id	sid	tid	token	lemma	pos
ejpam-6251	1	1	european	european	PROPN
ejpam-6251	1	2	journal	journal	PROPN
ejpam-6251	1	3	of	of	ADP
ejpam-6251	1	4	pure	pure	ADJ
ejpam-6251	1	5	and	and	CCONJ
ejpam-6251	1	6	applied	applied	ADJ
ejpam-6251	1	7	mathematics	mathematic	NOUN
ejpam-6251	1	8	2025	2025	NUM
ejpam-6251	1	9	,	,	PUNCT
ejpam-6251	1	10	vol	vol	NOUN
ejpam-6251	1	11	.	.	PROPN
ejpam-6251	1	12	18	18	NUM
ejpam-6251	1	13	,	,	PUNCT
ejpam-6251	1	14	issue	issue	NOUN
ejpam-6251	1	15	4	4	NUM
ejpam-6251	1	16	,	,	PUNCT
ejpam-6251	1	17	article	article	NOUN
ejpam-6251	1	18	number	number	NOUN
ejpam-6251	1	19	6251	6251	NUM
ejpam-6251	1	20	issn	issn	PROPN
ejpam-6251	1	21	1307	1307	NUM
ejpam-6251	1	22	-	-	SYM
ejpam-6251	1	23	5543	5543	NUM
ejpam-6251	1	24	–	–	PUNCT
ejpam-6251	1	25	ejpam.com	ejpam.com	X
ejpam-6251	1	26	published	publish	VERB
ejpam-6251	1	27	by	by	ADP
ejpam-6251	1	28	new	new	PROPN
ejpam-6251	1	29	york	york	PROPN
ejpam-6251	1	30	business	business	PROPN
ejpam-6251	1	31	global	global	ADJ
ejpam-6251	1	32	solving	solve	VERB
ejpam-6251	1	33	fractional	fractional	ADJ
ejpam-6251	1	34	differential	differential	ADJ
ejpam-6251	1	35	equations	equation	NOUN
ejpam-6251	1	36	and	and	CCONJ
ejpam-6251	1	37	integral	integral	ADJ
ejpam-6251	1	38	equations	equation	NOUN
ejpam-6251	1	39	via	via	ADP
ejpam-6251	1	40	neutrosophic	neutrosophic	ADJ
ejpam-6251	1	41	bipolar	bipolar	ADJ
ejpam-6251	1	42	metric	metric	ADJ
ejpam-6251	1	43	space	space	NOUN
ejpam-6251	1	44	rajagopalan	rajagopalan	VERB
ejpam-6251	1	45	ramaswamy	ramaswamy	ADJ
ejpam-6251	1	46	department	department	NOUN
ejpam-6251	1	47	of	of	ADP
ejpam-6251	1	48	mathematics	mathematics	PROPN
ejpam-6251	1	49	,	,	PUNCT
ejpam-6251	1	50	college	college	NOUN
ejpam-6251	1	51	of	of	ADP
ejpam-6251	1	52	science	science	NOUN
ejpam-6251	1	53	and	and	CCONJ
ejpam-6251	1	54	humanities	humanity	NOUN
ejpam-6251	1	55	in	in	ADP
ejpam-6251	1	56	alkharj	alkharj	NOUN
ejpam-6251	1	57	,	,	PUNCT
ejpam-6251	1	58	prince	prince	PROPN
ejpam-6251	1	59	sattam	sattam	PROPN
ejpam-6251	1	60	bin	bin	PROPN
ejpam-6251	1	61	abdulaziz	abdulaziz	PROPN
ejpam-6251	1	62	university	university	PROPN
ejpam-6251	1	63	,	,	PUNCT
ejpam-6251	1	64	alkharj	alkharj	VERB
ejpam-6251	1	65	11942	11942	NUM
ejpam-6251	1	66	,	,	PUNCT
ejpam-6251	1	67	saudi	saudi	PROPN
ejpam-6251	1	68	arabia	arabia	PROPN
ejpam-6251	1	69	abstract	abstract	NOUN
ejpam-6251	1	70	.	.	PUNCT
ejpam-6251	2	1	the	the	DET
ejpam-6251	2	2	theory	theory	NOUN
ejpam-6251	2	3	of	of	ADP
ejpam-6251	2	4	metric	metric	ADJ
ejpam-6251	2	5	spaces	space	NOUN
ejpam-6251	2	6	forms	form	VERB
ejpam-6251	2	7	the	the	DET
ejpam-6251	2	8	basis	basis	NOUN
ejpam-6251	2	9	of	of	ADP
ejpam-6251	2	10	metric	metric	ADJ
ejpam-6251	2	11	fixed	fix	VERB
ejpam-6251	2	12	point	point	NOUN
ejpam-6251	2	13	theory	theory	NOUN
ejpam-6251	2	14	,	,	PUNCT
ejpam-6251	2	15	which	which	PRON
ejpam-6251	2	16	has	have	VERB
ejpam-6251	2	17	varied	varied	ADJ
ejpam-6251	2	18	applications	application	NOUN
ejpam-6251	2	19	in	in	ADP
ejpam-6251	2	20	areas	area	NOUN
ejpam-6251	2	21	such	such	ADJ
ejpam-6251	2	22	as	as	ADP
ejpam-6251	2	23	engineering	engineering	NOUN
ejpam-6251	2	24	,	,	PUNCT
ejpam-6251	2	25	economics	economic	NOUN
ejpam-6251	2	26	,	,	PUNCT
ejpam-6251	2	27	medicine	medicine	NOUN
ejpam-6251	2	28	,	,	PUNCT
ejpam-6251	2	29	and	and	CCONJ
ejpam-6251	2	30	even	even	ADV
ejpam-6251	2	31	space	space	NOUN
ejpam-6251	2	32	science	science	NOUN
ejpam-6251	2	33	(	(	PUNCT
ejpam-6251	2	34	e.g.	e.g.	ADV
ejpam-6251	2	35	,	,	PUNCT
ejpam-6251	2	36	satellite	satellite	NOUN
ejpam-6251	2	37	launch	launch	NOUN
ejpam-6251	2	38	)	)	PUNCT
ejpam-6251	2	39	.	.	PUNCT
ejpam-6251	3	1	in	in	ADP
ejpam-6251	3	2	many	many	ADJ
ejpam-6251	3	3	generalizations	generalization	NOUN
ejpam-6251	3	4	of	of	ADP
ejpam-6251	3	5	metric	metric	ADJ
ejpam-6251	3	6	and	and	CCONJ
ejpam-6251	3	7	metric	metric	ADJ
ejpam-6251	3	8	-	-	PUNCT
ejpam-6251	3	9	like	like	ADJ
ejpam-6251	3	10	spaces	space	NOUN
ejpam-6251	3	11	,	,	PUNCT
ejpam-6251	3	12	fuzzy	fuzzy	ADJ
ejpam-6251	3	13	metric	metric	ADJ
ejpam-6251	3	14	spaces	space	NOUN
ejpam-6251	3	15	,	,	PUNCT
ejpam-6251	3	16	intuitionistic	intuitionistic	ADJ
ejpam-6251	3	17	fuzzy	fuzzy	ADJ
ejpam-6251	3	18	sets	set	NOUN
ejpam-6251	3	19	,	,	PUNCT
ejpam-6251	3	20	and	and	CCONJ
ejpam-6251	3	21	neutrosophic	neutrosophic	ADJ
ejpam-6251	3	22	sets	set	NOUN
ejpam-6251	3	23	have	have	AUX
ejpam-6251	3	24	evolved	evolve	VERB
ejpam-6251	3	25	.	.	PUNCT
ejpam-6251	4	1	while	while	SCONJ
ejpam-6251	4	2	both	both	CCONJ
ejpam-6251	4	3	metric	metric	ADJ
ejpam-6251	4	4	and	and	CCONJ
ejpam-6251	4	5	bipolar	bipolar	ADJ
ejpam-6251	4	6	metric	metric	NOUN
ejpam-6251	4	7	are	be	AUX
ejpam-6251	4	8	distance	distance	NOUN
ejpam-6251	4	9	functions	function	NOUN
ejpam-6251	4	10	,	,	PUNCT
ejpam-6251	4	11	the	the	DET
ejpam-6251	4	12	classical	classical	ADJ
ejpam-6251	4	13	metric	metric	NOUN
ejpam-6251	4	14	considers	consider	VERB
ejpam-6251	4	15	a	a	DET
ejpam-6251	4	16	single	single	ADJ
ejpam-6251	4	17	set	set	NOUN
ejpam-6251	4	18	,	,	PUNCT
ejpam-6251	4	19	whereas	whereas	SCONJ
ejpam-6251	4	20	the	the	DET
ejpam-6251	4	21	bipolar	bipolar	ADJ
ejpam-6251	4	22	metric	metric	NOUN
ejpam-6251	4	23	considers	consider	VERB
ejpam-6251	4	24	the	the	DET
ejpam-6251	4	25	distance	distance	NOUN
ejpam-6251	4	26	between	between	ADP
ejpam-6251	4	27	two	two	NUM
ejpam-6251	4	28	potentially	potentially	ADV
ejpam-6251	4	29	different	different	ADJ
ejpam-6251	4	30	sets	set	NOUN
ejpam-6251	4	31	.	.	PUNCT
ejpam-6251	5	1	it	it	PRON
ejpam-6251	5	2	is	be	AUX
ejpam-6251	5	3	also	also	ADV
ejpam-6251	5	4	well	well	ADV
ejpam-6251	5	5	known	know	VERB
ejpam-6251	5	6	that	that	SCONJ
ejpam-6251	5	7	fractional	fractional	ADJ
ejpam-6251	5	8	calculus	calculus	NOUN
ejpam-6251	5	9	has	have	VERB
ejpam-6251	5	10	broad	broad	ADJ
ejpam-6251	5	11	applications	application	NOUN
ejpam-6251	5	12	.	.	PUNCT
ejpam-6251	6	1	in	in	ADP
ejpam-6251	6	2	this	this	DET
ejpam-6251	6	3	work	work	NOUN
ejpam-6251	6	4	,	,	PUNCT
ejpam-6251	6	5	we	we	PRON
ejpam-6251	6	6	introduce	introduce	VERB
ejpam-6251	6	7	neutrosophic	neutrosophic	ADJ
ejpam-6251	6	8	bipolar	bipolar	ADJ
ejpam-6251	6	9	metric	metric	ADJ
ejpam-6251	6	10	spaces	space	NOUN
ejpam-6251	6	11	and	and	CCONJ
ejpam-6251	6	12	establish	establish	VERB
ejpam-6251	6	13	fixed	fix	VERB
ejpam-6251	6	14	point	point	NOUN
ejpam-6251	6	15	theorems	theorem	NOUN
ejpam-6251	6	16	in	in	ADP
ejpam-6251	6	17	these	these	DET
ejpam-6251	6	18	spaces	space	NOUN
ejpam-6251	6	19	.	.	PUNCT
ejpam-6251	7	1	our	our	PRON
ejpam-6251	7	2	main	main	ADJ
ejpam-6251	7	3	results	result	NOUN
ejpam-6251	7	4	generalize	generalize	VERB
ejpam-6251	7	5	several	several	ADJ
ejpam-6251	7	6	proven	prove	VERB
ejpam-6251	7	7	results	result	NOUN
ejpam-6251	7	8	in	in	ADP
ejpam-6251	7	9	the	the	DET
ejpam-6251	7	10	literature	literature	NOUN
ejpam-6251	7	11	.	.	PUNCT
ejpam-6251	8	1	the	the	DET
ejpam-6251	8	2	derived	derive	VERB
ejpam-6251	8	3	results	result	NOUN
ejpam-6251	8	4	are	be	AUX
ejpam-6251	8	5	supported	support	VERB
ejpam-6251	8	6	with	with	ADP
ejpam-6251	8	7	non	non	ADJ
ejpam-6251	8	8	-	-	ADJ
ejpam-6251	8	9	trivial	trivial	ADJ
ejpam-6251	8	10	illustrations	illustration	NOUN
ejpam-6251	8	11	.	.	PUNCT
ejpam-6251	9	1	three	three	NUM
ejpam-6251	9	2	applications	application	NOUN
ejpam-6251	9	3	are	be	AUX
ejpam-6251	9	4	presented	present	VERB
ejpam-6251	9	5	to	to	PART
ejpam-6251	9	6	supplement	supplement	VERB
ejpam-6251	9	7	the	the	DET
ejpam-6251	9	8	theoretical	theoretical	ADJ
ejpam-6251	9	9	findings	finding	NOUN
ejpam-6251	9	10	.	.	PUNCT
ejpam-6251	10	1	2020	2020	NUM
ejpam-6251	10	2	mathematics	mathematic	NOUN
ejpam-6251	10	3	subject	subject	NOUN
ejpam-6251	10	4	classifications	classification	NOUN
ejpam-6251	10	5	:	:	PUNCT
ejpam-6251	10	6	47h10	47h10	NUM
ejpam-6251	10	7	,	,	PUNCT
ejpam-6251	10	8	54h25	54h25	NUM
ejpam-6251	10	9	key	key	ADJ
ejpam-6251	10	10	words	word	NOUN
ejpam-6251	10	11	and	and	CCONJ
ejpam-6251	10	12	phrases	phrase	NOUN
ejpam-6251	10	13	:	:	PUNCT
ejpam-6251	10	14	fixed	fix	VERB
ejpam-6251	10	15	point	point	NOUN
ejpam-6251	10	16	,	,	PUNCT
ejpam-6251	10	17	neutrosophic	neutrosophic	ADJ
ejpam-6251	10	18	metric	metric	ADJ
ejpam-6251	10	19	space	space	NOUN
ejpam-6251	10	20	,	,	PUNCT
ejpam-6251	10	21	neutrosophic	neutrosophic	ADJ
ejpam-6251	10	22	bipolar	bipolar	ADJ
ejpam-6251	10	23	metric	metric	ADJ
ejpam-6251	10	24	space	space	NOUN
ejpam-6251	10	25	,	,	PUNCT
ejpam-6251	10	26	integral	integral	ADJ
ejpam-6251	10	27	equation	equation	NOUN
ejpam-6251	10	28	1	1	NUM
ejpam-6251	10	29	.	.	PUNCT
ejpam-6251	10	30	introduction	introduction	NOUN
ejpam-6251	10	31	the	the	DET
ejpam-6251	10	32	foundation	foundation	NOUN
ejpam-6251	10	33	of	of	ADP
ejpam-6251	10	34	metric	metric	ADJ
ejpam-6251	10	35	fixed	fix	VERB
ejpam-6251	10	36	point	point	NOUN
ejpam-6251	10	37	theory	theory	NOUN
ejpam-6251	10	38	lies	lie	VERB
ejpam-6251	10	39	on	on	ADP
ejpam-6251	10	40	the	the	DET
ejpam-6251	10	41	concept	concept	NOUN
ejpam-6251	10	42	of	of	ADP
ejpam-6251	10	43	metric	metric	ADJ
ejpam-6251	10	44	spaces	space	NOUN
ejpam-6251	10	45	and	and	CCONJ
ejpam-6251	10	46	the	the	DET
ejpam-6251	10	47	banach	banach	NOUN
ejpam-6251	10	48	contraction	contraction	NOUN
ejpam-6251	10	49	principle	principle	NOUN
ejpam-6251	10	50	[	[	X
ejpam-6251	10	51	1	1	X
ejpam-6251	10	52	]	]	PUNCT
ejpam-6251	10	53	.	.	PUNCT
ejpam-6251	11	1	an	an	DET
ejpam-6251	11	2	axiomatic	axiomatic	ADJ
ejpam-6251	11	3	grasp	grasp	NOUN
ejpam-6251	11	4	of	of	ADP
ejpam-6251	11	5	metric	metric	ADJ
ejpam-6251	11	6	space	space	NOUN
ejpam-6251	11	7	draws	draw	VERB
ejpam-6251	11	8	thousands	thousand	NOUN
ejpam-6251	11	9	of	of	ADP
ejpam-6251	11	10	scholars	scholar	NOUN
ejpam-6251	11	11	to	to	ADP
ejpam-6251	11	12	spaciousness	spaciousness	NOUN
ejpam-6251	11	13	.	.	PUNCT
ejpam-6251	12	1	metric	metric	ADJ
ejpam-6251	12	2	spaces	space	NOUN
ejpam-6251	12	3	have	have	AUX
ejpam-6251	12	4	seen	see	VERB
ejpam-6251	12	5	various	various	ADJ
ejpam-6251	12	6	changes	change	NOUN
ejpam-6251	12	7	in	in	ADP
ejpam-6251	12	8	the	the	DET
ejpam-6251	12	9	past	past	NOUN
ejpam-6251	12	10	.	.	PUNCT
ejpam-6251	13	1	here	here	ADV
ejpam-6251	13	2	,	,	PUNCT
ejpam-6251	13	3	we	we	PRON
ejpam-6251	13	4	notify	notify	VERB
ejpam-6251	13	5	that	that	SCONJ
ejpam-6251	13	6	the	the	DET
ejpam-6251	13	7	beauty	beauty	NOUN
ejpam-6251	13	8	,	,	PUNCT
ejpam-6251	13	9	attraction	attraction	NOUN
ejpam-6251	13	10	,	,	PUNCT
ejpam-6251	13	11	and	and	CCONJ
ejpam-6251	13	12	expansion	expansion	NOUN
ejpam-6251	13	13	of	of	ADP
ejpam-6251	13	14	the	the	DET
ejpam-6251	13	15	concept	concept	NOUN
ejpam-6251	13	16	of	of	ADP
ejpam-6251	13	17	metric	metric	ADJ
ejpam-6251	13	18	spaces	space	NOUN
ejpam-6251	13	19	.	.	PUNCT
ejpam-6251	14	1	fractal	fractal	PROPN
ejpam-6251	14	2	or	or	CCONJ
ejpam-6251	14	3	the	the	DET
ejpam-6251	14	4	hausdorff	hausdorff	NOUN
ejpam-6251	14	5	derivative	derivative	NOUN
ejpam-6251	14	6	of	of	ADP
ejpam-6251	14	7	mathematical	mathematical	ADJ
ejpam-6251	14	8	analysis	analysis	NOUN
ejpam-6251	14	9	,	,	PUNCT
ejpam-6251	14	10	which	which	PRON
ejpam-6251	14	11	is	be	AUX
ejpam-6251	14	12	a	a	DET
ejpam-6251	14	13	non	non	ADJ
ejpam-6251	14	14	neutonion	neutonion	NOUN
ejpam-6251	14	15	derivative	derivative	NOUN
ejpam-6251	14	16	,	,	PUNCT
ejpam-6251	14	17	deals	deal	NOUN
ejpam-6251	14	18	with	with	ADP
ejpam-6251	14	19	fractals	fractal	NOUN
ejpam-6251	14	20	defined	define	VERB
ejpam-6251	14	21	in	in	ADP
ejpam-6251	14	22	fractal	fractal	ADJ
ejpam-6251	14	23	geometry	geometry	NOUN
ejpam-6251	14	24	.	.	PUNCT
ejpam-6251	15	1	it	it	PRON
ejpam-6251	15	2	has	have	VERB
ejpam-6251	15	3	vast	vast	ADJ
ejpam-6251	15	4	applications	application	NOUN
ejpam-6251	15	5	.	.	PUNCT
ejpam-6251	16	1	to	to	PART
ejpam-6251	16	2	know	know	VERB
ejpam-6251	16	3	about	about	ADP
ejpam-6251	16	4	certain	certain	ADJ
ejpam-6251	16	5	fundamentals	fundamental	NOUN
ejpam-6251	16	6	of	of	ADP
ejpam-6251	16	7	fractal	fractal	ADJ
ejpam-6251	16	8	calculus	calculus	NOUN
ejpam-6251	16	9	and	and	CCONJ
ejpam-6251	16	10	its	its	PRON
ejpam-6251	16	11	application	application	NOUN
ejpam-6251	16	12	,	,	PUNCT
ejpam-6251	16	13	one	one	PRON
ejpam-6251	16	14	can	can	AUX
ejpam-6251	16	15	refer	refer	VERB
ejpam-6251	16	16	to	to	ADP
ejpam-6251	16	17	[	[	X
ejpam-6251	16	18	2–4	2–4	NUM
ejpam-6251	16	19	]	]	PUNCT
ejpam-6251	16	20	.	.	PUNCT
ejpam-6251	17	1	the	the	DET
ejpam-6251	17	2	notion	notion	NOUN
ejpam-6251	17	3	of	of	ADP
ejpam-6251	17	4	fuzzy	fuzzy	ADJ
ejpam-6251	17	5	set	set	NOUN
ejpam-6251	17	6	(	(	PUNCT
ejpam-6251	17	7	fs	fs	PROPN
ejpam-6251	17	8	)	)	PUNCT
ejpam-6251	17	9	was	be	AUX
ejpam-6251	17	10	introduced	introduce	VERB
ejpam-6251	17	11	by	by	ADP
ejpam-6251	17	12	l.	l.	PROPN
ejpam-6251	17	13	zadeh	zadeh	PROPN
ejpam-6251	18	1	[	[	X
ejpam-6251	18	2	5	5	NUM
ejpam-6251	18	3	]	]	PUNCT
ejpam-6251	18	4	in	in	ADP
ejpam-6251	18	5	1965	1965	NUM
ejpam-6251	18	6	,	,	PUNCT
ejpam-6251	18	7	where	where	SCONJ
ejpam-6251	18	8	each	each	DET
ejpam-6251	18	9	element	element	NOUN
ejpam-6251	18	10	had	have	VERB
ejpam-6251	18	11	a	a	DET
ejpam-6251	18	12	degree	degree	NOUN
ejpam-6251	18	13	of	of	ADP
ejpam-6251	18	14	membership	membership	NOUN
ejpam-6251	18	15	(	(	PUNCT
ejpam-6251	18	16	t	t	PROPN
ejpam-6251	18	17	)	)	PUNCT
ejpam-6251	18	18	.	.	PUNCT
ejpam-6251	19	1	the	the	DET
ejpam-6251	19	2	intuitionistic	intuitionistic	ADJ
ejpam-6251	19	3	fuzzy	fuzzy	ADJ
ejpam-6251	19	4	set	set	NOUN
ejpam-6251	19	5	(	(	PUNCT
ejpam-6251	19	6	ifs	ifs	PROPN
ejpam-6251	19	7	)	)	PUNCT
ejpam-6251	19	8	on	on	ADP
ejpam-6251	19	9	a	a	DET
ejpam-6251	19	10	universe	universe	NOUN
ejpam-6251	19	11	x	x	PRON
ejpam-6251	19	12	was	be	AUX
ejpam-6251	19	13	introduced	introduce	VERB
ejpam-6251	19	14	by	by	ADP
ejpam-6251	19	15	k.	k.	PROPN
ejpam-6251	19	16	atanassov	atanassov	PROPN
ejpam-6251	20	1	[	[	X
ejpam-6251	20	2	6	6	NUM
ejpam-6251	20	3	]	]	PUNCT
ejpam-6251	20	4	in	in	ADP
ejpam-6251	20	5	1986	1986	NUM
ejpam-6251	20	6	as	as	ADP
ejpam-6251	20	7	a	a	DET
ejpam-6251	20	8	generalization	generalization	NOUN
ejpam-6251	20	9	of	of	ADP
ejpam-6251	20	10	fs	f	NOUN
ejpam-6251	20	11	,	,	PUNCT
ejpam-6251	20	12	where	where	SCONJ
ejpam-6251	20	13	besides	besides	SCONJ
ejpam-6251	20	14	doi	doi	PROPN
ejpam-6251	20	15	:	:	PUNCT
ejpam-6251	20	16	https://doi.org/10.29020/nybg.ejpam.v18i4.6251	https://doi.org/10.29020/nybg.ejpam.v18i4.6251	PROPN
ejpam-6251	20	17	email	email	NOUN
ejpam-6251	20	18	address	address	NOUN
ejpam-6251	20	19	:	:	PUNCT
ejpam-6251	20	20	r.gopalan@psau.edu.sa	r.gopalan@psau.edu.sa	PROPN
ejpam-6251	20	21	(	(	PUNCT
ejpam-6251	20	22	r.	r.	PROPN
ejpam-6251	20	23	ramaswamy	ramaswamy	PROPN
ejpam-6251	20	24	)	)	PUNCT
ejpam-6251	20	25	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-6251	21	1	1	1	NUM
ejpam-6251	21	2	copyright	copyright	NOUN
ejpam-6251	21	3	:	:	PUNCT
ejpam-6251	21	4	©	©	PROPN
ejpam-6251	21	5	2025	2025	NUM
ejpam-6251	21	6	the	the	DET
ejpam-6251	21	7	author(s	author(s	NOUN
ejpam-6251	21	8	)	)	PUNCT
ejpam-6251	21	9	.	.	PUNCT
ejpam-6251	22	1	(	(	PUNCT
ejpam-6251	22	2	cc	cc	NOUN
ejpam-6251	22	3	by	by	ADP
ejpam-6251	22	4	-	-	PUNCT
ejpam-6251	22	5	nc	nc	PROPN
ejpam-6251	22	6	4.0	4.0	NUM
ejpam-6251	22	7	)	)	PUNCT
ejpam-6251	22	8	r.	r.	PROPN
ejpam-6251	22	9	ramaswamy	ramaswamy	PROPN
ejpam-6251	22	10	/	/	SYM
ejpam-6251	22	11	eur	eur	PROPN
ejpam-6251	22	12	.	.	PUNCT
ejpam-6251	23	1	j.	j.	PROPN
ejpam-6251	23	2	pure	pure	PROPN
ejpam-6251	23	3	appl	appl	PROPN
ejpam-6251	23	4	.	.	PROPN
ejpam-6251	23	5	math	math	PROPN
ejpam-6251	23	6	,	,	PUNCT
ejpam-6251	23	7	18	18	NUM
ejpam-6251	23	8	(	(	PUNCT
ejpam-6251	23	9	4	4	NUM
ejpam-6251	23	10	)	)	PUNCT
ejpam-6251	23	11	(	(	PUNCT
ejpam-6251	23	12	2025	2025	NUM
ejpam-6251	23	13	)	)	PUNCT
ejpam-6251	23	14	,	,	PUNCT
ejpam-6251	23	15	6251	6251	NUM
ejpam-6251	23	16	2	2	NUM
ejpam-6251	23	17	of	of	ADP
ejpam-6251	23	18	40	40	NUM
ejpam-6251	23	19	the	the	DET
ejpam-6251	23	20	degree	degree	NOUN
ejpam-6251	23	21	of	of	ADP
ejpam-6251	23	22	membership	membership	NOUN
ejpam-6251	23	23	µa(x	µa(x	NOUN
ejpam-6251	23	24	)	)	PUNCT
ejpam-6251	23	25	∈	∈	PROPN
ejpam-6251	24	1	[	[	X
ejpam-6251	24	2	0	0	NUM
ejpam-6251	24	3	,	,	PUNCT
ejpam-6251	24	4	1	1	NUM
ejpam-6251	24	5	]	]	PUNCT
ejpam-6251	24	6	of	of	ADP
ejpam-6251	24	7	each	each	DET
ejpam-6251	24	8	element	element	NOUN
ejpam-6251	24	9	x	x	SYM
ejpam-6251	24	10	∈	∈	NOUN
ejpam-6251	24	11	x	x	PUNCT
ejpam-6251	24	12	to	to	ADP
ejpam-6251	24	13	a	a	DET
ejpam-6251	24	14	set	set	NOUN
ejpam-6251	24	15	a	a	PRON
ejpam-6251	24	16	,	,	PUNCT
ejpam-6251	24	17	there	there	PRON
ejpam-6251	24	18	was	be	VERB
ejpam-6251	24	19	considered	consider	VERB
ejpam-6251	24	20	a	a	DET
ejpam-6251	24	21	degree	degree	NOUN
ejpam-6251	24	22	of	of	ADP
ejpam-6251	24	23	non	non	ADJ
ejpam-6251	24	24	-	-	NOUN
ejpam-6251	24	25	membership	membership	ADJ
ejpam-6251	24	26	νa(x	νa(x	NOUN
ejpam-6251	24	27	)	)	PUNCT
ejpam-6251	24	28	∈	∈	PROPN
ejpam-6251	25	1	[	[	X
ejpam-6251	25	2	0	0	NUM
ejpam-6251	25	3	,	,	PUNCT
ejpam-6251	25	4	1	1	NUM
ejpam-6251	25	5	]	]	PUNCT
ejpam-6251	25	6	,	,	PUNCT
ejpam-6251	25	7	∀x	∀x	VERB
ejpam-6251	25	8	∈	∈	PROPN
ejpam-6251	25	9	x,µa(x	x,µa(x	NOUN
ejpam-6251	25	10	)	)	PUNCT
ejpam-6251	25	11	+	+	NUM
ejpam-6251	25	12	νa(x	νa(x	NOUN
ejpam-6251	25	13	)	)	PUNCT
ejpam-6251	25	14	≤	≤	NUM
ejpam-6251	25	15	1	1	NUM
ejpam-6251	25	16	(	(	PUNCT
ejpam-6251	25	17	1	1	NUM
ejpam-6251	25	18	)	)	PUNCT
ejpam-6251	25	19	the	the	DET
ejpam-6251	25	20	neutrosophic	neutrosophic	ADJ
ejpam-6251	25	21	set	set	NOUN
ejpam-6251	25	22	(	(	PUNCT
ejpam-6251	25	23	ns	ns	NUM
ejpam-6251	25	24	)	)	PUNCT
ejpam-6251	25	25	was	be	AUX
ejpam-6251	25	26	introduced	introduce	VERB
ejpam-6251	25	27	by	by	ADP
ejpam-6251	25	28	f.	f.	PROPN
ejpam-6251	25	29	smarandache	smarandache	PROPN
ejpam-6251	26	1	[	[	X
ejpam-6251	26	2	7	7	NUM
ejpam-6251	26	3	]	]	SYM
ejpam-6251	26	4	degree	degree	NOUN
ejpam-6251	26	5	of	of	ADP
ejpam-6251	26	6	indeterminacy	indeterminacy	NOUN
ejpam-6251	26	7	as	as	ADP
ejpam-6251	26	8	independent	independent	ADJ
ejpam-6251	26	9	component	component	NOUN
ejpam-6251	26	10	.	.	PUNCT
ejpam-6251	27	1	in	in	ADP
ejpam-6251	27	2	the	the	DET
ejpam-6251	27	3	study	study	NOUN
ejpam-6251	27	4	on	on	ADP
ejpam-6251	27	5	analytical	analytical	ADJ
ejpam-6251	27	6	and	and	CCONJ
ejpam-6251	27	7	practical	practical	ADJ
ejpam-6251	27	8	applicability	applicability	NOUN
ejpam-6251	27	9	of	of	ADP
ejpam-6251	27	10	fuzzy	fuzzy	ADJ
ejpam-6251	27	11	sets	set	NOUN
ejpam-6251	27	12	and	and	CCONJ
ejpam-6251	27	13	their	their	PRON
ejpam-6251	27	14	generalisations	generalisation	NOUN
ejpam-6251	27	15	,	,	PUNCT
ejpam-6251	27	16	mathematicians	mathematician	NOUN
ejpam-6251	27	17	reported	report	VERB
ejpam-6251	27	18	many	many	ADJ
ejpam-6251	27	19	results	result	NOUN
ejpam-6251	27	20	including	include	VERB
ejpam-6251	27	21	analysing	analyse	VERB
ejpam-6251	27	22	the	the	DET
ejpam-6251	27	23	impact	impact	NOUN
ejpam-6251	27	24	of	of	ADP
ejpam-6251	27	25	fuzzy	fuzzy	ADJ
ejpam-6251	27	26	ideal	ideal	ADJ
ejpam-6251	27	27	extension	extension	NOUN
ejpam-6251	27	28	,	,	PUNCT
ejpam-6251	27	29	evaluating	evaluate	VERB
ejpam-6251	27	30	solutions	solution	NOUN
ejpam-6251	27	31	of	of	ADP
ejpam-6251	27	32	generalised	generalise	VERB
ejpam-6251	27	33	fuzzy	fuzzy	ADJ
ejpam-6251	27	34	differential	differential	ADJ
ejpam-6251	27	35	equations	equation	NOUN
ejpam-6251	27	36	,	,	PUNCT
ejpam-6251	27	37	intutionistic	intutionistic	ADJ
ejpam-6251	27	38	fuzzy	fuzzy	ADJ
ejpam-6251	27	39	linear	linear	ADJ
ejpam-6251	27	40	system	system	NOUN
ejpam-6251	27	41	of	of	ADP
ejpam-6251	27	42	equations	equation	NOUN
ejpam-6251	27	43	,	,	PUNCT
ejpam-6251	27	44	etc	etc	X
ejpam-6251	27	45	.	.	X
ejpam-6251	27	46	,	,	PUNCT
ejpam-6251	27	47	to	to	PART
ejpam-6251	27	48	name	name	VERB
ejpam-6251	27	49	a	a	DET
ejpam-6251	27	50	few	few	ADJ
ejpam-6251	27	51	.	.	PUNCT
ejpam-6251	27	52	,	,	PUNCT
ejpam-6251	27	53	see	see	VERB
ejpam-6251	27	54	[	[	X
ejpam-6251	27	55	8–11	8–11	X
ejpam-6251	27	56	]	]	PUNCT
ejpam-6251	27	57	.	.	PUNCT
ejpam-6251	28	1	in	in	ADP
ejpam-6251	28	2	contemporary	contemporary	ADJ
ejpam-6251	28	3	examinations	examination	NOUN
ejpam-6251	28	4	of	of	ADP
ejpam-6251	28	5	the	the	DET
ejpam-6251	28	6	set	set	NOUN
ejpam-6251	28	7	-	-	PUNCT
ejpam-6251	28	8	theoretical	theoretical	ADJ
ejpam-6251	28	9	and	and	CCONJ
ejpam-6251	28	10	logical	logical	ADJ
ejpam-6251	28	11	underpinnings	underpinning	NOUN
ejpam-6251	28	12	of	of	ADP
ejpam-6251	28	13	mathematics	mathematic	NOUN
ejpam-6251	28	14	,	,	PUNCT
ejpam-6251	28	15	the	the	DET
ejpam-6251	28	16	word	word	NOUN
ejpam-6251	28	17	“	"	PUNCT
ejpam-6251	28	18	fuzzy	fuzzy	ADJ
ejpam-6251	28	19	”	"	PUNCT
ejpam-6251	28	20	appears	appear	VERB
ejpam-6251	28	21	to	to	PART
ejpam-6251	28	22	be	be	AUX
ejpam-6251	28	23	prevalent	prevalent	ADJ
ejpam-6251	28	24	.	.	PUNCT
ejpam-6251	29	1	the	the	DET
ejpam-6251	29	2	primary	primary	ADJ
ejpam-6251	29	3	rationale	rationale	NOUN
ejpam-6251	29	4	for	for	ADP
ejpam-6251	29	5	this	this	DET
ejpam-6251	29	6	unexpected	unexpected	ADJ
ejpam-6251	29	7	development	development	NOUN
ejpam-6251	29	8	,	,	PUNCT
ejpam-6251	29	9	our	our	PRON
ejpam-6251	29	10	judgment	judgment	NOUN
ejpam-6251	29	11	,	,	PUNCT
ejpam-6251	29	12	is	be	AUX
ejpam-6251	29	13	straightforward	straightforward	ADJ
ejpam-6251	29	14	.	.	PUNCT
ejpam-6251	30	1	because	because	SCONJ
ejpam-6251	30	2	the	the	DET
ejpam-6251	30	3	information	information	NOUN
ejpam-6251	30	4	we	we	PRON
ejpam-6251	30	5	collect	collect	VERB
ejpam-6251	30	6	from	from	ADP
ejpam-6251	30	7	our	our	PRON
ejpam-6251	30	8	surroundings	surrounding	NOUN
ejpam-6251	30	9	,	,	PUNCT
ejpam-6251	30	10	we	we	PRON
ejpam-6251	30	11	employ	employ	VERB
ejpam-6251	30	12	the	the	DET
ejpam-6251	30	13	idea	idea	NOUN
ejpam-6251	30	14	of	of	ADP
ejpam-6251	30	15	resulting	result	VERB
ejpam-6251	30	16	from	from	ADP
ejpam-6251	30	17	our	our	PRON
ejpam-6251	30	18	observations	observation	NOUN
ejpam-6251	30	19	or	or	CCONJ
ejpam-6251	30	20	measurements	measurement	NOUN
ejpam-6251	30	21	are	be	AUX
ejpam-6251	30	22	all	all	ADV
ejpam-6251	30	23	hazy	hazy	ADJ
ejpam-6251	30	24	and	and	CCONJ
ejpam-6251	30	25	erroneous	erroneous	ADJ
ejpam-6251	30	26	,	,	PUNCT
ejpam-6251	30	27	the	the	DET
ejpam-6251	30	28	world	world	NOUN
ejpam-6251	30	29	around	around	ADP
ejpam-6251	30	30	us	we	PRON
ejpam-6251	30	31	is	be	AUX
ejpam-6251	30	32	full	full	ADJ
ejpam-6251	30	33	of	of	ADP
ejpam-6251	30	34	ambiguity	ambiguity	NOUN
ejpam-6251	30	35	.	.	PUNCT
ejpam-6251	31	1	so	so	ADV
ejpam-6251	31	2	,	,	PUNCT
ejpam-6251	31	3	every	every	DET
ejpam-6251	31	4	usual	usual	ADJ
ejpam-6251	31	5	illustration	illustration	NOUN
ejpam-6251	31	6	is	be	AUX
ejpam-6251	31	7	an	an	DET
ejpam-6251	31	8	approximation	approximation	NOUN
ejpam-6251	31	9	or	or	CCONJ
ejpam-6251	31	10	idealization	idealization	NOUN
ejpam-6251	31	11	of	of	ADP
ejpam-6251	31	12	truth	truth	NOUN
ejpam-6251	31	13	of	of	ADP
ejpam-6251	31	14	the	the	DET
ejpam-6251	31	15	real	real	ADJ
ejpam-6251	31	16	world	world	NOUN
ejpam-6251	31	17	or	or	CCONJ
ejpam-6251	31	18	a	a	DET
ejpam-6251	31	19	part	part	NOUN
ejpam-6251	31	20	of	of	ADP
ejpam-6251	31	21	it	it	PRON
ejpam-6251	31	22	.	.	PUNCT
ejpam-6251	32	1	fuzzy	fuzzy	ADJ
ejpam-6251	32	2	sets	set	NOUN
ejpam-6251	32	3	(	(	PUNCT
ejpam-6251	32	4	orderings	ordering	NOUN
ejpam-6251	32	5	,	,	PUNCT
ejpam-6251	32	6	languages	language	NOUN
ejpam-6251	32	7	,	,	PUNCT
ejpam-6251	32	8	etc	etc	X
ejpam-6251	32	9	.	.	X
ejpam-6251	32	10	)	)	PUNCT
ejpam-6251	33	1	and	and	CCONJ
ejpam-6251	33	2	other	other	ADJ
ejpam-6251	33	3	ideas	idea	NOUN
ejpam-6251	33	4	allow	allow	VERB
ejpam-6251	33	5	us	we	PRON
ejpam-6251	33	6	to	to	PART
ejpam-6251	33	7	deal	deal	VERB
ejpam-6251	33	8	with	with	ADP
ejpam-6251	33	9	analyze	analyze	NOUN
ejpam-6251	33	10	the	the	DET
ejpam-6251	33	11	mentioned	mention	VERB
ejpam-6251	33	12	in	in	ADP
ejpam-6251	33	13	a	a	DET
ejpam-6251	33	14	purely	purely	ADV
ejpam-6251	33	15	mathematical	mathematical	ADJ
ejpam-6251	33	16	and	and	CCONJ
ejpam-6251	33	17	formal	formal	ADJ
ejpam-6251	33	18	manner	manner	NOUN
ejpam-6251	33	19	of	of	ADP
ejpam-6251	33	20	uncertainty	uncertainty	NOUN
ejpam-6251	33	21	.	.	PUNCT
ejpam-6251	34	1	many	many	ADJ
ejpam-6251	34	2	mathematical	mathematical	ADJ
ejpam-6251	34	3	structures	structure	NOUN
ejpam-6251	34	4	have	have	AUX
ejpam-6251	34	5	moved	move	VERB
ejpam-6251	34	6	within	within	ADP
ejpam-6251	34	7	the	the	DET
ejpam-6251	34	8	concept	concept	NOUN
ejpam-6251	34	9	of	of	ADP
ejpam-6251	34	10	the	the	DET
ejpam-6251	34	11	fuzzy	fuzzy	ADJ
ejpam-6251	34	12	set	set	NOUN
ejpam-6251	34	13	.	.	PUNCT
ejpam-6251	35	1	schweizer	schweizer	PROPN
ejpam-6251	35	2	et	et	PROPN
ejpam-6251	35	3	al	al	PROPN
ejpam-6251	35	4	.	.	PUNCT
ejpam-6251	36	1	[	[	X
ejpam-6251	36	2	12	12	NUM
ejpam-6251	36	3	]	]	PUNCT
ejpam-6251	36	4	pioneered	pioneer	VERB
ejpam-6251	36	5	the	the	DET
ejpam-6251	36	6	conceit	conceit	NOUN
ejpam-6251	36	7	of	of	ADP
ejpam-6251	36	8	continuous	continuous	ADJ
ejpam-6251	36	9	criteria	criterion	NOUN
ejpam-6251	36	10	.	.	PUNCT
ejpam-6251	37	1	kramosil	kramosil	NOUN
ejpam-6251	37	2	et	et	PROPN
ejpam-6251	37	3	al	al	PROPN
ejpam-6251	37	4	.	.	PUNCT
ejpam-6251	38	1	[	[	X
ejpam-6251	38	2	13	13	NUM
ejpam-6251	38	3	]	]	PUNCT
ejpam-6251	38	4	initiated	initiate	VERB
ejpam-6251	38	5	fuzzy	fuzzy	ADJ
ejpam-6251	38	6	metric	metric	ADJ
ejpam-6251	38	7	spaces	space	NOUN
ejpam-6251	38	8	(	(	PUNCT
ejpam-6251	38	9	shortly	shortly	ADV
ejpam-6251	38	10	,	,	PUNCT
ejpam-6251	38	11	fms	fms	PROPN
ejpam-6251	38	12	)	)	PUNCT
ejpam-6251	38	13	.	.	PUNCT
ejpam-6251	39	1	they	they	PRON
ejpam-6251	39	2	used	use	VERB
ejpam-6251	39	3	continued	continue	VERB
ejpam-6251	39	4	norms	norm	NOUN
ejpam-6251	39	5	to	to	PART
ejpam-6251	39	6	apply	apply	VERB
ejpam-6251	39	7	the	the	DET
ejpam-6251	39	8	idea	idea	NOUN
ejpam-6251	39	9	of	of	ADP
ejpam-6251	39	10	fuzziness	fuzziness	NOUN
ejpam-6251	39	11	to	to	ADP
ejpam-6251	39	12	standard	standard	ADJ
ejpam-6251	39	13	concepts	concept	NOUN
ejpam-6251	39	14	of	of	ADP
ejpam-6251	39	15	probabilistic	probabilistic	ADJ
ejpam-6251	39	16	,	,	PUNCT
ejpam-6251	39	17	statistical	statistical	ADJ
ejpam-6251	39	18	extensions	extension	NOUN
ejpam-6251	39	19	of	of	ADP
ejpam-6251	39	20	metric	metric	ADJ
ejpam-6251	39	21	spaces	space	NOUN
ejpam-6251	39	22	and	and	CCONJ
ejpam-6251	39	23	compared	compare	VERB
ejpam-6251	39	24	the	the	DET
ejpam-6251	39	25	results	result	NOUN
ejpam-6251	39	26	to	to	ADP
ejpam-6251	39	27	these	these	PRON
ejpam-6251	39	28	obtained	obtain	VERB
ejpam-6251	39	29	from	from	ADP
ejpam-6251	39	30	other	other	ADJ
ejpam-6251	39	31	.	.	PUNCT
ejpam-6251	40	1	in	in	ADP
ejpam-6251	40	2	[	[	X
ejpam-6251	40	3	14	14	NUM
ejpam-6251	40	4	]	]	PUNCT
ejpam-6251	40	5	,	,	PUNCT
ejpam-6251	40	6	garbiec	garbiec	NOUN
ejpam-6251	40	7	established	establish	VERB
ejpam-6251	40	8	the	the	DET
ejpam-6251	40	9	banach	banach	NOUN
ejpam-6251	40	10	contraction	contraction	NOUN
ejpam-6251	40	11	concept	concept	NOUN
ejpam-6251	40	12	in	in	ADP
ejpam-6251	40	13	fms	fms	PROPN
ejpam-6251	40	14	.	.	PUNCT
ejpam-6251	41	1	rehmam	rehmam	PROPN
ejpam-6251	41	2	et	et	PROPN
ejpam-6251	41	3	al	al	PROPN
ejpam-6251	41	4	.	.	PUNCT
ejpam-6251	42	1	[	[	X
ejpam-6251	42	2	15	15	NUM
ejpam-6251	42	3	]	]	PUNCT
ejpam-6251	42	4	discovered	discover	VERB
ejpam-6251	42	5	numerous	numerous	ADJ
ejpam-6251	42	6	α	α	PROPN
ejpam-6251	42	7	−	−	NOUN
ejpam-6251	42	8	ϕ	ϕ	NOUN
ejpam-6251	42	9	contraction	contraction	NOUN
ejpam-6251	42	10	in	in	ADP
ejpam-6251	42	11	fuzzy	fuzzy	ADJ
ejpam-6251	42	12	cone	cone	NOUN
ejpam-6251	42	13	using	use	VERB
ejpam-6251	42	14	the	the	DET
ejpam-6251	42	15	integral	integral	ADJ
ejpam-6251	42	16	type	type	NOUN
ejpam-6251	42	17	,	,	PUNCT
ejpam-6251	42	18	mostly	mostly	ADV
ejpam-6251	42	19	considered	consider	VERB
ejpam-6251	42	20	membership	membership	NOUN
ejpam-6251	42	21	functions	function	NOUN
ejpam-6251	42	22	in	in	ADP
ejpam-6251	42	23	fms	fms	PROPN
ejpam-6251	42	24	.	.	PUNCT
ejpam-6251	43	1	park	park	NOUN
ejpam-6251	44	1	[	[	X
ejpam-6251	44	2	16	16	NUM
ejpam-6251	44	3	]	]	PUNCT
ejpam-6251	44	4	developed	develop	VERB
ejpam-6251	44	5	an	an	DET
ejpam-6251	44	6	intuitionistic	intuitionistic	ADJ
ejpam-6251	44	7	fms	fms	PROPN
ejpam-6251	44	8	for	for	ADP
ejpam-6251	44	9	dealing	deal	VERB
ejpam-6251	44	10	without	without	ADP
ejpam-6251	44	11	membership	membership	NOUN
ejpam-6251	44	12	and	and	CCONJ
ejpam-6251	44	13	nonmembership	nonmembership	NOUN
ejpam-6251	44	14	functions	function	NOUN
ejpam-6251	44	15	.	.	PUNCT
ejpam-6251	45	1	konwar	konwar	PROPN
ejpam-6251	46	1	[	[	X
ejpam-6251	46	2	17	17	NUM
ejpam-6251	46	3	]	]	PUNCT
ejpam-6251	46	4	introduced	introduce	VERB
ejpam-6251	46	5	an	an	DET
ejpam-6251	46	6	intuitionistic	intuitionistic	ADJ
ejpam-6251	46	7	fuzzy	fuzzy	ADJ
ejpam-6251	46	8	b	b	X
ejpam-6251	46	9	-	-	PUNCT
ejpam-6251	46	10	metric	metric	ADJ
ejpam-6251	46	11	space	space	NOUN
ejpam-6251	46	12	(	(	PUNCT
ejpam-6251	46	13	shortly	shortly	ADV
ejpam-6251	46	14	,	,	PUNCT
ejpam-6251	46	15	fbms	fbms	PROPN
ejpam-6251	46	16	)	)	PUNCT
ejpam-6251	46	17	and	and	CCONJ
ejpam-6251	46	18	proved	prove	VERB
ejpam-6251	46	19	many	many	ADJ
ejpam-6251	46	20	fixed	fix	VERB
ejpam-6251	46	21	-	-	PUNCT
ejpam-6251	46	22	point	point	NOUN
ejpam-6251	46	23	theorems	theorem	NOUN
ejpam-6251	46	24	.	.	PUNCT
ejpam-6251	47	1	mutlu	mutlu	PROPN
ejpam-6251	47	2	et	et	PROPN
ejpam-6251	47	3	al	al	PROPN
ejpam-6251	47	4	.	.	PUNCT
ejpam-6251	48	1	[	[	X
ejpam-6251	48	2	18	18	NUM
ejpam-6251	48	3	]	]	PUNCT
ejpam-6251	48	4	,	,	PUNCT
ejpam-6251	48	5	initiated	initiate	VERB
ejpam-6251	48	6	the	the	DET
ejpam-6251	48	7	concept	concept	NOUN
ejpam-6251	48	8	of	of	ADP
ejpam-6251	48	9	bipolar	bipolar	ADJ
ejpam-6251	48	10	metric	metric	ADJ
ejpam-6251	48	11	spaces	space	NOUN
ejpam-6251	48	12	(	(	PUNCT
ejpam-6251	48	13	shortly	shortly	ADV
ejpam-6251	48	14	,	,	PUNCT
ejpam-6251	48	15	bms	bms	PROPN
ejpam-6251	48	16	)	)	PUNCT
ejpam-6251	48	17	and	and	CCONJ
ejpam-6251	48	18	established	establish	VERB
ejpam-6251	48	19	fixed	fix	VERB
ejpam-6251	48	20	point	point	NOUN
ejpam-6251	48	21	theorems	theorem	NOUN
ejpam-6251	48	22	.	.	PUNCT
ejpam-6251	49	1	many	many	ADJ
ejpam-6251	49	2	researchers	researcher	NOUN
ejpam-6251	49	3	have	have	AUX
ejpam-6251	49	4	recently	recently	ADV
ejpam-6251	49	5	produced	produce	VERB
ejpam-6251	49	6	a	a	DET
ejpam-6251	49	7	slew	slew	NOUN
ejpam-6251	49	8	of	of	ADP
ejpam-6251	49	9	fixed	fix	VERB
ejpam-6251	49	10	point	point	NOUN
ejpam-6251	49	11	outcomes	outcome	NOUN
ejpam-6251	49	12	in	in	ADP
ejpam-6251	49	13	the	the	DET
ejpam-6251	49	14	constructions	construction	NOUN
ejpam-6251	49	15	of	of	ADP
ejpam-6251	49	16	bms	bms	PROPN
ejpam-6251	49	17	using	use	VERB
ejpam-6251	49	18	various	various	ADJ
ejpam-6251	49	19	extension	extension	NOUN
ejpam-6251	49	20	of	of	ADP
ejpam-6251	49	21	these	these	DET
ejpam-6251	49	22	spaces	space	NOUN
ejpam-6251	49	23	using	use	VERB
ejpam-6251	49	24	different	different	ADJ
ejpam-6251	49	25	contractions	contraction	NOUN
ejpam-6251	50	1	[	[	X
ejpam-6251	50	2	19–30	19–30	NUM
ejpam-6251	50	3	]	]	PUNCT
ejpam-6251	50	4	.	.	PUNCT
ejpam-6251	51	1	in	in	ADP
ejpam-6251	51	2	2019	2019	NUM
ejpam-6251	51	3	,	,	PUNCT
ejpam-6251	51	4	kiricsci	kiricsci	PROPN
ejpam-6251	51	5	et	et	PROPN
ejpam-6251	51	6	al	al	PROPN
ejpam-6251	51	7	.	.	PUNCT
ejpam-6251	52	1	[	[	X
ejpam-6251	52	2	31	31	NUM
ejpam-6251	52	3	]	]	PUNCT
ejpam-6251	52	4	introduced	introduce	VERB
ejpam-6251	52	5	the	the	DET
ejpam-6251	52	6	concept	concept	NOUN
ejpam-6251	52	7	of	of	ADP
ejpam-6251	52	8	neutrosophic	neutrosophic	ADJ
ejpam-6251	52	9	metric	metric	ADJ
ejpam-6251	52	10	spaces	space	NOUN
ejpam-6251	52	11	(	(	PUNCT
ejpam-6251	52	12	nms	nms	NOUN
ejpam-6251	52	13	)	)	PUNCT
ejpam-6251	52	14	,	,	PUNCT
ejpam-6251	52	15	which	which	PRON
ejpam-6251	52	16	deals	deal	VERB
ejpam-6251	52	17	with	with	ADP
ejpam-6251	52	18	membership	membership	NOUN
ejpam-6251	52	19	,	,	PUNCT
ejpam-6251	52	20	non	non	ADJ
ejpam-6251	52	21	-	-	NOUN
ejpam-6251	52	22	membership	membership	NOUN
ejpam-6251	52	23	,	,	PUNCT
ejpam-6251	52	24	and	and	CCONJ
ejpam-6251	52	25	naturalness	naturalness	NOUN
ejpam-6251	52	26	.	.	PUNCT
ejpam-6251	53	1	again	again	ADV
ejpam-6251	53	2	in	in	ADP
ejpam-6251	53	3	2020	2020	NUM
ejpam-6251	53	4	,	,	PUNCT
ejpam-6251	53	5	simsek	simsek	NOUN
ejpam-6251	53	6	et	et	NOUN
ejpam-6251	53	7	al	al	PROPN
ejpam-6251	53	8	.	.	PUNCT
ejpam-6251	54	1	[	[	X
ejpam-6251	54	2	32	32	NUM
ejpam-6251	54	3	]	]	PUNCT
ejpam-6251	54	4	established	establish	VERB
ejpam-6251	54	5	various	various	ADJ
ejpam-6251	54	6	fixed	fix	VERB
ejpam-6251	54	7	point	point	NOUN
ejpam-6251	54	8	results	result	NOUN
ejpam-6251	54	9	in	in	ADP
ejpam-6251	54	10	the	the	DET
ejpam-6251	54	11	setting	setting	NOUN
ejpam-6251	54	12	of	of	ADP
ejpam-6251	54	13	nms	nms	NOUN
ejpam-6251	54	14	.	.	PUNCT
ejpam-6251	55	1	later	later	ADV
ejpam-6251	55	2	in	in	ADP
ejpam-6251	55	3	2020	2020	NUM
ejpam-6251	55	4	,	,	PUNCT
ejpam-6251	55	5	sowndarrajan	sowndarrajan	NOUN
ejpam-6251	55	6	et	et	PROPN
ejpam-6251	55	7	al	al	PROPN
ejpam-6251	55	8	.	.	PUNCT
ejpam-6251	56	1	[	[	X
ejpam-6251	56	2	33	33	NUM
ejpam-6251	56	3	]	]	PUNCT
ejpam-6251	56	4	showed	show	VERB
ejpam-6251	56	5	several	several	ADJ
ejpam-6251	56	6	fixed	fix	VERB
ejpam-6251	56	7	point	point	NOUN
ejpam-6251	56	8	discoveries	discovery	NOUN
ejpam-6251	56	9	in	in	ADP
ejpam-6251	56	10	the	the	DET
ejpam-6251	56	11	context	context	NOUN
ejpam-6251	56	12	of	of	ADP
ejpam-6251	56	13	neutrosophic	neutrosophic	ADJ
ejpam-6251	56	14	metric	metric	ADJ
ejpam-6251	56	15	spaces	space	NOUN
ejpam-6251	56	16	.	.	PUNCT
ejpam-6251	57	1	in	in	ADP
ejpam-6251	57	2	the	the	DET
ejpam-6251	57	3	recent	recent	ADJ
ejpam-6251	57	4	past	past	NOUN
ejpam-6251	57	5	,	,	PUNCT
ejpam-6251	57	6	applications	application	NOUN
ejpam-6251	57	7	of	of	ADP
ejpam-6251	57	8	fixed	fix	VERB
ejpam-6251	57	9	point	point	NOUN
ejpam-6251	57	10	thoerems	thoerem	NOUN
ejpam-6251	57	11	to	to	PART
ejpam-6251	57	12	fractal	fractal	ADJ
ejpam-6251	57	13	calculus	calculus	NOUN
ejpam-6251	57	14	is	be	AUX
ejpam-6251	57	15	a	a	DET
ejpam-6251	57	16	matter	matter	NOUN
ejpam-6251	57	17	of	of	ADP
ejpam-6251	57	18	interest	interest	NOUN
ejpam-6251	57	19	.	.	PUNCT
ejpam-6251	58	1	many	many	ADJ
ejpam-6251	58	2	mathematicians	mathematician	NOUN
ejpam-6251	58	3	have	have	AUX
ejpam-6251	58	4	applied	apply	VERB
ejpam-6251	58	5	the	the	DET
ejpam-6251	58	6	results	result	NOUN
ejpam-6251	58	7	of	of	ADP
ejpam-6251	58	8	fixed	fix	VERB
ejpam-6251	58	9	point	point	NOUN
ejpam-6251	58	10	theorems	theorem	VERB
ejpam-6251	58	11	r.	r.	PROPN
ejpam-6251	58	12	ramaswamy	ramaswamy	PROPN
ejpam-6251	58	13	/	/	SYM
ejpam-6251	58	14	eur	eur	PROPN
ejpam-6251	58	15	.	.	PUNCT
ejpam-6251	59	1	j.	j.	PROPN
ejpam-6251	59	2	pure	pure	PROPN
ejpam-6251	59	3	appl	appl	PROPN
ejpam-6251	59	4	.	.	PROPN
ejpam-6251	59	5	math	math	PROPN
ejpam-6251	59	6	,	,	PUNCT
ejpam-6251	59	7	18	18	NUM
ejpam-6251	59	8	(	(	PUNCT
ejpam-6251	59	9	4	4	NUM
ejpam-6251	59	10	)	)	PUNCT
ejpam-6251	59	11	(	(	PUNCT
ejpam-6251	59	12	2025	2025	NUM
ejpam-6251	59	13	)	)	PUNCT
ejpam-6251	59	14	,	,	PUNCT
ejpam-6251	59	15	6251	6251	NUM
ejpam-6251	59	16	3	3	NUM
ejpam-6251	59	17	of	of	ADP
ejpam-6251	59	18	40	40	NUM
ejpam-6251	59	19	to	to	ADP
ejpam-6251	59	20	fractional	fractional	ADJ
ejpam-6251	59	21	calculus	calculus	NOUN
ejpam-6251	59	22	.	.	PUNCT
ejpam-6251	60	1	baleanu	baleanu	PROPN
ejpam-6251	60	2	et	et	PROPN
ejpam-6251	60	3	al	al	PROPN
ejpam-6251	60	4	.	.	PUNCT
ejpam-6251	61	1	[	[	X
ejpam-6251	61	2	34	34	NUM
ejpam-6251	61	3	]	]	PUNCT
ejpam-6251	61	4	studied	study	VERB
ejpam-6251	61	5	the	the	DET
ejpam-6251	61	6	existence	existence	NOUN
ejpam-6251	61	7	and	and	CCONJ
ejpam-6251	61	8	uniqueness	uniqueness	NOUN
ejpam-6251	61	9	of	of	ADP
ejpam-6251	61	10	a	a	DET
ejpam-6251	61	11	solution	solution	NOUN
ejpam-6251	61	12	to	to	ADP
ejpam-6251	61	13	non	non	ADJ
ejpam-6251	61	14	-	-	ADJ
ejpam-6251	61	15	linear	linear	ADJ
ejpam-6251	61	16	fractional	fractional	ADJ
ejpam-6251	61	17	differential	differential	NOUN
ejpam-6251	61	18	equation	equation	NOUN
ejpam-6251	61	19	.	.	PUNCT
ejpam-6251	62	1	more	more	ADV
ejpam-6251	62	2	recently	recently	ADV
ejpam-6251	62	3	,	,	PUNCT
ejpam-6251	62	4	in	in	ADP
ejpam-6251	62	5	2021	2021	NUM
ejpam-6251	62	6	,	,	PUNCT
ejpam-6251	62	7	zhu	zhu	PROPN
ejpam-6251	62	8	et	et	PROPN
ejpam-6251	62	9	al	al	PROPN
ejpam-6251	62	10	.	.	PUNCT
ejpam-6251	63	1	[	[	X
ejpam-6251	63	2	35	35	NUM
ejpam-6251	63	3	]	]	PUNCT
ejpam-6251	63	4	applied	apply	VERB
ejpam-6251	63	5	some	some	DET
ejpam-6251	63	6	fixed	fix	VERB
ejpam-6251	63	7	-	-	PUNCT
ejpam-6251	63	8	point	point	NOUN
ejpam-6251	63	9	theorems	theorem	NOUN
ejpam-6251	63	10	to	to	PART
ejpam-6251	63	11	discuss	discuss	VERB
ejpam-6251	63	12	the	the	DET
ejpam-6251	63	13	existence	existence	NOUN
ejpam-6251	63	14	of	of	ADP
ejpam-6251	63	15	solutions	solution	NOUN
ejpam-6251	63	16	for	for	ADP
ejpam-6251	63	17	fractional	fractional	ADJ
ejpam-6251	63	18	m	m	NOUN
ejpam-6251	63	19	-	-	PUNCT
ejpam-6251	63	20	point	point	NOUN
ejpam-6251	63	21	boundary	boundary	ADJ
ejpam-6251	63	22	value	value	NOUN
ejpam-6251	63	23	problems	problem	NOUN
ejpam-6251	63	24	.	.	PUNCT
ejpam-6251	64	1	more	more	ADV
ejpam-6251	64	2	recently	recently	ADV
ejpam-6251	64	3	,	,	PUNCT
ejpam-6251	64	4	chandok	chandok	NOUN
ejpam-6251	64	5	et	et	PROPN
ejpam-6251	64	6	al	al	PROPN
ejpam-6251	64	7	.	.	PUNCT
ejpam-6251	65	1	[	[	X
ejpam-6251	65	2	36	36	NUM
ejpam-6251	65	3	]	]	PUNCT
ejpam-6251	65	4	presented	present	VERB
ejpam-6251	65	5	application	application	NOUN
ejpam-6251	65	6	to	to	ADP
ejpam-6251	65	7	fractional	fractional	ADJ
ejpam-6251	65	8	calculus	calculus	NOUN
ejpam-6251	65	9	via	via	ADP
ejpam-6251	65	10	orthogonal	orthogonal	ADJ
ejpam-6251	65	11	contractions	contraction	NOUN
ejpam-6251	65	12	.	.	PUNCT
ejpam-6251	66	1	in	in	ADP
ejpam-6251	66	2	the	the	DET
ejpam-6251	66	3	recent	recent	ADJ
ejpam-6251	66	4	past	past	NOUN
ejpam-6251	66	5	,	,	PUNCT
ejpam-6251	66	6	mani	mani	PROPN
ejpam-6251	66	7	et	et	PROPN
ejpam-6251	66	8	al	al	PROPN
ejpam-6251	66	9	.	.	PUNCT
ejpam-6251	67	1	[	[	X
ejpam-6251	67	2	37	37	NUM
ejpam-6251	67	3	]	]	PUNCT
ejpam-6251	67	4	improved	improve	VERB
ejpam-6251	67	5	fixed	fix	VERB
ejpam-6251	67	6	point	point	NOUN
ejpam-6251	67	7	results	result	NOUN
ejpam-6251	67	8	and	and	CCONJ
ejpam-6251	67	9	to	to	PART
ejpam-6251	67	10	find	find	VERB
ejpam-6251	67	11	analytical	analytical	ADJ
ejpam-6251	67	12	solution	solution	NOUN
ejpam-6251	67	13	of	of	ADP
ejpam-6251	67	14	integral	integral	ADJ
ejpam-6251	67	15	equation	equation	NOUN
ejpam-6251	67	16	using	use	VERB
ejpam-6251	67	17	neutrosophic	neutrosophic	ADJ
ejpam-6251	67	18	triple	triple	ADJ
ejpam-6251	67	19	controlled	control	VERB
ejpam-6251	67	20	metric	metric	ADJ
ejpam-6251	67	21	spaces	space	NOUN
ejpam-6251	67	22	.	.	PUNCT
ejpam-6251	68	1	inspired	inspire	VERB
ejpam-6251	68	2	by	by	ADP
ejpam-6251	68	3	the	the	DET
ejpam-6251	68	4	reported	report	VERB
ejpam-6251	68	5	results	result	NOUN
ejpam-6251	68	6	in	in	ADP
ejpam-6251	68	7	the	the	DET
ejpam-6251	68	8	setting	setting	NOUN
ejpam-6251	68	9	of	of	ADP
ejpam-6251	68	10	bipolar	bipolar	ADJ
ejpam-6251	68	11	as	as	ADV
ejpam-6251	68	12	well	well	ADV
ejpam-6251	68	13	as	as	ADP
ejpam-6251	68	14	the	the	DET
ejpam-6251	68	15	neutrospohic	neutrospohic	ADJ
ejpam-6251	68	16	metric	metric	ADJ
ejpam-6251	68	17	spaces	space	NOUN
ejpam-6251	68	18	,	,	PUNCT
ejpam-6251	68	19	in	in	ADP
ejpam-6251	68	20	the	the	DET
ejpam-6251	68	21	present	present	ADJ
ejpam-6251	68	22	work	work	NOUN
ejpam-6251	68	23	,	,	PUNCT
ejpam-6251	68	24	the	the	DET
ejpam-6251	68	25	notion	notion	NOUN
ejpam-6251	68	26	of	of	ADP
ejpam-6251	68	27	nbms	nbms	NOUN
ejpam-6251	68	28	and	and	CCONJ
ejpam-6251	68	29	some	some	DET
ejpam-6251	68	30	related	relate	VERB
ejpam-6251	68	31	topological	topological	ADJ
ejpam-6251	68	32	concepts	concept	NOUN
ejpam-6251	68	33	are	be	AUX
ejpam-6251	68	34	introduced	introduce	VERB
ejpam-6251	68	35	and	and	CCONJ
ejpam-6251	68	36	fixed	fix	VERB
ejpam-6251	68	37	point	point	NOUN
ejpam-6251	68	38	results	result	NOUN
ejpam-6251	68	39	have	have	AUX
ejpam-6251	68	40	been	be	AUX
ejpam-6251	68	41	established	establish	VERB
ejpam-6251	68	42	in	in	ADP
ejpam-6251	68	43	the	the	DET
ejpam-6251	68	44	setting	setting	NOUN
ejpam-6251	68	45	of	of	ADP
ejpam-6251	68	46	this	this	DET
ejpam-6251	68	47	space	space	NOUN
ejpam-6251	68	48	and	and	CCONJ
ejpam-6251	68	49	the	the	DET
ejpam-6251	68	50	derived	derive	VERB
ejpam-6251	68	51	results	result	NOUN
ejpam-6251	68	52	are	be	AUX
ejpam-6251	68	53	supplemented	supplement	VERB
ejpam-6251	68	54	with	with	ADP
ejpam-6251	68	55	non	non	ADJ
ejpam-6251	68	56	-	-	ADJ
ejpam-6251	68	57	trivial	trivial	ADJ
ejpam-6251	68	58	examples	example	NOUN
ejpam-6251	68	59	.	.	PUNCT
ejpam-6251	69	1	this	this	DET
ejpam-6251	69	2	work	work	NOUN
ejpam-6251	69	3	also	also	ADV
ejpam-6251	69	4	presents	present	VERB
ejpam-6251	69	5	three	three	NUM
ejpam-6251	69	6	types	type	NOUN
ejpam-6251	69	7	of	of	ADP
ejpam-6251	69	8	applications	application	NOUN
ejpam-6251	69	9	of	of	ADP
ejpam-6251	69	10	the	the	DET
ejpam-6251	69	11	derived	derive	VERB
ejpam-6251	69	12	fixed	fix	VERB
ejpam-6251	69	13	point	point	NOUN
ejpam-6251	69	14	results	result	NOUN
ejpam-6251	69	15	:	:	PUNCT
ejpam-6251	69	16	(	(	PUNCT
ejpam-6251	69	17	a	a	X
ejpam-6251	69	18	)	)	PUNCT
ejpam-6251	69	19	to	to	PART
ejpam-6251	69	20	find	find	VERB
ejpam-6251	69	21	analytical	analytical	ADJ
ejpam-6251	69	22	and	and	CCONJ
ejpam-6251	69	23	closed	closed	ADJ
ejpam-6251	69	24	form	form	NOUN
ejpam-6251	69	25	solutions	solution	NOUN
ejpam-6251	69	26	of	of	ADP
ejpam-6251	69	27	an	an	DET
ejpam-6251	69	28	integral	integral	ADJ
ejpam-6251	69	29	equation	equation	NOUN
ejpam-6251	69	30	,	,	PUNCT
ejpam-6251	69	31	(	(	PUNCT
ejpam-6251	69	32	b	b	X
ejpam-6251	69	33	)	)	PUNCT
ejpam-6251	69	34	to	to	PART
ejpam-6251	69	35	find	find	VERB
ejpam-6251	69	36	the	the	DET
ejpam-6251	69	37	voltage	voltage	NOUN
ejpam-6251	69	38	in	in	ADP
ejpam-6251	69	39	an	an	DET
ejpam-6251	69	40	electrical	electrical	ADJ
ejpam-6251	69	41	circuit	circuit	NOUN
ejpam-6251	69	42	and	and	CCONJ
ejpam-6251	69	43	finally	finally	ADV
ejpam-6251	69	44	(	(	PUNCT
ejpam-6251	69	45	c	c	X
ejpam-6251	69	46	)	)	PUNCT
ejpam-6251	69	47	to	to	PART
ejpam-6251	69	48	find	find	VERB
ejpam-6251	69	49	the	the	DET
ejpam-6251	69	50	analytical	analytical	ADJ
ejpam-6251	69	51	solution	solution	NOUN
ejpam-6251	69	52	of	of	ADP
ejpam-6251	69	53	a	a	DET
ejpam-6251	69	54	fractional	fractional	ADJ
ejpam-6251	69	55	differential	differential	NOUN
ejpam-6251	69	56	equation	equation	NOUN
ejpam-6251	69	57	.	.	PUNCT
ejpam-6251	70	1	the	the	DET
ejpam-6251	70	2	results	result	NOUN
ejpam-6251	70	3	proven	prove	VERB
ejpam-6251	70	4	in	in	ADP
ejpam-6251	70	5	this	this	DET
ejpam-6251	70	6	manuscript	manuscript	NOUN
ejpam-6251	70	7	are	be	AUX
ejpam-6251	70	8	extensions	extension	NOUN
ejpam-6251	70	9	or	or	CCONJ
ejpam-6251	70	10	generalizations	generalization	NOUN
ejpam-6251	70	11	of	of	ADP
ejpam-6251	70	12	the	the	DET
ejpam-6251	70	13	result	result	NOUN
ejpam-6251	70	14	proven	prove	VERB
ejpam-6251	70	15	in	in	ADP
ejpam-6251	70	16	the	the	DET
ejpam-6251	70	17	past	past	NOUN
ejpam-6251	70	18	.	.	PUNCT
ejpam-6251	71	1	the	the	DET
ejpam-6251	71	2	rest	rest	NOUN
ejpam-6251	71	3	of	of	ADP
ejpam-6251	71	4	the	the	DET
ejpam-6251	71	5	paper	paper	NOUN
ejpam-6251	71	6	is	be	AUX
ejpam-6251	71	7	organized	organize	VERB
ejpam-6251	71	8	as	as	SCONJ
ejpam-6251	71	9	follows	follow	VERB
ejpam-6251	71	10	:	:	PUNCT
ejpam-6251	71	11	some	some	DET
ejpam-6251	71	12	definitions	definition	NOUN
ejpam-6251	71	13	and	and	CCONJ
ejpam-6251	71	14	theories	theory	NOUN
ejpam-6251	71	15	are	be	AUX
ejpam-6251	71	16	reviewed	review	VERB
ejpam-6251	71	17	in	in	ADP
ejpam-6251	71	18	section	section	NOUN
ejpam-6251	71	19	2.in	2.in	NUM
ejpam-6251	71	20	section	section	NOUN
ejpam-6251	71	21	3	3	NUM
ejpam-6251	71	22	,	,	PUNCT
ejpam-6251	71	23	the	the	DET
ejpam-6251	71	24	proposed	propose	VERB
ejpam-6251	71	25	neutrosophic	neutrosophic	ADJ
ejpam-6251	71	26	bipolar	bipolar	ADJ
ejpam-6251	71	27	metric	metric	ADJ
ejpam-6251	71	28	space	space	NOUN
ejpam-6251	71	29	and	and	CCONJ
ejpam-6251	71	30	associated	associate	VERB
ejpam-6251	71	31	concepts	concept	NOUN
ejpam-6251	71	32	are	be	AUX
ejpam-6251	71	33	defined	define	VERB
ejpam-6251	71	34	and	and	CCONJ
ejpam-6251	71	35	discussed	discuss	VERB
ejpam-6251	71	36	.	.	PUNCT
ejpam-6251	72	1	furthermore	furthermore	ADV
ejpam-6251	72	2	,	,	PUNCT
ejpam-6251	72	3	the	the	DET
ejpam-6251	72	4	main	main	ADJ
ejpam-6251	72	5	fixed	fix	VERB
ejpam-6251	72	6	point	point	NOUN
ejpam-6251	72	7	result	result	NOUN
ejpam-6251	72	8	is	be	AUX
ejpam-6251	72	9	presented	present	VERB
ejpam-6251	72	10	in	in	ADP
ejpam-6251	72	11	this	this	DET
ejpam-6251	72	12	section	section	NOUN
ejpam-6251	72	13	supported	support	VERB
ejpam-6251	72	14	with	with	ADP
ejpam-6251	72	15	non	non	ADJ
ejpam-6251	72	16	trivial	trivial	ADJ
ejpam-6251	72	17	examples	example	NOUN
ejpam-6251	72	18	to	to	PART
ejpam-6251	72	19	supplement	supplement	VERB
ejpam-6251	72	20	the	the	DET
ejpam-6251	72	21	derived	derive	VERB
ejpam-6251	72	22	results	result	NOUN
ejpam-6251	72	23	.	.	PUNCT
ejpam-6251	73	1	in	in	ADP
ejpam-6251	73	2	section	section	NOUN
ejpam-6251	73	3	4	4	NUM
ejpam-6251	73	4	,	,	PUNCT
ejpam-6251	73	5	an	an	DET
ejpam-6251	73	6	application	application	NOUN
ejpam-6251	73	7	of	of	ADP
ejpam-6251	73	8	the	the	DET
ejpam-6251	73	9	derived	derive	VERB
ejpam-6251	73	10	fixed	fix	VERB
ejpam-6251	73	11	point	point	NOUN
ejpam-6251	73	12	result	result	VERB
ejpam-6251	73	13	to	to	PART
ejpam-6251	73	14	find	find	VERB
ejpam-6251	73	15	the	the	DET
ejpam-6251	73	16	solution	solution	NOUN
ejpam-6251	73	17	of	of	ADP
ejpam-6251	73	18	the	the	DET
ejpam-6251	73	19	fredholm	fredholm	ADJ
ejpam-6251	73	20	integral	integral	ADJ
ejpam-6251	73	21	equation	equation	NOUN
ejpam-6251	73	22	is	be	AUX
ejpam-6251	73	23	given	give	VERB
ejpam-6251	73	24	.	.	PUNCT
ejpam-6251	74	1	this	this	PRON
ejpam-6251	74	2	is	be	AUX
ejpam-6251	74	3	followed	follow	VERB
ejpam-6251	74	4	by	by	ADP
ejpam-6251	74	5	the	the	DET
ejpam-6251	74	6	finding	finding	NOUN
ejpam-6251	74	7	an	an	DET
ejpam-6251	74	8	analytical	analytical	ADJ
ejpam-6251	74	9	solution	solution	NOUN
ejpam-6251	74	10	for	for	ADP
ejpam-6251	74	11	the	the	DET
ejpam-6251	74	12	voltage	voltage	NOUN
ejpam-6251	74	13	in	in	ADP
ejpam-6251	74	14	an	an	DET
ejpam-6251	74	15	electric	electric	ADJ
ejpam-6251	74	16	circuit	circuit	NOUN
ejpam-6251	74	17	in	in	ADP
ejpam-6251	74	18	section-5	section-5	ADP
ejpam-6251	74	19	along	along	ADV
ejpam-6251	74	20	with	with	ADP
ejpam-6251	74	21	the	the	DET
ejpam-6251	74	22	closed	closed	ADJ
ejpam-6251	74	23	form	form	NOUN
ejpam-6251	74	24	of	of	ADP
ejpam-6251	74	25	bvp	bvp	NOUN
ejpam-6251	74	26	and	and	CCONJ
ejpam-6251	74	27	finally	finally	ADV
ejpam-6251	74	28	,	,	PUNCT
ejpam-6251	74	29	an	an	DET
ejpam-6251	74	30	application	application	NOUN
ejpam-6251	74	31	to	to	PART
ejpam-6251	74	32	find	find	VERB
ejpam-6251	74	33	the	the	DET
ejpam-6251	74	34	analytical	analytical	ADJ
ejpam-6251	74	35	solution	solution	NOUN
ejpam-6251	74	36	of	of	ADP
ejpam-6251	74	37	the	the	DET
ejpam-6251	74	38	fractional	fractional	ADJ
ejpam-6251	74	39	differential	differential	NOUN
ejpam-6251	74	40	equation	equation	NOUN
ejpam-6251	74	41	is	be	AUX
ejpam-6251	74	42	also	also	ADV
ejpam-6251	74	43	presented	present	VERB
ejpam-6251	74	44	.	.	PUNCT
ejpam-6251	75	1	2	2	X
ejpam-6251	75	2	.	.	X
ejpam-6251	75	3	preliminaries	preliminary	NOUN
ejpam-6251	75	4	we	we	PRON
ejpam-6251	75	5	commence	commence	VERB
ejpam-6251	75	6	this	this	DET
ejpam-6251	75	7	section	section	NOUN
ejpam-6251	75	8	,	,	PUNCT
ejpam-6251	75	9	with	with	ADP
ejpam-6251	75	10	certain	certain	ADJ
ejpam-6251	75	11	abbreviations	abbreviation	NOUN
ejpam-6251	75	12	and	and	CCONJ
ejpam-6251	75	13	some	some	DET
ejpam-6251	75	14	symbols	symbol	NOUN
ejpam-6251	75	15	used	use	VERB
ejpam-6251	75	16	in	in	ADP
ejpam-6251	75	17	the	the	DET
ejpam-6251	75	18	manuscript	manuscript	NOUN
ejpam-6251	75	19	:	:	PUNCT
ejpam-6251	75	20	table	table	NOUN
ejpam-6251	75	21	1	1	NUM
ejpam-6251	75	22	:	:	PUNCT
ejpam-6251	75	23	list	list	NOUN
ejpam-6251	75	24	of	of	ADP
ejpam-6251	75	25	acronyms	acronym	NOUN
ejpam-6251	75	26	acronym	acronym	PROPN
ejpam-6251	75	27	full	full	ADJ
ejpam-6251	75	28	form	form	NOUN
ejpam-6251	75	29	fms	fms	PROPN
ejpam-6251	75	30	fuzzy	fuzzy	ADJ
ejpam-6251	75	31	metric	metric	ADJ
ejpam-6251	75	32	space	space	NOUN
ejpam-6251	75	33	nbms	nbms	NOUN
ejpam-6251	75	34	neutrosophic	neutrosophic	ADJ
ejpam-6251	75	35	bipolar	bipolar	ADJ
ejpam-6251	75	36	metric	metric	ADJ
ejpam-6251	75	37	space	space	NOUN
ejpam-6251	75	38	nms	nms	PROPN
ejpam-6251	75	39	neutrosophic	neutrosophic	ADJ
ejpam-6251	75	40	metric	metric	ADJ
ejpam-6251	75	41	space	space	NOUN
ejpam-6251	75	42	nb	nb	PROPN
ejpam-6251	75	43	neutrosophic	neutrosophic	ADJ
ejpam-6251	75	44	bipolar	bipolar	PROPN
ejpam-6251	75	45	r.	r.	PROPN
ejpam-6251	75	46	ramaswamy	ramaswamy	PROPN
ejpam-6251	75	47	/	/	SYM
ejpam-6251	75	48	eur	eur	PROPN
ejpam-6251	75	49	.	.	PUNCT
ejpam-6251	76	1	j.	j.	PROPN
ejpam-6251	76	2	pure	pure	PROPN
ejpam-6251	76	3	appl	appl	PROPN
ejpam-6251	76	4	.	.	PROPN
ejpam-6251	76	5	math	math	PROPN
ejpam-6251	76	6	,	,	PUNCT
ejpam-6251	76	7	18	18	NUM
ejpam-6251	76	8	(	(	PUNCT
ejpam-6251	76	9	4	4	NUM
ejpam-6251	76	10	)	)	PUNCT
ejpam-6251	76	11	(	(	PUNCT
ejpam-6251	76	12	2025	2025	NUM
ejpam-6251	76	13	)	)	PUNCT
ejpam-6251	76	14	,	,	PUNCT
ejpam-6251	76	15	6251	6251	NUM
ejpam-6251	76	16	4	4	NUM
ejpam-6251	76	17	of	of	ADP
ejpam-6251	76	18	40	40	NUM
ejpam-6251	76	19	table	table	NOUN
ejpam-6251	76	20	2	2	NUM
ejpam-6251	76	21	:	:	PUNCT
ejpam-6251	76	22	list	list	NOUN
ejpam-6251	76	23	of	of	ADP
ejpam-6251	76	24	symbols	symbol	NOUN
ejpam-6251	76	25	symbol	symbol	NOUN
ejpam-6251	76	26	meaning	mean	VERB
ejpam-6251	76	27	ct−||.||	ct−||.||	NOUN
ejpam-6251	76	28	continuous	continuous	ADJ
ejpam-6251	76	29	triangle	triangle	NOUN
ejpam-6251	76	30	norm	norm	NOUN
ejpam-6251	76	31	ct−co−||.||	ct−co−||.||	DET
ejpam-6251	76	32	continuous	continuous	ADJ
ejpam-6251	76	33	triangle	triangle	NOUN
ejpam-6251	76	34	co	co	NOUN
ejpam-6251	76	35	-	-	NOUN
ejpam-6251	76	36	norm	norm	ADJ
ejpam-6251	76	37	π	π	PROPN
ejpam-6251	76	38	,	,	PUNCT
ejpam-6251	76	39	ψ	ψ	SYM
ejpam-6251	76	40	,	,	PUNCT
ejpam-6251	76	41	ξ	ξ	PROPN
ejpam-6251	76	42	,	,	PUNCT
ejpam-6251	76	43	ω	ω	PROPN
ejpam-6251	76	44	functions	function	NOUN
ejpam-6251	76	45	𭟋	𭟋	NOUN
ejpam-6251	76	46	,	,	PUNCT
ejpam-6251	76	47	s	s	VERB
ejpam-6251	76	48	non	non	X
ejpam-6251	76	49	empty	empty	ADJ
ejpam-6251	76	50	sets	set	NOUN
ejpam-6251	76	51	⋇	⋇	NOUN
ejpam-6251	76	52	continuous	continuous	ADJ
ejpam-6251	76	53	triangle	triangle	NOUN
ejpam-6251	76	54	norm	norm	NOUN
ejpam-6251	76	55	♢	♢	PROPN
ejpam-6251	76	56	continuous	continuous	ADJ
ejpam-6251	76	57	triangle	triangle	NOUN
ejpam-6251	76	58	co	co	NOUN
ejpam-6251	76	59	-	-	NOUN
ejpam-6251	76	60	norm	norm	ADJ
ejpam-6251	76	61	u̇	u̇	PROPN
ejpam-6251	76	62	,	,	PUNCT
ejpam-6251	76	63	ż	ż	NOUN
ejpam-6251	76	64	,	,	PUNCT
ejpam-6251	76	65	ṫ	ṫ	PROPN
ejpam-6251	76	66	,	,	PUNCT
ejpam-6251	76	67	ṡ	ṡ	PRON
ejpam-6251	76	68	,	,	PUNCT
ejpam-6251	76	69	ẇ	ẇ	ADP
ejpam-6251	76	70	positive	positive	ADJ
ejpam-6251	76	71	reals	real	NOUN
ejpam-6251	76	72	the	the	DET
ejpam-6251	76	73	following	follow	VERB
ejpam-6251	76	74	definitions	definition	NOUN
ejpam-6251	76	75	are	be	AUX
ejpam-6251	76	76	required	require	VERB
ejpam-6251	76	77	in	in	ADP
ejpam-6251	76	78	the	the	DET
ejpam-6251	76	79	sequel	sequel	NOUN
ejpam-6251	76	80	.	.	PUNCT
ejpam-6251	77	1	definition	definition	NOUN
ejpam-6251	77	2	1	1	NUM
ejpam-6251	77	3	.	.	PUNCT
ejpam-6251	78	1	(	(	PUNCT
ejpam-6251	78	2	[	[	X
ejpam-6251	78	3	16	16	NUM
ejpam-6251	78	4	]	]	PUNCT
ejpam-6251	78	5	)	)	PUNCT
ejpam-6251	78	6	a	a	DET
ejpam-6251	78	7	binary	binary	PROPN
ejpam-6251	78	8	operation	operation	NOUN
ejpam-6251	78	9	⋇	⋇	NOUN
ejpam-6251	78	10	:	:	PUNCT
ejpam-6251	79	1	[	[	X
ejpam-6251	79	2	0	0	NUM
ejpam-6251	79	3	,	,	PUNCT
ejpam-6251	79	4	1]2	1]2	NUM
ejpam-6251	79	5	→	→	PUNCT
ejpam-6251	79	6	[	[	X
ejpam-6251	79	7	0	0	NUM
ejpam-6251	79	8	,	,	PUNCT
ejpam-6251	79	9	1	1	NUM
ejpam-6251	79	10	]	]	PUNCT
ejpam-6251	79	11	is	be	AUX
ejpam-6251	79	12	said	say	VERB
ejpam-6251	79	13	to	to	PART
ejpam-6251	79	14	be	be	AUX
ejpam-6251	79	15	a	a	DET
ejpam-6251	79	16	continuous	continuous	ADJ
ejpam-6251	79	17	triangle	triangle	NOUN
ejpam-6251	79	18	norm	norm	NOUN
ejpam-6251	79	19	(	(	PUNCT
ejpam-6251	79	20	shortly	shortly	ADV
ejpam-6251	79	21	,	,	PUNCT
ejpam-6251	79	22	ct−||.||	ct−||.||	NOUN
ejpam-6251	79	23	)	)	PUNCT
ejpam-6251	79	24	if	if	SCONJ
ejpam-6251	79	25	:	:	PUNCT
ejpam-6251	79	26	i.	i.	PROPN
ejpam-6251	79	27	i⋇	i⋇	PROPN
ejpam-6251	79	28	♭	♭	PROPN
ejpam-6251	80	1	=	=	PUNCT
ejpam-6251	80	2	♭	♭	PROPN
ejpam-6251	80	3	⋇	⋇	PROPN
ejpam-6251	80	4	i	i	PRON
ejpam-6251	80	5	,	,	PUNCT
ejpam-6251	80	6	(	(	PUNCT
ejpam-6251	80	7	∀)i	∀)i	NOUN
ejpam-6251	80	8	,	,	PUNCT
ejpam-6251	80	9	♭	♭	PROPN
ejpam-6251	80	10	∈	∈	PROPN
ejpam-6251	81	1	[	[	X
ejpam-6251	81	2	0	0	NUM
ejpam-6251	81	3	,	,	PUNCT
ejpam-6251	81	4	1	1	NUM
ejpam-6251	81	5	]	]	PUNCT
ejpam-6251	81	6	;	;	PUNCT
ejpam-6251	81	7	ii	ii	X
ejpam-6251	81	8	.	.	PUNCT
ejpam-6251	82	1	⋇	⋇	NOUN
ejpam-6251	82	2	is	be	AUX
ejpam-6251	82	3	continuous	continuous	ADJ
ejpam-6251	82	4	;	;	PUNCT
ejpam-6251	82	5	iii	iii	X
ejpam-6251	82	6	.	.	PUNCT
ejpam-6251	83	1	i⋇	i⋇	PROPN
ejpam-6251	83	2	1	1	NUM
ejpam-6251	83	3	=	=	SYM
ejpam-6251	83	4	i	i	PROPN
ejpam-6251	83	5	,	,	PUNCT
ejpam-6251	83	6	(	(	PUNCT
ejpam-6251	83	7	∀)i	∀)i	NOUN
ejpam-6251	83	8	∈	∈	PROPN
ejpam-6251	84	1	[	[	X
ejpam-6251	84	2	0	0	NUM
ejpam-6251	84	3	,	,	PUNCT
ejpam-6251	84	4	1	1	NUM
ejpam-6251	84	5	]	]	PUNCT
ejpam-6251	84	6	;	;	PUNCT
ejpam-6251	84	7	iv	iv	X
ejpam-6251	84	8	.	.	PUNCT
ejpam-6251	85	1	(	(	PUNCT
ejpam-6251	85	2	i⋇	i⋇	PROPN
ejpam-6251	85	3	♭	♭	PROPN
ejpam-6251	85	4	)	)	PUNCT
ejpam-6251	85	5	⋇	⋇	NOUN
ejpam-6251	85	6	ℏ	ℏ	NOUN
ejpam-6251	85	7	=	=	SYM
ejpam-6251	85	8	i⋇	i⋇	PROPN
ejpam-6251	85	9	(	(	PUNCT
ejpam-6251	85	10	♭	♭	PROPN
ejpam-6251	85	11	⋇	⋇	PROPN
ejpam-6251	85	12	ℏ	ℏ	PROPN
ejpam-6251	85	13	)	)	PUNCT
ejpam-6251	85	14	,	,	PUNCT
ejpam-6251	85	15	∀	∀	PUNCT
ejpam-6251	86	1	i	i	PRON
ejpam-6251	86	2	,	,	PUNCT
ejpam-6251	86	3	♭	♭	INTJ
ejpam-6251	86	4	,	,	PUNCT
ejpam-6251	86	5	ℏ	ℏ	PROPN
ejpam-6251	86	6	∈	∈	PROPN
ejpam-6251	87	1	[	[	X
ejpam-6251	87	2	0	0	NUM
ejpam-6251	87	3	,	,	PUNCT
ejpam-6251	87	4	1	1	NUM
ejpam-6251	87	5	]	]	PUNCT
ejpam-6251	87	6	;	;	PUNCT
ejpam-6251	87	7	v.	v.	CCONJ
ejpam-6251	87	8	if	if	SCONJ
ejpam-6251	87	9	i	i	PRON
ejpam-6251	87	10	≤	≤	X
ejpam-6251	87	11	ℏ	ℏ	PROPN
ejpam-6251	87	12	and	and	CCONJ
ejpam-6251	87	13	♭	♭	PROPN
ejpam-6251	88	1	≤	≤	NUM
ejpam-6251	88	2	j	j	PROPN
ejpam-6251	88	3	,	,	PUNCT
ejpam-6251	88	4	with	with	ADP
ejpam-6251	88	5	i	i	PRON
ejpam-6251	88	6	,	,	PUNCT
ejpam-6251	88	7	♭	♭	PROPN
ejpam-6251	88	8	,	,	PUNCT
ejpam-6251	88	9	ℏ	ℏ	PROPN
ejpam-6251	88	10	,	,	PUNCT
ejpam-6251	88	11	j	j	PROPN
ejpam-6251	88	12	∈	∈	PROPN
ejpam-6251	89	1	[	[	X
ejpam-6251	89	2	0	0	NUM
ejpam-6251	89	3	,	,	PUNCT
ejpam-6251	89	4	1	1	NUM
ejpam-6251	89	5	]	]	PUNCT
ejpam-6251	89	6	,	,	PUNCT
ejpam-6251	89	7	then	then	ADV
ejpam-6251	89	8	i⋇	i⋇	PROPN
ejpam-6251	89	9	♭	♭	PROPN
ejpam-6251	89	10	≤	≤	PROPN
ejpam-6251	89	11	ℏ	ℏ	PROPN
ejpam-6251	89	12	⋇	⋇	NOUN
ejpam-6251	89	13	j.	j.	PROPN
ejpam-6251	89	14	definition	definition	PROPN
ejpam-6251	89	15	2	2	NUM
ejpam-6251	89	16	.	.	PUNCT
ejpam-6251	90	1	(	(	PUNCT
ejpam-6251	90	2	[	[	X
ejpam-6251	90	3	16	16	NUM
ejpam-6251	90	4	]	]	PUNCT
ejpam-6251	90	5	)	)	PUNCT
ejpam-6251	90	6	a	a	DET
ejpam-6251	90	7	binary	binary	PROPN
ejpam-6251	90	8	operation	operation	NOUN
ejpam-6251	91	1	♢	♢	PROPN
ejpam-6251	91	2	:	:	PUNCT
ejpam-6251	92	1	[	[	X
ejpam-6251	92	2	0	0	NUM
ejpam-6251	92	3	,	,	PUNCT
ejpam-6251	92	4	1]2	1]2	NUM
ejpam-6251	92	5	→	→	PUNCT
ejpam-6251	92	6	[	[	X
ejpam-6251	92	7	0	0	NUM
ejpam-6251	92	8	,	,	PUNCT
ejpam-6251	92	9	1	1	NUM
ejpam-6251	92	10	]	]	PUNCT
ejpam-6251	92	11	is	be	AUX
ejpam-6251	92	12	said	say	VERB
ejpam-6251	92	13	to	to	PART
ejpam-6251	92	14	be	be	AUX
ejpam-6251	92	15	a	a	DET
ejpam-6251	92	16	continuous	continuous	ADJ
ejpam-6251	92	17	triangle	triangle	NOUN
ejpam-6251	92	18	co	co	NOUN
ejpam-6251	92	19	-	-	NOUN
ejpam-6251	92	20	norm	norm	ADJ
ejpam-6251	92	21	(	(	PUNCT
ejpam-6251	92	22	shortly	shortly	ADV
ejpam-6251	92	23	,	,	PUNCT
ejpam-6251	92	24	ct−co−||.||	ct−co−||.||	NOUN
ejpam-6251	92	25	)	)	PUNCT
ejpam-6251	92	26	if	if	SCONJ
ejpam-6251	92	27	:	:	PUNCT
ejpam-6251	92	28	i.	i.	PROPN
ejpam-6251	93	1	i	i	PRON
ejpam-6251	93	2	♢	♢	PROPN
ejpam-6251	93	3	♭	♭	PROPN
ejpam-6251	93	4	=	=	PUNCT
ejpam-6251	93	5	♭	♭	PROPN
ejpam-6251	93	6	♢	♢	PROPN
ejpam-6251	93	7	i	i	PROPN
ejpam-6251	93	8	,	,	PUNCT
ejpam-6251	93	9	∀	∀	VERB
ejpam-6251	93	10	i	i	PRON
ejpam-6251	93	11	,	,	PUNCT
ejpam-6251	93	12	♭	♭	PROPN
ejpam-6251	93	13	∈	∈	PROPN
ejpam-6251	94	1	[	[	X
ejpam-6251	94	2	0	0	NUM
ejpam-6251	94	3	,	,	PUNCT
ejpam-6251	94	4	1	1	NUM
ejpam-6251	94	5	]	]	PUNCT
ejpam-6251	94	6	;	;	PUNCT
ejpam-6251	94	7	ii	ii	PROPN
ejpam-6251	94	8	.	.	PUNCT
ejpam-6251	95	1	♢	♢	PROPN
ejpam-6251	95	2	is	be	AUX
ejpam-6251	95	3	continuous	continuous	ADJ
ejpam-6251	95	4	;	;	PUNCT
ejpam-6251	95	5	iii	iii	X
ejpam-6251	95	6	.	.	PUNCT
ejpam-6251	96	1	i	i	PRON
ejpam-6251	96	2	♢	♢	VERB
ejpam-6251	96	3	0	0	PROPN
ejpam-6251	96	4	=	=	SYM
ejpam-6251	96	5	0	0	NUM
ejpam-6251	96	6	,	,	PUNCT
ejpam-6251	96	7	∀	∀	VERB
ejpam-6251	97	1	i	i	PRON
ejpam-6251	97	2	∈	∈	VERB
ejpam-6251	98	1	[	[	X
ejpam-6251	98	2	0	0	NUM
ejpam-6251	98	3	,	,	PUNCT
ejpam-6251	98	4	1	1	NUM
ejpam-6251	98	5	]	]	PUNCT
ejpam-6251	98	6	;	;	PUNCT
ejpam-6251	98	7	iv	iv	X
ejpam-6251	98	8	.	.	PUNCT
ejpam-6251	99	1	(	(	PUNCT
ejpam-6251	99	2	i	i	PROPN
ejpam-6251	99	3	♢	♢	PROPN
ejpam-6251	99	4	♭	♭	PROPN
ejpam-6251	99	5	)	)	PUNCT
ejpam-6251	99	6	♢	♢	PROPN
ejpam-6251	99	7	ℏ	ℏ	PROPN
ejpam-6251	99	8	=	=	SYM
ejpam-6251	99	9	i	i	PRON
ejpam-6251	99	10	♢	♢	PROPN
ejpam-6251	99	11	(	(	PUNCT
ejpam-6251	99	12	♭	♭	PROPN
ejpam-6251	99	13	♢	♢	PROPN
ejpam-6251	99	14	ℏ	ℏ	PROPN
ejpam-6251	99	15	)	)	PUNCT
ejpam-6251	99	16	,	,	PUNCT
ejpam-6251	99	17	∀	∀	PUNCT
ejpam-6251	100	1	i	i	PRON
ejpam-6251	100	2	,	,	PUNCT
ejpam-6251	100	3	♭	♭	INTJ
ejpam-6251	100	4	,	,	PUNCT
ejpam-6251	100	5	ℏ	ℏ	PROPN
ejpam-6251	100	6	∈	∈	PROPN
ejpam-6251	101	1	[	[	X
ejpam-6251	101	2	0	0	NUM
ejpam-6251	101	3	,	,	PUNCT
ejpam-6251	101	4	1	1	NUM
ejpam-6251	101	5	]	]	PUNCT
ejpam-6251	101	6	;	;	PUNCT
ejpam-6251	101	7	v.	v.	CCONJ
ejpam-6251	101	8	if	if	SCONJ
ejpam-6251	101	9	i	i	PRON
ejpam-6251	101	10	≤	≤	X
ejpam-6251	101	11	ℏ	ℏ	PROPN
ejpam-6251	101	12	and	and	CCONJ
ejpam-6251	101	13	♭	♭	PROPN
ejpam-6251	102	1	≤	≤	NUM
ejpam-6251	102	2	j	j	PROPN
ejpam-6251	102	3	,	,	PUNCT
ejpam-6251	102	4	with	with	ADP
ejpam-6251	102	5	i	i	PRON
ejpam-6251	102	6	,	,	PUNCT
ejpam-6251	102	7	♭	♭	PROPN
ejpam-6251	102	8	,	,	PUNCT
ejpam-6251	102	9	ℏ	ℏ	PROPN
ejpam-6251	102	10	,	,	PUNCT
ejpam-6251	102	11	j	j	PROPN
ejpam-6251	102	12	∈	∈	PROPN
ejpam-6251	103	1	[	[	X
ejpam-6251	103	2	0	0	NUM
ejpam-6251	103	3	,	,	PUNCT
ejpam-6251	103	4	1	1	NUM
ejpam-6251	103	5	]	]	PUNCT
ejpam-6251	103	6	,	,	PUNCT
ejpam-6251	103	7	then	then	ADV
ejpam-6251	103	8	i	i	PRON
ejpam-6251	103	9	♢	♢	PROPN
ejpam-6251	103	10	♭	♭	PROPN
ejpam-6251	103	11	≤	≤	NUM
ejpam-6251	103	12	ℏ	ℏ	PROPN
ejpam-6251	103	13	♢	♢	PROPN
ejpam-6251	103	14	j.	j.	PROPN
ejpam-6251	103	15	definition	definition	PROPN
ejpam-6251	103	16	3	3	NUM
ejpam-6251	103	17	.	.	PUNCT
ejpam-6251	104	1	(	(	PUNCT
ejpam-6251	104	2	[	[	X
ejpam-6251	104	3	17	17	NUM
ejpam-6251	104	4	]	]	PUNCT
ejpam-6251	104	5	)	)	PUNCT
ejpam-6251	104	6	take	take	VERB
ejpam-6251	104	7	𭟋	𭟋	DET
ejpam-6251	104	8	̸=	̸=	PROPN
ejpam-6251	104	9	∅.	∅.	ADV
ejpam-6251	104	10	let	let	VERB
ejpam-6251	104	11	⋇	⋇	NOUN
ejpam-6251	104	12	be	be	AUX
ejpam-6251	104	13	a	a	DET
ejpam-6251	104	14	ct−||.||	ct−||.||	NOUN
ejpam-6251	104	15	,	,	PUNCT
ejpam-6251	104	16	♢	♢	PROPN
ejpam-6251	104	17	be	be	VERB
ejpam-6251	104	18	a	a	DET
ejpam-6251	104	19	ct−co−||.||	ct−co−||.||	NOUN
ejpam-6251	104	20	,	,	PUNCT
ejpam-6251	104	21	b	b	PROPN
ejpam-6251	104	22	≥	≥	NUM
ejpam-6251	104	23	1	1	NUM
ejpam-6251	104	24	and	and	CCONJ
ejpam-6251	104	25	π	π	PROPN
ejpam-6251	104	26	,	,	PUNCT
ejpam-6251	104	27	ψ	ψ	AUX
ejpam-6251	104	28	be	be	AUX
ejpam-6251	104	29	defined	define	VERB
ejpam-6251	104	30	on	on	ADP
ejpam-6251	104	31	fuzzy	fuzzy	ADJ
ejpam-6251	104	32	sets	set	NOUN
ejpam-6251	104	33	on	on	ADP
ejpam-6251	104	34	𭟋	𭟋	PRON
ejpam-6251	104	35	×	×	NOUN
ejpam-6251	104	36	𭟋	𭟋	PROPN
ejpam-6251	104	37	×	×	NOUN
ejpam-6251	104	38	(	(	PUNCT
ejpam-6251	104	39	0,+∞	0,+∞	NUM
ejpam-6251	104	40	)	)	PUNCT
ejpam-6251	104	41	.	.	PUNCT
ejpam-6251	105	1	if	if	SCONJ
ejpam-6251	105	2	(	(	PUNCT
ejpam-6251	105	3	𭟋	𭟋	NOUN
ejpam-6251	105	4	,	,	PUNCT
ejpam-6251	105	5	π	π	PROPN
ejpam-6251	105	6	,	,	PUNCT
ejpam-6251	105	7	ψ,⋇	ψ,⋇	PROPN
ejpam-6251	105	8	,	,	PUNCT
ejpam-6251	105	9	♢	♢	PROPN
ejpam-6251	105	10	)	)	PUNCT
ejpam-6251	105	11	fulfills	fulfill	VERB
ejpam-6251	105	12	all	all	DET
ejpam-6251	105	13	ς,ϖ	ς,ϖ	NUM
ejpam-6251	105	14	∈	∈	ADJ
ejpam-6251	105	15	𭟋	𭟋	NOUN
ejpam-6251	105	16	and	and	CCONJ
ejpam-6251	105	17	u̇	u̇	PROPN
ejpam-6251	105	18	,	,	PUNCT
ejpam-6251	105	19	ż	ż	NOUN
ejpam-6251	105	20	>	>	X
ejpam-6251	105	21	0	0	NUM
ejpam-6251	105	22	:	:	PUNCT
ejpam-6251	105	23	i.	i.	PROPN
ejpam-6251	105	24	π(ς,ϖ	π(ς,ϖ	NUM
ejpam-6251	105	25	,	,	PUNCT
ejpam-6251	105	26	ż	ż	NOUN
ejpam-6251	105	27	)	)	PUNCT
ejpam-6251	106	1	+	+	NUM
ejpam-6251	106	2	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	106	3	,	,	PUNCT
ejpam-6251	106	4	ż	ż	NOUN
ejpam-6251	106	5	)	)	PUNCT
ejpam-6251	106	6	≤	≤	NOUN
ejpam-6251	106	7	1	1	NUM
ejpam-6251	106	8	;	;	PUNCT
ejpam-6251	106	9	ii	ii	X
ejpam-6251	106	10	.	.	PUNCT
ejpam-6251	107	1	π(ς,ϖ	π(ς,ϖ	ADV
ejpam-6251	107	2	,	,	PUNCT
ejpam-6251	107	3	ż	ż	NOUN
ejpam-6251	107	4	)	)	PUNCT
ejpam-6251	107	5	>	>	X
ejpam-6251	107	6	0	0	NUM
ejpam-6251	107	7	;	;	PUNCT
ejpam-6251	107	8	iii	iii	X
ejpam-6251	107	9	.	.	PUNCT
ejpam-6251	108	1	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	108	2	,	,	PUNCT
ejpam-6251	108	3	ż	ż	NOUN
ejpam-6251	108	4	)	)	PUNCT
ejpam-6251	108	5	=	=	SYM
ejpam-6251	108	6	1	1	NUM
ejpam-6251	108	7	⇔	⇔	X
ejpam-6251	108	8	ς	ς	PROPN
ejpam-6251	108	9	=	=	SYM
ejpam-6251	108	10	ϖ	ϖ	PROPN
ejpam-6251	108	11	;	;	PUNCT
ejpam-6251	108	12	r.	r.	PROPN
ejpam-6251	108	13	ramaswamy	ramaswamy	PROPN
ejpam-6251	108	14	/	/	SYM
ejpam-6251	108	15	eur	eur	PROPN
ejpam-6251	108	16	.	.	PUNCT
ejpam-6251	109	1	j.	j.	PROPN
ejpam-6251	109	2	pure	pure	PROPN
ejpam-6251	109	3	appl	appl	PROPN
ejpam-6251	109	4	.	.	PROPN
ejpam-6251	109	5	math	math	PROPN
ejpam-6251	109	6	,	,	PUNCT
ejpam-6251	109	7	18	18	NUM
ejpam-6251	109	8	(	(	PUNCT
ejpam-6251	109	9	4	4	NUM
ejpam-6251	109	10	)	)	PUNCT
ejpam-6251	109	11	(	(	PUNCT
ejpam-6251	109	12	2025	2025	NUM
ejpam-6251	109	13	)	)	PUNCT
ejpam-6251	109	14	,	,	PUNCT
ejpam-6251	109	15	6251	6251	NUM
ejpam-6251	109	16	5	5	NUM
ejpam-6251	109	17	of	of	ADP
ejpam-6251	109	18	40	40	NUM
ejpam-6251	109	19	iv	iv	NUM
ejpam-6251	109	20	.	.	PUNCT
ejpam-6251	110	1	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	110	2	,	,	PUNCT
ejpam-6251	110	3	ż	ż	NOUN
ejpam-6251	110	4	)	)	PUNCT
ejpam-6251	110	5	=	=	SYM
ejpam-6251	111	1	π(ϖ	π(ϖ	NOUN
ejpam-6251	111	2	,	,	PUNCT
ejpam-6251	111	3	ς	ς	PROPN
ejpam-6251	111	4	,	,	PUNCT
ejpam-6251	111	5	ż	ż	NOUN
ejpam-6251	111	6	)	)	PUNCT
ejpam-6251	111	7	;	;	PUNCT
ejpam-6251	111	8	v.	v.	CCONJ
ejpam-6251	111	9	π(ς,⋏	π(ς,⋏	X
ejpam-6251	111	10	,	,	PUNCT
ejpam-6251	111	11	b(ż+	b(ż+	PROPN
ejpam-6251	111	12	u̇	u̇	PROPN
ejpam-6251	111	13	)	)	PUNCT
ejpam-6251	111	14	)	)	PUNCT
ejpam-6251	111	15	≥	≥	NOUN
ejpam-6251	111	16	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	111	17	,	,	PUNCT
ejpam-6251	111	18	ż)⋇π(ϖ,⋏	ż)⋇π(ϖ,⋏	PROPN
ejpam-6251	111	19	,	,	PUNCT
ejpam-6251	111	20	u̇	u̇	PROPN
ejpam-6251	111	21	)	)	PUNCT
ejpam-6251	111	22	;	;	PUNCT
ejpam-6251	111	23	vi	vi	X
ejpam-6251	111	24	.	.	PUNCT
ejpam-6251	111	25	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	111	26	,	,	PUNCT
ejpam-6251	111	27	·	·	PUNCT
ejpam-6251	111	28	)	)	PUNCT
ejpam-6251	111	29	is	be	AUX
ejpam-6251	111	30	a	a	DET
ejpam-6251	111	31	non	non	ADJ
ejpam-6251	111	32	-	-	ADJ
ejpam-6251	111	33	decreasing	decrease	VERB
ejpam-6251	111	34	function	function	NOUN
ejpam-6251	111	35	of	of	ADP
ejpam-6251	111	36	r+	r+	NOUN
ejpam-6251	111	37	and	and	CCONJ
ejpam-6251	111	38	limż→+∞π(ς,ϖ	limż→+∞π(ς,ϖ	ADP
ejpam-6251	111	39	,	,	PUNCT
ejpam-6251	111	40	ż	ż	NOUN
ejpam-6251	111	41	)	)	PUNCT
ejpam-6251	111	42	=	=	SYM
ejpam-6251	111	43	1	1	NUM
ejpam-6251	111	44	;	;	PUNCT
ejpam-6251	111	45	vii	vii	PROPN
ejpam-6251	111	46	.	.	PROPN
ejpam-6251	111	47	ψ(ς,ϖ	ψ(ς,ϖ	PROPN
ejpam-6251	111	48	,	,	PUNCT
ejpam-6251	111	49	ż	ż	NOUN
ejpam-6251	111	50	)	)	PUNCT
ejpam-6251	111	51	>	>	X
ejpam-6251	111	52	0	0	NUM
ejpam-6251	111	53	;	;	PUNCT
ejpam-6251	111	54	viii	viii	VERB
ejpam-6251	111	55	.	.	PUNCT
ejpam-6251	112	1	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	112	2	,	,	PUNCT
ejpam-6251	112	3	ż	ż	NOUN
ejpam-6251	112	4	)	)	PUNCT
ejpam-6251	112	5	=	=	SYM
ejpam-6251	112	6	0	0	NUM
ejpam-6251	112	7	⇔	⇔	X
ejpam-6251	112	8	ς	ς	PROPN
ejpam-6251	112	9	=	=	SYM
ejpam-6251	112	10	ϖ	ϖ	NOUN
ejpam-6251	112	11	;	;	PUNCT
ejpam-6251	112	12	ix	ix	PROPN
ejpam-6251	112	13	.	.	PUNCT
ejpam-6251	113	1	ψ(ς,ϖ	ψ(ς,ϖ	PROPN
ejpam-6251	113	2	,	,	PUNCT
ejpam-6251	113	3	ż	ż	NOUN
ejpam-6251	113	4	)	)	PUNCT
ejpam-6251	113	5	=	=	SYM
ejpam-6251	114	1	ψ(ϖ	ψ(ϖ	NOUN
ejpam-6251	114	2	,	,	PUNCT
ejpam-6251	114	3	ς	ς	PROPN
ejpam-6251	114	4	,	,	PUNCT
ejpam-6251	114	5	ż	ż	NOUN
ejpam-6251	114	6	)	)	PUNCT
ejpam-6251	114	7	;	;	PUNCT
ejpam-6251	114	8	x.	x.	NOUN
ejpam-6251	114	9	ψ(ς,⋏	ψ(ς,⋏	PROPN
ejpam-6251	114	10	,	,	PUNCT
ejpam-6251	114	11	b(ż+	b(ż+	PROPN
ejpam-6251	114	12	u̇	u̇	PROPN
ejpam-6251	114	13	)	)	PUNCT
ejpam-6251	114	14	)	)	PUNCT
ejpam-6251	114	15	≤	≤	NUM
ejpam-6251	114	16	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	114	17	,	,	PUNCT
ejpam-6251	114	18	ż)	ż)	PROPN
ejpam-6251	114	19	♢	♢	PROPN
ejpam-6251	114	20	ψ(ϖ,⋏	ψ(ϖ,⋏	PROPN
ejpam-6251	114	21	,	,	PUNCT
ejpam-6251	114	22	u̇	u̇	PROPN
ejpam-6251	114	23	)	)	PUNCT
ejpam-6251	114	24	;	;	PUNCT
ejpam-6251	114	25	xi	xi	X
ejpam-6251	114	26	.	.	PUNCT
ejpam-6251	114	27	ψ(ς,ϖ	ψ(ς,ϖ	PROPN
ejpam-6251	114	28	,	,	PUNCT
ejpam-6251	114	29	·	·	PUNCT
ejpam-6251	114	30	)	)	PUNCT
ejpam-6251	114	31	is	be	AUX
ejpam-6251	114	32	a	a	DET
ejpam-6251	114	33	function	function	NOUN
ejpam-6251	114	34	of	of	ADP
ejpam-6251	114	35	non	non	ADJ
ejpam-6251	114	36	-	-	ADJ
ejpam-6251	114	37	increasing	increasing	ADJ
ejpam-6251	114	38	r+	r+	NOUN
ejpam-6251	114	39	and	and	CCONJ
ejpam-6251	114	40	limż→+∞ψ(ς,ϖ	limż→+∞ψ(ς,ϖ	NOUN
ejpam-6251	114	41	,	,	PUNCT
ejpam-6251	114	42	ż	ż	NOUN
ejpam-6251	114	43	)	)	PUNCT
ejpam-6251	114	44	=	=	SYM
ejpam-6251	114	45	0	0	NUM
ejpam-6251	114	46	,	,	PUNCT
ejpam-6251	114	47	then	then	ADV
ejpam-6251	114	48	,	,	PUNCT
ejpam-6251	114	49	(	(	PUNCT
ejpam-6251	114	50	𭟋	𭟋	NOUN
ejpam-6251	114	51	,	,	PUNCT
ejpam-6251	114	52	π	π	PROPN
ejpam-6251	114	53	,	,	PUNCT
ejpam-6251	114	54	ψ,⋇	ψ,⋇	PROPN
ejpam-6251	114	55	,	,	PUNCT
ejpam-6251	114	56	♢	♢	PROPN
ejpam-6251	114	57	)	)	PUNCT
ejpam-6251	114	58	is	be	AUX
ejpam-6251	114	59	an	an	DET
ejpam-6251	114	60	intuitionistic	intuitionistic	ADJ
ejpam-6251	114	61	fbms	fbms	NOUN
ejpam-6251	114	62	.	.	PUNCT
ejpam-6251	115	1	definition	definition	NOUN
ejpam-6251	115	2	4	4	NUM
ejpam-6251	115	3	.	.	PUNCT
ejpam-6251	116	1	(	(	PUNCT
ejpam-6251	116	2	[	[	X
ejpam-6251	116	3	31	31	NUM
ejpam-6251	116	4	]	]	PUNCT
ejpam-6251	116	5	)	)	PUNCT
ejpam-6251	116	6	let	let	VERB
ejpam-6251	116	7	𭟋	𭟋	ADP
ejpam-6251	116	8	̸=	̸=	PROPN
ejpam-6251	116	9	∅,⋇	∅,⋇	PROPN
ejpam-6251	116	10	and	and	CCONJ
ejpam-6251	116	11	♢	♢	PROPN
ejpam-6251	116	12	are	be	AUX
ejpam-6251	116	13	a	a	DET
ejpam-6251	116	14	ct−||.||	ct−||.||	NOUN
ejpam-6251	116	15	and	and	CCONJ
ejpam-6251	116	16	ct−co−||.||	ct−co−||.||	NOUN
ejpam-6251	116	17	.	.	PUNCT
ejpam-6251	117	1	here	here	ADV
ejpam-6251	117	2	π	π	X
ejpam-6251	117	3	,	,	PUNCT
ejpam-6251	117	4	ψ	ψ	PROPN
ejpam-6251	117	5	,	,	PUNCT
ejpam-6251	117	6	ω	ω	PROPN
ejpam-6251	117	7	defined	define	VERB
ejpam-6251	117	8	on	on	ADP
ejpam-6251	117	9	the	the	DET
ejpam-6251	117	10	neutrosophic	neutrosophic	ADJ
ejpam-6251	117	11	sets	set	NOUN
ejpam-6251	117	12	𭟋	𭟋	ADP
ejpam-6251	117	13	×	×	NOUN
ejpam-6251	117	14	𭟋	𭟋	PROPN
ejpam-6251	117	15	×	×	NOUN
ejpam-6251	117	16	(	(	PUNCT
ejpam-6251	117	17	0,+∞	0,+∞	NUM
ejpam-6251	117	18	)	)	PUNCT
ejpam-6251	117	19	is	be	AUX
ejpam-6251	117	20	said	say	VERB
ejpam-6251	117	21	to	to	PART
ejpam-6251	117	22	be	be	AUX
ejpam-6251	117	23	a	a	DET
ejpam-6251	117	24	neutrosophic	neutrosophic	ADJ
ejpam-6251	117	25	metric	metric	NOUN
ejpam-6251	117	26	on	on	ADP
ejpam-6251	117	27	𭟋	𭟋	ADP
ejpam-6251	117	28	,	,	PUNCT
ejpam-6251	117	29	if	if	SCONJ
ejpam-6251	117	30	∀	∀	NOUN
ejpam-6251	117	31	ς,ϖ,⋏	ς,ϖ,⋏	NOUN
ejpam-6251	117	32	∈	∈	PROPN
ejpam-6251	117	33	𭟋	𭟋	NOUN
ejpam-6251	117	34	,	,	PUNCT
ejpam-6251	117	35	the	the	DET
ejpam-6251	117	36	following	following	ADJ
ejpam-6251	117	37	axioms	axiom	NOUN
ejpam-6251	117	38	are	be	AUX
ejpam-6251	117	39	fulfilled	fulfil	VERB
ejpam-6251	117	40	:	:	PUNCT
ejpam-6251	117	41	i.	i.	NOUN
ejpam-6251	117	42	π(ς,ϖ	π(ς,ϖ	NUM
ejpam-6251	117	43	,	,	PUNCT
ejpam-6251	117	44	ż	ż	NOUN
ejpam-6251	117	45	)	)	PUNCT
ejpam-6251	118	1	+	+	NUM
ejpam-6251	118	2	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	118	3	,	,	PUNCT
ejpam-6251	118	4	ż	ż	NOUN
ejpam-6251	118	5	)	)	PUNCT
ejpam-6251	119	1	+	+	CCONJ
ejpam-6251	119	2	ω(ς,ϖ	ω(ς,ϖ	ADP
ejpam-6251	119	3	,	,	PUNCT
ejpam-6251	119	4	ż	ż	NOUN
ejpam-6251	119	5	)	)	PUNCT
ejpam-6251	119	6	≤	≤	NOUN
ejpam-6251	119	7	3	3	NUM
ejpam-6251	119	8	;	;	PUNCT
ejpam-6251	119	9	ii	ii	NOUN
ejpam-6251	119	10	.	.	PUNCT
ejpam-6251	120	1	π(ς,ϖ	π(ς,ϖ	ADV
ejpam-6251	120	2	,	,	PUNCT
ejpam-6251	120	3	ż	ż	NOUN
ejpam-6251	120	4	)	)	PUNCT
ejpam-6251	120	5	>	>	X
ejpam-6251	120	6	0	0	NUM
ejpam-6251	120	7	;	;	PUNCT
ejpam-6251	120	8	iii	iii	X
ejpam-6251	120	9	.	.	PUNCT
ejpam-6251	121	1	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	121	2	,	,	PUNCT
ejpam-6251	121	3	ż	ż	NOUN
ejpam-6251	121	4	)	)	PUNCT
ejpam-6251	121	5	=	=	SYM
ejpam-6251	121	6	1	1	NUM
ejpam-6251	121	7	∀	∀	NOUN
ejpam-6251	122	1	ż	ż	NOUN
ejpam-6251	122	2	>	>	X
ejpam-6251	122	3	0	0	NUM
ejpam-6251	123	1	⇔	⇔	X
ejpam-6251	123	2	ς	ς	PROPN
ejpam-6251	123	3	=	=	SYM
ejpam-6251	123	4	ϖ	ϖ	NOUN
ejpam-6251	123	5	;	;	PUNCT
ejpam-6251	123	6	iv	iv	X
ejpam-6251	123	7	.	.	PUNCT
ejpam-6251	124	1	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	124	2	,	,	PUNCT
ejpam-6251	124	3	ż	ż	NOUN
ejpam-6251	124	4	)	)	PUNCT
ejpam-6251	124	5	=	=	SYM
ejpam-6251	125	1	π(ϖ	π(ϖ	NOUN
ejpam-6251	125	2	,	,	PUNCT
ejpam-6251	125	3	ς	ς	PROPN
ejpam-6251	125	4	,	,	PUNCT
ejpam-6251	125	5	ż	ż	NOUN
ejpam-6251	125	6	)	)	PUNCT
ejpam-6251	125	7	;	;	PUNCT
ejpam-6251	125	8	v.	v.	CCONJ
ejpam-6251	125	9	π(ς,⋏	π(ς,⋏	X
ejpam-6251	125	10	,	,	PUNCT
ejpam-6251	125	11	ż+	ż+	PROPN
ejpam-6251	125	12	u̇	u̇	PROPN
ejpam-6251	125	13	)	)	PUNCT
ejpam-6251	125	14	≥	≥	NOUN
ejpam-6251	125	15	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	125	16	,	,	PUNCT
ejpam-6251	125	17	ż)⋇π(ϖ,⋏	ż)⋇π(ϖ,⋏	PROPN
ejpam-6251	125	18	,	,	PUNCT
ejpam-6251	125	19	u̇	u̇	PROPN
ejpam-6251	125	20	)	)	PUNCT
ejpam-6251	125	21	;	;	PUNCT
ejpam-6251	125	22	vi	vi	X
ejpam-6251	125	23	.	.	PUNCT
ejpam-6251	125	24	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	125	25	,	,	PUNCT
ejpam-6251	125	26	·	·	PUNCT
ejpam-6251	125	27	)	)	PUNCT
ejpam-6251	125	28	:	:	PUNCT
ejpam-6251	125	29	(	(	PUNCT
ejpam-6251	125	30	0,+∞	0,+∞	NUM
ejpam-6251	125	31	)	)	PUNCT
ejpam-6251	125	32	→	→	PUNCT
ejpam-6251	126	1	[	[	X
ejpam-6251	126	2	0	0	NUM
ejpam-6251	126	3	,	,	PUNCT
ejpam-6251	126	4	1	1	NUM
ejpam-6251	126	5	]	]	PUNCT
ejpam-6251	126	6	is	be	AUX
ejpam-6251	126	7	continuous	continuous	ADJ
ejpam-6251	126	8	and	and	CCONJ
ejpam-6251	126	9	limż→+∞π(ς,ϖ	limż→+∞π(ς,ϖ	ADP
ejpam-6251	126	10	,	,	PUNCT
ejpam-6251	126	11	ż	ż	NOUN
ejpam-6251	126	12	)	)	PUNCT
ejpam-6251	126	13	=	=	SYM
ejpam-6251	126	14	1	1	NUM
ejpam-6251	126	15	;	;	PUNCT
ejpam-6251	127	1	vii	vii	PROPN
ejpam-6251	127	2	.	.	PROPN
ejpam-6251	127	3	ψ(ς,ϖ	ψ(ς,ϖ	PROPN
ejpam-6251	127	4	,	,	PUNCT
ejpam-6251	127	5	ż	ż	NOUN
ejpam-6251	127	6	)	)	PUNCT
ejpam-6251	127	7	<	<	X
ejpam-6251	127	8	1	1	NUM
ejpam-6251	127	9	;	;	PUNCT
ejpam-6251	127	10	viii	viii	NOUN
ejpam-6251	127	11	.	.	PUNCT
ejpam-6251	128	1	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	128	2	,	,	PUNCT
ejpam-6251	128	3	ż	ż	NOUN
ejpam-6251	128	4	)	)	PUNCT
ejpam-6251	128	5	=	=	SYM
ejpam-6251	128	6	0	0	NUM
ejpam-6251	128	7	∀	∀	NOUN
ejpam-6251	129	1	ż	ż	X
ejpam-6251	129	2	>	>	X
ejpam-6251	129	3	0	0	NUM
ejpam-6251	130	1	⇔	⇔	X
ejpam-6251	130	2	ς	ς	PROPN
ejpam-6251	130	3	=	=	SYM
ejpam-6251	130	4	ϖ	ϖ	NOUN
ejpam-6251	130	5	;	;	PUNCT
ejpam-6251	130	6	ix	ix	PROPN
ejpam-6251	130	7	.	.	PUNCT
ejpam-6251	131	1	ψ(ς,ϖ	ψ(ς,ϖ	PROPN
ejpam-6251	131	2	,	,	PUNCT
ejpam-6251	131	3	ż	ż	NOUN
ejpam-6251	131	4	)	)	PUNCT
ejpam-6251	131	5	=	=	SYM
ejpam-6251	132	1	ψ(ϖ	ψ(ϖ	NOUN
ejpam-6251	132	2	,	,	PUNCT
ejpam-6251	132	3	ς	ς	PROPN
ejpam-6251	132	4	,	,	PUNCT
ejpam-6251	132	5	ż	ż	NOUN
ejpam-6251	132	6	)	)	PUNCT
ejpam-6251	132	7	;	;	PUNCT
ejpam-6251	132	8	x.	x.	NOUN
ejpam-6251	132	9	ψ(ς,⋏	ψ(ς,⋏	PROPN
ejpam-6251	132	10	,	,	PUNCT
ejpam-6251	132	11	ż+	ż+	PROPN
ejpam-6251	132	12	u̇	u̇	PROPN
ejpam-6251	132	13	)	)	PUNCT
ejpam-6251	132	14	≤	≤	NOUN
ejpam-6251	132	15	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	132	16	,	,	PUNCT
ejpam-6251	132	17	ż)	ż)	PROPN
ejpam-6251	132	18	♢	♢	PROPN
ejpam-6251	132	19	ψ(ϖ,⋏	ψ(ϖ,⋏	PROPN
ejpam-6251	132	20	,	,	PUNCT
ejpam-6251	132	21	u̇	u̇	PROPN
ejpam-6251	132	22	)	)	PUNCT
ejpam-6251	132	23	;	;	PUNCT
ejpam-6251	132	24	xi	xi	X
ejpam-6251	132	25	.	.	PUNCT
ejpam-6251	132	26	ψ(ς,ϖ	ψ(ς,ϖ	PROPN
ejpam-6251	132	27	,	,	PUNCT
ejpam-6251	132	28	·	·	PUNCT
ejpam-6251	132	29	)	)	PUNCT
ejpam-6251	132	30	:	:	PUNCT
ejpam-6251	132	31	(	(	PUNCT
ejpam-6251	132	32	0,+∞	0,+∞	NUM
ejpam-6251	132	33	)	)	PUNCT
ejpam-6251	132	34	→	→	PUNCT
ejpam-6251	133	1	[	[	X
ejpam-6251	133	2	0	0	NUM
ejpam-6251	133	3	,	,	PUNCT
ejpam-6251	133	4	1	1	NUM
ejpam-6251	133	5	]	]	PUNCT
ejpam-6251	133	6	is	be	AUX
ejpam-6251	133	7	continuous	continuous	ADJ
ejpam-6251	133	8	and	and	CCONJ
ejpam-6251	133	9	limż→+∞ψ(ς,ϖ	limż→+∞ψ(ς,ϖ	NOUN
ejpam-6251	133	10	,	,	PUNCT
ejpam-6251	133	11	ż	ż	NOUN
ejpam-6251	133	12	)	)	PUNCT
ejpam-6251	133	13	=	=	SYM
ejpam-6251	134	1	0	0	NUM
ejpam-6251	134	2	;	;	PUNCT
ejpam-6251	134	3	xii	xii	PROPN
ejpam-6251	134	4	.	.	PUNCT
ejpam-6251	135	1	ω(ς,ϖ	ω(ς,ϖ	ADP
ejpam-6251	135	2	,	,	PUNCT
ejpam-6251	135	3	ż	ż	NOUN
ejpam-6251	135	4	)	)	PUNCT
ejpam-6251	135	5	<	<	X
ejpam-6251	135	6	1	1	NUM
ejpam-6251	135	7	;	;	PUNCT
ejpam-6251	135	8	xiii	xiii	PROPN
ejpam-6251	135	9	.	.	PUNCT
ejpam-6251	136	1	ω(ς,ϖ	ω(ς,ϖ	ADP
ejpam-6251	136	2	,	,	PUNCT
ejpam-6251	136	3	ż	ż	NOUN
ejpam-6251	136	4	)	)	PUNCT
ejpam-6251	136	5	=	=	SYM
ejpam-6251	136	6	0	0	NUM
ejpam-6251	136	7	∀	∀	NOUN
ejpam-6251	137	1	ż	ż	X
ejpam-6251	137	2	>	>	X
ejpam-6251	137	3	0	0	NUM
ejpam-6251	138	1	⇔	⇔	X
ejpam-6251	138	2	ς	ς	PROPN
ejpam-6251	138	3	=	=	SYM
ejpam-6251	138	4	ϖ	ϖ	PROPN
ejpam-6251	138	5	;	;	PUNCT
ejpam-6251	138	6	xiv	xiv	PROPN
ejpam-6251	138	7	.	.	PUNCT
ejpam-6251	139	1	ω(ς,ϖ	ω(ς,ϖ	ADP
ejpam-6251	139	2	,	,	PUNCT
ejpam-6251	139	3	ż	ż	NOUN
ejpam-6251	139	4	)	)	PUNCT
ejpam-6251	139	5	=	=	SYM
ejpam-6251	139	6	ω(ϖ	ω(ϖ	PROPN
ejpam-6251	139	7	,	,	PUNCT
ejpam-6251	139	8	ς	ς	PROPN
ejpam-6251	139	9	,	,	PUNCT
ejpam-6251	139	10	ż	ż	NOUN
ejpam-6251	139	11	)	)	PUNCT
ejpam-6251	139	12	;	;	PUNCT
ejpam-6251	139	13	xv	xv	PROPN
ejpam-6251	139	14	.	.	PROPN
ejpam-6251	139	15	ω(ς,⋏	ω(ς,⋏	NOUN
ejpam-6251	139	16	,	,	PUNCT
ejpam-6251	139	17	ż+	ż+	PROPN
ejpam-6251	139	18	u̇	u̇	PROPN
ejpam-6251	139	19	)	)	PUNCT
ejpam-6251	139	20	≤	≤	NOUN
ejpam-6251	139	21	ω(ς,ϖ	ω(ς,ϖ	ADP
ejpam-6251	139	22	,	,	PUNCT
ejpam-6251	139	23	ż)	ż)	PROPN
ejpam-6251	139	24	♢	♢	PROPN
ejpam-6251	139	25	ω(ϖ,⋏	ω(ϖ,⋏	PROPN
ejpam-6251	139	26	,	,	PUNCT
ejpam-6251	139	27	u̇	u̇	PROPN
ejpam-6251	139	28	)	)	PUNCT
ejpam-6251	139	29	;	;	PUNCT
ejpam-6251	139	30	r.	r.	PROPN
ejpam-6251	139	31	ramaswamy	ramaswamy	PROPN
ejpam-6251	139	32	/	/	SYM
ejpam-6251	139	33	eur	eur	PROPN
ejpam-6251	139	34	.	.	PUNCT
ejpam-6251	140	1	j.	j.	PROPN
ejpam-6251	140	2	pure	pure	PROPN
ejpam-6251	140	3	appl	appl	PROPN
ejpam-6251	140	4	.	.	PROPN
ejpam-6251	140	5	math	math	PROPN
ejpam-6251	140	6	,	,	PUNCT
ejpam-6251	140	7	18	18	NUM
ejpam-6251	140	8	(	(	PUNCT
ejpam-6251	140	9	4	4	NUM
ejpam-6251	140	10	)	)	PUNCT
ejpam-6251	140	11	(	(	PUNCT
ejpam-6251	140	12	2025	2025	NUM
ejpam-6251	140	13	)	)	PUNCT
ejpam-6251	140	14	,	,	PUNCT
ejpam-6251	140	15	6251	6251	NUM
ejpam-6251	140	16	6	6	NUM
ejpam-6251	140	17	of	of	ADP
ejpam-6251	140	18	40	40	NUM
ejpam-6251	140	19	xvi	xvi	NOUN
ejpam-6251	140	20	.	.	PUNCT
ejpam-6251	141	1	ω(ς,ϖ	ω(ς,ϖ	ADP
ejpam-6251	141	2	,	,	PUNCT
ejpam-6251	141	3	·	·	PUNCT
ejpam-6251	141	4	)	)	PUNCT
ejpam-6251	141	5	:	:	PUNCT
ejpam-6251	141	6	(	(	PUNCT
ejpam-6251	141	7	0,+∞	0,+∞	NUM
ejpam-6251	141	8	)	)	PUNCT
ejpam-6251	141	9	→	→	PUNCT
ejpam-6251	142	1	[	[	X
ejpam-6251	142	2	0	0	NUM
ejpam-6251	142	3	,	,	PUNCT
ejpam-6251	142	4	1	1	NUM
ejpam-6251	142	5	]	]	PUNCT
ejpam-6251	142	6	is	be	AUX
ejpam-6251	142	7	continuous	continuous	ADJ
ejpam-6251	142	8	and	and	CCONJ
ejpam-6251	142	9	limż→+∞ω(ς,ϖ	limż→+∞ω(ς,ϖ	NUM
ejpam-6251	142	10	,	,	PUNCT
ejpam-6251	142	11	ż	ż	NOUN
ejpam-6251	142	12	)	)	PUNCT
ejpam-6251	142	13	=	=	SYM
ejpam-6251	142	14	0	0	NUM
ejpam-6251	142	15	;	;	PUNCT
ejpam-6251	142	16	xvii	xvii	PROPN
ejpam-6251	142	17	.	.	PUNCT
ejpam-6251	143	1	if	if	SCONJ
ejpam-6251	143	2	ż	ż	ADJ
ejpam-6251	143	3	≤	≤	NOUN
ejpam-6251	143	4	0	0	NUM
ejpam-6251	143	5	,	,	PUNCT
ejpam-6251	143	6	then	then	ADV
ejpam-6251	143	7	π(ς,ϖ	π(ς,ϖ	NUM
ejpam-6251	143	8	,	,	PUNCT
ejpam-6251	143	9	ż	ż	NOUN
ejpam-6251	143	10	)	)	PUNCT
ejpam-6251	143	11	=	=	SYM
ejpam-6251	143	12	0,ψ(ς,ϖ	0,ψ(ς,ϖ	NUM
ejpam-6251	143	13	,	,	PUNCT
ejpam-6251	143	14	ż	ż	NOUN
ejpam-6251	143	15	)	)	PUNCT
ejpam-6251	143	16	=	=	SYM
ejpam-6251	143	17	0	0	NUM
ejpam-6251	143	18	;	;	PUNCT
ejpam-6251	143	19	then	then	ADV
ejpam-6251	143	20	,	,	PUNCT
ejpam-6251	143	21	(	(	PUNCT
ejpam-6251	143	22	𭟋	𭟋	X
ejpam-6251	143	23	,	,	PUNCT
ejpam-6251	143	24	π	π	PROPN
ejpam-6251	143	25	,	,	PUNCT
ejpam-6251	143	26	ψ	ψ	NOUN
ejpam-6251	143	27	,	,	PUNCT
ejpam-6251	143	28	ω,⋇	ω,⋇	PROPN
ejpam-6251	143	29	,	,	PUNCT
ejpam-6251	143	30	♢	♢	PROPN
ejpam-6251	143	31	)	)	PUNCT
ejpam-6251	143	32	is	be	AUX
ejpam-6251	143	33	said	say	VERB
ejpam-6251	143	34	to	to	PART
ejpam-6251	143	35	be	be	AUX
ejpam-6251	143	36	a	a	DET
ejpam-6251	143	37	neutrosophic	neutrosophic	ADJ
ejpam-6251	143	38	metric	metric	ADJ
ejpam-6251	143	39	space	space	NOUN
ejpam-6251	143	40	.	.	PUNCT
ejpam-6251	144	1	definition	definition	NOUN
ejpam-6251	144	2	5	5	NUM
ejpam-6251	144	3	.	.	PUNCT
ejpam-6251	145	1	[	[	X
ejpam-6251	145	2	18	18	NUM
ejpam-6251	145	3	]	]	PUNCT
ejpam-6251	145	4	let	let	VERB
ejpam-6251	145	5	𭟋	𭟋	NOUN
ejpam-6251	145	6	and	and	CCONJ
ejpam-6251	145	7	s	s	AUX
ejpam-6251	145	8	be	be	AUX
ejpam-6251	145	9	non	non	ADJ
ejpam-6251	145	10	-	-	ADJ
ejpam-6251	145	11	void	void	ADJ
ejpam-6251	145	12	sets	set	NOUN
ejpam-6251	145	13	and	and	CCONJ
ejpam-6251	145	14	ϱ	ϱ	ADP
ejpam-6251	145	15	:	:	PUNCT
ejpam-6251	145	16	𭟋×s	𭟋×s	PUNCT
ejpam-6251	145	17	→	→	X
ejpam-6251	145	18	[	[	X
ejpam-6251	145	19	0,+∞	0,+∞	NUM
ejpam-6251	145	20	)	)	PUNCT
ejpam-6251	145	21	be	be	AUX
ejpam-6251	145	22	a	a	DET
ejpam-6251	145	23	function	function	NOUN
ejpam-6251	145	24	,	,	PUNCT
ejpam-6251	145	25	such	such	ADJ
ejpam-6251	145	26	that	that	DET
ejpam-6251	145	27	i.	i.	NOUN
ejpam-6251	145	28	ϱ(ς,ϖ	ϱ(ς,ϖ	ADP
ejpam-6251	145	29	)	)	PUNCT
ejpam-6251	146	1	=	=	SYM
ejpam-6251	146	2	0	0	NUM
ejpam-6251	147	1	iff	iff	PROPN
ejpam-6251	147	2	ς	ς	PROPN
ejpam-6251	147	3	=	=	SYM
ejpam-6251	147	4	ϖ	ϖ	PROPN
ejpam-6251	147	5	,	,	PUNCT
ejpam-6251	147	6	∀	∀	X
ejpam-6251	147	7	(	(	PUNCT
ejpam-6251	147	8	ς,ϖ	ς,ϖ	X
ejpam-6251	147	9	)	)	PUNCT
ejpam-6251	147	10	∈	∈	PROPN
ejpam-6251	147	11	𭟋×	𭟋×	PROPN
ejpam-6251	147	12	s	s	PART
ejpam-6251	147	13	ii	ii	PROPN
ejpam-6251	147	14	.	.	PUNCT
ejpam-6251	148	1	ϱ(ς,ϖ	ϱ(ς,ϖ	ADP
ejpam-6251	148	2	)	)	PUNCT
ejpam-6251	148	3	=	=	SYM
ejpam-6251	148	4	ϱ(ς,ϖ	ϱ(ς,ϖ	NUM
ejpam-6251	148	5	)	)	PUNCT
ejpam-6251	148	6	,	,	PUNCT
ejpam-6251	148	7	∀	∀	X
ejpam-6251	148	8	(	(	PUNCT
ejpam-6251	148	9	ς,ϖ	ς,ϖ	NUM
ejpam-6251	148	10	)	)	PUNCT
ejpam-6251	148	11	∈	∈	PROPN
ejpam-6251	148	12	𭟋	𭟋	ADP
ejpam-6251	148	13	∩	∩	PROPN
ejpam-6251	148	14	s	s	PART
ejpam-6251	148	15	iii	iii	NOUN
ejpam-6251	148	16	.	.	PUNCT
ejpam-6251	148	17	ϱ(ς,ϖ	ϱ(ς,ϖ	ADP
ejpam-6251	148	18	)	)	PUNCT
ejpam-6251	148	19	≤	≤	PROPN
ejpam-6251	148	20	ϱ(ς	ϱ(ς	PROPN
ejpam-6251	148	21	,	,	PUNCT
ejpam-6251	148	22	γ	γ	NOUN
ejpam-6251	148	23	)	)	PUNCT
ejpam-6251	148	24	+	+	CCONJ
ejpam-6251	148	25	ϱ(ς1	ϱ(ς1	NOUN
ejpam-6251	148	26	,	,	PUNCT
ejpam-6251	148	27	γ	γ	NOUN
ejpam-6251	148	28	)	)	PUNCT
ejpam-6251	148	29	+	+	CCONJ
ejpam-6251	148	30	ϱ(ς1	ϱ(ς1	NOUN
ejpam-6251	148	31	,	,	PUNCT
ejpam-6251	148	32	ϖ	ϖ	NOUN
ejpam-6251	148	33	)	)	PUNCT
ejpam-6251	148	34	,	,	PUNCT
ejpam-6251	148	35	∀	∀	X
ejpam-6251	148	36	ς	ς	NOUN
ejpam-6251	148	37	,	,	PUNCT
ejpam-6251	148	38	ς1	ς1	PROPN
ejpam-6251	148	39	∈	∈	NOUN
ejpam-6251	148	40	𭟋	𭟋	NOUN
ejpam-6251	148	41	and	and	CCONJ
ejpam-6251	148	42	γ,ϖ	γ,ϖ	PROPN
ejpam-6251	148	43	∈	∈	PROPN
ejpam-6251	148	44	s.	s.	PROPN
ejpam-6251	148	45	we	we	PRON
ejpam-6251	148	46	say	say	VERB
ejpam-6251	148	47	that	that	SCONJ
ejpam-6251	148	48	the	the	DET
ejpam-6251	148	49	pair	pair	NOUN
ejpam-6251	148	50	(	(	PUNCT
ejpam-6251	148	51	𭟋	𭟋	NOUN
ejpam-6251	148	52	,	,	PUNCT
ejpam-6251	148	53	s	s	NOUN
ejpam-6251	148	54	,	,	PUNCT
ejpam-6251	148	55	ϱ	ϱ	NOUN
ejpam-6251	148	56	)	)	PUNCT
ejpam-6251	148	57	is	be	AUX
ejpam-6251	148	58	a	a	DET
ejpam-6251	148	59	bipolar	bipolar	ADJ
ejpam-6251	148	60	metric	metric	ADJ
ejpam-6251	148	61	space	space	NOUN
ejpam-6251	148	62	.	.	PUNCT
ejpam-6251	149	1	3	3	X
ejpam-6251	149	2	.	.	X
ejpam-6251	149	3	main	main	ADJ
ejpam-6251	149	4	results	result	NOUN
ejpam-6251	149	5	in	in	ADP
ejpam-6251	149	6	this	this	DET
ejpam-6251	149	7	section	section	NOUN
ejpam-6251	149	8	,	,	PUNCT
ejpam-6251	149	9	we	we	PRON
ejpam-6251	149	10	define	define	VERB
ejpam-6251	149	11	nbms	nbms	NOUN
ejpam-6251	149	12	and	and	CCONJ
ejpam-6251	149	13	prove	prove	VERB
ejpam-6251	149	14	few	few	ADJ
ejpam-6251	149	15	fixed	fix	VERB
ejpam-6251	149	16	-	-	PUNCT
ejpam-6251	149	17	point	point	NOUN
ejpam-6251	149	18	theorems	theorem	NOUN
ejpam-6251	149	19	.	.	PUNCT
ejpam-6251	150	1	definition	definition	NOUN
ejpam-6251	150	2	6	6	NUM
ejpam-6251	150	3	.	.	PUNCT
ejpam-6251	151	1	let	let	VERB
ejpam-6251	151	2	𭟋	𭟋	ADP
ejpam-6251	151	3	̸=	̸=	PROPN
ejpam-6251	151	4	∅	∅	NOUN
ejpam-6251	151	5	,	,	PUNCT
ejpam-6251	151	6	s	s	PART
ejpam-6251	151	7	̸=	̸=	PROPN
ejpam-6251	151	8	∅	∅	NOUN
ejpam-6251	151	9	be	be	AUX
ejpam-6251	151	10	two	two	NUM
ejpam-6251	151	11	sets	set	NOUN
ejpam-6251	151	12	and	and	CCONJ
ejpam-6251	151	13	⋇	⋇	NOUN
ejpam-6251	151	14	be	be	AUX
ejpam-6251	151	15	a	a	DET
ejpam-6251	151	16	ct−||.||	ct−||.||	NOUN
ejpam-6251	151	17	,	,	PUNCT
ejpam-6251	151	18	♢	♢	PROPN
ejpam-6251	151	19	be	be	AUX
ejpam-6251	151	20	a	a	DET
ejpam-6251	151	21	ct−co−||.||	ct−co−||.||	NOUN
ejpam-6251	151	22	.	.	PUNCT
ejpam-6251	152	1	then	then	ADV
ejpam-6251	152	2	,	,	PUNCT
ejpam-6251	152	3	π	π	PROPN
ejpam-6251	152	4	,	,	PUNCT
ejpam-6251	152	5	ψ	ψ	PROPN
ejpam-6251	152	6	,	,	PUNCT
ejpam-6251	152	7	ξ	ξ	PROPN
ejpam-6251	152	8	defined	define	VERB
ejpam-6251	152	9	on	on	ADP
ejpam-6251	152	10	neutrosophic	neutrosophic	ADJ
ejpam-6251	152	11	sets	set	NOUN
ejpam-6251	152	12	𭟋×s×(0,+∞	𭟋×s×(0,+∞	PUNCT
ejpam-6251	152	13	)	)	PUNCT
ejpam-6251	152	14	is	be	AUX
ejpam-6251	152	15	called	call	VERB
ejpam-6251	152	16	a	a	DET
ejpam-6251	152	17	neutrosophic	neutrosophic	ADJ
ejpam-6251	152	18	bipolar	bipolar	ADJ
ejpam-6251	152	19	metric	metric	NOUN
ejpam-6251	152	20	on	on	ADP
ejpam-6251	152	21	𭟋×	𭟋×	PROPN
ejpam-6251	152	22	s	s	X
ejpam-6251	152	23	,	,	PUNCT
ejpam-6251	152	24	if	if	SCONJ
ejpam-6251	152	25	∀	∀	NOUN
ejpam-6251	152	26	ς	ς	NOUN
ejpam-6251	152	27	,	,	PUNCT
ejpam-6251	152	28	x	x	SYM
ejpam-6251	152	29	∈	∈	PROPN
ejpam-6251	152	30	𭟋	𭟋	ADP
ejpam-6251	152	31	,	,	PUNCT
ejpam-6251	152	32	ϖ,⋏	ϖ,⋏	PROPN
ejpam-6251	152	33	∈	∈	PROPN
ejpam-6251	152	34	s	s	PART
ejpam-6251	152	35	and	and	CCONJ
ejpam-6251	152	36	ż	ż	NOUN
ejpam-6251	152	37	,	,	PUNCT
ejpam-6251	152	38	ŝ	ŝ	PROPN
ejpam-6251	152	39	,	,	PUNCT
ejpam-6251	152	40	ŵ	ŵ	X
ejpam-6251	152	41	>	>	X
ejpam-6251	152	42	0	0	NUM
ejpam-6251	152	43	,	,	PUNCT
ejpam-6251	152	44	the	the	DET
ejpam-6251	152	45	following	following	ADJ
ejpam-6251	152	46	axioms	axiom	NOUN
ejpam-6251	152	47	are	be	AUX
ejpam-6251	152	48	fulfilled	fulfil	VERB
ejpam-6251	152	49	:	:	PUNCT
ejpam-6251	152	50	i.	i.	NOUN
ejpam-6251	152	51	π(ς,ϖ	π(ς,ϖ	NUM
ejpam-6251	152	52	,	,	PUNCT
ejpam-6251	152	53	ż	ż	NOUN
ejpam-6251	152	54	)	)	PUNCT
ejpam-6251	153	1	+	+	NUM
ejpam-6251	153	2	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	153	3	,	,	PUNCT
ejpam-6251	153	4	ż	ż	NOUN
ejpam-6251	153	5	)	)	PUNCT
ejpam-6251	154	1	+	+	CCONJ
ejpam-6251	154	2	ξ(ς,ϖ	ξ(ς,ϖ	ADV
ejpam-6251	154	3	,	,	PUNCT
ejpam-6251	154	4	ż	ż	NOUN
ejpam-6251	154	5	)	)	PUNCT
ejpam-6251	154	6	≤	≤	NOUN
ejpam-6251	154	7	3	3	NUM
ejpam-6251	154	8	;	;	PUNCT
ejpam-6251	154	9	ii	ii	NOUN
ejpam-6251	154	10	.	.	PUNCT
ejpam-6251	155	1	π(ς,ϖ	π(ς,ϖ	ADV
ejpam-6251	155	2	,	,	PUNCT
ejpam-6251	155	3	ż	ż	NOUN
ejpam-6251	155	4	)	)	PUNCT
ejpam-6251	155	5	>	>	X
ejpam-6251	155	6	0	0	NUM
ejpam-6251	155	7	;	;	PUNCT
ejpam-6251	155	8	iii	iii	X
ejpam-6251	155	9	.	.	PUNCT
ejpam-6251	156	1	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	156	2	,	,	PUNCT
ejpam-6251	156	3	ż	ż	NOUN
ejpam-6251	156	4	)	)	PUNCT
ejpam-6251	156	5	=	=	SYM
ejpam-6251	156	6	1	1	NUM
ejpam-6251	156	7	∀	∀	NOUN
ejpam-6251	157	1	ż	ż	NOUN
ejpam-6251	157	2	>	>	X
ejpam-6251	157	3	0	0	NUM
ejpam-6251	158	1	⇔	⇔	X
ejpam-6251	158	2	ς	ς	PROPN
ejpam-6251	158	3	=	=	SYM
ejpam-6251	158	4	ϖ	ϖ	NOUN
ejpam-6251	158	5	;	;	PUNCT
ejpam-6251	158	6	iv	iv	X
ejpam-6251	158	7	.	.	PUNCT
ejpam-6251	159	1	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	159	2	,	,	PUNCT
ejpam-6251	159	3	ż	ż	NOUN
ejpam-6251	159	4	)	)	PUNCT
ejpam-6251	159	5	=	=	SYM
ejpam-6251	160	1	π(ϖ	π(ϖ	NOUN
ejpam-6251	160	2	,	,	PUNCT
ejpam-6251	160	3	ς	ς	PROPN
ejpam-6251	160	4	,	,	PUNCT
ejpam-6251	160	5	ż	ż	NOUN
ejpam-6251	160	6	)	)	PUNCT
ejpam-6251	160	7	;	;	PUNCT
ejpam-6251	160	8	v.	v.	CCONJ
ejpam-6251	160	9	π(ς,⋏	π(ς,⋏	X
ejpam-6251	160	10	,	,	PUNCT
ejpam-6251	160	11	ż+	ż+	PROPN
ejpam-6251	160	12	u̇+	u̇+	PROPN
ejpam-6251	160	13	ṫ	ṫ	PROPN
ejpam-6251	160	14	)	)	PUNCT
ejpam-6251	160	15	≥	≥	PROPN
ejpam-6251	161	1	π	π	PROPN
ejpam-6251	161	2	(	(	PUNCT
ejpam-6251	161	3	ς,ϖ	ς,ϖ	NUM
ejpam-6251	161	4	,	,	PUNCT
ejpam-6251	161	5	ż	ż	NOUN
ejpam-6251	161	6	)	)	PUNCT
ejpam-6251	161	7	⋇π	⋇π	X
ejpam-6251	161	8	(	(	PUNCT
ejpam-6251	161	9	x	x	X
ejpam-6251	161	10	,	,	PUNCT
ejpam-6251	161	11	ϖ	ϖ	PROPN
ejpam-6251	161	12	,	,	PUNCT
ejpam-6251	161	13	u̇	u̇	PROPN
ejpam-6251	161	14	)	)	PUNCT
ejpam-6251	162	1	⋇π	⋇π	X
ejpam-6251	162	2	(	(	PUNCT
ejpam-6251	162	3	x,⋏	x,⋏	PROPN
ejpam-6251	162	4	,	,	PUNCT
ejpam-6251	162	5	ṫ	ṫ	PROPN
ejpam-6251	162	6	)	)	PUNCT
ejpam-6251	162	7	;	;	PUNCT
ejpam-6251	163	1	vi	vi	X
ejpam-6251	163	2	.	.	PUNCT
ejpam-6251	163	3	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	163	4	,	,	PUNCT
ejpam-6251	163	5	·	·	PUNCT
ejpam-6251	163	6	)	)	PUNCT
ejpam-6251	163	7	:	:	PUNCT
ejpam-6251	163	8	(	(	PUNCT
ejpam-6251	163	9	0,+∞	0,+∞	NUM
ejpam-6251	163	10	)	)	PUNCT
ejpam-6251	163	11	→	→	PUNCT
ejpam-6251	164	1	[	[	X
ejpam-6251	164	2	0	0	NUM
ejpam-6251	164	3	,	,	PUNCT
ejpam-6251	164	4	1	1	NUM
ejpam-6251	164	5	]	]	PUNCT
ejpam-6251	164	6	is	be	AUX
ejpam-6251	164	7	continuous	continuous	ADJ
ejpam-6251	164	8	and	and	CCONJ
ejpam-6251	164	9	lim	lim	PROPN
ejpam-6251	164	10	ż→+∞	ż→+∞	PROPN
ejpam-6251	164	11	π(ς,ϖ	π(ς,ϖ	ADV
ejpam-6251	164	12	,	,	PUNCT
ejpam-6251	164	13	ż	ż	NOUN
ejpam-6251	164	14	)	)	PUNCT
ejpam-6251	164	15	=	=	SYM
ejpam-6251	164	16	1	1	NUM
ejpam-6251	164	17	;	;	PUNCT
ejpam-6251	165	1	vii	vii	PROPN
ejpam-6251	165	2	.	.	PROPN
ejpam-6251	165	3	ψ(ς,ϖ	ψ(ς,ϖ	PROPN
ejpam-6251	165	4	,	,	PUNCT
ejpam-6251	165	5	ż	ż	NOUN
ejpam-6251	165	6	)	)	PUNCT
ejpam-6251	165	7	<	<	X
ejpam-6251	165	8	1	1	NUM
ejpam-6251	165	9	;	;	PUNCT
ejpam-6251	165	10	viii	viii	NOUN
ejpam-6251	165	11	.	.	PUNCT
ejpam-6251	166	1	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	166	2	,	,	PUNCT
ejpam-6251	166	3	ż	ż	NOUN
ejpam-6251	166	4	)	)	PUNCT
ejpam-6251	166	5	=	=	SYM
ejpam-6251	166	6	0	0	NUM
ejpam-6251	166	7	∀	∀	NOUN
ejpam-6251	167	1	ż	ż	X
ejpam-6251	167	2	>	>	X
ejpam-6251	167	3	0	0	NUM
ejpam-6251	168	1	⇔	⇔	X
ejpam-6251	168	2	ς	ς	PROPN
ejpam-6251	168	3	=	=	SYM
ejpam-6251	168	4	ϖ	ϖ	NOUN
ejpam-6251	168	5	;	;	PUNCT
ejpam-6251	168	6	ix	ix	PROPN
ejpam-6251	168	7	.	.	PUNCT
ejpam-6251	169	1	ψ(ς,ϖ	ψ(ς,ϖ	PROPN
ejpam-6251	169	2	,	,	PUNCT
ejpam-6251	169	3	ż	ż	NOUN
ejpam-6251	169	4	)	)	PUNCT
ejpam-6251	169	5	=	=	SYM
ejpam-6251	170	1	ψ(ϖ	ψ(ϖ	NOUN
ejpam-6251	170	2	,	,	PUNCT
ejpam-6251	170	3	ς	ς	PROPN
ejpam-6251	170	4	,	,	PUNCT
ejpam-6251	170	5	ż	ż	NOUN
ejpam-6251	170	6	)	)	PUNCT
ejpam-6251	170	7	;	;	PUNCT
ejpam-6251	170	8	x.	x.	NOUN
ejpam-6251	170	9	ψ(ς,⋏	ψ(ς,⋏	PROPN
ejpam-6251	170	10	,	,	PUNCT
ejpam-6251	170	11	ż+	ż+	PROPN
ejpam-6251	170	12	u̇+	u̇+	PROPN
ejpam-6251	170	13	ṫ	ṫ	PROPN
ejpam-6251	170	14	)	)	PUNCT
ejpam-6251	170	15	≤	≤	NOUN
ejpam-6251	171	1	ψ	ψ	X
ejpam-6251	171	2	(	(	PUNCT
ejpam-6251	171	3	ς,ϖ	ς,ϖ	NUM
ejpam-6251	171	4	,	,	PUNCT
ejpam-6251	171	5	ż	ż	NOUN
ejpam-6251	171	6	)	)	PUNCT
ejpam-6251	171	7	♢	♢	PROPN
ejpam-6251	171	8	ψ	ψ	X
ejpam-6251	171	9	(	(	PUNCT
ejpam-6251	171	10	x	x	NOUN
ejpam-6251	171	11	,	,	PUNCT
ejpam-6251	171	12	ϖ	ϖ	PROPN
ejpam-6251	171	13	,	,	PUNCT
ejpam-6251	171	14	u̇	u̇	PROPN
ejpam-6251	171	15	)	)	PUNCT
ejpam-6251	171	16	♢	♢	PROPN
ejpam-6251	171	17	ψ	ψ	X
ejpam-6251	171	18	(	(	PUNCT
ejpam-6251	171	19	x,⋏	x,⋏	PROPN
ejpam-6251	171	20	,	,	PUNCT
ejpam-6251	171	21	ṫ	ṫ	PROPN
ejpam-6251	171	22	)	)	PUNCT
ejpam-6251	171	23	;	;	PUNCT
ejpam-6251	171	24	xi	xi	X
ejpam-6251	171	25	.	.	PUNCT
ejpam-6251	171	26	ψ(ς,ϖ	ψ(ς,ϖ	PROPN
ejpam-6251	171	27	,	,	PUNCT
ejpam-6251	171	28	·	·	PUNCT
ejpam-6251	171	29	)	)	PUNCT
ejpam-6251	171	30	:	:	PUNCT
ejpam-6251	171	31	(	(	PUNCT
ejpam-6251	171	32	0,+∞	0,+∞	NUM
ejpam-6251	171	33	)	)	PUNCT
ejpam-6251	171	34	→	→	PUNCT
ejpam-6251	172	1	[	[	X
ejpam-6251	172	2	0	0	NUM
ejpam-6251	172	3	,	,	PUNCT
ejpam-6251	172	4	1	1	NUM
ejpam-6251	172	5	]	]	PUNCT
ejpam-6251	172	6	is	be	AUX
ejpam-6251	172	7	continuous	continuous	ADJ
ejpam-6251	172	8	and	and	CCONJ
ejpam-6251	172	9	lim	lim	PROPN
ejpam-6251	172	10	ż→+∞	ż→+∞	PROPN
ejpam-6251	172	11	ψ(ς,ϖ	ψ(ς,ϖ	PROPN
ejpam-6251	172	12	,	,	PUNCT
ejpam-6251	172	13	ż	ż	NOUN
ejpam-6251	172	14	)	)	PUNCT
ejpam-6251	172	15	=	=	SYM
ejpam-6251	173	1	0	0	NUM
ejpam-6251	173	2	;	;	PUNCT
ejpam-6251	173	3	xii	xii	NOUN
ejpam-6251	173	4	.	.	PUNCT
ejpam-6251	174	1	ξ(ς,ϖ	ξ(ς,ϖ	ADP
ejpam-6251	174	2	,	,	PUNCT
ejpam-6251	174	3	ż	ż	NOUN
ejpam-6251	174	4	)	)	PUNCT
ejpam-6251	174	5	<	<	X
ejpam-6251	174	6	1	1	NUM
ejpam-6251	174	7	;	;	PUNCT
ejpam-6251	174	8	xiii	xiii	PROPN
ejpam-6251	174	9	.	.	PUNCT
ejpam-6251	175	1	ξ(ς,ϖ	ξ(ς,ϖ	X
ejpam-6251	175	2	,	,	PUNCT
ejpam-6251	175	3	ż	ż	NOUN
ejpam-6251	175	4	)	)	PUNCT
ejpam-6251	175	5	=	=	SYM
ejpam-6251	175	6	0	0	NUM
ejpam-6251	175	7	∀	∀	NOUN
ejpam-6251	176	1	ż	ż	X
ejpam-6251	176	2	>	>	X
ejpam-6251	176	3	0	0	NUM
ejpam-6251	177	1	⇔	⇔	X
ejpam-6251	177	2	ς	ς	PROPN
ejpam-6251	177	3	=	=	SYM
ejpam-6251	177	4	ϖ	ϖ	PROPN
ejpam-6251	177	5	;	;	PUNCT
ejpam-6251	177	6	r.	r.	PROPN
ejpam-6251	177	7	ramaswamy	ramaswamy	PROPN
ejpam-6251	177	8	/	/	SYM
ejpam-6251	177	9	eur	eur	PROPN
ejpam-6251	177	10	.	.	PUNCT
ejpam-6251	178	1	j.	j.	PROPN
ejpam-6251	178	2	pure	pure	PROPN
ejpam-6251	178	3	appl	appl	PROPN
ejpam-6251	178	4	.	.	PROPN
ejpam-6251	178	5	math	math	PROPN
ejpam-6251	178	6	,	,	PUNCT
ejpam-6251	178	7	18	18	NUM
ejpam-6251	178	8	(	(	PUNCT
ejpam-6251	178	9	4	4	NUM
ejpam-6251	178	10	)	)	PUNCT
ejpam-6251	178	11	(	(	PUNCT
ejpam-6251	178	12	2025	2025	NUM
ejpam-6251	178	13	)	)	PUNCT
ejpam-6251	178	14	,	,	PUNCT
ejpam-6251	178	15	6251	6251	NUM
ejpam-6251	178	16	7	7	NUM
ejpam-6251	178	17	of	of	ADP
ejpam-6251	178	18	40	40	NUM
ejpam-6251	178	19	xiv	xiv	NOUN
ejpam-6251	178	20	.	.	PUNCT
ejpam-6251	179	1	ξ(ς,ϖ	ξ(ς,ϖ	ADV
ejpam-6251	179	2	,	,	PUNCT
ejpam-6251	179	3	ż	ż	NOUN
ejpam-6251	179	4	)	)	PUNCT
ejpam-6251	179	5	=	=	SYM
ejpam-6251	180	1	ξ(ϖ	ξ(ϖ	PROPN
ejpam-6251	180	2	,	,	PUNCT
ejpam-6251	180	3	ς	ς	PROPN
ejpam-6251	180	4	,	,	PUNCT
ejpam-6251	180	5	ż	ż	NOUN
ejpam-6251	180	6	)	)	PUNCT
ejpam-6251	180	7	;	;	PUNCT
ejpam-6251	180	8	xv	xv	PROPN
ejpam-6251	180	9	.	.	PUNCT
ejpam-6251	180	10	ξ(ς,⋏	ξ(ς,⋏	NOUN
ejpam-6251	180	11	,	,	PUNCT
ejpam-6251	180	12	ż+	ż+	PROPN
ejpam-6251	180	13	u̇+	u̇+	PROPN
ejpam-6251	180	14	ṫ	ṫ	PROPN
ejpam-6251	180	15	)	)	PUNCT
ejpam-6251	180	16	≤	≤	NOUN
ejpam-6251	181	1	ξ	ξ	PROPN
ejpam-6251	181	2	(	(	PUNCT
ejpam-6251	181	3	ς,ϖ	ς,ϖ	NUM
ejpam-6251	181	4	,	,	PUNCT
ejpam-6251	181	5	ż	ż	NOUN
ejpam-6251	181	6	)	)	PUNCT
ejpam-6251	181	7	♢	♢	PROPN
ejpam-6251	181	8	ξ	ξ	X
ejpam-6251	181	9	(	(	PUNCT
ejpam-6251	181	10	x	x	NOUN
ejpam-6251	181	11	,	,	PUNCT
ejpam-6251	181	12	ϖ	ϖ	PROPN
ejpam-6251	181	13	,	,	PUNCT
ejpam-6251	181	14	u̇	u̇	PROPN
ejpam-6251	181	15	)	)	PUNCT
ejpam-6251	181	16	♢	♢	PROPN
ejpam-6251	181	17	ξ	ξ	X
ejpam-6251	181	18	(	(	PUNCT
ejpam-6251	181	19	x,⋏	x,⋏	PROPN
ejpam-6251	181	20	,	,	PUNCT
ejpam-6251	181	21	ṫ	ṫ	PROPN
ejpam-6251	181	22	)	)	PUNCT
ejpam-6251	181	23	;	;	PUNCT
ejpam-6251	181	24	xvi	xvi	NOUN
ejpam-6251	181	25	.	.	PUNCT
ejpam-6251	182	1	ξ(ς,ϖ	ξ(ς,ϖ	X
ejpam-6251	182	2	,	,	PUNCT
ejpam-6251	182	3	·	·	PUNCT
ejpam-6251	182	4	)	)	PUNCT
ejpam-6251	183	1	:	:	PUNCT
ejpam-6251	183	2	(	(	PUNCT
ejpam-6251	183	3	0,+∞	0,+∞	NUM
ejpam-6251	183	4	)	)	PUNCT
ejpam-6251	183	5	→	→	PUNCT
ejpam-6251	184	1	[	[	X
ejpam-6251	184	2	0	0	NUM
ejpam-6251	184	3	,	,	PUNCT
ejpam-6251	184	4	1	1	NUM
ejpam-6251	184	5	]	]	PUNCT
ejpam-6251	184	6	is	be	AUX
ejpam-6251	184	7	continuous	continuous	ADJ
ejpam-6251	184	8	and	and	CCONJ
ejpam-6251	184	9	lim	lim	PROPN
ejpam-6251	184	10	ż→+∞	ż→+∞	PROPN
ejpam-6251	184	11	ξ(ς,ϖ	ξ(ς,ϖ	ADP
ejpam-6251	184	12	,	,	PUNCT
ejpam-6251	184	13	ż	ż	NOUN
ejpam-6251	184	14	)	)	PUNCT
ejpam-6251	184	15	=	=	SYM
ejpam-6251	184	16	0	0	NUM
ejpam-6251	184	17	;	;	PUNCT
ejpam-6251	184	18	xvii	xvii	PROPN
ejpam-6251	184	19	.	.	PUNCT
ejpam-6251	185	1	if	if	SCONJ
ejpam-6251	185	2	ż	ż	ADJ
ejpam-6251	185	3	≤	≤	NOUN
ejpam-6251	185	4	0	0	NUM
ejpam-6251	185	5	,	,	PUNCT
ejpam-6251	185	6	then	then	ADV
ejpam-6251	185	7	π(ς,ϖ	π(ς,ϖ	NUM
ejpam-6251	185	8	,	,	PUNCT
ejpam-6251	185	9	ż	ż	NOUN
ejpam-6251	185	10	)	)	PUNCT
ejpam-6251	185	11	=	=	SYM
ejpam-6251	186	1	0,ψ(ς,ϖ	0,ψ(ς,ϖ	NUM
ejpam-6251	186	2	,	,	PUNCT
ejpam-6251	186	3	ż	ż	NOUN
ejpam-6251	186	4	)	)	PUNCT
ejpam-6251	186	5	=	=	SYM
ejpam-6251	186	6	1	1	NUM
ejpam-6251	186	7	and	and	CCONJ
ejpam-6251	186	8	ξ(ς,ϖ	ξ(ς,ϖ	ADV
ejpam-6251	186	9	,	,	PUNCT
ejpam-6251	186	10	ż	ż	NOUN
ejpam-6251	186	11	)	)	PUNCT
ejpam-6251	186	12	=	=	SYM
ejpam-6251	187	1	1	1	X
ejpam-6251	187	2	.	.	PUNCT
ejpam-6251	187	3	then	then	ADV
ejpam-6251	187	4	,	,	PUNCT
ejpam-6251	187	5	(	(	PUNCT
ejpam-6251	187	6	𭟋	𭟋	NOUN
ejpam-6251	187	7	,	,	PUNCT
ejpam-6251	187	8	s	s	PROPN
ejpam-6251	187	9	,	,	PUNCT
ejpam-6251	187	10	π	π	PROPN
ejpam-6251	187	11	,	,	PUNCT
ejpam-6251	187	12	ψ	ψ	PROPN
ejpam-6251	187	13	,	,	PUNCT
ejpam-6251	187	14	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	187	15	,	,	PUNCT
ejpam-6251	187	16	♢	♢	PROPN
ejpam-6251	187	17	)	)	PUNCT
ejpam-6251	187	18	is	be	AUX
ejpam-6251	187	19	said	say	VERB
ejpam-6251	187	20	to	to	PART
ejpam-6251	187	21	be	be	AUX
ejpam-6251	187	22	a	a	DET
ejpam-6251	187	23	nbms	nbms	NOUN
ejpam-6251	187	24	.	.	PUNCT
ejpam-6251	188	1	an	an	DET
ejpam-6251	188	2	illustrative	illustrative	ADJ
ejpam-6251	188	3	example	example	NOUN
ejpam-6251	188	4	of	of	ADP
ejpam-6251	188	5	nbms	nbms	NOUN
ejpam-6251	188	6	is	be	AUX
ejpam-6251	188	7	presented	present	VERB
ejpam-6251	188	8	below	below	ADP
ejpam-6251	188	9	:	:	PUNCT
ejpam-6251	188	10	example	example	NOUN
ejpam-6251	189	1	1	1	X
ejpam-6251	189	2	.	.	PUNCT
ejpam-6251	189	3	let	let	VERB
ejpam-6251	189	4	𭟋	𭟋	VERB
ejpam-6251	189	5	=	=	PUNCT
ejpam-6251	189	6	{	{	PUNCT
ejpam-6251	189	7	1	1	NUM
ejpam-6251	189	8	,	,	PUNCT
ejpam-6251	189	9	3	3	NUM
ejpam-6251	189	10	,	,	PUNCT
ejpam-6251	189	11	5	5	NUM
ejpam-6251	189	12	,	,	PUNCT
ejpam-6251	189	13	7	7	NUM
ejpam-6251	189	14	}	}	PUNCT
ejpam-6251	189	15	,	,	PUNCT
ejpam-6251	189	16	s	s	X
ejpam-6251	189	17	=	=	PUNCT
ejpam-6251	189	18	{	{	PUNCT
ejpam-6251	189	19	1	1	NUM
ejpam-6251	189	20	,	,	PUNCT
ejpam-6251	189	21	2	2	NUM
ejpam-6251	189	22	,	,	PUNCT
ejpam-6251	189	23	6	6	NUM
ejpam-6251	189	24	,	,	PUNCT
ejpam-6251	189	25	4	4	NUM
ejpam-6251	189	26	}	}	PUNCT
ejpam-6251	189	27	.	.	PUNCT
ejpam-6251	190	1	define	define	VERB
ejpam-6251	190	2	π	π	PROPN
ejpam-6251	190	3	,	,	PUNCT
ejpam-6251	190	4	ψ	ψ	X
ejpam-6251	190	5	,	,	PUNCT
ejpam-6251	190	6	ξ	ξ	PROPN
ejpam-6251	190	7	:	:	PUNCT
ejpam-6251	190	8	𭟋×s×(0,+∞	𭟋×s×(0,+∞	X
ejpam-6251	190	9	)	)	PUNCT
ejpam-6251	190	10	→	→	PUNCT
ejpam-6251	191	1	[	[	X
ejpam-6251	191	2	0	0	NUM
ejpam-6251	191	3	,	,	PUNCT
ejpam-6251	191	4	1	1	NUM
ejpam-6251	191	5	]	]	PUNCT
ejpam-6251	191	6	as	as	ADP
ejpam-6251	191	7	π(ς,ϖ	π(ς,ϖ	NOUN
ejpam-6251	191	8	,	,	PUNCT
ejpam-6251	191	9	ż	ż	NOUN
ejpam-6251	191	10	)	)	PUNCT
ejpam-6251	191	11	=	=	PUNCT
ejpam-6251	191	12	{	{	PUNCT
ejpam-6251	191	13	1	1	NUM
ejpam-6251	191	14	,	,	PUNCT
ejpam-6251	191	15	if	if	SCONJ
ejpam-6251	191	16	ς	ς	PROPN
ejpam-6251	191	17	=	=	PUNCT
ejpam-6251	191	18	ϖ	ϖ	PROPN
ejpam-6251	191	19	ż	ż	NOUN
ejpam-6251	191	20	ż+max{ς,ϖ	ż+max{ς,ϖ	PROPN
ejpam-6251	191	21	}	}	PUNCT
ejpam-6251	191	22	,	,	PUNCT
ejpam-6251	191	23	if	if	SCONJ
ejpam-6251	191	24	otherwise	otherwise	ADV
ejpam-6251	191	25	,	,	PUNCT
ejpam-6251	191	26	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	191	27	,	,	PUNCT
ejpam-6251	191	28	ż	ż	NOUN
ejpam-6251	191	29	)	)	PUNCT
ejpam-6251	191	30	=	=	PUNCT
ejpam-6251	191	31	{	{	PUNCT
ejpam-6251	191	32	0	0	NUM
ejpam-6251	191	33	,	,	PUNCT
ejpam-6251	191	34	if	if	SCONJ
ejpam-6251	191	35	ς	ς	PROPN
ejpam-6251	191	36	=	=	VERB
ejpam-6251	191	37	ϖ	ϖ	NOUN
ejpam-6251	191	38	max{ς,ϖ	max{ς,ϖ	PROPN
ejpam-6251	191	39	}	}	PUNCT
ejpam-6251	191	40	ż+max{ς,ϖ	ż+max{ς,ϖ	NOUN
ejpam-6251	191	41	}	}	PUNCT
ejpam-6251	191	42	,	,	PUNCT
ejpam-6251	191	43	if	if	SCONJ
ejpam-6251	191	44	otherwise	otherwise	ADV
ejpam-6251	191	45	,	,	PUNCT
ejpam-6251	191	46	and	and	CCONJ
ejpam-6251	191	47	ξ(ς,ϖ	ξ(ς,ϖ	ADP
ejpam-6251	191	48	,	,	PUNCT
ejpam-6251	191	49	ż	ż	NOUN
ejpam-6251	191	50	)	)	PUNCT
ejpam-6251	191	51	=	=	PRON
ejpam-6251	191	52	{	{	PUNCT
ejpam-6251	191	53	0	0	NUM
ejpam-6251	191	54	,	,	PUNCT
ejpam-6251	191	55	if	if	SCONJ
ejpam-6251	191	56	ς	ς	PROPN
ejpam-6251	191	57	=	=	VERB
ejpam-6251	191	58	ϖ	ϖ	NOUN
ejpam-6251	191	59	max{ς,ϖ	max{ς,ϖ	PROPN
ejpam-6251	191	60	}	}	PUNCT
ejpam-6251	191	61	ż	ż	NOUN
ejpam-6251	191	62	,	,	PUNCT
ejpam-6251	191	63	if	if	SCONJ
ejpam-6251	191	64	otherwise	otherwise	ADV
ejpam-6251	191	65	.	.	PUNCT
ejpam-6251	192	1	let	let	VERB
ejpam-6251	192	2	ς	ς	PROPN
ejpam-6251	192	3	=	=	SYM
ejpam-6251	192	4	1	1	PROPN
ejpam-6251	192	5	,	,	PUNCT
ejpam-6251	192	6	ϖ	ϖ	NOUN
ejpam-6251	192	7	=	=	SYM
ejpam-6251	192	8	2	2	NUM
ejpam-6251	192	9	,	,	PUNCT
ejpam-6251	192	10	x	x	SYM
ejpam-6251	192	11	=	=	SYM
ejpam-6251	192	12	3	3	NUM
ejpam-6251	192	13	and	and	CCONJ
ejpam-6251	192	14	⋏	⋏	PROPN
ejpam-6251	192	15	=	=	SYM
ejpam-6251	192	16	4	4	X
ejpam-6251	192	17	.	.	PUNCT
ejpam-6251	192	18	then	then	ADV
ejpam-6251	192	19	from	from	ADP
ejpam-6251	192	20	,	,	PUNCT
ejpam-6251	192	21	(	(	PUNCT
ejpam-6251	192	22	v	v	NOUN
ejpam-6251	192	23	)	)	PUNCT
ejpam-6251	192	24	,	,	PUNCT
ejpam-6251	192	25	(	(	PUNCT
ejpam-6251	192	26	x	x	X
ejpam-6251	192	27	)	)	PUNCT
ejpam-6251	192	28	and	and	CCONJ
ejpam-6251	192	29	(	(	PUNCT
ejpam-6251	192	30	xv	xv	PROPN
ejpam-6251	192	31	)	)	PUNCT
ejpam-6251	192	32	and	and	CCONJ
ejpam-6251	192	33	obviously	obviously	ADV
ejpam-6251	192	34	others	other	NOUN
ejpam-6251	192	35	.	.	PUNCT
ejpam-6251	193	1	π(1	π(1	NOUN
ejpam-6251	193	2	,	,	PUNCT
ejpam-6251	193	3	4	4	NUM
ejpam-6251	193	4	,	,	PUNCT
ejpam-6251	193	5	ż+	ż+	PROPN
ejpam-6251	193	6	u̇+	u̇+	PROPN
ejpam-6251	193	7	ṫ	ṫ	PROPN
ejpam-6251	193	8	)	)	PUNCT
ejpam-6251	193	9	=	=	PUNCT
ejpam-6251	193	10	ż+	ż+	PROPN
ejpam-6251	193	11	u̇+	u̇+	PROPN
ejpam-6251	193	12	ṫ	ṫ	PROPN
ejpam-6251	193	13	ż+	ż+	PROPN
ejpam-6251	193	14	u̇+	u̇+	PROPN
ejpam-6251	193	15	ṫ+max{1	ṫ+max{1	PROPN
ejpam-6251	193	16	,	,	PUNCT
ejpam-6251	193	17	4	4	NUM
ejpam-6251	193	18	}	}	PUNCT
ejpam-6251	193	19	=	=	SYM
ejpam-6251	193	20	ż+	ż+	PROPN
ejpam-6251	193	21	u̇+	u̇+	PROPN
ejpam-6251	193	22	ṫ	ṫ	PROPN
ejpam-6251	193	23	ż+	ż+	PROPN
ejpam-6251	193	24	u̇+	u̇+	PROPN
ejpam-6251	193	25	ṫ+	ṫ+	PROPN
ejpam-6251	193	26	4	4	NUM
ejpam-6251	193	27	.	.	PUNCT
ejpam-6251	194	1	further	far	ADV
ejpam-6251	194	2	,	,	PUNCT
ejpam-6251	194	3	π	π	PROPN
ejpam-6251	194	4	(	(	PUNCT
ejpam-6251	194	5	1	1	NUM
ejpam-6251	194	6	,	,	PUNCT
ejpam-6251	194	7	2	2	NUM
ejpam-6251	194	8	,	,	PUNCT
ejpam-6251	194	9	ż	ż	NOUN
ejpam-6251	194	10	)	)	PUNCT
ejpam-6251	195	1	=	=	PUNCT
ejpam-6251	195	2	ż	ż	NOUN
ejpam-6251	195	3	˙̇z+max{1	˙̇z+max{1	PROPN
ejpam-6251	195	4	,	,	PUNCT
ejpam-6251	195	5	2	2	NUM
ejpam-6251	195	6	}	}	PUNCT
ejpam-6251	195	7	=	=	PUNCT
ejpam-6251	195	8	ż	ż	NOUN
ejpam-6251	195	9	ż+	ż+	PROPN
ejpam-6251	195	10	2	2	NUM
ejpam-6251	195	11	=	=	SYM
ejpam-6251	195	12	ż	ż	PROPN
ejpam-6251	195	13	ż+	ż+	PROPN
ejpam-6251	195	14	2	2	NUM
ejpam-6251	195	15	,	,	PUNCT
ejpam-6251	195	16	π	π	X
ejpam-6251	195	17	(	(	PUNCT
ejpam-6251	195	18	2	2	NUM
ejpam-6251	195	19	,	,	PUNCT
ejpam-6251	195	20	3	3	NUM
ejpam-6251	195	21	,	,	PUNCT
ejpam-6251	195	22	u̇	u̇	PROPN
ejpam-6251	195	23	)	)	PUNCT
ejpam-6251	196	1	=	=	SYM
ejpam-6251	196	2	u̇	u̇	PROPN
ejpam-6251	197	1	u̇+max{2	u̇+max{2	PROPN
ejpam-6251	197	2	,	,	PUNCT
ejpam-6251	197	3	3	3	X
ejpam-6251	197	4	}	}	PUNCT
ejpam-6251	197	5	=	=	SYM
ejpam-6251	197	6	u̇	u̇	NOUN
ejpam-6251	197	7	u̇+	u̇+	NOUN
ejpam-6251	197	8	3	3	NUM
ejpam-6251	197	9	=	=	SYM
ejpam-6251	197	10	u̇	u̇	NOUN
ejpam-6251	197	11	u̇+	u̇+	PROPN
ejpam-6251	197	12	3	3	NUM
ejpam-6251	197	13	and	and	CCONJ
ejpam-6251	197	14	π	π	PROPN
ejpam-6251	197	15	(	(	PUNCT
ejpam-6251	197	16	3	3	NUM
ejpam-6251	197	17	,	,	PUNCT
ejpam-6251	197	18	4	4	NUM
ejpam-6251	197	19	,	,	PUNCT
ejpam-6251	197	20	ṫ	ṫ	PROPN
ejpam-6251	197	21	)	)	PUNCT
ejpam-6251	198	1	=	=	SYM
ejpam-6251	198	2	ṫ	ṫ	PROPN
ejpam-6251	198	3	ṫ+max{3	ṫ+max{3	NOUN
ejpam-6251	198	4	,	,	PUNCT
ejpam-6251	198	5	4	4	NUM
ejpam-6251	198	6	}	}	PUNCT
ejpam-6251	198	7	=	=	PUNCT
ejpam-6251	198	8	ṫ	ṫ	PROPN
ejpam-6251	198	9	ṫ+	ṫ+	ADJ
ejpam-6251	198	10	4	4	NUM
ejpam-6251	198	11	=	=	SYM
ejpam-6251	198	12	ṫ	ṫ	NOUN
ejpam-6251	198	13	ṫ+	ṫ+	ADJ
ejpam-6251	198	14	4	4	NUM
ejpam-6251	198	15	.	.	PUNCT
ejpam-6251	199	1	r.	r.	PROPN
ejpam-6251	199	2	ramaswamy	ramaswamy	PROPN
ejpam-6251	199	3	/	/	SYM
ejpam-6251	199	4	eur	eur	PROPN
ejpam-6251	199	5	.	.	PUNCT
ejpam-6251	200	1	j.	j.	PROPN
ejpam-6251	200	2	pure	pure	PROPN
ejpam-6251	200	3	appl	appl	PROPN
ejpam-6251	200	4	.	.	PROPN
ejpam-6251	200	5	math	math	PROPN
ejpam-6251	200	6	,	,	PUNCT
ejpam-6251	200	7	18	18	NUM
ejpam-6251	200	8	(	(	PUNCT
ejpam-6251	200	9	4	4	NUM
ejpam-6251	200	10	)	)	PUNCT
ejpam-6251	200	11	(	(	PUNCT
ejpam-6251	200	12	2025	2025	NUM
ejpam-6251	200	13	)	)	PUNCT
ejpam-6251	200	14	,	,	PUNCT
ejpam-6251	200	15	6251	6251	NUM
ejpam-6251	200	16	8	8	NUM
ejpam-6251	200	17	of	of	ADP
ejpam-6251	200	18	40	40	NUM
ejpam-6251	200	19	that	that	PRON
ejpam-6251	200	20	is	be	AUX
ejpam-6251	200	21	,	,	PUNCT
ejpam-6251	200	22	ż+	ż+	PROPN
ejpam-6251	200	23	u̇+	u̇+	PROPN
ejpam-6251	200	24	ṫ	ṫ	PROPN
ejpam-6251	200	25	ż+	ż+	PROPN
ejpam-6251	201	1	u̇+	u̇+	PROPN
ejpam-6251	201	2	ṫ+	ṫ+	PROPN
ejpam-6251	201	3	3	3	NUM
ejpam-6251	201	4	≥	≥	NOUN
ejpam-6251	201	5	ż	ż	PROPN
ejpam-6251	201	6	ż+	ż+	PROPN
ejpam-6251	201	7	2	2	NUM
ejpam-6251	201	8	·	·	PUNCT
ejpam-6251	201	9	u̇	u̇	PROPN
ejpam-6251	201	10	u̇+	u̇+	NOUN
ejpam-6251	201	11	3	3	NUM
ejpam-6251	201	12	.	.	PUNCT
ejpam-6251	202	1	ṫ	ṫ	PROPN
ejpam-6251	202	2	ṫ+	ṫ+	ADJ
ejpam-6251	202	3	4	4	NUM
ejpam-6251	202	4	.	.	PUNCT
ejpam-6251	203	1	since	since	SCONJ
ejpam-6251	203	2	each	each	PRON
ejpam-6251	203	3	of	of	ADP
ejpam-6251	203	4	ż	ż	PROPN
ejpam-6251	203	5	,	,	PUNCT
ejpam-6251	203	6	u̇	u̇	PROPN
ejpam-6251	203	7	,	,	PUNCT
ejpam-6251	203	8	ṫ	ṫ	PROPN
ejpam-6251	203	9	>	>	X
ejpam-6251	203	10	0	0	PROPN
ejpam-6251	203	11	,	,	PUNCT
ejpam-6251	203	12	the	the	DET
ejpam-6251	203	13	above	above	ADJ
ejpam-6251	203	14	inequality	inequality	NOUN
ejpam-6251	203	15	holds	hold	VERB
ejpam-6251	203	16	.	.	PUNCT
ejpam-6251	204	1	π(ς,⋏	π(ς,⋏	ADJ
ejpam-6251	204	2	,	,	PUNCT
ejpam-6251	204	3	ż+	ż+	PROPN
ejpam-6251	204	4	u̇+	u̇+	PROPN
ejpam-6251	204	5	ṫ	ṫ	PROPN
ejpam-6251	204	6	)	)	PUNCT
ejpam-6251	204	7	≥	≥	PROPN
ejpam-6251	204	8	π	π	PROPN
ejpam-6251	204	9	(	(	PUNCT
ejpam-6251	204	10	ς,ϖ	ς,ϖ	NUM
ejpam-6251	204	11	,	,	PUNCT
ejpam-6251	204	12	ż	ż	NOUN
ejpam-6251	204	13	)	)	PUNCT
ejpam-6251	205	1	⋇π	⋇π	X
ejpam-6251	205	2	(	(	PUNCT
ejpam-6251	205	3	ϖ	ϖ	NOUN
ejpam-6251	205	4	,	,	PUNCT
ejpam-6251	205	5	x	x	NOUN
ejpam-6251	205	6	,	,	PUNCT
ejpam-6251	205	7	u̇	u̇	PROPN
ejpam-6251	205	8	)	)	PUNCT
ejpam-6251	205	9	⋇π	⋇π	X
ejpam-6251	205	10	(	(	PUNCT
ejpam-6251	205	11	x,⋏	x,⋏	PROPN
ejpam-6251	205	12	,	,	PUNCT
ejpam-6251	205	13	ṫ	ṫ	PROPN
ejpam-6251	205	14	)	)	PUNCT
ejpam-6251	205	15	.	.	PUNCT
ejpam-6251	206	1	now	now	ADV
ejpam-6251	206	2	,	,	PUNCT
ejpam-6251	206	3	ψ(1	ψ(1	PROPN
ejpam-6251	206	4	,	,	PUNCT
ejpam-6251	206	5	4	4	NUM
ejpam-6251	206	6	,	,	PUNCT
ejpam-6251	206	7	ż+	ż+	PROPN
ejpam-6251	206	8	u̇+	u̇+	PROPN
ejpam-6251	206	9	ṫ	ṫ	PROPN
ejpam-6251	206	10	)	)	PUNCT
ejpam-6251	206	11	=	=	PUNCT
ejpam-6251	206	12	max{1	max{1	NOUN
ejpam-6251	206	13	,	,	PUNCT
ejpam-6251	206	14	4	4	NUM
ejpam-6251	206	15	}	}	PUNCT
ejpam-6251	206	16	ż+	ż+	PROPN
ejpam-6251	206	17	u̇+	u̇+	NOUN
ejpam-6251	206	18	ṫ+max{1	ṫ+max{1	PROPN
ejpam-6251	206	19	,	,	PUNCT
ejpam-6251	206	20	4	4	NUM
ejpam-6251	206	21	}	}	PUNCT
ejpam-6251	206	22	=	=	SYM
ejpam-6251	206	23	4	4	NUM
ejpam-6251	206	24	ż+	ż+	PROPN
ejpam-6251	206	25	u̇+	u̇+	NOUN
ejpam-6251	206	26	ṫ+	ṫ+	ADJ
ejpam-6251	206	27	4	4	NUM
ejpam-6251	206	28	.	.	PUNCT
ejpam-6251	207	1	on	on	ADP
ejpam-6251	207	2	the	the	DET
ejpam-6251	207	3	other	other	ADJ
ejpam-6251	207	4	hand	hand	NOUN
ejpam-6251	207	5	,	,	PUNCT
ejpam-6251	207	6	ψ	ψ	X
ejpam-6251	207	7	(	(	PUNCT
ejpam-6251	207	8	1	1	NUM
ejpam-6251	207	9	,	,	PUNCT
ejpam-6251	207	10	2	2	NUM
ejpam-6251	207	11	,	,	PUNCT
ejpam-6251	207	12	ż	ż	NOUN
ejpam-6251	207	13	)	)	PUNCT
ejpam-6251	207	14	=	=	SYM
ejpam-6251	207	15	max{1	max{1	NOUN
ejpam-6251	207	16	,	,	PUNCT
ejpam-6251	207	17	2	2	NUM
ejpam-6251	207	18	}	}	PUNCT
ejpam-6251	207	19	ż+max{1	ż+max{1	NOUN
ejpam-6251	207	20	,	,	PUNCT
ejpam-6251	207	21	2	2	NUM
ejpam-6251	207	22	}	}	PUNCT
ejpam-6251	207	23	=	=	SYM
ejpam-6251	207	24	2	2	NUM
ejpam-6251	207	25	ż+	ż+	NUM
ejpam-6251	207	26	2	2	NUM
ejpam-6251	207	27	=	=	SYM
ejpam-6251	207	28	2	2	NUM
ejpam-6251	207	29	ż+	ż+	PROPN
ejpam-6251	207	30	2	2	NUM
ejpam-6251	207	31	,	,	PUNCT
ejpam-6251	207	32	ψ	ψ	X
ejpam-6251	207	33	(	(	PUNCT
ejpam-6251	207	34	2	2	NUM
ejpam-6251	207	35	,	,	PUNCT
ejpam-6251	207	36	3	3	NUM
ejpam-6251	207	37	,	,	PUNCT
ejpam-6251	207	38	u̇	u̇	PROPN
ejpam-6251	207	39	)	)	PUNCT
ejpam-6251	207	40	=	=	SYM
ejpam-6251	207	41	max{2	max{2	PROPN
ejpam-6251	207	42	,	,	PUNCT
ejpam-6251	207	43	3	3	NUM
ejpam-6251	207	44	}	}	PUNCT
ejpam-6251	207	45	u̇+max{2	u̇+max{2	PROPN
ejpam-6251	207	46	,	,	PUNCT
ejpam-6251	207	47	3	3	NUM
ejpam-6251	207	48	}	}	PUNCT
ejpam-6251	207	49	=	=	SYM
ejpam-6251	207	50	3	3	NUM
ejpam-6251	207	51	u̇+	u̇+	NOUN
ejpam-6251	207	52	3	3	NUM
ejpam-6251	207	53	=	=	SYM
ejpam-6251	207	54	3	3	NUM
ejpam-6251	207	55	u̇+	u̇+	NOUN
ejpam-6251	207	56	3	3	NUM
ejpam-6251	207	57	and	and	CCONJ
ejpam-6251	207	58	ψ	ψ	X
ejpam-6251	207	59	(	(	PUNCT
ejpam-6251	207	60	3	3	NUM
ejpam-6251	207	61	,	,	PUNCT
ejpam-6251	207	62	4	4	NUM
ejpam-6251	207	63	,	,	PUNCT
ejpam-6251	207	64	ṫ	ṫ	PROPN
ejpam-6251	207	65	)	)	PUNCT
ejpam-6251	207	66	=	=	SYM
ejpam-6251	208	1	max{3	max{3	NOUN
ejpam-6251	208	2	,	,	PUNCT
ejpam-6251	208	3	4	4	NUM
ejpam-6251	208	4	}	}	PUNCT
ejpam-6251	208	5	ṫ+max{3	ṫ+max{3	NOUN
ejpam-6251	208	6	,	,	PUNCT
ejpam-6251	208	7	4	4	NUM
ejpam-6251	208	8	}	}	PUNCT
ejpam-6251	208	9	=	=	SYM
ejpam-6251	208	10	4	4	NUM
ejpam-6251	208	11	ṫ+	ṫ+	NOUN
ejpam-6251	208	12	4	4	NUM
ejpam-6251	208	13	=	=	SYM
ejpam-6251	208	14	4	4	NUM
ejpam-6251	208	15	ṫ+	ṫ+	NOUN
ejpam-6251	208	16	4	4	NUM
ejpam-6251	208	17	.	.	PUNCT
ejpam-6251	209	1	that	that	PRON
ejpam-6251	209	2	is	be	AUX
ejpam-6251	209	3	,	,	PUNCT
ejpam-6251	209	4	4	4	NUM
ejpam-6251	209	5	ż+	ż+	PROPN
ejpam-6251	209	6	u̇+	u̇+	NOUN
ejpam-6251	209	7	ṫ+	ṫ+	ADJ
ejpam-6251	209	8	4	4	NUM
ejpam-6251	209	9	≤	≤	NUM
ejpam-6251	209	10	max	max	NOUN
ejpam-6251	209	11	{	{	PUNCT
ejpam-6251	209	12	2	2	NUM
ejpam-6251	209	13	ż+	ż+	PROPN
ejpam-6251	209	14	2	2	NUM
ejpam-6251	209	15	,	,	PUNCT
ejpam-6251	209	16	3	3	NUM
ejpam-6251	209	17	u̇+	u̇+	PROPN
ejpam-6251	209	18	3	3	NUM
ejpam-6251	209	19	,	,	PUNCT
ejpam-6251	209	20	4	4	NUM
ejpam-6251	209	21	ṫ+	ṫ+	NOUN
ejpam-6251	209	22	4	4	NUM
ejpam-6251	209	23	}	}	PUNCT
ejpam-6251	209	24	.	.	PUNCT
ejpam-6251	210	1	here	here	ADV
ejpam-6251	210	2	again	again	ADV
ejpam-6251	210	3	,	,	PUNCT
ejpam-6251	210	4	ż	ż	NOUN
ejpam-6251	210	5	,	,	PUNCT
ejpam-6251	210	6	u̇	u̇	PROPN
ejpam-6251	210	7	,	,	PUNCT
ejpam-6251	210	8	ṫ	ṫ	PROPN
ejpam-6251	210	9	>	>	X
ejpam-6251	210	10	0	0	PUNCT
ejpam-6251	211	1	the	the	DET
ejpam-6251	211	2	above	above	ADJ
ejpam-6251	211	3	inequality	inequality	NOUN
ejpam-6251	211	4	is	be	AUX
ejpam-6251	211	5	true	true	ADJ
ejpam-6251	211	6	and	and	CCONJ
ejpam-6251	211	7	so	so	ADV
ejpam-6251	211	8	,	,	PUNCT
ejpam-6251	211	9	ψ(ς,⋏	ψ(ς,⋏	ADJ
ejpam-6251	211	10	,	,	PUNCT
ejpam-6251	211	11	ż+	ż+	PROPN
ejpam-6251	211	12	u̇+	u̇+	PROPN
ejpam-6251	211	13	ṫ	ṫ	PROPN
ejpam-6251	211	14	)	)	PUNCT
ejpam-6251	211	15	≤	≤	NOUN
ejpam-6251	212	1	ψ	ψ	X
ejpam-6251	212	2	(	(	PUNCT
ejpam-6251	212	3	ς,ϖ	ς,ϖ	NUM
ejpam-6251	212	4	,	,	PUNCT
ejpam-6251	212	5	ż	ż	NOUN
ejpam-6251	212	6	)	)	PUNCT
ejpam-6251	212	7	♢	♢	PROPN
ejpam-6251	212	8	ψ	ψ	X
ejpam-6251	212	9	(	(	PUNCT
ejpam-6251	212	10	x,⋏	x,⋏	PROPN
ejpam-6251	212	11	,	,	PUNCT
ejpam-6251	212	12	u̇	u̇	PROPN
ejpam-6251	212	13	)	)	PUNCT
ejpam-6251	212	14	♢	♢	PROPN
ejpam-6251	212	15	ψ	ψ	X
ejpam-6251	212	16	(	(	PUNCT
ejpam-6251	212	17	x,⋏	x,⋏	PROPN
ejpam-6251	212	18	,	,	PUNCT
ejpam-6251	212	19	ṫ	ṫ	PROPN
ejpam-6251	212	20	)	)	PUNCT
ejpam-6251	212	21	.	.	PUNCT
ejpam-6251	213	1	finally	finally	ADV
ejpam-6251	213	2	,	,	PUNCT
ejpam-6251	213	3	ξ(1	ξ(1	PROPN
ejpam-6251	213	4	,	,	PUNCT
ejpam-6251	213	5	3	3	NUM
ejpam-6251	213	6	,	,	PUNCT
ejpam-6251	213	7	ż+	ż+	PROPN
ejpam-6251	213	8	u̇+	u̇+	PROPN
ejpam-6251	213	9	ṫ	ṫ	PROPN
ejpam-6251	213	10	)	)	PUNCT
ejpam-6251	213	11	=	=	PUNCT
ejpam-6251	213	12	max{1	max{1	NOUN
ejpam-6251	213	13	,	,	PUNCT
ejpam-6251	213	14	3	3	NUM
ejpam-6251	213	15	}	}	PUNCT
ejpam-6251	213	16	ż+	ż+	PROPN
ejpam-6251	213	17	u̇+	u̇+	PROPN
ejpam-6251	213	18	ṫ	ṫ	PROPN
ejpam-6251	213	19	=	=	SYM
ejpam-6251	213	20	3	3	NUM
ejpam-6251	213	21	ż+	ż+	PROPN
ejpam-6251	213	22	u̇+	u̇+	PROPN
ejpam-6251	213	23	ṫ	ṫ	PROPN
ejpam-6251	213	24	.	.	PUNCT
ejpam-6251	214	1	on	on	ADP
ejpam-6251	214	2	the	the	DET
ejpam-6251	214	3	other	other	ADJ
ejpam-6251	214	4	hand	hand	NOUN
ejpam-6251	214	5	,	,	PUNCT
ejpam-6251	214	6	ξ	ξ	X
ejpam-6251	214	7	(	(	PUNCT
ejpam-6251	214	8	1	1	NUM
ejpam-6251	214	9	,	,	PUNCT
ejpam-6251	214	10	2	2	NUM
ejpam-6251	214	11	,	,	PUNCT
ejpam-6251	214	12	ż	ż	NOUN
ejpam-6251	214	13	)	)	PUNCT
ejpam-6251	214	14	=	=	SYM
ejpam-6251	214	15	max{1	max{1	NOUN
ejpam-6251	214	16	,	,	PUNCT
ejpam-6251	214	17	2	2	NUM
ejpam-6251	214	18	}	}	PUNCT
ejpam-6251	214	19	ż	ż	NOUN
ejpam-6251	214	20	=	=	SYM
ejpam-6251	214	21	2	2	NUM
ejpam-6251	214	22	ż	ż	NOUN
ejpam-6251	214	23	,	,	PUNCT
ejpam-6251	214	24	ξ	ξ	PROPN
ejpam-6251	214	25	(	(	PUNCT
ejpam-6251	214	26	2	2	NUM
ejpam-6251	214	27	,	,	PUNCT
ejpam-6251	214	28	3	3	NUM
ejpam-6251	214	29	,	,	PUNCT
ejpam-6251	214	30	u̇	u̇	PROPN
ejpam-6251	214	31	)	)	PUNCT
ejpam-6251	214	32	=	=	SYM
ejpam-6251	214	33	max{2	max{2	PROPN
ejpam-6251	214	34	,	,	PUNCT
ejpam-6251	214	35	3	3	X
ejpam-6251	214	36	}	}	PUNCT
ejpam-6251	214	37	u̇	u̇	NOUN
ejpam-6251	214	38	=	=	SYM
ejpam-6251	214	39	3	3	NUM
ejpam-6251	214	40	u̇	u̇	NOUN
ejpam-6251	214	41	=	=	SYM
ejpam-6251	214	42	3	3	NUM
ejpam-6251	214	43	u̇	u̇	PROPN
ejpam-6251	214	44	r.	r.	PROPN
ejpam-6251	214	45	ramaswamy	ramaswamy	PROPN
ejpam-6251	214	46	/	/	SYM
ejpam-6251	214	47	eur	eur	PROPN
ejpam-6251	214	48	.	.	PUNCT
ejpam-6251	215	1	j.	j.	PROPN
ejpam-6251	215	2	pure	pure	PROPN
ejpam-6251	215	3	appl	appl	PROPN
ejpam-6251	215	4	.	.	PROPN
ejpam-6251	215	5	math	math	PROPN
ejpam-6251	215	6	,	,	PUNCT
ejpam-6251	215	7	18	18	NUM
ejpam-6251	215	8	(	(	PUNCT
ejpam-6251	215	9	4	4	NUM
ejpam-6251	215	10	)	)	PUNCT
ejpam-6251	215	11	(	(	PUNCT
ejpam-6251	215	12	2025	2025	NUM
ejpam-6251	215	13	)	)	PUNCT
ejpam-6251	215	14	,	,	PUNCT
ejpam-6251	215	15	6251	6251	NUM
ejpam-6251	215	16	9	9	NUM
ejpam-6251	215	17	of	of	ADP
ejpam-6251	215	18	40	40	NUM
ejpam-6251	215	19	and	and	CCONJ
ejpam-6251	215	20	ξ	ξ	PROPN
ejpam-6251	215	21	(	(	PUNCT
ejpam-6251	215	22	3	3	NUM
ejpam-6251	215	23	,	,	PUNCT
ejpam-6251	215	24	4	4	NUM
ejpam-6251	215	25	,	,	PUNCT
ejpam-6251	215	26	ṫ	ṫ	PROPN
ejpam-6251	215	27	)	)	PUNCT
ejpam-6251	216	1	=	=	SYM
ejpam-6251	216	2	max{3	max{3	NOUN
ejpam-6251	216	3	,	,	PUNCT
ejpam-6251	216	4	4	4	NUM
ejpam-6251	216	5	}	}	PUNCT
ejpam-6251	216	6	ṫ	ṫ	PROPN
ejpam-6251	216	7	=	=	SYM
ejpam-6251	216	8	4	4	NUM
ejpam-6251	216	9	ṫ	ṫ	NOUN
ejpam-6251	216	10	=	=	SYM
ejpam-6251	216	11	4	4	NUM
ejpam-6251	216	12	ṫ	ṫ	NOUN
ejpam-6251	216	13	.	.	PUNCT
ejpam-6251	217	1	that	that	PRON
ejpam-6251	217	2	is	be	AUX
ejpam-6251	217	3	,	,	PUNCT
ejpam-6251	217	4	3	3	NUM
ejpam-6251	217	5	ż+	ż+	PROPN
ejpam-6251	217	6	u̇+	u̇+	PROPN
ejpam-6251	217	7	ṫ	ṫ	PROPN
ejpam-6251	217	8	≤	≤	PROPN
ejpam-6251	217	9	max	max	PROPN
ejpam-6251	217	10	{	{	PUNCT
ejpam-6251	217	11	2	2	NUM
ejpam-6251	217	12	ż	ż	NOUN
ejpam-6251	217	13	,	,	PUNCT
ejpam-6251	217	14	3	3	NUM
ejpam-6251	217	15	u̇	u̇	NOUN
ejpam-6251	217	16	,	,	PUNCT
ejpam-6251	217	17	4	4	NUM
ejpam-6251	217	18	ṫ	ṫ	NOUN
ejpam-6251	217	19	}	}	PUNCT
ejpam-6251	217	20	.	.	PUNCT
ejpam-6251	218	1	the	the	DET
ejpam-6251	218	2	above	above	ADJ
ejpam-6251	218	3	inequality	inequality	NOUN
ejpam-6251	218	4	holds	hold	VERB
ejpam-6251	218	5	as	as	ADP
ejpam-6251	218	6	ż	ż	NOUN
ejpam-6251	218	7	,	,	PUNCT
ejpam-6251	218	8	u̇	u̇	PROPN
ejpam-6251	218	9	>	>	X
ejpam-6251	218	10	0	0	X
ejpam-6251	218	11	.	.	PUNCT
ejpam-6251	219	1	thus	thus	ADV
ejpam-6251	219	2	,	,	PUNCT
ejpam-6251	219	3	,	,	PUNCT
ejpam-6251	219	4	ξ(ς,⋏	ξ(ς,⋏	NOUN
ejpam-6251	219	5	,	,	PUNCT
ejpam-6251	219	6	ż+	ż+	PROPN
ejpam-6251	219	7	u̇+	u̇+	PROPN
ejpam-6251	219	8	ṫ	ṫ	PROPN
ejpam-6251	219	9	)	)	PUNCT
ejpam-6251	219	10	≤	≤	NOUN
ejpam-6251	220	1	ξ	ξ	PROPN
ejpam-6251	220	2	(	(	PUNCT
ejpam-6251	220	3	ς,ϖ	ς,ϖ	NUM
ejpam-6251	220	4	,	,	PUNCT
ejpam-6251	220	5	ż	ż	NOUN
ejpam-6251	220	6	)	)	PUNCT
ejpam-6251	220	7	♢	♢	PROPN
ejpam-6251	220	8	ξ	ξ	X
ejpam-6251	220	9	(	(	PUNCT
ejpam-6251	220	10	ϖ	ϖ	NOUN
ejpam-6251	220	11	,	,	PUNCT
ejpam-6251	220	12	x	x	NOUN
ejpam-6251	220	13	,	,	PUNCT
ejpam-6251	220	14	u̇	u̇	PROPN
ejpam-6251	220	15	)	)	PUNCT
ejpam-6251	220	16	♢	♢	PROPN
ejpam-6251	220	17	ξ	ξ	X
ejpam-6251	220	18	(	(	PUNCT
ejpam-6251	220	19	x,⋏	x,⋏	PROPN
ejpam-6251	220	20	,	,	PUNCT
ejpam-6251	220	21	u̇	u̇	PROPN
ejpam-6251	220	22	)	)	PUNCT
ejpam-6251	220	23	.	.	PUNCT
ejpam-6251	221	1	thus	thus	ADV
ejpam-6251	221	2	,	,	PUNCT
ejpam-6251	221	3	(	(	PUNCT
ejpam-6251	221	4	𭟋	𭟋	X
ejpam-6251	221	5	,	,	PUNCT
ejpam-6251	221	6	π	π	PROPN
ejpam-6251	221	7	,	,	PUNCT
ejpam-6251	221	8	ψ	ψ	PROPN
ejpam-6251	221	9	,	,	PUNCT
ejpam-6251	221	10	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	221	11	,	,	PUNCT
ejpam-6251	221	12	♢	♢	PROPN
ejpam-6251	221	13	)	)	PUNCT
ejpam-6251	221	14	is	be	AUX
ejpam-6251	221	15	a	a	DET
ejpam-6251	221	16	nbms	nbms	NOUN
ejpam-6251	221	17	with	with	ADP
ejpam-6251	221	18	i	i	PRON
ejpam-6251	221	19	⋇	⋇	VERB
ejpam-6251	221	20	♭	♭	PROPN
ejpam-6251	222	1	=	=	PUNCT
ejpam-6251	222	2	i	i	PRON
ejpam-6251	222	3	♭	♭	PROPN
ejpam-6251	222	4	and	and	CCONJ
ejpam-6251	222	5	i	i	PRON
ejpam-6251	222	6	♢	♢	PROPN
ejpam-6251	222	7	♭	♭	X
ejpam-6251	222	8	=	=	PUNCT
ejpam-6251	222	9	max{i	max{i	X
ejpam-6251	222	10	,	,	PUNCT
ejpam-6251	222	11	♭	♭	X
ejpam-6251	222	12	}	}	PUNCT
ejpam-6251	222	13	by	by	ADP
ejpam-6251	222	14	ct−||.||	ct−||.||	NOUN
ejpam-6251	222	15	and	and	CCONJ
ejpam-6251	222	16	ct−co−||.||	ct−co−||.||	NOUN
ejpam-6251	222	17	,	,	PUNCT
ejpam-6251	222	18	respectively	respectively	ADV
ejpam-6251	222	19	.	.	PUNCT
ejpam-6251	223	1	remark	remark	PROPN
ejpam-6251	223	2	1	1	NUM
ejpam-6251	223	3	.	.	PUNCT
ejpam-6251	224	1	it	it	PRON
ejpam-6251	224	2	is	be	AUX
ejpam-6251	224	3	to	to	PART
ejpam-6251	224	4	be	be	AUX
ejpam-6251	224	5	noted	note	VERB
ejpam-6251	224	6	that	that	SCONJ
ejpam-6251	224	7	every	every	DET
ejpam-6251	224	8	nbms	nbms	NOUN
ejpam-6251	224	9	is	be	AUX
ejpam-6251	224	10	a	a	DET
ejpam-6251	224	11	neutrosophic	neutrosophic	ADJ
ejpam-6251	224	12	metric	metric	ADJ
ejpam-6251	224	13	space	space	NOUN
ejpam-6251	224	14	nms	nms	NOUN
ejpam-6251	224	15	,	,	PUNCT
ejpam-6251	224	16	but	but	CCONJ
ejpam-6251	224	17	the	the	DET
ejpam-6251	224	18	converse	converse	NOUN
ejpam-6251	224	19	is	be	AUX
ejpam-6251	224	20	not	not	PART
ejpam-6251	224	21	always	always	ADV
ejpam-6251	224	22	true	true	ADJ
ejpam-6251	224	23	because	because	SCONJ
ejpam-6251	224	24	,	,	PUNCT
ejpam-6251	224	25	nms	nms	PROPN
ejpam-6251	224	26	is	be	AUX
ejpam-6251	224	27	a	a	DET
ejpam-6251	224	28	particular	particular	ADJ
ejpam-6251	224	29	case	case	NOUN
ejpam-6251	224	30	of	of	ADP
ejpam-6251	224	31	nbms	nbms	NOUN
ejpam-6251	224	32	where	where	SCONJ
ejpam-6251	224	33	f	f	PROPN
ejpam-6251	224	34	=	=	SYM
ejpam-6251	224	35	s.	s.	PROPN
ejpam-6251	224	36	definition	definition	NOUN
ejpam-6251	224	37	7	7	NUM
ejpam-6251	224	38	.	.	PUNCT
ejpam-6251	225	1	let	let	VERB
ejpam-6251	225	2	p	p	NOUN
ejpam-6251	225	3	:	:	PUNCT
ejpam-6251	225	4	𭟋1	𭟋1	NOUN
ejpam-6251	225	5	∪s1	∪s1	PROPN
ejpam-6251	226	1	→	→	PUNCT
ejpam-6251	226	2	𭟋2	𭟋2	PROPN
ejpam-6251	226	3	∪s2	∪s2	AUX
ejpam-6251	226	4	be	be	AUX
ejpam-6251	226	5	a	a	DET
ejpam-6251	226	6	mapping	mapping	NOUN
ejpam-6251	226	7	,	,	PUNCT
ejpam-6251	226	8	where	where	SCONJ
ejpam-6251	226	9	(	(	PUNCT
ejpam-6251	226	10	𭟋1,s1	𭟋1,s1	PROPN
ejpam-6251	226	11	)	)	PUNCT
ejpam-6251	226	12	and	and	CCONJ
ejpam-6251	226	13	(	(	PUNCT
ejpam-6251	226	14	𭟋2,s2	𭟋2,s2	PROPN
ejpam-6251	226	15	)	)	PUNCT
ejpam-6251	226	16	pairs	pair	NOUN
ejpam-6251	226	17	of	of	ADP
ejpam-6251	226	18	sets	set	NOUN
ejpam-6251	226	19	.	.	PUNCT
ejpam-6251	227	1	i.	i.	NOUN
ejpam-6251	227	2	if	if	SCONJ
ejpam-6251	227	3	p(𭟋1	p(𭟋1	NOUN
ejpam-6251	227	4	)	)	PUNCT
ejpam-6251	227	5	⊆	⊆	NUM
ejpam-6251	227	6	𭟋2	𭟋2	NOUN
ejpam-6251	227	7	and	and	CCONJ
ejpam-6251	227	8	p(s1	p(s1	NOUN
ejpam-6251	227	9	)	)	PUNCT
ejpam-6251	227	10	⊆	⊆	NUM
ejpam-6251	227	11	s2	s2	NOUN
ejpam-6251	227	12	,	,	PUNCT
ejpam-6251	227	13	then	then	ADV
ejpam-6251	227	14	p	p	NOUN
ejpam-6251	227	15	is	be	AUX
ejpam-6251	227	16	said	say	VERB
ejpam-6251	227	17	to	to	PART
ejpam-6251	227	18	be	be	AUX
ejpam-6251	227	19	a	a	DET
ejpam-6251	227	20	covariant	covariant	ADJ
ejpam-6251	227	21	map	map	NOUN
ejpam-6251	227	22	,	,	PUNCT
ejpam-6251	227	23	or	or	CCONJ
ejpam-6251	227	24	a	a	DET
ejpam-6251	227	25	map	map	NOUN
ejpam-6251	227	26	from	from	ADP
ejpam-6251	227	27	(	(	PUNCT
ejpam-6251	227	28	𭟋1,s1,π1,ψ1,ξ1,⋇	𭟋1,s1,π1,ψ1,ξ1,⋇	PROPN
ejpam-6251	227	29	,	,	PUNCT
ejpam-6251	227	30	♢	♢	PROPN
ejpam-6251	227	31	)	)	PUNCT
ejpam-6251	227	32	to	to	ADP
ejpam-6251	227	33	(	(	PUNCT
ejpam-6251	227	34	𭟋2,s2,π2,ψ2,ξ2,⋇	𭟋2,s2,π2,ψ2,ξ2,⋇	PROPN
ejpam-6251	227	35	,	,	PUNCT
ejpam-6251	227	36	♢	♢	PROPN
ejpam-6251	227	37	)	)	PUNCT
ejpam-6251	227	38	and	and	CCONJ
ejpam-6251	227	39	this	this	PRON
ejpam-6251	227	40	is	be	AUX
ejpam-6251	227	41	written	write	VERB
ejpam-6251	227	42	as	as	ADP
ejpam-6251	227	43	,	,	PUNCT
ejpam-6251	227	44	p	p	X
ejpam-6251	227	45	:	:	PUNCT
ejpam-6251	227	46	(	(	PUNCT
ejpam-6251	227	47	𭟋1,s1,π1,ψ1,ξ1,⋇	𭟋1,s1,π1,ψ1,ξ1,⋇	PROPN
ejpam-6251	227	48	,	,	PUNCT
ejpam-6251	227	49	♢	♢	PROPN
ejpam-6251	227	50	)	)	PUNCT
ejpam-6251	227	51	⇒	⇒	PROPN
ejpam-6251	227	52	(	(	PUNCT
ejpam-6251	227	53	𭟋2,s2,π2,ψ2,ξ2,⋇	𭟋2,s2,π2,ψ2,ξ2,⋇	PROPN
ejpam-6251	227	54	,	,	PUNCT
ejpam-6251	227	55	♢	♢	PROPN
ejpam-6251	227	56	)	)	PUNCT
ejpam-6251	227	57	.	.	PUNCT
ejpam-6251	228	1	ii	ii	PROPN
ejpam-6251	228	2	.	.	PUNCT
ejpam-6251	229	1	if	if	SCONJ
ejpam-6251	229	2	p(𭟋1	p(𭟋1	NOUN
ejpam-6251	229	3	)	)	PUNCT
ejpam-6251	229	4	⊆	⊆	NUM
ejpam-6251	229	5	s2	s2	NOUN
ejpam-6251	229	6	and	and	CCONJ
ejpam-6251	229	7	p(s1	p(s1	ADJ
ejpam-6251	229	8	)	)	PUNCT
ejpam-6251	229	9	⊆	⊆	NUM
ejpam-6251	229	10	𭟋2	𭟋2	NOUN
ejpam-6251	229	11	,	,	PUNCT
ejpam-6251	229	12	then	then	ADV
ejpam-6251	229	13	p	p	NOUN
ejpam-6251	229	14	is	be	AUX
ejpam-6251	229	15	said	say	VERB
ejpam-6251	229	16	to	to	PART
ejpam-6251	229	17	be	be	AUX
ejpam-6251	229	18	a	a	DET
ejpam-6251	229	19	contravariant	contravariant	ADJ
ejpam-6251	229	20	map	map	NOUN
ejpam-6251	229	21	from	from	ADP
ejpam-6251	229	22	(	(	PUNCT
ejpam-6251	229	23	𭟋1,s1,π1,ψ1,ξ1,⋇	𭟋1,s1,π1,ψ1,ξ1,⋇	PROPN
ejpam-6251	229	24	,	,	PUNCT
ejpam-6251	229	25	♢	♢	PROPN
ejpam-6251	229	26	)	)	PUNCT
ejpam-6251	229	27	to	to	ADP
ejpam-6251	229	28	(	(	PUNCT
ejpam-6251	229	29	𭟋2,s2,π2,ψ2,ξ2,⋇	𭟋2,s2,π2,ψ2,ξ2,⋇	PROPN
ejpam-6251	229	30	,	,	PUNCT
ejpam-6251	229	31	♢	♢	PROPN
ejpam-6251	229	32	)	)	PUNCT
ejpam-6251	229	33	and	and	CCONJ
ejpam-6251	229	34	this	this	PRON
ejpam-6251	229	35	is	be	AUX
ejpam-6251	229	36	denoted	denote	VERB
ejpam-6251	229	37	as	as	ADP
ejpam-6251	229	38	:	:	PUNCT
ejpam-6251	229	39	p	p	X
ejpam-6251	229	40	:	:	PUNCT
ejpam-6251	229	41	(	(	PUNCT
ejpam-6251	229	42	𭟋1,s1,π1,ψ1,ξ1,⋇	𭟋1,s1,π1,ψ1,ξ1,⋇	PROPN
ejpam-6251	229	43	,	,	PUNCT
ejpam-6251	229	44	♢	♢	PROPN
ejpam-6251	229	45	)	)	PUNCT
ejpam-6251	229	46	⇆	⇆	PROPN
ejpam-6251	229	47	(	(	PUNCT
ejpam-6251	229	48	𭟋2,s2,π2,ψ2,ξ2,⋇	𭟋2,s2,π2,ψ2,ξ2,⋇	PROPN
ejpam-6251	229	49	,	,	PUNCT
ejpam-6251	229	50	♢	♢	PROPN
ejpam-6251	229	51	)	)	PUNCT
ejpam-6251	229	52	.	.	PUNCT
ejpam-6251	230	1	3.1	3.1	NUM
ejpam-6251	230	2	.	.	PUNCT
ejpam-6251	231	1	some	some	DET
ejpam-6251	231	2	topological	topological	ADJ
ejpam-6251	231	3	properties	property	NOUN
ejpam-6251	231	4	of	of	ADP
ejpam-6251	231	5	neutrosophic	neutrosophic	ADJ
ejpam-6251	231	6	bipolar	bipolar	ADJ
ejpam-6251	231	7	metric	metric	ADJ
ejpam-6251	231	8	space	space	NOUN
ejpam-6251	231	9	definition	definition	NOUN
ejpam-6251	231	10	8	8	NUM
ejpam-6251	231	11	.	.	PUNCT
ejpam-6251	232	1	let	let	VERB
ejpam-6251	232	2	(	(	PUNCT
ejpam-6251	232	3	𭟋	𭟋	NOUN
ejpam-6251	232	4	,	,	PUNCT
ejpam-6251	232	5	s	s	PROPN
ejpam-6251	232	6	,	,	PUNCT
ejpam-6251	232	7	π	π	PROPN
ejpam-6251	232	8	,	,	PUNCT
ejpam-6251	232	9	ψ	ψ	PROPN
ejpam-6251	232	10	,	,	PUNCT
ejpam-6251	232	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	232	12	,	,	PUNCT
ejpam-6251	232	13	♢	♢	PROPN
ejpam-6251	232	14	)	)	PUNCT
ejpam-6251	232	15	is	be	AUX
ejpam-6251	232	16	a	a	DET
ejpam-6251	232	17	nbms	nbms	NOUN
ejpam-6251	232	18	,	,	PUNCT
ejpam-6251	232	19	and	and	CCONJ
ejpam-6251	232	20	define	define	VERB
ejpam-6251	232	21	a	a	DET
ejpam-6251	232	22	right	right	ADJ
ejpam-6251	232	23	open	open	NOUN
ejpam-6251	232	24	ball	ball	NOUN
ejpam-6251	232	25	b(ς	b(ς	PROPN
ejpam-6251	232	26	,	,	PUNCT
ejpam-6251	232	27	r	r	NOUN
ejpam-6251	232	28	,	,	PUNCT
ejpam-6251	232	29	ż	ż	NOUN
ejpam-6251	232	30	)	)	PUNCT
ejpam-6251	232	31	with	with	ADP
ejpam-6251	232	32	center	center	NOUN
ejpam-6251	232	33	ς	ς	PROPN
ejpam-6251	232	34	∈	∈	PROPN
ejpam-6251	232	35	𭟋	𭟋	NOUN
ejpam-6251	232	36	,	,	PUNCT
ejpam-6251	232	37	radius	radius	NOUN
ejpam-6251	232	38	r	r	NOUN
ejpam-6251	232	39	,	,	PUNCT
ejpam-6251	232	40	r	r	NOUN
ejpam-6251	232	41	∈	∈	PROPN
ejpam-6251	232	42	(	(	PUNCT
ejpam-6251	232	43	0	0	NUM
ejpam-6251	232	44	,	,	PUNCT
ejpam-6251	232	45	1	1	NUM
ejpam-6251	232	46	)	)	PUNCT
ejpam-6251	232	47	,	,	PUNCT
ejpam-6251	232	48	ż	ż	NOUN
ejpam-6251	232	49	>	>	X
ejpam-6251	232	50	0	0	PUNCT
ejpam-6251	233	1	as	as	SCONJ
ejpam-6251	233	2	follows	follow	VERB
ejpam-6251	233	3	:	:	PUNCT
ejpam-6251	234	1	b(ς	b(ς	PROPN
ejpam-6251	234	2	,	,	PUNCT
ejpam-6251	234	3	r	r	NOUN
ejpam-6251	234	4	,	,	PUNCT
ejpam-6251	234	5	ż	ż	NOUN
ejpam-6251	234	6	)	)	PUNCT
ejpam-6251	234	7	=	=	PRON
ejpam-6251	234	8	{	{	PUNCT
ejpam-6251	234	9	ϖ	ϖ	PUNCT
ejpam-6251	234	10	∈	∈	PROPN
ejpam-6251	234	11	s	s	PART
ejpam-6251	234	12	:	:	PUNCT
ejpam-6251	234	13	π(ς,ϖ	π(ς,ϖ	NUM
ejpam-6251	234	14	,	,	PUNCT
ejpam-6251	234	15	ż	ż	NOUN
ejpam-6251	234	16	)	)	PUNCT
ejpam-6251	234	17	>	>	X
ejpam-6251	235	1	1−	1−	NUM
ejpam-6251	235	2	r	r	NOUN
ejpam-6251	235	3	,	,	PUNCT
ejpam-6251	235	4	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	235	5	,	,	PUNCT
ejpam-6251	235	6	ż	ż	NOUN
ejpam-6251	235	7	)	)	PUNCT
ejpam-6251	235	8	<	<	X
ejpam-6251	235	9	r	r	NOUN
ejpam-6251	235	10	,	,	PUNCT
ejpam-6251	235	11	ξ(ς,ϖ	ξ(ς,ϖ	NOUN
ejpam-6251	235	12	,	,	PUNCT
ejpam-6251	235	13	ż	ż	NOUN
ejpam-6251	235	14	)	)	PUNCT
ejpam-6251	235	15	<	<	X
ejpam-6251	235	16	r	r	X
ejpam-6251	235	17	}	}	PUNCT
ejpam-6251	235	18	.	.	PUNCT
ejpam-6251	236	1	definition	definition	NOUN
ejpam-6251	236	2	9	9	NUM
ejpam-6251	236	3	.	.	PUNCT
ejpam-6251	237	1	let	let	VERB
ejpam-6251	237	2	(	(	PUNCT
ejpam-6251	237	3	𭟋	𭟋	NOUN
ejpam-6251	237	4	,	,	PUNCT
ejpam-6251	237	5	s	s	PROPN
ejpam-6251	237	6	,	,	PUNCT
ejpam-6251	237	7	π	π	PROPN
ejpam-6251	237	8	,	,	PUNCT
ejpam-6251	237	9	ψ	ψ	PROPN
ejpam-6251	237	10	,	,	PUNCT
ejpam-6251	237	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	237	12	,	,	PUNCT
ejpam-6251	237	13	♢	♢	PROPN
ejpam-6251	237	14	)	)	PUNCT
ejpam-6251	237	15	is	be	AUX
ejpam-6251	237	16	a	a	DET
ejpam-6251	237	17	nbms	nbms	NOUN
ejpam-6251	237	18	,	,	PUNCT
ejpam-6251	237	19	and	and	CCONJ
ejpam-6251	237	20	define	define	VERB
ejpam-6251	237	21	a	a	DET
ejpam-6251	237	22	left	left	ADJ
ejpam-6251	237	23	open	open	ADJ
ejpam-6251	237	24	ball	ball	NOUN
ejpam-6251	237	25	b(ϖ	b(ϖ	NOUN
ejpam-6251	237	26	,	,	PUNCT
ejpam-6251	237	27	r	r	NOUN
ejpam-6251	237	28	,	,	PUNCT
ejpam-6251	237	29	ż	ż	NOUN
ejpam-6251	237	30	)	)	PUNCT
ejpam-6251	237	31	with	with	ADP
ejpam-6251	237	32	center	center	NOUN
ejpam-6251	237	33	ϖ	ϖ	INTJ
ejpam-6251	237	34	∈	∈	PROPN
ejpam-6251	237	35	s	s	PROPN
ejpam-6251	237	36	,	,	PUNCT
ejpam-6251	237	37	radius	radius	NOUN
ejpam-6251	237	38	r	r	NOUN
ejpam-6251	237	39	,	,	PUNCT
ejpam-6251	237	40	r	r	NOUN
ejpam-6251	237	41	∈	∈	PROPN
ejpam-6251	237	42	(	(	PUNCT
ejpam-6251	237	43	0	0	NUM
ejpam-6251	237	44	,	,	PUNCT
ejpam-6251	237	45	1	1	NUM
ejpam-6251	237	46	)	)	PUNCT
ejpam-6251	237	47	,	,	PUNCT
ejpam-6251	237	48	ż	ż	NOUN
ejpam-6251	237	49	>	>	X
ejpam-6251	237	50	0	0	PUNCT
ejpam-6251	238	1	as	as	SCONJ
ejpam-6251	238	2	follows	follow	VERB
ejpam-6251	238	3	:	:	PUNCT
ejpam-6251	238	4	b(ϖ	b(ϖ	NOUN
ejpam-6251	238	5	,	,	PUNCT
ejpam-6251	238	6	r	r	NOUN
ejpam-6251	238	7	,	,	PUNCT
ejpam-6251	238	8	ż	ż	NOUN
ejpam-6251	238	9	)	)	PUNCT
ejpam-6251	238	10	=	=	PRON
ejpam-6251	238	11	{	{	PUNCT
ejpam-6251	238	12	ς	ς	PROPN
ejpam-6251	238	13	∈	∈	PROPN
ejpam-6251	238	14	𭟋	𭟋	NOUN
ejpam-6251	238	15	:	:	PUNCT
ejpam-6251	238	16	π(ς,ϖ	π(ς,ϖ	ADV
ejpam-6251	238	17	,	,	PUNCT
ejpam-6251	238	18	ż	ż	NOUN
ejpam-6251	238	19	)	)	PUNCT
ejpam-6251	238	20	>	>	X
ejpam-6251	239	1	1−	1−	NUM
ejpam-6251	239	2	r	r	NOUN
ejpam-6251	239	3	,	,	PUNCT
ejpam-6251	239	4	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	239	5	,	,	PUNCT
ejpam-6251	239	6	ż	ż	NOUN
ejpam-6251	239	7	)	)	PUNCT
ejpam-6251	239	8	<	<	X
ejpam-6251	239	9	r	r	NOUN
ejpam-6251	239	10	,	,	PUNCT
ejpam-6251	239	11	ξ(ς,ϖ	ξ(ς,ϖ	NOUN
ejpam-6251	239	12	,	,	PUNCT
ejpam-6251	239	13	ż	ż	NOUN
ejpam-6251	239	14	)	)	PUNCT
ejpam-6251	239	15	<	<	X
ejpam-6251	239	16	r	r	X
ejpam-6251	239	17	}	}	PUNCT
ejpam-6251	239	18	.	.	PUNCT
ejpam-6251	240	1	definition	definition	NOUN
ejpam-6251	240	2	10	10	NUM
ejpam-6251	240	3	.	.	PUNCT
ejpam-6251	241	1	let	let	VERB
ejpam-6251	241	2	(	(	PUNCT
ejpam-6251	241	3	𭟋	𭟋	NOUN
ejpam-6251	241	4	,	,	PUNCT
ejpam-6251	241	5	s	s	PROPN
ejpam-6251	241	6	,	,	PUNCT
ejpam-6251	241	7	π	π	PROPN
ejpam-6251	241	8	,	,	PUNCT
ejpam-6251	241	9	ψ	ψ	PROPN
ejpam-6251	241	10	,	,	PUNCT
ejpam-6251	241	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	241	12	,	,	PUNCT
ejpam-6251	241	13	♢	♢	PROPN
ejpam-6251	241	14	)	)	PUNCT
ejpam-6251	241	15	is	be	AUX
ejpam-6251	241	16	a	a	DET
ejpam-6251	241	17	nbms	nbms	NOUN
ejpam-6251	241	18	.	.	PUNCT
ejpam-6251	242	1	a	a	DET
ejpam-6251	242	2	subset	subset	NOUN
ejpam-6251	242	3	p	p	NOUN
ejpam-6251	242	4	of	of	ADP
ejpam-6251	242	5	s	s	PRON
ejpam-6251	242	6	is	be	AUX
ejpam-6251	242	7	said	say	VERB
ejpam-6251	242	8	to	to	PART
ejpam-6251	242	9	be	be	AUX
ejpam-6251	242	10	right	right	ADV
ejpam-6251	242	11	open	open	ADJ
ejpam-6251	242	12	set	set	VERB
ejpam-6251	242	13	if	if	SCONJ
ejpam-6251	242	14	for	for	ADP
ejpam-6251	242	15	every	every	DET
ejpam-6251	242	16	ϖ	ϖ	NOUN
ejpam-6251	242	17	∈	∈	PROPN
ejpam-6251	242	18	p	p	NOUN
ejpam-6251	242	19	,	,	PUNCT
ejpam-6251	242	20	there	there	PRON
ejpam-6251	242	21	exists	exist	VERB
ejpam-6251	242	22	r	r	NOUN
ejpam-6251	243	1	such	such	ADJ
ejpam-6251	243	2	that	that	SCONJ
ejpam-6251	243	3	ϖ	ϖ	PROPN
ejpam-6251	243	4	∈	∈	PROPN
ejpam-6251	243	5	b(ς	b(ς	PROPN
ejpam-6251	243	6	,	,	PUNCT
ejpam-6251	243	7	r	r	NOUN
ejpam-6251	243	8	,	,	PUNCT
ejpam-6251	243	9	ż	ż	NOUN
ejpam-6251	243	10	)	)	PUNCT
ejpam-6251	243	11	⊆	⊆	PROPN
ejpam-6251	243	12	p.	p.	PROPN
ejpam-6251	243	13	r.	r.	PROPN
ejpam-6251	243	14	ramaswamy	ramaswamy	PROPN
ejpam-6251	243	15	/	/	SYM
ejpam-6251	243	16	eur	eur	PROPN
ejpam-6251	243	17	.	.	PUNCT
ejpam-6251	244	1	j.	j.	PROPN
ejpam-6251	244	2	pure	pure	PROPN
ejpam-6251	244	3	appl	appl	PROPN
ejpam-6251	244	4	.	.	PROPN
ejpam-6251	244	5	math	math	PROPN
ejpam-6251	244	6	,	,	PUNCT
ejpam-6251	244	7	18	18	NUM
ejpam-6251	244	8	(	(	PUNCT
ejpam-6251	244	9	4	4	NUM
ejpam-6251	244	10	)	)	PUNCT
ejpam-6251	244	11	(	(	PUNCT
ejpam-6251	244	12	2025	2025	NUM
ejpam-6251	244	13	)	)	PUNCT
ejpam-6251	244	14	,	,	PUNCT
ejpam-6251	244	15	6251	6251	NUM
ejpam-6251	244	16	10	10	NUM
ejpam-6251	244	17	of	of	ADP
ejpam-6251	244	18	40	40	NUM
ejpam-6251	244	19	definition	definition	NOUN
ejpam-6251	244	20	11	11	NUM
ejpam-6251	244	21	.	.	PUNCT
ejpam-6251	245	1	let	let	VERB
ejpam-6251	245	2	(	(	PUNCT
ejpam-6251	245	3	𭟋	𭟋	NOUN
ejpam-6251	245	4	,	,	PUNCT
ejpam-6251	245	5	s	s	PROPN
ejpam-6251	245	6	,	,	PUNCT
ejpam-6251	245	7	π	π	PROPN
ejpam-6251	245	8	,	,	PUNCT
ejpam-6251	245	9	ψ	ψ	PROPN
ejpam-6251	245	10	,	,	PUNCT
ejpam-6251	245	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	245	12	,	,	PUNCT
ejpam-6251	245	13	♢	♢	PROPN
ejpam-6251	245	14	)	)	PUNCT
ejpam-6251	245	15	is	be	AUX
ejpam-6251	245	16	a	a	DET
ejpam-6251	245	17	nbms	nbms	NOUN
ejpam-6251	245	18	.	.	PUNCT
ejpam-6251	246	1	a	a	DET
ejpam-6251	246	2	subset	subset	NOUN
ejpam-6251	246	3	k	k	PROPN
ejpam-6251	246	4	of	of	ADP
ejpam-6251	246	5	𭟋	𭟋	PROPN
ejpam-6251	246	6	is	be	AUX
ejpam-6251	246	7	said	say	VERB
ejpam-6251	246	8	to	to	PART
ejpam-6251	246	9	be	be	AUX
ejpam-6251	246	10	left	leave	VERB
ejpam-6251	246	11	open	open	ADJ
ejpam-6251	246	12	set	set	VERB
ejpam-6251	246	13	if	if	SCONJ
ejpam-6251	246	14	for	for	ADP
ejpam-6251	246	15	every	every	DET
ejpam-6251	246	16	ς	ς	PROPN
ejpam-6251	246	17	∈	∈	PROPN
ejpam-6251	246	18	k	k	NOUN
ejpam-6251	246	19	,	,	PUNCT
ejpam-6251	246	20	there	there	PRON
ejpam-6251	246	21	exists	exist	VERB
ejpam-6251	246	22	r	r	NOUN
ejpam-6251	246	23	such	such	ADJ
ejpam-6251	246	24	that	that	SCONJ
ejpam-6251	246	25	ς	ς	PROPN
ejpam-6251	246	26	∈	∈	PROPN
ejpam-6251	246	27	b(ϖ	b(ϖ	PROPN
ejpam-6251	246	28	,	,	PUNCT
ejpam-6251	246	29	r	r	NOUN
ejpam-6251	246	30	,	,	PUNCT
ejpam-6251	246	31	ż	ż	NOUN
ejpam-6251	246	32	)	)	PUNCT
ejpam-6251	246	33	⊆	⊆	NUM
ejpam-6251	246	34	k.	k.	NOUN
ejpam-6251	246	35	definition	definition	NOUN
ejpam-6251	246	36	12	12	NUM
ejpam-6251	246	37	.	.	PUNCT
ejpam-6251	247	1	let	let	VERB
ejpam-6251	247	2	(	(	PUNCT
ejpam-6251	247	3	𭟋	𭟋	NOUN
ejpam-6251	247	4	,	,	PUNCT
ejpam-6251	247	5	s	s	PROPN
ejpam-6251	247	6	,	,	PUNCT
ejpam-6251	247	7	π	π	PROPN
ejpam-6251	247	8	,	,	PUNCT
ejpam-6251	247	9	ψ	ψ	PROPN
ejpam-6251	247	10	,	,	PUNCT
ejpam-6251	247	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	247	12	,	,	PUNCT
ejpam-6251	247	13	♢	♢	PROPN
ejpam-6251	247	14	)	)	PUNCT
ejpam-6251	247	15	is	be	AUX
ejpam-6251	247	16	a	a	DET
ejpam-6251	247	17	nbms	nbms	NOUN
ejpam-6251	247	18	.	.	PUNCT
ejpam-6251	248	1	let	let	VERB
ejpam-6251	248	2	g	g	PROPN
ejpam-6251	248	3	⊆	⊆	NUM
ejpam-6251	248	4	𭟋	𭟋	NOUN
ejpam-6251	248	5	and	and	CCONJ
ejpam-6251	248	6	h	h	PROPN
ejpam-6251	248	7	⊆	⊆	NUM
ejpam-6251	248	8	s.	s.	PROPN
ejpam-6251	248	9	then	then	ADV
ejpam-6251	248	10	g	g	PROPN
ejpam-6251	248	11	×h	×h	PROPN
ejpam-6251	248	12	is	be	AUX
ejpam-6251	248	13	called	call	VERB
ejpam-6251	248	14	an	an	DET
ejpam-6251	248	15	open	open	ADJ
ejpam-6251	248	16	set	set	NOUN
ejpam-6251	248	17	if	if	SCONJ
ejpam-6251	248	18	g	g	PROPN
ejpam-6251	248	19	is	be	AUX
ejpam-6251	248	20	left	leave	VERB
ejpam-6251	248	21	open	open	ADJ
ejpam-6251	248	22	set	set	VERB
ejpam-6251	248	23	and	and	CCONJ
ejpam-6251	248	24	h	h	NOUN
ejpam-6251	248	25	is	be	AUX
ejpam-6251	248	26	right	right	ADV
ejpam-6251	248	27	open	open	ADJ
ejpam-6251	248	28	set	set	NOUN
ejpam-6251	248	29	.	.	PUNCT
ejpam-6251	249	1	definition	definition	NOUN
ejpam-6251	249	2	13	13	NUM
ejpam-6251	249	3	.	.	PUNCT
ejpam-6251	250	1	let	let	VERB
ejpam-6251	250	2	(	(	PUNCT
ejpam-6251	250	3	𭟋	𭟋	NOUN
ejpam-6251	250	4	,	,	PUNCT
ejpam-6251	250	5	s	s	PROPN
ejpam-6251	250	6	,	,	PUNCT
ejpam-6251	250	7	π	π	PROPN
ejpam-6251	250	8	,	,	PUNCT
ejpam-6251	250	9	ψ	ψ	PROPN
ejpam-6251	250	10	,	,	PUNCT
ejpam-6251	250	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	250	12	,	,	PUNCT
ejpam-6251	250	13	♢	♢	PROPN
ejpam-6251	250	14	)	)	PUNCT
ejpam-6251	250	15	is	be	AUX
ejpam-6251	250	16	a	a	DET
ejpam-6251	250	17	nbms	nbms	NOUN
ejpam-6251	250	18	.	.	PUNCT
ejpam-6251	251	1	let	let	VERB
ejpam-6251	251	2	g	g	PROPN
ejpam-6251	251	3	⊆	⊆	NUM
ejpam-6251	251	4	𭟋	𭟋	NOUN
ejpam-6251	251	5	and	and	CCONJ
ejpam-6251	251	6	h	h	NOUN
ejpam-6251	251	7	⊆	⊆	NUM
ejpam-6251	251	8	s.	s.	PROPN
ejpam-6251	251	9	we	we	PRON
ejpam-6251	251	10	say	say	VERB
ejpam-6251	251	11	that	that	SCONJ
ejpam-6251	251	12	a	a	DET
ejpam-6251	251	13	subset	subset	NOUN
ejpam-6251	251	14	g	g	NOUN
ejpam-6251	251	15	×h	×h	PROPN
ejpam-6251	251	16	of	of	ADP
ejpam-6251	251	17	𭟋×	𭟋×	PROPN
ejpam-6251	251	18	s	s	PART
ejpam-6251	251	19	is	be	AUX
ejpam-6251	251	20	closed	close	VERB
ejpam-6251	251	21	if	if	SCONJ
ejpam-6251	251	22	(	(	PUNCT
ejpam-6251	251	23	𭟋−	𭟋−	PROPN
ejpam-6251	251	24	g)×	g)×	NOUN
ejpam-6251	251	25	(	(	PUNCT
ejpam-6251	251	26	s	s	NOUN
ejpam-6251	251	27	−h	−h	ADV
ejpam-6251	251	28	)	)	PUNCT
ejpam-6251	251	29	is	be	AUX
ejpam-6251	251	30	open	open	ADJ
ejpam-6251	251	31	.	.	PUNCT
ejpam-6251	252	1	theorem	theorem	NOUN
ejpam-6251	252	2	1	1	NUM
ejpam-6251	252	3	.	.	PUNCT
ejpam-6251	253	1	every	every	DET
ejpam-6251	253	2	right	right	ADJ
ejpam-6251	253	3	open	open	ADJ
ejpam-6251	253	4	ball	ball	PROPN
ejpam-6251	253	5	b(ς	b(ς	PROPN
ejpam-6251	253	6	,	,	PUNCT
ejpam-6251	253	7	r	r	NOUN
ejpam-6251	253	8	,	,	PUNCT
ejpam-6251	253	9	ż	ż	NOUN
ejpam-6251	253	10	)	)	PUNCT
ejpam-6251	253	11	is	be	AUX
ejpam-6251	253	12	a	a	DET
ejpam-6251	253	13	right	right	ADV
ejpam-6251	253	14	open	open	ADJ
ejpam-6251	253	15	set	set	NOUN
ejpam-6251	253	16	.	.	PUNCT
ejpam-6251	254	1	proof	proof	NOUN
ejpam-6251	254	2	.	.	PUNCT
ejpam-6251	255	1	take	take	VERB
ejpam-6251	255	2	b(ς	b(ς	PROPN
ejpam-6251	255	3	,	,	PUNCT
ejpam-6251	255	4	r	r	NOUN
ejpam-6251	255	5	,	,	PUNCT
ejpam-6251	255	6	ż	ż	NOUN
ejpam-6251	255	7	)	)	PUNCT
ejpam-6251	255	8	be	be	AUX
ejpam-6251	255	9	a	a	DET
ejpam-6251	255	10	right	right	ADJ
ejpam-6251	255	11	open	open	ADJ
ejpam-6251	255	12	ball	ball	NOUN
ejpam-6251	255	13	.	.	PUNCT
ejpam-6251	256	1	choose	choose	VERB
ejpam-6251	256	2	ϖ	ϖ	PRON
ejpam-6251	256	3	∈	∈	PROPN
ejpam-6251	256	4	b(ς	b(ς	PROPN
ejpam-6251	256	5	,	,	PUNCT
ejpam-6251	256	6	r	r	NOUN
ejpam-6251	256	7	,	,	PUNCT
ejpam-6251	256	8	ż	ż	NOUN
ejpam-6251	256	9	)	)	PUNCT
ejpam-6251	256	10	.	.	PUNCT
ejpam-6251	257	1	therefore	therefore	ADV
ejpam-6251	257	2	,	,	PUNCT
ejpam-6251	257	3	π(ς,ϖ	π(ς,ϖ	ADV
ejpam-6251	257	4	,	,	PUNCT
ejpam-6251	257	5	ż	ż	NOUN
ejpam-6251	257	6	)	)	PUNCT
ejpam-6251	257	7	>	>	X
ejpam-6251	258	1	1	1	NUM
ejpam-6251	258	2	−	−	NOUN
ejpam-6251	258	3	r	r	NOUN
ejpam-6251	258	4	,	,	PUNCT
ejpam-6251	258	5	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	258	6	,	,	PUNCT
ejpam-6251	258	7	ż	ż	NOUN
ejpam-6251	258	8	)	)	PUNCT
ejpam-6251	259	1	<	<	X
ejpam-6251	259	2	r	r	NOUN
ejpam-6251	259	3	,	,	PUNCT
ejpam-6251	259	4	ξ(ς,ϖ	ξ(ς,ϖ	NOUN
ejpam-6251	259	5	,	,	PUNCT
ejpam-6251	259	6	ż	ż	NOUN
ejpam-6251	259	7	)	)	PUNCT
ejpam-6251	259	8	<	<	X
ejpam-6251	259	9	r.	r.	PROPN
ejpam-6251	259	10	there	there	PRON
ejpam-6251	259	11	exists	exist	VERB
ejpam-6251	259	12	ż0	ż0	PROPN
ejpam-6251	259	13	∈	∈	PROPN
ejpam-6251	259	14	(	(	PUNCT
ejpam-6251	259	15	0	0	NUM
ejpam-6251	259	16	,	,	PUNCT
ejpam-6251	259	17	ż	ż	NOUN
ejpam-6251	259	18	)	)	PUNCT
ejpam-6251	259	19	such	such	ADJ
ejpam-6251	259	20	that	that	SCONJ
ejpam-6251	259	21	π(ς,ϖ	π(ς,ϖ	NUM
ejpam-6251	259	22	,	,	PUNCT
ejpam-6251	259	23	ż0	ż0	PROPN
ejpam-6251	259	24	)	)	PUNCT
ejpam-6251	259	25	>	>	X
ejpam-6251	259	26	1−r	1−r	NUM
ejpam-6251	259	27	,	,	PUNCT
ejpam-6251	259	28	ψ(ς,ϖ	ψ(ς,ϖ	X
ejpam-6251	259	29	,	,	PUNCT
ejpam-6251	259	30	ż0	ż0	NOUN
ejpam-6251	259	31	)	)	PUNCT
ejpam-6251	259	32	<	<	X
ejpam-6251	259	33	r	r	NOUN
ejpam-6251	259	34	,	,	PUNCT
ejpam-6251	259	35	ξ(ς,ϖ	ξ(ς,ϖ	NOUN
ejpam-6251	259	36	,	,	PUNCT
ejpam-6251	259	37	ż0	ż0	NOUN
ejpam-6251	259	38	)	)	PUNCT
ejpam-6251	259	39	<	<	X
ejpam-6251	259	40	r	r	NOUN
ejpam-6251	259	41	because	because	SCONJ
ejpam-6251	259	42	of	of	ADP
ejpam-6251	259	43	π(ς,ϖ	π(ς,ϖ	PRON
ejpam-6251	259	44	,	,	PUNCT
ejpam-6251	259	45	ż	ż	NOUN
ejpam-6251	259	46	)	)	PUNCT
ejpam-6251	259	47	>	>	X
ejpam-6251	260	1	1−r	1−r	NUM
ejpam-6251	260	2	.	.	PUNCT
ejpam-6251	261	1	if	if	SCONJ
ejpam-6251	261	2	we	we	PRON
ejpam-6251	261	3	take	take	VERB
ejpam-6251	261	4	r0	r0	NOUN
ejpam-6251	261	5	=	=	PUNCT
ejpam-6251	261	6	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	261	7	,	,	PUNCT
ejpam-6251	261	8	ż0	ż0	NOUN
ejpam-6251	261	9	)	)	PUNCT
ejpam-6251	261	10	,	,	PUNCT
ejpam-6251	261	11	then	then	ADV
ejpam-6251	261	12	for	for	ADP
ejpam-6251	261	13	r0	r0	PROPN
ejpam-6251	261	14	>	>	X
ejpam-6251	261	15	1−r	1−r	NUM
ejpam-6251	261	16	,	,	PUNCT
ejpam-6251	261	17	θ	θ	PROPN
ejpam-6251	261	18	∈	∈	PROPN
ejpam-6251	261	19	(	(	PUNCT
ejpam-6251	261	20	0	0	NUM
ejpam-6251	261	21	,	,	PUNCT
ejpam-6251	261	22	1	1	NUM
ejpam-6251	261	23	)	)	PUNCT
ejpam-6251	261	24	will	will	AUX
ejpam-6251	261	25	exist	exist	VERB
ejpam-6251	261	26	such	such	ADJ
ejpam-6251	261	27	that	that	DET
ejpam-6251	261	28	r0	r0	NOUN
ejpam-6251	261	29	>	>	X
ejpam-6251	261	30	1−θ	1−θ	PROPN
ejpam-6251	261	31	>	>	X
ejpam-6251	261	32	1−r	1−r	NUM
ejpam-6251	261	33	.	.	PUNCT
ejpam-6251	262	1	give	give	VERB
ejpam-6251	262	2	r0	r0	NOUN
ejpam-6251	262	3	and	and	CCONJ
ejpam-6251	262	4	θ	θ	NOUN
ejpam-6251	262	5	such	such	ADJ
ejpam-6251	262	6	that	that	DET
ejpam-6251	262	7	r0	r0	NOUN
ejpam-6251	262	8	>	>	X
ejpam-6251	262	9	1−θ	1−θ	PROPN
ejpam-6251	262	10	.	.	PUNCT
ejpam-6251	263	1	then	then	ADV
ejpam-6251	263	2	,	,	PUNCT
ejpam-6251	263	3	r1	r1	PROPN
ejpam-6251	263	4	,	,	PUNCT
ejpam-6251	263	5	r2	r2	PROPN
ejpam-6251	263	6	,	,	PUNCT
ejpam-6251	263	7	r3	r3	PROPN
ejpam-6251	263	8	∈	∈	PROPN
ejpam-6251	263	9	(	(	PUNCT
ejpam-6251	263	10	0	0	NUM
ejpam-6251	263	11	,	,	PUNCT
ejpam-6251	263	12	1	1	NUM
ejpam-6251	263	13	)	)	PUNCT
ejpam-6251	263	14	will	will	AUX
ejpam-6251	263	15	exist	exist	VERB
ejpam-6251	263	16	such	such	ADJ
ejpam-6251	263	17	that	that	DET
ejpam-6251	263	18	r0⋇	r0⋇	PROPN
ejpam-6251	263	19	r1	r1	PROPN
ejpam-6251	263	20	>	>	X
ejpam-6251	263	21	1−θ	1−θ	PROPN
ejpam-6251	263	22	,	,	PUNCT
ejpam-6251	263	23	(	(	PUNCT
ejpam-6251	263	24	1−	1−	NUM
ejpam-6251	263	25	r0)⋄	r0)⋄	NOUN
ejpam-6251	263	26	(	(	PUNCT
ejpam-6251	263	27	1−	1−	NUM
ejpam-6251	263	28	r2	r2	NOUN
ejpam-6251	263	29	)	)	PUNCT
ejpam-6251	263	30	≤	≤	NUM
ejpam-6251	263	31	θ	θ	PROPN
ejpam-6251	263	32	and	and	CCONJ
ejpam-6251	263	33	(	(	PUNCT
ejpam-6251	263	34	1	1	NUM
ejpam-6251	263	35	−	−	NOUN
ejpam-6251	263	36	r0	r0	NOUN
ejpam-6251	263	37	)	)	PUNCT
ejpam-6251	263	38	⋄	⋄	NOUN
ejpam-6251	263	39	(	(	PUNCT
ejpam-6251	263	40	1	1	NUM
ejpam-6251	263	41	−	−	PROPN
ejpam-6251	263	42	r3	r3	PROPN
ejpam-6251	263	43	)	)	PUNCT
ejpam-6251	264	1	≤	≤	NUM
ejpam-6251	264	2	θ	θ	PROPN
ejpam-6251	264	3	.	.	PUNCT
ejpam-6251	264	4	choose	choose	VERB
ejpam-6251	264	5	r4	r4	NOUN
ejpam-6251	264	6	=	=	PROPN
ejpam-6251	264	7	max{r1	max{r1	NOUN
ejpam-6251	264	8	,	,	PUNCT
ejpam-6251	264	9	r2	r2	PROPN
ejpam-6251	264	10	,	,	PUNCT
ejpam-6251	264	11	r3	r3	PROPN
ejpam-6251	264	12	}	}	PUNCT
ejpam-6251	264	13	.	.	PUNCT
ejpam-6251	265	1	consider	consider	VERB
ejpam-6251	265	2	the	the	DET
ejpam-6251	265	3	right	right	ADJ
ejpam-6251	265	4	open	open	ADJ
ejpam-6251	265	5	ball	ball	PROPN
ejpam-6251	265	6	b(ϖ	b(ϖ	NOUN
ejpam-6251	265	7	,	,	PUNCT
ejpam-6251	265	8	1	1	NUM
ejpam-6251	265	9	−	−	NOUN
ejpam-6251	265	10	r4	r4	NOUN
ejpam-6251	265	11	,	,	PUNCT
ejpam-6251	265	12	ż	ż	NOUN
ejpam-6251	265	13	−	−	PROPN
ejpam-6251	265	14	ż0	ż0	PROPN
ejpam-6251	265	15	)	)	PUNCT
ejpam-6251	265	16	.	.	PUNCT
ejpam-6251	266	1	we	we	PRON
ejpam-6251	266	2	will	will	AUX
ejpam-6251	266	3	show	show	VERB
ejpam-6251	266	4	that	that	SCONJ
ejpam-6251	266	5	b(ϖ	b(ϖ	NOUN
ejpam-6251	266	6	,	,	PUNCT
ejpam-6251	266	7	1	1	NUM
ejpam-6251	266	8	−	−	NOUN
ejpam-6251	266	9	r4	r4	NOUN
ejpam-6251	266	10	,	,	PUNCT
ejpam-6251	266	11	ż	ż	NOUN
ejpam-6251	266	12	−	−	PROPN
ejpam-6251	266	13	ż0	ż0	PROPN
ejpam-6251	266	14	)	)	PUNCT
ejpam-6251	266	15	⊂	⊂	PROPN
ejpam-6251	267	1	b(ς	b(ς	PROPN
ejpam-6251	267	2	,	,	PUNCT
ejpam-6251	267	3	r	r	NOUN
ejpam-6251	267	4	,	,	PUNCT
ejpam-6251	267	5	ż	ż	NOUN
ejpam-6251	267	6	)	)	PUNCT
ejpam-6251	267	7	.	.	PUNCT
ejpam-6251	268	1	if	if	SCONJ
ejpam-6251	268	2	we	we	PRON
ejpam-6251	268	3	take	take	VERB
ejpam-6251	268	4	θ1	θ1	NOUN
ejpam-6251	268	5	∈	∈	PROPN
ejpam-6251	268	6	b(ϖ	b(ϖ	NOUN
ejpam-6251	268	7	,	,	PUNCT
ejpam-6251	268	8	1−r4	1−r4	NUM
ejpam-6251	268	9	,	,	PUNCT
ejpam-6251	268	10	ż−	ż−	NOUN
ejpam-6251	268	11	ż0	ż0	NOUN
ejpam-6251	268	12	)	)	PUNCT
ejpam-6251	268	13	,	,	PUNCT
ejpam-6251	268	14	then	then	ADV
ejpam-6251	268	15	π(ϖ	π(ϖ	PROPN
ejpam-6251	268	16	,	,	PUNCT
ejpam-6251	268	17	θ1	θ1	NOUN
ejpam-6251	268	18	,	,	PUNCT
ejpam-6251	268	19	ż−	ż−	NOUN
ejpam-6251	268	20	ż0	ż0	PROPN
ejpam-6251	268	21	)	)	PUNCT
ejpam-6251	268	22	>	>	X
ejpam-6251	268	23	r4,ψ(ϖ	r4,ψ(ϖ	NOUN
ejpam-6251	268	24	,	,	PUNCT
ejpam-6251	268	25	θ1	θ1	NOUN
ejpam-6251	268	26	,	,	PUNCT
ejpam-6251	268	27	ż−	ż−	NOUN
ejpam-6251	268	28	ż0	ż0	NOUN
ejpam-6251	268	29	)	)	PUNCT
ejpam-6251	268	30	<	<	X
ejpam-6251	268	31	r4,ξ(ϖ	r4,ξ(ϖ	PROPN
ejpam-6251	268	32	,	,	PUNCT
ejpam-6251	268	33	θ1	θ1	NOUN
ejpam-6251	268	34	,	,	PUNCT
ejpam-6251	268	35	ż−	ż−	NOUN
ejpam-6251	268	36	ż0	ż0	PROPN
ejpam-6251	268	37	)	)	PUNCT
ejpam-6251	268	38	<	<	X
ejpam-6251	268	39	r4	r4	PROPN
ejpam-6251	268	40	.	.	PUNCT
ejpam-6251	269	1	then	then	ADV
ejpam-6251	269	2	,	,	PUNCT
ejpam-6251	269	3	π(ς	π(ς	PROPN
ejpam-6251	269	4	,	,	PUNCT
ejpam-6251	269	5	θ1	θ1	NOUN
ejpam-6251	269	6	,	,	PUNCT
ejpam-6251	269	7	ż	ż	NOUN
ejpam-6251	269	8	)	)	PUNCT
ejpam-6251	269	9	≥	≥	NOUN
ejpam-6251	269	10	π(ς,ϖ	π(ς,ϖ	NOUN
ejpam-6251	269	11	,	,	PUNCT
ejpam-6251	269	12	ż0)⋇π(ϖ	ż0)⋇π(ϖ	NOUN
ejpam-6251	269	13	,	,	PUNCT
ejpam-6251	269	14	θ1	θ1	NOUN
ejpam-6251	269	15	,	,	PUNCT
ejpam-6251	269	16	ż−	ż−	NOUN
ejpam-6251	269	17	ż0	ż0	PROPN
ejpam-6251	269	18	)	)	PUNCT
ejpam-6251	269	19	≥	≥	NOUN
ejpam-6251	269	20	r0	r0	NOUN
ejpam-6251	269	21	⋇	⋇	NOUN
ejpam-6251	269	22	r4	r4	VERB
ejpam-6251	269	23	≥	≥	NUM
ejpam-6251	269	24	r0	r0	NOUN
ejpam-6251	269	25	⋇	⋇	NOUN
ejpam-6251	269	26	r1	r1	PROPN
ejpam-6251	269	27	≥	≥	NUM
ejpam-6251	269	28	1−	1−	NUM
ejpam-6251	269	29	θ	θ	SYM
ejpam-6251	269	30	>	>	X
ejpam-6251	269	31	1−	1−	NUM
ejpam-6251	269	32	r	r	NOUN
ejpam-6251	269	33	,	,	PUNCT
ejpam-6251	269	34	ψ(ς	ψ(ς	NOUN
ejpam-6251	269	35	,	,	PUNCT
ejpam-6251	269	36	θ1	θ1	NOUN
ejpam-6251	269	37	,	,	PUNCT
ejpam-6251	269	38	ż	ż	NOUN
ejpam-6251	269	39	)	)	PUNCT
ejpam-6251	269	40	≤	≤	NUM
ejpam-6251	269	41	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	269	42	,	,	PUNCT
ejpam-6251	269	43	ż0)	ż0)	PROPN
ejpam-6251	269	44	♢	♢	PART
ejpam-6251	269	45	ψ(ϖ	ψ(ϖ	NOUN
ejpam-6251	269	46	,	,	PUNCT
ejpam-6251	269	47	θ1	θ1	NOUN
ejpam-6251	269	48	,	,	PUNCT
ejpam-6251	269	49	ż−	ż−	NOUN
ejpam-6251	269	50	ż0	ż0	PROPN
ejpam-6251	269	51	)	)	PUNCT
ejpam-6251	269	52	≤	≤	NOUN
ejpam-6251	269	53	(	(	PUNCT
ejpam-6251	269	54	1−	1−	NUM
ejpam-6251	269	55	r0)	r0)	PROPN
ejpam-6251	269	56	♢	♢	PROPN
ejpam-6251	269	57	(1−	(1−	PROPN
ejpam-6251	269	58	r4	r4	PROPN
ejpam-6251	269	59	)	)	PUNCT
ejpam-6251	269	60	≤	≤	NOUN
ejpam-6251	269	61	(	(	PUNCT
ejpam-6251	269	62	1−	1−	NUM
ejpam-6251	269	63	r0)	r0)	PROPN
ejpam-6251	269	64	♢	♢	PROPN
ejpam-6251	269	65	(1−	(1−	PROPN
ejpam-6251	269	66	r2	r2	PROPN
ejpam-6251	269	67	)	)	PUNCT
ejpam-6251	269	68	≤	≤	PUNCT
ejpam-6251	270	1	θ	θ	NOUN
ejpam-6251	270	2	<	<	X
ejpam-6251	270	3	r	r	NOUN
ejpam-6251	270	4	,	,	PUNCT
ejpam-6251	270	5	ξ(ς	ξ(ς	NOUN
ejpam-6251	270	6	,	,	PUNCT
ejpam-6251	270	7	θ1	θ1	NOUN
ejpam-6251	270	8	,	,	PUNCT
ejpam-6251	270	9	ż	ż	NOUN
ejpam-6251	270	10	)	)	PUNCT
ejpam-6251	270	11	≤	≤	NOUN
ejpam-6251	270	12	ξ(ς,ϖ	ξ(ς,ϖ	ADP
ejpam-6251	270	13	,	,	PUNCT
ejpam-6251	270	14	ż0)	ż0)	PROPN
ejpam-6251	270	15	♢	♢	PROPN
ejpam-6251	270	16	ξ(ϖ	ξ(ϖ	PROPN
ejpam-6251	270	17	,	,	PUNCT
ejpam-6251	270	18	θ1	θ1	NOUN
ejpam-6251	270	19	,	,	PUNCT
ejpam-6251	270	20	ż−	ż−	NOUN
ejpam-6251	270	21	ż0	ż0	PROPN
ejpam-6251	270	22	)	)	PUNCT
ejpam-6251	270	23	≤	≤	NOUN
ejpam-6251	270	24	(	(	PUNCT
ejpam-6251	270	25	1−	1−	NUM
ejpam-6251	270	26	r0)	r0)	PROPN
ejpam-6251	270	27	♢	♢	PROPN
ejpam-6251	270	28	(1−	(1−	PROPN
ejpam-6251	270	29	r4	r4	PROPN
ejpam-6251	270	30	)	)	PUNCT
ejpam-6251	270	31	≤	≤	NOUN
ejpam-6251	270	32	(	(	PUNCT
ejpam-6251	270	33	1−	1−	NUM
ejpam-6251	270	34	r0)	r0)	PROPN
ejpam-6251	270	35	♢	♢	PROPN
ejpam-6251	270	36	(1−	(1−	PROPN
ejpam-6251	270	37	r2	r2	PROPN
ejpam-6251	270	38	)	)	PUNCT
ejpam-6251	270	39	≤	≤	PUNCT
ejpam-6251	271	1	θ	θ	X
ejpam-6251	271	2	<	<	X
ejpam-6251	271	3	r.	r.	PROPN
ejpam-6251	271	4	therefore	therefore	ADV
ejpam-6251	271	5	θ1	θ1	PROPN
ejpam-6251	271	6	∈	∈	PROPN
ejpam-6251	271	7	b(ς	b(ς	PROPN
ejpam-6251	271	8	,	,	PUNCT
ejpam-6251	271	9	r	r	NOUN
ejpam-6251	271	10	,	,	PUNCT
ejpam-6251	271	11	ż	ż	NOUN
ejpam-6251	271	12	)	)	PUNCT
ejpam-6251	271	13	.	.	PUNCT
ejpam-6251	272	1	similarly	similarly	ADV
ejpam-6251	272	2	,	,	PUNCT
ejpam-6251	272	3	we	we	PRON
ejpam-6251	272	4	can	can	AUX
ejpam-6251	272	5	prove	prove	VERB
ejpam-6251	272	6	the	the	DET
ejpam-6251	272	7	following	follow	VERB
ejpam-6251	272	8	theorems	theorem	NOUN
ejpam-6251	272	9	.	.	PUNCT
ejpam-6251	273	1	theorem	theorem	NOUN
ejpam-6251	273	2	2	2	NUM
ejpam-6251	273	3	.	.	PUNCT
ejpam-6251	274	1	every	every	PRON
ejpam-6251	274	2	left	leave	VERB
ejpam-6251	274	3	open	open	ADJ
ejpam-6251	274	4	ball	ball	PROPN
ejpam-6251	274	5	b(ϖ	b(ϖ	NOUN
ejpam-6251	274	6	,	,	PUNCT
ejpam-6251	274	7	r	r	NOUN
ejpam-6251	274	8	,	,	PUNCT
ejpam-6251	274	9	ż	ż	NOUN
ejpam-6251	274	10	)	)	PUNCT
ejpam-6251	274	11	is	be	AUX
ejpam-6251	274	12	a	a	DET
ejpam-6251	274	13	left	left	ADJ
ejpam-6251	274	14	open	open	ADJ
ejpam-6251	274	15	set	set	NOUN
ejpam-6251	274	16	.	.	PUNCT
ejpam-6251	275	1	theorem	theorem	VERB
ejpam-6251	275	2	3	3	NUM
ejpam-6251	275	3	.	.	PUNCT
ejpam-6251	276	1	every	every	DET
ejpam-6251	276	2	open	open	ADJ
ejpam-6251	276	3	ball	ball	NOUN
ejpam-6251	276	4	is	be	AUX
ejpam-6251	276	5	an	an	DET
ejpam-6251	276	6	open	open	ADJ
ejpam-6251	276	7	set	set	NOUN
ejpam-6251	276	8	.	.	PUNCT
ejpam-6251	277	1	remark	remark	PROPN
ejpam-6251	277	2	2	2	NUM
ejpam-6251	277	3	.	.	PUNCT
ejpam-6251	278	1	we	we	PRON
ejpam-6251	278	2	can	can	AUX
ejpam-6251	278	3	say	say	VERB
ejpam-6251	278	4	that	that	SCONJ
ejpam-6251	278	5	τp	τp	PROPN
ejpam-6251	278	6	=	=	X
ejpam-6251	278	7	{	{	PUNCT
ejpam-6251	278	8	g	g	PROPN
ejpam-6251	278	9	⊂	⊂	PROPN
ejpam-6251	278	10	𭟋	𭟋	ADP
ejpam-6251	278	11	:	:	PUNCT
ejpam-6251	278	12	there	there	PRON
ejpam-6251	278	13	exist	exist	VERB
ejpam-6251	278	14	ż	ż	PROPN
ejpam-6251	278	15	>	>	X
ejpam-6251	278	16	0	0	PUNCT
ejpam-6251	279	1	and	and	CCONJ
ejpam-6251	279	2	r	r	PROPN
ejpam-6251	279	3	∈	∈	PROPN
ejpam-6251	279	4	(	(	PUNCT
ejpam-6251	279	5	0	0	NUM
ejpam-6251	279	6	,	,	PUNCT
ejpam-6251	279	7	1	1	NUM
ejpam-6251	279	8	)	)	PUNCT
ejpam-6251	279	9	such	such	ADJ
ejpam-6251	279	10	that	that	SCONJ
ejpam-6251	279	11	b(ς	b(ς	PROPN
ejpam-6251	279	12	,	,	PUNCT
ejpam-6251	279	13	r	r	NOUN
ejpam-6251	279	14	,	,	PUNCT
ejpam-6251	279	15	ż	ż	NOUN
ejpam-6251	279	16	)	)	PUNCT
ejpam-6251	279	17	⊆	⊆	NUM
ejpam-6251	279	18	g	g	NOUN
ejpam-6251	279	19	for	for	ADP
ejpam-6251	279	20	each	each	DET
ejpam-6251	279	21	ς	ς	PROPN
ejpam-6251	279	22	∈	∈	PROPN
ejpam-6251	279	23	g}×{h	g}×{h	NOUN
ejpam-6251	279	24	⊂	⊂	ADJ
ejpam-6251	279	25	s	s	VERB
ejpam-6251	279	26	:	:	PUNCT
ejpam-6251	279	27	there	there	PRON
ejpam-6251	279	28	exist	exist	VERB
ejpam-6251	279	29	ż	ż	NOUN
ejpam-6251	279	30	>	>	X
ejpam-6251	279	31	0	0	PUNCT
ejpam-6251	280	1	and	and	CCONJ
ejpam-6251	280	2	r	r	PROPN
ejpam-6251	280	3	∈	∈	PROPN
ejpam-6251	280	4	(	(	PUNCT
ejpam-6251	280	5	0	0	NUM
ejpam-6251	280	6	,	,	PUNCT
ejpam-6251	280	7	1	1	NUM
ejpam-6251	280	8	)	)	PUNCT
ejpam-6251	280	9	such	such	ADJ
ejpam-6251	280	10	that	that	SCONJ
ejpam-6251	280	11	b(ϖ	b(ϖ	NOUN
ejpam-6251	280	12	,	,	PUNCT
ejpam-6251	280	13	r	r	NOUN
ejpam-6251	280	14	,	,	PUNCT
ejpam-6251	280	15	ż	ż	NOUN
ejpam-6251	280	16	)	)	PUNCT
ejpam-6251	280	17	⊆	⊆	NUM
ejpam-6251	280	18	g	g	NOUN
ejpam-6251	280	19	for	for	ADP
ejpam-6251	280	20	each	each	DET
ejpam-6251	280	21	ϖ	ϖ	PROPN
ejpam-6251	280	22	∈	∈	PROPN
ejpam-6251	280	23	h	h	NOUN
ejpam-6251	280	24	}	}	PUNCT
ejpam-6251	280	25	is	be	AUX
ejpam-6251	280	26	a	a	DET
ejpam-6251	280	27	product	product	NOUN
ejpam-6251	280	28	topology	topology	NOUN
ejpam-6251	280	29	on	on	ADP
ejpam-6251	280	30	𭟋×s	𭟋×s	PROPN
ejpam-6251	280	31	.	.	PUNCT
ejpam-6251	281	1	in	in	ADP
ejpam-6251	281	2	that	that	DET
ejpam-6251	281	3	case	case	NOUN
ejpam-6251	281	4	every	every	DET
ejpam-6251	281	5	nbms	nbms	NOUN
ejpam-6251	281	6	p	p	NOUN
ejpam-6251	281	7	on	on	ADP
ejpam-6251	281	8	𭟋×s	𭟋×s	PUNCT
ejpam-6251	281	9	produces	produce	VERB
ejpam-6251	281	10	a	a	DET
ejpam-6251	281	11	product	product	NOUN
ejpam-6251	281	12	topology	topology	NOUN
ejpam-6251	281	13	τp	τp	NOUN
ejpam-6251	281	14	on	on	ADP
ejpam-6251	281	15	𭟋×	𭟋×	PROPN
ejpam-6251	281	16	s	s	PART
ejpam-6251	281	17	which	which	PRON
ejpam-6251	281	18	has	have	VERB
ejpam-6251	281	19	a	a	DET
ejpam-6251	281	20	base	base	NOUN
ejpam-6251	281	21	the	the	DET
ejpam-6251	281	22	family	family	NOUN
ejpam-6251	281	23	of	of	ADP
ejpam-6251	281	24	open	open	ADJ
ejpam-6251	281	25	sets	set	NOUN
ejpam-6251	281	26	.	.	PUNCT
ejpam-6251	282	1	theorem	theorem	ADJ
ejpam-6251	282	2	4	4	NUM
ejpam-6251	282	3	.	.	PUNCT
ejpam-6251	283	1	every	every	DET
ejpam-6251	283	2	nbms	nbms	NOUN
ejpam-6251	283	3	is	be	AUX
ejpam-6251	283	4	hausdorff	hausdorff	NOUN
ejpam-6251	283	5	.	.	PUNCT
ejpam-6251	284	1	proof	proof	NOUN
ejpam-6251	284	2	.	.	PUNCT
ejpam-6251	285	1	let	let	VERB
ejpam-6251	285	2	(	(	PUNCT
ejpam-6251	285	3	𭟋	𭟋	NOUN
ejpam-6251	285	4	,	,	PUNCT
ejpam-6251	285	5	s	s	PROPN
ejpam-6251	285	6	,	,	PUNCT
ejpam-6251	285	7	π	π	PROPN
ejpam-6251	285	8	,	,	PUNCT
ejpam-6251	285	9	ψ	ψ	PROPN
ejpam-6251	285	10	,	,	PUNCT
ejpam-6251	285	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	285	12	,	,	PUNCT
ejpam-6251	285	13	♢	♢	PROPN
ejpam-6251	285	14	)	)	PUNCT
ejpam-6251	285	15	is	be	AUX
ejpam-6251	285	16	a	a	DET
ejpam-6251	285	17	nbms	nbms	NOUN
ejpam-6251	285	18	.	.	PUNCT
ejpam-6251	286	1	choose	choose	VERB
ejpam-6251	286	2	ς	ς	PROPN
ejpam-6251	286	3	and	and	CCONJ
ejpam-6251	286	4	ϖ	ϖ	PROPN
ejpam-6251	286	5	as	as	ADP
ejpam-6251	286	6	two	two	NUM
ejpam-6251	286	7	distinct	distinct	ADJ
ejpam-6251	286	8	points	point	NOUN
ejpam-6251	286	9	in	in	ADP
ejpam-6251	286	10	𭟋	𭟋	NOUN
ejpam-6251	286	11	and	and	CCONJ
ejpam-6251	286	12	s.	s.	PROPN
ejpam-6251	286	13	hence	hence	ADV
ejpam-6251	286	14	,	,	PUNCT
ejpam-6251	286	15	0	0	PUNCT
ejpam-6251	286	16	<	<	X
ejpam-6251	286	17	π(ς,ϖ	π(ς,ϖ	NUM
ejpam-6251	286	18	,	,	PUNCT
ejpam-6251	286	19	ż	ż	NOUN
ejpam-6251	286	20	)	)	PUNCT
ejpam-6251	286	21	<	<	X
ejpam-6251	287	1	1	1	NUM
ejpam-6251	287	2	,	,	PUNCT
ejpam-6251	287	3	0	0	NUM
ejpam-6251	287	4	<	<	X
ejpam-6251	287	5	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	287	6	,	,	PUNCT
ejpam-6251	287	7	ż	ż	NOUN
ejpam-6251	287	8	)	)	PUNCT
ejpam-6251	287	9	<	<	X
ejpam-6251	287	10	1	1	NUM
ejpam-6251	287	11	,	,	PUNCT
ejpam-6251	287	12	0	0	NUM
ejpam-6251	287	13	<	<	X
ejpam-6251	287	14	ξ(ς,ϖ	ξ(ς,ϖ	X
ejpam-6251	287	15	,	,	PUNCT
ejpam-6251	287	16	ż	ż	NOUN
ejpam-6251	287	17	)	)	PUNCT
ejpam-6251	287	18	<	<	X
ejpam-6251	287	19	1	1	X
ejpam-6251	287	20	.	.	X
ejpam-6251	287	21	take	take	VERB
ejpam-6251	287	22	r.	r.	PROPN
ejpam-6251	287	23	ramaswamy	ramaswamy	PROPN
ejpam-6251	287	24	/	/	SYM
ejpam-6251	287	25	eur	eur	PROPN
ejpam-6251	287	26	.	.	PUNCT
ejpam-6251	288	1	j.	j.	PROPN
ejpam-6251	288	2	pure	pure	PROPN
ejpam-6251	288	3	appl	appl	PROPN
ejpam-6251	288	4	.	.	PROPN
ejpam-6251	288	5	math	math	PROPN
ejpam-6251	288	6	,	,	PUNCT
ejpam-6251	288	7	18	18	NUM
ejpam-6251	288	8	(	(	PUNCT
ejpam-6251	288	9	4	4	NUM
ejpam-6251	288	10	)	)	PUNCT
ejpam-6251	288	11	(	(	PUNCT
ejpam-6251	288	12	2025	2025	NUM
ejpam-6251	288	13	)	)	PUNCT
ejpam-6251	288	14	,	,	PUNCT
ejpam-6251	288	15	6251	6251	NUM
ejpam-6251	288	16	11	11	NUM
ejpam-6251	288	17	of	of	ADP
ejpam-6251	288	18	40	40	NUM
ejpam-6251	288	19	r1	r1	NOUN
ejpam-6251	288	20	=	=	PUNCT
ejpam-6251	288	21	π(ς,ϖ	π(ς,ϖ	NOUN
ejpam-6251	288	22	,	,	PUNCT
ejpam-6251	288	23	ż	ż	NOUN
ejpam-6251	288	24	)	)	PUNCT
ejpam-6251	288	25	,	,	PUNCT
ejpam-6251	288	26	r2	r2	PROPN
ejpam-6251	288	27	=	=	SYM
ejpam-6251	288	28	ψ(ς,ϖ	ψ(ς,ϖ	PROPN
ejpam-6251	288	29	,	,	PUNCT
ejpam-6251	288	30	ż	ż	NOUN
ejpam-6251	288	31	)	)	PUNCT
ejpam-6251	288	32	,	,	PUNCT
ejpam-6251	288	33	r3	r3	PROPN
ejpam-6251	288	34	=	=	SYM
ejpam-6251	288	35	ξ(ς,ϖ	ξ(ς,ϖ	NOUN
ejpam-6251	288	36	,	,	PUNCT
ejpam-6251	288	37	ż	ż	NOUN
ejpam-6251	288	38	)	)	PUNCT
ejpam-6251	288	39	and	and	CCONJ
ejpam-6251	288	40	r	r	NOUN
ejpam-6251	288	41	=	=	PUNCT
ejpam-6251	288	42	max{r1	max{r1	NOUN
ejpam-6251	288	43	,	,	PUNCT
ejpam-6251	288	44	1	1	NUM
ejpam-6251	288	45	−	−	NOUN
ejpam-6251	288	46	r2	r2	NOUN
ejpam-6251	288	47	,	,	PUNCT
ejpam-6251	288	48	1	1	NUM
ejpam-6251	288	49	−	−	PROPN
ejpam-6251	288	50	r3	r3	PROPN
ejpam-6251	288	51	}	}	PUNCT
ejpam-6251	288	52	.	.	PUNCT
ejpam-6251	289	1	if	if	SCONJ
ejpam-6251	289	2	we	we	PRON
ejpam-6251	289	3	take	take	VERB
ejpam-6251	289	4	r0	r0	NOUN
ejpam-6251	289	5	∈	∈	PROPN
ejpam-6251	289	6	(	(	PUNCT
ejpam-6251	289	7	r	r	NOUN
ejpam-6251	289	8	,	,	PUNCT
ejpam-6251	289	9	1	1	NUM
ejpam-6251	289	10	)	)	PUNCT
ejpam-6251	289	11	,	,	PUNCT
ejpam-6251	289	12	then	then	ADV
ejpam-6251	289	13	there	there	PRON
ejpam-6251	289	14	exist	exist	VERB
ejpam-6251	289	15	r4	r4	NOUN
ejpam-6251	289	16	,	,	PUNCT
ejpam-6251	289	17	r5	r5	PROPN
ejpam-6251	289	18	,	,	PUNCT
ejpam-6251	289	19	r6	r6	VERB
ejpam-6251	289	20	such	such	ADJ
ejpam-6251	289	21	that	that	SCONJ
ejpam-6251	289	22	r4	r4	PROPN
ejpam-6251	289	23	⋇	⋇	NOUN
ejpam-6251	289	24	r4	r4	VERB
ejpam-6251	289	25	≥	≥	NUM
ejpam-6251	289	26	r0	r0	NOUN
ejpam-6251	289	27	,	,	PUNCT
ejpam-6251	289	28	(	(	PUNCT
ejpam-6251	289	29	1	1	NUM
ejpam-6251	289	30	−	−	PROPN
ejpam-6251	289	31	r5)	r5)	NOUN
ejpam-6251	289	32	♢	♢	PROPN
ejpam-6251	289	33	(1	(1	PROPN
ejpam-6251	289	34	−	−	PROPN
ejpam-6251	289	35	r5	r5	PROPN
ejpam-6251	289	36	)	)	PUNCT
ejpam-6251	289	37	≤	≤	NOUN
ejpam-6251	289	38	1−	1−	NUM
ejpam-6251	289	39	r0,(1−	r0,(1−	PROPN
ejpam-6251	289	40	r6)	r6)	PROPN
ejpam-6251	289	41	♢	♢	PROPN
ejpam-6251	289	42	(1−	(1−	PROPN
ejpam-6251	289	43	r6	r6	PROPN
ejpam-6251	289	44	)	)	PUNCT
ejpam-6251	289	45	≤	≤	NOUN
ejpam-6251	289	46	1−	1−	NUM
ejpam-6251	289	47	r0	r0	NOUN
ejpam-6251	289	48	.	.	PUNCT
ejpam-6251	290	1	let	let	VERB
ejpam-6251	290	2	r7	r7	PROPN
ejpam-6251	290	3	=	=	SYM
ejpam-6251	290	4	max{r4	max{r4	X
ejpam-6251	290	5	,	,	PUNCT
ejpam-6251	290	6	r5	r5	PROPN
ejpam-6251	290	7	,	,	PUNCT
ejpam-6251	290	8	r6	r6	NOUN
ejpam-6251	290	9	}	}	PUNCT
ejpam-6251	290	10	.	.	PUNCT
ejpam-6251	291	1	if	if	SCONJ
ejpam-6251	291	2	we	we	PRON
ejpam-6251	291	3	consider	consider	VERB
ejpam-6251	291	4	the	the	DET
ejpam-6251	291	5	right	right	ADJ
ejpam-6251	291	6	open	open	ADJ
ejpam-6251	291	7	ball	ball	PROPN
ejpam-6251	291	8	b(ς	b(ς	PROPN
ejpam-6251	291	9	,	,	PUNCT
ejpam-6251	291	10	r7	r7	NOUN
ejpam-6251	291	11	,	,	PUNCT
ejpam-6251	291	12	ż2	ż2	PROPN
ejpam-6251	291	13	)	)	PUNCT
ejpam-6251	291	14	and	and	CCONJ
ejpam-6251	291	15	left	leave	VERB
ejpam-6251	291	16	open	open	ADJ
ejpam-6251	291	17	ball	ball	PROPN
ejpam-6251	291	18	b(ϖ	b(ϖ	NOUN
ejpam-6251	291	19	,	,	PUNCT
ejpam-6251	291	20	r7	r7	NOUN
ejpam-6251	291	21	,	,	PUNCT
ejpam-6251	291	22	ż2	ż2	PROPN
ejpam-6251	291	23	)	)	PUNCT
ejpam-6251	291	24	,	,	PUNCT
ejpam-6251	291	25	then	then	ADV
ejpam-6251	291	26	clearly	clearly	ADV
ejpam-6251	291	27	b(ς	b(ς	PROPN
ejpam-6251	291	28	,	,	PUNCT
ejpam-6251	291	29	r7	r7	NOUN
ejpam-6251	291	30	,	,	PUNCT
ejpam-6251	291	31	ż2)∩b(ϖ	ż2)∩b(ϖ	PROPN
ejpam-6251	291	32	,	,	PUNCT
ejpam-6251	291	33	r7	r7	NOUN
ejpam-6251	291	34	,	,	PUNCT
ejpam-6251	291	35	ż2	ż2	PROPN
ejpam-6251	291	36	)	)	PUNCT
ejpam-6251	291	37	=	=	VERB
ejpam-6251	291	38	∅.	∅.	NOUN
ejpam-6251	291	39	suppose	suppose	VERB
ejpam-6251	291	40	that	that	SCONJ
ejpam-6251	291	41	θ1	θ1	PROPN
ejpam-6251	291	42	∈	∈	PROPN
ejpam-6251	291	43	b(ς	b(ς	PROPN
ejpam-6251	291	44	,	,	PUNCT
ejpam-6251	291	45	r7	r7	PROPN
ejpam-6251	291	46	,	,	PUNCT
ejpam-6251	291	47	ż2	ż2	NOUN
ejpam-6251	291	48	)	)	PUNCT
ejpam-6251	291	49	∩	∩	ADJ
ejpam-6251	291	50	b(ϖ	b(ϖ	PROPN
ejpam-6251	291	51	,	,	PUNCT
ejpam-6251	291	52	r7	r7	NOUN
ejpam-6251	291	53	,	,	PUNCT
ejpam-6251	291	54	ż2	ż2	PROPN
ejpam-6251	291	55	)	)	PUNCT
ejpam-6251	291	56	,	,	PUNCT
ejpam-6251	291	57	then	then	ADV
ejpam-6251	291	58	r1	r1	PROPN
ejpam-6251	291	59	=	=	PUNCT
ejpam-6251	291	60	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	291	61	,	,	PUNCT
ejpam-6251	291	62	ż	ż	NOUN
ejpam-6251	291	63	)	)	PUNCT
ejpam-6251	291	64	≥	≥	NOUN
ejpam-6251	291	65	π(ς	π(ς	PROPN
ejpam-6251	291	66	,	,	PUNCT
ejpam-6251	291	67	θ1	θ1	NOUN
ejpam-6251	291	68	,	,	PUNCT
ejpam-6251	291	69	ż	ż	NOUN
ejpam-6251	291	70	2	2	NUM
ejpam-6251	291	71	)	)	PUNCT
ejpam-6251	291	72	⋇π(θ1	⋇π(θ1	PROPN
ejpam-6251	291	73	,	,	PUNCT
ejpam-6251	291	74	ϖ	ϖ	PROPN
ejpam-6251	291	75	,	,	PUNCT
ejpam-6251	291	76	ż	ż	NOUN
ejpam-6251	291	77	2	2	X
ejpam-6251	291	78	)	)	PUNCT
ejpam-6251	291	79	≥	≥	NOUN
ejpam-6251	291	80	r7	r7	PROPN
ejpam-6251	291	81	⋇	⋇	PROPN
ejpam-6251	291	82	r7	r7	PROPN
ejpam-6251	291	83	≥	≥	PRON
ejpam-6251	291	84	r4	r4	PROPN
ejpam-6251	291	85	⋇	⋇	NOUN
ejpam-6251	291	86	r4	r4	VERB
ejpam-6251	291	87	≥	≥	NUM
ejpam-6251	291	88	r0	r0	PROPN
ejpam-6251	291	89	>	>	X
ejpam-6251	291	90	r1	r1	PROPN
ejpam-6251	291	91	,	,	PUNCT
ejpam-6251	291	92	r2	r2	PROPN
ejpam-6251	291	93	=	=	SYM
ejpam-6251	291	94	ψ(ς,ϖ	ψ(ς,ϖ	PROPN
ejpam-6251	291	95	,	,	PUNCT
ejpam-6251	291	96	ż	ż	NOUN
ejpam-6251	291	97	)	)	PUNCT
ejpam-6251	291	98	≤	≤	NOUN
ejpam-6251	291	99	ψ(ς	ψ(ς	NOUN
ejpam-6251	291	100	,	,	PUNCT
ejpam-6251	291	101	θ1	θ1	NOUN
ejpam-6251	291	102	,	,	PUNCT
ejpam-6251	291	103	ż	ż	NOUN
ejpam-6251	291	104	2	2	NUM
ejpam-6251	291	105	)	)	PUNCT
ejpam-6251	291	106	♢	♢	PROPN
ejpam-6251	291	107	ψ(θ1	ψ(θ1	PROPN
ejpam-6251	291	108	,	,	PUNCT
ejpam-6251	291	109	ϖ	ϖ	PROPN
ejpam-6251	291	110	,	,	PUNCT
ejpam-6251	291	111	ż	ż	NOUN
ejpam-6251	291	112	2	2	X
ejpam-6251	291	113	)	)	PUNCT
ejpam-6251	291	114	≤	≤	NOUN
ejpam-6251	291	115	(	(	PUNCT
ejpam-6251	291	116	1−	1−	NUM
ejpam-6251	291	117	r7)	r7)	PROPN
ejpam-6251	291	118	♢	♢	PROPN
ejpam-6251	291	119	(1−	(1−	PROPN
ejpam-6251	291	120	r7	r7	PROPN
ejpam-6251	291	121	)	)	PUNCT
ejpam-6251	291	122	≤	≤	NOUN
ejpam-6251	291	123	(	(	PUNCT
ejpam-6251	291	124	1−	1−	NUM
ejpam-6251	291	125	r5)	r5)	NOUN
ejpam-6251	291	126	♢	♢	PROPN
ejpam-6251	291	127	(1−	(1−	PROPN
ejpam-6251	291	128	r5	r5	PROPN
ejpam-6251	291	129	)	)	PUNCT
ejpam-6251	291	130	≤	≤	NOUN
ejpam-6251	291	131	1−	1−	NUM
ejpam-6251	291	132	r0	r0	NOUN
ejpam-6251	291	133	<	<	X
ejpam-6251	291	134	r2	r2	PROPN
ejpam-6251	291	135	,	,	PUNCT
ejpam-6251	291	136	r3	r3	PROPN
ejpam-6251	291	137	=	=	SYM
ejpam-6251	291	138	ξ(ς,ϖ	ξ(ς,ϖ	NOUN
ejpam-6251	291	139	,	,	PUNCT
ejpam-6251	291	140	ż	ż	NOUN
ejpam-6251	291	141	)	)	PUNCT
ejpam-6251	291	142	≤	≤	NOUN
ejpam-6251	291	143	ξ(ς	ξ(ς	NOUN
ejpam-6251	291	144	,	,	PUNCT
ejpam-6251	291	145	θ1	θ1	NOUN
ejpam-6251	291	146	,	,	PUNCT
ejpam-6251	291	147	ż	ż	NOUN
ejpam-6251	291	148	2	2	NUM
ejpam-6251	291	149	)	)	PUNCT
ejpam-6251	291	150	♢	♢	PROPN
ejpam-6251	291	151	ξ(θ1	ξ(θ1	PROPN
ejpam-6251	291	152	,	,	PUNCT
ejpam-6251	291	153	ϖ	ϖ	PROPN
ejpam-6251	291	154	ż	ż	NOUN
ejpam-6251	291	155	2	2	X
ejpam-6251	291	156	)	)	PUNCT
ejpam-6251	291	157	≤	≤	NOUN
ejpam-6251	291	158	(	(	PUNCT
ejpam-6251	291	159	1−	1−	NUM
ejpam-6251	291	160	r7)	r7)	PROPN
ejpam-6251	291	161	♢	♢	PROPN
ejpam-6251	291	162	(1−	(1−	PROPN
ejpam-6251	291	163	r7	r7	PROPN
ejpam-6251	291	164	)	)	PUNCT
ejpam-6251	291	165	≤	≤	NOUN
ejpam-6251	291	166	(	(	PUNCT
ejpam-6251	291	167	1−	1−	NUM
ejpam-6251	291	168	r6)	r6)	PROPN
ejpam-6251	291	169	♢	♢	PROPN
ejpam-6251	291	170	(1−	(1−	PROPN
ejpam-6251	291	171	r6	r6	PROPN
ejpam-6251	291	172	)	)	PUNCT
ejpam-6251	291	173	≤	≤	NOUN
ejpam-6251	291	174	1−	1−	NUM
ejpam-6251	291	175	r0	r0	NOUN
ejpam-6251	291	176	<	<	X
ejpam-6251	291	177	r3	r3	PROPN
ejpam-6251	291	178	,	,	PUNCT
ejpam-6251	291	179	which	which	PRON
ejpam-6251	291	180	is	be	AUX
ejpam-6251	291	181	a	a	DET
ejpam-6251	291	182	contradiction	contradiction	NOUN
ejpam-6251	291	183	.	.	PUNCT
ejpam-6251	292	1	definition	definition	NOUN
ejpam-6251	292	2	14	14	NUM
ejpam-6251	292	3	.	.	PUNCT
ejpam-6251	293	1	let	let	VERB
ejpam-6251	293	2	(	(	PUNCT
ejpam-6251	293	3	𭟋	𭟋	NOUN
ejpam-6251	293	4	,	,	PUNCT
ejpam-6251	293	5	s	s	PROPN
ejpam-6251	293	6	,	,	PUNCT
ejpam-6251	293	7	π	π	PROPN
ejpam-6251	293	8	,	,	PUNCT
ejpam-6251	293	9	ψ	ψ	PROPN
ejpam-6251	293	10	,	,	PUNCT
ejpam-6251	293	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	293	12	,	,	PUNCT
ejpam-6251	293	13	♢	♢	PROPN
ejpam-6251	293	14	)	)	PUNCT
ejpam-6251	293	15	is	be	AUX
ejpam-6251	293	16	a	a	DET
ejpam-6251	293	17	nbms	nbms	NOUN
ejpam-6251	293	18	.	.	PUNCT
ejpam-6251	294	1	i.	i.	PROPN
ejpam-6251	294	2	a	a	DET
ejpam-6251	294	3	point	point	NOUN
ejpam-6251	294	4	ς	ς	PROPN
ejpam-6251	294	5	∈	∈	PROPN
ejpam-6251	294	6	𭟋	𭟋	ADP
ejpam-6251	294	7	∪	∪	NOUN
ejpam-6251	294	8	s	s	NOUN
ejpam-6251	294	9	is	be	AUX
ejpam-6251	294	10	said	say	VERB
ejpam-6251	294	11	to	to	PART
ejpam-6251	294	12	be	be	AUX
ejpam-6251	294	13	a	a	DET
ejpam-6251	294	14	left	left	ADJ
ejpam-6251	294	15	point	point	NOUN
ejpam-6251	294	16	if	if	SCONJ
ejpam-6251	294	17	ς	ς	PROPN
ejpam-6251	294	18	∈	∈	PROPN
ejpam-6251	294	19	𭟋	𭟋	PROPN
ejpam-6251	294	20	,	,	PUNCT
ejpam-6251	294	21	a	a	DET
ejpam-6251	294	22	right	right	ADJ
ejpam-6251	294	23	point	point	NOUN
ejpam-6251	294	24	if	if	SCONJ
ejpam-6251	294	25	ς	ς	PROPN
ejpam-6251	294	26	∈	∈	PROPN
ejpam-6251	294	27	s	s	X
ejpam-6251	294	28	and	and	CCONJ
ejpam-6251	294	29	a	a	DET
ejpam-6251	294	30	central	central	ADJ
ejpam-6251	294	31	point	point	NOUN
ejpam-6251	294	32	if	if	SCONJ
ejpam-6251	294	33	both	both	PRON
ejpam-6251	294	34	hold	hold	VERB
ejpam-6251	294	35	.	.	PUNCT
ejpam-6251	295	1	ii	ii	PROPN
ejpam-6251	295	2	.	.	PUNCT
ejpam-6251	296	1	a	a	DET
ejpam-6251	296	2	sequence	sequence	NOUN
ejpam-6251	296	3	{	{	PUNCT
ejpam-6251	296	4	ςµ	ςµ	NOUN
ejpam-6251	296	5	}	}	PUNCT
ejpam-6251	296	6	⊂	⊂	PROPN
ejpam-6251	296	7	𭟋	𭟋	VERB
ejpam-6251	296	8	is	be	AUX
ejpam-6251	296	9	said	say	VERB
ejpam-6251	296	10	to	to	PART
ejpam-6251	296	11	be	be	AUX
ejpam-6251	296	12	a	a	DET
ejpam-6251	296	13	left	left	ADJ
ejpam-6251	296	14	sequence	sequence	NOUN
ejpam-6251	296	15	and	and	CCONJ
ejpam-6251	296	16	a	a	DET
ejpam-6251	296	17	sequence	sequence	NOUN
ejpam-6251	296	18	{	{	PUNCT
ejpam-6251	296	19	βn	βn	NOUN
ejpam-6251	296	20	}	}	PUNCT
ejpam-6251	296	21	⊂	⊂	PRON
ejpam-6251	296	22	s	s	VERB
ejpam-6251	296	23	is	be	AUX
ejpam-6251	296	24	said	say	VERB
ejpam-6251	296	25	to	to	PART
ejpam-6251	296	26	be	be	AUX
ejpam-6251	296	27	a	a	DET
ejpam-6251	296	28	right	right	ADJ
ejpam-6251	296	29	sequence	sequence	NOUN
ejpam-6251	296	30	.	.	PUNCT
ejpam-6251	297	1	iii	iii	X
ejpam-6251	297	2	.	.	PUNCT
ejpam-6251	298	1	a	a	DET
ejpam-6251	298	2	sequence	sequence	NOUN
ejpam-6251	298	3	{	{	PUNCT
ejpam-6251	298	4	ςµ	ςµ	NOUN
ejpam-6251	298	5	}	}	PUNCT
ejpam-6251	298	6	⊂	⊂	PRON
ejpam-6251	298	7	𭟋∪	𭟋∪	X
ejpam-6251	298	8	s	s	X
ejpam-6251	298	9	is	be	AUX
ejpam-6251	298	10	said	say	VERB
ejpam-6251	298	11	to	to	PART
ejpam-6251	298	12	converge	converge	VERB
ejpam-6251	298	13	to	to	ADP
ejpam-6251	298	14	a	a	DET
ejpam-6251	298	15	point	point	NOUN
ejpam-6251	298	16	ς	ς	PROPN
ejpam-6251	298	17	if	if	SCONJ
ejpam-6251	298	18	and	and	CCONJ
ejpam-6251	298	19	only	only	ADV
ejpam-6251	298	20	if	if	SCONJ
ejpam-6251	298	21	{	{	PUNCT
ejpam-6251	298	22	ςµ	ςµ	NOUN
ejpam-6251	298	23	}	}	PUNCT
ejpam-6251	298	24	is	be	AUX
ejpam-6251	298	25	a	a	DET
ejpam-6251	298	26	left	left	ADJ
ejpam-6251	298	27	sequence	sequence	NOUN
ejpam-6251	298	28	,	,	PUNCT
ejpam-6251	298	29	ς	ς	PROPN
ejpam-6251	298	30	is	be	AUX
ejpam-6251	298	31	a	a	DET
ejpam-6251	298	32	right	right	ADJ
ejpam-6251	298	33	point	point	NOUN
ejpam-6251	298	34	and	and	CCONJ
ejpam-6251	298	35	lim	lim	PROPN
ejpam-6251	298	36	µ→+∞	µ→+∞	VERB
ejpam-6251	298	37	π(ςµ	π(ςµ	PROPN
ejpam-6251	298	38	,	,	PUNCT
ejpam-6251	298	39	ς	ς	NOUN
ejpam-6251	298	40	,	,	PUNCT
ejpam-6251	298	41	ż	ż	NOUN
ejpam-6251	298	42	)	)	PUNCT
ejpam-6251	298	43	=	=	SYM
ejpam-6251	298	44	1	1	NUM
ejpam-6251	298	45	,	,	PUNCT
ejpam-6251	298	46	lim	lim	PROPN
ejpam-6251	298	47	µ→+∞	µ→+∞	VERB
ejpam-6251	298	48	ψ(ςµ	ψ(ςµ	PROPN
ejpam-6251	298	49	,	,	PUNCT
ejpam-6251	298	50	ς	ς	NOUN
ejpam-6251	298	51	,	,	PUNCT
ejpam-6251	298	52	ż	ż	NOUN
ejpam-6251	298	53	)	)	PUNCT
ejpam-6251	298	54	=	=	SYM
ejpam-6251	298	55	0	0	PROPN
ejpam-6251	298	56	,	,	PUNCT
ejpam-6251	298	57	lim	lim	PROPN
ejpam-6251	298	58	µ→+∞	µ→+∞	VERB
ejpam-6251	298	59	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	298	60	,	,	PUNCT
ejpam-6251	298	61	ς	ς	NOUN
ejpam-6251	298	62	,	,	PUNCT
ejpam-6251	298	63	ż	ż	NOUN
ejpam-6251	298	64	)	)	PUNCT
ejpam-6251	299	1	=	=	SYM
ejpam-6251	299	2	0	0	NUM
ejpam-6251	299	3	∀	∀	NOUN
ejpam-6251	299	4	ż	ż	NOUN
ejpam-6251	299	5	>	>	X
ejpam-6251	299	6	0	0	PUNCT
ejpam-6251	299	7	or	or	CCONJ
ejpam-6251	299	8	{	{	PUNCT
ejpam-6251	299	9	ςµ	ςµ	NOUN
ejpam-6251	299	10	}	}	PUNCT
ejpam-6251	299	11	is	be	AUX
ejpam-6251	299	12	a	a	DET
ejpam-6251	299	13	right	right	ADJ
ejpam-6251	299	14	sequence	sequence	NOUN
ejpam-6251	299	15	,	,	PUNCT
ejpam-6251	299	16	ς	ς	PROPN
ejpam-6251	299	17	is	be	AUX
ejpam-6251	299	18	a	a	DET
ejpam-6251	299	19	left	left	ADJ
ejpam-6251	299	20	point	point	NOUN
ejpam-6251	299	21	and	and	CCONJ
ejpam-6251	299	22	lim	lim	PROPN
ejpam-6251	299	23	µ→+∞	µ→+∞	PROPN
ejpam-6251	299	24	π(ς	π(ς	PROPN
ejpam-6251	299	25	,	,	PUNCT
ejpam-6251	299	26	ςµ	ςµ	NOUN
ejpam-6251	299	27	,	,	PUNCT
ejpam-6251	299	28	ż	ż	NOUN
ejpam-6251	299	29	)	)	PUNCT
ejpam-6251	299	30	=	=	SYM
ejpam-6251	299	31	1	1	NUM
ejpam-6251	299	32	,	,	PUNCT
ejpam-6251	299	33	lim	lim	PROPN
ejpam-6251	299	34	µ→+∞	µ→+∞	PROPN
ejpam-6251	299	35	ψ(ς	ψ(ς	NOUN
ejpam-6251	299	36	,	,	PUNCT
ejpam-6251	299	37	ςµ	ςµ	NOUN
ejpam-6251	299	38	,	,	PUNCT
ejpam-6251	299	39	ż	ż	NOUN
ejpam-6251	299	40	)	)	PUNCT
ejpam-6251	299	41	=	=	SYM
ejpam-6251	299	42	0	0	PROPN
ejpam-6251	299	43	,	,	PUNCT
ejpam-6251	299	44	lim	lim	PROPN
ejpam-6251	299	45	µ→+∞	µ→+∞	VERB
ejpam-6251	299	46	ξ(ς	ξ(ς	PROPN
ejpam-6251	299	47	,	,	PUNCT
ejpam-6251	299	48	ςµ	ςµ	NOUN
ejpam-6251	299	49	,	,	PUNCT
ejpam-6251	299	50	ż	ż	NOUN
ejpam-6251	299	51	)	)	PUNCT
ejpam-6251	299	52	=	=	SYM
ejpam-6251	299	53	0	0	NUM
ejpam-6251	299	54	∀	∀	NOUN
ejpam-6251	300	1	ż	ż	NOUN
ejpam-6251	300	2	>	>	X
ejpam-6251	300	3	0	0	X
ejpam-6251	300	4	.	.	X
ejpam-6251	300	5	iv	iv	X
ejpam-6251	300	6	.	.	PUNCT
ejpam-6251	301	1	a	a	DET
ejpam-6251	301	2	sequence	sequence	NOUN
ejpam-6251	301	3	{	{	PUNCT
ejpam-6251	301	4	(	(	PUNCT
ejpam-6251	301	5	ςµ	ςµ	NOUN
ejpam-6251	301	6	,	,	PUNCT
ejpam-6251	301	7	βµ	βµ	NOUN
ejpam-6251	301	8	)	)	PUNCT
ejpam-6251	301	9	}	}	PUNCT
ejpam-6251	301	10	⊂	⊂	PRON
ejpam-6251	301	11	𭟋×	𭟋×	PUNCT
ejpam-6251	302	1	s	s	PART
ejpam-6251	302	2	is	be	AUX
ejpam-6251	302	3	said	say	VERB
ejpam-6251	302	4	to	to	PART
ejpam-6251	302	5	be	be	AUX
ejpam-6251	302	6	a	a	DET
ejpam-6251	302	7	bisequence	bisequence	NOUN
ejpam-6251	302	8	.	.	PUNCT
ejpam-6251	303	1	if	if	SCONJ
ejpam-6251	303	2	the	the	DET
ejpam-6251	303	3	sequences	sequence	NOUN
ejpam-6251	303	4	{	{	PUNCT
ejpam-6251	303	5	ςµ	ςµ	NOUN
ejpam-6251	303	6	}	}	PUNCT
ejpam-6251	303	7	and	and	CCONJ
ejpam-6251	303	8	{	{	PUNCT
ejpam-6251	303	9	βµ	βµ	NOUN
ejpam-6251	303	10	}	}	PUNCT
ejpam-6251	303	11	both	both	PRON
ejpam-6251	303	12	converge	converge	VERB
ejpam-6251	303	13	then	then	ADV
ejpam-6251	303	14	the	the	DET
ejpam-6251	303	15	bisequence	bisequence	NOUN
ejpam-6251	303	16	{	{	PUNCT
ejpam-6251	303	17	(	(	PUNCT
ejpam-6251	303	18	ςµ	ςµ	NOUN
ejpam-6251	303	19	,	,	PUNCT
ejpam-6251	303	20	βµ	βµ	NOUN
ejpam-6251	303	21	)	)	PUNCT
ejpam-6251	303	22	}	}	PUNCT
ejpam-6251	303	23	is	be	AUX
ejpam-6251	303	24	said	say	VERB
ejpam-6251	303	25	to	to	PART
ejpam-6251	303	26	be	be	AUX
ejpam-6251	303	27	convergent	convergent	ADJ
ejpam-6251	303	28	in	in	ADP
ejpam-6251	303	29	𭟋×s	𭟋×s	PROPN
ejpam-6251	303	30	.	.	PUNCT
ejpam-6251	304	1	v.	v.	INTJ
ejpam-6251	304	2	if	if	SCONJ
ejpam-6251	304	3	{	{	PUNCT
ejpam-6251	304	4	ςµ	ςµ	NOUN
ejpam-6251	304	5	}	}	PUNCT
ejpam-6251	304	6	and	and	CCONJ
ejpam-6251	304	7	{	{	PUNCT
ejpam-6251	304	8	βµ	βµ	NOUN
ejpam-6251	304	9	}	}	PUNCT
ejpam-6251	304	10	both	both	PRON
ejpam-6251	304	11	converge	converge	VERB
ejpam-6251	304	12	to	to	ADP
ejpam-6251	304	13	a	a	DET
ejpam-6251	304	14	point	point	NOUN
ejpam-6251	304	15	β	β	X
ejpam-6251	304	16	∈	∈	NOUN
ejpam-6251	304	17	𭟋	𭟋	ADP
ejpam-6251	304	18	∩	∩	X
ejpam-6251	304	19	s	s	PART
ejpam-6251	304	20	then	then	ADV
ejpam-6251	304	21	the	the	DET
ejpam-6251	304	22	bisequence	bisequence	NOUN
ejpam-6251	304	23	{	{	PUNCT
ejpam-6251	304	24	(	(	PUNCT
ejpam-6251	304	25	ςµ	ςµ	NOUN
ejpam-6251	304	26	,	,	PUNCT
ejpam-6251	304	27	βµ	βµ	NOUN
ejpam-6251	304	28	)	)	PUNCT
ejpam-6251	304	29	}	}	PUNCT
ejpam-6251	304	30	is	be	AUX
ejpam-6251	304	31	said	say	VERB
ejpam-6251	304	32	to	to	PART
ejpam-6251	304	33	be	be	AUX
ejpam-6251	304	34	biconvergent	biconvergent	NOUN
ejpam-6251	304	35	.	.	PUNCT
ejpam-6251	305	1	a	a	DET
ejpam-6251	305	2	sequence	sequence	NOUN
ejpam-6251	305	3	{	{	PUNCT
ejpam-6251	305	4	(	(	PUNCT
ejpam-6251	305	5	ςµ	ςµ	NOUN
ejpam-6251	305	6	,	,	PUNCT
ejpam-6251	305	7	βµ	βµ	NOUN
ejpam-6251	305	8	)	)	PUNCT
ejpam-6251	305	9	}	}	PUNCT
ejpam-6251	305	10	is	be	AUX
ejpam-6251	305	11	a	a	DET
ejpam-6251	305	12	cauchy	cauchy	ADJ
ejpam-6251	305	13	bisequence	bisequence	NOUN
ejpam-6251	305	14	if	if	SCONJ
ejpam-6251	305	15	lim	lim	PROPN
ejpam-6251	305	16	µ,m→+∞	µ,m→+∞	NUM
ejpam-6251	305	17	π(ςµ	π(ςµ	NUM
ejpam-6251	305	18	,	,	PUNCT
ejpam-6251	305	19	βm	βm	VERB
ejpam-6251	305	20	,	,	PUNCT
ejpam-6251	305	21	ż	ż	NOUN
ejpam-6251	305	22	)	)	PUNCT
ejpam-6251	305	23	=	=	SYM
ejpam-6251	305	24	1	1	NUM
ejpam-6251	305	25	,	,	PUNCT
ejpam-6251	305	26	lim	lim	PROPN
ejpam-6251	305	27	µ,m→+∞	µ,m→+∞	NUM
ejpam-6251	305	28	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	305	29	,	,	PUNCT
ejpam-6251	305	30	βm	βm	VERB
ejpam-6251	305	31	,	,	PUNCT
ejpam-6251	305	32	ż	ż	NOUN
ejpam-6251	305	33	)	)	PUNCT
ejpam-6251	305	34	=	=	SYM
ejpam-6251	305	35	0	0	PROPN
ejpam-6251	305	36	,	,	PUNCT
ejpam-6251	305	37	lim	lim	PROPN
ejpam-6251	305	38	µ,m→+∞	µ,m→+∞	NUM
ejpam-6251	305	39	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	305	40	,	,	PUNCT
ejpam-6251	305	41	βm	βm	VERB
ejpam-6251	305	42	,	,	PUNCT
ejpam-6251	305	43	ż	ż	NOUN
ejpam-6251	305	44	)	)	PUNCT
ejpam-6251	305	45	=	=	SYM
ejpam-6251	305	46	0	0	NUM
ejpam-6251	305	47	,	,	PUNCT
ejpam-6251	306	1	∀	∀	X
ejpam-6251	306	2	ż	ż	NOUN
ejpam-6251	306	3	>	>	X
ejpam-6251	306	4	0	0	NUM
ejpam-6251	306	5	.	.	PUNCT
ejpam-6251	306	6	vi	vi	PROPN
ejpam-6251	306	7	.	.	PUNCT
ejpam-6251	307	1	a	a	DET
ejpam-6251	307	2	nbms	nbms	NOUN
ejpam-6251	307	3	is	be	AUX
ejpam-6251	307	4	said	say	VERB
ejpam-6251	307	5	to	to	PART
ejpam-6251	307	6	be	be	AUX
ejpam-6251	307	7	complete	complete	ADJ
ejpam-6251	307	8	if	if	SCONJ
ejpam-6251	307	9	every	every	DET
ejpam-6251	307	10	cauchy	cauchy	ADJ
ejpam-6251	307	11	bisequence	bisequence	NOUN
ejpam-6251	307	12	is	be	AUX
ejpam-6251	307	13	convergent	convergent	NOUN
ejpam-6251	307	14	.	.	PUNCT
ejpam-6251	308	1	now	now	ADV
ejpam-6251	308	2	we	we	PRON
ejpam-6251	308	3	establish	establish	VERB
ejpam-6251	308	4	our	our	PRON
ejpam-6251	308	5	main	main	ADJ
ejpam-6251	308	6	results	result	NOUN
ejpam-6251	308	7	.	.	PUNCT
ejpam-6251	309	1	r.	r.	PROPN
ejpam-6251	309	2	ramaswamy	ramaswamy	PROPN
ejpam-6251	309	3	/	/	SYM
ejpam-6251	309	4	eur	eur	PROPN
ejpam-6251	309	5	.	.	PUNCT
ejpam-6251	310	1	j.	j.	PROPN
ejpam-6251	310	2	pure	pure	PROPN
ejpam-6251	310	3	appl	appl	PROPN
ejpam-6251	310	4	.	.	PROPN
ejpam-6251	310	5	math	math	PROPN
ejpam-6251	310	6	,	,	PUNCT
ejpam-6251	310	7	18	18	NUM
ejpam-6251	310	8	(	(	PUNCT
ejpam-6251	310	9	4	4	NUM
ejpam-6251	310	10	)	)	PUNCT
ejpam-6251	310	11	(	(	PUNCT
ejpam-6251	310	12	2025	2025	NUM
ejpam-6251	310	13	)	)	PUNCT
ejpam-6251	310	14	,	,	PUNCT
ejpam-6251	310	15	6251	6251	NUM
ejpam-6251	310	16	12	12	NUM
ejpam-6251	310	17	of	of	ADP
ejpam-6251	310	18	40	40	NUM
ejpam-6251	310	19	3.2	3.2	NUM
ejpam-6251	310	20	.	.	PUNCT
ejpam-6251	311	1	main	main	ADJ
ejpam-6251	311	2	results	result	NOUN
ejpam-6251	311	3	lemma	lemma	PROPN
ejpam-6251	311	4	1	1	X
ejpam-6251	311	5	.	.	PUNCT
ejpam-6251	312	1	let	let	VERB
ejpam-6251	312	2	{	{	PUNCT
ejpam-6251	312	3	ςµ	ςµ	NOUN
ejpam-6251	312	4	}	}	PUNCT
ejpam-6251	312	5	be	be	AUX
ejpam-6251	312	6	a	a	DET
ejpam-6251	312	7	cauchy	cauchy	ADJ
ejpam-6251	312	8	sequence	sequence	NOUN
ejpam-6251	312	9	in	in	ADP
ejpam-6251	312	10	nbms	nbms	NOUN
ejpam-6251	312	11	(	(	PUNCT
ejpam-6251	312	12	𭟋	𭟋	NOUN
ejpam-6251	312	13	,	,	PUNCT
ejpam-6251	312	14	s	s	PROPN
ejpam-6251	312	15	,	,	PUNCT
ejpam-6251	312	16	π	π	PROPN
ejpam-6251	312	17	,	,	PUNCT
ejpam-6251	312	18	ψ	ψ	PROPN
ejpam-6251	312	19	,	,	PUNCT
ejpam-6251	312	20	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	312	21	,	,	PUNCT
ejpam-6251	312	22	♢	♢	PROPN
ejpam-6251	312	23	)	)	PUNCT
ejpam-6251	312	24	such	such	ADJ
ejpam-6251	312	25	that	that	DET
ejpam-6251	312	26	ςµ	ςµ	NOUN
ejpam-6251	312	27	̸=	̸=	PROPN
ejpam-6251	312	28	ςm	ςm	NOUN
ejpam-6251	312	29	for	for	ADP
ejpam-6251	312	30	every	every	DET
ejpam-6251	312	31	m	m	NOUN
ejpam-6251	312	32	,	,	PUNCT
ejpam-6251	313	1	µ(̸=	µ(̸=	PROPN
ejpam-6251	313	2	m	m	PROPN
ejpam-6251	313	3	)	)	PUNCT
ejpam-6251	313	4	∈	∈	PROPN
ejpam-6251	313	5	n.	n.	NOUN
ejpam-6251	313	6	then	then	ADV
ejpam-6251	313	7	,	,	PUNCT
ejpam-6251	313	8	at	at	ADP
ejpam-6251	313	9	most	most	ADJ
ejpam-6251	313	10	,	,	PUNCT
ejpam-6251	313	11	the	the	DET
ejpam-6251	313	12	sequence	sequence	NOUN
ejpam-6251	313	13	{	{	PUNCT
ejpam-6251	313	14	ςµ	ςµ	NOUN
ejpam-6251	313	15	}	}	PUNCT
ejpam-6251	313	16	converge	converge	NOUN
ejpam-6251	313	17	to	to	ADP
ejpam-6251	313	18	one	one	NUM
ejpam-6251	313	19	limit	limit	NOUN
ejpam-6251	313	20	point	point	NOUN
ejpam-6251	313	21	.	.	PUNCT
ejpam-6251	314	1	proof	proof	NOUN
ejpam-6251	314	2	.	.	PUNCT
ejpam-6251	315	1	conversely	conversely	ADV
ejpam-6251	315	2	,	,	PUNCT
ejpam-6251	315	3	suppose	suppose	VERB
ejpam-6251	315	4	that	that	SCONJ
ejpam-6251	315	5	ςµ	ςµ	NOUN
ejpam-6251	315	6	→	→	SYM
ejpam-6251	315	7	ς	ς	PROPN
ejpam-6251	315	8	∈	∈	PROPN
ejpam-6251	315	9	s	s	PART
ejpam-6251	315	10	and	and	CCONJ
ejpam-6251	315	11	ςµ	ςµ	NOUN
ejpam-6251	315	12	→	→	PUNCT
ejpam-6251	315	13	ϖ	ϖ	X
ejpam-6251	315	14	∈	∈	NOUN
ejpam-6251	315	15	𭟋	𭟋	ADP
ejpam-6251	315	16	∩	∩	NOUN
ejpam-6251	315	17	s	s	PART
ejpam-6251	315	18	,	,	PUNCT
ejpam-6251	315	19	for	for	SCONJ
ejpam-6251	315	20	ς	ς	PROPN
ejpam-6251	315	21	̸=	̸=	PROPN
ejpam-6251	315	22	ϖ.	ϖ.	VERB
ejpam-6251	315	23	then	then	ADV
ejpam-6251	315	24	,	,	PUNCT
ejpam-6251	315	25	limµ→+∞π(ςµ	limµ→+∞π(ςµ	NOUN
ejpam-6251	315	26	,	,	PUNCT
ejpam-6251	315	27	ς	ς	NOUN
ejpam-6251	315	28	,	,	PUNCT
ejpam-6251	315	29	ż	ż	NOUN
ejpam-6251	315	30	)	)	PUNCT
ejpam-6251	315	31	=	=	SYM
ejpam-6251	315	32	1	1	NUM
ejpam-6251	315	33	,	,	PUNCT
ejpam-6251	315	34	limµ→+∞ψ(ςµ	limµ→+∞ψ(ςµ	ADJ
ejpam-6251	315	35	,	,	PUNCT
ejpam-6251	315	36	ς	ς	NOUN
ejpam-6251	315	37	,	,	PUNCT
ejpam-6251	315	38	ż	ż	NOUN
ejpam-6251	315	39	)	)	PUNCT
ejpam-6251	315	40	=	=	SYM
ejpam-6251	315	41	0	0	NUM
ejpam-6251	315	42	,	,	PUNCT
ejpam-6251	315	43	limµ→+∞	limµ→+∞	VERB
ejpam-6251	315	44	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	315	45	,	,	PUNCT
ejpam-6251	315	46	ς	ς	NOUN
ejpam-6251	315	47	,	,	PUNCT
ejpam-6251	315	48	ż	ż	NOUN
ejpam-6251	315	49	)	)	PUNCT
ejpam-6251	315	50	=	=	SYM
ejpam-6251	315	51	0	0	NUM
ejpam-6251	315	52	,	,	PUNCT
ejpam-6251	315	53	and	and	CCONJ
ejpam-6251	315	54	limµ→+∞π(ςµ	limµ→+∞π(ςµ	NOUN
ejpam-6251	315	55	,	,	PUNCT
ejpam-6251	315	56	ϖ	ϖ	NOUN
ejpam-6251	315	57	,	,	PUNCT
ejpam-6251	315	58	ż	ż	NOUN
ejpam-6251	315	59	)	)	PUNCT
ejpam-6251	315	60	=	=	SYM
ejpam-6251	315	61	1	1	NUM
ejpam-6251	315	62	,	,	PUNCT
ejpam-6251	315	63	limµ→+∞ψ(ςµ	limµ→+∞ψ(ςµ	ADJ
ejpam-6251	315	64	,	,	PUNCT
ejpam-6251	315	65	ϖ	ϖ	NOUN
ejpam-6251	315	66	,	,	PUNCT
ejpam-6251	315	67	ż	ż	NOUN
ejpam-6251	315	68	)	)	PUNCT
ejpam-6251	315	69	=	=	SYM
ejpam-6251	315	70	0	0	NUM
ejpam-6251	315	71	,	,	PUNCT
ejpam-6251	315	72	limµ→+∞	limµ→+∞	VERB
ejpam-6251	315	73	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	315	74	,	,	PUNCT
ejpam-6251	315	75	ϖ	ϖ	NOUN
ejpam-6251	315	76	,	,	PUNCT
ejpam-6251	315	77	ż	ż	NOUN
ejpam-6251	315	78	)	)	PUNCT
ejpam-6251	315	79	=	=	SYM
ejpam-6251	315	80	0	0	NUM
ejpam-6251	315	81	,	,	PUNCT
ejpam-6251	315	82	∀	∀	X
ejpam-6251	315	83	ż	ż	NOUN
ejpam-6251	315	84	>	>	X
ejpam-6251	315	85	0	0	X
ejpam-6251	315	86	.	.	PUNCT
ejpam-6251	315	87	suppose	suppose	VERB
ejpam-6251	315	88	π(ς,ϖ	π(ς,ϖ	NOUN
ejpam-6251	315	89	,	,	PUNCT
ejpam-6251	315	90	ż	ż	NOUN
ejpam-6251	315	91	)	)	PUNCT
ejpam-6251	315	92	≥	≥	NOUN
ejpam-6251	315	93	π	π	PROPN
ejpam-6251	315	94	(	(	PUNCT
ejpam-6251	315	95	ς	ς	PROPN
ejpam-6251	315	96	,	,	PUNCT
ejpam-6251	315	97	ςµ	ςµ	NOUN
ejpam-6251	315	98	,	,	PUNCT
ejpam-6251	315	99	ż	ż	NOUN
ejpam-6251	315	100	3	3	NUM
ejpam-6251	315	101	)	)	PUNCT
ejpam-6251	315	102	⋇π	⋇π	NOUN
ejpam-6251	315	103	(	(	PUNCT
ejpam-6251	315	104	ςµ	ςµ	NOUN
ejpam-6251	315	105	,	,	PUNCT
ejpam-6251	315	106	ςµ+1	ςµ+1	NUM
ejpam-6251	315	107	,	,	PUNCT
ejpam-6251	315	108	ż	ż	NOUN
ejpam-6251	315	109	3	3	NUM
ejpam-6251	315	110	)	)	PUNCT
ejpam-6251	315	111	⋇π	⋇π	NOUN
ejpam-6251	315	112	(	(	PUNCT
ejpam-6251	315	113	ςµ+1	ςµ+1	NUM
ejpam-6251	315	114	,	,	PUNCT
ejpam-6251	315	115	ϖ	ϖ	NOUN
ejpam-6251	315	116	,	,	PUNCT
ejpam-6251	315	117	ż	ż	NOUN
ejpam-6251	315	118	3	3	NUM
ejpam-6251	315	119	)	)	PUNCT
ejpam-6251	315	120	→	→	PUNCT
ejpam-6251	316	1	1⋇	1⋇	NUM
ejpam-6251	316	2	1⋇	1⋇	NUM
ejpam-6251	316	3	1	1	NUM
ejpam-6251	316	4	,	,	PUNCT
ejpam-6251	316	5	as	as	ADP
ejpam-6251	316	6	µ→	µ→	PRON
ejpam-6251	316	7	+	+	NOUN
ejpam-6251	316	8	∞	∞	PROPN
ejpam-6251	316	9	,	,	PUNCT
ejpam-6251	316	10	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	316	11	,	,	PUNCT
ejpam-6251	316	12	ż	ż	NOUN
ejpam-6251	316	13	)	)	PUNCT
ejpam-6251	316	14	≤	≤	NOUN
ejpam-6251	316	15	ψ	ψ	X
ejpam-6251	316	16	(	(	PUNCT
ejpam-6251	316	17	ς	ς	PROPN
ejpam-6251	316	18	,	,	PUNCT
ejpam-6251	316	19	ςµ	ςµ	NOUN
ejpam-6251	316	20	,	,	PUNCT
ejpam-6251	316	21	ż	ż	NOUN
ejpam-6251	316	22	3	3	X
ejpam-6251	316	23	)	)	PUNCT
ejpam-6251	316	24	♢	♢	PROPN
ejpam-6251	316	25	ψ	ψ	X
ejpam-6251	316	26	(	(	PUNCT
ejpam-6251	316	27	ςµ	ςµ	NOUN
ejpam-6251	316	28	,	,	PUNCT
ejpam-6251	316	29	ςµ+1	ςµ+1	NUM
ejpam-6251	316	30	,	,	PUNCT
ejpam-6251	316	31	ż	ż	NOUN
ejpam-6251	316	32	3	3	X
ejpam-6251	316	33	)	)	PUNCT
ejpam-6251	316	34	♢	♢	PROPN
ejpam-6251	316	35	ψ	ψ	X
ejpam-6251	316	36	(	(	PUNCT
ejpam-6251	316	37	ςµ+1	ςµ+1	NUM
ejpam-6251	316	38	,	,	PUNCT
ejpam-6251	316	39	ϖ	ϖ	NOUN
ejpam-6251	316	40	,	,	PUNCT
ejpam-6251	316	41	ż	ż	NOUN
ejpam-6251	316	42	3	3	NUM
ejpam-6251	316	43	)	)	PUNCT
ejpam-6251	316	44	→	→	SYM
ejpam-6251	316	45	0	0	NUM
ejpam-6251	316	46	♢	♢	PROPN
ejpam-6251	316	47	0	0	PROPN
ejpam-6251	316	48	♢	♢	PROPN
ejpam-6251	316	49	0	0	NUM
ejpam-6251	316	50	,	,	PUNCT
ejpam-6251	316	51	as	as	ADP
ejpam-6251	316	52	µ→	µ→	X
ejpam-6251	316	53	+	+	NOUN
ejpam-6251	316	54	∞	∞	PROPN
ejpam-6251	316	55	,	,	PUNCT
ejpam-6251	316	56	ξ(ς,ϖ	ξ(ς,ϖ	ADV
ejpam-6251	316	57	,	,	PUNCT
ejpam-6251	316	58	ż	ż	NOUN
ejpam-6251	316	59	)	)	PUNCT
ejpam-6251	316	60	≤	≤	NOUN
ejpam-6251	316	61	ξ	ξ	X
ejpam-6251	316	62	(	(	PUNCT
ejpam-6251	316	63	ς	ς	PROPN
ejpam-6251	316	64	,	,	PUNCT
ejpam-6251	316	65	ςµ	ςµ	NOUN
ejpam-6251	316	66	,	,	PUNCT
ejpam-6251	316	67	ż	ż	NOUN
ejpam-6251	316	68	3	3	X
ejpam-6251	316	69	)	)	PUNCT
ejpam-6251	316	70	♢	♢	PROPN
ejpam-6251	316	71	ξ	ξ	X
ejpam-6251	316	72	(	(	PUNCT
ejpam-6251	316	73	ςµ	ςµ	NOUN
ejpam-6251	316	74	,	,	PUNCT
ejpam-6251	316	75	ςµ+1	ςµ+1	NUM
ejpam-6251	316	76	,	,	PUNCT
ejpam-6251	316	77	ż	ż	NOUN
ejpam-6251	316	78	3	3	X
ejpam-6251	316	79	)	)	PUNCT
ejpam-6251	316	80	♢	♢	PROPN
ejpam-6251	316	81	ξ	ξ	X
ejpam-6251	316	82	(	(	PUNCT
ejpam-6251	316	83	ςµ+1	ςµ+1	NUM
ejpam-6251	316	84	,	,	PUNCT
ejpam-6251	316	85	ϖ	ϖ	NOUN
ejpam-6251	316	86	,	,	PUNCT
ejpam-6251	316	87	ż	ż	NOUN
ejpam-6251	316	88	3	3	NUM
ejpam-6251	316	89	)	)	PUNCT
ejpam-6251	316	90	→	→	SYM
ejpam-6251	316	91	0	0	NUM
ejpam-6251	316	92	♢	♢	PROPN
ejpam-6251	316	93	0	0	PROPN
ejpam-6251	316	94	♢	♢	PROPN
ejpam-6251	316	95	0	0	NUM
ejpam-6251	316	96	,	,	PUNCT
ejpam-6251	316	97	as	as	ADP
ejpam-6251	316	98	µ→	µ→	PROPN
ejpam-6251	316	99	+	+	ADJ
ejpam-6251	316	100	∞.	∞.	PROPN
ejpam-6251	316	101	that	that	PRON
ejpam-6251	316	102	is	be	AUX
ejpam-6251	316	103	π(ς,ϖ	π(ς,ϖ	NUM
ejpam-6251	316	104	,	,	PUNCT
ejpam-6251	316	105	ż	ż	NOUN
ejpam-6251	316	106	)	)	PUNCT
ejpam-6251	316	107	≥	≥	NOUN
ejpam-6251	316	108	1	1	NUM
ejpam-6251	316	109	⋇	⋇	NOUN
ejpam-6251	316	110	1	1	NUM
ejpam-6251	316	111	⋇	⋇	NOUN
ejpam-6251	316	112	1	1	NUM
ejpam-6251	316	113	=	=	SYM
ejpam-6251	316	114	1,ψ(ς,ϖ	1,ψ(ς,ϖ	NUM
ejpam-6251	316	115	,	,	PUNCT
ejpam-6251	316	116	ż	ż	NOUN
ejpam-6251	316	117	)	)	PUNCT
ejpam-6251	316	118	≤	≤	NOUN
ejpam-6251	316	119	0	0	NUM
ejpam-6251	316	120	♢	♢	PROPN
ejpam-6251	316	121	0	0	PROPN
ejpam-6251	316	122	♢	♢	PROPN
ejpam-6251	316	123	0	0	PROPN
ejpam-6251	316	124	=	=	SYM
ejpam-6251	316	125	0	0	NUM
ejpam-6251	316	126	and	and	CCONJ
ejpam-6251	316	127	ξ(ς,ϖ	ξ(ς,ϖ	NOUN
ejpam-6251	316	128	,	,	PUNCT
ejpam-6251	316	129	ż	ż	NOUN
ejpam-6251	316	130	)	)	PUNCT
ejpam-6251	316	131	≤	≤	NOUN
ejpam-6251	316	132	0	0	NUM
ejpam-6251	316	133	♢	♢	PROPN
ejpam-6251	316	134	0	0	PROPN
ejpam-6251	316	135	♢	♢	PROPN
ejpam-6251	316	136	0	0	PROPN
ejpam-6251	316	137	=	=	SYM
ejpam-6251	316	138	0	0	PROPN
ejpam-6251	316	139	.	.	PUNCT
ejpam-6251	317	1	hence	hence	ADV
ejpam-6251	317	2	ς	ς	PROPN
ejpam-6251	317	3	=	=	SYM
ejpam-6251	317	4	ϖ	ϖ	NOUN
ejpam-6251	317	5	,	,	PUNCT
ejpam-6251	317	6	i.e.	i.e.	X
ejpam-6251	317	7	,	,	PUNCT
ejpam-6251	317	8	the	the	DET
ejpam-6251	317	9	sequence	sequence	NOUN
ejpam-6251	317	10	converges	converge	VERB
ejpam-6251	317	11	to	to	ADP
ejpam-6251	317	12	unique	unique	ADJ
ejpam-6251	317	13	limit	limit	NOUN
ejpam-6251	317	14	point	point	NOUN
ejpam-6251	317	15	at	at	ADV
ejpam-6251	317	16	most	most	ADV
ejpam-6251	317	17	.	.	PUNCT
ejpam-6251	318	1	lemma	lemma	PROPN
ejpam-6251	318	2	2	2	X
ejpam-6251	318	3	.	.	PUNCT
ejpam-6251	319	1	let	let	AUX
ejpam-6251	319	2	(	(	PUNCT
ejpam-6251	319	3	𭟋	𭟋	NOUN
ejpam-6251	319	4	,	,	PUNCT
ejpam-6251	319	5	s	s	PROPN
ejpam-6251	319	6	,	,	PUNCT
ejpam-6251	319	7	π	π	PROPN
ejpam-6251	319	8	,	,	PUNCT
ejpam-6251	319	9	ψ	ψ	PROPN
ejpam-6251	319	10	,	,	PUNCT
ejpam-6251	319	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	319	12	,	,	PUNCT
ejpam-6251	319	13	♢	♢	PROPN
ejpam-6251	319	14	)	)	PUNCT
ejpam-6251	319	15	be	be	AUX
ejpam-6251	319	16	a	a	DET
ejpam-6251	319	17	nbms	nbms	NOUN
ejpam-6251	319	18	.	.	PUNCT
ejpam-6251	320	1	if	if	SCONJ
ejpam-6251	320	2	ζ	ζ	PROPN
ejpam-6251	320	3	∈	∈	NOUN
ejpam-6251	320	4	(	(	PUNCT
ejpam-6251	320	5	0	0	NUM
ejpam-6251	320	6	,	,	PUNCT
ejpam-6251	320	7	1	1	NUM
ejpam-6251	320	8	)	)	PUNCT
ejpam-6251	320	9	and	and	CCONJ
ejpam-6251	320	10	for	for	ADP
ejpam-6251	320	11	some	some	DET
ejpam-6251	320	12	ς,ϖ	ς,ϖ	NUM
ejpam-6251	320	13	∈	∈	PROPN
ejpam-6251	320	14	𭟋	𭟋	PROPN
ejpam-6251	320	15	,	,	PUNCT
ejpam-6251	320	16	ż	ż	NOUN
ejpam-6251	320	17	>	>	X
ejpam-6251	320	18	0	0	PROPN
ejpam-6251	320	19	,	,	PUNCT
ejpam-6251	320	20	π(ς,ϖ	π(ς,ϖ	NUM
ejpam-6251	320	21	,	,	PUNCT
ejpam-6251	320	22	ż	ż	NOUN
ejpam-6251	320	23	)	)	PUNCT
ejpam-6251	320	24	≥	≥	NOUN
ejpam-6251	320	25	π	π	PROPN
ejpam-6251	320	26	(	(	PUNCT
ejpam-6251	320	27	ς,ϖ	ς,ϖ	NUM
ejpam-6251	320	28	,	,	PUNCT
ejpam-6251	320	29	ż	ż	NOUN
ejpam-6251	320	30	ζ	ζ	NOUN
ejpam-6251	320	31	)	)	PUNCT
ejpam-6251	320	32	,	,	PUNCT
ejpam-6251	320	33	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	320	34	,	,	PUNCT
ejpam-6251	320	35	ż	ż	NOUN
ejpam-6251	320	36	)	)	PUNCT
ejpam-6251	320	37	≤	≤	NOUN
ejpam-6251	321	1	ψ	ψ	X
ejpam-6251	321	2	(	(	PUNCT
ejpam-6251	321	3	ς,ϖ	ς,ϖ	NUM
ejpam-6251	321	4	,	,	PUNCT
ejpam-6251	321	5	ż	ż	NOUN
ejpam-6251	321	6	ζ	ζ	NOUN
ejpam-6251	321	7	)	)	PUNCT
ejpam-6251	321	8	,	,	PUNCT
ejpam-6251	321	9	ξ(ς,ϖ	ξ(ς,ϖ	ADV
ejpam-6251	321	10	,	,	PUNCT
ejpam-6251	321	11	ż	ż	NOUN
ejpam-6251	321	12	)	)	PUNCT
ejpam-6251	321	13	≤	≤	NOUN
ejpam-6251	322	1	ξ	ξ	PROPN
ejpam-6251	322	2	(	(	PUNCT
ejpam-6251	322	3	ς,ϖ	ς,ϖ	NUM
ejpam-6251	322	4	,	,	PUNCT
ejpam-6251	322	5	ż	ż	NOUN
ejpam-6251	322	6	ζ	ζ	NOUN
ejpam-6251	322	7	)	)	PUNCT
ejpam-6251	322	8	(	(	PUNCT
ejpam-6251	322	9	2	2	X
ejpam-6251	322	10	)	)	PUNCT
ejpam-6251	322	11	then	then	ADV
ejpam-6251	322	12	ς	ς	PROPN
ejpam-6251	322	13	=	=	PUNCT
ejpam-6251	322	14	ϖ.	ϖ.	ADJ
ejpam-6251	322	15	proof	proof	NOUN
ejpam-6251	322	16	.	.	PUNCT
ejpam-6251	323	1	(	(	PUNCT
ejpam-6251	323	2	2	2	X
ejpam-6251	323	3	)	)	PUNCT
ejpam-6251	323	4	implies	imply	VERB
ejpam-6251	323	5	that	that	SCONJ
ejpam-6251	323	6	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	323	7	,	,	PUNCT
ejpam-6251	323	8	ż	ż	NOUN
ejpam-6251	323	9	)	)	PUNCT
ejpam-6251	323	10	≥	≥	NOUN
ejpam-6251	323	11	π	π	PROPN
ejpam-6251	323	12	(	(	PUNCT
ejpam-6251	323	13	ς,ϖ	ς,ϖ	NUM
ejpam-6251	323	14	,	,	PUNCT
ejpam-6251	323	15	ż	ż	NOUN
ejpam-6251	323	16	ζµ	ζµ	X
ejpam-6251	323	17	)	)	PUNCT
ejpam-6251	323	18	,	,	PUNCT
ejpam-6251	323	19	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	323	20	,	,	PUNCT
ejpam-6251	323	21	ż	ż	NOUN
ejpam-6251	323	22	)	)	PUNCT
ejpam-6251	323	23	≤	≤	NOUN
ejpam-6251	324	1	ψ	ψ	X
ejpam-6251	324	2	(	(	PUNCT
ejpam-6251	324	3	ς,ϖ	ς,ϖ	NUM
ejpam-6251	324	4	,	,	PUNCT
ejpam-6251	324	5	ż	ż	NOUN
ejpam-6251	324	6	ζµ	ζµ	X
ejpam-6251	324	7	)	)	PUNCT
ejpam-6251	324	8	,	,	PUNCT
ejpam-6251	324	9	ξ(ς,ϖ	ξ(ς,ϖ	ADV
ejpam-6251	324	10	,	,	PUNCT
ejpam-6251	324	11	ż	ż	NOUN
ejpam-6251	324	12	)	)	PUNCT
ejpam-6251	324	13	≤	≤	NOUN
ejpam-6251	324	14	ξ	ξ	PROPN
ejpam-6251	324	15	(	(	PUNCT
ejpam-6251	324	16	ς,ϖ	ς,ϖ	NUM
ejpam-6251	324	17	,	,	PUNCT
ejpam-6251	324	18	ż	ż	NOUN
ejpam-6251	324	19	ζµ	ζµ	X
ejpam-6251	324	20	)	)	PUNCT
ejpam-6251	324	21	,	,	PUNCT
ejpam-6251	324	22	µ	µ	X
ejpam-6251	324	23	∈	∈	PROPN
ejpam-6251	324	24	n	n	CCONJ
ejpam-6251	324	25	,	,	PUNCT
ejpam-6251	324	26	ż	ż	NOUN
ejpam-6251	324	27	>	>	X
ejpam-6251	324	28	0	0	X
ejpam-6251	324	29	.	.	PUNCT
ejpam-6251	325	1	now	now	ADV
ejpam-6251	325	2	π(ς,ϖ	π(ς,ϖ	NUM
ejpam-6251	325	3	,	,	PUNCT
ejpam-6251	325	4	ż	ż	NOUN
ejpam-6251	325	5	)	)	PUNCT
ejpam-6251	325	6	≥	≥	NOUN
ejpam-6251	325	7	lim	lim	PROPN
ejpam-6251	325	8	µ→+∞	µ→+∞	VERB
ejpam-6251	325	9	π	π	PROPN
ejpam-6251	325	10	(	(	PUNCT
ejpam-6251	325	11	ς,ϖ	ς,ϖ	NUM
ejpam-6251	325	12	,	,	PUNCT
ejpam-6251	325	13	ż	ż	NOUN
ejpam-6251	325	14	ζµ	ζµ	X
ejpam-6251	325	15	)	)	PUNCT
ejpam-6251	325	16	=	=	SYM
ejpam-6251	325	17	1	1	NUM
ejpam-6251	325	18	,	,	PUNCT
ejpam-6251	325	19	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	325	20	,	,	PUNCT
ejpam-6251	325	21	ż	ż	NOUN
ejpam-6251	325	22	)	)	PUNCT
ejpam-6251	325	23	≤	≤	NOUN
ejpam-6251	326	1	lim	lim	PROPN
ejpam-6251	326	2	µ→+∞	µ→+∞	PROPN
ejpam-6251	326	3	ψ	ψ	PROPN
ejpam-6251	326	4	(	(	PUNCT
ejpam-6251	326	5	ς,ϖ	ς,ϖ	NUM
ejpam-6251	326	6	,	,	PUNCT
ejpam-6251	326	7	ż	ż	NOUN
ejpam-6251	326	8	ζµ	ζµ	X
ejpam-6251	326	9	)	)	PUNCT
ejpam-6251	326	10	=	=	SYM
ejpam-6251	326	11	0	0	NUM
ejpam-6251	326	12	,	,	PUNCT
ejpam-6251	326	13	ξ(ς,ϖ	ξ(ς,ϖ	ADV
ejpam-6251	326	14	,	,	PUNCT
ejpam-6251	326	15	ż	ż	NOUN
ejpam-6251	326	16	)	)	PUNCT
ejpam-6251	326	17	≤	≤	NOUN
ejpam-6251	326	18	lim	lim	PROPN
ejpam-6251	326	19	µ→+∞	µ→+∞	VERB
ejpam-6251	326	20	ξ	ξ	PROPN
ejpam-6251	326	21	(	(	PUNCT
ejpam-6251	326	22	ς,ϖ	ς,ϖ	NUM
ejpam-6251	326	23	,	,	PUNCT
ejpam-6251	326	24	ż	ż	NOUN
ejpam-6251	326	25	ζµ	ζµ	X
ejpam-6251	326	26	)	)	PUNCT
ejpam-6251	326	27	=	=	SYM
ejpam-6251	327	1	0	0	NUM
ejpam-6251	327	2	,	,	PUNCT
ejpam-6251	327	3	ż	ż	NOUN
ejpam-6251	327	4	>	>	X
ejpam-6251	328	1	0	0	X
ejpam-6251	328	2	.	.	PUNCT
ejpam-6251	329	1	also	also	ADV
ejpam-6251	329	2	,	,	PUNCT
ejpam-6251	329	3	by	by	ADP
ejpam-6251	329	4	definition	definition	NOUN
ejpam-6251	329	5	of	of	ADP
ejpam-6251	329	6	iii	iii	PROPN
ejpam-6251	329	7	,	,	PUNCT
ejpam-6251	329	8	viii	viii	NOUN
ejpam-6251	329	9	,	,	PUNCT
ejpam-6251	329	10	xiii	xiii	PROPN
ejpam-6251	329	11	,	,	PUNCT
ejpam-6251	329	12	that	that	ADV
ejpam-6251	329	13	is	is	ADV
ejpam-6251	329	14	,	,	PUNCT
ejpam-6251	329	15	ς	ς	PROPN
ejpam-6251	329	16	=	=	PUNCT
ejpam-6251	329	17	ϖ.	ϖ.	PROPN
ejpam-6251	329	18	r.	r.	PROPN
ejpam-6251	329	19	ramaswamy	ramaswamy	PROPN
ejpam-6251	329	20	/	/	SYM
ejpam-6251	329	21	eur	eur	PROPN
ejpam-6251	329	22	.	.	PUNCT
ejpam-6251	330	1	j.	j.	PROPN
ejpam-6251	330	2	pure	pure	PROPN
ejpam-6251	330	3	appl	appl	PROPN
ejpam-6251	330	4	.	.	PROPN
ejpam-6251	330	5	math	math	PROPN
ejpam-6251	330	6	,	,	PUNCT
ejpam-6251	330	7	18	18	NUM
ejpam-6251	330	8	(	(	PUNCT
ejpam-6251	330	9	4	4	NUM
ejpam-6251	330	10	)	)	PUNCT
ejpam-6251	330	11	(	(	PUNCT
ejpam-6251	330	12	2025	2025	NUM
ejpam-6251	330	13	)	)	PUNCT
ejpam-6251	330	14	,	,	PUNCT
ejpam-6251	330	15	6251	6251	NUM
ejpam-6251	330	16	13	13	NUM
ejpam-6251	330	17	of	of	ADP
ejpam-6251	330	18	40	40	NUM
ejpam-6251	330	19	theorem	theorem	NOUN
ejpam-6251	330	20	5	5	NUM
ejpam-6251	330	21	.	.	PUNCT
ejpam-6251	330	22	suppose	suppose	VERB
ejpam-6251	330	23	(	(	PUNCT
ejpam-6251	330	24	𭟋	𭟋	NOUN
ejpam-6251	330	25	,	,	PUNCT
ejpam-6251	330	26	s	s	PROPN
ejpam-6251	330	27	,	,	PUNCT
ejpam-6251	330	28	π	π	PROPN
ejpam-6251	330	29	,	,	PUNCT
ejpam-6251	330	30	ψ	ψ	PROPN
ejpam-6251	330	31	,	,	PUNCT
ejpam-6251	330	32	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	330	33	,	,	PUNCT
ejpam-6251	330	34	♢	♢	PROPN
ejpam-6251	330	35	)	)	PUNCT
ejpam-6251	330	36	is	be	AUX
ejpam-6251	330	37	a	a	DET
ejpam-6251	330	38	complete	complete	ADJ
ejpam-6251	330	39	nbms	nbms	NOUN
ejpam-6251	330	40	with	with	ADP
ejpam-6251	330	41	0	0	NUM
ejpam-6251	330	42	<	<	X
ejpam-6251	330	43	ζ	ζ	X
ejpam-6251	330	44	<	<	X
ejpam-6251	330	45	1	1	NUM
ejpam-6251	330	46	.	.	PUNCT
ejpam-6251	331	1	let	let	VERB
ejpam-6251	331	2	p	p	NOUN
ejpam-6251	331	3	:	:	PUNCT
ejpam-6251	331	4	𭟋	𭟋	ADP
ejpam-6251	331	5	∪	∪	ADP
ejpam-6251	331	6	s	s	X
ejpam-6251	331	7	→	→	SYM
ejpam-6251	331	8	𭟋	𭟋	ADP
ejpam-6251	331	9	∪	∪	NOUN
ejpam-6251	331	10	s	s	AUX
ejpam-6251	331	11	be	be	VERB
ejpam-6251	331	12	a	a	DET
ejpam-6251	331	13	mapping	mapping	NOUN
ejpam-6251	331	14	satisfying	satisfy	VERB
ejpam-6251	331	15	i.	i.	NOUN
ejpam-6251	331	16	p(𭟋	p(𭟋	PROPN
ejpam-6251	331	17	)	)	PUNCT
ejpam-6251	332	1	⊆	⊆	NUM
ejpam-6251	332	2	𭟋	𭟋	NOUN
ejpam-6251	332	3	and	and	CCONJ
ejpam-6251	332	4	p(s	p(s	NUM
ejpam-6251	332	5	)	)	PUNCT
ejpam-6251	332	6	⊆	⊆	NUM
ejpam-6251	332	7	s	s	NOUN
ejpam-6251	332	8	;	;	PUNCT
ejpam-6251	332	9	ii	ii	X
ejpam-6251	332	10	.	.	PUNCT
ejpam-6251	333	1	π(pς	π(pς	NOUN
ejpam-6251	333	2	,	,	PUNCT
ejpam-6251	333	3	pϖ	pϖ	ADP
ejpam-6251	333	4	,	,	PUNCT
ejpam-6251	333	5	ζ	ζ	NOUN
ejpam-6251	333	6	ż	ż	NOUN
ejpam-6251	333	7	)	)	PUNCT
ejpam-6251	333	8	≥	≥	NOUN
ejpam-6251	333	9	π(ς,ϖ	π(ς,ϖ	ADP
ejpam-6251	333	10	,	,	PUNCT
ejpam-6251	333	11	ż	ż	NOUN
ejpam-6251	333	12	)	)	PUNCT
ejpam-6251	333	13	,	,	PUNCT
ejpam-6251	333	14	ψ(pς	ψ(pς	NOUN
ejpam-6251	333	15	,	,	PUNCT
ejpam-6251	333	16	pϖ	pϖ	ADP
ejpam-6251	333	17	,	,	PUNCT
ejpam-6251	333	18	ζ	ζ	NOUN
ejpam-6251	333	19	ż	ż	NOUN
ejpam-6251	333	20	)	)	PUNCT
ejpam-6251	333	21	≤	≤	NOUN
ejpam-6251	333	22	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	333	23	,	,	PUNCT
ejpam-6251	333	24	ż	ż	NOUN
ejpam-6251	333	25	)	)	PUNCT
ejpam-6251	333	26	and	and	CCONJ
ejpam-6251	333	27	ξ(pς	ξ(pς	NOUN
ejpam-6251	333	28	,	,	PUNCT
ejpam-6251	333	29	pϖ	pϖ	ADP
ejpam-6251	333	30	,	,	PUNCT
ejpam-6251	333	31	ζ	ζ	NOUN
ejpam-6251	333	32	ż	ż	NOUN
ejpam-6251	333	33	)	)	PUNCT
ejpam-6251	333	34	≤	≤	NOUN
ejpam-6251	333	35	ξ(ς,ϖ	ξ(ς,ϖ	ADP
ejpam-6251	333	36	,	,	PUNCT
ejpam-6251	333	37	ż	ż	NOUN
ejpam-6251	333	38	)	)	PUNCT
ejpam-6251	333	39	(	(	PUNCT
ejpam-6251	333	40	3	3	X
ejpam-6251	333	41	)	)	PUNCT
ejpam-6251	333	42	∀	∀	NOUN
ejpam-6251	334	1	ς	ς	PROPN
ejpam-6251	334	2	∈	∈	X
ejpam-6251	334	3	𭟋	𭟋	X
ejpam-6251	334	4	,	,	PUNCT
ejpam-6251	334	5	ϖ	ϖ	PROPN
ejpam-6251	334	6	∈	∈	PROPN
ejpam-6251	334	7	s	s	PART
ejpam-6251	334	8	and	and	CCONJ
ejpam-6251	334	9	ż	ż	X
ejpam-6251	334	10	>	>	X
ejpam-6251	334	11	0	0	X
ejpam-6251	334	12	.	.	PUNCT
ejpam-6251	335	1	then	then	ADV
ejpam-6251	335	2	p	p	X
ejpam-6251	335	3	has	have	VERB
ejpam-6251	335	4	a	a	DET
ejpam-6251	335	5	unique	unique	ADJ
ejpam-6251	335	6	fixed	fix	VERB
ejpam-6251	335	7	point	point	NOUN
ejpam-6251	335	8	.	.	PUNCT
ejpam-6251	336	1	proof	proof	NOUN
ejpam-6251	336	2	.	.	PUNCT
ejpam-6251	337	1	let	let	VERB
ejpam-6251	337	2	ς0	ς0	PROPN
ejpam-6251	337	3	∈	∈	PROPN
ejpam-6251	337	4	𭟋	𭟋	NOUN
ejpam-6251	337	5	and	and	CCONJ
ejpam-6251	337	6	ϖ0	ϖ0	NOUN
ejpam-6251	337	7	∈	∈	NOUN
ejpam-6251	337	8	s	s	PART
ejpam-6251	337	9	and	and	CCONJ
ejpam-6251	337	10	assume	assume	VERB
ejpam-6251	337	11	that	that	SCONJ
ejpam-6251	337	12	p(ςµ	p(ςµ	NOUN
ejpam-6251	337	13	)	)	PUNCT
ejpam-6251	337	14	=	=	SYM
ejpam-6251	337	15	ςµ+1	ςµ+1	NUM
ejpam-6251	337	16	and	and	CCONJ
ejpam-6251	337	17	p(ϖµ	p(ϖµ	NOUN
ejpam-6251	337	18	)	)	PUNCT
ejpam-6251	338	1	=	=	SYM
ejpam-6251	338	2	ϖµ+1	ϖµ+1	NUM
ejpam-6251	338	3	∀	∀	NOUN
ejpam-6251	338	4	µ	µ	PRON
ejpam-6251	338	5	∈	∈	NOUN
ejpam-6251	338	6	n	n	NOUN
ejpam-6251	338	7	∪	∪	X
ejpam-6251	338	8	{	{	PUNCT
ejpam-6251	338	9	0	0	NUM
ejpam-6251	338	10	}	}	PUNCT
ejpam-6251	338	11	.	.	PUNCT
ejpam-6251	339	1	then	then	ADV
ejpam-6251	339	2	we	we	PRON
ejpam-6251	339	3	get	get	VERB
ejpam-6251	339	4	(	(	PUNCT
ejpam-6251	339	5	ςµ	ςµ	NOUN
ejpam-6251	339	6	,	,	PUNCT
ejpam-6251	339	7	ϖµ	ϖµ	NOUN
ejpam-6251	339	8	)	)	PUNCT
ejpam-6251	339	9	as	as	ADP
ejpam-6251	339	10	a	a	DET
ejpam-6251	339	11	bisequence	bisequence	NOUN
ejpam-6251	339	12	on	on	ADP
ejpam-6251	339	13	nbms	nbms	NOUN
ejpam-6251	339	14	(	(	PUNCT
ejpam-6251	339	15	𭟋	𭟋	NOUN
ejpam-6251	339	16	,	,	PUNCT
ejpam-6251	339	17	s	s	PROPN
ejpam-6251	339	18	,	,	PUNCT
ejpam-6251	339	19	π	π	PROPN
ejpam-6251	339	20	,	,	PUNCT
ejpam-6251	339	21	ψ	ψ	PROPN
ejpam-6251	339	22	,	,	PUNCT
ejpam-6251	339	23	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	339	24	,	,	PUNCT
ejpam-6251	339	25	♢	♢	PROPN
ejpam-6251	339	26	)	)	PUNCT
ejpam-6251	339	27	.	.	PUNCT
ejpam-6251	340	1	now	now	ADV
ejpam-6251	340	2	,	,	PUNCT
ejpam-6251	340	3	we	we	PRON
ejpam-6251	340	4	have	have	VERB
ejpam-6251	340	5	π(ς1	π(ς1	NOUN
ejpam-6251	340	6	,	,	PUNCT
ejpam-6251	340	7	ϖ1	ϖ1	VERB
ejpam-6251	340	8	,	,	PUNCT
ejpam-6251	340	9	ż	ż	NOUN
ejpam-6251	340	10	)	)	PUNCT
ejpam-6251	341	1	=	=	SYM
ejpam-6251	341	2	π(pς0	π(pς0	PROPN
ejpam-6251	341	3	,	,	PUNCT
ejpam-6251	341	4	pϖ0	pϖ0	PROPN
ejpam-6251	341	5	,	,	PUNCT
ejpam-6251	341	6	ż	ż	NOUN
ejpam-6251	341	7	)	)	PUNCT
ejpam-6251	341	8	≥	≥	NOUN
ejpam-6251	341	9	π(ς0	π(ς0	NOUN
ejpam-6251	341	10	,	,	PUNCT
ejpam-6251	341	11	ϖ0	ϖ0	NOUN
ejpam-6251	341	12	,	,	PUNCT
ejpam-6251	341	13	ż	ż	NOUN
ejpam-6251	341	14	ζ	ζ	NOUN
ejpam-6251	341	15	)	)	PUNCT
ejpam-6251	341	16	,	,	PUNCT
ejpam-6251	341	17	ψ(ς1	ψ(ς1	NOUN
ejpam-6251	341	18	,	,	PUNCT
ejpam-6251	341	19	ϖ1	ϖ1	PROPN
ejpam-6251	341	20	,	,	PUNCT
ejpam-6251	341	21	ż	ż	NOUN
ejpam-6251	341	22	)	)	PUNCT
ejpam-6251	341	23	=	=	PUNCT
ejpam-6251	342	1	ψ(pς0	ψ(pς0	ADJ
ejpam-6251	342	2	,	,	PUNCT
ejpam-6251	342	3	pϖ0	pϖ0	PROPN
ejpam-6251	342	4	,	,	PUNCT
ejpam-6251	342	5	ż	ż	NOUN
ejpam-6251	342	6	)	)	PUNCT
ejpam-6251	342	7	≤	≤	NOUN
ejpam-6251	342	8	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	342	9	,	,	PUNCT
ejpam-6251	342	10	ϖ0	ϖ0	NOUN
ejpam-6251	342	11	,	,	PUNCT
ejpam-6251	342	12	ż	ż	NOUN
ejpam-6251	342	13	ζ	ζ	NOUN
ejpam-6251	342	14	)	)	PUNCT
ejpam-6251	342	15	and	and	CCONJ
ejpam-6251	342	16	ξ(ς1	ξ(ς1	NOUN
ejpam-6251	342	17	,	,	PUNCT
ejpam-6251	342	18	ϖ1	ϖ1	VERB
ejpam-6251	342	19	,	,	PUNCT
ejpam-6251	342	20	ż	ż	NOUN
ejpam-6251	342	21	)	)	PUNCT
ejpam-6251	342	22	=	=	SYM
ejpam-6251	342	23	ξ(pς0	ξ(pς0	PROPN
ejpam-6251	342	24	,	,	PUNCT
ejpam-6251	342	25	pϖ0	pϖ0	PROPN
ejpam-6251	342	26	,	,	PUNCT
ejpam-6251	342	27	ż	ż	NOUN
ejpam-6251	342	28	)	)	PUNCT
ejpam-6251	342	29	≤	≤	NOUN
ejpam-6251	342	30	ξ(ς0	ξ(ς0	NOUN
ejpam-6251	342	31	,	,	PUNCT
ejpam-6251	342	32	ϖ0	ϖ0	NOUN
ejpam-6251	342	33	,	,	PUNCT
ejpam-6251	342	34	ż	ż	NOUN
ejpam-6251	342	35	ζ	ζ	NOUN
ejpam-6251	342	36	)	)	PUNCT
ejpam-6251	342	37	,	,	PUNCT
ejpam-6251	342	38	∀	∀	PUNCT
ejpam-6251	343	1	ż	ż	VERB
ejpam-6251	343	2	>	>	X
ejpam-6251	343	3	0	0	NUM
ejpam-6251	343	4	and	and	CCONJ
ejpam-6251	343	5	µ	µ	PRON
ejpam-6251	343	6	∈	∈	PROPN
ejpam-6251	343	7	n.	n.	NOUN
ejpam-6251	343	8	by	by	ADP
ejpam-6251	343	9	simple	simple	ADJ
ejpam-6251	343	10	induction	induction	NOUN
ejpam-6251	343	11	,	,	PUNCT
ejpam-6251	343	12	we	we	PRON
ejpam-6251	343	13	get	get	VERB
ejpam-6251	343	14	π(ςµ	π(ςµ	NUM
ejpam-6251	343	15	,	,	PUNCT
ejpam-6251	343	16	ϖµ	ϖµ	NOUN
ejpam-6251	343	17	,	,	PUNCT
ejpam-6251	343	18	ż	ż	NOUN
ejpam-6251	343	19	)	)	PUNCT
ejpam-6251	343	20	=	=	PUNCT
ejpam-6251	343	21	π(pςµ−1	π(pςµ−1	PROPN
ejpam-6251	343	22	,	,	PUNCT
ejpam-6251	343	23	pϖµ−1	pϖµ−1	PROPN
ejpam-6251	343	24	,	,	PUNCT
ejpam-6251	343	25	ż	ż	NOUN
ejpam-6251	343	26	)	)	PUNCT
ejpam-6251	343	27	≥	≥	NOUN
ejpam-6251	343	28	π(ςµ−1	π(ςµ−1	PROPN
ejpam-6251	343	29	,	,	PUNCT
ejpam-6251	343	30	ϖµ−1	ϖµ−1	VERB
ejpam-6251	343	31	,	,	PUNCT
ejpam-6251	343	32	ż	ż	NOUN
ejpam-6251	343	33	ζ	ζ	NOUN
ejpam-6251	343	34	)	)	PUNCT
ejpam-6251	343	35	≥	≥	NOUN
ejpam-6251	343	36	π	π	PROPN
ejpam-6251	343	37	(	(	PUNCT
ejpam-6251	343	38	ςµ−2	ςµ−2	PROPN
ejpam-6251	343	39	,	,	PUNCT
ejpam-6251	343	40	ϖµ−2	ϖµ−2	NOUN
ejpam-6251	343	41	,	,	PUNCT
ejpam-6251	343	42	ż	ż	NOUN
ejpam-6251	343	43	ζ2	ζ2	NOUN
ejpam-6251	343	44	)	)	PUNCT
ejpam-6251	343	45	≥	≥	NOUN
ejpam-6251	344	1	π	π	PROPN
ejpam-6251	344	2	(	(	PUNCT
ejpam-6251	344	3	ςµ−3	ςµ−3	NOUN
ejpam-6251	344	4	,	,	PUNCT
ejpam-6251	344	5	ϖµ−3	ϖµ−3	ADJ
ejpam-6251	344	6	,	,	PUNCT
ejpam-6251	344	7	ż	ż	NOUN
ejpam-6251	344	8	ζ3	ζ3	NOUN
ejpam-6251	344	9	)	)	PUNCT
ejpam-6251	344	10	≥	≥	X
ejpam-6251	344	11	·	·	PUNCT
ejpam-6251	344	12	·	·	PUNCT
ejpam-6251	344	13	·	·	PUNCT
ejpam-6251	344	14	≥	≥	NUM
ejpam-6251	345	1	π	π	NOUN
ejpam-6251	345	2	(	(	PUNCT
ejpam-6251	345	3	ς0	ς0	PROPN
ejpam-6251	345	4	,	,	PUNCT
ejpam-6251	345	5	ϖ0	ϖ0	NOUN
ejpam-6251	345	6	,	,	PUNCT
ejpam-6251	345	7	ż	ż	NOUN
ejpam-6251	345	8	ζµ	ζµ	X
ejpam-6251	345	9	)	)	PUNCT
ejpam-6251	345	10	,	,	PUNCT
ejpam-6251	345	11	ψ(ςµ	ψ(ςµ	PROPN
ejpam-6251	345	12	,	,	PUNCT
ejpam-6251	345	13	ϖµ	ϖµ	NOUN
ejpam-6251	345	14	,	,	PUNCT
ejpam-6251	345	15	ż	ż	NOUN
ejpam-6251	345	16	)	)	PUNCT
ejpam-6251	345	17	=	=	PUNCT
ejpam-6251	345	18	ψ(pςµ−1	ψ(pςµ−1	PROPN
ejpam-6251	345	19	,	,	PUNCT
ejpam-6251	345	20	pϖµ−1	pϖµ−1	PROPN
ejpam-6251	345	21	,	,	PUNCT
ejpam-6251	345	22	ż	ż	NOUN
ejpam-6251	345	23	)	)	PUNCT
ejpam-6251	345	24	≤	≤	NOUN
ejpam-6251	345	25	ψ(ςµ−1	ψ(ςµ−1	PUNCT
ejpam-6251	345	26	,	,	PUNCT
ejpam-6251	345	27	ϖµ−1	ϖµ−1	ADJ
ejpam-6251	345	28	,	,	PUNCT
ejpam-6251	345	29	ż	ż	NOUN
ejpam-6251	345	30	ζ	ζ	NOUN
ejpam-6251	345	31	)	)	PUNCT
ejpam-6251	345	32	≤	≤	NOUN
ejpam-6251	346	1	ψ	ψ	X
ejpam-6251	346	2	(	(	PUNCT
ejpam-6251	346	3	ςµ−2	ςµ−2	PROPN
ejpam-6251	346	4	,	,	PUNCT
ejpam-6251	346	5	ϖµ−2	ϖµ−2	NOUN
ejpam-6251	346	6	,	,	PUNCT
ejpam-6251	346	7	ż	ż	NOUN
ejpam-6251	346	8	ζ2	ζ2	NOUN
ejpam-6251	346	9	)	)	PUNCT
ejpam-6251	346	10	≤	≤	NUM
ejpam-6251	346	11	ψ	ψ	X
ejpam-6251	346	12	(	(	PUNCT
ejpam-6251	346	13	ςµ−3	ςµ−3	NOUN
ejpam-6251	346	14	,	,	PUNCT
ejpam-6251	346	15	ϖµ−3	ϖµ−3	ADJ
ejpam-6251	346	16	,	,	PUNCT
ejpam-6251	346	17	ż	ż	NOUN
ejpam-6251	346	18	ζ3	ζ3	NOUN
ejpam-6251	346	19	)	)	PUNCT
ejpam-6251	346	20	≤	≤	NOUN
ejpam-6251	346	21	·	·	PUNCT
ejpam-6251	346	22	·	·	PUNCT
ejpam-6251	346	23	·	·	PUNCT
ejpam-6251	347	1	≤	≤	NUM
ejpam-6251	347	2	ψ	ψ	X
ejpam-6251	347	3	(	(	PUNCT
ejpam-6251	347	4	ς0	ς0	PROPN
ejpam-6251	347	5	,	,	PUNCT
ejpam-6251	347	6	ϖ0	ϖ0	NOUN
ejpam-6251	347	7	,	,	PUNCT
ejpam-6251	347	8	ż	ż	NOUN
ejpam-6251	347	9	ζµ	ζµ	ADP
ejpam-6251	347	10	)	)	PUNCT
ejpam-6251	347	11	.	.	PUNCT
ejpam-6251	347	12	and	and	CCONJ
ejpam-6251	347	13	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	347	14	,	,	PUNCT
ejpam-6251	347	15	ϖµ	ϖµ	NOUN
ejpam-6251	347	16	,	,	PUNCT
ejpam-6251	347	17	ż	ż	NOUN
ejpam-6251	347	18	)	)	PUNCT
ejpam-6251	347	19	=	=	SYM
ejpam-6251	347	20	ξ(pςµ−1	ξ(pςµ−1	PROPN
ejpam-6251	347	21	,	,	PUNCT
ejpam-6251	347	22	pϖµ−1	pϖµ−1	PROPN
ejpam-6251	347	23	,	,	PUNCT
ejpam-6251	347	24	ż	ż	NOUN
ejpam-6251	347	25	)	)	PUNCT
ejpam-6251	347	26	≤	≤	NOUN
ejpam-6251	347	27	ξ(ςµ−1	ξ(ςµ−1	NUM
ejpam-6251	347	28	,	,	PUNCT
ejpam-6251	347	29	ϖµ−1	ϖµ−1	ADJ
ejpam-6251	347	30	,	,	PUNCT
ejpam-6251	347	31	ż	ż	NOUN
ejpam-6251	347	32	ζ	ζ	NOUN
ejpam-6251	347	33	)	)	PUNCT
ejpam-6251	347	34	≤	≤	NUM
ejpam-6251	347	35	ξ	ξ	PROPN
ejpam-6251	347	36	(	(	PUNCT
ejpam-6251	347	37	ςµ−2	ςµ−2	PROPN
ejpam-6251	347	38	,	,	PUNCT
ejpam-6251	347	39	ϖµ−2	ϖµ−2	NOUN
ejpam-6251	347	40	,	,	PUNCT
ejpam-6251	347	41	ż	ż	NOUN
ejpam-6251	347	42	ζ2	ζ2	NOUN
ejpam-6251	347	43	)	)	PUNCT
ejpam-6251	347	44	≤	≤	NUM
ejpam-6251	347	45	ξ	ξ	X
ejpam-6251	347	46	(	(	PUNCT
ejpam-6251	347	47	ςµ−3	ςµ−3	NOUN
ejpam-6251	347	48	,	,	PUNCT
ejpam-6251	347	49	ϖµ−3	ϖµ−3	ADJ
ejpam-6251	347	50	,	,	PUNCT
ejpam-6251	347	51	ż	ż	NOUN
ejpam-6251	347	52	ζ3	ζ3	NOUN
ejpam-6251	347	53	)	)	PUNCT
ejpam-6251	347	54	≤	≤	NOUN
ejpam-6251	347	55	·	·	PUNCT
ejpam-6251	347	56	·	·	PUNCT
ejpam-6251	347	57	·	·	PUNCT
ejpam-6251	348	1	≤	≤	NUM
ejpam-6251	348	2	ξ	ξ	X
ejpam-6251	348	3	(	(	PUNCT
ejpam-6251	348	4	ς0	ς0	PROPN
ejpam-6251	348	5	,	,	PUNCT
ejpam-6251	348	6	ϖ0	ϖ0	NOUN
ejpam-6251	348	7	,	,	PUNCT
ejpam-6251	348	8	ż	ż	NOUN
ejpam-6251	348	9	ζµ	ζµ	ADP
ejpam-6251	348	10	)	)	PUNCT
ejpam-6251	348	11	.	.	PUNCT
ejpam-6251	349	1	r.	r.	PROPN
ejpam-6251	349	2	ramaswamy	ramaswamy	PROPN
ejpam-6251	349	3	/	/	SYM
ejpam-6251	349	4	eur	eur	PROPN
ejpam-6251	349	5	.	.	PUNCT
ejpam-6251	350	1	j.	j.	PROPN
ejpam-6251	350	2	pure	pure	PROPN
ejpam-6251	350	3	appl	appl	PROPN
ejpam-6251	350	4	.	.	PROPN
ejpam-6251	350	5	math	math	PROPN
ejpam-6251	350	6	,	,	PUNCT
ejpam-6251	350	7	18	18	NUM
ejpam-6251	350	8	(	(	PUNCT
ejpam-6251	350	9	4	4	NUM
ejpam-6251	350	10	)	)	PUNCT
ejpam-6251	350	11	(	(	PUNCT
ejpam-6251	350	12	2025	2025	NUM
ejpam-6251	350	13	)	)	PUNCT
ejpam-6251	350	14	,	,	PUNCT
ejpam-6251	350	15	6251	6251	NUM
ejpam-6251	350	16	14	14	NUM
ejpam-6251	350	17	of	of	ADP
ejpam-6251	350	18	40	40	NUM
ejpam-6251	350	19	we	we	PRON
ejpam-6251	350	20	obtain	obtain	VERB
ejpam-6251	350	21	π(ςµ	π(ςµ	NUM
ejpam-6251	350	22	,	,	PUNCT
ejpam-6251	350	23	ϖµ	ϖµ	NOUN
ejpam-6251	350	24	,	,	PUNCT
ejpam-6251	350	25	ż	ż	NOUN
ejpam-6251	350	26	)	)	PUNCT
ejpam-6251	350	27	≥	≥	NOUN
ejpam-6251	351	1	π	π	PROPN
ejpam-6251	351	2	(	(	PUNCT
ejpam-6251	351	3	ς0	ς0	PROPN
ejpam-6251	351	4	,	,	PUNCT
ejpam-6251	351	5	ϖ0	ϖ0	NOUN
ejpam-6251	351	6	,	,	PUNCT
ejpam-6251	351	7	ż	ż	NOUN
ejpam-6251	351	8	ζµ	ζµ	X
ejpam-6251	351	9	)	)	PUNCT
ejpam-6251	351	10	,	,	PUNCT
ejpam-6251	351	11	ψ(ςµ	ψ(ςµ	PROPN
ejpam-6251	351	12	,	,	PUNCT
ejpam-6251	351	13	ϖµ	ϖµ	NOUN
ejpam-6251	351	14	,	,	PUNCT
ejpam-6251	351	15	ż	ż	NOUN
ejpam-6251	351	16	)	)	PUNCT
ejpam-6251	351	17	≤	≤	NOUN
ejpam-6251	352	1	ψ	ψ	X
ejpam-6251	352	2	(	(	PUNCT
ejpam-6251	352	3	ς0	ς0	PROPN
ejpam-6251	352	4	,	,	PUNCT
ejpam-6251	352	5	ϖ0	ϖ0	NOUN
ejpam-6251	352	6	,	,	PUNCT
ejpam-6251	352	7	ż	ż	NOUN
ejpam-6251	352	8	ζµ	ζµ	X
ejpam-6251	352	9	)	)	PUNCT
ejpam-6251	352	10	,	,	PUNCT
ejpam-6251	352	11	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	352	12	,	,	PUNCT
ejpam-6251	352	13	ϖµ	ϖµ	NOUN
ejpam-6251	352	14	,	,	PUNCT
ejpam-6251	352	15	ż	ż	NOUN
ejpam-6251	352	16	)	)	PUNCT
ejpam-6251	353	1	≤	≤	NOUN
ejpam-6251	353	2	ξ	ξ	PROPN
ejpam-6251	353	3	(	(	PUNCT
ejpam-6251	353	4	ς0	ς0	PROPN
ejpam-6251	353	5	,	,	PUNCT
ejpam-6251	353	6	ϖ0	ϖ0	NOUN
ejpam-6251	353	7	,	,	PUNCT
ejpam-6251	353	8	ż	ż	NOUN
ejpam-6251	353	9	ζµ	ζµ	X
ejpam-6251	353	10	)	)	PUNCT
ejpam-6251	353	11	(	(	PUNCT
ejpam-6251	353	12	4	4	NUM
ejpam-6251	353	13	)	)	PUNCT
ejpam-6251	353	14	and	and	CCONJ
ejpam-6251	353	15	π(ςµ+1	π(ςµ+1	PROPN
ejpam-6251	353	16	,	,	PUNCT
ejpam-6251	353	17	ϖµ	ϖµ	NOUN
ejpam-6251	353	18	,	,	PUNCT
ejpam-6251	353	19	ż	ż	NOUN
ejpam-6251	353	20	)	)	PUNCT
ejpam-6251	353	21	≥	≥	NOUN
ejpam-6251	353	22	π	π	PROPN
ejpam-6251	353	23	(	(	PUNCT
ejpam-6251	353	24	ς1	ς1	NOUN
ejpam-6251	353	25	,	,	PUNCT
ejpam-6251	353	26	ϖ0	ϖ0	NOUN
ejpam-6251	353	27	,	,	PUNCT
ejpam-6251	353	28	ż	ż	NOUN
ejpam-6251	353	29	ζµ	ζµ	X
ejpam-6251	353	30	)	)	PUNCT
ejpam-6251	353	31	,	,	PUNCT
ejpam-6251	353	32	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	353	33	,	,	PUNCT
ejpam-6251	353	34	ϖµ	ϖµ	NOUN
ejpam-6251	353	35	,	,	PUNCT
ejpam-6251	353	36	ż	ż	NOUN
ejpam-6251	353	37	)	)	PUNCT
ejpam-6251	353	38	≤	≤	NOUN
ejpam-6251	353	39	ψ	ψ	X
ejpam-6251	353	40	(	(	PUNCT
ejpam-6251	353	41	ς1	ς1	NOUN
ejpam-6251	353	42	,	,	PUNCT
ejpam-6251	353	43	ϖ0	ϖ0	NOUN
ejpam-6251	353	44	,	,	PUNCT
ejpam-6251	353	45	ż	ż	NOUN
ejpam-6251	353	46	ζµ	ζµ	X
ejpam-6251	353	47	)	)	PUNCT
ejpam-6251	353	48	,	,	PUNCT
ejpam-6251	353	49	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	353	50	,	,	PUNCT
ejpam-6251	353	51	ϖµ	ϖµ	NOUN
ejpam-6251	353	52	,	,	PUNCT
ejpam-6251	353	53	ż	ż	NOUN
ejpam-6251	353	54	)	)	PUNCT
ejpam-6251	353	55	≤	≤	NOUN
ejpam-6251	353	56	ξ	ξ	PROPN
ejpam-6251	353	57	(	(	PUNCT
ejpam-6251	353	58	ς1	ς1	NOUN
ejpam-6251	353	59	,	,	PUNCT
ejpam-6251	353	60	ϖ0	ϖ0	NOUN
ejpam-6251	353	61	,	,	PUNCT
ejpam-6251	353	62	ż	ż	NOUN
ejpam-6251	353	63	ζµ	ζµ	ADP
ejpam-6251	353	64	)	)	PUNCT
ejpam-6251	353	65	.	.	PUNCT
ejpam-6251	354	1	(	(	PUNCT
ejpam-6251	354	2	5	5	X
ejpam-6251	354	3	)	)	PUNCT
ejpam-6251	354	4	letting	let	VERB
ejpam-6251	354	5	µ	µ	PRON
ejpam-6251	354	6	<	<	X
ejpam-6251	354	7	m	m	PROPN
ejpam-6251	354	8	,	,	PUNCT
ejpam-6251	354	9	for	for	ADP
ejpam-6251	354	10	µ,m	µ,m	PROPN
ejpam-6251	354	11	∈	∈	PROPN
ejpam-6251	354	12	n.	n.	NOUN
ejpam-6251	354	13	then	then	ADV
ejpam-6251	354	14	,	,	PUNCT
ejpam-6251	354	15	π(ςµ	π(ςµ	PROPN
ejpam-6251	354	16	,	,	PUNCT
ejpam-6251	354	17	ϖm	ϖm	ADJ
ejpam-6251	354	18	,	,	PUNCT
ejpam-6251	354	19	ż	ż	NOUN
ejpam-6251	354	20	)	)	PUNCT
ejpam-6251	354	21	≥	≥	NOUN
ejpam-6251	354	22	π(ςµ	π(ςµ	PROPN
ejpam-6251	354	23	,	,	PUNCT
ejpam-6251	354	24	ϖµ	ϖµ	NOUN
ejpam-6251	354	25	,	,	PUNCT
ejpam-6251	354	26	ż	ż	NOUN
ejpam-6251	354	27	3	3	X
ejpam-6251	354	28	)	)	PUNCT
ejpam-6251	354	29	⋇π(ςµ+1	⋇π(ςµ+1	PROPN
ejpam-6251	354	30	,	,	PUNCT
ejpam-6251	354	31	ϖµ	ϖµ	NOUN
ejpam-6251	354	32	,	,	PUNCT
ejpam-6251	354	33	ż	ż	NOUN
ejpam-6251	354	34	3	3	X
ejpam-6251	354	35	)	)	PUNCT
ejpam-6251	354	36	⋇π(ςµ+1	⋇π(ςµ+1	PROPN
ejpam-6251	354	37	,	,	PUNCT
ejpam-6251	354	38	ϖm	ϖm	NOUN
ejpam-6251	354	39	,	,	PUNCT
ejpam-6251	354	40	ż	ż	NOUN
ejpam-6251	354	41	3	3	NUM
ejpam-6251	354	42	)	)	PUNCT
ejpam-6251	354	43	...	...	PUNCT
ejpam-6251	355	1	≥	≥	NUM
ejpam-6251	355	2	π(ςµ	π(ςµ	NOUN
ejpam-6251	355	3	,	,	PUNCT
ejpam-6251	355	4	ϖµ	ϖµ	NOUN
ejpam-6251	355	5	,	,	PUNCT
ejpam-6251	355	6	ż	ż	NOUN
ejpam-6251	355	7	3	3	X
ejpam-6251	355	8	)	)	PUNCT
ejpam-6251	355	9	⋇π(ςµ+1	⋇π(ςµ+1	PROPN
ejpam-6251	355	10	,	,	PUNCT
ejpam-6251	355	11	ϖµ	ϖµ	NOUN
ejpam-6251	355	12	,	,	PUNCT
ejpam-6251	355	13	ż	ż	NOUN
ejpam-6251	355	14	3	3	NUM
ejpam-6251	355	15	)	)	PUNCT
ejpam-6251	355	16	⋇	⋇	NOUN
ejpam-6251	355	17	·	·	PUNCT
ejpam-6251	355	18	·	·	PUNCT
ejpam-6251	356	1	·	·	PUNCT
ejpam-6251	356	2	⋇π(ςm−1	⋇π(ςm−1	PROPN
ejpam-6251	356	3	,	,	PUNCT
ejpam-6251	356	4	ϖm−1	ϖm−1	PROPN
ejpam-6251	356	5	,	,	PUNCT
ejpam-6251	356	6	ż	ż	PROPN
ejpam-6251	356	7	3m−1	3m−1	PROPN
ejpam-6251	356	8	)	)	PUNCT
ejpam-6251	357	1	⋇π(ςm	⋇π(ςm	PROPN
ejpam-6251	357	2	,	,	PUNCT
ejpam-6251	357	3	ϖm−1	ϖm−1	PROPN
ejpam-6251	357	4	,	,	PUNCT
ejpam-6251	357	5	ż	ż	NOUN
ejpam-6251	357	6	3m−1	3m−1	PROPN
ejpam-6251	357	7	)	)	PUNCT
ejpam-6251	357	8	⋇π(ςm	⋇π(ςm	PROPN
ejpam-6251	357	9	,	,	PUNCT
ejpam-6251	357	10	ϖm	ϖm	NOUN
ejpam-6251	357	11	,	,	PUNCT
ejpam-6251	357	12	ż	ż	NOUN
ejpam-6251	357	13	3m−1	3m−1	PROPN
ejpam-6251	357	14	)	)	PUNCT
ejpam-6251	357	15	,	,	PUNCT
ejpam-6251	357	16	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	357	17	,	,	PUNCT
ejpam-6251	357	18	ϖm	ϖm	ADJ
ejpam-6251	357	19	,	,	PUNCT
ejpam-6251	357	20	ż	ż	NOUN
ejpam-6251	357	21	)	)	PUNCT
ejpam-6251	357	22	≤	≤	PROPN
ejpam-6251	357	23	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	357	24	,	,	PUNCT
ejpam-6251	357	25	ϖµ	ϖµ	NOUN
ejpam-6251	357	26	,	,	PUNCT
ejpam-6251	357	27	ż	ż	NOUN
ejpam-6251	357	28	3	3	NUM
ejpam-6251	357	29	)	)	PUNCT
ejpam-6251	357	30	♢	♢	PROPN
ejpam-6251	357	31	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	357	32	,	,	PUNCT
ejpam-6251	357	33	ϖµ	ϖµ	NOUN
ejpam-6251	357	34	,	,	PUNCT
ejpam-6251	357	35	ż	ż	NOUN
ejpam-6251	357	36	3	3	NUM
ejpam-6251	357	37	)	)	PUNCT
ejpam-6251	357	38	♢	♢	PROPN
ejpam-6251	357	39	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	357	40	,	,	PUNCT
ejpam-6251	357	41	ϖm	ϖm	ADJ
ejpam-6251	357	42	,	,	PUNCT
ejpam-6251	357	43	ż	ż	NOUN
ejpam-6251	357	44	3	3	NUM
ejpam-6251	357	45	)	)	PUNCT
ejpam-6251	357	46	...	...	PUNCT
ejpam-6251	358	1	≤	≤	NUM
ejpam-6251	358	2	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	358	3	,	,	PUNCT
ejpam-6251	358	4	ϖµ	ϖµ	NOUN
ejpam-6251	358	5	,	,	PUNCT
ejpam-6251	358	6	ż	ż	NOUN
ejpam-6251	358	7	3	3	NUM
ejpam-6251	358	8	)	)	PUNCT
ejpam-6251	358	9	♢	♢	PROPN
ejpam-6251	358	10	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	358	11	,	,	PUNCT
ejpam-6251	358	12	ϖµ	ϖµ	NOUN
ejpam-6251	358	13	,	,	PUNCT
ejpam-6251	358	14	ż	ż	NOUN
ejpam-6251	358	15	3	3	NUM
ejpam-6251	358	16	)	)	PUNCT
ejpam-6251	358	17	♢	♢	PROPN
ejpam-6251	358	18	·	·	PUNCT
ejpam-6251	358	19	·	·	PUNCT
ejpam-6251	358	20	·	·	PUNCT
ejpam-6251	358	21	♢	♢	PROPN
ejpam-6251	358	22	ψ(ςm−1	ψ(ςm−1	PROPN
ejpam-6251	358	23	,	,	PUNCT
ejpam-6251	358	24	ϖm−1	ϖm−1	PROPN
ejpam-6251	358	25	,	,	PUNCT
ejpam-6251	358	26	ż	ż	PROPN
ejpam-6251	358	27	3m−1	3m−1	PROPN
ejpam-6251	358	28	)	)	PUNCT
ejpam-6251	358	29	♢	♢	PROPN
ejpam-6251	358	30	ψ(ςm	ψ(ςm	PROPN
ejpam-6251	358	31	,	,	PUNCT
ejpam-6251	358	32	ϖm−1	ϖm−1	PROPN
ejpam-6251	358	33	,	,	PUNCT
ejpam-6251	358	34	ż	ż	PROPN
ejpam-6251	358	35	3m−1	3m−1	PROPN
ejpam-6251	358	36	)	)	PUNCT
ejpam-6251	358	37	♢	♢	PROPN
ejpam-6251	358	38	ψ(ςm	ψ(ςm	PROPN
ejpam-6251	358	39	,	,	PUNCT
ejpam-6251	358	40	ϖm	ϖm	NOUN
ejpam-6251	358	41	,	,	PUNCT
ejpam-6251	358	42	ż	ż	NOUN
ejpam-6251	358	43	3m−1	3m−1	PROPN
ejpam-6251	358	44	)	)	PUNCT
ejpam-6251	358	45	,	,	PUNCT
ejpam-6251	358	46	and	and	CCONJ
ejpam-6251	358	47	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	358	48	,	,	PUNCT
ejpam-6251	358	49	ϖm	ϖm	ADJ
ejpam-6251	358	50	,	,	PUNCT
ejpam-6251	358	51	ż	ż	NOUN
ejpam-6251	358	52	)	)	PUNCT
ejpam-6251	358	53	≤	≤	NUM
ejpam-6251	358	54	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	358	55	,	,	PUNCT
ejpam-6251	358	56	ϖµ	ϖµ	NOUN
ejpam-6251	358	57	,	,	PUNCT
ejpam-6251	358	58	ż	ż	NOUN
ejpam-6251	358	59	3	3	NUM
ejpam-6251	358	60	)	)	PUNCT
ejpam-6251	358	61	♢	♢	PROPN
ejpam-6251	358	62	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	358	63	,	,	PUNCT
ejpam-6251	358	64	ϖµ	ϖµ	NOUN
ejpam-6251	358	65	,	,	PUNCT
ejpam-6251	358	66	ż	ż	NOUN
ejpam-6251	358	67	3	3	NUM
ejpam-6251	358	68	)	)	PUNCT
ejpam-6251	358	69	♢	♢	PROPN
ejpam-6251	358	70	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	358	71	,	,	PUNCT
ejpam-6251	358	72	ϖm	ϖm	ADJ
ejpam-6251	358	73	,	,	PUNCT
ejpam-6251	358	74	ż	ż	NOUN
ejpam-6251	358	75	3	3	NUM
ejpam-6251	358	76	)	)	PUNCT
ejpam-6251	358	77	...	...	PUNCT
ejpam-6251	359	1	≤	≤	NUM
ejpam-6251	359	2	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	359	3	,	,	PUNCT
ejpam-6251	359	4	ϖµ	ϖµ	NOUN
ejpam-6251	359	5	,	,	PUNCT
ejpam-6251	359	6	ż	ż	NOUN
ejpam-6251	359	7	3	3	NUM
ejpam-6251	359	8	)	)	PUNCT
ejpam-6251	359	9	♢	♢	PROPN
ejpam-6251	359	10	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	359	11	,	,	PUNCT
ejpam-6251	359	12	ϖµ	ϖµ	NOUN
ejpam-6251	359	13	,	,	PUNCT
ejpam-6251	359	14	ż	ż	NOUN
ejpam-6251	359	15	3	3	NUM
ejpam-6251	359	16	)	)	PUNCT
ejpam-6251	359	17	♢	♢	PROPN
ejpam-6251	359	18	·	·	PUNCT
ejpam-6251	359	19	·	·	PUNCT
ejpam-6251	359	20	·	·	PUNCT
ejpam-6251	359	21	♢	♢	PROPN
ejpam-6251	359	22	ξ(ςm−1	ξ(ςm−1	PROPN
ejpam-6251	359	23	,	,	PUNCT
ejpam-6251	359	24	ϖm−1	ϖm−1	PROPN
ejpam-6251	359	25	,	,	PUNCT
ejpam-6251	359	26	ż	ż	PROPN
ejpam-6251	359	27	3m−1	3m−1	PROPN
ejpam-6251	359	28	)	)	PUNCT
ejpam-6251	359	29	♢	♢	PROPN
ejpam-6251	359	30	ξ(ςm	ξ(ςm	PROPN
ejpam-6251	359	31	,	,	PUNCT
ejpam-6251	359	32	ϖm−1	ϖm−1	PROPN
ejpam-6251	359	33	,	,	PUNCT
ejpam-6251	359	34	ż	ż	PROPN
ejpam-6251	359	35	3m−1	3m−1	PROPN
ejpam-6251	359	36	)	)	PUNCT
ejpam-6251	359	37	♢	♢	PROPN
ejpam-6251	359	38	ξ(ςm	ξ(ςm	PROPN
ejpam-6251	359	39	,	,	PUNCT
ejpam-6251	359	40	ϖm	ϖm	NOUN
ejpam-6251	359	41	,	,	PUNCT
ejpam-6251	359	42	ż	ż	NOUN
ejpam-6251	359	43	3m−1	3m−1	PROPN
ejpam-6251	359	44	)	)	PUNCT
ejpam-6251	359	45	.	.	PUNCT
ejpam-6251	360	1	therefore	therefore	ADV
ejpam-6251	360	2	,	,	PUNCT
ejpam-6251	360	3	π(ςµ	π(ςµ	NUM
ejpam-6251	360	4	,	,	PUNCT
ejpam-6251	360	5	ϖm	ϖm	ADJ
ejpam-6251	360	6	,	,	PUNCT
ejpam-6251	360	7	ż	ż	NOUN
ejpam-6251	360	8	)	)	PUNCT
ejpam-6251	360	9	≥	≥	NOUN
ejpam-6251	360	10	π(ςµ	π(ςµ	PROPN
ejpam-6251	360	11	,	,	PUNCT
ejpam-6251	360	12	ϖµ	ϖµ	NOUN
ejpam-6251	360	13	,	,	PUNCT
ejpam-6251	360	14	ż	ż	NOUN
ejpam-6251	360	15	3	3	X
ejpam-6251	360	16	)	)	PUNCT
ejpam-6251	360	17	⋇π(ςµ+1	⋇π(ςµ+1	PROPN
ejpam-6251	360	18	,	,	PUNCT
ejpam-6251	360	19	ϖµ	ϖµ	NOUN
ejpam-6251	360	20	,	,	PUNCT
ejpam-6251	360	21	ż	ż	NOUN
ejpam-6251	360	22	3	3	NUM
ejpam-6251	360	23	)	)	PUNCT
ejpam-6251	360	24	⋇	⋇	NOUN
ejpam-6251	360	25	·	·	PUNCT
ejpam-6251	360	26	·	·	PUNCT
ejpam-6251	360	27	·	·	PUNCT
ejpam-6251	360	28	⋇π(ςm−1	⋇π(ςm−1	PROPN
ejpam-6251	360	29	,	,	PUNCT
ejpam-6251	360	30	ϖm−1	ϖm−1	PROPN
ejpam-6251	360	31	,	,	PUNCT
ejpam-6251	360	32	ż	ż	PROPN
ejpam-6251	360	33	3m−1	3m−1	PROPN
ejpam-6251	360	34	)	)	PUNCT
ejpam-6251	360	35	r.	r.	PROPN
ejpam-6251	360	36	ramaswamy	ramaswamy	PROPN
ejpam-6251	360	37	/	/	SYM
ejpam-6251	360	38	eur	eur	PROPN
ejpam-6251	360	39	.	.	PUNCT
ejpam-6251	361	1	j.	j.	PROPN
ejpam-6251	361	2	pure	pure	PROPN
ejpam-6251	361	3	appl	appl	PROPN
ejpam-6251	361	4	.	.	PROPN
ejpam-6251	361	5	math	math	PROPN
ejpam-6251	361	6	,	,	PUNCT
ejpam-6251	361	7	18	18	NUM
ejpam-6251	361	8	(	(	PUNCT
ejpam-6251	361	9	4	4	NUM
ejpam-6251	361	10	)	)	PUNCT
ejpam-6251	361	11	(	(	PUNCT
ejpam-6251	361	12	2025	2025	NUM
ejpam-6251	361	13	)	)	PUNCT
ejpam-6251	361	14	,	,	PUNCT
ejpam-6251	361	15	6251	6251	NUM
ejpam-6251	361	16	15	15	NUM
ejpam-6251	361	17	of	of	ADP
ejpam-6251	361	18	40	40	NUM
ejpam-6251	361	19	⋇π(ςm	⋇π(ςm	NOUN
ejpam-6251	361	20	,	,	PUNCT
ejpam-6251	361	21	ϖm−1	ϖm−1	PROPN
ejpam-6251	361	22	,	,	PUNCT
ejpam-6251	361	23	ż	ż	NOUN
ejpam-6251	361	24	3m−1	3m−1	PROPN
ejpam-6251	361	25	)	)	PUNCT
ejpam-6251	362	1	⋇π(ςm	⋇π(ςm	PROPN
ejpam-6251	362	2	,	,	PUNCT
ejpam-6251	362	3	ϖm	ϖm	NOUN
ejpam-6251	362	4	,	,	PUNCT
ejpam-6251	362	5	ż	ż	NOUN
ejpam-6251	362	6	3m−1	3m−1	PROPN
ejpam-6251	362	7	)	)	PUNCT
ejpam-6251	362	8	≥	≥	NOUN
ejpam-6251	362	9	π(ς0	π(ς0	NOUN
ejpam-6251	362	10	,	,	PUNCT
ejpam-6251	362	11	ϖ0	ϖ0	NOUN
ejpam-6251	362	12	,	,	PUNCT
ejpam-6251	362	13	ż	ż	NOUN
ejpam-6251	362	14	3ζµ	3ζµ	NOUN
ejpam-6251	362	15	)	)	PUNCT
ejpam-6251	363	1	⋇π(ς1	⋇π(ς1	NOUN
ejpam-6251	363	2	,	,	PUNCT
ejpam-6251	363	3	ϖ0	ϖ0	NOUN
ejpam-6251	363	4	,	,	PUNCT
ejpam-6251	363	5	ż	ż	ADJ
ejpam-6251	363	6	3ζµ	3ζµ	NOUN
ejpam-6251	363	7	)	)	PUNCT
ejpam-6251	363	8	⋇	⋇	NOUN
ejpam-6251	363	9	·	·	PUNCT
ejpam-6251	363	10	·	·	PUNCT
ejpam-6251	363	11	·	·	PUNCT
ejpam-6251	363	12	⋇π(ς0	⋇π(ς0	PROPN
ejpam-6251	363	13	,	,	PUNCT
ejpam-6251	363	14	ϖ0	ϖ0	NOUN
ejpam-6251	363	15	,	,	PUNCT
ejpam-6251	363	16	ż	ż	NOUN
ejpam-6251	363	17	3m−1ζm−1	3m−1ζm−1	NOUN
ejpam-6251	363	18	)	)	PUNCT
ejpam-6251	363	19	⋇π(ς1	⋇π(ς1	NOUN
ejpam-6251	363	20	,	,	PUNCT
ejpam-6251	363	21	ϖ0	ϖ0	NOUN
ejpam-6251	363	22	,	,	PUNCT
ejpam-6251	363	23	ż	ż	ADJ
ejpam-6251	363	24	3m−1ζm−1	3m−1ζm−1	NOUN
ejpam-6251	363	25	)	)	PUNCT
ejpam-6251	364	1	⋇π(ς0	⋇π(ς0	PROPN
ejpam-6251	364	2	,	,	PUNCT
ejpam-6251	364	3	ϖ0	ϖ0	NOUN
ejpam-6251	364	4	,	,	PUNCT
ejpam-6251	364	5	ż	ż	NOUN
ejpam-6251	364	6	3m−1ζm	3m−1ζm	PROPN
ejpam-6251	364	7	)	)	PUNCT
ejpam-6251	364	8	,	,	PUNCT
ejpam-6251	364	9	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	364	10	,	,	PUNCT
ejpam-6251	364	11	ϖm	ϖm	ADJ
ejpam-6251	364	12	,	,	PUNCT
ejpam-6251	364	13	ż	ż	NOUN
ejpam-6251	364	14	)	)	PUNCT
ejpam-6251	364	15	≤	≤	PROPN
ejpam-6251	364	16	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	364	17	,	,	PUNCT
ejpam-6251	364	18	ϖµ	ϖµ	NOUN
ejpam-6251	364	19	,	,	PUNCT
ejpam-6251	364	20	ż	ż	NOUN
ejpam-6251	364	21	3	3	NUM
ejpam-6251	364	22	)	)	PUNCT
ejpam-6251	364	23	♢	♢	PROPN
ejpam-6251	364	24	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	364	25	,	,	PUNCT
ejpam-6251	364	26	ϖµ	ϖµ	NOUN
ejpam-6251	364	27	,	,	PUNCT
ejpam-6251	364	28	ż	ż	NOUN
ejpam-6251	364	29	3	3	NUM
ejpam-6251	364	30	)	)	PUNCT
ejpam-6251	364	31	♢	♢	PROPN
ejpam-6251	364	32	·	·	PUNCT
ejpam-6251	364	33	·	·	PUNCT
ejpam-6251	364	34	·	·	PUNCT
ejpam-6251	364	35	♢	♢	PROPN
ejpam-6251	364	36	ψ(ςm−1	ψ(ςm−1	PROPN
ejpam-6251	364	37	,	,	PUNCT
ejpam-6251	364	38	ϖm−1	ϖm−1	PROPN
ejpam-6251	364	39	,	,	PUNCT
ejpam-6251	364	40	ż	ż	PROPN
ejpam-6251	364	41	3m−1	3m−1	PROPN
ejpam-6251	364	42	)	)	PUNCT
ejpam-6251	364	43	♢	♢	PROPN
ejpam-6251	364	44	ψ(ςm	ψ(ςm	PROPN
ejpam-6251	364	45	,	,	PUNCT
ejpam-6251	364	46	ϖm−1	ϖm−1	PROPN
ejpam-6251	364	47	,	,	PUNCT
ejpam-6251	364	48	ż	ż	PROPN
ejpam-6251	364	49	3m−1	3m−1	PROPN
ejpam-6251	364	50	)	)	PUNCT
ejpam-6251	364	51	♢	♢	PROPN
ejpam-6251	364	52	ψ(ςm	ψ(ςm	PROPN
ejpam-6251	364	53	,	,	PUNCT
ejpam-6251	364	54	ϖm	ϖm	NOUN
ejpam-6251	364	55	,	,	PUNCT
ejpam-6251	364	56	ż	ż	NOUN
ejpam-6251	364	57	3m−1	3m−1	PROPN
ejpam-6251	364	58	)	)	PUNCT
ejpam-6251	364	59	≤	≤	NOUN
ejpam-6251	364	60	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	364	61	,	,	PUNCT
ejpam-6251	364	62	ϖ0	ϖ0	NOUN
ejpam-6251	364	63	,	,	PUNCT
ejpam-6251	364	64	ż	ż	NOUN
ejpam-6251	364	65	3ζµ	3ζµ	NOUN
ejpam-6251	364	66	)	)	PUNCT
ejpam-6251	364	67	♢	♢	PROPN
ejpam-6251	364	68	ψ(ς1	ψ(ς1	NOUN
ejpam-6251	364	69	,	,	PUNCT
ejpam-6251	364	70	ϖ0	ϖ0	NOUN
ejpam-6251	364	71	,	,	PUNCT
ejpam-6251	364	72	ż	ż	NOUN
ejpam-6251	364	73	3ζµ	3ζµ	NOUN
ejpam-6251	364	74	)	)	PUNCT
ejpam-6251	364	75	♢	♢	PROPN
ejpam-6251	364	76	·	·	PUNCT
ejpam-6251	364	77	·	·	PUNCT
ejpam-6251	364	78	·	·	PUNCT
ejpam-6251	364	79	♢	♢	PROPN
ejpam-6251	364	80	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	364	81	,	,	PUNCT
ejpam-6251	364	82	ϖ0	ϖ0	NOUN
ejpam-6251	364	83	,	,	PUNCT
ejpam-6251	364	84	ż	ż	ADJ
ejpam-6251	364	85	3m−1ζm−1	3m−1ζm−1	NOUN
ejpam-6251	364	86	)	)	PUNCT
ejpam-6251	364	87	♢	♢	PROPN
ejpam-6251	364	88	ψ(ς1	ψ(ς1	NOUN
ejpam-6251	364	89	,	,	PUNCT
ejpam-6251	364	90	ϖ0	ϖ0	NOUN
ejpam-6251	364	91	,	,	PUNCT
ejpam-6251	364	92	ż	ż	ADJ
ejpam-6251	364	93	3m−1ζm−1	3m−1ζm−1	NOUN
ejpam-6251	364	94	)	)	PUNCT
ejpam-6251	365	1	♢	♢	PROPN
ejpam-6251	365	2	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	365	3	,	,	PUNCT
ejpam-6251	365	4	ϖ0	ϖ0	NOUN
ejpam-6251	365	5	,	,	PUNCT
ejpam-6251	365	6	ż	ż	NOUN
ejpam-6251	365	7	3m−1ζm	3m−1ζm	PROPN
ejpam-6251	365	8	)	)	PUNCT
ejpam-6251	365	9	,	,	PUNCT
ejpam-6251	365	10	and	and	CCONJ
ejpam-6251	365	11	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	365	12	,	,	PUNCT
ejpam-6251	365	13	ϖm	ϖm	ADJ
ejpam-6251	365	14	,	,	PUNCT
ejpam-6251	365	15	ż	ż	NOUN
ejpam-6251	365	16	)	)	PUNCT
ejpam-6251	365	17	≤	≤	NUM
ejpam-6251	365	18	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	365	19	,	,	PUNCT
ejpam-6251	365	20	ϖµ	ϖµ	NOUN
ejpam-6251	365	21	,	,	PUNCT
ejpam-6251	365	22	ż	ż	NOUN
ejpam-6251	365	23	3	3	NUM
ejpam-6251	365	24	)	)	PUNCT
ejpam-6251	365	25	♢	♢	PROPN
ejpam-6251	365	26	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	365	27	,	,	PUNCT
ejpam-6251	365	28	ϖµ	ϖµ	NOUN
ejpam-6251	365	29	,	,	PUNCT
ejpam-6251	365	30	ż	ż	NOUN
ejpam-6251	365	31	3	3	NUM
ejpam-6251	365	32	)	)	PUNCT
ejpam-6251	365	33	♢	♢	PROPN
ejpam-6251	365	34	·	·	PUNCT
ejpam-6251	365	35	·	·	PUNCT
ejpam-6251	365	36	·	·	PUNCT
ejpam-6251	365	37	♢	♢	PROPN
ejpam-6251	365	38	ξ(ςm−1	ξ(ςm−1	PROPN
ejpam-6251	365	39	,	,	PUNCT
ejpam-6251	365	40	ϖm−1	ϖm−1	PROPN
ejpam-6251	365	41	,	,	PUNCT
ejpam-6251	365	42	ż	ż	PROPN
ejpam-6251	365	43	3m−1	3m−1	PROPN
ejpam-6251	365	44	)	)	PUNCT
ejpam-6251	365	45	♢	♢	PROPN
ejpam-6251	365	46	ξ(ςm	ξ(ςm	PROPN
ejpam-6251	365	47	,	,	PUNCT
ejpam-6251	365	48	ϖm−1	ϖm−1	PROPN
ejpam-6251	365	49	,	,	PUNCT
ejpam-6251	365	50	ż	ż	PROPN
ejpam-6251	365	51	3m−1	3m−1	PROPN
ejpam-6251	365	52	)	)	PUNCT
ejpam-6251	365	53	♢	♢	PROPN
ejpam-6251	365	54	ξ(ςm	ξ(ςm	PROPN
ejpam-6251	365	55	,	,	PUNCT
ejpam-6251	365	56	ϖm	ϖm	NOUN
ejpam-6251	365	57	,	,	PUNCT
ejpam-6251	365	58	ż	ż	NOUN
ejpam-6251	365	59	3m−1	3m−1	PROPN
ejpam-6251	365	60	)	)	PUNCT
ejpam-6251	365	61	≤	≤	NOUN
ejpam-6251	365	62	ξ(ς0	ξ(ς0	NOUN
ejpam-6251	365	63	,	,	PUNCT
ejpam-6251	365	64	ϖ0	ϖ0	NOUN
ejpam-6251	365	65	,	,	PUNCT
ejpam-6251	365	66	ż	ż	NOUN
ejpam-6251	365	67	3ζµ	3ζµ	NOUN
ejpam-6251	365	68	)	)	PUNCT
ejpam-6251	365	69	♢	♢	PROPN
ejpam-6251	365	70	ξ(ς1	ξ(ς1	NOUN
ejpam-6251	365	71	,	,	PUNCT
ejpam-6251	365	72	ϖ0	ϖ0	NOUN
ejpam-6251	365	73	,	,	PUNCT
ejpam-6251	365	74	ż	ż	NOUN
ejpam-6251	365	75	3ζµ	3ζµ	NOUN
ejpam-6251	365	76	)	)	PUNCT
ejpam-6251	365	77	♢	♢	PROPN
ejpam-6251	365	78	·	·	PUNCT
ejpam-6251	365	79	·	·	PUNCT
ejpam-6251	365	80	·	·	PUNCT
ejpam-6251	365	81	♢	♢	PROPN
ejpam-6251	365	82	ξ(ς0	ξ(ς0	ADV
ejpam-6251	365	83	,	,	PUNCT
ejpam-6251	365	84	ϖ0	ϖ0	NOUN
ejpam-6251	365	85	,	,	PUNCT
ejpam-6251	365	86	ż	ż	ADJ
ejpam-6251	365	87	3m−1ζm−1	3m−1ζm−1	NOUN
ejpam-6251	365	88	)	)	PUNCT
ejpam-6251	365	89	♢	♢	PROPN
ejpam-6251	365	90	ξ(ς1	ξ(ς1	PROPN
ejpam-6251	365	91	,	,	PUNCT
ejpam-6251	365	92	ϖ0	ϖ0	NOUN
ejpam-6251	365	93	,	,	PUNCT
ejpam-6251	365	94	ż	ż	ADJ
ejpam-6251	365	95	3m−1ζm−1	3m−1ζm−1	NOUN
ejpam-6251	365	96	)	)	PUNCT
ejpam-6251	365	97	♢	♢	PROPN
ejpam-6251	365	98	ξ(ς0	ξ(ς0	ADV
ejpam-6251	365	99	,	,	PUNCT
ejpam-6251	365	100	ϖ0	ϖ0	NOUN
ejpam-6251	365	101	,	,	PUNCT
ejpam-6251	365	102	ż	ż	NOUN
ejpam-6251	365	103	3m−1ζm	3m−1ζm	PROPN
ejpam-6251	365	104	)	)	PUNCT
ejpam-6251	365	105	.	.	PUNCT
ejpam-6251	366	1	which	which	PRON
ejpam-6251	366	2	implies	imply	VERB
ejpam-6251	366	3	that	that	SCONJ
ejpam-6251	366	4	,	,	PUNCT
ejpam-6251	366	5	π(ςµ	π(ςµ	NUM
ejpam-6251	366	6	,	,	PUNCT
ejpam-6251	366	7	ϖm	ϖm	ADJ
ejpam-6251	366	8	,	,	PUNCT
ejpam-6251	366	9	ż	ż	NOUN
ejpam-6251	366	10	)	)	PUNCT
ejpam-6251	366	11	≥	≥	NOUN
ejpam-6251	366	12	π(ς0	π(ς0	NOUN
ejpam-6251	366	13	,	,	PUNCT
ejpam-6251	366	14	ϖ0	ϖ0	NOUN
ejpam-6251	366	15	,	,	PUNCT
ejpam-6251	366	16	ż	ż	NOUN
ejpam-6251	366	17	3ζµ	3ζµ	NOUN
ejpam-6251	366	18	)	)	PUNCT
ejpam-6251	367	1	⋇π(ς1	⋇π(ς1	NOUN
ejpam-6251	367	2	,	,	PUNCT
ejpam-6251	367	3	ϖ0	ϖ0	NOUN
ejpam-6251	367	4	,	,	PUNCT
ejpam-6251	367	5	ż	ż	ADJ
ejpam-6251	367	6	3ζµ	3ζµ	NOUN
ejpam-6251	367	7	)	)	PUNCT
ejpam-6251	367	8	⋇	⋇	NOUN
ejpam-6251	367	9	·	·	PUNCT
ejpam-6251	367	10	·	·	PUNCT
ejpam-6251	367	11	·	·	PUNCT
ejpam-6251	367	12	⋇π(ς0	⋇π(ς0	PROPN
ejpam-6251	367	13	,	,	PUNCT
ejpam-6251	367	14	ϖ0	ϖ0	NOUN
ejpam-6251	367	15	,	,	PUNCT
ejpam-6251	367	16	ż	ż	NOUN
ejpam-6251	367	17	3m−1ζm−1	3m−1ζm−1	NOUN
ejpam-6251	367	18	)	)	PUNCT
ejpam-6251	367	19	⋇π(ς1	⋇π(ς1	NOUN
ejpam-6251	367	20	,	,	PUNCT
ejpam-6251	367	21	ϖ0	ϖ0	NOUN
ejpam-6251	367	22	,	,	PUNCT
ejpam-6251	367	23	ż	ż	ADJ
ejpam-6251	367	24	3m−1ζm−1	3m−1ζm−1	NOUN
ejpam-6251	367	25	)	)	PUNCT
ejpam-6251	368	1	⋇π(ς0	⋇π(ς0	PROPN
ejpam-6251	368	2	,	,	PUNCT
ejpam-6251	368	3	ϖ0	ϖ0	NOUN
ejpam-6251	368	4	,	,	PUNCT
ejpam-6251	368	5	ż	ż	NOUN
ejpam-6251	368	6	3m−1ζm	3m−1ζm	PROPN
ejpam-6251	368	7	)	)	PUNCT
ejpam-6251	368	8	,	,	PUNCT
ejpam-6251	368	9	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	368	10	,	,	PUNCT
ejpam-6251	368	11	ϖm	ϖm	ADJ
ejpam-6251	368	12	,	,	PUNCT
ejpam-6251	368	13	ż	ż	NOUN
ejpam-6251	368	14	)	)	PUNCT
ejpam-6251	368	15	≤	≤	NOUN
ejpam-6251	368	16	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	368	17	,	,	PUNCT
ejpam-6251	368	18	ϖ0	ϖ0	NOUN
ejpam-6251	368	19	,	,	PUNCT
ejpam-6251	368	20	ż	ż	NOUN
ejpam-6251	368	21	3ζµ	3ζµ	NOUN
ejpam-6251	368	22	)	)	PUNCT
ejpam-6251	368	23	♢	♢	PROPN
ejpam-6251	368	24	ψ(ς1	ψ(ς1	NOUN
ejpam-6251	368	25	,	,	PUNCT
ejpam-6251	368	26	ϖ0	ϖ0	NOUN
ejpam-6251	368	27	,	,	PUNCT
ejpam-6251	368	28	ż	ż	NOUN
ejpam-6251	368	29	3ζµ	3ζµ	NOUN
ejpam-6251	368	30	)	)	PUNCT
ejpam-6251	368	31	♢	♢	PROPN
ejpam-6251	368	32	·	·	PUNCT
ejpam-6251	368	33	·	·	PUNCT
ejpam-6251	368	34	·	·	PUNCT
ejpam-6251	368	35	♢	♢	PROPN
ejpam-6251	368	36	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	368	37	,	,	PUNCT
ejpam-6251	368	38	ϖ0	ϖ0	NOUN
ejpam-6251	368	39	,	,	PUNCT
ejpam-6251	368	40	ż	ż	ADJ
ejpam-6251	368	41	3m−1ζm−1	3m−1ζm−1	NOUN
ejpam-6251	368	42	)	)	PUNCT
ejpam-6251	368	43	♢	♢	PROPN
ejpam-6251	368	44	ψ(ς1	ψ(ς1	NOUN
ejpam-6251	368	45	,	,	PUNCT
ejpam-6251	368	46	ϖ0	ϖ0	NOUN
ejpam-6251	368	47	,	,	PUNCT
ejpam-6251	368	48	ż	ż	ADJ
ejpam-6251	368	49	3m−1ζm−1	3m−1ζm−1	NOUN
ejpam-6251	368	50	)	)	PUNCT
ejpam-6251	368	51	♢	♢	PROPN
ejpam-6251	368	52	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	368	53	,	,	PUNCT
ejpam-6251	368	54	ϖ0	ϖ0	NOUN
ejpam-6251	368	55	,	,	PUNCT
ejpam-6251	368	56	ż	ż	NOUN
ejpam-6251	368	57	3m−1ζm	3m−1ζm	PROPN
ejpam-6251	368	58	)	)	PUNCT
ejpam-6251	368	59	,	,	PUNCT
ejpam-6251	368	60	and	and	CCONJ
ejpam-6251	368	61	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	368	62	,	,	PUNCT
ejpam-6251	368	63	ϖm	ϖm	ADJ
ejpam-6251	368	64	,	,	PUNCT
ejpam-6251	368	65	ż	ż	NOUN
ejpam-6251	368	66	)	)	PUNCT
ejpam-6251	368	67	≤	≤	NOUN
ejpam-6251	368	68	ξ(ς0	ξ(ς0	NOUN
ejpam-6251	368	69	,	,	PUNCT
ejpam-6251	368	70	ϖ0	ϖ0	NOUN
ejpam-6251	368	71	,	,	PUNCT
ejpam-6251	368	72	ż	ż	NOUN
ejpam-6251	368	73	3ζµ	3ζµ	NOUN
ejpam-6251	368	74	)	)	PUNCT
ejpam-6251	368	75	♢	♢	PROPN
ejpam-6251	368	76	ξ(ς1	ξ(ς1	NOUN
ejpam-6251	368	77	,	,	PUNCT
ejpam-6251	368	78	ϖ0	ϖ0	NOUN
ejpam-6251	368	79	,	,	PUNCT
ejpam-6251	368	80	ż	ż	NOUN
ejpam-6251	368	81	3ζµ	3ζµ	NOUN
ejpam-6251	368	82	)	)	PUNCT
ejpam-6251	368	83	♢	♢	PROPN
ejpam-6251	368	84	·	·	PUNCT
ejpam-6251	368	85	·	·	PUNCT
ejpam-6251	368	86	·	·	PUNCT
ejpam-6251	368	87	♢	♢	PROPN
ejpam-6251	368	88	ξ(ς0	ξ(ς0	ADV
ejpam-6251	368	89	,	,	PUNCT
ejpam-6251	368	90	ϖ0	ϖ0	NOUN
ejpam-6251	368	91	,	,	PUNCT
ejpam-6251	368	92	ż	ż	ADJ
ejpam-6251	368	93	3m−1ζm−1	3m−1ζm−1	NOUN
ejpam-6251	368	94	)	)	PUNCT
ejpam-6251	368	95	♢	♢	PROPN
ejpam-6251	368	96	ξ(ς1	ξ(ς1	PROPN
ejpam-6251	368	97	,	,	PUNCT
ejpam-6251	368	98	ϖ0	ϖ0	NOUN
ejpam-6251	368	99	,	,	PUNCT
ejpam-6251	368	100	ż	ż	ADJ
ejpam-6251	368	101	3m−1ζm−1	3m−1ζm−1	NOUN
ejpam-6251	368	102	)	)	PUNCT
ejpam-6251	368	103	♢	♢	PROPN
ejpam-6251	368	104	ξ(ς0	ξ(ς0	ADV
ejpam-6251	368	105	,	,	PUNCT
ejpam-6251	368	106	ϖ0	ϖ0	NOUN
ejpam-6251	368	107	,	,	PUNCT
ejpam-6251	368	108	ż	ż	NOUN
ejpam-6251	368	109	3m−1ζm	3m−1ζm	PROPN
ejpam-6251	368	110	)	)	PUNCT
ejpam-6251	368	111	.	.	PUNCT
ejpam-6251	369	1	r.	r.	PROPN
ejpam-6251	369	2	ramaswamy	ramaswamy	PROPN
ejpam-6251	369	3	/	/	SYM
ejpam-6251	369	4	eur	eur	PROPN
ejpam-6251	369	5	.	.	PUNCT
ejpam-6251	370	1	j.	j.	PROPN
ejpam-6251	370	2	pure	pure	PROPN
ejpam-6251	370	3	appl	appl	PROPN
ejpam-6251	370	4	.	.	PROPN
ejpam-6251	370	5	math	math	PROPN
ejpam-6251	370	6	,	,	PUNCT
ejpam-6251	370	7	18	18	NUM
ejpam-6251	370	8	(	(	PUNCT
ejpam-6251	370	9	4	4	NUM
ejpam-6251	370	10	)	)	PUNCT
ejpam-6251	370	11	(	(	PUNCT
ejpam-6251	370	12	2025	2025	NUM
ejpam-6251	370	13	)	)	PUNCT
ejpam-6251	370	14	,	,	PUNCT
ejpam-6251	370	15	6251	6251	NUM
ejpam-6251	370	16	16	16	NUM
ejpam-6251	370	17	of	of	ADP
ejpam-6251	370	18	40	40	NUM
ejpam-6251	370	19	as	as	ADP
ejpam-6251	370	20	µ,m	µ,m	PROPN
ejpam-6251	370	21	→	→	SYM
ejpam-6251	370	22	+	+	NOUN
ejpam-6251	370	23	∞	∞	PROPN
ejpam-6251	370	24	,	,	PUNCT
ejpam-6251	370	25	we	we	PRON
ejpam-6251	370	26	deduce	deduce	VERB
ejpam-6251	370	27	lim	lim	PROPN
ejpam-6251	370	28	µ,m→+∞	µ,m→+∞	NUM
ejpam-6251	370	29	π(ςµ	π(ςµ	PROPN
ejpam-6251	370	30	,	,	PUNCT
ejpam-6251	370	31	ϖm	ϖm	ADJ
ejpam-6251	370	32	,	,	PUNCT
ejpam-6251	370	33	ż	ż	NOUN
ejpam-6251	370	34	)	)	PUNCT
ejpam-6251	370	35	=	=	PUNCT
ejpam-6251	371	1	1⋇	1⋇	NUM
ejpam-6251	371	2	1⋇	1⋇	NUM
ejpam-6251	371	3	·	·	PUNCT
ejpam-6251	371	4	·	·	PUNCT
ejpam-6251	371	5	·	·	PUNCT
ejpam-6251	371	6	⋇	⋇	NOUN
ejpam-6251	371	7	1	1	NUM
ejpam-6251	371	8	=	=	SYM
ejpam-6251	371	9	1	1	NUM
ejpam-6251	371	10	,	,	PUNCT
ejpam-6251	371	11	lim	lim	PROPN
ejpam-6251	371	12	µ,m→+∞	µ,m→+∞	NUM
ejpam-6251	371	13	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	371	14	,	,	PUNCT
ejpam-6251	371	15	ϖm	ϖm	ADJ
ejpam-6251	371	16	,	,	PUNCT
ejpam-6251	371	17	ż	ż	NOUN
ejpam-6251	371	18	)	)	PUNCT
ejpam-6251	371	19	=	=	SYM
ejpam-6251	371	20	0	0	NUM
ejpam-6251	371	21	♢	♢	PROPN
ejpam-6251	371	22	0	0	PROPN
ejpam-6251	371	23	♢	♢	PROPN
ejpam-6251	371	24	·	·	PUNCT
ejpam-6251	371	25	·	·	PUNCT
ejpam-6251	371	26	·	·	PUNCT
ejpam-6251	371	27	♢	♢	PROPN
ejpam-6251	371	28	0	0	PROPN
ejpam-6251	371	29	=	=	SYM
ejpam-6251	371	30	0	0	PROPN
ejpam-6251	371	31	and	and	CCONJ
ejpam-6251	371	32	lim	lim	PROPN
ejpam-6251	371	33	µ,m→+∞	µ,m→+∞	NUM
ejpam-6251	371	34	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	371	35	,	,	PUNCT
ejpam-6251	371	36	ϖm	ϖm	ADJ
ejpam-6251	371	37	,	,	PUNCT
ejpam-6251	371	38	ż	ż	NOUN
ejpam-6251	371	39	)	)	PUNCT
ejpam-6251	371	40	=	=	SYM
ejpam-6251	371	41	0	0	NUM
ejpam-6251	371	42	♢	♢	PROPN
ejpam-6251	371	43	0	0	PROPN
ejpam-6251	371	44	♢	♢	PROPN
ejpam-6251	371	45	·	·	PUNCT
ejpam-6251	371	46	·	·	PUNCT
ejpam-6251	371	47	·	·	PUNCT
ejpam-6251	371	48	♢	♢	PROPN
ejpam-6251	371	49	0	0	PROPN
ejpam-6251	371	50	=	=	SYM
ejpam-6251	371	51	0	0	PROPN
ejpam-6251	371	52	.	.	NOUN
ejpam-6251	371	53	which	which	PRON
ejpam-6251	371	54	implies	imply	VERB
ejpam-6251	371	55	that	that	PRON
ejpam-6251	371	56	bisequence	bisequence	NOUN
ejpam-6251	371	57	(	(	PUNCT
ejpam-6251	371	58	ςµ	ςµ	NOUN
ejpam-6251	371	59	,	,	PUNCT
ejpam-6251	371	60	ϖµ	ϖµ	NOUN
ejpam-6251	371	61	)	)	PUNCT
ejpam-6251	371	62	is	be	AUX
ejpam-6251	371	63	a	a	DET
ejpam-6251	371	64	cauchy	cauchy	ADJ
ejpam-6251	371	65	bisequence	bisequence	NOUN
ejpam-6251	371	66	.	.	PUNCT
ejpam-6251	372	1	since	since	SCONJ
ejpam-6251	372	2	(	(	PUNCT
ejpam-6251	372	3	𭟋	𭟋	PROPN
ejpam-6251	372	4	,	,	PUNCT
ejpam-6251	372	5	s	s	PROPN
ejpam-6251	372	6	,	,	PUNCT
ejpam-6251	372	7	π	π	PROPN
ejpam-6251	372	8	,	,	PUNCT
ejpam-6251	372	9	ψ	ψ	PROPN
ejpam-6251	372	10	,	,	PUNCT
ejpam-6251	372	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	372	12	,	,	PUNCT
ejpam-6251	372	13	♢	♢	PROPN
ejpam-6251	372	14	)	)	PUNCT
ejpam-6251	372	15	is	be	AUX
ejpam-6251	372	16	a	a	DET
ejpam-6251	372	17	complete	complete	ADJ
ejpam-6251	372	18	nbms	nbms	NOUN
ejpam-6251	372	19	.	.	PUNCT
ejpam-6251	373	1	then	then	ADV
ejpam-6251	373	2	,	,	PUNCT
ejpam-6251	373	3	{	{	PUNCT
ejpam-6251	373	4	ςµ	ςµ	NOUN
ejpam-6251	373	5	}	}	PUNCT
ejpam-6251	373	6	→	→	SYM
ejpam-6251	373	7	ς	ς	PROPN
ejpam-6251	373	8	and	and	CCONJ
ejpam-6251	373	9	{	{	PUNCT
ejpam-6251	373	10	ϖµ	ϖµ	NOUN
ejpam-6251	373	11	}	}	PUNCT
ejpam-6251	373	12	→	→	SYM
ejpam-6251	373	13	ς	ς	PROPN
ejpam-6251	373	14	,	,	PUNCT
ejpam-6251	373	15	where	where	SCONJ
ejpam-6251	373	16	ς	ς	PROPN
ejpam-6251	373	17	∈	∈	PROPN
ejpam-6251	373	18	𭟋	𭟋	ADP
ejpam-6251	373	19	∩	∩	NOUN
ejpam-6251	373	20	s.	s.	PROPN
ejpam-6251	373	21	using	use	VERB
ejpam-6251	373	22	v	v	NOUN
ejpam-6251	373	23	,	,	PUNCT
ejpam-6251	373	24	x	x	PUNCT
ejpam-6251	373	25	and	and	CCONJ
ejpam-6251	373	26	xv	xv	PROPN
ejpam-6251	373	27	,	,	PUNCT
ejpam-6251	373	28	we	we	PRON
ejpam-6251	373	29	get	get	VERB
ejpam-6251	373	30	π(ς	π(ς	PROPN
ejpam-6251	373	31	,	,	PUNCT
ejpam-6251	373	32	pς	pς	ADP
ejpam-6251	373	33	,	,	PUNCT
ejpam-6251	373	34	ż	ż	NOUN
ejpam-6251	373	35	)	)	PUNCT
ejpam-6251	373	36	≥	≥	NOUN
ejpam-6251	373	37	π	π	PROPN
ejpam-6251	373	38	(	(	PUNCT
ejpam-6251	373	39	ς	ς	PROPN
ejpam-6251	373	40	,	,	PUNCT
ejpam-6251	373	41	ςµ+1	ςµ+1	NUM
ejpam-6251	373	42	,	,	PUNCT
ejpam-6251	373	43	ż	ż	NOUN
ejpam-6251	373	44	3	3	NUM
ejpam-6251	373	45	)	)	PUNCT
ejpam-6251	373	46	⋇π	⋇π	NOUN
ejpam-6251	373	47	(	(	PUNCT
ejpam-6251	373	48	ςµ+1	ςµ+1	NUM
ejpam-6251	373	49	,	,	PUNCT
ejpam-6251	373	50	ςµ+1	ςµ+1	NUM
ejpam-6251	373	51	,	,	PUNCT
ejpam-6251	373	52	ż	ż	NOUN
ejpam-6251	373	53	3	3	NUM
ejpam-6251	373	54	)	)	PUNCT
ejpam-6251	373	55	⋇π	⋇π	NOUN
ejpam-6251	373	56	(	(	PUNCT
ejpam-6251	373	57	ςµ+1	ςµ+1	NUM
ejpam-6251	373	58	,	,	PUNCT
ejpam-6251	373	59	pς	pς	ADP
ejpam-6251	373	60	,	,	PUNCT
ejpam-6251	373	61	ż	ż	NOUN
ejpam-6251	373	62	3	3	NUM
ejpam-6251	373	63	)	)	PUNCT
ejpam-6251	373	64	=	=	PUNCT
ejpam-6251	374	1	π	π	X
ejpam-6251	374	2	(	(	PUNCT
ejpam-6251	374	3	ς	ς	PROPN
ejpam-6251	374	4	,	,	PUNCT
ejpam-6251	374	5	ςµ+1	ςµ+1	NUM
ejpam-6251	374	6	,	,	PUNCT
ejpam-6251	374	7	ż	ż	NOUN
ejpam-6251	374	8	3	3	NUM
ejpam-6251	374	9	)	)	PUNCT
ejpam-6251	374	10	⋇π	⋇π	NOUN
ejpam-6251	374	11	(	(	PUNCT
ejpam-6251	374	12	pςµ	pςµ	PROPN
ejpam-6251	374	13	,	,	PUNCT
ejpam-6251	374	14	pςµ	pςµ	PROPN
ejpam-6251	374	15	,	,	PUNCT
ejpam-6251	374	16	ż	ż	NOUN
ejpam-6251	374	17	3	3	NUM
ejpam-6251	374	18	)	)	PUNCT
ejpam-6251	374	19	⋇π	⋇π	NOUN
ejpam-6251	374	20	(	(	PUNCT
ejpam-6251	374	21	pςµ	pςµ	PROPN
ejpam-6251	374	22	,	,	PUNCT
ejpam-6251	374	23	pς	pς	ADP
ejpam-6251	374	24	,	,	PUNCT
ejpam-6251	374	25	ż	ż	NOUN
ejpam-6251	374	26	3	3	NUM
ejpam-6251	374	27	)	)	PUNCT
ejpam-6251	374	28	→	→	PUNCT
ejpam-6251	374	29	1⋇	1⋇	NUM
ejpam-6251	374	30	1⋇	1⋇	NUM
ejpam-6251	374	31	1	1	NUM
ejpam-6251	374	32	=	=	SYM
ejpam-6251	374	33	1	1	NUM
ejpam-6251	374	34	as	as	ADP
ejpam-6251	374	35	µ→	µ→	PROPN
ejpam-6251	374	36	+	+	NOUN
ejpam-6251	374	37	∞	∞	PROPN
ejpam-6251	374	38	,	,	PUNCT
ejpam-6251	374	39	ψ(ς	ψ(ς	NOUN
ejpam-6251	374	40	,	,	PUNCT
ejpam-6251	374	41	pς	pς	ADP
ejpam-6251	374	42	,	,	PUNCT
ejpam-6251	374	43	ż	ż	NOUN
ejpam-6251	374	44	)	)	PUNCT
ejpam-6251	374	45	≤	≤	NOUN
ejpam-6251	374	46	ψ	ψ	X
ejpam-6251	374	47	(	(	PUNCT
ejpam-6251	374	48	ς	ς	PROPN
ejpam-6251	374	49	,	,	PUNCT
ejpam-6251	374	50	ςµ+1	ςµ+1	NUM
ejpam-6251	374	51	,	,	PUNCT
ejpam-6251	374	52	ż	ż	NOUN
ejpam-6251	374	53	3	3	X
ejpam-6251	374	54	)	)	PUNCT
ejpam-6251	374	55	♢	♢	PROPN
ejpam-6251	374	56	ψ	ψ	X
ejpam-6251	374	57	(	(	PUNCT
ejpam-6251	374	58	ςµ+1	ςµ+1	NUM
ejpam-6251	374	59	,	,	PUNCT
ejpam-6251	374	60	ςµ+1	ςµ+1	NUM
ejpam-6251	374	61	,	,	PUNCT
ejpam-6251	374	62	ż	ż	NOUN
ejpam-6251	374	63	3	3	X
ejpam-6251	374	64	)	)	PUNCT
ejpam-6251	374	65	♢	♢	PROPN
ejpam-6251	374	66	ψ	ψ	X
ejpam-6251	374	67	(	(	PUNCT
ejpam-6251	374	68	ςµ+1	ςµ+1	NUM
ejpam-6251	374	69	,	,	PUNCT
ejpam-6251	374	70	pς	pς	ADP
ejpam-6251	374	71	,	,	PUNCT
ejpam-6251	374	72	ż	ż	NOUN
ejpam-6251	374	73	3	3	NUM
ejpam-6251	374	74	)	)	PUNCT
ejpam-6251	374	75	=	=	SYM
ejpam-6251	374	76	ψ	ψ	X
ejpam-6251	374	77	(	(	PUNCT
ejpam-6251	374	78	ς	ς	PROPN
ejpam-6251	374	79	,	,	PUNCT
ejpam-6251	374	80	ςµ+1	ςµ+1	NUM
ejpam-6251	374	81	,	,	PUNCT
ejpam-6251	374	82	ż	ż	NOUN
ejpam-6251	374	83	3	3	X
ejpam-6251	374	84	)	)	PUNCT
ejpam-6251	374	85	♢	♢	PROPN
ejpam-6251	374	86	ψ	ψ	X
ejpam-6251	374	87	(	(	PUNCT
ejpam-6251	374	88	pςµ+1	pςµ+1	NOUN
ejpam-6251	374	89	,	,	PUNCT
ejpam-6251	374	90	pςµ+1	pςµ+1	NOUN
ejpam-6251	374	91	,	,	PUNCT
ejpam-6251	374	92	ż	ż	NOUN
ejpam-6251	374	93	3	3	NUM
ejpam-6251	374	94	)	)	PUNCT
ejpam-6251	374	95	♢	♢	PROPN
ejpam-6251	374	96	ψ	ψ	X
ejpam-6251	374	97	(	(	PUNCT
ejpam-6251	374	98	pςµ+1	pςµ+1	NOUN
ejpam-6251	374	99	,	,	PUNCT
ejpam-6251	374	100	pς	pς	ADP
ejpam-6251	374	101	,	,	PUNCT
ejpam-6251	374	102	ż	ż	NOUN
ejpam-6251	374	103	3	3	NUM
ejpam-6251	374	104	)	)	PUNCT
ejpam-6251	374	105	→	→	SYM
ejpam-6251	374	106	0	0	NUM
ejpam-6251	374	107	♢	♢	PROPN
ejpam-6251	374	108	0	0	PROPN
ejpam-6251	374	109	♢	♢	PROPN
ejpam-6251	374	110	0	0	PROPN
ejpam-6251	374	111	=	=	SYM
ejpam-6251	374	112	0	0	PUNCT
ejpam-6251	374	113	as	as	ADP
ejpam-6251	374	114	µ→	µ→	PROPN
ejpam-6251	374	115	+	+	NOUN
ejpam-6251	374	116	∞	∞	PROPN
ejpam-6251	374	117	and	and	CCONJ
ejpam-6251	374	118	ξ(ς	ξ(ς	NOUN
ejpam-6251	374	119	,	,	PUNCT
ejpam-6251	374	120	pς	pς	ADP
ejpam-6251	374	121	,	,	PUNCT
ejpam-6251	374	122	ż	ż	NOUN
ejpam-6251	374	123	)	)	PUNCT
ejpam-6251	375	1	≤	≤	NOUN
ejpam-6251	375	2	ξ	ξ	X
ejpam-6251	375	3	(	(	PUNCT
ejpam-6251	375	4	ς	ς	PROPN
ejpam-6251	375	5	,	,	PUNCT
ejpam-6251	375	6	ςµ+1	ςµ+1	NUM
ejpam-6251	375	7	,	,	PUNCT
ejpam-6251	375	8	ż	ż	NOUN
ejpam-6251	375	9	3	3	X
ejpam-6251	375	10	)	)	PUNCT
ejpam-6251	375	11	♢	♢	PROPN
ejpam-6251	375	12	ξ	ξ	X
ejpam-6251	375	13	(	(	PUNCT
ejpam-6251	375	14	ςµ+1	ςµ+1	NUM
ejpam-6251	375	15	,	,	PUNCT
ejpam-6251	375	16	ςµ+1	ςµ+1	NUM
ejpam-6251	375	17	,	,	PUNCT
ejpam-6251	375	18	ż	ż	NOUN
ejpam-6251	375	19	3	3	X
ejpam-6251	375	20	)	)	PUNCT
ejpam-6251	375	21	♢	♢	PROPN
ejpam-6251	375	22	ξ	ξ	X
ejpam-6251	375	23	(	(	PUNCT
ejpam-6251	375	24	ςµ+1	ςµ+1	NUM
ejpam-6251	375	25	,	,	PUNCT
ejpam-6251	375	26	pς	pς	ADP
ejpam-6251	375	27	,	,	PUNCT
ejpam-6251	375	28	ż	ż	NOUN
ejpam-6251	375	29	3	3	NUM
ejpam-6251	375	30	)	)	PUNCT
ejpam-6251	375	31	=	=	SYM
ejpam-6251	376	1	ξ	ξ	PROPN
ejpam-6251	376	2	(	(	PUNCT
ejpam-6251	376	3	ς	ς	PROPN
ejpam-6251	376	4	,	,	PUNCT
ejpam-6251	376	5	ςµ+1	ςµ+1	NUM
ejpam-6251	376	6	,	,	PUNCT
ejpam-6251	376	7	ż	ż	NOUN
ejpam-6251	376	8	3	3	X
ejpam-6251	376	9	)	)	PUNCT
ejpam-6251	376	10	♢	♢	PROPN
ejpam-6251	376	11	ξ	ξ	X
ejpam-6251	376	12	(	(	PUNCT
ejpam-6251	376	13	pςµ+1	pςµ+1	NOUN
ejpam-6251	376	14	,	,	PUNCT
ejpam-6251	376	15	pςµ+1	pςµ+1	NOUN
ejpam-6251	376	16	,	,	PUNCT
ejpam-6251	376	17	ż	ż	NOUN
ejpam-6251	376	18	3	3	X
ejpam-6251	376	19	)	)	PUNCT
ejpam-6251	376	20	♢	♢	PROPN
ejpam-6251	376	21	ξ	ξ	X
ejpam-6251	376	22	(	(	PUNCT
ejpam-6251	376	23	pςµ+1	pςµ+1	NOUN
ejpam-6251	376	24	,	,	PUNCT
ejpam-6251	376	25	pς	pς	ADP
ejpam-6251	376	26	,	,	PUNCT
ejpam-6251	376	27	ż	ż	NOUN
ejpam-6251	376	28	3	3	NUM
ejpam-6251	376	29	)	)	PUNCT
ejpam-6251	376	30	→	→	SYM
ejpam-6251	376	31	0	0	NUM
ejpam-6251	376	32	♢	♢	PROPN
ejpam-6251	376	33	0	0	PROPN
ejpam-6251	376	34	♢	♢	PROPN
ejpam-6251	376	35	0	0	PROPN
ejpam-6251	376	36	=	=	SYM
ejpam-6251	376	37	0	0	PUNCT
ejpam-6251	376	38	as	as	ADP
ejpam-6251	376	39	µ→	µ→	PROPN
ejpam-6251	376	40	+	+	NOUN
ejpam-6251	376	41	∞.	∞.	PROPN
ejpam-6251	376	42	hence	hence	ADV
ejpam-6251	376	43	,	,	PUNCT
ejpam-6251	376	44	pς	pς	ADP
ejpam-6251	376	45	=	=	SYM
ejpam-6251	376	46	ς	ς	PROPN
ejpam-6251	376	47	.	.	PUNCT
ejpam-6251	376	48	let	let	VERB
ejpam-6251	376	49	pη	pη	VERB
ejpam-6251	376	50	=	=	SYM
ejpam-6251	376	51	η	η	PROPN
ejpam-6251	376	52	for	for	ADP
ejpam-6251	376	53	any	any	DET
ejpam-6251	376	54	η	η	PROPN
ejpam-6251	376	55	∈	∈	PROPN
ejpam-6251	376	56	𭟋	𭟋	ADP
ejpam-6251	376	57	∩	∩	NOUN
ejpam-6251	376	58	s	s	SYM
ejpam-6251	376	59	,	,	PUNCT
ejpam-6251	376	60	then	then	ADV
ejpam-6251	376	61	1	1	NUM
ejpam-6251	376	62	≥	≥	NOUN
ejpam-6251	376	63	π(η	π(η	PROPN
ejpam-6251	376	64	,	,	PUNCT
ejpam-6251	376	65	ς	ς	PROPN
ejpam-6251	376	66	,	,	PUNCT
ejpam-6251	376	67	ż	ż	NOUN
ejpam-6251	376	68	)	)	PUNCT
ejpam-6251	376	69	=	=	SYM
ejpam-6251	376	70	π(pη	π(pη	NOUN
ejpam-6251	376	71	,	,	PUNCT
ejpam-6251	376	72	pς	pς	ADP
ejpam-6251	376	73	,	,	PUNCT
ejpam-6251	376	74	ż	ż	NOUN
ejpam-6251	376	75	)	)	PUNCT
ejpam-6251	376	76	≥	≥	NOUN
ejpam-6251	376	77	π	π	PROPN
ejpam-6251	376	78	(	(	PUNCT
ejpam-6251	376	79	η	η	PROPN
ejpam-6251	376	80	,	,	PUNCT
ejpam-6251	376	81	ς	ς	PROPN
ejpam-6251	376	82	,	,	PUNCT
ejpam-6251	376	83	ż	ż	NOUN
ejpam-6251	376	84	ζ	ζ	NOUN
ejpam-6251	376	85	)	)	PUNCT
ejpam-6251	376	86	=	=	PUNCT
ejpam-6251	377	1	π	π	X
ejpam-6251	377	2	(	(	PUNCT
ejpam-6251	377	3	pη	pη	NOUN
ejpam-6251	377	4	,	,	PUNCT
ejpam-6251	377	5	pς	pς	ADP
ejpam-6251	377	6	,	,	PUNCT
ejpam-6251	377	7	ż	ż	NOUN
ejpam-6251	377	8	ζ	ζ	NOUN
ejpam-6251	377	9	)	)	PUNCT
ejpam-6251	377	10	≥	≥	NOUN
ejpam-6251	377	11	π	π	PROPN
ejpam-6251	377	12	(	(	PUNCT
ejpam-6251	377	13	η	η	PROPN
ejpam-6251	377	14	,	,	PUNCT
ejpam-6251	377	15	ς	ς	PROPN
ejpam-6251	377	16	,	,	PUNCT
ejpam-6251	377	17	ż	ż	NOUN
ejpam-6251	377	18	ζ2	ζ2	NOUN
ejpam-6251	377	19	)	)	PUNCT
ejpam-6251	377	20	≥	≥	NOUN
ejpam-6251	377	21	·	·	PUNCT
ejpam-6251	377	22	·	·	PUNCT
ejpam-6251	377	23	·	·	PUNCT
ejpam-6251	377	24	≥	≥	NUM
ejpam-6251	377	25	π	π	PROPN
ejpam-6251	377	26	(	(	PUNCT
ejpam-6251	377	27	η	η	PROPN
ejpam-6251	377	28	,	,	PUNCT
ejpam-6251	377	29	ς	ς	PROPN
ejpam-6251	377	30	,	,	PUNCT
ejpam-6251	377	31	ż	ż	NOUN
ejpam-6251	377	32	ζµ	ζµ	X
ejpam-6251	377	33	)	)	PUNCT
ejpam-6251	377	34	→	→	SYM
ejpam-6251	377	35	1	1	NUM
ejpam-6251	377	36	as	as	ADP
ejpam-6251	377	37	µ→	µ→	PROPN
ejpam-6251	377	38	+	+	NOUN
ejpam-6251	377	39	∞	∞	PROPN
ejpam-6251	377	40	,	,	PUNCT
ejpam-6251	377	41	0	0	NUM
ejpam-6251	377	42	≤	≤	NUM
ejpam-6251	377	43	ψ(η	ψ(η	NOUN
ejpam-6251	377	44	,	,	PUNCT
ejpam-6251	377	45	ς	ς	NOUN
ejpam-6251	377	46	,	,	PUNCT
ejpam-6251	377	47	ż	ż	NOUN
ejpam-6251	377	48	)	)	PUNCT
ejpam-6251	377	49	=	=	PUNCT
ejpam-6251	378	1	ψ(pη	ψ(pη	NOUN
ejpam-6251	378	2	,	,	PUNCT
ejpam-6251	378	3	pς	pς	ADP
ejpam-6251	378	4	,	,	PUNCT
ejpam-6251	378	5	ż	ż	NOUN
ejpam-6251	378	6	)	)	PUNCT
ejpam-6251	378	7	≤	≤	NOUN
ejpam-6251	378	8	ψ	ψ	X
ejpam-6251	378	9	(	(	PUNCT
ejpam-6251	378	10	η	η	PROPN
ejpam-6251	378	11	,	,	PUNCT
ejpam-6251	378	12	ς	ς	PROPN
ejpam-6251	378	13	,	,	PUNCT
ejpam-6251	378	14	ż	ż	NOUN
ejpam-6251	378	15	ζ	ζ	NOUN
ejpam-6251	378	16	)	)	PUNCT
ejpam-6251	378	17	=	=	SYM
ejpam-6251	378	18	ψ	ψ	X
ejpam-6251	378	19	(	(	PUNCT
ejpam-6251	378	20	pη	pη	NOUN
ejpam-6251	378	21	,	,	PUNCT
ejpam-6251	378	22	pς	pς	ADP
ejpam-6251	378	23	,	,	PUNCT
ejpam-6251	378	24	ż	ż	NOUN
ejpam-6251	378	25	ζ	ζ	NOUN
ejpam-6251	378	26	)	)	PUNCT
ejpam-6251	378	27	r.	r.	PROPN
ejpam-6251	378	28	ramaswamy	ramaswamy	PROPN
ejpam-6251	378	29	/	/	SYM
ejpam-6251	378	30	eur	eur	PROPN
ejpam-6251	378	31	.	.	PUNCT
ejpam-6251	379	1	j.	j.	PROPN
ejpam-6251	379	2	pure	pure	PROPN
ejpam-6251	379	3	appl	appl	PROPN
ejpam-6251	379	4	.	.	PROPN
ejpam-6251	379	5	math	math	PROPN
ejpam-6251	379	6	,	,	PUNCT
ejpam-6251	379	7	18	18	NUM
ejpam-6251	379	8	(	(	PUNCT
ejpam-6251	379	9	4	4	NUM
ejpam-6251	379	10	)	)	PUNCT
ejpam-6251	379	11	(	(	PUNCT
ejpam-6251	379	12	2025	2025	NUM
ejpam-6251	379	13	)	)	PUNCT
ejpam-6251	379	14	,	,	PUNCT
ejpam-6251	379	15	6251	6251	NUM
ejpam-6251	379	16	17	17	NUM
ejpam-6251	379	17	of	of	ADP
ejpam-6251	379	18	40	40	NUM
ejpam-6251	379	19	≤	≤	NOUN
ejpam-6251	379	20	ψ	ψ	X
ejpam-6251	379	21	(	(	PUNCT
ejpam-6251	379	22	η	η	PROPN
ejpam-6251	379	23	,	,	PUNCT
ejpam-6251	379	24	ς	ς	PROPN
ejpam-6251	379	25	,	,	PUNCT
ejpam-6251	379	26	ż	ż	NOUN
ejpam-6251	379	27	ζ2	ζ2	NOUN
ejpam-6251	379	28	)	)	PUNCT
ejpam-6251	379	29	≤	≤	NOUN
ejpam-6251	379	30	·	·	PUNCT
ejpam-6251	379	31	·	·	PUNCT
ejpam-6251	379	32	·	·	PUNCT
ejpam-6251	380	1	≤	≤	NUM
ejpam-6251	380	2	ψ	ψ	X
ejpam-6251	380	3	(	(	PUNCT
ejpam-6251	380	4	η	η	PROPN
ejpam-6251	380	5	,	,	PUNCT
ejpam-6251	380	6	ς	ς	PROPN
ejpam-6251	380	7	,	,	PUNCT
ejpam-6251	380	8	ż	ż	NOUN
ejpam-6251	380	9	ζµ	ζµ	X
ejpam-6251	380	10	)	)	PUNCT
ejpam-6251	380	11	→	→	SYM
ejpam-6251	380	12	0	0	PUNCT
ejpam-6251	380	13	as	as	ADP
ejpam-6251	380	14	µ→	µ→	PROPN
ejpam-6251	380	15	+	+	NOUN
ejpam-6251	380	16	∞	∞	PROPN
ejpam-6251	380	17	,	,	PUNCT
ejpam-6251	380	18	and	and	CCONJ
ejpam-6251	380	19	0	0	NUM
ejpam-6251	380	20	≤	≤	NUM
ejpam-6251	380	21	ξ(η	ξ(η	PROPN
ejpam-6251	380	22	,	,	PUNCT
ejpam-6251	380	23	ς	ς	NOUN
ejpam-6251	380	24	,	,	PUNCT
ejpam-6251	380	25	ż	ż	NOUN
ejpam-6251	380	26	)	)	PUNCT
ejpam-6251	380	27	=	=	PUNCT
ejpam-6251	380	28	ξ(pη	ξ(pη	NOUN
ejpam-6251	380	29	,	,	PUNCT
ejpam-6251	380	30	pς	pς	ADP
ejpam-6251	380	31	,	,	PUNCT
ejpam-6251	380	32	ż	ż	NOUN
ejpam-6251	380	33	)	)	PUNCT
ejpam-6251	380	34	≤	≤	NOUN
ejpam-6251	380	35	ξ	ξ	PROPN
ejpam-6251	380	36	(	(	PUNCT
ejpam-6251	380	37	η	η	PROPN
ejpam-6251	380	38	,	,	PUNCT
ejpam-6251	380	39	ς	ς	PROPN
ejpam-6251	380	40	,	,	PUNCT
ejpam-6251	380	41	ż	ż	NOUN
ejpam-6251	380	42	ζ	ζ	NOUN
ejpam-6251	380	43	)	)	PUNCT
ejpam-6251	380	44	=	=	SYM
ejpam-6251	381	1	ξ	ξ	PROPN
ejpam-6251	381	2	(	(	PUNCT
ejpam-6251	381	3	pη	pη	NOUN
ejpam-6251	381	4	,	,	PUNCT
ejpam-6251	381	5	pς	pς	ADP
ejpam-6251	381	6	,	,	PUNCT
ejpam-6251	381	7	ż	ż	NOUN
ejpam-6251	381	8	ζ	ζ	NOUN
ejpam-6251	381	9	)	)	PUNCT
ejpam-6251	381	10	≤	≤	NUM
ejpam-6251	381	11	ξ	ξ	PROPN
ejpam-6251	381	12	(	(	PUNCT
ejpam-6251	381	13	η	η	PROPN
ejpam-6251	381	14	,	,	PUNCT
ejpam-6251	381	15	ς	ς	PROPN
ejpam-6251	381	16	,	,	PUNCT
ejpam-6251	381	17	ż	ż	NOUN
ejpam-6251	381	18	ζ2	ζ2	NOUN
ejpam-6251	381	19	)	)	PUNCT
ejpam-6251	381	20	≤	≤	NOUN
ejpam-6251	381	21	·	·	PUNCT
ejpam-6251	381	22	·	·	PUNCT
ejpam-6251	381	23	·	·	PUNCT
ejpam-6251	382	1	≤	≤	NUM
ejpam-6251	382	2	ξ	ξ	X
ejpam-6251	382	3	(	(	PUNCT
ejpam-6251	382	4	η	η	PROPN
ejpam-6251	382	5	,	,	PUNCT
ejpam-6251	382	6	ς	ς	PROPN
ejpam-6251	382	7	,	,	PUNCT
ejpam-6251	382	8	ż	ż	NOUN
ejpam-6251	382	9	ζµ	ζµ	X
ejpam-6251	382	10	)	)	PUNCT
ejpam-6251	382	11	→	→	SYM
ejpam-6251	382	12	0	0	PUNCT
ejpam-6251	382	13	as	as	ADP
ejpam-6251	382	14	µ→	µ→	PROPN
ejpam-6251	382	15	+	+	NOUN
ejpam-6251	382	16	∞	∞	PROPN
ejpam-6251	382	17	,	,	PUNCT
ejpam-6251	382	18	since	since	SCONJ
ejpam-6251	382	19	iii	iii	NOUN
ejpam-6251	382	20	,	,	PUNCT
ejpam-6251	382	21	viii	viii	NOUN
ejpam-6251	382	22	and	and	CCONJ
ejpam-6251	382	23	xiii	xiii	PROPN
ejpam-6251	382	24	,	,	PUNCT
ejpam-6251	382	25	we	we	PRON
ejpam-6251	382	26	get	get	VERB
ejpam-6251	382	27	ς	ς	PROPN
ejpam-6251	382	28	=	=	SYM
ejpam-6251	382	29	η	η	PROPN
ejpam-6251	382	30	.	.	PROPN
ejpam-6251	382	31	theorem	theorem	NOUN
ejpam-6251	382	32	6	6	NUM
ejpam-6251	382	33	.	.	PUNCT
ejpam-6251	382	34	suppose	suppose	VERB
ejpam-6251	382	35	(	(	PUNCT
ejpam-6251	382	36	𭟋	𭟋	NOUN
ejpam-6251	382	37	,	,	PUNCT
ejpam-6251	382	38	s	s	PROPN
ejpam-6251	382	39	,	,	PUNCT
ejpam-6251	382	40	π	π	PROPN
ejpam-6251	382	41	,	,	PUNCT
ejpam-6251	382	42	ψ	ψ	PROPN
ejpam-6251	382	43	,	,	PUNCT
ejpam-6251	382	44	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	382	45	,	,	PUNCT
ejpam-6251	382	46	♢	♢	PROPN
ejpam-6251	382	47	)	)	PUNCT
ejpam-6251	382	48	is	be	AUX
ejpam-6251	382	49	a	a	DET
ejpam-6251	382	50	complete	complete	ADJ
ejpam-6251	382	51	nbms	nbms	NOUN
ejpam-6251	382	52	with	with	ADP
ejpam-6251	382	53	0	0	NUM
ejpam-6251	382	54	<	<	X
ejpam-6251	382	55	ζ	ζ	X
ejpam-6251	382	56	<	<	X
ejpam-6251	382	57	1	1	NUM
ejpam-6251	382	58	.	.	PUNCT
ejpam-6251	383	1	let	let	VERB
ejpam-6251	383	2	p	p	NOUN
ejpam-6251	383	3	:	:	PUNCT
ejpam-6251	383	4	𭟋	𭟋	ADP
ejpam-6251	383	5	∪	∪	ADP
ejpam-6251	383	6	s	s	X
ejpam-6251	383	7	→	→	SYM
ejpam-6251	383	8	𭟋	𭟋	ADP
ejpam-6251	383	9	∪	∪	NOUN
ejpam-6251	383	10	s	s	AUX
ejpam-6251	383	11	be	be	VERB
ejpam-6251	383	12	a	a	DET
ejpam-6251	383	13	mapping	mapping	NOUN
ejpam-6251	383	14	satisfying	satisfy	VERB
ejpam-6251	383	15	i.	i.	NOUN
ejpam-6251	383	16	p(𭟋	p(𭟋	PROPN
ejpam-6251	383	17	)	)	PUNCT
ejpam-6251	383	18	⊆	⊆	NUM
ejpam-6251	383	19	s	s	NOUN
ejpam-6251	383	20	and	and	CCONJ
ejpam-6251	383	21	p(s	p(s	NUM
ejpam-6251	383	22	)	)	PUNCT
ejpam-6251	383	23	⊆	⊆	NUM
ejpam-6251	383	24	𭟋	𭟋	ADP
ejpam-6251	383	25	;	;	PUNCT
ejpam-6251	383	26	ii	ii	X
ejpam-6251	383	27	.	.	PUNCT
ejpam-6251	384	1	π(pς	π(pς	NOUN
ejpam-6251	384	2	,	,	PUNCT
ejpam-6251	384	3	pϖ	pϖ	ADP
ejpam-6251	384	4	,	,	PUNCT
ejpam-6251	384	5	ζ	ζ	NOUN
ejpam-6251	384	6	ż	ż	NOUN
ejpam-6251	384	7	)	)	PUNCT
ejpam-6251	384	8	≥	≥	NOUN
ejpam-6251	384	9	π(ϖ	π(ϖ	PROPN
ejpam-6251	384	10	,	,	PUNCT
ejpam-6251	384	11	ς	ς	PROPN
ejpam-6251	384	12	,	,	PUNCT
ejpam-6251	384	13	ż	ż	NOUN
ejpam-6251	384	14	)	)	PUNCT
ejpam-6251	384	15	,	,	PUNCT
ejpam-6251	384	16	ψ(pς	ψ(pς	NOUN
ejpam-6251	384	17	,	,	PUNCT
ejpam-6251	384	18	pϖ	pϖ	ADP
ejpam-6251	384	19	,	,	PUNCT
ejpam-6251	384	20	ζ	ζ	NOUN
ejpam-6251	384	21	ż	ż	NOUN
ejpam-6251	384	22	)	)	PUNCT
ejpam-6251	384	23	≤	≤	PUNCT
ejpam-6251	385	1	ψ(ϖ	ψ(ϖ	NOUN
ejpam-6251	385	2	,	,	PUNCT
ejpam-6251	385	3	ς	ς	PROPN
ejpam-6251	385	4	,	,	PUNCT
ejpam-6251	385	5	ż	ż	NOUN
ejpam-6251	385	6	)	)	PUNCT
ejpam-6251	385	7	and	and	CCONJ
ejpam-6251	385	8	ξ(pς	ξ(pς	NOUN
ejpam-6251	385	9	,	,	PUNCT
ejpam-6251	385	10	pϖ	pϖ	ADP
ejpam-6251	385	11	,	,	PUNCT
ejpam-6251	385	12	ζ	ζ	NOUN
ejpam-6251	385	13	ż	ż	NOUN
ejpam-6251	385	14	)	)	PUNCT
ejpam-6251	385	15	≤	≤	NOUN
ejpam-6251	386	1	ξ(ϖ	ξ(ϖ	PROPN
ejpam-6251	386	2	,	,	PUNCT
ejpam-6251	386	3	ς	ς	PROPN
ejpam-6251	386	4	,	,	PUNCT
ejpam-6251	386	5	ż	ż	NOUN
ejpam-6251	386	6	)	)	PUNCT
ejpam-6251	386	7	(	(	PUNCT
ejpam-6251	386	8	6	6	NUM
ejpam-6251	386	9	)	)	PUNCT
ejpam-6251	386	10	∀	∀	NOUN
ejpam-6251	387	1	ς	ς	PROPN
ejpam-6251	387	2	∈	∈	X
ejpam-6251	387	3	𭟋	𭟋	X
ejpam-6251	387	4	,	,	PUNCT
ejpam-6251	387	5	ϖ	ϖ	PROPN
ejpam-6251	387	6	∈	∈	PROPN
ejpam-6251	387	7	s	s	PART
ejpam-6251	387	8	and	and	CCONJ
ejpam-6251	387	9	ż	ż	X
ejpam-6251	387	10	>	>	X
ejpam-6251	387	11	0	0	X
ejpam-6251	387	12	.	.	PUNCT
ejpam-6251	388	1	then	then	ADV
ejpam-6251	388	2	p	p	X
ejpam-6251	388	3	has	have	VERB
ejpam-6251	388	4	a	a	DET
ejpam-6251	388	5	unique	unique	ADJ
ejpam-6251	388	6	fixed	fix	VERB
ejpam-6251	388	7	point	point	NOUN
ejpam-6251	388	8	.	.	PUNCT
ejpam-6251	389	1	proof	proof	NOUN
ejpam-6251	389	2	.	.	PUNCT
ejpam-6251	390	1	let	let	VERB
ejpam-6251	390	2	ς0	ς0	PROPN
ejpam-6251	390	3	∈	∈	PROPN
ejpam-6251	390	4	𭟋	𭟋	NOUN
ejpam-6251	390	5	and	and	CCONJ
ejpam-6251	390	6	ϖ0	ϖ0	NOUN
ejpam-6251	390	7	∈	∈	NOUN
ejpam-6251	390	8	s	s	PART
ejpam-6251	390	9	and	and	CCONJ
ejpam-6251	390	10	assume	assume	VERB
ejpam-6251	390	11	that	that	SCONJ
ejpam-6251	390	12	p(ςµ	p(ςµ	NOUN
ejpam-6251	390	13	)	)	PUNCT
ejpam-6251	390	14	=	=	SYM
ejpam-6251	390	15	ϖµ	ϖµ	NOUN
ejpam-6251	390	16	and	and	CCONJ
ejpam-6251	390	17	p(ϖµ	p(ϖµ	NOUN
ejpam-6251	390	18	)	)	PUNCT
ejpam-6251	390	19	=	=	SYM
ejpam-6251	390	20	ςµ+1	ςµ+1	NUM
ejpam-6251	390	21	∀	∀	NOUN
ejpam-6251	390	22	µ	µ	PRON
ejpam-6251	390	23	∈	∈	NOUN
ejpam-6251	390	24	n	n	NOUN
ejpam-6251	390	25	∪	∪	X
ejpam-6251	390	26	{	{	PUNCT
ejpam-6251	390	27	0	0	NUM
ejpam-6251	390	28	}	}	PUNCT
ejpam-6251	390	29	.	.	PUNCT
ejpam-6251	391	1	then	then	ADV
ejpam-6251	391	2	we	we	PRON
ejpam-6251	391	3	get	get	VERB
ejpam-6251	391	4	(	(	PUNCT
ejpam-6251	391	5	ςµ	ςµ	NOUN
ejpam-6251	391	6	,	,	PUNCT
ejpam-6251	391	7	ϖµ	ϖµ	NOUN
ejpam-6251	391	8	)	)	PUNCT
ejpam-6251	391	9	as	as	ADP
ejpam-6251	391	10	a	a	DET
ejpam-6251	391	11	bisequence	bisequence	NOUN
ejpam-6251	391	12	on	on	ADP
ejpam-6251	391	13	nbms	nbms	NOUN
ejpam-6251	391	14	(	(	PUNCT
ejpam-6251	391	15	𭟋	𭟋	NOUN
ejpam-6251	391	16	,	,	PUNCT
ejpam-6251	391	17	s	s	PROPN
ejpam-6251	391	18	,	,	PUNCT
ejpam-6251	391	19	π	π	PROPN
ejpam-6251	391	20	,	,	PUNCT
ejpam-6251	391	21	ψ	ψ	PROPN
ejpam-6251	391	22	,	,	PUNCT
ejpam-6251	391	23	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	391	24	,	,	PUNCT
ejpam-6251	391	25	♢	♢	PROPN
ejpam-6251	391	26	)	)	PUNCT
ejpam-6251	391	27	.	.	PUNCT
ejpam-6251	392	1	now	now	ADV
ejpam-6251	392	2	,	,	PUNCT
ejpam-6251	392	3	we	we	PRON
ejpam-6251	392	4	have	have	VERB
ejpam-6251	392	5	π(ς1	π(ς1	NOUN
ejpam-6251	392	6	,	,	PUNCT
ejpam-6251	392	7	ϖ0	ϖ0	NOUN
ejpam-6251	392	8	,	,	PUNCT
ejpam-6251	392	9	ż	ż	NOUN
ejpam-6251	392	10	)	)	PUNCT
ejpam-6251	393	1	=	=	SYM
ejpam-6251	393	2	π(pϖ0	π(pϖ0	PROPN
ejpam-6251	393	3	,	,	PUNCT
ejpam-6251	393	4	pς0	pς0	PROPN
ejpam-6251	393	5	,	,	PUNCT
ejpam-6251	393	6	ż	ż	NOUN
ejpam-6251	393	7	)	)	PUNCT
ejpam-6251	393	8	≥	≥	NOUN
ejpam-6251	393	9	π(ς0	π(ς0	NOUN
ejpam-6251	393	10	,	,	PUNCT
ejpam-6251	393	11	ϖ0	ϖ0	NOUN
ejpam-6251	393	12	,	,	PUNCT
ejpam-6251	393	13	ż	ż	NOUN
ejpam-6251	393	14	ζ	ζ	NOUN
ejpam-6251	393	15	)	)	PUNCT
ejpam-6251	393	16	,	,	PUNCT
ejpam-6251	393	17	ψ(ς1	ψ(ς1	NOUN
ejpam-6251	393	18	,	,	PUNCT
ejpam-6251	393	19	ϖ0	ϖ0	NOUN
ejpam-6251	393	20	,	,	PUNCT
ejpam-6251	393	21	ż	ż	NOUN
ejpam-6251	393	22	)	)	PUNCT
ejpam-6251	393	23	=	=	SYM
ejpam-6251	393	24	ψ(pϖ0	ψ(pϖ0	PROPN
ejpam-6251	393	25	,	,	PUNCT
ejpam-6251	393	26	pς0	pς0	PROPN
ejpam-6251	393	27	,	,	PUNCT
ejpam-6251	393	28	ż	ż	NOUN
ejpam-6251	393	29	)	)	PUNCT
ejpam-6251	393	30	≤	≤	NOUN
ejpam-6251	393	31	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	393	32	,	,	PUNCT
ejpam-6251	393	33	ϖ0	ϖ0	NOUN
ejpam-6251	393	34	,	,	PUNCT
ejpam-6251	393	35	ż	ż	NOUN
ejpam-6251	393	36	ζ	ζ	NOUN
ejpam-6251	393	37	)	)	PUNCT
ejpam-6251	393	38	and	and	CCONJ
ejpam-6251	393	39	ξ(ς1	ξ(ς1	NOUN
ejpam-6251	393	40	,	,	PUNCT
ejpam-6251	393	41	ϖ0	ϖ0	NOUN
ejpam-6251	393	42	,	,	PUNCT
ejpam-6251	393	43	ż	ż	NOUN
ejpam-6251	393	44	)	)	PUNCT
ejpam-6251	393	45	=	=	SYM
ejpam-6251	393	46	ξ(pϖ0	ξ(pϖ0	PROPN
ejpam-6251	393	47	,	,	PUNCT
ejpam-6251	393	48	pς0	pς0	PROPN
ejpam-6251	393	49	,	,	PUNCT
ejpam-6251	393	50	ż	ż	NOUN
ejpam-6251	393	51	)	)	PUNCT
ejpam-6251	393	52	≤	≤	NOUN
ejpam-6251	393	53	ξ(ς0	ξ(ς0	NOUN
ejpam-6251	393	54	,	,	PUNCT
ejpam-6251	393	55	ϖ0	ϖ0	NOUN
ejpam-6251	393	56	,	,	PUNCT
ejpam-6251	393	57	ż	ż	NOUN
ejpam-6251	393	58	ζ	ζ	NOUN
ejpam-6251	393	59	)	)	PUNCT
ejpam-6251	393	60	,	,	PUNCT
ejpam-6251	393	61	∀	∀	PUNCT
ejpam-6251	394	1	ż	ż	VERB
ejpam-6251	394	2	>	>	X
ejpam-6251	394	3	0	0	NUM
ejpam-6251	394	4	and	and	CCONJ
ejpam-6251	394	5	µ	µ	PRON
ejpam-6251	394	6	∈	∈	PROPN
ejpam-6251	394	7	n.	n.	NOUN
ejpam-6251	394	8	by	by	ADP
ejpam-6251	394	9	simple	simple	ADJ
ejpam-6251	394	10	induction	induction	NOUN
ejpam-6251	394	11	,	,	PUNCT
ejpam-6251	394	12	we	we	PRON
ejpam-6251	394	13	get	get	VERB
ejpam-6251	394	14	π(ςµ	π(ςµ	NUM
ejpam-6251	394	15	,	,	PUNCT
ejpam-6251	394	16	ϖµ	ϖµ	NOUN
ejpam-6251	394	17	,	,	PUNCT
ejpam-6251	394	18	ż	ż	NOUN
ejpam-6251	394	19	)	)	PUNCT
ejpam-6251	394	20	=	=	SYM
ejpam-6251	394	21	π(pϖµ−1	π(pϖµ−1	PROPN
ejpam-6251	394	22	,	,	PUNCT
ejpam-6251	394	23	pςµ	pςµ	PROPN
ejpam-6251	394	24	,	,	PUNCT
ejpam-6251	394	25	ż	ż	NOUN
ejpam-6251	394	26	)	)	PUNCT
ejpam-6251	394	27	≥	≥	NOUN
ejpam-6251	394	28	π	π	PROPN
ejpam-6251	394	29	(	(	PUNCT
ejpam-6251	394	30	ς0	ς0	PROPN
ejpam-6251	394	31	,	,	PUNCT
ejpam-6251	394	32	ϖ0	ϖ0	NOUN
ejpam-6251	394	33	,	,	PUNCT
ejpam-6251	394	34	ż	ż	PROPN
ejpam-6251	394	35	ζ2µ	ζ2µ	PROPN
ejpam-6251	394	36	)	)	PUNCT
ejpam-6251	394	37	,	,	PUNCT
ejpam-6251	394	38	ψ(ςµ	ψ(ςµ	PROPN
ejpam-6251	394	39	,	,	PUNCT
ejpam-6251	394	40	ϖµ	ϖµ	NOUN
ejpam-6251	394	41	,	,	PUNCT
ejpam-6251	394	42	ż	ż	NOUN
ejpam-6251	394	43	)	)	PUNCT
ejpam-6251	394	44	=	=	PUNCT
ejpam-6251	394	45	ψ(pϖµ−1	ψ(pϖµ−1	PROPN
ejpam-6251	394	46	,	,	PUNCT
ejpam-6251	394	47	pςµ	pςµ	PROPN
ejpam-6251	394	48	,	,	PUNCT
ejpam-6251	394	49	ż	ż	NOUN
ejpam-6251	394	50	)	)	PUNCT
ejpam-6251	394	51	≤	≤	NOUN
ejpam-6251	395	1	ψ	ψ	X
ejpam-6251	395	2	(	(	PUNCT
ejpam-6251	395	3	ς0	ς0	PROPN
ejpam-6251	395	4	,	,	PUNCT
ejpam-6251	395	5	ϖ0	ϖ0	NOUN
ejpam-6251	395	6	,	,	PUNCT
ejpam-6251	395	7	ż	ż	PROPN
ejpam-6251	395	8	ζ2µ	ζ2µ	PROPN
ejpam-6251	395	9	)	)	PUNCT
ejpam-6251	395	10	,	,	PUNCT
ejpam-6251	395	11	r.	r.	PROPN
ejpam-6251	395	12	ramaswamy	ramaswamy	PROPN
ejpam-6251	395	13	/	/	SYM
ejpam-6251	395	14	eur	eur	PROPN
ejpam-6251	395	15	.	.	PUNCT
ejpam-6251	396	1	j.	j.	PROPN
ejpam-6251	396	2	pure	pure	PROPN
ejpam-6251	396	3	appl	appl	PROPN
ejpam-6251	396	4	.	.	PROPN
ejpam-6251	396	5	math	math	PROPN
ejpam-6251	396	6	,	,	PUNCT
ejpam-6251	396	7	18	18	NUM
ejpam-6251	396	8	(	(	PUNCT
ejpam-6251	396	9	4	4	NUM
ejpam-6251	396	10	)	)	PUNCT
ejpam-6251	396	11	(	(	PUNCT
ejpam-6251	396	12	2025	2025	NUM
ejpam-6251	396	13	)	)	PUNCT
ejpam-6251	396	14	,	,	PUNCT
ejpam-6251	396	15	6251	6251	NUM
ejpam-6251	396	16	18	18	NUM
ejpam-6251	396	17	of	of	ADP
ejpam-6251	396	18	40	40	NUM
ejpam-6251	396	19	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	396	20	,	,	PUNCT
ejpam-6251	396	21	ϖµ	ϖµ	NOUN
ejpam-6251	396	22	,	,	PUNCT
ejpam-6251	396	23	ż	ż	NOUN
ejpam-6251	396	24	)	)	PUNCT
ejpam-6251	396	25	=	=	SYM
ejpam-6251	396	26	ξ(pϖµ−1	ξ(pϖµ−1	PROPN
ejpam-6251	396	27	,	,	PUNCT
ejpam-6251	396	28	pςµ	pςµ	PROPN
ejpam-6251	396	29	,	,	PUNCT
ejpam-6251	396	30	ż	ż	NOUN
ejpam-6251	396	31	)	)	PUNCT
ejpam-6251	397	1	≤	≤	NOUN
ejpam-6251	397	2	ξ	ξ	PROPN
ejpam-6251	397	3	(	(	PUNCT
ejpam-6251	397	4	ς0	ς0	PROPN
ejpam-6251	397	5	,	,	PUNCT
ejpam-6251	397	6	ϖ0	ϖ0	NOUN
ejpam-6251	397	7	,	,	PUNCT
ejpam-6251	397	8	ż	ż	NOUN
ejpam-6251	397	9	ζ2µ	ζ2µ	PROPN
ejpam-6251	397	10	)	)	PUNCT
ejpam-6251	397	11	and	and	CCONJ
ejpam-6251	397	12	π(ςµ+1	π(ςµ+1	PROPN
ejpam-6251	397	13	,	,	PUNCT
ejpam-6251	397	14	ϖµ	ϖµ	NOUN
ejpam-6251	397	15	,	,	PUNCT
ejpam-6251	397	16	ż	ż	NOUN
ejpam-6251	397	17	)	)	PUNCT
ejpam-6251	397	18	=	=	PUNCT
ejpam-6251	398	1	π(pϖµ	π(pϖµ	INTJ
ejpam-6251	398	2	,	,	PUNCT
ejpam-6251	398	3	pςµ	pςµ	PROPN
ejpam-6251	398	4	,	,	PUNCT
ejpam-6251	398	5	ż	ż	NOUN
ejpam-6251	398	6	)	)	PUNCT
ejpam-6251	398	7	≥	≥	NOUN
ejpam-6251	398	8	π	π	PROPN
ejpam-6251	398	9	(	(	PUNCT
ejpam-6251	398	10	ς0	ς0	PROPN
ejpam-6251	398	11	,	,	PUNCT
ejpam-6251	398	12	ϖ0	ϖ0	NOUN
ejpam-6251	398	13	,	,	PUNCT
ejpam-6251	398	14	ż	ż	NOUN
ejpam-6251	398	15	ζ2µ+1	ζ2µ+1	NOUN
ejpam-6251	398	16	)	)	PUNCT
ejpam-6251	398	17	,	,	PUNCT
ejpam-6251	398	18	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	398	19	,	,	PUNCT
ejpam-6251	398	20	ϖµ	ϖµ	NOUN
ejpam-6251	398	21	,	,	PUNCT
ejpam-6251	398	22	ż	ż	NOUN
ejpam-6251	398	23	)	)	PUNCT
ejpam-6251	398	24	=	=	SYM
ejpam-6251	398	25	ψ(pϖµ	ψ(pϖµ	PROPN
ejpam-6251	398	26	,	,	PUNCT
ejpam-6251	398	27	pςµ	pςµ	PROPN
ejpam-6251	398	28	,	,	PUNCT
ejpam-6251	398	29	ż	ż	NOUN
ejpam-6251	398	30	)	)	PUNCT
ejpam-6251	398	31	≤	≤	NOUN
ejpam-6251	398	32	ψ	ψ	X
ejpam-6251	398	33	(	(	PUNCT
ejpam-6251	398	34	ς0	ς0	PROPN
ejpam-6251	398	35	,	,	PUNCT
ejpam-6251	398	36	ϖ0	ϖ0	NOUN
ejpam-6251	398	37	,	,	PUNCT
ejpam-6251	398	38	ż	ż	NOUN
ejpam-6251	398	39	ζ2µ+1	ζ2µ+1	NOUN
ejpam-6251	398	40	)	)	PUNCT
ejpam-6251	398	41	,	,	PUNCT
ejpam-6251	398	42	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	398	43	,	,	PUNCT
ejpam-6251	398	44	ϖµ	ϖµ	NOUN
ejpam-6251	398	45	,	,	PUNCT
ejpam-6251	398	46	ż	ż	NOUN
ejpam-6251	398	47	)	)	PUNCT
ejpam-6251	398	48	=	=	SYM
ejpam-6251	398	49	ξ(pϖµ	ξ(pϖµ	PROPN
ejpam-6251	398	50	,	,	PUNCT
ejpam-6251	398	51	pςµ	pςµ	PROPN
ejpam-6251	398	52	,	,	PUNCT
ejpam-6251	398	53	ż	ż	NOUN
ejpam-6251	398	54	)	)	PUNCT
ejpam-6251	398	55	≤	≤	NOUN
ejpam-6251	398	56	ξ	ξ	PROPN
ejpam-6251	398	57	(	(	PUNCT
ejpam-6251	398	58	ς0	ς0	PROPN
ejpam-6251	398	59	,	,	PUNCT
ejpam-6251	398	60	ϖ0	ϖ0	NOUN
ejpam-6251	398	61	,	,	PUNCT
ejpam-6251	398	62	ż	ż	NOUN
ejpam-6251	398	63	ζ2µ+1	ζ2µ+1	NOUN
ejpam-6251	398	64	)	)	PUNCT
ejpam-6251	398	65	.	.	PUNCT
ejpam-6251	399	1	letting	let	VERB
ejpam-6251	399	2	µ	µ	PRON
ejpam-6251	399	3	<	<	X
ejpam-6251	399	4	m	m	PROPN
ejpam-6251	399	5	,	,	PUNCT
ejpam-6251	399	6	for	for	ADP
ejpam-6251	399	7	µ,m	µ,m	PROPN
ejpam-6251	399	8	∈	∈	PROPN
ejpam-6251	399	9	n.	n.	NOUN
ejpam-6251	399	10	then	then	ADV
ejpam-6251	399	11	,	,	PUNCT
ejpam-6251	399	12	π(ςµ	π(ςµ	PROPN
ejpam-6251	399	13	,	,	PUNCT
ejpam-6251	399	14	ϖm	ϖm	ADJ
ejpam-6251	399	15	,	,	PUNCT
ejpam-6251	399	16	ż	ż	NOUN
ejpam-6251	399	17	)	)	PUNCT
ejpam-6251	399	18	≥	≥	NOUN
ejpam-6251	399	19	π(ςµ	π(ςµ	PROPN
ejpam-6251	399	20	,	,	PUNCT
ejpam-6251	399	21	ϖµ	ϖµ	NOUN
ejpam-6251	399	22	,	,	PUNCT
ejpam-6251	399	23	ż	ż	NOUN
ejpam-6251	399	24	3	3	X
ejpam-6251	399	25	)	)	PUNCT
ejpam-6251	399	26	⋇π(ςµ+1	⋇π(ςµ+1	PROPN
ejpam-6251	399	27	,	,	PUNCT
ejpam-6251	399	28	ϖµ	ϖµ	NOUN
ejpam-6251	399	29	,	,	PUNCT
ejpam-6251	399	30	ż	ż	NOUN
ejpam-6251	399	31	3	3	X
ejpam-6251	399	32	)	)	PUNCT
ejpam-6251	399	33	⋇π(ςµ+1	⋇π(ςµ+1	PROPN
ejpam-6251	399	34	,	,	PUNCT
ejpam-6251	399	35	ϖm	ϖm	NOUN
ejpam-6251	399	36	,	,	PUNCT
ejpam-6251	399	37	ż	ż	NOUN
ejpam-6251	399	38	3	3	NUM
ejpam-6251	399	39	)	)	PUNCT
ejpam-6251	399	40	...	...	PUNCT
ejpam-6251	399	41	≥	≥	NUM
ejpam-6251	399	42	π(ςµ	π(ςµ	NOUN
ejpam-6251	399	43	,	,	PUNCT
ejpam-6251	399	44	ϖµ	ϖµ	NOUN
ejpam-6251	399	45	,	,	PUNCT
ejpam-6251	399	46	ż	ż	NOUN
ejpam-6251	399	47	3	3	X
ejpam-6251	399	48	)	)	PUNCT
ejpam-6251	399	49	⋇π(ςµ+1	⋇π(ςµ+1	PROPN
ejpam-6251	399	50	,	,	PUNCT
ejpam-6251	399	51	ϖµ	ϖµ	NOUN
ejpam-6251	399	52	,	,	PUNCT
ejpam-6251	399	53	ż	ż	NOUN
ejpam-6251	399	54	3	3	NUM
ejpam-6251	399	55	)	)	PUNCT
ejpam-6251	399	56	⋇	⋇	NOUN
ejpam-6251	399	57	·	·	PUNCT
ejpam-6251	399	58	·	·	PUNCT
ejpam-6251	399	59	·	·	PUNCT
ejpam-6251	399	60	⋇π(ςm−1	⋇π(ςm−1	PROPN
ejpam-6251	399	61	,	,	PUNCT
ejpam-6251	399	62	ϖm−1	ϖm−1	PROPN
ejpam-6251	399	63	,	,	PUNCT
ejpam-6251	399	64	ż	ż	PROPN
ejpam-6251	399	65	3m−1	3m−1	PROPN
ejpam-6251	399	66	)	)	PUNCT
ejpam-6251	400	1	⋇π(ςm	⋇π(ςm	PROPN
ejpam-6251	400	2	,	,	PUNCT
ejpam-6251	400	3	ϖm−1	ϖm−1	PROPN
ejpam-6251	400	4	,	,	PUNCT
ejpam-6251	400	5	ż	ż	NOUN
ejpam-6251	400	6	3m−1	3m−1	PROPN
ejpam-6251	400	7	)	)	PUNCT
ejpam-6251	400	8	⋇π(ςm	⋇π(ςm	PROPN
ejpam-6251	400	9	,	,	PUNCT
ejpam-6251	400	10	ϖm	ϖm	NOUN
ejpam-6251	400	11	,	,	PUNCT
ejpam-6251	400	12	ż	ż	NOUN
ejpam-6251	400	13	3m−1	3m−1	PROPN
ejpam-6251	400	14	)	)	PUNCT
ejpam-6251	400	15	,	,	PUNCT
ejpam-6251	400	16	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	400	17	,	,	PUNCT
ejpam-6251	400	18	ϖm	ϖm	ADJ
ejpam-6251	400	19	,	,	PUNCT
ejpam-6251	400	20	ż	ż	NOUN
ejpam-6251	400	21	)	)	PUNCT
ejpam-6251	400	22	≤	≤	PROPN
ejpam-6251	400	23	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	400	24	,	,	PUNCT
ejpam-6251	400	25	ϖµ	ϖµ	NOUN
ejpam-6251	400	26	,	,	PUNCT
ejpam-6251	400	27	ż	ż	NOUN
ejpam-6251	400	28	3	3	NUM
ejpam-6251	400	29	)	)	PUNCT
ejpam-6251	400	30	♢	♢	PROPN
ejpam-6251	400	31	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	400	32	,	,	PUNCT
ejpam-6251	400	33	ϖµ	ϖµ	NOUN
ejpam-6251	400	34	,	,	PUNCT
ejpam-6251	400	35	ż	ż	NOUN
ejpam-6251	400	36	3	3	NUM
ejpam-6251	400	37	)	)	PUNCT
ejpam-6251	400	38	♢	♢	PROPN
ejpam-6251	400	39	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	400	40	,	,	PUNCT
ejpam-6251	400	41	ϖm	ϖm	ADJ
ejpam-6251	400	42	,	,	PUNCT
ejpam-6251	400	43	ż	ż	NOUN
ejpam-6251	400	44	3	3	NUM
ejpam-6251	400	45	)	)	PUNCT
ejpam-6251	400	46	...	...	PUNCT
ejpam-6251	401	1	≤	≤	NUM
ejpam-6251	401	2	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	401	3	,	,	PUNCT
ejpam-6251	401	4	ϖµ	ϖµ	NOUN
ejpam-6251	401	5	,	,	PUNCT
ejpam-6251	401	6	ż	ż	NOUN
ejpam-6251	401	7	3	3	NUM
ejpam-6251	401	8	)	)	PUNCT
ejpam-6251	401	9	♢	♢	PROPN
ejpam-6251	401	10	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	401	11	,	,	PUNCT
ejpam-6251	401	12	ϖµ	ϖµ	NOUN
ejpam-6251	401	13	,	,	PUNCT
ejpam-6251	401	14	ż	ż	NOUN
ejpam-6251	401	15	3	3	NUM
ejpam-6251	401	16	)	)	PUNCT
ejpam-6251	401	17	♢	♢	PROPN
ejpam-6251	401	18	·	·	PUNCT
ejpam-6251	401	19	·	·	PUNCT
ejpam-6251	401	20	·	·	PUNCT
ejpam-6251	401	21	♢	♢	PROPN
ejpam-6251	401	22	ψ(ςm−1	ψ(ςm−1	PROPN
ejpam-6251	401	23	,	,	PUNCT
ejpam-6251	401	24	ϖm−1	ϖm−1	PROPN
ejpam-6251	401	25	,	,	PUNCT
ejpam-6251	401	26	ż	ż	PROPN
ejpam-6251	401	27	3m−1	3m−1	PROPN
ejpam-6251	401	28	)	)	PUNCT
ejpam-6251	401	29	♢	♢	PROPN
ejpam-6251	401	30	ψ(ςm	ψ(ςm	PROPN
ejpam-6251	401	31	,	,	PUNCT
ejpam-6251	401	32	ϖm−1	ϖm−1	PROPN
ejpam-6251	401	33	,	,	PUNCT
ejpam-6251	401	34	ż	ż	PROPN
ejpam-6251	401	35	3m−1	3m−1	PROPN
ejpam-6251	401	36	)	)	PUNCT
ejpam-6251	401	37	♢	♢	PROPN
ejpam-6251	401	38	ψ(ςm	ψ(ςm	PROPN
ejpam-6251	401	39	,	,	PUNCT
ejpam-6251	401	40	ϖm	ϖm	NOUN
ejpam-6251	401	41	,	,	PUNCT
ejpam-6251	401	42	ż	ż	NOUN
ejpam-6251	401	43	3m−1	3m−1	PROPN
ejpam-6251	401	44	)	)	PUNCT
ejpam-6251	401	45	and	and	CCONJ
ejpam-6251	401	46	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	401	47	,	,	PUNCT
ejpam-6251	401	48	ϖm	ϖm	ADJ
ejpam-6251	401	49	,	,	PUNCT
ejpam-6251	401	50	ż	ż	NOUN
ejpam-6251	401	51	)	)	PUNCT
ejpam-6251	401	52	≤	≤	NUM
ejpam-6251	401	53	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	401	54	,	,	PUNCT
ejpam-6251	401	55	ϖµ	ϖµ	NOUN
ejpam-6251	401	56	,	,	PUNCT
ejpam-6251	401	57	ż	ż	NOUN
ejpam-6251	401	58	3	3	NUM
ejpam-6251	401	59	)	)	PUNCT
ejpam-6251	401	60	♢	♢	PROPN
ejpam-6251	401	61	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	401	62	,	,	PUNCT
ejpam-6251	401	63	ϖµ	ϖµ	NOUN
ejpam-6251	401	64	,	,	PUNCT
ejpam-6251	401	65	ż	ż	NOUN
ejpam-6251	401	66	3	3	NUM
ejpam-6251	401	67	)	)	PUNCT
ejpam-6251	401	68	♢	♢	PROPN
ejpam-6251	401	69	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	401	70	,	,	PUNCT
ejpam-6251	401	71	ϖm	ϖm	ADJ
ejpam-6251	401	72	,	,	PUNCT
ejpam-6251	401	73	ż	ż	NOUN
ejpam-6251	401	74	3	3	NUM
ejpam-6251	401	75	)	)	PUNCT
ejpam-6251	401	76	...	...	PUNCT
ejpam-6251	402	1	≤	≤	NUM
ejpam-6251	402	2	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	402	3	,	,	PUNCT
ejpam-6251	402	4	ϖµ	ϖµ	NOUN
ejpam-6251	402	5	,	,	PUNCT
ejpam-6251	402	6	ż	ż	NOUN
ejpam-6251	402	7	3	3	NUM
ejpam-6251	402	8	)	)	PUNCT
ejpam-6251	402	9	♢	♢	PROPN
ejpam-6251	402	10	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	402	11	,	,	PUNCT
ejpam-6251	402	12	ϖµ	ϖµ	NOUN
ejpam-6251	402	13	,	,	PUNCT
ejpam-6251	402	14	ż	ż	NOUN
ejpam-6251	402	15	3	3	NUM
ejpam-6251	402	16	)	)	PUNCT
ejpam-6251	402	17	♢	♢	PROPN
ejpam-6251	402	18	·	·	PUNCT
ejpam-6251	402	19	·	·	PUNCT
ejpam-6251	402	20	·	·	PUNCT
ejpam-6251	402	21	♢	♢	PROPN
ejpam-6251	402	22	ξ(ςm−1	ξ(ςm−1	PROPN
ejpam-6251	402	23	,	,	PUNCT
ejpam-6251	402	24	ϖm−1	ϖm−1	PROPN
ejpam-6251	402	25	,	,	PUNCT
ejpam-6251	402	26	ż	ż	PROPN
ejpam-6251	402	27	3m−1	3m−1	PROPN
ejpam-6251	402	28	)	)	PUNCT
ejpam-6251	402	29	♢	♢	PROPN
ejpam-6251	402	30	ξ(ςm	ξ(ςm	PROPN
ejpam-6251	402	31	,	,	PUNCT
ejpam-6251	402	32	ϖm−1	ϖm−1	PROPN
ejpam-6251	402	33	,	,	PUNCT
ejpam-6251	402	34	ż	ż	PROPN
ejpam-6251	402	35	3m−1	3m−1	PROPN
ejpam-6251	402	36	)	)	PUNCT
ejpam-6251	402	37	♢	♢	PROPN
ejpam-6251	402	38	ξ(ςm	ξ(ςm	PROPN
ejpam-6251	402	39	,	,	PUNCT
ejpam-6251	402	40	ϖm	ϖm	NOUN
ejpam-6251	402	41	,	,	PUNCT
ejpam-6251	402	42	ż	ż	NOUN
ejpam-6251	402	43	3m−1	3m−1	PROPN
ejpam-6251	402	44	)	)	PUNCT
ejpam-6251	402	45	.	.	PUNCT
ejpam-6251	403	1	therefore	therefore	ADV
ejpam-6251	403	2	,	,	PUNCT
ejpam-6251	403	3	π(ςµ	π(ςµ	NUM
ejpam-6251	403	4	,	,	PUNCT
ejpam-6251	403	5	ϖm	ϖm	ADJ
ejpam-6251	403	6	,	,	PUNCT
ejpam-6251	403	7	ż	ż	NOUN
ejpam-6251	403	8	)	)	PUNCT
ejpam-6251	403	9	≥	≥	NOUN
ejpam-6251	403	10	π(ςµ	π(ςµ	PROPN
ejpam-6251	403	11	,	,	PUNCT
ejpam-6251	403	12	ϖµ	ϖµ	NOUN
ejpam-6251	403	13	,	,	PUNCT
ejpam-6251	403	14	ż	ż	NOUN
ejpam-6251	403	15	3	3	X
ejpam-6251	403	16	)	)	PUNCT
ejpam-6251	403	17	⋇π(ςµ+1	⋇π(ςµ+1	PROPN
ejpam-6251	403	18	,	,	PUNCT
ejpam-6251	403	19	ϖµ	ϖµ	NOUN
ejpam-6251	403	20	,	,	PUNCT
ejpam-6251	403	21	ż	ż	NOUN
ejpam-6251	403	22	3	3	NUM
ejpam-6251	403	23	)	)	PUNCT
ejpam-6251	403	24	⋇	⋇	NOUN
ejpam-6251	403	25	·	·	PUNCT
ejpam-6251	403	26	·	·	PUNCT
ejpam-6251	403	27	·	·	PUNCT
ejpam-6251	403	28	⋇π(ςm−1	⋇π(ςm−1	PROPN
ejpam-6251	403	29	,	,	PUNCT
ejpam-6251	403	30	ϖm−1	ϖm−1	PROPN
ejpam-6251	403	31	,	,	PUNCT
ejpam-6251	403	32	ż	ż	PROPN
ejpam-6251	403	33	3m−1	3m−1	PROPN
ejpam-6251	403	34	)	)	PUNCT
ejpam-6251	403	35	r.	r.	PROPN
ejpam-6251	403	36	ramaswamy	ramaswamy	PROPN
ejpam-6251	403	37	/	/	SYM
ejpam-6251	403	38	eur	eur	PROPN
ejpam-6251	403	39	.	.	PUNCT
ejpam-6251	404	1	j.	j.	PROPN
ejpam-6251	404	2	pure	pure	PROPN
ejpam-6251	404	3	appl	appl	PROPN
ejpam-6251	404	4	.	.	PROPN
ejpam-6251	404	5	math	math	PROPN
ejpam-6251	404	6	,	,	PUNCT
ejpam-6251	404	7	18	18	NUM
ejpam-6251	404	8	(	(	PUNCT
ejpam-6251	404	9	4	4	NUM
ejpam-6251	404	10	)	)	PUNCT
ejpam-6251	404	11	(	(	PUNCT
ejpam-6251	404	12	2025	2025	NUM
ejpam-6251	404	13	)	)	PUNCT
ejpam-6251	404	14	,	,	PUNCT
ejpam-6251	404	15	6251	6251	NUM
ejpam-6251	404	16	19	19	NUM
ejpam-6251	404	17	of	of	ADP
ejpam-6251	404	18	40	40	NUM
ejpam-6251	404	19	⋇π(ςm	⋇π(ςm	NOUN
ejpam-6251	404	20	,	,	PUNCT
ejpam-6251	404	21	ϖm−1	ϖm−1	PROPN
ejpam-6251	404	22	,	,	PUNCT
ejpam-6251	404	23	ż	ż	NOUN
ejpam-6251	404	24	3m−1	3m−1	PROPN
ejpam-6251	404	25	)	)	PUNCT
ejpam-6251	405	1	⋇π(ςm	⋇π(ςm	PROPN
ejpam-6251	405	2	,	,	PUNCT
ejpam-6251	405	3	ϖm	ϖm	NOUN
ejpam-6251	405	4	,	,	PUNCT
ejpam-6251	405	5	ż	ż	NOUN
ejpam-6251	405	6	3m−1	3m−1	PROPN
ejpam-6251	405	7	)	)	PUNCT
ejpam-6251	405	8	≥	≥	NOUN
ejpam-6251	405	9	π(ς0	π(ς0	NOUN
ejpam-6251	405	10	,	,	PUNCT
ejpam-6251	405	11	ϖ0	ϖ0	NOUN
ejpam-6251	405	12	,	,	PUNCT
ejpam-6251	405	13	ż	ż	NOUN
ejpam-6251	405	14	3ζ2µ	3ζ2µ	NOUN
ejpam-6251	405	15	)	)	PUNCT
ejpam-6251	406	1	⋇π(ς0	⋇π(ς0	PROPN
ejpam-6251	406	2	,	,	PUNCT
ejpam-6251	406	3	ϖ0	ϖ0	NOUN
ejpam-6251	406	4	,	,	PUNCT
ejpam-6251	406	5	ż	ż	NOUN
ejpam-6251	406	6	3ζ2µ+1	3ζ2µ+1	NUM
ejpam-6251	406	7	)	)	PUNCT
ejpam-6251	406	8	⋇	⋇	NOUN
ejpam-6251	406	9	·	·	PUNCT
ejpam-6251	406	10	·	·	PUNCT
ejpam-6251	406	11	·	·	PUNCT
ejpam-6251	406	12	⋇π(ς0	⋇π(ς0	PROPN
ejpam-6251	406	13	,	,	PUNCT
ejpam-6251	406	14	ϖ0	ϖ0	NOUN
ejpam-6251	406	15	,	,	PUNCT
ejpam-6251	406	16	ż	ż	PROPN
ejpam-6251	406	17	3m−1ζ2m−2	3m−1ζ2m−2	NUM
ejpam-6251	406	18	)	)	PUNCT
ejpam-6251	406	19	⋇π(ς0	⋇π(ς0	PROPN
ejpam-6251	406	20	,	,	PUNCT
ejpam-6251	406	21	ϖ0	ϖ0	NOUN
ejpam-6251	406	22	,	,	PUNCT
ejpam-6251	406	23	ż	ż	NOUN
ejpam-6251	406	24	3m−1ζ2m−1	3m−1ζ2m−1	NUM
ejpam-6251	406	25	)	)	PUNCT
ejpam-6251	406	26	⋇π(ς0	⋇π(ς0	PROPN
ejpam-6251	406	27	,	,	PUNCT
ejpam-6251	406	28	ϖ0	ϖ0	NOUN
ejpam-6251	406	29	,	,	PUNCT
ejpam-6251	406	30	ż	ż	NOUN
ejpam-6251	406	31	3m−1ζ2	3m−1ζ2	NUM
ejpam-6251	406	32	m	m	NOUN
ejpam-6251	406	33	)	)	PUNCT
ejpam-6251	406	34	,	,	PUNCT
ejpam-6251	406	35	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	406	36	,	,	PUNCT
ejpam-6251	406	37	ϖm	ϖm	ADJ
ejpam-6251	406	38	,	,	PUNCT
ejpam-6251	406	39	ż	ż	NOUN
ejpam-6251	406	40	)	)	PUNCT
ejpam-6251	406	41	≤	≤	PROPN
ejpam-6251	406	42	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	406	43	,	,	PUNCT
ejpam-6251	406	44	ϖµ	ϖµ	NOUN
ejpam-6251	406	45	,	,	PUNCT
ejpam-6251	406	46	ż	ż	NOUN
ejpam-6251	406	47	3	3	NUM
ejpam-6251	406	48	)	)	PUNCT
ejpam-6251	406	49	♢	♢	PROPN
ejpam-6251	406	50	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	406	51	,	,	PUNCT
ejpam-6251	406	52	ϖµ	ϖµ	NOUN
ejpam-6251	406	53	,	,	PUNCT
ejpam-6251	406	54	ż	ż	NOUN
ejpam-6251	406	55	3	3	NUM
ejpam-6251	406	56	)	)	PUNCT
ejpam-6251	406	57	♢	♢	PROPN
ejpam-6251	406	58	·	·	PUNCT
ejpam-6251	406	59	·	·	PUNCT
ejpam-6251	406	60	·	·	PUNCT
ejpam-6251	406	61	♢	♢	PROPN
ejpam-6251	406	62	ψ(ςm−1	ψ(ςm−1	PROPN
ejpam-6251	406	63	,	,	PUNCT
ejpam-6251	406	64	ϖm−1	ϖm−1	PROPN
ejpam-6251	406	65	,	,	PUNCT
ejpam-6251	406	66	ż	ż	PROPN
ejpam-6251	406	67	3m−1	3m−1	PROPN
ejpam-6251	406	68	)	)	PUNCT
ejpam-6251	406	69	♢	♢	PROPN
ejpam-6251	406	70	ψ(ςm	ψ(ςm	PROPN
ejpam-6251	406	71	,	,	PUNCT
ejpam-6251	406	72	ϖm−1	ϖm−1	PROPN
ejpam-6251	406	73	,	,	PUNCT
ejpam-6251	406	74	ż	ż	PROPN
ejpam-6251	406	75	3m−1	3m−1	PROPN
ejpam-6251	406	76	)	)	PUNCT
ejpam-6251	406	77	♢	♢	PROPN
ejpam-6251	406	78	ψ(ςm	ψ(ςm	PROPN
ejpam-6251	406	79	,	,	PUNCT
ejpam-6251	406	80	ϖm	ϖm	NOUN
ejpam-6251	406	81	,	,	PUNCT
ejpam-6251	406	82	ż	ż	NOUN
ejpam-6251	406	83	3m−1	3m−1	PROPN
ejpam-6251	406	84	)	)	PUNCT
ejpam-6251	406	85	≤	≤	NOUN
ejpam-6251	406	86	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	406	87	,	,	PUNCT
ejpam-6251	406	88	ϖ0	ϖ0	NOUN
ejpam-6251	406	89	,	,	PUNCT
ejpam-6251	406	90	ż	ż	NOUN
ejpam-6251	406	91	3ζ2µ	3ζ2µ	NOUN
ejpam-6251	406	92	)	)	PUNCT
ejpam-6251	406	93	♢	♢	PROPN
ejpam-6251	406	94	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	406	95	,	,	PUNCT
ejpam-6251	406	96	ϖ0	ϖ0	NOUN
ejpam-6251	406	97	,	,	PUNCT
ejpam-6251	406	98	ż	ż	NOUN
ejpam-6251	406	99	3ζ2µ+1	3ζ2µ+1	NUM
ejpam-6251	406	100	)	)	PUNCT
ejpam-6251	406	101	♢	♢	PROPN
ejpam-6251	406	102	·	·	PUNCT
ejpam-6251	406	103	·	·	PUNCT
ejpam-6251	406	104	·	·	PUNCT
ejpam-6251	406	105	♢	♢	PROPN
ejpam-6251	406	106	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	406	107	,	,	PUNCT
ejpam-6251	406	108	ϖ0	ϖ0	NOUN
ejpam-6251	406	109	,	,	PUNCT
ejpam-6251	406	110	ż	ż	PROPN
ejpam-6251	406	111	3m−1ζ2m−2	3m−1ζ2m−2	NUM
ejpam-6251	406	112	)	)	PUNCT
ejpam-6251	406	113	♢	♢	PROPN
ejpam-6251	406	114	ψ(ς0	ψ(ς0	PROPN
ejpam-6251	406	115	,	,	PUNCT
ejpam-6251	406	116	ϖ0	ϖ0	NOUN
ejpam-6251	406	117	,	,	PUNCT
ejpam-6251	406	118	ż	ż	NOUN
ejpam-6251	406	119	3m−1ζ2m−1	3m−1ζ2m−1	NUM
ejpam-6251	406	120	)	)	PUNCT
ejpam-6251	406	121	♢	♢	PROPN
ejpam-6251	406	122	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	406	123	,	,	PUNCT
ejpam-6251	406	124	ϖ0	ϖ0	NOUN
ejpam-6251	406	125	,	,	PUNCT
ejpam-6251	406	126	ż	ż	NOUN
ejpam-6251	406	127	3m−1ζ2	3m−1ζ2	NUM
ejpam-6251	406	128	m	m	NOUN
ejpam-6251	406	129	)	)	PUNCT
ejpam-6251	406	130	,	,	PUNCT
ejpam-6251	406	131	and	and	CCONJ
ejpam-6251	406	132	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	406	133	,	,	PUNCT
ejpam-6251	406	134	ϖm	ϖm	ADJ
ejpam-6251	406	135	,	,	PUNCT
ejpam-6251	406	136	ż	ż	NOUN
ejpam-6251	406	137	)	)	PUNCT
ejpam-6251	406	138	≤	≤	NUM
ejpam-6251	406	139	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	406	140	,	,	PUNCT
ejpam-6251	406	141	ϖµ	ϖµ	NOUN
ejpam-6251	406	142	,	,	PUNCT
ejpam-6251	406	143	ż	ż	NOUN
ejpam-6251	406	144	3	3	NUM
ejpam-6251	406	145	)	)	PUNCT
ejpam-6251	406	146	♢	♢	PROPN
ejpam-6251	406	147	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	406	148	,	,	PUNCT
ejpam-6251	406	149	ϖµ	ϖµ	NOUN
ejpam-6251	406	150	,	,	PUNCT
ejpam-6251	406	151	ż	ż	NOUN
ejpam-6251	406	152	3	3	NUM
ejpam-6251	406	153	)	)	PUNCT
ejpam-6251	406	154	♢	♢	PROPN
ejpam-6251	406	155	·	·	PUNCT
ejpam-6251	406	156	·	·	PUNCT
ejpam-6251	406	157	·	·	PUNCT
ejpam-6251	406	158	♢	♢	PROPN
ejpam-6251	406	159	ξ(ςm−1	ξ(ςm−1	PROPN
ejpam-6251	406	160	,	,	PUNCT
ejpam-6251	406	161	ϖm−1	ϖm−1	PROPN
ejpam-6251	406	162	,	,	PUNCT
ejpam-6251	406	163	ż	ż	PROPN
ejpam-6251	406	164	3m−1	3m−1	PROPN
ejpam-6251	406	165	)	)	PUNCT
ejpam-6251	406	166	♢	♢	PROPN
ejpam-6251	406	167	ξ(ςm	ξ(ςm	PROPN
ejpam-6251	406	168	,	,	PUNCT
ejpam-6251	406	169	ϖm−1	ϖm−1	PROPN
ejpam-6251	406	170	,	,	PUNCT
ejpam-6251	406	171	ż	ż	PROPN
ejpam-6251	406	172	3m−1	3m−1	PROPN
ejpam-6251	406	173	)	)	PUNCT
ejpam-6251	406	174	♢	♢	PROPN
ejpam-6251	406	175	ξ(ςm	ξ(ςm	PROPN
ejpam-6251	406	176	,	,	PUNCT
ejpam-6251	406	177	ϖm	ϖm	NOUN
ejpam-6251	406	178	,	,	PUNCT
ejpam-6251	406	179	ż	ż	NOUN
ejpam-6251	406	180	3m−1	3m−1	PROPN
ejpam-6251	406	181	)	)	PUNCT
ejpam-6251	406	182	≤	≤	NOUN
ejpam-6251	406	183	ξ(ς0	ξ(ς0	NOUN
ejpam-6251	406	184	,	,	PUNCT
ejpam-6251	406	185	ϖ0	ϖ0	NOUN
ejpam-6251	406	186	,	,	PUNCT
ejpam-6251	406	187	ż	ż	NOUN
ejpam-6251	406	188	3ζ2µ	3ζ2µ	NOUN
ejpam-6251	406	189	)	)	PUNCT
ejpam-6251	407	1	♢	♢	PROPN
ejpam-6251	407	2	ξ(ς0	ξ(ς0	ADV
ejpam-6251	407	3	,	,	PUNCT
ejpam-6251	407	4	ϖ0	ϖ0	NOUN
ejpam-6251	407	5	,	,	PUNCT
ejpam-6251	407	6	ż	ż	NOUN
ejpam-6251	407	7	3ζ2µ+1	3ζ2µ+1	NUM
ejpam-6251	407	8	)	)	PUNCT
ejpam-6251	407	9	♢	♢	PROPN
ejpam-6251	407	10	·	·	PUNCT
ejpam-6251	407	11	·	·	PUNCT
ejpam-6251	407	12	·	·	PUNCT
ejpam-6251	407	13	♢	♢	PROPN
ejpam-6251	407	14	ξ(ς0	ξ(ς0	ADV
ejpam-6251	407	15	,	,	PUNCT
ejpam-6251	407	16	ϖ0	ϖ0	NOUN
ejpam-6251	407	17	,	,	PUNCT
ejpam-6251	407	18	ż	ż	PROPN
ejpam-6251	407	19	3m−1ζ2m−2	3m−1ζ2m−2	NUM
ejpam-6251	407	20	)	)	PUNCT
ejpam-6251	407	21	♢	♢	PROPN
ejpam-6251	407	22	ξ(ς0	ξ(ς0	ADV
ejpam-6251	407	23	,	,	PUNCT
ejpam-6251	407	24	ϖ0	ϖ0	NOUN
ejpam-6251	407	25	,	,	PUNCT
ejpam-6251	407	26	ż	ż	NOUN
ejpam-6251	407	27	3m−1ζ2m−1	3m−1ζ2m−1	NUM
ejpam-6251	407	28	)	)	PUNCT
ejpam-6251	407	29	♢	♢	PROPN
ejpam-6251	407	30	ξ(ς0	ξ(ς0	ADV
ejpam-6251	407	31	,	,	PUNCT
ejpam-6251	407	32	ϖ0	ϖ0	NOUN
ejpam-6251	407	33	,	,	PUNCT
ejpam-6251	407	34	ż	ż	NOUN
ejpam-6251	407	35	3m−1ζ2	3m−1ζ2	NUM
ejpam-6251	407	36	m	m	NOUN
ejpam-6251	407	37	)	)	PUNCT
ejpam-6251	407	38	.	.	PUNCT
ejpam-6251	408	1	which	which	PRON
ejpam-6251	408	2	implies	imply	VERB
ejpam-6251	408	3	that	that	SCONJ
ejpam-6251	408	4	,	,	PUNCT
ejpam-6251	408	5	π(ςµ	π(ςµ	NUM
ejpam-6251	408	6	,	,	PUNCT
ejpam-6251	408	7	ϖm	ϖm	ADJ
ejpam-6251	408	8	,	,	PUNCT
ejpam-6251	408	9	ż	ż	NOUN
ejpam-6251	408	10	)	)	PUNCT
ejpam-6251	408	11	≥	≥	NOUN
ejpam-6251	408	12	π(ς0	π(ς0	NOUN
ejpam-6251	408	13	,	,	PUNCT
ejpam-6251	408	14	ϖ0	ϖ0	NOUN
ejpam-6251	408	15	,	,	PUNCT
ejpam-6251	408	16	ż	ż	NOUN
ejpam-6251	408	17	3ζ2µ	3ζ2µ	NOUN
ejpam-6251	408	18	)	)	PUNCT
ejpam-6251	409	1	⋇π(ς0	⋇π(ς0	PROPN
ejpam-6251	409	2	,	,	PUNCT
ejpam-6251	409	3	ϖ0	ϖ0	NOUN
ejpam-6251	409	4	,	,	PUNCT
ejpam-6251	409	5	ż	ż	NOUN
ejpam-6251	409	6	3ζ2µ+1	3ζ2µ+1	NUM
ejpam-6251	409	7	)	)	PUNCT
ejpam-6251	409	8	⋇	⋇	NOUN
ejpam-6251	409	9	·	·	PUNCT
ejpam-6251	409	10	·	·	PUNCT
ejpam-6251	409	11	·	·	PUNCT
ejpam-6251	409	12	⋇π(ς0	⋇π(ς0	PROPN
ejpam-6251	409	13	,	,	PUNCT
ejpam-6251	409	14	ϖ0	ϖ0	NOUN
ejpam-6251	409	15	,	,	PUNCT
ejpam-6251	409	16	ż	ż	PROPN
ejpam-6251	409	17	3m−1ζ2m−2	3m−1ζ2m−2	NUM
ejpam-6251	409	18	)	)	PUNCT
ejpam-6251	409	19	⋇π(ς0	⋇π(ς0	PROPN
ejpam-6251	409	20	,	,	PUNCT
ejpam-6251	409	21	ϖ0	ϖ0	NOUN
ejpam-6251	409	22	,	,	PUNCT
ejpam-6251	409	23	ż	ż	NOUN
ejpam-6251	409	24	3m−1ζ2m−1	3m−1ζ2m−1	NUM
ejpam-6251	409	25	)	)	PUNCT
ejpam-6251	409	26	⋇π(ς0	⋇π(ς0	PROPN
ejpam-6251	409	27	,	,	PUNCT
ejpam-6251	409	28	ϖ0	ϖ0	NOUN
ejpam-6251	409	29	,	,	PUNCT
ejpam-6251	409	30	ż	ż	NOUN
ejpam-6251	409	31	3m−1ζ2	3m−1ζ2	NUM
ejpam-6251	409	32	m	m	NOUN
ejpam-6251	409	33	)	)	PUNCT
ejpam-6251	409	34	,	,	PUNCT
ejpam-6251	409	35	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	409	36	,	,	PUNCT
ejpam-6251	409	37	ϖm	ϖm	ADJ
ejpam-6251	409	38	,	,	PUNCT
ejpam-6251	409	39	ż	ż	NOUN
ejpam-6251	409	40	)	)	PUNCT
ejpam-6251	409	41	≤	≤	NOUN
ejpam-6251	409	42	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	409	43	,	,	PUNCT
ejpam-6251	409	44	ϖ0	ϖ0	NOUN
ejpam-6251	409	45	,	,	PUNCT
ejpam-6251	409	46	ż	ż	NOUN
ejpam-6251	409	47	3ζ2µ	3ζ2µ	NOUN
ejpam-6251	409	48	)	)	PUNCT
ejpam-6251	409	49	♢	♢	PROPN
ejpam-6251	409	50	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	409	51	,	,	PUNCT
ejpam-6251	409	52	ϖ0	ϖ0	NOUN
ejpam-6251	409	53	,	,	PUNCT
ejpam-6251	409	54	ż	ż	NOUN
ejpam-6251	409	55	3ζ2µ+1	3ζ2µ+1	NUM
ejpam-6251	409	56	)	)	PUNCT
ejpam-6251	409	57	♢	♢	PROPN
ejpam-6251	409	58	·	·	PUNCT
ejpam-6251	409	59	·	·	PUNCT
ejpam-6251	409	60	·	·	PUNCT
ejpam-6251	409	61	♢	♢	PROPN
ejpam-6251	409	62	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	409	63	,	,	PUNCT
ejpam-6251	409	64	ϖ0	ϖ0	NOUN
ejpam-6251	409	65	,	,	PUNCT
ejpam-6251	409	66	ż	ż	PROPN
ejpam-6251	409	67	3m−1ζ2m−2	3m−1ζ2m−2	NUM
ejpam-6251	409	68	)	)	PUNCT
ejpam-6251	409	69	♢	♢	PROPN
ejpam-6251	409	70	ψ(ς0	ψ(ς0	PROPN
ejpam-6251	409	71	,	,	PUNCT
ejpam-6251	409	72	ϖ0	ϖ0	NOUN
ejpam-6251	409	73	,	,	PUNCT
ejpam-6251	409	74	ż	ż	NOUN
ejpam-6251	409	75	3m−1ζ2m−1	3m−1ζ2m−1	NUM
ejpam-6251	409	76	)	)	PUNCT
ejpam-6251	409	77	♢	♢	PROPN
ejpam-6251	409	78	ψ(ς0	ψ(ς0	NOUN
ejpam-6251	409	79	,	,	PUNCT
ejpam-6251	409	80	ϖ0	ϖ0	NOUN
ejpam-6251	409	81	,	,	PUNCT
ejpam-6251	409	82	ż	ż	NOUN
ejpam-6251	409	83	3m−1ζ2	3m−1ζ2	NUM
ejpam-6251	409	84	m	m	NOUN
ejpam-6251	409	85	)	)	PUNCT
ejpam-6251	409	86	,	,	PUNCT
ejpam-6251	409	87	and	and	CCONJ
ejpam-6251	409	88	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	409	89	,	,	PUNCT
ejpam-6251	409	90	ϖm	ϖm	ADJ
ejpam-6251	409	91	,	,	PUNCT
ejpam-6251	409	92	ż	ż	NOUN
ejpam-6251	409	93	)	)	PUNCT
ejpam-6251	409	94	≤	≤	NOUN
ejpam-6251	409	95	ξ(ς0	ξ(ς0	NOUN
ejpam-6251	409	96	,	,	PUNCT
ejpam-6251	409	97	ϖ0	ϖ0	NOUN
ejpam-6251	409	98	,	,	PUNCT
ejpam-6251	409	99	ż	ż	NOUN
ejpam-6251	409	100	3ζ2µ	3ζ2µ	NOUN
ejpam-6251	409	101	)	)	PUNCT
ejpam-6251	409	102	♢	♢	PROPN
ejpam-6251	409	103	ξ(ς0	ξ(ς0	ADV
ejpam-6251	409	104	,	,	PUNCT
ejpam-6251	409	105	ϖ0	ϖ0	NOUN
ejpam-6251	409	106	,	,	PUNCT
ejpam-6251	409	107	ż	ż	NOUN
ejpam-6251	409	108	3ζ2µ+1	3ζ2µ+1	NUM
ejpam-6251	409	109	)	)	PUNCT
ejpam-6251	409	110	♢	♢	PROPN
ejpam-6251	409	111	·	·	PUNCT
ejpam-6251	409	112	·	·	PUNCT
ejpam-6251	409	113	·	·	PUNCT
ejpam-6251	409	114	♢	♢	PROPN
ejpam-6251	409	115	ξ(ς0	ξ(ς0	ADV
ejpam-6251	409	116	,	,	PUNCT
ejpam-6251	409	117	ϖ0	ϖ0	NOUN
ejpam-6251	409	118	,	,	PUNCT
ejpam-6251	409	119	ż	ż	PROPN
ejpam-6251	409	120	3m−1ζ2m−2	3m−1ζ2m−2	NUM
ejpam-6251	409	121	)	)	PUNCT
ejpam-6251	409	122	♢	♢	PROPN
ejpam-6251	409	123	ξ(ς0	ξ(ς0	ADV
ejpam-6251	409	124	,	,	PUNCT
ejpam-6251	409	125	ϖ0	ϖ0	NOUN
ejpam-6251	409	126	,	,	PUNCT
ejpam-6251	409	127	ż	ż	NOUN
ejpam-6251	409	128	3m−1ζ2m−1	3m−1ζ2m−1	NUM
ejpam-6251	409	129	)	)	PUNCT
ejpam-6251	409	130	♢	♢	PROPN
ejpam-6251	409	131	ξ(ς0	ξ(ς0	ADV
ejpam-6251	409	132	,	,	PUNCT
ejpam-6251	409	133	ϖ0	ϖ0	NOUN
ejpam-6251	409	134	,	,	PUNCT
ejpam-6251	409	135	ż	ż	NOUN
ejpam-6251	409	136	3m−1ζ2	3m−1ζ2	NUM
ejpam-6251	409	137	m	m	NOUN
ejpam-6251	409	138	)	)	PUNCT
ejpam-6251	409	139	.	.	PUNCT
ejpam-6251	410	1	r.	r.	PROPN
ejpam-6251	410	2	ramaswamy	ramaswamy	PROPN
ejpam-6251	410	3	/	/	SYM
ejpam-6251	410	4	eur	eur	PROPN
ejpam-6251	410	5	.	.	PUNCT
ejpam-6251	411	1	j.	j.	PROPN
ejpam-6251	411	2	pure	pure	PROPN
ejpam-6251	411	3	appl	appl	PROPN
ejpam-6251	411	4	.	.	PROPN
ejpam-6251	411	5	math	math	PROPN
ejpam-6251	411	6	,	,	PUNCT
ejpam-6251	411	7	18	18	NUM
ejpam-6251	411	8	(	(	PUNCT
ejpam-6251	411	9	4	4	NUM
ejpam-6251	411	10	)	)	PUNCT
ejpam-6251	411	11	(	(	PUNCT
ejpam-6251	411	12	2025	2025	NUM
ejpam-6251	411	13	)	)	PUNCT
ejpam-6251	411	14	,	,	PUNCT
ejpam-6251	411	15	6251	6251	NUM
ejpam-6251	411	16	20	20	NUM
ejpam-6251	411	17	of	of	ADP
ejpam-6251	411	18	40	40	NUM
ejpam-6251	411	19	as	as	ADP
ejpam-6251	411	20	µ,m	µ,m	PROPN
ejpam-6251	411	21	→	→	SYM
ejpam-6251	411	22	+	+	NOUN
ejpam-6251	411	23	∞	∞	PROPN
ejpam-6251	411	24	,	,	PUNCT
ejpam-6251	411	25	we	we	PRON
ejpam-6251	411	26	deduce	deduce	VERB
ejpam-6251	411	27	lim	lim	PROPN
ejpam-6251	411	28	µ,m→+∞	µ,m→+∞	NUM
ejpam-6251	411	29	π(ςµ	π(ςµ	PROPN
ejpam-6251	411	30	,	,	PUNCT
ejpam-6251	411	31	ϖm	ϖm	ADJ
ejpam-6251	411	32	,	,	PUNCT
ejpam-6251	411	33	ż	ż	NOUN
ejpam-6251	411	34	)	)	PUNCT
ejpam-6251	411	35	=	=	PUNCT
ejpam-6251	412	1	1⋇	1⋇	NUM
ejpam-6251	412	2	1⋇	1⋇	NUM
ejpam-6251	412	3	·	·	PUNCT
ejpam-6251	412	4	·	·	PUNCT
ejpam-6251	412	5	·	·	PUNCT
ejpam-6251	412	6	⋇	⋇	NOUN
ejpam-6251	412	7	1	1	NUM
ejpam-6251	412	8	=	=	SYM
ejpam-6251	412	9	1	1	NUM
ejpam-6251	412	10	,	,	PUNCT
ejpam-6251	412	11	lim	lim	PROPN
ejpam-6251	412	12	µ,m→+∞	µ,m→+∞	NUM
ejpam-6251	412	13	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	412	14	,	,	PUNCT
ejpam-6251	412	15	ϖm	ϖm	ADJ
ejpam-6251	412	16	,	,	PUNCT
ejpam-6251	412	17	ż	ż	NOUN
ejpam-6251	412	18	)	)	PUNCT
ejpam-6251	412	19	=	=	SYM
ejpam-6251	412	20	0	0	NUM
ejpam-6251	412	21	♢	♢	PROPN
ejpam-6251	412	22	0	0	PROPN
ejpam-6251	412	23	♢	♢	PROPN
ejpam-6251	412	24	·	·	PUNCT
ejpam-6251	412	25	·	·	PUNCT
ejpam-6251	412	26	·	·	PUNCT
ejpam-6251	412	27	♢	♢	PROPN
ejpam-6251	412	28	0	0	PROPN
ejpam-6251	412	29	=	=	SYM
ejpam-6251	412	30	0	0	PROPN
ejpam-6251	412	31	and	and	CCONJ
ejpam-6251	412	32	lim	lim	PROPN
ejpam-6251	412	33	µ,m→+∞	µ,m→+∞	NUM
ejpam-6251	412	34	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	412	35	,	,	PUNCT
ejpam-6251	412	36	ϖm	ϖm	ADJ
ejpam-6251	412	37	,	,	PUNCT
ejpam-6251	412	38	ż	ż	NOUN
ejpam-6251	412	39	)	)	PUNCT
ejpam-6251	412	40	=	=	SYM
ejpam-6251	412	41	0	0	NUM
ejpam-6251	412	42	♢	♢	PROPN
ejpam-6251	412	43	0	0	PROPN
ejpam-6251	412	44	♢	♢	PROPN
ejpam-6251	412	45	·	·	PUNCT
ejpam-6251	412	46	·	·	PUNCT
ejpam-6251	412	47	·	·	PUNCT
ejpam-6251	412	48	♢	♢	PROPN
ejpam-6251	412	49	0	0	PROPN
ejpam-6251	412	50	=	=	SYM
ejpam-6251	412	51	0	0	PROPN
ejpam-6251	412	52	.	.	NOUN
ejpam-6251	412	53	which	which	PRON
ejpam-6251	412	54	implies	imply	VERB
ejpam-6251	412	55	that	that	PRON
ejpam-6251	412	56	bisequence	bisequence	NOUN
ejpam-6251	412	57	(	(	PUNCT
ejpam-6251	412	58	ςµ	ςµ	NOUN
ejpam-6251	412	59	,	,	PUNCT
ejpam-6251	412	60	ϖµ	ϖµ	NOUN
ejpam-6251	412	61	)	)	PUNCT
ejpam-6251	412	62	is	be	AUX
ejpam-6251	412	63	a	a	DET
ejpam-6251	412	64	cauchy	cauchy	ADJ
ejpam-6251	412	65	bisequence	bisequence	NOUN
ejpam-6251	412	66	.	.	PUNCT
ejpam-6251	413	1	since	since	SCONJ
ejpam-6251	413	2	(	(	PUNCT
ejpam-6251	413	3	𭟋	𭟋	PROPN
ejpam-6251	413	4	,	,	PUNCT
ejpam-6251	413	5	s	s	PROPN
ejpam-6251	413	6	,	,	PUNCT
ejpam-6251	413	7	π	π	PROPN
ejpam-6251	413	8	,	,	PUNCT
ejpam-6251	413	9	ψ	ψ	PROPN
ejpam-6251	413	10	,	,	PUNCT
ejpam-6251	413	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	413	12	,	,	PUNCT
ejpam-6251	413	13	♢	♢	PROPN
ejpam-6251	413	14	)	)	PUNCT
ejpam-6251	413	15	is	be	AUX
ejpam-6251	413	16	a	a	DET
ejpam-6251	413	17	complete	complete	ADJ
ejpam-6251	413	18	nbms	nbms	NOUN
ejpam-6251	413	19	.	.	PUNCT
ejpam-6251	414	1	then	then	ADV
ejpam-6251	414	2	,	,	PUNCT
ejpam-6251	414	3	{	{	PUNCT
ejpam-6251	414	4	ςµ	ςµ	NOUN
ejpam-6251	414	5	}	}	PUNCT
ejpam-6251	414	6	→	→	SYM
ejpam-6251	414	7	ς	ς	PROPN
ejpam-6251	414	8	and	and	CCONJ
ejpam-6251	414	9	{	{	PUNCT
ejpam-6251	414	10	ϖµ	ϖµ	NOUN
ejpam-6251	414	11	}	}	PUNCT
ejpam-6251	414	12	→	→	SYM
ejpam-6251	414	13	ς	ς	PROPN
ejpam-6251	414	14	,	,	PUNCT
ejpam-6251	414	15	where	where	SCONJ
ejpam-6251	414	16	ς	ς	PROPN
ejpam-6251	414	17	∈	∈	PROPN
ejpam-6251	414	18	𭟋	𭟋	ADP
ejpam-6251	414	19	∩	∩	NOUN
ejpam-6251	414	20	s.	s.	PROPN
ejpam-6251	414	21	using	use	VERB
ejpam-6251	414	22	v	v	NOUN
ejpam-6251	414	23	,	,	PUNCT
ejpam-6251	414	24	x	x	PUNCT
ejpam-6251	414	25	and	and	CCONJ
ejpam-6251	414	26	xv	xv	PROPN
ejpam-6251	414	27	,	,	PUNCT
ejpam-6251	414	28	we	we	PRON
ejpam-6251	414	29	get	get	VERB
ejpam-6251	414	30	π(ς	π(ς	PROPN
ejpam-6251	414	31	,	,	PUNCT
ejpam-6251	414	32	pς	pς	ADP
ejpam-6251	414	33	,	,	PUNCT
ejpam-6251	414	34	ż	ż	NOUN
ejpam-6251	414	35	)	)	PUNCT
ejpam-6251	414	36	≥	≥	NOUN
ejpam-6251	414	37	π	π	PROPN
ejpam-6251	414	38	(	(	PUNCT
ejpam-6251	414	39	ς	ς	PROPN
ejpam-6251	414	40	,	,	PUNCT
ejpam-6251	414	41	ςµ+1	ςµ+1	NUM
ejpam-6251	414	42	,	,	PUNCT
ejpam-6251	414	43	ż	ż	NOUN
ejpam-6251	414	44	3	3	NUM
ejpam-6251	414	45	)	)	PUNCT
ejpam-6251	414	46	⋇π	⋇π	NOUN
ejpam-6251	414	47	(	(	PUNCT
ejpam-6251	414	48	ςµ+1	ςµ+1	NUM
ejpam-6251	414	49	,	,	PUNCT
ejpam-6251	414	50	ςµ+1	ςµ+1	NUM
ejpam-6251	414	51	,	,	PUNCT
ejpam-6251	414	52	ż	ż	NOUN
ejpam-6251	414	53	3	3	NUM
ejpam-6251	414	54	)	)	PUNCT
ejpam-6251	414	55	⋇π	⋇π	NOUN
ejpam-6251	414	56	(	(	PUNCT
ejpam-6251	414	57	ςµ+1	ςµ+1	NUM
ejpam-6251	414	58	,	,	PUNCT
ejpam-6251	414	59	pς	pς	ADP
ejpam-6251	414	60	,	,	PUNCT
ejpam-6251	414	61	ż	ż	NOUN
ejpam-6251	414	62	3	3	NUM
ejpam-6251	414	63	)	)	PUNCT
ejpam-6251	414	64	=	=	PUNCT
ejpam-6251	415	1	π	π	X
ejpam-6251	415	2	(	(	PUNCT
ejpam-6251	415	3	ς	ς	PROPN
ejpam-6251	415	4	,	,	PUNCT
ejpam-6251	415	5	ςµ+1	ςµ+1	NUM
ejpam-6251	415	6	,	,	PUNCT
ejpam-6251	415	7	ż	ż	NOUN
ejpam-6251	415	8	3	3	NUM
ejpam-6251	415	9	)	)	PUNCT
ejpam-6251	415	10	⋇π	⋇π	NOUN
ejpam-6251	415	11	(	(	PUNCT
ejpam-6251	415	12	pςµ	pςµ	PROPN
ejpam-6251	415	13	,	,	PUNCT
ejpam-6251	415	14	pςµ	pςµ	PROPN
ejpam-6251	415	15	,	,	PUNCT
ejpam-6251	415	16	ż	ż	NOUN
ejpam-6251	415	17	3	3	NUM
ejpam-6251	415	18	)	)	PUNCT
ejpam-6251	415	19	⋇π	⋇π	NOUN
ejpam-6251	415	20	(	(	PUNCT
ejpam-6251	415	21	pςµ	pςµ	PROPN
ejpam-6251	415	22	,	,	PUNCT
ejpam-6251	415	23	pς	pς	ADP
ejpam-6251	415	24	,	,	PUNCT
ejpam-6251	415	25	ż	ż	NOUN
ejpam-6251	415	26	3	3	NUM
ejpam-6251	415	27	)	)	PUNCT
ejpam-6251	415	28	→	→	PUNCT
ejpam-6251	415	29	1⋇	1⋇	NUM
ejpam-6251	415	30	1⋇	1⋇	NUM
ejpam-6251	415	31	1	1	NUM
ejpam-6251	415	32	=	=	SYM
ejpam-6251	415	33	1	1	NUM
ejpam-6251	415	34	as	as	ADP
ejpam-6251	415	35	µ→	µ→	PROPN
ejpam-6251	415	36	+	+	NOUN
ejpam-6251	415	37	∞	∞	PROPN
ejpam-6251	415	38	,	,	PUNCT
ejpam-6251	415	39	ψ(ς	ψ(ς	NOUN
ejpam-6251	415	40	,	,	PUNCT
ejpam-6251	415	41	pς	pς	ADP
ejpam-6251	415	42	,	,	PUNCT
ejpam-6251	415	43	ż	ż	NOUN
ejpam-6251	415	44	)	)	PUNCT
ejpam-6251	415	45	≤	≤	NOUN
ejpam-6251	415	46	ψ	ψ	X
ejpam-6251	415	47	(	(	PUNCT
ejpam-6251	415	48	ς	ς	PROPN
ejpam-6251	415	49	,	,	PUNCT
ejpam-6251	415	50	ςµ+1	ςµ+1	NUM
ejpam-6251	415	51	,	,	PUNCT
ejpam-6251	415	52	ż	ż	NOUN
ejpam-6251	415	53	3	3	X
ejpam-6251	415	54	)	)	PUNCT
ejpam-6251	415	55	♢	♢	PROPN
ejpam-6251	415	56	ψ	ψ	X
ejpam-6251	415	57	(	(	PUNCT
ejpam-6251	415	58	ςµ+1	ςµ+1	NUM
ejpam-6251	415	59	,	,	PUNCT
ejpam-6251	415	60	ςµ+1	ςµ+1	NUM
ejpam-6251	415	61	,	,	PUNCT
ejpam-6251	415	62	ż	ż	NOUN
ejpam-6251	415	63	3	3	X
ejpam-6251	415	64	)	)	PUNCT
ejpam-6251	415	65	♢	♢	PROPN
ejpam-6251	415	66	ψ	ψ	X
ejpam-6251	415	67	(	(	PUNCT
ejpam-6251	415	68	ςµ+1	ςµ+1	NUM
ejpam-6251	415	69	,	,	PUNCT
ejpam-6251	415	70	pς	pς	ADP
ejpam-6251	415	71	,	,	PUNCT
ejpam-6251	415	72	ż	ż	NOUN
ejpam-6251	415	73	3	3	NUM
ejpam-6251	415	74	)	)	PUNCT
ejpam-6251	415	75	=	=	SYM
ejpam-6251	415	76	ψ	ψ	X
ejpam-6251	415	77	(	(	PUNCT
ejpam-6251	415	78	ς	ς	PROPN
ejpam-6251	415	79	,	,	PUNCT
ejpam-6251	415	80	ςµ+1	ςµ+1	NUM
ejpam-6251	415	81	,	,	PUNCT
ejpam-6251	415	82	ż	ż	NOUN
ejpam-6251	415	83	3	3	X
ejpam-6251	415	84	)	)	PUNCT
ejpam-6251	415	85	♢	♢	PROPN
ejpam-6251	415	86	ψ	ψ	X
ejpam-6251	415	87	(	(	PUNCT
ejpam-6251	415	88	pςµ+1	pςµ+1	NOUN
ejpam-6251	415	89	,	,	PUNCT
ejpam-6251	415	90	pςµ+1	pςµ+1	NOUN
ejpam-6251	415	91	,	,	PUNCT
ejpam-6251	415	92	ż	ż	NOUN
ejpam-6251	415	93	3	3	NUM
ejpam-6251	415	94	)	)	PUNCT
ejpam-6251	415	95	♢	♢	PROPN
ejpam-6251	415	96	ψ	ψ	X
ejpam-6251	415	97	(	(	PUNCT
ejpam-6251	415	98	pςµ+1	pςµ+1	NOUN
ejpam-6251	415	99	,	,	PUNCT
ejpam-6251	415	100	pς	pς	ADP
ejpam-6251	415	101	,	,	PUNCT
ejpam-6251	415	102	ż	ż	NOUN
ejpam-6251	415	103	3	3	NUM
ejpam-6251	415	104	)	)	PUNCT
ejpam-6251	415	105	→	→	SYM
ejpam-6251	415	106	0	0	NUM
ejpam-6251	415	107	♢	♢	PROPN
ejpam-6251	415	108	0	0	PROPN
ejpam-6251	415	109	♢	♢	PROPN
ejpam-6251	415	110	0	0	PROPN
ejpam-6251	415	111	=	=	SYM
ejpam-6251	415	112	0	0	PUNCT
ejpam-6251	415	113	as	as	ADP
ejpam-6251	415	114	µ→	µ→	PROPN
ejpam-6251	415	115	+	+	NOUN
ejpam-6251	415	116	∞	∞	PROPN
ejpam-6251	415	117	and	and	CCONJ
ejpam-6251	415	118	ξ(ς	ξ(ς	NOUN
ejpam-6251	415	119	,	,	PUNCT
ejpam-6251	415	120	pς	pς	ADP
ejpam-6251	415	121	,	,	PUNCT
ejpam-6251	415	122	ż	ż	NOUN
ejpam-6251	415	123	)	)	PUNCT
ejpam-6251	416	1	≤	≤	NOUN
ejpam-6251	416	2	ξ	ξ	X
ejpam-6251	416	3	(	(	PUNCT
ejpam-6251	416	4	ς	ς	PROPN
ejpam-6251	416	5	,	,	PUNCT
ejpam-6251	416	6	ςµ+1	ςµ+1	NUM
ejpam-6251	416	7	,	,	PUNCT
ejpam-6251	416	8	ż	ż	NOUN
ejpam-6251	416	9	3	3	X
ejpam-6251	416	10	)	)	PUNCT
ejpam-6251	416	11	♢	♢	PROPN
ejpam-6251	416	12	ξ	ξ	X
ejpam-6251	416	13	(	(	PUNCT
ejpam-6251	416	14	ςµ+1	ςµ+1	NUM
ejpam-6251	416	15	,	,	PUNCT
ejpam-6251	416	16	ςµ+1	ςµ+1	NUM
ejpam-6251	416	17	,	,	PUNCT
ejpam-6251	416	18	ż	ż	NOUN
ejpam-6251	416	19	3	3	X
ejpam-6251	416	20	)	)	PUNCT
ejpam-6251	416	21	♢	♢	PROPN
ejpam-6251	416	22	ξ	ξ	X
ejpam-6251	416	23	(	(	PUNCT
ejpam-6251	416	24	ςµ+1	ςµ+1	NUM
ejpam-6251	416	25	,	,	PUNCT
ejpam-6251	416	26	pς	pς	ADP
ejpam-6251	416	27	,	,	PUNCT
ejpam-6251	416	28	ż	ż	NOUN
ejpam-6251	416	29	3	3	NUM
ejpam-6251	416	30	)	)	PUNCT
ejpam-6251	416	31	=	=	SYM
ejpam-6251	417	1	ξ	ξ	PROPN
ejpam-6251	417	2	(	(	PUNCT
ejpam-6251	417	3	ς	ς	PROPN
ejpam-6251	417	4	,	,	PUNCT
ejpam-6251	417	5	ςµ+1	ςµ+1	NUM
ejpam-6251	417	6	,	,	PUNCT
ejpam-6251	417	7	ż	ż	NOUN
ejpam-6251	417	8	3	3	X
ejpam-6251	417	9	)	)	PUNCT
ejpam-6251	417	10	♢	♢	PROPN
ejpam-6251	417	11	ξ	ξ	X
ejpam-6251	417	12	(	(	PUNCT
ejpam-6251	417	13	pςµ+1	pςµ+1	NOUN
ejpam-6251	417	14	,	,	PUNCT
ejpam-6251	417	15	pςµ+1	pςµ+1	NOUN
ejpam-6251	417	16	,	,	PUNCT
ejpam-6251	417	17	ż	ż	NOUN
ejpam-6251	417	18	3	3	X
ejpam-6251	417	19	)	)	PUNCT
ejpam-6251	417	20	♢	♢	PROPN
ejpam-6251	417	21	ξ	ξ	X
ejpam-6251	417	22	(	(	PUNCT
ejpam-6251	417	23	pςµ+1	pςµ+1	NOUN
ejpam-6251	417	24	,	,	PUNCT
ejpam-6251	417	25	pς	pς	ADP
ejpam-6251	417	26	,	,	PUNCT
ejpam-6251	417	27	ż	ż	NOUN
ejpam-6251	417	28	3	3	NUM
ejpam-6251	417	29	)	)	PUNCT
ejpam-6251	417	30	→	→	SYM
ejpam-6251	417	31	0	0	NUM
ejpam-6251	417	32	♢	♢	PROPN
ejpam-6251	417	33	0	0	PROPN
ejpam-6251	417	34	♢	♢	PROPN
ejpam-6251	417	35	0	0	PROPN
ejpam-6251	417	36	=	=	SYM
ejpam-6251	417	37	0	0	PUNCT
ejpam-6251	417	38	as	as	ADP
ejpam-6251	417	39	µ→	µ→	PROPN
ejpam-6251	417	40	+	+	NOUN
ejpam-6251	417	41	∞.	∞.	PROPN
ejpam-6251	417	42	hence	hence	ADV
ejpam-6251	417	43	,	,	PUNCT
ejpam-6251	417	44	pς	pς	ADP
ejpam-6251	417	45	=	=	SYM
ejpam-6251	417	46	ς	ς	PROPN
ejpam-6251	417	47	.	.	PUNCT
ejpam-6251	417	48	let	let	VERB
ejpam-6251	417	49	pη	pη	VERB
ejpam-6251	417	50	=	=	SYM
ejpam-6251	417	51	η	η	PROPN
ejpam-6251	417	52	for	for	ADP
ejpam-6251	417	53	some	some	DET
ejpam-6251	417	54	η	η	PROPN
ejpam-6251	417	55	∈	∈	PROPN
ejpam-6251	417	56	𭟋	𭟋	ADP
ejpam-6251	417	57	∩	∩	NOUN
ejpam-6251	417	58	s	s	SYM
ejpam-6251	417	59	,	,	PUNCT
ejpam-6251	417	60	then	then	ADV
ejpam-6251	417	61	1	1	NUM
ejpam-6251	417	62	≥	≥	NOUN
ejpam-6251	417	63	π(η	π(η	PROPN
ejpam-6251	417	64	,	,	PUNCT
ejpam-6251	417	65	ς	ς	PROPN
ejpam-6251	417	66	,	,	PUNCT
ejpam-6251	417	67	ż	ż	NOUN
ejpam-6251	417	68	)	)	PUNCT
ejpam-6251	417	69	=	=	SYM
ejpam-6251	417	70	π(pς	π(pς	NOUN
ejpam-6251	417	71	,	,	PUNCT
ejpam-6251	417	72	pη	pη	NOUN
ejpam-6251	417	73	,	,	PUNCT
ejpam-6251	417	74	ż	ż	NOUN
ejpam-6251	417	75	)	)	PUNCT
ejpam-6251	417	76	≥	≥	NOUN
ejpam-6251	417	77	π	π	PROPN
ejpam-6251	417	78	(	(	PUNCT
ejpam-6251	417	79	η	η	PROPN
ejpam-6251	417	80	,	,	PUNCT
ejpam-6251	417	81	ς	ς	PROPN
ejpam-6251	417	82	,	,	PUNCT
ejpam-6251	417	83	ż	ż	NOUN
ejpam-6251	417	84	ζ	ζ	NOUN
ejpam-6251	417	85	)	)	PUNCT
ejpam-6251	417	86	=	=	PUNCT
ejpam-6251	418	1	π	π	X
ejpam-6251	418	2	(	(	PUNCT
ejpam-6251	418	3	pς	pς	ADP
ejpam-6251	418	4	,	,	PUNCT
ejpam-6251	418	5	pη	pη	ADP
ejpam-6251	418	6	,	,	PUNCT
ejpam-6251	418	7	ż	ż	NOUN
ejpam-6251	418	8	ζ	ζ	NOUN
ejpam-6251	418	9	)	)	PUNCT
ejpam-6251	418	10	≥	≥	NOUN
ejpam-6251	418	11	π	π	PROPN
ejpam-6251	418	12	(	(	PUNCT
ejpam-6251	418	13	η	η	PROPN
ejpam-6251	418	14	,	,	PUNCT
ejpam-6251	418	15	ς	ς	PROPN
ejpam-6251	418	16	,	,	PUNCT
ejpam-6251	418	17	ż	ż	NOUN
ejpam-6251	418	18	ζ2	ζ2	NOUN
ejpam-6251	418	19	)	)	PUNCT
ejpam-6251	418	20	≥	≥	NOUN
ejpam-6251	418	21	·	·	PUNCT
ejpam-6251	418	22	·	·	PUNCT
ejpam-6251	418	23	·	·	PUNCT
ejpam-6251	418	24	≥	≥	NUM
ejpam-6251	419	1	π	π	PROPN
ejpam-6251	419	2	(	(	PUNCT
ejpam-6251	419	3	η	η	PROPN
ejpam-6251	419	4	,	,	PUNCT
ejpam-6251	419	5	ς	ς	PROPN
ejpam-6251	419	6	,	,	PUNCT
ejpam-6251	419	7	ż	ż	NOUN
ejpam-6251	419	8	ζµ	ζµ	X
ejpam-6251	419	9	)	)	PUNCT
ejpam-6251	419	10	→	→	SYM
ejpam-6251	419	11	1	1	NUM
ejpam-6251	419	12	as	as	ADP
ejpam-6251	419	13	µ→	µ→	PROPN
ejpam-6251	419	14	+	+	NOUN
ejpam-6251	419	15	∞	∞	PROPN
ejpam-6251	419	16	,	,	PUNCT
ejpam-6251	419	17	0	0	NUM
ejpam-6251	419	18	≤	≤	NUM
ejpam-6251	419	19	ψ(η	ψ(η	NOUN
ejpam-6251	419	20	,	,	PUNCT
ejpam-6251	419	21	ς	ς	NOUN
ejpam-6251	419	22	,	,	PUNCT
ejpam-6251	419	23	ż	ż	NOUN
ejpam-6251	419	24	)	)	PUNCT
ejpam-6251	419	25	=	=	SYM
ejpam-6251	419	26	ψ(pς	ψ(pς	NOUN
ejpam-6251	419	27	,	,	PUNCT
ejpam-6251	419	28	pη	pη	NOUN
ejpam-6251	419	29	,	,	PUNCT
ejpam-6251	419	30	ż	ż	NOUN
ejpam-6251	419	31	)	)	PUNCT
ejpam-6251	419	32	≤	≤	NOUN
ejpam-6251	419	33	ψ	ψ	X
ejpam-6251	419	34	(	(	PUNCT
ejpam-6251	419	35	η	η	PROPN
ejpam-6251	419	36	,	,	PUNCT
ejpam-6251	419	37	ς	ς	PROPN
ejpam-6251	419	38	,	,	PUNCT
ejpam-6251	419	39	ż	ż	NOUN
ejpam-6251	419	40	ζ	ζ	NOUN
ejpam-6251	419	41	)	)	PUNCT
ejpam-6251	420	1	=	=	SYM
ejpam-6251	420	2	ψ	ψ	X
ejpam-6251	420	3	(	(	PUNCT
ejpam-6251	420	4	pς	pς	ADP
ejpam-6251	420	5	,	,	PUNCT
ejpam-6251	420	6	pη	pη	ADP
ejpam-6251	420	7	,	,	PUNCT
ejpam-6251	420	8	ż	ż	NOUN
ejpam-6251	420	9	ζ	ζ	NOUN
ejpam-6251	420	10	)	)	PUNCT
ejpam-6251	420	11	r.	r.	PROPN
ejpam-6251	420	12	ramaswamy	ramaswamy	PROPN
ejpam-6251	420	13	/	/	SYM
ejpam-6251	420	14	eur	eur	PROPN
ejpam-6251	420	15	.	.	PUNCT
ejpam-6251	421	1	j.	j.	PROPN
ejpam-6251	421	2	pure	pure	PROPN
ejpam-6251	421	3	appl	appl	PROPN
ejpam-6251	421	4	.	.	PROPN
ejpam-6251	421	5	math	math	PROPN
ejpam-6251	421	6	,	,	PUNCT
ejpam-6251	421	7	18	18	NUM
ejpam-6251	421	8	(	(	PUNCT
ejpam-6251	421	9	4	4	NUM
ejpam-6251	421	10	)	)	PUNCT
ejpam-6251	421	11	(	(	PUNCT
ejpam-6251	421	12	2025	2025	NUM
ejpam-6251	421	13	)	)	PUNCT
ejpam-6251	421	14	,	,	PUNCT
ejpam-6251	421	15	6251	6251	NUM
ejpam-6251	421	16	21	21	NUM
ejpam-6251	421	17	of	of	ADP
ejpam-6251	421	18	40	40	NUM
ejpam-6251	421	19	≤	≤	NOUN
ejpam-6251	421	20	ψ	ψ	X
ejpam-6251	421	21	(	(	PUNCT
ejpam-6251	421	22	η	η	PROPN
ejpam-6251	421	23	,	,	PUNCT
ejpam-6251	421	24	ς	ς	PROPN
ejpam-6251	421	25	,	,	PUNCT
ejpam-6251	421	26	ż	ż	NOUN
ejpam-6251	421	27	ζ2	ζ2	NOUN
ejpam-6251	421	28	)	)	PUNCT
ejpam-6251	421	29	≤	≤	NOUN
ejpam-6251	421	30	·	·	PUNCT
ejpam-6251	421	31	·	·	PUNCT
ejpam-6251	421	32	·	·	PUNCT
ejpam-6251	422	1	≤	≤	NUM
ejpam-6251	422	2	ψ	ψ	X
ejpam-6251	422	3	(	(	PUNCT
ejpam-6251	422	4	η	η	PROPN
ejpam-6251	422	5	,	,	PUNCT
ejpam-6251	422	6	ς	ς	PROPN
ejpam-6251	422	7	,	,	PUNCT
ejpam-6251	422	8	ż	ż	NOUN
ejpam-6251	422	9	ζµ	ζµ	X
ejpam-6251	422	10	)	)	PUNCT
ejpam-6251	422	11	→	→	SYM
ejpam-6251	422	12	0	0	PUNCT
ejpam-6251	422	13	as	as	ADP
ejpam-6251	422	14	µ→	µ→	PROPN
ejpam-6251	422	15	+	+	NOUN
ejpam-6251	422	16	∞	∞	PROPN
ejpam-6251	422	17	,	,	PUNCT
ejpam-6251	422	18	and	and	CCONJ
ejpam-6251	422	19	0	0	NUM
ejpam-6251	422	20	≤	≤	NUM
ejpam-6251	422	21	ξ(η	ξ(η	PROPN
ejpam-6251	422	22	,	,	PUNCT
ejpam-6251	422	23	ς	ς	NOUN
ejpam-6251	422	24	,	,	PUNCT
ejpam-6251	422	25	ż	ż	NOUN
ejpam-6251	422	26	)	)	PUNCT
ejpam-6251	422	27	=	=	SYM
ejpam-6251	422	28	ξ(pς	ξ(pς	PROPN
ejpam-6251	422	29	,	,	PUNCT
ejpam-6251	422	30	pη	pη	ADP
ejpam-6251	422	31	,	,	PUNCT
ejpam-6251	422	32	ż	ż	NOUN
ejpam-6251	422	33	)	)	PUNCT
ejpam-6251	422	34	≤	≤	NOUN
ejpam-6251	422	35	ξ	ξ	PROPN
ejpam-6251	422	36	(	(	PUNCT
ejpam-6251	422	37	η	η	PROPN
ejpam-6251	422	38	,	,	PUNCT
ejpam-6251	422	39	ς	ς	PROPN
ejpam-6251	422	40	,	,	PUNCT
ejpam-6251	422	41	ż	ż	NOUN
ejpam-6251	422	42	ζ	ζ	NOUN
ejpam-6251	422	43	)	)	PUNCT
ejpam-6251	422	44	=	=	SYM
ejpam-6251	422	45	ξ	ξ	PROPN
ejpam-6251	422	46	(	(	PUNCT
ejpam-6251	422	47	pς	pς	ADP
ejpam-6251	422	48	,	,	PUNCT
ejpam-6251	422	49	pη	pη	ADP
ejpam-6251	422	50	,	,	PUNCT
ejpam-6251	422	51	ż	ż	NOUN
ejpam-6251	422	52	ζ	ζ	NOUN
ejpam-6251	422	53	)	)	PUNCT
ejpam-6251	422	54	≤	≤	NUM
ejpam-6251	422	55	ξ	ξ	PROPN
ejpam-6251	422	56	(	(	PUNCT
ejpam-6251	422	57	η	η	PROPN
ejpam-6251	422	58	,	,	PUNCT
ejpam-6251	422	59	ς	ς	PROPN
ejpam-6251	422	60	,	,	PUNCT
ejpam-6251	422	61	ż	ż	NOUN
ejpam-6251	422	62	ζ2	ζ2	NOUN
ejpam-6251	422	63	)	)	PUNCT
ejpam-6251	422	64	≤	≤	NOUN
ejpam-6251	422	65	·	·	PUNCT
ejpam-6251	422	66	·	·	PUNCT
ejpam-6251	422	67	·	·	PUNCT
ejpam-6251	422	68	≤	≤	NUM
ejpam-6251	422	69	ξ	ξ	X
ejpam-6251	422	70	(	(	PUNCT
ejpam-6251	422	71	η	η	PROPN
ejpam-6251	422	72	,	,	PUNCT
ejpam-6251	422	73	ς	ς	PROPN
ejpam-6251	422	74	,	,	PUNCT
ejpam-6251	422	75	ż	ż	NOUN
ejpam-6251	422	76	ζµ	ζµ	X
ejpam-6251	422	77	)	)	PUNCT
ejpam-6251	422	78	→	→	SYM
ejpam-6251	422	79	0	0	PUNCT
ejpam-6251	422	80	as	as	ADP
ejpam-6251	422	81	µ→	µ→	PROPN
ejpam-6251	422	82	+	+	NOUN
ejpam-6251	422	83	∞	∞	PROPN
ejpam-6251	422	84	,	,	PUNCT
ejpam-6251	422	85	since	since	SCONJ
ejpam-6251	422	86	iii	iii	NOUN
ejpam-6251	422	87	,	,	PUNCT
ejpam-6251	422	88	viii	viii	NOUN
ejpam-6251	422	89	and	and	CCONJ
ejpam-6251	422	90	xiii	xiii	PROPN
ejpam-6251	422	91	,	,	PUNCT
ejpam-6251	422	92	we	we	PRON
ejpam-6251	422	93	get	get	VERB
ejpam-6251	422	94	ς	ς	PROPN
ejpam-6251	422	95	=	=	SYM
ejpam-6251	422	96	η	η	PROPN
ejpam-6251	422	97	.	.	PROPN
ejpam-6251	422	98	definition	definition	NOUN
ejpam-6251	422	99	15	15	NUM
ejpam-6251	422	100	.	.	PUNCT
ejpam-6251	423	1	let	let	AUX
ejpam-6251	423	2	(	(	PUNCT
ejpam-6251	423	3	𭟋	𭟋	NOUN
ejpam-6251	423	4	,	,	PUNCT
ejpam-6251	423	5	s	s	PROPN
ejpam-6251	423	6	,	,	PUNCT
ejpam-6251	423	7	π	π	PROPN
ejpam-6251	423	8	,	,	PUNCT
ejpam-6251	423	9	ψ	ψ	PROPN
ejpam-6251	423	10	,	,	PUNCT
ejpam-6251	423	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	423	12	,	,	PUNCT
ejpam-6251	423	13	♢	♢	PROPN
ejpam-6251	423	14	)	)	PUNCT
ejpam-6251	423	15	be	be	AUX
ejpam-6251	423	16	a	a	DET
ejpam-6251	423	17	nbms	nbms	NOUN
ejpam-6251	423	18	.	.	PUNCT
ejpam-6251	424	1	a	a	DET
ejpam-6251	424	2	map	map	NOUN
ejpam-6251	424	3	p	p	X
ejpam-6251	424	4	:	:	PUNCT
ejpam-6251	424	5	𭟋	𭟋	ADP
ejpam-6251	424	6	∪	∪	ADP
ejpam-6251	424	7	s	s	X
ejpam-6251	424	8	→	→	SYM
ejpam-6251	424	9	𭟋	𭟋	ADP
ejpam-6251	424	10	∪	∪	ADJ
ejpam-6251	424	11	s	s	NOUN
ejpam-6251	424	12	is	be	AUX
ejpam-6251	424	13	an	an	DET
ejpam-6251	424	14	nb(neutrosophic	nb(neutrosophic	PROPN
ejpam-6251	424	15	bipolar)-contraction	bipolar)-contraction	NOUN
ejpam-6251	424	16	if	if	SCONJ
ejpam-6251	424	17	we	we	PRON
ejpam-6251	424	18	can	can	AUX
ejpam-6251	424	19	find	find	VERB
ejpam-6251	424	20	0	0	NUM
ejpam-6251	424	21	<	<	X
ejpam-6251	424	22	ζ	ζ	X
ejpam-6251	424	23	<	<	X
ejpam-6251	424	24	1	1	NUM
ejpam-6251	424	25	,	,	PUNCT
ejpam-6251	424	26	satisfying	satisfy	VERB
ejpam-6251	424	27	1	1	NUM
ejpam-6251	424	28	π(pς	π(pς	NOUN
ejpam-6251	424	29	,	,	PUNCT
ejpam-6251	424	30	pϖ	pϖ	ADP
ejpam-6251	424	31	,	,	PUNCT
ejpam-6251	424	32	ż	ż	NOUN
ejpam-6251	424	33	)	)	PUNCT
ejpam-6251	425	1	−	−	PROPN
ejpam-6251	425	2	1	1	NUM
ejpam-6251	425	3	≤	≤	NUM
ejpam-6251	425	4	ζ	ζ	NOUN
ejpam-6251	425	5	[	[	PUNCT
ejpam-6251	425	6	1	1	NUM
ejpam-6251	425	7	π(ς,ϖ	π(ς,ϖ	NUM
ejpam-6251	425	8	,	,	PUNCT
ejpam-6251	425	9	ż	ż	NOUN
ejpam-6251	425	10	)	)	PUNCT
ejpam-6251	425	11	−	−	PROPN
ejpam-6251	425	12	1	1	NUM
ejpam-6251	425	13	]	]	PUNCT
ejpam-6251	425	14	(	(	PUNCT
ejpam-6251	425	15	7	7	X
ejpam-6251	425	16	)	)	PUNCT
ejpam-6251	425	17	ψ(pς	ψ(pς	NOUN
ejpam-6251	425	18	,	,	PUNCT
ejpam-6251	425	19	pϖ	pϖ	ADP
ejpam-6251	425	20	,	,	PUNCT
ejpam-6251	425	21	ż	ż	NOUN
ejpam-6251	425	22	)	)	PUNCT
ejpam-6251	425	23	≤	≤	NOUN
ejpam-6251	425	24	ζψ(ς,ϖ	ζψ(ς,ϖ	ADP
ejpam-6251	425	25	,	,	PUNCT
ejpam-6251	425	26	ż	ż	NOUN
ejpam-6251	425	27	)	)	PUNCT
ejpam-6251	425	28	,	,	PUNCT
ejpam-6251	425	29	(	(	PUNCT
ejpam-6251	425	30	8)	8)	NUM
ejpam-6251	425	31	and	and	CCONJ
ejpam-6251	425	32	ξ(pς	ξ(pς	NOUN
ejpam-6251	425	33	,	,	PUNCT
ejpam-6251	425	34	pϖ	pϖ	ADP
ejpam-6251	425	35	,	,	PUNCT
ejpam-6251	425	36	ż	ż	NOUN
ejpam-6251	425	37	)	)	PUNCT
ejpam-6251	425	38	≤	≤	NOUN
ejpam-6251	425	39	ζξ(ς,ϖ	ζξ(ς,ϖ	NOUN
ejpam-6251	425	40	,	,	PUNCT
ejpam-6251	425	41	ż	ż	NOUN
ejpam-6251	425	42	)	)	PUNCT
ejpam-6251	425	43	,	,	PUNCT
ejpam-6251	425	44	(	(	PUNCT
ejpam-6251	425	45	9	9	X
ejpam-6251	425	46	)	)	PUNCT
ejpam-6251	425	47	∀	∀	NOUN
ejpam-6251	425	48	ς	ς	PROPN
ejpam-6251	425	49	∈	∈	X
ejpam-6251	425	50	𭟋	𭟋	X
ejpam-6251	425	51	,	,	PUNCT
ejpam-6251	425	52	ϖ	ϖ	PROPN
ejpam-6251	425	53	∈	∈	PROPN
ejpam-6251	425	54	s	s	PART
ejpam-6251	425	55	and	and	CCONJ
ejpam-6251	425	56	ż	ż	X
ejpam-6251	425	57	>	>	X
ejpam-6251	425	58	0	0	X
ejpam-6251	425	59	.	.	PUNCT
ejpam-6251	426	1	now	now	ADV
ejpam-6251	426	2	,	,	PUNCT
ejpam-6251	426	3	we	we	PRON
ejpam-6251	426	4	present	present	VERB
ejpam-6251	426	5	the	the	DET
ejpam-6251	426	6	following	follow	VERB
ejpam-6251	426	7	theorem	theorem	NOUN
ejpam-6251	426	8	for	for	ADP
ejpam-6251	426	9	nb(neutrosophic	nb(neutrosophic	PROPN
ejpam-6251	426	10	bipolar)-contraction	bipolar)-contraction	PROPN
ejpam-6251	426	11	.	.	PUNCT
ejpam-6251	427	1	theorem	theorem	ADJ
ejpam-6251	427	2	7	7	NUM
ejpam-6251	427	3	.	.	PUNCT
ejpam-6251	428	1	let	let	AUX
ejpam-6251	428	2	(	(	PUNCT
ejpam-6251	428	3	𭟋	𭟋	NOUN
ejpam-6251	428	4	,	,	PUNCT
ejpam-6251	428	5	s	s	PROPN
ejpam-6251	428	6	,	,	PUNCT
ejpam-6251	428	7	π	π	PROPN
ejpam-6251	428	8	,	,	PUNCT
ejpam-6251	428	9	ψ	ψ	PROPN
ejpam-6251	428	10	,	,	PUNCT
ejpam-6251	428	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	428	12	,	,	PUNCT
ejpam-6251	428	13	♢	♢	PROPN
ejpam-6251	428	14	)	)	PUNCT
ejpam-6251	428	15	be	be	AUX
ejpam-6251	428	16	a	a	DET
ejpam-6251	428	17	complete	complete	ADJ
ejpam-6251	428	18	nbms	nbms	NOUN
ejpam-6251	428	19	.	.	PUNCT
ejpam-6251	429	1	let	let	VERB
ejpam-6251	429	2	p	p	NOUN
ejpam-6251	429	3	:	:	PUNCT
ejpam-6251	429	4	𭟋	𭟋	ADP
ejpam-6251	429	5	∪	∪	ADP
ejpam-6251	429	6	s	s	X
ejpam-6251	429	7	→	→	SYM
ejpam-6251	429	8	𭟋	𭟋	ADP
ejpam-6251	429	9	∪	∪	NOUN
ejpam-6251	429	10	s	s	AUX
ejpam-6251	429	11	be	be	VERB
ejpam-6251	429	12	a	a	DET
ejpam-6251	429	13	mapping	mapping	NOUN
ejpam-6251	429	14	satisfying	satisfy	VERB
ejpam-6251	429	15	i.	i.	NOUN
ejpam-6251	429	16	p(𭟋	p(𭟋	PROPN
ejpam-6251	429	17	)	)	PUNCT
ejpam-6251	430	1	⊆	⊆	NUM
ejpam-6251	430	2	𭟋	𭟋	NOUN
ejpam-6251	430	3	and	and	CCONJ
ejpam-6251	430	4	p(s	p(s	NUM
ejpam-6251	430	5	)	)	PUNCT
ejpam-6251	430	6	⊆	⊆	NUM
ejpam-6251	430	7	s	s	NOUN
ejpam-6251	430	8	;	;	PUNCT
ejpam-6251	430	9	ii	ii	NOUN
ejpam-6251	430	10	.	.	PUNCT
ejpam-6251	431	1	p	p	PROPN
ejpam-6251	431	2	is	be	AUX
ejpam-6251	431	3	nb	nb	NOUN
ejpam-6251	431	4	-	-	PUNCT
ejpam-6251	431	5	contraction	contraction	NOUN
ejpam-6251	431	6	,	,	PUNCT
ejpam-6251	431	7	∀	∀	X
ejpam-6251	431	8	ς	ς	NOUN
ejpam-6251	431	9	∈	∈	PROPN
ejpam-6251	431	10	𭟋	𭟋	X
ejpam-6251	431	11	,	,	PUNCT
ejpam-6251	431	12	ϖ	ϖ	PROPN
ejpam-6251	431	13	∈	∈	PROPN
ejpam-6251	431	14	s	s	PART
ejpam-6251	431	15	and	and	CCONJ
ejpam-6251	431	16	ż	ż	X
ejpam-6251	431	17	>	>	X
ejpam-6251	432	1	0	0	X
ejpam-6251	432	2	.	.	PUNCT
ejpam-6251	433	1	then	then	ADV
ejpam-6251	433	2	,	,	PUNCT
ejpam-6251	433	3	p	p	PROPN
ejpam-6251	433	4	has	have	VERB
ejpam-6251	433	5	a	a	DET
ejpam-6251	433	6	unique	unique	ADJ
ejpam-6251	433	7	fixed	fix	VERB
ejpam-6251	433	8	point	point	NOUN
ejpam-6251	433	9	.	.	PUNCT
ejpam-6251	434	1	proof	proof	NOUN
ejpam-6251	434	2	.	.	PUNCT
ejpam-6251	435	1	let	let	VERB
ejpam-6251	435	2	ς0	ς0	PROPN
ejpam-6251	435	3	∈	∈	PROPN
ejpam-6251	435	4	𭟋	𭟋	NOUN
ejpam-6251	435	5	and	and	CCONJ
ejpam-6251	435	6	ϖ0	ϖ0	NOUN
ejpam-6251	435	7	∈	∈	NOUN
ejpam-6251	435	8	s	s	PART
ejpam-6251	435	9	and	and	CCONJ
ejpam-6251	435	10	assume	assume	VERB
ejpam-6251	435	11	that	that	SCONJ
ejpam-6251	435	12	p(ςµ	p(ςµ	NOUN
ejpam-6251	435	13	)	)	PUNCT
ejpam-6251	435	14	=	=	SYM
ejpam-6251	435	15	ςµ+1	ςµ+1	NUM
ejpam-6251	435	16	and	and	CCONJ
ejpam-6251	435	17	p(ϖµ	p(ϖµ	NOUN
ejpam-6251	435	18	)	)	PUNCT
ejpam-6251	436	1	=	=	SYM
ejpam-6251	436	2	ϖµ+1	ϖµ+1	NUM
ejpam-6251	436	3	∀	∀	NOUN
ejpam-6251	436	4	µ	µ	PRON
ejpam-6251	436	5	∈	∈	NOUN
ejpam-6251	436	6	n	n	NOUN
ejpam-6251	436	7	∪	∪	X
ejpam-6251	436	8	{	{	PUNCT
ejpam-6251	436	9	0	0	NUM
ejpam-6251	436	10	}	}	PUNCT
ejpam-6251	436	11	.	.	PUNCT
ejpam-6251	437	1	then	then	ADV
ejpam-6251	437	2	we	we	PRON
ejpam-6251	437	3	get	get	VERB
ejpam-6251	437	4	(	(	PUNCT
ejpam-6251	437	5	ςµ	ςµ	NOUN
ejpam-6251	437	6	,	,	PUNCT
ejpam-6251	437	7	ϖµ)as	ϖµ)as	ADP
ejpam-6251	437	8	a	a	DET
ejpam-6251	437	9	bisequence	bisequence	NOUN
ejpam-6251	437	10	on	on	ADP
ejpam-6251	437	11	nbms	nbms	NOUN
ejpam-6251	437	12	(	(	PUNCT
ejpam-6251	437	13	𭟋	𭟋	NOUN
ejpam-6251	437	14	,	,	PUNCT
ejpam-6251	437	15	s	s	PROPN
ejpam-6251	437	16	,	,	PUNCT
ejpam-6251	437	17	π	π	PROPN
ejpam-6251	437	18	,	,	PUNCT
ejpam-6251	437	19	ψ	ψ	PROPN
ejpam-6251	437	20	,	,	PUNCT
ejpam-6251	437	21	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	437	22	,	,	PUNCT
ejpam-6251	437	23	♢	♢	PROPN
ejpam-6251	437	24	)	)	PUNCT
ejpam-6251	437	25	.	.	PUNCT
ejpam-6251	438	1	by	by	ADP
ejpam-6251	438	2	using	use	VERB
ejpam-6251	438	3	(	(	PUNCT
ejpam-6251	438	4	7	7	NUM
ejpam-6251	438	5	)	)	PUNCT
ejpam-6251	438	6	,	,	PUNCT
ejpam-6251	438	7	(	(	PUNCT
ejpam-6251	438	8	8)	8)	NUM
ejpam-6251	438	9	and	and	CCONJ
ejpam-6251	438	10	(	(	PUNCT
ejpam-6251	438	11	9	9	NUM
ejpam-6251	438	12	)	)	PUNCT
ejpam-6251	438	13	∀	∀	NOUN
ejpam-6251	439	1	ż	ż	NOUN
ejpam-6251	439	2	>	>	X
ejpam-6251	439	3	0	0	NUM
ejpam-6251	439	4	,	,	PUNCT
ejpam-6251	439	5	we	we	PRON
ejpam-6251	439	6	deduce	deduce	VERB
ejpam-6251	439	7	1	1	NUM
ejpam-6251	439	8	π(ςµ	π(ςµ	NUM
ejpam-6251	439	9	,	,	PUNCT
ejpam-6251	439	10	ϖµ	ϖµ	NOUN
ejpam-6251	439	11	,	,	PUNCT
ejpam-6251	439	12	ż	ż	NOUN
ejpam-6251	439	13	)	)	PUNCT
ejpam-6251	439	14	−	−	PROPN
ejpam-6251	440	1	1	1	NUM
ejpam-6251	440	2	=	=	SYM
ejpam-6251	440	3	1	1	NUM
ejpam-6251	440	4	π(pςµ−1	π(pςµ−1	NUM
ejpam-6251	440	5	,	,	PUNCT
ejpam-6251	440	6	pϖµ−1	pϖµ−1	PROPN
ejpam-6251	440	7	,	,	PUNCT
ejpam-6251	440	8	ż	ż	NOUN
ejpam-6251	440	9	)	)	PUNCT
ejpam-6251	440	10	−	−	PROPN
ejpam-6251	440	11	1	1	NUM
ejpam-6251	440	12	≤	≤	NUM
ejpam-6251	440	13	ζ	ζ	NOUN
ejpam-6251	440	14	[	[	PUNCT
ejpam-6251	440	15	1	1	NUM
ejpam-6251	440	16	π(ςµ−1	π(ςµ−1	NUM
ejpam-6251	440	17	,	,	PUNCT
ejpam-6251	440	18	ϖµ−1	ϖµ−1	ADJ
ejpam-6251	440	19	,	,	PUNCT
ejpam-6251	440	20	ż	ż	NOUN
ejpam-6251	440	21	)	)	PUNCT
ejpam-6251	440	22	]	]	PUNCT
ejpam-6251	441	1	=	=	PUNCT
ejpam-6251	441	2	ζ	ζ	X
ejpam-6251	441	3	π(ςµ−1	π(ςµ−1	NUM
ejpam-6251	441	4	,	,	PUNCT
ejpam-6251	441	5	ϖµ−1	ϖµ−1	ADJ
ejpam-6251	441	6	,	,	PUNCT
ejpam-6251	441	7	ż	ż	NOUN
ejpam-6251	441	8	)	)	PUNCT
ejpam-6251	441	9	−	−	PROPN
ejpam-6251	441	10	ζ	ζ	PROPN
ejpam-6251	441	11	⇒	⇒	NOUN
ejpam-6251	441	12	1	1	NUM
ejpam-6251	441	13	π(ςµ	π(ςµ	NUM
ejpam-6251	441	14	,	,	PUNCT
ejpam-6251	441	15	ϖµ	ϖµ	NOUN
ejpam-6251	441	16	,	,	PUNCT
ejpam-6251	441	17	ż	ż	NOUN
ejpam-6251	441	18	)	)	PUNCT
ejpam-6251	441	19	≤	≤	NUM
ejpam-6251	441	20	ζ	ζ	NOUN
ejpam-6251	441	21	π(ςµ−1	π(ςµ−1	NUM
ejpam-6251	441	22	,	,	PUNCT
ejpam-6251	441	23	ϖµ−1	ϖµ−1	ADJ
ejpam-6251	441	24	,	,	PUNCT
ejpam-6251	441	25	ż	ż	NOUN
ejpam-6251	441	26	)	)	PUNCT
ejpam-6251	441	27	+	+	CCONJ
ejpam-6251	441	28	(	(	PUNCT
ejpam-6251	441	29	1−	1−	NUM
ejpam-6251	441	30	ζ	ζ	NOUN
ejpam-6251	441	31	)	)	PUNCT
ejpam-6251	441	32	≤	≤	NUM
ejpam-6251	441	33	ζ2	ζ2	NOUN
ejpam-6251	441	34	π(ςµ−2	π(ςµ−2	NOUN
ejpam-6251	441	35	,	,	PUNCT
ejpam-6251	441	36	ϖµ−2	ϖµ−2	NOUN
ejpam-6251	441	37	,	,	PUNCT
ejpam-6251	441	38	ż	ż	NOUN
ejpam-6251	441	39	)	)	PUNCT
ejpam-6251	441	40	+	+	PUNCT
ejpam-6251	441	41	ζ(1−	ζ(1−	PROPN
ejpam-6251	441	42	ζ	ζ	NOUN
ejpam-6251	441	43	)	)	PUNCT
ejpam-6251	441	44	+	+	CCONJ
ejpam-6251	441	45	(	(	PUNCT
ejpam-6251	441	46	1−	1−	NUM
ejpam-6251	441	47	ζ	ζ	NOUN
ejpam-6251	441	48	)	)	PUNCT
ejpam-6251	441	49	.	.	PUNCT
ejpam-6251	442	1	r.	r.	PROPN
ejpam-6251	442	2	ramaswamy	ramaswamy	PROPN
ejpam-6251	442	3	/	/	SYM
ejpam-6251	442	4	eur	eur	PROPN
ejpam-6251	442	5	.	.	PUNCT
ejpam-6251	443	1	j.	j.	PROPN
ejpam-6251	443	2	pure	pure	PROPN
ejpam-6251	443	3	appl	appl	PROPN
ejpam-6251	443	4	.	.	PROPN
ejpam-6251	443	5	math	math	PROPN
ejpam-6251	443	6	,	,	PUNCT
ejpam-6251	443	7	18	18	NUM
ejpam-6251	443	8	(	(	PUNCT
ejpam-6251	443	9	4	4	NUM
ejpam-6251	443	10	)	)	PUNCT
ejpam-6251	443	11	(	(	PUNCT
ejpam-6251	443	12	2025	2025	NUM
ejpam-6251	443	13	)	)	PUNCT
ejpam-6251	443	14	,	,	PUNCT
ejpam-6251	443	15	6251	6251	NUM
ejpam-6251	443	16	22	22	NUM
ejpam-6251	443	17	of	of	ADP
ejpam-6251	443	18	40	40	NUM
ejpam-6251	443	19	in	in	ADP
ejpam-6251	443	20	this	this	DET
ejpam-6251	443	21	manner	manner	NOUN
ejpam-6251	443	22	,	,	PUNCT
ejpam-6251	443	23	we	we	PRON
ejpam-6251	443	24	obtain	obtain	VERB
ejpam-6251	443	25	1	1	NUM
ejpam-6251	443	26	π(ςµ	π(ςµ	NUM
ejpam-6251	443	27	,	,	PUNCT
ejpam-6251	443	28	ϖµ	ϖµ	NOUN
ejpam-6251	443	29	,	,	PUNCT
ejpam-6251	443	30	ż	ż	NOUN
ejpam-6251	443	31	)	)	PUNCT
ejpam-6251	443	32	≤	≤	NOUN
ejpam-6251	443	33	ζµ	ζµ	PRON
ejpam-6251	443	34	π(ς0	π(ς0	NOUN
ejpam-6251	443	35	,	,	PUNCT
ejpam-6251	443	36	ϖ0	ϖ0	NOUN
ejpam-6251	443	37	,	,	PUNCT
ejpam-6251	443	38	ż	ż	NOUN
ejpam-6251	443	39	)	)	PUNCT
ejpam-6251	444	1	+	+	NUM
ejpam-6251	444	2	ζµ−1(1−	ζµ−1(1−	ADJ
ejpam-6251	444	3	ζ	ζ	NOUN
ejpam-6251	444	4	)	)	PUNCT
ejpam-6251	444	5	+	+	CCONJ
ejpam-6251	444	6	ζµ−2(1−	ζµ−2(1−	PROPN
ejpam-6251	444	7	ζ	ζ	NOUN
ejpam-6251	444	8	)	)	PUNCT
ejpam-6251	444	9	+	+	CCONJ
ejpam-6251	444	10	·	·	PUNCT
ejpam-6251	444	11	·	·	PUNCT
ejpam-6251	444	12	·	·	PUNCT
ejpam-6251	444	13	+	+	NUM
ejpam-6251	444	14	ζ(1−	ζ(1−	PROPN
ejpam-6251	444	15	ζ	ζ	X
ejpam-6251	444	16	)	)	PUNCT
ejpam-6251	444	17	+	+	CCONJ
ejpam-6251	444	18	(	(	PUNCT
ejpam-6251	444	19	1−	1−	NUM
ejpam-6251	444	20	ζ	ζ	NOUN
ejpam-6251	444	21	)	)	PUNCT
ejpam-6251	444	22	≤	≤	NOUN
ejpam-6251	444	23	ζµ	ζµ	PRON
ejpam-6251	444	24	π(ς0	π(ς0	NOUN
ejpam-6251	444	25	,	,	PUNCT
ejpam-6251	444	26	ϖ0	ϖ0	NOUN
ejpam-6251	444	27	,	,	PUNCT
ejpam-6251	444	28	ż	ż	NOUN
ejpam-6251	444	29	)	)	PUNCT
ejpam-6251	445	1	+	+	CCONJ
ejpam-6251	445	2	(	(	PUNCT
ejpam-6251	445	3	ζµ−1	ζµ−1	ADJ
ejpam-6251	445	4	+	+	CCONJ
ejpam-6251	445	5	ζµ−2	ζµ−2	NOUN
ejpam-6251	445	6	+	+	NOUN
ejpam-6251	445	7	·	·	PUNCT
ejpam-6251	445	8	·	·	PUNCT
ejpam-6251	445	9	·	·	PUNCT
ejpam-6251	446	1	+	+	NUM
ejpam-6251	446	2	1)(1−	1)(1−	NUM
ejpam-6251	446	3	ζ	ζ	NOUN
ejpam-6251	446	4	)	)	PUNCT
ejpam-6251	446	5	≤	≤	NOUN
ejpam-6251	446	6	ζµ	ζµ	PRON
ejpam-6251	446	7	π(ς0	π(ς0	NOUN
ejpam-6251	446	8	,	,	PUNCT
ejpam-6251	446	9	ϖ0	ϖ0	NOUN
ejpam-6251	446	10	,	,	PUNCT
ejpam-6251	446	11	ż	ż	NOUN
ejpam-6251	446	12	)	)	PUNCT
ejpam-6251	447	1	+	+	CCONJ
ejpam-6251	447	2	(	(	PUNCT
ejpam-6251	447	3	1−	1−	NUM
ejpam-6251	447	4	ζµ	ζµ	NOUN
ejpam-6251	447	5	)	)	PUNCT
ejpam-6251	447	6	we	we	PRON
ejpam-6251	447	7	obtain	obtain	VERB
ejpam-6251	447	8	1	1	NUM
ejpam-6251	447	9	ζµ	ζµ	NOUN
ejpam-6251	447	10	π(ς0,ϖ0,ż	π(ς0,ϖ0,ż	NOUN
ejpam-6251	447	11	)	)	PUNCT
ejpam-6251	448	1	+	+	CCONJ
ejpam-6251	448	2	(	(	PUNCT
ejpam-6251	448	3	1−	1−	NUM
ejpam-6251	448	4	ζµ	ζµ	NOUN
ejpam-6251	448	5	)	)	PUNCT
ejpam-6251	448	6	≤	≤	NOUN
ejpam-6251	448	7	π(ςµ	π(ςµ	PROPN
ejpam-6251	448	8	,	,	PUNCT
ejpam-6251	448	9	ϖµ	ϖµ	NOUN
ejpam-6251	448	10	,	,	PUNCT
ejpam-6251	448	11	ż	ż	NOUN
ejpam-6251	448	12	)	)	PUNCT
ejpam-6251	448	13	(	(	PUNCT
ejpam-6251	448	14	10	10	NUM
ejpam-6251	448	15	)	)	PUNCT
ejpam-6251	448	16	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	448	17	,	,	PUNCT
ejpam-6251	448	18	ϖµ	ϖµ	NOUN
ejpam-6251	448	19	,	,	PUNCT
ejpam-6251	448	20	ż	ż	NOUN
ejpam-6251	448	21	)	)	PUNCT
ejpam-6251	448	22	=	=	PUNCT
ejpam-6251	448	23	ψ(pςµ−1	ψ(pςµ−1	PROPN
ejpam-6251	448	24	,	,	PUNCT
ejpam-6251	448	25	pϖµ−1	pϖµ−1	PROPN
ejpam-6251	448	26	,	,	PUNCT
ejpam-6251	448	27	ż	ż	NOUN
ejpam-6251	448	28	)	)	PUNCT
ejpam-6251	448	29	≤	≤	NOUN
ejpam-6251	448	30	ζψ(ςµ−1	ζψ(ςµ−1	NOUN
ejpam-6251	448	31	,	,	PUNCT
ejpam-6251	448	32	ϖµ−1	ϖµ−1	ADJ
ejpam-6251	448	33	,	,	PUNCT
ejpam-6251	448	34	ż	ż	NOUN
ejpam-6251	448	35	)	)	PUNCT
ejpam-6251	448	36	=	=	SYM
ejpam-6251	448	37	ψ(pςµ−2	ψ(pςµ−2	PROPN
ejpam-6251	448	38	,	,	PUNCT
ejpam-6251	448	39	pϖµ−2	pϖµ−2	PROPN
ejpam-6251	448	40	,	,	PUNCT
ejpam-6251	448	41	ż	ż	NOUN
ejpam-6251	448	42	)	)	PUNCT
ejpam-6251	448	43	≤	≤	NUM
ejpam-6251	448	44	ζ2ψ(ςµ−2	ζ2ψ(ςµ−2	PROPN
ejpam-6251	448	45	,	,	PUNCT
ejpam-6251	448	46	ςϖ−2	ςϖ−2	PROPN
ejpam-6251	448	47	,	,	PUNCT
ejpam-6251	448	48	ż	ż	NOUN
ejpam-6251	448	49	)	)	PUNCT
ejpam-6251	448	50	≤	≤	NOUN
ejpam-6251	448	51	·	·	PUNCT
ejpam-6251	448	52	·	·	PUNCT
ejpam-6251	448	53	·	·	PUNCT
ejpam-6251	448	54	≤	≤	NUM
ejpam-6251	448	55	ζµψ(ς0	ζµψ(ς0	PROPN
ejpam-6251	448	56	,	,	PUNCT
ejpam-6251	448	57	ϖ0	ϖ0	NOUN
ejpam-6251	448	58	,	,	PUNCT
ejpam-6251	448	59	ż	ż	NOUN
ejpam-6251	448	60	)	)	PUNCT
ejpam-6251	448	61	,	,	PUNCT
ejpam-6251	448	62	(	(	PUNCT
ejpam-6251	448	63	11	11	NUM
ejpam-6251	448	64	)	)	PUNCT
ejpam-6251	448	65	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	448	66	,	,	PUNCT
ejpam-6251	448	67	ϖµ	ϖµ	NOUN
ejpam-6251	448	68	,	,	PUNCT
ejpam-6251	448	69	ż	ż	NOUN
ejpam-6251	448	70	)	)	PUNCT
ejpam-6251	448	71	=	=	SYM
ejpam-6251	449	1	ξ(pςµ−1	ξ(pςµ−1	PROPN
ejpam-6251	449	2	,	,	PUNCT
ejpam-6251	449	3	pϖµ−1	pϖµ−1	PROPN
ejpam-6251	449	4	,	,	PUNCT
ejpam-6251	449	5	ż	ż	NOUN
ejpam-6251	449	6	)	)	PUNCT
ejpam-6251	449	7	≤	≤	NOUN
ejpam-6251	449	8	ζξ(ςµ−1	ζξ(ςµ−1	VERB
ejpam-6251	449	9	,	,	PUNCT
ejpam-6251	449	10	ϖµ−1	ϖµ−1	ADJ
ejpam-6251	449	11	,	,	PUNCT
ejpam-6251	449	12	ż	ż	NOUN
ejpam-6251	449	13	)	)	PUNCT
ejpam-6251	449	14	=	=	SYM
ejpam-6251	449	15	ξ(pςµ−2	ξ(pςµ−2	PROPN
ejpam-6251	449	16	,	,	PUNCT
ejpam-6251	449	17	pϖµ−2	pϖµ−2	PROPN
ejpam-6251	449	18	,	,	PUNCT
ejpam-6251	449	19	ż	ż	NOUN
ejpam-6251	449	20	)	)	PUNCT
ejpam-6251	449	21	≤	≤	NOUN
ejpam-6251	450	1	ζ2ξ(ςµ−2	ζ2ξ(ςµ−2	PROPN
ejpam-6251	450	2	,	,	PUNCT
ejpam-6251	450	3	ϖµ−2	ϖµ−2	NOUN
ejpam-6251	450	4	,	,	PUNCT
ejpam-6251	450	5	ż	ż	NOUN
ejpam-6251	450	6	)	)	PUNCT
ejpam-6251	450	7	≤	≤	NOUN
ejpam-6251	450	8	·	·	PUNCT
ejpam-6251	450	9	·	·	PUNCT
ejpam-6251	450	10	·	·	PUNCT
ejpam-6251	451	1	≤	≤	ADV
ejpam-6251	451	2	ζµξ(ς0	ζµξ(ς0	ADV
ejpam-6251	451	3	,	,	PUNCT
ejpam-6251	451	4	ϖ0	ϖ0	NOUN
ejpam-6251	451	5	,	,	PUNCT
ejpam-6251	451	6	ż	ż	NOUN
ejpam-6251	451	7	)	)	PUNCT
ejpam-6251	451	8	(	(	PUNCT
ejpam-6251	451	9	12	12	NUM
ejpam-6251	451	10	)	)	PUNCT
ejpam-6251	451	11	and	and	CCONJ
ejpam-6251	451	12	1	1	NUM
ejpam-6251	451	13	ζµ	ζµ	NOUN
ejpam-6251	451	14	π(ς1,ϖ0,ż	π(ς1,ϖ0,ż	PROPN
ejpam-6251	451	15	)	)	PUNCT
ejpam-6251	452	1	+	+	CCONJ
ejpam-6251	452	2	(	(	PUNCT
ejpam-6251	452	3	1−	1−	NUM
ejpam-6251	452	4	ζµ	ζµ	NOUN
ejpam-6251	452	5	)	)	PUNCT
ejpam-6251	452	6	≤	≤	NOUN
ejpam-6251	452	7	π(ςµ+1	π(ςµ+1	PROPN
ejpam-6251	452	8	,	,	PUNCT
ejpam-6251	452	9	ϖµ	ϖµ	NOUN
ejpam-6251	452	10	,	,	PUNCT
ejpam-6251	452	11	ż	ż	NOUN
ejpam-6251	452	12	)	)	PUNCT
ejpam-6251	452	13	(	(	PUNCT
ejpam-6251	452	14	13	13	NUM
ejpam-6251	452	15	)	)	PUNCT
ejpam-6251	452	16	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	452	17	,	,	PUNCT
ejpam-6251	452	18	ϖµ	ϖµ	NOUN
ejpam-6251	452	19	,	,	PUNCT
ejpam-6251	452	20	ż	ż	NOUN
ejpam-6251	452	21	)	)	PUNCT
ejpam-6251	452	22	=	=	PUNCT
ejpam-6251	452	23	ψ(pςµ	ψ(pςµ	PROPN
ejpam-6251	452	24	,	,	PUNCT
ejpam-6251	452	25	pϖµ−1	pϖµ−1	PROPN
ejpam-6251	452	26	,	,	PUNCT
ejpam-6251	452	27	ż	ż	NOUN
ejpam-6251	452	28	)	)	PUNCT
ejpam-6251	452	29	≤	≤	PROPN
ejpam-6251	452	30	ζψ(ςµ	ζψ(ςµ	PROPN
ejpam-6251	452	31	,	,	PUNCT
ejpam-6251	452	32	ϖµ−1	ϖµ−1	PROPN
ejpam-6251	452	33	,	,	PUNCT
ejpam-6251	452	34	ż	ż	NOUN
ejpam-6251	452	35	)	)	PUNCT
ejpam-6251	452	36	=	=	SYM
ejpam-6251	452	37	ψ(pςµ−1	ψ(pςµ−1	PROPN
ejpam-6251	452	38	,	,	PUNCT
ejpam-6251	452	39	pϖµ−2	pϖµ−2	NOUN
ejpam-6251	452	40	,	,	PUNCT
ejpam-6251	452	41	ż	ż	NOUN
ejpam-6251	452	42	)	)	PUNCT
ejpam-6251	452	43	≤	≤	NOUN
ejpam-6251	452	44	ζ2ψ(ςµ−1	ζ2ψ(ςµ−1	PROPN
ejpam-6251	452	45	,	,	PUNCT
ejpam-6251	452	46	ςϖ−2	ςϖ−2	PROPN
ejpam-6251	452	47	,	,	PUNCT
ejpam-6251	452	48	ż	ż	NOUN
ejpam-6251	452	49	)	)	PUNCT
ejpam-6251	452	50	≤	≤	NOUN
ejpam-6251	452	51	·	·	PUNCT
ejpam-6251	452	52	·	·	PUNCT
ejpam-6251	452	53	·	·	PUNCT
ejpam-6251	453	1	≤	≤	NUM
ejpam-6251	453	2	ζµψ(ς1	ζµψ(ς1	NOUN
ejpam-6251	453	3	,	,	PUNCT
ejpam-6251	453	4	ϖ0	ϖ0	NOUN
ejpam-6251	453	5	,	,	PUNCT
ejpam-6251	453	6	ż	ż	NOUN
ejpam-6251	453	7	)	)	PUNCT
ejpam-6251	453	8	,	,	PUNCT
ejpam-6251	453	9	(	(	PUNCT
ejpam-6251	453	10	14	14	NUM
ejpam-6251	453	11	)	)	PUNCT
ejpam-6251	453	12	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	453	13	,	,	PUNCT
ejpam-6251	453	14	ϖµ	ϖµ	NOUN
ejpam-6251	453	15	,	,	PUNCT
ejpam-6251	453	16	ż	ż	NOUN
ejpam-6251	453	17	)	)	PUNCT
ejpam-6251	453	18	=	=	PUNCT
ejpam-6251	453	19	ξ(pςµ	ξ(pςµ	PROPN
ejpam-6251	453	20	,	,	PUNCT
ejpam-6251	453	21	pϖµ−1	pϖµ−1	PROPN
ejpam-6251	453	22	,	,	PUNCT
ejpam-6251	453	23	ż	ż	NOUN
ejpam-6251	453	24	)	)	PUNCT
ejpam-6251	453	25	≤	≤	PROPN
ejpam-6251	453	26	ζξ(ςµ	ζξ(ςµ	NOUN
ejpam-6251	453	27	,	,	PUNCT
ejpam-6251	453	28	ϖµ−1	ϖµ−1	ADJ
ejpam-6251	453	29	,	,	PUNCT
ejpam-6251	453	30	ż	ż	NOUN
ejpam-6251	453	31	)	)	PUNCT
ejpam-6251	453	32	=	=	SYM
ejpam-6251	453	33	ξ(pςµ−1	ξ(pςµ−1	PROPN
ejpam-6251	453	34	,	,	PUNCT
ejpam-6251	453	35	pϖµ−2	pϖµ−2	NOUN
ejpam-6251	453	36	,	,	PUNCT
ejpam-6251	453	37	ż	ż	NOUN
ejpam-6251	453	38	)	)	PUNCT
ejpam-6251	453	39	≤	≤	NOUN
ejpam-6251	454	1	ζ2ξ(ςµ−1	ζ2ξ(ςµ−1	PROPN
ejpam-6251	454	2	,	,	PUNCT
ejpam-6251	454	3	ϖµ−2	ϖµ−2	NOUN
ejpam-6251	454	4	,	,	PUNCT
ejpam-6251	454	5	ż	ż	NOUN
ejpam-6251	454	6	)	)	PUNCT
ejpam-6251	454	7	≤	≤	NOUN
ejpam-6251	454	8	·	·	PUNCT
ejpam-6251	454	9	·	·	PUNCT
ejpam-6251	454	10	·	·	PUNCT
ejpam-6251	455	1	≤	≤	NUM
ejpam-6251	455	2	ζµξ(ς1	ζµξ(ς1	NOUN
ejpam-6251	455	3	,	,	PUNCT
ejpam-6251	455	4	ϖ0	ϖ0	NOUN
ejpam-6251	455	5	,	,	PUNCT
ejpam-6251	455	6	ż	ż	NOUN
ejpam-6251	455	7	)	)	PUNCT
ejpam-6251	455	8	.	.	PUNCT
ejpam-6251	456	1	(	(	PUNCT
ejpam-6251	456	2	15	15	X
ejpam-6251	456	3	)	)	PUNCT
ejpam-6251	456	4	letting	let	VERB
ejpam-6251	456	5	µ	µ	PRON
ejpam-6251	456	6	<	<	X
ejpam-6251	456	7	m	m	PROPN
ejpam-6251	456	8	,	,	PUNCT
ejpam-6251	456	9	for	for	ADP
ejpam-6251	456	10	µ,m	µ,m	PROPN
ejpam-6251	456	11	∈	∈	PROPN
ejpam-6251	456	12	n.	n.	NOUN
ejpam-6251	456	13	then	then	ADV
ejpam-6251	456	14	,	,	PUNCT
ejpam-6251	456	15	π(ςµ	π(ςµ	PROPN
ejpam-6251	456	16	,	,	PUNCT
ejpam-6251	456	17	ϖm	ϖm	ADJ
ejpam-6251	456	18	,	,	PUNCT
ejpam-6251	456	19	ż	ż	NOUN
ejpam-6251	456	20	)	)	PUNCT
ejpam-6251	456	21	≥	≥	NOUN
ejpam-6251	456	22	π(ςµ	π(ςµ	PROPN
ejpam-6251	456	23	,	,	PUNCT
ejpam-6251	456	24	ϖµ	ϖµ	NOUN
ejpam-6251	456	25	,	,	PUNCT
ejpam-6251	456	26	ż	ż	NOUN
ejpam-6251	456	27	3	3	X
ejpam-6251	456	28	)	)	PUNCT
ejpam-6251	456	29	⋇π(ςµ+1	⋇π(ςµ+1	PROPN
ejpam-6251	456	30	,	,	PUNCT
ejpam-6251	456	31	ϖµ	ϖµ	NOUN
ejpam-6251	456	32	,	,	PUNCT
ejpam-6251	456	33	ż	ż	NOUN
ejpam-6251	456	34	3	3	X
ejpam-6251	456	35	)	)	PUNCT
ejpam-6251	456	36	⋇π(ςµ+1	⋇π(ςµ+1	PROPN
ejpam-6251	456	37	,	,	PUNCT
ejpam-6251	456	38	ϖm	ϖm	NOUN
ejpam-6251	456	39	,	,	PUNCT
ejpam-6251	456	40	ż	ż	NOUN
ejpam-6251	456	41	3	3	NUM
ejpam-6251	456	42	)	)	PUNCT
ejpam-6251	456	43	...	...	PUNCT
ejpam-6251	457	1	≥	≥	NUM
ejpam-6251	457	2	π(ςµ	π(ςµ	NOUN
ejpam-6251	457	3	,	,	PUNCT
ejpam-6251	457	4	ϖµ	ϖµ	NOUN
ejpam-6251	457	5	,	,	PUNCT
ejpam-6251	457	6	ż	ż	NOUN
ejpam-6251	457	7	3	3	X
ejpam-6251	457	8	)	)	PUNCT
ejpam-6251	457	9	⋇π(ςµ+1	⋇π(ςµ+1	PROPN
ejpam-6251	457	10	,	,	PUNCT
ejpam-6251	457	11	ϖµ	ϖµ	NOUN
ejpam-6251	457	12	,	,	PUNCT
ejpam-6251	457	13	ż	ż	NOUN
ejpam-6251	457	14	3	3	NUM
ejpam-6251	457	15	)	)	PUNCT
ejpam-6251	457	16	⋇	⋇	NOUN
ejpam-6251	457	17	·	·	PUNCT
ejpam-6251	457	18	·	·	PUNCT
ejpam-6251	458	1	·	·	PUNCT
ejpam-6251	458	2	⋇π(ςm−1	⋇π(ςm−1	PROPN
ejpam-6251	458	3	,	,	PUNCT
ejpam-6251	458	4	ϖm−1	ϖm−1	PROPN
ejpam-6251	458	5	,	,	PUNCT
ejpam-6251	458	6	ż	ż	PROPN
ejpam-6251	458	7	3m−1	3m−1	PROPN
ejpam-6251	458	8	)	)	PUNCT
ejpam-6251	459	1	⋇π(ςm	⋇π(ςm	PROPN
ejpam-6251	459	2	,	,	PUNCT
ejpam-6251	459	3	ϖm−1	ϖm−1	PROPN
ejpam-6251	459	4	,	,	PUNCT
ejpam-6251	459	5	ż	ż	NOUN
ejpam-6251	459	6	3m−1	3m−1	PROPN
ejpam-6251	459	7	)	)	PUNCT
ejpam-6251	459	8	⋇π(ςm	⋇π(ςm	PROPN
ejpam-6251	459	9	,	,	PUNCT
ejpam-6251	459	10	ϖm	ϖm	NOUN
ejpam-6251	459	11	,	,	PUNCT
ejpam-6251	459	12	ż	ż	NOUN
ejpam-6251	459	13	3m−1	3m−1	PROPN
ejpam-6251	459	14	)	)	PUNCT
ejpam-6251	459	15	,	,	PUNCT
ejpam-6251	459	16	r.	r.	PROPN
ejpam-6251	459	17	ramaswamy	ramaswamy	PROPN
ejpam-6251	459	18	/	/	SYM
ejpam-6251	459	19	eur	eur	PROPN
ejpam-6251	459	20	.	.	PUNCT
ejpam-6251	460	1	j.	j.	PROPN
ejpam-6251	460	2	pure	pure	PROPN
ejpam-6251	460	3	appl	appl	PROPN
ejpam-6251	460	4	.	.	PROPN
ejpam-6251	460	5	math	math	PROPN
ejpam-6251	460	6	,	,	PUNCT
ejpam-6251	460	7	18	18	NUM
ejpam-6251	460	8	(	(	PUNCT
ejpam-6251	460	9	4	4	NUM
ejpam-6251	460	10	)	)	PUNCT
ejpam-6251	460	11	(	(	PUNCT
ejpam-6251	460	12	2025	2025	NUM
ejpam-6251	460	13	)	)	PUNCT
ejpam-6251	460	14	,	,	PUNCT
ejpam-6251	460	15	6251	6251	NUM
ejpam-6251	460	16	23	23	NUM
ejpam-6251	460	17	of	of	ADP
ejpam-6251	460	18	40	40	NUM
ejpam-6251	460	19	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	460	20	,	,	PUNCT
ejpam-6251	460	21	ϖm	ϖm	ADJ
ejpam-6251	460	22	,	,	PUNCT
ejpam-6251	460	23	ż	ż	NOUN
ejpam-6251	460	24	)	)	PUNCT
ejpam-6251	460	25	≤	≤	PROPN
ejpam-6251	460	26	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	460	27	,	,	PUNCT
ejpam-6251	460	28	ϖµ	ϖµ	NOUN
ejpam-6251	460	29	,	,	PUNCT
ejpam-6251	460	30	ż	ż	NOUN
ejpam-6251	460	31	3	3	NUM
ejpam-6251	460	32	)	)	PUNCT
ejpam-6251	460	33	♢	♢	PROPN
ejpam-6251	460	34	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	460	35	,	,	PUNCT
ejpam-6251	460	36	ϖµ	ϖµ	NOUN
ejpam-6251	460	37	,	,	PUNCT
ejpam-6251	460	38	ż	ż	NOUN
ejpam-6251	460	39	3	3	NUM
ejpam-6251	460	40	)	)	PUNCT
ejpam-6251	460	41	♢	♢	PROPN
ejpam-6251	460	42	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	460	43	,	,	PUNCT
ejpam-6251	460	44	ϖm	ϖm	ADJ
ejpam-6251	460	45	,	,	PUNCT
ejpam-6251	460	46	ż	ż	NOUN
ejpam-6251	460	47	3	3	NUM
ejpam-6251	460	48	)	)	PUNCT
ejpam-6251	460	49	...	...	PUNCT
ejpam-6251	461	1	≤	≤	NUM
ejpam-6251	461	2	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	461	3	,	,	PUNCT
ejpam-6251	461	4	ϖµ	ϖµ	NOUN
ejpam-6251	461	5	,	,	PUNCT
ejpam-6251	461	6	ż	ż	NOUN
ejpam-6251	461	7	3	3	NUM
ejpam-6251	461	8	)	)	PUNCT
ejpam-6251	461	9	♢	♢	PROPN
ejpam-6251	461	10	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	461	11	,	,	PUNCT
ejpam-6251	461	12	ϖµ	ϖµ	NOUN
ejpam-6251	461	13	,	,	PUNCT
ejpam-6251	461	14	ż	ż	NOUN
ejpam-6251	461	15	3	3	NUM
ejpam-6251	461	16	)	)	PUNCT
ejpam-6251	461	17	♢	♢	PROPN
ejpam-6251	461	18	·	·	PUNCT
ejpam-6251	461	19	·	·	PUNCT
ejpam-6251	461	20	·	·	PUNCT
ejpam-6251	461	21	♢	♢	PROPN
ejpam-6251	461	22	ψ(ςm−1	ψ(ςm−1	PROPN
ejpam-6251	461	23	,	,	PUNCT
ejpam-6251	461	24	ϖm−1	ϖm−1	PROPN
ejpam-6251	461	25	,	,	PUNCT
ejpam-6251	461	26	ż	ż	PROPN
ejpam-6251	461	27	3m−1	3m−1	PROPN
ejpam-6251	461	28	)	)	PUNCT
ejpam-6251	461	29	♢	♢	PROPN
ejpam-6251	461	30	ψ(ςm	ψ(ςm	PROPN
ejpam-6251	461	31	,	,	PUNCT
ejpam-6251	461	32	ϖm−1	ϖm−1	PROPN
ejpam-6251	461	33	,	,	PUNCT
ejpam-6251	461	34	ż	ż	PROPN
ejpam-6251	461	35	3m−1	3m−1	PROPN
ejpam-6251	461	36	)	)	PUNCT
ejpam-6251	461	37	♢	♢	PROPN
ejpam-6251	461	38	ψ(ςm	ψ(ςm	PROPN
ejpam-6251	461	39	,	,	PUNCT
ejpam-6251	461	40	ϖm	ϖm	NOUN
ejpam-6251	461	41	,	,	PUNCT
ejpam-6251	461	42	ż	ż	NOUN
ejpam-6251	461	43	3m−1	3m−1	PROPN
ejpam-6251	461	44	)	)	PUNCT
ejpam-6251	461	45	,	,	PUNCT
ejpam-6251	461	46	and	and	CCONJ
ejpam-6251	461	47	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	461	48	,	,	PUNCT
ejpam-6251	461	49	ϖm	ϖm	ADJ
ejpam-6251	461	50	,	,	PUNCT
ejpam-6251	461	51	ż	ż	NOUN
ejpam-6251	461	52	)	)	PUNCT
ejpam-6251	461	53	≤	≤	NUM
ejpam-6251	461	54	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	461	55	,	,	PUNCT
ejpam-6251	461	56	ϖµ	ϖµ	NOUN
ejpam-6251	461	57	,	,	PUNCT
ejpam-6251	461	58	ż	ż	NOUN
ejpam-6251	461	59	3	3	NUM
ejpam-6251	461	60	)	)	PUNCT
ejpam-6251	461	61	♢	♢	PROPN
ejpam-6251	461	62	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	461	63	,	,	PUNCT
ejpam-6251	461	64	ϖµ	ϖµ	NOUN
ejpam-6251	461	65	,	,	PUNCT
ejpam-6251	461	66	ż	ż	NOUN
ejpam-6251	461	67	3	3	NUM
ejpam-6251	461	68	)	)	PUNCT
ejpam-6251	461	69	♢	♢	PROPN
ejpam-6251	461	70	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	461	71	,	,	PUNCT
ejpam-6251	461	72	ϖm	ϖm	ADJ
ejpam-6251	461	73	,	,	PUNCT
ejpam-6251	461	74	ż	ż	NOUN
ejpam-6251	461	75	3	3	NUM
ejpam-6251	461	76	)	)	PUNCT
ejpam-6251	461	77	...	...	PUNCT
ejpam-6251	462	1	≤	≤	NUM
ejpam-6251	462	2	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	462	3	,	,	PUNCT
ejpam-6251	462	4	ϖµ	ϖµ	NOUN
ejpam-6251	462	5	,	,	PUNCT
ejpam-6251	462	6	ż	ż	NOUN
ejpam-6251	462	7	3	3	NUM
ejpam-6251	462	8	)	)	PUNCT
ejpam-6251	462	9	♢	♢	PROPN
ejpam-6251	462	10	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	462	11	,	,	PUNCT
ejpam-6251	462	12	ϖµ	ϖµ	NOUN
ejpam-6251	462	13	,	,	PUNCT
ejpam-6251	462	14	ż	ż	NOUN
ejpam-6251	462	15	3	3	NUM
ejpam-6251	462	16	)	)	PUNCT
ejpam-6251	462	17	♢	♢	PROPN
ejpam-6251	462	18	·	·	PUNCT
ejpam-6251	462	19	·	·	PUNCT
ejpam-6251	462	20	·	·	PUNCT
ejpam-6251	462	21	♢	♢	PROPN
ejpam-6251	462	22	ξ(ςm−1	ξ(ςm−1	PROPN
ejpam-6251	462	23	,	,	PUNCT
ejpam-6251	462	24	ϖm−1	ϖm−1	PROPN
ejpam-6251	462	25	,	,	PUNCT
ejpam-6251	462	26	ż	ż	PROPN
ejpam-6251	462	27	3m−1	3m−1	PROPN
ejpam-6251	462	28	)	)	PUNCT
ejpam-6251	462	29	♢	♢	PROPN
ejpam-6251	462	30	ξ(ςm	ξ(ςm	PROPN
ejpam-6251	462	31	,	,	PUNCT
ejpam-6251	462	32	ϖm−1	ϖm−1	PROPN
ejpam-6251	462	33	,	,	PUNCT
ejpam-6251	462	34	ż	ż	PROPN
ejpam-6251	462	35	3m−1	3m−1	PROPN
ejpam-6251	462	36	)	)	PUNCT
ejpam-6251	462	37	♢	♢	PROPN
ejpam-6251	462	38	ξ(ςm	ξ(ςm	PROPN
ejpam-6251	462	39	,	,	PUNCT
ejpam-6251	462	40	ϖm	ϖm	NOUN
ejpam-6251	462	41	,	,	PUNCT
ejpam-6251	462	42	ż	ż	NOUN
ejpam-6251	462	43	3m−1	3m−1	PROPN
ejpam-6251	462	44	)	)	PUNCT
ejpam-6251	462	45	.	.	PUNCT
ejpam-6251	463	1	therefore	therefore	ADV
ejpam-6251	463	2	,	,	PUNCT
ejpam-6251	463	3	π(ςµ	π(ςµ	NUM
ejpam-6251	463	4	,	,	PUNCT
ejpam-6251	463	5	ϖm	ϖm	ADJ
ejpam-6251	463	6	,	,	PUNCT
ejpam-6251	463	7	ż	ż	NOUN
ejpam-6251	463	8	)	)	PUNCT
ejpam-6251	463	9	≥	≥	NOUN
ejpam-6251	463	10	π(ςµ	π(ςµ	PROPN
ejpam-6251	463	11	,	,	PUNCT
ejpam-6251	463	12	ϖµ	ϖµ	NOUN
ejpam-6251	463	13	,	,	PUNCT
ejpam-6251	463	14	ż	ż	NOUN
ejpam-6251	463	15	3	3	X
ejpam-6251	463	16	)	)	PUNCT
ejpam-6251	463	17	⋇π(ςµ+1	⋇π(ςµ+1	PROPN
ejpam-6251	463	18	,	,	PUNCT
ejpam-6251	463	19	ϖµ	ϖµ	NOUN
ejpam-6251	463	20	,	,	PUNCT
ejpam-6251	463	21	ż	ż	NOUN
ejpam-6251	463	22	3	3	NUM
ejpam-6251	463	23	)	)	PUNCT
ejpam-6251	463	24	⋇	⋇	NOUN
ejpam-6251	463	25	·	·	PUNCT
ejpam-6251	463	26	·	·	PUNCT
ejpam-6251	463	27	·	·	PUNCT
ejpam-6251	463	28	⋇π(ςm−1	⋇π(ςm−1	PROPN
ejpam-6251	463	29	,	,	PUNCT
ejpam-6251	463	30	ϖm−1	ϖm−1	PROPN
ejpam-6251	463	31	,	,	PUNCT
ejpam-6251	463	32	ż	ż	PROPN
ejpam-6251	463	33	3m−1	3m−1	PROPN
ejpam-6251	463	34	)	)	PUNCT
ejpam-6251	464	1	⋇π(ςm	⋇π(ςm	PROPN
ejpam-6251	464	2	,	,	PUNCT
ejpam-6251	464	3	ϖm−1	ϖm−1	PROPN
ejpam-6251	464	4	,	,	PUNCT
ejpam-6251	464	5	ż	ż	NOUN
ejpam-6251	464	6	3m−1	3m−1	PROPN
ejpam-6251	464	7	)	)	PUNCT
ejpam-6251	464	8	⋇π(ςm	⋇π(ςm	PROPN
ejpam-6251	464	9	,	,	PUNCT
ejpam-6251	464	10	ϖm	ϖm	NOUN
ejpam-6251	464	11	,	,	PUNCT
ejpam-6251	464	12	ż	ż	NOUN
ejpam-6251	464	13	3m−1	3m−1	PROPN
ejpam-6251	464	14	)	)	PUNCT
ejpam-6251	464	15	≥	≥	NOUN
ejpam-6251	464	16	1	1	NUM
ejpam-6251	464	17	ζµ	ζµ	ADP
ejpam-6251	464	18	π(ς0,ϖ0	π(ς0,ϖ0	ADV
ejpam-6251	464	19	,	,	PUNCT
ejpam-6251	464	20	ż	ż	NOUN
ejpam-6251	464	21	3	3	NUM
ejpam-6251	464	22	)	)	PUNCT
ejpam-6251	465	1	+	+	CCONJ
ejpam-6251	465	2	(	(	PUNCT
ejpam-6251	465	3	1−	1−	NUM
ejpam-6251	465	4	ζµ	ζµ	NOUN
ejpam-6251	465	5	)	)	PUNCT
ejpam-6251	465	6	⋇	⋇	NOUN
ejpam-6251	465	7	1	1	NUM
ejpam-6251	465	8	ζµ	ζµ	NOUN
ejpam-6251	465	9	π(ς1,ϖ0	π(ς1,ϖ0	AUX
ejpam-6251	465	10	,	,	PUNCT
ejpam-6251	465	11	ż	ż	NOUN
ejpam-6251	465	12	3	3	NUM
ejpam-6251	465	13	)	)	PUNCT
ejpam-6251	465	14	+	+	CCONJ
ejpam-6251	466	1	(	(	PUNCT
ejpam-6251	466	2	1−	1−	NUM
ejpam-6251	466	3	ζµ	ζµ	NOUN
ejpam-6251	466	4	)	)	PUNCT
ejpam-6251	466	5	⋇	⋇	NOUN
ejpam-6251	466	6	·	·	PUNCT
ejpam-6251	466	7	·	·	PUNCT
ejpam-6251	466	8	·	·	PUNCT
ejpam-6251	466	9	⋇	⋇	VERB
ejpam-6251	466	10	1	1	NUM
ejpam-6251	466	11	ζm−1	ζm−1	PROPN
ejpam-6251	466	12	π(ς0,ϖ0	π(ς0,ϖ0	ADV
ejpam-6251	466	13	,	,	PUNCT
ejpam-6251	466	14	ż	ż	NOUN
ejpam-6251	466	15	3m−1	3m−1	PROPN
ejpam-6251	466	16	)	)	PUNCT
ejpam-6251	466	17	+	+	CCONJ
ejpam-6251	466	18	(	(	PUNCT
ejpam-6251	466	19	1−	1−	NUM
ejpam-6251	466	20	ζm−1	ζm−1	PROPN
ejpam-6251	466	21	)	)	PUNCT
ejpam-6251	466	22	⋇	⋇	VERB
ejpam-6251	466	23	1	1	NUM
ejpam-6251	466	24	ζm−1	ζm−1	PROPN
ejpam-6251	466	25	π(ς1,ϖ0	π(ς1,ϖ0	AUX
ejpam-6251	466	26	,	,	PUNCT
ejpam-6251	466	27	ż	ż	NOUN
ejpam-6251	466	28	3m−1	3m−1	PROPN
ejpam-6251	466	29	)	)	PUNCT
ejpam-6251	467	1	+	+	CCONJ
ejpam-6251	467	2	(	(	PUNCT
ejpam-6251	467	3	1−	1−	NUM
ejpam-6251	467	4	ζm−1	ζm−1	PROPN
ejpam-6251	467	5	)	)	PUNCT
ejpam-6251	467	6	⋇	⋇	VERB
ejpam-6251	467	7	1	1	NUM
ejpam-6251	467	8	ζm	ζm	VERB
ejpam-6251	467	9	π(ς0,ϖ0	π(ς0,ϖ0	ADV
ejpam-6251	467	10	,	,	PUNCT
ejpam-6251	467	11	ż	ż	NOUN
ejpam-6251	467	12	3m−1	3m−1	PROPN
ejpam-6251	467	13	)	)	PUNCT
ejpam-6251	468	1	+	+	CCONJ
ejpam-6251	468	2	(	(	PUNCT
ejpam-6251	468	3	1−	1−	NUM
ejpam-6251	468	4	ζm	ζm	NOUN
ejpam-6251	468	5	)	)	PUNCT
ejpam-6251	468	6	,	,	PUNCT
ejpam-6251	468	7	ψ(ςµ	ψ(ςµ	PROPN
ejpam-6251	468	8	,	,	PUNCT
ejpam-6251	468	9	ϖm	ϖm	ADJ
ejpam-6251	468	10	,	,	PUNCT
ejpam-6251	468	11	ż	ż	NOUN
ejpam-6251	468	12	)	)	PUNCT
ejpam-6251	468	13	≤	≤	PROPN
ejpam-6251	468	14	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	468	15	,	,	PUNCT
ejpam-6251	468	16	ϖµ	ϖµ	NOUN
ejpam-6251	468	17	,	,	PUNCT
ejpam-6251	468	18	ż	ż	NOUN
ejpam-6251	468	19	3	3	NUM
ejpam-6251	468	20	)	)	PUNCT
ejpam-6251	468	21	♢	♢	PROPN
ejpam-6251	468	22	ψ(ςµ+1	ψ(ςµ+1	PROPN
ejpam-6251	468	23	,	,	PUNCT
ejpam-6251	468	24	ϖµ	ϖµ	NOUN
ejpam-6251	468	25	,	,	PUNCT
ejpam-6251	468	26	ż	ż	NOUN
ejpam-6251	468	27	3	3	NUM
ejpam-6251	468	28	)	)	PUNCT
ejpam-6251	468	29	♢	♢	PROPN
ejpam-6251	468	30	·	·	PUNCT
ejpam-6251	468	31	·	·	PUNCT
ejpam-6251	468	32	·	·	PUNCT
ejpam-6251	468	33	♢	♢	PROPN
ejpam-6251	468	34	ψ(ςm−1	ψ(ςm−1	PROPN
ejpam-6251	468	35	,	,	PUNCT
ejpam-6251	468	36	ϖm−1	ϖm−1	PROPN
ejpam-6251	468	37	,	,	PUNCT
ejpam-6251	468	38	ż	ż	PROPN
ejpam-6251	468	39	3m−1	3m−1	PROPN
ejpam-6251	468	40	)	)	PUNCT
ejpam-6251	468	41	♢	♢	PROPN
ejpam-6251	468	42	ψ(ςm	ψ(ςm	PROPN
ejpam-6251	468	43	,	,	PUNCT
ejpam-6251	468	44	ϖm−1	ϖm−1	PROPN
ejpam-6251	468	45	,	,	PUNCT
ejpam-6251	468	46	ż	ż	PROPN
ejpam-6251	468	47	3m−1	3m−1	PROPN
ejpam-6251	468	48	)	)	PUNCT
ejpam-6251	468	49	♢	♢	PROPN
ejpam-6251	468	50	ψ(ςm	ψ(ςm	PROPN
ejpam-6251	468	51	,	,	PUNCT
ejpam-6251	468	52	ϖm	ϖm	NOUN
ejpam-6251	468	53	,	,	PUNCT
ejpam-6251	468	54	ż	ż	NOUN
ejpam-6251	468	55	3m−1	3m−1	PROPN
ejpam-6251	468	56	)	)	PUNCT
ejpam-6251	468	57	≤	≤	PROPN
ejpam-6251	468	58	ζµψ(ς0	ζµψ(ς0	PROPN
ejpam-6251	468	59	,	,	PUNCT
ejpam-6251	468	60	ϖ0	ϖ0	NOUN
ejpam-6251	468	61	,	,	PUNCT
ejpam-6251	468	62	ż	ż	NOUN
ejpam-6251	468	63	3	3	NUM
ejpam-6251	468	64	)	)	PUNCT
ejpam-6251	469	1	♢	♢	PROPN
ejpam-6251	469	2	ζµψ(ς1	ζµψ(ς1	NOUN
ejpam-6251	469	3	,	,	PUNCT
ejpam-6251	469	4	ϖ0	ϖ0	NOUN
ejpam-6251	469	5	,	,	PUNCT
ejpam-6251	469	6	ż	ż	NOUN
ejpam-6251	469	7	3m−1	3m−1	PROPN
ejpam-6251	469	8	)	)	PUNCT
ejpam-6251	469	9	♢	♢	PROPN
ejpam-6251	469	10	·	·	PUNCT
ejpam-6251	469	11	·	·	PUNCT
ejpam-6251	469	12	·	·	PUNCT
ejpam-6251	469	13	♢	♢	PROPN
ejpam-6251	469	14	ζm−1ψ(ς0	ζm−1ψ(ς0	PROPN
ejpam-6251	469	15	,	,	PUNCT
ejpam-6251	469	16	ϖ0	ϖ0	NOUN
ejpam-6251	469	17	,	,	PUNCT
ejpam-6251	469	18	ż	ż	PROPN
ejpam-6251	469	19	3m−1	3m−1	PROPN
ejpam-6251	469	20	)	)	PUNCT
ejpam-6251	469	21	♢	♢	PROPN
ejpam-6251	469	22	ζm−1ψ(ς1	ζm−1ψ(ς1	NOUN
ejpam-6251	469	23	,	,	PUNCT
ejpam-6251	469	24	ϖ0	ϖ0	NOUN
ejpam-6251	469	25	,	,	PUNCT
ejpam-6251	469	26	ż	ż	PROPN
ejpam-6251	469	27	3m−1	3m−1	PROPN
ejpam-6251	469	28	)	)	PUNCT
ejpam-6251	469	29	♢	♢	PROPN
ejpam-6251	469	30	ζmψ(ς0	ζmψ(ς0	PROPN
ejpam-6251	469	31	,	,	PUNCT
ejpam-6251	469	32	ϖ0	ϖ0	NOUN
ejpam-6251	469	33	,	,	PUNCT
ejpam-6251	469	34	ż	ż	NOUN
ejpam-6251	469	35	3m−1	3m−1	PROPN
ejpam-6251	469	36	)	)	PUNCT
ejpam-6251	469	37	,	,	PUNCT
ejpam-6251	469	38	and	and	CCONJ
ejpam-6251	469	39	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	469	40	,	,	PUNCT
ejpam-6251	469	41	ϖm	ϖm	ADJ
ejpam-6251	469	42	,	,	PUNCT
ejpam-6251	469	43	ż	ż	NOUN
ejpam-6251	469	44	)	)	PUNCT
ejpam-6251	469	45	≤	≤	NUM
ejpam-6251	469	46	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	469	47	,	,	PUNCT
ejpam-6251	469	48	ϖµ	ϖµ	NOUN
ejpam-6251	469	49	,	,	PUNCT
ejpam-6251	469	50	ż	ż	NOUN
ejpam-6251	469	51	3	3	NUM
ejpam-6251	469	52	)	)	PUNCT
ejpam-6251	469	53	♢	♢	PROPN
ejpam-6251	469	54	ξ(ςµ+1	ξ(ςµ+1	NOUN
ejpam-6251	469	55	,	,	PUNCT
ejpam-6251	469	56	ϖµ	ϖµ	NOUN
ejpam-6251	469	57	,	,	PUNCT
ejpam-6251	469	58	ż	ż	NOUN
ejpam-6251	469	59	3	3	NUM
ejpam-6251	469	60	)	)	PUNCT
ejpam-6251	469	61	♢	♢	PROPN
ejpam-6251	469	62	·	·	PUNCT
ejpam-6251	469	63	·	·	PUNCT
ejpam-6251	469	64	·	·	PUNCT
ejpam-6251	469	65	♢	♢	PROPN
ejpam-6251	469	66	ξ(ςm−1	ξ(ςm−1	PROPN
ejpam-6251	469	67	,	,	PUNCT
ejpam-6251	469	68	ϖm−1	ϖm−1	PROPN
ejpam-6251	469	69	,	,	PUNCT
ejpam-6251	469	70	ż	ż	PROPN
ejpam-6251	469	71	3m−1	3m−1	PROPN
ejpam-6251	469	72	)	)	PUNCT
ejpam-6251	469	73	r.	r.	PROPN
ejpam-6251	469	74	ramaswamy	ramaswamy	PROPN
ejpam-6251	469	75	/	/	SYM
ejpam-6251	469	76	eur	eur	PROPN
ejpam-6251	469	77	.	.	PUNCT
ejpam-6251	470	1	j.	j.	PROPN
ejpam-6251	470	2	pure	pure	PROPN
ejpam-6251	470	3	appl	appl	PROPN
ejpam-6251	470	4	.	.	PROPN
ejpam-6251	470	5	math	math	PROPN
ejpam-6251	470	6	,	,	PUNCT
ejpam-6251	470	7	18	18	NUM
ejpam-6251	470	8	(	(	PUNCT
ejpam-6251	470	9	4	4	NUM
ejpam-6251	470	10	)	)	PUNCT
ejpam-6251	470	11	(	(	PUNCT
ejpam-6251	470	12	2025	2025	NUM
ejpam-6251	470	13	)	)	PUNCT
ejpam-6251	470	14	,	,	PUNCT
ejpam-6251	470	15	6251	6251	NUM
ejpam-6251	470	16	24	24	NUM
ejpam-6251	470	17	of	of	ADP
ejpam-6251	470	18	40	40	NUM
ejpam-6251	470	19	♢	♢	NOUN
ejpam-6251	470	20	ξ(ςm	ξ(ςm	PROPN
ejpam-6251	470	21	,	,	PUNCT
ejpam-6251	470	22	ϖm−1	ϖm−1	PROPN
ejpam-6251	470	23	,	,	PUNCT
ejpam-6251	470	24	ż	ż	PROPN
ejpam-6251	470	25	3m−1	3m−1	PROPN
ejpam-6251	470	26	)	)	PUNCT
ejpam-6251	470	27	♢	♢	PROPN
ejpam-6251	470	28	ξ(ςm	ξ(ςm	PROPN
ejpam-6251	470	29	,	,	PUNCT
ejpam-6251	470	30	ϖm	ϖm	NOUN
ejpam-6251	470	31	,	,	PUNCT
ejpam-6251	470	32	ż	ż	NOUN
ejpam-6251	470	33	3m−1	3m−1	PROPN
ejpam-6251	470	34	)	)	PUNCT
ejpam-6251	470	35	≤	≤	NOUN
ejpam-6251	470	36	ζµξ(ς0	ζµξ(ς0	ADV
ejpam-6251	470	37	,	,	PUNCT
ejpam-6251	470	38	ϖ0	ϖ0	NOUN
ejpam-6251	470	39	,	,	PUNCT
ejpam-6251	470	40	ż	ż	NOUN
ejpam-6251	470	41	3	3	NUM
ejpam-6251	470	42	)	)	PUNCT
ejpam-6251	470	43	♢	♢	PROPN
ejpam-6251	470	44	ζµξ(ς1	ζµξ(ς1	NOUN
ejpam-6251	470	45	,	,	PUNCT
ejpam-6251	470	46	ϖ0	ϖ0	NOUN
ejpam-6251	470	47	,	,	PUNCT
ejpam-6251	470	48	ż	ż	NOUN
ejpam-6251	470	49	3m−1	3m−1	PROPN
ejpam-6251	470	50	)	)	PUNCT
ejpam-6251	470	51	♢	♢	PROPN
ejpam-6251	470	52	·	·	PUNCT
ejpam-6251	470	53	·	·	PUNCT
ejpam-6251	470	54	·	·	PUNCT
ejpam-6251	470	55	♢	♢	PROPN
ejpam-6251	470	56	ζm−1ξ(ς0	ζm−1ξ(ς0	PROPN
ejpam-6251	470	57	,	,	PUNCT
ejpam-6251	470	58	ϖ0	ϖ0	NOUN
ejpam-6251	470	59	,	,	PUNCT
ejpam-6251	470	60	ż	ż	PROPN
ejpam-6251	470	61	3m−1	3m−1	PROPN
ejpam-6251	470	62	)	)	PUNCT
ejpam-6251	470	63	♢	♢	PROPN
ejpam-6251	470	64	ζm−1ξ(ς1	ζm−1ξ(ς1	NOUN
ejpam-6251	470	65	,	,	PUNCT
ejpam-6251	470	66	ϖ0	ϖ0	NOUN
ejpam-6251	470	67	,	,	PUNCT
ejpam-6251	470	68	ż	ż	PROPN
ejpam-6251	470	69	3m−1	3m−1	PROPN
ejpam-6251	470	70	)	)	PUNCT
ejpam-6251	470	71	♢	♢	PROPN
ejpam-6251	470	72	ζmξ(ς0	ζmξ(ς0	PROPN
ejpam-6251	470	73	,	,	PUNCT
ejpam-6251	470	74	ϖ0	ϖ0	NOUN
ejpam-6251	470	75	,	,	PUNCT
ejpam-6251	470	76	ż	ż	NOUN
ejpam-6251	470	77	3m−1	3m−1	PROPN
ejpam-6251	470	78	)	)	PUNCT
ejpam-6251	470	79	.	.	PUNCT
ejpam-6251	471	1	which	which	PRON
ejpam-6251	471	2	implies	imply	VERB
ejpam-6251	471	3	that	that	SCONJ
ejpam-6251	471	4	,	,	PUNCT
ejpam-6251	471	5	π(ςµ	π(ςµ	NUM
ejpam-6251	471	6	,	,	PUNCT
ejpam-6251	471	7	ϖm	ϖm	ADJ
ejpam-6251	471	8	,	,	PUNCT
ejpam-6251	471	9	ż	ż	NOUN
ejpam-6251	471	10	)	)	PUNCT
ejpam-6251	471	11	≥	≥	NOUN
ejpam-6251	471	12	1	1	NUM
ejpam-6251	471	13	ζµ	ζµ	ADP
ejpam-6251	471	14	π(ς0,ϖ0	π(ς0,ϖ0	ADV
ejpam-6251	471	15	,	,	PUNCT
ejpam-6251	471	16	ż	ż	NOUN
ejpam-6251	471	17	3	3	NUM
ejpam-6251	471	18	)	)	PUNCT
ejpam-6251	472	1	+	+	CCONJ
ejpam-6251	472	2	(	(	PUNCT
ejpam-6251	472	3	1−	1−	NUM
ejpam-6251	472	4	ζµ	ζµ	NOUN
ejpam-6251	472	5	)	)	PUNCT
ejpam-6251	472	6	⋇	⋇	NOUN
ejpam-6251	472	7	1	1	NUM
ejpam-6251	472	8	ζµ	ζµ	NOUN
ejpam-6251	472	9	π(ς1,ϖ0	π(ς1,ϖ0	AUX
ejpam-6251	472	10	,	,	PUNCT
ejpam-6251	472	11	ż	ż	NOUN
ejpam-6251	472	12	3	3	NUM
ejpam-6251	472	13	)	)	PUNCT
ejpam-6251	472	14	+	+	CCONJ
ejpam-6251	473	1	(	(	PUNCT
ejpam-6251	473	2	1−	1−	NUM
ejpam-6251	473	3	ζµ	ζµ	NOUN
ejpam-6251	473	4	)	)	PUNCT
ejpam-6251	473	5	⋇	⋇	NOUN
ejpam-6251	473	6	·	·	PUNCT
ejpam-6251	473	7	·	·	PUNCT
ejpam-6251	473	8	·	·	PUNCT
ejpam-6251	473	9	⋇	⋇	VERB
ejpam-6251	473	10	1	1	NUM
ejpam-6251	473	11	ζm−1	ζm−1	PROPN
ejpam-6251	473	12	π(ς0,ϖ0	π(ς0,ϖ0	ADV
ejpam-6251	473	13	,	,	PUNCT
ejpam-6251	473	14	ż	ż	NOUN
ejpam-6251	473	15	3m−1	3m−1	PROPN
ejpam-6251	473	16	)	)	PUNCT
ejpam-6251	473	17	+	+	CCONJ
ejpam-6251	473	18	(	(	PUNCT
ejpam-6251	473	19	1−	1−	NUM
ejpam-6251	473	20	ζm−1	ζm−1	PROPN
ejpam-6251	473	21	)	)	PUNCT
ejpam-6251	473	22	⋇	⋇	VERB
ejpam-6251	473	23	1	1	NUM
ejpam-6251	473	24	ζm−1	ζm−1	PROPN
ejpam-6251	473	25	π(ς1,ϖ0	π(ς1,ϖ0	AUX
ejpam-6251	473	26	,	,	PUNCT
ejpam-6251	473	27	ż	ż	NOUN
ejpam-6251	473	28	3m−1	3m−1	PROPN
ejpam-6251	473	29	)	)	PUNCT
ejpam-6251	474	1	+	+	CCONJ
ejpam-6251	474	2	(	(	PUNCT
ejpam-6251	474	3	1−	1−	NUM
ejpam-6251	474	4	ζm−1	ζm−1	PROPN
ejpam-6251	474	5	)	)	PUNCT
ejpam-6251	474	6	⋇	⋇	VERB
ejpam-6251	474	7	1	1	NUM
ejpam-6251	474	8	ζm	ζm	VERB
ejpam-6251	474	9	π(ς0,ϖ0	π(ς0,ϖ0	ADV
ejpam-6251	474	10	,	,	PUNCT
ejpam-6251	474	11	ż	ż	NOUN
ejpam-6251	474	12	3m−1	3m−1	PROPN
ejpam-6251	474	13	)	)	PUNCT
ejpam-6251	475	1	+	+	CCONJ
ejpam-6251	475	2	(	(	PUNCT
ejpam-6251	475	3	1−	1−	NUM
ejpam-6251	475	4	ζm	ζm	NOUN
ejpam-6251	475	5	)	)	PUNCT
ejpam-6251	475	6	,	,	PUNCT
ejpam-6251	475	7	ψ(ςµ	ψ(ςµ	PROPN
ejpam-6251	475	8	,	,	PUNCT
ejpam-6251	475	9	ϖm	ϖm	ADJ
ejpam-6251	475	10	,	,	PUNCT
ejpam-6251	475	11	ż	ż	NOUN
ejpam-6251	475	12	)	)	PUNCT
ejpam-6251	475	13	≤	≤	NUM
ejpam-6251	475	14	ζµψ(ς0	ζµψ(ς0	PROPN
ejpam-6251	475	15	,	,	PUNCT
ejpam-6251	475	16	ϖ0	ϖ0	NOUN
ejpam-6251	475	17	,	,	PUNCT
ejpam-6251	475	18	ż	ż	NOUN
ejpam-6251	475	19	3	3	NUM
ejpam-6251	475	20	)	)	PUNCT
ejpam-6251	476	1	♢	♢	PROPN
ejpam-6251	476	2	ζµψ(ς1	ζµψ(ς1	NOUN
ejpam-6251	476	3	,	,	PUNCT
ejpam-6251	476	4	ϖ0	ϖ0	NOUN
ejpam-6251	476	5	,	,	PUNCT
ejpam-6251	476	6	ż	ż	NOUN
ejpam-6251	476	7	3m−1	3m−1	PROPN
ejpam-6251	476	8	)	)	PUNCT
ejpam-6251	476	9	♢	♢	PROPN
ejpam-6251	476	10	·	·	PUNCT
ejpam-6251	476	11	·	·	PUNCT
ejpam-6251	476	12	·	·	PUNCT
ejpam-6251	476	13	♢	♢	PROPN
ejpam-6251	476	14	ζm−1ψ(ς0	ζm−1ψ(ς0	PROPN
ejpam-6251	476	15	,	,	PUNCT
ejpam-6251	476	16	ϖ0	ϖ0	NOUN
ejpam-6251	476	17	,	,	PUNCT
ejpam-6251	476	18	ż	ż	PROPN
ejpam-6251	476	19	3m−1	3m−1	PROPN
ejpam-6251	476	20	)	)	PUNCT
ejpam-6251	476	21	♢	♢	PROPN
ejpam-6251	476	22	ζm−1ψ(ς1	ζm−1ψ(ς1	NOUN
ejpam-6251	476	23	,	,	PUNCT
ejpam-6251	476	24	ϖ0	ϖ0	NOUN
ejpam-6251	476	25	,	,	PUNCT
ejpam-6251	476	26	ż	ż	PROPN
ejpam-6251	476	27	3m−1	3m−1	PROPN
ejpam-6251	476	28	)	)	PUNCT
ejpam-6251	476	29	♢	♢	PROPN
ejpam-6251	476	30	ζmψ(ς0	ζmψ(ς0	PROPN
ejpam-6251	476	31	,	,	PUNCT
ejpam-6251	476	32	ϖ0	ϖ0	NOUN
ejpam-6251	476	33	,	,	PUNCT
ejpam-6251	476	34	ż	ż	NOUN
ejpam-6251	476	35	3m−1	3m−1	PROPN
ejpam-6251	476	36	)	)	PUNCT
ejpam-6251	476	37	,	,	PUNCT
ejpam-6251	476	38	and	and	CCONJ
ejpam-6251	476	39	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	476	40	,	,	PUNCT
ejpam-6251	476	41	ϖm	ϖm	ADJ
ejpam-6251	476	42	,	,	PUNCT
ejpam-6251	476	43	ż	ż	NOUN
ejpam-6251	476	44	)	)	PUNCT
ejpam-6251	476	45	≤	≤	NOUN
ejpam-6251	476	46	ζµξ(ς0	ζµξ(ς0	ADV
ejpam-6251	476	47	,	,	PUNCT
ejpam-6251	476	48	ϖ0	ϖ0	NOUN
ejpam-6251	476	49	,	,	PUNCT
ejpam-6251	476	50	ż	ż	NOUN
ejpam-6251	476	51	3	3	NUM
ejpam-6251	476	52	)	)	PUNCT
ejpam-6251	476	53	♢	♢	PROPN
ejpam-6251	476	54	ζµξ(ς1	ζµξ(ς1	NOUN
ejpam-6251	476	55	,	,	PUNCT
ejpam-6251	476	56	ϖ0	ϖ0	NOUN
ejpam-6251	476	57	,	,	PUNCT
ejpam-6251	476	58	ż	ż	NOUN
ejpam-6251	476	59	3m−1	3m−1	PROPN
ejpam-6251	476	60	)	)	PUNCT
ejpam-6251	476	61	♢	♢	PROPN
ejpam-6251	476	62	·	·	PUNCT
ejpam-6251	476	63	·	·	PUNCT
ejpam-6251	477	1	·	·	PUNCT
ejpam-6251	477	2	♢	♢	PROPN
ejpam-6251	477	3	ζm−1ξ(ς0	ζm−1ξ(ς0	PROPN
ejpam-6251	477	4	,	,	PUNCT
ejpam-6251	477	5	ϖ0	ϖ0	NOUN
ejpam-6251	477	6	,	,	PUNCT
ejpam-6251	477	7	ż	ż	PROPN
ejpam-6251	477	8	3m−1	3m−1	PROPN
ejpam-6251	477	9	)	)	PUNCT
ejpam-6251	477	10	♢	♢	PROPN
ejpam-6251	477	11	ζm−1ξ(ς1	ζm−1ξ(ς1	NOUN
ejpam-6251	477	12	,	,	PUNCT
ejpam-6251	477	13	ϖ0	ϖ0	NOUN
ejpam-6251	477	14	,	,	PUNCT
ejpam-6251	477	15	ż	ż	PROPN
ejpam-6251	477	16	3m−1	3m−1	PROPN
ejpam-6251	477	17	)	)	PUNCT
ejpam-6251	477	18	♢	♢	PROPN
ejpam-6251	477	19	ζmξ(ς0	ζmξ(ς0	PROPN
ejpam-6251	477	20	,	,	PUNCT
ejpam-6251	477	21	ϖ0	ϖ0	NOUN
ejpam-6251	477	22	,	,	PUNCT
ejpam-6251	477	23	ż	ż	NOUN
ejpam-6251	477	24	3m−1	3m−1	PROPN
ejpam-6251	477	25	)	)	PUNCT
ejpam-6251	477	26	.	.	PUNCT
ejpam-6251	478	1	as	as	ADP
ejpam-6251	478	2	µ,m	µ,m	PROPN
ejpam-6251	478	3	→	→	SYM
ejpam-6251	478	4	+	+	NOUN
ejpam-6251	478	5	∞	∞	PROPN
ejpam-6251	478	6	,	,	PUNCT
ejpam-6251	478	7	we	we	PRON
ejpam-6251	478	8	deduce	deduce	VERB
ejpam-6251	478	9	lim	lim	PROPN
ejpam-6251	478	10	µ,m→+∞	µ,m→+∞	NUM
ejpam-6251	478	11	π(ςµ	π(ςµ	PROPN
ejpam-6251	478	12	,	,	PUNCT
ejpam-6251	478	13	ϖm	ϖm	ADJ
ejpam-6251	478	14	,	,	PUNCT
ejpam-6251	478	15	ż	ż	NOUN
ejpam-6251	478	16	)	)	PUNCT
ejpam-6251	478	17	=	=	PUNCT
ejpam-6251	479	1	1⋇	1⋇	NUM
ejpam-6251	479	2	1⋇	1⋇	NUM
ejpam-6251	479	3	·	·	PUNCT
ejpam-6251	479	4	·	·	PUNCT
ejpam-6251	479	5	·	·	PUNCT
ejpam-6251	479	6	⋇	⋇	NOUN
ejpam-6251	479	7	1	1	NUM
ejpam-6251	479	8	=	=	SYM
ejpam-6251	479	9	1	1	NUM
ejpam-6251	479	10	,	,	PUNCT
ejpam-6251	479	11	lim	lim	PROPN
ejpam-6251	479	12	µ,m→+∞	µ,m→+∞	NUM
ejpam-6251	479	13	ψ(ςµ	ψ(ςµ	NOUN
ejpam-6251	479	14	,	,	PUNCT
ejpam-6251	479	15	ϖm	ϖm	ADJ
ejpam-6251	479	16	,	,	PUNCT
ejpam-6251	479	17	ż	ż	NOUN
ejpam-6251	479	18	)	)	PUNCT
ejpam-6251	479	19	=	=	SYM
ejpam-6251	479	20	0	0	NUM
ejpam-6251	479	21	♢	♢	PROPN
ejpam-6251	479	22	0	0	PROPN
ejpam-6251	479	23	♢	♢	PROPN
ejpam-6251	479	24	·	·	PUNCT
ejpam-6251	479	25	·	·	PUNCT
ejpam-6251	479	26	·	·	PUNCT
ejpam-6251	479	27	♢	♢	PROPN
ejpam-6251	479	28	0	0	PROPN
ejpam-6251	479	29	=	=	SYM
ejpam-6251	479	30	0	0	PROPN
ejpam-6251	479	31	and	and	CCONJ
ejpam-6251	479	32	lim	lim	PROPN
ejpam-6251	479	33	µ,m→+∞	µ,m→+∞	NUM
ejpam-6251	479	34	ξ(ςµ	ξ(ςµ	NUM
ejpam-6251	479	35	,	,	PUNCT
ejpam-6251	479	36	ϖm	ϖm	ADJ
ejpam-6251	479	37	,	,	PUNCT
ejpam-6251	479	38	ż	ż	NOUN
ejpam-6251	479	39	)	)	PUNCT
ejpam-6251	479	40	=	=	SYM
ejpam-6251	479	41	0	0	NUM
ejpam-6251	479	42	♢	♢	PROPN
ejpam-6251	479	43	0	0	PROPN
ejpam-6251	479	44	♢	♢	PROPN
ejpam-6251	479	45	·	·	PUNCT
ejpam-6251	479	46	·	·	PUNCT
ejpam-6251	479	47	·	·	PUNCT
ejpam-6251	479	48	♢	♢	PROPN
ejpam-6251	479	49	0	0	PROPN
ejpam-6251	479	50	=	=	SYM
ejpam-6251	479	51	0	0	PROPN
ejpam-6251	479	52	.	.	NOUN
ejpam-6251	479	53	which	which	PRON
ejpam-6251	479	54	implies	imply	VERB
ejpam-6251	479	55	that	that	PRON
ejpam-6251	479	56	bisequence	bisequence	NOUN
ejpam-6251	479	57	(	(	PUNCT
ejpam-6251	479	58	ςµ	ςµ	NOUN
ejpam-6251	479	59	,	,	PUNCT
ejpam-6251	479	60	ϖµ	ϖµ	NOUN
ejpam-6251	479	61	)	)	PUNCT
ejpam-6251	479	62	is	be	AUX
ejpam-6251	479	63	a	a	DET
ejpam-6251	479	64	cauchy	cauchy	ADJ
ejpam-6251	479	65	bisequence	bisequence	NOUN
ejpam-6251	479	66	.	.	PUNCT
ejpam-6251	480	1	since	since	SCONJ
ejpam-6251	480	2	(	(	PUNCT
ejpam-6251	480	3	𭟋	𭟋	PROPN
ejpam-6251	480	4	,	,	PUNCT
ejpam-6251	480	5	s	s	PROPN
ejpam-6251	480	6	,	,	PUNCT
ejpam-6251	480	7	π	π	PROPN
ejpam-6251	480	8	,	,	PUNCT
ejpam-6251	480	9	ψ	ψ	PROPN
ejpam-6251	480	10	,	,	PUNCT
ejpam-6251	480	11	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	480	12	,	,	PUNCT
ejpam-6251	480	13	♢	♢	PROPN
ejpam-6251	480	14	)	)	PUNCT
ejpam-6251	480	15	is	be	AUX
ejpam-6251	480	16	a	a	DET
ejpam-6251	480	17	complete	complete	ADJ
ejpam-6251	480	18	nbms	nbms	NOUN
ejpam-6251	480	19	.	.	PUNCT
ejpam-6251	481	1	then	then	ADV
ejpam-6251	481	2	,	,	PUNCT
ejpam-6251	481	3	{	{	PUNCT
ejpam-6251	481	4	ςµ	ςµ	NOUN
ejpam-6251	481	5	}	}	PUNCT
ejpam-6251	481	6	→	→	SYM
ejpam-6251	481	7	ς	ς	PROPN
ejpam-6251	481	8	and	and	CCONJ
ejpam-6251	481	9	{	{	PUNCT
ejpam-6251	481	10	ϖµ	ϖµ	NOUN
ejpam-6251	481	11	}	}	PUNCT
ejpam-6251	481	12	→	→	SYM
ejpam-6251	481	13	ς	ς	PROPN
ejpam-6251	481	14	,	,	PUNCT
ejpam-6251	481	15	where	where	SCONJ
ejpam-6251	481	16	ς	ς	PROPN
ejpam-6251	481	17	∈	∈	PROPN
ejpam-6251	481	18	𭟋	𭟋	ADP
ejpam-6251	481	19	∩	∩	NOUN
ejpam-6251	481	20	s.	s.	PROPN
ejpam-6251	481	21	using	use	VERB
ejpam-6251	481	22	v	v	NOUN
ejpam-6251	481	23	,	,	PUNCT
ejpam-6251	481	24	x	x	PUNCT
ejpam-6251	481	25	and	and	CCONJ
ejpam-6251	481	26	xv	xv	PROPN
ejpam-6251	481	27	,	,	PUNCT
ejpam-6251	481	28	we	we	PRON
ejpam-6251	481	29	get	get	VERB
ejpam-6251	481	30	π(ς	π(ς	PROPN
ejpam-6251	481	31	,	,	PUNCT
ejpam-6251	481	32	pς	pς	ADP
ejpam-6251	481	33	,	,	PUNCT
ejpam-6251	481	34	ż	ż	NOUN
ejpam-6251	481	35	)	)	PUNCT
ejpam-6251	481	36	≥	≥	NOUN
ejpam-6251	481	37	π	π	PROPN
ejpam-6251	481	38	(	(	PUNCT
ejpam-6251	481	39	ς	ς	PROPN
ejpam-6251	481	40	,	,	PUNCT
ejpam-6251	481	41	ςµ+1	ςµ+1	NUM
ejpam-6251	481	42	,	,	PUNCT
ejpam-6251	481	43	ż	ż	NOUN
ejpam-6251	481	44	3	3	NUM
ejpam-6251	481	45	)	)	PUNCT
ejpam-6251	481	46	⋇π	⋇π	NOUN
ejpam-6251	481	47	(	(	PUNCT
ejpam-6251	481	48	ςµ+1	ςµ+1	NUM
ejpam-6251	481	49	,	,	PUNCT
ejpam-6251	481	50	ςµ+1	ςµ+1	NUM
ejpam-6251	481	51	,	,	PUNCT
ejpam-6251	481	52	ż	ż	NOUN
ejpam-6251	481	53	3	3	NUM
ejpam-6251	481	54	)	)	PUNCT
ejpam-6251	481	55	⋇π	⋇π	NOUN
ejpam-6251	481	56	(	(	PUNCT
ejpam-6251	481	57	ςµ+1	ςµ+1	NUM
ejpam-6251	481	58	,	,	PUNCT
ejpam-6251	481	59	pς	pς	ADP
ejpam-6251	481	60	,	,	PUNCT
ejpam-6251	481	61	ż	ż	NOUN
ejpam-6251	481	62	3	3	X
ejpam-6251	481	63	)	)	PUNCT
ejpam-6251	481	64	r.	r.	PROPN
ejpam-6251	481	65	ramaswamy	ramaswamy	PROPN
ejpam-6251	481	66	/	/	SYM
ejpam-6251	481	67	eur	eur	PROPN
ejpam-6251	481	68	.	.	PUNCT
ejpam-6251	482	1	j.	j.	PROPN
ejpam-6251	482	2	pure	pure	PROPN
ejpam-6251	482	3	appl	appl	PROPN
ejpam-6251	482	4	.	.	PROPN
ejpam-6251	482	5	math	math	PROPN
ejpam-6251	482	6	,	,	PUNCT
ejpam-6251	482	7	18	18	NUM
ejpam-6251	482	8	(	(	PUNCT
ejpam-6251	482	9	4	4	NUM
ejpam-6251	482	10	)	)	PUNCT
ejpam-6251	482	11	(	(	PUNCT
ejpam-6251	482	12	2025	2025	NUM
ejpam-6251	482	13	)	)	PUNCT
ejpam-6251	482	14	,	,	PUNCT
ejpam-6251	482	15	6251	6251	NUM
ejpam-6251	482	16	25	25	NUM
ejpam-6251	482	17	of	of	ADP
ejpam-6251	482	18	40	40	NUM
ejpam-6251	482	19	=	=	SYM
ejpam-6251	482	20	π	π	X
ejpam-6251	482	21	(	(	PUNCT
ejpam-6251	482	22	ς	ς	PROPN
ejpam-6251	482	23	,	,	PUNCT
ejpam-6251	482	24	ςµ+1	ςµ+1	NUM
ejpam-6251	482	25	,	,	PUNCT
ejpam-6251	482	26	ż	ż	NOUN
ejpam-6251	482	27	3	3	NUM
ejpam-6251	482	28	)	)	PUNCT
ejpam-6251	482	29	⋇π	⋇π	NOUN
ejpam-6251	482	30	(	(	PUNCT
ejpam-6251	482	31	pςµ	pςµ	PROPN
ejpam-6251	482	32	,	,	PUNCT
ejpam-6251	482	33	pςµ	pςµ	PROPN
ejpam-6251	482	34	,	,	PUNCT
ejpam-6251	482	35	ż	ż	NOUN
ejpam-6251	482	36	3	3	NUM
ejpam-6251	482	37	)	)	PUNCT
ejpam-6251	482	38	⋇π	⋇π	NOUN
ejpam-6251	482	39	(	(	PUNCT
ejpam-6251	482	40	pςµ	pςµ	PROPN
ejpam-6251	482	41	,	,	PUNCT
ejpam-6251	482	42	pς	pς	ADP
ejpam-6251	482	43	,	,	PUNCT
ejpam-6251	482	44	ż	ż	NOUN
ejpam-6251	482	45	3	3	NUM
ejpam-6251	482	46	)	)	PUNCT
ejpam-6251	482	47	≥	≥	NOUN
ejpam-6251	483	1	π	π	PROPN
ejpam-6251	483	2	(	(	PUNCT
ejpam-6251	483	3	ς	ς	PROPN
ejpam-6251	483	4	,	,	PUNCT
ejpam-6251	483	5	ςµ+1	ςµ+1	NUM
ejpam-6251	483	6	,	,	PUNCT
ejpam-6251	483	7	ż	ż	NOUN
ejpam-6251	483	8	3	3	NUM
ejpam-6251	483	9	)	)	PUNCT
ejpam-6251	483	10	⋇	⋇	VERB
ejpam-6251	483	11	1	1	NUM
ejpam-6251	483	12	ζµ+1	ζµ+1	NUM
ejpam-6251	483	13	π(ς0,ϖ0	π(ς0,ϖ0	ADV
ejpam-6251	483	14	,	,	PUNCT
ejpam-6251	483	15	ż	ż	NOUN
ejpam-6251	483	16	3	3	NUM
ejpam-6251	483	17	)	)	PUNCT
ejpam-6251	483	18	+	+	CCONJ
ejpam-6251	483	19	(	(	PUNCT
ejpam-6251	483	20	1−	1−	NUM
ejpam-6251	483	21	ζµ+1	ζµ+1	NUM
ejpam-6251	483	22	)	)	PUNCT
ejpam-6251	483	23	⋇π	⋇π	NOUN
ejpam-6251	483	24	(	(	PUNCT
ejpam-6251	483	25	pςµ	pςµ	PROPN
ejpam-6251	483	26	,	,	PUNCT
ejpam-6251	483	27	pς	pς	ADP
ejpam-6251	483	28	,	,	PUNCT
ejpam-6251	483	29	ż	ż	NOUN
ejpam-6251	483	30	3	3	NUM
ejpam-6251	483	31	)	)	PUNCT
ejpam-6251	483	32	→	→	PUNCT
ejpam-6251	483	33	1⋇	1⋇	NUM
ejpam-6251	483	34	1⋇	1⋇	NUM
ejpam-6251	483	35	1	1	NUM
ejpam-6251	483	36	=	=	SYM
ejpam-6251	483	37	1	1	NUM
ejpam-6251	483	38	as	as	ADP
ejpam-6251	483	39	µ→	µ→	PROPN
ejpam-6251	483	40	+	+	NOUN
ejpam-6251	483	41	∞	∞	PROPN
ejpam-6251	483	42	,	,	PUNCT
ejpam-6251	483	43	ψ(ς	ψ(ς	NOUN
ejpam-6251	483	44	,	,	PUNCT
ejpam-6251	483	45	pς	pς	ADP
ejpam-6251	483	46	,	,	PUNCT
ejpam-6251	483	47	ż	ż	NOUN
ejpam-6251	483	48	)	)	PUNCT
ejpam-6251	483	49	≤	≤	NOUN
ejpam-6251	483	50	ψ	ψ	X
ejpam-6251	483	51	(	(	PUNCT
ejpam-6251	483	52	ς	ς	PROPN
ejpam-6251	483	53	,	,	PUNCT
ejpam-6251	483	54	ςµ+1	ςµ+1	NUM
ejpam-6251	483	55	,	,	PUNCT
ejpam-6251	483	56	ż	ż	NOUN
ejpam-6251	483	57	3	3	X
ejpam-6251	483	58	)	)	PUNCT
ejpam-6251	483	59	♢	♢	PROPN
ejpam-6251	483	60	ψ	ψ	X
ejpam-6251	483	61	(	(	PUNCT
ejpam-6251	483	62	ςµ+1	ςµ+1	NUM
ejpam-6251	483	63	,	,	PUNCT
ejpam-6251	483	64	ςµ+1	ςµ+1	NUM
ejpam-6251	483	65	,	,	PUNCT
ejpam-6251	483	66	ż	ż	NOUN
ejpam-6251	483	67	3	3	X
ejpam-6251	483	68	)	)	PUNCT
ejpam-6251	483	69	♢	♢	PROPN
ejpam-6251	483	70	ψ	ψ	X
ejpam-6251	483	71	(	(	PUNCT
ejpam-6251	483	72	ςµ+1	ςµ+1	NUM
ejpam-6251	483	73	,	,	PUNCT
ejpam-6251	483	74	pς	pς	ADP
ejpam-6251	483	75	,	,	PUNCT
ejpam-6251	483	76	ż	ż	NOUN
ejpam-6251	483	77	3	3	NUM
ejpam-6251	483	78	)	)	PUNCT
ejpam-6251	483	79	=	=	SYM
ejpam-6251	483	80	ψ	ψ	X
ejpam-6251	483	81	(	(	PUNCT
ejpam-6251	483	82	ς	ς	PROPN
ejpam-6251	483	83	,	,	PUNCT
ejpam-6251	483	84	ςµ+1	ςµ+1	NUM
ejpam-6251	483	85	,	,	PUNCT
ejpam-6251	483	86	ż	ż	NOUN
ejpam-6251	483	87	3	3	X
ejpam-6251	483	88	)	)	PUNCT
ejpam-6251	483	89	♢	♢	PROPN
ejpam-6251	483	90	ψ	ψ	X
ejpam-6251	483	91	(	(	PUNCT
ejpam-6251	483	92	pςµ+1	pςµ+1	NOUN
ejpam-6251	483	93	,	,	PUNCT
ejpam-6251	483	94	pςµ+1	pςµ+1	NOUN
ejpam-6251	483	95	,	,	PUNCT
ejpam-6251	483	96	ż	ż	NOUN
ejpam-6251	483	97	3	3	NUM
ejpam-6251	483	98	)	)	PUNCT
ejpam-6251	483	99	♢	♢	PROPN
ejpam-6251	483	100	ψ	ψ	X
ejpam-6251	483	101	(	(	PUNCT
ejpam-6251	483	102	pςµ+1	pςµ+1	NOUN
ejpam-6251	483	103	,	,	PUNCT
ejpam-6251	483	104	pς	pς	ADP
ejpam-6251	483	105	,	,	PUNCT
ejpam-6251	483	106	ż	ż	NOUN
ejpam-6251	483	107	3	3	NUM
ejpam-6251	483	108	)	)	PUNCT
ejpam-6251	483	109	≤	≤	NOUN
ejpam-6251	483	110	ψ	ψ	X
ejpam-6251	483	111	(	(	PUNCT
ejpam-6251	483	112	ς	ς	PROPN
ejpam-6251	483	113	,	,	PUNCT
ejpam-6251	483	114	ςµ+1	ςµ+1	NUM
ejpam-6251	483	115	,	,	PUNCT
ejpam-6251	483	116	ż	ż	NOUN
ejpam-6251	483	117	3	3	X
ejpam-6251	483	118	)	)	PUNCT
ejpam-6251	483	119	♢	♢	PROPN
ejpam-6251	483	120	ζµ+1ψ(ς0	ζµ+1ψ(ς0	PROPN
ejpam-6251	483	121	,	,	PUNCT
ejpam-6251	483	122	ϖ0	ϖ0	NOUN
ejpam-6251	483	123	,	,	PUNCT
ejpam-6251	483	124	ż	ż	NOUN
ejpam-6251	483	125	3	3	NUM
ejpam-6251	483	126	)	)	PUNCT
ejpam-6251	483	127	♢	♢	PROPN
ejpam-6251	483	128	ψ	ψ	X
ejpam-6251	483	129	(	(	PUNCT
ejpam-6251	483	130	pςµ+1	pςµ+1	NOUN
ejpam-6251	483	131	,	,	PUNCT
ejpam-6251	483	132	pς	pς	ADP
ejpam-6251	483	133	,	,	PUNCT
ejpam-6251	483	134	ż	ż	NOUN
ejpam-6251	483	135	3	3	NUM
ejpam-6251	483	136	)	)	PUNCT
ejpam-6251	483	137	→	→	SYM
ejpam-6251	483	138	0	0	NUM
ejpam-6251	483	139	♢	♢	PROPN
ejpam-6251	483	140	0	0	PROPN
ejpam-6251	483	141	♢	♢	PROPN
ejpam-6251	483	142	0	0	PROPN
ejpam-6251	484	1	=	=	SYM
ejpam-6251	484	2	0	0	PUNCT
ejpam-6251	484	3	as	as	ADP
ejpam-6251	484	4	µ→	µ→	PROPN
ejpam-6251	484	5	+	+	NOUN
ejpam-6251	484	6	∞	∞	PROPN
ejpam-6251	484	7	and	and	CCONJ
ejpam-6251	484	8	ξ(ς	ξ(ς	NOUN
ejpam-6251	484	9	,	,	PUNCT
ejpam-6251	484	10	pς	pς	ADP
ejpam-6251	484	11	,	,	PUNCT
ejpam-6251	484	12	ż	ż	NOUN
ejpam-6251	484	13	)	)	PUNCT
ejpam-6251	484	14	≤	≤	NOUN
ejpam-6251	484	15	ξ	ξ	X
ejpam-6251	484	16	(	(	PUNCT
ejpam-6251	484	17	ς	ς	PROPN
ejpam-6251	484	18	,	,	PUNCT
ejpam-6251	484	19	ςµ+1	ςµ+1	NUM
ejpam-6251	484	20	,	,	PUNCT
ejpam-6251	484	21	ż	ż	NOUN
ejpam-6251	484	22	3	3	X
ejpam-6251	484	23	)	)	PUNCT
ejpam-6251	484	24	♢	♢	PROPN
ejpam-6251	484	25	ξ	ξ	X
ejpam-6251	484	26	(	(	PUNCT
ejpam-6251	484	27	ςµ+1	ςµ+1	NUM
ejpam-6251	484	28	,	,	PUNCT
ejpam-6251	484	29	ςµ+1	ςµ+1	NUM
ejpam-6251	484	30	,	,	PUNCT
ejpam-6251	484	31	ż	ż	NOUN
ejpam-6251	484	32	3	3	X
ejpam-6251	484	33	)	)	PUNCT
ejpam-6251	484	34	♢	♢	PROPN
ejpam-6251	484	35	ξ	ξ	X
ejpam-6251	484	36	(	(	PUNCT
ejpam-6251	484	37	ςµ+1	ςµ+1	NUM
ejpam-6251	484	38	,	,	PUNCT
ejpam-6251	484	39	pς	pς	ADP
ejpam-6251	484	40	,	,	PUNCT
ejpam-6251	484	41	ż	ż	NOUN
ejpam-6251	484	42	3	3	NUM
ejpam-6251	484	43	)	)	PUNCT
ejpam-6251	484	44	=	=	SYM
ejpam-6251	485	1	ξ	ξ	PROPN
ejpam-6251	485	2	(	(	PUNCT
ejpam-6251	485	3	ς	ς	PROPN
ejpam-6251	485	4	,	,	PUNCT
ejpam-6251	485	5	ςµ+1	ςµ+1	NUM
ejpam-6251	485	6	,	,	PUNCT
ejpam-6251	485	7	ż	ż	NOUN
ejpam-6251	485	8	3	3	X
ejpam-6251	485	9	)	)	PUNCT
ejpam-6251	485	10	♢	♢	PROPN
ejpam-6251	485	11	ξ	ξ	X
ejpam-6251	485	12	(	(	PUNCT
ejpam-6251	485	13	pςµ+1	pςµ+1	NOUN
ejpam-6251	485	14	,	,	PUNCT
ejpam-6251	485	15	pςµ+1	pςµ+1	NOUN
ejpam-6251	485	16	,	,	PUNCT
ejpam-6251	485	17	ż	ż	NOUN
ejpam-6251	485	18	3	3	X
ejpam-6251	485	19	)	)	PUNCT
ejpam-6251	485	20	♢	♢	PROPN
ejpam-6251	485	21	ξ	ξ	X
ejpam-6251	485	22	(	(	PUNCT
ejpam-6251	485	23	pςµ+1	pςµ+1	NOUN
ejpam-6251	485	24	,	,	PUNCT
ejpam-6251	485	25	pς	pς	ADP
ejpam-6251	485	26	,	,	PUNCT
ejpam-6251	485	27	ż	ż	NOUN
ejpam-6251	485	28	3	3	NUM
ejpam-6251	485	29	)	)	PUNCT
ejpam-6251	485	30	≤	≤	NOUN
ejpam-6251	486	1	ξ	ξ	PROPN
ejpam-6251	486	2	(	(	PUNCT
ejpam-6251	486	3	ς	ς	PROPN
ejpam-6251	486	4	,	,	PUNCT
ejpam-6251	486	5	ςµ+1	ςµ+1	NUM
ejpam-6251	486	6	,	,	PUNCT
ejpam-6251	486	7	ż	ż	NOUN
ejpam-6251	486	8	3	3	X
ejpam-6251	486	9	)	)	PUNCT
ejpam-6251	486	10	♢	♢	PROPN
ejpam-6251	486	11	ζµ+1ψ(ς0	ζµ+1ψ(ς0	PROPN
ejpam-6251	486	12	,	,	PUNCT
ejpam-6251	486	13	ϖ0	ϖ0	NOUN
ejpam-6251	486	14	,	,	PUNCT
ejpam-6251	486	15	ż	ż	NOUN
ejpam-6251	486	16	3	3	NUM
ejpam-6251	486	17	)	)	PUNCT
ejpam-6251	486	18	♢	♢	PROPN
ejpam-6251	486	19	ξ	ξ	X
ejpam-6251	486	20	(	(	PUNCT
ejpam-6251	486	21	pςµ+1	pςµ+1	NOUN
ejpam-6251	486	22	,	,	PUNCT
ejpam-6251	486	23	pς	pς	ADP
ejpam-6251	486	24	,	,	PUNCT
ejpam-6251	486	25	ż	ż	NOUN
ejpam-6251	486	26	3	3	NUM
ejpam-6251	486	27	)	)	PUNCT
ejpam-6251	486	28	→	→	SYM
ejpam-6251	486	29	0	0	NUM
ejpam-6251	486	30	♢	♢	PROPN
ejpam-6251	486	31	0	0	PROPN
ejpam-6251	486	32	♢	♢	PROPN
ejpam-6251	486	33	0	0	PROPN
ejpam-6251	487	1	=	=	SYM
ejpam-6251	488	1	0	0	PUNCT
ejpam-6251	489	1	as	as	ADP
ejpam-6251	489	2	µ→	µ→	PROPN
ejpam-6251	489	3	+	+	NOUN
ejpam-6251	489	4	∞.	∞.	PROPN
ejpam-6251	489	5	hence	hence	ADV
ejpam-6251	489	6	,	,	PUNCT
ejpam-6251	489	7	pς	pς	ADP
ejpam-6251	489	8	=	=	SYM
ejpam-6251	489	9	ς	ς	PROPN
ejpam-6251	489	10	.	.	PUNCT
ejpam-6251	489	11	let	let	VERB
ejpam-6251	489	12	pη	pη	VERB
ejpam-6251	489	13	=	=	SYM
ejpam-6251	489	14	η	η	PROPN
ejpam-6251	489	15	for	for	ADP
ejpam-6251	489	16	some	some	DET
ejpam-6251	489	17	η	η	PROPN
ejpam-6251	489	18	∈	∈	PROPN
ejpam-6251	489	19	𭟋	𭟋	PROPN
ejpam-6251	489	20	,	,	PUNCT
ejpam-6251	489	21	then	then	ADV
ejpam-6251	489	22	1	1	NUM
ejpam-6251	489	23	π(ς	π(ς	PROPN
ejpam-6251	489	24	,	,	PUNCT
ejpam-6251	489	25	η	η	PROPN
ejpam-6251	489	26	,	,	PUNCT
ejpam-6251	489	27	ż	ż	NOUN
ejpam-6251	489	28	)	)	PUNCT
ejpam-6251	489	29	−	−	PROPN
ejpam-6251	489	30	1	1	NUM
ejpam-6251	489	31	=	=	SYM
ejpam-6251	489	32	1	1	NUM
ejpam-6251	489	33	π(pς	π(pς	NOUN
ejpam-6251	489	34	,	,	PUNCT
ejpam-6251	489	35	pη	pη	NOUN
ejpam-6251	489	36	,	,	PUNCT
ejpam-6251	489	37	ż	ż	NOUN
ejpam-6251	489	38	)	)	PUNCT
ejpam-6251	490	1	−	−	PROPN
ejpam-6251	490	2	1	1	NUM
ejpam-6251	490	3	≤	≤	NUM
ejpam-6251	490	4	ζ	ζ	NOUN
ejpam-6251	490	5	[	[	PUNCT
ejpam-6251	490	6	1	1	NUM
ejpam-6251	490	7	π(ς	π(ς	PROPN
ejpam-6251	490	8	,	,	PUNCT
ejpam-6251	490	9	η	η	PROPN
ejpam-6251	490	10	,	,	PUNCT
ejpam-6251	490	11	ż	ż	NOUN
ejpam-6251	490	12	)	)	PUNCT
ejpam-6251	490	13	−	−	PROPN
ejpam-6251	490	14	1	1	NUM
ejpam-6251	490	15	]	]	PUNCT
ejpam-6251	490	16	<	<	X
ejpam-6251	490	17	1	1	NUM
ejpam-6251	490	18	π(ς	π(ς	PROPN
ejpam-6251	490	19	,	,	PUNCT
ejpam-6251	490	20	η	η	PROPN
ejpam-6251	490	21	,	,	PUNCT
ejpam-6251	490	22	ż	ż	NOUN
ejpam-6251	490	23	)	)	PUNCT
ejpam-6251	490	24	−	−	PROPN
ejpam-6251	490	25	1	1	NUM
ejpam-6251	490	26	,	,	PUNCT
ejpam-6251	490	27	which	which	PRON
ejpam-6251	490	28	is	be	AUX
ejpam-6251	490	29	a	a	DET
ejpam-6251	490	30	contradiction	contradiction	NOUN
ejpam-6251	490	31	.	.	PUNCT
ejpam-6251	491	1	ψ(ς	ψ(ς	PROPN
ejpam-6251	491	2	,	,	PUNCT
ejpam-6251	491	3	η	η	PROPN
ejpam-6251	491	4	,	,	PUNCT
ejpam-6251	491	5	ż	ż	NOUN
ejpam-6251	491	6	)	)	PUNCT
ejpam-6251	491	7	=	=	SYM
ejpam-6251	491	8	ψ(pς	ψ(pς	NOUN
ejpam-6251	491	9	,	,	PUNCT
ejpam-6251	491	10	pη	pη	NOUN
ejpam-6251	491	11	,	,	PUNCT
ejpam-6251	491	12	ż	ż	NOUN
ejpam-6251	491	13	)	)	PUNCT
ejpam-6251	491	14	≤	≤	NOUN
ejpam-6251	491	15	ζψ(ς	ζψ(ς	NOUN
ejpam-6251	491	16	,	,	PUNCT
ejpam-6251	491	17	η	η	PROPN
ejpam-6251	491	18	,	,	PUNCT
ejpam-6251	491	19	ż	ż	NOUN
ejpam-6251	491	20	)	)	PUNCT
ejpam-6251	491	21	<	<	X
ejpam-6251	491	22	ψ(ς	ψ(ς	PROPN
ejpam-6251	491	23	,	,	PUNCT
ejpam-6251	491	24	η	η	PROPN
ejpam-6251	491	25	,	,	PUNCT
ejpam-6251	491	26	ż	ż	NOUN
ejpam-6251	491	27	)	)	PUNCT
ejpam-6251	491	28	,	,	PUNCT
ejpam-6251	491	29	which	which	PRON
ejpam-6251	491	30	is	be	AUX
ejpam-6251	491	31	a	a	DET
ejpam-6251	491	32	contradiction	contradiction	NOUN
ejpam-6251	491	33	and	and	CCONJ
ejpam-6251	491	34	ξ(ς	ξ(ς	NOUN
ejpam-6251	491	35	,	,	PUNCT
ejpam-6251	491	36	η	η	PROPN
ejpam-6251	491	37	,	,	PUNCT
ejpam-6251	491	38	ż	ż	NOUN
ejpam-6251	491	39	)	)	PUNCT
ejpam-6251	491	40	=	=	SYM
ejpam-6251	491	41	ξ(pς	ξ(pς	PROPN
ejpam-6251	491	42	,	,	PUNCT
ejpam-6251	491	43	pη	pη	ADP
ejpam-6251	491	44	,	,	PUNCT
ejpam-6251	491	45	ż	ż	NOUN
ejpam-6251	491	46	)	)	PUNCT
ejpam-6251	491	47	≤	≤	NOUN
ejpam-6251	491	48	ζξ(ς	ζξ(ς	NUM
ejpam-6251	491	49	,	,	PUNCT
ejpam-6251	491	50	η	η	PROPN
ejpam-6251	491	51	,	,	PUNCT
ejpam-6251	491	52	ż	ż	NOUN
ejpam-6251	491	53	)	)	PUNCT
ejpam-6251	491	54	<	<	X
ejpam-6251	491	55	ξ(ς	ξ(ς	PROPN
ejpam-6251	491	56	,	,	PUNCT
ejpam-6251	491	57	η	η	PROPN
ejpam-6251	491	58	,	,	PUNCT
ejpam-6251	491	59	ż	ż	NOUN
ejpam-6251	491	60	)	)	PUNCT
ejpam-6251	491	61	,	,	PUNCT
ejpam-6251	491	62	which	which	PRON
ejpam-6251	491	63	is	be	AUX
ejpam-6251	491	64	a	a	DET
ejpam-6251	491	65	contradiction	contradiction	NOUN
ejpam-6251	491	66	.	.	PUNCT
ejpam-6251	492	1	therefore	therefore	ADV
ejpam-6251	492	2	,	,	PUNCT
ejpam-6251	492	3	we	we	PRON
ejpam-6251	492	4	get	get	VERB
ejpam-6251	492	5	π(ς	π(ς	PROPN
ejpam-6251	492	6	,	,	PUNCT
ejpam-6251	492	7	η	η	PROPN
ejpam-6251	492	8	,	,	PUNCT
ejpam-6251	492	9	ż	ż	NOUN
ejpam-6251	492	10	)	)	PUNCT
ejpam-6251	493	1	=	=	SYM
ejpam-6251	493	2	1,ψ(ς	1,ψ(ς	NUM
ejpam-6251	493	3	,	,	PUNCT
ejpam-6251	493	4	η	η	PROPN
ejpam-6251	493	5	,	,	PUNCT
ejpam-6251	493	6	ż	ż	NOUN
ejpam-6251	493	7	)	)	PUNCT
ejpam-6251	493	8	=	=	SYM
ejpam-6251	493	9	0	0	NUM
ejpam-6251	493	10	and	and	CCONJ
ejpam-6251	493	11	ξ(ς	ξ(ς	PROPN
ejpam-6251	493	12	,	,	PUNCT
ejpam-6251	493	13	η	η	PROPN
ejpam-6251	493	14	,	,	PUNCT
ejpam-6251	493	15	ż	ż	NOUN
ejpam-6251	493	16	)	)	PUNCT
ejpam-6251	493	17	=	=	SYM
ejpam-6251	493	18	0	0	NUM
ejpam-6251	493	19	,	,	PUNCT
ejpam-6251	493	20	hence	hence	ADV
ejpam-6251	493	21	,	,	PUNCT
ejpam-6251	493	22	ς	ς	PROPN
ejpam-6251	493	23	=	=	SYM
ejpam-6251	493	24	η	η	PROPN
ejpam-6251	493	25	.	.	PROPN
ejpam-6251	493	26	r.	r.	PROPN
ejpam-6251	493	27	ramaswamy	ramaswamy	PROPN
ejpam-6251	493	28	/	/	SYM
ejpam-6251	493	29	eur	eur	PROPN
ejpam-6251	493	30	.	.	PUNCT
ejpam-6251	494	1	j.	j.	PROPN
ejpam-6251	494	2	pure	pure	PROPN
ejpam-6251	494	3	appl	appl	PROPN
ejpam-6251	494	4	.	.	PROPN
ejpam-6251	494	5	math	math	PROPN
ejpam-6251	494	6	,	,	PUNCT
ejpam-6251	494	7	18	18	NUM
ejpam-6251	494	8	(	(	PUNCT
ejpam-6251	494	9	4	4	NUM
ejpam-6251	494	10	)	)	PUNCT
ejpam-6251	494	11	(	(	PUNCT
ejpam-6251	494	12	2025	2025	NUM
ejpam-6251	494	13	)	)	PUNCT
ejpam-6251	494	14	,	,	PUNCT
ejpam-6251	494	15	6251	6251	NUM
ejpam-6251	494	16	26	26	NUM
ejpam-6251	494	17	of	of	ADP
ejpam-6251	494	18	40	40	NUM
ejpam-6251	494	19	example	example	NOUN
ejpam-6251	494	20	2	2	NUM
ejpam-6251	494	21	.	.	PUNCT
ejpam-6251	495	1	let	let	VERB
ejpam-6251	495	2	𭟋	𭟋	VERB
ejpam-6251	495	3	=	=	PUNCT
ejpam-6251	496	1	[	[	X
ejpam-6251	496	2	0	0	NUM
ejpam-6251	496	3	,	,	PUNCT
ejpam-6251	496	4	1	1	NUM
ejpam-6251	496	5	]	]	PUNCT
ejpam-6251	496	6	and	and	CCONJ
ejpam-6251	496	7	s	s	X
ejpam-6251	496	8	=	=	X
ejpam-6251	496	9	{	{	PUNCT
ejpam-6251	496	10	0}∪n−{1	0}∪n−{1	ADJ
ejpam-6251	496	11	}	}	PUNCT
ejpam-6251	496	12	.	.	PUNCT
ejpam-6251	497	1	define	define	VERB
ejpam-6251	497	2	π	π	PROPN
ejpam-6251	497	3	,	,	PUNCT
ejpam-6251	497	4	ψ	ψ	X
ejpam-6251	497	5	,	,	PUNCT
ejpam-6251	497	6	ξ	ξ	PROPN
ejpam-6251	497	7	:	:	PUNCT
ejpam-6251	497	8	𭟋×s×(0,+∞	𭟋×s×(0,+∞	X
ejpam-6251	497	9	)	)	PUNCT
ejpam-6251	497	10	→	→	PUNCT
ejpam-6251	498	1	[	[	X
ejpam-6251	498	2	0	0	NUM
ejpam-6251	498	3	,	,	PUNCT
ejpam-6251	498	4	1	1	NUM
ejpam-6251	498	5	]	]	PUNCT
ejpam-6251	498	6	as	as	ADP
ejpam-6251	498	7	π(ς,ϖ	π(ς,ϖ	NOUN
ejpam-6251	498	8	,	,	PUNCT
ejpam-6251	498	9	ż	ż	NOUN
ejpam-6251	498	10	)	)	PUNCT
ejpam-6251	498	11	=	=	PUNCT
ejpam-6251	498	12	ż	ż	PROPN
ejpam-6251	498	13	ż+	ż+	PROPN
ejpam-6251	498	14	|ς	|ς	PART
ejpam-6251	498	15	−ϖ|	−ϖ|	NOUN
ejpam-6251	498	16	,	,	PUNCT
ejpam-6251	498	17	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	498	18	,	,	PUNCT
ejpam-6251	498	19	ż	ż	NOUN
ejpam-6251	498	20	)	)	PUNCT
ejpam-6251	499	1	=	=	SYM
ejpam-6251	499	2	|ς	|ς	VERB
ejpam-6251	499	3	−ϖ|	−ϖ|	PROPN
ejpam-6251	499	4	ż+	ż+	PROPN
ejpam-6251	499	5	|ς	|ς	PART
ejpam-6251	499	6	−ϖ|	−ϖ|	NOUN
ejpam-6251	499	7	,	,	PUNCT
ejpam-6251	499	8	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	499	9	,	,	PUNCT
ejpam-6251	499	10	ż	ż	NOUN
ejpam-6251	499	11	)	)	PUNCT
ejpam-6251	499	12	=	=	PUNCT
ejpam-6251	500	1	|ς	|ς	ADJ
ejpam-6251	500	2	−ϖ|	−ϖ|	NOUN
ejpam-6251	501	1	ż	ż	INTJ
ejpam-6251	501	2	.	.	PUNCT
ejpam-6251	502	1	then	then	ADV
ejpam-6251	502	2	,	,	PUNCT
ejpam-6251	502	3	(	(	PUNCT
ejpam-6251	502	4	𭟋	𭟋	NOUN
ejpam-6251	502	5	,	,	PUNCT
ejpam-6251	502	6	s	s	PROPN
ejpam-6251	502	7	,	,	PUNCT
ejpam-6251	502	8	π	π	PROPN
ejpam-6251	502	9	,	,	PUNCT
ejpam-6251	502	10	ψ	ψ	PROPN
ejpam-6251	502	11	,	,	PUNCT
ejpam-6251	502	12	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	502	13	,	,	PUNCT
ejpam-6251	502	14	♢	♢	PROPN
ejpam-6251	502	15	)	)	PUNCT
ejpam-6251	502	16	is	be	AUX
ejpam-6251	502	17	a	a	DET
ejpam-6251	502	18	complete	complete	ADJ
ejpam-6251	502	19	nbms	nbms	NOUN
ejpam-6251	502	20	with	with	ADP
ejpam-6251	502	21	ct−||.||	ct−||.||	PROPN
ejpam-6251	502	22	ė	ė	PROPN
ejpam-6251	502	23	⋇	⋇	PROPN
ejpam-6251	502	24	ȧ	ȧ	PROPN
ejpam-6251	502	25	=	=	PROPN
ejpam-6251	502	26	ėȧ	ėȧ	PROPN
ejpam-6251	502	27	and	and	CCONJ
ejpam-6251	502	28	ct−co−||.||	ct−co−||.||	PRON
ejpam-6251	502	29	ė	ė	PROPN
ejpam-6251	502	30	♢	♢	PROPN
ejpam-6251	502	31	ȧ	ȧ	PROPN
ejpam-6251	502	32	=	=	PROPN
ejpam-6251	502	33	max{ė	max{ė	PROPN
ejpam-6251	502	34	,	,	PUNCT
ejpam-6251	502	35	ȧ	ȧ	PROPN
ejpam-6251	502	36	}	}	PUNCT
ejpam-6251	502	37	.	.	PUNCT
ejpam-6251	503	1	define	define	VERB
ejpam-6251	503	2	p	p	X
ejpam-6251	503	3	:	:	PUNCT
ejpam-6251	503	4	(	(	PUNCT
ejpam-6251	503	5	𭟋	𭟋	NOUN
ejpam-6251	503	6	,	,	PUNCT
ejpam-6251	503	7	s	s	PROPN
ejpam-6251	503	8	,	,	PUNCT
ejpam-6251	503	9	π	π	PROPN
ejpam-6251	503	10	,	,	PUNCT
ejpam-6251	503	11	ψ	ψ	PROPN
ejpam-6251	503	12	,	,	PUNCT
ejpam-6251	503	13	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	503	14	,	,	PUNCT
ejpam-6251	503	15	♢	♢	PROPN
ejpam-6251	503	16	)	)	PUNCT
ejpam-6251	503	17	⇒	⇒	NOUN
ejpam-6251	503	18	(	(	PUNCT
ejpam-6251	503	19	𭟋	𭟋	PROPN
ejpam-6251	503	20	,	,	PUNCT
ejpam-6251	503	21	s	s	PROPN
ejpam-6251	503	22	,	,	PUNCT
ejpam-6251	503	23	π	π	PROPN
ejpam-6251	503	24	,	,	PUNCT
ejpam-6251	503	25	ψ	ψ	PROPN
ejpam-6251	503	26	,	,	PUNCT
ejpam-6251	503	27	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	503	28	,	,	PUNCT
ejpam-6251	503	29	♢	♢	PROPN
ejpam-6251	503	30	)	)	PUNCT
ejpam-6251	503	31	by	by	ADP
ejpam-6251	503	32	p(ς	p(ς	PROPN
ejpam-6251	503	33	)	)	PUNCT
ejpam-6251	503	34	=	=	PRON
ejpam-6251	503	35	{	{	PUNCT
ejpam-6251	503	36	1−3−ς	1−3−ς	NUM
ejpam-6251	503	37	5	5	NUM
ejpam-6251	503	38	,	,	PUNCT
ejpam-6251	503	39	if	if	SCONJ
ejpam-6251	503	40	ς	ς	PROPN
ejpam-6251	503	41	∈	∈	PROPN
ejpam-6251	504	1	[	[	X
ejpam-6251	504	2	0	0	NUM
ejpam-6251	504	3	,	,	PUNCT
ejpam-6251	504	4	1	1	NUM
ejpam-6251	504	5	]	]	PUNCT
ejpam-6251	504	6	,	,	PUNCT
ejpam-6251	504	7	0	0	NUM
ejpam-6251	504	8	,	,	PUNCT
ejpam-6251	504	9	if	if	SCONJ
ejpam-6251	504	10	ς	ς	PROPN
ejpam-6251	504	11	∈	∈	PROPN
ejpam-6251	504	12	n−	n−	NOUN
ejpam-6251	504	13	{	{	PUNCT
ejpam-6251	504	14	1	1	NUM
ejpam-6251	504	15	}	}	PUNCT
ejpam-6251	504	16	,	,	PUNCT
ejpam-6251	504	17	∀	∀	PUNCT
ejpam-6251	504	18	ς	ς	PROPN
ejpam-6251	504	19	∈	∈	PROPN
ejpam-6251	504	20	𭟋	𭟋	ADP
ejpam-6251	504	21	∪	∪	NOUN
ejpam-6251	504	22	s	s	NOUN
ejpam-6251	505	1	and	and	CCONJ
ejpam-6251	505	2	take	take	VERB
ejpam-6251	505	3	ζ	ζ	NOUN
ejpam-6251	505	4	∈	∈	NOUN
ejpam-6251	506	1	[	[	X
ejpam-6251	506	2	12	12	NUM
ejpam-6251	506	3	,	,	PUNCT
ejpam-6251	506	4	1	1	NUM
ejpam-6251	506	5	)	)	PUNCT
ejpam-6251	506	6	,	,	PUNCT
ejpam-6251	506	7	then	then	ADV
ejpam-6251	506	8	π(pς	π(pς	NOUN
ejpam-6251	506	9	,	,	PUNCT
ejpam-6251	506	10	pϖ	pϖ	ADP
ejpam-6251	506	11	,	,	PUNCT
ejpam-6251	506	12	ζ	ζ	NOUN
ejpam-6251	506	13	ż	ż	NOUN
ejpam-6251	506	14	)	)	PUNCT
ejpam-6251	507	1	=	=	PUNCT
ejpam-6251	507	2	π	π	X
ejpam-6251	507	3	(	(	PUNCT
ejpam-6251	507	4	1−	1−	NUM
ejpam-6251	507	5	3−ς	3−ς	NUM
ejpam-6251	507	6	5	5	NUM
ejpam-6251	507	7	,	,	PUNCT
ejpam-6251	507	8	1−	1−	NUM
ejpam-6251	507	9	3−ϖ	3−ϖ	NUM
ejpam-6251	507	10	5	5	NUM
ejpam-6251	507	11	,	,	PUNCT
ejpam-6251	507	12	ζ	ζ	NOUN
ejpam-6251	507	13	ż	ż	NOUN
ejpam-6251	507	14	)	)	PUNCT
ejpam-6251	508	1	=	=	PUNCT
ejpam-6251	508	2	ζ	ζ	NOUN
ejpam-6251	508	3	ż	ż	NOUN
ejpam-6251	508	4	ζ	ζ	PROPN
ejpam-6251	508	5	ż+	ż+	PROPN
ejpam-6251	508	6	∣∣∣∣1−3−ς	∣∣∣∣1−3−ς	VERB
ejpam-6251	508	7	5	5	NUM
ejpam-6251	508	8	−	−	NOUN
ejpam-6251	508	9	1−3−ϖ	1−3−ϖ	NUM
ejpam-6251	508	10	5	5	NUM
ejpam-6251	508	11	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6251	508	12	=	=	PUNCT
ejpam-6251	508	13	ζ	ζ	NOUN
ejpam-6251	508	14	ż	ż	NOUN
ejpam-6251	508	15	ζ	ζ	PROPN
ejpam-6251	508	16	ż+	ż+	PROPN
ejpam-6251	508	17	|3−ς−3−ϖ|	|3−ς−3−ϖ|	NOUN
ejpam-6251	508	18	5	5	NUM
ejpam-6251	508	19	≥	≥	NOUN
ejpam-6251	508	20	ζ	ζ	NOUN
ejpam-6251	508	21	ż	ż	NOUN
ejpam-6251	508	22	ζ	ζ	PROPN
ejpam-6251	508	23	ż+	ż+	PROPN
ejpam-6251	508	24	|ς−ϖ|	|ς−ϖ|	PUNCT
ejpam-6251	508	25	5	5	NUM
ejpam-6251	508	26	=	=	SYM
ejpam-6251	508	27	5ζ	5ζ	PROPN
ejpam-6251	508	28	ż	ż	NOUN
ejpam-6251	508	29	5ζ	5ζ	PROPN
ejpam-6251	508	30	ż+	ż+	PROPN
ejpam-6251	508	31	|ς	|ς	PART
ejpam-6251	508	32	−ϖ|	−ϖ|	NOUN
ejpam-6251	508	33	≥	≥	PROPN
ejpam-6251	508	34	ż	ż	PROPN
ejpam-6251	508	35	ż+	ż+	PROPN
ejpam-6251	508	36	|ς	|ς	PART
ejpam-6251	508	37	−ϖ|	−ϖ|	NOUN
ejpam-6251	508	38	=	=	SYM
ejpam-6251	509	1	π(ς,ϖ	π(ς,ϖ	X
ejpam-6251	509	2	,	,	PUNCT
ejpam-6251	509	3	ż	ż	NOUN
ejpam-6251	509	4	)	)	PUNCT
ejpam-6251	509	5	,	,	PUNCT
ejpam-6251	509	6	ψ(pς	ψ(pς	NOUN
ejpam-6251	509	7	,	,	PUNCT
ejpam-6251	509	8	pϖ	pϖ	ADP
ejpam-6251	509	9	,	,	PUNCT
ejpam-6251	509	10	ζ	ζ	NOUN
ejpam-6251	509	11	ż	ż	NOUN
ejpam-6251	509	12	)	)	PUNCT
ejpam-6251	509	13	=	=	SYM
ejpam-6251	509	14	ψ	ψ	X
ejpam-6251	509	15	(	(	PUNCT
ejpam-6251	509	16	1−	1−	NUM
ejpam-6251	509	17	3−ς	3−ς	NUM
ejpam-6251	509	18	5	5	NUM
ejpam-6251	509	19	,	,	PUNCT
ejpam-6251	509	20	1−	1−	NUM
ejpam-6251	509	21	3−ϖ	3−ϖ	NUM
ejpam-6251	509	22	5	5	NUM
ejpam-6251	509	23	,	,	PUNCT
ejpam-6251	509	24	ζ	ζ	NOUN
ejpam-6251	509	25	ż	ż	NOUN
ejpam-6251	509	26	)	)	PUNCT
ejpam-6251	510	1	=	=	SYM
ejpam-6251	510	2	∣∣∣∣1−3−ς	∣∣∣∣1−3−ς	PUNCT
ejpam-6251	510	3	5	5	NUM
ejpam-6251	510	4	−	−	NOUN
ejpam-6251	510	5	1−3−ϖ	1−3−ϖ	NUM
ejpam-6251	510	6	5	5	NUM
ejpam-6251	510	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6251	510	8	ζ	ζ	PROPN
ejpam-6251	510	9	ż+	ż+	PROPN
ejpam-6251	510	10	∣∣∣∣1−3−ς	∣∣∣∣1−3−ς	VERB
ejpam-6251	511	1	5	5	NUM
ejpam-6251	511	2	−	−	NOUN
ejpam-6251	511	3	1−3−ϖ	1−3−ϖ	NUM
ejpam-6251	511	4	5	5	NUM
ejpam-6251	511	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6251	511	6	=	=	NOUN
ejpam-6251	511	7	|3−ς−3−ϖ|	|3−ς−3−ϖ|	NOUN
ejpam-6251	511	8	5	5	NUM
ejpam-6251	511	9	ζ	ζ	PROPN
ejpam-6251	511	10	ż+	ż+	PROPN
ejpam-6251	511	11	|3−ς−3−ϖ|	|3−ς−3−ϖ|	NOUN
ejpam-6251	511	12	5	5	NUM
ejpam-6251	511	13	=	=	PUNCT
ejpam-6251	511	14	|3−ς	|3−ς	PRON
ejpam-6251	511	15	−	−	PROPN
ejpam-6251	511	16	3−ϖ|	3−ϖ|	NUM
ejpam-6251	511	17	5ζ	5ζ	PROPN
ejpam-6251	511	18	ż+	ż+	PROPN
ejpam-6251	511	19	|3−ς	|3−ς	PUNCT
ejpam-6251	511	20	−	−	PROPN
ejpam-6251	511	21	3−ϖ|	3−ϖ|	PROPN
ejpam-6251	511	22	≤	≤	NUM
ejpam-6251	511	23	|ς	|ς	VERB
ejpam-6251	511	24	−ϖ|	−ϖ|	NOUN
ejpam-6251	511	25	5ζ	5ζ	PROPN
ejpam-6251	511	26	ż+	ż+	PROPN
ejpam-6251	511	27	|ς	|ς	PART
ejpam-6251	512	1	−ϖ|	−ϖ|	NOUN
ejpam-6251	512	2	≤	≤	X
ejpam-6251	512	3	|ς	|ς	VERB
ejpam-6251	512	4	−ϖ|	−ϖ|	NOUN
ejpam-6251	512	5	ż+	ż+	PROPN
ejpam-6251	512	6	|ς	|ς	PART
ejpam-6251	512	7	−ϖ|	−ϖ|	NOUN
ejpam-6251	512	8	=	=	SYM
ejpam-6251	512	9	ψ(ς,ϖ	ψ(ς,ϖ	NOUN
ejpam-6251	512	10	,	,	PUNCT
ejpam-6251	512	11	ż	ż	NOUN
ejpam-6251	512	12	)	)	PUNCT
ejpam-6251	512	13	and	and	CCONJ
ejpam-6251	512	14	ξ(pς	ξ(pς	NOUN
ejpam-6251	512	15	,	,	PUNCT
ejpam-6251	512	16	pϖ	pϖ	ADP
ejpam-6251	512	17	,	,	PUNCT
ejpam-6251	512	18	ζ	ζ	NOUN
ejpam-6251	512	19	ż	ż	NOUN
ejpam-6251	512	20	)	)	PUNCT
ejpam-6251	512	21	=	=	SYM
ejpam-6251	512	22	ξ	ξ	PROPN
ejpam-6251	512	23	(	(	PUNCT
ejpam-6251	512	24	1−	1−	NUM
ejpam-6251	512	25	3−ς	3−ς	NUM
ejpam-6251	512	26	5	5	NUM
ejpam-6251	512	27	,	,	PUNCT
ejpam-6251	512	28	1−	1−	NUM
ejpam-6251	512	29	3−ϖ	3−ϖ	NUM
ejpam-6251	512	30	5	5	NUM
ejpam-6251	512	31	,	,	PUNCT
ejpam-6251	512	32	ζ	ζ	NOUN
ejpam-6251	512	33	ż	ż	NOUN
ejpam-6251	512	34	)	)	PUNCT
ejpam-6251	512	35	=	=	SYM
ejpam-6251	512	36	∣∣∣∣1−3−ς	∣∣∣∣1−3−ς	PUNCT
ejpam-6251	512	37	5	5	NUM
ejpam-6251	512	38	−	−	NOUN
ejpam-6251	512	39	1−3−ϖ	1−3−ϖ	NUM
ejpam-6251	512	40	5	5	NUM
ejpam-6251	512	41	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6251	512	42	ζ	ζ	NOUN
ejpam-6251	512	43	ż	ż	NOUN
ejpam-6251	512	44	=	=	NOUN
ejpam-6251	512	45	|3−ς−3−ϖ|	|3−ς−3−ϖ|	NOUN
ejpam-6251	512	46	5	5	NUM
ejpam-6251	512	47	ζ	ζ	NOUN
ejpam-6251	512	48	ż	ż	PROPN
ejpam-6251	512	49	r.	r.	PROPN
ejpam-6251	512	50	ramaswamy	ramaswamy	PROPN
ejpam-6251	512	51	/	/	SYM
ejpam-6251	512	52	eur	eur	PROPN
ejpam-6251	512	53	.	.	PUNCT
ejpam-6251	513	1	j.	j.	PROPN
ejpam-6251	513	2	pure	pure	PROPN
ejpam-6251	513	3	appl	appl	PROPN
ejpam-6251	513	4	.	.	PROPN
ejpam-6251	513	5	math	math	PROPN
ejpam-6251	513	6	,	,	PUNCT
ejpam-6251	513	7	18	18	NUM
ejpam-6251	513	8	(	(	PUNCT
ejpam-6251	513	9	4	4	NUM
ejpam-6251	513	10	)	)	PUNCT
ejpam-6251	513	11	(	(	PUNCT
ejpam-6251	513	12	2025	2025	NUM
ejpam-6251	513	13	)	)	PUNCT
ejpam-6251	513	14	,	,	PUNCT
ejpam-6251	513	15	6251	6251	NUM
ejpam-6251	513	16	27	27	NUM
ejpam-6251	513	17	of	of	ADP
ejpam-6251	513	18	40	40	NUM
ejpam-6251	513	19	=	=	SYM
ejpam-6251	513	20	|3−ς	|3−ς	PRON
ejpam-6251	513	21	−	−	NOUN
ejpam-6251	513	22	3−ϖ|	3−ϖ|	NUM
ejpam-6251	513	23	5ζ	5ζ	PROPN
ejpam-6251	513	24	ż	ż	PROPN
ejpam-6251	513	25	≤	≤	PROPN
ejpam-6251	513	26	|ς	|ς	VERB
ejpam-6251	513	27	−ϖ|	−ϖ|	NOUN
ejpam-6251	514	1	5ζ	5ζ	PROPN
ejpam-6251	514	2	ż	ż	PROPN
ejpam-6251	514	3	≤	≤	PROPN
ejpam-6251	514	4	|ς	|ς	VERB
ejpam-6251	514	5	−ϖ|	−ϖ|	NOUN
ejpam-6251	514	6	ż	ż	NOUN
ejpam-6251	514	7	=	=	PUNCT
ejpam-6251	514	8	ξ(ς,ϖ	ξ(ς,ϖ	NOUN
ejpam-6251	514	9	,	,	PUNCT
ejpam-6251	514	10	ż	ż	NOUN
ejpam-6251	514	11	)	)	PUNCT
ejpam-6251	514	12	.	.	PUNCT
ejpam-6251	515	1	therefore	therefore	ADV
ejpam-6251	515	2	,	,	PUNCT
ejpam-6251	515	3	all	all	DET
ejpam-6251	515	4	the	the	DET
ejpam-6251	515	5	hypothesis	hypothesis	NOUN
ejpam-6251	515	6	of	of	ADP
ejpam-6251	515	7	theorem	theorem	NOUN
ejpam-6251	515	8	5	5	NUM
ejpam-6251	515	9	are	be	AUX
ejpam-6251	515	10	satisfied	satisfied	ADJ
ejpam-6251	515	11	,	,	PUNCT
ejpam-6251	515	12	and	and	CCONJ
ejpam-6251	515	13	0	0	NUM
ejpam-6251	515	14	is	be	AUX
ejpam-6251	515	15	the	the	DET
ejpam-6251	515	16	only	only	ADJ
ejpam-6251	515	17	fixed	fix	VERB
ejpam-6251	515	18	point	point	NOUN
ejpam-6251	515	19	for	for	ADP
ejpam-6251	515	20	p.	p.	NOUN
ejpam-6251	515	21	example	example	NOUN
ejpam-6251	516	1	3	3	X
ejpam-6251	516	2	.	.	PUNCT
ejpam-6251	516	3	let	let	VERB
ejpam-6251	516	4	𭟋	𭟋	VERB
ejpam-6251	516	5	=	=	VERB
ejpam-6251	516	6	{	{	PUNCT
ejpam-6251	516	7	uµ(r	uµ(r	NUM
ejpam-6251	516	8	)	)	PUNCT
ejpam-6251	516	9	:	:	PUNCT
ejpam-6251	516	10	uµ(r	uµ(r	NUM
ejpam-6251	516	11	)	)	PUNCT
ejpam-6251	516	12	is	be	AUX
ejpam-6251	516	13	an	an	DET
ejpam-6251	516	14	upper	upper	ADJ
ejpam-6251	516	15	triangular	triangular	NOUN
ejpam-6251	516	16	matrices	matrix	NOUN
ejpam-6251	516	17	over	over	ADP
ejpam-6251	516	18	r	r	NOUN
ejpam-6251	516	19	}	}	PUNCT
ejpam-6251	516	20	and	and	CCONJ
ejpam-6251	516	21	s	s	NOUN
ejpam-6251	516	22	=	=	X
ejpam-6251	516	23	{	{	PUNCT
ejpam-6251	516	24	lµ(r	lµ(r	NOUN
ejpam-6251	516	25	)	)	PUNCT
ejpam-6251	516	26	:	:	PUNCT
ejpam-6251	517	1	lµ(r	lµ(r	X
ejpam-6251	517	2	)	)	PUNCT
ejpam-6251	517	3	is	be	AUX
ejpam-6251	517	4	an	an	DET
ejpam-6251	517	5	upper	upper	ADJ
ejpam-6251	517	6	triangular	triangular	NOUN
ejpam-6251	517	7	matrices	matrix	NOUN
ejpam-6251	517	8	over	over	ADP
ejpam-6251	517	9	r	r	NOUN
ejpam-6251	517	10	}	}	PUNCT
ejpam-6251	517	11	.	.	PUNCT
ejpam-6251	518	1	define	define	VERB
ejpam-6251	518	2	π	π	PROPN
ejpam-6251	518	3	,	,	PUNCT
ejpam-6251	518	4	ψ	ψ	SYM
ejpam-6251	518	5	,	,	PUNCT
ejpam-6251	518	6	ξ	ξ	PROPN
ejpam-6251	518	7	:	:	PUNCT
ejpam-6251	518	8	𭟋×	𭟋×	PROPN
ejpam-6251	518	9	s	s	X
ejpam-6251	518	10	×	×	NOUN
ejpam-6251	518	11	(	(	PUNCT
ejpam-6251	518	12	0,+∞	0,+∞	NUM
ejpam-6251	518	13	)	)	PUNCT
ejpam-6251	518	14	→	→	PUNCT
ejpam-6251	519	1	[	[	X
ejpam-6251	519	2	0	0	NUM
ejpam-6251	519	3	,	,	PUNCT
ejpam-6251	519	4	1	1	NUM
ejpam-6251	519	5	]	]	PUNCT
ejpam-6251	519	6	as	as	ADP
ejpam-6251	519	7	π(r	π(r	PROPN
ejpam-6251	519	8	,	,	PUNCT
ejpam-6251	519	9	q	q	NOUN
ejpam-6251	519	10	,	,	PUNCT
ejpam-6251	519	11	ż	ż	NOUN
ejpam-6251	519	12	)	)	PUNCT
ejpam-6251	519	13	=	=	PUNCT
ejpam-6251	520	1	ż	ż	PROPN
ejpam-6251	520	2	ż+	ż+	PROPN
ejpam-6251	520	3	∑µ	∑µ	PROPN
ejpam-6251	521	1	i	i	PROPN
ejpam-6251	521	2	,	,	PUNCT
ejpam-6251	521	3	j=1	j=1	PROPN
ejpam-6251	521	4	|rij	|rij	PROPN
ejpam-6251	521	5	−	−	NOUN
ejpam-6251	521	6	qij|	qij|	NOUN
ejpam-6251	521	7	,	,	PUNCT
ejpam-6251	521	8	ψ(r	ψ(r	PROPN
ejpam-6251	521	9	,	,	PUNCT
ejpam-6251	521	10	q	q	NOUN
ejpam-6251	521	11	,	,	PUNCT
ejpam-6251	521	12	ż	ż	NOUN
ejpam-6251	521	13	)	)	PUNCT
ejpam-6251	521	14	=	=	PUNCT
ejpam-6251	522	1	∑µ	∑µ	PROPN
ejpam-6251	522	2	i	i	PROPN
ejpam-6251	522	3	,	,	PUNCT
ejpam-6251	522	4	j=1	j=1	PROPN
ejpam-6251	522	5	|rij	|rij	PROPN
ejpam-6251	522	6	−	−	NOUN
ejpam-6251	522	7	qij|	qij|	NOUN
ejpam-6251	522	8	ż+	ż+	PROPN
ejpam-6251	522	9	∑µ	∑µ	PROPN
ejpam-6251	523	1	i	i	PROPN
ejpam-6251	523	2	,	,	PUNCT
ejpam-6251	523	3	j=1	j=1	PROPN
ejpam-6251	523	4	|rij	|rij	PROPN
ejpam-6251	523	5	−	−	NOUN
ejpam-6251	523	6	qij|	qij|	NOUN
ejpam-6251	523	7	,	,	PUNCT
ejpam-6251	523	8	ψ(r	ψ(r	PROPN
ejpam-6251	523	9	,	,	PUNCT
ejpam-6251	523	10	q	q	NOUN
ejpam-6251	523	11	,	,	PUNCT
ejpam-6251	523	12	ż	ż	NOUN
ejpam-6251	523	13	)	)	PUNCT
ejpam-6251	523	14	=	=	PUNCT
ejpam-6251	524	1	∑µ	∑µ	PROPN
ejpam-6251	524	2	i	i	PROPN
ejpam-6251	524	3	,	,	PUNCT
ejpam-6251	524	4	j=1	j=1	PROPN
ejpam-6251	524	5	|rij	|rij	PROPN
ejpam-6251	524	6	−	−	NUM
ejpam-6251	524	7	qij|	qij|	NOUN
ejpam-6251	524	8	ż	ż	NOUN
ejpam-6251	524	9	,	,	PUNCT
ejpam-6251	524	10	for	for	ADP
ejpam-6251	524	11	all	all	DET
ejpam-6251	524	12	r	r	NOUN
ejpam-6251	524	13	=	=	SYM
ejpam-6251	524	14	(	(	PUNCT
ejpam-6251	524	15	rij)µ×µ	rij)µ×µ	NOUN
ejpam-6251	524	16	∈	∈	PROPN
ejpam-6251	524	17	𭟋	𭟋	NOUN
ejpam-6251	524	18	and	and	CCONJ
ejpam-6251	524	19	q	q	NOUN
ejpam-6251	524	20	=	=	PUNCT
ejpam-6251	524	21	(	(	PUNCT
ejpam-6251	524	22	qij)µ×µ	qij)µ×µ	PROPN
ejpam-6251	524	23	∈	∈	PROPN
ejpam-6251	524	24	s	s	PROPN
ejpam-6251	524	25	,	,	PUNCT
ejpam-6251	524	26	then	then	ADV
ejpam-6251	524	27	,	,	PUNCT
ejpam-6251	524	28	(	(	PUNCT
ejpam-6251	524	29	𭟋	𭟋	NOUN
ejpam-6251	524	30	,	,	PUNCT
ejpam-6251	524	31	s	s	PROPN
ejpam-6251	524	32	,	,	PUNCT
ejpam-6251	524	33	π	π	PROPN
ejpam-6251	524	34	,	,	PUNCT
ejpam-6251	524	35	ψ	ψ	PROPN
ejpam-6251	524	36	,	,	PUNCT
ejpam-6251	524	37	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	524	38	,	,	PUNCT
ejpam-6251	524	39	♢	♢	PROPN
ejpam-6251	524	40	)	)	PUNCT
ejpam-6251	524	41	is	be	AUX
ejpam-6251	524	42	a	a	DET
ejpam-6251	524	43	complete	complete	ADJ
ejpam-6251	524	44	nbms	nbms	NOUN
ejpam-6251	524	45	with	with	ADP
ejpam-6251	524	46	ct−||.||	ct−||.||	PROPN
ejpam-6251	524	47	ė⋇	ė⋇	PROPN
ejpam-6251	524	48	ȧ	ȧ	PROPN
ejpam-6251	525	1	=	=	PROPN
ejpam-6251	525	2	ėȧ	ėȧ	PROPN
ejpam-6251	525	3	and	and	CCONJ
ejpam-6251	525	4	ct−co−||.||	ct−co−||.||	DET
ejpam-6251	525	5	ė	ė	PROPN
ejpam-6251	525	6	♢	♢	PROPN
ejpam-6251	525	7	ȧ	ȧ	PROPN
ejpam-6251	525	8	=	=	PROPN
ejpam-6251	525	9	max{ė	max{ė	PROPN
ejpam-6251	525	10	,	,	PUNCT
ejpam-6251	525	11	ȧ	ȧ	PROPN
ejpam-6251	525	12	}	}	PUNCT
ejpam-6251	525	13	.	.	PUNCT
ejpam-6251	526	1	define	define	VERB
ejpam-6251	526	2	p	p	X
ejpam-6251	526	3	:	:	PUNCT
ejpam-6251	526	4	(	(	PUNCT
ejpam-6251	526	5	𭟋	𭟋	NOUN
ejpam-6251	526	6	,	,	PUNCT
ejpam-6251	526	7	s	s	PROPN
ejpam-6251	526	8	,	,	PUNCT
ejpam-6251	526	9	π	π	PROPN
ejpam-6251	526	10	,	,	PUNCT
ejpam-6251	526	11	ψ	ψ	PROPN
ejpam-6251	526	12	,	,	PUNCT
ejpam-6251	526	13	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	526	14	,	,	PUNCT
ejpam-6251	526	15	♢	♢	PROPN
ejpam-6251	526	16	)	)	PUNCT
ejpam-6251	526	17	⇒	⇒	NOUN
ejpam-6251	526	18	(	(	PUNCT
ejpam-6251	526	19	𭟋	𭟋	PROPN
ejpam-6251	526	20	,	,	PUNCT
ejpam-6251	526	21	s	s	PROPN
ejpam-6251	526	22	,	,	PUNCT
ejpam-6251	526	23	π	π	PROPN
ejpam-6251	526	24	,	,	PUNCT
ejpam-6251	526	25	ψ	ψ	PROPN
ejpam-6251	526	26	,	,	PUNCT
ejpam-6251	526	27	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	526	28	,	,	PUNCT
ejpam-6251	526	29	♢	♢	PROPN
ejpam-6251	526	30	)	)	PUNCT
ejpam-6251	526	31	by	by	ADP
ejpam-6251	526	32	p((rij)µ×µ	p((rij)µ×µ	NOUN
ejpam-6251	526	33	)	)	PUNCT
ejpam-6251	526	34	=	=	PUNCT
ejpam-6251	527	1	(	(	PUNCT
ejpam-6251	527	2	rij	rij	X
ejpam-6251	527	3	5	5	NUM
ejpam-6251	527	4	)	)	PUNCT
ejpam-6251	527	5	µ×µ	µ×µ	X
ejpam-6251	527	6	,	,	PUNCT
ejpam-6251	527	7	∀	∀	X
ejpam-6251	527	8	(	(	PUNCT
ejpam-6251	527	9	rij)µ×µ	rij)µ×µ	NOUN
ejpam-6251	527	10	∈	∈	PROPN
ejpam-6251	527	11	𭟋	𭟋	ADP
ejpam-6251	527	12	∪	∪	NOUN
ejpam-6251	527	13	s	s	NOUN
ejpam-6251	527	14	and	and	CCONJ
ejpam-6251	527	15	take	take	VERB
ejpam-6251	527	16	ζ	ζ	NOUN
ejpam-6251	527	17	∈	∈	NOUN
ejpam-6251	528	1	[	[	X
ejpam-6251	528	2	12	12	NUM
ejpam-6251	528	3	,	,	PUNCT
ejpam-6251	528	4	1	1	NUM
ejpam-6251	528	5	)	)	PUNCT
ejpam-6251	528	6	,	,	PUNCT
ejpam-6251	528	7	then	then	ADV
ejpam-6251	528	8	π(pr	π(pr	NOUN
ejpam-6251	528	9	,	,	PUNCT
ejpam-6251	528	10	pq	pq	INTJ
ejpam-6251	528	11	,	,	PUNCT
ejpam-6251	528	12	ζ	ζ	NOUN
ejpam-6251	528	13	ż	ż	NOUN
ejpam-6251	528	14	)	)	PUNCT
ejpam-6251	529	1	=	=	SYM
ejpam-6251	529	2	π	π	X
ejpam-6251	529	3	(	(	PUNCT
ejpam-6251	529	4	(	(	PUNCT
ejpam-6251	529	5	rij	rij	X
ejpam-6251	529	6	5	5	NUM
ejpam-6251	529	7	)	)	PUNCT
ejpam-6251	529	8	µ×µ	µ×µ	X
ejpam-6251	529	9	,	,	PUNCT
ejpam-6251	529	10	(	(	PUNCT
ejpam-6251	529	11	qij	qij	NOUN
ejpam-6251	529	12	5	5	NUM
ejpam-6251	529	13	)	)	PUNCT
ejpam-6251	529	14	µ×µ	µ×µ	SYM
ejpam-6251	529	15	,	,	PUNCT
ejpam-6251	529	16	ζ	ζ	NOUN
ejpam-6251	529	17	ż	ż	NOUN
ejpam-6251	529	18	)	)	PUNCT
ejpam-6251	529	19	=	=	PUNCT
ejpam-6251	529	20	ζ	ζ	NOUN
ejpam-6251	529	21	ż	ż	NOUN
ejpam-6251	529	22	ζ	ζ	PROPN
ejpam-6251	529	23	ż+	ż+	PROPN
ejpam-6251	529	24	1	1	NUM
ejpam-6251	529	25	5	5	NUM
ejpam-6251	529	26	∑µ	∑µ	PROPN
ejpam-6251	529	27	i	i	PROPN
ejpam-6251	529	28	,	,	PUNCT
ejpam-6251	529	29	j=1	j=1	PROPN
ejpam-6251	529	30	|rij	|rij	PROPN
ejpam-6251	529	31	−	−	NOUN
ejpam-6251	529	32	qij|	qij|	NOUN
ejpam-6251	529	33	≥	≥	NOUN
ejpam-6251	529	34	ζ	ζ	NOUN
ejpam-6251	529	35	ż	ż	NOUN
ejpam-6251	529	36	ζ	ζ	PROPN
ejpam-6251	529	37	ż+	ż+	PROPN
ejpam-6251	529	38	∑µ	∑µ	PROPN
ejpam-6251	530	1	i	i	PROPN
ejpam-6251	530	2	,	,	PUNCT
ejpam-6251	530	3	j=1	j=1	PROPN
ejpam-6251	530	4	|rij	|rij	PROPN
ejpam-6251	530	5	−	−	NOUN
ejpam-6251	530	6	qij|	qij|	NOUN
ejpam-6251	530	7	≥	≥	NOUN
ejpam-6251	530	8	ż	ż	PROPN
ejpam-6251	530	9	ż+	ż+	PROPN
ejpam-6251	530	10	∑µ	∑µ	PROPN
ejpam-6251	531	1	i	i	PROPN
ejpam-6251	531	2	,	,	PUNCT
ejpam-6251	531	3	j=1	j=1	PROPN
ejpam-6251	531	4	|rij	|rij	PROPN
ejpam-6251	531	5	−	−	NOUN
ejpam-6251	531	6	qij|	qij|	NOUN
ejpam-6251	531	7	=	=	SYM
ejpam-6251	531	8	π(r	π(r	PROPN
ejpam-6251	531	9	,	,	PUNCT
ejpam-6251	531	10	q	q	NOUN
ejpam-6251	531	11	,	,	PUNCT
ejpam-6251	531	12	ż	ż	NOUN
ejpam-6251	531	13	)	)	PUNCT
ejpam-6251	531	14	,	,	PUNCT
ejpam-6251	531	15	ψ(pr	ψ(pr	PROPN
ejpam-6251	531	16	,	,	PUNCT
ejpam-6251	531	17	pq	pq	NOUN
ejpam-6251	531	18	,	,	PUNCT
ejpam-6251	531	19	ζ	ζ	NOUN
ejpam-6251	531	20	ż	ż	NOUN
ejpam-6251	531	21	)	)	PUNCT
ejpam-6251	531	22	=	=	SYM
ejpam-6251	531	23	π	π	X
ejpam-6251	531	24	(	(	PUNCT
ejpam-6251	531	25	(	(	PUNCT
ejpam-6251	531	26	rij	rij	X
ejpam-6251	531	27	5	5	NUM
ejpam-6251	531	28	)	)	PUNCT
ejpam-6251	531	29	µ×µ	µ×µ	X
ejpam-6251	531	30	,	,	PUNCT
ejpam-6251	531	31	(	(	PUNCT
ejpam-6251	531	32	qij	qij	NOUN
ejpam-6251	531	33	5	5	NUM
ejpam-6251	531	34	)	)	PUNCT
ejpam-6251	531	35	µ×µ	µ×µ	SYM
ejpam-6251	531	36	,	,	PUNCT
ejpam-6251	531	37	ζ	ζ	NOUN
ejpam-6251	531	38	ż	ż	NOUN
ejpam-6251	531	39	)	)	PUNCT
ejpam-6251	531	40	=	=	SYM
ejpam-6251	531	41	1	1	NUM
ejpam-6251	531	42	5	5	NUM
ejpam-6251	531	43	∑µ	∑µ	PROPN
ejpam-6251	531	44	i	i	PROPN
ejpam-6251	531	45	,	,	PUNCT
ejpam-6251	531	46	j=1	j=1	PROPN
ejpam-6251	531	47	|rij	|rij	PROPN
ejpam-6251	531	48	−	−	NOUN
ejpam-6251	531	49	qij|	qij|	NOUN
ejpam-6251	531	50	ζ	ζ	PROPN
ejpam-6251	531	51	ż+	ż+	PROPN
ejpam-6251	531	52	1	1	NUM
ejpam-6251	531	53	5	5	NUM
ejpam-6251	531	54	∑µ	∑µ	PROPN
ejpam-6251	531	55	i	i	PROPN
ejpam-6251	531	56	,	,	PUNCT
ejpam-6251	531	57	j=1	j=1	PROPN
ejpam-6251	531	58	|rij	|rij	PROPN
ejpam-6251	531	59	−	−	NOUN
ejpam-6251	531	60	qij|	qij|	NOUN
ejpam-6251	531	61	=	=	SYM
ejpam-6251	531	62	∑µ	∑µ	PROPN
ejpam-6251	531	63	i	i	PROPN
ejpam-6251	531	64	,	,	PUNCT
ejpam-6251	531	65	j=1	j=1	PROPN
ejpam-6251	531	66	|rij	|rij	PROPN
ejpam-6251	531	67	−	−	NOUN
ejpam-6251	531	68	qij|	qij|	NOUN
ejpam-6251	531	69	5ζ	5ζ	PROPN
ejpam-6251	531	70	ż+	ż+	PROPN
ejpam-6251	531	71	∑µ	∑µ	PROPN
ejpam-6251	532	1	i	i	PROPN
ejpam-6251	532	2	,	,	PUNCT
ejpam-6251	532	3	j=1	j=1	PROPN
ejpam-6251	532	4	|rij	|rij	PROPN
ejpam-6251	532	5	−	−	NOUN
ejpam-6251	532	6	qij|	qij|	NOUN
ejpam-6251	532	7	≤	≤	PUNCT
ejpam-6251	532	8	∑µ	∑µ	PROPN
ejpam-6251	532	9	i	i	PROPN
ejpam-6251	532	10	,	,	PUNCT
ejpam-6251	532	11	j=1	j=1	PROPN
ejpam-6251	532	12	|rij	|rij	PROPN
ejpam-6251	532	13	−	−	NOUN
ejpam-6251	532	14	qij|	qij|	NOUN
ejpam-6251	532	15	ż+	ż+	PROPN
ejpam-6251	532	16	∑µ	∑µ	PROPN
ejpam-6251	533	1	i	i	PROPN
ejpam-6251	533	2	,	,	PUNCT
ejpam-6251	533	3	j=1	j=1	PROPN
ejpam-6251	533	4	|rij	|rij	PROPN
ejpam-6251	533	5	−	−	NOUN
ejpam-6251	533	6	qij|	qij|	NOUN
ejpam-6251	533	7	=	=	SYM
ejpam-6251	533	8	ψ(r	ψ(r	NOUN
ejpam-6251	533	9	,	,	PUNCT
ejpam-6251	533	10	q	q	NOUN
ejpam-6251	533	11	,	,	PUNCT
ejpam-6251	533	12	ż	ż	NOUN
ejpam-6251	533	13	)	)	PUNCT
ejpam-6251	533	14	r.	r.	PROPN
ejpam-6251	533	15	ramaswamy	ramaswamy	PROPN
ejpam-6251	533	16	/	/	SYM
ejpam-6251	533	17	eur	eur	PROPN
ejpam-6251	533	18	.	.	PUNCT
ejpam-6251	534	1	j.	j.	PROPN
ejpam-6251	534	2	pure	pure	PROPN
ejpam-6251	534	3	appl	appl	PROPN
ejpam-6251	534	4	.	.	PROPN
ejpam-6251	534	5	math	math	PROPN
ejpam-6251	534	6	,	,	PUNCT
ejpam-6251	534	7	18	18	NUM
ejpam-6251	534	8	(	(	PUNCT
ejpam-6251	534	9	4	4	NUM
ejpam-6251	534	10	)	)	PUNCT
ejpam-6251	534	11	(	(	PUNCT
ejpam-6251	534	12	2025	2025	NUM
ejpam-6251	534	13	)	)	PUNCT
ejpam-6251	534	14	,	,	PUNCT
ejpam-6251	534	15	6251	6251	NUM
ejpam-6251	534	16	28	28	NUM
ejpam-6251	534	17	of	of	ADP
ejpam-6251	534	18	40	40	NUM
ejpam-6251	534	19	and	and	CCONJ
ejpam-6251	534	20	ξ(pr	ξ(pr	NOUN
ejpam-6251	534	21	,	,	PUNCT
ejpam-6251	534	22	pq	pq	NOUN
ejpam-6251	534	23	,	,	PUNCT
ejpam-6251	534	24	ζ	ζ	NOUN
ejpam-6251	534	25	ż	ż	NOUN
ejpam-6251	534	26	)	)	PUNCT
ejpam-6251	534	27	=	=	SYM
ejpam-6251	535	1	ξ	ξ	X
ejpam-6251	535	2	(	(	PUNCT
ejpam-6251	535	3	(	(	PUNCT
ejpam-6251	535	4	rij	rij	X
ejpam-6251	535	5	5	5	NUM
ejpam-6251	535	6	)	)	PUNCT
ejpam-6251	535	7	µ×µ	µ×µ	X
ejpam-6251	535	8	,	,	PUNCT
ejpam-6251	535	9	(	(	PUNCT
ejpam-6251	535	10	qij	qij	NOUN
ejpam-6251	535	11	5	5	NUM
ejpam-6251	535	12	)	)	PUNCT
ejpam-6251	535	13	µ×µ	µ×µ	SYM
ejpam-6251	535	14	,	,	PUNCT
ejpam-6251	535	15	ζ	ζ	NOUN
ejpam-6251	535	16	ż	ż	NOUN
ejpam-6251	535	17	)	)	PUNCT
ejpam-6251	535	18	=	=	SYM
ejpam-6251	535	19	1	1	NUM
ejpam-6251	535	20	5	5	NUM
ejpam-6251	535	21	∑µ	∑µ	PROPN
ejpam-6251	535	22	i	i	PROPN
ejpam-6251	535	23	,	,	PUNCT
ejpam-6251	535	24	j=1	j=1	PROPN
ejpam-6251	535	25	|rij	|rij	PROPN
ejpam-6251	535	26	−	−	NOUN
ejpam-6251	535	27	qij|	qij|	NOUN
ejpam-6251	535	28	ζ	ζ	PROPN
ejpam-6251	535	29	ż	ż	NOUN
ejpam-6251	535	30	≤	≤	PUNCT
ejpam-6251	536	1	∑µ	∑µ	PROPN
ejpam-6251	537	1	i	i	PROPN
ejpam-6251	537	2	,	,	PUNCT
ejpam-6251	537	3	j=1	j=1	PROPN
ejpam-6251	537	4	|rij	|rij	PROPN
ejpam-6251	537	5	−	−	NOUN
ejpam-6251	537	6	qij|	qij|	NOUN
ejpam-6251	537	7	ζ	ζ	PROPN
ejpam-6251	537	8	ż	ż	NOUN
ejpam-6251	537	9	≤	≤	PUNCT
ejpam-6251	538	1	∑µ	∑µ	PROPN
ejpam-6251	539	1	i	i	PROPN
ejpam-6251	539	2	,	,	PUNCT
ejpam-6251	539	3	j=1	j=1	PROPN
ejpam-6251	539	4	|rij	|rij	PROPN
ejpam-6251	539	5	−	−	NUM
ejpam-6251	539	6	qij|	qij|	NOUN
ejpam-6251	539	7	ż	ż	NOUN
ejpam-6251	539	8	=	=	SYM
ejpam-6251	539	9	ξ(r	ξ(r	PROPN
ejpam-6251	539	10	,	,	PUNCT
ejpam-6251	539	11	q	q	NOUN
ejpam-6251	539	12	,	,	PUNCT
ejpam-6251	539	13	ż	ż	NOUN
ejpam-6251	539	14	)	)	PUNCT
ejpam-6251	539	15	.	.	PUNCT
ejpam-6251	540	1	therefore	therefore	ADV
ejpam-6251	540	2	,	,	PUNCT
ejpam-6251	540	3	all	all	DET
ejpam-6251	540	4	the	the	DET
ejpam-6251	540	5	hypothesis	hypothesis	NOUN
ejpam-6251	540	6	of	of	ADP
ejpam-6251	540	7	theorem	theorem	NOUN
ejpam-6251	540	8	5	5	NUM
ejpam-6251	540	9	are	be	AUX
ejpam-6251	540	10	satisfied	satisfied	ADJ
ejpam-6251	540	11	,	,	PUNCT
ejpam-6251	540	12	and	and	CCONJ
ejpam-6251	540	13	oµ×µ	oµ×µ	PROPN
ejpam-6251	540	14	is	be	AUX
ejpam-6251	540	15	the	the	DET
ejpam-6251	540	16	unique	unique	ADJ
ejpam-6251	540	17	fixed	fix	VERB
ejpam-6251	540	18	point	point	NOUN
ejpam-6251	540	19	for	for	ADP
ejpam-6251	540	20	p	p	X
ejpam-6251	540	21	,	,	PUNCT
ejpam-6251	540	22	where	where	SCONJ
ejpam-6251	540	23	oµ×µ	oµ×µ	PROPN
ejpam-6251	540	24	is	be	AUX
ejpam-6251	540	25	the	the	DET
ejpam-6251	540	26	null	null	ADJ
ejpam-6251	540	27	matrix	matrix	NOUN
ejpam-6251	540	28	of	of	ADP
ejpam-6251	540	29	order	order	NOUN
ejpam-6251	540	30	µ.	µ.	NOUN
ejpam-6251	540	31	4	4	NUM
ejpam-6251	540	32	.	.	PUNCT
ejpam-6251	540	33	application	application	NOUN
ejpam-6251	540	34	1	1	NUM
ejpam-6251	540	35	consider	consider	VERB
ejpam-6251	540	36	the	the	DET
ejpam-6251	540	37	set	set	NOUN
ejpam-6251	540	38	of	of	ADP
ejpam-6251	540	39	all	all	DET
ejpam-6251	540	40	continuous	continuous	ADJ
ejpam-6251	540	41	functions	function	NOUN
ejpam-6251	540	42	𭟋	𭟋	ADP
ejpam-6251	540	43	=	=	SYM
ejpam-6251	540	44	c([c	c([c	PROPN
ejpam-6251	540	45	,	,	PUNCT
ejpam-6251	540	46	a	a	PRON
ejpam-6251	540	47	]	]	X
ejpam-6251	540	48	,	,	PUNCT
ejpam-6251	540	49	[	[	X
ejpam-6251	540	50	0,+∞	0,+∞	NUM
ejpam-6251	540	51	)	)	PUNCT
ejpam-6251	540	52	)	)	PUNCT
ejpam-6251	541	1	defined	define	VERB
ejpam-6251	541	2	on	on	ADP
ejpam-6251	541	3	[	[	X
ejpam-6251	541	4	c	c	X
ejpam-6251	541	5	,	,	PUNCT
ejpam-6251	541	6	a	a	X
ejpam-6251	541	7	]	]	X
ejpam-6251	541	8	with	with	ADP
ejpam-6251	541	9	values	value	NOUN
ejpam-6251	541	10	in	in	ADP
ejpam-6251	541	11	the	the	DET
ejpam-6251	541	12	interval	interval	NOUN
ejpam-6251	541	13	[	[	X
ejpam-6251	541	14	0,+∞	0,+∞	NUM
ejpam-6251	541	15	)	)	PUNCT
ejpam-6251	541	16	and	and	CCONJ
ejpam-6251	541	17	s	s	NOUN
ejpam-6251	541	18	=	=	VERB
ejpam-6251	541	19	c([c	c([c	PROPN
ejpam-6251	541	20	,	,	PUNCT
ejpam-6251	541	21	a	a	DET
ejpam-6251	541	22	]	]	X
ejpam-6251	541	23	,	,	PUNCT
ejpam-6251	541	24	(	(	PUNCT
ejpam-6251	541	25	−∞	−∞	NOUN
ejpam-6251	541	26	,	,	PUNCT
ejpam-6251	541	27	0	0	NUM
ejpam-6251	541	28	]	]	PUNCT
ejpam-6251	541	29	)	)	PUNCT
ejpam-6251	541	30	defined	define	VERB
ejpam-6251	541	31	on	on	ADP
ejpam-6251	541	32	[	[	X
ejpam-6251	541	33	c	c	X
ejpam-6251	541	34	,	,	PUNCT
ejpam-6251	541	35	a	a	X
ejpam-6251	541	36	]	]	X
ejpam-6251	541	37	with	with	ADP
ejpam-6251	541	38	values	value	NOUN
ejpam-6251	541	39	in	in	ADP
ejpam-6251	541	40	the	the	DET
ejpam-6251	541	41	interval	interval	NOUN
ejpam-6251	541	42	(	(	PUNCT
ejpam-6251	541	43	−∞	−∞	NOUN
ejpam-6251	541	44	,	,	PUNCT
ejpam-6251	541	45	0	0	NUM
ejpam-6251	541	46	]	]	PUNCT
ejpam-6251	541	47	.	.	PUNCT
ejpam-6251	542	1	suppose	suppose	VERB
ejpam-6251	542	2	the	the	DET
ejpam-6251	542	3	integral	integral	ADJ
ejpam-6251	542	4	equation	equation	NOUN
ejpam-6251	542	5	:	:	PUNCT
ejpam-6251	542	6	ς(l	ς(l	PROPN
ejpam-6251	542	7	)	)	PUNCT
ejpam-6251	542	8	=	=	SYM
ejpam-6251	542	9	∧(l	∧(l	X
ejpam-6251	542	10	)	)	PUNCT
ejpam-6251	543	1	+	+	CCONJ
ejpam-6251	543	2	δ	δ	PROPN
ejpam-6251	543	3	∫	∫	PROPN
ejpam-6251	543	4	a	a	DET
ejpam-6251	543	5	c	c	PROPN
ejpam-6251	543	6	℧	℧	PROPN
ejpam-6251	543	7	(	(	PUNCT
ejpam-6251	543	8	l	l	NOUN
ejpam-6251	543	9	,	,	PUNCT
ejpam-6251	543	10	ε)ς(l)dε	ε)ς(l)dε	NOUN
ejpam-6251	543	11	for	for	ADP
ejpam-6251	543	12	l	l	NOUN
ejpam-6251	543	13	,	,	PUNCT
ejpam-6251	543	14	ε	ε	PROPN
ejpam-6251	543	15	∈	∈	PROPN
ejpam-6251	544	1	[	[	X
ejpam-6251	544	2	c	c	X
ejpam-6251	544	3	,	,	PUNCT
ejpam-6251	544	4	a	a	X
ejpam-6251	544	5	]	]	X
ejpam-6251	544	6	(	(	PUNCT
ejpam-6251	544	7	16	16	NUM
ejpam-6251	544	8	)	)	PUNCT
ejpam-6251	544	9	where	where	SCONJ
ejpam-6251	544	10	δ	δ	X
ejpam-6251	544	11	>	>	X
ejpam-6251	544	12	0	0	PROPN
ejpam-6251	544	13	,	,	PUNCT
ejpam-6251	544	14	℧	℧	PROPN
ejpam-6251	544	15	:	:	PUNCT
ejpam-6251	544	16	c([c	c([c	PROPN
ejpam-6251	544	17	,	,	PUNCT
ejpam-6251	544	18	a	a	DET
ejpam-6251	544	19	]	]	X
ejpam-6251	544	20	×	×	NOUN
ejpam-6251	544	21	r	r	NOUN
ejpam-6251	544	22	)	)	PUNCT
ejpam-6251	544	23	→	→	NOUN
ejpam-6251	544	24	r+	r+	X
ejpam-6251	544	25	,	,	PUNCT
ejpam-6251	544	26	∧(ε	∧(ε	PROPN
ejpam-6251	544	27	)	)	PUNCT
ejpam-6251	544	28	is	be	AUX
ejpam-6251	544	29	a	a	DET
ejpam-6251	544	30	fuzzy	fuzzy	ADJ
ejpam-6251	544	31	function	function	NOUN
ejpam-6251	544	32	of	of	ADP
ejpam-6251	544	33	ε	ε	PROPN
ejpam-6251	544	34	:	:	PUNCT
ejpam-6251	544	35	ε	ε	PROPN
ejpam-6251	544	36	∈	∈	PROPN
ejpam-6251	545	1	[	[	X
ejpam-6251	545	2	c	c	X
ejpam-6251	545	3	,	,	PUNCT
ejpam-6251	545	4	a	a	PRON
ejpam-6251	545	5	]	]	X
ejpam-6251	545	6	.	.	PUNCT
ejpam-6251	546	1	define	define	VERB
ejpam-6251	546	2	π	π	PROPN
ejpam-6251	546	3	,	,	PUNCT
ejpam-6251	546	4	ψ	ψ	NOUN
ejpam-6251	546	5	and	and	CCONJ
ejpam-6251	546	6	ξ	ξ	X
ejpam-6251	546	7	by	by	ADP
ejpam-6251	546	8	π(ς(l	π(ς(l	PROPN
ejpam-6251	546	9	)	)	PUNCT
ejpam-6251	546	10	,	,	PUNCT
ejpam-6251	546	11	ϖ(l	ϖ(l	PROPN
ejpam-6251	546	12	)	)	PUNCT
ejpam-6251	546	13	,	,	PUNCT
ejpam-6251	546	14	ż	ż	NOUN
ejpam-6251	546	15	)	)	PUNCT
ejpam-6251	546	16	=	=	SYM
ejpam-6251	546	17	sup	sup	NOUN
ejpam-6251	546	18	l∈[c	l∈[c	PROPN
ejpam-6251	546	19	,	,	PUNCT
ejpam-6251	546	20	a	a	PRON
ejpam-6251	546	21	]	]	X
ejpam-6251	546	22	ż	ż	PROPN
ejpam-6251	546	23	ż+	ż+	PROPN
ejpam-6251	546	24	|ς(l)−ϖ(l)|	|ς(l)−ϖ(l)|	ADP
ejpam-6251	546	25	∀	∀	PUNCT
ejpam-6251	547	1	ς,ϖ	ς,ϖ	NUM
ejpam-6251	547	2	∈	∈	PROPN
ejpam-6251	547	3	𭟋	𭟋	NOUN
ejpam-6251	547	4	and	and	CCONJ
ejpam-6251	547	5	ż	ż	X
ejpam-6251	547	6	>	>	X
ejpam-6251	547	7	0	0	NUM
ejpam-6251	547	8	,	,	PUNCT
ejpam-6251	547	9	ψ(ς(o	ψ(ς(o	NOUN
ejpam-6251	547	10	)	)	PUNCT
ejpam-6251	547	11	,	,	PUNCT
ejpam-6251	547	12	ϖ(o	ϖ(o	NOUN
ejpam-6251	547	13	)	)	PUNCT
ejpam-6251	547	14	,	,	PUNCT
ejpam-6251	547	15	ż	ż	NOUN
ejpam-6251	547	16	)	)	PUNCT
ejpam-6251	547	17	=	=	SYM
ejpam-6251	547	18	1−	1−	NUM
ejpam-6251	547	19	sup	sup	NOUN
ejpam-6251	547	20	o∈[c	o∈[c	ADP
ejpam-6251	547	21	,	,	PUNCT
ejpam-6251	547	22	a	a	PRON
ejpam-6251	547	23	]	]	X
ejpam-6251	547	24	ż	ż	PROPN
ejpam-6251	547	25	ż+	ż+	PROPN
ejpam-6251	547	26	|ς(o)−ϖ(o)|	|ς(o)−ϖ(o)|	ADP
ejpam-6251	547	27	∀	∀	NOUN
ejpam-6251	548	1	ς,ϖ	ς,ϖ	NUM
ejpam-6251	548	2	∈	∈	NUM
ejpam-6251	548	3	𭟋	𭟋	NOUN
ejpam-6251	548	4	and	and	CCONJ
ejpam-6251	548	5	ż	ż	X
ejpam-6251	548	6	>	>	X
ejpam-6251	548	7	0	0	NUM
ejpam-6251	548	8	,	,	PUNCT
ejpam-6251	548	9	and	and	CCONJ
ejpam-6251	548	10	ξ(ς(o	ξ(ς(o	NOUN
ejpam-6251	548	11	)	)	PUNCT
ejpam-6251	548	12	,	,	PUNCT
ejpam-6251	548	13	ϖ(o	ϖ(o	NOUN
ejpam-6251	548	14	)	)	PUNCT
ejpam-6251	548	15	,	,	PUNCT
ejpam-6251	548	16	ż	ż	NOUN
ejpam-6251	548	17	)	)	PUNCT
ejpam-6251	548	18	=	=	SYM
ejpam-6251	548	19	sup	sup	NOUN
ejpam-6251	548	20	o∈[c	o∈[c	ADV
ejpam-6251	548	21	,	,	PUNCT
ejpam-6251	548	22	a	a	PRON
ejpam-6251	548	23	]	]	X
ejpam-6251	548	24	|ς(o)−ϖ(o)|	|ς(o)−ϖ(o)|	NOUN
ejpam-6251	548	25	ż	ż	NOUN
ejpam-6251	548	26	∀	∀	NOUN
ejpam-6251	549	1	ς,ϖ	ς,ϖ	NUM
ejpam-6251	549	2	∈	∈	PROPN
ejpam-6251	549	3	𭟋	𭟋	NOUN
ejpam-6251	549	4	and	and	CCONJ
ejpam-6251	549	5	ż	ż	X
ejpam-6251	549	6	>	>	X
ejpam-6251	549	7	0	0	NUM
ejpam-6251	549	8	,	,	PUNCT
ejpam-6251	549	9	with	with	ADP
ejpam-6251	549	10	ct−||.||	ct−||.||	NOUN
ejpam-6251	549	11	and	and	CCONJ
ejpam-6251	549	12	ct−co−||.||	ct−co−||.||	PRON
ejpam-6251	549	13	define	define	VERB
ejpam-6251	549	14	by	by	ADP
ejpam-6251	549	15	i⋇	i⋇	PROPN
ejpam-6251	549	16	♭	♭	PROPN
ejpam-6251	550	1	=	=	PUNCT
ejpam-6251	550	2	i	i	PRON
ejpam-6251	550	3	♭	♭	PROPN
ejpam-6251	550	4	and	and	CCONJ
ejpam-6251	550	5	i	i	PRON
ejpam-6251	550	6	♢	♢	PROPN
ejpam-6251	550	7	♭	♭	X
ejpam-6251	550	8	=	=	PUNCT
ejpam-6251	550	9	max{i	max{i	X
ejpam-6251	550	10	,	,	PUNCT
ejpam-6251	550	11	♭	♭	PROPN
ejpam-6251	550	12	}	}	PUNCT
ejpam-6251	550	13	.	.	PUNCT
ejpam-6251	551	1	then	then	ADV
ejpam-6251	551	2	(	(	PUNCT
ejpam-6251	551	3	𭟋	𭟋	X
ejpam-6251	551	4	,	,	PUNCT
ejpam-6251	551	5	π	π	PROPN
ejpam-6251	551	6	,	,	PUNCT
ejpam-6251	551	7	ψ	ψ	PROPN
ejpam-6251	551	8	,	,	PUNCT
ejpam-6251	551	9	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	551	10	,	,	PUNCT
ejpam-6251	551	11	♢	♢	PROPN
ejpam-6251	551	12	)	)	PUNCT
ejpam-6251	551	13	is	be	AUX
ejpam-6251	551	14	a	a	DET
ejpam-6251	551	15	complete	complete	ADJ
ejpam-6251	551	16	nbms	nbms	NOUN
ejpam-6251	551	17	.	.	PUNCT
ejpam-6251	552	1	consider	consider	VERB
ejpam-6251	552	2	|	|	ADV
ejpam-6251	552	3	℧	℧	VERB
ejpam-6251	552	4	(o	(o	NOUN
ejpam-6251	552	5	,	,	PUNCT
ejpam-6251	552	6	ε)ς(o)−	ε)ς(o)−	PRON
ejpam-6251	552	7	℧	℧	PROPN
ejpam-6251	552	8	(	(	PUNCT
ejpam-6251	552	9	o	o	NOUN
ejpam-6251	552	10	,	,	PUNCT
ejpam-6251	552	11	ε)ϖ(o)|	ε)ϖ(o)|	PROPN
ejpam-6251	552	12	≤	≤	NUM
ejpam-6251	552	13	|ς(o)−ϖ(o)|	|ς(o)−ϖ(o)|	VERB
ejpam-6251	552	14	for	for	ADP
ejpam-6251	552	15	ς	ς	PROPN
ejpam-6251	552	16	∈	∈	PROPN
ejpam-6251	552	17	𭟋	𭟋	PROPN
ejpam-6251	552	18	,	,	PUNCT
ejpam-6251	552	19	ϖ	ϖ	PROPN
ejpam-6251	552	20	∈	∈	PROPN
ejpam-6251	552	21	s	s	NOUN
ejpam-6251	552	22	,	,	PUNCT
ejpam-6251	552	23	ζ	ζ	PROPN
ejpam-6251	552	24	∈	∈	PROPN
ejpam-6251	552	25	(	(	PUNCT
ejpam-6251	552	26	0	0	NUM
ejpam-6251	552	27	,	,	PUNCT
ejpam-6251	552	28	1	1	NUM
ejpam-6251	552	29	)	)	PUNCT
ejpam-6251	552	30	and	and	CCONJ
ejpam-6251	552	31	∀o	∀o	PROPN
ejpam-6251	552	32	,	,	PUNCT
ejpam-6251	552	33	ε	ε	PROPN
ejpam-6251	552	34	∈	∈	PROPN
ejpam-6251	553	1	[	[	X
ejpam-6251	553	2	c	c	X
ejpam-6251	553	3	,	,	PUNCT
ejpam-6251	553	4	a	a	PRON
ejpam-6251	553	5	]	]	X
ejpam-6251	553	6	.	.	PUNCT
ejpam-6251	554	1	also	also	ADV
ejpam-6251	554	2	,	,	PUNCT
ejpam-6251	554	3	let	let	VERB
ejpam-6251	554	4	℧	℧	VERB
ejpam-6251	554	5	(	(	PUNCT
ejpam-6251	554	6	o	o	NOUN
ejpam-6251	554	7	,	,	PUNCT
ejpam-6251	554	8	ε)(δ	ε)(δ	PROPN
ejpam-6251	554	9	∫	∫	PROPN
ejpam-6251	554	10	a	a	DET
ejpam-6251	554	11	c	c	NOUN
ejpam-6251	554	12	dε	dε	NOUN
ejpam-6251	554	13	)	)	PUNCT
ejpam-6251	554	14	≤	≤	NUM
ejpam-6251	554	15	ζ	ζ	NOUN
ejpam-6251	554	16	<	<	X
ejpam-6251	554	17	1	1	NUM
ejpam-6251	554	18	.	.	PUNCT
ejpam-6251	555	1	then	then	ADV
ejpam-6251	555	2	,	,	PUNCT
ejpam-6251	555	3	the	the	DET
ejpam-6251	555	4	integral	integral	ADJ
ejpam-6251	555	5	equation	equation	NOUN
ejpam-6251	555	6	(	(	PUNCT
ejpam-6251	555	7	16	16	NUM
ejpam-6251	555	8	)	)	PUNCT
ejpam-6251	555	9	has	have	VERB
ejpam-6251	555	10	a	a	DET
ejpam-6251	555	11	unique	unique	ADJ
ejpam-6251	555	12	solution	solution	NOUN
ejpam-6251	555	13	.	.	PUNCT
ejpam-6251	556	1	proof	proof	NOUN
ejpam-6251	556	2	.	.	PUNCT
ejpam-6251	557	1	define	define	VERB
ejpam-6251	557	2	p	p	X
ejpam-6251	557	3	:	:	PUNCT
ejpam-6251	557	4	(	(	PUNCT
ejpam-6251	557	5	𭟋	𭟋	NOUN
ejpam-6251	557	6	,	,	PUNCT
ejpam-6251	557	7	s	s	PROPN
ejpam-6251	557	8	,	,	PUNCT
ejpam-6251	557	9	π	π	PROPN
ejpam-6251	557	10	,	,	PUNCT
ejpam-6251	557	11	ψ	ψ	PROPN
ejpam-6251	557	12	,	,	PUNCT
ejpam-6251	557	13	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	557	14	,	,	PUNCT
ejpam-6251	557	15	♢	♢	PROPN
ejpam-6251	557	16	)	)	PUNCT
ejpam-6251	557	17	⇒	⇒	NOUN
ejpam-6251	557	18	(	(	PUNCT
ejpam-6251	557	19	𭟋	𭟋	PROPN
ejpam-6251	557	20	,	,	PUNCT
ejpam-6251	557	21	s	s	PROPN
ejpam-6251	557	22	,	,	PUNCT
ejpam-6251	557	23	π	π	PROPN
ejpam-6251	557	24	,	,	PUNCT
ejpam-6251	557	25	ψ	ψ	PROPN
ejpam-6251	557	26	,	,	PUNCT
ejpam-6251	557	27	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	557	28	,	,	PUNCT
ejpam-6251	557	29	♢	♢	PROPN
ejpam-6251	557	30	)	)	PUNCT
ejpam-6251	557	31	by	by	ADP
ejpam-6251	557	32	pς(o	pς(o	NUM
ejpam-6251	557	33	)	)	PUNCT
ejpam-6251	557	34	=	=	SYM
ejpam-6251	557	35	∧(o	∧(o	PROPN
ejpam-6251	557	36	)	)	PUNCT
ejpam-6251	558	1	+	+	CCONJ
ejpam-6251	558	2	δ	δ	PROPN
ejpam-6251	558	3	∫	∫	PROPN
ejpam-6251	558	4	a	a	DET
ejpam-6251	558	5	c	c	PROPN
ejpam-6251	558	6	℧	℧	PROPN
ejpam-6251	558	7	(	(	PUNCT
ejpam-6251	558	8	o	o	PROPN
ejpam-6251	558	9	,	,	PUNCT
ejpam-6251	558	10	ε)ς(o)dε	ε)ς(o)dε	VERB
ejpam-6251	558	11	∀	∀	X
ejpam-6251	558	12	o	o	NOUN
ejpam-6251	558	13	,	,	PUNCT
ejpam-6251	558	14	ε	ε	PROPN
ejpam-6251	558	15	∈	∈	PROPN
ejpam-6251	559	1	[	[	X
ejpam-6251	559	2	c	c	X
ejpam-6251	559	3	,	,	PUNCT
ejpam-6251	559	4	a	a	PRON
ejpam-6251	559	5	]	]	X
ejpam-6251	559	6	.	.	PUNCT
ejpam-6251	560	1	r.	r.	PROPN
ejpam-6251	560	2	ramaswamy	ramaswamy	PROPN
ejpam-6251	560	3	/	/	SYM
ejpam-6251	560	4	eur	eur	PROPN
ejpam-6251	560	5	.	.	PUNCT
ejpam-6251	561	1	j.	j.	PROPN
ejpam-6251	561	2	pure	pure	PROPN
ejpam-6251	561	3	appl	appl	PROPN
ejpam-6251	561	4	.	.	PROPN
ejpam-6251	561	5	math	math	PROPN
ejpam-6251	561	6	,	,	PUNCT
ejpam-6251	561	7	18	18	NUM
ejpam-6251	561	8	(	(	PUNCT
ejpam-6251	561	9	4	4	NUM
ejpam-6251	561	10	)	)	PUNCT
ejpam-6251	561	11	(	(	PUNCT
ejpam-6251	561	12	2025	2025	NUM
ejpam-6251	561	13	)	)	PUNCT
ejpam-6251	561	14	,	,	PUNCT
ejpam-6251	561	15	6251	6251	NUM
ejpam-6251	561	16	29	29	NUM
ejpam-6251	561	17	of	of	ADP
ejpam-6251	561	18	40	40	NUM
ejpam-6251	561	19	now	now	ADV
ejpam-6251	561	20	,	,	PUNCT
ejpam-6251	561	21	∀	∀	X
ejpam-6251	561	22	ς,ϖ	ς,ϖ	NUM
ejpam-6251	561	23	∈	∈	PROPN
ejpam-6251	561	24	𭟋	𭟋	VERB
ejpam-6251	561	25	∪	∪	ADP
ejpam-6251	561	26	s	s	PROPN
ejpam-6251	561	27	,	,	PUNCT
ejpam-6251	561	28	we	we	PRON
ejpam-6251	561	29	deduce	deduce	VERB
ejpam-6251	561	30	π(pς(o),pϖ(o	π(pς(o),pϖ(o	NOUN
ejpam-6251	561	31	)	)	PUNCT
ejpam-6251	561	32	,	,	PUNCT
ejpam-6251	561	33	ζ	ζ	NOUN
ejpam-6251	561	34	ż	ż	NOUN
ejpam-6251	561	35	)	)	PUNCT
ejpam-6251	561	36	=	=	SYM
ejpam-6251	561	37	sup	sup	NOUN
ejpam-6251	561	38	o∈[c	o∈[c	ADV
ejpam-6251	561	39	,	,	PUNCT
ejpam-6251	561	40	a	a	DET
ejpam-6251	561	41	]	]	X
ejpam-6251	561	42	ζ	ζ	NOUN
ejpam-6251	561	43	ż	ż	NOUN
ejpam-6251	561	44	ζ	ζ	PROPN
ejpam-6251	561	45	ż+	ż+	PROPN
ejpam-6251	561	46	|pς(o)−	|pς(o)−	PROPN
ejpam-6251	561	47	pϖ(o)|	pϖ(o)|	NOUN
ejpam-6251	562	1	=	=	NOUN
ejpam-6251	563	1	sup	sup	NOUN
ejpam-6251	563	2	o∈[c	o∈[c	ADV
ejpam-6251	563	3	,	,	PUNCT
ejpam-6251	563	4	a	a	PRON
ejpam-6251	563	5	]	]	X
ejpam-6251	563	6	ζ	ζ	NOUN
ejpam-6251	563	7	ż	ż	NOUN
ejpam-6251	563	8	ζ	ζ	PROPN
ejpam-6251	563	9	ż+	ż+	PROPN
ejpam-6251	563	10	|	|	CCONJ
ejpam-6251	563	11	∧	∧	PROPN
ejpam-6251	563	12	(	(	PUNCT
ejpam-6251	563	13	o	o	NOUN
ejpam-6251	563	14	)	)	PUNCT
ejpam-6251	564	1	+	+	CCONJ
ejpam-6251	564	2	δ	δ	PROPN
ejpam-6251	564	3	∫	∫	PROPN
ejpam-6251	564	4	a	a	DET
ejpam-6251	564	5	c	c	PROPN
ejpam-6251	564	6	℧	℧	PROPN
ejpam-6251	564	7	(	(	PUNCT
ejpam-6251	564	8	o	o	NOUN
ejpam-6251	564	9	,	,	PUNCT
ejpam-6251	564	10	ε)ς(o)dε−	ε)ς(o)dε−	PROPN
ejpam-6251	564	11	∧(o)−	∧(o)−	NUM
ejpam-6251	564	12	δ	δ	PROPN
ejpam-6251	564	13	∫	∫	PROPN
ejpam-6251	564	14	a	a	DET
ejpam-6251	564	15	c	c	PROPN
ejpam-6251	564	16	℧	℧	PROPN
ejpam-6251	564	17	(	(	PUNCT
ejpam-6251	564	18	o	o	NOUN
ejpam-6251	564	19	,	,	PUNCT
ejpam-6251	564	20	ε)ς(o)dε|	ε)ς(o)dε|	ADJ
ejpam-6251	564	21	=	=	PUNCT
ejpam-6251	564	22	sup	sup	NOUN
ejpam-6251	564	23	o∈[c	o∈[c	ADV
ejpam-6251	564	24	,	,	PUNCT
ejpam-6251	564	25	a	a	DET
ejpam-6251	564	26	]	]	X
ejpam-6251	564	27	ζ	ζ	NOUN
ejpam-6251	564	28	ż	ż	NOUN
ejpam-6251	564	29	ζ	ζ	PROPN
ejpam-6251	564	30	ż+	ż+	PROPN
ejpam-6251	564	31	|δ	|δ	NOUN
ejpam-6251	564	32	∫	∫	PROPN
ejpam-6251	564	33	a	a	PRON
ejpam-6251	564	34	c	c	PROPN
ejpam-6251	564	35	℧	℧	PROPN
ejpam-6251	564	36	(	(	PUNCT
ejpam-6251	564	37	o	o	NOUN
ejpam-6251	564	38	,	,	PUNCT
ejpam-6251	564	39	ε)ς(o)dε−	ε)ς(o)dε−	PROPN
ejpam-6251	564	40	δ	δ	PROPN
ejpam-6251	564	41	∫	∫	PROPN
ejpam-6251	564	42	a	a	DET
ejpam-6251	564	43	c	c	PROPN
ejpam-6251	564	44	℧	℧	PROPN
ejpam-6251	564	45	(	(	PUNCT
ejpam-6251	564	46	o	o	NOUN
ejpam-6251	564	47	,	,	PUNCT
ejpam-6251	564	48	ε)ς(o)dε|	ε)ς(o)dε|	ADJ
ejpam-6251	564	49	=	=	PUNCT
ejpam-6251	564	50	sup	sup	NOUN
ejpam-6251	564	51	o∈[c	o∈[c	ADV
ejpam-6251	564	52	,	,	PUNCT
ejpam-6251	564	53	a	a	PRON
ejpam-6251	564	54	]	]	X
ejpam-6251	564	55	ζ	ζ	NOUN
ejpam-6251	564	56	ż	ż	NOUN
ejpam-6251	564	57	ζ	ζ	PROPN
ejpam-6251	564	58	ż+	ż+	PROPN
ejpam-6251	564	59	|	|	CCONJ
ejpam-6251	564	60	℧	℧	PROPN
ejpam-6251	564	61	(o	(o	PROPN
ejpam-6251	564	62	,	,	PUNCT
ejpam-6251	564	63	ε)ς(o)−	ε)ς(o)−	DET
ejpam-6251	564	64	℧	℧	PROPN
ejpam-6251	564	65	(	(	PUNCT
ejpam-6251	564	66	o	o	NOUN
ejpam-6251	564	67	,	,	PUNCT
ejpam-6251	564	68	ε)ϖ(o)|(δ	ε)ϖ(o)|(δ	VERB
ejpam-6251	564	69	∫	∫	PROPN
ejpam-6251	564	70	a	a	DET
ejpam-6251	564	71	c	c	NOUN
ejpam-6251	564	72	dε	dε	NOUN
ejpam-6251	564	73	)	)	PUNCT
ejpam-6251	564	74	≥	≥	PROPN
ejpam-6251	564	75	sup	sup	NOUN
ejpam-6251	564	76	o∈[c	o∈[c	PROPN
ejpam-6251	564	77	,	,	PUNCT
ejpam-6251	564	78	a	a	DET
ejpam-6251	564	79	]	]	X
ejpam-6251	564	80	ż	ż	PROPN
ejpam-6251	564	81	ż+	ż+	PROPN
ejpam-6251	564	82	|ς(o)−ϖ(o)|	|ς(o)−ϖ(o)|	PROPN
ejpam-6251	564	83	≥	≥	NOUN
ejpam-6251	564	84	π(ς(o	π(ς(o	NOUN
ejpam-6251	564	85	)	)	PUNCT
ejpam-6251	564	86	,	,	PUNCT
ejpam-6251	564	87	ϖ(o	ϖ(o	NOUN
ejpam-6251	564	88	)	)	PUNCT
ejpam-6251	564	89	,	,	PUNCT
ejpam-6251	564	90	ż	ż	NOUN
ejpam-6251	564	91	)	)	PUNCT
ejpam-6251	564	92	,	,	PUNCT
ejpam-6251	564	93	ψ(pς(o	ψ(pς(o	PROPN
ejpam-6251	564	94	)	)	PUNCT
ejpam-6251	564	95	,	,	PUNCT
ejpam-6251	564	96	pϖ(o	pϖ(o	NUM
ejpam-6251	564	97	)	)	PUNCT
ejpam-6251	564	98	,	,	PUNCT
ejpam-6251	564	99	ζ	ζ	NOUN
ejpam-6251	564	100	ż	ż	NOUN
ejpam-6251	564	101	)	)	PUNCT
ejpam-6251	564	102	=	=	SYM
ejpam-6251	564	103	1−	1−	NUM
ejpam-6251	564	104	sup	sup	NOUN
ejpam-6251	564	105	o∈[c	o∈[c	ADP
ejpam-6251	564	106	,	,	PUNCT
ejpam-6251	564	107	a	a	DET
ejpam-6251	564	108	]	]	X
ejpam-6251	564	109	ζ	ζ	NOUN
ejpam-6251	564	110	ż	ż	NOUN
ejpam-6251	564	111	ζ	ζ	PROPN
ejpam-6251	564	112	ż+	ż+	PROPN
ejpam-6251	564	113	|pς(o)−	|pς(o)−	PROPN
ejpam-6251	564	114	pϖ(o)|	pϖ(o)|	NOUN
ejpam-6251	564	115	=	=	SYM
ejpam-6251	564	116	1−	1−	NUM
ejpam-6251	564	117	sup	sup	NOUN
ejpam-6251	564	118	o∈[c	o∈[c	ADP
ejpam-6251	564	119	,	,	PUNCT
ejpam-6251	564	120	a	a	PRON
ejpam-6251	564	121	]	]	X
ejpam-6251	564	122	ζ	ζ	NOUN
ejpam-6251	564	123	ż	ż	NOUN
ejpam-6251	564	124	ζ	ζ	PROPN
ejpam-6251	564	125	ż+	ż+	PROPN
ejpam-6251	564	126	|	|	CCONJ
ejpam-6251	564	127	∧	∧	PROPN
ejpam-6251	564	128	(	(	PUNCT
ejpam-6251	564	129	o	o	NOUN
ejpam-6251	564	130	)	)	PUNCT
ejpam-6251	565	1	+	+	CCONJ
ejpam-6251	565	2	δ	δ	PROPN
ejpam-6251	565	3	∫	∫	PROPN
ejpam-6251	565	4	a	a	DET
ejpam-6251	565	5	c	c	PROPN
ejpam-6251	565	6	℧	℧	PROPN
ejpam-6251	565	7	(	(	PUNCT
ejpam-6251	565	8	o	o	NOUN
ejpam-6251	565	9	,	,	PUNCT
ejpam-6251	565	10	ε)ς(o)dε−	ε)ς(o)dε−	PROPN
ejpam-6251	565	11	∧(o)−	∧(o)−	NUM
ejpam-6251	565	12	δ	δ	PROPN
ejpam-6251	565	13	∫	∫	PROPN
ejpam-6251	565	14	a	a	DET
ejpam-6251	565	15	c	c	PROPN
ejpam-6251	565	16	℧	℧	PROPN
ejpam-6251	565	17	(	(	PUNCT
ejpam-6251	565	18	o	o	NOUN
ejpam-6251	565	19	,	,	PUNCT
ejpam-6251	565	20	ε)ς(o)dε|	ε)ς(o)dε|	NOUN
ejpam-6251	565	21	=	=	SYM
ejpam-6251	565	22	1−	1−	NUM
ejpam-6251	565	23	sup	sup	NOUN
ejpam-6251	565	24	o∈[c	o∈[c	ADP
ejpam-6251	565	25	,	,	PUNCT
ejpam-6251	565	26	a	a	DET
ejpam-6251	565	27	]	]	X
ejpam-6251	565	28	ζ	ζ	NOUN
ejpam-6251	565	29	ż	ż	NOUN
ejpam-6251	565	30	ζ	ζ	PROPN
ejpam-6251	565	31	ż+	ż+	PROPN
ejpam-6251	565	32	|δ	|δ	NOUN
ejpam-6251	565	33	∫	∫	PROPN
ejpam-6251	565	34	a	a	PRON
ejpam-6251	565	35	c	c	PROPN
ejpam-6251	565	36	℧	℧	PROPN
ejpam-6251	565	37	(	(	PUNCT
ejpam-6251	565	38	o	o	NOUN
ejpam-6251	565	39	,	,	PUNCT
ejpam-6251	565	40	ε)ς(o)dε−	ε)ς(o)dε−	PROPN
ejpam-6251	565	41	δ	δ	PROPN
ejpam-6251	565	42	∫	∫	PROPN
ejpam-6251	565	43	a	a	PRON
ejpam-6251	565	44	c	c	PROPN
ejpam-6251	565	45	℧	℧	PROPN
ejpam-6251	565	46	(	(	PUNCT
ejpam-6251	565	47	o	o	NOUN
ejpam-6251	565	48	,	,	PUNCT
ejpam-6251	565	49	ε)ς(o)dε|	ε)ς(o)dε|	NOUN
ejpam-6251	565	50	=	=	SYM
ejpam-6251	565	51	1−	1−	NUM
ejpam-6251	565	52	sup	sup	NOUN
ejpam-6251	565	53	o∈[c	o∈[c	ADP
ejpam-6251	565	54	,	,	PUNCT
ejpam-6251	565	55	a	a	PRON
ejpam-6251	565	56	]	]	X
ejpam-6251	565	57	ζ	ζ	NOUN
ejpam-6251	565	58	ż	ż	NOUN
ejpam-6251	565	59	ζ	ζ	PROPN
ejpam-6251	565	60	ż+	ż+	PROPN
ejpam-6251	565	61	|	|	CCONJ
ejpam-6251	565	62	℧	℧	PROPN
ejpam-6251	565	63	(o	(o	PROPN
ejpam-6251	565	64	,	,	PUNCT
ejpam-6251	565	65	ε)ς(o)−	ε)ς(o)−	DET
ejpam-6251	565	66	℧	℧	PROPN
ejpam-6251	565	67	(	(	PUNCT
ejpam-6251	565	68	o	o	NOUN
ejpam-6251	565	69	,	,	PUNCT
ejpam-6251	565	70	ε)ϖ(o)|(δ	ε)ϖ(o)|(δ	VERB
ejpam-6251	565	71	∫	∫	PROPN
ejpam-6251	565	72	a	a	DET
ejpam-6251	565	73	c	c	NOUN
ejpam-6251	565	74	dε	dε	NOUN
ejpam-6251	565	75	)	)	PUNCT
ejpam-6251	565	76	≤	≤	NOUN
ejpam-6251	565	77	1−	1−	NUM
ejpam-6251	565	78	sup	sup	NOUN
ejpam-6251	565	79	o∈[c	o∈[c	ADP
ejpam-6251	565	80	,	,	PUNCT
ejpam-6251	565	81	a	a	DET
ejpam-6251	565	82	]	]	X
ejpam-6251	565	83	ż	ż	PROPN
ejpam-6251	565	84	ż+	ż+	PROPN
ejpam-6251	565	85	|ς(o)−ϖ(o)|	|ς(o)−ϖ(o)|	PROPN
ejpam-6251	565	86	≤	≤	NUM
ejpam-6251	565	87	ψ(ς(o	ψ(ς(o	NOUN
ejpam-6251	565	88	)	)	PUNCT
ejpam-6251	565	89	,	,	PUNCT
ejpam-6251	565	90	ϖ(o	ϖ(o	NOUN
ejpam-6251	565	91	)	)	PUNCT
ejpam-6251	565	92	,	,	PUNCT
ejpam-6251	565	93	ż	ż	NOUN
ejpam-6251	565	94	)	)	PUNCT
ejpam-6251	565	95	,	,	PUNCT
ejpam-6251	565	96	and	and	CCONJ
ejpam-6251	565	97	ξ(pς(o	ξ(pς(o	NUM
ejpam-6251	565	98	)	)	PUNCT
ejpam-6251	565	99	,	,	PUNCT
ejpam-6251	565	100	pϖ(o),ζ	pϖ(o),ζ	NOUN
ejpam-6251	565	101	ż	ż	NOUN
ejpam-6251	565	102	)	)	PUNCT
ejpam-6251	565	103	=	=	SYM
ejpam-6251	565	104	sup	sup	NOUN
ejpam-6251	565	105	o∈[c	o∈[c	ADV
ejpam-6251	565	106	,	,	PUNCT
ejpam-6251	565	107	a	a	DET
ejpam-6251	565	108	]	]	X
ejpam-6251	565	109	|pς(o)−	|pς(o)−	NOUN
ejpam-6251	565	110	pϖ(o)|	pϖ(o)|	ADJ
ejpam-6251	565	111	ζ	ζ	NOUN
ejpam-6251	565	112	ż	ż	NOUN
ejpam-6251	565	113	=	=	NOUN
ejpam-6251	565	114	sup	sup	NOUN
ejpam-6251	565	115	o∈[c	o∈[c	ADV
ejpam-6251	565	116	,	,	PUNCT
ejpam-6251	565	117	a	a	PRON
ejpam-6251	565	118	]	]	X
ejpam-6251	565	119	|	|	ADV
ejpam-6251	565	120	∧	∧	PROPN
ejpam-6251	565	121	(	(	PUNCT
ejpam-6251	565	122	o	o	NOUN
ejpam-6251	565	123	)	)	PUNCT
ejpam-6251	566	1	+	+	CCONJ
ejpam-6251	566	2	δ	δ	PROPN
ejpam-6251	566	3	∫	∫	PROPN
ejpam-6251	566	4	a	a	DET
ejpam-6251	566	5	c	c	PROPN
ejpam-6251	566	6	℧	℧	PROPN
ejpam-6251	566	7	(	(	PUNCT
ejpam-6251	566	8	o	o	NOUN
ejpam-6251	566	9	,	,	PUNCT
ejpam-6251	566	10	ε)ς(o)dε−	ε)ς(o)dε−	PROPN
ejpam-6251	566	11	∧(o)−	∧(o)−	NUM
ejpam-6251	566	12	δ	δ	PROPN
ejpam-6251	566	13	∫	∫	PROPN
ejpam-6251	566	14	a	a	DET
ejpam-6251	566	15	c	c	PROPN
ejpam-6251	566	16	℧	℧	PROPN
ejpam-6251	566	17	(	(	PUNCT
ejpam-6251	566	18	o	o	NOUN
ejpam-6251	566	19	,	,	PUNCT
ejpam-6251	566	20	ε)ς(o)dε|	ε)ς(o)dε|	ADJ
ejpam-6251	566	21	ζ	ζ	NOUN
ejpam-6251	566	22	ż	ż	NOUN
ejpam-6251	566	23	=	=	NOUN
ejpam-6251	566	24	sup	sup	NOUN
ejpam-6251	566	25	o∈[c	o∈[c	ADV
ejpam-6251	566	26	,	,	PUNCT
ejpam-6251	566	27	a	a	DET
ejpam-6251	566	28	]	]	PUNCT
ejpam-6251	566	29	|δ	|δ	NOUN
ejpam-6251	566	30	∫	∫	PROPN
ejpam-6251	566	31	a	a	PRON
ejpam-6251	566	32	c	c	PROPN
ejpam-6251	566	33	℧	℧	PROPN
ejpam-6251	566	34	(	(	PUNCT
ejpam-6251	566	35	o	o	NOUN
ejpam-6251	566	36	,	,	PUNCT
ejpam-6251	566	37	ε)ς(o)dε−	ε)ς(o)dε−	PROPN
ejpam-6251	566	38	δ	δ	PROPN
ejpam-6251	566	39	∫	∫	PROPN
ejpam-6251	566	40	a	a	DET
ejpam-6251	566	41	c	c	PROPN
ejpam-6251	566	42	℧	℧	PROPN
ejpam-6251	566	43	(	(	PUNCT
ejpam-6251	566	44	o	o	NOUN
ejpam-6251	566	45	,	,	PUNCT
ejpam-6251	566	46	ε)ς(o)dε|	ε)ς(o)dε|	ADJ
ejpam-6251	566	47	ζ	ζ	NOUN
ejpam-6251	566	48	ż	ż	NOUN
ejpam-6251	566	49	=	=	NOUN
ejpam-6251	566	50	sup	sup	NOUN
ejpam-6251	566	51	o∈[c	o∈[c	ADV
ejpam-6251	566	52	,	,	PUNCT
ejpam-6251	566	53	a	a	DET
ejpam-6251	566	54	]	]	X
ejpam-6251	566	55	|	|	NOUN
ejpam-6251	566	56	℧	℧	NOUN
ejpam-6251	566	57	(o	(o	NOUN
ejpam-6251	566	58	,	,	PUNCT
ejpam-6251	566	59	ε)ς(o)−	ε)ς(o)−	PRON
ejpam-6251	566	60	℧	℧	PROPN
ejpam-6251	566	61	(	(	PUNCT
ejpam-6251	566	62	o	o	NOUN
ejpam-6251	566	63	,	,	PUNCT
ejpam-6251	566	64	ε)ϖ(o)|(δ	ε)ϖ(o)|(δ	VERB
ejpam-6251	566	65	∫	∫	PROPN
ejpam-6251	566	66	a	a	DET
ejpam-6251	566	67	c	c	NOUN
ejpam-6251	566	68	dε	dε	NOUN
ejpam-6251	566	69	)	)	PUNCT
ejpam-6251	566	70	ζ	ζ	NOUN
ejpam-6251	566	71	ż	ż	NOUN
ejpam-6251	566	72	≤	≤	NUM
ejpam-6251	566	73	sup	sup	NOUN
ejpam-6251	566	74	o∈[c	o∈[c	PROPN
ejpam-6251	566	75	,	,	PUNCT
ejpam-6251	566	76	a	a	DET
ejpam-6251	566	77	]	]	X
ejpam-6251	566	78	|ς(o)−ϖ(o)|	|ς(o)−ϖ(o)|	PROPN
ejpam-6251	566	79	ż	ż	PROPN
ejpam-6251	566	80	r.	r.	PROPN
ejpam-6251	566	81	ramaswamy	ramaswamy	PROPN
ejpam-6251	566	82	/	/	SYM
ejpam-6251	566	83	eur	eur	PROPN
ejpam-6251	566	84	.	.	PUNCT
ejpam-6251	567	1	j.	j.	PROPN
ejpam-6251	567	2	pure	pure	PROPN
ejpam-6251	567	3	appl	appl	PROPN
ejpam-6251	567	4	.	.	PROPN
ejpam-6251	567	5	math	math	PROPN
ejpam-6251	567	6	,	,	PUNCT
ejpam-6251	567	7	18	18	NUM
ejpam-6251	567	8	(	(	PUNCT
ejpam-6251	567	9	4	4	NUM
ejpam-6251	567	10	)	)	PUNCT
ejpam-6251	567	11	(	(	PUNCT
ejpam-6251	567	12	2025	2025	NUM
ejpam-6251	567	13	)	)	PUNCT
ejpam-6251	567	14	,	,	PUNCT
ejpam-6251	567	15	6251	6251	NUM
ejpam-6251	567	16	30	30	NUM
ejpam-6251	567	17	of	of	ADP
ejpam-6251	567	18	40	40	NUM
ejpam-6251	567	19	≤	≤	NUM
ejpam-6251	567	20	ξ(ς(o	ξ(ς(o	NOUN
ejpam-6251	567	21	)	)	PUNCT
ejpam-6251	567	22	,	,	PUNCT
ejpam-6251	567	23	ϖ(o	ϖ(o	NOUN
ejpam-6251	567	24	)	)	PUNCT
ejpam-6251	567	25	,	,	PUNCT
ejpam-6251	567	26	ż	ż	NOUN
ejpam-6251	567	27	)	)	PUNCT
ejpam-6251	567	28	.	.	PUNCT
ejpam-6251	568	1	therefore	therefore	ADV
ejpam-6251	568	2	,	,	PUNCT
ejpam-6251	568	3	all	all	DET
ejpam-6251	568	4	the	the	DET
ejpam-6251	568	5	hypothesis	hypothesis	NOUN
ejpam-6251	568	6	of	of	ADP
ejpam-6251	568	7	theorem	theorem	NOUN
ejpam-6251	568	8	5	5	NUM
ejpam-6251	568	9	are	be	AUX
ejpam-6251	568	10	satisfied	satisfied	ADJ
ejpam-6251	568	11	and	and	CCONJ
ejpam-6251	568	12	p	p	NOUN
ejpam-6251	568	13	has	have	VERB
ejpam-6251	568	14	a	a	DET
ejpam-6251	568	15	unique	unique	ADJ
ejpam-6251	568	16	fixed	fix	VERB
ejpam-6251	568	17	point	point	NOUN
ejpam-6251	568	18	and	and	CCONJ
ejpam-6251	568	19	the	the	DET
ejpam-6251	568	20	integral	integral	ADJ
ejpam-6251	568	21	equation	equation	NOUN
ejpam-6251	568	22	(	(	PUNCT
ejpam-6251	568	23	16	16	NUM
ejpam-6251	568	24	)	)	PUNCT
ejpam-6251	568	25	has	have	VERB
ejpam-6251	568	26	a	a	DET
ejpam-6251	568	27	unique	unique	ADJ
ejpam-6251	568	28	solution	solution	NOUN
ejpam-6251	568	29	.	.	PUNCT
ejpam-6251	569	1	example	example	NOUN
ejpam-6251	570	1	4	4	X
ejpam-6251	570	2	.	.	X
ejpam-6251	570	3	consider	consider	VERB
ejpam-6251	570	4	the	the	DET
ejpam-6251	570	5	the	the	DET
ejpam-6251	570	6	non	non	ADJ
ejpam-6251	570	7	-	-	ADJ
ejpam-6251	570	8	linear	linear	ADJ
ejpam-6251	570	9	integral	integral	ADJ
ejpam-6251	570	10	equation	equation	NOUN
ejpam-6251	570	11	.	.	PUNCT
ejpam-6251	571	1	ς(o	ς(o	NOUN
ejpam-6251	571	2	)	)	PUNCT
ejpam-6251	572	1	=	=	PUNCT
ejpam-6251	573	1	|	|	ADV
ejpam-6251	574	1	cos	cos	ADP
ejpam-6251	574	2	o|+	o|+	PROPN
ejpam-6251	574	3	1	1	NUM
ejpam-6251	574	4	9	9	NUM
ejpam-6251	574	5	∫	∫	NOUN
ejpam-6251	574	6	1	1	NUM
ejpam-6251	574	7	0	0	NUM
ejpam-6251	574	8	ες(ε)dε	ες(ε)dε	NOUN
ejpam-6251	574	9	,	,	PUNCT
ejpam-6251	574	10	∀	∀	NOUN
ejpam-6251	574	11	ε	ε	NOUN
ejpam-6251	574	12	∈	∈	PROPN
ejpam-6251	575	1	[	[	X
ejpam-6251	575	2	0	0	NUM
ejpam-6251	575	3	,	,	PUNCT
ejpam-6251	575	4	1	1	NUM
ejpam-6251	575	5	]	]	PUNCT
ejpam-6251	575	6	then	then	ADV
ejpam-6251	575	7	it	it	PRON
ejpam-6251	575	8	has	have	VERB
ejpam-6251	575	9	a	a	DET
ejpam-6251	575	10	solution	solution	NOUN
ejpam-6251	575	11	in	in	ADP
ejpam-6251	575	12	𭟋	𭟋	PROPN
ejpam-6251	575	13	.	.	PUNCT
ejpam-6251	575	14	proof	proof	NOUN
ejpam-6251	575	15	.	.	PUNCT
ejpam-6251	576	1	let	let	VERB
ejpam-6251	576	2	p	p	NOUN
ejpam-6251	576	3	:	:	PUNCT
ejpam-6251	576	4	(	(	PUNCT
ejpam-6251	576	5	𭟋	𭟋	NOUN
ejpam-6251	576	6	,	,	PUNCT
ejpam-6251	576	7	s	s	PROPN
ejpam-6251	576	8	,	,	PUNCT
ejpam-6251	576	9	π	π	PROPN
ejpam-6251	576	10	,	,	PUNCT
ejpam-6251	576	11	ψ	ψ	PROPN
ejpam-6251	576	12	,	,	PUNCT
ejpam-6251	576	13	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	576	14	,	,	PUNCT
ejpam-6251	576	15	♢	♢	PROPN
ejpam-6251	576	16	)	)	PUNCT
ejpam-6251	576	17	⇒	⇒	NOUN
ejpam-6251	576	18	(	(	PUNCT
ejpam-6251	576	19	𭟋	𭟋	PROPN
ejpam-6251	576	20	,	,	PUNCT
ejpam-6251	576	21	s	s	PROPN
ejpam-6251	576	22	,	,	PUNCT
ejpam-6251	576	23	π	π	PROPN
ejpam-6251	576	24	,	,	PUNCT
ejpam-6251	576	25	ψ	ψ	PROPN
ejpam-6251	576	26	,	,	PUNCT
ejpam-6251	576	27	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	576	28	,	,	PUNCT
ejpam-6251	576	29	♢	♢	PROPN
ejpam-6251	576	30	)	)	PUNCT
ejpam-6251	576	31	be	be	AUX
ejpam-6251	576	32	defined	define	VERB
ejpam-6251	576	33	by	by	ADP
ejpam-6251	576	34	pς(o	pς(o	NOUN
ejpam-6251	576	35	)	)	PUNCT
ejpam-6251	577	1	=	=	PUNCT
ejpam-6251	578	1	|	|	ADV
ejpam-6251	578	2	cos	cos	ADP
ejpam-6251	578	3	o|+	o|+	PROPN
ejpam-6251	578	4	1	1	NUM
ejpam-6251	578	5	9	9	NUM
ejpam-6251	578	6	∫	∫	NOUN
ejpam-6251	578	7	1	1	NUM
ejpam-6251	578	8	0	0	NUM
ejpam-6251	578	9	ες(ε)dε	ες(ε)dε	NOUN
ejpam-6251	578	10	,	,	PUNCT
ejpam-6251	578	11	and	and	CCONJ
ejpam-6251	578	12	set	set	VERB
ejpam-6251	578	13	℧	℧	PROPN
ejpam-6251	578	14	(	(	PUNCT
ejpam-6251	578	15	o	o	NOUN
ejpam-6251	578	16	,	,	PUNCT
ejpam-6251	578	17	ε)ς(o	ε)ς(o	NOUN
ejpam-6251	578	18	)	)	PUNCT
ejpam-6251	578	19	=	=	SYM
ejpam-6251	578	20	1	1	NUM
ejpam-6251	578	21	9ες(ε	9ες(ε	NUM
ejpam-6251	578	22	)	)	PUNCT
ejpam-6251	578	23	and	and	CCONJ
ejpam-6251	578	24	℧	℧	PROPN
ejpam-6251	578	25	(	(	PUNCT
ejpam-6251	578	26	o	o	NOUN
ejpam-6251	578	27	,	,	PUNCT
ejpam-6251	578	28	ε)ϖ(o	ε)ϖ(o	PROPN
ejpam-6251	578	29	)	)	PUNCT
ejpam-6251	578	30	=	=	SYM
ejpam-6251	579	1	1	1	NUM
ejpam-6251	579	2	9εϖ(ε	9εϖ(ε	NUM
ejpam-6251	579	3	)	)	PUNCT
ejpam-6251	579	4	,	,	PUNCT
ejpam-6251	579	5	where	where	SCONJ
ejpam-6251	579	6	ς,ϖ	ς,ϖ	PROPN
ejpam-6251	579	7	∈	∈	PROPN
ejpam-6251	579	8	𭟋	𭟋	VERB
ejpam-6251	579	9	∪	∪	ADP
ejpam-6251	579	10	s	s	PROPN
ejpam-6251	579	11	,	,	PUNCT
ejpam-6251	579	12	and	and	CCONJ
ejpam-6251	579	13	∀	∀	NOUN
ejpam-6251	579	14	o	o	NOUN
ejpam-6251	579	15	,	,	PUNCT
ejpam-6251	579	16	ε	ε	PROPN
ejpam-6251	579	17	∈	∈	PROPN
ejpam-6251	580	1	[	[	X
ejpam-6251	580	2	0	0	NUM
ejpam-6251	580	3	,	,	PUNCT
ejpam-6251	580	4	1	1	NUM
ejpam-6251	580	5	]	]	PUNCT
ejpam-6251	580	6	.	.	PUNCT
ejpam-6251	581	1	then	then	ADV
ejpam-6251	581	2	we	we	PRON
ejpam-6251	581	3	have	have	VERB
ejpam-6251	581	4	|	|	ADV
ejpam-6251	581	5	℧	℧	VERB
ejpam-6251	581	6	(o	(o	NOUN
ejpam-6251	581	7	,	,	PUNCT
ejpam-6251	581	8	ε)ς(o)−	ε)ς(o)−	PRON
ejpam-6251	581	9	℧	℧	PROPN
ejpam-6251	581	10	(	(	PUNCT
ejpam-6251	581	11	o	o	NOUN
ejpam-6251	581	12	,	,	PUNCT
ejpam-6251	581	13	ε)ϖ(o)|	ε)ϖ(o)|	PROPN
ejpam-6251	581	14	=	=	PUNCT
ejpam-6251	581	15	|1	|1	NUM
ejpam-6251	581	16	9	9	NUM
ejpam-6251	581	17	ες(ε)−	ες(ε)−	PROPN
ejpam-6251	581	18	1	1	NUM
ejpam-6251	581	19	9	9	NUM
ejpam-6251	581	20	εϖ(ε)|	εϖ(ε)|	X
ejpam-6251	581	21	=	=	SYM
ejpam-6251	581	22	ε	ε	PROPN
ejpam-6251	581	23	9	9	NUM
ejpam-6251	581	24	|ς(ε)−ϖ(ε)|	|ς(ε)−ϖ(ε)|	PROPN
ejpam-6251	581	25	≤	≤	PROPN
ejpam-6251	581	26	|ς(ε)−ϖ(ε)|	|ς(ε)−ϖ(ε)|	NOUN
ejpam-6251	581	27	.	.	PUNCT
ejpam-6251	582	1	furthermore	furthermore	ADV
ejpam-6251	582	2	,	,	PUNCT
ejpam-6251	582	3	we	we	PRON
ejpam-6251	582	4	have	have	VERB
ejpam-6251	582	5	1	1	NUM
ejpam-6251	582	6	9	9	NUM
ejpam-6251	582	7	∫	∫	NOUN
ejpam-6251	582	8	1	1	NUM
ejpam-6251	582	9	0	0	NUM
ejpam-6251	582	10	εdε	εdε	NOUN
ejpam-6251	582	11	=	=	SYM
ejpam-6251	582	12	1	1	NUM
ejpam-6251	582	13	9	9	NUM
ejpam-6251	582	14	(	(	PUNCT
ejpam-6251	582	15	(	(	PUNCT
ejpam-6251	582	16	1)2	1)2	NUM
ejpam-6251	582	17	2	2	NUM
ejpam-6251	582	18	−	−	NOUN
ejpam-6251	582	19	(	(	PUNCT
ejpam-6251	582	20	0)2	0)2	NUM
ejpam-6251	582	21	2	2	NUM
ejpam-6251	582	22	)	)	PUNCT
ejpam-6251	582	23	=	=	SYM
ejpam-6251	582	24	1	1	NUM
ejpam-6251	582	25	18	18	NUM
ejpam-6251	582	26	=	=	SYM
ejpam-6251	582	27	ζ	ζ	NOUN
ejpam-6251	582	28	<	<	X
ejpam-6251	582	29	1	1	NUM
ejpam-6251	582	30	,	,	PUNCT
ejpam-6251	582	31	with	with	ADP
ejpam-6251	582	32	δ	δ	PROPN
ejpam-6251	582	33	=	=	SYM
ejpam-6251	582	34	1	1	NUM
ejpam-6251	582	35	9	9	NUM
ejpam-6251	582	36	.	.	PUNCT
ejpam-6251	583	1	hence	hence	ADV
ejpam-6251	583	2	,	,	PUNCT
ejpam-6251	583	3	all	all	DET
ejpam-6251	583	4	the	the	DET
ejpam-6251	583	5	conditions	condition	NOUN
ejpam-6251	583	6	of	of	ADP
ejpam-6251	583	7	the	the	DET
ejpam-6251	583	8	application	application	NOUN
ejpam-6251	583	9	are	be	AUX
ejpam-6251	583	10	easy	easy	ADJ
ejpam-6251	583	11	to	to	PART
ejpam-6251	583	12	verify	verify	VERB
ejpam-6251	583	13	and	and	CCONJ
ejpam-6251	583	14	the	the	DET
ejpam-6251	583	15	integral	integral	ADJ
ejpam-6251	583	16	equation	equation	NOUN
ejpam-6251	583	17	(	(	PUNCT
ejpam-6251	583	18	16	16	NUM
ejpam-6251	583	19	)	)	PUNCT
ejpam-6251	583	20	has	have	VERB
ejpam-6251	583	21	a	a	DET
ejpam-6251	583	22	unique	unique	ADJ
ejpam-6251	583	23	solution	solution	NOUN
ejpam-6251	583	24	𭟋	𭟋	ADP
ejpam-6251	583	25	∪	∪	ADJ
ejpam-6251	583	26	s.	s.	PROPN
ejpam-6251	583	27	using	use	VERB
ejpam-6251	583	28	mathematica	mathematica	PROPN
ejpam-6251	583	29	software	software	PROPN
ejpam-6251	583	30	,	,	PUNCT
ejpam-6251	583	31	near	near	ADP
ejpam-6251	583	32	to	to	ADP
ejpam-6251	583	33	the	the	DET
ejpam-6251	583	34	unique	unique	ADJ
ejpam-6251	583	35	solution	solution	NOUN
ejpam-6251	583	36	for	for	ADP
ejpam-6251	583	37	the	the	DET
ejpam-6251	583	38	integral	integral	ADJ
ejpam-6251	583	39	equation	equation	NOUN
ejpam-6251	583	40	of	of	ADP
ejpam-6251	583	41	example	example	NOUN
ejpam-6251	583	42	4	4	NUM
ejpam-6251	583	43	is	be	AUX
ejpam-6251	583	44	found	find	VERB
ejpam-6251	583	45	to	to	PART
ejpam-6251	583	46	be	be	AUX
ejpam-6251	583	47	a(τ	a(τ	PROPN
ejpam-6251	583	48	)	)	PUNCT
ejpam-6251	583	49	=	=	PUNCT
ejpam-6251	584	1	|	|	ADV
ejpam-6251	584	2	cos	cos	ADP
ejpam-6251	584	3	τ	τ	PROPN
ejpam-6251	584	4	|+	|+	X
ejpam-6251	584	5	0.0444392	0.0444392	NUM
ejpam-6251	584	6	,	,	PUNCT
ejpam-6251	584	7	and	and	CCONJ
ejpam-6251	584	8	the	the	DET
ejpam-6251	584	9	graph	graph	NOUN
ejpam-6251	584	10	of	of	ADP
ejpam-6251	584	11	the	the	DET
ejpam-6251	584	12	solution	solution	NOUN
ejpam-6251	584	13	is	be	AUX
ejpam-6251	584	14	shown	show	VERB
ejpam-6251	584	15	in	in	ADP
ejpam-6251	584	16	figure	figure	NOUN
ejpam-6251	584	17	1	1	NUM
ejpam-6251	584	18	.	.	NOUN
ejpam-6251	585	1	5	5	NUM
ejpam-6251	585	2	.	.	X
ejpam-6251	585	3	application	application	NOUN
ejpam-6251	585	4	2	2	NUM
ejpam-6251	585	5	consider	consider	VERB
ejpam-6251	585	6	the	the	DET
ejpam-6251	585	7	definition	definition	NOUN
ejpam-6251	585	8	of	of	ADP
ejpam-6251	585	9	the	the	DET
ejpam-6251	585	10	intensity	intensity	NOUN
ejpam-6251	585	11	of	of	ADP
ejpam-6251	585	12	a	a	DET
ejpam-6251	585	13	series	series	NOUN
ejpam-6251	585	14	electric	electric	PROPN
ejpam-6251	585	15	circuit	circuit	PROPN
ejpam-6251	586	1	i	i	PRON
ejpam-6251	586	2	=	=	PUNCT
ejpam-6251	586	3	dϖ	dϖ	PART
ejpam-6251	586	4	dl	dl	INTJ
ejpam-6251	586	5	,	,	PUNCT
ejpam-6251	586	6	where	where	SCONJ
ejpam-6251	586	7	ϖ	ϖ	PRON
ejpam-6251	586	8	denote	denote	VERB
ejpam-6251	586	9	the	the	DET
ejpam-6251	586	10	electric	electric	ADJ
ejpam-6251	586	11	charge	charge	NOUN
ejpam-6251	586	12	and	and	CCONJ
ejpam-6251	586	13	l	l	NOUN
ejpam-6251	586	14	-	-	NOUN
ejpam-6251	586	15	the	the	DET
ejpam-6251	586	16	time	time	NOUN
ejpam-6251	586	17	,	,	PUNCT
ejpam-6251	586	18	let	let	VERB
ejpam-6251	586	19	us	we	PRON
ejpam-6251	586	20	recall	recall	VERB
ejpam-6251	586	21	the	the	DET
ejpam-6251	586	22	following	following	NOUN
ejpam-6251	586	23	usually	usually	ADV
ejpam-6251	586	24	formulas	formula	VERB
ejpam-6251	586	25	•	•	NOUN
ejpam-6251	586	26	v	v	NOUN
ejpam-6251	586	27	=	=	SYM
ejpam-6251	586	28	ir	ir	NOUN
ejpam-6251	586	29	;	;	PUNCT
ejpam-6251	586	30	•	•	NUM
ejpam-6251	586	31	v	v	X
ejpam-6251	586	32	=	=	SYM
ejpam-6251	586	33	ϖ	ϖ	X
ejpam-6251	586	34	c	c	PROPN
ejpam-6251	586	35	r.	r.	PROPN
ejpam-6251	586	36	ramaswamy	ramaswamy	PROPN
ejpam-6251	586	37	/	/	SYM
ejpam-6251	586	38	eur	eur	PROPN
ejpam-6251	586	39	.	.	PUNCT
ejpam-6251	587	1	j.	j.	PROPN
ejpam-6251	587	2	pure	pure	PROPN
ejpam-6251	587	3	appl	appl	PROPN
ejpam-6251	587	4	.	.	PROPN
ejpam-6251	587	5	math	math	PROPN
ejpam-6251	587	6	,	,	PUNCT
ejpam-6251	587	7	18	18	NUM
ejpam-6251	587	8	(	(	PUNCT
ejpam-6251	587	9	4	4	NUM
ejpam-6251	587	10	)	)	PUNCT
ejpam-6251	587	11	(	(	PUNCT
ejpam-6251	587	12	2025	2025	NUM
ejpam-6251	587	13	)	)	PUNCT
ejpam-6251	587	14	,	,	PUNCT
ejpam-6251	587	15	6251	6251	NUM
ejpam-6251	587	16	31	31	NUM
ejpam-6251	587	17	of	of	ADP
ejpam-6251	587	18	40	40	NUM
ejpam-6251	587	19	figure	figure	NOUN
ejpam-6251	587	20	1	1	NUM
ejpam-6251	587	21	:	:	PUNCT
ejpam-6251	587	22	solution	solution	NOUN
ejpam-6251	587	23	of	of	ADP
ejpam-6251	587	24	example	example	NOUN
ejpam-6251	587	25	4.1	4.1	NUM
ejpam-6251	587	26	.	.	NOUN
ejpam-6251	588	1	•	•	NUM
ejpam-6251	588	2	v	v	NOUN
ejpam-6251	588	3	=	=	SYM
ejpam-6251	588	4	l	l	NOUN
ejpam-6251	588	5	di	di	X
ejpam-6251	588	6	dl	dl	PROPN
ejpam-6251	588	7	,	,	PUNCT
ejpam-6251	588	8	here	here	ADV
ejpam-6251	588	9	i.	i.	PROPN
ejpam-6251	588	10	r	r	NOUN
ejpam-6251	588	11	(	(	PUNCT
ejpam-6251	588	12	ohms	ohm	NOUN
ejpam-6251	588	13	)	)	PUNCT
ejpam-6251	588	14	is	be	AUX
ejpam-6251	588	15	a	a	DET
ejpam-6251	588	16	resistor	resistor	NOUN
ejpam-6251	588	17	,	,	PUNCT
ejpam-6251	588	18	ii	ii	PROPN
ejpam-6251	588	19	.	.	PUNCT
ejpam-6251	589	1	c	c	PROPN
ejpam-6251	589	2	(	(	PUNCT
ejpam-6251	589	3	faradays	faraday	NOUN
ejpam-6251	589	4	)	)	PUNCT
ejpam-6251	589	5	is	be	AUX
ejpam-6251	589	6	a	a	DET
ejpam-6251	589	7	capacitor	capacitor	NOUN
ejpam-6251	589	8	,	,	PUNCT
ejpam-6251	589	9	iii	iii	PROPN
ejpam-6251	589	10	.	.	PUNCT
ejpam-6251	590	1	l	l	NOUN
ejpam-6251	590	2	(	(	PUNCT
ejpam-6251	590	3	henries	henry	NOUN
ejpam-6251	590	4	)	)	PUNCT
ejpam-6251	590	5	is	be	AUX
ejpam-6251	590	6	an	an	DET
ejpam-6251	590	7	inductor	inductor	NOUN
ejpam-6251	590	8	,	,	PUNCT
ejpam-6251	590	9	iv	iv	NUM
ejpam-6251	590	10	.	.	PROPN
ejpam-6251	590	11	v	v	NUM
ejpam-6251	590	12	(	(	PUNCT
ejpam-6251	590	13	volts	volt	NOUN
ejpam-6251	590	14	)	)	PUNCT
ejpam-6251	590	15	is	be	AUX
ejpam-6251	590	16	an	an	DET
ejpam-6251	590	17	voltage	voltage	NOUN
ejpam-6251	590	18	and	and	CCONJ
ejpam-6251	590	19	v.	v.	ADP
ejpam-6251	590	20	e	e	PROPN
ejpam-6251	590	21	(	(	PUNCT
ejpam-6251	590	22	volts	volt	NOUN
ejpam-6251	590	23	)	)	PUNCT
ejpam-6251	590	24	is	be	AUX
ejpam-6251	590	25	an	an	DET
ejpam-6251	590	26	electromotive	electromotive	ADJ
ejpam-6251	590	27	force	force	NOUN
ejpam-6251	590	28	.	.	PUNCT
ejpam-6251	591	1	because	because	SCONJ
ejpam-6251	591	2	there	there	PRON
ejpam-6251	591	3	is	be	VERB
ejpam-6251	591	4	only	only	ADV
ejpam-6251	591	5	one	one	NUM
ejpam-6251	591	6	current	current	ADJ
ejpam-6251	591	7	flowing	flow	VERB
ejpam-6251	591	8	in	in	ADP
ejpam-6251	591	9	a	a	DET
ejpam-6251	591	10	series	series	NOUN
ejpam-6251	591	11	circuit	circuit	NOUN
ejpam-6251	591	12	,	,	PUNCT
ejpam-6251	591	13	mathcali	mathcali	PROPN
ejpam-6251	591	14	has	have	VERB
ejpam-6251	591	15	the	the	DET
ejpam-6251	591	16	same	same	ADJ
ejpam-6251	591	17	value	value	NOUN
ejpam-6251	591	18	throughout	throughout	ADP
ejpam-6251	591	19	the	the	DET
ejpam-6251	591	20	circuit	circuit	NOUN
ejpam-6251	591	21	.	.	PUNCT
ejpam-6251	592	1	kirchhoff	kirchhoff	PROPN
ejpam-6251	592	2	’s	’s	PART
ejpam-6251	592	3	voltage	voltage	NOUN
ejpam-6251	592	4	law	law	NOUN
ejpam-6251	592	5	is	be	AUX
ejpam-6251	592	6	the	the	DET
ejpam-6251	592	7	second	second	ADJ
ejpam-6251	592	8	of	of	ADP
ejpam-6251	592	9	his	his	PRON
ejpam-6251	592	10	fundamental	fundamental	ADJ
ejpam-6251	592	11	laws	law	NOUN
ejpam-6251	592	12	that	that	PRON
ejpam-6251	592	13	can	can	AUX
ejpam-6251	592	14	be	be	AUX
ejpam-6251	592	15	used	use	VERB
ejpam-6251	592	16	to	to	PART
ejpam-6251	592	17	analyse	analyse	VERB
ejpam-6251	592	18	circuits	circuit	NOUN
ejpam-6251	592	19	.	.	PUNCT
ejpam-6251	593	1	his	his	PRON
ejpam-6251	593	2	voltage	voltage	NOUN
ejpam-6251	593	3	law	law	NOUN
ejpam-6251	593	4	states	state	VERB
ejpam-6251	593	5	that	that	SCONJ
ejpam-6251	593	6	the	the	DET
ejpam-6251	593	7	algebraic	algebraic	ADJ
ejpam-6251	593	8	sum	sum	NOUN
ejpam-6251	593	9	of	of	ADP
ejpam-6251	593	10	all	all	DET
ejpam-6251	593	11	voltages	voltage	NOUN
ejpam-6251	593	12	around	around	ADP
ejpam-6251	593	13	any	any	DET
ejpam-6251	593	14	closed	closed	ADJ
ejpam-6251	593	15	loop	loop	NOUN
ejpam-6251	593	16	in	in	ADP
ejpam-6251	593	17	a	a	DET
ejpam-6251	593	18	circuit	circuit	NOUN
ejpam-6251	593	19	is	be	AUX
ejpam-6251	593	20	equal	equal	ADJ
ejpam-6251	593	21	to	to	ADP
ejpam-6251	593	22	zero	zero	NUM
ejpam-6251	593	23	for	for	ADP
ejpam-6251	593	24	a	a	DET
ejpam-6251	593	25	closed	closed	ADJ
ejpam-6251	593	26	loop	loop	NOUN
ejpam-6251	593	27	series	series	PROPN
ejpam-6251	593	28	path	path	PROPN
ejpam-6251	593	29	.	.	PUNCT
ejpam-6251	594	1	the	the	DET
ejpam-6251	594	2	r.	r.	PROPN
ejpam-6251	594	3	ramaswamy	ramaswamy	PROPN
ejpam-6251	594	4	/	/	SYM
ejpam-6251	594	5	eur	eur	PROPN
ejpam-6251	594	6	.	.	PUNCT
ejpam-6251	595	1	j.	j.	PROPN
ejpam-6251	595	2	pure	pure	PROPN
ejpam-6251	595	3	appl	appl	PROPN
ejpam-6251	595	4	.	.	PROPN
ejpam-6251	595	5	math	math	PROPN
ejpam-6251	595	6	,	,	PUNCT
ejpam-6251	595	7	18	18	NUM
ejpam-6251	595	8	(	(	PUNCT
ejpam-6251	595	9	4	4	NUM
ejpam-6251	595	10	)	)	PUNCT
ejpam-6251	595	11	(	(	PUNCT
ejpam-6251	595	12	2025	2025	NUM
ejpam-6251	595	13	)	)	PUNCT
ejpam-6251	595	14	,	,	PUNCT
ejpam-6251	595	15	6251	6251	NUM
ejpam-6251	595	16	32	32	NUM
ejpam-6251	595	17	of	of	ADP
ejpam-6251	595	18	40	40	NUM
ejpam-6251	595	19	algebraic	algebraic	ADJ
ejpam-6251	595	20	sum	sum	NOUN
ejpam-6251	595	21	of	of	ADP
ejpam-6251	595	22	all	all	DET
ejpam-6251	595	23	the	the	DET
ejpam-6251	595	24	voltages	voltage	NOUN
ejpam-6251	595	25	around	around	ADP
ejpam-6251	595	26	any	any	DET
ejpam-6251	595	27	closed	closed	ADJ
ejpam-6251	595	28	loop	loop	NOUN
ejpam-6251	595	29	in	in	ADP
ejpam-6251	595	30	a	a	DET
ejpam-6251	595	31	circuit	circuit	NOUN
ejpam-6251	595	32	equals	equal	VERB
ejpam-6251	595	33	zero	zero	NUM
ejpam-6251	595	34	,	,	PUNCT
ejpam-6251	595	35	according	accord	VERB
ejpam-6251	595	36	to	to	ADP
ejpam-6251	595	37	kirchhoff	kirchhoff	PROPN
ejpam-6251	595	38	’s	’s	PART
ejpam-6251	595	39	voltage	voltage	NOUN
ejpam-6251	595	40	law	law	NOUN
ejpam-6251	595	41	.	.	PUNCT
ejpam-6251	596	1	the	the	DET
ejpam-6251	596	2	main	main	ADJ
ejpam-6251	596	3	idea	idea	NOUN
ejpam-6251	596	4	behind	behind	ADP
ejpam-6251	596	5	kirchhoff	kirchhoff	PROPN
ejpam-6251	596	6	’s	’s	PART
ejpam-6251	596	7	voltage	voltage	NOUN
ejpam-6251	596	8	law	law	NOUN
ejpam-6251	596	9	is	be	AUX
ejpam-6251	596	10	that	that	SCONJ
ejpam-6251	596	11	as	as	SCONJ
ejpam-6251	596	12	you	you	PRON
ejpam-6251	596	13	move	move	VERB
ejpam-6251	596	14	around	around	ADP
ejpam-6251	596	15	a	a	DET
ejpam-6251	596	16	closed	closed	ADJ
ejpam-6251	596	17	loop	loop	NOUN
ejpam-6251	596	18	/	/	SYM
ejpam-6251	596	19	circuit	circuit	NOUN
ejpam-6251	596	20	,	,	PUNCT
ejpam-6251	596	21	you	you	PRON
ejpam-6251	596	22	will	will	AUX
ejpam-6251	596	23	end	end	VERB
ejpam-6251	596	24	up	up	ADP
ejpam-6251	596	25	back	back	ADV
ejpam-6251	596	26	where	where	SCONJ
ejpam-6251	596	27	you	you	PRON
ejpam-6251	596	28	started	start	VERB
ejpam-6251	596	29	.	.	PUNCT
ejpam-6251	597	1	as	as	ADP
ejpam-6251	597	2	a	a	DET
ejpam-6251	597	3	result	result	NOUN
ejpam-6251	597	4	,	,	PUNCT
ejpam-6251	597	5	you	you	PRON
ejpam-6251	597	6	return	return	VERB
ejpam-6251	597	7	to	to	ADP
ejpam-6251	597	8	the	the	DET
ejpam-6251	597	9	same	same	ADJ
ejpam-6251	597	10	initial	initial	ADJ
ejpam-6251	597	11	potential	potential	NOUN
ejpam-6251	597	12	without	without	ADP
ejpam-6251	597	13	any	any	DET
ejpam-6251	597	14	voltage	voltage	NOUN
ejpam-6251	597	15	losses	loss	NOUN
ejpam-6251	597	16	around	around	ADP
ejpam-6251	597	17	the	the	DET
ejpam-6251	597	18	loop	loop	NOUN
ejpam-6251	597	19	.	.	PUNCT
ejpam-6251	598	1	as	as	ADP
ejpam-6251	598	2	a	a	DET
ejpam-6251	598	3	result	result	NOUN
ejpam-6251	598	4	,	,	PUNCT
ejpam-6251	598	5	any	any	DET
ejpam-6251	598	6	voltage	voltage	NOUN
ejpam-6251	598	7	drop	drop	NOUN
ejpam-6251	598	8	around	around	ADP
ejpam-6251	598	9	the	the	DET
ejpam-6251	598	10	loop	loop	NOUN
ejpam-6251	598	11	must	must	AUX
ejpam-6251	598	12	be	be	AUX
ejpam-6251	598	13	equal	equal	ADJ
ejpam-6251	598	14	to	to	ADP
ejpam-6251	598	15	any	any	DET
ejpam-6251	598	16	voltage	voltage	NOUN
ejpam-6251	598	17	source	source	NOUN
ejpam-6251	598	18	encountered	encounter	VERB
ejpam-6251	598	19	along	along	ADP
ejpam-6251	598	20	the	the	DET
ejpam-6251	598	21	way	way	NOUN
ejpam-6251	598	22	.	.	PUNCT
ejpam-6251	599	1	the	the	DET
ejpam-6251	599	2	mathematical	mathematical	ADJ
ejpam-6251	599	3	expression	expression	NOUN
ejpam-6251	599	4	for	for	ADP
ejpam-6251	599	5	this	this	DET
ejpam-6251	599	6	consequence	consequence	NOUN
ejpam-6251	599	7	of	of	ADP
ejpam-6251	599	8	kirchhoff	kirchhoff	PROPN
ejpam-6251	599	9	’s	’s	PART
ejpam-6251	599	10	voltage	voltage	NOUN
ejpam-6251	599	11	law	law	NOUN
ejpam-6251	599	12	is	be	AUX
ejpam-6251	599	13	:	:	PUNCT
ejpam-6251	599	14	the	the	DET
ejpam-6251	599	15	sum	sum	NOUN
ejpam-6251	599	16	of	of	ADP
ejpam-6251	599	17	voltage	voltage	NOUN
ejpam-6251	599	18	rises	rise	VERB
ejpam-6251	599	19	across	across	ADP
ejpam-6251	599	20	any	any	DET
ejpam-6251	599	21	loop	loop	NOUN
ejpam-6251	599	22	is	be	AUX
ejpam-6251	599	23	equal	equal	ADJ
ejpam-6251	599	24	to	to	ADP
ejpam-6251	599	25	the	the	DET
ejpam-6251	599	26	sum	sum	NOUN
ejpam-6251	599	27	of	of	ADP
ejpam-6251	599	28	voltage	voltage	NOUN
ejpam-6251	599	29	drops	drop	NOUN
ejpam-6251	599	30	across	across	ADP
ejpam-6251	599	31	that	that	DET
ejpam-6251	599	32	loop	loop	NOUN
ejpam-6251	599	33	.	.	PUNCT
ejpam-6251	600	1	then	then	ADV
ejpam-6251	600	2	we	we	PRON
ejpam-6251	600	3	have	have	VERB
ejpam-6251	600	4	the	the	DET
ejpam-6251	600	5	following	follow	VERB
ejpam-6251	600	6	relation	relation	NOUN
ejpam-6251	600	7	:	:	PUNCT
ejpam-6251	600	8	ir+	ir+	VERB
ejpam-6251	601	1	ϖ	ϖ	X
ejpam-6251	601	2	c	c	PROPN
ejpam-6251	602	1	+	+	CCONJ
ejpam-6251	602	2	ldi	ldi	PROPN
ejpam-6251	602	3	dl	dl	PROPN
ejpam-6251	602	4	=	=	PROPN
ejpam-6251	602	5	v(l	v(l	PROPN
ejpam-6251	602	6	)	)	PUNCT
ejpam-6251	602	7	.	.	PUNCT
ejpam-6251	603	1	the	the	DET
ejpam-6251	603	2	voltage	voltage	NOUN
ejpam-6251	603	3	equation	equation	NOUN
ejpam-6251	603	4	can	can	AUX
ejpam-6251	603	5	be	be	AUX
ejpam-6251	603	6	expressed	express	VERB
ejpam-6251	603	7	as	as	ADP
ejpam-6251	603	8	in	in	ADP
ejpam-6251	603	9	the	the	DET
ejpam-6251	603	10	second	second	ADJ
ejpam-6251	603	11	-	-	PUNCT
ejpam-6251	603	12	order	order	NOUN
ejpam-6251	603	13	differential	differential	ADJ
ejpam-6251	603	14	equations	equation	NOUN
ejpam-6251	603	15	with	with	ADP
ejpam-6251	603	16	parameters	parameter	NOUN
ejpam-6251	603	17	as	as	SCONJ
ejpam-6251	603	18	follows	follow	VERB
ejpam-6251	603	19	.	.	PUNCT
ejpam-6251	604	1	ld2ϖ	ld2ϖ	PROPN
ejpam-6251	604	2	dl2	dl2	VERB
ejpam-6251	604	3	+	+	NOUN
ejpam-6251	604	4	rdϖ	rdϖ	NOUN
ejpam-6251	604	5	dl	dl	X
ejpam-6251	604	6	+	+	CCONJ
ejpam-6251	604	7	ϖ	ϖ	NOUN
ejpam-6251	604	8	c	c	NOUN
ejpam-6251	604	9	=	=	SYM
ejpam-6251	604	10	v(l	v(l	PROPN
ejpam-6251	604	11	)	)	PUNCT
ejpam-6251	604	12	=	=	PUNCT
ejpam-6251	605	1	h(l	h(l	PROPN
ejpam-6251	605	2	,	,	PUNCT
ejpam-6251	605	3	ς(l	ς(l	NOUN
ejpam-6251	605	4	)	)	PUNCT
ejpam-6251	605	5	)	)	PUNCT
ejpam-6251	605	6	,	,	PUNCT
ejpam-6251	605	7	with	with	ADP
ejpam-6251	605	8	the	the	DET
ejpam-6251	605	9	initial	initial	ADJ
ejpam-6251	605	10	conditions	condition	NOUN
ejpam-6251	605	11	,	,	PUNCT
ejpam-6251	605	12	ϖ(0	ϖ(0	PROPN
ejpam-6251	605	13	)	)	PUNCT
ejpam-6251	605	14	=	=	SYM
ejpam-6251	605	15	0	0	NUM
ejpam-6251	605	16	,	,	PUNCT
ejpam-6251	605	17	ϖ	ϖ	NOUN
ejpam-6251	605	18	′	′	NUM
ejpam-6251	605	19	(	(	PUNCT
ejpam-6251	605	20	0	0	NUM
ejpam-6251	605	21	)	)	PUNCT
ejpam-6251	605	22	=	=	SYM
ejpam-6251	605	23	0	0	NUM
ejpam-6251	605	24	,	,	PUNCT
ejpam-6251	605	25	(	(	PUNCT
ejpam-6251	605	26	17	17	NUM
ejpam-6251	605	27	)	)	PUNCT
ejpam-6251	605	28	where	where	SCONJ
ejpam-6251	605	29	c	c	NOUN
ejpam-6251	605	30	=	=	SYM
ejpam-6251	605	31	4l	4l	NOUN
ejpam-6251	605	32	r2	r2	PROPN
ejpam-6251	605	33	and	and	CCONJ
ejpam-6251	605	34	τ	τ	PROPN
ejpam-6251	605	35	=	=	SYM
ejpam-6251	605	36	r	r	NOUN
ejpam-6251	605	37	2l	2l	NUM
ejpam-6251	605	38	the	the	DET
ejpam-6251	605	39	non	non	ADJ
ejpam-6251	605	40	dimensional	dimensional	ADJ
ejpam-6251	605	41	time	time	NOUN
ejpam-6251	605	42	for	for	ADP
ejpam-6251	605	43	physics	physics	NOUN
ejpam-6251	605	44	.	.	PUNCT
ejpam-6251	606	1	the	the	DET
ejpam-6251	606	2	following	follow	VERB
ejpam-6251	606	3	green	green	ADJ
ejpam-6251	606	4	function	function	NOUN
ejpam-6251	606	5	associated	associate	VERB
ejpam-6251	606	6	with	with	ADP
ejpam-6251	606	7	equation	equation	NOUN
ejpam-6251	606	8	17	17	NUM
ejpam-6251	606	9	is	be	AUX
ejpam-6251	606	10	q(l	q(l	NOUN
ejpam-6251	606	11	,	,	PUNCT
ejpam-6251	606	12	s	s	PART
ejpam-6251	606	13	)	)	PUNCT
ejpam-6251	606	14	=	=	SYM
ejpam-6251	606	15	{	{	PUNCT
ejpam-6251	606	16	−si−τ(s−l	−si−τ(s−l	NOUN
ejpam-6251	606	17	)	)	PUNCT
ejpam-6251	606	18	,	,	PUNCT
ejpam-6251	606	19	if0	if0	VERB
ejpam-6251	607	1	≤	≤	PROPN
ejpam-6251	607	2	s	s	PART
ejpam-6251	607	3	≤	≤	NUM
ejpam-6251	607	4	l	l	NOUN
ejpam-6251	607	5	≤	≤	NUM
ejpam-6251	607	6	1	1	NUM
ejpam-6251	607	7	;	;	PUNCT
ejpam-6251	607	8	−li−τ(s−l	−li−τ(s−l	NOUN
ejpam-6251	607	9	)	)	PUNCT
ejpam-6251	607	10	,	,	PUNCT
ejpam-6251	607	11	if0	if0	VERB
ejpam-6251	607	12	≤	≤	NUM
ejpam-6251	608	1	l	l	NOUN
ejpam-6251	608	2	≤	≤	PROPN
ejpam-6251	608	3	s	s	PART
ejpam-6251	608	4	≤	≤	NOUN
ejpam-6251	608	5	1	1	NUM
ejpam-6251	608	6	.	.	PUNCT
ejpam-6251	609	1	in	in	ADP
ejpam-6251	609	2	equation	equation	NOUN
ejpam-6251	609	3	17	17	NUM
ejpam-6251	609	4	can	can	AUX
ejpam-6251	609	5	be	be	AUX
ejpam-6251	609	6	expressed	express	VERB
ejpam-6251	609	7	as	as	ADP
ejpam-6251	609	8	in	in	ADP
ejpam-6251	609	9	the	the	DET
ejpam-6251	609	10	integral	integral	ADJ
ejpam-6251	609	11	equation	equation	NOUN
ejpam-6251	609	12	with	with	ADP
ejpam-6251	609	13	the	the	DET
ejpam-6251	609	14	above	above	ADJ
ejpam-6251	609	15	condition	condition	NOUN
ejpam-6251	609	16	is	be	AUX
ejpam-6251	609	17	ς(l	ς(l	NOUN
ejpam-6251	609	18	)	)	PUNCT
ejpam-6251	609	19	=	=	SYM
ejpam-6251	610	1	∫	∫	PROPN
ejpam-6251	610	2	l	l	NOUN
ejpam-6251	610	3	0	0	NUM
ejpam-6251	610	4	q(l	q(l	NOUN
ejpam-6251	610	5	,	,	PUNCT
ejpam-6251	610	6	s)h(s	s)h(s	NOUN
ejpam-6251	610	7	,	,	PUNCT
ejpam-6251	610	8	ς(s))ds	ς(s))ds	PROPN
ejpam-6251	610	9	,	,	PUNCT
ejpam-6251	610	10	for	for	ADP
ejpam-6251	610	11	all	all	DET
ejpam-6251	610	12	l	l	NOUN
ejpam-6251	610	13	∈	∈	PROPN
ejpam-6251	611	1	[	[	X
ejpam-6251	611	2	0	0	NUM
ejpam-6251	611	3	,	,	PUNCT
ejpam-6251	611	4	1	1	NUM
ejpam-6251	611	5	]	]	PUNCT
ejpam-6251	611	6	(	(	PUNCT
ejpam-6251	611	7	18	18	NUM
ejpam-6251	611	8	)	)	PUNCT
ejpam-6251	611	9	and	and	CCONJ
ejpam-6251	611	10	h(s	h(s	PROPN
ejpam-6251	611	11	,	,	PUNCT
ejpam-6251	611	12	·	·	PUNCT
ejpam-6251	611	13	)	)	PUNCT
ejpam-6251	611	14	:	:	PUNCT
ejpam-6251	612	1	[	[	X
ejpam-6251	612	2	0	0	NUM
ejpam-6251	612	3	,	,	PUNCT
ejpam-6251	612	4	1]×	1]×	NUM
ejpam-6251	612	5	r	r	NOUN
ejpam-6251	612	6	→	→	SYM
ejpam-6251	612	7	r	r	NOUN
ejpam-6251	612	8	is	be	AUX
ejpam-6251	612	9	a	a	DET
ejpam-6251	612	10	monotone	monotone	ADJ
ejpam-6251	612	11	non	non	ADJ
ejpam-6251	612	12	-	-	ADJ
ejpam-6251	612	13	decreasing	decrease	VERB
ejpam-6251	612	14	mapping	mapping	NOUN
ejpam-6251	612	15	∀	∀	NOUN
ejpam-6251	612	16	s	s	PART
ejpam-6251	612	17	∈	∈	NOUN
ejpam-6251	613	1	[	[	X
ejpam-6251	613	2	0	0	NUM
ejpam-6251	613	3	,	,	PUNCT
ejpam-6251	613	4	1	1	NUM
ejpam-6251	613	5	]	]	PUNCT
ejpam-6251	613	6	.	.	PUNCT
ejpam-6251	614	1	consider	consider	VERB
ejpam-6251	614	2	the	the	DET
ejpam-6251	614	3	set	set	NOUN
ejpam-6251	614	4	of	of	ADP
ejpam-6251	614	5	all	all	DET
ejpam-6251	614	6	continuous	continuous	ADJ
ejpam-6251	614	7	functions	function	NOUN
ejpam-6251	614	8	𭟋	𭟋	ADP
ejpam-6251	614	9	=	=	SYM
ejpam-6251	614	10	(	(	PUNCT
ejpam-6251	614	11	c[0	c[0	PROPN
ejpam-6251	614	12	,	,	PUNCT
ejpam-6251	614	13	1	1	NUM
ejpam-6251	614	14	]	]	PUNCT
ejpam-6251	614	15	,	,	PUNCT
ejpam-6251	614	16	[	[	X
ejpam-6251	614	17	0,+∞	0,+∞	NUM
ejpam-6251	614	18	)	)	PUNCT
ejpam-6251	614	19	)	)	PUNCT
ejpam-6251	615	1	defined	define	VERB
ejpam-6251	615	2	on	on	ADP
ejpam-6251	615	3	[	[	X
ejpam-6251	615	4	0	0	NUM
ejpam-6251	615	5	,	,	PUNCT
ejpam-6251	615	6	1	1	NUM
ejpam-6251	615	7	]	]	PUNCT
ejpam-6251	615	8	with	with	ADP
ejpam-6251	615	9	values	value	NOUN
ejpam-6251	615	10	in	in	ADP
ejpam-6251	615	11	[	[	X
ejpam-6251	615	12	0,+∞	0,+∞	NUM
ejpam-6251	615	13	)	)	PUNCT
ejpam-6251	615	14	and	and	CCONJ
ejpam-6251	615	15	s	s	NOUN
ejpam-6251	615	16	=	=	SYM
ejpam-6251	615	17	(	(	PUNCT
ejpam-6251	615	18	c[0	c[0	PROPN
ejpam-6251	615	19	,	,	PUNCT
ejpam-6251	615	20	1	1	NUM
ejpam-6251	615	21	]	]	PUNCT
ejpam-6251	615	22	,	,	PUNCT
ejpam-6251	615	23	(	(	PUNCT
ejpam-6251	615	24	−∞	−∞	NOUN
ejpam-6251	615	25	,	,	PUNCT
ejpam-6251	615	26	0	0	NUM
ejpam-6251	615	27	]	]	PUNCT
ejpam-6251	615	28	)	)	PUNCT
ejpam-6251	615	29	defined	define	VERB
ejpam-6251	615	30	on	on	ADP
ejpam-6251	615	31	[	[	X
ejpam-6251	615	32	0	0	NUM
ejpam-6251	615	33	,	,	PUNCT
ejpam-6251	615	34	1	1	NUM
ejpam-6251	615	35	]	]	PUNCT
ejpam-6251	615	36	with	with	ADP
ejpam-6251	615	37	values	value	NOUN
ejpam-6251	615	38	in	in	ADP
ejpam-6251	615	39	(	(	PUNCT
ejpam-6251	615	40	−∞	−∞	NOUN
ejpam-6251	615	41	,	,	PUNCT
ejpam-6251	615	42	0	0	NUM
ejpam-6251	615	43	]	]	PUNCT
ejpam-6251	615	44	.	.	PUNCT
ejpam-6251	616	1	define	define	VERB
ejpam-6251	616	2	π	π	PROPN
ejpam-6251	616	3	,	,	PUNCT
ejpam-6251	616	4	ψ	ψ	NOUN
ejpam-6251	616	5	and	and	CCONJ
ejpam-6251	616	6	ξ	ξ	X
ejpam-6251	616	7	by	by	ADP
ejpam-6251	616	8	π(ς(o	π(ς(o	NOUN
ejpam-6251	616	9	)	)	PUNCT
ejpam-6251	616	10	,	,	PUNCT
ejpam-6251	616	11	ϖ(o	ϖ(o	NOUN
ejpam-6251	616	12	)	)	PUNCT
ejpam-6251	616	13	,	,	PUNCT
ejpam-6251	616	14	ż	ż	NOUN
ejpam-6251	616	15	)	)	PUNCT
ejpam-6251	616	16	=	=	SYM
ejpam-6251	616	17	sup	sup	NOUN
ejpam-6251	616	18	o∈[c	o∈[c	ADV
ejpam-6251	616	19	,	,	PUNCT
ejpam-6251	616	20	a	a	DET
ejpam-6251	616	21	]	]	X
ejpam-6251	616	22	ż	ż	PROPN
ejpam-6251	616	23	ż+	ż+	PROPN
ejpam-6251	616	24	|ς(o)−ϖ(o)|	|ς(o)−ϖ(o)|	ADP
ejpam-6251	616	25	∀	∀	NOUN
ejpam-6251	617	1	ς,ϖ	ς,ϖ	NUM
ejpam-6251	617	2	∈	∈	NUM
ejpam-6251	617	3	𭟋	𭟋	NOUN
ejpam-6251	617	4	and	and	CCONJ
ejpam-6251	617	5	ż	ż	X
ejpam-6251	617	6	>	>	X
ejpam-6251	617	7	0	0	NUM
ejpam-6251	617	8	,	,	PUNCT
ejpam-6251	617	9	ψ(ς(o	ψ(ς(o	NOUN
ejpam-6251	617	10	)	)	PUNCT
ejpam-6251	617	11	,	,	PUNCT
ejpam-6251	617	12	ϖ(o	ϖ(o	NOUN
ejpam-6251	617	13	)	)	PUNCT
ejpam-6251	617	14	,	,	PUNCT
ejpam-6251	617	15	ż	ż	NOUN
ejpam-6251	617	16	)	)	PUNCT
ejpam-6251	617	17	=	=	SYM
ejpam-6251	617	18	1−	1−	NUM
ejpam-6251	617	19	sup	sup	NOUN
ejpam-6251	617	20	o∈[c	o∈[c	ADP
ejpam-6251	617	21	,	,	PUNCT
ejpam-6251	617	22	a	a	PRON
ejpam-6251	617	23	]	]	X
ejpam-6251	617	24	ż	ż	PROPN
ejpam-6251	617	25	ż+	ż+	PROPN
ejpam-6251	617	26	|ς(o)−ϖ(o)|	|ς(o)−ϖ(o)|	ADP
ejpam-6251	617	27	∀	∀	NOUN
ejpam-6251	618	1	ς,ϖ	ς,ϖ	NUM
ejpam-6251	618	2	∈	∈	NUM
ejpam-6251	618	3	𭟋	𭟋	NOUN
ejpam-6251	618	4	and	and	CCONJ
ejpam-6251	618	5	ż	ż	X
ejpam-6251	618	6	>	>	X
ejpam-6251	618	7	0	0	NUM
ejpam-6251	618	8	,	,	PUNCT
ejpam-6251	618	9	and	and	CCONJ
ejpam-6251	618	10	ξ(ς(o	ξ(ς(o	NOUN
ejpam-6251	618	11	)	)	PUNCT
ejpam-6251	618	12	,	,	PUNCT
ejpam-6251	618	13	ϖ(o	ϖ(o	NOUN
ejpam-6251	618	14	)	)	PUNCT
ejpam-6251	618	15	,	,	PUNCT
ejpam-6251	618	16	ż	ż	NOUN
ejpam-6251	618	17	)	)	PUNCT
ejpam-6251	618	18	=	=	SYM
ejpam-6251	618	19	sup	sup	NOUN
ejpam-6251	618	20	o∈[c	o∈[c	ADV
ejpam-6251	618	21	,	,	PUNCT
ejpam-6251	618	22	a	a	PRON
ejpam-6251	618	23	]	]	X
ejpam-6251	618	24	|ς(o)−ϖ(o)|	|ς(o)−ϖ(o)|	NOUN
ejpam-6251	618	25	ż	ż	NOUN
ejpam-6251	618	26	∀	∀	NOUN
ejpam-6251	619	1	ς,ϖ	ς,ϖ	NUM
ejpam-6251	619	2	∈	∈	PROPN
ejpam-6251	619	3	𭟋	𭟋	NOUN
ejpam-6251	619	4	and	and	CCONJ
ejpam-6251	619	5	ż	ż	X
ejpam-6251	619	6	>	>	X
ejpam-6251	619	7	0	0	PROPN
ejpam-6251	619	8	,	,	PUNCT
ejpam-6251	619	9	r.	r.	PROPN
ejpam-6251	619	10	ramaswamy	ramaswamy	PROPN
ejpam-6251	619	11	/	/	SYM
ejpam-6251	619	12	eur	eur	PROPN
ejpam-6251	619	13	.	.	PUNCT
ejpam-6251	620	1	j.	j.	PROPN
ejpam-6251	620	2	pure	pure	PROPN
ejpam-6251	620	3	appl	appl	PROPN
ejpam-6251	620	4	.	.	PROPN
ejpam-6251	620	5	math	math	PROPN
ejpam-6251	620	6	,	,	PUNCT
ejpam-6251	620	7	18	18	NUM
ejpam-6251	620	8	(	(	PUNCT
ejpam-6251	620	9	4	4	NUM
ejpam-6251	620	10	)	)	PUNCT
ejpam-6251	620	11	(	(	PUNCT
ejpam-6251	620	12	2025	2025	NUM
ejpam-6251	620	13	)	)	PUNCT
ejpam-6251	620	14	,	,	PUNCT
ejpam-6251	620	15	6251	6251	NUM
ejpam-6251	620	16	33	33	NUM
ejpam-6251	620	17	of	of	ADP
ejpam-6251	620	18	40	40	NUM
ejpam-6251	620	19	figure	figure	NOUN
ejpam-6251	620	20	2	2	NUM
ejpam-6251	620	21	:	:	PUNCT
ejpam-6251	620	22	series	series	PROPN
ejpam-6251	620	23	rlc	rlc	PROPN
ejpam-6251	620	24	circuit	circuit	PROPN
ejpam-6251	620	25	.	.	PUNCT
ejpam-6251	621	1	with	with	ADP
ejpam-6251	621	2	ct−||.||	ct−||.||	PROPN
ejpam-6251	621	3	and	and	CCONJ
ejpam-6251	621	4	ct−co−||.||	ct−co−||.||	PRON
ejpam-6251	621	5	define	define	VERB
ejpam-6251	621	6	by	by	ADP
ejpam-6251	621	7	i⋇	i⋇	PROPN
ejpam-6251	621	8	♭	♭	PROPN
ejpam-6251	622	1	=	=	PUNCT
ejpam-6251	622	2	i	i	PRON
ejpam-6251	622	3	♭	♭	PROPN
ejpam-6251	622	4	and	and	CCONJ
ejpam-6251	622	5	i	i	PRON
ejpam-6251	622	6	♢	♢	PROPN
ejpam-6251	622	7	♭	♭	X
ejpam-6251	622	8	=	=	PUNCT
ejpam-6251	622	9	max{i	max{i	X
ejpam-6251	622	10	,	,	PUNCT
ejpam-6251	622	11	♭	♭	PROPN
ejpam-6251	622	12	}	}	PUNCT
ejpam-6251	622	13	.	.	PUNCT
ejpam-6251	623	1	then	then	ADV
ejpam-6251	623	2	(	(	PUNCT
ejpam-6251	623	3	𭟋	𭟋	X
ejpam-6251	623	4	,	,	PUNCT
ejpam-6251	623	5	π	π	PROPN
ejpam-6251	623	6	,	,	PUNCT
ejpam-6251	623	7	ψ	ψ	PROPN
ejpam-6251	623	8	,	,	PUNCT
ejpam-6251	623	9	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	623	10	,	,	PUNCT
ejpam-6251	623	11	♢	♢	PROPN
ejpam-6251	623	12	)	)	PUNCT
ejpam-6251	623	13	is	be	AUX
ejpam-6251	623	14	a	a	DET
ejpam-6251	623	15	complete	complete	ADJ
ejpam-6251	623	16	nbms	nbms	NOUN
ejpam-6251	623	17	.	.	PUNCT
ejpam-6251	624	1	theorem	theorem	ADJ
ejpam-6251	624	2	8	8	NUM
ejpam-6251	624	3	.	.	PUNCT
ejpam-6251	625	1	let	let	VERB
ejpam-6251	625	2	p	p	NOUN
ejpam-6251	625	3	:	:	PUNCT
ejpam-6251	625	4	(	(	PUNCT
ejpam-6251	625	5	𭟋	𭟋	NOUN
ejpam-6251	625	6	,	,	PUNCT
ejpam-6251	625	7	s	s	PROPN
ejpam-6251	625	8	,	,	PUNCT
ejpam-6251	625	9	π	π	PROPN
ejpam-6251	625	10	,	,	PUNCT
ejpam-6251	625	11	ψ	ψ	PROPN
ejpam-6251	625	12	,	,	PUNCT
ejpam-6251	625	13	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	625	14	,	,	PUNCT
ejpam-6251	625	15	♢	♢	PROPN
ejpam-6251	625	16	)	)	PUNCT
ejpam-6251	625	17	⇒	⇒	NOUN
ejpam-6251	625	18	(	(	PUNCT
ejpam-6251	625	19	𭟋	𭟋	PROPN
ejpam-6251	625	20	,	,	PUNCT
ejpam-6251	625	21	s	s	PROPN
ejpam-6251	625	22	,	,	PUNCT
ejpam-6251	625	23	π	π	PROPN
ejpam-6251	625	24	,	,	PUNCT
ejpam-6251	625	25	ψ	ψ	PROPN
ejpam-6251	625	26	,	,	PUNCT
ejpam-6251	625	27	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	625	28	,	,	PUNCT
ejpam-6251	625	29	♢	♢	PROPN
ejpam-6251	625	30	)	)	PUNCT
ejpam-6251	625	31	be	be	VERB
ejpam-6251	625	32	a	a	DET
ejpam-6251	625	33	map	map	NOUN
ejpam-6251	625	34	such	such	ADJ
ejpam-6251	625	35	that	that	SCONJ
ejpam-6251	625	36	the	the	DET
ejpam-6251	625	37	following	follow	VERB
ejpam-6251	625	38	axioms	axiom	NOUN
ejpam-6251	625	39	hold	hold	VERB
ejpam-6251	625	40	:	:	PUNCT
ejpam-6251	626	1	i.	i.	PROPN
ejpam-6251	626	2	q	q	PROPN
ejpam-6251	626	3	:	:	PUNCT
ejpam-6251	627	1	[	[	X
ejpam-6251	627	2	0	0	NUM
ejpam-6251	627	3	,	,	PUNCT
ejpam-6251	627	4	1]2	1]2	NUM
ejpam-6251	627	5	→	→	PUNCT
ejpam-6251	627	6	[	[	X
ejpam-6251	627	7	0,∞	0,∞	NUM
ejpam-6251	627	8	)	)	PUNCT
ejpam-6251	627	9	is	be	AUX
ejpam-6251	627	10	a	a	DET
ejpam-6251	627	11	continuous	continuous	ADJ
ejpam-6251	627	12	function	function	NOUN
ejpam-6251	627	13	;	;	PUNCT
ejpam-6251	627	14	ii	ii	X
ejpam-6251	627	15	.	.	PUNCT
ejpam-6251	628	1	h(s	h(s	PROPN
ejpam-6251	628	2	,	,	PUNCT
ejpam-6251	628	3	·	·	PUNCT
ejpam-6251	628	4	)	)	PUNCT
ejpam-6251	628	5	:	:	PUNCT
ejpam-6251	629	1	[	[	X
ejpam-6251	629	2	0	0	NUM
ejpam-6251	629	3	,	,	PUNCT
ejpam-6251	629	4	1	1	NUM
ejpam-6251	629	5	]	]	SYM
ejpam-6251	629	6	×	×	NOUN
ejpam-6251	629	7	r	r	NOUN
ejpam-6251	629	8	→	→	SYM
ejpam-6251	629	9	r	r	NOUN
ejpam-6251	629	10	is	be	AUX
ejpam-6251	629	11	a	a	DET
ejpam-6251	629	12	monotone	monotone	ADJ
ejpam-6251	629	13	nondecreasing	nondecrease	VERB
ejpam-6251	629	14	mapping	mapping	NOUN
ejpam-6251	629	15	∀	∀	NOUN
ejpam-6251	629	16	s	s	PART
ejpam-6251	629	17	∈	∈	NOUN
ejpam-6251	630	1	[	[	X
ejpam-6251	630	2	0	0	NUM
ejpam-6251	630	3	,	,	PUNCT
ejpam-6251	630	4	1	1	NUM
ejpam-6251	630	5	]	]	X
ejpam-6251	630	6	satisfying	satisfy	VERB
ejpam-6251	630	7	(	(	PUNCT
ejpam-6251	630	8	ς,ϖ	ς,ϖ	NUM
ejpam-6251	630	9	)	)	PUNCT
ejpam-6251	630	10	∈	∈	PROPN
ejpam-6251	630	11	(	(	PUNCT
ejpam-6251	630	12	𭟋	𭟋	NOUN
ejpam-6251	630	13	,	,	PUNCT
ejpam-6251	630	14	s	s	NOUN
ejpam-6251	630	15	)	)	PUNCT
ejpam-6251	630	16	,	,	PUNCT
ejpam-6251	630	17	|h(l	|h(l	PROPN
ejpam-6251	630	18	,	,	PUNCT
ejpam-6251	630	19	ς)−	ς)−	PROPN
ejpam-6251	630	20	h(l	h(l	PROPN
ejpam-6251	630	21	,	,	PUNCT
ejpam-6251	630	22	ϖ	ϖ	NOUN
ejpam-6251	630	23	)	)	PUNCT
ejpam-6251	630	24	≤	≤	NOUN
ejpam-6251	631	1	|ς(l)−ϖ(l)|	|ς(l)−ϖ(l)|	PROPN
ejpam-6251	631	2	.	.	PUNCT
ejpam-6251	632	1	iii	iii	PROPN
ejpam-6251	632	2	.	.	PUNCT
ejpam-6251	633	1	∫	∫	PROPN
ejpam-6251	633	2	l	l	NOUN
ejpam-6251	633	3	0	0	NUM
ejpam-6251	633	4	q(l	q(l	NOUN
ejpam-6251	633	5	,	,	PUNCT
ejpam-6251	633	6	s)ds	s)ds	PROPN
ejpam-6251	633	7	≤	≤	NOUN
ejpam-6251	633	8	ζ	ζ	NOUN
ejpam-6251	633	9	<	<	X
ejpam-6251	633	10	1	1	NUM
ejpam-6251	633	11	then	then	ADV
ejpam-6251	633	12	the	the	DET
ejpam-6251	633	13	voltage	voltage	NOUN
ejpam-6251	633	14	differential	differential	NOUN
ejpam-6251	633	15	equation	equation	NOUN
ejpam-6251	633	16	(	(	PUNCT
ejpam-6251	633	17	17	17	NUM
ejpam-6251	633	18	)	)	PUNCT
ejpam-6251	633	19	has	have	VERB
ejpam-6251	633	20	a	a	DET
ejpam-6251	633	21	unique	unique	ADJ
ejpam-6251	633	22	solution	solution	NOUN
ejpam-6251	633	23	.	.	PUNCT
ejpam-6251	634	1	proof	proof	NOUN
ejpam-6251	634	2	.	.	PUNCT
ejpam-6251	635	1	define	define	VERB
ejpam-6251	635	2	p	p	X
ejpam-6251	635	3	:	:	PUNCT
ejpam-6251	635	4	(	(	PUNCT
ejpam-6251	635	5	𭟋	𭟋	NOUN
ejpam-6251	635	6	,	,	PUNCT
ejpam-6251	635	7	s	s	PROPN
ejpam-6251	635	8	,	,	PUNCT
ejpam-6251	635	9	π	π	PROPN
ejpam-6251	635	10	,	,	PUNCT
ejpam-6251	635	11	ψ	ψ	PROPN
ejpam-6251	635	12	,	,	PUNCT
ejpam-6251	635	13	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	635	14	,	,	PUNCT
ejpam-6251	635	15	♢	♢	PROPN
ejpam-6251	635	16	)	)	PUNCT
ejpam-6251	635	17	⇒	⇒	NOUN
ejpam-6251	635	18	(	(	PUNCT
ejpam-6251	635	19	𭟋	𭟋	PROPN
ejpam-6251	635	20	,	,	PUNCT
ejpam-6251	635	21	s	s	PROPN
ejpam-6251	635	22	,	,	PUNCT
ejpam-6251	635	23	π	π	PROPN
ejpam-6251	635	24	,	,	PUNCT
ejpam-6251	635	25	ψ	ψ	PROPN
ejpam-6251	635	26	,	,	PUNCT
ejpam-6251	635	27	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	635	28	,	,	PUNCT
ejpam-6251	635	29	♢	♢	PROPN
ejpam-6251	635	30	)	)	PUNCT
ejpam-6251	635	31	by	by	ADP
ejpam-6251	635	32	pς(l	pς(l	NOUN
ejpam-6251	635	33	)	)	PUNCT
ejpam-6251	635	34	=	=	SYM
ejpam-6251	636	1	∫	∫	PROPN
ejpam-6251	636	2	l	l	NOUN
ejpam-6251	636	3	0	0	NUM
ejpam-6251	636	4	q(l	q(l	NOUN
ejpam-6251	636	5	,	,	PUNCT
ejpam-6251	636	6	s)h(s	s)h(s	NOUN
ejpam-6251	636	7	,	,	PUNCT
ejpam-6251	636	8	ς(s))ds	ς(s))ds	PROPN
ejpam-6251	636	9	,	,	PUNCT
ejpam-6251	636	10	where	where	SCONJ
ejpam-6251	636	11	l	l	PROPN
ejpam-6251	636	12	∈	∈	PROPN
ejpam-6251	637	1	[	[	X
ejpam-6251	637	2	0	0	NUM
ejpam-6251	637	3	,	,	PUNCT
ejpam-6251	637	4	1	1	NUM
ejpam-6251	637	5	]	]	X
ejpam-6251	637	6	r.	r.	PROPN
ejpam-6251	637	7	ramaswamy	ramaswamy	PROPN
ejpam-6251	637	8	/	/	SYM
ejpam-6251	637	9	eur	eur	PROPN
ejpam-6251	637	10	.	.	PUNCT
ejpam-6251	638	1	j.	j.	PROPN
ejpam-6251	638	2	pure	pure	PROPN
ejpam-6251	638	3	appl	appl	PROPN
ejpam-6251	638	4	.	.	PROPN
ejpam-6251	638	5	math	math	PROPN
ejpam-6251	638	6	,	,	PUNCT
ejpam-6251	638	7	18	18	NUM
ejpam-6251	638	8	(	(	PUNCT
ejpam-6251	638	9	4	4	NUM
ejpam-6251	638	10	)	)	PUNCT
ejpam-6251	638	11	(	(	PUNCT
ejpam-6251	638	12	2025	2025	NUM
ejpam-6251	638	13	)	)	PUNCT
ejpam-6251	638	14	,	,	PUNCT
ejpam-6251	638	15	6251	6251	NUM
ejpam-6251	638	16	34	34	NUM
ejpam-6251	638	17	of	of	ADP
ejpam-6251	638	18	40	40	NUM
ejpam-6251	638	19	now	now	ADV
ejpam-6251	638	20	,	,	PUNCT
ejpam-6251	638	21	∀	∀	X
ejpam-6251	638	22	ς,ϖ	ς,ϖ	NUM
ejpam-6251	638	23	∈	∈	PROPN
ejpam-6251	638	24	𭟋	𭟋	VERB
ejpam-6251	638	25	∪	∪	ADP
ejpam-6251	638	26	s	s	PROPN
ejpam-6251	638	27	,	,	PUNCT
ejpam-6251	638	28	we	we	PRON
ejpam-6251	638	29	deduce	deduce	VERB
ejpam-6251	638	30	π(pς(l	π(pς(l	NOUN
ejpam-6251	638	31	)	)	PUNCT
ejpam-6251	638	32	,	,	PUNCT
ejpam-6251	638	33	pϖ(l	pϖ(l	NOUN
ejpam-6251	638	34	)	)	PUNCT
ejpam-6251	638	35	,	,	PUNCT
ejpam-6251	638	36	ζ	ζ	NOUN
ejpam-6251	638	37	ż	ż	NOUN
ejpam-6251	638	38	)	)	PUNCT
ejpam-6251	638	39	=	=	NOUN
ejpam-6251	638	40	sup	sup	NOUN
ejpam-6251	638	41	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	638	42	]	]	X
ejpam-6251	638	43	ζ	ζ	NOUN
ejpam-6251	638	44	ż	ż	NOUN
ejpam-6251	638	45	ζ	ζ	PROPN
ejpam-6251	638	46	ż+	ż+	PROPN
ejpam-6251	638	47	|pς(l)−	|pς(l)−	PROPN
ejpam-6251	638	48	pϖ(l)|	pϖ(l)|	NOUN
ejpam-6251	638	49	=	=	SYM
ejpam-6251	638	50	sup	sup	NOUN
ejpam-6251	638	51	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	638	52	]	]	X
ejpam-6251	638	53	ζ	ζ	NOUN
ejpam-6251	638	54	ż	ż	NOUN
ejpam-6251	638	55	ζ	ζ	PROPN
ejpam-6251	638	56	ż+	ż+	PROPN
ejpam-6251	638	57	|	|	CCONJ
ejpam-6251	638	58	∫	∫	PROPN
ejpam-6251	638	59	l	l	NOUN
ejpam-6251	638	60	0	0	NUM
ejpam-6251	638	61	q(l	q(l	NOUN
ejpam-6251	638	62	,	,	PUNCT
ejpam-6251	638	63	s)h(s	s)h(s	NOUN
ejpam-6251	638	64	,	,	PUNCT
ejpam-6251	638	65	ς(s))ds−	ς(s))ds−	NOUN
ejpam-6251	638	66	∫	∫	PROPN
ejpam-6251	638	67	l	l	NOUN
ejpam-6251	638	68	0	0	NUM
ejpam-6251	638	69	q(l	q(l	NOUN
ejpam-6251	638	70	,	,	PUNCT
ejpam-6251	638	71	s)h(s	s)h(s	NOUN
ejpam-6251	638	72	,	,	PUNCT
ejpam-6251	638	73	ϖ(s))ds|	ϖ(s))ds|	NOUN
ejpam-6251	638	74	=	=	NOUN
ejpam-6251	638	75	sup	sup	NOUN
ejpam-6251	638	76	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	638	77	]	]	X
ejpam-6251	638	78	ζ	ζ	NOUN
ejpam-6251	638	79	ż	ż	NOUN
ejpam-6251	638	80	ζ	ζ	PROPN
ejpam-6251	638	81	ż+	ż+	PROPN
ejpam-6251	638	82	∫	∫	PROPN
ejpam-6251	639	1	l	l	NOUN
ejpam-6251	639	2	0	0	NUM
ejpam-6251	639	3	q(l	q(l	NOUN
ejpam-6251	639	4	,	,	PUNCT
ejpam-6251	639	5	s)|h(s	s)|h(s	PROPN
ejpam-6251	639	6	,	,	PUNCT
ejpam-6251	639	7	ς(s))−	ς(s))−	NOUN
ejpam-6251	639	8	h(s	h(	NOUN
ejpam-6251	639	9	,	,	PUNCT
ejpam-6251	639	10	ϖ(s))|ds	ϖ(s))|ds	NOUN
ejpam-6251	639	11	=	=	SYM
ejpam-6251	639	12	sup	sup	NOUN
ejpam-6251	639	13	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	639	14	]	]	X
ejpam-6251	639	15	ζ	ζ	NOUN
ejpam-6251	639	16	ż	ż	NOUN
ejpam-6251	639	17	ζ	ζ	PROPN
ejpam-6251	639	18	ż+	ż+	PROPN
ejpam-6251	639	19	|h(s	|h(s	PROPN
ejpam-6251	639	20	,	,	PUNCT
ejpam-6251	639	21	ς(s))−	ς(s))−	NOUN
ejpam-6251	639	22	h(s	h(s	PROPN
ejpam-6251	639	23	,	,	PUNCT
ejpam-6251	639	24	ϖ(s))|	ϖ(s))|	NOUN
ejpam-6251	639	25	≥	≥	NUM
ejpam-6251	639	26	sup	sup	NOUN
ejpam-6251	639	27	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	639	28	]	]	PUNCT
ejpam-6251	639	29	ż	ż	PROPN
ejpam-6251	639	30	ż+	ż+	PROPN
ejpam-6251	639	31	|ς(l)−ϖ(l)|	|ς(l)−ϖ(l)|	ADP
ejpam-6251	639	32	≥	≥	NOUN
ejpam-6251	639	33	π(ς(l	π(ς(l	PROPN
ejpam-6251	639	34	)	)	PUNCT
ejpam-6251	639	35	,	,	PUNCT
ejpam-6251	639	36	ϖ(l	ϖ(l	PROPN
ejpam-6251	639	37	)	)	PUNCT
ejpam-6251	639	38	,	,	PUNCT
ejpam-6251	639	39	ż	ż	NOUN
ejpam-6251	639	40	)	)	PUNCT
ejpam-6251	639	41	,	,	PUNCT
ejpam-6251	639	42	ψ(pς(l	ψ(pς(l	NOUN
ejpam-6251	639	43	)	)	PUNCT
ejpam-6251	639	44	,	,	PUNCT
ejpam-6251	639	45	pϖ(l	pϖ(l	NOUN
ejpam-6251	639	46	)	)	PUNCT
ejpam-6251	639	47	,	,	PUNCT
ejpam-6251	639	48	ζ	ζ	NOUN
ejpam-6251	639	49	ż	ż	NOUN
ejpam-6251	639	50	)	)	PUNCT
ejpam-6251	639	51	=	=	SYM
ejpam-6251	640	1	1−	1−	NUM
ejpam-6251	640	2	sup	sup	NOUN
ejpam-6251	640	3	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	640	4	]	]	X
ejpam-6251	640	5	ζ	ζ	NOUN
ejpam-6251	640	6	ż	ż	NOUN
ejpam-6251	640	7	ζ	ζ	PROPN
ejpam-6251	640	8	ż+	ż+	PROPN
ejpam-6251	640	9	|pς(l)−	|pς(l)−	PROPN
ejpam-6251	640	10	pϖ(l)|	pϖ(l)|	NOUN
ejpam-6251	640	11	=	=	SYM
ejpam-6251	640	12	1−	1−	NUM
ejpam-6251	640	13	sup	sup	NOUN
ejpam-6251	640	14	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	640	15	]	]	X
ejpam-6251	640	16	ζ	ζ	NOUN
ejpam-6251	640	17	ż	ż	NOUN
ejpam-6251	640	18	ζ	ζ	PROPN
ejpam-6251	640	19	ż+	ż+	PROPN
ejpam-6251	640	20	|	|	CCONJ
ejpam-6251	640	21	∫	∫	PROPN
ejpam-6251	640	22	l	l	NOUN
ejpam-6251	640	23	0	0	NUM
ejpam-6251	640	24	q(l	q(l	NOUN
ejpam-6251	640	25	,	,	PUNCT
ejpam-6251	640	26	s)h(s	s)h(s	NOUN
ejpam-6251	640	27	,	,	PUNCT
ejpam-6251	640	28	ς(s))ds−	ς(s))ds−	NOUN
ejpam-6251	640	29	∫	∫	PROPN
ejpam-6251	640	30	l	l	NOUN
ejpam-6251	640	31	0	0	NUM
ejpam-6251	640	32	q(l	q(l	NOUN
ejpam-6251	640	33	,	,	PUNCT
ejpam-6251	640	34	s)h(s	s)h(s	NOUN
ejpam-6251	640	35	,	,	PUNCT
ejpam-6251	640	36	ϖ(s))ds|	ϖ(s))ds|	NOUN
ejpam-6251	640	37	=	=	NOUN
ejpam-6251	640	38	1−	1−	NUM
ejpam-6251	640	39	sup	sup	NOUN
ejpam-6251	640	40	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	640	41	]	]	X
ejpam-6251	640	42	ζ	ζ	NOUN
ejpam-6251	640	43	ż	ż	NOUN
ejpam-6251	640	44	ζ	ζ	PROPN
ejpam-6251	640	45	ż+	ż+	PROPN
ejpam-6251	640	46	∫	∫	PROPN
ejpam-6251	640	47	l	l	NOUN
ejpam-6251	640	48	0	0	NUM
ejpam-6251	640	49	q(l	q(l	NOUN
ejpam-6251	640	50	,	,	PUNCT
ejpam-6251	640	51	s)|h(s	s)|h(s	PROPN
ejpam-6251	640	52	,	,	PUNCT
ejpam-6251	640	53	ς(s))−	ς(s))−	NOUN
ejpam-6251	640	54	h(s	h(s	PROPN
ejpam-6251	640	55	,	,	PUNCT
ejpam-6251	640	56	ϖ(s))|ds	ϖ(s))|d	VERB
ejpam-6251	640	57	≤	≤	NUM
ejpam-6251	640	58	1−	1−	NUM
ejpam-6251	640	59	sup	sup	NOUN
ejpam-6251	640	60	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	640	61	]	]	PUNCT
ejpam-6251	641	1	ż	ż	PROPN
ejpam-6251	641	2	ż+	ż+	PROPN
ejpam-6251	641	3	|ς(l)−ϖ(l)|	|ς(l)−ϖ(l)|	CCONJ
ejpam-6251	641	4	≤	≤	ADJ
ejpam-6251	641	5	ψ(ς(l	ψ(ς(l	PROPN
ejpam-6251	641	6	)	)	PUNCT
ejpam-6251	641	7	,	,	PUNCT
ejpam-6251	641	8	ϖ(l	ϖ(l	PROPN
ejpam-6251	641	9	)	)	PUNCT
ejpam-6251	641	10	,	,	PUNCT
ejpam-6251	641	11	ż	ż	NOUN
ejpam-6251	641	12	)	)	PUNCT
ejpam-6251	641	13	,	,	PUNCT
ejpam-6251	641	14	and	and	CCONJ
ejpam-6251	641	15	ξ(pς(l	ξ(pς(l	NOUN
ejpam-6251	641	16	)	)	PUNCT
ejpam-6251	641	17	,	,	PUNCT
ejpam-6251	641	18	pϖ(l	pϖ(l	NOUN
ejpam-6251	641	19	)	)	PUNCT
ejpam-6251	641	20	,	,	PUNCT
ejpam-6251	641	21	ζ	ζ	NOUN
ejpam-6251	641	22	ż	ż	NOUN
ejpam-6251	641	23	)	)	PUNCT
ejpam-6251	641	24	=	=	NOUN
ejpam-6251	641	25	sup	sup	NOUN
ejpam-6251	641	26	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	641	27	]	]	PUNCT
ejpam-6251	641	28	|pς(l)−	|pς(l)−	NOUN
ejpam-6251	641	29	pϖ(l)|	pϖ(l)|	PUNCT
ejpam-6251	641	30	ζ	ζ	PROPN
ejpam-6251	641	31	ż	ż	NOUN
ejpam-6251	641	32	=	=	NOUN
ejpam-6251	641	33	sup	sup	NOUN
ejpam-6251	641	34	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	641	35	]	]	PUNCT
ejpam-6251	642	1	|	|	ADV
ejpam-6251	642	2	∫	∫	PROPN
ejpam-6251	642	3	l	l	NOUN
ejpam-6251	642	4	0	0	NUM
ejpam-6251	642	5	q(l	q(l	NOUN
ejpam-6251	642	6	,	,	PUNCT
ejpam-6251	642	7	s)h(s	s)h(s	NOUN
ejpam-6251	642	8	,	,	PUNCT
ejpam-6251	642	9	ς(s))ds−	ς(s))ds−	NOUN
ejpam-6251	642	10	∫	∫	PROPN
ejpam-6251	642	11	l	l	NOUN
ejpam-6251	642	12	0	0	NUM
ejpam-6251	642	13	q(l	q(l	NOUN
ejpam-6251	642	14	,	,	PUNCT
ejpam-6251	642	15	s)h(s	s)h(s	NOUN
ejpam-6251	642	16	,	,	PUNCT
ejpam-6251	642	17	ϖ(s))ds|	ϖ(s))ds|	VERB
ejpam-6251	642	18	ζ	ζ	NOUN
ejpam-6251	642	19	ż	ż	NOUN
ejpam-6251	642	20	=	=	NOUN
ejpam-6251	642	21	sup	sup	NOUN
ejpam-6251	642	22	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	642	23	]	]	PUNCT
ejpam-6251	642	24	∫	∫	PROPN
ejpam-6251	643	1	l	l	NOUN
ejpam-6251	643	2	0	0	NUM
ejpam-6251	643	3	q(l	q(l	NOUN
ejpam-6251	643	4	,	,	PUNCT
ejpam-6251	643	5	s)|h(s	s)|h(s	PROPN
ejpam-6251	643	6	,	,	PUNCT
ejpam-6251	643	7	ς(s))−	ς(s))−	NOUN
ejpam-6251	643	8	h(s	h(s	PROPN
ejpam-6251	643	9	,	,	PUNCT
ejpam-6251	643	10	ϖ(s))|ds	ϖ(s))|ds	ADP
ejpam-6251	643	11	ζ	ζ	PROPN
ejpam-6251	643	12	ż	ż	NOUN
ejpam-6251	643	13	≤	≤	NUM
ejpam-6251	643	14	sup	sup	NOUN
ejpam-6251	643	15	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	643	16	]	]	PUNCT
ejpam-6251	644	1	|ς(l)−ϖ(l)|	|ς(l)−ϖ(l)|	X
ejpam-6251	645	1	ż	ż	NOUN
ejpam-6251	645	2	≤	≤	NUM
ejpam-6251	645	3	ξ(ς(l	ξ(ς(l	NOUN
ejpam-6251	645	4	)	)	PUNCT
ejpam-6251	645	5	,	,	PUNCT
ejpam-6251	645	6	ϖ(l	ϖ(l	PROPN
ejpam-6251	645	7	)	)	PUNCT
ejpam-6251	645	8	,	,	PUNCT
ejpam-6251	645	9	ż	ż	NOUN
ejpam-6251	645	10	)	)	PUNCT
ejpam-6251	645	11	.	.	PUNCT
ejpam-6251	646	1	it	it	PRON
ejpam-6251	646	2	can	can	AUX
ejpam-6251	646	3	be	be	AUX
ejpam-6251	646	4	seen	see	VERB
ejpam-6251	646	5	that	that	SCONJ
ejpam-6251	646	6	all	all	DET
ejpam-6251	646	7	conditions	condition	NOUN
ejpam-6251	646	8	of	of	ADP
ejpam-6251	646	9	theorem	theorem	NOUN
ejpam-6251	646	10	(	(	PUNCT
ejpam-6251	646	11	5	5	NUM
ejpam-6251	646	12	)	)	PUNCT
ejpam-6251	646	13	are	be	AUX
ejpam-6251	646	14	satisfied	satisfied	ADJ
ejpam-6251	646	15	and	and	CCONJ
ejpam-6251	646	16	p	p	NOUN
ejpam-6251	646	17	has	have	VERB
ejpam-6251	646	18	a	a	DET
ejpam-6251	646	19	unique	unique	ADJ
ejpam-6251	646	20	fixed	fix	VERB
ejpam-6251	646	21	point	point	NOUN
ejpam-6251	646	22	and	and	CCONJ
ejpam-6251	646	23	the	the	DET
ejpam-6251	646	24	differential	differential	ADJ
ejpam-6251	646	25	voltage	voltage	NOUN
ejpam-6251	646	26	equation	equation	NOUN
ejpam-6251	646	27	(	(	PUNCT
ejpam-6251	646	28	17	17	NUM
ejpam-6251	646	29	)	)	PUNCT
ejpam-6251	646	30	has	have	VERB
ejpam-6251	646	31	a	a	DET
ejpam-6251	646	32	unique	unique	ADJ
ejpam-6251	646	33	solution	solution	NOUN
ejpam-6251	646	34	.	.	PUNCT
ejpam-6251	647	1	r.	r.	PROPN
ejpam-6251	647	2	ramaswamy	ramaswamy	PROPN
ejpam-6251	647	3	/	/	SYM
ejpam-6251	647	4	eur	eur	PROPN
ejpam-6251	647	5	.	.	PUNCT
ejpam-6251	648	1	j.	j.	PROPN
ejpam-6251	648	2	pure	pure	PROPN
ejpam-6251	648	3	appl	appl	PROPN
ejpam-6251	648	4	.	.	PROPN
ejpam-6251	648	5	math	math	PROPN
ejpam-6251	648	6	,	,	PUNCT
ejpam-6251	648	7	18	18	NUM
ejpam-6251	648	8	(	(	PUNCT
ejpam-6251	648	9	4	4	NUM
ejpam-6251	648	10	)	)	PUNCT
ejpam-6251	648	11	(	(	PUNCT
ejpam-6251	648	12	2025	2025	NUM
ejpam-6251	648	13	)	)	PUNCT
ejpam-6251	648	14	,	,	PUNCT
ejpam-6251	648	15	6251	6251	NUM
ejpam-6251	648	16	35	35	NUM
ejpam-6251	648	17	of	of	ADP
ejpam-6251	648	18	40	40	NUM
ejpam-6251	648	19	now	now	ADV
ejpam-6251	648	20	assume	assume	VERB
ejpam-6251	648	21	that	that	SCONJ
ejpam-6251	648	22	r	r	NOUN
ejpam-6251	648	23	=	=	SYM
ejpam-6251	648	24	10	10	NUM
ejpam-6251	648	25	,	,	PUNCT
ejpam-6251	648	26	c	c	NOUN
ejpam-6251	648	27	=	=	SYM
ejpam-6251	648	28	1	1	NUM
ejpam-6251	648	29	and	and	CCONJ
ejpam-6251	648	30	l	l	NOUN
ejpam-6251	648	31	=	=	NOUN
ejpam-6251	648	32	1	1	NUM
ejpam-6251	648	33	whereas	whereas	SCONJ
ejpam-6251	648	34	the	the	DET
ejpam-6251	648	35	voltage	voltage	NOUN
ejpam-6251	648	36	source	source	NOUN
ejpam-6251	648	37	is	be	AUX
ejpam-6251	648	38	given	give	VERB
ejpam-6251	648	39	by	by	ADP
ejpam-6251	648	40	v(t	v(t	ADJ
ejpam-6251	648	41	)	)	PUNCT
ejpam-6251	648	42	=	=	SYM
ejpam-6251	648	43	5sin(t	5sin(t	NUM
ejpam-6251	648	44	)	)	PUNCT
ejpam-6251	648	45	.	.	PUNCT
ejpam-6251	649	1	thus	thus	ADV
ejpam-6251	649	2	,	,	PUNCT
ejpam-6251	649	3	the	the	DET
ejpam-6251	649	4	nearer	nearer	ADJ
ejpam-6251	649	5	form	form	NOUN
ejpam-6251	649	6	of	of	ADP
ejpam-6251	649	7	the	the	DET
ejpam-6251	649	8	unique	unique	ADJ
ejpam-6251	649	9	solution	solution	NOUN
ejpam-6251	649	10	for	for	ADP
ejpam-6251	649	11	circuit	circuit	NOUN
ejpam-6251	649	12	ivp	ivp	NOUN
ejpam-6251	649	13	is	be	AUX
ejpam-6251	649	14	found	find	VERB
ejpam-6251	649	15	using	use	VERB
ejpam-6251	649	16	mathematica	mathematica	PROPN
ejpam-6251	649	17	software	software	NOUN
ejpam-6251	649	18	and	and	CCONJ
ejpam-6251	649	19	expressed	express	VERB
ejpam-6251	649	20	as	as	ADP
ejpam-6251	649	21	q(t	q(t	ADJ
ejpam-6251	649	22	)	)	PUNCT
ejpam-6251	649	23	=	=	SYM
ejpam-6251	649	24	1	1	NUM
ejpam-6251	649	25	24	24	NUM
ejpam-6251	649	26	e−5	e−5	PROPN
ejpam-6251	649	27	t	t	PROPN
ejpam-6251	649	28	(	(	PUNCT
ejpam-6251	649	29	5	5	NUM
ejpam-6251	649	30	√	√	NUM
ejpam-6251	649	31	6	6	NUM
ejpam-6251	649	32	sinh	sinh	NOUN
ejpam-6251	649	33	(	(	PUNCT
ejpam-6251	649	34	2	2	NUM
ejpam-6251	649	35	√	√	NUM
ejpam-6251	649	36	6	6	NUM
ejpam-6251	649	37	t	t	NOUN
ejpam-6251	649	38	)	)	PUNCT
ejpam-6251	650	1	+	+	CCONJ
ejpam-6251	650	2	12	12	NUM
ejpam-6251	650	3	cosh	cosh	NOUN
ejpam-6251	650	4	(	(	PUNCT
ejpam-6251	650	5	2	2	NUM
ejpam-6251	650	6	√	√	NUM
ejpam-6251	650	7	6	6	NUM
ejpam-6251	650	8	t	t	NOUN
ejpam-6251	650	9	)	)	PUNCT
ejpam-6251	650	10	)	)	PUNCT
ejpam-6251	651	1	−	−	PROPN
ejpam-6251	651	2	cos(t	cos(t	X
ejpam-6251	651	3	)	)	PUNCT
ejpam-6251	651	4	2	2	NUM
ejpam-6251	651	5	,	,	PUNCT
ejpam-6251	651	6	and	and	CCONJ
ejpam-6251	651	7	the	the	DET
ejpam-6251	651	8	graph	graph	NOUN
ejpam-6251	651	9	of	of	ADP
ejpam-6251	651	10	the	the	DET
ejpam-6251	651	11	solution	solution	NOUN
ejpam-6251	651	12	is	be	AUX
ejpam-6251	651	13	shown	show	VERB
ejpam-6251	651	14	in	in	ADP
ejpam-6251	651	15	figure	figure	NOUN
ejpam-6251	651	16	3	3	NUM
ejpam-6251	651	17	.	.	PUNCT
ejpam-6251	651	18	figure	figure	VERB
ejpam-6251	651	19	3	3	NUM
ejpam-6251	651	20	:	:	PUNCT
ejpam-6251	651	21	solution	solution	NOUN
ejpam-6251	651	22	of	of	ADP
ejpam-6251	651	23	(	(	PUNCT
ejpam-6251	651	24	5.1	5.1	NUM
ejpam-6251	651	25	)	)	PUNCT
ejpam-6251	651	26	.	.	PUNCT
ejpam-6251	652	1	r.	r.	PROPN
ejpam-6251	652	2	ramaswamy	ramaswamy	PROPN
ejpam-6251	652	3	/	/	SYM
ejpam-6251	652	4	eur	eur	PROPN
ejpam-6251	652	5	.	.	PUNCT
ejpam-6251	653	1	j.	j.	PROPN
ejpam-6251	653	2	pure	pure	PROPN
ejpam-6251	653	3	appl	appl	PROPN
ejpam-6251	653	4	.	.	PROPN
ejpam-6251	653	5	math	math	PROPN
ejpam-6251	653	6	,	,	PUNCT
ejpam-6251	653	7	18	18	NUM
ejpam-6251	653	8	(	(	PUNCT
ejpam-6251	653	9	4	4	NUM
ejpam-6251	653	10	)	)	PUNCT
ejpam-6251	653	11	(	(	PUNCT
ejpam-6251	653	12	2025	2025	NUM
ejpam-6251	653	13	)	)	PUNCT
ejpam-6251	653	14	,	,	PUNCT
ejpam-6251	653	15	6251	6251	NUM
ejpam-6251	653	16	36	36	NUM
ejpam-6251	653	17	of	of	ADP
ejpam-6251	653	18	40	40	NUM
ejpam-6251	653	19	6	6	NUM
ejpam-6251	653	20	.	.	PUNCT
ejpam-6251	654	1	application	application	NOUN
ejpam-6251	654	2	to	to	ADP
ejpam-6251	654	3	fractional	fractional	ADJ
ejpam-6251	654	4	differential	differential	NOUN
ejpam-6251	654	5	equation	equation	NOUN
ejpam-6251	654	6	consider	consider	VERB
ejpam-6251	654	7	the	the	DET
ejpam-6251	654	8	definition	definition	NOUN
ejpam-6251	654	9	of	of	ADP
ejpam-6251	654	10	caputo	caputo	PROPN
ejpam-6251	654	11	derivative	derivative	PROPN
ejpam-6251	654	12	of	of	ADP
ejpam-6251	654	13	a	a	DET
ejpam-6251	654	14	continuous	continuous	ADJ
ejpam-6251	654	15	function	function	NOUN
ejpam-6251	654	16	p̄	p̄	NOUN
ejpam-6251	654	17	:	:	PUNCT
ejpam-6251	655	1	[	[	X
ejpam-6251	655	2	0,+∞	0,+∞	NUM
ejpam-6251	655	3	)	)	PUNCT
ejpam-6251	655	4	→	→	SYM
ejpam-6251	655	5	r	r	NOUN
ejpam-6251	655	6	order	order	NOUN
ejpam-6251	655	7	β̄	β̄	X
ejpam-6251	655	8	>	>	X
ejpam-6251	655	9	0	0	PUNCT
ejpam-6251	655	10	(	(	PUNCT
ejpam-6251	655	11	see[2	see[2	NUM
ejpam-6251	655	12	,	,	PUNCT
ejpam-6251	655	13	3	3	NUM
ejpam-6251	655	14	]	]	X
ejpam-6251	655	15	):	):	PUNCT
ejpam-6251	655	16	cdβ̄(p̄(l	cdβ̄(p̄(l	NOUN
ejpam-6251	655	17	)	)	PUNCT
ejpam-6251	655	18	)	)	PUNCT
ejpam-6251	655	19	:	:	PUNCT
ejpam-6251	656	1	=	=	SYM
ejpam-6251	656	2	1	1	NUM
ejpam-6251	656	3	γ(µ−	γ(µ−	NOUN
ejpam-6251	656	4	β̄	β̄	NOUN
ejpam-6251	656	5	)	)	PUNCT
ejpam-6251	656	6	∫	∫	PROPN
ejpam-6251	657	1	l	l	NOUN
ejpam-6251	657	2	0	0	PUNCT
ejpam-6251	658	1	(	(	PUNCT
ejpam-6251	658	2	l−	l−	NOUN
ejpam-6251	658	3	s)µ−β̄−1p̄(µ)(s)ds(µ−	s)µ−β̄−1p̄(µ)(s)ds(µ−	NOUN
ejpam-6251	658	4	1	1	NUM
ejpam-6251	658	5	<	<	X
ejpam-6251	658	6	β̄	β̄	PROPN
ejpam-6251	658	7	<	<	X
ejpam-6251	658	8	µ	µ	X
ejpam-6251	658	9	,	,	PUNCT
ejpam-6251	658	10	µ	µ	X
ejpam-6251	658	11	=	=	SYM
ejpam-6251	659	1	[	[	X
ejpam-6251	659	2	β̄	β̄	X
ejpam-6251	659	3	]	]	X
ejpam-6251	659	4	+	+	NUM
ejpam-6251	659	5	1	1	NUM
ejpam-6251	659	6	)	)	PUNCT
ejpam-6251	659	7	,	,	PUNCT
ejpam-6251	659	8	where	where	SCONJ
ejpam-6251	659	9	γ	γ	PROPN
ejpam-6251	659	10	is	be	AUX
ejpam-6251	659	11	a	a	DET
ejpam-6251	659	12	gamma	gamma	NOUN
ejpam-6251	659	13	function	function	NOUN
ejpam-6251	659	14	and	and	CCONJ
ejpam-6251	659	15	[	[	X
ejpam-6251	659	16	β̄	β̄	X
ejpam-6251	659	17	]	]	AUX
ejpam-6251	659	18	denotes	denote	VERB
ejpam-6251	659	19	the	the	DET
ejpam-6251	659	20	integer	integer	NOUN
ejpam-6251	659	21	part	part	NOUN
ejpam-6251	659	22	of	of	ADP
ejpam-6251	659	23	the	the	DET
ejpam-6251	659	24	real	real	ADJ
ejpam-6251	659	25	number	number	NOUN
ejpam-6251	659	26	β̄	β̄	PROPN
ejpam-6251	659	27	>	>	X
ejpam-6251	659	28	0	0	X
ejpam-6251	659	29	.	.	PUNCT
ejpam-6251	660	1	additionally	additionally	ADV
ejpam-6251	660	2	,	,	PUNCT
ejpam-6251	660	3	we	we	PRON
ejpam-6251	660	4	provide	provide	VERB
ejpam-6251	660	5	an	an	DET
ejpam-6251	660	6	application	application	NOUN
ejpam-6251	660	7	of	of	ADP
ejpam-6251	660	8	the	the	DET
ejpam-6251	660	9	theorem	theorem	NOUN
ejpam-6251	660	10	5	5	NUM
ejpam-6251	660	11	for	for	ADP
ejpam-6251	660	12	proving	prove	VERB
ejpam-6251	660	13	the	the	DET
ejpam-6251	660	14	existence	existence	NOUN
ejpam-6251	660	15	solution	solution	NOUN
ejpam-6251	660	16	of	of	ADP
ejpam-6251	660	17	the	the	DET
ejpam-6251	660	18	nonlinear	nonlinear	ADJ
ejpam-6251	660	19	fractional	fractional	ADJ
ejpam-6251	660	20	differential	differential	NOUN
ejpam-6251	660	21	equation	equation	NOUN
ejpam-6251	660	22	cdβ̄(ς(l	cdβ̄(ς(l	NOUN
ejpam-6251	660	23	)	)	PUNCT
ejpam-6251	660	24	)	)	PUNCT
ejpam-6251	661	1	+	+	CCONJ
ejpam-6251	661	2	h(l	h(l	PROPN
ejpam-6251	661	3	,	,	PUNCT
ejpam-6251	661	4	ς(l	ς(l	NOUN
ejpam-6251	661	5	)	)	PUNCT
ejpam-6251	661	6	)	)	PUNCT
ejpam-6251	662	1	=	=	SYM
ejpam-6251	662	2	0	0	PUNCT
ejpam-6251	662	3	(	(	PUNCT
ejpam-6251	662	4	0	0	NUM
ejpam-6251	662	5	≤	≤	NUM
ejpam-6251	662	6	l	l	NOUN
ejpam-6251	662	7	≤	≤	NUM
ejpam-6251	662	8	1	1	NUM
ejpam-6251	662	9	,	,	PUNCT
ejpam-6251	662	10	β̄	β̄	PROPN
ejpam-6251	662	11	<	<	X
ejpam-6251	662	12	1	1	NUM
ejpam-6251	662	13	)	)	PUNCT
ejpam-6251	662	14	(	(	PUNCT
ejpam-6251	662	15	19	19	NUM
ejpam-6251	662	16	)	)	PUNCT
ejpam-6251	662	17	with	with	ADP
ejpam-6251	662	18	ς(0	ς(0	PROPN
ejpam-6251	662	19	)	)	PUNCT
ejpam-6251	662	20	=	=	SYM
ejpam-6251	662	21	0	0	PUNCT
ejpam-6251	662	22	=	=	SYM
ejpam-6251	662	23	ς(1	ς(1	NOUN
ejpam-6251	662	24	)	)	PUNCT
ejpam-6251	662	25	and	and	CCONJ
ejpam-6251	662	26	h	h	NOUN
ejpam-6251	662	27	:	:	PUNCT
ejpam-6251	663	1	[	[	X
ejpam-6251	663	2	0	0	NUM
ejpam-6251	663	3	,	,	PUNCT
ejpam-6251	663	4	1	1	NUM
ejpam-6251	663	5	]	]	SYM
ejpam-6251	663	6	×	×	NOUN
ejpam-6251	663	7	r	r	NOUN
ejpam-6251	663	8	→	→	SYM
ejpam-6251	663	9	r	r	NOUN
ejpam-6251	663	10	is	be	AUX
ejpam-6251	663	11	a	a	DET
ejpam-6251	663	12	continuous	continuous	ADJ
ejpam-6251	663	13	function	function	NOUN
ejpam-6251	663	14	(	(	PUNCT
ejpam-6251	663	15	see[4	see[4	NOUN
ejpam-6251	663	16	,	,	PUNCT
ejpam-6251	663	17	34–36	34–36	NUM
ejpam-6251	663	18	]	]	PUNCT
ejpam-6251	663	19	)	)	PUNCT
ejpam-6251	663	20	.	.	PUNCT
ejpam-6251	664	1	the	the	DET
ejpam-6251	664	2	green	green	ADJ
ejpam-6251	664	3	function	function	NOUN
ejpam-6251	664	4	related	relate	VERB
ejpam-6251	664	5	with	with	ADP
ejpam-6251	664	6	(	(	PUNCT
ejpam-6251	664	7	19	19	NUM
ejpam-6251	664	8	)	)	PUNCT
ejpam-6251	664	9	is	be	AUX
ejpam-6251	664	10	q(l	q(l	NOUN
ejpam-6251	664	11	,	,	PUNCT
ejpam-6251	664	12	s	s	X
ejpam-6251	664	13	)	)	PUNCT
ejpam-6251	664	14	=	=	SYM
ejpam-6251	664	15	{	{	PUNCT
ejpam-6251	664	16	(	(	PUNCT
ejpam-6251	664	17	l(1−	l(1−	PROPN
ejpam-6251	664	18	s))α−1	s))α−1	PROPN
ejpam-6251	664	19	−	−	PROPN
ejpam-6251	664	20	(	(	PUNCT
ejpam-6251	664	21	l−	l−	PROPN
ejpam-6251	664	22	s)α−1	s)α−1	NOUN
ejpam-6251	664	23	,	,	PUNCT
ejpam-6251	664	24	if	if	SCONJ
ejpam-6251	664	25	0	0	NUM
ejpam-6251	664	26	≤	≤	NUM
ejpam-6251	664	27	s	s	PART
ejpam-6251	664	28	≤	≤	NUM
ejpam-6251	664	29	l	l	NOUN
ejpam-6251	664	30	≤	≤	NUM
ejpam-6251	664	31	1	1	NUM
ejpam-6251	664	32	(	(	PUNCT
ejpam-6251	664	33	l(1−s))α−1	l(1−s))α−1	NOUN
ejpam-6251	664	34	γ(α	γ(α	NOUN
ejpam-6251	664	35	)	)	PUNCT
ejpam-6251	664	36	,	,	PUNCT
ejpam-6251	664	37	if	if	SCONJ
ejpam-6251	664	38	0	0	NUM
ejpam-6251	664	39	≤	≤	NUM
ejpam-6251	664	40	l	l	NOUN
ejpam-6251	664	41	≤	≤	PROPN
ejpam-6251	664	42	s	s	PART
ejpam-6251	664	43	≤	≤	NUM
ejpam-6251	664	44	1	1	NUM
ejpam-6251	664	45	.	.	PUNCT
ejpam-6251	665	1	obviously	obviously	ADV
ejpam-6251	665	2	ς∗	ς∗	VERB
ejpam-6251	665	3	∈	∈	PROPN
ejpam-6251	665	4	𭟋	𭟋	NOUN
ejpam-6251	665	5	is	be	AUX
ejpam-6251	665	6	a	a	DET
ejpam-6251	665	7	solution	solution	NOUN
ejpam-6251	665	8	of	of	ADP
ejpam-6251	665	9	(	(	PUNCT
ejpam-6251	665	10	19	19	NUM
ejpam-6251	665	11	)	)	PUNCT
ejpam-6251	665	12	if	if	SCONJ
ejpam-6251	665	13	and	and	CCONJ
ejpam-6251	665	14	only	only	ADV
ejpam-6251	665	15	if	if	SCONJ
ejpam-6251	665	16	ς∗	ς∗	PROPN
ejpam-6251	665	17	∈	∈	PROPN
ejpam-6251	665	18	𭟋	𭟋	NOUN
ejpam-6251	665	19	is	be	AUX
ejpam-6251	665	20	a	a	DET
ejpam-6251	665	21	solution	solution	NOUN
ejpam-6251	665	22	of	of	ADP
ejpam-6251	665	23	the	the	DET
ejpam-6251	665	24	equation	equation	NOUN
ejpam-6251	665	25	ς(l	ς(l	NOUN
ejpam-6251	665	26	)	)	PUNCT
ejpam-6251	665	27	=	=	SYM
ejpam-6251	666	1	∫	∫	PROPN
ejpam-6251	666	2	l	l	NOUN
ejpam-6251	666	3	0	0	NUM
ejpam-6251	666	4	q(l	q(l	NOUN
ejpam-6251	666	5	,	,	PUNCT
ejpam-6251	666	6	s)h(s	s)h(s	NOUN
ejpam-6251	666	7	,	,	PUNCT
ejpam-6251	666	8	ς(s))ds	ς(s))ds	NUM
ejpam-6251	666	9	∀	∀	X
ejpam-6251	667	1	l	l	NOUN
ejpam-6251	667	2	∈	∈	PROPN
ejpam-6251	668	1	[	[	X
ejpam-6251	668	2	0	0	NUM
ejpam-6251	668	3	,	,	PUNCT
ejpam-6251	668	4	1	1	NUM
ejpam-6251	668	5	]	]	PUNCT
ejpam-6251	668	6	.	.	PUNCT
ejpam-6251	669	1	let	let	VERB
ejpam-6251	669	2	the	the	DET
ejpam-6251	669	3	set	set	NOUN
ejpam-6251	669	4	of	of	ADP
ejpam-6251	669	5	all	all	DET
ejpam-6251	669	6	continuous	continuous	ADJ
ejpam-6251	669	7	functions	function	NOUN
ejpam-6251	669	8	𭟋	𭟋	ADP
ejpam-6251	669	9	=	=	SYM
ejpam-6251	669	10	(	(	PUNCT
ejpam-6251	669	11	c[0	c[0	PROPN
ejpam-6251	669	12	,	,	PUNCT
ejpam-6251	669	13	1	1	NUM
ejpam-6251	669	14	]	]	PUNCT
ejpam-6251	669	15	,	,	PUNCT
ejpam-6251	670	1	[	[	X
ejpam-6251	670	2	0,+∞	0,+∞	NUM
ejpam-6251	670	3	)	)	PUNCT
ejpam-6251	670	4	)	)	PUNCT
ejpam-6251	671	1	defined	define	VERB
ejpam-6251	671	2	on	on	ADP
ejpam-6251	671	3	[	[	X
ejpam-6251	671	4	0	0	NUM
ejpam-6251	671	5	,	,	PUNCT
ejpam-6251	671	6	1	1	NUM
ejpam-6251	671	7	]	]	PUNCT
ejpam-6251	671	8	with	with	ADP
ejpam-6251	671	9	values	value	NOUN
ejpam-6251	671	10	in	in	ADP
ejpam-6251	671	11	[	[	X
ejpam-6251	671	12	0,+∞	0,+∞	NUM
ejpam-6251	671	13	)	)	PUNCT
ejpam-6251	671	14	and	and	CCONJ
ejpam-6251	671	15	s	s	NOUN
ejpam-6251	671	16	=	=	SYM
ejpam-6251	671	17	(	(	PUNCT
ejpam-6251	671	18	c[0	c[0	PROPN
ejpam-6251	671	19	,	,	PUNCT
ejpam-6251	671	20	1	1	NUM
ejpam-6251	671	21	]	]	PUNCT
ejpam-6251	671	22	,	,	PUNCT
ejpam-6251	671	23	(	(	PUNCT
ejpam-6251	671	24	−∞	−∞	NOUN
ejpam-6251	671	25	,	,	PUNCT
ejpam-6251	671	26	0	0	NUM
ejpam-6251	671	27	]	]	PUNCT
ejpam-6251	671	28	)	)	PUNCT
ejpam-6251	671	29	defined	define	VERB
ejpam-6251	671	30	on	on	ADP
ejpam-6251	671	31	[	[	X
ejpam-6251	671	32	0	0	NUM
ejpam-6251	671	33	,	,	PUNCT
ejpam-6251	671	34	1	1	NUM
ejpam-6251	671	35	]	]	PUNCT
ejpam-6251	671	36	with	with	ADP
ejpam-6251	671	37	values	value	NOUN
ejpam-6251	671	38	in	in	ADP
ejpam-6251	671	39	(	(	PUNCT
ejpam-6251	671	40	−∞	−∞	NOUN
ejpam-6251	671	41	,	,	PUNCT
ejpam-6251	671	42	0	0	NUM
ejpam-6251	671	43	]	]	PUNCT
ejpam-6251	671	44	.	.	PUNCT
ejpam-6251	672	1	define	define	VERB
ejpam-6251	672	2	π	π	PROPN
ejpam-6251	672	3	,	,	PUNCT
ejpam-6251	672	4	ψ	ψ	NOUN
ejpam-6251	672	5	and	and	CCONJ
ejpam-6251	672	6	ξ	ξ	X
ejpam-6251	672	7	by	by	ADP
ejpam-6251	672	8	π(ς(o	π(ς(o	NOUN
ejpam-6251	672	9	)	)	PUNCT
ejpam-6251	672	10	,	,	PUNCT
ejpam-6251	672	11	ϖ(o	ϖ(o	NOUN
ejpam-6251	672	12	)	)	PUNCT
ejpam-6251	672	13	,	,	PUNCT
ejpam-6251	672	14	ż	ż	NOUN
ejpam-6251	672	15	)	)	PUNCT
ejpam-6251	672	16	=	=	SYM
ejpam-6251	672	17	sup	sup	NOUN
ejpam-6251	672	18	o∈[c	o∈[c	ADV
ejpam-6251	672	19	,	,	PUNCT
ejpam-6251	672	20	a	a	DET
ejpam-6251	672	21	]	]	X
ejpam-6251	672	22	ż	ż	PROPN
ejpam-6251	672	23	ż+	ż+	PROPN
ejpam-6251	672	24	|ς(o)−ϖ(o)|	|ς(o)−ϖ(o)|	ADP
ejpam-6251	672	25	∀	∀	NOUN
ejpam-6251	673	1	ς,ϖ	ς,ϖ	NUM
ejpam-6251	673	2	∈	∈	NUM
ejpam-6251	673	3	𭟋	𭟋	NOUN
ejpam-6251	673	4	and	and	CCONJ
ejpam-6251	673	5	ż	ż	X
ejpam-6251	673	6	>	>	X
ejpam-6251	673	7	0	0	NUM
ejpam-6251	673	8	,	,	PUNCT
ejpam-6251	673	9	ψ(ς(o	ψ(ς(o	NOUN
ejpam-6251	673	10	)	)	PUNCT
ejpam-6251	673	11	,	,	PUNCT
ejpam-6251	673	12	ϖ(o	ϖ(o	NOUN
ejpam-6251	673	13	)	)	PUNCT
ejpam-6251	673	14	,	,	PUNCT
ejpam-6251	673	15	ż	ż	NOUN
ejpam-6251	673	16	)	)	PUNCT
ejpam-6251	673	17	=	=	SYM
ejpam-6251	673	18	1−	1−	NUM
ejpam-6251	673	19	sup	sup	NOUN
ejpam-6251	673	20	o∈[c	o∈[c	ADP
ejpam-6251	673	21	,	,	PUNCT
ejpam-6251	673	22	a	a	PRON
ejpam-6251	673	23	]	]	X
ejpam-6251	673	24	ż	ż	PROPN
ejpam-6251	673	25	ż+	ż+	PROPN
ejpam-6251	673	26	|ς(o)−ϖ(o)|	|ς(o)−ϖ(o)|	ADP
ejpam-6251	673	27	∀	∀	NOUN
ejpam-6251	674	1	ς,ϖ	ς,ϖ	NUM
ejpam-6251	674	2	∈	∈	NUM
ejpam-6251	674	3	𭟋	𭟋	NOUN
ejpam-6251	674	4	and	and	CCONJ
ejpam-6251	674	5	ż	ż	X
ejpam-6251	674	6	>	>	X
ejpam-6251	674	7	0	0	NUM
ejpam-6251	674	8	,	,	PUNCT
ejpam-6251	674	9	and	and	CCONJ
ejpam-6251	674	10	ξ(ς(o	ξ(ς(o	NOUN
ejpam-6251	674	11	)	)	PUNCT
ejpam-6251	674	12	,	,	PUNCT
ejpam-6251	674	13	ϖ(o	ϖ(o	NOUN
ejpam-6251	674	14	)	)	PUNCT
ejpam-6251	674	15	,	,	PUNCT
ejpam-6251	674	16	ż	ż	NOUN
ejpam-6251	674	17	)	)	PUNCT
ejpam-6251	674	18	=	=	SYM
ejpam-6251	674	19	sup	sup	NOUN
ejpam-6251	674	20	o∈[c	o∈[c	ADV
ejpam-6251	674	21	,	,	PUNCT
ejpam-6251	674	22	a	a	PRON
ejpam-6251	674	23	]	]	X
ejpam-6251	674	24	|ς(o)−ϖ(o)|	|ς(o)−ϖ(o)|	NOUN
ejpam-6251	674	25	ż	ż	NOUN
ejpam-6251	674	26	∀	∀	NOUN
ejpam-6251	675	1	ς,ϖ	ς,ϖ	NUM
ejpam-6251	675	2	∈	∈	PROPN
ejpam-6251	675	3	𭟋	𭟋	NOUN
ejpam-6251	675	4	and	and	CCONJ
ejpam-6251	675	5	ż	ż	X
ejpam-6251	675	6	>	>	X
ejpam-6251	675	7	0	0	NUM
ejpam-6251	675	8	,	,	PUNCT
ejpam-6251	675	9	with	with	ADP
ejpam-6251	675	10	ct−||.||	ct−||.||	NOUN
ejpam-6251	675	11	and	and	CCONJ
ejpam-6251	675	12	ct−co−||.||	ct−co−||.||	PRON
ejpam-6251	675	13	define	define	VERB
ejpam-6251	675	14	by	by	ADP
ejpam-6251	675	15	i⋇	i⋇	PROPN
ejpam-6251	675	16	♭	♭	PROPN
ejpam-6251	676	1	=	=	PUNCT
ejpam-6251	676	2	i	i	PRON
ejpam-6251	676	3	♭	♭	PROPN
ejpam-6251	676	4	and	and	CCONJ
ejpam-6251	676	5	i	i	PRON
ejpam-6251	676	6	♢	♢	PROPN
ejpam-6251	676	7	♭	♭	X
ejpam-6251	676	8	=	=	PUNCT
ejpam-6251	676	9	max{i	max{i	X
ejpam-6251	676	10	,	,	PUNCT
ejpam-6251	676	11	♭	♭	PROPN
ejpam-6251	676	12	}	}	PUNCT
ejpam-6251	676	13	.	.	PUNCT
ejpam-6251	677	1	then	then	ADV
ejpam-6251	677	2	(	(	PUNCT
ejpam-6251	677	3	𭟋	𭟋	X
ejpam-6251	677	4	,	,	PUNCT
ejpam-6251	677	5	π	π	PROPN
ejpam-6251	677	6	,	,	PUNCT
ejpam-6251	677	7	ψ	ψ	PROPN
ejpam-6251	677	8	,	,	PUNCT
ejpam-6251	677	9	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	677	10	,	,	PUNCT
ejpam-6251	677	11	♢	♢	PROPN
ejpam-6251	677	12	)	)	PUNCT
ejpam-6251	677	13	is	be	AUX
ejpam-6251	677	14	a	a	DET
ejpam-6251	677	15	complete	complete	ADJ
ejpam-6251	677	16	nbms	nbms	NOUN
ejpam-6251	677	17	.	.	PUNCT
ejpam-6251	678	1	theorem	theorem	NOUN
ejpam-6251	678	2	9	9	NUM
ejpam-6251	678	3	.	.	PUNCT
ejpam-6251	679	1	let	let	VERB
ejpam-6251	679	2	p	p	NOUN
ejpam-6251	679	3	:	:	PUNCT
ejpam-6251	679	4	(	(	PUNCT
ejpam-6251	679	5	𭟋	𭟋	NOUN
ejpam-6251	679	6	,	,	PUNCT
ejpam-6251	679	7	s	s	PROPN
ejpam-6251	679	8	,	,	PUNCT
ejpam-6251	679	9	π	π	PROPN
ejpam-6251	679	10	,	,	PUNCT
ejpam-6251	679	11	ψ	ψ	PROPN
ejpam-6251	679	12	,	,	PUNCT
ejpam-6251	679	13	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	679	14	,	,	PUNCT
ejpam-6251	679	15	♢	♢	PROPN
ejpam-6251	679	16	)	)	PUNCT
ejpam-6251	679	17	⇒	⇒	NOUN
ejpam-6251	679	18	(	(	PUNCT
ejpam-6251	679	19	𭟋	𭟋	PROPN
ejpam-6251	679	20	,	,	PUNCT
ejpam-6251	679	21	s	s	PROPN
ejpam-6251	679	22	,	,	PUNCT
ejpam-6251	679	23	π	π	PROPN
ejpam-6251	679	24	,	,	PUNCT
ejpam-6251	679	25	ψ	ψ	PROPN
ejpam-6251	679	26	,	,	PUNCT
ejpam-6251	679	27	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	679	28	,	,	PUNCT
ejpam-6251	679	29	♢	♢	PROPN
ejpam-6251	679	30	)	)	PUNCT
ejpam-6251	679	31	be	be	VERB
ejpam-6251	679	32	a	a	DET
ejpam-6251	679	33	map	map	NOUN
ejpam-6251	679	34	such	such	ADJ
ejpam-6251	679	35	that	that	SCONJ
ejpam-6251	679	36	the	the	DET
ejpam-6251	679	37	following	follow	VERB
ejpam-6251	679	38	axioms	axiom	NOUN
ejpam-6251	679	39	hold	hold	VERB
ejpam-6251	679	40	:	:	PUNCT
ejpam-6251	680	1	i.	i.	PROPN
ejpam-6251	680	2	q	q	PROPN
ejpam-6251	680	3	:	:	PUNCT
ejpam-6251	681	1	[	[	X
ejpam-6251	681	2	0	0	NUM
ejpam-6251	681	3	,	,	PUNCT
ejpam-6251	681	4	1]2	1]2	NUM
ejpam-6251	681	5	→	→	PUNCT
ejpam-6251	681	6	[	[	X
ejpam-6251	681	7	0,∞	0,∞	NUM
ejpam-6251	681	8	)	)	PUNCT
ejpam-6251	681	9	is	be	AUX
ejpam-6251	681	10	a	a	DET
ejpam-6251	681	11	continuous	continuous	ADJ
ejpam-6251	681	12	function	function	NOUN
ejpam-6251	681	13	;	;	PUNCT
ejpam-6251	681	14	r.	r.	PROPN
ejpam-6251	681	15	ramaswamy	ramaswamy	PROPN
ejpam-6251	681	16	/	/	SYM
ejpam-6251	681	17	eur	eur	PROPN
ejpam-6251	681	18	.	.	PUNCT
ejpam-6251	682	1	j.	j.	PROPN
ejpam-6251	682	2	pure	pure	PROPN
ejpam-6251	682	3	appl	appl	PROPN
ejpam-6251	682	4	.	.	PROPN
ejpam-6251	682	5	math	math	PROPN
ejpam-6251	682	6	,	,	PUNCT
ejpam-6251	682	7	18	18	NUM
ejpam-6251	682	8	(	(	PUNCT
ejpam-6251	682	9	4	4	NUM
ejpam-6251	682	10	)	)	PUNCT
ejpam-6251	682	11	(	(	PUNCT
ejpam-6251	682	12	2025	2025	NUM
ejpam-6251	682	13	)	)	PUNCT
ejpam-6251	682	14	,	,	PUNCT
ejpam-6251	682	15	6251	6251	NUM
ejpam-6251	682	16	37	37	NUM
ejpam-6251	682	17	of	of	ADP
ejpam-6251	682	18	40	40	NUM
ejpam-6251	682	19	ii	ii	NOUN
ejpam-6251	682	20	.	.	PUNCT
ejpam-6251	683	1	h(s	h(s	PROPN
ejpam-6251	683	2	,	,	PUNCT
ejpam-6251	683	3	·	·	PUNCT
ejpam-6251	683	4	)	)	PUNCT
ejpam-6251	683	5	:	:	PUNCT
ejpam-6251	684	1	[	[	X
ejpam-6251	684	2	0	0	NUM
ejpam-6251	684	3	,	,	PUNCT
ejpam-6251	684	4	1	1	NUM
ejpam-6251	684	5	]	]	SYM
ejpam-6251	684	6	×	×	NOUN
ejpam-6251	684	7	r	r	NOUN
ejpam-6251	684	8	→	→	SYM
ejpam-6251	684	9	r	r	NOUN
ejpam-6251	684	10	is	be	AUX
ejpam-6251	684	11	a	a	DET
ejpam-6251	684	12	monotone	monotone	ADJ
ejpam-6251	684	13	non	non	NOUN
ejpam-6251	684	14	decreasing	decrease	VERB
ejpam-6251	684	15	function	function	NOUN
ejpam-6251	684	16	∀	∀	X
ejpam-6251	684	17	s	s	PART
ejpam-6251	684	18	∈	∈	NOUN
ejpam-6251	685	1	[	[	X
ejpam-6251	685	2	0	0	NUM
ejpam-6251	685	3	,	,	PUNCT
ejpam-6251	685	4	1	1	NUM
ejpam-6251	685	5	]	]	PUNCT
ejpam-6251	685	6	such	such	ADJ
ejpam-6251	685	7	that	that	SCONJ
ejpam-6251	685	8	(	(	PUNCT
ejpam-6251	685	9	ς,ϖ	ς,ϖ	NUM
ejpam-6251	685	10	)	)	PUNCT
ejpam-6251	685	11	∈	∈	PROPN
ejpam-6251	685	12	(	(	PUNCT
ejpam-6251	685	13	𭟋	𭟋	NOUN
ejpam-6251	685	14	,	,	PUNCT
ejpam-6251	685	15	s	s	PART
ejpam-6251	685	16	)	)	PUNCT
ejpam-6251	685	17	,	,	PUNCT
ejpam-6251	685	18	we	we	PRON
ejpam-6251	685	19	have	have	VERB
ejpam-6251	685	20	|h(l	|h(l	PROPN
ejpam-6251	685	21	,	,	PUNCT
ejpam-6251	685	22	ς)−	ς)−	PROPN
ejpam-6251	685	23	h(l	h(l	PROPN
ejpam-6251	685	24	,	,	PUNCT
ejpam-6251	685	25	ϖ	ϖ	NOUN
ejpam-6251	685	26	)	)	PUNCT
ejpam-6251	685	27	≤	≤	NOUN
ejpam-6251	686	1	|ς(l)−ϖ(l)|	|ς(l)−ϖ(l)|	PROPN
ejpam-6251	686	2	;	;	PUNCT
ejpam-6251	686	3	iii	iii	X
ejpam-6251	686	4	.	.	PUNCT
ejpam-6251	687	1	supl∈[0,1	supl∈[0,1	PROPN
ejpam-6251	687	2	]	]	PUNCT
ejpam-6251	687	3	∫	∫	PROPN
ejpam-6251	688	1	l	l	NOUN
ejpam-6251	688	2	0	0	NUM
ejpam-6251	688	3	q(l	q(l	NOUN
ejpam-6251	688	4	,	,	PUNCT
ejpam-6251	688	5	s	s	X
ejpam-6251	688	6	)	)	PUNCT
ejpam-6251	688	7	≤	≤	NUM
ejpam-6251	688	8	ζ	ζ	NOUN
ejpam-6251	688	9	<	<	X
ejpam-6251	688	10	1	1	NUM
ejpam-6251	688	11	.	.	PUNCT
ejpam-6251	689	1	then	then	ADV
ejpam-6251	689	2	the	the	DET
ejpam-6251	689	3	fractional	fractional	ADJ
ejpam-6251	689	4	differential	differential	ADJ
ejpam-6251	689	5	equation	equation	NOUN
ejpam-6251	689	6	(	(	PUNCT
ejpam-6251	689	7	19	19	NUM
ejpam-6251	689	8	)	)	PUNCT
ejpam-6251	689	9	has	have	VERB
ejpam-6251	689	10	a	a	DET
ejpam-6251	689	11	unique	unique	ADJ
ejpam-6251	689	12	solution	solution	NOUN
ejpam-6251	689	13	.	.	PUNCT
ejpam-6251	690	1	proof	proof	NOUN
ejpam-6251	690	2	.	.	PUNCT
ejpam-6251	691	1	define	define	VERB
ejpam-6251	691	2	p	p	X
ejpam-6251	691	3	:	:	PUNCT
ejpam-6251	691	4	(	(	PUNCT
ejpam-6251	691	5	𭟋	𭟋	NOUN
ejpam-6251	691	6	,	,	PUNCT
ejpam-6251	691	7	s	s	PROPN
ejpam-6251	691	8	,	,	PUNCT
ejpam-6251	691	9	π	π	PROPN
ejpam-6251	691	10	,	,	PUNCT
ejpam-6251	691	11	ψ	ψ	PROPN
ejpam-6251	691	12	,	,	PUNCT
ejpam-6251	691	13	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	691	14	,	,	PUNCT
ejpam-6251	691	15	♢	♢	PROPN
ejpam-6251	691	16	)	)	PUNCT
ejpam-6251	691	17	⇒	⇒	NOUN
ejpam-6251	691	18	(	(	PUNCT
ejpam-6251	691	19	𭟋	𭟋	PROPN
ejpam-6251	691	20	,	,	PUNCT
ejpam-6251	691	21	s	s	PROPN
ejpam-6251	691	22	,	,	PUNCT
ejpam-6251	691	23	π	π	PROPN
ejpam-6251	691	24	,	,	PUNCT
ejpam-6251	691	25	ψ	ψ	PROPN
ejpam-6251	691	26	,	,	PUNCT
ejpam-6251	691	27	ξ,⋇	ξ,⋇	PROPN
ejpam-6251	691	28	,	,	PUNCT
ejpam-6251	691	29	♢	♢	PROPN
ejpam-6251	691	30	)	)	PUNCT
ejpam-6251	691	31	by	by	ADP
ejpam-6251	691	32	pς(l	pς(l	NOUN
ejpam-6251	691	33	)	)	PUNCT
ejpam-6251	691	34	=	=	SYM
ejpam-6251	692	1	∫	∫	PROPN
ejpam-6251	692	2	l	l	NOUN
ejpam-6251	692	3	0	0	NUM
ejpam-6251	692	4	q(l	q(l	NOUN
ejpam-6251	692	5	,	,	PUNCT
ejpam-6251	692	6	s)h(s	s)h(s	NOUN
ejpam-6251	692	7	,	,	PUNCT
ejpam-6251	692	8	ς(s))ds	ς(s))ds	PROPN
ejpam-6251	692	9	,	,	PUNCT
ejpam-6251	692	10	where	where	SCONJ
ejpam-6251	692	11	l	l	PROPN
ejpam-6251	692	12	∈	∈	PROPN
ejpam-6251	693	1	[	[	X
ejpam-6251	693	2	0	0	NUM
ejpam-6251	693	3	,	,	PUNCT
ejpam-6251	693	4	1	1	NUM
ejpam-6251	693	5	]	]	PUNCT
ejpam-6251	693	6	now	now	ADV
ejpam-6251	693	7	,	,	PUNCT
ejpam-6251	693	8	∀	∀	X
ejpam-6251	693	9	ς,ϖ	ς,ϖ	NUM
ejpam-6251	693	10	∈	∈	PROPN
ejpam-6251	693	11	𭟋	𭟋	VERB
ejpam-6251	693	12	∪	∪	ADP
ejpam-6251	693	13	s	s	PROPN
ejpam-6251	693	14	,	,	PUNCT
ejpam-6251	693	15	we	we	PRON
ejpam-6251	693	16	deduce	deduce	VERB
ejpam-6251	693	17	π(pς(l	π(pς(l	NOUN
ejpam-6251	693	18	)	)	PUNCT
ejpam-6251	693	19	,	,	PUNCT
ejpam-6251	693	20	pϖ(l),ζ	pϖ(l),ζ	NOUN
ejpam-6251	693	21	ż	ż	NOUN
ejpam-6251	693	22	)	)	PUNCT
ejpam-6251	693	23	=	=	NOUN
ejpam-6251	693	24	sup	sup	NOUN
ejpam-6251	693	25	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	693	26	]	]	X
ejpam-6251	693	27	ζ	ζ	NOUN
ejpam-6251	693	28	ż	ż	NOUN
ejpam-6251	693	29	ζ	ζ	PROPN
ejpam-6251	693	30	ż+	ż+	PROPN
ejpam-6251	693	31	|pς(l)−	|pς(l)−	PROPN
ejpam-6251	693	32	pϖ(l)|	pϖ(l)|	NOUN
ejpam-6251	693	33	=	=	SYM
ejpam-6251	693	34	sup	sup	NOUN
ejpam-6251	693	35	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	693	36	]	]	X
ejpam-6251	693	37	ζ	ζ	NOUN
ejpam-6251	693	38	ż	ż	NOUN
ejpam-6251	693	39	ζ	ζ	PROPN
ejpam-6251	693	40	ż+	ż+	PROPN
ejpam-6251	693	41	|	|	CCONJ
ejpam-6251	693	42	∫	∫	PROPN
ejpam-6251	693	43	l	l	NOUN
ejpam-6251	693	44	0	0	NUM
ejpam-6251	693	45	q(l	q(l	NOUN
ejpam-6251	693	46	,	,	PUNCT
ejpam-6251	693	47	s)h(s	s)h(s	NOUN
ejpam-6251	693	48	,	,	PUNCT
ejpam-6251	693	49	ς(s))ds−	ς(s))ds−	NOUN
ejpam-6251	693	50	∫	∫	PROPN
ejpam-6251	693	51	l	l	NOUN
ejpam-6251	693	52	0	0	NUM
ejpam-6251	693	53	q(l	q(l	NOUN
ejpam-6251	693	54	,	,	PUNCT
ejpam-6251	693	55	s)h(s	s)h(s	NOUN
ejpam-6251	693	56	,	,	PUNCT
ejpam-6251	693	57	ϖ(s))ds|	ϖ(s))ds|	NOUN
ejpam-6251	693	58	=	=	NOUN
ejpam-6251	693	59	sup	sup	NOUN
ejpam-6251	693	60	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	693	61	]	]	X
ejpam-6251	693	62	ζ	ζ	NOUN
ejpam-6251	693	63	ż	ż	NOUN
ejpam-6251	693	64	ζ	ζ	PROPN
ejpam-6251	693	65	ż+	ż+	PROPN
ejpam-6251	693	66	∫	∫	PROPN
ejpam-6251	693	67	l	l	NOUN
ejpam-6251	693	68	0	0	NUM
ejpam-6251	693	69	q(l	q(l	NOUN
ejpam-6251	693	70	,	,	PUNCT
ejpam-6251	693	71	s)|h(s	s)|h(s	PROPN
ejpam-6251	693	72	,	,	PUNCT
ejpam-6251	693	73	ς(s))−	ς(s))−	NOUN
ejpam-6251	693	74	h(s	h(	NOUN
ejpam-6251	693	75	,	,	PUNCT
ejpam-6251	693	76	ϖ(s))|ds	ϖ(s))|ds	NOUN
ejpam-6251	693	77	=	=	SYM
ejpam-6251	693	78	sup	sup	NOUN
ejpam-6251	693	79	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	693	80	]	]	X
ejpam-6251	693	81	ζ	ζ	NOUN
ejpam-6251	693	82	ż	ż	NOUN
ejpam-6251	693	83	ζ	ζ	PROPN
ejpam-6251	693	84	ż+	ż+	PROPN
ejpam-6251	693	85	|h(s	|h(s	PROPN
ejpam-6251	693	86	,	,	PUNCT
ejpam-6251	693	87	ς(s))−	ς(s))−	NOUN
ejpam-6251	693	88	h(s	h(s	PROPN
ejpam-6251	693	89	,	,	PUNCT
ejpam-6251	693	90	ϖ(s))|	ϖ(s))|	NOUN
ejpam-6251	693	91	≥	≥	NUM
ejpam-6251	693	92	sup	sup	NOUN
ejpam-6251	693	93	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	693	94	]	]	PUNCT
ejpam-6251	693	95	ż	ż	PROPN
ejpam-6251	693	96	ż+	ż+	PROPN
ejpam-6251	693	97	|ς(l)−ϖ(l)|	|ς(l)−ϖ(l)|	ADP
ejpam-6251	693	98	≥	≥	NOUN
ejpam-6251	693	99	π(ς(l	π(ς(l	PROPN
ejpam-6251	693	100	)	)	PUNCT
ejpam-6251	693	101	,	,	PUNCT
ejpam-6251	693	102	ϖ(l	ϖ(l	PROPN
ejpam-6251	693	103	)	)	PUNCT
ejpam-6251	693	104	,	,	PUNCT
ejpam-6251	693	105	ż	ż	NOUN
ejpam-6251	693	106	)	)	PUNCT
ejpam-6251	693	107	,	,	PUNCT
ejpam-6251	693	108	ψ(pς(l),pϖ(l	ψ(pς(l),pϖ(l	NOUN
ejpam-6251	693	109	)	)	PUNCT
ejpam-6251	693	110	,	,	PUNCT
ejpam-6251	693	111	ζ	ζ	NOUN
ejpam-6251	693	112	ż	ż	NOUN
ejpam-6251	693	113	)	)	PUNCT
ejpam-6251	693	114	=	=	SYM
ejpam-6251	694	1	1−	1−	NUM
ejpam-6251	694	2	sup	sup	NOUN
ejpam-6251	694	3	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	694	4	]	]	X
ejpam-6251	694	5	ζ	ζ	NOUN
ejpam-6251	694	6	ż	ż	NOUN
ejpam-6251	694	7	ζ	ζ	PROPN
ejpam-6251	694	8	ż+	ż+	PROPN
ejpam-6251	694	9	|pς(l)−	|pς(l)−	PROPN
ejpam-6251	694	10	pϖ(l)|	pϖ(l)|	NOUN
ejpam-6251	694	11	=	=	SYM
ejpam-6251	694	12	1−	1−	NUM
ejpam-6251	694	13	sup	sup	NOUN
ejpam-6251	694	14	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	694	15	]	]	X
ejpam-6251	694	16	ζ	ζ	NOUN
ejpam-6251	694	17	ż	ż	NOUN
ejpam-6251	694	18	ζ	ζ	PROPN
ejpam-6251	694	19	ż+	ż+	PROPN
ejpam-6251	694	20	|	|	CCONJ
ejpam-6251	694	21	∫	∫	PROPN
ejpam-6251	694	22	l	l	NOUN
ejpam-6251	694	23	0	0	NUM
ejpam-6251	694	24	q(l	q(l	NOUN
ejpam-6251	694	25	,	,	PUNCT
ejpam-6251	694	26	s)h(s	s)h(s	NOUN
ejpam-6251	694	27	,	,	PUNCT
ejpam-6251	694	28	ς(s))ds−	ς(s))ds−	NOUN
ejpam-6251	694	29	∫	∫	PROPN
ejpam-6251	694	30	l	l	NOUN
ejpam-6251	694	31	0	0	NUM
ejpam-6251	694	32	q(l	q(l	NOUN
ejpam-6251	694	33	,	,	PUNCT
ejpam-6251	694	34	s)h(s	s)h(s	NOUN
ejpam-6251	694	35	,	,	PUNCT
ejpam-6251	694	36	ϖ(s))ds|	ϖ(s))ds|	NOUN
ejpam-6251	694	37	=	=	NOUN
ejpam-6251	694	38	1−	1−	NUM
ejpam-6251	694	39	sup	sup	NOUN
ejpam-6251	694	40	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	694	41	]	]	X
ejpam-6251	694	42	ζ	ζ	NOUN
ejpam-6251	694	43	ż	ż	NOUN
ejpam-6251	694	44	ζ	ζ	PROPN
ejpam-6251	694	45	ż+	ż+	PROPN
ejpam-6251	694	46	∫	∫	PROPN
ejpam-6251	694	47	l	l	NOUN
ejpam-6251	694	48	0	0	NUM
ejpam-6251	694	49	q(l	q(l	NOUN
ejpam-6251	694	50	,	,	PUNCT
ejpam-6251	694	51	s)|h(s	s)|h(s	PROPN
ejpam-6251	694	52	,	,	PUNCT
ejpam-6251	694	53	ς(s))−	ς(s))−	NOUN
ejpam-6251	694	54	h(s	h(s	PROPN
ejpam-6251	694	55	,	,	PUNCT
ejpam-6251	694	56	ϖ(s))|ds	ϖ(s))|d	VERB
ejpam-6251	694	57	≤	≤	NUM
ejpam-6251	694	58	1−	1−	NUM
ejpam-6251	694	59	sup	sup	NOUN
ejpam-6251	694	60	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	694	61	]	]	PUNCT
ejpam-6251	695	1	ż	ż	PROPN
ejpam-6251	695	2	ż+	ż+	PROPN
ejpam-6251	695	3	|ς(l)−ϖ(l)|	|ς(l)−ϖ(l)|	CCONJ
ejpam-6251	695	4	≤	≤	ADJ
ejpam-6251	695	5	ψ(ς(l	ψ(ς(l	PROPN
ejpam-6251	695	6	)	)	PUNCT
ejpam-6251	695	7	,	,	PUNCT
ejpam-6251	695	8	ϖ(l	ϖ(l	PROPN
ejpam-6251	695	9	)	)	PUNCT
ejpam-6251	695	10	,	,	PUNCT
ejpam-6251	695	11	ż	ż	NOUN
ejpam-6251	695	12	)	)	PUNCT
ejpam-6251	695	13	,	,	PUNCT
ejpam-6251	695	14	and	and	CCONJ
ejpam-6251	695	15	ξ(pς(l	ξ(pς(l	NOUN
ejpam-6251	695	16	)	)	PUNCT
ejpam-6251	695	17	,	,	PUNCT
ejpam-6251	695	18	pϖ(l	pϖ(l	NOUN
ejpam-6251	695	19	)	)	PUNCT
ejpam-6251	695	20	,	,	PUNCT
ejpam-6251	695	21	ζ	ζ	NOUN
ejpam-6251	695	22	ż	ż	NOUN
ejpam-6251	695	23	)	)	PUNCT
ejpam-6251	695	24	=	=	NOUN
ejpam-6251	695	25	sup	sup	NOUN
ejpam-6251	695	26	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	695	27	]	]	PUNCT
ejpam-6251	695	28	|pς(l)−	|pς(l)−	NOUN
ejpam-6251	695	29	pϖ(l)|	pϖ(l)|	PUNCT
ejpam-6251	695	30	ζ	ζ	PROPN
ejpam-6251	695	31	ż	ż	PROPN
ejpam-6251	695	32	r.	r.	PROPN
ejpam-6251	695	33	ramaswamy	ramaswamy	PROPN
ejpam-6251	695	34	/	/	SYM
ejpam-6251	695	35	eur	eur	PROPN
ejpam-6251	695	36	.	.	PUNCT
ejpam-6251	696	1	j.	j.	PROPN
ejpam-6251	696	2	pure	pure	PROPN
ejpam-6251	696	3	appl	appl	PROPN
ejpam-6251	696	4	.	.	PROPN
ejpam-6251	696	5	math	math	PROPN
ejpam-6251	696	6	,	,	PUNCT
ejpam-6251	696	7	18	18	NUM
ejpam-6251	696	8	(	(	PUNCT
ejpam-6251	696	9	4	4	NUM
ejpam-6251	696	10	)	)	PUNCT
ejpam-6251	696	11	(	(	PUNCT
ejpam-6251	696	12	2025	2025	NUM
ejpam-6251	696	13	)	)	PUNCT
ejpam-6251	696	14	,	,	PUNCT
ejpam-6251	696	15	6251	6251	NUM
ejpam-6251	696	16	38	38	NUM
ejpam-6251	696	17	of	of	ADP
ejpam-6251	696	18	40	40	NUM
ejpam-6251	696	19	=	=	NOUN
ejpam-6251	696	20	sup	sup	NOUN
ejpam-6251	696	21	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	696	22	]	]	PUNCT
ejpam-6251	697	1	|	|	ADV
ejpam-6251	697	2	∫	∫	PROPN
ejpam-6251	697	3	l	l	NOUN
ejpam-6251	697	4	0	0	NUM
ejpam-6251	697	5	q(l	q(l	NOUN
ejpam-6251	697	6	,	,	PUNCT
ejpam-6251	697	7	s)h(s	s)h(s	NOUN
ejpam-6251	697	8	,	,	PUNCT
ejpam-6251	697	9	ς(s))ds−	ς(s))ds−	NOUN
ejpam-6251	697	10	∫	∫	PROPN
ejpam-6251	697	11	l	l	NOUN
ejpam-6251	697	12	0	0	NUM
ejpam-6251	697	13	q(l	q(l	NOUN
ejpam-6251	697	14	,	,	PUNCT
ejpam-6251	697	15	s)h(s	s)h(s	NOUN
ejpam-6251	697	16	,	,	PUNCT
ejpam-6251	697	17	ϖ(s))ds|	ϖ(s))ds|	VERB
ejpam-6251	697	18	ζ	ζ	NOUN
ejpam-6251	697	19	ż	ż	NOUN
ejpam-6251	697	20	=	=	NOUN
ejpam-6251	697	21	sup	sup	NOUN
ejpam-6251	697	22	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	697	23	]	]	PUNCT
ejpam-6251	697	24	∫	∫	PROPN
ejpam-6251	698	1	l	l	NOUN
ejpam-6251	698	2	0	0	NUM
ejpam-6251	698	3	q(l	q(l	NOUN
ejpam-6251	698	4	,	,	PUNCT
ejpam-6251	698	5	s)|h(s	s)|h(s	PROPN
ejpam-6251	698	6	,	,	PUNCT
ejpam-6251	698	7	ς(s))−	ς(s))−	NOUN
ejpam-6251	698	8	h(s	h(s	PROPN
ejpam-6251	698	9	,	,	PUNCT
ejpam-6251	698	10	ϖ(s))|ds	ϖ(s))|ds	ADP
ejpam-6251	698	11	ζ	ζ	PROPN
ejpam-6251	698	12	ż	ż	NOUN
ejpam-6251	698	13	≤	≤	NUM
ejpam-6251	698	14	sup	sup	NOUN
ejpam-6251	698	15	l∈[0,1	l∈[0,1	NOUN
ejpam-6251	698	16	]	]	PUNCT
ejpam-6251	699	1	|ς(l)−ϖ(l)|	|ς(l)−ϖ(l)|	X
ejpam-6251	700	1	ż	ż	NOUN
ejpam-6251	700	2	≤	≤	NUM
ejpam-6251	700	3	ξ(ς(l	ξ(ς(l	NOUN
ejpam-6251	700	4	)	)	PUNCT
ejpam-6251	700	5	,	,	PUNCT
ejpam-6251	700	6	ϖ(l	ϖ(l	PROPN
ejpam-6251	700	7	)	)	PUNCT
ejpam-6251	700	8	,	,	PUNCT
ejpam-6251	700	9	ż	ż	NOUN
ejpam-6251	700	10	)	)	PUNCT
ejpam-6251	700	11	.	.	PUNCT
ejpam-6251	701	1	it	it	PRON
ejpam-6251	701	2	can	can	AUX
ejpam-6251	701	3	be	be	AUX
ejpam-6251	701	4	seen	see	VERB
ejpam-6251	701	5	that	that	SCONJ
ejpam-6251	701	6	all	all	DET
ejpam-6251	701	7	conditions	condition	NOUN
ejpam-6251	701	8	of	of	ADP
ejpam-6251	701	9	theorem	theorem	NOUN
ejpam-6251	701	10	5	5	NUM
ejpam-6251	701	11	are	be	AUX
ejpam-6251	701	12	satisfied	satisfied	ADJ
ejpam-6251	701	13	and	and	CCONJ
ejpam-6251	701	14	p	p	NOUN
ejpam-6251	701	15	has	have	VERB
ejpam-6251	701	16	a	a	DET
ejpam-6251	701	17	unique	unique	ADJ
ejpam-6251	701	18	fixed	fix	VERB
ejpam-6251	701	19	point	point	NOUN
ejpam-6251	701	20	and	and	CCONJ
ejpam-6251	701	21	the	the	DET
ejpam-6251	701	22	fractional	fractional	ADJ
ejpam-6251	701	23	differential	differential	ADJ
ejpam-6251	701	24	equation	equation	NOUN
ejpam-6251	701	25	(	(	PUNCT
ejpam-6251	701	26	19	19	NUM
ejpam-6251	701	27	)	)	PUNCT
ejpam-6251	701	28	has	have	VERB
ejpam-6251	701	29	a	a	DET
ejpam-6251	701	30	unique	unique	ADJ
ejpam-6251	701	31	solution	solution	NOUN
ejpam-6251	701	32	.	.	PUNCT
ejpam-6251	702	1	7	7	X
ejpam-6251	702	2	.	.	X
ejpam-6251	702	3	conclusion	conclusion	NOUN
ejpam-6251	702	4	in	in	ADP
ejpam-6251	702	5	this	this	DET
ejpam-6251	702	6	paper	paper	NOUN
ejpam-6251	702	7	,	,	PUNCT
ejpam-6251	702	8	the	the	DET
ejpam-6251	702	9	notion	notion	NOUN
ejpam-6251	702	10	of	of	ADP
ejpam-6251	702	11	neutrosophic	neutrosophic	ADJ
ejpam-6251	702	12	bipolar	bipolar	ADJ
ejpam-6251	702	13	metric	metric	ADJ
ejpam-6251	702	14	space	space	NOUN
ejpam-6251	702	15	has	have	AUX
ejpam-6251	702	16	been	be	AUX
ejpam-6251	702	17	introduced	introduce	VERB
ejpam-6251	702	18	and	and	CCONJ
ejpam-6251	702	19	fixed	fix	VERB
ejpam-6251	702	20	point	point	NOUN
ejpam-6251	702	21	results	result	NOUN
ejpam-6251	702	22	in	in	ADP
ejpam-6251	702	23	nbms	nbms	NOUN
ejpam-6251	702	24	have	have	AUX
ejpam-6251	702	25	been	be	AUX
ejpam-6251	702	26	established	establish	VERB
ejpam-6251	702	27	.	.	PUNCT
ejpam-6251	703	1	some	some	PRON
ejpam-6251	703	2	of	of	ADP
ejpam-6251	703	3	the	the	DET
ejpam-6251	703	4	topological	topological	ADJ
ejpam-6251	703	5	properties	property	NOUN
ejpam-6251	703	6	of	of	ADP
ejpam-6251	703	7	the	the	DET
ejpam-6251	703	8	nbms	nbms	NOUN
ejpam-6251	703	9	have	have	AUX
ejpam-6251	703	10	also	also	ADV
ejpam-6251	703	11	been	be	AUX
ejpam-6251	703	12	presented	present	VERB
ejpam-6251	703	13	in	in	ADP
ejpam-6251	703	14	the	the	DET
ejpam-6251	703	15	manuscript	manuscript	NOUN
ejpam-6251	703	16	.	.	PUNCT
ejpam-6251	704	1	it	it	PRON
ejpam-6251	704	2	can	can	AUX
ejpam-6251	704	3	be	be	AUX
ejpam-6251	704	4	seen	see	VERB
ejpam-6251	704	5	that	that	SCONJ
ejpam-6251	704	6	an	an	DET
ejpam-6251	704	7	analogue	analogue	NOUN
ejpam-6251	704	8	of	of	ADP
ejpam-6251	704	9	the	the	DET
ejpam-6251	704	10	banach	banach	ADV
ejpam-6251	704	11	fixed	fix	VERB
ejpam-6251	704	12	point	point	NOUN
ejpam-6251	704	13	theorem	theorem	NOUN
ejpam-6251	704	14	has	have	AUX
ejpam-6251	704	15	been	be	AUX
ejpam-6251	704	16	established	establish	VERB
ejpam-6251	704	17	supplemented	supplement	VERB
ejpam-6251	704	18	with	with	ADP
ejpam-6251	704	19	suitable	suitable	ADJ
ejpam-6251	704	20	non	non	ADJ
ejpam-6251	704	21	trivial	trivial	ADJ
ejpam-6251	704	22	examples	example	NOUN
ejpam-6251	704	23	.	.	PUNCT
ejpam-6251	705	1	the	the	DET
ejpam-6251	705	2	results	result	NOUN
ejpam-6251	705	3	have	have	AUX
ejpam-6251	705	4	been	be	AUX
ejpam-6251	705	5	applied	apply	VERB
ejpam-6251	705	6	to	to	PART
ejpam-6251	705	7	find	find	VERB
ejpam-6251	705	8	solution	solution	NOUN
ejpam-6251	705	9	to	to	ADP
ejpam-6251	705	10	integral	integral	ADJ
ejpam-6251	705	11	equation	equation	NOUN
ejpam-6251	705	12	,	,	PUNCT
ejpam-6251	705	13	voltage	voltage	NOUN
ejpam-6251	705	14	differential	differential	NOUN
ejpam-6251	705	15	equation	equation	NOUN
ejpam-6251	705	16	and	and	CCONJ
ejpam-6251	705	17	fractional	fractional	ADJ
ejpam-6251	705	18	differential	differential	ADJ
ejpam-6251	705	19	equation	equation	NOUN
ejpam-6251	705	20	.	.	PUNCT
ejpam-6251	706	1	simulation	simulation	NOUN
ejpam-6251	706	2	has	have	AUX
ejpam-6251	706	3	also	also	ADV
ejpam-6251	706	4	been	be	AUX
ejpam-6251	706	5	presented	present	VERB
ejpam-6251	706	6	for	for	ADP
ejpam-6251	706	7	the	the	DET
ejpam-6251	706	8	analytical	analytical	ADJ
ejpam-6251	706	9	results	result	NOUN
ejpam-6251	706	10	using	use	VERB
ejpam-6251	706	11	mathematica	mathematica	PROPN
ejpam-6251	706	12	software	software	PROPN
ejpam-6251	706	13	.	.	PUNCT
ejpam-6251	707	1	since	since	SCONJ
ejpam-6251	707	2	the	the	DET
ejpam-6251	707	3	space	space	NOUN
ejpam-6251	707	4	nbms	nbms	NOUN
ejpam-6251	707	5	generalises	generalise	VERB
ejpam-6251	707	6	neutrosophic	neutrosophic	ADJ
ejpam-6251	707	7	metric	metric	ADJ
ejpam-6251	707	8	space	space	NOUN
ejpam-6251	707	9	nms	nms	NOUN
ejpam-6251	707	10	and	and	CCONJ
ejpam-6251	707	11	its	its	PRON
ejpam-6251	707	12	seeds	seed	NOUN
ejpam-6251	707	13	,	,	PUNCT
ejpam-6251	707	14	the	the	DET
ejpam-6251	707	15	results	result	NOUN
ejpam-6251	707	16	established	establish	VERB
ejpam-6251	707	17	vide	vide	ADP
ejpam-6251	707	18	the	the	DET
ejpam-6251	707	19	contractions	contraction	NOUN
ejpam-6251	707	20	considered	consider	VERB
ejpam-6251	707	21	in	in	ADP
ejpam-6251	707	22	this	this	DET
ejpam-6251	707	23	manuscript	manuscript	NOUN
ejpam-6251	707	24	will	will	AUX
ejpam-6251	707	25	not	not	PART
ejpam-6251	707	26	be	be	AUX
ejpam-6251	707	27	satisfied	satisfied	ADJ
ejpam-6251	707	28	in	in	ADP
ejpam-6251	707	29	the	the	DET
ejpam-6251	707	30	setting	setting	NOUN
ejpam-6251	707	31	of	of	ADP
ejpam-6251	707	32	nms	nms	NOUN
ejpam-6251	707	33	or	or	CCONJ
ejpam-6251	707	34	general	general	ADJ
ejpam-6251	707	35	metric	metric	ADJ
ejpam-6251	707	36	spaces	space	NOUN
ejpam-6251	707	37	.	.	PUNCT
ejpam-6251	708	1	it	it	PRON
ejpam-6251	708	2	will	will	AUX
ejpam-6251	708	3	also	also	ADV
ejpam-6251	708	4	be	be	AUX
ejpam-6251	708	5	an	an	DET
ejpam-6251	708	6	open	open	ADJ
ejpam-6251	708	7	question	question	NOUN
ejpam-6251	708	8	to	to	PART
ejpam-6251	708	9	establish	establish	VERB
ejpam-6251	708	10	fixed	fix	VERB
ejpam-6251	708	11	point	point	NOUN
ejpam-6251	708	12	results	result	NOUN
ejpam-6251	708	13	using	use	VERB
ejpam-6251	708	14	different	different	ADJ
ejpam-6251	708	15	types	type	NOUN
ejpam-6251	708	16	of	of	ADP
ejpam-6251	708	17	contractions	contraction	NOUN
ejpam-6251	708	18	,	,	PUNCT
ejpam-6251	708	19	such	such	ADJ
ejpam-6251	708	20	as	as	ADP
ejpam-6251	708	21	kannan	kannan	PROPN
ejpam-6251	708	22	type	type	PROPN
ejpam-6251	708	23	,	,	PUNCT
ejpam-6251	708	24	ciric	ciric	ADJ
ejpam-6251	708	25	type	type	NOUN
ejpam-6251	708	26	,	,	PUNCT
ejpam-6251	708	27	reich	reich	PROPN
ejpam-6251	708	28	type	type	NOUN
ejpam-6251	708	29	,	,	PUNCT
ejpam-6251	708	30	meir	meir	PROPN
ejpam-6251	708	31	-	-	PUNCT
ejpam-6251	708	32	keeler	keeler	PROPN
ejpam-6251	708	33	type	type	NOUN
ejpam-6251	708	34	,	,	PUNCT
ejpam-6251	708	35	to	to	PART
ejpam-6251	708	36	name	name	VERB
ejpam-6251	708	37	a	a	DET
ejpam-6251	708	38	few	few	ADJ
ejpam-6251	708	39	in	in	ADP
ejpam-6251	708	40	the	the	DET
ejpam-6251	708	41	setting	setting	NOUN
ejpam-6251	708	42	of	of	ADP
ejpam-6251	708	43	neutrosophic	neutrosophic	ADJ
ejpam-6251	708	44	bipolar	bipolar	ADJ
ejpam-6251	708	45	metric	metric	ADJ
ejpam-6251	708	46	spaces	space	NOUN
ejpam-6251	708	47	and	and	CCONJ
ejpam-6251	708	48	also	also	ADV
ejpam-6251	708	49	finding	find	VERB
ejpam-6251	708	50	applications	application	NOUN
ejpam-6251	708	51	in	in	ADP
ejpam-6251	708	52	other	other	ADJ
ejpam-6251	708	53	fields	field	NOUN
ejpam-6251	708	54	such	such	ADJ
ejpam-6251	708	55	as	as	ADP
ejpam-6251	708	56	neural	neural	ADJ
ejpam-6251	708	57	networking	networking	NOUN
ejpam-6251	708	58	,	,	PUNCT
ejpam-6251	708	59	stochastic	stochastic	ADJ
ejpam-6251	708	60	process	process	NOUN
ejpam-6251	708	61	etc	etc	X
ejpam-6251	708	62	.	.	X
ejpam-6251	708	63	acknowledgements	acknowledgement	VERB
ejpam-6251	708	64	the	the	DET
ejpam-6251	708	65	author	author	NOUN
ejpam-6251	708	66	extend	extend	VERB
ejpam-6251	708	67	his	his	PRON
ejpam-6251	708	68	appreciation	appreciation	NOUN
ejpam-6251	708	69	to	to	ADP
ejpam-6251	708	70	prince	prince	PROPN
ejpam-6251	708	71	sattam	sattam	PROPN
ejpam-6251	708	72	bin	bin	PROPN
ejpam-6251	708	73	adbulaziz	adbulaziz	PROPN
ejpam-6251	708	74	university	university	PROPN
ejpam-6251	708	75	for	for	ADP
ejpam-6251	708	76	funding	fund	VERB
ejpam-6251	708	77	this	this	DET
ejpam-6251	708	78	research	research	NOUN
ejpam-6251	708	79	work	work	NOUN
ejpam-6251	708	80	through	through	ADP
ejpam-6251	708	81	the	the	DET
ejpam-6251	708	82	project	project	NOUN
ejpam-6251	708	83	number	number	NOUN
ejpam-6251	708	84	psau/2025/01/33096	psau/2025/01/33096	NOUN
ejpam-6251	708	85	.	.	PUNCT
ejpam-6251	709	1	references	reference	NOUN
ejpam-6251	709	2	[	[	X
ejpam-6251	709	3	1	1	X
ejpam-6251	709	4	]	]	PUNCT
ejpam-6251	709	5	s.	s.	PROPN
ejpam-6251	709	6	banach	banach	PROPN
ejpam-6251	709	7	.	.	PUNCT
ejpam-6251	710	1	sur	sur	PROPN
ejpam-6251	710	2	les	les	X
ejpam-6251	710	3	opérations	opération	NOUN
ejpam-6251	710	4	dans	dan	NOUN
ejpam-6251	710	5	les	les	X
ejpam-6251	710	6	ensembles	ensemble	NOUN
ejpam-6251	710	7	abstraits	abstrait	NOUN
ejpam-6251	710	8	et	et	PROPN
ejpam-6251	710	9	leur	leur	X
ejpam-6251	710	10	application	application	PROPN
ejpam-6251	710	11	aux	aux	PROPN
ejpam-6251	710	12	équations	équations	PROPN
ejpam-6251	710	13	intégrales	intégrale	NOUN
ejpam-6251	710	14	.	.	PUNCT
ejpam-6251	711	1	fundamenta	fundamenta	PROPN
ejpam-6251	711	2	mathematicae	mathematicae	PROPN
ejpam-6251	711	3	,	,	PUNCT
ejpam-6251	711	4	3(1):133–181	3(1):133–181	NUM
ejpam-6251	711	5	,	,	PUNCT
ejpam-6251	711	6	1922	1922	NUM
ejpam-6251	711	7	.	.	PUNCT
ejpam-6251	712	1	[	[	X
ejpam-6251	712	2	2	2	X
ejpam-6251	712	3	]	]	X
ejpam-6251	712	4	g.	g.	PROPN
ejpam-6251	712	5	g.	g.	PROPN
ejpam-6251	712	6	samko	samko	PROPN
ejpam-6251	712	7	,	,	PUNCT
ejpam-6251	712	8	a.	a.	NOUN
ejpam-6251	712	9	a.	a.	NOUN
ejpam-6251	712	10	kilbas	kilbas	PROPN
ejpam-6251	712	11	,	,	PUNCT
ejpam-6251	712	12	and	and	CCONJ
ejpam-6251	712	13	o.	o.	PROPN
ejpam-6251	712	14	i.	i.	PROPN
ejpam-6251	712	15	marichev	marichev	PROPN
ejpam-6251	712	16	.	.	PUNCT
ejpam-6251	713	1	fractional	fractional	ADJ
ejpam-6251	713	2	integral	integral	ADJ
ejpam-6251	713	3	and	and	CCONJ
ejpam-6251	713	4	derivative	derivative	ADJ
ejpam-6251	713	5	.	.	PUNCT
ejpam-6251	714	1	gordon	gordon	PROPN
ejpam-6251	714	2	and	and	CCONJ
ejpam-6251	714	3	breach	breach	VERB
ejpam-6251	714	4	,	,	PUNCT
ejpam-6251	714	5	2023	2023	NUM
ejpam-6251	714	6	.	.	PUNCT
ejpam-6251	715	1	[	[	X
ejpam-6251	715	2	3	3	NUM
ejpam-6251	715	3	]	]	X
ejpam-6251	715	4	i.	i.	NOUN
ejpam-6251	715	5	podlubny	podlubny	PROPN
ejpam-6251	715	6	.	.	PUNCT
ejpam-6251	716	1	fractional	fractional	ADJ
ejpam-6251	716	2	differential	differential	ADJ
ejpam-6251	716	3	equations	equation	NOUN
ejpam-6251	716	4	.	.	PUNCT
ejpam-6251	717	1	academic	academic	ADJ
ejpam-6251	717	2	press	press	NOUN
ejpam-6251	717	3	,	,	PUNCT
ejpam-6251	717	4	san	san	PROPN
ejpam-6251	717	5	diego	diego	PROPN
ejpam-6251	717	6	,	,	PUNCT
ejpam-6251	717	7	ca	ca	PROPN
ejpam-6251	717	8	,	,	PUNCT
ejpam-6251	717	9	usa	usa	PROPN
ejpam-6251	717	10	,	,	PUNCT
ejpam-6251	717	11	1999	1999	NUM
ejpam-6251	717	12	.	.	PUNCT
ejpam-6251	718	1	r.	r.	PROPN
ejpam-6251	718	2	ramaswamy	ramaswamy	PROPN
ejpam-6251	718	3	/	/	SYM
ejpam-6251	718	4	eur	eur	PROPN
ejpam-6251	718	5	.	.	PUNCT
ejpam-6251	719	1	j.	j.	PROPN
ejpam-6251	719	2	pure	pure	PROPN
ejpam-6251	719	3	appl	appl	PROPN
ejpam-6251	719	4	.	.	PROPN
ejpam-6251	719	5	math	math	PROPN
ejpam-6251	719	6	,	,	PUNCT
ejpam-6251	719	7	18	18	NUM
ejpam-6251	719	8	(	(	PUNCT
ejpam-6251	719	9	4	4	NUM
ejpam-6251	719	10	)	)	PUNCT
ejpam-6251	719	11	(	(	PUNCT
ejpam-6251	719	12	2025	2025	NUM
ejpam-6251	719	13	)	)	PUNCT
ejpam-6251	719	14	,	,	PUNCT
ejpam-6251	719	15	6251	6251	NUM
ejpam-6251	719	16	39	39	NUM
ejpam-6251	719	17	of	of	ADP
ejpam-6251	719	18	40	40	NUM
ejpam-6251	720	1	[	[	SYM
ejpam-6251	720	2	4	4	NUM
ejpam-6251	720	3	]	]	PUNCT
ejpam-6251	720	4	a.	a.	NOUN
ejpam-6251	720	5	a.	a.	NOUN
ejpam-6251	720	6	kilbas	kilbas	PROPN
ejpam-6251	720	7	,	,	PUNCT
ejpam-6251	720	8	h.	h.	PROPN
ejpam-6251	720	9	m.	m.	PROPN
ejpam-6251	720	10	srivastava	srivastava	PROPN
ejpam-6251	720	11	,	,	PUNCT
ejpam-6251	720	12	and	and	CCONJ
ejpam-6251	720	13	j.	j.	PROPN
ejpam-6251	720	14	j.	j.	PROPN
ejpam-6251	720	15	trujillo	trujillo	PROPN
ejpam-6251	720	16	.	.	PUNCT
ejpam-6251	720	17	theory	theory	NOUN
ejpam-6251	720	18	and	and	CCONJ
ejpam-6251	720	19	applications	application	NOUN
ejpam-6251	720	20	of	of	ADP
ejpam-6251	720	21	fractional	fractional	ADJ
ejpam-6251	720	22	differential	differential	ADJ
ejpam-6251	720	23	equations	equation	NOUN
ejpam-6251	720	24	.	.	PUNCT
ejpam-6251	721	1	north	north	NOUN
ejpam-6251	721	2	-	-	PUNCT
ejpam-6251	721	3	holland	holland	PROPN
ejpam-6251	721	4	mathematics	mathematics	PROPN
ejpam-6251	721	5	studies	study	NOUN
ejpam-6251	721	6	,	,	PUNCT
ejpam-6251	721	7	204	204	NUM
ejpam-6251	721	8	,	,	PUNCT
ejpam-6251	721	9	2006	2006	NUM
ejpam-6251	721	10	.	.	PUNCT
ejpam-6251	722	1	[	[	X
ejpam-6251	722	2	5	5	X
ejpam-6251	722	3	]	]	PUNCT
ejpam-6251	722	4	l.	l.	PROPN
ejpam-6251	722	5	zadeh	zadeh	PROPN
ejpam-6251	722	6	.	.	PUNCT
ejpam-6251	722	7	fuzzy	fuzzy	ADJ
ejpam-6251	722	8	sets	set	NOUN
ejpam-6251	722	9	.	.	PUNCT
ejpam-6251	723	1	information	information	NOUN
ejpam-6251	723	2	and	and	CCONJ
ejpam-6251	723	3	control	control	NOUN
ejpam-6251	723	4	,	,	PUNCT
ejpam-6251	723	5	8:338–353	8:338–353	NUM
ejpam-6251	723	6	,	,	PUNCT
ejpam-6251	723	7	1965	1965	NUM
ejpam-6251	723	8	.	.	PUNCT
ejpam-6251	724	1	[	[	X
ejpam-6251	724	2	6	6	NUM
ejpam-6251	724	3	]	]	PUNCT
ejpam-6251	724	4	k.	k.	PROPN
ejpam-6251	724	5	atanassov	atanassov	PROPN
ejpam-6251	724	6	.	.	PUNCT
ejpam-6251	725	1	intuitionistic	intuitionistic	ADJ
ejpam-6251	725	2	fuzzy	fuzzy	ADJ
ejpam-6251	725	3	sets	set	NOUN
ejpam-6251	725	4	.	.	PUNCT
ejpam-6251	726	1	fuzzy	fuzzy	ADJ
ejpam-6251	726	2	sets	set	NOUN
ejpam-6251	726	3	and	and	CCONJ
ejpam-6251	726	4	systems	system	NOUN
ejpam-6251	726	5	,	,	PUNCT
ejpam-6251	726	6	20:87–96	20:87–96	NUM
ejpam-6251	726	7	,	,	PUNCT
ejpam-6251	726	8	1986	1986	NUM
ejpam-6251	726	9	.	.	PUNCT
ejpam-6251	727	1	[	[	X
ejpam-6251	727	2	7	7	X
ejpam-6251	727	3	]	]	X
ejpam-6251	727	4	f.	f.	PROPN
ejpam-6251	727	5	smarandache	smarandache	PROPN
ejpam-6251	727	6	.	.	PUNCT
ejpam-6251	728	1	neutrosophy	neutrosophy	NOUN
ejpam-6251	728	2	:	:	PUNCT
ejpam-6251	728	3	neutrosophic	neutrosophic	ADJ
ejpam-6251	728	4	probability	probability	NOUN
ejpam-6251	728	5	,	,	PUNCT
ejpam-6251	728	6	set	set	NOUN
ejpam-6251	728	7	,	,	PUNCT
ejpam-6251	728	8	and	and	CCONJ
ejpam-6251	728	9	logic	logic	NOUN
ejpam-6251	728	10	.	.	PUNCT
ejpam-6251	729	1	american	american	ADJ
ejpam-6251	729	2	research	research	PROPN
ejpam-6251	729	3	press	press	PROPN
ejpam-6251	729	4	,	,	PUNCT
ejpam-6251	729	5	rehoboth	rehoboth	PROPN
ejpam-6251	729	6	,	,	PUNCT
ejpam-6251	729	7	usa	usa	PROPN
ejpam-6251	729	8	,	,	PUNCT
ejpam-6251	729	9	2006	2006	NUM
ejpam-6251	729	10	.	.	PUNCT
ejpam-6251	730	1	[	[	X
ejpam-6251	730	2	8	8	X
ejpam-6251	730	3	]	]	PUNCT
ejpam-6251	730	4	v.	v.	CCONJ
ejpam-6251	730	5	s.	s.	PROPN
ejpam-6251	730	6	gadipally	gadipally	PROPN
ejpam-6251	730	7	.	.	PUNCT
ejpam-6251	731	1	impact	impact	VERB
ejpam-6251	731	2	fuzzy	fuzzy	ADJ
ejpam-6251	731	3	ideal	ideal	ADJ
ejpam-6251	731	4	extension	extension	NOUN
ejpam-6251	731	5	in	in	ADP
ejpam-6251	731	6	terms	term	NOUN
ejpam-6251	731	7	of	of	ADP
ejpam-6251	731	8	gamma	gamma	PROPN
ejpam-6251	731	9	semigroup	semigroup	PROPN
ejpam-6251	731	10	.	.	PUNCT
ejpam-6251	732	1	communications	communication	NOUN
ejpam-6251	732	2	on	on	ADP
ejpam-6251	732	3	applied	apply	VERB
ejpam-6251	732	4	nonlinear	nonlinear	ADJ
ejpam-6251	732	5	analysis	analysis	NOUN
ejpam-6251	732	6	,	,	PUNCT
ejpam-6251	732	7	32(9	32(9	NUM
ejpam-6251	732	8	)	)	PUNCT
ejpam-6251	732	9	,	,	PUNCT
ejpam-6251	732	10	2025	2025	NUM
ejpam-6251	732	11	.	.	PUNCT
ejpam-6251	733	1	[	[	X
ejpam-6251	733	2	9	9	NUM
ejpam-6251	733	3	]	]	PUNCT
ejpam-6251	733	4	m.	m.	NOUN
ejpam-6251	733	5	shams	sham	NOUN
ejpam-6251	733	6	,	,	PUNCT
ejpam-6251	733	7	n.	n.	PROPN
ejpam-6251	733	8	kausar	kausar	PROPN
ejpam-6251	733	9	,	,	PUNCT
ejpam-6251	733	10	k.	k.	PROPN
ejpam-6251	733	11	alayyash	alayyash	PROPN
ejpam-6251	733	12	,	,	PUNCT
ejpam-6251	733	13	m.	m.	NOUN
ejpam-6251	733	14	m.	m.	PROPN
ejpam-6251	733	15	al	al	PROPN
ejpam-6251	733	16	-	-	PUNCT
ejpam-6251	733	17	shamiri	shamiri	PROPN
ejpam-6251	733	18	,	,	PUNCT
ejpam-6251	733	19	n.	n.	PROPN
ejpam-6251	733	20	arif	arif	PROPN
ejpam-6251	733	21	,	,	PUNCT
ejpam-6251	733	22	and	and	CCONJ
ejpam-6251	733	23	r.	r.	PROPN
ejpam-6251	733	24	ismail	ismail	PROPN
ejpam-6251	733	25	.	.	PUNCT
ejpam-6251	734	1	semi	semi	ADJ
ejpam-6251	734	2	-	-	ADJ
ejpam-6251	734	3	analytical	analytical	ADJ
ejpam-6251	734	4	scheme	scheme	NOUN
ejpam-6251	734	5	for	for	ADP
ejpam-6251	734	6	solving	solve	VERB
ejpam-6251	734	7	intuitionistic	intuitionistic	ADJ
ejpam-6251	734	8	fuzzy	fuzzy	ADJ
ejpam-6251	734	9	system	system	NOUN
ejpam-6251	734	10	of	of	ADP
ejpam-6251	734	11	differential	differential	ADJ
ejpam-6251	734	12	equations	equation	NOUN
ejpam-6251	734	13	.	.	PUNCT
ejpam-6251	735	1	ieee	ieee	NOUN
ejpam-6251	735	2	access	access	NOUN
ejpam-6251	735	3	,	,	PUNCT
ejpam-6251	735	4	11:33205–33223	11:33205–33223	NUM
ejpam-6251	735	5	,	,	PUNCT
ejpam-6251	735	6	2023	2023	NUM
ejpam-6251	735	7	.	.	PUNCT
ejpam-6251	736	1	[	[	X
ejpam-6251	736	2	10	10	NUM
ejpam-6251	736	3	]	]	PUNCT
ejpam-6251	736	4	m.	m.	NOUN
ejpam-6251	736	5	shams	sham	NOUN
ejpam-6251	736	6	,	,	PUNCT
ejpam-6251	736	7	n.	n.	PROPN
ejpam-6251	736	8	kausar	kausar	PROPN
ejpam-6251	736	9	,	,	PUNCT
ejpam-6251	736	10	n.	n.	PROPN
ejpam-6251	736	11	yaqoob	yaqoob	PROPN
ejpam-6251	736	12	,	,	PUNCT
ejpam-6251	736	13	a.	a.	NOUN
ejpam-6251	736	14	nayyab	nayyab	PROPN
ejpam-6251	736	15	,	,	PUNCT
ejpam-6251	736	16	and	and	CCONJ
ejpam-6251	736	17	g.	g.	PROPN
ejpam-6251	736	18	mulat	mulat	PROPN
ejpam-6251	736	19	addis	addis	PROPN
ejpam-6251	736	20	.	.	PUNCT
ejpam-6251	737	1	techniques	technique	NOUN
ejpam-6251	737	2	for	for	ADP
ejpam-6251	737	3	finding	find	VERB
ejpam-6251	737	4	analytical	analytical	ADJ
ejpam-6251	737	5	solution	solution	NOUN
ejpam-6251	737	6	of	of	ADP
ejpam-6251	737	7	generalized	generalized	ADJ
ejpam-6251	737	8	fuzzy	fuzzy	ADJ
ejpam-6251	737	9	differential	differential	ADJ
ejpam-6251	737	10	equations	equation	NOUN
ejpam-6251	737	11	with	with	ADP
ejpam-6251	737	12	applications	application	NOUN
ejpam-6251	737	13	.	.	PUNCT
ejpam-6251	738	1	complexity	complexity	NOUN
ejpam-6251	738	2	,	,	PUNCT
ejpam-6251	738	3	2023:3000653	2023:3000653	NUM
ejpam-6251	738	4	,	,	PUNCT
ejpam-6251	738	5	2023	2023	NUM
ejpam-6251	738	6	.	.	PUNCT
ejpam-6251	739	1	[	[	X
ejpam-6251	739	2	11	11	NUM
ejpam-6251	739	3	]	]	PUNCT
ejpam-6251	739	4	m.	m.	NOUN
ejpam-6251	739	5	shams	sham	NOUN
ejpam-6251	739	6	,	,	PUNCT
ejpam-6251	739	7	n.	n.	PROPN
ejpam-6251	739	8	kausar	kausar	PROPN
ejpam-6251	739	9	,	,	PUNCT
ejpam-6251	739	10	p.	p.	PROPN
ejpam-6251	739	11	agarwal	agarwal	PROPN
ejpam-6251	739	12	,	,	PUNCT
ejpam-6251	739	13	and	and	CCONJ
ejpam-6251	739	14	m.	m.	NOUN
ejpam-6251	739	15	a.	a.	NOUN
ejpam-6251	739	16	shah	shah	PROPN
ejpam-6251	739	17	.	.	PUNCT
ejpam-6251	740	1	triangular	triangular	PROPN
ejpam-6251	740	2	intuitionistic	intuitionistic	ADJ
ejpam-6251	740	3	fuzzy	fuzzy	ADJ
ejpam-6251	740	4	linear	linear	ADJ
ejpam-6251	740	5	system	system	NOUN
ejpam-6251	740	6	of	of	ADP
ejpam-6251	740	7	equations	equation	NOUN
ejpam-6251	740	8	with	with	ADP
ejpam-6251	740	9	applications	application	NOUN
ejpam-6251	740	10	:	:	PUNCT
ejpam-6251	740	11	an	an	DET
ejpam-6251	740	12	analytical	analytical	ADJ
ejpam-6251	740	13	approach	approach	NOUN
ejpam-6251	740	14	.	.	PUNCT
ejpam-6251	741	1	applied	apply	VERB
ejpam-6251	741	2	mathematics	mathematic	NOUN
ejpam-6251	741	3	in	in	ADP
ejpam-6251	741	4	science	science	NOUN
ejpam-6251	741	5	and	and	CCONJ
ejpam-6251	741	6	engineering	engineering	NOUN
ejpam-6251	741	7	,	,	PUNCT
ejpam-6251	741	8	32(1	32(1	NUM
ejpam-6251	741	9	)	)	PUNCT
ejpam-6251	741	10	,	,	PUNCT
ejpam-6251	741	11	2024	2024	NUM
ejpam-6251	741	12	.	.	PUNCT
ejpam-6251	742	1	[	[	X
ejpam-6251	742	2	12	12	NUM
ejpam-6251	742	3	]	]	PUNCT
ejpam-6251	742	4	b.	b.	PROPN
ejpam-6251	742	5	schweizer	schweizer	PROPN
ejpam-6251	742	6	and	and	CCONJ
ejpam-6251	742	7	a.	a.	NOUN
ejpam-6251	742	8	sklar	sklar	PROPN
ejpam-6251	742	9	.	.	PUNCT
ejpam-6251	743	1	statistical	statistical	ADJ
ejpam-6251	743	2	metric	metric	ADJ
ejpam-6251	743	3	spaces	space	NOUN
ejpam-6251	743	4	.	.	PUNCT
ejpam-6251	744	1	pacific	pacific	PROPN
ejpam-6251	744	2	journal	journal	PROPN
ejpam-6251	744	3	of	of	ADP
ejpam-6251	744	4	mathematics	mathematic	NOUN
ejpam-6251	744	5	,	,	PUNCT
ejpam-6251	744	6	10:314–334	10:314–334	PROPN
ejpam-6251	744	7	,	,	PUNCT
ejpam-6251	744	8	1960	1960	NUM
ejpam-6251	744	9	.	.	PUNCT
ejpam-6251	745	1	[	[	X
ejpam-6251	745	2	13	13	NUM
ejpam-6251	745	3	]	]	PUNCT
ejpam-6251	745	4	i.	i.	NOUN
ejpam-6251	745	5	kramosil	kramosil	PROPN
ejpam-6251	745	6	and	and	CCONJ
ejpam-6251	745	7	j.	j.	PROPN
ejpam-6251	745	8	michlek	michlek	PROPN
ejpam-6251	745	9	.	.	PUNCT
ejpam-6251	746	1	fuzzy	fuzzy	ADJ
ejpam-6251	746	2	metric	metric	ADJ
ejpam-6251	746	3	and	and	CCONJ
ejpam-6251	746	4	statistical	statistical	ADJ
ejpam-6251	746	5	metric	metric	ADJ
ejpam-6251	746	6	spaces	space	NOUN
ejpam-6251	746	7	.	.	PUNCT
ejpam-6251	747	1	kybernetika	kybernetika	PROPN
ejpam-6251	747	2	,	,	PUNCT
ejpam-6251	747	3	11:336–344	11:336–344	PROPN
ejpam-6251	747	4	,	,	PUNCT
ejpam-6251	747	5	1975	1975	NUM
ejpam-6251	747	6	.	.	PUNCT
ejpam-6251	748	1	[	[	X
ejpam-6251	748	2	14	14	NUM
ejpam-6251	748	3	]	]	PUNCT
ejpam-6251	748	4	m.	m.	NOUN
ejpam-6251	748	5	grabiec	grabiec	PROPN
ejpam-6251	748	6	.	.	PUNCT
ejpam-6251	749	1	fixed	fix	VERB
ejpam-6251	749	2	points	point	NOUN
ejpam-6251	749	3	in	in	ADP
ejpam-6251	749	4	fuzzy	fuzzy	ADJ
ejpam-6251	749	5	metric	metric	ADJ
ejpam-6251	749	6	spaces	space	NOUN
ejpam-6251	749	7	.	.	PUNCT
ejpam-6251	750	1	fuzzy	fuzzy	ADJ
ejpam-6251	750	2	sets	set	NOUN
ejpam-6251	750	3	and	and	CCONJ
ejpam-6251	750	4	systems	system	NOUN
ejpam-6251	750	5	,	,	PUNCT
ejpam-6251	750	6	27:385–389	27:385–389	NUM
ejpam-6251	750	7	,	,	PUNCT
ejpam-6251	750	8	1988	1988	NUM
ejpam-6251	750	9	.	.	PUNCT
ejpam-6251	751	1	[	[	X
ejpam-6251	751	2	15	15	NUM
ejpam-6251	751	3	]	]	X
ejpam-6251	751	4	s.	s.	PROPN
ejpam-6251	751	5	u.	u.	PROPN
ejpam-6251	751	6	rehman	rehman	PROPN
ejpam-6251	751	7	,	,	PUNCT
ejpam-6251	751	8	s.	s.	PROPN
ejpam-6251	751	9	jabeen	jabeen	PROPN
ejpam-6251	751	10	,	,	PUNCT
ejpam-6251	751	11	s.	s.	PROPN
ejpam-6251	751	12	u.	u.	PROPN
ejpam-6251	751	13	khan	khan	PROPN
ejpam-6251	751	14	,	,	PUNCT
ejpam-6251	751	15	and	and	CCONJ
ejpam-6251	751	16	m.	m.	NOUN
ejpam-6251	751	17	m.	m.	PROPN
ejpam-6251	751	18	m.	m.	PROPN
ejpam-6251	751	19	jaradat	jaradat	PROPN
ejpam-6251	751	20	.	.	PUNCT
ejpam-6251	752	1	some	some	DET
ejpam-6251	752	2	α	α	NOUN
ejpam-6251	752	3	ϕ	ϕ	X
ejpam-6251	752	4	fuzzy	fuzzy	ADJ
ejpam-6251	752	5	cone	cone	NOUN
ejpam-6251	752	6	contraction	contraction	NOUN
ejpam-6251	752	7	results	result	VERB
ejpam-6251	752	8	with	with	ADP
ejpam-6251	752	9	integral	integral	ADJ
ejpam-6251	752	10	type	type	NOUN
ejpam-6251	752	11	application	application	NOUN
ejpam-6251	752	12	.	.	PUNCT
ejpam-6251	753	1	journal	journal	NOUN
ejpam-6251	753	2	of	of	ADP
ejpam-6251	753	3	mathematics	mathematic	NOUN
ejpam-6251	753	4	,	,	PUNCT
ejpam-6251	753	5	2021(1566348	2021(1566348	NOUN
ejpam-6251	753	6	)	)	PUNCT
ejpam-6251	753	7	,	,	PUNCT
ejpam-6251	753	8	2021	2021	NUM
ejpam-6251	753	9	.	.	PUNCT
ejpam-6251	754	1	[	[	X
ejpam-6251	754	2	16	16	NUM
ejpam-6251	754	3	]	]	PUNCT
ejpam-6251	754	4	j.	j.	PROPN
ejpam-6251	754	5	h.	h.	PROPN
ejpam-6251	754	6	park	park	PROPN
ejpam-6251	754	7	.	.	PUNCT
ejpam-6251	755	1	intuitionistic	intuitionistic	ADJ
ejpam-6251	755	2	fuzzy	fuzzy	ADJ
ejpam-6251	755	3	metric	metric	ADJ
ejpam-6251	755	4	spaces	space	NOUN
ejpam-6251	755	5	.	.	PUNCT
ejpam-6251	756	1	chaos	chaos	NOUN
ejpam-6251	756	2	,	,	PUNCT
ejpam-6251	756	3	solitons	soliton	NOUN
ejpam-6251	756	4	fractals	fractal	NOUN
ejpam-6251	756	5	,	,	PUNCT
ejpam-6251	756	6	22:1039–1046	22:1039–1046	NUM
ejpam-6251	756	7	,	,	PUNCT
ejpam-6251	756	8	2004	2004	NUM
ejpam-6251	756	9	.	.	PUNCT
ejpam-6251	757	1	[	[	X
ejpam-6251	757	2	17	17	NUM
ejpam-6251	757	3	]	]	X
ejpam-6251	757	4	n.	n.	PROPN
ejpam-6251	757	5	konwar	konwar	PROPN
ejpam-6251	757	6	.	.	PUNCT
ejpam-6251	758	1	extension	extension	NOUN
ejpam-6251	758	2	of	of	ADP
ejpam-6251	758	3	fixed	fix	VERB
ejpam-6251	758	4	results	result	NOUN
ejpam-6251	758	5	in	in	ADP
ejpam-6251	758	6	intuitionistic	intuitionistic	ADJ
ejpam-6251	758	7	fuzzy	fuzzy	ADJ
ejpam-6251	758	8	b	b	NOUN
ejpam-6251	758	9	-	-	PUNCT
ejpam-6251	758	10	metric	metric	ADJ
ejpam-6251	758	11	spaces	space	NOUN
ejpam-6251	758	12	.	.	PUNCT
ejpam-6251	759	1	journal	journal	NOUN
ejpam-6251	759	2	of	of	ADP
ejpam-6251	759	3	intelligent	intelligent	ADJ
ejpam-6251	759	4	fuzzy	fuzzy	ADJ
ejpam-6251	759	5	systems	system	NOUN
ejpam-6251	759	6	,	,	PUNCT
ejpam-6251	759	7	39:7831–7841	39:7831–7841	NUM
ejpam-6251	759	8	,	,	PUNCT
ejpam-6251	759	9	2020	2020	NUM
ejpam-6251	759	10	.	.	PUNCT
ejpam-6251	760	1	[	[	X
ejpam-6251	760	2	18	18	NUM
ejpam-6251	760	3	]	]	PUNCT
ejpam-6251	760	4	a.	a.	NOUN
ejpam-6251	760	5	mutlu	mutlu	PROPN
ejpam-6251	760	6	and	and	CCONJ
ejpam-6251	760	7	u.	u.	PROPN
ejpam-6251	760	8	gürdal	gürdal	PROPN
ejpam-6251	760	9	.	.	PUNCT
ejpam-6251	761	1	bipolar	bipolar	ADJ
ejpam-6251	761	2	metric	metric	ADJ
ejpam-6251	761	3	spaces	space	NOUN
ejpam-6251	761	4	and	and	CCONJ
ejpam-6251	761	5	some	some	DET
ejpam-6251	761	6	fixed	fix	VERB
ejpam-6251	761	7	point	point	NOUN
ejpam-6251	761	8	theorems	theorem	NOUN
ejpam-6251	761	9	.	.	PUNCT
ejpam-6251	761	10	journal	journal	PROPN
ejpam-6251	761	11	of	of	ADP
ejpam-6251	761	12	nonlinear	nonlinear	PROPN
ejpam-6251	761	13	sciences	sciences	PROPN
ejpam-6251	761	14	and	and	CCONJ
ejpam-6251	761	15	applications	application	NOUN
ejpam-6251	761	16	,	,	PUNCT
ejpam-6251	761	17	9:5362–5373	9:5362–5373	NUM
ejpam-6251	761	18	,	,	PUNCT
ejpam-6251	761	19	2016	2016	NUM
ejpam-6251	761	20	.	.	PUNCT
ejpam-6251	762	1	[	[	X
ejpam-6251	762	2	19	19	NUM
ejpam-6251	762	3	]	]	PUNCT
ejpam-6251	762	4	a.	a.	NOUN
ejpam-6251	762	5	mutlu	mutlu	PROPN
ejpam-6251	762	6	,	,	PUNCT
ejpam-6251	762	7	a.	a.	PROPN
ejpam-6251	762	8	özkan	özkan	PROPN
ejpam-6251	762	9	,	,	PUNCT
ejpam-6251	762	10	and	and	CCONJ
ejpam-6251	762	11	u.	u.	PROPN
ejpam-6251	762	12	gürdal	gürdal	PROPN
ejpam-6251	762	13	.	.	PUNCT
ejpam-6251	763	1	locally	locally	ADV
ejpam-6251	763	2	and	and	CCONJ
ejpam-6251	763	3	weakly	weakly	ADJ
ejpam-6251	763	4	contractive	contractive	ADJ
ejpam-6251	763	5	principle	principle	NOUN
ejpam-6251	763	6	in	in	ADP
ejpam-6251	763	7	bipolar	bipolar	ADJ
ejpam-6251	763	8	metric	metric	ADJ
ejpam-6251	763	9	spaces	space	NOUN
ejpam-6251	763	10	.	.	PUNCT
ejpam-6251	764	1	twms	twms	PROPN
ejpam-6251	764	2	journal	journal	PROPN
ejpam-6251	764	3	of	of	ADP
ejpam-6251	764	4	applied	apply	VERB
ejpam-6251	764	5	and	and	CCONJ
ejpam-6251	764	6	engineering	engineering	NOUN
ejpam-6251	764	7	mathematics	mathematic	NOUN
ejpam-6251	764	8	,	,	PUNCT
ejpam-6251	764	9	10(2):379–388	10(2):379–388	NUM
ejpam-6251	764	10	,	,	PUNCT
ejpam-6251	764	11	2020	2020	NUM
ejpam-6251	764	12	.	.	PUNCT
ejpam-6251	765	1	[	[	X
ejpam-6251	765	2	20	20	NUM
ejpam-6251	765	3	]	]	PUNCT
ejpam-6251	765	4	b.	b.	PROPN
ejpam-6251	765	5	s.	s.	PROPN
ejpam-6251	765	6	rao	rao	PROPN
ejpam-6251	765	7	,	,	PUNCT
ejpam-6251	765	8	g.	g.	PROPN
ejpam-6251	765	9	n.	n.	PROPN
ejpam-6251	765	10	v.	v.	PROPN
ejpam-6251	765	11	kishore	kishore	PROPN
ejpam-6251	765	12	,	,	PUNCT
ejpam-6251	765	13	and	and	CCONJ
ejpam-6251	765	14	g.	g.	PROPN
ejpam-6251	765	15	k.	k.	PROPN
ejpam-6251	765	16	kumar	kumar	PROPN
ejpam-6251	765	17	.	.	PUNCT
ejpam-6251	766	1	geraghty	geraghty	PROPN
ejpam-6251	766	2	type	type	NOUN
ejpam-6251	766	3	contraction	contraction	NOUN
ejpam-6251	766	4	and	and	CCONJ
ejpam-6251	766	5	common	common	ADJ
ejpam-6251	766	6	coupled	couple	VERB
ejpam-6251	766	7	fixed	fix	VERB
ejpam-6251	766	8	point	point	NOUN
ejpam-6251	766	9	theorems	theorem	NOUN
ejpam-6251	766	10	in	in	ADP
ejpam-6251	766	11	bipolar	bipolar	ADJ
ejpam-6251	766	12	metric	metric	ADJ
ejpam-6251	766	13	spaces	space	NOUN
ejpam-6251	766	14	with	with	ADP
ejpam-6251	766	15	applications	application	NOUN
ejpam-6251	766	16	to	to	PART
ejpam-6251	766	17	homotopy	homotopy	VERB
ejpam-6251	766	18	.	.	PUNCT
ejpam-6251	767	1	international	international	ADJ
ejpam-6251	767	2	journal	journal	PROPN
ejpam-6251	767	3	of	of	ADP
ejpam-6251	767	4	mathematics	mathematics	NOUN
ejpam-6251	767	5	trends	trend	NOUN
ejpam-6251	767	6	and	and	CCONJ
ejpam-6251	767	7	technology	technology	NOUN
ejpam-6251	767	8	,	,	PUNCT
ejpam-6251	767	9	63	63	NUM
ejpam-6251	767	10	,	,	PUNCT
ejpam-6251	767	11	2018	2018	NUM
ejpam-6251	767	12	.	.	PUNCT
ejpam-6251	768	1	[	[	X
ejpam-6251	768	2	21	21	NUM
ejpam-6251	768	3	]	]	X
ejpam-6251	768	4	g.	g.	PROPN
ejpam-6251	768	5	n.	n.	PROPN
ejpam-6251	768	6	v.	v.	PROPN
ejpam-6251	768	7	kishore	kishore	PROPN
ejpam-6251	768	8	,	,	PUNCT
ejpam-6251	768	9	d.	d.	PROPN
ejpam-6251	768	10	r.	r.	PROPN
ejpam-6251	768	11	prasad	prasad	PROPN
ejpam-6251	768	12	,	,	PUNCT
ejpam-6251	768	13	b.	b.	PROPN
ejpam-6251	768	14	s.	s.	PROPN
ejpam-6251	768	15	rao	rao	PROPN
ejpam-6251	768	16	,	,	PUNCT
ejpam-6251	768	17	and	and	CCONJ
ejpam-6251	768	18	v.	v.	PROPN
ejpam-6251	768	19	s.	s.	PROPN
ejpam-6251	768	20	baghavan	baghavan	PROPN
ejpam-6251	768	21	.	.	PUNCT
ejpam-6251	769	1	some	some	DET
ejpam-6251	769	2	applications	application	NOUN
ejpam-6251	769	3	via	via	ADP
ejpam-6251	769	4	common	common	ADJ
ejpam-6251	769	5	coupled	couple	VERB
ejpam-6251	769	6	fixed	fix	VERB
ejpam-6251	769	7	point	point	NOUN
ejpam-6251	769	8	theorems	theorem	NOUN
ejpam-6251	769	9	in	in	ADP
ejpam-6251	769	10	bipolar	bipolar	ADJ
ejpam-6251	769	11	metric	metric	ADJ
ejpam-6251	769	12	spaces	space	NOUN
ejpam-6251	769	13	.	.	PUNCT
ejpam-6251	770	1	journal	journal	NOUN
ejpam-6251	770	2	of	of	ADP
ejpam-6251	770	3	critical	critical	ADJ
ejpam-6251	770	4	reviews	review	NOUN
ejpam-6251	770	5	,	,	PUNCT
ejpam-6251	770	6	7(2):601–607	7(2):601–607	NUM
ejpam-6251	770	7	,	,	PUNCT
ejpam-6251	770	8	2019	2019	NUM
ejpam-6251	770	9	.	.	PUNCT
ejpam-6251	771	1	[	[	X
ejpam-6251	771	2	22	22	NUM
ejpam-6251	771	3	]	]	X
ejpam-6251	771	4	g.	g.	PROPN
ejpam-6251	771	5	mani	mani	PROPN
ejpam-6251	771	6	,	,	PUNCT
ejpam-6251	771	7	r.	r.	PROPN
ejpam-6251	771	8	ramaswamy	ramaswamy	PROPN
ejpam-6251	771	9	,	,	PUNCT
ejpam-6251	771	10	a.	a.	PROPN
ejpam-6251	771	11	j.	j.	PROPN
ejpam-6251	771	12	gnanaprakasam	gnanaprakasam	PROPN
ejpam-6251	771	13	,	,	PUNCT
ejpam-6251	771	14	a.	a.	NOUN
ejpam-6251	771	15	elsonbaty	elsonbaty	NOUN
ejpam-6251	771	16	,	,	PUNCT
ejpam-6251	771	17	o.	o.	PROPN
ejpam-6251	771	18	a.	a.	PROPN
ejpam-6251	771	19	a.	a.	PROPN
ejpam-6251	771	20	abdelnaby	abdelnaby	PROPN
ejpam-6251	771	21	,	,	PUNCT
ejpam-6251	771	22	and	and	CCONJ
ejpam-6251	771	23	s.	s.	PROPN
ejpam-6251	772	1	radenović.	radenović.	PROPN
ejpam-6251	772	2	application	application	NOUN
ejpam-6251	772	3	of	of	ADP
ejpam-6251	772	4	fixed	fix	VERB
ejpam-6251	772	5	points	point	NOUN
ejpam-6251	772	6	in	in	ADP
ejpam-6251	772	7	bipolar	bipolar	ADJ
ejpam-6251	772	8	controlled	control	VERB
ejpam-6251	772	9	metric	metric	ADJ
ejpam-6251	772	10	space	space	NOUN
ejpam-6251	772	11	to	to	PART
ejpam-6251	772	12	r.	r.	VERB
ejpam-6251	772	13	ramaswamy	ramaswamy	PROPN
ejpam-6251	772	14	/	/	SYM
ejpam-6251	772	15	eur	eur	PROPN
ejpam-6251	772	16	.	.	PUNCT
ejpam-6251	773	1	j.	j.	PROPN
ejpam-6251	773	2	pure	pure	PROPN
ejpam-6251	773	3	appl	appl	PROPN
ejpam-6251	773	4	.	.	PROPN
ejpam-6251	773	5	math	math	PROPN
ejpam-6251	773	6	,	,	PUNCT
ejpam-6251	773	7	18	18	NUM
ejpam-6251	773	8	(	(	PUNCT
ejpam-6251	773	9	4	4	NUM
ejpam-6251	773	10	)	)	PUNCT
ejpam-6251	773	11	(	(	PUNCT
ejpam-6251	773	12	2025	2025	NUM
ejpam-6251	773	13	)	)	PUNCT
ejpam-6251	773	14	,	,	PUNCT
ejpam-6251	773	15	6251	6251	NUM
ejpam-6251	773	16	40	40	NUM
ejpam-6251	773	17	of	of	ADP
ejpam-6251	773	18	40	40	NUM
ejpam-6251	773	19	solve	solve	NOUN
ejpam-6251	773	20	fractional	fractional	ADJ
ejpam-6251	773	21	differential	differential	NOUN
ejpam-6251	773	22	equation	equation	NOUN
ejpam-6251	773	23	.	.	PUNCT
ejpam-6251	774	1	fractal	fractal	ADJ
ejpam-6251	774	2	and	and	CCONJ
ejpam-6251	774	3	fractional	fractional	ADJ
ejpam-6251	774	4	,	,	PUNCT
ejpam-6251	774	5	7(2):601–607	7(2):601–607	NUM
ejpam-6251	774	6	,	,	PUNCT
ejpam-6251	774	7	2019	2019	NUM
ejpam-6251	774	8	.	.	PUNCT
ejpam-6251	775	1	[	[	X
ejpam-6251	775	2	23	23	NUM
ejpam-6251	775	3	]	]	X
ejpam-6251	775	4	g.	g.	PROPN
ejpam-6251	775	5	n.	n.	PROPN
ejpam-6251	775	6	v.	v.	PROPN
ejpam-6251	775	7	kishore	kishore	PROPN
ejpam-6251	775	8	,	,	PUNCT
ejpam-6251	775	9	k.	k.	PROPN
ejpam-6251	776	1	p.	p.	PROPN
ejpam-6251	776	2	r.	r.	PROPN
ejpam-6251	776	3	rao	rao	PROPN
ejpam-6251	776	4	,	,	PUNCT
ejpam-6251	776	5	b.	b.	PROPN
ejpam-6251	776	6	s.	s.	PROPN
ejpam-6251	776	7	rao	rao	PROPN
ejpam-6251	776	8	,	,	PUNCT
ejpam-6251	776	9	and	and	CCONJ
ejpam-6251	776	10	a.	a.	PROPN
ejpam-6251	776	11	sombabu	sombabu	PROPN
ejpam-6251	776	12	.	.	PUNCT
ejpam-6251	777	1	covariant	covariant	ADJ
ejpam-6251	777	2	mappings	mapping	NOUN
ejpam-6251	777	3	and	and	CCONJ
ejpam-6251	777	4	coupled	couple	VERB
ejpam-6251	777	5	fixed	fix	VERB
ejpam-6251	777	6	point	point	NOUN
ejpam-6251	777	7	results	result	NOUN
ejpam-6251	777	8	in	in	ADP
ejpam-6251	777	9	bipolar	bipolar	ADJ
ejpam-6251	777	10	metric	metric	ADJ
ejpam-6251	777	11	spaces	space	NOUN
ejpam-6251	777	12	.	.	PUNCT
ejpam-6251	778	1	international	international	ADJ
ejpam-6251	778	2	journal	journal	PROPN
ejpam-6251	778	3	of	of	ADP
ejpam-6251	778	4	nonlinear	nonlinear	ADJ
ejpam-6251	778	5	analysis	analysis	NOUN
ejpam-6251	778	6	and	and	CCONJ
ejpam-6251	778	7	applications	application	NOUN
ejpam-6251	778	8	,	,	PUNCT
ejpam-6251	778	9	12(1):1–15	12(1):1–15	NUM
ejpam-6251	778	10	,	,	PUNCT
ejpam-6251	778	11	2021	2021	NUM
ejpam-6251	778	12	.	.	PUNCT
ejpam-6251	779	1	[	[	X
ejpam-6251	779	2	24	24	NUM
ejpam-6251	779	3	]	]	X
ejpam-6251	779	4	g.	g.	PROPN
ejpam-6251	779	5	n.	n.	PROPN
ejpam-6251	779	6	v.	v.	PROPN
ejpam-6251	779	7	kishore	kishore	PROPN
ejpam-6251	779	8	,	,	PUNCT
ejpam-6251	779	9	r.	r.	PROPN
ejpam-6251	779	10	p.	p.	PROPN
ejpam-6251	779	11	agarwal	agarwal	PROPN
ejpam-6251	779	12	,	,	PUNCT
ejpam-6251	779	13	b.	b.	PROPN
ejpam-6251	779	14	s.	s.	PROPN
ejpam-6251	779	15	rao	rao	PROPN
ejpam-6251	779	16	,	,	PUNCT
ejpam-6251	779	17	and	and	CCONJ
ejpam-6251	779	18	r.	r.	PROPN
ejpam-6251	779	19	v.	v.	ADP
ejpam-6251	779	20	n.	n.	PROPN
ejpam-6251	779	21	s.	s.	PROPN
ejpam-6251	779	22	rao	rao	PROPN
ejpam-6251	779	23	.	.	PUNCT
ejpam-6251	780	1	caristi	caristi	PROPN
ejpam-6251	780	2	type	type	NOUN
ejpam-6251	780	3	cyclic	cyclic	ADJ
ejpam-6251	780	4	contraction	contraction	NOUN
ejpam-6251	780	5	and	and	CCONJ
ejpam-6251	780	6	common	common	ADJ
ejpam-6251	780	7	fixed	fix	VERB
ejpam-6251	780	8	point	point	NOUN
ejpam-6251	780	9	theorems	theorem	NOUN
ejpam-6251	780	10	in	in	ADP
ejpam-6251	780	11	bipolar	bipolar	ADJ
ejpam-6251	780	12	metric	metric	ADJ
ejpam-6251	780	13	spaces	space	NOUN
ejpam-6251	780	14	with	with	ADP
ejpam-6251	780	15	applications	application	NOUN
ejpam-6251	780	16	.	.	PUNCT
ejpam-6251	781	1	fixed	fix	VERB
ejpam-6251	781	2	point	point	NOUN
ejpam-6251	781	3	theory	theory	NOUN
ejpam-6251	781	4	and	and	CCONJ
ejpam-6251	781	5	applications	application	NOUN
ejpam-6251	781	6	,	,	PUNCT
ejpam-6251	781	7	2018(21	2018(21	NUM
ejpam-6251	781	8	)	)	PUNCT
ejpam-6251	781	9	,	,	PUNCT
ejpam-6251	781	10	2018	2018	NUM
ejpam-6251	781	11	.	.	PUNCT
ejpam-6251	782	1	[	[	X
ejpam-6251	782	2	25	25	NUM
ejpam-6251	782	3	]	]	X
ejpam-6251	782	4	g.	g.	PROPN
ejpam-6251	782	5	n.	n.	PROPN
ejpam-6251	782	6	v.	v.	PROPN
ejpam-6251	782	7	kishore	kishore	PROPN
ejpam-6251	782	8	,	,	PUNCT
ejpam-6251	782	9	k.	k.	PROPN
ejpam-6251	783	1	p.	p.	PROPN
ejpam-6251	783	2	r.	r.	PROPN
ejpam-6251	783	3	rao	rao	PROPN
ejpam-6251	783	4	,	,	PUNCT
ejpam-6251	783	5	b.	b.	PROPN
ejpam-6251	783	6	s.	s.	PROPN
ejpam-6251	783	7	rao	rao	PROPN
ejpam-6251	783	8	,	,	PUNCT
ejpam-6251	783	9	and	and	CCONJ
ejpam-6251	783	10	a.	a.	PROPN
ejpam-6251	783	11	sombabu	sombabu	PROPN
ejpam-6251	783	12	.	.	PUNCT
ejpam-6251	784	1	covariant	covariant	ADJ
ejpam-6251	784	2	mappings	mapping	NOUN
ejpam-6251	784	3	and	and	CCONJ
ejpam-6251	784	4	coupled	couple	VERB
ejpam-6251	784	5	fixed	fix	VERB
ejpam-6251	784	6	point	point	NOUN
ejpam-6251	784	7	results	result	NOUN
ejpam-6251	784	8	in	in	ADP
ejpam-6251	784	9	bipolar	bipolar	ADJ
ejpam-6251	784	10	metric	metric	ADJ
ejpam-6251	784	11	spaces	space	NOUN
ejpam-6251	784	12	.	.	PUNCT
ejpam-6251	785	1	international	international	ADJ
ejpam-6251	785	2	journal	journal	PROPN
ejpam-6251	785	3	of	of	ADP
ejpam-6251	785	4	nonlinear	nonlinear	ADJ
ejpam-6251	785	5	analysis	analysis	NOUN
ejpam-6251	785	6	and	and	CCONJ
ejpam-6251	785	7	applications	application	NOUN
ejpam-6251	785	8	,	,	PUNCT
ejpam-6251	785	9	12(1):1–15	12(1):1–15	NUM
ejpam-6251	785	10	,	,	PUNCT
ejpam-6251	785	11	2021	2021	NUM
ejpam-6251	785	12	.	.	PUNCT
ejpam-6251	786	1	[	[	X
ejpam-6251	786	2	26	26	NUM
ejpam-6251	786	3	]	]	PUNCT
ejpam-6251	786	4	m.	m.	NOUN
ejpam-6251	786	5	kumar	kumar	PROPN
ejpam-6251	786	6	,	,	PUNCT
ejpam-6251	786	7	p.	p.	PROPN
ejpam-6251	786	8	kumar	kumar	PROPN
ejpam-6251	786	9	,	,	PUNCT
ejpam-6251	786	10	r.	r.	PROPN
ejpam-6251	786	11	ramaswamy	ramaswamy	PROPN
ejpam-6251	786	12	,	,	PUNCT
ejpam-6251	786	13	o.	o.	PROPN
ejpam-6251	786	14	a.	a.	PROPN
ejpam-6251	786	15	a.	a.	PROPN
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ejpam-6251	786	17	,	,	PUNCT
ejpam-6251	786	18	a.	a.	NOUN
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ejpam-6251	786	20	,	,	PUNCT
ejpam-6251	786	21	and	and	CCONJ
ejpam-6251	786	22	s.	s.	PROPN
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ejpam-6251	786	24	(	(	PUNCT
ejpam-6251	786	25	α	α	NOUN
ejpam-6251	786	26	ψ	ψ	NOUN
ejpam-6251	786	27	)	)	PUNCT
ejpam-6251	786	28	meir	meir	ADJ
ejpam-6251	786	29	-	-	PUNCT
ejpam-6251	786	30	keeler	keeler	PROPN
ejpam-6251	786	31	contractions	contraction	NOUN
ejpam-6251	786	32	in	in	ADP
ejpam-6251	786	33	bipolar	bipolar	ADJ
ejpam-6251	786	34	metric	metric	ADJ
ejpam-6251	786	35	spaces	space	NOUN
ejpam-6251	786	36	.	.	PUNCT
ejpam-6251	787	1	mathematics	mathematic	NOUN
ejpam-6251	787	2	,	,	PUNCT
ejpam-6251	787	3	11(1310	11(1310	NUM
ejpam-6251	787	4	)	)	PUNCT
ejpam-6251	787	5	,	,	PUNCT
ejpam-6251	787	6	2023	2023	NUM
ejpam-6251	787	7	.	.	PUNCT
ejpam-6251	788	1	[	[	X
ejpam-6251	788	2	27	27	NUM
ejpam-6251	788	3	]	]	X
ejpam-6251	788	4	r.	r.	PROPN
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ejpam-6251	788	6	,	,	PUNCT
ejpam-6251	788	7	g.	g.	PROPN
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ejpam-6251	788	9	,	,	PUNCT
ejpam-6251	788	10	a.	a.	PROPN
ejpam-6251	788	11	j.	j.	PROPN
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ejpam-6251	788	13	,	,	PUNCT
ejpam-6251	788	14	o.	o.	PROPN
ejpam-6251	788	15	a.	a.	PROPN
ejpam-6251	788	16	a.	a.	PROPN
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ejpam-6251	788	18	,	,	PUNCT
ejpam-6251	788	19	v.	v.	ADP
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ejpam-6251	788	21	,	,	PUNCT
ejpam-6251	788	22	s.	s.	PROPN
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ejpam-6251	788	24	,	,	PUNCT
ejpam-6251	788	25	and	and	CCONJ
ejpam-6251	788	26	s.	s.	PROPN
ejpam-6251	789	1	radenović.	radenović.	PROPN
ejpam-6251	789	2	fixed	fix	VERB
ejpam-6251	789	3	points	point	NOUN
ejpam-6251	789	4	on	on	ADP
ejpam-6251	789	5	covariant	covariant	NOUN
ejpam-6251	789	6	and	and	CCONJ
ejpam-6251	789	7	contravariant	contravariant	PROPN
ejpam-6251	789	8	maps	map	NOUN
ejpam-6251	789	9	with	with	ADP
ejpam-6251	789	10	an	an	DET
ejpam-6251	789	11	application	application	NOUN
ejpam-6251	789	12	.	.	PUNCT
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ejpam-6251	790	2	,	,	PUNCT
ejpam-6251	790	3	10(4385	10(4385	NUM
ejpam-6251	790	4	)	)	PUNCT
ejpam-6251	790	5	,	,	PUNCT
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ejpam-6251	790	7	.	.	PUNCT
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ejpam-6251	791	2	28	28	NUM
ejpam-6251	791	3	]	]	X
ejpam-6251	791	4	s.	s.	PROPN
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ejpam-6251	791	6	,	,	PUNCT
ejpam-6251	791	7	r.	r.	PROPN
ejpam-6251	791	8	c.	c.	PROPN
ejpam-6251	791	9	dimri	dimri	PROPN
ejpam-6251	791	10	,	,	PUNCT
ejpam-6251	791	11	and	and	CCONJ
ejpam-6251	791	12	a.	a.	NOUN
ejpam-6251	791	13	bartwal	bartwal	NOUN
ejpam-6251	791	14	.	.	PUNCT
ejpam-6251	792	1	f	f	X
ejpam-6251	792	2	-	-	PUNCT
ejpam-6251	792	3	bipolar	bipolar	ADJ
ejpam-6251	792	4	metric	metric	ADJ
ejpam-6251	792	5	spaces	space	NOUN
ejpam-6251	792	6	and	and	CCONJ
ejpam-6251	792	7	fixed	fix	VERB
ejpam-6251	792	8	point	point	NOUN
ejpam-6251	792	9	theorems	theorem	NOUN
ejpam-6251	792	10	with	with	ADP
ejpam-6251	792	11	applications	application	NOUN
ejpam-6251	792	12	.	.	PUNCT
ejpam-6251	793	1	journal	journal	NOUN
ejpam-6251	793	2	of	of	ADP
ejpam-6251	793	3	mathematics	mathematic	NOUN
ejpam-6251	793	4	and	and	CCONJ
ejpam-6251	793	5	computer	computer	NOUN
ejpam-6251	793	6	science	science	NOUN
ejpam-6251	793	7	,	,	PUNCT
ejpam-6251	793	8	26:184	26:184	NUM
ejpam-6251	793	9	–	–	PUNCT
ejpam-6251	793	10	195	195	NUM
ejpam-6251	793	11	,	,	PUNCT
ejpam-6251	793	12	2022	2022	NUM
ejpam-6251	793	13	.	.	PUNCT
ejpam-6251	794	1	[	[	X
ejpam-6251	794	2	29	29	NUM
ejpam-6251	794	3	]	]	X
ejpam-6251	794	4	u.	u.	NOUN
ejpam-6251	794	5	gürdal	gürdal	PROPN
ejpam-6251	794	6	,	,	PUNCT
ejpam-6251	794	7	a.	a.	NOUN
ejpam-6251	794	8	mutlu	mutlu	PROPN
ejpam-6251	794	9	,	,	PUNCT
ejpam-6251	794	10	and	and	CCONJ
ejpam-6251	794	11	a.	a.	NOUN
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ejpam-6251	794	13	.	.	PUNCT
ejpam-6251	794	14	fixed	fix	VERB
ejpam-6251	794	15	point	point	NOUN
ejpam-6251	794	16	results	result	NOUN
ejpam-6251	794	17	for	for	ADP
ejpam-6251	794	18	ψ−ϕ	ψ−ϕ	NOUN
ejpam-6251	794	19	contractive	contractive	ADJ
ejpam-6251	794	20	mappings	mapping	NOUN
ejpam-6251	794	21	in	in	ADP
ejpam-6251	794	22	bipolar	bipolar	ADJ
ejpam-6251	794	23	metric	metric	ADJ
ejpam-6251	794	24	spaces	space	NOUN
ejpam-6251	794	25	.	.	PUNCT
ejpam-6251	795	1	journal	journal	NOUN
ejpam-6251	795	2	of	of	ADP
ejpam-6251	795	3	inequalities	inequality	NOUN
ejpam-6251	795	4	and	and	CCONJ
ejpam-6251	795	5	special	special	ADJ
ejpam-6251	795	6	functions	function	NOUN
ejpam-6251	795	7	,	,	PUNCT
ejpam-6251	795	8	11(1	11(1	NUM
ejpam-6251	795	9	)	)	PUNCT
ejpam-6251	795	10	,	,	PUNCT
ejpam-6251	795	11	2020	2020	NUM
ejpam-6251	795	12	.	.	PUNCT
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ejpam-6251	796	2	30	30	NUM
ejpam-6251	796	3	]	]	X
ejpam-6251	796	4	y.	y.	PROPN
ejpam-6251	796	5	u.	u.	PROPN
ejpam-6251	796	6	gaba	gaba	PROPN
ejpam-6251	796	7	,	,	PUNCT
ejpam-6251	796	8	m.	m.	NOUN
ejpam-6251	796	9	aphane	aphane	PROPN
ejpam-6251	796	10	,	,	PUNCT
ejpam-6251	796	11	and	and	CCONJ
ejpam-6251	796	12	h.	h.	PROPN
ejpam-6251	796	13	aydi	aydi	VERB
ejpam-6251	796	14	.	.	PUNCT
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ejpam-6251	797	2	in	in	ADP
ejpam-6251	797	3	bipolar	bipolar	ADJ
ejpam-6251	797	4	metric	metric	ADJ
ejpam-6251	797	5	spaces	space	NOUN
ejpam-6251	797	6	.	.	PUNCT
ejpam-6251	798	1	journal	journal	NOUN
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ejpam-6251	798	4	,	,	PUNCT
ejpam-6251	798	5	2021(5562651	2021(5562651	NUM
ejpam-6251	798	6	)	)	PUNCT
ejpam-6251	798	7	,	,	PUNCT
ejpam-6251	798	8	2021	2021	NUM
ejpam-6251	798	9	.	.	PUNCT
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ejpam-6251	799	2	31	31	NUM
ejpam-6251	799	3	]	]	X
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ejpam-6251	799	7	m.	m.	PROPN
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ejpam-6251	799	9	.	.	PUNCT
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ejpam-6251	800	2	metric	metric	ADJ
ejpam-6251	800	3	spaces	space	NOUN
ejpam-6251	800	4	.	.	PUNCT
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ejpam-6251	801	2	sciences	sciences	PROPN
ejpam-6251	801	3	,	,	PUNCT
ejpam-6251	801	4	14:241–248	14:241–248	PROPN
ejpam-6251	801	5	,	,	PUNCT
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ejpam-6251	801	7	.	.	PUNCT
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ejpam-6251	802	2	32	32	NUM
ejpam-6251	802	3	]	]	X
ejpam-6251	802	4	n.	n.	NOUN
ejpam-6251	802	5	simsek	simsek	NOUN
ejpam-6251	802	6	and	and	CCONJ
ejpam-6251	802	7	m.	m.	NOUN
ejpam-6251	802	8	kirisci	kirisci	PROPN
ejpam-6251	802	9	.	.	PUNCT
ejpam-6251	803	1	fixed	fix	VERB
ejpam-6251	803	2	point	point	NOUN
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ejpam-6251	803	5	neutrosophic	neutrosophic	ADJ
ejpam-6251	803	6	metric	metric	ADJ
ejpam-6251	803	7	spaces	space	NOUN
ejpam-6251	803	8	.	.	PUNCT
ejpam-6251	804	1	sigma	sigma	PROPN
ejpam-6251	804	2	journal	journal	PROPN
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ejpam-6251	804	4	engineering	engineering	NOUN
ejpam-6251	804	5	and	and	CCONJ
ejpam-6251	804	6	natural	natural	ADJ
ejpam-6251	804	7	sciences	science	NOUN
ejpam-6251	804	8	,	,	PUNCT
ejpam-6251	804	9	10:221–230	10:221–230	NUM
ejpam-6251	804	10	,	,	PUNCT
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ejpam-6251	804	12	.	.	PUNCT
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ejpam-6251	805	3	]	]	PUNCT
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ejpam-6251	805	6	,	,	PUNCT
ejpam-6251	805	7	m.	m.	NOUN
ejpam-6251	805	8	jeyarama	jeyarama	PROPN
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ejpam-6251	805	11	f.	f.	PROPN
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ejpam-6251	805	13	.	.	PUNCT
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ejpam-6251	806	2	point	point	NOUN
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ejpam-6251	806	5	contraction	contraction	NOUN
ejpam-6251	806	6	theorems	theorem	NOUN
ejpam-6251	806	7	in	in	ADP
ejpam-6251	806	8	neutrosophic	neutrosophic	ADJ
ejpam-6251	806	9	metric	metric	ADJ
ejpam-6251	806	10	spaces	space	NOUN
ejpam-6251	806	11	.	.	PUNCT
ejpam-6251	807	1	neutrosophic	neutrosophic	ADJ
ejpam-6251	807	2	sets	set	NOUN
ejpam-6251	807	3	and	and	CCONJ
ejpam-6251	807	4	systems	system	NOUN
ejpam-6251	807	5	,	,	PUNCT
ejpam-6251	807	6	36(23	36(23	NOUN
ejpam-6251	807	7	)	)	PUNCT
ejpam-6251	807	8	,	,	PUNCT
ejpam-6251	807	9	2020	2020	NUM
ejpam-6251	807	10	.	.	PUNCT
ejpam-6251	808	1	[	[	X
ejpam-6251	808	2	34	34	NUM
ejpam-6251	808	3	]	]	X
ejpam-6251	808	4	d.	d.	PROPN
ejpam-6251	808	5	baleanu	baleanu	PROPN
ejpam-6251	808	6	,	,	PUNCT
ejpam-6251	808	7	s.	s.	PROPN
ejpam-6251	808	8	rezapour	rezapour	PROPN
ejpam-6251	808	9	,	,	PUNCT
ejpam-6251	808	10	and	and	CCONJ
ejpam-6251	808	11	m.	m.	NOUN
ejpam-6251	808	12	mohammadi	mohammadi	NOUN
ejpam-6251	808	13	.	.	PUNCT
ejpam-6251	809	1	some	some	DET
ejpam-6251	809	2	existence	existence	NOUN
ejpam-6251	809	3	results	result	VERB
ejpam-6251	809	4	on	on	ADP
ejpam-6251	809	5	nonlinear	nonlinear	ADJ
ejpam-6251	809	6	fractional	fractional	ADJ
ejpam-6251	809	7	differential	differential	ADJ
ejpam-6251	809	8	equations	equation	NOUN
ejpam-6251	809	9	.	.	PUNCT
ejpam-6251	810	1	philosophical	philosophical	ADJ
ejpam-6251	810	2	transactions	transaction	NOUN
ejpam-6251	810	3	of	of	ADP
ejpam-6251	810	4	the	the	DET
ejpam-6251	810	5	royal	royal	ADJ
ejpam-6251	810	6	society	society	NOUN
ejpam-6251	810	7	a	a	DET
ejpam-6251	810	8	:	:	PUNCT
ejpam-6251	810	9	mathematical	mathematical	ADJ
ejpam-6251	810	10	,	,	PUNCT
ejpam-6251	810	11	physical	physical	ADJ
ejpam-6251	810	12	and	and	CCONJ
ejpam-6251	810	13	engineering	engineering	NOUN
ejpam-6251	810	14	sciences	science	NOUN
ejpam-6251	810	15	,	,	PUNCT
ejpam-6251	810	16	371(20120144	371(20120144	NUM
ejpam-6251	810	17	)	)	PUNCT
ejpam-6251	810	18	,	,	PUNCT
ejpam-6251	810	19	2013	2013	NUM
ejpam-6251	810	20	.	.	PUNCT
ejpam-6251	811	1	[	[	X
ejpam-6251	811	2	35	35	NUM
ejpam-6251	811	3	]	]	X
ejpam-6251	811	4	h.	h.	PROPN
ejpam-6251	811	5	zhu	zhu	PROPN
ejpam-6251	811	6	,	,	PUNCT
ejpam-6251	811	7	s.	s.	PROPN
ejpam-6251	811	8	han	han	PROPN
ejpam-6251	811	9	,	,	PUNCT
ejpam-6251	811	10	and	and	CCONJ
ejpam-6251	811	11	j.	j.	PROPN
ejpam-6251	811	12	shen	shen	PROPN
ejpam-6251	811	13	.	.	PUNCT
ejpam-6251	812	1	some	some	DET
ejpam-6251	812	2	results	result	NOUN
ejpam-6251	812	3	on	on	ADP
ejpam-6251	812	4	fractional	fractional	ADJ
ejpam-6251	812	5	m	m	NOUN
ejpam-6251	812	6	-	-	PUNCT
ejpam-6251	812	7	point	point	NOUN
ejpam-6251	812	8	boundary	boundary	ADJ
ejpam-6251	812	9	value	value	NOUN
ejpam-6251	812	10	problems	problem	NOUN
ejpam-6251	812	11	.	.	PUNCT
ejpam-6251	813	1	journal	journal	NOUN
ejpam-6251	813	2	of	of	ADP
ejpam-6251	813	3	function	function	NOUN
ejpam-6251	813	4	spaces	space	NOUN
ejpam-6251	813	5	,	,	PUNCT
ejpam-6251	813	6	2021(3152688	2021(3152688	NUM
ejpam-6251	813	7	)	)	PUNCT
ejpam-6251	813	8	,	,	PUNCT
ejpam-6251	813	9	2021	2021	NUM
ejpam-6251	813	10	.	.	PUNCT
ejpam-6251	814	1	[	[	X
ejpam-6251	814	2	36	36	NUM
ejpam-6251	814	3	]	]	X
ejpam-6251	814	4	s.	s.	PROPN
ejpam-6251	814	5	chandok	chandok	PROPN
ejpam-6251	814	6	,	,	PUNCT
ejpam-6251	814	7	r.	r.	PROPN
ejpam-6251	814	8	k.	k.	PROPN
ejpam-6251	814	9	sharma	sharma	PROPN
ejpam-6251	814	10	,	,	PUNCT
ejpam-6251	814	11	and	and	CCONJ
ejpam-6251	814	12	s.	s.	PROPN
ejpam-6251	814	13	radenović.	radenović.	PROPN
ejpam-6251	814	14	multivalued	multivalue	VERB
ejpam-6251	814	15	problems	problem	NOUN
ejpam-6251	814	16	via	via	ADP
ejpam-6251	814	17	orthogonal	orthogonal	ADJ
ejpam-6251	814	18	contraction	contraction	NOUN
ejpam-6251	814	19	mappings	mapping	NOUN
ejpam-6251	814	20	with	with	ADP
ejpam-6251	814	21	application	application	NOUN
ejpam-6251	814	22	to	to	ADP
ejpam-6251	814	23	fractional	fractional	ADJ
ejpam-6251	814	24	differential	differential	ADJ
ejpam-6251	814	25	equation	equation	NOUN
ejpam-6251	814	26	.	.	PUNCT
ejpam-6251	815	1	journal	journal	NOUN
ejpam-6251	815	2	of	of	ADP
ejpam-6251	815	3	fixed	fix	VERB
ejpam-6251	815	4	point	point	NOUN
ejpam-6251	815	5	theory	theory	NOUN
ejpam-6251	815	6	and	and	CCONJ
ejpam-6251	815	7	applications	application	NOUN
ejpam-6251	815	8	,	,	PUNCT
ejpam-6251	815	9	23(14	23(14	NUM
ejpam-6251	815	10	)	)	PUNCT
ejpam-6251	815	11	,	,	PUNCT
ejpam-6251	815	12	2021	2021	NUM
ejpam-6251	815	13	.	.	PUNCT
ejpam-6251	816	1	[	[	X
ejpam-6251	816	2	37	37	NUM
ejpam-6251	816	3	]	]	PUNCT
ejpam-6251	816	4	g.	g.	PROPN
ejpam-6251	816	5	mani	mani	PROPN
ejpam-6251	816	6	,	,	PUNCT
ejpam-6251	816	7	r.	r.	PROPN
ejpam-6251	816	8	ramaswamy	ramaswamy	PROPN
ejpam-6251	816	9	,	,	PUNCT
ejpam-6251	816	10	a.	a.	PROPN
ejpam-6251	816	11	j.	j.	PROPN
ejpam-6251	816	12	gnanaprakasam	gnanaprakasam	PROPN
ejpam-6251	816	13	,	,	PUNCT
ejpam-6251	816	14	o.	o.	PROPN
ejpam-6251	816	15	a.	a.	PROPN
ejpam-6251	816	16	a.	a.	PROPN
ejpam-6251	816	17	abdelnaby	abdelnaby	PROPN
ejpam-6251	816	18	,	,	PUNCT
ejpam-6251	816	19	s.	s.	PROPN
ejpam-6251	816	20	radojević	radojević	PROPN
ejpam-6251	816	21	,	,	PUNCT
ejpam-6251	816	22	and	and	CCONJ
ejpam-6251	816	23	s.	s.	PROPN
ejpam-6251	817	1	radenović.	radenović.	PRON
ejpam-6251	817	2	solution	solution	NOUN
ejpam-6251	817	3	of	of	ADP
ejpam-6251	817	4	integral	integral	ADJ
ejpam-6251	817	5	equation	equation	NOUN
ejpam-6251	817	6	with	with	ADP
ejpam-6251	817	7	neutrosophic	neutrosophic	ADJ
ejpam-6251	817	8	rectangular	rectangular	ADJ
ejpam-6251	817	9	triple	triple	ADV
ejpam-6251	817	10	controlled	control	VERB
ejpam-6251	817	11	metric	metric	ADJ
ejpam-6251	817	12	spaces	space	NOUN
ejpam-6251	817	13	.	.	PUNCT
ejpam-6251	818	1	symmetry	symmetry	NOUN
ejpam-6251	818	2	,	,	PUNCT
ejpam-6251	818	3	14(2074	14(2074	NUM
ejpam-6251	818	4	)	)	PUNCT
ejpam-6251	818	5	,	,	PUNCT
ejpam-6251	818	6	2022	2022	NUM
ejpam-6251	818	7	.	.	PUNCT