id	sid	tid	token	lemma	pos
asir-1642	1	1	applied	apply	VERB
asir-1642	1	2	science	science	NOUN
asir-1642	1	3	and	and	CCONJ
asir-1642	1	4	innovative	innovative	ADJ
asir-1642	1	5	research	research	NOUN
asir-1642	1	6	issn	issn	VERB
asir-1642	1	7	2474	2474	NUM
asir-1642	1	8	-	-	SYM
asir-1642	1	9	4972	4972	NUM
asir-1642	1	10	(	(	PUNCT
asir-1642	1	11	print	print	NOUN
asir-1642	1	12	)	)	PUNCT
asir-1642	1	13	issn	issn	VERB
asir-1642	1	14	2474	2474	NUM
asir-1642	1	15	-	-	SYM
asir-1642	1	16	4980	4980	NUM
asir-1642	1	17	(	(	PUNCT
asir-1642	1	18	online	online	ADJ
asir-1642	1	19	)	)	PUNCT
asir-1642	1	20	vol	vol	NOUN
asir-1642	1	21	.	.	PROPN
asir-1642	2	1	2	2	NUM
asir-1642	2	2	,	,	PUNCT
asir-1642	2	3	no	no	INTJ
asir-1642	2	4	.	.	NOUN
asir-1642	2	5	4	4	NUM
asir-1642	2	6	,	,	PUNCT
asir-1642	2	7	2018	2018	NUM
asir-1642	2	8	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	2	9	155	155	NUM
asir-1642	2	10	original	original	ADJ
asir-1642	2	11	paper	paper	NOUN
asir-1642	2	12	the	the	DET
asir-1642	2	13	gravity	gravity	NOUN
asir-1642	2	14	and	and	CCONJ
asir-1642	2	15	photons	photon	NOUN
asir-1642	2	16	markos	markos	PROPN
asir-1642	2	17	georgallides1	georgallides1	PROPN
asir-1642	2	18	*	*	PROPN
asir-1642	2	19	1	1	NUM
asir-1642	2	20	civil	civil	ADJ
asir-1642	2	21	-	-	PUNCT
asir-1642	2	22	structural	structural	ADJ
asir-1642	2	23	engineer	engineer	NOUN
asir-1642	2	24	(	(	PUNCT
asir-1642	2	25	natua	natua	NOUN
asir-1642	2	26	)	)	PUNCT
asir-1642	2	27	,	,	PUNCT
asir-1642	2	28	athens	athens	PROPN
asir-1642	2	29	,	,	PUNCT
asir-1642	2	30	cyprus	cyprus	PROPN
asir-1642	2	31	*	*	PUNCT
asir-1642	2	32	markos	markos	PROPN
asir-1642	2	33	georgallides	georgallide	NOUN
asir-1642	2	34	,	,	PUNCT
asir-1642	2	35	civil	civil	ADJ
asir-1642	2	36	-	-	PUNCT
asir-1642	2	37	structural	structural	ADJ
asir-1642	2	38	engineer	engineer	NOUN
asir-1642	2	39	(	(	PUNCT
asir-1642	2	40	natua	natua	NOUN
asir-1642	2	41	)	)	PUNCT
asir-1642	2	42	,	,	PUNCT
asir-1642	2	43	athens	athens	PROPN
asir-1642	2	44	,	,	PUNCT
asir-1642	2	45	cyprus	cyprus	PROPN
asir-1642	2	46	received	receive	VERB
asir-1642	2	47	:	:	PUNCT
asir-1642	2	48	september	september	PROPN
asir-1642	2	49	19	19	NUM
asir-1642	2	50	,	,	PUNCT
asir-1642	2	51	2018	2018	NUM
asir-1642	2	52	accepted	accept	VERB
asir-1642	2	53	:	:	PUNCT
asir-1642	2	54	october	october	PROPN
asir-1642	2	55	9	9	NUM
asir-1642	2	56	,	,	PUNCT
asir-1642	2	57	2018	2018	NUM
asir-1642	2	58	online	online	ADV
asir-1642	2	59	published	publish	VERB
asir-1642	2	60	:	:	PUNCT
asir-1642	2	61	october	october	PROPN
asir-1642	2	62	18	18	NUM
asir-1642	2	63	,	,	PUNCT
asir-1642	2	64	2018	2018	NUM
asir-1642	2	65	doi:10.22158	doi:10.22158	NOUN
asir-1642	2	66	/	/	SYM
asir-1642	2	67	asir.v2n4p155	asir.v2n4p155	PROPN
asir-1642	2	68	url	url	PROPN
asir-1642	2	69	:	:	PUNCT
asir-1642	2	70	http://dx.doi.org/10.22158/asir.v2n4p155	http://dx.doi.org/10.22158/asir.v2n4p155	X
asir-1642	2	71	abstract	abstract	ADJ
asir-1642	2	72	one	one	NUM
asir-1642	2	73	of	of	ADP
asir-1642	2	74	the	the	DET
asir-1642	2	75	most	most	ADV
asir-1642	2	76	important	important	ADJ
asir-1642	2	77	concept	concept	NOUN
asir-1642	2	78	in	in	ADP
asir-1642	2	79	geometry	geometry	NOUN
asir-1642	2	80	is	be	AUX
asir-1642	2	81	,	,	PUNCT
asir-1642	2	82	distance	distance	NOUN
asir-1642	2	83	,	,	PUNCT
asir-1642	2	84	which	which	PRON
asir-1642	2	85	is	be	AUX
asir-1642	2	86	the	the	DET
asir-1642	2	87	quanta	quanta	PROPN
asir-1642	2	88	in	in	ADP
asir-1642	2	89	geometry	geometry	NOUN
asir-1642	2	90	,	,	PUNCT
asir-1642	2	91	while	while	SCONJ
asir-1642	2	92	in	in	ADP
asir-1642	2	93	material	material	NOUN
asir-1642	2	94	-	-	PUNCT
asir-1642	2	95	geometry	geometry	NOUN
asir-1642	2	96	the	the	DET
asir-1642	2	97	composition	composition	NOUN
asir-1642	2	98	of	of	ADP
asir-1642	2	99	opposites	opposite	NOUN
asir-1642	2	100	,	,	PUNCT
asir-1642	2	101	the	the	DET
asir-1642	2	102	material	material	NOUN
asir-1642	2	103	-	-	PUNCT
asir-1642	2	104	point	point	NOUN
asir-1642	2	105	which	which	PRON
asir-1642	2	106	is	be	AUX
asir-1642	2	107	the	the	DET
asir-1642	2	108	quanta	quanta	PROPN
asir-1642	2	109	in	in	ADP
asir-1642	2	110	chemistry	chemistry	NOUN
asir-1642	2	111	and	and	CCONJ
asir-1642	2	112	physics	physics	NOUN
asir-1642	2	113	.	.	PUNCT
asir-1642	3	1	as	as	ADP
asir-1642	3	2	in	in	ADP
asir-1642	3	3	algebra	algebra	NOUN
asir-1642	3	4	zero	zero	NUM
asir-1642	3	5	,	,	PUNCT
asir-1642	3	6	0	0	NUM
asir-1642	3	7	,	,	PUNCT
asir-1642	3	8	is	be	AUX
asir-1642	3	9	the	the	DET
asir-1642	3	10	master	master	NOUN
asir-1642	3	11	-	-	PUNCT
asir-1642	3	12	key	key	NOUN
asir-1642	3	13	number	number	NOUN
asir-1642	3	14	for	for	ADP
asir-1642	3	15	all	all	DET
asir-1642	3	16	positive	positive	ADJ
asir-1642	3	17	and	and	CCONJ
asir-1642	3	18	negative	negative	ADJ
asir-1642	3	19	numbers	number	NOUN
asir-1642	3	20	and	and	CCONJ
asir-1642	3	21	this	this	PRON
asir-1642	3	22	because	because	SCONJ
asir-1642	3	23	their	their	PRON
asir-1642	3	24	sum	sum	NOUN
asir-1642	3	25	and	and	CCONJ
asir-1642	3	26	multiplication	multiplication	NOUN
asir-1642	3	27	becomes	become	VERB
asir-1642	3	28	zero	zero	NUM
asir-1642	3	29	,	,	PUNCT
asir-1642	3	30	and	and	CCONJ
asir-1642	3	31	the	the	DET
asir-1642	3	32	same	same	ADJ
asir-1642	3	33	on	on	ADP
asir-1642	3	34	any	any	DET
asir-1642	3	35	coordinate	coordinate	NOUN
asir-1642	3	36	-	-	PUNCT
asir-1642	3	37	system	system	NOUN
asir-1642	3	38	where	where	SCONJ
asir-1642	3	39	±	±	NUM
asir-1642	3	40	axes	axis	NOUN
asir-1642	3	41	pass	pass	VERB
asir-1642	3	42	from	from	ADP
asir-1642	3	43	zero	zero	NUM
asir-1642	3	44	,	,	PUNCT
asir-1642	3	45	exists	exist	VERB
asir-1642	3	46	also	also	ADV
asir-1642	3	47	apriori	apriori	ADV
asir-1642	3	48	in	in	ADP
asir-1642	3	49	geometry	geometry	NOUN
asir-1642	3	50	the	the	DET
asir-1642	3	51	material	material	NOUN
asir-1642	3	52	-	-	PUNCT
asir-1642	3	53	point	point	NOUN
asir-1642	3	54	in	in	ADP
asir-1642	3	55	where	where	SCONJ
asir-1642	3	56	the	the	DET
asir-1642	3	57	rolling	rolling	NOUN
asir-1642	3	58	of	of	ADP
asir-1642	3	59	positive	positive	ADJ
asir-1642	3	60	⊕	⊕	PROPN
asir-1642	3	61	,	,	PUNCT
asir-1642	3	62	constituent	constituent	NOUN
asir-1642	3	63	on	on	ADP
asir-1642	3	64	the	the	DET
asir-1642	3	65	negative	negative	ADJ
asir-1642	3	66	⊝	⊝	NOUN
asir-1642	3	67	,	,	PUNCT
asir-1642	3	68	constituent	constituent	NOUN
asir-1642	3	69	,	,	PUNCT
asir-1642	3	70	creates	create	VERB
asir-1642	3	71	the	the	DET
asir-1642	3	72	neutral	neutral	ADJ
asir-1642	3	73	material	material	NOUN
asir-1642	3	74	point	point	NOUN
asir-1642	3	75	which	which	DET
asir-1642	3	76	equilibrium	equilibrium	NOUN
asir-1642	3	77	.	.	PUNCT
asir-1642	4	1	angular	angular	ADJ
asir-1642	4	2	momentum	momentum	NOUN
asir-1642	4	3	is	be	AUX
asir-1642	4	4	identical	identical	ADJ
asir-1642	4	5	with	with	ADP
asir-1642	4	6	spin	spin	NOUN
asir-1642	4	7	and	and	CCONJ
asir-1642	4	8	consists	consist	VERB
asir-1642	4	9	the	the	DET
asir-1642	4	10	first	first	ADJ
asir-1642	4	11	-	-	PUNCT
asir-1642	4	12	discrete	discrete	NOUN
asir-1642	4	13	-	-	PUNCT
asir-1642	4	14	energy	energy	NOUN
asir-1642	4	15	-	-	PUNCT
asir-1642	4	16	monad	monad	PROPN
asir-1642	4	17	which	which	PRON
asir-1642	4	18	occupies	occupy	VERB
asir-1642	4	19	,	,	PUNCT
asir-1642	4	20	discrete	discrete	ADJ
asir-1642	4	21	value	value	NOUN
asir-1642	4	22	and	and	CCONJ
asir-1642	4	23	direction	direction	NOUN
asir-1642	4	24	,	,	PUNCT
asir-1642	4	25	in	in	ADP
asir-1642	4	26	contradiction	contradiction	NOUN
asir-1642	4	27	to	to	ADP
asir-1642	4	28	the	the	DET
asir-1642	4	29	point	point	NOUN
asir-1642	4	30	which	which	PRON
asir-1642	4	31	is	be	AUX
asir-1642	4	32	nothing	nothing	PRON
asir-1642	4	33	,	,	PUNCT
asir-1642	4	34	dimensionless	dimensionless	NOUN
asir-1642	4	35	and	and	CCONJ
asir-1642	4	36	without	without	ADP
asir-1642	4	37	any	any	DET
asir-1642	4	38	direction	direction	NOUN
asir-1642	4	39	.	.	PUNCT
asir-1642	5	1	from	from	ADP
asir-1642	5	2	the	the	DET
asir-1642	5	3	definition	definition	NOUN
asir-1642	5	4	,	,	PUNCT
asir-1642	5	5	work	work	NOUN
asir-1642	5	6	=	=	SYM
asir-1642	5	7	motion	motion	NOUN
asir-1642	5	8	=	=	SYM
asir-1642	5	9	force	force	NOUN
asir-1642	5	10	x	x	NOUN
asir-1642	5	11	displacement	displacement	ADJ
asir-1642	5	12	=	=	SYM
asir-1642	5	13	energy	energy	NOUN
asir-1642	5	14	,	,	PUNCT
asir-1642	5	15	results	result	VERB
asir-1642	5	16	the	the	PRON
asir-1642	5	17	where	where	SCONJ
asir-1642	5	18	this	this	DET
asir-1642	5	19	energy	energy	NOUN
asir-1642	5	20	as	as	ADP
asir-1642	5	21	,	,	PUNCT
asir-1642	5	22	momentum	momentum	NOUN
asir-1642	5	23	vector	vector	NOUN
asir-1642	5	24	�	�	PROPN
asir-1642	5	25	̅	̅	NOUN
asir-1642	5	26	�	�	PROPN
asir-1642	5	27	≡	≡	PROPN
asir-1642	5	28	spin	spin	PROPN
asir-1642	5	29	≡	≡	PROPN
asir-1642	5	30	energy	energy	NOUN
asir-1642	5	31	is	be	AUX
asir-1642	5	32	stored	store	VERB
asir-1642	5	33	,	,	PUNCT
asir-1642	5	34	and	and	CCONJ
asir-1642	5	35	it	it	PRON
asir-1642	5	36	is	be	AUX
asir-1642	5	37	the	the	DET
asir-1642	5	38	,	,	PUNCT
asir-1642	5	39	r	r	NOUN
asir-1642	5	40	cave	cave	NOUN
asir-1642	5	41	.	.	PUNCT
asir-1642	6	1	it	it	PRON
asir-1642	6	2	was	be	AUX
asir-1642	6	3	proved	prove	VERB
asir-1642	6	4	that	that	SCONJ
asir-1642	6	5	,	,	PUNCT
asir-1642	6	6	the	the	DET
asir-1642	6	7	r	r	NOUN
asir-1642	6	8	cave	cave	NOUN
asir-1642	6	9	≡	≡	PROPN
asir-1642	6	10	the	the	DET
asir-1642	6	11	particle	particle	NOUN
asir-1642	6	12	,	,	PUNCT
asir-1642	6	13	is	be	AUX
asir-1642	6	14	,	,	PUNCT
asir-1642	6	15	outward	outward	VERB
asir-1642	6	16	a	a	DET
asir-1642	6	17	stationary	stationary	ADJ
asir-1642	6	18	box	box	NOUN
asir-1642	6	19	,	,	PUNCT
asir-1642	6	20	inward	inward	ADP
asir-1642	6	21	a	a	DET
asir-1642	6	22	stationary	stationary	ADJ
asir-1642	6	23	wave	wave	NOUN
asir-1642	6	24	with	with	ADP
asir-1642	6	25	infinite	infinite	ADJ
asir-1642	6	26	frequencies	frequency	NOUN
asir-1642	6	27	...	...	PUNCT
asir-1642	7	1	𝑛	𝑛	X
asir-1642	7	2	→	→	SYM
asir-1642	7	3	∞	∞	PROPN
asir-1642	7	4	and	and	CCONJ
asir-1642	7	5	with	with	ADP
asir-1642	7	6	energy	energy	NOUN
asir-1642	7	7	,	,	PUNCT
asir-1642	7	8	the	the	DET
asir-1642	7	9	wave	wave	NOUN
asir-1642	7	10	,	,	PUNCT
asir-1642	7	11	e	e	PROPN
asir-1642	7	12	=	=	PUNCT
asir-1642	7	13	h.	h.	PROPN
asir-1642	7	14	𝑛	𝑛	PROPN
asir-1642	8	1	=	=	SYM
asir-1642	8	2	(	(	PUNCT
asir-1642	8	3	nσ/8r²).	nσ/8r²).	X
asir-1642	8	4	�	�	PROPN
asir-1642	8	5	̅	̅	NOUN
asir-1642	8	6	�	�	NOUN
asir-1642	8	7	.	.	PUNCT
asir-1642	9	1	[	[	X
asir-1642	9	2	70	70	NUM
asir-1642	9	3	]	]	PUNCT
asir-1642	9	4	.	.	PUNCT
asir-1642	10	1	in	in	ADP
asir-1642	10	2	all	all	PRON
asir-1642	10	3	above	above	ADP
asir-1642	10	4	issue	issue	VERB
asir-1642	10	5	the	the	DET
asir-1642	10	6	kepler	kepler	NOUN
asir-1642	10	7	-	-	PUNCT
asir-1642	10	8	laws	law	NOUN
asir-1642	10	9	,	,	PUNCT
asir-1642	10	10	denoting	denote	VERB
asir-1642	10	11	that	that	SCONJ
asir-1642	10	12	both	both	PRON
asir-1642	10	13	macrocosm	macrocosm	PROPN
asir-1642	10	14	and	and	CCONJ
asir-1642	10	15	microcosm	microcosm	PROPN
asir-1642	10	16	obey	obey	VERB
asir-1642	10	17	the	the	DET
asir-1642	10	18	newton	newton	PROPN
asir-1642	10	19	’s	’s	PART
asir-1642	10	20	laws	law	NOUN
asir-1642	10	21	of	of	ADP
asir-1642	10	22	motion	motion	NOUN
asir-1642	10	23	in	in	ADP
asir-1642	10	24	all	all	DET
asir-1642	10	25	scales	scale	NOUN
asir-1642	10	26	.	.	PUNCT
asir-1642	11	1	keywords	keyword	VERB
asir-1642	11	2	what	what	PRON
asir-1642	11	3	is	be	AUX
asir-1642	11	4	gravity	gravity	NOUN
asir-1642	11	5	,	,	PUNCT
asir-1642	11	6	gravity	gravity	NOUN
asir-1642	11	7	and	and	CCONJ
asir-1642	11	8	planet	planet	NOUN
asir-1642	11	9	-	-	PUNCT
asir-1642	11	10	orbits	orbit	NOUN
asir-1642	11	11	,	,	PUNCT
asir-1642	11	12	gravity	gravity	NOUN
asir-1642	11	13	and	and	CCONJ
asir-1642	11	14	black	black	ADJ
asir-1642	11	15	-	-	PUNCT
asir-1642	11	16	holes	hole	NOUN
asir-1642	11	17	,	,	PUNCT
asir-1642	11	18	gravity	gravity	NOUN
asir-1642	11	19	and	and	CCONJ
asir-1642	11	20	atom	atom	NOUN
asir-1642	11	21	-	-	PUNCT
asir-1642	11	22	rims	rim	NOUN
asir-1642	11	23	1	1	NUM
asir-1642	11	24	.	.	PUNCT
asir-1642	12	1	introduction	introduction	NOUN
asir-1642	12	2	a	a	PRON
asir-1642	12	3	..	..	PUNCT
asir-1642	13	1	it	it	PRON
asir-1642	13	2	was	be	AUX
asir-1642	13	3	shown	show	VERB
asir-1642	13	4	[	[	PUNCT
asir-1642	13	5	33	33	NUM
asir-1642	13	6	-	-	SYM
asir-1642	13	7	36	36	NUM
asir-1642	13	8	]	]	PUNCT
asir-1642	13	9	that	that	SCONJ
asir-1642	13	10	un	un	PROPN
asir-1642	13	11	-	-	ADJ
asir-1642	13	12	clashed	clash	VERB
asir-1642	13	13	fragments	fragment	NOUN
asir-1642	13	14	through	through	ADP
asir-1642	13	15	the	the	DET
asir-1642	13	16	center	center	NOUN
asir-1642	13	17	,	,	PUNCT
asir-1642	13	18	o	o	NOUN
asir-1642	13	19	,	,	PUNCT
asir-1642	13	20	consist	consist	VERB
asir-1642	13	21	the	the	DET
asir-1642	13	22	medium	medium	ADJ
asir-1642	13	23	-	-	PUNCT
asir-1642	13	24	field	field	NOUN
asir-1642	13	25	material	material	NOUN
asir-1642	13	26	-	-	PUNCT
asir-1642	13	27	fragment	fragment	NOUN
asir-1642	13	28	→	→	PUNCT
asir-1642	13	29	[	[	PUNCT
asir-1642	13	30	±	±	NUM
asir-1642	13	31	s²	s²	NOUN
asir-1642	13	32	]	]	PUNCT
asir-1642	13	33	=	=	PUNCT
asir-1642	14	1	[	[	X
asir-1642	14	2	mfmf	mfmf	X
asir-1642	14	3	]	]	X
asir-1642	14	4	≡	≡	PROPN
asir-1642	14	5	the	the	DET
asir-1642	14	6	chaos	chaos	NOUN
asir-1642	14	7	,	,	PUNCT
asir-1642	14	8	as	as	ADP
asir-1642	14	9	base	base	NOUN
asir-1642	14	10	for	for	ADP
asir-1642	14	11	all	all	DET
asir-1642	14	12	motions	motion	NOUN
asir-1642	14	13	,	,	PUNCT
asir-1642	14	14	and	and	CCONJ
asir-1642	14	15	gravity	gravity	NOUN
asir-1642	14	16	as	as	ADP
asir-1642	14	17	force	force	NOUN
asir-1642	14	18	[	[	X
asir-1642	14	19	i	i	PROPN
asir-1642	14	20	]	]	PUNCT
asir-1642	14	21	,	,	PUNCT
asir-1642	14	22	while	while	SCONJ
asir-1642	14	23	the	the	PRON
asir-1642	14	24	clashed	clash	VERB
asir-1642	14	25	with	with	ADP
asir-1642	14	26	the	the	DET
asir-1642	14	27	constant	constant	ADJ
asir-1642	14	28	velocity	velocity	NOUN
asir-1642	14	29	,	,	PUNCT
asir-1642	14	30	c̅	c̅	PROPN
asir-1642	14	31	,	,	PUNCT
asir-1642	14	32	consist	consist	VERB
asir-1642	14	33	the	the	DET
asir-1642	14	34	dark	dark	ADJ
asir-1642	14	35	matter	matter	NOUN
asir-1642	15	1	[	[	X
asir-1642	15	2	±.c̅.s	±.c̅.s	X
asir-1642	15	3	]	]	X
asir-1642	15	4	and	and	CCONJ
asir-1642	15	5	the	the	DET
asir-1642	15	6	dark	dark	ADJ
asir-1642	15	7	energy	energy	NOUN
asir-1642	15	8	[	[	X
asir-1642	15	9	c̅.i	c̅.i	NOUN
asir-1642	15	10	]	]	PUNCT
asir-1642	15	11	,	,	PUNCT
asir-1642	15	12	declaring	declare	VERB
asir-1642	15	13	that	that	SCONJ
asir-1642	15	14	→	→	NOUN
asir-1642	15	15	antimatter	antimatter	NOUN
asir-1642	15	16	-	-	PUNCT
asir-1642	15	17	galaxies	galaxy	NOUN
asir-1642	15	18	and	and	CCONJ
asir-1642	15	19	antimatter	antimatter	NOUN
asir-1642	15	20	-	-	PUNCT
asir-1642	15	21	asteroids	asteroid	NOUN
asir-1642	15	22	can	can	AUX
asir-1642	15	23	exist	exist	VERB
asir-1642	15	24	only	only	ADV
asir-1642	15	25	as	as	ADP
asir-1642	15	26	dark	dark	ADJ
asir-1642	15	27	-	-	PUNCT
asir-1642	15	28	matter	matter	NOUN
asir-1642	15	29	or	or	CCONJ
asir-1642	15	30	/	/	SYM
asir-1642	15	31	and	and	CCONJ
asir-1642	15	32	dark	dark	ADJ
asir-1642	15	33	-	-	PUNCT
asir-1642	15	34	energy	energy	NOUN
asir-1642	15	35	and	and	CCONJ
asir-1642	15	36	not	not	PART
asir-1642	15	37	as	as	ADP
asir-1642	15	38	antimatter	antimatter	NOUN
asir-1642	15	39	light	light	NOUN
asir-1642	15	40	,	,	PUNCT
asir-1642	15	41	c	c	NOUN
asir-1642	15	42	,	,	PUNCT
asir-1642	15	43	alone	alone	ADV
asir-1642	15	44	,	,	PUNCT
asir-1642	15	45	or	or	CCONJ
asir-1642	15	46	from	from	ADP
asir-1642	15	47	→	→	PUNCT
asir-1642	15	48	velocity	velocity	NOUN
asir-1642	15	49	breakages	breakage	NOUN
asir-1642	15	50	,	,	PUNCT
asir-1642	15	51	[	[	PUNCT
asir-1642	15	52	±	±	NOUN
asir-1642	15	53	s²	s²	NOUN
asir-1642	15	54	=	=	SYM
asir-1642	15	55	±	±	PROPN
asir-1642	15	56	(	(	PUNCT
asir-1642	15	57	wr)²	wr)²	PROPN
asir-1642	15	58	]	]	PUNCT
asir-1642	15	59	and	and	CCONJ
asir-1642	15	60	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	15	61	applied	apply	VERB
asir-1642	15	62	science	science	NOUN
asir-1642	15	63	and	and	CCONJ
asir-1642	15	64	innovative	innovative	ADJ
asir-1642	15	65	research	research	NOUN
asir-1642	15	66	vol	vol	NOUN
asir-1642	15	67	.	.	PROPN
asir-1642	16	1	2	2	NUM
asir-1642	16	2	,	,	PUNCT
asir-1642	16	3	no	no	INTJ
asir-1642	16	4	.	.	NOUN
asir-1642	16	5	4	4	NUM
asir-1642	16	6	,	,	PUNCT
asir-1642	16	7	2018	2018	NUM
asir-1642	16	8	156	156	NUM
asir-1642	16	9	published	publish	VERB
asir-1642	16	10	by	by	ADP
asir-1642	16	11	scholink	scholink	PROPN
asir-1642	16	12	inc	inc	PROPN
asir-1642	16	13	.	.	PUNCT
asir-1642	17	1	[	[	X
asir-1642	17	2	i	i	PROPN
asir-1642	17	3	=	=	SYM
asir-1642	17	4	2(wr)²	2(wr)²	NUM
asir-1642	17	5	]	]	PUNCT
asir-1642	17	6	,	,	PUNCT
asir-1642	17	7	where	where	SCONJ
asir-1642	17	8	then	then	ADV
asir-1642	17	9	become	become	VERB
asir-1642	17	10	waves	wave	NOUN
asir-1642	17	11	[	[	X
asir-1642	17	12	the	the	DET
asir-1642	17	13	distance	distance	NOUN
asir-1642	17	14	ds	ds	NOUN
asir-1642	17	15	=	=	PUNCT
asir-1642	17	16	|a	|a	PUNCT
asir-1642	17	17	|	|	ADV
asir-1642	17	18	is	be	AUX
asir-1642	17	19	the	the	DET
asir-1642	17	20	work	work	NOUN
asir-1642	17	21	embedded	embed	VERB
asir-1642	17	22	in	in	ADP
asir-1642	17	23	monads	monad	NOUN
asir-1642	17	24	and	and	CCONJ
asir-1642	17	25	it	it	PRON
asir-1642	17	26	is	be	AUX
asir-1642	17	27	what	what	PRON
asir-1642	17	28	is	be	AUX
asir-1642	17	29	vibrated	vibrate	VERB
asir-1642	17	30	]	]	PUNCT
asir-1642	17	31	with	with	ADP
asir-1642	17	32	the	the	DET
asir-1642	17	33	vibrating	vibrating	NOUN
asir-1642	17	34	equations	equation	NOUN
asir-1642	17	35	of	of	ADP
asir-1642	17	36	motion	motion	NOUN
asir-1642	17	37	,	,	PUNCT
asir-1642	17	38	to	to	PART
asir-1642	17	39	become	become	VERB
asir-1642	17	40	,	,	PUNCT
asir-1642	17	41	a	a	DET
asir-1642	17	42	→	→	NOUN
asir-1642	17	43	particles	particle	NOUN
asir-1642	17	44	,	,	PUNCT
asir-1642	17	45	with	with	ADP
asir-1642	17	46	inherent	inherent	ADJ
asir-1642	17	47	vibration	vibration	NOUN
asir-1642	17	48	occupying	occupy	VERB
asir-1642	17	49	distance	distance	NOUN
asir-1642	17	50	r	r	NOUN
asir-1642	17	51	=	=	NOUN
asir-1642	17	52	ds	ds	NOUN
asir-1642	17	53	=	=	NOUN
asir-1642	17	54	|a	|a	VERB
asir-1642	17	55	|	|	NOUN
asir-1642	17	56	,	,	PUNCT
asir-1642	17	57	b	b	X
asir-1642	17	58	→	→	SYM
asir-1642	17	59	gravity	gravity	NOUN
asir-1642	17	60	-	-	PUNCT
asir-1642	17	61	field	field	NOUN
asir-1642	17	62	-	-	PUNCT
asir-1642	17	63	energy	energy	NOUN
asir-1642	17	64	without	without	ADP
asir-1642	17	65	vibration	vibration	NOUN
asir-1642	17	66	,	,	PUNCT
asir-1642	17	67	the	the	DET
asir-1642	17	68	only	only	ADJ
asir-1642	17	69	stationary	stationary	ADJ
asir-1642	17	70	-	-	PUNCT
asir-1642	17	71	rotating	rotate	VERB
asir-1642	17	72	material	material	NOUN
asir-1642	17	73	-	-	PUNCT
asir-1642	17	74	points	point	NOUN
asir-1642	17	75	.	.	PUNCT
asir-1642	18	1	c	c	NOUN
asir-1642	18	2	→	→	SYM
asir-1642	18	3	dark	dark	ADJ
asir-1642	18	4	-	-	PUNCT
asir-1642	18	5	matter	matter	NOUN
asir-1642	18	6	-	-	PUNCT
asir-1642	18	7	energy	energy	NOUN
asir-1642	18	8	constituents	constituent	NOUN
asir-1642	18	9	as	as	ADP
asir-1642	18	10	below	below	ADV
asir-1642	18	11	,	,	PUNCT
asir-1642	18	12	a	a	PRON
asir-1642	18	13	..	..	PUNCT
asir-1642	19	1	[	[	X
asir-1642	19	2	±v̅.s²	±v̅.s²	X
asir-1642	19	3	]	]	X
asir-1642	19	4	→	→	SYM
asir-1642	19	5	fermions	fermion	NOUN
asir-1642	19	6	,	,	PUNCT
asir-1642	19	7	quarks	quark	NOUN
asir-1642	19	8	and	and	CCONJ
asir-1642	19	9	leptons	lepton	NOUN
asir-1642	19	10	,	,	PUNCT
asir-1642	19	11	and	and	CCONJ
asir-1642	19	12	→	→	SYM
asir-1642	19	13	[	[	X
asir-1642	19	14	v̅.i	v̅.i	X
asir-1642	19	15	]	]	X
asir-1642	19	16	→	→	SYM
asir-1642	19	17	bosons	boson	NOUN
asir-1642	19	18	,	,	PUNCT
asir-1642	19	19	b	b	X
asir-1642	19	20	..	..	PUNCT
asir-1642	20	1	[	[	X
asir-1642	20	2	±	±	NUM
asir-1642	20	3	s²	s²	NOUN
asir-1642	20	4	]	]	PUNCT
asir-1642	20	5	→	→	SYM
asir-1642	20	6	[	[	X
asir-1642	20	7	mfmf	mfmf	X
asir-1642	20	8	]	]	X
asir-1642	20	9	neutral	neutral	ADJ
asir-1642	20	10	field	field	NOUN
asir-1642	20	11	≡	≡	PROPN
asir-1642	20	12	the	the	DET
asir-1642	20	13	energy	energy	NOUN
asir-1642	20	14	chaos	chaos	NOUN
asir-1642	20	15	,	,	PUNCT
asir-1642	20	16	and	and	CCONJ
asir-1642	20	17	the	the	DET
asir-1642	20	18	negative	negative	ADJ
asir-1642	20	19	-	-	PUNCT
asir-1642	20	20	energy	energy	NOUN
asir-1642	20	21	binder	binder	NOUN
asir-1642	20	22	field	field	NOUN
asir-1642	20	23	is	be	AUX
asir-1642	20	24	[	[	X
asir-1642	20	25	i	i	X
asir-1642	20	26	]	]	X
asir-1642	20	27	→	→	SYM
asir-1642	20	28	gravity	gravity	NOUN
asir-1642	20	29	force	force	NOUN
asir-1642	20	30	as	as	ADP
asir-1642	20	31	dipole	dipole	NOUN
asir-1642	20	32	,	,	PUNCT
asir-1642	20	33	c	c	X
asir-1642	20	34	..	..	PUNCT
asir-1642	20	35	[	[	PUNCT
asir-1642	20	36	±c̅.s²	±c̅.s²	X
asir-1642	20	37	]	]	X
asir-1642	20	38	→	→	SYM
asir-1642	20	39	dark	dark	ADJ
asir-1642	20	40	matter	matter	NOUN
asir-1642	20	41	,	,	PUNCT
asir-1642	20	42	and	and	CCONJ
asir-1642	20	43	the	the	DET
asir-1642	20	44	binder	binder	NOUN
asir-1642	20	45	gravity	gravity	NOUN
asir-1642	20	46	force	force	NOUN
asir-1642	20	47	[	[	X
asir-1642	20	48	i	i	PROPN
asir-1642	20	49	]	]	PUNCT
asir-1642	20	50	,	,	PUNCT
asir-1642	20	51	[	[	X
asir-1642	20	52	c̅.i	c̅.i	NOUN
asir-1642	20	53	]	]	X
asir-1642	20	54	→	→	PUNCT
asir-1642	20	55	the	the	DET
asir-1642	20	56	expanding	expand	VERB
asir-1642	20	57	dark	dark	ADJ
asir-1642	20	58	energy	energy	NOUN
asir-1642	20	59	,	,	PUNCT
asir-1642	20	60	positive	positive	ADJ
asir-1642	20	61	-	-	PUNCT
asir-1642	20	62	energy	energy	NOUN
asir-1642	20	63	,	,	PUNCT
asir-1642	20	64	which	which	PRON
asir-1642	20	65	both	both	PRON
asir-1642	20	66	are	be	AUX
asir-1642	20	67	moving	move	VERB
asir-1642	20	68	with	with	ADP
asir-1642	20	69	light	light	ADJ
asir-1642	20	70	velocity	velocity	NOUN
asir-1642	20	71	,	,	PUNCT
asir-1642	20	72	c	c	AUX
asir-1642	20	73	,	,	PUNCT
asir-1642	20	74	causing	cause	VERB
asir-1642	20	75	the	the	DET
asir-1642	20	76	universe	universe	NOUN
asir-1642	20	77	to	to	PART
asir-1642	20	78	grow	grow	VERB
asir-1642	20	79	.	.	PUNCT
asir-1642	21	1	from	from	ADP
asir-1642	21	2	above	above	ADP
asir-1642	21	3	in	in	ADP
asir-1642	21	4	,	,	PUNCT
asir-1642	21	5	a	a	PRON
asir-1642	21	6	,	,	PUNCT
asir-1642	21	7	and	and	CCONJ
asir-1642	21	8	c	c	NOUN
asir-1642	21	9	,	,	PUNCT
asir-1642	21	10	case	case	NOUN
asir-1642	21	11	→	→	SYM
asir-1642	21	12	energy	energy	NOUN
asir-1642	21	13	as	as	ADP
asir-1642	21	14	velocity	velocity	NOUN
asir-1642	21	15	,	,	PUNCT
asir-1642	21	16	v̅	v̅	PROPN
asir-1642	21	17	,	,	PUNCT
asir-1642	21	18	exists	exist	VERB
asir-1642	21	19	in	in	ADP
asir-1642	21	20	the	the	DET
asir-1642	21	21	discrete	discrete	ADJ
asir-1642	21	22	monads	monad	NOUN
asir-1642	21	23	,	,	PUNCT
asir-1642	21	24	±	±	NUM
asir-1642	21	25	v̅.s²	v̅.s²	PROPN
asir-1642	21	26	and	and	CCONJ
asir-1642	21	27	±	±	NUM
asir-1642	21	28	c̅.s²	c̅.s²	PROPN
asir-1642	21	29	.	.	PUNCT
asir-1642	22	1	b	b	X
asir-1642	22	2	,	,	PUNCT
asir-1642	22	3	case	case	NOUN
asir-1642	22	4	is	be	AUX
asir-1642	22	5	the	the	DET
asir-1642	22	6	transportation	transportation	NOUN
asir-1642	22	7	of	of	ADP
asir-1642	22	8	energy	energy	NOUN
asir-1642	22	9	,	,	PUNCT
asir-1642	22	10	from	from	ADP
asir-1642	22	11	chaos	chaos	NOUN
asir-1642	22	12	to	to	ADP
asir-1642	22	13	stationary	stationary	ADJ
asir-1642	22	14	material	material	NOUN
asir-1642	22	15	points	point	NOUN
asir-1642	22	16	.	.	PUNCT
asir-1642	23	1	dark	dark	ADJ
asir-1642	23	2	energy	energy	PROPN
asir-1642	23	3	de	de	X
asir-1642	23	4	≡	≡	PROPN
asir-1642	23	5	[	[	PUNCT
asir-1642	23	6	�	�	PROPN
asir-1642	23	7	̅	̅	NOUN
asir-1642	23	8	�	�	NOUN
asir-1642	23	9	.i	.i	PROPN
asir-1642	23	10	]	]	X
asir-1642	23	11	(	(	PUNCT
asir-1642	23	12	©	©	PROPN
asir-1642	23	13	)	)	PUNCT
asir-1642	23	14	→	→	SYM
asir-1642	23	15	acting	act	VERB
asir-1642	23	16	,	,	PUNCT
asir-1642	23	17	positive	positive	ADJ
asir-1642	23	18	-	-	PUNCT
asir-1642	23	19	energy	energy	NOUN
asir-1642	23	20	,	,	PUNCT
asir-1642	23	21	on	on	ADP
asir-1642	23	22	the	the	DET
asir-1642	23	23	five	five	NUM
asir-1642	23	24	constituents	constituent	NOUN
asir-1642	23	25	→	→	SYM
asir-1642	23	26	{	{	PUNCT
asir-1642	23	27	(	(	PUNCT
asir-1642	23	28	i),(+s²),(-s²),(+cs²),(-cs²	i),(+s²),(-s²),(+cs²),(-cs²	NOUN
asir-1642	23	29	)	)	PUNCT
asir-1642	23	30	}	}	PUNCT
asir-1642	23	31	gives	give	VERB
asir-1642	23	32	[	[	PUNCT
asir-1642	23	33	±	±	NUM
asir-1642	23	34	s²	s²	NOUN
asir-1642	23	35	]	]	PUNCT
asir-1642	23	36	→	→	SYM
asir-1642	23	37	mfmf	mfmf	NOUN
asir-1642	23	38	field	field	NOUN
asir-1642	23	39	[	[	X
asir-1642	23	40	±	±	NUM
asir-1642	23	41	c̅.s²	c̅.s²	PROPN
asir-1642	23	42	]	]	PUNCT
asir-1642	24	1	→	→	PUNCT
asir-1642	24	2	dm	dm	NOUN
asir-1642	24	3	-	-	PUNCT
asir-1642	24	4	de	de	X
asir-1642	24	5	field	field	NOUN
asir-1642	24	6	,	,	PUNCT
asir-1642	24	7	of	of	ADP
asir-1642	24	8	,	,	PUNCT
asir-1642	24	9	dark	dark	ADJ
asir-1642	24	10	matter	matter	NOUN
asir-1642	24	11	and	and	CCONJ
asir-1642	24	12	anti	anti	ADJ
asir-1642	24	13	-	-	NOUN
asir-1642	24	14	matter	matter	NOUN
asir-1642	24	15	[	[	X
asir-1642	24	16	±v̅.s²	±v̅.s²	X
asir-1642	24	17	]	]	X
asir-1642	24	18	→	→	SYM
asir-1642	24	19	fermions	fermion	NOUN
asir-1642	25	1	[	[	X
asir-1642	25	2	i	i	X
asir-1642	25	3	]	]	PUNCT
asir-1642	25	4	→	→	PUNCT
asir-1642	25	5	gf	gf	PROPN
asir-1642	25	6	≡	≡	PROPN
asir-1642	25	7	gravity	gravity	NOUN
asir-1642	25	8	-	-	PUNCT
asir-1642	25	9	force	force	NOUN
asir-1642	25	10	in	in	ADP
asir-1642	25	11	dm	dm	PROPN
asir-1642	25	12	-	-	PUNCT
asir-1642	25	13	de	de	X
asir-1642	25	14	stationary	stationary	ADJ
asir-1642	25	15	field	field	NOUN
asir-1642	25	16	.	.	PUNCT
asir-1642	26	1	[	[	X
asir-1642	26	2	v̅.i	v̅.i	X
asir-1642	26	3	]	]	X
asir-1642	26	4	→	→	SYM
asir-1642	26	5	bosons	boson	NOUN
asir-1642	26	6	,	,	PUNCT
asir-1642	26	7	[	[	X
asir-1642	26	8	c̅.i	c̅.i	NOUN
asir-1642	26	9	]	]	X
asir-1642	26	10	≡	≡	PROPN
asir-1642	26	11	de	de	PROPN
asir-1642	26	12	→	→	SYM
asir-1642	26	13	dark	dark	ADJ
asir-1642	26	14	energy	energy	NOUN
asir-1642	26	15	c	c	NOUN
asir-1642	26	16	x	x	SYM
asir-1642	26	17	(	(	PUNCT
asir-1642	26	18	©	©	NOUN
asir-1642	26	19	)	)	PUNCT
asir-1642	27	1	[	[	X
asir-1642	27	2	i	i	X
asir-1642	27	3	]	]	X
asir-1642	27	4	→	→	SYM
asir-1642	27	5	gravity	gravity	NOUN
asir-1642	27	6	force	force	NOUN
asir-1642	27	7	de	de	PROPN
asir-1642	27	8	≡	≡	PROPN
asir-1642	27	9	[	[	X
asir-1642	27	10	c̅.i	c̅.i	NOUN
asir-1642	27	11	]	]	X
asir-1642	27	12	=	=	SYM
asir-1642	27	13	c̅	c̅	PROPN
asir-1642	28	1	[	[	X
asir-1642	28	2	i	i	NOUN
asir-1642	28	3	]	]	X
asir-1642	28	4	=	=	PUNCT
asir-1642	28	5	the	the	DET
asir-1642	28	6	travelling	travel	VERB
asir-1642	28	7	-	-	PUNCT
asir-1642	28	8	energy	energy	NOUN
asir-1642	28	9	with	with	ADP
asir-1642	28	10	,	,	PUNCT
asir-1642	28	11	c	c	NOUN
asir-1642	28	12	,	,	PUNCT
asir-1642	28	13	velocity	velocity	NOUN
asir-1642	28	14	.	.	PUNCT
asir-1642	29	1	in	in	ADP
asir-1642	29	2	all	all	PRON
asir-1642	29	3	above	above	ADP
asir-1642	29	4	issue	issue	NOUN
asir-1642	29	5	kepler	kepler	NOUN
asir-1642	29	6	-	-	PUNCT
asir-1642	29	7	laws	law	NOUN
asir-1642	29	8	,	,	PUNCT
asir-1642	29	9	denoting	denote	VERB
asir-1642	29	10	that	that	DET
asir-1642	29	11	macrocosm	macrocosm	PROPN
asir-1642	29	12	and	and	CCONJ
asir-1642	29	13	microcosm	microcosm	PROPN
asir-1642	29	14	.	.	PUNCT
asir-1642	30	1	obey	obey	PROPN
asir-1642	30	2	newton	newton	PROPN
asir-1642	30	3	’s	’s	PART
asir-1642	30	4	laws	law	NOUN
asir-1642	30	5	of	of	ADP
asir-1642	30	6	motion	motion	NOUN
asir-1642	30	7	in	in	ADP
asir-1642	30	8	all	all	DET
asir-1642	30	9	scales	scale	NOUN
asir-1642	30	10	,	,	PUNCT
asir-1642	30	11	as	as	SCONJ
asir-1642	30	12	is	be	AUX
asir-1642	30	13	proofed	proof	VERB
asir-1642	30	14	.	.	PUNCT
asir-1642	31	1	it	it	PRON
asir-1642	31	2	is	be	AUX
asir-1642	31	3	shown	show	VERB
asir-1642	31	4	that	that	SCONJ
asir-1642	31	5	motion	motion	NOUN
asir-1642	31	6	may	may	AUX
asir-1642	31	7	be	be	AUX
asir-1642	31	8	linear	linear	ADJ
asir-1642	31	9	or	or	CCONJ
asir-1642	31	10	rotational	rotational	ADJ
asir-1642	31	11	for	for	ADP
asir-1642	31	12	any	any	DET
asir-1642	31	13	displacement	displacement	NOUN
asir-1642	31	14	,	,	PUNCT
asir-1642	31	15	r	r	NOUN
asir-1642	31	16	,	,	PUNCT
asir-1642	31	17	so	so	ADV
asir-1642	31	18	exists	exist	VERB
asir-1642	31	19	a	a	DET
asir-1642	31	20	constant	constant	ADJ
asir-1642	31	21	-	-	PUNCT
asir-1642	31	22	work	work	NOUN
asir-1642	31	23	w	w	NOUN
asir-1642	31	24	=	=	SYM
asir-1642	31	25	k	k	PROPN
asir-1642	31	26	and	and	CCONJ
asir-1642	31	27	conserved	conserve	VERB
asir-1642	31	28	in	in	ADP
asir-1642	31	29	orbits	orbit	NOUN
asir-1642	31	30	,	,	PUNCT
asir-1642	31	31	during	during	ADP
asir-1642	31	32	these	these	DET
asir-1642	31	33	motions	motion	NOUN
asir-1642	31	34	as	as	ADP
asir-1642	31	35	,	,	PUNCT
asir-1642	31	36	k	k	PROPN
asir-1642	31	37	=	=	SYM
asir-1642	31	38	�	�	PROPN
asir-1642	31	39	̅	̅	NOUN
asir-1642	31	40	�	�	NOUN
asir-1642	31	41	x	x	SYM
asir-1642	31	42	�	�	PROPN
asir-1642	31	43	̅	̅	NOUN
asir-1642	31	44	�	�	PROPN
asir-1642	31	45	.	.	PUNCT
asir-1642	31	46	�	�	PROPN
asir-1642	31	47	̅	̅	NOUN
asir-1642	31	48	�	�	NOUN
asir-1642	31	49	=	=	SYM
asir-1642	31	50	v².r	v².r	PROPN
asir-1642	31	51	.	.	PUNCT
asir-1642	31	52	�	�	PROPN
asir-1642	31	53	̅	̅	NOUN
asir-1642	31	54	�	�	NOUN
asir-1642	31	55	.	.	PUNCT
asir-1642	32	1	=	=	SYM
asir-1642	32	2	v²	v²	PROPN
asir-1642	32	3	.	.	PUNCT
asir-1642	33	1	r	r	NOUN
asir-1642	33	2	=	=	PUNCT
asir-1642	33	3	(	(	PUNCT
asir-1642	33	4	wr)².r	wr)².r	NOUN
asir-1642	33	5	=	=	PUNCT
asir-1642	33	6	[	[	PUNCT
asir-1642	33	7	𝟐𝛑	𝟐𝛑	X
asir-1642	33	8	𝐓	𝐓	PROPN
asir-1642	33	9	r]².r	r]².r	PROPN
asir-1642	33	10	=	=	PUNCT
asir-1642	33	11	𝟒𝛑²	𝟒𝛑²	PRON
asir-1642	33	12	𝐫²	𝐫²	NOUN
asir-1642	33	13	𝐓²	𝐓²	VERB
asir-1642	33	14	.	.	PUNCT
asir-1642	34	1	r	r	NOUN
asir-1642	34	2	=	=	PUNCT
asir-1642	34	3	𝟒𝛑²	𝟒𝛑²	NOUN
asir-1642	34	4	𝐫	𝐫	PROPN
asir-1642	34	5	³	³	PROPN
asir-1642	34	6	𝐓²	𝐓²	PROPN
asir-1642	34	7	=	=	SYM
asir-1642	34	8	4π²	4π²	NUM
asir-1642	34	9	.	.	PUNCT
asir-1642	35	1	𝐫³	𝐫³	PROPN
asir-1642	35	2	𝐓²	𝐓²	PROPN
asir-1642	36	1	=	=	SYM
asir-1642	36	2	4π².r³.𝐟²𝐩	4π².r³.𝐟²𝐩	PROPN
asir-1642	36	3	a	a	DET
asir-1642	36	4	photon	photon	NOUN
asir-1642	36	5	during	during	ADP
asir-1642	36	6	motion	motion	NOUN
asir-1642	36	7	in	in	ADP
asir-1642	36	8	[	[	X
asir-1642	36	9	mfmf	mfmf	NOUN
asir-1642	36	10	]	]	X
asir-1642	36	11	chaos	chaos	NOUN
asir-1642	36	12	,	,	PUNCT
asir-1642	36	13	collides	collide	VERB
asir-1642	36	14	with	with	ADP
asir-1642	36	15	other	other	ADJ
asir-1642	36	16	photons	photon	NOUN
asir-1642	36	17	by	by	ADP
asir-1642	36	18	means	mean	NOUN
asir-1642	36	19	of	of	ADP
asir-1642	36	20	cross	cross	NOUN
asir-1642	36	21	-	-	NOUN
asir-1642	36	22	product	product	NOUN
asir-1642	36	23	and	and	CCONJ
asir-1642	36	24	produces	produce	VERB
asir-1642	36	25	a	a	DET
asir-1642	36	26	constant	constant	ADJ
asir-1642	36	27	work	work	NOUN
asir-1642	36	28	which	which	PRON
asir-1642	36	29	is	be	AUX
asir-1642	36	30	stored	store	VERB
asir-1642	36	31	into	into	ADP
asir-1642	36	32	the	the	DET
asir-1642	36	33	only	only	ADJ
asir-1642	36	34	-	-	PUNCT
asir-1642	36	35	four	four	NUM
asir-1642	36	36	energy	energy	NOUN
asir-1642	36	37	-	-	PUNCT
asir-1642	36	38	geometrical	geometrical	ADJ
asir-1642	36	39	-	-	PUNCT
asir-1642	36	40	shapes	shape	NOUN
asir-1642	36	41	,	,	PUNCT
asir-1642	36	42	of	of	ADP
asir-1642	36	43	the	the	DET
asir-1642	36	44	motion	motion	NOUN
asir-1642	36	45	which	which	PRON
asir-1642	36	46	shapes	shape	NOUN
asir-1642	36	47	are	be	AUX
asir-1642	36	48	the	the	DET
asir-1642	36	49	conic	conic	ADJ
asir-1642	36	50	-	-	PUNCT
asir-1642	36	51	sections	section	NOUN
asir-1642	36	52	.	.	PUNCT
asir-1642	37	1	the	the	DET
asir-1642	37	2	interior	interior	ADJ
asir-1642	37	3	motion	motion	NOUN
asir-1642	37	4	is	be	AUX
asir-1642	37	5	kept	keep	VERB
asir-1642	37	6	in	in	ADP
asir-1642	37	7	its	its	PRON
asir-1642	37	8	wavelength	wavelength	NOUN
asir-1642	37	9	-	-	PUNCT
asir-1642	37	10	tank	tank	NOUN
asir-1642	37	11	2r	2r	NUM
asir-1642	37	12	=	=	SYM
asir-1642	37	13	nλ	nλ	NOUN
asir-1642	37	14	while	while	SCONJ
asir-1642	37	15	the	the	DET
asir-1642	37	16	linear	linear	ADJ
asir-1642	37	17	motion	motion	NOUN
asir-1642	37	18	is	be	AUX
asir-1642	37	19	continued	continue	VERB
asir-1642	37	20	by	by	ADP
asir-1642	37	21	the	the	DET
asir-1642	37	22	propagating	propagate	VERB
asir-1642	37	23	electromagnetic	electromagnetic	ADJ
asir-1642	37	24	-	-	PUNCT
asir-1642	37	25	wave	wave	NOUN
asir-1642	37	26	→	→	PUNCT
asir-1642	37	27	it	it	PRON
asir-1642	37	28	is	be	AUX
asir-1642	37	29	the	the	DET
asir-1642	37	30	energy	energy	NOUN
asir-1642	37	31	-	-	PUNCT
asir-1642	37	32	conveyer	conveyer	NOUN
asir-1642	37	33	,	,	PUNCT
asir-1642	37	34	i.e.	i.e.	X
asir-1642	37	35	,	,	PUNCT
asir-1642	37	36	the	the	DET
asir-1642	37	37	stored	store	VERB
asir-1642	37	38	energy	energy	NOUN
asir-1642	37	39	in	in	ADP
asir-1642	37	40	the	the	DET
asir-1642	37	41	loop	loop	NOUN
asir-1642	37	42	is	be	AUX
asir-1642	37	43	→	→	SYM
asir-1642	37	44	=	=	SYM
asir-1642	37	45	v²	v²	PROPN
asir-1642	37	46	[	[	PUNCT
asir-1642	37	47	𝟐𝛑	𝟐𝛑	NOUN
asir-1642	37	48	]	]	PUNCT
asir-1642	37	49	=	=	PUNCT
asir-1642	37	50	4π².r³.	4π².r³.	NUM
asir-1642	37	51	²	²	NUM
asir-1642	37	52	,	,	PUNCT
asir-1642	37	53	it	it	PRON
asir-1642	37	54	is	be	AUX
asir-1642	37	55	the	the	DET
asir-1642	37	56	particle	particle	NOUN
asir-1642	37	57	and	and	CCONJ
asir-1642	37	58	dependent	dependent	ADJ
asir-1642	37	59	on	on	ADP
asir-1642	37	60	velocity	velocity	NOUN
asir-1642	37	61	,	,	PUNCT
asir-1642	37	62	v	v	NOUN
asir-1642	37	63	,	,	PUNCT
asir-1642	37	64	and	and	CCONJ
asir-1642	37	65	planck	planck	NOUN
asir-1642	37	66	’s	’s	PART
asir-1642	37	67	constant	constant	ADJ
asir-1642	37	68	h	h	NOUN
asir-1642	37	69	,	,	PUNCT
asir-1642	37	70	or	or	CCONJ
asir-1642	37	71	on	on	ADP
asir-1642	37	72	loop	loop	NOUN
asir-1642	37	73	,	,	PUNCT
asir-1642	37	74	r	r	NOUN
asir-1642	37	75	,	,	PUNCT
asir-1642	37	76	and	and	CCONJ
asir-1642	37	77	frequency	frequency	NOUN
asir-1642	37	78	,	,	PUNCT
asir-1642	37	79	𝐟𝐩	𝐟𝐩	ADP
asir-1642	37	80	,	,	PUNCT
asir-1642	37	81	which	which	PRON
asir-1642	37	82	is	be	AUX
asir-1642	37	83	the	the	DET
asir-1642	37	84	wave	wave	NOUN
asir-1642	37	85	.	.	PUNCT
asir-1642	38	1	it	it	PRON
asir-1642	38	2	is	be	AUX
asir-1642	38	3	proved	prove	VERB
asir-1642	38	4	that	that	SCONJ
asir-1642	38	5	this	this	DET
asir-1642	38	6	minimum	minimum	ADJ
asir-1642	38	7	energy	energy	NOUN
asir-1642	38	8	-	-	PUNCT
asir-1642	38	9	constant	constant	ADJ
asir-1642	38	10	→	→	X
asir-1642	38	11	k	k	X
asir-1642	38	12	=	=	PUNCT
asir-1642	38	13	g.	g.	PROPN
asir-1642	38	14	b	b	PROPN
asir-1642	38	15	..	..	PUNCT
asir-1642	38	16	kinetic	kinetic	ADJ
asir-1642	38	17	energy	energy	NOUN
asir-1642	38	18	,	,	PUNCT
asir-1642	38	19	motion	motion	NOUN
asir-1642	38	20	,	,	PUNCT
asir-1642	38	21	in	in	ADP
asir-1642	38	22	orbits	orbit	NOUN
asir-1642	38	23	becomes	become	VERB
asir-1642	38	24	from	from	ADP
asir-1642	38	25	the	the	DET
asir-1642	38	26	,	,	PUNCT
asir-1642	38	27	piezoelectric	piezoelectric	NOUN
asir-1642	38	28	-	-	PUNCT
asir-1642	38	29	effect	effect	NOUN
asir-1642	38	30	,	,	PUNCT
asir-1642	38	31	where	where	SCONJ
asir-1642	38	32	orbit	orbit	NOUN
asir-1642	38	33	is	be	AUX
asir-1642	38	34	subjected	subject	VERB
asir-1642	38	35	to	to	ADP
asir-1642	38	36	a	a	DET
asir-1642	38	37	mechanical	mechanical	ADJ
asir-1642	38	38	-	-	PUNCT
asir-1642	38	39	stress	stress	NOUN
asir-1642	38	40	,	,	PUNCT
asir-1642	38	41	σ	σ	PROPN
asir-1642	38	42	=	=	SYM
asir-1642	38	43	±	±	NUM
asir-1642	38	44	𝟒𝛑𝐫	𝟒𝛑𝐫	NOUN
asir-1642	38	45	(	(	PUNCT
asir-1642	38	46	+	+	NOUN
asir-1642	38	47	√𝟓	√𝟓	NOUN
asir-1642	38	48	)	)	PUNCT
asir-1642	38	49	.	.	PUNCT
asir-1642	39	1	𝐟𝐩	𝐟𝐩	PROPN
asir-1642	39	2	,	,	PUNCT
asir-1642	39	3	becoming	become	VERB
asir-1642	39	4	from	from	ADP
asir-1642	39	5	the	the	DET
asir-1642	39	6	centripetal	centripetal	ADJ
asir-1642	39	7	-	-	PUNCT
asir-1642	39	8	acceleration	acceleration	NOUN
asir-1642	39	9	�	�	NOUN
asir-1642	39	10	̅	̅	NOUN
asir-1642	39	11	�	�	NOUN
asir-1642	39	12	𝐏	𝐏	PROPN
asir-1642	39	13	of	of	ADP
asir-1642	39	14	the	the	DET
asir-1642	39	15	planet	planet	NOUN
asir-1642	39	16	and	and	CCONJ
asir-1642	39	17	thus	thus	ADV
asir-1642	39	18	is	be	AUX
asir-1642	39	19	appeared	appear	VERB
asir-1642	39	20	a	a	DET
asir-1642	39	21	positive	positive	ADJ
asir-1642	39	22	charge	charge	NOUN
asir-1642	39	23	at	at	ADP
asir-1642	39	24	the	the	DET
asir-1642	39	25	nucleus	nucleus	NOUN
asir-1642	39	26	and	and	CCONJ
asir-1642	39	27	a	a	DET
asir-1642	39	28	negative	negative	ADJ
asir-1642	39	29	-	-	PUNCT
asir-1642	39	30	charge	charge	NOUN
asir-1642	39	31	at	at	ADP
asir-1642	39	32	the	the	DET
asir-1642	39	33	planet	planet	NOUN
asir-1642	39	34	,	,	PUNCT
asir-1642	39	35	so	so	ADV
asir-1642	39	36	is	be	AUX
asir-1642	39	37	created	create	VERB
asir-1642	39	38	an	an	DET
asir-1642	39	39	electric	electric	NOUN
asir-1642	39	40	-	-	PUNCT
asir-1642	39	41	signal	signal	NOUN
asir-1642	39	42	with	with	ADP
asir-1642	39	43	a	a	DET
asir-1642	39	44	given	give	VERB
asir-1642	39	45	frequency	frequency	NOUN
asir-1642	39	46	𝐟𝐩.	𝐟𝐩.	NOUN
asir-1642	39	47	the	the	DET
asir-1642	39	48	two	two	NUM
asir-1642	39	49	faces	face	NOUN
asir-1642	39	50	at	at	ADP
asir-1642	39	51	n	n	PROPN
asir-1642	39	52	and	and	CCONJ
asir-1642	39	53	p	p	NOUN
asir-1642	39	54	are	be	AUX
asir-1642	39	55	connected	connect	VERB
asir-1642	39	56	by	by	ADP
asir-1642	39	57	the	the	DET
asir-1642	39	58	in	in	NOUN
asir-1642	39	59	-	-	PUNCT
asir-1642	39	60	between	between	ADP
asir-1642	39	61	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	39	62	applied	apply	VERB
asir-1642	39	63	science	science	NOUN
asir-1642	39	64	and	and	CCONJ
asir-1642	39	65	innovative	innovative	ADJ
asir-1642	39	66	research	research	NOUN
asir-1642	39	67	vol	vol	NOUN
asir-1642	39	68	.	.	PROPN
asir-1642	40	1	2	2	NUM
asir-1642	40	2	,	,	PUNCT
asir-1642	40	3	no	no	INTJ
asir-1642	40	4	.	.	NOUN
asir-1642	40	5	4	4	NUM
asir-1642	40	6	,	,	PUNCT
asir-1642	40	7	2018	2018	NUM
asir-1642	40	8	157	157	NUM
asir-1642	40	9	published	publish	VERB
asir-1642	40	10	by	by	ADP
asir-1642	40	11	scholink	scholink	PROPN
asir-1642	40	12	inc	inc	PROPN
asir-1642	40	13	.	.	PROPN
asir-1642	40	14	energy	energy	NOUN
asir-1642	40	15	-	-	PUNCT
asir-1642	40	16	vectors	vector	NOUN
asir-1642	40	17	b̅	b̅	NOUN
asir-1642	40	18	=	=	SYM
asir-1642	40	19	³	³	PUNCT
asir-1642	41	1	[	[	X
asir-1642	41	2	1	1	NUM
asir-1642	41	3	+	+	NUM
asir-1642	41	4	√	√	NUM
asir-1642	41	5	]	]	PUNCT
asir-1642	41	6	of	of	ADP
asir-1642	41	7	gravity	gravity	NOUN
asir-1642	41	8	-	-	PUNCT
asir-1642	41	9	field	field	NOUN
asir-1642	41	10	-	-	PUNCT
asir-1642	41	11	pointy	pointy	NOUN
asir-1642	41	12	material	material	NOUN
asir-1642	41	13	-	-	PUNCT
asir-1642	41	14	point	point	NOUN
asir-1642	41	15	[	[	X
asir-1642	41	16	i	i	X
asir-1642	41	17	]	]	X
asir-1642	41	18	=	=	PUNCT
asir-1642	41	19	[	[	X
asir-1642	41	20	⊕	⊕	NOUN
asir-1642	41	21	↻	↻	NOUN
asir-1642	41	22	↺	↺	NOUN
asir-1642	41	23	⊝	⊝	NUM
asir-1642	41	24	]	]	PUNCT
asir-1642	41	25	.	.	PUNCT
asir-1642	42	1	c	c	X
asir-1642	42	2	..	..	PUNCT
asir-1642	42	3	orbit	orbit	NOUN
asir-1642	42	4	or	or	CCONJ
asir-1642	42	5	,	,	PUNCT
asir-1642	42	6	negative	negative	ADJ
asir-1642	42	7	-	-	PUNCT
asir-1642	42	8	energy	energy	NOUN
asir-1642	42	9	-	-	PUNCT
asir-1642	42	10	rim	rim	NOUN
asir-1642	42	11	in	in	ADP
asir-1642	42	12	monad	monad	PROPN
asir-1642	42	13	,	,	PUNCT
asir-1642	42	14	the	the	DET
asir-1642	42	15	-	-	PUNCT
asir-1642	42	16	atom	atom	NOUN
asir-1642	42	17	,	,	PUNCT
asir-1642	42	18	is	be	AUX
asir-1642	42	19	the	the	DET
asir-1642	42	20	stable	stable	ADJ
asir-1642	42	21	and	and	CCONJ
asir-1642	42	22	stationary	stationary	ADJ
asir-1642	42	23	granular	granular	ADJ
asir-1642	42	24	-	-	PUNCT
asir-1642	42	25	lattice	lattice	NOUN
asir-1642	42	26	-	-	PUNCT
asir-1642	42	27	energy	energy	NOUN
asir-1642	42	28	-	-	PUNCT
asir-1642	42	29	disk	disk	NOUN
asir-1642	42	30	,	,	PUNCT
asir-1642	42	31	which	which	PRON
asir-1642	42	32	is	be	AUX
asir-1642	42	33	kept	keep	VERB
asir-1642	42	34	in	in	ADP
asir-1642	42	35	the	the	DET
asir-1642	42	36	plane	plane	NOUN
asir-1642	42	37	-	-	PUNCT
asir-1642	42	38	orbit	orbit	NOUN
asir-1642	42	39	of	of	ADP
asir-1642	42	40	motion	motion	NOUN
asir-1642	42	41	,	,	PUNCT
asir-1642	42	42	ellipse	ellipse	NOUN
asir-1642	42	43	area	area	NOUN
asir-1642	42	44	,	,	PUNCT
asir-1642	42	45	πab	πab	INTJ
asir-1642	42	46	,	,	PUNCT
asir-1642	42	47	in	in	ADP
asir-1642	42	48	gravity	gravity	NOUN
asir-1642	42	49	-	-	PUNCT
asir-1642	42	50	field	field	NOUN
asir-1642	42	51	,	,	PUNCT
asir-1642	42	52	and	and	CCONJ
asir-1642	42	53	in	in	ADP
asir-1642	42	54	a	a	DET
asir-1642	42	55	way	way	NOUN
asir-1642	42	56	is	be	AUX
asir-1642	42	57	opposite	opposite	ADJ
asir-1642	42	58	to	to	ADP
asir-1642	42	59	that	that	PRON
asir-1642	42	60	which	which	PRON
asir-1642	42	61	follows	follow	VERB
asir-1642	42	62	the	the	DET
asir-1642	42	63	central	central	ADJ
asir-1642	42	64	motion	motion	NOUN
asir-1642	42	65	,	,	PUNCT
asir-1642	42	66	i.e.	i.e.	X
asir-1642	42	67	,	,	PUNCT
asir-1642	42	68	the	the	DET
asir-1642	42	69	gravity	gravity	NOUN
asir-1642	42	70	-	-	PUNCT
asir-1642	42	71	force	force	NOUN
asir-1642	42	72	-	-	PUNCT
asir-1642	42	73	vectors	vector	NOUN
asir-1642	42	74	b̅	b̅	NOUN
asir-1642	42	75	,	,	PUNCT
asir-1642	42	76	which	which	PRON
asir-1642	42	77	is	be	AUX
asir-1642	42	78	the	the	DET
asir-1642	42	79	spin	spin	NOUN
asir-1642	42	80	[	[	PUNCT
asir-1642	42	81	⊕	⊕	PROPN
asir-1642	42	82	↻	↻	PROPN
asir-1642	42	83	↺	↺	NOUN
asir-1642	42	84	⊝	⊝	NOUN
asir-1642	42	85	]	]	PUNCT
asir-1642	42	86	of	of	ADP
asir-1642	42	87	the	the	DET
asir-1642	42	88	material	material	NOUN
asir-1642	42	89	-	-	PUNCT
asir-1642	42	90	points	point	NOUN
asir-1642	42	91	.	.	PUNCT
asir-1642	43	1	these	these	PRON
asir-1642	43	2	are	be	AUX
asir-1642	43	3	spinning	spinning	ADJ
asir-1642	43	4	-	-	PUNCT
asir-1642	43	5	plane	plane	NOUN
asir-1642	43	6	-	-	PUNCT
asir-1642	43	7	packets	packet	NOUN
asir-1642	43	8	into	into	ADP
asir-1642	43	9	the	the	DET
asir-1642	43	10	orbit	orbit	NOUN
asir-1642	43	11	-	-	PUNCT
asir-1642	43	12	rim	rim	NOUN
asir-1642	43	13	as	as	ADP
asir-1642	43	14	the	the	DET
asir-1642	43	15	energy	energy	NOUN
asir-1642	43	16	-	-	PUNCT
asir-1642	43	17	granular	granular	ADJ
asir-1642	43	18	-	-	PUNCT
asir-1642	43	19	conveyers	conveyer	NOUN
asir-1642	43	20	for	for	ADP
asir-1642	43	21	the	the	DET
asir-1642	43	22	interactions	interaction	NOUN
asir-1642	43	23	between	between	ADP
asir-1642	43	24	,	,	PUNCT
asir-1642	43	25	nucleus	nucleus	NOUN
asir-1642	43	26	n	n	PROPN
asir-1642	43	27	and	and	CCONJ
asir-1642	43	28	the	the	DET
asir-1642	43	29	orbiting	orbiting	ADJ
asir-1642	43	30	object	object	NOUN
asir-1642	43	31	,	,	PUNCT
asir-1642	43	32	the	the	DET
asir-1642	43	33	planet	planet	NOUN
asir-1642	43	34	p	p	X
asir-1642	43	35	,	,	PUNCT
asir-1642	43	36	and	and	CCONJ
asir-1642	43	37	consists	consist	VERB
asir-1642	43	38	the	the	DET
asir-1642	43	39	quanta	quanta	PROPN
asir-1642	43	40	,	,	PUNCT
asir-1642	43	41	the	the	DET
asir-1642	43	42	minimum	minimum	ADJ
asir-1642	43	43	constant	constant	ADJ
asir-1642	43	44	energy	energy	NOUN
asir-1642	43	45	,	,	PUNCT
asir-1642	43	46	of	of	ADP
asir-1642	43	47	rotational	rotational	ADJ
asir-1642	43	48	motion	motion	NOUN
asir-1642	43	49	→	→	PUNCT
asir-1642	43	50	[	[	X
asir-1642	43	51	⊕	⊕	NOUN
asir-1642	43	52	↻	↻	NOUN
asir-1642	43	53	↺	↺	NOUN
asir-1642	43	54	⊝	⊝	NOUN
asir-1642	43	55	]	]	PUNCT
asir-1642	43	56	←	←	PROPN
asir-1642	43	57	and	and	CCONJ
asir-1642	43	58	is	be	AUX
asir-1642	43	59	equal	equal	ADJ
asir-1642	43	60	to	to	ADP
asir-1642	43	61	g.	g.	PROPN
asir-1642	43	62	d	d	PROPN
asir-1642	43	63	..	..	PUNCT
asir-1642	43	64	black	black	ADJ
asir-1642	43	65	holes	hole	NOUN
asir-1642	43	66	follow	follow	VERB
asir-1642	43	67	kepler	kepler	NOUN
asir-1642	43	68	laws	law	NOUN
asir-1642	43	69	where	where	SCONJ
asir-1642	43	70	,	,	PUNCT
asir-1642	43	71	on	on	ADP
asir-1642	43	72	any	any	DET
asir-1642	43	73	moving	move	VERB
asir-1642	43	74	particle	particle	NOUN
asir-1642	43	75	when	when	SCONJ
asir-1642	43	76	is	be	AUX
asir-1642	43	77	tangentially	tangentially	ADV
asir-1642	43	78	-	-	PUNCT
asir-1642	43	79	colliding	collide	VERB
asir-1642	43	80	or	or	CCONJ
asir-1642	43	81	under	under	ADP
asir-1642	43	82	any	any	DET
asir-1642	43	83	angle	angle	NOUN
asir-1642	43	84	φ	φ	NOUN
asir-1642	43	85	with	with	ADP
asir-1642	43	86	a	a	DET
asir-1642	43	87	material	material	NOUN
asir-1642	43	88	-	-	PUNCT
asir-1642	43	89	point	point	NOUN
asir-1642	43	90	executing	execute	VERB
asir-1642	43	91	circular	circular	ADJ
asir-1642	43	92	motion	motion	NOUN
asir-1642	43	93	,	,	PUNCT
asir-1642	43	94	then	then	ADV
asir-1642	43	95	the	the	DET
asir-1642	43	96	total	total	ADJ
asir-1642	43	97	energy	energy	NOUN
asir-1642	43	98	is	be	AUX
asir-1642	43	99	negative	negative	ADJ
asir-1642	43	100	,	,	PUNCT
asir-1642	43	101	the	the	DET
asir-1642	43	102	particle	particle	NOUN
asir-1642	43	103	follows	follow	VERB
asir-1642	43	104	constant	constant	ADJ
asir-1642	43	105	elliptical	elliptical	ADJ
asir-1642	43	106	-	-	PUNCT
asir-1642	43	107	energy	energy	NOUN
asir-1642	43	108	-	-	PUNCT
asir-1642	43	109	orbits	orbit	NOUN
asir-1642	43	110	on	on	ADP
asir-1642	43	111	the	the	DET
asir-1642	43	112	same	same	ADJ
asir-1642	43	113	semi	semi	ADJ
asir-1642	43	114	major	major	ADJ
asir-1642	43	115	axis	axis	NOUN
asir-1642	43	116	as	as	ADP
asir-1642	43	117	,	,	PUNCT
asir-1642	43	118	1	1	NUM
asir-1642	43	119	=	=	SYM
asir-1642	43	120	c.	c.	NOUN
asir-1642	43	121	𝐟𝐧²	𝐟𝐧²	VERB
asir-1642	43	122	.	.	PUNCT
asir-1642	44	1	a³	a³	PROPN
asir-1642	44	2	,	,	PUNCT
asir-1642	44	3	and	and	CCONJ
asir-1642	44	4	of	of	ADP
asir-1642	44	5	the	the	DET
asir-1642	44	6	same	same	ADJ
asir-1642	44	7	constant	constant	ADJ
asir-1642	44	8	energy	energy	NOUN
asir-1642	44	9	.	.	PUNCT
asir-1642	45	1	semi	semi	ADJ
asir-1642	45	2	major	major	ADJ
asir-1642	45	3	axis	axis	NOUN
asir-1642	45	4	,	,	PUNCT
asir-1642	45	5	a	a	PRON
asir-1642	45	6	,	,	PUNCT
asir-1642	45	7	is	be	AUX
asir-1642	45	8	related	relate	VERB
asir-1642	45	9	to	to	ADP
asir-1642	45	10	energy	energy	NOUN
asir-1642	45	11	as	as	ADP
asir-1642	45	12	→	→	SYM
asir-1642	45	13	a	a	DET
asir-1642	45	14	=	=	X
asir-1642	45	15	gmm	gmm	X
asir-1642	45	16	/	/	SYM
asir-1642	45	17	2e	2e	NOUN
asir-1642	45	18	,	,	PUNCT
asir-1642	45	19	i.e.	i.e.	X
asir-1642	45	20	,	,	PUNCT
asir-1642	45	21	for	for	ADP
asir-1642	45	22	very	very	ADV
asir-1642	45	23	large	large	ADJ
asir-1642	45	24	energies	energy	NOUN
asir-1642	45	25	,	,	PUNCT
asir-1642	45	26	semi	semi	ADV
asir-1642	45	27	major	major	ADJ
asir-1642	45	28	axis	axis	NOUN
asir-1642	45	29	a	a	PRON
asir-1642	45	30	,	,	PUNCT
asir-1642	45	31	tents	tent	NOUN
asir-1642	45	32	to	to	ADP
asir-1642	45	33	a	a	DET
asir-1642	45	34	negative	negative	ADJ
asir-1642	45	35	-	-	PUNCT
asir-1642	45	36	energy	energy	NOUN
asir-1642	45	37	-	-	PUNCT
asir-1642	45	38	point	point	NOUN
asir-1642	45	39	,	,	PUNCT
asir-1642	45	40	which	which	PRON
asir-1642	45	41	is	be	AUX
asir-1642	45	42	the	the	DET
asir-1642	45	43	beginning	beginning	NOUN
asir-1642	45	44	of	of	ADP
asir-1642	45	45	the	the	DET
asir-1642	45	46	black	black	ADJ
asir-1642	45	47	hole	hole	NOUN
asir-1642	45	48	such	such	ADJ
asir-1642	45	49	as	as	ADP
asir-1642	45	50	in	in	ADP
asir-1642	45	51	microcosm	microcosm	PROPN
asir-1642	45	52	and	and	CCONJ
asir-1642	45	53	macrocosm	macrocosm	PROPN
asir-1642	45	54	.	.	PUNCT
asir-1642	46	1	for	for	ADP
asir-1642	46	2	axis	axis	NOUN
asir-1642	46	3	a	a	DET
asir-1642	46	4	→	→	SYM
asir-1642	46	5	0	0	NUM
asir-1642	46	6	,	,	PUNCT
asir-1642	46	7	then	then	ADV
asir-1642	46	8	→	→	SYM
asir-1642	46	9	∞	∞	PROPN
asir-1642	46	10	,	,	PUNCT
asir-1642	46	11	which	which	PRON
asir-1642	46	12	is	be	AUX
asir-1642	46	13	a	a	DET
asir-1642	46	14	black	black	ADJ
asir-1642	46	15	-	-	PUNCT
asir-1642	46	16	hole	hole	NOUN
asir-1642	46	17	.	.	PUNCT
asir-1642	47	1	from	from	ADP
asir-1642	47	2	equation	equation	NOUN
asir-1642	47	3	is	be	AUX
asir-1642	47	4	seen	see	VERB
asir-1642	47	5	the	the	DET
asir-1642	47	6	way	way	NOUN
asir-1642	47	7	that	that	PRON
asir-1642	47	8	energy	energy	NOUN
asir-1642	47	9	as	as	ADP
asir-1642	47	10	,	,	PUNCT
asir-1642	47	11	frequency	frequency	NOUN
asir-1642	47	12	or	or	CCONJ
asir-1642	47	13	velocity	velocity	NOUN
asir-1642	47	14	or	or	CCONJ
asir-1642	47	15	acceleration	acceleration	NOUN
asir-1642	47	16	or	or	CCONJ
asir-1642	47	17	any	any	DET
asir-1642	47	18	other	other	ADJ
asir-1642	47	19	mode	mode	NOUN
asir-1642	47	20	of	of	ADP
asir-1642	47	21	motion	motion	NOUN
asir-1642	47	22	,	,	PUNCT
asir-1642	47	23	response	response	NOUN
asir-1642	47	24	on	on	ADP
asir-1642	47	25	space	space	NOUN
asir-1642	47	26	,	,	PUNCT
asir-1642	47	27	a	a	DET
asir-1642	47	28	axis	axis	NOUN
asir-1642	47	29	.	.	PUNCT
asir-1642	48	1	e	e	X
asir-1642	48	2	..	..	PUNCT
asir-1642	48	3	the	the	DET
asir-1642	48	4	{	{	PUNCT
asir-1642	48	5	n	n	CCONJ
asir-1642	48	6	}	}	PUNCT
asir-1642	48	7	energy	energy	NOUN
asir-1642	48	8	-	-	PUNCT
asir-1642	48	9	storages	storage	NOUN
asir-1642	48	10	of	of	ADP
asir-1642	48	11	the	the	DET
asir-1642	48	12	moving	moving	NOUN
asir-1642	48	13	-	-	PUNCT
asir-1642	48	14	monads	monad	NOUN
asir-1642	48	15	.	.	PUNCT
asir-1642	49	1	figure-1	figure-1	NOUN
asir-1642	49	2	.	.	PUNCT
asir-1642	50	1	in	in	ADP
asir-1642	50	2	store	store	NOUN
asir-1642	50	3	,	,	PUNCT
asir-1642	50	4	r	r	NOUN
asir-1642	50	5	,	,	PUNCT
asir-1642	50	6	wavelength	wavelength	NOUN
asir-1642	50	7	λ	λ	NOUN
asir-1642	50	8	=	=	SYM
asir-1642	50	9	2	2	NUM
asir-1642	50	10	,	,	PUNCT
asir-1642	50	11	fundamental	fundamental	ADJ
asir-1642	50	12	-	-	PUNCT
asir-1642	50	13	frequency	frequency	NOUN
asir-1642	50	14	=	=	SYM
asir-1642	50	15	[	[	PUNCT
asir-1642	50	16	(	(	PUNCT
asir-1642	50	17	+	+	NOUN
asir-1642	50	18	√	√	NUM
asir-1642	50	19	)	)	PUNCT
asir-1642	50	20	]	]	PUNCT
asir-1642	50	21	,	,	PUNCT
asir-1642	50	22	work	work	NOUN
asir-1642	50	23	=	=	PUNCT
asir-1642	50	24	h.	h.	PROPN
asir-1642	51	1	the	the	DET
asir-1642	51	2	energy	energy	NOUN
asir-1642	51	3	-	-	PUNCT
asir-1642	51	4	storage	storage	NOUN
asir-1642	51	5	length	length	NOUN
asir-1642	51	6	e	e	NOUN
asir-1642	51	7	-	-	NOUN
asir-1642	51	8	p	p	X
asir-1642	51	9	=	=	NOUN
asir-1642	51	10	λ/2	λ/2	NUM
asir-1642	51	11	,	,	PUNCT
asir-1642	51	12	and	and	CCONJ
asir-1642	51	13	is	be	AUX
asir-1642	51	14	composed	compose	VERB
asir-1642	51	15	of	of	ADP
asir-1642	51	16	4	4	NUM
asir-1642	51	17	lobes	lobe	NOUN
asir-1642	51	18	with	with	ADP
asir-1642	51	19	wavelength	wavelength	NOUN
asir-1642	51	20	λ	λ	NOUN
asir-1642	51	21	=	=	SYM
asir-1642	51	22	2	2	NUM
asir-1642	51	23	,	,	PUNCT
asir-1642	51	24	=	=	NOUN
asir-1642	51	25	v	v	ADP
asir-1642	51	26	2	2	NUM
asir-1642	51	27	=	=	SYM
asir-1642	51	28	4	4	NUM
asir-1642	51	29	o	o	NOUN
asir-1642	51	30	,	,	PUNCT
asir-1642	51	31	w	w	PROPN
asir-1642	51	32	=	=	SYM
asir-1642	51	33	h	h	NOUN
asir-1642	51	34	2	2	NUM
asir-1642	51	35	v	v	NOUN
asir-1642	51	36	and	and	CCONJ
asir-1642	51	37	for	for	ADP
asir-1642	51	38	→	→	SYM
asir-1642	51	39	total	total	ADJ
asir-1642	51	40	-	-	PUNCT
asir-1642	51	41	work	work	NOUN
asir-1642	51	42	w	w	NOUN
asir-1642	52	1	=	=	PUNCT
asir-1642	52	2	[	[	PUNCT
asir-1642	52	3	𝜋	𝜋	NOUN
asir-1642	52	4	²f	²f	NOUN
asir-1642	52	5	3	3	NUM
asir-1642	52	6	]	]	PUNCT
asir-1642	52	7	.n.(n+1	.n.(n+1	X
asir-1642	52	8	)	)	PUNCT
asir-1642	52	9	or	or	CCONJ
asir-1642	52	10	w	w	NOUN
asir-1642	52	11	=	=	ADJ
asir-1642	52	12	0.𝜋	0.𝜋	NUM
asir-1642	52	13	²f	²f	NOUN
asir-1642	52	14	3	3	NUM
asir-1642	52	15	,	,	PUNCT
asir-1642	52	16	v	v	NOUN
asir-1642	52	17	=	=	SYM
asir-1642	52	18	λ	λ	NOUN
asir-1642	52	19	.	.	PUNCT
asir-1642	53	1	=	=	PUNCT
asir-1642	53	2	4.λ	4.λ	NUM
asir-1642	53	3	.	.	PUNCT
asir-1642	54	1	o	o	NOUN
asir-1642	55	1	n	n	NOUN
asir-1642	55	2	=	=	SYM
asir-1642	55	3	1→	1→	NUM
asir-1642	55	4	=	=	SYM
asir-1642	55	5	1	1	NUM
asir-1642	55	6	.	.	PUNCT
asir-1642	55	7	[	[	PUNCT
asir-1642	55	8	(	(	PUNCT
asir-1642	55	9	+	+	NOUN
asir-1642	55	10	√	√	NUM
asir-1642	55	11	)	)	PUNCT
asir-1642	56	1	]	]	PUNCT
asir-1642	56	2	,	,	PUNCT
asir-1642	56	3	wavelength	wavelength	NOUN
asir-1642	56	4	λ	λ	PROPN
asir-1642	56	5	=	=	SYM
asir-1642	56	6	2	2	NUM
asir-1642	56	7	,	,	PUNCT
asir-1642	56	8	energy	energy	NOUN
asir-1642	56	9	w	w	NOUN
asir-1642	56	10	=	=	PUNCT
asir-1642	57	1	[	[	PUNCT
asir-1642	57	2	𝜋𝑟²	𝜋𝑟²	NOUN
asir-1642	57	3	3	3	NUM
asir-1642	57	4	]	]	PUNCT
asir-1642	57	5	.	.	PUNCT
asir-1642	58	1	=	=	SYM
asir-1642	58	2	1	1	X
asir-1642	58	3	.	.	PUNCT
asir-1642	59	1	(	(	PUNCT
asir-1642	59	2	+	+	X
asir-1642	59	3	√𝟓	√𝟓	NOUN
asir-1642	59	4	)	)	PUNCT
asir-1642	59	5	𝐫	𝐫	ADP
asir-1642	59	6	𝟑	𝟑	NUM
asir-1642	59	7	n	n	NOUN
asir-1642	59	8	=	=	SYM
asir-1642	59	9	2→	2→	NUM
asir-1642	59	10	2	2	NUM
asir-1642	59	11	=	=	SYM
asir-1642	59	12	2	2	NUM
asir-1642	59	13	.	.	PUNCT
asir-1642	59	14	[	[	PUNCT
asir-1642	59	15	(	(	PUNCT
asir-1642	59	16	+	+	NOUN
asir-1642	59	17	√	√	NUM
asir-1642	59	18	)	)	PUNCT
asir-1642	60	1	]	]	PUNCT
asir-1642	60	2	,	,	PUNCT
asir-1642	60	3	wavelength	wavelength	NOUN
asir-1642	60	4	λ	λ	NOUN
asir-1642	60	5	2	2	NUM
asir-1642	60	6	=	=	SYM
asir-1642	60	7	2	2	NUM
asir-1642	60	8	2	2	NUM
asir-1642	60	9	,	,	PUNCT
asir-1642	60	10	energy	energy	NOUN
asir-1642	60	11	w	w	NOUN
asir-1642	60	12	2	2	NUM
asir-1642	60	13	=	=	SYM
asir-1642	60	14	[	[	PUNCT
asir-1642	60	15	𝜋𝑟²	𝜋𝑟²	NOUN
asir-1642	60	16	3	3	NUM
asir-1642	60	17	]	]	PUNCT
asir-1642	60	18	.	.	PUNCT
asir-1642	61	1	2	2	NUM
asir-1642	61	2	=	=	SYM
asir-1642	61	3	2	2	NUM
asir-1642	61	4	.	.	PUNCT
asir-1642	62	1	(	(	PUNCT
asir-1642	62	2	+	+	X
asir-1642	62	3	√𝟓	√𝟓	NOUN
asir-1642	62	4	)	)	PUNCT
asir-1642	62	5	𝐫	𝐫	ADP
asir-1642	62	6	𝟑	𝟑	NUM
asir-1642	62	7	n	n	NOUN
asir-1642	62	8	=	=	SYM
asir-1642	62	9	3→	3→	NUM
asir-1642	62	10	3	3	NUM
asir-1642	62	11	=	=	SYM
asir-1642	62	12	3	3	NUM
asir-1642	62	13	.	.	PUNCT
asir-1642	62	14	[	[	PUNCT
asir-1642	62	15	(	(	PUNCT
asir-1642	62	16	+	+	NOUN
asir-1642	62	17	√	√	NUM
asir-1642	62	18	)	)	PUNCT
asir-1642	63	1	]	]	PUNCT
asir-1642	63	2	,	,	PUNCT
asir-1642	63	3	wavelength	wavelength	NOUN
asir-1642	63	4	λ	λ	PROPN
asir-1642	63	5	3	3	NUM
asir-1642	63	6	=	=	SYM
asir-1642	63	7	2	2	NUM
asir-1642	63	8	3	3	NUM
asir-1642	63	9	,	,	PUNCT
asir-1642	63	10	energy	energy	NOUN
asir-1642	63	11	w	w	NOUN
asir-1642	63	12	3	3	NUM
asir-1642	63	13	=	=	PUNCT
asir-1642	63	14	[	[	PUNCT
asir-1642	63	15	𝜋𝑟²	𝜋𝑟²	NOUN
asir-1642	63	16	3	3	NUM
asir-1642	63	17	]	]	PUNCT
asir-1642	63	18	.	.	PUNCT
asir-1642	64	1	3	3	NUM
asir-1642	64	2	=	=	SYM
asir-1642	64	3	3	3	X
asir-1642	64	4	.	.	PUNCT
asir-1642	65	1	(	(	PUNCT
asir-1642	65	2	+	+	X
asir-1642	65	3	√𝟓	√𝟓	NOUN
asir-1642	65	4	)	)	PUNCT
asir-1642	65	5	𝐫	𝐫	ADP
asir-1642	65	6	𝟑	𝟑	NUM
asir-1642	65	7	n	n	NOUN
asir-1642	65	8	=	=	SYM
asir-1642	65	9	4→	4→	NUM
asir-1642	65	10	=	=	SYM
asir-1642	65	11	4	4	NUM
asir-1642	65	12	.	.	PUNCT
asir-1642	65	13	[	[	PUNCT
asir-1642	65	14	(	(	PUNCT
asir-1642	65	15	+	+	NOUN
asir-1642	65	16	√	√	NUM
asir-1642	65	17	)	)	PUNCT
asir-1642	66	1	]	]	PUNCT
asir-1642	66	2	,	,	PUNCT
asir-1642	66	3	wavelength	wavelength	NOUN
asir-1642	66	4	λ	λ	PROPN
asir-1642	66	5	=	=	SYM
asir-1642	66	6	2	2	NUM
asir-1642	66	7	,	,	PUNCT
asir-1642	66	8	energy	energy	NOUN
asir-1642	66	9	w	w	NOUN
asir-1642	66	10	=	=	PUNCT
asir-1642	67	1	[	[	PUNCT
asir-1642	67	2	𝜋𝑟²	𝜋𝑟²	NOUN
asir-1642	67	3	3	3	NUM
asir-1642	67	4	]	]	PUNCT
asir-1642	67	5	.	.	PUNCT
asir-1642	68	1	=	=	SYM
asir-1642	68	2	4	4	X
asir-1642	68	3	.	.	PUNCT
asir-1642	69	1	(	(	PUNCT
asir-1642	69	2	+	+	X
asir-1642	69	3	√𝟓	√𝟓	NOUN
asir-1642	69	4	)	)	PUNCT
asir-1642	69	5	𝐫	𝐫	NUM
asir-1642	69	6	𝟑	𝟑	NUM
asir-1642	69	7	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	69	8	applied	apply	VERB
asir-1642	69	9	science	science	NOUN
asir-1642	69	10	and	and	CCONJ
asir-1642	69	11	innovative	innovative	ADJ
asir-1642	69	12	research	research	NOUN
asir-1642	69	13	vol	vol	NOUN
asir-1642	69	14	.	.	PROPN
asir-1642	70	1	2	2	NUM
asir-1642	70	2	,	,	PUNCT
asir-1642	70	3	no	no	INTJ
asir-1642	70	4	.	.	NOUN
asir-1642	70	5	4	4	NUM
asir-1642	70	6	,	,	PUNCT
asir-1642	70	7	2018	2018	NUM
asir-1642	70	8	158	158	NUM
asir-1642	70	9	published	publish	VERB
asir-1642	70	10	by	by	ADP
asir-1642	70	11	scholink	scholink	PROPN
asir-1642	70	12	inc	inc	PROPN
asir-1642	70	13	.	.	PROPN
asir-1642	70	14	figure	figure	NOUN
asir-1642	70	15	1	1	NUM
asir-1642	70	16	.	.	PUNCT
asir-1642	71	1	the	the	DET
asir-1642	71	2	photon	photon	NOUN
asir-1642	71	3	as	as	ADP
asir-1642	71	4	n	n	NOUN
asir-1642	71	5	-	-	PUNCT
asir-1642	71	6	lobes	lobe	NOUN
asir-1642	71	7	energy	energy	NOUN
asir-1642	71	8	-	-	PUNCT
asir-1642	71	9	store≡particle	store≡particle	NOUN
asir-1642	71	10	≡	≡	PROPN
asir-1642	72	1	[	[	X
asir-1642	72	2	nλ=2r	nλ=2r	X
asir-1642	72	3	]	]	PUNCT
asir-1642	72	4	and	and	CCONJ
asir-1642	72	5	e	e	NOUN
asir-1642	72	6	-	-	NOUN
asir-1642	72	7	m	m	PROPN
asir-1642	72	8	wave	wave	NOUN
asir-1642	72	9	≡	≡	PROPN
asir-1642	72	10	[	[	PUNCT
asir-1642	72	11	λ	λ	X
asir-1642	72	12	=	=	PUNCT
asir-1642	72	13	cf	cf	X
asir-1642	72	14	]	]	PUNCT
asir-1642	72	15	in	in	ADP
asir-1642	72	16	figure	figure	NOUN
asir-1642	72	17	1	1	NUM
asir-1642	72	18	,	,	PUNCT
asir-1642	73	1	r	r	NOUN
asir-1642	73	2	=	=	NOUN
asir-1642	73	3	λ/2	λ/2	PUNCT
asir-1642	73	4	=	=	SYM
asir-1642	73	5	ep	ep	PROPN
asir-1642	73	6	is	be	AUX
asir-1642	73	7	the	the	DET
asir-1642	73	8	energy	energy	NOUN
asir-1642	73	9	-	-	PUNCT
asir-1642	73	10	storage	storage	NOUN
asir-1642	73	11	-	-	PUNCT
asir-1642	73	12	monad	monad	PROPN
asir-1642	74	1	[	[	X
asir-1642	74	2	s≡em	s≡em	VERB
asir-1642	74	3	-	-	PUNCT
asir-1642	74	4	r	r	NOUN
asir-1642	74	5	≡	≡	PROPN
asir-1642	74	6	,	,	PUNCT
asir-1642	74	7	2	2	NUM
asir-1642	74	8	,	,	PUNCT
asir-1642	74	9	3	3	NUM
asir-1642	74	10	,	,	PUNCT
asir-1642	74	11	,	,	PUNCT
asir-1642	74	12	,	,	PUNCT
asir-1642	74	13	]	]	PUNCT
asir-1642	74	14	with	with	ADP
asir-1642	74	15	wavelength	wavelength	NOUN
asir-1642	74	16	λ	λ	PROPN
asir-1642	74	17	=	=	PRON
asir-1642	74	18	.	.	PUNCT
asir-1642	75	1	(	(	PUNCT
asir-1642	75	2	+	+	ADV
asir-1642	75	3	√	√	ADJ
asir-1642	75	4	)	)	PUNCT
asir-1642	76	1	=	=	PUNCT
asir-1642	76	2	𝑛.b̅	𝑛.b̅	PROPN
asir-1642	76	3	²	²	NUM
asir-1642	76	4	≡	≡	PROPN
asir-1642	76	5	particle	particle	NOUN
asir-1642	76	6	,	,	PUNCT
asir-1642	76	7	where	where	SCONJ
asir-1642	76	8	velocity	velocity	NOUN
asir-1642	76	9	v̅	v̅	X
asir-1642	76	10	=	=	SYM
asir-1642	76	11	w.r	w.r	PROPN
asir-1642	76	12	,	,	PUNCT
asir-1642	76	13	follows	follow	VERB
asir-1642	76	14	the	the	DET
asir-1642	76	15	breakage	breakage	NOUN
asir-1642	76	16	-	-	PUNCT
asir-1642	76	17	principle	principle	NOUN
asir-1642	76	18	which	which	PRON
asir-1642	76	19	is	be	AUX
asir-1642	76	20	quaternion	quaternion	NOUN
asir-1642	76	21	̅	̅	NOUN
asir-1642	76	22	=	=	PUNCT
asir-1642	77	1	[	[	X
asir-1642	77	2	s	s	X
asir-1642	77	3	+	+	NOUN
asir-1642	77	4	v̅	v̅	X
asir-1642	77	5	]	]	PUNCT
asir-1642	77	6	or	or	CCONJ
asir-1642	77	7	→	→	SYM
asir-1642	77	8	s²	s²	NOUN
asir-1642	77	9	|	|	ADV
asir-1642	77	10	̅|²	̅|²	PROPN
asir-1642	78	1	+	+	CCONJ
asir-1642	78	2	2|s|².i	2|s|².i	NUM
asir-1642	78	3	←	←	PROPN
asir-1642	78	4	≡	≡	PROPN
asir-1642	79	1	[	[	X
asir-1642	79	2	εe²	εe²	NOUN
asir-1642	79	3	+	+	CCONJ
asir-1642	79	4	μb²	μb²	NOUN
asir-1642	79	5	]	]	X
asir-1642	79	6	≡	≡	PROPN
asir-1642	79	7	the	the	DET
asir-1642	79	8	energy	energy	NOUN
asir-1642	79	9	-	-	PUNCT
asir-1642	79	10	monad	monad	PROPN
asir-1642	79	11	ep	ep	PROPN
asir-1642	79	12	,	,	PUNCT
asir-1642	79	13	the	the	DET
asir-1642	79	14	wave	wave	NOUN
asir-1642	79	15	,	,	PUNCT
asir-1642	79	16	as	as	ADP
asir-1642	79	17	,	,	PUNCT
asir-1642	79	18	matter	matter	NOUN
asir-1642	79	19	(	(	PUNCT
asir-1642	79	20	+	+	ADJ
asir-1642	79	21	)	)	PUNCT
asir-1642	79	22	≡	≡	PROPN
asir-1642	79	23	magnetic	magnetic	ADJ
asir-1642	79	24	-	-	PUNCT
asir-1642	79	25	field	field	NOUN
asir-1642	79	26	→	→	SYM
asir-1642	79	27	[	[	X
asir-1642	79	28	μb²	μb²	X
asir-1642	79	29	]	]	X
asir-1642	79	30	antimatter	antimatter	NOUN
asir-1642	79	31	(	(	PUNCT
asir-1642	79	32	-	-	PUNCT
asir-1642	79	33	)	)	PUNCT
asir-1642	79	34	≡	≡	PROPN
asir-1642	79	35	electric	electric	NOUN
asir-1642	79	36	-	-	PUNCT
asir-1642	79	37	field	field	NOUN
asir-1642	79	38	→	→	PUNCT
asir-1642	79	39	[	[	X
asir-1642	79	40	εe²	εe²	NOUN
asir-1642	79	41	]	]	PUNCT
asir-1642	79	42	energy	energy	NOUN
asir-1642	79	43	(	(	PUNCT
asir-1642	79	44	+	+	NOUN
asir-1642	79	45	↔	↔	PROPN
asir-1642	79	46	-	-	PUNCT
asir-1642	79	47	)	)	PUNCT
asir-1642	79	48	≡	≡	PROPN
asir-1642	79	49	motion	motion	NOUN
asir-1642	79	50	in	in	ADP
asir-1642	79	51	n	n	DET
asir-1642	79	52	lobes	lobe	NOUN
asir-1642	79	53	→	→	SYM
asir-1642	79	54	[	[	PUNCT
asir-1642	79	55	,	,	PUNCT
asir-1642	79	56	]	]	X
asir-1642	79	57	,	,	PUNCT
asir-1642	79	58	i.e.	i.e.	X
asir-1642	79	59	,	,	PUNCT
asir-1642	79	60	the	the	DET
asir-1642	79	61	stationary	stationary	ADJ
asir-1642	79	62	-	-	PUNCT
asir-1642	79	63	cave	cave	NOUN
asir-1642	79	64	-	-	PUNCT
asir-1642	79	65	lobes	lobe	NOUN
asir-1642	79	66	,	,	PUNCT
asir-1642	79	67	consist	consist	VERB
asir-1642	79	68	the	the	DET
asir-1642	79	69	particle	particle	NOUN
asir-1642	79	70	-	-	PUNCT
asir-1642	79	71	photon	photon	NOUN
asir-1642	79	72	with	with	ADP
asir-1642	79	73	the	the	DET
asir-1642	79	74	inside	inside	ADJ
asir-1642	79	75	motion	motion	NOUN
asir-1642	79	76	,	,	PUNCT
asir-1642	79	77	in	in	ADP
asir-1642	79	78	the	the	DET
asir-1642	79	79	r	r	NOUN
asir-1642	79	80	=	=	SYM
asir-1642	79	81	n	n	X
asir-1642	79	82	[	[	X
asir-1642	79	83	λ/2	λ/2	NUM
asir-1642	79	84	]	]	PUNCT
asir-1642	79	85	energy	energy	NOUN
asir-1642	79	86	-	-	PUNCT
asir-1642	79	87	storage	storage	NOUN
asir-1642	79	88	,	,	PUNCT
asir-1642	79	89	and	and	CCONJ
asir-1642	79	90	[	[	X
asir-1642	79	91	e²	e²	X
asir-1642	79	92	+	+	CCONJ
asir-1642	79	93	h²	h²	PROPN
asir-1642	79	94	]	]	X
asir-1642	79	95	=	=	SYM
asir-1642	79	96	2.(2r).c.𝐬𝐢𝐧𝟐𝛗	2.(2r).c.𝐬𝐢𝐧𝟐𝛗	NOUN
asir-1642	79	97	,	,	PUNCT
asir-1642	79	98	the	the	DET
asir-1642	79	99	wave	wave	NOUN
asir-1642	79	100	photon	photon	NOUN
asir-1642	79	101	as	as	ADP
asir-1642	79	102	the	the	DET
asir-1642	79	103	outward	outward	ADJ
asir-1642	79	104	motion	motion	NOUN
asir-1642	79	105	.	.	PUNCT
asir-1642	80	1	energy	energy	NOUN
asir-1642	80	2	-	-	PUNCT
asir-1642	80	3	storage	storage	NOUN
asir-1642	80	4	-	-	PUNCT
asir-1642	80	5	monads	monad	NOUN
asir-1642	80	6	are	be	AUX
asir-1642	80	7	consisted	consist	VERB
asir-1642	80	8	of	of	ADP
asir-1642	80	9	the	the	DET
asir-1642	80	10	above	above	ADJ
asir-1642	80	11	three	three	NUM
asir-1642	80	12	-	-	PUNCT
asir-1642	80	13	constituents	constituent	NOUN
asir-1642	80	14	all	all	ADV
asir-1642	80	15	-	-	PUNCT
asir-1642	80	16	together	together	ADV
asir-1642	80	17	,	,	PUNCT
asir-1642	80	18	or	or	CCONJ
asir-1642	80	19	each	each	DET
asir-1642	80	20	-	-	PUNCT
asir-1642	80	21	one	one	NUM
asir-1642	80	22	of	of	ADP
asir-1642	80	23	them	they	PRON
asir-1642	80	24	work	work	NOUN
asir-1642	80	25	ratio	ratio	NOUN
asir-1642	80	26	is	be	AUX
asir-1642	80	27	→	→	SYM
asir-1642	80	28	w	w	X
asir-1642	80	29	/	/	SYM
asir-1642	80	30	w	w	NOUN
asir-1642	80	31	=	=	PUNCT
asir-1642	80	32	/	/	SYM
asir-1642	81	1	=	=	PROPN
asir-1642	81	2	n	n	PROPN
asir-1642	81	3	(	(	PUNCT
asir-1642	81	4	n+1).[v	n+1).[v	X
asir-1642	81	5	/	/	SYM
asir-1642	81	6	v	v	NOUN
asir-1642	81	7	]	]	PUNCT
asir-1642	81	8	=	=	SYM
asir-1642	82	1	n	n	PROPN
asir-1642	82	2	(	(	PUNCT
asir-1642	82	3	n+1	n+1	PROPN
asir-1642	82	4	)	)	PUNCT
asir-1642	82	5	f	f	PROPN
asir-1642	83	1	f	f	PROPN
asir-1642	83	2	=	=	SYM
asir-1642	83	3	n	n	PROPN
asir-1642	83	4	(	(	PUNCT
asir-1642	83	5	n+1	n+1	PROPN
asir-1642	83	6	)	)	PUNCT
asir-1642	83	7	𝑛.	𝑛.	NOUN
asir-1642	83	8	f	f	PROPN
asir-1642	83	9	2𝑟.f	2𝑟.f	NUM
asir-1642	83	10	=	=	SYM
asir-1642	83	11	n²(n+1	n²(n+1	PROPN
asir-1642	83	12	)	)	PUNCT
asir-1642	83	13	2	2	NUM
asir-1642	83	14	=	=	SYM
asir-1642	83	15	n	n	PROPN
asir-1642	83	16	(	(	PUNCT
asir-1642	83	17	n+1	n+1	PROPN
asir-1642	83	18	)	)	PUNCT
asir-1642	83	19	and	and	CCONJ
asir-1642	83	20	for	for	ADP
asir-1642	83	21	λ	λ	PROPN
asir-1642	83	22	=	=	SYM
asir-1642	83	23	2r	2r	NUM
asir-1642	83	24	,	,	PUNCT
asir-1642	83	25	v	v	NOUN
asir-1642	83	26	=	=	SYM
asir-1642	83	27	v	v	NOUN
asir-1642	83	28	then	then	ADV
asir-1642	83	29	,	,	PUNCT
asir-1642	83	30	n.	n.	PROPN
asir-1642	83	31	𝐧	𝐧	NOUN
asir-1642	83	32	=	=	PUNCT
asir-1642	83	33	2.r	2.r	NUM
asir-1642	83	34	,	,	PUNCT
asir-1642	83	35	or	or	CCONJ
asir-1642	83	36	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	83	37	applied	apply	VERB
asir-1642	83	38	science	science	NOUN
asir-1642	83	39	and	and	CCONJ
asir-1642	83	40	innovative	innovative	ADJ
asir-1642	83	41	research	research	NOUN
asir-1642	83	42	vol	vol	NOUN
asir-1642	83	43	.	.	PROPN
asir-1642	84	1	2	2	NUM
asir-1642	84	2	,	,	PUNCT
asir-1642	84	3	no	no	INTJ
asir-1642	84	4	.	.	NOUN
asir-1642	84	5	4	4	NUM
asir-1642	84	6	,	,	PUNCT
asir-1642	84	7	2018	2018	NUM
asir-1642	84	8	159	159	NUM
asir-1642	84	9	published	publish	VERB
asir-1642	84	10	by	by	ADP
asir-1642	84	11	scholink	scholink	PROPN
asir-1642	84	12	inc	inc	PROPN
asir-1642	84	13	.	.	PUNCT
asir-1642	85	1	the	the	DET
asir-1642	85	2	work	work	NOUN
asir-1642	85	3	,	,	PUNCT
asir-1642	85	4	w	w	PROPN
asir-1642	85	5	,	,	PUNCT
asir-1642	85	6	produced	produce	VERB
asir-1642	85	7	from	from	ADP
asir-1642	85	8	the	the	DET
asir-1642	85	9	wave	wave	NOUN
asir-1642	85	10	-	-	PUNCT
asir-1642	85	11	energy	energy	NOUN
asir-1642	85	12	-	-	PUNCT
asir-1642	85	13	pattern	pattern	NOUN
asir-1642	85	14	with	with	ADP
asir-1642	85	15	wavelengths	wavelength	NOUN
asir-1642	85	16	𝐧	𝐧	ADP
asir-1642	85	17	,	,	PUNCT
asir-1642	85	18	and	and	CCONJ
asir-1642	85	19	created	create	VERB
asir-1642	85	20	from	from	ADP
asir-1642	85	21	all	all	DET
asir-1642	85	22	points	point	NOUN
asir-1642	85	23	of	of	ADP
asir-1642	85	24	the	the	DET
asir-1642	85	25	periodic	periodic	ADJ
asir-1642	85	26	oscillation	oscillation	NOUN
asir-1642	85	27	in	in	ADP
asir-1642	85	28	the	the	DET
asir-1642	85	29	cave	cave	NOUN
asir-1642	85	30	,	,	PUNCT
asir-1642	85	31	r	r	PROPN
asir-1642	85	32	,	,	PUNCT
asir-1642	85	33	is	be	AUX
asir-1642	85	34	stored	store	VERB
asir-1642	85	35	into	into	ADP
asir-1642	85	36	the	the	DET
asir-1642	85	37	,	,	PUNCT
asir-1642	85	38	n	n	CCONJ
asir-1642	85	39	,	,	PUNCT
asir-1642	85	40	integer	integer	NOUN
asir-1642	85	41	and	and	CCONJ
asir-1642	85	42	energy	energy	NOUN
asir-1642	85	43	-	-	PUNCT
asir-1642	85	44	lobes	lobe	NOUN
asir-1642	85	45	of	of	ADP
asir-1642	85	46	cave	cave	PROPN
asir-1642	85	47	r.	r.	PROPN
asir-1642	85	48	from	from	ADP
asir-1642	85	49	mechanics	mechanic	NOUN
asir-1642	85	50	,	,	PUNCT
asir-1642	85	51	the	the	DET
asir-1642	85	52	only	only	ADJ
asir-1642	85	53	-	-	PUNCT
asir-1642	85	54	possible	possible	ADJ
asir-1642	85	55	motions	motion	NOUN
asir-1642	85	56	are	be	AUX
asir-1642	85	57	,	,	PUNCT
asir-1642	85	58	the	the	DET
asir-1642	85	59	periodic	periodic	ADJ
asir-1642	85	60	excitation	excitation	NOUN
asir-1642	85	61	,	,	PUNCT
asir-1642	85	62	and	and	CCONJ
asir-1642	85	63	the	the	DET
asir-1642	85	64	revolving	revolve	VERB
asir-1642	85	65	motion	motion	NOUN
asir-1642	85	66	therefore	therefore	ADV
asir-1642	85	67	all	all	DET
asir-1642	85	68	moving	move	VERB
asir-1642	85	69	-	-	PUNCT
asir-1642	85	70	energy	energy	NOUN
asir-1642	85	71	-	-	PUNCT
asir-1642	85	72	stores	store	NOUN
asir-1642	85	73	travel	travel	VERB
asir-1642	85	74	as	as	ADP
asir-1642	85	75	a	a	DET
asir-1642	85	76	wave	wave	NOUN
asir-1642	85	77	and	and	CCONJ
asir-1642	85	78	not	not	PART
asir-1642	85	79	as	as	ADP
asir-1642	85	80	a	a	DET
asir-1642	85	81	particle	particle	NOUN
asir-1642	85	82	.	.	PUNCT
asir-1642	86	1	the	the	DET
asir-1642	86	2	n	n	NOUN
asir-1642	86	3	,	,	PUNCT
asir-1642	86	4	energy	energy	NOUN
asir-1642	86	5	-	-	PUNCT
asir-1642	86	6	tanks	tank	NOUN
asir-1642	86	7	,	,	PUNCT
asir-1642	86	8	the	the	DET
asir-1642	86	9	n	n	PRON
asir-1642	86	10	antinodes	antinode	NOUN
asir-1642	86	11	in	in	ADP
asir-1642	86	12	its	its	PRON
asir-1642	86	13	store	store	NOUN
asir-1642	86	14	2λ	2λ	NOUN
asir-1642	87	1	=	=	SYM
asir-1642	87	2	r	r	NOUN
asir-1642	87	3	=	=	SYM
asir-1642	87	4	h	h	NOUN
asir-1642	87	5	/	/	SYM
asir-1642	87	6	p	p	PRON
asir-1642	87	7	≡	≡	PROPN
asir-1642	87	8	[	[	PUNCT
asir-1642	87	9	,	,	PUNCT
asir-1642	87	10	2	2	NUM
asir-1642	87	11	,	,	PUNCT
asir-1642	87	12	≡	≡	PROPN
asir-1642	87	13	n	n	PRON
asir-1642	87	14	lobes	lobe	NOUN
asir-1642	87	15	]	]	PUNCT
asir-1642	87	16	follows	follow	VERB
asir-1642	87	17	the	the	DET
asir-1642	87	18	stationary	stationary	ADJ
asir-1642	87	19	-	-	PUNCT
asir-1642	87	20	wave	wave	NOUN
asir-1642	87	21	-	-	PUNCT
asir-1642	87	22	nodes	node	NOUN
asir-1642	87	23	-	-	NOUN
asir-1642	87	24	principle	principle	ADJ
asir-1642	87	25	,	,	PUNCT
asir-1642	87	26	i.e.	i.e.	X
asir-1642	87	27	,	,	PUNCT
asir-1642	87	28	the	the	DET
asir-1642	87	29	glue	glue	NOUN
asir-1642	87	30	-	-	PUNCT
asir-1642	87	31	bond	bond	NOUN
asir-1642	87	32	-	-	PUNCT
asir-1642	87	33	stress	stress	NOUN
asir-1642	87	34	rotation	rotation	NOUN
asir-1642	87	35	of	of	ADP
asir-1642	87	36	opposites	opposite	NOUN
asir-1642	87	37	on	on	ADP
asir-1642	87	38	small	small	ADJ
asir-1642	87	39	-	-	PUNCT
asir-1642	87	40	circles	circle	NOUN
asir-1642	87	41	creates	create	VERB
asir-1642	87	42	integer	integer	NOUN
asir-1642	87	43	number	number	NOUN
asir-1642	87	44	of	of	ADP
asir-1642	87	45	lobes	lobe	NOUN
asir-1642	87	46	,	,	PUNCT
asir-1642	87	47	which	which	PRON
asir-1642	87	48	is	be	AUX
asir-1642	87	49	the	the	DET
asir-1642	87	50	wave	wave	NOUN
asir-1642	87	51	-	-	PUNCT
asir-1642	87	52	nodes	node	NOUN
asir-1642	87	53	-	-	NOUN
asir-1642	87	54	principle	principle	NOUN
asir-1642	87	55	of	of	ADP
asir-1642	87	56	the	the	DET
asir-1642	87	57	moving	move	VERB
asir-1642	87	58	-	-	PUNCT
asir-1642	87	59	energy	energy	NOUN
asir-1642	87	60	-	-	PUNCT
asir-1642	87	61	stores	store	NOUN
asir-1642	87	62	,	,	PUNCT
asir-1642	87	63	one	one	NUM
asir-1642	87	64	of	of	ADP
asir-1642	87	65	which	which	PRON
asir-1642	87	66	is	be	AUX
asir-1642	87	67	the	the	DET
asir-1642	87	68	photon	photon	NOUN
asir-1642	87	69	.	.	PUNCT
asir-1642	88	1	f	f	X
asir-1642	88	2	..	..	PUNCT
asir-1642	88	3	the	the	DET
asir-1642	88	4	photon	photon	NOUN
asir-1642	88	5	:	:	PUNCT
asir-1642	88	6	electromagnetic	electromagnetic	ADJ
asir-1642	88	7	waves	wave	NOUN
asir-1642	88	8	are	be	AUX
asir-1642	88	9	created	create	VERB
asir-1642	88	10	by	by	ADP
asir-1642	88	11	the	the	DET
asir-1642	88	12	vibration	vibration	NOUN
asir-1642	88	13	of	of	ADP
asir-1642	88	14	an	an	DET
asir-1642	88	15	electric	electric	ADJ
asir-1642	88	16	charge	charge	NOUN
asir-1642	88	17	.	.	PUNCT
asir-1642	89	1	in	in	ADP
asir-1642	89	2	material	material	NOUN
asir-1642	89	3	-	-	PUNCT
asir-1642	89	4	point	point	NOUN
asir-1642	89	5	,	,	PUNCT
asir-1642	89	6	the	the	DET
asir-1642	89	7	eternal	eternal	ADJ
asir-1642	89	8	rotation	rotation	NOUN
asir-1642	89	9	of	of	ADP
asir-1642	89	10	the	the	DET
asir-1642	89	11	⊕	⊕	PROPN
asir-1642	89	12	constituent	constituent	NOUN
asir-1642	89	13	around	around	ADP
asir-1642	89	14	the	the	DET
asir-1642	89	15	⊝	⊝	NUM
asir-1642	89	16	constituent	constituent	NOUN
asir-1642	89	17	creates	create	VERB
asir-1642	89	18	the	the	DET
asir-1642	89	19	,	,	PUNCT
asir-1642	89	20	n	n	CCONJ
asir-1642	89	21	,	,	PUNCT
asir-1642	89	22	energy	energy	NOUN
asir-1642	89	23	-	-	PUNCT
asir-1642	89	24	lobes	lobe	NOUN
asir-1642	89	25	in	in	ADP
asir-1642	89	26	a	a	DET
asir-1642	89	27	tank	tank	NOUN
asir-1642	89	28	r	r	NOUN
asir-1642	89	29	=	=	SYM
asir-1642	89	30	n	n	CCONJ
asir-1642	89	31	𝟐	𝟐	NUM
asir-1642	89	32	or	or	CCONJ
asir-1642	89	33	λ	λ	PROPN
asir-1642	89	34	=	=	NOUN
asir-1642	89	35	𝟐𝐫	𝟐𝐫	PROPN
asir-1642	89	36	𝐧	𝐧	ADV
asir-1642	89	37	since	since	SCONJ
asir-1642	89	38	the	the	DET
asir-1642	89	39	velocity	velocity	NOUN
asir-1642	89	40	of	of	ADP
asir-1642	89	41	the	the	DET
asir-1642	89	42	wave	wave	NOUN
asir-1642	89	43	is	be	AUX
asir-1642	89	44	�	�	NOUN
asir-1642	89	45	̅	̅	NOUN
asir-1642	89	46	�	�	NOUN
asir-1642	89	47	=	=	SYM
asir-1642	89	48	f	f	PROPN
asir-1642	89	49	x	x	SYM
asir-1642	89	50	λ	λ	PROPN
asir-1642	89	51	.	.	PUNCT
asir-1642	90	1	the	the	DET
asir-1642	90	2	frequency	frequency	NOUN
asir-1642	90	3	is	be	AUX
asir-1642	90	4	f	f	PROPN
asir-1642	90	5	=	=	SYM
asir-1642	90	6	𝐧.	𝐧.	PROPN
asir-1642	90	7	�	�	PROPN
asir-1642	90	8	̅	̅	NOUN
asir-1642	90	9	�	�	NOUN
asir-1642	90	10	𝟐.𝐫	𝟐.𝐫	PROPN
asir-1642	90	11	where	where	SCONJ
asir-1642	90	12	n	n	PRON
asir-1642	90	13	is	be	AUX
asir-1642	90	14	a	a	DET
asir-1642	90	15	positive	positive	ADJ
asir-1642	90	16	integer	integer	NOUN
asir-1642	90	17	number	number	NOUN
asir-1642	90	18	.	.	PUNCT
asir-1642	91	1	because	because	SCONJ
asir-1642	91	2	in	in	ADP
asir-1642	91	3	lobes	lobe	NOUN
asir-1642	91	4	the	the	DET
asir-1642	91	5	inner	inner	ADJ
asir-1642	91	6	particles	particle	NOUN
asir-1642	91	7	are	be	AUX
asir-1642	91	8	the	the	PRON
asir-1642	91	9	[	[	X
asir-1642	91	10	+	+	NOUN
asir-1642	91	11	]	]	X
asir-1642	91	12	,	,	PUNCT
asir-1642	91	13	[	[	X
asir-1642	91	14	-	-	PUNCT
asir-1642	91	15	]	]	X
asir-1642	91	16	constituents	constituent	NOUN
asir-1642	91	17	of	of	ADP
asir-1642	91	18	space	space	NOUN
asir-1642	91	19	and	and	CCONJ
asir-1642	91	20	of	of	ADP
asir-1642	91	21	anti	anti	ADJ
asir-1642	91	22	-	-	NOUN
asir-1642	91	23	space	space	NOUN
asir-1642	91	24	,	,	PUNCT
asir-1642	91	25	the	the	DET
asir-1642	91	26	maximum	maximum	ADJ
asir-1642	91	27	amplitude	amplitude	NOUN
asir-1642	91	28	of	of	ADP
asir-1642	91	29	each	each	DET
asir-1642	91	30	constituent	constituent	NOUN
asir-1642	91	31	is	be	AUX
asir-1642	91	32	related	relate	VERB
asir-1642	91	33	with	with	ADP
asir-1642	91	34	its	its	PRON
asir-1642	91	35	position	position	NOUN
asir-1642	91	36	and	and	CCONJ
asir-1642	91	37	each	each	DET
asir-1642	91	38	amplitude	amplitude	NOUN
asir-1642	91	39	oscillates	oscillate	NOUN
asir-1642	91	40	periodically	periodically	ADV
asir-1642	91	41	as	as	ADP
asir-1642	91	42	the	the	DET
asir-1642	91	43	wave	wave	NOUN
asir-1642	91	44	equation	equation	NOUN
asir-1642	91	45	,	,	PUNCT
asir-1642	91	46	x	x	PROPN
asir-1642	91	47	=	=	PUNCT
asir-1642	91	48	𝐯	𝐯	X
asir-1642	91	49	.	.	PUNCT
asir-1642	92	1	𝐬𝐢𝐧	𝐬𝐢𝐧	ADP
asir-1642	92	2	=	=	VERB
asir-1642	92	3	a.sin	a.sin	PROPN
asir-1642	92	4	[	[	X
asir-1642	92	5	√(𝐚	√(𝐚	NOUN
asir-1642	92	6	)	)	PUNCT
asir-1642	92	7	.	.	PUNCT
asir-1642	93	1	+	+	CCONJ
asir-1642	93	2	π/2	π/2	NUM
asir-1642	93	3	]	]	PUNCT
asir-1642	93	4	,	,	PUNCT
asir-1642	93	5	(	(	PUNCT
asir-1642	93	6	1	1	X
asir-1642	93	7	)	)	PUNCT
asir-1642	93	8	where	where	SCONJ
asir-1642	93	9	a	a	DET
asir-1642	93	10	..	..	PUNCT
asir-1642	93	11	velocity	velocity	NOUN
asir-1642	93	12	→	→	SYM
asir-1642	93	13	|v̅|	|v̅|	NOUN
asir-1642	93	14	=	=	PUNCT
asir-1642	94	1	w.r/2	w.r/2	PROPN
asir-1642	94	2	=	=	SYM
asir-1642	94	3	2	2	NUM
asir-1642	94	4	2	2	NUM
asir-1642	94	5	t	t	NOUN
asir-1642	94	6	.r	.r	NOUN
asir-1642	95	1	=	=	PUNCT
asir-1642	95	2	4πr	4πr	PROPN
asir-1642	95	3	.	.	PUNCT
asir-1642	95	4	,	,	PUNCT
asir-1642	95	5	and	and	CCONJ
asir-1642	95	6	=	=	SYM
asir-1642	95	7	.v	.v	ADJ
asir-1642	96	1	𝑟	𝑟	X
asir-1642	97	1	[	[	X
asir-1642	97	2	1	1	NUM
asir-1642	97	3	+	+	NUM
asir-1642	97	4	√	√	NUM
asir-1642	97	5	]	]	PUNCT
asir-1642	97	6	,	,	PUNCT
asir-1642	97	7	b	b	X
asir-1642	97	8	..	..	PUNCT
asir-1642	97	9	angular	angular	ADJ
asir-1642	97	10	velocity	velocity	NOUN
asir-1642	97	11	→	→	SYM
asir-1642	97	12	|w̅|	|w̅|	NOUN
asir-1642	97	13	=	=	SYM
asir-1642	97	14	2𝑟	2𝑟	NUM
asir-1642	98	1	[	[	X
asir-1642	98	2	1	1	NUM
asir-1642	98	3	+	+	NUM
asir-1642	98	4	√	√	NOUN
asir-1642	98	5	]	]	PUNCT
asir-1642	98	6	and	and	CCONJ
asir-1642	98	7	fundamental	fundamental	ADJ
asir-1642	98	8	frequency	frequency	NOUN
asir-1642	98	9	f	f	NOUN
asir-1642	98	10	=	=	PUNCT
asir-1642	98	11	(	(	PUNCT
asir-1642	98	12	+	+	CCONJ
asir-1642	98	13	√	√	NUM
asir-1642	98	14	)	)	PUNCT
asir-1642	98	15	.	.	PUNCT
asir-1642	99	1	in	in	ADP
asir-1642	99	2	cave	cave	PROPN
asir-1642	99	3	,	,	PUNCT
asir-1642	99	4	r.	r.	PROPN
asir-1642	99	5	and	and	CCONJ
asir-1642	99	6	then	then	ADV
asir-1642	99	7	,	,	PUNCT
asir-1642	99	8	wave	wave	NOUN
asir-1642	99	9	propagate	propagate	VERB
asir-1642	99	10	,	,	PUNCT
asir-1642	99	11	as	as	ADP
asir-1642	99	12	in	in	ADP
asir-1642	99	13	a	a	DET
asir-1642	99	14	magnetic	magnetic	ADJ
asir-1642	99	15	-	-	PUNCT
asir-1642	99	16	device	device	NOUN
asir-1642	99	17	the	the	DET
asir-1642	99	18	arced	arced	ADJ
asir-1642	99	19	pattern	pattern	NOUN
asir-1642	99	20	,	,	PUNCT
asir-1642	99	21	by	by	ADP
asir-1642	99	22	travelling	travel	VERB
asir-1642	99	23	from	from	ADP
asir-1642	99	24	north	north	NOUN
asir-1642	99	25	to	to	ADP
asir-1642	99	26	the	the	DET
asir-1642	99	27	south	south	ADJ
asir-1642	99	28	pole	pole	NOUN
asir-1642	99	29	and	and	CCONJ
asir-1642	99	30	thus	thus	ADV
asir-1642	99	31	creating	create	VERB
asir-1642	99	32	the	the	DET
asir-1642	99	33	inner	inner	ADJ
asir-1642	99	34	-	-	PUNCT
asir-1642	99	35	electromagnetic	electromagnetic	NOUN
asir-1642	99	36	-	-	PUNCT
asir-1642	99	37	displacement	displacement	NOUN
asir-1642	99	38	-	-	PUNCT
asir-1642	99	39	current	current	NOUN
asir-1642	99	40	→	→	PUNCT
asir-1642	99	41	,	,	PUNCT
asir-1642	99	42	←	←	PROPN
asir-1642	99	43	and	and	CCONJ
asir-1642	99	44	when	when	SCONJ
asir-1642	99	45	reduced	reduce	VERB
asir-1642	99	46	to	to	ADP
asir-1642	99	47	one	one	NUM
asir-1642	99	48	line	line	NOUN
asir-1642	99	49	is	be	AUX
asir-1642	99	50	as	as	ADP
asir-1642	99	51	,	,	PUNCT
asir-1642	99	52	e	e	NOUN
asir-1642	99	53	→	→	PUNCT
asir-1642	99	54	𝛛𝐄	𝛛𝐄	NOUN
asir-1642	99	55	𝛛	𝛛	PROPN
asir-1642	99	56	→	→	SYM
asir-1642	99	57	h	h	NOUN
asir-1642	99	58	→	→	SYM
asir-1642	99	59	𝛛	𝛛	ADJ
asir-1642	99	60	→	→	NOUN
asir-1642	99	61	𝐇.	𝐇.	NOUN
asir-1642	99	62	this	this	DET
asir-1642	99	63	vibration	vibration	NOUN
asir-1642	99	64	of	of	ADP
asir-1642	99	65	opposites	opposite	NOUN
asir-1642	99	66	creates	create	VERB
asir-1642	99	67	a	a	DET
asir-1642	99	68	wave	wave	NOUN
asir-1642	99	69	which	which	PRON
asir-1642	99	70	has	have	VERB
asir-1642	99	71	both	both	CCONJ
asir-1642	99	72	an	an	DET
asir-1642	99	73	electric	electric	NOUN
asir-1642	99	74	,	,	PUNCT
asir-1642	99	75	e	e	NOUN
asir-1642	99	76	,	,	PUNCT
asir-1642	99	77	and	and	CCONJ
asir-1642	99	78	an	an	DET
asir-1642	99	79	magnetic	magnetic	ADJ
asir-1642	99	80	component	component	NOUN
asir-1642	99	81	,	,	PUNCT
asir-1642	99	82	h	h	NOUN
asir-1642	99	83	,	,	PUNCT
asir-1642	99	84	perpendicular	perpendicular	ADJ
asir-1642	99	85	each	each	DET
asir-1642	99	86	other	other	ADJ
asir-1642	99	87	and	and	CCONJ
asir-1642	99	88	is	be	AUX
asir-1642	99	89	as	as	ADP
asir-1642	99	90	equation	equation	NOUN
asir-1642	99	91	,	,	PUNCT
asir-1642	99	92	[	[	X
asir-1642	99	93	e²	e²	X
asir-1642	99	94	+	+	CCONJ
asir-1642	99	95	h²	h²	PROPN
asir-1642	99	96	]	]	X
asir-1642	99	97	=	=	SYM
asir-1642	99	98	2.(2r).c.𝐬𝐢𝐧𝟐𝛗	2.(2r).c.𝐬𝐢𝐧𝟐𝛗	NUM
asir-1642	99	99	(	(	PUNCT
asir-1642	99	100	2	2	NUM
asir-1642	99	101	)	)	PUNCT
asir-1642	99	102	in	in	ADP
asir-1642	99	103	where	where	SCONJ
asir-1642	99	104	exists	exist	VERB
asir-1642	99	105	the	the	DET
asir-1642	99	106	skin	skin	NOUN
asir-1642	99	107	-	-	PUNCT
asir-1642	99	108	effect	effect	NOUN
asir-1642	99	109	.	.	PUNCT
asir-1642	100	1	this	this	PRON
asir-1642	100	2	happens	happen	VERB
asir-1642	100	3	because	because	SCONJ
asir-1642	100	4	of	of	ADP
asir-1642	100	5	the	the	DET
asir-1642	100	6	difference	difference	NOUN
asir-1642	100	7	in	in	ADP
asir-1642	100	8	density	density	NOUN
asir-1642	100	9	on	on	ADP
asir-1642	100	10	stress	stress	NOUN
asir-1642	100	11	-	-	PUNCT
asir-1642	100	12	common	common	ADJ
asir-1642	100	13	-	-	PUNCT
asir-1642	100	14	curve	curve	NOUN
asir-1642	100	15	ρ	ρ	NOUN
asir-1642	100	16	=	=	SYM
asir-1642	100	17	σ	σ	PROPN
asir-1642	100	18	instead	instead	ADV
asir-1642	100	19	–	–	PUNCT
asir-1642	100	20	of	of	ADP
asir-1642	100	21	ρ	ρ	PROPN
asir-1642	100	22	=	=	SYM
asir-1642	100	23	0	0	NUM
asir-1642	101	1	at	at	ADP
asir-1642	101	2	the	the	DET
asir-1642	101	3	center	center	NOUN
asir-1642	101	4	.	.	PUNCT
asir-1642	102	1	this	this	DET
asir-1642	102	2	property	property	NOUN
asir-1642	102	3	in	in	ADP
asir-1642	102	4	material	material	NOUN
asir-1642	102	5	-	-	PUNCT
asir-1642	102	6	point	point	NOUN
asir-1642	102	7	launches	launch	VERB
asir-1642	102	8	the	the	DET
asir-1642	102	9	inner	inner	ADJ
asir-1642	102	10	-	-	PUNCT
asir-1642	102	11	electromagnetic	electromagnetic	NOUN
asir-1642	102	12	-	-	PUNCT
asir-1642	102	13	wave	wave	NOUN
asir-1642	102	14	,	,	PUNCT
asir-1642	102	15	the	the	DET
asir-1642	102	16	-	-	PUNCT
asir-1642	102	17	particle	particle	NOUN
asir-1642	102	18	≡	≡	PROPN
asir-1642	103	1	[	[	X
asir-1642	103	2	e²	e²	X
asir-1642	103	3	+	+	CCONJ
asir-1642	103	4	h²	h²	PROPN
asir-1642	103	5	]	]	X
asir-1642	103	6	=	=	SYM
asir-1642	103	7	2(2r).c.𝐬𝐢𝐧	2(2r).c.𝐬𝐢𝐧	NUM
asir-1642	103	8	𝟐𝛗	𝟐𝛗	NOUN
asir-1642	103	9	,	,	PUNCT
asir-1642	103	10	of	of	ADP
asir-1642	103	11	wavelength	wavelength	NOUN
asir-1642	103	12	,	,	PUNCT
asir-1642	103	13	λ	λ	NOUN
asir-1642	103	14	,	,	PUNCT
asir-1642	103	15	outward	outward	ADV
asir-1642	103	16	λ	λ	NOUN
asir-1642	103	17	,	,	PUNCT
asir-1642	103	18	as	as	ADP
asir-1642	103	19	the	the	DET
asir-1642	103	20	outer	outer	ADJ
asir-1642	103	21	propagating	propagate	VERB
asir-1642	103	22	electromagnetic	electromagnetic	ADJ
asir-1642	103	23	-	-	PUNCT
asir-1642	103	24	wave	wave	NOUN
asir-1642	103	25	→	→	PUNCT
asir-1642	103	26	{	{	PUNCT
asir-1642	103	27	the	the	DET
asir-1642	103	28	-	-	PUNCT
asir-1642	103	29	wave	wave	NOUN
asir-1642	103	30	≡	≡	PROPN
asir-1642	104	1	[	[	X
asir-1642	104	2	εe²	εe²	NOUN
asir-1642	104	3	+	+	CCONJ
asir-1642	104	4	μb²	μb²	NOUN
asir-1642	104	5	]	]	X
asir-1642	104	6	=	=	SYM
asir-1642	105	1	2.λc.sin.2φ	2.λc.sin.2φ	NUM
asir-1642	105	2	}	}	PUNCT
asir-1642	105	3	←	←	PROPN
asir-1642	105	4	which	which	PRON
asir-1642	105	5	is	be	AUX
asir-1642	105	6	the	the	DET
asir-1642	105	7	conveyer	conveyer	NOUN
asir-1642	105	8	of	of	ADP
asir-1642	105	9	the	the	DET
asir-1642	105	10	-	-	PUNCT
asir-1642	105	11	particle	particle	NOUN
asir-1642	105	12	,	,	PUNCT
asir-1642	105	13	and	and	CCONJ
asir-1642	105	14	allows	allow	VERB
asir-1642	105	15	all	all	DET
asir-1642	105	16	the	the	DET
asir-1642	105	17	energy	energy	NOUN
asir-1642	105	18	-	-	PUNCT
asir-1642	105	19	wave	wave	NOUN
asir-1642	105	20	-	-	PUNCT
asir-1642	105	21	storages	storage	NOUN
asir-1642	105	22	to	to	PART
asir-1642	105	23	propagate	propagate	VERB
asir-1642	105	24	any	any	DET
asir-1642	105	25	distance	distance	NOUN
asir-1642	105	26	in	in	ADP
asir-1642	105	27	vacuum	vacuum	NOUN
asir-1642	105	28	without	without	ADP
asir-1642	105	29	dissipation	dissipation	NOUN
asir-1642	105	30	.	.	PUNCT
asir-1642	106	1	this	this	DET
asir-1642	106	2	inner	inner	ADJ
asir-1642	106	3	-	-	PUNCT
asir-1642	106	4	motion	motion	NOUN
asir-1642	106	5	≡	≡	PROPN
asir-1642	106	6	work	work	VERB
asir-1642	106	7	w	w	PROPN
asir-1642	106	8	,	,	PUNCT
asir-1642	106	9	from	from	ADP
asir-1642	106	10	the	the	DET
asir-1642	106	11	wave	wave	NOUN
asir-1642	106	12	-	-	PUNCT
asir-1642	106	13	energy	energy	NOUN
asir-1642	106	14	-	-	PUNCT
asir-1642	106	15	pattern	pattern	NOUN
asir-1642	106	16	with	with	ADP
asir-1642	106	17	wavelengths	wavelength	NOUN
asir-1642	106	18	𝐧	𝐧	ADV
asir-1642	106	19	,	,	PUNCT
asir-1642	106	20	is	be	AUX
asir-1642	106	21	created	create	VERB
asir-1642	106	22	from	from	ADP
asir-1642	106	23	all	all	DET
asir-1642	106	24			PROPN
asir-1642	106	25	points	point	NOUN
asir-1642	106	26	of	of	ADP
asir-1642	106	27	the	the	DET
asir-1642	106	28	periodic	periodic	ADJ
asir-1642	106	29	oscillation	oscillation	NOUN
asir-1642	106	30	in	in	ADP
asir-1642	106	31	any	any	DET
asir-1642	106	32	cave	cave	NOUN
asir-1642	106	33	r	r	NOUN
asir-1642	106	34	,	,	PUNCT
asir-1642	106	35	and	and	CCONJ
asir-1642	106	36	is	be	AUX
asir-1642	106	37	stored	store	VERB
asir-1642	106	38	in	in	ADP
asir-1642	106	39	the	the	DET
asir-1642	106	40	n	n	NOUN
asir-1642	106	41	lobes	lobe	NOUN
asir-1642	106	42	as	as	ADP
asir-1642	106	43	motion	motion	NOUN
asir-1642	106	44	.	.	PUNCT
asir-1642	107	1	this	this	DET
asir-1642	107	2	motion	motion	NOUN
asir-1642	107	3	is	be	AUX
asir-1642	107	4	conserved	conserve	VERB
asir-1642	107	5	and	and	CCONJ
asir-1642	107	6	is	be	AUX
asir-1642	107	7	transported	transport	VERB
asir-1642	107	8	through	through	ADP
asir-1642	107	9	vacuum	vacuum	NOUN
asir-1642	107	10	at	at	ADP
asir-1642	107	11	the	the	DET
asir-1642	107	12	speed	speed	NOUN
asir-1642	107	13	of	of	ADP
asir-1642	107	14	light	light	ADJ
asir-1642	107	15	c.	c.	NOUN
asir-1642	107	16	since	since	SCONJ
asir-1642	107	17	the	the	DET
asir-1642	107	18	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	107	19	applied	apply	VERB
asir-1642	107	20	science	science	NOUN
asir-1642	107	21	and	and	CCONJ
asir-1642	107	22	innovative	innovative	ADJ
asir-1642	107	23	research	research	NOUN
asir-1642	107	24	vol	vol	NOUN
asir-1642	107	25	.	.	PROPN
asir-1642	108	1	2	2	NUM
asir-1642	108	2	,	,	PUNCT
asir-1642	108	3	no	no	INTJ
asir-1642	108	4	.	.	NOUN
asir-1642	108	5	4	4	NUM
asir-1642	108	6	,	,	PUNCT
asir-1642	108	7	2018	2018	NUM
asir-1642	108	8	160	160	NUM
asir-1642	108	9	published	publish	VERB
asir-1642	108	10	by	by	ADP
asir-1642	108	11	scholink	scholink	PROPN
asir-1642	108	12	inc	inc	PROPN
asir-1642	108	13	.	.	PROPN
asir-1642	108	14	medium	medium	ADJ
asir-1642	108	15	-	-	PUNCT
asir-1642	108	16	field	field	NOUN
asir-1642	108	17	-	-	PUNCT
asir-1642	108	18	material	material	NOUN
asir-1642	108	19	-	-	PUNCT
asir-1642	108	20	fragment	fragment	NOUN
asir-1642	108	21	→	→	PUNCT
asir-1642	108	22	[	[	X
asir-1642	108	23	±	±	NUM
asir-1642	108	24	s²	s²	NOUN
asir-1642	108	25	]	]	PUNCT
asir-1642	109	1	=	=	PUNCT
asir-1642	109	2	[	[	X
asir-1642	109	3	mfmf	mfmf	X
asir-1642	109	4	]	]	X
asir-1642	109	5	≡	≡	PROPN
asir-1642	109	6	the	the	DET
asir-1642	109	7	chaos	chaos	NOUN
asir-1642	109	8	,	,	PUNCT
asir-1642	109	9	is	be	AUX
asir-1642	109	10	the	the	DET
asir-1642	109	11	base	base	NOUN
asir-1642	109	12	for	for	ADP
asir-1642	109	13	all	all	DET
asir-1642	109	14	motions	motion	NOUN
asir-1642	109	15	,	,	PUNCT
asir-1642	109	16	then	then	ADV
asir-1642	109	17	it	it	PRON
asir-1642	109	18	is	be	AUX
asir-1642	109	19	,	,	PUNCT
asir-1642	109	20	the	the	DET
asir-1642	109	21	motion	motion	NOUN
asir-1642	109	22	of	of	ADP
asir-1642	109	23	photons	photon	NOUN
asir-1642	109	24	:	:	PUNCT
asir-1642	109	25	all	all	DET
asir-1642	109	26	motions	motion	NOUN
asir-1642	109	27	create	create	VERB
asir-1642	109	28	work	work	NOUN
asir-1642	109	29	which	which	PRON
asir-1642	109	30	is	be	AUX
asir-1642	109	31	conservated	conservate	VERB
asir-1642	109	32	.	.	PUNCT
asir-1642	110	1	motion	motion	NOUN
asir-1642	110	2	presupposes	presuppose	VERB
asir-1642	110	3	velocity	velocity	NOUN
asir-1642	110	4	vector	vector	NOUN
asir-1642	110	5	�	�	PROPN
asir-1642	110	6	̅	̅	NOUN
asir-1642	110	7	�	�	PROPN
asir-1642	110	8	which	which	PRON
asir-1642	110	9	,	,	PUNCT
asir-1642	110	10	when	when	SCONJ
asir-1642	110	11	it	it	PRON
asir-1642	110	12	is	be	AUX
asir-1642	110	13	in	in	ADP
asir-1642	110	14	motion	motion	NOUN
asir-1642	110	15	collides	collide	NOUN
asir-1642	110	16	with	with	ADP
asir-1642	110	17	other	other	ADJ
asir-1642	110	18	velocity	velocity	NOUN
asir-1642	110	19	vectors	vector	NOUN
asir-1642	110	20	,	,	PUNCT
asir-1642	110	21	creating	create	VERB
asir-1642	110	22	a	a	DET
asir-1642	110	23	constant	constant	ADJ
asir-1642	110	24	work	work	NOUN
asir-1642	110	25	k.	k.	PROPN
asir-1642	110	26	motion	motion	NOUN
asir-1642	110	27	may	may	AUX
asir-1642	110	28	be	be	AUX
asir-1642	110	29	linear	linear	ADJ
asir-1642	110	30	or	or	CCONJ
asir-1642	110	31	rotational	rotational	ADJ
asir-1642	110	32	for	for	ADP
asir-1642	110	33	any	any	DET
asir-1642	110	34	displacement	displacement	NOUN
asir-1642	110	35	,	,	PUNCT
asir-1642	110	36	r	r	NOUN
asir-1642	110	37	,	,	PUNCT
asir-1642	110	38	so	so	ADV
asir-1642	110	39	exists	exist	VERB
asir-1642	110	40	in	in	ADP
asir-1642	110	41	vectors	vector	NOUN
asir-1642	110	42	the	the	DET
asir-1642	110	43	constant	constant	ADJ
asir-1642	110	44	-	-	PUNCT
asir-1642	110	45	work	work	NOUN
asir-1642	110	46	→	→	SYM
asir-1642	110	47	k	k	X
asir-1642	110	48	=	=	PUNCT
asir-1642	110	49	�	�	PROPN
asir-1642	110	50	̅	̅	NOUN
asir-1642	110	51	�	�	NOUN
asir-1642	110	52	x	x	SYM
asir-1642	110	53	�	�	PROPN
asir-1642	110	54	̅	̅	NOUN
asir-1642	110	55	�	�	PROPN
asir-1642	110	56	.	.	PUNCT
asir-1642	110	57	�	�	PROPN
asir-1642	110	58	̅	̅	NOUN
asir-1642	110	59	�	�	NOUN
asir-1642	110	60	=	=	SYM
asir-1642	110	61	v².r	v².r	PROPN
asir-1642	110	62	,	,	PUNCT
asir-1642	110	63	and	and	CCONJ
asir-1642	110	64	is	be	AUX
asir-1642	110	65	as	as	SCONJ
asir-1642	110	66	follows	follow	VERB
asir-1642	110	67	,	,	PUNCT
asir-1642	110	68	from	from	ADP
asir-1642	110	69	relation	relation	NOUN
asir-1642	110	70	nλ	nλ	NOUN
asir-1642	110	71	=	=	SYM
asir-1642	110	72	2r	2r	NUM
asir-1642	110	73	and	and	CCONJ
asir-1642	110	74	2r	2r	NUM
asir-1642	110	75	=	=	SYM
asir-1642	110	76	nv	nv	PROPN
asir-1642	110	77	/	/	SYM
asir-1642	110	78	f	f	PROPN
asir-1642	110	79	,	,	PUNCT
asir-1642	110	80	issues	issue	VERB
asir-1642	110	81	v	v	ADJ
asir-1642	110	82	=	=	NOUN
asir-1642	110	83	λf	λf	PROPN
asir-1642	110	84	→	→	SYM
asir-1642	110	85	�	�	NOUN
asir-1642	110	86	̅	̅	NOUN
asir-1642	110	87	�	�	PROPN
asir-1642	110	88	=	=	SYM
asir-1642	110	89	�	�	PROPN
asir-1642	110	90	̅	̅	NOUN
asir-1642	110	91	�	�	NOUN
asir-1642	110	92	=	=	SYM
asir-1642	110	93	λf	λf	PROPN
asir-1642	110	94	.	.	PUNCT
asir-1642	110	95	constant	constant	ADJ
asir-1642	110	96	-	-	PUNCT
asir-1642	110	97	work	work	NOUN
asir-1642	110	98	k	k	NOUN
asir-1642	110	99	=	=	SYM
asir-1642	110	100	v²	v²	PROPN
asir-1642	110	101	.	.	PUNCT
asir-1642	111	1	r	r	NOUN
asir-1642	111	2	=	=	PUNCT
asir-1642	111	3	(	(	PUNCT
asir-1642	111	4	wr)²	wr)²	PROPN
asir-1642	111	5	.	.	PUNCT
asir-1642	112	1	r	r	NOUN
asir-1642	112	2	=	=	PUNCT
asir-1642	112	3	[	[	PUNCT
asir-1642	112	4	𝟐𝛑	𝟐𝛑	NOUN
asir-1642	112	5	𝐓	𝐓	PROPN
asir-1642	112	6	r]².r	r]².r	PROPN
asir-1642	112	7	=	=	PUNCT
asir-1642	112	8	𝟒𝛑²	𝟒𝛑²	PRON
asir-1642	112	9	𝐫²	𝐫²	NOUN
asir-1642	112	10	𝐓²	𝐓²	VERB
asir-1642	112	11	.	.	PUNCT
asir-1642	113	1	r	r	NOUN
asir-1642	113	2	=	=	PUNCT
asir-1642	113	3	𝟒𝛑²	𝟒𝛑²	NOUN
asir-1642	113	4	𝐫	𝐫	PROPN
asir-1642	113	5	³	³	PROPN
asir-1642	113	6	𝐓²	𝐓²	PROPN
asir-1642	113	7	=	=	SYM
asir-1642	113	8	4π²	4π²	NUM
asir-1642	113	9	.	.	PUNCT
asir-1642	114	1	𝐫³	𝐫³	PROPN
asir-1642	114	2	𝐓²	𝐓²	PROPN
asir-1642	114	3	=	=	SYM
asir-1642	114	4	4π².r³.𝐟²𝐩	4π².r³.𝐟²𝐩	PROPN
asir-1642	114	5	→	→	SYM
asir-1642	114	6	which	which	PRON
asir-1642	114	7	are	be	AUX
asir-1642	114	8	the	the	DET
asir-1642	114	9	universal	universal	ADJ
asir-1642	114	10	kepler	kepler	NOUN
asir-1642	114	11	laws	law	NOUN
asir-1642	114	12	for	for	ADP
asir-1642	114	13	macrocosm	macrocosm	PROPN
asir-1642	114	14	.	.	PUNCT
asir-1642	115	1	i.e.	i.e.	X
asir-1642	115	2	,	,	PUNCT
asir-1642	115	3	photon	photon	NOUN
asir-1642	115	4	during	during	ADP
asir-1642	115	5	motion	motion	NOUN
asir-1642	115	6	in	in	ADP
asir-1642	115	7	[	[	X
asir-1642	115	8	mfmf	mfmf	NOUN
asir-1642	115	9	]	]	PUNCT
asir-1642	115	10	chaos	chaos	NOUN
asir-1642	115	11	collides	collide	VERB
asir-1642	115	12	with	with	ADP
asir-1642	115	13	other	other	ADJ
asir-1642	115	14	photons	photon	NOUN
asir-1642	115	15	,	,	PUNCT
asir-1642	115	16	by	by	ADP
asir-1642	115	17	means	mean	NOUN
asir-1642	115	18	of	of	ADP
asir-1642	115	19	cross	cross	NOUN
asir-1642	115	20	-	-	NOUN
asir-1642	115	21	product	product	NOUN
asir-1642	115	22	produces	produce	VERB
asir-1642	115	23	a	a	DET
asir-1642	115	24	constant	constant	ADJ
asir-1642	115	25	work	work	NOUN
asir-1642	115	26	which	which	PRON
asir-1642	115	27	is	be	AUX
asir-1642	115	28	stored	store	VERB
asir-1642	115	29	into	into	ADP
asir-1642	115	30	the	the	DET
asir-1642	115	31	only	only	ADJ
asir-1642	115	32	-	-	PUNCT
asir-1642	115	33	four	four	NUM
asir-1642	115	34	energy	energy	NOUN
asir-1642	115	35	-geometrical	-geometrical	ADJ
asir-1642	115	36	shapes	shape	NOUN
asir-1642	115	37	,	,	PUNCT
asir-1642	115	38	of	of	ADP
asir-1642	115	39	the	the	DET
asir-1642	115	40	motion	motion	NOUN
asir-1642	115	41	which	which	PRON
asir-1642	115	42	are	be	AUX
asir-1642	115	43	the	the	DET
asir-1642	115	44	conic	conic	ADJ
asir-1642	115	45	-	-	PUNCT
asir-1642	115	46	sections	section	NOUN
asir-1642	115	47	.	.	PUNCT
asir-1642	116	1	the	the	DET
asir-1642	116	2	interior	interior	ADJ
asir-1642	116	3	motion	motion	NOUN
asir-1642	116	4	is	be	AUX
asir-1642	116	5	kept	keep	VERB
asir-1642	116	6	in	in	ADP
asir-1642	116	7	its	its	PRON
asir-1642	116	8	wavelength	wavelength	NOUN
asir-1642	116	9	-	-	PUNCT
asir-1642	116	10	storage	storage	NOUN
asir-1642	116	11	2r	2r	NUM
asir-1642	116	12	=	=	SYM
asir-1642	116	13	n	n	PART
asir-1642	116	14	λ	λ	NOUN
asir-1642	116	15	,	,	PUNCT
asir-1642	116	16	and	and	CCONJ
asir-1642	116	17	the	the	DET
asir-1642	116	18	linear	linear	NOUN
asir-1642	116	19	outward	outward	ADJ
asir-1642	116	20	motion	motion	NOUN
asir-1642	116	21	is	be	AUX
asir-1642	116	22	continued	continue	VERB
asir-1642	116	23	by	by	ADP
asir-1642	116	24	the	the	DET
asir-1642	116	25	propagating	propagate	VERB
asir-1642	116	26	electromagnetic	electromagnetic	NOUN
asir-1642	116	27	-	-	PUNCT
asir-1642	116	28	wave	wave	NOUN
asir-1642	116	29	,	,	PUNCT
asir-1642	116	30	the	the	DET
asir-1642	116	31	conveyer	conveyer	NOUN
asir-1642	116	32	.	.	PUNCT
asir-1642	117	1	the	the	DET
asir-1642	117	2	mechanism	mechanism	NOUN
asir-1642	117	3	of	of	ADP
asir-1642	117	4	energy	energy	NOUN
asir-1642	117	5	-	-	PUNCT
asir-1642	117	6	transport	transport	NOUN
asir-1642	117	7	through	through	ADP
asir-1642	117	8	a	a	DET
asir-1642	117	9	medium	medium	NOUN
asir-1642	117	10	involves	involve	VERB
asir-1642	117	11	the	the	DET
asir-1642	117	12	absorption	absorption	NOUN
asir-1642	117	13	and	and	CCONJ
asir-1642	117	14	the	the	DET
asir-1642	117	15	reemission	reemission	NOUN
asir-1642	117	16	of	of	ADP
asir-1642	117	17	the	the	DET
asir-1642	117	18	wave	wave	NOUN
asir-1642	117	19	-	-	PUNCT
asir-1642	117	20	energy	energy	NOUN
asir-1642	117	21	by	by	ADP
asir-1642	117	22	the	the	DET
asir-1642	117	23	atoms	atom	NOUN
asir-1642	117	24	of	of	ADP
asir-1642	117	25	the	the	DET
asir-1642	117	26	material	material	NOUN
asir-1642	117	27	.	.	PUNCT
asir-1642	118	1	since	since	SCONJ
asir-1642	118	2	quanta	quanta	PROPN
asir-1642	118	3	of	of	ADP
asir-1642	118	4	energy	energy	NOUN
asir-1642	118	5	occupy	occupy	VERB
asir-1642	118	6	a	a	DET
asir-1642	118	7	finite	finite	ADJ
asir-1642	118	8	space	space	NOUN
asir-1642	118	9	λ	λ	NOUN
asir-1642	118	10	=	=	SYM
asir-1642	118	11	2r	2r	NUM
asir-1642	118	12	,	,	PUNCT
asir-1642	118	13	as	as	ADP
asir-1642	118	14	motion	motion	NOUN
asir-1642	118	15	,	,	PUNCT
asir-1642	118	16	then	then	ADV
asir-1642	118	17	an	an	DET
asir-1642	118	18	electromagnetic	electromagnetic	ADJ
asir-1642	118	19	wave	wave	NOUN
asir-1642	118	20	impinging	impinge	VERB
asir-1642	118	21	upon	upon	SCONJ
asir-1642	118	22	the	the	DET
asir-1642	118	23	atoms	atom	NOUN
asir-1642	118	24	of	of	ADP
asir-1642	118	25	a	a	DET
asir-1642	118	26	material	material	NOUN
asir-1642	118	27	,	,	PUNCT
asir-1642	118	28	its	its	PRON
asir-1642	118	29	energy	energy	NOUN
asir-1642	118	30	is	be	AUX
asir-1642	118	31	absorbed	absorb	VERB
asir-1642	118	32	by	by	ADP
asir-1642	118	33	the	the	DET
asir-1642	118	34	atoms	atom	NOUN
asir-1642	118	35	of	of	ADP
asir-1642	118	36	the	the	DET
asir-1642	118	37	material	material	NOUN
asir-1642	118	38	,	,	PUNCT
asir-1642	118	39	and	and	CCONJ
asir-1642	118	40	since	since	SCONJ
asir-1642	118	41	energy	energy	NOUN
asir-1642	118	42	≡	≡	PROPN
asir-1642	118	43	motion	motion	NOUN
asir-1642	118	44	then	then	ADV
asir-1642	118	45	occurs	occur	VERB
asir-1642	118	46	resonance	resonance	NOUN
asir-1642	118	47	,	,	PUNCT
asir-1642	118	48	and	and	CCONJ
asir-1642	118	49	electrons	electron	NOUN
asir-1642	118	50	within	within	ADP
asir-1642	118	51	the	the	DET
asir-1642	118	52	atoms	atom	NOUN
asir-1642	118	53	undergo	undergo	VERB
asir-1642	118	54	vibrations	vibration	NOUN
asir-1642	118	55	.	.	PUNCT
asir-1642	119	1	after	after	ADP
asir-1642	119	2	a	a	DET
asir-1642	119	3	short	short	ADJ
asir-1642	119	4	period	period	NOUN
asir-1642	119	5	of	of	ADP
asir-1642	119	6	vibrational	vibrational	NOUN
asir-1642	119	7	-	-	PUNCT
asir-1642	119	8	motion	motion	NOUN
asir-1642	119	9	,	,	PUNCT
asir-1642	119	10	the	the	DET
asir-1642	119	11	vibrating	vibrate	VERB
asir-1642	119	12	electrons	electron	NOUN
asir-1642	119	13	create	create	VERB
asir-1642	119	14	a	a	DET
asir-1642	119	15	new	new	ADJ
asir-1642	119	16	electromagnetic	electromagnetic	ADJ
asir-1642	119	17	wave	wave	NOUN
asir-1642	119	18	with	with	ADP
asir-1642	119	19	the	the	DET
asir-1642	119	20	same	same	ADJ
asir-1642	119	21	frequency	frequency	NOUN
asir-1642	119	22	as	as	ADP
asir-1642	119	23	the	the	DET
asir-1642	119	24	first	first	ADJ
asir-1642	119	25	one	one	NUM
asir-1642	119	26	and	and	CCONJ
asir-1642	119	27	thus	thus	ADV
asir-1642	119	28	delay	delay	VERB
asir-1642	119	29	motion	motion	NOUN
asir-1642	119	30	through	through	ADP
asir-1642	119	31	the	the	DET
asir-1642	119	32	medium	medium	NOUN
asir-1642	119	33	.	.	PUNCT
asir-1642	120	1	because	because	SCONJ
asir-1642	120	2	energy	energy	NOUN
asir-1642	120	3	is	be	AUX
asir-1642	120	4	related	relate	VERB
asir-1642	120	5	to	to	PART
asir-1642	120	6	wavelength	wavelength	VERB
asir-1642	120	7	λ	λ	PROPN
asir-1642	120	8	,	,	PUNCT
asir-1642	120	9	then	then	ADV
asir-1642	120	10	once	once	SCONJ
asir-1642	120	11	the	the	DET
asir-1642	120	12	energy	energy	NOUN
asir-1642	120	13	of	of	ADP
asir-1642	120	14	em	em	NOUN
asir-1642	120	15	-	-	NOUN
asir-1642	120	16	wave	wave	NOUN
asir-1642	120	17	is	be	AUX
asir-1642	120	18	reemitted	reemitte	VERB
asir-1642	120	19	then	then	ADV
asir-1642	120	20	it	it	PRON
asir-1642	120	21	travels	travel	VERB
asir-1642	120	22	through	through	ADP
asir-1642	120	23	a	a	DET
asir-1642	120	24	small	small	ADJ
asir-1642	120	25	region	region	NOUN
asir-1642	120	26	of	of	ADP
asir-1642	120	27	space	space	NOUN
asir-1642	120	28	between	between	ADP
asir-1642	120	29	atoms	atom	NOUN
asir-1642	120	30	and	and	CCONJ
asir-1642	120	31	once	once	SCONJ
asir-1642	120	32	it	it	PRON
asir-1642	120	33	reaches	reach	VERB
asir-1642	120	34	the	the	DET
asir-1642	120	35	next	next	ADJ
asir-1642	120	36	atom	atom	NOUN
asir-1642	120	37	the	the	DET
asir-1642	120	38	em	em	NOUN
asir-1642	120	39	-	-	NOUN
asir-1642	120	40	wave	wave	NOUN
asir-1642	120	41	is	be	AUX
asir-1642	120	42	absorbed	absorb	VERB
asir-1642	120	43	and	and	CCONJ
asir-1642	120	44	transformed	transform	VERB
asir-1642	120	45	into	into	ADP
asir-1642	120	46	electron	electron	NOUN
asir-1642	120	47	vibrations	vibration	NOUN
asir-1642	120	48	and	and	CCONJ
asir-1642	120	49	then	then	ADV
asir-1642	120	50	reemitted	reemitte	VERB
asir-1642	120	51	as	as	ADP
asir-1642	120	52	an	an	DET
asir-1642	120	53	electromagnetic	electromagnetic	ADJ
asir-1642	120	54	-	-	PUNCT
asir-1642	120	55	wave	wave	NOUN
asir-1642	120	56	.	.	PUNCT
asir-1642	121	1	the	the	DET
asir-1642	121	2	actual	actual	ADJ
asir-1642	121	3	speed	speed	NOUN
asir-1642	121	4	of	of	ADP
asir-1642	121	5	an	an	DET
asir-1642	121	6	electromagnetic	electromagnetic	ADJ
asir-1642	121	7	-	-	PUNCT
asir-1642	121	8	wave	wave	NOUN
asir-1642	121	9	through	through	ADP
asir-1642	121	10	a	a	DET
asir-1642	121	11	material	material	NOUN
asir-1642	121	12	-	-	PUNCT
asir-1642	121	13	medium	medium	NOUN
asir-1642	121	14	,	,	PUNCT
asir-1642	121	15	due	due	ADP
asir-1642	121	16	to	to	ADP
asir-1642	121	17	the	the	DET
asir-1642	121	18	absorption	absorption	NOUN
asir-1642	121	19	and	and	CCONJ
asir-1642	121	20	reemission	reemission	NOUN
asir-1642	121	21	-	-	PUNCT
asir-1642	121	22	process	process	NOUN
asir-1642	121	23	,	,	PUNCT
asir-1642	121	24	is	be	AUX
asir-1642	121	25	dependent	dependent	ADJ
asir-1642	121	26	upon	upon	SCONJ
asir-1642	121	27	the	the	DET
asir-1642	121	28	optical	optical	ADJ
asir-1642	121	29	-	-	PUNCT
asir-1642	121	30	density	density	NOUN
asir-1642	121	31	of	of	ADP
asir-1642	121	32	the	the	DET
asir-1642	121	33	medium	medium	NOUN
asir-1642	121	34	,	,	PUNCT
asir-1642	121	35	or	or	CCONJ
asir-1642	121	36	when	when	SCONJ
asir-1642	121	37	their	their	PRON
asir-1642	121	38	atoms	atom	NOUN
asir-1642	121	39	are	be	AUX
asir-1642	121	40	closely	closely	ADV
asir-1642	121	41	packed	pack	VERB
asir-1642	121	42	upon	upon	SCONJ
asir-1642	121	43	their	their	PRON
asir-1642	121	44	,	,	PUNCT
asir-1642	121	45	material	material	NOUN
asir-1642	121	46	-	-	PUNCT
asir-1642	121	47	density	density	NOUN
asir-1642	121	48	.	.	PUNCT
asir-1642	122	1	i.e.	i.e.	X
asir-1642	122	2	,	,	PUNCT
asir-1642	122	3	photon	photon	NOUN
asir-1642	122	4	is	be	AUX
asir-1642	122	5	an	an	DET
asir-1642	122	6	energy	energy	NOUN
asir-1642	122	7	-	-	PUNCT
asir-1642	122	8	store	store	NOUN
asir-1642	122	9	,	,	PUNCT
asir-1642	122	10	r	r	NOUN
asir-1642	122	11	,	,	PUNCT
asir-1642	122	12	in	in	ADP
asir-1642	122	13	a	a	DET
asir-1642	122	14	stationary	stationary	ADJ
asir-1642	122	15	-	-	PUNCT
asir-1642	122	16	wave	wave	NOUN
asir-1642	122	17	of	of	ADP
asir-1642	122	18	wavelength	wavelength	NOUN
asir-1642	122	19	n	n	PROPN
asir-1642	122	20	λ	λ	PROPN
asir-1642	122	21	=	=	SYM
asir-1642	122	22	2r	2r	NUM
asir-1642	122	23	,	,	PUNCT
asir-1642	122	24	consisted	consist	VERB
asir-1642	122	25	of	of	ADP
asir-1642	122	26	n	n	PRON
asir-1642	122	27	stationary	stationary	ADJ
asir-1642	122	28	lobes	lobe	NOUN
asir-1642	122	29	filled	fill	VERB
asir-1642	122	30	in	in	ADP
asir-1642	122	31	λ	λ	PROPN
asir-1642	122	32	with	with	ADP
asir-1642	122	33	inner	inner	ADJ
asir-1642	122	34	motion	motion	NOUN
asir-1642	122	35	the	the	DET
asir-1642	122	36	electromagnetic	electromagnetic	ADJ
asir-1642	122	37	-	-	PUNCT
asir-1642	122	38	displacement	displacement	NOUN
asir-1642	122	39	-	-	PUNCT
asir-1642	122	40	current	current	NOUN
asir-1642	122	41	,	,	PUNCT
asir-1642	122	42	while	while	SCONJ
asir-1642	122	43	is	be	AUX
asir-1642	122	44	outward	outward	ADV
asir-1642	122	45	propagating	propagate	VERB
asir-1642	122	46	with	with	ADP
asir-1642	122	47	light	light	ADJ
asir-1642	122	48	speed	speed	NOUN
asir-1642	122	49	as	as	ADP
asir-1642	122	50	energy	energy	NOUN
asir-1642	122	51	-	-	PUNCT
asir-1642	122	52	store	store	NOUN
asir-1642	122	53	λ	λ	NOUN
asir-1642	122	54	=	=	SYM
asir-1642	122	55	2r	2r	NUM
asir-1642	122	56	/	/	SYM
asir-1642	122	57	n	n	CCONJ
asir-1642	122	58	,	,	PUNCT
asir-1642	122	59	[	[	X
asir-1642	122	60	+	+	X
asir-1642	122	61	]	]	X
asir-1642	122	62	electric	electric	ADJ
asir-1642	122	63	-	-	PUNCT
asir-1642	122	64	field	field	NOUN
asir-1642	122	65	as	as	ADP
asir-1642	122	66	space	space	NOUN
asir-1642	122	67	,	,	PUNCT
asir-1642	122	68	[	[	X
asir-1642	122	69	-	-	PUNCT
asir-1642	122	70	]	]	X
asir-1642	122	71	magnetic	magnetic	ADJ
asir-1642	122	72	-	-	PUNCT
asir-1642	122	73	field	field	NOUN
asir-1642	122	74	as	as	ADP
asir-1642	122	75	anti	anti	ADJ
asir-1642	122	76	-	-	NOUN
asir-1642	122	77	space	space	NOUN
asir-1642	122	78	.	.	PUNCT
asir-1642	123	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-1642	123	2	applied	apply	VERB
asir-1642	123	3	science	science	NOUN
asir-1642	123	4	and	and	CCONJ
asir-1642	123	5	innovative	innovative	ADJ
asir-1642	123	6	research	research	NOUN
asir-1642	123	7	vol	vol	NOUN
asir-1642	123	8	.	.	PROPN
asir-1642	124	1	2	2	NUM
asir-1642	124	2	,	,	PUNCT
asir-1642	124	3	no	no	INTJ
asir-1642	124	4	.	.	NOUN
asir-1642	124	5	4	4	NUM
asir-1642	124	6	,	,	PUNCT
asir-1642	124	7	2018	2018	NUM
asir-1642	124	8	161	161	NUM
asir-1642	124	9	published	publish	VERB
asir-1642	124	10	by	by	ADP
asir-1642	124	11	scholink	scholink	PROPN
asir-1642	124	12	inc	inc	PROPN
asir-1642	124	13	.	.	PROPN
asir-1642	124	14	figure	figure	NOUN
asir-1642	124	15	2	2	NUM
asir-1642	124	16	.	.	PUNCT
asir-1642	125	1	the	the	DET
asir-1642	125	2	wave	wave	NOUN
asir-1642	125	3	[	[	X
asir-1642	125	4	𝐟	𝐟	X
asir-1642	125	5	=	=	PUNCT
asir-1642	125	6	(	(	PUNCT
asir-1642	125	7	e²	e²	PROPN
asir-1642	125	8	+	+	CCONJ
asir-1642	125	9	h²	h²	NOUN
asir-1642	125	10	)	)	PUNCT
asir-1642	125	11	]	]	PUNCT
asir-1642	125	12	particle	particle	NOUN
asir-1642	126	1	[	[	X
asir-1642	126	2	�	�	NOUN
asir-1642	126	3	̅	̅	NOUN
asir-1642	126	4	�	�	PROPN
asir-1642	126	5	=	=	SYM
asir-1642	126	6	�	�	PROPN
asir-1642	126	7	̅	̅	NOUN
asir-1642	126	8	�	�	NOUN
asir-1642	126	9	=	=	PUNCT
asir-1642	126	10	λf	λf	PROPN
asir-1642	126	11	]	]	X
asir-1642	126	12	→	→	PUNCT
asir-1642	126	13	duality	duality	NOUN
asir-1642	126	14	the	the	DET
asir-1642	126	15	outward	outward	ADJ
asir-1642	126	16	propagating	propagate	VERB
asir-1642	126	17	electromagnetic	electromagnetic	ADJ
asir-1642	126	18	-	-	PUNCT
asir-1642	126	19	wave	wave	NOUN
asir-1642	126	20	→	→	PUNCT
asir-1642	126	21	[	[	X
asir-1642	126	22	𝐟	𝐟	X
asir-1642	126	23	=	=	SYM
asir-1642	126	24	(	(	PUNCT
asir-1642	126	25	e²	e²	PROPN
asir-1642	126	26	+	+	CCONJ
asir-1642	126	27	h²	h²	PROPN
asir-1642	126	28	)	)	PUNCT
asir-1642	126	29	]	]	PUNCT
asir-1642	126	30	is	be	AUX
asir-1642	126	31	the	the	DET
asir-1642	126	32	conveyer	conveyer	NOUN
asir-1642	126	33	,	,	PUNCT
asir-1642	126	34	of	of	ADP
asir-1642	126	35	the	the	DET
asir-1642	126	36	stationary	stationary	ADJ
asir-1642	126	37	-	-	PUNCT
asir-1642	126	38	wave	wave	NOUN
asir-1642	126	39	particle	particle	NOUN
asir-1642	126	40	→	→	SYM
asir-1642	126	41	[	[	X
asir-1642	126	42	�	�	NOUN
asir-1642	126	43	̅	̅	NOUN
asir-1642	126	44	�	�	PROPN
asir-1642	126	45	=	=	SYM
asir-1642	126	46	�	�	PROPN
asir-1642	126	47	̅	̅	NOUN
asir-1642	126	48	�	�	NOUN
asir-1642	126	49	=	=	PUNCT
asir-1642	126	50	λf	λf	PROPN
asir-1642	126	51	=	=	SYM
asir-1642	126	52	2r.f	2r.f	NUM
asir-1642	126	53	]	]	PUNCT
asir-1642	126	54	≡	≡	PROPN
asir-1642	126	55	[	[	PUNCT
asir-1642	126	56	,	,	PUNCT
asir-1642	126	57	2	2	NUM
asir-1642	126	58	,	,	PUNCT
asir-1642	126	59	≡	≡	PROPN
asir-1642	126	60	n	n	PRON
asir-1642	126	61	lobes	lobe	NOUN
asir-1642	126	62	]	]	PUNCT
asir-1642	127	1	1	1	X
asir-1642	127	2	..	..	PUNCT
asir-1642	127	3	the	the	DET
asir-1642	127	4	experiment	experiment	NOUN
asir-1642	127	5	of	of	ADP
asir-1642	127	6	a	a	DET
asir-1642	127	7	-	-	PUNCT
asir-1642	127	8	compton	compton	NOUN
asir-1642	127	9	,	,	PUNCT
asir-1642	127	10	light	light	NOUN
asir-1642	127	11	behaves	behave	VERB
asir-1642	127	12	as	as	ADP
asir-1642	127	13	a	a	DET
asir-1642	127	14	wave	wave	NOUN
asir-1642	127	15	,	,	PUNCT
asir-1642	127	16	is	be	AUX
asir-1642	127	17	consisted	consist	VERB
asir-1642	127	18	on	on	ADP
asir-1642	127	19	an	an	DET
asir-1642	127	20	x	x	ADJ
asir-1642	127	21	-	-	NOUN
asir-1642	127	22	ray	ray	NOUN
asir-1642	127	23	photon	photon	NOUN
asir-1642	127	24	of	of	ADP
asir-1642	127	25	frequency	frequency	NOUN
asir-1642	127	26	which	which	PRON
asir-1642	127	27	collides	collide	VERB
asir-1642	127	28	with	with	ADP
asir-1642	127	29	a	a	DET
asir-1642	127	30	stationary	stationary	ADJ
asir-1642	127	31	electron	electron	NOUN
asir-1642	127	32	and	and	CCONJ
asir-1642	127	33	scattered	scatter	VERB
asir-1642	127	34	with	with	ADP
asir-1642	127	35	frequency	frequency	NOUN
asir-1642	127	36	2	2	NUM
asir-1642	127	37	<	<	X
asir-1642	127	38	which	which	PRON
asir-1642	127	39	is	be	AUX
asir-1642	127	40	energy	energy	NOUN
asir-1642	127	41	loss	loss	NOUN
asir-1642	127	42	.	.	PUNCT
asir-1642	128	1	2	2	NUM
asir-1642	128	2	..	..	PUNCT
asir-1642	128	3	the	the	DET
asir-1642	128	4	uncertainty	uncertainty	NOUN
asir-1642	128	5	principle	principle	NOUN
asir-1642	128	6	for	for	ADP
asir-1642	128	7	the	the	DET
asir-1642	128	8	wave	wave	NOUN
asir-1642	128	9	-	-	PUNCT
asir-1642	128	10	particle	particle	NOUN
asir-1642	128	11	accepts	accept	VERB
asir-1642	128	12	each	each	DET
asir-1642	128	13	particle	particle	NOUN
asir-1642	128	14	with	with	ADP
asir-1642	128	15	a	a	DET
asir-1642	128	16	definite	definite	ADJ
asir-1642	128	17	momentum	momentum	NOUN
asir-1642	128	18	can	can	AUX
asir-1642	128	19	be	be	AUX
asir-1642	128	20	described	describe	VERB
asir-1642	128	21	by	by	ADP
asir-1642	128	22	a	a	DET
asir-1642	128	23	wave	wave	NOUN
asir-1642	128	24	-	-	PUNCT
asir-1642	128	25	function	function	NOUN
asir-1642	128	26	,	,	PUNCT
asir-1642	128	27	which	which	PRON
asir-1642	128	28	created	create	VERB
asir-1642	128	29	the	the	DET
asir-1642	128	30	suspicious	suspicious	ADJ
asir-1642	128	31	of	of	ADP
asir-1642	128	32	finding	find	VERB
asir-1642	128	33	a	a	DET
asir-1642	128	34	particle	particle	NOUN
asir-1642	128	35	in	in	ADP
asir-1642	128	36	the	the	DET
asir-1642	128	37	biggest	big	ADJ
asir-1642	128	38	envelope	envelope	NOUN
asir-1642	128	39	of	of	ADP
asir-1642	128	40	the	the	DET
asir-1642	128	41	wave	wave	NOUN
asir-1642	128	42	.	.	PUNCT
asir-1642	129	1	instead	instead	ADV
asir-1642	129	2	of	of	ADP
asir-1642	129	3	it	it	PRON
asir-1642	129	4	momentum	momentum	NOUN
asir-1642	129	5	b	b	NOUN
asir-1642	129	6	,	,	PUNCT
asir-1642	129	7	rotates	rotate	VERB
asir-1642	129	8	into	into	ADP
asir-1642	129	9	the	the	DET
asir-1642	129	10	,	,	PUNCT
asir-1642	129	11	angular	angular	ADJ
asir-1642	129	12	-	-	PUNCT
asir-1642	129	13	velocity	velocity	NOUN
asir-1642	129	14	-	-	PUNCT
asir-1642	129	15	cone	cone	NOUN
asir-1642	129	16	.	.	PUNCT
asir-1642	130	1	3	3	X
asir-1642	130	2	..	..	PUNCT
asir-1642	130	3	the	the	DET
asir-1642	130	4	material	material	NOUN
asir-1642	130	5	wave	wave	NOUN
asir-1642	130	6	-	-	PUNCT
asir-1642	130	7	particle	particle	NOUN
asir-1642	130	8	duality	duality	NOUN
asir-1642	130	9	.	.	PUNCT
asir-1642	131	1	all	all	PRON
asir-1642	131	2	moving	move	VERB
asir-1642	131	3	energy	energy	NOUN
asir-1642	131	4	-	-	PUNCT
asir-1642	131	5	storages	storage	NOUN
asir-1642	131	6	are	be	AUX
asir-1642	131	7	standing	stand	VERB
asir-1642	131	8	-	-	PUNCT
asir-1642	131	9	waves	wave	NOUN
asir-1642	131	10	-	-	PUNCT
asir-1642	131	11	particles	particle	NOUN
asir-1642	131	12	as	as	ADP
asir-1642	131	13	all	all	DET
asir-1642	131	14	quantum	quantum	NOUN
asir-1642	131	15	-	-	NOUN
asir-1642	131	16	particles	particle	NOUN
asir-1642	131	17	,	,	PUNCT
asir-1642	131	18	and	and	CCONJ
asir-1642	131	19	the	the	DET
asir-1642	131	20	propagating	propagate	VERB
asir-1642	131	21	-	-	PUNCT
asir-1642	131	22	energy	energy	NOUN
asir-1642	131	23	as	as	ADP
asir-1642	131	24	electromagnetic	electromagnetic	ADJ
asir-1642	131	25	-	-	PUNCT
asir-1642	131	26	wave	wave	NOUN
asir-1642	131	27	is	be	AUX
asir-1642	131	28	the	the	DET
asir-1642	131	29	wave	wave	NOUN
asir-1642	131	30	and	and	CCONJ
asir-1642	131	31	is	be	AUX
asir-1642	131	32	their	their	PRON
asir-1642	131	33	conveyer	conveyer	NOUN
asir-1642	131	34	.	.	PUNCT
asir-1642	132	1	in	in	ADP
asir-1642	132	2	energy	energy	NOUN
asir-1642	132	3	-	-	PUNCT
asir-1642	132	4	storages	storage	NOUN
asir-1642	132	5	issues	issue	VERB
asir-1642	132	6	the	the	DET
asir-1642	132	7	stability	stability	NOUN
asir-1642	132	8	of	of	ADP
asir-1642	132	9	equilibrium	equilibrium	NOUN
asir-1642	132	10	as	as	ADP
asir-1642	132	11	this	this	PRON
asir-1642	132	12	in	in	ADP
asir-1642	132	13	energy	energy	NOUN
asir-1642	132	14	-	-	PUNCT
asir-1642	132	15	rims	rim	NOUN
asir-1642	132	16	=	=	NOUN
asir-1642	132	17	orbitals	orbital	NOUN
asir-1642	132	18	,	,	PUNCT
asir-1642	132	19	also	also	ADV
asir-1642	132	20	.	.	PUNCT
asir-1642	133	1	a	a	DET
asir-1642	133	2	..	..	PUNCT
asir-1642	133	3	compton	compton	PROPN
asir-1642	133	4	effect	effect	NOUN
asir-1642	133	5	:	:	PUNCT
asir-1642	133	6	the	the	DET
asir-1642	133	7	moving	move	VERB
asir-1642	133	8	stores	store	NOUN
asir-1642	133	9	which	which	PRON
asir-1642	133	10	are	be	AUX
asir-1642	133	11	the	the	DET
asir-1642	133	12	em	em	NOUN
asir-1642	133	13	-	-	PUNCT
asir-1642	133	14	waves	wave	NOUN
asir-1642	133	15	are	be	AUX
asir-1642	133	16	consisted	consist	VERB
asir-1642	133	17	of	of	ADP
asir-1642	133	18	three	three	NUM
asir-1642	133	19	parts	part	NOUN
asir-1642	133	20	,	,	PUNCT
asir-1642	133	21	1	1	NUM
asir-1642	133	22	..	..	PUNCT
asir-1642	133	23	the	the	DET
asir-1642	133	24	energy	energy	NOUN
asir-1642	133	25	-	-	PUNCT
asir-1642	133	26	store	store	NOUN
asir-1642	133	27	r	r	NOUN
asir-1642	133	28	=	=	PUNCT
asir-1642	133	29	n.	n.	NOUN
asir-1642	133	30	𝝀	𝝀	X
asir-1642	133	31	𝟐	𝟐	NUM
asir-1642	133	32	,	,	PUNCT
asir-1642	133	33	is	be	AUX
asir-1642	133	34	consisted	consist	VERB
asir-1642	133	35	of	of	ADP
asir-1642	133	36	,	,	PUNCT
asir-1642	133	37	n	n	CCONJ
asir-1642	133	38	,	,	PUNCT
asir-1642	133	39	energy	energy	NOUN
asir-1642	133	40	lobes	lobe	NOUN
asir-1642	133	41	in	in	ADP
asir-1642	133	42	the	the	DET
asir-1642	133	43	stationary	stationary	ADJ
asir-1642	133	44	-	-	PUNCT
asir-1642	133	45	wave	wave	NOUN
asir-1642	133	46	of	of	ADP
asir-1642	133	47	cave	cave	NOUN
asir-1642	133	48	,	,	PUNCT
asir-1642	133	49	r	r	NOUN
asir-1642	133	50	,	,	PUNCT
asir-1642	133	51	as	as	SCONJ
asir-1642	133	52	the	the	DET
asir-1642	133	53	frequency	frequency	NOUN
asir-1642	133	54	𝐟𝐧	𝐟𝐧	ADP
asir-1642	133	55	𝐧	𝐧	ADJ
asir-1642	133	56	𝟖𝒓	𝟖𝒓	NOUN
asir-1642	134	1	[	[	X
asir-1642	134	2	1	1	NUM
asir-1642	134	3	+	+	NUM
asir-1642	134	4	√𝟓	√𝟓	NOUN
asir-1642	134	5	]	]	PUNCT
asir-1642	134	6	,	,	PUNCT
asir-1642	134	7	and	and	CCONJ
asir-1642	134	8	consists	consist	VERB
asir-1642	134	9	the	the	DET
asir-1642	134	10	massive	massive	ADJ
asir-1642	134	11	-	-	PUNCT
asir-1642	134	12	particle	particle	NOUN
asir-1642	134	13	-	-	PUNCT
asir-1642	134	14	energy	energy	NOUN
asir-1642	134	15	-	-	PUNCT
asir-1642	134	16	part	part	NOUN
asir-1642	134	17	of	of	ADP
asir-1642	134	18	photon	photon	NOUN
asir-1642	134	19	,	,	PUNCT
asir-1642	134	20	p.	p.	NOUN
asir-1642	134	21	2	2	NUM
asir-1642	134	22	..	..	PUNCT
asir-1642	134	23	the	the	DET
asir-1642	134	24	vertical	vertical	ADJ
asir-1642	134	25	electric	electric	NOUN
asir-1642	134	26	-	-	PUNCT
asir-1642	134	27	field	field	NOUN
asir-1642	134	28	e	e	NOUN
asir-1642	134	29	is	be	AUX
asir-1642	134	30	perpendicular	perpendicular	ADJ
asir-1642	134	31	to	to	ADP
asir-1642	134	32	r	r	NOUN
asir-1642	134	33	,	,	PUNCT
asir-1642	134	34	axis	axis	NOUN
asir-1642	134	35	and	and	CCONJ
asir-1642	134	36	consists	consist	VERB
asir-1642	134	37	the	the	DET
asir-1642	134	38	space	space	NOUN
asir-1642	134	39	-	-	PUNCT
asir-1642	134	40	wave	wave	NOUN
asir-1642	134	41	-	-	PUNCT
asir-1642	134	42	energy	energy	NOUN
asir-1642	134	43	-	-	PUNCT
asir-1642	134	44	part	part	NOUN
asir-1642	134	45	of	of	ADP
asir-1642	134	46	photon	photon	NOUN
asir-1642	134	47	.	.	PUNCT
asir-1642	135	1	3	3	X
asir-1642	135	2	..	..	PUNCT
asir-1642	135	3	the	the	DET
asir-1642	135	4	horizontal	horizontal	ADJ
asir-1642	135	5	magnetic	magnetic	ADJ
asir-1642	135	6	-	-	PUNCT
asir-1642	135	7	field	field	NOUN
asir-1642	135	8	p	p	NOUN
asir-1642	135	9	perpendicular	perpendicular	NOUN
asir-1642	135	10	to	to	ADP
asir-1642	135	11	r	r	NOUN
asir-1642	135	12	axis	axis	NOUN
asir-1642	135	13	and	and	CCONJ
asir-1642	135	14	field	field	NOUN
asir-1642	135	15	e	e	NOUN
asir-1642	135	16	,	,	PUNCT
asir-1642	135	17	both	both	PRON
asir-1642	135	18	being	be	AUX
asir-1642	135	19	always	always	ADV
asir-1642	135	20	in	in	ADP
asir-1642	135	21	phase	phase	NOUN
asir-1642	135	22	and	and	CCONJ
asir-1642	135	23	consists	consist	VERB
asir-1642	135	24	the	the	DET
asir-1642	135	25	anti	anti	ADJ
asir-1642	135	26	-	-	ADJ
asir-1642	135	27	space	space	ADJ
asir-1642	135	28	-	-	PUNCT
asir-1642	135	29	wave	wave	NOUN
asir-1642	135	30	-	-	PUNCT
asir-1642	135	31	energy	energy	NOUN
asir-1642	135	32	-	-	PUNCT
asir-1642	135	33	part	part	NOUN
asir-1642	135	34	of	of	ADP
asir-1642	135	35	photon	photon	NOUN
asir-1642	135	36	.	.	PUNCT
asir-1642	136	1	b	b	X
asir-1642	136	2	..	..	PUNCT
asir-1642	136	3	wave	wave	NOUN
asir-1642	136	4	-	-	PUNCT
asir-1642	136	5	particle	particle	NOUN
asir-1642	136	6	duality	duality	NOUN
asir-1642	136	7	and	and	CCONJ
asir-1642	136	8	uncertainty	uncertainty	NOUN
asir-1642	136	9	principles	principle	NOUN
asir-1642	136	10	:	:	PUNCT
asir-1642	136	11	all	all	DET
asir-1642	136	12	quantum	quantum	ADJ
asir-1642	136	13	objects	object	NOUN
asir-1642	136	14	and	and	CCONJ
asir-1642	136	15	photon	photon	NOUN
asir-1642	136	16	,	,	PUNCT
asir-1642	136	17	exhibit	exhibit	VERB
asir-1642	136	18	wave	wave	NOUN
asir-1642	136	19	-	-	PUNCT
asir-1642	136	20	like	like	ADJ
asir-1642	136	21	and	and	CCONJ
asir-1642	136	22	particle	particle	NOUN
asir-1642	136	23	-	-	PUNCT
asir-1642	136	24	like	like	ADJ
asir-1642	136	25	properties	property	NOUN
asir-1642	136	26	such	such	ADJ
asir-1642	136	27	as	as	ADP
asir-1642	136	28	diffraction	diffraction	NOUN
asir-1642	136	29	and	and	CCONJ
asir-1642	136	30	interference	interference	NOUN
asir-1642	136	31	on	on	ADP
asir-1642	136	32	the	the	DET
asir-1642	136	33	length	length	NOUN
asir-1642	136	34	scale	scale	NOUN
asir-1642	136	35	of	of	ADP
asir-1642	136	36	their	their	PRON
asir-1642	136	37	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	136	38	applied	apply	VERB
asir-1642	136	39	science	science	NOUN
asir-1642	136	40	and	and	CCONJ
asir-1642	136	41	innovative	innovative	ADJ
asir-1642	136	42	research	research	NOUN
asir-1642	136	43	vol	vol	NOUN
asir-1642	136	44	.	.	PROPN
asir-1642	137	1	2	2	NUM
asir-1642	137	2	,	,	PUNCT
asir-1642	137	3	no	no	INTJ
asir-1642	137	4	.	.	NOUN
asir-1642	137	5	4	4	NUM
asir-1642	137	6	,	,	PUNCT
asir-1642	137	7	2018	2018	NUM
asir-1642	137	8	162	162	NUM
asir-1642	137	9	published	publish	VERB
asir-1642	137	10	by	by	ADP
asir-1642	137	11	scholink	scholink	PROPN
asir-1642	137	12	inc	inc	PROPN
asir-1642	137	13	.	.	PROPN
asir-1642	137	14	wavelength	wavelength	NOUN
asir-1642	137	15	.	.	PUNCT
asir-1642	138	1	experiments	experiment	NOUN
asir-1642	138	2	confirm	confirm	VERB
asir-1642	138	3	that	that	SCONJ
asir-1642	138	4	the	the	DET
asir-1642	138	5	photon	photon	NOUN
asir-1642	138	6	is	be	AUX
asir-1642	138	7	not	not	PART
asir-1642	138	8	a	a	DET
asir-1642	138	9	short	short	ADJ
asir-1642	138	10	pulse	pulse	NOUN
asir-1642	138	11	of	of	ADP
asir-1642	138	12	electromagnetic	electromagnetic	ADJ
asir-1642	138	13	radiation	radiation	NOUN
asir-1642	138	14	because	because	SCONJ
asir-1642	138	15	it	it	PRON
asir-1642	138	16	does	do	AUX
asir-1642	138	17	not	not	PART
asir-1642	138	18	spread	spread	VERB
asir-1642	138	19	-	-	PUNCT
asir-1642	138	20	out	out	NOUN
asir-1642	138	21	as	as	SCONJ
asir-1642	138	22	it	it	PRON
asir-1642	138	23	propagates	propagate	VERB
asir-1642	138	24	,	,	PUNCT
asir-1642	138	25	nor	nor	CCONJ
asir-1642	138	26	does	do	AUX
asir-1642	138	27	it	it	PRON
asir-1642	138	28	divide	divide	VERB
asir-1642	138	29	when	when	SCONJ
asir-1642	138	30	it	it	PRON
asir-1642	138	31	encounters	encounter	VERB
asir-1642	138	32	a	a	DET
asir-1642	138	33	beam	beam	NOUN
asir-1642	138	34	splitter	splitter	NOUN
asir-1642	138	35	.	.	PUNCT
asir-1642	139	1	because	because	SCONJ
asir-1642	139	2	photon	photon	NOUN
asir-1642	139	3	is	be	AUX
asir-1642	139	4	a	a	DET
asir-1642	139	5	material	material	NOUN
asir-1642	139	6	-	-	PUNCT
asir-1642	139	7	point	point	NOUN
asir-1642	139	8	is	be	AUX
asir-1642	139	9	absorbed	absorb	VERB
asir-1642	139	10	or	or	CCONJ
asir-1642	139	11	emitted	emit	VERB
asir-1642	139	12	as	as	ADP
asir-1642	139	13	a	a	DET
asir-1642	139	14	whole	whole	NOUN
asir-1642	139	15	by	by	ADP
asir-1642	139	16	arbitrary	arbitrary	ADJ
asir-1642	139	17	smaller	small	ADJ
asir-1642	139	18	than	than	ADP
asir-1642	139	19	its	its	PRON
asir-1642	139	20	wavelength	wavelength	NOUN
asir-1642	139	21	or	or	CCONJ
asir-1642	139	22	even	even	ADV
asir-1642	139	23	point	point	ADV
asir-1642	139	24	-	-	PUNCT
asir-1642	139	25	like	like	ADJ
asir-1642	139	26	electrons	electron	NOUN
asir-1642	139	27	or	or	CCONJ
asir-1642	139	28	small	small	ADJ
asir-1642	139	29	-	-	PUNCT
asir-1642	139	30	systems	system	NOUN
asir-1642	139	31	.	.	PUNCT
asir-1642	140	1	it	it	PRON
asir-1642	140	2	was	be	AUX
asir-1642	140	3	shown	show	VERB
asir-1642	140	4	[	[	PUNCT
asir-1642	140	5	66	66	NUM
asir-1642	140	6	]	]	PUNCT
asir-1642	140	7	that	that	DET
asir-1642	140	8	photon	photon	NOUN
asir-1642	140	9	which	which	PRON
asir-1642	140	10	is	be	AUX
asir-1642	140	11	an	an	DET
asir-1642	140	12	energy	energy	NOUN
asir-1642	140	13	-	-	PUNCT
asir-1642	140	14	storage	storage	NOUN
asir-1642	140	15	-	-	PUNCT
asir-1642	140	16	monad	monad	PROPN
asir-1642	140	17	is	be	AUX
asir-1642	140	18	consisted	consist	VERB
asir-1642	140	19	of	of	ADP
asir-1642	140	20	two	two	NUM
asir-1642	140	21	-	-	PUNCT
asir-1642	140	22	real	real	ADJ
asir-1642	140	23	-	-	PUNCT
asir-1642	140	24	constituents	constituent	NOUN
asir-1642	140	25	,	,	PUNCT
asir-1642	140	26	and	and	CCONJ
asir-1642	140	27	one	one	NUM
asir-1642	140	28	energy	energy	NOUN
asir-1642	140	29	.	.	PUNCT
asir-1642	141	1	that	that	SCONJ
asir-1642	141	2	imaginary	imaginary	ADJ
asir-1642	141	3	-	-	PUNCT
asir-1642	141	4	constituent	constituent	NOUN
asir-1642	141	5	which	which	PRON
asir-1642	141	6	creates	create	VERB
asir-1642	141	7	the	the	DET
asir-1642	141	8	electromagnetic	electromagnetic	ADJ
asir-1642	141	9	field	field	NOUN
asir-1642	141	10	,	,	PUNCT
asir-1642	141	11	is	be	AUX
asir-1642	141	12	resulting	result	VERB
asir-1642	141	13	from	from	ADP
asir-1642	141	14	the	the	DET
asir-1642	141	15	local	local	ADJ
asir-1642	141	16	and	and	CCONJ
asir-1642	141	17	energy	energy	NOUN
asir-1642	141	18	-	-	PUNCT
asir-1642	141	19	cave	cave	NOUN
asir-1642	141	20	,	,	PUNCT
asir-1642	141	21	by	by	ADP
asir-1642	141	22	launching	launch	VERB
asir-1642	141	23	the	the	DET
asir-1642	141	24	inner	inner	ADJ
asir-1642	141	25	-	-	PUNCT
asir-1642	141	26	electromagnetic	electromagnetic	NOUN
asir-1642	141	27	-	-	PUNCT
asir-1642	141	28	wave	wave	NOUN
asir-1642	141	29	of	of	ADP
asir-1642	141	30	monad	monad	PROPN
asir-1642	141	31	λ	λ	PROPN
asir-1642	141	32	=	=	SYM
asir-1642	141	33	2r	2r	NUM
asir-1642	141	34	/n	/n	PUNCT
asir-1642	141	35	outward	outward	VERB
asir-1642	141	36	the	the	DET
asir-1642	141	37	λ	λ	NOUN
asir-1642	141	38	.	.	PROPN
asir-1642	142	1	c	c	X
asir-1642	142	2	..	..	PUNCT
asir-1642	142	3	material	material	ADJ
asir-1642	142	4	wave	wave	NOUN
asir-1642	142	5	-	-	PUNCT
asir-1642	142	6	particle	particle	NOUN
asir-1642	142	7	duality	duality	NOUN
asir-1642	142	8	:	:	PUNCT
asir-1642	142	9	the	the	DET
asir-1642	142	10	recoiled	recoil	VERB
asir-1642	142	11	-	-	PUNCT
asir-1642	142	12	electron	electron	NOUN
asir-1642	142	13	position	position	NOUN
asir-1642	142	14	can	can	AUX
asir-1642	142	15	be	be	AUX
asir-1642	142	16	resolved	resolve	VERB
asir-1642	142	17	to	to	ADP
asir-1642	142	18	the	the	DET
asir-1642	142	19	new	new	ADJ
asir-1642	142	20	position	position	NOUN
asir-1642	142	21	as	as	ADV
asir-1642	142	22	well	well	ADV
asir-1642	142	23	as	as	ADP
asir-1642	142	24	the	the	DET
asir-1642	142	25	scattered	scatter	VERB
asir-1642	142	26	photon	photon	NOUN
asir-1642	142	27	of	of	ADP
asir-1642	142	28	the	the	DET
asir-1642	142	29	energy	energy	NOUN
asir-1642	142	30	-	-	PUNCT
asir-1642	142	31	storage	storage	NOUN
asir-1642	142	32	by	by	ADP
asir-1642	142	33	its	its	PRON
asir-1642	142	34	new	new	ADJ
asir-1642	142	35	frequency	frequency	NOUN
asir-1642	142	36	.	.	PUNCT
asir-1642	143	1	momentum	momentum	NOUN
asir-1642	143	2	equal	equal	ADJ
asir-1642	143	3	to	to	PART
asir-1642	143	4	spin	spin	VERB
asir-1642	143	5	is	be	AUX
asir-1642	143	6	not	not	PART
asir-1642	143	7	changed	change	VERB
asir-1642	143	8	because	because	SCONJ
asir-1642	143	9	issues	issue	VERB
asir-1642	143	10	the	the	DET
asir-1642	143	11	law	law	NOUN
asir-1642	143	12	of	of	ADP
asir-1642	143	13	energy	energy	NOUN
asir-1642	143	14	-	-	PUNCT
asir-1642	143	15	conservation	conservation	NOUN
asir-1642	143	16	.	.	PUNCT
asir-1642	144	1	electromagnetic	electromagnetic	ADJ
asir-1642	144	2	energy	energy	NOUN
asir-1642	144	3	is	be	AUX
asir-1642	144	4	supplemented	supplement	VERB
asir-1642	144	5	by	by	ADP
asir-1642	144	6	the	the	DET
asir-1642	144	7	incoming	incoming	ADJ
asir-1642	144	8	wavelength	wavelength	NOUN
asir-1642	144	9	λ	λ	X
asir-1642	144	10	=	=	SYM
asir-1642	144	11	2r	2r	NUM
asir-1642	144	12	/	/	SYM
asir-1642	144	13	n	n	CCONJ
asir-1642	144	14	,	,	PUNCT
asir-1642	144	15	or	or	CCONJ
asir-1642	144	16	by	by	ADP
asir-1642	144	17	angle	angle	NOUN
asir-1642	144	18	φ	φ	PROPN
asir-1642	144	19	.	.	PUNCT
asir-1642	145	1	the	the	DET
asir-1642	145	2	storage	storage	NOUN
asir-1642	145	3	r	r	NOUN
asir-1642	145	4	,	,	PUNCT
asir-1642	145	5	which	which	PRON
asir-1642	145	6	is	be	AUX
asir-1642	145	7	the	the	DET
asir-1642	145	8	particle	particle	NOUN
asir-1642	145	9	photon	photon	NOUN
asir-1642	145	10	,	,	PUNCT
asir-1642	145	11	modifies	modify	VERB
asir-1642	145	12	the	the	DET
asir-1642	145	13	intrinsic	intrinsic	ADJ
asir-1642	145	14	-	-	PUNCT
asir-1642	145	15	radiation	radiation	NOUN
asir-1642	145	16	and	and	CCONJ
asir-1642	145	17	avoids	avoid	VERB
asir-1642	145	18	spontaneous	spontaneous	ADJ
asir-1642	145	19	emission	emission	NOUN
asir-1642	145	20	.	.	PUNCT
asir-1642	146	1	a	a	DET
asir-1642	146	2	photon	photon	NOUN
asir-1642	146	3	with	with	ADP
asir-1642	146	4	e	e	PROPN
asir-1642	146	5			PROPN
asir-1642	146	6	b	b	PROPN
asir-1642	146	7	wave	wave	NOUN
asir-1642	146	8	when	when	SCONJ
asir-1642	146	9	entering	enter	VERB
asir-1642	146	10	a	a	DET
asir-1642	146	11	transparent	transparent	ADJ
asir-1642	146	12	material	material	NOUN
asir-1642	146	13	,	,	PUNCT
asir-1642	146	14	photon	photon	NOUN
asir-1642	146	15	is	be	AUX
asir-1642	146	16	absorbed	absorb	VERB
asir-1642	146	17	by	by	ADP
asir-1642	146	18	an	an	DET
asir-1642	146	19	atom	atom	NOUN
asir-1642	146	20	and	and	CCONJ
asir-1642	146	21	the	the	DET
asir-1642	146	22	reemitted	reemitte	VERB
asir-1642	146	23	,	,	PUNCT
asir-1642	146	24	because	because	SCONJ
asir-1642	146	25	wave	wave	NOUN
asir-1642	146	26	vector	vector	NOUN
asir-1642	146	27	would	would	AUX
asir-1642	146	28	not	not	PART
asir-1642	146	29	be	be	AUX
asir-1642	146	30	preserved	preserve	VERB
asir-1642	146	31	,	,	PUNCT
asir-1642	146	32	by	by	ADP
asir-1642	146	33	the	the	DET
asir-1642	146	34	material	material	NOUN
asir-1642	146	35	and	and	CCONJ
asir-1642	146	36	there	there	PRON
asir-1642	146	37	would	would	AUX
asir-1642	146	38	be	be	AUX
asir-1642	146	39	scattering	scatter	VERB
asir-1642	146	40	.	.	PUNCT
asir-1642	147	1	light	light	ADJ
asir-1642	147	2	storage	storage	NOUN
asir-1642	147	3	,	,	PUNCT
asir-1642	147	4	r	r	PROPN
asir-1642	147	5	≡	≡	PROPN
asir-1642	147	6	eh	eh	NOUN
asir-1642	147	7	,	,	PUNCT
asir-1642	147	8	using	use	VERB
asir-1642	147	9	electromagnetically	electromagnetically	ADV
asir-1642	147	10	-	-	PUNCT
asir-1642	147	11	induced	induce	VERB
asir-1642	147	12	transparency	transparency	NOUN
asir-1642	147	13	,	,	PUNCT
asir-1642	147	14	interaction	interaction	NOUN
asir-1642	147	15	between	between	ADP
asir-1642	147	16	photon	photon	NOUN
asir-1642	147	17	and	and	CCONJ
asir-1642	147	18	an	an	DET
asir-1642	147	19	ensemble	ensemble	NOUN
asir-1642	147	20	of	of	ADP
asir-1642	147	21	atoms	atom	NOUN
asir-1642	147	22	is	be	AUX
asir-1642	147	23	tuned	tune	VERB
asir-1642	147	24	,	,	PUNCT
asir-1642	147	25	to	to	ADP
asir-1642	147	26	the	the	DET
asir-1642	147	27	group	group	NOUN
asir-1642	147	28	velocity	velocity	NOUN
asir-1642	147	29	of	of	ADP
asir-1642	147	30	the	the	DET
asir-1642	147	31	photon	photon	NOUN
asir-1642	147	32	and	and	CCONJ
asir-1642	147	33	e	e	NOUN
asir-1642	147	34	-	-	NOUN
asir-1642	147	35	m	m	NOUN
asir-1642	147	36	wave	wave	NOUN
asir-1642	147	37	is	be	AUX
asir-1642	147	38	reduced	reduce	VERB
asir-1642	147	39	to	to	ADP
asir-1642	147	40	zero	zero	NUM
asir-1642	147	41	and	and	CCONJ
asir-1642	147	42	to	to	ADP
asir-1642	147	43	the	the	DET
asir-1642	147	44	remaining	remain	VERB
asir-1642	147	45	eb	eb	PROPN
asir-1642	147	46	-	-	PUNCT
asir-1642	147	47	storage	storage	NOUN
asir-1642	147	48	-	-	PUNCT
asir-1642	147	49	field	field	NOUN
asir-1642	147	50	-	-	PUNCT
asir-1642	147	51	particle	particle	NOUN
asir-1642	147	52	within	within	ADP
asir-1642	147	53	the	the	DET
asir-1642	147	54	interaction	interaction	NOUN
asir-1642	147	55	zone	zone	NOUN
asir-1642	147	56	.	.	PUNCT
asir-1642	148	1	the	the	DET
asir-1642	148	2	excitation	excitation	NOUN
asir-1642	148	3	is	be	AUX
asir-1642	148	4	not	not	PART
asir-1642	148	5	purely	purely	ADV
asir-1642	148	6	photonic	photonic	ADJ
asir-1642	148	7	,	,	PUNCT
asir-1642	148	8	but	but	CCONJ
asir-1642	148	9	instead	instead	ADV
asir-1642	148	10	has	have	AUX
asir-1642	148	11	been	be	AUX
asir-1642	148	12	mapped	map	VERB
asir-1642	148	13	smoothly	smoothly	ADV
asir-1642	148	14	from	from	ADP
asir-1642	148	15	a	a	DET
asir-1642	148	16	single	single	ADJ
asir-1642	148	17	photon	photon	NOUN
asir-1642	148	18	to	to	ADP
asir-1642	148	19	an	an	DET
asir-1642	148	20	ensemble	ensemble	NOUN
asir-1642	148	21	of	of	ADP
asir-1642	148	22	eb	eb	PROPN
asir-1642	148	23	-	-	PUNCT
asir-1642	148	24	storage	storage	NOUN
asir-1642	148	25	atoms	atom	NOUN
asir-1642	148	26	.	.	PUNCT
asir-1642	149	1	photon	photon	NOUN
asir-1642	149	2	is	be	AUX
asir-1642	149	3	regenerated	regenerate	VERB
asir-1642	149	4	by	by	ADP
asir-1642	149	5	its	its	PRON
asir-1642	149	6	intrinsic	intrinsic	ADJ
asir-1642	149	7	electromagnetic	electromagnetic	ADJ
asir-1642	149	8	wave	wave	NOUN
asir-1642	149	9	e	e	PROPN
asir-1642	149	10			NOUN
asir-1642	149	11	b	b	PROPN
asir-1642	149	12	and	and	CCONJ
asir-1642	149	13	is	be	AUX
asir-1642	149	14	indistinguishable	indistinguishable	ADJ
asir-1642	149	15	from	from	ADP
asir-1642	149	16	the	the	DET
asir-1642	149	17	input	input	NOUN
asir-1642	149	18	one	one	NOUN
asir-1642	149	19	,	,	PUNCT
asir-1642	149	20	exactly	exactly	ADV
asir-1642	149	21	the	the	DET
asir-1642	149	22	same	same	ADJ
asir-1642	149	23	.	.	PUNCT
asir-1642	150	1	the	the	DET
asir-1642	150	2	interpretation	interpretation	NOUN
asir-1642	150	3	that	that	PRON
asir-1642	150	4	the	the	DET
asir-1642	150	5	photon	photon	NOUN
asir-1642	150	6	has	have	AUX
asir-1642	150	7	been	be	AUX
asir-1642	150	8	stored	store	VERB
asir-1642	150	9	within	within	ADP
asir-1642	150	10	the	the	DET
asir-1642	150	11	material	material	NOUN
asir-1642	150	12	is	be	AUX
asir-1642	150	13	false	false	ADJ
asir-1642	150	14	,	,	PUNCT
asir-1642	150	15	on	on	ADP
asir-1642	150	16	the	the	DET
asir-1642	150	17	contrary	contrary	ADJ
asir-1642	150	18	storage	storage	NOUN
asir-1642	150	19	is	be	AUX
asir-1642	150	20	the	the	DET
asir-1642	150	21	e	e	PROPN
asir-1642	150	22	,	,	PUNCT
asir-1642	150	23	h	h	NOUN
asir-1642	150	24	,	,	PUNCT
asir-1642	150	25	energy	energy	NOUN
asir-1642	150	26	-	-	PUNCT
asir-1642	150	27	tank	tank	NOUN
asir-1642	150	28	with	with	ADP
asir-1642	150	29	the	the	DET
asir-1642	150	30	n	n	NOUN
asir-1642	150	31	,	,	PUNCT
asir-1642	150	32	frequencies,𝐟𝐧	frequencies,𝐟𝐧	NOUN
asir-1642	150	33	in	in	ADP
asir-1642	150	34	photon	photon	NOUN
asir-1642	150	35	,	,	PUNCT
asir-1642	150	36	and	and	CCONJ
asir-1642	150	37	the	the	DET
asir-1642	150	38	electromagnetic	electromagnetic	ADJ
asir-1642	150	39	radiation	radiation	NOUN
asir-1642	150	40	e	e	NOUN
asir-1642	150	41	,	,	PUNCT
asir-1642	150	42	b	b	PROPN
asir-1642	150	43	,	,	PUNCT
asir-1642	150	44	which	which	PRON
asir-1642	150	45	is	be	AUX
asir-1642	150	46	the	the	DET
asir-1642	150	47	conveyer	conveyer	NOUN
asir-1642	150	48	→	→	PUNCT
asir-1642	150	49	the	the	DET
asir-1642	150	50	carrier	carrier	NOUN
asir-1642	150	51	.	.	PUNCT
asir-1642	151	1	g	g	X
asir-1642	151	2	..	..	PUNCT
asir-1642	151	3	the	the	DET
asir-1642	151	4	total	total	ADJ
asir-1642	151	5	-	-	PUNCT
asir-1642	151	6	energy	energy	NOUN
asir-1642	151	7	in	in	ADP
asir-1642	151	8	loops	loop	NOUN
asir-1642	151	9	:	:	PUNCT
asir-1642	151	10	it	it	PRON
asir-1642	151	11	was	be	AUX
asir-1642	151	12	shown	show	VERB
asir-1642	151	13	[	[	X
asir-1642	151	14	58	58	NUM
asir-1642	151	15	]	]	PUNCT
asir-1642	151	16	that	that	SCONJ
asir-1642	151	17	the	the	DET
asir-1642	151	18	maximum	maximum	ADJ
asir-1642	151	19	velocity	velocity	NOUN
asir-1642	151	20	in	in	ADP
asir-1642	151	21	a	a	DET
asir-1642	151	22	closed	closed	ADJ
asir-1642	151	23	system	system	NOUN
asir-1642	151	24	occurs	occur	VERB
asir-1642	151	25	in	in	ADP
asir-1642	151	26	common	common	ADJ
asir-1642	151	27	circle	circle	NOUN
asir-1642	151	28	,	,	PUNCT
asir-1642	151	29	when	when	SCONJ
asir-1642	151	30	the	the	DET
asir-1642	151	31	two	two	NUM
asir-1642	151	32	velocities	velocity	NOUN
asir-1642	151	33	,	,	PUNCT
asir-1642	151	34	c̅	c̅	PROPN
asir-1642	151	35	,	,	PUNCT
asir-1642	151	36	v̅	v̅	PROPN
asir-1642	151	37	are	be	AUX
asir-1642	151	38	perpendicular	perpendicular	ADJ
asir-1642	151	39	between	between	ADP
asir-1642	151	40	them	they	PRON
asir-1642	151	41	,	,	PUNCT
asir-1642	151	42	and	and	CCONJ
asir-1642	151	43	are	be	AUX
asir-1642	151	44	not	not	PART
asir-1642	151	45	producing	produce	VERB
asir-1642	151	46	work	work	NOUN
asir-1642	151	47	,	,	PUNCT
asir-1642	151	48	from	from	ADP
asir-1642	151	49	where	where	SCONJ
asir-1642	151	50	then	then	ADV
asir-1642	151	51	dispersion	dispersion	NOUN
asir-1642	151	52	follows	follow	VERB
asir-1642	151	53	pythagoras	pythagoras	PROPN
asir-1642	151	54	theorem	theorem	PROPN
asir-1642	151	55	and	and	CCONJ
asir-1642	151	56	the	the	DET
asir-1642	151	57	resultant	resultant	NOUN
asir-1642	151	58	quantized	quantize	VERB
asir-1642	151	59	linear	linear	NOUN
asir-1642	151	60	space	space	NOUN
asir-1642	151	61	length	length	NOUN
asir-1642	151	62	,	,	PUNCT
asir-1642	151	63	r	r	NOUN
asir-1642	151	64	,	,	PUNCT
asir-1642	151	65	becomes	become	VERB
asir-1642	151	66	,	,	PUNCT
asir-1642	151	67	as	as	ADP
asir-1642	151	68	the	the	DET
asir-1642	151	69	resultant	resultant	NOUN
asir-1642	151	70	of	of	ADP
asir-1642	151	71	energy	energy	NOUN
asir-1642	151	72	vectors	vector	NOUN
asir-1642	151	73	,	,	PUNCT
asir-1642	152	1	r	r	NOUN
asir-1642	152	2	=	=	NOUN
asir-1642	152	3	|(c̅.t)|	|(c̅.t)|	NOUN
asir-1642	152	4	=	=	X
asir-1642	152	5	√v²	√v²	X
asir-1642	152	6	+	+	CCONJ
asir-1642	152	7	c²	c²	NOUN
asir-1642	152	8	and	and	CCONJ
asir-1642	152	9	by	by	ADP
asir-1642	152	10	using	use	VERB
asir-1642	152	11	space	space	NOUN
asir-1642	152	12	vector	vector	NOUN
asir-1642	152	13	r̅	r̅	ADP
asir-1642	152	14	=	=	PUNCT
asir-1642	152	15	|(c̅.t)|	|(c̅.t)|	NOUN
asir-1642	152	16	=	=	SYM
asir-1642	152	17	√v²	√v²	PROPN
asir-1642	152	18	+	+	NUM
asir-1642	152	19	c²	c²	NOUN
asir-1642	152	20	then	then	ADV
asir-1642	152	21	,	,	PUNCT
asir-1642	152	22	the	the	DET
asir-1642	152	23	total	total	ADJ
asir-1642	152	24	rotating	rotate	VERB
asir-1642	152	25	energy	energy	NOUN
asir-1642	152	26	is	be	AUX
asir-1642	152	27	→	→	SYM
asir-1642	152	28	±	±	NUM
asir-1642	152	29	λ̅	λ̅	NOUN
asir-1642	152	30	=	=	SYM
asir-1642	152	31	p̅.r	p̅.r	NOUN
asir-1642	152	32	=	=	PUNCT
asir-1642	152	33	(	(	PUNCT
asir-1642	152	34	m.c).r	m.c).r	NOUN
asir-1642	152	35	=	=	SYM
asir-1642	152	36	(	(	PUNCT
asir-1642	152	37	m.c	m.c	PROPN
asir-1642	152	38	)	)	PUNCT
asir-1642	152	39	.	.	PUNCT
asir-1642	153	1	√v²	√v²	PUNCT
asir-1642	154	1	+	+	CCONJ
asir-1642	154	2	c²	c²	NOUN
asir-1642	154	3	and	and	CCONJ
asir-1642	154	4	squaring	square	VERB
asir-1642	154	5	both	both	DET
asir-1642	154	6	sites	site	NOUN
asir-1642	154	7	[	[	X
asir-1642	154	8	±	±	X
asir-1642	154	9	λ̅	λ̅	X
asir-1642	154	10	]	]	PUNCT
asir-1642	154	11	²	²	PROPN
asir-1642	154	12	=	=	SYM
asir-1642	154	13	p².r²	p².r²	NOUN
asir-1642	154	14	=	=	PUNCT
asir-1642	154	15	m	m	AUX
asir-1642	154	16	².c².(v²+c²	².c².(v²+c²	ADJ
asir-1642	154	17	)	)	PUNCT
asir-1642	154	18	=	=	PUNCT
asir-1642	154	19	(	(	PUNCT
asir-1642	154	20	m².v²).c²	m².v²).c²	X
asir-1642	154	21	+	+	CCONJ
asir-1642	154	22	m².c	m².c	NOUN
asir-1642	154	23	=	=	SYM
asir-1642	154	24	(	(	PUNCT
asir-1642	154	25	p².c²	p².c²	NOUN
asir-1642	154	26	)	)	PUNCT
asir-1642	155	1	+	+	CCONJ
asir-1642	155	2	m².c	m².c	NOUN
asir-1642	155	3	=	=	PUNCT
asir-1642	156	1	[	[	X
asir-1642	156	2	p.c]²	p.c]²	X
asir-1642	156	3	+	+	PUNCT
asir-1642	156	4	[	[	X
asir-1642	156	5	mo.c²]²	mo.c²]²	X
asir-1642	156	6	or	or	CCONJ
asir-1642	156	7	is	be	AUX
asir-1642	156	8	t	t	NOUN
asir-1642	156	9	=	=	PUNCT
asir-1642	156	10	r+	r+	PUNCT
asir-1642	156	11	k	k	PROPN
asir-1642	156	12	→	→	SYM
asir-1642	156	13	total	total	ADJ
asir-1642	156	14	-	-	PUNCT
asir-1642	156	15	energy	energy	NOUN
asir-1642	156	16	of	of	ADP
asir-1642	156	17	elementary	elementary	ADJ
asir-1642	156	18	-	-	PUNCT
asir-1642	156	19	particle	particle	NOUN
asir-1642	156	20	=	=	VERB
asir-1642	156	21	intrinsic	intrinsic	ADJ
asir-1642	156	22	rotational	rotational	ADJ
asir-1642	156	23	+	+	CCONJ
asir-1642	156	24	kinetic	kinetic	ADJ
asir-1642	156	25	energy	energy	NOUN
asir-1642	156	26	,	,	PUNCT
asir-1642	156	27	the	the	DET
asir-1642	156	28	velocity	velocity	NOUN
asir-1642	156	29	of	of	ADP
asir-1642	156	30	elementary	elementary	ADJ
asir-1642	156	31	particles	particle	NOUN
asir-1642	156	32	is	be	AUX
asir-1642	156	33	the	the	DET
asir-1642	156	34	light	light	ADJ
asir-1642	156	35	velocity	velocity	NOUN
asir-1642	156	36	c	c	NOUN
asir-1642	156	37	=	=	SYM
asir-1642	156	38	v	v	PROPN
asir-1642	156	39	=	=	SYM
asir-1642	156	40	2πr	2πr	NOUN
asir-1642	156	41	.	.	PUNCT
asir-1642	157	1	e	e	NOUN
asir-1642	157	2	and	and	CCONJ
asir-1642	157	3	frequency	frequency	PROPN
asir-1642	157	4	→	→	SYM
asir-1642	157	5	e=	e=	CCONJ
asir-1642	157	6	𝐜	𝐜	PROPN
asir-1642	157	7	𝟐𝛑.𝐫	𝟐𝛑.𝐫	PUNCT
asir-1642	157	8	…	…	PUNCT
asir-1642	157	9	…	…	PUNCT
asir-1642	157	10	..	..	PUNCT
asir-1642	157	11	(	(	PUNCT
asir-1642	157	12	a	a	X
asir-1642	157	13	)	)	PUNCT
asir-1642	157	14	rotational	rotational	ADJ
asir-1642	157	15	energy	energy	NOUN
asir-1642	157	16	r	r	NOUN
asir-1642	157	17	=	=	SYM
asir-1642	157	18	b̅.	b̅.	NUM
asir-1642	157	19	w̅	w̅	PUNCT
asir-1642	157	20	=	=	SYM
asir-1642	157	21	2l=	2l=	NUM
asir-1642	157	22	j.w²	j.w²	NOUN
asir-1642	157	23	and	and	CCONJ
asir-1642	157	24	→	→	SYM
asir-1642	157	25	r	r	NOUN
asir-1642	157	26	=	=	PUNCT
asir-1642	157	27	[	[	PUNCT
asir-1642	157	28	⁴	⁴	NUM
asir-1642	157	29	]	]	PUNCT
asir-1642	157	30	.	.	PUNCT
asir-1642	158	1	[	[	PUNCT
asir-1642	158	2	c²	c²	NOUN
asir-1642	158	3	]	]	PUNCT
asir-1642	158	4	=	=	SYM
asir-1642	158	5	c²	c²	NOUN
asir-1642	158	6	r²	r²	NOUN
asir-1642	158	7	=	=	PUNCT
asir-1642	158	8	3,535.10	3,535.10	NUM
asir-1642	158	9	6	6	NUM
asir-1642	158	10	.	.	PUNCT
asir-1642	159	1	r²	r²	VERB
asir-1642	159	2	…	…	PUNCT
asir-1642	159	3	…	…	PUNCT
asir-1642	159	4	.(b	.(b	NUM
asir-1642	159	5	)	)	PUNCT
asir-1642	159	6	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	159	7	applied	apply	VERB
asir-1642	159	8	science	science	NOUN
asir-1642	159	9	and	and	CCONJ
asir-1642	159	10	innovative	innovative	ADJ
asir-1642	159	11	research	research	NOUN
asir-1642	159	12	vol	vol	NOUN
asir-1642	159	13	.	.	PROPN
asir-1642	160	1	2	2	NUM
asir-1642	160	2	,	,	PUNCT
asir-1642	160	3	no	no	INTJ
asir-1642	160	4	.	.	NOUN
asir-1642	160	5	4	4	NUM
asir-1642	160	6	,	,	PUNCT
asir-1642	160	7	2018	2018	NUM
asir-1642	160	8	163	163	NUM
asir-1642	160	9	published	publish	VERB
asir-1642	160	10	by	by	ADP
asir-1642	160	11	scholink	scholink	PROPN
asir-1642	160	12	inc	inc	PROPN
asir-1642	160	13	.	.	PROPN
asir-1642	160	14	energy	energy	NOUN
asir-1642	160	15	and	and	CCONJ
asir-1642	160	16	frequency	frequency	NOUN
asir-1642	160	17	of	of	ADP
asir-1642	160	18	elementary	elementary	ADJ
asir-1642	160	19	particles	particle	NOUN
asir-1642	160	20	can	can	AUX
asir-1642	160	21	be	be	AUX
asir-1642	160	22	found	find	VERB
asir-1642	160	23	from	from	ADP
asir-1642	160	24	cave	cave	NOUN
asir-1642	160	25	r	r	NOUN
asir-1642	160	26	,	,	PUNCT
asir-1642	160	27	only	only	ADV
asir-1642	160	28	since	since	SCONJ
asir-1642	160	29	,	,	PUNCT
asir-1642	160	30	c	c	X
asir-1642	160	31	,	,	PUNCT
asir-1642	160	32	constant	constant	ADJ
asir-1642	160	33	,	,	PUNCT
asir-1642	160	34	total	total	ADJ
asir-1642	160	35	-	-	PUNCT
asir-1642	160	36	energy	energy	NOUN
asir-1642	160	37	→	→	SYM
asir-1642	160	38	𝐄	𝐄	NOUN
asir-1642	160	39	𝐓	𝐓	NOUN
asir-1642	160	40	=	=	PUNCT
asir-1642	160	41	r+	r+	X
asir-1642	160	42	k=	k=	X
asir-1642	160	43	c²	c²	NOUN
asir-1642	160	44	r²	r²	VERB
asir-1642	160	45	+	+	CCONJ
asir-1642	160	46	2	2	NUM
asir-1642	160	47	m.v²	m.v²	NOUN
asir-1642	160	48	=	=	SYM
asir-1642	160	49	3,535	3,535	NUM
asir-1642	160	50	.	.	PUNCT
asir-1642	160	51	𝟎	𝟎	NUM
asir-1642	161	1	𝟔.	𝟔.	X
asir-1642	161	2	r²	r²	VERB
asir-1642	161	3	+	+	CCONJ
asir-1642	161	4	𝟐	𝟐	NUM
asir-1642	161	5	m.v²	m.v²	NOUN
asir-1642	161	6	…	…	PUNCT
asir-1642	161	7	…	…	PUNCT
asir-1642	161	8	…	…	PUNCT
asir-1642	161	9	(	(	PUNCT
asir-1642	161	10	c	c	NOUN
asir-1642	161	11	)	)	PUNCT
asir-1642	161	12	mass	mass	NOUN
asir-1642	161	13	of	of	ADP
asir-1642	161	14	elementary	elementary	ADJ
asir-1642	161	15	particles	particle	NOUN
asir-1642	161	16	is	be	AUX
asir-1642	161	17	m	m	NOUN
asir-1642	161	18	=	=	SYM
asir-1642	161	19	2	2	NUM
asir-1642	161	20	².w²	².w²	NOUN
asir-1642	161	21	=	=	SYM
asir-1642	161	22	j.w²	j.w²	NOUN
asir-1642	161	23	2	2	NUM
asir-1642	161	24	.	.	NOUN
asir-1642	161	25	2	2	NUM
asir-1642	161	26	².w²	².w²	NOUN
asir-1642	161	27	=	=	SYM
asir-1642	161	28	j	j	PROPN
asir-1642	161	29	.	.	PUNCT
asir-1642	162	1	²	²	NUM
asir-1642	162	2	=	=	NOUN
asir-1642	162	3	𝛑.𝐫²	𝛑.𝐫²	X
asir-1642	162	4	𝟔	𝟔	NUM
asir-1642	162	5	,	,	PUNCT
asir-1642	162	6	i.e.	i.e.	X
asir-1642	162	7	,	,	PUNCT
asir-1642	162	8	dependent	dependent	ADJ
asir-1642	162	9	on	on	ADP
asir-1642	162	10	radius	radius	NOUN
asir-1642	162	11	of	of	ADP
asir-1642	162	12	cave	cave	NOUN
asir-1642	162	13	.	.	PUNCT
asir-1642	163	1	dot	dot	NOUN
asir-1642	163	2	product	product	NOUN
asir-1642	163	3	and	and	CCONJ
asir-1642	163	4	cross	cross	NOUN
asir-1642	163	5	product	product	NOUN
asir-1642	163	6	:	:	PUNCT
asir-1642	163	7	the	the	DET
asir-1642	163	8	dot	dot	NOUN
asir-1642	163	9	-	-	PUNCT
asir-1642	163	10	product	product	NOUN
asir-1642	163	11	happens	happen	VERB
asir-1642	163	12	for	for	ADP
asir-1642	163	13	interactions	interaction	NOUN
asir-1642	163	14	between	between	ADP
asir-1642	163	15	similar	similar	ADJ
asir-1642	163	16	dimensions	dimension	NOUN
asir-1642	163	17	,	,	PUNCT
asir-1642	163	18	while	while	SCONJ
asir-1642	163	19	the	the	DET
asir-1642	163	20	cross	cross	NOUN
asir-1642	163	21	-	-	NOUN
asir-1642	163	22	product	product	NOUN
asir-1642	163	23	between	between	ADP
asir-1642	163	24	different	different	ADJ
asir-1642	163	25	-	-	PUNCT
asir-1642	163	26	dimensions	dimension	NOUN
asir-1642	163	27	.	.	PUNCT
asir-1642	164	1	cross	cross	NOUN
asir-1642	164	2	-	-	NOUN
asir-1642	164	3	product	product	NOUN
asir-1642	164	4	of	of	ADP
asir-1642	164	5	two	two	NUM
asir-1642	164	6	vectors	vector	NOUN
asir-1642	164	7	̅	̅	NOUN
asir-1642	164	8	,	,	PUNCT
asir-1642	164	9	̅	̅	NOUN
asir-1642	164	10	is	be	AUX
asir-1642	164	11	̅	̅	NOUN
asir-1642	164	12	x	x	SYM
asir-1642	164	13	̅	̅	NOUN
asir-1642	164	14	=	=	SYM
asir-1642	165	1	|	|	ADV
asir-1642	165	2	̅|.|	̅|.|	X
asir-1642	165	3	̅|	̅|	INTJ
asir-1642	165	4	.	.	PUNCT
asir-1642	166	1	̅	̅	NOUN
asir-1642	166	2	and	and	CCONJ
asir-1642	166	3	for	for	ADP
asir-1642	166	4	̅	̅	NOUN
asir-1642	166	5	=	=	SYM
asir-1642	166	6	̅	̅	NOUN
asir-1642	166	7	and	and	CCONJ
asir-1642	166	8	θ=90ᵒ	θ=90ᵒ	PROPN
asir-1642	166	9	then	then	ADV
asir-1642	166	10	̅	̅	VERB
asir-1642	166	11	x	x	SYM
asir-1642	166	12	̅	̅	NOUN
asir-1642	166	13	=	=	SYM
asir-1642	166	14	̅²	̅²	NOUN
asir-1642	166	15	,	,	PUNCT
asir-1642	166	16	and	and	CCONJ
asir-1642	166	17	for	for	ADP
asir-1642	166	18	quaternion	quaternion	NOUN
asir-1642	166	19	,	,	PUNCT
asir-1642	166	20	s	s	PROPN
asir-1642	166	21	,	,	PUNCT
asir-1642	166	22	which	which	PRON
asir-1642	166	23	performs	perform	VERB
asir-1642	166	24	the	the	DET
asir-1642	166	25	work	work	NOUN
asir-1642	166	26	of	of	ADP
asir-1642	166	27	rotating	rotate	VERB
asir-1642	166	28	the	the	DET
asir-1642	166	29	one	one	NUM
asir-1642	166	30	vector	vector	NOUN
asir-1642	166	31	around	around	ADP
asir-1642	166	32	the	the	DET
asir-1642	166	33	other	other	ADJ
asir-1642	166	34	→work	→work	PUNCT
asir-1642	166	35	=	=	SYM
asir-1642	166	36	̅	̅	NOUN
asir-1642	166	37	x	x	SYM
asir-1642	166	38	̅	̅	NOUN
asir-1642	166	39	=	=	SYM
asir-1642	166	40	̅².r̅	̅².r̅	NUM
asir-1642	166	41	,	,	PUNCT
asir-1642	166	42	and	and	CCONJ
asir-1642	166	43	for	for	ADP
asir-1642	166	44	̅	̅	NOUN
asir-1642	166	45	=	=	SYM
asir-1642	166	46	v̅	v̅	NOUN
asir-1642	166	47	then	then	ADV
asir-1642	166	48	,	,	PUNCT
asir-1642	166	49	work	work	NOUN
asir-1642	166	50	=	=	PUNCT
asir-1642	166	51	v̅².r̅	v̅².r̅	VERB
asir-1642	166	52	=	=	VERB
asir-1642	166	53	|v̅|.|v̅|.r̅	|v̅|.|v̅|.r̅	NOUN
asir-1642	166	54	=	=	SYM
asir-1642	166	55	v²	v²	PROPN
asir-1642	166	56	.	.	PUNCT
asir-1642	167	1	r.	r.	PROPN
asir-1642	167	2	̅	̅	PROPN
asir-1642	167	3	=	=	SYM
asir-1642	167	4	(	(	PUNCT
asir-1642	167	5	wr)²r	wr)²r	NOUN
asir-1642	167	6	.	.	PUNCT
asir-1642	167	7	̅	̅	NOUN
asir-1642	168	1	=	=	SYM
asir-1642	168	2	(	(	PUNCT
asir-1642	168	3	2πr	2πr	ADJ
asir-1642	168	4	/	/	SYM
asir-1642	168	5	t)²	t)²	NOUN
asir-1642	168	6	̅	̅	NOUN
asir-1642	168	7	=	=	SYM
asir-1642	168	8	(	(	PUNCT
asir-1642	168	9	4π²r²/	4π²r²/	NUM
asir-1642	168	10	t²	t²	NOUN
asir-1642	168	11	)	)	PUNCT
asir-1642	168	12	.	.	PUNCT
asir-1642	169	1	r.	r.	PROPN
asir-1642	169	2	̅	̅	PROPN
asir-1642	169	3	=	=	SYM
asir-1642	169	4	²	²	NUM
asir-1642	169	5	³	³	NUM
asir-1642	169	6	t²	t²	NOUN
asir-1642	169	7	.	.	PUNCT
asir-1642	170	1	̅	̅	NOUN
asir-1642	170	2	=	=	SYM
asir-1642	170	3	w	w	PROPN
asir-1642	170	4	=	=	SYM
asir-1642	170	5	4π²	4π²	NUM
asir-1642	170	6	.	.	PUNCT
asir-1642	171	1	𝐫³	𝐫³	PROPN
asir-1642	171	2	𝐓²	𝐓²	PROPN
asir-1642	171	3	.	.	PUNCT
asir-1642	172	1	�	�	PROPN
asir-1642	172	2	̅	̅	NOUN
asir-1642	172	3	�	�	PROPN
asir-1642	172	4	,	,	PUNCT
asir-1642	172	5	which	which	PRON
asir-1642	172	6	is	be	AUX
asir-1642	172	7	the	the	DET
asir-1642	172	8	kepler	kepler	ADJ
asir-1642	172	9	celestial	celestial	ADJ
asir-1642	172	10	law	law	NOUN
asir-1642	172	11	for	for	ADP
asir-1642	172	12	microcosm	microcosm	PROPN
asir-1642	172	13	.	.	PUNCT
asir-1642	173	1	since	since	SCONJ
asir-1642	173	2	in	in	ADP
asir-1642	173	3	mechanics	mechanic	NOUN
asir-1642	173	4	issues	issue	NOUN
asir-1642	173	5	z²	z²	NOUN
asir-1642	173	6	=	=	SYM
asir-1642	173	7	s²	s²	ADJ
asir-1642	173	8	s²	s²	NOUN
asir-1642	173	9	+	+	CCONJ
asir-1642	173	10	2.s.s	2.s.s	NUM
asir-1642	173	11	=	=	SYM
asir-1642	173	12	1	1	NUM
asir-1642	173	13	,	,	PUNCT
asir-1642	173	14	and	and	CCONJ
asir-1642	173	15	from	from	ADP
asir-1642	173	16	unit	unit	NOUN
asir-1642	173	17	-	-	PUNCT
asir-1642	173	18	quaternion	quaternion	NOUN
asir-1642	173	19	s	s	NOUN
asir-1642	173	20	²	²	NUM
asir-1642	173	21	+	+	CCONJ
asir-1642	173	22	[	[	X
asir-1642	173	23	iv	iv	X
asir-1642	173	24	]	]	PUNCT
asir-1642	173	25	²	²	PROPN
asir-1642	173	26	=	=	SYM
asir-1642	173	27	1	1	NUM
asir-1642	173	28	then	then	ADV
asir-1642	173	29	is	be	AUX
asir-1642	173	30	→	→	SYM
asir-1642	173	31	s²	s²	ADJ
asir-1642	173	32	v²	v²	PROPN
asir-1642	173	33	=	=	SYM
asir-1642	173	34	1	1	NUM
asir-1642	173	35	…	…	SYM
asir-1642	173	36	…	…	PUNCT
asir-1642	173	37	.(d	.(d	NUM
asir-1642	173	38	)	)	PUNCT
asir-1642	173	39	equation	equation	NOUN
asir-1642	173	40	(	(	PUNCT
asir-1642	173	41	d	d	X
asir-1642	173	42	)	)	PUNCT
asir-1642	173	43	is	be	AUX
asir-1642	173	44	a	a	DET
asir-1642	173	45	cone	cone	NOUN
asir-1642	173	46	relation	relation	NOUN
asir-1642	173	47	on	on	ADP
asir-1642	173	48	where	where	SCONJ
asir-1642	173	49	total	total	ADJ
asir-1642	173	50	-	-	PUNCT
asir-1642	173	51	energy	energy	NOUN
asir-1642	173	52	,	,	PUNCT
asir-1642	173	53	kinetic	kinetic	ADJ
asir-1642	173	54	and	and	CCONJ
asir-1642	173	55	potential	potential	NOUN
asir-1642	173	56	is	be	AUX
asir-1642	173	57	conserved	conserve	VERB
asir-1642	173	58	and	and	CCONJ
asir-1642	173	59	for	for	ADP
asir-1642	173	60	photon	photon	NOUN
asir-1642	173	61	,	,	PUNCT
asir-1642	173	62	electromagnetic	electromagnetic	ADJ
asir-1642	173	63	radiation	radiation	NOUN
asir-1642	173	64	is	be	AUX
asir-1642	173	65	the	the	DET
asir-1642	173	66	kinetic	kinetic	NOUN
asir-1642	173	67	-	-	PUNCT
asir-1642	173	68	energy	energy	NOUN
asir-1642	173	69	and	and	CCONJ
asir-1642	173	70	the	the	DET
asir-1642	173	71	velocity	velocity	NOUN
asir-1642	173	72	-	-	PUNCT
asir-1642	173	73	vector	vector	NOUN
asir-1642	173	74	-	-	PUNCT
asir-1642	173	75	energy	energy	NOUN
asir-1642	173	76	-	-	PUNCT
asir-1642	173	77	tank	tank	NOUN
asir-1642	173	78	is	be	AUX
asir-1642	173	79	the	the	DET
asir-1642	173	80	potential	potential	NOUN
asir-1642	173	81	.	.	PUNCT
asir-1642	174	1	photon	photon	NOUN
asir-1642	174	2	is	be	AUX
asir-1642	174	3	an	an	DET
asir-1642	174	4	energy	energy	NOUN
asir-1642	174	5	-	-	PUNCT
asir-1642	174	6	store	store	NOUN
asir-1642	174	7	,	,	PUNCT
asir-1642	174	8	r	r	NOUN
asir-1642	174	9	,	,	PUNCT
asir-1642	174	10	in	in	ADP
asir-1642	174	11	a	a	DET
asir-1642	174	12	stationary	stationary	ADJ
asir-1642	174	13	-	-	PUNCT
asir-1642	174	14	wave	wave	NOUN
asir-1642	174	15	of	of	ADP
asir-1642	174	16	wavelength	wavelength	NOUN
asir-1642	174	17	n	n	PRON
asir-1642	174	18	λ=	λ=	VERB
asir-1642	174	19	2r	2r	NUM
asir-1642	174	20	consisted	consist	VERB
asir-1642	174	21	of	of	ADP
asir-1642	174	22	n	n	PRON
asir-1642	174	23	stationary	stationary	ADJ
asir-1642	174	24	lobes	lobe	NOUN
asir-1642	174	25	filled	fill	VERB
asir-1642	174	26	in	in	ADP
asir-1642	174	27	λ	λ	PROPN
asir-1642	174	28	with	with	ADP
asir-1642	174	29	inner	inner	ADJ
asir-1642	174	30	motion	motion	NOUN
asir-1642	174	31	the	the	DET
asir-1642	174	32	electromagnetic	electromagnetic	ADJ
asir-1642	174	33	-	-	PUNCT
asir-1642	174	34	displacement	displacement	NOUN
asir-1642	174	35	-	-	PUNCT
asir-1642	174	36	current	current	NOUN
asir-1642	174	37	and	and	CCONJ
asir-1642	174	38	outward	outward	VERB
asir-1642	174	39	the	the	DET
asir-1642	174	40	propagating	propagating	NOUN
asir-1642	174	41	,	,	PUNCT
asir-1642	174	42	energy	energy	NOUN
asir-1642	174	43	-	-	PUNCT
asir-1642	174	44	store	store	NOUN
asir-1642	174	45	λ	λ	NOUN
asir-1642	174	46	=	=	SYM
asir-1642	174	47	2r	2r	NUM
asir-1642	174	48	/	/	SYM
asir-1642	174	49	n	n	CCONJ
asir-1642	174	50	,	,	PUNCT
asir-1642	174	51	with	with	ADP
asir-1642	174	52	the	the	DET
asir-1642	174	53	light	light	ADJ
asir-1642	174	54	speed	speed	NOUN
asir-1642	174	55	,	,	PUNCT
asir-1642	174	56	c	c	X
asir-1642	174	57	,	,	PUNCT
asir-1642	174	58	the	the	DET
asir-1642	174	59	two	two	NUM
asir-1642	174	60	transverse	transverse	NOUN
asir-1642	174	61	fields	field	NOUN
asir-1642	174	62	,	,	PUNCT
asir-1642	174	63	[	[	X
asir-1642	174	64	the	the	DET
asir-1642	174	65	+	+	CCONJ
asir-1642	174	66	electric	electric	ADJ
asir-1642	174	67	-	-	PUNCT
asir-1642	174	68	field	field	NOUN
asir-1642	174	69	and	and	CCONJ
asir-1642	174	70	the	the	DET
asir-1642	174	71	magnetic	magnetic	ADJ
asir-1642	174	72	-	-	PUNCT
asir-1642	174	73	field	field	NOUN
asir-1642	174	74	]	]	PUNCT
asir-1642	174	75	.	.	PUNCT
asir-1642	175	1	figure	figure	NOUN
asir-1642	175	2	3	3	NUM
asir-1642	175	3	.	.	PUNCT
asir-1642	176	1	the	the	DET
asir-1642	176	2	three	three	NUM
asir-1642	176	3	constituents	constituent	NOUN
asir-1642	176	4	in	in	ADP
asir-1642	176	5	bohr	bohr	PROPN
asir-1642	176	6	-	-	PUNCT
asir-1642	176	7	atom	atom	NOUN
asir-1642	176	8	and	and	CCONJ
asir-1642	176	9	the	the	DET
asir-1642	176	10	spinning	spinning	NOUN
asir-1642	176	11	-	-	PUNCT
asir-1642	176	12	gravity	gravity	NOUN
asir-1642	176	13	in	in	ADP
asir-1642	176	14	-	-	PUNCT
asir-1642	176	15	orbit	orbit	NOUN
asir-1642	176	16	energy	energy	NOUN
asir-1642	176	17	-	-	PUNCT
asir-1642	176	18	rim	rim	NOUN
asir-1642	176	19	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	176	20	applied	apply	VERB
asir-1642	176	21	science	science	NOUN
asir-1642	176	22	and	and	CCONJ
asir-1642	176	23	innovative	innovative	ADJ
asir-1642	176	24	research	research	NOUN
asir-1642	176	25	vol	vol	NOUN
asir-1642	176	26	.	.	PROPN
asir-1642	177	1	2	2	NUM
asir-1642	177	2	,	,	PUNCT
asir-1642	177	3	no	no	INTJ
asir-1642	177	4	.	.	NOUN
asir-1642	177	5	4	4	NUM
asir-1642	177	6	,	,	PUNCT
asir-1642	177	7	2018	2018	NUM
asir-1642	177	8	164	164	NUM
asir-1642	177	9	published	publish	VERB
asir-1642	177	10	by	by	ADP
asir-1642	177	11	scholink	scholink	PROPN
asir-1642	177	12	inc	inc	PROPN
asir-1642	177	13	.	.	PROPN
asir-1642	177	14	proton	proton	PROPN
asir-1642	177	15	,	,	PUNCT
asir-1642	177	16	in	in	ADP
asir-1642	177	17	bohr	bohr	PROPN
asir-1642	177	18	-	-	PUNCT
asir-1642	177	19	model	model	PROPN
asir-1642	177	20	,	,	PUNCT
asir-1642	177	21	consists	consist	VERB
asir-1642	177	22	the	the	DET
asir-1642	177	23	→	→	NOUN
asir-1642	177	24	positive	positive	ADJ
asir-1642	177	25	breakage	breakage	NOUN
asir-1642	177	26	(	(	PUNCT
asir-1642	177	27	+	+	NOUN
asir-1642	177	28	)	)	PUNCT
asir-1642	177	29	of	of	ADP
asir-1642	177	30	the	the	DET
asir-1642	177	31	three	three	NUM
asir-1642	177	32	constituents	constituent	NOUN
asir-1642	177	33	,	,	PUNCT
asir-1642	177	34	electron	electron	NOUN
asir-1642	177	35	consists	consist	VERB
asir-1642	177	36	the	the	DET
asir-1642	177	37	→	→	NOUN
asir-1642	177	38	negative	negative	ADJ
asir-1642	177	39	breakage	breakage	NOUN
asir-1642	177	40	(	(	PUNCT
asir-1642	177	41	-	-	PUNCT
asir-1642	177	42	)	)	PUNCT
asir-1642	177	43	of	of	ADP
asir-1642	177	44	the	the	DET
asir-1642	177	45	three	three	NUM
asir-1642	177	46	constituents	constituent	NOUN
asir-1642	177	47	,	,	PUNCT
asir-1642	177	48	neutron	neutron	NOUN
asir-1642	177	49	consists	consist	VERB
asir-1642	177	50	the	the	DET
asir-1642	177	51	→	→	SYM
asir-1642	177	52	equilibrium	equilibrium	NOUN
asir-1642	177	53	material	material	NOUN
asir-1642	177	54	point	point	NOUN
asir-1642	177	55	(	(	PUNCT
asir-1642	177	56	+	+	NUM
asir-1642	177	57	-	-	PUNCT
asir-1642	177	58	)	)	PUNCT
asir-1642	177	59	of	of	ADP
asir-1642	177	60	the	the	DET
asir-1642	177	61	spaces	space	NOUN
asir-1642	177	62	and	and	CCONJ
asir-1642	177	63	anti	anti	NOUN
asir-1642	177	64	-	-	ADJ
asir-1642	177	65	spaces	space	NOUN
asir-1642	177	66	.	.	PUNCT
asir-1642	178	1	nucleus	nucleus	PROPN
asir-1642	178	2	consists	consist	VERB
asir-1642	178	3	the	the	DET
asir-1642	178	4	→	→	SYM
asir-1642	178	5	equilibrium	equilibrium	NOUN
asir-1642	178	6	positive	positive	ADJ
asir-1642	178	7	breakage	breakage	NOUN
asir-1642	178	8	store	store	NOUN
asir-1642	178	9	,	,	PUNCT
asir-1642	178	10	in	in	ADP
asir-1642	178	11	atom	atom	NOUN
asir-1642	178	12	-	-	PUNCT
asir-1642	178	13	model	model	NOUN
asir-1642	178	14	.	.	PUNCT
asir-1642	179	1	electron	electron	NOUN
asir-1642	179	2	orbits	orbit	NOUN
asir-1642	179	3	are	be	AUX
asir-1642	179	4	the	the	DET
asir-1642	179	5	→	→	NOUN
asir-1642	179	6	equilibrium	equilibrium	NOUN
asir-1642	179	7	negative	negative	ADJ
asir-1642	179	8	breakage	breakage	NOUN
asir-1642	179	9	store	store	NOUN
asir-1642	179	10	-	-	PUNCT
asir-1642	179	11	rims	rim	NOUN
asir-1642	179	12	in	in	ADP
asir-1642	179	13	atom	atom	NOUN
asir-1642	179	14	.	.	PUNCT
asir-1642	180	1	orbital	orbital	ADJ
asir-1642	180	2	electron	electron	NOUN
asir-1642	180	3	is	be	AUX
asir-1642	180	4	the	the	DET
asir-1642	180	5	→	→	SYM
asir-1642	180	6	moving	move	VERB
asir-1642	180	7	-	-	PUNCT
asir-1642	180	8	charge	charge	NOUN
asir-1642	180	9	-	-	PUNCT
asir-1642	180	10	carrier	carrier	NOUN
asir-1642	180	11	of	of	ADP
asir-1642	180	12	energy	energy	NOUN
asir-1642	180	13	in	in	ADP
asir-1642	180	14	atom	atom	NOUN
asir-1642	180	15	–	–	PUNCT
asir-1642	180	16	model	model	NOUN
asir-1642	180	17	.	.	PUNCT
asir-1642	181	1	it	it	PRON
asir-1642	181	2	was	be	AUX
asir-1642	181	3	prior	prior	ADV
asir-1642	181	4	referred	refer	VERB
asir-1642	181	5	that	that	SCONJ
asir-1642	181	6	,	,	PUNCT
asir-1642	181	7	when	when	SCONJ
asir-1642	181	8	matter	matter	NOUN
asir-1642	181	9	and	and	CCONJ
asir-1642	181	10	antimatter	antimatter	NOUN
asir-1642	181	11	annihilate	annihilate	NOUN
asir-1642	181	12	at	at	ADP
asir-1642	181	13	rest	rest	NOUN
asir-1642	181	14	or	or	CCONJ
asir-1642	181	15	when	when	SCONJ
asir-1642	181	16	anti	anti	ADJ
asir-1642	181	17	-	-	ADJ
asir-1642	181	18	space	space	NOUN
asir-1642	181	19	comes	come	VERB
asir-1642	181	20	in	in	ADP
asir-1642	181	21	contact	contact	NOUN
asir-1642	181	22	with	with	ADP
asir-1642	181	23	its	its	PRON
asir-1642	181	24	regular	regular	ADJ
asir-1642	181	25	space	space	NOUN
asir-1642	181	26	counterpart	counterpart	NOUN
asir-1642	181	27	,	,	PUNCT
asir-1642	181	28	they	they	PRON
asir-1642	181	29	mutually	mutually	ADV
asir-1642	181	30	destroy	destroy	VERB
asir-1642	181	31	each	each	DET
asir-1642	181	32	other	other	ADJ
asir-1642	181	33	and	and	CCONJ
asir-1642	181	34	all	all	PRON
asir-1642	181	35	of	of	ADP
asir-1642	181	36	their	their	PRON
asir-1642	181	37	energy	energy	NOUN
asir-1642	181	38	is	be	AUX
asir-1642	181	39	converted	convert	VERB
asir-1642	181	40	to	to	ADP
asir-1642	181	41	the	the	DET
asir-1642	181	42	three	three	NUM
asir-1642	181	43	breakages	breakage	NOUN
asir-1642	181	44	→	→	SYM
asir-1642	181	45	s²	s²	PROPN
asir-1642	181	46	,	,	PUNCT
asir-1642	181	47	-|	-|	PROPN
asir-1642	181	48	�	�	PROPN
asir-1642	181	49	̅	̅	NOUN
asir-1642	181	50	�	�	NOUN
asir-1642	181	51	|	|	ADV
asir-1642	181	52	²	²	NUM
asir-1642	181	53	,	,	PUNCT
asir-1642	181	54	[	[	X
asir-1642	181	55	2	2	NUM
asir-1642	181	56	̅].|s|	̅].|s|	NOUN
asir-1642	181	57	|r|.i	|r|.i	NOUN
asir-1642	181	58	←	←	VERB
asir-1642	181	59	where	where	SCONJ
asir-1642	181	60	for	for	ADP
asir-1642	181	61	,	,	PUNCT
asir-1642	181	62	�	�	NOUN
asir-1642	181	63	̅	̅	NOUN
asir-1642	181	64	�	�	NOUN
asir-1642	181	65	=	=	SYM
asir-1642	181	66	s	s	PART
asir-1642	181	67	≡	≡	PROPN
asir-1642	181	68	the	the	DET
asir-1642	181	69	cave	cave	NOUN
asir-1642	181	70	,	,	PUNCT
asir-1642	181	71	[	[	PUNCT
asir-1642	181	72	s²	s²	NOUN
asir-1642	181	73	]	]	PUNCT
asir-1642	181	74	→	→	PUNCT
asir-1642	181	75	is	be	AUX
asir-1642	181	76	the	the	DET
asir-1642	181	77	real	real	ADJ
asir-1642	181	78	part	part	NOUN
asir-1642	181	79	,	,	PUNCT
asir-1642	181	80	matter	matter	NOUN
asir-1642	181	81	,	,	PUNCT
asir-1642	181	82	of	of	ADP
asir-1642	181	83	the	the	DET
asir-1642	181	84	new	new	ADJ
asir-1642	181	85	monad	monad	PROPN
asir-1642	181	86	,	,	PUNCT
asir-1642	181	87	and	and	CCONJ
asir-1642	181	88	is	be	AUX
asir-1642	181	89	a	a	DET
asir-1642	181	90	positive	positive	ADJ
asir-1642	181	91	scalar	scalar	ADJ
asir-1642	181	92	magnitude	magnitude	NOUN
asir-1642	181	93	-	-	PUNCT
asir-1642	181	94	[	[	PUNCT
asir-1642	181	95	s²	s²	NOUN
asir-1642	181	96	]	]	PUNCT
asir-1642	181	97	→	→	SYM
asir-1642	181	98	is	be	AUX
asir-1642	181	99	the	the	DET
asir-1642	181	100	always	always	ADV
asir-1642	181	101	negative	negative	ADJ
asir-1642	181	102	part	part	NOUN
asir-1642	181	103	,	,	PUNCT
asir-1642	181	104	anti	anti	ADJ
asir-1642	181	105	-	-	ADJ
asir-1642	181	106	matter	matter	NOUN
asir-1642	181	107	,	,	PUNCT
asir-1642	181	108	which	which	PRON
asir-1642	181	109	is	be	AUX
asir-1642	181	110	always	always	ADV
asir-1642	181	111	a	a	DET
asir-1642	181	112	negative	negative	ADJ
asir-1642	181	113	scalar	scalar	ADJ
asir-1642	181	114	-	-	PUNCT
asir-1642	181	115	magnitude	magnitude	NOUN
asir-1642	181	116	.	.	PUNCT
asir-1642	182	1	2	2	NUM
asir-1642	182	2	s².i	s².i	NOUN
asir-1642	182	3	→	→	SYM
asir-1642	182	4	is	be	AUX
asir-1642	182	5	the	the	DET
asir-1642	182	6	double	double	ADJ
asir-1642	182	7	angular	angular	ADJ
asir-1642	182	8	-	-	PUNCT
asir-1642	182	9	velocity	velocity	NOUN
asir-1642	182	10	term	term	NOUN
asir-1642	182	11	,	,	PUNCT
asir-1642	182	12	the	the	DET
asir-1642	182	13	energy	energy	NOUN
asir-1642	182	14	term	term	NOUN
asir-1642	182	15	,	,	PUNCT
asir-1642	182	16	and	and	CCONJ
asir-1642	182	17	which	which	PRON
asir-1642	182	18	is	be	AUX
asir-1642	182	19	a	a	DET
asir-1642	182	20	vector	vector	NOUN
asir-1642	182	21	magnitude	magnitude	NOUN
asir-1642	182	22	.	.	PUNCT
asir-1642	183	1	photon	photon	NOUN
asir-1642	183	2	is	be	AUX
asir-1642	183	3	a	a	DET
asir-1642	183	4	material	material	NOUN
asir-1642	183	5	-	-	PUNCT
asir-1642	183	6	point	point	NOUN
asir-1642	183	7	in	in	ADP
asir-1642	183	8	cave	cave	NOUN
asir-1642	183	9	r	r	NOUN
asir-1642	183	10	,	,	PUNCT
asir-1642	183	11	where	where	SCONJ
asir-1642	183	12	its	its	PRON
asir-1642	183	13	inner	inner	NOUN
asir-1642	183	14	is	be	AUX
asir-1642	183	15	the	the	DET
asir-1642	183	16	stationary	stationary	ADJ
asir-1642	183	17	-	-	PUNCT
asir-1642	183	18	standing	standing	ADJ
asir-1642	183	19	-	-	PUNCT
asir-1642	183	20	wave	wave	NOUN
asir-1642	183	21	electromagnetic	electromagnetic	ADJ
asir-1642	183	22	-	-	PUNCT
asir-1642	183	23	wave	wave	NOUN
asir-1642	183	24	[	[	X
asir-1642	183	25	e²+h²	e²+h²	NOUN
asir-1642	183	26	]	]	X
asir-1642	183	27	=	=	NOUN
asir-1642	183	28	2(2r).c	2(2r).c	NOUN
asir-1642	183	29	.	.	PUNCT
asir-1642	184	1	with	with	ADP
asir-1642	184	2	n	n	ADP
asir-1642	184	3	lobes	lobe	NOUN
asir-1642	184	4	representing	represent	VERB
asir-1642	184	5	the	the	DET
asir-1642	184	6	normal	normal	ADJ
asir-1642	184	7	mode	mode	NOUN
asir-1642	184	8	vibration	vibration	NOUN
asir-1642	184	9	with	with	ADP
asir-1642	184	10	frequencies	frequency	NOUN
asir-1642	184	11	=	=	PUNCT
asir-1642	184	12	n.	n.	NOUN
asir-1642	184	13	=	=	PUNCT
asir-1642	184	14	h	h	NOUN
asir-1642	184	15	=	=	PUNCT
asir-1642	184	16	.v	.v	ADJ
asir-1642	185	1	𝑟	𝑟	X
asir-1642	186	1	[	[	X
asir-1642	186	2	1	1	NUM
asir-1642	186	3	+	+	NUM
asir-1642	186	4	√	√	NUM
asir-1642	186	5	]	]	PUNCT
asir-1642	186	6	,	,	PUNCT
asir-1642	186	7	its	its	PRON
asir-1642	186	8	outward	outward	ADV
asir-1642	186	9	as	as	ADP
asir-1642	186	10	the	the	DET
asir-1642	186	11	propagating	propagate	VERB
asir-1642	186	12	electromagnetic	electromagnetic	ADJ
asir-1642	186	13	-	-	PUNCT
asir-1642	186	14	wave	wave	NOUN
asir-1642	186	15	→{[εe²	→{[εe²	NOUN
asir-1642	186	16	+	+	CCONJ
asir-1642	186	17	μb²	μb²	NOUN
asir-1642	186	18	]	]	X
asir-1642	186	19	=	=	SYM
asir-1642	186	20	2.λc.sin.2φ	2.λc.sin.2φ	NUM
asir-1642	186	21	}	}	PUNCT
asir-1642	186	22	←	←	PROPN
asir-1642	186	23	where	where	SCONJ
asir-1642	186	24	particle	particle	NOUN
asir-1642	186	25	2r	2r	NUM
asir-1642	186	26	=	=	SYM
asir-1642	186	27	n	n	PRON
asir-1642	186	28	λ	λ	PROPN
asir-1642	186	29	,	,	PUNCT
asir-1642	186	30	cave	cave	NOUN
asir-1642	186	31	r	r	NOUN
asir-1642	186	32	,	,	PUNCT
asir-1642	186	33	is	be	AUX
asir-1642	186	34	the	the	DET
asir-1642	186	35	electromagnetic	electromagnetic	ADJ
asir-1642	186	36	-	-	PUNCT
asir-1642	186	37	energy	energy	NOUN
asir-1642	186	38	-	-	PUNCT
asir-1642	186	39	storage	storage	NOUN
asir-1642	186	40	,	,	PUNCT
asir-1642	186	41	and	and	CCONJ
asir-1642	186	42	electromagnetic	electromagnetic	ADJ
asir-1642	186	43	-	-	PUNCT
asir-1642	186	44	radiation	radiation	NOUN
asir-1642	186	45	e	e	NOUN
asir-1642	186	46	,	,	PUNCT
asir-1642	186	47	b	b	PROPN
asir-1642	186	48	is	be	AUX
asir-1642	186	49	the	the	DET
asir-1642	186	50	wave	wave	NOUN
asir-1642	186	51	conveyer	conveyer	NOUN
asir-1642	186	52	.	.	PUNCT
asir-1642	187	1	following	follow	VERB
asir-1642	187	2	above	above	ADP
asir-1642	187	3	constituents	constituent	NOUN
asir-1642	187	4	of	of	ADP
asir-1642	187	5	photon	photon	NOUN
asir-1642	187	6	then	then	ADV
asir-1642	187	7	,	,	PUNCT
asir-1642	187	8	since	since	SCONJ
asir-1642	187	9	energy	energy	NOUN
asir-1642	187	10	is	be	AUX
asir-1642	187	11	motion	motion	NOUN
asir-1642	187	12	and	and	CCONJ
asir-1642	187	13	the	the	DET
asir-1642	187	14	,	,	PUNCT
asir-1642	187	15	total	total	ADJ
asir-1642	187	16	-	-	PUNCT
asir-1642	187	17	energy	energy	NOUN
asir-1642	187	18	of	of	ADP
asir-1642	187	19	elementary	elementary	ADJ
asir-1642	187	20	-	-	PUNCT
asir-1642	187	21	particle	particle	NOUN
asir-1642	187	22	is	be	AUX
asir-1642	187	23	equal	equal	ADJ
asir-1642	187	24	to	to	ADP
asir-1642	187	25	the	the	DET
asir-1642	187	26	→	→	SYM
asir-1642	187	27	intrinsic	intrinsic	ADJ
asir-1642	187	28	rotational	rotational	ADJ
asir-1642	187	29	+	+	CCONJ
asir-1642	187	30	kinetic	kinetic	ADJ
asir-1642	187	31	energy	energy	NOUN
asir-1642	187	32	from	from	ADP
asir-1642	187	33	velocity	velocity	NOUN
asir-1642	187	34	,	,	PUNCT
asir-1642	187	35	then	then	ADV
asir-1642	187	36	according	accord	VERB
asir-1642	187	37	to	to	ADP
asir-1642	187	38	the	the	DET
asir-1642	187	39	conservation	conservation	NOUN
asir-1642	187	40	law	law	NOUN
asir-1642	187	41	of	of	ADP
asir-1642	187	42	energy	energy	NOUN
asir-1642	187	43	,	,	PUNCT
asir-1642	187	44	this	this	DET
asir-1642	187	45	energy	energy	NOUN
asir-1642	187	46	is	be	AUX
asir-1642	187	47	stored	store	VERB
asir-1642	187	48	into	into	ADP
asir-1642	187	49	neutral	neutral	ADJ
asir-1642	187	50	caves	cave	NOUN
asir-1642	187	51	as	as	ADP
asir-1642	187	52	stationary	stationary	ADJ
asir-1642	187	53	loops	loop	NOUN
asir-1642	187	54	consisting	consist	VERB
asir-1642	187	55	the	the	DET
asir-1642	187	56	lobes	lobe	NOUN
asir-1642	187	57	,	,	PUNCT
asir-1642	187	58	and	and	CCONJ
asir-1642	187	59	thus	thus	ADV
asir-1642	187	60	producing	produce	VERB
asir-1642	187	61	the	the	DET
asir-1642	187	62	space	space	NOUN
asir-1642	187	63	and	and	CCONJ
asir-1642	187	64	the	the	DET
asir-1642	187	65	anti	anti	ADJ
asir-1642	187	66	space	space	NOUN
asir-1642	187	67	particles	particle	NOUN
asir-1642	187	68	with	with	ADP
asir-1642	187	69	velocity	velocity	NOUN
asir-1642	187	70	vector	vector	NOUN
asir-1642	187	71	the	the	DET
asir-1642	187	72	remaining	remain	VERB
asir-1642	187	73	of	of	ADP
asir-1642	187	74	the	the	DET
asir-1642	187	75	energy	energy	NOUN
asir-1642	187	76	term	term	NOUN
asir-1642	187	77	.	.	PUNCT
asir-1642	188	1	the	the	DET
asir-1642	188	2	breakage	breakage	NOUN
asir-1642	188	3	-	-	PUNCT
asir-1642	188	4	principle	principle	NOUN
asir-1642	188	5	,	,	PUNCT
asir-1642	188	6	is	be	AUX
asir-1642	188	7	the	the	DET
asir-1642	188	8	way	way	NOUN
asir-1642	188	9	of	of	ADP
asir-1642	188	10	energy	energy	NOUN
asir-1642	188	11	conservation	conservation	NOUN
asir-1642	188	12	,	,	PUNCT
asir-1642	188	13	where	where	SCONJ
asir-1642	188	14	energy	energy	NOUN
asir-1642	188	15	never	never	ADV
asir-1642	188	16	annihilates	annihilate	VERB
asir-1642	188	17	and	and	CCONJ
asir-1642	188	18	which	which	PRON
asir-1642	188	19	is	be	AUX
asir-1642	188	20	always	always	ADV
asir-1642	188	21	reverted	revert	VERB
asir-1642	188	22	into	into	ADP
asir-1642	188	23	→	→	SYM
asir-1642	188	24	the	the	DET
asir-1642	188	25	two	two	NUM
asir-1642	188	26	opposites	opposite	NOUN
asir-1642	188	27	[	[	X
asir-1642	188	28	(	(	PUNCT
asir-1642	188	29	±	±	NUM
asir-1642	188	30	w	w	NOUN
asir-1642	188	31	)	)	PUNCT
asir-1642	188	32	or	or	CCONJ
asir-1642	188	33	the	the	DET
asir-1642	188	34	conveyers	conveyer	NOUN
asir-1642	188	35	≡	≡	PROPN
asir-1642	188	36	carriers	carrier	NOUN
asir-1642	188	37	]	]	PUNCT
asir-1642	188	38	and	and	CCONJ
asir-1642	188	39	an	an	DET
asir-1642	188	40	neutral	neutral	ADJ
asir-1642	188	41	part	part	NOUN
asir-1642	188	42	2	2	NUM
asir-1642	188	43	.	.	PUNCT
asir-1642	188	44	i	i	PROPN
asir-1642	188	45	which	which	PRON
asir-1642	188	46	is	be	AUX
asir-1642	188	47	the	the	DET
asir-1642	188	48	energy	energy	NOUN
asir-1642	188	49	-	-	PUNCT
asir-1642	188	50	store	store	NOUN
asir-1642	188	51	≡	≡	PROPN
asir-1642	188	52	tank	tank	NOUN
asir-1642	188	53	energy	energy	NOUN
asir-1642	188	54	≡	≡	PROPN
asir-1642	188	55	or	or	CCONJ
asir-1642	188	56	as	as	ADV
asir-1642	188	57	matter	matter	ADV
asir-1642	188	58	(	(	PUNCT
asir-1642	188	59	+	+	NUM
asir-1642	188	60	w	w	NOUN
asir-1642	188	61	)	)	PUNCT
asir-1642	188	62	,	,	PUNCT
asir-1642	188	63	as	as	ADP
asir-1642	188	64	antimatter	antimatter	NOUN
asir-1642	188	65	(	(	PUNCT
asir-1642	188	66	w	w	NOUN
asir-1642	188	67	)	)	PUNCT
asir-1642	188	68	and	and	CCONJ
asir-1642	188	69	as	as	ADP
asir-1642	188	70	energy	energy	NOUN
asir-1642	188	71	part	part	NOUN
asir-1642	188	72	,	,	PUNCT
asir-1642	188	73	2l	2l	PROPN
asir-1642	188	74	=	=	SYM
asir-1642	188	75	b̅.	b̅.	NUM
asir-1642	188	76	w̅	w̅	X
asir-1642	188	77	i.e.	i.e.	X
asir-1642	188	78	,	,	PUNCT
asir-1642	188	79	energy	energy	NOUN
asir-1642	188	80	≡	≡	PROPN
asir-1642	188	81	motion	motion	NOUN
asir-1642	188	82	≡	≡	PROPN
asir-1642	188	83	space	space	NOUN
asir-1642	188	84	+	+	CCONJ
asir-1642	188	85	anti	anti	ADJ
asir-1642	188	86	space	space	NOUN
asir-1642	188	87	+	+	CCONJ
asir-1642	188	88	kinetic	kinetic	ADJ
asir-1642	188	89	energy	energy	NOUN
asir-1642	188	90	,	,	PUNCT
asir-1642	188	91	vibrations	vibration	NOUN
asir-1642	188	92	of	of	ADP
asir-1642	188	93	systems	system	NOUN
asir-1642	188	94	issues	issue	NOUN
asir-1642	188	95	for	for	ADP
asir-1642	188	96	orbits	orbit	NOUN
asir-1642	188	97	as	as	ADP
asir-1642	188	98	→	→	SYM
asir-1642	188	99	w	w	PROPN
asir-1642	188	100	=	=	SYM
asir-1642	188	101	4π²	4π²	NUM
asir-1642	188	102	.	.	PUNCT
asir-1642	189	1	𝐫³	𝐫³	PROPN
asir-1642	189	2	𝐓²	𝐓²	PROPN
asir-1642	189	3	.	.	PUNCT
asir-1642	190	1	�	�	PROPN
asir-1642	190	2	̅	̅	NOUN
asir-1642	190	3	�	�	NOUN
asir-1642	190	4	=	=	SYM
asir-1642	190	5	4π².r	4π².r	NUM
asir-1642	190	6	³.	³.	X
asir-1642	190	7	𝐟²𝐩.	𝐟²𝐩.	PROPN
asir-1642	190	8	�	�	PROPN
asir-1642	190	9	̅	̅	PROPN
asir-1642	190	10	�	�	PROPN
asir-1642	190	11	←	←	PROPN
asir-1642	190	12	and	and	CCONJ
asir-1642	190	13	agree	agree	VERB
asir-1642	190	14	,	,	PUNCT
asir-1642	190	15	to	to	ADP
asir-1642	190	16	kepler	kepler	ADJ
asir-1642	190	17	celestial	celestial	ADJ
asir-1642	190	18	law	law	NOUN
asir-1642	190	19	such	such	ADJ
asir-1642	190	20	as	as	ADP
asir-1642	190	21	for	for	ADP
asir-1642	190	22	macrocosm	macrocosm	NOUN
asir-1642	190	23	and	and	CCONJ
asir-1642	190	24	microcosm	microcosm	PROPN
asir-1642	190	25	.	.	PUNCT
asir-1642	191	1	h	h	X
asir-1642	191	2	..	..	PUNCT
asir-1642	191	3	the	the	DET
asir-1642	191	4	permeable	permeable	ADJ
asir-1642	191	5	resonance	resonance	NOUN
asir-1642	191	6	-	-	PUNCT
asir-1642	191	7	path	path	NOUN
asir-1642	191	8	:	:	PUNCT
asir-1642	191	9	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	191	10	applied	apply	VERB
asir-1642	191	11	science	science	NOUN
asir-1642	191	12	and	and	CCONJ
asir-1642	191	13	innovative	innovative	ADJ
asir-1642	191	14	research	research	NOUN
asir-1642	191	15	vol	vol	NOUN
asir-1642	191	16	.	.	PROPN
asir-1642	192	1	2	2	NUM
asir-1642	192	2	,	,	PUNCT
asir-1642	192	3	no	no	INTJ
asir-1642	192	4	.	.	NOUN
asir-1642	192	5	4	4	NUM
asir-1642	192	6	,	,	PUNCT
asir-1642	192	7	2018	2018	NUM
asir-1642	192	8	165	165	NUM
asir-1642	192	9	published	publish	VERB
asir-1642	192	10	by	by	ADP
asir-1642	192	11	scholink	scholink	PROPN
asir-1642	192	12	inc	inc	PROPN
asir-1642	192	13	.	.	PROPN
asir-1642	192	14	figure	figure	NOUN
asir-1642	192	15	4	4	NUM
asir-1642	192	16	.	.	PUNCT
asir-1642	193	1	the	the	DET
asir-1642	193	2	permeable	permeable	ADJ
asir-1642	193	3	resonanace	resonanace	NOUN
asir-1642	193	4	path	path	NOUN
asir-1642	193	5	of	of	ADP
asir-1642	193	6	photon	photon	NOUN
asir-1642	193	7	in	in	ADP
asir-1642	193	8	material	material	NOUN
asir-1642	193	9	systems	system	NOUN
asir-1642	193	10	a	a	X
asir-1642	193	11	)	)	PUNCT
asir-1642	193	12	the	the	DET
asir-1642	193	13	transmitted	transmit	VERB
asir-1642	193	14	electromagnetic	electromagnetic	ADJ
asir-1642	193	15	wave	wave	NOUN
asir-1642	193	16	of	of	ADP
asir-1642	193	17	wavelength	wavelength	NOUN
asir-1642	193	18	λ	λ	PROPN
asir-1642	193	19	=	=	NOUN
asir-1642	193	20	2πc	2πc	ADJ
asir-1642	193	21	/	/	SYM
asir-1642	193	22	w	w	PROPN
asir-1642	193	23	≡	≡	PROPN
asir-1642	193	24	c	c	PROPN
asir-1642	193	25	/	/	SYM
asir-1642	193	26	f	f	PROPN
asir-1642	193	27	follows	follow	VERB
asir-1642	193	28	the	the	DET
asir-1642	193	29	hook	hook	NOUN
asir-1642	193	30	’s	’s	PART
asir-1642	193	31	elastic	elastic	ADJ
asir-1642	193	32	deformation	deformation	NOUN
asir-1642	193	33	and	and	CCONJ
asir-1642	193	34	resolves	resolve	NOUN
asir-1642	193	35	into	into	ADP
asir-1642	193	36	the	the	DET
asir-1642	193	37	principal	principal	ADJ
asir-1642	193	38	stresses	stress	NOUN
asir-1642	193	39	-	-	PUNCT
asir-1642	193	40	pattern	pattern	NOUN
asir-1642	193	41	,	,	PUNCT
asir-1642	193	42	2	2	X
asir-1642	193	43	.	.	SYM
asir-1642	193	44	b	b	X
asir-1642	193	45	)	)	PUNCT
asir-1642	193	46	the	the	DET
asir-1642	193	47	permeable	permeable	ADJ
asir-1642	193	48	–	–	PUNCT
asir-1642	193	49	resonance	resonance	NOUN
asir-1642	193	50	path	path	NOUN
asir-1642	193	51	is	be	AUX
asir-1642	193	52	for	for	ADP
asir-1642	193	53	,	,	PUNCT
asir-1642	193	54	1	1	X
asir-1642	193	55	)	)	PUNCT
asir-1642	193	56	solids	solid	NOUN
asir-1642	193	57	→	→	PUNCT
asir-1642	193	58	the	the	DET
asir-1642	193	59	normal	normal	ADJ
asir-1642	193	60	-	-	PUNCT
asir-1642	193	61	mode	mode	NOUN
asir-1642	193	62	-	-	PUNCT
asir-1642	193	63	vibration	vibration	NOUN
asir-1642	193	64	system	system	NOUN
asir-1642	193	65	{	{	PUNCT
asir-1642	193	66	w²	w²	PROPN
asir-1642	193	67	[	[	X
asir-1642	193	68	m	m	X
asir-1642	193	69	]	]	X
asir-1642	194	1	+	+	CCONJ
asir-1642	194	2	[	[	X
asir-1642	194	3	k	k	X
asir-1642	194	4	]	]	X
asir-1642	194	5	(	(	PUNCT
asir-1642	194	6	x	x	NOUN
asir-1642	194	7	)	)	PUNCT
asir-1642	194	8	}	}	PUNCT
asir-1642	194	9	=	=	SYM
asir-1642	194	10	0	0	NUM
asir-1642	194	11	2	2	NUM
asir-1642	194	12	)	)	PUNCT
asir-1642	194	13	liquids	liquid	NOUN
asir-1642	194	14	→the	→the	PRON
asir-1642	194	15	cauchy	cauchy	ADJ
asir-1642	194	16	stress	stress	NOUN
asir-1642	194	17	-	-	PUNCT
asir-1642	194	18	tensor	tensor	NOUN
asir-1642	194	19	as	as	ADP
asir-1642	194	20	momentum	momentum	NOUN
asir-1642	194	21	equation	equation	NOUN
asir-1642	194	22	.σ	.σ	NOUN
asir-1642	195	1	=	=	PUNCT
asir-1642	196	1	p	p	X
asir-1642	196	2	+	+	CCONJ
asir-1642	196	3	.τ	.τ	ADJ
asir-1642	196	4	3	3	NUM
asir-1642	196	5	)	)	PUNCT
asir-1642	196	6	gases	gas	NOUN
asir-1642	196	7	→	→	PUNCT
asir-1642	196	8	the	the	DET
asir-1642	196	9	combined	combine	VERB
asir-1642	196	10	avogadro	avogadro	PROPN
asir-1642	196	11	’s	’s	PART
asir-1642	196	12	pressure	pressure	NOUN
asir-1642	196	13	-	-	PUNCT
asir-1642	196	14	law	law	NOUN
asir-1642	196	15	pv	pv	NOUN
asir-1642	196	16	=	=	SYM
asir-1642	196	17	n	n	CCONJ
asir-1642	196	18	rt	rt	NOUN
asir-1642	196	19	=	=	SYM
asir-1642	196	20	n.mv²/3	n.mv²/3	PROPN
asir-1642	196	21	4	4	NUM
asir-1642	196	22	)	)	PUNCT
asir-1642	196	23	crystals	crystal	NOUN
asir-1642	196	24	→	→	PUNCT
asir-1642	196	25	the	the	DET
asir-1642	196	26	cauchy	cauchy	ADJ
asir-1642	196	27	ellipsoid	ellipsoid	NOUN
asir-1642	196	28	-	-	PUNCT
asir-1642	196	29	stress	stress	NOUN
asir-1642	196	30	-	-	PUNCT
asir-1642	196	31	tensor	tensor	NOUN
asir-1642	196	32	where	where	SCONJ
asir-1642	196	33	ebr	ebr	PROPN
asir-1642	196	34	≡	≡	PROPN
asir-1642	196	35			NOUN
asir-1642	196	36	2	2	NUM
asir-1642	196	37	3	3	NUM
asir-1642	196	38	5	5	NUM
asir-1642	196	39	)	)	PUNCT
asir-1642	196	40	molecules	molecule	NOUN
asir-1642	196	41	→	→	PUNCT
asir-1642	196	42	the	the	DET
asir-1642	196	43	lattice	lattice	PROPN
asir-1642	196	44	crystal	crystal	PROPN
asir-1642	196	45	-arrangement	-arrangement	PROPN
asir-1642	196	46	6	6	NUM
asir-1642	196	47	)	)	PUNCT
asir-1642	196	48	atoms	atom	NOUN
asir-1642	196	49	→	→	PUNCT
asir-1642	196	50	the	the	DET
asir-1642	196	51	chemical	chemical	NOUN
asir-1642	196	52	bonds	bond	NOUN
asir-1642	196	53	relation	relation	NOUN
asir-1642	196	54	7	7	NUM
asir-1642	196	55	)	)	PUNCT
asir-1642	196	56	particles	particle	NOUN
asir-1642	196	57	→	→	PUNCT
asir-1642	196	58	the	the	DET
asir-1642	196	59	resultance	resultance	ADJ
asir-1642	196	60	one	one	NUM
asir-1642	196	61	-	-	PUNCT
asir-1642	196	62	dimensional	dimensional	ADJ
asir-1642	196	63	-	-	PUNCT
asir-1642	196	64	collision	collision	NOUN
asir-1642	196	65	v̅	v̅	NOUN
asir-1642	196	66	=	=	PUNCT
asir-1642	196	67	v̅	v̅	NOUN
asir-1642	196	68	v̅	v̅	X
asir-1642	196	69	=	=	SYM
asir-1642	196	70	w̅	w̅	PROPN
asir-1642	196	71	.	.	PUNCT
asir-1642	197	1	r̅	r̅	ADP
asir-1642	197	2	8)	8)	NUM
asir-1642	197	3	m	m	NOUN
asir-1642	197	4	-	-	PUNCT
asir-1642	197	5	points	point	NOUN
asir-1642	197	6	→	→	PUNCT
asir-1642	198	1	the	the	DET
asir-1642	198	2	resonance	resonance	NOUN
asir-1642	198	3	-	-	PUNCT
asir-1642	198	4	frequencies	frequency	NOUN
asir-1642	198	5	𝐟	𝐟	NOUN
asir-1642	199	1	[	[	X
asir-1642	199	2	s≡	s≡	NOUN
asir-1642	199	3	,	,	PUNCT
asir-1642	199	4	2	2	NUM
asir-1642	199	5	,	,	PUNCT
asir-1642	199	6	3	3	NUM
asir-1642	199	7	,	,	PUNCT
asir-1642	199	8	r	r	NOUN
asir-1642	199	9	w²	w²	NOUN
asir-1642	199	10	]	]	PUNCT
asir-1642	199	11	=	=	PUNCT
asir-1642	200	1	𝐟𝐧=	𝐟𝐧=	NOUN
asir-1642	200	2	n	n	CCONJ
asir-1642	200	3	(	(	PUNCT
asir-1642	200	4	+	+	ADV
asir-1642	200	5	√	√	ADJ
asir-1642	200	6	)	)	PUNCT
asir-1642	201	1	=	=	PUNCT
asir-1642	201	2	.b̅	.b̅	PROPN
asir-1642	201	3	²	²	NUM
asir-1642	201	4	9	9	NUM
asir-1642	201	5	)	)	PUNCT
asir-1642	201	6	cave	cave	NOUN
asir-1642	201	7	-	-	PUNCT
asir-1642	201	8	orbit→	orbit→	PROPN
asir-1642	201	9	the	the	DET
asir-1642	201	10	relation	relation	NOUN
asir-1642	201	11	c.	c.	PROPN
asir-1642	201	12	=	=	PROPN
asir-1642	201	13	v	v	PROPN
asir-1642	201	14	,	,	PUNCT
asir-1642	201	15	light	light	NOUN
asir-1642	201	16	-	-	PUNCT
asir-1642	201	17	velocity	velocity	NOUN
asir-1642	201	18	3.10	3.10	NUM
asir-1642	201	19	m	m	NOUN
asir-1642	201	20	/	/	SYM
asir-1642	201	21	s*1.10	s*1.10	ADJ
asir-1642	201	22	2	2	NUM
asir-1642	201	23	m	m	NOUN
asir-1642	201	24	cave	cave	NOUN
asir-1642	201	25	=	=	NOUN
asir-1642	201	26	3.10	3.10	NUM
asir-1642	201	27	3	3	NUM
asir-1642	201	28	m²/s	m²/s	NOUN
asir-1642	201	29	are	be	AUX
asir-1642	201	30	the	the	DET
asir-1642	201	31	cave	cave	NOUN
asir-1642	201	32	-	-	PUNCT
asir-1642	201	33	energy	energy	NOUN
asir-1642	201	34	-	-	PUNCT
asir-1642	201	35	plane	plane	NOUN
asir-1642	201	36	-	-	PUNCT
asir-1642	201	37	rims	rim	NOUN
asir-1642	201	38	in	in	ADP
asir-1642	201	39	atom	atom	NOUN
asir-1642	201	40	’s	’s	PART
asir-1642	201	41	,	,	PUNCT
asir-1642	201	42	planet	planet	NOUN
asir-1642	201	43	orbits	orbit	NOUN
asir-1642	201	44	remarks	remark	VERB
asir-1642	201	45	:	:	PUNCT
asir-1642	201	46	the	the	DET
asir-1642	201	47	path	path	NOUN
asir-1642	201	48	permeable	permeable	ADJ
asir-1642	201	49	to	to	ADP
asir-1642	201	50	a	a	DET
asir-1642	201	51	common	common	ADJ
asir-1642	201	52	motion	motion	NOUN
asir-1642	201	53	is	be	AUX
asir-1642	201	54	following	follow	VERB
asir-1642	201	55	one	one	NUM
asir-1642	201	56	of	of	ADP
asir-1642	201	57	,	,	PUNCT
asir-1642	201	58	w	w	PROPN
asir-1642	201	59	,	,	PUNCT
asir-1642	201	60	f	f	PROPN
asir-1642	201	61	,	,	PUNCT
asir-1642	201	62	𝐧	𝐧	INTJ
asir-1642	201	63	,	,	PUNCT
asir-1642	201	64	quantities	quantity	NOUN
asir-1642	201	65	as	as	ADP
asir-1642	201	66	below	below	ADP
asir-1642	201	67	procedure	procedure	NOUN
asir-1642	201	68	,	,	PUNCT
asir-1642	201	69	1	1	NUM
asir-1642	201	70	..	..	PUNCT
asir-1642	201	71	a	a	DET
asir-1642	201	72	transmitted	transmit	VERB
asir-1642	201	73	electromagnetic	electromagnetic	ADJ
asir-1642	201	74	wave	wave	NOUN
asir-1642	201	75	with	with	ADP
asir-1642	201	76	angular	angular	ADJ
asir-1642	201	77	velocity	velocity	NOUN
asir-1642	201	78	vector	vector	NOUN
asir-1642	201	79	w	w	NOUN
asir-1642	201	80	=	=	SYM
asir-1642	201	81	2πf	2πf	NOUN
asir-1642	202	1	=	=	PUNCT
asir-1642	202	2	2πc	2πc	ADJ
asir-1642	202	3	/	/	SYM
asir-1642	202	4	λ	λ	NOUN
asir-1642	202	5	strikes	strike	NOUN
asir-1642	202	6	on	on	ADP
asir-1642	202	7	a	a	DET
asir-1642	202	8	body	body	NOUN
asir-1642	202	9	.	.	PUNCT
asir-1642	203	1	2	2	X
asir-1642	203	2	..	..	PUNCT
asir-1642	203	3	the	the	DET
asir-1642	203	4	electromagnetic	electromagnetic	ADJ
asir-1642	203	5	wave	wave	NOUN
asir-1642	203	6	entering	enter	VERB
asir-1642	203	7	into	into	ADP
asir-1642	203	8	the	the	DET
asir-1642	203	9	body	body	NOUN
asir-1642	203	10	follows	follow	VERB
asir-1642	203	11	hook	hook	NOUN
asir-1642	203	12	’s	’s	PART
asir-1642	203	13	elastic	elastic	ADJ
asir-1642	203	14	deformation	deformation	NOUN
asir-1642	203	15	,	,	PUNCT
asir-1642	203	16	and	and	CCONJ
asir-1642	203	17	resolves	resolve	NOUN
asir-1642	203	18	into	into	ADP
asir-1642	203	19	the	the	DET
asir-1642	203	20	principal	principal	ADJ
asir-1642	203	21	net	net	ADJ
asir-1642	203	22	-	-	PUNCT
asir-1642	203	23	stresses	stress	NOUN
asir-1642	203	24	-	-	PUNCT
asir-1642	203	25	pattern	pattern	NOUN
asir-1642	203	26	.	.	PUNCT
asir-1642	204	1	3	3	X
asir-1642	204	2	..	..	PUNCT
asir-1642	204	3	because	because	SCONJ
asir-1642	204	4	of	of	ADP
asir-1642	204	5	principal	principal	ADJ
asir-1642	204	6	-	-	PUNCT
asir-1642	204	7	stresses	stress	NOUN
asir-1642	204	8	resolving	resolve	VERB
asir-1642	204	9	,	,	PUNCT
asir-1642	204	10	different	different	ADJ
asir-1642	204	11	refractive	refractive	ADJ
asir-1642	204	12	-	-	PUNCT
asir-1642	204	13	indices	index	NOUN
asir-1642	204	14	are	be	AUX
asir-1642	204	15	experienced	experience	VERB
asir-1642	204	16	on	on	ADP
asir-1642	204	17	their	their	PRON
asir-1642	204	18	perpendicular	perpendicular	ADJ
asir-1642	204	19	components	component	NOUN
asir-1642	204	20	due	due	ADP
asir-1642	204	21	to	to	ADP
asir-1642	204	22	the	the	DET
asir-1642	204	23	birefringence	birefringence	NOUN
asir-1642	204	24	.	.	PUNCT
asir-1642	205	1	4	4	NUM
asir-1642	205	2	..	..	PUNCT
asir-1642	205	3	the	the	DET
asir-1642	205	4	difference	difference	NOUN
asir-1642	205	5	in	in	ADP
asir-1642	205	6	the	the	DET
asir-1642	205	7	refractive	refractive	ADJ
asir-1642	205	8	-	-	PUNCT
asir-1642	205	9	indices	index	NOUN
asir-1642	205	10	leads	lead	VERB
asir-1642	205	11	to	to	ADP
asir-1642	205	12	a	a	DET
asir-1642	205	13	relative	relative	ADJ
asir-1642	205	14	-	-	PUNCT
asir-1642	205	15	phase	phase	NOUN
asir-1642	205	16	-	-	PUNCT
asir-1642	205	17	retardation	retardation	NOUN
asir-1642	205	18	between	between	ADP
asir-1642	205	19	the	the	DET
asir-1642	205	20	components	component	NOUN
asir-1642	205	21	given	give	VERB
asir-1642	205	22	as	as	ADP
asir-1642	205	23	∆	∆	PROPN
asir-1642	205	24	=	=	SYM
asir-1642	205	25	(	(	PUNCT
asir-1642	205	26	2πc	2πc	ADJ
asir-1642	205	27	/	/	SYM
asir-1642	205	28	λ).k	λ).k	PROPN
asir-1642	205	29	.	.	PUNCT
asir-1642	206	1	(	(	PUNCT
asir-1642	206	2	2	2	NUM
asir-1642	206	3	)	)	PUNCT
asir-1642	206	4	or	or	CCONJ
asir-1642	206	5	as	as	ADP
asir-1642	206	6	2	2	NUM
asir-1642	206	7	=	=	SYM
asir-1642	206	8	[	[	PUNCT
asir-1642	206	9	]	]	X
asir-1642	206	10	.	.	PUNCT
asir-1642	207	1	∆	∆	PROPN
asir-1642	207	2	2	2	NUM
asir-1642	207	3	c	c	X
asir-1642	207	4	=	=	PUNCT
asir-1642	207	5	k.	k.	PROPN
asir-1642	208	1	[	[	X
asir-1642	208	2	]	]	X
asir-1642	208	3	…	…	PUNCT
asir-1642	208	4	…	…	PUNCT
asir-1642	208	5	…	…	PUNCT
asir-1642	208	6	.(a	.(a	PUNCT
asir-1642	208	7	)	)	PUNCT
asir-1642	208	8	where	where	SCONJ
asir-1642	208	9	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	208	10	applied	apply	VERB
asir-1642	208	11	science	science	NOUN
asir-1642	208	12	and	and	CCONJ
asir-1642	208	13	innovative	innovative	ADJ
asir-1642	208	14	research	research	NOUN
asir-1642	208	15	vol	vol	NOUN
asir-1642	208	16	.	.	PROPN
asir-1642	209	1	2	2	NUM
asir-1642	209	2	,	,	PUNCT
asir-1642	209	3	no	no	INTJ
asir-1642	209	4	.	.	NOUN
asir-1642	209	5	4	4	NUM
asir-1642	209	6	,	,	PUNCT
asir-1642	209	7	2018	2018	NUM
asir-1642	209	8	166	166	NUM
asir-1642	209	9	published	publish	VERB
asir-1642	209	10	by	by	ADP
asir-1642	209	11	scholink	scholink	PROPN
asir-1642	209	12	inc	inc	PROPN
asir-1642	209	13	.	.	PUNCT
asir-1642	209	14	∆	∆	PROPN
asir-1642	210	1	=	=	PUNCT
asir-1642	210	2	the	the	DET
asir-1642	210	3	controlled	control	VERB
asir-1642	210	4	phase	phase	NOUN
asir-1642	210	5	-	-	PUNCT
asir-1642	210	6	retardation	retardation	NOUN
asir-1642	210	7	from	from	ADP
asir-1642	210	8	the	the	DET
asir-1642	210	9	transmitted	transmit	VERB
asir-1642	210	10	electromagnetic	electromagnetic	ADJ
asir-1642	210	11	wave	wave	NOUN
asir-1642	210	12	λ	λ	NOUN
asir-1642	210	13	=	=	SYM
asir-1642	210	14	2	2	NUM
asir-1642	210	15	c	c	NOUN
asir-1642	210	16	w	w	VERB
asir-1642	210	17	,	,	PUNCT
asir-1642	210	18	is	be	AUX
asir-1642	210	19	the	the	DET
asir-1642	210	20	vacuum	vacuum	NOUN
asir-1642	210	21	wavelength	wavelength	NOUN
asir-1642	210	22	d	d	PROPN
asir-1642	210	23	=	=	PUNCT
asir-1642	210	24	the	the	DET
asir-1642	210	25	thickness	thickness	NOUN
asir-1642	210	26	of	of	ADP
asir-1642	210	27	the	the	DET
asir-1642	210	28	body	body	NOUN
asir-1642	210	29	or	or	CCONJ
asir-1642	210	30	of	of	ADP
asir-1642	210	31	specimen	speciman	NOUN
asir-1642	210	32	5	5	NUM
asir-1642	210	33	..	..	PUNCT
asir-1642	210	34	the	the	DET
asir-1642	210	35	relative	relative	ADJ
asir-1642	210	36	phase	phase	NOUN
asir-1642	210	37	retardation	retardation	NOUN
asir-1642	210	38	changes	change	VERB
asir-1642	210	39	the	the	DET
asir-1642	210	40	polarization	polarization	NOUN
asir-1642	210	41	of	of	ADP
asir-1642	210	42	the	the	DET
asir-1642	210	43	transmitted	transmit	VERB
asir-1642	210	44	em	em	PRON
asir-1642	210	45	wave	wave	NOUN
asir-1642	210	46	,	,	PUNCT
asir-1642	210	47	which	which	PRON
asir-1642	210	48	changes	change	VERB
asir-1642	210	49	also	also	ADV
asir-1642	210	50	the	the	DET
asir-1642	210	51	polarization	polarization	NOUN
asir-1642	210	52	of	of	ADP
asir-1642	210	53	the	the	DET
asir-1642	210	54	principal	principal	NOUN
asir-1642	210	55	stresses	stress	NOUN
asir-1642	210	56	,	,	PUNCT
asir-1642	210	57	and	and	CCONJ
asir-1642	210	58	thus	thus	ADV
asir-1642	210	59	many	many	ADJ
asir-1642	210	60	different	different	ADJ
asir-1642	210	61	waves	wave	NOUN
asir-1642	210	62	are	be	AUX
asir-1642	210	63	so	so	ADV
asir-1642	210	64	produced	produce	VERB
asir-1642	210	65	.	.	PUNCT
asir-1642	211	1	the	the	DET
asir-1642	211	2	optical	optical	ADJ
asir-1642	211	3	interference	interference	NOUN
asir-1642	211	4	of	of	ADP
asir-1642	211	5	the	the	DET
asir-1642	211	6	waves	wave	NOUN
asir-1642	211	7	fringe	fringe	NOUN
asir-1642	211	8	-	-	PUNCT
asir-1642	211	9	pattern	pattern	NOUN
asir-1642	211	10	are	be	AUX
asir-1642	211	11	revealed	reveal	VERB
asir-1642	211	12	with	with	ADP
asir-1642	211	13	fringe	fringe	NOUN
asir-1642	211	14	-	-	PUNCT
asir-1642	211	15	order	order	NOUN
asir-1642	211	16	n	n	PRON
asir-1642	211	17	=	=	NOUN
asir-1642	211	18	∆/2π	∆/2π	NOUN
asir-1642	211	19	dependent	dependent	ADJ
asir-1642	211	20	on	on	ADP
asir-1642	211	21	relative	relative	ADJ
asir-1642	211	22	-	-	PUNCT
asir-1642	211	23	retardation	retardation	NOUN
asir-1642	211	24	.	.	PUNCT
asir-1642	212	1	6	6	NUM
asir-1642	212	2	..	..	PUNCT
asir-1642	212	3	by	by	ADP
asir-1642	212	4	studying	study	VERB
asir-1642	212	5	the	the	DET
asir-1642	212	6	fringe	fringe	NOUN
asir-1642	212	7	-	-	PUNCT
asir-1642	212	8	pattern	pattern	NOUN
asir-1642	212	9	one	one	PRON
asir-1642	212	10	can	can	AUX
asir-1642	212	11	determine	determine	VERB
asir-1642	212	12	the	the	DET
asir-1642	212	13	state	state	NOUN
asir-1642	212	14	of	of	ADP
asir-1642	212	15	stress	stress	NOUN
asir-1642	212	16	at	at	ADP
asir-1642	212	17	various	various	ADJ
asir-1642	212	18	points	point	NOUN
asir-1642	212	19	of	of	ADP
asir-1642	212	20	the	the	DET
asir-1642	212	21	material	material	NOUN
asir-1642	212	22	and	and	CCONJ
asir-1642	212	23	the	the	DET
asir-1642	212	24	general	general	ADJ
asir-1642	212	25	permeable	permeable	ADJ
asir-1642	212	26	paths	path	NOUN
asir-1642	212	27	of	of	ADP
asir-1642	212	28	the	the	DET
asir-1642	212	29	electromagnetic	electromagnetic	ADJ
asir-1642	212	30	-	-	PUNCT
asir-1642	212	31	state	state	NOUN
asir-1642	212	32	of	of	ADP
asir-1642	212	33	the	the	DET
asir-1642	212	34	body	body	NOUN
asir-1642	212	35	.	.	PUNCT
asir-1642	213	1	in	in	ADP
asir-1642	213	2	figure	figure	NOUN
asir-1642	213	3	4	4	NUM
asir-1642	213	4	is	be	AUX
asir-1642	213	5	seen	see	VERB
asir-1642	213	6	the	the	DET
asir-1642	213	7	energy	energy	NOUN
asir-1642	213	8	-	-	PUNCT
asir-1642	213	9	storage	storage	NOUN
asir-1642	213	10	p	p	NOUN
asir-1642	213	11	,	,	PUNCT
asir-1642	213	12	which	which	PRON
asir-1642	213	13	is	be	AUX
asir-1642	213	14	transported	transport	VERB
asir-1642	213	15	by	by	ADP
asir-1642	213	16	the	the	DET
asir-1642	213	17	electromagnetic	electromagnetic	ADJ
asir-1642	213	18	conveyer	conveyer	NOUN
asir-1642	213	19	.	.	PUNCT
asir-1642	214	1	the	the	DET
asir-1642	214	2	energy	energy	NOUN
asir-1642	214	3	-	-	PUNCT
asir-1642	214	4	storages	storage	NOUN
asir-1642	214	5	r	r	NOUN
asir-1642	214	6	=	=	SYM
asir-1642	214	7	n.	n.	NOUN
asir-1642	214	8	[	[	PUNCT
asir-1642	214	9	2	2	NUM
asir-1642	214	10	]	]	PUNCT
asir-1642	214	11	≡	≡	PROPN
asir-1642	214	12	w	w	PROPN
asir-1642	214	13	(	(	PUNCT
asir-1642	214	14	+	+	X
asir-1642	214	15	)	)	PUNCT
asir-1642	214	16	=	=	SYM
asir-1642	215	1	[	[	PUNCT
asir-1642	215	2	𝜋	𝜋	NOUN
asir-1642	215	3	²f	²f	NOUN
asir-1642	215	4	3	3	NUM
asir-1642	215	5	]	]	PUNCT
asir-1642	215	6	.n.(n+1	.n.(n+1	NUM
asir-1642	215	7	)	)	PUNCT
asir-1642	215	8	,	,	PUNCT
asir-1642	215	9	are	be	AUX
asir-1642	215	10	travelling	travel	VERB
asir-1642	215	11	through	through	ADP
asir-1642	215	12	bodies	body	NOUN
asir-1642	215	13	and	and	CCONJ
asir-1642	215	14	follow	follow	VERB
asir-1642	215	15	,	,	PUNCT
asir-1642	215	16	lame	lame	ADJ
asir-1642	215	17	stress	stress	NOUN
asir-1642	215	18	ellipsoid	ellipsoid	NOUN
asir-1642	215	19	²	²	PROPN
asir-1642	216	1	+	+	NOUN
asir-1642	216	2	2²	2²	NUM
asir-1642	216	3	+	+	SYM
asir-1642	216	4	3²	3²	NUM
asir-1642	216	5	=	=	SYM
asir-1642	216	6	t	t	NOUN
asir-1642	216	7	²	²	NUM
asir-1642	216	8	²	²	PROPN
asir-1642	216	9	+	+	NUM
asir-1642	216	10	t	t	PROPN
asir-1642	216	11	²	²	NUM
asir-1642	216	12	²	²	PROPN
asir-1642	216	13	+	+	NUM
asir-1642	216	14	t	t	PROPN
asir-1642	216	15	²	²	NUM
asir-1642	216	16	²	²	NUM
asir-1642	216	17	=	=	SYM
asir-1642	216	18	1	1	NUM
asir-1642	216	19	on	on	ADP
asir-1642	216	20	principal	principal	NOUN
asir-1642	216	21	stresses	stress	NOUN
asir-1642	216	22			PROPN
asir-1642	216	23	,	,	PUNCT
asir-1642	216	24			PROPN
asir-1642	216	25	2	2	NUM
asir-1642	216	26	,	,	PUNCT
asir-1642	216	27			PROPN
asir-1642	216	28	3	3	NUM
asir-1642	216	29	,	,	PUNCT
asir-1642	216	30	which	which	PRON
asir-1642	216	31	is	be	AUX
asir-1642	216	32	the	the	DET
asir-1642	216	33	passage	passage	NOUN
asir-1642	216	34	through	through	ADP
asir-1642	216	35	which	which	PRON
asir-1642	216	36	forces	force	NOUN
asir-1642	216	37	(	(	PUNCT
asir-1642	216	38	the	the	DET
asir-1642	216	39	em	em	NOUN
asir-1642	216	40	-	-	PUNCT
asir-1642	216	41	radiation	radiation	NOUN
asir-1642	216	42	)	)	PUNCT
asir-1642	216	43	travel	travel	NOUN
asir-1642	216	44	in	in	ADP
asir-1642	216	45	any	any	DET
asir-1642	216	46	solid	solid	ADJ
asir-1642	216	47	either	either	CCONJ
asir-1642	216	48	in	in	ADP
asir-1642	216	49	motion	motion	NOUN
asir-1642	216	50	or	or	CCONJ
asir-1642	216	51	at	at	ADP
asir-1642	216	52	rest	rest	NOUN
asir-1642	216	53	.	.	PUNCT
asir-1642	217	1	laplace	laplace	PROPN
asir-1642	217	2	’s	’s	PART
asir-1642	217	3	orbital	orbital	ADJ
asir-1642	217	4	angular	angular	ADJ
asir-1642	217	5	-	-	PUNCT
asir-1642	217	6	momentum	momentum	NOUN
asir-1642	217	7	e	e	NOUN
asir-1642	217	8	.2	.2	NUM
asir-1642	217	9	=	=	SYM
asir-1642	217	10	1	1	NUM
asir-1642	217	11	and	and	CCONJ
asir-1642	217	12	for	for	ADP
asir-1642	217	13	n	n	NOUN
asir-1642	217	14	=	=	SYM
asir-1642	217	15	0,1,2,3,.	0,1,2,3,.	NUM
asir-1642	217	16	n	n	CCONJ
asir-1642	217	17	,	,	PUNCT
asir-1642	217	18	consist	consist	VERB
asir-1642	217	19	the	the	DET
asir-1642	217	20	eigenvalues	eigenvalue	NOUN
asir-1642	217	21	operator	operator	NOUN
asir-1642	217	22	z	z	NOUN
asir-1642	217	23	which	which	PRON
asir-1642	217	24	agree	agree	VERB
asir-1642	217	25	with	with	ADP
asir-1642	217	26	prior	prior	ADJ
asir-1642	217	27	resonance	resonance	NOUN
asir-1642	217	28	-	-	PUNCT
asir-1642	217	29	frequencies	frequency	NOUN
asir-1642	217	30	𝐟	𝐟	NOUN
asir-1642	218	1	[	[	X
asir-1642	218	2	s≡	s≡	NOUN
asir-1642	218	3	,	,	PUNCT
asir-1642	218	4	2	2	NUM
asir-1642	218	5	,	,	PUNCT
asir-1642	218	6	3	3	NUM
asir-1642	218	7	,	,	PUNCT
asir-1642	218	8	r	r	NOUN
asir-1642	218	9	w²	w²	NOUN
asir-1642	218	10	]	]	PUNCT
asir-1642	218	11	as	as	ADP
asir-1642	218	12	wavelengths	wavelength	NOUN
asir-1642	218	13	λ	λ	PROPN
asir-1642	218	14	≡	≡	PROPN
asir-1642	218	15	[	[	PUNCT
asir-1642	218	16	,	,	PUNCT
asir-1642	218	17	2	2	NUM
asir-1642	218	18	…	…	PUNCT
asir-1642	218	19	=	=	SYM
asir-1642	218	20	w²]≡	w²]≡	VERB
asir-1642	218	21	the	the	DET
asir-1642	218	22	n	n	DET
asir-1642	218	23	lobes	lobe	NOUN
asir-1642	218	24	,	,	PUNCT
asir-1642	218	25	or	or	CCONJ
asir-1642	218	26	→	→	SYM
asir-1642	218	27	=	=	SYM
asir-1642	218	28	n	n	CCONJ
asir-1642	218	29	(	(	PUNCT
asir-1642	218	30	+	+	NOUN
asir-1642	218	31	√	√	ADJ
asir-1642	218	32	)	)	PUNCT
asir-1642	219	1	=	=	PUNCT
asir-1642	219	2	.b̅	.b̅	PROPN
asir-1642	219	3	²	²	NUM
asir-1642	219	4	,	,	PUNCT
asir-1642	219	5	a	a	DET
asir-1642	219	6	principal	principal	NOUN
asir-1642	219	7	-	-	PUNCT
asir-1642	219	8	stresses	stress	NOUN
asir-1642	219	9	σ	σ	NOUN
asir-1642	219	10	,	,	PUNCT
asir-1642	219	11	and	and	CCONJ
asir-1642	219	12	a	a	DET
asir-1642	219	13	resonance	resonance	NOUN
asir-1642	219	14	-	-	PUNCT
asir-1642	219	15	frequencies	frequency	NOUN
asir-1642	219	16	𝐟	𝐟	PRON
asir-1642	219	17	relation	relation	NOUN
asir-1642	219	18	,	,	PUNCT
asir-1642	219	19	which	which	PRON
asir-1642	219	20	is	be	AUX
asir-1642	219	21	the	the	DET
asir-1642	219	22	energy	energy	NOUN
asir-1642	219	23	stored	store	VERB
asir-1642	219	24	in	in	ADP
asir-1642	219	25	the	the	DET
asir-1642	219	26	material	material	ADJ
asir-1642	219	27	-	-	PUNCT
asir-1642	219	28	points	point	NOUN
asir-1642	219	29	-	-	PUNCT
asir-1642	219	30	lobes	lobe	NOUN
asir-1642	219	31	.	.	PUNCT
asir-1642	220	1	[	[	X
asir-1642	220	2	70	70	NUM
asir-1642	220	3	]	]	X
asir-1642	220	4	physical	physical	ADJ
asir-1642	220	5	properties	property	NOUN
asir-1642	220	6	and	and	CCONJ
asir-1642	220	7	crystal	crystal	NOUN
asir-1642	220	8	-	-	PUNCT
asir-1642	220	9	types	type	NOUN
asir-1642	220	10	:	:	PUNCT
asir-1642	220	11	the	the	DET
asir-1642	220	12	physical	physical	ADJ
asir-1642	220	13	properties	property	NOUN
asir-1642	220	14	of	of	ADP
asir-1642	220	15	crystals	crystal	NOUN
asir-1642	220	16	,	,	PUNCT
asir-1642	220	17	depend	depend	VERB
asir-1642	220	18	on	on	ADP
asir-1642	220	19	the	the	DET
asir-1642	220	20	kinds	kind	NOUN
asir-1642	220	21	and	and	CCONJ
asir-1642	220	22	strengths	strength	NOUN
asir-1642	220	23	of	of	ADP
asir-1642	220	24	the	the	DET
asir-1642	220	25	attractive	attractive	ADJ
asir-1642	220	26	forces	force	NOUN
asir-1642	220	27	that	that	PRON
asir-1642	220	28	hold	hold	VERB
asir-1642	220	29	the	the	DET
asir-1642	220	30	particles	particle	NOUN
asir-1642	220	31	together	together	ADV
asir-1642	220	32	in	in	ADP
asir-1642	220	33	the	the	DET
asir-1642	220	34	bodies	body	NOUN
asir-1642	220	35	[	[	X
asir-1642	220	36	solids	solid	NOUN
asir-1642	220	37	,	,	PUNCT
asir-1642	220	38	liquids	liquid	NOUN
asir-1642	220	39	,	,	PUNCT
asir-1642	220	40	gases	gas	NOUN
asir-1642	220	41	,	,	PUNCT
asir-1642	220	42	crystals	crystal	NOUN
asir-1642	220	43	etc	etc	X
asir-1642	220	44	.	.	X
asir-1642	220	45	]	]	PUNCT
asir-1642	220	46	while	while	SCONJ
asir-1642	220	47	the	the	DET
asir-1642	220	48	types	type	NOUN
asir-1642	220	49	depend	depend	VERB
asir-1642	220	50	upon	upon	SCONJ
asir-1642	220	51	the	the	DET
asir-1642	220	52	kinds	kind	NOUN
asir-1642	220	53	of	of	ADP
asir-1642	220	54	particles	particle	NOUN
asir-1642	220	55	located	locate	VERB
asir-1642	220	56	at	at	ADP
asir-1642	220	57	sites	site	NOUN
asir-1642	220	58	in	in	ADP
asir-1642	220	59	the	the	DET
asir-1642	220	60	lattice	lattice	NOUN
asir-1642	220	61	-	-	PUNCT
asir-1642	220	62	material	material	NOUN
asir-1642	220	63	-	-	PUNCT
asir-1642	220	64	geometry	geometry	NOUN
asir-1642	220	65	-	-	PUNCT
asir-1642	220	66	formation	formation	NOUN
asir-1642	220	67	.	.	PUNCT
asir-1642	221	1	an	an	DET
asir-1642	221	2	ion	ion	NOUN
asir-1642	221	3	is	be	AUX
asir-1642	221	4	an	an	DET
asir-1642	221	5	atom	atom	NOUN
asir-1642	221	6	or	or	CCONJ
asir-1642	221	7	molecule	molecule	NOUN
asir-1642	221	8	in	in	ADP
asir-1642	221	9	which	which	PRON
asir-1642	221	10	the	the	DET
asir-1642	221	11	number	number	NOUN
asir-1642	221	12	of	of	ADP
asir-1642	221	13	electrons	electron	NOUN
asir-1642	221	14	differs	differ	VERB
asir-1642	221	15	the	the	DET
asir-1642	221	16	number	number	NOUN
asir-1642	221	17	of	of	ADP
asir-1642	221	18	protons	proton	NOUN
asir-1642	221	19	,	,	PUNCT
asir-1642	221	20	or	or	CCONJ
asir-1642	221	21	≠	≠	PROPN
asir-1642	221	22	p	p	NOUN
asir-1642	221	23	,	,	PUNCT
asir-1642	221	24	and	and	CCONJ
asir-1642	221	25	if	if	SCONJ
asir-1642	221	26	>	>	X
asir-1642	221	27	p	p	NOUN
asir-1642	221	28	or	or	CCONJ
asir-1642	221	29	<	<	X
asir-1642	221	30	p	p	X
asir-1642	221	31	then	then	ADV
asir-1642	221	32	is	be	AUX
asir-1642	221	33	negative	negative	ADJ
asir-1642	221	34	or	or	CCONJ
asir-1642	221	35	positive	positive	ADJ
asir-1642	221	36	ion	ion	NOUN
asir-1642	221	37	.	.	PUNCT
asir-1642	222	1	lattice	lattice	PROPN
asir-1642	222	2	-	-	PUNCT
asir-1642	222	3	crystal	crystal	NOUN
asir-1642	222	4	is	be	AUX
asir-1642	222	5	a	a	DET
asir-1642	222	6	regular	regular	ADJ
asir-1642	222	7	3d	3d	NOUN
asir-1642	222	8	geometrical	geometrical	ADJ
asir-1642	222	9	arrangement	arrangement	NOUN
asir-1642	222	10	of	of	ADP
asir-1642	222	11	atoms	atom	NOUN
asir-1642	222	12	,	,	PUNCT
asir-1642	222	13	molecules	molecule	NOUN
asir-1642	222	14	or	or	CCONJ
asir-1642	222	15	ions	ion	NOUN
asir-1642	222	16	in	in	ADP
asir-1642	222	17	a	a	DET
asir-1642	222	18	crystal	crystal	NOUN
asir-1642	222	19	,	,	PUNCT
asir-1642	222	20	which	which	PRON
asir-1642	222	21	follows	follow	VERB
asir-1642	222	22	the	the	DET
asir-1642	222	23	material	material	NOUN
asir-1642	222	24	-	-	PUNCT
asir-1642	222	25	geometry	geometry	NOUN
asir-1642	222	26	rules	rule	NOUN
asir-1642	222	27	.	.	PUNCT
asir-1642	223	1	[	[	X
asir-1642	223	2	70	70	NUM
asir-1642	223	3	]	]	X
asir-1642	223	4	lattice	lattice	NOUN
asir-1642	223	5	-	-	PUNCT
asir-1642	223	6	energy	energy	NOUN
asir-1642	223	7	is	be	AUX
asir-1642	223	8	the	the	DET
asir-1642	223	9	energy	energy	NOUN
asir-1642	223	10	required	require	VERB
asir-1642	223	11	to	to	PART
asir-1642	223	12	separate	separate	VERB
asir-1642	223	13	the	the	DET
asir-1642	223	14	ions	ion	NOUN
asir-1642	223	15	of	of	ADP
asir-1642	223	16	an	an	DET
asir-1642	223	17	ionic	ionic	ADJ
asir-1642	223	18	,	,	PUNCT
asir-1642	223	19	with	with	ADP
asir-1642	223	20	atoms	atom	NOUN
asir-1642	223	21	or	or	CCONJ
asir-1642	223	22	molecules	molecule	NOUN
asir-1642	223	23	solid	solid	ADJ
asir-1642	223	24	.	.	PUNCT
asir-1642	224	1	the	the	DET
asir-1642	224	2	mapping	mapping	NOUN
asir-1642	224	3	of	of	ADP
asir-1642	224	4	crystal	crystal	NOUN
asir-1642	224	5	-	-	PUNCT
asir-1642	224	6	types	type	NOUN
asir-1642	224	7	is	be	AUX
asir-1642	224	8	as	as	ADV
asir-1642	224	9	below	below	ADV
asir-1642	224	10	,	,	PUNCT
asir-1642	224	11	type	type	NOUN
asir-1642	224	12	-	-	PUNCT
asir-1642	224	13	particles	particle	NOUN
asir-1642	224	14	at	at	ADP
asir-1642	224	15	sites	site	NOUN
asir-1642	224	16	-	-	PUNCT
asir-1642	224	17	type	type	NOUN
asir-1642	224	18	of	of	ADP
asir-1642	224	19	bounding	bounding	NOUN
asir-1642	224	20	-	-	PUNCT
asir-1642	224	21	force	force	NOUN
asir-1642	224	22	-	-	PUNCT
asir-1642	224	23	properties	property	NOUN
asir-1642	224	24	-	-	PUNCT
asir-1642	224	25	em	em	NOUN
asir-1642	224	26	-	-	PUNCT
asir-1642	224	27	radiation	radiation	NOUN
asir-1642	224	28	ionic	ionic	NOUN
asir-1642	224	29	:	:	PUNCT
asir-1642	224	30	⊕	⊕	PROPN
asir-1642	224	31	,	,	PUNCT
asir-1642	224	32	⊝	⊝	VERB
asir-1642	224	33	ions	ion	NOUN
asir-1642	224	34	electrostatic	electrostatic	ADJ
asir-1642	224	35	⊕	⊕	PROPN
asir-1642	224	36	↔⊝	↔⊝	PROPN
asir-1642	224	37	non	non	ADJ
asir-1642	224	38	-	-	ADJ
asir-1642	224	39	conductors	conductor	NOUN
asir-1642	224	40	infrared	infrared	ADJ
asir-1642	224	41	molecular	molecular	NOUN
asir-1642	224	42	:	:	PUNCT
asir-1642	224	43	atoms	atom	NOUN
asir-1642	224	44	or	or	CCONJ
asir-1642	224	45	molecules	molecule	NOUN
asir-1642	224	46	-	-	PUNCT
asir-1642	224	47	dipole	dipole	NOUN
asir-1642	224	48	attraction	attraction	NOUN
asir-1642	224	49	-	-	PUNCT
asir-1642	224	50	repulsion	repulsion	NOUN
asir-1642	224	51	-	-	PUNCT
asir-1642	224	52	non	non	NOUN
asir-1642	224	53	-	-	ADJ
asir-1642	224	54	conductors	conductor	NOUN
asir-1642	224	55	-	-	PUNCT
asir-1642	224	56	chemical	chemical	NOUN
asir-1642	224	57	-	-	PUNCT
asir-1642	224	58	bonds	bond	NOUN
asir-1642	224	59	.	.	PUNCT
asir-1642	225	1	covalent	covalent	NOUN
asir-1642	225	2	:	:	PUNCT
asir-1642	225	3	atoms	atom	NOUN
asir-1642	225	4	-	-	PUNCT
asir-1642	225	5	network	network	NOUN
asir-1642	225	6	-	-	PUNCT
asir-1642	225	7	bonds	bond	NOUN
asir-1642	225	8	between	between	ADP
asir-1642	225	9	atoms	atom	NOUN
asir-1642	225	10	-	-	PUNCT
asir-1642	225	11	non	non	NOUN
asir-1642	225	12	-	-	NOUN
asir-1642	225	13	conductors	conductor	NOUN
asir-1642	225	14	-	-	PUNCT
asir-1642	225	15	em	em	NOUN
asir-1642	225	16	-	-	NOUN
asir-1642	225	17	spectrum	spectrum	ADJ
asir-1642	225	18	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	225	19	applied	apply	VERB
asir-1642	225	20	science	science	NOUN
asir-1642	225	21	and	and	CCONJ
asir-1642	225	22	innovative	innovative	ADJ
asir-1642	225	23	research	research	NOUN
asir-1642	225	24	vol	vol	NOUN
asir-1642	225	25	.	.	PROPN
asir-1642	226	1	2	2	NUM
asir-1642	226	2	,	,	PUNCT
asir-1642	226	3	no	no	INTJ
asir-1642	226	4	.	.	NOUN
asir-1642	226	5	4	4	NUM
asir-1642	226	6	,	,	PUNCT
asir-1642	226	7	2018	2018	NUM
asir-1642	226	8	167	167	NUM
asir-1642	226	9	published	publish	VERB
asir-1642	226	10	by	by	ADP
asir-1642	226	11	scholink	scholink	PROPN
asir-1642	226	12	inc	inc	PROPN
asir-1642	226	13	.	.	PROPN
asir-1642	226	14	metallic	metallic	PROPN
asir-1642	226	15	:	:	PUNCT
asir-1642	226	16	atoms	atom	NOUN
asir-1642	226	17	-	-	PUNCT
asir-1642	226	18	ions	ion	NOUN
asir-1642	226	19	and	and	CCONJ
asir-1642	226	20	electrons	electron	NOUN
asir-1642	226	21	attraction	attraction	NOUN
asir-1642	226	22	conductors	conductor	NOUN
asir-1642	226	23	e	e	NOUN
asir-1642	226	24	-	-	NOUN
asir-1642	226	25	conduction	conduction	NOUN
asir-1642	226	26	.	.	PUNCT
asir-1642	227	1	the	the	DET
asir-1642	227	2	kinetic	kinetic	NOUN
asir-1642	227	3	-	-	PUNCT
asir-1642	227	4	energy	energy	NOUN
asir-1642	227	5	k	k	NOUN
asir-1642	227	6	of	of	ADP
asir-1642	227	7	a	a	DET
asir-1642	227	8	moving	move	VERB
asir-1642	227	9	material	material	NOUN
asir-1642	227	10	-	-	PUNCT
asir-1642	227	11	point	point	NOUN
asir-1642	227	12	,	,	PUNCT
asir-1642	227	13	as	as	SCONJ
asir-1642	227	14	this	this	PRON
asir-1642	227	15	is	be	AUX
asir-1642	227	16	the	the	DET
asir-1642	227	17	photon	photon	NOUN
asir-1642	227	18	,	,	PUNCT
asir-1642	227	19	is	be	AUX
asir-1642	227	20	stored	store	VERB
asir-1642	227	21	as	as	ADP
asir-1642	227	22	motion	motion	NOUN
asir-1642	227	23	in	in	ADP
asir-1642	227	24	its	its	PRON
asir-1642	227	25	storage	storage	NOUN
asir-1642	227	26	,	,	PUNCT
asir-1642	227	27	r	r	NOUN
asir-1642	227	28	=	=	PUNCT
asir-1642	228	1	[	[	X
asir-1642	228	2	n.λ/2	n.λ/2	PROPN
asir-1642	228	3	]	]	PUNCT
asir-1642	228	4	with	with	ADP
asir-1642	228	5	the	the	DET
asir-1642	228	6	,	,	PUNCT
asir-1642	228	7	n	n	PRON
asir-1642	228	8	frequencies	frequency	NOUN
asir-1642	228	9	=	=	PUNCT
asir-1642	228	10	n.	n.	NOUN
asir-1642	228	11	,	,	PUNCT
asir-1642	228	12	with	with	ADP
asir-1642	228	13	n	n	ADP
asir-1642	228	14	lobes	lobe	NOUN
asir-1642	228	15	and	and	CCONJ
asir-1642	228	16	fundamental	fundamental	ADJ
asir-1642	228	17	frequency	frequency	NOUN
asir-1642	228	18	.	.	PUNCT
asir-1642	229	1	from	from	ADP
asir-1642	229	2	above	above	ADV
asir-1642	229	3	is	be	AUX
asir-1642	229	4	seen	see	VERB
asir-1642	229	5	the	the	DET
asir-1642	229	6	passage	passage	NOUN
asir-1642	229	7	and	and	CCONJ
asir-1642	229	8	the	the	DET
asir-1642	229	9	-	-	PUNCT
asir-1642	229	10	how	how	SCONJ
asir-1642	229	11	em	em	NOUN
asir-1642	229	12	-	-	NOUN
asir-1642	229	13	radiation	radiation	NOUN
asir-1642	229	14	can	can	AUX
asir-1642	229	15	travel	travel	VERB
asir-1642	229	16	in	in	ADP
asir-1642	229	17	crystals	crystal	NOUN
asir-1642	229	18	and	and	CCONJ
asir-1642	229	19	which	which	PRON
asir-1642	229	20	are	be	AUX
asir-1642	229	21	the	the	DET
asir-1642	229	22	cauchy	cauchy	NOUN
asir-1642	229	23	-	-	PUNCT
asir-1642	229	24	stress	stress	NOUN
asir-1642	229	25	-	-	PUNCT
asir-1642	229	26	tensor	tensor	NOUN
asir-1642	229	27	where	where	SCONJ
asir-1642	229	28	e	e	X
asir-1642	229	29			PROPN
asir-1642	229	30	b	b	PROPN
asir-1642	229	31			NOUN
asir-1642	229	32	r	r	PROPN
asir-1642	229	33	≡	≡	PROPN
asir-1642	229	34			NOUN
asir-1642	229	35	2	2	NUM
asir-1642	229	36			NOUN
asir-1642	229	37	3	3	NUM
asir-1642	229	38	,	,	PUNCT
asir-1642	229	39	in	in	ADP
asir-1642	229	40	-	-	PUNCT
asir-1642	229	41	where	where	SCONJ
asir-1642	229	42	energy	energy	NOUN
asir-1642	229	43	propagates	propagate	VERB
asir-1642	229	44	along	along	ADP
asir-1642	229	45	directions	direction	NOUN
asir-1642	229	46	without	without	ADP
asir-1642	229	47	birefringence	birefringence	NOUN
asir-1642	229	48	,	,	PUNCT
asir-1642	229	49	and	and	CCONJ
asir-1642	229	50	carries	carry	VERB
asir-1642	229	51	the	the	DET
asir-1642	229	52	energy	energy	NOUN
asir-1642	229	53	-	-	PUNCT
asir-1642	229	54	storage	storage	NOUN
asir-1642	229	55	r	r	NOUN
asir-1642	229	56	,	,	PUNCT
asir-1642	229	57	which	which	DET
asir-1642	229	58	radiation	radiation	NOUN
asir-1642	229	59	is	be	AUX
asir-1642	229	60	the	the	DET
asir-1642	229	61	conveyer	conveyer	NOUN
asir-1642	229	62	.	.	PUNCT
asir-1642	230	1	above	above	ADP
asir-1642	230	2	procedure	procedure	NOUN
asir-1642	230	3	can	can	AUX
asir-1642	230	4	be	be	AUX
asir-1642	230	5	used	use	VERB
asir-1642	230	6	in	in	ADP
asir-1642	230	7	cells	cell	NOUN
asir-1642	230	8	,	,	PUNCT
asir-1642	230	9	where	where	SCONJ
asir-1642	230	10	cells	cell	NOUN
asir-1642	230	11	are	be	AUX
asir-1642	230	12	cases	case	NOUN
asir-1642	230	13	of	of	ADP
asir-1642	230	14	a	a	DET
asir-1642	230	15	birefringence	birefringence	NOUN
asir-1642	230	16	material	material	NOUN
asir-1642	230	17	and	and	CCONJ
asir-1642	230	18	the	the	DET
asir-1642	230	19	resonance	resonance	NOUN
asir-1642	230	20	-	-	PUNCT
asir-1642	230	21	passage	passage	NOUN
asir-1642	230	22	happens	happen	VERB
asir-1642	230	23	as	as	ADP
asir-1642	230	24	the	the	DET
asir-1642	230	25	force	force	NOUN
asir-1642	230	26	,	,	PUNCT
asir-1642	230	27	em	em	NOUN
asir-1642	230	28	-	-	NOUN
asir-1642	230	29	radiation	radiation	NOUN
asir-1642	230	30	in	in	ADP
asir-1642	230	31	two	two	NUM
asir-1642	230	32	directions	direction	NOUN
asir-1642	230	33	,	,	PUNCT
asir-1642	230	34	can	can	AUX
asir-1642	230	35	travel	travel	VERB
asir-1642	230	36	in	in	ADP
asir-1642	230	37	cell	cell	NOUN
asir-1642	230	38	through	through	ADP
asir-1642	230	39	cauchy	cauchy	NOUN
asir-1642	230	40	-	-	PUNCT
asir-1642	230	41	stress	stress	NOUN
asir-1642	230	42	-	-	PUNCT
asir-1642	230	43	tensor	tensor	NOUN
asir-1642	230	44	where	where	SCONJ
asir-1642	230	45	the	the	DET
asir-1642	230	46	two	two	NUM
asir-1642	230	47	conveyers	conveyer	NOUN
asir-1642	230	48	e	e	X
asir-1642	230	49			NOUN
asir-1642	230	50	b	b	PROPN
asir-1642	230	51			NOUN
asir-1642	230	52	r	r	PROPN
asir-1642	230	53	≡	≡	PROPN
asir-1642	230	54			NOUN
asir-1642	230	55	2	2	NUM
asir-1642	230	56			NOUN
asir-1642	230	57	3	3	NUM
asir-1642	230	58	,	,	PUNCT
asir-1642	230	59	can	can	AUX
asir-1642	230	60	carry	carry	VERB
asir-1642	230	61	the	the	DET
asir-1642	230	62	energy	energy	NOUN
asir-1642	230	63	-	-	PUNCT
asir-1642	230	64	storage	storage	NOUN
asir-1642	230	65	,	,	PUNCT
asir-1642	230	66	r	r	NOUN
asir-1642	230	67	,	,	PUNCT
asir-1642	230	68	in	in	ADP
asir-1642	230	69	cell	cell	NOUN
asir-1642	230	70	,	,	PUNCT
asir-1642	230	71	and	and	CCONJ
asir-1642	230	72	change	change	VERB
asir-1642	230	73	the	the	DET
asir-1642	230	74	inner	inner	ADJ
asir-1642	230	75	-	-	PUNCT
asir-1642	230	76	structure	structure	NOUN
asir-1642	230	77	of	of	ADP
asir-1642	230	78	cell	cell	NOUN
asir-1642	230	79	to	to	ADP
asir-1642	230	80	another	another	DET
asir-1642	230	81	desirable	desirable	ADJ
asir-1642	230	82	property	property	NOUN
asir-1642	230	83	.	.	PUNCT
asir-1642	231	1	from	from	ADP
asir-1642	231	2	inner	inner	ADJ
asir-1642	231	3	-	-	PUNCT
asir-1642	231	4	velocity	velocity	NOUN
asir-1642	231	5	equation	equation	NOUN
asir-1642	231	6	v	v	ADP
asir-1642	231	7	=	=	SYM
asir-1642	231	8	wr	wr	NOUN
asir-1642	231	9	=	=	PUNCT
asir-1642	231	10	(	(	PUNCT
asir-1642	231	11	2π	2π	NOUN
asir-1642	231	12	/	/	SYM
asir-1642	231	13	t).r	t).r	NUM
asir-1642	231	14	=	=	NOUN
asir-1642	231	15	2π	2π	NOUN
asir-1642	231	16	.	.	PUNCT
asir-1642	232	1	r	r	NOUN
asir-1642	232	2	,	,	PUNCT
asir-1642	232	3	wavelength	wavelength	NOUN
asir-1642	232	4	λ	λ	PROPN
asir-1642	232	5	=	=	SYM
asir-1642	232	6	ct	ct	PROPN
asir-1642	232	7	=	=	PROPN
asir-1642	232	8	c	c	NOUN
asir-1642	232	9	/	/	SYM
asir-1642	232	10	,	,	PUNCT
asir-1642	232	11	cave	cave	NOUN
asir-1642	232	12	r	r	NOUN
asir-1642	232	13	=	=	SYM
asir-1642	232	14	n.[λ/2	n.[λ/2	PROPN
asir-1642	232	15	]	]	PUNCT
asir-1642	232	16	,	,	PUNCT
asir-1642	232	17	then	then	ADV
asir-1642	232	18	r	r	NOUN
asir-1642	232	19	=	=	PUNCT
asir-1642	232	20	n.(c/2	n.(c/2	ADV
asir-1642	232	21	)	)	PUNCT
asir-1642	232	22	and	and	CCONJ
asir-1642	232	23	v	v	X
asir-1642	232	24	=	=	NOUN
asir-1642	232	25	2π	2π	NOUN
asir-1642	232	26	.	.	PUNCT
asir-1642	233	1	[	[	X
asir-1642	233	2	n.c/2	n.c/2	NOUN
asir-1642	233	3	]	]	X
asir-1642	233	4	=	=	PUNCT
asir-1642	233	5	n.π.c	n.π.c	ADJ
asir-1642	233	6	or	or	CCONJ
asir-1642	233	7	v	v	NOUN
asir-1642	233	8	=	=	PUNCT
asir-1642	233	9	n.π.c	n.π.c	X
asir-1642	233	10	(	(	PUNCT
asir-1642	233	11	4	4	X
asir-1642	233	12	)	)	PUNCT
asir-1642	233	13	showing	show	VERB
asir-1642	233	14	that	that	SCONJ
asir-1642	233	15	velocities	velocity	NOUN
asir-1642	233	16	in	in	ADP
asir-1642	233	17	lobes	lobe	NOUN
asir-1642	233	18	are	be	AUX
asir-1642	233	19	,	,	PUNCT
asir-1642	233	20	n.π	n.π	PROPN
asir-1642	233	21	,	,	PUNCT
asir-1642	233	22	times	time	VERB
asir-1642	233	23	that	that	PRON
asir-1642	233	24	of	of	ADP
asir-1642	233	25	light	light	NOUN
asir-1642	233	26	and	and	CCONJ
asir-1642	233	27	for	for	ADP
asir-1642	233	28	n	n	NOUN
asir-1642	233	29	=	=	SYM
asir-1642	233	30	1	1	NUM
asir-1642	233	31	then	then	ADV
asir-1642	233	32	v	v	NOUN
asir-1642	233	33	=	=	PUNCT
asir-1642	233	34	π.c	π.c	NOUN
asir-1642	233	35	more	more	ADJ
asir-1642	233	36	than	than	ADP
asir-1642	233	37	three	three	NUM
asir-1642	233	38	times	time	NOUN
asir-1642	233	39	faster	fast	ADV
asir-1642	233	40	of	of	ADP
asir-1642	233	41	light	light	ADJ
asir-1642	233	42	velocity	velocity	NOUN
asir-1642	233	43	.	.	PUNCT
asir-1642	234	1	because	because	SCONJ
asir-1642	234	2	of	of	ADP
asir-1642	234	3	the	the	DET
asir-1642	234	4	above	above	ADJ
asir-1642	234	5	velocity	velocity	NOUN
asir-1642	234	6	v	v	NOUN
asir-1642	234	7	,	,	PUNCT
asir-1642	234	8	an	an	DET
asir-1642	234	9	e	e	NOUN
asir-1642	234	10	field	field	NOUN
asir-1642	234	11	is	be	AUX
asir-1642	234	12	produced	produce	VERB
asir-1642	234	13	,	,	PUNCT
asir-1642	234	14	which	which	PRON
asir-1642	234	15	produces	produce	VERB
asir-1642	234	16	the	the	DET
asir-1642	234	17	field	field	NOUN
asir-1642	234	18	,	,	PUNCT
asir-1642	234	19	which	which	PRON
asir-1642	234	20	in	in	ADP
asir-1642	234	21	turn	turn	NOUN
asir-1642	234	22	produces	produce	VERB
asir-1642	234	23	the	the	DET
asir-1642	234	24	h	h	NOUN
asir-1642	234	25	field	field	NOUN
asir-1642	234	26	which	which	PRON
asir-1642	234	27	produces	produce	VERB
asir-1642	234	28	the	the	DET
asir-1642	234	29	b	b	PROPN
asir-1642	234	30	field	field	NOUN
asir-1642	234	31	and	and	CCONJ
asir-1642	234	32	which	which	PRON
asir-1642	234	33	again	again	ADV
asir-1642	234	34	produces	produce	VERB
asir-1642	234	35	the	the	DET
asir-1642	234	36	e	e	NOUN
asir-1642	234	37	field	field	NOUN
asir-1642	234	38	,	,	PUNCT
asir-1642	234	39	i.e.	i.e.	X
asir-1642	234	40	,	,	PUNCT
asir-1642	234	41	the	the	DET
asir-1642	234	42	total	total	ADJ
asir-1642	234	43	em	em	NOUN
asir-1642	234	44	-	-	PUNCT
asir-1642	234	45	field	field	NOUN
asir-1642	234	46	regenerates	regenerate	VERB
asir-1642	234	47	itself	itself	PRON
asir-1642	234	48	as	as	SCONJ
asir-1642	234	49	it	it	PRON
asir-1642	234	50	rotates	rotate	VERB
asir-1642	234	51	,	,	PUNCT
asir-1642	234	52	and	and	CCONJ
asir-1642	234	53	is	be	AUX
asir-1642	234	54	a	a	DET
asir-1642	234	55	phenomenon	phenomenon	NOUN
asir-1642	234	56	happening	happen	VERB
asir-1642	234	57	in	in	ADP
asir-1642	234	58	a	a	DET
asir-1642	234	59	propagating	propagate	VERB
asir-1642	234	60	plane	plane	NOUN
asir-1642	234	61	-	-	PUNCT
asir-1642	234	62	wave	wave	NOUN
asir-1642	234	63	.	.	PUNCT
asir-1642	235	1	permeable	permeable	ADJ
asir-1642	235	2	-	-	PUNCT
asir-1642	235	3	resonance	resonance	NOUN
asir-1642	235	4	-	-	PUNCT
asir-1642	235	5	path	path	NOUN
asir-1642	235	6	is	be	AUX
asir-1642	235	7	impossible	impossible	ADJ
asir-1642	235	8	in	in	ADP
asir-1642	235	9	a	a	DET
asir-1642	235	10	three	three	NUM
asir-1642	235	11	-	-	PUNCT
asir-1642	235	12	times	time	NOUN
asir-1642	235	13	stronger	strong	ADJ
asir-1642	235	14	em	em	NOUN
asir-1642	235	15	-	-	NOUN
asir-1642	235	16	field	field	NOUN
asir-1642	235	17	.	.	PUNCT
asir-1642	236	1	i	i	PRON
asir-1642	236	2	..	..	PUNCT
asir-1642	236	3	the	the	DET
asir-1642	236	4	conic	conic	ADJ
asir-1642	236	5	sections	section	NOUN
asir-1642	236	6	and	and	CCONJ
asir-1642	236	7	planar	planar	ADJ
asir-1642	236	8	-	-	PUNCT
asir-1642	236	9	curves	curve	NOUN
asir-1642	236	10	:	:	PUNCT
asir-1642	236	11	menaechmus	menaechmus	NOUN
asir-1642	236	12	came	come	VERB
asir-1642	236	13	to	to	PART
asir-1642	236	14	think	think	VERB
asir-1642	236	15	of	of	ADP
asir-1642	236	16	producing	produce	VERB
asir-1642	236	17	curves	curve	NOUN
asir-1642	236	18	by	by	ADP
asir-1642	236	19	cutting	cut	VERB
asir-1642	236	20	a	a	DET
asir-1642	236	21	cone	cone	NOUN
asir-1642	236	22	from	from	ADP
asir-1642	236	23	the	the	DET
asir-1642	236	24	circle	circle	NOUN
asir-1642	236	25	definition	definition	NOUN
asir-1642	236	26	which	which	PRON
asir-1642	236	27	is	be	AUX
asir-1642	236	28	→	→	PUNCT
asir-1642	236	29	since	since	SCONJ
asir-1642	236	30	the	the	DET
asir-1642	236	31	center	center	NOUN
asir-1642	236	32	o	o	NOUN
asir-1642	236	33	of	of	ADP
asir-1642	236	34	a	a	DET
asir-1642	236	35	circle	circle	NOUN
asir-1642	236	36	is	be	AUX
asir-1642	236	37	of	of	ADP
asir-1642	236	38	equal	equal	ADJ
asir-1642	236	39	distance	distance	NOUN
asir-1642	236	40	to	to	ADP
asir-1642	236	41	all	all	DET
asir-1642	236	42	points	point	NOUN
asir-1642	236	43	in	in	ADP
asir-1642	236	44	plane	plane	NOUN
asir-1642	236	45	of	of	ADP
asir-1642	236	46	the	the	DET
asir-1642	236	47	circumference	circumference	NOUN
asir-1642	236	48	the	the	DET
asir-1642	236	49	same	same	ADJ
asir-1642	236	50	also	also	ADV
asir-1642	236	51	to	to	ADP
asir-1642	236	52	all	all	DET
asir-1642	236	53	centers	center	NOUN
asir-1642	236	54	𝐎𝐧	𝐎𝐧	PROPN
asir-1642	236	55	from	from	ADP
asir-1642	236	56	center	center	PROPN
asir-1642	236	57	o	o	NOUN
asir-1642	236	58	which	which	PRON
asir-1642	236	59	are	be	AUX
asir-1642	236	60	on	on	ADP
asir-1642	236	61	line	line	NOUN
asir-1642	236	62	𝐎𝐎𝐧	𝐎𝐎𝐧	NOUN
asir-1642	236	63	and	and	CCONJ
asir-1642	236	64	perpendicular	perpendicular	ADJ
asir-1642	236	65	to	to	ADP
asir-1642	236	66	this	this	DET
asir-1642	236	67	plane	plane	NOUN
asir-1642	236	68	←	←	PROPN
asir-1642	236	69	in	in	ADP
asir-1642	236	70	figure	figure	NOUN
asir-1642	236	71	-5	-5	INTJ
asir-1642	236	72	,	,	PUNCT
asir-1642	236	73	line	line	NOUN
asir-1642	236	74	oo	oo	INTJ
asir-1642	236	75	is	be	AUX
asir-1642	236	76	the	the	DET
asir-1642	236	77	generator	generator	NOUN
asir-1642	236	78	axis	axis	NOUN
asir-1642	236	79	of	of	ADP
asir-1642	236	80	a	a	DET
asir-1642	236	81	right	right	ADV
asir-1642	236	82	-	-	PUNCT
asir-1642	236	83	angled	angle	VERB
asir-1642	236	84	cone	cone	NOUN
asir-1642	236	85	and	and	CCONJ
asir-1642	236	86	all	all	DET
asir-1642	236	87	the	the	DET
asir-1642	236	88	shapes	shape	NOUN
asir-1642	236	89	of	of	ADP
asir-1642	236	90	the	the	DET
asir-1642	236	91	curve	curve	NOUN
asir-1642	236	92	produced	produce	VERB
asir-1642	236	93	by	by	ADP
asir-1642	236	94	cutting	cut	VERB
asir-1642	236	95	a	a	DET
asir-1642	236	96	right	right	NOUN
asir-1642	236	97	-	-	PUNCT
asir-1642	236	98	cone	cone	NOUN
asir-1642	236	99	by	by	ADP
asir-1642	236	100	a	a	DET
asir-1642	236	101	plane	plane	NOUN
asir-1642	236	102	obliquely	obliquely	ADV
asir-1642	236	103	inclined	incline	VERB
asir-1642	236	104	to	to	ADP
asir-1642	236	105	its	its	PRON
asir-1642	236	106	axis	axis	NOUN
asir-1642	236	107	is	be	AUX
asir-1642	236	108	a	a	DET
asir-1642	236	109	conic	conic	ADJ
asir-1642	236	110	section	section	NOUN
asir-1642	236	111	.	.	PUNCT
asir-1642	237	1	in	in	ADP
asir-1642	237	2	circle	circle	NOUN
asir-1642	237	3	[	[	X
asir-1642	237	4	o	o	NOUN
asir-1642	237	5	,	,	PUNCT
asir-1642	237	6	op	op	NOUN
asir-1642	237	7	]	]	PUNCT
asir-1642	237	8	with	with	ADP
asir-1642	237	9	only	only	ADV
asir-1642	237	10	one	one	NUM
asir-1642	237	11	center	center	NOUN
asir-1642	237	12	issues	issue	NOUN
asir-1642	237	13	for	for	ADP
asir-1642	237	14	point	point	NOUN
asir-1642	237	15	p	p	X
asir-1642	237	16	,	,	PUNCT
asir-1642	237	17	op	op	NOUN
asir-1642	237	18	+	+	CCONJ
asir-1642	237	19	po	po	X
asir-1642	237	20	=	=	SYM
asir-1642	237	21	2r	2r	NUM
asir-1642	237	22	is	be	AUX
asir-1642	237	23	constant	constant	ADJ
asir-1642	237	24	,	,	PUNCT
asir-1642	237	25	while	while	SCONJ
asir-1642	237	26	in	in	ADP
asir-1642	237	27	ellipse	ellipse	NOUN
asir-1642	238	1	[	[	X
asir-1642	238	2	o	o	X
asir-1642	238	3	p	p	X
asir-1642	238	4	,	,	PUNCT
asir-1642	238	5	po2	po2	PROPN
asir-1642	238	6	]	]	PUNCT
asir-1642	238	7	of	of	ADP
asir-1642	238	8	two	two	NUM
asir-1642	238	9	centerso	centerso	NOUN
asir-1642	238	10	,	,	PUNCT
asir-1642	238	11	o2	o2	ADJ
asir-1642	238	12	issues	issue	NOUN
asir-1642	238	13	for	for	ADP
asir-1642	238	14	point	point	NOUN
asir-1642	238	15	p	p	X
asir-1642	238	16	,	,	PUNCT
asir-1642	238	17	po	po	NOUN
asir-1642	238	18	+	+	CCONJ
asir-1642	238	19	po2=	po2=	NOUN
asir-1642	238	20	major	major	ADJ
asir-1642	238	21	-	-	PUNCT
asir-1642	238	22	axis	axis	NOUN
asir-1642	238	23	,	,	PUNCT
asir-1642	238	24	is	be	AUX
asir-1642	238	25	constant	constant	ADJ
asir-1642	238	26	.	.	PUNCT
asir-1642	239	1	this	this	DET
asir-1642	239	2	property	property	NOUN
asir-1642	239	3	allows	allow	VERB
asir-1642	239	4	central	central	ADJ
asir-1642	239	5	-	-	PUNCT
asir-1642	239	6	motion	motion	NOUN
asir-1642	239	7	to	to	PART
asir-1642	239	8	be	be	AUX
asir-1642	239	9	seen	see	VERB
asir-1642	239	10	as	as	ADP
asir-1642	239	11	a	a	DET
asir-1642	239	12	geometrical	geometrical	ADJ
asir-1642	239	13	problem	problem	NOUN
asir-1642	239	14	of	of	ADP
asir-1642	239	15	proportionals	proportional	NOUN
asir-1642	239	16	on	on	ADP
asir-1642	239	17	points	point	NOUN
asir-1642	239	18	and	and	CCONJ
asir-1642	239	19	lines	line	NOUN
asir-1642	239	20	[	[	X
asir-1642	239	21	44	44	NUM
asir-1642	239	22	]	]	PUNCT
asir-1642	239	23	.	.	PUNCT
asir-1642	240	1	in	in	ADP
asir-1642	240	2	[	[	X
asir-1642	240	3	70	70	NUM
asir-1642	240	4	]	]	PUNCT
asir-1642	240	5	is	be	AUX
asir-1642	240	6	m̅	m̅	PROPN
asir-1642	240	7	=	=	PUNCT
asir-1642	241	1	[	[	X
asir-1642	241	2	r̅xp̅	r̅xp̅	NOUN
asir-1642	241	3	]	]	X
asir-1642	241	4	=	=	SYM
asir-1642	241	5	�	�	PROPN
asir-1642	241	6	̅	̅	NOUN
asir-1642	241	7	�	�	PROPN
asir-1642	241	8	t	t	PROPN
asir-1642	241	9	→	→	PUNCT
asir-1642	241	10	the	the	DET
asir-1642	241	11	theorem	theorem	NOUN
asir-1642	241	12	of	of	ADP
asir-1642	241	13	equal	equal	ADJ
asir-1642	241	14	-	-	PUNCT
asir-1642	241	15	areas	area	NOUN
asir-1642	241	16	and	and	CCONJ
asir-1642	241	17	kepler	kepler	NOUN
asir-1642	241	18	’s	’s	PART
asir-1642	241	19	1st	1st	ADJ
asir-1642	241	20	law	law	NOUN
asir-1642	241	21	,	,	PUNCT
asir-1642	241	22	i.e.	i.e.	X
asir-1642	241	23	,	,	PUNCT
asir-1642	241	24	momentum	momentum	NOUN
asir-1642	241	25	p̅	p̅	NOUN
asir-1642	241	26	,	,	PUNCT
asir-1642	241	27	of	of	ADP
asir-1642	241	28	a	a	DET
asir-1642	241	29	force	force	NOUN
asir-1642	241	30	p̅	p̅	NOUN
asir-1642	241	31	,	,	PUNCT
asir-1642	241	32	to	to	ADP
asir-1642	241	33	a	a	DET
asir-1642	241	34	constant	constant	ADJ
asir-1642	241	35	center	center	NOUN
asir-1642	241	36	o	o	NOUN
asir-1642	241	37	,	,	PUNCT
asir-1642	241	38	of	of	ADP
asir-1642	241	39	radius	radius	NOUN
asir-1642	241	40	r̅	r̅	PROPN
asir-1642	241	41	,	,	PUNCT
asir-1642	241	42	is	be	AUX
asir-1642	241	43	equal	equal	ADJ
asir-1642	241	44	to	to	ADP
asir-1642	241	45	the	the	DET
asir-1642	241	46	change	change	NOUN
asir-1642	241	47	of	of	ADP
asir-1642	241	48	the	the	DET
asir-1642	241	49	angular	angular	ADJ
asir-1642	241	50	-momentum	-momentum	NOUN
asir-1642	241	51	b̅	b̅	NOUN
asir-1642	241	52	at	at	ADP
asir-1642	241	53	time	time	NOUN
asir-1642	241	54	t	t	PROPN
asir-1642	241	55	,	,	PUNCT
asir-1642	241	56	related	relate	VERB
asir-1642	241	57	to	to	ADP
asir-1642	241	58	the	the	DET
asir-1642	241	59	same	same	ADJ
asir-1642	241	60	center	center	NOUN
asir-1642	241	61	o	o	NOUN
asir-1642	241	62	,	,	PUNCT
asir-1642	241	63	and	and	CCONJ
asir-1642	241	64	its	its	PRON
asir-1642	241	65	trajectory	trajectory	NOUN
asir-1642	241	66	lies	lie	VERB
asir-1642	241	67	on	on	ADP
asir-1642	241	68	the	the	DET
asir-1642	241	69	same	same	ADJ
asir-1642	241	70	plane	plane	NOUN
asir-1642	241	71	.	.	PUNCT
asir-1642	242	1	a	a	DET
asir-1642	242	2	..	..	PUNCT
asir-1642	242	3	the	the	DET
asir-1642	242	4	geometrical	geometrical	ADJ
asir-1642	242	5	central	central	ADJ
asir-1642	242	6	motion	motion	NOUN
asir-1642	242	7	:	:	PUNCT
asir-1642	242	8	huygens	huygen	NOUN
asir-1642	242	9	and	and	CCONJ
asir-1642	242	10	johannes	johannes	PROPN
asir-1642	242	11	bernoulli	bernoulli	PROPN
asir-1642	242	12	came	come	VERB
asir-1642	242	13	to	to	PART
asir-1642	242	14	think	think	VERB
asir-1642	242	15	of	of	ADP
asir-1642	242	16	producing	produce	VERB
asir-1642	242	17	the	the	DET
asir-1642	242	18	shortest	short	ADJ
asir-1642	242	19	-	-	PUNCT
asir-1642	242	20	time	time	NOUN
asir-1642	242	21	curve	curve	NOUN
asir-1642	242	22	between	between	ADP
asir-1642	242	23	two	two	NUM
asir-1642	242	24	points	point	NOUN
asir-1642	242	25	on	on	ADP
asir-1642	242	26	a	a	DET
asir-1642	242	27	vertical	vertical	ADJ
asir-1642	242	28	plane	plane	NOUN
asir-1642	242	29	by	by	ADP
asir-1642	242	30	a	a	DET
asir-1642	242	31	point	point	NOUN
asir-1642	242	32	acted	act	VERB
asir-1642	242	33	only	only	ADV
asir-1642	242	34	by	by	ADP
asir-1642	242	35	gravity	gravity	NOUN
asir-1642	242	36	and	and	CCONJ
asir-1642	242	37	which	which	PRON
asir-1642	242	38	is	be	AUX
asir-1642	242	39	,	,	PUNCT
asir-1642	242	40	→	→	PUNCT
asir-1642	242	41	to	to	PART
asir-1642	242	42	find	find	VERB
asir-1642	242	43	the	the	DET
asir-1642	242	44	path	path	NOUN
asir-1642	242	45	-	-	PUNCT
asir-1642	242	46	curve	curve	NOUN
asir-1642	242	47	or	or	CCONJ
asir-1642	242	48	surface	surface	NOUN
asir-1642	242	49	for	for	ADP
asir-1642	242	50	which	which	PRON
asir-1642	242	51	a	a	DET
asir-1642	242	52	given	give	VERB
asir-1642	242	53	variation	variation	NOUN
asir-1642	242	54	has	have	VERB
asir-1642	242	55	a	a	DET
asir-1642	242	56	stationary	stationary	ADJ
asir-1642	242	57	value	value	NOUN
asir-1642	242	58	,	,	PUNCT
asir-1642	242	59	stationary	stationary	ADJ
asir-1642	242	60	or	or	CCONJ
asir-1642	242	61	extrema	extrema	NOUN
asir-1642	242	62	is	be	AUX
asir-1642	242	63	the	the	DET
asir-1642	242	64	maximum	maximum	ADJ
asir-1642	242	65	or	or	CCONJ
asir-1642	242	66	minimum	minimum	NOUN
asir-1642	242	67	between	between	ADP
asir-1642	242	68	two	two	NUM
asir-1642	242	69	points	point	NOUN
asir-1642	242	70	(	(	PUNCT
asir-1642	242	71	1	1	NUM
asir-1642	242	72	)	)	PUNCT
asir-1642	242	73	,	,	PUNCT
asir-1642	242	74	(	(	PUNCT
asir-1642	242	75	2	2	X
asir-1642	242	76	)	)	PUNCT
asir-1642	242	77	←	←	PROPN
asir-1642	242	78	it	it	PRON
asir-1642	242	79	was	be	AUX
asir-1642	242	80	proved	prove	VERB
asir-1642	242	81	the	the	DET
asir-1642	242	82	cycloid	cycloid	NOUN
asir-1642	242	83	.	.	PUNCT
asir-1642	243	1	from	from	ADP
asir-1642	243	2	geometry	geometry	NOUN
asir-1642	243	3	figure	figure	NOUN
asir-1642	243	4	5	5	NUM
asir-1642	243	5	,	,	PUNCT
asir-1642	243	6	equality	equality	NOUN
asir-1642	243	7	o	o	NOUN
asir-1642	243	8	=	=	PUNCT
asir-1642	243	9	p	p	X
asir-1642	243	10	/	/	SYM
asir-1642	243	11	e	e	NOUN
asir-1642	243	12	=	=	PROPN
asir-1642	243	13	ap	ap	PROPN
asir-1642	243	14	+	+	CCONJ
asir-1642	244	1	op.co	op.co	ADJ
asir-1642	244	2	=	=	SYM
asir-1642	244	3	r	r	NOUN
asir-1642	244	4	/	/	SYM
asir-1642	244	5	e	e	NOUN
asir-1642	244	6	+	+	CCONJ
asir-1642	245	1	r.co	r.co	VERB
asir-1642	245	2	and	and	CCONJ
asir-1642	245	3	is	be	AUX
asir-1642	245	4	→	→	SYM
asir-1642	245	5	p	p	X
asir-1642	245	6	=	=	PUNCT
asir-1642	246	1	r	r	NOUN
asir-1642	246	2	+	+	NOUN
asir-1642	246	3	r	r	NOUN
asir-1642	246	4	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	246	5	applied	apply	VERB
asir-1642	246	6	science	science	NOUN
asir-1642	246	7	and	and	CCONJ
asir-1642	246	8	innovative	innovative	ADJ
asir-1642	246	9	research	research	NOUN
asir-1642	246	10	vol	vol	NOUN
asir-1642	246	11	.	.	PROPN
asir-1642	247	1	2	2	NUM
asir-1642	247	2	,	,	PUNCT
asir-1642	247	3	no	no	INTJ
asir-1642	247	4	.	.	NOUN
asir-1642	247	5	4	4	NUM
asir-1642	247	6	,	,	PUNCT
asir-1642	247	7	2018	2018	NUM
asir-1642	247	8	168	168	NUM
asir-1642	247	9	published	publish	VERB
asir-1642	247	10	by	by	ADP
asir-1642	247	11	scholink	scholink	PROPN
asir-1642	247	12	inc	inc	PROPN
asir-1642	247	13	.	.	PUNCT
asir-1642	248	1	e.co	e.co	NOUN
asir-1642	248	2	=	=	NOUN
asir-1642	248	3	r	r	NOUN
asir-1642	248	4	(	(	PUNCT
asir-1642	248	5	1	1	NUM
asir-1642	248	6	+	+	NUM
asir-1642	248	7	e.𝐜	e.𝐜	NOUN
asir-1642	248	8	𝐬𝛗	𝐬𝛗	NOUN
asir-1642	248	9	)	)	PUNCT
asir-1642	248	10	…	…	PUNCT
asir-1642	248	11	..	..	PUNCT
asir-1642	248	12	(	(	PUNCT
asir-1642	248	13	1	1	X
asir-1642	248	14	)	)	PUNCT
asir-1642	248	15	where	where	SCONJ
asir-1642	248	16	,	,	PUNCT
asir-1642	248	17	p	p	X
asir-1642	248	18	=	=	PUNCT
asir-1642	248	19	a	a	DET
asir-1642	248	20	constant	constant	ADJ
asir-1642	248	21	parameter	parameter	NOUN
asir-1642	248	22	,	,	PUNCT
asir-1642	248	23	r	r	NOUN
asir-1642	248	24	=	=	PUNCT
asir-1642	248	25	the	the	DET
asir-1642	248	26	orbit	orbit	NOUN
asir-1642	248	27	radius	radius	NOUN
asir-1642	248	28	from	from	ADP
asir-1642	248	29	o.	o.	PROPN
asir-1642	248	30	inversing	inversing	NOUN
asir-1642	248	31	(	(	PUNCT
asir-1642	248	32	1	1	NUM
asir-1642	248	33	)	)	PUNCT
asir-1642	248	34	then	then	ADV
asir-1642	248	35	→	→	SYM
asir-1642	248	36	=	=	PUNCT
asir-1642	248	37	+	+	PUNCT
asir-1642	248	38	e.co	e.co	PROPN
asir-1642	248	39	φ	φ	NOUN
asir-1642	248	40	and	and	CCONJ
asir-1642	248	41	derivative	derivative	ADJ
asir-1642	248	42	→	→	SYM
asir-1642	248	43	²	²	NUM
asir-1642	248	44	φ²	φ²	NOUN
asir-1642	248	45	=	=	SYM
asir-1642	248	46	e.co	e.co	NOUN
asir-1642	248	47	φ	φ	X
asir-1642	248	48	,	,	PUNCT
asir-1642	248	49	→	→	SYM
asir-1642	248	50	²	²	NUM
asir-1642	248	51	φ²	φ²	NOUN
asir-1642	248	52	+	+	CCONJ
asir-1642	248	53	=	=	SYM
asir-1642	248	54	…	…	PUNCT
asir-1642	248	55	…	…	PUNCT
asir-1642	248	56	(	(	PUNCT
asir-1642	248	57	2	2	X
asir-1642	248	58	)	)	PUNCT
asir-1642	248	59	integrating	integrating	NOUN
asir-1642	248	60	(	(	PUNCT
asir-1642	248	61	2	2	NUM
asir-1642	248	62	)	)	PUNCT
asir-1642	248	63	is	be	AUX
asir-1642	248	64	the	the	DET
asir-1642	248	65	acceleration	acceleration	NOUN
asir-1642	248	66	at	at	ADP
asir-1642	248	67	point	point	NOUN
asir-1642	248	68	p	p	NOUN
asir-1642	248	69	and	and	CCONJ
asir-1642	248	70	equal	equal	ADJ
asir-1642	248	71	to	to	ADP
asir-1642	248	72	→	→	SYM
asir-1642	248	73	a	a	DET
asir-1642	248	74	=	=	X
asir-1642	248	75	a²	a²	NOUN
asir-1642	248	76	²	²	NUM
asir-1642	248	77	…	…	PUNCT
asir-1642	248	78	…	…	PUNCT
asir-1642	248	79	…	…	PUNCT
asir-1642	248	80	(	(	PUNCT
asir-1642	248	81	3	3	NUM
asir-1642	248	82	)	)	PUNCT
asir-1642	248	83	where	where	SCONJ
asir-1642	248	84	the	the	DET
asir-1642	248	85	constant	constant	ADJ
asir-1642	248	86	area	area	NOUN
asir-1642	248	87	o	o	NOUN
asir-1642	248	88	,	,	PUNCT
asir-1642	248	89	p	p	X
asir-1642	248	90	,	,	PUNCT
asir-1642	248	91	p	p	X
asir-1642	248	92	=	=	PUNCT
asir-1642	248	93	a	a	NOUN
asir-1642	248	94	=	=	SYM
asir-1642	248	95	2	2	NUM
asir-1642	248	96	.	.	PUNCT
asir-1642	249	1	r²	r²	VERB
asir-1642	249	2	.	.	PUNCT
asir-1642	250	1	φ	φ	PROPN
asir-1642	250	2	t	t	PROPN
asir-1642	250	3	,	,	PUNCT
asir-1642	250	4	and	and	CCONJ
asir-1642	250	5	for	for	ADP
asir-1642	250	6	ellipse	ellipse	NOUN
asir-1642	250	7	the	the	DET
asir-1642	250	8	area	area	NOUN
asir-1642	250	9	=	=	SYM
asir-1642	250	10	(	(	PUNCT
asir-1642	250	11	π	π	X
asir-1642	250	12	e	e	X
asir-1642	250	13	e	e	NOUN
asir-1642	250	14	)	)	PUNCT
asir-1642	250	15	.	.	PUNCT
asir-1642	251	1	for	for	ADP
asir-1642	251	2	ellipse	ellipse	NOUN
asir-1642	251	3	²p	²p	NOUN
asir-1642	252	1	=	=	PROPN
asir-1642	252	2	p.	p.	NOUN
asir-1642	252	3	p	p	X
asir-1642	252	4	,	,	PUNCT
asir-1642	252	5	or	or	CCONJ
asir-1642	252	6	=	=	SYM
asir-1642	252	7	ap	ap	PROPN
asir-1642	252	8	b²p	b²p	PROPN
asir-1642	252	9	and	and	CCONJ
asir-1642	252	10	period	period	NOUN
asir-1642	252	11	of	of	ADP
asir-1642	252	12	rotation	rotation	PROPN
asir-1642	252	13	t	t	PROPN
asir-1642	252	14	,	,	PUNCT
asir-1642	252	15	then	then	ADV
asir-1642	252	16	the	the	DET
asir-1642	252	17	constant	constant	ADJ
asir-1642	252	18	area	area	NOUN
asir-1642	252	19	for	for	ADP
asir-1642	252	20	a	a	DET
asir-1642	252	21	period	period	NOUN
asir-1642	252	22	,	,	PUNCT
asir-1642	252	23	t	t	PROPN
asir-1642	252	24	,	,	PUNCT
asir-1642	252	25	is	be	AUX
asir-1642	252	26	a	a	DET
asir-1642	252	27	=	=	PUNCT
asir-1642	252	28	(	(	PUNCT
asir-1642	252	29	π	π	PROPN
asir-1642	252	30	p	p	X
asir-1642	252	31	p	p	PROPN
asir-1642	252	32	)	)	PUNCT
asir-1642	252	33	/	/	SYM
asir-1642	252	34	t	t	PROPN
asir-1642	252	35	and	and	CCONJ
asir-1642	252	36	(	(	PUNCT
asir-1642	252	37	3	3	X
asir-1642	252	38	)	)	PUNCT
asir-1642	252	39	becomes	become	VERB
asir-1642	252	40	a	a	PRON
asir-1642	252	41	=	=	SYM
asir-1642	252	42	²	²	NUM
asir-1642	252	43	.	.	PUNCT
asir-1642	252	44	t	t	NOUN
asir-1642	252	45	²	²	NUM
asir-1642	252	46	²	²	NUM
asir-1642	252	47	²p	²p	NOUN
asir-1642	252	48	²p	²p	NOUN
asir-1642	252	49	ap	ap	ADP
asir-1642	252	50	b²p	b²p	PROPN
asir-1642	252	51	=	=	PUNCT
asir-1642	252	52	[	[	PUNCT
asir-1642	252	53	²	²	NUM
asir-1642	252	54	t	t	NOUN
asir-1642	252	55	²	²	NUM
asir-1642	252	56	³p	³p	NOUN
asir-1642	252	57	]	]	PUNCT
asir-1642	252	58	²	²	NUM
asir-1642	252	59	=	=	SYM
asir-1642	252	60	[	[	PUNCT
asir-1642	252	61	²	²	NUM
asir-1642	252	62	t	t	NOUN
asir-1642	252	63	²	²	NUM
asir-1642	252	64	]	]	PUNCT
asir-1642	252	65	a³p	a³p	PROPN
asir-1642	252	66	²	²	PROPN
asir-1642	252	67	=	=	SYM
asir-1642	252	68	k	k	PROPN
asir-1642	252	69	²	²	NUM
asir-1642	252	70	…	…	PUNCT
asir-1642	252	71	.(4	.(4	NUM
asir-1642	252	72	)	)	PUNCT
asir-1642	252	73	or	or	CCONJ
asir-1642	252	74	acceleration	acceleration	NOUN
asir-1642	253	1	a	a	PRON
asir-1642	254	1	=	=	X
asir-1642	254	2	[	[	PUNCT
asir-1642	254	3	²	²	NUM
asir-1642	254	4	t	t	NOUN
asir-1642	254	5	²	²	NUM
asir-1642	254	6	]	]	PUNCT
asir-1642	254	7	a³p	a³p	PROPN
asir-1642	254	8	²	²	PROPN
asir-1642	254	9	=	=	SYM
asir-1642	254	10	k	k	NOUN
asir-1642	254	11	²	²	NUM
asir-1642	254	12	,	,	PUNCT
asir-1642	254	13	where	where	SCONJ
asir-1642	254	14	k	k	NOUN
asir-1642	254	15	=	=	PRON
asir-1642	255	1	[	[	PUNCT
asir-1642	255	2	²a³p	²a³p	NOUN
asir-1642	255	3	t	t	PROPN
asir-1642	255	4	²	²	X
asir-1642	255	5	]	]	PUNCT
asir-1642	255	6	=	=	SYM
asir-1642	255	7	4π²	4π²	NUM
asir-1642	255	8	.	.	PUNCT
asir-1642	256	1	³p.f	³p.f	VERB
asir-1642	256	2	²	²	PROPN
asir-1642	256	3	→	→	SYM
asir-1642	256	4	a	a	DET
asir-1642	256	5	constant	constant	ADJ
asir-1642	256	6	…	…	PUNCT
asir-1642	256	7	…	…	PUNCT
asir-1642	256	8	..	..	PUNCT
asir-1642	256	9	(	(	PUNCT
asir-1642	256	10	4a	4a	NUM
asir-1642	256	11	)	)	PUNCT
asir-1642	256	12	equation	equation	NOUN
asir-1642	256	13	(	(	PUNCT
asir-1642	256	14	4a	4a	NUM
asir-1642	256	15	)	)	PUNCT
asir-1642	256	16	is	be	AUX
asir-1642	256	17	kepler	kepler	PROPN
asir-1642	256	18	second	second	ADJ
asir-1642	256	19	planetary	planetary	ADJ
asir-1642	256	20	law	law	NOUN
asir-1642	256	21	,	,	PUNCT
asir-1642	256	22	spotting	spot	VERB
asir-1642	256	23	constant	constant	ADJ
asir-1642	256	24	k	k	NOUN
asir-1642	256	25	,	,	PUNCT
asir-1642	256	26	to	to	PART
asir-1642	256	27	be	be	AUX
asir-1642	256	28	a	a	DET
asir-1642	256	29	function	function	NOUN
asir-1642	256	30	of	of	ADP
asir-1642	256	31	the	the	DET
asir-1642	256	32	orbit	orbit	NOUN
asir-1642	256	33	≡	≡	PROPN
asir-1642	256	34	³p≡	³p≡	PROPN
asir-1642	256	35	the	the	DET
asir-1642	256	36	semi	semi	ADJ
asir-1642	256	37	-	-	ADJ
asir-1642	256	38	major	major	ADJ
asir-1642	256	39	axis	axis	ADJ
asir-1642	256	40	≡	≡	PROPN
asir-1642	256	41	space	space	NOUN
asir-1642	256	42	and	and	CCONJ
asir-1642	256	43	as	as	ADP
asir-1642	256	44	a	a	DET
asir-1642	256	45	function	function	NOUN
asir-1642	256	46	of	of	ADP
asir-1642	256	47	time	time	NOUN
asir-1642	256	48	,	,	PUNCT
asir-1642	256	49	t	t	PROPN
asir-1642	256	50	,	,	PUNCT
asir-1642	256	51	or	or	CCONJ
asir-1642	256	52	the	the	DET
asir-1642	256	53	frequency	frequency	NOUN
asir-1642	256	54	p	p	NOUN
asir-1642	256	55	of	of	ADP
asir-1642	256	56	orbiting	orbiting	NOUN
asir-1642	256	57	.	.	PUNCT
asir-1642	257	1	this	this	DET
asir-1642	257	2	significant	significant	ADJ
asir-1642	257	3	property	property	NOUN
asir-1642	257	4	is	be	AUX
asir-1642	257	5	used	use	VERB
asir-1642	257	6	also	also	ADV
asir-1642	257	7	in	in	ADP
asir-1642	257	8	atom	atom	NOUN
asir-1642	257	9	’s	’s	PART
asir-1642	257	10	structure	structure	NOUN
asir-1642	257	11	.	.	PUNCT
asir-1642	258	1	for	for	ADP
asir-1642	258	2	circular	circular	ADJ
asir-1642	258	3	motion	motion	NOUN
asir-1642	258	4	³e=	³e=	NOUN
asir-1642	258	5	r	r	NOUN
asir-1642	258	6	,	,	PUNCT
asir-1642	258	7	then	then	ADV
asir-1642	258	8	(	(	PUNCT
asir-1642	258	9	4a	4a	NUM
asir-1642	258	10	)	)	PUNCT
asir-1642	258	11	becomes	become	VERB
asir-1642	258	12	a	a	PRON
asir-1642	258	13	=	=	X
asir-1642	258	14	[	[	PUNCT
asir-1642	258	15	²	²	NUM
asir-1642	258	16	t	t	NOUN
asir-1642	258	17	²	²	X
asir-1642	258	18	]	]	PUNCT
asir-1642	258	19	³	³	X
asir-1642	258	20	²	²	PROPN
asir-1642	258	21	=	=	X
asir-1642	258	22	-	-	PUNCT
asir-1642	258	23	[	[	PUNCT
asir-1642	258	24	²	²	NUM
asir-1642	258	25	t	t	NOUN
asir-1642	258	26	²	²	X
asir-1642	258	27	]	]	PUNCT
asir-1642	258	28	=	=	SYM
asir-1642	258	29	4π².r.f²	4π².r.f²	NUM
asir-1642	258	30	and	and	CCONJ
asir-1642	258	31	k	k	NOUN
asir-1642	259	1	=	=	PRON
asir-1642	259	2	[	[	PUNCT
asir-1642	259	3	²	²	PROPN
asir-1642	259	4	³	³	NUM
asir-1642	259	5	t	t	NOUN
asir-1642	259	6	²	²	NUM
asir-1642	259	7	]	]	PUNCT
asir-1642	259	8	=	=	SYM
asir-1642	259	9	4π².r³	4π².r³	NUM
asir-1642	259	10	e²	e²	VERB
asir-1642	259	11	,	,	PUNCT
asir-1642	259	12	i.e.	i.e.	X
asir-1642	259	13	,	,	PUNCT
asir-1642	259	14	1	1	X
asir-1642	259	15	..	..	PUNCT
asir-1642	259	16	kepler	kepler	PROPN
asir-1642	259	17	’s	’s	PART
asir-1642	259	18	first	first	ADJ
asir-1642	259	19	law	law	NOUN
asir-1642	259	20	of	of	ADP
asir-1642	259	21	orbits	orbit	NOUN
asir-1642	259	22	:	:	PUNCT
asir-1642	259	23	all	all	DET
asir-1642	259	24	planets	planet	NOUN
asir-1642	259	25	move	move	VERB
asir-1642	259	26	in	in	ADP
asir-1642	259	27	elliptical	elliptical	ADJ
asir-1642	259	28	orbits	orbit	NOUN
asir-1642	259	29	,	,	PUNCT
asir-1642	259	30	with	with	ADP
asir-1642	259	31	the	the	DET
asir-1642	259	32	sun	sun	NOUN
asir-1642	259	33	at	at	ADP
asir-1642	259	34	one	one	NUM
asir-1642	259	35	focus	focus	NOUN
asir-1642	259	36	.	.	PUNCT
asir-1642	260	1	2	2	X
asir-1642	260	2	..	..	PUNCT
asir-1642	260	3	kepler	kepler	PROPN
asir-1642	260	4	’s	’s	PART
asir-1642	260	5	second	second	ADJ
asir-1642	260	6	law	law	NOUN
asir-1642	260	7	of	of	ADP
asir-1642	260	8	areas	area	NOUN
asir-1642	260	9	:	:	PUNCT
asir-1642	260	10	a	a	DET
asir-1642	260	11	line	line	NOUN
asir-1642	260	12	that	that	PRON
asir-1642	260	13	connects	connect	VERB
asir-1642	260	14	a	a	DET
asir-1642	260	15	planet	planet	NOUN
asir-1642	260	16	to	to	ADP
asir-1642	260	17	the	the	DET
asir-1642	260	18	sun	sun	NOUN
asir-1642	260	19	sweeps	sweep	VERB
asir-1642	260	20	out	out	ADP
asir-1642	260	21	equal	equal	ADJ
asir-1642	260	22	areas	area	NOUN
asir-1642	260	23	in	in	ADP
asir-1642	260	24	equal	equal	ADJ
asir-1642	260	25	times	time	NOUN
asir-1642	260	26	.	.	PUNCT
asir-1642	261	1	3	3	X
asir-1642	261	2	..	..	PUNCT
asir-1642	261	3	kepler	kepler	PROPN
asir-1642	261	4	’s	’s	PART
asir-1642	261	5	third	third	ADJ
asir-1642	261	6	law	law	NOUN
asir-1642	261	7	of	of	ADP
asir-1642	261	8	periods	period	NOUN
asir-1642	261	9	:	:	PUNCT
asir-1642	261	10	the	the	DET
asir-1642	261	11	square	square	NOUN
asir-1642	261	12	of	of	ADP
asir-1642	261	13	the	the	DET
asir-1642	261	14	period	period	NOUN
asir-1642	261	15	of	of	ADP
asir-1642	261	16	any	any	DET
asir-1642	261	17	planet	planet	NOUN
asir-1642	261	18	is	be	AUX
asir-1642	261	19	proportional	proportional	ADJ
asir-1642	261	20	to	to	ADP
asir-1642	261	21	the	the	DET
asir-1642	261	22	cube	cube	NOUN
asir-1642	261	23	of	of	ADP
asir-1642	261	24	the	the	DET
asir-1642	261	25	semimajor	semimajor	NOUN
asir-1642	261	26	axis	axis	NOUN
asir-1642	261	27	of	of	ADP
asir-1642	261	28	its	its	PRON
asir-1642	261	29	orbit	orbit	NOUN
asir-1642	261	30	.	.	PUNCT
asir-1642	262	1	4	4	X
asir-1642	262	2	..	..	PUNCT
asir-1642	262	3	kepler	kepler	PROPN
asir-1642	262	4	’s	’s	PART
asir-1642	262	5	constant	constant	ADJ
asir-1642	262	6	k=	k=	ADJ
asir-1642	262	7	4π²r³(1	4π²r³(1	PROPN
asir-1642	262	8	/	/	SYM
asir-1642	262	9	t)²	t)²	PROPN
asir-1642	262	10	:	:	PUNCT
asir-1642	262	11	the	the	DET
asir-1642	262	12	constant	constant	ADJ
asir-1642	262	13	k	k	NOUN
asir-1642	262	14	,	,	PUNCT
asir-1642	262	15	is	be	AUX
asir-1642	262	16	not	not	PART
asir-1642	262	17	-	-	PUNCT
asir-1642	262	18	only	only	ADV
asir-1642	262	19	constant	constant	ADJ
asir-1642	262	20	during	during	ADP
asir-1642	262	21	the	the	DET
asir-1642	262	22	motion	motion	NOUN
asir-1642	262	23	of	of	ADP
asir-1642	262	24	a	a	DET
asir-1642	262	25	planet	planet	NOUN
asir-1642	262	26	,	,	PUNCT
asir-1642	262	27	because	because	SCONJ
asir-1642	262	28	being	be	AUX
asir-1642	262	29	also	also	ADV
asir-1642	262	30	k	k	PROPN
asir-1642	262	31	≅	≅	PROPN
asir-1642	262	32	r³.(1	r³.(1	PROPN
asir-1642	262	33	/	/	SYM
asir-1642	262	34	t)²	t)²	NOUN
asir-1642	262	35	=	=	PUNCT
asir-1642	262	36	constant	constant	ADJ
asir-1642	262	37	for	for	ADP
asir-1642	262	38	all	all	DET
asir-1642	262	39	planets	planet	NOUN
asir-1642	262	40	.	.	PUNCT
asir-1642	263	1	5	5	X
asir-1642	263	2	..	..	PUNCT
asir-1642	263	3	spotting	spot	VERB
asir-1642	263	4	on	on	ADP
asir-1642	263	5	kepler	kepler	PROPN
asir-1642	263	6	’s	’s	PART
asir-1642	263	7	constant	constant	ADJ
asir-1642	263	8	k	k	NOUN
asir-1642	263	9	:	:	PUNCT
asir-1642	263	10	during	during	ADP
asir-1642	263	11	the	the	DET
asir-1642	263	12	central	central	ADJ
asir-1642	263	13	-	-	PUNCT
asir-1642	263	14	plane	plane	NOUN
asir-1642	263	15	-	-	PUNCT
asir-1642	263	16	motion	motion	NOUN
asir-1642	263	17	of	of	ADP
asir-1642	263	18	a	a	DET
asir-1642	263	19	planet	planet	NOUN
asir-1642	263	20	≡	≡	PROPN
asir-1642	263	21	momentum	momentum	NOUN
asir-1642	263	22	b̅	b̅	PROPN
asir-1642	263	23	and	and	CCONJ
asir-1642	263	24	a	a	DET
asir-1642	263	25	sun	sun	NOUN
asir-1642	263	26	≡	≡	PROPN
asir-1642	263	27	focus	focus	VERB
asir-1642	263	28	o	o	PROPN
asir-1642	263	29	,	,	PUNCT
asir-1642	263	30	the	the	DET
asir-1642	263	31	coefficient	coefficient	NOUN
asir-1642	263	32	r³.(1	r³.(1	PROPN
asir-1642	263	33	/	/	SYM
asir-1642	263	34	t)²	t)²	NOUN
asir-1642	263	35	=	=	PUNCT
asir-1642	264	1	r³.	r³.	NOUN
asir-1642	264	2	p²	p²	NOUN
asir-1642	264	3	is	be	AUX
asir-1642	264	4	constant	constant	ADJ
asir-1642	264	5	.	.	PUNCT
asir-1642	265	1	applying	apply	VERB
asir-1642	265	2	above	above	ADP
asir-1642	265	3	property	property	NOUN
asir-1642	265	4	to	to	ADP
asir-1642	265	5	caves	cave	NOUN
asir-1642	265	6	≡	≡	PROPN
asir-1642	265	7	energy	energy	NOUN
asir-1642	265	8	-	-	PUNCT
asir-1642	265	9	storages	storage	NOUN
asir-1642	265	10	≡	≡	PROPN
asir-1642	265	11	orbits	orbit	NOUN
asir-1642	265	12	,	,	PUNCT
asir-1642	265	13	then	then	ADV
asir-1642	265	14	since	since	SCONJ
asir-1642	265	15	r³.	r³.	NOUN
asir-1642	265	16	p²	p²	NOUN
asir-1642	265	17	=	=	SYM
asir-1642	266	1	c	c	NOUN
asir-1642	266	2	=	=	SYM
asir-1642	266	3	constant	constant	ADJ
asir-1642	266	4	,	,	PUNCT
asir-1642	266	5	then	then	ADV
asir-1642	266	6	change	change	NOUN
asir-1642	266	7	of	of	ADP
asir-1642	266	8	,	,	PUNCT
asir-1642	266	9	r	r	PROPN
asir-1642	266	10	,	,	PUNCT
asir-1642	266	11	follows	follow	VERB
asir-1642	266	12	change	change	NOUN
asir-1642	266	13	of	of	ADP
asir-1642	266	14	p	p	NOUN
asir-1642	266	15	,	,	PUNCT
asir-1642	266	16	or	or	CCONJ
asir-1642	266	17	in	in	ADP
asir-1642	266	18	cave	cave	NOUN
asir-1642	266	19	,	,	PUNCT
asir-1642	266	20	electromagnetic	electromagnetic	ADJ
asir-1642	266	21	-	-	PUNCT
asir-1642	266	22	wave	wave	NOUN
asir-1642	266	23	𝐄	𝐄	NOUN
asir-1642	266	24	=	=	SYM
asir-1642	266	25	[	[	PUNCT
asir-1642	266	26	𝟒𝝅𝒓²	𝟒𝝅𝒓²	X
asir-1642	266	27	𝟑	𝟑	NUM
asir-1642	266	28	]	]	PUNCT
asir-1642	266	29	.𝐟	.𝐟	X
asir-1642	267	1	=	=	SYM
asir-1642	267	2	c	c	X
asir-1642	267	3	,	,	PUNCT
asir-1642	267	4	constant	constant	ADJ
asir-1642	267	5	,	,	PUNCT
asir-1642	267	6	is	be	AUX
asir-1642	267	7	absorbed	absorb	VERB
asir-1642	267	8	or	or	CCONJ
asir-1642	267	9	emitted	emit	VERB
asir-1642	267	10	.	.	PUNCT
asir-1642	268	1	remark	remark	NOUN
asir-1642	268	2	:	:	PUNCT
asir-1642	268	3	1	1	X
asir-1642	268	4	..	..	PUNCT
asir-1642	268	5	since	since	ADV
asir-1642	268	6	,	,	PUNCT
asir-1642	268	7	caves	cave	VERB
asir-1642	268	8	≡	≡	PROPN
asir-1642	268	9	energy	energy	NOUN
asir-1642	268	10	-	-	PUNCT
asir-1642	268	11	storages	storage	NOUN
asir-1642	268	12	≡	≡	PROPN
asir-1642	268	13	orbits	orbit	NOUN
asir-1642	268	14	≡	≡	PROPN
asir-1642	268	15	stationary	stationary	ADJ
asir-1642	268	16	-	-	PUNCT
asir-1642	268	17	lobes	lobe	NOUN
asir-1642	268	18	≡	≡	PROPN
asir-1642	268	19	energy	energy	NOUN
asir-1642	268	20	-	-	PUNCT
asir-1642	268	21	rims	rim	NOUN
asir-1642	268	22	≡	≡	PROPN
asir-1642	268	23	r³.	r³.	NOUN
asir-1642	268	24	p²	p²	PROPN
asir-1642	268	25	,	,	PUNCT
asir-1642	268	26	and	and	CCONJ
asir-1642	268	27	energy	energy	NOUN
asir-1642	268	28	=	=	SYM
asir-1642	268	29	n.	n.	NOUN
asir-1642	268	30	[	[	PUNCT
asir-1642	268	31	𝜋𝑟²	𝜋𝑟²	NOUN
asir-1642	268	32	3	3	NUM
asir-1642	268	33	]	]	PUNCT
asir-1642	268	34	.	.	PUNCT
asir-1642	269	1	=	=	PUNCT
asir-1642	269	2	c	c	X
asir-1642	269	3	,	,	PUNCT
asir-1642	269	4	therefore	therefore	ADV
asir-1642	269	5	,	,	PUNCT
asir-1642	269	6	atoms	atom	NOUN
asir-1642	269	7	are	be	AUX
asir-1642	269	8	wheel	wheel	NOUN
asir-1642	269	9	-	-	PUNCT
asir-1642	269	10	rim	rim	NOUN
asir-1642	269	11	,	,	PUNCT
asir-1642	269	12	the	the	DET
asir-1642	269	13	protons	proton	NOUN
asir-1642	269	14	-	-	PUNCT
asir-1642	269	15	neutrons	neutron	NOUN
asir-1642	269	16	in	in	ADP
asir-1642	269	17	nucleus	nucleus	NOUN
asir-1642	269	18	and	and	CCONJ
asir-1642	269	19	electrons	electron	NOUN
asir-1642	269	20	in	in	ADP
asir-1642	269	21	orbits	orbit	NOUN
asir-1642	269	22	is	be	AUX
asir-1642	269	23	an	an	DET
asir-1642	269	24	energy	energy	NOUN
asir-1642	269	25	-	-	PUNCT
asir-1642	269	26	rim	rim	NOUN
asir-1642	269	27	also	also	ADV
asir-1642	269	28	,	,	PUNCT
asir-1642	269	29	for	for	ADP
asir-1642	269	30	each	each	DET
asir-1642	269	31	electron	electron	NOUN
asir-1642	269	32	-	-	PUNCT
asir-1642	269	33	energy	energy	NOUN
asir-1642	269	34	-	-	PUNCT
asir-1642	269	35	orbit	orbit	NOUN
asir-1642	269	36	.	.	PUNCT
asir-1642	270	1	2	2	X
asir-1642	270	2	..	..	PUNCT
asir-1642	270	3	it	it	PRON
asir-1642	270	4	was	be	AUX
asir-1642	270	5	shown	show	VERB
asir-1642	270	6	that	that	SCONJ
asir-1642	270	7	all	all	DET
asir-1642	270	8	particles	particle	NOUN
asir-1642	270	9	have	have	VERB
asir-1642	270	10	the	the	DET
asir-1642	270	11	same	same	ADJ
asir-1642	270	12	acceleration	acceleration	NOUN
asir-1642	270	13	,	,	PUNCT
asir-1642	270	14	g	g	NOUN
asir-1642	270	15	,	,	PUNCT
asir-1642	270	16	in	in	ADP
asir-1642	270	17	our	our	PRON
asir-1642	270	18	gravitational	gravitational	ADJ
asir-1642	270	19	field	field	NOUN
asir-1642	270	20	with	with	ADP
asir-1642	270	21	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	270	22	applied	apply	VERB
asir-1642	270	23	science	science	NOUN
asir-1642	270	24	and	and	CCONJ
asir-1642	270	25	innovative	innovative	ADJ
asir-1642	270	26	research	research	NOUN
asir-1642	270	27	vol	vol	NOUN
asir-1642	270	28	.	.	PROPN
asir-1642	271	1	2	2	NUM
asir-1642	271	2	,	,	PUNCT
asir-1642	271	3	no	no	INTJ
asir-1642	271	4	.	.	NOUN
asir-1642	271	5	4	4	NUM
asir-1642	271	6	,	,	PUNCT
asir-1642	271	7	2018	2018	NUM
asir-1642	271	8	169	169	NUM
asir-1642	271	9	published	publish	VERB
asir-1642	271	10	by	by	ADP
asir-1642	271	11	scholink	scholink	PROPN
asir-1642	271	12	inc	inc	PROPN
asir-1642	271	13	.	.	PROPN
asir-1642	271	14	frequency	frequency	PROPN
asir-1642	271	15	unchanged	unchanged	ADJ
asir-1642	271	16	,	,	PUNCT
asir-1642	271	17	and	and	CCONJ
asir-1642	271	18	→	→	PUNCT
asir-1642	271	19	velocity	velocity	NOUN
asir-1642	271	20	,	,	PUNCT
asir-1642	271	21	dv̅	dv̅	NOUN
asir-1642	271	22	,	,	PUNCT
asir-1642	271	23	with	with	ADP
asir-1642	271	24	wavelength	wavelength	NOUN
asir-1642	271	25	,	,	PUNCT
asir-1642	271	26	λ	λ	PROPN
asir-1642	271	27	,	,	PUNCT
asir-1642	271	28	to	to	PART
asir-1642	271	29	be	be	AUX
asir-1642	271	30	changed	change	VERB
asir-1642	271	31	←	←	PROPN
asir-1642	272	1	so	so	ADV
asir-1642	272	2	light	light	ADJ
asir-1642	272	3	being	be	AUX
asir-1642	272	4	a	a	DET
asir-1642	272	5	particle	particle	NOUN
asir-1642	272	6	also	also	ADV
asir-1642	272	7	is	be	AUX
asir-1642	272	8	deviated	deviate	VERB
asir-1642	272	9	in	in	ADP
asir-1642	272	10	gravity	gravity	NOUN
asir-1642	272	11	field	field	NOUN
asir-1642	272	12	and	and	CCONJ
asir-1642	272	13	,	,	PUNCT
asir-1642	272	14	inertial	inertial	ADJ
asir-1642	272	15	mass	mass	NOUN
asir-1642	272	16	is	be	AUX
asir-1642	272	17	equal	equal	ADJ
asir-1642	272	18	to	to	ADP
asir-1642	272	19	the	the	DET
asir-1642	272	20	gravitational	gravitational	ADJ
asir-1642	272	21	mass	mass	NOUN
asir-1642	272	22	which	which	PRON
asir-1642	272	23	is	be	AUX
asir-1642	272	24	the	the	DET
asir-1642	272	25	necessary	necessary	ADJ
asir-1642	272	26	and	and	CCONJ
asir-1642	272	27	sufficient	sufficient	ADJ
asir-1642	272	28	condition	condition	NOUN
asir-1642	272	29	only	only	ADV
asir-1642	272	30	in	in	ADP
asir-1642	272	31	mass	mass	NOUN
asir-1642	272	32	of	of	ADP
asir-1642	272	33	material	material	NOUN
asir-1642	272	34	-	-	PUNCT
asir-1642	272	35	point	point	NOUN
asir-1642	272	36	where	where	SCONJ
asir-1642	272	37	c	c	NOUN
asir-1642	272	38	t	t	NOUN
asir-1642	273	1	=	=	SYM
asir-1642	273	2	λ	λ	X
asir-1642	273	3	=	=	PUNCT
asir-1642	273	4	c	c	PROPN
asir-1642	273	5	/	/	SYM
asir-1642	273	6	f	f	NOUN
asir-1642	273	7	,	,	PUNCT
asir-1642	273	8	of	of	ADP
asir-1642	273	9	this	this	DET
asir-1642	273	10	isochronous	isochronous	ADJ
asir-1642	273	11	motion	motion	NOUN
asir-1642	273	12	.	.	PUNCT
asir-1642	274	1	3	3	X
asir-1642	274	2	..	..	PUNCT
asir-1642	274	3	the	the	DET
asir-1642	274	4	spotting	spotting	NOUN
asir-1642	274	5	on	on	ADP
asir-1642	274	6	kepler	kepler	PROPN
asir-1642	274	7	’s	’s	PART
asir-1642	274	8	constant	constant	ADJ
asir-1642	274	9	k	k	NOUN
asir-1642	274	10	:	:	PUNCT
asir-1642	274	11	question	question	NOUN
asir-1642	274	12	:	:	PUNCT
asir-1642	274	13	since	since	SCONJ
asir-1642	274	14	the	the	DET
asir-1642	274	15	central	central	ADJ
asir-1642	274	16	-	-	PUNCT
asir-1642	274	17	plane	plane	NOUN
asir-1642	274	18	-	-	PUNCT
asir-1642	274	19	motion	motion	NOUN
asir-1642	274	20	of	of	ADP
asir-1642	274	21	point	point	NOUN
asir-1642	274	22	p	p	X
asir-1642	274	23	=	=	ADJ
asir-1642	274	24	planet	planet	ADJ
asir-1642	274	25	≡	≡	PROPN
asir-1642	274	26	momentum	momentum	NOUN
asir-1642	274	27	b̅	b̅	PROPN
asir-1642	274	28	,	,	PUNCT
asir-1642	274	29	and	and	CCONJ
asir-1642	274	30	a	a	DET
asir-1642	274	31	sun	sun	NOUN
asir-1642	274	32	≡	≡	PROPN
asir-1642	274	33	focus	focus	NOUN
asir-1642	274	34	o	o	NOUN
asir-1642	274	35	is	be	AUX
asir-1642	274	36	a	a	DET
asir-1642	274	37	conic	conic	ADJ
asir-1642	274	38	-	-	PUNCT
asir-1642	274	39	section	section	NOUN
asir-1642	274	40	,	,	PUNCT
asir-1642	274	41	to	to	PART
asir-1642	274	42	find	find	VERB
asir-1642	274	43	of	of	ADP
asir-1642	274	44	producing	produce	VERB
asir-1642	274	45	the	the	DET
asir-1642	274	46	shortest	shortest	ADV
asir-1642	274	47	-	-	PUNCT
asir-1642	274	48	closed	close	VERB
asir-1642	274	49	-	-	PUNCT
asir-1642	274	50	surface	surface	NOUN
asir-1642	274	51	on	on	ADP
asir-1642	274	52	any	any	DET
asir-1642	274	53	plane	plane	NOUN
asir-1642	274	54	,	,	PUNCT
asir-1642	274	55	such	such	ADJ
asir-1642	274	56	that	that	SCONJ
asir-1642	274	57	energy	energy	NOUN
asir-1642	274	58	≡	≡	PROPN
asir-1642	274	59	motion	motion	NOUN
asir-1642	274	60	,	,	PUNCT
asir-1642	274	61	to	to	PART
asir-1642	274	62	be	be	AUX
asir-1642	274	63	constant	constant	ADJ
asir-1642	274	64	≡	≡	PROPN
asir-1642	274	65	the	the	DET
asir-1642	274	66	closed	close	VERB
asir-1642	274	67	-	-	PUNCT
asir-1642	274	68	surface	surface	NOUN
asir-1642	274	69	of	of	ADP
asir-1642	274	70	the	the	DET
asir-1642	274	71	two	two	NUM
asir-1642	274	72	points	point	NOUN
asir-1642	274	73	,	,	PUNCT
asir-1642	274	74	and	and	CCONJ
asir-1642	274	75	which	which	PRON
asir-1642	274	76	is	be	AUX
asir-1642	274	77	,	,	PUNCT
asir-1642	274	78	→	→	PUNCT
asir-1642	274	79	to	to	PART
asir-1642	274	80	find	find	VERB
asir-1642	274	81	the	the	DET
asir-1642	274	82	energy	energy	NOUN
asir-1642	274	83	-	-	PUNCT
asir-1642	274	84	path	path	NOUN
asir-1642	274	85	-	-	PUNCT
asir-1642	274	86	closed	closed	ADJ
asir-1642	274	87	-	-	PUNCT
asir-1642	274	88	curve	curve	NOUN
asir-1642	274	89	of	of	ADP
asir-1642	274	90	the	the	DET
asir-1642	274	91	two	two	NUM
asir-1642	274	92	points	point	NOUN
asir-1642	274	93	which	which	DET
asir-1642	274	94	surface	surface	NOUN
asir-1642	274	95	is	be	AUX
asir-1642	274	96	of	of	ADP
asir-1642	274	97	constant	constant	ADJ
asir-1642	274	98	-	-	PUNCT
asir-1642	274	99	energy	energy	NOUN
asir-1642	274	100	.	.	PUNCT
asir-1642	275	1	constant	constant	ADJ
asir-1642	275	2	is	be	AUX
asir-1642	275	3	not	not	PART
asir-1642	275	4	a	a	DET
asir-1642	275	5	maximum	maximum	ADJ
asir-1642	275	6	or	or	CCONJ
asir-1642	275	7	minimum	minimum	ADJ
asir-1642	275	8	magnitude	magnitude	NOUN
asir-1642	275	9	between	between	ADP
asir-1642	275	10	the	the	DET
asir-1642	275	11	two	two	NUM
asir-1642	275	12	points	point	NOUN
asir-1642	275	13	p	p	NOUN
asir-1642	275	14	and	and	CCONJ
asir-1642	275	15	o	o	NOUN
asir-1642	275	16	,	,	PUNCT
asir-1642	275	17	instead	instead	ADV
asir-1642	275	18	it	it	PRON
asir-1642	275	19	is	be	AUX
asir-1642	275	20	a	a	DET
asir-1642	275	21	fixed	fix	VERB
asir-1642	275	22	sum	sum	NOUN
asir-1642	275	23	from	from	ADP
asir-1642	275	24	rotation	rotation	NOUN
asir-1642	275	25	≡	≡	PROPN
asir-1642	276	1	[	[	X
asir-1642	276	2	⊕	⊕	NOUN
asir-1642	276	3	↻	↻	NOUN
asir-1642	276	4	↺	↺	NOUN
asir-1642	276	5	⊝	⊝	NOUN
asir-1642	276	6	]	]	PUNCT
asir-1642	276	7	≡	≡	PROPN
asir-1642	276	8	motion	motion	NOUN
asir-1642	276	9	,	,	PUNCT
asir-1642	276	10	trapped	trap	VERB
asir-1642	276	11	in	in	ADP
asir-1642	276	12	a	a	DET
asir-1642	276	13	closed	closed	ADJ
asir-1642	276	14	-	-	PUNCT
asir-1642	276	15	curve	curve	NOUN
asir-1642	276	16	←	←	PROPN
asir-1642	276	17	the	the	DET
asir-1642	276	18	energy	energy	NOUN
asir-1642	276	19	-	-	PUNCT
asir-1642	276	20	quantity	quantity	NOUN
asir-1642	276	21	k	k	NOUN
asir-1642	276	22	is	be	AUX
asir-1642	276	23	constant	constant	ADJ
asir-1642	276	24	in	in	ADP
asir-1642	276	25	planck	planck	NOUN
asir-1642	276	26	’s	’s	PART
asir-1642	276	27	scale	scale	NOUN
asir-1642	276	28	cave	cave	NOUN
asir-1642	276	29	10	10	NUM
asir-1642	276	30	3	3	NUM
asir-1642	276	31	m	m	NOUN
asir-1642	276	32	and	and	CCONJ
asir-1642	276	33	exist	exist	VERB
asir-1642	276	34	,	,	PUNCT
asir-1642	276	35	in	in	ADP
asir-1642	276	36	plane	plane	NOUN
asir-1642	276	37	rims	rim	NOUN
asir-1642	276	38	,	,	PUNCT
asir-1642	276	39	becoming	become	VERB
asir-1642	276	40	from	from	ADP
asir-1642	276	41	the	the	DET
asir-1642	276	42	continuous	continuous	ADJ
asir-1642	276	43	central	central	ADJ
asir-1642	276	44	-	-	PUNCT
asir-1642	276	45	rotation	rotation	NOUN
asir-1642	276	46	of	of	ADP
asir-1642	276	47	masses	masse	NOUN
asir-1642	276	48	in	in	ADP
asir-1642	276	49	scales	scale	NOUN
asir-1642	276	50	.	.	PUNCT
asir-1642	277	1	it	it	PRON
asir-1642	277	2	is	be	AUX
asir-1642	277	3	shown	show	VERB
asir-1642	277	4	in	in	ADP
asir-1642	277	5	,	,	PUNCT
asir-1642	277	6	kepler	kepler	PROPN
asir-1642	277	7	’s	’s	PART
asir-1642	277	8	third	third	ADJ
asir-1642	277	9	law	law	NOUN
asir-1642	277	10	,	,	PUNCT
asir-1642	277	11	that	that	SCONJ
asir-1642	277	12	this	this	DET
asir-1642	277	13	constant	constant	ADJ
asir-1642	277	14	is	be	AUX
asir-1642	277	15	k	k	X
asir-1642	277	16	=	=	PRON
asir-1642	277	17	[	[	PUNCT
asir-1642	277	18	²	²	PROPN
asir-1642	277	19	³	³	NUM
asir-1642	277	20	t	t	NOUN
asir-1642	277	21	²	²	NUM
asir-1642	277	22	]	]	PUNCT
asir-1642	277	23	=	=	SYM
asir-1642	277	24	4π².r³	4π².r³	NUM
asir-1642	277	25	p²	p²	PROPN
asir-1642	277	26	,	,	PUNCT
asir-1642	277	27	where	where	SCONJ
asir-1642	277	28	for	for	ADP
asir-1642	277	29	the	the	DET
asir-1642	277	30	sun	sun	NOUN
asir-1642	277	31	-	-	PUNCT
asir-1642	277	32	earth	earth	NOUN
asir-1642	277	33	-	-	PUNCT
asir-1642	277	34	rim	rim	NOUN
asir-1642	277	35	semi	semi	ADJ
asir-1642	277	36	-	-	ADJ
asir-1642	277	37	major	major	ADJ
asir-1642	277	38	-	-	PUNCT
asir-1642	277	39	axis	axis	NOUN
asir-1642	277	40	,	,	PUNCT
asir-1642	277	41	r	r	NOUN
asir-1642	277	42	=	=	SYM
asir-1642	277	43	15.10	15.10	NUM
asir-1642	277	44	0	0	NUM
asir-1642	277	45	m	m	NOUN
asir-1642	277	46	,	,	PUNCT
asir-1642	277	47	and	and	CCONJ
asir-1642	277	48	the	the	DET
asir-1642	277	49	period	period	NOUN
asir-1642	277	50	t	t	NOUN
asir-1642	277	51	=	=	SYM
asir-1642	277	52	1	1	NUM
asir-1642	277	53	year	year	NOUN
asir-1642	277	54	the	the	DET
asir-1642	277	55	energy	energy	NOUN
asir-1642	277	56	in	in	ADP
asir-1642	277	57	this	this	DET
asir-1642	277	58	plane	plane	NOUN
asir-1642	277	59	-	-	PUNCT
asir-1642	277	60	sun	sun	NOUN
asir-1642	277	61	-	-	PUNCT
asir-1642	277	62	earth	earth	NOUN
asir-1642	277	63	rim	rim	NOUN
asir-1642	277	64	is	be	AUX
asir-1642	277	65	k	k	NOUN
asir-1642	277	66	=	=	PUNCT
asir-1642	277	67	3.10	3.10	NUM
asir-1642	277	68	3	3	NUM
asir-1642	277	69	=	=	PUNCT
asir-1642	278	1	[	[	X
asir-1642	278	2	3.10	3.10	NUM
asir-1642	278	3	]	]	SYM
asir-1642	278	4	.10	.10	NUM
asir-1642	278	5	2	2	NUM
asir-1642	278	6	y²/m³.	y²/m³.	PROPN
asir-1642	278	7	figure	figure	NOUN
asir-1642	278	8	5	5	NUM
asir-1642	278	9	.	.	PUNCT
asir-1642	279	1	the	the	DET
asir-1642	279	2	conic	conic	ADJ
asir-1642	279	3	-	-	PUNCT
asir-1642	279	4	sections	section	NOUN
asir-1642	279	5	as	as	ADP
asir-1642	279	6	planar	planar	ADJ
asir-1642	279	7	and	and	CCONJ
asir-1642	279	8	atoms	atom	NOUN
asir-1642	279	9	-	-	PUNCT
asir-1642	279	10	curves	curve	NOUN
asir-1642	279	11	under	under	ADP
asir-1642	279	12	equilibrium	equilibrium	NOUN
asir-1642	279	13	of	of	ADP
asir-1642	279	14	forces	force	NOUN
asir-1642	279	15	1	1	NUM
asir-1642	279	16	..	..	PUNCT
asir-1642	279	17	the	the	DET
asir-1642	279	18	generation	generation	NOUN
asir-1642	279	19	of	of	ADP
asir-1642	279	20	the	the	DET
asir-1642	279	21	conic	conic	ADJ
asir-1642	279	22	-	-	PUNCT
asir-1642	279	23	sections	section	NOUN
asir-1642	279	24	:	:	PUNCT
asir-1642	280	1	o	o	X
asir-1642	280	2	=	=	PUNCT
asir-1642	280	3	the	the	DET
asir-1642	280	4	constant	constant	ADJ
asir-1642	280	5	center	center	NOUN
asir-1642	280	6	of	of	ADP
asir-1642	280	7	rotation	rotation	NOUN
asir-1642	280	8	,	,	PUNCT
asir-1642	280	9	p	p	X
asir-1642	280	10	=	=	PUNCT
asir-1642	280	11	the	the	DET
asir-1642	280	12	movable	movable	ADJ
asir-1642	280	13	point	point	NOUN
asir-1642	280	14	on	on	ADP
asir-1642	280	15	orbit	orbit	NOUN
asir-1642	280	16	,	,	PUNCT
asir-1642	280	17	p	p	X
asir-1642	280	18	=	=	PUNCT
asir-1642	280	19	the	the	DET
asir-1642	280	20	parameter	parameter	NOUN
asir-1642	280	21	of	of	ADP
asir-1642	280	22	the	the	DET
asir-1642	280	23	conic	conic	NOUN
asir-1642	280	24	,	,	PUNCT
asir-1642	280	25	e	e	X
asir-1642	280	26	=	=	PUNCT
asir-1642	280	27	the	the	DET
asir-1642	280	28	eccentricity	eccentricity	NOUN
asir-1642	280	29	of	of	ADP
asir-1642	280	30	the	the	DET
asir-1642	280	31	conic	conic	ADJ
asir-1642	280	32	0	0	NUM
asir-1642	280	33	≤	≤	NUM
asir-1642	280	34	e	e	X
asir-1642	280	35	≤1	≤1	PROPN
asir-1642	280	36	2	2	NUM
asir-1642	280	37	..	..	PUNCT
asir-1642	280	38	the	the	DET
asir-1642	280	39	central	central	ADJ
asir-1642	280	40	ellipse	ellipse	NOUN
asir-1642	280	41	and	and	CCONJ
asir-1642	280	42	gravity	gravity	NOUN
asir-1642	280	43	relation	relation	NOUN
asir-1642	280	44	for	for	ADP
asir-1642	280	45	mass	mass	NOUN
asir-1642	280	46	m	m	VERB
asir-1642	280	47	p→	p→	ADJ
asir-1642	280	48	planet	planet	NOUN
asir-1642	280	49	,	,	PUNCT
asir-1642	280	50	on	on	ADP
asir-1642	280	51	m	m	PROPN
asir-1642	280	52	s→	s→	PRON
asir-1642	280	53	sun	sun	NOUN
asir-1642	280	54	.	.	PUNCT
asir-1642	281	1	3	3	NUM
asir-1642	281	2	..	..	PUNCT
asir-1642	281	3	the	the	DET
asir-1642	281	4	energy	energy	NOUN
asir-1642	281	5	-	-	PUNCT
asir-1642	281	6	rim	rim	NOUN
asir-1642	281	7	r	r	NOUN
asir-1642	281	8	is	be	AUX
asir-1642	281	9	circle	circle	NOUN
asir-1642	281	10	because	because	SCONJ
asir-1642	281	11	focus	focus	NOUN
asir-1642	281	12	f	f	PROPN
asir-1642	281	13	is	be	AUX
asir-1642	281	14	consisted	consist	VERB
asir-1642	281	15	of	of	ADP
asir-1642	281	16	one	one	NUM
asir-1642	281	17	center	center	NOUN
asir-1642	281	18	,	,	PUNCT
asir-1642	281	19	while	while	SCONJ
asir-1642	281	20	the	the	DET
asir-1642	281	21	others	other	NOUN
asir-1642	281	22	for	for	ADP
asir-1642	281	23	focus	focus	NOUN
asir-1642	281	24	f	f	PROPN
asir-1642	281	25	is	be	AUX
asir-1642	281	26	of	of	ADP
asir-1642	281	27	2,3,4,n	2,3,4,n	NUM
asir-1642	281	28	.	.	PUNCT
asir-1642	282	1	centers	center	NOUN
asir-1642	282	2	due	due	ADP
asir-1642	282	3	to	to	ADP
asir-1642	282	4	⊕	⊕	PROPN
asir-1642	282	5	elements	element	NOUN
asir-1642	282	6	are	be	AUX
asir-1642	282	7	ellipse	ellipse	NOUN
asir-1642	282	8	for	for	ADP
asir-1642	282	9	every	every	DET
asir-1642	282	10	one	one	NUM
asir-1642	282	11	⊝	⊝	NOUN
asir-1642	282	12	mass	mass	NOUN
asir-1642	282	13	m	m	PROPN
asir-1642	282	14	p.	p.	NOUN
asir-1642	282	15	kepler	kepler	PROPN
asir-1642	282	16	’s	’s	PART
asir-1642	282	17	constant	constant	ADJ
asir-1642	282	18	planets	planet	NOUN
asir-1642	282	19	relation	relation	NOUN
asir-1642	282	20	is	be	AUX
asir-1642	282	21	t	t	PROPN
asir-1642	282	22	²	²	NUM
asir-1642	282	23	a³	a³	PROPN
asir-1642	283	1	=	=	SYM
asir-1642	283	2	k	k	NOUN
asir-1642	283	3	=	=	PUNCT
asir-1642	283	4	[	[	PUNCT
asir-1642	283	5	²	²	PROPN
asir-1642	283	6	g.m	g.m	NOUN
asir-1642	283	7	]	]	PUNCT
asir-1642	284	1	=	=	PUNCT
asir-1642	284	2	2,97.10	2,97.10	NUM
asir-1642	284	3	9	9	NUM
asir-1642	284	4	(	(	PUNCT
asir-1642	284	5	s²/m³	s²/m³	PROPN
asir-1642	284	6	)	)	PUNCT
asir-1642	284	7	,	,	PUNCT
asir-1642	284	8	where	where	SCONJ
asir-1642	284	9	g	g	NOUN
asir-1642	284	10	=	=	SYM
asir-1642	284	11	6,67.10	6,67.10	NUM
asir-1642	284	12	(	(	PUNCT
asir-1642	284	13	nm²/kg²	nm²/kg²	NOUN
asir-1642	284	14	)	)	PUNCT
asir-1642	284	15	becomes	become	VERB
asir-1642	284	16	from	from	ADP
asir-1642	284	17	the	the	DET
asir-1642	284	18	light	light	ADJ
asir-1642	284	19	-	-	PUNCT
asir-1642	284	20	velocity	velocity	NOUN
asir-1642	284	21	-	-	PUNCT
asir-1642	284	22	storage	storage	NOUN
asir-1642	284	23	,	,	PUNCT
asir-1642	284	24	v̅	v̅	PROPN
asir-1642	284	25	,	,	PUNCT
asir-1642	284	26	when	when	SCONJ
asir-1642	284	27	,	,	PUNCT
asir-1642	284	28	v̅	v̅	PROPN
asir-1642	284	29	,	,	PUNCT
asir-1642	284	30	is	be	AUX
asir-1642	284	31	entering	enter	VERB
asir-1642	284	32	the	the	DET
asir-1642	284	33	cave	cave	NOUN
asir-1642	284	34	r	r	NOUN
asir-1642	284	35	=	=	NOUN
asir-1642	284	36	1.10	1.10	NUM
asir-1642	284	37	2	2	NUM
asir-1642	284	38	m	m	NOUN
asir-1642	284	39	,	,	PUNCT
asir-1642	284	40	where	where	SCONJ
asir-1642	284	41	is	be	AUX
asir-1642	284	42	produced	produce	VERB
asir-1642	284	43	the	the	DET
asir-1642	284	44	energy	energy	NOUN
asir-1642	284	45	plane	plane	NOUN
asir-1642	284	46	-	-	PUNCT
asir-1642	284	47	cave	cave	NOUN
asir-1642	284	48	-	-	PUNCT
asir-1642	284	49	rim	rim	NOUN
asir-1642	284	50	equal	equal	ADJ
asir-1642	284	51	to	to	ADP
asir-1642	284	52	r	r	NOUN
asir-1642	284	53	=	=	PUNCT
asir-1642	284	54	3.10	3.10	NUM
asir-1642	284	55	3	3	NUM
asir-1642	284	56	m²/s	m²/s	NOUN
asir-1642	284	57	.	.	PUNCT
asir-1642	285	1	since	since	SCONJ
asir-1642	285	2	also	also	ADV
asir-1642	285	3	exists	exist	VERB
asir-1642	285	4	the	the	DET
asir-1642	285	5	relation	relation	NOUN
asir-1642	285	6	→	→	PUNCT
asir-1642	285	7	k.	k.	PROPN
asir-1642	285	8	².r³	².r³	PROPN
asir-1642	286	1	=	=	PUNCT
asir-1642	286	2	1	1	NUM
asir-1642	286	3	←	←	PROPN
asir-1642	286	4	where	where	SCONJ
asir-1642	286	5	r	r	NOUN
asir-1642	286	6	=	=	PUNCT
asir-1642	286	7	semi	semi	ADV
asir-1642	286	8	major	major	ADJ
asir-1642	286	9	axis	axis	NOUN
asir-1642	286	10	a	a	PRON
asir-1642	286	11	,	,	PUNCT
asir-1642	286	12	then	then	ADV
asir-1642	286	13	,	,	PUNCT
asir-1642	286	14	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	286	15	applied	apply	VERB
asir-1642	286	16	science	science	NOUN
asir-1642	286	17	and	and	CCONJ
asir-1642	286	18	innovative	innovative	ADJ
asir-1642	286	19	research	research	NOUN
asir-1642	286	20	vol	vol	NOUN
asir-1642	286	21	.	.	PROPN
asir-1642	287	1	2	2	NUM
asir-1642	287	2	,	,	PUNCT
asir-1642	287	3	no	no	INTJ
asir-1642	287	4	.	.	NOUN
asir-1642	287	5	4	4	NUM
asir-1642	287	6	,	,	PUNCT
asir-1642	287	7	2018	2018	NUM
asir-1642	287	8	170	170	NUM
asir-1642	287	9	published	publish	VERB
asir-1642	287	10	by	by	ADP
asir-1642	287	11	scholink	scholink	PROPN
asir-1642	287	12	inc	inc	PROPN
asir-1642	287	13	.	.	PUNCT
asir-1642	288	1	an	an	DET
asir-1642	288	2	energy	energy	NOUN
asir-1642	288	3	-	-	PUNCT
asir-1642	288	4	rim	rim	NOUN
asir-1642	288	5	is	be	AUX
asir-1642	288	6	a	a	DET
asir-1642	288	7	plane	plane	NOUN
asir-1642	288	8	-	-	PUNCT
asir-1642	288	9	surface	surface	NOUN
asir-1642	288	10	representing	represent	VERB
asir-1642	288	11	a	a	DET
asir-1642	288	12	constant	constant	ADJ
asir-1642	288	13	-	-	PUNCT
asir-1642	288	14	energy	energy	NOUN
asir-1642	288	15	becoming	become	VERB
asir-1642	288	16	from	from	ADP
asir-1642	288	17	the	the	DET
asir-1642	288	18	squared	square	VERB
asir-1642	288	19	frequency	frequency	NOUN
asir-1642	288	20	𝐟𝐧²	𝐟𝐧²	VERB
asir-1642	288	21	,	,	PUNCT
asir-1642	288	22	representing	represent	VERB
asir-1642	288	23	the	the	DET
asir-1642	288	24	imaginary	imaginary	ADJ
asir-1642	288	25	energy	energy	NOUN
asir-1642	288	26	part	part	NOUN
asir-1642	288	27	of	of	ADP
asir-1642	288	28	monad	monad	PROPN
asir-1642	288	29	,	,	PUNCT
asir-1642	288	30	and	and	CCONJ
asir-1642	288	31	𝐫𝐧³	𝐫𝐧³	NOUN
asir-1642	288	32	representing	represent	VERB
asir-1642	288	33	the	the	DET
asir-1642	288	34	real	real	ADJ
asir-1642	288	35	-	-	PUNCT
asir-1642	288	36	space	space	NOUN
asir-1642	288	37	-	-	PUNCT
asir-1642	288	38	part	part	NOUN
asir-1642	288	39	of	of	ADP
asir-1642	288	40	monad	monad	PROPN
asir-1642	288	41	1	1	PROPN
asir-1642	288	42	=	=	SYM
asir-1642	288	43	k.	k.	NOUN
asir-1642	288	44	².r³.	².r³.	NOUN
asir-1642	288	45	all	all	DET
asir-1642	288	46	these	these	DET
asir-1642	288	47	energy	energy	NOUN
asir-1642	288	48	-	-	PUNCT
asir-1642	288	49	rims	rim	NOUN
asir-1642	288	50	consist	consist	VERB
asir-1642	288	51	the	the	DET
asir-1642	288	52	quantized	quantize	VERB
asir-1642	288	53	-	-	PUNCT
asir-1642	288	54	plane	plane	NOUN
asir-1642	288	55	-	-	PUNCT
asir-1642	288	56	curves	curve	NOUN
asir-1642	288	57	4	4	NUM
asir-1642	288	58	..	..	PUNCT
asir-1642	288	59	central	central	ADJ
asir-1642	288	60	motion	motion	NOUN
asir-1642	288	61	and	and	CCONJ
asir-1642	288	62	gravity	gravity	NOUN
asir-1642	288	63	:	:	PUNCT
asir-1642	288	64	kepler	kepler	PROPN
asir-1642	288	65	’s	’s	PART
asir-1642	288	66	third	third	ADJ
asir-1642	288	67	law	law	NOUN
asir-1642	288	68	of	of	ADP
asir-1642	288	69	harmonics	harmonic	NOUN
asir-1642	288	70	suggested	suggest	VERB
asir-1642	288	71	that	that	SCONJ
asir-1642	288	72	,	,	PUNCT
asir-1642	288	73	the	the	DET
asir-1642	288	74	ratio	ratio	NOUN
asir-1642	288	75	of	of	ADP
asir-1642	288	76	the	the	DET
asir-1642	288	77	period	period	NOUN
asir-1642	288	78	of	of	ADP
asir-1642	288	79	orbit	orbit	NOUN
asir-1642	288	80	squared	square	VERB
asir-1642	288	81	(	(	PUNCT
asir-1642	288	82	t²	t²	NOUN
asir-1642	288	83	)	)	PUNCT
asir-1642	288	84	to	to	ADP
asir-1642	288	85	the	the	DET
asir-1642	288	86	mean	mean	ADJ
asir-1642	288	87	radius	radius	NOUN
asir-1642	288	88	of	of	ADP
asir-1642	288	89	orbit	orbit	NOUN
asir-1642	288	90	cubed	cubed	PROPN
asir-1642	288	91	(	(	PUNCT
asir-1642	288	92	r³	r³	PROPN
asir-1642	288	93	)	)	PUNCT
asir-1642	288	94	is	be	AUX
asir-1642	288	95	the	the	DET
asir-1642	288	96	same	same	ADJ
asir-1642	288	97	value	value	NOUN
asir-1642	288	98	,	,	PUNCT
asir-1642	288	99	k	k	PROPN
asir-1642	289	1	=	=	SYM
asir-1642	289	2	2,97.10	2,97.10	NUM
asir-1642	289	3	9	9	NUM
asir-1642	289	4	s²/m³	s²/m³	NOUN
asir-1642	289	5	=	=	SYM
asir-1642	289	6	t²/r³	t²/r³	NOUN
asir-1642	289	7	,	,	PUNCT
asir-1642	289	8	for	for	ADP
asir-1642	289	9	all	all	DET
asir-1642	289	10	the	the	DET
asir-1642	289	11	planets	planet	NOUN
asir-1642	289	12	that	that	PRON
asir-1642	289	13	orbit	orbit	VERB
asir-1642	289	14	the	the	DET
asir-1642	289	15	sun	sun	PROPN
asir-1642	289	16	.	.	PUNCT
asir-1642	289	17	centripetal	centripetal	PROPN
asir-1642	289	18	force	force	NOUN
asir-1642	290	1	c	c	PROPN
asir-1642	290	2	f	f	PROPN
asir-1642	291	1	=	=	PUNCT
asir-1642	291	2	m	m	VERB
asir-1642	291	3	pv²	pv²	NOUN
asir-1642	291	4	/	/	SYM
asir-1642	291	5	r	r	NOUN
asir-1642	291	6	is	be	AUX
asir-1642	291	7	the	the	DET
asir-1642	291	8	result	result	NOUN
asir-1642	291	9	of	of	ADP
asir-1642	291	10	the	the	DET
asir-1642	291	11	gravitational	gravitational	ADJ
asir-1642	291	12	force	force	NOUN
asir-1642	291	13	that	that	PRON
asir-1642	291	14	attracts	attract	VERB
asir-1642	291	15	the	the	DET
asir-1642	291	16	planet	planet	NOUN
asir-1642	291	17	towards	towards	ADP
asir-1642	291	18	the	the	DET
asir-1642	291	19	sun	sun	NOUN
asir-1642	291	20	and	and	CCONJ
asir-1642	291	21	can	can	AUX
asir-1642	291	22	be	be	AUX
asir-1642	291	23	represented	represent	VERB
asir-1642	291	24	as	as	ADP
asir-1642	291	25	gravity	gravity	NOUN
asir-1642	291	26	-	-	PUNCT
asir-1642	291	27	force	force	NOUN
asir-1642	291	28	→	→	PUNCT
asir-1642	291	29	g	g	NOUN
asir-1642	291	30	f	f	PROPN
asir-1642	291	31	=	=	X
asir-1642	291	32	[	[	PUNCT
asir-1642	291	33	g.m	g.m	PROPN
asir-1642	291	34	pm	pm	NOUN
asir-1642	291	35	s	s	X
asir-1642	291	36	]	]	X
asir-1642	291	37	/	/	SYM
asir-1642	291	38	r²	r²	NOUN
asir-1642	291	39	and	and	CCONJ
asir-1642	291	40	is	be	AUX
asir-1642	291	41	𝐂	𝐂	ADJ
asir-1642	291	42	𝐅	𝐅	NOUN
asir-1642	291	43	=	=	SYM
asir-1642	291	44	𝐆	𝐆	NOUN
asir-1642	291	45	𝐅	𝐅	PROPN
asir-1642	291	46	.	.	PUNCT
asir-1642	292	1	since	since	SCONJ
asir-1642	292	2	the	the	DET
asir-1642	292	3	mean	mean	ADJ
asir-1642	292	4	-	-	PUNCT
asir-1642	292	5	velocity	velocity	NOUN
asir-1642	292	6	of	of	ADP
asir-1642	292	7	a	a	DET
asir-1642	292	8	planet	planet	NOUN
asir-1642	292	9	is	be	AUX
asir-1642	292	10	v	v	ADP
asir-1642	292	11	p	p	NOUN
asir-1642	292	12	=	=	PUNCT
asir-1642	292	13	(	(	PUNCT
asir-1642	292	14	2πr	2πr	NOUN
asir-1642	292	15	)	)	PUNCT
asir-1642	292	16	/	/	SYM
asir-1642	293	1	t	t	NOUN
asir-1642	293	2	then	then	ADV
asir-1642	293	3	v²	v²	PROPN
asir-1642	293	4	=	=	SYM
asir-1642	293	5	(	(	PUNCT
asir-1642	293	6	4π²r²	4π²r²	NOUN
asir-1642	293	7	)	)	PUNCT
asir-1642	293	8	/	/	SYM
asir-1642	293	9	t²	t²	NOUN
asir-1642	293	10	and	and	CCONJ
asir-1642	293	11	substituting	substitute	VERB
asir-1642	293	12	to	to	ADP
asir-1642	293	13	prior	prior	ADV
asir-1642	293	14	,	,	PUNCT
asir-1642	293	15	centripetal	centripetal	ADJ
asir-1642	293	16	force	force	NOUN
asir-1642	294	1	m	m	VERB
asir-1642	294	2	p	p	NOUN
asir-1642	295	1	[	[	X
asir-1642	295	2	4π²r²	4π²r²	X
asir-1642	295	3	]	]	PUNCT
asir-1642	295	4	/	/	SYM
asir-1642	295	5	rt²	rt²	NOUN
asir-1642	295	6	=	=	PUNCT
asir-1642	296	1	[	[	PUNCT
asir-1642	296	2	g.m	g.m	PROPN
asir-1642	296	3	pm	pm	NOUN
asir-1642	296	4	s	s	X
asir-1642	296	5	]	]	X
asir-1642	296	6	/	/	SYM
asir-1642	296	7	r²	r²	NOUN
asir-1642	296	8	and	and	CCONJ
asir-1642	296	9	by	by	ADP
asir-1642	296	10	cross	cross	ADJ
asir-1642	296	11	-	-	ADJ
asir-1642	296	12	multiplication	multiplication	NOUN
asir-1642	296	13	is	be	AUX
asir-1642	296	14	transformed	transform	VERB
asir-1642	296	15	to	to	ADP
asir-1642	296	16	t²	t²	NOUN
asir-1642	296	17	/	/	SYM
asir-1642	296	18	r³	r³	PROPN
asir-1642	296	19	=	=	PUNCT
asir-1642	297	1	[	[	X
asir-1642	297	2	m	m	X
asir-1642	297	3	p4π²	p4π²	X
asir-1642	297	4	]	]	X
asir-1642	297	5	/	/	PUNCT
asir-1642	298	1	[	[	X
asir-1642	298	2	g.	g.	NOUN
asir-1642	298	3	m	m	VERB
asir-1642	298	4	pm	pm	PROPN
asir-1642	298	5	s	s	X
asir-1642	298	6	]	]	PUNCT
asir-1642	298	7	and	and	CCONJ
asir-1642	298	8	canceling	cancel	VERB
asir-1642	298	9	the	the	DET
asir-1642	298	10	same	same	ADJ
asir-1642	298	11	from	from	ADP
asir-1642	298	12	numerator	numerator	NOUN
asir-1642	298	13	and	and	CCONJ
asir-1642	298	14	the	the	DET
asir-1642	298	15	denominator	denominator	NOUN
asir-1642	298	16	then	then	ADV
asir-1642	298	17	t²/r³	t²/r³	NOUN
asir-1642	298	18	=	=	PUNCT
asir-1642	299	1	[	[	X
asir-1642	299	2	4π²	4π²	X
asir-1642	299	3	]	]	PUNCT
asir-1642	299	4	/	/	PUNCT
asir-1642	300	1	[	[	X
asir-1642	300	2	g.ms	g.ms	X
asir-1642	300	3	]	]	X
asir-1642	300	4	or	or	CCONJ
asir-1642	300	5	gm	gm	PROPN
asir-1642	300	6	s	s	PART
asir-1642	300	7	=	=	PUNCT
asir-1642	301	1	[	[	X
asir-1642	301	2	4π²	4π²	NUM
asir-1642	301	3	.	.	PUNCT
asir-1642	302	1	p²	p²	PROPN
asir-1642	302	2	]	]	PUNCT
asir-1642	302	3	r³	r³	PROPN
asir-1642	302	4	=	=	PUNCT
asir-1642	303	1	w²r³	w²r³	X
asir-1642	303	2	where	where	SCONJ
asir-1642	303	3	=	=	PUNCT
asir-1642	303	4	[	[	PUNCT
asir-1642	303	5	𝜋𝑟²	𝜋𝑟²	NOUN
asir-1642	303	6	3	3	NUM
asir-1642	303	7	]	]	PUNCT
asir-1642	303	8	.	.	PUNCT
asir-1642	304	1	p	p	X
asir-1642	304	2	,	,	PUNCT
asir-1642	304	3	k	k	PROPN
asir-1642	304	4	=	=	PUNCT
asir-1642	304	5	r³.	r³.	NOUN
asir-1642	304	6	p²	p²	VERB
asir-1642	304	7	the	the	DET
asir-1642	304	8	period	period	NOUN
asir-1642	304	9	t(s	t(s	PROPN
asir-1642	304	10	)	)	PUNCT
asir-1642	304	11	for	for	ADP
asir-1642	304	12	an	an	DET
asir-1642	304	13	elliptical	elliptical	ADJ
asir-1642	304	14	orbit	orbit	NOUN
asir-1642	304	15	is	be	AUX
asir-1642	304	16	t	t	NOUN
asir-1642	304	17	=	=	PUNCT
asir-1642	304	18	2π√	2π√	PROPN
asir-1642	304	19	a	a	DET
asir-1642	304	20	³	³	X
asir-1642	304	21	g[m	g[m	NOUN
asir-1642	304	22	+	+	NOUN
asir-1642	304	23	m2	m2	PROPN
asir-1642	304	24	(	(	PUNCT
asir-1642	304	25	1	1	NUM
asir-1642	304	26	)	)	PUNCT
asir-1642	304	27	,	,	PUNCT
asir-1642	304	28	which	which	PRON
asir-1642	304	29	is	be	AUX
asir-1642	304	30	the	the	DET
asir-1642	304	31	same	same	ADJ
asir-1642	304	32	for	for	ADP
asir-1642	304	33	all	all	DET
asir-1642	304	34	ellipse	ellipse	NOUN
asir-1642	304	35	with	with	ADP
asir-1642	304	36	the	the	DET
asir-1642	304	37	same	same	ADJ
asir-1642	304	38	semi	semi	ADJ
asir-1642	304	39	-	-	ADJ
asir-1642	304	40	major	major	ADJ
asir-1642	304	41	-	-	PUNCT
asir-1642	304	42	axis	axis	NOUN
asir-1642	304	43	a.	a.	NOUN
asir-1642	304	44	inversely	inversely	ADV
asir-1642	304	45	for	for	ADP
asir-1642	304	46	calculating	calculate	VERB
asir-1642	304	47	the	the	DET
asir-1642	304	48	distance	distance	NOUN
asir-1642	304	49	in	in	ADP
asir-1642	304	50	meters	meter	NOUN
asir-1642	304	51	,	,	PUNCT
asir-1642	304	52	where	where	SCONJ
asir-1642	304	53	a	a	DET
asir-1642	304	54	body	body	NOUN
asir-1642	304	55	has	have	VERB
asir-1642	304	56	to	to	PART
asir-1642	304	57	orbit	orbit	VERB
asir-1642	304	58	in	in	ADP
asir-1642	304	59	order	order	NOUN
asir-1642	304	60	to	to	PART
asir-1642	304	61	have	have	AUX
asir-1642	304	62	a	a	DET
asir-1642	304	63	given	give	VERB
asir-1642	304	64	orbital	orbital	ADJ
asir-1642	304	65	period	period	NOUN
asir-1642	304	66	,	,	PUNCT
asir-1642	304	67	in	in	ADP
asir-1642	304	68	second	second	ADJ
asir-1642	304	69	,	,	PUNCT
asir-1642	304	70	a	a	DET
asir-1642	304	71	=	=	NOUN
asir-1642	304	72	√	√	NOUN
asir-1642	304	73	g[m	g[m	NOUN
asir-1642	304	74	+	+	CCONJ
asir-1642	304	75	m	m	NOUN
asir-1642	304	76	t²	t²	NOUN
asir-1642	304	77	²	²	NUM
asir-1642	304	78	(	(	PUNCT
asir-1642	304	79	2	2	NUM
asir-1642	304	80	)	)	PUNCT
asir-1642	305	1	where	where	SCONJ
asir-1642	305	2	,	,	PUNCT
asir-1642	305	3	g	g	PROPN
asir-1642	305	4	=	=	PUNCT
asir-1642	305	5	the	the	DET
asir-1642	305	6	gravitational	gravitational	ADJ
asir-1642	305	7	constant	constant	ADJ
asir-1642	305	8	=	=	SYM
asir-1642	305	9	6,67.10	6,67.10	NUM
asir-1642	305	10	nm²/kg²	nm²/kg²	NOUN
asir-1642	305	11	,	,	PUNCT
asir-1642	305	12	m	m	PROPN
asir-1642	305	13	,	,	PUNCT
asir-1642	305	14	m2	m2	PROPN
asir-1642	305	15	the	the	DET
asir-1642	305	16	masses	masse	NOUN
asir-1642	305	17	of	of	ADP
asir-1642	305	18	any	any	DET
asir-1642	305	19	two	two	NUM
asir-1642	305	20	material	material	NOUN
asir-1642	305	21	-	-	PUNCT
asir-1642	305	22	points	point	NOUN
asir-1642	305	23	.	.	PUNCT
asir-1642	306	1	from	from	ADP
asir-1642	306	2	above	above	ADP
asir-1642	306	3	relation	relation	NOUN
asir-1642	306	4	is	be	AUX
asir-1642	306	5	seen	see	VERB
asir-1642	306	6	that	that	SCONJ
asir-1642	306	7	energy	energy	NOUN
asir-1642	306	8	-	-	PUNCT
asir-1642	306	9	rim	rim	NOUN
asir-1642	306	10	-	-	PUNCT
asir-1642	306	11	shapes	shape	NOUN
asir-1642	306	12	c	c	NOUN
asir-1642	306	13	,	,	PUNCT
asir-1642	306	14	are	be	AUX
asir-1642	306	15	discrete	discrete	ADJ
asir-1642	306	16	-	-	PUNCT
asir-1642	306	17	packets	packet	NOUN
asir-1642	306	18	of	of	ADP
asir-1642	306	19	energy	energy	NOUN
asir-1642	306	20	-	-	PUNCT
asir-1642	306	21	levels	level	NOUN
asir-1642	306	22	,	,	PUNCT
asir-1642	306	23	i.e.	i.e.	X
asir-1642	306	24	,	,	PUNCT
asir-1642	306	25	1	1	X
asir-1642	306	26	..	..	SYM
asir-1642	306	27	attraction	attraction	NOUN
asir-1642	306	28	of	of	ADP
asir-1642	306	29	opposite	opposite	ADJ
asir-1642	306	30	forces	force	NOUN
asir-1642	306	31	fo↔f	fo↔f	VERB
asir-1642	306	32	p	p	NOUN
asir-1642	306	33	at	at	ADP
asir-1642	306	34	points	point	NOUN
asir-1642	306	35	o	o	NOUN
asir-1642	306	36	,	,	PUNCT
asir-1642	306	37	p	p	PRON
asir-1642	306	38	creates	create	VERB
asir-1642	306	39	the	the	DET
asir-1642	306	40	central	central	ADJ
asir-1642	306	41	motion	motion	NOUN
asir-1642	306	42	and	and	CCONJ
asir-1642	306	43	kepler	kepler	NOUN
asir-1642	306	44	’s	’s	PART
asir-1642	306	45	laws	law	NOUN
asir-1642	306	46	where	where	SCONJ
asir-1642	306	47	orbits	orbit	NOUN
asir-1642	306	48	are	be	AUX
asir-1642	306	49	plane	plane	NOUN
asir-1642	306	50	-	-	PUNCT
asir-1642	306	51	curves	curve	NOUN
asir-1642	306	52	representing	represent	VERB
asir-1642	306	53	a	a	DET
asir-1642	306	54	constant	constant	ADJ
asir-1642	306	55	-	-	PUNCT
asir-1642	306	56	energy	energy	NOUN
asir-1642	306	57	becoming	become	VERB
asir-1642	306	58	from	from	ADP
asir-1642	306	59	the	the	DET
asir-1642	306	60	squared	square	VERB
asir-1642	306	61	periods	period	NOUN
asir-1642	306	62	t²	t²	NOUN
asir-1642	306	63	,	,	PUNCT
asir-1642	306	64	or	or	CCONJ
asir-1642	306	65	frequency	frequency	NOUN
asir-1642	306	66	²	²	NUM
asir-1642	306	67	,	,	PUNCT
asir-1642	306	68	representing	represent	VERB
asir-1642	306	69	the	the	DET
asir-1642	306	70	imaginary	imaginary	ADJ
asir-1642	306	71	-	-	PUNCT
asir-1642	306	72	energy	energy	NOUN
asir-1642	306	73	-	-	PUNCT
asir-1642	306	74	part	part	NOUN
asir-1642	306	75	of	of	ADP
asir-1642	306	76	monad	monad	PROPN
asir-1642	306	77	and	and	CCONJ
asir-1642	306	78	𝐫𝐧	𝐫𝐧	PROPN
asir-1642	306	79	³	³	X
asir-1642	306	80	representing	represent	VERB
asir-1642	306	81	the	the	DET
asir-1642	306	82	real	real	ADJ
asir-1642	306	83	-	-	PUNCT
asir-1642	306	84	space	space	NOUN
asir-1642	306	85	-	-	PUNCT
asir-1642	306	86	part	part	NOUN
asir-1642	306	87	of	of	ADP
asir-1642	306	88	monad	monad	PROPN
asir-1642	306	89	1	1	NUM
asir-1642	306	90	=	=	SYM
asir-1642	306	91	c.	c.	NOUN
asir-1642	306	92	².r³.	².r³.	NOUN
asir-1642	306	93	these	these	DET
asir-1642	306	94	constants	constant	NOUN
asir-1642	306	95	are	be	AUX
asir-1642	306	96	the	the	DET
asir-1642	306	97	quantized	quantize	VERB
asir-1642	306	98	-	-	PUNCT
asir-1642	306	99	curve	curve	NOUN
asir-1642	306	100	-	-	PUNCT
asir-1642	306	101	rims	rims	NOUN
asir-1642	306	102	.	.	PUNCT
asir-1642	307	1	2	2	NUM
asir-1642	307	2	..	..	PUNCT
asir-1642	307	3	since	since	SCONJ
asir-1642	307	4	both	both	DET
asir-1642	307	5	semi	semi	ADJ
asir-1642	307	6	-	-	ADJ
asir-1642	307	7	major	major	ADJ
asir-1642	307	8	axis	axis	NOUN
asir-1642	307	9	̅	̅	NOUN
asir-1642	307	10	,	,	PUNCT
asir-1642	307	11	the	the	DET
asir-1642	307	12	position	position	NOUN
asir-1642	307	13	-	-	PUNCT
asir-1642	307	14	vector	vector	NOUN
asir-1642	307	15	,	,	PUNCT
asir-1642	307	16	and	and	CCONJ
asir-1642	307	17	velocity	velocity	NOUN
asir-1642	307	18	v̅	v̅	PROPN
asir-1642	307	19	,	,	PUNCT
asir-1642	307	20	the	the	DET
asir-1642	307	21	velocity	velocity	NOUN
asir-1642	307	22	-	-	PUNCT
asir-1642	307	23	vector	vector	NOUN
asir-1642	307	24	,	,	PUNCT
asir-1642	307	25	define	define	VERB
asir-1642	307	26	the	the	DET
asir-1642	307	27	orbital	orbital	ADJ
asir-1642	307	28	-	-	PUNCT
asir-1642	307	29	plane	plane	NOUN
asir-1642	307	30	,	,	PUNCT
asir-1642	307	31	then	then	ADV
asir-1642	307	32	angular	angular	ADJ
asir-1642	307	33	-	-	PUNCT
asir-1642	307	34	momentum	momentum	NOUN
asir-1642	307	35	-	-	PUNCT
asir-1642	307	36	vector	vector	NOUN
asir-1642	307	37	̅	̅	NOUN
asir-1642	307	38	,	,	PUNCT
asir-1642	307	39	is	be	AUX
asir-1642	307	40	perpendicular	perpendicular	ADJ
asir-1642	307	41	to	to	ADP
asir-1642	307	42	vectors	vector	NOUN
asir-1642	307	43	̅	̅	NOUN
asir-1642	307	44	,	,	PUNCT
asir-1642	307	45	v̅	v̅	PROPN
asir-1642	307	46	,	,	PUNCT
asir-1642	307	47	and	and	CCONJ
asir-1642	307	48	is	be	AUX
asir-1642	307	49	̅	̅	NOUN
asir-1642	307	50			NOUN
asir-1642	307	51	̅.	̅.	PROPN
asir-1642	307	52	v̅	v̅	PROPN
asir-1642	307	53	,	,	PUNCT
asir-1642	307	54	or	or	CCONJ
asir-1642	307	55	the	the	DET
asir-1642	307	56	magnitude	magnitude	NOUN
asir-1642	307	57	�	�	NOUN
asir-1642	307	58	̅	̅	NOUN
asir-1642	307	59	�	�	PROPN
asir-1642	307	60	=	=	SYM
asir-1642	307	61	�	�	PROPN
asir-1642	307	62	̅	̅	NOUN
asir-1642	307	63	�	�	PROPN
asir-1642	307	64	x	x	SYM
asir-1642	307	65	�	�	PROPN
asir-1642	307	66	̅	̅	NOUN
asir-1642	307	67	�	�	NOUN
asir-1642	307	68	=	=	NOUN
asir-1642	307	69	constant	constant	ADJ
asir-1642	307	70	for	for	ADP
asir-1642	307	71	all	all	DET
asir-1642	307	72	central	central	ADJ
asir-1642	307	73	motions	motion	NOUN
asir-1642	307	74	.	.	PUNCT
asir-1642	308	1	for	for	ADP
asir-1642	308	2	circular	circular	ADJ
asir-1642	308	3	orbits	orbit	NOUN
asir-1642	308	4	gravitational	gravitational	ADJ
asir-1642	308	5	force	force	NOUN
asir-1642	308	6	g	g	PROPN
asir-1642	308	7	f	f	PROPN
asir-1642	308	8	equals	equal	VERB
asir-1642	308	9	the	the	DET
asir-1642	308	10	centripetal	centripetal	ADJ
asir-1642	308	11	force	force	NOUN
asir-1642	308	12	c	c	PROPN
asir-1642	308	13	f	f	PROPN
asir-1642	308	14	,	,	PUNCT
asir-1642	309	1	so	so	ADV
asir-1642	309	2	c	c	NOUN
asir-1642	309	3	f	f	PROPN
asir-1642	309	4	=	=	SYM
asir-1642	309	5	g	g	PROPN
asir-1642	309	6	f	f	PROPN
asir-1642	309	7	and	and	CCONJ
asir-1642	309	8	m	m	PROPN
asir-1642	309	9	pv²	pv²	NOUN
asir-1642	309	10	/	/	SYM
asir-1642	309	11	r	r	NOUN
asir-1642	309	12	=	=	PUNCT
asir-1642	310	1	[	[	X
asir-1642	310	2	g.m	g.m	X
asir-1642	310	3	pm	pm	NOUN
asir-1642	310	4	s	s	X
asir-1642	310	5	]	]	X
asir-1642	310	6	/	/	SYM
asir-1642	310	7	r²	r²	NOUN
asir-1642	310	8	and	and	CCONJ
asir-1642	310	9	velocity	velocity	NOUN
asir-1642	310	10	v²	v²	PROPN
asir-1642	311	1	=	=	SYM
asir-1642	311	2	gm	gm	PROPN
asir-1642	311	3	/	/	SYM
asir-1642	311	4	r	r	NOUN
asir-1642	311	5	…	…	PUNCT
asir-1642	311	6	…	…	PUNCT
asir-1642	311	7	…	…	PUNCT
asir-1642	311	8	.	.	PUNCT
asir-1642	312	1	(	(	PUNCT
asir-1642	312	2	1	1	X
asir-1642	312	3	)	)	PUNCT
asir-1642	312	4	substituting	substitute	VERB
asir-1642	312	5	the	the	DET
asir-1642	312	6	expression	expression	NOUN
asir-1642	312	7	into	into	ADP
asir-1642	312	8	the	the	DET
asir-1642	312	9	formula	formula	NOUN
asir-1642	312	10	for	for	ADP
asir-1642	312	11	kinetic	kinetic	ADJ
asir-1642	312	12	energy	energy	NOUN
asir-1642	312	13	then	then	ADV
asir-1642	312	14	,	,	PUNCT
asir-1642	312	15	k	k	PROPN
asir-1642	312	16	=	=	PUNCT
asir-1642	312	17	mv²	mv²	ADJ
asir-1642	312	18	2	2	X
asir-1642	312	19	=	=	SYM
asir-1642	312	20	m.gm	m.gm	NOUN
asir-1642	312	21	2.r	2.r	NUM
asir-1642	312	22	=	=	PUNCT
asir-1642	312	23	gmm	gmm	X
asir-1642	312	24	2.r	2.r	NUM
asir-1642	312	25	…	…	NUM
asir-1642	312	26	……	……	X
asir-1642	312	27	(	(	PUNCT
asir-1642	312	28	2	2	NUM
asir-1642	312	29	)	)	PUNCT
asir-1642	312	30	or	or	CCONJ
asir-1642	312	31	k	k	NOUN
asir-1642	312	32	=	=	PUNCT
asir-1642	312	33	(	(	PUNCT
asir-1642	312	34	1/2	1/2	NUM
asir-1642	312	35	)	)	PUNCT
asir-1642	312	36	(	(	PUNCT
asir-1642	312	37	-p	-p	X
asir-1642	312	38	)	)	PUNCT
asir-1642	312	39	=	=	PUNCT
asir-1642	313	1	p	p	X
asir-1642	313	2	e	e	X
asir-1642	313	3	2	2	NUM
asir-1642	313	4	and	and	CCONJ
asir-1642	313	5	p	p	NOUN
asir-1642	313	6	=	=	PROPN
asir-1642	313	7	2.k	2.k	NUM
asir-1642	313	8	…	…	PUNCT
asir-1642	313	9	…	…	PUNCT
asir-1642	313	10	…	…	PUNCT
asir-1642	313	11	.	.	PUNCT
asir-1642	314	1	(	(	PUNCT
asir-1642	314	2	3	3	X
asir-1642	314	3	)	)	PUNCT
asir-1642	314	4	the	the	DET
asir-1642	314	5	total	total	ADJ
asir-1642	314	6	-	-	PUNCT
asir-1642	314	7	energy	energy	NOUN
asir-1642	314	8	e	e	NOUN
asir-1642	314	9	=	=	SYM
asir-1642	314	10	k	k	PROPN
asir-1642	315	1	+	+	CCONJ
asir-1642	315	2	p	p	X
asir-1642	315	3	=	=	PUNCT
asir-1642	315	4	k	k	X
asir-1642	315	5	–	–	PUNCT
asir-1642	315	6	2.k	2.k	NUM
asir-1642	315	7	=	=	SYM
asir-1642	315	8	k	k	X
asir-1642	315	9	…	…	PUNCT
asir-1642	315	10	…	…	PUNCT
asir-1642	315	11	…	…	PUNCT
asir-1642	315	12	.	.	PUNCT
asir-1642	316	1	(	(	PUNCT
asir-1642	316	2	4	4	NUM
asir-1642	316	3	)	)	PUNCT
asir-1642	316	4	,	,	PUNCT
asir-1642	316	5	i.e.	i.e.	X
asir-1642	316	6	,	,	PUNCT
asir-1642	316	7	the	the	DET
asir-1642	316	8	potential	potential	ADJ
asir-1642	316	9	-	-	PUNCT
asir-1642	316	10	energy	energy	NOUN
asir-1642	316	11	is	be	AUX
asir-1642	316	12	always	always	ADV
asir-1642	316	13	-	-	PUNCT
asir-1642	316	14	negative	negative	ADJ
asir-1642	316	15	and	and	CCONJ
asir-1642	316	16	twice	twice	DET
asir-1642	316	17	the	the	DET
asir-1642	316	18	kinetic	kinetic	NOUN
asir-1642	316	19	-	-	PUNCT
asir-1642	316	20	energy	energy	NOUN
asir-1642	316	21	while	while	SCONJ
asir-1642	316	22	the	the	DET
asir-1642	316	23	total	total	ADJ
asir-1642	316	24	-	-	PUNCT
asir-1642	316	25	energy	energy	NOUN
asir-1642	316	26	of	of	ADP
asir-1642	316	27	an	an	DET
asir-1642	316	28	central	central	ADJ
asir-1642	316	29	-	-	PUNCT
asir-1642	316	30	orbiting	orbit	VERB
asir-1642	316	31	-	-	PUNCT
asir-1642	316	32	system	system	NOUN
asir-1642	316	33	is	be	AUX
asir-1642	316	34	negative	negative	ADJ
asir-1642	316	35	.	.	PUNCT
asir-1642	317	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	317	2	applied	apply	VERB
asir-1642	317	3	science	science	NOUN
asir-1642	317	4	and	and	CCONJ
asir-1642	317	5	innovative	innovative	ADJ
asir-1642	317	6	research	research	NOUN
asir-1642	317	7	vol	vol	NOUN
asir-1642	317	8	.	.	PROPN
asir-1642	318	1	2	2	NUM
asir-1642	318	2	,	,	PUNCT
asir-1642	318	3	no	no	INTJ
asir-1642	318	4	.	.	NOUN
asir-1642	318	5	4	4	NUM
asir-1642	318	6	,	,	PUNCT
asir-1642	318	7	2018	2018	NUM
asir-1642	318	8	171	171	NUM
asir-1642	318	9	published	publish	VERB
asir-1642	318	10	by	by	ADP
asir-1642	318	11	scholink	scholink	PROPN
asir-1642	318	12	inc	inc	PROPN
asir-1642	318	13	.	.	PROPN
asir-1642	318	14	5	5	NUM
asir-1642	318	15	..	..	PUNCT
asir-1642	318	16	conservation	conservation	NOUN
asir-1642	318	17	laws	law	NOUN
asir-1642	318	18	in	in	ADP
asir-1642	318	19	astronomy	astronomy	NOUN
asir-1642	318	20	:	:	PUNCT
asir-1642	318	21	1	1	NUM
asir-1642	318	22	..	..	PUNCT
asir-1642	318	23	newton	newton	PROPN
asir-1642	318	24	’s	’s	PART
asir-1642	318	25	second	second	ADJ
asir-1642	318	26	law	law	NOUN
asir-1642	318	27	tell	tell	VERB
asir-1642	318	28	us	we	PRON
asir-1642	318	29	that	that	DET
asir-1642	318	30	acceleration	acceleration	NOUN
asir-1642	318	31	on	on	ADP
asir-1642	318	32	an	an	DET
asir-1642	318	33	object	object	NOUN
asir-1642	318	34	is	be	AUX
asir-1642	318	35	proportional	proportional	ADJ
asir-1642	318	36	to	to	ADP
asir-1642	318	37	the	the	DET
asir-1642	318	38	net	net	ADJ
asir-1642	318	39	force	force	NOUN
asir-1642	318	40	acting	act	VERB
asir-1642	318	41	on	on	ADP
asir-1642	318	42	it	it	PRON
asir-1642	318	43	so	so	ADV
asir-1642	318	44	objects	object	VERB
asir-1642	318	45	move	move	VERB
asir-1642	318	46	at	at	ADP
asir-1642	318	47	constant	constant	ADJ
asir-1642	318	48	velocity	velocity	NOUN
asir-1642	318	49	if	if	SCONJ
asir-1642	318	50	no	no	DET
asir-1642	318	51	force	force	NOUN
asir-1642	318	52	acts	act	VERB
asir-1642	318	53	on	on	ADP
asir-1642	318	54	them	they	PRON
asir-1642	318	55	.	.	PUNCT
asir-1642	319	1	because	because	SCONJ
asir-1642	319	2	of	of	ADP
asir-1642	319	3	conservation	conservation	NOUN
asir-1642	319	4	of	of	ADP
asir-1642	319	5	momentum	momentum	NOUN
asir-1642	319	6	the	the	DET
asir-1642	319	7	interacting	interact	VERB
asir-1642	319	8	objects	object	NOUN
asir-1642	319	9	exchange	exchange	NOUN
asir-1642	319	10	momentum	momentum	NOUN
asir-1642	319	11	through	through	ADP
asir-1642	319	12	equal	equal	ADJ
asir-1642	319	13	and	and	CCONJ
asir-1642	319	14	opposite	opposite	ADJ
asir-1642	319	15	forces	force	NOUN
asir-1642	319	16	[	[	X
asir-1642	319	17	⊕↔⊝	⊕↔⊝	X
asir-1642	319	18	]	]	X
asir-1642	319	19	≡	≡	PROPN
asir-1642	319	20	[	[	PUNCT
asir-1642	319	21	v̅	v̅	PROPN
asir-1642	319	22	.i	.i	NOUN
asir-1642	319	23	]	]	PUNCT
asir-1642	319	24	,	,	PUNCT
asir-1642	319	25	therefore	therefore	ADV
asir-1642	319	26	constant	constant	ADJ
asir-1642	319	27	c	c	NOUN
asir-1642	319	28	=	=	SYM
asir-1642	319	29	r³.	r³.	NOUN
asir-1642	319	30	e	e	X
asir-1642	319	31	²	²	NUM
asir-1642	319	32	,	,	PUNCT
asir-1642	319	33	is	be	AUX
asir-1642	319	34	a	a	DET
asir-1642	319	35	quantized	quantize	VERB
asir-1642	319	36	-	-	PUNCT
asir-1642	319	37	energy	energy	NOUN
asir-1642	319	38	-	-	PUNCT
asir-1642	319	39	storage	storage	NOUN
asir-1642	319	40	,	,	PUNCT
asir-1642	319	41	a	a	DET
asir-1642	319	42	constant	constant	ADJ
asir-1642	319	43	energy	energy	NOUN
asir-1642	319	44	-	-	PUNCT
asir-1642	319	45	plane	plane	NOUN
asir-1642	319	46	-	-	PUNCT
asir-1642	319	47	rim	rim	NOUN
asir-1642	319	48	,	,	PUNCT
asir-1642	319	49	in	in	ADP
asir-1642	319	50	where	where	SCONJ
asir-1642	319	51	planets	planet	NOUN
asir-1642	319	52	move	move	VERB
asir-1642	319	53	at	at	ADP
asir-1642	319	54	constant	constant	ADJ
asir-1642	319	55	velocities	velocity	NOUN
asir-1642	319	56	without	without	ADP
asir-1642	319	57	any	any	DET
asir-1642	319	58	force	force	NOUN
asir-1642	319	59	acting	act	VERB
asir-1642	319	60	on	on	ADP
asir-1642	319	61	them	they	PRON
asir-1642	319	62	.	.	PUNCT
asir-1642	320	1	2	2	X
asir-1642	320	2	..	..	PUNCT
asir-1642	320	3	in	in	ADP
asir-1642	320	4	[	[	X
asir-1642	320	5	70	70	NUM
asir-1642	320	6	]	]	PUNCT
asir-1642	320	7	,	,	PUNCT
asir-1642	320	8	the	the	DET
asir-1642	320	9	work	work	NOUN
asir-1642	320	10	produced	produce	VERB
asir-1642	320	11	in	in	ADP
asir-1642	320	12	material	material	NOUN
asir-1642	320	13	-	-	PUNCT
asir-1642	320	14	point	point	NOUN
asir-1642	320	15	b	b	X
asir-1642	320	16	⃡	⃡	NOUN
asir-1642	320	17	is	be	AUX
asir-1642	320	18	equal	equal	ADJ
asir-1642	320	19	to	to	ADP
asir-1642	320	20	→	→	SYM
asir-1642	320	21	w	w	NOUN
asir-1642	320	22	=	=	VERB
asir-1642	320	23	2l	2l	NOUN
asir-1642	320	24	=	=	SYM
asir-1642	320	25	b̅.	b̅.	NUM
asir-1642	320	26	w̅	w̅	PUNCT
asir-1642	320	27	=	=	SYM
asir-1642	320	28	j.w²	j.w²	PROPN
asir-1642	320	29	←	←	PROPN
asir-1642	320	30	consisting	consist	VERB
asir-1642	320	31	the	the	DET
asir-1642	320	32	first	first	ADJ
asir-1642	320	33	-	-	PUNCT
asir-1642	320	34	energy	energy	NOUN
asir-1642	320	35	-	-	PUNCT
asir-1642	320	36	store	store	NOUN
asir-1642	320	37	which	which	PRON
asir-1642	320	38	is	be	AUX
asir-1642	320	39	a	a	DET
asir-1642	320	40	stationary	stationary	ADJ
asir-1642	320	41	wave	wave	NOUN
asir-1642	320	42	with	with	ADP
asir-1642	320	43	,	,	PUNCT
asir-1642	320	44	n	n	CCONJ
asir-1642	320	45	,	,	PUNCT
asir-1642	320	46	lobes	lobe	NOUN
asir-1642	320	47	as	as	ADP
asir-1642	320	48	,	,	PUNCT
asir-1642	320	49	w	w	PROPN
asir-1642	320	50	(	(	PUNCT
asir-1642	320	51	+	+	X
asir-1642	320	52	)	)	PUNCT
asir-1642	321	1	=	=	PUNCT
asir-1642	321	2	[	[	PUNCT
asir-1642	321	3	𝜋	𝜋	NOUN
asir-1642	321	4	²f	²f	NOUN
asir-1642	321	5	3	3	NUM
asir-1642	321	6	]	]	PUNCT
asir-1642	321	7	.n.(n+1	.n.(n+1	NUM
asir-1642	321	8	)	)	PUNCT
asir-1642	321	9	and	and	CCONJ
asir-1642	321	10	wavelength	wavelength	NOUN
asir-1642	321	11	λ	λ	PROPN
asir-1642	321	12	=	=	PRON
asir-1642	321	13	.	.	PUNCT
asir-1642	322	1	(	(	PUNCT
asir-1642	322	2	+	+	ADV
asir-1642	322	3	√	√	ADJ
asir-1642	322	4	)	)	PUNCT
asir-1642	323	1	=	=	SYM
asir-1642	323	2	𝑛.b̅	𝑛.b̅	PROPN
asir-1642	323	3	²	²	NUM
asir-1642	323	4	,	,	PUNCT
asir-1642	323	5	i.e.	i.e.	X
asir-1642	323	6	,	,	PUNCT
asir-1642	323	7	that	that	PRON
asir-1642	323	8	which	which	PRON
asir-1642	323	9	happens	happen	VERB
asir-1642	323	10	in	in	ADP
asir-1642	323	11	material	material	NOUN
asir-1642	323	12	point	point	NOUN
asir-1642	323	13	,	,	PUNCT
asir-1642	323	14	momentum	momentum	NOUN
asir-1642	323	15	as	as	ADP
asir-1642	323	16	work	work	NOUN
asir-1642	323	17	is	be	AUX
asir-1642	323	18	w	w	ADP
asir-1642	323	19	(	(	PUNCT
asir-1642	323	20	+	+	X
asir-1642	323	21	)	)	PUNCT
asir-1642	323	22	=	=	SYM
asir-1642	323	23	constant	constant	ADJ
asir-1642	323	24	in	in	ADP
asir-1642	323	25	n	n	CCONJ
asir-1642	323	26	-	-	PUNCT
asir-1642	323	27	lobe	lobe	NOUN
asir-1642	323	28	,	,	PUNCT
asir-1642	323	29	happens	happen	VERB
asir-1642	323	30	to	to	ADP
asir-1642	323	31	planets	planet	NOUN
asir-1642	323	32	orbiting	orbit	VERB
asir-1642	323	33	the	the	DET
asir-1642	323	34	sun	sun	NOUN
asir-1642	323	35	,	,	PUNCT
asir-1642	323	36	so	so	ADV
asir-1642	323	37	because	because	SCONJ
asir-1642	323	38	of	of	ADP
asir-1642	323	39	conservation	conservation	NOUN
asir-1642	323	40	of	of	ADP
asir-1642	323	41	angular	angular	ADJ
asir-1642	323	42	momentum	momentum	NOUN
asir-1642	323	43	in	in	ADP
asir-1642	323	44	the	the	DET
asir-1642	323	45	constant	constant	ADJ
asir-1642	323	46	energy	energy	NOUN
asir-1642	323	47	-	-	PUNCT
asir-1642	323	48	plane	plane	NOUN
asir-1642	323	49	-	-	PUNCT
asir-1642	323	50	rim	rim	NOUN
asir-1642	323	51	-	-	PUNCT
asir-1642	323	52	orbits	orbit	NOUN
asir-1642	323	53	,	,	PUNCT
asir-1642	323	54	planets	planet	NOUN
asir-1642	323	55	with	with	ADP
asir-1642	323	56	no	no	DET
asir-1642	323	57	twisting	twisting	NOUN
asir-1642	323	58	forces	force	NOUN
asir-1642	323	59	are	be	AUX
asir-1642	323	60	continually	continually	ADV
asir-1642	323	61	rotating	rotate	VERB
asir-1642	323	62	and	and	CCONJ
asir-1642	323	63	orbiting	orbit	VERB
asir-1642	323	64	the	the	DET
asir-1642	323	65	sun	sun	NOUN
asir-1642	323	66	.	.	PUNCT
asir-1642	324	1	energy	energy	NOUN
asir-1642	324	2	is	be	AUX
asir-1642	324	3	concentrated	concentrate	VERB
asir-1642	324	4	at	at	ADP
asir-1642	324	5	the	the	DET
asir-1642	324	6	trajectories	trajectory	NOUN
asir-1642	324	7	≡	≡	PROPN
asir-1642	324	8	rims	rims	PROPN
asir-1642	324	9	≡	≡	PROPN
asir-1642	324	10	orbits	orbit	NOUN
asir-1642	324	11	because	because	SCONJ
asir-1642	324	12	there	there	PRON
asir-1642	324	13	exists	exist	VERB
asir-1642	324	14	the	the	DET
asir-1642	324	15	pressure	pressure	NOUN
asir-1642	324	16	of	of	ADP
asir-1642	324	17	centripetal	centripetal	ADJ
asir-1642	324	18	force	force	NOUN
asir-1642	324	19	as	as	ADP
asir-1642	324	20	in	in	ADP
asir-1642	324	21	figure	figure	NOUN
asir-1642	324	22	6	6	NUM
asir-1642	324	23	.	.	NOUN
asir-1642	324	24	3	3	NUM
asir-1642	324	25	..	..	PUNCT
asir-1642	324	26	energy	energy	NOUN
asir-1642	324	27	=	=	NOUN
asir-1642	324	28	motion	motion	NOUN
asir-1642	324	29	=	=	NOUN
asir-1642	324	30	work	work	NOUN
asir-1642	324	31	,	,	PUNCT
asir-1642	324	32	and	and	CCONJ
asir-1642	324	33	makes	make	VERB
asir-1642	324	34	the	the	DET
asir-1642	324	35	matter	matter	NOUN
asir-1642	324	36	move	move	NOUN
asir-1642	324	37	.	.	PUNCT
asir-1642	325	1	in	in	ADP
asir-1642	325	2	[	[	X
asir-1642	325	3	70	70	NUM
asir-1642	325	4	]	]	PUNCT
asir-1642	325	5	the	the	DET
asir-1642	325	6	work	work	NOUN
asir-1642	325	7	produced	produce	VERB
asir-1642	325	8	in	in	ADP
asir-1642	325	9	material	material	NOUN
asir-1642	325	10	-	-	PUNCT
asir-1642	325	11	point	point	NOUN
asir-1642	325	12	is	be	AUX
asir-1642	325	13	conserved	conserve	VERB
asir-1642	325	14	but	but	CCONJ
asir-1642	325	15	can	can	AUX
asir-1642	325	16	travel	travel	VERB
asir-1642	325	17	from	from	ADP
asir-1642	325	18	one	one	NUM
asir-1642	325	19	object	object	NOUN
asir-1642	325	20	to	to	ADP
asir-1642	325	21	another	another	PRON
asir-1642	325	22	,	,	PUNCT
asir-1642	325	23	or	or	CCONJ
asir-1642	325	24	change	change	VERB
asir-1642	325	25	in	in	ADP
asir-1642	325	26	form	form	NOUN
asir-1642	325	27	.	.	PUNCT
asir-1642	326	1	from	from	ADP
asir-1642	326	2	figure	figure	NOUN
asir-1642	326	3	-1	-1	ADP
asir-1642	326	4	energy	energy	PROPN
asir-1642	326	5	≡	≡	PROPN
asir-1642	326	6	motion	motion	NOUN
asir-1642	326	7	is	be	AUX
asir-1642	326	8	kept	keep	VERB
asir-1642	326	9	in	in	ADP
asir-1642	326	10	the	the	DET
asir-1642	326	11	storages	storage	NOUN
asir-1642	326	12	r	r	NOUN
asir-1642	326	13	=	=	SYM
asir-1642	326	14	n	n	PROPN
asir-1642	326	15	(	(	PUNCT
asir-1642	326	16	λ/2	λ/2	NUM
asir-1642	326	17	)	)	PUNCT
asir-1642	326	18	,	,	PUNCT
asir-1642	326	19	and	and	CCONJ
asir-1642	326	20	is	be	AUX
asir-1642	326	21	so	so	ADV
asir-1642	326	22	conserved	conserved	ADJ
asir-1642	326	23	and	and	CCONJ
asir-1642	326	24	transferred	transfer	VERB
asir-1642	326	25	from	from	ADP
asir-1642	326	26	one	one	NUM
asir-1642	326	27	object	object	NOUN
asir-1642	326	28	to	to	ADP
asir-1642	326	29	another	another	PRON
asir-1642	326	30	,	,	PUNCT
asir-1642	326	31	or	or	CCONJ
asir-1642	326	32	change	change	VERB
asir-1642	326	33	in	in	ADP
asir-1642	326	34	form	form	NOUN
asir-1642	326	35	.	.	PUNCT
asir-1642	327	1	the	the	DET
asir-1642	327	2	types	type	NOUN
asir-1642	327	3	of	of	ADP
asir-1642	327	4	energy	energy	NOUN
asir-1642	327	5	-	-	PUNCT
asir-1642	327	6	forms	form	NOUN
asir-1642	327	7	are	be	AUX
asir-1642	327	8	,	,	PUNCT
asir-1642	327	9	the	the	DET
asir-1642	327	10	rotational	rotational	ADJ
asir-1642	327	11	,	,	PUNCT
asir-1642	327	12	the	the	DET
asir-1642	327	13	eternal	eternal	ADJ
asir-1642	327	14	rotation	rotation	NOUN
asir-1642	327	15	of	of	ADP
asir-1642	327	16	positive	positive	ADJ
asir-1642	327	17	⊕	⊕	PROPN
asir-1642	327	18	around	around	ADP
asir-1642	327	19	the	the	DET
asir-1642	327	20	negative	negative	ADJ
asir-1642	327	21	⊝	⊝	NOUN
asir-1642	327	22	,	,	PUNCT
asir-1642	327	23	the	the	DET
asir-1642	327	24	kinetic	kinetic	NOUN
asir-1642	327	25	,	,	PUNCT
asir-1642	327	26	motion	motion	NOUN
asir-1642	327	27	,	,	PUNCT
asir-1642	327	28	the	the	DET
asir-1642	327	29	potential	potential	NOUN
asir-1642	327	30	,	,	PUNCT
asir-1642	327	31	stored	store	VERB
asir-1642	327	32	motion	motion	NOUN
asir-1642	327	33	,	,	PUNCT
asir-1642	327	34	the	the	DET
asir-1642	327	35	radioactive	radioactive	ADJ
asir-1642	327	36	,	,	PUNCT
asir-1642	327	37	wave	wave	NOUN
asir-1642	327	38	motion	motion	NOUN
asir-1642	327	39	,	,	PUNCT
asir-1642	327	40	so	so	ADV
asir-1642	327	41	,	,	PUNCT
asir-1642	327	42	objects	object	NOUN
asir-1642	327	43	get	get	VERB
asir-1642	327	44	their	their	PRON
asir-1642	327	45	energy	energy	NOUN
asir-1642	327	46	=	=	NOUN
asir-1642	327	47	motion	motion	NOUN
asir-1642	327	48	from	from	ADP
asir-1642	327	49	the	the	DET
asir-1642	327	50	primary	primary	ADJ
asir-1642	327	51	m	m	NOUN
asir-1642	327	52	-	-	PUNCT
asir-1642	327	53	points	point	NOUN
asir-1642	327	54	in	in	ADP
asir-1642	327	55	-	-	PUNCT
asir-1642	327	56	which	which	PRON
asir-1642	327	57	motion	motion	NOUN
asir-1642	327	58	exists	exist	VERB
asir-1642	327	59	apriori	apriori	ADV
asir-1642	327	60	,	,	PUNCT
asir-1642	327	61	and	and	CCONJ
asir-1642	327	62	transformed	transform	VERB
asir-1642	327	63	from	from	ADP
asir-1642	327	64	one	one	NUM
asir-1642	327	65	type	type	NOUN
asir-1642	327	66	to	to	ADP
asir-1642	327	67	another	another	PRON
asir-1642	327	68	.	.	PUNCT
asir-1642	328	1	4	4	NUM
asir-1642	328	2	..	..	PUNCT
asir-1642	328	3	angular	angular	ADJ
asir-1642	328	4	momentum	momentum	NOUN
asir-1642	328	5	is	be	AUX
asir-1642	328	6	the	the	DET
asir-1642	328	7	constant	constant	ADJ
asir-1642	328	8	energy	energy	NOUN
asir-1642	328	9	-	-	PUNCT
asir-1642	328	10	plane	plane	NOUN
asir-1642	328	11	-	-	PUNCT
asir-1642	328	12	rim	rim	NOUN
asir-1642	328	13	-	-	PUNCT
asir-1642	328	14	orbits	orbit	NOUN
asir-1642	328	15	of	of	ADP
asir-1642	328	16	the	the	DET
asir-1642	328	17	system	system	NOUN
asir-1642	328	18	sun	sun	NOUN
asir-1642	328	19	-	-	PUNCT
asir-1642	328	20	planet	planet	NOUN
asir-1642	328	21	.	.	PUNCT
asir-1642	329	1	only	only	ADV
asir-1642	329	2	friction	friction	NOUN
asir-1642	329	3	or	or	CCONJ
asir-1642	329	4	atmospheric	atmospheric	ADJ
asir-1642	329	5	drag	drag	NOUN
asir-1642	329	6	can	can	AUX
asir-1642	329	7	change	change	VERB
asir-1642	329	8	the	the	DET
asir-1642	329	9	orbit	orbit	NOUN
asir-1642	329	10	,	,	PUNCT
asir-1642	329	11	and	and	CCONJ
asir-1642	329	12	if	if	SCONJ
asir-1642	329	13	an	an	DET
asir-1642	329	14	object	object	NOUN
asir-1642	329	15	gains	gain	VERB
asir-1642	329	16	orbital	orbital	ADJ
asir-1642	329	17	energy	energy	NOUN
asir-1642	329	18	it	it	PRON
asir-1642	329	19	moves	move	VERB
asir-1642	329	20	to	to	ADP
asir-1642	329	21	a	a	DET
asir-1642	329	22	more	more	ADV
asir-1642	329	23	distant	distant	ADJ
asir-1642	329	24	orbit	orbit	NOUN
asir-1642	329	25	with	with	ADP
asir-1642	329	26	more	more	ADJ
asir-1642	329	27	energy	energy	NOUN
asir-1642	329	28	.	.	PUNCT
asir-1642	330	1	this	this	PRON
asir-1642	330	2	is	be	AUX
asir-1642	330	3	obvious	obvious	ADJ
asir-1642	330	4	from	from	ADP
asir-1642	330	5	planets	planet	NOUN
asir-1642	330	6	constant	constant	ADJ
asir-1642	330	7	c	c	NOUN
asir-1642	330	8	=	=	SYM
asir-1642	330	9	r³.	r³.	NOUN
asir-1642	330	10	e²	e²	NOUN
asir-1642	330	11	,	,	PUNCT
asir-1642	330	12	since	since	SCONJ
asir-1642	330	13	frequency	frequency	NOUN
asir-1642	330	14	is	be	AUX
asir-1642	330	15	increased	increase	VERB
asir-1642	330	16	.	.	PUNCT
asir-1642	331	1	the	the	DET
asir-1642	331	2	kepler	kepler	PROPN
asir-1642	331	3	’s	’s	PART
asir-1642	331	4	planar	planar	ADJ
asir-1642	331	5	constant	constant	ADJ
asir-1642	331	6	principle	principle	NOUN
asir-1642	331	7	:	:	PUNCT
asir-1642	331	8	planet	planet	NOUN
asir-1642	331	9	:	:	PUNCT
asir-1642	331	10	period	period	NOUN
asir-1642	331	11	of	of	ADP
asir-1642	331	12	rotation	rotation	NOUN
asir-1642	331	13	(	(	PUNCT
asir-1642	331	14	y	y	NOUN
asir-1642	331	15	)	)	PUNCT
asir-1642	331	16	:	:	PUNCT
asir-1642	331	17	frequency	frequency	NOUN
asir-1642	331	18	(	(	PUNCT
asir-1642	331	19	n	n	CCONJ
asir-1642	331	20	)	)	PUNCT
asir-1642	331	21	:	:	PUNCT
asir-1642	331	22	semi	semi	ADJ
asir-1642	331	23	-	-	ADJ
asir-1642	331	24	major	major	ADJ
asir-1642	331	25	axis	axis	NOUN
asir-1642	331	26	(	(	PUNCT
asir-1642	331	27	m	m	NOUN
asir-1642	331	28	)	)	PUNCT
asir-1642	331	29	:	:	PUNCT
asir-1642	331	30	t²	t²	NOUN
asir-1642	331	31	/	/	SYM
asir-1642	331	32	r³	r³	PROPN
asir-1642	331	33	(	(	PUNCT
asir-1642	331	34	s²/m³	s²/m³	PROPN
asir-1642	331	35	)	)	PUNCT
asir-1642	331	36	:	:	PUNCT
asir-1642	331	37	k.	k.	PROPN
asir-1642	331	38	².r³	².r³	PROPN
asir-1642	332	1	=	=	SYM
asir-1642	332	2	1	1	NUM
asir-1642	332	3	mercury	mercury	NOUN
asir-1642	332	4	→	→	SYM
asir-1642	332	5	0,2410	0,2410	NUM
asir-1642	332	6	4,1494	4,1494	NUM
asir-1642	332	7	5,79	5,79	NOUN
asir-1642	332	8	.	.	PUNCT
asir-1642	333	1	10	10	NUM
asir-1642	333	2	0	0	NUM
asir-1642	333	3	2	2	NUM
asir-1642	333	4	,	,	PUNCT
asir-1642	333	5	993	993	NUM
asir-1642	333	6	1	1	NUM
asir-1642	333	7	earth	earth	NOUN
asir-1642	333	8	→	→	SYM
asir-1642	333	9	1,0000	1,0000	NUM
asir-1642	333	10	1,0000	1,0000	NUM
asir-1642	333	11	15,00	15,00	NUM
asir-1642	333	12	.	.	PUNCT
asir-1642	334	1	10	10	NUM
asir-1642	334	2	0	0	NUM
asir-1642	334	3	2	2	NUM
asir-1642	334	4	,	,	PUNCT
asir-1642	334	5	974	974	NUM
asir-1642	334	6	1	1	NUM
asir-1642	334	7	pluto	pluto	NOUN
asir-1642	334	8	→	→	SYM
asir-1642	334	9	248,3000	248,3000	NUM
asir-1642	334	10	0,0040	0,0040	X
asir-1642	334	11	590,00	590,00	NUM
asir-1642	334	12	.	.	PUNCT
asir-1642	335	1	10	10	NUM
asir-1642	335	2	0	0	NUM
asir-1642	335	3	2	2	NUM
asir-1642	335	4	,	,	PUNCT
asir-1642	335	5	993	993	NUM
asir-1642	335	6	10	10	NUM
asir-1642	335	7	2	2	NUM
asir-1642	335	8	≡	≡	PROPN
asir-1642	335	9	1	1	NUM
asir-1642	335	10	each	each	PRON
asir-1642	335	11	of	of	ADP
asir-1642	335	12	the	the	DET
asir-1642	335	13	above	above	ADJ
asir-1642	335	14	orbits	orbit	NOUN
asir-1642	335	15	consist	consist	VERB
asir-1642	335	16	an	an	DET
asir-1642	335	17	energy	energy	NOUN
asir-1642	335	18	-	-	PUNCT
asir-1642	335	19	plane	plane	NOUN
asir-1642	335	20	-	-	PUNCT
asir-1642	335	21	monad	monad	PROPN
asir-1642	335	22	with	with	ADP
asir-1642	335	23	a	a	DET
asir-1642	335	24	constant	constant	ADJ
asir-1642	335	25	-	-	PUNCT
asir-1642	335	26	quantized	quantize	VERB
asir-1642	335	27	energy	energy	NOUN
asir-1642	335	28	.	.	PUNCT
asir-1642	336	1	we	we	PRON
asir-1642	336	2	will	will	AUX
asir-1642	336	3	show	show	VERB
asir-1642	336	4	that	that	SCONJ
asir-1642	336	5	above	above	ADP
asir-1642	336	6	issues	issue	NOUN
asir-1642	336	7	for	for	ADP
asir-1642	336	8	atom	atom	NOUN
asir-1642	336	9	’s	’s	PART
asir-1642	336	10	structure	structure	NOUN
asir-1642	336	11	,	,	PUNCT
asir-1642	336	12	where	where	SCONJ
asir-1642	336	13	nucleus	nucleus	NOUN
asir-1642	336	14	at	at	ADP
asir-1642	336	15	focus	focus	NOUN
asir-1642	336	16	is	be	AUX
asir-1642	336	17	consisted	consist	VERB
asir-1642	336	18	of	of	ADP
asir-1642	336	19	1	1	NUM
asir-1642	336	20	,	,	PUNCT
asir-1642	336	21	2	2	NUM
asir-1642	336	22	,	,	PUNCT
asir-1642	336	23	3,4	3,4	NUM
asir-1642	336	24	,	,	PUNCT
asir-1642	336	25	n	n	CCONJ
asir-1642	336	26	,	,	PUNCT
asir-1642	336	27	,	,	PUNCT
asir-1642	336	28	,	,	PUNCT
asir-1642	336	29	[	[	X
asir-1642	336	30	⊕	⊕	NOUN
asir-1642	336	31	]	]	X
asir-1642	336	32	protons	proton	NOUN
asir-1642	336	33	which	which	PRON
asir-1642	336	34	define	define	VERB
asir-1642	336	35	the	the	DET
asir-1642	336	36	figure	figure	NOUN
asir-1642	336	37	of	of	ADP
asir-1642	336	38	(	(	PUNCT
asir-1642	336	39	1	1	NUM
asir-1642	336	40	)	)	PUNCT
asir-1642	336	41	focus	focus	NOUN
asir-1642	336	42	to	to	PART
asir-1642	336	43	be	be	AUX
asir-1642	336	44	circular	circular	ADJ
asir-1642	336	45	-	-	PUNCT
asir-1642	336	46	rim	rim	NOUN
asir-1642	336	47	and	and	CCONJ
asir-1642	336	48	for	for	ADP
asir-1642	336	49	(	(	PUNCT
asir-1642	336	50	2	2	NUM
asir-1642	336	51	)	)	PUNCT
asir-1642	336	52	and	and	CCONJ
asir-1642	336	53	more	more	ADJ
asir-1642	336	54	focus	focus	NOUN
asir-1642	336	55	to	to	PART
asir-1642	336	56	be	be	AUX
asir-1642	336	57	ellipse	ellipse	NOUN
asir-1642	336	58	-	-	PUNCT
asir-1642	336	59	rim	rim	NOUN
asir-1642	336	60	.	.	PUNCT
asir-1642	337	1	each	each	DET
asir-1642	337	2	proton	proton	NOUN
asir-1642	337	3	in	in	ADP
asir-1642	337	4	atom	atom	NOUN
asir-1642	337	5	creates	create	VERB
asir-1642	337	6	only	only	ADV
asir-1642	337	7	one	one	NUM
asir-1642	337	8	energy	energy	NOUN
asir-1642	337	9	-	-	PUNCT
asir-1642	337	10	rim	rim	NOUN
asir-1642	337	11	.	.	PUNCT
asir-1642	338	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-1642	338	2	applied	apply	VERB
asir-1642	338	3	science	science	NOUN
asir-1642	338	4	and	and	CCONJ
asir-1642	338	5	innovative	innovative	ADJ
asir-1642	338	6	research	research	NOUN
asir-1642	338	7	vol	vol	NOUN
asir-1642	338	8	.	.	PROPN
asir-1642	339	1	2	2	NUM
asir-1642	339	2	,	,	PUNCT
asir-1642	339	3	no	no	INTJ
asir-1642	339	4	.	.	NOUN
asir-1642	339	5	4	4	NUM
asir-1642	339	6	,	,	PUNCT
asir-1642	339	7	2018	2018	NUM
asir-1642	339	8	172	172	NUM
asir-1642	339	9	published	publish	VERB
asir-1642	339	10	by	by	ADP
asir-1642	339	11	scholink	scholink	PROPN
asir-1642	339	12	inc	inc	PROPN
asir-1642	339	13	.	.	PROPN
asir-1642	340	1	since	since	SCONJ
asir-1642	340	2	medium	medium	ADJ
asir-1642	340	3	-	-	PUNCT
asir-1642	340	4	field	field	NOUN
asir-1642	340	5	material	material	NOUN
asir-1642	340	6	-	-	PUNCT
asir-1642	340	7	fragment	fragment	NOUN
asir-1642	340	8	→	→	PUNCT
asir-1642	340	9	[	[	X
asir-1642	340	10	±	±	NUM
asir-1642	340	11	s²	s²	NOUN
asir-1642	340	12	]	]	PUNCT
asir-1642	340	13	=	=	PUNCT
asir-1642	341	1	[	[	X
asir-1642	341	2	mfmf	mfmf	X
asir-1642	341	3	]	]	X
asir-1642	341	4	≡	≡	PROPN
asir-1642	341	5	the	the	DET
asir-1642	341	6	chaos	chaos	NOUN
asir-1642	341	7	,	,	PUNCT
asir-1642	341	8	is	be	AUX
asir-1642	341	9	the	the	DET
asir-1642	341	10	base	base	NOUN
asir-1642	341	11	for	for	ADP
asir-1642	341	12	all	all	DET
asir-1642	341	13	motions	motion	NOUN
asir-1642	341	14	,	,	PUNCT
asir-1642	341	15	the	the	DET
asir-1642	341	16	scales	scale	NOUN
asir-1642	341	17	of	of	ADP
asir-1642	341	18	the	the	DET
asir-1642	341	19	universe	universe	NOUN
asir-1642	341	20	occupy	occupy	VERB
asir-1642	341	21	the	the	DET
asir-1642	341	22	same	same	ADJ
asir-1642	341	23	work	work	NOUN
asir-1642	341	24	.	.	PUNCT
asir-1642	342	1	all	all	DET
asir-1642	342	2	motions	motion	NOUN
asir-1642	342	3	create	create	VERB
asir-1642	342	4	work	work	NOUN
asir-1642	342	5	which	which	PRON
asir-1642	342	6	is	be	AUX
asir-1642	342	7	conserved	conserve	VERB
asir-1642	342	8	.	.	PUNCT
asir-1642	343	1	motion	motion	NOUN
asir-1642	343	2	presupposes	presuppose	VERB
asir-1642	343	3	velocity	velocity	NOUN
asir-1642	343	4	vector	vector	NOUN
asir-1642	343	5	�	�	PROPN
asir-1642	343	6	̅	̅	NOUN
asir-1642	343	7	�	�	PROPN
asir-1642	343	8	which	which	PRON
asir-1642	343	9	,	,	PUNCT
asir-1642	343	10	when	when	SCONJ
asir-1642	343	11	it	it	PRON
asir-1642	343	12	is	be	AUX
asir-1642	343	13	in	in	ADP
asir-1642	343	14	motion	motion	NOUN
asir-1642	343	15	collides	collide	NOUN
asir-1642	343	16	with	with	ADP
asir-1642	343	17	other	other	ADJ
asir-1642	343	18	velocity	velocity	NOUN
asir-1642	343	19	vectors	vector	NOUN
asir-1642	343	20	and	and	CCONJ
asir-1642	343	21	creates	create	VERB
asir-1642	343	22	constant	constant	ADJ
asir-1642	343	23	work	work	NOUN
asir-1642	343	24	,	,	PUNCT
asir-1642	343	25	k.	k.	PROPN
asir-1642	343	26	motion	motion	PROPN
asir-1642	343	27	may	may	AUX
asir-1642	343	28	be	be	AUX
asir-1642	343	29	linear	linear	ADJ
asir-1642	343	30	,	,	PUNCT
asir-1642	343	31	or	or	CCONJ
asir-1642	343	32	rotational	rotational	ADJ
asir-1642	343	33	for	for	ADP
asir-1642	343	34	any	any	DET
asir-1642	343	35	displacement	displacement	NOUN
asir-1642	343	36	,	,	PUNCT
asir-1642	343	37	r	r	NOUN
asir-1642	343	38	,	,	PUNCT
asir-1642	343	39	so	so	ADV
asir-1642	343	40	exists	exist	VERB
asir-1642	343	41	the	the	DET
asir-1642	343	42	-	-	PUNCT
asir-1642	343	43	constant	constant	ADJ
asir-1642	343	44	-	-	PUNCT
asir-1642	343	45	work	work	NOUN
asir-1642	343	46	→	→	SYM
asir-1642	343	47	k	k	PROPN
asir-1642	343	48	=	=	SYM
asir-1642	343	49	�	�	PROPN
asir-1642	343	50	̅	̅	NOUN
asir-1642	343	51	�	�	NOUN
asir-1642	343	52	x	x	SYM
asir-1642	343	53	�	�	PROPN
asir-1642	343	54	̅	̅	NOUN
asir-1642	343	55	�	�	PROPN
asir-1642	343	56	.	.	PUNCT
asir-1642	343	57	�	�	PROPN
asir-1642	343	58	̅	̅	NOUN
asir-1642	343	59	�	�	NOUN
asir-1642	343	60	=	=	SYM
asir-1642	343	61	v².r	v².r	VERB
asir-1642	343	62	this	this	DET
asir-1642	343	63	constant	constant	ADJ
asir-1642	343	64	-	-	PUNCT
asir-1642	343	65	work	work	NOUN
asir-1642	343	66	is	be	AUX
asir-1642	343	67	→	→	SYM
asir-1642	343	68	k	k	X
asir-1642	343	69	=	=	SYM
asir-1642	343	70	v²	v²	PROPN
asir-1642	343	71	.	.	PUNCT
asir-1642	344	1	r	r	NOUN
asir-1642	344	2	=	=	PUNCT
asir-1642	344	3	(	(	PUNCT
asir-1642	344	4	w	w	NOUN
asir-1642	344	5	r	r	NOUN
asir-1642	344	6	)	)	PUNCT
asir-1642	344	7	².r	².r	PROPN
asir-1642	344	8	=	=	PUNCT
asir-1642	344	9	[	[	PUNCT
asir-1642	344	10	𝟐𝛑	𝟐𝛑	X
asir-1642	344	11	𝐓	𝐓	PROPN
asir-1642	344	12	𝐫	𝐫	PROPN
asir-1642	344	13	]	]	X
asir-1642	344	14	².r	².r	X
asir-1642	344	15	=	=	SYM
asir-1642	344	16	𝟒𝛑²	𝟒𝛑²	PRON
asir-1642	344	17	𝐫²	𝐫²	NOUN
asir-1642	344	18	𝐓²	𝐓²	VERB
asir-1642	344	19	.	.	PUNCT
asir-1642	345	1	r	r	NOUN
asir-1642	345	2	=	=	PUNCT
asir-1642	345	3	𝟒𝛑²	𝟒𝛑²	NOUN
asir-1642	345	4	𝐫	𝐫	PROPN
asir-1642	345	5	³	³	PROPN
asir-1642	345	6	𝐓²	𝐓²	PROPN
asir-1642	345	7	=	=	SYM
asir-1642	345	8	4π²	4π²	NUM
asir-1642	345	9	.	.	PUNCT
asir-1642	346	1	𝐫³	𝐫³	PROPN
asir-1642	346	2	𝐓²	𝐓²	PROPN
asir-1642	346	3	=	=	SYM
asir-1642	346	4	4π².r³.𝐟²𝐩	4π².r³.𝐟²𝐩	NUM
asir-1642	346	5	…	…	PUNCT
asir-1642	346	6	(	(	PUNCT
asir-1642	346	7	k	k	NOUN
asir-1642	346	8	)	)	PUNCT
asir-1642	346	9	equation	equation	NOUN
asir-1642	346	10	(	(	PUNCT
asir-1642	346	11	k	k	NOUN
asir-1642	346	12	)	)	PUNCT
asir-1642	346	13	is	be	AUX
asir-1642	346	14	kepler	kepler	NOUN
asir-1642	346	15	-	-	PUNCT
asir-1642	346	16	third	third	ADJ
asir-1642	346	17	-	-	PUNCT
asir-1642	346	18	law	law	NOUN
asir-1642	346	19	,	,	PUNCT
asir-1642	346	20	denoting	denote	VERB
asir-1642	346	21	that	that	DET
asir-1642	346	22	macrocosm	macrocosm	PROPN
asir-1642	346	23	and	and	CCONJ
asir-1642	346	24	microcosm	microcosm	PROPN
asir-1642	346	25	obey	obey	PROPN
asir-1642	346	26	newton	newton	PROPN
asir-1642	346	27	’s	’s	PART
asir-1642	346	28	laws	law	NOUN
asir-1642	346	29	of	of	ADP
asir-1642	346	30	motion	motion	NOUN
asir-1642	346	31	in	in	ADP
asir-1642	346	32	all	all	DET
asir-1642	346	33	scales	scale	NOUN
asir-1642	346	34	.	.	PUNCT
asir-1642	347	1	photon	photon	NOUN
asir-1642	347	2	during	during	ADP
asir-1642	347	3	motion	motion	NOUN
asir-1642	347	4	in	in	ADP
asir-1642	347	5	[	[	X
asir-1642	347	6	mfmf	mfmf	NOUN
asir-1642	347	7	]	]	X
asir-1642	347	8	chaos	chaos	NOUN
asir-1642	347	9	,	,	PUNCT
asir-1642	347	10	collides	collide	VERB
asir-1642	347	11	with	with	ADP
asir-1642	347	12	other	other	ADJ
asir-1642	347	13	photons	photon	NOUN
asir-1642	347	14	,	,	PUNCT
asir-1642	347	15	by	by	ADP
asir-1642	347	16	means	mean	NOUN
asir-1642	347	17	of	of	ADP
asir-1642	347	18	vectors	vector	NOUN
asir-1642	347	19	-	-	PUNCT
asir-1642	347	20	cross	cross	NOUN
asir-1642	347	21	-	-	NOUN
asir-1642	347	22	product	product	NOUN
asir-1642	347	23	,	,	PUNCT
asir-1642	347	24	and	and	CCONJ
asir-1642	347	25	produces	produce	VERB
asir-1642	347	26	a	a	DET
asir-1642	347	27	constant	constant	ADJ
asir-1642	347	28	work	work	NOUN
asir-1642	347	29	which	which	PRON
asir-1642	347	30	is	be	AUX
asir-1642	347	31	stored	store	VERB
asir-1642	347	32	into	into	ADP
asir-1642	347	33	the	the	DET
asir-1642	347	34	only	only	ADJ
asir-1642	347	35	-	-	PUNCT
asir-1642	347	36	four	four	NUM
asir-1642	347	37	energy	energy	NOUN
asir-1642	347	38	-	-	PUNCT
asir-1642	347	39	geometricalshapes	geometricalshape	NOUN
asir-1642	347	40	,	,	PUNCT
asir-1642	347	41	of	of	ADP
asir-1642	347	42	the	the	DET
asir-1642	347	43	motion	motion	NOUN
asir-1642	347	44	.	.	PUNCT
asir-1642	348	1	the	the	DET
asir-1642	348	2	interior	interior	ADJ
asir-1642	348	3	motion	motion	NOUN
asir-1642	348	4	is	be	AUX
asir-1642	348	5	kept	keep	VERB
asir-1642	348	6	in	in	ADP
asir-1642	348	7	its	its	PRON
asir-1642	348	8	wavelength	wavelength	NOUN
asir-1642	348	9	-	-	PUNCT
asir-1642	348	10	tank	tank	NOUN
asir-1642	348	11	2r	2r	NUM
asir-1642	348	12	=	=	SYM
asir-1642	348	13	n	n	PART
asir-1642	348	14	λ	λ	NOUN
asir-1642	348	15	,	,	PUNCT
asir-1642	348	16	and	and	CCONJ
asir-1642	348	17	the	the	DET
asir-1642	348	18	linear	linear	ADJ
asir-1642	348	19	motion	motion	NOUN
asir-1642	348	20	is	be	AUX
asir-1642	348	21	continued	continue	VERB
asir-1642	348	22	by	by	ADP
asir-1642	348	23	the	the	DET
asir-1642	348	24	propagating	propagate	VERB
asir-1642	348	25	electromagnetic	electromagnetic	ADJ
asir-1642	348	26	-	-	PUNCT
asir-1642	348	27	wave	wave	NOUN
asir-1642	348	28	-	-	PUNCT
asir-1642	348	29	conveyer	conveyer	NOUN
asir-1642	348	30	.	.	PUNCT
asir-1642	349	1	figure	figure	NOUN
asir-1642	349	2	6	6	NUM
asir-1642	349	3	.	.	PUNCT
asir-1642	350	1	velocities	velocity	NOUN
asir-1642	350	2	and	and	CCONJ
asir-1642	350	3	accelerations	acceleration	NOUN
asir-1642	350	4	on	on	ADP
asir-1642	350	5	,	,	PUNCT
asir-1642	350	6	planar	planar	ADJ
asir-1642	350	7	and	and	CCONJ
asir-1642	350	8	atom	atom	NOUN
asir-1642	350	9	,	,	PUNCT
asir-1642	350	10	orbits	orbit	NOUN
asir-1642	350	11	after	after	ADP
asir-1642	350	12	collision	collision	NOUN
asir-1642	350	13	in	in	ADP
asir-1642	350	14	(	(	PUNCT
asir-1642	350	15	1	1	X
asir-1642	350	16	)	)	PUNCT
asir-1642	350	17	is	be	AUX
asir-1642	350	18	presented	present	VERB
asir-1642	350	19	the	the	DET
asir-1642	350	20	circular	circular	ADJ
asir-1642	350	21	motion	motion	NOUN
asir-1642	350	22	where	where	SCONJ
asir-1642	350	23	the	the	DET
asir-1642	350	24	constant	constant	ADJ
asir-1642	350	25	velocity	velocity	NOUN
asir-1642	350	26	is	be	AUX
asir-1642	350	27	equal	equal	ADJ
asir-1642	350	28	to	to	ADP
asir-1642	350	29	v	v	NOUN
asir-1642	350	30	=	=	SYM
asir-1642	350	31	𝐯	𝐯	X
asir-1642	350	32	𝐩	𝐩	NOUN
asir-1642	350	33	=	=	PUNCT
asir-1642	350	34	wr	wr	PROPN
asir-1642	350	35	and	and	CCONJ
asir-1642	350	36	the	the	DET
asir-1642	350	37	centripetal	centripetal	NOUN
asir-1642	350	38	-	-	PUNCT
asir-1642	350	39	acceleration	acceleration	NOUN
asir-1642	350	40	𝐚	𝐚	X
asir-1642	350	41	𝐩	𝐩	NOUN
asir-1642	350	42	=	=	PUNCT
asir-1642	350	43	v²	v²	PROPN
asir-1642	350	44	in	in	ADP
asir-1642	350	45	(	(	PUNCT
asir-1642	350	46	2	2	NUM
asir-1642	350	47	)	)	PUNCT
asir-1642	350	48	is	be	AUX
asir-1642	350	49	presented	present	VERB
asir-1642	350	50	the	the	DET
asir-1642	350	51	elliptical	elliptical	ADJ
asir-1642	350	52	motion	motion	NOUN
asir-1642	350	53	after	after	ADP
asir-1642	350	54	collision	collision	NOUN
asir-1642	350	55	,	,	PUNCT
asir-1642	350	56	where	where	SCONJ
asir-1642	350	57	the	the	DET
asir-1642	350	58	acceleration	acceleration	NOUN
asir-1642	350	59	is	be	AUX
asir-1642	350	60	increased	increase	VERB
asir-1642	350	61	,	,	PUNCT
asir-1642	350	62	the	the	DET
asir-1642	350	63	velocity	velocity	NOUN
asir-1642	350	64	is	be	AUX
asir-1642	350	65	equal	equal	ADJ
asir-1642	350	66	to	to	ADP
asir-1642	350	67	𝐯²𝐩	𝐯²𝐩	NOUN
asir-1642	350	68	=	=	SYM
asir-1642	350	69	4	4	NUM
asir-1642	350	70	π²a³.	π²a³.	NOUN
asir-1642	350	71	²	²	NUM
asir-1642	350	72	[	[	PUNCT
asir-1642	350	73	+	+	NOUN
asir-1642	350	74	e	e	NOUN
asir-1642	350	75	]	]	PUNCT
asir-1642	350	76	and	and	CCONJ
asir-1642	350	77	the	the	DET
asir-1642	350	78	centripetal	centripetal	NOUN
asir-1642	350	79	-	-	PUNCT
asir-1642	350	80	acceleration	acceleration	NOUN
asir-1642	350	81	𝐚𝐩	𝐚𝐩	NOUN
asir-1642	350	82	=	=	SYM
asir-1642	350	83	32c²a²	32c²a²	NUM
asir-1642	350	84	5	5	NUM
asir-1642	350	85	=	=	SYM
asir-1642	350	86	32	32	NUM
asir-1642	350	87	a4	a4	NOUN
asir-1642	350	88	[	[	PUNCT
asir-1642	350	89	t²	t²	NOUN
asir-1642	350	90	4	4	NUM
asir-1642	350	91	[	[	SYM
asir-1642	350	92	5	5	NUM
asir-1642	350	93	,	,	PUNCT
asir-1642	350	94	and	and	CCONJ
asir-1642	350	95	for	for	ADP
asir-1642	350	96	r	r	NOUN
asir-1642	350	97	=	=	PUNCT
asir-1642	350	98	a	a	PRON
asir-1642	350	99	→	→	SYM
asir-1642	350	100	=	=	SYM
asir-1642	350	101	32	32	NUM
asir-1642	350	102	t²	t²	NOUN
asir-1642	350	103	5	5	NUM
asir-1642	350	104	,	,	PUNCT
asir-1642	350	105	where	where	SCONJ
asir-1642	350	106	c	c	NOUN
asir-1642	350	107	=	=	SYM
asir-1642	350	108	s	s	PROPN
asir-1642	350	109	t	t	NOUN
asir-1642	350	110	=	=	SYM
asir-1642	350	111	r²dφ/2	r²dφ/2	ADJ
asir-1642	350	112	=	=	PUNCT
asir-1642	350	113	constant	constant	ADJ
asir-1642	350	114	=	=	NOUN
asir-1642	350	115	area	area	NOUN
asir-1642	350	116	covered	cover	VERB
asir-1642	350	117	in	in	ADP
asir-1642	350	118	equal	equal	ADJ
asir-1642	350	119	times	time	NOUN
asir-1642	350	120	.	.	PUNCT
asir-1642	351	1	in	in	ADP
asir-1642	351	2	(	(	PUNCT
asir-1642	351	3	3	3	X
asir-1642	351	4	)	)	PUNCT
asir-1642	351	5	are	be	AUX
asir-1642	351	6	presented	present	VERB
asir-1642	351	7	the	the	DET
asir-1642	351	8	circular	circular	ADJ
asir-1642	351	9	,	,	PUNCT
asir-1642	351	10	elliptical	elliptical	ADJ
asir-1642	351	11	,	,	PUNCT
asir-1642	351	12	parabola	parabola	PROPN
asir-1642	351	13	,	,	PUNCT
asir-1642	351	14	hyperbola	hyperbola	PROPN
asir-1642	351	15	motion	motion	NOUN
asir-1642	351	16	after	after	ADP
asir-1642	351	17	collision	collision	NOUN
asir-1642	351	18	,	,	PUNCT
asir-1642	351	19	where	where	SCONJ
asir-1642	351	20	acceleration	acceleration	NOUN
asir-1642	351	21	is	be	AUX
asir-1642	351	22	increased	increase	VERB
asir-1642	351	23	.	.	PUNCT
asir-1642	352	1	the	the	DET
asir-1642	352	2	velocity	velocity	NOUN
asir-1642	352	3	is	be	AUX
asir-1642	352	4	equal	equal	ADJ
asir-1642	352	5	to	to	ADP
asir-1642	352	6	𝐯²𝐩	𝐯²𝐩	NOUN
asir-1642	352	7	=	=	SYM
asir-1642	352	8	4π²	4π²	NUM
asir-1642	353	1	a³	a³	ADJ
asir-1642	353	2	t²	t²	NOUN
asir-1642	353	3	[	[	PUNCT
asir-1642	353	4	+	+	NOUN
asir-1642	353	5	e	e	NOUN
asir-1642	353	6	]	]	X
asir-1642	353	7	=	=	PUNCT
asir-1642	353	8	4π²a³	4π²a³	NOUN
asir-1642	353	9	²	²	NUM
asir-1642	353	10	[	[	PUNCT
asir-1642	353	11	+	+	NOUN
asir-1642	353	12	e	e	NOUN
asir-1642	353	13	]	]	PUNCT
asir-1642	354	1	=	=	SYM
asir-1642	354	2	k	k	X
asir-1642	354	3	[	[	PUNCT
asir-1642	354	4	2	2	NUM
asir-1642	354	5	e²	e²	NOUN
asir-1642	354	6	]	]	PUNCT
asir-1642	354	7	and	and	CCONJ
asir-1642	354	8	the	the	DET
asir-1642	354	9	centripetal	centripetal	NOUN
asir-1642	354	10	-	-	PUNCT
asir-1642	354	11	acceleration	acceleration	NOUN
asir-1642	354	12	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	354	13	applied	apply	VERB
asir-1642	354	14	science	science	NOUN
asir-1642	354	15	and	and	CCONJ
asir-1642	354	16	innovative	innovative	ADJ
asir-1642	354	17	research	research	NOUN
asir-1642	354	18	vol	vol	NOUN
asir-1642	354	19	.	.	PROPN
asir-1642	355	1	2	2	NUM
asir-1642	355	2	,	,	PUNCT
asir-1642	355	3	no	no	INTJ
asir-1642	355	4	.	.	NOUN
asir-1642	355	5	4	4	NUM
asir-1642	355	6	,	,	PUNCT
asir-1642	355	7	2018	2018	NUM
asir-1642	355	8	173	173	NUM
asir-1642	355	9	published	publish	VERB
asir-1642	355	10	by	by	ADP
asir-1642	355	11	scholink	scholink	PROPN
asir-1642	355	12	inc	inc	PROPN
asir-1642	355	13	.	.	PROPN
asir-1642	355	14	𝐚𝐩	𝐚𝐩	PROPN
asir-1642	356	1	=	=	NOUN
asir-1642	356	2	²	²	NUM
asir-1642	356	3	t	t	NOUN
asir-1642	356	4	c	c	NOUN
asir-1642	356	5	²	²	PROPN
asir-1642	356	6	z	z	NOUN
asir-1642	356	7	,	,	PUNCT
asir-1642	356	8	where	where	SCONJ
asir-1642	356	9	k	k	PROPN
asir-1642	356	10	=	=	SYM
asir-1642	356	11	c²	c²	NOUN
asir-1642	356	12	=	=	SYM
asir-1642	356	13	constant	constant	ADJ
asir-1642	356	14	,	,	PUNCT
asir-1642	356	15	²	²	NUM
asir-1642	356	16	t	t	NOUN
asir-1642	356	17	=	=	SYM
asir-1642	356	18	natural	natural	ADJ
asir-1642	356	19	acceleration	acceleration	NOUN
asir-1642	356	20	5	5	NUM
asir-1642	356	21	..	..	PUNCT
asir-1642	356	22	the	the	DET
asir-1642	356	23	conservative	conservative	ADJ
asir-1642	356	24	system	system	NOUN
asir-1642	356	25	,	,	PUNCT
asir-1642	356	26	mechanical	mechanical	ADJ
asir-1642	356	27	-	-	PUNCT
asir-1642	356	28	energy	energy	NOUN
asir-1642	356	29	and	and	CCONJ
asir-1642	356	30	shapes	shape	NOUN
asir-1642	356	31	:	:	PUNCT
asir-1642	356	32	conservative	conservative	ADJ
asir-1642	356	33	system	system	NOUN
asir-1642	356	34	is	be	AUX
asir-1642	356	35	that	that	SCONJ
asir-1642	356	36	,	,	PUNCT
asir-1642	356	37	when	when	SCONJ
asir-1642	356	38	the	the	DET
asir-1642	356	39	total	total	ADJ
asir-1642	356	40	energy	energy	NOUN
asir-1642	356	41	e	e	NOUN
asir-1642	356	42	=	=	PUNCT
asir-1642	356	43	k	k	PROPN
asir-1642	357	1	+	+	NOUN
asir-1642	357	2	p	p	X
asir-1642	357	3	,	,	PUNCT
asir-1642	357	4	is	be	AUX
asir-1642	357	5	constant	constant	ADJ
asir-1642	357	6	where	where	SCONJ
asir-1642	357	7	k	k	NOUN
asir-1642	357	8	=	=	PUNCT
asir-1642	357	9	the	the	DET
asir-1642	357	10	kinetic	kinetic	ADJ
asir-1642	357	11	energy	energy	NOUN
asir-1642	357	12	and	and	CCONJ
asir-1642	357	13	p	p	NOUN
asir-1642	357	14	=	=	PUNCT
asir-1642	357	15	the	the	DET
asir-1642	357	16	potential	potential	ADJ
asir-1642	357	17	energy	energy	NOUN
asir-1642	357	18	and	and	CCONJ
asir-1642	357	19	k	k	NOUN
asir-1642	357	20	+	+	CCONJ
asir-1642	357	21	p	p	X
asir-1642	357	22	=	=	NOUN
asir-1642	357	23	constant	constant	ADJ
asir-1642	357	24	or	or	CCONJ
asir-1642	357	25	t	t	X
asir-1642	358	1	[	[	X
asir-1642	358	2	k	k	X
asir-1642	359	1	+	+	X
asir-1642	359	2	p	p	X
asir-1642	359	3	]	]	X
asir-1642	359	4	=	=	SYM
asir-1642	359	5	0	0	NUM
asir-1642	359	6	,	,	PUNCT
asir-1642	359	7	from	from	ADP
asir-1642	359	8	the	the	DET
asir-1642	359	9	conservation	conservation	NOUN
asir-1642	359	10	of	of	ADP
asir-1642	359	11	energy	energy	NOUN
asir-1642	359	12	can	can	AUX
asir-1642	359	13	be	be	AUX
asir-1642	359	14	written	write	VERB
asir-1642	359	15	e	e	X
asir-1642	360	1	=	=	SYM
asir-1642	360	2	k	k	PROPN
asir-1642	360	3	+	+	NUM
asir-1642	360	4	p	p	X
asir-1642	360	5	=	=	PROPN
asir-1642	360	6	k2	k2	PROPN
asir-1642	360	7	+	+	CCONJ
asir-1642	360	8	p2	p2	NOUN
asir-1642	360	9	,	,	PUNCT
asir-1642	360	10	where	where	SCONJ
asir-1642	360	11	,	,	PUNCT
asir-1642	360	12	1	1	NUM
asir-1642	360	13	,	,	PUNCT
asir-1642	360	14	2	2	NUM
asir-1642	360	15	,	,	PUNCT
asir-1642	360	16	represent	represent	VERB
asir-1642	360	17	two	two	NUM
asir-1642	360	18	instances	instance	NOUN
asir-1642	360	19	of	of	ADP
asir-1642	360	20	time	time	NOUN
asir-1642	360	21	.	.	PUNCT
asir-1642	361	1	if	if	SCONJ
asir-1642	361	2	at	at	ADP
asir-1642	361	3	time	time	NOUN
asir-1642	361	4	,	,	PUNCT
asir-1642	361	5	2	2	NUM
asir-1642	361	6	,	,	PUNCT
asir-1642	361	7	is	be	AUX
asir-1642	361	8	the	the	DET
asir-1642	361	9	time	time	NOUN
asir-1642	361	10	corresponding	correspond	VERB
asir-1642	361	11	to	to	ADP
asir-1642	361	12	the	the	DET
asir-1642	361	13	maximum	maximum	ADJ
asir-1642	361	14	displacement	displacement	NOUN
asir-1642	361	15	of	of	ADP
asir-1642	361	16	the	the	DET
asir-1642	361	17	mass	mass	NOUN
asir-1642	361	18	then	then	ADV
asir-1642	361	19	velocity	velocity	NOUN
asir-1642	361	20	of	of	ADP
asir-1642	361	21	the	the	DET
asir-1642	361	22	mass	mass	NOUN
asir-1642	361	23	is	be	AUX
asir-1642	361	24	zero	zero	NUM
asir-1642	361	25	and	and	CCONJ
asir-1642	361	26	k2	k2	NOUN
asir-1642	361	27	=	=	SYM
asir-1642	361	28	0	0	PROPN
asir-1642	361	29	,	,	PUNCT
asir-1642	361	30	where	where	SCONJ
asir-1642	362	1	k	k	PROPN
asir-1642	362	2	+	+	NOUN
asir-1642	362	3	0	0	NUM
asir-1642	362	4	=	=	SYM
asir-1642	362	5	0	0	PUNCT
asir-1642	362	6	+	+	NUM
asir-1642	362	7	p2	p2	NOUN
asir-1642	362	8	.	.	PUNCT
asir-1642	363	1	if	if	SCONJ
asir-1642	363	2	the	the	DET
asir-1642	363	3	system	system	NOUN
asir-1642	363	4	is	be	AUX
asir-1642	363	5	undergoing	undergo	VERB
asir-1642	363	6	harmonic	harmonic	ADJ
asir-1642	363	7	motion	motion	NOUN
asir-1642	363	8	,	,	PUNCT
asir-1642	363	9	the	the	DET
asir-1642	363	10	motion	motion	NOUN
asir-1642	363	11	is	be	AUX
asir-1642	363	12	repeated	repeat	VERB
asir-1642	363	13	in	in	ADP
asir-1642	363	14	equal	equal	ADJ
asir-1642	363	15	intervals	interval	NOUN
asir-1642	363	16	of	of	ADP
asir-1642	363	17	time	time	NOUN
asir-1642	363	18	t	t	PROPN
asir-1642	363	19	,	,	PUNCT
asir-1642	363	20	and	and	CCONJ
asir-1642	363	21	x(t	x(t	PROPN
asir-1642	363	22	)	)	PUNCT
asir-1642	363	23	=	=	PUNCT
asir-1642	364	1	x(t	x(t	PROPN
asir-1642	364	2	+	+	CCONJ
asir-1642	364	3	w	w	NOUN
asir-1642	364	4	)	)	PUNCT
asir-1642	364	5	,	,	PUNCT
asir-1642	364	6	then	then	ADV
asir-1642	364	7	k	k	PROPN
asir-1642	364	8	and	and	CCONJ
asir-1642	364	9	p2	p2	PROPN
asir-1642	364	10	are	be	AUX
asir-1642	364	11	maximum	maximum	ADJ
asir-1642	364	12	values	value	NOUN
asir-1642	364	13	and	and	CCONJ
asir-1642	364	14	issues	issue	NOUN
asir-1642	364	15	kmax	kmax	NOUN
asir-1642	364	16	=	=	SYM
asir-1642	364	17	pmax	pmax	NOUN
asir-1642	364	18	.	.	PUNCT
asir-1642	365	1	summing	sum	VERB
asir-1642	365	2	the	the	DET
asir-1642	365	3	kinetic	kinetic	ADJ
asir-1642	365	4	and	and	CCONJ
asir-1642	365	5	potential	potential	ADJ
asir-1642	365	6	energy	energy	NOUN
asir-1642	365	7	we	we	PRON
asir-1642	365	8	have	have	VERB
asir-1642	365	9	ẋ²	ẋ²	PROPN
asir-1642	365	10	/2	/2	PUNCT
asir-1642	366	1	+	+	PUNCT
asir-1642	366	2	p(x	p(x	NOUN
asir-1642	366	3	)	)	PUNCT
asir-1642	366	4	=	=	SYM
asir-1642	366	5	e	e	X
asir-1642	366	6	=	=	NOUN
asir-1642	366	7	constant	constant	ADJ
asir-1642	366	8	(	(	PUNCT
asir-1642	366	9	1	1	NUM
asir-1642	366	10	)	)	PUNCT
asir-1642	366	11	and	and	CCONJ
asir-1642	366	12	solving	solve	VERB
asir-1642	366	13	for	for	ADP
asir-1642	366	14	ẋ	ẋ	PROPN
asir-1642	367	1	=	=	SYM
asir-1642	367	2	y	y	PROPN
asir-1642	367	3	then	then	ADV
asir-1642	367	4	y	y	PROPN
asir-1642	368	1	=	=	PUNCT
asir-1642	368	2	ẋ	ẋ	PROPN
asir-1642	368	3	=	=	SYM
asir-1642	368	4	±	±	NUM
asir-1642	368	5	√	√	PROPN
asir-1642	369	1	[	[	PUNCT
asir-1642	369	2	−	−	PROPN
asir-1642	369	3	p(x	p(x	PROPN
asir-1642	369	4	)	)	PUNCT
asir-1642	369	5	…	…	PUNCT
asir-1642	369	6	(	(	PUNCT
asir-1642	369	7	2	2	NUM
asir-1642	369	8	)	)	PUNCT
asir-1642	369	9	where	where	SCONJ
asir-1642	369	10	trajectories	trajectory	NOUN
asir-1642	369	11	must	must	AUX
asir-1642	369	12	be	be	AUX
asir-1642	369	13	symmetric	symmetric	ADJ
asir-1642	369	14	about	about	ADP
asir-1642	369	15	the	the	DET
asir-1642	369	16	x	x	NOUN
asir-1642	369	17	-	-	NOUN
asir-1642	369	18	axis	axis	ADJ
asir-1642	369	19	,	,	PUNCT
asir-1642	369	20	ẍ	ẍ	X
asir-1642	369	21	=	=	SYM
asir-1642	369	22	f(x	f(x	PROPN
asir-1642	369	23	)	)	PUNCT
asir-1642	369	24	(	(	PUNCT
asir-1642	369	25	3	3	X
asir-1642	369	26	)	)	PUNCT
asir-1642	369	27	or	or	CCONJ
asir-1642	369	28	ẍ	ẍ	X
asir-1642	369	29	=	=	SYM
asir-1642	369	30	ẋ	ẋ	PROPN
asir-1642	369	31	(	(	PUNCT
asir-1642	369	32	dẋ/dt	dẋ/dt	PROPN
asir-1642	369	33	)	)	PUNCT
asir-1642	369	34	=	=	SYM
asir-1642	369	35	f(x	f(x	PROPN
asir-1642	369	36	)	)	PUNCT
asir-1642	369	37	and	and	CCONJ
asir-1642	369	38	(	(	PUNCT
asir-1642	369	39	3	3	X
asir-1642	369	40	)	)	PUNCT
asir-1642	369	41	is	be	AUX
asir-1642	369	42	written	write	VERB
asir-1642	369	43	ẋ.dẋ	ẋ.dẋ	ADJ
asir-1642	369	44	f(x).dx	f(x).dx	PROPN
asir-1642	370	1	=	=	SYM
asir-1642	370	2	0	0	NUM
asir-1642	370	3	…	…	PUNCT
asir-1642	370	4	…	…	PUNCT
asir-1642	370	5	(	(	PUNCT
asir-1642	370	6	4	4	X
asir-1642	370	7	)	)	PUNCT
asir-1642	370	8	integrating	integrate	VERB
asir-1642	370	9	ẋ	ẋ	PROPN
asir-1642	370	10	²	²	NUM
asir-1642	370	11	2	2	NUM
asir-1642	370	12	∫	∫	NOUN
asir-1642	370	13	(	(	PUNCT
asir-1642	370	14	x)dx	x)dx	NOUN
asir-1642	370	15	x	x	SYM
asir-1642	370	16	0	0	PUNCT
asir-1642	370	17	=	=	SYM
asir-1642	370	18	e	e	NOUN
asir-1642	370	19	and	and	CCONJ
asir-1642	370	20	by	by	ADP
asir-1642	370	21	comparison	comparison	NOUN
asir-1642	370	22	with	with	ADP
asir-1642	370	23	(	(	PUNCT
asir-1642	370	24	1	1	NUM
asir-1642	370	25	)	)	PUNCT
asir-1642	370	26	then	then	ADV
asir-1642	370	27	p(x	p(x	VERB
asir-1642	370	28	)	)	PUNCT
asir-1642	370	29	=	=	SYM
asir-1642	370	30	∫	∫	PROPN
asir-1642	371	1	(	(	PUNCT
asir-1642	371	2	x)dx	x)dx	PROPN
asir-1642	371	3	x	x	SYM
asir-1642	371	4	0	0	NUM
asir-1642	371	5	and	and	CCONJ
asir-1642	371	6	f(x	f(x	PROPN
asir-1642	371	7	)	)	PUNCT
asir-1642	372	1	=	=	PUNCT
asir-1642	372	2	dp	dp	PROPN
asir-1642	372	3	/	/	SYM
asir-1642	372	4	dx	dx	PROPN
asir-1642	372	5	,	,	PUNCT
asir-1642	372	6	i.e.	i.e.	X
asir-1642	372	7	,	,	PUNCT
asir-1642	372	8	for	for	ADP
asir-1642	372	9	a	a	DET
asir-1642	372	10	conservative	conservative	ADJ
asir-1642	372	11	system	system	NOUN
asir-1642	372	12	the	the	DET
asir-1642	372	13	force	force	NOUN
asir-1642	372	14	is	be	AUX
asir-1642	372	15	equal	equal	ADJ
asir-1642	372	16	to	to	ADP
asir-1642	372	17	the	the	DET
asir-1642	372	18	negative	negative	ADJ
asir-1642	372	19	gradient	gradient	NOUN
asir-1642	372	20	of	of	ADP
asir-1642	372	21	the	the	DET
asir-1642	372	22	potential	potential	ADJ
asir-1642	372	23	-	-	PUNCT
asir-1642	372	24	energy	energy	NOUN
asir-1642	372	25	,	,	PUNCT
asir-1642	372	26	and	and	CCONJ
asir-1642	372	27	is	be	AUX
asir-1642	372	28	y	y	PROPN
asir-1642	372	29	x	x	PROPN
asir-1642	372	30	=	=	SYM
asir-1642	372	31	f(x	f(x	PROPN
asir-1642	372	32	)	)	PUNCT
asir-1642	372	33	y	y	PROPN
asir-1642	372	34	…	…	PUNCT
asir-1642	372	35	.	.	PUNCT
asir-1642	373	1	(	(	PUNCT
asir-1642	373	2	5	5	X
asir-1642	373	3	)	)	PUNCT
asir-1642	373	4	equations	equation	NOUN
asir-1642	373	5	note	note	VERB
asir-1642	373	6	that	that	SCONJ
asir-1642	373	7	,	,	PUNCT
asir-1642	373	8	at	at	ADP
asir-1642	373	9	the	the	DET
asir-1642	373	10	equilibrium	equilibrium	NOUN
asir-1642	373	11	points	point	NOUN
asir-1642	373	12	the	the	DET
asir-1642	373	13	slope	slope	NOUN
asir-1642	373	14	of	of	ADP
asir-1642	373	15	the	the	DET
asir-1642	373	16	potential	potential	ADJ
asir-1642	373	17	energy	energy	NOUN
asir-1642	373	18	curve	curve	NOUN
asir-1642	373	19	p(x	p(x	NOUN
asir-1642	373	20	)	)	PUNCT
asir-1642	373	21	=	=	SYM
asir-1642	373	22	0	0	X
asir-1642	373	23	.	.	PUNCT
asir-1642	374	1	it	it	PRON
asir-1642	374	2	can	can	AUX
asir-1642	374	3	be	be	AUX
asir-1642	374	4	shown	show	VERB
asir-1642	374	5	that	that	SCONJ
asir-1642	374	6	the	the	DET
asir-1642	374	7	minima	minima	NOUN
asir-1642	374	8	of	of	ADP
asir-1642	374	9	p(x	p(x	PROPN
asir-1642	374	10	)	)	PUNCT
asir-1642	374	11	are	be	AUX
asir-1642	374	12	stable	stable	ADJ
asir-1642	374	13	equilibrium	equilibrium	NOUN
asir-1642	374	14	while	while	NOUN
asir-1642	374	15	,	,	PUNCT
asir-1642	374	16	positions	position	NOUN
asir-1642	374	17	corresponding	correspond	VERB
asir-1642	374	18	to	to	ADP
asir-1642	374	19	the	the	DET
asir-1642	374	20	maxima	maxima	NOUN
asir-1642	374	21	of	of	ADP
asir-1642	374	22	p(x	p(x	PROPN
asir-1642	374	23	)	)	PUNCT
asir-1642	374	24	and	and	CCONJ
asir-1642	374	25	are	be	AUX
asir-1642	374	26	positions	position	NOUN
asir-1642	374	27	of	of	ADP
asir-1642	374	28	unstable	unstable	ADJ
asir-1642	374	29	equilibrium	equilibrium	NOUN
asir-1642	374	30	.	.	PUNCT
asir-1642	375	1	since	since	SCONJ
asir-1642	375	2	the	the	DET
asir-1642	375	3	trajectories	trajectory	NOUN
asir-1642	375	4	maybe	maybe	ADV
asir-1642	375	5	closed	close	VERB
asir-1642	375	6	curves	curve	NOUN
asir-1642	375	7	as	as	SCONJ
asir-1642	375	8	this	this	PRON
asir-1642	375	9	happens	happen	VERB
asir-1642	375	10	in	in	ADP
asir-1642	375	11	orbitals	orbital	NOUN
asir-1642	375	12	,	,	PUNCT
asir-1642	375	13	the	the	DET
asir-1642	375	14	period	period	NOUN
asir-1642	375	15	associated	associate	VERB
asir-1642	375	16	with	with	ADP
asir-1642	375	17	them	they	PRON
asir-1642	375	18	is	be	AUX
asir-1642	375	19	t	t	PROPN
asir-1642	375	20	=	=	SYM
asir-1642	375	21	2∫	2∫	NUM
asir-1642	375	22	dx	dx	NOUN
asir-1642	375	23	√	√	PROPN
asir-1642	375	24	[	[	PUNCT
asir-1642	375	25	−	−	PROPN
asir-1642	375	26	p(x	p(x	PROPN
asir-1642	375	27	)	)	PUNCT
asir-1642	375	28	x2	x2	NOUN
asir-1642	375	29	x	x	PUNCT
asir-1642	375	30	where	where	SCONJ
asir-1642	375	31	x	x	X
asir-1642	375	32	,	,	PUNCT
asir-1642	375	33	x2	x2	PROPN
asir-1642	375	34	,	,	PUNCT
asir-1642	375	35	are	be	AUX
asir-1642	375	36	extreme	extreme	ADJ
asir-1642	375	37	points	point	NOUN
asir-1642	375	38	of	of	ADP
asir-1642	375	39	the	the	DET
asir-1642	375	40	trajectory	trajectory	NOUN
asir-1642	375	41	on	on	ADP
asir-1642	375	42	x	x	NOUN
asir-1642	375	43	-	-	NOUN
asir-1642	375	44	axis	axis	ADJ
asir-1642	375	45	.	.	PUNCT
asir-1642	376	1	in	in	ADP
asir-1642	376	2	figure	figure	NOUN
asir-1642	376	3	6	6	NUM
asir-1642	376	4	,	,	PUNCT
asir-1642	376	5	mass	mass	NOUN
asir-1642	376	6	m	m	PROPN
asir-1642	376	7	,	,	PUNCT
asir-1642	376	8	at	at	ADP
asir-1642	376	9	point	point	NOUN
asir-1642	376	10	p	p	NOUN
asir-1642	376	11	,	,	PUNCT
asir-1642	376	12	is	be	AUX
asir-1642	376	13	orbiting	orbit	VERB
asir-1642	376	14	with	with	ADP
asir-1642	376	15	velocity	velocity	NOUN
asir-1642	376	16	vector	vector	NOUN
asir-1642	376	17	�	�	PROPN
asir-1642	376	18	̅	̅	NOUN
asir-1642	376	19	�	�	PROPN
asir-1642	376	20	,	,	PUNCT
asir-1642	376	21	analyzed	analyze	VERB
asir-1642	376	22	into	into	ADP
asir-1642	376	23	the	the	DET
asir-1642	376	24	radial	radial	ADJ
asir-1642	376	25	v	v	NOUN
asir-1642	376	26	̅̅̅̅	̅̅̅̅	NOUN
asir-1642	376	27	,	,	PUNCT
asir-1642	376	28	and	and	CCONJ
asir-1642	376	29	the	the	DET
asir-1642	376	30	tangential	tangential	ADJ
asir-1642	376	31	v2̅̅̅̅	v2̅̅̅̅	PROPN
asir-1642	376	32	,	,	PUNCT
asir-1642	376	33	both	both	CCONJ
asir-1642	376	34	perpendicular	perpendicular	ADJ
asir-1642	376	35	to	to	ADP
asir-1642	376	36	pf	pf	PROPN
asir-1642	376	37	,	,	PUNCT
asir-1642	376	38	pf2	pf2	VERB
asir-1642	376	39	.	.	PUNCT
asir-1642	377	1	since	since	SCONJ
asir-1642	377	2	sum	sum	NOUN
asir-1642	377	3	pf	pf	NOUN
asir-1642	377	4	+	+	CCONJ
asir-1642	377	5	pf2	pf2	NOUN
asir-1642	377	6	=	=	SYM
asir-1642	377	7	2a	2a	NUM
asir-1642	377	8	=	=	SYM
asir-1642	377	9	constant	constant	ADJ
asir-1642	377	10	,	,	PUNCT
asir-1642	377	11	therefore	therefore	ADV
asir-1642	377	12	v	v	ADP
asir-1642	377	13	+	+	NOUN
asir-1642	377	14	v2=	v2=	NOUN
asir-1642	377	15	0	0	NUM
asir-1642	377	16	,	,	PUNCT
asir-1642	377	17	and	and	CCONJ
asir-1642	377	18	v	v	X
asir-1642	377	19	=	=	SYM
asir-1642	377	20	v2	v2	PROPN
asir-1642	377	21	,	,	PUNCT
asir-1642	377	22	i.e.	i.e.	X
asir-1642	377	23	,	,	PUNCT
asir-1642	377	24	the	the	DET
asir-1642	377	25	two	two	NUM
asir-1642	377	26	velocities	velocity	NOUN
asir-1642	377	27	are	be	AUX
asir-1642	377	28	of	of	ADP
asir-1642	377	29	equal	equal	ADJ
asir-1642	377	30	magnitude	magnitude	NOUN
asir-1642	377	31	and	and	CCONJ
asir-1642	377	32	opposite	opposite	ADJ
asir-1642	377	33	sign	sign	NOUN
asir-1642	377	34	and	and	CCONJ
asir-1642	377	35	,	,	PUNCT
asir-1642	377	36	velocity	velocity	NOUN
asir-1642	377	37	on	on	ADP
asir-1642	377	38	tangent	tangent	NOUN
asir-1642	377	39	at	at	ADP
asir-1642	377	40	p	p	NOUN
asir-1642	377	41	,	,	PUNCT
asir-1642	377	42	is	be	AUX
asir-1642	377	43	the	the	DET
asir-1642	377	44	external	external	ADJ
asir-1642	377	45	bisector	bisector	NOUN
asir-1642	377	46	of	of	ADP
asir-1642	377	47	pf	pf	PROPN
asir-1642	377	48	,	,	PUNCT
asir-1642	377	49	pf2	pf2	PROPN
asir-1642	377	50	vectors	vector	NOUN
asir-1642	377	51	.	.	PUNCT
asir-1642	378	1	the	the	DET
asir-1642	378	2	kinetic	kinetic	ADJ
asir-1642	378	3	energy	energy	NOUN
asir-1642	378	4	breaks	break	NOUN
asir-1642	378	5	into	into	ADP
asir-1642	378	6	two	two	NUM
asir-1642	378	7	parts	part	NOUN
asir-1642	378	8	as	as	ADP
asir-1642	378	9	k	k	PROPN
asir-1642	378	10	=	=	PUNCT
asir-1642	378	11	mv	mv	PROPN
asir-1642	378	12	²/2	²/2	PROPN
asir-1642	378	13	+	+	CCONJ
asir-1642	378	14	mv2²/2	mv2²/2	PROPN
asir-1642	378	15	(	(	PUNCT
asir-1642	378	16	a	a	NOUN
asir-1642	378	17	)	)	PUNCT
asir-1642	378	18	,	,	PUNCT
asir-1642	378	19	and	and	CCONJ
asir-1642	378	20	the	the	DET
asir-1642	378	21	magnitude	magnitude	NOUN
asir-1642	378	22	of	of	ADP
asir-1642	378	23	the	the	DET
asir-1642	378	24	angular	angular	ADJ
asir-1642	378	25	-	-	PUNCT
asir-1642	378	26	momentum	momentum	NOUN
asir-1642	378	27	l	l	NOUN
asir-1642	378	28	=	=	PUNCT
asir-1642	378	29	r	r	NOUN
asir-1642	378	30	m	m	NOUN
asir-1642	378	31	v2	v2	NOUN
asir-1642	378	32	,	,	PUNCT
asir-1642	378	33	and	and	CCONJ
asir-1642	378	34	in	in	ADP
asir-1642	378	35	terms	term	NOUN
asir-1642	378	36	of	of	ADP
asir-1642	378	37	l	l	NOUN
asir-1642	378	38	,	,	PUNCT
asir-1642	378	39	then	then	ADV
asir-1642	378	40	k	k	PROPN
asir-1642	378	41	=	=	SYM
asir-1642	378	42	2	2	NUM
asir-1642	378	43	mv	mv	NOUN
asir-1642	378	44	²	²	NUM
asir-1642	378	45	+	+	CCONJ
asir-1642	378	46	l²	l²	VERB
asir-1642	378	47	2	2	NUM
asir-1642	378	48	m	m	NOUN
asir-1642	378	49	²	²	NUM
asir-1642	378	50	and	and	CCONJ
asir-1642	378	51	adding	add	VERB
asir-1642	378	52	the	the	DET
asir-1642	378	53	negative	negative	ADJ
asir-1642	378	54	potential	potential	ADJ
asir-1642	378	55	energy	energy	NOUN
asir-1642	378	56	p	p	NOUN
asir-1642	379	1	=	=	NOUN
asir-1642	379	2	g	g	NOUN
asir-1642	379	3	mm	mm	INTJ
asir-1642	379	4	then	then	ADV
asir-1642	379	5	total	total	VERB
asir-1642	379	6	energy	energy	NOUN
asir-1642	379	7	e	e	NOUN
asir-1642	379	8	=	=	SYM
asir-1642	379	9	k	k	PROPN
asir-1642	380	1	+	+	CCONJ
asir-1642	380	2	p	p	X
asir-1642	380	3	=	=	SYM
asir-1642	380	4	𝟐	𝟐	NUM
asir-1642	380	5	m𝐯	m𝐯	NOUN
asir-1642	380	6	²	²	NUM
asir-1642	380	7	+	+	CCONJ
asir-1642	380	8	𝐋²	𝐋²	NOUN
asir-1642	380	9	𝟐	𝟐	NUM
asir-1642	380	10	𝐫	𝐫	ADP
asir-1642	380	11	²	²	NUM
asir-1642	380	12	g	g	PROPN
asir-1642	380	13	𝐌	𝐌	PROPN
asir-1642	380	14	𝐫	𝐫	PROPN
asir-1642	380	15	(	(	PUNCT
asir-1642	380	16	b	b	NOUN
asir-1642	380	17	)	)	PUNCT
asir-1642	380	18	turning	turn	VERB
asir-1642	380	19	points	point	NOUN
asir-1642	380	20	,	,	PUNCT
asir-1642	380	21	r	r	NOUN
asir-1642	380	22	perihelion	perihelion	NOUN
asir-1642	380	23	,	,	PUNCT
asir-1642	380	24	ra	ra	PROPN
asir-1642	380	25	aphelion	aphelion	NOUN
asir-1642	380	26	,	,	PUNCT
asir-1642	380	27	are	be	AUX
asir-1642	380	28	the	the	DET
asir-1642	380	29	distances	distance	NOUN
asir-1642	380	30	of	of	ADP
asir-1642	380	31	closest	close	ADJ
asir-1642	380	32	approach	approach	NOUN
asir-1642	380	33	and	and	CCONJ
asir-1642	380	34	further	further	ADJ
asir-1642	380	35	recession	recession	NOUN
asir-1642	380	36	,	,	PUNCT
asir-1642	380	37	where	where	SCONJ
asir-1642	380	38	v	v	NOUN
asir-1642	380	39	=	=	SYM
asir-1642	380	40	0	0	NUM
asir-1642	380	41	,	,	PUNCT
asir-1642	380	42	v2=	v2=	PROPN
asir-1642	380	43	0	0	NUM
asir-1642	380	44	,	,	PUNCT
asir-1642	380	45	and	and	CCONJ
asir-1642	380	46	(	(	PUNCT
asir-1642	380	47	b	b	NOUN
asir-1642	380	48	)	)	PUNCT
asir-1642	380	49	becomes	become	VERB
asir-1642	380	50	l²	l²	PROPN
asir-1642	380	51	2	2	NUM
asir-1642	380	52	m	m	NOUN
asir-1642	380	53	²	²	NUM
asir-1642	380	54	g	g	NOUN
asir-1642	380	55	mm	mm	NOUN
asir-1642	380	56	=	=	SYM
asir-1642	380	57	e	e	PROPN
asir-1642	380	58	or	or	CCONJ
asir-1642	380	59	→	→	SYM
asir-1642	380	60	e	e	X
asir-1642	380	61	=	=	PUNCT
asir-1642	380	62	r²	r²	VERB
asir-1642	380	63	+	+	CCONJ
asir-1642	380	64	g	g	NOUN
asir-1642	380	65	mm	mm	NOUN
asir-1642	380	66	r	r	NOUN
asir-1642	380	67	l²	l²	NOUN
asir-1642	380	68	2	2	NUM
asir-1642	380	69	m	m	NOUN
asir-1642	380	70	=	=	SYM
asir-1642	380	71	0	0	NUM
asir-1642	380	72	,	,	PUNCT
asir-1642	380	73	an	an	DET
asir-1642	380	74	equation	equation	NOUN
asir-1642	380	75	with	with	ADP
asir-1642	380	76	the	the	DET
asir-1642	380	77	two	two	NUM
asir-1642	380	78	roots	root	NOUN
asir-1642	380	79	r	r	NOUN
asir-1642	380	80	and	and	CCONJ
asir-1642	380	81	ra	ra	NOUN
asir-1642	380	82	,	,	PUNCT
asir-1642	380	83	as	as	ADP
asir-1642	380	84	(	(	PUNCT
asir-1642	380	85	r	r	NOUN
asir-1642	380	86	r	r	NOUN
asir-1642	380	87	)	)	PUNCT
asir-1642	380	88	.	.	PUNCT
asir-1642	381	1	(	(	PUNCT
asir-1642	381	2	r	r	NOUN
asir-1642	381	3	ra	ra	NOUN
asir-1642	381	4	)	)	PUNCT
asir-1642	381	5	=	=	SYM
asir-1642	382	1	0	0	NUM
asir-1642	382	2	,	,	PUNCT
asir-1642	382	3	or	or	CCONJ
asir-1642	382	4	r²	r²	VERB
asir-1642	382	5	(	(	PUNCT
asir-1642	382	6	r	r	NOUN
asir-1642	382	7	+	+	NOUN
asir-1642	382	8	ra).r	ra).r	NOUN
asir-1642	383	1	+	+	SYM
asir-1642	383	2	(	(	PUNCT
asir-1642	383	3	r	r	NOUN
asir-1642	383	4	ra	ra	PROPN
asir-1642	383	5	)	)	PUNCT
asir-1642	384	1	=	=	SYM
asir-1642	384	2	0	0	NUM
asir-1642	385	1	where	where	SCONJ
asir-1642	385	2	is	be	AUX
asir-1642	385	3	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	385	4	applied	apply	VERB
asir-1642	385	5	science	science	NOUN
asir-1642	385	6	and	and	CCONJ
asir-1642	385	7	innovative	innovative	ADJ
asir-1642	385	8	research	research	NOUN
asir-1642	385	9	vol	vol	NOUN
asir-1642	385	10	.	.	PROPN
asir-1642	386	1	2	2	NUM
asir-1642	386	2	,	,	PUNCT
asir-1642	386	3	no	no	INTJ
asir-1642	386	4	.	.	NOUN
asir-1642	386	5	4	4	NUM
asir-1642	386	6	,	,	PUNCT
asir-1642	386	7	2018	2018	NUM
asir-1642	386	8	174	174	NUM
asir-1642	386	9	published	publish	VERB
asir-1642	386	10	by	by	ADP
asir-1642	386	11	scholink	scholink	PROPN
asir-1642	386	12	inc	inc	PROPN
asir-1642	386	13	.	.	PUNCT
asir-1642	387	1	the	the	DET
asir-1642	387	2	sum	sum	NOUN
asir-1642	387	3	of	of	ADP
asir-1642	387	4	roots	root	NOUN
asir-1642	387	5	[	[	X
asir-1642	387	6	r	r	X
asir-1642	387	7	+	+	NUM
asir-1642	387	8	ra	ra	NOUN
asir-1642	387	9	]	]	X
asir-1642	388	1	=	=	PUNCT
asir-1642	388	2	g	g	NOUN
asir-1642	388	3	mm	mm	NOUN
asir-1642	388	4	=	=	SYM
asir-1642	388	5	2a	2a	NUM
asir-1642	388	6	from	from	ADP
asir-1642	388	7	where	where	SCONJ
asir-1642	388	8	2	2	NUM
asir-1642	388	9	m	m	NOUN
asir-1642	388	10	=	=	NOUN
asir-1642	388	11	gm	gm	PROPN
asir-1642	388	12	a	a	PRON
asir-1642	388	13	,	,	PUNCT
asir-1642	388	14	and	and	CCONJ
asir-1642	388	15	product	product	NOUN
asir-1642	388	16	of	of	ADP
asir-1642	388	17	roots	root	NOUN
asir-1642	388	18	[	[	X
asir-1642	388	19	r	r	NOUN
asir-1642	388	20	.ra	.ra	PUNCT
asir-1642	388	21	]	]	PUNCT
asir-1642	389	1	=	=	SYM
asir-1642	389	2	l²	l²	NOUN
asir-1642	389	3	2	2	NUM
asir-1642	389	4	m	m	VERB
asir-1642	389	5	from	from	ADP
asir-1642	389	6	where	where	SCONJ
asir-1642	389	7	l	l	NOUN
asir-1642	389	8	=	=	SYM
asir-1642	389	9	r.mv	r.mv	PROPN
asir-1642	389	10	,	,	PUNCT
asir-1642	389	11	v	v	NOUN
asir-1642	389	12	=	=	SYM
asir-1642	389	13	l	l	NOUN
asir-1642	389	14	/	/	SYM
asir-1642	389	15	r.m	r.m	PROPN
asir-1642	389	16	,	,	PUNCT
asir-1642	389	17	and	and	CCONJ
asir-1642	389	18	the	the	DET
asir-1642	389	19	total	total	ADJ
asir-1642	389	20	-	-	PUNCT
asir-1642	389	21	energy	energy	NOUN
asir-1642	389	22	is	be	AUX
asir-1642	389	23	e	e	NOUN
asir-1642	389	24	=	=	SYM
asir-1642	389	25	2	2	NUM
asir-1642	389	26	m	m	NOUN
asir-1642	389	27	[	[	PUNCT
asir-1642	389	28	l	l	NOUN
asir-1642	389	29	m	m	X
asir-1642	389	30	]	]	X
asir-1642	389	31	²	²	X
asir-1642	389	32	=	=	SYM
asir-1642	389	33	l²	l²	NOUN
asir-1642	389	34	2	2	NUM
asir-1642	389	35	m	m	NOUN
asir-1642	389	36	²	²	NUM
asir-1642	389	37	the	the	DET
asir-1642	389	38	turning	turning	NOUN
asir-1642	389	39	points	point	NOUN
asir-1642	389	40	are	be	AUX
asir-1642	389	41	related	relate	VERB
asir-1642	389	42	to	to	ADP
asir-1642	389	43	the	the	DET
asir-1642	389	44	axes	axis	NOUN
asir-1642	389	45	of	of	ADP
asir-1642	389	46	the	the	DET
asir-1642	389	47	ellipse	ellipse	NOUN
asir-1642	389	48	by	by	ADP
asir-1642	389	49	r	r	NOUN
asir-1642	389	50	+	+	NUM
asir-1642	389	51	ra	ra	NOUN
asir-1642	389	52	=	=	PUNCT
asir-1642	389	53	2a	2a	NUM
asir-1642	389	54	,	,	PUNCT
asir-1642	389	55	and	and	CCONJ
asir-1642	389	56	r	r	NOUN
asir-1642	389	57	.ra	.ra	PUNCT
asir-1642	390	1	=	=	SYM
asir-1642	390	2	b²	b²	NOUN
asir-1642	390	3	=	=	PROPN
asir-1642	390	4	l²	l²	NOUN
asir-1642	390	5	2	2	NUM
asir-1642	390	6	m	m	NOUN
asir-1642	390	7	so	so	ADV
asir-1642	390	8	,	,	PUNCT
asir-1642	390	9	energy	energy	NOUN
asir-1642	390	10	on	on	ADP
asir-1642	390	11	orbit	orbit	NOUN
asir-1642	390	12	e	e	NOUN
asir-1642	390	13	=	=	SYM
asir-1642	390	14	𝐆𝐌	𝐆𝐌	PROPN
asir-1642	390	15	𝟐𝐚	𝟐𝐚	ADV
asir-1642	390	16	,	,	PUNCT
asir-1642	390	17	angular	angular	ADJ
asir-1642	390	18	-	-	PUNCT
asir-1642	390	19	momentum	momentum	NOUN
asir-1642	390	20	l²	l²	NOUN
asir-1642	390	21	=	=	NOUN
asir-1642	391	1	2m.e.b²	2m.e.b²	NUM
asir-1642	391	2	(	(	PUNCT
asir-1642	391	3	c	c	NOUN
asir-1642	391	4	)	)	PUNCT
asir-1642	391	5	from	from	ADP
asir-1642	391	6	kepler	kepler	PROPN
asir-1642	391	7	laws	law	NOUN
asir-1642	391	8	,	,	PUNCT
asir-1642	391	9	the	the	DET
asir-1642	391	10	area	area	NOUN
asir-1642	391	11	,	,	PUNCT
asir-1642	391	12	s	s	AUX
asir-1642	391	13	,	,	PUNCT
asir-1642	391	14	swept	sweep	VERB
asir-1642	391	15	out	out	ADP
asir-1642	391	16	by	by	ADP
asir-1642	391	17	the	the	DET
asir-1642	391	18	line	line	NOUN
asir-1642	391	19	pf	pf	NOUN
asir-1642	391	20	=	=	NOUN
asir-1642	391	21	r	r	NOUN
asir-1642	391	22	is	be	AUX
asir-1642	391	23	ds	ds	ADJ
asir-1642	391	24	=	=	SYM
asir-1642	391	25	r².dθ/2	r².dθ/2	NOUN
asir-1642	391	26	and	and	CCONJ
asir-1642	391	27	the	the	DET
asir-1642	391	28	rate	rate	NOUN
asir-1642	391	29	of	of	ADP
asir-1642	391	30	swept	sweep	VERB
asir-1642	391	31	is	be	AUX
asir-1642	391	32	s	s	PROPN
asir-1642	391	33	t	t	NOUN
asir-1642	391	34	=	=	PUNCT
asir-1642	391	35	(	(	PUNCT
asir-1642	391	36	r²	r²	VERB
asir-1642	391	37	/	/	SYM
asir-1642	391	38	2).(dθ	2).(dθ	NUM
asir-1642	391	39	/	/	SYM
asir-1642	391	40	dt	dt	NOUN
asir-1642	391	41	)	)	PUNCT
asir-1642	391	42	=	=	SYM
asir-1642	391	43	2	2	NUM
asir-1642	391	44	r²	r²	NOUN
asir-1642	391	45	w	w	NOUN
asir-1642	391	46	=	=	SYM
asir-1642	391	47	2	2	NUM
asir-1642	391	48	r	r	NOUN
asir-1642	391	49	(	(	PUNCT
asir-1642	391	50	r	r	NOUN
asir-1642	391	51	w	w	PROPN
asir-1642	391	52	)	)	PUNCT
asir-1642	391	53	=	=	PUNCT
asir-1642	392	1	l	l	NOUN
asir-1642	392	2	2	2	NUM
asir-1642	392	3	m	m	NOUN
asir-1642	392	4	,	,	PUNCT
asir-1642	392	5	since	since	SCONJ
asir-1642	392	6	r	r	NOUN
asir-1642	392	7	w	w	PROPN
asir-1642	392	8	=	=	SYM
asir-1642	392	9	v	v	PROPN
asir-1642	392	10	and	and	CCONJ
asir-1642	392	11	,	,	PUNCT
asir-1642	392	12	m	m	VERB
asir-1642	392	13	r²	r²	VERB
asir-1642	392	14	w	w	PROPN
asir-1642	392	15	=	=	SYM
asir-1642	392	16	l.	l.	NOUN
asir-1642	392	17	²	²	NUM
asir-1642	392	18	.	.	PUNCT
asir-1642	393	1	since	since	SCONJ
asir-1642	393	2	also	also	ADV
asir-1642	393	3	l	l	PROPN
asir-1642	393	4	is	be	AUX
asir-1642	393	5	a	a	DET
asir-1642	393	6	constant	constant	ADJ
asir-1642	393	7	,	,	PUNCT
asir-1642	393	8	according	accord	VERB
asir-1642	393	9	to	to	ADP
asir-1642	393	10	kepler	kepler	PROPN
asir-1642	393	11	second	second	ADJ
asir-1642	393	12	law	law	NOUN
asir-1642	393	13	radius	radius	NOUN
asir-1642	393	14	r	r	NOUN
asir-1642	393	15	,	,	PUNCT
asir-1642	393	16	sweeps	sweep	VERB
asir-1642	393	17	out	out	ADP
asir-1642	393	18	equal	equal	ADJ
asir-1642	393	19	areas	area	NOUN
asir-1642	393	20	during	during	ADP
asir-1642	393	21	equal	equal	ADJ
asir-1642	393	22	intervals	interval	NOUN
asir-1642	393	23	of	of	ADP
asir-1642	393	24	time	time	NOUN
asir-1642	393	25	and	and	CCONJ
asir-1642	393	26	for	for	ADP
asir-1642	393	27	the	the	DET
asir-1642	393	28	total	total	ADJ
asir-1642	393	29	area	area	NOUN
asir-1642	393	30	→	→	PUNCT
asir-1642	393	31	π	π	X
asir-1642	393	32	ab	ab	X
asir-1642	393	33	=	=	PUNCT
asir-1642	393	34	s	s	PART
asir-1642	393	35	=	=	NOUN
asir-1642	393	36	∫	∫	PROPN
asir-1642	393	37	l	l	NOUN
asir-1642	393	38	2	2	NUM
asir-1642	393	39	m	m	NOUN
asir-1642	393	40	dt	dt	NOUN
asir-1642	394	1	=	=	SYM
asir-1642	394	2	lt	lt	PRON
asir-1642	394	3	2	2	NUM
asir-1642	394	4	m	m	NOUN
asir-1642	394	5	,	,	PUNCT
asir-1642	394	6	and	and	CCONJ
asir-1642	394	7	t	t	PROPN
asir-1642	394	8	is	be	AUX
asir-1642	394	9	the	the	DET
asir-1642	394	10	period	period	NOUN
asir-1642	394	11	of	of	ADP
asir-1642	394	12	rotation	rotation	NOUN
asir-1642	394	13	.	.	PUNCT
asir-1642	395	1	from	from	ADP
asir-1642	395	2	above	above	ADP
asir-1642	395	3	s²	s²	NOUN
asir-1642	395	4	=	=	SYM
asir-1642	395	5	l²	l²	NOUN
asir-1642	395	6	t²	t²	NOUN
asir-1642	395	7	m²	m²	PROPN
asir-1642	395	8	=	=	SYM
asir-1642	395	9	π²a²	π²a²	X
asir-1642	395	10	[	[	PUNCT
asir-1642	395	11	b	b	X
asir-1642	395	12	=	=	SYM
asir-1642	395	13	π	π	X
asir-1642	395	14	a	a	X
asir-1642	395	15	(	(	PUNCT
asir-1642	395	16	l²	l²	NOUN
asir-1642	395	17	2	2	NUM
asir-1642	395	18	m	m	NOUN
asir-1642	395	19	)	)	PUNCT
asir-1642	395	20	]	]	PUNCT
asir-1642	395	21	,	,	PUNCT
asir-1642	395	22	or	or	CCONJ
asir-1642	395	23	t	t	X
asir-1642	395	24	²	²	NUM
asir-1642	395	25	a	a	DET
asir-1642	395	26	²	²	NUM
asir-1642	395	27	=	=	PUNCT
asir-1642	395	28	²m	²m	ADJ
asir-1642	395	29	2	2	NUM
asir-1642	395	30	=	=	SYM
asir-1642	395	31	²	²	NUM
asir-1642	395	32	2	2	NUM
asir-1642	395	33	m	m	NOUN
asir-1642	395	34	=	=	NUM
asir-1642	395	35	²	²	NUM
asir-1642	395	36	a	a	DET
asir-1642	395	37	gm	gm	PROPN
asir-1642	395	38	and	and	CCONJ
asir-1642	395	39	→	→	SYM
asir-1642	395	40	𝐓	𝐓	PROPN
asir-1642	395	41	²	²	PROPN
asir-1642	395	42	𝐚	𝐚	PROPN
asir-1642	395	43	³	³	X
asir-1642	395	44	=	=	X
asir-1642	395	45	𝟒𝛑²	𝟒𝛑²	NOUN
asir-1642	395	46	𝐆𝐌	𝐆𝐌	NOUN
asir-1642	395	47	=	=	PUNCT
asir-1642	395	48	constant	constant	ADJ
asir-1642	395	49	.	.	PUNCT
asir-1642	396	1	from	from	ADP
asir-1642	396	2	relation	relation	NOUN
asir-1642	396	3	t	t	PROPN
asir-1642	396	4	²	²	NUM
asir-1642	396	5	a	a	DET
asir-1642	396	6	³	³	X
asir-1642	396	7	=	=	SYM
asir-1642	396	8	²	²	NUM
asir-1642	396	9	gm	gm	NOUN
asir-1642	396	10	=	=	PUNCT
asir-1642	396	11	k	k	PROPN
asir-1642	396	12	=	=	SYM
asir-1642	396	13	f	f	PROPN
asir-1642	396	14	²	²	NUM
asir-1642	396	15	.a	.a	NOUN
asir-1642	396	16	³	³	NUM
asir-1642	396	17	becomes	become	VERB
asir-1642	396	18	→	→	SYM
asir-1642	396	19	1	1	NUM
asir-1642	396	20	=	=	SYM
asir-1642	396	21	k.𝐟	k.𝐟	PROPN
asir-1642	396	22	²𝐧.	²𝐧.	PROPN
asir-1642	396	23	𝐚𝟑	𝐚𝟑	PROPN
asir-1642	397	1	=	=	X
asir-1642	397	2	𝟒𝛑²	𝟒𝛑²	PRON
asir-1642	397	3	𝐆𝐌	𝐆𝐌	PROPN
asir-1642	397	4	.	.	PUNCT
asir-1642	398	1	𝐟	𝐟	PRON
asir-1642	398	2	²𝐧.	²𝐧.	PROPN
asir-1642	398	3	𝐚𝟑	𝐚𝟑	PROPN
asir-1642	398	4	…	…	PUNCT
asir-1642	398	5	…	…	PUNCT
asir-1642	398	6	(	(	PUNCT
asir-1642	398	7	d	d	X
asir-1642	398	8	)	)	PUNCT
asir-1642	398	9	from	from	ADP
asir-1642	398	10	web	web	NOUN
asir-1642	398	11	r²(θ	r²(θ	PROPN
asir-1642	398	12	)	)	PUNCT
asir-1642	398	13	=	=	PUNCT
asir-1642	399	1	[	[	PUNCT
asir-1642	399	2	l²	l²	NOUN
asir-1642	399	3	m	m	NOUN
asir-1642	399	4			PROPN
asir-1642	399	5	√	√	PROPN
asir-1642	399	6	²	²	NUM
asir-1642	399	7	kl	kl	NOUN
asir-1642	399	8	m	m	PROPN
asir-1642	399	9	)	)	PUNCT
asir-1642	399	10	2(θ	2(θ	NUM
asir-1642	399	11	θ0	θ0	PROPN
asir-1642	399	12	)	)	PUNCT
asir-1642	399	13	]	]	PUNCT
asir-1642	399	14	…	…	PUNCT
asir-1642	399	15	…	…	PUNCT
asir-1642	399	16	.	.	PUNCT
asir-1642	400	1	(	(	PUNCT
asir-1642	400	2	e	e	NOUN
asir-1642	400	3	)	)	PUNCT
asir-1642	400	4	which	which	PRON
asir-1642	400	5	is	be	AUX
asir-1642	400	6	an	an	DET
asir-1642	400	7	ellipse	ellipse	NOUN
asir-1642	400	8	.	.	PUNCT
asir-1642	401	1	equation	equation	NOUN
asir-1642	401	2	(	(	PUNCT
asir-1642	401	3	e	e	NOUN
asir-1642	401	4	)	)	PUNCT
asir-1642	401	5	denotes	denote	NOUN
asir-1642	401	6	ellipses	ellipsis	NOUN
asir-1642	401	7	and	and	CCONJ
asir-1642	401	8	circle	circle	NOUN
asir-1642	401	9	,	,	PUNCT
asir-1642	401	10	having	have	VERB
asir-1642	401	11	a	a	DET
asir-1642	401	12	constant	constant	ADJ
asir-1642	401	13	energy	energy	NOUN
asir-1642	401	14	-	-	PUNCT
asir-1642	401	15	shape	shape	NOUN
asir-1642	401	16	when	when	SCONJ
asir-1642	401	17	are	be	AUX
asir-1642	401	18	given	give	VERB
asir-1642	401	19	the	the	DET
asir-1642	401	20	geometrical	geometrical	ADJ
asir-1642	401	21	parameters	parameter	NOUN
asir-1642	401	22	related	relate	VERB
asir-1642	401	23	to	to	ADP
asir-1642	401	24	the	the	DET
asir-1642	401	25	physical	physical	ADJ
asir-1642	401	26	parameters	parameter	NOUN
asir-1642	401	27	,	,	PUNCT
asir-1642	401	28	angular	angular	ADJ
asir-1642	401	29	momentum	momentum	NOUN
asir-1642	401	30	(	(	PUNCT
asir-1642	401	31	l	l	NOUN
asir-1642	401	32	)	)	PUNCT
asir-1642	401	33	,	,	PUNCT
asir-1642	401	34	total	total	ADJ
asir-1642	401	35	energy	energy	NOUN
asir-1642	401	36	(	(	PUNCT
asir-1642	401	37	e	e	NOUN
asir-1642	401	38	)	)	PUNCT
asir-1642	401	39	.	.	PUNCT
asir-1642	402	1	for	for	ADP
asir-1642	402	2	a	a	DET
asir-1642	402	3	central	central	ADJ
asir-1642	402	4	gravitational	gravitational	ADJ
asir-1642	402	5	force	force	NOUN
asir-1642	402	6	,	,	PUNCT
asir-1642	402	7	the	the	DET
asir-1642	402	8	potential	potential	ADJ
asir-1642	402	9	-	-	PUNCT
asir-1642	402	10	energy	energy	NOUN
asir-1642	402	11	p	p	NOUN
asir-1642	402	12	=	=	X
asir-1642	402	13	gmm	gmm	X
asir-1642	402	14	/	/	SYM
asir-1642	402	15	r	r	NOUN
asir-1642	402	16	and	and	CCONJ
asir-1642	402	17	,	,	PUNCT
asir-1642	402	18	θ(r	θ(r	X
asir-1642	402	19	)	)	PUNCT
asir-1642	403	1	=	=	SYM
asir-1642	403	2	∫𝑑𝜃	∫𝑑𝜃	NOUN
asir-1642	403	3	=	=	PUNCT
asir-1642	404	1			PROPN
asir-1642	404	2	𝑙	𝑙	PROPN
asir-1642	404	3	√2	√2	PROPN
asir-1642	404	4	m	m	NOUN
asir-1642	404	5	∫	∫	PROPN
asir-1642	404	6	𝑑𝑟	𝑑𝑟	PROPN
asir-1642	404	7	𝑟²	𝑟²	PROPN
asir-1642	404	8	√	√	PUNCT
asir-1642	404	9	²+	²+	PROPN
asir-1642	404	10	gmm	gmm	PROPN
asir-1642	404	11	l	l	PROPN
asir-1642	404	12	2	2	NUM
asir-1642	404	13	m	m	NOUN
asir-1642	404	14	𝑟	𝑟	NOUN
asir-1642	404	15	0	0	NUM
asir-1642	404	16	…	…	PUNCT
asir-1642	404	17	……	……	NOUN
asir-1642	404	18	(	(	PUNCT
asir-1642	404	19	f	f	X
asir-1642	404	20	)	)	PUNCT
asir-1642	404	21	placing	placing	NOUN
asir-1642	404	22	,	,	PUNCT
asir-1642	404	23	a	a	PRON
asir-1642	404	24	=	=	X
asir-1642	404	25	l²/2	l²/2	PROPN
asir-1642	404	26	m	m	PROPN
asir-1642	404	27	,	,	PUNCT
asir-1642	404	28	b	b	X
asir-1642	404	29	=	=	SYM
asir-1642	404	30	gmm	gmm	PROPN
asir-1642	404	31	,	,	PUNCT
asir-1642	404	32	c	c	X
asir-1642	404	33	=	=	SYM
asir-1642	404	34	e	e	NOUN
asir-1642	404	35	,	,	PUNCT
asir-1642	404	36	then	then	ADV
asir-1642	404	37	,	,	PUNCT
asir-1642	404	38	∫	∫	PROPN
asir-1642	404	39	𝑑𝑟	𝑑𝑟	VERB
asir-1642	404	40	𝑟	𝑟	PRON
asir-1642	404	41	√a+	√a+	PROPN
asir-1642	404	42	b	b	PROPN
asir-1642	405	1	+	+	CCONJ
asir-1642	405	2	c	c	NOUN
asir-1642	405	3	𝑟	𝑟	NOUN
asir-1642	405	4	0	0	PUNCT
asir-1642	406	1	=	=	SYM
asir-1642	406	2	√	√	NUM
asir-1642	406	3	𝑎	𝑎	NOUN
asir-1642	406	4	.	.	PUNCT
asir-1642	407	1	(	(	PUNCT
asir-1642	407	2	b	b	X
asir-1642	407	3	+2a	+2a	NUM
asir-1642	407	4	𝑟√b²	𝑟√b²	NUM
asir-1642	407	5	ac	ac	PROPN
asir-1642	407	6	)	)	PUNCT
asir-1642	407	7	…	…	PUNCT
asir-1642	407	8	…	…	PUNCT
asir-1642	407	9	(	(	PUNCT
asir-1642	407	10	f1	f1	NOUN
asir-1642	407	11	)	)	PUNCT
asir-1642	407	12	and	and	CCONJ
asir-1642	407	13	θ	θ	PROPN
asir-1642	407	14	0	0	PUNCT
asir-1642	408	1	=	=	SYM
asir-1642	408	2			PROPN
asir-1642	408	3	(	(	PUNCT
asir-1642	408	4	gmm²	gmm²	PROPN
asir-1642	408	5	l²	l²	PROPN
asir-1642	408	6	𝐺𝑀𝑚²𝑟	𝐺𝑀𝑚²𝑟	PROPN
asir-1642	408	7	)	)	PUNCT
asir-1642	408	8	and	and	CCONJ
asir-1642	408	9	eccentricity	eccentricity	NOUN
asir-1642	408	10	e	e	X
asir-1642	408	11	=	=	PUNCT
asir-1642	408	12	√1	√1	PROPN
asir-1642	408	13	+	+	CCONJ
asir-1642	408	14	²	²	NUM
asir-1642	408	15	g²m²m³	g²m²m³	NOUN
asir-1642	408	16	…	…	PUNCT
asir-1642	408	17	…	…	PUNCT
asir-1642	408	18	(	(	PUNCT
asir-1642	408	19	f2	f2	PROPN
asir-1642	408	20	)	)	PUNCT
asir-1642	408	21	where	where	SCONJ
asir-1642	408	22	0	0	NUM
asir-1642	408	23	is	be	AUX
asir-1642	408	24	a	a	DET
asir-1642	408	25	constant	constant	ADJ
asir-1642	408	26	of	of	ADP
asir-1642	408	27	integration	integration	NOUN
asir-1642	408	28	.	.	PUNCT
asir-1642	409	1	solving	solve	VERB
asir-1642	409	2	for	for	ADP
asir-1642	409	3	r	r	NOUN
asir-1642	409	4	then	then	ADV
asir-1642	409	5	r	r	NOUN
asir-1642	409	6	=	=	SYM
asir-1642	409	7	l²	l²	NOUN
asir-1642	409	8	gmm²	gmm²	PROPN
asir-1642	409	9			PROPN
asir-1642	409	10	e	e	PROPN
asir-1642	409	11	(	(	PUNCT
asir-1642	409	12	θ	θ	PROPN
asir-1642	409	13	θ0	θ0	PROPN
asir-1642	409	14	)	)	PUNCT
asir-1642	409	15	=	=	SYM
asir-1642	409	16	l²	l²	VERB
asir-1642	409	17	gmm²	gmm²	PROPN
asir-1642	409	18	+	+	CCONJ
asir-1642	409	19	e.co	e.co	PROPN
asir-1642	409	20	θ	θ	NOUN
asir-1642	409	21	at	at	ADP
asir-1642	409	22	periapsis	periapsis	NOUN
asir-1642	409	23	…	…	PUNCT
asir-1642	409	24	(f3	(f3	X
asir-1642	409	25	)	)	PUNCT
asir-1642	409	26	creates	create	VERB
asir-1642	409	27	only	only	ADV
asir-1642	409	28	one	one	NUM
asir-1642	409	29	energy	energy	NOUN
asir-1642	409	30	-	-	PUNCT
asir-1642	409	31	rim	rim	NOUN
asir-1642	409	32	.	.	PUNCT
asir-1642	410	1	velocity	velocity	NOUN
asir-1642	410	2	related	relate	VERB
asir-1642	410	3	to	to	ADP
asir-1642	410	4	the	the	DET
asir-1642	410	5	distance	distance	NOUN
asir-1642	411	1	[	[	X
asir-1642	411	2	r	r	X
asir-1642	411	3	]	]	X
asir-1642	411	4	of	of	ADP
asir-1642	411	5	the	the	DET
asir-1642	411	6	planet	planet	NOUN
asir-1642	411	7	[	[	X
asir-1642	411	8	the	the	DET
asir-1642	411	9	orbiter	orbiter	NOUN
asir-1642	411	10	]	]	PUNCT
asir-1642	411	11	,	,	PUNCT
asir-1642	411	12	to	to	ADP
asir-1642	411	13	the	the	DET
asir-1642	411	14	sun	sun	NOUN
asir-1642	411	15	[	[	X
asir-1642	411	16	the	the	DET
asir-1642	411	17	focus	focus	NOUN
asir-1642	411	18	]	]	PUNCT
asir-1642	411	19	,	,	PUNCT
asir-1642	411	20	is	be	AUX
asir-1642	411	21	from	from	ADP
asir-1642	411	22	figure	figure	NOUN
asir-1642	411	23	6	6	NUM
asir-1642	411	24	,	,	PUNCT
asir-1642	411	25	the	the	DET
asir-1642	411	26	velocity	velocity	NOUN
asir-1642	411	27	equation	equation	NOUN
asir-1642	411	28	in	in	ADP
asir-1642	411	29	a	a	DET
asir-1642	411	30	central	central	ADJ
asir-1642	411	31	motion	motion	NOUN
asir-1642	411	32	is	be	AUX
asir-1642	411	33	v²	v²	PROPN
asir-1642	411	34	=	=	SYM
asir-1642	411	35	4c²	4c²	PROPN
asir-1642	411	36	.	.	PUNCT
asir-1642	412	1	[	[	PUNCT
asir-1642	412	2	e²	e²	AUX
asir-1642	412	3	²φ	²φ	VERB
asir-1642	412	4	+	+	CCONJ
asir-1642	412	5	𝑟²	𝑟²	PROPN
asir-1642	412	6	]	]	X
asir-1642	412	7	…	…	PUNCT
asir-1642	412	8	(	(	PUNCT
asir-1642	412	9	f4	f4	NOUN
asir-1642	412	10	)	)	PUNCT
asir-1642	412	11	where	where	SCONJ
asir-1642	412	12	constant	constant	ADJ
asir-1642	412	13	c	c	X
asir-1642	412	14	=	=	SYM
asir-1642	412	15	ab	ab	PROPN
asir-1642	412	16	t	t	PROPN
asir-1642	412	17	=	=	PUNCT
asir-1642	412	18	π	π	PROPN
asir-1642	412	19	ab	ab	PROPN
asir-1642	412	20	,	,	PUNCT
asir-1642	412	21	=	=	PROPN
asir-1642	412	22	s	s	PROPN
asir-1642	412	23	t	t	NOUN
asir-1642	412	24	=	=	SYM
asir-1642	412	25	r²dφ/2	r²dφ/2	VERB
asir-1642	412	26	=	=	NOUN
asir-1642	412	27	the	the	DET
asir-1642	412	28	covered	cover	VERB
asir-1642	412	29	orbiting	orbit	VERB
asir-1642	412	30	area	area	NOUN
asir-1642	412	31	per	per	ADP
asir-1642	412	32	time	time	NOUN
asir-1642	412	33	second	second	ADJ
asir-1642	412	34	,	,	PUNCT
asir-1642	412	35	and	and	CCONJ
asir-1642	412	36	(	(	PUNCT
asir-1642	412	37	)	)	PUNCT
asir-1642	412	38	φ	φ	PROPN
asir-1642	412	39	=	=	SYM
asir-1642	412	40	e	e	PROPN
asir-1642	412	41	φ	φ	PROPN
asir-1642	412	42	.	.	PUNCT
asir-1642	413	1	from	from	ADP
asir-1642	413	2	a(1	a(1	ADJ
asir-1642	413	3	)	)	PUNCT
asir-1642	413	4	r	r	NOUN
asir-1642	414	1	=	=	PUNCT
asir-1642	414	2	+	+	PROPN
asir-1642	414	3	eco	eco	PROPN
asir-1642	414	4	φ	φ	NOUN
asir-1642	414	5	and	and	CCONJ
asir-1642	414	6	velocity	velocity	NOUN
asir-1642	414	7	is	be	AUX
asir-1642	414	8	,	,	PUNCT
asir-1642	414	9	v²	v²	PROPN
asir-1642	414	10	=	=	SYM
asir-1642	414	11	4c²	4c²	PROPN
asir-1642	414	12	.	.	PUNCT
asir-1642	415	1	[	[	PUNCT
asir-1642	415	2	e²	e²	AUX
asir-1642	415	3	²φ	²φ	VERB
asir-1642	415	4	²	²	NUM
asir-1642	415	5	+	+	CCONJ
asir-1642	416	1	+	+	ADP
asir-1642	416	2	e²	e²	PROPN
asir-1642	416	3	co	co	X
asir-1642	416	4	²φ+2eco	²φ+2eco	PROPN
asir-1642	416	5	φ	φ	PROPN
asir-1642	416	6	²	²	PROPN
asir-1642	416	7	]=	]=	NUM
asir-1642	416	8	𝐶²	𝐶²	NOUN
asir-1642	416	9	𝑝²	𝑝²	NOUN
asir-1642	416	10	[	[	X
asir-1642	416	11	e²+1	e²+1	PROPN
asir-1642	416	12	+	+	ADJ
asir-1642	416	13	2eco	2eco	NOUN
asir-1642	416	14	]=	]=	NUM
asir-1642	416	15	c²	c²	NOUN
asir-1642	416	16	[	[	PUNCT
asir-1642	416	17	e²+	e²+	PROPN
asir-1642	416	18	+	+	CCONJ
asir-1642	416	19	2	2	NUM
asir-1642	416	20	2	2	NUM
asir-1642	416	21	]	]	PUNCT
asir-1642	416	22	=	=	SYM
asir-1642	416	23	c²	c²	NOUN
asir-1642	416	24	[	[	PUNCT
asir-1642	416	25	2	2	NUM
asir-1642	416	26	e²	e²	NOUN
asir-1642	416	27	]	]	PUNCT
asir-1642	416	28	…	…	PUNCT
asir-1642	416	29	(	(	PUNCT
asir-1642	416	30	f5	f5	NOUN
asir-1642	416	31	)	)	PUNCT
asir-1642	416	32	and	and	CCONJ
asir-1642	416	33	for	for	ADP
asir-1642	416	34	ellipse	ellipse	NOUN
asir-1642	416	35	issuing	issue	VERB
asir-1642	416	36	2a	2a	NUM
asir-1642	416	37	=	=	SYM
asir-1642	416	38	rφ	rφ	VERB
asir-1642	416	39	0+rφ	0+rφ	X
asir-1642	416	40	a	a	DET
asir-1642	416	41	=	=	SYM
asir-1642	416	42	+	+	NOUN
asir-1642	416	43	e	e	NOUN
asir-1642	416	44	+	+	NOUN
asir-1642	416	45	e	e	NOUN
asir-1642	416	46	=	=	SYM
asir-1642	416	47	2	2	NUM
asir-1642	416	48	e²	e²	NOUN
asir-1642	416	49	therefore	therefore	ADV
asir-1642	416	50	,	,	PUNCT
asir-1642	416	51	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	416	52	applied	apply	VERB
asir-1642	416	53	science	science	NOUN
asir-1642	416	54	and	and	CCONJ
asir-1642	416	55	innovative	innovative	ADJ
asir-1642	416	56	research	research	NOUN
asir-1642	416	57	vol	vol	NOUN
asir-1642	416	58	.	.	PROPN
asir-1642	417	1	2	2	NUM
asir-1642	417	2	,	,	PUNCT
asir-1642	417	3	no	no	INTJ
asir-1642	417	4	.	.	NOUN
asir-1642	417	5	4	4	NUM
asir-1642	417	6	,	,	PUNCT
asir-1642	417	7	2018	2018	NUM
asir-1642	417	8	175	175	NUM
asir-1642	417	9	published	publish	VERB
asir-1642	417	10	by	by	ADP
asir-1642	417	11	scholink	scholink	PROPN
asir-1642	417	12	inc	inc	PROPN
asir-1642	417	13	.	.	PROPN
asir-1642	417	14	v²	v²	PROPN
asir-1642	417	15	=	=	SYM
asir-1642	417	16	c²	c²	PROPN
asir-1642	417	17	[	[	PUNCT
asir-1642	417	18	2	2	NUM
asir-1642	417	19	e²	e²	NOUN
asir-1642	417	20	]	]	PUNCT
asir-1642	418	1	=	=	PUNCT
asir-1642	418	2	𝟒𝐂²	𝟒𝐂²	PUNCT
asir-1642	419	1	𝐩	𝐩	X
asir-1642	419	2	[	[	PUNCT
asir-1642	419	3	𝟐	𝟐	NUM
asir-1642	419	4	𝐫	𝐫	SYM
asir-1642	419	5	𝐚	𝐚	X
asir-1642	419	6	]	]	PUNCT
asir-1642	419	7	…	…	PUNCT
asir-1642	419	8	…	…	PUNCT
asir-1642	419	9	.(f6	.(f6	NOUN
asir-1642	419	10	)	)	PUNCT
asir-1642	419	11	from	from	ADP
asir-1642	419	12	(	(	PUNCT
asir-1642	419	13	f6	f6	PROPN
asir-1642	419	14	)	)	PUNCT
asir-1642	419	15	,	,	PUNCT
asir-1642	419	16	when	when	SCONJ
asir-1642	419	17	planet	planet	NOUN
asir-1642	419	18	is	be	AUX
asir-1642	419	19	at	at	ADP
asir-1642	419	20	perihelion	perihelion	NOUN
asir-1642	419	21	near	near	ADP
asir-1642	419	22	the	the	DET
asir-1642	419	23	sun	sun	NOUN
asir-1642	419	24	=	=	PUNCT
asir-1642	420	1	+	+	NUM
asir-1642	420	2	e	e	NOUN
asir-1642	420	3	,	,	PUNCT
asir-1642	420	4	then	then	ADV
asir-1642	420	5	velocity	velocity	NOUN
asir-1642	420	6	is	be	AUX
asir-1642	420	7	v²	v²	PROPN
asir-1642	420	8	=	=	SYM
asir-1642	420	9	c²	c²	PROPN
asir-1642	420	10	[	[	PUNCT
asir-1642	420	11	2	2	NUM
asir-1642	420	12	e²	e²	NOUN
asir-1642	420	13	]	]	PUNCT
asir-1642	421	1	=	=	PUNCT
asir-1642	421	2	c²	c²	NOUN
asir-1642	421	3	[	[	PUNCT
asir-1642	421	4	2	2	NUM
asir-1642	421	5	e	e	NOUN
asir-1642	421	6	]	]	PUNCT
asir-1642	421	7	=	=	SYM
asir-1642	421	8	𝟒𝐂²	𝟒𝐂²	NOUN
asir-1642	421	9	𝐩	𝐩	X
asir-1642	421	10	[	[	PUNCT
asir-1642	421	11	+	+	NOUN
asir-1642	421	12	𝐞	𝐞	NOUN
asir-1642	421	13	𝐫	𝐫	X
asir-1642	421	14	]	]	PUNCT
asir-1642	421	15	,	,	PUNCT
asir-1642	421	16	where	where	SCONJ
asir-1642	421	17	c²	c²	NOUN
asir-1642	421	18	=	=	PRON
asir-1642	421	19	(	(	PUNCT
asir-1642	421	20	ab	ab	PROPN
asir-1642	421	21	t)²	t)²	PROPN
asir-1642	421	22	b²	b²	VERB
asir-1642	421	23	a	a	PRON
asir-1642	421	24	=	=	SYM
asir-1642	421	25	4π²	4π²	NUM
asir-1642	421	26	a³	a³	PROPN
asir-1642	421	27	t²	t²	NOUN
asir-1642	421	28	,	,	PUNCT
asir-1642	421	29	which	which	PRON
asir-1642	421	30	is	be	AUX
asir-1642	421	31	the	the	DET
asir-1642	421	32	kepler	kepler	PROPN
asir-1642	421	33	constant	constant	ADJ
asir-1642	421	34	,	,	PUNCT
asir-1642	421	35	and	and	CCONJ
asir-1642	421	36	v²	v²	PROPN
asir-1642	421	37	=	=	SYM
asir-1642	421	38	4π²	4π²	NUM
asir-1642	422	1	a³	a³	ADJ
asir-1642	422	2	t²	t²	NOUN
asir-1642	422	3	[	[	PUNCT
asir-1642	422	4	+	+	NOUN
asir-1642	422	5	e	e	NOUN
asir-1642	422	6	]	]	PUNCT
asir-1642	422	7	=	=	PUNCT
asir-1642	423	1	[	[	X
asir-1642	423	2	4	4	NUM
asir-1642	423	3	π²a³.	π²a³.	NOUN
asir-1642	423	4	²	²	NUM
asir-1642	423	5	]	]	PUNCT
asir-1642	423	6	.	.	PUNCT
asir-1642	424	1	[	[	PUNCT
asir-1642	424	2	+	+	NOUN
asir-1642	424	3	e	e	X
asir-1642	424	4	]	]	PUNCT
asir-1642	424	5	=	=	SYM
asir-1642	424	6	k	k	X
asir-1642	424	7	[	[	PUNCT
asir-1642	424	8	+	+	NOUN
asir-1642	424	9	e	e	X
asir-1642	424	10	]	]	PUNCT
asir-1642	424	11	…	…	PUNCT
asir-1642	424	12	…	…	PUNCT
asir-1642	424	13	.(f6a	.(f6a	NUM
asir-1642	424	14	)	)	PUNCT
asir-1642	424	15	,	,	PUNCT
asir-1642	424	16	the	the	DET
asir-1642	424	17	velocity	velocity	NOUN
asir-1642	424	18	at	at	ADP
asir-1642	424	19	perihelion	perihelion	NOUN
asir-1642	424	20	for	for	ADP
asir-1642	424	21	eccentricity	eccentricity	NOUN
asir-1642	424	22	e	e	X
asir-1642	424	23	<	<	X
asir-1642	424	24	1	1	NUM
asir-1642	424	25	→	→	SYM
asir-1642	424	26	v²	v²	PROPN
asir-1642	424	27	=	=	SYM
asir-1642	424	28	k	k	PROPN
asir-1642	425	1	[	[	PUNCT
asir-1642	425	2	+	+	NOUN
asir-1642	425	3	e	e	NOUN
asir-1642	425	4	]	]	PUNCT
asir-1642	425	5	<	<	X
asir-1642	425	6	k	k	PROPN
asir-1642	425	7	2	2	NUM
asir-1642	425	8	and	and	CCONJ
asir-1642	425	9	planet	planet	NOUN
asir-1642	425	10	follows	follow	VERB
asir-1642	425	11	elliptic	elliptic	ADJ
asir-1642	425	12	orbit	orbit	NOUN
asir-1642	425	13	.	.	PUNCT
asir-1642	426	1	for	for	ADP
asir-1642	426	2	eccentricity	eccentricity	NOUN
asir-1642	426	3	e	e	NOUN
asir-1642	426	4	=	=	SYM
asir-1642	426	5	1	1	NUM
asir-1642	426	6	→	→	SYM
asir-1642	426	7	v²	v²	PROPN
asir-1642	426	8	=	=	SYM
asir-1642	426	9	k	k	PROPN
asir-1642	426	10	[	[	PUNCT
asir-1642	426	11	+	+	NOUN
asir-1642	426	12	e	e	NOUN
asir-1642	426	13	]	]	PUNCT
asir-1642	426	14	=	=	SYM
asir-1642	426	15	k	k	PROPN
asir-1642	426	16	2	2	NUM
asir-1642	426	17	and	and	CCONJ
asir-1642	426	18	planet	planet	NOUN
asir-1642	426	19	follows	follow	VERB
asir-1642	426	20	parabolic	parabolic	NOUN
asir-1642	426	21	-	-	PUNCT
asir-1642	426	22	orbit	orbit	NOUN
asir-1642	426	23	for	for	ADP
asir-1642	427	1	eccentricity	eccentricity	NOUN
asir-1642	427	2	e	e	X
asir-1642	427	3	>	>	X
asir-1642	427	4	1	1	NUM
asir-1642	427	5	→	→	SYM
asir-1642	427	6	v²	v²	PROPN
asir-1642	427	7	=	=	SYM
asir-1642	427	8	k	k	PROPN
asir-1642	428	1	[	[	PUNCT
asir-1642	428	2	+	+	NOUN
asir-1642	428	3	e	e	NOUN
asir-1642	428	4	]	]	PUNCT
asir-1642	428	5	>	>	X
asir-1642	428	6	k	k	PROPN
asir-1642	428	7	2	2	NUM
asir-1642	428	8	and	and	CCONJ
asir-1642	428	9	planet	planet	NOUN
asir-1642	428	10	follows	follow	VERB
asir-1642	428	11	hyperbolic	hyperbolic	ADJ
asir-1642	428	12	-	-	PUNCT
asir-1642	428	13	orbit	orbit	NOUN
asir-1642	428	14	in	in	ADP
asir-1642	428	15	a	a	DET
asir-1642	428	16	circular	circular	ADJ
asir-1642	428	17	motion	motion	NOUN
asir-1642	428	18	is	be	AUX
asir-1642	428	19	shown	show	VERB
asir-1642	428	20	that	that	SCONJ
asir-1642	428	21	,	,	PUNCT
asir-1642	428	22	velocity	velocity	NOUN
asir-1642	428	23	is	be	AUX
asir-1642	428	24	proportional	proportional	ADJ
asir-1642	428	25	to	to	ADP
asir-1642	428	26	the	the	DET
asir-1642	428	27	inverse	inverse	NOUN
asir-1642	428	28	square	square	NOUN
asir-1642	428	29	of	of	ADP
asir-1642	428	30	radius	radius	NOUN
asir-1642	428	31	r	r	NOUN
asir-1642	428	32	,	,	PUNCT
asir-1642	428	33	and	and	CCONJ
asir-1642	428	34	newton	newton	PROPN
asir-1642	428	35	-	-	PUNCT
asir-1642	428	36	force	force	NOUN
asir-1642	428	37	,	,	PUNCT
asir-1642	428	38	acceleration	acceleration	NOUN
asir-1642	428	39	,	,	PUNCT
asir-1642	428	40	the	the	DET
asir-1642	428	41	fifth	fifth	ADJ
asir-1642	428	42	,	,	PUNCT
asir-1642	428	43	where	where	SCONJ
asir-1642	428	44	c	c	NOUN
asir-1642	428	45	=	=	SYM
asir-1642	428	46	ab	ab	PROPN
asir-1642	428	47	t	t	PROPN
asir-1642	428	48	=	=	PUNCT
asir-1642	428	49	a	a	DET
asir-1642	428	50	t	t	NOUN
asir-1642	428	51	[	[	PUNCT
asir-1642	428	52	²	²	X
asir-1642	428	53	]	]	PUNCT
asir-1642	428	54	=	=	PUNCT
asir-1642	428	55	a	a	DET
asir-1642	428	56	t	t	NOUN
asir-1642	428	57	²	²	NUM
asir-1642	428	58	,	,	PUNCT
asir-1642	428	59	from	from	ADP
asir-1642	428	60	relation	relation	NOUN
asir-1642	428	61	r	r	NOUN
asir-1642	428	62	=	=	SYM
asir-1642	428	63	2a.co	2a.co	NUM
asir-1642	428	64	is	be	AUX
asir-1642	428	65	,	,	PUNCT
asir-1642	428	66	co	co	ADJ
asir-1642	428	67	=	=	NOUN
asir-1642	428	68	2a	2a	NUM
asir-1642	428	69	and	and	CCONJ
asir-1642	428	70	=	=	SYM
asir-1642	428	71	2aco	2aco	NUM
asir-1642	428	72	φ	φ	PROPN
asir-1642	428	73	also	also	ADV
asir-1642	428	74	𝑑	𝑑	PROPN
asir-1642	428	75	𝑟	𝑟	NOUN
asir-1642	428	76	𝑑𝜑	𝑑𝜑	ADP
asir-1642	428	77	=	=	PUNCT
asir-1642	428	78	,	,	PUNCT
asir-1642	428	79	and	and	CCONJ
asir-1642	428	80	(	(	PUNCT
asir-1642	428	81	f4	f4	NOUN
asir-1642	428	82	)	)	PUNCT
asir-1642	428	83	is	be	AUX
asir-1642	428	84	v²	v²	PROPN
asir-1642	428	85	=	=	SYM
asir-1642	428	86	4c²	4c²	PROPN
asir-1642	428	87	.	.	PUNCT
asir-1642	429	1	[	[	PUNCT
asir-1642	429	2	²	²	NUM
asir-1642	429	3	+	+	NOUN
asir-1642	429	4	1	1	NUM
asir-1642	429	5	]	]	X
asir-1642	429	6	=	=	SYM
asir-1642	429	7	c²	c²	NOUN
asir-1642	429	8	²	²	NUM
asir-1642	429	9	co	co	NOUN
asir-1642	429	10	²φ	²φ	NOUN
asir-1642	429	11	=	=	SYM
asir-1642	429	12	6c²a²	6c²a²	NUM
asir-1642	429	13	4	4	NUM
asir-1642	429	14	and	and	CCONJ
asir-1642	429	15	velocity	velocity	NOUN
asir-1642	429	16	becomes	become	VERB
asir-1642	429	17	v	v	ADP
asir-1642	429	18	=	=	PUNCT
asir-1642	429	19	𝟒𝐂𝐚	𝟒𝐂𝐚	PROPN
asir-1642	429	20	𝐫	𝐫	ADP
asir-1642	429	21	𝟐	𝟐	NUM
asir-1642	429	22	…	…	SYM
asir-1642	429	23	…	…	SYM
asir-1642	429	24	……	……	X
asir-1642	429	25	(	(	PUNCT
asir-1642	429	26	f7	f7	PROPN
asir-1642	429	27	)	)	PUNCT
asir-1642	429	28	centripetal	centripetal	NOUN
asir-1642	429	29	-	-	PUNCT
asir-1642	429	30	acceleration	acceleration	NOUN
asir-1642	429	31	=	=	PUNCT
asir-1642	429	32	v²	v²	NOUN
asir-1642	429	33	=	=	SYM
asir-1642	430	1	6c²a²	6c²a²	NUM
asir-1642	430	2	4	4	NUM
asir-1642	430	3	a	a	DET
asir-1642	430	4	=	=	SYM
asir-1642	430	5	6	6	NUM
asir-1642	430	6	c²a	c²a	NOUN
asir-1642	430	7	4	4	NUM
asir-1642	430	8	and	and	CCONJ
asir-1642	430	9	equal	equal	ADJ
asir-1642	430	10	to	to	ADP
asir-1642	430	11	ap	ap	PROPN
asir-1642	430	12	co	co	PROPN
asir-1642	430	13	φ	φ	PROPN
asir-1642	430	14	,	,	PUNCT
asir-1642	430	15	so	so	ADV
asir-1642	430	16	centripetal	centripetal	ADJ
asir-1642	430	17	acceleration	acceleration	NOUN
asir-1642	430	18	𝐚𝐩	𝐚𝐩	PROPN
asir-1642	430	19	=	=	PUNCT
asir-1642	430	20	𝟑𝟐𝐂²𝐚²	𝟑𝟐𝐂²𝐚²	NOUN
asir-1642	430	21	𝐫	𝐫	ADP
asir-1642	430	22	𝟓	𝟓	NUM
asir-1642	430	23	=	=	SYM
asir-1642	430	24	𝟑𝟐𝛑𝐚𝟒	𝟑𝟐𝛑𝐚𝟒	NOUN
asir-1642	430	25	[	[	PUNCT
asir-1642	430	26	𝐓²	𝐓²	PROPN
asir-1642	430	27	𝐫	𝐫	PROPN
asir-1642	430	28	𝟒	𝟒	PROPN
asir-1642	430	29	[	[	PUNCT
asir-1642	430	30	𝐫	𝐫	ADP
asir-1642	430	31	𝟓	𝟓	NUM
asir-1642	430	32	,	,	PUNCT
asir-1642	430	33	for	for	ADP
asir-1642	430	34	r	r	NOUN
asir-1642	430	35	=	=	PUNCT
asir-1642	430	36	a	a	PRON
asir-1642	430	37	then	then	ADV
asir-1642	430	38	𝐚𝐩=	𝐚𝐩=	ADJ
asir-1642	430	39	𝟑𝟐	𝟑𝟐	NUM
asir-1642	430	40	𝛑	𝛑	ADP
asir-1642	430	41	𝐓²𝐫𝟓	𝐓²𝐫𝟓	NOUN
asir-1642	430	42	…	…	PUNCT
asir-1642	430	43	……	……	NOUN
asir-1642	430	44	(	(	PUNCT
asir-1642	430	45	f8	f8	PROPN
asir-1642	430	46	)	)	PUNCT
asir-1642	430	47	2	2	NUM
asir-1642	430	48	.	.	X
asir-1642	430	49	conclusion	conclusion	NOUN
asir-1642	430	50	1	1	NUM
asir-1642	430	51	..	..	PUNCT
asir-1642	430	52	orbits	orbit	NOUN
asir-1642	430	53	:	:	PUNCT
asir-1642	430	54	in	in	ADP
asir-1642	430	55	orbits	orbit	NOUN
asir-1642	430	56	issues	issue	VERB
asir-1642	430	57	the	the	DET
asir-1642	430	58	piezoelectric	piezoelectric	NOUN
asir-1642	430	59	-	-	PUNCT
asir-1642	430	60	effect	effect	NOUN
asir-1642	430	61	,	,	PUNCT
asir-1642	430	62	as	as	SCONJ
asir-1642	430	63	this	this	PRON
asir-1642	430	64	is	be	AUX
asir-1642	430	65	used	use	VERB
asir-1642	430	66	in	in	ADP
asir-1642	430	67	a	a	DET
asir-1642	430	68	,	,	PUNCT
asir-1642	430	69	lattice	lattice	NOUN
asir-1642	430	70	-	-	PUNCT
asir-1642	430	71	disk	disk	NOUN
asir-1642	430	72	(	(	PUNCT
asir-1642	430	73	orbits	orbit	NOUN
asir-1642	430	74	,	,	PUNCT
asir-1642	430	75	caves	cave	NOUN
asir-1642	430	76	,	,	PUNCT
asir-1642	430	77	material	material	NOUN
asir-1642	430	78	-	-	PUNCT
asir-1642	430	79	points	point	NOUN
asir-1642	430	80	,	,	PUNCT
asir-1642	430	81	particles	particle	NOUN
asir-1642	430	82	,	,	PUNCT
asir-1642	430	83	atoms	atom	NOUN
asir-1642	430	84	,	,	PUNCT
asir-1642	430	85	molecule	molecule	NOUN
asir-1642	430	86	,	,	PUNCT
asir-1642	430	87	crystals	crystal	NOUN
asir-1642	430	88	,	,	PUNCT
asir-1642	430	89	microchips	microchip	NOUN
asir-1642	430	90	,	,	PUNCT
asir-1642	430	91	etc	etc	X
asir-1642	430	92	.	.	X
asir-1642	430	93	)	)	PUNCT
asir-1642	430	94	where	where	SCONJ
asir-1642	430	95	is	be	AUX
asir-1642	430	96	converted	convert	VERB
asir-1642	430	97	the	the	DET
asir-1642	430	98	mechanical	mechanical	ADJ
asir-1642	430	99	energy	energy	NOUN
asir-1642	430	100	which	which	PRON
asir-1642	430	101	is	be	AUX
asir-1642	430	102	work	work	NOUN
asir-1642	430	103	,	,	PUNCT
asir-1642	430	104	into	into	ADP
asir-1642	430	105	electricity	electricity	NOUN
asir-1642	430	106	(	(	PUNCT
asir-1642	430	107	electrical	electrical	ADJ
asir-1642	430	108	potential	potential	NOUN
asir-1642	430	109	as	as	ADP
asir-1642	430	110	a	a	DET
asir-1642	430	111	voltage	voltage	NOUN
asir-1642	430	112	)	)	PUNCT
asir-1642	430	113	,	,	PUNCT
asir-1642	430	114	across	across	ADP
asir-1642	430	115	the	the	DET
asir-1642	430	116	sides	side	NOUN
asir-1642	430	117	of	of	ADP
asir-1642	430	118	the	the	DET
asir-1642	430	119	disk	disk	NOUN
asir-1642	430	120	or	or	CCONJ
asir-1642	430	121	vice	vice	NOUN
asir-1642	430	122	versa	versa	ADV
asir-1642	430	123	,	,	PUNCT
asir-1642	430	124	i.e.	i.e.	X
asir-1642	430	125	,	,	PUNCT
asir-1642	430	126	when	when	SCONJ
asir-1642	430	127	on	on	ADP
asir-1642	430	128	a	a	DET
asir-1642	430	129	lattice	lattice	NOUN
asir-1642	430	130	-	-	PUNCT
asir-1642	430	131	disk	disk	NOUN
asir-1642	430	132	,	,	PUNCT
asir-1642	430	133	is	be	AUX
asir-1642	430	134	put	put	VERB
asir-1642	430	135	a	a	DET
asir-1642	430	136	voltage	voltage	NOUN
asir-1642	430	137	across	across	ADP
asir-1642	430	138	the	the	DET
asir-1642	430	139	disk	disk	NOUN
asir-1642	430	140	,	,	PUNCT
asir-1642	430	141	so	so	ADV
asir-1642	430	142	thus	thus	ADV
asir-1642	430	143	its	its	PRON
asir-1642	430	144	inside	inside	NOUN
asir-1642	430	145	-	-	PUNCT
asir-1642	430	146	content	content	NOUN
asir-1642	430	147	is	be	AUX
asir-1642	430	148	subjecting	subject	VERB
asir-1642	430	149	to	to	ADP
asir-1642	430	150	an	an	DET
asir-1642	430	151	electrical	electrical	ADJ
asir-1642	430	152	-	-	PUNCT
asir-1642	430	153	pressure	pressure	NOUN
asir-1642	430	154	,	,	PUNCT
asir-1642	430	155	inside	inside	NOUN
asir-1642	430	156	-	-	PUNCT
asir-1642	430	157	content	content	NOUN
asir-1642	430	158	has	have	VERB
asir-1642	430	159	to	to	PART
asir-1642	430	160	move	move	VERB
asir-1642	430	161	to	to	ADP
asir-1642	430	162	rebalance	rebalance	NOUN
asir-1642	430	163	,	,	PUNCT
asir-1642	430	164	and	and	CCONJ
asir-1642	430	165	thus	thus	ADV
asir-1642	430	166	deformed	deform	VERB
asir-1642	430	167	.	.	PUNCT
asir-1642	431	1	gravity	gravity	NOUN
asir-1642	431	2	is	be	AUX
asir-1642	431	3	potential	potential	ADJ
asir-1642	431	4	-	-	PUNCT
asir-1642	431	5	energy	energy	NOUN
asir-1642	431	6	with	with	ADP
asir-1642	431	7	binder	binder	NOUN
asir-1642	431	8	energy	energy	NOUN
asir-1642	431	9	-	-	PUNCT
asir-1642	431	10	field	field	NOUN
asir-1642	431	11	{	{	PUNCT
asir-1642	431	12	[	[	X
asir-1642	431	13	i	i	X
asir-1642	431	14	]	]	X
asir-1642	431	15	=	=	PUNCT
asir-1642	432	1	[	[	X
asir-1642	432	2	±	±	NUM
asir-1642	432	3	s²	s²	NOUN
asir-1642	432	4	]	]	PUNCT
asir-1642	432	5	a	a	DET
asir-1642	432	6	constituent	constituent	NOUN
asir-1642	432	7	in	in	ADP
asir-1642	432	8	mfmf	mfmf	NOUN
asir-1642	432	9	field	field	NOUN
asir-1642	432	10	,	,	PUNCT
asir-1642	432	11	the	the	DET
asir-1642	432	12	called	call	VERB
asir-1642	432	13	gravity	gravity	NOUN
asir-1642	432	14	force	force	NOUN
asir-1642	432	15	without	without	ADP
asir-1642	432	16	vibration	vibration	NOUN
asir-1642	432	17	but	but	CCONJ
asir-1642	432	18	only	only	ADV
asir-1642	432	19	local	local	ADJ
asir-1642	432	20	rotation	rotation	NOUN
asir-1642	432	21	}	}	PUNCT
asir-1642	432	22	,	,	PUNCT
asir-1642	432	23	from	from	ADP
asir-1642	432	24	energy	energy	NOUN
asir-1642	432	25	-	-	PUNCT
asir-1642	432	26	vectors	vector	NOUN
asir-1642	432	27	occurring	occur	VERB
asir-1642	432	28	in	in	ADP
asir-1642	432	29	any	any	DET
asir-1642	432	30	material	material	NOUN
asir-1642	432	31	-	-	PUNCT
asir-1642	432	32	point	point	NOUN
asir-1642	432	33	[	[	X
asir-1642	432	34	⊕	⊕	NOUN
asir-1642	432	35	↻	↻	NOUN
asir-1642	432	36	↺	↺	NOUN
asir-1642	432	37	⊝	⊝	NOUN
asir-1642	432	38	]	]	PUNCT
asir-1642	432	39	in	in	ADP
asir-1642	432	40	gravity	gravity	NOUN
asir-1642	432	41	-	-	PUNCT
asir-1642	432	42	field	field	NOUN
asir-1642	432	43	,	,	PUNCT
asir-1642	432	44	and	and	CCONJ
asir-1642	432	45	this	this	PRON
asir-1642	432	46	because	because	SCONJ
asir-1642	432	47	are	be	AUX
asir-1642	432	48	axially	axially	ADV
asir-1642	432	49	on	on	ADP
asir-1642	432	50	their	their	PRON
asir-1642	432	51	spin	spin	NOUN
asir-1642	432	52	-	-	PUNCT
asir-1642	432	53	vector	vector	NOUN
asir-1642	432	54	b̅	b̅	PROPN
asir-1642	432	55	≡	≡	PROPN
asir-1642	432	56	spin	spin	VERB
asir-1642	432	57	≡	≡	PROPN
asir-1642	432	58	rotational	rotational	ADJ
asir-1642	432	59	-	-	PUNCT
asir-1642	432	60	energy	energy	NOUN
asir-1642	432	61	,	,	PUNCT
asir-1642	432	62	and	and	CCONJ
asir-1642	432	63	which	which	DET
asir-1642	432	64	energy	energy	NOUN
asir-1642	432	65	-	-	PUNCT
asir-1642	432	66	vectors	vector	NOUN
asir-1642	432	67	≡	≡	PROPN
asir-1642	432	68	spin	spin	NOUN
asir-1642	432	69	,	,	PUNCT
asir-1642	432	70	is	be	AUX
asir-1642	432	71	the	the	DET
asir-1642	432	72	inside	inside	NOUN
asir-1642	432	73	-	-	PUNCT
asir-1642	432	74	content	content	NOUN
asir-1642	432	75	of	of	ADP
asir-1642	432	76	the	the	DET
asir-1642	432	77	gravity	gravity	NOUN
asir-1642	432	78	-	-	PUNCT
asir-1642	432	79	field	field	NOUN
asir-1642	432	80	.	.	PUNCT
asir-1642	433	1	the	the	DET
asir-1642	433	2	dot	dot	NOUN
asir-1642	433	3	-	-	PUNCT
asir-1642	433	4	product	product	NOUN
asir-1642	433	5	happens	happen	VERB
asir-1642	433	6	for	for	ADP
asir-1642	433	7	interactions	interaction	NOUN
asir-1642	433	8	between	between	ADP
asir-1642	433	9	similar	similar	ADJ
asir-1642	433	10	dimensions	dimension	NOUN
asir-1642	433	11	,	,	PUNCT
asir-1642	433	12	while	while	SCONJ
asir-1642	433	13	the	the	DET
asir-1642	433	14	cross	cross	NOUN
asir-1642	433	15	-	-	NOUN
asir-1642	433	16	product	product	NOUN
asir-1642	433	17	between	between	ADP
asir-1642	433	18	different	different	ADJ
asir-1642	433	19	-	-	PUNCT
asir-1642	433	20	dimensions	dimension	NOUN
asir-1642	433	21	.	.	PUNCT
asir-1642	434	1	cross	cross	NOUN
asir-1642	434	2	-	-	NOUN
asir-1642	434	3	product	product	NOUN
asir-1642	434	4	of	of	ADP
asir-1642	434	5	two	two	NUM
asir-1642	434	6	vectors	vector	NOUN
asir-1642	434	7	̅	̅	NOUN
asir-1642	434	8	,	,	PUNCT
asir-1642	434	9	̅	̅	NOUN
asir-1642	434	10	is	be	AUX
asir-1642	434	11	̅	̅	NOUN
asir-1642	434	12	x	x	SYM
asir-1642	434	13	̅	̅	NOUN
asir-1642	434	14	=	=	SYM
asir-1642	435	1	|	|	ADV
asir-1642	435	2	̅|.|	̅|.|	X
asir-1642	435	3	̅|	̅|	INTJ
asir-1642	435	4	.	.	PUNCT
asir-1642	436	1	̅	̅	NOUN
asir-1642	436	2	and	and	CCONJ
asir-1642	436	3	for	for	ADP
asir-1642	436	4	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	436	5	applied	apply	VERB
asir-1642	436	6	science	science	NOUN
asir-1642	436	7	and	and	CCONJ
asir-1642	436	8	innovative	innovative	ADJ
asir-1642	436	9	research	research	NOUN
asir-1642	436	10	vol	vol	NOUN
asir-1642	436	11	.	.	PROPN
asir-1642	437	1	2	2	NUM
asir-1642	437	2	,	,	PUNCT
asir-1642	437	3	no	no	INTJ
asir-1642	437	4	.	.	NOUN
asir-1642	437	5	4	4	NUM
asir-1642	437	6	,	,	PUNCT
asir-1642	437	7	2018	2018	NUM
asir-1642	437	8	176	176	NUM
asir-1642	437	9	published	publish	VERB
asir-1642	437	10	by	by	ADP
asir-1642	437	11	scholink	scholink	PROPN
asir-1642	437	12	inc	inc	PROPN
asir-1642	437	13	.	.	PROPN
asir-1642	437	14	̅	̅	PROPN
asir-1642	437	15	=	=	SYM
asir-1642	437	16	̅	̅	NOUN
asir-1642	437	17	and	and	CCONJ
asir-1642	437	18	θ	θ	NOUN
asir-1642	437	19	=	=	NOUN
asir-1642	437	20	90ᵒ	90ᵒ	NOUN
asir-1642	437	21	then	then	ADV
asir-1642	437	22	̅	̅	VERB
asir-1642	437	23	x	x	SYM
asir-1642	437	24	̅	̅	NOUN
asir-1642	437	25	=	=	SYM
asir-1642	437	26	̅	̅	NOUN
asir-1642	437	27	²	²	NUM
asir-1642	437	28	,	,	PUNCT
asir-1642	437	29	and	and	CCONJ
asir-1642	437	30	for	for	ADP
asir-1642	437	31	quaternion	quaternion	NOUN
asir-1642	437	32	,	,	PUNCT
asir-1642	437	33	s	s	PROPN
asir-1642	437	34	,	,	PUNCT
asir-1642	437	35	which	which	PRON
asir-1642	437	36	performs	perform	VERB
asir-1642	437	37	the	the	DET
asir-1642	437	38	work	work	NOUN
asir-1642	437	39	of	of	ADP
asir-1642	437	40	rotating	rotate	VERB
asir-1642	437	41	the	the	DET
asir-1642	437	42	one	one	NUM
asir-1642	437	43	vector	vector	NOUN
asir-1642	437	44	around	around	ADP
asir-1642	437	45	the	the	DET
asir-1642	437	46	other	other	ADJ
asir-1642	437	47	is	be	AUX
asir-1642	437	48	→	→	SYM
asir-1642	437	49	work	work	NOUN
asir-1642	437	50	=	=	SYM
asir-1642	437	51	̅	̅	NOUN
asir-1642	437	52	x	x	SYM
asir-1642	437	53	̅	̅	NOUN
asir-1642	437	54	=	=	SYM
asir-1642	437	55	̅	̅	NOUN
asir-1642	437	56	².r̅	².r̅	ADJ
asir-1642	437	57	,	,	PUNCT
asir-1642	437	58	and	and	CCONJ
asir-1642	437	59	for	for	ADP
asir-1642	437	60	̅	̅	NOUN
asir-1642	437	61	=	=	SYM
asir-1642	437	62	v̅	v̅	NOUN
asir-1642	437	63	then	then	ADV
asir-1642	437	64	→	→	SYM
asir-1642	437	65	work	work	NOUN
asir-1642	437	66	=	=	SYM
asir-1642	437	67	v̅	v̅	NOUN
asir-1642	437	68	².r̅	².r̅	ADJ
asir-1642	437	69	=	=	VERB
asir-1642	437	70	|v̅|.|v̅|.r̅	|v̅|.|v̅|.r̅	NOUN
asir-1642	437	71	=	=	SYM
asir-1642	437	72	v²	v²	PROPN
asir-1642	437	73	.	.	PUNCT
asir-1642	438	1	r.	r.	PROPN
asir-1642	438	2	̅	̅	PROPN
asir-1642	438	3	=	=	SYM
asir-1642	438	4	(	(	PUNCT
asir-1642	438	5	wr)²r	wr)²r	NOUN
asir-1642	438	6	.	.	PUNCT
asir-1642	438	7	̅	̅	VERB
asir-1642	438	8	,	,	PUNCT
asir-1642	438	9	or	or	CCONJ
asir-1642	438	10	work	work	NOUN
asir-1642	438	11	=	=	SYM
asir-1642	438	12	(	(	PUNCT
asir-1642	438	13	wr)²r	wr)²r	NOUN
asir-1642	438	14	.	.	PUNCT
asir-1642	438	15	̅	̅	NOUN
asir-1642	439	1	=	=	SYM
asir-1642	439	2	(	(	PUNCT
asir-1642	439	3	2πr	2πr	ADJ
asir-1642	439	4	/	/	SYM
asir-1642	439	5	t)²	t)²	NOUN
asir-1642	439	6	r	r	NOUN
asir-1642	439	7	̅	̅	NOUN
asir-1642	439	8	=	=	SYM
asir-1642	439	9	(	(	PUNCT
asir-1642	439	10	4π²r²/	4π²r²/	NUM
asir-1642	439	11	t²	t²	NOUN
asir-1642	439	12	)	)	PUNCT
asir-1642	439	13	.	.	PUNCT
asir-1642	440	1	r.	r.	PROPN
asir-1642	440	2	̅	̅	PROPN
asir-1642	440	3	=	=	SYM
asir-1642	440	4	²	²	NUM
asir-1642	440	5	³	³	NUM
asir-1642	440	6	t²	t²	NOUN
asir-1642	440	7	.	.	PUNCT
asir-1642	441	1	̅	̅	VERB
asir-1642	441	2	←	←	PROPN
asir-1642	441	3	w	w	PROPN
asir-1642	441	4	=	=	SYM
asir-1642	441	5	4π²	4π²	PROPN
asir-1642	441	6	.	.	PUNCT
asir-1642	442	1	𝐫³	𝐫³	PROPN
asir-1642	442	2	𝐓²	𝐓²	PROPN
asir-1642	442	3	.	.	PUNCT
asir-1642	443	1	�	�	PROPN
asir-1642	443	2	̅	̅	NOUN
asir-1642	443	3	�	�	NOUN
asir-1642	443	4	=	=	SYM
asir-1642	443	5	4π².r	4π².r	NUM
asir-1642	443	6	³.	³.	X
asir-1642	443	7	𝐟²𝐩.	𝐟²𝐩.	PROPN
asir-1642	443	8	�	�	PROPN
asir-1642	443	9	̅	̅	NOUN
asir-1642	443	10	�	�	NOUN
asir-1642	443	11	i.e.	i.e.	X
asir-1642	443	12	,	,	PUNCT
asir-1642	443	13	kepler	kepler	NOUN
asir-1642	443	14	constant	constant	ADJ
asir-1642	443	15	celestial	celestial	ADJ
asir-1642	443	16	law	law	NOUN
asir-1642	443	17	for	for	ADP
asir-1642	443	18	microcosm	microcosm	NOUN
asir-1642	443	19	.	.	PUNCT
asir-1642	444	1	kinetic	kinetic	ADJ
asir-1642	444	2	energy	energy	NOUN
asir-1642	444	3	,	,	PUNCT
asir-1642	444	4	motion	motion	NOUN
asir-1642	444	5	,	,	PUNCT
asir-1642	444	6	in	in	ADP
asir-1642	444	7	orbits	orbit	NOUN
asir-1642	444	8	becomes	become	VERB
asir-1642	444	9	from	from	ADP
asir-1642	444	10	the	the	DET
asir-1642	444	11	,	,	PUNCT
asir-1642	444	12	piezoelectric	piezoelectric	NOUN
asir-1642	444	13	-	-	PUNCT
asir-1642	444	14	effect	effect	NOUN
asir-1642	444	15	,	,	PUNCT
asir-1642	444	16	where	where	SCONJ
asir-1642	444	17	orbit	orbit	NOUN
asir-1642	444	18	is	be	AUX
asir-1642	444	19	subject	subject	ADJ
asir-1642	444	20	to	to	ADP
asir-1642	444	21	a	a	DET
asir-1642	444	22	mechanical	mechanical	ADJ
asir-1642	444	23	-	-	PUNCT
asir-1642	444	24	stress	stress	NOUN
asir-1642	444	25	,	,	PUNCT
asir-1642	444	26	σ	σ	PROPN
asir-1642	444	27	=	=	SYM
asir-1642	444	28	±	±	NUM
asir-1642	444	29	𝟒𝛑𝐫	𝟒𝛑𝐫	NOUN
asir-1642	444	30	(	(	PUNCT
asir-1642	444	31	+	+	NOUN
asir-1642	444	32	√𝟓	√𝟓	NOUN
asir-1642	444	33	)	)	PUNCT
asir-1642	444	34	.	.	PUNCT
asir-1642	445	1	𝐟𝐩	𝐟𝐩	PROPN
asir-1642	445	2	,	,	PUNCT
asir-1642	445	3	becoming	become	VERB
asir-1642	445	4	from	from	ADP
asir-1642	445	5	the	the	DET
asir-1642	445	6	centripetal	centripetal	ADJ
asir-1642	445	7	-	-	PUNCT
asir-1642	445	8	acceleration	acceleration	NOUN
asir-1642	445	9	�	�	NOUN
asir-1642	445	10	̅	̅	NOUN
asir-1642	445	11	�	�	NOUN
asir-1642	445	12	𝐏	𝐏	PROPN
asir-1642	445	13	of	of	ADP
asir-1642	445	14	the	the	DET
asir-1642	445	15	planet	planet	NOUN
asir-1642	445	16	and	and	CCONJ
asir-1642	445	17	thus	thus	ADV
asir-1642	445	18	is	be	AUX
asir-1642	445	19	appeared	appear	VERB
asir-1642	445	20	a	a	DET
asir-1642	445	21	positive	positive	ADJ
asir-1642	445	22	charge	charge	NOUN
asir-1642	445	23	at	at	ADP
asir-1642	445	24	the	the	DET
asir-1642	445	25	nucleus	nucleus	NOUN
asir-1642	445	26	and	and	CCONJ
asir-1642	445	27	a	a	DET
asir-1642	445	28	negative	negative	ADJ
asir-1642	445	29	-	-	PUNCT
asir-1642	445	30	charge	charge	NOUN
asir-1642	445	31	at	at	ADP
asir-1642	445	32	the	the	DET
asir-1642	445	33	planet	planet	NOUN
asir-1642	445	34	,	,	PUNCT
asir-1642	445	35	so	so	ADV
asir-1642	445	36	is	be	AUX
asir-1642	445	37	created	create	VERB
asir-1642	445	38	an	an	DET
asir-1642	445	39	electric	electric	NOUN
asir-1642	445	40	-	-	PUNCT
asir-1642	445	41	signal	signal	NOUN
asir-1642	445	42	with	with	ADP
asir-1642	445	43	a	a	DET
asir-1642	445	44	given	give	VERB
asir-1642	445	45	frequency	frequency	NOUN
asir-1642	445	46	𝐟𝐩.	𝐟𝐩.	NOUN
asir-1642	445	47	the	the	DET
asir-1642	445	48	two	two	NUM
asir-1642	445	49	faces	face	NOUN
asir-1642	445	50	at	at	ADP
asir-1642	445	51	n	n	PROPN
asir-1642	445	52	and	and	CCONJ
asir-1642	445	53	p	p	NOUN
asir-1642	445	54	are	be	AUX
asir-1642	445	55	connected	connect	VERB
asir-1642	445	56	by	by	ADP
asir-1642	445	57	the	the	DET
asir-1642	445	58	in	in	NOUN
asir-1642	445	59	-	-	PUNCT
asir-1642	445	60	between	between	ADP
asir-1642	445	61	energy	energy	NOUN
asir-1642	445	62	-	-	PUNCT
asir-1642	445	63	vectors	vector	NOUN
asir-1642	445	64	b̅	b̅	PROPN
asir-1642	445	65	≡	≡	PROPN
asir-1642	445	66	spin	spin	NOUN
asir-1642	445	67	,	,	PUNCT
asir-1642	445	68	of	of	ADP
asir-1642	445	69	the	the	DET
asir-1642	445	70	oriented	orient	VERB
asir-1642	445	71	gravity	gravity	NOUN
asir-1642	445	72	-	-	PUNCT
asir-1642	445	73	field	field	NOUN
asir-1642	445	74	[	[	X
asir-1642	445	75	i	i	NOUN
asir-1642	445	76	]	]	X
asir-1642	445	77	=	=	PUNCT
asir-1642	446	1	[	[	X
asir-1642	446	2	⊕	⊕	NOUN
asir-1642	446	3	↻	↻	NOUN
asir-1642	446	4	↺	↺	NOUN
asir-1642	446	5	⊝	⊝	PUNCT
asir-1642	446	6	]	]	PUNCT
asir-1642	446	7	.	.	PUNCT
asir-1642	447	1	in	in	ADP
asir-1642	447	2	orbits	orbit	NOUN
asir-1642	447	3	which	which	PRON
asir-1642	447	4	are	be	AUX
asir-1642	447	5	negative	negative	ADJ
asir-1642	447	6	-	-	PUNCT
asir-1642	447	7	energy	energy	NOUN
asir-1642	447	8	-	-	PUNCT
asir-1642	447	9	rims	rim	NOUN
asir-1642	447	10	,	,	PUNCT
asir-1642	447	11	with	with	ADP
asir-1642	447	12	binder	binder	NOUN
asir-1642	447	13	energy	energy	NOUN
asir-1642	447	14	the	the	DET
asir-1642	447	15	atraction	atraction	NOUN
asir-1642	447	16	between	between	ADP
asir-1642	447	17	the	the	DET
asir-1642	447	18	two	two	NUM
asir-1642	447	19	opposite	opposite	ADJ
asir-1642	447	20	forces	force	NOUN
asir-1642	447	21	p	p	X
asir-1642	447	22	↔pp	↔pp	NOUN
asir-1642	447	23	at	at	ADP
asir-1642	447	24	points	point	NOUN
asir-1642	447	25	focus	focus	NOUN
asir-1642	447	26	n	n	NOUN
asir-1642	447	27	and	and	CCONJ
asir-1642	447	28	planet	planet	NOUN
asir-1642	447	29	p	p	X
asir-1642	447	30	,	,	PUNCT
asir-1642	447	31	is	be	AUX
asir-1642	447	32	created	create	VERB
asir-1642	447	33	the	the	DET
asir-1642	447	34	central	central	ADJ
asir-1642	447	35	motion	motion	NOUN
asir-1642	447	36	where	where	SCONJ
asir-1642	447	37	,	,	PUNCT
asir-1642	447	38	orbital	orbital	ADJ
asir-1642	447	39	-	-	PUNCT
asir-1642	447	40	resonance	resonance	NOUN
asir-1642	447	41	is	be	AUX
asir-1642	447	42	the	the	DET
asir-1642	447	43	plane	plane	NOUN
asir-1642	447	44	surfaces	surface	NOUN
asir-1642	447	45	,	,	PUNCT
asir-1642	447	46	representing	represent	VERB
asir-1642	447	47	a	a	DET
asir-1642	447	48	constant	constant	ADJ
asir-1642	447	49	-	-	PUNCT
asir-1642	447	50	energy	energy	NOUN
asir-1642	447	51	-	-	PUNCT
asir-1642	447	52	rim	rim	NOUN
asir-1642	447	53	following	follow	VERB
asir-1642	447	54	the	the	DET
asir-1642	447	55	celestial	celestial	ADJ
asir-1642	447	56	kepler	kepler	NOUN
asir-1642	447	57	laws	law	NOUN
asir-1642	447	58	and	and	CCONJ
asir-1642	447	59	say	say	VERB
asir-1642	447	60	this	this	PRON
asir-1642	447	61	as	as	ADP
asir-1642	447	62	an	an	DET
asir-1642	447	63	plane	plane	NOUN
asir-1642	447	64	energy	energy	NOUN
asir-1642	447	65	-	-	PUNCT
asir-1642	447	66	resonance	resonance	NOUN
asir-1642	447	67	,	,	PUNCT
asir-1642	447	68	because	because	SCONJ
asir-1642	447	69	happens	happen	VERB
asir-1642	447	70	in	in	ADP
asir-1642	447	71	-	-	PUNCT
asir-1642	447	72	plane	plane	NOUN
asir-1642	447	73	and	and	CCONJ
asir-1642	447	74	on	on	ADP
asir-1642	447	75	energy	energy	NOUN
asir-1642	447	76	-	-	PUNCT
asir-1642	447	77	field	field	NOUN
asir-1642	447	78	-	-	PUNCT
asir-1642	447	79	vectors	vector	NOUN
asir-1642	447	80	of	of	ADP
asir-1642	447	81	spins	spin	NOUN
asir-1642	447	82	b̅	b̅	NOUN
asir-1642	447	83	in	in	ADP
asir-1642	447	84	figures	figure	NOUN
asir-1642	447	85	3	3	NUM
asir-1642	447	86	,	,	PUNCT
asir-1642	447	87	6	6	NUM
asir-1642	447	88	are	be	AUX
asir-1642	447	89	shown	show	VERB
asir-1642	447	90	the	the	DET
asir-1642	447	91	ellipse	ellipse	NOUN
asir-1642	447	92	-	-	PUNCT
asir-1642	447	93	orbits	orbit	NOUN
asir-1642	447	94	,	,	PUNCT
asir-1642	447	95	1	1	NUM
asir-1642	447	96	=	=	SYM
asir-1642	447	97	c.	c.	PROPN
asir-1642	447	98	².r³	².r³	PROPN
asir-1642	447	99	,	,	PUNCT
asir-1642	447	100	with	with	ADP
asir-1642	447	101	their	their	PRON
asir-1642	447	102	content	content	NOUN
asir-1642	447	103	which	which	PRON
asir-1642	447	104	is	be	AUX
asir-1642	447	105	the	the	DET
asir-1642	447	106	spin	spin	NOUN
asir-1642	447	107	-	-	PUNCT
asir-1642	447	108	field	field	NOUN
asir-1642	447	109	-	-	PUNCT
asir-1642	447	110	vectors	vector	NOUN
asir-1642	447	111	b̅	b̅	NOUN
asir-1642	447	112	in	in	ADP
asir-1642	447	113	all	all	DET
asir-1642	447	114	area	area	NOUN
asir-1642	447	115	πab	πab	ADV
asir-1642	447	116	of	of	ADP
asir-1642	447	117	mfmf	mfmf	NOUN
asir-1642	447	118	field	field	NOUN
asir-1642	447	119	.	.	PUNCT
asir-1642	448	1	during	during	ADP
asir-1642	448	2	orbiting	orbit	VERB
asir-1642	448	3	centripetal	centripetal	ADJ
asir-1642	448	4	acceleration	acceleration	NOUN
asir-1642	448	5	�	�	PROPN
asir-1642	448	6	̅	̅	NOUN
asir-1642	448	7	�	�	NOUN
asir-1642	448	8	𝐏	𝐏	NOUN
asir-1642	448	9	=	=	SYM
asir-1642	448	10	σ	σ	PROPN
asir-1642	448	11	=	=	SYM
asir-1642	448	12	±	±	NUM
asir-1642	448	13	𝟒𝛑𝐫	𝟒𝛑𝐫	NOUN
asir-1642	448	14	(	(	PUNCT
asir-1642	448	15	+	+	NOUN
asir-1642	448	16	√𝟓	√𝟓	NOUN
asir-1642	448	17	)	)	PUNCT
asir-1642	448	18	.	.	PUNCT
asir-1642	449	1	𝐟	𝐟	NOUN
asir-1642	449	2	is	be	AUX
asir-1642	449	3	directed	direct	VERB
asir-1642	449	4	to	to	PART
asir-1642	449	5	focus	focus	VERB
asir-1642	449	6	n	n	CCONJ
asir-1642	449	7	,	,	PUNCT
asir-1642	449	8	i.e.	i.e.	X
asir-1642	449	9	,	,	PUNCT
asir-1642	449	10	orbit	orbit	NOUN
asir-1642	449	11	is	be	AUX
asir-1642	449	12	subject	subject	ADJ
asir-1642	449	13	to	to	ADP
asir-1642	449	14	a	a	DET
asir-1642	449	15	mechanical	mechanical	ADJ
asir-1642	449	16	-	-	PUNCT
asir-1642	449	17	stress	stress	NOUN
asir-1642	449	18	σ	σ	NOUN
asir-1642	449	19	,	,	PUNCT
asir-1642	449	20	becoming	become	VERB
asir-1642	449	21	from	from	ADP
asir-1642	449	22	a	a	DET
asir-1642	449	23	centripetal	centripetal	ADJ
asir-1642	449	24	-	-	PUNCT
asir-1642	449	25	acceleration	acceleration	NOUN
asir-1642	449	26	�	�	NOUN
asir-1642	449	27	̅	̅	NOUN
asir-1642	449	28	�	�	NOUN
asir-1642	449	29	𝐏	𝐏	PROPN
asir-1642	449	30	,	,	PUNCT
asir-1642	449	31	and	and	CCONJ
asir-1642	449	32	so	so	ADV
asir-1642	449	33	is	be	AUX
asir-1642	449	34	appeared	appear	VERB
asir-1642	449	35	the	the	DET
asir-1642	449	36	piezoelectric	piezoelectric	NOUN
asir-1642	449	37	-	-	PUNCT
asir-1642	449	38	effect	effect	NOUN
asir-1642	449	39	with	with	ADP
asir-1642	449	40	positive	positive	ADJ
asir-1642	449	41	-	-	PUNCT
asir-1642	449	42	charge	charge	NOUN
asir-1642	449	43	at	at	ADP
asir-1642	449	44	the	the	DET
asir-1642	449	45	nucleus	nucleus	NOUN
asir-1642	449	46	and	and	CCONJ
asir-1642	449	47	negative	negative	ADJ
asir-1642	449	48	-	-	PUNCT
asir-1642	449	49	charge	charge	NOUN
asir-1642	449	50	at	at	ADP
asir-1642	449	51	the	the	DET
asir-1642	449	52	planet	planet	NOUN
asir-1642	449	53	≡	≡	PROPN
asir-1642	449	54	material	material	NOUN
asir-1642	449	55	-	-	PUNCT
asir-1642	449	56	point	point	NOUN
asir-1642	449	57	.	.	PUNCT
asir-1642	450	1	the	the	DET
asir-1642	450	2	two	two	NUM
asir-1642	450	3	faces	face	NOUN
asir-1642	450	4	at	at	ADP
asir-1642	450	5	n	n	CCONJ
asir-1642	450	6	,	,	PUNCT
asir-1642	450	7	p	p	NOUN
asir-1642	450	8	are	be	AUX
asir-1642	450	9	connected	connect	VERB
asir-1642	450	10	by	by	ADP
asir-1642	450	11	the	the	DET
asir-1642	450	12	in	in	NOUN
asir-1642	450	13	-	-	PUNCT
asir-1642	450	14	between	between	ADP
asir-1642	450	15	gravity	gravity	NOUN
asir-1642	450	16	-	-	PUNCT
asir-1642	450	17	field	field	NOUN
asir-1642	450	18	[	[	X
asir-1642	450	19	i	i	NOUN
asir-1642	450	20	]	]	X
asir-1642	450	21	=	=	PUNCT
asir-1642	451	1	[	[	X
asir-1642	451	2	±	±	NUM
asir-1642	451	3	s²	s²	NOUN
asir-1642	451	4	]	]	PUNCT
asir-1642	451	5	in	in	ADP
asir-1642	451	6	[	[	X
asir-1642	451	7	mfmf	mfmf	NOUN
asir-1642	451	8	]	]	PUNCT
asir-1642	451	9	field	field	NOUN
asir-1642	451	10	and	and	CCONJ
asir-1642	451	11	flows	flow	VERB
asir-1642	451	12	current	current	ADJ
asir-1642	451	13	,	,	PUNCT
asir-1642	451	14	motion	motion	NOUN
asir-1642	451	15	is	be	AUX
asir-1642	451	16	realized	realize	VERB
asir-1642	451	17	by	by	ADP
asir-1642	451	18	the	the	DET
asir-1642	451	19	orientation	orientation	NOUN
asir-1642	451	20	of	of	ADP
asir-1642	451	21	the	the	DET
asir-1642	451	22	infinite	infinite	ADJ
asir-1642	451	23	spin	spin	NOUN
asir-1642	451	24	-	-	PUNCT
asir-1642	451	25	energy	energy	NOUN
asir-1642	451	26	-	-	PUNCT
asir-1642	451	27	vectors	vector	NOUN
asir-1642	451	28	,	,	PUNCT
asir-1642	451	29	which	which	PRON
asir-1642	451	30	is	be	AUX
asir-1642	451	31	the	the	DET
asir-1642	451	32	resonance	resonance	NOUN
asir-1642	451	33	on	on	ADP
asir-1642	451	34	orbit	orbit	NOUN
asir-1642	451	35	,	,	PUNCT
asir-1642	451	36	the	the	DET
asir-1642	451	37	gravity	gravity	NOUN
asir-1642	451	38	force	force	NOUN
asir-1642	451	39	,	,	PUNCT
asir-1642	451	40	g.	g.	PROPN
asir-1642	451	41	in	in	ADP
asir-1642	451	42	the	the	DET
asir-1642	451	43	inverse	inverse	NOUN
asir-1642	451	44	piezoelectric	piezoelectric	NOUN
asir-1642	451	45	-	-	PUNCT
asir-1642	451	46	effect	effect	NOUN
asir-1642	451	47	on	on	ADP
asir-1642	451	48	orbit	orbit	NOUN
asir-1642	451	49	,	,	PUNCT
asir-1642	451	50	when	when	SCONJ
asir-1642	451	51	a	a	DET
asir-1642	451	52	voltage	voltage	NOUN
asir-1642	451	53	is	be	AUX
asir-1642	451	54	applied	apply	VERB
asir-1642	451	55	across	across	ADP
asir-1642	451	56	its	its	PRON
asir-1642	451	57	opposite	opposite	ADJ
asir-1642	451	58	faces	face	NOUN
asir-1642	451	59	at	at	ADP
asir-1642	451	60	n	n	CCONJ
asir-1642	451	61	,	,	PUNCT
asir-1642	451	62	p	p	X
asir-1642	451	63	,	,	PUNCT
asir-1642	451	64	becoming	become	VERB
asir-1642	451	65	from	from	ADP
asir-1642	451	66	the	the	DET
asir-1642	451	67	[	[	X
asir-1642	451	68	⊕↔⊝	⊕↔⊝	NOUN
asir-1642	451	69	]	]	X
asir-1642	451	70	stretching	stretching	NOUN
asir-1642	451	71	,	,	PUNCT
asir-1642	451	72	then	then	ADV
asir-1642	451	73	orbit	orbit	NOUN
asir-1642	451	74	becomes	become	VERB
asir-1642	451	75	mechanically	mechanically	ADV
asir-1642	451	76	stressed	stressed	ADJ
asir-1642	451	77	,	,	PUNCT
asir-1642	451	78	deformed	deform	VERB
asir-1642	451	79	in	in	ADP
asir-1642	451	80	shape	shape	NOUN
asir-1642	451	81	by	by	ADP
asir-1642	451	82	the	the	DET
asir-1642	451	83	resonance	resonance	NOUN
asir-1642	451	84	at	at	ADP
asir-1642	451	85	n	n	PROPN
asir-1642	451	86	and	and	CCONJ
asir-1642	451	87	p.	p.	NOUN
asir-1642	451	88	further	far	ADV
asir-1642	451	89	is	be	AUX
asir-1642	451	90	seen	see	VERB
asir-1642	451	91	,	,	PUNCT
asir-1642	451	92	orbit	orbit	NOUN
asir-1642	451	93	or	or	CCONJ
asir-1642	451	94	,	,	PUNCT
asir-1642	451	95	a	a	DET
asir-1642	451	96	negative	negative	ADJ
asir-1642	451	97	-	-	PUNCT
asir-1642	451	98	energy	energy	NOUN
asir-1642	451	99	-	-	PUNCT
asir-1642	451	100	rim	rim	NOUN
asir-1642	451	101	,	,	PUNCT
asir-1642	451	102	is	be	AUX
asir-1642	451	103	the	the	DET
asir-1642	451	104	stable	stable	ADJ
asir-1642	451	105	and	and	CCONJ
asir-1642	451	106	stationary	stationary	ADJ
asir-1642	451	107	granular	granular	ADJ
asir-1642	451	108	-	-	PUNCT
asir-1642	451	109	lattice	lattice	NOUN
asir-1642	451	110	energy	energy	NOUN
asir-1642	451	111	-	-	PUNCT
asir-1642	451	112	disk	disk	NOUN
asir-1642	451	113	,	,	PUNCT
asir-1642	451	114	which	which	PRON
asir-1642	451	115	is	be	AUX
asir-1642	451	116	kept	keep	VERB
asir-1642	451	117	in	in	ADP
asir-1642	451	118	the	the	DET
asir-1642	451	119	plane	plane	NOUN
asir-1642	451	120	-	-	PUNCT
asir-1642	451	121	orbit	orbit	NOUN
asir-1642	451	122	of	of	ADP
asir-1642	451	123	motion	motion	NOUN
asir-1642	451	124	,	,	PUNCT
asir-1642	451	125	ellipse	ellipse	NOUN
asir-1642	451	126	area	area	NOUN
asir-1642	451	127	πab	πab	ADJ
asir-1642	451	128	,	,	PUNCT
asir-1642	451	129	in	in	ADP
asir-1642	451	130	gravity	gravity	NOUN
asir-1642	451	131	field	field	NOUN
asir-1642	451	132	,	,	PUNCT
asir-1642	451	133	and	and	CCONJ
asir-1642	451	134	in	in	ADP
asir-1642	451	135	a	a	DET
asir-1642	451	136	way	way	NOUN
asir-1642	451	137	it	it	PRON
asir-1642	451	138	is	be	AUX
asir-1642	451	139	opposite	opposite	ADJ
asir-1642	451	140	to	to	ADP
asir-1642	451	141	that	that	PRON
asir-1642	451	142	which	which	PRON
asir-1642	451	143	follows	follow	VERB
asir-1642	451	144	the	the	DET
asir-1642	451	145	central	central	ADJ
asir-1642	451	146	motion	motion	NOUN
asir-1642	451	147	,	,	PUNCT
asir-1642	451	148	i.e.	i.e.	X
asir-1642	451	149	,	,	PUNCT
asir-1642	451	150	either	either	CCONJ
asir-1642	451	151	for	for	ADP
asir-1642	451	152	macrocosm	macrocosm	PROPN
asir-1642	451	153	or	or	CCONJ
asir-1642	451	154	microcosm	microcosm	NOUN
asir-1642	451	155	,	,	PUNCT
asir-1642	451	156	gravity	gravity	NOUN
asir-1642	451	157	-	-	PUNCT
asir-1642	451	158	force	force	NOUN
asir-1642	451	159	-	-	PUNCT
asir-1642	451	160	vectors	vector	NOUN
asir-1642	451	161	b̅	b̅	PROPN
asir-1642	451	162	≡	≡	PROPN
asir-1642	451	163	spin	spin	NOUN
asir-1642	451	164	,	,	PUNCT
asir-1642	451	165	of	of	ADP
asir-1642	451	166	material	material	NOUN
asir-1642	451	167	-	-	PUNCT
asir-1642	451	168	points	point	NOUN
asir-1642	451	169	as	as	ADP
asir-1642	451	170	spin	spin	NOUN
asir-1642	451	171	[	[	X
asir-1642	451	172	⊕	⊕	NOUN
asir-1642	451	173	↻	↻	NOUN
asir-1642	451	174	↺	↺	NOUN
asir-1642	451	175	⊝	⊝	X
asir-1642	451	176	]	]	PUNCT
asir-1642	452	1	is	be	AUX
asir-1642	452	2	packet	packet	NOUN
asir-1642	452	3	into	into	ADP
asir-1642	452	4	the	the	DET
asir-1642	452	5	orbit	orbit	NOUN
asir-1642	452	6	-	-	PUNCT
asir-1642	452	7	rim	rim	NOUN
asir-1642	452	8	as	as	ADP
asir-1642	452	9	energy	energy	NOUN
asir-1642	452	10	-	-	PUNCT
asir-1642	452	11	conveyer	conveyer	NOUN
asir-1642	452	12	for	for	ADP
asir-1642	452	13	the	the	DET
asir-1642	452	14	interactions	interaction	NOUN
asir-1642	452	15	between	between	ADP
asir-1642	452	16	,	,	PUNCT
asir-1642	452	17	the	the	DET
asir-1642	452	18	nucleus	nucleus	NOUN
asir-1642	452	19	n	n	CCONJ
asir-1642	452	20	,	,	PUNCT
asir-1642	452	21	and	and	CCONJ
asir-1642	452	22	the	the	DET
asir-1642	452	23	orbiting	orbiting	ADJ
asir-1642	452	24	object	object	NOUN
asir-1642	452	25	,	,	PUNCT
asir-1642	452	26	the	the	DET
asir-1642	452	27	planet	planet	NOUN
asir-1642	452	28	p	p	X
asir-1642	452	29	,	,	PUNCT
asir-1642	452	30	and	and	CCONJ
asir-1642	452	31	consists	consist	VERB
asir-1642	452	32	the	the	DET
asir-1642	452	33	energy	energy	NOUN
asir-1642	452	34	-	-	PUNCT
asir-1642	452	35	quanta	quanta	PROPN
asir-1642	452	36	,	,	PUNCT
asir-1642	452	37	the	the	DET
asir-1642	452	38	minimum	minimum	ADJ
asir-1642	452	39	constant	constant	ADJ
asir-1642	452	40	energy	energy	NOUN
asir-1642	452	41	,	,	PUNCT
asir-1642	452	42	for	for	ADP
asir-1642	452	43	motion	motion	NOUN
asir-1642	452	44	→	→	PUNCT
asir-1642	452	45	[	[	X
asir-1642	452	46	⊕	⊕	NOUN
asir-1642	452	47	↻	↻	NOUN
asir-1642	452	48	↺	↺	NOUN
asir-1642	452	49	⊝	⊝	NOUN
asir-1642	452	50	]	]	PUNCT
asir-1642	452	51	←	←	PROPN
asir-1642	452	52	in	in	ADP
asir-1642	452	53	the	the	DET
asir-1642	452	54	monad	monad	PROPN
asir-1642	452	55	atom	atom	PROPN
asir-1642	452	56	-	-	PUNCT
asir-1642	452	57	rim	rim	NOUN
asir-1642	452	58	.	.	PUNCT
asir-1642	453	1	2	2	NUM
asir-1642	453	2	..	..	PUNCT
asir-1642	453	3	the	the	DET
asir-1642	453	4	minimum	minimum	ADJ
asir-1642	453	5	energy	energy	NOUN
asir-1642	453	6	rim	rim	NOUN
asir-1642	453	7	:	:	PUNCT
asir-1642	453	8	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	NOUN
asir-1642	453	9	applied	apply	VERB
asir-1642	453	10	science	science	NOUN
asir-1642	453	11	and	and	CCONJ
asir-1642	453	12	innovative	innovative	ADJ
asir-1642	453	13	research	research	NOUN
asir-1642	453	14	vol	vol	NOUN
asir-1642	453	15	.	.	PROPN
asir-1642	454	1	2	2	NUM
asir-1642	454	2	,	,	PUNCT
asir-1642	454	3	no	no	INTJ
asir-1642	454	4	.	.	NOUN
asir-1642	454	5	4	4	NUM
asir-1642	454	6	,	,	PUNCT
asir-1642	454	7	2018	2018	NUM
asir-1642	454	8	177	177	NUM
asir-1642	454	9	published	publish	VERB
asir-1642	454	10	by	by	ADP
asir-1642	454	11	scholink	scholink	PROPN
asir-1642	454	12	inc	inc	PROPN
asir-1642	454	13	.	.	PROPN
asir-1642	454	14	a	a	PRON
asir-1642	454	15	..	..	PUNCT
asir-1642	454	16	from	from	ADP
asir-1642	454	17	orbiting	orbit	VERB
asir-1642	454	18	equation	equation	NOUN
asir-1642	454	19	t	t	PROPN
asir-1642	454	20	²	²	NUM
asir-1642	454	21	a	a	DET
asir-1642	454	22	²	²	NUM
asir-1642	454	23	=	=	PUNCT
asir-1642	454	24	²m	²m	ADJ
asir-1642	454	25	2	2	NUM
asir-1642	454	26	=	=	SYM
asir-1642	454	27	²	²	NUM
asir-1642	454	28	2	2	NUM
asir-1642	454	29	m	m	NOUN
asir-1642	454	30	=	=	NUM
asir-1642	454	31	²	²	PROPN
asir-1642	454	32	a	a	DET
asir-1642	454	33	gm	gm	NOUN
asir-1642	454	34	then	then	ADV
asir-1642	454	35	𝐓	𝐓	PROPN
asir-1642	454	36	²	²	PROPN
asir-1642	454	37	𝐚	𝐚	PROPN
asir-1642	454	38	³	³	X
asir-1642	454	39	=	=	X
asir-1642	454	40	𝟒𝛑²	𝟒𝛑²	ADJ
asir-1642	454	41	𝐆𝐌	𝐆𝐌	NOUN
asir-1642	455	1	=	=	PUNCT
asir-1642	455	2	constant	constant	ADJ
asir-1642	455	3	k	k	X
asir-1642	455	4	=	=	SYM
asir-1642	455	5	f	f	PROPN
asir-1642	455	6	²	²	NUM
asir-1642	455	7	.a	.a	NOUN
asir-1642	455	8	³	³	NUM
asir-1642	455	9	or	or	CCONJ
asir-1642	455	10	1	1	NUM
asir-1642	455	11	=	=	SYM
asir-1642	455	12	k.	k.	NOUN
asir-1642	455	13	𝐟	𝐟	PROPN
asir-1642	456	1	²𝐧.	²𝐧.	PROPN
asir-1642	456	2	𝐚𝟑	𝐚𝟑	PROPN
asir-1642	457	1	=	=	X
asir-1642	457	2	𝟒𝛑²	𝟒𝛑²	PRON
asir-1642	457	3	𝐆𝐌	𝐆𝐌	PROPN
asir-1642	457	4	.	.	PUNCT
asir-1642	458	1	𝐟	𝐟	PRON
asir-1642	458	2	²𝐧.	²𝐧.	PROPN
asir-1642	458	3	𝐚𝟑	𝐚𝟑	PROPN
asir-1642	458	4	,	,	PUNCT
asir-1642	458	5	the	the	DET
asir-1642	458	6	constant	constant	ADJ
asir-1642	458	7	work	work	NOUN
asir-1642	458	8	1	1	NUM
asir-1642	458	9	/	/	SYM
asir-1642	458	10	k	k	NOUN
asir-1642	458	11	=	=	PUNCT
asir-1642	458	12	².a³	².a³	NOUN
asir-1642	458	13	and	and	CCONJ
asir-1642	458	14	the	the	DET
asir-1642	458	15	constant	constant	ADJ
asir-1642	458	16	energy	energy	NOUN
asir-1642	458	17	e	e	NOUN
asir-1642	458	18	,	,	PUNCT
asir-1642	458	19	in	in	ADP
asir-1642	458	20	orbit	orbit	NOUN
asir-1642	458	21	,	,	PUNCT
asir-1642	458	22	is	be	AUX
asir-1642	458	23	k	k	NOUN
asir-1642	458	24	=	=	SYM
asir-1642	458	25	e	e	NOUN
asir-1642	458	26	=	=	NOUN
asir-1642	458	27	t²	t²	NOUN
asir-1642	458	28	a³	a³	ADV
asir-1642	458	29	from	from	ADP
asir-1642	458	30	equation	equation	NOUN
asir-1642	458	31	1	1	NUM
asir-1642	458	32	=	=	SYM
asir-1642	458	33	c.	c.	PROPN
asir-1642	458	34	².a³	².a³	PROPN
asir-1642	458	35	,	,	PUNCT
asir-1642	458	36	and	and	CCONJ
asir-1642	458	37	constant	constant	ADJ
asir-1642	458	38	work	work	NOUN
asir-1642	458	39	1	1	NUM
asir-1642	458	40	/	/	SYM
asir-1642	458	41	k	k	NOUN
asir-1642	458	42	=	=	SYM
asir-1642	458	43	².a³	².a³	NOUN
asir-1642	458	44	the	the	DET
asir-1642	458	45	constant	constant	ADJ
asir-1642	458	46	energy	energy	NOUN
asir-1642	458	47	in	in	ADP
asir-1642	458	48	orbit	orbit	NOUN
asir-1642	458	49	is	be	AUX
asir-1642	458	50	k	k	NOUN
asir-1642	458	51	=	=	PROPN
asir-1642	458	52	t²	t²	NOUN
asir-1642	458	53	a³	a³	PROPN
asir-1642	458	54	…	…	PUNCT
asir-1642	458	55	..	..	PUNCT
asir-1642	458	56	(	(	PUNCT
asir-1642	458	57	e	e	X
asir-1642	458	58	)	)	PUNCT
asir-1642	458	59	it	it	PRON
asir-1642	458	60	was	be	AUX
asir-1642	458	61	shown	show	VERB
asir-1642	458	62	that	that	SCONJ
asir-1642	458	63	the	the	DET
asir-1642	458	64	maximum	maximum	ADJ
asir-1642	458	65	energy	energy	NOUN
asir-1642	458	66	in	in	ADP
asir-1642	458	67	hydrogen	hydrogen	NOUN
asir-1642	458	68	atom	atom	NOUN
asir-1642	458	69	is	be	AUX
asir-1642	458	70	e	e	NOUN
asir-1642	458	71	=	=	SYM
asir-1642	459	1	h	h	NOUN
asir-1642	459	2	f	f	NOUN
asir-1642	460	1	=	=	NOUN
asir-1642	460	2	-13,6	-13,6	PUNCT
asir-1642	460	3	ev	ev	PROPN
asir-1642	460	4	=	=	SYM
asir-1642	460	5	13,6	13,6	NUM
asir-1642	460	6	x	x	SYM
asir-1642	460	7	1,6.10	1,6.10	NUM
asir-1642	460	8	9	9	NUM
asir-1642	460	9	=	=	SYM
asir-1642	460	10	2,176.10	2,176.10	NUM
asir-1642	460	11	joule	joule	NOUN
asir-1642	460	12	,	,	PUNCT
asir-1642	460	13	the	the	DET
asir-1642	460	14	frequency	frequency	NOUN
asir-1642	460	15	is	be	AUX
asir-1642	460	16	f	f	NOUN
asir-1642	460	17	=	=	SYM
asir-1642	460	18	e	e	PROPN
asir-1642	460	19	/	/	SYM
asir-1642	460	20	h	h	NOUN
asir-1642	460	21	or	or	CCONJ
asir-1642	460	22	,	,	PUNCT
asir-1642	460	23	f	f	PROPN
asir-1642	460	24	=	=	PROPN
asir-1642	460	25	2,176.10	2,176.10	NUM
asir-1642	460	26	j	j	PROPN
asir-1642	460	27	/	/	SYM
asir-1642	460	28	6,6262.10	6,6262.10	NUM
asir-1642	460	29	3	3	NUM
asir-1642	460	30	j.s	j.s	PROPN
asir-1642	460	31	=	=	SYM
asir-1642	460	32	3	3	NUM
asir-1642	460	33	,	,	PUNCT
asir-1642	460	34	28393.10	28393.10	NUM
asir-1642	460	35	/s	/	NOUN
asir-1642	460	36	,	,	PUNCT
asir-1642	460	37	and	and	CCONJ
asir-1642	460	38	the	the	DET
asir-1642	460	39	period	period	NOUN
asir-1642	460	40	in	in	ADP
asir-1642	460	41	orbit	orbit	NOUN
asir-1642	460	42	,	,	PUNCT
asir-1642	460	43	t	t	NOUN
asir-1642	460	44	=	=	PUNCT
asir-1642	460	45	=	=	SYM
asir-1642	460	46	3,04513.10	3,04513.10	NUM
asir-1642	460	47	6	6	NUM
asir-1642	460	48	s.	s.	NOUN
asir-1642	460	49	the	the	DET
asir-1642	460	50	motion	motion	NOUN
asir-1642	460	51	of	of	ADP
asir-1642	460	52	all	all	DET
asir-1642	460	53	moving	move	VERB
asir-1642	460	54	energy	energy	NOUN
asir-1642	460	55	-	-	PUNCT
asir-1642	460	56	tanks	tank	NOUN
asir-1642	460	57	is	be	AUX
asir-1642	460	58	sinusoidal	sinusoidal	ADJ
asir-1642	460	59	as	as	ADP
asir-1642	460	60	equation	equation	NOUN
asir-1642	460	61	→	→	SYM
asir-1642	460	62	{	{	PUNCT
asir-1642	460	63	[	[	X
asir-1642	460	64	εe²	εe²	NOUN
asir-1642	460	65	+	+	CCONJ
asir-1642	460	66	μb²	μb²	NOUN
asir-1642	460	67	]	]	X
asir-1642	460	68	=	=	SYM
asir-1642	460	69	2.λc.sin.2φ	2.λc.sin.2φ	NUM
asir-1642	460	70	}	}	PUNCT
asir-1642	460	71	←	←	PROPN
asir-1642	460	72	(	(	PUNCT
asir-1642	460	73	e1	e1	PROPN
asir-1642	460	74	)	)	PUNCT
asir-1642	460	75	and	and	CCONJ
asir-1642	460	76	the	the	DET
asir-1642	460	77	work	work	NOUN
asir-1642	460	78	produced	produce	VERB
asir-1642	460	79	is	be	AUX
asir-1642	460	80	stored	store	VERB
asir-1642	460	81	in	in	ADP
asir-1642	460	82	their	their	PRON
asir-1642	460	83	sine	sine	NOUN
asir-1642	460	84	-	-	PUNCT
asir-1642	460	85	curve	curve	NOUN
asir-1642	460	86	-	-	PUNCT
asir-1642	460	87	area	area	NOUN
asir-1642	460	88	of	of	ADP
asir-1642	460	89	x	x	PROPN
asir-1642	460	90	,	,	PUNCT
asir-1642	460	91	y	y	PROPN
asir-1642	460	92	,	,	PUNCT
asir-1642	460	93	coordinate	coordinate	VERB
asir-1642	460	94	axis	axis	NOUN
asir-1642	460	95	as	as	ADP
asir-1642	460	96	∫	∫	PROPN
asir-1642	460	97	x	x	PROPN
asir-1642	460	98	dx	dx	PROPN
asir-1642	460	99	0	0	NUM
asir-1642	461	1	=	=	SYM
asir-1642	461	2	2	2	NUM
asir-1642	461	3	as	as	ADP
asir-1642	461	4	equation	equation	NOUN
asir-1642	461	5	(	(	PUNCT
asir-1642	461	6	e1	e1	PROPN
asir-1642	461	7	)	)	PUNCT
asir-1642	461	8	.	.	PUNCT
asir-1642	462	1	simultaneously	simultaneously	ADV
asir-1642	462	2	work	work	VERB
asir-1642	462	3	=	=	PUNCT
asir-1642	462	4	sine	sine	ADJ
asir-1642	462	5	integral	integral	ADJ
asir-1642	462	6	=	=	ADJ
asir-1642	462	7	∫	∫	PROPN
asir-1642	462	8	t	t	PROPN
asir-1642	462	9	t	t	NOUN
asir-1642	462	10	0	0	PUNCT
asir-1642	463	1	d	d	NOUN
asir-1642	463	2	=	=	SYM
asir-1642	463	3	1	1	NUM
asir-1642	463	4	,	,	PUNCT
asir-1642	463	5	at	at	ADP
asir-1642	463	6	critical	critical	ADJ
asir-1642	463	7	-	-	PUNCT
asir-1642	463	8	energy	energy	NOUN
asir-1642	463	9	-	-	PUNCT
asir-1642	463	10	point	point	NOUN
asir-1642	463	11	where	where	SCONJ
asir-1642	463	12	point	point	NOUN
asir-1642	463	13	is	be	AUX
asir-1642	463	14	such	such	ADJ
asir-1642	463	15	that	that	DET
asir-1642	463	16	si(x	si(x	NOUN
asir-1642	463	17	=	=	SYM
asir-1642	463	18	1	1	X
asir-1642	463	19	)	)	PUNCT
asir-1642	463	20	becomes	become	VERB
asir-1642	463	21	equal	equal	ADJ
asir-1642	463	22	to	to	ADP
asir-1642	463	23	monad	monad	PROPN
asir-1642	463	24	1	1	NUM
asir-1642	463	25	,	,	PUNCT
asir-1642	463	26	and	and	CCONJ
asir-1642	463	27	this	this	DET
asir-1642	463	28	critical	critical	ADJ
asir-1642	463	29	-	-	PUNCT
asir-1642	463	30	energy	energy	NOUN
asir-1642	463	31	-	-	PUNCT
asir-1642	463	32	unit	unit	NOUN
asir-1642	463	33	happens	happen	VERB
asir-1642	463	34	at	at	ADP
asir-1642	463	35	the	the	DET
asir-1642	463	36	point	point	NOUN
asir-1642	463	37	x	x	PUNCT
asir-1642	463	38	=	=	SYM
asir-1642	463	39	1	1	NUM
asir-1642	463	40	,	,	PUNCT
asir-1642	463	41	0572508754	0572508754	NUM
asir-1642	463	42	,	,	PUNCT
asir-1642	463	43	or	or	CCONJ
asir-1642	463	44	at	at	ADP
asir-1642	463	45	axis	axis	NOUN
asir-1642	463	46	→	→	PUNCT
asir-1642	463	47	a	a	DET
asir-1642	463	48	=	=	SYM
asir-1642	463	49	2x	2x	NOUN
asir-1642	463	50	=	=	SYM
asir-1642	463	51	2,1145016	2,1145016	PROPN
asir-1642	463	52	m.	m.	NOUN
asir-1642	463	53	from	from	ADP
asir-1642	463	54	relation	relation	NOUN
asir-1642	463	55	(	(	PUNCT
asir-1642	463	56	4πa³/3)³	4πa³/3)³	NOUN
asir-1642	463	57	=	=	SYM
asir-1642	463	58	1,616229.10	1,616229.10	NUM
asir-1642	463	59	3	3	NUM
asir-1642	463	60	,	,	PUNCT
asir-1642	463	61	a	a	DET
asir-1642	463	62	=	=	SYM
asir-1642	463	63	5,447.10	5,447.10	NUM
asir-1642	463	64	,	,	PUNCT
asir-1642	463	65	or	or	CCONJ
asir-1642	463	66	semi	semi	ADJ
asir-1642	463	67	-	-	ADJ
asir-1642	463	68	major	major	ADJ
asir-1642	463	69	axis	axis	NOUN
asir-1642	463	70	in	in	ADP
asir-1642	463	71	hydrogen	hydrogen	NOUN
asir-1642	463	72	cave	cave	NOUN
asir-1642	463	73	is	be	AUX
asir-1642	463	74	a	a	DET
asir-1642	463	75	=	=	NUM
asir-1642	463	76	10	10	NUM
asir-1642	463	77	m	m	NOUN
asir-1642	463	78	,	,	PUNCT
asir-1642	463	79	and	and	CCONJ
asir-1642	463	80	the	the	DET
asir-1642	463	81	basic	basic	ADJ
asir-1642	463	82	-	-	PUNCT
asir-1642	463	83	coefficient	coefficient	NOUN
asir-1642	463	84	[	[	X
asir-1642	463	85	2si(1	2si(1	NUM
asir-1642	463	86	)	)	PUNCT
asir-1642	463	87	]	]	PUNCT
asir-1642	463	88	,	,	PUNCT
asir-1642	463	89	is	be	AUX
asir-1642	463	90	the	the	DET
asir-1642	463	91	constant	constant	ADJ
asir-1642	463	92	a	a	DET
asir-1642	463	93	=	=	SYM
asir-1642	463	94	2x	2x	NUM
asir-1642	463	95	=	=	SYM
asir-1642	463	96	2,1145016.10	2,1145016.10	NUM
asir-1642	463	97	m.	m.	NOUN
asir-1642	463	98	placing	place	VERB
asir-1642	463	99	in	in	ADP
asir-1642	463	100	hydrogen	hydrogen	NOUN
asir-1642	463	101	-	-	PUNCT
asir-1642	463	102	rim	rim	NOUN
asir-1642	463	103	the	the	DET
asir-1642	463	104	period	period	NOUN
asir-1642	463	105	t	t	PROPN
asir-1642	463	106	,	,	PUNCT
asir-1642	463	107	and	and	CCONJ
asir-1642	463	108	the	the	DET
asir-1642	463	109	prior	prior	ADJ
asir-1642	463	110	semi	semi	ADJ
asir-1642	463	111	-	-	ADJ
asir-1642	463	112	major	major	ADJ
asir-1642	463	113	axis	axis	NOUN
asir-1642	463	114	a	a	PRON
asir-1642	463	115	,	,	PUNCT
asir-1642	464	1	then	then	ADV
asir-1642	464	2	k	k	PROPN
asir-1642	464	3	=	=	PUNCT
asir-1642	464	4	𝐓²	𝐓²	ADV
asir-1642	464	5	𝐚³	𝐚³	ADV
asir-1642	464	6	=	=	PUNCT
asir-1642	465	1	[	[	X
asir-1642	465	2	3,0	3,0	NUM
asir-1642	465	3	3	3	NUM
asir-1642	465	4	.	.	NOUN
asir-1642	465	5	0	0	NUM
asir-1642	465	6	²	²	NUM
asir-1642	466	1	[	[	X
asir-1642	466	2	2	2	NUM
asir-1642	466	3	,	,	PUNCT
asir-1642	466	4	0	0	NUM
asir-1642	466	5	6	6	NUM
asir-1642	466	6	.	.	SYM
asir-1642	466	7	0	0	NUM
asir-1642	466	8	³	³	X
asir-1642	466	9	=	=	SYM
asir-1642	466	10	9,2	9,2	NUM
asir-1642	466	11	2	2	NUM
asir-1642	466	12	.	.	NOUN
asir-1642	466	13	0	0	NUM
asir-1642	467	1	9	9	NUM
asir-1642	467	2	,	,	PUNCT
asir-1642	467	3	6	6	NUM
asir-1642	467	4	.	.	NOUN
asir-1642	467	5	0	0	NUM
asir-1642	468	1	=	=	SYM
asir-1642	468	2	9	9	NUM
asir-1642	468	3	,	,	PUNCT
asir-1642	468	4	808238	808238	NUM
asir-1642	468	5	²	²	NUM
asir-1642	468	6	m³	m³	VERB
asir-1642	468	7	=	=	SYM
asir-1642	468	8	k	k	PROPN
asir-1642	468	9	,	,	PUNCT
asir-1642	468	10	agreeing	agree	VERB
asir-1642	468	11	with	with	ADP
asir-1642	468	12	gravity	gravity	NOUN
asir-1642	468	13	g	g	NOUN
asir-1642	468	14	,	,	PUNCT
asir-1642	468	15	as	as	SCONJ
asir-1642	468	16	is	be	AUX
asir-1642	468	17	measured	measure	VERB
asir-1642	468	18	.	.	PUNCT
asir-1642	469	1	i.e.	i.e.	X
asir-1642	469	2	,	,	PUNCT
asir-1642	469	3	the	the	DET
asir-1642	469	4	minimum	minimum	NOUN
asir-1642	469	5	-	-	PUNCT
asir-1642	469	6	work	work	NOUN
asir-1642	469	7	→	→	SYM
asir-1642	469	8	w	w	NOUN
asir-1642	469	9	=	=	SYM
asir-1642	469	10	4π²	4π²	NUM
asir-1642	469	11	𝐫³	𝐫³	NOUN
asir-1642	469	12	𝐓²	𝐓²	PROPN
asir-1642	469	13	.	.	PUNCT
asir-1642	470	1	�	�	PROPN
asir-1642	470	2	̅	̅	NOUN
asir-1642	470	3	�	�	PROPN
asir-1642	470	4	=	=	SYM
asir-1642	470	5	4π².r³.𝐟²𝐩.	4π².r³.𝐟²𝐩.	PROPN
asir-1642	470	6	�	�	PROPN
asir-1642	470	7	̅	̅	NOUN
asir-1642	470	8	�	�	PROPN
asir-1642	470	9	←	←	PROPN
asir-1642	470	10	in	in	ADP
asir-1642	470	11	an	an	DET
asir-1642	470	12	negative	negative	ADJ
asir-1642	470	13	-	-	PUNCT
asir-1642	470	14	elliptic	elliptic	ADJ
asir-1642	470	15	-	-	PUNCT
asir-1642	470	16	energy	energy	NOUN
asir-1642	470	17	-	-	PUNCT
asir-1642	470	18	field	field	NOUN
asir-1642	470	19	-	-	PUNCT
asir-1642	470	20	disk	disk	NOUN
asir-1642	470	21	as	as	SCONJ
asir-1642	470	22	this	this	PRON
asir-1642	470	23	is	be	AUX
asir-1642	470	24	pns	pns	NOUN
asir-1642	470	25	,	,	PUNCT
asir-1642	470	26	is	be	AUX
asir-1642	470	27	stored	store	VERB
asir-1642	470	28	as	as	ADP
asir-1642	470	29	a	a	DET
asir-1642	470	30	voltage	voltage	NOUN
asir-1642	470	31	[	[	X
asir-1642	470	32	n≡⊕↔⊝≡p	n≡⊕↔⊝≡p	X
asir-1642	470	33	]	]	PUNCT
asir-1642	470	34	across	across	ADP
asir-1642	470	35	the	the	DET
asir-1642	470	36	disk	disk	NOUN
asir-1642	470	37	between	between	ADP
asir-1642	470	38	the	the	DET
asir-1642	470	39	rotating	rotate	VERB
asir-1642	470	40	planet	planet	NOUN
asir-1642	470	41	p	p	NOUN
asir-1642	470	42	and	and	CCONJ
asir-1642	470	43	nucleus	nucleus	PROPN
asir-1642	470	44	n	n	CCONJ
asir-1642	470	45	,	,	PUNCT
asir-1642	470	46	produced	produce	VERB
asir-1642	470	47	from	from	ADP
asir-1642	470	48	the	the	DET
asir-1642	470	49	pressure	pressure	NOUN
asir-1642	470	50	,	,	PUNCT
asir-1642	470	51	σ	σ	PROPN
asir-1642	470	52	,	,	PUNCT
asir-1642	470	53	of	of	ADP
asir-1642	470	54	the	the	DET
asir-1642	470	55	frequency	frequency	NOUN
asir-1642	470	56	𝐟𝐩	𝐟𝐩	NOUN
asir-1642	470	57	and	and	CCONJ
asir-1642	470	58	of	of	ADP
asir-1642	470	59	the	the	DET
asir-1642	470	60	semi	semi	ADJ
asir-1642	470	61	-	-	ADJ
asir-1642	470	62	major	major	ADJ
asir-1642	470	63	axis	axis	NOUN
asir-1642	470	64	𝐚	𝐚	ADP
asir-1642	470	65	𝐩	𝐩	PROPN
asir-1642	470	66	of	of	ADP
asir-1642	470	67	the	the	DET
asir-1642	470	68	planet	planet	NOUN
asir-1642	470	69	.	.	PUNCT
asir-1642	471	1	motion	motion	NOUN
asir-1642	471	2	is	be	AUX
asir-1642	471	3	kept	keep	VERB
asir-1642	471	4	,	,	PUNCT
asir-1642	471	5	is	be	AUX
asir-1642	471	6	quantized	quantize	VERB
asir-1642	471	7	,	,	PUNCT
asir-1642	471	8	as	as	ADP
asir-1642	471	9	work	work	NOUN
asir-1642	471	10	→	→	SYM
asir-1642	471	11	w	w	NOUN
asir-1642	471	12	=	=	SYM
asir-1642	471	13	1=	1=	X
asir-1642	471	14	k	k	X
asir-1642	471	15	≡	≡	PROPN
asir-1642	471	16	[	[	X
asir-1642	471	17	i].[±s²	i].[±s²	X
asir-1642	471	18	]	]	X
asir-1642	471	19	≡	≡	PROPN
asir-1642	471	20	mfmf	mfmf	PROPN
asir-1642	471	21	field	field	PROPN
asir-1642	471	22	←	←	PROPN
asir-1642	471	23	in	in	ADP
asir-1642	471	24	the	the	DET
asir-1642	471	25	orbit	orbit	NOUN
asir-1642	471	26	-	-	PUNCT
asir-1642	471	27	area	area	NOUN
asir-1642	471	28	,	,	PUNCT
asir-1642	471	29	πab	πab	INTJ
asir-1642	471	30	,	,	PUNCT
asir-1642	471	31	upon	upon	SCONJ
asir-1642	471	32	the	the	DET
asir-1642	471	33	spin	spin	NOUN
asir-1642	471	34	�	�	PROPN
asir-1642	471	35	̅	̅	NOUN
asir-1642	471	36	�	�	NOUN
asir-1642	471	37	orientation	orientation	NOUN
asir-1642	471	38	of	of	ADP
asir-1642	471	39	the	the	DET
asir-1642	471	40	pointy	pointy	ADJ
asir-1642	471	41	-	-	PUNCT
asir-1642	471	42	material	material	NOUN
asir-1642	471	43	-	-	PUNCT
asir-1642	471	44	points	point	NOUN
asir-1642	472	1	[	[	X
asir-1642	472	2	±s²].orientation	±s²].orientation	NOUN
asir-1642	472	3	of	of	ADP
asir-1642	472	4	spin	spin	NOUN
asir-1642	472	5	becomes	become	VERB
asir-1642	472	6	from	from	ADP
asir-1642	472	7	the	the	DET
asir-1642	472	8	energy	energy	NOUN
asir-1642	472	9	in	in	ADP
asir-1642	472	10	the	the	DET
asir-1642	472	11	sinusoidal	sinusoidal	ADJ
asir-1642	472	12	gravity	gravity	NOUN
asir-1642	472	13	-	-	PUNCT
asir-1642	472	14	fields	field	NOUN
asir-1642	472	15	in	in	ADP
asir-1642	472	16	orbit	orbit	NOUN
asir-1642	472	17	,	,	PUNCT
asir-1642	472	18	created	create	VERB
asir-1642	472	19	by	by	ADP
asir-1642	472	20	the	the	DET
asir-1642	472	21	motion	motion	NOUN
asir-1642	472	22	of	of	ADP
asir-1642	472	23	oscillation	oscillation	NOUN
asir-1642	472	24	of	of	ADP
asir-1642	472	25	the	the	DET
asir-1642	472	26	material	material	NOUN
asir-1642	472	27	points	point	NOUN
asir-1642	473	1	[	[	X
asir-1642	473	2	⊕	⊕	NOUN
asir-1642	473	3	↻	↻	NOUN
asir-1642	473	4	↺	↺	NOUN
asir-1642	473	5	⊝	⊝	NOUN
asir-1642	473	6	]	]	PUNCT
asir-1642	473	7	.	.	PUNCT
asir-1642	474	1	any	any	DET
asir-1642	474	2	interaction	interaction	NOUN
asir-1642	474	3	between	between	ADP
asir-1642	474	4	this	this	DET
asir-1642	474	5	oriented	orient	VERB
asir-1642	474	6	-	-	PUNCT
asir-1642	474	7	energy	energy	NOUN
asir-1642	474	8	disk	disk	NOUN
asir-1642	474	9	-	-	PUNCT
asir-1642	474	10	rim	rim	NOUN
asir-1642	474	11	and	and	CCONJ
asir-1642	474	12	a	a	DET
asir-1642	474	13	body	body	NOUN
asir-1642	474	14	-	-	PUNCT
asir-1642	474	15	planet	planet	NOUN
asir-1642	474	16	creates	create	VERB
asir-1642	474	17	disturbances	disturbance	NOUN
asir-1642	474	18	in	in	ADP
asir-1642	474	19	disk	disk	NOUN
asir-1642	474	20	and	and	CCONJ
asir-1642	474	21	reorientation	reorientation	NOUN
asir-1642	474	22	of	of	ADP
asir-1642	474	23	spin	spin	NOUN
asir-1642	474	24	�	�	PROPN
asir-1642	474	25	̅	̅	NOUN
asir-1642	474	26	�	�	PROPN
asir-1642	474	27	≡	≡	PROPN
asir-1642	474	28	motion	motion	NOUN
asir-1642	474	29	≡	≡	PROPN
asir-1642	474	30	work	work	NOUN
asir-1642	475	1	≡	≡	PROPN
asir-1642	475	2	k	k	PROPN
asir-1642	476	1	=	=	PUNCT
asir-1642	476	2	constant	constant	ADJ
asir-1642	476	3	=	=	PUNCT
asir-1642	476	4	quanta	quanta	PROPN
asir-1642	476	5	and	and	CCONJ
asir-1642	476	6	transformed	transform	VERB
asir-1642	476	7	as	as	ADP
asir-1642	476	8	,	,	PUNCT
asir-1642	476	9	the	the	DET
asir-1642	476	10	gravity	gravity	NOUN
asir-1642	476	11	-	-	PUNCT
asir-1642	476	12	force	force	NOUN
asir-1642	476	13	in	in	ADP
asir-1642	476	14	disk	disk	NOUN
asir-1642	476	15	,	,	PUNCT
asir-1642	476	16	and	and	CCONJ
asir-1642	476	17	which	which	DET
asir-1642	476	18	energy	energy	NOUN
asir-1642	476	19	is	be	AUX
asir-1642	476	20	equal	equal	ADJ
asir-1642	476	21	to	to	ADP
asir-1642	476	22	the	the	DET
asir-1642	476	23	gravity	gravity	NOUN
asir-1642	476	24	acceleration	acceleration	NOUN
asir-1642	476	25	g	g	NOUN
asir-1642	476	26	,	,	PUNCT
asir-1642	476	27	and	and	CCONJ
asir-1642	476	28	this	this	PRON
asir-1642	476	29	because	because	SCONJ
asir-1642	476	30	g	g	PROPN
asir-1642	476	31	=	=	PUNCT
asir-1642	476	32	force	force	NOUN
asir-1642	476	33	,	,	PUNCT
asir-1642	476	34	as	as	SCONJ
asir-1642	476	35	equation	equation	NOUN
asir-1642	476	36	g	g	NOUN
asir-1642	476	37	=	=	SYM
asir-1642	476	38	f	f	X
asir-1642	476	39	/	/	SYM
asir-1642	476	40	m.	m.	NOUN
asir-1642	476	41	bodies	body	NOUN
asir-1642	476	42	produce	produce	VERB
asir-1642	476	43	gravity	gravity	NOUN
asir-1642	476	44	{	{	PUNCT
asir-1642	476	45	the	the	DET
asir-1642	476	46	change	change	NOUN
asir-1642	476	47	of	of	ADP
asir-1642	476	48	spin	spin	NOUN
asir-1642	476	49	-	-	PUNCT
asir-1642	476	50	direction	direction	NOUN
asir-1642	476	51	of	of	ADP
asir-1642	476	52	m	m	NOUN
asir-1642	476	53	-	-	ADJ
asir-1642	476	54	p	p	NOUN
asir-1642	476	55	-	-	PUNCT
asir-1642	476	56	dipole	dipole	NOUN
asir-1642	476	57	[	[	X
asir-1642	476	58	⊕s²	⊕s²	NUM
asir-1642	476	59	↻	↻	NOUN
asir-1642	476	60	↺	↺	NOUN
asir-1642	476	61	⊝s²	⊝s²	NOUN
asir-1642	476	62	]	]	PUNCT
asir-1642	476	63	in	in	ADP
asir-1642	476	64	mfmf	mfmf	PROPN
asir-1642	476	65	field	field	PROPN
asir-1642	476	66	}	}	PUNCT
asir-1642	476	67	from	from	ADP
asir-1642	476	68	stationary	stationary	ADJ
asir-1642	476	69	force	force	NOUN
asir-1642	476	70	[	[	X
asir-1642	476	71	i	i	X
asir-1642	476	72	]	]	PUNCT
asir-1642	476	73	=	=	PUNCT
asir-1642	476	74			PROPN
asir-1642	476	75	s²	s²	NOUN
asir-1642	476	76	,	,	PUNCT
asir-1642	476	77	and	and	CCONJ
asir-1642	476	78	because	because	SCONJ
asir-1642	476	79	gravity	gravity	NOUN
asir-1642	476	80	≡	≡	PROPN
asir-1642	476	81	acceleration	acceleration	NOUN
asir-1642	476	82	and	and	CCONJ
asir-1642	476	83	not	not	PART
asir-1642	476	84	change	change	NOUN
asir-1642	476	85	of	of	ADP
asir-1642	476	86	velocity	velocity	NOUN
asir-1642	476	87	vector	vector	NOUN
asir-1642	476	88	,	,	PUNCT
asir-1642	476	89	it	it	PRON
asir-1642	476	90	is	be	AUX
asir-1642	476	91	by	by	ADP
asir-1642	476	92	changing	change	VERB
asir-1642	476	93	the	the	DET
asir-1642	476	94	direction	direction	NOUN
asir-1642	476	95	of	of	ADP
asir-1642	476	96	the	the	DET
asir-1642	476	97	above	above	ADJ
asir-1642	476	98	dipole	dipole	NOUN
asir-1642	476	99	.	.	PUNCT
asir-1642	477	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-1642	477	2	applied	apply	VERB
asir-1642	477	3	science	science	NOUN
asir-1642	477	4	and	and	CCONJ
asir-1642	477	5	innovative	innovative	ADJ
asir-1642	477	6	research	research	NOUN
asir-1642	477	7	vol	vol	NOUN
asir-1642	477	8	.	.	PROPN
asir-1642	478	1	2	2	NUM
asir-1642	478	2	,	,	PUNCT
asir-1642	478	3	no	no	INTJ
asir-1642	478	4	.	.	NOUN
asir-1642	478	5	4	4	NUM
asir-1642	478	6	,	,	PUNCT
asir-1642	478	7	2018	2018	NUM
asir-1642	478	8	178	178	NUM
asir-1642	478	9	published	publish	VERB
asir-1642	478	10	by	by	ADP
asir-1642	478	11	scholink	scholink	PROPN
asir-1642	478	12	inc	inc	PROPN
asir-1642	478	13	.	.	PROPN
asir-1642	479	1	b	b	X
asir-1642	479	2	..	..	PUNCT
asir-1642	479	3	motion	motion	NOUN
asir-1642	479	4	with	with	ADP
asir-1642	479	5	velocity	velocity	NOUN
asir-1642	479	6	vector	vector	NOUN
asir-1642	479	7	v	v	NOUN
asir-1642	479	8	,	,	PUNCT
asir-1642	479	9	may	may	AUX
asir-1642	479	10	be	be	AUX
asir-1642	479	11	linear	linear	ADJ
asir-1642	479	12	or	or	CCONJ
asir-1642	479	13	rotational	rotational	ADJ
asir-1642	479	14	for	for	ADP
asir-1642	479	15	all	all	DET
asir-1642	479	16	displacements	displacement	NOUN
asir-1642	479	17	r	r	NOUN
asir-1642	479	18	,	,	PUNCT
asir-1642	479	19	and	and	CCONJ
asir-1642	479	20	thus	thus	ADV
asir-1642	479	21	exists	exist	VERB
asir-1642	479	22	a	a	DET
asir-1642	479	23	constant	constant	ADJ
asir-1642	479	24	work	work	NOUN
asir-1642	479	25	w	w	NOUN
asir-1642	479	26	=	=	PUNCT
asir-1642	479	27	k	k	PROPN
asir-1642	479	28	=	=	PUNCT
asir-1642	479	29	�	�	PROPN
asir-1642	479	30	̅	̅	NOUN
asir-1642	479	31	�	�	NOUN
asir-1642	479	32	x	x	SYM
asir-1642	479	33	�	�	PROPN
asir-1642	479	34	̅	̅	NOUN
asir-1642	479	35	�	�	PROPN
asir-1642	479	36	.	.	PUNCT
asir-1642	479	37	�	�	PROPN
asir-1642	479	38	̅	̅	NOUN
asir-1642	480	1	�	�	NOUN
asir-1642	480	2	=	=	SYM
asir-1642	480	3	v².r	v².r	PROPN
asir-1642	480	4	.	.	PUNCT
asir-1642	480	5	�	�	PROPN
asir-1642	480	6	̅	̅	NOUN
asir-1642	480	7	�	�	PROPN
asir-1642	480	8	.	.	PUNCT
asir-1642	481	1	i.e.	i.e.	X
asir-1642	481	2	,	,	PUNCT
asir-1642	481	3	constant	constant	ADJ
asir-1642	481	4	-	-	PUNCT
asir-1642	481	5	work	work	NOUN
asir-1642	481	6	=	=	SYM
asir-1642	481	7	k	k	NOUN
asir-1642	481	8	=	=	SYM
asir-1642	481	9	v²	v²	PROPN
asir-1642	481	10	.	.	PUNCT
asir-1642	482	1	r	r	NOUN
asir-1642	482	2	=	=	PUNCT
asir-1642	482	3	(	(	PUNCT
asir-1642	482	4	wr)².r	wr)².r	NOUN
asir-1642	482	5	=	=	PUNCT
asir-1642	482	6	[	[	PUNCT
asir-1642	482	7	𝟐𝛑	𝟐𝛑	X
asir-1642	482	8	𝐓	𝐓	PROPN
asir-1642	482	9	r]².r	r]².r	PROPN
asir-1642	482	10	=	=	PUNCT
asir-1642	482	11	𝟒𝛑²	𝟒𝛑²	PRON
asir-1642	482	12	𝐫²	𝐫²	NOUN
asir-1642	482	13	𝐓²	𝐓²	VERB
asir-1642	482	14	.	.	PUNCT
asir-1642	483	1	r	r	NOUN
asir-1642	483	2	=	=	PUNCT
asir-1642	483	3	𝟒𝛑²	𝟒𝛑²	NOUN
asir-1642	483	4	𝐫	𝐫	PROPN
asir-1642	483	5	³	³	PROPN
asir-1642	483	6	𝐓²	𝐓²	PROPN
asir-1642	483	7	=	=	SYM
asir-1642	483	8	4π²	4π²	NUM
asir-1642	483	9	.	.	PUNCT
asir-1642	484	1	𝐫³	𝐫³	PROPN
asir-1642	484	2	𝐓²	𝐓²	PROPN
asir-1642	485	1	=	=	SYM
asir-1642	485	2	4π².r³.𝐟²𝐩	4π².r³.𝐟²𝐩	PROPN
asir-1642	485	3	because	because	SCONJ
asir-1642	485	4	gravity	gravity	NOUN
asir-1642	485	5	-	-	PUNCT
asir-1642	485	6	force	force	NOUN
asir-1642	485	7	fg	fg	NOUN
asir-1642	485	8	becomes	become	VERB
asir-1642	485	9	from	from	ADP
asir-1642	485	10	the	the	DET
asir-1642	485	11	in	in	ADP
asir-1642	485	12	-	-	PUNCT
asir-1642	485	13	storages	storage	NOUN
asir-1642	485	14	acceleration	acceleration	VERB
asir-1642	485	15	a	a	DET
asir-1642	485	16	=	=	NOUN
asir-1642	485	17	v²/r	v²/r	NOUN
asir-1642	485	18	of	of	ADP
asir-1642	485	19	the	the	DET
asir-1642	485	20	mfmf	mfmf	NOUN
asir-1642	485	21	material	material	NOUN
asir-1642	485	22	points	point	NOUN
asir-1642	485	23	and	and	CCONJ
asir-1642	485	24	force	force	NOUN
asir-1642	486	1	[	[	X
asir-1642	486	2	i	i	X
asir-1642	486	3	]	]	PUNCT
asir-1642	486	4	is	be	AUX
asir-1642	486	5	stationary	stationary	ADJ
asir-1642	486	6	,	,	PUNCT
asir-1642	486	7	and	and	CCONJ
asir-1642	486	8	this	this	PRON
asir-1642	486	9	because	because	SCONJ
asir-1642	486	10	from	from	ADP
asir-1642	486	11	the	the	DET
asir-1642	486	12	pointy	pointy	ADV
asir-1642	486	13	-	-	PUNCT
asir-1642	486	14	rotated	rotate	VERB
asir-1642	486	15	-	-	PUNCT
asir-1642	486	16	dipole	dipole	NOUN
asir-1642	486	17	[	[	X
asir-1642	486	18	-s²	-s²	NOUN
asir-1642	486	19	↻	↻	PROPN
asir-1642	486	20	↺	↺	NOUN
asir-1642	486	21	+s²	+s²	PROPN
asir-1642	486	22	]	]	X
asir-1642	486	23	,	,	PUNCT
asir-1642	486	24	then	then	ADV
asir-1642	486	25	for	for	ADP
asir-1642	486	26	planck	planck	NOUN
asir-1642	486	27	length	length	NOUN
asir-1642	486	28	is	be	AUX
asir-1642	486	29	,	,	PUNCT
asir-1642	486	30	gravity	gravity	NOUN
asir-1642	486	31	force	force	NOUN
asir-1642	486	32	[	[	X
asir-1642	486	33	i	i	X
asir-1642	486	34	]	]	X
asir-1642	486	35	≡	≡	PROPN
asir-1642	486	36	fg	fg	PROPN
asir-1642	486	37	≡	≡	PROPN
asir-1642	486	38	mgg	mgg	PROPN
asir-1642	486	39	=	=	SYM
asir-1642	486	40	g.	g.	PROPN
asir-1642	486	41	[	[	PUNCT
asir-1642	486	42	𝜎	𝜎	X
asir-1642	486	43	𝑐²	𝑐²	NOUN
asir-1642	486	44	]	]	SYM
asir-1642	486	45	².r	².r	PROPN
asir-1642	486	46	=	=	SYM
asir-1642	486	47	mg	mg	NUM
asir-1642	486	48	v²	v²	PROPN
asir-1642	486	49	=	=	PUNCT
asir-1642	486	50	jw².gg	jw².gg	PROPN
asir-1642	487	1	=	=	PUNCT
asir-1642	488	1	[	[	PUNCT
asir-1642	488	2	4	4	NUM
asir-1642	488	3	2	2	NUM
asir-1642	488	4	]	]	PUNCT
asir-1642	488	5	w²	w²	NOUN
asir-1642	488	6	.	.	PUNCT
asir-1642	489	1	v²	v²	NOUN
asir-1642	489	2	=	=	SYM
asir-1642	489	3	v²	v²	PROPN
asir-1642	489	4	[	[	PUNCT
asir-1642	489	5	4	4	NUM
asir-1642	489	6	2	2	NUM
asir-1642	489	7	]	]	PUNCT
asir-1642	489	8	v²	v²	PROPN
asir-1642	489	9	²	²	NUM
asir-1642	489	10	=	=	SYM
asir-1642	489	11	[	[	PUNCT
asir-1642	489	12	v4	v4	NOUN
asir-1642	489	13	2	2	NUM
asir-1642	489	14	]	]	PUNCT
asir-1642	489	15	…	…	PUNCT
asir-1642	489	16	…	…	PUNCT
asir-1642	489	17	..	..	PUNCT
asir-1642	489	18	(	(	PUNCT
asir-1642	489	19	b	b	NOUN
asir-1642	489	20	)	)	PUNCT
asir-1642	489	21	and	and	CCONJ
asir-1642	489	22	from	from	ADP
asir-1642	489	23	relation	relation	NOUN
asir-1642	489	24	,	,	PUNCT
asir-1642	489	25	spin	spin	NOUN
asir-1642	489	26	s	s	PART
asir-1642	489	27	=	=	ADJ
asir-1642	489	28	�	�	PROPN
asir-1642	489	29	̅	̅	NOUN
asir-1642	489	30	�	�	NOUN
asir-1642	489	31	=	=	PUNCT
asir-1642	489	32	h√3	h√3	X
asir-1642	489	33	then	then	ADV
asir-1642	489	34	,	,	PUNCT
asir-1642	489	35	gravity	gravity	NOUN
asir-1642	489	36	-	-	PUNCT
asir-1642	489	37	force	force	NOUN
asir-1642	489	38	→	→	SYM
asir-1642	489	39	fg	fg	PROPN
asir-1642	489	40	≡	≡	PROPN
asir-1642	489	41	[	[	PUNCT
asir-1642	489	42	v4	v4	NOUN
asir-1642	489	43	2	2	NUM
asir-1642	489	44	]	]	PUNCT
asir-1642	489	45	𝝅	𝝅	PRON
asir-1642	489	46	𝟐	𝟐	NUM
asir-1642	489	47	(	(	PUNCT
asir-1642	489	48	+	+	ADJ
asir-1642	489	49	√𝟓	√𝟓	PROPN
asir-1642	489	50	)	)	PUNCT
asir-1642	489	51	�	�	PROPN
asir-1642	489	52	̅	̅	NOUN
asir-1642	489	53	�	�	NOUN
asir-1642	489	54	=	=	PUNCT
asir-1642	489	55	[	[	PUNCT
asir-1642	489	56	𝐧𝛑²	𝐧𝛑²	NOUN
asir-1642	489	57	𝟒	𝟒	NUM
asir-1642	489	58	(	(	PUNCT
asir-1642	489	59	+	+	NOUN
asir-1642	489	60	√𝟓	√𝟓	NOUN
asir-1642	489	61	)	)	PUNCT
asir-1642	489	62	]	]	PUNCT
asir-1642	489	63	�	�	SYM
asir-1642	489	64	̅	̅	NOUN
asir-1642	489	65	�	�	NOUN
asir-1642	489	66	v	v	NOUN
asir-1642	489	67	and	and	CCONJ
asir-1642	489	68	so	so	ADV
asir-1642	489	69	fg	fg	PROPN
asir-1642	489	70	≡	≡	PROPN
asir-1642	489	71	𝝅√𝟑	𝝅√𝟑	ADV
asir-1642	489	72	𝟔	𝟔	NUM
asir-1642	489	73	(	(	PUNCT
asir-1642	489	74	+	+	ADJ
asir-1642	489	75	√𝟓	√𝟓	NOUN
asir-1642	489	76	)	)	PUNCT
asir-1642	489	77	v	v	NOUN
asir-1642	489	78	=	=	PUNCT
asir-1642	490	1	𝐧√𝟑𝛑	𝐧√𝟑𝛑	PROPN
asir-1642	490	2	(	(	PUNCT
asir-1642	490	3	+	+	NOUN
asir-1642	490	4	√𝟓	√𝟓	NOUN
asir-1642	490	5	)	)	PUNCT
asir-1642	490	6	(	(	PUNCT
asir-1642	490	7	2	2	X
asir-1642	490	8	)	)	PUNCT
asir-1642	490	9	and	and	CCONJ
asir-1642	490	10	it	it	PRON
asir-1642	490	11	is	be	AUX
asir-1642	490	12	the	the	DET
asir-1642	490	13	black	black	ADJ
asir-1642	490	14	-	-	PUNCT
asir-1642	490	15	hole	hole	NOUN
asir-1642	490	16	-	-	PUNCT
asir-1642	490	17	gravity	gravity	NOUN
asir-1642	490	18	-	-	PUNCT
asir-1642	490	19	equation	equation	NOUN
asir-1642	490	20	which	which	PRON
asir-1642	490	21	is	be	AUX
asir-1642	490	22	related	relate	VERB
asir-1642	490	23	to	to	ADP
asir-1642	490	24	the	the	DET
asir-1642	490	25	inner	inner	ADJ
asir-1642	490	26	velocity	velocity	NOUN
asir-1642	490	27	v	v	NOUN
asir-1642	490	28	,	,	PUNCT
asir-1642	490	29	and	and	CCONJ
asir-1642	490	30	to	to	ADP
asir-1642	490	31	its	its	PRON
asir-1642	490	32	n	n	PRON
asir-1642	490	33	lobes	lobe	NOUN
asir-1642	490	34	.	.	PUNCT
asir-1642	491	1	gravity	gravity	NOUN
asir-1642	491	2	-	-	PUNCT
asir-1642	491	3	acceleration	acceleration	NOUN
asir-1642	491	4	in	in	ADP
asir-1642	491	5	black	black	ADJ
asir-1642	491	6	-	-	PUNCT
asir-1642	491	7	holes	hole	NOUN
asir-1642	491	8	is	be	AUX
asir-1642	491	9	gg=	gg=	PROPN
asir-1642	491	10	s	s	PROPN
asir-1642	491	11	[	[	PUNCT
asir-1642	491	12	v4	v4	PROPN
asir-1642	491	13	2	2	NUM
asir-1642	491	14	]	]	PUNCT
asir-1642	491	15	=[	=[	NOUN
asir-1642	491	16	3	3	NUM
asir-1642	491	17	,	,	PUNCT
asir-1642	491	18	926([√	926([√	NUM
asir-1642	491	19	+	+	NUM
asir-1642	491	20	]	]	PUNCT
asir-1642	491	21	.	.	PUNCT
asir-1642	492	1	√2	√2	NOUN
asir-1642	492	2	4	4	NUM
asir-1642	492	3	.	.	PUNCT
asir-1642	492	4	0	0	NUM
asir-1642	493	1	5).(299	5).(299	NUM
asir-1642	493	2	93	93	NUM
asir-1642	493	3	)	)	PUNCT
asir-1642	493	4	4	4	NUM
asir-1642	493	5	2	2	NUM
asir-1642	493	6	]	]	PUNCT
asir-1642	493	7	.𝑒3	.𝑒3	PUNCT
asir-1642	494	1	=	=	PUNCT
asir-1642	495	1	6,044981.10	6,044981.10	NUM
asir-1642	495	2	3	3	NUM
asir-1642	495	3	.80,776078.1032.20,085536	.80,776078.1032.20,085536	PUNCT
asir-1642	495	4	=	=	SYM
asir-1642	495	5	gg	gg	NOUN
asir-1642	495	6	=	=	SYM
asir-1642	495	7	9,8075633	9,8075633	NUM
asir-1642	495	8	,	,	PUNCT
asir-1642	495	9	near	near	ADP
asir-1642	495	10	all	all	DET
asir-1642	495	11	the	the	DET
asir-1642	495	12	prio	prio	NOUN
asir-1642	495	13	,	,	PUNCT
asir-1642	495	14	where	where	SCONJ
asir-1642	495	15	1	1	NUM
asir-1642	495	16	/	/	SYM
asir-1642	495	17	mg	mg	PROPN
asir-1642	495	18	=	=	SYM
asir-1642	495	19	s	s	PART
asir-1642	495	20	=	=	NOUN
asir-1642	495	21	mass	mass	NOUN
asir-1642	495	22	-	-	PUNCT
asir-1642	495	23	coefficient	coefficient	NOUN
asir-1642	495	24	[	[	X
asir-1642	495	25	√5	√5	PROPN
asir-1642	495	26	+	+	NOUN
asir-1642	495	27	1	1	NUM
asir-1642	495	28	]	]	PUNCT
asir-1642	495	29	.	.	PUNCT
asir-1642	496	1	√	√	NUM
asir-1642	496	2	4	4	NUM
asir-1642	496	3	.	.	PUNCT
asir-1642	497	1	e3	e3	NOUN
asir-1642	497	2	,	,	PUNCT
asir-1642	497	3	because	because	SCONJ
asir-1642	497	4	the	the	DET
asir-1642	497	5	constant	constant	ADJ
asir-1642	497	6	tensor	tensor	NOUN
asir-1642	497	7	tz	tz	NOUN
asir-1642	497	8	is	be	AUX
asir-1642	497	9	the	the	DET
asir-1642	497	10	length	length	NOUN
asir-1642	497	11	of	of	ADP
asir-1642	497	12	vector	vector	NOUN
asir-1642	497	13	,	,	PUNCT
asir-1642	497	14	z	z	PROPN
asir-1642	497	15	≡	≡	PROPN
asir-1642	497	16	m	m	PROPN
asir-1642	497	17	,	,	PUNCT
asir-1642	497	18	in	in	ADP
asir-1642	497	19	euclidean	euclidean	ADJ
asir-1642	497	20	coordinates	coordinate	NOUN
asir-1642	497	21	and	and	CCONJ
asir-1642	497	22	which	which	DET
asir-1642	497	23	magnitude	magnitude	NOUN
asir-1642	497	24	is	be	AUX
asir-1642	497	25	k	k	NOUN
asir-1642	497	26	=	=	PUNCT
asir-1642	497	27	tz	tz	PROPN
asir-1642	497	28	=	=	PUNCT
asir-1642	497	29	√y	√y	ADP
asir-1642	497	30	²	²	NUM
asir-1642	497	31	+	+	CCONJ
asir-1642	497	32	y2²	y2²	NOUN
asir-1642	497	33	+	+	CCONJ
asir-1642	497	34	y3²	y3²	NOUN
asir-1642	497	35	+	+	CCONJ
asir-1642	497	36	y	y	PROPN
asir-1642	497	37	²	²	NUM
asir-1642	497	38	,	,	PUNCT
asir-1642	497	39	denoting	denote	VERB
asir-1642	497	40	the	the	DET
asir-1642	497	41	energy	energy	NOUN
asir-1642	497	42	-	-	PUNCT
asir-1642	497	43	space	space	NOUN
asir-1642	497	44	relation	relation	NOUN
asir-1642	497	45	.	.	PUNCT
asir-1642	498	1	from	from	ADP
asir-1642	498	2	above	above	ADP
asir-1642	498	3	the	the	DET
asir-1642	498	4	dimensionless	dimensionless	ADJ
asir-1642	498	5	coefficient	coefficient	NOUN
asir-1642	498	6	of	of	ADP
asir-1642	498	7	work	work	NOUN
asir-1642	498	8	w	w	NOUN
asir-1642	498	9	is	be	AUX
asir-1642	498	10	[	[	X
asir-1642	498	11	√5	√5	PROPN
asir-1642	498	12	+	+	NOUN
asir-1642	498	13	1	1	NUM
asir-1642	498	14	]	]	PUNCT
asir-1642	498	15	for	for	ADP
asir-1642	498	16	any	any	DET
asir-1642	498	17	material	material	NOUN
asir-1642	498	18	cave	cave	NOUN
asir-1642	498	19	,	,	PUNCT
asir-1642	498	20	r	r	NOUN
asir-1642	498	21	,	,	PUNCT
asir-1642	498	22	coefficient	coefficient	NOUN
asir-1642	498	23	for	for	ADP
asir-1642	498	24	the	the	DET
asir-1642	498	25	unity	unity	NOUN
asir-1642	498	26	-	-	PUNCT
asir-1642	498	27	plane	plane	NOUN
asir-1642	498	28	quaternion	quaternion	NOUN
asir-1642	498	29	is	be	AUX
asir-1642	498	30	√√	√√	ADV
asir-1642	498	31	=	=	SYM
asir-1642	498	32	√	√	ADP
asir-1642	498	33	4	4	NUM
asir-1642	498	34	,	,	PUNCT
asir-1642	498	35	or	or	CCONJ
asir-1642	498	36	the	the	DET
asir-1642	498	37	same	same	ADJ
asir-1642	498	38	i	i	PRON
asir-1642	498	39			VERB
asir-1642	498	40	j	j	PROPN
asir-1642	498	41	≡	≡	PROPN
asir-1642	498	42	√	√	PROPN
asir-1642	498	43	⃡	⃡	NOUN
asir-1642	499	1	+	+	CCONJ
asir-1642	499	2	k	k	PROPN
asir-1642	499	3	√	√	PUNCT
asir-1642	499	4	≡	≡	PROPN
asir-1642	499	5	√√	√√	ADV
asir-1642	499	6	⃡	⃡	VERB
asir-1642	499	7	=	=	PUNCT
asir-1642	500	1	√	√	ADP
asir-1642	500	2	4	4	NUM
asir-1642	500	3	and	and	CCONJ
asir-1642	500	4	for	for	ADP
asir-1642	500	5	the	the	DET
asir-1642	500	6	three	three	NUM
asir-1642	500	7	dimensions	dimension	NOUN
asir-1642	500	8	euler	euler	NOUN
asir-1642	500	9	rotation	rotation	NOUN
asir-1642	500	10	number	number	NOUN
asir-1642	500	11	-	-	PUNCT
asir-1642	500	12	system	system	NOUN
asir-1642	500	13	as	as	ADP
asir-1642	500	14	e.	e.	PROPN
asir-1642	500	15	e.	e.	PROPN
asir-1642	500	16	e	e	PROPN
asir-1642	500	17	=	=	PROPN
asir-1642	500	18	𝑒3	𝑒3	PROPN
asir-1642	500	19	.	.	PUNCT
asir-1642	501	1	bodies	body	NOUN
asir-1642	501	2	produce	produce	VERB
asir-1642	501	3	gravity	gravity	NOUN
asir-1642	501	4	{	{	PUNCT
asir-1642	501	5	the	the	DET
asir-1642	501	6	change	change	NOUN
asir-1642	501	7	of	of	ADP
asir-1642	501	8	spin	spin	NOUN
asir-1642	501	9	-	-	PUNCT
asir-1642	501	10	direction	direction	NOUN
asir-1642	501	11	of	of	ADP
asir-1642	501	12	m	m	NOUN
asir-1642	501	13	-	-	ADJ
asir-1642	501	14	p	p	NOUN
asir-1642	501	15	-	-	PUNCT
asir-1642	501	16	dipole	dipole	NOUN
asir-1642	501	17	[	[	X
asir-1642	501	18	⊕s²	⊕s²	NUM
asir-1642	501	19	↻	↻	NOUN
asir-1642	501	20	↺	↺	NOUN
asir-1642	501	21	⊝s²	⊝s²	NOUN
asir-1642	501	22	]	]	PUNCT
asir-1642	501	23	in	in	ADP
asir-1642	501	24	mfmf	mfmf	NOUN
asir-1642	501	25	field	field	PROPN
asir-1642	501	26	}	}	PUNCT
asir-1642	501	27	from	from	ADP
asir-1642	501	28	stationary	stationary	ADJ
asir-1642	501	29	forces	force	NOUN
asir-1642	501	30	[	[	X
asir-1642	501	31	i	i	X
asir-1642	501	32	]	]	PUNCT
asir-1642	501	33	=	=	SYM
asir-1642	501	34			PROPN
asir-1642	501	35	s²	s²	NOUN
asir-1642	501	36	,	,	PUNCT
asir-1642	501	37	as	as	ADP
asir-1642	501	38	dipole	dipole	NOUN
asir-1642	501	39	,	,	PUNCT
asir-1642	501	40	and	and	CCONJ
asir-1642	501	41	this	this	PRON
asir-1642	501	42	because	because	SCONJ
asir-1642	501	43	gravity	gravity	NOUN
asir-1642	501	44	≡	≡	PROPN
asir-1642	501	45	acceleration	acceleration	NOUN
asir-1642	501	46	and	and	CCONJ
asir-1642	501	47	not	not	PART
asir-1642	501	48	by	by	ADP
asir-1642	501	49	the	the	DET
asir-1642	501	50	change	change	NOUN
asir-1642	501	51	of	of	ADP
asir-1642	501	52	velocity	velocity	NOUN
asir-1642	501	53	vector	vector	NOUN
asir-1642	501	54	,	,	PUNCT
asir-1642	501	55	but	but	CCONJ
asir-1642	501	56	,	,	PUNCT
asir-1642	501	57	by	by	ADP
asir-1642	501	58	the	the	DET
asir-1642	501	59	changing	changing	NOUN
asir-1642	501	60	of	of	ADP
asir-1642	501	61	direction	direction	NOUN
asir-1642	501	62	of	of	ADP
asir-1642	501	63	the	the	DET
asir-1642	501	64	above	above	ADJ
asir-1642	501	65	dipole	dipole	NOUN
asir-1642	501	66	[	[	X
asir-1642	501	67	⊕s²	⊕s²	NUM
asir-1642	501	68	↻	↻	NOUN
asir-1642	501	69	↺	↺	NOUN
asir-1642	501	70	⊝s²	⊝s²	NOUN
asir-1642	501	71	]	]	PUNCT
asir-1642	501	72	.	.	PUNCT
asir-1642	502	1	the	the	DET
asir-1642	502	2	produced	produce	VERB
asir-1642	502	3	work	work	NOUN
asir-1642	502	4	≡	≡	PROPN
asir-1642	502	5	gravity	gravity	NOUN
asir-1642	502	6	≡	≡	PROPN
asir-1642	502	7	energy	energy	NOUN
asir-1642	502	8	≡	≡	PROPN
asir-1642	502	9	constant	constant	ADJ
asir-1642	502	10	becomes	become	VERB
asir-1642	502	11	from	from	ADP
asir-1642	502	12	the	the	DET
asir-1642	502	13	eternal	eternal	ADJ
asir-1642	502	14	-	-	PUNCT
asir-1642	502	15	motion	motion	NOUN
asir-1642	502	16	on	on	ADP
asir-1642	502	17	orbits	orbit	NOUN
asir-1642	502	18	for	for	ADP
asir-1642	502	19	any	any	DET
asir-1642	502	20	planet	planet	NOUN
asir-1642	502	21	,	,	PUNCT
asir-1642	502	22	and	and	CCONJ
asir-1642	502	23	is	be	AUX
asir-1642	502	24	stored	store	VERB
asir-1642	502	25	or	or	CCONJ
asir-1642	502	26	taken	take	VERB
asir-1642	502	27	from	from	ADP
asir-1642	502	28	the	the	DET
asir-1642	502	29	pointy	pointy	NOUN
asir-1642	502	30	-	-	PUNCT
asir-1642	502	31	dipole	dipole	NOUN
asir-1642	502	32	in	in	ADP
asir-1642	502	33	orbits	orbit	NOUN
asir-1642	502	34	,	,	PUNCT
asir-1642	502	35	either	either	CCONJ
asir-1642	502	36	in	in	ADP
asir-1642	502	37	microcosm	microcosm	PROPN
asir-1642	502	38	or	or	CCONJ
asir-1642	502	39	macrocosm	macrocosm	PROPN
asir-1642	502	40	.	.	PROPN
asir-1642	503	1	3	3	X
asir-1642	503	2	.	.	X
asir-1642	503	3	discussion	discussion	NOUN
asir-1642	503	4	the	the	DET
asir-1642	503	5	way	way	NOUN
asir-1642	503	6	that	that	PRON
asir-1642	503	7	potential	potential	ADJ
asir-1642	503	8	-	-	PUNCT
asir-1642	503	9	energy	energy	NOUN
asir-1642	503	10	is	be	AUX
asir-1642	503	11	stored	store	VERB
asir-1642	503	12	,	,	PUNCT
asir-1642	503	13	is	be	AUX
asir-1642	503	14	that	that	PRON
asir-1642	503	15	of	of	ADP
asir-1642	503	16	material	material	NOUN
asir-1642	503	17	-	-	PUNCT
asir-1642	503	18	lrc	lrc	NOUN
asir-1642	503	19	-	-	PUNCT
asir-1642	503	20	circuit	circuit	NOUN
asir-1642	503	21	,	,	PUNCT
asir-1642	503	22	which	which	PRON
asir-1642	503	23	is	be	AUX
asir-1642	503	24	for	for	ADP
asir-1642	503	25	the	the	DET
asir-1642	503	26	gravitational	gravitational	ADJ
asir-1642	503	27	potential	potential	ADJ
asir-1642	503	28	-	-	PUNCT
asir-1642	503	29	energy	energy	NOUN
asir-1642	503	30	the	the	DET
asir-1642	503	31	material	material	NOUN
asir-1642	503	32	-	-	PUNCT
asir-1642	503	33	capacitor	capacitor	NOUN
asir-1642	503	34	or	or	CCONJ
asir-1642	503	35	the	the	DET
asir-1642	503	36	→	→	PUNCT
asir-1642	503	37	focus	focus	NOUN
asir-1642	503	38	-	-	PUNCT
asir-1642	503	39	planet	planet	NOUN
asir-1642	503	40	-	-	PUNCT
asir-1642	503	41	sector	sector	NOUN
asir-1642	503	42	-	-	PUNCT
asir-1642	503	43	stores	store	NOUN
asir-1642	503	44	-	-	PUNCT
asir-1642	503	45	charge	charge	NOUN
asir-1642	503	46	←	←	PROPN
asir-1642	503	47	which	which	PRON
asir-1642	503	48	develop	develop	VERB
asir-1642	503	49	a	a	DET
asir-1642	503	50	voltage	voltage	NOUN
asir-1642	503	51	in	in	ADP
asir-1642	503	52	response	response	NOUN
asir-1642	503	53	to	to	ADP
asir-1642	503	54	that	that	DET
asir-1642	503	55	charge	charge	NOUN
asir-1642	503	56	.	.	PUNCT
asir-1642	504	1	the	the	DET
asir-1642	504	2	coil	coil	NOUN
asir-1642	504	3	of	of	ADP
asir-1642	504	4	wire	wire	NOUN
asir-1642	504	5	is	be	AUX
asir-1642	504	6	the	the	DET
asir-1642	504	7	infinite	infinite	ADJ
asir-1642	504	8	stationary	stationary	ADJ
asir-1642	504	9	-	-	PUNCT
asir-1642	504	10	dipole	dipole	NOUN
asir-1642	504	11	-	-	PUNCT
asir-1642	504	12	spinning	spin	VERB
asir-1642	504	13	material	material	NOUN
asir-1642	504	14	points	point	NOUN
asir-1642	504	15	of	of	ADP
asir-1642	504	16	this	this	DET
asir-1642	504	17	→	→	SYM
asir-1642	504	18	focus	focus	NOUN
asir-1642	504	19	-	-	PUNCT
asir-1642	504	20	planet	planet	NOUN
asir-1642	504	21	-	-	PUNCT
asir-1642	504	22	sector	sector	NOUN
asir-1642	504	23	←	←	PROPN
asir-1642	504	24	which	which	PRON
asir-1642	504	25	develops	develop	VERB
asir-1642	504	26	the	the	DET
asir-1642	504	27	back	back	NOUN
asir-1642	504	28	-	-	PUNCT
asir-1642	504	29	emf	emf	NOUN
asir-1642	504	30	,	,	PUNCT
asir-1642	504	31	when	when	SCONJ
asir-1642	504	32	the	the	DET
asir-1642	504	33	current	current	NOUN
asir-1642	504	34	through	through	ADP
asir-1642	504	35	them	they	PRON
asir-1642	504	36	changes	change	NOUN
asir-1642	504	37	.	.	PUNCT
asir-1642	505	1	a	a	DET
asir-1642	505	2	wide	wide	ADJ
asir-1642	505	3	analysis	analysis	NOUN
asir-1642	505	4	in	in	ADP
asir-1642	505	5	[	[	X
asir-1642	505	6	68	68	NUM
asir-1642	505	7	]	]	PUNCT
asir-1642	505	8	.	.	PUNCT
asir-1642	506	1	www.scholink.org/ojs/index.php/asir	www.scholink.org/ojs/index.php/asir	PROPN
asir-1642	506	2	applied	apply	VERB
asir-1642	506	3	science	science	NOUN
asir-1642	506	4	and	and	CCONJ
asir-1642	506	5	innovative	innovative	ADJ
asir-1642	506	6	research	research	NOUN
asir-1642	506	7	vol	vol	NOUN
asir-1642	506	8	.	.	PROPN
asir-1642	507	1	2	2	NUM
asir-1642	507	2	,	,	PUNCT
asir-1642	507	3	no	no	INTJ
asir-1642	507	4	.	.	NOUN
asir-1642	507	5	4	4	NUM
asir-1642	507	6	,	,	PUNCT
asir-1642	507	7	2018	2018	NUM
asir-1642	507	8	179	179	NUM
asir-1642	507	9	published	publish	VERB
asir-1642	507	10	by	by	ADP
asir-1642	507	11	scholink	scholink	PROPN
asir-1642	507	12	inc	inc	PROPN
asir-1642	507	13	.	.	PROPN
asir-1642	507	14	acknowledges	acknowledge	VERB
asir-1642	507	15	the	the	DET
asir-1642	507	16	essence	essence	NOUN
asir-1642	507	17	of	of	ADP
asir-1642	507	18	ideas	idea	NOUN
asir-1642	507	19	contained	contain	VERB
asir-1642	507	20	in	in	ADP
asir-1642	507	21	the	the	DET
asir-1642	507	22	article	article	NOUN
asir-1642	507	23	were	be	AUX
asir-1642	507	24	formulated	formulate	VERB
asir-1642	507	25	many	many	ADJ
asir-1642	507	26	years	year	NOUN
asir-1642	507	27	ago	ago	ADV
asir-1642	507	28	after	after	ADP
asir-1642	507	29	a	a	DET
asir-1642	507	30	pedant	pedant	ADJ
asir-1642	507	31	continuous	continuous	ADJ
asir-1642	507	32	conceptual	conceptual	ADJ
asir-1642	507	33	understandable	understandable	ADJ
asir-1642	507	34	to	to	ADP
asir-1642	507	35	assimilation	assimilation	NOUN
asir-1642	507	36	in	in	ADP
asir-1642	507	37	the	the	DET
asir-1642	507	38	euclidean	euclidean	ADJ
asir-1642	507	39	and	and	CCONJ
asir-1642	507	40	mechanical	mechanical	ADJ
asir-1642	507	41	logic	logic	NOUN
asir-1642	507	42	,	,	PUNCT
asir-1642	507	43	not	not	PART
asir-1642	507	44	only	only	ADV
asir-1642	507	45	for	for	ADP
asir-1642	507	46	this	this	DET
asir-1642	507	47	particular	particular	ADJ
asir-1642	507	48	problem	problem	NOUN
asir-1642	507	49	but	but	CCONJ
asir-1642	507	50	on	on	ADP
asir-1642	507	51	all	all	DET
asir-1642	507	52	related	relate	VERB
asir-1642	507	53	-	-	PUNCT
asir-1642	507	54	subjects	subject	NOUN
asir-1642	507	55	which	which	PRON
asir-1642	507	56	are	be	AUX
asir-1642	507	57	connected	connect	VERB
asir-1642	507	58	to	to	ADP
asir-1642	507	59	the	the	DET
asir-1642	507	60	physical	physical	ADJ
asir-1642	507	61	world	world	NOUN
asir-1642	507	62	.	.	PUNCT
asir-1642	508	1	many	many	ADJ
asir-1642	508	2	questions	question	NOUN
asir-1642	508	3	by	by	ADP
asir-1642	508	4	mathematicians	mathematician	NOUN
asir-1642	508	5	gave	give	VERB
asir-1642	508	6	me	i	PRON
asir-1642	508	7	the	the	DET
asir-1642	508	8	chance	chance	NOUN
asir-1642	508	9	for	for	ADP
asir-1642	508	10	a	a	DET
asir-1642	508	11	better	well	ADV
asir-1642	508	12	critical	critical	ADJ
asir-1642	508	13	understanding	understanding	NOUN
asir-1642	508	14	.	.	PUNCT
asir-1642	509	1	references	reference	NOUN
asir-1642	509	2	der	der	PROPN
asir-1642	509	3	zweck	zweck	PROPN
asir-1642	510	1	i	i	PRON
asir-1642	510	2	m	m	VERB
asir-1642	510	3	rect	rect	ADJ
asir-1642	510	4	by	by	ADP
asir-1642	510	5	rudolf	rudolf	NOUN
asir-1642	510	6	v.	v.	ADP
asir-1642	510	7	jhering	jhering	PROPN
asir-1642	510	8	.	.	PUNCT
asir-1642	511	1	(	(	PUNCT
asir-1642	511	2	1935	1935	NUM
asir-1642	511	3	)	)	PUNCT
asir-1642	511	4	.	.	PUNCT
asir-1642	512	1	greek	greek	NOUN
asir-1642	512	2	mathematics	mathematic	NOUN
asir-1642	512	3	.	.	PUNCT
asir-1642	513	1	(	(	PUNCT
asir-1642	513	2	n.d	n.d	PROPN
asir-1642	513	3	.	.	PROPN
asir-1642	513	4	)	)	PUNCT
asir-1642	513	5	.	.	PUNCT
asir-1642	514	1	sir	sir	PROPN
asir-1642	514	2	thomas	thomas	PROPN
asir-1642	514	3	l.heath	l.heath	PROPN
asir-1642	514	4	-	-	PUNCT
asir-1642	514	5	dover	dover	PROPN
asir-1642	514	6	publications	publications	PROPN
asir-1642	514	7	,	,	PUNCT
asir-1642	514	8	inc	inc	PROPN
asir-1642	514	9	.	.	PROPN
asir-1642	514	10	new	new	PROPN
asir-1642	514	11	york	york	PROPN
asir-1642	514	12	.	.	PUNCT
asir-1642	515	1	material	material	NOUN
asir-1642	515	2	geometry	geometry	NOUN
asir-1642	515	3	and	and	CCONJ
asir-1642	515	4	,	,	PUNCT
asir-1642	515	5	the	the	DET
asir-1642	515	6	origin	origin	NOUN
asir-1642	515	7	of	of	ADP
asir-1642	515	8	black	black	ADJ
asir-1642	515	9	-	-	PUNCT
asir-1642	515	10	holes	hole	NOUN
asir-1642	515	11	,	,	PUNCT
asir-1642	515	12	black	black	NOUN
asir-1642	515	13	-	-	PUNCT
asir-1642	515	14	matter	matter	NOUN
asir-1642	515	15	.	.	PUNCT
asir-1642	516	1	(	(	PUNCT
asir-1642	516	2	n.d	n.d	PROPN
asir-1642	516	3	.	.	PROPN
asir-1642	516	4	)	)	PUNCT
asir-1642	516	5	.	.	PUNCT
asir-1642	517	1	retrieved	retrieve	VERB
asir-1642	517	2	from	from	ADP
asir-1642	517	3	http://www.sciencempg	http://www.sciencempg	ADJ
asir-1642	517	4	matrix	matrix	NOUN
asir-1642	517	5	structure	structure	NOUN
asir-1642	517	6	of	of	ADP
asir-1642	517	7	analysis	analysis	NOUN
asir-1642	517	8	by	by	ADP
asir-1642	517	9	j.l.meek	j.l.meek	ADJ
asir-1642	517	10	library	library	NOUN
asir-1642	517	11	of	of	ADP
asir-1642	517	12	congress	congress	PROPN
asir-1642	517	13	catalog	catalog	NOUN
asir-1642	517	14	.	.	PUNCT
asir-1642	518	1	(	(	PUNCT
asir-1642	518	2	1971	1971	NUM
asir-1642	518	3	)	)	PUNCT
asir-1642	518	4	.	.	PUNCT
asir-1642	519	1	the	the	DET
asir-1642	519	2	energy	energy	NOUN
asir-1642	519	3	structure	structure	NOUN
asir-1642	519	4	of	of	ADP
asir-1642	519	5	atoms	atom	NOUN
asir-1642	519	6	and	and	CCONJ
asir-1642	519	7	photon	photon	NOUN
asir-1642	519	8	.	.	PUNCT
asir-1642	520	1	(	(	PUNCT
asir-1642	520	2	n.d	n.d	PROPN
asir-1642	520	3	.	.	PROPN
asir-1642	520	4	)	)	PUNCT
asir-1642	520	5	.	.	PUNCT
asir-1642	521	1	retrieved	retrieve	VERB
asir-1642	521	2	from	from	ADP
asir-1642	521	3	http://www.vixra.org	http://www.vixra.org	PROPN
asir-1642	521	4	the	the	DET
asir-1642	521	5	energy	energy	NOUN
asir-1642	521	6	-	-	PUNCT
asir-1642	521	7	stores	store	NOUN
asir-1642	521	8	in	in	ADP
asir-1642	521	9	photon	photon	NOUN
asir-1642	521	10	.	.	PUNCT
asir-1642	522	1	(	(	PUNCT
asir-1642	522	2	n.d	n.d	PROPN
asir-1642	522	3	.	.	PROPN
asir-1642	522	4	)	)	PUNCT
asir-1642	522	5	.	.	PUNCT
asir-1642	523	1	retrieved	retrieve	VERB
asir-1642	523	2	from	from	ADP
asir-1642	523	3	http://www.i-b-r.org	http://www.i-b-r.org	ADJ
asir-1642	523	4	the	the	DET
asir-1642	523	5	geometrical	geometrical	ADJ
asir-1642	523	6	solution	solution	NOUN
asir-1642	523	7	of	of	ADP
asir-1642	523	8	the	the	DET
asir-1642	523	9	regular	regular	ADJ
asir-1642	523	10	-	-	PUNCT
asir-1642	523	11	polygons	polygon	NOUN
asir-1642	523	12	,	,	PUNCT
asir-1642	523	13	the	the	DET
asir-1642	523	14	special	special	ADJ
asir-1642	523	15	-	-	PUNCT
asir-1642	523	16	greek	greek	NOUN
asir-1642	523	17	-	-	PUNCT
asir-1642	523	18	problems	problem	NOUN
asir-1642	523	19	and	and	CCONJ
asir-1642	523	20	,	,	PUNCT
asir-1642	523	21	their	their	PRON
asir-1642	523	22	nature	nature	NOUN
asir-1642	523	23	.	.	PUNCT
asir-1642	524	1	(	(	PUNCT
asir-1642	524	2	n.d	n.d	PROPN
asir-1642	524	3	.	.	PROPN
asir-1642	524	4	)	)	PUNCT
asir-1642	524	5	.	.	PUNCT
asir-1642	525	1	retrieved	retrieve	VERB
asir-1642	525	2	from	from	ADP
asir-1642	525	3	http://www.iosrmail.org/	http://www.iosrmail.org/	NOUN
asir-1642	525	4	the	the	DET
asir-1642	525	5	great	great	ADJ
asir-1642	525	6	text	text	NOUN
asir-1642	525	7	of	of	ADP
asir-1642	525	8	j.	j.	PROPN
asir-1642	525	9	l.heisenberg	l.heisenberg	PROPN
asir-1642	525	10	.	.	PUNCT
asir-1642	526	1	(	(	PUNCT
asir-1642	526	2	1883	1883	NUM
asir-1642	526	3	-	-	SYM
asir-1642	526	4	1886	1886	NUM
asir-1642	526	5	)	)	PUNCT
asir-1642	526	6	.	.	PUNCT
asir-1642	527	1	english	english	ADJ
asir-1642	527	2	translation	translation	NOUN
asir-1642	527	3	by	by	ADP
asir-1642	527	4	richard	richard	PROPN
asir-1642	527	5	elements	element	NOUN
asir-1642	527	6	book	book	NOUN
asir-1642	527	7	1	1	NUM
asir-1642	527	8	.	.	PUNCT
asir-1642	527	9	fitzpatrick	fitzpatrick	PROPN
asir-1642	527	10	wikipedia.org	wikipedia.org	PROPN
asir-1642	527	11	,	,	PUNCT
asir-1642	527	12	the	the	DET
asir-1642	527	13	free	free	ADJ
asir-1642	527	14	encyclopedia	encyclopedia	NOUN
asir-1642	527	15	.	.	PUNCT
asir-1642	528	1	the	the	DET
asir-1642	528	2	how	how	SCONJ
asir-1642	528	3	energy	energy	NOUN
asir-1642	528	4	from	from	ADP
asir-1642	528	5	chaos	chaos	NOUN
asir-1642	528	6	becomes	become	VERB
asir-1642	528	7	the	the	DET
asir-1642	528	8	→	→	SYM
asir-1642	528	9	spin	spin	NOUN
asir-1642	528	10	,	,	PUNCT
asir-1642	528	11	of	of	ADP
asir-1642	528	12	the	the	DET
asir-1642	528	13	discrete	discrete	ADJ
asir-1642	528	14	elementary	elementary	ADJ
asir-1642	528	15	monads	monad	NOUN
asir-1642	528	16	.	.	PUNCT
asir-1642	529	1	(	(	PUNCT
asir-1642	529	2	n.d	n.d	PROPN
asir-1642	529	3	.	.	PROPN
asir-1642	529	4	)	)	PUNCT
asir-1642	529	5	.	.	PUNCT
asir-1642	530	1	retrieved	retrieve	VERB
asir-1642	530	2	from	from	ADP
asir-1642	530	3	http://www.ijrdo.org/	http://www.ijrdo.org/	NOUN
asir-1642	530	4	the	the	DET
asir-1642	530	5	how	how	SCONJ
asir-1642	530	6	energy	energy	NOUN
asir-1642	530	7	from	from	ADP
asir-1642	530	8	chaos	chaos	NOUN
asir-1642	530	9	becomes	become	VERB
asir-1642	530	10	the	the	DET
asir-1642	530	11	spin	spin	NOUN
asir-1642	530	12	of	of	ADP
asir-1642	530	13	monads	monad	NOUN
asir-1642	530	14	and	and	CCONJ
asir-1642	530	15	photon	photon	NOUN
asir-1642	530	16	.	.	PUNCT
asir-1642	531	1	(	(	PUNCT
asir-1642	531	2	n.d	n.d	PROPN
asir-1642	531	3	.	.	PROPN
asir-1642	531	4	)	)	PUNCT
asir-1642	531	5	.	.	PUNCT
asir-1642	532	1	retrieved	retrieve	VERB
asir-1642	532	2	from	from	ADP
asir-1642	532	3	http://www.ijrdo.org/	http://www.ijrdo.org/	NOUN
asir-1642	532	4	the	the	DET
asir-1642	532	5	moving	move	VERB
asir-1642	532	6	energy	energy	NOUN
asir-1642	532	7	-	-	PUNCT
asir-1642	532	8	stores	store	NOUN
asir-1642	532	9	and	and	CCONJ
asir-1642	532	10	photon	photon	NOUN
asir-1642	532	11	.	.	PUNCT
asir-1642	533	1	(	(	PUNCT
asir-1642	533	2	n.d	n.d	PROPN
asir-1642	533	3	.	.	PROPN
asir-1642	533	4	)	)	PUNCT
asir-1642	533	5	.	.	PUNCT
asir-1642	534	1	retrieved	retrieve	VERB
asir-1642	534	2	from	from	ADP
asir-1642	534	3	http://www.sciencempg	http://www.sciencempg	VERB
asir-1642	534	4	the	the	DET
asir-1642	534	5	moving	move	VERB
asir-1642	534	6	particles	particle	NOUN
asir-1642	534	7	and	and	CCONJ
asir-1642	534	8	photon	photon	NOUN
asir-1642	534	9	.	.	PUNCT
asir-1642	535	1	(	(	PUNCT
asir-1642	535	2	n.d	n.d	PROPN
asir-1642	535	3	.	.	PROPN
asir-1642	535	4	)	)	PUNCT
asir-1642	535	5	.	.	PUNCT
asir-1642	536	1	retrieved	retrieve	VERB
asir-1642	536	2	from	from	ADP
asir-1642	536	3	http://www.sciencempg	http://www.sciencempg	VERB
asir-1642	536	4	the	the	DET
asir-1642	536	5	spin	spin	NOUN
asir-1642	536	6	of	of	ADP
asir-1642	536	7	monads	monad	NOUN
asir-1642	536	8	and	and	CCONJ
asir-1642	536	9	their	their	PRON
asir-1642	536	10	energy	energy	NOUN
asir-1642	536	11	-	-	PUNCT
asir-1642	536	12	stores	store	NOUN
asir-1642	536	13	.	.	PUNCT
asir-1642	537	1	(	(	PUNCT
asir-1642	537	2	n.d	n.d	PROPN
asir-1642	537	3	.	.	PROPN
asir-1642	537	4	)	)	PUNCT
asir-1642	537	5	.	.	PUNCT
asir-1642	538	1	retrieved	retrieve	VERB
asir-1642	538	2	from	from	ADP
asir-1642	538	3	http://www.ajer.org	http://www.ajer.org	PROPN
asir-1642	538	4	theory	theory	NOUN
asir-1642	538	5	of	of	ADP
asir-1642	538	6	vibrations	vibration	NOUN
asir-1642	538	7	by	by	ADP
asir-1642	538	8	william	william	PROPN
asir-1642	538	9	t.	t.	PROPN
asir-1642	538	10	thomson	thomson	PROPN
asir-1642	538	11	(	(	PUNCT
asir-1642	538	12	4th	4th	PROPN
asir-1642	538	13	ed	ed	NOUN
asir-1642	538	14	.	.	PUNCT
asir-1642	538	15	)	)	PUNCT
asir-1642	538	16	.	.	PUNCT
asir-1642	539	1	(	(	PUNCT
asir-1642	539	2	n.d	n.d	PROPN
asir-1642	539	3	.	.	PROPN
asir-1642	539	4	)	)	PUNCT
asir-1642	539	5	.	.	PUNCT