X
m-1112	2533	12	a	a	X
m-1112	2533	13	]	]	X
m-1112	2533	14	≡	≡	PROPN
m-1112	2533	15	[	[	X
m-1112	2533	16	c	c	X
m-1112	2533	17	]	]	X
m-1112	2533	18	+	+	ADJ
m-1112	2533	19	{	{	PUNCT
m-1112	2533	20	𝐗	𝐗	PROPN
m-1112	2533	21	𝐍	𝐍	PROPN
m-1112	2533	22	}	}	PUNCT
m-1112	2534	1	[	[	X
m-1112	2534	2	a	a	X
m-1112	2534	3	]	]	X
m-1112	2534	4	=	=	PUNCT
m-1112	2534	5	the	the	DET
m-1112	2534	6	initial	initial	NOUN
m-1112	2534	7	,	,	PUNCT
m-1112	2535	1	[	[	X
m-1112	2535	2	c	c	X
m-1112	2535	3	]	]	X
m-1112	2535	4	=	=	PUNCT
m-1112	2535	5	the	the	DET
m-1112	2535	6	final	final	ADJ
m-1112	2535	7	,	,	PUNCT
m-1112	2535	8	[	[	PUNCT
m-1112	2535	9	x	x	X
m-1112	2535	10	n	n	X
m-1112	2535	11	]	]	PUNCT
m-1112	2535	12	=	=	PUNCT
m-1112	2535	13	{	{	PUNCT
m-1112	2535	14	[	[	X
m-1112	2535	15	b	b	X
m-1112	2535	16	]	]	X
m-1112	2535	17	±	±	NOUN
m-1112	2536	1	[	[	X
m-1112	2536	2	en	en	X
m-1112	2536	3	]	]	X
m-1112	2536	4	}	}	PUNCT
m-1112	2536	5	≡	≡	PROPN
m-1112	2536	6	the	the	DET
m-1112	2536	7	antidote	antidote	NOUN
m-1112	2536	8	.	.	PUNCT
m-1112	2537	1	the	the	DET
m-1112	2537	2	atoms	atom	NOUN
m-1112	2537	3	action	action	NOUN
m-1112	2537	4	(	(	PUNCT
m-1112	2537	5	2	2	NUM
m-1112	2537	6	)	)	PUNCT
m-1112	2537	7	…	…	PUNCT
m-1112	2537	8	.	.	PUNCT
m-1112	2538	1	[	[	X
m-1112	2538	2	a	a	X
m-1112	2538	3	]	]	X
m-1112	2538	4	→	→	X
m-1112	2538	5	[	[	PUNCT
m-1112	2538	6	±	±	NUM
m-1112	2538	7	e	e	NOUN
m-1112	2538	8	n	n	X
m-1112	2538	9	]	]	PUNCT
m-1112	2538	10	≡	≡	PROPN
m-1112	2539	1	[	[	X
m-1112	2539	2	c	c	X
m-1112	2539	3	]	]	X
m-1112	2539	4	≡≡≡	≡≡≡	PROPN
m-1112	2539	5	±	±	NOUN
m-1112	2540	1	𝐄𝒏	𝐄𝒏	PROPN
m-1112	2540	2	+	+	PROPN
m-1112	2541	1	[	[	X
m-1112	2541	2	a	a	X
m-1112	2541	3	]	]	X
m-1112	2541	4	,	,	PUNCT
m-1112	2541	5	,	,	PUNCT
m-1112	2541	6	,	,	PUNCT
m-1112	2541	7	,	,	PUNCT
m-1112	2541	8	[	[	X
m-1112	2541	9	a	a	X
m-1112	2541	10	]	]	X
m-1112	2541	11	≡	≡	PROPN
m-1112	2542	1	[	[	X
m-1112	2542	2	c	c	X
m-1112	2542	3	]	]	X
m-1112	2543	1	+	+	CCONJ
m-1112	2543	2	[	[	PUNCT
m-1112	2543	3	e	e	X
m-1112	2543	4	n	n	X
m-1112	2543	5	]	]	PUNCT
m-1112	2544	1	[	[	X
m-1112	2544	2	a	a	X
m-1112	2544	3	]	]	X
m-1112	2544	4	=	=	PUNCT
m-1112	2544	5	the	the	DET
m-1112	2544	6	initial	initial	NOUN
m-1112	2544	7	,	,	PUNCT
m-1112	2544	8	[	[	X
m-1112	2544	9	c	c	X
m-1112	2544	10	}	}	PUNCT
m-1112	2544	11	=	=	PUNCT
m-1112	2544	12	the	the	DET
m-1112	2544	13	final	final	ADJ
m-1112	2544	14	,	,	PUNCT
m-1112	2544	15	[	[	PUNCT
m-1112	2544	16	e	e	NOUN
m-1112	2544	17	n	n	X
m-1112	2544	18	]	]	PUNCT
m-1112	2544	19	≡	≡	PROPN
m-1112	2544	20	the	the	DET
m-1112	2544	21	antidote	antidote	NOUN
m-1112	2544	22	,	,	PUNCT
m-1112	2544	23	the	the	DET
m-1112	2544	24	circular	circular	ADJ
m-1112	2544	25	-	-	PUNCT
m-1112	2544	26	signal	signal	NOUN
m-1112	2544	27	-	-	PUNCT
m-1112	2544	28	action	action	NOUN
m-1112	2544	29	is	be	AUX
m-1112	2544	30	as	as	ADP
m-1112	2544	31	,	,	PUNCT
m-1112	2544	32	i	i	PROPN
m-1112	2544	33	→	→	SYM
m-1112	2544	34	f	f	X
m-1112	2545	1	=	=	X
m-1112	2545	2	[	[	PUNCT
m-1112	2545	3	i	i	X
m-1112	2545	4	+	+	X
m-1112	2545	5	f	f	X
m-1112	2545	6	]	]	PUNCT
m-1112	2545	7	and	and	CCONJ
m-1112	2545	8	[	[	PUNCT
m-1112	2545	9	i	i	PRON
m-1112	2545	10	+	+	X
m-1112	2545	11	f	f	X
m-1112	2545	12	]	]	X
m-1112	2546	1	↔	↔	PROPN
m-1112	2546	2	[	[	PUNCT
m-1112	2546	3	dm	dm	X
m-1112	2546	4	]	]	PUNCT
m-1112	2546	5	≡	≡	PROPN
m-1112	2546	6	antidote	antidote	NOUN
m-1112	2546	7	,	,	PUNCT
m-1112	2546	8	or	or	CCONJ
m-1112	2546	9	still	still	ADV
m-1112	2546	10	-	-	PUNCT
m-1112	2546	11	actions	action	NOUN
m-1112	2546	12	[	[	PUNCT
m-1112	2546	13	i	i	NOUN
m-1112	2546	14	=	=	SYM
m-1112	2546	15	carrier	carrier	NOUN
m-1112	2546	16	]	]	PUNCT
m-1112	2546	17	→	→	ADP
m-1112	2546	18	[	[	PUNCT
m-1112	2546	19	f	f	NOUN
m-1112	2546	20	=	=	NOUN
m-1112	2546	21	modulator	modulator	NOUN
m-1112	2546	22	]	]	X
m-1112	2546	23	→	→	ADP
m-1112	2546	24	[	[	PUNCT
m-1112	2546	25	i+f	i+f	ADJ
m-1112	2546	26	=	=	PRON
m-1112	2546	27	modulated	modulate	VERB
m-1112	2546	28	]	]	PUNCT
m-1112	2546	29	→	→	X
m-1112	2546	30	→	→	X
m-1112	2546	31	[	[	PUNCT
m-1112	2546	32	i+f	i+f	X
m-1112	2546	33	]	]	PUNCT
m-1112	2547	1	+	+	CCONJ
m-1112	2547	2	m	m	VERB
m-1112	2547	3	↔	↔	NOUN
m-1112	2547	4	[	[	PUNCT
m-1112	2547	5	dm	dm	NOUN
m-1112	2547	6	=	=	PUNCT
m-1112	2547	7	antidotes	antidote	NOUN
m-1112	2547	8	]	]	PUNCT
m-1112	2547	9	=	=	PUNCT
m-1112	2547	10	the	the	DET
m-1112	2547	11	demodulation	demodulation	NOUN
m-1112	2547	12	]	]	PUNCT
m-1112	2547	13	the	the	DET
m-1112	2547	14	communications	communication	NOUN
m-1112	2547	15	–	–	PUNCT
m-1112	2547	16	frequencies	frequency	NOUN
m-1112	2547	17	in	in	ADP
m-1112	2547	18	atoms	atom	NOUN
m-1112	2547	19	caves	cave	NOUN
m-1112	2547	20	,	,	PUNCT
m-1112	2547	21	are	be	AUX
m-1112	2547	22	their	their	PRON
m-1112	2547	23	wave	wave	NOUN
m-1112	2547	24	resonances	resonance	NOUN
m-1112	2547	25	which	which	PRON
m-1112	2547	26	consist	consist	VERB
m-1112	2547	27	the	the	DET
m-1112	2547	28	master	master	NOUN
m-1112	2547	29	-	-	PUNCT
m-1112	2547	30	keys	key	NOUN
m-1112	2547	31	of	of	ADP
m-1112	2547	32	all	all	DET
m-1112	2547	33	the	the	DET
m-1112	2547	34	wave	wave	NOUN
m-1112	2547	35	caves	cave	NOUN
m-1112	2547	36	.	.	PUNCT
m-1112	2548	1	6c5	6c5	NUM
m-1112	2548	2	..	..	PUNCT
m-1112	2548	3	the	the	DET
m-1112	2548	4	energy	energy	NOUN
m-1112	2548	5	superflow	superflow	NOUN
m-1112	2548	6	in	in	ADP
m-1112	2548	7	mfmf	mfmf	NOUN
m-1112	2548	8	-	-	PUNCT
m-1112	2548	9	pns	pns	NOUN
m-1112	2548	10	space	space	NOUN
m-1112	2548	11	-	-	PUNCT
m-1112	2548	12	levels	level	NOUN
m-1112	2548	13	for	for	ADP
m-1112	2548	14	black	black	ADJ
m-1112	2548	15	-	-	PUNCT
m-1112	2548	16	holes	hole	NOUN
m-1112	2548	17	origination	origination	NOUN
m-1112	2548	18	.	.	PUNCT
m-1112	2549	1	1)	1)	NUM
m-1112	2549	2	..	..	PUNCT
m-1112	2549	3	it	it	PRON
m-1112	2549	4	was	be	AUX
m-1112	2549	5	prior	prior	ADV
m-1112	2549	6	proved	prove	VERB
m-1112	2549	7	that	that	SCONJ
m-1112	2549	8	angular	angular	ADJ
m-1112	2549	9	-	-	PUNCT
m-1112	2549	10	momentum	momentum	NOUN
m-1112	2549	11	of	of	ADP
m-1112	2549	12	the	the	DET
m-1112	2549	13	primary	primary	ADJ
m-1112	2549	14	-	-	PUNCT
m-1112	2549	15	motion	motion	NOUN
m-1112	2549	16	in	in	ADP
m-1112	2549	17	pns	pns	PROPN
m-1112	2549	18	space	space	NOUN
m-1112	2549	19	is	be	AUX
m-1112	2549	20	a	a	DET
m-1112	2549	21	quaternion	quaternion	NOUN
m-1112	2549	22	of	of	ADP
m-1112	2549	23	dimension	dimension	NOUN
m-1112	2549	24	power	power	NOUN
m-1112	2549	25	(	(	PUNCT
m-1112	2549	26	s	s	NOUN
m-1112	2549	27	+	+	NUM
m-1112	2549	28	�	�	NOUN
m-1112	2549	29	̅	̅	NOUN
m-1112	2549	30	�	�	PROPN
m-1112	2549	31	i	i	NOUN
m-1112	2549	32	)	)	PUNCT
m-1112	2550	1	¹/	¹/	PROPN
m-1112	2550	2	d	d	X
m-1112	2550	3	=	=	PUNCT
m-1112	2550	4	√	√	PROPN
m-1112	2550	5	(	(	PUNCT
m-1112	2550	6	s	s	PART
m-1112	2550	7	+	+	NUM
m-1112	2550	8	�	�	NOUN
m-1112	2550	9	̅	̅	NOUN
m-1112	2550	10	�	�	PROPN
m-1112	2550	11	i	i	NOUN
m-1112	2550	12	)	)	PUNCT
m-1112	2550	13	d	d	NOUN
m-1112	2550	14	,	,	PUNCT
m-1112	2550	15	which	which	PRON
m-1112	2550	16	follows	follow	VERB
m-1112	2550	17	that	that	PRON
m-1112	2550	18	of	of	ADP
m-1112	2550	19	spaces	space	NOUN
m-1112	2550	20	origination	origination	NOUN
m-1112	2550	21	.	.	PUNCT
m-1112	2551	1	2)it	2)it	PROPN
m-1112	2551	2	was	be	AUX
m-1112	2551	3	prior	prior	ADV
m-1112	2551	4	proved	prove	VERB
m-1112	2551	5	[	[	X
m-1112	2551	6	70	70	NUM
m-1112	2551	7	]	]	PUNCT
m-1112	2551	8	that	that	SCONJ
m-1112	2551	9	in	in	ADP
m-1112	2551	10	pns	pns	PROPN
m-1112	2551	11	space	space	NOUN
m-1112	2551	12	the	the	DET
m-1112	2551	13	inner	inner	ADJ
m-1112	2551	14	forces	force	NOUN
m-1112	2551	15	of	of	ADP
m-1112	2551	16	a	a	DET
m-1112	2551	17	system	system	NOUN
m-1112	2551	18	,	,	PUNCT
m-1112	2551	19	are	be	AUX
m-1112	2551	20	the	the	DET
m-1112	2551	21	two	two	NUM
m-1112	2551	22	equilibrium	equilibrium	NOUN
m-1112	2551	23	centripetal	centripetal	ADJ
m-1112	2551	24	and	and	CCONJ
m-1112	2551	25	centrifugal	centrifugal	ADJ
m-1112	2551	26	forces	force	NOUN
m-1112	2551	27	due	due	ADP
m-1112	2551	28	to	to	ADP
m-1112	2551	29	the	the	DET
m-1112	2551	30	eternal	eternal	ADJ
m-1112	2551	31	,	,	PUNCT
m-1112	2551	32	±	±	NUM
m-1112	2551	33	σ	σ	NOUN
m-1112	2551	34	,	,	PUNCT
m-1112	2551	35	stresses	stress	NOUN
m-1112	2551	36	of	of	ADP
m-1112	2551	37	opposites	opposite	NOUN
m-1112	2551	38	[	[	X
m-1112	2551	39	⊕↔⊝	⊕↔⊝	X
m-1112	2551	40	]	]	X
m-1112	2551	41	originate	originate	ADJ
m-1112	2551	42	motion	motion	NOUN
m-1112	2551	43	u	u	NOUN
m-1112	2551	44	,	,	PUNCT
m-1112	2551	45	as	as	SCONJ
m-1112	2551	46	𝐉𝟏.	𝐉𝟏.	PROPN
m-1112	2551	47	𝐮²	𝐮²	PROPN
m-1112	2551	48	𝐜𝐨𝐬𝛝	𝐜𝐨𝐬𝛝	PROPN
m-1112	2551	49	𝐉𝟑	𝐉𝟑	PROPN
m-1112	2551	50	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2551	51	.u	.u	PROPN
m-1112	2552	1	+	+	X
m-1112	2552	2	s	s	X
m-1112	2552	3	.	.	PUNCT
m-1112	2552	4	q	q	PUNCT
m-1112	2553	1	=	=	NOUN
m-1112	2553	2	0	0	NUM
m-1112	2553	3	.	.	PUNCT
m-1112	2554	1	this	this	DET
m-1112	2554	2	quadratic	quadratic	ADJ
m-1112	2554	3	equation	equation	NOUN
m-1112	2554	4	has	have	VERB
m-1112	2554	5	4	4	NUM
m-1112	2554	6	solutions	solution	NOUN
m-1112	2554	7	where	where	SCONJ
m-1112	2554	8	the	the	DET
m-1112	2554	9	angular	angular	ADJ
m-1112	2554	10	velocity	velocity	NOUN
m-1112	2554	11	complex	complex	ADJ
m-1112	2554	12	number	number	NOUN
m-1112	2554	13	u	u	NOUN
m-1112	2554	14	=	=	NOUN
m-1112	2554	15	|	|	NUM
m-1112	2554	16	�	�	NOUN
m-1112	2554	17	̅	̅	NOUN
m-1112	2554	18	�	�	NOUN
m-1112	2554	19	|	|	NOUN
m-1112	2554	20	=	=	SYM
m-1112	2554	21	s	s	VERB
m-1112	2554	22	q	q	PROPN
m-1112	2554	23	b	b	PROPN
m-1112	2554	24	=	=	SYM
m-1112	2554	25	s	s	X
m-1112	2554	26	q	q	NOUN
m-1112	2554	27	j3w	j3w	PROPN
m-1112	2554	28	=	=	SYM
m-1112	2554	29	|	|	NUM
m-1112	2554	30	�	�	NOUN
m-1112	2554	31	̅	̅	NOUN
m-1112	2554	32	�	�	NOUN
m-1112	2554	33	|	|	NOUN
m-1112	2554	34	=	=	NOUN
m-1112	2554	35	dφ	dφ	X
m-1112	2554	36	dt	dt	NOUN
m-1112	2554	37	=	=	PUNCT
m-1112	2554	38	[	[	PUNCT
m-1112	2554	39	j3	j3	PROPN
m-1112	2554	40	.	.	PROPN
m-1112	2555	1	w3	w3	PROPN
m-1112	2555	2	2	2	NUM
m-1112	2555	3	j1.cos	j1.co	NOUN
m-1112	2555	4	ϑ	ϑ	X
m-1112	2555	5	]	]	X
m-1112	2555	6	±	±	NOUN
m-1112	2555	7	[	[	PUNCT
m-1112	2555	8	k	k	PROPN
m-1112	2555	9	pns	pns	PROPN
m-1112	2555	10	2	2	NUM
m-1112	2555	11	j1.cos	j1.co	NOUN
m-1112	2555	12	ϑ	ϑ	X
m-1112	2555	13	]	]	X
m-1112	2555	14	.i	.i	PUNCT
m-1112	2556	1	=	=	PUNCT
m-1112	2556	2	s	s	PART
m-1112	2556	3	±	±	NUM
m-1112	2556	4	v	v	NOUN
m-1112	2556	5	i	i	PRON
m-1112	2556	6	,	,	PUNCT
m-1112	2556	7	or	or	CCONJ
m-1112	2556	8	→	→	ADP
m-1112	2556	9	angular	angular	ADJ
m-1112	2556	10	-	-	PUNCT
m-1112	2556	11	velocity	velocity	NOUN
m-1112	2556	12	|	|	NOUN
m-1112	2556	13	�	�	NOUN
m-1112	2556	14	̅	̅	NOUN
m-1112	2556	15	�	�	NOUN
m-1112	2556	16	|	|	NOUN
m-1112	2556	17	=	=	SYM
m-1112	2556	18	𝐉𝟑.	𝐉𝟑.	NOUN
m-1112	2556	19	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2556	20	𝟐	𝟐	NUM
m-1112	2556	21	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2556	22	±	±	NUM
m-1112	2556	23	√−	√−	NOUN
m-1112	2556	24	𝐬𝐐	𝐬𝐐	PROPN
m-1112	2556	25	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2556	26	+	+	CCONJ
m-1112	2556	27	(	(	PUNCT
m-1112	2556	28	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2556	29	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2556	30	𝟐	𝟐	PROPN
m-1112	2556	31	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2556	32	)	)	PUNCT
m-1112	2556	33	²	²	NUM
m-1112	2556	34	𝟐	𝟐	NUM
m-1112	2556	35	=	=	SYM
m-1112	2556	36	s	s	PART
m-1112	2556	37	±	±	NUM
m-1112	2556	38	{	{	PUNCT
m-1112	2556	39	√	√	NUM
m-1112	2556	40	�	�	SYM
m-1112	2556	41	̅	̅	NOUN
m-1112	2556	42	�	�	PROPN
m-1112	2556	43	}	}	PUNCT
m-1112	2556	44	.i	.i	PROPN
m-1112	2557	1	←	←	PROPN
m-1112	2557	2	where	where	SCONJ
m-1112	2557	3	s	s	VERB
m-1112	2557	4	=	=	X
m-1112	2557	5	[	[	PUNCT
m-1112	2557	6	j3	j3	PROPN
m-1112	2557	7	.	.	PROPN
m-1112	2557	8	w3	w3	PROPN
m-1112	2557	9	2	2	NUM
m-1112	2557	10	j1.cos	j1.co	NOUN
m-1112	2557	11	ϑ	ϑ	X
m-1112	2557	12	]	]	PUNCT
m-1112	2557	13	,	,	PUNCT
m-1112	2557	14	�	�	PROPN
m-1112	2557	15	̅	̅	NOUN
m-1112	2557	16	�	�	NOUN
m-1112	2557	17	=	=	SYM
m-1112	2557	18	[	[	PUNCT
m-1112	2557	19	k	k	X
m-1112	2557	20	pns	pns	PROPN
m-1112	2557	21	2	2	PROPN
m-1112	2557	22	j1.cosϑ	j1.cosϑ	ADV
m-1112	2557	23	]	]	PUNCT
m-1112	2557	24	,	,	PUNCT
m-1112	2557	25	𝐤	𝐤	X
m-1112	2557	26	𝐏𝐍𝐒	𝐏𝐍𝐒	PROPN
m-1112	2557	27	=	=	SYM
m-1112	2557	28	√	√	PROPN
m-1112	2557	29	[	[	PUNCT
m-1112	2557	30	j3	j3	PROPN
m-1112	2557	31	.	.	PUNCT
m-1112	2558	1	w3]²	w3]²	ADP
m-1112	2558	2	−	−	NOUN
m-1112	2558	3	4	4	X
m-1112	2558	4	.	.	X
m-1112	2559	1	sq	sq	PROPN
m-1112	2559	2	.	.	PROPN
m-1112	2559	3	j1	j1	PROPN
m-1112	2559	4	cos	cos	PROPN
m-1112	2559	5	ϑ	ϑ	PROPN
m-1112	2559	6	2	2	NUM
m-1112	2559	7	the	the	DET
m-1112	2559	8	constant	constant	ADJ
m-1112	2559	9	work	work	NOUN
m-1112	2559	10	exists	exist	VERB
m-1112	2559	11	on	on	ADP
m-1112	2559	12	the	the	DET
m-1112	2559	13	common	common	ADJ
m-1112	2559	14	central	central	ADJ
m-1112	2559	15	axes	axis	NOUN
m-1112	2559	16	of	of	ADP
m-1112	2559	17	rotation	rotation	NOUN
m-1112	2559	18	which	which	PRON
m-1112	2559	19	is	be	AUX
m-1112	2559	20	fixed	fix	VERB
m-1112	2559	21	to	to	ADP
m-1112	2559	22	the	the	DET
m-1112	2559	23	tangential	tangential	ADJ
m-1112	2559	24	-	-	PUNCT
m-1112	2559	25	planes	plane	NOUN
m-1112	2559	26	of	of	ADP
m-1112	2559	27	�	�	PROPN
m-1112	2559	28	̅	̅	NOUN
m-1112	2559	29	�	�	PROPN
m-1112	2559	30	&	&	CCONJ
m-1112	2559	31	�	�	PROPN
m-1112	2559	32	̅	̅	PROPN
m-1112	2559	33	�	�	NOUN
m-1112	2559	34	nib	nib	NOUN
m-1112	2559	35	,	,	PUNCT
m-1112	2559	36	being	be	AUX
m-1112	2559	37	alternately	alternately	ADV
m-1112	2559	38	perpendicular	perpendicular	ADJ
m-1112	2559	39	to	to	ADP
m-1112	2559	40	,	,	PUNCT
m-1112	2559	41	b̅	b̅	PROPN
m-1112	2559	42	,	,	PUNCT
m-1112	2559	43	and	and	CCONJ
m-1112	2559	44	,	,	PUNCT
m-1112	2559	45	w̅	w̅	PROPN
m-1112	2559	46	,	,	PUNCT
m-1112	2559	47	and	and	CCONJ
m-1112	2559	48	found	find	VERB
m-1112	2559	49	to	to	PART
m-1112	2559	50	be	be	AUX
m-1112	2559	51	as	as	ADP
m-1112	2559	52	�	�	NOUN
m-1112	2559	53	̅	̅	NOUN
m-1112	2559	54	�	�	PROPN
m-1112	2559	55	.	.	PUNCT
m-1112	2560	1	�	�	PROPN
m-1112	2560	2	̅	̅	NOUN
m-1112	2560	3	�	�	NOUN
m-1112	2560	4	=	=	SYM
m-1112	2560	5	2l	2l	NUM
m-1112	2560	6	=	=	NOUN
m-1112	2560	7	j.w²	j.w²	NOUN
m-1112	2560	8	.	.	PUNCT
m-1112	2561	1	the	the	DET
m-1112	2561	2	frequency	frequency	NOUN
m-1112	2561	3	monad	monad	PROPN
m-1112	2561	4	of	of	ADP
m-1112	2561	5	rotation	rotation	NOUN
m-1112	2561	6	in	in	ADP
m-1112	2561	7	the	the	DET
m-1112	2561	8	pns	pns	NOUN
m-1112	2561	9	space	space	NOUN
m-1112	2561	10	is	be	AUX
m-1112	2561	11	as	as	ADP
m-1112	2561	12	→	→	SYM
m-1112	2561	13	𝐟	𝐟	NOUN
m-1112	2561	14	𝐏𝐍𝐒	𝐏𝐍𝐒	NOUN
m-1112	2561	15	=	=	PUNCT
m-1112	2561	16	𝐬	𝐬	PROPN
m-1112	2561	17	𝐐	𝐐	PROPN
m-1112	2561	18	𝟐𝛑.𝐉𝟐.𝐰	𝟐𝛑.𝐉𝟐.𝐰	PROPN
m-1112	2561	19	←	←	PROPN
m-1112	2561	20	with	with	ADP
m-1112	2561	21	the	the	DET
m-1112	2561	22	following	follow	VERB
m-1112	2561	23	4	4	NUM
m-1112	2561	24	solutions	solution	NOUN
m-1112	2561	25	for	for	ADP
m-1112	2561	26	|	|	PRON
m-1112	2561	27	�	�	NOUN
m-1112	2561	28	̅	̅	NOUN
m-1112	2561	29	�	�	NOUN
m-1112	2561	30	|	|	NOUN
m-1112	2561	31	,	,	PUNCT
m-1112	2561	32	solution-1	solution-1	ADP
m-1112	2561	33			VERB
m-1112	2561	34	|	|	ADV
m-1112	2561	35	𝑤	𝑤	ADV
m-1112	2561	36	1	1	NUM
m-1112	2561	37	|	|	ADV
m-1112	2561	38	=	=	PUNCT
m-1112	2561	39	[	[	PUNCT
m-1112	2561	40	s	s	X
m-1112	2561	41	]	]	X
m-1112	2561	42	+	+	CCONJ
m-1112	2561	43	[	[	PUNCT
m-1112	2561	44	√	√	NUM
m-1112	2561	45	�	�	SYM
m-1112	2561	46	̅	̅	NOUN
m-1112	2561	47	�	�	NOUN
m-1112	2561	48	]	]	PUNCT
m-1112	2561	49	→	→	SYM
m-1112	2561	50	real	real	ADJ
m-1112	2561	51	root	root	NOUN
m-1112	2561	52	≡	≡	ADJ
m-1112	2561	53	huge	huge	ADJ
m-1112	2561	54	minerals	mineral	NOUN
m-1112	2561	55	at	at	ADP
m-1112	2561	56	edge	edge	NOUN
m-1112	2561	57	of	of	ADP
m-1112	2561	58	universe	universe	NOUN
m-1112	2561	59	.	.	PUNCT
m-1112	2562	1	solution-2	solution-2	NUM
m-1112	2562	2			NOUN
m-1112	2562	3	|	|	NOUN
m-1112	2562	4	𝑤	𝑤	ADP
m-1112	2562	5	2	2	NUM
m-1112	2562	6	|	|	NOUN
m-1112	2562	7	=	=	PUNCT
m-1112	2562	8	[	[	PUNCT
m-1112	2562	9	s	s	X
m-1112	2562	10	]	]	X
m-1112	2562	11	[	[	PUNCT
m-1112	2562	12	√	√	NUM
m-1112	2562	13	�	�	SYM
m-1112	2562	14	̅	̅	NOUN
m-1112	2562	15	�	�	NOUN
m-1112	2562	16	]	]	PUNCT
m-1112	2562	17	→	→	SYM
m-1112	2562	18	real	real	ADJ
m-1112	2562	19	root	root	NOUN
m-1112	2562	20	≡	≡	PROPN
m-1112	2562	21	atoms	atom	NOUN
m-1112	2562	22	&	&	CCONJ
m-1112	2562	23	compounds	compound	NOUN
m-1112	2562	24	into	into	ADP
m-1112	2562	25	structures	structure	NOUN
m-1112	2562	26	.	.	PUNCT
m-1112	2563	1	solution-3	solution-3	NUM
m-1112	2563	2			NOUN
m-1112	2563	3	|	|	ADV
m-1112	2563	4	𝑤	𝑤	ADP
m-1112	2563	5	3	3	NUM
m-1112	2563	6	|	|	ADV
m-1112	2564	1	=	=	PUNCT
m-1112	2564	2	[	[	PUNCT
m-1112	2564	3	s	s	X
m-1112	2564	4	]	]	X
m-1112	2564	5	+	+	CCONJ
m-1112	2564	6	[	[	PUNCT
m-1112	2564	7	√	√	NUM
m-1112	2564	8	�	�	SYM
m-1112	2564	9	̅	̅	NOUN
m-1112	2564	10	�	�	NOUN
m-1112	2564	11	]	]	SYM
m-1112	2564	12	.i	.i	X
m-1112	2565	1	→	→	PUNCT
m-1112	2565	2	imaginary	imaginary	ADJ
m-1112	2565	3	root	root	NOUN
m-1112	2565	4	≡	≡	PROPN
m-1112	2565	5	huge	huge	ADJ
m-1112	2565	6	bh	bh	NOUN
m-1112	2565	7	at	at	ADP
m-1112	2565	8	centres	centre	NOUN
m-1112	2565	9	of	of	ADP
m-1112	2565	10	galaxies	galaxy	NOUN
m-1112	2565	11	.	.	PUNCT
m-1112	2566	1	ijo	ijo	PROPN
m-1112	2566	2	international	international	PROPN
m-1112	2566	3	journal	journal	PROPN
m-1112	2566	4	of	of	ADP
m-1112	2566	5	mathematics	mathematics	PROPN
m-1112	2566	6	(	(	PUNCT
m-1112	2566	7	issn	issn	PROPN
m-1112	2566	8	:	:	PUNCT
m-1112	2566	9	2992	2992	NUM
m-1112	2566	10	-	-	SYM
m-1112	2566	11	4421	4421	NUM
m-1112	2566	12	)	)	PUNCT
m-1112	2566	13	volume	volume	NOUN
m-1112	2566	14	08	08	NUM
m-1112	2567	1	|	|	ADV
m-1112	2567	2	issue	issue	NOUN
m-1112	2567	3	08	08	NUM
m-1112	2568	1	|	|	ADV
m-1112	2568	2	august	august	PROPN
m-1112	2568	3	2025	2025	NUM
m-1112	2568	4	|	|	ADV
m-1112	2568	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2568	6	ijo	ijo	PROPN
m-1112	2568	7	journals	journal	NOUN
m-1112	2568	8	89	89	NUM
m-1112	2568	9	the	the	DET
m-1112	2568	10	fundamental	fundamental	ADJ
m-1112	2568	11	particles	particle	NOUN
m-1112	2568	12	origination	origination	NOUN
m-1112	2568	13	mechanism	mechanism	NOUN
m-1112	2568	14	in	in	ADP
m-1112	2568	15	mfmf	mfmf	PROPN
m-1112	2568	16	pns	pns	PROPN
m-1112	2568	17	caves	cave	NOUN
m-1112	2568	18	.	.	PUNCT
m-1112	2569	1	solution-4	solution-4	NUM
m-1112	2569	2			NOUN
m-1112	2569	3	|	|	ADV
m-1112	2569	4	𝑤	𝑤	ADP
m-1112	2569	5	4	4	NUM
m-1112	2569	6	|	|	ADV
m-1112	2570	1	=	=	PUNCT
m-1112	2571	1	[	[	PUNCT
m-1112	2571	2	s	s	X
m-1112	2571	3	]	]	X
m-1112	2571	4	[	[	PUNCT
m-1112	2571	5	√	√	NUM
m-1112	2571	6	�	�	SYM
m-1112	2571	7	̅	̅	NOUN
m-1112	2571	8	�	�	NOUN
m-1112	2571	9	]	]	SYM
m-1112	2571	10	.i	.i	X
m-1112	2572	1	→	→	PUNCT
m-1112	2572	2	imaginary	imaginary	ADJ
m-1112	2572	3	root	root	NOUN
m-1112	2572	4	≡	≡	PROPN
m-1112	2572	5	micro	micro	PROPN
m-1112	2572	6	bh	bh	PROPN
m-1112	2572	7	at	at	ADP
m-1112	2572	8	centre	centre	NOUN
m-1112	2572	9	of	of	ADP
m-1112	2572	10	molecules	molecule	NOUN
m-1112	2572	11	.	.	PUNCT
m-1112	2573	1	where	where	SCONJ
m-1112	2573	2	bh	bh	NOUN
m-1112	2573	3	=	=	PUNCT
m-1112	2573	4	black	black	ADJ
m-1112	2573	5	hole	hole	NOUN
m-1112	2573	6	.	.	PUNCT
m-1112	2574	1	from	from	ADP
m-1112	2574	2	4	4	NUM
m-1112	2574	3	-	-	PUNCT
m-1112	2574	4	above	above	ADJ
m-1112	2574	5	issues	issue	NOUN
m-1112	2574	6	,	,	PUNCT
m-1112	2574	7	a	a	DET
m-1112	2574	8	-	-	PUNCT
m-1112	2574	9	velocity	velocity	NOUN
m-1112	2574	10	|𝑤1	|𝑤1	NOUN
m-1112	2574	11	̅̅	̅̅	NOUN
m-1112	2574	12	̅̅	̅̅	PROPN
m-1112	2574	13	|	|	ADV
m-1112	2574	14	=	=	SYM
m-1112	2574	15	𝐉𝟑.	𝐉𝟑.	NOUN
m-1112	2574	16	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2574	17	𝟐	𝟐	NUM
m-1112	2574	18	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2574	19	±√−	±√−	NOUN
m-1112	2574	20	𝐬𝐐	𝐬𝐐	X
m-1112	2574	21	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2574	22	+	+	CCONJ
m-1112	2574	23	(	(	PUNCT
m-1112	2574	24	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2574	25	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2574	26	𝟐	𝟐	PROPN
m-1112	2574	27	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2574	28	)	)	PUNCT
m-1112	2574	29	²	²	PROPN
m-1112	2574	30	𝟐	𝟐	NUM
m-1112	2574	31	≡	≡	PROPN
m-1112	2574	32	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2574	33	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2574	34	𝟐	𝟐	NUM
m-1112	2574	35	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2574	36	+	+	NOUN
m-1112	2574	37	√−	√−	NOUN
m-1112	2574	38	𝐬𝐐	𝐬𝐐	X
m-1112	2574	39	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2574	40	+	+	CCONJ
m-1112	2574	41	(	(	PUNCT
m-1112	2574	42	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2574	43	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2574	44	𝟐	𝟐	PROPN
m-1112	2574	45	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2574	46	)	)	PUNCT
m-1112	2574	47	²	²	PROPN
m-1112	2574	48	𝟐	𝟐	NUM
m-1112	2574	49	a	a	DET
m-1112	2574	50	-	-	PUNCT
m-1112	2574	51	velocity	velocity	NOUN
m-1112	2574	52	|𝑤2	|𝑤2	PROPN
m-1112	2574	53	̅̅	̅̅	PROPN
m-1112	2574	54	̅̅	̅̅	PROPN
m-1112	2574	55	|	|	ADV
m-1112	2574	56	=	=	SYM
m-1112	2574	57	𝐉𝟑.	𝐉𝟑.	NOUN
m-1112	2574	58	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2574	59	𝟐	𝟐	NUM
m-1112	2574	60	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2574	61	±√−	±√−	NOUN
m-1112	2574	62	𝐬𝐐	𝐬𝐐	X
m-1112	2574	63	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2574	64	+	+	CCONJ
m-1112	2574	65	(	(	PUNCT
m-1112	2574	66	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2574	67	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2574	68	𝟐	𝟐	PROPN
m-1112	2574	69	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2574	70	)	)	PUNCT
m-1112	2574	71	²	²	PROPN
m-1112	2574	72	𝟐	𝟐	NUM
m-1112	2574	73	≡	≡	PROPN
m-1112	2574	74	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2574	75	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2574	76	𝟐	𝟐	NUM
m-1112	2574	77	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2574	78	-√−	-√−	ADJ
m-1112	2574	79	𝐬𝐐	𝐬𝐐	X
m-1112	2574	80	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2574	81	+	+	CCONJ
m-1112	2574	82	(	(	PUNCT
m-1112	2574	83	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2574	84	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2574	85	𝟐	𝟐	PROPN
m-1112	2574	86	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2574	87	)	)	PUNCT
m-1112	2574	88	²	²	PROPN
m-1112	2574	89	𝟐	𝟐	NUM
m-1112	2574	90	a	a	DET
m-1112	2574	91	-	-	PUNCT
m-1112	2574	92	velocity	velocity	NOUN
m-1112	2574	93	|𝑤3	|𝑤3	PROPN
m-1112	2574	94	̅̅	̅̅	PROPN
m-1112	2574	95	̅̅	̅̅	PROPN
m-1112	2574	96	|	|	ADV
m-1112	2574	97	=	=	SYM
m-1112	2574	98	𝐉𝟑.	𝐉𝟑.	NOUN
m-1112	2574	99	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2574	100	𝟐	𝟐	NUM
m-1112	2574	101	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2574	102	±√−	±√−	NOUN
m-1112	2574	103	𝐬𝐐	𝐬𝐐	X
m-1112	2574	104	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2574	105	+	+	CCONJ
m-1112	2574	106	(	(	PUNCT
m-1112	2574	107	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2574	108	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2574	109	𝟐	𝟐	PROPN
m-1112	2574	110	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2574	111	)	)	PUNCT
m-1112	2574	112	²	²	PROPN
m-1112	2574	113	𝟐	𝟐	NUM
m-1112	2574	114	≡	≡	PROPN
m-1112	2574	115	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2574	116	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2574	117	𝟐	𝟐	NUM
m-1112	2574	118	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2574	119	+	+	NOUN
m-1112	2574	120	√−	√−	NOUN
m-1112	2574	121	𝐬𝐐	𝐬𝐐	PROPN
m-1112	2574	122	𝐉𝟏.𝐜𝐨𝐬	𝐉𝟏.𝐜𝐨𝐬	PROPN
m-1112	2574	123	𝛝	𝛝	PROPN
m-1112	2574	124	+	+	CCONJ
m-1112	2574	125	(	(	PUNCT
m-1112	2574	126	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2574	127	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2574	128	𝟐	𝟐	PROPN
m-1112	2574	129	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2574	130	)	)	PUNCT
m-1112	2574	131	²	²	PROPN
m-1112	2574	132	𝟐	𝟐	NUM
m-1112	2574	133	.	.	PUNCT
m-1112	2575	1	i	i	PRON
m-1112	2575	2	a	a	DET
m-1112	2575	3	-	-	PUNCT
m-1112	2575	4	velocity	velocity	NOUN
m-1112	2575	5	|𝑤4	|𝑤4	PROPN
m-1112	2575	6	̅̅	̅̅	PROPN
m-1112	2575	7	̅̅	̅̅	PROPN
m-1112	2575	8	|	|	ADV
m-1112	2575	9	=	=	SYM
m-1112	2575	10	𝐉𝟑.	𝐉𝟑.	NOUN
m-1112	2575	11	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2575	12	𝟐	𝟐	NUM
m-1112	2575	13	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2575	14	±√−	±√−	NOUN
m-1112	2575	15	𝐬𝐐	𝐬𝐐	X
m-1112	2575	16	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2575	17	+	+	CCONJ
m-1112	2575	18	(	(	PUNCT
m-1112	2575	19	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2575	20	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2575	21	𝟐	𝟐	PROPN
m-1112	2575	22	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2575	23	)	)	PUNCT
m-1112	2575	24	²	²	PROPN
m-1112	2575	25	𝟐	𝟐	NUM
m-1112	2575	26	≡	≡	PROPN
m-1112	2575	27	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2575	28	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2575	29	𝟐	𝟐	NUM
m-1112	2575	30	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2575	31	-√−	-√−	ADJ
m-1112	2575	32	𝐬𝐐	𝐬𝐐	X
m-1112	2575	33	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2575	34	+	+	CCONJ
m-1112	2575	35	(	(	PUNCT
m-1112	2575	36	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2575	37	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2575	38	𝟐	𝟐	PROPN
m-1112	2575	39	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2575	40	)	)	PUNCT
m-1112	2575	41	²	²	PROPN
m-1112	2575	42	𝟐	𝟐	NUM
m-1112	2575	43	.	.	PUNCT
m-1112	2576	1	i	i	PRON
m-1112	2576	2	angular	angular	ADJ
m-1112	2576	3	-	-	PUNCT
m-1112	2576	4	velocity	velocity	NOUN
m-1112	2576	5	�	�	NOUN
m-1112	2576	6	̅	̅	NOUN
m-1112	2576	7	�	�	NOUN
m-1112	2576	8	is	be	AUX
m-1112	2576	9	a	a	DET
m-1112	2576	10	vector	vector	NOUN
m-1112	2576	11	,	,	PUNCT
m-1112	2576	12	and	and	CCONJ
m-1112	2576	13	rotates	rotate	NOUN
m-1112	2576	14	in	in	ADP
m-1112	2576	15	one	one	NUM
m-1112	2576	16	axis	axis	NOUN
m-1112	2576	17	k	k	NOUN
m-1112	2576	18	with	with	ADP
m-1112	2576	19	respect	respect	NOUN
m-1112	2576	20	to	to	ADP
m-1112	2576	21	variable	variable	ADJ
m-1112	2576	22	�	�	PROPN
m-1112	2576	23	̅	̅	NOUN
m-1112	2576	24	�	�	NOUN
m-1112	2576	25	momentum	momentum	NOUN
m-1112	2576	26	and	and	CCONJ
m-1112	2576	27	,	,	PUNCT
m-1112	2576	28	the	the	DET
m-1112	2576	29	ellipsoid	ellipsoid	NOUN
m-1112	2576	30	of	of	ADP
m-1112	2576	31	|	|	PRON
m-1112	2576	32	�	�	NOUN
m-1112	2576	33	̅	̅	NOUN
m-1112	2576	34	�	�	PROPN
m-1112	2576	35	|	|	ADV
m-1112	2576	36	≡	≡	PROPN
m-1112	2576	37	quaternion	quaternion	NOUN
m-1112	2576	38	of	of	ADP
m-1112	2576	39	dimension	dimension	NOUN
m-1112	2576	40	power	power	NOUN
m-1112	2576	41	(	(	PUNCT
m-1112	2576	42	s	s	NOUN
m-1112	2576	43	±	±	NUM
m-1112	2576	44	�	�	PROPN
m-1112	2576	45	̅	̅	NOUN
m-1112	2576	46	�	�	PROPN
m-1112	2576	47	i)¹/d	i)¹/d	VERB
m-1112	2576	48	the	the	DET
m-1112	2576	49	inertia	inertia	NOUN
m-1112	2576	50	j	j	PROPN
m-1112	2576	51	-	-	NOUN
m-1112	2576	52	ellipsoid	ellipsoid	NOUN
m-1112	2576	53	of	of	ADP
m-1112	2576	54	|	|	PRON
m-1112	2576	55	�	�	NOUN
m-1112	2576	56	̅	̅	NOUN
m-1112	2576	57	�	�	NOUN
m-1112	2576	58	|	|	ADV
m-1112	2576	59	gives	give	VERB
m-1112	2576	60	two	two	NUM
m-1112	2576	61	anti	anti	ADJ
m-1112	2576	62	-	-	ADJ
m-1112	2576	63	symmetrical	symmetrical	ADJ
m-1112	2576	64	inertial	inertial	ADJ
m-1112	2576	65	ellipsoids	ellipsoid	NOUN
m-1112	2576	66	,	,	PUNCT
m-1112	2576	67	a	a	DET
m-1112	2576	68	real	real	ADJ
m-1112	2576	69	and	and	CCONJ
m-1112	2576	70	an	an	DET
m-1112	2576	71	imaginary	imaginary	ADJ
m-1112	2576	72	in	in	ADP
m-1112	2576	73	their	their	PRON
m-1112	2576	74	polhode	polhode	NOUN
m-1112	2576	75	and	and	CCONJ
m-1112	2576	76	herpolhode	herpolhode	ADJ
m-1112	2576	77	cones	cone	NOUN
m-1112	2576	78	as	as	ADP
m-1112	2576	79	below	below	ADV
m-1112	2576	80	,	,	PUNCT
m-1112	2576	81	the	the	ADJ
m-1112	2576	82	-	-	PUNCT
m-1112	2576	83	real	real	ADJ
m-1112	2576	84	�	�	PROPN
m-1112	2576	85	̅	̅	NOUN
m-1112	2576	86	�	�	PROPN
m-1112	2576	87	≡	≡	PROPN
m-1112	2576	88	{	{	PUNCT
m-1112	2576	89	polhode	polhode	PROPN
m-1112	2576	90	≡	≡	PROPN
m-1112	2576	91	cone	cone	NOUN
m-1112	2576	92	ops	op	NOUN
m-1112	2576	93	,	,	PUNCT
m-1112	2576	94	herpolhode	herpolhode	PROPN
m-1112	2576	95	≡	≡	PROPN
m-1112	2576	96	cone	cone	NOUN
m-1112	2576	97	opt	opt	NOUN
m-1112	2576	98	,	,	PUNCT
m-1112	2576	99	[	[	PUNCT
m-1112	2576	100	↻	↻	NOUN
m-1112	2576	101	rolling	roll	VERB
m-1112	2576	102	]	]	PUNCT
m-1112	2576	103	on	on	ADP
m-1112	2576	104	the	the	DET
m-1112	2576	105	the	the	DET
m-1112	2576	106	ellipsoid	ellipsoid	NOUN
m-1112	2576	107	axis	axis	NOUN
m-1112	2576	108	,	,	PUNCT
m-1112	2576	109	↓	↓	PROPN
m-1112	2576	110	normal	normal	ADJ
m-1112	2576	111	on	on	ADP
m-1112	2576	112	the	the	DET
m-1112	2576	113	unmovable	unmovable	ADJ
m-1112	2576	114	&	&	CCONJ
m-1112	2576	115	attitude	attitude	NOUN
m-1112	2576	116	-	-	PUNCT
m-1112	2576	117	plane	plane	NOUN
m-1112	2576	118	of	of	ADP
m-1112	2576	119	the	the	DET
m-1112	2576	120	[	[	PUNCT
m-1112	2576	121	pspt	pspt	NOUN
m-1112	2576	122	]	]	PUNCT
m-1112	2576	123	truncated	truncate	VERB
m-1112	2576	124	-	-	PUNCT
m-1112	2576	125	polar	polar	ADJ
m-1112	2576	126	-	-	PUNCT
m-1112	2576	127	cone	cone	NOUN
m-1112	2576	128	}	}	PUNCT
m-1112	2576	129	.	.	PUNCT
m-1112	2577	1	the	the	ADJ
m-1112	2577	2	-	-	ADJ
m-1112	2577	3	imaginary	imaginary	ADJ
m-1112	2577	4	�	�	PROPN
m-1112	2577	5	̅	̅	NOUN
m-1112	2577	6	�	�	PROPN
m-1112	2577	7	≡	≡	PROPN
m-1112	2577	8	{	{	PUNCT
m-1112	2577	9	polhode	polhode	NOUN
m-1112	2577	10	=	=	PUNCT
m-1112	2577	11	cone	cone	NOUN
m-1112	2577	12	ops	op	NOUN
m-1112	2577	13	,	,	PUNCT
m-1112	2577	14	herpolhode	herpolhode	PROPN
m-1112	2577	15	=	=	PUNCT
m-1112	2577	16	cone	cone	NOUN
m-1112	2577	17	opt	opt	NOUN
m-1112	2577	18	[	[	PUNCT
m-1112	2577	19	↺	↺	NOUN
m-1112	2577	20	rolling	roll	VERB
m-1112	2577	21	]	]	PUNCT
m-1112	2577	22	on	on	ADP
m-1112	2577	23	the	the	DET
m-1112	2577	24	anti	anti	ADJ
m-1112	2577	25	-	-	ADJ
m-1112	2577	26	symmetrically	symmetrically	ADV
m-1112	2577	27	-	-	PUNCT
m-1112	2577	28	ellipsoid	ellipsoid	NOUN
m-1112	2577	29	-	-	PUNCT
m-1112	2577	30	axis	axis	NOUN
m-1112	2577	31	,	,	PUNCT
m-1112	2577	32	↑	↑	NOUN
m-1112	2577	33	normal	normal	ADJ
m-1112	2577	34	on	on	ADP
m-1112	2577	35	the	the	DET
m-1112	2577	36	unmovable	unmovable	ADJ
m-1112	2577	37	&	&	CCONJ
m-1112	2577	38	attitude	attitude	NOUN
m-1112	2577	39	-	-	PUNCT
m-1112	2577	40	plane	plane	NOUN
m-1112	2577	41	of	of	ADP
m-1112	2577	42	the	the	DET
m-1112	2577	43	[	[	PUNCT
m-1112	2577	44	pspt	pspt	NOUN
m-1112	2577	45	]	]	PUNCT
m-1112	2577	46	truncated	truncate	VERB
m-1112	2577	47	-	-	PUNCT
m-1112	2577	48	polar	polar	ADJ
m-1112	2577	49	-	-	PUNCT
m-1112	2577	50	cone	cone	NOUN
m-1112	2577	51	}	}	PUNCT
m-1112	2577	52	.	.	PUNCT
m-1112	2578	1	it	it	PRON
m-1112	2578	2	has	have	AUX
m-1112	2578	3	been	be	AUX
m-1112	2578	4	proved	prove	VERB
m-1112	2578	5	that	that	SCONJ
m-1112	2578	6	�	�	PROPN
m-1112	2578	7	̅	̅	NOUN
m-1112	2578	8	�	�	PROPN
m-1112	2578	9	,	,	PUNCT
m-1112	2578	10	�	�	PROPN
m-1112	2578	11	̅	̅	NOUN
m-1112	2578	12	�	�	NOUN
m-1112	2578	13	vectors	vector	NOUN
m-1112	2578	14	exist	exist	VERB
m-1112	2578	15	as	as	ADP
m-1112	2578	16	,	,	PUNCT
m-1112	2578	17	e	e	NOUN
m-1112	2578	18	=	=	NOUN
m-1112	2578	19	energy	energy	NOUN
m-1112	2578	20	=	=	NOUN
m-1112	2578	21	motion	motion	NOUN
m-1112	2578	22	,	,	PUNCT
m-1112	2578	23	s	s	NOUN
m-1112	2578	24	=	=	NOUN
m-1112	2578	25	space	space	NOUN
m-1112	2578	26	=	=	NOUN
m-1112	2578	27	length	length	NOUN
m-1112	2578	28	---------------------------------------------------------------------------------------------------------------	---------------------------------------------------------------------------------------------------------------	PUNCT
m-1112	2578	29	both	both	DET
m-1112	2578	30	magnitudes	magnitude	NOUN
m-1112	2578	31	define	define	VERB
m-1112	2578	32	the	the	DET
m-1112	2578	33	unit	unit	NOUN
m-1112	2578	34	-	-	PUNCT
m-1112	2578	35	energy	energy	NOUN
m-1112	2578	36	vectors	vector	NOUN
m-1112	2578	37	→	→	SYM
m-1112	2578	38	{	{	PUNCT
m-1112	2578	39	unit	unit	NOUN
m-1112	2578	40	-	-	PUNCT
m-1112	2578	41	e	e	NOUN
m-1112	2578	42	vector	vector	NOUN
m-1112	2578	43	r	r	NOUN
m-1112	2578	44	=	=	SYM
m-1112	2578	45	σ	σ	X
m-1112	2578	46	j.w²	j.w²	NOUN
m-1112	2578	47	=	=	SYM
m-1112	2578	48	𝛔	𝛔	PART
m-1112	2578	49	�	�	PROPN
m-1112	2578	50	̅	̅	NOUN
m-1112	2578	51	�	�	PROPN
m-1112	2578	52	}	}	PUNCT
m-1112	2578	53	←	←	PROPN
m-1112	2578	54	when	when	SCONJ
m-1112	2578	55	the	the	DET
m-1112	2578	56	unit-e.vector	unit-e.vector	PROPN
m-1112	2578	57	r	r	NOUN
m-1112	2578	58	is	be	AUX
m-1112	2578	59	placed	place	VERB
m-1112	2578	60	on	on	ADP
m-1112	2578	61	[	[	X
m-1112	2578	62	ab≡2r	ab≡2r	ADP
m-1112	2578	63	s.diameter	s.diameter	NOUN
m-1112	2578	64	of	of	ADP
m-1112	2578	65	spaces	space	NOUN
m-1112	2578	66	-	-	PUNCT
m-1112	2578	67	neutral	neutral	ADJ
m-1112	2578	68	-	-	PUNCT
m-1112	2578	69	circle	circle	NOUN
m-1112	2578	70	]	]	PUNCT
m-1112	2578	71	then	then	ADV
m-1112	2578	72	energy	energy	NOUN
m-1112	2578	73	-	-	PUNCT
m-1112	2578	74	monad	monad	PROPN
m-1112	2578	75	|	|	NOUN
m-1112	2578	76	�	�	PROPN
m-1112	2578	77	̅	̅	NOUN
m-1112	2578	78	�	�	NOUN
m-1112	2578	79	|	|	ADV
m-1112	2578	80	,	,	PUNCT
m-1112	2578	81	exists	exist	VERB
m-1112	2578	82	on	on	ADP
m-1112	2578	83	,	,	PUNCT
m-1112	2578	84	space	space	NOUN
m-1112	2578	85	-	-	PUNCT
m-1112	2578	86	monad	monad	PROPN
m-1112	2578	87	|ab|	|ab|	NUM
m-1112	2578	88	≡	≡	PROPN
m-1112	2578	89	|	|	NOUN
m-1112	2578	90	�	�	PROPN
m-1112	2578	91	̅	̅	NOUN
m-1112	2578	92	�	�	NOUN
m-1112	2578	93	|	|	NOUN
m-1112	2578	94	and	and	CCONJ
m-1112	2578	95	is	be	AUX
m-1112	2578	96	{	{	PUNCT
m-1112	2578	97	e+s	e+s	NUM
m-1112	2578	98	-monad	-monad	PROPN
m-1112	2578	99	|	|	NOUN
m-1112	2578	100	�	�	NOUN
m-1112	2578	101	̅	̅	NOUN
m-1112	2578	102	�	�	NOUN
m-1112	2578	103	|	|	NOUN
m-1112	2578	104	}	}	PUNCT
m-1112	2578	105	or	or	CCONJ
m-1112	2578	106	is	be	AUX
m-1112	2578	107	the	the	DET
m-1112	2578	108	{	{	PUNCT
m-1112	2578	109	energy	energy	NOUN
m-1112	2578	110	–	–	PUNCT
m-1112	2578	111	space	space	NOUN
m-1112	2579	1	monad	monad	PROPN
m-1112	2579	2	|	|	NOUN
m-1112	2579	3	�	�	PROPN
m-1112	2579	4	̅	̅	NOUN
m-1112	2579	5	�	�	PROPN
m-1112	2579	6	|	|	ADV
m-1112	2579	7	≡	≡	PROPN
m-1112	2579	8	|ab|	|ab|	PROPN
m-1112	2579	9	}	}	PUNCT
m-1112	2579	10	,	,	PUNCT
m-1112	2579	11	where	where	SCONJ
m-1112	2579	12	the	the	DET
m-1112	2579	13	magnitudes	magnitude	NOUN
m-1112	2579	14	,	,	PUNCT
m-1112	2579	15	spaces	space	VERB
m-1112	2579	16	sides	side	NOUN
m-1112	2579	17	𝛌𝐧	𝛌𝐧	ADP
m-1112	2579	18	=	=	SYM
m-1112	2579	19	2,√r2	2,√r2	PROPN
m-1112	2579	20	−	−	PROPN
m-1112	2579	21	a²n	a²n	PROPN
m-1112	2579	22	,	,	PUNCT
m-1112	2579	23	&	&	CCONJ
m-1112	2579	24	the	the	DET
m-1112	2579	25	quantum	quantum	ADJ
m-1112	2579	26	critical	critical	ADJ
m-1112	2579	27	-	-	PUNCT
m-1112	2579	28	side	side	NOUN
m-1112	2579	29	𝐚𝐧	𝐚𝐧	NOUN
m-1112	2579	30	=	=	SYM
m-1112	2579	31	1	1	NUM
m-1112	2579	32	2	2	NUM
m-1112	2579	33	√4r2	√4r2	PROPN
m-1112	2579	34	−	−	PROPN
m-1112	2579	35	λ²n	λ²n	X
m-1112	2579	36	,	,	PUNCT
m-1112	2579	37	every	every	DET
m-1112	2579	38	=	=	NOUN
m-1112	2579	39	monad	monad	PROPN
m-1112	2579	40	occupies	occupy	VERB
m-1112	2579	41	ab	ab	PROPN
m-1112	2579	42	=	=	SYM
m-1112	2579	43	2|r|	2|r|	NUM
m-1112	2579	44	diameter	diameter	NOUN
m-1112	2579	45	=	=	SYM
m-1112	2579	46	space	space	NOUN
m-1112	2579	47	&	&	CCONJ
m-1112	2579	48	unit	unit	PROPN
m-1112	2579	49	-	-	PUNCT
m-1112	2579	50	e	e	NOUN
m-1112	2579	51	-	-	NOUN
m-1112	2579	52	vector	vector	ADJ
m-1112	2579	53	r=	r=	ADJ
m-1112	2579	54	σ	σ	NOUN
m-1112	2579	55	j.w²	j.w²	X
m-1112	2580	1	=	=	SYM
m-1112	2580	2	σ	σ	NUM
m-1112	2580	3	b̅	b̅	PUNCT
m-1112	2580	4	=	=	PUNCT
m-1112	2580	5	motion	motion	NOUN
m-1112	2580	6	the	the	DET
m-1112	2580	7	quantization	quantization	NOUN
m-1112	2580	8	of	of	ADP
m-1112	2580	9	energy	energy	NOUN
m-1112	2580	10	in	in	ADP
m-1112	2580	11	spaces	space	NOUN
m-1112	2580	12	happens	happen	VERB
m-1112	2580	13	by	by	ADP
m-1112	2580	14	following	follow	VERB
m-1112	2580	15	the	the	DET
m-1112	2580	16	archimedes	archimede	NOUN
m-1112	2580	17	formula	formula	NOUN
m-1112	2580	18	for	for	ADP
m-1112	2580	19	duplication	duplication	NOUN
m-1112	2580	20	of	of	ADP
m-1112	2580	21	sides	side	NOUN
m-1112	2580	22	as	as	ADP
m-1112	2580	23	𝛌𝟐𝐧=√2r2	𝛌𝟐𝐧=√2r2	NOUN
m-1112	2580	24	−	−	PROPN
m-1112	2580	25	r√4r2	r√4r2	PROPN
m-1112	2580	26	−	−	PROPN
m-1112	2580	27	λ²n	λ²n	X
m-1112	2580	28	&	&	CCONJ
m-1112	2580	29	critical	critical	ADJ
m-1112	2580	30	-	-	PUNCT
m-1112	2580	31	sides	side	NOUN
m-1112	2580	32	𝐚𝟐𝐧=	𝐚𝟐𝐧=	VERB
m-1112	2580	33	1	1	NUM
m-1112	2580	34	2	2	NUM
m-1112	2580	35	√4r2	√4r2	NOUN
m-1112	2580	36	−	−	PROPN
m-1112	2580	37	λ²2n	λ²2n	NOUN
m-1112	2581	1	the	the	DET
m-1112	2581	2	energy	energy	NOUN
m-1112	2581	3	-	-	PUNCT
m-1112	2581	4	monad	monad	PROPN
m-1112	2581	5	|	|	NOUN
m-1112	2581	6	�	�	NOUN
m-1112	2581	7	̅	̅	NOUN
m-1112	2581	8	�	�	NOUN
m-1112	2581	9	|	|	NOUN
m-1112	2581	10	=	=	SYM
m-1112	2581	11	σ	σ	X
m-1112	2581	12	j.w²	j.w²	NOUN
m-1112	2581	13	=	=	SYM
m-1112	2581	14	𝛔	𝛔	PART
m-1112	2581	15	�	�	PROPN
m-1112	2581	16	̅	̅	NOUN
m-1112	2581	17	�	�	NOUN
m-1112	2581	18	remains	remain	VERB
m-1112	2581	19	the	the	DET
m-1112	2581	20	same	same	ADJ
m-1112	2581	21	in	in	ADP
m-1112	2581	22	pns	pns	PROPN
m-1112	2581	23	space	space	NOUN
m-1112	2581	24	while	while	SCONJ
m-1112	2581	25	the	the	DET
m-1112	2581	26	spaces	space	NOUN
m-1112	2581	27	sides	side	NOUN
m-1112	2581	28	change	change	VERB
m-1112	2581	29	as	as	ADP
m-1112	2581	30	𝛌𝟐𝐧	𝛌𝟐𝐧	ADV
m-1112	2581	31	,	,	PUNCT
m-1112	2581	32	𝐚𝟐𝐧	𝐚𝟐𝐧	PROPN
m-1112	2581	33	,	,	PUNCT
m-1112	2581	34	when	when	SCONJ
m-1112	2581	35	the	the	DET
m-1112	2581	36	monad	monad	PROPN
m-1112	2581	37	|	|	NOUN
m-1112	2581	38	�	�	PROPN
m-1112	2581	39	̅	̅	NOUN
m-1112	2581	40	�	�	NOUN
m-1112	2581	41	|	|	NOUN
m-1112	2581	42	enters	enter	VERB
m-1112	2581	43	the	the	DET
m-1112	2581	44	2n	2n	NUM
m-1112	2581	45	.	.	PUNCT
m-1112	2582	1	-------------------------------------------------------------------------------------------------------------------------	-------------------------------------------------------------------------------------------------------------------------	PUNCT
m-1112	2582	2	the	the	DET
m-1112	2582	3	4	4	NUM
m-1112	2582	4	solution	solution	NOUN
m-1112	2582	5	for	for	ADP
m-1112	2582	6	real	real	ADJ
m-1112	2582	7	and	and	CCONJ
m-1112	2582	8	imaginary	imaginary	ADJ
m-1112	2582	9	root	root	NOUN
m-1112	2582	10	is	be	AUX
m-1112	2582	11	as	as	ADP
m-1112	2582	12	below	below	ADV
m-1112	2582	13	,	,	PUNCT
m-1112	2582	14	the	the	DET
m-1112	2582	15	|w1	|w1	PROPN
m-1112	2582	16	̅̅	̅̅	PROPN
m-1112	2582	17	̅̅	̅̅	PROPN
m-1112	2583	1	|	|	ADJ
m-1112	2583	2	solution	solution	NOUN
m-1112	2583	3	is	be	AUX
m-1112	2583	4	the	the	DET
m-1112	2583	5	real	real	ADJ
m-1112	2583	6	-root	-root	NOUN
m-1112	2583	7	giving	give	VERB
m-1112	2583	8	the	the	DET
m-1112	2583	9	strongest	strong	ADJ
m-1112	2583	10	in	in	ADP
m-1112	2583	11	amplitude	amplitude	NOUN
m-1112	2583	12	energy	energy	NOUN
m-1112	2583	13	-	-	PUNCT
m-1112	2583	14	structions	struction	NOUN
m-1112	2583	15	.	.	PUNCT
m-1112	2584	1	the	the	DET
m-1112	2584	2	|w2	|w2	PROPN
m-1112	2584	3	̅̅	̅̅	PROPN
m-1112	2584	4	̅̅	̅̅	PROPN
m-1112	2584	5	|	|	ADJ
m-1112	2584	6	solution	solution	NOUN
m-1112	2584	7	is	be	AUX
m-1112	2584	8	the	the	DET
m-1112	2584	9	real	real	ADJ
m-1112	2584	10	-root	-root	NOUN
m-1112	2584	11	giving	give	VERB
m-1112	2584	12	the	the	DET
m-1112	2584	13	weakest	weak	ADJ
m-1112	2584	14	in	in	ADP
m-1112	2584	15	amplitude	amplitude	NOUN
m-1112	2584	16	energy	energy	NOUN
m-1112	2584	17	-	-	PUNCT
m-1112	2584	18	structions	struction	NOUN
m-1112	2584	19	.	.	PUNCT
m-1112	2585	1	the	the	DET
m-1112	2585	2	|𝑤3	|𝑤3	PROPN
m-1112	2585	3	̅̅	̅̅	PROPN
m-1112	2585	4	̅̅	̅̅	PROPN
m-1112	2586	1	|	|	ADJ
m-1112	2586	2	solution	solution	NOUN
m-1112	2586	3	is	be	AUX
m-1112	2586	4	the	the	DET
m-1112	2586	5	imaginary	imaginary	ADJ
m-1112	2586	6	-	-	PUNCT
m-1112	2586	7	root	root	NOUN
m-1112	2586	8	giving	give	VERB
m-1112	2586	9	the	the	DET
m-1112	2586	10	mega	mega	ADJ
m-1112	2586	11	tapered	taper	VERB
m-1112	2586	12	-	-	PUNCT
m-1112	2586	13	amplitude	amplitude	NOUN
m-1112	2586	14	e	e	NOUN
m-1112	2586	15	-	-	NOUN
m-1112	2586	16	structions	struction	NOUN
m-1112	2586	17	.	.	PUNCT
m-1112	2587	1	the	the	DET
m-1112	2587	2	|𝑤4	|𝑤4	PROPN
m-1112	2587	3	̅̅	̅̅	PROPN
m-1112	2587	4	̅̅	̅̅	PROPN
m-1112	2588	1	|	|	ADJ
m-1112	2588	2	solution	solution	NOUN
m-1112	2588	3	is	be	AUX
m-1112	2588	4	the	the	DET
m-1112	2588	5	imaginary	imaginary	ADJ
m-1112	2588	6	-	-	PUNCT
m-1112	2588	7	root	root	NOUN
m-1112	2588	8	giving	give	VERB
m-1112	2588	9	the	the	DET
m-1112	2588	10	micro	micro	ADJ
m-1112	2588	11	black	black	ADJ
m-1112	2588	12	-	-	PUNCT
m-1112	2588	13	holes	hole	NOUN
m-1112	2588	14	structions	struction	NOUN
m-1112	2588	15	.	.	PUNCT
m-1112	2589	1	from	from	ADP
m-1112	2589	2	gravity	gravity	NOUN
m-1112	2589	3	relation	relation	NOUN
m-1112	2589	4	g	g	PROPN
m-1112	2589	5	=	=	SYM
m-1112	2589	6	g	g	PROPN
m-1112	2589	7	𝐤𝐄	𝐤𝐄	NOUN
m-1112	2589	8	=	=	NOUN
m-1112	2589	9	9,8076941.6,8116.10−12=	9,8076941.6,8116.10−12=	PROPN
m-1112	2589	10	6,68056.𝟏𝟎−𝟏𝟏	6,68056.𝟏𝟎−𝟏𝟏	NUM
m-1112	2589	11	m3/	m3/	ADP
m-1112	2589	12	n.s²	n.s²	ADV
m-1112	2589	13	from	from	ADP
m-1112	2589	14	ijo	ijo	PROPN
m-1112	2589	15	international	international	PROPN
m-1112	2589	16	journal	journal	PROPN
m-1112	2589	17	of	of	ADP
m-1112	2589	18	mathematics	mathematics	PROPN
m-1112	2589	19	(	(	PUNCT
m-1112	2589	20	issn	issn	PROPN
m-1112	2589	21	:	:	PUNCT
m-1112	2589	22	2992	2992	NUM
m-1112	2589	23	-	-	SYM
m-1112	2589	24	4421	4421	NUM
m-1112	2589	25	)	)	PUNCT
m-1112	2589	26	volume	volume	NOUN
m-1112	2589	27	08	08	NUM
m-1112	2590	1	|	|	ADV
m-1112	2590	2	issue	issue	NOUN
m-1112	2590	3	08	08	NUM
m-1112	2591	1	|	|	ADV
m-1112	2591	2	august	august	PROPN
m-1112	2591	3	2025	2025	NUM
m-1112	2591	4	|	|	ADV
m-1112	2591	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2591	6	ijo	ijo	PROPN
m-1112	2591	7	journals	journal	NOUN
m-1112	2591	8	90	90	NUM
m-1112	2591	9	the	the	DET
m-1112	2591	10	fundamental	fundamental	ADJ
m-1112	2591	11	particles	particle	NOUN
m-1112	2591	12	origination	origination	NOUN
m-1112	2591	13	mechanism	mechanism	NOUN
m-1112	2591	14	in	in	ADP
m-1112	2591	15	mfmf	mfmf	PROPN
m-1112	2591	16	pns	pns	PROPN
m-1112	2591	17	caves	cave	NOUN
m-1112	2591	18	.	.	PUNCT
m-1112	2592	1	energy	energy	NOUN
m-1112	2592	2	-	-	PUNCT
m-1112	2592	3	loop	loop	NOUN
m-1112	2592	4	relation	relation	NOUN
m-1112	2592	5	1	1	NUM
m-1112	2592	6	=	=	SYM
m-1112	2592	7	c.	c.	PROPN
m-1112	2592	8	r³.	r³.	NOUN
m-1112	2592	9	𝐟𝐏²	𝐟𝐏²	PROPN
m-1112	2592	10	→	→	SYM
m-1112	2592	11	fp=√1	fp=√1	PROPN
m-1112	2592	12	/	/	SYM
m-1112	2592	13	cr³	cr³	NOUN
m-1112	2592	14	,	,	PUNCT
m-1112	2592	15	and	and	CCONJ
m-1112	2592	16	from	from	ADP
m-1112	2592	17	f	f	PROPN
m-1112	2592	18	=	=	SYM
m-1112	2592	19	e	e	PROPN
m-1112	2592	20	/	/	SYM
m-1112	2592	21	h	h	NOUN
m-1112	2593	1	then	then	ADV
m-1112	2593	2	f	f	PROPN
m-1112	2593	3	=	=	SYM
m-1112	2593	4	𝐄	𝐄	PROPN
m-1112	2593	5	𝐡	𝐡	NOUN
m-1112	2593	6	=	=	PUNCT
m-1112	2593	7	√1	√1	PROPN
m-1112	2593	8	/	/	SYM
m-1112	2593	9	cr³	cr³	ADJ
m-1112	2593	10	or	or	CCONJ
m-1112	2593	11	→	→	SYM
m-1112	2593	12	e	e	NOUN
m-1112	2593	13	=	=	SYM
m-1112	2593	14	h	h	PROPN
m-1112	2593	15	.√1	.√1	PROPN
m-1112	2593	16	/	/	SYM
m-1112	2593	17	c.	c.	PROPN
m-1112	2593	18	r³	r³	PROPN
m-1112	2593	19	,	,	PUNCT
m-1112	2593	20	and	and	CCONJ
m-1112	2593	21	e²	e²	VERB
m-1112	2593	22	h²	h²	PROPN
m-1112	2594	1	=	=	SYM
m-1112	2594	2	1	1	NUM
m-1112	2594	3	c	c	X
m-1112	2594	4	r³	r³	PROPN
m-1112	2594	5	or	or	CCONJ
m-1112	2594	6	,	,	PUNCT
m-1112	2594	7	e	e	X
m-1112	2594	8	²	²	PROPN
m-1112	2594	9	=	=	SYM
m-1112	2594	10	h²	h²	PROPN
m-1112	2594	11	c	c	PROPN
m-1112	2594	12	r³	r³	PROPN
m-1112	2594	13	,	,	PUNCT
m-1112	2594	14	an	an	DET
m-1112	2594	15	energy	energy	NOUN
m-1112	2594	16	relation	relation	NOUN
m-1112	2594	17	between	between	ADP
m-1112	2594	18	the	the	PRON
m-1112	2594	19	,	,	PUNCT
m-1112	2594	20	c	c	NOUN
m-1112	2594	21	,	,	PUNCT
m-1112	2595	1	r	r	NOUN
m-1112	2595	2	.	.	PUNCT
m-1112	2596	1	this	this	DET
m-1112	2596	2	relation	relation	NOUN
m-1112	2596	3	is	be	AUX
m-1112	2596	4	used	use	VERB
m-1112	2596	5	for	for	ADP
m-1112	2596	6	blackholes	blackhole	NOUN
m-1112	2596	7	energy	energy	NOUN
m-1112	2596	8	where	where	SCONJ
m-1112	2596	9	r	r	NOUN
m-1112	2596	10	,	,	PUNCT
m-1112	2596	11	result	result	VERB
m-1112	2596	12	to	to	ADP
m-1112	2596	13	zero	zero	NUM
m-1112	2596	14	,	,	PUNCT
m-1112	2596	15	the	the	DET
m-1112	2596	16	permissible	permissible	ADJ
m-1112	2596	17	-	-	PUNCT
m-1112	2596	18	permeable	permeable	ADJ
m-1112	2596	19	-	-	PUNCT
m-1112	2596	20	resonance	resonance	NOUN
m-1112	2596	21	-	-	PUNCT
m-1112	2596	22	paths	path	NOUN
m-1112	2596	23	for	for	ADP
m-1112	2596	24	their	their	PRON
m-1112	2596	25	means	mean	NOUN
m-1112	2596	26	are	be	AUX
m-1112	2596	27	for	for	ADP
m-1112	2596	28	,	,	PUNCT
m-1112	2596	29	7	7	X
m-1112	2596	30	)	)	PUNCT
m-1112	2596	31	particles	particle	NOUN
m-1112	2596	32	→	→	PUNCT
m-1112	2596	33	the	the	DET
m-1112	2596	34	resultance	resultance	NOUN
m-1112	2596	35	of	of	ADP
m-1112	2596	36	the	the	DET
m-1112	2596	37	one	one	NUM
m-1112	2596	38	-	-	PUNCT
m-1112	2596	39	dimensional	dimensional	ADJ
m-1112	2596	40	-	-	PUNCT
m-1112	2596	41	collision	collision	NOUN
m-1112	2596	42	v̅ij=	v̅ij=	NOUN
m-1112	2597	1	v̅j	v̅j	PROPN
m-1112	2597	2	v̅i	v̅i	PUNCT
m-1112	2597	3	=	=	PUNCT
m-1112	2597	4	w̅ij	w̅ij	PROPN
m-1112	2597	5	.	.	PUNCT
m-1112	2598	1	r̅ij	r̅ij	NOUN
m-1112	2598	2	8)	8)	NUM
m-1112	2598	3	particles	particle	NOUN
m-1112	2598	4	→	→	PUNCT
m-1112	2598	5	the	the	DET
m-1112	2598	6	cauchy	cauchy	ADJ
m-1112	2598	7	ellipsoid	ellipsoid	NOUN
m-1112	2598	8	-	-	PUNCT
m-1112	2598	9	stress	stress	NOUN
m-1112	2598	10	-	-	PUNCT
m-1112	2598	11	tensor	tensor	NOUN
m-1112	2598	12	where	where	SCONJ
m-1112	2598	13	{	{	PUNCT
m-1112	2598	14	w̅	w̅	PROPN
m-1112	2598	15	⊥	⊥	NUM
m-1112	2598	16	b̅	b̅	PROPN
m-1112	2598	17	⊥	⊥	X
m-1112	2598	18	r̅	r̅	NUM
m-1112	2598	19	≡	≡	PROPN
m-1112	2598	20	σ1⊥	σ1⊥	NOUN
m-1112	2598	21	σ2⊥σ3	σ2⊥σ3	PUNCT
m-1112	2599	1	}	}	PUNCT
m-1112	2599	2	9	9	X
m-1112	2599	3	)	)	PUNCT
m-1112	2599	4	m	m	NOUN
m-1112	2599	5	-	-	PUNCT
m-1112	2599	6	points	point	NOUN
m-1112	2599	7	→	→	PUNCT
m-1112	2599	8	the	the	DET
m-1112	2599	9	resonance	resonance	NOUN
m-1112	2599	10	-	-	PUNCT
m-1112	2599	11	frequencies	frequency	NOUN
m-1112	2599	12	𝐟𝐑	𝐟𝐑	NOUN
m-1112	2600	1	[	[	X
m-1112	2600	2	s	s	X
m-1112	2600	3	≡	≡	PROPN
m-1112	2600	4	f1=	f1=	PROPN
m-1112	2600	5	n	n	PROPN
m-1112	2600	6	,	,	PUNCT
m-1112	2600	7	f2	f2	PROPN
m-1112	2600	8	,	,	PUNCT
m-1112	2600	9	f3,fr	f3,fr	NOUN
m-1112	2600	10	=	=	NOUN
m-1112	2600	11	w²]=	w²]=	NOUN
m-1112	2600	12	𝐟𝐧	𝐟𝐧	ADP
m-1112	2600	13	=	=	NOUN
m-1112	2601	1	[	[	X
m-1112	2601	2	⊕↔⊝	⊕↔⊝	X
m-1112	2601	3	]	]	X
m-1112	2601	4	=	=	SYM
m-1112	2601	5	n	n	SYM
m-1112	2601	6	(	(	PUNCT
m-1112	2601	7	1+√5)σ	1+√5)σ	NUM
m-1112	2601	8	4πr	4πr	NOUN
m-1112	2601	9	=	=	PUNCT
m-1112	2601	10	n.σ.b̅	n.σ.b̅	ADJ
m-1112	2601	11	8	8	NUM
m-1112	2601	12	r²	r²	NOUN
m-1112	2601	13	→	→	SYM
m-1112	2601	14	i.e.	i.e.	X
m-1112	2601	15	the	the	DET
m-1112	2601	16	golden	golden	ADJ
m-1112	2601	17	-	-	PUNCT
m-1112	2601	18	ratio	ratio	NOUN
m-1112	2601	19	-	-	PUNCT
m-1112	2601	20	pattern	pattern	NOUN
m-1112	2601	21	,	,	PUNCT
m-1112	2601	22	which	which	PRON
m-1112	2601	23	is	be	AUX
m-1112	2601	24	related	relate	VERB
m-1112	2601	25	to	to	PART
m-1112	2601	26	spin	spin	VERB
m-1112	2601	27	.	.	PUNCT
m-1112	2602	1	-------------------------------------------------------------------------------------------------------------	-------------------------------------------------------------------------------------------------------------	PROPN
m-1112	2603	1	from	from	ADP
m-1112	2603	2	solution-3	solution-3	NUM
m-1112	2603	3	the	the	DET
m-1112	2603	4	magnitude	magnitude	NOUN
m-1112	2603	5	d	d	NOUN
m-1112	2603	6	becomes	become	VERB
m-1112	2603	7	maximum	maximum	ADJ
m-1112	2603	8	when	when	SCONJ
m-1112	2603	9	𝐬𝐐	𝐬𝐐	PROPN
m-1112	2603	10	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2603	11	≡	≡	PROPN
m-1112	2603	12	maximum	maximum	NOUN
m-1112	2603	13	or	or	CCONJ
m-1112	2603	14	,	,	PUNCT
m-1112	2604	1	when	when	SCONJ
m-1112	2604	2	|θr̅|	|θr̅|	NUM
m-1112	2604	3	axis	axis	NOUN
m-1112	2604	4	is	be	AUX
m-1112	2604	5	⊥	⊥	ADJ
m-1112	2604	6	b̅	b̅	PROPN
m-1112	2604	7	and	and	CCONJ
m-1112	2604	8	cone	cone	NOUN
m-1112	2604	9	-	-	PUNCT
m-1112	2604	10	angle	angle	NOUN
m-1112	2604	11	𝛉	𝛉	PROPN
m-1112	2604	12			NOUN
m-1112	2604	13	90	90	NUM
m-1112	2604	14	.	.	PUNCT
m-1112	2605	1	from	from	ADP
m-1112	2605	2	energy	energy	NOUN
m-1112	2605	3	relation	relation	NOUN
m-1112	2605	4	e	e	NOUN
m-1112	2605	5	=	=	SYM
m-1112	2605	6	w	w	PROPN
m-1112	2605	7	=	=	PUNCT
m-1112	2605	8	2l	2l	NUM
m-1112	2605	9	=	=	SYM
m-1112	2605	10	b̅	b̅	X
m-1112	2605	11	.w̅	.w̅	PUNCT
m-1112	2605	12	=	=	SYM
m-1112	2605	13	j.w²	j.w²	X
m-1112	2605	14	angular	angular	ADJ
m-1112	2605	15	-	-	PUNCT
m-1112	2605	16	momentum	momentum	NOUN
m-1112	2605	17	�	�	NOUN
m-1112	2605	18	̅	̅	NOUN
m-1112	2605	19	�	�	NOUN
m-1112	2605	20	=	=	PUNCT
m-1112	2606	1	[	[	X
m-1112	2606	2	3	3	NUM
m-1112	2606	3	,	,	PUNCT
m-1112	2606	4	3770539.10−96j].[5,613308.1045hz	3770539.10−96j].[5,613308.1045hz	NUM
m-1112	2606	5	]	]	X
m-1112	2606	6	=	=	SYM
m-1112	2606	7	1,895644.𝟏𝟎−𝟓𝟎	1,895644.𝟏𝟎−𝟓𝟎	NUM
m-1112	2606	8	j	j	PROPN
m-1112	2606	9	/	/	SYM
m-1112	2606	10	s	s	PROPN
m-1112	2606	11	,	,	PUNCT
m-1112	2606	12	i.e.	i.e.	X
m-1112	2606	13	the	the	DET
m-1112	2606	14	planck`s	planck`s	NOUN
m-1112	2606	15	cave	cave	NOUN
m-1112	2606	16	,	,	PUNCT
m-1112	2606	17	10−35	10−35	PROPN
m-1112	2606	18	m	m	NOUN
m-1112	2606	19	,	,	PUNCT
m-1112	2606	20	is	be	AUX
m-1112	2606	21	the	the	DET
m-1112	2606	22	safety	safety	NOUN
m-1112	2606	23	-	-	PUNCT
m-1112	2606	24	valve	valve	NOUN
m-1112	2606	25	≡	≡	NOUN
m-1112	2606	26	the	the	DET
m-1112	2606	27	critical	critical	ADJ
m-1112	2606	28	state	state	NOUN
m-1112	2606	29	for	for	ADP
m-1112	2606	30	the	the	DET
m-1112	2606	31	stress	stress	NOUN
m-1112	2606	32	ellipsoids	ellipsoid	NOUN
m-1112	2606	33	,	,	PUNCT
m-1112	2606	34	b̅	b̅	PROPN
m-1112	2606	35	w̅	w̅	PROPN
m-1112	2606	36	,	,	PUNCT
m-1112	2606	37	vectors	vector	NOUN
m-1112	2606	38	in	in	ADP
m-1112	2606	39	order	order	NOUN
m-1112	2606	40	that	that	SCONJ
m-1112	2606	41	this	this	DET
m-1112	2606	42	total	total	ADJ
m-1112	2606	43	-	-	PUNCT
m-1112	2606	44	energy	energy	NOUN
m-1112	2606	45	to	to	PART
m-1112	2606	46	superflow	superflow	VERB
m-1112	2606	47	and	and	CCONJ
m-1112	2606	48	be	be	AUX
m-1112	2606	49	still	still	ADV
m-1112	2606	50	into	into	ADP
m-1112	2606	51	vacuum	vacuum	PROPN
m-1112	2606	52	≡	≡	PROPN
m-1112	2607	1	[	[	X
m-1112	2607	2	10−62	10−62	NUM
m-1112	2607	3	-	-	PUNCT
m-1112	2607	4	10−35	10−35	NOUN
m-1112	2607	5	m	m	NOUN
m-1112	2607	6	]	]	X
m-1112	2607	7	.	.	PUNCT
m-1112	2608	1	this	this	DET
m-1112	2608	2	vacuum	vacuum	NOUN
m-1112	2608	3	between	between	ADP
m-1112	2608	4	the	the	DET
m-1112	2608	5	|gravity	|gravity	NOUN
m-1112	2608	6	cave	cave	NOUN
m-1112	2608	7	planck`s	planck`s	NOUN
m-1112	2608	8	cave|	cave|	PROPN
m-1112	2608	9	consists	consist	VERB
m-1112	2608	10	the	the	DET
m-1112	2608	11	black	black	ADJ
m-1112	2608	12	holes	hole	NOUN
m-1112	2608	13	chaos	chaos	NOUN
m-1112	2608	14	,	,	PUNCT
m-1112	2608	15	as	as	ADP
m-1112	2608	16	the	the	DET
m-1112	2608	17	recycling	recycling	NOUN
m-1112	2608	18	–	–	PUNCT
m-1112	2608	19	energy	energy	NOUN
m-1112	2608	20	into	into	ADP
m-1112	2608	21	which	which	PRON
m-1112	2608	22	→	→	PUNCT
m-1112	2608	23	the	the	DET
m-1112	2608	24	{	{	PUNCT
m-1112	2608	25	energy	energy	NOUN
m-1112	2608	26	–	–	PUNCT
m-1112	2608	27	space	space	NOUN
m-1112	2609	1	monad	monad	PROPN
m-1112	2609	2	|	|	NOUN
m-1112	2609	3	�	�	PROPN
m-1112	2609	4	̅	̅	NOUN
m-1112	2609	5	�	�	PROPN
m-1112	2609	6	|	|	ADV
m-1112	2609	7	≡	≡	PROPN
m-1112	2609	8	|ab|	|ab|	PROPN
m-1112	2609	9	}	}	PUNCT
m-1112	2609	10	,	,	PUNCT
m-1112	2609	11	vanishes	vanish	VERB
m-1112	2609	12	≡	≡	PROPN
m-1112	2609	13	decomposes	decompose	VERB
m-1112	2609	14	←	←	PROPN
m-1112	2609	15	-------------------------------------------------------------------------------------------------------------	-------------------------------------------------------------------------------------------------------------	PROPN
m-1112	2609	16	in	in	ADP
m-1112	2609	17	physics	physics	NOUN
m-1112	2609	18	exist	exist	VERB
m-1112	2609	19	,	,	PUNCT
m-1112	2609	20	two	two	NUM
m-1112	2609	21	different	different	ADJ
m-1112	2609	22	potential	potential	ADJ
m-1112	2609	23	-	-	PUNCT
m-1112	2609	24	energies	energy	NOUN
m-1112	2609	25	between	between	ADP
m-1112	2609	26	planck	planck	NOUN
m-1112	2609	27	spaces	space	NOUN
m-1112	2609	28	and	and	CCONJ
m-1112	2609	29	gravity	gravity	NOUN
m-1112	2609	30	spaces	space	NOUN
m-1112	2609	31	as	as	ADP
m-1112	2609	32	uplanc	uplanc	NOUN
m-1112	2609	33	and	and	CCONJ
m-1112	2609	34	ugravity	ugravity	NOUN
m-1112	2609	35	.the	.the	DET
m-1112	2609	36	difference	difference	NOUN
m-1112	2610	1	∆u	∆u	ADV
m-1112	2610	2	=	=	PUNCT
m-1112	2610	3	ugraupla	ugraupla	NOUN
m-1112	2610	4	is	be	AUX
m-1112	2610	5	the	the	DET
m-1112	2610	6	flow	flow	NOUN
m-1112	2610	7	-	-	PUNCT
m-1112	2610	8	energy	energy	NOUN
m-1112	2610	9	between	between	ADP
m-1112	2610	10	the	the	DET
m-1112	2610	11	two	two	NUM
m-1112	2610	12	energy	energy	NOUN
m-1112	2610	13	levels	level	NOUN
m-1112	2610	14	l	l	NOUN
m-1112	2610	15	pla	pla	NOUN
m-1112	2610	16	=	=	PUNCT
m-1112	2611	1	6,6262.10−34	6,6262.10−34	NUM
m-1112	2611	2	m	m	NOUN
m-1112	2611	3	,	,	PUNCT
m-1112	2611	4	and	and	CCONJ
m-1112	2611	5	l	l	X
m-1112	2612	1	gra=	gra=	NOUN
m-1112	2612	2	1,777.10−62	1,777.10−62	NUM
m-1112	2612	3	m	m	NOUN
m-1112	2612	4	,	,	PUNCT
m-1112	2612	5	from	from	ADP
m-1112	2612	6	cave	cave	PROPN
m-1112	2612	7	l	l	NOUN
m-1112	2612	8	pla	pla	NOUN
m-1112	2612	9	=	=	PUNCT
m-1112	2612	10	6,6262.10−34	6,6262.10−34	NUM
m-1112	2612	11	m	m	NOUN
m-1112	2612	12	and	and	CCONJ
m-1112	2612	13	fp	fp	X
m-1112	2612	14	=	=	NOUN
m-1112	2612	15	√	√	PROPN
m-1112	2612	16	g	g	NOUN
m-1112	2612	17	a³	a³	PROPN
m-1112	2612	18	2	2	NUM
m-1112	2612	19	=	=	SYM
m-1112	2612	20	√	√	NUM
m-1112	2612	21	9,8078	9,8078	NOUN
m-1112	2612	22	(	(	PUNCT
m-1112	2612	23	6,6262.10−34)³	6,6262.10−34)³	NUM
m-1112	2612	24	2	2	NUM
m-1112	2612	25	=	=	SYM
m-1112	2612	26	1,83585.10	1,83585.10	NUM
m-1112	2612	27	50	50	NUM
m-1112	2612	28	h	h	NOUN
m-1112	2612	29	then	then	ADV
m-1112	2612	30	→	→	SYM
m-1112	2612	31	e	e	PROPN
m-1112	2612	32	pla	pla	NOUN
m-1112	2612	33	=	=	SYM
m-1112	2612	34	h.fp	h.fp	PROPN
m-1112	2612	35	=	=	NOUN
m-1112	2612	36	6.62607.10−34	6.62607.10−34	NUM
m-1112	2612	37	.	.	PUNCT
m-1112	2613	1	1,83585.10	1,83585.10	NUM
m-1112	2613	2	50	50	NUM
m-1112	2613	3	=	=	SYM
m-1112	2613	4	1,216447	1,216447	NUM
m-1112	2613	5	.	.	PUNCT
m-1112	2614	1	1017	1017	NUM
m-1112	2614	2	j	j	NOUN
m-1112	2614	3	the	the	DET
m-1112	2614	4	minimum	minimum	ADJ
m-1112	2614	5	charge	charge	NOUN
m-1112	2614	6	in	in	ADP
m-1112	2614	7	planck`s	planck`s	NOUN
m-1112	2614	8	cave	cave	NOUN
m-1112	2614	9	→	→	SYM
m-1112	2614	10	q	q	NOUN
m-1112	2614	11	pla	pla	NOUN
m-1112	2614	12	=	=	PUNCT
m-1112	2614	13	1cb	1cb	NOUN
m-1112	2614	14	=	=	SYM
m-1112	2614	15	1,6	1,6	NUM
m-1112	2614	16	.10−19	.10−19	PUNCT
m-1112	2614	17	ev	ev	X
m-1112	2614	18	,	,	PUNCT
m-1112	2614	19	from	from	ADP
m-1112	2614	20	voltage	voltage	NOUN
m-1112	2614	21	relation	relation	NOUN
m-1112	2614	22	∆u	∆u	PROPN
m-1112	2614	23	=	=	SYM
m-1112	2614	24	energy	energy	NOUN
m-1112	2614	25	charge	charge	NOUN
m-1112	2614	26	issues	issue	NOUN
m-1112	2614	27	,	,	PUNCT
m-1112	2614	28	1volt	1volt	NUM
m-1112	2614	29	=	=	SYM
m-1112	2614	30	1joule	1joule	NUM
m-1112	2614	31	1culomb	1culomb	NUM
m-1112	2614	32	or	or	CCONJ
m-1112	2614	33	1v	1v	NUM
m-1112	2614	34	=	=	PUNCT
m-1112	2614	35	𝟏𝐉	𝟏𝐉	NOUN
m-1112	2614	36	𝟏𝐂	𝟏𝐂	NOUN
m-1112	2614	37	…	…	PUNCT
m-1112	2614	38	.(v	.(v	NUM
m-1112	2614	39	)	)	PUNCT
m-1112	2614	40	in	in	ADP
m-1112	2614	41	order	order	NOUN
m-1112	2614	42	that	that	SCONJ
m-1112	2614	43	1cb	1cb	NOUN
m-1112	2614	44	may	may	AUX
m-1112	2614	45	overflow	overflow	VERB
m-1112	2614	46	and	and	CCONJ
m-1112	2614	47	flow	flow	VERB
m-1112	2614	48	from	from	ADP
m-1112	2614	49	planck`s	planck`s	NOUN
m-1112	2614	50	cave	cave	NOUN
m-1112	2614	51	to	to	ADP
m-1112	2614	52	the	the	DET
m-1112	2614	53	gravity	gravity	NOUN
m-1112	2614	54	cave	cave	NOUN
m-1112	2614	55	,	,	PUNCT
m-1112	2614	56	then	then	ADV
m-1112	2614	57	must	must	AUX
m-1112	2614	58	exist	exist	VERB
m-1112	2614	59	a	a	DET
m-1112	2614	60	voltage	voltage	NOUN
m-1112	2614	61	∆u	∆u	ADV
m-1112	2614	62	>	>	X
m-1112	2614	63	=	=	PUNCT
m-1112	2615	1	7,593.10	7,593.10	NUM
m-1112	2615	2	35	35	NUM
m-1112	2615	3	ev	ev	NOUN
m-1112	2615	4	,	,	PUNCT
m-1112	2615	5	and	and	CCONJ
m-1112	2615	6	be	be	AUX
m-1112	2615	7	as	as	ADP
m-1112	2615	8	....	....	PUNCT
m-1112	2615	9	(	(	PUNCT
m-1112	2615	10	v	v	NOUN
m-1112	2615	11	)	)	PUNCT
m-1112	2615	12	𝐕	𝐕	NOUN
m-1112	2615	13	𝐆𝐑𝐀	𝐆𝐑𝐀	NOUN
m-1112	2615	14	=	=	X
m-1112	2615	15	𝐡.𝐟𝐏	𝐡.𝐟𝐏	X
m-1112	2615	16	.	.	PUNCT
m-1112	2616	1	𝟏𝐂𝐛	𝟏𝐂𝐛	X
m-1112	2617	1	=	=	SYM
m-1112	2617	2	1	1	NUM
m-1112	2617	3	,	,	PUNCT
m-1112	2617	4	216447.1017	216447.1017	NUM
m-1112	2617	5	j	j	NOUN
m-1112	2617	6	1,6022.10−19ev	1,6022.10−19ev	NUM
m-1112	2617	7	=	=	SYM
m-1112	2617	8	7,593.𝟏𝟎	7,593.𝟏𝟎	NUM
m-1112	2617	9	𝟑𝟓	𝟑𝟓	NUM
m-1112	2617	10	v	v	NOUN
m-1112	2617	11	,	,	PUNCT
m-1112	2617	12	i.e.	i.e.	X
m-1112	2617	13	→	→	PUNCT
m-1112	2617	14	when	when	SCONJ
m-1112	2617	15	the	the	DET
m-1112	2617	16	energy	energy	NOUN
m-1112	2617	17	in	in	ADP
m-1112	2617	18	planck`s	planck`s	NOUN
m-1112	2617	19	cave	cave	NOUN
m-1112	2617	20	lpla	lpla	NOUN
m-1112	2617	21	,	,	PUNCT
m-1112	2617	22	increases	increase	VERB
m-1112	2617	23	to	to	ADP
m-1112	2617	24	an	an	DET
m-1112	2617	25	voltage	voltage	NOUN
m-1112	2617	26	>	>	PUNCT
m-1112	2617	27	=	=	X
m-1112	2617	28	7,593.10	7,593.10	NUM
m-1112	2617	29	35	35	NUM
m-1112	2617	30	v	v	NOUN
m-1112	2617	31	then	then	ADV
m-1112	2617	32	the	the	DET
m-1112	2617	33	motion≡	motion≡	PROPN
m-1112	2617	34	energy	energy	NOUN
m-1112	2617	35	between	between	ADP
m-1112	2617	36	the	the	DET
m-1112	2617	37	two	two	NUM
m-1112	2617	38	opposite	opposite	ADJ
m-1112	2617	39	elements	element	NOUN
m-1112	2617	40	of	of	ADP
m-1112	2617	41	mp	mp	NOUN
m-1112	2617	42	-	-	PUNCT
m-1112	2617	43	dipole	dipole	NOUN
m-1112	2617	44	[	[	X
m-1112	2617	45	⊕↔⊝	⊕↔⊝	NOUN
m-1112	2617	46	]	]	X
m-1112	2617	47	becomes	become	VERB
m-1112	2617	48	a	a	DET
m-1112	2617	49	stationary	stationary	ADJ
m-1112	2617	50	flow	flow	NOUN
m-1112	2617	51	[	[	X
m-1112	2617	52	⊕,⊝	⊕,⊝	X
m-1112	2617	53	]	]	X
m-1112	2617	54	≡	≡	PROPN
m-1112	2617	55	charges	charge	VERB
m-1112	2617	56	[	[	X
m-1112	2617	57	⊕--⊝	⊕--⊝	X
m-1112	2617	58	]	]	PUNCT
m-1112	2617	59	in	in	ADP
m-1112	2617	60	gravity	gravity	NOUN
m-1112	2617	61	cave	cave	NOUN
m-1112	2617	62	l	l	PROPN
m-1112	2617	63	gra	gra	PROPN
m-1112	2617	64	.	.	PUNCT
m-1112	2618	1	so	so	ADV
m-1112	2618	2	energy	energy	NOUN
m-1112	2618	3	≡	≡	PROPN
m-1112	2618	4	motion	motion	NOUN
m-1112	2618	5	,	,	PUNCT
m-1112	2618	6	exists	exist	VERB
m-1112	2618	7	in	in	ADP
m-1112	2618	8	l	l	PROPN
m-1112	2618	9	gra	gra	PROPN
m-1112	2618	10	as	as	ADP
m-1112	2618	11	an	an	DET
m-1112	2618	12	→	→	SYM
m-1112	2618	13	pointy	pointy	ADJ
m-1112	2618	14	rotational	rotational	ADJ
m-1112	2618	15	centripetal	centripetal	ADJ
m-1112	2618	16	force	force	PROPN
m-1112	2618	17	←	←	PROPN
m-1112	2618	18	ijo	ijo	PROPN
m-1112	2618	19	international	international	PROPN
m-1112	2618	20	journal	journal	PROPN
m-1112	2618	21	of	of	ADP
m-1112	2618	22	mathematics	mathematics	PROPN
m-1112	2618	23	(	(	PUNCT
m-1112	2618	24	issn	issn	PROPN
m-1112	2618	25	:	:	PUNCT
m-1112	2618	26	2992	2992	NUM
m-1112	2618	27	-	-	SYM
m-1112	2618	28	4421	4421	NUM
m-1112	2618	29	)	)	PUNCT
m-1112	2618	30	volume	volume	NOUN
m-1112	2618	31	08	08	NUM
m-1112	2619	1	|	|	ADV
m-1112	2619	2	issue	issue	NOUN
m-1112	2619	3	08	08	NUM
m-1112	2620	1	|	|	ADV
m-1112	2620	2	august	august	PROPN
m-1112	2620	3	2025	2025	NUM
m-1112	2620	4	|	|	ADV
m-1112	2620	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2620	6	ijo	ijo	PROPN
m-1112	2620	7	journals	journal	NOUN
m-1112	2620	8	91	91	NUM
m-1112	2620	9	the	the	DET
m-1112	2620	10	fundamental	fundamental	ADJ
m-1112	2620	11	particles	particle	NOUN
m-1112	2620	12	origination	origination	NOUN
m-1112	2620	13	mechanism	mechanism	NOUN
m-1112	2620	14	in	in	ADP
m-1112	2620	15	mfmf	mfmf	PROPN
m-1112	2620	16	pns	pns	PROPN
m-1112	2620	17	caves	cave	NOUN
m-1112	2620	18	.	.	PUNCT
m-1112	2621	1	→	→	PUNCT
m-1112	2621	2	when	when	SCONJ
m-1112	2621	3	the	the	DET
m-1112	2621	4	energy	energy	NOUN
m-1112	2621	5	in	in	ADP
m-1112	2621	6	planck`s	planck`s	NOUN
m-1112	2621	7	cave	cave	NOUN
m-1112	2621	8	lpla	lpla	NOUN
m-1112	2621	9	,	,	PUNCT
m-1112	2621	10	decreases	decrease	VERB
m-1112	2621	11	to	to	ADP
m-1112	2621	12	an	an	DET
m-1112	2621	13	voltage	voltage	NOUN
m-1112	2621	14	=	=	NOUN
m-1112	2621	15	<	<	X
m-1112	2621	16	7,593.10	7,593.10	NUM
m-1112	2621	17	35	35	NUM
m-1112	2621	18	v	v	NOUN
m-1112	2621	19	then	then	ADV
m-1112	2621	20	motion	motion	NOUN
m-1112	2621	21	≡	≡	PROPN
m-1112	2621	22	energy	energy	NOUN
m-1112	2621	23	between	between	ADP
m-1112	2621	24	the	the	DET
m-1112	2621	25	two	two	NUM
m-1112	2621	26	opposite	opposite	ADJ
m-1112	2621	27	elements	element	NOUN
m-1112	2621	28	of	of	ADP
m-1112	2621	29	m	m	PROPN
m-1112	2621	30	-	-	ADJ
m-1112	2621	31	p	p	NOUN
m-1112	2621	32	-	-	PUNCT
m-1112	2621	33	dipole	dipole	NOUN
m-1112	2621	34	[	[	X
m-1112	2621	35	⊕	⊕	NOUN
m-1112	2621	36	↻	↻	NOUN
m-1112	2621	37	↺	↺	NOUN
m-1112	2621	38	⊝	⊝	X
m-1112	2621	39	]	]	PUNCT
m-1112	2621	40	creates	create	VERB
m-1112	2621	41	the	the	DET
m-1112	2621	42	a	a	DET
m-1112	2621	43	-	-	PUNCT
m-1112	2621	44	velocity	velocity	NOUN
m-1112	2621	45	-	-	PUNCT
m-1112	2621	46	vector	vector	NOUN
m-1112	2621	47	�	�	PROPN
m-1112	2621	48	̅	̅	NOUN
m-1112	2621	49	�	�	NUM
m-1112	2621	50	which	which	PRON
m-1112	2621	51	rotates	rotate	VERB
m-1112	2621	52	in	in	ADP
m-1112	2621	53	the	the	DET
m-1112	2621	54	axis	axis	NOUN
m-1112	2621	55	k	k	PROPN
m-1112	2621	56	with	with	ADP
m-1112	2621	57	respect	respect	NOUN
m-1112	2621	58	to	to	ADP
m-1112	2621	59	variable	variable	ADJ
m-1112	2621	60	�	�	PROPN
m-1112	2621	61	̅	̅	NOUN
m-1112	2621	62	�	�	PROPN
m-1112	2621	63	.	.	PUNCT
m-1112	2622	1	so	so	ADV
m-1112	2622	2	when	when	SCONJ
m-1112	2622	3	unit	unit	NOUN
m-1112	2622	4	-	-	PUNCT
m-1112	2622	5	energy	energy	NOUN
m-1112	2622	6	vectors	vector	NOUN
m-1112	2622	7	�	�	NOUN
m-1112	2622	8	̅	̅	NOUN
m-1112	2622	9	�	�	NOUN
m-1112	2622	10	=	=	SYM
m-1112	2622	11	σ	σ	PROPN
m-1112	2622	12	/	/	SYM
m-1112	2622	13	�	�	PROPN
m-1112	2622	14	̅	̅	NOUN
m-1112	2622	15	�	�	NOUN
m-1112	2622	16	exists	exist	VERB
m-1112	2622	17	on	on	ADP
m-1112	2622	18	the	the	DET
m-1112	2622	19	unit	unit	NOUN
m-1112	2622	20	-	-	PUNCT
m-1112	2622	21	space	space	NOUN
m-1112	2622	22	-	-	PUNCT
m-1112	2622	23	monad	monad	PROPN
m-1112	2622	24	|ab|	|ab|	NUM
m-1112	2622	25	≡	≡	PROPN
m-1112	2622	26	|	|	NOUN
m-1112	2622	27	�	�	PROPN
m-1112	2622	28	̅	̅	NOUN
m-1112	2622	29	�	�	NOUN
m-1112	2622	30	|	|	NOUN
m-1112	2622	31	,	,	PUNCT
m-1112	2622	32	then	then	ADV
m-1112	2622	33	is	be	AUX
m-1112	2622	34	→	→	PUNCT
m-1112	2622	35	{	{	PUNCT
m-1112	2622	36	the	the	DET
m-1112	2622	37	energy	energy	NOUN
m-1112	2622	38	–	–	PUNCT
m-1112	2622	39	space	space	NOUN
m-1112	2623	1	monad	monad	PROPN
m-1112	2623	2	|	|	NOUN
m-1112	2623	3	�	�	PROPN
m-1112	2623	4	̅	̅	NOUN
m-1112	2623	5	�	�	NOUN
m-1112	2623	6	|	|	ADV
m-1112	2623	7	≡	≡	PROPN
m-1112	2623	8	|ab|	|ab|	PROPN
m-1112	2623	9	≡	≡	PROPN
m-1112	2623	10	the	the	DET
m-1112	2623	11	existing	exist	VERB
m-1112	2623	12	universe	universe	NOUN
m-1112	2623	13	}	}	PUNCT
m-1112	2623	14	←	←	PROPN
m-1112	2623	15	for	for	ADP
m-1112	2623	16	the	the	DET
m-1112	2623	17	chaos	chaos	NOUN
m-1112	2623	18	motion	motion	NOUN
m-1112	2623	19	→	→	PUNCT
m-1112	2623	20	angular	angular	ADJ
m-1112	2623	21	–	–	PUNCT
m-1112	2623	22	momentum	momentum	NOUN
m-1112	2623	23	≡	≡	PROPN
m-1112	2623	24	the	the	DET
m-1112	2623	25	rotational	rotational	ADJ
m-1112	2623	26	energy	energy	NOUN
m-1112	2623	27	�	�	PROPN
m-1112	2623	28	̅	̅	NOUN
m-1112	2623	29	�	�	PROPN
m-1112	2623	30	←	←	PROPN
m-1112	2623	31	for	for	ADP
m-1112	2623	32	the	the	DET
m-1112	2623	33	pns	pns	NOUN
m-1112	2623	34	–	–	PUNCT
m-1112	2623	35	spaces	space	NOUN
m-1112	2623	36	→	→	PUNCT
m-1112	2623	37	angular	angular	ADJ
m-1112	2623	38	–	–	PUNCT
m-1112	2623	39	momentum	momentum	NOUN
m-1112	2623	40	≡	≡	PROPN
m-1112	2623	41	the	the	DET
m-1112	2623	42	rotational	rotational	ADJ
m-1112	2623	43	energy	energy	NOUN
m-1112	2623	44	�	�	PROPN
m-1112	2623	45	̅	̅	NOUN
m-1112	2623	46	�	�	PROPN
m-1112	2623	47	←	←	PROPN
m-1112	2623	48	from	from	ADP
m-1112	2623	49	fig-13	fig-13	NUM
m-1112	2623	50	and	and	CCONJ
m-1112	2623	51	solution-3	solution-3	NUM
m-1112	2623	52	,	,	PUNCT
m-1112	2623	53	magnitude	magnitude	NOUN
m-1112	2623	54	d	d	NOUN
m-1112	2623	55	becomes	become	VERB
m-1112	2623	56	maximum	maximum	ADJ
m-1112	2623	57	when	when	SCONJ
m-1112	2623	58	𝐬𝐐	𝐬𝐐	PROPN
m-1112	2623	59	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2623	60	≡	≡	PROPN
m-1112	2623	61	maximum	maximum	NOUN
m-1112	2623	62	or	or	CCONJ
m-1112	2623	63	,	,	PUNCT
m-1112	2624	1	when	when	SCONJ
m-1112	2624	2	|θr̅|	|θr̅|	NUM
m-1112	2624	3	axis	axis	NOUN
m-1112	2624	4	is	be	AUX
m-1112	2624	5	⊥	⊥	ADJ
m-1112	2624	6	b̅	b̅	PROPN
m-1112	2624	7	and	and	CCONJ
m-1112	2624	8	cone	cone	NOUN
m-1112	2624	9	-	-	PUNCT
m-1112	2624	10	angle	angle	NOUN
m-1112	2624	11	θ	θ	PROPN
m-1112	2624	12			NOUN
m-1112	2624	13	90	90	NUM
m-1112	2624	14	,	,	PUNCT
m-1112	2624	15	where	where	SCONJ
m-1112	2624	16	energy	energy	NOUN
m-1112	2624	17	e	e	NOUN
m-1112	2624	18	=	=	NOUN
m-1112	2624	19	w=	w=	NOUN
m-1112	2624	20	2l=	2l=	NUM
m-1112	2624	21	b̅	b̅	X
m-1112	2624	22	.w̅	.w̅	PUNCT
m-1112	2625	1	=	=	SYM
m-1112	2625	2	j.w²	j.w²	X
m-1112	2625	3	angular	angular	ADJ
m-1112	2625	4	-	-	PUNCT
m-1112	2625	5	momentum	momentum	NOUN
m-1112	2625	6	�	�	NOUN
m-1112	2625	7	̅	̅	NOUN
m-1112	2625	8	�	�	NOUN
m-1112	2625	9	=	=	PUNCT
m-1112	2626	1	[	[	X
m-1112	2626	2	3	3	NUM
m-1112	2626	3	,	,	PUNCT
m-1112	2626	4	3770539.10−96j].[1,15346.1051hz	3770539.10−96j].[1,15346.1051hz	NOUN
m-1112	2626	5	]	]	X
m-1112	2626	6	=	=	SYM
m-1112	2627	1	3,895312.𝟏𝟎−𝟒𝟓	3,895312.𝟏𝟎−𝟒𝟓	NUM
m-1112	2627	2	j	j	PROPN
m-1112	2627	3	/	/	SYM
m-1112	2627	4	s	s	PROPN
m-1112	2627	5	,	,	PUNCT
m-1112	2627	6	i.e.	i.e.	X
m-1112	2627	7	the	the	DET
m-1112	2627	8	planck`s	planck`s	NOUN
m-1112	2627	9	cave	cave	NOUN
m-1112	2627	10	,	,	PUNCT
m-1112	2627	11	10−35	10−35	NOUN
m-1112	2627	12	m	m	NOUN
m-1112	2627	13	,	,	PUNCT
m-1112	2627	14	is	be	AUX
m-1112	2627	15	the	the	DET
m-1112	2627	16	safety	safety	NOUN
m-1112	2627	17	-	-	PUNCT
m-1112	2627	18	valve	valve	NOUN
m-1112	2627	19	≡	≡	NOUN
m-1112	2627	20	the	the	DET
m-1112	2627	21	critical	critical	ADJ
m-1112	2627	22	state	state	NOUN
m-1112	2627	23	for	for	ADP
m-1112	2627	24	the	the	DET
m-1112	2627	25	stress	stress	NOUN
m-1112	2627	26	ellipsoids	ellipsoid	NOUN
m-1112	2627	27	,	,	PUNCT
m-1112	2627	28	b̅	b̅	PROPN
m-1112	2627	29	w̅	w̅	PROPN
m-1112	2627	30	,	,	PUNCT
m-1112	2627	31	vectors	vector	NOUN
m-1112	2627	32	in	in	ADP
m-1112	2627	33	order	order	NOUN
m-1112	2627	34	that	that	SCONJ
m-1112	2627	35	this	this	DET
m-1112	2627	36	total	total	ADJ
m-1112	2627	37	-	-	PUNCT
m-1112	2627	38	energy	energy	NOUN
m-1112	2627	39	to	to	PART
m-1112	2627	40	superflow	superflow	VERB
m-1112	2627	41	and	and	CCONJ
m-1112	2627	42	be	be	AUX
m-1112	2627	43	still	still	ADV
m-1112	2627	44	into	into	ADP
m-1112	2627	45	vacuum	vacuum	PROPN
m-1112	2627	46	≡	≡	PROPN
m-1112	2628	1	[	[	X
m-1112	2628	2	10−62	10−62	NUM
m-1112	2628	3	-	-	PUNCT
m-1112	2628	4	10−35	10−35	NUM
m-1112	2628	5	m	m	NOUN
m-1112	2628	6	]	]	PUNCT
m-1112	2628	7	.	.	PUNCT
m-1112	2629	1	this	this	DET
m-1112	2629	2	vacuum	vacuum	NOUN
m-1112	2629	3	between	between	ADP
m-1112	2629	4	the	the	DET
m-1112	2629	5	|gravity	|gravity	NOUN
m-1112	2629	6	cave	cave	NOUN
m-1112	2629	7	planck`s	planck`s	NOUN
m-1112	2629	8	cave|	cave|	PROPN
m-1112	2629	9	consists	consist	VERB
m-1112	2629	10	the	the	DET
m-1112	2629	11	black	black	ADJ
m-1112	2629	12	holes	hole	NOUN
m-1112	2629	13	chaos	chaos	NOUN
m-1112	2629	14	,	,	PUNCT
m-1112	2629	15	as	as	ADP
m-1112	2629	16	the	the	DET
m-1112	2629	17	recycling	recycling	NOUN
m-1112	2629	18	–	–	PUNCT
m-1112	2629	19	energy	energy	NOUN
m-1112	2629	20	into	into	ADP
m-1112	2629	21	which	which	PRON
m-1112	2629	22	→	→	PUNCT
m-1112	2629	23	the	the	DET
m-1112	2629	24	{	{	PUNCT
m-1112	2629	25	energy	energy	NOUN
m-1112	2629	26	–	–	PUNCT
m-1112	2629	27	space	space	NOUN
m-1112	2630	1	monad	monad	PROPN
m-1112	2630	2	|	|	NOUN
m-1112	2630	3	�	�	PROPN
m-1112	2630	4	̅	̅	NOUN
m-1112	2630	5	�	�	PROPN
m-1112	2630	6	|	|	ADV
m-1112	2630	7	≡	≡	PROPN
m-1112	2630	8	|ab|	|ab|	PROPN
m-1112	2630	9	}	}	PUNCT
m-1112	2630	10	,	,	PUNCT
m-1112	2630	11	decomposes	decompose	VERB
m-1112	2630	12	←	←	PROPN
m-1112	2630	13	{	{	PUNCT
m-1112	2630	14	fig-13	fig-13	X
m-1112	2630	15	}	}	PUNCT
m-1112	2630	16	in	in	ADP
m-1112	2630	17	figure	figure	NOUN
m-1112	2630	18	,	,	PUNCT
m-1112	2630	19	the	the	DET
m-1112	2630	20	herpolhodecone	herpolhodecone	NOUN
m-1112	2630	21	plane	plane	NOUN
m-1112	2630	22	is	be	AUX
m-1112	2630	23	a	a	DET
m-1112	2630	24	circle	circle	NOUN
m-1112	2630	25	where	where	SCONJ
m-1112	2630	26	vector	vector	NOUN
m-1112	2630	27	b̅	b̅	NOUN
m-1112	2630	28	rotates	rotate	NOUN
m-1112	2630	29	,	,	PUNCT
m-1112	2630	30	and	and	CCONJ
m-1112	2630	31	when	when	SCONJ
m-1112	2630	32	𝛉	𝛉	X
m-1112	2630	33			NOUN
m-1112	2630	34	90	90	NUM
m-1112	2630	35	.	.	PUNCT
m-1112	2631	1	then	then	ADV
m-1112	2631	2	cone	cone	NOUN
m-1112	2631	3	becomes	become	VERB
m-1112	2631	4	a	a	DET
m-1112	2631	5	circle	circle	NOUN
m-1112	2631	6	,	,	PUNCT
m-1112	2631	7	where	where	SCONJ
m-1112	2631	8	energy	energy	NOUN
m-1112	2631	9	follows	follow	VERB
m-1112	2631	10	[	[	PUNCT
m-1112	2631	11	⊕	⊕	PROPN
m-1112	2631	12			PROPN
m-1112	2631	13	⊝	⊝	NUM
m-1112	2631	14	]	]	PUNCT
m-1112	2631	15	mode	mode	NOUN
m-1112	2631	16	as	as	ADP
m-1112	2631	17	→	→	PUNCT
m-1112	2631	18	+	+	X
m-1112	2631	19	when	when	SCONJ
m-1112	2631	20	𝛉	𝛉	X
m-1112	2631	21	=	=	SYM
m-1112	2631	22	0	0	PUNCT
m-1112	2632	1	=	=	PUNCT
m-1112	2632	2	<	<	X
m-1112	2632	3	90	90	NUM
m-1112	2632	4	,	,	PUNCT
m-1112	2632	5	and	and	CCONJ
m-1112	2632	6	when	when	SCONJ
m-1112	2632	7	𝛉	𝛉	X
m-1112	2632	8	=	=	SYM
m-1112	2632	9	90	90	NUM
m-1112	2632	10	–	–	PUNCT
m-1112	2632	11	180	180	NUM
m-1112	2632	12	←	←	PROPN
m-1112	2632	13	it	it	PRON
m-1112	2632	14	was	be	AUX
m-1112	2632	15	shown	show	VERB
m-1112	2632	16	that	that	SCONJ
m-1112	2632	17	,	,	PUNCT
m-1112	2632	18	the	the	DET
m-1112	2632	19	energy	energy	NOUN
m-1112	2632	20	from	from	ADP
m-1112	2632	21	chaos	chaos	NOUN
m-1112	2632	22	[	[	X
m-1112	2632	23	⊕	⊕	PROPN
m-1112	2632	24			PROPN
m-1112	2632	25	⊝	⊝	NUM
m-1112	2632	26	becomes	become	VERB
m-1112	2632	27	momentum	momentum	NOUN
m-1112	2632	28	�	�	NOUN
m-1112	2632	29	̅	̅	NOUN
m-1112	2632	30	�	�	PROPN
m-1112	2632	31	,	,	PUNCT
m-1112	2632	32	�	�	PROPN
m-1112	2632	33	̅	̅	NOUN
m-1112	2632	34	�	�	PROPN
m-1112	2632	35	,	,	PUNCT
m-1112	2632	36	and	and	CCONJ
m-1112	2632	37	is	be	AUX
m-1112	2632	38	composed	compose	VERB
m-1112	2632	39	≡	≡	PROPN
m-1112	2632	40	quantized	quantize	VERB
m-1112	2632	41	through	through	ADP
m-1112	2632	42	the	the	DET
m-1112	2632	43	physical-[stpl]-line	physical-[stpl]-line	NOUN
m-1112	2632	44	-	-	NOUN
m-1112	2632	45	mechanism	mechanism	NOUN
m-1112	2632	46	,	,	PUNCT
m-1112	2632	47	in	in	ADP
m-1112	2632	48	-	-	PUNCT
m-1112	2632	49	circle	circle	NOUN
m-1112	2632	50			NOUN
m-1112	2632	51	triangles	triangles	PROPN
m-1112	2632	52			NOUN
m-1112	2633	1	ex	ex	NOUN
m-1112	2633	2	-	-	NOUN
m-1112	2633	3	circle	circle	ADJ
m-1112	2633	4			NOUN
m-1112	2633	5	ex	ex	NOUN
m-1112	2633	6	-	-	NOUN
m-1112	2633	7	triangles	triangle	NOUN
m-1112	2633	8	consisted	consist	VERB
m-1112	2633	9	with	with	ADP
m-1112	2633	10	the	the	DET
m-1112	2633	11	three	three	NUM
m-1112	2633	12	spaces	space	NOUN
m-1112	2633	13	.	.	PUNCT
m-1112	2634	1	on	on	ADP
m-1112	2634	2	this	this	DET
m-1112	2634	3	pm	pm	NOUN
m-1112	2634	4	exist	exist	VERB
m-1112	2634	5	the	the	DET
m-1112	2634	6	three	three	NUM
m-1112	2634	7	breakages	breakage	NOUN
m-1112	2634	8	[	[	X
m-1112	2634	9	s²	s²	NOUN
m-1112	2634	10	=	=	SYM
m-1112	2634	11	⊕	⊕	PROPN
m-1112	2634	12	,	,	PUNCT
m-1112	2634	13	2s	2s	PROPN
m-1112	2634	14	²	²	NUM
m-1112	2634	15	=	=	SYM
m-1112	2634	16			ADJ
m-1112	2634	17	,	,	PUNCT
m-1112	2634	18	s	s	NOUN
m-1112	2634	19	²	²	NUM
m-1112	2634	20	=	=	PUNCT
m-1112	2634	21	⊝	⊝	X
m-1112	2634	22	]	]	PUNCT
m-1112	2634	23	which	which	DET
m-1112	2634	24	circularly	circularly	ADV
m-1112	2634	25	-	-	PUNCT
m-1112	2634	26	charge	charge	NOUN
m-1112	2634	27	on	on	ADP
m-1112	2634	28	the	the	DET
m-1112	2634	29	three	three	NUM
m-1112	2634	30	–	–	PUNCT
m-1112	2634	31	extreme	extreme	ADJ
m-1112	2634	32	triangles	triangle	NOUN
m-1112	2634	33	{	{	PUNCT
m-1112	2634	34	a	a	DET
m-1112	2634	35	b	b	NOUN
m-1112	2634	36	c	c	NOUN
m-1112	2634	37	}	}	PUNCT
m-1112	2634	38	,	,	PUNCT
m-1112	2634	39	{	{	PUNCT
m-1112	2634	40	ka	ka	PROPN
m-1112	2634	41	kb	kb	PROPN
m-1112	2634	42	kc	kc	PROPN
m-1112	2634	43	}	}	PUNCT
m-1112	2634	44	,	,	PUNCT
m-1112	2634	45	{	{	PUNCT
m-1112	2634	46	ae	ae	PROPN
m-1112	2634	47	be	be	VERB
m-1112	2634	48	ce	ce	PROPN
m-1112	2634	49	}	}	PUNCT
m-1112	2634	50	and	and	CCONJ
m-1112	2634	51	thus	thus	ADV
m-1112	2634	52	launch	launch	VERB
m-1112	2634	53	the	the	DET
m-1112	2634	54	energy	energy	NOUN
m-1112	2634	55	-	-	PUNCT
m-1112	2634	56	quantity	quantity	NOUN
m-1112	2634	57	±	±	NOUN
m-1112	2634	58	𝐐𝐩−𝐩=	𝐐𝐩−𝐩=	ADV
m-1112	2634	59	[	[	PUNCT
m-1112	2634	60	𝒄.𝑺	𝒄.𝑺	NOUN
m-1112	2634	61	𝒓	𝒓	X
m-1112	2634	62	]	]	PUNCT
m-1112	2634	63	≡	≡	PROPN
m-1112	2634	64	centripetal	centripetal	ADJ
m-1112	2634	65	-	-	PUNCT
m-1112	2634	66	force	force	NOUN
m-1112	2634	67	from	from	ADP
m-1112	2634	68	chaos	chaos	NOUN
m-1112	2634	69	to	to	ADP
m-1112	2634	70	pns	pns	PROPN
m-1112	2634	71	space	space	NOUN
m-1112	2634	72	,	,	PUNCT
m-1112	2634	73	on	on	ADP
m-1112	2634	74	the	the	DET
m-1112	2634	75	pascal`s	pascal`s	NUM
m-1112	2634	76	-desargues	-desargue	NOUN
m-1112	2634	77	points	point	NOUN
m-1112	2634	78	-	-	PUNCT
m-1112	2634	79	line	line	NOUN
m-1112	2634	80	through	through	ADP
m-1112	2634	81	the	the	DET
m-1112	2634	82	stpl	stpl	PROPN
m-1112	2634	83	circuit	circuit	NOUN
m-1112	2634	84	caves	cave	VERB
m-1112	2634	85	r	r	NOUN
m-1112	2634	86	,	,	PUNCT
m-1112	2634	87	and	and	CCONJ
m-1112	2634	88	from	from	ADP
m-1112	2634	89	the	the	DET
m-1112	2634	90	ptolemy`s	ptolemy`s	PROPN
m-1112	2634	91	&	&	CCONJ
m-1112	2634	92	ceba`s	ceba`	NOUN
m-1112	2634	93	still	still	ADV
m-1112	2634	94	-	-	PUNCT
m-1112	2634	95	mechanism	mechanism	NOUN
m-1112	2634	96	.	.	PUNCT
m-1112	2635	1	{	{	PUNCT
m-1112	2635	2	fig-24	fig-24	NOUN
m-1112	2635	3	}	}	PUNCT
m-1112	2635	4	remark	remark	NOUN
m-1112	2635	5	.	.	PUNCT
m-1112	2636	1	1	1	X
m-1112	2636	2	..	..	PUNCT
m-1112	2636	3	electron	electron	NOUN
m-1112	2636	4	,	,	PUNCT
m-1112	2636	5	e	e	X
m-1112	2636	6	,	,	PUNCT
m-1112	2636	7	me	i	PRON
m-1112	2636	8	=	=	SYM
m-1112	2636	9	0	0	NUM
m-1112	2636	10	,	,	PUNCT
m-1112	2636	11	511mev	511mev	NUM
m-1112	2636	12	=	=	SYM
m-1112	2636	13	0	0	NUM
m-1112	2636	14	,	,	PUNCT
m-1112	2636	15	511.10−6	511.10−6	NUM
m-1112	2636	16	ev	ev	X
m-1112	2636	17	.	.	PUNCT
m-1112	2637	1	[	[	X
m-1112	2637	2	1,80	1,80	X
m-1112	2637	3	.	.	PUNCT
m-1112	2638	1	10−27	10−27	NUM
m-1112	2638	2	]	]	X
m-1112	2638	3	=	=	PUNCT
m-1112	2639	1	9,198.10−34	9,198.10−34	NUM
m-1112	2639	2	kg	kg	NOUN
m-1112	2639	3	𝐚𝐞	𝐚𝐞	NOUN
m-1112	2640	1	=	=	NOUN
m-1112	2641	1	5,0.10−18	5,0.10−18	NUM
m-1112	2641	2	m	m	VERB
m-1112	2641	3	,	,	PUNCT
m-1112	2641	4	charge	charge	VERB
m-1112	2641	5	𝐂	𝐂	PROPN
m-1112	2641	6	𝐞	𝐞	NOUN
m-1112	2641	7	=	=	NUM
m-1112	2641	8	1,602.10−19	1,602.10−19	NUM
m-1112	2641	9	c	c	NOUN
m-1112	2641	10	,	,	PUNCT
m-1112	2641	11	spin	spin	VERB
m-1112	2641	12	𝐒𝒆	𝐒𝒆	NOUN
m-1112	2641	13	=	=	SYM
m-1112	2641	14	𝐒	𝐒	PROPN
m-1112	2641	15	2	2	NUM
m-1112	2642	1	=	=	VERB
m-1112	2642	2	2,845976.10−34{kg	2,845976.10−34{kg	NUM
m-1112	2642	3	/	/	SYM
m-1112	2642	4	m	m	PROPN
m-1112	2642	5	/	/	SYM
m-1112	2642	6	s	s	PART
m-1112	2642	7	}	}	PUNCT
m-1112	2642	8	,	,	PUNCT
m-1112	2642	9	using	use	VERB
m-1112	2642	10	𝐄	𝐄	NOUN
m-1112	2642	11	𝐞𝐊	𝐞𝐊	NOUN
m-1112	2642	12	=	=	SYM
m-1112	2642	13	𝐤	𝐤	SYM
m-1112	2642	14	𝐫	𝐫	PROPN
m-1112	2642	15	+	+	CCONJ
m-1112	2642	16	𝒄𝐒	𝒄𝐒	NOUN
m-1112	2642	17	𝟐	𝟐	NUM
m-1112	2642	18	𝟐𝐦.𝐫𝟐	𝟐𝐦.𝐫𝟐	NOUN
m-1112	2642	19	=	=	SYM
m-1112	2642	20	36.10−20	36.10−20	NUM
m-1112	2642	21	7,10−18	7,10−18	NUM
m-1112	2643	1	+	+	CCONJ
m-1112	2643	2	3.108(5,691952.10−34)²	3.108(5,691952.10−34)²	NUM
m-1112	2643	3	2.9,198.10−34[5.10−18]²	2.9,198.10−34[5.10−18]²	NUM
m-1112	2643	4	=	=	NOUN
m-1112	2643	5	51,428	51,428	NUM
m-1112	2643	6	ev	ev	X
m-1112	2644	1	+	+	CCONJ
m-1112	2644	2	2,111843.1010j	2,111843.1010j	ADJ
m-1112	2644	3	=	=	SYM
m-1112	2644	4	51,43	51,43	NUM
m-1112	2644	5	ev+	ev+	NOUN
m-1112	2644	6	1,32	1,32	X
m-1112	2644	7	.1029	.1029	PROPN
m-1112	2644	8	ev	ev	X
m-1112	2644	9	,	,	PUNCT
m-1112	2644	10	i.e.	i.e.	X
m-1112	2644	11	the	the	DET
m-1112	2644	12	energy	energy	NOUN
m-1112	2644	13	increases	increase	VERB
m-1112	2644	14	inverse	inverse	NOUN
m-1112	2644	15	analogous	analogous	ADJ
m-1112	2644	16	to	to	ADP
m-1112	2644	17	the	the	DET
m-1112	2644	18	cave	cave	NOUN
m-1112	2644	19	.	.	PUNCT
m-1112	2645	1	2	2	NUM
m-1112	2645	2	…	…	PUNCT
m-1112	2645	3	since	since	SCONJ
m-1112	2645	4	primary	primary	ADJ
m-1112	2645	5	motion	motion	NOUN
m-1112	2645	6	≡	≡	PROPN
m-1112	2645	7	[	[	X
m-1112	2645	8	pm	pm	X
m-1112	2645	9	]	]	PUNCT
m-1112	2645	10	exist	exist	VERB
m-1112	2645	11	from	from	ADP
m-1112	2645	12	the	the	DET
m-1112	2645	13	three	three	NUM
m-1112	2645	14	breakages	breakage	NOUN
m-1112	2645	15	only	only	ADV
m-1112	2645	16	stpl	stpl	PROPN
m-1112	2645	17	is	be	AUX
m-1112	2645	18	the	the	PRON
m-1112	2645	19	n	n	ADV
m-1112	2645	20	=3	=3	VERB
m-1112	2645	21	mechanism	mechanism	NOUN
m-1112	2645	22	creating	create	VERB
m-1112	2645	23	elementary	elementary	ADJ
m-1112	2645	24	particles	particle	NOUN
m-1112	2645	25	as	as	ADP
m-1112	2645	26	[	[	NOUN
m-1112	2645	27	n	n	X
m-1112	2645	28	-	-	PUNCT
m-1112	2645	29	knots=3	knots=3	X
m-1112	2645	30	]	]	X
m-1112	2645	31	in	in	ADP
m-1112	2645	32	𝐕	𝐕	PROPN
m-1112	2645	33	gra	gra	NOUN
m-1112	2645	34	=	=	PROPN
m-1112	2645	35	7,593.1035	7,593.1035	NUM
m-1112	2645	36	v	v	NOUN
m-1112	2645	37	.	.	PUNCT
m-1112	2646	1	ijo	ijo	PROPN
m-1112	2646	2	international	international	PROPN
m-1112	2646	3	journal	journal	PROPN
m-1112	2646	4	of	of	ADP
m-1112	2646	5	mathematics	mathematics	PROPN
m-1112	2646	6	(	(	PUNCT
m-1112	2646	7	issn	issn	PROPN
m-1112	2646	8	:	:	PUNCT
m-1112	2646	9	2992	2992	NUM
m-1112	2646	10	-	-	SYM
m-1112	2646	11	4421	4421	NUM
m-1112	2646	12	)	)	PUNCT
m-1112	2646	13	volume	volume	NOUN
m-1112	2646	14	08	08	NUM
m-1112	2647	1	|	|	ADV
m-1112	2647	2	issue	issue	NOUN
m-1112	2647	3	08	08	NUM
m-1112	2648	1	|	|	ADV
m-1112	2648	2	august	august	PROPN
m-1112	2648	3	2025	2025	NUM
m-1112	2648	4	|	|	ADV
m-1112	2648	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2648	6	ijo	ijo	PROPN
m-1112	2648	7	journals	journal	NOUN
m-1112	2648	8	92	92	NUM
m-1112	2648	9	the	the	DET
m-1112	2648	10	fundamental	fundamental	ADJ
m-1112	2648	11	particles	particle	NOUN
m-1112	2648	12	origination	origination	NOUN
m-1112	2648	13	mechanism	mechanism	NOUN
m-1112	2648	14	in	in	ADP
m-1112	2648	15	mfmf	mfmf	PROPN
m-1112	2648	16	pns	pns	PROPN
m-1112	2648	17	caves	cave	NOUN
m-1112	2648	18	.	.	PUNCT
m-1112	2649	1	the	the	DET
m-1112	2649	2	unit	unit	NOUN
m-1112	2649	3	-	-	PUNCT
m-1112	2649	4	space	space	NOUN
m-1112	2649	5	-vectors	-vector	NOUN
m-1112	2649	6	,	,	PUNCT
m-1112	2649	7	�	�	NOUN
m-1112	2649	8	̅	̅	NOUN
m-1112	2649	9	�	�	PROPN
m-1112	2649	10	.	.	PUNCT
m-1112	2649	11	�	�	PROPN
m-1112	2649	12	̅	̅	NOUN
m-1112	2649	13	�	�	PROPN
m-1112	2649	14	,	,	PUNCT
m-1112	2649	15	&	&	CCONJ
m-1112	2649	16	the	the	DET
m-1112	2649	17	unit	unit	NOUN
m-1112	2649	18	-	-	PUNCT
m-1112	2649	19	energy	energy	NOUN
m-1112	2649	20	-	-	PUNCT
m-1112	2649	21	vectors	vector	NOUN
m-1112	2649	22	,	,	PUNCT
m-1112	2649	23	�	�	NOUN
m-1112	2649	24	̅	̅	NOUN
m-1112	2649	25	�	�	PROPN
m-1112	2649	26	.	.	PUNCT
m-1112	2649	27	�	�	PROPN
m-1112	2649	28	̅	̅	NOUN
m-1112	2649	29	�	�	PROPN
m-1112	2649	30	,	,	PUNCT
m-1112	2649	31	ellipsoids	ellipsoid	NOUN
m-1112	2649	32	.	.	PUNCT
m-1112	2650	1	figure.17c	figure.17c	PROPN
m-1112	2650	2	..	..	PUNCT
m-1112	2650	3	shown	show	VERB
m-1112	2650	4	the	the	DET
m-1112	2650	5	geometrical	geometrical	ADJ
m-1112	2650	6	-	-	PUNCT
m-1112	2650	7	meaning	meaning	NOUN
m-1112	2650	8	of	of	ADP
m-1112	2650	9	ao̅̅	ao̅̅	NOUN
m-1112	2650	10	̅	̅	NOUN
m-1112	2650	11	ri̅	ri̅	NOUN
m-1112	2650	12	,	,	PUNCT
m-1112	2650	13	√ri²	√ri²	PROPN
m-1112	2650	14	−	−	PROPN
m-1112	2650	15	(	(	PUNCT
m-1112	2650	16	ao̅̅	ao̅̅	NOUN
m-1112	2650	17	̅	̅	NOUN
m-1112	2650	18	ri̅)²	ri̅)²	NOUN
m-1112	2650	19	terms	term	NOUN
m-1112	2650	20	of	of	ADP
m-1112	2650	21	radius	radius	NOUN
m-1112	2650	22	oa	oa	INTJ
m-1112	2650	23	i	i	PRON
m-1112	2650	24	in	in	ADP
m-1112	2650	25	(	(	PUNCT
m-1112	2650	26	1	1	X
m-1112	2650	27	)	)	PUNCT
m-1112	2650	28	is	be	AUX
m-1112	2650	29	shown	show	VERB
m-1112	2650	30	the	the	DET
m-1112	2650	31	inertial	inertial	ADJ
m-1112	2650	32	ellipsoid	ellipsoid	NOUN
m-1112	2650	33	(	(	PUNCT
m-1112	2650	34	o	o	NOUN
m-1112	2650	35	,	,	PUNCT
m-1112	2650	36	a̅	a̅	PROPN
m-1112	2650	37	)	)	PUNCT
m-1112	2650	38	of	of	ADP
m-1112	2650	39	radii	radius	NOUN
m-1112	2650	40	,	,	PUNCT
m-1112	2650	41	a̅	a̅	PROPN
m-1112	2650	42	,	,	PUNCT
m-1112	2650	43	and	and	CCONJ
m-1112	2650	44	the	the	DET
m-1112	2650	45	interchangable	interchangable	ADJ
m-1112	2650	46	momentum	momentum	NOUN
m-1112	2650	47	–	–	PUNCT
m-1112	2650	48	ellipsoid	ellipsoid	NOUN
m-1112	2650	49	(	(	PUNCT
m-1112	2650	50	o	o	NOUN
m-1112	2650	51	,	,	PUNCT
m-1112	2650	52	ρ̅	ρ̅	PROPN
m-1112	2650	53	)	)	PUNCT
m-1112	2650	54	of	of	ADP
m-1112	2650	55	radii	radius	NOUN
m-1112	2650	56	,	,	PUNCT
m-1112	2650	57	ρ̅.	ρ̅.	NOUN
m-1112	2650	58	(	(	PUNCT
m-1112	2650	59	o	o	NOUN
m-1112	2650	60	,	,	PUNCT
m-1112	2650	61	ρ̅	ρ̅	PROPN
m-1112	2650	62	)	)	PUNCT
m-1112	2650	63	.	.	PUNCT
m-1112	2651	1	the	the	DET
m-1112	2651	2	same	same	ADJ
m-1112	2651	3	for	for	ADP
m-1112	2651	4	{	{	PUNCT
m-1112	2651	5	b̅	b̅	PROPN
m-1112	2651	6	,	,	PUNCT
m-1112	2651	7	(	(	PUNCT
m-1112	2651	8	o	o	NOUN
m-1112	2651	9	,	,	PUNCT
m-1112	2651	10	b̅	b̅	NOUN
m-1112	2651	11	)	)	PUNCT
m-1112	2651	12	}	}	PUNCT
m-1112	2651	13	in	in	ADP
m-1112	2651	14	(	(	PUNCT
m-1112	2651	15	2	2	X
m-1112	2651	16	)	)	PUNCT
m-1112	2651	17	is	be	AUX
m-1112	2651	18	shown	show	VERB
m-1112	2651	19	the	the	DET
m-1112	2651	20	momentum	momentum	NOUN
m-1112	2651	21	energy	energy	NOUN
m-1112	2651	22	ellipsoid	ellipsoid	NOUN
m-1112	2651	23	(	(	PUNCT
m-1112	2651	24	o	o	NOUN
m-1112	2651	25	,	,	PUNCT
m-1112	2651	26	b̅	b̅	PROPN
m-1112	2651	27	)	)	PUNCT
m-1112	2651	28	of	of	ADP
m-1112	2651	29	radii	radius	NOUN
m-1112	2651	30	,	,	PUNCT
m-1112	2651	31	b̅	b̅	PROPN
m-1112	2651	32	,	,	PUNCT
m-1112	2651	33	and	and	CCONJ
m-1112	2651	34	the	the	DET
m-1112	2651	35	interchangable	interchangable	ADJ
m-1112	2651	36	angular	angular	ADJ
m-1112	2651	37	velocity	velocity	NOUN
m-1112	2651	38	–	–	PUNCT
m-1112	2651	39	ellipsoid	ellipsoid	NOUN
m-1112	2651	40	(	(	PUNCT
m-1112	2651	41	o	o	NOUN
m-1112	2651	42	,	,	PUNCT
m-1112	2651	43	w̅	w̅	PROPN
m-1112	2651	44	)	)	PUNCT
m-1112	2651	45	of	of	ADP
m-1112	2651	46	radii	radius	NOUN
m-1112	2651	47	,	,	PUNCT
m-1112	2651	48	w̅	w̅	PROPN
m-1112	2651	49	.	.	PUNCT
m-1112	2652	1	s	s	PART
m-1112	2653	1	=	=	NOUN
m-1112	2653	2	space	space	NOUN
m-1112	2653	3	in	in	ADP
m-1112	2653	4	(	(	PUNCT
m-1112	2653	5	3	3	X
m-1112	2653	6	)	)	PUNCT
m-1112	2653	7	is	be	AUX
m-1112	2653	8	shown	show	VERB
m-1112	2653	9	in	in	ADP
m-1112	2653	10	mohr	mohr	PROPN
m-1112	2653	11	-	-	PUNCT
m-1112	2653	12	method	method	NOUN
m-1112	2653	13	,	,	PUNCT
m-1112	2653	14	the	the	DET
m-1112	2653	15	geometrical	geometrical	ADJ
m-1112	2653	16	construction	construction	NOUN
m-1112	2653	17	from	from	ADP
m-1112	2653	18	the	the	DET
m-1112	2653	19	two	two	NUM
m-1112	2653	20	interchangable	interchangable	ADJ
m-1112	2653	21	ellipsoids→the	ellipsoids→the	PRON
m-1112	2653	22	energy	energy	NOUN
m-1112	2653	23	-	-	PUNCT
m-1112	2653	24	rotational	rotational	ADJ
m-1112	2653	25	momentum	momentum	NOUN
m-1112	2653	26	–	–	PUNCT
m-1112	2653	27	ellipsoid	ellipsoid	NOUN
m-1112	2653	28	(	(	PUNCT
m-1112	2653	29	o	o	NOUN
m-1112	2653	30	,	,	PUNCT
m-1112	2653	31	ρ̅	ρ̅	PROPN
m-1112	2653	32	)	)	PUNCT
m-1112	2653	33	,	,	PUNCT
m-1112	2653	34	where	where	SCONJ
m-1112	2653	35	{	{	PUNCT
m-1112	2653	36	work	work	NOUN
m-1112	2653	37	}	}	PUNCT
m-1112	2653	38	=	=	PUNCT
m-1112	2653	39	the	the	DET
m-1112	2653	40	angular	angular	ADJ
m-1112	2653	41	-	-	PUNCT
m-1112	2653	42	velocity	velocity	NOUN
m-1112	2653	43	-	-	PUNCT
m-1112	2653	44	vector	vector	NOUN
m-1112	2653	45	-unit	-unit	NOUN
m-1112	2653	46	-	-	PUNCT
m-1112	2653	47	sphere	sphere	NOUN
m-1112	2653	48	,	,	PUNCT
m-1112	2653	49	s	s	VERB
m-1112	2653	50	=	=	NOUN
m-1112	2653	51	the	the	DET
m-1112	2653	52	inertialellipsoid	inertialellipsoid	NOUN
m-1112	2653	53	(	(	PUNCT
m-1112	2653	54	o	o	NOUN
m-1112	2653	55	,	,	PUNCT
m-1112	2653	56	a̅	a̅	PROPN
m-1112	2653	57	)	)	PUNCT
m-1112	2653	58	,	,	PUNCT
m-1112	2653	59	{	{	PUNCT
m-1112	2653	60	force	force	NOUN
m-1112	2653	61	}	}	PUNCT
m-1112	2653	62	=	=	PUNCT
m-1112	2653	63	the	the	DET
m-1112	2653	64	reaction	reaction	NOUN
m-1112	2653	65	to	to	ADP
m-1112	2653	66	the	the	DET
m-1112	2653	67	velocity	velocity	NOUN
m-1112	2653	68	-	-	PUNCT
m-1112	2653	69	change	change	NOUN
m-1112	2653	70	-	-	PUNCT
m-1112	2653	71	motion	motion	NOUN
m-1112	2653	72	,	,	PUNCT
m-1112	2653	73	s	s	PART
m-1112	2653	74	=	=	PUNCT
m-1112	2653	75	the	the	DET
m-1112	2653	76	mass	mass	PROPN
m-1112	2653	77	ellipsoid	ellipsoid	NOUN
m-1112	2653	78	{	{	PUNCT
m-1112	2653	79	mass	mass	NOUN
m-1112	2653	80	}	}	PUNCT
m-1112	2653	81	=	=	SYM
m-1112	2653	82	(	(	PUNCT
m-1112	2653	83	gd	gd	NOUN
m-1112	2653	84	=	=	SYM
m-1112	2653	85	ja	ja	PROPN
m-1112	2653	86	≡	≡	PROPN
m-1112	2653	87	m̅	m̅	PROPN
m-1112	2653	88	)	)	PUNCT
m-1112	2653	89	,	,	PUNCT
m-1112	2653	90	and	and	CCONJ
m-1112	2653	91	between	between	ADP
m-1112	2653	92	the	the	DET
m-1112	2653	93	types	type	NOUN
m-1112	2653	94	of	of	ADP
m-1112	2653	95	ellipsoids	ellipsoid	NOUN
m-1112	2653	96	issues	issue	NOUN
m-1112	2653	97	ρ̅	ρ̅	PRON
m-1112	2653	98	.	.	PUNCT
m-1112	2654	1	a̅	a̅	PROPN
m-1112	2655	1	=	=	PUNCT
m-1112	2655	2	j	j	PROPN
m-1112	2655	3	a	a	X
m-1112	2655	4	..	..	PUNCT
m-1112	2655	5	(	(	PUNCT
m-1112	2655	6	12	12	NUM
m-1112	2655	7	)	)	PUNCT
m-1112	2655	8	the	the	DET
m-1112	2655	9	above	above	ADJ
m-1112	2655	10	property	property	NOUN
m-1112	2655	11	of	of	ADP
m-1112	2655	12	the	the	DET
m-1112	2655	13	two	two	NUM
m-1112	2655	14	interchangable	interchangable	ADJ
m-1112	2655	15	-	-	PUNCT
m-1112	2655	16	ellipsoids	ellipsoid	NOUN
m-1112	2655	17	defines	define	VERB
m-1112	2655	18	the	the	DET
m-1112	2655	19	deep	deep	ADJ
m-1112	2655	20	relation	relation	NOUN
m-1112	2655	21	between	between	ADP
m-1112	2655	22	,	,	PUNCT
m-1112	2655	23	the	the	DET
m-1112	2655	24	angular	angular	ADJ
m-1112	2655	25	-	-	PUNCT
m-1112	2655	26	velocity	velocity	NOUN
m-1112	2655	27	-	-	PUNCT
m-1112	2655	28	ellipsoid	ellipsoid	NOUN
m-1112	2655	29	→	→	SYM
m-1112	2655	30	j1w1²	j1w1²	NOUN
m-1112	2655	31	+	+	X
m-1112	2656	1	j2w2²	j2w2²	X
m-1112	2656	2	+	+	CCONJ
m-1112	2656	3	j3w3²	j3w3²	ADJ
m-1112	2656	4	=	=	VERB
m-1112	2656	5	2l	2l	NOUN
m-1112	2656	6	=	=	SYM
m-1112	2656	7	c	c	X
m-1112	2656	8	=	=	SYM
m-1112	2656	9	ja	ja	PROPN
m-1112	2656	10	w̅	w̅	PROPN
m-1112	2656	11	²	²	NUM
m-1112	2656	12	…	…	PUNCT
m-1112	2656	13	.(13	.(13	NUM
m-1112	2656	14	)	)	PUNCT
m-1112	2656	15	and	and	CCONJ
m-1112	2656	16	the	the	DET
m-1112	2656	17	momentum	momentum	NOUN
m-1112	2656	18	-	-	PUNCT
m-1112	2656	19	energy	energy	NOUN
m-1112	2656	20	-	-	PUNCT
m-1112	2656	21	ellipsoid	ellipsoid	NOUN
m-1112	2656	22	→	→	SYM
m-1112	2656	23	1	1	NUM
m-1112	2656	24	j1	j1	NOUN
m-1112	2656	25	b1²	b1²	NOUN
m-1112	2656	26	+	+	CCONJ
m-1112	2656	27	1	1	NUM
m-1112	2656	28	j2	j2	PROPN
m-1112	2656	29	b2²	b2²	NOUN
m-1112	2656	30	+	+	CCONJ
m-1112	2656	31	1	1	NUM
m-1112	2656	32	j3	j3	PROPN
m-1112	2656	33	b3²	b3²	NOUN
m-1112	2656	34	=	=	SYM
m-1112	2656	35	2l	2l	NUM
m-1112	2656	36	=	=	SYM
m-1112	2656	37	c	c	X
m-1112	2656	38	=	=	SYM
m-1112	2656	39	ja	ja	PROPN
m-1112	2656	40	w̅	w̅	PROPN
m-1112	2656	41	²	²	NUM
m-1112	2656	42	.....	.....	PUNCT
m-1112	2656	43	(	(	PUNCT
m-1112	2656	44	13a	13a	NOUN
m-1112	2656	45	)	)	PUNCT
m-1112	2656	46	conclusions	conclusion	NOUN
m-1112	2656	47	:	:	PUNCT
m-1112	2656	48	1	1	X
m-1112	2656	49	..	..	PUNCT
m-1112	2656	50	from	from	ADP
m-1112	2656	51	the	the	DET
m-1112	2656	52	generated	generate	VERB
m-1112	2656	53	radius	radius	NOUN
m-1112	2656	54	�	�	PROPN
m-1112	2656	55	̅	̅	NOUN
m-1112	2656	56	�	�	NOUN
m-1112	2656	57	=	=	NOUN
m-1112	2656	58	the	the	DET
m-1112	2656	59	inertial	inertial	NOUN
m-1112	2656	60	-	-	PUNCT
m-1112	2656	61	ellipsoid	ellipsoid	NOUN
m-1112	2656	62	of	of	ADP
m-1112	2656	63	a	a	DET
m-1112	2656	64	solid	solid	ADJ
m-1112	2656	65	fig-17	fig-17	NOUN
m-1112	2656	66	-	-	SYM
m-1112	2656	67	1	1	NUM
m-1112	2656	68	corresponds	correspond	VERB
m-1112	2656	69	another	another	DET
m-1112	2656	70	radius	radius	NOUN
m-1112	2656	71	b̅	b̅	NOUN
m-1112	2656	72	,	,	PUNCT
m-1112	2656	73	fig-17	fig-17	NOUN
m-1112	2656	74	-	-	SYM
m-1112	2656	75	2	2	NUM
m-1112	2656	76	momentum	momentum	NOUN
m-1112	2656	77	–	–	PUNCT
m-1112	2656	78	energy	energy	NOUN
m-1112	2656	79	–	–	PUNCT
m-1112	2656	80	ellipsoid	ellipsoid	NOUN
m-1112	2656	81	,	,	PUNCT
m-1112	2656	82	to	to	ADP
m-1112	2656	83	the	the	DET
m-1112	2656	84	common	common	ADJ
m-1112	2656	85	-	-	PUNCT
m-1112	2656	86	point	point	NOUN
m-1112	2656	87	o	o	NOUN
m-1112	2656	88	of	of	ADP
m-1112	2656	89	rotation	rotation	NOUN
m-1112	2656	90	.the	.the	PROPN
m-1112	2657	1	radius	radius	PROPN
m-1112	2657	2	�	�	PROPN
m-1112	2657	3	̅	̅	NOUN
m-1112	2657	4	�	�	NOUN
m-1112	2657	5	is	be	AUX
m-1112	2657	6	perpendicular	perpendicular	ADJ
m-1112	2657	7	to	to	ADP
m-1112	2657	8	the	the	DET
m-1112	2657	9	tangential	tangential	ADJ
m-1112	2657	10	-	-	PUNCT
m-1112	2657	11	plane	plane	NOUN
m-1112	2657	12	at	at	ADP
m-1112	2657	13	the	the	DET
m-1112	2657	14	nib	nib	NOUN
m-1112	2657	15	of	of	ADP
m-1112	2657	16	the	the	DET
m-1112	2657	17	�	�	PROPN
m-1112	2657	18	̅	̅	NOUN
m-1112	2657	19	�	�	NOUN
m-1112	2657	20	angular	angular	ADJ
m-1112	2657	21	velocity	velocity	NOUN
m-1112	2657	22	-	-	PUNCT
m-1112	2657	23	ellipsoid	ellipsoid	NOUN
m-1112	2657	24	.	.	PUNCT
m-1112	2658	1	similarly	similarly	ADV
m-1112	2658	2	the	the	DET
m-1112	2658	3	radius	radius	NOUN
m-1112	2658	4	�	�	PROPN
m-1112	2658	5	̅	̅	NOUN
m-1112	2658	6	�	�	NOUN
m-1112	2658	7	is	be	AUX
m-1112	2658	8	perpendicular	perpendicular	ADJ
m-1112	2658	9	to	to	ADP
m-1112	2658	10	the	the	DET
m-1112	2658	11	tangential	tangential	ADJ
m-1112	2658	12	-	-	PUNCT
m-1112	2658	13	plane	plane	NOUN
m-1112	2658	14	at	at	ADP
m-1112	2658	15	the	the	DET
m-1112	2658	16	nib	nib	NOUN
m-1112	2658	17	of	of	ADP
m-1112	2658	18	the	the	DET
m-1112	2658	19	�	�	PROPN
m-1112	2658	20	̅	̅	NOUN
m-1112	2658	21	�	�	PROPN
m-1112	2658	22	of	of	ADP
m-1112	2658	23	the	the	DET
m-1112	2658	24	angular	angular	ADJ
m-1112	2658	25	-	-	PUNCT
m-1112	2658	26	momentum	momentum	NOUN
m-1112	2658	27	-	-	PUNCT
m-1112	2658	28	ellipsoid	ellipsoid	NOUN
m-1112	2658	29	.	.	PUNCT
m-1112	2659	1	relation	relation	NOUN
m-1112	2659	2	ρ̅	ρ̅	PROPN
m-1112	2659	3	.	.	PUNCT
m-1112	2660	1	a̅	a̅	PROPN
m-1112	2661	1	=	=	PUNCT
m-1112	2661	2	j	j	PROPN
m-1112	2661	3	a=	a=	VERB
m-1112	2661	4	a	a	DET
m-1112	2661	5	constant	constant	ADJ
m-1112	2661	6	,	,	PUNCT
m-1112	2661	7	means	mean	VERB
m-1112	2661	8	ρ̅	ρ̅	PROPN
m-1112	2661	9	⊥	⊥	PROPN
m-1112	2661	10	a̅	a̅	PROPN
m-1112	2661	11	≡	≡	PROPN
m-1112	2661	12	space	space	NOUN
m-1112	2661	13	+	+	CCONJ
m-1112	2661	14	anti	anti	ADJ
m-1112	2661	15	-	-	ADJ
m-1112	2661	16	space	space	ADJ
m-1112	2661	17	≡	≡	PROPN
m-1112	2661	18	motion	motion	PROPN
m-1112	2661	19			PROPN
m-1112	2661	20	�	�	PROPN
m-1112	2661	21	̅	̅	NOUN
m-1112	2661	22	�	�	SYM
m-1112	2661	23	≡	≡	PROPN
m-1112	2662	1	[	[	PUNCT
m-1112	2662	2	i	i	PRON
m-1112	2662	3	≡	≡	PROPN
m-1112	2662	4	√−1	√−1	VERB
m-1112	2662	5	2	2	NUM
m-1112	2662	6	]	]	PUNCT
m-1112	2662	7	*	*	PUNCT
m-1112	2662	8	ρ̅	ρ̅	NUM
m-1112	2662	9	≡	≡	PROPN
m-1112	2662	10	the	the	DET
m-1112	2662	11	argand	argand	NOUN
m-1112	2662	12	-	-	PUNCT
m-1112	2662	13	diagram	diagram	NOUN
m-1112	2662	14	.	.	PUNCT
m-1112	2663	1	from	from	ADP
m-1112	2663	2	relation	relation	NOUN
m-1112	2663	3	(	(	PUNCT
m-1112	2663	4	12	12	NUM
m-1112	2663	5	)	)	PUNCT
m-1112	2663	6	,	,	PUNCT
m-1112	2663	7	the	the	DET
m-1112	2663	8	vertical	vertical	ADJ
m-1112	2663	9	-	-	PUNCT
m-1112	2663	10	projection	projection	NOUN
m-1112	2663	11	of	of	ADP
m-1112	2663	12	the	the	DET
m-1112	2663	13	radius	radius	NOUN
m-1112	2663	14	,	,	PUNCT
m-1112	2663	15	ρ̅	ρ̅	PROPN
m-1112	2663	16	,	,	PUNCT
m-1112	2663	17	at	at	ADP
m-1112	2663	18	the	the	DET
m-1112	2663	19	corresponding	corresponding	ADJ
m-1112	2663	20	conjugate	conjugate	ADJ
m-1112	2663	21	radius	radius	NOUN
m-1112	2663	22	a̅	a̅	PROPN
m-1112	2663	23	,	,	PUNCT
m-1112	2663	24	of	of	ADP
m-1112	2663	25	the	the	DET
m-1112	2663	26	unit	unit	NOUN
m-1112	2663	27	sphere	sphere	ADV
m-1112	2663	28	,	,	PUNCT
m-1112	2663	29	denotes	denote	VERB
m-1112	2663	30	the	the	DET
m-1112	2663	31	meter	meter	NOUN
m-1112	2663	32	to	to	ADP
m-1112	2663	33	the	the	DET
m-1112	2663	34	solid	solid	ADJ
m-1112	2663	35	last	last	ADJ
m-1112	2663	36	angular	angular	ADJ
m-1112	2663	37	momentum	momentum	NOUN
m-1112	2663	38	.	.	PUNCT
m-1112	2664	1	because	because	SCONJ
m-1112	2664	2	the	the	DET
m-1112	2664	3	unit	unit	NOUN
m-1112	2664	4	-	-	PUNCT
m-1112	2664	5	energy	energy	NOUN
m-1112	2664	6	-	-	PUNCT
m-1112	2664	7	vectors	vector	NOUN
m-1112	2664	8	,	,	PUNCT
m-1112	2664	9	�	�	NOUN
m-1112	2664	10	̅	̅	NOUN
m-1112	2664	11	�	�	PROPN
m-1112	2664	12	.	.	PUNCT
m-1112	2664	13	�	�	PROPN
m-1112	2664	14	̅	̅	NOUN
m-1112	2664	15	�	�	PROPN
m-1112	2664	16	,	,	PUNCT
m-1112	2664	17	are	be	AUX
m-1112	2664	18	related	relate	VERB
m-1112	2664	19	as	as	ADP
m-1112	2664	20	�	�	NOUN
m-1112	2664	21	̅	̅	NOUN
m-1112	2664	22	�	�	NOUN
m-1112	2664	23	=	=	SYM
m-1112	2664	24	ab	ab	PROPN
m-1112	2664	25	=	=	PROPN
m-1112	2664	26	σ	σ	PROPN
m-1112	2664	27	/	/	SYM
m-1112	2664	28	b̅	b̅	PROPN
m-1112	2664	29	=	=	SYM
m-1112	2664	30	σ	σ	PROPN
m-1112	2664	31	/	/	SYM
m-1112	2664	32	j.w²	j.w²	NOUN
m-1112	2664	33	,	,	PUNCT
m-1112	2664	34	i.e.	i.e.	X
m-1112	2664	35	the	the	DET
m-1112	2664	36	common	common	ADJ
m-1112	2664	37	velocity	velocity	NOUN
m-1112	2664	38	vector	vector	NOUN
m-1112	2664	39	c	c	NOUN
m-1112	2664	40	=	=	SYM
m-1112	2664	41	w	w	NOUN
m-1112	2664	42	r	r	NOUN
m-1112	2664	43	=	=	SYM
m-1112	2664	44	2.b	2.b	NUM
m-1112	2664	45	/	/	SYM
m-1112	2664	46	π	π	PROPN
m-1112	2664	47	r	r	NOUN
m-1112	2664	48	³	³	PROPN
m-1112	2664	49	,	,	PUNCT
m-1112	2664	50	therefore	therefore	ADV
m-1112	2664	51	issues	issue	NOUN
m-1112	2664	52	and	and	CCONJ
m-1112	2664	53	for	for	ADP
m-1112	2664	54	all	all	DET
m-1112	2664	55	the	the	DET
m-1112	2664	56	5	5	NUM
m-1112	2664	57	-	-	PUNCT
m-1112	2664	58	spaces	space	NOUN
m-1112	2664	59	.	.	PUNCT
m-1112	2665	1	2	2	X
m-1112	2665	2	..	..	PUNCT
m-1112	2665	3	inversely	inversely	ADV
m-1112	2665	4	the	the	DET
m-1112	2665	5	unit	unit	NOUN
m-1112	2665	6	-	-	PUNCT
m-1112	2665	7	energy	energy	NOUN
m-1112	2665	8	-	-	PUNCT
m-1112	2665	9	vectors	vector	NOUN
m-1112	2665	10	,	,	PUNCT
m-1112	2665	11	�	�	NOUN
m-1112	2665	12	̅	̅	NOUN
m-1112	2665	13	�	�	PROPN
m-1112	2665	14	.	.	PUNCT
m-1112	2665	15	�	�	PROPN
m-1112	2665	16	̅	̅	NOUN
m-1112	2665	17	�	�	PROPN
m-1112	2665	18	,	,	PUNCT
m-1112	2665	19	decompose	decompose	VERB
m-1112	2665	20	when	when	SCONJ
m-1112	2665	21	bcrit	bcrit	NOUN
m-1112	2665	22	=	=	PROPN
m-1112	2665	23	j	j	PROPN
m-1112	2665	24	w	w	PROPN
m-1112	2665	25	=	=	PUNCT
m-1112	2665	26	𝜋r3	𝜋r3	NOUN
m-1112	2665	27	2	2	NUM
m-1112	2666	1	[	[	X
m-1112	2666	2	c	c	X
m-1112	2666	3	/	/	SYM
m-1112	2666	4	r	r	NOUN
m-1112	2666	5	]	]	PUNCT
m-1112	2666	6	=	=	PUNCT
m-1112	2667	1	[	[	PUNCT
m-1112	2667	2	𝜋r2	𝜋r2	ADJ
m-1112	2667	3	2	2	NUM
m-1112	2667	4	]	]	SYM
m-1112	2667	5	c	c	NOUN
m-1112	2667	6	or	or	CCONJ
m-1112	2667	7	when	when	SCONJ
m-1112	2667	8	�	�	NOUN
m-1112	2667	9	̅	̅	NOUN
m-1112	2667	10	�	�	NOUN
m-1112	2667	11	becomes	become	VERB
m-1112	2667	12	maximum	maximum	ADJ
m-1112	2667	13	,	,	PUNCT
m-1112	2667	14	i.e.	i.e.	X
m-1112	2667	15	for	for	ADP
m-1112	2667	16	gravity	gravity	NOUN
m-1112	2667	17	and	and	CCONJ
m-1112	2667	18	antigravity	antigravity	NOUN
m-1112	2667	19	happens	happen	VERB
m-1112	2667	20	when	when	SCONJ
m-1112	2667	21	|θr̅|	|θr̅|	NUM
m-1112	2667	22	axis	axis	NOUN
m-1112	2667	23	is	be	AUX
m-1112	2667	24	perpendicular	perpendicular	ADJ
m-1112	2667	25	(	(	PUNCT
m-1112	2667	26	⊥	⊥	NOUN
m-1112	2667	27	)	)	PUNCT
m-1112	2667	28	to	to	ADP
m-1112	2667	29	b̅	b̅	PROPN
m-1112	2667	30	and	and	CCONJ
m-1112	2667	31	the	the	DET
m-1112	2667	32	cone	cone	NOUN
m-1112	2667	33	-	-	PUNCT
m-1112	2667	34	angle	angle	NOUN
m-1112	2667	35	θ	θ	PROPN
m-1112	2667	36			NOUN
m-1112	2667	37	90	90	NUM
m-1112	2667	38	,	,	PUNCT
m-1112	2667	39	and	and	CCONJ
m-1112	2667	40	energy	energy	NOUN
m-1112	2668	1	e	e	NOUN
m-1112	2668	2	=	=	NOUN
m-1112	2668	3	w=	w=	NOUN
m-1112	2668	4	2l=	2l=	NUM
m-1112	2668	5	b̅	b̅	X
m-1112	2668	6	.w̅	.w̅	PUNCT
m-1112	2668	7	=	=	PUNCT
m-1112	2668	8	j.w²	j.w²	PROPN
m-1112	2668	9	.	.	PUNCT
m-1112	2668	10	from	from	ADP
m-1112	2668	11	the	the	DET
m-1112	2668	12	�	�	PROPN
m-1112	2668	13	̅	̅	NOUN
m-1112	2668	14	�	�	PROPN
m-1112	2668	15	physical	physical	ADJ
m-1112	2668	16	-magnet	-magnet	PROPN
m-1112	2668	17	,	,	PUNCT
m-1112	2668	18	�	�	PROPN
m-1112	2668	19	̅	̅	NOUN
m-1112	2668	20	�	�	NOUN
m-1112	2668	21	is	be	AUX
m-1112	2668	22	quantized	quantize	VERB
m-1112	2668	23	to	to	ADP
m-1112	2668	24	the	the	DET
m-1112	2668	25	2	2	NUM
m-1112	2668	26	-	-	PUNCT
m-1112	2668	27	constitutes	constitute	VERB
m-1112	2668	28	⊕	⊕	PROPN
m-1112	2668	29	⇉	⇉	PROPN
m-1112	2669	1	⊝	⊝	PUNCT
m-1112	2669	2	as	as	ADP
m-1112	2669	3	the	the	DET
m-1112	2669	4	prior	prior	ADJ
m-1112	2669	5	.	.	PUNCT
m-1112	2670	1	ijo	ijo	PROPN
m-1112	2670	2	international	international	PROPN
m-1112	2670	3	journal	journal	PROPN
m-1112	2670	4	of	of	ADP
m-1112	2670	5	mathematics	mathematics	PROPN
m-1112	2670	6	(	(	PUNCT
m-1112	2670	7	issn	issn	PROPN
m-1112	2670	8	:	:	PUNCT
m-1112	2670	9	2992	2992	NUM
m-1112	2670	10	-	-	SYM
m-1112	2670	11	4421	4421	NUM
m-1112	2670	12	)	)	PUNCT
m-1112	2670	13	volume	volume	NOUN
m-1112	2670	14	08	08	NUM
m-1112	2671	1	|	|	ADV
m-1112	2671	2	issue	issue	NOUN
m-1112	2671	3	08	08	NUM
m-1112	2672	1	|	|	ADV
m-1112	2672	2	august	august	PROPN
m-1112	2672	3	2025	2025	NUM
m-1112	2672	4	|	|	ADV
m-1112	2672	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2672	6	ijo	ijo	PROPN
m-1112	2672	7	journals	journal	NOUN
m-1112	2672	8	93	93	NUM
m-1112	2672	9	the	the	DET
m-1112	2672	10	fundamental	fundamental	ADJ
m-1112	2672	11	particles	particle	NOUN
m-1112	2672	12	origination	origination	NOUN
m-1112	2672	13	mechanism	mechanism	NOUN
m-1112	2672	14	in	in	ADP
m-1112	2672	15	mfmf	mfmf	PROPN
m-1112	2672	16	pns	pns	PROPN
m-1112	2672	17	caves	cave	NOUN
m-1112	2672	18	.	.	PUNCT
m-1112	2673	1	6c6	6c6	X
m-1112	2673	2	..	..	PUNCT
m-1112	2673	3	the	the	DET
m-1112	2673	4	de	de	NOUN
m-1112	2673	5	-	-	NOUN
m-1112	2673	6	quantization	quantization	NOUN
m-1112	2673	7	of	of	ADP
m-1112	2673	8	energy	energy	NOUN
m-1112	2673	9	from	from	ADP
m-1112	2673	10	,	,	PUNCT
m-1112	2673	11	pns	pns	PROPN
m-1112	2673	12			PROPN
m-1112	2673	13	mfmf	mfmf	NOUN
m-1112	2673	14	,	,	PUNCT
m-1112	2673	15	≡	≡	PROPN
m-1112	2673	16	empty	empty	ADJ
m-1112	2673	17	space	space	NOUN
m-1112	2673	18	.	.	PUNCT
m-1112	2674	1	figure.17d	figure.17d	PROPN
m-1112	2674	2	..	..	PUNCT
m-1112	2674	3	the	the	DET
m-1112	2674	4	angular	angular	ADJ
m-1112	2674	5	-	-	PUNCT
m-1112	2674	6	velocity	velocity	NOUN
m-1112	2674	7	|	|	NOUN
m-1112	2674	8	�	�	NOUN
m-1112	2674	9	̅	̅	NOUN
m-1112	2674	10	�	�	NOUN
m-1112	2674	11	|	|	NOUN
m-1112	2674	12	=	=	SYM
m-1112	2674	13	𝐉𝟑.	𝐉𝟑.	NOUN
m-1112	2674	14	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2674	15	𝟐	𝟐	NUM
m-1112	2674	16	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2674	17	±√−	±√−	NOUN
m-1112	2674	18	𝐬𝐐	𝐬𝐐	X
m-1112	2674	19	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2674	20	+	+	CCONJ
m-1112	2674	21	(	(	PUNCT
m-1112	2674	22	𝐉𝟑.	𝐉𝟑.	PROPN
m-1112	2674	23	𝐰𝟑	𝐰𝟑	PROPN
m-1112	2674	24	𝟐	𝟐	PROPN
m-1112	2674	25	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	NOUN
m-1112	2674	26	)	)	PUNCT
m-1112	2674	27	²	²	NUM
m-1112	2674	28	𝟐	𝟐	NUM
m-1112	2674	29	=	=	SYM
m-1112	2674	30	s	s	PART
m-1112	2674	31	±	±	NUM
m-1112	2674	32	{	{	PUNCT
m-1112	2674	33	√	√	NUM
m-1112	2674	34	�	�	SYM
m-1112	2674	35	̅	̅	NOUN
m-1112	2674	36	�	�	PROPN
m-1112	2674	37	}	}	PUNCT
m-1112	2674	38	.i	.i	PROPN
m-1112	2674	39			PROPN
m-1112	2675	1	|𝑤3	|𝑤3	NOUN
m-1112	2675	2	|=	|=	PUNCT
m-1112	2676	1	[	[	X
m-1112	2676	2	s]+[√	s]+[√	X
m-1112	2676	3	�	�	NOUN
m-1112	2676	4	̅	̅	NOUN
m-1112	2676	5	�	�	PROPN
m-1112	2676	6	]	]	SYM
m-1112	2676	7	.i	.i	NOUN
m-1112	2676	8	,	,	PUNCT
m-1112	2676	9	s	s	NOUN
m-1112	2676	10	=	=	PUNCT
m-1112	2676	11	[	[	PUNCT
m-1112	2676	12	j3	j3	PROPN
m-1112	2676	13	.	.	PROPN
m-1112	2677	1	w3	w3	PROPN
m-1112	2677	2	2	2	NUM
m-1112	2677	3	j1.cos	j1.co	NOUN
m-1112	2677	4	ϑ	ϑ	X
m-1112	2677	5	]	]	PUNCT
m-1112	2677	6	,	,	PUNCT
m-1112	2677	7	�	�	PROPN
m-1112	2677	8	̅	̅	NOUN
m-1112	2677	9	�	�	NOUN
m-1112	2678	1	=	=	SYM
m-1112	2679	1	[	[	PUNCT
m-1112	2679	2	k	k	X
m-1112	2679	3	pns	pns	PROPN
m-1112	2679	4	2	2	PROPN
m-1112	2679	5	j1.cosϑ	j1.cosϑ	ADV
m-1112	2679	6	]	]	PUNCT
m-1112	2679	7	,	,	PUNCT
m-1112	2679	8	𝐤	𝐤	X
m-1112	2679	9	𝐏𝐍𝐒	𝐏𝐍𝐒	PROPN
m-1112	2679	10	=	=	SYM
m-1112	2679	11	√	√	PROPN
m-1112	2679	12	[	[	PUNCT
m-1112	2679	13	j3	j3	PROPN
m-1112	2679	14	.	.	PUNCT
m-1112	2680	1	w3]²	w3]²	ADP
m-1112	2680	2	−	−	NOUN
m-1112	2680	3	4	4	X
m-1112	2680	4	.	.	X
m-1112	2680	5	sq	sq	PROPN
m-1112	2680	6	.	.	PROPN
m-1112	2680	7	j1	j1	PROPN
m-1112	2680	8	cos	cos	PROPN
m-1112	2680	9	ϑ	ϑ	PROPN
m-1112	2680	10	2	2	NUM
m-1112	2680	11	from	from	ADP
m-1112	2680	12	10.c	10.c	NUM
m-1112	2680	13	,	,	PUNCT
m-1112	2680	14	the	the	DET
m-1112	2680	15	unit	unit	NOUN
m-1112	2680	16	-	-	PUNCT
m-1112	2680	17	energy	energy	NOUN
m-1112	2680	18	-	-	PUNCT
m-1112	2680	19	vectors	vector	NOUN
m-1112	2680	20	,	,	PUNCT
m-1112	2680	21	�	�	NOUN
m-1112	2680	22	̅	̅	NOUN
m-1112	2680	23	�	�	PROPN
m-1112	2680	24	.	.	PUNCT
m-1112	2680	25	�	�	PROPN
m-1112	2680	26	̅	̅	NOUN
m-1112	2680	27	�	�	PROPN
m-1112	2680	28	,	,	PUNCT
m-1112	2680	29	fp	fp	PROPN
m-1112	2680	30	=	=	SYM
m-1112	2680	31	1,836.1045hz	1,836.1045hz	PROPN
m-1112	2680	32	in	in	ADP
m-1112	2680	33	pns	pns	PROPN
m-1112	2680	34	–	–	PUNCT
m-1112	2680	35	space	space	NOUN
m-1112	2680	36	become	become	VERB
m-1112	2680	37	1	1	NUM
m-1112	2680	38	)	)	PUNCT
m-1112	2680	39	..	..	PUNCT
m-1112	2680	40	from	from	ADP
m-1112	2680	41	relation	relation	NOUN
m-1112	2680	42	w̅	w̅	PUNCT
m-1112	2681	1	=	=	SYM
m-1112	2681	2	2π.f	2π.f	NUM
m-1112	2681	3	pns	pns	NOUN
m-1112	2681	4	,	,	PUNCT
m-1112	2681	5	then	then	ADV
m-1112	2681	6	𝐰	𝐰	PROPN
m-1112	2681	7	pns	pns	X
m-1112	2681	8	=	=	SYM
m-1112	2681	9	56,13308	56,13308	NUM
m-1112	2681	10	.1044hz	.1044hz	PUNCT
m-1112	2682	1	=	=	PUNCT
m-1112	2682	2	5,613308	5,613308	NUM
m-1112	2682	3	.1045hz	.1045hz	PROPN
m-1112	2682	4	,	,	PUNCT
m-1112	2682	5	2	2	NUM
m-1112	2682	6	)	)	PUNCT
m-1112	2682	7	..	..	PUNCT
m-1112	2682	8	from	from	ADP
m-1112	2682	9	centripetal	centripetal	ADJ
m-1112	2682	10	force	force	NOUN
m-1112	2682	11	in	in	ADP
m-1112	2682	12	mfmf	mfmf	NOUN
m-1112	2682	13	space	space	NOUN
m-1112	2682	14	fc	fc	PROPN
m-1112	2682	15	=	=	PUNCT
m-1112	2682	16	σ	σ	PROPN
m-1112	2682	17	=	=	PUNCT
m-1112	2682	18	m.v³	m.v³	NOUN
m-1112	2682	19	r	r	NOUN
m-1112	2682	20	=	=	PROPN
m-1112	2682	21	j	j	PROPN
m-1112	2682	22	w²	w²	PROPN
m-1112	2682	23	r	r	NOUN
m-1112	2682	24	=	=	NOUN
m-1112	2682	25	b̅	b̅	NOUN
m-1112	2682	26	w	w	NOUN
m-1112	2682	27	r	r	NOUN
m-1112	2682	28	,	,	PUNCT
m-1112	2682	29	then	then	ADV
m-1112	2682	30	b̅	b̅	PROPN
m-1112	2682	31	=	=	NUM
m-1112	2682	32	j	j	PROPN
m-1112	2682	33	w	w	NOUN
m-1112	2682	34	,	,	PUNCT
m-1112	2682	35	or	or	CCONJ
m-1112	2682	36	b̅	b̅	PROPN
m-1112	2682	37	=	=	SYM
m-1112	2682	38	j	j	PROPN
m-1112	2682	39	w	w	NOUN
m-1112	2683	1	=	=	PRON
m-1112	2683	2	[	[	PUNCT
m-1112	2683	3	π.r4	π.r4	NOUN
m-1112	2683	4	2	2	NUM
m-1112	2683	5	]	]	PUNCT
m-1112	2683	6	.w	.w	PUNCT
m-1112	2684	1	=	=	X
m-1112	2684	2	π[1,6162.10−35]4	π[1,6162.10−35]4	X
m-1112	2684	3	(	(	PUNCT
m-1112	2684	4	5,613308	5,613308	NUM
m-1112	2684	5	.1045	.1045	NOUN
m-1112	2684	6	)	)	PUNCT
m-1112	2684	7	2	2	NUM
m-1112	2684	8	=	=	SYM
m-1112	2684	9	3	3	NUM
m-1112	2684	10	,	,	PUNCT
m-1112	2684	11	3770539.10−96	3770539.10−96	NUM
m-1112	2684	12	j	j	NOUN
m-1112	2684	13	and	and	CCONJ
m-1112	2684	14	for	for	ADP
m-1112	2684	15	ev	ev	INTJ
m-1112	2684	16	,	,	PUNCT
m-1112	2684	17	b̅	b̅	PROPN
m-1112	2684	18	=	=	SYM
m-1112	2684	19	3	3	NUM
m-1112	2684	20	,	,	PUNCT
m-1112	2684	21	3770539.10−96	3770539.10−96	PROPN
m-1112	2684	22	j	j	PROPN
m-1112	2684	23	/	/	SYM
m-1112	2684	24	1,6022	1,6022	PROPN
m-1112	2684	25	.10−19	.10−19	PUNCT
m-1112	2684	26	c	c	X
m-1112	2684	27	=	=	SYM
m-1112	2684	28	3,754935.10−76	3,754935.10−76	NUM
m-1112	2684	29	ev	ev	NOUN
m-1112	2684	30	.	.	PROPN
m-1112	2684	31	3	3	NUM
m-1112	2684	32	)	)	PUNCT
m-1112	2684	33	..	..	PUNCT
m-1112	2684	34	from	from	ADP
m-1112	2684	35	sol	sol	PROPN
m-1112	2684	36	-3	-3	PUNCT
m-1112	2684	37	the	the	DET
m-1112	2684	38	magnitude	magnitude	NOUN
m-1112	2684	39	d	d	NOUN
m-1112	2684	40	becomes	become	VERB
m-1112	2684	41	maximum	maximum	ADJ
m-1112	2684	42	when	when	SCONJ
m-1112	2684	43	𝐬𝐐	𝐬𝐐	PROPN
m-1112	2684	44	𝐉𝟏.𝐜𝐨𝐬𝛝	𝐉𝟏.𝐜𝐨𝐬𝛝	PROPN
m-1112	2684	45	≡	≡	PROPN
m-1112	2684	46	maximum	maximum	NOUN
m-1112	2684	47	or	or	CCONJ
m-1112	2684	48	,	,	PUNCT
m-1112	2684	49	when	when	SCONJ
m-1112	2684	50	|θr̅|	|θr̅|	NUM
m-1112	2684	51	axis	axis	VERB
m-1112	2684	52	⊥	⊥	ADJ
m-1112	2684	53	b̅	b̅	PROPN
m-1112	2684	54	and	and	CCONJ
m-1112	2684	55	cone	cone	NOUN
m-1112	2684	56	-	-	PUNCT
m-1112	2684	57	angle	angle	NOUN
m-1112	2684	58	𝛉	𝛉	PROPN
m-1112	2684	59			NOUN
m-1112	2684	60	90	90	NUM
m-1112	2684	61	.	.	PUNCT
m-1112	2685	1	from	from	ADP
m-1112	2685	2	energy	energy	NOUN
m-1112	2685	3	relation	relation	NOUN
m-1112	2685	4	e	e	NOUN
m-1112	2685	5	=	=	SYM
m-1112	2685	6	w	w	PROPN
m-1112	2685	7	=	=	PUNCT
m-1112	2685	8	2l	2l	NUM
m-1112	2685	9	=	=	SYM
m-1112	2685	10	b̅	b̅	X
m-1112	2685	11	.w̅	.w̅	PUNCT
m-1112	2685	12	=	=	SYM
m-1112	2685	13	j.w²	j.w²	X
m-1112	2685	14	angular	angular	ADJ
m-1112	2685	15	-	-	PUNCT
m-1112	2685	16	momentum	momentum	NOUN
m-1112	2685	17	�	�	NOUN
m-1112	2685	18	̅	̅	NOUN
m-1112	2685	19	�	�	NOUN
m-1112	2685	20	=	=	PUNCT
m-1112	2686	1	[	[	X
m-1112	2686	2	3	3	NUM
m-1112	2686	3	,	,	PUNCT
m-1112	2686	4	3770539.10−96j].[5,613308.1045hz	3770539.10−96j].[5,613308.1045hz	NUM
m-1112	2686	5	]	]	PUNCT
m-1112	2686	6	=	=	SYM
m-1112	2686	7	1,895644.𝟏𝟎−𝟓𝟎	1,895644.𝟏𝟎−𝟓𝟎	NUM
m-1112	2686	8	j	j	PROPN
m-1112	2686	9	/	/	SYM
m-1112	2686	10	s	s	PROPN
m-1112	2686	11	,	,	PUNCT
m-1112	2686	12	i.e.	i.e.	X
m-1112	2686	13	the	the	DET
m-1112	2686	14	planck`s	planck`s	NOUN
m-1112	2686	15	cave	cave	NOUN
m-1112	2686	16	,	,	PUNCT
m-1112	2686	17	10−35	10−35	PROPN
m-1112	2686	18	m	m	NOUN
m-1112	2686	19	,	,	PUNCT
m-1112	2686	20	is	be	AUX
m-1112	2686	21	the	the	DET
m-1112	2686	22	safety	safety	NOUN
m-1112	2686	23	-	-	PUNCT
m-1112	2686	24	valve	valve	NOUN
m-1112	2686	25	≡	≡	NOUN
m-1112	2686	26	the	the	DET
m-1112	2686	27	critical	critical	ADJ
m-1112	2686	28	state	state	NOUN
m-1112	2686	29	for	for	ADP
m-1112	2686	30	the	the	DET
m-1112	2686	31	stress	stress	NOUN
m-1112	2686	32	ellipsoids	ellipsoid	NOUN
m-1112	2686	33	,	,	PUNCT
m-1112	2686	34	b̅	b̅	PROPN
m-1112	2686	35	w̅	w̅	PROPN
m-1112	2686	36	,	,	PUNCT
m-1112	2686	37	vectors	vector	NOUN
m-1112	2686	38	in	in	ADP
m-1112	2686	39	order	order	NOUN
m-1112	2686	40	that	that	SCONJ
m-1112	2686	41	this	this	DET
m-1112	2686	42	total	total	ADJ
m-1112	2686	43	-	-	PUNCT
m-1112	2686	44	energy	energy	NOUN
m-1112	2686	45	to	to	PART
m-1112	2686	46	superflow	superflow	VERB
m-1112	2686	47	and	and	CCONJ
m-1112	2686	48	be	be	AUX
m-1112	2686	49	still	still	ADV
m-1112	2686	50	into	into	ADP
m-1112	2686	51	vacuum	vacuum	PROPN
m-1112	2686	52	≡	≡	PROPN
m-1112	2687	1	[	[	X
m-1112	2687	2	10−62	10−62	NUM
m-1112	2687	3	-	-	PUNCT
m-1112	2687	4	10−35	10−35	NOUN
m-1112	2687	5	m	m	NOUN
m-1112	2687	6	]	]	X
m-1112	2687	7	.	.	PUNCT
m-1112	2688	1	this	this	DET
m-1112	2688	2	vacuum	vacuum	NOUN
m-1112	2688	3	between	between	ADP
m-1112	2688	4	the	the	DET
m-1112	2688	5	|gravity	|gravity	NOUN
m-1112	2688	6	cave	cave	NOUN
m-1112	2688	7	planck`s	planck`s	VERB
m-1112	2688	8	cave|	cave|	PROPN
m-1112	2688	9	ijo	ijo	PROPN
m-1112	2688	10	international	international	PROPN
m-1112	2688	11	journal	journal	PROPN
m-1112	2688	12	of	of	ADP
m-1112	2688	13	mathematics	mathematics	PROPN
m-1112	2688	14	(	(	PUNCT
m-1112	2688	15	issn	issn	PROPN
m-1112	2688	16	:	:	PUNCT
m-1112	2688	17	2992	2992	NUM
m-1112	2688	18	-	-	SYM
m-1112	2688	19	4421	4421	NUM
m-1112	2688	20	)	)	PUNCT
m-1112	2688	21	volume	volume	NOUN
m-1112	2688	22	08	08	NUM
m-1112	2689	1	|	|	ADV
m-1112	2689	2	issue	issue	NOUN
m-1112	2689	3	08	08	NUM
m-1112	2690	1	|	|	ADV
m-1112	2690	2	august	august	PROPN
m-1112	2690	3	2025	2025	NUM
m-1112	2690	4	|	|	ADV
m-1112	2690	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2690	6	ijo	ijo	PROPN
m-1112	2690	7	journals	journal	NOUN
m-1112	2690	8	94	94	NUM
m-1112	2690	9	the	the	DET
m-1112	2690	10	fundamental	fundamental	ADJ
m-1112	2690	11	particles	particle	NOUN
m-1112	2690	12	origination	origination	NOUN
m-1112	2690	13	mechanism	mechanism	NOUN
m-1112	2690	14	in	in	ADP
m-1112	2690	15	mfmf	mfmf	PROPN
m-1112	2690	16	pns	pns	PROPN
m-1112	2690	17	caves	cave	NOUN
m-1112	2690	18	.	.	PUNCT
m-1112	2691	1	consists	consist	VERB
m-1112	2691	2	the	the	DET
m-1112	2691	3	black	black	ADJ
m-1112	2691	4	holes	hole	NOUN
m-1112	2691	5	chaos	chaos	NOUN
m-1112	2691	6	,	,	PUNCT
m-1112	2691	7	as	as	ADP
m-1112	2691	8	the	the	DET
m-1112	2691	9	recycling	recycling	NOUN
m-1112	2691	10	–	–	PUNCT
m-1112	2691	11	energy	energy	NOUN
m-1112	2691	12	,	,	PUNCT
m-1112	2691	13	into	into	ADP
m-1112	2691	14	which	which	PRON
m-1112	2691	15	→	→	PUNCT
m-1112	2691	16	the	the	DET
m-1112	2691	17	{	{	PUNCT
m-1112	2691	18	energy	energy	NOUN
m-1112	2691	19	–	–	PUNCT
m-1112	2691	20	space	space	NOUN
m-1112	2692	1	monad	monad	PROPN
m-1112	2692	2	|	|	NOUN
m-1112	2692	3	�	�	PROPN
m-1112	2692	4	̅	̅	NOUN
m-1112	2692	5	�	�	PROPN
m-1112	2692	6	|	|	ADV
m-1112	2692	7	≡	≡	PROPN
m-1112	2692	8	|ab|	|ab|	PROPN
m-1112	2692	9	}	}	PUNCT
m-1112	2692	10	,	,	PUNCT
m-1112	2692	11	vanishes	vanish	VERB
m-1112	2692	12	≡	≡	PROPN
m-1112	2692	13	decomposes	decompose	VERB
m-1112	2692	14	←	←	PROPN
m-1112	2692	15	→	→	PUNCT
m-1112	2692	16	in	in	ADP
m-1112	2692	17	physics	physics	NOUN
m-1112	2692	18	exist	exist	VERB
m-1112	2692	19	,	,	PUNCT
m-1112	2692	20	two	two	NUM
m-1112	2692	21	different	different	ADJ
m-1112	2692	22	potential	potential	ADJ
m-1112	2692	23	-	-	PUNCT
m-1112	2692	24	energies	energy	NOUN
m-1112	2692	25	between	between	ADP
m-1112	2692	26	planck	planck	NOUN
m-1112	2692	27	spaces	space	NOUN
m-1112	2692	28	and	and	CCONJ
m-1112	2692	29	gravity	gravity	NOUN
m-1112	2692	30	spaces	space	NOUN
m-1112	2692	31	as	as	ADP
m-1112	2692	32	uplanc	uplanc	NOUN
m-1112	2692	33	and	and	CCONJ
m-1112	2692	34	ugravity	ugravity	NOUN
m-1112	2692	35	.the	.the	DET
m-1112	2692	36	difference	difference	NOUN
m-1112	2693	1	∆u	∆u	ADV
m-1112	2693	2	=	=	PUNCT
m-1112	2693	3	ugraupla	ugraupla	NOUN
m-1112	2693	4	is	be	AUX
m-1112	2693	5	the	the	DET
m-1112	2693	6	flow	flow	NOUN
m-1112	2693	7	-	-	PUNCT
m-1112	2693	8	energy	energy	NOUN
m-1112	2693	9	between	between	ADP
m-1112	2693	10	the	the	DET
m-1112	2693	11	two	two	NUM
m-1112	2693	12	energy	energy	NOUN
m-1112	2693	13	levels	level	NOUN
m-1112	2693	14	l	l	NOUN
m-1112	2693	15	pla	pla	NOUN
m-1112	2693	16	=	=	PUNCT
m-1112	2694	1	6,6262.10−34	6,6262.10−34	NUM
m-1112	2694	2	m	m	NOUN
m-1112	2694	3	,	,	PUNCT
m-1112	2694	4	and	and	CCONJ
m-1112	2694	5	l	l	X
m-1112	2695	1	gra=	gra=	NOUN
m-1112	2695	2	1,777.10−62	1,777.10−62	NUM
m-1112	2695	3	m	m	NOUN
m-1112	2695	4	,	,	PUNCT
m-1112	2695	5	the	the	DET
m-1112	2695	6	total	total	ADJ
m-1112	2695	7	energy	energy	NOUN
m-1112	2695	8	in	in	ADP
m-1112	2695	9	planck`s	planck`s	NOUN
m-1112	2695	10	cave	cave	NOUN
m-1112	2695	11	is	be	AUX
m-1112	2695	12	→	→	SYM
m-1112	2695	13	e	e	X
m-1112	2695	14	pla	pla	NOUN
m-1112	2695	15	=	=	SYM
m-1112	2695	16	1,216447	1,216447	NUM
m-1112	2695	17	.	.	PUNCT
m-1112	2696	1	1017	1017	NUM
m-1112	2696	2	j	j	NOUN
m-1112	2696	3	,	,	PUNCT
m-1112	2696	4	and	and	CCONJ
m-1112	2696	5	the	the	DET
m-1112	2696	6	minimum	minimum	ADJ
m-1112	2696	7	charge	charge	NOUN
m-1112	2696	8	in	in	ADP
m-1112	2696	9	planck`s	planck`s	NOUN
m-1112	2696	10	cave	cave	NOUN
m-1112	2696	11	→	→	SYM
m-1112	2696	12	q	q	NOUN
m-1112	2696	13	pla	pla	NOUN
m-1112	2696	14	=	=	PUNCT
m-1112	2696	15	1cb	1cb	NOUN
m-1112	2696	16	=	=	SYM
m-1112	2696	17	1,6	1,6	NUM
m-1112	2696	18	.10−19	.10−19	PUNCT
m-1112	2696	19	ev	ev	X
m-1112	2696	20	,	,	PUNCT
m-1112	2696	21	from	from	ADP
m-1112	2696	22	voltage	voltage	NOUN
m-1112	2696	23	relation	relation	NOUN
m-1112	2696	24	∆u	∆u	PROPN
m-1112	2696	25	=	=	SYM
m-1112	2696	26	energy	energy	NOUN
m-1112	2696	27	charge	charge	NOUN
m-1112	2696	28	issues	issue	NOUN
m-1112	2696	29	,	,	PUNCT
m-1112	2696	30	1volt	1volt	NUM
m-1112	2696	31	=	=	SYM
m-1112	2696	32	1−joule	1−joule	NUM
m-1112	2696	33	1−culomb	1−culomb	NUM
m-1112	2696	34	or	or	CCONJ
m-1112	2696	35	1v	1v	NUM
m-1112	2696	36	=	=	SYM
m-1112	2696	37	𝟏𝐉	𝟏𝐉	NOUN
m-1112	2696	38	𝟏𝐂	𝟏𝐂	NOUN
m-1112	2696	39	…	…	PUNCT
m-1112	2696	40	.(v	.(v	NUM
m-1112	2696	41	)	)	PUNCT
m-1112	2696	42	in	in	ADP
m-1112	2696	43	order	order	NOUN
m-1112	2696	44	that	that	SCONJ
m-1112	2696	45	1cb	1cb	NOUN
m-1112	2696	46	may	may	AUX
m-1112	2696	47	overflow	overflow	VERB
m-1112	2696	48	and	and	CCONJ
m-1112	2696	49	flow	flow	VERB
m-1112	2696	50	from	from	ADP
m-1112	2696	51	planck`s	planck`s	NOUN
m-1112	2696	52	cave	cave	NOUN
m-1112	2696	53	to	to	ADP
m-1112	2696	54	the	the	DET
m-1112	2696	55	gravity	gravity	NOUN
m-1112	2696	56	cave	cave	NOUN
m-1112	2696	57	,	,	PUNCT
m-1112	2696	58	then	then	ADV
m-1112	2696	59	must	must	AUX
m-1112	2696	60	exist	exist	VERB
m-1112	2696	61	a	a	DET
m-1112	2696	62	voltage	voltage	NOUN
m-1112	2696	63	∆u	∆u	ADV
m-1112	2696	64	>	>	X
m-1112	2696	65	=	=	PUNCT
m-1112	2696	66	7,592354	7,592354	NOUN
m-1112	2696	67	.10	.10	NUM
m-1112	2696	68	35	35	NUM
m-1112	2696	69	ev	ev	NOUN
m-1112	2696	70	,	,	PUNCT
m-1112	2696	71	and	and	CCONJ
m-1112	2696	72	be	be	AUX
m-1112	2696	73	as	as	ADP
m-1112	2696	74	..	..	PUNCT
m-1112	2696	75	…	…	PUNCT
m-1112	2696	76	.(v	.(v	NUM
m-1112	2696	77	)	)	PUNCT
m-1112	2697	1	𝐕	𝐕	NOUN
m-1112	2697	2	𝐆𝐑𝐀	𝐆𝐑𝐀	NOUN
m-1112	2697	3	=	=	X
m-1112	2697	4	𝐡.𝐟𝐏	𝐡.𝐟𝐏	X
m-1112	2697	5	.	.	PUNCT
m-1112	2698	1	𝟏𝐂𝐛	𝟏𝐂𝐛	X
m-1112	2699	1	=	=	SYM
m-1112	2699	2	1	1	NUM
m-1112	2699	3	,	,	PUNCT
m-1112	2699	4	216447.1017	216447.1017	NUM
m-1112	2699	5	j	j	NOUN
m-1112	2699	6	1,6022.10−19ev	1,6022.10−19ev	NUM
m-1112	2699	7	=	=	SYM
m-1112	2699	8	7,593.𝟏𝟎	7,593.𝟏𝟎	NUM
m-1112	2699	9	𝟑𝟓	𝟑𝟓	NUM
m-1112	2699	10	v	v	NOUN
m-1112	2699	11	,	,	PUNCT
m-1112	2699	12	i.e.	i.e.	X
m-1112	2699	13			NOUN
m-1112	2699	14	when	when	SCONJ
m-1112	2699	15	the	the	DET
m-1112	2699	16	energy	energy	NOUN
m-1112	2699	17	in	in	ADP
m-1112	2699	18	planck`s	planck`s	NOUN
m-1112	2699	19	cave	cave	NOUN
m-1112	2699	20	=	=	PUNCT
m-1112	2699	21	lpla	lpla	NOUN
m-1112	2699	22	,	,	PUNCT
m-1112	2699	23	increases	increase	VERB
m-1112	2699	24	to	to	ADP
m-1112	2699	25	an	an	DET
m-1112	2699	26	voltage	voltage	NOUN
m-1112	2699	27	=	=	SYM
m-1112	2699	28	7,593.10	7,593.10	NUM
m-1112	2699	29	35	35	NUM
m-1112	2699	30	v	v	NOUN
m-1112	2699	31	then	then	ADV
m-1112	2699	32	the	the	DET
m-1112	2699	33	motion≡	motion≡	PROPN
m-1112	2699	34	energy	energy	NOUN
m-1112	2699	35	between	between	ADP
m-1112	2699	36	the	the	DET
m-1112	2699	37	two	two	NUM
m-1112	2699	38	opposite	opposite	ADJ
m-1112	2699	39	elements	element	NOUN
m-1112	2699	40	of	of	ADP
m-1112	2699	41	mp	mp	NOUN
m-1112	2699	42	-	-	PUNCT
m-1112	2699	43	dipole	dipole	NOUN
m-1112	2699	44	[	[	X
m-1112	2699	45	⊕↔⊝	⊕↔⊝	NOUN
m-1112	2699	46	]	]	X
m-1112	2699	47	becomes	become	VERB
m-1112	2699	48	a	a	DET
m-1112	2699	49	stationary	stationary	ADJ
m-1112	2699	50	flow	flow	NOUN
m-1112	2699	51	[	[	X
m-1112	2699	52	⊕,⊝	⊕,⊝	X
m-1112	2699	53	]	]	X
m-1112	2699	54	≡	≡	PROPN
m-1112	2699	55	charges	charge	VERB
m-1112	2699	56	[	[	X
m-1112	2699	57	⊕	⊕	X
m-1112	2699	58			PROPN
m-1112	2699	59	⊝	⊝	NUM
m-1112	2699	60	]	]	PUNCT
m-1112	2699	61	in	in	ADP
m-1112	2699	62	gravity	gravity	NOUN
m-1112	2699	63	cave	cave	NOUN
m-1112	2699	64	l	l	PROPN
m-1112	2699	65	gra	gra	PROPN
m-1112	2699	66	.	.	PUNCT
m-1112	2700	1	so	so	ADV
m-1112	2700	2	energy	energy	NOUN
m-1112	2700	3	≡	≡	PROPN
m-1112	2700	4	motion	motion	NOUN
m-1112	2700	5	,	,	PUNCT
m-1112	2700	6	exists	exist	VERB
m-1112	2700	7	in	in	ADP
m-1112	2700	8	l	l	PROPN
m-1112	2700	9	gra	gra	PROPN
m-1112	2700	10	as	as	ADP
m-1112	2700	11	an	an	DET
m-1112	2700	12	→	→	SYM
m-1112	2700	13	pointy	pointy	ADJ
m-1112	2700	14	rotational	rotational	ADJ
m-1112	2700	15	centripetal	centripetal	ADJ
m-1112	2700	16	force	force	NOUN
m-1112	2700	17	←	←	PROPN
m-1112	2700	18			PROPN
m-1112	2700	19	when	when	SCONJ
m-1112	2700	20	the	the	DET
m-1112	2700	21	energy	energy	NOUN
m-1112	2700	22	in	in	ADP
m-1112	2700	23	planck`s	planck`s	NOUN
m-1112	2700	24	cave	cave	NOUN
m-1112	2700	25	lpla	lpla	NOUN
m-1112	2700	26	,	,	PUNCT
m-1112	2700	27	increases	increase	VERB
m-1112	2700	28	to	to	ADP
m-1112	2700	29	an	an	DET
m-1112	2700	30	voltage	voltage	NOUN
m-1112	2700	31	𝐕𝐂𝐑	𝐕𝐂𝐑	PROPN
m-1112	2700	32	>	>	X
m-1112	2700	33	7,593.10	7,593.10	NUM
m-1112	2700	34	35	35	NUM
m-1112	2700	35	v	v	NOUN
m-1112	2700	36	then	then	ADV
m-1112	2700	37	motion	motion	NOUN
m-1112	2700	38	≡	≡	PROPN
m-1112	2700	39	⇄	⇄	PROPN
m-1112	2700	40	≡	≡	PROPN
m-1112	2700	41	energy	energy	NOUN
m-1112	2700	42	between	between	ADP
m-1112	2700	43	the	the	DET
m-1112	2700	44	two	two	NUM
m-1112	2700	45	opposite	opposite	ADJ
m-1112	2700	46	elements	element	NOUN
m-1112	2700	47	of	of	ADP
m-1112	2700	48	m	m	PROPN
m-1112	2700	49	-	-	ADJ
m-1112	2700	50	p	p	NOUN
m-1112	2700	51	-	-	PUNCT
m-1112	2700	52	dipole	dipole	NOUN
m-1112	2700	53	[	[	X
m-1112	2700	54	⊕	⊕	NOUN
m-1112	2700	55	↻	↻	NOUN
m-1112	2700	56	↺	↺	NOUN
m-1112	2700	57	⊝	⊝	X
m-1112	2700	58	]	]	PUNCT
m-1112	2700	59	creates	create	VERB
m-1112	2700	60	the	the	DET
m-1112	2700	61	negative	negative	ADJ
m-1112	2700	62	-	-	PUNCT
m-1112	2700	63	angular	angular	ADJ
m-1112	2700	64	-velocity	-velocity	NOUN
m-1112	2700	65	-	-	PUNCT
m-1112	2700	66	vector	vector	NOUN
m-1112	2700	67	�	�	PROPN
m-1112	2700	68	̅	̅	NOUN
m-1112	2700	69	�	�	PROPN
m-1112	2700	70	↓	↓	NOUN
m-1112	2700	71	,	,	PUNCT
m-1112	2700	72	which	which	PRON
m-1112	2700	73	rotates	rotate	VERB
m-1112	2700	74	in	in	ADP
m-1112	2700	75	the	the	DET
m-1112	2700	76	symmetrical	symmetrical	ADJ
m-1112	2700	77	to	to	ADP
m-1112	2700	78	neutral	neutral	ADJ
m-1112	2700	79	circle	circle	NOUN
m-1112	2700	80	axis	axis	NOUN
m-1112	2700	81	k	k	PROPN
m-1112	2700	82	=	=	PUNCT
m-1112	2700	83	↓	↓	PROPN
m-1112	2700	84	with	with	ADP
m-1112	2700	85	respect	respect	NOUN
m-1112	2700	86	to	to	ADP
m-1112	2700	87	the	the	DET
m-1112	2700	88	interchangable	interchangable	ADJ
m-1112	2700	89	variable	variable	ADJ
m-1112	2700	90	�	�	PROPN
m-1112	2700	91	̅	̅	NOUN
m-1112	2700	92	�	�	PROPN
m-1112	2700	93	↓	↓	NOUN
m-1112	2700	94	.	.	PUNCT
m-1112	2701	1	this	this	PRON
m-1112	2701	2	is	be	AUX
m-1112	2701	3	the	the	DET
m-1112	2701	4	case	case	NOUN
m-1112	2701	5	of	of	ADP
m-1112	2701	6	the	the	DET
m-1112	2701	7	black	black	ADJ
m-1112	2701	8	-	-	PUNCT
m-1112	2701	9	holes	hole	NOUN
m-1112	2701	10	origination	origination	NOUN
m-1112	2701	11	.	.	PUNCT
m-1112	2702	1			NOUN
m-1112	2702	2	when	when	SCONJ
m-1112	2702	3	the	the	DET
m-1112	2702	4	energy	energy	NOUN
m-1112	2702	5	in	in	ADP
m-1112	2702	6	planck`s	planck`s	NOUN
m-1112	2702	7	cave	cave	NOUN
m-1112	2702	8	lpla	lpla	NOUN
m-1112	2702	9	,	,	PUNCT
m-1112	2702	10	decreases	decrease	VERB
m-1112	2702	11	to	to	ADP
m-1112	2702	12	an	an	DET
m-1112	2702	13	voltage	voltage	NOUN
m-1112	2702	14	=	=	PUNCT
m-1112	2702	15	<	<	X
m-1112	2702	16	3,695.10	3,695.10	NUM
m-1112	2702	17	30	30	NUM
m-1112	2702	18	v	v	NOUN
m-1112	2702	19	then	then	ADV
m-1112	2702	20	motion	motion	NOUN
m-1112	2702	21	≡	≡	PROPN
m-1112	2702	22	⇄	⇄	PROPN
m-1112	2702	23	≡	≡	PROPN
m-1112	2702	24	energy	energy	NOUN
m-1112	2702	25	between	between	ADP
m-1112	2702	26	the	the	DET
m-1112	2702	27	two	two	NUM
m-1112	2702	28	opposite	opposite	ADJ
m-1112	2702	29	elements	element	NOUN
m-1112	2702	30	of	of	ADP
m-1112	2702	31	m	m	PROPN
m-1112	2702	32	-	-	ADJ
m-1112	2702	33	p	p	NOUN
m-1112	2702	34	-	-	PUNCT
m-1112	2702	35	dipole	dipole	NOUN
m-1112	2702	36	[	[	X
m-1112	2702	37	⊕	⊕	NOUN
m-1112	2702	38	↻	↻	NOUN
m-1112	2702	39	↺	↺	NOUN
m-1112	2702	40	⊝	⊝	X
m-1112	2702	41	]	]	PUNCT
m-1112	2702	42	creates	create	VERB
m-1112	2702	43	the	the	DET
m-1112	2702	44	positive	positive	ADJ
m-1112	2702	45	-	-	PUNCT
m-1112	2702	46	angular	angular	ADJ
m-1112	2702	47	-velocity	-velocity	NOUN
m-1112	2702	48	-	-	PUNCT
m-1112	2702	49	vector	vector	NOUN
m-1112	2702	50	�	�	PROPN
m-1112	2702	51	̅	̅	NOUN
m-1112	2702	52	�	�	PROPN
m-1112	2702	53	↑	↑	PROPN
m-1112	2702	54	,	,	PUNCT
m-1112	2702	55	which	which	PRON
m-1112	2702	56	rotates	rotate	VERB
m-1112	2702	57	in	in	ADP
m-1112	2702	58	the	the	DET
m-1112	2702	59	symmetrical	symmetrical	ADJ
m-1112	2702	60	to	to	ADP
m-1112	2702	61	neutral	neutral	ADJ
m-1112	2702	62	circle	circle	NOUN
m-1112	2702	63	axis	axis	NOUN
m-1112	2702	64	k	k	PROPN
m-1112	2702	65	=	=	PUNCT
m-1112	2702	66	↑	↑	PROPN
m-1112	2702	67	with	with	ADP
m-1112	2702	68	respect	respect	NOUN
m-1112	2702	69	to	to	ADP
m-1112	2702	70	the	the	DET
m-1112	2702	71	interchangable	interchangable	ADJ
m-1112	2702	72	variable	variable	ADJ
m-1112	2702	73	�	�	PROPN
m-1112	2702	74	̅	̅	NOUN
m-1112	2702	75	�	�	PROPN
m-1112	2702	76	↑	↑	PROPN
m-1112	2702	77	.	.	PUNCT
m-1112	2703	1	this	this	PRON
m-1112	2703	2	is	be	AUX
m-1112	2703	3	the	the	DET
m-1112	2703	4	case	case	NOUN
m-1112	2703	5	of	of	ADP
m-1112	2703	6	the	the	DET
m-1112	2703	7	universe	universe	ADJ
m-1112	2703	8	origination	origination	NOUN
m-1112	2703	9	.	.	PUNCT
m-1112	2704	1	so	so	ADV
m-1112	2704	2	thus	thus	ADV
m-1112	2704	3	,	,	PUNCT
m-1112	2704	4	are	be	AUX
m-1112	2704	5	defined	define	VERB
m-1112	2704	6	the	the	DET
m-1112	2704	7	unit	unit	NOUN
m-1112	2704	8	-	-	PUNCT
m-1112	2704	9	energy	energy	NOUN
m-1112	2704	10	vectors	vector	NOUN
m-1112	2704	11	,	,	PUNCT
m-1112	2704	12	�	�	NOUN
m-1112	2704	13	̅	̅	NOUN
m-1112	2704	14	�	�	NOUN
m-1112	2704	15	=	=	SYM
m-1112	2704	16	σ	σ	PROPN
m-1112	2704	17	/	/	SYM
m-1112	2704	18	�	�	PROPN
m-1112	2704	19	̅	̅	NOUN
m-1112	2704	20	�	�	NOUN
m-1112	2704	21	=	=	SYM
m-1112	2704	22	σ	σ	PROPN
m-1112	2704	23	/	/	SYM
m-1112	2704	24	j.w²	j.w²	NOUN
m-1112	2704	25	,	,	PUNCT
m-1112	2704	26	which	which	PRON
m-1112	2704	27	exist	exist	VERB
m-1112	2704	28	on	on	ADP
m-1112	2704	29	the	the	DET
m-1112	2704	30	unit	unit	NOUN
m-1112	2704	31	–	–	PUNCT
m-1112	2704	32	space	space	NOUN
m-1112	2704	33	–	–	PUNCT
m-1112	2704	34	monad	monad	PROPN
m-1112	2704	35	|ab|	|ab|	NUM
m-1112	2704	36	≡	≡	PROPN
m-1112	2704	37	|	|	NOUN
m-1112	2704	38	�	�	PROPN
m-1112	2704	39	̅	̅	NOUN
m-1112	2704	40	�	�	NOUN
m-1112	2704	41	|	|	NOUN
m-1112	2704	42	,	,	PUNCT
m-1112	2704	43	and	and	CCONJ
m-1112	2704	44	which	which	PRON
m-1112	2704	45	is	be	AUX
m-1112	2704	46	{	{	PUNCT
m-1112	2704	47	the	the	DET
m-1112	2704	48	energy	energy	NOUN
m-1112	2704	49	–	–	PUNCT
m-1112	2704	50	space	space	NOUN
m-1112	2704	51	–	–	PUNCT
m-1112	2704	52	monad	monad	PROPN
m-1112	2704	53	|	|	NOUN
m-1112	2704	54	�	�	PROPN
m-1112	2704	55	̅	̅	NOUN
m-1112	2704	56	�	�	NOUN
m-1112	2704	57	|	|	ADV
m-1112	2704	58	≡	≡	PROPN
m-1112	2704	59	|ab|	|ab|	PROPN
m-1112	2704	60	≡	≡	PROPN
m-1112	2704	61	the	the	DET
m-1112	2704	62	existing	exist	VERB
m-1112	2704	63	universe	universe	NOUN
m-1112	2704	64	}	}	PUNCT
m-1112	2704	65	.	.	PUNCT
m-1112	2705	1	in	in	ADP
m-1112	2705	2	fig-14	fig-14	NUM
m-1112	2705	3	are	be	AUX
m-1112	2705	4	shown	show	VERB
m-1112	2705	5	the	the	DET
m-1112	2705	6	5	5	NUM
m-1112	2705	7	-	-	PUNCT
m-1112	2705	8	states	state	NOUN
m-1112	2705	9	for	for	ADP
m-1112	2705	10	angle	angle	NOUN
m-1112	2705	11	→	→	SYM
m-1112	2705	12	θ	θ	PROPN
m-1112	2705	13			NOUN
m-1112	2705	14	0ᶱ	0ᶱ	NOUN
m-1112	2705	15	,	,	PUNCT
m-1112	2705	16	45ᶱ	45ᶱ	X
m-1112	2705	17	,	,	PUNCT
m-1112	2705	18	90ᶱ	90ᶱ	NOUN
m-1112	2705	19	,	,	PUNCT
m-1112	2705	20	135ᶱ	135ᶱ	NUM
m-1112	2705	21	,	,	PUNCT
m-1112	2705	22	180ᶱ	180ᶱ	PROPN
m-1112	2705	23	.	.	PUNCT
m-1112	2706	1	1	1	X
m-1112	2706	2	..	..	PUNCT
m-1112	2706	3	for	for	ADP
m-1112	2706	4	angle	angle	NOUN
m-1112	2706	5	→	→	SYM
m-1112	2706	6	θ	θ	PROPN
m-1112	2706	7			NOUN
m-1112	2706	8	00ᶱ	00ᶱ	NOUN
m-1112	2706	9	,	,	PUNCT
m-1112	2706	10	�	�	PROPN
m-1112	2706	11	̅	̅	NOUN
m-1112	2706	12	�	�	PROPN
m-1112	2706	13	≡	≡	PROPN
m-1112	2706	14	�	�	PROPN
m-1112	2706	15	̅	̅	NOUN
m-1112	2706	16	�	�	NOUN
m-1112	2706	17	,	,	PUNCT
m-1112	2706	18	voltage	voltage	NOUN
m-1112	2706	19	=	=	NOUN
m-1112	2706	20	7,593.10	7,593.10	NUM
m-1112	2706	21	35	35	NUM
m-1112	2706	22	v	v	NOUN
m-1112	2706	23	,	,	PUNCT
m-1112	2706	24	↑	↑	PROPN
m-1112	2706	25	on	on	ADP
m-1112	2706	26	neutral	neutral	ADJ
m-1112	2706	27	–	–	PUNCT
m-1112	2706	28	circle	circle	NOUN
m-1112	2706	29	2	2	NUM
m-1112	2706	30	..	..	PUNCT
m-1112	2706	31	for	for	ADP
m-1112	2706	32	angle	angle	NOUN
m-1112	2706	33	→	→	SYM
m-1112	2706	34	θ	θ	PROPN
m-1112	2706	35			NOUN
m-1112	2706	36	45ᶱ	45ᶱ	X
m-1112	2706	37	,	,	PUNCT
m-1112	2706	38	�	�	PROPN
m-1112	2706	39	̅	̅	NOUN
m-1112	2706	40	�	�	PROPN
m-1112	2706	41	/	/	SYM
m-1112	2706	42	�	�	PROPN
m-1112	2706	43	̅	̅	NOUN
m-1112	2706	44	�	�	NOUN
m-1112	2706	45	,	,	PUNCT
m-1112	2706	46	voltage	voltage	VERB
m-1112	2706	47	<	<	X
m-1112	2706	48	7,593.10	7,593.10	NUM
m-1112	2706	49	35	35	NUM
m-1112	2706	50	v	v	NOUN
m-1112	2706	51	,	,	PUNCT
m-1112	2706	52	<	<	X
m-1112	2706	53	≠	≠	ADJ
m-1112	2706	54	neutral	neutral	ADJ
m-1112	2706	55	–	–	PUNCT
m-1112	2706	56	circle	circle	NOUN
m-1112	2706	57	3	3	NUM
m-1112	2706	58	..	..	PUNCT
m-1112	2706	59	for	for	ADP
m-1112	2706	60	angle	angle	NOUN
m-1112	2706	61	→	→	SYM
m-1112	2706	62	θ	θ	PROPN
m-1112	2706	63			NOUN
m-1112	2706	64	90ᶱ	90ᶱ	PROPN
m-1112	2706	65	,	,	PUNCT
m-1112	2706	66	�	�	PROPN
m-1112	2706	67	̅	̅	NOUN
m-1112	2706	68	�	�	PROPN
m-1112	2706	69	⏊	⏊	SYM
m-1112	2706	70	�	�	PROPN
m-1112	2706	71	̅	̅	NOUN
m-1112	2706	72	�	�	NOUN
m-1112	2706	73	,	,	PUNCT
m-1112	2706	74	voltage	voltage	NOUN
m-1112	2706	75	≡	≡	PROPN
m-1112	2706	76	7,593.10	7,593.10	NUM
m-1112	2706	77	35	35	NUM
m-1112	2706	78	v	v	NOUN
m-1112	2706	79	,	,	PUNCT
m-1112	2706	80	⇉	⇉	PROPN
m-1112	2707	1	in	in	ADP
m-1112	2707	2	neutral	neutral	ADJ
m-1112	2707	3	circle	circle	NOUN
m-1112	2707	4	4	4	NUM
m-1112	2707	5	..	..	PUNCT
m-1112	2707	6	for	for	ADP
m-1112	2707	7	angle	angle	NOUN
m-1112	2707	8	→	→	SYM
m-1112	2707	9	θ	θ	PROPN
m-1112	2707	10			NOUN
m-1112	2707	11	135ᶱ	135ᶱ	NUM
m-1112	2707	12	,	,	PUNCT
m-1112	2707	13	�	�	PROPN
m-1112	2707	14	̅	̅	NOUN
m-1112	2707	15	�	�	PROPN
m-1112	2707	16	\	\	PROPN
m-1112	2707	17	�	�	PROPN
m-1112	2707	18	̅	̅	NOUN
m-1112	2707	19	�	�	PROPN
m-1112	2707	20	,	,	PUNCT
m-1112	2707	21	voltage	voltage	VERB
m-1112	2707	22	>	>	X
m-1112	2707	23	7,593.10	7,593.10	NUM
m-1112	2707	24	35	35	NUM
m-1112	2707	25	v	v	NOUN
m-1112	2707	26	,	,	PUNCT
m-1112	2707	27	≠	≠	PROPN
m-1112	2707	28	>	>	SYM
m-1112	2707	29	neutral	neutral	ADJ
m-1112	2707	30	–	–	PUNCT
m-1112	2707	31	circle	circle	NOUN
m-1112	2707	32	5	5	NUM
m-1112	2707	33	..	..	PUNCT
m-1112	2707	34	for	for	ADP
m-1112	2707	35	angle	angle	NOUN
m-1112	2707	36	→	→	SYM
m-1112	2707	37	θ	θ	PROPN
m-1112	2707	38			NOUN
m-1112	2707	39	180ᶱ	180ᶱ	PROPN
m-1112	2707	40	,	,	PUNCT
m-1112	2707	41	�	�	PROPN
m-1112	2707	42	̅	̅	NOUN
m-1112	2707	43	�	�	PROPN
m-1112	2707	44	⏊	⏊	SYM
m-1112	2707	45	�	�	PROPN
m-1112	2707	46	̅	̅	NOUN
m-1112	2707	47	�	�	PROPN
m-1112	2707	48	,	,	PUNCT
m-1112	2707	49	voltage	voltage	NOUN
m-1112	2707	50	>	>	PUNCT
m-1112	2708	1	=	=	NOUN
m-1112	2708	2	7,593.10	7,593.10	NUM
m-1112	2708	3	35	35	NUM
m-1112	2708	4	v	v	NOUN
m-1112	2708	5	,	,	PUNCT
m-1112	2708	6	⇅	⇅	VERB
m-1112	2708	7	off	off	ADP
m-1112	2708	8	neutral	neutral	ADJ
m-1112	2708	9	-	-	PUNCT
m-1112	2708	10	circle	circle	NOUN
m-1112	2708	11	4	4	NUM
m-1112	2708	12	)	)	PUNCT
m-1112	2708	13	..	..	PUNCT
m-1112	2709	1	from	from	ADP
m-1112	2709	2	solution-4	solution-4	NUM
m-1112	2709	3	,	,	PUNCT
m-1112	2709	4	the	the	DET
m-1112	2709	5	{	{	PUNCT
m-1112	2709	6	energy	energy	NOUN
m-1112	2709	7	-	-	PUNCT
m-1112	2709	8	space	space	NOUN
m-1112	2709	9	-	-	PUNCT
m-1112	2709	10	monad	monad	PROPN
m-1112	2709	11	|r̅|	|r̅|	PROPN
m-1112	2709	12	≡	≡	PROPN
m-1112	2709	13	|ab|	|ab|	PROPN
m-1112	2709	14	}	}	PUNCT
m-1112	2709	15	vanishes	vanish	VERB
m-1112	2709	16	in	in	ADP
m-1112	2709	17	bh	bh	NOUN
m-1112	2709	18	-	-	NOUN
m-1112	2709	19	chaos	chaos	NOUN
m-1112	2709	20	,	,	PUNCT
m-1112	2709	21	where	where	SCONJ
m-1112	2709	22	energy	energy	NOUN
m-1112	2709	23	increases	increase	VERB
m-1112	2709	24	to	to	ADP
m-1112	2709	25	an	an	DET
m-1112	2709	26	voltage	voltage	NOUN
m-1112	2709	27	>	>	PUNCT
m-1112	2709	28	>	>	X
m-1112	2709	29	7,593.10	7,593.10	NUM
m-1112	2709	30	35	35	NUM
m-1112	2709	31	v	v	NOUN
m-1112	2709	32	and	and	CCONJ
m-1112	2709	33	then	then	ADV
m-1112	2709	34	motion	motion	PROPN
m-1112	2709	35	≡	≡	PROPN
m-1112	2709	36	energy	energy	NOUN
m-1112	2709	37	between	between	ADP
m-1112	2709	38	the	the	DET
m-1112	2709	39	two	two	NUM
m-1112	2709	40	opposite	opposite	ADJ
m-1112	2709	41	elements	element	NOUN
m-1112	2709	42	collides	collide	VERB
m-1112	2709	43	them	they	PRON
m-1112	2709	44	to	to	ADP
m-1112	2709	45	the	the	DET
m-1112	2709	46	mp	mp	NOUN
m-1112	2709	47	-	-	PUNCT
m-1112	2709	48	dipole	dipole	NOUN
m-1112	2710	1	[	[	X
m-1112	2710	2	⊕↔⊝	⊕↔⊝	NOUN
m-1112	2710	3	]	]	PUNCT
m-1112	2710	4	.	.	PUNCT
m-1112	2711	1	ijo	ijo	PROPN
m-1112	2711	2	international	international	PROPN
m-1112	2711	3	journal	journal	PROPN
m-1112	2711	4	of	of	ADP
m-1112	2711	5	mathematics	mathematics	PROPN
m-1112	2711	6	(	(	PUNCT
m-1112	2711	7	issn	issn	PROPN
m-1112	2711	8	:	:	PUNCT
m-1112	2711	9	2992	2992	NUM
m-1112	2711	10	-	-	SYM
m-1112	2711	11	4421	4421	NUM
m-1112	2711	12	)	)	PUNCT
m-1112	2711	13	volume	volume	NOUN
m-1112	2711	14	08	08	NUM
m-1112	2712	1	|	|	ADV
m-1112	2712	2	issue	issue	NOUN
m-1112	2712	3	08	08	NUM
m-1112	2713	1	|	|	ADV
m-1112	2713	2	august	august	PROPN
m-1112	2713	3	2025	2025	NUM
m-1112	2713	4	|	|	ADV
m-1112	2713	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2713	6	ijo	ijo	PROPN
m-1112	2713	7	journals	journal	NOUN
m-1112	2713	8	95	95	NUM
m-1112	2713	9	the	the	DET
m-1112	2713	10	fundamental	fundamental	ADJ
m-1112	2713	11	particles	particle	NOUN
m-1112	2713	12	origination	origination	NOUN
m-1112	2713	13	mechanism	mechanism	NOUN
m-1112	2713	14	in	in	ADP
m-1112	2713	15	mfmf	mfmf	PROPN
m-1112	2713	16	pns	pns	PROPN
m-1112	2713	17	caves	cave	NOUN
m-1112	2713	18	.	.	PUNCT
m-1112	2714	1	5	5	X
m-1112	2714	2	)	)	PUNCT
m-1112	2714	3	..	..	PUNCT
m-1112	2714	4	from	from	ADP
m-1112	2714	5	solution-5	solution-5	NUM
m-1112	2714	6	,	,	PUNCT
m-1112	2714	7	the	the	DET
m-1112	2714	8	{	{	PUNCT
m-1112	2714	9	energy	energy	NOUN
m-1112	2714	10	-	-	PUNCT
m-1112	2714	11	space	space	NOUN
m-1112	2714	12	-	-	PUNCT
m-1112	2714	13	monad	monad	PROPN
m-1112	2714	14	|r̅|	|r̅|	PROPN
m-1112	2714	15	≡	≡	PROPN
m-1112	2714	16	|ab|	|ab|	PROPN
m-1112	2714	17	}	}	PUNCT
m-1112	2714	18	vanishes	vanish	VERB
m-1112	2714	19	in	in	ADP
m-1112	2714	20	bh	bh	NOUN
m-1112	2714	21	-	-	NOUN
m-1112	2714	22	chaos	chaos	NOUN
m-1112	2714	23	,	,	PUNCT
m-1112	2714	24	&	&	CCONJ
m-1112	2714	25	energy	energy	NOUN
m-1112	2714	26	is	be	AUX
m-1112	2714	27	quantized	quantize	VERB
m-1112	2714	28	to	to	ADP
m-1112	2714	29	the	the	DET
m-1112	2714	30	2	2	NUM
m-1112	2714	31	-	-	PUNCT
m-1112	2714	32	constitutes	constitute	NOUN
m-1112	2714	33	from	from	ADP
m-1112	2714	34	the	the	DET
m-1112	2714	35	�	�	PROPN
m-1112	2714	36	̅	̅	NOUN
m-1112	2714	37	�	�	PROPN
m-1112	2714	38	,	,	PUNCT
m-1112	2714	39	physical	physical	ADJ
m-1112	2714	40	-	-	PUNCT
m-1112	2714	41	magnet	magnet	NOUN
m-1112	2714	42	⊕	⊕	PROPN
m-1112	2714	43	⇉	⇉	PUNCT
m-1112	2715	1	⊝.	⊝.	PROPN
m-1112	2716	1	figure.17e	figure.17e	PROPN
m-1112	2716	2	..	..	PUNCT
m-1112	2716	3	the	the	DET
m-1112	2716	4	stability	stability	NOUN
m-1112	2716	5	of	of	ADP
m-1112	2716	6	photon	photon	NOUN
m-1112	2716	7	as	as	ADP
m-1112	2716	8	electromagnetic	electromagnetic	ADJ
m-1112	2716	9	wave	wave	NOUN
m-1112	2716	10	with	with	ADP
m-1112	2716	11	the	the	DET
m-1112	2716	12	two	two	NUM
m-1112	2716	13	frequencies	frequency	NOUN
m-1112	2716	14	.	.	PUNCT
m-1112	2717	1	the	the	DET
m-1112	2717	2	dual	dual	ADJ
m-1112	2717	3	property	property	NOUN
m-1112	2717	4	of	of	ADP
m-1112	2717	5	the	the	DET
m-1112	2717	6	simultaneous	simultaneous	ADJ
m-1112	2717	7	existence	existence	NOUN
m-1112	2717	8	as	as	ADP
m-1112	2717	9	electric	electric	ADJ
m-1112	2717	10	and	and	CCONJ
m-1112	2717	11	as	as	ADP
m-1112	2717	12	magnetic	magnetic	ADJ
m-1112	2717	13	fields	field	NOUN
m-1112	2717	14	in	in	ADP
m-1112	2717	15	wavelengths	wavelength	NOUN
m-1112	2717	16	,	,	PUNCT
m-1112	2717	17	λ	λ	X
m-1112	2717	18	x	x	X
m-1112	2717	19	,	,	PUNCT
m-1112	2717	20	λ	λ	X
m-1112	2717	21	y	y	PROPN
m-1112	2717	22	,	,	PUNCT
m-1112	2717	23	as	as	ADP
m-1112	2717	24	effective	effective	ADJ
m-1112	2717	25	range	range	NOUN
m-1112	2717	26	.which	.which	PRON
m-1112	2717	27	is	be	AUX
m-1112	2717	28	thrusted	thrust	VERB
m-1112	2717	29	through	through	ADP
m-1112	2717	30	the	the	DET
m-1112	2717	31	newton	newton	PROPN
m-1112	2717	32	’s	’s	PART
m-1112	2717	33	gravitational	gravitational	ADJ
m-1112	2717	34	force	force	NOUN
m-1112	2717	35	g	g	PROPN
m-1112	2717	36	only	only	ADV
m-1112	2717	37	,	,	PUNCT
m-1112	2717	38	becoming	become	VERB
m-1112	2717	39	from	from	ADP
m-1112	2717	40	the	the	DET
m-1112	2717	41	trigonometry	trigonometry	NOUN
m-1112	2717	42	relations	relation	NOUN
m-1112	2717	43	[	[	X
m-1112	2717	44	the	the	DET
m-1112	2717	45	space	space	NOUN
m-1112	2717	46	]	]	PUNCT
m-1112	2717	47	,	,	PUNCT
m-1112	2717	48	sin(2φ	sin(2φ	NOUN
m-1112	2717	49	)	)	PUNCT
m-1112	2718	1	=	=	PUNCT
m-1112	2718	2	sin(𝜋	sin(𝜋	NOUN
m-1112	2718	3	−	−	NOUN
m-1112	2718	4	2φ	2φ	NUM
m-1112	2718	5	)	)	PUNCT
m-1112	2719	1	=	=	VERB
m-1112	2719	2	sin	sin	NOUN
m-1112	2719	3	(	(	PUNCT
m-1112	2719	4	𝜋	𝜋	NOUN
m-1112	2719	5	2	2	NUM
m-1112	2719	6	−	−	PROPN
m-1112	2719	7	φ	φ	PROPN
m-1112	2719	8	)	)	PUNCT
m-1112	2719	9	,	,	PUNCT
m-1112	2719	10	and	and	CCONJ
m-1112	2719	11	from	from	ADP
m-1112	2719	12	physics	physics	NOUN
m-1112	2719	13	[	[	X
m-1112	2719	14	energy	energy	NOUN
m-1112	2719	15	]	]	PUNCT
m-1112	2719	16	e	e	NOUN
m-1112	2719	17	x	x	X
m-1112	2719	18	=	=	SYM
m-1112	2719	19	g	g	PROPN
m-1112	2719	20	,	,	PUNCT
m-1112	2719	21	maxwel	maxwel	PROPN
m-1112	2719	22	electric	electric	PROPN
m-1112	2719	23	displacement	displacement	PROPN
m-1112	2719	24	current	current	NOUN
m-1112	2719	25	𝝑d	𝝑d	PROPN
m-1112	2719	26	/	/	SYM
m-1112	2719	27	𝝑t	𝝑t	PROPN
m-1112	2719	28	is	be	AUX
m-1112	2719	29	created	create	VERB
m-1112	2719	30	from	from	ADP
m-1112	2719	31	the	the	DET
m-1112	2719	32	(	(	PUNCT
m-1112	2719	33	𝐜𝐱	𝐜𝐱	NOUN
m-1112	2719	34	,	,	PUNCT
m-1112	2719	35	𝐜𝐲	𝐜𝐲	ADJ
m-1112	2719	36	)	)	PUNCT
m-1112	2719	37	vectors	vector	NOUN
m-1112	2719	38	motion	motion	NOUN
m-1112	2719	39	happening	happen	VERB
m-1112	2719	40	from	from	ADP
m-1112	2719	41	gravity	gravity	NOUN
m-1112	2719	42	continuous	continuous	ADJ
m-1112	2719	43	action	action	NOUN
m-1112	2719	44	,	,	PUNCT
m-1112	2719	45	and	and	CCONJ
m-1112	2719	46	producing	produce	VERB
m-1112	2719	47	the	the	DET
m-1112	2719	48	work	work	NOUN
m-1112	2719	49	w	w	NOUN
m-1112	2719	50	=	=	PUNCT
m-1112	2719	51	𝐜	𝐜	PROPN
m-1112	2719	52	𝐲	𝐲	ADP
m-1112	2719	53	g	g	NOUN
m-1112	2719	54	for	for	ADP
m-1112	2719	55	photon	photon	NOUN
m-1112	2719	56	{	{	PUNCT
m-1112	2719	57	markos	markos	NOUN
m-1112	2719	58	rotating	rotating	NOUN
m-1112	2719	59	method	method	NOUN
m-1112	2719	60	of	of	ADP
m-1112	2719	61	{	{	PUNCT
m-1112	2719	62	2	2	NUM
m-1112	2719	63	-	-	PUNCT
m-1112	2719	64	vectors	vector	NOUN
m-1112	2719	65	3	3	NUM
m-1112	2719	66	-	-	PUNCT
m-1112	2719	67	poles	pole	NOUN
m-1112	2719	68	mechanism	mechanism	NOUN
m-1112	2719	69	}	}	PUNCT
m-1112	2719	70	which	which	DET
m-1112	2719	71	circles	circle	NOUN
m-1112	2719	72	and	and	CCONJ
m-1112	2719	73	squares	square	NOUN
m-1112	2719	74	as	as	SCONJ
m-1112	2719	75	areas	area	NOUN
m-1112	2719	76	pass	pass	VERB
m-1112	2719	77	from	from	ADP
m-1112	2719	78	the	the	DET
m-1112	2719	79	point	point	NOUN
m-1112	2719	80	m	m	AUX
m-1112	2719	81	determined	determine	VERB
m-1112	2719	82	by	by	ADP
m-1112	2719	83	the	the	DET
m-1112	2719	84	position	position	NOUN
m-1112	2719	85	𝐀	𝐀	PROPN
m-1112	2719	86	𝐞	𝐞	NOUN
m-1112	2719	87	,	,	PUNCT
m-1112	2719	88	and	and	CCONJ
m-1112	2719	89	where	where	SCONJ
m-1112	2719	90	is	be	AUX
m-1112	2719	91	such	such	ADJ
m-1112	2719	92	that	that	SCONJ
m-1112	2719	93	issues	issue	NOUN
m-1112	2719	94	π	π	NOUN
m-1112	2719	95	r	r	NOUN
m-1112	2719	96	²	²	NUM
m-1112	2719	97	=	=	SYM
m-1112	2719	98	cmnh	cmnh	NOUN
m-1112	2719	99	square	square	NOUN
m-1112	2719	100	then	then	ADV
m-1112	2719	101	.the	.the	SCONJ
m-1112	2719	102	squaring	squaring	NOUN
m-1112	2719	103	of	of	ADP
m-1112	2719	104	the	the	DET
m-1112	2719	105	circle	circle	NOUN
m-1112	2719	106	becomes	become	VERB
m-1112	2719	107	at	at	ADP
m-1112	2719	108	the	the	DET
m-1112	2719	109	equilibrium	equilibrium	NOUN
m-1112	2719	110	positions	position	NOUN
m-1112	2719	111	which	which	PRON
m-1112	2719	112	are	be	AUX
m-1112	2719	113	from	from	ADP
m-1112	2719	114	relation	relation	NOUN
m-1112	2719	115	→	→	SYM
m-1112	2719	116	π	π	PROPN
m-1112	2719	117	[	[	PUNCT
m-1112	2719	118	𝐂𝐀	𝐂𝐀	PROPN
m-1112	2719	119	√𝟐	√𝟐	PROPN
m-1112	2719	120	]	]	PUNCT
m-1112	2719	121	²	²	NUM
m-1112	2719	122	=	=	NOUN
m-1112	2719	123	cm²	cm²	ADP
m-1112	2719	124	=	=	SYM
m-1112	2719	125	|cm`|²	|cm`|²	X
m-1112	2719	126	←	←	X
m-1112	2719	127	namely	namely	ADV
m-1112	2719	128	the	the	DET
m-1112	2719	129	square	square	ADJ
m-1112	2719	130	|	|	ADV
m-1112	2719	131	cmnh	cmnh	NOUN
m-1112	2720	1	|	|	NOUN
m-1112	2720	2	=	=	SYM
m-1112	2720	3	square	square	ADJ
m-1112	2720	4	|	|	CCONJ
m-1112	2720	5	cm`n`h`|	cm`n`h`|	X
m-1112	2720	6	.	.	PUNCT
m-1112	2721	1	because	because	SCONJ
m-1112	2721	2	of	of	ADP
m-1112	2721	3	the	the	DET
m-1112	2721	4	bellow	bellow	ADJ
m-1112	2721	5	motion	motion	NOUN
m-1112	2721	6	then	then	ADV
m-1112	2721	7	,	,	PUNCT
m-1112	2721	8	the	the	DET
m-1112	2721	9	total	total	ADJ
m-1112	2721	10	motion	motion	NOUN
m-1112	2721	11	in	in	ADP
m-1112	2721	12	the	the	DET
m-1112	2721	13	wavelength	wavelength	NOUN
m-1112	2721	14	,	,	PUNCT
m-1112	2721	15	λ	λ	INTJ
m-1112	2721	16	,	,	PUNCT
m-1112	2721	17	corresponds	correspond	VERB
m-1112	2721	18	to	to	ADP
m-1112	2721	19	the	the	DET
m-1112	2721	20	angle	angle	NOUN
m-1112	2721	21	a	a	DET
m-1112	2721	22	=	=	SYM
m-1112	2721	23	45	45	NUM
m-1112	2721	24	°	°	NOUN
m-1112	2721	25	,	,	PUNCT
m-1112	2721	26	meaning	mean	VERB
m-1112	2721	27	that	that	SCONJ
m-1112	2721	28	the	the	DET
m-1112	2721	29	motion	motion	NOUN
m-1112	2721	30	of	of	ADP
m-1112	2721	31	space	space	NOUN
m-1112	2721	32	≡	≡	PROPN
m-1112	2721	33	the	the	DET
m-1112	2721	34	electric	electric	NOUN
m-1112	2721	35	-	-	PUNCT
m-1112	2721	36	field	field	NOUN
m-1112	2721	37	,	,	PUNCT
m-1112	2721	38	and	and	CCONJ
m-1112	2721	39	anti	anti	ADJ
m-1112	2721	40	-	-	ADJ
m-1112	2721	41	space	space	ADJ
m-1112	2721	42	≡	≡	PROPN
m-1112	2721	43	the	the	DET
m-1112	2721	44	magnetic	magnetic	ADJ
m-1112	2721	45	-	-	PUNCT
m-1112	2721	46	field	field	NOUN
m-1112	2721	47	equilibrium	equilibrium	NOUN
m-1112	2721	48	as	as	ADP
m-1112	2721	49	an	an	DET
m-1112	2721	50	bellow	bellow	NOUN
m-1112	2721	51	.	.	PUNCT
m-1112	2722	1	the	the	DET
m-1112	2722	2	two	two	NUM
m-1112	2722	3	wings	wing	NOUN
m-1112	2722	4	in	in	ADP
m-1112	2722	5	90	90	NUM
m-1112	2722	6	°	°	NOUN
m-1112	2722	7	type	type	NOUN
m-1112	2722	8	simultaneously	simultaneously	ADV
m-1112	2722	9	oscillate	oscillate	ADJ
m-1112	2722	10	to	to	ADP
m-1112	2722	11	its	its	PRON
m-1112	2722	12	45	45	NUM
m-1112	2722	13	°	°	NUM
m-1112	2722	14	bisector	bisector	NOUN
m-1112	2722	15	-axis	-axis	NOUN
m-1112	2722	16	,	,	PUNCT
m-1112	2722	17	and	and	CCONJ
m-1112	2722	18	the	the	DET
m-1112	2722	19	produced	produce	VERB
m-1112	2722	20	work	work	NOUN
m-1112	2722	21	from	from	ADP
m-1112	2722	22	the	the	DET
m-1112	2722	23	electric	electric	ADJ
m-1112	2722	24	-	-	PUNCT
m-1112	2722	25	field	field	NOUN
m-1112	2722	26	-	-	PUNCT
m-1112	2722	27	area	area	NOUN
m-1112	2722	28	is	be	AUX
m-1112	2722	29	stored	store	VERB
m-1112	2722	30	into	into	ADP
m-1112	2722	31	the	the	DET
m-1112	2722	32	conjugate	conjugate	ADJ
m-1112	2722	33	magnetic	magnetic	ADJ
m-1112	2722	34	-	-	PUNCT
m-1112	2722	35	field	field	NOUN
m-1112	2722	36	-	-	PUNCT
m-1112	2722	37	area	area	NOUN
m-1112	2722	38	.	.	PUNCT
m-1112	2723	1	the	the	DET
m-1112	2723	2	common	common	ADJ
m-1112	2723	3	axis	axis	NOUN
m-1112	2723	4	of	of	ADP
m-1112	2723	5	the	the	DET
m-1112	2723	6	two	two	NUM
m-1112	2723	7	perpendicular	perpendicular	ADJ
m-1112	2723	8	fields	field	NOUN
m-1112	2723	9	,	,	PUNCT
m-1112	2723	10	carry	carry	VERB
m-1112	2723	11	the	the	DET
m-1112	2723	12	golden	golden	ADJ
m-1112	2723	13	-	-	PUNCT
m-1112	2723	14	ratio	ratio	NOUN
m-1112	2723	15	energy	energy	NOUN
m-1112	2723	16	-	-	PUNCT
m-1112	2723	17	surfaces	surface	NOUN
m-1112	2723	18	,	,	PUNCT
m-1112	2723	19	and	and	CCONJ
m-1112	2723	20	runs	run	VERB
m-1112	2723	21	with	with	ADP
m-1112	2723	22	the	the	DET
m-1112	2723	23	same	same	ADJ
m-1112	2723	24	velocity	velocity	NOUN
m-1112	2723	25	c	c	NOUN
m-1112	2723	26	̅	̅	NOUN
m-1112	2723	27	to	to	ADP
m-1112	2723	28	the	the	DET
m-1112	2723	29	direction	direction	NOUN
m-1112	2723	30	of	of	ADP
m-1112	2723	31	the	the	DET
m-1112	2723	32	inner	inner	ADJ
m-1112	2723	33	motion	motion	NOUN
m-1112	2723	34	.	.	PUNCT
m-1112	2724	1	the	the	DET
m-1112	2724	2	epilogus	epilogus	ADJ
m-1112	2724	3	in	in	ADP
m-1112	2724	4	[	[	X
m-1112	2724	5	89	89	NUM
m-1112	2724	6	96	96	NUM
m-1112	2724	7	]	]	PUNCT
m-1112	2724	8	it	it	PRON
m-1112	2724	9	was	be	AUX
m-1112	2724	10	proved	prove	VERB
m-1112	2724	11	and	and	CCONJ
m-1112	2724	12	elucidated	elucidate	VERB
m-1112	2724	13	that	that	SCONJ
m-1112	2724	14	,	,	PUNCT
m-1112	2724	15	a	a	PRON
m-1112	2724	16	..	..	PUNCT
m-1112	2724	17	monad	monad	PROPN
m-1112	2724	18	is	be	AUX
m-1112	2724	19	quaternion	quaternion	ADJ
m-1112	2725	1	[	[	X
m-1112	2725	2	x	x	X
m-1112	2726	1	+	+	NUM
m-1112	2726	2	i	i	PRON
m-1112	2726	3	y	y	X
m-1112	2726	4	]	]	X
m-1112	2726	5	=	=	SYM
m-1112	2726	6	λ̅	λ̅	NOUN
m-1112	2726	7	type	type	NOUN
m-1112	2726	8	,	,	PUNCT
m-1112	2726	9	and	and	CCONJ
m-1112	2726	10	its	its	PRON
m-1112	2726	11	energy	energy	NOUN
m-1112	2726	12	is	be	AUX
m-1112	2726	13	vector	vector	NOUN
m-1112	2726	14	as	as	ADP
m-1112	2726	15	q⃗⃗	q⃗⃗	ADJ
m-1112	2726	16	=	=	PUNCT
m-1112	2726	17	{	{	PUNCT
m-1112	2726	18	λ}.x	λ}.x	X
m-1112	2726	19	,	,	PUNCT
m-1112	2726	20	where	where	SCONJ
m-1112	2726	21	x	x	X
m-1112	2726	22	=	=	PUNCT
m-1112	2726	23	the	the	DET
m-1112	2726	24	displacement	displacement	NOUN
m-1112	2726	25	.	.	PUNCT
m-1112	2727	1	since	since	SCONJ
m-1112	2727	2	1	1	NUM
m-1112	2727	3	=	=	SYM
m-1112	2727	4	c.	c.	NOUN
m-1112	2727	5	r³.	r³.	NOUN
m-1112	2727	6	fp²	fp²	NOUN
m-1112	2727	7	=	=	SYM
m-1112	2727	8	constant	constant	ADJ
m-1112	2727	9	,	,	PUNCT
m-1112	2727	10	so	so	CCONJ
m-1112	2727	11	→	→	SYM
m-1112	2727	12	r³.	r³.	NOUN
m-1112	2727	13	fp²	fp²	NOUN
m-1112	2727	14	=	=	SYM
m-1112	2727	15	constant	constant	ADJ
m-1112	2727	16	.	.	PUNCT
m-1112	2728	1	since	since	SCONJ
m-1112	2728	2	also	also	ADV
m-1112	2728	3	ijo	ijo	PROPN
m-1112	2728	4	international	international	ADJ
m-1112	2728	5	journal	journal	PROPN
m-1112	2728	6	of	of	ADP
m-1112	2728	7	mathematics	mathematics	PROPN
m-1112	2728	8	(	(	PUNCT
m-1112	2728	9	issn	issn	PROPN
m-1112	2728	10	:	:	PUNCT
m-1112	2728	11	2992	2992	NUM
m-1112	2728	12	-	-	SYM
m-1112	2728	13	4421	4421	NUM
m-1112	2728	14	)	)	PUNCT
m-1112	2728	15	volume	volume	NOUN
m-1112	2728	16	08	08	NUM
m-1112	2729	1	|	|	ADV
m-1112	2729	2	issue	issue	NOUN
m-1112	2729	3	08	08	NUM
m-1112	2730	1	|	|	ADV
m-1112	2730	2	august	august	PROPN
m-1112	2730	3	2025	2025	NUM
m-1112	2730	4	|	|	ADV
m-1112	2730	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2730	6	ijo	ijo	PROPN
m-1112	2730	7	journals	journal	NOUN
m-1112	2730	8	96	96	NUM
m-1112	2730	9	the	the	DET
m-1112	2730	10	fundamental	fundamental	ADJ
m-1112	2730	11	particles	particle	NOUN
m-1112	2730	12	origination	origination	NOUN
m-1112	2730	13	mechanism	mechanism	NOUN
m-1112	2730	14	in	in	ADP
m-1112	2730	15	mfmf	mfmf	PROPN
m-1112	2730	16	pns	pns	PROPN
m-1112	2730	17	caves	cave	NOUN
m-1112	2730	18	.	.	PUNCT
m-1112	2731	1	λ	λ	X
m-1112	2731	2	=	=	SYM
m-1112	2732	1	2r	2r	NUM
m-1112	2732	2	then	then	ADV
m-1112	2732	3	r³.	r³.	NOUN
m-1112	2732	4	fp²	fp²	VERB
m-1112	2733	1	=	=	PUNCT
m-1112	2733	2	λ	λ	X
m-1112	2733	3	³.	³.	PUNCT
m-1112	2733	4	fp²	fp²	VERB
m-1112	2733	5	=	=	SYM
m-1112	2733	6	c	c	NOUN
m-1112	2733	7	,	,	PUNCT
m-1112	2733	8	and	and	CCONJ
m-1112	2733	9	energy	energy	NOUN
m-1112	2733	10	becomes	become	VERB
m-1112	2733	11	→vector	→vector	X
m-1112	2733	12	q⃗⃗	q⃗⃗	NOUN
m-1112	2733	13	=	=	PUNCT
m-1112	2733	14	{	{	PUNCT
m-1112	2733	15	λ}.√c/	λ}.√c/	PUNCT
m-1112	2733	16	fp²	fp²	VERB
m-1112	2733	17	3	3	NUM
m-1112	2733	18	←	←	PROPN
m-1112	2734	1	[	[	X
m-1112	2734	2	𝐄	𝐄	PROPN
m-1112	2734	3	𝟏	𝟏	NUM
m-1112	2734	4	]	]	SYM
m-1112	2734	5	b	b	X
m-1112	2734	6	..	..	PUNCT
m-1112	2734	7	in	in	ADP
m-1112	2734	8	mechanics	mechanic	NOUN
m-1112	2734	9	an	an	DET
m-1112	2734	10	energy	energy	NOUN
m-1112	2734	11	-	-	PUNCT
m-1112	2734	12	vector	vector	NOUN
m-1112	2734	13	is	be	AUX
m-1112	2734	14	an	an	DET
m-1112	2734	15	conductor	conductor	NOUN
m-1112	2734	16	aka	aka	ADV
m-1112	2734	17	⃗⃗	⃗⃗	PROPN
m-1112	2734	18	⃗⃗	⃗⃗	PROPN
m-1112	2734	19	⃗⃗	⃗⃗	PROPN
m-1112	2734	20	⃗⃗	⃗⃗	PROPN
m-1112	2735	1	=	=	PUNCT
m-1112	2735	2	|q⃗⃗	|q⃗⃗	PROPN
m-1112	2736	1	|	|	ADV
m-1112	2736	2			PROPN
m-1112	2736	3	,	,	PUNCT
m-1112	2736	4	and	and	CCONJ
m-1112	2736	5	is	be	AUX
m-1112	2736	6	the	the	DET
m-1112	2736	7	quaternion	quaternion	NOUN
m-1112	2736	8	in	in	ADP
m-1112	2736	9	material	material	NOUN
m-1112	2736	10	-	-	PUNCT
m-1112	2736	11	geometry	geometry	NOUN
m-1112	2736	12	where	where	SCONJ
m-1112	2736	13	zero	zero	NUM
m-1112	2736	14	-	-	PUNCT
m-1112	2736	15	point	point	NOUN
m-1112	2736	16	0	0	NUM
m-1112	2736	17	≡	≡	PROPN
m-1112	2736	18			PROPN
m-1112	2736	19	≡	≡	PROPN
m-1112	2736	20	{	{	PUNCT
m-1112	2736	21	⊕+⊝}on	⊕+⊝}on	NOUN
m-1112	2736	22	where	where	SCONJ
m-1112	2736	23	motion	motion	NOUN
m-1112	2736	24	|q⃗⃗	|q⃗⃗	ADV
m-1112	2736	25	|	|	ADV
m-1112	2736	26	≡	≡	VERB
m-1112	2736	27	�	�	NOUN
m-1112	2736	28	̅	̅	NOUN
m-1112	2736	29	�	�	NOUN
m-1112	2736	30	𝐱	𝐱	PROPN
m-1112	2736	31	as	as	ADP
m-1112	2736	32	an	an	DET
m-1112	2736	33	electric	electric	ADJ
m-1112	2736	34	field	field	NOUN
m-1112	2736	35	on	on	ADP
m-1112	2736	36	aka	aka	ADV
m-1112	2736	37	axis	axis	NOUN
m-1112	2736	38	and	and	CCONJ
m-1112	2736	39	as	as	ADP
m-1112	2736	40	q⃗⃗	q⃗⃗	ADJ
m-1112	2736	41	|	|	ADV
m-1112	2736	42			PROPN
m-1112	2736	43	≡	≡	PROPN
m-1112	2736	44	�	�	PROPN
m-1112	2736	45	̅	̅	NOUN
m-1112	2736	46	�	�	PROPN
m-1112	2736	47	𝐲	𝐲	ADP
m-1112	2736	48	≡	≡	PROPN
m-1112	2736	49	magnetic	magnetic	ADJ
m-1112	2736	50	field	field	NOUN
m-1112	2736	51	⊥	⊥	PROPN
m-1112	2736	52	aka	aka	ADV
m-1112	2736	53	,	,	PUNCT
m-1112	2736	54	is	be	AUX
m-1112	2736	55	transferred	transfer	VERB
m-1112	2736	56	from	from	ADP
m-1112	2736	57	one	one	NUM
m-1112	2736	58	edge	edge	NOUN
m-1112	2736	59	point	point	NOUN
m-1112	2736	60	a	a	PRON
m-1112	2736	61	,	,	PUNCT
m-1112	2736	62	to	to	ADP
m-1112	2736	63	the	the	DET
m-1112	2736	64	other	other	ADJ
m-1112	2736	65	edge	edge	NOUN
m-1112	2736	66	point	point	NOUN
m-1112	2736	67	k	k	PROPN
m-1112	2736	68	a	a	PRON
m-1112	2736	69	as	as	ADP
m-1112	2736	70	→	→	SYM
m-1112	2736	71	�	�	NOUN
m-1112	2736	72	̅	̅	NOUN
m-1112	2736	73	�	�	PROPN
m-1112	2736	74	,	,	PUNCT
m-1112	2736	75	�	�	PROPN
m-1112	2736	76	̅	̅	NOUN
m-1112	2736	77	�	�	PROPN
m-1112	2736	78	𝐱	𝐱	PROPN
m-1112	2736	79	,	,	PUNCT
m-1112	2736	80	�	�	PROPN
m-1112	2736	81	̅	̅	NOUN
m-1112	2736	82	�	�	PROPN
m-1112	2736	83	𝐲	𝐲	ADP
m-1112	2736	84	←	←	PROPN
m-1112	2736	85	[	[	X
m-1112	2736	86	𝐄	𝐄	PROPN
m-1112	2736	87	𝟐	𝟐	NUM
m-1112	2736	88	]	]	SYM
m-1112	2736	89	c	c	X
m-1112	2736	90	..	..	PUNCT
m-1112	2736	91	energy	energy	NOUN
m-1112	2736	92	is	be	AUX
m-1112	2736	93	the	the	DET
m-1112	2736	94	work	work	NOUN
m-1112	2736	95	,	,	PUNCT
m-1112	2736	96	the	the	DET
m-1112	2736	97	motion	motion	NOUN
m-1112	2736	98	,	,	PUNCT
m-1112	2736	99	produced	produce	VERB
m-1112	2736	100	in	in	ADP
m-1112	2736	101	energy	energy	NOUN
m-1112	2736	102	-	-	PUNCT
m-1112	2736	103	monads	monad	NOUN
m-1112	2736	104	and	and	CCONJ
m-1112	2736	105	for	for	ADP
m-1112	2736	106	photon	photon	NOUN
m-1112	2736	107	is	be	AUX
m-1112	2736	108	equal	equal	ADJ
m-1112	2736	109	to	to	ADP
m-1112	2736	110	w	w	NOUN
m-1112	2736	111	=	=	PUNCT
m-1112	2736	112	2l	2l	NOUN
m-1112	2736	113	=	=	SYM
m-1112	2736	114	b̅	b̅	PROPN
m-1112	2736	115	.	.	PUNCT
m-1112	2736	116	w̅	w̅	X
m-1112	2737	1	=	=	PUNCT
m-1112	2738	1	r	r	NOUN
m-1112	2738	2	m	m	VERB
m-1112	2738	3	v	v	NOUN
m-1112	2738	4	=	=	X
m-1112	2739	1	[	[	X
m-1112	2739	2	r.	r.	NOUN
m-1112	2739	3	p	p	X
m-1112	2739	4	]	]	X
m-1112	2739	5	=	=	SYM
m-1112	2739	6	j	j	PROPN
m-1112	2739	7	w²	w²	PROPN
m-1112	2739	8	≡	≡	PROPN
m-1112	2739	9	[	[	PUNCT
m-1112	2739	10	�	�	NOUN
m-1112	2739	11	̅	̅	NOUN
m-1112	2739	12	�	�	PROPN
m-1112	2739	13	𝐱	𝐱	PROPN
m-1112	2739	14	⊥	⊥	PROPN
m-1112	2739	15	�	�	PROPN
m-1112	2739	16	̅	̅	NOUN
m-1112	2739	17	�	�	NOUN
m-1112	2739	18	𝐲	𝐲	ADP
m-1112	2739	19	]	]	PUNCT
m-1112	2739	20	where	where	SCONJ
m-1112	2739	21	�	�	PROPN
m-1112	2739	22	̅	̅	VERB
m-1112	2739	23	�	�	PROPN
m-1112	2739	24	𝐱	𝐱	PROPN
m-1112	2739	25	=	=	PUNCT
m-1112	2739	26	�	�	PROPN
m-1112	2739	27	̅	̅	NOUN
m-1112	2739	28	�	�	PROPN
m-1112	2739	29	𝐲	𝐲	ADP
m-1112	2739	30	,	,	PUNCT
m-1112	2739	31	in	in	ADP
m-1112	2739	32	the	the	DET
m-1112	2739	33	conductor	conductor	NOUN
m-1112	2739	34	aka	aka	ADV
m-1112	2739	35	⃗⃗	⃗⃗	PROPN
m-1112	2739	36	⃗⃗	⃗⃗	PROPN
m-1112	2739	37	⃗⃗	⃗⃗	PROPN
m-1112	2739	38	⃗⃗	⃗⃗	PROPN
m-1112	2739	39	=	=	SYM
m-1112	2739	40	2.r	2.r	NUM
m-1112	2739	41	≡	≡	PROPN
m-1112	2739	42	λ	λ	PROPN
m-1112	2739	43	where	where	SCONJ
m-1112	2739	44	,	,	PUNCT
m-1112	2739	45	λ	λ	PROPN
m-1112	2739	46	is	be	AUX
m-1112	2739	47	-the	-the	DET
m-1112	2739	48	-wavelength	-wavelength	NOUN
m-1112	2739	49	and	and	CCONJ
m-1112	2739	50	p	p	NOUN
m-1112	2739	51	=	=	NOUN
m-1112	2739	52	m	m	NOUN
m-1112	2739	53	c	c	NOUN
m-1112	2739	54	=	=	PUNCT
m-1112	2739	55	the	the	DET
m-1112	2739	56	momentum	momentum	NOUN
m-1112	2739	57	.	.	PUNCT
m-1112	2740	1	[	[	X
m-1112	2740	2	𝐄	𝐄	NOUN
m-1112	2740	3	𝟑	𝟑	X
m-1112	2740	4	]	]	X
m-1112	2740	5	d	d	X
m-1112	2740	6	..	..	PUNCT
m-1112	2740	7	it	it	PRON
m-1112	2740	8	was	be	AUX
m-1112	2740	9	prooved	proove	VERB
m-1112	2740	10	that	that	SCONJ
m-1112	2740	11	→	→	PUNCT
m-1112	2740	12	any	any	DET
m-1112	2740	13	diameter	diameter	NOUN
m-1112	2740	14	d	d	NOUN
m-1112	2740	15	of	of	ADP
m-1112	2740	16	a	a	DET
m-1112	2740	17	circle	circle	NOUN
m-1112	2740	18	in	in	ADP
m-1112	2740	19	the	the	DET
m-1112	2740	20	stpl	stpl	PROPN
m-1112	2740	21	–	–	PUNCT
m-1112	2740	22	circuit	circuit	NOUN
m-1112	2740	23	,	,	PUNCT
m-1112	2740	24	the	the	DET
m-1112	2740	25	three	three	NUM
m-1112	2740	26	–	–	PUNCT
m-1112	2740	27	poles	pole	NOUN
m-1112	2740	28	–	–	PUNCT
m-1112	2740	29	squares	square	NOUN
m-1112	2740	30	-	-	PUNCT
m-1112	2740	31	rotational	rotational	ADJ
m-1112	2740	32	system	system	NOUN
m-1112	2740	33	is	be	AUX
m-1112	2740	34	an	an	DET
m-1112	2740	35	conductor	conductor	NOUN
m-1112	2740	36	where	where	SCONJ
m-1112	2740	37	d	d	NOUN
m-1112	2740	38	=	=	SYM
m-1112	2740	39	aka	aka	ADP
m-1112	2740	40	⃗⃗	⃗⃗	PROPN
m-1112	2740	41	⃗⃗	⃗⃗	PROPN
m-1112	2740	42	⃗⃗	⃗⃗	PROPN
m-1112	2740	43	⃗⃗	⃗⃗	PROPN
m-1112	2741	1	=	=	PUNCT
m-1112	2741	2	|q⃗⃗	|q⃗⃗	PROPN
m-1112	2742	1	|	|	ADV
m-1112	2742	2			PROPN
m-1112	2742	3	=	=	PUNCT
m-1112	2742	4	|	|	ADV
m-1112	2742	5	𝐜.	𝐜.	NOUN
m-1112	2742	6	�	�	PROPN
m-1112	2742	7	̅	̅	NOUN
m-1112	2742	8	�	�	PROPN
m-1112	2742	9	𝐫	𝐫	ADP
m-1112	2742	10	²	²	NUM
m-1112	2742	11	|	|	NOUN
m-1112	2742	12	=	=	SYM
m-1112	2742	13	𝐈𝐄	𝐈𝐄	PROPN
m-1112	2742	14	the	the	DET
m-1112	2742	15	electric	electric	ADJ
m-1112	2742	16	-	-	PUNCT
m-1112	2742	17	wave	wave	NOUN
m-1112	2742	18	-	-	PUNCT
m-1112	2742	19	intensity	intensity	NOUN
m-1112	2742	20	,	,	PUNCT
m-1112	2742	21	and	and	CCONJ
m-1112	2742	22	a	a	DET
m-1112	2742	23	↑	↑	PROPN
m-1112	2742	24	ka	ka	PROPN
m-1112	2742	25	⃗⃗	⃗⃗	PROPN
m-1112	2742	26	⃗⃗	⃗⃗	PROPN
m-1112	2742	27	⃗⃗	⃗⃗	PROPN
m-1112	2742	28	⃗⃗	⃗⃗	PROPN
m-1112	2742	29	⃗⃗	⃗⃗	PROPN
m-1112	2742	30	⃗⃗	⃗⃗	PROPN
m-1112	2742	31	⃗	⃗	PROPN
m-1112	2742	32	≡	≡	PROPN
m-1112	2742	33	𝐈𝐌	𝐈𝐌	PROPN
m-1112	2742	34	is	be	AUX
m-1112	2742	35	the	the	DET
m-1112	2742	36	magnetic	magnetic	ADJ
m-1112	2742	37	–	–	PUNCT
m-1112	2742	38	wave	wave	NOUN
m-1112	2742	39	intensity	intensity	NOUN
m-1112	2742	40	.	.	PUNCT
m-1112	2743	1	their	their	PRON
m-1112	2743	2	square	square	ADJ
m-1112	2743	3	-vectors	-vector	NOUN
m-1112	2743	4	–	–	PUNCT
m-1112	2743	5	area	area	NOUN
m-1112	2743	6	=	=	PUNCT
m-1112	2743	7	[	[	PUNCT
m-1112	2743	8	aka	aka	ADV
m-1112	2743	9	⃗⃗	⃗⃗	PROPN
m-1112	2743	10	⃗⃗	⃗⃗	PROPN
m-1112	2743	11	⃗⃗	⃗⃗	PROPN
m-1112	2743	12	⃗⃗	⃗⃗	PROPN
m-1112	2743	13	⃗⃗	⃗⃗	PROPN
m-1112	2743	14	]	]	X
m-1112	2743	15	x[a	x[a	PROPN
m-1112	2743	16	↑	↑	PROPN
m-1112	2743	17	ka	ka	PROPN
m-1112	2743	18	⃗⃗	⃗⃗	PROPN
m-1112	2743	19	⃗⃗	⃗⃗	PROPN
m-1112	2743	20	⃗⃗	⃗⃗	PROPN
m-1112	2743	21	⃗⃗	⃗⃗	PROPN
m-1112	2743	22	⃗⃗	⃗⃗	PROPN
m-1112	2743	23	⃗⃗	⃗⃗	PROPN
m-1112	2743	24	⃗	⃗	PROPN
m-1112	2743	25	]	]	PUNCT
m-1112	2744	1	=	=	PUNCT
m-1112	2744	2	[	[	PUNCT
m-1112	2744	3	�	�	NOUN
m-1112	2744	4	̅	̅	NOUN
m-1112	2744	5	�	�	PROPN
m-1112	2744	6	𝐱	𝐱	PROPN
m-1112	2744	7	�	�	PROPN
m-1112	2744	8	̅	̅	NOUN
m-1112	2744	9	�	�	NOUN
m-1112	2744	10	𝐲	𝐲	ADP
m-1112	2744	11	]	]	PUNCT
m-1112	2744	12	=	=	PUNCT
m-1112	2744	13	the	the	DET
m-1112	2744	14	energy	energy	NOUN
m-1112	2744	15	square	square	PROPN
m-1112	2744	16	≡	≡	PROPN
m-1112	2744	17	cm	cm	NOUN
m-1112	2744	18	x	x	SYM
m-1112	2744	19	cm	cm	NOUN
m-1112	2744	20	=	=	SYM
m-1112	2744	21	cmnh	cmnh	NOUN
m-1112	2744	22	square	square	NOUN
m-1112	2744	23	=	=	PUNCT
m-1112	2744	24	on	on	ADP
m-1112	2744	25	circle	circle	NOUN
m-1112	2744	26	(	(	PUNCT
m-1112	2744	27	e	e	NOUN
m-1112	2744	28	,	,	PUNCT
m-1112	2744	29	ea	ea	PROPN
m-1112	2744	30	)	)	PUNCT
m-1112	2744	31	,	,	PUNCT
m-1112	2744	32	and	and	CCONJ
m-1112	2744	33	from	from	ADP
m-1112	2744	34	relation	relation	NOUN
m-1112	2744	35	�	�	PROPN
m-1112	2744	36	̅	̅	NOUN
m-1112	2744	37	�	�	NOUN
m-1112	2744	38	=	=	SYM
m-1112	2744	39	σ	σ	PROPN
m-1112	2744	40	.	.	PUNCT
m-1112	2745	1	φ	φ	PROPN
m-1112	2745	2	=	=	X
m-1112	2746	1	f	f	PROPN
m-1112	2746	2	a	a	DET
m-1112	2746	3	φ	φ	PROPN
m-1112	2746	4	area	area	NOUN
m-1112	2746	5	a	a	PRON
m-1112	2746	6	=	=	X
m-1112	2746	7	f	f	PROPN
m-1112	2746	8	/	/	SYM
m-1112	2746	9	σ	σ	PROPN
m-1112	2746	10	=	=	PUNCT
m-1112	2746	11	|cm|²	|cm|²	PUNCT
m-1112	2746	12	/	/	SYM
m-1112	2746	13	σ	σ	PROPN
m-1112	2746	14	,	,	PUNCT
m-1112	2746	15	i.e.	i.e.	X
m-1112	2746	16	plane	plane	NOUN
m-1112	2746	17	-	-	PUNCT
m-1112	2746	18	force	force	NOUN
m-1112	2746	19	f	f	NOUN
m-1112	2746	20	=	=	SYM
m-1112	2746	21	σ	σ	PROPN
m-1112	2746	22	.	.	PUNCT
m-1112	2746	23	|cm|²	|cm|²	PUNCT
m-1112	2746	24	,	,	PUNCT
m-1112	2746	25	and	and	CCONJ
m-1112	2746	26	in	in	ADP
m-1112	2746	27	space	space	NOUN
m-1112	2746	28	volume	volume	NOUN
m-1112	2746	29	-	-	PUNCT
m-1112	2746	30	force	force	NOUN
m-1112	2746	31	f	f	NOUN
m-1112	2746	32	=	=	SYM
m-1112	2746	33	σ	σ	PROPN
m-1112	2746	34	.	.	PUNCT
m-1112	2747	1	|cm|	|cm|	PROPN
m-1112	2747	2	³	³	X
m-1112	2747	3	≡	≡	PROPN
m-1112	2747	4	[	[	X
m-1112	2747	5	𝐄	𝐄	PROPN
m-1112	2747	6	𝟒	𝟒	NUM
m-1112	2747	7	]	]	PUNCT
m-1112	2747	8	or	or	CCONJ
m-1112	2747	9	[	[	PUNCT
m-1112	2747	10	aka	aka	ADV
m-1112	2747	11	⃗⃗	⃗⃗	PROPN
m-1112	2747	12	⃗⃗	⃗⃗	PROPN
m-1112	2747	13	⃗⃗	⃗⃗	PROPN
m-1112	2747	14	⃗⃗	⃗⃗	PROPN
m-1112	2747	15	⃗⃗	⃗⃗	PROPN
m-1112	2747	16	]	]	X
m-1112	2747	17	x[a	x[a	PROPN
m-1112	2747	18	↑	↑	PROPN
m-1112	2747	19	ka	ka	PROPN
m-1112	2747	20	⃗⃗	⃗⃗	PROPN
m-1112	2747	21	⃗⃗	⃗⃗	PROPN
m-1112	2747	22	⃗⃗	⃗⃗	PROPN
m-1112	2747	23	⃗⃗	⃗⃗	PROPN
m-1112	2747	24	⃗⃗	⃗⃗	PROPN
m-1112	2747	25	⃗⃗	⃗⃗	PROPN
m-1112	2747	26	⃗	⃗	PROPN
m-1112	2747	27	]	]	X
m-1112	2747	28	x[d	x[d	X
m-1112	2747	29	]	]	X
m-1112	2747	30	=	=	SYM
m-1112	2747	31	cmnh	cmnh	NOUN
m-1112	2747	32	x	x	PUNCT
m-1112	2747	33	𝐐	𝐐	PROPN
m-1112	2747	34	⤱	⤱	VERB
m-1112	2747	35	⇉	⇉	PROPN
m-1112	2747	36	⃗⃗	⃗⃗	PROPN
m-1112	2747	37	⃗⃗	⃗⃗	PROPN
m-1112	2747	38	⃗⃗	⃗⃗	PROPN
m-1112	2747	39	⃗⃗	⃗⃗	PROPN
m-1112	2747	40	⃗⃗	⃗⃗	PROPN
m-1112	2747	41	⃗⃗	⃗⃗	PROPN
m-1112	2747	42	⃗	⃗	PROPN
m-1112	2747	43	=	=	SYM
m-1112	2747	44	cmnh	cmnh	PROPN
m-1112	2747	45	x	x	SYM
m-1112	2747	46	�	�	PROPN
m-1112	2747	47	̅	̅	NOUN
m-1112	2747	48	�	�	NOUN
m-1112	2747	49	⤱	⤱	NOUN
m-1112	2747	50	⇉	⇉	PROPN
m-1112	2747	51	,	,	PUNCT
m-1112	2747	52	where	where	SCONJ
m-1112	2747	53	|𝐐	|𝐐	X
m-1112	2747	54	⤱	⤱	PROPN
m-1112	2747	55	⇉	⇉	PROPN
m-1112	2747	56	⃗⃗⃗⃗	⃗⃗⃗⃗	PUNCT
m-1112	2748	1	⃗⃗	⃗⃗	PROPN
m-1112	2748	2	⃗⃗	⃗⃗	PROPN
m-1112	2748	3	⃗⃗	⃗⃗	PROPN
m-1112	2748	4	⃗⃗	⃗⃗	PROPN
m-1112	2748	5	|	|	PROPN
m-1112	2748	6	≡	≡	PROPN
m-1112	2748	7	�	�	PROPN
m-1112	2748	8	⃗⃗	⃗⃗	PROPN
m-1112	2748	9	�	�	PROPN
m-1112	2748	10	,	,	PUNCT
m-1112	2748	11	which	which	PRON
m-1112	2748	12	is	be	AUX
m-1112	2748	13	the	the	DET
m-1112	2748	14	energy	energy	NOUN
m-1112	2748	15	-	-	PUNCT
m-1112	2748	16	quantum	quantum	NOUN
m-1112	2748	17	in	in	ADP
m-1112	2748	18	the	the	DET
m-1112	2748	19	propagating	propagate	VERB
m-1112	2748	20	electromagnetic	electromagnetic	ADJ
m-1112	2748	21	wave	wave	NOUN
m-1112	2748	22	where	where	SCONJ
m-1112	2748	23	|	|	ADV
m-1112	2748	24	𝐈𝐄	𝐈𝐄	PROPN
m-1112	2748	25	⊥	⊥	PROPN
m-1112	2748	26	𝐈𝐌	𝐈𝐌	PROPN
m-1112	2748	27	|	|	ADV
m-1112	2748	28	.	.	PUNCT
m-1112	2749	1	since	since	SCONJ
m-1112	2749	2	motions	motion	NOUN
m-1112	2749	3	b̅xw̅	b̅xw̅	PROPN
m-1112	2749	4	,	,	PUNCT
m-1112	2749	5	are	be	AUX
m-1112	2749	6	constants	constant	NOUN
m-1112	2749	7	from	from	ADP
m-1112	2749	8	(	(	PUNCT
m-1112	2749	9	b	b	NOUN
m-1112	2749	10	)	)	PUNCT
m-1112	2749	11	and	and	CCONJ
m-1112	2749	12	from	from	ADP
m-1112	2749	13	poinsot`s	poinsot`s	NOUN
m-1112	2749	14	solution	solution	NOUN
m-1112	2749	15	w1²	w1²	NOUN
m-1112	2749	16	+	+	CCONJ
m-1112	2749	17	j2	j2	PROPN
m-1112	2749	18	w2²	w2²	NOUN
m-1112	2749	19	=	=	SYM
m-1112	2749	20	a²	a²	NOUN
m-1112	2749	21	,	,	PUNCT
m-1112	2749	22	then	then	ADV
m-1112	2749	23	angular	angular	ADJ
m-1112	2749	24	velocity	velocity	NOUN
m-1112	2749	25	-	-	PUNCT
m-1112	2749	26	ellipsoid	ellipsoid	NOUN
m-1112	2749	27	polar	polar	ADJ
m-1112	2749	28	-	-	PUNCT
m-1112	2749	29	paths	path	NOUN
m-1112	2749	30	are	be	AUX
m-1112	2749	31	the	the	DET
m-1112	2749	32	parallel	parallel	ADJ
m-1112	2749	33	circles	circle	NOUN
m-1112	2749	34	and	and	CCONJ
m-1112	2749	35	perpendicular	perpendicular	NOUN
m-1112	2749	36	to	to	ADP
m-1112	2749	37	the	the	DET
m-1112	2749	38	angular	angular	ADJ
m-1112	2749	39	-	-	PUNCT
m-1112	2749	40	momentum	momentum	NOUN
m-1112	2749	41	ellipsoid	ellipsoid	NOUN
m-1112	2749	42	nibs	nibs	NOUN
m-1112	2749	43	..	..	PUNCT
m-1112	2750	1	[	[	X
m-1112	2750	2	𝐄	𝐄	NOUN
m-1112	2750	3	𝟓	𝟓	NUM
m-1112	2750	4	]	]	PUNCT
m-1112	2750	5	,	,	PUNCT
m-1112	2750	6	[	[	X
m-1112	2750	7	70	70	NUM
m-1112	2750	8	]	]	X
m-1112	2750	9	e	e	X
m-1112	2750	10	..	..	PUNCT
m-1112	2750	11	when	when	SCONJ
m-1112	2750	12	is	be	AUX
m-1112	2750	13	found	find	VERB
m-1112	2750	14	an	an	DET
m-1112	2750	15	obstacle	obstacle	NOUN
m-1112	2750	16	at	at	ADP
m-1112	2750	17	point	point	NOUN
m-1112	2750	18	𝐊𝐀	𝐊𝐀	INTJ
m-1112	2750	19	,	,	PUNCT
m-1112	2750	20	then	then	ADV
m-1112	2750	21	the	the	DET
m-1112	2750	22	particles	particle	NOUN
m-1112	2750	23	of	of	ADP
m-1112	2750	24	conductor	conductor	NOUN
m-1112	2750	25	medium	medium	NOUN
m-1112	2750	26	oscillate	oscillate	NOUN
m-1112	2750	27	perpendicular	perpendicular	NOUN
m-1112	2750	28	.	.	PUNCT
m-1112	2751	1	this	this	DET
m-1112	2751	2	obstacle	obstacle	NOUN
m-1112	2751	3	at	at	ADP
m-1112	2751	4	ka	ka	PROPN
m-1112	2751	5	point	point	PROPN
m-1112	2751	6	,	,	PUNCT
m-1112	2751	7	is	be	AUX
m-1112	2751	8	the	the	DET
m-1112	2751	9	presentation	presentation	NOUN
m-1112	2751	10	of	of	ADP
m-1112	2751	11	the	the	DET
m-1112	2751	12	,	,	PUNCT
m-1112	2751	13	⊕	⊕	NOUN
m-1112	2751	14	constituent	constituent	NOUN
m-1112	2751	15	and	and	CCONJ
m-1112	2751	16	the	the	DET
m-1112	2751	17	absent	absent	NOUN
m-1112	2751	18	of	of	ADP
m-1112	2751	19	⊝	⊝	NUM
m-1112	2751	20	constituent	constituent	NOUN
m-1112	2751	21	and	and	CCONJ
m-1112	2751	22	so	so	ADV
m-1112	2751	23			PROPN
m-1112	2751	24	,	,	PUNCT
m-1112	2751	25	transversepropagating	transversepropagate	VERB
m-1112	2751	26	-	-	PUNCT
m-1112	2751	27	wave	wave	NOUN
m-1112	2751	28	,	,	PUNCT
m-1112	2751	29	or	or	CCONJ
m-1112	2751	30	moving	move	VERB
m-1112	2751	31	energy	energy	NOUN
m-1112	2751	32	-	-	PUNCT
m-1112	2751	33	vector	vector	NOUN
m-1112	2751	34	|⊕	|⊕	PROPN
m-1112	2751	35	𝐐	𝐐	PROPN
m-1112	2751	36	⇈	⇈	PROPN
m-1112	2751	37	aka⃗⃗	aka⃗⃗	PROPN
m-1112	2751	38	⃗⃗	⃗⃗	PROPN
m-1112	2751	39	⃗⃗	⃗⃗	PROPN
m-1112	2751	40	⃗⃗	⃗⃗	PROPN
m-1112	2751	41	⃗	⃗	PROPN
m-1112	2751	42	|=|	|=|	PROPN
m-1112	2751	43	↕	↕	PROPN
m-1112	2751	44	|	|	NOUN
m-1112	2751	45	at	at	ADP
m-1112	2751	46	node	node	PROPN
m-1112	2751	47	ka	ka	PROPN
m-1112	2751	48	is	be	AUX
m-1112	2751	49	equal	equal	ADJ
m-1112	2751	50	to	to	ADP
m-1112	2751	51	e	e	NOUN
m-1112	2751	52	-	-	NOUN
m-1112	2751	53	vector|	vector|	NOUN
m-1112	2751	54	⊕	⊕	PROPN
m-1112	2751	55	𝐐	𝐐	PROPN
m-1112	2751	56	⇉	⇉	PROPN
m-1112	2752	1	aka⃗⃗	aka⃗⃗	PROPN
m-1112	2752	2	⃗⃗	⃗⃗	PROPN
m-1112	2752	3	⃗⃗	⃗⃗	PROPN
m-1112	2752	4	⃗⃗	⃗⃗	PROPN
m-1112	2752	5	⃗	⃗	PROPN
m-1112	2752	6	|≡	|≡	ADP
m-1112	2752	7	|↔|	|↔|	PROPN
m-1112	2752	8	at	at	ADP
m-1112	2752	9	node	node	PROPN
m-1112	2752	10	a	a	PRON
m-1112	2752	11	,	,	PUNCT
m-1112	2752	12	and	and	CCONJ
m-1112	2752	13	energy	energy	NOUN
m-1112	2752	14	volume	volume	NOUN
m-1112	2752	15	is	be	AUX
m-1112	2752	16	doubled	double	VERB
m-1112	2752	17	as	as	ADP
m-1112	2752	18	,	,	PUNCT
m-1112	2752	19	2l	2l	NUM
m-1112	2752	20	=	=	SYM
m-1112	2752	21	b̅	b̅	PROPN
m-1112	2752	22	.w̅	.w̅	PUNCT
m-1112	2752	23	,	,	PUNCT
m-1112	2752	24	in	in	ADP
m-1112	2752	25	kaa⃐⃗⃗⃗	kaa⃐⃗⃗⃗	PROPN
m-1112	2752	26	⃗⃗	⃗⃗	PROPN
m-1112	2752	27	⃗⃗⃗	⃗⃗⃗	PROPN
m-1112	2752	28	conductor	conductor	NOUN
m-1112	2752	29	meaning	mean	VERB
m-1112	2752	30	that	that	SCONJ
m-1112	2752	31	the	the	DET
m-1112	2752	32	meter	meter	NOUN
m-1112	2752	33	of	of	ADP
m-1112	2752	34	volume	volume	NOUN
m-1112	2752	35	is	be	AUX
m-1112	2752	36	the	the	DET
m-1112	2752	37	duplication	duplication	NOUN
m-1112	2752	38	of	of	ADP
m-1112	2752	39	total	total	ADJ
m-1112	2752	40	energy	energy	NOUN
m-1112	2752	41	l	l	NOUN
m-1112	2752	42	.the	.the	PRON
m-1112	2753	1	reaction	reaction	NOUN
m-1112	2753	2	to	to	ADP
m-1112	2753	3	the	the	DET
m-1112	2753	4	motion	motion	NOUN
m-1112	2753	5	of	of	ADP
m-1112	2753	6	squares	square	NOUN
m-1112	2753	7	{	{	PUNCT
m-1112	2753	8	|qx	|qx	X
m-1112	2753	9	=	=	PROPN
m-1112	2753	10	co	co	NOUN
m-1112	2753	11	⇉	⇉	NOUN
m-1112	2753	12	|	|	PROPN
m-1112	2753	13	x|qy=	x|qy=	PROPN
m-1112	2753	14	cb	cb	PROPN
m-1112	2753	15	⇈	⇈	PROPN
m-1112	2753	16	|	|	PRON
m-1112	2753	17	}	}	PUNCT
m-1112	2753	18	≡	≡	PROPN
m-1112	2753	19	|𝐐	|𝐐	NOUN
m-1112	2753	20	⤱	⤱	PROPN
m-1112	2753	21	⇉	⇉	PROPN
m-1112	2753	22	⃗⃗⃗⃗	⃗⃗⃗⃗	PUNCT
m-1112	2754	1	⃗⃗	⃗⃗	PROPN
m-1112	2754	2	⃗⃗	⃗⃗	PROPN
m-1112	2754	3	⃗⃗	⃗⃗	PROPN
m-1112	2754	4	⃗⃗	⃗⃗	PROPN
m-1112	2754	5	|	|	PROPN
m-1112	2754	6	≡	≡	PROPN
m-1112	2754	7	[	[	PUNCT
m-1112	2754	8	𝐜𝐒	𝐜𝐒	ADJ
m-1112	2754	9	𝐫²	𝐫²	NOUN
m-1112	2754	10	]	]	PUNCT
m-1112	2754	11	.|𝐐	.|𝐐	PUNCT
m-1112	2755	1	⇉	⇉	PROPN
m-1112	2755	2	⃗⃗⃗⃗⃗⃗	⃗⃗⃗⃗⃗⃗	X
m-1112	2756	1	⃗⃗	⃗⃗	PROPN
m-1112	2756	2	|	|	ADV
m-1112	2756	3	is	be	AUX
m-1112	2756	4	equal	equal	ADJ
m-1112	2756	5	to	to	ADP
m-1112	2756	6	quantum	quantum	PROPN
m-1112	2756	7	�	�	PROPN
m-1112	2756	8	⃗⃗	⃗⃗	PROPN
m-1112	2756	9	�	�	PROPN
m-1112	2756	10	.	.	PUNCT
m-1112	2757	1	[	[	X
m-1112	2757	2	𝐄	𝐄	NOUN
m-1112	2757	3	𝟔	𝟔	NUM
m-1112	2757	4	]	]	SYM
m-1112	2757	5	f	f	X
m-1112	2757	6	..	..	PUNCT
m-1112	2757	7	any	any	DET
m-1112	2757	8	two	two	NUM
m-1112	2757	9	perpendicular	perpendicular	ADJ
m-1112	2757	10	energy	energy	NOUN
m-1112	2757	11	-	-	PUNCT
m-1112	2757	12	vectors	vector	NOUN
m-1112	2757	13	,	,	PUNCT
m-1112	2757	14	|𝐐	|𝐐	VERB
m-1112	2757	15	⇉	⇉	PROPN
m-1112	2758	1	aka⃗⃗	aka⃗⃗	PROPN
m-1112	2758	2	⃗⃗	⃗⃗	PROPN
m-1112	2758	3	⃗⃗	⃗⃗	PROPN
m-1112	2758	4	⃗⃗	⃗⃗	PROPN
m-1112	2758	5	⃗	⃗	PROPN
m-1112	2758	6	=	=	SYM
m-1112	2758	7	↔	↔	PROPN
m-1112	2758	8	|	|	ADV
m-1112	2758	9	,	,	PUNCT
m-1112	2758	10	|𝐐	|𝐐	PROPN
m-1112	2758	11	⇈	⇈	NUM
m-1112	2758	12	aka⃗⃗	aka⃗⃗	PROPN
m-1112	2758	13	⃗⃗	⃗⃗	PROPN
m-1112	2758	14	⃗⃗	⃗⃗	PROPN
m-1112	2758	15	⃗⃗	⃗⃗	PROPN
m-1112	2758	16	⃗	⃗	PROPN
m-1112	2758	17	=	=	SYM
m-1112	2758	18	↕	↕	PROPN
m-1112	2759	1	|	|	ADV
m-1112	2759	2	of	of	ADP
m-1112	2759	3	this	this	DET
m-1112	2759	4	propagating	propagate	VERB
m-1112	2759	5	energy	energy	NOUN
m-1112	2759	6	,	,	PUNCT
m-1112	2760	1	form	form	VERB
m-1112	2760	2	the	the	DET
m-1112	2760	3	energy	energy	NOUN
m-1112	2760	4	-	-	PUNCT
m-1112	2760	5	square	square	NOUN
m-1112	2760	6	,	,	PUNCT
m-1112	2760	7	|↔|.|	|↔|.|	NUM
m-1112	2760	8	↕	↕	PROPN
m-1112	2760	9	|≡|𝐐	|≡|𝐐	NUM
m-1112	2760	10	⇉	⇉	PROPN
m-1112	2760	11	|.|	|.|	NOUN
m-1112	2760	12	𝐐	𝐐	PROPN
m-1112	2760	13	⇈	⇈	PROPN
m-1112	2760	14	|	|	ADV
m-1112	2760	15	≡	≡	PROPN
m-1112	2760	16	q0	q0	PROPN
m-1112	2760	17	,	,	PUNCT
m-1112	2760	18	on	on	ADP
m-1112	2760	19	conductor	conductor	NOUN
m-1112	2760	20	aka	aka	ADV
m-1112	2760	21	and	and	CCONJ
m-1112	2760	22	then	then	ADV
m-1112	2760	23	energy	energy	NOUN
m-1112	2760	24	-	-	PUNCT
m-1112	2760	25	circular	circular	ADJ
m-1112	2760	26	-	-	PUNCT
m-1112	2760	27	prism	prism	NOUN
m-1112	2760	28	=	=	PROPN
m-1112	2760	29	|aka|	|aka|	PROPN
m-1112	2760	30	.{𝐐	.{𝐐	PUNCT
m-1112	2761	1	⇉	⇉	X
m-1112	2761	2	aka⃗⃗	aka⃗⃗	PROPN
m-1112	2761	3	⃗⃗	⃗⃗	PROPN
m-1112	2761	4	⃗⃗	⃗⃗	PROPN
m-1112	2761	5	⃗⃗	⃗⃗	PROPN
m-1112	2761	6	⃗	⃗	PROPN
m-1112	2761	7	}	}	PUNCT
m-1112	2761	8	.	.	PUNCT
m-1112	2761	9	{	{	PUNCT
m-1112	2762	1	𝐐	𝐐	PROPN
m-1112	2762	2	⇈	⇈	PROPN
m-1112	2762	3	aka⃗⃗	aka⃗⃗	PROPN
m-1112	2762	4	⃗⃗	⃗⃗	PROPN
m-1112	2762	5	⃗⃗	⃗⃗	PROPN
m-1112	2762	6	⃗⃗	⃗⃗	PROPN
m-1112	2762	7	⃗	⃗	PROPN
m-1112	2762	8	}	}	PUNCT
m-1112	2762	9	≡	≡	PROPN
m-1112	2762	10	≡	≡	PROPN
m-1112	2763	1	[	[	X
m-1112	2763	2	�	�	NOUN
m-1112	2763	3	̅	̅	VERB
m-1112	2763	4	�	�	PROPN
m-1112	2763	5	𝐱	𝐱	PROPN
m-1112	2763	6	�	�	PROPN
m-1112	2763	7	̅	̅	NOUN
m-1112	2763	8	�	�	NOUN
m-1112	2763	9	𝐲].|aka|	𝐲].|aka|	X
m-1112	2763	10	=	=	PUNCT
m-1112	2763	11	|	|	ADV
m-1112	2763	12	↔	↔	PROPN
m-1112	2763	13	|.|	|.|	NOUN
m-1112	2763	14	↕	↕	NOUN
m-1112	2763	15	|.|aka|	|.|aka|	NOUN
m-1112	2763	16	,	,	PUNCT
m-1112	2763	17	i.e.	i.e.	X
m-1112	2763	18	an	an	DET
m-1112	2763	19	energy	energy	NOUN
m-1112	2763	20	-	-	PUNCT
m-1112	2763	21	circular	circular	ADJ
m-1112	2763	22	-	-	PUNCT
m-1112	2763	23	cone	cone	NOUN
m-1112	2763	24	which	which	PRON
m-1112	2763	25	is	be	AUX
m-1112	2763	26	a	a	DET
m-1112	2763	27	moving	move	VERB
m-1112	2763	28	energy	energy	NOUN
m-1112	2763	29	-volume	-volume	NOUN
m-1112	2763	30	and	and	CCONJ
m-1112	2763	31	because	because	SCONJ
m-1112	2763	32	from	from	ADP
m-1112	2763	33	cauchy	cauchy	PROPN
m-1112	2763	34	equations	equation	NOUN
m-1112	2763	35	of	of	ADP
m-1112	2763	36	stresses	stress	NOUN
m-1112	2763	37	in	in	ADP
m-1112	2763	38	three	three	NUM
m-1112	2763	39	dimensions	dimension	NOUN
m-1112	2763	40	,	,	PUNCT
m-1112	2763	41	the	the	DET
m-1112	2763	42	energy	energy	NOUN
m-1112	2763	43	stress	stress	NOUN
m-1112	2763	44	remains	remain	VERB
m-1112	2763	45	flat	flat	ADJ
m-1112	2763	46	onlywhen	onlywhen	NOUN
m-1112	2763	47	the	the	DET
m-1112	2763	48	plane	plane	NOUN
m-1112	2763	49	-	-	PUNCT
m-1112	2763	50	section	section	NOUN
m-1112	2763	51	is	be	AUX
m-1112	2763	52	a	a	DET
m-1112	2763	53	circle	circle	NOUN
m-1112	2764	1	[	[	X
m-1112	2764	2	𝐄𝟐	𝐄𝟐	X
m-1112	2764	3	]	]	PUNCT
m-1112	2764	4	and	and	CCONJ
m-1112	2764	5	the	the	DET
m-1112	2764	6	square	square	NOUN
m-1112	2764	7	becomes	become	VERB
m-1112	2764	8	circle	circle	NOUN
m-1112	2764	9	,	,	PUNCT
m-1112	2764	10	anti	anti	ADJ
m-1112	2764	11	-	-	ADJ
m-1112	2764	12	quadrature	quadrature	NOUN
m-1112	2764	13	.	.	PUNCT
m-1112	2765	1	because	because	SCONJ
m-1112	2765	2	from	from	ADP
m-1112	2765	3	mechanics	mechanic	NOUN
m-1112	2765	4	,	,	PUNCT
m-1112	2765	5	the	the	DET
m-1112	2765	6	sphere	sphere	NOUN
m-1112	2765	7	occupies	occupy	VERB
m-1112	2765	8	the	the	DET
m-1112	2765	9	least	least	ADJ
m-1112	2765	10	-	-	PUNCT
m-1112	2765	11	resistance	resistance	NOUN
m-1112	2765	12	to	to	ADP
m-1112	2765	13	motion	motion	NOUN
m-1112	2765	14	where	where	SCONJ
m-1112	2765	15	the	the	DET
m-1112	2765	16	geometrical	geometrical	ADJ
m-1112	2765	17	square	square	NOUN
m-1112	2765	18	–	–	PUNCT
m-1112	2765	19	cone	cone	NOUN
m-1112	2766	1	[	[	X
m-1112	2766	2	cm	cm	X
m-1112	2766	3	x	x	SYM
m-1112	2766	4	ch	ch	NOUN
m-1112	2766	5	x[co⃗⃗⃗⃗	x[co⃗⃗⃗⃗	PROPN
m-1112	2767	1	⃗	⃗	PROPN
m-1112	2767	2	↑	↑	PROPN
m-1112	2767	3	]	]	X
m-1112	2767	4	ijo	ijo	PROPN
m-1112	2767	5	international	international	PROPN
m-1112	2767	6	journal	journal	PROPN
m-1112	2767	7	of	of	ADP
m-1112	2767	8	mathematics	mathematics	PROPN
m-1112	2767	9	(	(	PUNCT
m-1112	2767	10	issn	issn	PROPN
m-1112	2767	11	:	:	PUNCT
m-1112	2767	12	2992	2992	NUM
m-1112	2767	13	-	-	SYM
m-1112	2767	14	4421	4421	NUM
m-1112	2767	15	)	)	PUNCT
m-1112	2767	16	volume	volume	NOUN
m-1112	2767	17	08	08	NUM
m-1112	2768	1	|	|	ADV
m-1112	2768	2	issue	issue	NOUN
m-1112	2768	3	08	08	NUM
m-1112	2769	1	|	|	ADV
m-1112	2769	2	august	august	PROPN
m-1112	2769	3	2025	2025	NUM
m-1112	2769	4	|	|	ADV
m-1112	2769	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2769	6	ijo	ijo	PROPN
m-1112	2769	7	journals	journal	NOUN
m-1112	2769	8	97	97	NUM
m-1112	2769	9	the	the	DET
m-1112	2769	10	fundamental	fundamental	ADJ
m-1112	2769	11	particles	particle	NOUN
m-1112	2769	12	origination	origination	NOUN
m-1112	2769	13	mechanism	mechanism	NOUN
m-1112	2769	14	in	in	ADP
m-1112	2769	15	mfmf	mfmf	PROPN
m-1112	2769	16	pns	pns	PROPN
m-1112	2769	17	caves	cave	NOUN
m-1112	2769	18	.	.	PUNCT
m-1112	2770	1	is	be	AUX
m-1112	2770	2	altered	alter	VERB
m-1112	2770	3	to	to	AUX
m-1112	2770	4	equivalent	equivalent	VERB
m-1112	2770	5	energycircular	energycircular	ADJ
m-1112	2770	6	cone	cone	NOUN
m-1112	2771	1	[	[	X
m-1112	2771	2	π	π	X
m-1112	2771	3	.	.	PUNCT
m-1112	2771	4	[	[	PUNCT
m-1112	2771	5	𝐂𝐌	𝐂𝐌	PROPN
m-1112	2771	6	𝟐	𝟐	NUM
m-1112	2771	7	]	]	SYM
m-1112	2771	8	²	²	X
m-1112	2771	9	(	(	PUNCT
m-1112	2771	10	x	x	X
m-1112	2771	11	)	)	PUNCT
m-1112	2771	12	[	[	X
m-1112	2771	13	co⃗⃗⃗⃗	co⃗⃗⃗⃗	NOUN
m-1112	2771	14	⃗	⃗	PROPN
m-1112	2771	15	↑	↑	X
m-1112	2771	16	]	]	PUNCT
m-1112	2771	17	and	and	CCONJ
m-1112	2771	18	to	to	ADP
m-1112	2771	19	the	the	DET
m-1112	2771	20	energy	energy	NOUN
m-1112	2771	21	unit	unit	NOUN
m-1112	2771	22	-volume	-volume	PROPN
m-1112	2771	23	co³.[𝐐	co³.[𝐐	PROPN
m-1112	2771	24	⇉	⇉	NOUN
m-1112	2771	25	⃗⃗⃗⃗⃗⃗	⃗⃗⃗⃗⃗⃗	X
m-1112	2772	1	⃗⃗	⃗⃗	PROPN
m-1112	2772	2	]	]	PUNCT
m-1112	2772	3	≡	≡	PROPN
m-1112	2772	4	2	2	NUM
m-1112	2772	5	.sphere	.sphere	ADP
m-1112	2772	6	𝟒𝛑	𝟒𝛑	VERB
m-1112	2772	7	𝟑	𝟑	NUM
m-1112	2772	8	r	r	NOUN
m-1112	2772	9	³	³	NOUN
m-1112	2772	10	and	and	CCONJ
m-1112	2772	11	to	to	ADP
m-1112	2772	12	energy	energy	NOUN
m-1112	2772	13	-	-	PUNCT
m-1112	2772	14	sphere	sphere	NOUN
m-1112	2772	15	cone	cone	NOUN
m-1112	2772	16	⸿	⸿	PROPN
m-1112	2772	17	=	=	PROPN
m-1112	2772	18	k	k	PROPN
m-1112	2772	19	π	π	PROPN
m-1112	2772	20	r³	r³	PROPN
m-1112	2772	21	,	,	PUNCT
m-1112	2772	22	where	where	SCONJ
m-1112	2772	23	the	the	DET
m-1112	2772	24	geometrycube	geometrycube	NOUN
m-1112	2772	25	[	[	X
m-1112	2772	26	|↔|.|	|↔|.|	NOUN
m-1112	2772	27	↕	↕	PROPN
m-1112	2772	28	|.|𝐀𝐊𝐀|	|.|𝐀𝐊𝐀|	PROPN
m-1112	2772	29	]	]	X
m-1112	2772	30	=	=	SYM
m-1112	2772	31	x	x	SYM
m-1112	2772	32	³	³	PROPN
m-1112	2772	33	so	so	ADV
m-1112	2772	34	becomes	become	VERB
m-1112	2772	35	the	the	DET
m-1112	2772	36	energy	energy	NOUN
m-1112	2772	37	-sphere	-sphere	NOUN
m-1112	2772	38	–	–	PUNCT
m-1112	2772	39	cone	cone	NOUN
m-1112	2772	40	as	as	SCONJ
m-1112	2772	41	→	→	SYM
m-1112	2772	42	k	k	PROPN
m-1112	2772	43	π	π	PROPN
m-1112	2772	44	r³	r³	PROPN
m-1112	2772	45	=	=	SYM
m-1112	2772	46	x	x	SYM
m-1112	2772	47	³	³	X
m-1112	2772	48	←	←	PROPN
m-1112	2772	49	[	[	X
m-1112	2772	50	𝐄	𝐄	PROPN
m-1112	2772	51	𝟕	𝟕	NUM
m-1112	2772	52	]	]	X
m-1112	2772	53	g	g	PROPN
m-1112	2772	54	..	..	PUNCT
m-1112	2772	55	since	since	SCONJ
m-1112	2772	56	frequencies	frequency	NOUN
m-1112	2772	57	fn	fn	VERB
m-1112	2772	58	are	be	AUX
m-1112	2772	59	the	the	DET
m-1112	2772	60	quantum	quantum	NOUN
m-1112	2772	61	of	of	ADP
m-1112	2772	62	energy	energy	NOUN
m-1112	2772	63	,	,	PUNCT
m-1112	2772	64	and	and	CCONJ
m-1112	2772	65	electromagnetic	electromagnetic	ADJ
m-1112	2772	66	vectors	vector	NOUN
m-1112	2772	67	are	be	AUX
m-1112	2772	68	always	always	ADV
m-1112	2772	69	perpendicular	perpendicular	ADJ
m-1112	2772	70	between	between	ADP
m-1112	2772	71	them	they	PRON
m-1112	2772	72	as	as	ADP
m-1112	2772	73	|	|	ADV
m-1112	2772	74	𝐅	𝐅	NOUN
m-1112	2772	75	𝐄	𝐄	NOUN
m-1112	2773	1	⊥	⊥	NOUN
m-1112	2773	2	𝐅	𝐅	PROPN
m-1112	2773	3	𝐌	𝐌	PROPN
m-1112	2774	1	|	|	ADV
m-1112	2774	2	,	,	PUNCT
m-1112	2774	3	so	so	ADV
m-1112	2774	4	are	be	AUX
m-1112	2774	5	everywhere	everywhere	ADV
m-1112	2774	6	in	in	ADP
m-1112	2774	7	nature	nature	NOUN
m-1112	2774	8	from	from	ADP
m-1112	2774	9	microcosm	microcosm	PROPN
m-1112	2774	10	to	to	ADP
m-1112	2774	11	macrocosm	macrocosm	PROPN
m-1112	2774	12	.	.	PUNCT
m-1112	2775	1	because	because	SCONJ
m-1112	2775	2	gravitational	gravitational	ADJ
m-1112	2775	3	force	force	NOUN
m-1112	2775	4	exists	exist	VERB
m-1112	2775	5	beyond	beyond	ADP
m-1112	2775	6	planck`s	planck`s	NOUN
m-1112	2775	7	length	length	NOUN
m-1112	2775	8	therefore	therefore	ADV
m-1112	2775	9	the	the	DET
m-1112	2775	10	propagating	propagate	VERB
m-1112	2775	11	-	-	PUNCT
m-1112	2775	12	plane	plane	NOUN
m-1112	2775	13	-	-	PUNCT
m-1112	2775	14	force	force	NOUN
m-1112	2775	15	𝐅𝐏	𝐅𝐏	PROPN
m-1112	2775	16	=	=	PROPN
m-1112	2775	17	σ	σ	PROPN
m-1112	2775	18	.	.	PUNCT
m-1112	2775	19	|cm|²	|cm|²	PUNCT
m-1112	2775	20	,	,	PUNCT
m-1112	2775	21	is	be	AUX
m-1112	2775	22	continually	continually	ADV
m-1112	2775	23	perpendicular	perpendicular	ADJ
m-1112	2775	24	to	to	ADP
m-1112	2775	25	the	the	DET
m-1112	2775	26	two	two	NUM
m-1112	2775	27	perpendicular	perpendicular	ADJ
m-1112	2775	28	constituents	constituent	NOUN
m-1112	2775	29	of	of	ADP
m-1112	2775	30	electromagnetic	electromagnetic	ADJ
m-1112	2775	31	vectors	vector	NOUN
m-1112	2775	32	as	as	ADP
m-1112	2775	33	|𝐅𝐏	|𝐅𝐏	NOUN
m-1112	2775	34	⊥	⊥	NUM
m-1112	2775	35	𝐅	𝐅	NOUN
m-1112	2775	36	𝐄	𝐄	NOUN
m-1112	2775	37	⊥	⊥	NOUN
m-1112	2775	38	𝐅	𝐅	PROPN
m-1112	2775	39	𝐌	𝐌	PROPN
m-1112	2775	40	|	|	NOUN
m-1112	2775	41	.	.	PUNCT
m-1112	2776	1	distance	distance	NOUN
m-1112	2776	2	is	be	AUX
m-1112	2776	3	the	the	DET
m-1112	2776	4	quantum	quantum	NOUN
m-1112	2776	5	of	of	ADP
m-1112	2776	6	e	e	NOUN
m-1112	2776	7	-	-	NOUN
m-1112	2776	8	geometry	geometry	NOUN
m-1112	2776	9	,	,	PUNCT
m-1112	2776	10	while	while	SCONJ
m-1112	2776	11	material	material	NOUN
m-1112	2776	12	-	-	PUNCT
m-1112	2776	13	point	point	NOUN
m-1112	2776	14	is	be	AUX
m-1112	2776	15	the	the	DET
m-1112	2776	16	quantum	quantum	NOUN
m-1112	2776	17	in	in	ADP
m-1112	2776	18	physics	physics	NOUN
m-1112	2776	19	and	and	CCONJ
m-1112	2776	20	in	in	ADP
m-1112	2776	21	material	material	NOUN
m-1112	2776	22	–	–	PUNCT
m-1112	2776	23	geometry	geometry	NOUN
m-1112	2776	24	which	which	PRON
m-1112	2776	25	is	be	AUX
m-1112	2776	26	the	the	DET
m-1112	2776	27	composition	composition	NOUN
m-1112	2776	28	of	of	ADP
m-1112	2776	29	opposites	opposite	NOUN
m-1112	2776	30	and	and	CCONJ
m-1112	2776	31	are	be	AUX
m-1112	2776	32	the	the	DET
m-1112	2776	33	elements	element	NOUN
m-1112	2776	34	in	in	ADP
m-1112	2776	35	chemistry	chemistry	NOUN
m-1112	2776	36	and	and	CCONJ
m-1112	2776	37	physics	physics	NOUN
m-1112	2776	38	.	.	PUNCT
m-1112	2777	1	as	as	ADP
m-1112	2777	2	in	in	ADP
m-1112	2777	3	algebra	algebra	NOUN
m-1112	2777	4	zero	zero	NUM
m-1112	2777	5	,	,	PUNCT
m-1112	2777	6	0	0	NUM
m-1112	2777	7	,	,	PUNCT
m-1112	2777	8	is	be	AUX
m-1112	2777	9	the	the	DET
m-1112	2777	10	master	master	NOUN
m-1112	2777	11	-	-	PUNCT
m-1112	2777	12	key	key	NOUN
m-1112	2777	13	number	number	NOUN
m-1112	2777	14	for	for	ADP
m-1112	2777	15	all	all	DET
m-1112	2777	16	positive	positive	ADJ
m-1112	2777	17	and	and	CCONJ
m-1112	2777	18	negative	negative	ADJ
m-1112	2777	19	numbers	number	NOUN
m-1112	2777	20	because	because	SCONJ
m-1112	2777	21	their	their	PRON
m-1112	2777	22	sum	sum	NOUN
m-1112	2777	23	and	and	CCONJ
m-1112	2777	24	multiplication	multiplication	NOUN
m-1112	2777	25	is	be	AUX
m-1112	2777	26	zero	zero	NUM
m-1112	2777	27	,	,	PUNCT
m-1112	2777	28	and	and	CCONJ
m-1112	2777	29	the	the	DET
m-1112	2777	30	same	same	ADJ
m-1112	2777	31	on	on	ADP
m-1112	2777	32	coordinate	coordinate	NOUN
m-1112	2777	33	system	system	NOUN
m-1112	2777	34	,	,	PUNCT
m-1112	2777	35	±	±	NUM
m-1112	2777	36	,	,	PUNCT
m-1112	2777	37	axes	axis	NOUN
m-1112	2777	38	pass	pass	VERB
m-1112	2777	39	from	from	ADP
m-1112	2777	40	zero	zero	NUM
m-1112	2777	41	.	.	PUNCT
m-1112	2778	1	[	[	X
m-1112	2778	2	𝐄	𝐄	NOUN
m-1112	2778	3	𝟖	𝟖	NUM
m-1112	2778	4	]	]	X
m-1112	2778	5	the	the	DET
m-1112	2778	6	rolling	rolling	NOUN
m-1112	2778	7	of	of	ADP
m-1112	2778	8	positive	positive	ADJ
m-1112	2778	9	⊕	⊕	PROPN
m-1112	2778	10	,	,	PUNCT
m-1112	2778	11	constituent	constituent	NOUN
m-1112	2778	12	on	on	ADP
m-1112	2778	13	the	the	DET
m-1112	2778	14	negative	negative	ADJ
m-1112	2778	15	⊝	⊝	NOUN
m-1112	2778	16	,	,	PUNCT
m-1112	2778	17	constituent	constituent	NOUN
m-1112	2778	18	,	,	PUNCT
m-1112	2778	19	creates	create	VERB
m-1112	2778	20	the	the	DET
m-1112	2778	21	neutral	neutral	ADJ
m-1112	2778	22	material	material	NOUN
m-1112	2778	23	point	point	NOUN
m-1112	2778	24	which	which	DET
m-1112	2778	25	equilibrium	equilibrium	NOUN
m-1112	2778	26	.	.	PUNCT
m-1112	2779	1	spin	spin	PROPN
m-1112	2779	2	�	�	PROPN
m-1112	2779	3	̅	̅	NOUN
m-1112	2779	4	�	�	PROPN
m-1112	2779	5	,	,	PUNCT
m-1112	2779	6	is	be	AUX
m-1112	2779	7	its	its	PRON
m-1112	2779	8	angular	angular	ADJ
m-1112	2779	9	momentum	momentum	NOUN
m-1112	2779	10	and	and	CCONJ
m-1112	2779	11	also	also	ADV
m-1112	2779	12	the	the	DET
m-1112	2779	13	first	first	ADJ
m-1112	2779	14	-discrete	-discrete	ADJ
m-1112	2779	15	-	-	PUNCT
m-1112	2779	16	energy	energy	NOUN
m-1112	2779	17	-	-	PUNCT
m-1112	2779	18	monad	monad	PROPN
m-1112	2779	19	which	which	PRON
m-1112	2779	20	occupies	occupy	VERB
m-1112	2779	21	discrete	discrete	ADJ
m-1112	2779	22	-	-	PUNCT
m-1112	2779	23	value	value	NOUN
m-1112	2779	24	and	and	CCONJ
m-1112	2779	25	direction	direction	NOUN
m-1112	2779	26	,	,	PUNCT
m-1112	2779	27	in	in	ADP
m-1112	2779	28	contradiction	contradiction	NOUN
m-1112	2779	29	to	to	ADP
m-1112	2779	30	the	the	DET
m-1112	2779	31	point	point	NOUN
m-1112	2779	32	which	which	PRON
m-1112	2779	33	is	be	AUX
m-1112	2779	34	nothing	nothing	PRON
m-1112	2779	35	,	,	PUNCT
m-1112	2779	36	dimensionless	dimensionless	NOUN
m-1112	2779	37	and	and	CCONJ
m-1112	2779	38	without	without	ADP
m-1112	2779	39	any	any	DET
m-1112	2779	40	direction	direction	NOUN
m-1112	2779	41	.	.	PUNCT
m-1112	2780	1	point	point	NOUN
m-1112	2780	2	-	-	PUNCT
m-1112	2780	3	caves	cave	NOUN
m-1112	2780	4	are	be	AUX
m-1112	2780	5	the	the	DET
m-1112	2780	6	energy	energy	NOUN
m-1112	2780	7	-	-	PUNCT
m-1112	2780	8	magnets	magnet	NOUN
m-1112	2780	9	from	from	ADP
m-1112	2780	10	which	which	PRON
m-1112	2780	11	the	the	DET
m-1112	2780	12	quantum	quantum	NOUN
m-1112	2780	13	of	of	ADP
m-1112	2780	14	energy	energy	NOUN
m-1112	2780	15	are	be	AUX
m-1112	2780	16	generated	generate	VERB
m-1112	2780	17	.	.	PUNCT
m-1112	2781	1	h	h	X
m-1112	2781	2	..	..	PUNCT
m-1112	2781	3	the	the	DET
m-1112	2781	4	space	space	NOUN
m-1112	2781	5	is	be	AUX
m-1112	2781	6	quantized	quantize	VERB
m-1112	2781	7	as	as	ADP
m-1112	2781	8	energy	energy	NOUN
m-1112	2781	9	-	-	PUNCT
m-1112	2781	10	caves	cave	NOUN
m-1112	2781	11	under	under	ADP
m-1112	2781	12	the	the	DET
m-1112	2781	13	effect	effect	NOUN
m-1112	2781	14	of	of	ADP
m-1112	2781	15	gravitational	gravitational	ADJ
m-1112	2781	16	-	-	PUNCT
m-1112	2781	17	force	force	NOUN
m-1112	2781	18	g	g	NOUN
m-1112	2781	19	,	,	PUNCT
m-1112	2781	20	as	as	ADV
m-1112	2781	21	well	well	ADV
m-1112	2781	22	in	in	ADP
m-1112	2781	23	conductors	conductor	NOUN
m-1112	2781	24	and	and	CCONJ
m-1112	2781	25	this	this	DET
m-1112	2781	26	energy	energy	NOUN
m-1112	2781	27	or	or	CCONJ
m-1112	2781	28	motion	motion	NOUN
m-1112	2781	29	is	be	AUX
m-1112	2781	30	quantized	quantize	VERB
m-1112	2781	31	as	as	ADP
m-1112	2781	32	frequency	frequency	NOUN
m-1112	2781	33	in	in	ADP
m-1112	2781	34	energy	energy	NOUN
m-1112	2781	35	caves	cave	NOUN
m-1112	2781	36	,	,	PUNCT
m-1112	2781	37	or	or	CCONJ
m-1112	2781	38	in	in	ADP
m-1112	2781	39	conductors	conductor	NOUN
m-1112	2781	40	,	,	PUNCT
m-1112	2781	41	following	follow	VERB
m-1112	2781	42	the	the	DET
m-1112	2781	43	kepler`s	kepler`s	NOUN
m-1112	2781	44	first	first	ADJ
m-1112	2781	45	-	-	PUNCT
m-1112	2781	46	law	law	NOUN
m-1112	2781	47	of	of	ADP
m-1112	2781	48	equal	equal	ADJ
m-1112	2781	49	areas	area	NOUN
m-1112	2781	50	where	where	SCONJ
m-1112	2781	51	in	in	ADP
m-1112	2781	52	equal	equal	ADJ
m-1112	2781	53	intervals	interval	NOUN
m-1112	2781	54	and	and	CCONJ
m-1112	2781	55	in	in	ADP
m-1112	2781	56	conductors	conductor	NOUN
m-1112	2781	57	,	,	PUNCT
m-1112	2781	58	is	be	AUX
m-1112	2781	59	the	the	DET
m-1112	2781	60	electricity	electricity	NOUN
m-1112	2781	61	or	or	CCONJ
m-1112	2781	62	electromagnetic	electromagnetic	ADJ
m-1112	2781	63	waves	wave	NOUN
m-1112	2781	64	.	.	PUNCT
m-1112	2782	1	[	[	X
m-1112	2782	2	𝐄	𝐄	NOUN
m-1112	2782	3	𝟗	𝟗	NUM
m-1112	2782	4	]	]	PUNCT
m-1112	2782	5	quaternion	quaternion	NOUN
m-1112	2782	6	[	[	X
m-1112	2782	7	(	(	PUNCT
m-1112	2782	8	+	+	ADJ
m-1112	2782	9	)	)	PUNCT
m-1112	2782	10	↻	↻	NOUN
m-1112	2782	11	↺	↺	NOUN
m-1112	2782	12	(	(	PUNCT
m-1112	2782	13	-	-	PUNCT
m-1112	2782	14	)	)	PUNCT
m-1112	2782	15	]	]	PUNCT
m-1112	2782	16	is	be	AUX
m-1112	2782	17	a	a	DET
m-1112	2782	18	quantum	quantum	NOUN
m-1112	2782	19	-	-	PUNCT
m-1112	2782	20	mould	mould	NOUN
m-1112	2782	21	for	for	ADP
m-1112	2782	22	space	space	NOUN
m-1112	2782	23	[	[	X
m-1112	2782	24	(	(	PUNCT
m-1112	2782	25	+	+	NOUN
m-1112	2782	26	)	)	PUNCT
m-1112	2782	27	(	(	PUNCT
m-1112	2782	28	-	-	PUNCT
m-1112	2782	29	)	)	PUNCT
m-1112	2782	30	]	]	PUNCT
m-1112	2782	31	and	and	CCONJ
m-1112	2782	32	energy	energy	PROPN
m-1112	2782	33	≡	≡	PROPN
m-1112	2782	34	motion	motion	NOUN
m-1112	2782	35	≡	≡	PROPN
m-1112	2782	36	force	force	NOUN
m-1112	2782	37	x	x	PUNCT
m-1112	2782	38	displacement	displacement	NOUN
m-1112	2782	39	as	as	ADP
m-1112	2782	40	[	[	X
m-1112	2782	41	↻	↻	NOUN
m-1112	2782	42	↺	↺	NOUN
m-1112	2782	43	or	or	CCONJ
m-1112	2782	44	↑↔↓	↑↔↓	PROPN
m-1112	2782	45	]	]	X
m-1112	2782	46	≡	≡	PROPN
m-1112	2782	47	standing	standing	PROPN
m-1112	2782	48	box	box	PROPN
m-1112	2782	49	𝐁𝐐	𝐁𝐐	PROPN
m-1112	2782	50	≡	≡	PROPN
m-1112	2782	51	an	an	DET
m-1112	2782	52	material	material	NOUN
m-1112	2782	53	point	point	NOUN
m-1112	2782	54	which	which	PRON
m-1112	2782	55	carries	carry	VERB
m-1112	2782	56	the	the	DET
m-1112	2782	57	principal	principal	ADJ
m-1112	2782	58	stress	stress	NOUN
m-1112	2782	59	σ	σ	NOUN
m-1112	2782	60	between	between	ADP
m-1112	2782	61	positions	position	NOUN
m-1112	2782	62	a	a	DET
m-1112	2782	63	(	(	PUNCT
m-1112	2782	64	+	+	NOUN
m-1112	2782	65	)	)	PUNCT
m-1112	2782	66	,	,	PUNCT
m-1112	2782	67	b	b	X
m-1112	2782	68	(	(	PUNCT
m-1112	2782	69	-	-	PUNCT
m-1112	2782	70	)	)	PUNCT
m-1112	2782	71	,	,	PUNCT
m-1112	2782	72	and	and	CCONJ
m-1112	2782	73	σ	σ	PROPN
m-1112	2782	74	,	,	PUNCT
m-1112	2782	75	is	be	AUX
m-1112	2782	76	the	the	DET
m-1112	2782	77	centripetal	centripetal	ADJ
m-1112	2782	78	acceleration	acceleration	NOUN
m-1112	2782	79	of	of	ADP
m-1112	2782	80	minimum	minimum	ADJ
m-1112	2782	81	energy	energy	NOUN
m-1112	2782	82	becoming	become	VERB
m-1112	2782	83	from	from	ADP
m-1112	2782	84	the	the	DET
m-1112	2782	85	in	in	ADP
m-1112	2782	86	-	-	PUNCT
m-1112	2782	87	storage	storage	NOUN
m-1112	2782	88	ab	ab	NOUN
m-1112	2782	89	acceleration	acceleration	NOUN
m-1112	2782	90	and	and	CCONJ
m-1112	2782	91	which	which	PRON
m-1112	2782	92	is	be	AUX
m-1112	2782	93	equal	equal	ADJ
m-1112	2782	94	to	to	ADP
m-1112	2782	95	the	the	DET
m-1112	2782	96	gravity	gravity	NOUN
m-1112	2782	97	g	g	NOUN
m-1112	2782	98	.	.	PUNCT
m-1112	2783	1	from	from	ADP
m-1112	2783	2	quaternion	quaternion	ADJ
m-1112	2783	3	quantum	quantum	ADJ
m-1112	2783	4	mould	mould	NOUN
m-1112	2784	1	[	[	X
m-1112	2784	2	r	r	X
m-1112	2784	3	+	+	NUM
m-1112	2784	4	v̅	v̅	NOUN
m-1112	2784	5	i	i	PRON
m-1112	2784	6	]	]	PUNCT
m-1112	2784	7	𝟏/𝐰	𝟏/𝐰	X
m-1112	2784	8	=	=	SYM
m-1112	2784	9	𝐞−	𝐞−	PROPN
m-1112	2784	10	𝐢.(𝛑/𝟐+𝟐𝐤𝛑).𝐰	𝐢.(𝛑/𝟐+𝟐𝐤𝛑).𝐰	NOUN
m-1112	2784	11	is	be	AUX
m-1112	2784	12	created	create	VERB
m-1112	2784	13	the	the	DET
m-1112	2784	14	min	min	NOUN
m-1112	2784	15	-	-	ADJ
m-1112	2784	16	space	space	ADJ
m-1112	2784	17	≡	≡	PROPN
m-1112	2784	18	cave	cave	NOUN
m-1112	2784	19	r	r	NOUN
m-1112	2784	20	=	=	SYM
m-1112	2784	21	1	1	NUM
m-1112	2784	22	,	,	PUNCT
m-1112	2784	23	07.𝟏𝟎−𝟕	07.𝟏𝟎−𝟕	PROPN
m-1112	2784	24	m	m	PROPN
m-1112	2784	25	and	and	CCONJ
m-1112	2784	26	the	the	DET
m-1112	2784	27	min	min	NOUN
m-1112	2784	28	-	-	ADJ
m-1112	2784	29	energy	energy	ADJ
m-1112	2784	30	≡	≡	PROPN
m-1112	2784	31	v̅	v̅	PUNCT
m-1112	2785	1	=	=	PUNCT
m-1112	2785	2	w	w	NOUN
m-1112	2785	3	r	r	NOUN
m-1112	2785	4	=	=	PUNCT
m-1112	2785	5	2πr	2πr	NOUN
m-1112	2785	6	f	f	X
m-1112	2785	7	,	,	PUNCT
m-1112	2785	8	as	as	ADP
m-1112	2785	9	frequency	frequency	NOUN
m-1112	2785	10	𝐟𝐦=	𝐟𝐦=	NOUN
m-1112	2785	11	2,839844	2,839844	NOUN
m-1112	2785	12	.	.	PUNCT
m-1112	2786	1	𝟏𝟎𝟏𝟎	𝟏𝟎𝟏𝟎	NUM
m-1112	2786	2	h	h	NOUN
m-1112	2786	3	.	.	PUNCT
m-1112	2787	1	g	g	PROPN
m-1112	2787	2	pushes	push	VERB
m-1112	2787	3	the	the	DET
m-1112	2787	4	→	→	SYM
m-1112	2787	5	min	min	ADJ
m-1112	2787	6	-	-	PUNCT
m-1112	2787	7	quantum	quantum	ADJ
m-1112	2787	8	-	-	PUNCT
m-1112	2787	9	energy	energy	NOUN
m-1112	2787	10	≡	≡	PROPN
m-1112	2787	11	motion	motion	NOUN
m-1112	2787	12	𝛔𝐄	𝛔𝐄	PROPN
m-1112	2787	13	,	,	PUNCT
m-1112	2787	14	into	into	ADP
m-1112	2787	15	the	the	DET
m-1112	2787	16	inscribed	inscribe	VERB
m-1112	2787	17	-	-	PUNCT
m-1112	2787	18	cave	cave	NOUN
m-1112	2787	19	π	π	PROPN
m-1112	2787	20	.	.	PUNCT
m-1112	2788	1	[	[	PUNCT
m-1112	2788	2	𝐂𝐌	𝐂𝐌	PROPN
m-1112	2788	3	𝟐	𝟐	NUM
m-1112	2788	4	]	]	PUNCT
m-1112	2788	5	²	²	NUM
m-1112	2788	6	≡	≡	PROPN
m-1112	2788	7	π.ea²	π.ea²	PROPN
m-1112	2788	8	.	.	PUNCT
m-1112	2789	1	gravitational	gravitational	ADJ
m-1112	2789	2	-	-	PUNCT
m-1112	2789	3	force	force	NOUN
m-1112	2789	4	g	g	NOUN
m-1112	2789	5	effecting	effect	VERB
m-1112	2789	6	on	on	ADP
m-1112	2789	7	light	light	ADJ
m-1112	2789	8	velocity	velocity	NOUN
m-1112	2789	9	�	�	NOUN
m-1112	2789	10	̅	̅	NOUN
m-1112	2789	11	�	�	NOUN
m-1112	2789	12	creates	create	VERB
m-1112	2789	13	the	the	DET
m-1112	2789	14	electron	electron	NOUN
m-1112	2789	15	-	-	PUNCT
m-1112	2789	16	charge	charge	NOUN
m-1112	2789	17	�	�	PROPN
m-1112	2789	18	̅	̅	NOUN
m-1112	2789	19	�	�	PROPN
m-1112	2789	20	and	and	CCONJ
m-1112	2789	21	electron	electron	VERB
m-1112	2789	22	𝐞	𝐞	PROPN
m-1112	2789	23	̅	̅	NOUN
m-1112	2789	24	,	,	PUNCT
m-1112	2789	25	while	while	SCONJ
m-1112	2789	26	acting	act	VERB
m-1112	2789	27	on	on	ADP
m-1112	2789	28	planck`s	planck`s	NOUN
m-1112	2789	29	-	-	NOUN
m-1112	2789	30	cave	cave	NOUN
m-1112	2789	31	on	on	ADP
m-1112	2789	32	the	the	DET
m-1112	2789	33	gravity	gravity	NOUN
m-1112	2789	34	g	g	PROPN
m-1112	2789	35	≡	≡	PROPN
m-1112	2789	36			PROPN
m-1112	2789	37	σ	σ	PROPN
m-1112	2789	38	,	,	PUNCT
m-1112	2789	39	as	as	ADP
m-1112	2789	40	g	g	PROPN
m-1112	2789	41	=	=	SYM
m-1112	2789	42	g	g	NOUN
m-1112	2790	1	k	k	PROPN
m-1112	2790	2	=	=	PUNCT
m-1112	2790	3	𝐤𝐄	𝐤𝐄	NOUN
m-1112	2790	4	g	g	NOUN
m-1112	2790	5	=	=	SYM
m-1112	2790	6	𝐤𝐋	𝐤𝐋	NOUN
m-1112	2790	7	σ	σ	NOUN
m-1112	2790	8	=	=	SYM
m-1112	2790	9	g.gl	g.gl	PROPN
m-1112	2790	10	kl	kl	NOUN
m-1112	2790	11	,	,	PUNCT
m-1112	2790	12	and	and	CCONJ
m-1112	2790	13	�	�	PROPN
m-1112	2790	14	̅	̅	NOUN
m-1112	2790	15	�	�	NOUN
m-1112	2790	16	effecting	effect	VERB
m-1112	2790	17	on	on	ADP
m-1112	2790	18	the	the	DET
m-1112	2790	19	min	min	NOUN
m-1112	2790	20	-	-	PUNCT
m-1112	2790	21	planck	planck	NOUN
m-1112	2790	22	-	-	PUNCT
m-1112	2790	23	cave	cave	NOUN
m-1112	2790	24	in	in	ADP
m-1112	2790	25	lp	lp	NOUN
m-1112	2790	26	formulates	formulate	VERB
m-1112	2790	27	hydrogen	hydrogen	NOUN
m-1112	2790	28	-	-	PUNCT
m-1112	2790	29	cave	cave	NOUN
m-1112	2790	30	h	h	NOUN
m-1112	2790	31	with	with	ADP
m-1112	2790	32	its	its	PRON
m-1112	2790	33	electron	electron	NOUN
m-1112	2790	34	as	as	ADP
m-1112	2790	35	he	he	PRON
m-1112	2790	36	.	.	PUNCT
m-1112	2791	1	[	[	X
m-1112	2791	2	𝐄	𝐄	NOUN
m-1112	2791	3	𝟏𝟎	𝟏𝟎	NUM
m-1112	2791	4	]	]	PUNCT
m-1112	2791	5	,	,	PUNCT
m-1112	2791	6	[	[	X
m-1112	2791	7	109	109	NUM
m-1112	2791	8	]	]	PUNCT
m-1112	2791	9	i	i	PRON
m-1112	2791	10	..	..	PUNCT
m-1112	2791	11	the	the	DET
m-1112	2791	12	physical	physical	NOUN
m-1112	2791	13	-	-	PUNCT
m-1112	2791	14	notion	notion	NOUN
m-1112	2791	15	of	of	ADP
m-1112	2791	16	the	the	DET
m-1112	2791	17	duplication	duplication	NOUN
m-1112	2791	18	of	of	ADP
m-1112	2791	19	the	the	DET
m-1112	2791	20	cube	cube	NOUN
m-1112	2791	21	,	,	PUNCT
m-1112	2791	22	in	in	ADP
m-1112	2791	23	the	the	DET
m-1112	2791	24	quadrature	quadrature	NOUN
m-1112	2791	25	physical	physical	ADJ
m-1112	2791	26	energy	energy	NOUN
m-1112	2791	27	mould	mould	NOUN
m-1112	2791	28	shows	show	VERB
m-1112	2791	29	that	that	SCONJ
m-1112	2791	30	nature	nature	NOUN
m-1112	2791	31	follows	follow	VERB
m-1112	2791	32	the	the	DET
m-1112	2791	33	geometry	geometry	NOUN
m-1112	2791	34	-	-	PUNCT
m-1112	2791	35	rules	rule	NOUN
m-1112	2791	36	in	in	ADP
m-1112	2791	37	order	order	NOUN
m-1112	2791	38	to	to	PART
m-1112	2791	39	exist	exist	VERB
m-1112	2791	40	as	as	ADP
m-1112	2791	41	space	space	NOUN
m-1112	2791	42	and	and	CCONJ
m-1112	2791	43	as	as	ADP
m-1112	2791	44	energy	energy	NOUN
m-1112	2791	45	,	,	PUNCT
m-1112	2791	46	which	which	PRON
m-1112	2791	47	is	be	AUX
m-1112	2791	48	motion	motion	NOUN
m-1112	2791	49	of	of	ADP
m-1112	2791	50	the	the	DET
m-1112	2791	51	,	,	PUNCT
m-1112	2791	52	+	+	ADJ
m-1112	2791	53	,	,	PUNCT
m-1112	2791	54	constituent	constituent	NOUN
m-1112	2791	55	to	to	ADP
m-1112	2791	56	the	the	DET
m-1112	2791	57	,	,	PUNCT
m-1112	2791	58	,	,	PUNCT
m-1112	2791	59	constituent	constituent	NOUN
m-1112	2791	60	.	.	PUNCT
m-1112	2792	1	this	this	DET
m-1112	2792	2	motion	motion	NOUN
m-1112	2792	3	is	be	AUX
m-1112	2792	4	conserved	conserve	VERB
m-1112	2792	5	by	by	ADP
m-1112	2792	6	propagating	propagate	VERB
m-1112	2792	7	in	in	ADP
m-1112	2792	8	caves	cave	NOUN
m-1112	2792	9	either	either	CCONJ
m-1112	2792	10	for	for	ADP
m-1112	2792	11	standing	standing	PROPN
m-1112	2792	12	≡	≡	PROPN
m-1112	2792	13	|	|	ADV
m-1112	2792	14	𝐯	𝐯	X
m-1112	2792	15	𝛑².𝐫⁴𝐧	𝛑².𝐫⁴𝐧	NOUN
m-1112	2792	16	|	|	NOUN
m-1112	2792	17	.	.	PUNCT
m-1112	2793	1	b̅n	b̅n	PROPN
m-1112	2793	2	or	or	CCONJ
m-1112	2793	3	for	for	ADP
m-1112	2793	4	moving	move	VERB
m-1112	2793	5	caves	cave	NOUN
m-1112	2793	6	as	as	SCONJ
m-1112	2793	7	this	this	PRON
m-1112	2793	8	is	be	AUX
m-1112	2793	9	the	the	DET
m-1112	2793	10	duality	duality	NOUN
m-1112	2793	11	-	-	PUNCT
m-1112	2793	12	photon	photon	NOUN
m-1112	2793	13	→	→	NOUN
m-1112	2793	14	v̅	v̅	NOUN
m-1112	2793	15	.	.	PUNCT
m-1112	2794	1	[	[	PUNCT
m-1112	2794	2	fn̅	fn̅	PROPN
m-1112	2794	3	+	+	NUM
m-1112	2794	4	fn	fn	NOUN
m-1112	2794	5	]	]	PUNCT
m-1112	2794	6	≡	≡	PROPN
m-1112	2794	7	|	|	ADV
m-1112	2794	8	𝐯	𝐯	X
m-1112	2794	9	𝛑².𝐫⁴𝐧	𝛑².𝐫⁴𝐧	NOUN
m-1112	2794	10	|	|	NOUN
m-1112	2794	11	.	.	PUNCT
m-1112	2795	1	b̅n	b̅n	PROPN
m-1112	2795	2	+	+	CCONJ
m-1112	2796	1	|	|	ADV
m-1112	2796	2	c̅	c̅	ADP
m-1112	2796	3	|	|	ADV
m-1112	2796	4	fn	fn	NOUN
m-1112	2796	5	.material	.material	ADJ
m-1112	2796	6	-	-	PUNCT
m-1112	2796	7	geometry	geometry	NOUN
m-1112	2796	8	meters	meter	NOUN
m-1112	2796	9	for	for	ADP
m-1112	2796	10	quantum	quantum	NOUN
m-1112	2796	11	-	-	PUNCT
m-1112	2796	12	length	length	NOUN
m-1112	2796	13	is	be	AUX
m-1112	2796	14	the	the	DET
m-1112	2796	15	quaternion	quaternion	ADJ
m-1112	2796	16	≡	≡	ADJ
m-1112	2796	17	dipole	dipole	NOUN
m-1112	2796	18	≡	≡	PROPN
m-1112	2796	19	the	the	DET
m-1112	2796	20	two	two	NUM
m-1112	2796	21	-	-	PUNCT
m-1112	2796	22	points	point	NOUN
m-1112	2796	23	joint	joint	NOUN
m-1112	2796	24	with	with	ADP
m-1112	2796	25	motion	motion	NOUN
m-1112	2796	26	between	between	ADP
m-1112	2796	27	them	they	PRON
m-1112	2796	28	,	,	PUNCT
m-1112	2796	29	while	while	SCONJ
m-1112	2796	30	for	for	ADP
m-1112	2796	31	the	the	DET
m-1112	2796	32	quantum	quantum	NOUN
m-1112	2796	33	-	-	PUNCT
m-1112	2796	34	surface	surface	NOUN
m-1112	2796	35	is	be	AUX
m-1112	2796	36	the	the	DET
m-1112	2796	37	unit	unit	NOUN
m-1112	2796	38	circle	circle	NOUN
m-1112	2796	39	π.r	π.r	PUNCT
m-1112	2796	40	²	²	PROPN
m-1112	2796	41	=	=	SYM
m-1112	2796	42	π	π	NOUN
m-1112	2796	43	,	,	PUNCT
m-1112	2796	44	and	and	CCONJ
m-1112	2796	45	is	be	AUX
m-1112	2796	46	r	r	NOUN
m-1112	2796	47	=	=	NOUN
m-1112	2796	48	unit	unit	NOUN
m-1112	2796	49	1	1	NUM
m-1112	2796	50	.	.	PUNCT
m-1112	2796	51	ijo	ijo	PROPN
m-1112	2796	52	international	international	PROPN
m-1112	2796	53	journal	journal	PROPN
m-1112	2796	54	of	of	ADP
m-1112	2796	55	mathematics	mathematics	PROPN
m-1112	2796	56	(	(	PUNCT
m-1112	2796	57	issn	issn	PROPN
m-1112	2796	58	:	:	PUNCT
m-1112	2796	59	2992	2992	NUM
m-1112	2796	60	-	-	SYM
m-1112	2796	61	4421	4421	NUM
m-1112	2796	62	)	)	PUNCT
m-1112	2797	1	volume	volume	NOUN
m-1112	2797	2	08	08	NUM
m-1112	2798	1	|	|	ADV
m-1112	2798	2	issue	issue	NOUN
m-1112	2798	3	08	08	NUM
m-1112	2799	1	|	|	ADV
m-1112	2799	2	august	august	PROPN
m-1112	2799	3	2025	2025	NUM
m-1112	2799	4	|	|	ADV
m-1112	2799	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2799	6	ijo	ijo	NOUN
m-1112	2799	7	journals	journal	NOUN
m-1112	2799	8	98	98	NUM
m-1112	2799	9	the	the	DET
m-1112	2799	10	fundamental	fundamental	ADJ
m-1112	2799	11	particles	particle	NOUN
m-1112	2799	12	origination	origination	NOUN
m-1112	2799	13	mechanism	mechanism	NOUN
m-1112	2799	14	in	in	ADP
m-1112	2799	15	mfmf	mfmf	PROPN
m-1112	2799	16	pns	pns	PROPN
m-1112	2799	17	caves	cave	NOUN
m-1112	2799	18	.	.	PUNCT
m-1112	2800	1	for	for	ADP
m-1112	2800	2	the	the	DET
m-1112	2800	3	quantum	quantum	NOUN
m-1112	2800	4	-	-	PUNCT
m-1112	2800	5	volumes	volume	NOUN
m-1112	2800	6	,	,	PUNCT
m-1112	2800	7	is	be	AUX
m-1112	2800	8	the	the	DET
m-1112	2800	9	.	.	PUNCT
m-1112	2800	10	unit	unit	NOUN
m-1112	2800	11	volume	volume	NOUN
m-1112	2800	12	sphere	sphere	ADV
m-1112	2800	13	4	4	NUM
m-1112	2800	14	3	3	NUM
m-1112	2800	15	π.r	π.r	X
m-1112	2800	16	³	³	X
m-1112	2800	17	=	=	X
m-1112	2800	18	[	[	PUNCT
m-1112	2800	19	4.r	4.r	NUM
m-1112	2800	20	3	3	NUM
m-1112	2800	21	]	]	PUNCT
m-1112	2800	22	(	(	PUNCT
m-1112	2800	23	π.r	π.r	X
m-1112	2800	24	²	²	NUM
m-1112	2800	25	)	)	PUNCT
m-1112	2800	26	=	=	SYM
m-1112	2800	27	4	4	NUM
m-1112	2800	28	π	π	SYM
m-1112	2800	29	3	3	NUM
m-1112	2800	30	,	,	PUNCT
m-1112	2800	31	for	for	ADP
m-1112	2800	32	r	r	NOUN
m-1112	2800	33	=	=	SYM
m-1112	2800	34	unit	unit	NOUN
m-1112	2800	35	1	1	NUM
m-1112	2800	36	.	.	PUNCT
m-1112	2801	1	the	the	DET
m-1112	2801	2	unit	unit	NOUN
m-1112	2801	3	-	-	PUNCT
m-1112	2801	4	volume	volume	NOUN
m-1112	2801	5	is	be	AUX
m-1112	2801	6	formulated	formulate	VERB
m-1112	2801	7	from	from	ADP
m-1112	2801	8	the	the	DET
m-1112	2801	9	inscribed	inscribed	NOUN
m-1112	2801	10	-	-	PUNCT
m-1112	2801	11	square	square	NOUN
m-1112	2801	12	of	of	ADP
m-1112	2801	13	unit	unit	NOUN
m-1112	2801	14	circle	circle	NOUN
m-1112	2801	15	-	-	PUNCT
m-1112	2801	16	side	side	NOUN
m-1112	2801	17	co	co	NOUN
m-1112	2801	18	=	=	NOUN
m-1112	2801	19	cb	cb	PROPN
m-1112	2801	20	=	=	SYM
m-1112	2801	21	1	1	NUM
m-1112	2801	22	/√2	/√2	PUNCT
m-1112	2801	23	,	,	PUNCT
m-1112	2801	24	and	and	CCONJ
m-1112	2801	25	when	when	SCONJ
m-1112	2801	26	placed	place	VERB
m-1112	2801	27	the	the	DET
m-1112	2801	28	-	-	PUNCT
m-1112	2801	29	unit	unit	NOUN
m-1112	2801	30	-	-	PUNCT
m-1112	2801	31	energy	energy	NOUN
m-1112	2801	32	-	-	PUNCT
m-1112	2801	33	magnitude	magnitude	NOUN
m-1112	2801	34	oc	oc	NOUN
m-1112	2801	35	on	on	ADP
m-1112	2801	36	square	square	ADJ
m-1112	2801	37	co	co	NOUN
m-1112	2801	38	x	x	PROPN
m-1112	2801	39	co	co	NOUN
m-1112	2801	40	then	then	ADV
m-1112	2801	41	is	be	AUX
m-1112	2802	1	unit	unit	NOUN
m-1112	2802	2	-	-	PUNCT
m-1112	2802	3	volume	volume	NOUN
m-1112	2803	1	[	[	X
m-1112	2803	2	co	co	NOUN
m-1112	2803	3	x	x	X
m-1112	2803	4	co	co	NOUN
m-1112	2803	5	x	x	PROPN
m-1112	2803	6	co⃗⃗⃗⃗	co⃗⃗⃗⃗	PROPN
m-1112	2803	7	⃗	⃗	PROPN
m-1112	2803	8	↑	↑	X
m-1112	2803	9	]	]	PUNCT
m-1112	2803	10	.	.	PUNCT
m-1112	2804	1	this	this	DET
m-1112	2804	2	unit	unit	NOUN
m-1112	2804	3	-	-	PUNCT
m-1112	2804	4	volume	volume	NOUN
m-1112	2804	5	when	when	SCONJ
m-1112	2804	6	placed	place	VERB
m-1112	2804	7	in	in	ADP
m-1112	2804	8	,	,	PUNCT
m-1112	2804	9	the	the	DET
m-1112	2804	10	three	three	NUM
m-1112	2804	11	-poles	-pole	NOUN
m-1112	2804	12	squares	square	NOUN
m-1112	2804	13	-	-	PUNCT
m-1112	2804	14	rotating	rotate	VERB
m-1112	2804	15	-	-	PUNCT
m-1112	2804	16	system	system	NOUN
m-1112	2804	17	,	,	PUNCT
m-1112	2804	18	then	then	ADV
m-1112	2804	19	at	at	ADP
m-1112	2804	20	point	point	NOUN
m-1112	2804	21	kn	kn	PROPN
m-1112	2804	22	,	,	PUNCT
m-1112	2804	23	unit	unit	NOUN
m-1112	2804	24	volume	volume	NOUN
m-1112	2805	1	[	[	X
m-1112	2805	2	co	co	NOUN
m-1112	2805	3	x	x	X
m-1112	2805	4	co	co	NOUN
m-1112	2805	5	x	x	X
m-1112	2805	6	[	[	X
m-1112	2805	7	co⃗⃗⃗⃗	co⃗⃗⃗⃗	NOUN
m-1112	2805	8	⃗	⃗	PROPN
m-1112	2805	9	↑	↑	X
m-1112	2805	10	]	]	PUNCT
m-1112	2805	11	becomes	become	VERB
m-1112	2805	12	[	[	X
m-1112	2805	13	cm	cm	X
m-1112	2805	14	x	x	SYM
m-1112	2805	15	ch	ch	NOUN
m-1112	2805	16	]	]	PUNCT
m-1112	2805	17	x	x	SYM
m-1112	2805	18	ch⃗⃗⃗⃗	ch⃗⃗⃗⃗	X
m-1112	2805	19	⃗	⃗	PROPN
m-1112	2805	20	↑	↑	X
m-1112	2805	21	]	]	X
m-1112	2805	22	=	=	SYM
m-1112	2805	23	circular	circular	ADJ
m-1112	2805	24	-	-	PUNCT
m-1112	2805	25	cone	cone	NOUN
m-1112	2806	1	[	[	X
m-1112	2806	2	π	π	X
m-1112	2806	3	.	.	PUNCT
m-1112	2806	4	(	(	PUNCT
m-1112	2806	5	𝐂𝐁	𝐂𝐁	PROPN
m-1112	2806	6	√𝟐	√𝟐	PROPN
m-1112	2806	7	)	)	PUNCT
m-1112	2806	8	²	²	PROPN
m-1112	2806	9	]	]	PUNCT
m-1112	2806	10	.	.	PUNCT
m-1112	2807	1	[	[	X
m-1112	2807	2	co⃗⃗⃗⃗	co⃗⃗⃗⃗	NOUN
m-1112	2807	3	⃗	⃗	PROPN
m-1112	2807	4	↑	↑	X
m-1112	2807	5	]	]	X
m-1112	2807	6	=	=	SYM
m-1112	2807	7	unit	unit	NOUN
m-1112	2807	8	sphere	sphere	ADV
m-1112	2807	9	4π	4π	NUM
m-1112	2807	10	3	3	NUM
m-1112	2807	11	r	r	NOUN
m-1112	2807	12	³	³	NOUN
m-1112	2807	13	,	,	PUNCT
m-1112	2807	14	equal	equal	ADJ
m-1112	2807	15	to	to	ADP
m-1112	2807	16	quantum	quantum	NOUN
m-1112	2807	17	of	of	ADP
m-1112	2807	18	energy	energy	NOUN
m-1112	2807	19	.	.	PUNCT
m-1112	2808	1	because	because	SCONJ
m-1112	2808	2	physical	physical	ADJ
m-1112	2808	3	-	-	PUNCT
m-1112	2808	4	magnet	magnet	NOUN
m-1112	2808	5	⊕	⊕	PROPN
m-1112	2808	6	⇉	⇉	PROPN
m-1112	2809	1	⊝	⊝	NUM
m-1112	2809	2	compels	compel	VERB
m-1112	2809	3	force	force	NOUN
m-1112	2809	4	�	�	PROPN
m-1112	2809	5	̅	̅	NOUN
m-1112	2809	6	�	�	PROPN
m-1112	2809	7	⇉	⇉	PROPN
m-1112	2810	1	aka⃗⃗	aka⃗⃗	PROPN
m-1112	2810	2	⃗⃗	⃗⃗	PROPN
m-1112	2810	3	⃗⃗	⃗⃗	PROPN
m-1112	2810	4	⃗⃗	⃗⃗	PROPN
m-1112	2810	5	⃗	⃗	PROPN
m-1112	2810	6	,	,	PUNCT
m-1112	2810	7	between	between	ADP
m-1112	2810	8	a	a	PRON
m-1112	2810	9	and	and	CCONJ
m-1112	2810	10	ka	ka	PROPN
m-1112	2810	11	points	point	NOUN
m-1112	2810	12	and	and	CCONJ
m-1112	2810	13	then	then	ADV
m-1112	2810	14	unit	unit	NOUN
m-1112	2810	15	-	-	PUNCT
m-1112	2810	16	sphere	sphere	NOUN
m-1112	2810	17	4π	4π	NUM
m-1112	2810	18	3	3	NUM
m-1112	2810	19	r	r	NOUN
m-1112	2810	20	³	³	NUM
m-1112	2810	21	becomes	become	VERB
m-1112	2810	22	the	the	DET
m-1112	2810	23	double	double	ADJ
m-1112	2810	24	unit	unit	NOUN
m-1112	2810	25	-	-	PUNCT
m-1112	2810	26	sphere	sphere	NOUN
m-1112	2810	27	2	2	NUM
m-1112	2810	28	.	.	PUNCT
m-1112	2810	29	{	{	PUNCT
m-1112	2811	1	4π	4π	NUM
m-1112	2811	2	3	3	NUM
m-1112	2811	3	r³	r³	PROPN
m-1112	2811	4	}	}	PUNCT
m-1112	2811	5	and	and	CCONJ
m-1112	2811	6	because	because	SCONJ
m-1112	2811	7	the	the	DET
m-1112	2811	8	energy	energy	NOUN
m-1112	2811	9	square	square	NOUN
m-1112	2811	10	[	[	X
m-1112	2811	11	cakap	cakap	X
m-1112	2811	12	]	]	X
m-1112	2811	13	is	be	AUX
m-1112	2811	14	double	double	ADJ
m-1112	2811	15	that	that	SCONJ
m-1112	2811	16	the	the	DET
m-1112	2811	17	unit	unit	NOUN
m-1112	2811	18	square	square	VERB
m-1112	2811	19	|cb	|cb	PROPN
m-1112	2811	20	x	x	AUX
m-1112	2811	21	co|	co|	PROPN
m-1112	2811	22	,	,	PUNCT
m-1112	2811	23	then	then	ADV
m-1112	2811	24	force	force	VERB
m-1112	2811	25	�	�	PROPN
m-1112	2811	26	̅	̅	NOUN
m-1112	2811	27	�	�	PROPN
m-1112	2811	28	⇉	⇉	PROPN
m-1112	2812	1	aka⃗⃗	aka⃗⃗	PROPN
m-1112	2812	2	⃗⃗	⃗⃗	PROPN
m-1112	2812	3	⃗⃗	⃗⃗	PROPN
m-1112	2812	4	⃗⃗	⃗⃗	PROPN
m-1112	2812	5	⃗	⃗	PROPN
m-1112	2812	6	is	be	AUX
m-1112	2812	7	the	the	DET
m-1112	2812	8	pivot	pivot	NOUN
m-1112	2812	9	of	of	ADP
m-1112	2812	10	spinning	spin	VERB
m-1112	2812	11	indicating	indicate	VERB
m-1112	2812	12	±	±	NUM
m-1112	2812	13	�	�	PROPN
m-1112	2812	14	̅	̅	NOUN
m-1112	2812	15	�	�	PROPN
m-1112	2812	16	≡	≡	PROPN
m-1112	2812	17	�	�	PROPN
m-1112	2812	18	̅	̅	NOUN
m-1112	2812	19	�	�	PROPN
m-1112	2812	20	,	,	PUNCT
m-1112	2812	21	in	in	ADP
m-1112	2812	22	all	all	DET
m-1112	2812	23	energy	energy	NOUN
m-1112	2812	24	monads	monad	NOUN
m-1112	2813	1	.[𝐄	.[𝐄	ADV
m-1112	2814	1	𝟏𝟏	𝟏𝟏	NUM
m-1112	2814	2	]	]	PUNCT
m-1112	2814	3	j	j	PROPN
m-1112	2814	4	..	..	PUNCT
m-1112	2814	5	gravity	gravity	NOUN
m-1112	2814	6	and	and	CCONJ
m-1112	2814	7	antigravity	antigravity	NOUN
m-1112	2814	8	are	be	AUX
m-1112	2814	9	the	the	DET
m-1112	2814	10	two	two	NUM
m-1112	2814	11	halve	halve	NOUN
m-1112	2814	12	spins	spin	VERB
m-1112	2814	13	from	from	ADP
m-1112	2814	14	the	the	DET
m-1112	2814	15	angular	angular	ADJ
m-1112	2814	16	momentum	momentum	NOUN
m-1112	2814	17	�	�	NOUN
m-1112	2814	18	̅	̅	NOUN
m-1112	2814	19	�	�	PROPN
m-1112	2814	20	≡	≡	PROPN
m-1112	2814	21	±	±	PROPN
m-1112	2814	22	work	work	NOUN
m-1112	2814	23	created	create	VERB
m-1112	2814	24	from	from	ADP
m-1112	2814	25	the	the	DET
m-1112	2814	26	velocity	velocity	NOUN
m-1112	2814	27	vector	vector	NOUN
m-1112	2814	28	�	�	PROPN
m-1112	2814	29	̅	̅	NOUN
m-1112	2814	30	�	�	NOUN
m-1112	2814	31	by	by	ADP
m-1112	2814	32	rotating	rotate	VERB
m-1112	2814	33	↻	↻	NOUN
m-1112	2814	34	on	on	ADP
m-1112	2814	35	planck`s	planck`s	NOUN
m-1112	2814	36	cave	cave	NOUN
m-1112	2814	37	diameter.[𝐄𝟏𝟐	diameter.[𝐄𝟏𝟐	PROPN
m-1112	2814	38	]	]	X
m-1112	2814	39	this	this	DET
m-1112	2814	40	property	property	NOUN
m-1112	2814	41	,	,	PUNCT
m-1112	2814	42	±	±	NUM
m-1112	2814	43	�	�	PROPN
m-1112	2814	44	̅	̅	NOUN
m-1112	2814	45	�	�	PROPN
m-1112	2814	46	≡	≡	PROPN
m-1112	2814	47	�	�	PROPN
m-1112	2814	48	̅	̅	NOUN
m-1112	2814	49	�	�	PROPN
m-1112	2814	50	,	,	PUNCT
m-1112	2814	51	is	be	AUX
m-1112	2814	52	in	in	ADP
m-1112	2814	53	all	all	DET
m-1112	2814	54	energy	energy	NOUN
m-1112	2814	55	monads	monad	NOUN
m-1112	2814	56	and	and	CCONJ
m-1112	2814	57	when	when	SCONJ
m-1112	2814	58	applied	apply	VERB
m-1112	2814	59	on	on	ADP
m-1112	2814	60	initial	initial	ADJ
m-1112	2814	61	,	,	PUNCT
m-1112	2814	62	⊕	⊕	PROPN
m-1112	2814	63	⇉	⇉	PROPN
m-1112	2814	64	⊝	⊝	NUM
m-1112	2814	65	,	,	PUNCT
m-1112	2814	66	answers	answer	NOUN
m-1112	2814	67	to	to	ADP
m-1112	2814	68	the	the	DET
m-1112	2814	69	3d	3d	NUM
m-1112	2814	70	-	-	PUNCT
m-1112	2814	71	stability	stability	NOUN
m-1112	2814	72	of	of	ADP
m-1112	2814	73	all	all	DET
m-1112	2814	74	elementary	elementary	ADJ
m-1112	2814	75	-	-	PUNCT
m-1112	2814	76	particles	particle	NOUN
m-1112	2814	77	and	and	CCONJ
m-1112	2814	78	cosmology	cosmology	NOUN
m-1112	2814	79	equilibrium	equilibrium	NOUN
m-1112	2814	80	.	.	PUNCT
m-1112	2815	1	gravity	gravity	NOUN
m-1112	2815	2	+	+	CCONJ
m-1112	2815	3	g	g	PROPN
m-1112	2815	4	≡	≡	PROPN
m-1112	2815	5	the	the	DET
m-1112	2815	6	vector	vector	NOUN
m-1112	2815	7	of	of	ADP
m-1112	2815	8	angular	angular	ADJ
m-1112	2815	9	-	-	PUNCT
m-1112	2815	10	momentum	momentum	NOUN
m-1112	2815	11	�	�	NOUN
m-1112	2815	12	̅	̅	NOUN
m-1112	2815	13	�	�	PROPN
m-1112	2815	14	≡	≡	PROPN
m-1112	2815	15	+	+	CCONJ
m-1112	2815	16	spin	spin	PROPN
m-1112	2815	17	≡	≡	PROPN
m-1112	2815	18	↓	↓	PROPN
m-1112	2815	19	↻	↻	PROPN
m-1112	2815	20	≡	≡	PROPN
m-1112	2815	21	the	the	DET
m-1112	2815	22	work	work	NOUN
m-1112	2815	23	stored	store	VERB
m-1112	2815	24	in	in	ADP
m-1112	2815	25	the	the	DET
m-1112	2815	26	[	[	X
m-1112	2815	27	4	4	NUM
m-1112	2815	28	-	-	SYM
m-1112	2815	29	1	1	NUM
m-1112	2815	30	-	-	SYM
m-1112	2815	31	3	3	NUM
m-1112	2815	32	]	]	PUNCT
m-1112	2815	33	semi	semi	ADJ
m-1112	2815	34	circle	circle	NOUN
m-1112	2815	35	of	of	ADP
m-1112	2815	36	the	the	DET
m-1112	2815	37	,	,	PUNCT
m-1112	2815	38	�	�	PROPN
m-1112	2815	39	̅	̅	NOUN
m-1112	2815	40	�	�	PROPN
m-1112	2815	41	�	�	NOUN
m-1112	2815	42	̅	̅	NOUN
m-1112	2815	43	�	�	PROPN
m-1112	2815	44	vectors	vector	NOUN
m-1112	2815	45	circle	circle	NOUN
m-1112	2815	46	-	-	PUNCT
m-1112	2815	47	surface	surface	NOUN
m-1112	2815	48	,	,	PUNCT
m-1112	2815	49	produced	produce	VERB
m-1112	2815	50	from	from	ADP
m-1112	2815	51	the	the	DET
m-1112	2815	52	gravitational	gravitational	ADJ
m-1112	2815	53	-	-	PUNCT
m-1112	2815	54	force	force	NOUN
m-1112	2815	55	,	,	PUNCT
m-1112	2815	56	g	g	PROPN
m-1112	2815	57	,	,	PUNCT
m-1112	2815	58	as	as	ADP
m-1112	2815	59	acting	act	VERB
m-1112	2815	60	into	into	ADP
m-1112	2815	61	the	the	DET
m-1112	2815	62	-planckcave	-planckcave	NOUN
m-1112	2815	63	,	,	PUNCT
m-1112	2815	64	and	and	CCONJ
m-1112	2815	65	on	on	ADP
m-1112	2815	66	the	the	DET
m-1112	2815	67	light	light	ADJ
m-1112	2815	68	velocity	velocity	NOUN
m-1112	2815	69	vector	vector	NOUN
m-1112	2815	70	of	of	ADP
m-1112	2815	71	,	,	PUNCT
m-1112	2815	72	+	+	CCONJ
m-1112	2815	73	↓	↓	PROPN
m-1112	2815	74	�	�	PROPN
m-1112	2815	75	̅	̅	NOUN
m-1112	2815	76	�	�	NOUN
m-1112	2815	77	direction	direction	NOUN
m-1112	2815	78	.	.	PUNCT
m-1112	2816	1	[	[	X
m-1112	2816	2	107	107	NUM
m-1112	2816	3	]	]	PUNCT
m-1112	2816	4	antigravity	antigravity	NOUN
m-1112	2816	5	g	g	PROPN
m-1112	2816	6	≡	≡	PROPN
m-1112	2816	7	the	the	DET
m-1112	2816	8	vector	vector	NOUN
m-1112	2816	9	of	of	ADP
m-1112	2816	10	angular	angular	ADJ
m-1112	2816	11	-momentum	-momentum	PROPN
m-1112	2816	12	�	�	PROPN
m-1112	2816	13	̅	̅	NOUN
m-1112	2816	14	�	�	PROPN
m-1112	2816	15	≡	≡	PROPN
m-1112	2816	16	spin	spin	PROPN
m-1112	2816	17	≡	≡	PROPN
m-1112	2816	18	↑	↑	PROPN
m-1112	2816	19	↺	↺	NOUN
m-1112	2816	20	≡	≡	PROPN
m-1112	2816	21	the	the	DET
m-1112	2816	22	work	work	NOUN
m-1112	2816	23	stored	store	VERB
m-1112	2816	24	in	in	ADP
m-1112	2816	25	the	the	DET
m-1112	2816	26	complementary	complementary	ADJ
m-1112	2816	27	[	[	X
m-1112	2816	28	4	4	NUM
m-1112	2816	29	-	-	SYM
m-1112	2816	30	2	2	NUM
m-1112	2816	31	-	-	SYM
m-1112	2816	32	3	3	NUM
m-1112	2816	33	]	]	PUNCT
m-1112	2816	34	semi	semi	ADJ
m-1112	2816	35	circle	circle	NOUN
m-1112	2816	36	of	of	ADP
m-1112	2816	37	the	the	DET
m-1112	2816	38	,	,	PUNCT
m-1112	2816	39	�	�	PROPN
m-1112	2816	40	̅	̅	NOUN
m-1112	2816	41	�	�	PROPN
m-1112	2816	42	�	�	NOUN
m-1112	2816	43	̅	̅	NOUN
m-1112	2816	44	�	�	PROPN
m-1112	2816	45	vectors	vector	NOUN
m-1112	2816	46	circle	circle	NOUN
m-1112	2816	47	surface	surface	NOUN
m-1112	2816	48	which	which	PRON
m-1112	2816	49	is	be	AUX
m-1112	2816	50	produced	produce	VERB
m-1112	2816	51	from	from	ADP
m-1112	2816	52	the	the	DET
m-1112	2816	53	gravitational	gravitational	ADJ
m-1112	2816	54	-	-	PUNCT
m-1112	2816	55	force	force	NOUN
m-1112	2816	56	g	g	NOUN
m-1112	2816	57	,	,	PUNCT
m-1112	2816	58	as	as	ADP
m-1112	2816	59	acting	act	VERB
m-1112	2816	60	into	into	ADP
m-1112	2816	61	the	the	DET
m-1112	2816	62	-	-	PUNCT
m-1112	2816	63	planck	planck	NOUN
m-1112	2816	64	-	-	PUNCT
m-1112	2816	65	cave	cave	NOUN
m-1112	2816	66	,	,	PUNCT
m-1112	2816	67	and	and	CCONJ
m-1112	2816	68	on	on	ADP
m-1112	2816	69	the	the	DET
m-1112	2816	70	light	light	ADJ
m-1112	2816	71	velocity	velocity	NOUN
m-1112	2816	72	vector	vector	NOUN
m-1112	2816	73	of	of	ADP
m-1112	2816	74	the	the	DET
m-1112	2816	75	,	,	PUNCT
m-1112	2816	76	↑	↑	PROPN
m-1112	2816	77	�	�	PROPN
m-1112	2816	78	̅	̅	NOUN
m-1112	2816	79	�	�	NOUN
m-1112	2816	80	direction	direction	NOUN
m-1112	2816	81	.	.	PUNCT
m-1112	2817	1	k	k	X
m-1112	2817	2	..	..	PUNCT
m-1112	2817	3	the	the	DET
m-1112	2817	4	black	black	ADJ
m-1112	2817	5	-	-	PUNCT
m-1112	2817	6	holes	hole	NOUN
m-1112	2817	7	exist	exist	VERB
m-1112	2817	8	as	as	ADP
m-1112	2817	9	parallel	parallel	ADJ
m-1112	2817	10	origination	origination	NOUN
m-1112	2817	11	either	either	CCONJ
m-1112	2817	12	as	as	SCONJ
m-1112	2817	13			PROPN
m-1112	2817	14	planar	planar	ADJ
m-1112	2817	15	black	black	ADJ
m-1112	2817	16	-	-	PUNCT
m-1112	2817	17	holes	hole	NOUN
m-1112	2817	18	or	or	CCONJ
m-1112	2817	19			NOUN
m-1112	2817	20	atoms	atom	NOUN
m-1112	2817	21	black	black	ADJ
m-1112	2817	22	–	–	PUNCT
m-1112	2817	23	holes	hole	NOUN
m-1112	2817	24	,	,	PUNCT
m-1112	2817	25	when	when	SCONJ
m-1112	2817	26	g	g	NOUN
m-1112	2817	27	force	force	NOUN
m-1112	2817	28	is	be	AUX
m-1112	2817	29	acting	act	VERB
m-1112	2817	30	on	on	ADP
m-1112	2817	31	the	the	DET
m-1112	2817	32	-planck	-planck	NOUN
m-1112	2817	33	–	–	PUNCT
m-1112	2817	34	cave	cave	NOUN
m-1112	2817	35	.	.	PUNCT
m-1112	2818	1	[	[	X
m-1112	2818	2	𝐄	𝐄	NOUN
m-1112	2818	3	𝟏𝟑	𝟏𝟑	NUM
m-1112	2818	4	]	]	PUNCT
m-1112	2818	5	momentum	momentum	NOUN
m-1112	2818	6	b̅	b̅	PROPN
m-1112	2818	7	&	&	CCONJ
m-1112	2818	8	w̅	w̅	PROPN
m-1112	2818	9	,	,	PUNCT
m-1112	2818	10	as	as	ADP
m-1112	2818	11	real	real	ADJ
m-1112	2818	12	≡	≡	PROPN
m-1112	2818	13	the	the	DET
m-1112	2818	14	existing	exist	VERB
m-1112	2818	15	universe	universe	NOUN
m-1112	2818	16	as	as	SCONJ
m-1112	2818	17	is	be	AUX
m-1112	2818	18	the	the	DET
m-1112	2818	19	real	real	ADJ
m-1112	2818	20	objective	objective	ADJ
m-1112	2818	21	reality	reality	NOUN
m-1112	2818	22	|	|	NOUN
m-1112	2818	23	�	�	NOUN
m-1112	2818	24	̅	̅	NOUN
m-1112	2818	25	�	�	PROPN
m-1112	2818	26	|	|	ADV
m-1112	2818	27	≡	≡	PROPN
m-1112	2818	28	the	the	DET
m-1112	2818	29	numeric	numeric	ADJ
m-1112	2818	30	vector	vector	NOUN
m-1112	2818	31	-	-	PUNCT
m-1112	2818	32	value	value	NOUN
m-1112	2818	33	of	of	ADP
m-1112	2818	34	the	the	DET
m-1112	2818	35	material	material	NOUN
m-1112	2818	36	-	-	PUNCT
m-1112	2818	37	point	point	NOUN
m-1112	2818	38	[	[	X
m-1112	2818	39	⊕	⊕	NOUN
m-1112	2818	40	,	,	PUNCT
m-1112	2818	41	r	r	NOUN
m-1112	2818	42	,	,	PUNCT
m-1112	2818	43	⊝	⊝	X
m-1112	2818	44	]	]	PUNCT
m-1112	2818	45	in	in	ADP
m-1112	2818	46	[	[	PUNCT
m-1112	2818	47	pns	pns	X
m-1112	2818	48	]	]	X
m-1112	2818	49	≡	≡	PROPN
m-1112	2818	50	the	the	DET
m-1112	2818	51	work	work	NOUN
m-1112	2818	52	stored	store	VERB
m-1112	2818	53	in	in	ADP
m-1112	2818	54	polhode	polhode	NOUN
m-1112	2818	55	cone	cone	NOUN
m-1112	2818	56	of	of	ADP
m-1112	2818	57	the	the	DET
m-1112	2818	58	|𝐎𝐒̅̅	|𝐎𝐒̅̅	PROPN
m-1112	2818	59	̅̅	̅̅	NOUN
m-1112	2818	60	|	|	ADV
m-1112	2818	61	rolling	roll	VERB
m-1112	2818	62	nib	nib	NOUN
m-1112	2818	63	-vector	-vector	NOUN
m-1112	2818	64	produced	produce	VERB
m-1112	2818	65	from	from	ADP
m-1112	2818	66	the	the	DET
m-1112	2818	67	eternal	eternal	ADJ
m-1112	2818	68	centripetal	centripetal	ADJ
m-1112	2818	69	force	force	NOUN
m-1112	2818	70	,	,	PUNCT
m-1112	2818	71	𝐅	𝐅	PROPN
m-1112	2818	72	𝐂	𝐂	PROPN
m-1112	2818	73	as	as	ADP
m-1112	2818	74	the	the	DET
m-1112	2818	75	newton`s	newton`s	NOUN
m-1112	2818	76	action	action	NOUN
m-1112	2818	77	in	in	ADP
m-1112	2818	78	the	the	DET
m-1112	2818	79	planck`s	planck`s	NOUN
m-1112	2818	80	cave	cave	NOUN
m-1112	2818	81	,	,	PUNCT
m-1112	2818	82	and	and	CCONJ
m-1112	2818	83	from	from	ADP
m-1112	2818	84	the	the	DET
m-1112	2818	85	�	�	PROPN
m-1112	2818	86	̅	̅	NOUN
m-1112	2818	87	�	�	NOUN
m-1112	2818	88	angular	angular	ADJ
m-1112	2818	89	momentum	momentum	NOUN
m-1112	2818	90	in	in	ADP
m-1112	2818	91	the	the	PRON
m-1112	2818	92	,	,	PUNCT
m-1112	2818	93	+	+	CCONJ
m-1112	2818	94	↓	↓	X
m-1112	2818	95	b̅	b̅	NOUN
m-1112	2818	96	,	,	PUNCT
m-1112	2818	97	direction	direction	NOUN
m-1112	2818	98	.	.	PUNCT
m-1112	2819	1	the	the	DET
m-1112	2819	2	real	real	ADJ
m-1112	2819	3	type	type	NOUN
m-1112	2819	4	is	be	AUX
m-1112	2819	5	applied	apply	VERB
m-1112	2819	6	on	on	ADP
m-1112	2819	7	all	all	DET
m-1112	2819	8	different	different	ADJ
m-1112	2819	9	monads	monad	NOUN
m-1112	2819	10	and	and	CCONJ
m-1112	2819	11	their	their	PRON
m-1112	2819	12	compounds	compound	NOUN
m-1112	2819	13	monads	monad	NOUN
m-1112	2819	14	.	.	PUNCT
m-1112	2820	1	[	[	X
m-1112	2820	2	109	109	NUM
m-1112	2820	3	]	]	SYM
m-1112	2820	4	momentum	momentum	NOUN
m-1112	2820	5	b̅	b̅	PROPN
m-1112	2820	6	&	&	CCONJ
m-1112	2820	7	w̅	w̅	PROPN
m-1112	2820	8	,	,	PUNCT
m-1112	2820	9	as	as	ADP
m-1112	2820	10	imaginary	imaginary	ADJ
m-1112	2820	11	≡	≡	PROPN
m-1112	2820	12	the	the	DET
m-1112	2820	13	black	black	ADJ
m-1112	2820	14	holes	hole	NOUN
m-1112	2820	15	as	as	SCONJ
m-1112	2820	16	is	be	AUX
m-1112	2820	17	their	their	PRON
m-1112	2820	18	real	real	ADJ
m-1112	2820	19	objective	objective	ADJ
m-1112	2820	20	reality	reality	NOUN
m-1112	2820	21	±	±	NUM
m-1112	2820	22	�	�	PROPN
m-1112	2820	23	̅	̅	NOUN
m-1112	2820	24	�	�	PROPN
m-1112	2820	25	.i	.i	NOUN
m-1112	2820	26	≡	≡	PROPN
m-1112	2820	27	s	s	PROPN
m-1112	2820	28			NOUN
m-1112	2820	29	the	the	DET
m-1112	2820	30	numeric	numeric	ADJ
m-1112	2820	31	amplitude	amplitude	NOUN
m-1112	2820	32	-	-	PUNCT
m-1112	2820	33	vector	vector	NOUN
m-1112	2820	34	-	-	PUNCT
m-1112	2820	35	value	value	NOUN
m-1112	2820	36	of	of	ADP
m-1112	2820	37	material	material	NOUN
m-1112	2820	38	-	-	PUNCT
m-1112	2820	39	point	point	NOUN
m-1112	2820	40	[	[	X
m-1112	2820	41	⊕,r,⊝	⊕,r,⊝	X
m-1112	2820	42	]	]	X
m-1112	2820	43	in	in	ADP
m-1112	2820	44	[	[	X
m-1112	2820	45	pns	pns	NOUN
m-1112	2820	46	]	]	PUNCT
m-1112	2820	47	and	and	CCONJ
m-1112	2820	48	the	the	DET
m-1112	2820	49	imaginary	imaginary	ADJ
m-1112	2820	50	�	�	PROPN
m-1112	2820	51	̅	̅	NOUN
m-1112	2820	52	�	�	SYM
m-1112	2820	53	.i	.i	PROPN
m-1112	2820	54	≡	≡	PROPN
m-1112	2820	55	centripetal	centripetal	ADJ
m-1112	2820	56	force	force	NOUN
m-1112	2820	57	𝐅	𝐅	PROPN
m-1112	2820	58	𝐂	𝐂	PROPN
m-1112	2820	59	≡	≡	PROPN
m-1112	2820	60	the	the	DET
m-1112	2820	61	wave	wave	NOUN
m-1112	2820	62	amplitude	amplitude	NOUN
m-1112	2820	63	-value	-value	PROPN
m-1112	2820	64	≡	≡	PROPN
m-1112	2820	65	the	the	DET
m-1112	2820	66	work	work	NOUN
m-1112	2820	67	stored	store	VERB
m-1112	2820	68	in	in	ADP
m-1112	2820	69	the	the	DET
m-1112	2820	70	herpolhode	herpolhode	ADJ
m-1112	2820	71	cone	cone	NOUN
m-1112	2820	72	of	of	ADP
m-1112	2820	73	the	the	DET
m-1112	2820	74	|𝐎𝐁̅̅	|𝐎𝐁̅̅	PROPN
m-1112	2820	75	̅̅	̅̅	NOUN
m-1112	2820	76	|	|	ADV
m-1112	2820	77	rotating	rotate	VERB
m-1112	2820	78	�	�	NOUN
m-1112	2820	79	̅	̅	NOUN
m-1112	2820	80	�	�	NOUN
m-1112	2820	81	-vector	-vector	NOUN
m-1112	2820	82	and	and	CCONJ
m-1112	2820	83	also	also	ADV
m-1112	2820	84	produced	produce	VERB
m-1112	2820	85	from	from	ADP
m-1112	2820	86	the	the	DET
m-1112	2820	87	eternal	eternal	ADJ
m-1112	2820	88	centripetal	centripetal	ADJ
m-1112	2820	89	force	force	NOUN
m-1112	2820	90	𝐅	𝐅	PROPN
m-1112	2820	91	𝐂	𝐂	PROPN
m-1112	2820	92	,	,	PUNCT
m-1112	2820	93	as	as	ADP
m-1112	2820	94	the	the	DET
m-1112	2820	95	newton`s	newton`s	NOUN
m-1112	2820	96	reaction	reaction	NOUN
m-1112	2820	97	into	into	ADP
m-1112	2820	98	the	the	DET
m-1112	2820	99	planck`s	planck`s	NOUN
m-1112	2820	100	cave	cave	NOUN
m-1112	2820	101	and	and	CCONJ
m-1112	2820	102	from	from	ADP
m-1112	2820	103	the	the	DET
m-1112	2820	104	�	�	PROPN
m-1112	2820	105	̅	̅	NOUN
m-1112	2820	106	�	�	NOUN
m-1112	2820	107	angular	angular	ADJ
m-1112	2820	108	momentum	momentum	NOUN
m-1112	2820	109	in	in	ADP
m-1112	2820	110	,	,	PUNCT
m-1112	2820	111	↑	↑	PROPN
m-1112	2820	112	�	�	PROPN
m-1112	2820	113	̅	̅	NOUN
m-1112	2820	114	�	�	PROPN
m-1112	2820	115	direction	direction	NOUN
m-1112	2820	116	.	.	PUNCT
m-1112	2821	1	ijo	ijo	PROPN
m-1112	2821	2	international	international	PROPN
m-1112	2821	3	journal	journal	PROPN
m-1112	2821	4	of	of	ADP
m-1112	2821	5	mathematics	mathematics	PROPN
m-1112	2821	6	(	(	PUNCT
m-1112	2821	7	issn	issn	PROPN
m-1112	2821	8	:	:	PUNCT
m-1112	2821	9	2992	2992	NUM
m-1112	2821	10	-	-	SYM
m-1112	2821	11	4421	4421	NUM
m-1112	2821	12	)	)	PUNCT
m-1112	2821	13	volume	volume	NOUN
m-1112	2821	14	08	08	NUM
m-1112	2822	1	|	|	ADV
m-1112	2822	2	issue	issue	NOUN
m-1112	2822	3	08	08	NUM
m-1112	2823	1	|	|	ADV
m-1112	2823	2	august	august	PROPN
m-1112	2823	3	2025	2025	NUM
m-1112	2823	4	|	|	ADV
m-1112	2823	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2823	6	ijo	ijo	PROPN
m-1112	2823	7	journals	journal	NOUN
m-1112	2823	8	99	99	NUM
m-1112	2823	9	the	the	DET
m-1112	2823	10	fundamental	fundamental	ADJ
m-1112	2823	11	particles	particle	NOUN
m-1112	2823	12	origination	origination	NOUN
m-1112	2823	13	mechanism	mechanism	NOUN
m-1112	2823	14	in	in	ADP
m-1112	2823	15	mfmf	mfmf	PROPN
m-1112	2823	16	pns	pns	PROPN
m-1112	2823	17	caves	cave	NOUN
m-1112	2823	18	.	.	PUNCT
m-1112	2824	1	l	l	X
m-1112	2824	2	..	..	PUNCT
m-1112	2824	3	in	in	ADP
m-1112	2824	4	case	case	NOUN
m-1112	2824	5	of	of	ADP
m-1112	2824	6	points	point	NOUN
m-1112	2824	7	a	a	DET
m-1112	2824	8	,	,	PUNCT
m-1112	2824	9	b	b	NOUN
m-1112	2824	10	,	,	PUNCT
m-1112	2824	11	c	c	PROPN
m-1112	2825	1	being	be	AUX
m-1112	2825	2	on	on	ADP
m-1112	2825	3	a	a	DET
m-1112	2825	4	sphere	sphere	NOUN
m-1112	2825	5	then	then	ADV
m-1112	2825	6	[	[	X
m-1112	2825	7	stpl	stpl	X
m-1112	2825	8	]	]	PUNCT
m-1112	2825	9	becomes	become	VERB
m-1112	2825	10	a	a	DET
m-1112	2825	11	cylinder	cylinder	NOUN
m-1112	2825	12	as	as	SCONJ
m-1112	2825	13	this	this	PRON
m-1112	2825	14	is	be	AUX
m-1112	2825	15	the	the	DET
m-1112	2825	16	angular	angular	ADJ
m-1112	2825	17	-	-	PUNCT
m-1112	2825	18	momentum	momentum	NOUN
m-1112	2825	19	�	�	NOUN
m-1112	2825	20	̅	̅	NOUN
m-1112	2825	21	�	�	NOUN
m-1112	2825	22	=	=	SYM
m-1112	2825	23	2l	2l	NOUN
m-1112	2825	24	w̅	w̅	PUNCT
m-1112	2826	1	=	=	SYM
m-1112	2826	2	2l	2l	NUM
m-1112	2826	3	2πf	2πf	NOUN
m-1112	2827	1	=	=	PUNCT
m-1112	2828	1	[	[	PUNCT
m-1112	2828	2	2l	2l	NUM
m-1112	2828	3	2π	2π	NOUN
m-1112	2828	4	]	]	PUNCT
m-1112	2828	5	.	.	PUNCT
m-1112	2829	1	[	[	PUNCT
m-1112	2829	2	1	1	NUM
m-1112	2829	3	f	f	NOUN
m-1112	2829	4	]	]	X
m-1112	2829	5	=	=	PUNCT
m-1112	2829	6	constant	constant	ADJ
m-1112	2829	7	2π	2π	NOUN
m-1112	2829	8	[	[	PUNCT
m-1112	2829	9	1	1	NUM
m-1112	2829	10	fm	fm	NOUN
m-1112	2829	11	]	]	PUNCT
m-1112	2829	12	=	=	PUNCT
m-1112	2830	1	spin	spin	NOUN
m-1112	2831	1	[	[	X
m-1112	2831	2	89	89	NUM
m-1112	2831	3	]	]	X
m-1112	2831	4	d	d	X
m-1112	2831	5	...	...	PUNCT
m-1112	2831	6	the	the	DET
m-1112	2831	7	origination	origination	NOUN
m-1112	2831	8	of	of	ADP
m-1112	2831	9	the	the	DET
m-1112	2831	10	fundamental	fundamental	ADJ
m-1112	2831	11	particles	particle	NOUN
m-1112	2831	12	1d	1d	NUM
m-1112	2831	13	…	…	PUNCT
m-1112	2831	14	the	the	DET
m-1112	2831	15	balancing	balancing	NOUN
m-1112	2831	16	of	of	ADP
m-1112	2831	17	the	the	DET
m-1112	2831	18	space	space	NOUN
m-1112	2831	19	and	and	CCONJ
m-1112	2831	20	anti	anti	ADJ
m-1112	2831	21	-	-	NOUN
m-1112	2831	22	space	space	NOUN
m-1112	2831	23	.	.	PUNCT
m-1112	2832	1	[	[	X
m-1112	2832	2	64	64	NUM
m-1112	2832	3	]	]	PUNCT
m-1112	2832	4	↺	↺	NOUN
m-1112	2832	5	↻	↻	NOUN
m-1112	2832	6	↻	↻	VERB
m-1112	2832	7	↺	↺	NOUN
m-1112	2832	8	→	→	SYM
m-1112	2832	9	↻	↻	NOUN
m-1112	2832	10	↺	↺	NOUN
m-1112	2832	11	+	+	CCONJ
m-1112	2832	12	↺	↺	NOUN
m-1112	2832	13	+	+	NUM
m-1112	2832	14	↻	↻	NOUN
m-1112	2832	15	figure	figure	NOUN
m-1112	2832	16	-18	-18	PROPN
m-1112	2832	17	:	:	PUNCT
m-1112	2832	18	the	the	DET
m-1112	2832	19	work	work	NOUN
m-1112	2832	20	w	w	NOUN
m-1112	2832	21	,	,	PUNCT
m-1112	2832	22	of	of	ADP
m-1112	2832	23	two	two	NUM
m-1112	2832	24	-	-	PUNCT
m-1112	2832	25	quaternion	quaternion	NOUN
m-1112	2832	26	-	-	PUNCT
m-1112	2832	27	monads	monad	NOUN
m-1112	2832	28	𝐳	𝐳	X
m-1112	2832	29	=	=	X
m-1112	2832	30	(	(	PUNCT
m-1112	2832	31	s	s	NUM
m-1112	2832	32	+	+	NUM
m-1112	2832	33	v̅.	v̅.	NOUN
m-1112	2832	34	i	i	NOUN
m-1112	2832	35	)	)	PUNCT
m-1112	2833	1	≡	≡	PROPN
m-1112	2833	2	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	2833	3	̅̅	̅̅	PROPN
m-1112	2833	4	≡	≡	PROPN
m-1112	2833	5	�	�	PROPN
m-1112	2833	6	⃗⃗	⃗⃗	PROPN
m-1112	2833	7	�	�	PROPN
m-1112	2833	8	is	be	AUX
m-1112	2833	9	the	the	DET
m-1112	2833	10	action	action	NOUN
m-1112	2833	11	of	of	ADP
m-1112	2833	12	any	any	DET
m-1112	2833	13	two	two	NUM
m-1112	2833	14	tangential	tangential	ADJ
m-1112	2833	15	&	&	CCONJ
m-1112	2833	16	opposite	opposite	ADJ
m-1112	2833	17	equilibrium	equilibrium	NOUN
m-1112	2833	18	-	-	PUNCT
m-1112	2833	19	dipole	dipole	NOUN
m-1112	2833	20	[	[	X
m-1112	2833	21	⊕↔⊝	⊕↔⊝	X
m-1112	2833	22	]	]	X
m-1112	2833	23	with	with	ADP
m-1112	2833	24	v	v	NOUN
m-1112	2833	25	=	=	NOUN
m-1112	2833	26	w⃗⃗⃗	w⃗⃗⃗	NOUN
m-1112	2833	27	.r	.r	NOUN
m-1112	2833	28	.	.	PUNCT
m-1112	2834	1	for	for	ADP
m-1112	2834	2	quaternion	quaternion	NOUN
m-1112	2834	3	actions	action	NOUN
m-1112	2834	4	exists	exist	VERB
m-1112	2834	5	the	the	DET
m-1112	2834	6	square	square	ADJ
m-1112	2834	7	law	law	NOUN
m-1112	2834	8	for	for	ADP
m-1112	2834	9	both	both	CCONJ
m-1112	2834	10	real	real	ADJ
m-1112	2834	11	and	and	CCONJ
m-1112	2834	12	imaginary	imaginary	ADJ
m-1112	2834	13	part	part	NOUN
m-1112	2834	14	,	,	PUNCT
m-1112	2834	15	as	as	ADP
m-1112	2834	16	𝐳	𝐳	X
m-1112	2834	17	*	*	PUNCT
m-1112	2834	18	𝐳	𝐳	X
m-1112	2834	19	=	=	X
m-1112	2834	20	(	(	PUNCT
m-1112	2834	21	s	s	NOUN
m-1112	2834	22	+	+	CCONJ
m-1112	2834	23	v̅.	v̅.	NOUN
m-1112	2834	24	i	i	NOUN
m-1112	2834	25	)	)	PUNCT
m-1112	2834	26	²	²	PROPN
m-1112	2834	27	=	=	PUNCT
m-1112	2834	28	s²	s²	NOUN
m-1112	2835	1	+	+	PROPN
m-1112	2835	2	[	[	X
m-1112	2835	3	v̅.	v̅.	NOUN
m-1112	2835	4	]	]	PUNCT
m-1112	2835	5	²	²	NUM
m-1112	2835	6	+2.sv̅.	+2.sv̅.	NOUN
m-1112	2835	7	i	i	NOUN
m-1112	2835	8	=	=	SYM
m-1112	2835	9	s²	s²	ADJ
m-1112	2835	10	–	–	PUNCT
m-1112	2835	11	v̅	v̅	NOUN
m-1112	2835	12	²	²	NUM
m-1112	2835	13	±	±	NUM
m-1112	2835	14	2.s	2.s	NUM
m-1112	2835	15	v̅	v̅	NOUN
m-1112	2836	1	=	=	NOUN
m-1112	2836	2	|s|²	|s|²	PROPN
m-1112	2836	3	-|s̅|²	-|s̅|²	NOUN
m-1112	2836	4	±	±	NOUN
m-1112	2836	5	2.|s|.|s̅|	2.|s|.|s̅|	NUM
m-1112	2836	6	,	,	PUNCT
m-1112	2836	7	for	for	ADP
m-1112	2836	8	|v̅|	|v̅|	PROPN
m-1112	2836	9	=	=	SYM
m-1112	2836	10	s	s	PART
m-1112	2836	11	vorticities	vorticitie	NOUN
m-1112	2836	12	±	±	NUM
m-1112	2836	13	λ	λ	PROPN
m-1112	2836	14	(	(	PUNCT
m-1112	2836	15	rotating	rotate	VERB
m-1112	2836	16	energy	energy	NOUN
m-1112	2836	17	)	)	PUNCT
m-1112	2836	18	,	,	PUNCT
m-1112	2836	19	becomes	become	VERB
m-1112	2836	20	from	from	ADP
m-1112	2836	21	the	the	DET
m-1112	2836	22	collision	collision	NOUN
m-1112	2836	23	on	on	ADP
m-1112	2836	24	common	common	ADJ
m-1112	2836	25	-	-	PUNCT
m-1112	2836	26	circle	circle	NOUN
m-1112	2836	27	and	and	CCONJ
m-1112	2836	28	from	from	ADP
m-1112	2836	29	the	the	DET
m-1112	2836	30	thrust	thrust	NOUN
m-1112	2836	31	on	on	ADP
m-1112	2836	32	the	the	DET
m-1112	2836	33	velocity	velocity	NOUN
m-1112	2836	34	-	-	PUNCT
m-1112	2836	35	breakages	breakage	NOUN
m-1112	2836	36	.the	.the	PRON
m-1112	2836	37	work	work	NOUN
m-1112	2836	38	is	be	AUX
m-1112	2836	39	,	,	PUNCT
m-1112	2836	40	w	w	PROPN
m-1112	2836	41	=	=	PUNCT
m-1112	2836	42	[	[	PUNCT
m-1112	2836	43	n	n	NOUN
m-1112	2836	44	.	.	PUNCT
m-1112	2837	1	p	p	X
m-1112	2837	2	]	]	X
m-1112	2838	1	=	=	PUNCT
m-1112	2838	2	[	[	PUNCT
m-1112	2838	3	λ.λ	λ.λ	X
m-1112	2838	4	]	]	X
m-1112	2838	5	,	,	PUNCT
m-1112	2838	6	where	where	SCONJ
m-1112	2838	7	λ	λ	PROPN
m-1112	2838	8	=	=	SYM
m-1112	2838	9	displacement	displacement	NOUN
m-1112	2838	10	of	of	ADP
m-1112	2838	11	a	a	DET
m-1112	2838	12	to	to	ADP
m-1112	2838	13	b	b	NOUN
m-1112	2838	14	and	and	CCONJ
m-1112	2838	15	it	it	PRON
m-1112	2838	16	is	be	AUX
m-1112	2838	17	a	a	DET
m-1112	2838	18	scalar	scalar	ADJ
m-1112	2838	19	magnitude	magnitude	NOUN
m-1112	2838	20	called	call	VERB
m-1112	2838	21	wavelength	wavelength	NOUN
m-1112	2838	22	of	of	ADP
m-1112	2838	23	dipole	dipole	PROPN
m-1112	2838	24	ab	ab	PROPN
m-1112	2838	25	.	.	PUNCT
m-1112	2839	1	λ	λ	X
m-1112	2839	2	=	=	NOUN
m-1112	2839	3	the	the	DET
m-1112	2839	4	amount	amount	NOUN
m-1112	2839	5	of	of	ADP
m-1112	2839	6	rotation	rotation	NOUN
m-1112	2839	7	on	on	ADP
m-1112	2839	8	dipole	dipole	NOUN
m-1112	2839	9	ab	ab	PROPN
m-1112	2840	1	(	(	PUNCT
m-1112	2840	2	this	this	PRON
m-1112	2840	3	is	be	AUX
m-1112	2840	4	angular	angular	ADJ
m-1112	2840	5	momentum	momentum	NOUN
m-1112	2840	6	and	and	CCONJ
m-1112	2840	7	it	it	PRON
m-1112	2840	8	is	be	AUX
m-1112	2840	9	a	a	DET
m-1112	2840	10	vector	vector	NOUN
m-1112	2840	11	)	)	PUNCT
m-1112	2840	12	.	.	PUNCT
m-1112	2841	1	momentum	momentum	NOUN
m-1112	2841	2	±	±	NOUN
m-1112	2841	3	λ̅	λ̅	X
m-1112	2841	4	=	=	PUNCT
m-1112	2841	5	r.m.v	r.m.v	NOUN
m-1112	2841	6	=	=	NOUN
m-1112	2842	1	r	r	NOUN
m-1112	2842	2	m	m	NOUN
m-1112	2842	3	wr	wr	NOUN
m-1112	2842	4	=	=	PUNCT
m-1112	2842	5	mr².w̅	mr².w̅	NOUN
m-1112	2842	6	,	,	PUNCT
m-1112	2842	7	where	where	SCONJ
m-1112	2842	8	w̅	w̅	PROPN
m-1112	2842	9	is	be	AUX
m-1112	2842	10	the	the	DET
m-1112	2842	11	angular	angular	ADJ
m-1112	2842	12	velocity	velocity	NOUN
m-1112	2842	13	(	(	PUNCT
m-1112	2842	14	spin	spin	NOUN
m-1112	2842	15	)	)	PUNCT
m-1112	2842	16	which	which	PRON
m-1112	2842	17	maps	map	VERB
m-1112	2842	18	velocity	velocity	NOUN
m-1112	2842	19	vector	vector	NOUN
m-1112	2842	20	v̅	v̅	NOUN
m-1112	2842	21	on	on	ADP
m-1112	2842	22	the	the	DET
m-1112	2842	23	perpendicular	perpendicular	NOUN
m-1112	2842	24	to	to	ADP
m-1112	2842	25	±	±	NUM
m-1112	2842	26	λ̅	λ̅	PROPN
m-1112	2842	27	plane	plane	NOUN
m-1112	2842	28	with	with	ADP
m-1112	2842	29	two	two	NUM
m-1112	2842	30	components	component	NOUN
m-1112	2842	31	v̅	v̅	PROPN
m-1112	2842	32	e	e	PROPN
m-1112	2842	33	⊥	⊥	PROPN
m-1112	2842	34	v̅	v̅	PROPN
m-1112	2842	35	b	b	PROPN
m-1112	2842	36	.	.	PUNCT
m-1112	2843	1	the	the	DET
m-1112	2843	2	tangential	tangential	ADJ
m-1112	2843	3	velocity	velocity	NOUN
m-1112	2843	4	v̅	v̅	NOUN
m-1112	2843	5	e	e	NOUN
m-1112	2843	6	=	=	NOUN
m-1112	2843	7	wr	wr	PROPN
m-1112	2843	8	,	,	PUNCT
m-1112	2843	9	is	be	AUX
m-1112	2843	10	the	the	DET
m-1112	2843	11	quaternion	quaternion	NOUN
m-1112	2843	12	v̅	v̅	NOUN
m-1112	2843	13	e	e	NOUN
m-1112	2843	14	=	=	SYM
m-1112	2843	15	w	w	NOUN
m-1112	2843	16	r	r	NOUN
m-1112	2843	17	=	=	PUNCT
m-1112	2843	18	z̅	z̅	SYM
m-1112	2843	19	=	=	PUNCT
m-1112	2844	1	[	[	PUNCT
m-1112	2844	2	s	s	X
m-1112	2844	3	+	+	CCONJ
m-1112	2844	4	v̅.	v̅.	NOUN
m-1112	2844	5	i	i	NOUN
m-1112	2844	6	]	]	PUNCT
m-1112	2844	7	where	where	SCONJ
m-1112	2844	8	s	s	VERB
m-1112	2844	9	=	=	SYM
m-1112	2844	10	v̅	v̅	PROPN
m-1112	2844	11	e	e	NOUN
m-1112	2844	12	=	=	SYM
m-1112	2844	13	|r.w̅|	|r.w̅|	PROPN
m-1112	2844	14	and	and	CCONJ
m-1112	2844	15	v̅.	v̅.	NOUN
m-1112	2844	16	i	i	NOUN
m-1112	2844	17	=	=	SYM
m-1112	2844	18	|w̅	|w̅	PROPN
m-1112	2844	19	x	x	X
m-1112	2845	1	r̅	r̅	ADP
m-1112	2845	2	|	|	ADV
m-1112	2845	3	.	.	PUNCT
m-1112	2846	1	in	in	ADP
m-1112	2846	2	a	a	DET
m-1112	2846	3	spherical	spherical	ADJ
m-1112	2846	4	cave	cave	NOUN
m-1112	2846	5	the	the	DET
m-1112	2846	6	biaxial	biaxial	ADJ
m-1112	2846	7	ellipsoid	ellipsoid	NOUN
m-1112	2846	8	(	(	PUNCT
m-1112	2846	9	σx	σx	NOUN
m-1112	2846	10	=	=	SYM
m-1112	2846	11	σy	σy	NOUN
m-1112	2846	12	)	)	PUNCT
m-1112	2846	13	exists	exist	VERB
m-1112	2846	14	as	as	ADP
m-1112	2846	15	momentum	momentum	NOUN
m-1112	2846	16	+	+	NOUN
m-1112	2846	17	λ	λ	NOUN
m-1112	2846	18	on	on	ADP
m-1112	2846	19	caves	cave	NOUN
m-1112	2846	20	of	of	ADP
m-1112	2846	21	diameter	diameter	NOUN
m-1112	2846	22	2r	2r	NUM
m-1112	2846	23	with	with	ADP
m-1112	2846	24	parallel	parallel	ADJ
m-1112	2846	25	circles	circle	NOUN
m-1112	2846	26	→	→	SYM
m-1112	2846	27	0	0	NUM
m-1112	2846	28	.the	.the	PRON
m-1112	2846	29	biaxial	biaxial	ADJ
m-1112	2846	30	anti	anti	NOUN
m-1112	2846	31	-	-	NOUN
m-1112	2846	32	ellipsoid	ellipsoid	ADJ
m-1112	2846	33	(	(	PUNCT
m-1112	2846	34	σx	σx	NOUN
m-1112	2846	35	=	=	SYM
m-1112	2846	36	σy	σy	NOUN
m-1112	2846	37	)	)	PUNCT
m-1112	2846	38	exists	exist	VERB
m-1112	2846	39	as	as	ADP
m-1112	2846	40	equal	equal	ADJ
m-1112	2846	41	and	and	CCONJ
m-1112	2846	42	opposite	opposite	ADJ
m-1112	2846	43	momentum	momentum	NOUN
m-1112	2846	44	λ	λ	NOUN
m-1112	2846	45	on	on	ADP
m-1112	2846	46	the	the	DET
m-1112	2846	47	same	same	ADJ
m-1112	2846	48	diameter	diameter	NOUN
m-1112	2846	49	2r	2r	NUM
m-1112	2846	50	with	with	ADP
m-1112	2846	51	anti	anti	ADJ
m-1112	2846	52	parallel	parallel	ADJ
m-1112	2846	53	circles	circle	NOUN
m-1112	2846	54	→	→	SYM
m-1112	2846	55	0	0	NUM
m-1112	2846	56	.	.	PUNCT
m-1112	2847	1	equilibrium	equilibrium	NOUN
m-1112	2847	2	of	of	ADP
m-1112	2847	3	the	the	DET
m-1112	2847	4	two	two	NUM
m-1112	2847	5	ellipsoids	ellipsoid	NOUN
m-1112	2847	6	±	±	PROPN
m-1112	2847	7	λ	λ	PROPN
m-1112	2847	8	,	,	PUNCT
m-1112	2847	9	presupposes	presuppose	VERB
m-1112	2847	10	a	a	DET
m-1112	2847	11	stabilizersystem	stabilizersystem	NOUN
m-1112	2847	12	attached	attach	VERB
m-1112	2847	13	to	to	ADP
m-1112	2847	14	ellipsoids	ellipsoid	NOUN
m-1112	2847	15	such	such	ADJ
m-1112	2847	16	that	that	SCONJ
m-1112	2847	17	opposite	opposite	ADJ
m-1112	2847	18	momentum	momentum	NOUN
m-1112	2847	19	is	be	AUX
m-1112	2847	20	distributed	distribute	VERB
m-1112	2847	21	to	to	ADP
m-1112	2847	22	the	the	DET
m-1112	2847	23	center	center	NOUN
m-1112	2847	24	of	of	ADP
m-1112	2847	25	mass	mass	NOUN
m-1112	2847	26	of	of	ADP
m-1112	2847	27	the	the	DET
m-1112	2847	28	total	total	ADJ
m-1112	2847	29	system	system	NOUN
m-1112	2847	30	,	,	PUNCT
m-1112	2847	31	recover	recover	VERB
m-1112	2847	32	equilibrium	equilibrium	NOUN
m-1112	2847	33	,	,	PUNCT
m-1112	2847	34	which	which	PRON
m-1112	2847	35	is	be	AUX
m-1112	2847	36	the	the	DET
m-1112	2847	37	center	center	NOUN
m-1112	2847	38	of	of	ADP
m-1112	2847	39	the	the	DET
m-1112	2847	40	spherical	spherical	ADJ
m-1112	2847	41	cave	cave	NOUN
m-1112	2847	42	.	.	PUNCT
m-1112	2848	1	ijo	ijo	PROPN
m-1112	2848	2	international	international	PROPN
m-1112	2848	3	journal	journal	PROPN
m-1112	2848	4	of	of	ADP
m-1112	2848	5	mathematics	mathematics	PROPN
m-1112	2848	6	(	(	PUNCT
m-1112	2848	7	issn	issn	PROPN
m-1112	2848	8	:	:	PUNCT
m-1112	2848	9	2992	2992	NUM
m-1112	2848	10	-	-	SYM
m-1112	2848	11	4421	4421	NUM
m-1112	2848	12	)	)	PUNCT
m-1112	2848	13	volume	volume	NOUN
m-1112	2848	14	08	08	NUM
m-1112	2849	1	|	|	ADV
m-1112	2849	2	issue	issue	NOUN
m-1112	2849	3	08	08	NUM
m-1112	2850	1	|	|	ADV
m-1112	2850	2	august	august	PROPN
m-1112	2850	3	2025	2025	NUM
m-1112	2850	4	|	|	ADV
m-1112	2850	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2850	6	ijo	ijo	PROPN
m-1112	2850	7	journals	journal	NOUN
m-1112	2850	8	100	100	NUM
m-1112	2850	9	the	the	DET
m-1112	2850	10	fundamental	fundamental	ADJ
m-1112	2850	11	particles	particle	NOUN
m-1112	2850	12	origination	origination	NOUN
m-1112	2850	13	mechanism	mechanism	NOUN
m-1112	2850	14	in	in	ADP
m-1112	2850	15	mfmf	mfmf	PROPN
m-1112	2850	16	pns	pns	PROPN
m-1112	2850	17	caves	cave	NOUN
m-1112	2850	18	.	.	PUNCT
m-1112	2851	1	the	the	DET
m-1112	2851	2	biaxial	biaxial	ADJ
m-1112	2851	3	ellipsoid	ellipsoid	NOUN
m-1112	2851	4	and	and	CCONJ
m-1112	2851	5	anti	anti	ADJ
m-1112	2851	6	-	-	ADJ
m-1112	2851	7	ellipsoid	ellipsoid	ADJ
m-1112	2851	8	are	be	AUX
m-1112	2851	9	inversely	inversely	ADV
m-1112	2851	10	directed	direct	VERB
m-1112	2851	11	and	and	CCONJ
m-1112	2851	12	rotated	rotate	VERB
m-1112	2851	13	in	in	ADP
m-1112	2851	14	the	the	DET
m-1112	2851	15	same	same	ADJ
m-1112	2851	16	circle	circle	NOUN
m-1112	2851	17	,	,	PUNCT
m-1112	2851	18	so	so	CCONJ
m-1112	2851	19	the	the	DET
m-1112	2851	20	two	two	NUM
m-1112	2851	21	velocity	velocity	NOUN
m-1112	2851	22	vectors	vector	NOUN
m-1112	2851	23	,	,	PUNCT
m-1112	2851	24	v̅	v̅	PROPN
m-1112	2851	25	,	,	PUNCT
m-1112	2851	26	−	−	PROPN
m-1112	2851	27	v̅	v̅	NOUN
m-1112	2851	28	,	,	PUNCT
m-1112	2851	29	collide	collide	VERB
m-1112	2851	30	.this	.this	PRON
m-1112	2851	31	collision	collision	NOUN
m-1112	2851	32	of	of	ADP
m-1112	2851	33	the	the	DET
m-1112	2851	34	two	two	NUM
m-1112	2851	35	opposite	opposite	ADJ
m-1112	2851	36	velocity	velocity	NOUN
m-1112	2851	37	-	-	PUNCT
m-1112	2851	38	vectors	vector	NOUN
m-1112	2851	39	is	be	AUX
m-1112	2851	40	the	the	DET
m-1112	2851	41	physical	physical	ADJ
m-1112	2851	42	-	-	PUNCT
m-1112	2851	43	action	action	NOUN
m-1112	2851	44	(	(	PUNCT
m-1112	2851	45	thrust	thrust	NOUN
m-1112	2851	46	)	)	PUNCT
m-1112	2851	47	of	of	ADP
m-1112	2851	48	the	the	DET
m-1112	2851	49	two	two	NUM
m-1112	2851	50	-	-	PUNCT
m-1112	2851	51	quaternion	quaternion	NOUN
m-1112	2851	52	and	and	CCONJ
m-1112	2851	53	their	their	PRON
m-1112	2851	54	action	action	NOUN
m-1112	2851	55	is	be	AUX
m-1112	2851	56	,	,	PUNCT
m-1112	2851	57	(	(	PUNCT
m-1112	2851	58	s	s	X
m-1112	2852	1	+	+	CCONJ
m-1112	2852	2	v̅.	v̅.	NOUN
m-1112	2852	3	i	i	NOUN
m-1112	2852	4	)	)	PUNCT
m-1112	2852	5	(	(	PUNCT
m-1112	2852	6	©	©	NOUN
m-1112	2852	7	)	)	PUNCT
m-1112	2852	8	(	(	PUNCT
m-1112	2852	9	s	s	X
m-1112	2852	10	+	+	CCONJ
m-1112	2852	11	v̅.	v̅.	NOUN
m-1112	2852	12	i	i	NOUN
m-1112	2852	13	)	)	PUNCT
m-1112	2852	14	=	=	PUNCT
m-1112	2853	1	[	[	X
m-1112	2853	2	s	s	X
m-1112	2853	3	+	+	ADJ
m-1112	2853	4	v̅	v̅	X
m-1112	2853	5	.	.	PUNCT
m-1112	2854	1	i	i	PRON
m-1112	2854	2	]	]	X
m-1112	2854	3	²	²	PROPN
m-1112	2854	4	=	=	SYM
m-1112	2854	5	s²	s²	PROPN
m-1112	2854	6	+	+	CCONJ
m-1112	2854	7	|	|	ADV
m-1112	2854	8	v̅|	v̅|	NOUN
m-1112	2854	9	²	²	NUM
m-1112	2854	10	.	.	PUNCT
m-1112	2855	1	i	i	PRON
m-1112	2855	2	²	²	NUM
m-1112	2856	1	+	+	CCONJ
m-1112	2856	2	2|s|.|v̅	2|s|.|v̅	NUM
m-1112	2856	3	|	|	NOUN
m-1112	2856	4	.	.	PUNCT
m-1112	2857	1	i	i	PRON
m-1112	2857	2	=	=	SYM
m-1112	2857	3	s²	s²	PROPN
m-1112	2857	4	|v̅|	|v̅|	PROPN
m-1112	2857	5	²	²	NUM
m-1112	2857	6	+	+	NUM
m-1112	2857	7	2|s|.|	2|s|.|	NUM
m-1112	2857	8	w̅	w̅	NUM
m-1112	2857	9	r|	r|	NOUN
m-1112	2857	10	.	.	PUNCT
m-1112	2858	1	i	i	PRON
m-1112	2858	2	=	=	SYM
m-1112	2858	3	s²	s²	PROPN
m-1112	2858	4	|v̅|	|v̅|	NOUN
m-1112	2858	5	²	²	NUM
m-1112	2858	6	+	+	CCONJ
m-1112	2859	1	[	[	X
m-1112	2859	2	2w̅].|s|	2w̅].|s|	NUM
m-1112	2859	3	|r|	|r|	PROPN
m-1112	2859	4	.	.	PUNCT
m-1112	2860	1	i	i	PRON
m-1112	2860	2	,	,	PUNCT
m-1112	2860	3	where	where	SCONJ
m-1112	2860	4	,	,	PUNCT
m-1112	2860	5	s²	s²	NOUN
m-1112	2860	6	=	=	SYM
m-1112	2860	7	(	(	PUNCT
m-1112	2860	8	r	r	NOUN
m-1112	2860	9	w	w	PROPN
m-1112	2860	10	)	)	PUNCT
m-1112	2860	11	²	²	NUM
m-1112	2860	12	→	→	X
m-1112	2860	13	is	be	AUX
m-1112	2860	14	the	the	DET
m-1112	2860	15	real	real	ADJ
m-1112	2860	16	-	-	PUNCT
m-1112	2860	17	part	part	NOUN
m-1112	2860	18	of	of	ADP
m-1112	2860	19	the	the	DET
m-1112	2860	20	new	new	ADJ
m-1112	2860	21	-	-	PUNCT
m-1112	2860	22	quaternion	quaternion	NOUN
m-1112	2860	23	,	,	PUNCT
m-1112	2860	24	|v̅|²	|v̅|²	NOUN
m-1112	2860	25	=	=	SYM
m-1112	2860	26	|w̅	|w̅	PROPN
m-1112	2860	27	x	x	PUNCT
m-1112	2860	28	r̅|²	r̅|²	NOUN
m-1112	2860	29	=	=	SYM
m-1112	2860	30	(	(	PUNCT
m-1112	2860	31	w.r	w.r	PROPN
m-1112	2860	32	)	)	PUNCT
m-1112	2860	33	²	²	PROPN
m-1112	2860	34	→	→	SYM
m-1112	2860	35	the	the	DET
m-1112	2860	36	always	always	ADV
m-1112	2860	37	negative	negative	ADJ
m-1112	2860	38	-	-	PUNCT
m-1112	2860	39	anti	anti	ADJ
m-1112	2860	40	-	-	NOUN
m-1112	2860	41	space	space	NOUN
m-1112	2860	42	(	(	PUNCT
m-1112	2860	43	a	a	DET
m-1112	2860	44	vector	vector	NOUN
m-1112	2860	45	⊥	⊥	X
m-1112	2860	46	to	to	ADP
m-1112	2860	47	w	w	NOUN
m-1112	2860	48	r	r	NOUN
m-1112	2860	49	plane	plane	NOUN
m-1112	2860	50	)	)	PUNCT
m-1112	2860	51	,	,	PUNCT
m-1112	2860	52	[	[	X
m-1112	2860	53	2	2	NUM
m-1112	2860	54	�	�	NOUN
m-1112	2860	55	̅	̅	NOUN
m-1112	2860	56	�	�	PROPN
m-1112	2860	57	].|s|.|	].|s|.|	NOUN
m-1112	2860	58	�	�	NOUN
m-1112	2860	59	̅	̅	NOUN
m-1112	2860	60	�	�	NOUN
m-1112	2860	61	.	.	PUNCT
m-1112	2861	1	i	i	PRON
m-1112	2861	2	=	=	PUNCT
m-1112	2862	1	2w.(sr	2w.(sr	NUM
m-1112	2862	2	)	)	PUNCT
m-1112	2862	3	.	.	PUNCT
m-1112	2863	1	i	i	PRON
m-1112	2863	2	→	→	PUNCT
m-1112	2863	3	the	the	DET
m-1112	2863	4	double	double	ADJ
m-1112	2863	5	angular	angular	ADJ
m-1112	2863	6	-	-	PUNCT
m-1112	2863	7	velocity	velocity	NOUN
m-1112	2863	8	-	-	PUNCT
m-1112	2863	9	term	term	NOUN
m-1112	2863	10	,	,	PUNCT
m-1112	2863	11	and	and	CCONJ
m-1112	2863	12	for	for	ADP
m-1112	2863	13	the	the	DET
m-1112	2863	14	pns	pns	PROPN
m-1112	2863	15	space	space	NOUN
m-1112	2863	16	where	where	SCONJ
m-1112	2863	17	|s|	|s|	VERB
m-1112	2863	18	=	=	SYM
m-1112	2863	19	|v̅|²	|v̅|²	PRON
m-1112	2863	20	then	then	ADV
m-1112	2863	21	s²	s²	PROPN
m-1112	2863	22	=	=	SYM
m-1112	2863	23	(	(	PUNCT
m-1112	2863	24	w.r	w.r	PROPN
m-1112	2863	25	)	)	PUNCT
m-1112	2863	26	²	²	NUM
m-1112	2863	27	≡	≡	PROPN
m-1112	2863	28	⊕	⊕	PROPN
m-1112	2863	29	≡	≡	PROPN
m-1112	2863	30	s	s	PART
m-1112	2863	31	²	²	PROPN
m-1112	2863	32	=	=	PUNCT
m-1112	2863	33	+	+	NOUN
m-1112	2863	34	charge	charge	NOUN
m-1112	2863	35	|v̅|²	|v̅|²	NOUN
m-1112	2863	36	=	=	SYM
m-1112	2863	37	|w̅xr̅|²	|w̅xr̅|²	NOUN
m-1112	2863	38	=	=	SYM
m-1112	2863	39	(	(	PUNCT
m-1112	2863	40	w.r	w.r	PROPN
m-1112	2863	41	)	)	PUNCT
m-1112	2863	42	²	²	NUM
m-1112	2863	43	≡	≡	PROPN
m-1112	2863	44	⊝	⊝	PUNCT
m-1112	2864	1	≡	≡	PROPN
m-1112	2864	2	s	s	PART
m-1112	2864	3	²	²	NUM
m-1112	2864	4	=	=	PUNCT
m-1112	2864	5	charge	charge	NOUN
m-1112	2864	6	[	[	X
m-1112	2864	7	2w̅].|v̅||.r̅.	2w̅].|v̅||.r̅.	NUM
m-1112	2864	8	i	i	NOUN
m-1112	2864	9	=	=	NOUN
m-1112	2864	10	2	2	NUM
m-1112	2864	11	|v̅|²	|v̅|²	NUM
m-1112	2864	12	=	=	SYM
m-1112	2864	13	2	2	NUM
m-1112	2864	14	(	(	PUNCT
m-1112	2864	15	w̅.r	w̅.r	X
m-1112	2864	16	)	)	PUNCT
m-1112	2864	17	≡	≡	PROPN
m-1112	2864	18	2[⊕↔⊝	2[⊕↔⊝	NUM
m-1112	2864	19	]	]	X
m-1112	2864	20	≡	≡	PROPN
m-1112	2864	21	2s	2s	NOUN
m-1112	2864	22	²	²	PROPN
m-1112	2864	23	=	=	SYM
m-1112	2864	24	0	0	NUM
m-1112	2864	25	charge	charge	NOUN
m-1112	2864	26	i.e.	i.e.	X
m-1112	2864	27	for	for	ADP
m-1112	2864	28	the	the	DET
m-1112	2864	29	equilibrium	equilibrium	NOUN
m-1112	2864	30	-	-	PUNCT
m-1112	2864	31	recovery	recovery	NOUN
m-1112	2864	32	(	(	PUNCT
m-1112	2864	33	maybe	maybe	ADV
m-1112	2864	34	a	a	DET
m-1112	2864	35	surface	surface	NOUN
m-1112	2864	36	cylinder	cylinder	NOUN
m-1112	2864	37	with	with	ADP
m-1112	2864	38	2r	2r	NUM
m-1112	2864	39	diameter	diameter	NOUN
m-1112	2864	40	)	)	PUNCT
m-1112	2864	41	,	,	PUNCT
m-1112	2864	42	fig-16	fig-16	PROPN
m-1112	2864	43	-	-	PUNCT
m-1112	2864	44	17	17	NUM
m-1112	2864	45	2d	2d	NOUN
m-1112	2864	46	..	..	PUNCT
m-1112	2865	1	the	the	DET
m-1112	2865	2	vibration	vibration	NOUN
m-1112	2865	3	of	of	ADP
m-1112	2865	4	particles	particle	NOUN
m-1112	2865	5	in	in	ADP
m-1112	2865	6	all	all	DET
m-1112	2865	7	levels	level	NOUN
m-1112	2865	8	[	[	X
m-1112	2865	9	54	54	NUM
m-1112	2865	10	]	]	PUNCT
m-1112	2865	11	.	.	PUNCT
m-1112	2866	1	figure	figure	VERB
m-1112	2866	2	19	19	NUM
m-1112	2866	3	:	:	PUNCT
m-1112	2866	4	the	the	DET
m-1112	2866	5	glue	glue	NOUN
m-1112	2866	6	-	-	PUNCT
m-1112	2866	7	bond	bond	NOUN
m-1112	2866	8	electrons	electron	NOUN
m-1112	2866	9	of	of	ADP
m-1112	2866	10	nucleus	nucleus	ADJ
m-1112	2866	11	rotor	rotor	NOUN
m-1112	2866	12	,	,	PUNCT
m-1112	2866	13	form	form	VERB
m-1112	2866	14	rhodonea	rhodonea	NOUN
m-1112	2866	15	-	-	PUNCT
m-1112	2866	16	like	like	ADJ
m-1112	2866	17	curves	curve	NOUN
m-1112	2866	18	curves	curve	NOUN
m-1112	2866	19	created	create	VERB
m-1112	2866	20	by	by	ADP
m-1112	2866	21	rotor`s	rotor`s	NOUN
m-1112	2866	22	electron	electron	NOUN
m-1112	2866	23	are	be	AUX
m-1112	2866	24	such	such	ADJ
m-1112	2866	25	that	that	SCONJ
m-1112	2866	26	they	they	PRON
m-1112	2866	27	keep	keep	VERB
m-1112	2866	28	a	a	DET
m-1112	2866	29	continuous	continuous	ADJ
m-1112	2866	30	pressure	pressure	NOUN
m-1112	2866	31	on	on	ADP
m-1112	2866	32	protons	proton	NOUN
m-1112	2866	33	.	.	PUNCT
m-1112	2867	1	1	1	NUM
m-1112	2867	2	..	..	PUNCT
m-1112	2867	3	the	the	DET
m-1112	2867	4	continuous	continuous	ADJ
m-1112	2867	5	action	action	NOUN
m-1112	2867	6	of	of	ADP
m-1112	2867	7	negative	negative	ADJ
m-1112	2867	8	⊝	⊝	NOUN
m-1112	2867	9	,	,	PUNCT
m-1112	2867	10	on	on	ADP
m-1112	2867	11	one	one	NUM
m-1112	2867	12	positive	positive	ADJ
m-1112	2867	13	⊕	⊕	PROPN
m-1112	2867	14	,	,	PUNCT
m-1112	2867	15	is	be	AUX
m-1112	2867	16	equivalent	equivalent	ADJ
m-1112	2867	17	to	to	ADP
m-1112	2867	18	a	a	DET
m-1112	2867	19	circular	circular	ADJ
m-1112	2867	20	motion	motion	NOUN
m-1112	2867	21	of	of	ADP
m-1112	2867	22	the	the	DET
m-1112	2867	23	⊝	⊝	PROPN
m-1112	2867	24	,	,	PUNCT
m-1112	2867	25	⊕	⊕	PROPN
m-1112	2867	26	,	,	PUNCT
m-1112	2867	27	with	with	ADP
m-1112	2867	28	velocity	velocity	NOUN
m-1112	2867	29	v	v	ADP
m-1112	2867	30	=	=	SYM
m-1112	2867	31	√f	√f	NOUN
m-1112	2867	32	.	.	PUNCT
m-1112	2868	1	r	r	X
m-1112	2868	2	/	/	SYM
m-1112	2868	3	m	m	PROPN
m-1112	2868	4	,	,	PUNCT
m-1112	2868	5	and	and	CCONJ
m-1112	2868	6	this	this	PRON
m-1112	2868	7	because	because	SCONJ
m-1112	2868	8	exists	exist	VERB
m-1112	2868	9	l	l	NOUN
m-1112	2868	10	=	=	SYM
m-1112	2868	11	r	r	NOUN
m-1112	2868	12	=	=	NOUN
m-1112	2868	13	constant	constant	ADJ
m-1112	2868	14	.	.	PUNCT
m-1112	2869	1	2	2	X
m-1112	2869	2	..	..	PUNCT
m-1112	2869	3	the	the	DET
m-1112	2869	4	continuous	continuous	ADJ
m-1112	2869	5	action	action	NOUN
m-1112	2869	6	of	of	ADP
m-1112	2869	7	negative	negative	ADJ
m-1112	2869	8	⊝	⊝	NOUN
m-1112	2869	9	,	,	PUNCT
m-1112	2869	10	on	on	ADP
m-1112	2869	11	two	two	NUM
m-1112	2869	12	positive	positive	ADJ
m-1112	2869	13	⊕⊕	⊕⊕	NOUN
m-1112	2869	14	of	of	ADP
m-1112	2869	15	glued	glue	VERB
m-1112	2869	16	bond	bond	NOUN
m-1112	2869	17	,	,	PUNCT
m-1112	2869	18	is	be	AUX
m-1112	2869	19	equal	equal	ADJ
m-1112	2869	20	to	to	ADP
m-1112	2869	21	a	a	DET
m-1112	2869	22	circular	circular	ADJ
m-1112	2869	23	and	and	CCONJ
m-1112	2869	24	other	other	ADJ
m-1112	2869	25	of	of	ADP
m-1112	2869	26	one	one	NUM
m-1112	2869	27	-	-	PUNCT
m-1112	2869	28	step	step	NOUN
m-1112	2869	29	longer	long	ADJ
m-1112	2869	30	motion	motion	NOUN
m-1112	2869	31	of	of	ADP
m-1112	2869	32	⊝	⊝	NUM
m-1112	2869	33	to	to	ADP
m-1112	2869	34	⊕⊕	⊕⊕	PROPN
m-1112	2869	35	,	,	PUNCT
m-1112	2869	36	or	or	CCONJ
m-1112	2869	37	circular	circular	ADJ
m-1112	2869	38	motion	motion	NOUN
m-1112	2869	39	on	on	ADP
m-1112	2869	40	ijo	ijo	PROPN
m-1112	2869	41	international	international	PROPN
m-1112	2869	42	journal	journal	PROPN
m-1112	2869	43	of	of	ADP
m-1112	2869	44	mathematics	mathematics	PROPN
m-1112	2869	45	(	(	PUNCT
m-1112	2869	46	issn	issn	PROPN
m-1112	2869	47	:	:	PUNCT
m-1112	2869	48	2992	2992	NUM
m-1112	2869	49	-	-	SYM
m-1112	2869	50	4421	4421	NUM
m-1112	2869	51	)	)	PUNCT
m-1112	2870	1	volume	volume	NOUN
m-1112	2870	2	08	08	NUM
m-1112	2871	1	|	|	ADV
m-1112	2871	2	issue	issue	NOUN
m-1112	2871	3	08	08	NUM
m-1112	2872	1	|	|	ADV
m-1112	2872	2	august	august	PROPN
m-1112	2872	3	2025	2025	NUM
m-1112	2872	4	|	|	ADV
m-1112	2872	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2872	6	ijo	ijo	NOUN
m-1112	2872	7	journals	journal	NOUN
m-1112	2872	8	101	101	NUM
m-1112	2872	9	the	the	DET
m-1112	2872	10	fundamental	fundamental	ADJ
m-1112	2872	11	particles	particle	NOUN
m-1112	2872	12	origination	origination	NOUN
m-1112	2872	13	mechanism	mechanism	NOUN
m-1112	2872	14	in	in	ADP
m-1112	2872	15	mfmf	mfmf	PROPN
m-1112	2872	16	pns	pns	PROPN
m-1112	2872	17	caves	cave	NOUN
m-1112	2872	18	.	.	PUNCT
m-1112	2873	1	the	the	DET
m-1112	2873	2	common	common	ADJ
m-1112	2873	3	–	–	PUNCT
m-1112	2873	4	length	length	NOUN
m-1112	2873	5	,	,	PUNCT
m-1112	2873	6	l	l	NOUN
m-1112	2873	7	,	,	PUNCT
m-1112	2873	8	in	in	ADP
m-1112	2873	9	polar	polar	ADJ
m-1112	2873	10	equations	equation	NOUN
m-1112	2873	11	is	be	AUX
m-1112	2873	12	,	,	PUNCT
m-1112	2873	13	l	l	X
m-1112	2873	14	=	=	PUNCT
m-1112	2873	15	a	a	PRON
m-1112	2873	16	.	.	PUNCT
m-1112	2874	1	cos(c.θ	cos(c.θ	NOUN
m-1112	2874	2	)	)	PUNCT
m-1112	2875	1	or	or	CCONJ
m-1112	2875	2	l	l	NOUN
m-1112	2875	3	=	=	PUNCT
m-1112	2875	4	a	a	PRON
m-1112	2875	5	.	.	PUNCT
m-1112	2875	6	sin(c.θ	sin(c.θ	NOUN
m-1112	2875	7	)	)	PUNCT
m-1112	2875	8	where	where	SCONJ
m-1112	2875	9	a	a	DET
m-1112	2875	10	=	=	X
m-1112	2875	11	the	the	DET
m-1112	2875	12	length	length	NOUN
m-1112	2875	13	of	of	ADP
m-1112	2875	14	the	the	DET
m-1112	2875	15	base	base	NOUN
m-1112	2875	16	=	=	SYM
m-1112	2876	1	2r+2r	2r+2r	NUM
m-1112	2876	2	=	=	SYM
m-1112	2876	3	4r	4r	NOUN
m-1112	2876	4	,	,	PUNCT
m-1112	2876	5	c	c	NOUN
m-1112	2876	6	=	=	SYM
m-1112	2876	7	rim`s	rim`s	PROPN
m-1112	2876	8	number	number	NOUN
m-1112	2876	9	which	which	PRON
m-1112	2876	10	produce	produce	VERB
m-1112	2876	11	a	a	DET
m-1112	2876	12	c	c	NOUN
m-1112	2876	13	-	-	PUNCT
m-1112	2876	14	petaled	petaled	ADJ
m-1112	2876	15	rose	rise	VERB
m-1112	2876	16	,	,	PUNCT
m-1112	2876	17	if	if	SCONJ
m-1112	2876	18	c	c	PROPN
m-1112	2876	19	is	be	AUX
m-1112	2876	20	odd	odd	ADJ
m-1112	2876	21	or	or	CCONJ
m-1112	2876	22	2c	2c	NOUN
m-1112	2876	23	-	-	PUNCT
m-1112	2876	24	petaled	petaled	ADJ
m-1112	2876	25	rose	rise	VERB
m-1112	2876	26	and	and	CCONJ
m-1112	2876	27	if	if	SCONJ
m-1112	2876	28	c	c	NOUN
m-1112	2876	29	is	be	AUX
m-1112	2876	30	even	even	ADV
m-1112	2876	31	number	number	NOUN
m-1112	2876	32	.	.	PUNCT
m-1112	2877	1	the	the	DET
m-1112	2877	2	period	period	NOUN
m-1112	2877	3	of	of	ADP
m-1112	2877	4	both	both	DET
m-1112	2877	5	cos(cθ	cos(cθ	NUM
m-1112	2877	6	)	)	PUNCT
m-1112	2877	7	,	,	PUNCT
m-1112	2877	8	sin(cθ	sin(cθ	NUM
m-1112	2877	9	)	)	PUNCT
m-1112	2877	10	is	be	AUX
m-1112	2877	11	2π	2π	NOUN
m-1112	2877	12	/	/	SYM
m-1112	2877	13	c	c	NOUN
m-1112	2877	14	,	,	PUNCT
m-1112	2877	15	and	and	CCONJ
m-1112	2877	16	the	the	DET
m-1112	2877	17	number	number	NOUN
m-1112	2877	18	of	of	ADP
m-1112	2877	19	petals	petal	NOUN
m-1112	2877	20	for	for	ADP
m-1112	2877	21	the	the	DET
m-1112	2877	22	period	period	NOUN
m-1112	2877	23	is	be	AUX
m-1112	2877	24	[	[	PUNCT
m-1112	2877	25	0	0	NUM
m-1112	2877	26	,	,	PUNCT
m-1112	2877	27	2π	2π	NOUN
m-1112	2877	28	/	/	SYM
m-1112	2877	29	c	c	X
m-1112	2877	30	]	]	PUNCT
m-1112	2877	31	will	will	AUX
m-1112	2877	32	be	be	AUX
m-1112	2877	33	c	c	NOUN
m-1112	2877	34	or	or	CCONJ
m-1112	2877	35	2c	2c	NUM
m-1112	2877	36	,	,	PUNCT
m-1112	2877	37	according	accord	VERB
m-1112	2877	38	to	to	ADP
m-1112	2877	39	as	as	SCONJ
m-1112	2877	40	c	c	PROPN
m-1112	2877	41	is	be	AUX
m-1112	2877	42	odd	odd	ADJ
m-1112	2877	43	or	or	CCONJ
m-1112	2877	44	c	c	NOUN
m-1112	2877	45	is	be	AUX
m-1112	2877	46	even	even	ADV
m-1112	2877	47	,	,	PUNCT
m-1112	2877	48	so	so	ADV
m-1112	2877	49	the	the	DET
m-1112	2877	50	degree	degree	NOUN
m-1112	2877	51	of	of	ADP
m-1112	2877	52	the	the	DET
m-1112	2877	53	cartesian	cartesian	ADJ
m-1112	2877	54	equation	equation	NOUN
m-1112	2877	55	of	of	ADP
m-1112	2877	56	the	the	DET
m-1112	2877	57	curve	curve	NOUN
m-1112	2877	58	is	be	AUX
m-1112	2877	59	,	,	PUNCT
m-1112	2877	60	c	c	X
m-1112	2877	61	+1	+1	PROPN
m-1112	2877	62	for	for	ADP
m-1112	2877	63	odd	odd	ADJ
m-1112	2877	64	-	-	PUNCT
m-1112	2877	65	c	c	NOUN
m-1112	2877	66	,	,	PUNCT
m-1112	2877	67	and	and	CCONJ
m-1112	2877	68	2(c+1	2(c+1	NOUN
m-1112	2877	69	)	)	PUNCT
m-1112	2877	70	for	for	ADP
m-1112	2877	71	even	even	ADV
m-1112	2877	72	-	-	PUNCT
m-1112	2877	73	c	c	NOUN
m-1112	2877	74	.	.	PUNCT
m-1112	2878	1	3	3	X
m-1112	2878	2	..	..	PUNCT
m-1112	2878	3	the	the	DET
m-1112	2878	4	continuous	continuous	ADJ
m-1112	2878	5	action	action	NOUN
m-1112	2878	6	of	of	ADP
m-1112	2878	7	negative	negative	ADJ
m-1112	2878	8	⊝	⊝	NOUN
m-1112	2878	9	,	,	PUNCT
m-1112	2878	10	on	on	ADP
m-1112	2878	11	three	three	NUM
m-1112	2878	12	positive	positive	ADJ
m-1112	2878	13	⊕⊕⊕	⊕⊕⊕	NOUN
m-1112	2878	14	of	of	ADP
m-1112	2878	15	glued	glue	VERB
m-1112	2878	16	bond	bond	NOUN
m-1112	2878	17	,	,	PUNCT
m-1112	2878	18	is	be	AUX
m-1112	2878	19	equivalent	equivalent	ADJ
m-1112	2878	20	to	to	ADP
m-1112	2878	21	a	a	DET
m-1112	2878	22	circular	circular	ADJ
m-1112	2878	23	-	-	PUNCT
m-1112	2878	24	and	and	CCONJ
m-1112	2878	25	other	other	ADJ
m-1112	2878	26	of	of	ADP
m-1112	2878	27	two	two	NUM
m-1112	2878	28	-	-	PUNCT
m-1112	2878	29	step	step	NOUN
m-1112	2878	30	longer	long	ADJ
m-1112	2878	31	motion	motion	NOUN
m-1112	2878	32	of	of	ADP
m-1112	2878	33	⊝	⊝	NUM
m-1112	2878	34	to	to	ADP
m-1112	2878	35	⊕⊕⊕	⊕⊕⊕	NOUN
m-1112	2878	36	,	,	PUNCT
m-1112	2878	37	or	or	CCONJ
m-1112	2878	38	circular	circular	ADJ
m-1112	2878	39	motion	motion	NOUN
m-1112	2878	40	on	on	ADP
m-1112	2878	41	the	the	DET
m-1112	2878	42	common	common	ADJ
m-1112	2878	43	–	–	PUNCT
m-1112	2878	44	length	length	NOUN
m-1112	2878	45	.	.	PUNCT
m-1112	2879	1	length	length	NOUN
m-1112	2879	2	,	,	PUNCT
m-1112	2879	3	l	l	NOUN
m-1112	2879	4	,	,	PUNCT
m-1112	2879	5	in	in	ADP
m-1112	2879	6	polar	polar	ADJ
m-1112	2879	7	equations	equation	NOUN
m-1112	2879	8	is	be	AUX
m-1112	2879	9	,	,	PUNCT
m-1112	2879	10	l	l	X
m-1112	2879	11	=	=	PUNCT
m-1112	2879	12	a	a	PRON
m-1112	2879	13	.	.	PUNCT
m-1112	2880	1	cos(c.θ	cos(c.θ	NOUN
m-1112	2880	2	)	)	PUNCT
m-1112	2881	1	or	or	CCONJ
m-1112	2881	2	l	l	NOUN
m-1112	2881	3	=	=	PUNCT
m-1112	2881	4	a	a	PRON
m-1112	2881	5	.	.	PUNCT
m-1112	2881	6	sin(c.θ	sin(c.θ	NOUN
m-1112	2881	7	)	)	PUNCT
m-1112	2881	8	,	,	PUNCT
m-1112	2881	9	where	where	SCONJ
m-1112	2881	10	a	a	PRON
m-1112	2881	11	is	be	AUX
m-1112	2881	12	the	the	DET
m-1112	2881	13	length	length	NOUN
m-1112	2881	14	of	of	ADP
m-1112	2881	15	the	the	DET
m-1112	2881	16	base	base	NOUN
m-1112	2881	17	=	=	SYM
m-1112	2881	18	2r	2r	NUM
m-1112	2882	1	+	+	NUM
m-1112	2882	2	2r	2r	NUM
m-1112	2882	3	+	+	CCONJ
m-1112	2882	4	2r	2r	NUM
m-1112	2882	5	=	=	SYM
m-1112	2882	6	6r	6r	NUM
m-1112	2882	7	,	,	PUNCT
m-1112	2882	8	c	c	NOUN
m-1112	2882	9	=	=	SYM
m-1112	2882	10	rim`s	rim`s	PROPN
m-1112	2882	11	number	number	NOUN
m-1112	2882	12	which	which	PRON
m-1112	2882	13	produce	produce	VERB
m-1112	2882	14	a	a	DET
m-1112	2882	15	c	c	NOUN
m-1112	2882	16	-	-	PUNCT
m-1112	2882	17	petaled	petaled	ADJ
m-1112	2882	18	rose	rise	VERB
m-1112	2882	19	,	,	PUNCT
m-1112	2882	20	where	where	SCONJ
m-1112	2882	21	c	c	PROPN
m-1112	2882	22	is	be	AUX
m-1112	2882	23	odd	odd	ADJ
m-1112	2882	24	or	or	CCONJ
m-1112	2882	25	2c	2c	NUM
m-1112	2882	26	petaled	petale	VERB
m-1112	2882	27	rose	rise	VERB
m-1112	2882	28	number	number	NOUN
m-1112	2882	29	.	.	PUNCT
m-1112	2883	1	this	this	PRON
m-1112	2883	2	is	be	AUX
m-1112	2883	3	seen	see	VERB
m-1112	2883	4	and	and	CCONJ
m-1112	2883	5	from	from	ADP
m-1112	2883	6	equations	equation	NOUN
m-1112	2883	7	issuing	issue	VERB
m-1112	2883	8	in	in	ADP
m-1112	2883	9	figure.21	figure.21	NOUN
m-1112	2883	10	-	-	SYM
m-1112	2883	11	2	2	NUM
m-1112	2883	12	→	→	SYM
m-1112	2883	13	r	r	NOUN
m-1112	2883	14	=	=	SYM
m-1112	2883	15	rd.sin	rd.sin	PROPN
m-1112	2883	16	φ	φ	NOUN
m-1112	2883	17	and	and	CCONJ
m-1112	2883	18	r	r	NOUN
m-1112	2883	19	=	=	NOUN
m-1112	2883	20	rd.sinφ	rd.sinφ	NOUN
m-1112	2883	21	where	where	SCONJ
m-1112	2883	22	a	a	PRON
m-1112	2883	23	,	,	PUNCT
m-1112	2883	24	are	be	AUX
m-1112	2883	25	the	the	DET
m-1112	2883	26	equal	equal	ADJ
m-1112	2883	27	radius	radius	NOUN
m-1112	2883	28	of	of	ADP
m-1112	2883	29	point	point	NOUN
m-1112	2883	30	a	a	PRON
m-1112	2883	31	of	of	ADP
m-1112	2883	32	polar	polar	ADJ
m-1112	2883	33	path	path	NOUN
m-1112	2883	34	.	.	PUNCT
m-1112	2884	1	rhodonea	rhodonea	PROPN
m-1112	2884	2	curves	curve	NOUN
m-1112	2884	3	follow	follow	VERB
m-1112	2884	4	the	the	DET
m-1112	2884	5	odd	odd	ADJ
m-1112	2884	6	or	or	CCONJ
m-1112	2884	7	and	and	CCONJ
m-1112	2884	8	even	even	ADV
m-1112	2884	9	number	number	NOUN
m-1112	2884	10	of	of	ADP
m-1112	2884	11	protons	proton	NOUN
m-1112	2884	12	in	in	ADP
m-1112	2884	13	nucleus	nucleus	NOUN
m-1112	2884	14	by	by	ADP
m-1112	2884	15	changing	change	VERB
m-1112	2884	16	their	their	PRON
m-1112	2884	17	rolling	rolling	NOUN
m-1112	2884	18	length	length	NOUN
m-1112	2884	19	a	a	DET
m-1112	2884	20	=	=	X
m-1112	2884	21	(	(	PUNCT
m-1112	2884	22	2r	2r	NUM
m-1112	2884	23	)	)	PUNCT
m-1112	2884	24	,	,	PUNCT
m-1112	2884	25	and	and	CCONJ
m-1112	2884	26	the	the	DET
m-1112	2884	27	polar	polar	ADJ
m-1112	2884	28	–	–	PUNCT
m-1112	2884	29	length	length	NOUN
m-1112	2884	30	l	l	NOUN
m-1112	2884	31	=	=	PUNCT
m-1112	2884	32	a	a	PRON
m-1112	2884	33	.	.	PUNCT
m-1112	2884	34	cos(c.θ	cos(c.θ	NOUN
m-1112	2884	35	)	)	PUNCT
m-1112	2884	36	depending	depend	VERB
m-1112	2884	37	on	on	ADP
m-1112	2884	38	,	,	PUNCT
m-1112	2884	39	θ	θ	PROPN
m-1112	2884	40	,	,	PUNCT
m-1112	2884	41	as	as	ADP
m-1112	2884	42	above	above	ADV
m-1112	2884	43	.	.	PUNCT
m-1112	2885	1	the	the	DET
m-1112	2885	2	common	common	ADJ
m-1112	2885	3	bonding	bonding	NOUN
m-1112	2885	4	point	point	NOUN
m-1112	2885	5	of	of	ADP
m-1112	2885	6	the	the	DET
m-1112	2885	7	negative	negative	ADJ
m-1112	2885	8	circle	circle	NOUN
m-1112	2885	9	and	and	CCONJ
m-1112	2885	10	the	the	DET
m-1112	2885	11	positive	positive	ADJ
m-1112	2885	12	line	line	NOUN
m-1112	2885	13	of	of	ADP
m-1112	2885	14	the	the	DET
m-1112	2885	15	rolling	rolling	ADJ
m-1112	2885	16	circle	circle	NOUN
m-1112	2885	17	obliges	oblige	VERB
m-1112	2885	18	that	that	DET
m-1112	2885	19	point	point	NOUN
m-1112	2885	20	to	to	PART
m-1112	2885	21	follow	follow	VERB
m-1112	2885	22	the	the	DET
m-1112	2885	23	cycloid	cycloid	NOUN
m-1112	2885	24	motion	motion	NOUN
m-1112	2885	25	in	in	ADP
m-1112	2885	26	maximum	maximum	ADJ
m-1112	2885	27	degree	degree	NOUN
m-1112	2885	28	and	and	CCONJ
m-1112	2885	29	thus	thus	ADV
m-1112	2885	30	executing	execute	VERB
m-1112	2885	31	hypocycloid	hypocycloid	ADJ
m-1112	2885	32	motion	motion	NOUN
m-1112	2885	33	.	.	PUNCT
m-1112	2886	1	particles	particle	NOUN
m-1112	2886	2	vibration	vibration	NOUN
m-1112	2886	3	in	in	ADP
m-1112	2886	4	all	all	DET
m-1112	2886	5	levels	level	NOUN
m-1112	2886	6	of	of	ADP
m-1112	2886	7	material	material	NOUN
m-1112	2886	8	-	-	PUNCT
m-1112	2886	9	geometry	geometry	NOUN
m-1112	2886	10	.	.	PUNCT
m-1112	2887	1	4	4	X
m-1112	2887	2	..	..	PUNCT
m-1112	2887	3	the	the	DET
m-1112	2887	4	n	n	CCONJ
m-1112	2887	5	-	-	PUNCT
m-1112	2887	6	knots	knot	NOUN
m-1112	2887	7	figures	figure	NOUN
m-1112	2887	8	exist	exist	VERB
m-1112	2887	9	in	in	ADP
m-1112	2887	10	figures	figure	NOUN
m-1112	2887	11	where	where	SCONJ
m-1112	2887	12	the	the	DET
m-1112	2887	13	vector	vector	NOUN
m-1112	2887	14	-force	-force	NOUN
m-1112	2887	15	polygons	polygon	NOUN
m-1112	2887	16	have	have	VERB
m-1112	2887	17	the	the	DET
m-1112	2887	18	same	same	ADJ
m-1112	2887	19	number	number	NOUN
m-1112	2887	20	n	n	NOUN
m-1112	2887	21	,	,	PUNCT
m-1112	2887	22	as	as	SCONJ
m-1112	2887	23	the	the	DET
m-1112	2887	24	in	in	ADP
m-1112	2887	25	figures	figure	NOUN
m-1112	2887	26	.	.	PUNCT
m-1112	2888	1	for	for	ADP
m-1112	2888	2	the	the	DET
m-1112	2888	3	circularlycharged	circularlycharged	ADJ
m-1112	2888	4	breakages	breakage	NOUN
m-1112	2888	5	the	the	DET
m-1112	2888	6	3	3	NUM
m-1112	2888	7	-	-	PUNCT
m-1112	2888	8	elements	element	NOUN
m-1112	2888	9	[	[	X
m-1112	2888	10	σ	σ	X
m-1112	2888	11	=	=	SYM
m-1112	2888	12	n	n	PROPN
m-1112	2888	13	.	.	PUNCT
m-1112	2889	1	h	h	X
m-1112	2889	2	]	]	X
m-1112	2889	3			NOUN
m-1112	2890	1	[	[	X
m-1112	2890	2	s²	s²	NOUN
m-1112	2890	3	=	=	SYM
m-1112	2890	4	⊕	⊕	PROPN
m-1112	2890	5	,	,	PUNCT
m-1112	2890	6	2s²=	2s²=	NUM
m-1112	2890	7	,	,	PUNCT
m-1112	2890	8	s²	s²	NOUN
m-1112	2890	9	=	=	SYM
m-1112	2890	10	⊝	⊝	X
m-1112	2890	11	]	]	PUNCT
m-1112	2890	12	formulate	formulate	VERB
m-1112	2890	13	the	the	DET
m-1112	2890	14	primary	primary	ADJ
m-1112	2890	15	-	-	PUNCT
m-1112	2890	16	particles	particle	NOUN
m-1112	2890	17	3	3	NUM
m-1112	2890	18	-	-	SYM
m-1112	2890	19	k	k	NOUN
m-1112	2890	20	,	,	PUNCT
m-1112	2890	21	figures	figure	NOUN
m-1112	2890	22	.	.	PUNCT
m-1112	2891	1	since	since	SCONJ
m-1112	2891	2	n	n	ADV
m-1112	2891	3	=3	=3	NOUN
m-1112	2891	4	,	,	PUNCT
m-1112	2891	5	the	the	DET
m-1112	2891	6	only	only	ADJ
m-1112	2891	7	shape	shape	NOUN
m-1112	2891	8	in	in	ADP
m-1112	2891	9	spaces	space	NOUN
m-1112	2891	10	is	be	AUX
m-1112	2891	11	the	the	DET
m-1112	2891	12	regular	regular	ADJ
m-1112	2891	13	triangle	triangle	NOUN
m-1112	2891	14	,	,	PUNCT
m-1112	2891	15	and	and	CCONJ
m-1112	2891	16	from	from	ADP
m-1112	2891	17	this	this	PRON
m-1112	2891	18	n	n	NOUN
m-1112	2891	19	<	<	X
m-1112	2891	20	4→	4→	NUM
m-1112	2891	21	n	n	CCONJ
m-1112	2891	22	there	there	PRON
m-1112	2891	23	are	be	VERB
m-1112	2891	24	vast	vast	ADJ
m-1112	2891	25	regions	region	NOUN
m-1112	2891	26	of	of	ADP
m-1112	2891	27	space	space	NOUN
m-1112	2891	28	that	that	PRON
m-1112	2891	29	are	be	AUX
m-1112	2891	30	very	very	ADV
m-1112	2891	31	nearly	nearly	ADV
m-1112	2891	32	empty	empty	ADJ
m-1112	2891	33	of	of	ADP
m-1112	2891	34	them	they	PRON
m-1112	2891	35	,	,	PUNCT
m-1112	2891	36	5	5	NUM
m-1112	2891	37	..	..	PUNCT
m-1112	2891	38	the	the	DET
m-1112	2891	39	case	case	NOUN
m-1112	2891	40	of	of	ADP
m-1112	2891	41	{	{	PUNCT
m-1112	2891	42	tcic}≡	tcic}≡	PROPN
m-1112	2891	43	[	[	PUNCT
m-1112	2891	44	σ	σ	X
m-1112	2891	45	=	=	SYM
m-1112	2891	46	n	n	PROPN
m-1112	2891	47	.	.	PUNCT
m-1112	2892	1	h	h	NOUN
m-1112	2892	2	]	]	PUNCT
m-1112	2893	1			NOUN
m-1112	2893	2	8	8	NUM
m-1112	2893	3	x	x	SYM
m-1112	2893	4	①	①	PROPN
m-1112	2893	5	which	which	PRON
m-1112	2893	6	is	be	AUX
m-1112	2893	7	the	the	DET
m-1112	2893	8	physical	physical	ADJ
m-1112	2893	9	mechanism	mechanism	NOUN
m-1112	2893	10	,	,	PUNCT
m-1112	2893	11	gives	give	VERB
m-1112	2893	12	the	the	DET
m-1112	2893	13	n	n	NOUN
m-1112	2893	14	-	-	PUNCT
m-1112	2893	15	masses	masse	NOUN
m-1112	2893	16	of	of	ADP
m-1112	2893	17	atom`s	atom`s	PROPN
m-1112	2893	18	&	&	CCONJ
m-1112	2893	19	compounds	compound	NOUN
m-1112	2893	20	determining	determine	VERB
m-1112	2893	21	the	the	DET
m-1112	2893	22	atoms	atom	NOUN
m-1112	2893	23	complex	complex	ADJ
m-1112	2893	24	-	-	PUNCT
m-1112	2893	25	vector	vector	NOUN
m-1112	2893	26	-	-	PUNCT
m-1112	2893	27	response	response	NOUN
m-1112	2893	28	.	.	PUNCT
m-1112	2894	1	these	these	DET
m-1112	2894	2	particles	particle	NOUN
m-1112	2894	3	exist	exist	VERB
m-1112	2894	4	in	in	ADP
m-1112	2894	5	all	all	PRON
m-1112	2894	6	of	of	ADP
m-1112	2894	7	the	the	DET
m-1112	2894	8	universe	universe	NOUN
m-1112	2894	9	in	in	ADP
m-1112	2894	10	the	the	DET
m-1112	2894	11	sense	sense	NOUN
m-1112	2894	12	that	that	SCONJ
m-1112	2894	13	they	they	PRON
m-1112	2894	14	are	be	AUX
m-1112	2894	15	uniformly	uniformly	ADV
m-1112	2894	16	distributed	distribute	VERB
m-1112	2894	17	throughout	throughout	ADP
m-1112	2894	18	space	space	NOUN
m-1112	2894	19	and	and	CCONJ
m-1112	2894	20	consist	consist	VERB
m-1112	2894	21	the	the	DET
m-1112	2894	22	objective	objective	ADJ
m-1112	2894	23	reality	reality	NOUN
m-1112	2894	24	which	which	PRON
m-1112	2894	25	is	be	AUX
m-1112	2894	26	the	the	DET
m-1112	2894	27	existing	exist	VERB
m-1112	2894	28	universe	universe	ADJ
m-1112	2894	29	ijo	ijo	PROPN
m-1112	2894	30	international	international	ADJ
m-1112	2894	31	journal	journal	PROPN
m-1112	2894	32	of	of	ADP
m-1112	2894	33	mathematics	mathematics	PROPN
m-1112	2894	34	(	(	PUNCT
m-1112	2894	35	issn	issn	PROPN
m-1112	2894	36	:	:	PUNCT
m-1112	2894	37	2992	2992	NUM
m-1112	2894	38	-	-	SYM
m-1112	2894	39	4421	4421	NUM
m-1112	2894	40	)	)	PUNCT
m-1112	2894	41	volume	volume	NOUN
m-1112	2894	42	08	08	NUM
m-1112	2895	1	|	|	ADV
m-1112	2895	2	issue	issue	NOUN
m-1112	2895	3	08	08	NUM
m-1112	2896	1	|	|	ADV
m-1112	2896	2	august	august	PROPN
m-1112	2896	3	2025	2025	NUM
m-1112	2896	4	|	|	ADV
m-1112	2896	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2896	6	ijo	ijo	PROPN
m-1112	2896	7	journals	journal	NOUN
m-1112	2896	8	102	102	NUM
m-1112	2896	9	the	the	DET
m-1112	2896	10	fundamental	fundamental	ADJ
m-1112	2896	11	particles	particle	NOUN
m-1112	2896	12	origination	origination	NOUN
m-1112	2896	13	mechanism	mechanism	NOUN
m-1112	2896	14	in	in	ADP
m-1112	2896	15	mfmf	mfmf	PROPN
m-1112	2896	16	pns	pns	PROPN
m-1112	2896	17	caves	cave	NOUN
m-1112	2896	18	.	.	PUNCT
m-1112	2897	1	figure	figure	NOUN
m-1112	2897	2	–	–	PUNCT
m-1112	2897	3	20	20	NUM
m-1112	2897	4	:	:	PUNCT
m-1112	2897	5	the	the	DET
m-1112	2897	6	carbon	carbon	NOUN
m-1112	2897	7	,	,	PUNCT
m-1112	2897	8	nitrogen	nitrogen	NOUN
m-1112	2897	9	,	,	PUNCT
m-1112	2897	10	oxygen	oxygen	NOUN
m-1112	2897	11	,	,	PUNCT
m-1112	2897	12	sulfur	sulfur	NOUN
m-1112	2897	13	,	,	PUNCT
m-1112	2897	14	atoms	atom	NOUN
m-1112	2897	15	-	-	PUNCT
m-1112	2897	16	conductors	conductor	NOUN
m-1112	2897	17	sustains	sustain	VERB
m-1112	2897	18	into	into	ADP
m-1112	2897	19	the	the	DET
m-1112	2897	20	first	first	ADJ
m-1112	2897	21	4	4	NUM
m-1112	2897	22	-	-	PUNCT
m-1112	2897	23	dimentional	dimentional	ADJ
m-1112	2897	24	spinning	spinning	NOUN
m-1112	2897	25	,	,	PUNCT
m-1112	2897	26	tetrahedron	tetrahedron	NOUN
m-1112	2897	27	cube	cube	NOUN
m-1112	2897	28	–	–	PUNCT
m-1112	2897	29	sphere	sphere	NOUN
m-1112	2897	30	mould	mould	NOUN
m-1112	2897	31	.	.	PUNCT
m-1112	2898	1	figure	figure	NOUN
m-1112	2898	2	–	–	PUNCT
m-1112	2898	3	20a	20a	NUM
m-1112	2898	4	:	:	PUNCT
m-1112	2898	5	the	the	DET
m-1112	2898	6	hydrogen	hydrogen	NOUN
m-1112	2898	7	,	,	PUNCT
m-1112	2898	8	carbon	carbon	NOUN
m-1112	2898	9	,	,	PUNCT
m-1112	2898	10	oxygen	oxygen	NOUN
m-1112	2898	11	,	,	PUNCT
m-1112	2898	12	atoms	atom	NOUN
m-1112	2898	13	-	-	PUNCT
m-1112	2898	14	conductors	conductor	NOUN
m-1112	2898	15	into	into	ADP
m-1112	2898	16	the	the	DET
m-1112	2898	17	sphere	sphere	NOUN
m-1112	2898	18	-	-	PUNCT
m-1112	2898	19	cube	cube	NOUN
m-1112	2898	20	mould	mould	NOUN
m-1112	2898	21	.	.	PUNCT
m-1112	2899	1	deka	deka	PROPN
m-1112	2899	2	hexahedron	hexahedron	NOUN
m-1112	2899	3	,	,	PUNCT
m-1112	2899	4	octahedron	octahedron	NOUN
m-1112	2899	5	≡	≡	PROPN
m-1112	2899	6	cube	cube	NOUN
m-1112	2899	7	,	,	PUNCT
m-1112	2899	8	tetrahedron	tetrahedron	NOUN
m-1112	2899	9	≡	≡	PROPN
m-1112	2899	10	4	4	NUM
m-1112	2899	11	-	-	PUNCT
m-1112	2899	12	points	point	NOUN
m-1112	2899	13	,	,	PUNCT
m-1112	2899	14	triangle	triangle	NOUN
m-1112	2899	15	≡	≡	PROPN
m-1112	2899	16	3	3	NUM
m-1112	2899	17	-	-	PUNCT
m-1112	2899	18	points	point	NOUN
m-1112	2899	19	,	,	PUNCT
m-1112	2899	20	vector	vector	NOUN
m-1112	2899	21	≡	≡	PROPN
m-1112	2899	22	2	2	NUM
m-1112	2899	23	-	-	PUNCT
m-1112	2899	24	points	point	NOUN
m-1112	2899	25	≡	≡	PROPN
m-1112	2899	26	the	the	DET
m-1112	2899	27	closed	close	VERB
m-1112	2899	28	-	-	PUNCT
m-1112	2899	29	conductor	conductor	NOUN
m-1112	2899	30	,	,	PUNCT
m-1112	2899	31	1	1	NUM
m-1112	2899	32	-	-	PUNCT
m-1112	2899	33	point	point	NOUN
m-1112	2899	34	≡	≡	PROPN
m-1112	2899	35	the	the	DET
m-1112	2899	36	opened	open	VERB
m-1112	2899	37	-conductor	-conductor	NOUN
m-1112	2899	38	≡	≡	PROPN
m-1112	2899	39	the	the	DET
m-1112	2899	40	bracket	bracket	NOUN
m-1112	2899	41	-	-	PUNCT
m-1112	2899	42	hook	hook	NOUN
m-1112	2899	43	.	.	PUNCT
m-1112	2900	1	oxygen	oxygen	NOUN
m-1112	2900	2	is	be	AUX
m-1112	2900	3	the	the	DET
m-1112	2900	4	element	element	NOUN
m-1112	2900	5	which	which	PRON
m-1112	2900	6	fills	fill	VERB
m-1112	2900	7	8	8	NUM
m-1112	2900	8	2	2	NUM
m-1112	2900	9	=	=	SYM
m-1112	2900	10	6	6	NUM
m-1112	2900	11	vertices	vertex	NOUN
m-1112	2900	12	of	of	ADP
m-1112	2900	13	cube	cube	NOUN
m-1112	2900	14	as	as	ADP
m-1112	2900	15	el	el	PROPN
m-1112	2900	16	→	→	PUNCT
m-1112	2900	17	{	{	PUNCT
m-1112	2900	18	1𝑒	1𝑒	NUM
m-1112	2900	19	0𝑒	0𝑒	VERB
m-1112	2900	20	1𝑒	1𝑒	PROPN
m-1112	2900	21	1	1	NUM
m-1112	2900	22	𝑒	𝑒	PROPN
m-1112	2900	23	2⃡	2⃡	NUM
m-1112	2900	24	0	0	PUNCT
m-1112	2900	25	𝑒	𝑒	PROPN
m-1112	2900	26	1𝑒	1𝑒	NUM
m-1112	2900	27	1𝑒	1𝑒	PROPN
m-1112	2900	28	1𝑒	1𝑒	PROPN
m-1112	2900	29	}	}	PUNCT
m-1112	2900	30	≡	≡	PROPN
m-1112	2900	31	(	(	PUNCT
m-1112	2900	32	±	±	NOUN
m-1112	2900	33	2	2	NUM
m-1112	2900	34	2	2	NUM
m-1112	2900	35	)	)	PUNCT
m-1112	2900	36	,	,	PUNCT
m-1112	2900	37	where	where	SCONJ
m-1112	2900	38	⓪	⓪	X
m-1112	2900	39	is	be	AUX
m-1112	2900	40	the	the	DET
m-1112	2900	41	first	first	ADJ
m-1112	2900	42	,	,	PUNCT
m-1112	2900	43	zero	zero	NUM
m-1112	2900	44	-	-	PUNCT
m-1112	2900	45	acting	act	VERB
m-1112	2900	46	cube	cube	NOUN
m-1112	2900	47	filled	fill	VERB
m-1112	2900	48	with	with	ADP
m-1112	2900	49	1e	1e	PROPN
m-1112	2900	50	,	,	PUNCT
m-1112	2900	51	therefore	therefore	ADV
m-1112	2900	52	is	be	AUX
m-1112	2900	53	the	the	DET
m-1112	2900	54	only	only	ADJ
m-1112	2900	55	steady	steady	ADJ
m-1112	2900	56	element	element	NOUN
m-1112	2900	57	which	which	PRON
m-1112	2900	58	occupies	occupy	VERB
m-1112	2900	59	the	the	DET
m-1112	2900	60	first	first	ADJ
m-1112	2900	61	energy	energy	NOUN
m-1112	2900	62	-	-	PUNCT
m-1112	2900	63	level	level	NOUN
m-1112	2900	64	①	①	NOUN
m-1112	2900	65	with	with	ADP
m-1112	2900	66	2	2	NUM
m-1112	2900	67	electron	electron	NOUN
m-1112	2900	68	-	-	PUNCT
m-1112	2900	69	positions	position	NOUN
m-1112	2900	70	as	as	ADP
m-1112	2900	71	①	①	X
m-1112	2900	72	=	=	SYM
m-1112	2900	73	2e	2e	NOUN
m-1112	2900	74	=	=	SYM
m-1112	2900	75	2⃡	2⃡	NOUN
m-1112	2900	76	positions	position	NOUN
m-1112	2900	77	at	at	ADP
m-1112	2900	78	1⃗	1⃗	NUM
m-1112	2900	79	,	,	PUNCT
m-1112	2900	80	1⃗⃖	1⃗⃖	NUM
m-1112	2900	81	the	the	DET
m-1112	2900	82	electron	electron	NOUN
m-1112	2900	83	being	be	AUX
m-1112	2900	84	in	in	ADP
m-1112	2900	85	the	the	DET
m-1112	2900	86	hydrogen	hydrogen	NOUN
m-1112	2900	87	-	-	PUNCT
m-1112	2900	88	cave	cave	NOUN
m-1112	2900	89	precesses	precesse	NOUN
m-1112	2900	90	because	because	SCONJ
m-1112	2900	91	of	of	ADP
m-1112	2900	92	the	the	DET
m-1112	2900	93	different	different	ADJ
m-1112	2900	94	axis	axis	NOUN
m-1112	2900	95	of	of	ADP
m-1112	2900	96	rotation	rotation	NOUN
m-1112	2900	97	and	and	CCONJ
m-1112	2900	98	nutation`s	nutation`s	ADP
m-1112	2900	99	,	,	PUNCT
m-1112	2900	100	from	from	ADP
m-1112	2900	101	the	the	DET
m-1112	2900	102	continuous	continuous	ADJ
m-1112	2900	103	and	and	CCONJ
m-1112	2900	104	immense	immense	ADJ
m-1112	2900	105	-	-	PUNCT
m-1112	2900	106	communication	communication	NOUN
m-1112	2900	107	to	to	ADP
m-1112	2900	108	the	the	DET
m-1112	2900	109	effect	effect	NOUN
m-1112	2900	110	of	of	ADP
m-1112	2900	111	gravity	gravity	NOUN
m-1112	2900	112	g	g	NOUN
m-1112	2900	113	.	.	PUNCT
m-1112	2901	1	since	since	SCONJ
m-1112	2901	2	electron	electron	NOUN
m-1112	2901	3	is	be	AUX
m-1112	2901	4	continually	continually	ADV
m-1112	2901	5	oscillating	oscillate	VERB
m-1112	2901	6	,	,	PUNCT
m-1112	2901	7	with	with	ADP
m-1112	2901	8	the	the	DET
m-1112	2901	9	nutation	nutation	NOUN
m-1112	2901	10	-	-	PUNCT
m-1112	2901	11	frequency	frequency	NOUN
m-1112	2901	12	𝐟	𝐟	NOUN
m-1112	2901	13	𝐍	𝐍	NOUN
m-1112	2901	14	,	,	PUNCT
m-1112	2901	15	so	so	ADV
m-1112	2901	16	produces	produce	VERB
m-1112	2901	17	a	a	DET
m-1112	2901	18	continuous	continuous	ADJ
m-1112	2901	19	and	and	CCONJ
m-1112	2901	20	oscillating	oscillate	VERB
m-1112	2901	21	magnetic	magnetic	ADJ
m-1112	2901	22	-	-	PUNCT
m-1112	2901	23	field	field	NOUN
m-1112	2901	24	–	–	PUNCT
m-1112	2901	25	mwhich	mwhich	NOUN
m-1112	2901	26	in	in	ADP
m-1112	2901	27	turn	turn	NOUN
m-1112	2901	28	is	be	AUX
m-1112	2901	29	the	the	DET
m-1112	2901	30	source	source	NOUN
m-1112	2901	31	of	of	ADP
m-1112	2901	32	an	an	DET
m-1112	2901	33	oscillating	oscillate	VERB
m-1112	2901	34	electric	electric	NOUN
m-1112	2901	35	-	-	PUNCT
m-1112	2901	36	field	field	NOUN
m-1112	2901	37	–	–	PUNCT
m-1112	2901	38	e	e	NOUN
m-1112	2901	39	which	which	PRON
m-1112	2901	40	implies	imply	VERB
m-1112	2901	41	the	the	DET
m-1112	2901	42	regeneration	regeneration	NOUN
m-1112	2901	43	of	of	ADP
m-1112	2901	44	each	each	DET
m-1112	2901	45	other	other	ADJ
m-1112	2901	46	,	,	PUNCT
m-1112	2901	47	i.e.	i.e.	X
m-1112	2901	48	it	it	PRON
m-1112	2901	49	is	be	AUX
m-1112	2901	50	a	a	DET
m-1112	2901	51	propagating	propagate	VERB
m-1112	2901	52	electromagnetic	electromagnetic	ADJ
m-1112	2901	53	-	-	PUNCT
m-1112	2901	54	wave	wave	NOUN
m-1112	2902	1	where	where	SCONJ
m-1112	2902	2	e	e	NOUN
m-1112	2902	3	=	=	SYM
m-1112	2902	4	b	b	PROPN
m-1112	2902	5	c	c	NOUN
m-1112	2902	6	,	,	PUNCT
m-1112	2902	7	and	and	CCONJ
m-1112	2902	8	with	with	ADP
m-1112	2902	9	a	a	DET
m-1112	2902	10	quantum	quantum	NOUN
m-1112	2902	11	-	-	PUNCT
m-1112	2902	12	energy	energy	NOUN
m-1112	2902	13	e	e	NOUN
m-1112	2902	14	=	=	NOUN
m-1112	2902	15	h	h	PROPN
m-1112	2902	16	fn	fn	NOUN
m-1112	2902	17	or	or	CCONJ
m-1112	2902	18	e	e	X
m-1112	2902	19	=	=	SYM
m-1112	2902	20	2μ.b	2μ.b	NUM
m-1112	2902	21	,	,	PUNCT
m-1112	2902	22	this	this	DET
m-1112	2902	23	energy	energy	NOUN
m-1112	2902	24	e	e	NOUN
m-1112	2902	25	consists	consist	VERB
m-1112	2902	26	the	the	DET
m-1112	2902	27	hydrogen	hydrogen	NOUN
m-1112	2902	28	bracket	bracket	NOUN
m-1112	2902	29	hook	hook	NOUN
m-1112	2902	30	hbh	hbh	PROPN
m-1112	2902	31	,	,	PUNCT
m-1112	2902	32	or	or	CCONJ
m-1112	2902	33	[	[	X
m-1112	2902	34	bh⃗⃗⃗⃗	bh⃗⃗⃗⃗	NOUN
m-1112	2902	35	⃗	⃗	NOUN
m-1112	2902	36	]	]	X
m-1112	2902	37	and	and	CCONJ
m-1112	2902	38	it	it	PRON
m-1112	2902	39	is	be	AUX
m-1112	2902	40	the	the	DET
m-1112	2902	41	only	only	ADJ
m-1112	2902	42	free	free	ADJ
m-1112	2902	43	monad	monad	PROPN
m-1112	2902	44	which	which	PRON
m-1112	2902	45	can	can	AUX
m-1112	2902	46	bond	bond	VERB
m-1112	2902	47	to	to	ADP
m-1112	2902	48	all	all	DET
m-1112	2902	49	energy	energy	NOUN
m-1112	2902	50	structures	structure	NOUN
m-1112	2902	51	.	.	PUNCT
m-1112	2903	1	5d	5d	NUM
m-1112	2903	2	..	..	PUNCT
m-1112	2904	1	the	the	DET
m-1112	2904	2	natural	natural	ADJ
m-1112	2904	3	electromagnetic	electromagnetic	ADJ
m-1112	2904	4	energy	energy	NOUN
m-1112	2904	5	-	-	PUNCT
m-1112	2904	6	tetrahedron	tetrahedron	NOUN
m-1112	2904	7	and	and	CCONJ
m-1112	2904	8	,	,	PUNCT
m-1112	2904	9	the	the	DET
m-1112	2904	10	3conductors	3conductor	NOUN
m-1112	2904	11	into	into	ADP
m-1112	2904	12	the	the	DET
m-1112	2904	13	energy	energy	NOUN
m-1112	2904	14	cube	cube	NOUN
m-1112	2904	15	and	and	CCONJ
m-1112	2904	16	spheres	sphere	NOUN
m-1112	2904	17	:	:	PUNCT
m-1112	2904	18	[	[	X
m-1112	2904	19	102	102	NUM
m-1112	2904	20	]	]	X
m-1112	2904	21	ijo	ijo	PROPN
m-1112	2904	22	international	international	PROPN
m-1112	2904	23	journal	journal	PROPN
m-1112	2904	24	of	of	ADP
m-1112	2904	25	mathematics	mathematics	PROPN
m-1112	2904	26	(	(	PUNCT
m-1112	2904	27	issn	issn	PROPN
m-1112	2904	28	:	:	PUNCT
m-1112	2904	29	2992	2992	NUM
m-1112	2904	30	-	-	SYM
m-1112	2904	31	4421	4421	NUM
m-1112	2904	32	)	)	PUNCT
m-1112	2904	33	volume	volume	NOUN
m-1112	2904	34	08	08	NUM
m-1112	2905	1	|	|	ADV
m-1112	2905	2	issue	issue	NOUN
m-1112	2905	3	08	08	NUM
m-1112	2906	1	|	|	ADV
m-1112	2906	2	august	august	PROPN
m-1112	2906	3	2025	2025	NUM
m-1112	2906	4	|	|	ADV
m-1112	2906	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2906	6	ijo	ijo	PROPN
m-1112	2906	7	journals	journal	NOUN
m-1112	2906	8	103	103	NUM
m-1112	2906	9	the	the	DET
m-1112	2906	10	fundamental	fundamental	ADJ
m-1112	2906	11	particles	particle	NOUN
m-1112	2906	12	origination	origination	NOUN
m-1112	2906	13	mechanism	mechanism	NOUN
m-1112	2906	14	in	in	ADP
m-1112	2906	15	mfmf	mfmf	PROPN
m-1112	2906	16	pns	pns	PROPN
m-1112	2906	17	caves	cave	NOUN
m-1112	2906	18	.	.	PUNCT
m-1112	2907	1	figure	figure	NOUN
m-1112	2907	2	–	–	PUNCT
m-1112	2907	3	20.athe	20.athe	DET
m-1112	2907	4	dynamic	dynamic	ADJ
m-1112	2907	5	loading	loading	NOUN
m-1112	2907	6	of	of	ADP
m-1112	2907	7	→	→	PUNCT
m-1112	2907	8	tetrahedron	tetrahedron	NOUN
m-1112	2907	9	–	–	PUNCT
m-1112	2907	10	cube	cube	NOUN
m-1112	2907	11	sphere	sphere	NOUN
m-1112	2907	12	←	←	PROPN
m-1112	2907	13	atom	atom	NOUN
m-1112	2907	14	–	–	PUNCT
m-1112	2907	15	structure	structure	NOUN
m-1112	2907	16	.	.	PUNCT
m-1112	2908	1	material	material	NOUN
m-1112	2908	2	geometry	geometry	NOUN
m-1112	2908	3	uses	use	VERB
m-1112	2908	4	the	the	DET
m-1112	2908	5	only	only	ADV
m-1112	2908	6	-	-	PUNCT
m-1112	2908	7	three	three	NUM
m-1112	2908	8	elements	element	NOUN
m-1112	2908	9	for	for	ADP
m-1112	2908	10	the	the	DET
m-1112	2908	11	origination	origination	NOUN
m-1112	2908	12	of	of	ADP
m-1112	2908	13	primary	primary	ADJ
m-1112	2908	14	particles	particle	NOUN
m-1112	2908	15	,	,	PUNCT
m-1112	2908	16	as	as	ADP
m-1112	2908	17	weak	weak	ADJ
m-1112	2908	18	,	,	PUNCT
m-1112	2908	19	w−zo	w−zo	VERB
m-1112	2908	20	and	and	CCONJ
m-1112	2908	21	strong	strong	ADJ
m-1112	2908	22	w+z+0,−	w+z+0,−	NOUN
m-1112	2908	23	forces	force	NOUN
m-1112	2908	24	,	,	PUNCT
m-1112	2908	25	spin	spin	VERB
m-1112	2908	26	b̅	b̅	NOUN
m-1112	2908	27	=	=	PUNCT
m-1112	2908	28	s̅	s̅	NOUN
m-1112	2908	29	,	,	PUNCT
m-1112	2908	30	hydrogen	hydrogen	NOUN
m-1112	2908	31	cave	cave	NOUN
m-1112	2908	32	,	,	PUNCT
m-1112	2908	33	r	r	NOUN
m-1112	2908	34	h	h	NOUN
m-1112	2908	35	,	,	PUNCT
m-1112	2908	36	and	and	CCONJ
m-1112	2908	37	electron	electron	NOUN
m-1112	2908	38	e−.	e−.	NOUN
m-1112	2909	1	where	where	SCONJ
m-1112	2909	2	[	[	X
m-1112	2909	3	0	0	NUM
m-1112	2909	4	]	]	X
m-1112	2909	5	≡	≡	PROPN
m-1112	2909	6			PROPN
m-1112	2909	7	≡	≡	PROPN
m-1112	2909	8	the	the	DET
m-1112	2909	9	rest	rest	NOUN
m-1112	2909	10	-	-	PUNCT
m-1112	2909	11	energy	energy	NOUN
m-1112	2909	12	≡	≡	PROPN
m-1112	2910	1	[	[	X
m-1112	2910	2	⊕	⊕	PROPN
m-1112	2910	3	↔	↔	PROPN
m-1112	2910	4	⊝	⊝	X
m-1112	2910	5	]	]	PUNCT
m-1112	2910	6	→	→	PUNCT
m-1112	2910	7	[	[	PUNCT
m-1112	2910	8	⊕	⊕	NOUN
m-1112	2910	9	∷	∷	NOUN
m-1112	2910	10	2	2	NUM
m-1112	2910	11	+	+	NOUN
m-1112	2910	12	⊝	⊝	NOUN
m-1112	2910	13	∷	∷	NOUN
m-1112	2910	14	2	2	NUM
m-1112	2910	15	]	]	PUNCT
m-1112	2910	16	,	,	PUNCT
m-1112	2910	17	split	split	VERB
m-1112	2910	18	into	into	ADP
m-1112	2910	19	two	two	NUM
m-1112	2910	20	.	.	PUNCT
m-1112	2911	1	and	and	CCONJ
m-1112	2911	2	,	,	PUNCT
m-1112	2911	3	[	[	X
m-1112	2911	4	0	0	X
m-1112	2911	5	]	]	X
m-1112	2911	6	≡	≡	PROPN
m-1112	2911	7	zd̅̅̅̅	zd̅̅̅̅	PROPN
m-1112	2911	8	≡	≡	PROPN
m-1112	2911	9	the	the	DET
m-1112	2911	10	rest	rest	NOUN
m-1112	2911	11	space	space	NOUN
m-1112	2911	12	≡	≡	PROPN
m-1112	2911	13	conductor	conductor	NOUN
m-1112	2911	14	−	−	PROPN
m-1112	2911	15	dm⃗⃗⃗⃖	dm⃗⃗⃗⃖	PROPN
m-1112	2911	16	←	←	PROPN
m-1112	2912	1	+	+	SYM
m-1112	2912	2	z	z	PROPN
m-1112	2912	3	e⃗⃗	e⃗⃗	PROPN
m-1112	2912	4	⃗	⃗	PROPN
m-1112	2912	5	→	→	SYM
m-1112	2912	6	,	,	PUNCT
m-1112	2912	7	from	from	ADP
m-1112	2912	8	relation	relation	NOUN
m-1112	2912	9	[	[	X
m-1112	2912	10	⊕←ds→⊝	⊕←ds→⊝	X
m-1112	2912	11	]	]	X
m-1112	2912	12	,	,	PUNCT
m-1112	2912	13	where	where	SCONJ
m-1112	2912	14	their	their	PRON
m-1112	2912	15	properties	property	NOUN
m-1112	2912	16	and	and	CCONJ
m-1112	2912	17	corelations	corelation	NOUN
m-1112	2912	18	are	be	AUX
m-1112	2912	19	all	all	PRON
m-1112	2912	20	motions	motion	NOUN
m-1112	2912	21	into	into	ADP
m-1112	2912	22	their	their	PRON
m-1112	2912	23	spaces	space	NOUN
m-1112	2912	24	,	,	PUNCT
m-1112	2912	25	from	from	ADP
m-1112	2912	26	energy	energy	NOUN
m-1112	2912	27	.	.	PUNCT
m-1112	2913	1	in	in	ADP
m-1112	2913	2	fig-20b	fig-20b	NUM
m-1112	2913	3	the	the	DET
m-1112	2913	4	electric	electric	PROPN
m-1112	2913	5	magnetic	magnetic	ADJ
m-1112	2913	6	field	field	NOUN
m-1112	2913	7	of	of	ADP
m-1112	2913	8	3	3	NUM
m-1112	2913	9	-	-	PUNCT
m-1112	2913	10	conductors	conductor	NOUN
m-1112	2913	11	which	which	PRON
m-1112	2913	12	lie	lie	VERB
m-1112	2913	13	on	on	ADP
m-1112	2913	14	the	the	DET
m-1112	2913	15	dabc	dabc	ADJ
m-1112	2913	16	tetrahedron	tetrahedron	PROPN
m-1112	2913	17	.the	.the	DET
m-1112	2913	18	stability	stability	NOUN
m-1112	2913	19	of	of	ADP
m-1112	2913	20	the	the	DET
m-1112	2913	21	→	→	PUNCT
m-1112	2913	22	{	{	PUNCT
m-1112	2913	23	⊕	⊕	NOUN
m-1112	2913	24	4	4	NUM
m-1112	2913	25	-	-	PUNCT
m-1112	2913	26	space	space	NOUN
m-1112	2914	1	[	[	X
m-1112	2914	2	d	d	X
m-1112	2914	3	a	a	DET
m-1112	2914	4	b	b	X
m-1112	2914	5	c	c	NOUN
m-1112	2914	6	]	]	X
m-1112	2914	7	}	}	PUNCT
m-1112	2914	8	regular	regular	ADJ
m-1112	2914	9	–	–	PUNCT
m-1112	2914	10	tetrahedron	tetrahedron	NOUN
m-1112	2914	11	,	,	PUNCT
m-1112	2914	12	occurs	occur	VERB
m-1112	2914	13	into	into	ADP
m-1112	2914	14	the	the	DET
m-1112	2914	15	{	{	PUNCT
m-1112	2914	16	⊝	⊝	NOUN
m-1112	2914	17	8	8	NUM
m-1112	2914	18	-	-	PUNCT
m-1112	2914	19	anti	anti	ADJ
m-1112	2914	20	-	-	ADJ
m-1112	2914	21	space	space	ADJ
m-1112	2914	22	cube	cube	NOUN
m-1112	2914	23	,	,	PUNCT
m-1112	2915	1	[	[	X
m-1112	2915	2	da1a	da1a	ADP
m-1112	2915	3	d1	d1	PROPN
m-1112	2915	4	,	,	PUNCT
m-1112	2915	5	b	b	NOUN
m-1112	2915	6	b1cc1	b1cc1	NOUN
m-1112	2915	7	]	]	PUNCT
m-1112	2915	8	}	}	PUNCT
m-1112	2915	9	,	,	PUNCT
m-1112	2915	10	and	and	CCONJ
m-1112	2915	11	the	the	DET
m-1112	2915	12	positive	positive	ADJ
m-1112	2915	13	→	→	PUNCT
m-1112	2915	14	{	{	PUNCT
m-1112	2915	15	⊕	⊕	NOUN
m-1112	2915	16	8	8	NUM
m-1112	2915	17	space	space	NOUN
m-1112	2915	18	–	–	PUNCT
m-1112	2915	19	cube	cube	NOUN
m-1112	2915	20	,	,	PUNCT
m-1112	2915	21	[	[	X
m-1112	2915	22	da1a	da1a	ADP
m-1112	2915	23	d1	d1	PROPN
m-1112	2915	24	,	,	PUNCT
m-1112	2915	25	b	b	X
m-1112	2915	26	b1cc1	b1cc1	NOUN
m-1112	2915	27	]	]	PUNCT
m-1112	2915	28	}	}	PUNCT
m-1112	2915	29	,	,	PUNCT
m-1112	2915	30	into	into	ADP
m-1112	2915	31	the	the	DET
m-1112	2915	32	{	{	PUNCT
m-1112	2915	33	⊝	⊝	NUM
m-1112	2915	34	16	16	NUM
m-1112	2915	35	-	-	PUNCT
m-1112	2915	36	anti	anti	NOUN
m-1112	2915	37	-	-	NOUN
m-1112	2915	38	space	space	ADJ
m-1112	2915	39	[	[	PUNCT
m-1112	2915	40	1	1	NUM
m-1112	2915	41	,	,	PUNCT
m-1112	2915	42	2	2	NUM
m-1112	2915	43	,	,	PUNCT
m-1112	2915	44	3	3	NUM
m-1112	2915	45	,	,	PUNCT
m-1112	2915	46	4	4	NUM
m-1112	2915	47	,	,	PUNCT
m-1112	2915	48	5	5	NUM
m-1112	2915	49	,	,	PUNCT
m-1112	2915	50	6	6	NUM
m-1112	2915	51	,	,	PUNCT
m-1112	2915	52	7	7	NUM
m-1112	2915	53	,	,	PUNCT
m-1112	2915	54	8	8	NUM
m-1112	2915	55	9	9	NUM
m-1112	2915	56	,	,	PUNCT
m-1112	2915	57	10	10	NUM
m-1112	2915	58	,	,	PUNCT
m-1112	2915	59	11	11	NUM
m-1112	2915	60	,	,	PUNCT
m-1112	2915	61	12	12	NUM
m-1112	2915	62	,	,	PUNCT
m-1112	2915	63	13	13	NUM
m-1112	2915	64	,	,	PUNCT
m-1112	2915	65	14	14	NUM
m-1112	2915	66	,	,	PUNCT
m-1112	2915	67	15	15	NUM
m-1112	2915	68	,	,	PUNCT
m-1112	2915	69	16	16	NUM
m-1112	2915	70	]	]	PUNCT
m-1112	2915	71	}	}	PUNCT
m-1112	2915	72	sphere	sphere	NOUN
m-1112	2915	73	cube	cube	NOUN
m-1112	2915	74	on	on	ADP
m-1112	2915	75	vertices.=	vertices.=	PROPN
m-1112	2915	76	point	point	NOUN
m-1112	2915	77	[	[	X
m-1112	2915	78	the	the	DET
m-1112	2915	79	point	point	NOUN
m-1112	2915	80	16	16	NUM
m-1112	2915	81	≡	≡	PROPN
m-1112	2915	82	|	|	ADV
m-1112	2915	83	⇉	⇉	NOUN
m-1112	2915	84	|z|	|z|	NOUN
m-1112	2915	85	]	]	PUNCT
m-1112	2915	86	consists	consist	VERB
m-1112	2915	87	the	the	DET
m-1112	2915	88	navel	navel	NOUN
m-1112	2915	89	-	-	PUNCT
m-1112	2915	90	string	string	NOUN
m-1112	2915	91	gate	gate	NOUN
m-1112	2915	92	into	into	ADP
m-1112	2915	93	the	the	DET
m-1112	2915	94	triangle	triangle	NOUN
m-1112	2915	95	-	-	PUNCT
m-1112	2915	96	circle	circle	NOUN
m-1112	2915	97	-	-	PUNCT
m-1112	2915	98	system	system	NOUN
m-1112	2915	99	{	{	PUNCT
m-1112	2915	100	z-(∆d	z-(∆d	NOUN
m-1112	2915	101	,	,	PUNCT
m-1112	2915	102	abc	abc	PROPN
m-1112	2915	103	)	)	PUNCT
m-1112	2915	104	,	,	PUNCT
m-1112	2915	105	∆[t1t2	∆[t1t2	PROPN
m-1112	2915	106	t3	t3	PROPN
m-1112	2915	107	]	]	X
m-1112	2915	108	}	}	PUNCT
m-1112	2915	109	of	of	ADP
m-1112	2915	110	the	the	DET
m-1112	2915	111	stationary	stationary	ADJ
m-1112	2915	112	bases	basis	NOUN
m-1112	2915	113	which	which	PRON
m-1112	2915	114	results	result	VERB
m-1112	2915	115	on	on	ADP
m-1112	2915	116	the	the	DET
m-1112	2915	117	2	2	NUM
m-1112	2915	118	-anti	-anti	NOUN
m-1112	2915	119	-	-	PUNCT
m-1112	2915	120	parallel	parallel	ADJ
m-1112	2915	121	-	-	PUNCT
m-1112	2915	122	strands	strand	NOUN
m-1112	2915	123	.	.	PUNCT
m-1112	2916	1	the	the	DET
m-1112	2916	2	dual	dual	ADJ
m-1112	2916	3	photon	photon	NOUN
m-1112	2916	4	v̅	v̅	PROPN
m-1112	2916	5	[	[	PUNCT
m-1112	2916	6	σφ	σφ	NOUN
m-1112	2916	7	2πr	2πr	NOUN
m-1112	2917	1	+	+	CCONJ
m-1112	2917	2	σ	σ	NUM
m-1112	2917	3	2πr	2πr	NOUN
m-1112	2917	4	]	]	PUNCT
m-1112	2918	1	≡	≡	PROPN
m-1112	2918	2	v̅.	v̅.	PROPN
m-1112	2918	3	[	[	PUNCT
m-1112	2918	4	fn̅	fn̅	PROPN
m-1112	2918	5	+	+	NUM
m-1112	2918	6	fn	fn	NOUN
m-1112	2918	7	]	]	PUNCT
m-1112	2918	8	,	,	PUNCT
m-1112	2918	9	occupies	occupy	VERB
m-1112	2918	10	stresses	stress	NOUN
m-1112	2918	11	=	=	SYM
m-1112	2918	12	σ	σ	PROPN
m-1112	2918	13	and	and	CCONJ
m-1112	2918	14	velocities	velocity	NOUN
m-1112	2918	15	v̅	v̅	VERB
m-1112	2918	16	,	,	PUNCT
m-1112	2918	17	in	in	ADP
m-1112	2918	18	the	the	DET
m-1112	2918	19	tiny	tiny	ADJ
m-1112	2918	20	-	-	PUNCT
m-1112	2918	21	caves	cave	NOUN
m-1112	2918	22	r	r	NOUN
m-1112	2918	23	.	.	PUNCT
m-1112	2919	1	the	the	DET
m-1112	2919	2	colours	colour	NOUN
m-1112	2919	3	in	in	ADP
m-1112	2919	4	light	light	NOUN
m-1112	2919	5	,	,	PUNCT
m-1112	2919	6	are	be	AUX
m-1112	2919	7	the	the	DET
m-1112	2919	8	still	still	ADV
m-1112	2919	9	-	-	PUNCT
m-1112	2919	10	sub	sub	NOUN
m-1112	2919	11	-	-	NOUN
m-1112	2919	12	units	unit	NOUN
m-1112	2919	13	in	in	ADP
m-1112	2919	14	storage	storage	NOUN
m-1112	2919	15	→[v̅	→[v̅	PROPN
m-1112	2919	16	.	.	PUNCT
m-1112	2920	1	fn̅	fn̅	PROPN
m-1112	2920	2	]	]	PUNCT
m-1112	2920	3	←	←	PROPN
m-1112	2921	1	and	and	CCONJ
m-1112	2921	2	exist	exist	VERB
m-1112	2921	3	as	as	ADP
m-1112	2921	4	frequencies	frequency	NOUN
m-1112	2921	5	of	of	ADP
m-1112	2921	6	→	→	SYM
m-1112	2921	7	violet	violet	NOUN
m-1112	2921	8	,	,	PUNCT
m-1112	2921	9	blue	blue	ADJ
m-1112	2921	10	,	,	PUNCT
m-1112	2921	11	green	green	ADJ
m-1112	2921	12	,	,	PUNCT
m-1112	2921	13	with	with	ADP
m-1112	2921	14	their	their	PRON
m-1112	2921	15	complementary	complementary	ADJ
m-1112	2921	16	yellow	yellow	NOUN
m-1112	2921	17	,	,	PUNCT
m-1112	2921	18	orange	orange	PROPN
m-1112	2921	19	,	,	PUNCT
m-1112	2921	20	red	red	ADJ
m-1112	2921	21	←	←	PROPN
m-1112	2922	1	every	every	DET
m-1112	2922	2	8	8	NUM
m-1112	2922	3	-	-	PUNCT
m-1112	2922	4	electrons	electron	NOUN
m-1112	2922	5	are	be	AUX
m-1112	2922	6	vibrations	vibration	NOUN
m-1112	2922	7	on	on	ADP
m-1112	2922	8	atoms	atom	NOUN
m-1112	2922	9	-	-	PUNCT
m-1112	2922	10	cube	cube	NOUN
m-1112	2922	11	-	-	PUNCT
m-1112	2922	12	structure	structure	NOUN
m-1112	2922	13	{	{	PUNCT
m-1112	2922	14	a	a	DET
m-1112	2922	15	tetrahedron	tetrahedron	NOUN
m-1112	2922	16	in	in	ADP
m-1112	2922	17	cube	cube	NOUN
m-1112	2922	18	in	in	ADP
m-1112	2922	19	a	a	DET
m-1112	2922	20	sphere	sphere	NOUN
m-1112	2922	21	}	}	PUNCT
m-1112	2922	22	whether	whether	SCONJ
m-1112	2922	23	it	it	PRON
m-1112	2922	24	be	be	AUX
m-1112	2922	25	sound	sound	ADJ
m-1112	2922	26	or	or	CCONJ
m-1112	2922	27	light	light	NOUN
m-1112	2922	28	.	.	PUNCT
m-1112	2923	1	above	above	ADP
m-1112	2923	2	structure	structure	NOUN
m-1112	2923	3	is	be	AUX
m-1112	2923	4	followed	follow	VERB
m-1112	2923	5	by	by	ADP
m-1112	2923	6	all	all	DET
m-1112	2923	7	compounds	compound	NOUN
m-1112	2923	8	.	.	PUNCT
m-1112	2924	1	molecules	molecule	NOUN
m-1112	2924	2	are	be	AUX
m-1112	2924	3	systems	system	NOUN
m-1112	2924	4	consisted	consist	VERB
m-1112	2924	5	of	of	ADP
m-1112	2924	6	the	the	DET
m-1112	2924	7	periferal	periferal	PROPN
m-1112	2924	8	≡	≡	PROPN
m-1112	2924	9	skeleton	skeleton	PROPN
m-1112	2924	10	𝐌	𝐌	PROPN
m-1112	2924	11	𝟏𝟔	𝟏𝟔	NUM
m-1112	2924	12	and	and	CCONJ
m-1112	2924	13	the	the	DET
m-1112	2924	14	central	central	ADJ
m-1112	2924	15	≡	≡	PROPN
m-1112	2924	16	fittings	fitting	NOUN
m-1112	2924	17	𝐌	𝐌	PROPN
m-1112	2924	18	𝟖	𝟖	NUM
m-1112	2924	19	,	,	PUNCT
m-1112	2924	20	and	and	CCONJ
m-1112	2924	21	the	the	DET
m-1112	2924	22	accessories	accessory	NOUN
m-1112	2924	23	≡	≡	PROPN
m-1112	2924	24	𝐌	𝐌	ADP
m-1112	2924	25	𝟒	𝟒	PROPN
m-1112	2924	26	or	or	CCONJ
m-1112	2924	27	𝐌	𝐌	PROPN
m-1112	2924	28	𝟐	𝟐	NUM
m-1112	2924	29	,	,	PUNCT
m-1112	2924	30	𝐌	𝐌	PROPN
m-1112	2924	31	𝟏	𝟏	NUM
m-1112	2924	32	.	.	PUNCT
m-1112	2925	1	this	this	DET
m-1112	2925	2	property	property	NOUN
m-1112	2925	3	of	of	ADP
m-1112	2925	4	atoms	atom	NOUN
m-1112	2925	5	and	and	CCONJ
m-1112	2925	6	of	of	ADP
m-1112	2925	7	the	the	DET
m-1112	2925	8	compounds	compound	NOUN
m-1112	2925	9	is	be	AUX
m-1112	2925	10	the	the	DET
m-1112	2925	11	critical	critical	ADJ
m-1112	2925	12	-	-	PUNCT
m-1112	2925	13	valve	valve	NOUN
m-1112	2925	14	of	of	ADP
m-1112	2925	15	switching	switch	VERB
m-1112	2925	16	the	the	DET
m-1112	2925	17	motion	motion	NOUN
m-1112	2925	18	as	as	SCONJ
m-1112	2925	19	this	this	PRON
m-1112	2925	20	happens	happen	VERB
m-1112	2925	21	in	in	ADP
m-1112	2925	22	the	the	DET
m-1112	2925	23	electro	electro	ADJ
m-1112	2925	24	-	-	PUNCT
m-1112	2925	25	magnetic	magnetic	ADJ
m-1112	2925	26	solenoid	solenoid	NOUN
m-1112	2925	27	valves	valve	NOUN
m-1112	2925	28	with	with	ADP
m-1112	2925	29	high	high	ADJ
m-1112	2925	30	or	or	CCONJ
m-1112	2925	31	low	low	ADJ
m-1112	2925	32	pressure	pressure	NOUN
m-1112	2925	33	and	and	CCONJ
m-1112	2925	34	flow	flow	NOUN
m-1112	2925	35	rates	rate	NOUN
m-1112	2925	36	directly	directly	ADV
m-1112	2925	37	or	or	CCONJ
m-1112	2925	38	not	not	PART
m-1112	2925	39	.	.	PUNCT
m-1112	2926	1	figure	figure	VERB
m-1112	2926	2	–	–	PUNCT
m-1112	2926	3	20.b	20.b	NUM
m-1112	2926	4	:	:	PUNCT
m-1112	2926	5	the	the	DET
m-1112	2926	6	electric	electric	PROPN
m-1112	2926	7	magnetic	magnetic	ADJ
m-1112	2926	8	field	field	NOUN
m-1112	2926	9	of	of	ADP
m-1112	2926	10	3	3	NUM
m-1112	2926	11	,	,	PUNCT
m-1112	2926	12	conductors	conductor	NOUN
m-1112	2926	13	results	result	VERB
m-1112	2926	14	on	on	ADP
m-1112	2926	15	2	2	NUM
m-1112	2926	16	-anti	-anti	NOUN
m-1112	2926	17	-	-	ADJ
m-1112	2926	18	parallel	parallel	ADJ
m-1112	2926	19	strands	strand	NOUN
m-1112	2926	20	.the	.the	PUNCT
m-1112	2926	21	stability	stability	NOUN
m-1112	2926	22	of	of	ADP
m-1112	2926	23	→	→	NOUN
m-1112	2926	24	{	{	PUNCT
m-1112	2926	25	⊕	⊕	PROPN
m-1112	2926	26	4	4	NUM
m-1112	2926	27	-	-	PUNCT
m-1112	2926	28	space	space	NOUN
m-1112	2927	1	[	[	X
m-1112	2927	2	d	d	X
m-1112	2927	3	a	a	DET
m-1112	2927	4	b	b	X
m-1112	2927	5	c	c	NOUN
m-1112	2927	6	]	]	X
m-1112	2927	7	}	}	PUNCT
m-1112	2927	8	regular	regular	ADJ
m-1112	2927	9	tetrahedron	tetrahedron	NOUN
m-1112	2927	10	,	,	PUNCT
m-1112	2927	11	in	in	ADP
m-1112	2927	12	{	{	PUNCT
m-1112	2927	13	⊝	⊝	NUM
m-1112	2927	14	8	8	NUM
m-1112	2927	15	-	-	PUNCT
m-1112	2927	16	antispace	antispace	NOUN
m-1112	2927	17	cube	cube	NOUN
m-1112	2927	18	,	,	PUNCT
m-1112	2927	19	[	[	PUNCT
m-1112	2927	20	da1b	da1b	VERB
m-1112	2927	21	d1	d1	PROPN
m-1112	2927	22	,	,	PUNCT
m-1112	2927	23	c	c	PROPN
m-1112	2927	24	c1ab1	c1ab1	NOUN
m-1112	2927	25	]	]	PUNCT
m-1112	2927	26	}	}	PUNCT
m-1112	2927	27	,	,	PUNCT
m-1112	2927	28	and	and	CCONJ
m-1112	2927	29	the	the	DET
m-1112	2927	30	→	→	NOUN
m-1112	2927	31	{	{	PUNCT
m-1112	2927	32	⊕	⊕	PROPN
m-1112	2927	33	8space	8space	PROPN
m-1112	2927	34	[	[	PUNCT
m-1112	2927	35	da1bd1	da1bd1	NOUN
m-1112	2927	36	,	,	PUNCT
m-1112	2927	37	cc1ab1	cc1ab1	X
m-1112	2927	38	]	]	PUNCT
m-1112	2927	39	}	}	PUNCT
m-1112	2927	40	cube	cube	NOUN
m-1112	2927	41	,	,	PUNCT
m-1112	2927	42	into	into	ADP
m-1112	2927	43	the	the	DET
m-1112	2927	44	{	{	PUNCT
m-1112	2927	45	⊝	⊝	NUM
m-1112	2927	46	16	16	NUM
m-1112	2927	47	-	-	PUNCT
m-1112	2927	48	anti	anti	NOUN
m-1112	2927	49	-	-	NOUN
m-1112	2927	50	space	space	ADJ
m-1112	2927	51	[	[	PUNCT
m-1112	2927	52	1	1	NUM
m-1112	2927	53	,	,	PUNCT
m-1112	2927	54	2	2	NUM
m-1112	2927	55	,	,	PUNCT
m-1112	2927	56	3	3	NUM
m-1112	2927	57	,	,	PUNCT
m-1112	2927	58	4	4	NUM
m-1112	2927	59	,	,	PUNCT
m-1112	2927	60	5	5	NUM
m-1112	2927	61	,	,	PUNCT
m-1112	2927	62	6	6	NUM
m-1112	2927	63	,	,	PUNCT
m-1112	2927	64	7	7	NUM
m-1112	2927	65	,	,	PUNCT
m-1112	2927	66	8	8	NUM
m-1112	2927	67	9	9	NUM
m-1112	2927	68	,	,	PUNCT
m-1112	2927	69	10	10	NUM
m-1112	2927	70	,	,	PUNCT
m-1112	2927	71	11	11	NUM
m-1112	2927	72	,	,	PUNCT
m-1112	2927	73	12	12	NUM
m-1112	2927	74	,	,	PUNCT
m-1112	2927	75	13	13	NUM
m-1112	2927	76	,	,	PUNCT
m-1112	2927	77	14	14	NUM
m-1112	2927	78	,	,	PUNCT
m-1112	2927	79	15	15	NUM
m-1112	2927	80	,	,	PUNCT
m-1112	2927	81	16	16	NUM
m-1112	2927	82	]	]	PUNCT
m-1112	2927	83	}	}	PUNCT
m-1112	2927	84	sphere	sphere	NOUN
m-1112	2927	85	ijo	ijo	PROPN
m-1112	2927	86	international	international	PROPN
m-1112	2927	87	journal	journal	PROPN
m-1112	2927	88	of	of	ADP
m-1112	2927	89	mathematics	mathematics	PROPN
m-1112	2927	90	(	(	PUNCT
m-1112	2927	91	issn	issn	PROPN
m-1112	2927	92	:	:	PUNCT
m-1112	2927	93	2992	2992	NUM
m-1112	2927	94	-	-	SYM
m-1112	2927	95	4421	4421	NUM
m-1112	2927	96	)	)	PUNCT
m-1112	2927	97	volume	volume	NOUN
m-1112	2927	98	08	08	NUM
m-1112	2928	1	|	|	ADV
m-1112	2928	2	issue	issue	NOUN
m-1112	2928	3	08	08	NUM
m-1112	2929	1	|	|	ADV
m-1112	2929	2	august	august	PROPN
m-1112	2929	3	2025	2025	NUM
m-1112	2929	4	|	|	ADV
m-1112	2929	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2929	6	ijo	ijo	PROPN
m-1112	2929	7	journals	journal	NOUN
m-1112	2929	8	104	104	NUM
m-1112	2929	9	the	the	DET
m-1112	2929	10	fundamental	fundamental	ADJ
m-1112	2929	11	particles	particle	NOUN
m-1112	2929	12	origination	origination	NOUN
m-1112	2929	13	mechanism	mechanism	NOUN
m-1112	2929	14	in	in	ADP
m-1112	2929	15	mfmf	mfmf	PROPN
m-1112	2929	16	pns	pns	PROPN
m-1112	2929	17	caves	cave	NOUN
m-1112	2929	18	.	.	PUNCT
m-1112	2930	1	cube	cube	NOUN
m-1112	2930	2	vertices	vertex	NOUN
m-1112	2930	3	.	.	PUNCT
m-1112	2931	1	point	point	NOUN
m-1112	2932	1	[	[	X
m-1112	2932	2	16	16	NUM
m-1112	2932	3	≡	≡	PROPN
m-1112	2932	4	|	|	ADV
m-1112	2932	5	⇉	⇉	NOUN
m-1112	2932	6	|z|	|z|	NOUN
m-1112	2932	7	]	]	PUNCT
m-1112	2932	8	consists	consist	VERB
m-1112	2932	9	the	the	DET
m-1112	2932	10	navel	navel	NOUN
m-1112	2932	11	-	-	PUNCT
m-1112	2932	12	string	string	NOUN
m-1112	2932	13	gate	gate	NOUN
m-1112	2932	14	in	in	ADP
m-1112	2932	15	{	{	PUNCT
m-1112	2932	16	z-(∆d	z-(∆d	NOUN
m-1112	2932	17	,	,	PUNCT
m-1112	2932	18	abc),∆[t1	abc),∆[t1	PROPN
m-1112	2932	19	t2	t2	PROPN
m-1112	2932	20	t3	t3	PROPN
m-1112	2932	21	]	]	X
m-1112	2932	22	}	}	PUNCT
m-1112	2932	23	stationary	stationary	ADJ
m-1112	2932	24	bases	basis	NOUN
m-1112	2932	25	.	.	PUNCT
m-1112	2933	1	stability	stability	NOUN
m-1112	2933	2	analysis	analysis	NOUN
m-1112	2933	3	in	in	ADP
m-1112	2933	4	[	[	X
m-1112	2933	5	88	88	NUM
m-1112	2933	6	]	]	PUNCT
m-1112	2933	7	data	datum	NOUN
m-1112	2933	8	:	:	PUNCT
m-1112	2933	9	a	a	X
m-1112	2933	10	..	..	PUNCT
m-1112	2933	11	the	the	DET
m-1112	2933	12	atoms	atom	NOUN
m-1112	2933	13	cube	cube	NOUN
m-1112	2933	14	coordinate	coordinate	NOUN
m-1112	2933	15	-	-	PUNCT
m-1112	2933	16	system	system	NOUN
m-1112	2933	17	:	:	PUNCT
m-1112	2933	18	the	the	DET
m-1112	2933	19	relation	relation	NOUN
m-1112	2933	20	of	of	ADP
m-1112	2933	21	a	a	DET
m-1112	2933	22	cube	cube	NOUN
m-1112	2933	23	of	of	ADP
m-1112	2933	24	side	side	NOUN
m-1112	2933	25	a	a	PRON
m-1112	2933	26	,	,	PUNCT
m-1112	2933	27	inscribed	inscribe	VERB
m-1112	2933	28	in	in	ADP
m-1112	2933	29	a	a	DET
m-1112	2933	30	sphere	sphere	NOUN
m-1112	2933	31	of	of	ADP
m-1112	2933	32	diameter	diameter	NOUN
m-1112	2934	1	d	d	PROPN
m-1112	2934	2	=	=	SYM
m-1112	2934	3	2r	2r	NUM
m-1112	2934	4	,	,	PUNCT
m-1112	2934	5	is	be	AUX
m-1112	2934	6	in	in	ADP
m-1112	2934	7	their	their	PRON
m-1112	2934	8	volumes	volume	NOUN
m-1112	2934	9	as	as	ADP
m-1112	2934	10	v	v	ADP
m-1112	2934	11	sphere	sphere	NOUN
m-1112	2934	12	=	=	PUNCT
m-1112	2935	1	4.𝜋	4.𝜋	PROPN
m-1112	2935	2	r	r	NOUN
m-1112	2935	3	³.	³.	X
m-1112	2935	4	3	3	NUM
m-1112	2935	5	=	=	SYM
m-1112	2935	6	𝜋	𝜋	X
m-1112	2935	7	d	d	X
m-1112	2935	8	³.	³.	X
m-1112	2935	9	6	6	NUM
m-1112	2935	10	,	,	PUNCT
m-1112	2935	11	v	v	NOUN
m-1112	2935	12	cube	cube	NOUN
m-1112	2935	13	=	=	SYM
m-1112	2935	14	a³	a³	PROPN
m-1112	2935	15	and	and	CCONJ
m-1112	2935	16	since	since	SCONJ
m-1112	2935	17	d²	d²	NOUN
m-1112	2935	18	=	=	SYM
m-1112	2935	19	2a²	2a²	NUM
m-1112	2935	20	+	+	CCONJ
m-1112	2935	21	a²	a²	NOUN
m-1112	2935	22	=	=	SYM
m-1112	2935	23	3,a²	3,a²	NOUN
m-1112	2935	24	,	,	PUNCT
m-1112	2935	25	then	then	ADV
m-1112	2935	26	a	a	DET
m-1112	2935	27	=	=	X
m-1112	2935	28	d.	d.	PROPN
m-1112	2935	29	√3	√3	PROPN
m-1112	2935	30	=	=	PUNCT
m-1112	2935	31	d.	d.	PROPN
m-1112	2935	32	,√3	,√3	PUNCT
m-1112	2935	33	3	3	NUM
m-1112	2935	34	=	=	NOUN
m-1112	2935	35	√3,d	√3,d	NUM
m-1112	2935	36	3	3	NUM
m-1112	2935	37	=	=	SYM
m-1112	2935	38	2√3,r	2√3,r	NUM
m-1112	2935	39	3	3	NUM
m-1112	2935	40	,	,	PUNCT
m-1112	2935	41	and	and	CCONJ
m-1112	2935	42	the	the	DET
m-1112	2935	43	coordinates	coordinate	NOUN
m-1112	2935	44	of	of	ADP
m-1112	2935	45	the	the	DET
m-1112	2935	46	8	8	NUM
m-1112	2935	47	-	-	PUNCT
m-1112	2935	48	cube	cube	NOUN
m-1112	2935	49	-	-	PUNCT
m-1112	2935	50	vertices	vertex	NOUN
m-1112	2935	51	are	be	AUX
m-1112	2935	52	for	for	ADP
m-1112	2935	53	center	center	NOUN
m-1112	2935	54	o	o	NOUN
m-1112	2935	55	→	→	PUNCT
m-1112	2935	56	𝐗	𝐗	NOUN
m-1112	2935	57	𝐎	𝐎	NOUN
m-1112	2935	58	=	=	SYM
m-1112	2935	59	0	0	NUM
m-1112	2935	60	,	,	PUNCT
m-1112	2935	61	𝐘	𝐘	NOUN
m-1112	2935	62	𝟎	𝟎	NUM
m-1112	2935	63	=	=	SYM
m-1112	2935	64	0	0	NUM
m-1112	2935	65	,	,	PUNCT
m-1112	2935	66	𝐙	𝐙	NOUN
m-1112	2935	67	𝟎	𝟎	ADV
m-1112	2935	68	=	=	SYM
m-1112	2935	69	0	0	NUM
m-1112	2935	70	←	←	PROPN
m-1112	2935	71	𝐗	𝐗	PROPN
m-1112	2935	72	𝟏	𝟏	PROPN
m-1112	2935	73	=	=	SYM
m-1112	2935	74	−	−	PROPN
m-1112	2935	75	a.	a.	NOUN
m-1112	2935	76	2	2	NUM
m-1112	2935	77	,	,	PUNCT
m-1112	2935	78	𝐘	𝐘	NOUN
m-1112	2935	79	𝟏	𝟏	NUM
m-1112	2935	80	=	=	SYM
m-1112	2936	1	−	−	PROPN
m-1112	2936	2	a.	a.	NOUN
m-1112	2936	3	2	2	NUM
m-1112	2936	4	,	,	PUNCT
m-1112	2936	5	𝐙	𝐙	NOUN
m-1112	2936	6	𝟏	𝟏	NUM
m-1112	2936	7	=	=	SYM
m-1112	2936	8	−	−	PROPN
m-1112	2936	9	a.	a.	NOUN
m-1112	2936	10	2	2	NUM
m-1112	2936	11	,	,	PUNCT
m-1112	2936	12	𝐗	𝐗	PROPN
m-1112	2936	13	𝟐	𝟐	NUM
m-1112	2936	14	=	=	PUNCT
m-1112	2936	15	+	+	NUM
m-1112	2936	16	a.	a.	NOUN
m-1112	2936	17	2	2	NUM
m-1112	2936	18	,	,	PUNCT
m-1112	2936	19	𝐘	𝐘	NOUN
m-1112	2936	20	𝟐	𝟐	NUM
m-1112	2936	21	=	=	SYM
m-1112	2936	22	−	−	PROPN
m-1112	2936	23	a.	a.	NOUN
m-1112	2936	24	2	2	NUM
m-1112	2936	25	,	,	PUNCT
m-1112	2936	26	𝐙	𝐙	NOUN
m-1112	2936	27	𝟐	𝟐	NUM
m-1112	2936	28	=	=	SYM
m-1112	2936	29	−	−	PROPN
m-1112	2936	30	a.	a.	NOUN
m-1112	2936	31	2	2	NUM
m-1112	2936	32	,	,	PUNCT
m-1112	2936	33	𝐗	𝐗	PROPN
m-1112	2936	34	𝟑	𝟑	X
m-1112	2936	35	=	=	SYM
m-1112	2936	36	+	+	NUM
m-1112	2936	37	a.	a.	NOUN
m-1112	2936	38	2	2	NUM
m-1112	2936	39	,	,	PUNCT
m-1112	2936	40	𝐘	𝐘	NOUN
m-1112	2936	41	𝟑	𝟑	X
m-1112	2936	42	=	=	SYM
m-1112	2936	43	+	+	NUM
m-1112	2936	44	a.	a.	NOUN
m-1112	2936	45	2	2	NUM
m-1112	2936	46	,	,	PUNCT
m-1112	2936	47	𝐙	𝐙	NOUN
m-1112	2936	48	𝟑	𝟑	X
m-1112	2936	49	=	=	SYM
m-1112	2936	50	−	−	PROPN
m-1112	2936	51	a.	a.	NOUN
m-1112	2936	52	2	2	NUM
m-1112	2936	53	,	,	PUNCT
m-1112	2936	54	𝐗	𝐗	PROPN
m-1112	2936	55	𝟒	𝟒	PROPN
m-1112	2936	56	=	=	SYM
m-1112	2936	57	−	−	PROPN
m-1112	2936	58	a.	a.	NOUN
m-1112	2936	59	2	2	NUM
m-1112	2936	60	,	,	PUNCT
m-1112	2936	61	𝐘	𝐘	NOUN
m-1112	2936	62	𝟒	𝟒	NUM
m-1112	2936	63	=	=	SYM
m-1112	2936	64	+	+	NUM
m-1112	2936	65	a.	a.	NOUN
m-1112	2936	66	2	2	NUM
m-1112	2936	67	,	,	PUNCT
m-1112	2936	68	𝐙	𝐙	NOUN
m-1112	2936	69	𝟒	𝟒	PROPN
m-1112	2936	70	=	=	SYM
m-1112	2936	71	−	−	PROPN
m-1112	2936	72	a.	a.	NOUN
m-1112	2936	73	2	2	NUM
m-1112	2936	74	,	,	PUNCT
m-1112	2936	75	𝐗	𝐗	PROPN
m-1112	2936	76	𝟓	𝟓	NUM
m-1112	2936	77	=	=	SYM
m-1112	2936	78	−	−	PROPN
m-1112	2936	79	a.	a.	NOUN
m-1112	2936	80	2	2	NUM
m-1112	2936	81	,	,	PUNCT
m-1112	2936	82	𝐘	𝐘	NOUN
m-1112	2936	83	𝟓	𝟓	NUM
m-1112	2936	84	=	=	SYM
m-1112	2936	85	+	+	NUM
m-1112	2936	86	a.	a.	NOUN
m-1112	2936	87	2	2	NUM
m-1112	2936	88	,	,	PUNCT
m-1112	2936	89	𝐙	𝐙	NOUN
m-1112	2936	90	𝟓	𝟓	NUM
m-1112	2936	91	=	=	SYM
m-1112	2936	92	+	+	NUM
m-1112	2936	93	a.	a.	NOUN
m-1112	2936	94	2	2	NUM
m-1112	2936	95	,	,	PUNCT
m-1112	2936	96	𝐗	𝐗	PROPN
m-1112	2936	97	𝟔	𝟔	NUM
m-1112	2936	98	=	=	SYM
m-1112	2936	99	−	−	PROPN
m-1112	2936	100	a.	a.	NOUN
m-1112	2936	101	2	2	NUM
m-1112	2936	102	,	,	PUNCT
m-1112	2936	103	𝐘	𝐘	NOUN
m-1112	2936	104	𝟔	𝟔	NUM
m-1112	2936	105	=	=	SYM
m-1112	2936	106	−	−	PROPN
m-1112	2936	107	a.	a.	NOUN
m-1112	2936	108	2	2	NUM
m-1112	2936	109	,	,	PUNCT
m-1112	2936	110	𝐙	𝐙	NOUN
m-1112	2936	111	𝟔	𝟔	NUM
m-1112	2936	112	=	=	PUNCT
m-1112	2936	113	+	+	NUM
m-1112	2936	114	a.	a.	NOUN
m-1112	2936	115	2	2	NUM
m-1112	2936	116	,	,	PUNCT
m-1112	2936	117	𝐗	𝐗	PROPN
m-1112	2936	118	𝟕	𝟕	NOUN
m-1112	2936	119	=	=	SYM
m-1112	2936	120	+	+	NUM
m-1112	2936	121	a.	a.	NOUN
m-1112	2936	122	2	2	NUM
m-1112	2936	123	,	,	PUNCT
m-1112	2936	124	𝐘	𝐘	NOUN
m-1112	2936	125	𝟕	𝟕	NUM
m-1112	2936	126	=	=	SYM
m-1112	2937	1	−	−	PROPN
m-1112	2937	2	a.	a.	NOUN
m-1112	2937	3	2	2	NUM
m-1112	2937	4	,	,	PUNCT
m-1112	2937	5	𝐙	𝐙	NOUN
m-1112	2937	6	𝟕	𝟕	NOUN
m-1112	2937	7	=	=	SYM
m-1112	2937	8	+	+	NUM
m-1112	2937	9	a.	a.	NOUN
m-1112	2937	10	2	2	NUM
m-1112	2937	11	,	,	PUNCT
m-1112	2937	12	𝐗	𝐗	PROPN
m-1112	2937	13	𝟖	𝟖	PROPN
m-1112	2937	14	=	=	SYM
m-1112	2937	15	+	+	NUM
m-1112	2937	16	a.	a.	NOUN
m-1112	2937	17	2	2	NUM
m-1112	2937	18	,	,	PUNCT
m-1112	2937	19	𝐘	𝐘	NOUN
m-1112	2937	20	𝟖	𝟖	NUM
m-1112	2937	21	=	=	SYM
m-1112	2937	22	+	+	NUM
m-1112	2937	23	a.	a.	NOUN
m-1112	2937	24	2	2	NUM
m-1112	2937	25	,	,	PUNCT
m-1112	2937	26	𝐙	𝐙	NOUN
m-1112	2937	27	𝟖	𝟖	X
m-1112	2937	28	=	=	SYM
m-1112	2937	29	+	+	NUM
m-1112	2937	30	a.	a.	NOUN
m-1112	2937	31	2	2	NUM
m-1112	2937	32	,	,	PUNCT
m-1112	2937	33	since	since	SCONJ
m-1112	2937	34	tetrahedron	tetrahedron	NOUN
m-1112	2937	35	in	in	ADP
m-1112	2937	36	cube	cube	NOUN
m-1112	2937	37	is	be	AUX
m-1112	2937	38	formed	form	VERB
m-1112	2937	39	in	in	ADP
m-1112	2937	40	three	three	NUM
m-1112	2937	41	equal	equal	ADJ
m-1112	2937	42	-	-	PUNCT
m-1112	2937	43	diagonals	diagonal	NOUN
m-1112	2937	44	𝐝	𝐝	X
m-1112	2937	45	𝟏−𝟑	𝟏−𝟑	X
m-1112	2937	46	=	=	SYM
m-1112	2937	47	a.√2	a.√2	PROPN
m-1112	2937	48	,	,	PUNCT
m-1112	2937	49	𝐝	𝐝	PROPN
m-1112	2937	50	𝟏−𝟓	𝟏−𝟓	PROPN
m-1112	2937	51	=	=	SYM
m-1112	2937	52	a.√2	a.√2	PROPN
m-1112	2937	53	,	,	PUNCT
m-1112	2937	54	𝐝	𝐝	PROPN
m-1112	2937	55	𝟏−𝟕	𝟏−𝟕	PROPN
m-1112	2937	56	=	=	SYM
m-1112	2937	57	a.√2	a.√2	PROPN
m-1112	2937	58	of	of	ADP
m-1112	2937	59	the	the	DET
m-1112	2937	60	perpendicular	perpendicular	ADJ
m-1112	2937	61	3	3	NUM
m-1112	2937	62	-	-	PUNCT
m-1112	2937	63	planes	plane	NOUN
m-1112	2937	64	,	,	PUNCT
m-1112	2937	65	p	p	X
m-1112	2937	66	x−y	x−y	PROPN
m-1112	2937	67	=	=	PROPN
m-1112	2938	1	p	p	X
m-1112	2938	2	y−z	y−z	PROPN
m-1112	2938	3	=	=	PUNCT
m-1112	2938	4	p	p	X
m-1112	2938	5	z−x	z−x	NOUN
m-1112	2938	6	=	=	SYM
m-1112	2938	7	a²	a²	NOUN
m-1112	2938	8	,	,	PUNCT
m-1112	2938	9	and	and	CCONJ
m-1112	2938	10	since	since	SCONJ
m-1112	2938	11	issues	issue	NOUN
m-1112	2938	12	𝐝	𝐝	PRON
m-1112	2939	1	𝟏−𝟑	𝟏−𝟑	ADJ
m-1112	2939	2	⏊	⏊	PROPN
m-1112	2939	3	𝐝	𝐝	PROPN
m-1112	2939	4	𝟏−𝟓	𝟏−𝟓	PROPN
m-1112	2939	5	⏊	⏊	PROPN
m-1112	2939	6	𝐝	𝐝	SYM
m-1112	2939	7	𝟏−𝟕	𝟏−𝟕	PROPN
m-1112	2939	8	,	,	PUNCT
m-1112	2939	9	these	these	PRON
m-1112	2939	10	consist	consist	VERB
m-1112	2939	11	the	the	PRON
m-1112	2939	12	-	-	PUNCT
m-1112	2939	13	scanning	scan	VERB
m-1112	2939	14	vectors	vector	NOUN
m-1112	2939	15	-	-	PUNCT
m-1112	2939	16	plotting	plot	VERB
m-1112	2939	17	for	for	ADP
m-1112	2939	18	all	all	DET
m-1112	2939	19	systems	system	NOUN
m-1112	2939	20	.	.	PUNCT
m-1112	2940	1	since	since	SCONJ
m-1112	2940	2	the	the	DET
m-1112	2940	3	cube	cube	NOUN
m-1112	2940	4	’s	’s	PART
m-1112	2940	5	outer	outer	ADJ
m-1112	2940	6	-	-	PUNCT
m-1112	2940	7	sphere	sphere	NOUN
m-1112	2940	8	diameter	diameter	NOUN
m-1112	2940	9	d	d	NOUN
m-1112	2940	10	,	,	PUNCT
m-1112	2940	11	is	be	AUX
m-1112	2940	12	equal	equal	ADJ
m-1112	2940	13	to	to	ADP
m-1112	2940	14	the	the	DET
m-1112	2940	15	cube	cube	NOUN
m-1112	2940	16	-	-	PUNCT
m-1112	2940	17	diagonals	diagonal	NOUN
m-1112	2940	18	[	[	X
m-1112	2940	19	1	1	NUM
m-1112	2940	20	-	-	SYM
m-1112	2940	21	8	8	NUM
m-1112	2940	22	]	]	PUNCT
m-1112	2940	23	,	,	PUNCT
m-1112	2941	1	[	[	X
m-1112	2941	2	2	2	NUM
m-1112	2941	3	-	-	SYM
m-1112	2941	4	5	5	NUM
m-1112	2941	5	]	]	PUNCT
m-1112	2941	6	,	,	PUNCT
m-1112	2941	7	[	[	X
m-1112	2941	8	3	3	NUM
m-1112	2941	9	-	-	SYM
m-1112	2941	10	6	6	NUM
m-1112	2941	11	]	]	PUNCT
m-1112	2941	12	,	,	PUNCT
m-1112	2941	13	[	[	X
m-1112	2941	14	4	4	NUM
m-1112	2941	15	-	-	SYM
m-1112	2941	16	7	7	NUM
m-1112	2941	17	]	]	PUNCT
m-1112	2941	18	,	,	PUNCT
m-1112	2941	19	therefore	therefore	ADV
m-1112	2941	20	consist	consist	VERB
m-1112	2941	21	4	4	NUM
m-1112	2941	22	-	-	PUNCT
m-1112	2941	23	big	big	ADJ
m-1112	2941	24	circles	circle	NOUN
m-1112	2941	25	on	on	ADP
m-1112	2941	26	sphere	sphere	NOUN
m-1112	2941	27	and	and	CCONJ
m-1112	2941	28	perpendicular	perpendicular	ADJ
m-1112	2941	29	between	between	ADP
m-1112	2941	30	them	they	PRON
m-1112	2941	31	,	,	PUNCT
m-1112	2941	32	in	in	ADP
m-1112	2941	33	contradiction	contradiction	NOUN
m-1112	2941	34	to	to	ADP
m-1112	2941	35	the	the	DET
m-1112	2941	36	3	3	NUM
m-1112	2941	37	circles	circle	NOUN
m-1112	2941	38	in	in	ADP
m-1112	2941	39	the	the	DET
m-1112	2941	40	3	3	NUM
m-1112	2941	41	-	-	PUNCT
m-1112	2941	42	planes	plane	NOUN
m-1112	2941	43	which	which	PRON
m-1112	2941	44	consist	consist	VERB
m-1112	2941	45	the	the	DET
m-1112	2941	46	small	small	ADJ
m-1112	2941	47	circles	circle	NOUN
m-1112	2941	48	.	.	PUNCT
m-1112	2942	1	the	the	DET
m-1112	2942	2	geometrical	geometrical	ADJ
m-1112	2942	3	matric	matric	NOUN
m-1112	2942	4	of	of	ADP
m-1112	2942	5	tetrahedron	tetrahedron	NOUN
m-1112	2942	6	-	-	PUNCT
m-1112	2942	7	cube	cube	NOUN
m-1112	2942	8	-	-	PUNCT
m-1112	2942	9	sphere	sphere	NOUN
m-1112	2942	10	mould	mould	NOUN
m-1112	2942	11	=	=	PUNCT
m-1112	2942	12	(	(	PUNCT
m-1112	2942	13	stcs	stcs	NOUN
m-1112	2942	14	)	)	PUNCT
m-1112	2942	15	where	where	SCONJ
m-1112	2942	16	,	,	PUNCT
m-1112	2942	17	𝐏𝟏	𝐏𝟏	PROPN
m-1112	2942	18	𝐏𝟐	𝐏𝟐	PROPN
m-1112	2942	19	𝐏𝟑	𝐏𝟑	PROPN
m-1112	2942	20	𝐏𝟓	𝐏𝟓	PROPN
m-1112	2943	1	𝐏𝐨	𝐏𝐨	PROPN
m-1112	2943	2	𝐏𝟒	𝐏𝟒	NOUN
m-1112	2943	3	𝐏𝟔	𝐏𝟔	PROPN
m-1112	2943	4	𝐏𝟕	𝐏𝟕	PROPN
m-1112	2943	5	𝐏𝟖	𝐏𝟖	PROPN
m-1112	2943	6	p	p	PROPN
m-1112	2943	7	o	o	PROPN
m-1112	2944	1	=	=	PUNCT
m-1112	2944	2	the	the	DET
m-1112	2944	3	coordinates	coordinate	NOUN
m-1112	2944	4	x	x	X
m-1112	2944	5	o	o	INTJ
m-1112	2944	6	,	,	PUNCT
m-1112	2944	7	y	y	PROPN
m-1112	2944	8	o	o	INTJ
m-1112	2944	9	,	,	PUNCT
m-1112	2944	10	z	z	NOUN
m-1112	2944	11	o	o	NOUN
m-1112	2944	12	of	of	ADP
m-1112	2944	13	the	the	DET
m-1112	2944	14	common	common	ADJ
m-1112	2944	15	center	center	NOUN
m-1112	2944	16	of	of	ADP
m-1112	2944	17	2	2	NUM
m-1112	2944	18	-	-	PUNCT
m-1112	2944	19	spheres	sphere	NOUN
m-1112	2944	20	.	.	PUNCT
m-1112	2945	1	p	p	NOUN
m-1112	2945	2	1	1	NUM
m-1112	2945	3	=	=	SYM
m-1112	2945	4	the	the	DET
m-1112	2945	5	coordinates	coordinate	NOUN
m-1112	2945	6	x	x	SYM
m-1112	2945	7	1	1	X
m-1112	2945	8	,	,	PUNCT
m-1112	2945	9	y	y	PROPN
m-1112	2945	10	1	1	NUM
m-1112	2945	11	,	,	PUNCT
m-1112	2945	12	z	z	NOUN
m-1112	2945	13	1	1	NUM
m-1112	2945	14	of	of	ADP
m-1112	2945	15	the	the	DET
m-1112	2945	16	tetrahedroncube	tetrahedroncube	NOUN
m-1112	2945	17	point	point	NOUN
m-1112	2945	18	-1	-1	PUNCT
m-1112	2945	19	p	p	X
m-1112	2945	20	2	2	NUM
m-1112	2945	21	=	=	SYM
m-1112	2945	22	the	the	DET
m-1112	2945	23	coordinates	coordinate	NOUN
m-1112	2945	24	x	x	SYM
m-1112	2945	25	2	2	NUM
m-1112	2945	26	,	,	PUNCT
m-1112	2945	27	y	y	PROPN
m-1112	2945	28	2	2	NUM
m-1112	2945	29	,	,	PUNCT
m-1112	2945	30	z	z	NOUN
m-1112	2945	31	2	2	NUM
m-1112	2945	32	of	of	ADP
m-1112	2945	33	the	the	DET
m-1112	2945	34	sphere	sphere	NOUN
m-1112	2945	35	cube	cube	NOUN
m-1112	2945	36	point	point	NOUN
m-1112	2945	37	2	2	NUM
m-1112	2945	38	p	p	NOUN
m-1112	2945	39	3	3	NUM
m-1112	2945	40	=	=	SYM
m-1112	2945	41	the	the	DET
m-1112	2945	42	coordinates	coordinate	NOUN
m-1112	2945	43	x	x	SYM
m-1112	2945	44	3	3	X
m-1112	2945	45	,	,	PUNCT
m-1112	2945	46	y	y	PROPN
m-1112	2945	47	3	3	NUM
m-1112	2945	48	,	,	PUNCT
m-1112	2945	49	z	z	NOUN
m-1112	2945	50	3	3	NUM
m-1112	2945	51	of	of	ADP
m-1112	2945	52	the	the	DET
m-1112	2945	53	tetrahedroncube	tetrahedroncube	NOUN
m-1112	2945	54	point	point	NOUN
m-1112	2945	55	-3	-3	PUNCT
m-1112	2945	56	p	p	X
m-1112	2945	57	4	4	NUM
m-1112	2945	58	=	=	SYM
m-1112	2945	59	the	the	DET
m-1112	2945	60	coordinates	coordinate	NOUN
m-1112	2945	61	x	x	SYM
m-1112	2945	62	4	4	NUM
m-1112	2945	63	,	,	PUNCT
m-1112	2945	64	y	y	PROPN
m-1112	2945	65	4	4	NUM
m-1112	2945	66	,	,	PUNCT
m-1112	2945	67	z	z	NOUN
m-1112	2945	68	4	4	NUM
m-1112	2945	69	of	of	ADP
m-1112	2945	70	the	the	DET
m-1112	2945	71	sphere	sphere	NOUN
m-1112	2945	72	cube	cube	NOUN
m-1112	2945	73	point	point	NOUN
m-1112	2945	74	4	4	NUM
m-1112	2945	75	p	p	NOUN
m-1112	2945	76	5	5	NUM
m-1112	2945	77	=	=	SYM
m-1112	2945	78	the	the	DET
m-1112	2945	79	coordinates	coordinate	NOUN
m-1112	2945	80	x	x	SYM
m-1112	2945	81	5	5	NUM
m-1112	2945	82	,	,	PUNCT
m-1112	2945	83	y	y	PROPN
m-1112	2945	84	5	5	NUM
m-1112	2945	85	,	,	PUNCT
m-1112	2945	86	z	z	NOUN
m-1112	2945	87	5	5	NUM
m-1112	2945	88	of	of	ADP
m-1112	2945	89	the	the	DET
m-1112	2945	90	tetrahedroncube	tetrahedroncube	NOUN
m-1112	2945	91	point	point	NOUN
m-1112	2945	92	-5	-5	PUNCT
m-1112	2945	93	p	p	X
m-1112	2945	94	6	6	NUM
m-1112	2945	95	=	=	NOUN
m-1112	2945	96	the	the	DET
m-1112	2945	97	coordinates	coordinate	NOUN
m-1112	2945	98	x	x	PUNCT
m-1112	2945	99	6	6	NUM
m-1112	2945	100	,	,	PUNCT
m-1112	2945	101	y	y	PROPN
m-1112	2945	102	6	6	NUM
m-1112	2945	103	,	,	PUNCT
m-1112	2945	104	z	z	NOUN
m-1112	2945	105	6	6	NUM
m-1112	2945	106	of	of	ADP
m-1112	2945	107	the	the	DET
m-1112	2945	108	sphere	sphere	NOUN
m-1112	2945	109	cube	cube	NOUN
m-1112	2945	110	point	point	NOUN
m-1112	2945	111	6	6	NUM
m-1112	2945	112	p	p	NOUN
m-1112	2945	113	7	7	NUM
m-1112	2945	114	=	=	SYM
m-1112	2945	115	the	the	DET
m-1112	2945	116	coordinates	coordinate	NOUN
m-1112	2945	117	x	x	SYM
m-1112	2945	118	7	7	NUM
m-1112	2945	119	,	,	PUNCT
m-1112	2945	120	y	y	PROPN
m-1112	2945	121	7	7	NUM
m-1112	2945	122	,	,	PUNCT
m-1112	2945	123	z	z	PROPN
m-1112	2945	124	7	7	NUM
m-1112	2945	125	of	of	ADP
m-1112	2945	126	the	the	DET
m-1112	2945	127	tetrahedroncube	tetrahedroncube	NOUN
m-1112	2945	128	point	point	NOUN
m-1112	2945	129	-7	-7	INTJ
m-1112	2946	1	p	p	NOUN
m-1112	2946	2	8	8	NUM
m-1112	2946	3	=	=	SYM
m-1112	2946	4	the	the	DET
m-1112	2946	5	coordinates	coordinate	NOUN
m-1112	2946	6	x	x	SYM
m-1112	2946	7	8	8	NUM
m-1112	2946	8	,	,	PUNCT
m-1112	2946	9	y	y	PROPN
m-1112	2946	10	8	8	NUM
m-1112	2946	11	,	,	PUNCT
m-1112	2946	12	z	z	NOUN
m-1112	2946	13	8	8	NUM
m-1112	2946	14	of	of	ADP
m-1112	2946	15	the	the	DET
m-1112	2946	16	sphere	sphere	NOUN
m-1112	2946	17	cube	cube	NOUN
m-1112	2946	18	point	point	NOUN
m-1112	2946	19	8	8	NUM
m-1112	2946	20	on	on	ADP
m-1112	2946	21	the	the	DET
m-1112	2946	22	above	above	ADJ
m-1112	2946	23	geometrical	geometrical	ADJ
m-1112	2946	24	coordinates	coordinate	NOUN
m-1112	2946	25	system	system	NOUN
m-1112	2946	26	are	be	AUX
m-1112	2946	27	placed	place	VERB
m-1112	2946	28	the	the	DET
m-1112	2946	29	4	4	NUM
m-1112	2946	30	-	-	PUNCT
m-1112	2946	31	spaces	space	NOUN
m-1112	2946	32	from	from	ADP
m-1112	2946	33	the	the	DET
m-1112	2946	34	oz	oz	NOUN
m-1112	2946	35	=	=	SYM
m-1112	2946	36	od	od	NUM
m-1112	2946	37	extended	extend	VERB
m-1112	2946	38	conductor	conductor	NOUN
m-1112	2946	39	and	and	CCONJ
m-1112	2946	40	equal	equal	ADJ
m-1112	2946	41	to	to	ADP
m-1112	2946	42	monads	monad	NOUN
m-1112	2946	43	.	.	PUNCT
m-1112	2947	1	for	for	ADP
m-1112	2947	2	the	the	DET
m-1112	2947	3	cave	cave	NOUN
m-1112	2947	4	-	-	PUNCT
m-1112	2947	5	spin	spin	NOUN
m-1112	2947	6	,	,	PUNCT
m-1112	2947	7	�	�	NOUN
m-1112	2947	8	̅	̅	NOUN
m-1112	2947	9	�	�	NOUN
m-1112	2947	10	=	=	SYM
m-1112	2947	11	r	r	NOUN
m-1112	2947	12	m	m	VERB
m-1112	2947	13	v	v	NOUN
m-1112	2947	14	which	which	PRON
m-1112	2947	15	is	be	AUX
m-1112	2947	16	a	a	DET
m-1112	2947	17	monad	monad	PROPN
m-1112	2947	18	,	,	PUNCT
m-1112	2947	19	exist	exist	VERB
m-1112	2947	20	the	the	DET
m-1112	2947	21	4	4	NUM
m-1112	2947	22	-	-	PUNCT
m-1112	2947	23	spaces	space	NOUN
m-1112	2947	24	as	as	ADP
m-1112	2947	25	fig-1	fig-1	NOUN
m-1112	2947	26	→	→	PUNCT
m-1112	2947	27	(	(	PUNCT
m-1112	2947	28	(	(	PUNCT
m-1112	2947	29	the	the	DET
m-1112	2947	30	n	n	DET
m-1112	2947	31	spaces	space	NOUN
m-1112	2947	32	of	of	ADP
m-1112	2947	33	spin	spin	NOUN
m-1112	2947	34	�	�	NOUN
m-1112	2947	35	̅	̅	NOUN
m-1112	2947	36	�	�	NOUN
m-1112	2947	37	are	be	AUX
m-1112	2947	38	the	the	DET
m-1112	2947	39	polygons	polygons	PROPN
m-1112	2947	40	𝐒𝐧	𝐒𝐧	PROPN
m-1112	2947	41	,	,	PUNCT
m-1112	2947	42	the	the	DET
m-1112	2947	43	n	n	ADV
m-1112	2947	44	anti	anti	NOUN
m-1112	2947	45	-	-	ADJ
m-1112	2947	46	spaces	space	NOUN
m-1112	2947	47	of	of	ADP
m-1112	2947	48	spin	spin	NOUN
m-1112	2947	49	�	�	NOUN
m-1112	2947	50	̅	̅	NOUN
m-1112	2947	51	�	�	NOUN
m-1112	2947	52	are	be	AUX
m-1112	2947	53	the	the	DET
m-1112	2947	54	polygons	polygon	NOUN
m-1112	2947	55	𝐒𝐧	𝐒𝐧	NOUN
m-1112	2947	56	)	)	PUNCT
m-1112	2947	57	)	)	PUNCT
m-1112	2948	1	←	←	PROPN
m-1112	2948	2	the	the	DET
m-1112	2948	3	sub	sub	ADJ
m-1112	2948	4	-	-	ADJ
m-1112	2948	5	spaces	spaces	ADJ
m-1112	2948	6	±	±	NOUN
m-1112	2948	7	√	√	NUM
m-1112	2948	8	�	�	NOUN
m-1112	2948	9	̅	̅	NOUN
m-1112	2948	10	�	�	NOUN
m-1112	2948	11	𝒏=𝟏−∞	𝒏=𝟏−∞	PROPN
m-1112	2948	12	are	be	AUX
m-1112	2948	13	the	the	DET
m-1112	2948	14	polygons	polygon	NOUN
m-1112	2948	15	with	with	ADP
m-1112	2948	16	n	n	NOUN
m-1112	2948	17	=	=	SYM
m-1112	2948	18	1	1	NUM
m-1112	2948	19	≈	≈	NUM
m-1112	2948	20	∞	∞	PROPN
m-1112	2948	21	knots	knot	NOUN
m-1112	2948	22	since	since	SCONJ
m-1112	2948	23	knots	knot	NOUN
m-1112	2948	24	are	be	AUX
m-1112	2948	25	the	the	DET
m-1112	2948	26	degrees	degree	NOUN
m-1112	2948	27	of	of	ADP
m-1112	2948	28	the	the	DET
m-1112	2948	29	polynomials	polynomial	NOUN
m-1112	2948	30	of	of	ADP
m-1112	2948	31	each	each	DET
m-1112	2948	32	monad	monad	PROPN
m-1112	2948	33	then	then	ADV
m-1112	2948	34	,	,	PUNCT
m-1112	2948	35	the	the	DET
m-1112	2948	36	oz	oz	X
m-1112	2948	37	monad	monad	PROPN
m-1112	2948	38	determines	determine	VERB
m-1112	2948	39	the	the	DET
m-1112	2948	40	number	number	NOUN
m-1112	2948	41	of	of	ADP
m-1112	2948	42	knots	knot	NOUN
m-1112	2948	43	beginning	begin	VERB
m-1112	2948	44	from	from	ADP
m-1112	2948	45	number	number	NOUN
m-1112	2948	46	3	3	NUM
m-1112	2948	47	,	,	PUNCT
m-1112	2948	48	ijo	ijo	PROPN
m-1112	2948	49	international	international	PROPN
m-1112	2948	50	journal	journal	PROPN
m-1112	2948	51	of	of	ADP
m-1112	2948	52	mathematics	mathematics	PROPN
m-1112	2948	53	(	(	PUNCT
m-1112	2948	54	issn	issn	PROPN
m-1112	2948	55	:	:	PUNCT
m-1112	2948	56	2992	2992	NUM
m-1112	2948	57	-	-	SYM
m-1112	2948	58	4421	4421	NUM
m-1112	2948	59	)	)	PUNCT
m-1112	2948	60	volume	volume	NOUN
m-1112	2948	61	08	08	NUM
m-1112	2949	1	|	|	ADV
m-1112	2949	2	issue	issue	NOUN
m-1112	2949	3	08	08	NUM
m-1112	2950	1	|	|	ADV
m-1112	2950	2	august	august	PROPN
m-1112	2950	3	2025	2025	NUM
m-1112	2950	4	|	|	ADV
m-1112	2950	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2950	6	ijo	ijo	PROPN
m-1112	2950	7	journals	journal	NOUN
m-1112	2950	8	105	105	NUM
m-1112	2950	9	the	the	DET
m-1112	2950	10	fundamental	fundamental	ADJ
m-1112	2950	11	particles	particle	NOUN
m-1112	2950	12	origination	origination	NOUN
m-1112	2950	13	mechanism	mechanism	NOUN
m-1112	2950	14	in	in	ADP
m-1112	2950	15	mfmf	mfmf	PROPN
m-1112	2950	16	pns	pns	PROPN
m-1112	2950	17	caves	cave	NOUN
m-1112	2950	18	.	.	PUNCT
m-1112	2951	1	3	3	NUM
m-1112	2951	2			NOUN
m-1112	2951	3	is	be	AUX
m-1112	2951	4	the	the	DET
m-1112	2951	5	figure	figure	NOUN
m-1112	2951	6	of	of	ADP
m-1112	2951	7	regular	regular	ADJ
m-1112	2951	8	triangle	triangle	NOUN
m-1112	2951	9	in	in	ADP
m-1112	2951	10	poly-3rd	poly-3rd	NOUN
m-1112	2951	11	degree	degree	NOUN
m-1112	2951	12	.	.	PUNCT
m-1112	2952	1	the	the	DET
m-1112	2952	2	3	3	NUM
m-1112	2952	3	and	and	CCONJ
m-1112	2952	4	±	±	NUM
m-1112	2952	5	√	√	PROPN
m-1112	2952	6	oz̅̅̅̅	oz̅̅̅̅	PROPN
m-1112	2952	7	𝑛=3	𝑛=3	PROPN
m-1112	2952	8	4	4	NUM
m-1112	2952	9			NOUN
m-1112	2952	10	is	be	AUX
m-1112	2952	11	the	the	DET
m-1112	2952	12	figure	figure	NOUN
m-1112	2952	13	of	of	ADP
m-1112	2952	14	regular	regular	ADJ
m-1112	2952	15	square	square	NOUN
m-1112	2952	16	in	in	ADP
m-1112	2952	17	poly-4rd	poly-4rd	NOUN
m-1112	2952	18	degree	degree	NOUN
m-1112	2952	19	.	.	PUNCT
m-1112	2953	1	the	the	DET
m-1112	2953	2	4	4	NUM
m-1112	2953	3	and	and	CCONJ
m-1112	2953	4	±	±	NUM
m-1112	2953	5	√	√	PROPN
m-1112	2953	6	oz̅̅̅̅	oz̅̅̅̅	NUM
m-1112	2953	7	𝑛=4	𝑛=4	NOUN
m-1112	2953	8	5	5	NUM
m-1112	2953	9			NOUN
m-1112	2953	10	is	be	AUX
m-1112	2953	11	the	the	DET
m-1112	2953	12	figure	figure	NOUN
m-1112	2953	13	of	of	ADP
m-1112	2953	14	regular	regular	ADJ
m-1112	2953	15	pentagon	pentagon	PROPN
m-1112	2953	16	in	in	ADP
m-1112	2953	17	poly-5rd	poly-5rd	NOUN
m-1112	2953	18	degree	degree	NOUN
m-1112	2953	19	.	.	PUNCT
m-1112	2954	1	the	the	DET
m-1112	2954	2	5	5	NUM
m-1112	2954	3	and	and	CCONJ
m-1112	2954	4	±	±	NUM
m-1112	2954	5	√	√	PROPN
m-1112	2954	6	oz̅̅̅̅	oz̅̅̅̅	NUM
m-1112	2954	7	𝑛=5	𝑛=5	PROPN
m-1112	2954	8	6	6	NUM
m-1112	2954	9			NOUN
m-1112	2954	10	is	be	AUX
m-1112	2954	11	the	the	DET
m-1112	2954	12	figure	figure	NOUN
m-1112	2954	13	of	of	ADP
m-1112	2954	14	regular	regular	ADJ
m-1112	2954	15	hexagon	hexagon	NOUN
m-1112	2954	16	in	in	ADP
m-1112	2954	17	poly-6rd	poly-6rd	NOUN
m-1112	2954	18	degree	degree	NOUN
m-1112	2954	19	.	.	PUNCT
m-1112	2955	1	the	the	DET
m-1112	2955	2	6	6	NUM
m-1112	2955	3	and	and	CCONJ
m-1112	2955	4	±	±	NUM
m-1112	2955	5	√	√	PROPN
m-1112	2955	6	oz̅̅̅̅	oz̅̅̅̅	PROPN
m-1112	2955	7	𝑛=6	𝑛=6	PROPN
m-1112	2955	8	7	7	NUM
m-1112	2955	9			NOUN
m-1112	2955	10	is	be	AUX
m-1112	2955	11	the	the	DET
m-1112	2955	12	figure	figure	NOUN
m-1112	2955	13	of	of	ADP
m-1112	2955	14	regular	regular	ADJ
m-1112	2955	15	heptagon	heptagon	NOUN
m-1112	2955	16	in	in	ADP
m-1112	2955	17	poly-7rd	poly-7rd	NOUN
m-1112	2955	18	degree	degree	NOUN
m-1112	2955	19	.	.	PUNCT
m-1112	2956	1	the	the	DET
m-1112	2956	2	7	7	NUM
m-1112	2956	3	and	and	CCONJ
m-1112	2956	4	±	±	NUM
m-1112	2956	5	√	√	PROPN
m-1112	2956	6	oz̅̅̅̅	oz̅̅̅̅	PROPN
m-1112	2956	7	𝑛=7	𝑛=7	PROPN
m-1112	2956	8	8	8	NUM
m-1112	2956	9			NOUN
m-1112	2956	10	is	be	AUX
m-1112	2956	11	the	the	DET
m-1112	2956	12	figure	figure	NOUN
m-1112	2956	13	of	of	ADP
m-1112	2956	14	regular	regular	ADJ
m-1112	2956	15	octagon	octagon	NOUN
m-1112	2956	16	in	in	ADP
m-1112	2956	17	poly-8rd	poly-8rd	PROPN
m-1112	2956	18	degree	degree	NOUN
m-1112	2956	19	.	.	PUNCT
m-1112	2957	1	the	the	DET
m-1112	2957	2	8	8	NUM
m-1112	2957	3	and	and	CCONJ
m-1112	2957	4	±	±	NUM
m-1112	2957	5	√	√	PROPN
m-1112	2957	6	oz̅̅̅̅	oz̅̅̅̅	PROPN
m-1112	2957	7	𝑛=8	𝑛=8	PROPN
m-1112	2957	8	9	9	NUM
m-1112	2957	9			NOUN
m-1112	2957	10	is	be	AUX
m-1112	2957	11	the	the	DET
m-1112	2957	12	figure	figure	NOUN
m-1112	2957	13	of	of	ADP
m-1112	2957	14	regular	regular	ADJ
m-1112	2957	15	eniagon	eniagon	NOUN
m-1112	2957	16	in	in	ADP
m-1112	2957	17	poly-9rd	poly-9rd	NOUN
m-1112	2957	18	degree	degree	NOUN
m-1112	2957	19	.	.	PUNCT
m-1112	2958	1	the	the	DET
m-1112	2958	2	9	9	NUM
m-1112	2958	3	and	and	CCONJ
m-1112	2958	4	±	±	NUM
m-1112	2958	5	√	√	PROPN
m-1112	2958	6	oz̅̅̅̅	oz̅̅̅̅	PROPN
m-1112	2958	7	𝑛=9	𝑛=9	PROPN
m-1112	2958	8	n	n	PROPN
m-1112	2958	9			NOUN
m-1112	2958	10	is	be	AUX
m-1112	2958	11	the	the	DET
m-1112	2958	12	figure	figure	NOUN
m-1112	2958	13	of	of	ADP
m-1112	2958	14	regular	regular	ADJ
m-1112	2958	15	n	n	CCONJ
m-1112	2958	16	-	-	PUNCT
m-1112	2958	17	gone	go	VERB
m-1112	2958	18	in	in	ADP
m-1112	2958	19	poly	poly	ADJ
m-1112	2958	20	-	-	PUNCT
m-1112	2958	21	nrd	nrd	NOUN
m-1112	2958	22	degree	degree	NOUN
m-1112	2958	23	.	.	PUNCT
m-1112	2959	1	the	the	DET
m-1112	2959	2	n	n	NOUN
m-1112	2959	3	and	and	CCONJ
m-1112	2959	4	±	±	NUM
m-1112	2959	5	√	√	PROPN
m-1112	2959	6	oz̅̅̅̅	oz̅̅̅̅	PROPN
m-1112	2959	7	𝑛=𝑁	𝑛=𝑁	ADJ
m-1112	2959	8	remarks	remark	NOUN
m-1112	2959	9	:	:	PUNCT
m-1112	2959	10	1	1	NUM
m-1112	2959	11	…	…	PUNCT
m-1112	2959	12	gravity	gravity	NOUN
m-1112	2959	13	force	force	NOUN
m-1112	2959	14	g	g	PROPN
m-1112	2959	15	≡	≡	PROPN
m-1112	2959	16	motion	motion	NOUN
m-1112	2959	17	,	,	PUNCT
m-1112	2959	18	exists	exist	VERB
m-1112	2959	19	without	without	ADP
m-1112	2959	20	mass	mass	NOUN
m-1112	2959	21	and	and	CCONJ
m-1112	2959	22	is	be	AUX
m-1112	2959	23	quantized	quantize	VERB
m-1112	2959	24	→	→	PUNCT
m-1112	2959	25	spread	spread	VERB
m-1112	2959	26	in	in	ADP
m-1112	2959	27	{	{	PUNCT
m-1112	2959	28	space	space	NOUN
m-1112	2959	29	and	and	CCONJ
m-1112	2959	30	anti	anti	ADJ
m-1112	2959	31	-	-	NOUN
m-1112	2959	32	space	space	ADJ
m-1112	2959	33	}	}	PUNCT
m-1112	2959	34	or	or	CCONJ
m-1112	2959	35	≡	≡	PROPN
m-1112	2959	36	qua	qua	PROPN
m-1112	2959	37	≡	≡	PROPN
m-1112	2959	38	{	{	PUNCT
m-1112	2959	39	is	be	AUX
m-1112	2959	40	the	the	DET
m-1112	2959	41	quantized	quantize	VERB
m-1112	2959	42	-	-	PUNCT
m-1112	2959	43	units	unit	NOUN
m-1112	2959	44	in	in	ADP
m-1112	2959	45	-	-	PUNCT
m-1112	2959	46	area	area	NOUN
m-1112	2959	47	of	of	ADP
m-1112	2959	48	space	space	NOUN
m-1112	2959	49	and	and	CCONJ
m-1112	2959	50	anti	anti	ADJ
m-1112	2959	51	-	-	NOUN
m-1112	2959	52	space	space	NOUN
m-1112	2959	53	}	}	PUNCT
m-1112	2959	54	,	,	PUNCT
m-1112	2959	55	and	and	CCONJ
m-1112	2959	56	as	as	ADP
m-1112	2959	57	a	a	DET
m-1112	2959	58	mould	mould	NOUN
m-1112	2959	59	𝚽	𝚽	PRON
m-1112	2959	60	golden	golden	ADJ
m-1112	2959	61	-	-	PUNCT
m-1112	2959	62	ratio	ratio	NOUN
m-1112	2959	63	,	,	PUNCT
m-1112	2959	64	exists	exist	VERB
m-1112	2959	65	in	in	ADP
m-1112	2959	66	the	the	DET
m-1112	2959	67	impedance	impedance	NOUN
m-1112	2959	68	b	b	PROPN
m-1112	2959	69	.	.	PROPN
m-1112	2960	1	2	2	NUM
m-1112	2960	2	…	…	PUNCT
m-1112	2960	3	the	the	DET
m-1112	2960	4	case	case	NOUN
m-1112	2960	5	of	of	ADP
m-1112	2960	6	{	{	PUNCT
m-1112	2960	7	qua	qua	ADJ
m-1112	2960	8	}	}	PUNCT
m-1112	2960	9	≡	≡	PROPN
m-1112	2960	10	[	[	PUNCT
m-1112	2960	11	σ	σ	PROPN
m-1112	2960	12	=	=	SYM
m-1112	2960	13	n	n	PROPN
m-1112	2960	14	.	.	PUNCT
m-1112	2961	1	h	h	NOUN
m-1112	2961	2	]	]	PUNCT
m-1112	2962	1			NOUN
m-1112	2963	1	∞	∞	NUM
m-1112	2963	2	x	x	PUNCT
m-1112	2963	3	𝚽	𝚽	NOUN
m-1112	2963	4	which	which	PRON
m-1112	2963	5	is	be	AUX
m-1112	2963	6	the	the	DET
m-1112	2963	7	physical	physical	ADJ
m-1112	2963	8	mechanism	mechanism	NOUN
m-1112	2963	9	,	,	PUNCT
m-1112	2963	10	gives	give	VERB
m-1112	2963	11	the	the	DET
m-1112	2963	12	∞	∞	NUM
m-1112	2963	13	impedance	impedance	NOUN
m-1112	2963	14	b	b	NOUN
m-1112	2963	15	determining	determine	VERB
m-1112	2963	16	the	the	DET
m-1112	2963	17	objective	objective	ADJ
m-1112	2963	18	reality	reality	NOUN
m-1112	2963	19	which	which	PRON
m-1112	2963	20	is	be	AUX
m-1112	2963	21	the	the	DET
m-1112	2963	22	existing	exist	VERB
m-1112	2963	23	universe	universe	NOUN
m-1112	2963	24	.	.	PUNCT
m-1112	2964	1	for	for	ADP
m-1112	2964	2	n	n	PRON
m-1112	2964	3	=	=	NOUN
m-1112	2964	4	2	2	NUM
m-1112	2964	5	then	then	ADV
m-1112	2964	6	[	[	X
m-1112	2964	7	σ	σ	X
m-1112	2964	8	=	=	SYM
m-1112	2964	9	n	n	PRON
m-1112	2964	10	h	h	NOUN
m-1112	2964	11	]	]	X
m-1112	2964	12			NOUN
m-1112	2964	13	2	2	NUM
m-1112	2964	14	x	x	SYM
m-1112	2964	15	g	g	PROPN
m-1112	2964	16	/φ	/φ	PUNCT
m-1112	2964	17	,	,	PUNCT
m-1112	2964	18	is	be	AUX
m-1112	2964	19	the	the	DET
m-1112	2964	20	light	light	ADJ
m-1112	2964	21	-	-	PUNCT
m-1112	2964	22	velocity	velocity	NOUN
m-1112	2964	23	�	�	NOUN
m-1112	2964	24	̅	̅	NOUN
m-1112	2964	25	�	�	NOUN
m-1112	2964	26	=	=	SYM
m-1112	2964	27	[	[	PUNCT
m-1112	2964	28	𝐆	𝐆	PROPN
m-1112	2964	29	𝚽	𝚽	PROPN
m-1112	2964	30	𝐀	𝐀	PROPN
m-1112	2964	31	]	]	X
m-1112	2965	1	=	=	VERB
m-1112	2965	2	2.9982.108	2.9982.108	NUM
m-1112	2965	3	m	m	NOUN
m-1112	2965	4	/	/	SYM
m-1112	2965	5	s.	s.	PROPN
m-1112	2965	6	for	for	ADP
m-1112	2965	7	n	n	PROPN
m-1112	2965	8	=	=	NOUN
m-1112	2965	9	1	1	NUM
m-1112	2965	10	then	then	ADV
m-1112	2965	11	[	[	X
m-1112	2965	12	σ	σ	X
m-1112	2965	13	=	=	SYM
m-1112	2965	14	n	n	PRON
m-1112	2965	15	h	h	NOUN
m-1112	2965	16	]	]	X
m-1112	2965	17			NOUN
m-1112	2965	18	g	g	PROPN
m-1112	2965	19	/	/	SYM
m-1112	2965	20	c	c	NOUN
m-1112	2965	21	=	=	NOUN
m-1112	2965	22	charge	charge	NOUN
m-1112	2965	23	q̅	q̅	PROPN
m-1112	2965	24	=	=	SYM
m-1112	2965	25	𝐆	𝐆	PROPN
m-1112	2965	26	𝐜	𝐜	NOUN
m-1112	2965	27	√𝟐	√𝟐	PROPN
m-1112	2965	28	=	=	SYM
m-1112	2965	29	1,58.10−19	1,58.10−19	NUM
m-1112	2965	30	coulomb	coulomb	NOUN
m-1112	2965	31	.	.	PUNCT
m-1112	2966	1	3	3	X
m-1112	2966	2	…	…	PUNCT
m-1112	2966	3	for	for	ADP
m-1112	2966	4	n	n	NOUN
m-1112	2966	5	=	=	SYM
m-1112	2966	6	3	3	NUM
m-1112	2966	7	is	be	AUX
m-1112	2966	8	stpl	stpl	ADJ
m-1112	2966	9	mechanism	mechanism	NOUN
m-1112	2966	10	which	which	PRON
m-1112	2966	11	creates	create	VERB
m-1112	2966	12	the	the	DET
m-1112	2966	13	elementary	elementary	ADJ
m-1112	2966	14	particles	particle	NOUN
m-1112	2966	15	,	,	PUNCT
m-1112	2966	16	[	[	X
m-1112	2966	17	n	n	CCONJ
m-1112	2966	18	-	-	PUNCT
m-1112	2966	19	knots	knot	NOUN
m-1112	2966	20	=	=	SYM
m-1112	2966	21	3	3	X
m-1112	2966	22	]	]	PUNCT
m-1112	2966	23	in	in	ADP
m-1112	2966	24	gravity	gravity	NOUN
m-1112	2966	25	-	-	PUNCT
m-1112	2966	26	voltage	voltage	NOUN
m-1112	2966	27	𝐕	𝐕	NOUN
m-1112	2966	28	gra	gra	NOUN
m-1112	2966	29	=	=	PUNCT
m-1112	2966	30	7,593.1035	7,593.1035	PROPN
m-1112	2966	31	v.	v.	ADP
m-1112	2966	32	this	this	PRON
m-1112	2966	33	is	be	AUX
m-1112	2966	34	because	because	SCONJ
m-1112	2966	35	the	the	DET
m-1112	2966	36	primary	primary	ADJ
m-1112	2966	37	motion	motion	NOUN
m-1112	2966	38	≡	≡	PROPN
m-1112	2967	1	[	[	X
m-1112	2967	2	pm	pm	X
m-1112	2967	3	]	]	PUNCT
m-1112	2967	4	exist	exist	VERB
m-1112	2967	5	from	from	ADP
m-1112	2967	6	the	the	DET
m-1112	2967	7	three	three	NUM
m-1112	2967	8	3	3	NUM
m-1112	2967	9	breakages	breakage	NOUN
m-1112	2967	10	elements	element	NOUN
m-1112	2967	11	[	[	X
m-1112	2967	12	σ	σ	X
m-1112	2967	13	=	=	SYM
m-1112	2967	14	n	n	PROPN
m-1112	2967	15	.	.	PUNCT
m-1112	2968	1	h	h	X
m-1112	2968	2	]	]	X
m-1112	2968	3			NOUN
m-1112	2969	1	[	[	X
m-1112	2969	2	s²	s²	NOUN
m-1112	2969	3	=	=	SYM
m-1112	2969	4	⊕	⊕	PROPN
m-1112	2969	5	,	,	PUNCT
m-1112	2969	6	2s²=	2s²=	NUM
m-1112	2969	7	,	,	PUNCT
m-1112	2969	8	s²	s²	NOUN
m-1112	2969	9	=	=	SYM
m-1112	2969	10	⊝	⊝	X
m-1112	2969	11	]	]	X
m-1112	2969	12	b	b	X
m-1112	2969	13	..	..	PUNCT
m-1112	2969	14	the	the	DET
m-1112	2969	15	atoms	atom	NOUN
m-1112	2969	16	-	-	PUNCT
m-1112	2969	17	elements	element	NOUN
m-1112	2969	18	mass	mass	NOUN
m-1112	2969	19	,	,	PUNCT
m-1112	2969	20	stiffness	stiffness	ADJ
m-1112	2969	21	flexibility	flexibility	NOUN
m-1112	2969	22	[	[	X
m-1112	2969	23	101	101	NUM
m-1112	2969	24	]	]	SYM
m-1112	2969	25	6d	6d	NUM
m-1112	2969	26	..	..	PUNCT
m-1112	2969	27	the	the	DET
m-1112	2969	28	dimensioning	dimensioning	NOUN
m-1112	2969	29	of	of	ADP
m-1112	2969	30	the	the	DET
m-1112	2969	31	[	[	X
m-1112	2969	32	stpl	stpl	X
m-1112	2969	33	]	]	PUNCT
m-1112	2969	34	–	–	PUNCT
m-1112	2969	35	mechanism	mechanism	NOUN
m-1112	2969	36	defining	define	VERB
m-1112	2969	37	the	the	DET
m-1112	2969	38	lengths	length	NOUN
m-1112	2969	39	,	,	PUNCT
m-1112	2969	40	a	a	DET
m-1112	2969	41	=	=	SYM
m-1112	2969	42	kb	kb	PROPN
m-1112	2969	43	kc	kc	PROPN
m-1112	2969	44	,	,	PUNCT
m-1112	2969	45	b	b	X
m-1112	2969	46	=	=	X
m-1112	2969	47	kc	kc	PROPN
m-1112	2969	48	ka	ka	PROPN
m-1112	2969	49	,	,	PUNCT
m-1112	2969	50	c	c	PROPN
m-1112	2969	51	=	=	SYM
m-1112	2969	52	ka	ka	PROPN
m-1112	2969	53	kb	kb	PROPN
m-1112	2969	54	,	,	PUNCT
m-1112	2969	55	d	d	PROPN
m-1112	2969	56	=	=	PUNCT
m-1112	2969	57	[	[	PUNCT
m-1112	2969	58	a+b+c	a+b+c	NOUN
m-1112	2969	59	2	2	NUM
m-1112	2969	60	]	]	PUNCT
m-1112	2970	1	=	=	NOUN
m-1112	2970	2	the	the	DET
m-1112	2970	3	semi	semi	ADJ
m-1112	2970	4	-	-	NOUN
m-1112	2970	5	perimeter	perimeter	NOUN
m-1112	2970	6	then	then	ADV
m-1112	2970	7	the	the	DET
m-1112	2970	8	inscribe	inscribe	NOUN
m-1112	2970	9	radius	radius	NOUN
m-1112	2970	10	r	r	NOUN
m-1112	2970	11	=	=	NOUN
m-1112	2970	12	√d(d−a)(d−b)(d−c	√d(d−a)(d−b)(d−c	X
m-1112	2970	13	)	)	PUNCT
m-1112	2970	14	d	d	NOUN
m-1112	2970	15	=	=	PUNCT
m-1112	2970	16	|oa|	|oa|	INTJ
m-1112	2970	17	,	,	PUNCT
m-1112	2970	18	the	the	DET
m-1112	2970	19	coordinates	coordinate	NOUN
m-1112	2970	20	for	for	ADP
m-1112	2970	21	the	the	DET
m-1112	2970	22	point	point	NOUN
m-1112	2970	23	k	k	X
m-1112	2970	24	=	=	X
m-1112	2970	25	da	da	NOUN
m-1112	2970	26	are	be	AUX
m-1112	2970	27	[	[	PUNCT
m-1112	2970	28	bc	bc	PROPN
m-1112	2970	29	b+c−a	b+c−a	PROPN
m-1112	2970	30	]	]	PUNCT
m-1112	2970	31	:	:	PUNCT
m-1112	2970	32	[	[	PUNCT
m-1112	2970	33	ca	can	AUX
m-1112	2970	34	c+a−b	c+a−b	VERB
m-1112	2970	35	]	]	PUNCT
m-1112	2970	36	:	:	PUNCT
m-1112	2970	37	[	[	PUNCT
m-1112	2970	38	ab	ab	PROPN
m-1112	2970	39	a+b−c	a+b−c	PROPN
m-1112	2970	40	]	]	PUNCT
m-1112	2970	41	,	,	PUNCT
m-1112	2970	42	while	while	SCONJ
m-1112	2970	43	for	for	ADP
m-1112	2970	44	point	point	NOUN
m-1112	2970	45	o	o	NOUN
m-1112	2970	46	are	be	AUX
m-1112	2970	47	[	[	PUNCT
m-1112	2970	48	b+c−a	b+c−a	PROPN
m-1112	2970	49	a	a	X
m-1112	2970	50	]	]	X
m-1112	2970	51	:	:	PUNCT
m-1112	2970	52	[	[	PUNCT
m-1112	2970	53	c+a−b	c+a−b	PROPN
m-1112	2970	54	b	b	PROPN
m-1112	2970	55	]	]	X
m-1112	2970	56	:	:	PUNCT
m-1112	2970	57	[	[	PUNCT
m-1112	2970	58	a+b−c	a+b−c	PROPN
m-1112	2970	59	c	c	NOUN
m-1112	2970	60	]	]	PUNCT
m-1112	2970	61	.	.	PUNCT
m-1112	2971	1	fig-17	fig-17	ADP
m-1112	2971	2	the	the	DET
m-1112	2971	3	stpl	stpl	PROPN
m-1112	2971	4	mechanism	mechanism	NOUN
m-1112	2971	5	is	be	AUX
m-1112	2971	6	the	the	DET
m-1112	2971	7	mould	mould	NOUN
m-1112	2971	8	consisted	consist	VERB
m-1112	2971	9	from	from	ADP
m-1112	2971	10	any	any	DET
m-1112	2971	11	common	common	ADJ
m-1112	2971	12	circle	circle	NOUN
m-1112	2971	13	o	o	NOUN
m-1112	2971	14	,	,	PUNCT
m-1112	2971	15	oa=[oa`≡	oa=[oa`≡	NOUN
m-1112	2971	16	oae	oae	PROPN
m-1112	2971	17	]	]	PUNCT
m-1112	2971	18	,	,	PUNCT
m-1112	2971	19	o	o	NOUN
m-1112	2971	20	,	,	PUNCT
m-1112	2971	21	ob	ob	NOUN
m-1112	2971	22	=	=	SYM
m-1112	2972	1	[	[	X
m-1112	2972	2	ob`≡	ob`≡	NOUN
m-1112	2972	3	obe	obe	NOUN
m-1112	2972	4	]	]	PUNCT
m-1112	2972	5	,	,	PUNCT
m-1112	2972	6	o	o	NOUN
m-1112	2972	7	,	,	PUNCT
m-1112	2972	8	oc	oc	ADP
m-1112	2972	9	=	=	PUNCT
m-1112	2973	1	[	[	X
m-1112	2973	2	oc`≡	oc`≡	NOUN
m-1112	2973	3	oce	oce	NOUN
m-1112	2973	4	]	]	PUNCT
m-1112	2973	5	,	,	PUNCT
m-1112	2973	6	and	and	CCONJ
m-1112	2973	7	the	the	DET
m-1112	2973	8	common	common	ADJ
m-1112	2973	9	lines	line	NOUN
m-1112	2973	10	da	da	PROPN
m-1112	2973	11	-	-	PROPN
m-1112	2973	12	pa	pa	PROPN
m-1112	2973	13	,	,	PUNCT
m-1112	2973	14	db	db	PROPN
m-1112	2973	15	-	-	PUNCT
m-1112	2973	16	pb	pb	NOUN
m-1112	2973	17	,	,	PUNCT
m-1112	2973	18	dc	dc	PROPN
m-1112	2973	19	-	-	PUNCT
m-1112	2973	20	pc	pc	NOUN
m-1112	2973	21	all	all	PRON
m-1112	2973	22	on	on	ADP
m-1112	2973	23	a	a	DET
m-1112	2973	24	line	line	NOUN
m-1112	2973	25	of	of	ADP
m-1112	2973	26	stpl	stpl	PROPN
m-1112	2973	27	.	.	PUNCT
m-1112	2974	1	on	on	ADP
m-1112	2974	2	the	the	DET
m-1112	2974	3	infinite	infinite	ADJ
m-1112	2974	4	sectors	sectors	PROPN
m-1112	2974	5	ada	ada	PROPN
m-1112	2974	6	-	-	PUNCT
m-1112	2974	7	apa	apa	PROPN
m-1112	2974	8	,	,	PUNCT
m-1112	2974	9	bdb	bdb	PROPN
m-1112	2974	10	-	-	PUNCT
m-1112	2974	11	bpb	bpb	PROPN
m-1112	2974	12	,	,	PUNCT
m-1112	2974	13	cdc	cdc	PROPN
m-1112	2974	14	-	-	PUNCT
m-1112	2974	15	cpc	cpc	PROPN
m-1112	2974	16	vibrate	vibrate	NOUN
m-1112	2974	17	,	,	PUNCT
m-1112	2974	18	the	the	DET
m-1112	2974	19	ijo	ijo	PROPN
m-1112	2974	20	international	international	PROPN
m-1112	2974	21	journal	journal	PROPN
m-1112	2974	22	of	of	ADP
m-1112	2974	23	mathematics	mathematics	PROPN
m-1112	2974	24	(	(	PUNCT
m-1112	2974	25	issn	issn	PROPN
m-1112	2974	26	:	:	PUNCT
m-1112	2974	27	2992	2992	NUM
m-1112	2974	28	-	-	SYM
m-1112	2974	29	4421	4421	NUM
m-1112	2974	30	)	)	PUNCT
m-1112	2974	31	volume	volume	NOUN
m-1112	2974	32	08	08	NUM
m-1112	2975	1	|	|	ADV
m-1112	2975	2	issue	issue	NOUN
m-1112	2975	3	08	08	NUM
m-1112	2976	1	|	|	ADV
m-1112	2976	2	august	august	PROPN
m-1112	2976	3	2025	2025	NUM
m-1112	2977	1	|	|	ADV
m-1112	2977	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	2977	3	ijo	ijo	PROPN
m-1112	2977	4	journals	journal	NOUN
m-1112	2977	5	106	106	NUM
m-1112	2977	6	the	the	DET
m-1112	2977	7	fundamental	fundamental	ADJ
m-1112	2977	8	particles	particle	NOUN
m-1112	2977	9	origination	origination	NOUN
m-1112	2977	10	mechanism	mechanism	NOUN
m-1112	2977	11	in	in	ADP
m-1112	2977	12	mfmf	mfmf	PROPN
m-1112	2977	13	pns	pns	PROPN
m-1112	2977	14	caves	cave	NOUN
m-1112	2977	15	.	.	PUNCT
m-1112	2978	1	breakages	breakage	NOUN
m-1112	2978	2	[	[	X
m-1112	2978	3	±	±	NOUN
m-1112	2978	4	s²	s²	NOUN
m-1112	2978	5	=	=	SYM
m-1112	2978	6	±	±	NOUN
m-1112	2978	7	(	(	PUNCT
m-1112	2978	8	w	w	NOUN
m-1112	2978	9	r)²	r)²	NOUN
m-1112	2978	10	]	]	PUNCT
m-1112	2978	11	and	and	CCONJ
m-1112	2978	12	[	[	PUNCT
m-1112	2978	13	i	i	NOUN
m-1112	2978	14	=	=	NOUN
m-1112	2978	15	2(w	2(w	NUM
m-1112	2978	16	r)²	r)²	NOUN
m-1112	2978	17	]	]	PUNCT
m-1112	2978	18	forming	form	VERB
m-1112	2978	19	all	all	DET
m-1112	2978	20	families	family	NOUN
m-1112	2978	21	of	of	ADP
m-1112	2978	22	curves	curve	NOUN
m-1112	2978	23	and	and	CCONJ
m-1112	2978	24	the	the	DET
m-1112	2978	25	euler	euler	PROPN
m-1112	2978	26	savary	savary	PROPN
m-1112	2978	27	coupler	coupler	PROPN
m-1112	2978	28	curves	curve	NOUN
m-1112	2978	29	of	of	ADP
m-1112	2978	30	the	the	DET
m-1112	2978	31	cubic	cubic	ADJ
m-1112	2978	32	-	-	PUNCT
m-1112	2978	33	of	of	ADP
m-1112	2978	34	-	-	PUNCT
m-1112	2978	35	stationary	stationary	ADJ
m-1112	2978	36	curvature	curvature	NOUN
m-1112	2978	37	mechanism	mechanism	NOUN
m-1112	2978	38	of	of	ADP
m-1112	2978	39	spaces	space	NOUN
m-1112	2978	40	,	,	PUNCT
m-1112	2978	41	anti	anti	ADJ
m-1112	2978	42	-	-	ADJ
m-1112	2978	43	spaces	space	NOUN
m-1112	2978	44	vibrating	vibrate	VERB
m-1112	2978	45	the	the	DET
m-1112	2978	46	end	end	NOUN
m-1112	2978	47	-	-	PUNCT
m-1112	2978	48	curves	curve	NOUN
m-1112	2978	49	.	.	PUNCT
m-1112	2979	1	the	the	DET
m-1112	2979	2	dimensioning	dimensioning	NOUN
m-1112	2979	3	of	of	ADP
m-1112	2979	4	the	the	DET
m-1112	2979	5	mechanism	mechanism	NOUN
m-1112	2979	6	is	be	AUX
m-1112	2979	7	possible	possible	ADJ
m-1112	2979	8	by	by	ADP
m-1112	2979	9	using	use	VERB
m-1112	2979	10	the	the	DET
m-1112	2979	11	analytical	analytical	ADJ
m-1112	2979	12	geometry	geometry	NOUN
m-1112	2979	13	.	.	PUNCT
m-1112	2980	1	[	[	X
m-1112	2980	2	91	91	NUM
m-1112	2980	3	]	]	PUNCT
m-1112	2980	4	the	the	DET
m-1112	2980	5	dimensioning	dimensioning	NOUN
m-1112	2980	6	of	of	ADP
m-1112	2980	7	proton	proton	NOUN
m-1112	2980	8	–	–	PUNCT
m-1112	2980	9	neutron	neutron	NOUN
m-1112	2980	10	in	in	ADP
m-1112	2980	11	fig-26	fig-26	NOUN
m-1112	2980	12	,	,	PUNCT
m-1112	2980	13	and	and	CCONJ
m-1112	2980	14	others	other	NOUN
m-1112	2980	15	with	with	ADP
m-1112	2980	16	compounds	compound	NOUN
m-1112	2980	17	in	in	ADP
m-1112	2980	18	fig-27	fig-27	NOUN
m-1112	2980	19	.the	.the	DET
m-1112	2980	20	dimensioning	dimensioning	NOUN
m-1112	2980	21	of	of	ADP
m-1112	2980	22	hydrogen	hydrogen	NOUN
m-1112	2980	23	and	and	CCONJ
m-1112	2980	24	atoms	atom	NOUN
m-1112	2980	25	in	in	ADP
m-1112	2980	26	fig-28	fig-28	PROPN
m-1112	2980	27	-	-	SYM
m-1112	2980	28	30	30	NUM
m-1112	2980	29	,	,	PUNCT
m-1112	2980	30	the	the	DET
m-1112	2980	31	linear	linear	NOUN
m-1112	2980	32	-	-	PUNCT
m-1112	2980	33	vibrations	vibration	NOUN
m-1112	2980	34	[	[	PUNCT
m-1112	2980	35	ẍ	ẍ	X
m-1112	2981	1	+	+	CCONJ
m-1112	2981	2	w	w	PROPN
m-1112	2981	3	²	²	NUM
m-1112	2981	4	x	x	SYM
m-1112	2981	5	=	=	NOUN
m-1112	2981	6	0	0	NUM
m-1112	2981	7	]	]	PUNCT
m-1112	2981	8	of	of	ADP
m-1112	2981	9	three	three	NUM
m-1112	2981	10	-	-	PUNCT
m-1112	2981	11	masses	masse	NOUN
m-1112	2981	12	,	,	PUNCT
m-1112	2981	13	occur	occur	VERB
m-1112	2981	14	on	on	ADP
m-1112	2981	15	two	two	NUM
m-1112	2981	16	-	-	PUNCT
m-1112	2981	17	line	line	NOUN
m-1112	2981	18	-	-	PUNCT
m-1112	2981	19	vectors	vector	NOUN
m-1112	2981	20	perpendicular	perpendicular	NOUN
m-1112	2981	21	each	each	DET
m-1112	2981	22	other	other	ADJ
m-1112	2981	23	,	,	PUNCT
m-1112	2981	24	vibrating	vibrate	VERB
m-1112	2981	25	on	on	ADP
m-1112	2981	26	straight	straight	ADJ
m-1112	2981	27	-	-	PUNCT
m-1112	2981	28	line	line	NOUN
m-1112	2981	29	,	,	PUNCT
m-1112	2981	30	ÿ	ÿ	PROPN
m-1112	2982	1	+	+	CCONJ
m-1112	2982	2	w	w	PROPN
m-1112	2982	3	²	²	NUM
m-1112	2982	4	y	y	NOUN
m-1112	2982	5	=	=	SYM
m-1112	2982	6	0	0	NUM
m-1112	2982	7	,	,	PUNCT
m-1112	2982	8	of	of	ADP
m-1112	2982	9	x	x	PROPN
m-1112	2982	10	⊥	⊥	PROPN
m-1112	2982	11	y	y	PROPN
m-1112	2982	12	plane	plane	NOUN
m-1112	2983	1	and	and	CCONJ
m-1112	2983	2	follow	follow	VERB
m-1112	2983	3	the	the	DET
m-1112	2983	4	lissajous	lissajous	ADJ
m-1112	2983	5	shapes	shape	NOUN
m-1112	2983	6	,	,	PUNCT
m-1112	2984	1	[	[	X
m-1112	2984	2	83	83	NUM
m-1112	2984	3	]	]	PUNCT
m-1112	2984	4	,	,	PUNCT
m-1112	2984	5	where	where	SCONJ
m-1112	2984	6	for	for	ADP
m-1112	2984	7	,	,	PUNCT
m-1112	2984	8	a	a	DET
m-1112	2984	9	..	..	PUNCT
m-1112	2984	10	difference	difference	NOUN
m-1112	2984	11	of	of	ADP
m-1112	2984	12	phase	phase	NOUN
m-1112	2984	13	dφ	dφ	ADP
m-1112	2984	14	=	=	SYM
m-1112	2984	15	90⁰	90⁰	NUM
m-1112	2984	16	emission	emission	NOUN
m-1112	2984	17	is	be	AUX
m-1112	2984	18	→	→	PUNCT
m-1112	2984	19	the	the	DET
m-1112	2984	20	eight	eight	NUM
m-1112	2984	21	-	-	PUNCT
m-1112	2984	22	shapes	shape	NOUN
m-1112	2984	23	ꝏ	ꝏ	X
m-1112	2984	24	.	.	PUNCT
m-1112	2985	1	b	b	X
m-1112	2985	2	..	..	PUNCT
m-1112	2985	3	difference	difference	NOUN
m-1112	2985	4	of	of	ADP
m-1112	2985	5	phase	phase	NOUN
m-1112	2985	6	dφ	dφ	ADP
m-1112	2985	7	=	=	PUNCT
m-1112	2985	8	0⁰	0⁰	NUM
m-1112	2985	9	emission	emission	NOUN
m-1112	2985	10	is	be	AUX
m-1112	2985	11	→	→	PUNCT
m-1112	2985	12	the	the	DET
m-1112	2985	13	ellipse	ellipse	NOUN
m-1112	2985	14	-	-	PUNCT
m-1112	2985	15	shapes	shape	NOUN
m-1112	2985	16	∝	∝	NOUN
m-1112	2985	17	.	.	PUNCT
m-1112	2986	1	c	c	X
m-1112	2986	2	..	..	PUNCT
m-1112	2986	3	difference	difference	NOUN
m-1112	2986	4	of	of	ADP
m-1112	2986	5	phase	phase	NOUN
m-1112	2986	6	dφ	dφ	ADP
m-1112	2986	7	=	=	SYM
m-1112	2986	8	45⁰	45⁰	NUM
m-1112	2986	9	emission	emission	NOUN
m-1112	2986	10	is	be	AUX
m-1112	2986	11	→	→	PUNCT
m-1112	2986	12	the	the	DET
m-1112	2986	13	double	double	ADJ
m-1112	2986	14	-	-	PUNCT
m-1112	2986	15	saddle	saddle	NOUN
m-1112	2986	16	-	-	PUNCT
m-1112	2986	17	shapes	shape	NOUN
m-1112	2986	18	.	.	PUNCT
m-1112	2987	1	ց	ց	INTJ
m-1112	2987	2	,	,	PUNCT
m-1112	2987	3	ѡ	ѡ	PROPN
m-1112	2987	4	.	.	PUNCT
m-1112	2988	1	for	for	ADP
m-1112	2988	2	planck	planck	NOUN
m-1112	2988	3	length	length	NOUN
m-1112	2988	4	[	[	X
m-1112	2988	5	73	73	NUM
m-1112	2988	6	]	]	SYM
m-1112	2988	7	p-49	p-49	NOUN
m-1112	2988	8	,	,	PUNCT
m-1112	2988	9	was	be	AUX
m-1112	2988	10	shown	show	VERB
m-1112	2988	11	that	that	SCONJ
m-1112	2988	12	the	the	DET
m-1112	2988	13	rotated	rotate	VERB
m-1112	2988	14	energy	energy	NOUN
m-1112	2988	15	case	case	NOUN
m-1112	2988	16	,	,	PUNCT
m-1112	2988	17	when	when	SCONJ
m-1112	2988	18	s	s	VERB
m-1112	2988	19	=	=	NOUN
m-1112	2988	20	0	0	NUM
m-1112	2988	21	and	and	CCONJ
m-1112	2988	22	cosφ	cosφ	NOUN
m-1112	2988	23	=	=	SYM
m-1112	2988	24	0	0	NUM
m-1112	2988	25	,	,	PUNCT
m-1112	2988	26	exists	exist	VERB
m-1112	2988	27	for	for	ADP
m-1112	2988	28	angle	angle	NOUN
m-1112	2988	29	φ	φ	PROPN
m-1112	2988	30	=	=	SYM
m-1112	2988	31	π	π	X
m-1112	2988	32	/2	/2	PUNCT
m-1112	2988	33	and	and	CCONJ
m-1112	2988	34	quaternion	quaternion	NOUN
m-1112	2988	35	(	(	PUNCT
m-1112	2988	36	s	s	VERB
m-1112	2988	37	+	+	CCONJ
m-1112	2988	38	v̅	v̅	PROPN
m-1112	2988	39	i	i	INTJ
m-1112	2988	40	)	)	PUNCT
m-1112	2988	41	𝟏/𝐰	𝟏/𝐰	PROPN
m-1112	2988	42	=	=	PUNCT
m-1112	2988	43	𝐞−	𝐞−	PROPN
m-1112	2988	44	𝐢.(𝛑/𝟐+𝟐𝐤𝛑).𝐰	𝐢.(𝛑/𝟐+𝟐𝐤𝛑).𝐰	PROPN
m-1112	2988	45	...	...	PUNCT
m-1112	2988	46	(1	(1	X
m-1112	2988	47	)	)	PUNCT
m-1112	2988	48	the	the	DET
m-1112	2988	49	dimension	dimension	NOUN
m-1112	2988	50	power	power	NOUN
m-1112	2988	51	→	→	SYM
m-1112	2988	52	w	w	PROPN
m-1112	2988	53	=	=	SYM
m-1112	2988	54	b	b	PROPN
m-1112	2988	55	←	←	PROPN
m-1112	2988	56	and	and	CCONJ
m-1112	2988	57	for	for	ADP
m-1112	2988	58	k	k	PROPN
m-1112	2988	59	=	=	SYM
m-1112	2988	60	1	1	NUM
m-1112	2988	61	then	then	ADV
m-1112	2988	62	(	(	PUNCT
m-1112	2988	63	1	1	X
m-1112	2988	64	)	)	PUNCT
m-1112	2988	65	becomes	become	VERB
m-1112	2988	66	,	,	PUNCT
m-1112	2988	67	[	[	X
m-1112	2988	68	84	84	NUM
m-1112	2988	69	]	]	PUNCT
m-1112	2988	70	-p.74	-p.74	ADJ
m-1112	2988	71	𝐞−	𝐞−	PROPN
m-1112	2988	72	𝐢.(𝛑/𝟐+𝟐𝐤𝛑).𝐰	𝐢.(𝛑/𝟐+𝟐𝐤𝛑).𝐰	NOUN
m-1112	2988	73	=	=	SYM
m-1112	2988	74	𝐞−	𝐞−	PROPN
m-1112	2988	75	𝐢.(𝛑/𝟐+𝟐𝐤𝛑).𝐛	𝐢.(𝛑/𝟐+𝟐𝐤𝛑).𝐛	NOUN
m-1112	2988	76	=	=	PUNCT
m-1112	2989	1	𝐞−	𝐞−	PROPN
m-1112	2989	2	𝐢.(𝟓𝛑/𝟐).𝐛	𝐢.(𝟓𝛑/𝟐).𝐛	NOUN
m-1112	2990	1	=	=	PUNCT
m-1112	2990	2	𝐞−	𝐞−	PROPN
m-1112	2990	3	𝐢.(𝟓𝛑/𝟐).𝟏𝟎	𝐢.(𝟓𝛑/𝟐).𝟏𝟎	NOUN
m-1112	2991	1	[	[	X
m-1112	2991	2	86	86	NUM
m-1112	2991	3	]	]	PUNCT
m-1112	2991	4	…	…	PUNCT
m-1112	2991	5	...	...	PUNCT
m-1112	2991	6	(	(	PUNCT
m-1112	2991	7	2	2	X
m-1112	2991	8	)	)	PUNCT
m-1112	2991	9	equation	equation	NOUN
m-1112	2991	10	(	(	PUNCT
m-1112	2991	11	2	2	X
m-1112	2991	12	)	)	PUNCT
m-1112	2991	13	fits	fit	VERB
m-1112	2991	14	,	,	PUNCT
m-1112	2991	15	as	as	ADP
m-1112	2991	16	minimum	minimum	NOUN
m-1112	2991	17	cave	cave	NOUN
m-1112	2991	18	,	,	PUNCT
m-1112	2991	19	in	in	ADP
m-1112	2991	20	the	the	DET
m-1112	2991	21	planck	planck	NOUN
m-1112	2991	22	length	length	NOUN
m-1112	2991	23	and	and	CCONJ
m-1112	2991	24	is	be	AUX
m-1112	2991	25	𝐋	𝐋	PROPN
m-1112	2991	26	𝐩	𝐩	PROPN
m-1112	2991	27	=	=	SYM
m-1112	2991	28	𝐞−	𝐞−	PROPN
m-1112	2991	29	𝐢.(𝟓𝛑/𝟐).𝟏𝟎	𝐢.(𝟓𝛑/𝟐).𝟏𝟎	NOUN
m-1112	2991	30	.....	.....	PUNCT
m-1112	2991	31	(	(	PUNCT
m-1112	2991	32	3	3	X
m-1112	2991	33	)	)	PUNCT
m-1112	2991	34	equation	equation	NOUN
m-1112	2991	35	(	(	PUNCT
m-1112	2991	36	3	3	X
m-1112	2991	37	)	)	PUNCT
m-1112	2991	38	is	be	AUX
m-1112	2991	39	the	the	DET
m-1112	2991	40	smallest	small	ADJ
m-1112	2991	41	energy	energy	NOUN
m-1112	2991	42	-	-	PUNCT
m-1112	2991	43	unit	unit	NOUN
m-1112	2991	44	of	of	ADP
m-1112	2991	45	space	space	NOUN
m-1112	2991	46	,	,	PUNCT
m-1112	2991	47	and	and	CCONJ
m-1112	2991	48	this	this	PRON
m-1112	2991	49	because	because	SCONJ
m-1112	2991	50	is	be	AUX
m-1112	2991	51	for	for	ADP
m-1112	2991	52	s	s	NOUN
m-1112	2991	53	=	=	SYM
m-1112	2991	54	0	0	PROPN
m-1112	2991	55	and	and	CCONJ
m-1112	2991	56	k	k	X
m-1112	2992	1	=	=	NOUN
m-1112	2992	2	1	1	X
m-1112	2992	3	.	.	PUNCT
m-1112	2993	1	it	it	PRON
m-1112	2993	2	was	be	AUX
m-1112	2993	3	shown	show	VERB
m-1112	2993	4	[	[	X
m-1112	2993	5	31	31	NUM
m-1112	2993	6	]	]	PUNCT
m-1112	2993	7	that	that	SCONJ
m-1112	2993	8	space	space	NOUN
m-1112	2993	9	and	and	CCONJ
m-1112	2993	10	energy	energy	NOUN
m-1112	2993	11	is	be	AUX
m-1112	2993	12	quantized	quantize	VERB
m-1112	2993	13	and	and	CCONJ
m-1112	2993	14	measured	measure	VERB
m-1112	2993	15	on	on	ADP
m-1112	2993	16	the	the	DET
m-1112	2993	17	two	two	NUM
m-1112	2993	18	constant	constant	ADJ
m-1112	2993	19	and	and	CCONJ
m-1112	2993	20	natural	natural	ADJ
m-1112	2993	21	numbers	number	NOUN
m-1112	2993	22	e	e	NOUN
m-1112	2993	23	,	,	PUNCT
m-1112	2993	24	π	π	PROPN
m-1112	2993	25	,	,	PUNCT
m-1112	2993	26	where	where	SCONJ
m-1112	2993	27	for	for	ADP
m-1112	2993	28	base	base	NOUN
m-1112	2993	29	the	the	DET
m-1112	2993	30	natural	natural	ADJ
m-1112	2993	31	logarithm	logarithm	NOUN
m-1112	2993	32	,	,	PUNCT
m-1112	2993	33	e	e	NOUN
m-1112	2993	34	,	,	PUNCT
m-1112	2993	35	and	and	CCONJ
m-1112	2993	36	exponent	exponent	VERB
m-1112	2993	37	the	the	DET
m-1112	2993	38	decimal	decimal	ADJ
m-1112	2993	39	base	base	NOUN
m-1112	2993	40	,	,	PUNCT
m-1112	2993	41	b	b	NOUN
m-1112	2993	42	=	=	SYM
m-1112	2993	43	10	10	NUM
m-1112	2993	44	.	.	PUNCT
m-1112	2994	1	from	from	ADP
m-1112	2994	2	→	→	X
m-1112	2994	3	z¹/w	z¹/w	NOUN
m-1112	2994	4	=	=	SYM
m-1112	2994	5	(	(	PUNCT
m-1112	2994	6	s	s	NOUN
m-1112	2994	7	+	+	NUM
m-1112	2994	8	�	�	NOUN
m-1112	2994	9	̅	̅	NOUN
m-1112	2994	10	�	�	PROPN
m-1112	2994	11	i	i	NOUN
m-1112	2994	12	)	)	PUNCT
m-1112	2995	1	¹/	¹/	PROPN
m-1112	2995	2	w	w	PROPN
m-1112	2995	3	=	=	PUNCT
m-1112	2995	4	|zo|−w.[cos.(φ	|zo|−w.[cos.(φ	PROPN
m-1112	2995	5	+	+	CCONJ
m-1112	2995	6	kπ)/w	kπ)/w	X
m-1112	2995	7	+	+	CCONJ
m-1112	2995	8	i.sin.(φ	i.sin.(φ	X
m-1112	2996	1	+	+	CCONJ
m-1112	2996	2	kπ)/w	kπ)/w	X
m-1112	2996	3	]	]	X
m-1112	2996	4	=	=	NOUN
m-1112	2996	5	|zo|−w	|zo|−w	X
m-1112	2996	6	.	.	PUNCT
m-1112	2997	1	e−i.(φ+kπ).w	e−i.(φ+kπ).w	PROPN
m-1112	2997	2	for	for	ADP
m-1112	2997	3	cos.(φ+kπ)/w	cos.(φ+kπ)/w	PRON
m-1112	2997	4	=	=	NOUN
m-1112	2997	5	0	0	PUNCT
m-1112	2997	6	then	then	ADV
m-1112	2997	7	exists	exist	VERB
m-1112	2997	8	only	only	ADV
m-1112	2997	9	the	the	DET
m-1112	2997	10	imaginary	imaginary	ADJ
m-1112	2997	11	part	part	NOUN
m-1112	2997	12	of	of	ADP
m-1112	2997	13	monad	monad	PROPN
m-1112	2997	14	(	(	PUNCT
m-1112	2997	15	�	�	NOUN
m-1112	2997	16	̅	̅	NOUN
m-1112	2997	17	�	�	PROPN
m-1112	2997	18	i	i	NOUN
m-1112	2997	19	)	)	PUNCT
m-1112	2997	20	≠	≠	PROPN
m-1112	2997	21	0	0	NUM
m-1112	2997	22	,	,	PUNCT
m-1112	2998	1	where	where	SCONJ
m-1112	2998	2	φ	φ	PROPN
m-1112	2998	3	=	=	SYM
m-1112	2998	4	π	π	PROPN
m-1112	2998	5	/2	/2	PUNCT
m-1112	2999	1	and	and	CCONJ
m-1112	2999	2	then	then	ADV
m-1112	2999	3	,	,	PUNCT
m-1112	2999	4	z¹/w	z¹/w	NOUN
m-1112	3000	1	=	=	SYM
m-1112	3000	2	|zo|	|zo|	PROPN
m-1112	3000	3	̄	̄	NOUN
m-1112	3000	4	w	w	PROPN
m-1112	3000	5	.	.	PUNCT
m-1112	3001	1	e	e	X
m-1112	3001	2	i.(φ+kπ)/w	i.(φ+kπ)/w	ADP
m-1112	3001	3	=	=	NOUN
m-1112	3001	4	e−i	e−i	NOUN
m-1112	3001	5	.	.	PUNCT
m-1112	3002	1	(	(	PUNCT
m-1112	3002	2	π	π	NOUN
m-1112	3002	3	2	2	NUM
m-1112	3003	1	+	+	NOUN
m-1112	3003	2	kπ).10	kπ).10	ADJ
m-1112	3003	3	which	which	PRON
m-1112	3003	4	is	be	AUX
m-1112	3003	5	the	the	DET
m-1112	3003	6	diffraction	diffraction	NOUN
m-1112	3003	7	energy	energy	NOUN
m-1112	3003	8	mechanism	mechanism	NOUN
m-1112	3003	9	for	for	ADP
m-1112	3003	10	all	all	DET
m-1112	3003	11	space	space	NOUN
m-1112	3003	12	levels	level	NOUN
m-1112	3003	13	of	of	ADP
m-1112	3003	14	quantization	quantization	NOUN
m-1112	3003	15	which	which	PRON
m-1112	3003	16	are	be	AUX
m-1112	3003	17	the	the	DET
m-1112	3003	18	energy	energy	NOUN
m-1112	3003	19	particles	particle	NOUN
m-1112	3003	20	only	only	ADV
m-1112	3003	21	i.e.	i.e.	X
m-1112	3003	22	the	the	DET
m-1112	3003	23	energy	energy	NOUN
m-1112	3003	24	particles	particle	NOUN
m-1112	3003	25	in	in	ADP
m-1112	3003	26	stationary	stationary	ADJ
m-1112	3003	27	caves	cave	NOUN
m-1112	3003	28	are	be	AUX
m-1112	3003	29	z¹/w	z¹/w	NOUN
m-1112	3003	30	=	=	SYM
m-1112	3004	1	|zo|	|zo|	PROPN
m-1112	3004	2	̄	̄	NOUN
m-1112	3004	3	w.	w.	PROPN
m-1112	3004	4	lv	lv	PROPN
m-1112	3005	1	=	=	PUNCT
m-1112	3006	1	e	e	X
m-1112	3006	2	-	-	PROPN
m-1112	3006	3	monad	monad	PROPN
m-1112	3006	4	.	.	PUNCT
m-1112	3007	1	extending	extend	VERB
m-1112	3007	2	quantization	quantization	NOUN
m-1112	3007	3	of	of	ADP
m-1112	3007	4	energy	energy	NOUN
m-1112	3007	5	according	accord	VERB
m-1112	3007	6	to	to	ADP
m-1112	3007	7	exponential	exponential	NOUN
m-1112	3007	8	formula→	formula→	PRON
m-1112	3007	9	𝐋	𝐋	PROPN
m-1112	3007	10	𝐯	𝐯	NOUN
m-1112	3007	11	=	=	X
m-1112	3007	12	𝐞−	𝐞−	PROPN
m-1112	3007	13	𝐢.(𝟓𝛑/𝟐).𝟏𝟎	𝐢.(𝟓𝛑/𝟐).𝟏𝟎	NOUN
m-1112	3007	14	then	then	ADV
m-1112	3007	15	𝐋	𝐋	PROPN
m-1112	3007	16	𝐯	𝐯	NOUN
m-1112	3007	17	on	on	ADP
m-1112	3007	18	the	the	DET
m-1112	3007	19	decimal	decimal	ADJ
m-1112	3007	20	base	base	PROPN
m-1112	3007	21	b	b	PROPN
m-1112	3007	22	=	=	SYM
m-1112	3007	23	10	10	NUM
m-1112	3007	24	and	and	CCONJ
m-1112	3007	25	for	for	ADP
m-1112	3007	26	k	k	PROPN
m-1112	3007	27	=	=	SYM
m-1112	3007	28	±	±	PROPN
m-1112	3007	29	0	0	NUM
m-1112	3007	30	→	→	SYM
m-1112	3007	31	±	±	NUM
m-1112	3007	32	∞	∞	PROPN
m-1112	3007	33	,	,	PUNCT
m-1112	3007	34	are	be	AUX
m-1112	3007	35	the	the	DET
m-1112	3007	36	energy	energy	NOUN
m-1112	3007	37	caves	cave	NOUN
m-1112	3007	38	as	as	ADP
m-1112	3007	39	,	,	PUNCT
m-1112	3007	40	for	for	ADP
m-1112	3007	41	base	base	NOUN
m-1112	3007	42	e	e	NOUN
m-1112	3007	43	=	=	SYM
m-1112	3007	44	2,71828	2,71828	PROPN
m-1112	3007	45	and	and	CCONJ
m-1112	3007	46	base	base	PROPN
m-1112	3007	47	b	b	NOUN
m-1112	3008	1	=	=	SYM
m-1112	3008	2	10	10	NUM
m-1112	3008	3	then	then	ADV
m-1112	3008	4	e^	e^	PROPN
m-1112	3008	5	(	(	PUNCT
m-1112	3008	6	13,8155	13,8155	NUM
m-1112	3008	7	)	)	PUNCT
m-1112	3008	8	=	=	SYM
m-1112	3009	1	1	1	NUM
m-1112	3009	2	.10	.10	NUM
m-1112	3009	3	̄	̄	NOUN
m-1112	3009	4	6	6	NUM
m-1112	3009	5	m	m	NOUN
m-1112	3009	6	for	for	ADP
m-1112	3009	7	base	base	NOUN
m-1112	3009	8	e	e	NOUN
m-1112	3009	9	=	=	PUNCT
m-1112	3009	10	2,71828	2,71828	PROPN
m-1112	3009	11	and	and	CCONJ
m-1112	3009	12	k	k	NOUN
m-1112	3009	13	=	=	SYM
m-1112	3009	14	0	0	NUM
m-1112	3009	15	lv	lv	PROPN
m-1112	3009	16	=	=	SYM
m-1112	3009	17	e^i	e^i	PROPN
m-1112	3009	18	.	.	PROPN
m-1112	3009	19	(	(	PUNCT
m-1112	3009	20	±	±	X
m-1112	3009	21	π/2)b	π/2)b	NOUN
m-1112	3009	22	then	then	ADV
m-1112	3009	23	e^	e^	PROPN
m-1112	3009	24	(	(	PUNCT
m-1112	3009	25	-15,7079	-15,7079	NOUN
m-1112	3009	26	)	)	PUNCT
m-1112	3009	27	=	=	PUNCT
m-1112	3010	1	1,78118	1,78118	NUM
m-1112	3010	2	.10	.10	NUM
m-1112	3010	3	̄	̄	NOUN
m-1112	3010	4	7	7	NUM
m-1112	3010	5	m	m	NOUN
m-1112	3010	6	for	for	ADP
m-1112	3010	7	base	base	NOUN
m-1112	3010	8	e	e	NOUN
m-1112	3010	9	=	=	SYM
m-1112	3010	10	2,71828	2,71828	PROPN
m-1112	3010	11	and	and	CCONJ
m-1112	3010	12	base	base	PROPN
m-1112	3010	13	b	b	NOUN
m-1112	3010	14	=	=	SYM
m-1112	3010	15	10	10	NUM
m-1112	3010	16	then	then	ADV
m-1112	3010	17	e^	e^	X
m-1112	3010	18	(	(	PUNCT
m-1112	3010	19	16,1181	16,1181	NUM
m-1112	3010	20	)	)	PUNCT
m-1112	3010	21	=	=	SYM
m-1112	3010	22	1	1	NUM
m-1112	3010	23	.10	.10	NUM
m-1112	3010	24	̄	̄	NOUN
m-1112	3010	25	7	7	NUM
m-1112	3010	26	or	or	CCONJ
m-1112	3010	27	r	r	NOUN
m-1112	3010	28	=	=	SYM
m-1112	3010	29	1,07.𝟏𝟎−𝟕	1,07.𝟏𝟎−𝟕	NOUN
m-1112	3010	30	m.	m.	NOUN
m-1112	3010	31	placing	place	VERB
m-1112	3010	32	r	r	NOUN
m-1112	3010	33	,	,	PUNCT
m-1112	3010	34	in	in	ADP
m-1112	3010	35	the	the	DET
m-1112	3010	36	dynamic	dynamic	ADJ
m-1112	3010	37	-	-	PUNCT
m-1112	3010	38	space	space	NOUN
m-1112	3010	39	-	-	PUNCT
m-1112	3010	40	energy	energy	NOUN
m-1112	3010	41	relation	relation	NOUN
m-1112	3010	42	when	when	SCONJ
m-1112	3010	43	g	g	PROPN
m-1112	3010	44	=	=	PROPN
m-1112	3010	45	1	1	NUM
m-1112	3010	46	then	then	ADV
m-1112	3010	47	r	r	NOUN
m-1112	3010	48	³.𝐟²𝐩=	³.𝐟²𝐩=	PROPN
m-1112	3010	49	1	1	NUM
m-1112	3010	50	and	and	CCONJ
m-1112	3010	51	𝐟²𝐩	𝐟²𝐩	VERB
m-1112	3010	52	=	=	SYM
m-1112	3010	53	1	1	NUM
m-1112	3010	54	r	r	NOUN
m-1112	3010	55	³	³	X
m-1112	3010	56	=	=	SYM
m-1112	3010	57	8,0647139.1020	8,0647139.1020	NUM
m-1112	3010	58	m	m	NOUN
m-1112	3010	59	and	and	CCONJ
m-1112	3010	60	occurs	occur	VERB
m-1112	3010	61	the	the	DET
m-1112	3010	62	,	,	PUNCT
m-1112	3010	63	minimum	minimum	ADJ
m-1112	3010	64	frequency	frequency	NOUN
m-1112	3010	65	𝐟𝐦𝐢𝐧	𝐟𝐦𝐢𝐧	NOUN
m-1112	3010	66	=	=	SYM
m-1112	3010	67	2,839844	2,839844	NOUN
m-1112	3010	68	.	.	NOUN
m-1112	3010	69	𝟏𝟎𝟏𝟎	𝟏𝟎𝟏𝟎	NUM
m-1112	3010	70	h	h	NOUN
m-1112	3010	71	…	…	PUNCT
m-1112	3010	72	(	(	PUNCT
m-1112	3010	73	4	4	NUM
m-1112	3010	74	)	)	PUNCT
m-1112	3010	75	7d	7d	NUM
m-1112	3010	76	..	..	PUNCT
m-1112	3010	77	the	the	DET
m-1112	3010	78	cosmic	cosmic	ADJ
m-1112	3010	79	particles	particle	NOUN
m-1112	3010	80	in	in	ADP
m-1112	3010	81	the	the	DET
m-1112	3010	82	cycloid	cycloid	NOUN
m-1112	3010	83	,	,	PUNCT
m-1112	3010	84	anti	anti	ADJ
m-1112	3010	85	-	-	ADJ
m-1112	3010	86	cycloid	cycloid	ADJ
m-1112	3010	87	evolute	evolute	NOUN
m-1112	3010	88	:	:	PUNCT
m-1112	3010	89	the	the	DET
m-1112	3010	90	moving	move	VERB
m-1112	3010	91	monads	monad	NOUN
m-1112	3010	92	in	in	ADP
m-1112	3010	93	cycloid	cycloid	NOUN
m-1112	3010	94	equilibrium	equilibrium	NOUN
m-1112	3010	95	in	in	ADP
m-1112	3010	96	the	the	DET
m-1112	3010	97	anti	anti	X
m-1112	3010	98	cycloid	cycloid	NOUN
m-1112	3010	99	(	(	PUNCT
m-1112	3010	100	evolute	evolute	PROPN
m-1112	3010	101	)	)	PUNCT
m-1112	3010	102	.	.	PUNCT
m-1112	3011	1	the	the	DET
m-1112	3011	2	equilibrium	equilibrium	NOUN
m-1112	3011	3	of	of	ADP
m-1112	3011	4	the	the	DET
m-1112	3011	5	resultant	resultant	NOUN
m-1112	3011	6	forces	force	NOUN
m-1112	3011	7	is	be	AUX
m-1112	3011	8	obtained	obtain	VERB
m-1112	3011	9	by	by	ADP
m-1112	3011	10	the	the	DET
m-1112	3011	11	above	above	ADJ
m-1112	3011	12	cycloid	cycloid	NOUN
m-1112	3011	13	,	,	PUNCT
m-1112	3011	14	anti	anti	ADJ
m-1112	3011	15	-	-	ADJ
m-1112	3011	16	cycloid	cycloid	ADJ
m-1112	3011	17	evolute	evolute	PROPN
m-1112	3011	18	forces	force	NOUN
m-1112	3011	19	,	,	PUNCT
m-1112	3011	20	or	or	CCONJ
m-1112	3011	21	by	by	ADP
m-1112	3011	22	the	the	DET
m-1112	3011	23	rotor	rotor	NOUN
m-1112	3011	24	and	and	CCONJ
m-1112	3011	25	spin	spin	VERB
m-1112	3011	26	in	in	ADP
m-1112	3011	27	one	one	NUM
m-1112	3011	28	rim	rim	NOUN
m-1112	3011	29	,	,	PUNCT
m-1112	3011	30	as	as	SCONJ
m-1112	3011	31	was	be	AUX
m-1112	3011	32	shown	show	VERB
m-1112	3011	33	.	.	PUNCT
m-1112	3012	1	ijo	ijo	PROPN
m-1112	3012	2	international	international	PROPN
m-1112	3012	3	journal	journal	PROPN
m-1112	3012	4	of	of	ADP
m-1112	3012	5	mathematics	mathematics	PROPN
m-1112	3012	6	(	(	PUNCT
m-1112	3012	7	issn	issn	PROPN
m-1112	3012	8	:	:	PUNCT
m-1112	3012	9	2992	2992	NUM
m-1112	3012	10	-	-	SYM
m-1112	3012	11	4421	4421	NUM
m-1112	3012	12	)	)	PUNCT
m-1112	3012	13	volume	volume	NOUN
m-1112	3012	14	08	08	NUM
m-1112	3013	1	|	|	ADV
m-1112	3013	2	issue	issue	NOUN
m-1112	3013	3	08	08	NUM
m-1112	3014	1	|	|	ADV
m-1112	3014	2	august	august	PROPN
m-1112	3014	3	2025	2025	NUM
m-1112	3014	4	|	|	ADV
m-1112	3014	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3014	6	ijo	ijo	PROPN
m-1112	3014	7	journals	journal	NOUN
m-1112	3014	8	107	107	NUM
m-1112	3014	9	the	the	DET
m-1112	3014	10	fundamental	fundamental	ADJ
m-1112	3014	11	particles	particle	NOUN
m-1112	3014	12	origination	origination	NOUN
m-1112	3014	13	mechanism	mechanism	NOUN
m-1112	3014	14	in	in	ADP
m-1112	3014	15	mfmf	mfmf	PROPN
m-1112	3014	16	pns	pns	PROPN
m-1112	3014	17	caves	cave	NOUN
m-1112	3014	18	.	.	PUNCT
m-1112	3015	1	in	in	ADP
m-1112	3015	2	rims	rim	NOUN
m-1112	3015	3	is	be	AUX
m-1112	3015	4	possible	possible	ADJ
m-1112	3015	5	the	the	DET
m-1112	3015	6	forming	form	VERB
m-1112	3015	7	velocities	velocity	NOUN
m-1112	3015	8	greater	great	ADJ
m-1112	3015	9	than	than	ADP
m-1112	3015	10	that	that	PRON
m-1112	3015	11	of	of	ADP
m-1112	3015	12	light	light	NOUN
m-1112	3015	13	,	,	PUNCT
m-1112	3015	14	and	and	CCONJ
m-1112	3015	15	this	this	PRON
m-1112	3015	16	because	because	SCONJ
m-1112	3015	17	of	of	ADP
m-1112	3015	18	different	different	ADJ
m-1112	3015	19	,	,	PUNCT
m-1112	3015	20	r	r	NOUN
m-1112	3015	21	,	,	PUNCT
m-1112	3015	22	and	and	CCONJ
m-1112	3015	23	the	the	DET
m-1112	3015	24	tangential	tangential	ADJ
m-1112	3015	25	velocities	velocity	NOUN
m-1112	3015	26	are	be	AUX
m-1112	3015	27	kept	keep	VERB
m-1112	3015	28	with	with	ADP
m-1112	3015	29	the	the	DET
m-1112	3015	30	same	same	ADJ
m-1112	3015	31	angular	angular	ADJ
m-1112	3015	32	velocity	velocity	NOUN
m-1112	3015	33	,	,	PUNCT
m-1112	3015	34	the	the	DET
m-1112	3015	35	spinning	spinning	NOUN
m-1112	3015	36	,	,	PUNCT
m-1112	3015	37	unless	unless	SCONJ
m-1112	3015	38	spinning	spinning	NOUN
m-1112	3015	39	changes	change	NOUN
m-1112	3015	40	in	in	ADP
m-1112	3015	41	such	such	ADJ
m-1112	3015	42	way	way	NOUN
m-1112	3015	43	to	to	PART
m-1112	3015	44	keep	keep	VERB
m-1112	3015	45	light	light	ADJ
m-1112	3015	46	-	-	PUNCT
m-1112	3015	47	velocity	velocity	NOUN
m-1112	3015	48	constant	constant	ADJ
m-1112	3015	49	.	.	PUNCT
m-1112	3016	1	figure	figure	VERB
m-1112	3016	2	25	25	NUM
m-1112	3016	3	the	the	DET
m-1112	3016	4	equilibrium	equilibrium	NOUN
m-1112	3016	5	of	of	ADP
m-1112	3016	6	the	the	DET
m-1112	3016	7	resultant	resultant	NOUN
m-1112	3016	8	forces	force	NOUN
m-1112	3016	9	,	,	PUNCT
m-1112	3016	10	in	in	ADP
m-1112	3016	11	the	the	DET
m-1112	3016	12	cycloid	cycloid	NOUN
m-1112	3016	13	and	and	CCONJ
m-1112	3016	14	for	for	ADP
m-1112	3016	15	motion	motion	NOUN
m-1112	3016	16	wavelength	wavelength	NOUN
m-1112	3016	17	,	,	PUNCT
m-1112	3016	18	and	and	CCONJ
m-1112	3016	19	of	of	ADP
m-1112	3016	20	any	any	DET
m-1112	3016	21	other	other	ADJ
m-1112	3016	22	removal	removal	NOUN
m-1112	3016	23	monad	monad	PROPN
m-1112	3016	24	.	.	PUNCT
m-1112	3017	1	the	the	DET
m-1112	3017	2	intrinsic	intrinsic	ADJ
m-1112	3017	3	space	space	NOUN
m-1112	3017	4	is	be	AUX
m-1112	3017	5	(	(	PUNCT
m-1112	3017	6	wavelength	wavelength	NOUN
m-1112	3017	7	=	=	PUNCT
m-1112	3018	1	[	[	X
m-1112	3018	2	λ	λ	X
m-1112	3018	3	]	]	X
m-1112	3018	4	)	)	PUNCT
m-1112	3018	5	,	,	PUNCT
m-1112	3018	6	as	as	ADP
m-1112	3018	7	the	the	DET
m-1112	3018	8	energy	energy	NOUN
m-1112	3018	9	quanta	quanta	PROPN
m-1112	3018	10	.	.	PUNCT
m-1112	3019	1	the	the	DET
m-1112	3019	2	equilibrium	equilibrium	NOUN
m-1112	3019	3	of	of	ADP
m-1112	3019	4	the	the	DET
m-1112	3019	5	three	three	NUM
m-1112	3019	6	-	-	PUNCT
m-1112	3019	7	spaces	space	NOUN
m-1112	3019	8	,	,	PUNCT
m-1112	3019	9	the	the	DET
m-1112	3019	10	space	space	NOUN
m-1112	3019	11	anti	anti	NOUN
m-1112	3019	12	-	-	ADJ
m-1112	3019	13	space	space	ADJ
m-1112	3019	14	,	,	PUNCT
m-1112	3019	15	neutral	neutral	ADJ
m-1112	3019	16	-	-	PUNCT
m-1112	3019	17	space	space	NOUN
m-1112	3019	18	:	:	PUNCT
m-1112	3020	1	[	[	X
m-1112	3020	2	60	60	NUM
m-1112	3020	3	]	]	PUNCT
m-1112	3020	4	the	the	DET
m-1112	3020	5	stability	stability	NOUN
m-1112	3020	6	of	of	ADP
m-1112	3020	7	elementary	elementary	ADJ
m-1112	3020	8	particles	particle	NOUN
m-1112	3020	9	,	,	PUNCT
m-1112	3020	10	conductors	conductor	NOUN
m-1112	3020	11	and	and	CCONJ
m-1112	3020	12	the	the	DET
m-1112	3020	13	atoms	atom	NOUN
m-1112	3020	14	-nucleus	-nucleus	NOUN
m-1112	3020	15	fig-24	fig-24	ADP
m-1112	3020	16	the	the	DET
m-1112	3020	17	equations	equation	NOUN
m-1112	3020	18	of	of	ADP
m-1112	3020	19	motion	motion	NOUN
m-1112	3020	20	become	become	VERB
m-1112	3020	21	everywhere	everywhere	ADV
m-1112	3020	22	from	from	ADP
m-1112	3020	23	any	any	DET
m-1112	3020	24	opposite	opposite	ADJ
m-1112	3020	25	space	space	NOUN
m-1112	3020	26	≡	≡	PROPN
m-1112	3020	27	⊕	⊕	PROPN
m-1112	3020	28	,	,	PUNCT
m-1112	3020	29	anti	anti	ADJ
m-1112	3020	30	space	space	NOUN
m-1112	3020	31	≡	≡	PROPN
m-1112	3020	32	⊝	⊝	PROPN
m-1112	3020	33	.	.	PUNCT
m-1112	3021	1	during	during	ADP
m-1112	3021	2	these	these	DET
m-1112	3021	3	motions	motion	NOUN
m-1112	3021	4	as	as	ADP
m-1112	3021	5	,	,	PUNCT
m-1112	3021	6	ds	ds	INTJ
m-1112	3021	7	.	.	PUNCT
m-1112	3021	8	is	be	AUX
m-1112	3021	9	done	do	VERB
m-1112	3021	10	a	a	DET
m-1112	3021	11	constant	constant	ADJ
m-1112	3021	12	-	-	PUNCT
m-1112	3021	13	work	work	NOUN
m-1112	3021	14	,	,	PUNCT
m-1112	3021	15	k	k	NOUN
m-1112	3021	16	,	,	PUNCT
m-1112	3021	17	or	or	CCONJ
m-1112	3021	18	and	and	CCONJ
m-1112	3021	19	from	from	ADP
m-1112	3021	20	their	their	PRON
m-1112	3021	21	velocities	velocity	NOUN
m-1112	3021	22	�	�	NOUN
m-1112	3021	23	̅	̅	NOUN
m-1112	3021	24	�	�	NOUN
m-1112	3021	25	and	and	CCONJ
m-1112	3021	26	this	this	DET
m-1112	3021	27	work	work	NOUN
m-1112	3021	28	may	may	AUX
m-1112	3021	29	be	be	AUX
m-1112	3021	30	positive	positive	ADJ
m-1112	3021	31	or	or	CCONJ
m-1112	3021	32	negative	negative	ADJ
m-1112	3021	33	for	for	ADP
m-1112	3021	34	equilibrium	equilibrium	NOUN
m-1112	3021	35	.	.	PUNCT
m-1112	3022	1	in	in	ADP
m-1112	3022	2	f-23	f-23	PROPN
m-1112	3022	3	cycloid	cycloid	NOUN
m-1112	3022	4	anti	anti	ADJ
m-1112	3022	5	-	-	ADJ
m-1112	3022	6	cycloid	cycloid	ADJ
m-1112	3022	7	motion	motion	NOUN
m-1112	3022	8	is	be	AUX
m-1112	3022	9	as	as	ADP
m-1112	3022	10	,	,	PUNCT
m-1112	3022	11	d.	d.	PROPN
m-1112	3022	12	the	the	DET
m-1112	3022	13	origination	origination	NOUN
m-1112	3022	14	of	of	ADP
m-1112	3022	15	gravity	gravity	NOUN
m-1112	3022	16	g	g	NOUN
m-1112	3022	17	,	,	PUNCT
m-1112	3022	18	antigravity	antigravity	NOUN
m-1112	3023	1	[	[	X
m-1112	3023	2	g	g	X
m-1112	3023	3	]	]	PUNCT
m-1112	3023	4	in	in	ADP
m-1112	3023	5	fig-20.b	fig-20.b	ADV
m-1112	3023	6	,	,	PUNCT
m-1112	3023	7	conductor	conductor	NOUN
m-1112	3023	8	d	d	NOUN
m-1112	3023	9	=	=	SYM
m-1112	3024	1	d	d	NOUN
m-1112	3024	2	=	=	PUNCT
m-1112	3024	3	aka	aka	ADV
m-1112	3024	4	where	where	SCONJ
m-1112	3024	5	⊕	⊕	PROPN
m-1112	3024	6	constituent	constituent	NOUN
m-1112	3024	7	attacks	attack	NOUN
m-1112	3024	8	⊝	⊝	VERB
m-1112	3024	9	by	by	ADP
m-1112	3024	10	a	a	DET
m-1112	3024	11	hook`s	hook`	NOUN
m-1112	3024	12	law	law	NOUN
m-1112	3024	13	force	force	NOUN
m-1112	3024	14	as	as	ADP
m-1112	3024	15	stress	stress	NOUN
m-1112	3024	16	σ	σ	NOUN
m-1112	3024	17	=	=	PUNCT
m-1112	3024	18	e	e	PROPN
m-1112	3024	19	u	u	PROPN
m-1112	3024	20	,	,	PUNCT
m-1112	3024	21	and	and	CCONJ
m-1112	3024	22	an	an	DET
m-1112	3024	23	coulomb	coulomb	NOUN
m-1112	3024	24	force	force	NOUN
m-1112	3024	25	f	f	PROPN
m-1112	3025	1	[	[	X
m-1112	3025	2	+	+	X
m-1112	3025	3	↔	↔	PROPN
m-1112	3025	4	−	−	NOUN
m-1112	3025	5	]	]	X
m-1112	3026	1	=	=	PUNCT
m-1112	3027	1	[	[	X
m-1112	3027	2	⊕↔⊝	⊕↔⊝	X
m-1112	3027	3	]	]	X
m-1112	3027	4	r²	r²	NOUN
m-1112	3027	5	=	=	PUNCT
m-1112	3028	1	[	[	X
m-1112	3028	2	2	2	NUM
m-1112	3028	3	σ	σ	NOUN
m-1112	3028	4	]	]	X
m-1112	3028	5	r²	r²	NOUN
m-1112	3028	6	,	,	PUNCT
m-1112	3028	7	creating	create	VERB
m-1112	3028	8	work	work	NOUN
m-1112	3028	9	≡	≡	PROPN
m-1112	3028	10	motion	motion	NOUN
m-1112	3028	11	as	as	SCONJ
m-1112	3028	12	was	be	AUX
m-1112	3028	13	shown	show	VERB
m-1112	3028	14	it	it	PRON
m-1112	3028	15	was	be	AUX
m-1112	3028	16	shown	show	VERB
m-1112	3028	17	that	that	SCONJ
m-1112	3028	18	,	,	PUNCT
m-1112	3028	19	the	the	DET
m-1112	3028	20	stability	stability	NOUN
m-1112	3028	21	of	of	ADP
m-1112	3028	22	nucleus	nucleus	ADJ
m-1112	3028	23	forces	force	NOUN
m-1112	3028	24	,	,	PUNCT
m-1112	3028	25	is	be	AUX
m-1112	3028	26	succeeded	succeed	VERB
m-1112	3028	27	through	through	ADP
m-1112	3028	28	the	the	DET
m-1112	3028	29	pascal`s	pascal`s	ADJ
m-1112	3028	30	ceba`s	ceba`s	NOUN
m-1112	3028	31	triangle	triangle	NOUN
m-1112	3028	32	launched	launch	VERB
m-1112	3028	33	caves	cave	NOUN
m-1112	3028	34	r	r	NOUN
m-1112	3028	35	,	,	PUNCT
m-1112	3028	36	while	while	SCONJ
m-1112	3028	37	leptons	lepton	NOUN
m-1112	3028	38	from	from	ADP
m-1112	3028	39	their	their	PRON
m-1112	3028	40	anti	anti	ADJ
m-1112	3028	41	leptons	lepton	NOUN
m-1112	3028	42	existence	existence	NOUN
m-1112	3028	43	in	in	ADP
m-1112	3028	44	the	the	DET
m-1112	3028	45	same	same	ADJ
m-1112	3028	46	launched	launch	VERB
m-1112	3028	47	pascal`s	pascal`s	NUM
m-1112	3028	48	caves	cave	NOUN
m-1112	3028	49	r	r	NOUN
m-1112	3028	50	.	.	PUNCT
m-1112	3029	1	[	[	X
m-1112	3029	2	58	58	NUM
m-1112	3029	3	]	]	PUNCT
m-1112	3029	4	the	the	DET
m-1112	3029	5	equilibrium	equilibrium	NOUN
m-1112	3029	6	of	of	ADP
m-1112	3029	7	the	the	DET
m-1112	3029	8	three	three	NUM
m-1112	3029	9	-	-	PUNCT
m-1112	3029	10	spaces	space	NOUN
m-1112	3029	11	is	be	AUX
m-1112	3029	12	done	do	VERB
m-1112	3029	13	on	on	ADP
m-1112	3029	14	the	the	DET
m-1112	3029	15	three	three	NUM
m-1112	3029	16	cyclic	cyclic	ADJ
m-1112	3029	17	-	-	PUNCT
m-1112	3029	18	quadrilaterals	quadrilateral	NOUN
m-1112	3029	19	(	(	PUNCT
m-1112	3029	20	abeaece	abeaece	NOUN
m-1112	3029	21	)	)	PUNCT
m-1112	3029	22	(	(	PUNCT
m-1112	3029	23	bcebeae	bcebeae	PROPN
m-1112	3029	24	)	)	PUNCT
m-1112	3029	25	,	,	PUNCT
m-1112	3029	26	(	(	PUNCT
m-1112	3029	27	caecebe	caecebe	NOUN
m-1112	3029	28	)	)	PUNCT
m-1112	3029	29	of	of	ADP
m-1112	3029	30	the	the	DET
m-1112	3029	31	6	6	NUM
m-1112	3029	32	conductors	conductor	NOUN
m-1112	3029	33	each	each	PRON
m-1112	3029	34	for	for	ADP
m-1112	3029	35	,	,	PUNCT
m-1112	3029	36	[	[	X
m-1112	3029	37	a	a	DET
m-1112	3029	38	,	,	PUNCT
m-1112	3029	39	b	b	NOUN
m-1112	3029	40	,	,	PUNCT
m-1112	3029	41	c	c	NOUN
m-1112	3029	42	,	,	PUNCT
m-1112	3029	43	d	d	PROPN
m-1112	3029	44	,	,	PUNCT
m-1112	3029	45	p	p	X
m-1112	3029	46	,	,	PUNCT
m-1112	3029	47	q	q	X
m-1112	3029	48	]	]	X
m-1112	3029	49	x	x	PUNCT
m-1112	3030	1	[	[	X
m-1112	3030	2	3	3	NUM
m-1112	3030	3	-	-	PUNCT
m-1112	3030	4	abc	abc	X
m-1112	3030	5	]	]	X
m-1112	3030	6	=	=	SYM
m-1112	3030	7	18	18	NUM
m-1112	3030	8	conductors	conductor	NOUN
m-1112	3030	9	.	.	PUNCT
m-1112	3031	1	linearly	linearly	ADV
m-1112	3031	2	is	be	AUX
m-1112	3031	3	through	through	ADP
m-1112	3031	4	the	the	DET
m-1112	3031	5	products	product	NOUN
m-1112	3031	6	of	of	ADP
m-1112	3031	7	the	the	DET
m-1112	3031	8	diagonal	diagonal	ADJ
m-1112	3031	9	connectors	connector	NOUN
m-1112	3031	10	as	as	ADP
m-1112	3031	11	,	,	PUNCT
m-1112	3031	12	→	→	SYM
m-1112	3031	13	→	→	SYM
m-1112	3031	14	→	→	SYM
m-1112	3031	15	[	[	X
m-1112	3031	16	aae].[bece	aae].[bece	X
m-1112	3031	17	]	]	X
m-1112	3031	18	=	=	PUNCT
m-1112	3032	1	[	[	X
m-1112	3032	2	ace].[aebe]+[abe].[aece	ace].[aebe]+[abe].[aece	NOUN
m-1112	3032	3	]	]	PUNCT
m-1112	3032	4	,	,	PUNCT
m-1112	3032	5	[	[	X
m-1112	3032	6	bbe].[ceae	bbe].[ceae	X
m-1112	3032	7	]	]	X
m-1112	3032	8	=	=	PUNCT
m-1112	3033	1	[	[	X
m-1112	3033	2	bae].[bece]+[bce].[beae	bae].[bece]+[bce].[beae	X
m-1112	3033	3	]	]	PUNCT
m-1112	3033	4	,	,	PUNCT
m-1112	3033	5	[	[	X
m-1112	3033	6	cce].[aebe	cce].[aebe	X
m-1112	3033	7	]	]	PUNCT
m-1112	3033	8	=	=	PUNCT
m-1112	3034	1	[	[	X
m-1112	3034	2	cae].[bece]+[cbe].[ceae	cae].[bece]+[cbe].[ceae	X
m-1112	3034	3	]	]	PUNCT
m-1112	3034	4	and	and	CCONJ
m-1112	3034	5	,	,	PUNCT
m-1112	3034	6	rotationally	rotationally	ADV
m-1112	3034	7	through	through	ADP
m-1112	3034	8	the	the	DET
m-1112	3034	9	ratio	ratio	NOUN
m-1112	3034	10	of	of	ADP
m-1112	3034	11	the	the	DET
m-1112	3034	12	diagonals	diagonal	NOUN
m-1112	3034	13	≡	≡	PROPN
m-1112	3034	14	the	the	DET
m-1112	3034	15	conductors	conductor	NOUN
m-1112	3035	1	|	|	ADV
m-1112	3035	2	akb	akb	PROPN
m-1112	3035	3	akc	akc	PROPN
m-1112	3035	4	|x|	|x|	PROPN
m-1112	3035	5	bkc	bkc	PROPN
m-1112	3035	6	bka	bka	PROPN
m-1112	3035	7	|x|	|x|	PROPN
m-1112	3035	8	cka	cka	PROPN
m-1112	3035	9	ckb	ckb	PROPN
m-1112	3035	10	|	|	ADV
m-1112	3035	11	=	=	SYM
m-1112	3035	12	1	1	NUM
m-1112	3035	13	or	or	CCONJ
m-1112	3035	14			PROPN
m-1112	3035	15	rotational	rotational	ADJ
m-1112	3035	16	-	-	PUNCT
m-1112	3035	17	equilibrium	equilibrium	NOUN
m-1112	3035	18	as	as	ADP
m-1112	3035	19	,	,	PUNCT
m-1112	3035	20	[	[	X
m-1112	3035	21	akb].[cka].[bkc	akb].[cka].[bkc	NOUN
m-1112	3035	22	]	]	X
m-1112	3035	23	=	=	PUNCT
m-1112	3036	1	[	[	X
m-1112	3036	2	akc].[bka].[ckb	akc].[bka].[ckb	X
m-1112	3036	3	]	]	X
m-1112	3036	4	,	,	PUNCT
m-1112	3036	5	of	of	ADP
m-1112	3036	6	all	all	DET
m-1112	3036	7	opposites	opposite	NOUN
m-1112	3036	8			VERB
m-1112	3036	9	tangential	tangential	ADJ
m-1112	3036	10	-	-	PUNCT
m-1112	3036	11	electromotive	electromotive	ADJ
m-1112	3036	12	forces	force	NOUN
m-1112	3036	13	.	.	PUNCT
m-1112	3037	1	from	from	ADP
m-1112	3037	2	mechanics	mechanic	NOUN
m-1112	3037	3	-	-	PUNCT
m-1112	3037	4	physics	physics	NOUN
m-1112	3037	5	,	,	PUNCT
m-1112	3037	6	all	all	DET
m-1112	3037	7	systems	system	NOUN
m-1112	3037	8	possessing	possess	VERB
m-1112	3037	9	elasticity	elasticity	NOUN
m-1112	3037	10	≡	≡	PROPN
m-1112	3037	11	motion	motion	NOUN
m-1112	3037	12	and	and	CCONJ
m-1112	3037	13	reaction	reaction	NOUN
m-1112	3037	14	to	to	ADP
m-1112	3037	15	motion	motion	NOUN
m-1112	3037	16	,	,	PUNCT
m-1112	3037	17	the	the	DET
m-1112	3037	18	called	call	VERB
m-1112	3037	19	mass	mass	NOUN
m-1112	3037	20	,	,	PUNCT
m-1112	3037	21	are	be	AUX
m-1112	3037	22	capable	capable	ADJ
m-1112	3037	23	of	of	ADP
m-1112	3037	24	free	free	ADJ
m-1112	3037	25	vibration	vibration	NOUN
m-1112	3037	26	or	or	CCONJ
m-1112	3037	27	vibration	vibration	NOUN
m-1112	3037	28	taking	take	VERB
m-1112	3037	29	place	place	NOUN
m-1112	3037	30	in	in	ADP
m-1112	3037	31	the	the	DET
m-1112	3037	32	absence	absence	NOUN
m-1112	3037	33	of	of	ADP
m-1112	3037	34	external	external	ADJ
m-1112	3037	35	excitation	excitation	NOUN
m-1112	3037	36	[	[	X
m-1112	3037	37	7	7	X
m-1112	3037	38	]	]	PUNCT
m-1112	3037	39	.this	.this	PRON
m-1112	3037	40	principle	principle	ADJ
m-1112	3037	41	issues	issue	NOUN
m-1112	3037	42	for	for	ADP
m-1112	3037	43	both	both	PRON
m-1112	3037	44	closed	closed	ADJ
m-1112	3037	45	or	or	CCONJ
m-1112	3037	46	open	open	ADJ
m-1112	3037	47	systems	system	NOUN
m-1112	3037	48	.	.	PUNCT
m-1112	3038	1	i.e.	i.e.	X
m-1112	3038	2	either	either	CCONJ
m-1112	3038	3	for	for	ADP
m-1112	3038	4	the	the	DET
m-1112	3038	5	nucleus	nucleus	NOUN
m-1112	3038	6	where	where	SCONJ
m-1112	3038	7	issues	issue	VERB
m-1112	3038	8	the	the	DET
m-1112	3038	9	pascal`s	pascal`s	ADJ
m-1112	3038	10	ceba`s	ceba`s	NOUN
m-1112	3038	11	triangle	triangle	VERB
m-1112	3038	12	stability	stability	NOUN
m-1112	3038	13	,	,	PUNCT
m-1112	3038	14	or	or	CCONJ
m-1112	3038	15	for	for	ADP
m-1112	3038	16	the	the	DET
m-1112	3038	17	orbitals	orbital	NOUN
m-1112	3038	18	where	where	SCONJ
m-1112	3038	19	issues	issue	VERB
m-1112	3038	20	the	the	DET
m-1112	3038	21	tetrahedron	tetrahedron	NOUN
m-1112	3038	22	cube	cube	NOUN
m-1112	3038	23	–	–	PUNCT
m-1112	3038	24	sphere	sphere	NOUN
m-1112	3038	25	–	–	PUNCT
m-1112	3038	26	mould	mould	NOUN
m-1112	3038	27	.	.	PUNCT
m-1112	3039	1	ijo	ijo	PROPN
m-1112	3039	2	international	international	PROPN
m-1112	3039	3	journal	journal	PROPN
m-1112	3039	4	of	of	ADP
m-1112	3039	5	mathematics	mathematics	PROPN
m-1112	3039	6	(	(	PUNCT
m-1112	3039	7	issn	issn	PROPN
m-1112	3039	8	:	:	PUNCT
m-1112	3039	9	2992	2992	NUM
m-1112	3039	10	-	-	SYM
m-1112	3039	11	4421	4421	NUM
m-1112	3039	12	)	)	PUNCT
m-1112	3039	13	volume	volume	NOUN
m-1112	3039	14	08	08	NUM
m-1112	3040	1	|	|	ADV
m-1112	3040	2	issue	issue	NOUN
m-1112	3040	3	08	08	NUM
m-1112	3041	1	|	|	ADV
m-1112	3041	2	august	august	PROPN
m-1112	3041	3	2025	2025	NUM
m-1112	3041	4	|	|	ADV
m-1112	3041	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3041	6	ijo	ijo	PROPN
m-1112	3041	7	journals	journal	NOUN
m-1112	3041	8	108	108	NUM
m-1112	3041	9	the	the	DET
m-1112	3041	10	fundamental	fundamental	ADJ
m-1112	3041	11	particles	particle	NOUN
m-1112	3041	12	origination	origination	NOUN
m-1112	3041	13	mechanism	mechanism	NOUN
m-1112	3041	14	in	in	ADP
m-1112	3041	15	mfmf	mfmf	PROPN
m-1112	3041	16	pns	pns	PROPN
m-1112	3041	17	caves	cave	NOUN
m-1112	3041	18	.	.	PUNCT
m-1112	3042	1	8d	8d	NUM
m-1112	3042	2	..	..	PUNCT
m-1112	3043	1	the	the	DET
m-1112	3043	2	stability	stability	NOUN
m-1112	3043	3	of	of	ADP
m-1112	3043	4	the	the	DET
m-1112	3043	5	cosmic	cosmic	ADJ
m-1112	3043	6	particles	particle	NOUN
m-1112	3043	7	conductors	conductor	NOUN
m-1112	3043	8	and	and	CCONJ
m-1112	3043	9	atoms	atom	NOUN
m-1112	3043	10	–	–	PUNCT
m-1112	3043	11	nucleus	nucleus	NOUN
m-1112	3043	12	.	.	PUNCT
m-1112	3044	1	figure	figure	NOUN
m-1112	3044	2	-26	-26	PROPN
m-1112	3044	3	:	:	PUNCT
m-1112	3044	4	the	the	DET
m-1112	3044	5	stability	stability	NOUN
m-1112	3044	6	of	of	ADP
m-1112	3044	7	→	→	SYM
m-1112	3044	8	{	{	PUNCT
m-1112	3044	9	⊕	⊕	NOUN
m-1112	3044	10	space	space	NOUN
m-1112	3045	1	[	[	X
m-1112	3045	2	a	a	DET
m-1112	3045	3	b	b	NOUN
m-1112	3045	4	c	c	NOUN
m-1112	3045	5	]	]	PUNCT
m-1112	3045	6	}	}	PUNCT
m-1112	3045	7	,	,	PUNCT
m-1112	3045	8	{	{	PUNCT
m-1112	3045	9	⊝	⊝	NUM
m-1112	3045	10	anti	anti	ADJ
m-1112	3045	11	-	-	ADJ
m-1112	3045	12	space	space	ADJ
m-1112	3045	13	[	[	X
m-1112	3045	14	ka	ka	X
m-1112	3045	15	kb	kb	PROPN
m-1112	3045	16	kc	kc	PROPN
m-1112	3045	17	]	]	PROPN
m-1112	3045	18	}	}	PUNCT
m-1112	3045	19	,	,	PUNCT
m-1112	3045	20	of	of	ADP
m-1112	3045	21	the	the	DET
m-1112	3045	22	sub	sub	NOUN
m-1112	3045	23	-	-	NOUN
m-1112	3045	24	space	space	NOUN
m-1112	3045	25	[	[	X
m-1112	3045	26	a	a	X
m-1112	3045	27	e	e	NOUN
m-1112	3045	28	,	,	PUNCT
m-1112	3045	29	b	b	PROPN
m-1112	3045	30	e	e	NOUN
m-1112	3045	31	,	,	PUNCT
m-1112	3045	32	c	c	PROPN
m-1112	3045	33	e	e	NOUN
m-1112	3045	34	]	]	PUNCT
m-1112	3045	35	}	}	PUNCT
m-1112	3045	36	,	,	PUNCT
m-1112	3045	37	and	and	CCONJ
m-1112	3045	38	neutral	neutral	ADJ
m-1112	3045	39	-	-	PUNCT
m-1112	3045	40	space	space	NOUN
m-1112	3045	41	{	{	PUNCT
m-1112	3045	42	[	[	X
m-1112	3045	43	⊕↔⊝	⊕↔⊝	X
m-1112	3045	44	]	]	X
m-1112	3045	45	≡	≡	PROPN
m-1112	3045	46	ds	ds	PROPN
m-1112	3045	47	≡	≡	PROPN
m-1112	3046	1	[	[	X
m-1112	3046	2	⊕←ds→⊝	⊕←ds→⊝	NOUN
m-1112	3046	3	]	]	PUNCT
m-1112	3046	4	}	}	PUNCT
m-1112	3046	5	.	.	PUNCT
m-1112	3047	1	since	since	SCONJ
m-1112	3047	2	,	,	PUNCT
m-1112	3047	3	energy	energy	NOUN
m-1112	3047	4	of	of	ADP
m-1112	3047	5	the	the	DET
m-1112	3047	6	first	first	ADJ
m-1112	3047	7	wheel	wheel	NOUN
m-1112	3047	8	-	-	PUNCT
m-1112	3047	9	rim	rim	NOUN
m-1112	3047	10	or	or	CCONJ
m-1112	3047	11	orbital	orbital	NOUN
m-1112	3047	12	is	be	AUX
m-1112	3047	13	distributed	distribute	VERB
m-1112	3047	14	to	to	ADP
m-1112	3047	15	the	the	DET
m-1112	3047	16	couple	couple	NOUN
m-1112	3047	17	of	of	ADP
m-1112	3047	18	(	(	PUNCT
m-1112	3047	19	2e	2e	NOUN
m-1112	3047	20	)	)	PUNCT
m-1112	3047	21	electrons	electron	NOUN
m-1112	3047	22	of	of	ADP
m-1112	3047	23	the	the	DET
m-1112	3047	24	orbital	orbital	NOUN
m-1112	3047	25	,	,	PUNCT
m-1112	3047	26	then	then	ADV
m-1112	3047	27	this	this	PRON
m-1112	3047	28	is	be	AUX
m-1112	3047	29	a	a	DET
m-1112	3047	30	cycloid	cycloid	NOUN
m-1112	3047	31	anti	anti	ADJ
m-1112	3047	32	-	-	ADJ
m-1112	3047	33	cycloid	cycloid	ADJ
m-1112	3047	34	stability	stability	NOUN
m-1112	3047	35	system	system	NOUN
m-1112	3047	36	.	.	PUNCT
m-1112	3048	1	this	this	DET
m-1112	3048	2	still	still	ADV
m-1112	3048	3	systems	system	NOUN
m-1112	3048	4	of	of	ADP
m-1112	3048	5	space	space	NOUN
m-1112	3048	6	–	–	PUNCT
m-1112	3048	7	anti	anti	ADJ
m-1112	3048	8	space	space	NOUN
m-1112	3048	9	does	do	AUX
m-1112	3048	10	not	not	PART
m-1112	3048	11	mean	mean	VERB
m-1112	3048	12	matter	matter	NOUN
m-1112	3048	13	–	–	PUNCT
m-1112	3048	14	antimatter	antimatter	NOUN
m-1112	3048	15	but	but	CCONJ
m-1112	3048	16	the	the	DET
m-1112	3048	17	state	state	NOUN
m-1112	3048	18	of	of	ADP
m-1112	3048	19	equilibrium	equilibrium	NOUN
m-1112	3048	20	in	in	ADP
m-1112	3048	21	caves	cave	NOUN
m-1112	3048	22	≡	≡	PROPN
m-1112	3048	23	the	the	DET
m-1112	3048	24	ceba`s	ceba`s	NOUN
m-1112	3048	25	energy	energy	NOUN
m-1112	3048	26	triangle	triangle	NOUN
m-1112	3048	27	.	.	PUNCT
m-1112	3049	1	a	a	DET
m-1112	3049	2	…	…	PUNCT
m-1112	3049	3	the	the	DET
m-1112	3049	4	space	space	NOUN
m-1112	3049	5	anti	anti	NOUN
m-1112	3049	6	-	-	NOUN
m-1112	3049	7	space	space	ADJ
m-1112	3049	8	and	and	CCONJ
m-1112	3049	9	,	,	PUNCT
m-1112	3049	10	neutral	neutral	ADJ
m-1112	3049	11	-	-	PUNCT
m-1112	3049	12	space	space	NOUN
m-1112	3049	13	conductors	conductor	NOUN
m-1112	3049	14	:	:	PUNCT
m-1112	3050	1	[	[	X
m-1112	3050	2	60	60	NUM
m-1112	3050	3	]	]	PUNCT
m-1112	3050	4	the	the	DET
m-1112	3050	5	equations	equation	NOUN
m-1112	3050	6	of	of	ADP
m-1112	3050	7	motion	motion	NOUN
m-1112	3050	8	become	become	VERB
m-1112	3050	9	everywhere	everywhere	ADV
m-1112	3050	10	from	from	ADP
m-1112	3050	11	any	any	DET
m-1112	3050	12	opposite	opposite	NOUN
m-1112	3050	13	,	,	PUNCT
m-1112	3050	14	space	space	NOUN
m-1112	3050	15	≡	≡	PROPN
m-1112	3050	16	⊕	⊕	PROPN
m-1112	3050	17	,	,	PUNCT
m-1112	3050	18	and	and	CCONJ
m-1112	3050	19	anti	anti	ADJ
m-1112	3050	20	-	-	ADJ
m-1112	3050	21	space	space	ADJ
m-1112	3050	22	≡	≡	PROPN
m-1112	3050	23	⊝	⊝	PROPN
m-1112	3050	24	.	.	PUNCT
m-1112	3051	1	during	during	ADP
m-1112	3051	2	these	these	DET
m-1112	3051	3	motions	motion	NOUN
m-1112	3051	4	as	as	ADP
m-1112	3051	5	,	,	PUNCT
m-1112	3051	6	ds	ds	INTJ
m-1112	3051	7	.	.	PUNCT
m-1112	3051	8	is	be	AUX
m-1112	3051	9	done	do	VERB
m-1112	3051	10	a	a	DET
m-1112	3051	11	constant	constant	ADJ
m-1112	3051	12	-	-	PUNCT
m-1112	3051	13	work	work	NOUN
m-1112	3051	14	,	,	PUNCT
m-1112	3051	15	k	k	NOUN
m-1112	3051	16	,	,	PUNCT
m-1112	3051	17	or	or	CCONJ
m-1112	3051	18	and	and	CCONJ
m-1112	3051	19	from	from	ADP
m-1112	3051	20	their	their	PRON
m-1112	3051	21	velocities	velocity	NOUN
m-1112	3051	22	�	�	NOUN
m-1112	3051	23	̅	̅	NOUN
m-1112	3051	24	�	�	PROPN
m-1112	3051	25	.	.	PUNCT
m-1112	3052	1	in	in	ADP
m-1112	3052	2	figure	figure	NOUN
m-1112	3052	3	conductor	conductor	NOUN
m-1112	3052	4	d	d	NOUN
m-1112	3052	5	=	=	SYM
m-1112	3052	6	d	d	PROPN
m-1112	3052	7	=	=	PUNCT
m-1112	3052	8	aka	aka	ADV
m-1112	3052	9	where	where	SCONJ
m-1112	3052	10	⊕	⊕	PROPN
m-1112	3052	11	constituent	constituent	NOUN
m-1112	3052	12	attacks	attack	NOUN
m-1112	3052	13	⊝	⊝	VERB
m-1112	3052	14	by	by	ADP
m-1112	3052	15	a	a	DET
m-1112	3052	16	hook`s	hook`	NOUN
m-1112	3052	17	law	law	NOUN
m-1112	3052	18	force	force	NOUN
m-1112	3052	19	as	as	ADP
m-1112	3052	20	stress	stress	NOUN
m-1112	3052	21	σ	σ	NOUN
m-1112	3052	22	=	=	PUNCT
m-1112	3052	23	e	e	PROPN
m-1112	3052	24	u	u	PROPN
m-1112	3052	25	,	,	PUNCT
m-1112	3052	26	and	and	CCONJ
m-1112	3052	27	an	an	DET
m-1112	3052	28	coulomb	coulomb	NOUN
m-1112	3052	29	force	force	NOUN
m-1112	3052	30	f	f	PROPN
m-1112	3053	1	[	[	X
m-1112	3053	2	+	+	X
m-1112	3053	3	↔	↔	PROPN
m-1112	3053	4	−	−	NOUN
m-1112	3053	5	]	]	X
m-1112	3054	1	=	=	PUNCT
m-1112	3055	1	[	[	X
m-1112	3055	2	⊕↔⊝	⊕↔⊝	X
m-1112	3055	3	]	]	X
m-1112	3055	4	r²	r²	NOUN
m-1112	3055	5	=	=	PUNCT
m-1112	3056	1	[	[	X
m-1112	3056	2	2	2	NUM
m-1112	3056	3	σ	σ	NOUN
m-1112	3056	4	]	]	X
m-1112	3056	5	r²	r²	NOUN
m-1112	3056	6	,	,	PUNCT
m-1112	3056	7	creating	create	VERB
m-1112	3056	8	work	work	NOUN
m-1112	3056	9	≡	≡	PROPN
m-1112	3056	10	motion	motion	NOUN
m-1112	3056	11	as	as	SCONJ
m-1112	3056	12	was	be	AUX
m-1112	3056	13	shown	show	VERB
m-1112	3056	14	.	.	PUNCT
m-1112	3057	1	[	[	X
m-1112	3057	2	58	58	NUM
m-1112	3057	3	]	]	PUNCT
m-1112	3057	4	it	it	PRON
m-1112	3057	5	was	be	AUX
m-1112	3057	6	shown	show	VERB
m-1112	3057	7	that	that	SCONJ
m-1112	3057	8	,	,	PUNCT
m-1112	3057	9	the	the	DET
m-1112	3057	10	stability	stability	NOUN
m-1112	3057	11	of	of	ADP
m-1112	3057	12	forces	force	NOUN
m-1112	3057	13	is	be	AUX
m-1112	3057	14	succeeded	succeed	VERB
m-1112	3057	15	in	in	ADP
m-1112	3057	16	the	the	DET
m-1112	3057	17	pascal`s	pascal`s	NUM
m-1112	3057	18	launched	launch	VERB
m-1112	3057	19	caves	cave	NOUN
m-1112	3057	20	r	r	NOUN
m-1112	3058	1	while	while	SCONJ
m-1112	3058	2	leptons	lepton	NOUN
m-1112	3058	3	,	,	PUNCT
m-1112	3058	4	from	from	ADP
m-1112	3058	5	their	their	PRON
m-1112	3058	6	anti	anti	ADJ
m-1112	3058	7	leptons	lepton	NOUN
m-1112	3058	8	existence	existence	NOUN
m-1112	3058	9	in	in	ADP
m-1112	3058	10	the	the	DET
m-1112	3058	11	same	same	ADJ
m-1112	3058	12	launched	launch	VERB
m-1112	3058	13	pascal`s	pascal`	NOUN
m-1112	3058	14	-	-	NOUN
m-1112	3058	15	caves	cave	NOUN
m-1112	3058	16	r	r	NOUN
m-1112	3058	17	.	.	PUNCT
m-1112	3059	1	the	the	DET
m-1112	3059	2	equilibrium	equilibrium	NOUN
m-1112	3059	3	of	of	ADP
m-1112	3059	4	the	the	DET
m-1112	3059	5	three	three	NUM
m-1112	3059	6	-	-	PUNCT
m-1112	3059	7	spaces	space	NOUN
m-1112	3059	8	is	be	AUX
m-1112	3059	9	succeeded	succeed	VERB
m-1112	3059	10	on	on	ADP
m-1112	3059	11	the	the	DET
m-1112	3059	12	three	three	NUM
m-1112	3059	13	cyclic	cyclic	ADJ
m-1112	3059	14	quadrilaterals	quadrilateral	NOUN
m-1112	3059	15	→	→	SYM
m-1112	3059	16	(	(	PUNCT
m-1112	3059	17	abeaece	abeaece	NOUN
m-1112	3059	18	)	)	PUNCT
m-1112	3059	19	,	,	PUNCT
m-1112	3059	20	(	(	PUNCT
m-1112	3059	21	bcebeae	bcebeae	PROPN
m-1112	3059	22	)	)	PUNCT
m-1112	3059	23	,	,	PUNCT
m-1112	3059	24	(	(	PUNCT
m-1112	3059	25	caecebe	caecebe	NOUN
m-1112	3059	26	)	)	PUNCT
m-1112	3059	27	of	of	ADP
m-1112	3059	28	6	6	NUM
m-1112	3059	29	conductors	conductor	NOUN
m-1112	3059	30	each	each	PRON
m-1112	3059	31	[	[	X
m-1112	3059	32	a	a	DET
m-1112	3059	33	,	,	PUNCT
m-1112	3059	34	b	b	NOUN
m-1112	3059	35	,	,	PUNCT
m-1112	3059	36	c	c	NOUN
m-1112	3059	37	,	,	PUNCT
m-1112	3059	38	d	d	PROPN
m-1112	3059	39	,	,	PUNCT
m-1112	3059	40	p	p	X
m-1112	3059	41	,	,	PUNCT
m-1112	3059	42	q	q	X
m-1112	3059	43	]	]	X
m-1112	3059	44	x	x	PUNCT
m-1112	3060	1	[	[	X
m-1112	3060	2	3	3	NUM
m-1112	3060	3	-	-	PUNCT
m-1112	3060	4	abc	abc	X
m-1112	3060	5	]	]	X
m-1112	3060	6	=	=	SYM
m-1112	3060	7	18	18	NUM
m-1112	3060	8	conductors	conductor	NOUN
m-1112	3060	9	.	.	PUNCT
m-1112	3061	1	linearly	linearly	ADV
m-1112	3061	2	is	be	AUX
m-1112	3061	3	through	through	ADP
m-1112	3061	4	the	the	DET
m-1112	3061	5	products	product	NOUN
m-1112	3061	6	of	of	ADP
m-1112	3061	7	the	the	DET
m-1112	3061	8	diagonal	diagonal	ADJ
m-1112	3061	9	connectors	connector	NOUN
m-1112	3061	10	as	as	ADP
m-1112	3061	11	,	,	PUNCT
m-1112	3061	12	→	→	SYM
m-1112	3061	13	→	→	SYM
m-1112	3061	14	→	→	SYM
m-1112	3061	15	[	[	X
m-1112	3061	16	aae].[bece	aae].[bece	X
m-1112	3061	17	]	]	X
m-1112	3061	18	=	=	PUNCT
m-1112	3062	1	[	[	X
m-1112	3062	2	ace].[aebe]+[abe].[aece	ace].[aebe]+[abe].[aece	NOUN
m-1112	3062	3	]	]	PUNCT
m-1112	3062	4	,	,	PUNCT
m-1112	3062	5	[	[	X
m-1112	3062	6	bbe].[ceae	bbe].[ceae	X
m-1112	3062	7	]	]	X
m-1112	3062	8	=	=	PUNCT
m-1112	3063	1	[	[	X
m-1112	3063	2	bae].[bece]+[bce].[beae	bae].[bece]+[bce].[beae	X
m-1112	3063	3	]	]	PUNCT
m-1112	3063	4	,	,	PUNCT
m-1112	3063	5	[	[	X
m-1112	3063	6	cce].[aebe	cce].[aebe	X
m-1112	3063	7	]	]	PUNCT
m-1112	3063	8	=	=	PUNCT
m-1112	3064	1	[	[	X
m-1112	3064	2	cae].[bece]+[cbe].[ceae	cae].[bece]+[cbe].[ceae	X
m-1112	3064	3	]	]	PUNCT
m-1112	3064	4	and	and	CCONJ
m-1112	3064	5	,	,	PUNCT
m-1112	3064	6	rotationally	rotationally	ADV
m-1112	3064	7	through	through	ADP
m-1112	3064	8	the	the	DET
m-1112	3064	9	ratio	ratio	NOUN
m-1112	3064	10	of	of	ADP
m-1112	3064	11	diagonals	diagonal	NOUN
m-1112	3064	12	≡	≡	PROPN
m-1112	3064	13	the	the	DET
m-1112	3064	14	conductors	conductor	NOUN
m-1112	3065	1	|	|	ADV
m-1112	3065	2	akb	akb	PROPN
m-1112	3065	3	akc	akc	PROPN
m-1112	3065	4	|x|	|x|	PROPN
m-1112	3065	5	bkc	bkc	PROPN
m-1112	3065	6	bka	bka	PROPN
m-1112	3065	7	|x|	|x|	PROPN
m-1112	3065	8	cka	cka	PROPN
m-1112	3065	9	ckb	ckb	PROPN
m-1112	3065	10	|	|	ADV
m-1112	3065	11	=	=	SYM
m-1112	3065	12	1	1	NUM
m-1112	3065	13	or	or	CCONJ
m-1112	3065	14	the	the	DET
m-1112	3065	15			PROPN
m-1112	3065	16	rotational	rotational	ADJ
m-1112	3065	17	-	-	PUNCT
m-1112	3065	18	equilibrium	equilibrium	NOUN
m-1112	3066	1	[	[	X
m-1112	3066	2	akb].[bkc].[cka	akb].[bkc].[cka	NOUN
m-1112	3066	3	]	]	X
m-1112	3066	4	=	=	PUNCT
m-1112	3067	1	[	[	X
m-1112	3067	2	akc].[bka].[ckb	akc].[bka].[ckb	X
m-1112	3067	3	]	]	X
m-1112	3067	4	,	,	PUNCT
m-1112	3067	5	of	of	ADP
m-1112	3067	6	all	all	PRON
m-1112	3067	7	above	above	ADP
m-1112	3067	8	opposites	opposite	NOUN
m-1112	3067	9	→	→	SYM
m-1112	3067	10	tangential	tangential	ADJ
m-1112	3067	11	-	-	PUNCT
m-1112	3067	12	electromotive	electromotive	ADJ
m-1112	3067	13	-	-	PUNCT
m-1112	3067	14	forces	force	NOUN
m-1112	3067	15	←	←	PROPN
m-1112	3067	16	from	from	ADP
m-1112	3067	17	mechanics	mechanic	NOUN
m-1112	3067	18	,	,	PUNCT
m-1112	3067	19	all	all	DET
m-1112	3067	20	systems	system	NOUN
m-1112	3067	21	possessing	possess	VERB
m-1112	3067	22	elasticity	elasticity	NOUN
m-1112	3067	23	≡	≡	PROPN
m-1112	3067	24	motion	motion	NOUN
m-1112	3067	25	and	and	CCONJ
m-1112	3067	26	reaction	reaction	NOUN
m-1112	3067	27	to	to	ADP
m-1112	3067	28	motion	motion	NOUN
m-1112	3067	29	,	,	PUNCT
m-1112	3067	30	called	call	VERB
m-1112	3067	31	mass	mass	NOUN
m-1112	3067	32	,	,	PUNCT
m-1112	3067	33	are	be	AUX
m-1112	3067	34	capable	capable	ADJ
m-1112	3067	35	of	of	ADP
m-1112	3067	36	free	free	ADJ
m-1112	3067	37	vibration	vibration	NOUN
m-1112	3067	38	or	or	CCONJ
m-1112	3067	39	vibration	vibration	NOUN
m-1112	3067	40	taking	take	VERB
m-1112	3067	41	place	place	NOUN
m-1112	3067	42	in	in	ADP
m-1112	3067	43	the	the	DET
m-1112	3067	44	absence	absence	NOUN
m-1112	3067	45	of	of	ADP
m-1112	3067	46	external	external	ADJ
m-1112	3067	47	excitation	excitation	NOUN
m-1112	3067	48	.	.	PUNCT
m-1112	3068	1	[	[	X
m-1112	3068	2	7	7	NUM
m-1112	3068	3	]	]	PUNCT
m-1112	3068	4	from	from	ADP
m-1112	3068	5	lorentz	lorentz	NOUN
m-1112	3068	6	-	-	PUNCT
m-1112	3068	7	force	force	NOUN
m-1112	3068	8	,	,	PUNCT
m-1112	3068	9	f	f	PROPN
m-1112	3068	10	=	=	SYM
m-1112	3068	11	�	�	PROPN
m-1112	3068	12	̅	̅	NOUN
m-1112	3068	13	�	�	PROPN
m-1112	3068	14	�	�	PROPN
m-1112	3068	15	̅	̅	NOUN
m-1112	3068	16	�	�	PROPN
m-1112	3068	17	x	x	SYM
m-1112	3068	18	�	�	PROPN
m-1112	3068	19	̅	̅	NOUN
m-1112	3068	20	�	�	NOUN
m-1112	3068	21	𝐅	𝐅	PROPN
m-1112	3068	22	,	,	PUNCT
m-1112	3068	23	where	where	SCONJ
m-1112	3068	24	,	,	PUNCT
m-1112	3068	25	q̅	q̅	PROPN
m-1112	3068	26	≡	≡	PROPN
m-1112	3068	27	charge	charge	NOUN
m-1112	3068	28	,	,	PUNCT
m-1112	3068	29	v̅	v̅	PROPN
m-1112	3068	30	≡	≡	PROPN
m-1112	3068	31	the	the	DET
m-1112	3068	32	velocity	velocity	NOUN
m-1112	3068	33	of	of	ADP
m-1112	3068	34	charge	charge	NOUN
m-1112	3068	35	,	,	PUNCT
m-1112	3068	36	b̅	b̅	PROPN
m-1112	3068	37	f	f	PROPN
m-1112	3068	38	≡	≡	PROPN
m-1112	3068	39	the	the	DET
m-1112	3068	40	strength	strength	NOUN
m-1112	3068	41	of	of	ADP
m-1112	3068	42	magnetic	magnetic	ADJ
m-1112	3068	43	field	field	NOUN
m-1112	3068	44	and	and	CCONJ
m-1112	3068	45	centrifugal	centrifugal	ADJ
m-1112	3068	46	force	force	NOUN
m-1112	3068	47	,	,	PUNCT
m-1112	3068	48	𝐅	𝐅	PROPN
m-1112	3068	49	𝐂𝐅	𝐂𝐅	PROPN
m-1112	3068	50	=	=	PUNCT
m-1112	3068	51	m.𝐰²𝐑.r	m.𝐰²𝐑.r	ADV
m-1112	3068	52	.	.	PUNCT
m-1112	3069	1	ijo	ijo	PROPN
m-1112	3069	2	international	international	PROPN
m-1112	3069	3	journal	journal	PROPN
m-1112	3069	4	of	of	ADP
m-1112	3069	5	mathematics	mathematics	PROPN
m-1112	3069	6	(	(	PUNCT
m-1112	3069	7	issn	issn	PROPN
m-1112	3069	8	:	:	PUNCT
m-1112	3069	9	2992	2992	NUM
m-1112	3069	10	-	-	SYM
m-1112	3069	11	4421	4421	NUM
m-1112	3069	12	)	)	PUNCT
m-1112	3069	13	volume	volume	NOUN
m-1112	3069	14	08	08	NUM
m-1112	3070	1	|	|	ADV
m-1112	3070	2	issue	issue	NOUN
m-1112	3070	3	08	08	NUM
m-1112	3071	1	|	|	ADV
m-1112	3071	2	august	august	PROPN
m-1112	3071	3	2025	2025	NUM
m-1112	3071	4	|	|	ADV
m-1112	3071	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3071	6	ijo	ijo	PROPN
m-1112	3071	7	journals	journal	NOUN
m-1112	3071	8	109	109	NUM
m-1112	3071	9	the	the	DET
m-1112	3071	10	fundamental	fundamental	ADJ
m-1112	3071	11	particles	particle	NOUN
m-1112	3071	12	origination	origination	NOUN
m-1112	3071	13	mechanism	mechanism	NOUN
m-1112	3071	14	in	in	ADP
m-1112	3071	15	mfmf	mfmf	PROPN
m-1112	3071	16	pns	pns	PROPN
m-1112	3071	17	caves	cave	NOUN
m-1112	3071	18	.	.	PUNCT
m-1112	3072	1	from	from	ADP
m-1112	3072	2	cave	cave	NOUN
m-1112	3072	3	-	-	PUNCT
m-1112	3072	4	spin	spin	NOUN
m-1112	3072	5	,	,	PUNCT
m-1112	3072	6	�	�	NOUN
m-1112	3072	7	̅	̅	NOUN
m-1112	3072	8	�	�	NOUN
m-1112	3072	9	=	=	SYM
m-1112	3073	1	r	r	NOUN
m-1112	3073	2	m	m	VERB
m-1112	3073	3	v	v	NOUN
m-1112	3073	4	then	then	ADV
m-1112	3073	5	mass	mass	NOUN
m-1112	3073	6	m	m	NOUN
m-1112	3073	7	=	=	PUNCT
m-1112	3073	8	(	(	PUNCT
m-1112	3073	9	s	s	AUX
m-1112	3073	10	r.v	r.v	NOUN
m-1112	3073	11	)	)	PUNCT
m-1112	3073	12	.equating	.equating	NUM
m-1112	3073	13	equations	equation	NOUN
m-1112	3073	14	then	then	ADV
m-1112	3074	1	,	,	PUNCT
m-1112	3074	2	f	f	PROPN
m-1112	3074	3	≡	≡	PROPN
m-1112	3074	4	fc	fc	PROPN
m-1112	3074	5	f	f	PROPN
m-1112	3074	6	≡	≡	PROPN
m-1112	3074	7	q̅	q̅	PROPN
m-1112	3074	8	v̅	v̅	PROPN
m-1112	3074	9	x	x	X
m-1112	3074	10	b̅	b̅	PROPN
m-1112	3074	11	f	f	X
m-1112	3074	12	,	,	PUNCT
m-1112	3074	13	and	and	CCONJ
m-1112	3074	14	𝐐	𝐐	PROPN
m-1112	3074	15			PROPN
m-1112	3074	16	=	=	PUNCT
m-1112	3074	17	m.w²r.r	m.w²r.r	NOUN
m-1112	3074	18	=	=	PUNCT
m-1112	3074	19	(	(	PUNCT
m-1112	3074	20	s	s	X
m-1112	3074	21	r.v	r.v	NOUN
m-1112	3074	22	)	)	PUNCT
m-1112	3074	23	.w².r	.w².r	PUNCT
m-1112	3075	1	=	=	SYM
m-1112	3075	2	s.w²	s.w²	NOUN
m-1112	3075	3	v	v	X
m-1112	3075	4	=	=	SYM
m-1112	3075	5	s.v	s.v	PROPN
m-1112	3075	6	²	²	NUM
m-1112	3075	7	r².v	r².v	PROPN
m-1112	3075	8	≡	≡	PROPN
m-1112	3075	9	|	|	ADV
m-1112	3075	10	𝐯.	𝐯.	PROPN
m-1112	3075	11	�	�	PROPN
m-1112	3075	12	̅	̅	NOUN
m-1112	3075	13	�	�	NOUN
m-1112	3075	14	𝐫²	𝐫²	NOUN
m-1112	3075	15	|	|	ADV
m-1112	3075	16	…	…	PUNCT
m-1112	3075	17	.(emf	.(emf	PROPN
m-1112	3075	18	)	)	PUNCT
m-1112	3075	19	where	where	SCONJ
m-1112	3075	20	exists	exist	VERB
m-1112	3075	21	rmin=	rmin=	NUM
m-1112	3075	22	√πb−n	√πb−n	SYM
m-1112	3075	23	2	2	NUM
m-1112	3075	24	,	,	PUNCT
m-1112	3075	25	[	[	X
m-1112	3075	26	95	95	NUM
m-1112	3075	27	]	]	PUNCT
m-1112	3075	28	,	,	PUNCT
m-1112	3076	1	[	[	X
m-1112	3076	2	96bb	96bb	NOUN
m-1112	3076	3	]	]	PUNCT
m-1112	3076	4	.	.	PUNCT
m-1112	3077	1	electromotive	electromotive	ADJ
m-1112	3077	2	-	-	PUNCT
m-1112	3077	3	forces	force	NOUN
m-1112	3077	4	,	,	PUNCT
m-1112	3077	5	f	f	PROPN
m-1112	3077	6	=	=	SYM
m-1112	3077	7	�	�	PROPN
m-1112	3077	8	̅	̅	NOUN
m-1112	3077	9	�	�	PROPN
m-1112	3077	10	�	�	PROPN
m-1112	3077	11	̅	̅	NOUN
m-1112	3077	12	�	�	PROPN
m-1112	3077	13	x	x	SYM
m-1112	3077	14	�	�	PROPN
m-1112	3077	15	̅	̅	NOUN
m-1112	3077	16	�	�	NOUN
m-1112	3077	17	𝐅	𝐅	NOUN
m-1112	3077	18	=	=	SYM
m-1112	3077	19	𝐐	𝐐	NOUN
m-1112	3077	20			PROPN
m-1112	3077	21	=	=	PUNCT
m-1112	3077	22	𝐯.	𝐯.	PROPN
m-1112	3077	23	�	�	PROPN
m-1112	3077	24	̅	̅	NOUN
m-1112	3077	25	�	�	PROPN
m-1112	3077	26	𝐫²	𝐫²	PROPN
m-1112	3077	27	≡	≡	PROPN
m-1112	3078	1	|	|	PROPN
m-1112	3078	2	𝐜.	𝐜.	PROPN
m-1112	3078	3	�	�	PROPN
m-1112	3078	4	̅	̅	NOUN
m-1112	3078	5	�	�	PROPN
m-1112	3078	6	𝐫	𝐫	ADP
m-1112	3078	7	²	²	NUM
m-1112	3078	8	|	|	NOUN
m-1112	3078	9	,	,	PUNCT
m-1112	3078	10	are	be	AUX
m-1112	3078	11	the	the	DET
m-1112	3078	12	elementary	elementary	ADJ
m-1112	3078	13	-	-	PUNCT
m-1112	3078	14	particles	particle	NOUN
m-1112	3078	15	{	{	PUNCT
m-1112	3078	16	f	f	NOUN
m-1112	3078	17	,	,	PUNCT
m-1112	3078	18	l	l	NOUN
m-1112	3078	19	,	,	PUNCT
m-1112	3078	20	q	q	X
m-1112	3078	21	}	}	PUNCT
m-1112	3078	22	.	.	PUNCT
m-1112	3079	1	from	from	ADP
m-1112	3079	2	electromotive	electromotive	ADJ
m-1112	3079	3	-	-	PUNCT
m-1112	3079	4	force	force	NOUN
m-1112	3079	5	in	in	ADP
m-1112	3079	6	min	min	ADJ
m-1112	3079	7	-	-	NOUN
m-1112	3079	8	cave	cave	NOUN
m-1112	3079	9	r	r	NOUN
m-1112	3079	10	=	=	SYM
m-1112	3079	11	1,7724538.10−3	1,7724538.10−3	NUM
m-1112	3079	12	m.	m.	NOUN
m-1112	3079	13	exists	exist	VERB
m-1112	3079	14	electron	electron	NOUN
m-1112	3079	15	force	force	NOUN
m-1112	3079	16	-	-	PUNCT
m-1112	3079	17	charge	charge	NOUN
m-1112	3079	18	q̅	q̅	PROPN
m-1112	3079	19	e	e	NOUN
m-1112	3079	20	as	as	ADP
m-1112	3079	21	𝐐	𝐐	PROPN
m-1112	3079	22			PROPN
m-1112	3079	23	=	=	PUNCT
m-1112	3080	1	|	|	ADV
m-1112	3080	2	𝐜.	𝐜.	NOUN
m-1112	3080	3	�	�	PROPN
m-1112	3080	4	̅	̅	NOUN
m-1112	3080	5	�	�	PROPN
m-1112	3080	6	𝐫	𝐫	ADP
m-1112	3080	7	²	²	NUM
m-1112	3080	8	|	|	NOUN
m-1112	3080	9	=	=	PUNCT
m-1112	3081	1	[	[	X
m-1112	3081	2	2,998.108].[1,0546.10−34]j	2,998.108].[1,0546.10−34]j	NUM
m-1112	3081	3	(	(	PUNCT
m-1112	3081	4	1,7724538.10−3	1,7724538.10−3	NUM
m-1112	3081	5	)	)	PUNCT
m-1112	3081	6	²	²	NUM
m-1112	3081	7	=	=	SYM
m-1112	3081	8	1,6022.10−19	1,6022.10−19	NUM
m-1112	3081	9	ev	ev	X
m-1112	3081	10	,	,	PUNCT
m-1112	3081	11	which	which	PRON
m-1112	3081	12	is	be	AUX
m-1112	3081	13	the	the	DET
m-1112	3081	14	electron	electron	NOUN
m-1112	3081	15	-	-	PUNCT
m-1112	3081	16	force	force	NOUN
m-1112	3081	17	-	-	PUNCT
m-1112	3081	18	charge	charge	NOUN
m-1112	3081	19	and	and	CCONJ
m-1112	3081	20	also	also	ADV
m-1112	3081	21	from	from	ADP
m-1112	3081	22	the	the	DET
m-1112	3081	23	gravitational	gravitational	ADJ
m-1112	3081	24	-	-	PUNCT
m-1112	3081	25	stress	stress	NOUN
m-1112	3081	26	-	-	PUNCT
m-1112	3081	27	charge	charge	NOUN
m-1112	3081	28	�	�	PROPN
m-1112	3081	29	̅	̅	NOUN
m-1112	3081	30	�	�	PROPN
m-1112	3081	31	electron	electron	NOUN
m-1112	3081	32	=	=	PUNCT
m-1112	3081	33	g	g	PROPN
m-1112	3081	34	c	c	PROPN
m-1112	3081	35	√2	√2	NOUN
m-1112	3081	36	=	=	SYM
m-1112	3081	37	6,6736923	6,6736923	PROPN
m-1112	3081	38	.10−11	.10−11	SYM
m-1112	3082	1	1,41429.2,9979346.108	1,41429.2,9979346.108	NUM
m-1112	3082	2	=	=	SYM
m-1112	3082	3	1,574.10−19	1,574.10−19	NUM
m-1112	3082	4	c	c	NOUN
m-1112	3082	5	.	.	PUNCT
m-1112	3083	1	electromotive	electromotive	ADJ
m-1112	3083	2	-	-	PUNCT
m-1112	3083	3	force	force	NOUN
m-1112	3083	4	in	in	ADP
m-1112	3083	5	the	the	DET
m-1112	3083	6	min	min	NOUN
m-1112	3083	7	-	-	NOUN
m-1112	3083	8	cave	cave	NOUN
m-1112	3083	9	𝑒−15,572707=	𝑒−15,572707=	NOUN
m-1112	3083	10	r	r	NOUN
m-1112	3083	11	=	=	SYM
m-1112	3083	12	1,7252787.10−7	1,7252787.10−7	NUM
m-1112	3083	13	m	m	NOUN
m-1112	3083	14	,	,	PUNCT
m-1112	3083	15	and	and	CCONJ
m-1112	3083	16	the	the	DET
m-1112	3083	17	gravitational	gravitational	ADJ
m-1112	3083	18	-	-	PUNCT
m-1112	3083	19	force	force	NOUN
m-1112	3083	20	g	g	NOUN
m-1112	3083	21	becomes	become	VERB
m-1112	3083	22	also	also	ADV
m-1112	3083	23	as	as	ADP
m-1112	3083	24	,	,	PUNCT
m-1112	3083	25	𝐐	𝐐	PROPN
m-1112	3083	26			PROPN
m-1112	3083	27	=	=	PUNCT
m-1112	3083	28	|	|	ADV
m-1112	3083	29	𝐜.	𝐜.	NOUN
m-1112	3083	30	�	�	PROPN
m-1112	3083	31	̅	̅	NOUN
m-1112	3083	32	�	�	PROPN
m-1112	3083	33	𝐫	𝐫	ADP
m-1112	3083	34	²	²	NUM
m-1112	3084	1	|	|	NOUN
m-1112	3084	2	=	=	PUNCT
m-1112	3085	1	[	[	X
m-1112	3085	2	2,998.108].[6,62606957.10−34	2,998.108].[6,62606957.10−34	NUM
m-1112	3085	3	]	]	X
m-1112	3085	4	(	(	PUNCT
m-1112	3085	5	1,7252787.10−7	1,7252787.10−7	NUM
m-1112	3085	6	)	)	PUNCT
m-1112	3085	7	²	²	NUM
m-1112	3085	8	=	=	SYM
m-1112	3085	9	6,673692	6,673692	NUM
m-1112	3085	10	.	.	PUNCT
m-1112	3086	1	10−11	10−11	NUM
m-1112	3086	2	,	,	PUNCT
m-1112	3086	3	which	which	PRON
m-1112	3086	4	is	be	AUX
m-1112	3086	5	the	the	DET
m-1112	3086	6	g	g	NOUN
m-1112	3086	7	physical	physical	ADJ
m-1112	3086	8	-	-	PUNCT
m-1112	3086	9	forcecharge	forcecharge	NOUN
m-1112	3086	10	.	.	PUNCT
m-1112	3087	1	when	when	SCONJ
m-1112	3087	2	the	the	DET
m-1112	3087	3	heap	heap	NOUN
m-1112	3087	4	of	of	ADP
m-1112	3087	5	the	the	DET
m-1112	3087	6	elementary	elementary	ADJ
m-1112	3087	7	particles	particle	NOUN
m-1112	3087	8	on	on	ADP
m-1112	3087	9	da	da	PROPN
m-1112	3087	10	-	-	PROPN
m-1112	3087	11	pa	pa	PROPN
m-1112	3087	12	line	line	NOUN
m-1112	3087	13	,	,	PUNCT
m-1112	3087	14	is	be	AUX
m-1112	3087	15	compressed	compress	VERB
m-1112	3087	16	and	and	CCONJ
m-1112	3087	17	gets	get	VERB
m-1112	3087	18	out	out	ADP
m-1112	3087	19	the	the	DET
m-1112	3087	20	line	line	NOUN
m-1112	3087	21	then	then	ADV
m-1112	3087	22	is	be	AUX
m-1112	3087	23	a	a	DET
m-1112	3087	24	reason	reason	NOUN
m-1112	3087	25	for	for	ADP
m-1112	3087	26	black	black	ADJ
m-1112	3087	27	hole	hole	NOUN
m-1112	3087	28	creation	creation	NOUN
m-1112	3087	29	.	.	PUNCT
m-1112	3088	1	b	b	X
m-1112	3088	2	…	…	PUNCT
m-1112	3088	3	the	the	DET
m-1112	3088	4	relation	relation	NOUN
m-1112	3088	5	of	of	ADP
m-1112	3088	6	the	the	DET
m-1112	3088	7	n	n	NOUN
m-1112	3088	8	,	,	PUNCT
m-1112	3088	9	degree	degree	NOUN
m-1112	3088	10	of	of	ADP
m-1112	3088	11	polynomials	polynomial	NOUN
m-1112	3088	12	and	and	CCONJ
m-1112	3088	13	electromotive	electromotive	ADJ
m-1112	3088	14	-	-	PUNCT
m-1112	3088	15	forces	force	NOUN
m-1112	3088	16	vibration	vibration	NOUN
m-1112	3088	17	.	.	PUNCT
m-1112	3089	1	the	the	DET
m-1112	3089	2	transportation	transportation	NOUN
m-1112	3089	3	of	of	ADP
m-1112	3089	4	energy	energy	NOUN
m-1112	3089	5	on	on	ADP
m-1112	3089	6	edge	edge	NOUN
m-1112	3089	7	-	-	PUNCT
m-1112	3089	8	points	point	NOUN
m-1112	3089	9	happens	happen	VERB
m-1112	3089	10	in	in	ADP
m-1112	3089	11	material	material	NOUN
m-1112	3089	12	geometry	geometry	NOUN
m-1112	3089	13	,	,	PUNCT
m-1112	3089	14	while	while	SCONJ
m-1112	3089	15	the	the	DET
m-1112	3089	16	transportation	transportation	NOUN
m-1112	3089	17	of	of	ADP
m-1112	3089	18	the	the	DET
m-1112	3089	19	edge	edge	NOUN
m-1112	3089	20	-	-	PUNCT
m-1112	3089	21	points	point	NOUN
m-1112	3089	22	as	as	ADP
m-1112	3089	23	,	,	PUNCT
m-1112	3089	24	positions	position	NOUN
m-1112	3089	25	,	,	PUNCT
m-1112	3089	26	exists	exist	VERB
m-1112	3089	27	in	in	ADP
m-1112	3089	28	vector	vector	NOUN
m-1112	3089	29	geometry	geometry	NOUN
m-1112	3089	30	only	only	ADV
m-1112	3089	31	.	.	PUNCT
m-1112	3090	1	since	since	SCONJ
m-1112	3090	2	in	in	ADP
m-1112	3090	3	vibrations	vibration	NOUN
m-1112	3090	4	the	the	DET
m-1112	3090	5	deformation	deformation	NOUN
m-1112	3090	6	of	of	ADP
m-1112	3090	7	the	the	DET
m-1112	3090	8	spring	spring	NOUN
m-1112	3090	9	is	be	AUX
m-1112	3090	10	an	an	DET
m-1112	3090	11	equilibrium	equilibrium	NOUN
m-1112	3090	12	position	position	NOUN
m-1112	3090	13	in	in	ADP
m-1112	3090	14	∆	∆	PROPN
m-1112	3090	15	,	,	PUNCT
m-1112	3090	16	and	and	CCONJ
m-1112	3090	17	the	the	DET
m-1112	3090	18	spring	spring	NOUN
m-1112	3090	19	-	-	PUNCT
m-1112	3090	20	forse	forse	PROPN
m-1112	3090	21	k	k	PROPN
m-1112	3090	22	∆	∆	PROPN
m-1112	3091	1	=	=	PUNCT
m-1112	3091	2	w	w	PROPN
m-1112	3091	3	=	=	VERB
m-1112	3091	4	m	m	PROPN
m-1112	3091	5	g	g	NOUN
m-1112	3091	6	=	=	SYM
m-1112	3091	7	gravitational	gravitational	ADJ
m-1112	3091	8	force	force	NOUN
m-1112	3091	9	w	w	VERB
m-1112	3091	10	acting	act	VERB
m-1112	3091	11	on	on	ADP
m-1112	3091	12	mass	mass	PROPN
m-1112	3091	13	m	m	PROPN
m-1112	3091	14	,	,	PUNCT
m-1112	3091	15	then	then	ADV
m-1112	3091	16	exists	exist	VERB
m-1112	3091	17	→	→	PUNCT
m-1112	3091	18	m	m	VERB
m-1112	3091	19	�	�	PROPN
m-1112	3091	20	̈	̈	X
m-1112	3091	21	�	�	NOUN
m-1112	3091	22	=	=	SYM
m-1112	3091	23	σf	σf	NOUN
m-1112	3091	24	=	=	PUNCT
m-1112	3091	25	w	w	PROPN
m-1112	3091	26	=	=	SYM
m-1112	3091	27	k	k	PROPN
m-1112	3091	28	[	[	PUNCT
m-1112	3091	29	∆	∆	X
m-1112	3091	30	+	+	CCONJ
m-1112	3091	31	x	x	X
m-1112	3091	32	]	]	X
m-1112	3091	33	…	…	PUNCT
m-1112	3091	34	.(1	.(1	NUM
m-1112	3091	35	)	)	PUNCT
m-1112	3091	36	,	,	PUNCT
m-1112	3091	37	and	and	CCONJ
m-1112	3091	38	because	because	SCONJ
m-1112	3091	39	k	k	PROPN
m-1112	3091	40	∆	∆	PROPN
m-1112	3091	41	=	=	PUNCT
m-1112	3091	42	w	w	NOUN
m-1112	3091	43	we	we	PRON
m-1112	3091	44	obtain	obtain	VERB
m-1112	3091	45	w	w	ADJ
m-1112	3091	46	²n	²n	NOUN
m-1112	3091	47	=	=	SYM
m-1112	3092	1	k	k	X
m-1112	3092	2	/	/	SYM
m-1112	3092	3	m	m	PROPN
m-1112	3092	4	..	..	PUNCT
m-1112	3092	5	(	(	PUNCT
m-1112	3092	6	2	2	X
m-1112	3092	7	)	)	PUNCT
m-1112	3092	8	and	and	CCONJ
m-1112	3092	9	(	(	PUNCT
m-1112	3092	10	1	1	X
m-1112	3092	11	)	)	PUNCT
m-1112	3092	12	becomes	become	VERB
m-1112	3092	13	→	→	SYM
m-1112	3092	14	�	�	NOUN
m-1112	3092	15	̈	̈	X
m-1112	3092	16	�	�	NOUN
m-1112	3092	17	+	+	CCONJ
m-1112	3092	18	𝐰	𝐰	ADJ
m-1112	3092	19	²𝐧	²𝐧	NOUN
m-1112	3092	20	=	=	SYM
m-1112	3092	21	0	0	NUM
m-1112	3092	22	,	,	PUNCT
m-1112	3092	23	…	…	PUNCT
m-1112	3092	24	(	(	PUNCT
m-1112	3092	25	3	3	X
m-1112	3092	26	)	)	PUNCT
m-1112	3092	27	←	←	PROPN
m-1112	3092	28	i.e.	i.e.	X
m-1112	3092	29	the	the	DET
m-1112	3092	30	transportation	transportation	NOUN
m-1112	3092	31	of	of	ADP
m-1112	3092	32	energy	energy	NOUN
m-1112	3092	33	is	be	AUX
m-1112	3092	34	a	a	DET
m-1112	3092	35	harmonic	harmonic	ADJ
m-1112	3092	36	vibration	vibration	NOUN
m-1112	3092	37	in	in	ADP
m-1112	3092	38	cave	cave	NOUN
m-1112	3092	39	∆	∆	PROPN
m-1112	3092	40	,	,	PUNCT
m-1112	3092	41	meaning	mean	VERB
m-1112	3092	42	the	the	DET
m-1112	3092	43	wave	wave	NOUN
m-1112	3092	44	pattern	pattern	NOUN
m-1112	3092	45	.	.	PUNCT
m-1112	3093	1	from	from	ADP
m-1112	3093	2	before	before	ADP
m-1112	3093	3	the	the	DET
m-1112	3093	4	cave	cave	NOUN
m-1112	3093	5	-	-	PUNCT
m-1112	3093	6	spin	spin	NOUN
m-1112	3093	7	,	,	PUNCT
m-1112	3093	8	�	�	NOUN
m-1112	3093	9	̅	̅	NOUN
m-1112	3093	10	�	�	NOUN
m-1112	3093	11	=	=	SYM
m-1112	3093	12	r	r	NOUN
m-1112	3093	13	m	m	NOUN
m-1112	3093	14	v	v	NOUN
m-1112	3093	15	is	be	AUX
m-1112	3093	16	a	a	DET
m-1112	3093	17	monad	monad	PROPN
m-1112	3093	18	,	,	PUNCT
m-1112	3093	19	and	and	CCONJ
m-1112	3093	20	occupies	occupy	VERB
m-1112	3093	21	the	the	DET
m-1112	3093	22	4	4	NUM
m-1112	3093	23	-	-	PUNCT
m-1112	3093	24	spaces	space	NOUN
m-1112	3093	25	as	as	ADP
m-1112	3093	26	the	the	DET
m-1112	3093	27	fig–1	fig–1	NOUN
m-1112	3093	28	.	.	PUNCT
m-1112	3094	1	i.e.	i.e.	X
m-1112	3094	2	→	→	X
m-1112	3094	3	(	(	PUNCT
m-1112	3094	4	(	(	PUNCT
m-1112	3094	5	the	the	DET
m-1112	3094	6	n	n	DET
m-1112	3094	7	spaces	space	NOUN
m-1112	3094	8	of	of	ADP
m-1112	3094	9	spin	spin	NOUN
m-1112	3094	10	�	�	NOUN
m-1112	3094	11	̅	̅	NOUN
m-1112	3094	12	�	�	NOUN
m-1112	3094	13	are	be	AUX
m-1112	3094	14	the	the	DET
m-1112	3094	15	polygons	polygons	PROPN
m-1112	3094	16	𝐒𝐧	𝐒𝐧	PROPN
m-1112	3094	17	,	,	PUNCT
m-1112	3094	18	the	the	DET
m-1112	3094	19	n	n	ADV
m-1112	3094	20	anti	anti	NOUN
m-1112	3094	21	-	-	ADJ
m-1112	3094	22	spaces	space	NOUN
m-1112	3094	23	of	of	ADP
m-1112	3094	24	spin	spin	NOUN
m-1112	3094	25	�	�	NOUN
m-1112	3094	26	̅	̅	NOUN
m-1112	3094	27	�	�	NOUN
m-1112	3094	28	are	be	AUX
m-1112	3094	29	the	the	DET
m-1112	3094	30	polygons	polygon	NOUN
m-1112	3094	31	𝐒𝐧	𝐒𝐧	NOUN
m-1112	3094	32	)	)	PUNCT
m-1112	3094	33	)	)	PUNCT
m-1112	3095	1	←	←	PROPN
m-1112	3095	2	the	the	DET
m-1112	3095	3	sub	sub	ADJ
m-1112	3095	4	-	-	ADJ
m-1112	3095	5	spaces	spaces	ADJ
m-1112	3095	6	±	±	NOUN
m-1112	3095	7	√	√	NUM
m-1112	3095	8	�	�	NOUN
m-1112	3095	9	̅	̅	NOUN
m-1112	3095	10	�	�	NOUN
m-1112	3095	11	𝒏=𝟏−∞	𝒏=𝟏−∞	PROPN
m-1112	3095	12	are	be	AUX
m-1112	3095	13	the	the	DET
m-1112	3095	14	polygons	polygon	NOUN
m-1112	3095	15	with	with	ADP
m-1112	3095	16	n	n	NOUN
m-1112	3095	17	=	=	SYM
m-1112	3095	18	1	1	NUM
m-1112	3095	19	≈	≈	NUM
m-1112	3095	20	∞	∞	PROPN
m-1112	3095	21	knots	knot	NOUN
m-1112	3095	22	since	since	SCONJ
m-1112	3095	23	the	the	DET
m-1112	3095	24	number	number	NOUN
m-1112	3095	25	of	of	ADP
m-1112	3095	26	knots	knot	NOUN
m-1112	3095	27	n	n	CCONJ
m-1112	3095	28	,	,	PUNCT
m-1112	3095	29	are	be	AUX
m-1112	3095	30	the	the	DET
m-1112	3095	31	degrees	degree	NOUN
m-1112	3095	32	n	n	ADP
m-1112	3095	33	of	of	ADP
m-1112	3095	34	the	the	DET
m-1112	3095	35	polynomials	polynomial	NOUN
m-1112	3095	36	of	of	ADP
m-1112	3095	37	each	each	DET
m-1112	3095	38	monad	monad	PROPN
m-1112	3095	39	and	and	CCONJ
m-1112	3095	40	since	since	SCONJ
m-1112	3095	41	the	the	DET
m-1112	3095	42	n	n	PRON
m-1112	3095	43	masses	masse	NOUN
m-1112	3095	44	spring	spring	VERB
m-1112	3095	45	𝐦	𝐦	PROPN
m-1112	3095	46	𝐧	𝐧	PROPN
m-1112	3095	47	is	be	AUX
m-1112	3095	48	an	an	DET
m-1112	3095	49	equilibrium	equilibrium	NOUN
m-1112	3095	50	position	position	NOUN
m-1112	3095	51	in	in	ADP
m-1112	3095	52	∆	∆	PROPN
m-1112	3095	53	,	,	PUNCT
m-1112	3095	54	of	of	ADP
m-1112	3095	55	the	the	DET
m-1112	3095	56	equation	equation	NOUN
m-1112	3095	57	of	of	ADP
m-1112	3095	58	motion	motion	NOUN
m-1112	3095	59	→	→	SYM
m-1112	3095	60	�	�	PROPN
m-1112	3095	61	̈	̈	X
m-1112	3095	62	�	�	NOUN
m-1112	3095	63	+	+	CCONJ
m-1112	3095	64	𝐰	𝐰	ADJ
m-1112	3095	65	²𝐧	²𝐧	NOUN
m-1112	3095	66	=	=	SYM
m-1112	3095	67	0	0	NUM
m-1112	3095	68	←	←	PROPN
m-1112	3095	69	then	then	ADV
m-1112	3095	70	the	the	DET
m-1112	3095	71	4	4	NUM
m-1112	3095	72	-	-	PUNCT
m-1112	3095	73	spaces	space	NOUN
m-1112	3095	74	of	of	ADP
m-1112	3095	75	monad	monad	PROPN
m-1112	3095	76	are	be	AUX
m-1112	3095	77	the	the	DET
m-1112	3095	78	polygons	polygon	NOUN
m-1112	3095	79	of	of	ADP
m-1112	3095	80	n	n	NOUN
m-1112	3095	81	-	-	PUNCT
m-1112	3095	82	knots	knot	NOUN
m-1112	3095	83	and	and	CCONJ
m-1112	3095	84	equal	equal	ADJ
m-1112	3095	85	to	to	ADP
m-1112	3095	86	the	the	DET
m-1112	3095	87	n	n	NOUN
m-1112	3095	88	degrees	degree	VERB
m-1112	3095	89	roots	root	NOUN
m-1112	3095	90	of	of	ADP
m-1112	3095	91	the	the	DET
m-1112	3095	92	polynomials	polynomial	NOUN
m-1112	3095	93	.	.	PUNCT
m-1112	3096	1	the	the	DET
m-1112	3096	2	process	process	NOUN
m-1112	3096	3	of	of	ADP
m-1112	3096	4	actions	action	NOUN
m-1112	3096	5	in	in	ADP
m-1112	3096	6	the	the	DET
m-1112	3096	7	4	4	NUM
m-1112	3096	8	=	=	NOUN
m-1112	3096	9	spaces	space	NOUN
m-1112	3096	10	1	1	NUM
m-1112	3096	11	…	…	SYM
m-1112	3096	12	a	a	DET
m-1112	3096	13	heap	heap	NOUN
m-1112	3096	14	of	of	ADP
m-1112	3096	15	n	n	NOUN
m-1112	3096	16	-	-	PUNCT
m-1112	3096	17	masses	masse	NOUN
m-1112	3096	18	vibrates	vibrate	NOUN
m-1112	3096	19	and	and	CCONJ
m-1112	3096	20	equilibrium	equilibrium	NOUN
m-1112	3096	21	.	.	PUNCT
m-1112	3097	1	2	2	NUM
m-1112	3097	2	…	…	SYM
m-1112	3097	3	a	a	DET
m-1112	3097	4	heap	heap	NOUN
m-1112	3097	5	of	of	ADP
m-1112	3097	6	n	n	CCONJ
m-1112	3097	7	-	-	PUNCT
m-1112	3097	8	masses	masse	NOUN
m-1112	3097	9	equilibrium	equilibrium	NOUN
m-1112	3097	10	at	at	ADP
m-1112	3097	11	the	the	DET
m-1112	3097	12	n	n	CCONJ
m-1112	3097	13	-	-	PUNCT
m-1112	3097	14	mode	mode	NOUN
m-1112	3097	15	shapes	shape	NOUN
m-1112	3097	16	waveform	waveform	VERB
m-1112	3097	17	.	.	PUNCT
m-1112	3098	1	3	3	NUM
m-1112	3098	2	…	…	SYM
m-1112	3098	3	a	a	DET
m-1112	3098	4	heap	heap	NOUN
m-1112	3098	5	of	of	ADP
m-1112	3098	6	n	n	NOUN
m-1112	3098	7	-	-	PUNCT
m-1112	3098	8	masses	masse	NOUN
m-1112	3098	9	of	of	ADP
m-1112	3098	10	n	n	CCONJ
m-1112	3098	11	-	-	PUNCT
m-1112	3098	12	mode	mode	NOUN
m-1112	3098	13	shapes	shape	NOUN
m-1112	3098	14	occupies	occupy	VERB
m-1112	3098	15	the	the	DET
m-1112	3098	16	resultant	resultant	NOUN
m-1112	3098	17	e	e	NOUN
m-1112	3098	18	-	-	NOUN
m-1112	3098	19	spectrum	spectrum	ADJ
m-1112	3098	20	4	4	NUM
m-1112	3098	21	…	…	PUNCT
m-1112	3098	22	each	each	PRON
m-1112	3098	23	-	-	PUNCT
m-1112	3098	24	one	one	NUM
m-1112	3098	25	of	of	ADP
m-1112	3098	26	the	the	DET
m-1112	3098	27	n	n	NUM
m-1112	3098	28	-	-	PUNCT
m-1112	3098	29	masses	masse	NOUN
m-1112	3098	30	occupies	occupy	VERB
m-1112	3098	31	n	n	CCONJ
m-1112	3098	32	-	-	PUNCT
m-1112	3098	33	mode	mode	NOUN
m-1112	3098	34	shapes	shape	NOUN
m-1112	3098	35	,	,	PUNCT
m-1112	3098	36	n	n	CCONJ
m-1112	3098	37	-	-	PUNCT
m-1112	3098	38	element	element	NOUN
m-1112	3098	39	.spectrum	.spectrum	X
m-1112	3098	40	,	,	PUNCT
m-1112	3098	41	4-p.spaces	4-p.spaces	NUM
m-1112	3098	42	,	,	PUNCT
m-1112	3098	43	4.n	4.n	NUM
m-1112	3098	44	..	..	PUNCT
m-1112	3098	45	regular	regular	ADJ
m-1112	3098	46	-	-	PUNCT
m-1112	3098	47	polygons	polygon	NOUN
m-1112	3098	48	of	of	ADP
m-1112	3098	49	n	n	CCONJ
m-1112	3098	50	-	-	PUNCT
m-1112	3098	51	degree	degree	NOUN
m-1112	3098	52	,	,	PUNCT
m-1112	3098	53	with	with	ADP
m-1112	3098	54	4.n	4.n	NUM
m-1112	3098	55	..	..	PUNCT
m-1112	3098	56	knots	knot	NOUN
m-1112	3098	57	and	and	CCONJ
m-1112	3098	58	roots	root	NOUN
m-1112	3098	59	.	.	PUNCT
m-1112	3099	1	5	5	NUM
m-1112	3099	2	…	…	PUNCT
m-1112	3099	3	each	each	DET
m-1112	3099	4	-	-	PUNCT
m-1112	3099	5	one	one	NUM
m-1112	3099	6	of	of	ADP
m-1112	3099	7	the	the	DET
m-1112	3099	8	n	n	NUM
m-1112	3099	9	-	-	PUNCT
m-1112	3099	10	masses	masse	NOUN
m-1112	3099	11	is	be	AUX
m-1112	3099	12	an	an	DET
m-1112	3099	13	e	e	NOUN
m-1112	3099	14	-monad	-monad	PROPN
m-1112	3099	15	occupying	occupy	VERB
m-1112	3099	16	4	4	NUM
m-1112	3099	17	-	-	PUNCT
m-1112	3099	18	primary	primary	ADJ
m-1112	3099	19	-	-	PUNCT
m-1112	3099	20	spaces	space	NOUN
m-1112	3099	21	,	,	PUNCT
m-1112	3099	22	and	and	CCONJ
m-1112	3099	23	ijo	ijo	PROPN
m-1112	3099	24	international	international	PROPN
m-1112	3099	25	journal	journal	PROPN
m-1112	3099	26	of	of	ADP
m-1112	3099	27	mathematics	mathematics	PROPN
m-1112	3099	28	(	(	PUNCT
m-1112	3099	29	issn	issn	PROPN
m-1112	3099	30	:	:	PUNCT
m-1112	3099	31	2992	2992	NUM
m-1112	3099	32	-	-	SYM
m-1112	3099	33	4421	4421	NUM
m-1112	3099	34	)	)	PUNCT
m-1112	3099	35	volume	volume	NOUN
m-1112	3099	36	08	08	NUM
m-1112	3100	1	|	|	ADV
m-1112	3100	2	issue	issue	NOUN
m-1112	3100	3	08	08	NUM
m-1112	3101	1	|	|	ADV
m-1112	3101	2	august	august	PROPN
m-1112	3101	3	2025	2025	NUM
m-1112	3101	4	|	|	ADV
m-1112	3101	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3101	6	ijo	ijo	NOUN
m-1112	3101	7	journals	journal	NOUN
m-1112	3101	8	110	110	NUM
m-1112	3101	9	the	the	DET
m-1112	3101	10	fundamental	fundamental	ADJ
m-1112	3101	11	particles	particle	NOUN
m-1112	3101	12	origination	origination	NOUN
m-1112	3101	13	mechanism	mechanism	NOUN
m-1112	3101	14	in	in	ADP
m-1112	3101	15	mfmf	mfmf	PROPN
m-1112	3101	16	pns	pns	PROPN
m-1112	3101	17	caves	cave	NOUN
m-1112	3101	18	.	.	PUNCT
m-1112	3102	1	forms	form	NOUN
m-1112	3102	2	4.n	4.n	NUM
m-1112	3102	3	..	..	PUNCT
m-1112	3103	1	regular	regular	ADJ
m-1112	3103	2	-	-	PUNCT
m-1112	3103	3	polygons	polygon	NOUN
m-1112	3103	4	of	of	ADP
m-1112	3103	5	the	the	DET
m-1112	3103	6	n	n	CCONJ
m-1112	3103	7	-	-	PUNCT
m-1112	3103	8	degree	degree	NOUN
m-1112	3103	9	,	,	PUNCT
m-1112	3103	10	and	and	CCONJ
m-1112	3103	11	with	with	ADP
m-1112	3103	12	4.n	4.n	NUM
m-1112	3103	13	..	..	PUNCT
m-1112	3103	14	knots	knot	NOUN
m-1112	3103	15	as	as	ADP
m-1112	3103	16	roots	root	NOUN
m-1112	3103	17	..	..	PUNCT
m-1112	3104	1	6	6	NUM
m-1112	3104	2	…	…	PUNCT
m-1112	3104	3	each	each	PRON
m-1112	3104	4	-	-	PUNCT
m-1112	3104	5	one	one	NUM
m-1112	3104	6	of	of	ADP
m-1112	3104	7	the	the	DET
m-1112	3104	8	n	n	NUM
m-1112	3104	9	-	-	PUNCT
m-1112	3104	10	masses	masse	NOUN
m-1112	3104	11	is	be	AUX
m-1112	3104	12	an	an	DET
m-1112	3104	13	e	e	NOUN
m-1112	3104	14	-	-	NOUN
m-1112	3104	15	monad	monad	PROPN
m-1112	3104	16	occupying	occupy	VERB
m-1112	3104	17	all	all	PRON
m-1112	3104	18	above	above	ADP
m-1112	3104	19	properties	property	NOUN
m-1112	3104	20	(	(	PUNCT
m-1112	3104	21	signals	signal	NOUN
m-1112	3104	22	)	)	PUNCT
m-1112	3104	23	.	.	PUNCT
m-1112	3105	1	9d	9d	NUM
m-1112	3105	2	..	..	PUNCT
m-1112	3105	3	the	the	DET
m-1112	3105	4	origination	origination	NOUN
m-1112	3105	5	of	of	ADP
m-1112	3105	6	proton	proton	NOUN
m-1112	3105	7	and	and	CCONJ
m-1112	3105	8	neutron	neutron	NOUN
m-1112	3105	9	cosmic	cosmic	ADJ
m-1112	3105	10	particles	particle	NOUN
m-1112	3105	11	.	.	PUNCT
m-1112	3106	1	the	the	DET
m-1112	3106	2	elements	element	NOUN
m-1112	3106	3	in	in	ADP
m-1112	3106	4	the	the	DET
m-1112	3106	5	proton	proton	NOUN
m-1112	3106	6	&	&	CCONJ
m-1112	3106	7	neutral	neutral	ADJ
m-1112	3106	8	-	-	PUNCT
m-1112	3106	9	caves	cave	NOUN
m-1112	3106	10	→	→	SYM
m-1112	3106	11	{	{	PUNCT
m-1112	3106	12	masses	masse	NOUN
m-1112	3106	13	–	–	PUNCT
m-1112	3106	14	charges	charge	NOUN
m-1112	3106	15	forces	force	NOUN
m-1112	3106	16	}	}	PUNCT
m-1112	3106	17	[	[	X
m-1112	3106	18	89	89	NUM
m-1112	3106	19	]	]	X
m-1112	3106	20	figure-27	figure-27	PROPN
m-1112	3106	21	:	:	PUNCT
m-1112	3106	22	the	the	DET
m-1112	3106	23	sphere	sphere	NOUN
m-1112	3106	24	-	-	PUNCT
m-1112	3106	25	structure	structure	NOUN
m-1112	3106	26	of	of	ADP
m-1112	3106	27	the	the	DET
m-1112	3106	28	hydrogen	hydrogen	NOUN
m-1112	3106	29	-	-	PUNCT
m-1112	3106	30	nucleus	nucleus	NOUN
m-1112	3106	31	,	,	PUNCT
m-1112	3106	32	⊕	⊕	PROPN
m-1112	3106	33	proton	proton	NOUN
m-1112	3106	34	,	,	PUNCT
m-1112	3106	35	[	[	X
m-1112	3106	36	⊕↔⊝]=neutron	⊕↔⊝]=neutron	NUM
m-1112	3106	37	proton	proton	NOUN
m-1112	3106	38	is	be	AUX
m-1112	3106	39	consisted	consist	VERB
m-1112	3106	40	of	of	ADP
m-1112	3106	41	three	three	NUM
m-1112	3106	42	-	-	PUNCT
m-1112	3106	43	primary	primary	ADJ
m-1112	3106	44	-	-	PUNCT
m-1112	3106	45	opposite	opposite	ADJ
m-1112	3106	46	-	-	PUNCT
m-1112	3106	47	spaces	space	NOUN
m-1112	3106	48	⊕	⊕	PROPN
m-1112	3106	49	,	,	PUNCT
m-1112	3106	50	⊝	⊝	NUM
m-1112	3106	51	,	,	PUNCT
m-1112	3107	1	[	[	X
m-1112	3107	2	⊕↔⊝	⊕↔⊝	X
m-1112	3107	3	]	]	X
m-1112	3107	4	,	,	PUNCT
m-1112	3107	5	having	have	VERB
m-1112	3107	6	masses	masse	NOUN
m-1112	3107	7	m	m	VERB
m-1112	3107	8	p	p	NOUN
m-1112	3107	9	,	,	PUNCT
m-1112	3107	10	charges	charge	NOUN
m-1112	3107	11	q̅p	q̅p	VERB
m-1112	3107	12	,	,	PUNCT
m-1112	3107	13	and	and	CCONJ
m-1112	3107	14	caves	cave	VERB
m-1112	3107	15	a	a	DET
m-1112	3107	16	p	p	NOUN
m-1112	3107	17	=	=	NOUN
m-1112	3107	18	r	r	NOUN
m-1112	3107	19	.	.	PUNCT
m-1112	3108	1	the	the	DET
m-1112	3108	2	nucleus`s	nucleus`s	PRON
m-1112	3108	3	cave	cave	NOUN
m-1112	3108	4	r	r	NOUN
m-1112	3108	5	,	,	PUNCT
m-1112	3108	6	exists	exist	VERB
m-1112	3108	7	in	in	ADP
m-1112	3108	8	the	the	DET
m-1112	3108	9	inscribed	inscribe	VERB
m-1112	3108	10	to	to	ADP
m-1112	3108	11	the	the	DET
m-1112	3108	12	tetrahedron	tetrahedron	NOUN
m-1112	3108	13	sphere	sphere	ADV
m-1112	3108	14	.	.	PUNCT
m-1112	3109	1	the	the	DET
m-1112	3109	2	elements	element	NOUN
m-1112	3109	3	in	in	ADP
m-1112	3109	4	proton	proton	NOUN
m-1112	3109	5	are	be	AUX
m-1112	3109	6	the	the	DET
m-1112	3109	7	two	two	NUM
m-1112	3109	8	u	u	NOUN
m-1112	3109	9	-	-	NOUN
m-1112	3109	10	quarks	quarks	NOUN
m-1112	3109	11	and	and	CCONJ
m-1112	3109	12	one	one	NUM
m-1112	3109	13	d	d	NOUN
m-1112	3109	14	-	-	NOUN
m-1112	3109	15	quark	quark	NOUN
m-1112	3109	16	.	.	PUNCT
m-1112	3110	1	the	the	DET
m-1112	3110	2	hydrogen	hydrogen	NOUN
m-1112	3110	3	-	-	PUNCT
m-1112	3110	4	nucleus	nucleus	NOUN
m-1112	3110	5	is	be	AUX
m-1112	3110	6	in	in	ADP
m-1112	3110	7	the	the	DET
m-1112	3110	8	inscribed	inscribe	VERB
m-1112	3110	9	sphere	sphere	NOUN
m-1112	3110	10	from	from	ADP
m-1112	3110	11	the	the	DET
m-1112	3110	12	{	{	PUNCT
m-1112	3110	13	inscribed	inscribe	VERB
m-1112	3110	14	sphere	sphere	PROPN
m-1112	3110	15	-tetrahedron	-tetrahedron	PROPN
m-1112	3110	16	–	–	PUNCT
m-1112	3110	17	cube	cube	NOUN
m-1112	3110	18	circumscribed	circumscribe	VERB
m-1112	3110	19	sphere	sphere	NOUN
m-1112	3110	20	system	system	NOUN
m-1112	3110	21	}	}	PUNCT
m-1112	3110	22	.	.	PUNCT
m-1112	3111	1	in	in	ADP
m-1112	3111	2	order	order	NOUN
m-1112	3111	3	to	to	PART
m-1112	3111	4	shift	shift	VERB
m-1112	3111	5	the	the	DET
m-1112	3111	6	u	u	NOUN
m-1112	3111	7	-	-	PROPN
m-1112	3111	8	d	d	NOUN
m-1112	3111	9	-	-	PUNCT
m-1112	3111	10	quarks	quarks	NOUN
m-1112	3111	11	of	of	ADP
m-1112	3111	12	an	an	DET
m-1112	3111	13	anti	anti	ADJ
m-1112	3111	14	-	-	NOUN
m-1112	3111	15	proton	proton	NOUN
m-1112	3111	16	into	into	ADP
m-1112	3111	17	a	a	DET
m-1112	3111	18	proton	proton	NOUN
m-1112	3111	19	spin	spin	NOUN
m-1112	3111	20	-	-	PUNCT
m-1112	3111	21	pair	pair	NOUN
m-1112	3111	22	require	require	VERB
m-1112	3111	23	an	an	DET
m-1112	3111	24	extra	extra	ADJ
m-1112	3111	25	input	input	NOUN
m-1112	3111	26	of	of	ADP
m-1112	3111	27	energy-(mev	energy-(mev	NOUN
m-1112	3111	28	)	)	PUNCT
m-1112	3111	29	,	,	PUNCT
m-1112	3111	30	so	so	ADV
m-1112	3111	31	would	would	AUX
m-1112	3111	32	proton	proton	VERB
m-1112	3111	33	paired	pair	VERB
m-1112	3111	34	with	with	ADP
m-1112	3111	35	a	a	DET
m-1112	3111	36	neutron	neutron	NOUN
m-1112	3111	37	be	be	AUX
m-1112	3111	38	stable	stable	ADJ
m-1112	3111	39	.	.	PUNCT
m-1112	3112	1	the	the	DET
m-1112	3112	2	total	total	ADJ
m-1112	3112	3	mass	mass	PROPN
m-1112	3112	4	mt	mt	PROPN
m-1112	3112	5	in	in	ADP
m-1112	3112	6	proton	proton	NOUN
m-1112	3112	7	follows	follow	VERB
m-1112	3112	8	,	,	PUNCT
m-1112	3112	9	the	the	DET
m-1112	3112	10	parallel	parallel	ADJ
m-1112	3112	11	connections	connection	NOUN
m-1112	3112	12	resistors	resistor	NOUN
m-1112	3112	13	inverse	inverse	NOUN
m-1112	3112	14	law	law	NOUN
m-1112	3112	15	,	,	PUNCT
m-1112	3112	16	where	where	SCONJ
m-1112	3112	17	the	the	DET
m-1112	3112	18	proton	proton	NOUN
m-1112	3112	19	total	total	NOUN
m-1112	3112	20	-	-	PUNCT
m-1112	3112	21	harmonic	harmonic	NOUN
m-1112	3112	22	mass	mass	PROPN
m-1112	3112	23	≡	≡	PROPN
m-1112	3112	24	mt	mt	PROPN
m-1112	3112	25	is	be	AUX
m-1112	3112	26	→	→	SYM
m-1112	3112	27	1	1	NUM
m-1112	3112	28	mt	mt	NOUN
m-1112	3112	29	=	=	SYM
m-1112	3112	30	1	1	NUM
m-1112	3112	31	mu	mu	NOUN
m-1112	3112	32	+	+	CCONJ
m-1112	3112	33	1	1	NUM
m-1112	3112	34	mu	mu	NOUN
m-1112	3112	35	+	+	CCONJ
m-1112	3112	36	1	1	NUM
m-1112	3112	37	md	md	NOUN
m-1112	3112	38	,	,	PUNCT
m-1112	3112	39	the	the	DET
m-1112	3112	40	system	system	NOUN
m-1112	3112	41	totalharmonic	totalharmonic	NOUN
m-1112	3112	42	-	-	PUNCT
m-1112	3112	43	charge	charge	NOUN
m-1112	3112	44	≡	≡	PROPN
m-1112	3112	45	qt	qt	ADP
m-1112	3112	46	≡	≡	PROPN
m-1112	3112	47	2.qu	2.qu	NUM
m-1112	3112	48	+	+	CCONJ
m-1112	3112	49	qd	qd	NOUN
m-1112	3112	50	=	=	SYM
m-1112	3112	51	2.(2/3).e	2.(2/3).e	PROPN
m-1112	3112	52	–	–	PUNCT
m-1112	3112	53	(	(	PUNCT
m-1112	3112	54	1/3	1/3	NUM
m-1112	3112	55	)	)	PUNCT
m-1112	3112	56	e	e	NOUN
m-1112	3113	1	=	=	PUNCT
m-1112	3113	2	+	+	CCONJ
m-1112	3113	3	3	3	NUM
m-1112	3113	4	3	3	NUM
m-1112	3113	5	e	e	NOUN
m-1112	3113	6	=	=	PUNCT
m-1112	3113	7	+	+	NUM
m-1112	3113	8	1,6022.10−19	1,6022.10−19	NUM
m-1112	3113	9	c	c	NOUN
m-1112	3113	10	,	,	PUNCT
m-1112	3113	11	and	and	CCONJ
m-1112	3113	12	the	the	DET
m-1112	3113	13	system	system	NOUN
m-1112	3113	14	-	-	PUNCT
m-1112	3113	15	resonance	resonance	NOUN
m-1112	3113	16	-	-	PUNCT
m-1112	3113	17	charge	charge	NOUN
m-1112	3113	18	qt	qt	NOUN
m-1112	3113	19	=	=	PUNCT
m-1112	3114	1	+	+	NUM
m-1112	3114	2	1	1	NUM
m-1112	3114	3	,	,	PUNCT
m-1112	3114	4	6022.10−19	6022.10−19	NUM
m-1112	3114	5	c	c	NOUN
m-1112	3114	6	...	...	PUNCT
m-1112	3114	7	(	(	PUNCT
m-1112	3114	8	2	2	X
m-1112	3114	9	)	)	PUNCT
m-1112	3114	10	the	the	DET
m-1112	3114	11	proton	proton	NOUN
m-1112	3114	12	totalharmoniccharge	totalharmoniccharge	NOUN
m-1112	3114	13	→	→	SYM
m-1112	3114	14	qt	qt	NOUN
m-1112	3114	15	≡	≡	PROPN
m-1112	3114	16	2.qu	2.qu	NUM
m-1112	3114	17	+	+	CCONJ
m-1112	3114	18	qd	qd	NOUN
m-1112	3114	19	,	,	PUNCT
m-1112	3114	20	and	and	CCONJ
m-1112	3114	21	for	for	ADP
m-1112	3114	22	the	the	DET
m-1112	3114	23	resonance	resonance	NOUN
m-1112	3114	24	frequency	frequency	NOUN
m-1112	3114	25	of	of	ADP
m-1112	3114	26	the	the	DET
m-1112	3114	27	unit	unit	NOUN
m-1112	3114	28	-	-	PUNCT
m-1112	3114	29	cave	cave	PROPN
m-1112	3114	30	is	be	AUX
m-1112	3114	31	the	the	DET
m-1112	3114	32	stationary	stationary	ADJ
m-1112	3114	33	-	-	PUNCT
m-1112	3114	34	system	system	NOUN
m-1112	3114	35	becoming	become	VERB
m-1112	3114	36	from	from	ADP
m-1112	3114	37	kepler	kepler	PROPN
m-1112	3114	38	second	second	ADJ
m-1112	3114	39	planetary	planetary	NOUN
m-1112	3114	40	-	-	PUNCT
m-1112	3114	41	law	law	NOUN
m-1112	3114	42	as	as	ADP
m-1112	3114	43	equation	equation	NOUN
m-1112	3114	44	,	,	PUNCT
m-1112	3114	45	4	4	NUM
m-1112	3114	46	π²	π²	NOUN
m-1112	3114	47	m	m	NOUN
m-1112	3114	48	f	f	NOUN
m-1112	3114	49	²o	²o	NOUN
m-1112	3114	50	=	=	SYM
m-1112	3114	51	k	k	PROPN
m-1112	3114	52	,	,	PUNCT
m-1112	3114	53	and	and	CCONJ
m-1112	3114	54	constant	constant	ADJ
m-1112	3114	55	law	law	NOUN
m-1112	3114	56	of	of	ADP
m-1112	3114	57	areas	area	NOUN
m-1112	3114	58	1	1	NUM
m-1112	3114	59	=	=	SYM
m-1112	3114	60	k	k	X
m-1112	3114	61	.𝐟	.𝐟	X
m-1112	3114	62	²𝐨	²𝐨	VERB
m-1112	3114	63	𝐚	𝐚	ADP
m-1112	3114	64	𝟑	𝟑	NUM
m-1112	3114	65	.	.	PUNCT
m-1112	3115	1	their	their	PRON
m-1112	3115	2	common	common	ADJ
m-1112	3115	3	k	k	PROPN
m-1112	3115	4	,	,	PUNCT
m-1112	3115	5	is	be	AUX
m-1112	3115	6	the	the	DET
m-1112	3115	7	ijo	ijo	PROPN
m-1112	3115	8	international	international	PROPN
m-1112	3115	9	journal	journal	PROPN
m-1112	3115	10	of	of	ADP
m-1112	3115	11	mathematics	mathematics	PROPN
m-1112	3115	12	(	(	PUNCT
m-1112	3115	13	issn	issn	PROPN
m-1112	3115	14	:	:	PUNCT
m-1112	3115	15	2992	2992	NUM
m-1112	3115	16	-	-	SYM
m-1112	3115	17	4421	4421	NUM
m-1112	3115	18	)	)	PUNCT
m-1112	3115	19	volume	volume	NOUN
m-1112	3115	20	08	08	NUM
m-1112	3116	1	|	|	ADV
m-1112	3116	2	issue	issue	NOUN
m-1112	3116	3	08	08	NUM
m-1112	3117	1	|	|	ADV
m-1112	3117	2	august	august	PROPN
m-1112	3117	3	2025	2025	NUM
m-1112	3117	4	|	|	ADV
m-1112	3117	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3117	6	ijo	ijo	PROPN
m-1112	3117	7	journals	journal	NOUN
m-1112	3117	8	111	111	NUM
m-1112	3117	9	the	the	DET
m-1112	3117	10	fundamental	fundamental	ADJ
m-1112	3117	11	particles	particle	NOUN
m-1112	3117	12	origination	origination	NOUN
m-1112	3117	13	mechanism	mechanism	NOUN
m-1112	3117	14	in	in	ADP
m-1112	3117	15	mfmf	mfmf	PROPN
m-1112	3117	16	pns	pns	PROPN
m-1112	3117	17	caves	cave	NOUN
m-1112	3117	18	.	.	PUNCT
m-1112	3118	1	constant	constant	ADJ
m-1112	3118	2	-	-	PUNCT
m-1112	3118	3	energy	energy	NOUN
m-1112	3118	4	→	→	SYM
m-1112	3118	5	k	k	NOUN
m-1112	3118	6	=	=	SYM
m-1112	3118	7	4	4	NUM
m-1112	3118	8	π²	π²	NOUN
m-1112	3118	9	m	m	PROPN
m-1112	3118	10	f	f	NOUN
m-1112	3118	11	²p	²p	NOUN
m-1112	3118	12	=	=	SYM
m-1112	3118	13	1	1	NUM
m-1112	3118	14	𝐟	𝐟	NUM
m-1112	3118	15	²𝐩	²𝐩	PROPN
m-1112	3118	16	𝐚𝟑	𝐚𝟑	PROPN
m-1112	3118	17	or	or	CCONJ
m-1112	3118	18	,	,	PUNCT
m-1112	3118	19	f	f	PROPN
m-1112	3118	20	⁴p	⁴p	NOUN
m-1112	3118	21	=	=	SYM
m-1112	3118	22	1	1	NUM
m-1112	3118	23	4π²ma3	4π²ma3	NUM
m-1112	3118	24	and	and	CCONJ
m-1112	3118	25	f	f	PROPN
m-1112	3118	26	p	p	NOUN
m-1112	3118	27	=	=	NOUN
m-1112	3119	1	√	√	NUM
m-1112	3119	2	1	1	NUM
m-1112	3119	3	4π²m.a3	4π²m.a3	NUM
m-1112	3119	4	4	4	NUM
m-1112	3119	5	.	.	PUNCT
m-1112	3120	1	the	the	DET
m-1112	3120	2	measured	measure	VERB
m-1112	3120	3	magnitudes	magnitude	NOUN
m-1112	3120	4	are	be	AUX
m-1112	3120	5	as	as	SCONJ
m-1112	3120	6	follows	follow	VERB
m-1112	3120	7	,	,	PUNCT
m-1112	3120	8	a	a	DET
m-1112	3120	9	-	-	PUNCT
m-1112	3120	10	proton⊕→	proton⊕→	VERB
m-1112	3120	11	mass	mass	NOUN
m-1112	3121	1	𝐦𝐩	𝐦𝐩	NOUN
m-1112	3121	2	=	=	SYM
m-1112	3121	3	1,672.10−27	1,672.10−27	NUM
m-1112	3121	4	kg	kg	NOUN
m-1112	3122	1	→charge	→charge	X
m-1112	3122	2	𝐂	𝐂	PROPN
m-1112	3122	3	𝐩	𝐩	PROPN
m-1112	3122	4	=	=	SYM
m-1112	3122	5	1,602.10−19	1,602.10−19	NUM
m-1112	3122	6	c	c	NOUN
m-1112	3122	7	→	→	SYM
m-1112	3122	8	a	a	DET
m-1112	3122	9	=	=	SYM
m-1112	3122	10	8,4.10−16	8,4.10−16	NUM
m-1112	3122	11	m	m	VERB
m-1112	3122	12	b	b	X
m-1112	3122	13	-	-	PUNCT
m-1112	3122	14	electron⊝→mass	electron⊝→mass	NOUN
m-1112	3122	15	𝐦𝐞	𝐦𝐞	NOUN
m-1112	3122	16	=	=	SYM
m-1112	3122	17	9,11.10−31	9,11.10−31	NUM
m-1112	3122	18	kg	kg	NOUN
m-1112	3123	1	→charge	→charge	NUM
m-1112	3123	2	𝐂	𝐂	PROPN
m-1112	3123	3	𝐞	𝐞	NOUN
m-1112	3123	4	=	=	SYM
m-1112	3123	5	1,602.10−19	1,602.10−19	NUM
m-1112	3123	6	c	c	NOUN
m-1112	3123	7	→	→	PUNCT
m-1112	3123	8	a	a	PRON
m-1112	3123	9	=	=	SYM
m-1112	3123	10	5,0.10−17	5,0.10−17	PROPN
m-1112	3123	11	m	m	NOUN
m-1112	3123	12	c	c	NOUN
m-1112	3123	13	-	-	PUNCT
m-1112	3123	14	neutron[⊕↔⊝]→mass	neutron[⊕↔⊝]→mass	NUM
m-1112	3123	15	𝐦𝐧	𝐦𝐧	PROPN
m-1112	3123	16	=	=	PROPN
m-1112	3123	17	1,672.10−27	1,672.10−27	NUM
m-1112	3123	18	kg	kg	NOUN
m-1112	3123	19	→charge	→charge	NUM
m-1112	3123	20	𝐂	𝐂	ADV
m-1112	3123	21	𝐧	𝐧	NOUN
m-1112	3123	22	=	=	SYM
m-1112	3123	23	0	0	NUM
m-1112	3123	24	,	,	PUNCT
m-1112	3123	25	0	0	NUM
m-1112	3123	26	c	c	NOUN
m-1112	3123	27	→	→	PUNCT
m-1112	3123	28	a	a	PRON
m-1112	3123	29	=	=	SYM
m-1112	3123	30	1,7.10−15	1,7.10−15	NUM
m-1112	3123	31	m	m	NOUN
m-1112	3123	32	d	d	NOUN
m-1112	3123	33	-	-	PUNCT
m-1112	3123	34	u	u	NOUN
m-1112	3123	35	-	-	NOUN
m-1112	3123	36	quark	quark	NOUN
m-1112	3123	37	→from	→from	ADP
m-1112	3123	38	equal	equal	ADJ
m-1112	3123	39	masses	masse	NOUN
m-1112	3123	40	mp	mp	NOUN
m-1112	3123	41	=	=	PROPN
m-1112	3123	42	2.mu	2.mu	NUM
m-1112	3123	43	+	+	CCONJ
m-1112	3123	44	md	md	PROPN
m-1112	3123	45	=	=	NUM
m-1112	3123	46	3.mu	3.mu	NUM
m-1112	3123	47	=	=	SYM
m-1112	3123	48	1,672.10−27	1,672.10−27	NUM
m-1112	3123	49	kg	kg	NOUN
m-1112	3123	50	and	and	CCONJ
m-1112	3123	51	quark	quark	ADJ
m-1112	3123	52	masses	masse	NOUN
m-1112	3123	53	𝐦𝐮	𝐦𝐮	NOUN
m-1112	3123	54	=	=	PUNCT
m-1112	3123	55	𝐦𝐝	𝐦𝐝	PROPN
m-1112	3123	56	=	=	SYM
m-1112	3123	57	mp	mp	PROPN
m-1112	3123	58	/	/	SYM
m-1112	3123	59	3	3	NUM
m-1112	3123	60	=	=	SYM
m-1112	3123	61	5,573.10−28	5,573.10−28	NUM
m-1112	3123	62	kg	kg	NOUN
m-1112	3123	63	,	,	PUNCT
m-1112	3123	64	and	and	CCONJ
m-1112	3123	65	1	1	NUM
m-1112	3123	66	mt	mt	NOUN
m-1112	3123	67	=	=	NOUN
m-1112	3123	68	1	1	NUM
m-1112	3123	69	mu	mu	NOUN
m-1112	3123	70	+	+	CCONJ
m-1112	3123	71	1	1	NUM
m-1112	3123	72	mu	mu	NOUN
m-1112	3123	73	+	+	CCONJ
m-1112	3123	74	1	1	NUM
m-1112	3123	75	md	md	NOUN
m-1112	3123	76	=	=	SYM
m-1112	3123	77	3	3	NUM
m-1112	3123	78	mp	mp	NOUN
m-1112	3123	79	+	+	CCONJ
m-1112	3123	80	2.3	2.3	NUM
m-1112	3123	81	mp	mp	NOUN
m-1112	3123	82	=	=	SYM
m-1112	3123	83	9	9	NUM
m-1112	3123	84	mp	mp	NOUN
m-1112	3123	85	and	and	CCONJ
m-1112	3123	86	proton	proton	NOUN
m-1112	3123	87	resonance	resonance	NOUN
m-1112	3123	88	mass	mass	PROPN
m-1112	3123	89	mt	mt	PROPN
m-1112	3124	1	=	=	PROPN
m-1112	3124	2	m	m	PROPN
m-1112	3124	3	p	p	NOUN
m-1112	3124	4	9	9	NUM
m-1112	3124	5	=	=	SYM
m-1112	3124	6	1,857777.10−28	1,857777.10−28	NUM
m-1112	3124	7	kg	kg	NOUN
m-1112	3125	1	≈	≈	PROPN
m-1112	3125	2	16,7267	16,7267	NUM
m-1112	3125	3	m	m	NOUN
m-1112	3125	4	ev	ev	ADJ
m-1112	3125	5	/	/	SYM
m-1112	3125	6	c²	c²	NOUN
m-1112	3125	7	…	…	PUNCT
m-1112	3125	8	…	…	PUNCT
m-1112	3125	9	.(m	.(m	NUM
m-1112	3125	10	)	)	PUNCT
m-1112	3125	11	for	for	ADP
m-1112	3125	12	proton	proton	NOUN
m-1112	3125	13	issues	issue	NOUN
m-1112	3125	14	qp	qp	ADP
m-1112	3125	15	=	=	NOUN
m-1112	3125	16	2.qu	2.qu	NUM
m-1112	3125	17	+	+	CCONJ
m-1112	3125	18	qd	qd	NOUN
m-1112	3125	19	=	=	SYM
m-1112	3125	20	2	2	NUM
m-1112	3125	21	.	.	NOUN
m-1112	3125	22	2	2	NUM
m-1112	3125	23	3	3	NUM
m-1112	3125	24	e	e	NOUN
m-1112	3125	25	1	1	NUM
m-1112	3125	26	3	3	NUM
m-1112	3125	27	e	e	NOUN
m-1112	3125	28	=	=	SYM
m-1112	3125	29	e	e	PROPN
m-1112	3125	30	,	,	PUNCT
m-1112	3125	31	and	and	CCONJ
m-1112	3125	32	the	the	DET
m-1112	3125	33	stability	stability	NOUN
m-1112	3125	34	of	of	ADP
m-1112	3125	35	forces	force	NOUN
m-1112	3125	36	is	be	AUX
m-1112	3125	37	axial	axial	ADJ
m-1112	3125	38	.	.	PUNCT
m-1112	3126	1	electron	electron	NOUN
m-1112	3126	2	-	-	PUNCT
m-1112	3126	3	charge	charge	NOUN
m-1112	3126	4	𝐂𝐞	𝐂𝐞	PROPN
m-1112	3126	5	=	=	NOUN
m-1112	3126	6	1,602	1,602	NUM
m-1112	3126	7	.	.	PUNCT
m-1112	3127	1	10−19	10−19	NUM
m-1112	3127	2	c	c	NOUN
m-1112	3127	3	,	,	PUNCT
m-1112	3127	4	while	while	SCONJ
m-1112	3127	5	𝐂𝐪𝐮	𝐂𝐪𝐮	PROPN
m-1112	3127	6	=	=	NOUN
m-1112	3127	7	2	2	NUM
m-1112	3127	8	3	3	NUM
m-1112	3127	9	e	e	NOUN
m-1112	3127	10	=	=	PUNCT
m-1112	3127	11	+	+	CCONJ
m-1112	3127	12	𝟐	𝟐	NUM
m-1112	3127	13	𝟑	𝟑	NUM
m-1112	3127	14	1,602.10−19	1,602.10−19	NUM
m-1112	3127	15	c	c	PROPN
m-1112	3127	16	𝐂𝐪𝐝	𝐂𝐪𝐝	PROPN
m-1112	3127	17	=	=	SYM
m-1112	3127	18	1	1	NUM
m-1112	3127	19	3	3	NUM
m-1112	3127	20	e	e	NOUN
m-1112	3127	21	=	=	SYM
m-1112	3127	22	𝟏	𝟏	NUM
m-1112	3127	23	𝟑	𝟑	NUM
m-1112	3127	24	1,602.10−19	1,602.10−19	NUM
m-1112	3127	25	c	c	NOUN
m-1112	3127	26	,	,	PUNCT
m-1112	3127	27	and	and	CCONJ
m-1112	3127	28	from	from	ADP
m-1112	3127	29	qt	qt	NOUN
m-1112	3127	30	≡	≡	PROPN
m-1112	3127	31	2.qu	2.qu	NUM
m-1112	3127	32	+	+	CCONJ
m-1112	3127	33	qd	qd	NOUN
m-1112	3127	34	,	,	PUNCT
m-1112	3127	35	then	then	ADV
m-1112	3127	36	proton	proton	NOUN
m-1112	3127	37	resonance	resonance	NOUN
m-1112	3127	38	charge	charge	NOUN
m-1112	3127	39	qt	qt	NOUN
m-1112	3127	40	=	=	SYM
m-1112	3127	41	3.q	3.q	NUM
m-1112	3128	1	p	p	NOUN
m-1112	3128	2	3	3	NUM
m-1112	3128	3	=	=	SYM
m-1112	3128	4	1,602.10−19	1,602.10−19	NUM
m-1112	3128	5	c	c	X
m-1112	3128	6	…	…	PUNCT
m-1112	3128	7	…	…	PUNCT
m-1112	3128	8	…	…	PUNCT
m-1112	3128	9	..	..	PUNCT
m-1112	3128	10	(	(	PUNCT
m-1112	3128	11	c	c	X
m-1112	3128	12	)	)	PUNCT
m-1112	3128	13	proton	proton	NOUN
m-1112	3128	14	-	-	PUNCT
m-1112	3128	15	resonance	resonance	NOUN
m-1112	3128	16	frequency	frequency	NOUN
m-1112	3128	17	f	f	X
m-1112	3129	1	p	p	PROPN
m-1112	3129	2	=	=	NOUN
m-1112	3129	3	√	√	ADJ
m-1112	3129	4	1	1	NUM
m-1112	3129	5	4π²m.a3	4π²m.a3	NUM
m-1112	3129	6	4	4	NUM
m-1112	3129	7	=	=	SYM
m-1112	3129	8	√	√	NUM
m-1112	3129	9	1	1	NUM
m-1112	3129	10	4π²5,573.10−28(8,4.10−16)³	4π²5,573.10−28(8,4.10−16)³	NUM
m-1112	3129	11	4	4	NUM
m-1112	3129	12	=	=	SYM
m-1112	3129	13	5,26241.1017	5,26241.1017	NUM
m-1112	3129	14	h	h	NOUN
m-1112	3129	15	using	use	VERB
m-1112	3129	16	the	the	DET
m-1112	3129	17	united	united	PROPN
m-1112	3129	18	newton	newton	PROPN
m-1112	3129	19	-	-	PUNCT
m-1112	3129	20	coulomb	coulomb	NOUN
m-1112	3129	21	electro	electro	ADJ
m-1112	3129	22	-	-	PUNCT
m-1112	3129	23	mechanical	mechanical	ADJ
m-1112	3129	24	equation	equation	NOUN
m-1112	3129	25	,	,	PUNCT
m-1112	3129	26	q	q	PUNCT
m-1112	3130	1	b̅l=2π.m	b̅l=2π.m	NOUN
m-1112	3130	2	f	f	X
m-1112	3130	3	,	,	PUNCT
m-1112	3130	4	the	the	DET
m-1112	3130	5	proton	proton	NOUN
m-1112	3130	6	magnetic	magnetic	ADJ
m-1112	3130	7	-	-	PUNCT
m-1112	3130	8	field	field	NOUN
m-1112	3130	9	b̅f	b̅f	NOUN
m-1112	3130	10	=	=	SYM
m-1112	3130	11	|2π.m	|2π.m	PROPN
m-1112	3130	12	t|	t|	PROPN
m-1112	3130	13	qt	qt	NOUN
m-1112	3130	14	f	f	PROPN
m-1112	3130	15	=	=	PUNCT
m-1112	3130	16	2𝜋.1,85777.10−285,262409.1017	2𝜋.1,85777.10−285,262409.1017	NUM
m-1112	3130	17	1,6022.10−19	1,6022.10−19	NUM
m-1112	3130	18	(	(	PUNCT
m-1112	3130	19	kg	kg	NOUN
m-1112	3130	20	/	/	SYM
m-1112	3130	21	cs	cs	PROPN
m-1112	3130	22	)	)	PUNCT
m-1112	3130	23	=	=	SYM
m-1112	3131	1	3,83389.109	3,83389.109	NUM
m-1112	3131	2	tesla	tesla	NOUN
m-1112	3131	3	which	which	PRON
m-1112	3131	4	is	be	AUX
m-1112	3131	5	the	the	DET
m-1112	3131	6	strength	strength	NOUN
m-1112	3131	7	of	of	ADP
m-1112	3131	8	a	a	DET
m-1112	3131	9	magnetar	magnetar	NOUN
m-1112	3131	10	,	,	PUNCT
m-1112	3131	11	i.e.	i.e.	X
m-1112	3131	12	a	a	DET
m-1112	3131	13	type	type	NOUN
m-1112	3131	14	of	of	ADP
m-1112	3131	15	neutron	neutron	NOUN
m-1112	3131	16	-	-	PUNCT
m-1112	3131	17	star	star	PROPN
m-1112	3131	18	having	have	VERB
m-1112	3131	19	an	an	DET
m-1112	3131	20	extremely	extremely	ADV
m-1112	3131	21	powerful	powerful	ADJ
m-1112	3131	22	magnetic	magnetic	ADJ
m-1112	3131	23	-	-	PUNCT
m-1112	3131	24	field	field	NOUN
m-1112	3131	25	,	,	PUNCT
m-1112	3131	26	and	and	CCONJ
m-1112	3131	27	electric	electric	NOUN
m-1112	3131	28	-	-	PUNCT
m-1112	3131	29	forces	force	NOUN
m-1112	3131	30	to	to	PART
m-1112	3131	31	be	be	AUX
m-1112	3131	32	over	over	ADP
m-1112	3131	33	ten	ten	NUM
m-1112	3131	34	-	-	PUNCT
m-1112	3131	35	thousands	thousand	NOUN
m-1112	3131	36	-	-	PUNCT
m-1112	3131	37	newton	newton	PROPN
m-1112	3131	38	.	.	PUNCT
m-1112	3132	1	the	the	DET
m-1112	3132	2	electric	electric	ADJ
m-1112	3132	3	force	force	NOUN
m-1112	3132	4	between	between	ADP
m-1112	3132	5	the	the	DET
m-1112	3132	6	u	u	NOUN
m-1112	3132	7	-	-	NOUN
m-1112	3132	8	quarks	quarks	NOUN
m-1112	3132	9	and	and	CCONJ
m-1112	3132	10	d	d	NOUN
m-1112	3132	11	-	-	PUNCT
m-1112	3132	12	quarks	quarks	NOUN
m-1112	3132	13	in	in	ADP
m-1112	3132	14	proton	proton	NOUN
m-1112	3132	15	is	be	AUX
m-1112	3132	16	from	from	ADP
m-1112	3132	17	coulomb	coulomb	NOUN
m-1112	3132	18	law	law	NOUN
m-1112	3132	19	𝐅𝐮𝐝−𝐩	𝐅𝐮𝐝−𝐩	NOUN
m-1112	3132	20	=	=	PUNCT
m-1112	3133	1	c	c	X
m-1112	3133	2	q1.q	q1.q	NUM
m-1112	3133	3	2	2	NUM
m-1112	3133	4	r	r	NOUN
m-1112	3133	5	²	²	NUM
m-1112	3133	6	=	=	SYM
m-1112	3133	7	8,9875.109(nm2	8,9875.109(nm2	NUM
m-1112	3133	8	/	/	SYM
m-1112	3133	9	c²	c²	NOUN
m-1112	3133	10	)	)	PUNCT
m-1112	3133	11	.	.	PUNCT
m-1112	3134	1	2	2	NUM
m-1112	3134	2	9	9	NUM
m-1112	3134	3	[	[	SYM
m-1112	3134	4	1,602.10−19	1,602.10−19	NUM
m-1112	3134	5	c]²	c]²	NOUN
m-1112	3134	6	1	1	NUM
m-1112	3134	7	(	(	PUNCT
m-1112	3134	8	10−16)²	10−16)²	NOUN
m-1112	3134	9	=	=	SYM
m-1112	3134	10	1,997222.10	1,997222.10	NUM
m-1112	3134	11	6	6	NUM
m-1112	3134	12	n	n	NOUN
m-1112	3134	13	...	...	PUNCT
m-1112	3134	14	(	(	PUNCT
m-1112	3134	15	f	f	PROPN
m-1112	3134	16	p	p	X
m-1112	3134	17	)	)	PUNCT
m-1112	3134	18	and	and	CCONJ
m-1112	3134	19	the	the	DET
m-1112	3134	20	electric	electric	ADJ
m-1112	3134	21	force	force	NOUN
m-1112	3134	22	between	between	ADP
m-1112	3134	23	the	the	DET
m-1112	3134	24	u	u	NOUN
m-1112	3134	25	-	-	NOUN
m-1112	3134	26	quarks	quarks	NOUN
m-1112	3134	27	and	and	CCONJ
m-1112	3134	28	d	d	NOUN
m-1112	3134	29	-	-	PUNCT
m-1112	3134	30	quarks	quarks	NOUN
m-1112	3134	31	in	in	ADP
m-1112	3134	32	neutron	neutron	NOUN
m-1112	3134	33	is	be	AUX
m-1112	3134	34	𝐅𝐮𝐝−𝐧	𝐅𝐮𝐝−𝐧	PROPN
m-1112	3134	35	=	=	SYM
m-1112	3134	36	c	c	NOUN
m-1112	3134	37	q1.q	q1.q	NUM
m-1112	3134	38	2	2	NUM
m-1112	3134	39	r	r	NOUN
m-1112	3134	40	²	²	NUM
m-1112	3134	41	=	=	SYM
m-1112	3134	42	8,9875.109(nm2	8,9875.109(nm2	NUM
m-1112	3134	43	/	/	SYM
m-1112	3134	44	c²	c²	NOUN
m-1112	3134	45	)	)	PUNCT
m-1112	3134	46	.	.	PUNCT
m-1112	3135	1	2	2	NUM
m-1112	3135	2	9	9	NUM
m-1112	3135	3	[	[	SYM
m-1112	3135	4	1,602.10−19	1,602.10−19	NUM
m-1112	3135	5	c]²	c]²	NOUN
m-1112	3135	6	1	1	NUM
m-1112	3135	7	(	(	PUNCT
m-1112	3135	8	10−16)²	10−16)²	NOUN
m-1112	3135	9	=	=	SYM
m-1112	3135	10	-1,997222.10	-1,997222.10	PROPN
m-1112	3135	11	6	6	NUM
m-1112	3135	12	n	n	NOUN
m-1112	3135	13	..	..	PUNCT
m-1112	3135	14	(	(	PUNCT
m-1112	3135	15	f	f	PROPN
m-1112	3135	16	n	n	CCONJ
m-1112	3135	17	)	)	PUNCT
m-1112	3135	18	i.e.	i.e.	X
m-1112	3135	19	forces	force	NOUN
m-1112	3135	20	between	between	ADP
m-1112	3135	21	the	the	DET
m-1112	3135	22	opposites	opposite	NOUN
m-1112	3135	23	equilibrium	equilibrium	NOUN
m-1112	3135	24	-	-	PUNCT
m-1112	3135	25	linearly	linearly	ADV
m-1112	3135	26	←[d	←[d	PROPN
m-1112	3135	27	-	-	PUNCT
m-1112	3135	28	u	u	NOUN
m-1112	3135	29	-	-	NOUN
m-1112	3135	30	d]→	d]→	ADJ
m-1112	3135	31	or	or	CCONJ
m-1112	3135	32	→[u	→[u	ADP
m-1112	3135	33	-	-	PUNCT
m-1112	3135	34	d	d	NOUN
m-1112	3135	35	-	-	NOUN
m-1112	3135	36	u]←	u]←	NOUN
m-1112	3135	37	for	for	ADP
m-1112	3135	38	the	the	DET
m-1112	3135	39	neutral	neutral	ADJ
m-1112	3135	40	-	-	PUNCT
m-1112	3135	41	cave	cave	NOUN
m-1112	3135	42	issues	issue	NOUN
m-1112	3135	43	qn	qn	NOUN
m-1112	3135	44	=	=	SYM
m-1112	3135	45	2.qd	2.qd	NUM
m-1112	3135	46	+	+	CCONJ
m-1112	3135	47	qu	qu	X
m-1112	3135	48	=	=	PROPN
m-1112	3135	49	2	2	NUM
m-1112	3135	50	.	.	NOUN
m-1112	3135	51	1	1	NUM
m-1112	3135	52	3	3	NUM
m-1112	3135	53	e	e	NOUN
m-1112	3135	54	+	+	NOUN
m-1112	3135	55	2	2	NUM
m-1112	3135	56	3	3	NUM
m-1112	3135	57	e	e	NOUN
m-1112	3135	58	=	=	NOUN
m-1112	3135	59	0.e	0.e	NUM
m-1112	3135	60	,	,	PUNCT
m-1112	3135	61	and	and	CCONJ
m-1112	3135	62	the	the	DET
m-1112	3135	63	stability	stability	NOUN
m-1112	3135	64	of	of	ADP
m-1112	3135	65	forces	force	NOUN
m-1112	3135	66	is	be	AUX
m-1112	3135	67	axial	axial	ADJ
m-1112	3135	68	as	as	ADP
m-1112	3135	69	in	in	ADP
m-1112	3135	70	proton	proton	NOUN
m-1112	3135	71	and	and	CCONJ
m-1112	3135	72	this	this	PRON
m-1112	3135	73	because	because	SCONJ
m-1112	3135	74	the	the	DET
m-1112	3135	75	dynamic	dynamic	ADJ
m-1112	3135	76	-	-	PUNCT
m-1112	3135	77	strip	strip	NOUN
m-1112	3135	78	-	-	PUNCT
m-1112	3135	79	polygon	polygon	NOUN
m-1112	3135	80	doesn`t	doesn`t	VERB
m-1112	3135	81	close	close	ADV
m-1112	3135	82	.	.	PUNCT
m-1112	3136	1	for	for	ADP
m-1112	3136	2	,	,	PUNCT
m-1112	3136	3	ijo	ijo	PROPN
m-1112	3136	4	international	international	PROPN
m-1112	3136	5	journal	journal	PROPN
m-1112	3136	6	of	of	ADP
m-1112	3136	7	mathematics	mathematics	PROPN
m-1112	3136	8	(	(	PUNCT
m-1112	3136	9	issn	issn	PROPN
m-1112	3136	10	:	:	PUNCT
m-1112	3136	11	2992	2992	NUM
m-1112	3136	12	-	-	SYM
m-1112	3136	13	4421	4421	NUM
m-1112	3136	14	)	)	PUNCT
m-1112	3136	15	volume	volume	NOUN
m-1112	3136	16	08	08	NUM
m-1112	3137	1	|	|	ADV
m-1112	3137	2	issue	issue	NOUN
m-1112	3137	3	08	08	NUM
m-1112	3138	1	|	|	ADV
m-1112	3138	2	august	august	PROPN
m-1112	3138	3	2025	2025	NUM
m-1112	3138	4	|	|	ADV
m-1112	3138	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3138	6	ijo	ijo	PROPN
m-1112	3138	7	journals	journal	NOUN
m-1112	3138	8	112	112	NUM
m-1112	3138	9	the	the	DET
m-1112	3138	10	fundamental	fundamental	ADJ
m-1112	3138	11	particles	particle	NOUN
m-1112	3138	12	origination	origination	NOUN
m-1112	3138	13	mechanism	mechanism	NOUN
m-1112	3138	14	in	in	ADP
m-1112	3138	15	mfmf	mfmf	PROPN
m-1112	3138	16	pns	pns	PROPN
m-1112	3138	17	caves	cave	NOUN
m-1112	3138	18	.	.	PUNCT
m-1112	3139	1	1	1	X
m-1112	3139	2	..	..	PUNCT
m-1112	3139	3	neutrinos	neutrino	NOUN
m-1112	3139	4	,	,	PUNCT
m-1112	3139	5	v	v	NOUN
m-1112	3139	6	,	,	PUNCT
m-1112	3139	7	mass	mass	NOUN
m-1112	3139	8	m	m	NOUN
m-1112	3139	9	=	=	SYM
m-1112	3139	10	(	(	PUNCT
m-1112	3139	11	3,11	3,11	NUM
m-1112	3139	12	.10−6	.10−6	PUNCT
m-1112	3139	13	)	)	PUNCT
m-1112	3140	1	mev	mev	PROPN
m-1112	3140	2	/	/	SYM
m-1112	3140	3	c²	c²	PROPN
m-1112	3140	4	x	x	X
m-1112	3140	5	1,8.10−28	1,8.10−28	NUM
m-1112	3140	6	=	=	SYM
m-1112	3140	7	5	5	NUM
m-1112	3140	8	,	,	PUNCT
m-1112	3140	9	598	598	NUM
m-1112	3140	10	.𝟏𝟎−𝟑𝟒	.𝟏𝟎−𝟑𝟒	PUNCT
m-1112	3140	11	kg	kg	NOUN
m-1112	3140	12	the	the	DET
m-1112	3140	13	spin	spin	NOUN
m-1112	3140	14	is	be	AUX
m-1112	3140	15	,	,	PUNCT
m-1112	3140	16	𝐒𝒗	𝐒𝒗	PROPN
m-1112	3140	17	=	=	PUNCT
m-1112	3140	18	5,691952.10−34{kg	5,691952.10−34{kg	NUM
m-1112	3140	19	/	/	SYM
m-1112	3140	20	m	m	PROPN
m-1112	3140	21	/	/	SYM
m-1112	3140	22	s	s	PART
m-1112	3140	23	}	}	PUNCT
m-1112	3140	24	,	,	PUNCT
m-1112	3140	25	𝐚𝐯	𝐚𝐯	PROPN
m-1112	3140	26	=	=	SYM
m-1112	3141	1	7,0.10−21	7,0.10−21	NUM
m-1112	3141	2	m	m	NOUN
m-1112	3141	3	,	,	PUNCT
m-1112	3141	4	𝐟𝐯	𝐟𝐯	PROPN
m-1112	3141	5	=	=	PUNCT
m-1112	3142	1	[	[	PUNCT
m-1112	3142	2	𝐄	𝐄	NOUN
m-1112	3142	3	𝐯𝐊	𝐯𝐊	VERB
m-1112	3142	4	=	=	SYM
m-1112	3142	5	mc²	mc²	X
m-1112	3142	6	]	]	X
m-1112	3142	7	/	/	SYM
m-1112	3142	8	h	h	NOUN
m-1112	3142	9	=	=	SYM
m-1112	3143	1	5,6.10−34	5,6.10−34	NUM
m-1112	3144	1	[	[	X
m-1112	3144	2	1017].1,6022.10−19	1017].1,6022.10−19	NUM
m-1112	3144	3	=	=	SYM
m-1112	3144	4	8,96912.10−36	8,96912.10−36	NUM
m-1112	3144	5	j/[6,626.10−34	j/[6,626.10−34	NOUN
m-1112	3144	6	js	js	PROPN
m-1112	3144	7	=	=	SYM
m-1112	3144	8	13,536244	13,536244	PROPN
m-1112	3144	9	.	.	PUNCT
m-1112	3144	10	𝟏𝟎𝟏/s	𝟏𝟎𝟏/s	PUNCT
m-1112	3145	1	from	from	ADP
m-1112	3145	2	cave	cave	NOUN
m-1112	3145	3	r	r	NOUN
m-1112	3145	4	=	=	PUNCT
m-1112	3145	5	7.10−21	7.10−21	NUM
m-1112	3145	6	m	m	VERB
m-1112	3145	7	then	then	ADV
m-1112	3145	8	f	f	PROPN
m-1112	3145	9	=	=	PUNCT
m-1112	3145	10	√	√	NUM
m-1112	3145	11	1	1	NUM
m-1112	3145	12	g.a³	g.a³	NOUN
m-1112	3145	13	2	2	NUM
m-1112	3145	14	=	=	SYM
m-1112	3145	15	√	√	ADP
m-1112	3145	16	1	1	NUM
m-1112	3145	17	9,81(7.10−21)³	9,81(7.10−21)³	NUM
m-1112	3145	18	2	2	NUM
m-1112	3145	19	=	=	SYM
m-1112	3145	20	5,347345.𝟏𝟎𝟑𝟎	5,347345.𝟏𝟎𝟑𝟎	NUM
m-1112	3145	21	h	h	NOUN
m-1112	3145	22	and	and	CCONJ
m-1112	3145	23	exists	exist	VERB
m-1112	3145	24	,	,	PUNCT
m-1112	3145	25	𝐄	𝐄	NOUN
m-1112	3145	26	𝐯𝐊	𝐯𝐊	VERB
m-1112	3145	27	=	=	NOUN
m-1112	3145	28	h	h	NOUN
m-1112	3145	29	𝐟𝐯	𝐟𝐯	NOUN
m-1112	3145	30	=	=	PUNCT
m-1112	3145	31	6,62607.10−34j	6,62607.10−34j	NUM
m-1112	3145	32	s.	s.	PROPN
m-1112	3145	33	[	[	PUNCT
m-1112	3145	34	5,347.1030	5,347.1030	NUM
m-1112	3145	35	]	]	PUNCT
m-1112	3145	36	/(1,6022.10−19	/(1,6022.10−19	PUNCT
m-1112	3145	37	ev	ev	X
m-1112	3145	38	)	)	PUNCT
m-1112	3145	39	=	=	SYM
m-1112	3145	40	2,2114518.𝟏𝟎	2,2114518.𝟏𝟎	NUM
m-1112	3145	41	𝟏𝟒ev	𝟏𝟒ev	NOUN
m-1112	3145	42	using	use	VERB
m-1112	3145	43	𝐄	𝐄	NOUN
m-1112	3145	44	𝐯𝐊	𝐯𝐊	VERB
m-1112	3145	45	=	=	PUNCT
m-1112	3145	46	𝐤	𝐤	X
m-1112	3145	47	𝐫	𝐫	PROPN
m-1112	3145	48	+	+	CCONJ
m-1112	3145	49	𝒄𝐒	𝒄𝐒	NOUN
m-1112	3145	50	𝟐	𝟐	NUM
m-1112	3145	51	𝟐𝐦.𝐫𝟐	𝟐𝐦.𝐫𝟐	NOUN
m-1112	3145	52	=	=	SYM
m-1112	3145	53	36.10−20	36.10−20	NUM
m-1112	3145	54	7,10−21	7,10−21	NUM
m-1112	3145	55	+	+	CCONJ
m-1112	3145	56	3.108(5,691952.10−34)²	3.108(5,691952.10−34)²	NUM
m-1112	3145	57	2.3,922.10−36[7,0.10−21]²	2.3,922.10−36[7,0.10−21]²	NUM
m-1112	3145	58	=	=	SYM
m-1112	3145	59	51,428	51,428	NUM
m-1112	3145	60	ev+	ev+	NOUN
m-1112	3145	61	2,528774.1017ev	2,528774.1017ev	NUM
m-1112	3145	62	=	=	SYM
m-1112	3145	63	252,8774	252,8774	NUM
m-1112	3145	64	,	,	PUNCT
m-1112	3145	65	[	[	X
m-1112	3145	66	1015	1015	NUM
m-1112	3145	67	]	]	PUNCT
m-1112	3145	68	tev	tev	PROPN
m-1112	3145	69	→	→	PUNCT
m-1112	3145	70	the	the	DET
m-1112	3145	71	total	total	ADJ
m-1112	3145	72	energy	energy	NOUN
m-1112	3145	73	of	of	ADP
m-1112	3145	74	the	the	DET
m-1112	3145	75	sun	sun	NOUN
m-1112	3145	76	striking	strike	VERB
m-1112	3145	77	earth	earth	NOUN
m-1112	3145	78	-	-	PUNCT
m-1112	3145	79	face	face	NOUN
m-1112	3145	80	per	per	ADP
m-1112	3145	81	second	second	NOUN
m-1112	3145	82	.	.	PUNCT
m-1112	3146	1	2	2	NUM
m-1112	3146	2	…	…	PUNCT
m-1112	3146	3	electron	electron	NOUN
m-1112	3146	4	,	,	PUNCT
m-1112	3146	5	e	e	X
m-1112	3146	6	,	,	PUNCT
m-1112	3146	7	me	i	PRON
m-1112	3146	8	=	=	SYM
m-1112	3146	9	0	0	NUM
m-1112	3146	10	,	,	PUNCT
m-1112	3146	11	511mev	511mev	NUM
m-1112	3146	12	=	=	SYM
m-1112	3146	13	0	0	NUM
m-1112	3146	14	,	,	PUNCT
m-1112	3146	15	511.10−5	511.10−5	NUM
m-1112	3146	16	ev	ev	X
m-1112	3146	17	.	.	PUNCT
m-1112	3147	1	[	[	X
m-1112	3147	2	1,80	1,80	X
m-1112	3147	3	.	.	PUNCT
m-1112	3148	1	10−27	10−27	NUM
m-1112	3148	2	]	]	X
m-1112	3149	1	=	=	PUNCT
m-1112	3150	1	9,198.10−31	9,198.10−31	NUM
m-1112	3150	2	kg	kg	INTJ
m-1112	3150	3	𝐚𝐞	𝐚𝐞	NOUN
m-1112	3151	1	=	=	NOUN
m-1112	3152	1	5,0.10−18	5,0.10−18	NUM
m-1112	3152	2	m	m	VERB
m-1112	3152	3	,	,	PUNCT
m-1112	3152	4	charge	charge	VERB
m-1112	3152	5	𝐂	𝐂	PROPN
m-1112	3152	6	𝐞	𝐞	NOUN
m-1112	3152	7	=	=	NUM
m-1112	3152	8	1,602.10−19	1,602.10−19	NUM
m-1112	3152	9	c	c	NOUN
m-1112	3152	10	,	,	PUNCT
m-1112	3152	11	spin	spin	VERB
m-1112	3152	12	𝐒𝒆	𝐒𝒆	NOUN
m-1112	3152	13	=	=	SYM
m-1112	3152	14	𝐒	𝐒	PROPN
m-1112	3152	15	2	2	NUM
m-1112	3153	1	=	=	VERB
m-1112	3153	2	2,845976.10−34{kg	2,845976.10−34{kg	NUM
m-1112	3153	3	/	/	SYM
m-1112	3153	4	m	m	PROPN
m-1112	3153	5	/	/	SYM
m-1112	3153	6	s	s	PART
m-1112	3153	7	}	}	PUNCT
m-1112	3153	8	,	,	PUNCT
m-1112	3153	9	from	from	ADP
m-1112	3153	10	cave	cave	NOUN
m-1112	3153	11	r	r	NOUN
m-1112	3153	12	=	=	PUNCT
m-1112	3153	13	5.10−18	5.10−18	NUM
m-1112	3153	14	m	m	VERB
m-1112	3153	15	then	then	ADV
m-1112	3153	16	f	f	PROPN
m-1112	3154	1	=	=	PUNCT
m-1112	3154	2	√	√	PROPN
m-1112	3154	3	g	g	NOUN
m-1112	3154	4	a³	a³	PRON
m-1112	3154	5	2	2	NUM
m-1112	3154	6	=	=	SYM
m-1112	3154	7	√	√	NUM
m-1112	3154	8	9,8078	9,8078	NOUN
m-1112	3154	9	(	(	PUNCT
m-1112	3154	10	5.10−18)³	5.10−18)³	NUM
m-1112	3154	11	2	2	NUM
m-1112	3154	12	=	=	SYM
m-1112	3154	13	2,801114.10	2,801114.10	NUM
m-1112	3154	14	26	26	NUM
m-1112	3154	15	h	h	NOUN
m-1112	3154	16	,	,	PUNCT
m-1112	3154	17	and	and	CCONJ
m-1112	3154	18	by	by	ADP
m-1112	3154	19	using	use	VERB
m-1112	3154	20	𝐄	𝐄	NOUN
m-1112	3154	21	𝐞𝐊	𝐞𝐊	NOUN
m-1112	3154	22	=	=	SYM
m-1112	3154	23	𝐤	𝐤	SYM
m-1112	3154	24	𝐫	𝐫	PROPN
m-1112	3155	1	+	+	CCONJ
m-1112	3155	2	𝒄𝐒	𝒄𝐒	NOUN
m-1112	3155	3	𝟐	𝟐	NUM
m-1112	3155	4	𝟐𝐦.𝐫𝟐	𝟐𝐦.𝐫𝟐	NOUN
m-1112	3155	5	=	=	SYM
m-1112	3155	6	36.10−20	36.10−20	NUM
m-1112	3155	7	7,10−18	7,10−18	NUM
m-1112	3156	1	+	+	CCONJ
m-1112	3156	2	3.108(5,691952.10−34)²	3.108(5,691952.10−34)²	NUM
m-1112	3156	3	2.9,198.10−34[5.10−18]²	2.9,198.10−34[5.10−18]²	NUM
m-1112	3156	4	=	=	NOUN
m-1112	3156	5	51,428	51,428	NUM
m-1112	3156	6	ev	ev	X
m-1112	3157	1	+	+	CCONJ
m-1112	3157	2	2,111843.1010j	2,111843.1010j	ADJ
m-1112	3157	3	=	=	SYM
m-1112	3157	4	51,43	51,43	NUM
m-1112	3157	5	ev+	ev+	NOUN
m-1112	3158	1	1,32	1,32	PROPN
m-1112	3158	2	.1029	.1029	PROPN
m-1112	3158	3	ev	ev	PROPN
m-1112	3158	4	→	→	PUNCT
m-1112	3158	5	the	the	DET
m-1112	3158	6	energy	energy	NOUN
m-1112	3158	7	of	of	ADP
m-1112	3158	8	133	133	NUM
m-1112	3158	9	gr	gr	NOUN
m-1112	3158	10	to	to	PART
m-1112	3158	11	fall	fall	VERB
m-1112	3158	12	1	1	NUM
m-1112	3158	13	meter	meter	NOUN
m-1112	3158	14	against	against	ADP
m-1112	3158	15	gravity	gravity	NOUN
m-1112	3158	16	.	.	PUNCT
m-1112	3159	1	remarks	remark	NOUN
m-1112	3159	2	:	:	PUNCT
m-1112	3159	3	1	1	X
m-1112	3159	4	..	..	PUNCT
m-1112	3159	5	gravitational	gravitational	ADJ
m-1112	3159	6	force	force	NOUN
m-1112	3159	7	→	→	PUNCT
m-1112	3159	8	g	g	PROPN
m-1112	3159	9	≡	≡	PROPN
m-1112	3159	10	σ	σ	PROPN
m-1112	3159	11	a	a	DET
m-1112	3159	12	≡	≡	PROPN
m-1112	3159	13	[	[	PUNCT
m-1112	3159	14	2πrf	2πrf	NUM
m-1112	3159	15	φ	φ	X
m-1112	3159	16	]	]	PUNCT
m-1112	3159	17	a	a	DET
m-1112	3159	18	≡	≡	PROPN
m-1112	3159	19	v̅	v̅	PROPN
m-1112	3159	20	[	[	PUNCT
m-1112	3159	21	𝐀	𝐀	PROPN
m-1112	3159	22	𝚽	𝚽	PROPN
m-1112	3159	23	]	]	PUNCT
m-1112	3159	24	≡	≡	PROPN
m-1112	3159	25	σ.φ³	σ.φ³	ADJ
m-1112	3159	26	≡	≡	PROPN
m-1112	3159	27	φ	φ	X
m-1112	3159	28	²	²	NUM
m-1112	3159	29	.	.	PUNCT
m-1112	3160	1	[	[	X
m-1112	3160	2	{	{	PUNCT
m-1112	3160	3	σ	σ	PROPN
m-1112	3160	4	φ	φ	PROPN
m-1112	3160	5	}	}	PUNCT
m-1112	3160	6	]	]	PUNCT
m-1112	3160	7	≡	≡	PROPN
m-1112	3160	8	g	g	PROPN
m-1112	3160	9	≡	≡	PROPN
m-1112	3160	10	φ²	φ²	PROPN
m-1112	3160	11	.	.	PUNCT
m-1112	3161	1	[	[	X
m-1112	3161	2	{	{	PUNCT
m-1112	3161	3	σ	σ	PROPN
m-1112	3161	4	φ}≡	φ}≡	PROPN
m-1112	3161	5	2πfp	2πfp	PROPN
m-1112	3161	6	r	r	NOUN
m-1112	3161	7	≡	≡	PROPN
m-1112	3161	8	w	w	PROPN
m-1112	3161	9	r	r	PROPN
m-1112	3161	10	≡	≡	PROPN
m-1112	3161	11	v̅	v̅	PROPN
m-1112	3161	12	≡	≡	PROPN
m-1112	3161	13	m	m	VERB
m-1112	3161	14	g	g	NOUN
m-1112	3161	15	=	=	SYM
m-1112	3161	16	c̅	c̅	PROPN
m-1112	3161	17	=	=	SYM
m-1112	3161	18	2.b	2.b	NUM
m-1112	3161	19	πr³	πr³	NOUN
m-1112	3161	20	]	]	PUNCT
m-1112	3161	21	→	→	PUNCT
m-1112	3161	22	i.e.	i.e.	X
m-1112	3161	23	g	g	PROPN
m-1112	3161	24	is	be	AUX
m-1112	3161	25	related	relate	VERB
m-1112	3161	26	to	to	ADP
m-1112	3161	27	→	→	SYM
m-1112	3161	28	motion	motion	NOUN
m-1112	3161	29	≡	≡	PROPN
m-1112	3161	30	work	work	NOUN
m-1112	3161	31	w	w	NOUN
m-1112	3161	32	,	,	PUNCT
m-1112	3161	33	spaces	space	NOUN
m-1112	3161	34	r	r	NOUN
m-1112	3161	35	,	,	PUNCT
m-1112	3161	36	anti	anti	ADJ
m-1112	3161	37	-	-	ADJ
m-1112	3161	38	spaces	spaces	ADJ
m-1112	3161	39	1	1	NUM
m-1112	3161	40	/	/	SYM
m-1112	3161	41	r	r	NOUN
m-1112	3161	42	,	,	PUNCT
m-1112	3161	43	stresses	stress	VERB
m-1112	3161	44	σ	σ	PROPN
m-1112	3161	45	,	,	PUNCT
m-1112	3161	46	areas	area	NOUN
m-1112	3161	47	a	a	PRON
m-1112	3161	48	,	,	PUNCT
m-1112	3161	49	caves	cave	VERB
m-1112	3161	50	a	a	DET
m-1112	3161	51	,	,	PUNCT
m-1112	3161	52	→	→	SYM
m-1112	3161	53	periods	periods	ADP
m-1112	3161	54	t	t	NOUN
m-1112	3161	55	,	,	PUNCT
m-1112	3161	56	frequencies	frequency	NOUN
m-1112	3161	57	f	f	PROPN
m-1112	3161	58	,	,	PUNCT
m-1112	3161	59	angular	angular	ADJ
m-1112	3161	60	-	-	PUNCT
m-1112	3161	61	waves	wave	NOUN
m-1112	3161	62	w	w	NOUN
m-1112	3161	63	,	,	PUNCT
m-1112	3161	64	angular	angular	ADJ
m-1112	3161	65	-	-	PUNCT
m-1112	3161	66	momentum	momentum	NOUN
m-1112	3161	67	b	b	NOUN
m-1112	3161	68	,	,	PUNCT
m-1112	3161	69	→	→	SYM
m-1112	3161	70	spin	spin	NOUN
m-1112	3161	71	b	b	PROPN
m-1112	3161	72	≡	≡	PROPN
m-1112	3161	73	s	s	PART
m-1112	3161	74	,	,	PUNCT
m-1112	3161	75	velocities	velocity	NOUN
m-1112	3161	76	v	v	ADP
m-1112	3161	77	,	,	PUNCT
m-1112	3161	78	light	light	ADJ
m-1112	3161	79	-	-	PUNCT
m-1112	3161	80	velocity	velocity	NOUN
m-1112	3161	81	c	c	NOUN
m-1112	3161	82	,	,	PUNCT
m-1112	3161	83	impedances	impedance	VERB
m-1112	3161	84	zn	zn	PROPN
m-1112	3161	85	,	,	PUNCT
m-1112	3161	86	masses	mass	VERB
m-1112	3161	87	m	m	VERB
m-1112	3161	88	,	,	PUNCT
m-1112	3161	89	→	→	SYM
m-1112	3161	90	gravity	gravity	NOUN
m-1112	3161	91	g̅	g̅	NOUN
m-1112	3161	92	,	,	PUNCT
m-1112	3162	1	charges	charge	NOUN
m-1112	3162	2	,	,	PUNCT
m-1112	3162	3	q̅	q̅	PROPN
m-1112	3162	4	,	,	PUNCT
m-1112	3162	5	electromagnetic	electromagnetic	ADJ
m-1112	3162	6	–	–	PUNCT
m-1112	3162	7	fields	field	NOUN
m-1112	3162	8	,	,	PUNCT
m-1112	3162	9	e̅	e̅	PRON
m-1112	3162	10	,	,	PUNCT
m-1112	3162	11	m̅	m̅	PROPN
m-1112	3162	12	,	,	PUNCT
m-1112	3162	13	hydrogen	hydrogen	NOUN
m-1112	3162	14	h	h	NOUN
m-1112	3162	15	,	,	PUNCT
m-1112	3162	16	→	→	SYM
m-1112	3162	17	atoms	atom	NOUN
m-1112	3162	18	,	,	PUNCT
m-1112	3162	19	molecules	molecule	NOUN
m-1112	3162	20	,	,	PUNCT
m-1112	3162	21	golden	golden	ADJ
m-1112	3162	22	-	-	PUNCT
m-1112	3162	23	ratio	ratio	NOUN
m-1112	3162	24	φ	φ	PROPN
m-1112	3162	25	,	,	PUNCT
m-1112	3162	26	i.e.	i.e.	X
m-1112	3162	27	all	all	ADV
m-1112	3162	28	-	-	PUNCT
m-1112	3162	29	universe	universe	NOUN
m-1112	3162	30	.	.	PUNCT
m-1112	3163	1	markos	markos	PROPN
m-1112	3163	2	9/4/2020	9/4/2020	PROPN
m-1112	3163	3	.	.	PUNCT
m-1112	3164	1	by	by	ADP
m-1112	3164	2	sweeping	sweep	VERB
m-1112	3164	3	the	the	DET
m-1112	3164	4	φ	φ	PROPN
m-1112	3164	5	surface	surface	NOUN
m-1112	3164	6	through	through	ADP
m-1112	3164	7	stresses	stress	NOUN
m-1112	3164	8	σ	σ	PROPN
m-1112	3164	9	≡	≡	PROPN
m-1112	3164	10	[	[	PUNCT
m-1112	3164	11	2πrf	2πrf	NUM
m-1112	3164	12	φ	φ	NUM
m-1112	3164	13	]	]	PUNCT
m-1112	3164	14	,	,	PUNCT
m-1112	3164	15	and	and	CCONJ
m-1112	3164	16	scanning	scan	VERB
m-1112	3164	17	frequencies	frequency	NOUN
m-1112	3164	18	f	f	NOUN
m-1112	3164	19	,	,	PUNCT
m-1112	3164	20	explanation	explanation	NOUN
m-1112	3164	21	:	:	PUNCT
m-1112	3164	22	the	the	DET
m-1112	3164	23	action	action	NOUN
m-1112	3164	24	-	-	PUNCT
m-1112	3164	25	spaces	space	NOUN
m-1112	3164	26	≡	≡	PROPN
m-1112	3164	27	the	the	DET
m-1112	3164	28	infinite	infinite	ADJ
m-1112	3164	29	quaternion	quaternion	NOUN
m-1112	3164	30	monads	monad	NOUN
m-1112	3164	31	→	→	SYM
m-1112	3164	32	�	�	NOUN
m-1112	3164	33	̅	̅	NOUN
m-1112	3164	34	�	�	PROPN
m-1112	3164	35	≡	≡	PROPN
m-1112	3164	36	(	(	PUNCT
m-1112	3164	37	s	s	NOUN
m-1112	3164	38	+	+	NUM
m-1112	3164	39	v̅.i	v̅.i	X
m-1112	3164	40	)	)	PUNCT
m-1112	3164	41	≡	≡	PROPN
m-1112	3164	42	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	3164	43	̅̅	̅̅	PROPN
m-1112	3164	44	≡	≡	PROPN
m-1112	3164	45	≡	≡	PROPN
m-1112	3164	46	√s2	√s2	PROPN
m-1112	3165	1	+	+	PUNCT
m-1112	3165	2	[	[	PUNCT
m-1112	3165	3	v̅.	v̅.	NOUN
m-1112	3165	4	i	i	X
m-1112	3165	5	]	]	X
m-1112	3165	6	²	²	X
m-1112	3165	7	]	]	PUNCT
m-1112	3165	8	,	,	PUNCT
m-1112	3165	9	or	or	CCONJ
m-1112	3165	10	�	�	PROPN
m-1112	3165	11	̅	̅	NOUN
m-1112	3165	12	�	�	NOUN
m-1112	3165	13	≡	≡	PROPN
m-1112	3165	14	x	x	PUNCT
m-1112	3166	1	+	+	CCONJ
m-1112	3166	2	i	i	PRON
m-1112	3166	3	.	.	PUNCT
m-1112	3167	1	y	y	PROPN
m-1112	3167	2	≡	≡	PROPN
m-1112	3167	3	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	3167	4	̅̅	̅̅	PROPN
m-1112	3167	5	≡	≡	PROPN
m-1112	3167	6	moduli	modulus	NOUN
m-1112	3167	7	,	,	PUNCT
m-1112	3167	8	r	r	NOUN
m-1112	3167	9	,	,	PUNCT
m-1112	3167	10	is	be	AUX
m-1112	3167	11	their	their	PRON
m-1112	3167	12	magnitude	magnitude	NOUN
m-1112	3167	13	[	[	PUNCT
m-1112	3167	14	r	r	NOUN
m-1112	3167	15	=	=	NOUN
m-1112	3167	16	|	|	ADV
m-1112	3167	17	r	r	NOUN
m-1112	3167	18	|	|	NOUN
m-1112	3167	19	=	=	PUNCT
m-1112	3168	1	√	√	PROPN
m-1112	3169	1	x2	x2	NOUN
m-1112	3170	1	+	+	CCONJ
m-1112	3171	1	y2	y2	NOUN
m-1112	3171	2	]	]	PUNCT
m-1112	3171	3	,	,	PUNCT
m-1112	3171	4	on	on	ADP
m-1112	3171	5	unit	unit	NOUN
m-1112	3171	6	-	-	PUNCT
m-1112	3171	7	diameter	diameter	NOUN
m-1112	3171	8	ab̅̅	ab̅̅	PROPN
m-1112	3171	9	̅̅	̅̅	PROPN
m-1112	3171	10	.	.	PUNCT
m-1112	3172	1	the	the	DET
m-1112	3172	2	[	[	X
m-1112	3172	3	qmas	qmas	NOUN
m-1112	3172	4	]	]	PUNCT
m-1112	3172	5	.	.	PUNCT
m-1112	3173	1	for	for	ADP
m-1112	3173	2	quaternion	quaternion	NOUN
m-1112	3173	3	|v̅|	|v̅|	NOUN
m-1112	3173	4	=	=	SYM
m-1112	3173	5	s	s	VERB
m-1112	3173	6	breakages	breakage	VERB
m-1112	3173	7	𝐳	𝐳	X
m-1112	3173	8	*	*	PUNCT
m-1112	3173	9	𝐳	𝐳	X
m-1112	3173	10	=	=	X
m-1112	3173	11	(	(	PUNCT
m-1112	3173	12	s	s	NOUN
m-1112	3173	13	+	+	NUM
m-1112	3173	14	v̅.i	v̅.i	X
m-1112	3173	15	)	)	PUNCT
m-1112	3173	16	²	²	PROPN
m-1112	3173	17	=	=	PUNCT
m-1112	3173	18	s²	s²	NOUN
m-1112	3174	1	+	+	PROPN
m-1112	3174	2	[	[	X
m-1112	3174	3	v̅]²	v̅]²	X
m-1112	3174	4	+2.sv̅.i	+2.sv̅.i	ADJ
m-1112	3174	5	=	=	SYM
m-1112	3174	6	s²	s²	PROPN
m-1112	3174	7	–	–	PUNCT
m-1112	3174	8	v̅	v̅	NOUN
m-1112	3174	9	²	²	NUM
m-1112	3174	10	±	±	NUM
m-1112	3174	11	2.s	2.s	NUM
m-1112	3174	12	v̅	v̅	NOUN
m-1112	3175	1	=	=	NOUN
m-1112	3175	2	|s|²	|s|²	PROPN
m-1112	3175	3	|	|	NOUN
m-1112	3175	4	�	�	NOUN
m-1112	3175	5	̅	̅	NOUN
m-1112	3175	6	�	�	PROPN
m-1112	3175	7	|²	|²	NUM
m-1112	3175	8	±	±	NUM
m-1112	3175	9	2.|s|.|s̅|	2.|s|.|s̅|	NUM
m-1112	3175	10	,	,	PUNCT
m-1112	3175	11	i.e.	i.e.	X
m-1112	3175	12	in	in	ADP
m-1112	3175	13	figure	figure	NOUN
m-1112	3175	14	-3	-3	PUNCT
m-1112	3175	15	the	the	DET
m-1112	3175	16	vector	vector	NOUN
m-1112	3175	17	of	of	ADP
m-1112	3175	18	amplitude	amplitude	NOUN
m-1112	3175	19	is	be	AUX
m-1112	3175	20	quaternion	quaternion	ADJ
m-1112	3175	21	�	�	NOUN
m-1112	3175	22	̅	̅	NOUN
m-1112	3175	23	�	�	NOUN
m-1112	3175	24	≡	≡	PROPN
m-1112	3175	25	x	x	PUNCT
m-1112	3176	1	+	+	CCONJ
m-1112	3176	2	i	i	PRON
m-1112	3176	3	.	.	PUNCT
m-1112	3177	1	y	y	PROPN
m-1112	3177	2	,	,	PUNCT
m-1112	3177	3	with	with	ADP
m-1112	3177	4	vector	vector	NOUN
m-1112	3177	5	�	�	PROPN
m-1112	3177	6	̅	̅	NOUN
m-1112	3177	7	�	�	PROPN
m-1112	3177	8	,	,	PUNCT
m-1112	3177	9	to	to	PART
m-1112	3177	10	be	be	AUX
m-1112	3177	11	from	from	ADP
m-1112	3177	12	definition	definition	NOUN
m-1112	3177	13	of	of	ADP
m-1112	3177	14	the	the	DET
m-1112	3177	15	complex	complex	ADJ
m-1112	3177	16	vector	vector	NOUN
m-1112	3177	17	space	space	NOUN
m-1112	3177	18	,	,	PUNCT
m-1112	3177	19	the	the	DET
m-1112	3177	20	set	set	NOUN
m-1112	3177	21	of	of	ADP
m-1112	3177	22	vectors	vector	NOUN
m-1112	3177	23	of	of	ADP
m-1112	3177	24	length	length	NOUN
m-1112	3177	25	(	(	PUNCT
m-1112	3177	26	the	the	DET
m-1112	3177	27	n	n	NOUN
m-1112	3177	28	vertices	vertex	NOUN
m-1112	3177	29	which	which	PRON
m-1112	3177	30	form	form	VERB
m-1112	3177	31	the	the	DET
m-1112	3177	32	n	n	NUM
m-1112	3177	33	polygon	polygon	NOUN
m-1112	3177	34	sides	side	NOUN
m-1112	3177	35	,	,	PUNCT
m-1112	3177	36	or	or	CCONJ
m-1112	3177	37	the	the	DET
m-1112	3177	38	norm	norm	NOUN
m-1112	3177	39	of	of	ADP
m-1112	3177	40	the	the	DET
m-1112	3177	41	complex	complex	ADJ
m-1112	3177	42	vectors	vector	NOUN
m-1112	3177	43	)	)	PUNCT
m-1112	3178	1	a	a	X
m-1112	3178	2	...	...	PUNCT
m-1112	3178	3	the	the	DET
m-1112	3178	4	4	4	NUM
m-1112	3178	5	-	-	PUNCT
m-1112	3178	6	geometrical	geometrical	ADJ
m-1112	3178	7	spaces	space	NOUN
m-1112	3178	8	,	,	PUNCT
m-1112	3178	9	[	[	PUNCT
m-1112	3178	10	space	space	NOUN
m-1112	3178	11	,	,	PUNCT
m-1112	3178	12	anti	anti	ADJ
m-1112	3178	13	-	-	ADJ
m-1112	3178	14	space	space	ADJ
m-1112	3178	15	,	,	PUNCT
m-1112	3178	16	neutral	neutral	ADJ
m-1112	3178	17	-	-	PUNCT
m-1112	3178	18	space	space	NOUN
m-1112	3178	19	,	,	PUNCT
m-1112	3178	20	sub	sub	NOUN
m-1112	3178	21	-	-	NOUN
m-1112	3178	22	space	space	NOUN
m-1112	3178	23	]	]	PUNCT
m-1112	3178	24	consist	consist	NOUN
m-1112	3178	25	→	→	PUNCT
m-1112	3178	26	the	the	DET
m-1112	3178	27	geometrical	geometrical	ADJ
m-1112	3178	28	mould	mould	NOUN
m-1112	3178	29	of	of	ADP
m-1112	3178	30	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	3178	31	̅̅	̅̅	PROPN
m-1112	3178	32	monad	monad	PROPN
m-1112	3178	33	≡	≡	PROPN
m-1112	3179	1	[	[	X
m-1112	3179	2	pm-2r	pm-2r	NOUN
m-1112	3179	3	-	-	PUNCT
m-1112	3179	4	m	m	NOUN
m-1112	3179	5	]	]	X
m-1112	3179	6	←	←	PROPN
m-1112	3179	7	b	b	X
m-1112	3179	8	...	...	PUNCT
m-1112	3179	9	the	the	DET
m-1112	3179	10	vectors	vector	NOUN
m-1112	3179	11	of	of	ADP
m-1112	3179	12	amplitude	amplitude	NOUN
m-1112	3179	13	z	z	NOUN
m-1112	3179	14	=	=	SYM
m-1112	3179	15	2r	2r	NUM
m-1112	3179	16	,	,	PUNCT
m-1112	3179	17	on	on	ADP
m-1112	3179	18	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	3179	19	̅̅	̅̅	PROPN
m-1112	3179	20	monad	monad	PROPN
m-1112	3179	21	,	,	PUNCT
m-1112	3179	22	consist	consist	VERB
m-1112	3179	23	the	the	DET
m-1112	3179	24	energy	energy	NOUN
m-1112	3179	25	-	-	PUNCT
m-1112	3179	26	mould	mould	NOUN
m-1112	3179	27	.	.	PUNCT
m-1112	3180	1	of	of	ADP
m-1112	3180	2	2r	2r	NUM
m-1112	3180	3	-	-	PUNCT
m-1112	3180	4	form	form	NOUN
m-1112	3180	5	.the	.the	DET
m-1112	3180	6	physical	physical	ADJ
m-1112	3180	7	-mechanisms	-mechanism	NOUN
m-1112	3180	8	→	→	PUNCT
m-1112	3180	9	[	[	PUNCT
m-1112	3180	10	physical	physical	ADJ
m-1112	3180	11	mould	mould	NOUN
m-1112	3180	12	of	of	ADP
m-1112	3180	13	2rmonad	2rmonad	NUM
m-1112	3180	14	]	]	PUNCT
m-1112	3180	15	≡	≡	PROPN
m-1112	3181	1	[	[	X
m-1112	3181	2	gm	gm	PROPN
m-1112	3181	3	-	-	PUNCT
m-1112	3181	4	ab	ab	PROPN
m-1112	3181	5	-	-	PUNCT
m-1112	3181	6	m	m	PROPN
m-1112	3181	7	]	]	X
m-1112	3181	8	←	←	PROPN
m-1112	3181	9	are	be	AUX
m-1112	3181	10	such	such	ADJ
m-1112	3181	11	and	and	CCONJ
m-1112	3181	12	dependent	dependent	ADJ
m-1112	3181	13	on	on	ADP
m-1112	3181	14	the	the	DET
m-1112	3181	15	n	n	ADJ
m-1112	3181	16	number	number	NOUN
m-1112	3181	17	of	of	ADP
m-1112	3181	18	accessories	accessory	NOUN
m-1112	3181	19	they	they	PRON
m-1112	3181	20	use	use	VERB
m-1112	3181	21	.	.	PUNCT
m-1112	3182	1	ijo	ijo	PROPN
m-1112	3182	2	international	international	PROPN
m-1112	3182	3	journal	journal	PROPN
m-1112	3182	4	of	of	ADP
m-1112	3182	5	mathematics	mathematics	PROPN
m-1112	3182	6	(	(	PUNCT
m-1112	3182	7	issn	issn	PROPN
m-1112	3182	8	:	:	PUNCT
m-1112	3182	9	2992	2992	NUM
m-1112	3182	10	-	-	SYM
m-1112	3182	11	4421	4421	NUM
m-1112	3182	12	)	)	PUNCT
m-1112	3182	13	volume	volume	NOUN
m-1112	3182	14	08	08	NUM
m-1112	3183	1	|	|	ADV
m-1112	3183	2	issue	issue	NOUN
m-1112	3183	3	08	08	NUM
m-1112	3184	1	|	|	ADV
m-1112	3184	2	august	august	PROPN
m-1112	3184	3	2025	2025	NUM
m-1112	3184	4	|	|	ADV
m-1112	3184	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3184	6	ijo	ijo	PROPN
m-1112	3184	7	journals	journal	NOUN
m-1112	3184	8	113	113	NUM
m-1112	3184	9	the	the	DET
m-1112	3184	10	fundamental	fundamental	ADJ
m-1112	3184	11	particles	particle	NOUN
m-1112	3184	12	origination	origination	NOUN
m-1112	3184	13	mechanism	mechanism	NOUN
m-1112	3184	14	in	in	ADP
m-1112	3184	15	mfmf	mfmf	PROPN
m-1112	3184	16	pns	pns	PROPN
m-1112	3184	17	caves	cave	NOUN
m-1112	3184	18	.	.	PUNCT
m-1112	3185	1	a	a	PRON
m-1112	3185	2	…	…	PUNCT
m-1112	3185	3	the	the	DET
m-1112	3185	4	gravity	gravity	NOUN
m-1112	3185	5	force	force	NOUN
m-1112	3185	6	g	g	PROPN
m-1112	3185	7	≡	≡	PROPN
m-1112	3185	8	motion	motion	NOUN
m-1112	3185	9	≡	≡	PROPN
m-1112	3185	10	σ.𝚽³	σ.𝚽³	NOUN
m-1112	3185	11	,	,	PUNCT
m-1112	3185	12	exists	exist	VERB
m-1112	3185	13	without	without	ADP
m-1112	3185	14	mass	mass	NOUN
m-1112	3185	15	and	and	CCONJ
m-1112	3185	16	is	be	AUX
m-1112	3185	17	quantized	quantize	VERB
m-1112	3185	18	spread	spread	VERB
m-1112	3185	19	in{space	in{space	NOUN
m-1112	3185	20	and	and	CCONJ
m-1112	3185	21	anti	anti	ADJ
m-1112	3185	22	-	-	ADJ
m-1112	3185	23	space	space	NOUN
m-1112	3185	24	or	or	CCONJ
m-1112	3185	25	≡	≡	PROPN
m-1112	3185	26	qua	qua	PROPN
m-1112	3185	27	≡	≡	PROPN
m-1112	3185	28	{	{	PUNCT
m-1112	3185	29	is	be	AUX
m-1112	3185	30	the	the	DET
m-1112	3185	31	quantized	quantize	VERB
m-1112	3185	32	-	-	PUNCT
m-1112	3185	33	units	unit	NOUN
m-1112	3185	34	in	in	ADP
m-1112	3185	35	-	-	PUNCT
m-1112	3185	36	area	area	NOUN
m-1112	3185	37	of	of	ADP
m-1112	3185	38	space	space	NOUN
m-1112	3185	39	and	and	CCONJ
m-1112	3185	40	anti	anti	ADJ
m-1112	3185	41	-	-	NOUN
m-1112	3185	42	space	space	NOUN
m-1112	3185	43	}	}	PUNCT
m-1112	3185	44	,	,	PUNCT
m-1112	3185	45	and	and	CCONJ
m-1112	3185	46	as	as	ADP
m-1112	3185	47	a	a	DET
m-1112	3185	48	mould	mould	NOUN
m-1112	3185	49	𝚽	𝚽	PRON
m-1112	3185	50	golden	golden	ADJ
m-1112	3185	51	-	-	PUNCT
m-1112	3185	52	ratio	ratio	NOUN
m-1112	3185	53	,	,	PUNCT
m-1112	3185	54	exists	exist	VERB
m-1112	3185	55	as	as	ADP
m-1112	3185	56	impedance	impedance	NOUN
m-1112	3185	57	b.	b.	NOUN
m-1112	3185	58	placing	placing	NOUN
m-1112	3185	59	[	[	PUNCT
m-1112	3185	60	physical	physical	ADJ
m-1112	3185	61	mould	mould	NOUN
m-1112	3185	62	of	of	ADP
m-1112	3185	63	2rmonad	2rmonad	NUM
m-1112	3185	64	]	]	PUNCT
m-1112	3185	65	on	on	ADP
m-1112	3185	66	[	[	PUNCT
m-1112	3185	67	geometrical	geometrical	ADJ
m-1112	3185	68	mould	mould	NOUN
m-1112	3185	69	of	of	ADP
m-1112	3185	70	𝐀𝐁̅̅	𝐀𝐁̅̅	PROPN
m-1112	3185	71	̅̅	̅̅	PROPN
m-1112	3185	72	monad	monad	PROPN
m-1112	3185	73	]	]	X
m-1112	3185	74	[	[	PUNCT
m-1112	3185	75	pm-2r	pm-2r	NOUN
m-1112	3185	76	-	-	PUNCT
m-1112	3185	77	m	m	NOUN
m-1112	3185	78	]	]	PUNCT
m-1112	3186	1	→	→	SYM
m-1112	3186	2	⇅	⇅	PROPN
m-1112	3186	3	←	←	PROPN
m-1112	3186	4	[	[	PUNCT
m-1112	3186	5	gm	gm	PROPN
m-1112	3186	6	-	-	PUNCT
m-1112	3186	7	ab	ab	PROPN
m-1112	3186	8	-	-	PROPN
m-1112	3186	9	m	m	VERB
m-1112	3186	10	]	]	PUNCT
m-1112	3186	11	then	then	ADV
m-1112	3186	12	→	→	PUNCT
m-1112	3186	13	gravitational	gravitational	ADJ
m-1112	3186	14	-	-	PUNCT
m-1112	3186	15	force	force	NOUN
m-1112	3186	16	g	g	PROPN
m-1112	3186	17	≡	≡	PROPN
m-1112	3186	18	[	[	PUNCT
m-1112	3186	19	σ	σ	X
m-1112	3186	20	=	=	SYM
m-1112	3186	21	n	n	PROPN
m-1112	3186	22	.	.	PUNCT
m-1112	3187	1	h	h	NOUN
m-1112	3187	2	]	]	PUNCT
m-1112	3187	3	,	,	PUNCT
m-1112	3187	4	and	and	CCONJ
m-1112	3187	5	n	n	CCONJ
m-1112	3187	6	-	-	PUNCT
m-1112	3187	7	na	na	NOUN
m-1112	3187	8	=	=	SYM
m-1112	3187	9	1	1	NUM
m-1112	3187	10			NOUN
m-1112	3187	11	creates	create	VERB
m-1112	3187	12	&	&	CCONJ
m-1112	3187	13	constructs	construct	NOUN
m-1112	3187	14	,	,	PUNCT
m-1112	3187	15	figure	figure	NOUN
m-1112	3187	16	-28	-28	PROPN
m-1112	3187	17	:	:	PUNCT
m-1112	3187	18	on	on	ADP
m-1112	3187	19	any	any	DET
m-1112	3187	20	energy	energy	NOUN
m-1112	3187	21	monad	monad	PROPN
m-1112	3187	22	a	a	DET
m-1112	3187	23	↔	↔	PROPN
m-1112	3187	24	b	b	PROPN
m-1112	3187	25	,	,	PUNCT
m-1112	3187	26	exist	exist	VERB
m-1112	3187	27	the	the	DET
m-1112	3187	28	4	4	NUM
m-1112	3187	29	-	-	PUNCT
m-1112	3187	30	primary	primary	ADJ
m-1112	3187	31	spaces	space	NOUN
m-1112	3187	32	which	which	PRON
m-1112	3187	33	are	be	AUX
m-1112	3187	34	the	the	DET
m-1112	3187	35	roots	root	NOUN
m-1112	3187	36	of	of	ADP
m-1112	3187	37	the	the	DET
m-1112	3187	38	nth	nth	NOUN
m-1112	3187	39	degree	degree	NOUN
m-1112	3187	40	polynomial	polynomial	ADJ
m-1112	3187	41	,	,	PUNCT
m-1112	3187	42	becoming	become	VERB
m-1112	3187	43	from	from	ADP
m-1112	3187	44	the	the	DET
m-1112	3187	45	equation	equation	NOUN
m-1112	3187	46	of	of	ADP
m-1112	3187	47	motion	motion	NOUN
m-1112	3187	48	.	.	PUNCT
m-1112	3188	1	f	f	X
m-1112	3188	2	...	...	PUNCT
m-1112	3188	3	references	reference	NOUN
m-1112	3188	4	:	:	PUNCT
m-1112	3188	5	[	[	PUNCT
m-1112	3188	6	1	1	NUM
m-1112	3188	7	]	]	PUNCT
m-1112	3188	8	matrix	matrix	NOUN
m-1112	3188	9	structure	structure	NOUN
m-1112	3188	10	of	of	ADP
m-1112	3188	11	analysis	analysis	NOUN
m-1112	3188	12	by	by	ADP
m-1112	3188	13	j.l.meek	j.l.meek	ADJ
m-1112	3188	14	library	library	NOUN
m-1112	3188	15	of	of	ADP
m-1112	3188	16	congress	congress	PROPN
m-1112	3188	17	catalog	catalog	PROPN
m-1112	3188	18	1971	1971	NUM
m-1112	3188	19	.	.	PUNCT
m-1112	3189	1	[	[	PUNCT
m-1112	3189	2	2	2	NUM
m-1112	3189	3	]	]	PUNCT
m-1112	3189	4	der	der	NOUN
m-1112	3189	5	zweck	zweck	PROPN
m-1112	3189	6	i	i	PRON
m-1112	3189	7	m	m	VERB
m-1112	3189	8	rect	rect	ADJ
m-1112	3189	9	by	by	ADP
m-1112	3189	10	rudolf	rudolf	NOUN
m-1112	3189	11	v.	v.	ADP
m-1112	3189	12	jhering	jhere	VERB
m-1112	3189	13	1935	1935	NUM
m-1112	3189	14	.	.	PUNCT
m-1112	3190	1	[	[	PUNCT
m-1112	3190	2	3	3	X
m-1112	3190	3	]	]	PUNCT
m-1112	3190	4	the	the	DET
m-1112	3190	5	great	great	ADJ
m-1112	3190	6	text	text	NOUN
m-1112	3190	7	of	of	ADP
m-1112	3190	8	j.	j.	PROPN
m-1112	3190	9	l.heisenberg	l.heisenberg	PROPN
m-1112	3190	10	(	(	PUNCT
m-1112	3190	11	1883	1883	NUM
m-1112	3190	12	-	-	SYM
m-1112	3190	13	1886	1886	NUM
m-1112	3190	14	)	)	PUNCT
m-1112	3190	15	english	english	ADJ
m-1112	3190	16	translation	translation	NOUN
m-1112	3190	17	,	,	PUNCT
m-1112	3190	18	richard	richard	PROPN
m-1112	3190	19	fitzpatrick	fitzpatrick	PROPN
m-1112	3190	20	[	[	PUNCT
m-1112	3190	21	4	4	NUM
m-1112	3190	22	]	]	PUNCT
m-1112	3190	23	elements	element	NOUN
m-1112	3190	24	book	book	NOUN
m-1112	3190	25	1	1	NUM
m-1112	3190	26	.	.	PUNCT
m-1112	3191	1	[	[	PUNCT
m-1112	3191	2	5	5	NUM
m-1112	3191	3	]	]	SYM
m-1112	3191	4	wikipedia.org	wikipedia.org	NUM
m-1112	3191	5	,	,	PUNCT
m-1112	3191	6	the	the	DET
m-1112	3191	7	free	free	ADJ
m-1112	3191	8	encyclopedia	encyclopedia	NOUN
m-1112	3191	9	.	.	PUNCT
m-1112	3192	1	[	[	PUNCT
m-1112	3192	2	6	6	NUM
m-1112	3192	3	]	]	PUNCT
m-1112	3192	4	greek	greek	NOUN
m-1112	3192	5	mathematics	mathematic	NOUN
m-1112	3192	6	,	,	PUNCT
m-1112	3192	7	sir	sir	PROPN
m-1112	3192	8	thomas	thomas	PROPN
m-1112	3192	9	l.heath	l.heath	PROPN
m-1112	3192	10	,	,	PUNCT
m-1112	3192	11	dover	dover	PROPN
m-1112	3192	12	publications	publications	PROPN
m-1112	3192	13	,	,	PUNCT
m-1112	3192	14	inc	inc	PROPN
m-1112	3192	15	,	,	PUNCT
m-1112	3192	16	new	new	PROPN
m-1112	3192	17	york	york	PROPN
m-1112	3192	18	.	.	PUNCT
m-1112	3193	1	63	63	NUM
m-1112	3193	2	-	-	SYM
m-1112	3193	3	3571	3571	NUM
m-1112	3193	4	[	[	PUNCT
m-1112	3193	5	7	7	NUM
m-1112	3193	6	]	]	PUNCT
m-1112	3193	7	[	[	X
m-1112	3193	8	t	t	X
m-1112	3193	9	]	]	PUNCT
m-1112	3193	10	theory	theory	NOUN
m-1112	3193	11	of	of	ADP
m-1112	3193	12	vibrations	vibration	NOUN
m-1112	3193	13	by	by	ADP
m-1112	3193	14	william	william	PROPN
m-1112	3193	15	t.	t.	PROPN
m-1112	3193	16	thomson	thomson	PROPN
m-1112	3193	17	(	(	PUNCT
m-1112	3193	18	fourth	fourth	PROPN
m-1112	3193	19	edition	edition	NOUN
m-1112	3193	20	)	)	PUNCT
m-1112	3193	21	.	.	PUNCT
m-1112	3194	1	[	[	PUNCT
m-1112	3194	2	8	8	X
m-1112	3194	3	]	]	PUNCT
m-1112	3194	4	a	a	DET
m-1112	3194	5	simplified	simplified	ADJ
m-1112	3194	6	approach	approach	NOUN
m-1112	3194	7	of	of	ADP
m-1112	3194	8	squaring	square	VERB
m-1112	3194	9	the	the	DET
m-1112	3194	10	circle	circle	NOUN
m-1112	3194	11	,	,	PUNCT
m-1112	3194	12	http://www.scribd.com/mobile/doc/33887739	http://www.scribd.com/mobile/doc/33887739	PROPN
m-1112	3195	1	[	[	X
m-1112	3195	2	9	9	NUM
m-1112	3195	3	]	]	PUNCT
m-1112	3195	4	the	the	DET
m-1112	3195	5	parallel	parallel	ADJ
m-1112	3195	6	postulate	postulate	NOUN
m-1112	3195	7	is	be	AUX
m-1112	3195	8	depended	depend	VERB
m-1112	3195	9	on	on	ADP
m-1112	3195	10	the	the	DET
m-1112	3195	11	other	other	ADJ
m-1112	3195	12	axioms	axiom	NOUN
m-1112	3195	13	,	,	PUNCT
m-1112	3195	14	http://vixra.org/abs/1103.0042	http://vixra.org/abs/1103.0042	NOUN
m-1112	3195	15	[	[	X
m-1112	3195	16	10	10	NUM
m-1112	3195	17	]	]	PUNCT
m-1112	3195	18	measuring	measure	VERB
m-1112	3195	19	regular	regular	ADJ
m-1112	3195	20	polygons	polygon	NOUN
m-1112	3195	21	and	and	CCONJ
m-1112	3195	22	heptagon	heptagon	PROPN
m-1112	3195	23	in	in	ADP
m-1112	3195	24	a	a	DET
m-1112	3195	25	circle	circle	NOUN
m-1112	3195	26	,	,	PUNCT
m-1112	3195	27	http://www.scribd.com/mobile/doc/33887268	http://www.scribd.com/mobile/doc/33887268	PROPN
m-1112	3196	1	[	[	X
m-1112	3196	2	11	11	NUM
m-1112	3196	3	]	]	PUNCT
m-1112	3196	4	the	the	DET
m-1112	3196	5	trisection	trisection	NOUN
m-1112	3196	6	of	of	ADP
m-1112	3196	7	any	any	DET
m-1112	3196	8	angle	angle	NOUN
m-1112	3196	9	,	,	PUNCT
m-1112	3196	10	http://vixra.org/abs/1103.0119	http://vixra.org/abs/1103.0119	PROPN
m-1112	3197	1	[	[	X
m-1112	3197	2	12	12	NUM
m-1112	3197	3	]	]	PUNCT
m-1112	3197	4	the	the	DET
m-1112	3197	5	euclidean	euclidean	ADJ
m-1112	3197	6	philosophy	philosophy	NOUN
m-1112	3197	7	of	of	ADP
m-1112	3197	8	universe	universe	NOUN
m-1112	3197	9	,	,	PUNCT
m-1112	3197	10	http://vixra.org/abs/1103.0043	http://vixra.org/abs/1103.0043	ADJ
m-1112	3197	11	[	[	X
m-1112	3197	12	13	13	NUM
m-1112	3197	13	]	]	PUNCT
m-1112	3197	14	universe	universe	NOUN
m-1112	3197	15	originated	originate	VERB
m-1112	3197	16	not	not	PART
m-1112	3197	17	with	with	ADP
m-1112	3197	18	big	big	PROPN
m-1112	3197	19	bang	bang	PROPN
m-1112	3197	20	,	,	PUNCT
m-1112	3197	21	http://www.vixra.org/pdf/1310.0146v1.pdf	http://www.vixra.org/pdf/1310.0146v1.pdf	PROPN
m-1112	3197	22	ijo	ijo	PROPN
m-1112	3197	23	international	international	PROPN
m-1112	3197	24	journal	journal	PROPN
m-1112	3197	25	of	of	ADP
m-1112	3197	26	mathematics	mathematics	PROPN
m-1112	3197	27	(	(	PUNCT
m-1112	3197	28	issn	issn	PROPN
m-1112	3197	29	:	:	PUNCT
m-1112	3197	30	2992	2992	NUM
m-1112	3197	31	-	-	SYM
m-1112	3197	32	4421	4421	NUM
m-1112	3197	33	)	)	PUNCT
m-1112	3198	1	volume	volume	NOUN
m-1112	3198	2	08	08	NUM
m-1112	3199	1	|	|	ADV
m-1112	3199	2	issue	issue	NOUN
m-1112	3199	3	08	08	NUM
m-1112	3200	1	|	|	ADV
m-1112	3200	2	august	august	PROPN
m-1112	3200	3	2025	2025	NUM
m-1112	3201	1	|	|	ADV
m-1112	3201	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3201	3	ijo	ijo	PROPN
m-1112	3201	4	journals	journal	NOUN
m-1112	3201	5	http://www.scribd.com/mobile/doc/33887739	http://www.scribd.com/mobile/doc/33887739	PROPN
m-1112	3201	6	http://vixra.org/abs/1103.0042	http://vixra.org/abs/1103.0042	NOUN
m-1112	3201	7	http://www.scribd.com/mobile/doc/33887268	http://www.scribd.com/mobile/doc/33887268	PROPN
m-1112	3201	8	http://vixra.org/abs/1103.0119	http://vixra.org/abs/1103.0119	PROPN
m-1112	3201	9	http://vixra.org/abs/1103.0043	http://vixra.org/abs/1103.0043	PROPN
m-1112	3201	10	http://www.vixra.org/pdf/1310.0146v1.pdf	http://www.vixra.org/pdf/1310.0146v1.pdf	PROPN
m-1112	3201	11	114	114	NUM
m-1112	3201	12	the	the	DET
m-1112	3201	13	fundamental	fundamental	ADJ
m-1112	3201	14	particles	particle	NOUN
m-1112	3201	15	origination	origination	NOUN
m-1112	3201	16	mechanism	mechanism	NOUN
m-1112	3201	17	in	in	ADP
m-1112	3201	18	mfmf	mfmf	PROPN
m-1112	3201	19	pns	pns	PROPN
m-1112	3201	20	caves	cave	NOUN
m-1112	3201	21	.	.	PUNCT
m-1112	3202	1	[	[	X
m-1112	3202	2	14	14	NUM
m-1112	3202	3	]	]	SYM
m-1112	3202	4	complex	complex	ADJ
m-1112	3202	5	numbers	number	NOUN
m-1112	3202	6	quantum	quantum	ADJ
m-1112	3202	7	mechanics	mechanic	NOUN
m-1112	3202	8	spring	spring	NOUN
m-1112	3202	9	from	from	ADP
m-1112	3202	10	euclidean	euclidean	ADJ
m-1112	3202	11	universe	universe	NOUN
m-1112	3202	12	,	,	PUNCT
m-1112	3202	13	http://www.scribd.com/mobile/doc/57533734	http://www.scribd.com/mobile/doc/57533734	PROPN
m-1112	3203	1	[	[	X
m-1112	3203	2	15	15	NUM
m-1112	3203	3	]	]	PUNCT
m-1112	3203	4	zeno`s	zeno`s	NUM
m-1112	3203	5	paradox	paradox	NOUN
m-1112	3203	6	,	,	PUNCT
m-1112	3203	7	nature	nature	NOUN
m-1112	3203	8	of	of	ADP
m-1112	3203	9	points	point	NOUN
m-1112	3203	10	in	in	ADP
m-1112	3203	11	quantized	quantize	VERB
m-1112	3203	12	euclidean	euclidean	ADJ
m-1112	3203	13	geometry	geometry	NOUN
m-1112	3203	14	,	,	PUNCT
m-1112	3203	15	http://www.scribd.com/mobile/doc/59304295	http://www.scribd.com/mobile/doc/59304295	PROPN
m-1112	3204	1	[	[	X
m-1112	3204	2	16	16	NUM
m-1112	3204	3	]	]	PUNCT
m-1112	3205	1	the	the	DET
m-1112	3205	2	decreasing	decrease	VERB
m-1112	3205	3	tunnel	tunnel	NOUN
m-1112	3205	4	,	,	PUNCT
m-1112	3205	5	by	by	ADP
m-1112	3205	6	pr	pr	NOUN
m-1112	3205	7	.	.	PUNCT
m-1112	3205	8	florentine	florentine	PROPN
m-1112	3205	9	smarandashe	smarandashe	PROPN
m-1112	3205	10	,	,	PUNCT
m-1112	3205	11	http://vixra.org/abs/111201.0047	http://vixra.org/abs/111201.0047	PROPN
m-1112	3205	12	[	[	X
m-1112	3205	13	17	17	NUM
m-1112	3205	14	]	]	PUNCT
m-1112	3205	15	the	the	DET
m-1112	3205	16	six	six	NUM
m-1112	3205	17	-	-	PUNCT
m-1112	3205	18	triple	triple	NOUN
m-1112	3205	19	concurrency	concurrency	NOUN
m-1112	3205	20	line	line	NOUN
m-1112	3205	21	–	–	PUNCT
m-1112	3205	22	points	point	NOUN
m-1112	3205	23	,	,	PUNCT
m-1112	3205	24	http://vixra.org/abs/1203.0006	http://vixra.org/abs/1203.0006	NOUN
m-1112	3205	25	[	[	X
m-1112	3205	26	18	18	NUM
m-1112	3205	27	]	]	PUNCT
m-1112	3205	28	energy	energy	NOUN
m-1112	3205	29	laws	law	NOUN
m-1112	3205	30	follow	follow	VERB
m-1112	3205	31	euclidean	euclidean	ADJ
m-1112	3205	32	moulds	mould	NOUN
m-1112	3205	33	,	,	PUNCT
m-1112	3205	34	http://vixra.org/abs/1203.006	http://vixra.org/abs/1203.006	NOUN
m-1112	3205	35	[	[	X
m-1112	3205	36	19	19	NUM
m-1112	3205	37	]	]	PUNCT
m-1112	3205	38	higgs	higgs	NOUN
m-1112	3205	39	particle	particle	NOUN
m-1112	3205	40	and	and	CCONJ
m-1112	3205	41	euclidean	euclidean	ADJ
m-1112	3205	42	geometry	geometry	NOUN
m-1112	3205	43	,	,	PUNCT
m-1112	3205	44	http://www.scribd.com/mobile/doc/105109978	http://www.scribd.com/mobile/doc/105109978	PROPN
m-1112	3205	45	[	[	X
m-1112	3205	46	20	20	NUM
m-1112	3205	47	]	]	PUNCT
m-1112	3205	48	higgs	higgs	PROPN
m-1112	3205	49	boson	boson	NOUN
m-1112	3205	50	and	and	CCONJ
m-1112	3205	51	euclidean	euclidean	ADJ
m-1112	3205	52	geometry	geometry	NOUN
m-1112	3205	53	,	,	PUNCT
m-1112	3205	54	http://vixra.org/abs/1209.0081	http://vixra.org/abs/1209.0081	PROPN
m-1112	3206	1	[	[	X
m-1112	3206	2	21	21	NUM
m-1112	3206	3	]	]	PUNCT
m-1112	3206	4	the	the	DET
m-1112	3206	5	outside	outside	ADJ
m-1112	3206	6	relativity	relativity	NOUN
m-1112	3206	7	space	space	NOUN
m-1112	3206	8	–	–	PUNCT
m-1112	3206	9	energy	energy	NOUN
m-1112	3206	10	universe	universe	NOUN
m-1112	3206	11	,	,	PUNCT
m-1112	3206	12	http://www.scribd.com/mobile/doc/223253928	http://www.scribd.com/mobile/doc/223253928	PROPN
m-1112	3207	1	[	[	X
m-1112	3207	2	22	22	NUM
m-1112	3207	3	]	]	PUNCT
m-1112	3207	4	quantization	quantization	NOUN
m-1112	3207	5	of	of	ADP
m-1112	3207	6	points	point	NOUN
m-1112	3207	7	and	and	CCONJ
m-1112	3207	8	of	of	ADP
m-1112	3207	9	energy	energy	NOUN
m-1112	3207	10	,	,	PUNCT
m-1112	3207	11	http://www.vixra.org/pdf/1303.015v21.pdf	http://www.vixra.org/pdf/1303.015v21.pdf	ADP
m-1112	3207	12	[	[	X
m-1112	3207	13	23	23	NUM
m-1112	3207	14	]	]	PUNCT
m-1112	3207	15	quantization	quantization	NOUN
m-1112	3207	16	of	of	ADP
m-1112	3207	17	points	point	NOUN
m-1112	3207	18	and	and	CCONJ
m-1112	3207	19	energy	energy	NOUN
m-1112	3207	20	on	on	ADP
m-1112	3207	21	dipole	dipole	NOUN
m-1112	3207	22	vectors	vector	NOUN
m-1112	3207	23	and	and	CCONJ
m-1112	3207	24	spin	spin	NOUN
m-1112	3207	25	,	,	PUNCT
m-1112	3207	26	http://vixra.org/abs/1303.0152	http://vixra.org/abs/1303.0152	X
m-1112	3208	1	[	[	X
m-1112	3208	2	24	24	NUM
m-1112	3208	3	]	]	PUNCT
m-1112	3208	4	quaternion`s	quaternion`s	NOUN
m-1112	3208	5	,	,	PUNCT
m-1112	3208	6	spaces	space	NOUN
m-1112	3208	7	and	and	CCONJ
m-1112	3208	8	the	the	DET
m-1112	3208	9	parallel	parallel	ADJ
m-1112	3208	10	postulate	postulate	NOUN
m-1112	3208	11	,	,	PUNCT
m-1112	3208	12	http://vixra.org/abs/1310.0146	http://vixra.org/abs/1310.0146	NOUN
m-1112	3208	13	[	[	X
m-1112	3208	14	25	25	NUM
m-1112	3208	15	]	]	PUNCT
m-1112	3208	16	gravity	gravity	NOUN
m-1112	3208	17	as	as	ADP
m-1112	3208	18	the	the	DET
m-1112	3208	19	intrinsic	intrinsic	ADJ
m-1112	3208	20	vorticity	vorticity	NOUN
m-1112	3208	21	of	of	ADP
m-1112	3208	22	points	point	NOUN
m-1112	3208	23	,	,	PUNCT
m-1112	3208	24	http://vixra.org/abs/1401.0062	http://vixra.org/abs/1401.0062	X
m-1112	3209	1	[	[	X
m-1112	3209	2	26	26	NUM
m-1112	3209	3	]	]	PUNCT
m-1112	3209	4	the	the	DET
m-1112	3209	5	beyond	beyond	ADJ
m-1112	3209	6	gravity	gravity	NOUN
m-1112	3209	7	forced	force	VERB
m-1112	3209	8	fields	field	NOUN
m-1112	3209	9	,	,	PUNCT
m-1112	3209	10	http://scribd.com/mobile/doc/203167317	http://scribd.com/mobile/doc/203167317	ADP
m-1112	3209	11	[	[	X
m-1112	3209	12	27	27	NUM
m-1112	3209	13	]	]	PUNCT
m-1112	3209	14	the	the	DET
m-1112	3209	15	wave	wave	NOUN
m-1112	3209	16	nature	nature	NOUN
m-1112	3209	17	of	of	ADP
m-1112	3209	18	the	the	DET
m-1112	3209	19	geometry	geometry	NOUN
m-1112	3209	20	dipole	dipole	NOUN
m-1112	3209	21	,	,	PUNCT
m-1112	3209	22	http://vixra.org/abs/1404.0023	http://vixra.org/abs/1404.0023	NOUN
m-1112	3209	23	[	[	X
m-1112	3209	24	28	28	NUM
m-1112	3209	25	]	]	X
m-1112	3209	26	planks	plank	NOUN
m-1112	3209	27	length	length	NOUN
m-1112	3209	28	as	as	ADP
m-1112	3209	29	geometrical	geometrical	ADJ
m-1112	3209	30	exponential	exponential	NOUN
m-1112	3209	31	of	of	ADP
m-1112	3209	32	spaces	space	NOUN
m-1112	3209	33	.	.	PUNCT
m-1112	3210	1	http:/vixra.org	http:/vixra.org	PROPN
m-1112	3210	2	/	/	SYM
m-1112	3210	3	abs/1406.0063	abs/1406.0063	ADV
m-1112	3210	4	[	[	X
m-1112	3210	5	29	29	NUM
m-1112	3210	6	]	]	PUNCT
m-1112	3210	7	the	the	DET
m-1112	3210	8	outside	outside	ADJ
m-1112	3210	9	relativity	relativity	NOUN
m-1112	3210	10	space	space	NOUN
m-1112	3210	11	–	–	PUNCT
m-1112	3210	12	energy	energy	NOUN
m-1112	3210	13	universe	universe	NOUN
m-1112	3210	14	,	,	PUNCT
m-1112	3210	15	http://www.scribd.com/mobile/doc/223253928	http://www.scribd.com/mobile/doc/223253928	X
m-1112	3211	1	[	[	X
m-1112	3211	2	30	30	NUM
m-1112	3211	3	]	]	X
m-1112	3211	4	universe	universe	NOUN
m-1112	3211	5	is	be	AUX
m-1112	3211	6	built	build	VERB
m-1112	3211	7	only	only	ADV
m-1112	3211	8	from	from	ADP
m-1112	3211	9	geometry	geometry	NOUN
m-1112	3211	10	dipole	dipole	NOUN
m-1112	3211	11	,	,	PUNCT
m-1112	3211	12	scribd	scribd	NOUN
m-1112	3211	13	:	:	PUNCT
m-1112	3211	14	http://www.scribd.com/mobile/doc/122970530	http://www.scribd.com/mobile/doc/122970530	PROPN
m-1112	3212	1	[	[	X
m-1112	3212	2	31	31	NUM
m-1112	3212	3	]	]	PUNCT
m-1112	3212	4	gravity	gravity	NOUN
m-1112	3212	5	and	and	CCONJ
m-1112	3212	6	planck`s	planck`s	NOUN
m-1112	3212	7	length	length	NOUN
m-1112	3212	8	as	as	ADP
m-1112	3212	9	the	the	DET
m-1112	3212	10	exponential	exponential	ADJ
m-1112	3212	11	geometry	geometry	NOUN
m-1112	3212	12	base	base	NOUN
m-1112	3212	13	of	of	ADP
m-1112	3212	14	spaces	space	NOUN
m-1112	3212	15	,	,	PUNCT
m-1112	3212	16	http://vixra.org/abs/1406.0063	http://vixra.org/abs/1406.0063	NOUN
m-1112	3213	1	[	[	X
m-1112	3213	2	32	32	NUM
m-1112	3213	3	]	]	PUNCT
m-1112	3213	4	the	the	DET
m-1112	3213	5	parallel	parallel	ADJ
m-1112	3213	6	postulate	postulate	NOUN
m-1112	3213	7	and	and	CCONJ
m-1112	3213	8	spaces	space	NOUN
m-1112	3213	9	(	(	PUNCT
m-1112	3213	10	in	in	ADP
m-1112	3213	11	sciep	sciep	PROPN
m-1112	3213	12	)	)	PUNCT
m-1112	3214	1	[	[	X
m-1112	3214	2	33	33	NUM
m-1112	3214	3	]	]	PUNCT
m-1112	3214	4	the	the	DET
m-1112	3214	5	fundamental	fundamental	ADJ
m-1112	3214	6	origin	origin	NOUN
m-1112	3214	7	of	of	ADP
m-1112	3214	8	particles	particle	NOUN
m-1112	3214	9	in	in	ADP
m-1112	3214	10	planck`s	planck`s	NOUN
m-1112	3214	11	confinement	confinement	ADJ
m-1112	3214	12	.	.	PUNCT
m-1112	3215	1	on	on	ADP
m-1112	3215	2	scribd	scribd	PROPN
m-1112	3215	3	&	&	CCONJ
m-1112	3215	4	vixra	vixra	PROPN
m-1112	3215	5	(	(	PUNCT
m-1112	3215	6	fundapar.doc	fundapar.doc	NOUN
m-1112	3215	7	)	)	PUNCT
m-1112	3215	8	[	[	X
m-1112	3215	9	34	34	NUM
m-1112	3215	10	]	]	PUNCT
m-1112	3215	11	the	the	DET
m-1112	3215	12	fundamental	fundamental	ADJ
m-1112	3215	13	particles	particle	NOUN
m-1112	3215	14	of	of	ADP
m-1112	3215	15	planck`s	planck`s	NOUN
m-1112	3215	16	confinement	confinement	ADJ
m-1112	3215	17	.	.	PUNCT
m-1112	3216	1	www.ijesi.com	www.ijesi.com	PROPN
m-1112	3216	2	(	(	PUNCT
m-1112	3216	3	ijpst14	ijpst14	NOUN
m-1112	3216	4	-	-	PUNCT
m-1112	3216	5	082601	082601	NUM
m-1112	3216	6	)	)	PUNCT
m-1112	3217	1	[	[	X
m-1112	3217	2	35	35	NUM
m-1112	3217	3	]	]	SYM
m-1112	3217	4	origin	origin	NOUN
m-1112	3217	5	of	of	ADP
m-1112	3217	6	fundamental	fundamental	ADJ
m-1112	3217	7	particles	particle	NOUN
m-1112	3217	8	www.ethanpublishing.com(ijpst	www.ethanpublishing.com(ijpst	NOUN
m-1112	3217	9	-	-	PUNCT
m-1112	3217	10	e140620	e140620	NOUN
m-1112	3217	11	-	-	PUNCT
m-1112	3217	12	01	01	NUM
m-1112	3217	13	)	)	PUNCT
m-1112	3218	1	[	[	X
m-1112	3218	2	36	36	NUM
m-1112	3218	3	]	]	PUNCT
m-1112	3218	4	the	the	DET
m-1112	3218	5	nature	nature	NOUN
m-1112	3218	6	of	of	ADP
m-1112	3218	7	fundamental	fundamental	ADJ
m-1112	3218	8	particles	particle	NOUN
m-1112	3218	9	,	,	PUNCT
m-1112	3218	10	.ijesit.com	.ijesit.com	PUNCT
m-1112	3218	11	–	–	PUNCT
m-1112	3218	12	paper	paper	NOUN
m-1112	3218	13	i	i	NOUN
m-1112	3218	14	d	d	PROPN
m-1112	3218	15	:	:	PUNCT
m-1112	3218	16	ijesit	ijesit	VERB
m-1112	3218	17	i	i	PROPN
m-1112	3218	18	d	d	PROPN
m-1112	3218	19	:	:	PUNCT
m-1112	3218	20	1491	1491	NUM
m-1112	3218	21	[	[	X
m-1112	3218	22	37	37	NUM
m-1112	3218	23	]	]	PUNCT
m-1112	3218	24	the	the	DET
m-1112	3218	25	energy	energy	NOUN
m-1112	3218	26	-	-	PUNCT
m-1112	3218	27	space	space	NOUN
m-1112	3218	28	universe	universe	NOUN
m-1112	3218	29	and	and	CCONJ
m-1112	3218	30	relativity	relativity	NOUN
m-1112	3218	31	ijism	ijism	NOUN
m-1112	3218	32	,	,	PUNCT
m-1112	3218	33	ijism.org	ijism.org	PROPN
m-1112	3218	34	–	–	PUNCT
m-1112	3218	35	paper	paper	NOUN
m-1112	3218	36	i	i	NOUN
m-1112	3218	37	d	d	PROPN
m-1112	3218	38	:	:	PUNCT
m-1112	3218	39	ijism	ijism	NOUN
m-1112	3218	40	–	–	PUNCT
m-1112	3218	41	294	294	NUM
m-1112	3219	1	[	[	X
m-1112	3219	2	v2,i6,2347	v2,i6,2347	NOUN
m-1112	3219	3	-	-	SYM
m-1112	3219	4	9051	9051	NUM
m-1112	3219	5	]	]	PUNCT
m-1112	3220	1	[	[	X
m-1112	3220	2	38	38	NUM
m-1112	3220	3	]	]	PUNCT
m-1112	3220	4	the	the	DET
m-1112	3220	5	parallel	parallel	ADJ
m-1112	3220	6	postulate	postulate	NOUN
m-1112	3220	7	,	,	PUNCT
m-1112	3220	8	the	the	DET
m-1112	3220	9	other	other	ADJ
m-1112	3220	10	four	four	NUM
m-1112	3220	11	and	and	CCONJ
m-1112	3220	12	relativity	relativity	NOUN
m-1112	3220	13	(	(	PUNCT
m-1112	3220	14	american	american	ADJ
m-1112	3220	15	journal	journal	PROPN
m-1112	3220	16	of	of	ADP
m-1112	3220	17	modern	modern	ADJ
m-1112	3220	18	physics	physics	NOUN
m-1112	3220	19	,	,	PUNCT
m-1112	3220	20	science	science	NOUN
m-1112	3220	21	pg	pg	PROPN
m-1112	3220	22	–	–	PUNCT
m-1112	3220	23	publication	publication	NOUN
m-1112	3220	24	group	group	PROPN
m-1112	3220	25	usa	usa	PROPN
m-1112	3220	26	)	)	PUNCT
m-1112	3220	27	,	,	PUNCT
m-1112	3220	28	1800978	1800978	NUM
m-1112	3220	29	paper	paper	NOUN
m-1112	3220	30	.	.	PUNCT
m-1112	3221	1	[	[	X
m-1112	3221	2	39	39	NUM
m-1112	3221	3	]	]	PUNCT
m-1112	3221	4	space	space	NOUN
m-1112	3221	5	-	-	PUNCT
m-1112	3221	6	time	time	NOUN
m-1112	3221	7	or	or	CCONJ
m-1112	3221	8	,	,	PUNCT
m-1112	3221	9	space	space	NOUN
m-1112	3221	10	-	-	PUNCT
m-1112	3221	11	energy	energy	NOUN
m-1112	3221	12	universe	universe	NOUN
m-1112	3221	13	(	(	PUNCT
m-1112	3221	14	american	american	ADJ
m-1112	3221	15	journal	journal	PROPN
m-1112	3221	16	of	of	ADP
m-1112	3221	17	modern	modern	ADJ
m-1112	3221	18	physics	physics	NOUN
m-1112	3221	19	,	,	PUNCT
m-1112	3221	20	science	science	NOUN
m-1112	3221	21	pg	pg	PROPN
m-1112	3221	22	publication	publication	PROPN
m-1112	3221	23	group	group	PROPN
m-1112	3221	24	usa	usa	PROPN
m-1112	3221	25	)	)	PUNCT
m-1112	3221	26	1221001	1221001	NUM
m-1112	3221	27	–	–	PUNCT
m-1112	3221	28	paper	paper	NOUN
m-1112	3221	29	.	.	PUNCT
m-1112	3222	1	[	[	X
m-1112	3222	2	40	40	NUM
m-1112	3222	3	]	]	PUNCT
m-1112	3222	4	the	the	DET
m-1112	3222	5	origin	origin	NOUN
m-1112	3222	6	of	of	ADP
m-1112	3222	7	,	,	PUNCT
m-1112	3222	8	maxwell`s	maxwell`	NOUN
m-1112	3222	9	-	-	PUNCT
m-1112	3222	10	gravity`s	gravity`s	NOUN
m-1112	3222	11	,	,	PUNCT
m-1112	3222	12	displacement	displacement	ADJ
m-1112	3222	13	current	current	NOUN
m-1112	3222	14	.	.	PUNCT
m-1112	3223	1	gjsfr	gjsfr	NOUN
m-1112	3223	2	(	(	PUNCT
m-1112	3223	3	journalofscience.org	journalofscience.org	NOUN
m-1112	3223	4	)	)	PUNCT
m-1112	3223	5	,	,	PUNCT
m-1112	3223	6	volume	volume	NOUN
m-1112	3223	7	15	15	NUM
m-1112	3223	8	-	-	PUNCT
m-1112	3223	9	a	a	PRON
m-1112	3223	10	,	,	PUNCT
m-1112	3223	11	issue	issue	NOUN
m-1112	3223	12	3	3	NUM
m-1112	3223	13	,	,	PUNCT
m-1112	3223	14	version	version	NOUN
m-1112	3223	15	1.0	1.0	NUM
m-1112	3223	16	[	[	X
m-1112	3223	17	41	41	NUM
m-1112	3223	18	]	]	PUNCT
m-1112	3223	19	young`s	young`s	NOUN
m-1112	3223	20	double	double	ADJ
m-1112	3223	21	slit	slit	ADJ
m-1112	3223	22	experiment	experiment	NOUN
m-1112	3223	23	[	[	PUNCT
m-1112	3223	24	vixra	vixra	NOUN
m-1112	3223	25	:	:	PUNCT
m-1112	3223	26	1505.0105	1505.0105	ADJ
m-1112	3223	27	]	]	X
m-1112	3223	28	scribd	scribd	NOUN
m-1112	3223	29	:	:	PUNCT
m-1112	3223	30	https://www.scribd.com/doc/265195121/	https://www.scribd.com/doc/265195121/	PROPN
m-1112	3224	1	[	[	X
m-1112	3224	2	42	42	NUM
m-1112	3224	3	]	]	PUNCT
m-1112	3224	4	the	the	DET
m-1112	3224	5	creation	creation	NOUN
m-1112	3224	6	hypothesis	hypothesis	NOUN
m-1112	3224	7	of	of	ADP
m-1112	3224	8	nature	nature	NOUN
m-1112	3224	9	without	without	ADP
m-1112	3224	10	big	big	ADJ
m-1112	3224	11	-	-	PUNCT
m-1112	3224	12	bang	bang	NOUN
m-1112	3224	13	.	.	PUNCT
m-1112	3225	1	scribd	scribd	NOUN
m-1112	3225	2	:	:	PUNCT
m-1112	3225	3	https://www.scribd.com/doc/267917624	https://www.scribd.com/doc/267917624	PROPN
m-1112	3225	4	/	/	PUNCT
m-1112	3226	1	[	[	X
m-1112	3226	2	43	43	NUM
m-1112	3226	3	]	]	PUNCT
m-1112	3226	4	the	the	DET
m-1112	3226	5	expanding	expand	VERB
m-1112	3226	6	universe	universe	NOUN
m-1112	3226	7	without	without	ADP
m-1112	3226	8	big	big	ADJ
m-1112	3226	9	-	-	PUNCT
m-1112	3226	10	bang	bang	NOUN
m-1112	3226	11	.	.	PUNCT
m-1112	3227	1	(	(	PUNCT
m-1112	3227	2	american	american	PROPN
m-1112	3227	3	journal	journal	PROPN
m-1112	3227	4	of	of	ADP
m-1112	3227	5	modern	modern	ADJ
m-1112	3227	6	ijo	ijo	PROPN
m-1112	3227	7	international	international	PROPN
m-1112	3227	8	journal	journal	PROPN
m-1112	3227	9	of	of	ADP
m-1112	3227	10	mathematics	mathematics	PROPN
m-1112	3227	11	(	(	PUNCT
m-1112	3227	12	issn	issn	PROPN
m-1112	3227	13	:	:	PUNCT
m-1112	3227	14	2992	2992	NUM
m-1112	3227	15	-	-	SYM
m-1112	3227	16	4421	4421	NUM
m-1112	3227	17	)	)	PUNCT
m-1112	3227	18	volume	volume	NOUN
m-1112	3227	19	08	08	NUM
m-1112	3228	1	|	|	ADV
m-1112	3228	2	issue	issue	NOUN
m-1112	3228	3	08	08	NUM
m-1112	3229	1	|	|	ADV
m-1112	3229	2	august	august	PROPN
m-1112	3229	3	2025	2025	NUM
m-1112	3229	4	|	|	ADV
m-1112	3229	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3229	6	ijo	ijo	PROPN
m-1112	3229	7	journals	journal	NOUN
m-1112	3229	8	http://www.scribd.com/mobile/doc/57533734	http://www.scribd.com/mobile/doc/57533734	PROPN
m-1112	3229	9	http://www.scribd.com/mobile/doc/59304295	http://www.scribd.com/mobile/doc/59304295	PROPN
m-1112	3229	10	http://vixra.org/abs/111201.0047	http://vixra.org/abs/111201.0047	ADJ
m-1112	3229	11	http://vixra.org/abs/1203.0006	http://vixra.org/abs/1203.0006	PROPN
m-1112	3229	12	http://vixra.org/abs/1203.006	http://vixra.org/abs/1203.006	PROPN
m-1112	3229	13	http://www.scribd.com/mobile/doc/105109978	http://www.scribd.com/mobile/doc/105109978	PROPN
m-1112	3229	14	http://vixra.org/abs/1209.0081	http://vixra.org/abs/1209.0081	ADJ
m-1112	3229	15	http://www.scribd.com/mobile/doc/223253928	http://www.scribd.com/mobile/doc/223253928	PROPN
m-1112	3229	16	http://www.vixra.org/pdf/1303.015v21.pdf	http://www.vixra.org/pdf/1303.015v21.pdf	X
m-1112	3229	17	http://vixra.org/abs/1303.0152	http://vixra.org/abs/1303.0152	PROPN
m-1112	3229	18	http://vixra.org/abs/1310.0146	http://vixra.org/abs/1310.0146	PROPN
m-1112	3229	19	http://vixra.org/abs/1401.0062	http://vixra.org/abs/1401.0062	PROPN
m-1112	3229	20	http://scribd.com/mobile/doc/203167317	http://scribd.com/mobile/doc/203167317	PROPN
m-1112	3229	21	http://vixra.org/abs/1404.0023	http://vixra.org/abs/1404.0023	PROPN
m-1112	3229	22	http://www.vixra.org/abs/1406.0063	http://www.vixra.org/abs/1406.0063	PROPN
m-1112	3229	23	http://www.scribd.com/mobile/doc/223253928	http://www.scribd.com/mobile/doc/223253928	PROPN
m-1112	3230	1	http://www.scribd.com/mobile/doc/122970530	http://www.scribd.com/mobile/doc/122970530	PROPN
m-1112	3230	2	http://vixra.org/abs/1406.0063	http://vixra.org/abs/1406.0063	PROPN
m-1112	3230	3	http://www.ijesi.com/	http://www.ijesi.com/	PROPN
m-1112	3230	4	http://www.ethanpublishing.com(ijpst-/	http://www.ethanpublishing.com(ijpst-/	PROPN
m-1112	3230	5	http://www.ijesit.com/	http://www.ijesit.com/	PROPN
m-1112	3230	6	http://www.ijism.org/	http://www.ijism.org/	X
m-1112	3230	7	https://www.scribd.com/doc/265195121/	https://www.scribd.com/doc/265195121/	ADP
m-1112	3231	1	https://www.scribd.com/doc/267917624	https://www.scribd.com/doc/267917624	PROPN
m-1112	3231	2	115	115	NUM
m-1112	3231	3	the	the	DET
m-1112	3231	4	fundamental	fundamental	ADJ
m-1112	3231	5	particles	particle	NOUN
m-1112	3231	6	origination	origination	NOUN
m-1112	3231	7	mechanism	mechanism	NOUN
m-1112	3231	8	in	in	ADP
m-1112	3231	9	mfmf	mfmf	PROPN
m-1112	3231	10	pns	pns	PROPN
m-1112	3231	11	caves	cave	NOUN
m-1112	3231	12	.	.	PUNCT
m-1112	3232	1	physics	physics	NOUN
m-1112	3232	2	and	and	CCONJ
m-1112	3232	3	applications	application	NOUN
m-1112	3232	4	special	special	ADJ
m-1112	3232	5	issue	issue	NOUN
m-1112	3232	6	:	:	PUNCT
m-1112	3232	7	http://www.sciencepublishinggroup.com/j	http://www.sciencepublishinggroup.com/j	PROPN
m-1112	3232	8	/	/	SYM
m-1112	3232	9	science	science	PROPN
m-1112	3232	10	pg	pg	PROPN
m-1112	3232	11	-	-	PUNCT
m-1112	3232	12	publication	publication	NOUN
m-1112	3232	13	group	group	NOUN
m-1112	3232	14	usa	usa	PROPN
m-1112	3232	15	–	–	PUNCT
m-1112	3232	16	622012001	622012001	NUM
m-1112	3232	17	–	–	PUNCT
m-1112	3232	18	paper	paper	NOUN
m-1112	3232	19	.	.	PUNCT
m-1112	3233	1	[	[	X
m-1112	3233	2	44	44	NUM
m-1112	3233	3	]	]	PUNCT
m-1112	3233	4	the	the	DET
m-1112	3233	5	parallel	parallel	ADJ
m-1112	3233	6	postulate	postulate	NOUN
m-1112	3233	7	and	and	CCONJ
m-1112	3233	8	the	the	DET
m-1112	3233	9	other	other	ADJ
m-1112	3233	10	four	four	NUM
m-1112	3233	11	,	,	PUNCT
m-1112	3233	12	the	the	DET
m-1112	3233	13	doubling	doubling	NOUN
m-1112	3233	14	of	of	ADP
m-1112	3233	15	the	the	DET
m-1112	3233	16	cube	cube	NOUN
m-1112	3233	17	,	,	PUNCT
m-1112	3233	18	the	the	DET
m-1112	3233	19	special	special	ADJ
m-1112	3233	20	problems	problem	NOUN
m-1112	3233	21	and	and	CCONJ
m-1112	3233	22	relativity	relativity	NOUN
m-1112	3233	23	.	.	PUNCT
m-1112	3234	1	https://www.lap-publishing.com/.	https://www.lap-publishing.com/.	PRON
m-1112	3234	2	e	e	NOUN
m-1112	3234	3	-	-	NOUN
m-1112	3234	4	book	book	NOUN
m-1112	3234	5	.	.	PUNCT
m-1112	3235	1	lambert	lambert	PROPN
m-1112	3235	2	academic	academic	ADJ
m-1112	3235	3	publication	publication	NOUN
m-1112	3235	4	.	.	PUNCT
m-1112	3236	1	[	[	X
m-1112	3236	2	45	45	NUM
m-1112	3236	3	]	]	PUNCT
m-1112	3236	4	the	the	DET
m-1112	3236	5	moulds	mould	NOUN
m-1112	3236	6	for	for	ADP
m-1112	3236	7	e	e	NOUN
m-1112	3236	8	-	-	NOUN
m-1112	3236	9	geometry	geometry	NOUN
m-1112	3236	10	quantization	quantization	NOUN
m-1112	3236	11	and	and	CCONJ
m-1112	3236	12	relativity	relativity	NOUN
m-1112	3236	13	,	,	PUNCT
m-1112	3236	14	international	international	ADJ
m-1112	3236	15	journal	journal	NOUN
m-1112	3236	16	of	of	ADP
m-1112	3236	17	advances	advance	NOUN
m-1112	3236	18	of	of	ADP
m-1112	3236	19	innovative	innovative	ADJ
m-1112	3236	20	research	research	NOUN
m-1112	3236	21	in	in	ADP
m-1112	3236	22	science	science	NOUN
m-1112	3236	23	engineering	engineering	NOUN
m-1112	3236	24	and	and	CCONJ
m-1112	3236	25	technology	technology	NOUN
m-1112	3236	26	ijirset	ijirset	VERB
m-1112	3236	27	:	:	PUNCT
m-1112	3236	28	http://www.ijirset.com/..markos	http://www.ijirset.com/..markos	DET
m-1112	3236	29	georgallides	georgallide	NOUN
m-1112	3236	30	[	[	X
m-1112	3236	31	46	46	NUM
m-1112	3236	32	]	]	X
m-1112	3237	1	[	[	X
m-1112	3237	2	m	m	X
m-1112	3237	3	]	]	X
m-1112	3237	4	the	the	DET
m-1112	3237	5	special	special	ADJ
m-1112	3237	6	problems	problem	NOUN
m-1112	3237	7	of	of	ADP
m-1112	3237	8	e	e	NOUN
m-1112	3237	9	-	-	NOUN
m-1112	3237	10	geometry	geometry	NOUN
m-1112	3237	11	and	and	CCONJ
m-1112	3237	12	relativity	relativity	NOUN
m-1112	3237	13	http://vixra.org/abs/1510.0328	http://vixra.org/abs/1510.0328	NOUN
m-1112	3237	14	[	[	X
m-1112	3237	15	47	47	NUM
m-1112	3237	16	]	]	PUNCT
m-1112	3238	1	[	[	X
m-1112	3238	2	m	m	X
m-1112	3238	3	]	]	X
m-1112	3238	4	the	the	DET
m-1112	3238	5	ancient	ancient	ADJ
m-1112	3238	6	greek	greek	ADJ
m-1112	3238	7	special	special	ADJ
m-1112	3238	8	problems	problem	NOUN
m-1112	3238	9	as	as	ADP
m-1112	3238	10	the	the	DET
m-1112	3238	11	quantization	quantization	NOUN
m-1112	3238	12	moulds	mould	NOUN
m-1112	3238	13	of	of	ADP
m-1112	3238	14	spaces	space	NOUN
m-1112	3238	15	.	.	PUNCT
m-1112	3239	1	www.submission.arpweb.com(id-44031	www.submission.arpweb.com(id-44031	NOUN
m-1112	3239	2	-	-	PUNCT
m-1112	3239	3	sr-015.0	sr-015.0	NOUN
m-1112	3239	4	[	[	X
m-1112	3239	5	48	48	NUM
m-1112	3239	6	]	]	PUNCT
m-1112	3240	1	[	[	X
m-1112	3240	2	m	m	X
m-1112	3240	3	]	]	X
m-1112	3240	4	the	the	DET
m-1112	3240	5	quantization	quantization	NOUN
m-1112	3240	6	of	of	ADP
m-1112	3240	7	e	e	NOUN
m-1112	3240	8	-	-	NOUN
m-1112	3240	9	geometry	geometry	NOUN
m-1112	3240	10	as	as	ADP
m-1112	3240	11	energy	energy	NOUN
m-1112	3240	12	monads	monad	NOUN
m-1112	3240	13	and	and	CCONJ
m-1112	3240	14	the	the	DET
m-1112	3240	15	unification	unification	NOUN
m-1112	3240	16	of	of	ADP
m-1112	3240	17	space	space	NOUN
m-1112	3240	18	and	and	CCONJ
m-1112	3240	19	energy	energy	NOUN
m-1112	3240	20	.	.	PUNCT
m-1112	3241	1	www.ijera.com(id-512080.0	www.ijera.com(id-512080.0	X
m-1112	3242	1	[	[	X
m-1112	3242	2	49	49	NUM
m-1112	3242	3	]	]	PUNCT
m-1112	3242	4	[	[	X
m-1112	3242	5	51	51	NUM
m-1112	3242	6	]	]	PUNCT
m-1112	3242	7	the	the	DET
m-1112	3242	8	why	why	SCONJ
m-1112	3242	9	intrinsic	intrinsic	ADJ
m-1112	3242	10	spin	spin	NOUN
m-1112	3242	11	(	(	PUNCT
m-1112	3242	12	angular	angular	ADJ
m-1112	3242	13	momentum	momentum	NOUN
m-1112	3242	14	)	)	PUNCT
m-1112	3242	15	½	½	NOUN
m-1112	3242	16	-1	-1	PUNCT
m-1112	3242	17	,	,	PUNCT
m-1112	3242	18	into	into	ADP
m-1112	3242	19	particles	particle	NOUN
m-1112	3242	20	.	.	PUNCT
m-1112	3243	1	www.oalib.com(id-1102480.0	www.oalib.com(id-1102480.0	VERB
m-1112	3243	2	[	[	X
m-1112	3243	3	50	50	NUM
m-1112	3243	4	]	]	PUNCT
m-1112	3244	1	[	[	X
m-1112	3244	2	m	m	X
m-1112	3244	3	]	]	X
m-1112	3244	4	the	the	DET
m-1112	3244	5	kinematic	kinematic	ADJ
m-1112	3244	6	geometrical	geometrical	ADJ
m-1112	3244	7	solution	solution	NOUN
m-1112	3244	8	of	of	ADP
m-1112	3244	9	the	the	DET
m-1112	3244	10	unsolved	unsolved	ADJ
m-1112	3244	11	ancient	ancient	ADJ
m-1112	3244	12	–	–	PUNCT
m-1112	3244	13	greek	greek	NOUN
m-1112	3244	14	problems	problem	NOUN
m-1112	3244	15	and	and	CCONJ
m-1112	3244	16	their	their	PRON
m-1112	3244	17	physical	physical	ADJ
m-1112	3244	18	nature	nature	NOUN
m-1112	3244	19	http	http	NOUN
m-1112	3244	20	:	:	PUNCT
m-1112	3244	21	www.jiaats.com	www.jiaats.com	X
m-1112	3244	22	/	/	SYM
m-1112	3244	23	paper/3068.iso	paper/3068.iso	NOUN
m-1112	3244	24	9001	9001	NUM
m-1112	3245	1	[	[	X
m-1112	3245	2	51	51	NUM
m-1112	3245	3	]	]	X
m-1112	3245	4	[	[	X
m-1112	3245	5	m	m	X
m-1112	3245	6	]	]	X
m-1112	3245	7	the	the	DET
m-1112	3245	8	nature	nature	NOUN
m-1112	3245	9	of	of	ADP
m-1112	3245	10	geometry	geometry	NOUN
m-1112	3245	11	the	the	DET
m-1112	3245	12	unsolved	unsolved	ADJ
m-1112	3245	13	ancient	ancient	ADJ
m-1112	3245	14	-	-	PUNCT
m-1112	3245	15	greek	greek	NOUN
m-1112	3245	16	problems	problem	NOUN
m-1112	3245	17	and	and	CCONJ
m-1112	3245	18	their	their	PRON
m-1112	3245	19	geometrical	geometrical	ADJ
m-1112	3245	20	solution	solution	NOUN
m-1112	3245	21	error	error	NOUN
m-1112	3245	22	!	!	PUNCT
m-1112	3246	1	hyperlink	hyperlink	PROPN
m-1112	3246	2	reference	reference	NOUN
m-1112	3246	3	not	not	PART
m-1112	3246	4	valid	valid	ADJ
m-1112	3246	5	.	.	PUNCT
m-1112	3247	1	http	http	ADJ
m-1112	3247	2	:	:	PUNCT
m-1112	3247	3	www.oalib.com	www.oalib.com	NUM
m-1112	3247	4	/	/	SYM
m-1112	3247	5	journal	journal	PROPN
m-1112	3247	6	:	:	PUNCT
m-1112	3247	7	paper/1102605	paper/1102605	PROPN
m-1112	3248	1	[	[	X
m-1112	3248	2	52	52	NUM
m-1112	3248	3	]	]	SYM
m-1112	3248	4	e	e	NOUN
m-1112	3248	5	-	-	NOUN
m-1112	3248	6	geometry	geometry	NOUN
m-1112	3248	7	,	,	PUNCT
m-1112	3248	8	mechanics	mechanic	NOUN
m-1112	3248	9	-	-	PUNCT
m-1112	3248	10	physics	physics	NOUN
m-1112	3248	11	and	and	CCONJ
m-1112	3248	12	relativity	relativity	NOUN
m-1112	3248	13	,	,	PUNCT
m-1112	3248	14	http	http	CCONJ
m-1112	3248	15	:	:	PUNCT
m-1112	3248	16	gpcpublishing.com	gpcpublishing.com	X
m-1112	3248	17	/	/	SYM
m-1112	3248	18	gpc	gpc	PROPN
m-1112	3248	19	:	:	PUNCT
m-1112	3248	20	volume	volume	NOUN
m-1112	3248	21	4	4	NUM
m-1112	3248	22	,	,	PUNCT
m-1112	3248	23	number	number	NOUN
m-1112	3248	24	2	2	NUM
m-1112	3248	25	journal	journal	NOUN
m-1112	3248	26	homepage	homepage	NOUN
m-1112	3248	27	[	[	X
m-1112	3248	28	53	53	NUM
m-1112	3248	29	]	]	PUNCT
m-1112	3248	30	material	material	NOUN
m-1112	3248	31	-	-	PUNCT
m-1112	3248	32	geometry	geometry	NOUN
m-1112	3248	33	and	and	CCONJ
m-1112	3248	34	the	the	DET
m-1112	3248	35	elements	element	NOUN
m-1112	3248	36	of	of	ADP
m-1112	3248	37	the	the	DET
m-1112	3248	38	periodic	periodic	ADJ
m-1112	3248	39	-	-	PUNCT
m-1112	3248	40	table	table	NOUN
m-1112	3248	41	www.ijerm.com(id-0306031.0	www.ijerm.com(id-0306031.0	NOUN
m-1112	3248	42	)	)	PUNCT
m-1112	3249	1	[	[	X
m-1112	3249	2	54	54	NUM
m-1112	3249	3	]	]	PUNCT
m-1112	3249	4	the	the	DET
m-1112	3249	5	material	material	NOUN
m-1112	3249	6	-	-	PUNCT
m-1112	3249	7	geometry	geometry	NOUN
m-1112	3249	8	periodic	periodic	ADJ
m-1112	3249	9	table	table	NOUN
m-1112	3249	10	of	of	ADP
m-1112	3249	11	particles	particle	NOUN
m-1112	3249	12	and	and	CCONJ
m-1112	3249	13	chemistry	chemistry	NOUN
m-1112	3249	14	.http://ijemcs.in/	.http://ijemcs.in/	PUNCT
m-1112	3250	1	[	[	X
m-1112	3250	2	54	54	NUM
m-1112	3250	3	]	]	PUNCT
m-1112	3250	4	the	the	DET
m-1112	3250	5	material	material	NOUN
m-1112	3250	6	-	-	PUNCT
m-1112	3250	7	geometry	geometry	NOUN
m-1112	3250	8	a	a	DET
m-1112	3250	9	-	-	PUNCT
m-1112	3250	10	periodic	periodic	ADJ
m-1112	3250	11	table	table	NOUN
m-1112	3250	12	of	of	ADP
m-1112	3250	13	particles	particle	NOUN
m-1112	3250	14	and	and	CCONJ
m-1112	3250	15	chemistry	chemistry	NOUN
m-1112	3250	16	.	.	PUNCT
m-1112	3251	1	www.iosrjournals.org	www.iosrjournals.org	NUM
m-1112	3251	2	)	)	PUNCT
m-1112	3252	1	[	[	X
m-1112	3252	2	55	55	NUM
m-1112	3252	3	]	]	PUNCT
m-1112	3252	4	material	material	NOUN
m-1112	3252	5	-	-	PUNCT
m-1112	3252	6	geometry	geometry	NOUN
m-1112	3252	7	,	,	PUNCT
m-1112	3252	8	the	the	DET
m-1112	3252	9	periodic	periodic	ADJ
m-1112	3252	10	table	table	NOUN
m-1112	3252	11	of	of	ADP
m-1112	3252	12	particles	particle	NOUN
m-1112	3252	13	&	&	CCONJ
m-1112	3252	14	physics	physics	PROPN
m-1112	3252	15	,	,	PUNCT
m-1112	3252	16	http://ephjournal.com	http://ephjournal.com	X
m-1112	3253	1	[	[	X
m-1112	3253	2	56	56	NUM
m-1112	3253	3	]	]	X
m-1112	3253	4	big	big	ADJ
m-1112	3253	5	-	-	PUNCT
m-1112	3253	6	bang	bang	NOUN
m-1112	3253	7	or	or	CCONJ
m-1112	3253	8	the	the	DET
m-1112	3253	9	glue	glue	NOUN
m-1112	3253	10	-	-	PUNCT
m-1112	3253	11	bond	bond	NOUN
m-1112	3253	12	of	of	ADP
m-1112	3253	13	space	space	NOUN
m-1112	3253	14	,	,	PUNCT
m-1112	3253	15	anti	anti	ADJ
m-1112	3253	16	-	-	NOUN
m-1112	3253	17	space	space	NOUN
m-1112	3253	18	?	?	PUNCT
m-1112	3253	19	?	?	PUNCT
m-1112	3253	20	.	.	PUNCT
m-1112	3254	1	(	(	PUNCT
m-1112	3254	2	www.technicaldean.org	www.technicaldean.org	X
m-1112	3254	3	)	)	PUNCT
m-1112	3255	1	[	[	X
m-1112	3255	2	57	57	NUM
m-1112	3255	3	]	]	PUNCT
m-1112	3255	4	the	the	DET
m-1112	3255	5	eternal	eternal	ADJ
m-1112	3255	6	glue	glue	NOUN
m-1112	3255	7	-	-	PUNCT
m-1112	3255	8	bond	bond	NOUN
m-1112	3255	9	of	of	ADP
m-1112	3255	10	space	space	NOUN
m-1112	3255	11	,	,	PUNCT
m-1112	3255	12	anti	anti	ADJ
m-1112	3255	13	-	-	ADJ
m-1112	3255	14	space	space	ADJ
m-1112	3255	15	,	,	PUNCT
m-1112	3255	16	chemistry	chemistry	NOUN
m-1112	3255	17	and	and	CCONJ
m-1112	3255	18	physics	physics	NOUN
m-1112	3255	19	www.globaljournals.org	www.globaljournals.org	NOUN
m-1112	3255	20	.	.	PUNCT
m-1112	3256	1	[	[	X
m-1112	3256	2	58	58	NUM
m-1112	3256	3	]	]	X
m-1112	3256	4	big	big	ADJ
m-1112	3256	5	-	-	PUNCT
m-1112	3256	6	bang	bang	NOUN
m-1112	3256	7	or	or	CCONJ
m-1112	3256	8	the	the	DET
m-1112	3256	9	rolling	rolling	ADJ
m-1112	3256	10	glue	glue	NOUN
m-1112	3256	11	-	-	PUNCT
m-1112	3256	12	bond	bond	NOUN
m-1112	3256	13	of	of	ADP
m-1112	3256	14	space	space	NOUN
m-1112	3256	15	,	,	PUNCT
m-1112	3256	16	anti	anti	ADJ
m-1112	3256	17	-	-	NOUN
m-1112	3256	18	space	space	ADJ
m-1112	3256	19	,	,	PUNCT
m-1112	3256	20	book@scirp.org	book@scirp.org	VERB
m-1112	3256	21	,	,	PUNCT
m-1112	3256	22	http://www.scirp.org/	http://www.scirp.org/	NOUN
m-1112	3256	23	[	[	X
m-1112	3256	24	59	59	NUM
m-1112	3256	25	]	]	PUNCT
m-1112	3256	26	stpl	stpl	ADJ
m-1112	3256	27	mechanism	mechanism	NOUN
m-1112	3256	28	is	be	AUX
m-1112	3256	29	the	the	DET
m-1112	3256	30	energy	energy	NOUN
m-1112	3256	31	–	–	PUNCT
m-1112	3256	32	space	space	NOUN
m-1112	3256	33	generator	generator	NOUN
m-1112	3256	34	.	.	PUNCT
m-1112	3257	1	http://vixra.org/abs/1612.0299	http://vixra.org/abs/1612.0299	PROPN
m-1112	3258	1	[	[	X
m-1112	3258	2	60	60	NUM
m-1112	3258	3	]	]	PUNCT
m-1112	3258	4	the	the	DET
m-1112	3258	5	chaos	chaos	NOUN
m-1112	3258	6	becomes	become	VERB
m-1112	3258	7	discrete	discrete	ADJ
m-1112	3258	8	through	through	ADP
m-1112	3258	9	the	the	DET
m-1112	3258	10	stpl	stpl	PROPN
m-1112	3258	11	mechanism	mechanism	NOUN
m-1112	3258	12	which	which	PRON
m-1112	3258	13	is	be	AUX
m-1112	3258	14	energy	energy	NOUN
m-1112	3258	15	-	-	PUNCT
m-1112	3258	16	space	space	NOUN
m-1112	3258	17	generator	generator	NOUN
m-1112	3258	18	(	(	PUNCT
m-1112	3258	19	http://www.ijrdo.org/	http://www.ijrdo.org/	NOUN
m-1112	3258	20	)	)	PUNCT
m-1112	3259	1	[	[	X
m-1112	3259	2	61	61	NUM
m-1112	3259	3	]	]	PUNCT
m-1112	3259	4	the	the	PRON
m-1112	3259	5	how	how	SCONJ
m-1112	3259	6	energy	energy	NOUN
m-1112	3259	7	from	from	ADP
m-1112	3259	8	chaos	chaos	NOUN
m-1112	3259	9	becomes	become	VERB
m-1112	3259	10	discrete	discrete	ADJ
m-1112	3259	11	monads	monad	NOUN
m-1112	3259	12	http://www.ephjournal.net/	http://www.ephjournal.net/	NOUN
m-1112	3259	13	[	[	X
m-1112	3259	14	61	61	NUM
m-1112	3259	15	-	-	SYM
m-1112	3259	16	a	a	NOUN
m-1112	3259	17	]	]	X
m-1112	3259	18	the	the	PRON
m-1112	3259	19	how	how	SCONJ
m-1112	3259	20	energy	energy	NOUN
m-1112	3259	21	from	from	ADP
m-1112	3259	22	chaos	chaos	NOUN
m-1112	3259	23	,	,	PUNCT
m-1112	3259	24	becomes	become	VERB
m-1112	3259	25	discrete	discrete	ADJ
m-1112	3259	26	monads	monad	NOUN
m-1112	3259	27	.	.	PUNCT
m-1112	3260	1	http://www.ijrdo.org/	http://www.ijrdo.org/	NOUN
m-1112	3261	1	[	[	PUNCT
m-1112	3261	2	62	62	NUM
m-1112	3261	3	-	-	SYM
m-1112	3261	4	b	b	NOUN
m-1112	3261	5	]	]	X
m-1112	3261	6	the	the	DET
m-1112	3261	7	geometrical	geometrical	ADJ
m-1112	3261	8	solution	solution	NOUN
m-1112	3261	9	of	of	ADP
m-1112	3261	10	all	all	DET
m-1112	3261	11	regular	regular	ADJ
m-1112	3261	12	n	n	CCONJ
m-1112	3261	13	-	-	PUNCT
m-1112	3261	14	polygons	polygon	NOUN
m-1112	3261	15	.	.	PUNCT
m-1112	3262	1	http://www.irjaes.com/	http://www.irjaes.com/	NOUN
m-1112	3263	1	[	[	X
m-1112	3263	2	62	62	NUM
m-1112	3263	3	]	]	PUNCT
m-1112	3263	4	the	the	DET
m-1112	3263	5	geometrical	geometrical	ADJ
m-1112	3263	6	solution	solution	NOUN
m-1112	3263	7	of	of	ADP
m-1112	3263	8	all	all	DET
m-1112	3263	9	odd	odd	ADJ
m-1112	3263	10	–	–	PUNCT
m-1112	3263	11	regular	regular	ADJ
m-1112	3263	12	–	–	PUNCT
m-1112	3263	13	polygons	polygon	NOUN
m-1112	3263	14	,	,	PUNCT
m-1112	3263	15	and	and	CCONJ
m-1112	3263	16	the	the	DET
m-1112	3263	17	special	special	ADJ
m-1112	3263	18	greek	greek	NOUN
m-1112	3263	19	problems	problem	NOUN
m-1112	3263	20	http://www.irjaes.com/	http://www.irjaes.com/	VERB
m-1112	3264	1	[	[	X
m-1112	3264	2	63	63	NUM
m-1112	3264	3	]	]	PUNCT
m-1112	3264	4	the	the	DET
m-1112	3264	5	geometrical	geometrical	ADJ
m-1112	3264	6	solution	solution	NOUN
m-1112	3264	7	of	of	ADP
m-1112	3264	8	all	all	DET
m-1112	3264	9	odd	odd	ADJ
m-1112	3264	10	–	–	PUNCT
m-1112	3264	11	regular	regular	ADJ
m-1112	3264	12	–	–	PUNCT
m-1112	3264	13	polygons	polygon	NOUN
m-1112	3264	14	,	,	PUNCT
m-1112	3264	15	the	the	DET
m-1112	3264	16	special	special	ADJ
m-1112	3264	17	greek	greek	NOUN
m-1112	3264	18	problems	problem	NOUN
m-1112	3264	19	and	and	CCONJ
m-1112	3264	20	their	their	PRON
m-1112	3264	21	nature	nature	NOUN
m-1112	3264	22	.	.	PUNCT
m-1112	3265	1	http://www.ijerd.com/	http://www.ijerd.com/	PROPN
m-1112	3266	1	[	[	X
m-1112	3266	2	63	63	NUM
m-1112	3266	3	]	]	PUNCT
m-1112	3266	4	[	[	X
m-1112	3266	5	a	a	X
m-1112	3266	6	]	]	X
m-1112	3266	7	the	the	DET
m-1112	3266	8	geometrical	geometrical	ADJ
m-1112	3266	9	solution	solution	NOUN
m-1112	3266	10	of	of	ADP
m-1112	3266	11	theregular	theregular	ADJ
m-1112	3266	12	–	–	PUNCT
m-1112	3266	13	polygons	polygon	NOUN
m-1112	3266	14	,	,	PUNCT
m-1112	3266	15	the	the	DET
m-1112	3266	16	special	special	ADJ
m-1112	3266	17	greek	greek	NOUN
m-1112	3266	18	problems	problem	NOUN
m-1112	3266	19	and	and	CCONJ
m-1112	3266	20	their	their	PRON
m-1112	3266	21	nature	nature	NOUN
m-1112	3266	22	.	.	PUNCT
m-1112	3267	1	http://vixra.org/	http://vixra.org/	PRON
m-1112	3268	1	[	[	X
m-1112	3268	2	63	63	NUM
m-1112	3268	3	]	]	PUNCT
m-1112	3269	1	[	[	X
m-1112	3269	2	b	b	X
m-1112	3269	3	]	]	X
m-1112	3269	4	the	the	DET
m-1112	3269	5	geometrical	geometrical	ADJ
m-1112	3269	6	solution	solution	NOUN
m-1112	3269	7	of	of	ADP
m-1112	3269	8	theregular	theregular	ADJ
m-1112	3269	9	–	–	PUNCT
m-1112	3269	10	polygons	polygon	NOUN
m-1112	3269	11	,	,	PUNCT
m-1112	3269	12	the	the	DET
m-1112	3269	13	special	special	ADJ
m-1112	3269	14	ijo	ijo	PROPN
m-1112	3269	15	international	international	PROPN
m-1112	3269	16	journal	journal	PROPN
m-1112	3269	17	of	of	ADP
m-1112	3269	18	mathematics	mathematics	PROPN
m-1112	3269	19	(	(	PUNCT
m-1112	3269	20	issn	issn	PROPN
m-1112	3269	21	:	:	PUNCT
m-1112	3269	22	2992	2992	NUM
m-1112	3269	23	-	-	SYM
m-1112	3269	24	4421	4421	NUM
m-1112	3269	25	)	)	PUNCT
m-1112	3269	26	volume	volume	NOUN
m-1112	3269	27	08	08	NUM
m-1112	3270	1	|	|	ADV
m-1112	3270	2	issue	issue	NOUN
m-1112	3270	3	08	08	NUM
m-1112	3271	1	|	|	ADV
m-1112	3271	2	august	august	PROPN
m-1112	3271	3	2025	2025	NUM
m-1112	3272	1	|	|	ADV
m-1112	3272	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3272	3	ijo	ijo	PROPN
m-1112	3272	4	journals	journal	NOUN
m-1112	3272	5	http://www.sciencepublishinggroup.com/j	http://www.sciencepublishinggroup.com/j	PROPN
m-1112	3272	6	https://www.lap-publishing.com/	https://www.lap-publishing.com/	ADJ
m-1112	3272	7	http://www.ijirset.com/	http://www.ijirset.com/	NOUN
m-1112	3272	8	http://vixra.org/abs/1510.0328	http://vixra.org/abs/1510.0328	PROPN
m-1112	3272	9	http://www.submission.arpweb.com(id-44031	http://www.submission.arpweb.com(id-44031	PROPN
m-1112	3272	10	-	-	PROPN
m-1112	3272	11	sr-015.0/	sr-015.0/	PROPN
m-1112	3272	12	http://www.ijera.com(id-512080.0/	http://www.ijera.com(id-512080.0/	NOUN
m-1112	3272	13	http://www.oalib.com(id-1102480.0/	http://www.oalib.com(id-1102480.0/	PRON
m-1112	3272	14	http://gpcpublishing.com/index.php?journal=gjp&page=index	http://gpcpublishing.com/index.php?journal=gjp&page=index	NOUN
m-1112	3272	15	http://www.ijerm.com(id-0306031.0/	http://www.ijerm.com(id-0306031.0/	PROPN
m-1112	3272	16	http://ijemcs.in/	http://ijemcs.in/	NOUN
m-1112	3272	17	http://www.iosrjournals.org/	http://www.iosrjournals.org/	X
m-1112	3272	18	http://ephjournal.com/	http://ephjournal.com/	PROPN
m-1112	3272	19	http://www.technicaldean.org/	http://www.technicaldean.org/	X
m-1112	3272	20	http://www.globaljoyrnals.org/	http://www.globaljoyrnals.org/	X
m-1112	3272	21	http://www.scirp.org/	http://www.scirp.org/	NOUN
m-1112	3272	22	http://vixra.org/abs/1612.0299	http://vixra.org/abs/1612.0299	NOUN
m-1112	3272	23	http://www.ijrdo.org/	http://www.ijrdo.org/	NOUN
m-1112	3272	24	http://www.ephjournal.net/	http://www.ephjournal.net/	NOUN
m-1112	3272	25	http://www.ijrdo.org/	http://www.ijrdo.org/	PROPN
m-1112	3272	26	http://www.irjaes.com/	http://www.irjaes.com/	PROPN
m-1112	3272	27	http://www.irjaes.com/	http://www.irjaes.com/	PROPN
m-1112	3272	28	http://www.ijerd.com/	http://www.ijerd.com/	PROPN
m-1112	3272	29	http://vixra.org/	http://vixra.org/	PROPN
m-1112	3272	30	116	116	NUM
m-1112	3272	31	the	the	DET
m-1112	3272	32	fundamental	fundamental	ADJ
m-1112	3272	33	particles	particle	NOUN
m-1112	3272	34	origination	origination	NOUN
m-1112	3272	35	mechanism	mechanism	NOUN
m-1112	3272	36	in	in	ADP
m-1112	3272	37	mfmf	mfmf	PROPN
m-1112	3272	38	pns	pns	PROPN
m-1112	3272	39	caves	cave	NOUN
m-1112	3272	40	.	.	PUNCT
m-1112	3273	1	greek	greek	ADJ
m-1112	3273	2	problems	problem	NOUN
m-1112	3273	3	and	and	CCONJ
m-1112	3273	4	their	their	PRON
m-1112	3273	5	nature	nature	NOUN
m-1112	3273	6	.	.	PUNCT
m-1112	3274	1	(	(	PUNCT
m-1112	3274	2	http://iosrmail.org/	http://iosrmail.org/	NOUN
m-1112	3274	3	)	)	PUNCT
m-1112	3275	1	[	[	X
m-1112	3275	2	64	64	NUM
m-1112	3275	3	]	]	PUNCT
m-1112	3276	1	[	[	X
m-1112	3276	2	a	a	X
m-1112	3276	3	]	]	X
m-1112	3276	4	the	the	DET
m-1112	3276	5	how	how	SCONJ
m-1112	3276	6	energy	energy	NOUN
m-1112	3276	7	from	from	ADP
m-1112	3276	8	chaos	chaos	NOUN
m-1112	3276	9	becomes	become	VERB
m-1112	3276	10	the	the	DET
m-1112	3276	11	→	→	SYM
m-1112	3276	12	spin	spin	NOUN
m-1112	3276	13	,	,	PUNCT
m-1112	3276	14	of	of	ADP
m-1112	3276	15	the	the	DET
m-1112	3276	16	discrete	discrete	ADJ
m-1112	3276	17	elementary	elementary	ADJ
m-1112	3276	18	monads	monad	NOUN
m-1112	3276	19	.	.	PUNCT
m-1112	3277	1	http://www.i-b-r.org	http://www.i-b-r.org	ADJ
m-1112	3277	2	.	.	PUNCT
m-1112	3277	3	/	/	PUNCT
m-1112	3277	4	.	.	PUNCT
m-1112	3277	5	?	?	PUNCT
m-1112	3277	6	?	?	PUNCT
m-1112	3278	1	[	[	X
m-1112	3278	2	64	64	NUM
m-1112	3278	3	]	]	PUNCT
m-1112	3278	4	the	the	DET
m-1112	3278	5	how	how	SCONJ
m-1112	3278	6	energy	energy	NOUN
m-1112	3278	7	from	from	ADP
m-1112	3278	8	chaos	chaos	NOUN
m-1112	3278	9	becomes	become	VERB
m-1112	3278	10	the	the	DET
m-1112	3278	11	→	→	SYM
m-1112	3278	12	spin	spin	NOUN
m-1112	3278	13	,	,	PUNCT
m-1112	3278	14	of	of	ADP
m-1112	3278	15	the	the	DET
m-1112	3278	16	discrete	discrete	ADJ
m-1112	3278	17	elementary	elementary	ADJ
m-1112	3278	18	monads	monad	NOUN
m-1112	3278	19	:	:	PUNCT
m-1112	3278	20	(	(	PUNCT
m-1112	3278	21	http://www.ijrdo.org/	http://www.ijrdo.org/	NOUN
m-1112	3278	22	)	)	PUNCT
m-1112	3279	1	[	[	X
m-1112	3279	2	65	65	NUM
m-1112	3279	3	]	]	X
m-1112	3279	4	the	the	DET
m-1112	3279	5	spin	spin	NOUN
m-1112	3279	6	of	of	ADP
m-1112	3279	7	monads	monad	NOUN
m-1112	3279	8	and	and	CCONJ
m-1112	3279	9	their	their	PRON
m-1112	3279	10	energy	energy	NOUN
m-1112	3279	11	-	-	PUNCT
m-1112	3279	12	stores	store	NOUN
m-1112	3279	13	.	.	PUNCT
m-1112	3280	1	www.ajer.org	www.ajer.org	X
m-1112	3280	2	.	.	PUNCT
m-1112	3281	1	[	[	X
m-1112	3281	2	66	66	NUM
m-1112	3281	3	]	]	PUNCT
m-1112	3281	4	the	the	DET
m-1112	3281	5	energy	energy	NOUN
m-1112	3281	6	-	-	PUNCT
m-1112	3281	7	stores	store	NOUN
m-1112	3281	8	in	in	ADP
m-1112	3281	9	photon	photon	NOUN
m-1112	3281	10	.	.	PUNCT
m-1112	3282	1	http://www.i-b-r.org	http://www.i-b-r.org	PROPN
m-1112	3282	2	.	.	PUNCT
m-1112	3282	3	/	/	PUNCT
m-1112	3282	4	.	.	PUNCT
m-1112	3282	5	?	?	PUNCT
m-1112	3282	6	?	?	PUNCT
m-1112	3282	7	?	?	PUNCT
m-1112	3283	1	[	[	X
m-1112	3283	2	67	67	NUM
m-1112	3283	3	]	]	PUNCT
m-1112	3283	4	the	the	DET
m-1112	3283	5	energy	energy	NOUN
m-1112	3283	6	structure	structure	NOUN
m-1112	3283	7	of	of	ADP
m-1112	3283	8	atoms	atom	NOUN
m-1112	3283	9	and	and	CCONJ
m-1112	3283	10	photon	photon	NOUN
m-1112	3283	11	.	.	PUNCT
m-1112	3284	1	http://vixra.org/.	http://vixra.org/.	PROPN
m-1112	3285	1	[	[	X
m-1112	3285	2	68	68	NUM
m-1112	3285	3	]	]	X
m-1112	3285	4	the	the	DET
m-1112	3285	5	moving	move	VERB
m-1112	3285	6	energy	energy	NOUN
m-1112	3285	7	storages	storage	NOUN
m-1112	3285	8	and	and	CCONJ
m-1112	3285	9	photon	photon	NOUN
m-1112	3285	10	.	.	PUNCT
m-1112	3285	11	www.sfjqp.com	www.sfjqp.com	X
m-1112	3286	1	[	[	X
m-1112	3286	2	69	69	NUM
m-1112	3286	3	]	]	PUNCT
m-1112	3286	4	the	the	DET
m-1112	3286	5	moving	move	VERB
m-1112	3286	6	and	and	CCONJ
m-1112	3286	7	the	the	DET
m-1112	3286	8	stationary	stationary	ADJ
m-1112	3286	9	particles	particle	NOUN
m-1112	3286	10	.	.	PUNCT
m-1112	3287	1	http://science	http://science	NOUN
m-1112	3287	2	mpg	mpg	NOUN
m-1112	3288	1	[	[	X
m-1112	3288	2	70	70	NUM
m-1112	3288	3	]	]	PUNCT
m-1112	3288	4	the	the	DET
m-1112	3288	5	how	how	SCONJ
m-1112	3288	6	energy	energy	NOUN
m-1112	3288	7	from	from	ADP
m-1112	3288	8	chaos	chaos	NOUN
m-1112	3288	9	becomes	become	VERB
m-1112	3288	10	the	the	DET
m-1112	3288	11	spin	spin	NOUN
m-1112	3288	12	of	of	ADP
m-1112	3288	13	monads	monad	NOUN
m-1112	3288	14	and	and	CCONJ
m-1112	3288	15	photon	photon	NOUN
m-1112	3288	16	http://www.ijrdo.org/	http://www.ijrdo.org/	NOUN
m-1112	3289	1	[	[	X
m-1112	3289	2	70	70	NUM
m-1112	3289	3	]	]	PUNCT
m-1112	3289	4	energy	energy	NOUN
m-1112	3289	5	from	from	ADP
m-1112	3289	6	chaos	chaos	NOUN
m-1112	3289	7	becomes	become	VERB
m-1112	3289	8	the	the	DET
m-1112	3289	9	spin	spin	NOUN
m-1112	3289	10	of	of	ADP
m-1112	3289	11	monads	monad	NOUN
m-1112	3289	12	&	&	CCONJ
m-1112	3289	13	photon	photon	NOUN
m-1112	3289	14	,	,	PUNCT
m-1112	3289	15	http://science	http://science	NOUN
m-1112	3289	16	mpg	mpg	NOUN
m-1112	3289	17	[	[	X
m-1112	3289	18	70	70	NUM
m-1112	3289	19	]	]	PUNCT
m-1112	3289	20	the	the	DET
m-1112	3289	21	how	how	SCONJ
m-1112	3289	22	energy	energy	NOUN
m-1112	3289	23	from	from	ADP
m-1112	3289	24	chaos	chaos	NOUN
m-1112	3289	25	becomes	become	VERB
m-1112	3289	26	the	the	DET
m-1112	3289	27	spin	spin	NOUN
m-1112	3289	28	of	of	ADP
m-1112	3289	29	monads	monad	NOUN
m-1112	3289	30	and	and	CCONJ
m-1112	3289	31	photon	photon	NOUN
m-1112	3289	32	.	.	PUNCT
m-1112	3290	1	www.ijera.com	www.ijera.com	X
m-1112	3290	2	.	.	PUNCT
m-1112	3291	1	[	[	X
m-1112	3291	2	71	71	NUM
m-1112	3291	3	]	]	PUNCT
m-1112	3291	4	the	the	DET
m-1112	3291	5	gravity	gravity	NOUN
m-1112	3291	6	and	and	CCONJ
m-1112	3291	7	photons	photon	NOUN
m-1112	3291	8	.	.	PUNCT
m-1112	3292	1	http://asir@sholink.org	http://asir@sholink.org	PUNCT
m-1112	3293	1	[	[	X
m-1112	3293	2	72	72	NUM
m-1112	3293	3	]	]	PUNCT
m-1112	3293	4	the	the	DET
m-1112	3293	5	origin	origin	NOUN
m-1112	3293	6	of	of	ADP
m-1112	3293	7	gravity	gravity	NOUN
m-1112	3293	8	and	and	CCONJ
m-1112	3293	9	universe	universe	NOUN
m-1112	3293	10	.	.	PUNCT
m-1112	3294	1	[	[	X
m-1112	3294	2	mailto:editorusa@globaljournals.org	mailto:editorusa@globaljournals.org	X
m-1112	3294	3	]	]	X
m-1112	3294	4	[	[	X
m-1112	3294	5	72a	72a	NOUN
m-1112	3294	6	]	]	X
m-1112	3294	7	[	[	X
m-1112	3294	8	m	m	X
m-1112	3294	9	]	]	X
m-1112	3294	10	the	the	DET
m-1112	3294	11	origin	origin	NOUN
m-1112	3294	12	of	of	ADP
m-1112	3294	13	gravity	gravity	NOUN
m-1112	3294	14	gravitational	gravitational	ADJ
m-1112	3294	15	constant	constant	ADJ
m-1112	3294	16	and	and	CCONJ
m-1112	3294	17	universe	universe	NOUN
m-1112	3294	18	.	.	PUNCT
m-1112	3295	1	http://saiconference.com/ftc	http://saiconference.com/ftc	PUNCT
m-1112	3296	1	[	[	X
m-1112	3296	2	73	73	NUM
m-1112	3296	3	]	]	PUNCT
m-1112	3296	4	[	[	X
m-1112	3296	5	m	m	X
m-1112	3296	6	]	]	X
m-1112	3296	7	planck`s	planck`s	NOUN
m-1112	3296	8	constant	constant	ADJ
m-1112	3296	9	,	,	PUNCT
m-1112	3296	10	the	the	DET
m-1112	3296	11	gravitational	gravitational	ADJ
m-1112	3296	12	and	and	CCONJ
m-1112	3296	13	gravity	gravity	NOUN
m-1112	3296	14	constant	constant	ADJ
m-1112	3296	15	.	.	PUNCT
m-1112	3297	1	:	:	PUNCT
m-1112	3298	1	https://ijrdo.org/index.php/mce/issue/current	https://ijrdo.org/index.php/mce/issue/current	NOUN
m-1112	3298	2	[	[	X
m-1112	3298	3	74	74	NUM
m-1112	3298	4	]	]	PUNCT
m-1112	3299	1	[	[	X
m-1112	3299	2	m	m	X
m-1112	3299	3	]	]	X
m-1112	3299	4	the	the	DET
m-1112	3299	5	newtonian	newtonian	ADJ
m-1112	3299	6	constant	constant	ADJ
m-1112	3299	7	of	of	ADP
m-1112	3299	8	gravitation	gravitation	NOUN
m-1112	3299	9	and	and	CCONJ
m-1112	3299	10	gravity	gravity	NOUN
m-1112	3299	11	constant	constant	ADJ
m-1112	3299	12	.	.	PUNCT
m-1112	3300	1	www.iosr.org	www.iosr.org	PROPN
m-1112	3301	1	[	[	X
m-1112	3301	2	75	75	NUM
m-1112	3301	3	]	]	PUNCT
m-1112	3302	1	[	[	X
m-1112	3302	2	m	m	X
m-1112	3302	3	]	]	X
m-1112	3302	4	the	the	DET
m-1112	3302	5	newtonian	newtonian	ADJ
m-1112	3302	6	constant	constant	ADJ
m-1112	3302	7	of	of	ADP
m-1112	3302	8	gravitation	gravitation	NOUN
m-1112	3302	9	and	and	CCONJ
m-1112	3302	10	gravity	gravity	NOUN
m-1112	3302	11	constant	constant	ADJ
m-1112	3302	12	.	.	PUNCT
m-1112	3303	1	the	the	DET
m-1112	3303	2	physical	physical	ADJ
m-1112	3303	3	interpretation	interpretation	NOUN
m-1112	3303	4	http://science	http://science	ADP
m-1112	3303	5	mpg	mpg	NOUN
m-1112	3303	6	[	[	X
m-1112	3303	7	76	76	NUM
m-1112	3303	8	]	]	X
m-1112	3304	1	[	[	X
m-1112	3304	2	m	m	X
m-1112	3304	3	]	]	X
m-1112	3304	4	the	the	DET
m-1112	3304	5	newtonian	newtonian	ADJ
m-1112	3304	6	constant	constant	ADJ
m-1112	3304	7	of	of	ADP
m-1112	3304	8	gravitation	gravitation	NOUN
m-1112	3304	9	gravity	gravity	NOUN
m-1112	3304	10	constant	constant	ADJ
m-1112	3304	11	,	,	PUNCT
m-1112	3304	12	and	and	CCONJ
m-1112	3304	13	the	the	DET
m-1112	3304	14	galileo	galileo	NOUN
m-1112	3304	15	principia	principia	PROPN
m-1112	3304	16	http://www.i-b-r.org	http://www.i-b-r.org	PROPN
m-1112	3304	17	.	.	PUNCT
m-1112	3304	18	/	/	PUNCT
m-1112	3304	19	.	.	PUNCT
m-1112	3305	1	[	[	X
m-1112	3305	2	76a	76a	NOUN
m-1112	3305	3	]	]	X
m-1112	3305	4	[	[	X
m-1112	3305	5	m	m	X
m-1112	3305	6	]	]	X
m-1112	3305	7	origination	origination	NOUN
m-1112	3305	8	of	of	ADP
m-1112	3305	9	the	the	DET
m-1112	3305	10	nutation	nutation	NOUN
m-1112	3305	11	-	-	PUNCT
m-1112	3305	12	motion	motion	NOUN
m-1112	3305	13	,	,	PUNCT
m-1112	3305	14	and	and	CCONJ
m-1112	3305	15	atom	atom	NOUN
m-1112	3305	16	-	-	PUNCT
m-1112	3305	17	model	model	NOUN
m-1112	3305	18	.http://www.i-b-r.org	.http://www.i-b-r.org	PROPN
m-1112	3305	19	.	.	PUNCT
m-1112	3305	20	/.	/.	PUNCT
m-1112	3305	21	?	?	PUNCT
m-1112	3306	1	[	[	X
m-1112	3306	2	77	77	X
m-1112	3306	3	]	]	X
m-1112	3306	4	[	[	X
m-1112	3306	5	m	m	X
m-1112	3306	6	]	]	X
m-1112	3306	7	the	the	DET
m-1112	3306	8	newtonian	newtonian	ADJ
m-1112	3306	9	constant	constant	ADJ
m-1112	3306	10	of	of	ADP
m-1112	3306	11	gravitation	gravitation	NOUN
m-1112	3306	12	and	and	CCONJ
m-1112	3306	13	gravity	gravity	NOUN
m-1112	3306	14	constant	constant	ADJ
m-1112	3306	15	.	.	PUNCT
m-1112	3307	1	their	their	PRON
m-1112	3307	2	physical	physical	ADJ
m-1112	3307	3	interpretation	interpretation	NOUN
m-1112	3307	4	..	..	PUNCT
m-1112	3308	1	[	[	X
m-1112	3308	2	78	78	X
m-1112	3308	3	]	]	PUNCT
m-1112	3308	4	[	[	X
m-1112	3308	5	m	m	X
m-1112	3308	6	]	]	X
m-1112	3308	7	the	the	DET
m-1112	3308	8	physical	physical	ADJ
m-1112	3308	9	interpretation	interpretation	NOUN
m-1112	3308	10	of	of	ADP
m-1112	3308	11	gravity	gravity	NOUN
m-1112	3308	12	-	-	PUNCT
m-1112	3308	13	constants	constant	NOUN
m-1112	3308	14	,	,	PUNCT
m-1112	3308	15	electron	electron	NOUN
m-1112	3308	16	and	and	CCONJ
m-1112	3308	17	photon	photon	VERB
m-1112	3308	18	https://saiconference.com/ficc2020/submit	https://saiconference.com/ficc2020/submit	PROPN
m-1112	3309	1	[	[	X
m-1112	3309	2	79	79	NUM
m-1112	3309	3	]	]	PUNCT
m-1112	3309	4	[	[	X
m-1112	3309	5	m	m	X
m-1112	3309	6	]	]	X
m-1112	3309	7	the	the	DET
m-1112	3309	8	planck`s	planck`s	NOUN
m-1112	3309	9	constant	constant	ADJ
m-1112	3309	10	and	and	CCONJ
m-1112	3309	11	speed	speed	NOUN
m-1112	3309	12	of	of	ADP
m-1112	3309	13	light	light	NOUN
m-1112	3309	14	.	.	PUNCT
m-1112	3310	1	http://science	http://science	NOUN
m-1112	3310	2	mpg	mpg	NOUN
m-1112	3311	1	[	[	X
m-1112	3311	2	80	80	NUM
m-1112	3311	3	]	]	X
m-1112	3311	4	[	[	X
m-1112	3311	5	m	m	X
m-1112	3311	6	]	]	X
m-1112	3311	7	the	the	DET
m-1112	3311	8	origination	origination	NOUN
m-1112	3311	9	of	of	ADP
m-1112	3311	10	the	the	DET
m-1112	3311	11	nutation	nutation	NOUN
m-1112	3311	12	-	-	PUNCT
m-1112	3311	13	motion	motion	NOUN
m-1112	3311	14	,	,	PUNCT
m-1112	3311	15	the	the	DET
m-1112	3311	16	new	new	ADJ
m-1112	3311	17	-	-	PUNCT
m-1112	3311	18	energy	energy	NOUN
m-1112	3311	19	-	-	PUNCT
m-1112	3311	20	atom	atom	NOUN
m-1112	3311	21	-	-	PUNCT
m-1112	3311	22	model	model	NOUN
m-1112	3311	23	and	and	CCONJ
m-1112	3311	24	the	the	DET
m-1112	3311	25	united	united	PROPN
m-1112	3311	26	-	-	PUNCT
m-1112	3311	27	coulomb	coulomb	PROPN
m-1112	3311	28	-	-	PUNCT
m-1112	3311	29	newton	newton	NOUN
m-1112	3311	30	-	-	PUNCT
m-1112	3311	31	laws	law	NOUN
m-1112	3311	32	for	for	ADP
m-1112	3311	33	interaction	interaction	NOUN
m-1112	3311	34	.	.	PUNCT
m-1112	3312	1	https://www.akinik.com/publishbookchapter/-research	https://www.akinik.com/publishbookchapter/-research	PROPN
m-1112	3313	1	[	[	X
m-1112	3313	2	81	81	NUM
m-1112	3313	3	]	]	PUNCT
m-1112	3314	1	[	[	X
m-1112	3314	2	m	m	X
m-1112	3314	3	]	]	X
m-1112	3314	4	the	the	DET
m-1112	3314	5	physical	physical	ADJ
m-1112	3314	6	interpretation	interpretation	NOUN
m-1112	3314	7	of	of	ADP
m-1112	3314	8	gravity	gravity	NOUN
m-1112	3314	9	–	–	PUNCT
m-1112	3314	10	constant	constant	ADJ
m-1112	3314	11	,	,	PUNCT
m-1112	3314	12	electron	electron	NOUN
m-1112	3314	13	and	and	CCONJ
m-1112	3314	14	photon	photon	PROPN
m-1112	3314	15	http://vixra.org/abs/1906.o468	http://vixra.org/abs/1906.o468	PROPN
m-1112	3314	16	,	,	PUNCT
m-1112	3314	17	https://www.scribd.com/doc/	https://www.scribd.com/doc/	X
m-1112	3314	18	[	[	X
m-1112	3314	19	82	82	NUM
m-1112	3314	20	]	]	X
m-1112	3315	1	[	[	X
m-1112	3315	2	m	m	X
m-1112	3315	3	]	]	X
m-1112	3315	4	the	the	DET
m-1112	3315	5	physical	physical	ADJ
m-1112	3315	6	interpretation	interpretation	NOUN
m-1112	3315	7	of	of	ADP
m-1112	3315	8	gravity	gravity	NOUN
m-1112	3315	9	–	–	PUNCT
m-1112	3315	10	constant	constant	ADJ
m-1112	3315	11	,	,	PUNCT
m-1112	3315	12	electron	electron	NOUN
m-1112	3315	13	and	and	CCONJ
m-1112	3315	14	chemistry	chemistry	NOUN
m-1112	3315	15	http://science	http://science	NOUN
m-1112	3315	16	mpg	mpg	NOUN
m-1112	3315	17	[	[	X
m-1112	3315	18	83	83	NUM
m-1112	3315	19	]	]	X
m-1112	3316	1	[	[	X
m-1112	3316	2	m	m	X
m-1112	3316	3	]	]	X
m-1112	3316	4	the	the	DET
m-1112	3316	5	epr	epr	ADJ
m-1112	3316	6	argument	argument	NOUN
m-1112	3316	7	and	and	CCONJ
m-1112	3316	8	the	the	DET
m-1112	3316	9	quantization	quantization	NOUN
m-1112	3316	10	of	of	ADP
m-1112	3316	11	energy	energy	NOUN
m-1112	3316	12	in	in	ADP
m-1112	3316	13	spaces	space	NOUN
m-1112	3316	14	http://www.ajer.org/volume9	http://www.ajer.org/volume9	NOUN
m-1112	3316	15	issue	issue	NOUN
m-1112	3316	16	1.html	1.html	NUM
m-1112	3316	17	[	[	NOUN
m-1112	3316	18	83a	83a	NOUN
m-1112	3316	19	]	]	X
m-1112	3317	1	[	[	X
m-1112	3317	2	m	m	X
m-1112	3317	3	]	]	X
m-1112	3317	4	the	the	DET
m-1112	3317	5	epr	epr	PROPN
m-1112	3317	6	argument	argument	NOUN
m-1112	3317	7	under	under	ADP
m-1112	3317	8	the	the	DET
m-1112	3317	9	critic	critic	NOUN
m-1112	3317	10	of	of	ADP
m-1112	3317	11	material	material	NOUN
m-1112	3317	12	-	-	PUNCT
m-1112	3317	13	geometry	geometry	NOUN
m-1112	3317	14	and	and	CCONJ
m-1112	3317	15	elementary	elementary	ADJ
m-1112	3317	16	particles	particle	NOUN
m-1112	3317	17	.	.	PUNCT
m-1112	3318	1	,	,	PUNCT
m-1112	3318	2	http://www.ajer.org/volume9	http://www.ajer.org/volume9	NOUN
m-1112	3318	3	issue	issue	VERB
m-1112	3318	4	1.html	1.html	NUM
m-1112	3318	5	[	[	X
m-1112	3318	6	84	84	NUM
m-1112	3318	7	]	]	PUNCT
m-1112	3319	1	[	[	X
m-1112	3319	2	m	m	X
m-1112	3319	3	]	]	X
m-1112	3319	4	the	the	DET
m-1112	3319	5	unification	unification	NOUN
m-1112	3319	6	of	of	ADP
m-1112	3319	7	energy	energy	NOUN
m-1112	3319	8	-	-	PUNCT
m-1112	3319	9	monads	monad	NOUN
m-1112	3319	10	,	,	PUNCT
m-1112	3319	11	black	black	ADJ
m-1112	3319	12	holes	hole	NOUN
m-1112	3319	13	,	,	PUNCT
m-1112	3319	14	with	with	ADP
m-1112	3319	15	geometry	geometry	NOUN
m-1112	3319	16	monads	monad	NOUN
m-1112	3319	17	,	,	PUNCT
m-1112	3319	18	black	black	ADJ
m-1112	3319	19	matter	matter	NOUN
m-1112	3319	20	,	,	PUNCT
m-1112	3319	21	through	through	ADP
m-1112	3319	22	automobile	automobile	NOUN
m-1112	3319	23	forces	force	NOUN
m-1112	3319	24	in	in	ADP
m-1112	3319	25	monads	monad	NOUN
m-1112	3319	26	.	.	PUNCT
m-1112	3320	1	[	[	X
m-1112	3320	2	85	85	NUM
m-1112	3320	3	]	]	X
m-1112	3320	4	[	[	X
m-1112	3320	5	m	m	X
m-1112	3320	6	]	]	X
m-1112	3320	7	quantization	quantization	NOUN
m-1112	3320	8	of	of	ADP
m-1112	3320	9	points	point	NOUN
m-1112	3320	10	and	and	CCONJ
m-1112	3320	11	potential	potential	NOUN
m-1112	3320	12	and	and	CCONJ
m-1112	3320	13	the	the	DET
m-1112	3320	14	unification	unification	NOUN
m-1112	3320	15	of	of	ADP
m-1112	3320	16	energy	energy	NOUN
m-1112	3320	17	-	-	PUNCT
m-1112	3320	18	space	space	NOUN
m-1112	3320	19	.	.	PUNCT
m-1112	3321	1	[	[	X
m-1112	3321	2	86	86	NUM
m-1112	3321	3	]	]	PUNCT
m-1112	3321	4	[	[	X
m-1112	3321	5	m	m	X
m-1112	3321	6	]	]	X
m-1112	3321	7	[	[	X
m-1112	3321	8	m	m	X
m-1112	3321	9	]	]	X
m-1112	3321	10	the	the	DET
m-1112	3321	11	physical	physical	ADJ
m-1112	3321	12	interpretation	interpretation	NOUN
m-1112	3321	13	of	of	ADP
m-1112	3321	14	gravity	gravity	NOUN
m-1112	3321	15	–	–	PUNCT
m-1112	3321	16	constant	constant	ADJ
m-1112	3321	17	,	,	PUNCT
m-1112	3321	18	and	and	CCONJ
m-1112	3321	19	ijo	ijo	PROPN
m-1112	3321	20	international	international	PROPN
m-1112	3321	21	journal	journal	PROPN
m-1112	3321	22	of	of	ADP
m-1112	3321	23	mathematics	mathematics	PROPN
m-1112	3321	24	(	(	PUNCT
m-1112	3321	25	issn	issn	PROPN
m-1112	3321	26	:	:	PUNCT
m-1112	3321	27	2992	2992	NUM
m-1112	3321	28	-	-	SYM
m-1112	3321	29	4421	4421	NUM
m-1112	3321	30	)	)	PUNCT
m-1112	3321	31	volume	volume	NOUN
m-1112	3321	32	08	08	NUM
m-1112	3322	1	|	|	ADV
m-1112	3322	2	issue	issue	NOUN
m-1112	3322	3	08	08	NUM
m-1112	3323	1	|	|	ADV
m-1112	3323	2	august	august	PROPN
m-1112	3323	3	2025	2025	NUM
m-1112	3324	1	|	|	ADV
m-1112	3324	2	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3324	3	ijo	ijo	PROPN
m-1112	3324	4	journals	journal	NOUN
m-1112	3324	5	http://vixra.org/	http://vixra.org/	PROPN
m-1112	3324	6	http://vixra.org/	http://vixra.org/	PROPN
m-1112	3324	7	http://www.ijrdo.org/	http://www.ijrdo.org/	VERB
m-1112	3324	8	http://www.ajer.org/	http://www.ajer.org/	VERB
m-1112	3324	9	http://vixra.org/	http://vixra.org/	PROPN
m-1112	3324	10	http://science/	http://science/	NOUN
m-1112	3324	11	http://www.ijrdo.org/	http://www.ijrdo.org/	NOUN
m-1112	3324	12	http://science/	http://science/	PROPN
m-1112	3325	1	mailto:editorusa@globaljournals.org	mailto:editorusa@globaljournals.org	PROPN
m-1112	3325	2	http://saiconference.com/ftc	http://saiconference.com/ftc	PROPN
m-1112	3326	1	https://ijrdo.org/index.php/mce/issue/current	https://ijrdo.org/index.php/mce/issue/current	ADJ
m-1112	3326	2	http://www.iosr.org/	http://www.iosr.org/	NOUN
m-1112	3326	3	http://science/	http://science/	VERB
m-1112	3326	4	http://vixra.org/	http://vixra.org/	PROPN
m-1112	3326	5	http://vixra.org/	http://vixra.org/	PROPN
m-1112	3326	6	https://saiconference.com/ficc2020/submit	https://saiconference.com/ficc2020/submit	NUM
m-1112	3326	7	http://science/	http://science/	NOUN
m-1112	3326	8	http://vixra.org/abs/	http://vixra.org/abs/	NOUN
m-1112	3326	9	https://www.scribd.com/doc/	https://www.scribd.com/doc/	PROPN
m-1112	3326	10	http://science/	http://science/	NOUN
m-1112	3326	11	http://www.ajer.org/volume9	http://www.ajer.org/volume9	NUM
m-1112	3326	12	http://www.ajer.org/volume9	http://www.ajer.org/volume9	NOUN
m-1112	3326	13	117	117	NUM
m-1112	3326	14	the	the	DET
m-1112	3326	15	fundamental	fundamental	ADJ
m-1112	3326	16	particles	particle	NOUN
m-1112	3326	17	origination	origination	NOUN
m-1112	3326	18	mechanism	mechanism	NOUN
m-1112	3326	19	in	in	ADP
m-1112	3326	20	mfmf	mfmf	PROPN
m-1112	3326	21	pns	pns	PROPN
m-1112	3326	22	caves	cave	NOUN
m-1112	3326	23	.	.	PUNCT
m-1112	3327	1	applications	application	NOUN
m-1112	3327	2	in	in	ADP
m-1112	3327	3	chemistry	chemistry	NOUN
m-1112	3327	4	http://science	http://science	ADP
m-1112	3327	5	mpg	mpg	NOUN
m-1112	3328	1	[	[	X
m-1112	3328	2	87	87	NUM
m-1112	3328	3	]	]	PUNCT
m-1112	3328	4	[	[	X
m-1112	3328	5	m	m	X
m-1112	3328	6	]	]	X
m-1112	3328	7	photon	photon	NOUN
m-1112	3328	8	particle	particle	NOUN
m-1112	3328	9	,	,	PUNCT
m-1112	3328	10	photon	photon	NOUN
m-1112	3328	11	wave	wave	NOUN
m-1112	3328	12	or	or	CCONJ
m-1112	3328	13	duality	duality	NOUN
m-1112	3328	14	photon	photon	NOUN
m-1112	3328	15	?	?	PUNCT
m-1112	3329	1	and	and	CCONJ
m-1112	3329	2	applications	application	NOUN
m-1112	3329	3	http://vixra.org/abs/2003.0601	http://vixra.org/abs/2003.0601	ADJ
m-1112	3329	4	[	[	X
m-1112	3329	5	87	87	NUM
m-1112	3329	6	]	]	PUNCT
m-1112	3329	7	[	[	X
m-1112	3329	8	m	m	X
m-1112	3329	9	]	]	X
m-1112	3329	10	photon	photon	NOUN
m-1112	3329	11	particle	particle	NOUN
m-1112	3329	12	,	,	PUNCT
m-1112	3329	13	photon	photon	NOUN
m-1112	3329	14	wave	wave	NOUN
m-1112	3329	15	or	or	CCONJ
m-1112	3329	16	duality	duality	NOUN
m-1112	3329	17	photon	photon	NOUN
m-1112	3329	18	?	?	PUNCT
m-1112	3329	19	and	and	CCONJ
m-1112	3329	20	future	future	ADJ
m-1112	3329	21	technologies	technology	NOUN
m-1112	3329	22	https://www.scribd.com/doc/1/	https://www.scribd.com/doc/1/	NOUN
m-1112	3329	23	[	[	X
m-1112	3329	24	87b	87b	NOUN
m-1112	3329	25	]	]	X
m-1112	3330	1	[	[	X
m-1112	3330	2	r	r	X
m-1112	3330	3	]	]	PUNCT
m-1112	3330	4	photon	photon	NOUN
m-1112	3330	5	particle	particle	NOUN
m-1112	3330	6	,	,	PUNCT
m-1112	3330	7	photon	photon	NOUN
m-1112	3330	8	wave	wave	NOUN
m-1112	3330	9	or	or	CCONJ
m-1112	3330	10	duality	duality	NOUN
m-1112	3330	11	photon	photon	NOUN
m-1112	3330	12	?	?	PUNCT
m-1112	3331	1	an	an	DET
m-1112	3331	2	answer	answer	NOUN
m-1112	3331	3	to	to	ADP
m-1112	3331	4	why	why	SCONJ
m-1112	3331	5	and	and	CCONJ
m-1112	3331	6	how	how	SCONJ
m-1112	3331	7	is	be	AUX
m-1112	3331	8	the	the	DET
m-1112	3331	9	objective	objective	ADJ
m-1112	3331	10	-	-	PUNCT
m-1112	3331	11	reality	reality	NOUN
m-1112	3331	12	www.ijrdo-journals.org	www.ijrdo-journals.org	NOUN
m-1112	3331	13	)	)	PUNCT
m-1112	3332	1	[	[	X
m-1112	3332	2	88	88	NUM
m-1112	3332	3	]	]	PUNCT
m-1112	3332	4	[	[	X
m-1112	3332	5	m	m	X
m-1112	3332	6	]	]	X
m-1112	3332	7	[	[	X
m-1112	3332	8	m	m	X
m-1112	3332	9	]	]	X
m-1112	3332	10	the	the	DET
m-1112	3332	11	origination	origination	NOUN
m-1112	3332	12	of	of	ADP
m-1112	3332	13	nutation	nutation	NOUN
m-1112	3332	14	motion	motion	NOUN
m-1112	3332	15	and	and	CCONJ
m-1112	3332	16	a	a	DET
m-1112	3332	17	new	new	ADJ
m-1112	3332	18	electromagnetic	electromagnetic	ADJ
m-1112	3332	19	structure	structure	NOUN
m-1112	3332	20	of	of	ADP
m-1112	3332	21	atom	atom	NOUN
m-1112	3332	22	http://science	http://science	NOUN
m-1112	3332	23	mpg	mpg	NOUN
m-1112	3333	1	[	[	X
m-1112	3333	2	89	89	NUM
m-1112	3333	3	]	]	X
m-1112	3333	4	[	[	X
m-1112	3333	5	m	m	X
m-1112	3333	6	]	]	X
m-1112	3333	7	the	the	DET
m-1112	3333	8	wave	wave	NOUN
m-1112	3333	9	&	&	CCONJ
m-1112	3333	10	particle	particle	PROPN
m-1112	3333	11	duality	duality	NOUN
m-1112	3333	12	photon	photon	NOUN
m-1112	3333	13	and	and	CCONJ
m-1112	3333	14	elementary	elementary	ADJ
m-1112	3333	15	particles	particle	NOUN
m-1112	3333	16	origination	origination	NOUN
m-1112	3333	17	.	.	PUNCT
m-1112	3334	1	http://science	http://science	NOUN
m-1112	3334	2	mpg	mpg	NOUN
m-1112	3334	3	≡	≡	PROPN
m-1112	3334	4	markos	markos	PROPN
m-1112	3334	5	georgallides	georgallide	VERB
m-1112	3334	6	[	[	X
m-1112	3334	7	89a	89a	NOUN
m-1112	3334	8	]	]	PUNCT
m-1112	3335	1	[	[	X
m-1112	3335	2	m	m	X
m-1112	3335	3	]	]	X
m-1112	3335	4	the	the	DET
m-1112	3335	5	duality	duality	NOUN
m-1112	3335	6	photon	photon	NOUN
m-1112	3335	7	and	and	CCONJ
m-1112	3335	8	the	the	DET
m-1112	3335	9	physical	physical	ADJ
m-1112	3335	10	interpretation	interpretation	NOUN
m-1112	3335	11	of	of	ADP
m-1112	3335	12	photon	photon	NOUN
m-1112	3335	13	spectrum	spectrum	NOUN
m-1112	3335	14	http://science	http://science	NOUN
m-1112	3335	15	mpg	mpg	NOUN
m-1112	3335	16	≡	≡	PROPN
m-1112	3335	17	markos	markos	PROPN
m-1112	3335	18	georgallides	georgallide	VERB
m-1112	3335	19	[	[	X
m-1112	3335	20	90	90	NUM
m-1112	3335	21	]	]	PUNCT
m-1112	3336	1	[	[	X
m-1112	3336	2	m	m	X
m-1112	3336	3	]	]	X
m-1112	3336	4	the	the	DET
m-1112	3336	5	new	new	ADJ
m-1112	3336	6	-	-	PUNCT
m-1112	3336	7	structure	structure	NOUN
m-1112	3336	8	of	of	ADP
m-1112	3336	9	atom	atom	NOUN
m-1112	3336	10	,	,	PUNCT
m-1112	3336	11	the	the	DET
m-1112	3336	12	nutation	nutation	NOUN
m-1112	3336	13	-	-	PUNCT
m-1112	3336	14	motion	motion	NOUN
m-1112	3336	15	and	and	CCONJ
m-1112	3336	16	their	their	PRON
m-1112	3336	17	application	application	NOUN
m-1112	3336	18	.	.	PUNCT
m-1112	3337	1	http://science	http://science	NOUN
m-1112	3337	2	mpg	mpg	NOUN
m-1112	3337	3	≡	≡	PROPN
m-1112	3337	4	markos	markos	PROPN
m-1112	3337	5	georgallides	georgallide	VERB
m-1112	3337	6	[	[	X
m-1112	3337	7	91	91	NUM
m-1112	3337	8	]	]	PUNCT
m-1112	3338	1	[	[	X
m-1112	3338	2	m	m	X
m-1112	3338	3	]	]	X
m-1112	3338	4	the	the	DET
m-1112	3338	5	origin	origin	NOUN
m-1112	3338	6	of	of	ADP
m-1112	3338	7	the	the	DET
m-1112	3338	8	fundamental	fundamental	ADJ
m-1112	3338	9	-	-	PUNCT
m-1112	3338	10	particles	particle	NOUN
m-1112	3338	11	in	in	ADP
m-1112	3338	12	planck`s	planck`s	NOUN
m-1112	3338	13	confinement	confinement	NOUN
m-1112	3338	14	.	.	PUNCT
m-1112	3339	1	http://science	http://science	NOUN
m-1112	3339	2	mpg	mpg	NOUN
m-1112	3339	3	≡	≡	PROPN
m-1112	3339	4	markos	markos	PROPN
m-1112	3339	5	georgallides	georgallide	VERB
m-1112	3339	6	[	[	X
m-1112	3339	7	92	92	NUM
m-1112	3339	8	]	]	PUNCT
m-1112	3340	1	[	[	X
m-1112	3340	2	m	m	X
m-1112	3340	3	]	]	X
m-1112	3340	4	the	the	DET
m-1112	3340	5	wave	wave	NOUN
m-1112	3340	6	&	&	CCONJ
m-1112	3340	7	particle	particle	PROPN
m-1112	3340	8	duality	duality	NOUN
m-1112	3340	9	-	-	PUNCT
m-1112	3340	10	photon	photon	NOUN
m-1112	3340	11	and	and	CCONJ
m-1112	3340	12	elementary	elementary	ADJ
m-1112	3340	13	particles	particle	NOUN
m-1112	3340	14	-	-	PUNCT
m-1112	3340	15	origination	origination	NOUN
m-1112	3340	16	.	.	PUNCT
m-1112	3341	1	www.ijrdo-journals.org	www.ijrdo-journals.org	NOUN
m-1112	3341	2	)	)	PUNCT
m-1112	3341	3	,	,	PUNCT
m-1112	3341	4	http://science	http://science	NUM
m-1112	3341	5	mpg	mpg	NOUN
m-1112	3341	6	≡	≡	PROPN
m-1112	3341	7	markos	markos	PROPN
m-1112	3342	1	[	[	X
m-1112	3342	2	93	93	NUM
m-1112	3342	3	]	]	PUNCT
m-1112	3343	1	[	[	X
m-1112	3343	2	m	m	X
m-1112	3343	3	]	]	X
m-1112	3343	4	the	the	DET
m-1112	3343	5	fundamental	fundamental	ADJ
m-1112	3343	6	-	-	PUNCT
m-1112	3343	7	particles	particle	NOUN
m-1112	3343	8	and	and	CCONJ
m-1112	3343	9	the	the	DET
m-1112	3343	10	fundamental	fundamental	ADJ
m-1112	3343	11	-	-	PUNCT
m-1112	3343	12	forces	force	NOUN
m-1112	3343	13	of	of	ADP
m-1112	3343	14	nature	nature	NOUN
m-1112	3343	15	.	.	PUNCT
m-1112	3344	1	http://science	http://science	NOUN
m-1112	3344	2	mpg	mpg	NOUN
m-1112	3344	3	≡	≡	PROPN
m-1112	3344	4	markos	markos	PROPN
m-1112	3344	5	georgallides	georgallide	VERB
m-1112	3344	6	[	[	X
m-1112	3344	7	94	94	X
m-1112	3344	8	]	]	PUNCT
m-1112	3345	1	[	[	X
m-1112	3345	2	m	m	X
m-1112	3345	3	]	]	X
m-1112	3345	4	the	the	DET
m-1112	3345	5	cosmic	cosmic	ADJ
m-1112	3345	6	-	-	PUNCT
m-1112	3345	7	particles	particle	NOUN
m-1112	3345	8	origination	origination	NOUN
m-1112	3345	9	and	and	CCONJ
m-1112	3345	10	their	their	PRON
m-1112	3345	11	bonding	bonding	NOUN
m-1112	3345	12	,	,	PUNCT
m-1112	3346	1	[	[	X
m-1112	3346	2	95	95	NUM
m-1112	3346	3	]	]	PUNCT
m-1112	3347	1	[	[	X
m-1112	3347	2	m	m	X
m-1112	3347	3	]	]	X
m-1112	3347	4	the	the	DET
m-1112	3347	5	wave	wave	NOUN
m-1112	3347	6	and	and	CCONJ
m-1112	3347	7	particle	particle	NOUN
m-1112	3347	8	duality	duality	NOUN
m-1112	3347	9	photon	photon	NOUN
m-1112	3347	10	,	,	PUNCT
m-1112	3347	11	cosmic	cosmic	ADJ
m-1112	3347	12	-	-	PUNCT
m-1112	3347	13	particles	particle	NOUN
m-1112	3347	14	-	-	PUNCT
m-1112	3347	15	origination	origination	NOUN
m-1112	3347	16	and	and	CCONJ
m-1112	3347	17	their	their	PRON
m-1112	3347	18	bonding	bonding	NOUN
m-1112	3347	19	stair	stair	NOUN
m-1112	3347	20	awards	award	NOUN
m-1112	3347	21	2021	2021	NUM
m-1112	3348	1	[	[	X
m-1112	3348	2	294	294	NUM
m-1112	3348	3	]	]	PUNCT
m-1112	3348	4	[	[	X
m-1112	3348	5	m	m	X
m-1112	3348	6	]	]	X
m-1112	3348	7	the	the	DET
m-1112	3348	8	wave	wave	NOUN
m-1112	3348	9	&	&	CCONJ
m-1112	3348	10	particle	particle	PROPN
m-1112	3348	11	duality	duality	NOUN
m-1112	3348	12	photon	photon	NOUN
m-1112	3348	13	,	,	PUNCT
m-1112	3348	14	cosmic	cosmic	ADJ
m-1112	3348	15	-	-	PUNCT
m-1112	3348	16	particles	particle	NOUN
m-1112	3348	17	origination	origination	NOUN
m-1112	3348	18	and	and	CCONJ
m-1112	3348	19	their	their	PRON
m-1112	3348	20	bonding	bonding	NOUN
m-1112	3348	21	http://science	http://science	ADP
m-1112	3348	22	mpg	mpg	NOUN
m-1112	3348	23	≡	≡	PROPN
m-1112	3348	24	markos	markos	PROPN
m-1112	3348	25	[	[	X
m-1112	3348	26	95	95	NUM
m-1112	3348	27	]	]	PUNCT
m-1112	3349	1	[	[	X
m-1112	3349	2	m	m	X
m-1112	3349	3	]	]	X
m-1112	3349	4	the	the	DET
m-1112	3349	5	how	how	SCONJ
m-1112	3349	6	intensity	intensity	NOUN
m-1112	3349	7	-	-	PUNCT
m-1112	3349	8	squares	square	NOUN
m-1112	3349	9	of	of	ADP
m-1112	3349	10	electromagnetic	electromagnetic	ADJ
m-1112	3349	11	-	-	PUNCT
m-1112	3349	12	cosmic	cosmic	ADJ
m-1112	3349	13	-	-	PUNCT
m-1112	3349	14	particles	particle	NOUN
m-1112	3349	15	follow	follow	VERB
m-1112	3349	16	quadrature	quadrature	NOUN
m-1112	3349	17	of	of	ADP
m-1112	3349	18	square	square	ADJ
m-1112	3349	19	-	-	PUNCT
m-1112	3349	20	prism	prism	NOUN
m-1112	3349	21	to	to	ADP
m-1112	3349	22	equivalent	equivalent	ADJ
m-1112	3349	23	-	-	PUNCT
m-1112	3349	24	energy	energy	NOUN
m-1112	3349	25	-	-	PUNCT
m-1112	3349	26	sphere	sphere	NOUN
m-1112	3349	27	-	-	PUNCT
m-1112	3349	28	cone	cone	NOUN
m-1112	3349	29	,	,	PUNCT
m-1112	3349	30	http://vixra.org/3	http://vixra.org/3	PROPN
m-1112	3349	31	/	/	SYM
m-1112	3349	32	2021	2021	NUM
m-1112	3349	33	[	[	X
m-1112	3349	34	96	96	NUM
m-1112	3349	35	]	]	X
m-1112	3349	36	aa	aa	NOUN
m-1112	3349	37	the	the	DET
m-1112	3349	38	wave	wave	NOUN
m-1112	3349	39	and	and	CCONJ
m-1112	3349	40	particle	particle	NOUN
m-1112	3349	41	duality	duality	NOUN
m-1112	3349	42	photon	photon	NOUN
m-1112	3349	43	,	,	PUNCT
m-1112	3349	44	cosmic	cosmic	ADJ
m-1112	3349	45	-	-	PUNCT
m-1112	3349	46	particles	particle	NOUN
m-1112	3349	47	-	-	PUNCT
m-1112	3349	48	origination	origination	NOUN
m-1112	3349	49	and	and	CCONJ
m-1112	3349	50	their	their	PRON
m-1112	3349	51	stability	stability	NOUN
m-1112	3349	52	in	in	ADP
m-1112	3349	53	cosmology	cosmology	NOUN
m-1112	3349	54	<	<	X
m-1112	3349	55	ejas@scholarpublishing.org	ejas@scholarpublishing.org	X
m-1112	3349	56	>	>	X
m-1112	3350	1	[	[	X
m-1112	3350	2	97a	97a	NOUN
m-1112	3350	3	]	]	X
m-1112	3350	4	[	[	X
m-1112	3350	5	m	m	X
m-1112	3350	6	]	]	X
m-1112	3350	7	duality	duality	NOUN
m-1112	3350	8	photon	photon	NOUN
m-1112	3350	9	and	and	CCONJ
m-1112	3350	10	the	the	DET
m-1112	3350	11	mechanical	mechanical	ADJ
m-1112	3350	12	and	and	CCONJ
m-1112	3350	13	chemical	chemical	NOUN
m-1112	3350	14	,	,	PUNCT
m-1112	3350	15	dna	dna	NOUN
m-1112	3350	16	-	-	PUNCT
m-1112	3350	17	helix	helix	NOUN
m-1112	3350	18	,	,	PUNCT
m-1112	3350	19	construction	construction	NOUN
m-1112	3350	20	functions	function	NOUN
m-1112	3350	21	<	<	X
m-1112	3350	22	ejas@scholarpublishing.org	ejas@scholarpublishing.org	X
m-1112	3350	23	>	>	X
m-1112	3350	24	,	,	PUNCT
m-1112	3350	25	http://science	http://science	NUM
m-1112	3350	26	mpg	mpg	NOUN
m-1112	3350	27	≡	≡	PROPN
m-1112	3350	28	markos	markos	PROPN
m-1112	3350	29	georgallides	georgallide	VERB
m-1112	3350	30	[	[	X
m-1112	3350	31	97b	97b	X
m-1112	3350	32	]	]	X
m-1112	3351	1	[	[	X
m-1112	3351	2	m	m	X
m-1112	3351	3	]	]	X
m-1112	3351	4	the	the	DET
m-1112	3351	5	duality	duality	NOUN
m-1112	3351	6	photon	photon	NOUN
m-1112	3351	7	,	,	PUNCT
m-1112	3351	8	dna	dna	PROPN
m-1112	3351	9	,	,	PUNCT
m-1112	3351	10	and	and	CCONJ
m-1112	3351	11	the	the	DET
m-1112	3351	12	cruise	cruise	NOUN
m-1112	3351	13	-	-	PUNCT
m-1112	3351	14	missile	missile	NOUN
m-1112	3351	15	elementary	elementary	ADJ
m-1112	3351	16	-	-	PUNCT
m-1112	3351	17	particles	particle	NOUN
m-1112	3351	18	,	,	PUNCT
m-1112	3351	19	conductors	conductor	NOUN
m-1112	3351	20	,	,	PUNCT
m-1112	3351	21	http://science	http://science	NOUN
m-1112	3351	22	mpg	mpg	NOUN
m-1112	3351	23	≡	≡	PROPN
m-1112	3351	24	markos	markos	PROPN
m-1112	3351	25	georgallides	georgallide	VERB
m-1112	3351	26	[	[	X
m-1112	3351	27	98a	98a	X
m-1112	3351	28	]	]	X
m-1112	3352	1	[	[	X
m-1112	3352	2	m	m	X
m-1112	3352	3	]	]	X
m-1112	3352	4	the	the	DET
m-1112	3352	5	nature	nature	NOUN
m-1112	3352	6	of	of	ADP
m-1112	3352	7	greek	greek	ADJ
m-1112	3352	8	-	-	PUNCT
m-1112	3352	9	special	special	ADJ
m-1112	3352	10	-	-	PUNCT
m-1112	3352	11	problems	problem	NOUN
m-1112	3352	12	&	&	CCONJ
m-1112	3352	13	their	their	PRON
m-1112	3352	14	functioning	functioning	NOUN
m-1112	3352	15	in	in	ADP
m-1112	3352	16	electromagnetic	electromagnetic	ADJ
m-1112	3352	17	forces	force	NOUN
m-1112	3352	18	in	in	ADP
m-1112	3352	19	dna	dna	PROPN
m-1112	3352	20	conductors	conductor	NOUN
m-1112	3352	21	,	,	PUNCT
m-1112	3352	22	https://www.lap-publishing.com/.	https://www.lap-publishing.com/.	PRON
m-1112	3352	23	e	e	NOUN
m-1112	3352	24	-	-	NOUN
m-1112	3352	25	book	book	NOUN
m-1112	3352	26	.	.	PUNCT
m-1112	3353	1	lap	lap	PROPN
m-1112	3353	2	lambert	lambert	PROPN
m-1112	3353	3	academic	academic	ADJ
m-1112	3353	4	publication	publication	NOUN
m-1112	3353	5	.	.	PUNCT
m-1112	3354	1	[	[	X
m-1112	3354	2	98b	98b	NOUN
m-1112	3354	3	]	]	X
m-1112	3354	4	[	[	X
m-1112	3354	5	m	m	X
m-1112	3354	6	]	]	X
m-1112	3354	7	the	the	DET
m-1112	3354	8	why	why	SCONJ
m-1112	3354	9	,	,	PUNCT
m-1112	3354	10	the	the	DET
m-1112	3354	11	how	how	SCONJ
m-1112	3354	12	and	and	CCONJ
m-1112	3354	13	when	when	SCONJ
m-1112	3354	14	,	,	PUNCT
m-1112	3354	15	the	the	DET
m-1112	3354	16	atoms	atom	NOUN
m-1112	3354	17	–	–	PUNCT
m-1112	3354	18	bond	bond	NOUN
m-1112	3354	19	.	.	PUNCT
m-1112	3355	1	http://science	http://science	NOUN
m-1112	3355	2	mpg	mpg	NOUN
m-1112	3355	3	≡	≡	PROPN
m-1112	3355	4	markos	markos	PROPN
m-1112	3355	5	georgallides	georgallide	VERB
m-1112	3355	6	[	[	X
m-1112	3355	7	99a	99a	NOUN
m-1112	3355	8	]	]	X
m-1112	3356	1	[	[	X
m-1112	3356	2	m	m	X
m-1112	3356	3	]	]	X
m-1112	3356	4	the	the	DET
m-1112	3356	5	how	how	SCONJ
m-1112	3356	6	,	,	PUNCT
m-1112	3356	7	why	why	SCONJ
m-1112	3356	8	and	and	CCONJ
m-1112	3356	9	when	when	SCONJ
m-1112	3356	10	,	,	PUNCT
m-1112	3356	11	the	the	DET
m-1112	3356	12	atoms	atom	NOUN
m-1112	3356	13	–	–	PUNCT
m-1112	3356	14	bond	bond	NOUN
m-1112	3356	15	.	.	PUNCT
m-1112	3356	16	https://mts.intechopen.com.book.process/	https://mts.intechopen.com.book.process/	PUNCT
m-1112	3357	1	≡	≡	PROPN
m-1112	3357	2	dragan	dragan	VERB
m-1112	3357	3	miljak	miljak	ADV
m-1112	3358	1	[	[	X
m-1112	3358	2	99aaa	99aaa	NOUN
m-1112	3358	3	]	]	X
m-1112	3359	1	[	[	X
m-1112	3359	2	m	m	X
m-1112	3359	3	]	]	X
m-1112	3359	4	the	the	DET
m-1112	3359	5	how	how	SCONJ
m-1112	3359	6	,	,	PUNCT
m-1112	3359	7	why	why	SCONJ
m-1112	3359	8	and	and	CCONJ
m-1112	3359	9	when	when	SCONJ
m-1112	3359	10	,	,	PUNCT
m-1112	3359	11	the	the	DET
m-1112	3359	12	atoms	atom	NOUN
m-1112	3359	13	–	–	PUNCT
m-1112	3359	14	bond	bond	NOUN
m-1112	3359	15	.	.	PUNCT
m-1112	3360	1	http://science	http://science	NOUN
m-1112	3360	2	mpg	mpg	NOUN
m-1112	3360	3	≡	≡	PROPN
m-1112	3360	4	markos	markos	PROPN
m-1112	3360	5	georgallides	georgallide	VERB
m-1112	3361	1	[	[	X
m-1112	3361	2	99ccc	99ccc	X
m-1112	3361	3	]	]	X
m-1112	3362	1	[	[	X
m-1112	3362	2	m	m	X
m-1112	3362	3	]	]	X
m-1112	3362	4	the	the	DET
m-1112	3362	5	4	4	NUM
m-1112	3362	6	-	-	PUNCT
m-1112	3362	7	frequencies	frequency	NOUN
m-1112	3362	8	of	of	ADP
m-1112	3362	9	atoms	atom	NOUN
m-1112	3362	10	–	–	PUNCT
m-1112	3362	11	bonding	bonding	NOUN
m-1112	3362	12	related	relate	VERB
m-1112	3362	13	to	to	PART
m-1112	3362	14	octave	octave	VERB
m-1112	3362	15	periodic	periodic	ADJ
m-1112	3362	16	-	-	PUNCT
m-1112	3362	17	table	table	NOUN
m-1112	3362	18	.	.	PUNCT
m-1112	3363	1	http://science	http://science	NOUN
m-1112	3363	2	mpg	mpg	NOUN
m-1112	3363	3	≡	≡	PROPN
m-1112	3363	4	markos	markos	PROPN
m-1112	3363	5	georgallides	georgallide	VERB
m-1112	3363	6	ijo	ijo	PROPN
m-1112	3363	7	international	international	PROPN
m-1112	3363	8	journal	journal	PROPN
m-1112	3363	9	of	of	ADP
m-1112	3363	10	mathematics	mathematics	PROPN
m-1112	3363	11	(	(	PUNCT
m-1112	3363	12	issn	issn	PROPN
m-1112	3363	13	:	:	PUNCT
m-1112	3363	14	2992	2992	NUM
m-1112	3363	15	-	-	SYM
m-1112	3363	16	4421	4421	NUM
m-1112	3363	17	)	)	PUNCT
m-1112	3363	18	volume	volume	NOUN
m-1112	3363	19	08	08	NUM
m-1112	3364	1	|	|	ADV
m-1112	3364	2	issue	issue	NOUN
m-1112	3364	3	08	08	NUM
m-1112	3365	1	|	|	ADV
m-1112	3365	2	august	august	PROPN
m-1112	3365	3	2025	2025	NUM
m-1112	3365	4	|	|	ADV
m-1112	3365	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3365	6	ijo	ijo	PROPN
m-1112	3365	7	journals	journal	NOUN
m-1112	3365	8	http://science/	http://science/	VERB
m-1112	3365	9	http://vixra.org/abs/2003.0601	http://vixra.org/abs/2003.0601	ADJ
m-1112	3365	10	https://www.scribd.com/doc/1/	https://www.scribd.com/doc/1/	PROPN
m-1112	3365	11	http://www.ijrdo-journals.org/	http://www.ijrdo-journals.org/	NOUN
m-1112	3365	12	http://science/	http://science/	VERB
m-1112	3365	13	http://science/	http://science/	PROPN
m-1112	3365	14	http://science/	http://science/	PROPN
m-1112	3365	15	http://science/	http://science/	PROPN
m-1112	3365	16	http://science/	http://science/	PROPN
m-1112	3366	1	http://www.ijrdo-journals.org/	http://www.ijrdo-journals.org/	NOUN
m-1112	3366	2	http://science/	http://science/	NOUN
m-1112	3366	3	http://science/	http://science/	PROPN
m-1112	3366	4	http://science/	http://science/	PROPN
m-1112	3366	5	http://vixra.org/3%20/%202021	http://vixra.org/3%20/%202021	PROPN
m-1112	3366	6	mailto:ejas@scholarpublishing.org	mailto:ejas@scholarpublishing.org	PROPN
m-1112	3366	7	mailto:ejas@scholarpublishing.org	mailto:ejas@scholarpublishing.org	PROPN
m-1112	3366	8	http://science/	http://science/	NOUN
m-1112	3366	9	http://science/	http://science/	PROPN
m-1112	3366	10	https://www.lap-publishing.com/	https://www.lap-publishing.com/	NUM
m-1112	3366	11	http://science/	http://science/	PROPN
m-1112	3366	12	http://science/	http://science/	PROPN
m-1112	3366	13	http://science/	http://science/	PROPN
m-1112	3366	14	118	118	NUM
m-1112	3366	15	the	the	DET
m-1112	3366	16	fundamental	fundamental	ADJ
m-1112	3366	17	particles	particle	NOUN
m-1112	3366	18	origination	origination	NOUN
m-1112	3366	19	mechanism	mechanism	NOUN
m-1112	3366	20	in	in	ADP
m-1112	3366	21	mfmf	mfmf	PROPN
m-1112	3366	22	pns	pns	PROPN
m-1112	3366	23	caves	cave	NOUN
m-1112	3366	24	.	.	PUNCT
m-1112	3367	1	[	[	X
m-1112	3367	2	99	99	NUM
m-1112	3367	3	]	]	X
m-1112	3367	4	[	[	X
m-1112	3367	5	m	m	X
m-1112	3367	6	]	]	X
m-1112	3367	7	the	the	DET
m-1112	3367	8	bonding	bonding	NOUN
m-1112	3367	9	of	of	ADP
m-1112	3367	10	cosmic	cosmic	ADJ
m-1112	3367	11	-	-	PUNCT
m-1112	3367	12	particles	particle	NOUN
m-1112	3367	13	and	and	CCONJ
m-1112	3367	14	resonance	resonance	NOUN
m-1112	3367	15	photoelasticity	photoelasticity	NOUN
m-1112	3367	16	,	,	PUNCT
m-1112	3367	17	http://science	http://science	NOUN
m-1112	3367	18	mpg	mpg	NOUN
m-1112	3367	19	≡	≡	PROPN
m-1112	3367	20	markos	markos	PROPN
m-1112	3367	21	georgallides	georgallide	VERB
m-1112	3367	22	[	[	X
m-1112	3367	23	100	100	NUM
m-1112	3367	24	]	]	PUNCT
m-1112	3368	1	[	[	X
m-1112	3368	2	m	m	X
m-1112	3368	3	]	]	X
m-1112	3368	4	programming	programming	NOUN
m-1112	3368	5	,	,	PUNCT
m-1112	3368	6	the	the	DET
m-1112	3368	7	atoms	atom	NOUN
m-1112	3368	8	and	and	CCONJ
m-1112	3368	9	their	their	PRON
m-1112	3368	10	compounds	compound	NOUN
m-1112	3368	11	energy	energy	NOUN
m-1112	3368	12	,	,	PUNCT
m-1112	3368	13	http://science	http://science	NUM
m-1112	3368	14	mpg	mpg	NOUN
m-1112	3368	15	≡	≡	PROPN
m-1112	3368	16	markos	markos	PROPN
m-1112	3368	17	georgallides	georgallide	VERB
m-1112	3368	18	[	[	X
m-1112	3368	19	101	101	NUM
m-1112	3368	20	]	]	PUNCT
m-1112	3369	1	[	[	X
m-1112	3369	2	m	m	X
m-1112	3369	3	]	]	X
m-1112	3369	4	the	the	DET
m-1112	3369	5	why	why	SCONJ
m-1112	3369	6	and	and	CCONJ
m-1112	3369	7	how	how	SCONJ
m-1112	3369	8	atoms	atom	NOUN
m-1112	3369	9	and	and	CCONJ
m-1112	3369	10	compounds	compound	VERB
m-1112	3369	11	bond	bond	NOUN
m-1112	3369	12	,	,	PUNCT
m-1112	3369	13	and	and	CCONJ
m-1112	3369	14	chemistry	chemistry	NOUN
m-1112	3369	15	-	-	PUNCT
m-1112	3369	16	programming	programming	NOUN
m-1112	3369	17	[	[	X
m-1112	3369	18	102	102	NUM
m-1112	3369	19	]	]	X
m-1112	3370	1	[	[	X
m-1112	3370	2	m	m	X
m-1112	3370	3	]	]	X
m-1112	3370	4	the	the	DET
m-1112	3370	5	markos	markos	PROPN
m-1112	3370	6	-	-	PUNCT
m-1112	3370	7	method	method	NOUN
m-1112	3370	8	of	of	ADP
m-1112	3370	9	conservation	conservation	NOUN
m-1112	3370	10	of	of	ADP
m-1112	3370	11	motion	motion	NOUN
m-1112	3370	12	=	=	NOUN
m-1112	3370	13	energy	energy	NOUN
m-1112	3370	14	,	,	PUNCT
m-1112	3370	15	by	by	ADP
m-1112	3370	16	division	division	NOUN
m-1112	3370	17	.	.	PUNCT
m-1112	3371	1	[	[	X
m-1112	3371	2	103	103	NUM
m-1112	3371	3	]	]	X
m-1112	3371	4	[	[	X
m-1112	3371	5	m	m	X
m-1112	3371	6	]	]	X
m-1112	3371	7	the	the	DET
m-1112	3371	8	markos	markos	PROPN
m-1112	3371	9	-	-	PUNCT
m-1112	3371	10	method	method	NOUN
m-1112	3371	11	of	of	ADP
m-1112	3371	12	conservation	conservation	NOUN
m-1112	3371	13	of	of	ADP
m-1112	3371	14	motion	motion	NOUN
m-1112	3371	15	in	in	ADP
m-1112	3371	16	nature	nature	NOUN
m-1112	3371	17	and	and	CCONJ
m-1112	3371	18	medicine	medicine	NOUN
m-1112	3371	19	.	.	PUNCT
m-1112	3372	1	[	[	X
m-1112	3372	2	104	104	X
m-1112	3372	3	]	]	X
m-1112	3372	4	[	[	X
m-1112	3372	5	m	m	X
m-1112	3372	6	]	]	X
m-1112	3372	7	programming	programming	NOUN
m-1112	3372	8	of	of	ADP
m-1112	3372	9	atoms	atom	NOUN
m-1112	3372	10	and	and	CCONJ
m-1112	3372	11	their	their	PRON
m-1112	3372	12	compounds	compound	NOUN
m-1112	3372	13	and	and	CCONJ
m-1112	3372	14	their	their	PRON
m-1112	3372	15	modulated	modulate	VERB
m-1112	3372	16	-	-	PUNCT
m-1112	3372	17	energy	energy	NOUN
m-1112	3372	18	,	,	PUNCT
m-1112	3372	19	http://science	http://science	NUM
m-1112	3372	20	mpg	mpg	NOUN
m-1112	3372	21	≡	≡	PROPN
m-1112	3372	22	markos	markos	PROPN
m-1112	3372	23	georgallides	georgallide	VERB
m-1112	3372	24	[	[	X
m-1112	3372	25	105	105	NUM
m-1112	3372	26	]	]	X
m-1112	3373	1	[	[	X
m-1112	3373	2	m	m	X
m-1112	3373	3	]	]	X
m-1112	3373	4	the	the	DET
m-1112	3373	5	erp	erp	NOUN
m-1112	3373	6	argument	argument	NOUN
m-1112	3373	7	,	,	PUNCT
m-1112	3373	8	under	under	ADP
m-1112	3373	9	the	the	DET
m-1112	3373	10	critic	critic	NOUN
m-1112	3373	11	of	of	ADP
m-1112	3373	12	the	the	DET
m-1112	3373	13	material	material	NOUN
m-1112	3373	14	—	—	PUNCT
m-1112	3373	15	geometry	geometry	NOUN
m-1112	3373	16	and	and	CCONJ
m-1112	3373	17	,	,	PUNCT
m-1112	3373	18	the	the	DET
m-1112	3373	19	space	space	NOUN
m-1112	3373	20	energy	energy	NOUN
m-1112	3373	21	universe	universe	NOUN
m-1112	3373	22	.	.	PUNCT
m-1112	3374	1	[	[	X
m-1112	3374	2	106	106	X
m-1112	3374	3	]	]	X
m-1112	3374	4	[	[	X
m-1112	3374	5	m	m	X
m-1112	3374	6	]	]	X
m-1112	3374	7	programming	program	VERB
m-1112	3374	8	the	the	DET
m-1112	3374	9	atoms	atom	NOUN
m-1112	3374	10	and	and	CCONJ
m-1112	3374	11	compounds	compound	NOUN
m-1112	3374	12	and	and	CCONJ
m-1112	3374	13	the	the	DET
m-1112	3374	14	unification	unification	NOUN
m-1112	3374	15	of	of	ADP
m-1112	3374	16	physics	physics	NOUN
m-1112	3374	17	and	and	CCONJ
m-1112	3374	18	chemistry	chemistry	NOUN
m-1112	3374	19	—	—	PUNCT
m-1112	3374	20	[	[	X
m-1112	3374	21	"	"	PUNCT
m-1112	3374	22	jmseat	jmseat	NOUN
m-1112	3374	23	2024	2024	NUM
m-1112	3374	24	"	"	PUNCT
m-1112	3374	25	]	]	PUNCT
m-1112	3374	26	atul@scientificadvances.co.in	atul@scientificadvances.co.in	VERB
m-1112	3374	27	[	[	X
m-1112	3374	28	106	106	NUM
m-1112	3374	29	]	]	X
m-1112	3375	1	[	[	X
m-1112	3375	2	m	m	X
m-1112	3375	3	]	]	X
m-1112	3375	4	programming	program	VERB
m-1112	3375	5	the	the	DET
m-1112	3375	6	atoms	atom	NOUN
m-1112	3375	7	and	and	CCONJ
m-1112	3375	8	compounds	compound	NOUN
m-1112	3375	9	and	and	CCONJ
m-1112	3375	10	the	the	DET
m-1112	3375	11	unification	unification	NOUN
m-1112	3375	12	of	of	ADP
m-1112	3375	13	physics	physics	NOUN
m-1112	3375	14	and	and	CCONJ
m-1112	3375	15	chemistry	chemistry	NOUN
m-1112	3375	16	—	—	PUNCT
m-1112	3375	17	asrp.hspublishing@gmail.con	asrp.hspublishing@gmail.con	PROPN
m-1112	3376	1	[	[	X
m-1112	3376	2	107	107	NUM
m-1112	3376	3	-	-	SYM
m-1112	3376	4	a	a	NOUN
m-1112	3376	5	]	]	X
m-1112	3376	6	[	[	X
m-1112	3376	7	m	m	X
m-1112	3376	8	]	]	X
m-1112	3376	9	the	the	DET
m-1112	3376	10	planck`s	planck`s	NOUN
m-1112	3376	11	<	<	X
m-1112	3376	12	<	<	X
m-1112	3376	13	duality	duality	NOUN
m-1112	3376	14	angular	angular	ADJ
m-1112	3376	15	momentum	momentum	NOUN
m-1112	3376	16	>	>	X
m-1112	3376	17	>	>	X
m-1112	3376	18	as	as	ADP
m-1112	3376	19	gravity	gravity	NOUN
m-1112	3376	20	and	and	CCONJ
m-1112	3376	21	.	.	PUNCT
m-1112	3377	1	antigravity	antigravity	NOUN
m-1112	3377	2	<	<	X
m-1112	3377	3	editor@granthaalayah.com	editor@granthaalayah.com	PROPN
m-1112	3377	4	>	>	X
m-1112	3377	5	research	research	PROPN
m-1112	3377	6	international	international	ADJ
m-1112	3377	7	journal	journal	NOUN
m-1112	3377	8	[	[	X
m-1112	3377	9	107	107	X
m-1112	3377	10	]	]	X
m-1112	3378	1	[	[	X
m-1112	3378	2	m	m	X
m-1112	3378	3	]	]	X
m-1112	3378	4	the	the	DET
m-1112	3378	5	planck`s	planck`s	NOUN
m-1112	3378	6	<	<	X
m-1112	3378	7	<	<	X
m-1112	3378	8	duality	duality	NOUN
m-1112	3378	9	angular	angular	ADJ
m-1112	3378	10	momentum	momentum	NOUN
m-1112	3378	11	>	>	X
m-1112	3378	12	>	>	X
m-1112	3378	13	as	as	ADP
m-1112	3378	14	gravity	gravity	NOUN
m-1112	3378	15	and	and	CCONJ
m-1112	3378	16	antigravity	antigravity	NOUN
m-1112	3378	17	http://science	http://science	NUM
m-1112	3378	18	mpg	mpg	NOUN
m-1112	3378	19	≡	≡	PROPN
m-1112	3378	20	markos	markos	PROPN
m-1112	3378	21	georgallides	georgallide	VERB
m-1112	3378	22	[	[	X
m-1112	3378	23	108	108	NUM
m-1112	3378	24	]	]	PUNCT
m-1112	3379	1	[	[	X
m-1112	3379	2	m	m	X
m-1112	3379	3	]	]	X
m-1112	3379	4	the	the	DET
m-1112	3379	5	planar	planar	ADJ
m-1112	3379	6	and	and	CCONJ
m-1112	3379	7	atoms	atom	VERB
m-1112	3379	8	black	black	ADJ
m-1112	3379	9	holes	hole	NOUN
m-1112	3379	10	,	,	PUNCT
m-1112	3379	11	under	under	ADP
m-1112	3379	12	the	the	DET
m-1112	3379	13	critic	critic	NOUN
m-1112	3379	14	of	of	ADP
m-1112	3379	15	material	material	NOUN
m-1112	3379	16	-	-	PUNCT
m-1112	3379	17	geometry	geometry	NOUN
m-1112	3379	18	&	&	CCONJ
m-1112	3379	19	planck	planck	NOUN
m-1112	3379	20	–	–	PUNCT
m-1112	3379	21	dual	dual	ADJ
m-1112	3379	22	spin	spin	NOUN
m-1112	3379	23	as	as	SCONJ
m-1112	3379	24	gravity	gravity	NOUN
m-1112	3379	25	-	-	PUNCT
m-1112	3379	26	antigravity	antigravity	NOUN
m-1112	3379	27	http://science	http://science	NUM
m-1112	3379	28	mpg	mpg	NOUN
m-1112	3379	29	≡	≡	PROPN
m-1112	3379	30	markos	markos	PROPN
m-1112	3379	31	georgallides	georgallide	VERB
m-1112	3380	1	[	[	X
m-1112	3380	2	109	109	NUM
m-1112	3380	3	]	]	PUNCT
m-1112	3380	4	[	[	X
m-1112	3380	5	m	m	X
m-1112	3380	6	]	]	X
m-1112	3380	7	the	the	DET
m-1112	3380	8	dual	dual	ADJ
m-1112	3380	9	quaternion	quaternion	NOUN
m-1112	3380	10	momentum	momentum	NOUN
m-1112	3380	11	-b	-b	PUNCT
m-1112	3380	12	as	as	ADP
m-1112	3380	13	{	{	PUNCT
m-1112	3380	14	the	the	DET
m-1112	3380	15	existing	exist	VERB
m-1112	3380	16	universe	universe	NOUN
m-1112	3380	17	}	}	PUNCT
m-1112	3380	18	&	&	CCONJ
m-1112	3380	19	the	the	DET
m-1112	3380	20	black	black	ADJ
m-1112	3380	21	-holes	-hole	NOUN
m-1112	3380	22	,	,	PUNCT
m-1112	3380	23	http://science	http://science	NUM
m-1112	3380	24	mpg	mpg	NOUN
m-1112	3380	25	≡	≡	PROPN
m-1112	3380	26	markos	markos	PROPN
m-1112	3380	27	georgallides	georgallide	VERB
m-1112	3380	28	[	[	X
m-1112	3380	29	110	110	NUM
m-1112	3380	30	]	]	X
m-1112	3381	1	[	[	X
m-1112	3381	2	m	m	X
m-1112	3381	3	]	]	X
m-1112	3381	4	the	the	DET
m-1112	3381	5	origination	origination	NOUN
m-1112	3381	6	-	-	PUNCT
m-1112	3381	7	mechanism	mechanism	NOUN
m-1112	3381	8	of	of	ADP
m-1112	3381	9	fundamental	fundamental	ADJ
m-1112	3381	10	particles	particle	NOUN
m-1112	3381	11	in	in	ADP
m-1112	3381	12	the	the	DET
m-1112	3381	13	energy	energy	NOUN
m-1112	3381	14	-	-	PUNCT
m-1112	3381	15	planck`s	planck`s	NOUN
m-1112	3381	16	confinement	confinement	NOUN
m-1112	3381	17	and	and	CCONJ
m-1112	3381	18	their	their	PRON
m-1112	3381	19	existence	existence	NOUN
m-1112	3381	20	,	,	PUNCT
m-1112	3381	21	http://science	http://science	NOUN
m-1112	3381	22	mpg	mpg	NOUN
m-1112	3381	23	≡	≡	PROPN
m-1112	3381	24	markos	markos	PROPN
m-1112	3381	25	georgallides	georgallide	VERB
m-1112	3381	26	[	[	X
m-1112	3381	27	111	111	NUM
m-1112	3381	28	]	]	PUNCT
m-1112	3382	1	[	[	X
m-1112	3382	2	m	m	X
m-1112	3382	3	]	]	X
m-1112	3382	4	the	the	DET
m-1112	3382	5	polynomials	polynomial	NOUN
m-1112	3382	6	,	,	PUNCT
m-1112	3382	7	n	n	CCONJ
m-1112	3382	8	-	-	PUNCT
m-1112	3382	9	knots	knot	NOUN
m-1112	3382	10	figures	figure	NOUN
m-1112	3382	11	,	,	PUNCT
m-1112	3382	12	edge	edge	NOUN
m-1112	3382	13	points	point	NOUN
m-1112	3382	14	vibration	vibration	NOUN
m-1112	3382	15	&	&	CCONJ
m-1112	3382	16	m	m	NOUN
m-1112	3382	17	-	-	NOUN
m-1112	3382	18	geometry	geometry	NOUN
m-1112	3382	19	.	.	PUNCT
m-1112	3383	1	by	by	ADP
m-1112	3383	2	http://science	http://science	NUM
m-1112	3383	3	mpg	mpg	NOUN
m-1112	3383	4	≡	≡	PROPN
m-1112	3383	5	markos	markos	PROPN
m-1112	3383	6	georgallides	georgallide	VERB
m-1112	3383	7	[	[	X
m-1112	3383	8	112	112	NUM
m-1112	3383	9	]	]	PUNCT
m-1112	3384	1	[	[	X
m-1112	3384	2	m	m	X
m-1112	3384	3	]	]	X
m-1112	3384	4	an	an	DET
m-1112	3384	5	way	way	NOUN
m-1112	3384	6	for	for	ADP
m-1112	3384	7	deceptioning	deceptione	VERB
m-1112	3384	8	the	the	DET
m-1112	3384	9	normal	normal	ADJ
m-1112	3384	10	or	or	CCONJ
m-1112	3384	11	the	the	DET
m-1112	3384	12	dangerous	dangerous	ADJ
m-1112	3384	13	cells	cell	NOUN
m-1112	3384	14	by	by	ADP
m-1112	3384	15	http://science	http://science	NUM
m-1112	3384	16	mpg	mpg	NOUN
m-1112	3384	17	≡	≡	PROPN
m-1112	3384	18	markos	markos	PROPN
m-1112	3384	19	georgallides	georgallide	VERB
m-1112	3384	20	[	[	X
m-1112	3384	21	113	113	NUM
m-1112	3384	22	]	]	PUNCT
m-1112	3385	1	[	[	X
m-1112	3385	2	m	m	X
m-1112	3385	3	]	]	X
m-1112	3385	4	the	the	DET
m-1112	3385	5	origination	origination	NOUN
m-1112	3385	6	of	of	ADP
m-1112	3385	7	universe	universe	NOUN
m-1112	3385	8	from	from	ADP
m-1112	3385	9	energy	energy	NOUN
m-1112	3385	10	≡	≡	PROPN
m-1112	3385	11	motion	motion	NOUN
m-1112	3385	12	into	into	ADP
m-1112	3385	13	the	the	DET
m-1112	3385	14	e	e	NOUN
m-1112	3385	15	-	-	NOUN
m-1112	3385	16	geometry	geometry	NOUN
m-1112	3385	17	.	.	PUNCT
m-1112	3386	1	markos	markos	PROPN
m-1112	3386	2	georgallides	georgallide	NOUN
m-1112	3386	3	comes	come	VERB
m-1112	3386	4	from	from	ADP
m-1112	3386	5	cyprus	cyprus	PROPN
m-1112	3386	6	and	and	CCONJ
m-1112	3386	7	currently	currently	ADV
m-1112	3386	8	resides	reside	VERB
m-1112	3386	9	in	in	ADP
m-1112	3386	10	the	the	DET
m-1112	3386	11	city	city	NOUN
m-1112	3386	12	larnaca	larnaca	PROPN
m-1112	3386	13	,	,	PUNCT
m-1112	3386	14	cyprus	cyprus	PROPN
m-1112	3386	15	after	after	ADP
m-1112	3386	16	being	be	AUX
m-1112	3386	17	expelled	expel	VERB
m-1112	3386	18	from	from	ADP
m-1112	3386	19	his	his	PRON
m-1112	3386	20	home	home	NOUN
m-1112	3386	21	town	town	NOUN
m-1112	3386	22	famagusta	famagusta	PROPN
m-1112	3386	23	-	-	PUNCT
m-1112	3386	24	varosha	varosha	PROPN
m-1112	3386	25	,	,	PUNCT
m-1112	3386	26	by	by	ADP
m-1112	3386	27	the	the	DET
m-1112	3386	28	barbaric	barbaric	ADJ
m-1112	3386	29	turks	turk	NOUN
m-1112	3386	30	in	in	ADP
m-1112	3386	31	august	august	PROPN
m-1112	3386	32	1974	1974	NUM
m-1112	3386	33	.	.	PUNCT
m-1112	3387	1	he	he	PRON
m-1112	3387	2	works	work	VERB
m-1112	3387	3	as	as	ADP
m-1112	3387	4	a	a	DET
m-1112	3387	5	consultant	consultant	NOUN
m-1112	3387	6	civil	civil	ADJ
m-1112	3387	7	and	and	CCONJ
m-1112	3387	8	architect	architect	NOUN
m-1112	3387	9	engineer	engineer	NOUN
m-1112	3387	10	having	have	VERB
m-1112	3387	11	his	his	PRON
m-1112	3387	12	own	own	ADJ
m-1112	3387	13	business	business	NOUN
m-1112	3387	14	.	.	PUNCT
m-1112	3388	1	he	he	PRON
m-1112	3388	2	is	be	AUX
m-1112	3388	3	also	also	ADV
m-1112	3388	4	the	the	DET
m-1112	3388	5	author	author	NOUN
m-1112	3388	6	of	of	ADP
m-1112	3388	7	numerous	numerous	ADJ
m-1112	3388	8	scholarly	scholarly	ADJ
m-1112	3388	9	articles	article	NOUN
m-1112	3388	10	focusing	focus	VERB
m-1112	3388	11	on	on	ADP
m-1112	3388	12	euclidean	euclidean	ADJ
m-1112	3388	13	and	and	CCONJ
m-1112	3388	14	material	material	NOUN
m-1112	3388	15	geometry	geometry	NOUN
m-1112	3388	16	,	,	PUNCT
m-1112	3388	17	and	and	CCONJ
m-1112	3388	18	mathematical	mathematical	ADJ
m-1112	3388	19	to	to	ADP
m-1112	3388	20	physics	physics	NOUN
m-1112	3388	21	and	and	CCONJ
m-1112	3388	22	mechanics	mechanic	NOUN
m-1112	3388	23	related	relate	VERB
m-1112	3388	24	subjects	subject	NOUN
m-1112	3388	25	.	.	PUNCT
m-1112	3389	1	he	he	PRON
m-1112	3389	2	obtained	obtain	VERB
m-1112	3389	3	his	his	PRON
m-1112	3389	4	degree	degree	NOUN
m-1112	3389	5	from	from	ADP
m-1112	3389	6	the	the	DET
m-1112	3389	7	athens	athens	PROPN
m-1112	3389	8	,	,	PUNCT
m-1112	3389	9	national	national	PROPN
m-1112	3389	10	technical	technical	ADJ
m-1112	3389	11	,	,	PUNCT
m-1112	3389	12	polytechnic	polytechnic	ADJ
m-1112	3389	13	university	university	NOUN
m-1112	3389	14	[	[	X
m-1112	3389	15	natua	natua	X
m-1112	3389	16	]	]	X
m-1112	3389	17	athensgreece	athensgreece	NOUN
m-1112	3389	18	,	,	PUNCT
m-1112	3389	19	and	and	CCONJ
m-1112	3389	20	subsequently	subsequently	ADV
m-1112	3389	21	studied	study	VERB
m-1112	3389	22	in	in	ADP
m-1112	3389	23	germany	germany	PROPN
m-1112	3389	24	,	,	PUNCT
m-1112	3389	25	math	math	NOUN
m-1112	3389	26	theory	theory	NOUN
m-1112	3389	27	of	of	ADP
m-1112	3389	28	photoelasticity	photoelasticity	NOUN
m-1112	3389	29	.	.	PUNCT
m-1112	3390	1	ijo	ijo	PROPN
m-1112	3390	2	international	international	PROPN
m-1112	3390	3	journal	journal	PROPN
m-1112	3390	4	of	of	ADP
m-1112	3390	5	mathematics	mathematics	PROPN
m-1112	3390	6	(	(	PUNCT
m-1112	3390	7	issn	issn	PROPN
m-1112	3390	8	:	:	PUNCT
m-1112	3390	9	2992	2992	NUM
m-1112	3390	10	-	-	SYM
m-1112	3390	11	4421	4421	NUM
m-1112	3390	12	)	)	PUNCT
m-1112	3390	13	volume	volume	NOUN
m-1112	3390	14	08	08	NUM
m-1112	3391	1	|	|	ADV
m-1112	3391	2	issue	issue	NOUN
m-1112	3391	3	08	08	NUM
m-1112	3392	1	|	|	ADV
m-1112	3392	2	august	august	PROPN
m-1112	3392	3	2025	2025	NUM
m-1112	3392	4	|	|	ADV
m-1112	3392	5	https://ijojournals.com/index.php/m/index	https://ijojournals.com/index.php/m/index	NOUN
m-1112	3392	6	ijo	ijo	PROPN
m-1112	3392	7	journals	journal	NOUN
m-1112	3392	8	http://science/	http://science/	VERB
m-1112	3392	9	http://science/	http://science/	PROPN
m-1112	3392	10	http://science/	http://science/	PROPN
m-1112	3392	11	mailto:atul@scientificadvances.co.in	mailto:atul@scientificadvances.co.in	NOUN
m-1112	3392	12	mailto:asrp.hspublishing@gmail.con	mailto:asrp.hspublishing@gmail.con	PROPN
m-1112	3392	13	mailto	mailto	PROPN
m-1112	3392	14	:	:	PUNCT
m-1112	3392	15	editor@g	editor@g	PRON
m-1112	3392	16	http://science/	http://science/	PROPN
m-1112	3392	17	http://science/	http://science/	PROPN
m-1112	3392	18	http://science/	http://science/	PROPN
m-1112	3392	19	http://science/	http://science/	PROPN
m-1112	3392	20	http://science/	http://science/	PROPN
m-1112	3392	21	http://science/	http://science/	PROPN