id	sid	tid	token	lemma	pos
ejpam-5641	1	1	european	european	PROPN
ejpam-5641	1	2	journal	journal	PROPN
ejpam-5641	1	3	of	of	ADP
ejpam-5641	1	4	pure	pure	ADJ
ejpam-5641	1	5	and	and	CCONJ
ejpam-5641	1	6	applied	applied	ADJ
ejpam-5641	1	7	mathematics	mathematic	NOUN
ejpam-5641	1	8	2025	2025	NUM
ejpam-5641	1	9	,	,	PUNCT
ejpam-5641	1	10	vol	vol	NOUN
ejpam-5641	1	11	.	.	PROPN
ejpam-5641	1	12	18	18	NUM
ejpam-5641	1	13	,	,	PUNCT
ejpam-5641	1	14	issue	issue	NOUN
ejpam-5641	1	15	1	1	NUM
ejpam-5641	1	16	,	,	PUNCT
ejpam-5641	1	17	article	article	NOUN
ejpam-5641	1	18	number	number	NOUN
ejpam-5641	1	19	5641	5641	NUM
ejpam-5641	1	20	issn	issn	PROPN
ejpam-5641	1	21	1307	1307	NUM
ejpam-5641	1	22	-	-	SYM
ejpam-5641	1	23	5543	5543	NUM
ejpam-5641	1	24	–	–	PUNCT
ejpam-5641	1	25	ejpam.com	ejpam.com	X
ejpam-5641	1	26	published	publish	VERB
ejpam-5641	1	27	by	by	ADP
ejpam-5641	1	28	new	new	PROPN
ejpam-5641	1	29	york	york	PROPN
ejpam-5641	1	30	business	business	PROPN
ejpam-5641	1	31	global	global	PROPN
ejpam-5641	1	32	on	on	ADP
ejpam-5641	1	33	a	a	DET
ejpam-5641	1	34	new	new	ADJ
ejpam-5641	1	35	stochastic	stochastic	ADJ
ejpam-5641	1	36	space	space	NOUN
ejpam-5641	1	37	with	with	ADP
ejpam-5641	1	38	applications	application	NOUN
ejpam-5641	1	39	to	to	ADP
ejpam-5641	1	40	nonlinear	nonlinear	ADJ
ejpam-5641	1	41	economic	economic	ADJ
ejpam-5641	1	42	model	model	NOUN
ejpam-5641	1	43	meshayil	meshayil	PROPN
ejpam-5641	1	44	m.	m.	PROPN
ejpam-5641	1	45	alsolmi1,∗	alsolmi1,∗	PROPN
ejpam-5641	1	46	,	,	PUNCT
ejpam-5641	1	47	salah	salah	PROPN
ejpam-5641	1	48	h.	h.	PROPN
ejpam-5641	1	49	alshabhi1	alshabhi1	PROPN
ejpam-5641	1	50	,	,	PUNCT
ejpam-5641	1	51	mustafa	mustafa	PROPN
ejpam-5641	1	52	m.	m.	PROPN
ejpam-5641	1	53	mohammed1	mohammed1	PROPN
ejpam-5641	1	54	,	,	PUNCT
ejpam-5641	1	55	thwiba	thwiba	PROPN
ejpam-5641	1	56	a.	a.	PROPN
ejpam-5641	1	57	khalid2	khalid2	PROPN
ejpam-5641	1	58	,	,	PUNCT
ejpam-5641	1	59	mona	mona	PROPN
ejpam-5641	1	60	magzoub1	magzoub1	PROPN
ejpam-5641	1	61	,	,	PUNCT
ejpam-5641	1	62	nidal	nidal	PROPN
ejpam-5641	1	63	e.	e.	PROPN
ejpam-5641	1	64	taha3	taha3	PROPN
ejpam-5641	1	65	,	,	PUNCT
ejpam-5641	1	66	khdija	khdija	ADJ
ejpam-5641	1	67	o.	o.	NOUN
ejpam-5641	1	68	taha3	taha3	PROPN
ejpam-5641	1	69	,	,	PUNCT
ejpam-5641	1	70	awad	awad	PROPN
ejpam-5641	1	71	a.	a.	PROPN
ejpam-5641	1	72	bakery1	bakery1	PROPN
ejpam-5641	1	73	1	1	NUM
ejpam-5641	1	74	university	university	NOUN
ejpam-5641	1	75	of	of	ADP
ejpam-5641	1	76	jeddah	jeddah	PROPN
ejpam-5641	1	77	,	,	PUNCT
ejpam-5641	1	78	applied	apply	VERB
ejpam-5641	1	79	college	college	NOUN
ejpam-5641	1	80	,	,	PUNCT
ejpam-5641	1	81	department	department	NOUN
ejpam-5641	1	82	of	of	ADP
ejpam-5641	1	83	mathematics	mathematics	PROPN
ejpam-5641	1	84	,	,	PUNCT
ejpam-5641	1	85	jeddah	jeddah	PROPN
ejpam-5641	1	86	,	,	PUNCT
ejpam-5641	1	87	saudi	saudi	PROPN
ejpam-5641	1	88	arabia	arabia	PROPN
ejpam-5641	1	89	2	2	NUM
ejpam-5641	1	90	department	department	NOUN
ejpam-5641	1	91	of	of	ADP
ejpam-5641	1	92	mathematics	mathematic	NOUN
ejpam-5641	1	93	,	,	PUNCT
ejpam-5641	1	94	faculty	faculty	NOUN
ejpam-5641	1	95	of	of	ADP
ejpam-5641	1	96	science	science	NOUN
ejpam-5641	1	97	,	,	PUNCT
ejpam-5641	1	98	al	al	PROPN
ejpam-5641	1	99	-	-	PUNCT
ejpam-5641	1	100	baha	baha	PROPN
ejpam-5641	1	101	university	university	PROPN
ejpam-5641	1	102	,	,	PUNCT
ejpam-5641	1	103	albaha	albaha	NOUN
ejpam-5641	1	104	65525	65525	NUM
ejpam-5641	1	105	,	,	PUNCT
ejpam-5641	1	106	saudi	saudi	PROPN
ejpam-5641	1	107	arabia	arabia	PROPN
ejpam-5641	1	108	3	3	NUM
ejpam-5641	1	109	department	department	NOUN
ejpam-5641	1	110	of	of	ADP
ejpam-5641	1	111	mathematics	mathematics	PROPN
ejpam-5641	1	112	,	,	PUNCT
ejpam-5641	1	113	college	college	NOUN
ejpam-5641	1	114	of	of	ADP
ejpam-5641	1	115	science	science	NOUN
ejpam-5641	1	116	,	,	PUNCT
ejpam-5641	1	117	qassim	qassim	PROPN
ejpam-5641	1	118	university	university	PROPN
ejpam-5641	1	119	,	,	PUNCT
ejpam-5641	1	120	buraidah	buraidah	NOUN
ejpam-5641	1	121	51452	51452	NUM
ejpam-5641	1	122	,	,	PUNCT
ejpam-5641	1	123	saudi	saudi	PROPN
ejpam-5641	1	124	arabia	arabia	PROPN
ejpam-5641	1	125	abstract	abstract	NOUN
ejpam-5641	1	126	.	.	PUNCT
ejpam-5641	2	1	this	this	DET
ejpam-5641	2	2	article	article	NOUN
ejpam-5641	2	3	will	will	AUX
ejpam-5641	2	4	utilize	utilize	VERB
ejpam-5641	2	5	a	a	DET
ejpam-5641	2	6	weighted	weighted	ADJ
ejpam-5641	2	7	regular	regular	ADJ
ejpam-5641	2	8	matrix	matrix	NOUN
ejpam-5641	2	9	composed	compose	VERB
ejpam-5641	2	10	of	of	ADP
ejpam-5641	2	11	fibonacci	fibonacci	NOUN
ejpam-5641	2	12	numbers	number	NOUN
ejpam-5641	2	13	and	and	CCONJ
ejpam-5641	2	14	variable	variable	ADJ
ejpam-5641	2	15	exponent	exponent	NOUN
ejpam-5641	2	16	sequence	sequence	NOUN
ejpam-5641	2	17	spaces	space	VERB
ejpam-5641	2	18	to	to	PART
ejpam-5641	2	19	create	create	VERB
ejpam-5641	2	20	a	a	DET
ejpam-5641	2	21	novel	novel	ADJ
ejpam-5641	2	22	stochastic	stochastic	ADJ
ejpam-5641	2	23	space	space	NOUN
ejpam-5641	2	24	with	with	ADP
ejpam-5641	2	25	certain	certain	ADJ
ejpam-5641	2	26	geometric	geometric	ADJ
ejpam-5641	2	27	and	and	CCONJ
ejpam-5641	2	28	topological	topological	ADJ
ejpam-5641	2	29	properties	property	NOUN
ejpam-5641	2	30	.	.	PUNCT
ejpam-5641	3	1	this	this	DET
ejpam-5641	3	2	area	area	NOUN
ejpam-5641	3	3	demonstrates	demonstrate	VERB
ejpam-5641	3	4	the	the	DET
ejpam-5641	3	5	new	new	ADJ
ejpam-5641	3	6	form	form	NOUN
ejpam-5641	3	7	of	of	ADP
ejpam-5641	3	8	the	the	DET
ejpam-5641	3	9	kannan	kannan	PROPN
ejpam-5641	3	10	contraction	contraction	NOUN
ejpam-5641	3	11	operator	operator	NOUN
ejpam-5641	3	12	with	with	ADP
ejpam-5641	3	13	a	a	DET
ejpam-5641	3	14	fixed	fix	VERB
ejpam-5641	3	15	point	point	NOUN
ejpam-5641	3	16	.	.	PUNCT
ejpam-5641	4	1	in	in	ADP
ejpam-5641	4	2	mathematical	mathematical	ADJ
ejpam-5641	4	3	economics	economic	NOUN
ejpam-5641	4	4	,	,	PUNCT
ejpam-5641	4	5	we	we	PRON
ejpam-5641	4	6	represent	represent	VERB
ejpam-5641	4	7	economic	economic	ADJ
ejpam-5641	4	8	entities	entity	NOUN
ejpam-5641	4	9	,	,	PUNCT
ejpam-5641	4	10	processes	process	NOUN
ejpam-5641	4	11	,	,	PUNCT
ejpam-5641	4	12	and	and	CCONJ
ejpam-5641	4	13	phenomena	phenomenon	NOUN
ejpam-5641	4	14	by	by	ADP
ejpam-5641	4	15	mathematically	mathematically	ADV
ejpam-5641	4	16	structured	structure	VERB
ejpam-5641	4	17	functional	functional	ADJ
ejpam-5641	4	18	equations	equation	NOUN
ejpam-5641	4	19	,	,	PUNCT
ejpam-5641	4	20	either	either	CCONJ
ejpam-5641	4	21	as	as	ADP
ejpam-5641	4	22	summable	summable	ADJ
ejpam-5641	4	23	equations	equation	NOUN
ejpam-5641	4	24	or	or	CCONJ
ejpam-5641	4	25	integral	integral	ADJ
ejpam-5641	4	26	equations	equation	NOUN
ejpam-5641	4	27	.	.	PUNCT
ejpam-5641	5	1	we	we	PRON
ejpam-5641	5	2	investigate	investigate	VERB
ejpam-5641	5	3	a	a	DET
ejpam-5641	5	4	category	category	NOUN
ejpam-5641	5	5	of	of	ADP
ejpam-5641	5	6	volterra	volterra	NOUN
ejpam-5641	5	7	-	-	PUNCT
ejpam-5641	5	8	type	type	NOUN
ejpam-5641	5	9	non	non	ADJ
ejpam-5641	5	10	-	-	ADJ
ejpam-5641	5	11	linear	linear	ADJ
ejpam-5641	5	12	dynamical	dynamical	ADJ
ejpam-5641	5	13	systems	system	NOUN
ejpam-5641	5	14	,	,	PUNCT
ejpam-5641	5	15	similar	similar	ADJ
ejpam-5641	5	16	to	to	ADP
ejpam-5641	5	17	an	an	DET
ejpam-5641	5	18	economic	economic	ADJ
ejpam-5641	5	19	model	model	NOUN
ejpam-5641	5	20	.	.	PUNCT
ejpam-5641	6	1	we	we	PRON
ejpam-5641	6	2	employ	employ	VERB
ejpam-5641	6	3	our	our	PRON
ejpam-5641	6	4	acquired	acquire	VERB
ejpam-5641	6	5	results	result	NOUN
ejpam-5641	6	6	to	to	PART
ejpam-5641	6	7	formulate	formulate	VERB
ejpam-5641	6	8	new	new	ADJ
ejpam-5641	6	9	solvability	solvability	NOUN
ejpam-5641	6	10	criteria	criterion	NOUN
ejpam-5641	6	11	for	for	ADP
ejpam-5641	6	12	a	a	DET
ejpam-5641	6	13	unique	unique	ADJ
ejpam-5641	6	14	solution	solution	NOUN
ejpam-5641	6	15	of	of	ADP
ejpam-5641	6	16	these	these	DET
ejpam-5641	6	17	non	non	ADJ
ejpam-5641	6	18	-	-	ADJ
ejpam-5641	6	19	linear	linear	ADJ
ejpam-5641	6	20	discrete	discrete	ADJ
ejpam-5641	6	21	economic	economic	ADJ
ejpam-5641	6	22	dynamical	dynamical	ADJ
ejpam-5641	6	23	systems	system	NOUN
ejpam-5641	6	24	.	.	PUNCT
ejpam-5641	7	1	ultimately	ultimately	ADV
ejpam-5641	7	2	,	,	PUNCT
ejpam-5641	7	3	we	we	PRON
ejpam-5641	7	4	illustrate	illustrate	VERB
ejpam-5641	7	5	our	our	PRON
ejpam-5641	7	6	findings	finding	NOUN
ejpam-5641	7	7	with	with	ADP
ejpam-5641	7	8	specific	specific	ADJ
ejpam-5641	7	9	instances	instance	NOUN
ejpam-5641	7	10	and	and	CCONJ
ejpam-5641	7	11	applications	application	NOUN
ejpam-5641	7	12	related	relate	VERB
ejpam-5641	7	13	to	to	ADP
ejpam-5641	7	14	the	the	DET
ejpam-5641	7	15	presence	presence	NOUN
ejpam-5641	7	16	of	of	ADP
ejpam-5641	7	17	solutions	solution	NOUN
ejpam-5641	7	18	in	in	ADP
ejpam-5641	7	19	non	non	ADJ
ejpam-5641	7	20	-	-	ADJ
ejpam-5641	7	21	linear	linear	ADJ
ejpam-5641	7	22	dynamical	dynamical	ADJ
ejpam-5641	7	23	systems	system	NOUN
ejpam-5641	7	24	of	of	ADP
ejpam-5641	7	25	volterra	volterra	NOUN
ejpam-5641	7	26	-	-	PUNCT
ejpam-5641	7	27	type	type	NOUN
ejpam-5641	7	28	.	.	PUNCT
ejpam-5641	8	1	2020	2020	NUM
ejpam-5641	8	2	mathematics	mathematic	NOUN
ejpam-5641	8	3	subject	subject	NOUN
ejpam-5641	8	4	classifications	classification	NOUN
ejpam-5641	8	5	:	:	PUNCT
ejpam-5641	8	6	46b15	46b15	NUM
ejpam-5641	8	7	,	,	PUNCT
ejpam-5641	8	8	46c05	46c05	NUM
ejpam-5641	8	9	,	,	PUNCT
ejpam-5641	8	10	46e05	46e05	NUM
ejpam-5641	8	11	key	key	ADJ
ejpam-5641	8	12	words	word	NOUN
ejpam-5641	8	13	and	and	CCONJ
ejpam-5641	8	14	phrases	phrase	NOUN
ejpam-5641	8	15	:	:	PUNCT
ejpam-5641	8	16	fibonacci	fibonacci	NOUN
ejpam-5641	8	17	numbers	number	NOUN
ejpam-5641	8	18	,	,	PUNCT
ejpam-5641	8	19	variable	variable	ADJ
ejpam-5641	8	20	exponent	exponent	NOUN
ejpam-5641	8	21	,	,	PUNCT
ejpam-5641	8	22	extended	extend	VERB
ejpam-5641	8	23	s−soft	s−soft	NUM
ejpam-5641	8	24	numbers	number	NOUN
ejpam-5641	8	25	,	,	PUNCT
ejpam-5641	8	26	new	new	ADJ
ejpam-5641	8	27	type	type	NOUN
ejpam-5641	8	28	of	of	ADP
ejpam-5641	8	29	kannan	kannan	PROPN
ejpam-5641	8	30	contraction	contraction	PROPN
ejpam-5641	8	31	.	.	PUNCT
ejpam-5641	9	1	abbreviations	abbreviation	NOUN
ejpam-5641	9	2	(	(	PUNCT
ejpam-5641	9	3	i	i	NOUN
ejpam-5641	9	4	)	)	PUNCT
ejpam-5641	9	5	p	p	PROPN
ejpam-5641	9	6	-	-	PUNCT
ejpam-5641	9	7	q.n	q.n	NOUN
ejpam-5641	9	8	:	:	PUNCT
ejpam-5641	9	9	pre	pre	ADJ
ejpam-5641	9	10	-	-	ADJ
ejpam-5641	9	11	quasi	quasi	ADJ
ejpam-5641	9	12	norm	norm	NOUN
ejpam-5641	9	13	.	.	PUNCT
ejpam-5641	10	1	(	(	PUNCT
ejpam-5641	10	2	ii	ii	NOUN
ejpam-5641	10	3	)	)	PUNCT
ejpam-5641	10	4	psssf	psssf	NOUN
ejpam-5641	10	5	:	:	PUNCT
ejpam-5641	10	6	private	private	ADJ
ejpam-5641	10	7	sequence	sequence	NOUN
ejpam-5641	10	8	space	space	NOUN
ejpam-5641	10	9	of	of	ADP
ejpam-5641	10	10	soft	soft	ADJ
ejpam-5641	10	11	functions	function	NOUN
ejpam-5641	10	12	.	.	PUNCT
ejpam-5641	11	1	(	(	PUNCT
ejpam-5641	11	2	iii	iii	X
ejpam-5641	11	3	)	)	PUNCT
ejpam-5641	11	4	p	p	NOUN
ejpam-5641	11	5	-	-	NOUN
ejpam-5641	11	6	m	m	NOUN
ejpam-5641	11	7	:	:	PUNCT
ejpam-5641	11	8	pre	pre	ADJ
ejpam-5641	11	9	-	-	ADJ
ejpam-5641	11	10	modular	modular	ADJ
ejpam-5641	11	11	.	.	PUNCT
ejpam-5641	12	1	∗corresponding	∗corresponde	VERB
ejpam-5641	12	2	author	author	NOUN
ejpam-5641	12	3	.	.	PUNCT
ejpam-5641	13	1	doi	doi	NOUN
ejpam-5641	13	2	:	:	PUNCT
ejpam-5641	13	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5641	https://doi.org/10.29020/nybg.ejpam.v18i1.5641	PROPN
ejpam-5641	13	4	email	email	NOUN
ejpam-5641	13	5	addresses	address	VERB
ejpam-5641	13	6	:	:	PUNCT
ejpam-5641	14	1	mmralsulami@uj.edu.sa	mmralsulami@uj.edu.sa	PROPN
ejpam-5641	14	2	(	(	PUNCT
ejpam-5641	14	3	m.	m.	NOUN
ejpam-5641	14	4	m.	m.	NOUN
ejpam-5641	14	5	alsolmi	alsolmi	PROPN
ejpam-5641	14	6	)	)	PUNCT
ejpam-5641	14	7	,	,	PUNCT
ejpam-5641	14	8	salsabieh@uj.edu.sa	salsabieh@uj.edu.sa	PROPN
ejpam-5641	14	9	(	(	PUNCT
ejpam-5641	14	10	s.	s.	PROPN
ejpam-5641	14	11	h.	h.	PROPN
ejpam-5641	14	12	alshabhi	alshabhi	PROPN
ejpam-5641	14	13	)	)	PUNCT
ejpam-5641	14	14	,	,	PUNCT
ejpam-5641	14	15	mustasta@yahoo.com	mustasta@yahoo.com	X
ejpam-5641	14	16	,	,	PUNCT
ejpam-5641	14	17	mmibrahim@uj.edu.sa	mmibrahim@uj.edu.sa	PROPN
ejpam-5641	14	18	(	(	PUNCT
ejpam-5641	14	19	m.	m.	NOUN
ejpam-5641	14	20	m.	m.	PROPN
ejpam-5641	14	21	mohammed	mohammed	PROPN
ejpam-5641	14	22	)	)	PUNCT
ejpam-5641	14	23	,	,	PUNCT
ejpam-5641	14	24	tabdulrhman@bu.edu.sa	tabdulrhman@bu.edu.sa	PROPN
ejpam-5641	14	25	(	(	PUNCT
ejpam-5641	14	26	t.	t.	PROPN
ejpam-5641	14	27	a.	a.	PROPN
ejpam-5641	14	28	khalid	khalid	PROPN
ejpam-5641	14	29	)	)	PUNCT
ejpam-5641	14	30	,	,	PUNCT
ejpam-5641	14	31	mmahmed@uj.edu.sa	mmahmed@uj.edu.sa	PROPN
ejpam-5641	14	32	(	(	PUNCT
ejpam-5641	14	33	m.	m.	NOUN
ejpam-5641	14	34	m.	m.	PROPN
ejpam-5641	14	35	ahmed	ahmed	PROPN
ejpam-5641	14	36	)	)	PUNCT
ejpam-5641	14	37	,	,	PUNCT
ejpam-5641	14	38	n.taha@qu.edu.sa	n.taha@qu.edu.sa	PROPN
ejpam-5641	14	39	(	(	PUNCT
ejpam-5641	14	40	n.	n.	PROPN
ejpam-5641	14	41	e.	e.	PROPN
ejpam-5641	14	42	taha	taha	PROPN
ejpam-5641	14	43	)	)	PUNCT
ejpam-5641	14	44	,	,	PUNCT
ejpam-5641	14	45	k.taha@qu.edu.sa	k.taha@qu.edu.sa	PROPN
ejpam-5641	14	46	(	(	PUNCT
ejpam-5641	14	47	k.	k.	PROPN
ejpam-5641	14	48	o.	o.	PROPN
ejpam-5641	14	49	taha	taha	PROPN
ejpam-5641	14	50	)	)	PUNCT
ejpam-5641	14	51	,	,	PUNCT
ejpam-5641	14	52	aabhassan@uj.edu.sa	aabhassan@uj.edu.sa	PROPN
ejpam-5641	14	53	(	(	PUNCT
ejpam-5641	14	54	a.	a.	NOUN
ejpam-5641	14	55	a.	a.	PROPN
ejpam-5641	14	56	bakery	bakery	PROPN
ejpam-5641	14	57	)	)	PUNCT
ejpam-5641	14	58	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5641	14	59	1	1	NUM
ejpam-5641	14	60	copyright	copyright	NOUN
ejpam-5641	14	61	:	:	PUNCT
ejpam-5641	14	62	©	©	PROPN
ejpam-5641	14	63	2025	2025	NUM
ejpam-5641	14	64	the	the	DET
ejpam-5641	14	65	author(s	author(s	NOUN
ejpam-5641	14	66	)	)	PUNCT
ejpam-5641	14	67	.	.	PUNCT
ejpam-5641	15	1	(	(	PUNCT
ejpam-5641	15	2	cc	cc	NOUN
ejpam-5641	15	3	by	by	ADP
ejpam-5641	15	4	-	-	PUNCT
ejpam-5641	15	5	nc	nc	PROPN
ejpam-5641	15	6	4.0	4.0	NUM
ejpam-5641	15	7	)	)	PUNCT
ejpam-5641	15	8	m.	m.	NOUN
ejpam-5641	15	9	m.	m.	NOUN
ejpam-5641	15	10	a	a	PRON
ejpam-5641	15	11	et	et	PROPN
ejpam-5641	15	12	al	al	PROPN
ejpam-5641	15	13	.	.	PUNCT
ejpam-5641	15	14	/	/	SYM
ejpam-5641	15	15	eur	eur	PROPN
ejpam-5641	15	16	.	.	PUNCT
ejpam-5641	16	1	j.	j.	PROPN
ejpam-5641	16	2	pure	pure	PROPN
ejpam-5641	16	3	appl	appl	PROPN
ejpam-5641	16	4	.	.	PROPN
ejpam-5641	16	5	math	math	PROPN
ejpam-5641	16	6	,	,	PUNCT
ejpam-5641	16	7	18	18	NUM
ejpam-5641	16	8	(	(	PUNCT
ejpam-5641	16	9	1	1	NUM
ejpam-5641	16	10	)	)	PUNCT
ejpam-5641	16	11	(	(	PUNCT
ejpam-5641	16	12	2025	2025	NUM
ejpam-5641	16	13	)	)	PUNCT
ejpam-5641	16	14	,	,	PUNCT
ejpam-5641	16	15	5641	5641	NUM
ejpam-5641	16	16	2	2	NUM
ejpam-5641	16	17	of	of	ADP
ejpam-5641	16	18	20	20	NUM
ejpam-5641	16	19	(	(	PUNCT
ejpam-5641	16	20	iv	iv	X
ejpam-5641	16	21	)	)	PUNCT
ejpam-5641	16	22	p	p	NOUN
ejpam-5641	16	23	-	-	PUNCT
ejpam-5641	16	24	q.b	q.b	NOUN
ejpam-5641	16	25	:	:	PUNCT
ejpam-5641	16	26	pre	pre	ADJ
ejpam-5641	16	27	-	-	ADJ
ejpam-5641	16	28	quasi	quasi	ADJ
ejpam-5641	16	29	banach	banach	NOUN
ejpam-5641	16	30	.	.	PUNCT
ejpam-5641	17	1	(	(	PUNCT
ejpam-5641	17	2	v	v	NOUN
ejpam-5641	17	3	)	)	PUNCT
ejpam-5641	17	4	bs	bs	NOUN
ejpam-5641	17	5	:	:	PUNCT
ejpam-5641	17	6	banach	banach	NOUN
ejpam-5641	17	7	space	space	NOUN
ejpam-5641	17	8	.	.	PUNCT
ejpam-5641	18	1	(	(	PUNCT
ejpam-5641	18	2	vi	vi	X
ejpam-5641	18	3	)	)	PUNCT
ejpam-5641	18	4	cs	cs	ADJ
ejpam-5641	18	5	:	:	PUNCT
ejpam-5641	18	6	cauchy	cauchy	ADJ
ejpam-5641	18	7	sequence	sequence	NOUN
ejpam-5641	18	8	.	.	PUNCT
ejpam-5641	19	1	(	(	PUNCT
ejpam-5641	19	2	vii	vii	PROPN
ejpam-5641	19	3	)	)	PUNCT
ejpam-5641	19	4	cms	cms	PROPN
ejpam-5641	19	5	:	:	PUNCT
ejpam-5641	19	6	complete	complete	ADJ
ejpam-5641	19	7	metric	metric	ADJ
ejpam-5641	19	8	space	space	NOUN
ejpam-5641	19	9	.	.	PUNCT
ejpam-5641	20	1	(	(	PUNCT
ejpam-5641	20	2	viii	viii	NOUN
ejpam-5641	20	3	)	)	PUNCT
ejpam-5641	20	4	nat	nat	NOUN
ejpam-5641	20	5	:	:	PUNCT
ejpam-5641	20	6	non	non	ADJ
ejpam-5641	20	7	-	-	ADJ
ejpam-5641	20	8	absolute	absolute	ADJ
ejpam-5641	20	9	type	type	NOUN
ejpam-5641	20	10	.	.	PUNCT
ejpam-5641	21	1	(	(	PUNCT
ejpam-5641	21	2	ix	ix	PROPN
ejpam-5641	21	3	)	)	PUNCT
ejpam-5641	21	4	fp	fp	ADJ
ejpam-5641	21	5	:	:	PUNCT
ejpam-5641	21	6	fatou	fatou	PROPN
ejpam-5641	21	7	property	property	NOUN
ejpam-5641	21	8	.	.	PUNCT
ejpam-5641	22	1	(	(	PUNCT
ejpam-5641	22	2	x	x	X
ejpam-5641	22	3	)	)	PUNCT
ejpam-5641	22	4	ntk-∥.∥p−qn	ntk-∥.∥p−qn	NOUN
ejpam-5641	22	5	-	-	SYM
ejpam-5641	22	6	c	c	NOUN
ejpam-5641	22	7	:	:	PUNCT
ejpam-5641	22	8	new	new	ADJ
ejpam-5641	22	9	type	type	NOUN
ejpam-5641	22	10	of	of	ADP
ejpam-5641	22	11	kannan	kannan	PROPN
ejpam-5641	22	12	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	22	13	-contraction	-contraction	PROPN
ejpam-5641	22	14	.	.	PUNCT
ejpam-5641	23	1	(	(	PUNCT
ejpam-5641	23	2	xi	xi	X
ejpam-5641	23	3	)	)	PUNCT
ejpam-5641	23	4	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	23	5	-	-	PUNCT
ejpam-5641	23	6	seq.c	seq.c	PROPN
ejpam-5641	23	7	:	:	PUNCT
ejpam-5641	23	8	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	23	9	-sequentially	-sequentially	ADV
ejpam-5641	23	10	continuous	continuous	ADJ
ejpam-5641	23	11	.	.	PUNCT
ejpam-5641	24	1	(	(	PUNCT
ejpam-5641	24	2	xii	xii	NOUN
ejpam-5641	24	3	)	)	PUNCT
ejpam-5641	24	4	ufp	ufp	NOUN
ejpam-5641	24	5	:	:	PUNCT
ejpam-5641	24	6	unique	unique	ADJ
ejpam-5641	24	7	fixed	fix	VERB
ejpam-5641	24	8	point	point	NOUN
ejpam-5641	24	9	.	.	PUNCT
ejpam-5641	25	1	(	(	PUNCT
ejpam-5641	25	2	xiii	xiii	X
ejpam-5641	25	3	)	)	PUNCT
ejpam-5641	25	4	nldes	nlde	NOUN
ejpam-5641	25	5	:	:	PUNCT
ejpam-5641	25	6	non	non	ADJ
ejpam-5641	25	7	-	-	ADJ
ejpam-5641	25	8	linear	linear	ADJ
ejpam-5641	25	9	difference	difference	NOUN
ejpam-5641	25	10	equations	equation	NOUN
ejpam-5641	25	11	.	.	PUNCT
ejpam-5641	26	1	notations	notation	NOUN
ejpam-5641	26	2	(	(	PUNCT
ejpam-5641	26	3	i	i	NOUN
ejpam-5641	26	4	)	)	PUNCT
ejpam-5641	26	5	n	n	CCONJ
ejpam-5641	26	6	:	:	PUNCT
ejpam-5641	26	7	=	=	SYM
ejpam-5641	26	8	{	{	PUNCT
ejpam-5641	26	9	0	0	NUM
ejpam-5641	26	10	,	,	PUNCT
ejpam-5641	26	11	1	1	NUM
ejpam-5641	26	12	,	,	PUNCT
ejpam-5641	26	13	2	2	NUM
ejpam-5641	26	14	,	,	PUNCT
ejpam-5641	26	15	...	...	PUNCT
ejpam-5641	26	16	}	}	PUNCT
ejpam-5641	26	17	and	and	CCONJ
ejpam-5641	26	18	r	r	NOUN
ejpam-5641	26	19	is	be	AUX
ejpam-5641	26	20	the	the	DET
ejpam-5641	26	21	set	set	NOUN
ejpam-5641	26	22	of	of	ADP
ejpam-5641	26	23	real	real	ADJ
ejpam-5641	26	24	numbers	number	NOUN
ejpam-5641	26	25	.	.	PUNCT
ejpam-5641	27	1	(	(	PUNCT
ejpam-5641	27	2	ii	ii	NOUN
ejpam-5641	27	3	)	)	PUNCT
ejpam-5641	27	4	r+n	r+n	NOUN
ejpam-5641	27	5	:	:	PUNCT
ejpam-5641	27	6	the	the	DET
ejpam-5641	27	7	space	space	NOUN
ejpam-5641	27	8	of	of	ADP
ejpam-5641	27	9	all	all	DET
ejpam-5641	27	10	sequences	sequence	NOUN
ejpam-5641	27	11	of	of	ADP
ejpam-5641	27	12	positive	positive	ADJ
ejpam-5641	27	13	reals	real	NOUN
ejpam-5641	27	14	.	.	PUNCT
ejpam-5641	28	1	(	(	PUNCT
ejpam-5641	28	2	iii	iii	X
ejpam-5641	28	3	)	)	PUNCT
ejpam-5641	28	4	ℓm	ℓm	NOUN
ejpam-5641	28	5	,	,	PUNCT
ejpam-5641	28	6	ℓ∞	ℓ∞	PROPN
ejpam-5641	28	7	,	,	PUNCT
ejpam-5641	28	8	and	and	CCONJ
ejpam-5641	28	9	c0	c0	NOUN
ejpam-5641	28	10	:	:	PUNCT
ejpam-5641	28	11	the	the	DET
ejpam-5641	28	12	spaces	space	NOUN
ejpam-5641	28	13	of	of	ADP
ejpam-5641	28	14	m	m	NOUN
ejpam-5641	28	15	-	-	PUNCT
ejpam-5641	28	16	absolutely	absolutely	ADV
ejpam-5641	28	17	summable	summable	ADJ
ejpam-5641	28	18	,	,	PUNCT
ejpam-5641	28	19	bounded	bound	VERB
ejpam-5641	28	20	,	,	PUNCT
ejpam-5641	28	21	and	and	CCONJ
ejpam-5641	28	22	convergent	convergent	NOUN
ejpam-5641	28	23	to	to	ADP
ejpam-5641	28	24	zero	zero	NUM
ejpam-5641	28	25	sequences	sequence	NOUN
ejpam-5641	28	26	of	of	ADP
ejpam-5641	28	27	reals	real	NOUN
ejpam-5641	28	28	,	,	PUNCT
ejpam-5641	28	29	respectively	respectively	ADV
ejpam-5641	28	30	.	.	PUNCT
ejpam-5641	29	1	(	(	PUNCT
ejpam-5641	29	2	iv	iv	X
ejpam-5641	29	3	)	)	PUNCT
ejpam-5641	29	4	b(r	b(r	PROPN
ejpam-5641	29	5	)	)	PUNCT
ejpam-5641	29	6	and	and	CCONJ
ejpam-5641	29	7	e	e	NOUN
ejpam-5641	29	8	:	:	PUNCT
ejpam-5641	29	9	the	the	DET
ejpam-5641	29	10	collection	collection	NOUN
ejpam-5641	29	11	of	of	ADP
ejpam-5641	29	12	all	all	DET
ejpam-5641	29	13	nonempty	nonempty	ADV
ejpam-5641	29	14	bounded	bound	VERB
ejpam-5641	29	15	subsets	subset	NOUN
ejpam-5641	29	16	of	of	ADP
ejpam-5641	29	17	r	r	NOUN
ejpam-5641	29	18	and	and	CCONJ
ejpam-5641	29	19	the	the	DET
ejpam-5641	29	20	set	set	NOUN
ejpam-5641	29	21	of	of	ADP
ejpam-5641	29	22	parameters	parameter	NOUN
ejpam-5641	29	23	,	,	PUNCT
ejpam-5641	29	24	respectively	respectively	ADV
ejpam-5641	29	25	.	.	PUNCT
ejpam-5641	30	1	(	(	PUNCT
ejpam-5641	30	2	v	v	NOUN
ejpam-5641	30	3	)	)	PUNCT
ejpam-5641	30	4	r(a)∗	r(a)∗	NOUN
ejpam-5641	30	5	and	and	CCONJ
ejpam-5641	30	6	r(a	r(a	NUM
ejpam-5641	30	7	):	):	PUNCT
ejpam-5641	30	8	the	the	DET
ejpam-5641	30	9	set	set	NOUN
ejpam-5641	30	10	of	of	ADP
ejpam-5641	30	11	nonnegative	nonnegative	ADJ
ejpam-5641	30	12	and	and	CCONJ
ejpam-5641	30	13	all	all	DET
ejpam-5641	30	14	soft	soft	ADJ
ejpam-5641	30	15	real	real	ADJ
ejpam-5641	30	16	numbers	number	NOUN
ejpam-5641	30	17	(	(	PUNCT
ejpam-5641	30	18	corresponding	correspond	VERB
ejpam-5641	30	19	to	to	ADP
ejpam-5641	30	20	a	a	PRON
ejpam-5641	30	21	)	)	PUNCT
ejpam-5641	30	22	,	,	PUNCT
ejpam-5641	30	23	where	where	SCONJ
ejpam-5641	30	24	a	a	DET
ejpam-5641	30	25	⊂	⊂	PROPN
ejpam-5641	30	26	e	e	NOUN
ejpam-5641	30	27	,	,	PUNCT
ejpam-5641	30	28	respectively	respectively	ADV
ejpam-5641	30	29	.	.	PUNCT
ejpam-5641	31	1	(	(	PUNCT
ejpam-5641	31	2	vi	vi	NOUN
ejpam-5641	31	3	)	)	PUNCT
ejpam-5641	31	4	0̃	0̃	NOUN
ejpam-5641	31	5	and	and	CCONJ
ejpam-5641	31	6	1̃	1̃	NUM
ejpam-5641	31	7	:	:	PUNCT
ejpam-5641	31	8	the	the	DET
ejpam-5641	31	9	additive	additive	ADJ
ejpam-5641	31	10	identity	identity	NOUN
ejpam-5641	31	11	and	and	CCONJ
ejpam-5641	31	12	multiplicative	multiplicative	ADJ
ejpam-5641	31	13	identity	identity	NOUN
ejpam-5641	31	14	in	in	ADP
ejpam-5641	31	15	r(a	r(a	PROPN
ejpam-5641	31	16	)	)	PUNCT
ejpam-5641	31	17	,	,	PUNCT
ejpam-5641	31	18	respectively	respectively	ADV
ejpam-5641	31	19	,	,	PUNCT
ejpam-5641	31	20	see	see	VERB
ejpam-5641	31	21	[	[	X
ejpam-5641	31	22	6	6	NUM
ejpam-5641	31	23	]	]	PUNCT
ejpam-5641	31	24	.	.	PUNCT
ejpam-5641	32	1	(	(	PUNCT
ejpam-5641	32	2	vii	vii	PROPN
ejpam-5641	32	3	)	)	PUNCT
ejpam-5641	32	4	µs	µs	X
ejpam-5641	32	5	:	:	PUNCT
ejpam-5641	32	6	the	the	DET
ejpam-5641	32	7	space	space	NOUN
ejpam-5641	32	8	of	of	ADP
ejpam-5641	32	9	all	all	DET
ejpam-5641	32	10	sequences	sequence	NOUN
ejpam-5641	32	11	of	of	ADP
ejpam-5641	32	12	soft	soft	ADJ
ejpam-5641	32	13	reals	real	NOUN
ejpam-5641	32	14	.	.	PUNCT
ejpam-5641	33	1	(	(	PUNCT
ejpam-5641	33	2	viii	viii	NOUN
ejpam-5641	33	3	)	)	PUNCT
ejpam-5641	33	4	g	g	NOUN
ejpam-5641	33	5	,	,	PUNCT
ejpam-5641	33	6	v	v	NOUN
ejpam-5641	33	7	:	:	PUNCT
ejpam-5641	33	8	infinite	infinite	ADJ
ejpam-5641	33	9	dimensional	dimensional	ADJ
ejpam-5641	33	10	banach	banach	NOUN
ejpam-5641	33	11	spaces	space	NOUN
ejpam-5641	33	12	.	.	PUNCT
ejpam-5641	34	1	(	(	PUNCT
ejpam-5641	34	2	ix	ix	INTJ
ejpam-5641	34	3	)	)	PUNCT
ejpam-5641	34	4	es	es	NOUN
ejpam-5641	34	5	:	:	PUNCT
ejpam-5641	34	6	the	the	DET
ejpam-5641	34	7	linear	linear	ADJ
ejpam-5641	34	8	space	space	NOUN
ejpam-5641	34	9	of	of	ADP
ejpam-5641	34	10	sequences	sequence	NOUN
ejpam-5641	34	11	of	of	ADP
ejpam-5641	34	12	soft	soft	ADJ
ejpam-5641	34	13	functions	function	NOUN
ejpam-5641	34	14	.	.	PUNCT
ejpam-5641	35	1	(	(	PUNCT
ejpam-5641	35	2	x	x	X
ejpam-5641	35	3	)	)	PUNCT
ejpam-5641	35	4	êd	êd	PROPN
ejpam-5641	35	5	:	:	PUNCT
ejpam-5641	35	6	=	=	SYM
ejpam-5641	35	7	(	(	PUNCT
ejpam-5641	35	8	0̂	0̂	PROPN
ejpam-5641	35	9	,	,	PUNCT
ejpam-5641	35	10	0̂	0̂	PROPN
ejpam-5641	35	11	,	,	PUNCT
ejpam-5641	35	12	...	...	PUNCT
ejpam-5641	35	13	,	,	PUNCT
ejpam-5641	35	14	1̂	1̂	NUM
ejpam-5641	35	15	,	,	PUNCT
ejpam-5641	35	16	0̂	0̂	PROPN
ejpam-5641	35	17	,	,	PUNCT
ejpam-5641	35	18	0̂	0̂	PROPN
ejpam-5641	35	19	,	,	PUNCT
ejpam-5641	35	20	·	·	PUNCT
ejpam-5641	35	21	·	·	PUNCT
ejpam-5641	35	22	·	·	PUNCT
ejpam-5641	35	23	)	)	PUNCT
ejpam-5641	35	24	,	,	PUNCT
ejpam-5641	35	25	while	while	SCONJ
ejpam-5641	35	26	1̂	1̂	NUM
ejpam-5641	35	27	displays	display	NOUN
ejpam-5641	35	28	at	at	ADP
ejpam-5641	35	29	the	the	DET
ejpam-5641	35	30	dth	dth	ADJ
ejpam-5641	35	31	place	place	NOUN
ejpam-5641	35	32	.	.	PUNCT
ejpam-5641	36	1	(	(	PUNCT
ejpam-5641	36	2	xi	xi	X
ejpam-5641	36	3	)	)	PUNCT
ejpam-5641	37	1	[	[	X
ejpam-5641	37	2	d	d	X
ejpam-5641	37	3	]	]	X
ejpam-5641	37	4	:	:	PUNCT
ejpam-5641	37	5	the	the	DET
ejpam-5641	37	6	integral	integral	ADJ
ejpam-5641	37	7	part	part	NOUN
ejpam-5641	37	8	of	of	ADP
ejpam-5641	37	9	real	real	ADJ
ejpam-5641	37	10	number	number	NOUN
ejpam-5641	37	11	d.	d.	NOUN
ejpam-5641	37	12	(	(	PUNCT
ejpam-5641	37	13	xii	xii	PROPN
ejpam-5641	37	14	)	)	PUNCT
ejpam-5641	37	15	ϑ̂	ϑ̂	ADV
ejpam-5641	37	16	:	:	PUNCT
ejpam-5641	37	17	=	=	SYM
ejpam-5641	37	18	(	(	PUNCT
ejpam-5641	37	19	0̂	0̂	PROPN
ejpam-5641	37	20	,	,	PUNCT
ejpam-5641	37	21	0̂	0̂	PROPN
ejpam-5641	37	22	,	,	PUNCT
ejpam-5641	37	23	0̂	0̂	PROPN
ejpam-5641	37	24	,	,	PUNCT
ejpam-5641	37	25	.	.	PUNCT
ejpam-5641	37	26	.	.	PUNCT
ejpam-5641	37	27	.	.	PUNCT
ejpam-5641	37	28	)	)	PUNCT
ejpam-5641	37	29	.	.	PUNCT
ejpam-5641	38	1	m.	m.	NOUN
ejpam-5641	38	2	m.	m.	PROPN
ejpam-5641	38	3	a	a	PRON
ejpam-5641	38	4	et	et	PROPN
ejpam-5641	38	5	al	al	PROPN
ejpam-5641	38	6	.	.	PUNCT
ejpam-5641	38	7	/	/	SYM
ejpam-5641	38	8	eur	eur	PROPN
ejpam-5641	38	9	.	.	PUNCT
ejpam-5641	39	1	j.	j.	PROPN
ejpam-5641	39	2	pure	pure	PROPN
ejpam-5641	39	3	appl	appl	PROPN
ejpam-5641	39	4	.	.	PROPN
ejpam-5641	39	5	math	math	PROPN
ejpam-5641	39	6	,	,	PUNCT
ejpam-5641	39	7	18	18	NUM
ejpam-5641	39	8	(	(	PUNCT
ejpam-5641	39	9	1	1	NUM
ejpam-5641	39	10	)	)	PUNCT
ejpam-5641	39	11	(	(	PUNCT
ejpam-5641	39	12	2025	2025	NUM
ejpam-5641	39	13	)	)	PUNCT
ejpam-5641	39	14	,	,	PUNCT
ejpam-5641	39	15	5641	5641	NUM
ejpam-5641	39	16	3	3	NUM
ejpam-5641	39	17	of	of	ADP
ejpam-5641	39	18	20	20	NUM
ejpam-5641	39	19	(	(	PUNCT
ejpam-5641	39	20	xiii	xiii	PROPN
ejpam-5641	39	21	)	)	PUNCT
ejpam-5641	39	22	f	f	NOUN
ejpam-5641	39	23	:	:	PUNCT
ejpam-5641	39	24	the	the	DET
ejpam-5641	39	25	space	space	NOUN
ejpam-5641	39	26	of	of	ADP
ejpam-5641	39	27	finite	finite	ADJ
ejpam-5641	39	28	sequences	sequence	NOUN
ejpam-5641	39	29	of	of	ADP
ejpam-5641	39	30	soft	soft	ADJ
ejpam-5641	39	31	numbers	number	NOUN
ejpam-5641	39	32	.	.	PUNCT
ejpam-5641	40	1	(	(	PUNCT
ejpam-5641	40	2	xiv	xiv	PROPN
ejpam-5641	40	3	)	)	PUNCT
ejpam-5641	40	4	n+	n+	PUNCT
ejpam-5641	40	5	and	and	CCONJ
ejpam-5641	40	6	d−	d−	PROPN
ejpam-5641	40	7	:	:	PUNCT
ejpam-5641	40	8	the	the	DET
ejpam-5641	40	9	space	space	NOUN
ejpam-5641	40	10	of	of	ADP
ejpam-5641	40	11	all	all	DET
ejpam-5641	40	12	monotonic	monotonic	ADJ
ejpam-5641	40	13	increasing	increase	VERB
ejpam-5641	40	14	and	and	CCONJ
ejpam-5641	40	15	decreasing	decrease	VERB
ejpam-5641	40	16	sequences	sequence	NOUN
ejpam-5641	40	17	of	of	ADP
ejpam-5641	40	18	positive	positive	ADJ
ejpam-5641	40	19	reals	real	NOUN
ejpam-5641	40	20	,	,	PUNCT
ejpam-5641	40	21	respectively	respectively	ADV
ejpam-5641	40	22	.	.	PUNCT
ejpam-5641	41	1	(	(	PUNCT
ejpam-5641	41	2	xv	xv	PROPN
ejpam-5641	41	3	)	)	PUNCT
ejpam-5641	41	4	ir	ir	PROPN
ejpam-5641	41	5	:	:	PUNCT
ejpam-5641	41	6	the	the	DET
ejpam-5641	41	7	identity	identity	NOUN
ejpam-5641	41	8	mapping	mapping	NOUN
ejpam-5641	41	9	on	on	ADP
ejpam-5641	41	10	ℓd2	ℓd2	PROPN
ejpam-5641	41	11	.	.	PUNCT
ejpam-5641	42	1	(	(	PUNCT
ejpam-5641	42	2	xvi	xvi	NOUN
ejpam-5641	42	3	)	)	PUNCT
ejpam-5641	42	4	jr	jr	PROPN
ejpam-5641	42	5	:	:	PUNCT
ejpam-5641	42	6	the	the	DET
ejpam-5641	42	7	natural	natural	ADJ
ejpam-5641	42	8	embedding	embed	VERB
ejpam-5641	42	9	mapping	mapping	NOUN
ejpam-5641	42	10	from	from	ADP
ejpam-5641	42	11	mr	mr	PROPN
ejpam-5641	42	12	into	into	ADP
ejpam-5641	42	13	v.	v.	PROPN
ejpam-5641	42	14	(	(	PUNCT
ejpam-5641	42	15	xvii	xvii	PROPN
ejpam-5641	42	16	)	)	PUNCT
ejpam-5641	42	17	tr	tr	VERB
ejpam-5641	42	18	:	:	PUNCT
ejpam-5641	42	19	the	the	DET
ejpam-5641	42	20	quotient	quotient	NOUN
ejpam-5641	42	21	mapping	mapping	NOUN
ejpam-5641	42	22	from	from	ADP
ejpam-5641	42	23	g	g	PRON
ejpam-5641	42	24	onto	onto	ADP
ejpam-5641	42	25	g	g	PROPN
ejpam-5641	42	26	/	/	SYM
ejpam-5641	42	27	yr	yr	NOUN
ejpam-5641	42	28	.	.	PUNCT
ejpam-5641	43	1	(	(	PUNCT
ejpam-5641	43	2	xviii	xviii	PROPN
ejpam-5641	43	3	)	)	PUNCT
ejpam-5641	43	4	dvoretzky	dvoretzky	PROPN
ejpam-5641	43	5	’s	’s	PART
ejpam-5641	43	6	theorem	theorem	NOUN
ejpam-5641	43	7	[	[	X
ejpam-5641	43	8	19	19	NUM
ejpam-5641	43	9	]	]	X
ejpam-5641	43	10	:	:	PUNCT
ejpam-5641	43	11	for	for	ADP
ejpam-5641	43	12	any	any	DET
ejpam-5641	43	13	d	d	PROPN
ejpam-5641	43	14	∈	∈	PROPN
ejpam-5641	43	15	n	n	X
ejpam-5641	43	16	,	,	PUNCT
ejpam-5641	43	17	we	we	PRON
ejpam-5641	43	18	have	have	VERB
ejpam-5641	43	19	quotient	quotient	NOUN
ejpam-5641	43	20	spaces	space	NOUN
ejpam-5641	43	21	g	g	NOUN
ejpam-5641	43	22	/	/	SYM
ejpam-5641	43	23	yd	yd	NOUN
ejpam-5641	43	24	and	and	CCONJ
ejpam-5641	43	25	subspaces	subspace	NOUN
ejpam-5641	43	26	md	md	PROPN
ejpam-5641	43	27	of	of	ADP
ejpam-5641	43	28	v	v	ADP
ejpam-5641	43	29	which	which	PRON
ejpam-5641	43	30	can	can	AUX
ejpam-5641	43	31	be	be	AUX
ejpam-5641	43	32	transformed	transform	VERB
ejpam-5641	43	33	onto	onto	ADP
ejpam-5641	43	34	ℓd2	ℓd2	NOUN
ejpam-5641	43	35	by	by	ADP
ejpam-5641	43	36	isomorphisms	isomorphism	NOUN
ejpam-5641	43	37	vd	vd	NOUN
ejpam-5641	43	38	and	and	CCONJ
ejpam-5641	43	39	xd	xd	INTJ
ejpam-5641	43	40	such	such	ADJ
ejpam-5641	43	41	that	that	PRON
ejpam-5641	43	42	∥wd∥∥w−1	∥wd∥∥w−1	PUNCT
ejpam-5641	44	1	d	d	X
ejpam-5641	44	2	∥	∥	PUNCT
ejpam-5641	44	3	≤	≤	NUM
ejpam-5641	44	4	2	2	NUM
ejpam-5641	44	5	and	and	CCONJ
ejpam-5641	44	6	∥xd∥∥x−1	∥xd∥∥x−1	NUM
ejpam-5641	44	7	d	d	NOUN
ejpam-5641	44	8	∥	∥	PUNCT
ejpam-5641	44	9	≤	≤	NUM
ejpam-5641	44	10	2	2	NUM
ejpam-5641	44	11	.	.	NOUN
ejpam-5641	44	12	1	1	NUM
ejpam-5641	44	13	.	.	X
ejpam-5641	44	14	introduction	introduction	NOUN
ejpam-5641	44	15	the	the	DET
ejpam-5641	44	16	ability	ability	NOUN
ejpam-5641	44	17	to	to	PART
ejpam-5641	44	18	mathematically	mathematically	ADV
ejpam-5641	44	19	simulate	simulate	VERB
ejpam-5641	44	20	non	non	ADJ
ejpam-5641	44	21	-	-	ADJ
ejpam-5641	44	22	newtonian	newtonian	ADJ
ejpam-5641	44	23	fluids	fluid	NOUN
ejpam-5641	44	24	in	in	ADP
ejpam-5641	44	25	hydrodynamics	hydrodynamic	NOUN
ejpam-5641	44	26	is	be	AUX
ejpam-5641	44	27	drawing	draw	VERB
ejpam-5641	44	28	more	more	ADJ
ejpam-5641	44	29	and	and	CCONJ
ejpam-5641	44	30	more	more	ADJ
ejpam-5641	44	31	attention	attention	NOUN
ejpam-5641	44	32	to	to	ADP
ejpam-5641	44	33	the	the	DET
ejpam-5641	44	34	study	study	NOUN
ejpam-5641	44	35	of	of	ADP
ejpam-5641	44	36	variable	variable	ADJ
ejpam-5641	44	37	exponent	exponent	NOUN
ejpam-5641	44	38	lebesgue	lebesgue	NOUN
ejpam-5641	44	39	spaces	space	NOUN
ejpam-5641	44	40	,	,	PUNCT
ejpam-5641	44	41	as	as	SCONJ
ejpam-5641	44	42	discussed	discuss	VERB
ejpam-5641	44	43	by	by	ADP
ejpam-5641	44	44	ruẑiĉka	ruẑiĉka	NOUN
ejpam-5641	44	45	[	[	X
ejpam-5641	44	46	20	20	NUM
ejpam-5641	44	47	]	]	PUNCT
ejpam-5641	44	48	.	.	PUNCT
ejpam-5641	45	1	a	a	DET
ejpam-5641	45	2	variety	variety	NOUN
ejpam-5641	45	3	of	of	ADP
ejpam-5641	45	4	disciplines	discipline	NOUN
ejpam-5641	45	5	,	,	PUNCT
ejpam-5641	45	6	including	include	VERB
ejpam-5641	45	7	orthopedics	orthopedic	NOUN
ejpam-5641	45	8	,	,	PUNCT
ejpam-5641	45	9	civil	civil	ADJ
ejpam-5641	45	10	engineering	engineering	NOUN
ejpam-5641	45	11	,	,	PUNCT
ejpam-5641	45	12	and	and	CCONJ
ejpam-5641	45	13	military	military	ADJ
ejpam-5641	45	14	science	science	NOUN
ejpam-5641	45	15	,	,	PUNCT
ejpam-5641	45	16	make	make	VERB
ejpam-5641	45	17	use	use	NOUN
ejpam-5641	45	18	of	of	ADP
ejpam-5641	45	19	electrorheological	electrorheological	ADJ
ejpam-5641	45	20	fluids	fluid	NOUN
ejpam-5641	45	21	,	,	PUNCT
ejpam-5641	45	22	a	a	DET
ejpam-5641	45	23	class	class	NOUN
ejpam-5641	45	24	of	of	ADP
ejpam-5641	45	25	non	non	ADJ
ejpam-5641	45	26	-	-	ADJ
ejpam-5641	45	27	newtonian	newtonian	ADJ
ejpam-5641	45	28	fluids	fluid	NOUN
ejpam-5641	45	29	.	.	PUNCT
ejpam-5641	46	1	the	the	DET
ejpam-5641	46	2	work	work	NOUN
ejpam-5641	46	3	of	of	ADP
ejpam-5641	46	4	diening	diene	VERB
ejpam-5641	46	5	et	et	PROPN
ejpam-5641	46	6	al	al	PROPN
ejpam-5641	46	7	.	.	PUNCT
ejpam-5641	47	1	[	[	X
ejpam-5641	47	2	7	7	X
ejpam-5641	47	3	]	]	PUNCT
ejpam-5641	47	4	covered	cover	VERB
ejpam-5641	47	5	the	the	DET
ejpam-5641	47	6	topic	topic	NOUN
ejpam-5641	47	7	of	of	ADP
ejpam-5641	47	8	lebesgue	lebesgue	NOUN
ejpam-5641	47	9	and	and	CCONJ
ejpam-5641	47	10	sobolev	sobolev	NOUN
ejpam-5641	47	11	spaces	space	NOUN
ejpam-5641	47	12	involving	involve	VERB
ejpam-5641	47	13	variable	variable	ADJ
ejpam-5641	47	14	exponents	exponent	NOUN
ejpam-5641	47	15	.	.	PUNCT
ejpam-5641	48	1	a	a	DET
ejpam-5641	48	2	particular	particular	ADJ
ejpam-5641	48	3	sequence	sequence	NOUN
ejpam-5641	48	4	space	space	NOUN
ejpam-5641	48	5	contains	contain	VERB
ejpam-5641	48	6	the	the	DET
ejpam-5641	48	7	solutions	solution	NOUN
ejpam-5641	48	8	of	of	ADP
ejpam-5641	48	9	discrete	discrete	ADJ
ejpam-5641	48	10	dynamical	dynamical	ADJ
ejpam-5641	48	11	systems	system	NOUN
ejpam-5641	48	12	.	.	PUNCT
ejpam-5641	49	1	according	accord	VERB
ejpam-5641	49	2	to	to	ADP
ejpam-5641	49	3	[	[	X
ejpam-5641	49	4	16	16	NUM
ejpam-5641	49	5	]	]	PUNCT
ejpam-5641	49	6	,	,	PUNCT
ejpam-5641	49	7	the	the	DET
ejpam-5641	49	8	construction	construction	NOUN
ejpam-5641	49	9	of	of	ADP
ejpam-5641	49	10	new	new	ADJ
ejpam-5641	49	11	sequence	sequence	NOUN
ejpam-5641	49	12	spaces	space	NOUN
ejpam-5641	49	13	is	be	AUX
ejpam-5641	49	14	a	a	DET
ejpam-5641	49	15	subject	subject	NOUN
ejpam-5641	49	16	of	of	ADP
ejpam-5641	49	17	significant	significant	ADJ
ejpam-5641	49	18	mathematical	mathematical	ADJ
ejpam-5641	49	19	interest	interest	NOUN
ejpam-5641	49	20	.	.	PUNCT
ejpam-5641	50	1	the	the	DET
ejpam-5641	50	2	domain	domain	NOUN
ejpam-5641	50	3	of	of	ADP
ejpam-5641	50	4	the	the	DET
ejpam-5641	50	5	cesàro	cesàro	NOUN
ejpam-5641	50	6	mean	mean	NOUN
ejpam-5641	50	7	of	of	ADP
ejpam-5641	50	8	order	order	NOUN
ejpam-5641	50	9	one	one	NUM
ejpam-5641	50	10	in	in	ADP
ejpam-5641	50	11	certain	certain	ADJ
ejpam-5641	50	12	spaces	space	NOUN
ejpam-5641	50	13	of	of	ADP
ejpam-5641	50	14	double	double	ADJ
ejpam-5641	50	15	sequences	sequence	NOUN
ejpam-5641	50	16	was	be	AUX
ejpam-5641	50	17	developed	develop	VERB
ejpam-5641	50	18	and	and	CCONJ
ejpam-5641	50	19	studied	study	VERB
ejpam-5641	50	20	by	by	ADP
ejpam-5641	50	21	mursaleen	mursaleen	NOUN
ejpam-5641	50	22	and	and	CCONJ
ejpam-5641	50	23	başar	başar	PROPN
ejpam-5641	51	1	[	[	X
ejpam-5641	51	2	15	15	NUM
ejpam-5641	51	3	]	]	PUNCT
ejpam-5641	51	4	,	,	PUNCT
ejpam-5641	51	5	while	while	SCONJ
ejpam-5641	51	6	noman	noman	PROPN
ejpam-5641	51	7	and	and	CCONJ
ejpam-5641	51	8	mursaleen	mursaleen	PROPN
ejpam-5641	52	1	[	[	X
ejpam-5641	52	2	17	17	NUM
ejpam-5641	52	3	]	]	PUNCT
ejpam-5641	52	4	investigated	investigate	VERB
ejpam-5641	52	5	novel	novel	ADJ
ejpam-5641	52	6	non	non	ADJ
ejpam-5641	52	7	-	-	ADJ
ejpam-5641	52	8	absolute	absolute	ADJ
ejpam-5641	52	9	sequence	sequence	NOUN
ejpam-5641	52	10	spaces	space	NOUN
ejpam-5641	52	11	that	that	PRON
ejpam-5641	52	12	are	be	AUX
ejpam-5641	52	13	connected	connect	VERB
ejpam-5641	52	14	to	to	ADP
ejpam-5641	52	15	ℓp	ℓp	NOUN
ejpam-5641	52	16	and	and	CCONJ
ejpam-5641	52	17	ℓ∞.	ℓ∞.	ADP
ejpam-5641	52	18	the	the	DET
ejpam-5641	52	19	notion	notion	NOUN
ejpam-5641	52	20	of	of	ADP
ejpam-5641	52	21	psssf	psssf	NOUN
ejpam-5641	52	22	was	be	AUX
ejpam-5641	52	23	first	first	ADV
ejpam-5641	52	24	proposed	propose	VERB
ejpam-5641	52	25	by	by	ADP
ejpam-5641	52	26	alsolmi	alsolmi	NOUN
ejpam-5641	52	27	and	and	CCONJ
ejpam-5641	52	28	bakery	bakery	NOUN
ejpam-5641	53	1	[	[	X
ejpam-5641	53	2	4	4	NUM
ejpam-5641	53	3	]	]	PUNCT
ejpam-5641	53	4	.	.	PUNCT
ejpam-5641	54	1	in	in	ADP
ejpam-5641	54	2	[	[	X
ejpam-5641	54	3	14	14	NUM
ejpam-5641	54	4	]	]	PUNCT
ejpam-5641	54	5	,	,	PUNCT
ejpam-5641	54	6	the	the	DET
ejpam-5641	54	7	researchers	researcher	NOUN
ejpam-5641	54	8	examined	examine	VERB
ejpam-5641	54	9	the	the	DET
ejpam-5641	54	10	distinctiveness	distinctiveness	NOUN
ejpam-5641	54	11	and	and	CCONJ
ejpam-5641	54	12	presence	presence	NOUN
ejpam-5641	54	13	of	of	ADP
ejpam-5641	54	14	solutions	solution	NOUN
ejpam-5641	54	15	inside	inside	ADP
ejpam-5641	54	16	a	a	DET
ejpam-5641	54	17	novel	novel	ADJ
ejpam-5641	54	18	complex	complex	ADJ
ejpam-5641	54	19	function	function	NOUN
ejpam-5641	54	20	space	space	NOUN
ejpam-5641	54	21	for	for	ADP
ejpam-5641	54	22	kannan	kannan	PROPN
ejpam-5641	54	23	nonlinear	nonlinear	ADJ
ejpam-5641	54	24	dynamical	dynamical	ADJ
ejpam-5641	54	25	systems	system	NOUN
ejpam-5641	54	26	.	.	PUNCT
ejpam-5641	55	1	supposing	suppose	VERB
ejpam-5641	55	2	that	that	PRON
ejpam-5641	55	3	(	(	PUNCT
ejpam-5641	55	4	fk	fk	INTJ
ejpam-5641	55	5	)	)	PUNCT
ejpam-5641	55	6	∞	∞	PROPN
ejpam-5641	55	7	k=0	k=0	PROPN
ejpam-5641	55	8	is	be	AUX
ejpam-5641	55	9	the	the	DET
ejpam-5641	55	10	sequence	sequence	NOUN
ejpam-5641	55	11	of	of	ADP
ejpam-5641	55	12	fibonacci	fibonacci	NOUN
ejpam-5641	55	13	numbers	number	NOUN
ejpam-5641	55	14	defined	define	VERB
ejpam-5641	55	15	by	by	ADP
ejpam-5641	55	16	the	the	DET
ejpam-5641	55	17	recurrence	recurrence	NOUN
ejpam-5641	55	18	relation	relation	NOUN
ejpam-5641	55	19	fv	fv	PROPN
ejpam-5641	56	1	=	=	SYM
ejpam-5641	56	2	fv−1	fv−1	PROPN
ejpam-5641	56	3	+	+	CCONJ
ejpam-5641	56	4	fv−2	fv−2	PROPN
ejpam-5641	56	5	,	,	PUNCT
ejpam-5641	56	6	v	v	PRON
ejpam-5641	56	7	≥	≥	NOUN
ejpam-5641	56	8	2	2	NUM
ejpam-5641	56	9	,	,	PUNCT
ejpam-5641	56	10	so	so	SCONJ
ejpam-5641	57	1	that	that	SCONJ
ejpam-5641	57	2	f0	f0	PROPN
ejpam-5641	57	3	=	=	SYM
ejpam-5641	57	4	1	1	NUM
ejpam-5641	57	5	and	and	CCONJ
ejpam-5641	57	6	f1	f1	NOUN
ejpam-5641	57	7	=	=	SYM
ejpam-5641	57	8	1	1	X
ejpam-5641	57	9	.	.	X
ejpam-5641	57	10	note	note	VERB
ejpam-5641	57	11	that	that	SCONJ
ejpam-5641	57	12	in	in	ADP
ejpam-5641	57	13	[	[	X
ejpam-5641	57	14	12	12	NUM
ejpam-5641	57	15	]	]	PUNCT
ejpam-5641	57	16	that	that	SCONJ
ejpam-5641	57	17	∑l	∑l	VERB
ejpam-5641	57	18	z=0	z=0	NUM
ejpam-5641	57	19	f	f	NOUN
ejpam-5641	57	20	2	2	NUM
ejpam-5641	57	21	z	z	NOUN
ejpam-5641	57	22	=	=	SYM
ejpam-5641	57	23	flfl+1	flfl+1	PROPN
ejpam-5641	57	24	,	,	PUNCT
ejpam-5641	57	25	and	and	CCONJ
ejpam-5641	57	26	∑∞	∑∞	NOUN
ejpam-5641	57	27	z=0	z=0	NUM
ejpam-5641	57	28	1	1	NUM
ejpam-5641	57	29	fz	fz	VERB
ejpam-5641	57	30	<	<	X
ejpam-5641	57	31	∞.	∞.	PROPN
ejpam-5641	57	32	kara	kara	NOUN
ejpam-5641	57	33	and	and	CCONJ
ejpam-5641	57	34	başarır	başarır	ADJ
ejpam-5641	57	35	further	far	ADV
ejpam-5641	57	36	strengthen	strengthen	VERB
ejpam-5641	57	37	the	the	DET
ejpam-5641	57	38	studies	study	NOUN
ejpam-5641	57	39	on	on	ADP
ejpam-5641	57	40	fibonacci	fibonacci	NOUN
ejpam-5641	57	41	sequence	sequence	NOUN
ejpam-5641	57	42	spaces	space	VERB
ejpam-5641	57	43	[	[	X
ejpam-5641	57	44	11	11	NUM
ejpam-5641	57	45	]	]	PUNCT
ejpam-5641	57	46	.	.	PUNCT
ejpam-5641	58	1	they	they	PRON
ejpam-5641	58	2	defined	define	VERB
ejpam-5641	58	3	and	and	CCONJ
ejpam-5641	58	4	studied	study	VERB
ejpam-5641	58	5	the	the	DET
ejpam-5641	58	6	matrix	matrix	NOUN
ejpam-5641	58	7	domains	domain	NOUN
ejpam-5641	58	8	ℓp(γf	ℓp(γf	NOUN
ejpam-5641	58	9	)	)	PUNCT
ejpam-5641	58	10	:	:	PUNCT
ejpam-5641	59	1	=	=	SYM
ejpam-5641	59	2	(	(	PUNCT
ejpam-5641	59	3	ℓp)γf	ℓp)γf	PUNCT
ejpam-5641	59	4	,	,	PUNCT
ejpam-5641	59	5	c0(γf	c0(γf	PROPN
ejpam-5641	59	6	)	)	PUNCT
ejpam-5641	59	7	:	:	PUNCT
ejpam-5641	59	8	=	=	SYM
ejpam-5641	59	9	(	(	PUNCT
ejpam-5641	59	10	c0)γf	c0)γf	PROPN
ejpam-5641	59	11	,	,	PUNCT
ejpam-5641	59	12	c(γf	c(γf	NUM
ejpam-5641	59	13	)	)	PUNCT
ejpam-5641	59	14	:	:	PUNCT
ejpam-5641	60	1	=	=	SYM
ejpam-5641	60	2	(	(	PUNCT
ejpam-5641	60	3	c)γf	c)γf	PROPN
ejpam-5641	60	4	and	and	CCONJ
ejpam-5641	60	5	ℓ∞(γf	ℓ∞(γf	NOUN
ejpam-5641	60	6	)	)	PUNCT
ejpam-5641	60	7	:	:	PUNCT
ejpam-5641	61	1	=	=	SYM
ejpam-5641	61	2	(	(	PUNCT
ejpam-5641	61	3	ℓ∞)γf	ℓ∞)γf	PROPN
ejpam-5641	61	4	.	.	PUNCT
ejpam-5641	61	5	assume	assume	VERB
ejpam-5641	61	6	that	that	SCONJ
ejpam-5641	61	7	(	(	PUNCT
ejpam-5641	61	8	tl	tl	PROPN
ejpam-5641	61	9	)	)	PUNCT
ejpam-5641	61	10	,	,	PUNCT
ejpam-5641	61	11	(	(	PUNCT
ejpam-5641	61	12	ql	ql	X
ejpam-5641	61	13	)	)	PUNCT
ejpam-5641	61	14	∈	∈	PROPN
ejpam-5641	61	15	r+n	r+n	PROPN
ejpam-5641	61	16	.	.	PUNCT
ejpam-5641	62	1	we	we	PRON
ejpam-5641	62	2	have	have	AUX
ejpam-5641	62	3	presented	present	VERB
ejpam-5641	62	4	a	a	DET
ejpam-5641	62	5	novel	novel	ADJ
ejpam-5641	62	6	stochastic	stochastic	ADJ
ejpam-5641	62	7	space	space	NOUN
ejpam-5641	62	8	(	(	PUNCT
ejpam-5641	62	9	γsf	γsf	X
ejpam-5641	62	10	(	(	PUNCT
ejpam-5641	62	11	q	q	NOUN
ejpam-5641	62	12	,	,	PUNCT
ejpam-5641	62	13	t	t	PROPN
ejpam-5641	62	14	)	)	PUNCT
ejpam-5641	62	15	)	)	PUNCT
ejpam-5641	63	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	63	2	of	of	ADP
ejpam-5641	63	3	soft	soft	ADJ
ejpam-5641	63	4	functions	function	NOUN
ejpam-5641	63	5	as	as	ADP
ejpam-5641	63	6	:(	:(	PUNCT
ejpam-5641	63	7	γsf	γsf	X
ejpam-5641	63	8	(	(	PUNCT
ejpam-5641	63	9	q	q	NOUN
ejpam-5641	63	10	,	,	PUNCT
ejpam-5641	63	11	t	t	PROPN
ejpam-5641	63	12	)	)	PUNCT
ejpam-5641	63	13	)	)	PUNCT
ejpam-5641	64	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	64	2	:	:	PUNCT
ejpam-5641	64	3	=	=	PRON
ejpam-5641	64	4	{	{	PUNCT
ejpam-5641	64	5	d̂	d̂	PROPN
ejpam-5641	64	6	=	=	SYM
ejpam-5641	64	7	(	(	PUNCT
ejpam-5641	64	8	d̂b	d̂b	PROPN
ejpam-5641	64	9	)	)	PUNCT
ejpam-5641	64	10	∈	∈	PROPN
ejpam-5641	64	11	µs	µs	NOUN
ejpam-5641	64	12	:	:	PUNCT
ejpam-5641	64	13	∥δd̂∥p−qn	∥δd̂∥p−qn	PROPN
ejpam-5641	64	14	<	<	X
ejpam-5641	64	15	∞	∞	PROPN
ejpam-5641	64	16	,	,	PUNCT
ejpam-5641	64	17	for	for	ADP
ejpam-5641	64	18	some	some	DET
ejpam-5641	64	19	δ	δ	PROPN
ejpam-5641	64	20	>	>	X
ejpam-5641	64	21	0	0	NUM
ejpam-5641	64	22	}	}	PUNCT
ejpam-5641	64	23	,	,	PUNCT
ejpam-5641	64	24	where	where	SCONJ
ejpam-5641	64	25	∥d̂∥p−qn	∥d̂∥p−qn	NOUN
ejpam-5641	64	26	=	=	PUNCT
ejpam-5641	64	27	∑	∑	PUNCT
ejpam-5641	64	28	l∈n	l∈n	ADP
ejpam-5641	64	29			PROPN
ejpam-5641	64	30	ℏ̂	ℏ̂	NUM
ejpam-5641	64	31	(	(	PUNCT
ejpam-5641	64	32	∑l	∑l	INTJ
ejpam-5641	64	33	z=0	z=0	NUM
ejpam-5641	64	34	f	f	NOUN
ejpam-5641	64	35	2	2	NUM
ejpam-5641	64	36	zqzd̂z	zqzd̂z	NOUN
ejpam-5641	64	37	,	,	PUNCT
ejpam-5641	64	38	0̂	0̂	PROPN
ejpam-5641	64	39	)	)	PUNCT
ejpam-5641	65	1	flfl+1	flfl+1	PROPN
ejpam-5641	65	2	tl	tl	PROPN
ejpam-5641	65	3	,	,	PUNCT
ejpam-5641	65	4	ℏ	ℏ	PROPN
ejpam-5641	65	5	:	:	PUNCT
ejpam-5641	65	6	r(a)×r(a	r(a)×r(a	NUM
ejpam-5641	65	7	)	)	PUNCT
ejpam-5641	65	8	→	→	SYM
ejpam-5641	65	9	r(a)∗	r(a)∗	PROPN
ejpam-5641	65	10	,	,	PUNCT
ejpam-5641	65	11	with	with	ADP
ejpam-5641	65	12	ℏ(f̂	ℏ(f̂	PROPN
ejpam-5641	65	13	,	,	PUNCT
ejpam-5641	65	14	ĝ	ĝ	X
ejpam-5641	65	15	)	)	PUNCT
ejpam-5641	65	16	=	=	PUNCT
ejpam-5641	65	17	|f̂	|f̂	ADP
ejpam-5641	65	18	−	−	PROPN
ejpam-5641	65	19	ĝ|	ĝ|	PROPN
ejpam-5641	65	20	,	,	PUNCT
ejpam-5641	65	21	for	for	ADP
ejpam-5641	65	22	all	all	DET
ejpam-5641	65	23	f̂	f̂	NUM
ejpam-5641	65	24	,	,	PUNCT
ejpam-5641	65	25	ĝ	ĝ	X
ejpam-5641	65	26	∈	∈	PROPN
ejpam-5641	65	27	r(a	r(a	PROPN
ejpam-5641	65	28	)	)	PUNCT
ejpam-5641	65	29	,	,	PUNCT
ejpam-5641	65	30	and	and	CCONJ
ejpam-5641	65	31	ℏ̂	ℏ̂	ADV
ejpam-5641	65	32	:	:	PUNCT
ejpam-5641	65	33	r(a)×r(a	r(a)×r(a	X
ejpam-5641	65	34	)	)	PUNCT
ejpam-5641	65	35	→	→	NOUN
ejpam-5641	65	36	r+	r+	PRON
ejpam-5641	65	37	is	be	AUX
ejpam-5641	65	38	defined	define	VERB
ejpam-5641	65	39	by	by	ADP
ejpam-5641	65	40	ℏ̂(f̂	ℏ̂(f̂	PROPN
ejpam-5641	65	41	,	,	PUNCT
ejpam-5641	65	42	ĝ	ĝ	X
ejpam-5641	65	43	)	)	PUNCT
ejpam-5641	65	44	=	=	SYM
ejpam-5641	65	45	max	max	PROPN
ejpam-5641	65	46	λ∈a	λ∈a	NOUN
ejpam-5641	65	47	ℏ(f̂	ℏ(f̂	NOUN
ejpam-5641	65	48	,	,	PUNCT
ejpam-5641	65	49	ĝ)(λ	ĝ)(λ	PROPN
ejpam-5641	65	50	)	)	PUNCT
ejpam-5641	65	51	.	.	PUNCT
ejpam-5641	66	1	m.	m.	NOUN
ejpam-5641	66	2	m.	m.	PROPN
ejpam-5641	66	3	a	a	PRON
ejpam-5641	66	4	et	et	PROPN
ejpam-5641	66	5	al	al	PROPN
ejpam-5641	66	6	.	.	PUNCT
ejpam-5641	66	7	/	/	SYM
ejpam-5641	66	8	eur	eur	PROPN
ejpam-5641	66	9	.	.	PUNCT
ejpam-5641	67	1	j.	j.	PROPN
ejpam-5641	67	2	pure	pure	PROPN
ejpam-5641	67	3	appl	appl	PROPN
ejpam-5641	67	4	.	.	PROPN
ejpam-5641	67	5	math	math	PROPN
ejpam-5641	67	6	,	,	PUNCT
ejpam-5641	67	7	18	18	NUM
ejpam-5641	67	8	(	(	PUNCT
ejpam-5641	67	9	1	1	NUM
ejpam-5641	67	10	)	)	PUNCT
ejpam-5641	67	11	(	(	PUNCT
ejpam-5641	67	12	2025	2025	NUM
ejpam-5641	67	13	)	)	PUNCT
ejpam-5641	67	14	,	,	PUNCT
ejpam-5641	67	15	5641	5641	NUM
ejpam-5641	67	16	4	4	NUM
ejpam-5641	67	17	of	of	ADP
ejpam-5641	67	18	20	20	NUM
ejpam-5641	67	19	if	if	SCONJ
ejpam-5641	67	20	(	(	PUNCT
ejpam-5641	67	21	tl	tl	PROPN
ejpam-5641	67	22	)	)	PUNCT
ejpam-5641	67	23	∈	∈	PROPN
ejpam-5641	67	24	r+n	r+n	NOUN
ejpam-5641	67	25	∩	∩	PROPN
ejpam-5641	67	26	ℓ∞	ℓ∞	NOUN
ejpam-5641	67	27	,	,	PUNCT
ejpam-5641	67	28	then	then	ADV
ejpam-5641	67	29	(	(	PUNCT
ejpam-5641	67	30	γsf	γsf	X
ejpam-5641	67	31	(	(	PUNCT
ejpam-5641	67	32	q	q	NOUN
ejpam-5641	67	33	,	,	PUNCT
ejpam-5641	67	34	t	t	PROPN
ejpam-5641	67	35	)	)	PUNCT
ejpam-5641	67	36	)	)	PUNCT
ejpam-5641	68	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	68	2	=	=	PUNCT
ejpam-5641	68	3	{	{	PUNCT
ejpam-5641	68	4	d̂	d̂	PROPN
ejpam-5641	68	5	=	=	SYM
ejpam-5641	68	6	(	(	PUNCT
ejpam-5641	68	7	d̂b	d̂b	PROPN
ejpam-5641	68	8	)	)	PUNCT
ejpam-5641	68	9	∈	∈	PROPN
ejpam-5641	68	10	µs	µs	NOUN
ejpam-5641	68	11	:	:	PUNCT
ejpam-5641	68	12	∥δd̂∥p−qn	∥δd̂∥p−qn	PROPN
ejpam-5641	68	13	<	<	X
ejpam-5641	68	14	∞	∞	PROPN
ejpam-5641	68	15	,	,	PUNCT
ejpam-5641	68	16	for	for	ADP
ejpam-5641	68	17	any	any	DET
ejpam-5641	68	18	δ	δ	PROPN
ejpam-5641	68	19	>	>	X
ejpam-5641	68	20	0	0	NUM
ejpam-5641	68	21	}	}	PUNCT
ejpam-5641	68	22	.	.	PUNCT
ejpam-5641	69	1	volterra	volterra	NOUN
ejpam-5641	69	2	-	-	PUNCT
ejpam-5641	69	3	type	type	NOUN
ejpam-5641	69	4	summable	summable	ADJ
ejpam-5641	69	5	equations	equation	NOUN
ejpam-5641	69	6	are	be	AUX
ejpam-5641	69	7	fundamental	fundamental	ADJ
ejpam-5641	69	8	in	in	ADP
ejpam-5641	69	9	investigating	investigate	VERB
ejpam-5641	69	10	dynamical	dynamical	ADJ
ejpam-5641	69	11	systems	system	NOUN
ejpam-5641	69	12	[	[	X
ejpam-5641	69	13	1	1	X
ejpam-5641	69	14	]	]	PUNCT
ejpam-5641	69	15	and	and	CCONJ
ejpam-5641	69	16	stochastic	stochastic	ADJ
ejpam-5641	69	17	processes	process	NOUN
ejpam-5641	69	18	[	[	X
ejpam-5641	69	19	9	9	NUM
ejpam-5641	69	20	,	,	PUNCT
ejpam-5641	69	21	13	13	NUM
ejpam-5641	69	22	]	]	PUNCT
ejpam-5641	69	23	.	.	PUNCT
ejpam-5641	70	1	assuming	assume	VERB
ejpam-5641	70	2	that	that	SCONJ
ejpam-5641	70	3	ν̂	ν̂	NUM
ejpam-5641	70	4	∈	∈	PROPN
ejpam-5641	70	5	γsf	γsf	X
ejpam-5641	70	6	(	(	PUNCT
ejpam-5641	70	7	q	q	NOUN
ejpam-5641	70	8	,	,	PUNCT
ejpam-5641	70	9	t	t	PROPN
ejpam-5641	70	10	)	)	PUNCT
ejpam-5641	70	11	,	,	PUNCT
ejpam-5641	70	12	γ	γ	X
ejpam-5641	70	13	:	:	PUNCT
ejpam-5641	70	14	n	n	PROPN
ejpam-5641	70	15	2	2	NUM
ejpam-5641	70	16	→	→	SYM
ejpam-5641	70	17	r	r	NOUN
ejpam-5641	70	18	,	,	PUNCT
ejpam-5641	70	19	ψ	ψ	X
ejpam-5641	70	20	:	:	PUNCT
ejpam-5641	70	21	n×r(a	n×r(a	NUM
ejpam-5641	70	22	)	)	PUNCT
ejpam-5641	70	23	→	→	SYM
ejpam-5641	70	24	r(a	r(a	NUM
ejpam-5641	70	25	)	)	PUNCT
ejpam-5641	70	26	,	,	PUNCT
ejpam-5641	70	27	ν̂	ν̂	NUM
ejpam-5641	70	28	:	:	PUNCT
ejpam-5641	70	29	n	n	X
ejpam-5641	70	30	→	→	SYM
ejpam-5641	70	31	r(a	r(a	NUM
ejpam-5641	70	32	)	)	PUNCT
ejpam-5641	70	33	,	,	PUNCT
ejpam-5641	70	34	and	and	CCONJ
ejpam-5641	70	35	β̂	β̂	ADP
ejpam-5641	70	36	:	:	PUNCT
ejpam-5641	70	37	n	n	X
ejpam-5641	70	38	→	→	SYM
ejpam-5641	70	39	r(a	r(a	NUM
ejpam-5641	70	40	)	)	PUNCT
ejpam-5641	70	41	.	.	PUNCT
ejpam-5641	71	1	consider	consider	VERB
ejpam-5641	71	2	the	the	DET
ejpam-5641	71	3	volterra	volterra	NOUN
ejpam-5641	71	4	-	-	PUNCT
ejpam-5641	71	5	type	type	NOUN
ejpam-5641	71	6	summable	summable	ADJ
ejpam-5641	71	7	equations	equation	NOUN
ejpam-5641	71	8	of	of	ADP
ejpam-5641	71	9	soft	soft	ADJ
ejpam-5641	71	10	functions	function	NOUN
ejpam-5641	71	11	[	[	X
ejpam-5641	71	12	4	4	NUM
ejpam-5641	71	13	]	]	PUNCT
ejpam-5641	71	14	:	:	PUNCT
ejpam-5641	71	15	ν̂d	ν̂d	X
ejpam-5641	71	16	=	=	SYM
ejpam-5641	71	17	β̂d	β̂d	PUNCT
ejpam-5641	72	1	+	+	CCONJ
ejpam-5641	72	2	∑	∑	ADP
ejpam-5641	72	3	v∈n	v∈n	NOUN
ejpam-5641	72	4	γd	γd	ADP
ejpam-5641	72	5	,	,	PUNCT
ejpam-5641	72	6	vψv	vψv	ADJ
ejpam-5641	72	7	,	,	PUNCT
ejpam-5641	72	8	ν̂v	ν̂v	VERB
ejpam-5641	72	9	,	,	PUNCT
ejpam-5641	72	10	(	(	PUNCT
ejpam-5641	72	11	1	1	X
ejpam-5641	72	12	)	)	PUNCT
ejpam-5641	72	13	and	and	CCONJ
ejpam-5641	72	14	when	when	SCONJ
ejpam-5641	72	15	φ	φ	PROPN
ejpam-5641	72	16	:	:	PUNCT
ejpam-5641	72	17	(	(	PUNCT
ejpam-5641	72	18	γsf	γsf	X
ejpam-5641	72	19	(	(	PUNCT
ejpam-5641	72	20	q	q	NOUN
ejpam-5641	72	21	,	,	PUNCT
ejpam-5641	72	22	t	t	PROPN
ejpam-5641	72	23	)	)	PUNCT
ejpam-5641	72	24	)	)	PUNCT
ejpam-5641	73	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	73	2	→	→	SYM
ejpam-5641	73	3	(	(	PUNCT
ejpam-5641	73	4	γsf	γsf	X
ejpam-5641	73	5	(	(	PUNCT
ejpam-5641	73	6	q	q	NOUN
ejpam-5641	73	7	,	,	PUNCT
ejpam-5641	73	8	t	t	PROPN
ejpam-5641	73	9	)	)	PUNCT
ejpam-5641	73	10	)	)	PUNCT
ejpam-5641	74	1	∥.∥p−qn	∥.∥p−qn	PRON
ejpam-5641	74	2	is	be	AUX
ejpam-5641	74	3	defined	define	VERB
ejpam-5641	74	4	as	as	ADP
ejpam-5641	74	5	φ(ν̂d)d∈n	φ(ν̂d)d∈n	NOUN
ejpam-5641	74	6	=	=	X
ejpam-5641	74	7	(	(	PUNCT
ejpam-5641	74	8	β̂d	β̂d	NUM
ejpam-5641	74	9	+	+	CCONJ
ejpam-5641	74	10	∑	∑	PUNCT
ejpam-5641	74	11	v∈n	v∈n	NOUN
ejpam-5641	74	12	γd	γd	ADP
ejpam-5641	74	13	,	,	PUNCT
ejpam-5641	74	14	vψv	vψv	ADJ
ejpam-5641	74	15	,	,	PUNCT
ejpam-5641	74	16	ν̂v	ν̂v	NUM
ejpam-5641	74	17	)	)	PUNCT
ejpam-5641	74	18	d∈n	d∈n	NOUN
ejpam-5641	74	19	.	.	PUNCT
ejpam-5641	75	1	(	(	PUNCT
ejpam-5641	75	2	2	2	X
ejpam-5641	75	3	)	)	PUNCT
ejpam-5641	75	4	considering	consider	VERB
ejpam-5641	75	5	the	the	DET
ejpam-5641	75	6	multitude	multitude	NOUN
ejpam-5641	75	7	of	of	ADP
ejpam-5641	75	8	fixed	fix	VERB
ejpam-5641	75	9	point	point	NOUN
ejpam-5641	75	10	theorems	theorem	NOUN
ejpam-5641	75	11	within	within	ADP
ejpam-5641	75	12	a	a	DET
ejpam-5641	75	13	specific	specific	ADJ
ejpam-5641	75	14	space	space	NOUN
ejpam-5641	75	15	,	,	PUNCT
ejpam-5641	75	16	it	it	PRON
ejpam-5641	75	17	is	be	AUX
ejpam-5641	75	18	necessary	necessary	ADJ
ejpam-5641	75	19	to	to	PART
ejpam-5641	75	20	either	either	CCONJ
ejpam-5641	75	21	enlarge	enlarge	VERB
ejpam-5641	75	22	the	the	DET
ejpam-5641	75	23	space	space	NOUN
ejpam-5641	75	24	itself	itself	PRON
ejpam-5641	75	25	or	or	CCONJ
ejpam-5641	75	26	to	to	PART
ejpam-5641	75	27	augment	augment	VERB
ejpam-5641	75	28	the	the	DET
ejpam-5641	75	29	self	self	NOUN
ejpam-5641	75	30	-	-	PUNCT
ejpam-5641	75	31	mapping	mapping	NOUN
ejpam-5641	75	32	that	that	PRON
ejpam-5641	75	33	operates	operate	VERB
ejpam-5641	75	34	within	within	ADP
ejpam-5641	75	35	it	it	PRON
ejpam-5641	75	36	;	;	PUNCT
ejpam-5641	75	37	both	both	DET
ejpam-5641	75	38	alternatives	alternative	NOUN
ejpam-5641	75	39	are	be	AUX
ejpam-5641	75	40	feasible	feasible	ADJ
ejpam-5641	75	41	.	.	PUNCT
ejpam-5641	76	1	examples	example	NOUN
ejpam-5641	76	2	include	include	VERB
ejpam-5641	76	3	granular	granular	ADJ
ejpam-5641	76	4	systems	system	NOUN
ejpam-5641	76	5	,	,	PUNCT
ejpam-5641	76	6	sweeping	sweeping	ADJ
ejpam-5641	76	7	processes	process	NOUN
ejpam-5641	76	8	,	,	PUNCT
ejpam-5641	76	9	oscillation	oscillation	NOUN
ejpam-5641	76	10	issues	issue	NOUN
ejpam-5641	76	11	,	,	PUNCT
ejpam-5641	76	12	control	control	NOUN
ejpam-5641	76	13	challenges	challenge	NOUN
ejpam-5641	76	14	,	,	PUNCT
ejpam-5641	76	15	and	and	CCONJ
ejpam-5641	76	16	decision	decision	NOUN
ejpam-5641	76	17	-	-	PUNCT
ejpam-5641	76	18	making	make	VERB
ejpam-5641	76	19	problems	problem	NOUN
ejpam-5641	76	20	,	,	PUNCT
ejpam-5641	76	21	among	among	ADP
ejpam-5641	76	22	others	other	NOUN
ejpam-5641	76	23	.	.	PUNCT
ejpam-5641	77	1	a	a	DET
ejpam-5641	77	2	particular	particular	ADJ
ejpam-5641	77	3	sequence	sequence	NOUN
ejpam-5641	77	4	space	space	NOUN
ejpam-5641	77	5	encompasses	encompass	VERB
ejpam-5641	77	6	the	the	DET
ejpam-5641	77	7	solutions	solution	NOUN
ejpam-5641	77	8	of	of	ADP
ejpam-5641	77	9	summable	summable	ADJ
ejpam-5641	77	10	equations	equation	NOUN
ejpam-5641	77	11	.	.	PUNCT
ejpam-5641	78	1	so	so	ADV
ejpam-5641	78	2	,	,	PUNCT
ejpam-5641	78	3	there	there	PRON
ejpam-5641	78	4	is	be	VERB
ejpam-5641	78	5	significant	significant	ADJ
ejpam-5641	78	6	interest	interest	NOUN
ejpam-5641	78	7	in	in	ADP
ejpam-5641	78	8	mathematics	mathematic	NOUN
ejpam-5641	78	9	to	to	PART
ejpam-5641	78	10	develop	develop	VERB
ejpam-5641	78	11	new	new	ADJ
ejpam-5641	78	12	sequence	sequence	NOUN
ejpam-5641	78	13	spaces	space	NOUN
ejpam-5641	78	14	.	.	PUNCT
ejpam-5641	79	1	this	this	DET
ejpam-5641	79	2	work	work	NOUN
ejpam-5641	79	3	aims	aim	VERB
ejpam-5641	79	4	to	to	PART
ejpam-5641	79	5	create	create	VERB
ejpam-5641	79	6	a	a	DET
ejpam-5641	79	7	new	new	ADJ
ejpam-5641	79	8	stochastic	stochastic	ADJ
ejpam-5641	79	9	space	space	NOUN
ejpam-5641	79	10	by	by	ADP
ejpam-5641	79	11	utilizing	utilize	VERB
ejpam-5641	79	12	a	a	DET
ejpam-5641	79	13	weighted	weight	VERB
ejpam-5641	79	14	regular	regular	ADJ
ejpam-5641	79	15	matrix	matrix	NOUN
ejpam-5641	79	16	based	base	VERB
ejpam-5641	79	17	on	on	ADP
ejpam-5641	79	18	fibonacci	fibonacci	NOUN
ejpam-5641	79	19	numbers	number	NOUN
ejpam-5641	79	20	and	and	CCONJ
ejpam-5641	79	21	variable	variable	ADJ
ejpam-5641	79	22	exponent	exponent	NOUN
ejpam-5641	79	23	sequence	sequence	NOUN
ejpam-5641	79	24	spaces	space	VERB
ejpam-5641	79	25	.	.	PUNCT
ejpam-5641	80	1	we	we	PRON
ejpam-5641	80	2	have	have	AUX
ejpam-5641	80	3	applied	apply	VERB
ejpam-5641	80	4	specific	specific	ADJ
ejpam-5641	80	5	geometric	geometric	ADJ
ejpam-5641	80	6	and	and	CCONJ
ejpam-5641	80	7	topological	topological	ADJ
ejpam-5641	80	8	structures	structure	NOUN
ejpam-5641	80	9	to	to	ADP
ejpam-5641	80	10	soft	soft	ADJ
ejpam-5641	80	11	functions	function	NOUN
ejpam-5641	80	12	represented	represent	VERB
ejpam-5641	80	13	as	as	ADP
ejpam-5641	80	14	(	(	PUNCT
ejpam-5641	80	15	γsf	γsf	X
ejpam-5641	80	16	(	(	PUNCT
ejpam-5641	80	17	q	q	NOUN
ejpam-5641	80	18	,	,	PUNCT
ejpam-5641	80	19	t	t	PROPN
ejpam-5641	80	20	)	)	PUNCT
ejpam-5641	80	21	)	)	PUNCT
ejpam-5641	81	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	81	2	.	.	PUNCT
ejpam-5641	82	1	the	the	DET
ejpam-5641	82	2	fixed	fix	VERB
ejpam-5641	82	3	point	point	NOUN
ejpam-5641	82	4	of	of	ADP
ejpam-5641	82	5	the	the	DET
ejpam-5641	82	6	new	new	ADJ
ejpam-5641	82	7	type	type	NOUN
ejpam-5641	82	8	of	of	ADP
ejpam-5641	82	9	pre	pre	ADJ
ejpam-5641	82	10	-	-	ADJ
ejpam-5641	82	11	quasi	quasi	ADJ
ejpam-5641	82	12	-	-	ADJ
ejpam-5641	82	13	kannan	kannan	ADJ
ejpam-5641	82	14	contraction	contraction	NOUN
ejpam-5641	82	15	operator	operator	NOUN
ejpam-5641	82	16	is	be	AUX
ejpam-5641	82	17	verified	verify	VERB
ejpam-5641	82	18	in	in	ADP
ejpam-5641	82	19	this	this	DET
ejpam-5641	82	20	context	context	NOUN
ejpam-5641	82	21	.	.	PUNCT
ejpam-5641	83	1	we	we	PRON
ejpam-5641	83	2	conclude	conclude	VERB
ejpam-5641	83	3	by	by	ADP
ejpam-5641	83	4	illustrating	illustrate	VERB
ejpam-5641	83	5	our	our	PRON
ejpam-5641	83	6	findings	finding	NOUN
ejpam-5641	83	7	with	with	ADP
ejpam-5641	83	8	several	several	ADJ
ejpam-5641	83	9	examples	example	NOUN
ejpam-5641	83	10	and	and	CCONJ
ejpam-5641	83	11	applications	application	NOUN
ejpam-5641	83	12	related	relate	VERB
ejpam-5641	83	13	to	to	ADP
ejpam-5641	83	14	the	the	DET
ejpam-5641	83	15	existence	existence	NOUN
ejpam-5641	83	16	of	of	ADP
ejpam-5641	83	17	solutions	solution	NOUN
ejpam-5641	83	18	to	to	ADP
ejpam-5641	83	19	non	non	ADJ
ejpam-5641	83	20	-	-	ADJ
ejpam-5641	83	21	linear	linear	ADJ
ejpam-5641	83	22	difference	difference	NOUN
ejpam-5641	83	23	equations	equation	NOUN
ejpam-5641	83	24	.	.	PUNCT
ejpam-5641	84	1	2	2	X
ejpam-5641	84	2	.	.	X
ejpam-5641	84	3	definitions	definition	NOUN
ejpam-5641	84	4	and	and	CCONJ
ejpam-5641	84	5	preliminaries	preliminary	NOUN
ejpam-5641	84	6	definition	definition	NOUN
ejpam-5641	84	7	1	1	NUM
ejpam-5641	84	8	.	.	PUNCT
ejpam-5641	85	1	[	[	X
ejpam-5641	85	2	4	4	X
ejpam-5641	85	3	]	]	SYM
ejpam-5641	85	4	es	es	X
ejpam-5641	85	5	is	be	AUX
ejpam-5641	85	6	referred	refer	VERB
ejpam-5641	85	7	to	to	ADP
ejpam-5641	85	8	as	as	ADP
ejpam-5641	85	9	a	a	DET
ejpam-5641	85	10	psssf	psssf	NOUN
ejpam-5641	85	11	if	if	SCONJ
ejpam-5641	85	12	it	it	PRON
ejpam-5641	85	13	meets	meet	VERB
ejpam-5641	85	14	the	the	DET
ejpam-5641	85	15	following	follow	VERB
ejpam-5641	85	16	criteria	criterion	NOUN
ejpam-5641	85	17	:	:	PUNCT
ejpam-5641	85	18	(	(	PUNCT
ejpam-5641	85	19	1c	1c	X
ejpam-5641	85	20	)	)	PUNCT
ejpam-5641	85	21	es	es	NOUN
ejpam-5641	85	22	is	be	AUX
ejpam-5641	85	23	linear	linear	ADJ
ejpam-5641	85	24	space	space	NOUN
ejpam-5641	85	25	and	and	CCONJ
ejpam-5641	85	26	êr	êr	NOUN
ejpam-5641	85	27	∈	∈	PROPN
ejpam-5641	85	28	es	es	NOUN
ejpam-5641	85	29	,	,	PUNCT
ejpam-5641	85	30	for	for	ADP
ejpam-5641	85	31	r	r	NOUN
ejpam-5641	85	32	∈	∈	PROPN
ejpam-5641	85	33	n	n	NOUN
ejpam-5641	85	34	,	,	PUNCT
ejpam-5641	85	35	(	(	PUNCT
ejpam-5641	85	36	2c	2c	NOUN
ejpam-5641	85	37	)	)	PUNCT
ejpam-5641	85	38	es	es	PROPN
ejpam-5641	85	39	is	be	AUX
ejpam-5641	85	40	solid	solid	ADJ
ejpam-5641	85	41	i.e.	i.e.	X
ejpam-5641	85	42	,	,	PUNCT
ejpam-5641	85	43	if	if	SCONJ
ejpam-5641	85	44	m̂	m̂	PROPN
ejpam-5641	85	45	=	=	SYM
ejpam-5641	85	46	(	(	PUNCT
ejpam-5641	85	47	m̂r	m̂r	NOUN
ejpam-5641	85	48	)	)	PUNCT
ejpam-5641	85	49	∈	∈	PROPN
ejpam-5641	85	50	µs	µs	NOUN
ejpam-5641	85	51	,	,	PUNCT
ejpam-5641	85	52	|k̂|	|k̂|	PROPN
ejpam-5641	85	53	=	=	SYM
ejpam-5641	85	54	(	(	PUNCT
ejpam-5641	85	55	|k̂r|	|k̂r|	PROPN
ejpam-5641	85	56	)	)	PUNCT
ejpam-5641	85	57	∈	∈	PROPN
ejpam-5641	85	58	es	es	NOUN
ejpam-5641	85	59	and	and	CCONJ
ejpam-5641	85	60	|m̂r|	|m̂r|	PROPN
ejpam-5641	85	61	≤	≤	PROPN
ejpam-5641	85	62	|k̂r|	|k̂r|	PROPN
ejpam-5641	85	63	,	,	PUNCT
ejpam-5641	85	64	where	where	SCONJ
ejpam-5641	85	65	r	r	NOUN
ejpam-5641	85	66	∈	∈	PROPN
ejpam-5641	85	67	n	n	NOUN
ejpam-5641	85	68	,	,	PUNCT
ejpam-5641	85	69	then	then	ADV
ejpam-5641	85	70	|m̂|	|m̂|	PROPN
ejpam-5641	85	71	∈	∈	PROPN
ejpam-5641	85	72	es	es	NOUN
ejpam-5641	85	73	,	,	PUNCT
ejpam-5641	85	74	(	(	PUNCT
ejpam-5641	85	75	3c	3c	NUM
ejpam-5641	85	76	)	)	PUNCT
ejpam-5641	85	77	(	(	PUNCT
ejpam-5641	85	78	∣∣∣k̂	∣∣∣k̂	PROPN
ejpam-5641	85	79	[	[	PUNCT
ejpam-5641	85	80	r	r	NOUN
ejpam-5641	85	81	2	2	NUM
ejpam-5641	85	82	]	]	SYM
ejpam-5641	85	83	∣∣∣	∣∣∣	ADJ
ejpam-5641	85	84	)	)	PUNCT
ejpam-5641	85	85	r∈n	r∈n	NOUN
ejpam-5641	85	86	∈	∈	PROPN
ejpam-5641	85	87	es	es	NOUN
ejpam-5641	85	88	,	,	PUNCT
ejpam-5641	85	89	if	if	SCONJ
ejpam-5641	85	90	(	(	PUNCT
ejpam-5641	85	91	∣∣∣k̂x∣∣∣	∣∣∣k̂x∣∣∣	ADJ
ejpam-5641	85	92	)	)	PUNCT
ejpam-5641	85	93	r∈n	r∈n	NOUN
ejpam-5641	85	94	∈	∈	PROPN
ejpam-5641	85	95	es	es	NOUN
ejpam-5641	85	96	.	.	NOUN
ejpam-5641	85	97	definition	definition	NOUN
ejpam-5641	85	98	2	2	NUM
ejpam-5641	85	99	.	.	PUNCT
ejpam-5641	86	1	[	[	X
ejpam-5641	86	2	4	4	X
ejpam-5641	86	3	]	]	X
ejpam-5641	86	4	a	a	DET
ejpam-5641	86	5	subspace	subspace	NOUN
ejpam-5641	86	6	psssf	psssf	NOUN
ejpam-5641	86	7	es	es	X
ejpam-5641	86	8	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	86	9	is	be	AUX
ejpam-5641	86	10	called	call	VERB
ejpam-5641	86	11	a	a	DET
ejpam-5641	86	12	p	p	ADJ
ejpam-5641	86	13	-	-	PUNCT
ejpam-5641	86	14	m	m	NOUN
ejpam-5641	86	15	psssf	psssf	NOUN
ejpam-5641	86	16	,	,	PUNCT
ejpam-5641	86	17	if	if	SCONJ
ejpam-5641	86	18	∥.∥p−qn	∥.∥p−qn	X
ejpam-5641	86	19	:	:	PUNCT
ejpam-5641	86	20	es	es	X
ejpam-5641	86	21	→	→	PUNCT
ejpam-5641	86	22	[	[	X
ejpam-5641	86	23	0,∞	0,∞	NOUN
ejpam-5641	86	24	)	)	PUNCT
ejpam-5641	86	25	meets	meet	VERB
ejpam-5641	86	26	the	the	DET
ejpam-5641	86	27	following	follow	VERB
ejpam-5641	86	28	criteria	criterion	NOUN
ejpam-5641	86	29	for	for	ADP
ejpam-5641	86	30	all	all	DET
ejpam-5641	86	31	m̂	m̂	PROPN
ejpam-5641	86	32	,	,	PUNCT
ejpam-5641	86	33	k̂	k̂	PROPN
ejpam-5641	86	34	∈	∈	PROPN
ejpam-5641	86	35	es	es	NOUN
ejpam-5641	86	36	,	,	PUNCT
ejpam-5641	86	37	and	and	CCONJ
ejpam-5641	86	38	δ	δ	PROPN
ejpam-5641	86	39	∈	∈	PROPN
ejpam-5641	86	40	r	r	NOUN
ejpam-5641	86	41	:	:	PUNCT
ejpam-5641	86	42	m.	m.	NOUN
ejpam-5641	86	43	m.	m.	NOUN
ejpam-5641	86	44	a	a	PRON
ejpam-5641	86	45	et	et	PROPN
ejpam-5641	86	46	al	al	PROPN
ejpam-5641	86	47	.	.	PUNCT
ejpam-5641	86	48	/	/	SYM
ejpam-5641	86	49	eur	eur	PROPN
ejpam-5641	86	50	.	.	PUNCT
ejpam-5641	87	1	j.	j.	PROPN
ejpam-5641	87	2	pure	pure	PROPN
ejpam-5641	87	3	appl	appl	PROPN
ejpam-5641	87	4	.	.	PROPN
ejpam-5641	87	5	math	math	PROPN
ejpam-5641	87	6	,	,	PUNCT
ejpam-5641	87	7	18	18	NUM
ejpam-5641	87	8	(	(	PUNCT
ejpam-5641	87	9	1	1	NUM
ejpam-5641	87	10	)	)	PUNCT
ejpam-5641	87	11	(	(	PUNCT
ejpam-5641	87	12	2025	2025	NUM
ejpam-5641	87	13	)	)	PUNCT
ejpam-5641	87	14	,	,	PUNCT
ejpam-5641	87	15	5641	5641	NUM
ejpam-5641	87	16	5	5	NUM
ejpam-5641	87	17	of	of	ADP
ejpam-5641	87	18	20	20	NUM
ejpam-5641	87	19	(	(	PUNCT
ejpam-5641	87	20	a1	a1	PROPN
ejpam-5641	87	21	)	)	PUNCT
ejpam-5641	87	22	k̂	k̂	NOUN
ejpam-5641	88	1	=	=	SYM
ejpam-5641	88	2	ϑ̂	ϑ̂	ADJ
ejpam-5641	88	3	⇐	⇐	ADJ
ejpam-5641	88	4	⇒	⇒	PROPN
ejpam-5641	88	5	∥(|k̂|)∥p−qn	∥(|k̂|)∥p−qn	NOUN
ejpam-5641	88	6	=	=	SYM
ejpam-5641	88	7	0	0	NUM
ejpam-5641	88	8	,	,	PUNCT
ejpam-5641	88	9	and	and	CCONJ
ejpam-5641	88	10	∥k̂∥p−qn	∥k̂∥p−qn	NOUN
ejpam-5641	88	11	≥	≥	NOUN
ejpam-5641	88	12	0	0	NUM
ejpam-5641	88	13	,	,	PUNCT
ejpam-5641	88	14	(	(	PUNCT
ejpam-5641	88	15	a2	a2	PROPN
ejpam-5641	88	16	)	)	PUNCT
ejpam-5641	88	17	there	there	PRON
ejpam-5641	88	18	are	be	VERB
ejpam-5641	88	19	c1	c1	PROPN
ejpam-5641	88	20	≥	≥	NUM
ejpam-5641	88	21	1	1	NUM
ejpam-5641	88	22	so	so	SCONJ
ejpam-5641	88	23	that	that	SCONJ
ejpam-5641	88	24	∥δm̂∥p−qn	∥δm̂∥p−qn	PROPN
ejpam-5641	88	25	≤	≤	NOUN
ejpam-5641	88	26	|δ|c1∥m̂∥p−qn	|δ|c1∥m̂∥p−qn	X
ejpam-5641	88	27	,	,	PUNCT
ejpam-5641	88	28	(	(	PUNCT
ejpam-5641	88	29	a3	a3	NOUN
ejpam-5641	88	30	)	)	PUNCT
ejpam-5641	88	31	∥m̂+	∥m̂+	PROPN
ejpam-5641	88	32	k̂∥p−qn	k̂∥p−qn	PROPN
ejpam-5641	88	33	≤	≤	PROPN
ejpam-5641	88	34	c2(∥m̂∥p−qn	c2(∥m̂∥p−qn	PUNCT
ejpam-5641	89	1	+	+	CCONJ
ejpam-5641	89	2	∥k̂∥p−qn	∥k̂∥p−qn	ADJ
ejpam-5641	89	3	)	)	PUNCT
ejpam-5641	89	4	verifies	verifie	NOUN
ejpam-5641	89	5	so	so	SCONJ
ejpam-5641	89	6	that	that	SCONJ
ejpam-5641	89	7	c2	c2	PROPN
ejpam-5641	89	8	≥	≥	NUM
ejpam-5641	89	9	1	1	NUM
ejpam-5641	89	10	,	,	PUNCT
ejpam-5641	89	11	(	(	PUNCT
ejpam-5641	89	12	a4	a4	INTJ
ejpam-5641	89	13	)	)	PUNCT
ejpam-5641	89	14	if	if	SCONJ
ejpam-5641	89	15	|m̂r|	|m̂r|	PROPN
ejpam-5641	89	16	≤	≤	PROPN
ejpam-5641	89	17	|k̂r|	|k̂r|	PROPN
ejpam-5641	89	18	,	,	PUNCT
ejpam-5641	89	19	then	then	ADV
ejpam-5641	89	20	∥(|m̂r|)∥p−qn	∥(|m̂r|)∥p−qn	PROPN
ejpam-5641	89	21	≤	≤	ADJ
ejpam-5641	89	22	∥(|k̂r|)∥p−qn	∥(|k̂r|)∥p−qn	NOUN
ejpam-5641	89	23	,	,	PUNCT
ejpam-5641	89	24	(	(	PUNCT
ejpam-5641	89	25	a5	a5	PROPN
ejpam-5641	89	26	)	)	PUNCT
ejpam-5641	89	27	the	the	DET
ejpam-5641	89	28	inequality	inequality	NOUN
ejpam-5641	89	29	,	,	PUNCT
ejpam-5641	89	30	∥(|k̂r|)∥p−qn	∥(|k̂r|)∥p−qn	ADJ
ejpam-5641	89	31	≤	≤	NOUN
ejpam-5641	89	32	∥(|k̂	∥(|k̂	NOUN
ejpam-5641	89	33	[	[	PUNCT
ejpam-5641	89	34	r	r	NOUN
ejpam-5641	89	35	2	2	NUM
ejpam-5641	89	36	]	]	PUNCT
ejpam-5641	89	37	|)∥p−qn	|)∥p−qn	NOUN
ejpam-5641	89	38	≤	≤	X
ejpam-5641	89	39	c3∥(|k̂r|)∥p−qn	c3∥(|k̂r|)∥p−qn	NOUN
ejpam-5641	89	40	holds	hold	VERB
ejpam-5641	89	41	,	,	PUNCT
ejpam-5641	89	42	for	for	ADP
ejpam-5641	89	43	c3	c3	PROPN
ejpam-5641	89	44	≥	≥	NUM
ejpam-5641	89	45	1	1	NUM
ejpam-5641	89	46	,	,	PUNCT
ejpam-5641	89	47	(	(	PUNCT
ejpam-5641	89	48	a6	a6	NOUN
ejpam-5641	89	49	)	)	PUNCT
ejpam-5641	89	50	the	the	DET
ejpam-5641	89	51	closure	closure	NOUN
ejpam-5641	89	52	f	f	PROPN
ejpam-5641	89	53	of	of	ADP
ejpam-5641	89	54	f	f	PROPN
ejpam-5641	89	55	=	=	PROPN
ejpam-5641	89	56	es	es	PROPN
ejpam-5641	89	57	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	89	58	,	,	PUNCT
ejpam-5641	89	59	(	(	PUNCT
ejpam-5641	89	60	a7	a7	PROPN
ejpam-5641	89	61	)	)	PUNCT
ejpam-5641	89	62	the	the	DET
ejpam-5641	89	63	inequality	inequality	NOUN
ejpam-5641	89	64	,	,	PUNCT
ejpam-5641	89	65	∥(m̂	∥(m̂	PROPN
ejpam-5641	89	66	,	,	PUNCT
ejpam-5641	89	67	0̂	0̂	PROPN
ejpam-5641	89	68	,	,	PUNCT
ejpam-5641	89	69	0̂	0̂	PROPN
ejpam-5641	89	70	,	,	PUNCT
ejpam-5641	89	71	0̂	0̂	PROPN
ejpam-5641	89	72	,	,	PUNCT
ejpam-5641	89	73	...	...	PUNCT
ejpam-5641	89	74	)	)	PUNCT
ejpam-5641	89	75	∥p−qn	∥p−qn	NOUN
ejpam-5641	89	76	≥	≥	NOUN
ejpam-5641	89	77	α|m|∥ê1∥p−qn	α|m|∥ê1∥p−qn	NOUN
ejpam-5641	89	78	verifies	verifie	NOUN
ejpam-5641	89	79	for	for	ADP
ejpam-5641	89	80	α	α	PROPN
ejpam-5641	89	81	>	>	X
ejpam-5641	89	82	0	0	PROPN
ejpam-5641	89	83	.	.	PUNCT
ejpam-5641	89	84	definition	definition	NOUN
ejpam-5641	89	85	3	3	NUM
ejpam-5641	89	86	.	.	PUNCT
ejpam-5641	90	1	[	[	X
ejpam-5641	90	2	4	4	X
ejpam-5641	90	3	]	]	PUNCT
ejpam-5641	90	4	the	the	DET
ejpam-5641	90	5	space	space	NOUN
ejpam-5641	90	6	psssf	psssf	NOUN
ejpam-5641	90	7	es	es	X
ejpam-5641	90	8	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	90	9	is	be	AUX
ejpam-5641	90	10	called	call	VERB
ejpam-5641	90	11	a	a	DET
ejpam-5641	90	12	p	p	ADJ
ejpam-5641	90	13	-	-	PUNCT
ejpam-5641	90	14	q.n	q.n	NOUN
ejpam-5641	90	15	psssf	psssf	NOUN
ejpam-5641	90	16	when	when	SCONJ
ejpam-5641	90	17	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	90	18	verifies	verify	VERB
ejpam-5641	90	19	the	the	DET
ejpam-5641	90	20	parts	part	NOUN
ejpam-5641	90	21	(	(	PUNCT
ejpam-5641	90	22	a1)-(a3	a1)-(a3	NOUN
ejpam-5641	90	23	)	)	PUNCT
ejpam-5641	90	24	of	of	ADP
ejpam-5641	90	25	definition	definition	NOUN
ejpam-5641	90	26	2	2	NUM
ejpam-5641	90	27	.	.	PUNCT
ejpam-5641	91	1	the	the	DET
ejpam-5641	91	2	space	space	NOUN
ejpam-5641	91	3	psssf	psssf	NOUN
ejpam-5641	91	4	es	es	X
ejpam-5641	91	5	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	91	6	is	be	AUX
ejpam-5641	91	7	said	say	VERB
ejpam-5641	91	8	to	to	PART
ejpam-5641	91	9	be	be	AUX
ejpam-5641	91	10	p	p	NOUN
ejpam-5641	91	11	-	-	PUNCT
ejpam-5641	91	12	q.b	q.b	NOUN
ejpam-5641	91	13	psssf	psssf	NOUN
ejpam-5641	91	14	if	if	SCONJ
ejpam-5641	91	15	the	the	DET
ejpam-5641	91	16	space	space	NOUN
ejpam-5641	91	17	psssf	psssf	NOUN
ejpam-5641	91	18	es	es	X
ejpam-5641	91	19	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	91	20	is	be	AUX
ejpam-5641	91	21	complete	complete	ADJ
ejpam-5641	91	22	equipped	equip	VERB
ejpam-5641	91	23	with	with	ADP
ejpam-5641	91	24	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	91	25	.	.	PUNCT
ejpam-5641	92	1	theorem	theorem	VERB
ejpam-5641	92	2	2.1	2.1	NUM
ejpam-5641	92	3	.	.	PUNCT
ejpam-5641	93	1	[	[	X
ejpam-5641	93	2	3	3	X
ejpam-5641	93	3	]	]	PUNCT
ejpam-5641	93	4	every	every	DET
ejpam-5641	93	5	p	p	PROPN
ejpam-5641	93	6	-	-	PUNCT
ejpam-5641	93	7	m	m	NOUN
ejpam-5641	93	8	psssf	psssf	NOUN
ejpam-5641	93	9	es	es	X
ejpam-5641	93	10	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	93	11	is	be	AUX
ejpam-5641	93	12	a	a	DET
ejpam-5641	93	13	p	p	ADJ
ejpam-5641	93	14	-	-	PUNCT
ejpam-5641	93	15	q.n	q.n	NOUN
ejpam-5641	93	16	psssf	psssf	NOUN
ejpam-5641	93	17	.	.	PUNCT
ejpam-5641	94	1	lemma	lemma	PROPN
ejpam-5641	94	2	2.2	2.2	NUM
ejpam-5641	94	3	.	.	PUNCT
ejpam-5641	95	1	[	[	X
ejpam-5641	95	2	5	5	X
ejpam-5641	95	3	]	]	PUNCT
ejpam-5641	95	4	suppose	suppose	VERB
ejpam-5641	95	5	rm	rm	PROPN
ejpam-5641	95	6	>	>	X
ejpam-5641	95	7	1	1	NUM
ejpam-5641	95	8	and	and	CCONJ
ejpam-5641	95	9	αm	αm	INTJ
ejpam-5641	95	10	,	,	PUNCT
ejpam-5641	95	11	δm	δm	PROPN
ejpam-5641	95	12	∈	∈	NOUN
ejpam-5641	95	13	r	r	NOUN
ejpam-5641	95	14	,	,	PUNCT
ejpam-5641	95	15	for	for	ADP
ejpam-5641	95	16	all	all	DET
ejpam-5641	95	17	m	m	NOUN
ejpam-5641	95	18	∈	∈	ADJ
ejpam-5641	95	19	n	n	NOUN
ejpam-5641	95	20	,	,	PUNCT
ejpam-5641	95	21	and	and	CCONJ
ejpam-5641	95	22	ℶ	ℶ	PROPN
ejpam-5641	95	23	=	=	SYM
ejpam-5641	95	24	supm	supm	PROPN
ejpam-5641	95	25	rm	rm	PROPN
ejpam-5641	95	26	,	,	PUNCT
ejpam-5641	95	27	one	one	PRON
ejpam-5641	95	28	has	have	VERB
ejpam-5641	95	29	|αm	|αm	NUM
ejpam-5641	95	30	+	+	NUM
ejpam-5641	95	31	δm|rm	δm|rm	VERB
ejpam-5641	95	32	≤	≤	NUM
ejpam-5641	95	33	2ℶ−1	2ℶ−1	NUM
ejpam-5641	95	34	(	(	PUNCT
ejpam-5641	95	35	|αm|rm	|αm|rm	X
ejpam-5641	95	36	+	+	CCONJ
ejpam-5641	95	37	|δm|rm	|δm|rm	NOUN
ejpam-5641	95	38	)	)	PUNCT
ejpam-5641	95	39	.	.	PUNCT
ejpam-5641	96	1	(	(	PUNCT
ejpam-5641	96	2	3	3	X
ejpam-5641	96	3	)	)	PUNCT
ejpam-5641	96	4	definition	definition	NOUN
ejpam-5641	96	5	4	4	NUM
ejpam-5641	96	6	.	.	PUNCT
ejpam-5641	97	1	[	[	X
ejpam-5641	97	2	3	3	X
ejpam-5641	97	3	]	]	PUNCT
ejpam-5641	97	4	a	a	DET
ejpam-5641	97	5	function	function	NOUN
ejpam-5641	97	6	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	97	7	on	on	ADP
ejpam-5641	97	8	es	es	X
ejpam-5641	97	9	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	97	10	satisfies	satisfie	NOUN
ejpam-5641	97	11	the	the	DET
ejpam-5641	97	12	fp	fp	INTJ
ejpam-5641	97	13	when	when	SCONJ
ejpam-5641	97	14	for	for	SCONJ
ejpam-5641	97	15	each	each	DET
ejpam-5641	97	16	{	{	PUNCT
ejpam-5641	97	17	k̂r	k̂r	NOUN
ejpam-5641	97	18	}	}	PUNCT
ejpam-5641	97	19	⊆	⊆	NUM
ejpam-5641	97	20	es	es	ADP
ejpam-5641	97	21	∥.∥p−qn	∥.∥p−qn	PRON
ejpam-5641	97	22	such	such	ADJ
ejpam-5641	97	23	that	that	SCONJ
ejpam-5641	97	24	limr→∞	limr→∞	PROPN
ejpam-5641	97	25	∥k̂r	∥k̂r	ADP
ejpam-5641	97	26	−	−	PROPN
ejpam-5641	97	27	k̂∥p−qn	k̂∥p−qn	PROPN
ejpam-5641	97	28	=	=	PUNCT
ejpam-5641	97	29	0	0	NUM
ejpam-5641	97	30	and	and	CCONJ
ejpam-5641	97	31	all	all	DET
ejpam-5641	97	32	û	û	NUM
ejpam-5641	97	33	∈	∈	PROPN
ejpam-5641	97	34	es	es	ADP
ejpam-5641	97	35	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	97	36	,	,	PUNCT
ejpam-5641	97	37	then	then	ADV
ejpam-5641	97	38	∥û	∥û	PROPN
ejpam-5641	97	39	−	−	PROPN
ejpam-5641	97	40	k̂∥p−qn	k̂∥p−qn	PROPN
ejpam-5641	97	41	≤	≤	PROPN
ejpam-5641	97	42	supm	supm	PROPN
ejpam-5641	97	43	infr≥m	infr≥m	PROPN
ejpam-5641	97	44	∥û−	∥û−	PROPN
ejpam-5641	97	45	k̂r∥p−qn	k̂r∥p−qn	PROPN
ejpam-5641	97	46	.	.	PUNCT
ejpam-5641	98	1	definition	definition	NOUN
ejpam-5641	98	2	5	5	NUM
ejpam-5641	98	3	.	.	PUNCT
ejpam-5641	99	1	[	[	X
ejpam-5641	99	2	4	4	X
ejpam-5641	99	3	]	]	PUNCT
ejpam-5641	99	4	supposing	suppose	VERB
ejpam-5641	99	5	that	that	SCONJ
ejpam-5641	99	6	es	es	X
ejpam-5641	99	7	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	99	8	is	be	AUX
ejpam-5641	99	9	a	a	DET
ejpam-5641	99	10	p	p	ADJ
ejpam-5641	99	11	-	-	PUNCT
ejpam-5641	99	12	q.n	q.n	NOUN
ejpam-5641	99	13	psssf	psssf	NOUN
ejpam-5641	99	14	,	,	PUNCT
ejpam-5641	99	15	m	m	VERB
ejpam-5641	99	16	:	:	PUNCT
ejpam-5641	99	17	es	es	X
ejpam-5641	99	18	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	99	19	→	→	SYM
ejpam-5641	99	20	es	es	X
ejpam-5641	99	21	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	99	22	and	and	CCONJ
ejpam-5641	99	23	d̂	d̂	NUM
ejpam-5641	99	24	∈	∈	PROPN
ejpam-5641	99	25	es	es	ADP
ejpam-5641	99	26	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	99	27	.	.	PUNCT
ejpam-5641	100	1	the	the	DET
ejpam-5641	100	2	mapping	mapping	NOUN
ejpam-5641	100	3	m	m	VERB
ejpam-5641	100	4	is	be	AUX
ejpam-5641	100	5	said	say	VERB
ejpam-5641	100	6	to	to	PART
ejpam-5641	100	7	be	be	AUX
ejpam-5641	100	8	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	100	9	-	-	PUNCT
ejpam-5641	100	10	seq.c	seq.c	PROPN
ejpam-5641	100	11	at	at	ADP
ejpam-5641	100	12	d̂	d̂	PROPN
ejpam-5641	100	13	,	,	PUNCT
ejpam-5641	100	14	if	if	SCONJ
ejpam-5641	100	15	and	and	CCONJ
ejpam-5641	100	16	only	only	ADV
ejpam-5641	100	17	if	if	SCONJ
ejpam-5641	100	18	,	,	PUNCT
ejpam-5641	100	19	for	for	ADP
ejpam-5641	100	20	any	any	DET
ejpam-5641	100	21	{	{	PUNCT
ejpam-5641	100	22	k̂r	k̂r	NOUN
ejpam-5641	100	23	}	}	PUNCT
ejpam-5641	100	24	⊆	⊆	NUM
ejpam-5641	100	25	es	es	ADP
ejpam-5641	100	26	∥.∥p−qn	∥.∥p−qn	PRON
ejpam-5641	100	27	such	such	ADJ
ejpam-5641	100	28	that	that	SCONJ
ejpam-5641	100	29	limr→∞	limr→∞	PROPN
ejpam-5641	100	30	∥k̂r	∥k̂r	CCONJ
ejpam-5641	100	31	−	−	PROPN
ejpam-5641	100	32	d̂∥p−qn	d̂∥p−qn	PROPN
ejpam-5641	100	33	=	=	PUNCT
ejpam-5641	100	34	0	0	PUNCT
ejpam-5641	101	1	then	then	ADV
ejpam-5641	101	2	limr→∞	limr→∞	PROPN
ejpam-5641	101	3	∥mk̂r	∥mk̂r	PROPN
ejpam-5641	101	4	−md̂∥p−qn	−md̂∥p−qn	ADV
ejpam-5641	101	5	=	=	NOUN
ejpam-5641	101	6	0	0	NUM
ejpam-5641	101	7	.	.	NOUN
ejpam-5641	102	1	3	3	X
ejpam-5641	102	2	.	.	X
ejpam-5641	102	3	configuration	configuration	NOUN
ejpam-5641	102	4	and	and	CCONJ
ejpam-5641	102	5	properties	property	NOUN
ejpam-5641	102	6	of	of	ADP
ejpam-5641	102	7	(	(	PUNCT
ejpam-5641	102	8	γs	γs	ADP
ejpam-5641	102	9	f	f	PROPN
ejpam-5641	102	10	(	(	PUNCT
ejpam-5641	102	11	q	q	PROPN
ejpam-5641	102	12	,	,	PUNCT
ejpam-5641	102	13	t	t	PROPN
ejpam-5641	102	14	)	)	PUNCT
ejpam-5641	102	15	)	)	PUNCT
ejpam-5641	103	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	103	2	this	this	DET
ejpam-5641	103	3	section	section	NOUN
ejpam-5641	103	4	introduces	introduce	VERB
ejpam-5641	103	5	the	the	DET
ejpam-5641	103	6	definition	definition	NOUN
ejpam-5641	103	7	and	and	CCONJ
ejpam-5641	103	8	inclusion	inclusion	NOUN
ejpam-5641	103	9	relations	relation	NOUN
ejpam-5641	103	10	of	of	ADP
ejpam-5641	103	11	the	the	DET
ejpam-5641	103	12	sequence	sequence	NOUN
ejpam-5641	103	13	space	space	NOUN
ejpam-5641	103	14	(	(	PUNCT
ejpam-5641	103	15	γsf	γsf	X
ejpam-5641	103	16	(	(	PUNCT
ejpam-5641	103	17	q	q	NOUN
ejpam-5641	103	18	,	,	PUNCT
ejpam-5641	103	19	t	t	PROPN
ejpam-5641	103	20	)	)	PUNCT
ejpam-5641	103	21	)	)	PUNCT
ejpam-5641	104	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	104	2	with	with	ADP
ejpam-5641	104	3	the	the	DET
ejpam-5641	104	4	function	function	NOUN
ejpam-5641	104	5	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	104	6	.	.	PUNCT
ejpam-5641	105	1	theorem	theorem	VERB
ejpam-5641	105	2	3.1	3.1	NUM
ejpam-5641	105	3	.	.	PUNCT
ejpam-5641	106	1	the	the	DET
ejpam-5641	106	2	space	space	NOUN
ejpam-5641	106	3	(	(	PUNCT
ejpam-5641	106	4	γsf	γsf	X
ejpam-5641	106	5	(	(	PUNCT
ejpam-5641	106	6	q	q	NOUN
ejpam-5641	106	7	,	,	PUNCT
ejpam-5641	106	8	t	t	PROPN
ejpam-5641	106	9	)	)	PUNCT
ejpam-5641	106	10	)	)	PUNCT
ejpam-5641	107	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	107	2	is	be	AUX
ejpam-5641	107	3	a	a	DET
ejpam-5641	107	4	nat	nat	NOUN
ejpam-5641	107	5	,	,	PUNCT
ejpam-5641	107	6	if	if	SCONJ
ejpam-5641	107	7	(	(	PUNCT
ejpam-5641	107	8	tl	tl	PROPN
ejpam-5641	107	9	)	)	PUNCT
ejpam-5641	107	10	∈	∈	PROPN
ejpam-5641	107	11	(	(	PUNCT
ejpam-5641	107	12	0,∞)n	0,∞)n	X
ejpam-5641	107	13	∩	∩	NOUN
ejpam-5641	107	14	ℓ∞.	ℓ∞.	ADP
ejpam-5641	107	15	proof	proof	NOUN
ejpam-5641	107	16	.	.	PUNCT
ejpam-5641	108	1	clearly	clearly	ADV
ejpam-5641	108	2	,	,	PUNCT
ejpam-5641	108	3	as	as	ADP
ejpam-5641	108	4	∥ê0	∥ê0	PROPN
ejpam-5641	108	5	−	−	PROPN
ejpam-5641	108	6	ê1∥p−qn	ê1∥p−qn	NOUN
ejpam-5641	108	7	=	=	PUNCT
ejpam-5641	108	8	(	(	PUNCT
ejpam-5641	108	9	q0	q0	PROPN
ejpam-5641	108	10	)	)	PUNCT
ejpam-5641	108	11	t0	t0	PROPN
ejpam-5641	108	12	+	+	CCONJ
ejpam-5641	108	13	(	(	PUNCT
ejpam-5641	108	14	|q0	|q0	NOUN
ejpam-5641	108	15	−	−	PROPN
ejpam-5641	108	16	q1|	q1|	ADV
ejpam-5641	108	17	2	2	NUM
ejpam-5641	108	18	)	)	PUNCT
ejpam-5641	108	19	t1	t1	NOUN
ejpam-5641	108	20	+	+	CCONJ
ejpam-5641	108	21	(	(	PUNCT
ejpam-5641	108	22	|q0	|q0	NOUN
ejpam-5641	108	23	−	−	PROPN
ejpam-5641	108	24	q1|	q1|	ADV
ejpam-5641	108	25	6	6	NUM
ejpam-5641	108	26	)	)	PUNCT
ejpam-5641	108	27	t2	t2	NOUN
ejpam-5641	108	28	+	+	CCONJ
ejpam-5641	108	29	·	·	PUNCT
ejpam-5641	108	30	·	·	PUNCT
ejpam-5641	108	31	·	·	PUNCT
ejpam-5641	109	1	̸=	̸=	PROPN
ejpam-5641	109	2	(	(	PUNCT
ejpam-5641	109	3	q0	q0	PROPN
ejpam-5641	109	4	)	)	PUNCT
ejpam-5641	109	5	t0	t0	PROPN
ejpam-5641	109	6	+	+	CCONJ
ejpam-5641	109	7	(	(	PUNCT
ejpam-5641	109	8	|q0	|q0	NOUN
ejpam-5641	109	9	+	+	CCONJ
ejpam-5641	109	10	q1|	q1|	ADV
ejpam-5641	109	11	2	2	NUM
ejpam-5641	109	12	)	)	PUNCT
ejpam-5641	109	13	t1	t1	NOUN
ejpam-5641	109	14	+	+	CCONJ
ejpam-5641	109	15	(	(	PUNCT
ejpam-5641	109	16	|q0	|q0	NOUN
ejpam-5641	109	17	+	+	CCONJ
ejpam-5641	109	18	q1|	q1|	ADV
ejpam-5641	109	19	6	6	NUM
ejpam-5641	109	20	)	)	PUNCT
ejpam-5641	109	21	t2	t2	NOUN
ejpam-5641	109	22	+	+	CCONJ
ejpam-5641	109	23	·	·	PUNCT
ejpam-5641	109	24	·	·	PUNCT
ejpam-5641	109	25	·	·	PUNCT
ejpam-5641	110	1	=	=	PUNCT
ejpam-5641	110	2	∥ê0	∥ê0	PROPN
ejpam-5641	110	3	+	+	NOUN
ejpam-5641	110	4	ê1∥p−qn	ê1∥p−qn	PROPN
ejpam-5641	110	5	.	.	PUNCT
ejpam-5641	111	1	m.	m.	NOUN
ejpam-5641	111	2	m.	m.	PROPN
ejpam-5641	111	3	a	a	PRON
ejpam-5641	111	4	et	et	PROPN
ejpam-5641	111	5	al	al	PROPN
ejpam-5641	111	6	.	.	PUNCT
ejpam-5641	111	7	/	/	SYM
ejpam-5641	111	8	eur	eur	PROPN
ejpam-5641	111	9	.	.	PUNCT
ejpam-5641	112	1	j.	j.	PROPN
ejpam-5641	112	2	pure	pure	PROPN
ejpam-5641	112	3	appl	appl	PROPN
ejpam-5641	112	4	.	.	PROPN
ejpam-5641	112	5	math	math	PROPN
ejpam-5641	112	6	,	,	PUNCT
ejpam-5641	112	7	18	18	NUM
ejpam-5641	112	8	(	(	PUNCT
ejpam-5641	112	9	1	1	NUM
ejpam-5641	112	10	)	)	PUNCT
ejpam-5641	112	11	(	(	PUNCT
ejpam-5641	112	12	2025	2025	NUM
ejpam-5641	112	13	)	)	PUNCT
ejpam-5641	112	14	,	,	PUNCT
ejpam-5641	112	15	5641	5641	NUM
ejpam-5641	112	16	6	6	NUM
ejpam-5641	112	17	of	of	ADP
ejpam-5641	112	18	20	20	NUM
ejpam-5641	112	19	definition	definition	NOUN
ejpam-5641	112	20	6	6	NUM
ejpam-5641	112	21	.	.	PUNCT
ejpam-5641	113	1	supposing	suppose	VERB
ejpam-5641	113	2	that	that	PRON
ejpam-5641	113	3	(	(	PUNCT
ejpam-5641	113	4	tl	tl	PROPN
ejpam-5641	113	5	)	)	PUNCT
ejpam-5641	113	6	∈	∈	PROPN
ejpam-5641	114	1	[	[	X
ejpam-5641	114	2	0.5,∞)n	0.5,∞)n	NUM
ejpam-5641	114	3	.	.	PUNCT
ejpam-5641	115	1	the	the	DET
ejpam-5641	115	2	absolute	absolute	ADJ
ejpam-5641	115	3	type	type	NOUN
ejpam-5641	115	4	space	space	NOUN
ejpam-5641	115	5	(	(	PUNCT
ejpam-5641	115	6	|γsf	|γsf	NOUN
ejpam-5641	115	7	|(q	|(q	PROPN
ejpam-5641	115	8	,	,	PUNCT
ejpam-5641	115	9	t	t	PROPN
ejpam-5641	115	10	)	)	PUNCT
ejpam-5641	115	11	)	)	PUNCT
ejpam-5641	116	1	φ	φ	PROPN
ejpam-5641	116	2	is	be	AUX
ejpam-5641	116	3	defined	define	VERB
ejpam-5641	116	4	as	as	ADP
ejpam-5641	116	5	(	(	PUNCT
ejpam-5641	116	6	|γsf	|γsf	X
ejpam-5641	116	7	|(q	|(q	PROPN
ejpam-5641	116	8	,	,	PUNCT
ejpam-5641	116	9	t	t	PROPN
ejpam-5641	116	10	)	)	PUNCT
ejpam-5641	116	11	)	)	PUNCT
ejpam-5641	117	1	φ	φ	X
ejpam-5641	117	2	:	:	PUNCT
ejpam-5641	117	3	=	=	X
ejpam-5641	117	4	{	{	PUNCT
ejpam-5641	117	5	ĵ	ĵ	X
ejpam-5641	117	6	=	=	SYM
ejpam-5641	117	7	(	(	PUNCT
ejpam-5641	117	8	ĵk	ĵk	NOUN
ejpam-5641	117	9	)	)	PUNCT
ejpam-5641	117	10	∈	∈	PROPN
ejpam-5641	117	11	µs	µs	NOUN
ejpam-5641	117	12	:	:	PUNCT
ejpam-5641	117	13	φ(δf	φ(δf	NOUN
ejpam-5641	117	14	)	)	PUNCT
ejpam-5641	117	15	<	<	X
ejpam-5641	117	16	∞	∞	PROPN
ejpam-5641	117	17	,	,	PUNCT
ejpam-5641	117	18	for	for	ADP
ejpam-5641	117	19	some	some	DET
ejpam-5641	117	20	δ	δ	PROPN
ejpam-5641	117	21	>	>	X
ejpam-5641	117	22	0	0	NUM
ejpam-5641	117	23	}	}	PUNCT
ejpam-5641	117	24	,	,	PUNCT
ejpam-5641	117	25	where	where	SCONJ
ejpam-5641	117	26	φ(ĵ	φ(ĵ	ADV
ejpam-5641	117	27	)	)	PUNCT
ejpam-5641	117	28	=	=	PUNCT
ejpam-5641	118	1	∞∑	∞∑	NUM
ejpam-5641	118	2	l=0	l=0	PROPN
ejpam-5641	118	3			PROPN
ejpam-5641	118	4	ℏ̂	ℏ̂	PUNCT
ejpam-5641	118	5	(	(	PUNCT
ejpam-5641	118	6	∑l	∑l	INTJ
ejpam-5641	118	7	z=0	z=0	PROPN
ejpam-5641	118	8	f	f	NOUN
ejpam-5641	118	9	2	2	NUM
ejpam-5641	118	10	zqz|ĵz|	zqz|ĵz|	NOUN
ejpam-5641	118	11	,	,	PUNCT
ejpam-5641	118	12	0̂	0̂	PROPN
ejpam-5641	118	13	)	)	PUNCT
ejpam-5641	119	1	flfl+1	flfl+1	PROPN
ejpam-5641	119	2	tl	tl	PROPN
ejpam-5641	119	3	.	.	PUNCT
ejpam-5641	120	1	theorem	theorem	VERB
ejpam-5641	120	2	3.2	3.2	NUM
ejpam-5641	120	3	.	.	PUNCT
ejpam-5641	121	1	if	if	SCONJ
ejpam-5641	121	2	(	(	PUNCT
ejpam-5641	121	3	tl	tl	PROPN
ejpam-5641	121	4	)	)	PUNCT
ejpam-5641	121	5	∈	∈	PROPN
ejpam-5641	121	6	[	[	X
ejpam-5641	121	7	0.5,∞)n	0.5,∞)n	NUM
ejpam-5641	121	8	∩	∩	X
ejpam-5641	121	9	ℓ∞	ℓ∞	NOUN
ejpam-5641	121	10	with	with	ADP
ejpam-5641	121	11	(	(	PUNCT
ejpam-5641	121	12	l+1	l+1	PROPN
ejpam-5641	121	13	flfl+1	flfl+1	PROPN
ejpam-5641	121	14	)	)	PUNCT
ejpam-5641	121	15	/∈	/∈	PUNCT
ejpam-5641	122	1	ℓ(tl	ℓ(tl	NUM
ejpam-5641	122	2	)	)	PUNCT
ejpam-5641	123	1	,	,	PUNCT
ejpam-5641	123	2	one	one	PRON
ejpam-5641	123	3	gets	get	VERB
ejpam-5641	123	4	(	(	PUNCT
ejpam-5641	123	5	|γsf	|γsf	NOUN
ejpam-5641	123	6	|(q	|(q	PROPN
ejpam-5641	123	7	,	,	PUNCT
ejpam-5641	123	8	t	t	PROPN
ejpam-5641	123	9	)	)	PUNCT
ejpam-5641	123	10	)	)	PUNCT
ejpam-5641	124	1	φ	φ	PROPN
ejpam-5641	124	2	⫋	⫋	PROPN
ejpam-5641	124	3	(	(	PUNCT
ejpam-5641	124	4	γsf	γsf	X
ejpam-5641	124	5	(	(	PUNCT
ejpam-5641	124	6	q	q	NOUN
ejpam-5641	124	7	,	,	PUNCT
ejpam-5641	124	8	t	t	PROPN
ejpam-5641	124	9	)	)	PUNCT
ejpam-5641	124	10	)	)	PUNCT
ejpam-5641	124	11	∥.∥p−qn	∥.∥p−qn	X
ejpam-5641	124	12	.	.	PUNCT
ejpam-5641	125	1	proof	proof	NOUN
ejpam-5641	125	2	.	.	PUNCT
ejpam-5641	126	1	if	if	SCONJ
ejpam-5641	126	2	d̂	d̂	PUNCT
ejpam-5641	126	3	∈	∈	PROPN
ejpam-5641	126	4	(	(	PUNCT
ejpam-5641	126	5	|γsf	|γsf	PROPN
ejpam-5641	126	6	|(q	|(q	PROPN
ejpam-5641	126	7	,	,	PUNCT
ejpam-5641	126	8	t	t	PROPN
ejpam-5641	126	9	)	)	PUNCT
ejpam-5641	126	10	)	)	PUNCT
ejpam-5641	126	11	φ	φ	PROPN
ejpam-5641	126	12	,	,	PUNCT
ejpam-5641	126	13	then	then	ADV
ejpam-5641	126	14	∑	∑	PUNCT
ejpam-5641	126	15	l∈n	l∈n	ADP
ejpam-5641	126	16			PROPN
ejpam-5641	126	17	ℏ̂	ℏ̂	NUM
ejpam-5641	126	18	(	(	PUNCT
ejpam-5641	126	19	∑l	∑l	INTJ
ejpam-5641	126	20	z=0	z=0	NUM
ejpam-5641	126	21	f	f	NOUN
ejpam-5641	126	22	2	2	NUM
ejpam-5641	126	23	zqzd̂z	zqzd̂z	NOUN
ejpam-5641	126	24	,	,	PUNCT
ejpam-5641	126	25	0̂	0̂	PROPN
ejpam-5641	126	26	)	)	PUNCT
ejpam-5641	127	1	flfl+1	flfl+1	PROPN
ejpam-5641	127	2	tl	tl	X
ejpam-5641	127	3	≤	≤	NOUN
ejpam-5641	127	4	∑	∑	PUNCT
ejpam-5641	127	5	l∈n	l∈n	ADP
ejpam-5641	127	6			PROPN
ejpam-5641	127	7	ℏ̂	ℏ̂	NUM
ejpam-5641	127	8	(	(	PUNCT
ejpam-5641	127	9	∑l	∑l	INTJ
ejpam-5641	127	10	z=0	z=0	PROPN
ejpam-5641	127	11	f	f	NOUN
ejpam-5641	127	12	2	2	NUM
ejpam-5641	127	13	zqz|d̂z|	zqz|d̂z|	NUM
ejpam-5641	127	14	,	,	PUNCT
ejpam-5641	127	15	0̂	0̂	PROPN
ejpam-5641	127	16	)	)	PUNCT
ejpam-5641	128	1	flfl+1	flfl+1	PROPN
ejpam-5641	128	2	tl	tl	PROPN
ejpam-5641	129	1	<	<	X
ejpam-5641	129	2	∞.	∞.	PROPN
ejpam-5641	129	3	therefore	therefore	ADV
ejpam-5641	129	4	,	,	PUNCT
ejpam-5641	129	5	d̂	d̂	PROPN
ejpam-5641	129	6	∈	∈	PROPN
ejpam-5641	129	7	(	(	PUNCT
ejpam-5641	129	8	γsf	γsf	X
ejpam-5641	129	9	(	(	PUNCT
ejpam-5641	129	10	q	q	NOUN
ejpam-5641	129	11	,	,	PUNCT
ejpam-5641	129	12	t	t	PROPN
ejpam-5641	129	13	)	)	PUNCT
ejpam-5641	129	14	)	)	PUNCT
ejpam-5641	129	15	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	129	16	.	.	PUNCT
ejpam-5641	130	1	if	if	SCONJ
ejpam-5641	130	2	ĵ	ĵ	PUNCT
ejpam-5641	130	3	=	=	SYM
ejpam-5641	130	4	(	(	PUNCT
ejpam-5641	130	5	(	(	PUNCT
ejpam-5641	130	6	−1̂)z	−1̂)z	NOUN
ejpam-5641	130	7	f2zqz	f2zqz	NUM
ejpam-5641	130	8	)	)	PUNCT
ejpam-5641	130	9	z∈n	z∈n	NOUN
ejpam-5641	130	10	,	,	PUNCT
ejpam-5641	130	11	one	one	PRON
ejpam-5641	130	12	has	have	VERB
ejpam-5641	130	13	ĵ	ĵ	PROPN
ejpam-5641	130	14	∈	∈	PROPN
ejpam-5641	130	15	(	(	PUNCT
ejpam-5641	130	16	γsf	γsf	X
ejpam-5641	130	17	(	(	PUNCT
ejpam-5641	130	18	q	q	NOUN
ejpam-5641	130	19	,	,	PUNCT
ejpam-5641	130	20	t	t	PROPN
ejpam-5641	130	21	)	)	PUNCT
ejpam-5641	130	22	)	)	PUNCT
ejpam-5641	130	23	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	130	24	and	and	CCONJ
ejpam-5641	130	25	ĵ	ĵ	PROPN
ejpam-5641	130	26	/∈	/∈	PUNCT
ejpam-5641	130	27	(	(	PUNCT
ejpam-5641	130	28	|γsf	|γsf	PROPN
ejpam-5641	130	29	|(q	|(q	PROPN
ejpam-5641	130	30	,	,	PUNCT
ejpam-5641	130	31	t	t	PROPN
ejpam-5641	130	32	)	)	PUNCT
ejpam-5641	130	33	)	)	PUNCT
ejpam-5641	131	1	φ	φ	INTJ
ejpam-5641	131	2	.	.	PUNCT
ejpam-5641	132	1	we	we	PRON
ejpam-5641	132	2	provide	provide	VERB
ejpam-5641	132	3	the	the	DET
ejpam-5641	132	4	sufficient	sufficient	ADJ
ejpam-5641	132	5	conditions	condition	NOUN
ejpam-5641	132	6	on	on	ADP
ejpam-5641	132	7	γsf	γsf	X
ejpam-5641	132	8	(	(	PUNCT
ejpam-5641	132	9	q	q	NOUN
ejpam-5641	132	10	,	,	PUNCT
ejpam-5641	132	11	t	t	PROPN
ejpam-5641	132	12	)	)	PUNCT
ejpam-5641	132	13	to	to	PART
ejpam-5641	132	14	form	form	VERB
ejpam-5641	132	15	a	a	DET
ejpam-5641	132	16	p	p	NOUN
ejpam-5641	132	17	-	-	PUNCT
ejpam-5641	132	18	q.b	q.b	NOUN
ejpam-5641	132	19	psssf	psssf	NOUN
ejpam-5641	132	20	.	.	PUNCT
ejpam-5641	133	1	theorem	theorem	VERB
ejpam-5641	133	2	3.3	3.3	NUM
ejpam-5641	133	3	.	.	PUNCT
ejpam-5641	134	1	γsf	γsf	VERB
ejpam-5641	134	2	(	(	PUNCT
ejpam-5641	134	3	q	q	NOUN
ejpam-5641	134	4	,	,	PUNCT
ejpam-5641	134	5	t	t	PROPN
ejpam-5641	134	6	)	)	PUNCT
ejpam-5641	134	7	is	be	AUX
ejpam-5641	134	8	a	a	DET
ejpam-5641	134	9	p	p	ADJ
ejpam-5641	134	10	-	-	PUNCT
ejpam-5641	134	11	m	m	NOUN
ejpam-5641	134	12	psssf	psssf	NOUN
ejpam-5641	134	13	,	,	PUNCT
ejpam-5641	134	14	if	if	SCONJ
ejpam-5641	134	15	(	(	PUNCT
ejpam-5641	134	16	o1	o1	NOUN
ejpam-5641	134	17	)	)	PUNCT
ejpam-5641	134	18	(	(	PUNCT
ejpam-5641	134	19	tl	tl	PROPN
ejpam-5641	134	20	)	)	PUNCT
ejpam-5641	134	21	∈	∈	PROPN
ejpam-5641	134	22	n+	n+	NUM
ejpam-5641	134	23	∩	∩	PROPN
ejpam-5641	134	24	ℓ∞	ℓ∞	PROPN
ejpam-5641	134	25	and	and	CCONJ
ejpam-5641	134	26	t0	t0	PROPN
ejpam-5641	134	27	≥	≥	NUM
ejpam-5641	134	28	0.5	0.5	NUM
ejpam-5641	134	29	.	.	PUNCT
ejpam-5641	135	1	(	(	PUNCT
ejpam-5641	135	2	o2	o2	PROPN
ejpam-5641	135	3	)	)	PUNCT
ejpam-5641	135	4	(	(	PUNCT
ejpam-5641	135	5	f2zqz	f2zqz	ADJ
ejpam-5641	135	6	)	)	PUNCT
ejpam-5641	135	7	z∈n	z∈n	NOUN
ejpam-5641	135	8	∈	∈	NOUN
ejpam-5641	135	9	d−	d−	PROPN
ejpam-5641	135	10	or	or	CCONJ
ejpam-5641	135	11	,	,	PUNCT
ejpam-5641	135	12	(	(	PUNCT
ejpam-5641	135	13	f2zqz	f2zqz	ADJ
ejpam-5641	135	14	)	)	PUNCT
ejpam-5641	135	15	z∈n	z∈n	NOUN
ejpam-5641	135	16	∈	∈	PROPN
ejpam-5641	135	17	n+∩	n+∩	PUNCT
ejpam-5641	135	18	ℓ∞	ℓ∞	NOUN
ejpam-5641	135	19	and	and	CCONJ
ejpam-5641	135	20	one	one	NUM
ejpam-5641	135	21	has	have	VERB
ejpam-5641	135	22	a	a	DET
ejpam-5641	135	23	≥	≥	NUM
ejpam-5641	135	24	1	1	NUM
ejpam-5641	135	25	such	such	ADJ
ejpam-5641	135	26	that	that	SCONJ
ejpam-5641	135	27	r2z+1q2z+1	r2z+1q2z+1	PROPN
ejpam-5641	135	28	≤	≤	ADV
ejpam-5641	135	29	af2zqz	af2zqz	ADJ
ejpam-5641	135	30	.	.	PUNCT
ejpam-5641	136	1	proof	proof	NOUN
ejpam-5641	136	2	.	.	PUNCT
ejpam-5641	137	1	assuming	assume	VERB
ejpam-5641	137	2	that	that	SCONJ
ejpam-5641	137	3	d̂	d̂	PROPN
ejpam-5641	137	4	,	,	PUNCT
ejpam-5641	137	5	k̂	k̂	PROPN
ejpam-5641	137	6	∈	∈	PROPN
ejpam-5641	137	7	γsf	γsf	X
ejpam-5641	137	8	(	(	PUNCT
ejpam-5641	137	9	q	q	NOUN
ejpam-5641	137	10	,	,	PUNCT
ejpam-5641	137	11	t	t	PROPN
ejpam-5641	137	12	)	)	PUNCT
ejpam-5641	137	13	,	,	PUNCT
ejpam-5641	137	14	and	and	CCONJ
ejpam-5641	137	15	δ	δ	PROPN
ejpam-5641	137	16	∈	∈	PROPN
ejpam-5641	137	17	r.	r.	PROPN
ejpam-5641	137	18	assume	assume	VERB
ejpam-5641	137	19	the	the	DET
ejpam-5641	137	20	setups	setup	NOUN
ejpam-5641	137	21	(	(	PUNCT
ejpam-5641	137	22	o1	o1	NOUN
ejpam-5641	137	23	)	)	PUNCT
ejpam-5641	137	24	and	and	CCONJ
ejpam-5641	137	25	(	(	PUNCT
ejpam-5641	137	26	o2	o2	PROPN
ejpam-5641	137	27	)	)	PUNCT
ejpam-5641	137	28	are	be	AUX
ejpam-5641	137	29	verified	verify	VERB
ejpam-5641	137	30	.	.	PUNCT
ejpam-5641	138	1	the	the	DET
ejpam-5641	138	2	condition	condition	NOUN
ejpam-5641	138	3	(	(	PUNCT
ejpam-5641	138	4	a1	a1	NOUN
ejpam-5641	138	5	):	):	PUNCT
ejpam-5641	138	6	clearly	clearly	ADV
ejpam-5641	138	7	,	,	PUNCT
ejpam-5641	138	8	∥d̂∥p−qn	∥d̂∥p−qn	ADJ
ejpam-5641	138	9	≥	≥	NOUN
ejpam-5641	138	10	0	0	NUM
ejpam-5641	138	11	and	and	CCONJ
ejpam-5641	138	12	∥(|d̂|)∥p−qn	∥(|d̂|)∥p−qn	NOUN
ejpam-5641	138	13	=	=	SYM
ejpam-5641	138	14	0	0	NUM
ejpam-5641	138	15	⇔	⇔	NOUN
ejpam-5641	138	16	d̂	d̂	PROPN
ejpam-5641	139	1	=	=	PRON
ejpam-5641	139	2	ϑ̂.	ϑ̂.	VERB
ejpam-5641	139	3	the	the	DET
ejpam-5641	139	4	conditions	condition	NOUN
ejpam-5641	139	5	(	(	PUNCT
ejpam-5641	139	6	1c	1c	X
ejpam-5641	139	7	)	)	PUNCT
ejpam-5641	139	8	and	and	CCONJ
ejpam-5641	139	9	(	(	PUNCT
ejpam-5641	139	10	a3	a3	NOUN
ejpam-5641	139	11	):	):	PUNCT
ejpam-5641	139	12	∥d̂+	∥d̂+	PROPN
ejpam-5641	139	13	k̂∥p−qn	k̂∥p−qn	PROPN
ejpam-5641	139	14	=	=	PUNCT
ejpam-5641	139	15	∑	∑	PUNCT
ejpam-5641	139	16	l∈n	l∈n	VERB
ejpam-5641	139	17			PROPN
ejpam-5641	139	18	ℏ̂	ℏ̂	NUM
ejpam-5641	139	19	(	(	PUNCT
ejpam-5641	139	20	∑l	∑l	INTJ
ejpam-5641	139	21	z=0	z=0	NUM
ejpam-5641	139	22	f	f	NOUN
ejpam-5641	139	23	2	2	NUM
ejpam-5641	139	24	zqz	zqz	NUM
ejpam-5641	139	25	(	(	PUNCT
ejpam-5641	139	26	d̂z	d̂z	PROPN
ejpam-5641	139	27	+	+	CCONJ
ejpam-5641	139	28	k̂z	k̂z	PROPN
ejpam-5641	139	29	)	)	PUNCT
ejpam-5641	139	30	,	,	PUNCT
ejpam-5641	139	31	0̂	0̂	PROPN
ejpam-5641	139	32	)	)	PUNCT
ejpam-5641	140	1	flfl+1	flfl+1	PROPN
ejpam-5641	140	2	tl	tl	VERB
ejpam-5641	140	3	≤	≤	NUM
ejpam-5641	140	4	2ℶ−1	2ℶ−1	NUM
ejpam-5641	140	5	∑	∑	ADV
ejpam-5641	140	6	l∈n	l∈n	ADJ
ejpam-5641	140	7			PROPN
ejpam-5641	140	8	ℏ̂	ℏ̂	NUM
ejpam-5641	140	9	(	(	PUNCT
ejpam-5641	140	10	∑l	∑l	INTJ
ejpam-5641	140	11	z=0	z=0	NUM
ejpam-5641	140	12	f	f	NOUN
ejpam-5641	140	13	2	2	NUM
ejpam-5641	140	14	zqzd̂z	zqzd̂z	NOUN
ejpam-5641	140	15	,	,	PUNCT
ejpam-5641	140	16	0̂	0̂	PROPN
ejpam-5641	140	17	)	)	PUNCT
ejpam-5641	140	18	flfl+1	flfl+1	PROPN
ejpam-5641	140	19	tl	tl	PUNCT
ejpam-5641	141	1	+	+	CCONJ
ejpam-5641	141	2	∑	∑	PUNCT
ejpam-5641	141	3	l∈n	l∈n	VERB
ejpam-5641	141	4			PROPN
ejpam-5641	141	5	ℏ̂	ℏ̂	NUM
ejpam-5641	141	6	(	(	PUNCT
ejpam-5641	141	7	∑l	∑l	INTJ
ejpam-5641	141	8	z=0	z=0	NUM
ejpam-5641	141	9	f	f	NOUN
ejpam-5641	141	10	2	2	NUM
ejpam-5641	141	11	zqzk̂z	zqzk̂z	NUM
ejpam-5641	141	12	,	,	PUNCT
ejpam-5641	141	13	0̂	0̂	PROPN
ejpam-5641	141	14	)	)	PUNCT
ejpam-5641	141	15	flfl+1	flfl+1	PROPN
ejpam-5641	141	16	tl	tl	PUNCT
ejpam-5641	142	1			PROPN
ejpam-5641	143	1	=	=	PUNCT
ejpam-5641	144	1	c2(∥d̂∥p−qn	c2(∥d̂∥p−qn	PROPN
ejpam-5641	145	1	+	+	NUM
ejpam-5641	145	2	∥k̂∥p−qn	∥k̂∥p−qn	NOUN
ejpam-5641	145	3	)	)	PUNCT
ejpam-5641	145	4	<	<	X
ejpam-5641	145	5	∞	∞	PROPN
ejpam-5641	145	6	,	,	PUNCT
ejpam-5641	145	7	m.	m.	NOUN
ejpam-5641	145	8	m.	m.	NOUN
ejpam-5641	145	9	a	a	PRON
ejpam-5641	145	10	et	et	NOUN
ejpam-5641	145	11	al	al	PROPN
ejpam-5641	145	12	.	.	PUNCT
ejpam-5641	145	13	/	/	SYM
ejpam-5641	145	14	eur	eur	PROPN
ejpam-5641	145	15	.	.	PUNCT
ejpam-5641	146	1	j.	j.	PROPN
ejpam-5641	146	2	pure	pure	PROPN
ejpam-5641	146	3	appl	appl	PROPN
ejpam-5641	146	4	.	.	PROPN
ejpam-5641	146	5	math	math	PROPN
ejpam-5641	146	6	,	,	PUNCT
ejpam-5641	146	7	18	18	NUM
ejpam-5641	146	8	(	(	PUNCT
ejpam-5641	146	9	1	1	NUM
ejpam-5641	146	10	)	)	PUNCT
ejpam-5641	146	11	(	(	PUNCT
ejpam-5641	146	12	2025	2025	NUM
ejpam-5641	146	13	)	)	PUNCT
ejpam-5641	146	14	,	,	PUNCT
ejpam-5641	146	15	5641	5641	NUM
ejpam-5641	146	16	7	7	NUM
ejpam-5641	146	17	of	of	ADP
ejpam-5641	146	18	20	20	NUM
ejpam-5641	146	19	therefore	therefore	ADV
ejpam-5641	146	20	,	,	PUNCT
ejpam-5641	146	21	d̂+	d̂+	PROPN
ejpam-5641	146	22	k̂	k̂	PROPN
ejpam-5641	146	23	∈	∈	PROPN
ejpam-5641	146	24	γsf	γsf	X
ejpam-5641	146	25	(	(	PUNCT
ejpam-5641	146	26	q	q	NOUN
ejpam-5641	146	27	,	,	PUNCT
ejpam-5641	146	28	t	t	PROPN
ejpam-5641	146	29	)	)	PUNCT
ejpam-5641	146	30	.	.	PUNCT
ejpam-5641	147	1	the	the	DET
ejpam-5641	147	2	conditions	condition	NOUN
ejpam-5641	147	3	(	(	PUNCT
ejpam-5641	147	4	1c	1c	X
ejpam-5641	147	5	)	)	PUNCT
ejpam-5641	147	6	and	and	CCONJ
ejpam-5641	147	7	(	(	PUNCT
ejpam-5641	147	8	a2	a2	PROPN
ejpam-5641	147	9	):	):	PUNCT
ejpam-5641	147	10	∥δd̂∥p−qn	∥δd̂∥p−qn	PROPN
ejpam-5641	147	11	=	=	SYM
ejpam-5641	147	12	∑	∑	PUNCT
ejpam-5641	147	13	l∈n	l∈n	VERB
ejpam-5641	147	14			PROPN
ejpam-5641	147	15	ℏ̂	ℏ̂	NUM
ejpam-5641	147	16	(	(	PUNCT
ejpam-5641	147	17	∑l	∑l	INTJ
ejpam-5641	147	18	z=0	z=0	PROPN
ejpam-5641	147	19	f	f	PROPN
ejpam-5641	147	20	2	2	NUM
ejpam-5641	147	21	zqzδd̂z	zqzδd̂z	PROPN
ejpam-5641	147	22	,	,	PUNCT
ejpam-5641	147	23	0̂	0̂	PROPN
ejpam-5641	147	24	)	)	PUNCT
ejpam-5641	148	1	flfl+1	flfl+1	PROPN
ejpam-5641	148	2	tl	tl	PROPN
ejpam-5641	148	3	≤	≤	NUM
ejpam-5641	148	4	sup	sup	NOUN
ejpam-5641	148	5	l	l	NOUN
ejpam-5641	148	6	|δ|tl	|δ|tl	ADJ
ejpam-5641	148	7	∑	∑	ADV
ejpam-5641	148	8	l∈n	l∈n	VERB
ejpam-5641	148	9			PROPN
ejpam-5641	148	10	ℏ̂	ℏ̂	NUM
ejpam-5641	148	11	(	(	PUNCT
ejpam-5641	148	12	∑l	∑l	INTJ
ejpam-5641	148	13	z=0	z=0	NUM
ejpam-5641	148	14	f	f	NOUN
ejpam-5641	148	15	2	2	NUM
ejpam-5641	148	16	zqzd̂z	zqzd̂z	NOUN
ejpam-5641	148	17	,	,	PUNCT
ejpam-5641	148	18	0̂	0̂	PROPN
ejpam-5641	148	19	)	)	PUNCT
ejpam-5641	149	1	flfl+1	flfl+1	PROPN
ejpam-5641	149	2	tl	tl	PUNCT
ejpam-5641	150	1	=	=	PUNCT
ejpam-5641	150	2	c1∥d̂∥p−qn	c1∥d̂∥p−qn	ADP
ejpam-5641	150	3	<	<	X
ejpam-5641	150	4	∞.	∞.	PROPN
ejpam-5641	150	5	hence	hence	ADV
ejpam-5641	150	6	,	,	PUNCT
ejpam-5641	150	7	δd̂	δd̂	PROPN
ejpam-5641	150	8	∈	∈	PROPN
ejpam-5641	150	9	γsf	γsf	X
ejpam-5641	150	10	(	(	PUNCT
ejpam-5641	150	11	q	q	NOUN
ejpam-5641	150	12	,	,	PUNCT
ejpam-5641	150	13	t	t	PROPN
ejpam-5641	150	14	)	)	PUNCT
ejpam-5641	150	15	.	.	PUNCT
ejpam-5641	151	1	hence	hence	ADV
ejpam-5641	151	2	γsf	γsf	VERB
ejpam-5641	151	3	(	(	PUNCT
ejpam-5641	151	4	q	q	NOUN
ejpam-5641	151	5	,	,	PUNCT
ejpam-5641	151	6	t	t	PROPN
ejpam-5641	151	7	)	)	PUNCT
ejpam-5641	151	8	is	be	AUX
ejpam-5641	151	9	a	a	DET
ejpam-5641	151	10	linear	linear	ADJ
ejpam-5641	151	11	space	space	NOUN
ejpam-5641	151	12	.	.	PUNCT
ejpam-5641	152	1	also	also	ADV
ejpam-5641	152	2	∑	∑	ADV
ejpam-5641	152	3	l∈n	l∈n	VERB
ejpam-5641	152	4			PROPN
ejpam-5641	152	5	ℏ̂	ℏ̂	NUM
ejpam-5641	152	6	(	(	PUNCT
ejpam-5641	152	7	∑l	∑l	INTJ
ejpam-5641	152	8	z=0	z=0	NUM
ejpam-5641	152	9	f	f	NOUN
ejpam-5641	152	10	2	2	NUM
ejpam-5641	152	11	zqz	zqz	NUM
ejpam-5641	152	12	(	(	PUNCT
ejpam-5641	152	13	̂eb)z	̂eb)z	PROPN
ejpam-5641	152	14	,	,	PUNCT
ejpam-5641	152	15	0̂	0̂	PROPN
ejpam-5641	152	16	)	)	PUNCT
ejpam-5641	153	1	flfl+1	flfl+1	PROPN
ejpam-5641	153	2	tl	tl	PUNCT
ejpam-5641	154	1	=	=	PUNCT
ejpam-5641	155	1	∞∑	∞∑	NUM
ejpam-5641	155	2	l	l	NOUN
ejpam-5641	155	3	=	=	SYM
ejpam-5641	155	4	b	b	X
ejpam-5641	155	5	(	(	PUNCT
ejpam-5641	155	6	f2bqb	f2bqb	PROPN
ejpam-5641	155	7	flfl+1	flfl+1	PROPN
ejpam-5641	155	8	)	)	PUNCT
ejpam-5641	155	9	tl	tl	PROPN
ejpam-5641	155	10	≤	≤	NUM
ejpam-5641	155	11	∞	∞	NUM
ejpam-5641	155	12	sup	sup	NOUN
ejpam-5641	155	13	l	l	NOUN
ejpam-5641	155	14	=	=	SYM
ejpam-5641	155	15	b	b	X
ejpam-5641	155	16	(	(	PUNCT
ejpam-5641	155	17	f2bqb	f2bqb	NOUN
ejpam-5641	155	18	)	)	PUNCT
ejpam-5641	155	19	tl	tl	PROPN
ejpam-5641	155	20	∞∑	∞∑	NUM
ejpam-5641	155	21	l	l	NOUN
ejpam-5641	155	22	=	=	SYM
ejpam-5641	155	23	b	b	X
ejpam-5641	155	24	(	(	PUNCT
ejpam-5641	155	25	1	1	NUM
ejpam-5641	155	26	flfl+1	flfl+1	NOUN
ejpam-5641	155	27	)	)	PUNCT
ejpam-5641	155	28	tl	tl	PROPN
ejpam-5641	155	29	<	<	X
ejpam-5641	155	30	∞.	∞.	PROPN
ejpam-5641	155	31	so	so	ADV
ejpam-5641	155	32	,	,	PUNCT
ejpam-5641	155	33	êb	êb	PROPN
ejpam-5641	155	34	∈	∈	PROPN
ejpam-5641	155	35	γsf	γsf	X
ejpam-5641	155	36	(	(	PUNCT
ejpam-5641	155	37	q	q	NOUN
ejpam-5641	155	38	,	,	PUNCT
ejpam-5641	155	39	t	t	PROPN
ejpam-5641	155	40	)	)	PUNCT
ejpam-5641	155	41	,	,	PUNCT
ejpam-5641	155	42	for	for	ADP
ejpam-5641	155	43	every	every	DET
ejpam-5641	155	44	b	b	PROPN
ejpam-5641	155	45	∈	∈	PROPN
ejpam-5641	155	46	n	n	NOUN
ejpam-5641	155	47	.	.	PUNCT
ejpam-5641	156	1	the	the	DET
ejpam-5641	156	2	conditions	condition	NOUN
ejpam-5641	156	3	(	(	PUNCT
ejpam-5641	156	4	2c	2c	NOUN
ejpam-5641	156	5	)	)	PUNCT
ejpam-5641	156	6	and	and	CCONJ
ejpam-5641	156	7	(	(	PUNCT
ejpam-5641	156	8	a4	a4	NUM
ejpam-5641	156	9	):	):	PUNCT
ejpam-5641	156	10	assume	assume	VERB
ejpam-5641	156	11	|d̂b|	|d̂b|	PROPN
ejpam-5641	156	12	≤	≤	PROPN
ejpam-5641	156	13	|k̂b|	|k̂b|	PROPN
ejpam-5641	156	14	,	,	PUNCT
ejpam-5641	156	15	for	for	ADP
ejpam-5641	156	16	b	b	PROPN
ejpam-5641	156	17	∈	∈	PROPN
ejpam-5641	156	18	n	n	NOUN
ejpam-5641	156	19	and	and	CCONJ
ejpam-5641	156	20	|k̂|	|k̂|	PROPN
ejpam-5641	156	21	∈	∈	PROPN
ejpam-5641	156	22	γsf	γsf	NOUN
ejpam-5641	156	23	(	(	PUNCT
ejpam-5641	156	24	q	q	NOUN
ejpam-5641	156	25	,	,	PUNCT
ejpam-5641	156	26	t	t	PROPN
ejpam-5641	156	27	)	)	PUNCT
ejpam-5641	156	28	.	.	PUNCT
ejpam-5641	157	1	hence	hence	ADV
ejpam-5641	157	2	∥(|d̂|)∥p−qn	∥(|d̂|)∥p−qn	NOUN
ejpam-5641	157	3	=	=	PUNCT
ejpam-5641	157	4	∑	∑	PUNCT
ejpam-5641	157	5	l∈n	l∈n	VERB
ejpam-5641	157	6			PROPN
ejpam-5641	157	7	ℏ̂	ℏ̂	NUM
ejpam-5641	157	8	(	(	PUNCT
ejpam-5641	157	9	∑l	∑l	INTJ
ejpam-5641	157	10	z=0	z=0	PROPN
ejpam-5641	157	11	f	f	NOUN
ejpam-5641	157	12	2	2	NUM
ejpam-5641	157	13	zqz|d̂z|	zqz|d̂z|	NUM
ejpam-5641	157	14	,	,	PUNCT
ejpam-5641	157	15	0̂	0̂	PROPN
ejpam-5641	157	16	)	)	PUNCT
ejpam-5641	158	1	flfl+1	flfl+1	PROPN
ejpam-5641	158	2	tl	tl	X
ejpam-5641	158	3	≤	≤	NOUN
ejpam-5641	158	4	∑	∑	PUNCT
ejpam-5641	158	5	l∈n	l∈n	ADP
ejpam-5641	158	6			PROPN
ejpam-5641	158	7	ℏ̂	ℏ̂	NUM
ejpam-5641	158	8	(	(	PUNCT
ejpam-5641	158	9	∑l	∑l	INTJ
ejpam-5641	158	10	z=0	z=0	PROPN
ejpam-5641	158	11	f	f	NOUN
ejpam-5641	158	12	2	2	NUM
ejpam-5641	158	13	zqz|k̂z|	zqz|k̂z|	NOUN
ejpam-5641	158	14	,	,	PUNCT
ejpam-5641	158	15	0̂	0̂	PROPN
ejpam-5641	158	16	)	)	PUNCT
ejpam-5641	159	1	flfl+1	flfl+1	PROPN
ejpam-5641	159	2	tl	tl	PUNCT
ejpam-5641	160	1	=	=	SYM
ejpam-5641	160	2	∥(|k̂|)∥p−qn	∥(|k̂|)∥p−qn	NOUN
ejpam-5641	160	3	<	<	X
ejpam-5641	160	4	∞	∞	PROPN
ejpam-5641	160	5	,	,	PUNCT
ejpam-5641	160	6	then	then	ADV
ejpam-5641	160	7	|d̂|	|d̂|	PROPN
ejpam-5641	160	8	∈	∈	PROPN
ejpam-5641	160	9	γsf	γsf	NOUN
ejpam-5641	160	10	(	(	PUNCT
ejpam-5641	160	11	q	q	NOUN
ejpam-5641	160	12	,	,	PUNCT
ejpam-5641	160	13	t	t	PROPN
ejpam-5641	160	14	)	)	PUNCT
ejpam-5641	160	15	.	.	PUNCT
ejpam-5641	161	1	the	the	DET
ejpam-5641	161	2	conditions	condition	NOUN
ejpam-5641	161	3	(	(	PUNCT
ejpam-5641	161	4	3c	3c	NUM
ejpam-5641	161	5	)	)	PUNCT
ejpam-5641	161	6	and	and	CCONJ
ejpam-5641	161	7	(	(	PUNCT
ejpam-5641	161	8	a5	a5	NOUN
ejpam-5641	161	9	):	):	PUNCT
ejpam-5641	161	10	let	let	VERB
ejpam-5641	161	11	(	(	PUNCT
ejpam-5641	161	12	|d̂z|	|d̂z|	NOUN
ejpam-5641	161	13	)	)	PUNCT
ejpam-5641	161	14	∈	∈	NOUN
ejpam-5641	161	15	γsf	γsf	NOUN
ejpam-5641	161	16	(	(	PUNCT
ejpam-5641	161	17	q	q	NOUN
ejpam-5641	161	18	,	,	PUNCT
ejpam-5641	161	19	t	t	PROPN
ejpam-5641	161	20	)	)	PUNCT
ejpam-5641	161	21	and	and	CCONJ
ejpam-5641	161	22	(	(	PUNCT
ejpam-5641	161	23	f2zqz	f2zqz	ADJ
ejpam-5641	161	24	)	)	PUNCT
ejpam-5641	161	25	z∈n	z∈n	NOUN
ejpam-5641	161	26	∈	∈	PROPN
ejpam-5641	161	27	d−	d−	PROPN
ejpam-5641	161	28	,	,	PUNCT
ejpam-5641	161	29	one	one	PRON
ejpam-5641	161	30	can	can	AUX
ejpam-5641	161	31	see	see	VERB
ejpam-5641	161	32	that	that	SCONJ
ejpam-5641	161	33	∥(|d̂	∥(|d̂	NOUN
ejpam-5641	161	34	[	[	PUNCT
ejpam-5641	161	35	z	z	NOUN
ejpam-5641	161	36	2	2	NUM
ejpam-5641	161	37	]	]	X
ejpam-5641	161	38	|)∥p−qn	|)∥p−qn	NOUN
ejpam-5641	161	39	=	=	SYM
ejpam-5641	161	40	∑	∑	PUNCT
ejpam-5641	161	41	l∈n	l∈n	VERB
ejpam-5641	161	42			PROPN
ejpam-5641	161	43	ℏ̂	ℏ̂	NUM
ejpam-5641	161	44	(	(	PUNCT
ejpam-5641	161	45	∑l	∑l	INTJ
ejpam-5641	161	46	z=0	z=0	NUM
ejpam-5641	161	47	f	f	NOUN
ejpam-5641	161	48	2	2	NUM
ejpam-5641	161	49	zqz|d̂	zqz|d̂	PROPN
ejpam-5641	161	50	[	[	PUNCT
ejpam-5641	161	51	z2	z2	NOUN
ejpam-5641	161	52	]	]	PUNCT
ejpam-5641	161	53	|	|	ADV
ejpam-5641	161	54	,	,	PUNCT
ejpam-5641	161	55	0̂	0̂	PROPN
ejpam-5641	161	56	)	)	PUNCT
ejpam-5641	162	1	flfl+1	flfl+1	PROPN
ejpam-5641	162	2	tl	tl	PUNCT
ejpam-5641	163	1	=	=	PUNCT
ejpam-5641	163	2	∑	∑	PUNCT
ejpam-5641	163	3	l∈n	l∈n	ADP
ejpam-5641	163	4			PROPN
ejpam-5641	163	5	ℏ̂	ℏ̂	NUM
ejpam-5641	163	6	(	(	PUNCT
ejpam-5641	163	7	∑2l	∑2l	PROPN
ejpam-5641	163	8	z=0	z=0	PROPN
ejpam-5641	163	9	f	f	NOUN
ejpam-5641	163	10	2	2	NUM
ejpam-5641	163	11	zqz|d̂	zqz|d̂	PROPN
ejpam-5641	163	12	[	[	PUNCT
ejpam-5641	163	13	z2	z2	NOUN
ejpam-5641	163	14	]	]	PUNCT
ejpam-5641	163	15	|	|	ADV
ejpam-5641	163	16	,	,	PUNCT
ejpam-5641	163	17	0̂	0̂	PROPN
ejpam-5641	163	18	)	)	PUNCT
ejpam-5641	163	19	f2lf2l+1	f2lf2l+1	PROPN
ejpam-5641	163	20	t2l	t2l	PROPN
ejpam-5641	164	1	+	+	CCONJ
ejpam-5641	164	2	∑	∑	PUNCT
ejpam-5641	164	3	l∈n	l∈n	VERB
ejpam-5641	164	4			PROPN
ejpam-5641	164	5	ℏ̂	ℏ̂	PUNCT
ejpam-5641	164	6	(	(	PUNCT
ejpam-5641	164	7	∑2l+1	∑2l+1	PROPN
ejpam-5641	164	8	z=0	z=0	PROPN
ejpam-5641	164	9	f2zqz|d̂	f2zqz|d̂	NOUN
ejpam-5641	164	10	[	[	PUNCT
ejpam-5641	164	11	z2	z2	NOUN
ejpam-5641	164	12	]	]	PUNCT
ejpam-5641	164	13	|	|	ADV
ejpam-5641	164	14	,	,	PUNCT
ejpam-5641	164	15	0̂	0̂	PROPN
ejpam-5641	164	16	)	)	PUNCT
ejpam-5641	164	17	f2l+1f2l+2	f2l+1f2l+2	PROPN
ejpam-5641	164	18	t2l+1	t2l+1	NOUN
ejpam-5641	164	19	≤	≤	NUM
ejpam-5641	164	20	∑	∑	PUNCT
ejpam-5641	164	21	l∈n	l∈n	ADP
ejpam-5641	164	22			PROPN
ejpam-5641	164	23	ℏ̂	ℏ̂	NUM
ejpam-5641	164	24	(	(	PUNCT
ejpam-5641	164	25	∑2l	∑2l	PROPN
ejpam-5641	164	26	z=0	z=0	PROPN
ejpam-5641	164	27	f	f	NOUN
ejpam-5641	164	28	2	2	NUM
ejpam-5641	164	29	zqz|d̂	zqz|d̂	PROPN
ejpam-5641	164	30	[	[	PUNCT
ejpam-5641	164	31	z2	z2	NOUN
ejpam-5641	164	32	]	]	PUNCT
ejpam-5641	164	33	|	|	ADV
ejpam-5641	164	34	,	,	PUNCT
ejpam-5641	164	35	0̂	0̂	PROPN
ejpam-5641	164	36	)	)	PUNCT
ejpam-5641	165	1	flfl+1	flfl+1	PROPN
ejpam-5641	165	2	tl	tl	PUNCT
ejpam-5641	166	1	+	+	CCONJ
ejpam-5641	166	2	∑	∑	PUNCT
ejpam-5641	166	3	l∈n	l∈n	VERB
ejpam-5641	166	4			PROPN
ejpam-5641	166	5	ℏ̂	ℏ̂	PUNCT
ejpam-5641	166	6	(	(	PUNCT
ejpam-5641	166	7	∑2l+1	∑2l+1	PROPN
ejpam-5641	166	8	z=0	z=0	PROPN
ejpam-5641	166	9	f2zqz|d̂	f2zqz|d̂	NOUN
ejpam-5641	166	10	[	[	PUNCT
ejpam-5641	166	11	z2	z2	NOUN
ejpam-5641	166	12	]	]	PUNCT
ejpam-5641	166	13	|	|	ADV
ejpam-5641	166	14	,	,	PUNCT
ejpam-5641	166	15	0̂	0̂	PROPN
ejpam-5641	166	16	)	)	PUNCT
ejpam-5641	167	1	flfl+1	flfl+1	PROPN
ejpam-5641	167	2	tl	tl	X
ejpam-5641	167	3	≤	≤	NOUN
ejpam-5641	167	4	∑	∑	PUNCT
ejpam-5641	167	5	l∈n	l∈n	ADP
ejpam-5641	167	6			PROPN
ejpam-5641	167	7	ℏ̂	ℏ̂	NUM
ejpam-5641	167	8	(	(	PUNCT
ejpam-5641	167	9	f22lq2l|d̂l|+	f22lq2l|d̂l|+	PROPN
ejpam-5641	167	10	∑l	∑l	PROPN
ejpam-5641	167	11	z=0	z=0	PROPN
ejpam-5641	167	12	(	(	PUNCT
ejpam-5641	167	13	f22zq2z	f22zq2z	X
ejpam-5641	168	1	+	+	NUM
ejpam-5641	168	2	f22z+1q2z+1	f22z+1q2z+1	PROPN
ejpam-5641	168	3	)	)	PUNCT
ejpam-5641	168	4	|d̂z|	|d̂z|	PROPN
ejpam-5641	168	5	,	,	PUNCT
ejpam-5641	168	6	0̂	0̂	PROPN
ejpam-5641	168	7	)	)	PUNCT
ejpam-5641	169	1	flfl+1	flfl+1	PROPN
ejpam-5641	169	2	tl	tl	PUNCT
ejpam-5641	170	1	+	+	CCONJ
ejpam-5641	170	2	∑	∑	PUNCT
ejpam-5641	170	3	l∈n	l∈n	VERB
ejpam-5641	170	4			PROPN
ejpam-5641	170	5	ℏ̂	ℏ̂	NUM
ejpam-5641	170	6	(	(	PUNCT
ejpam-5641	170	7	∑l	∑l	INTJ
ejpam-5641	170	8	z=0	z=0	PROPN
ejpam-5641	170	9	(	(	PUNCT
ejpam-5641	170	10	f22zq2z	f22zq2z	X
ejpam-5641	170	11	+	+	NUM
ejpam-5641	170	12	f22z+1q2z+1	f22z+1q2z+1	PROPN
ejpam-5641	170	13	)	)	PUNCT
ejpam-5641	170	14	|d̂z|	|d̂z|	PROPN
ejpam-5641	170	15	,	,	PUNCT
ejpam-5641	170	16	0̂	0̂	PROPN
ejpam-5641	170	17	)	)	PUNCT
ejpam-5641	171	1	flfl+1	flfl+1	PROPN
ejpam-5641	171	2	tl	tl	VERB
ejpam-5641	171	3	≤	≤	NUM
ejpam-5641	171	4	2ℶ−1	2ℶ−1	NUM
ejpam-5641	171	5	∑	∑	ADV
ejpam-5641	171	6	l∈n	l∈n	ADJ
ejpam-5641	171	7			PROPN
ejpam-5641	171	8	ℏ̂	ℏ̂	NUM
ejpam-5641	171	9	(	(	PUNCT
ejpam-5641	171	10	∑l	∑l	INTJ
ejpam-5641	171	11	z=0	z=0	PROPN
ejpam-5641	171	12	f	f	NOUN
ejpam-5641	171	13	2	2	NUM
ejpam-5641	171	14	zqz|d̂z|	zqz|d̂z|	NUM
ejpam-5641	171	15	,	,	PUNCT
ejpam-5641	171	16	0̂	0̂	PROPN
ejpam-5641	171	17	)	)	PUNCT
ejpam-5641	172	1	flfl+1	flfl+1	PROPN
ejpam-5641	172	2	tl	tl	PUNCT
ejpam-5641	173	1	+	+	CCONJ
ejpam-5641	173	2	∑	∑	PUNCT
ejpam-5641	173	3	l∈n	l∈n	VERB
ejpam-5641	173	4	2ℏ̂	2ℏ̂	NUM
ejpam-5641	173	5	(	(	PUNCT
ejpam-5641	173	6	∑l	∑l	INTJ
ejpam-5641	173	7	z=0	z=0	PROPN
ejpam-5641	173	8	f	f	NOUN
ejpam-5641	173	9	2	2	NUM
ejpam-5641	173	10	zqz|d̂z|	zqz|d̂z|	NUM
ejpam-5641	173	11	,	,	PUNCT
ejpam-5641	173	12	0̂	0̂	PROPN
ejpam-5641	173	13	)	)	PUNCT
ejpam-5641	174	1	flfl+1	flfl+1	PROPN
ejpam-5641	174	2	tl	tl	PUNCT
ejpam-5641	174	3	+	+	PROPN
ejpam-5641	174	4	∑	∑	PUNCT
ejpam-5641	174	5	l∈n	l∈n	VERB
ejpam-5641	174	6	2ℏ̂	2ℏ̂	NUM
ejpam-5641	174	7	(	(	PUNCT
ejpam-5641	174	8	∑l	∑l	INTJ
ejpam-5641	174	9	z=0	z=0	PROPN
ejpam-5641	174	10	f	f	NOUN
ejpam-5641	174	11	2	2	NUM
ejpam-5641	174	12	zqz|d̂z|	zqz|d̂z|	NUM
ejpam-5641	174	13	,	,	PUNCT
ejpam-5641	174	14	0̂	0̂	PROPN
ejpam-5641	174	15	)	)	PUNCT
ejpam-5641	175	1	flfl+1	flfl+1	PROPN
ejpam-5641	175	2	tl	tl	VERB
ejpam-5641	175	3	≤	≤	NUM
ejpam-5641	175	4	(	(	PUNCT
ejpam-5641	175	5	22ℶ−1	22ℶ−1	NUM
ejpam-5641	175	6	+	+	SYM
ejpam-5641	175	7	2ℶ−1	2ℶ−1	NUM
ejpam-5641	175	8	+	+	CCONJ
ejpam-5641	175	9	2ℶ	2ℶ	NOUN
ejpam-5641	175	10	)	)	PUNCT
ejpam-5641	175	11	∑	∑	PUNCT
ejpam-5641	175	12	l∈n	l∈n	VERB
ejpam-5641	175	13			PROPN
ejpam-5641	175	14	ℏ̂	ℏ̂	NUM
ejpam-5641	175	15	(	(	PUNCT
ejpam-5641	175	16	∑l	∑l	INTJ
ejpam-5641	175	17	z=0	z=0	PROPN
ejpam-5641	175	18	f	f	NOUN
ejpam-5641	175	19	2	2	NUM
ejpam-5641	175	20	zqz|d̂z|	zqz|d̂z|	NUM
ejpam-5641	175	21	,	,	PUNCT
ejpam-5641	175	22	0̂	0̂	PROPN
ejpam-5641	175	23	)	)	PUNCT
ejpam-5641	176	1	flfl+1	flfl+1	PROPN
ejpam-5641	176	2	tl	tl	PUNCT
ejpam-5641	177	1	=	=	PUNCT
ejpam-5641	177	2	c3∥(|d̂z|)∥p−qn	c3∥(|d̂z|)∥p−qn	X
ejpam-5641	177	3	<	<	X
ejpam-5641	177	4	∞	∞	PROPN
ejpam-5641	177	5	,	,	PUNCT
ejpam-5641	177	6	m.	m.	NOUN
ejpam-5641	177	7	m.	m.	NOUN
ejpam-5641	177	8	a	a	PRON
ejpam-5641	177	9	et	et	NOUN
ejpam-5641	177	10	al	al	PROPN
ejpam-5641	177	11	.	.	PUNCT
ejpam-5641	177	12	/	/	SYM
ejpam-5641	177	13	eur	eur	PROPN
ejpam-5641	177	14	.	.	PUNCT
ejpam-5641	178	1	j.	j.	PROPN
ejpam-5641	178	2	pure	pure	PROPN
ejpam-5641	178	3	appl	appl	PROPN
ejpam-5641	178	4	.	.	PROPN
ejpam-5641	178	5	math	math	PROPN
ejpam-5641	178	6	,	,	PUNCT
ejpam-5641	178	7	18	18	NUM
ejpam-5641	178	8	(	(	PUNCT
ejpam-5641	178	9	1	1	NUM
ejpam-5641	178	10	)	)	PUNCT
ejpam-5641	178	11	(	(	PUNCT
ejpam-5641	178	12	2025	2025	NUM
ejpam-5641	178	13	)	)	PUNCT
ejpam-5641	178	14	,	,	PUNCT
ejpam-5641	178	15	5641	5641	NUM
ejpam-5641	178	16	8	8	NUM
ejpam-5641	178	17	of	of	ADP
ejpam-5641	178	18	20	20	NUM
ejpam-5641	178	19	then	then	ADV
ejpam-5641	178	20	(	(	PUNCT
ejpam-5641	178	21	|d̂	|d̂	NOUN
ejpam-5641	178	22	[	[	PUNCT
ejpam-5641	178	23	z	z	NOUN
ejpam-5641	178	24	2	2	NUM
ejpam-5641	178	25	]	]	PUNCT
ejpam-5641	178	26	|	|	NOUN
ejpam-5641	178	27	)	)	PUNCT
ejpam-5641	178	28	∈	∈	NOUN
ejpam-5641	178	29	γsf	γsf	NOUN
ejpam-5641	178	30	(	(	PUNCT
ejpam-5641	178	31	q	q	NOUN
ejpam-5641	178	32	,	,	PUNCT
ejpam-5641	178	33	t	t	PROPN
ejpam-5641	178	34	)	)	PUNCT
ejpam-5641	178	35	.	.	PUNCT
ejpam-5641	179	1	evidently	evidently	ADV
ejpam-5641	179	2	,	,	PUNCT
ejpam-5641	179	3	the	the	DET
ejpam-5641	179	4	conditions	condition	NOUN
ejpam-5641	179	5	(	(	PUNCT
ejpam-5641	179	6	a6	a6	NOUN
ejpam-5641	179	7	)	)	PUNCT
ejpam-5641	179	8	and	and	CCONJ
ejpam-5641	179	9	(	(	PUNCT
ejpam-5641	179	10	a7	a7	PROPN
ejpam-5641	179	11	)	)	PUNCT
ejpam-5641	179	12	can	can	AUX
ejpam-5641	179	13	be	be	AUX
ejpam-5641	179	14	easily	easily	ADV
ejpam-5641	179	15	shown	show	VERB
ejpam-5641	179	16	.	.	PUNCT
ejpam-5641	180	1	assume	assume	VERB
ejpam-5641	180	2	here	here	ADV
ejpam-5641	180	3	and	and	CCONJ
ejpam-5641	180	4	after	after	SCONJ
ejpam-5641	180	5	the	the	DET
ejpam-5641	180	6	parts	part	NOUN
ejpam-5641	180	7	of	of	ADP
ejpam-5641	180	8	theorem	theorem	ADJ
ejpam-5641	180	9	3.3	3.3	NUM
ejpam-5641	180	10	are	be	AUX
ejpam-5641	180	11	verified	verify	VERB
ejpam-5641	180	12	.	.	PUNCT
ejpam-5641	181	1	theorem	theorem	VERB
ejpam-5641	181	2	3.4	3.4	NUM
ejpam-5641	181	3	.	.	PUNCT
ejpam-5641	182	1	(	(	PUNCT
ejpam-5641	182	2	γsf	γsf	X
ejpam-5641	182	3	(	(	PUNCT
ejpam-5641	182	4	q	q	X
ejpam-5641	182	5	,	,	PUNCT
ejpam-5641	182	6	t))∥.∥p−qn	t))∥.∥p−qn	PROPN
ejpam-5641	182	7	is	be	AUX
ejpam-5641	182	8	a	a	DET
ejpam-5641	182	9	p	p	NOUN
ejpam-5641	182	10	-	-	PUNCT
ejpam-5641	182	11	q.b	q.b	NOUN
ejpam-5641	182	12	psssf	psssf	NOUN
ejpam-5641	182	13	.	.	PUNCT
ejpam-5641	183	1	proof	proof	NOUN
ejpam-5641	183	2	.	.	PUNCT
ejpam-5641	184	1	in	in	ADP
ejpam-5641	184	2	view	view	NOUN
ejpam-5641	184	3	of	of	ADP
ejpam-5641	184	4	theorem	theorem	NOUN
ejpam-5641	184	5	2.1	2.1	NUM
ejpam-5641	184	6	,	,	PUNCT
ejpam-5641	184	7	then	then	ADV
ejpam-5641	184	8	(	(	PUNCT
ejpam-5641	184	9	γsf	γsf	X
ejpam-5641	184	10	(	(	PUNCT
ejpam-5641	184	11	q	q	X
ejpam-5641	184	12	,	,	PUNCT
ejpam-5641	184	13	t))∥.∥p−qn	t))∥.∥p−qn	PROPN
ejpam-5641	184	14	is	be	AUX
ejpam-5641	184	15	a	a	DET
ejpam-5641	184	16	p	p	ADJ
ejpam-5641	184	17	-	-	PUNCT
ejpam-5641	184	18	q.n	q.n	NOUN
ejpam-5641	184	19	psssf	psssf	NOUN
ejpam-5641	184	20	.	.	PUNCT
ejpam-5641	185	1	to	to	PART
ejpam-5641	185	2	prove	prove	VERB
ejpam-5641	185	3	that	that	SCONJ
ejpam-5641	185	4	(	(	PUNCT
ejpam-5641	185	5	γsf	γsf	X
ejpam-5641	185	6	(	(	PUNCT
ejpam-5641	185	7	q	q	X
ejpam-5641	185	8	,	,	PUNCT
ejpam-5641	185	9	t))∥.∥p−qn	t))∥.∥p−qn	PROPN
ejpam-5641	185	10	is	be	AUX
ejpam-5641	185	11	a	a	DET
ejpam-5641	185	12	p	p	NOUN
ejpam-5641	185	13	-	-	PUNCT
ejpam-5641	185	14	q.b	q.b	NOUN
ejpam-5641	185	15	psssf	psssf	NOUN
ejpam-5641	185	16	,	,	PUNCT
ejpam-5641	185	17	assume	assume	VERB
ejpam-5641	185	18	f̂a	f̂a	X
ejpam-5641	185	19	=	=	PRON
ejpam-5641	185	20	(	(	PUNCT
ejpam-5641	185	21	f̂a	f̂a	PROPN
ejpam-5641	185	22	z	z	PROPN
ejpam-5641	185	23	)	)	PUNCT
ejpam-5641	185	24	z∈n	z∈n	PROPN
ejpam-5641	185	25	is	be	AUX
ejpam-5641	185	26	a	a	DET
ejpam-5641	185	27	cs	cs	PROPN
ejpam-5641	185	28	in	in	ADP
ejpam-5641	185	29	(	(	PUNCT
ejpam-5641	185	30	γsf	γsf	X
ejpam-5641	185	31	(	(	PUNCT
ejpam-5641	185	32	q	q	NOUN
ejpam-5641	185	33	,	,	PUNCT
ejpam-5641	185	34	t))∥.∥p−qn	t))∥.∥p−qn	NOUN
ejpam-5641	185	35	,	,	PUNCT
ejpam-5641	185	36	then	then	ADV
ejpam-5641	185	37	for	for	ADP
ejpam-5641	185	38	λ	λ	PROPN
ejpam-5641	185	39	∈	∈	PROPN
ejpam-5641	185	40	(	(	PUNCT
ejpam-5641	185	41	0	0	NUM
ejpam-5641	185	42	,	,	PUNCT
ejpam-5641	185	43	1	1	NUM
ejpam-5641	185	44	)	)	PUNCT
ejpam-5641	185	45	,	,	PUNCT
ejpam-5641	185	46	we	we	PRON
ejpam-5641	185	47	get	get	VERB
ejpam-5641	185	48	m0	m0	PROPN
ejpam-5641	185	49	∈	∈	PROPN
ejpam-5641	185	50	n	n	X
ejpam-5641	185	51	for	for	ADP
ejpam-5641	185	52	every	every	DET
ejpam-5641	185	53	m	m	PROPN
ejpam-5641	185	54	,	,	PUNCT
ejpam-5641	185	55	j	j	PROPN
ejpam-5641	185	56	≥	≥	NUM
ejpam-5641	185	57	m0	m0	PROPN
ejpam-5641	185	58	,	,	PUNCT
ejpam-5641	186	1	so	so	SCONJ
ejpam-5641	186	2	∥d̂m	∥d̂m	NUM
ejpam-5641	186	3	−	−	PROPN
ejpam-5641	186	4	d̂j∥p−qn	d̂j∥p−qn	PROPN
ejpam-5641	186	5	=	=	SYM
ejpam-5641	186	6	∑	∑	PUNCT
ejpam-5641	186	7	l∈n	l∈n	ADJ
ejpam-5641	186	8			PROPN
ejpam-5641	186	9	ℏ̂	ℏ̂	ADP
ejpam-5641	186	10	(	(	PUNCT
ejpam-5641	186	11	∑l	∑l	INTJ
ejpam-5641	186	12	z=0	z=0	NUM
ejpam-5641	186	13	f	f	NOUN
ejpam-5641	186	14	2	2	NUM
ejpam-5641	186	15	zqz	zqz	NUM
ejpam-5641	186	16	(	(	PUNCT
ejpam-5641	186	17	d̂zz	d̂zz	NOUN
ejpam-5641	186	18	−	−	PROPN
ejpam-5641	186	19	d̂jz	d̂jz	NOUN
ejpam-5641	186	20	)	)	PUNCT
ejpam-5641	186	21	,	,	PUNCT
ejpam-5641	186	22	0̂	0̂	PROPN
ejpam-5641	186	23	)	)	PUNCT
ejpam-5641	187	1	flfl+1	flfl+1	PROPN
ejpam-5641	187	2			VERB
ejpam-5641	187	3	tl	tl	PROPN
ejpam-5641	187	4	<	<	X
ejpam-5641	187	5	λℶ.	λℶ.	PROPN
ejpam-5641	188	1	so	so	ADV
ejpam-5641	188	2	ℏ̂	ℏ̂	ADP
ejpam-5641	188	3	(	(	PUNCT
ejpam-5641	188	4	∑l	∑l	INTJ
ejpam-5641	188	5	z=0	z=0	NUM
ejpam-5641	188	6	f	f	NOUN
ejpam-5641	188	7	2	2	NUM
ejpam-5641	188	8	zqz	zqz	NUM
ejpam-5641	188	9	(	(	PUNCT
ejpam-5641	188	10	d̂mz	d̂mz	PROPN
ejpam-5641	188	11	−	−	PROPN
ejpam-5641	188	12	d̂jz	d̂jz	PROPN
ejpam-5641	188	13	)	)	PUNCT
ejpam-5641	188	14	,	,	PUNCT
ejpam-5641	188	15	0̂	0̂	PROPN
ejpam-5641	188	16	)	)	PUNCT
ejpam-5641	188	17	<	<	X
ejpam-5641	189	1	λ	λ	X
ejpam-5641	189	2	.	.	PUNCT
ejpam-5641	190	1	since	since	SCONJ
ejpam-5641	190	2	(	(	PUNCT
ejpam-5641	190	3	r(a	r(a	PROPN
ejpam-5641	190	4	)	)	PUNCT
ejpam-5641	190	5	,	,	PUNCT
ejpam-5641	190	6	ℏ̂	ℏ̂	ADV
ejpam-5641	190	7	)	)	PUNCT
ejpam-5641	190	8	is	be	AUX
ejpam-5641	190	9	a	a	DET
ejpam-5641	190	10	cms	cms	NOUN
ejpam-5641	190	11	.	.	PUNCT
ejpam-5641	191	1	therefore	therefore	ADV
ejpam-5641	191	2	,	,	PUNCT
ejpam-5641	191	3	(	(	PUNCT
ejpam-5641	191	4	d̂jz	d̂jz	NOUN
ejpam-5641	191	5	)	)	PUNCT
ejpam-5641	191	6	is	be	AUX
ejpam-5641	191	7	a	a	DET
ejpam-5641	191	8	cs	cs	PROPN
ejpam-5641	191	9	in	in	ADP
ejpam-5641	191	10	r(a	r(a	PROPN
ejpam-5641	191	11	)	)	PUNCT
ejpam-5641	191	12	,	,	PUNCT
ejpam-5641	191	13	for	for	ADP
ejpam-5641	191	14	fixed	fix	VERB
ejpam-5641	191	15	z	z	PROPN
ejpam-5641	191	16	∈	∈	PROPN
ejpam-5641	191	17	n	n	X
ejpam-5641	191	18	.	.	PUNCT
ejpam-5641	192	1	therefore	therefore	ADV
ejpam-5641	192	2	,	,	PUNCT
ejpam-5641	192	3	∥d̂m	∥d̂m	NUM
ejpam-5641	192	4	−	−	PROPN
ejpam-5641	192	5	d̂0∥p−qn	d̂0∥p−qn	NOUN
ejpam-5641	192	6	<	<	X
ejpam-5641	192	7	λℶ	λℶ	NOUN
ejpam-5641	192	8	,	,	PUNCT
ejpam-5641	192	9	for	for	ADP
ejpam-5641	192	10	any	any	DET
ejpam-5641	192	11	m	m	PROPN
ejpam-5641	192	12	≥	≥	NOUN
ejpam-5641	192	13	m0	m0	NOUN
ejpam-5641	192	14	.	.	PUNCT
ejpam-5641	193	1	obviously	obviously	ADV
ejpam-5641	193	2	from	from	ADP
ejpam-5641	193	3	the	the	DET
ejpam-5641	193	4	linearity	linearity	NOUN
ejpam-5641	193	5	,	,	PUNCT
ejpam-5641	193	6	d̂0	d̂0	NOUN
ejpam-5641	193	7	∈	∈	PROPN
ejpam-5641	193	8	(	(	PUNCT
ejpam-5641	193	9	γsf	γsf	X
ejpam-5641	193	10	(	(	PUNCT
ejpam-5641	193	11	q	q	NOUN
ejpam-5641	193	12	,	,	PUNCT
ejpam-5641	193	13	t))∥.∥p−qn	t))∥.∥p−qn	NUM
ejpam-5641	193	14	.	.	PUNCT
ejpam-5641	194	1	4	4	X
ejpam-5641	194	2	.	.	X
ejpam-5641	194	3	ntk-∥.∥p−qn	ntk-∥.∥p−qn	NOUN
ejpam-5641	194	4	-	-	SYM
ejpam-5641	194	5	c	c	NOUN
ejpam-5641	194	6	we	we	PRON
ejpam-5641	194	7	will	will	AUX
ejpam-5641	194	8	explore	explore	VERB
ejpam-5641	194	9	the	the	DET
ejpam-5641	194	10	existence	existence	NOUN
ejpam-5641	194	11	and	and	CCONJ
ejpam-5641	194	12	uniqueness	uniqueness	NOUN
ejpam-5641	194	13	of	of	ADP
ejpam-5641	194	14	the	the	DET
ejpam-5641	194	15	fixed	fix	VERB
ejpam-5641	194	16	point	point	NOUN
ejpam-5641	194	17	of	of	ADP
ejpam-5641	194	18	ntk-∥.∥p−qn	ntk-∥.∥p−qn	NOUN
ejpam-5641	194	19	-	-	PUNCT
ejpam-5641	194	20	c	c	NOUN
ejpam-5641	194	21	defined	define	VERB
ejpam-5641	194	22	on	on	ADP
ejpam-5641	194	23	γsf	γsf	X
ejpam-5641	194	24	(	(	PUNCT
ejpam-5641	194	25	q	q	NOUN
ejpam-5641	194	26	,	,	PUNCT
ejpam-5641	194	27	t	t	PROPN
ejpam-5641	194	28	)	)	PUNCT
ejpam-5641	194	29	in	in	ADP
ejpam-5641	194	30	this	this	DET
ejpam-5641	194	31	section	section	NOUN
ejpam-5641	194	32	.	.	PUNCT
ejpam-5641	195	1	supposing	suppose	VERB
ejpam-5641	195	2	that	that	SCONJ
ejpam-5641	195	3	the	the	DET
ejpam-5641	195	4	conditions	condition	NOUN
ejpam-5641	195	5	of	of	ADP
ejpam-5641	195	6	theorem	theorem	ADJ
ejpam-5641	195	7	3.3	3.3	NUM
ejpam-5641	195	8	are	be	AUX
ejpam-5641	195	9	confirmed	confirm	VERB
ejpam-5641	195	10	.	.	PUNCT
ejpam-5641	196	1	we	we	PRON
ejpam-5641	196	2	will	will	AUX
ejpam-5641	196	3	use	use	VERB
ejpam-5641	196	4	in	in	ADP
ejpam-5641	196	5	this	this	DET
ejpam-5641	196	6	part	part	NOUN
ejpam-5641	196	7	the	the	DET
ejpam-5641	196	8	following	follow	VERB
ejpam-5641	196	9	two	two	NUM
ejpam-5641	196	10	equivalent	equivalent	ADJ
ejpam-5641	196	11	p-q.ns	p-q.ns	NOUN
ejpam-5641	196	12	:	:	PUNCT
ejpam-5641	196	13	∥f̂∥p−qn	∥f̂∥p−qn	NOUN
ejpam-5641	196	14	=	=	SYM
ejpam-5641	196	15	∑	∑	NOUN
ejpam-5641	196	16	l∈n	l∈n	VERB
ejpam-5641	196	17			PROPN
ejpam-5641	196	18	ℏ̂	ℏ̂	NUM
ejpam-5641	196	19	(	(	PUNCT
ejpam-5641	196	20	∑l	∑l	INTJ
ejpam-5641	196	21	z=0	z=0	NUM
ejpam-5641	196	22	f	f	NOUN
ejpam-5641	196	23	2	2	NUM
ejpam-5641	196	24	zqz	zqz	NUM
ejpam-5641	196	25	f̂z	f̂z	NOUN
ejpam-5641	196	26	,	,	PUNCT
ejpam-5641	196	27	0̂	0̂	PROPN
ejpam-5641	196	28	)	)	PUNCT
ejpam-5641	197	1	flfl+1	flfl+1	PROPN
ejpam-5641	197	2	tl	tl	VERB
ejpam-5641	198	1			ADV
ejpam-5641	198	2	1	1	NUM
ejpam-5641	198	3	ℶ	ℶ	NOUN
ejpam-5641	198	4	and	and	CCONJ
ejpam-5641	198	5	∥f̂∥ℶp−qn	∥f̂∥ℶp−qn	NOUN
ejpam-5641	198	6	=	=	SYM
ejpam-5641	198	7	∑	∑	PUNCT
ejpam-5641	198	8	l∈n	l∈n	ADP
ejpam-5641	198	9			PROPN
ejpam-5641	198	10	ℏ̂	ℏ̂	NUM
ejpam-5641	198	11	(	(	PUNCT
ejpam-5641	198	12	∑l	∑l	INTJ
ejpam-5641	198	13	z=0	z=0	NUM
ejpam-5641	198	14	f	f	NOUN
ejpam-5641	198	15	2	2	NUM
ejpam-5641	198	16	zqz	zqz	NUM
ejpam-5641	198	17	f̂z	f̂z	NOUN
ejpam-5641	198	18	,	,	PUNCT
ejpam-5641	198	19	0̂	0̂	PROPN
ejpam-5641	198	20	)	)	PUNCT
ejpam-5641	199	1	flfl+1	flfl+1	PROPN
ejpam-5641	199	2	tl	tl	PROPN
ejpam-5641	199	3	,	,	PUNCT
ejpam-5641	199	4	for	for	ADP
ejpam-5641	199	5	every	every	DET
ejpam-5641	199	6	f̂	f̂	NUM
ejpam-5641	199	7	∈	∈	NOUN
ejpam-5641	199	8	γsf	γsf	NOUN
ejpam-5641	199	9	(	(	PUNCT
ejpam-5641	199	10	q	q	NOUN
ejpam-5641	199	11	,	,	PUNCT
ejpam-5641	199	12	t	t	PROPN
ejpam-5641	199	13	)	)	PUNCT
ejpam-5641	199	14	.	.	PUNCT
ejpam-5641	200	1	theorem	theorem	VERB
ejpam-5641	200	2	4.1	4.1	NUM
ejpam-5641	200	3	.	.	PUNCT
ejpam-5641	201	1	the	the	DET
ejpam-5641	201	2	p	p	PROPN
ejpam-5641	201	3	-	-	PUNCT
ejpam-5641	201	4	q.n	q.n	NOUN
ejpam-5641	201	5	∥f̂∥p−qn	∥f̂∥p−qn	NOUN
ejpam-5641	201	6	satisfies	satisfy	VERB
ejpam-5641	201	7	the	the	DET
ejpam-5641	201	8	fp	fp	PROPN
ejpam-5641	201	9	.	.	PROPN
ejpam-5641	201	10	m.	m.	PROPN
ejpam-5641	201	11	m.	m.	PROPN
ejpam-5641	201	12	a	a	PRON
ejpam-5641	201	13	et	et	PROPN
ejpam-5641	201	14	al	al	PROPN
ejpam-5641	201	15	.	.	PUNCT
ejpam-5641	201	16	/	/	SYM
ejpam-5641	201	17	eur	eur	PROPN
ejpam-5641	201	18	.	.	PUNCT
ejpam-5641	202	1	j.	j.	PROPN
ejpam-5641	202	2	pure	pure	PROPN
ejpam-5641	202	3	appl	appl	PROPN
ejpam-5641	202	4	.	.	PROPN
ejpam-5641	202	5	math	math	PROPN
ejpam-5641	202	6	,	,	PUNCT
ejpam-5641	202	7	18	18	NUM
ejpam-5641	202	8	(	(	PUNCT
ejpam-5641	202	9	1	1	NUM
ejpam-5641	202	10	)	)	PUNCT
ejpam-5641	202	11	(	(	PUNCT
ejpam-5641	202	12	2025	2025	NUM
ejpam-5641	202	13	)	)	PUNCT
ejpam-5641	202	14	,	,	PUNCT
ejpam-5641	202	15	5641	5641	NUM
ejpam-5641	202	16	9	9	NUM
ejpam-5641	202	17	of	of	ADP
ejpam-5641	202	18	20	20	NUM
ejpam-5641	202	19	proof	proof	NOUN
ejpam-5641	202	20	.	.	PUNCT
ejpam-5641	203	1	assume	assume	VERB
ejpam-5641	203	2	{	{	PUNCT
ejpam-5641	203	3	ûd	ûd	NOUN
ejpam-5641	203	4	}	}	SYM
ejpam-5641	203	5	⊆	⊆	NUM
ejpam-5641	203	6	(	(	PUNCT
ejpam-5641	203	7	γsf	γsf	X
ejpam-5641	203	8	(	(	PUNCT
ejpam-5641	203	9	q	q	NOUN
ejpam-5641	203	10	,	,	PUNCT
ejpam-5641	203	11	t	t	PROPN
ejpam-5641	203	12	)	)	PUNCT
ejpam-5641	203	13	)	)	PUNCT
ejpam-5641	204	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	204	2	with	with	ADP
ejpam-5641	204	3	limd→∞	limd→∞	PROPN
ejpam-5641	204	4	∥ûd−û∥p−qn	∥ûd−û∥p−qn	PROPN
ejpam-5641	204	5	=	=	SYM
ejpam-5641	204	6	0.as	0.as	X
ejpam-5641	204	7	(	(	PUNCT
ejpam-5641	204	8	γsf	γsf	X
ejpam-5641	204	9	(	(	PUNCT
ejpam-5641	204	10	q	q	NOUN
ejpam-5641	204	11	,	,	PUNCT
ejpam-5641	204	12	t	t	PROPN
ejpam-5641	204	13	)	)	PUNCT
ejpam-5641	204	14	)	)	PUNCT
ejpam-5641	205	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	205	2	is	be	AUX
ejpam-5641	205	3	a	a	DET
ejpam-5641	205	4	p	p	NOUN
ejpam-5641	205	5	-	-	PUNCT
ejpam-5641	205	6	q.b	q.b	NOUN
ejpam-5641	205	7	,	,	PUNCT
ejpam-5641	205	8	then	then	ADV
ejpam-5641	205	9	û	û	PRON
ejpam-5641	205	10	∈	∈	PROPN
ejpam-5641	205	11	(	(	PUNCT
ejpam-5641	205	12	γsf	γsf	X
ejpam-5641	205	13	(	(	PUNCT
ejpam-5641	205	14	q	q	NOUN
ejpam-5641	205	15	,	,	PUNCT
ejpam-5641	205	16	t	t	PROPN
ejpam-5641	205	17	)	)	PUNCT
ejpam-5641	205	18	)	)	PUNCT
ejpam-5641	206	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	206	2	.	.	PUNCT
ejpam-5641	207	1	hence	hence	ADV
ejpam-5641	207	2	∥f̂	∥f̂	PROPN
ejpam-5641	207	3	−	−	PROPN
ejpam-5641	207	4	û∥p−qn	û∥p−qn	PROPN
ejpam-5641	207	5	=	=	PROPN
ejpam-5641	207	6	∑	∑	NOUN
ejpam-5641	207	7	l∈n	l∈n	VERB
ejpam-5641	207	8			PROPN
ejpam-5641	207	9	ℏ̂	ℏ̂	NUM
ejpam-5641	207	10	(	(	PUNCT
ejpam-5641	207	11	∑l	∑l	INTJ
ejpam-5641	207	12	z=0	z=0	NUM
ejpam-5641	207	13	f	f	NOUN
ejpam-5641	207	14	2	2	NUM
ejpam-5641	207	15	zqz(f̂z	zqz(f̂z	PROPN
ejpam-5641	207	16	−	−	PROPN
ejpam-5641	207	17	ûz	ûz	NOUN
ejpam-5641	207	18	)	)	PUNCT
ejpam-5641	207	19	,	,	PUNCT
ejpam-5641	207	20	0̂	0̂	PROPN
ejpam-5641	207	21	)	)	PUNCT
ejpam-5641	208	1	flfl+1	flfl+1	PROPN
ejpam-5641	208	2	tl	tl	VERB
ejpam-5641	209	1			ADV
ejpam-5641	209	2	1	1	NUM
ejpam-5641	209	3	ℶ	ℶ	NOUN
ejpam-5641	209	4	≤	≤	NUM
ejpam-5641	209	5	∑	∑	NOUN
ejpam-5641	209	6	l∈n	l∈n	VERB
ejpam-5641	209	7			PROPN
ejpam-5641	209	8	ℏ̂	ℏ̂	NUM
ejpam-5641	209	9	(	(	PUNCT
ejpam-5641	209	10	∑l	∑l	INTJ
ejpam-5641	209	11	z=0	z=0	NUM
ejpam-5641	209	12	f	f	NOUN
ejpam-5641	209	13	2	2	NUM
ejpam-5641	209	14	zqz(f̂z	zqz(f̂z	PROPN
ejpam-5641	209	15	−	−	PROPN
ejpam-5641	209	16	ûdz	ûdz	NOUN
ejpam-5641	209	17	)	)	PUNCT
ejpam-5641	209	18	,	,	PUNCT
ejpam-5641	209	19	0̂	0̂	PROPN
ejpam-5641	209	20	)	)	PUNCT
ejpam-5641	210	1	flfl+1	flfl+1	PROPN
ejpam-5641	210	2	tl	tl	VERB
ejpam-5641	211	1			ADV
ejpam-5641	211	2	1	1	NUM
ejpam-5641	211	3	ℶ	ℶ	NOUN
ejpam-5641	211	4	+	+	NUM
ejpam-5641	211	5	∑	∑	NOUN
ejpam-5641	211	6	l∈n	l∈n	VERB
ejpam-5641	211	7			PROPN
ejpam-5641	211	8	ℏ̂	ℏ̂	NUM
ejpam-5641	211	9	(	(	PUNCT
ejpam-5641	211	10	∑l	∑l	INTJ
ejpam-5641	211	11	z=0	z=0	NUM
ejpam-5641	211	12	f	f	NOUN
ejpam-5641	211	13	2	2	NUM
ejpam-5641	211	14	zqz(û	zqz(û	NOUN
ejpam-5641	211	15	d	d	NOUN
ejpam-5641	211	16	z	z	NOUN
ejpam-5641	211	17	−	−	NOUN
ejpam-5641	211	18	ûz	ûz	NOUN
ejpam-5641	211	19	)	)	PUNCT
ejpam-5641	211	20	,	,	PUNCT
ejpam-5641	211	21	0̂	0̂	PROPN
ejpam-5641	211	22	)	)	PUNCT
ejpam-5641	212	1	flfl+1	flfl+1	PROPN
ejpam-5641	212	2	tl	tl	VERB
ejpam-5641	213	1			ADV
ejpam-5641	213	2	1	1	NUM
ejpam-5641	213	3	ℶ	ℶ	NOUN
ejpam-5641	213	4	≤	≤	NUM
ejpam-5641	213	5	sup	sup	NOUN
ejpam-5641	213	6	v	v	NOUN
ejpam-5641	213	7	inf	inf	NOUN
ejpam-5641	213	8	d≥v	d≥v	ADJ
ejpam-5641	213	9	∥f̂	∥f̂	PROPN
ejpam-5641	213	10	−	−	PROPN
ejpam-5641	213	11	ûd∥p−qn	ûd∥p−qn	PROPN
ejpam-5641	213	12	.	.	PUNCT
ejpam-5641	214	1	theorem	theorem	VERB
ejpam-5641	214	2	4.2	4.2	NUM
ejpam-5641	214	3	.	.	PUNCT
ejpam-5641	215	1	the	the	DET
ejpam-5641	215	2	p	p	PROPN
ejpam-5641	215	3	-	-	PUNCT
ejpam-5641	215	4	q.n	q.n	NOUN
ejpam-5641	215	5	∥f̂∥ℶp−qn	∥f̂∥ℶp−qn	NOUN
ejpam-5641	215	6	does	do	AUX
ejpam-5641	215	7	not	not	PART
ejpam-5641	215	8	hold	hold	VERB
ejpam-5641	215	9	the	the	DET
ejpam-5641	215	10	fp	fp	NOUN
ejpam-5641	215	11	under	under	ADP
ejpam-5641	215	12	t0	t0	PROPN
ejpam-5641	215	13	>	>	X
ejpam-5641	216	1	1	1	X
ejpam-5641	216	2	.	.	PUNCT
ejpam-5641	216	3	proof	proof	NOUN
ejpam-5641	216	4	.	.	PUNCT
ejpam-5641	217	1	when	when	SCONJ
ejpam-5641	217	2	{	{	PUNCT
ejpam-5641	217	3	ûd	ûd	NOUN
ejpam-5641	217	4	}	}	SYM
ejpam-5641	217	5	⊆	⊆	NUM
ejpam-5641	217	6	(	(	PUNCT
ejpam-5641	217	7	γsf	γsf	X
ejpam-5641	217	8	(	(	PUNCT
ejpam-5641	217	9	q	q	NOUN
ejpam-5641	217	10	,	,	PUNCT
ejpam-5641	217	11	t	t	PROPN
ejpam-5641	217	12	)	)	PUNCT
ejpam-5641	217	13	)	)	PUNCT
ejpam-5641	217	14	∥.∥ℶp−qn	∥.∥ℶp−qn	NOUN
ejpam-5641	217	15	with	with	ADP
ejpam-5641	217	16	limd→∞	limd→∞	PROPN
ejpam-5641	217	17	∥ûd−û∥ℶp−qn	∥ûd−û∥ℶp−qn	PROPN
ejpam-5641	217	18	=	=	SYM
ejpam-5641	217	19	0.as	0.as	X
ejpam-5641	217	20	(	(	PUNCT
ejpam-5641	217	21	γsf	γsf	X
ejpam-5641	217	22	(	(	PUNCT
ejpam-5641	217	23	q	q	NOUN
ejpam-5641	217	24	,	,	PUNCT
ejpam-5641	217	25	t	t	PROPN
ejpam-5641	217	26	)	)	PUNCT
ejpam-5641	217	27	)	)	PUNCT
ejpam-5641	218	1	∥.∥ℶp−qn	∥.∥ℶp−qn	NOUN
ejpam-5641	218	2	is	be	AUX
ejpam-5641	218	3	a	a	DET
ejpam-5641	218	4	p	p	NOUN
ejpam-5641	218	5	-	-	PUNCT
ejpam-5641	218	6	q.b	q.b	NOUN
ejpam-5641	218	7	,	,	PUNCT
ejpam-5641	218	8	then	then	ADV
ejpam-5641	218	9	û	û	PRON
ejpam-5641	218	10	∈	∈	PROPN
ejpam-5641	218	11	(	(	PUNCT
ejpam-5641	218	12	γsf	γsf	X
ejpam-5641	218	13	(	(	PUNCT
ejpam-5641	218	14	q	q	NOUN
ejpam-5641	218	15	,	,	PUNCT
ejpam-5641	218	16	t	t	PROPN
ejpam-5641	218	17	)	)	PUNCT
ejpam-5641	218	18	)	)	PUNCT
ejpam-5641	219	1	∥.∥ℶp−qn	∥.∥ℶp−qn	NOUN
ejpam-5641	219	2	.	.	PUNCT
ejpam-5641	220	1	so	so	ADV
ejpam-5641	220	2	∥f̂	∥f̂	PROPN
ejpam-5641	220	3	−	−	PROPN
ejpam-5641	220	4	û∥ℶp−qn	û∥ℶp−qn	NOUN
ejpam-5641	220	5	=	=	SYM
ejpam-5641	220	6	∑	∑	PUNCT
ejpam-5641	220	7	l∈n	l∈n	VERB
ejpam-5641	220	8			PROPN
ejpam-5641	220	9	ℏ̂	ℏ̂	NUM
ejpam-5641	220	10	(	(	PUNCT
ejpam-5641	220	11	∑l	∑l	INTJ
ejpam-5641	220	12	z=0	z=0	NUM
ejpam-5641	220	13	f	f	NOUN
ejpam-5641	220	14	2	2	NUM
ejpam-5641	220	15	zqz(f̂z	zqz(f̂z	PROPN
ejpam-5641	220	16	−	−	PROPN
ejpam-5641	220	17	ûz	ûz	NOUN
ejpam-5641	220	18	)	)	PUNCT
ejpam-5641	220	19	,	,	PUNCT
ejpam-5641	220	20	0̂	0̂	PROPN
ejpam-5641	220	21	)	)	PUNCT
ejpam-5641	221	1	flfl+1	flfl+1	PROPN
ejpam-5641	221	2	tl	tl	VERB
ejpam-5641	221	3	≤	≤	NUM
ejpam-5641	221	4	2ℶ−1	2ℶ−1	NUM
ejpam-5641	221	5	∑	∑	NOUN
ejpam-5641	221	6	l∈n	l∈n	VERB
ejpam-5641	221	7			PROPN
ejpam-5641	221	8	ℏ̂	ℏ̂	NUM
ejpam-5641	221	9	(	(	PUNCT
ejpam-5641	221	10	∑l	∑l	INTJ
ejpam-5641	221	11	z=0	z=0	NUM
ejpam-5641	221	12	f	f	NOUN
ejpam-5641	221	13	2	2	NUM
ejpam-5641	221	14	zqz(f̂z	zqz(f̂z	PROPN
ejpam-5641	221	15	−	−	PROPN
ejpam-5641	221	16	ûdz	ûdz	NOUN
ejpam-5641	221	17	)	)	PUNCT
ejpam-5641	221	18	,	,	PUNCT
ejpam-5641	221	19	0̂	0̂	PROPN
ejpam-5641	221	20	)	)	PUNCT
ejpam-5641	222	1	flfl+1	flfl+1	PROPN
ejpam-5641	222	2	tl	tl	PUNCT
ejpam-5641	223	1	+	+	CCONJ
ejpam-5641	223	2	∑	∑	PUNCT
ejpam-5641	223	3	l∈n	l∈n	VERB
ejpam-5641	223	4			PROPN
ejpam-5641	223	5	ℏ̂	ℏ̂	NUM
ejpam-5641	223	6	(	(	PUNCT
ejpam-5641	223	7	∑l	∑l	INTJ
ejpam-5641	223	8	z=0	z=0	NUM
ejpam-5641	223	9	f	f	NOUN
ejpam-5641	223	10	2	2	NUM
ejpam-5641	223	11	zqz(û	zqz(û	NOUN
ejpam-5641	223	12	d	d	NOUN
ejpam-5641	223	13	z	z	NOUN
ejpam-5641	223	14	−	−	NOUN
ejpam-5641	223	15	ûz	ûz	NOUN
ejpam-5641	223	16	)	)	PUNCT
ejpam-5641	223	17	,	,	PUNCT
ejpam-5641	223	18	0̂	0̂	PROPN
ejpam-5641	223	19	)	)	PUNCT
ejpam-5641	224	1	flfl+1	flfl+1	PROPN
ejpam-5641	224	2	tl	tl	VERB
ejpam-5641	225	1			NUM
ejpam-5641	225	2	≤	≤	NUM
ejpam-5641	225	3	2ℶ−1	2ℶ−1	NUM
ejpam-5641	225	4	sup	sup	NOUN
ejpam-5641	225	5	j	j	PROPN
ejpam-5641	225	6	inf	inf	PROPN
ejpam-5641	225	7	d≥j	d≥j	NOUN
ejpam-5641	225	8	∥f̂	∥f̂	PROPN
ejpam-5641	225	9	−	−	PROPN
ejpam-5641	225	10	ûd∥ℶp−qn	ûd∥ℶp−qn	NOUN
ejpam-5641	225	11	.	.	PUNCT
ejpam-5641	226	1	definition	definition	NOUN
ejpam-5641	226	2	7	7	NUM
ejpam-5641	226	3	.	.	PUNCT
ejpam-5641	227	1	a	a	DET
ejpam-5641	227	2	mapping	mapping	NOUN
ejpam-5641	227	3	m	m	VERB
ejpam-5641	227	4	:	:	PUNCT
ejpam-5641	227	5	es	es	X
ejpam-5641	227	6	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	227	7	→	→	SYM
ejpam-5641	227	8	es	es	X
ejpam-5641	227	9	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	227	10	is	be	AUX
ejpam-5641	227	11	said	say	VERB
ejpam-5641	227	12	to	to	PART
ejpam-5641	227	13	be	be	AUX
ejpam-5641	227	14	a	a	DET
ejpam-5641	227	15	ntk-∥.∥p−qn	ntk-∥.∥p−qn	NOUN
ejpam-5641	227	16	-	-	PUNCT
ejpam-5641	227	17	c	c	NOUN
ejpam-5641	227	18	if	if	SCONJ
ejpam-5641	227	19	there	there	PRON
ejpam-5641	227	20	are	be	VERB
ejpam-5641	227	21	{	{	PUNCT
ejpam-5641	227	22	αi}3i=1	αi}3i=1	NOUN
ejpam-5641	227	23	⊂	⊂	PROPN
ejpam-5641	228	1	[	[	X
ejpam-5641	228	2	0	0	NUM
ejpam-5641	228	3	,	,	PUNCT
ejpam-5641	228	4	1	1	NUM
ejpam-5641	228	5	)	)	PUNCT
ejpam-5641	228	6	with	with	ADP
ejpam-5641	228	7	α1	α1	PROPN
ejpam-5641	228	8	+	+	CCONJ
ejpam-5641	228	9	α2	α2	ADJ
ejpam-5641	228	10	+	+	CCONJ
ejpam-5641	228	11	α3	α3	ADJ
ejpam-5641	228	12	∈	∈	NOUN
ejpam-5641	229	1	[	[	X
ejpam-5641	229	2	0	0	NUM
ejpam-5641	229	3	,	,	PUNCT
ejpam-5641	229	4	1	1	NUM
ejpam-5641	229	5	)	)	PUNCT
ejpam-5641	229	6	so	so	SCONJ
ejpam-5641	229	7	that	that	SCONJ
ejpam-5641	229	8	∥mû−mk̂∥p−qn	∥mû−mk̂∥p−qn	PROPN
ejpam-5641	229	9	≤	≤	NOUN
ejpam-5641	230	1	α1∥mû−	α1∥mû−	X
ejpam-5641	231	1	û∥p−qn	û∥p−qn	PROPN
ejpam-5641	231	2	+	+	CCONJ
ejpam-5641	231	3	α2∥mk̂	α2∥mk̂	VERB
ejpam-5641	231	4	−	−	PROPN
ejpam-5641	232	1	k̂∥p−qn	k̂∥p−qn	PROPN
ejpam-5641	232	2	+	+	CCONJ
ejpam-5641	232	3	α3∥û−	α3∥û−	PROPN
ejpam-5641	232	4	k̂∥p−qn	k̂∥p−qn	PROPN
ejpam-5641	232	5	for	for	ADP
ejpam-5641	232	6	any	any	DET
ejpam-5641	232	7	û	û	NUM
ejpam-5641	232	8	,	,	PUNCT
ejpam-5641	232	9	k̂	k̂	PROPN
ejpam-5641	232	10	∈	∈	PROPN
ejpam-5641	232	11	es	es	ADP
ejpam-5641	232	12	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	232	13	.	.	PUNCT
ejpam-5641	233	1	if	if	SCONJ
ejpam-5641	233	2	m(û	m(û	PROPN
ejpam-5641	233	3	)	)	PUNCT
ejpam-5641	233	4	=	=	SYM
ejpam-5641	234	1	û	û	PROPN
ejpam-5641	234	2	,	,	PUNCT
ejpam-5641	234	3	we	we	PRON
ejpam-5641	234	4	say	say	VERB
ejpam-5641	234	5	û	û	NUM
ejpam-5641	234	6	∈	∈	NOUN
ejpam-5641	234	7	es	es	SCONJ
ejpam-5641	234	8	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	234	9	is	be	AUX
ejpam-5641	234	10	a	a	DET
ejpam-5641	234	11	fixed	fix	VERB
ejpam-5641	234	12	point	point	NOUN
ejpam-5641	234	13	of	of	ADP
ejpam-5641	234	14	m	m	PROPN
ejpam-5641	234	15	.	.	PUNCT
ejpam-5641	235	1	theorem	theorem	NOUN
ejpam-5641	235	2	4.3	4.3	NUM
ejpam-5641	235	3	.	.	PUNCT
ejpam-5641	236	1	assume	assume	VERB
ejpam-5641	236	2	w	w	NOUN
ejpam-5641	236	3	:	:	PUNCT
ejpam-5641	236	4	(	(	PUNCT
ejpam-5641	236	5	γsf	γsf	X
ejpam-5641	236	6	(	(	PUNCT
ejpam-5641	236	7	q	q	NOUN
ejpam-5641	236	8	,	,	PUNCT
ejpam-5641	236	9	t	t	PROPN
ejpam-5641	236	10	)	)	PUNCT
ejpam-5641	236	11	)	)	PUNCT
ejpam-5641	237	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	237	2	→	→	SYM
ejpam-5641	237	3	(	(	PUNCT
ejpam-5641	237	4	γsf	γsf	X
ejpam-5641	237	5	(	(	PUNCT
ejpam-5641	237	6	q	q	NOUN
ejpam-5641	237	7	,	,	PUNCT
ejpam-5641	237	8	t	t	PROPN
ejpam-5641	237	9	)	)	PUNCT
ejpam-5641	237	10	)	)	PUNCT
ejpam-5641	238	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	238	2	is	be	AUX
ejpam-5641	238	3	ntk-∥.∥p−qn	ntk-∥.∥p−qn	NOUN
ejpam-5641	238	4	-	-	PUNCT
ejpam-5641	238	5	c	c	NOUN
ejpam-5641	238	6	,	,	PUNCT
ejpam-5641	238	7	then	then	ADV
ejpam-5641	238	8	w	w	PROPN
ejpam-5641	238	9	has	have	VERB
ejpam-5641	238	10	a	a	DET
ejpam-5641	238	11	ufp	ufp	NOUN
ejpam-5641	238	12	.	.	PUNCT
ejpam-5641	239	1	m.	m.	NOUN
ejpam-5641	239	2	m.	m.	PROPN
ejpam-5641	239	3	a	a	PRON
ejpam-5641	239	4	et	et	PROPN
ejpam-5641	239	5	al	al	PROPN
ejpam-5641	239	6	.	.	PUNCT
ejpam-5641	239	7	/	/	SYM
ejpam-5641	239	8	eur	eur	PROPN
ejpam-5641	239	9	.	.	PUNCT
ejpam-5641	240	1	j.	j.	PROPN
ejpam-5641	240	2	pure	pure	PROPN
ejpam-5641	240	3	appl	appl	PROPN
ejpam-5641	240	4	.	.	PROPN
ejpam-5641	240	5	math	math	PROPN
ejpam-5641	240	6	,	,	PUNCT
ejpam-5641	240	7	18	18	NUM
ejpam-5641	240	8	(	(	PUNCT
ejpam-5641	240	9	1	1	NUM
ejpam-5641	240	10	)	)	PUNCT
ejpam-5641	240	11	(	(	PUNCT
ejpam-5641	240	12	2025	2025	NUM
ejpam-5641	240	13	)	)	PUNCT
ejpam-5641	240	14	,	,	PUNCT
ejpam-5641	240	15	5641	5641	NUM
ejpam-5641	240	16	10	10	NUM
ejpam-5641	240	17	of	of	ADP
ejpam-5641	240	18	20	20	NUM
ejpam-5641	240	19	proof	proof	NOUN
ejpam-5641	240	20	.	.	PUNCT
ejpam-5641	241	1	when	when	SCONJ
ejpam-5641	241	2	d̂	d̂	X
ejpam-5641	241	3	∈	∈	PROPN
ejpam-5641	241	4	γsf	γsf	VERB
ejpam-5641	241	5	(	(	PUNCT
ejpam-5641	241	6	q	q	NOUN
ejpam-5641	241	7	,	,	PUNCT
ejpam-5641	241	8	t	t	PROPN
ejpam-5641	241	9	)	)	PUNCT
ejpam-5641	241	10	,	,	PUNCT
ejpam-5641	241	11	then	then	ADV
ejpam-5641	241	12	wmd̂	wmd̂	PROPN
ejpam-5641	241	13	∈	∈	PROPN
ejpam-5641	241	14	γsf	γsf	NOUN
ejpam-5641	241	15	(	(	PUNCT
ejpam-5641	241	16	q	q	NOUN
ejpam-5641	241	17	,	,	PUNCT
ejpam-5641	241	18	t	t	PROPN
ejpam-5641	241	19	)	)	PUNCT
ejpam-5641	241	20	.	.	PUNCT
ejpam-5641	242	1	since	since	SCONJ
ejpam-5641	242	2	w	w	PROPN
ejpam-5641	242	3	is	be	AUX
ejpam-5641	242	4	a	a	DET
ejpam-5641	242	5	ntk-∥.∥p−qn	ntk-∥.∥p−qn	NOUN
ejpam-5641	242	6	-	-	PUNCT
ejpam-5641	242	7	c	c	NOUN
ejpam-5641	242	8	,	,	PUNCT
ejpam-5641	242	9	then	then	ADV
ejpam-5641	242	10	∥wm+1d̂−wmd̂∥p−qn	∥wm+1d̂−wmd̂∥p−qn	PROPN
ejpam-5641	242	11	≤	≤	X
ejpam-5641	242	12	α1∥wm+1d̂−wmd̂∥p−qn	α1∥wm+1d̂−wmd̂∥p−qn	X
ejpam-5641	242	13	+	+	CCONJ
ejpam-5641	242	14	α2∥wmd̂−wm−1d̂∥p−qn	α2∥wmd̂−wm−1d̂∥p−qn	PROPN
ejpam-5641	242	15	+	+	CCONJ
ejpam-5641	242	16	α3∥wmd̂−wm−1d̂∥p−qn	α3∥wmd̂−wm−1d̂∥p−qn	ADJ
ejpam-5641	242	17	⇒	⇒	NOUN
ejpam-5641	242	18	∥wm+1d̂−wmd̂∥p−qn	∥wm+1d̂−wmd̂∥p−qn	PROPN
ejpam-5641	242	19	≤	≤	ADV
ejpam-5641	242	20	α2	α2	PROPN
ejpam-5641	242	21	+	+	CCONJ
ejpam-5641	242	22	α3	α3	PROPN
ejpam-5641	242	23	1−	1−	NUM
ejpam-5641	242	24	α1	α1	PROPN
ejpam-5641	242	25	∥wmd̂−wm−1d̂∥p−qn	∥wmd̂−wm−1d̂∥p−qn	X
ejpam-5641	242	26	≤	≤	PROPN
ejpam-5641	242	27	(	(	PUNCT
ejpam-5641	242	28	α2	α2	ADJ
ejpam-5641	242	29	+	+	CCONJ
ejpam-5641	242	30	α3	α3	PROPN
ejpam-5641	242	31	1−	1−	NUM
ejpam-5641	242	32	α1	α1	PROPN
ejpam-5641	242	33	)	)	PUNCT
ejpam-5641	242	34	2	2	NUM
ejpam-5641	242	35	∥wm−1d̂−wm−2d̂∥p−qn	∥wm−1d̂−wm−2d̂∥p−qn	NOUN
ejpam-5641	242	36	≤	≤	NOUN
ejpam-5641	242	37	.	.	PUNCT
ejpam-5641	242	38	.	.	PUNCT
ejpam-5641	243	1	.	.	PUNCT
ejpam-5641	244	1	≤	≤	NUM
ejpam-5641	244	2	(	(	PUNCT
ejpam-5641	244	3	α2	α2	ADJ
ejpam-5641	244	4	+	+	CCONJ
ejpam-5641	244	5	α3	α3	ADJ
ejpam-5641	244	6	1−	1−	NUM
ejpam-5641	244	7	α1	α1	PROPN
ejpam-5641	244	8	)	)	PUNCT
ejpam-5641	244	9	m	m	AUX
ejpam-5641	244	10	∥wd̂−	∥wd̂−	ADJ
ejpam-5641	244	11	d̂∥p−qn	d̂∥p−qn	PROPN
ejpam-5641	244	12	.	.	PUNCT
ejpam-5641	245	1	for	for	ADP
ejpam-5641	245	2	every	every	DET
ejpam-5641	245	3	m	m	NOUN
ejpam-5641	245	4	,	,	PUNCT
ejpam-5641	245	5	n	n	PRON
ejpam-5641	245	6	∈	∈	PROPN
ejpam-5641	245	7	n	n	ADV
ejpam-5641	245	8	so	so	ADV
ejpam-5641	245	9	that	that	SCONJ
ejpam-5641	245	10	n	n	CCONJ
ejpam-5641	245	11	>	>	X
ejpam-5641	245	12	m	m	PROPN
ejpam-5641	245	13	,	,	PUNCT
ejpam-5641	245	14	we	we	PRON
ejpam-5641	245	15	obtain	obtain	VERB
ejpam-5641	245	16	∥wmd̂−wnd̂∥p−qn	∥wmd̂−wnd̂∥p−qn	PROPN
ejpam-5641	245	17	≤	≤	NUM
ejpam-5641	246	1	α1∥wmd̂−wm−1d̂∥p−qn	α1∥wmd̂−wm−1d̂∥p−qn	PROPN
ejpam-5641	246	2	+	+	CCONJ
ejpam-5641	246	3	α2∥wnd̂−wn−1d̂∥p−qn	α2∥wnd̂−wn−1d̂∥p−qn	PROPN
ejpam-5641	246	4	+	+	CCONJ
ejpam-5641	246	5	α3∥wm−1d̂−wn−1d̂∥p−qn	α3∥wm−1d̂−wn−1d̂∥p−qn	PROPN
ejpam-5641	246	6	≤	≤	NOUN
ejpam-5641	246	7	(	(	PUNCT
ejpam-5641	246	8	α1	α1	PROPN
ejpam-5641	246	9	(	(	PUNCT
ejpam-5641	246	10	α2	α2	ADJ
ejpam-5641	246	11	+	+	CCONJ
ejpam-5641	246	12	α3	α3	ADJ
ejpam-5641	246	13	1−	1−	NUM
ejpam-5641	246	14	α1	α1	PROPN
ejpam-5641	246	15	)	)	PUNCT
ejpam-5641	246	16	m−1	m−1	PROPN
ejpam-5641	246	17	+	+	CCONJ
ejpam-5641	246	18	α2	α2	ADJ
ejpam-5641	246	19	(	(	PUNCT
ejpam-5641	246	20	α2	α2	PROPN
ejpam-5641	246	21	+	+	CCONJ
ejpam-5641	246	22	α3	α3	ADJ
ejpam-5641	246	23	1−	1−	NUM
ejpam-5641	246	24	α1	α1	PROPN
ejpam-5641	246	25	)	)	PUNCT
ejpam-5641	246	26	n−1	n−1	PROPN
ejpam-5641	246	27	)	)	PUNCT
ejpam-5641	246	28	∥wd̂−	∥wd̂−	VERB
ejpam-5641	246	29	d̂∥p−qn	d̂∥p−qn	PROPN
ejpam-5641	246	30	+	+	CCONJ
ejpam-5641	246	31	α3∥wm−1d̂−wn−1d̂∥p−qn	α3∥wm−1d̂−wn−1d̂∥p−qn	PROPN
ejpam-5641	246	32	.	.	PUNCT
ejpam-5641	247	1	hence	hence	ADV
ejpam-5641	247	2	,	,	PUNCT
ejpam-5641	247	3	{	{	PUNCT
ejpam-5641	247	4	wmd̂	wmd̂	PROPN
ejpam-5641	247	5	}	}	PUNCT
ejpam-5641	247	6	is	be	AUX
ejpam-5641	247	7	a	a	DET
ejpam-5641	247	8	cs	cs	PROPN
ejpam-5641	247	9	in	in	ADP
ejpam-5641	247	10	(	(	PUNCT
ejpam-5641	247	11	γsf	γsf	X
ejpam-5641	247	12	(	(	PUNCT
ejpam-5641	247	13	q	q	NOUN
ejpam-5641	247	14	,	,	PUNCT
ejpam-5641	247	15	t	t	PROPN
ejpam-5641	247	16	)	)	PUNCT
ejpam-5641	247	17	)	)	PUNCT
ejpam-5641	248	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	248	2	.	.	PUNCT
ejpam-5641	249	1	since	since	SCONJ
ejpam-5641	249	2	(	(	PUNCT
ejpam-5641	249	3	γsf	γsf	X
ejpam-5641	249	4	(	(	PUNCT
ejpam-5641	249	5	q	q	NOUN
ejpam-5641	249	6	,	,	PUNCT
ejpam-5641	249	7	t	t	PROPN
ejpam-5641	249	8	)	)	PUNCT
ejpam-5641	249	9	)	)	PUNCT
ejpam-5641	250	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	250	2	is	be	AUX
ejpam-5641	250	3	p	p	NOUN
ejpam-5641	250	4	-	-	PUNCT
ejpam-5641	250	5	q.b	q.b	NOUN
ejpam-5641	250	6	.	.	PUNCT
ejpam-5641	251	1	one	one	NOUN
ejpam-5641	251	2	has	have	VERB
ejpam-5641	251	3	v̂	v̂	X
ejpam-5641	251	4	∈	∈	NOUN
ejpam-5641	251	5	(	(	PUNCT
ejpam-5641	251	6	γsf	γsf	X
ejpam-5641	251	7	(	(	PUNCT
ejpam-5641	251	8	q	q	NOUN
ejpam-5641	251	9	,	,	PUNCT
ejpam-5641	251	10	t	t	PROPN
ejpam-5641	251	11	)	)	PUNCT
ejpam-5641	251	12	)	)	PUNCT
ejpam-5641	252	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	252	2	with	with	ADP
ejpam-5641	252	3	limm→∞wmd̂	limm→∞wmd̂	PROPN
ejpam-5641	252	4	=	=	PUNCT
ejpam-5641	252	5	v̂.	v̂.	NOUN
ejpam-5641	252	6	as	as	SCONJ
ejpam-5641	252	7	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	252	8	has	have	VERB
ejpam-5641	252	9	the	the	DET
ejpam-5641	252	10	fp	fp	PROPN
ejpam-5641	252	11	,	,	PUNCT
ejpam-5641	252	12	so	so	ADV
ejpam-5641	252	13	∥wv̂	∥wv̂	ADP
ejpam-5641	252	14	−	−	PROPN
ejpam-5641	252	15	v̂∥p−qn	v̂∥p−qn	PROPN
ejpam-5641	252	16	≤	≤	NUM
ejpam-5641	252	17	sup	sup	NOUN
ejpam-5641	252	18	i	i	PRON
ejpam-5641	252	19	inf	inf	NOUN
ejpam-5641	252	20	m≥i	m≥i	NOUN
ejpam-5641	252	21	∥wm+1d̂−wmd̂∥p−qn	∥wm+1d̂−wmd̂∥p−qn	PROPN
ejpam-5641	252	22	≤	≤	PROPN
ejpam-5641	252	23	sup	sup	NOUN
ejpam-5641	253	1	i	i	PROPN
ejpam-5641	253	2	inf	inf	NOUN
ejpam-5641	253	3	m≥i	m≥i	NOUN
ejpam-5641	253	4	(	(	PUNCT
ejpam-5641	253	5	α2	α2	PROPN
ejpam-5641	253	6	+	+	CCONJ
ejpam-5641	253	7	α3	α3	PROPN
ejpam-5641	253	8	1−	1−	NUM
ejpam-5641	253	9	α1	α1	PROPN
ejpam-5641	253	10	)	)	PUNCT
ejpam-5641	253	11	m	m	VERB
ejpam-5641	253	12	∥wd̂−	∥wd̂−	VERB
ejpam-5641	253	13	d̂∥p−qn	d̂∥p−qn	PROPN
ejpam-5641	253	14	=	=	SYM
ejpam-5641	253	15	0	0	PROPN
ejpam-5641	253	16	,	,	PUNCT
ejpam-5641	253	17	then	then	ADV
ejpam-5641	253	18	wv̂	wv̂	PROPN
ejpam-5641	253	19	=	=	SYM
ejpam-5641	253	20	v̂.	v̂.	NOUN
ejpam-5641	253	21	hence	hence	ADV
ejpam-5641	253	22	,	,	PUNCT
ejpam-5641	253	23	v̂	v̂	PRON
ejpam-5641	253	24	is	be	AUX
ejpam-5641	253	25	a	a	DET
ejpam-5641	253	26	fp	fp	NOUN
ejpam-5641	253	27	of	of	ADP
ejpam-5641	253	28	w	w	PROPN
ejpam-5641	253	29	.	.	PUNCT
ejpam-5641	254	1	next	next	ADV
ejpam-5641	254	2	,	,	PUNCT
ejpam-5641	254	3	when	when	SCONJ
ejpam-5641	254	4	we	we	PRON
ejpam-5641	254	5	have	have	VERB
ejpam-5641	254	6	two	two	NUM
ejpam-5641	254	7	fp	fp	NOUN
ejpam-5641	254	8	â	â	PROPN
ejpam-5641	254	9	,	,	PUNCT
ejpam-5641	254	10	v̂	v̂	X
ejpam-5641	254	11	∈	∈	NOUN
ejpam-5641	254	12	(	(	PUNCT
ejpam-5641	254	13	γsf	γsf	X
ejpam-5641	254	14	(	(	PUNCT
ejpam-5641	254	15	q	q	NOUN
ejpam-5641	254	16	,	,	PUNCT
ejpam-5641	254	17	t	t	PROPN
ejpam-5641	254	18	)	)	PUNCT
ejpam-5641	254	19	)	)	PUNCT
ejpam-5641	255	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	255	2	of	of	ADP
ejpam-5641	255	3	w	w	PROPN
ejpam-5641	255	4	with	with	ADP
ejpam-5641	255	5	â	â	PRON
ejpam-5641	255	6	̸=	̸=	PROPN
ejpam-5641	255	7	v̂.	v̂.	NOUN
ejpam-5641	255	8	then	then	ADV
ejpam-5641	255	9	(	(	PUNCT
ejpam-5641	255	10	1−	1−	NUM
ejpam-5641	255	11	α3)∥â−	α3)∥â−	NUM
ejpam-5641	255	12	v̂∥p−qn	v̂∥p−qn	NOUN
ejpam-5641	255	13	≤	≤	PROPN
ejpam-5641	255	14	α1∥wâ−	α1∥wâ−	X
ejpam-5641	256	1	â∥p−qn	â∥p−qn	PROPN
ejpam-5641	256	2	+	+	CCONJ
ejpam-5641	256	3	α2∥wv̂	α2∥wv̂	PROPN
ejpam-5641	256	4	−	−	PROPN
ejpam-5641	256	5	v̂∥p−qn	v̂∥p−qn	NOUN
ejpam-5641	256	6	=	=	NOUN
ejpam-5641	256	7	0	0	NUM
ejpam-5641	256	8	.	.	PUNCT
ejpam-5641	257	1	so	so	ADV
ejpam-5641	257	2	â	â	X
ejpam-5641	257	3	=	=	PUNCT
ejpam-5641	257	4	v̂.	v̂.	PROPN
ejpam-5641	257	5	corollary	corollary	NOUN
ejpam-5641	257	6	4.4	4.4	NUM
ejpam-5641	257	7	.	.	PUNCT
ejpam-5641	258	1	suppose	suppose	VERB
ejpam-5641	258	2	w	w	X
ejpam-5641	258	3	:	:	PUNCT
ejpam-5641	258	4	(	(	PUNCT
ejpam-5641	258	5	γsf	γsf	X
ejpam-5641	258	6	(	(	PUNCT
ejpam-5641	258	7	q	q	NOUN
ejpam-5641	258	8	,	,	PUNCT
ejpam-5641	258	9	t	t	PROPN
ejpam-5641	258	10	)	)	PUNCT
ejpam-5641	258	11	)	)	PUNCT
ejpam-5641	259	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	259	2	→	→	SYM
ejpam-5641	259	3	(	(	PUNCT
ejpam-5641	259	4	γsf	γsf	X
ejpam-5641	259	5	(	(	PUNCT
ejpam-5641	259	6	q	q	NOUN
ejpam-5641	259	7	,	,	PUNCT
ejpam-5641	259	8	t	t	PROPN
ejpam-5641	259	9	)	)	PUNCT
ejpam-5641	259	10	)	)	PUNCT
ejpam-5641	260	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	260	2	is	be	AUX
ejpam-5641	260	3	ntk-∥.∥p−qn	ntk-∥.∥p−qn	NOUN
ejpam-5641	260	4	-	-	PUNCT
ejpam-5641	260	5	c	c	NOUN
ejpam-5641	260	6	,	,	PUNCT
ejpam-5641	260	7	then	then	ADV
ejpam-5641	260	8	w	w	PROPN
ejpam-5641	260	9	has	have	VERB
ejpam-5641	260	10	a	a	DET
ejpam-5641	260	11	ufp	ufp	NOUN
ejpam-5641	260	12	â	â	ADP
ejpam-5641	260	13	under	under	ADP
ejpam-5641	260	14	∥wmd̂−â∥p−qn	∥wmd̂−â∥p−qn	NOUN
ejpam-5641	260	15	≤	≤	ADJ
ejpam-5641	260	16	α1	α1	NOUN
ejpam-5641	260	17	(	(	PUNCT
ejpam-5641	260	18	α2+α3	α2+α3	NOUN
ejpam-5641	260	19	1−α1	1−α1	NUM
ejpam-5641	260	20	)	)	PUNCT
ejpam-5641	260	21	m−1	m−1	PROPN
ejpam-5641	260	22	∥wd̂−d̂∥p−qn+α3∥wm−1d̂−	∥wd̂−d̂∥p−qn+α3∥wm−1d̂−	VERB
ejpam-5641	260	23	â∥p−qn	â∥p−qn	PROPN
ejpam-5641	260	24	.	.	PUNCT
ejpam-5641	261	1	proof	proof	NOUN
ejpam-5641	261	2	.	.	PUNCT
ejpam-5641	262	1	by	by	ADP
ejpam-5641	262	2	theorem	theorem	NOUN
ejpam-5641	262	3	4.3	4.3	NUM
ejpam-5641	262	4	,	,	PUNCT
ejpam-5641	262	5	we	we	PRON
ejpam-5641	262	6	have	have	VERB
ejpam-5641	262	7	a	a	DET
ejpam-5641	262	8	ufp	ufp	NOUN
ejpam-5641	262	9	â	â	X
ejpam-5641	262	10	of	of	ADP
ejpam-5641	262	11	w	w	PROPN
ejpam-5641	262	12	.	.	PUNCT
ejpam-5641	263	1	hence	hence	ADV
ejpam-5641	263	2	∥wmd̂−	∥wmd̂−	ADJ
ejpam-5641	263	3	â∥p−qn	â∥p−qn	PROPN
ejpam-5641	263	4	=	=	SYM
ejpam-5641	263	5	∥wmd̂−wâ∥p−qn	∥wmd̂−wâ∥p−qn	PROPN
ejpam-5641	263	6	≤	≤	PUNCT
ejpam-5641	263	7	α1∥wmd̂−wm−1d̂∥p−qn	α1∥wmd̂−wm−1d̂∥p−qn	X
ejpam-5641	263	8	+	+	CCONJ
ejpam-5641	263	9	α2∥wâ−	α2∥wâ−	PROPN
ejpam-5641	263	10	â∥p−qn	â∥p−qn	PROPN
ejpam-5641	263	11	+	+	PROPN
ejpam-5641	263	12	α3∥wm−1d̂−	α3∥wm−1d̂−	PROPN
ejpam-5641	263	13	â∥p−qn	â∥p−qn	PROPN
ejpam-5641	263	14	=	=	SYM
ejpam-5641	263	15	α1	α1	PROPN
ejpam-5641	263	16	(	(	PUNCT
ejpam-5641	263	17	α2	α2	ADJ
ejpam-5641	263	18	+	+	CCONJ
ejpam-5641	263	19	α3	α3	ADJ
ejpam-5641	263	20	1−	1−	NUM
ejpam-5641	263	21	α1	α1	PROPN
ejpam-5641	263	22	)	)	PUNCT
ejpam-5641	263	23	m−1	m−1	PROPN
ejpam-5641	263	24	∥wd̂−	∥wd̂−	VERB
ejpam-5641	263	25	d̂∥p−qn	d̂∥p−qn	PROPN
ejpam-5641	263	26	+	+	CCONJ
ejpam-5641	263	27	α3∥wm−1d̂−	α3∥wm−1d̂−	PROPN
ejpam-5641	263	28	â∥p−qn	â∥p−qn	PROPN
ejpam-5641	263	29	.	.	PUNCT
ejpam-5641	264	1	m.	m.	PROPN
ejpam-5641	264	2	m.	m.	PROPN
ejpam-5641	264	3	a	a	PRON
ejpam-5641	264	4	et	et	PROPN
ejpam-5641	264	5	al	al	PROPN
ejpam-5641	264	6	.	.	PUNCT
ejpam-5641	264	7	/	/	SYM
ejpam-5641	264	8	eur	eur	PROPN
ejpam-5641	264	9	.	.	PUNCT
ejpam-5641	265	1	j.	j.	PROPN
ejpam-5641	265	2	pure	pure	PROPN
ejpam-5641	265	3	appl	appl	PROPN
ejpam-5641	265	4	.	.	PROPN
ejpam-5641	265	5	math	math	PROPN
ejpam-5641	265	6	,	,	PUNCT
ejpam-5641	265	7	18	18	NUM
ejpam-5641	265	8	(	(	PUNCT
ejpam-5641	265	9	1	1	NUM
ejpam-5641	265	10	)	)	PUNCT
ejpam-5641	265	11	(	(	PUNCT
ejpam-5641	265	12	2025	2025	NUM
ejpam-5641	265	13	)	)	PUNCT
ejpam-5641	265	14	,	,	PUNCT
ejpam-5641	265	15	5641	5641	NUM
ejpam-5641	265	16	11	11	NUM
ejpam-5641	265	17	of	of	ADP
ejpam-5641	265	18	20	20	NUM
ejpam-5641	265	19	theorem	theorem	VERB
ejpam-5641	265	20	4.5	4.5	NUM
ejpam-5641	265	21	.	.	PUNCT
ejpam-5641	266	1	assuming	assume	VERB
ejpam-5641	266	2	that	that	SCONJ
ejpam-5641	266	3	w	w	X
ejpam-5641	266	4	:	:	PUNCT
ejpam-5641	266	5	(	(	PUNCT
ejpam-5641	266	6	γsf	γsf	X
ejpam-5641	266	7	(	(	PUNCT
ejpam-5641	266	8	q	q	NOUN
ejpam-5641	266	9	,	,	PUNCT
ejpam-5641	266	10	t	t	PROPN
ejpam-5641	266	11	)	)	PUNCT
ejpam-5641	266	12	)	)	PUNCT
ejpam-5641	267	1	∥.∥ℶp−qn	∥.∥ℶp−qn	X
ejpam-5641	267	2	→	→	SYM
ejpam-5641	267	3	(	(	PUNCT
ejpam-5641	267	4	γsf	γsf	X
ejpam-5641	267	5	(	(	PUNCT
ejpam-5641	267	6	q	q	NOUN
ejpam-5641	267	7	,	,	PUNCT
ejpam-5641	267	8	t	t	PROPN
ejpam-5641	267	9	)	)	PUNCT
ejpam-5641	267	10	)	)	PUNCT
ejpam-5641	268	1	∥.∥ℶp−qn	∥.∥ℶp−qn	X
ejpam-5641	268	2	,	,	PUNCT
ejpam-5641	268	3	where	where	SCONJ
ejpam-5641	268	4	∥d̂∥ℶp−qn	∥d̂∥ℶp−qn	PRON
ejpam-5641	268	5	=	=	SYM
ejpam-5641	268	6	∑	∑	PUNCT
ejpam-5641	268	7	l∈n	l∈n	ADP
ejpam-5641	268	8			PROPN
ejpam-5641	268	9	ℏ̂	ℏ̂	NUM
ejpam-5641	268	10	(	(	PUNCT
ejpam-5641	268	11	∑l	∑l	INTJ
ejpam-5641	268	12	z=0	z=0	NUM
ejpam-5641	268	13	f	f	NOUN
ejpam-5641	268	14	2	2	NUM
ejpam-5641	268	15	zqzd̂z	zqzd̂z	NOUN
ejpam-5641	268	16	,	,	PUNCT
ejpam-5641	268	17	0̂	0̂	PROPN
ejpam-5641	268	18	)	)	PUNCT
ejpam-5641	269	1	flfl+1	flfl+1	PROPN
ejpam-5641	269	2	tl	tl	PROPN
ejpam-5641	269	3	,	,	PUNCT
ejpam-5641	269	4	for	for	ADP
ejpam-5641	269	5	all	all	DET
ejpam-5641	269	6	d̂	d̂	PRON
ejpam-5641	269	7	∈	∈	NOUN
ejpam-5641	269	8	γsf	γsf	X
ejpam-5641	269	9	(	(	PUNCT
ejpam-5641	269	10	q	q	NOUN
ejpam-5641	269	11	,	,	PUNCT
ejpam-5641	269	12	t	t	PROPN
ejpam-5641	269	13	)	)	PUNCT
ejpam-5641	269	14	under	under	ADP
ejpam-5641	269	15	t0	t0	PROPN
ejpam-5641	269	16	>	>	X
ejpam-5641	270	1	1	1	X
ejpam-5641	270	2	.	.	PUNCT
ejpam-5641	271	1	if	if	SCONJ
ejpam-5641	271	2	the	the	DET
ejpam-5641	271	3	following	follow	VERB
ejpam-5641	271	4	conditions	condition	NOUN
ejpam-5641	271	5	(	(	PUNCT
ejpam-5641	271	6	k1	k1	NOUN
ejpam-5641	271	7	)	)	PUNCT
ejpam-5641	271	8	w	w	PROPN
ejpam-5641	271	9	is	be	AUX
ejpam-5641	271	10	ntk-∥.∥ℶp−qn	ntk-∥.∥ℶp−qn	NOUN
ejpam-5641	271	11	-	-	PUNCT
ejpam-5641	271	12	c	c	NOUN
ejpam-5641	271	13	,	,	PUNCT
ejpam-5641	271	14	(	(	PUNCT
ejpam-5641	271	15	k2	k2	NOUN
ejpam-5641	271	16	)	)	PUNCT
ejpam-5641	271	17	w	w	PROPN
ejpam-5641	271	18	is	be	AUX
ejpam-5641	271	19	∥.∥ℶp−qn	∥.∥ℶp−qn	NUM
ejpam-5641	271	20	-	-	PUNCT
ejpam-5641	271	21	seq.c	seq.c	NOUN
ejpam-5641	271	22	at	at	ADP
ejpam-5641	271	23	v̂	v̂	X
ejpam-5641	271	24	∈	∈	NOUN
ejpam-5641	271	25	(	(	PUNCT
ejpam-5641	271	26	γsf	γsf	X
ejpam-5641	271	27	(	(	PUNCT
ejpam-5641	271	28	q	q	NOUN
ejpam-5641	271	29	,	,	PUNCT
ejpam-5641	271	30	t	t	PROPN
ejpam-5641	271	31	)	)	PUNCT
ejpam-5641	271	32	)	)	PUNCT
ejpam-5641	272	1	∥.∥ℶp−qn	∥.∥ℶp−qn	NOUN
ejpam-5641	272	2	,	,	PUNCT
ejpam-5641	272	3	and	and	CCONJ
ejpam-5641	272	4	(	(	PUNCT
ejpam-5641	272	5	k3	k3	PROPN
ejpam-5641	272	6	)	)	PUNCT
ejpam-5641	272	7	there	there	PRON
ejpam-5641	272	8	is	be	VERB
ejpam-5641	272	9	an	an	DET
ejpam-5641	272	10	element	element	NOUN
ejpam-5641	272	11	d̂	d̂	PRON
ejpam-5641	272	12	∈	∈	PROPN
ejpam-5641	272	13	(	(	PUNCT
ejpam-5641	272	14	γsf	γsf	X
ejpam-5641	272	15	(	(	PUNCT
ejpam-5641	272	16	q	q	NOUN
ejpam-5641	272	17	,	,	PUNCT
ejpam-5641	272	18	t	t	PROPN
ejpam-5641	272	19	)	)	PUNCT
ejpam-5641	272	20	)	)	PUNCT
ejpam-5641	273	1	∥.∥ℶp−qn	∥.∥ℶp−qn	ADV
ejpam-5641	273	2	so	so	SCONJ
ejpam-5641	273	3	that	that	SCONJ
ejpam-5641	273	4	the	the	DET
ejpam-5641	273	5	sequence	sequence	NOUN
ejpam-5641	273	6	of	of	ADP
ejpam-5641	273	7	iterates	iterate	NOUN
ejpam-5641	273	8	{	{	PUNCT
ejpam-5641	273	9	wmd̂	wmd̂	PROPN
ejpam-5641	273	10	}	}	PUNCT
ejpam-5641	273	11	has	have	VERB
ejpam-5641	273	12	a	a	DET
ejpam-5641	273	13	subsequence	subsequence	NOUN
ejpam-5641	273	14	{	{	PUNCT
ejpam-5641	273	15	wmi	wmi	NOUN
ejpam-5641	273	16	d̂	d̂	PROPN
ejpam-5641	273	17	}	}	PUNCT
ejpam-5641	273	18	converges	converge	VERB
ejpam-5641	273	19	to	to	ADP
ejpam-5641	273	20	v̂	v̂	NOUN
ejpam-5641	273	21	,	,	PUNCT
ejpam-5641	273	22	are	be	AUX
ejpam-5641	273	23	satisfied	satisfied	ADJ
ejpam-5641	273	24	,	,	PUNCT
ejpam-5641	273	25	then	then	ADV
ejpam-5641	273	26	the	the	DET
ejpam-5641	273	27	vector	vector	NOUN
ejpam-5641	273	28	v̂	v̂	X
ejpam-5641	273	29	∈	∈	NOUN
ejpam-5641	273	30	(	(	PUNCT
ejpam-5641	273	31	γsf	γsf	X
ejpam-5641	273	32	(	(	PUNCT
ejpam-5641	273	33	q	q	NOUN
ejpam-5641	273	34	,	,	PUNCT
ejpam-5641	273	35	t	t	PROPN
ejpam-5641	273	36	)	)	PUNCT
ejpam-5641	273	37	)	)	PUNCT
ejpam-5641	274	1	∥.∥ℶp−qn	∥.∥ℶp−qn	NOUN
ejpam-5641	274	2	is	be	AUX
ejpam-5641	274	3	the	the	DET
ejpam-5641	274	4	ufp	ufp	NOUN
ejpam-5641	274	5	of	of	ADP
ejpam-5641	274	6	w	w	PROPN
ejpam-5641	274	7	.	.	PUNCT
ejpam-5641	275	1	proof	proof	NOUN
ejpam-5641	275	2	.	.	PUNCT
ejpam-5641	276	1	let	let	VERB
ejpam-5641	276	2	wv̂	wv̂	NUM
ejpam-5641	276	3	̸=	̸=	PROPN
ejpam-5641	276	4	v̂.	v̂.	NOUN
ejpam-5641	276	5	from	from	ADP
ejpam-5641	276	6	parts	part	NOUN
ejpam-5641	276	7	(	(	PUNCT
ejpam-5641	276	8	k2	k2	NOUN
ejpam-5641	276	9	)	)	PUNCT
ejpam-5641	276	10	and	and	CCONJ
ejpam-5641	276	11	(	(	PUNCT
ejpam-5641	276	12	k3	k3	PROPN
ejpam-5641	276	13	)	)	PUNCT
ejpam-5641	276	14	,	,	PUNCT
ejpam-5641	276	15	one	one	PRON
ejpam-5641	276	16	obtains	obtain	VERB
ejpam-5641	276	17	lim	lim	NOUN
ejpam-5641	276	18	mi→∞	mi→∞	NUM
ejpam-5641	276	19	∥wmi	∥wmi	PROPN
ejpam-5641	276	20	d̂−	d̂−	ADJ
ejpam-5641	276	21	v̂∥ℶp−qn	v̂∥ℶp−qn	NOUN
ejpam-5641	276	22	=	=	SYM
ejpam-5641	276	23	0	0	PUNCT
ejpam-5641	277	1	and	and	CCONJ
ejpam-5641	277	2	lim	lim	PROPN
ejpam-5641	277	3	mi→∞	mi→∞	NUM
ejpam-5641	277	4	∥wmi+1d̂−wv̂∥ℶp−qn	∥wmi+1d̂−wv̂∥ℶp−qn	PROPN
ejpam-5641	277	5	=	=	SYM
ejpam-5641	277	6	0	0	NUM
ejpam-5641	277	7	.	.	PUNCT
ejpam-5641	278	1	since	since	SCONJ
ejpam-5641	278	2	w	w	PROPN
ejpam-5641	278	3	is	be	AUX
ejpam-5641	278	4	ntk-∥.∥ℶp−qn	ntk-∥.∥ℶp−qn	NOUN
ejpam-5641	278	5	-	-	PUNCT
ejpam-5641	278	6	c	c	NOUN
ejpam-5641	278	7	,	,	PUNCT
ejpam-5641	278	8	then	then	ADV
ejpam-5641	278	9	0	0	NUM
ejpam-5641	278	10	<	<	X
ejpam-5641	278	11	∥wv̂	∥wv̂	ADP
ejpam-5641	278	12	−	−	PROPN
ejpam-5641	278	13	v̂∥ℶp−qn	v̂∥ℶp−qn	NOUN
ejpam-5641	278	14	=	=	SYM
ejpam-5641	278	15	∥(wv̂	∥(wv̂	PROPN
ejpam-5641	278	16	−wmi+1d̂	−wmi+1d̂	NOUN
ejpam-5641	278	17	)	)	PUNCT
ejpam-5641	279	1	+	+	CCONJ
ejpam-5641	279	2	(	(	PUNCT
ejpam-5641	279	3	wmi	wmi	NOUN
ejpam-5641	279	4	d̂−	d̂−	PROPN
ejpam-5641	279	5	v̂	v̂	NUM
ejpam-5641	279	6	)	)	PUNCT
ejpam-5641	280	1	+	+	CCONJ
ejpam-5641	280	2	(	(	PUNCT
ejpam-5641	280	3	wmi+1d̂−wmi	wmi+1d̂−wmi	ADJ
ejpam-5641	280	4	d̂)∥ℶp−qn	d̂)∥ℶp−qn	VERB
ejpam-5641	280	5	≤	≤	NOUN
ejpam-5641	280	6	22ℶ−2∥wmi+1v̂	22ℶ−2∥wmi+1v̂	NUM
ejpam-5641	280	7	−wv̂∥ℶp−qn	−wv̂∥ℶp−qn	PUNCT
ejpam-5641	280	8	+	+	PROPN
ejpam-5641	280	9	22ℶ−2∥wmi	22ℶ−2∥wmi	PROPN
ejpam-5641	280	10	v̂	v̂	ADP
ejpam-5641	280	11	−	−	PROPN
ejpam-5641	280	12	v̂∥ℶp−qn	v̂∥ℶp−qn	NOUN
ejpam-5641	280	13	+	+	CCONJ
ejpam-5641	280	14	2ℶ−1	2ℶ−1	NUM
ejpam-5641	280	15	(	(	PUNCT
ejpam-5641	280	16	α2	α2	ADJ
ejpam-5641	280	17	+	+	CCONJ
ejpam-5641	280	18	α3	α3	ADJ
ejpam-5641	280	19	1−	1−	NUM
ejpam-5641	280	20	α1	α1	PROPN
ejpam-5641	280	21	)	)	PUNCT
ejpam-5641	280	22	mi	mi	PROPN
ejpam-5641	280	23	∥wd̂−	∥wd̂−	ADJ
ejpam-5641	280	24	d̂∥ℶp−qn	d̂∥ℶp−qn	PROPN
ejpam-5641	280	25	.	.	PUNCT
ejpam-5641	281	1	when	when	SCONJ
ejpam-5641	281	2	mi	mi	PROPN
ejpam-5641	281	3	→	→	SYM
ejpam-5641	281	4	∞	∞	PROPN
ejpam-5641	281	5	,	,	PUNCT
ejpam-5641	281	6	we	we	PRON
ejpam-5641	281	7	get	get	VERB
ejpam-5641	281	8	a	a	DET
ejpam-5641	281	9	contradiction	contradiction	NOUN
ejpam-5641	281	10	.	.	PUNCT
ejpam-5641	282	1	so	so	ADV
ejpam-5641	282	2	,	,	PUNCT
ejpam-5641	282	3	wv̂	wv̂	PROPN
ejpam-5641	282	4	=	=	PUNCT
ejpam-5641	282	5	v̂.	v̂.	NOUN
ejpam-5641	282	6	for	for	ADP
ejpam-5641	282	7	the	the	DET
ejpam-5641	282	8	uniqueness	uniqueness	NOUN
ejpam-5641	282	9	,	,	PUNCT
ejpam-5641	282	10	assume	assume	VERB
ejpam-5641	282	11	wv̂	wv̂	PROPN
ejpam-5641	282	12	=	=	PUNCT
ejpam-5641	282	13	v̂	v̂	X
ejpam-5641	282	14	and	and	CCONJ
ejpam-5641	282	15	wâ	wâ	NOUN
ejpam-5641	282	16	=	=	SYM
ejpam-5641	282	17	â	â	PROPN
ejpam-5641	282	18	,	,	PUNCT
ejpam-5641	282	19	where	where	SCONJ
ejpam-5641	282	20	v̂	v̂	NOUN
ejpam-5641	282	21	,	,	PUNCT
ejpam-5641	282	22	â	â	X
ejpam-5641	282	23	∈	∈	PROPN
ejpam-5641	282	24	(	(	PUNCT
ejpam-5641	282	25	γsf	γsf	X
ejpam-5641	282	26	(	(	PUNCT
ejpam-5641	282	27	q	q	NOUN
ejpam-5641	282	28	,	,	PUNCT
ejpam-5641	282	29	t	t	PROPN
ejpam-5641	282	30	)	)	PUNCT
ejpam-5641	282	31	)	)	PUNCT
ejpam-5641	283	1	∥.∥ℶp−qn	∥.∥ℶp−qn	ADV
ejpam-5641	283	2	and	and	CCONJ
ejpam-5641	283	3	v̂	v̂	NUM
ejpam-5641	283	4	̸=	̸=	PROPN
ejpam-5641	283	5	â.	â.	NOUN
ejpam-5641	283	6	hence	hence	ADV
ejpam-5641	283	7	∥v̂	∥v̂	PROPN
ejpam-5641	283	8	−	−	NOUN
ejpam-5641	283	9	â∥ℶp−qn	â∥ℶp−qn	ADJ
ejpam-5641	283	10	≤	≤	PUNCT
ejpam-5641	283	11	∥wv̂	∥wv̂	ADP
ejpam-5641	283	12	−wâ∥ℶp−qn	−wâ∥ℶp−qn	PRON
ejpam-5641	283	13	≤	≤	PROPN
ejpam-5641	283	14	α1∥wv̂	α1∥wv̂	NOUN
ejpam-5641	283	15	−	−	PROPN
ejpam-5641	283	16	v̂∥ℶp−qn	v̂∥ℶp−qn	NOUN
ejpam-5641	283	17	+	+	PUNCT
ejpam-5641	283	18	α2∥wâ−	α2∥wâ−	NUM
ejpam-5641	283	19	â∥ℶp−qn	â∥ℶp−qn	NOUN
ejpam-5641	283	20	+	+	CCONJ
ejpam-5641	283	21	α3∥v̂	α3∥v̂	NUM
ejpam-5641	283	22	−	−	NOUN
ejpam-5641	283	23	â∥ℶp−qn	â∥ℶp−qn	NOUN
ejpam-5641	283	24	.	.	PUNCT
ejpam-5641	284	1	so	so	ADV
ejpam-5641	284	2	,	,	PUNCT
ejpam-5641	284	3	v̂	v̂	NOUN
ejpam-5641	284	4	=	=	PUNCT
ejpam-5641	284	5	â.	â.	ADJ
ejpam-5641	284	6	example	example	NOUN
ejpam-5641	284	7	4.6	4.6	NUM
ejpam-5641	284	8	.	.	PUNCT
ejpam-5641	285	1	supposing	suppose	VERB
ejpam-5641	285	2	that	that	PRON
ejpam-5641	285	3	φ	φ	PROPN
ejpam-5641	285	4	:	:	PUNCT
ejpam-5641	285	5	(	(	PUNCT
ejpam-5641	285	6	γsf	γsf	X
ejpam-5641	285	7	(	(	PUNCT
ejpam-5641	285	8	(	(	PUNCT
ejpam-5641	285	9	1	1	NUM
ejpam-5641	285	10	(	(	PUNCT
ejpam-5641	285	11	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	285	12	)	)	PUNCT
ejpam-5641	285	13	l∈n	l∈n	ADJ
ejpam-5641	285	14	,	,	PUNCT
ejpam-5641	285	15	(	(	PUNCT
ejpam-5641	285	16	2l+3	2l+3	NOUN
ejpam-5641	285	17	l+2	l+2	NOUN
ejpam-5641	285	18	)	)	PUNCT
ejpam-5641	285	19	l∈n	l∈n	ADJ
ejpam-5641	285	20	)	)	PUNCT
ejpam-5641	285	21	)	)	PUNCT
ejpam-5641	285	22	∥.∥p−qn	∥.∥p−qn	PRON
ejpam-5641	285	23	→	→	PUNCT
ejpam-5641	285	24	(	(	PUNCT
ejpam-5641	285	25	γsf	γsf	X
ejpam-5641	285	26	(	(	PUNCT
ejpam-5641	285	27	(	(	PUNCT
ejpam-5641	285	28	1	1	NUM
ejpam-5641	285	29	(	(	PUNCT
ejpam-5641	285	30	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	285	31	)	)	PUNCT
ejpam-5641	285	32	l∈n	l∈n	ADJ
ejpam-5641	285	33	,	,	PUNCT
ejpam-5641	285	34	(	(	PUNCT
ejpam-5641	285	35	2l+3	2l+3	NOUN
ejpam-5641	285	36	l+2	l+2	NOUN
ejpam-5641	285	37	)	)	PUNCT
ejpam-5641	285	38	l∈n	l∈n	ADJ
ejpam-5641	285	39	)	)	PUNCT
ejpam-5641	285	40	)	)	PUNCT
ejpam-5641	286	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	286	2	,	,	PUNCT
ejpam-5641	286	3	where	where	SCONJ
ejpam-5641	286	4	∥d̂∥p−qn	∥d̂∥p−qn	NOUN
ejpam-5641	286	5	=	=	NOUN
ejpam-5641	286	6	√√√√√√∑	√√√√√√∑	NOUN
ejpam-5641	286	7	l∈n	l∈n	VERB
ejpam-5641	286	8			PROPN
ejpam-5641	286	9	ℏ̂	ℏ̂	NUM
ejpam-5641	286	10	(	(	PUNCT
ejpam-5641	286	11	∑l	∑l	PROPN
ejpam-5641	286	12	z=0	z=0	PROPN
ejpam-5641	286	13	d̂z	d̂z	NUM
ejpam-5641	286	14	z+5	z+5	NUM
ejpam-5641	286	15	,	,	PUNCT
ejpam-5641	286	16	0̂	0̂	PROPN
ejpam-5641	286	17	)	)	PUNCT
ejpam-5641	287	1	flfl+1	flfl+1	PROPN
ejpam-5641	287	2			PROPN
ejpam-5641	287	3	2l+3	2l+3	PROPN
ejpam-5641	287	4	l+2	l+2	NOUN
ejpam-5641	287	5	,	,	PUNCT
ejpam-5641	287	6	with	with	ADP
ejpam-5641	287	7	,	,	PUNCT
ejpam-5641	287	8	v̂	v̂	NOUN
ejpam-5641	287	9	,	,	PUNCT
ejpam-5641	287	10	d̂	d̂	PROPN
ejpam-5641	287	11	∈	∈	PROPN
ejpam-5641	287	12	(	(	PUNCT
ejpam-5641	287	13	γsf	γsf	X
ejpam-5641	287	14	(	(	PUNCT
ejpam-5641	287	15	(	(	PUNCT
ejpam-5641	287	16	1	1	NUM
ejpam-5641	287	17	(	(	PUNCT
ejpam-5641	287	18	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	287	19	)	)	PUNCT
ejpam-5641	287	20	l∈n	l∈n	ADJ
ejpam-5641	287	21	,	,	PUNCT
ejpam-5641	287	22	(	(	PUNCT
ejpam-5641	287	23	2l+3	2l+3	NOUN
ejpam-5641	287	24	l+2	l+2	NOUN
ejpam-5641	287	25	)	)	PUNCT
ejpam-5641	287	26	l∈n	l∈n	ADJ
ejpam-5641	287	27	)	)	PUNCT
ejpam-5641	287	28	)	)	PUNCT
ejpam-5641	287	29	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	287	30	and	and	CCONJ
ejpam-5641	287	31	φ(d̂	φ(d̂	NOUN
ejpam-5641	287	32	)	)	PUNCT
ejpam-5641	287	33	=	=	PRON
ejpam-5641	287	34	{	{	PUNCT
ejpam-5641	287	35	d̂	d̂	PROPN
ejpam-5641	287	36	4	4	NUM
ejpam-5641	287	37	,	,	PUNCT
ejpam-5641	287	38	∥d̂∥p−qn	∥d̂∥p−qn	NOUN
ejpam-5641	287	39	∈	∈	PROPN
ejpam-5641	288	1	[	[	X
ejpam-5641	288	2	0	0	NUM
ejpam-5641	288	3	,	,	PUNCT
ejpam-5641	288	4	1	1	NUM
ejpam-5641	288	5	)	)	PUNCT
ejpam-5641	288	6	,	,	PUNCT
ejpam-5641	288	7	d̂	d̂	PROPN
ejpam-5641	288	8	5	5	NUM
ejpam-5641	288	9	,	,	PUNCT
ejpam-5641	288	10	∥d̂∥p−qn	∥d̂∥p−qn	NOUN
ejpam-5641	288	11	∈	∈	PROPN
ejpam-5641	289	1	[	[	X
ejpam-5641	289	2	1,∞	1,∞	NUM
ejpam-5641	289	3	)	)	PUNCT
ejpam-5641	289	4	.	.	PUNCT
ejpam-5641	290	1	m.	m.	NOUN
ejpam-5641	290	2	m.	m.	PROPN
ejpam-5641	290	3	a	a	PRON
ejpam-5641	290	4	et	et	PROPN
ejpam-5641	290	5	al	al	PROPN
ejpam-5641	290	6	.	.	PUNCT
ejpam-5641	290	7	/	/	SYM
ejpam-5641	290	8	eur	eur	PROPN
ejpam-5641	290	9	.	.	PUNCT
ejpam-5641	291	1	j.	j.	PROPN
ejpam-5641	291	2	pure	pure	PROPN
ejpam-5641	291	3	appl	appl	PROPN
ejpam-5641	291	4	.	.	PROPN
ejpam-5641	291	5	math	math	PROPN
ejpam-5641	291	6	,	,	PUNCT
ejpam-5641	291	7	18	18	NUM
ejpam-5641	291	8	(	(	PUNCT
ejpam-5641	291	9	1	1	NUM
ejpam-5641	291	10	)	)	PUNCT
ejpam-5641	291	11	(	(	PUNCT
ejpam-5641	291	12	2025	2025	NUM
ejpam-5641	291	13	)	)	PUNCT
ejpam-5641	291	14	,	,	PUNCT
ejpam-5641	291	15	5641	5641	NUM
ejpam-5641	291	16	12	12	NUM
ejpam-5641	291	17	of	of	ADP
ejpam-5641	291	18	20	20	NUM
ejpam-5641	291	19	if	if	SCONJ
ejpam-5641	291	20	∥d̂∥p−qn	∥d̂∥p−qn	NOUN
ejpam-5641	291	21	,	,	PUNCT
ejpam-5641	291	22	∥v̂∥p−qn	∥v̂∥p−qn	NOUN
ejpam-5641	291	23	∈	∈	PROPN
ejpam-5641	292	1	[	[	X
ejpam-5641	292	2	0	0	NUM
ejpam-5641	292	3	,	,	PUNCT
ejpam-5641	292	4	1	1	NUM
ejpam-5641	292	5	)	)	PUNCT
ejpam-5641	292	6	,	,	PUNCT
ejpam-5641	292	7	one	one	NUM
ejpam-5641	292	8	has	have	VERB
ejpam-5641	292	9	∥φd̂−	∥φd̂−	ADJ
ejpam-5641	292	10	φv̂∥p−qn	φv̂∥p−qn	X
ejpam-5641	292	11	=	=	SYM
ejpam-5641	293	1	∥	∥	X
ejpam-5641	293	2	d̂	d̂	X
ejpam-5641	293	3	4	4	NUM
ejpam-5641	293	4	−	−	NOUN
ejpam-5641	293	5	v̂	v̂	ADP
ejpam-5641	293	6	4	4	NUM
ejpam-5641	293	7	∥p−qn	∥p−qn	ADJ
ejpam-5641	293	8	≤	≤	NUM
ejpam-5641	293	9	1	1	NUM
ejpam-5641	293	10	4	4	NUM
ejpam-5641	293	11	√	√	NUM
ejpam-5641	293	12	27	27	NUM
ejpam-5641	293	13	(	(	PUNCT
ejpam-5641	293	14	∥3d̂	∥3d̂	ADV
ejpam-5641	293	15	4	4	NUM
ejpam-5641	293	16	∥p−qn	∥p−qn	ADJ
ejpam-5641	293	17	+	+	CCONJ
ejpam-5641	293	18	∥3v̂	∥3v̂	PROPN
ejpam-5641	293	19	4	4	NUM
ejpam-5641	293	20	∥p−qn	∥p−qn	NOUN
ejpam-5641	293	21	)	)	PUNCT
ejpam-5641	294	1	+	+	CCONJ
ejpam-5641	295	1	0.1∥d̂−	0.1∥d̂−	PRON
ejpam-5641	295	2	v̂∥p−qn	v̂∥p−qn	NOUN
ejpam-5641	295	3	=	=	NOUN
ejpam-5641	295	4	1	1	NUM
ejpam-5641	295	5	4	4	NUM
ejpam-5641	295	6	√	√	NUM
ejpam-5641	295	7	27	27	NUM
ejpam-5641	295	8	(	(	PUNCT
ejpam-5641	295	9	∥φd̂−	∥φd̂−	ADJ
ejpam-5641	295	10	d̂∥p−qn	d̂∥p−qn	PROPN
ejpam-5641	295	11	+	+	CCONJ
ejpam-5641	295	12	∥φv̂	∥φv̂	PROPN
ejpam-5641	295	13	−	−	PROPN
ejpam-5641	295	14	v̂∥p−qn	v̂∥p−qn	NOUN
ejpam-5641	295	15	)	)	PUNCT
ejpam-5641	296	1	+	+	CCONJ
ejpam-5641	296	2	0.1∥d̂−	0.1∥d̂−	NUM
ejpam-5641	296	3	v̂∥p−qn	v̂∥p−qn	NOUN
ejpam-5641	296	4	.	.	PUNCT
ejpam-5641	297	1	if	if	SCONJ
ejpam-5641	297	2	∥d̂∥p−qn	∥d̂∥p−qn	NOUN
ejpam-5641	297	3	,	,	PUNCT
ejpam-5641	297	4	∥v̂∥p−qn	∥v̂∥p−qn	NOUN
ejpam-5641	297	5	∈	∈	PROPN
ejpam-5641	298	1	[	[	X
ejpam-5641	298	2	1,∞	1,∞	NUM
ejpam-5641	298	3	)	)	PUNCT
ejpam-5641	298	4	,	,	PUNCT
ejpam-5641	298	5	then	then	ADV
ejpam-5641	298	6	∥φd̂−	∥φd̂−	ADJ
ejpam-5641	298	7	φv̂∥p−qn	φv̂∥p−qn	X
ejpam-5641	298	8	=	=	SYM
ejpam-5641	299	1	∥	∥	X
ejpam-5641	299	2	d̂	d̂	X
ejpam-5641	299	3	5	5	NUM
ejpam-5641	299	4	−	−	NOUN
ejpam-5641	299	5	v̂	v̂	ADP
ejpam-5641	299	6	5	5	NUM
ejpam-5641	299	7	∥p−qn	∥p−qn	ADJ
ejpam-5641	299	8	≤	≤	NUM
ejpam-5641	299	9	1	1	NUM
ejpam-5641	299	10	4	4	NUM
ejpam-5641	299	11	√	√	NUM
ejpam-5641	299	12	64	64	NUM
ejpam-5641	299	13	(	(	PUNCT
ejpam-5641	299	14	∥4d̂	∥4d̂	ADJ
ejpam-5641	299	15	5	5	NUM
ejpam-5641	299	16	∥p−qn	∥p−qn	NOUN
ejpam-5641	299	17	+	+	CCONJ
ejpam-5641	299	18	∥4v̂	∥4v̂	PROPN
ejpam-5641	299	19	5	5	NUM
ejpam-5641	299	20	∥p−qn	∥p−qn	NOUN
ejpam-5641	299	21	)	)	PUNCT
ejpam-5641	300	1	+	+	NUM
ejpam-5641	301	1	0.2∥d̂−	0.2∥d̂−	NOUN
ejpam-5641	301	2	v̂∥p−qn	v̂∥p−qn	NOUN
ejpam-5641	301	3	=	=	NOUN
ejpam-5641	301	4	1	1	NUM
ejpam-5641	301	5	4	4	NUM
ejpam-5641	301	6	√	√	NUM
ejpam-5641	301	7	64	64	NUM
ejpam-5641	301	8	(	(	PUNCT
ejpam-5641	301	9	∥φd̂−	∥φd̂−	ADJ
ejpam-5641	301	10	d̂∥p−qn	d̂∥p−qn	PROPN
ejpam-5641	301	11	+	+	CCONJ
ejpam-5641	301	12	∥φv̂	∥φv̂	PROPN
ejpam-5641	301	13	−	−	PROPN
ejpam-5641	301	14	v̂∥p−qn	v̂∥p−qn	NOUN
ejpam-5641	301	15	)	)	PUNCT
ejpam-5641	302	1	+	+	NUM
ejpam-5641	302	2	0.2∥d̂−	0.2∥d̂−	NOUN
ejpam-5641	302	3	v̂∥p−qn	v̂∥p−qn	NOUN
ejpam-5641	302	4	.	.	PUNCT
ejpam-5641	303	1	suppose	suppose	VERB
ejpam-5641	303	2	∥d̂∥p−qn	∥d̂∥p−qn	PROPN
ejpam-5641	303	3	∈	∈	PROPN
ejpam-5641	304	1	[	[	X
ejpam-5641	304	2	0	0	NUM
ejpam-5641	304	3	,	,	PUNCT
ejpam-5641	304	4	1	1	NUM
ejpam-5641	304	5	)	)	PUNCT
ejpam-5641	304	6	and	and	CCONJ
ejpam-5641	304	7	∥v̂∥p−qn	∥v̂∥p−qn	NOUN
ejpam-5641	304	8	∈	∈	PROPN
ejpam-5641	305	1	[	[	X
ejpam-5641	305	2	1,∞	1,∞	NUM
ejpam-5641	305	3	)	)	PUNCT
ejpam-5641	305	4	,	,	PUNCT
ejpam-5641	305	5	then	then	ADV
ejpam-5641	305	6	∥φd̂−	∥φd̂−	ADJ
ejpam-5641	305	7	φv̂∥p−qn	φv̂∥p−qn	X
ejpam-5641	305	8	=	=	SYM
ejpam-5641	306	1	∥	∥	X
ejpam-5641	306	2	d̂	d̂	X
ejpam-5641	306	3	4	4	NUM
ejpam-5641	306	4	−	−	NOUN
ejpam-5641	306	5	v̂	v̂	ADP
ejpam-5641	306	6	5	5	NUM
ejpam-5641	306	7	∥p−qn	∥p−qn	ADJ
ejpam-5641	306	8	≤	≤	NUM
ejpam-5641	306	9	1	1	NUM
ejpam-5641	306	10	4	4	NUM
ejpam-5641	306	11	√	√	NUM
ejpam-5641	306	12	27	27	NUM
ejpam-5641	306	13	∥3d̂	∥3d̂	PROPN
ejpam-5641	306	14	4	4	NUM
ejpam-5641	306	15	∥p−qn	∥p−qn	ADJ
ejpam-5641	306	16	+	+	CCONJ
ejpam-5641	306	17	1	1	NUM
ejpam-5641	306	18	4	4	NUM
ejpam-5641	306	19	√	√	NUM
ejpam-5641	306	20	64	64	NUM
ejpam-5641	306	21	∥4v̂	∥4v̂	PROPN
ejpam-5641	306	22	5	5	NUM
ejpam-5641	306	23	∥p−qn	∥p−qn	NOUN
ejpam-5641	306	24	+	+	NUM
ejpam-5641	306	25	0.1∥d̂−	0.1∥d̂−	ADJ
ejpam-5641	306	26	v̂∥p−qn	v̂∥p−qn	NOUN
ejpam-5641	306	27	=	=	NOUN
ejpam-5641	306	28	1	1	NUM
ejpam-5641	306	29	4	4	NUM
ejpam-5641	306	30	√	√	NUM
ejpam-5641	306	31	27	27	NUM
ejpam-5641	306	32	∥φd̂−	∥φd̂−	ADJ
ejpam-5641	306	33	d̂∥p−qn	d̂∥p−qn	PROPN
ejpam-5641	306	34	+	+	CCONJ
ejpam-5641	306	35	1	1	NUM
ejpam-5641	306	36	4	4	NUM
ejpam-5641	306	37	√	√	NUM
ejpam-5641	306	38	64	64	NUM
ejpam-5641	306	39	∥φv̂	∥φv̂	NOUN
ejpam-5641	306	40	−	−	PROPN
ejpam-5641	307	1	v̂∥p−qn	v̂∥p−qn	NOUN
ejpam-5641	307	2	+	+	CCONJ
ejpam-5641	307	3	0.1∥d̂−	0.1∥d̂−	ADJ
ejpam-5641	307	4	v̂∥p−qn	v̂∥p−qn	NOUN
ejpam-5641	307	5	.	.	PUNCT
ejpam-5641	308	1	therefore	therefore	ADV
ejpam-5641	308	2	,	,	PUNCT
ejpam-5641	308	3	φ	φ	PROPN
ejpam-5641	308	4	is	be	AUX
ejpam-5641	308	5	ntk-∥.∥p−qn	ntk-∥.∥p−qn	NOUN
ejpam-5641	308	6	-	-	PUNCT
ejpam-5641	308	7	c.	c.	NOUN
ejpam-5641	308	8	since	since	SCONJ
ejpam-5641	308	9	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	308	10	verifies	verifie	NOUN
ejpam-5641	308	11	the	the	DET
ejpam-5641	308	12	fp	fp	NOUN
ejpam-5641	308	13	.	.	PUNCT
ejpam-5641	309	1	by	by	ADP
ejpam-5641	309	2	theorem	theorem	NOUN
ejpam-5641	309	3	4.3	4.3	NUM
ejpam-5641	309	4	,	,	PUNCT
ejpam-5641	309	5	one	one	NOUN
ejpam-5641	309	6	obtains	obtain	VERB
ejpam-5641	309	7	φ	φ	PROPN
ejpam-5641	309	8	has	have	VERB
ejpam-5641	310	1	a	a	DET
ejpam-5641	310	2	ufp	ufp	ADJ
ejpam-5641	310	3	ϑ̂.	ϑ̂.	NOUN
ejpam-5641	310	4	assume	assume	VERB
ejpam-5641	310	5	{	{	PUNCT
ejpam-5641	310	6	d̂(a	d̂(a	NOUN
ejpam-5641	310	7	)	)	PUNCT
ejpam-5641	310	8	}	}	PUNCT
ejpam-5641	310	9	⊆	⊆	NUM
ejpam-5641	310	10	(	(	PUNCT
ejpam-5641	310	11	γsf	γsf	X
ejpam-5641	310	12	(	(	PUNCT
ejpam-5641	310	13	(	(	PUNCT
ejpam-5641	310	14	1	1	NUM
ejpam-5641	310	15	(	(	PUNCT
ejpam-5641	310	16	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	310	17	)	)	PUNCT
ejpam-5641	310	18	l∈n	l∈n	ADJ
ejpam-5641	310	19	,	,	PUNCT
ejpam-5641	310	20	(	(	PUNCT
ejpam-5641	310	21	2l+3	2l+3	NOUN
ejpam-5641	310	22	l+2	l+2	NOUN
ejpam-5641	310	23	)	)	PUNCT
ejpam-5641	310	24	l∈n	l∈n	ADJ
ejpam-5641	310	25	)	)	PUNCT
ejpam-5641	310	26	)	)	PUNCT
ejpam-5641	311	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	311	2	under	under	ADP
ejpam-5641	311	3	lima→∞	lima→∞	PROPN
ejpam-5641	311	4	∥d̂(a)−d̂(0)∥p−qn	∥d̂(a)−d̂(0)∥p−qn	PROPN
ejpam-5641	311	5	=	=	PUNCT
ejpam-5641	311	6	0	0	PROPN
ejpam-5641	311	7	,	,	PUNCT
ejpam-5641	311	8	where	where	SCONJ
ejpam-5641	311	9	d̂(0	d̂(0	NOUN
ejpam-5641	311	10	)	)	PUNCT
ejpam-5641	311	11	∈	∈	PROPN
ejpam-5641	311	12	(	(	PUNCT
ejpam-5641	311	13	γsf	γsf	X
ejpam-5641	311	14	(	(	PUNCT
ejpam-5641	311	15	(	(	PUNCT
ejpam-5641	311	16	1	1	NUM
ejpam-5641	311	17	(	(	PUNCT
ejpam-5641	311	18	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	311	19	)	)	PUNCT
ejpam-5641	311	20	l∈n	l∈n	ADJ
ejpam-5641	311	21	,	,	PUNCT
ejpam-5641	311	22	(	(	PUNCT
ejpam-5641	311	23	2l+3	2l+3	NOUN
ejpam-5641	311	24	l+2	l+2	NOUN
ejpam-5641	311	25	)	)	PUNCT
ejpam-5641	311	26	l∈n	l∈n	ADJ
ejpam-5641	311	27	)	)	PUNCT
ejpam-5641	311	28	)	)	PUNCT
ejpam-5641	312	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	312	2	and	and	CCONJ
ejpam-5641	312	3	∥d̂(0)∥p−qn	∥d̂(0)∥p−qn	PROPN
ejpam-5641	312	4	=	=	PROPN
ejpam-5641	312	5	1	1	X
ejpam-5641	312	6	.	.	PUNCT
ejpam-5641	313	1	as	as	SCONJ
ejpam-5641	313	2	the	the	DET
ejpam-5641	313	3	p	p	PROPN
ejpam-5641	313	4	-	-	PUNCT
ejpam-5641	313	5	q.n	q.n	NOUN
ejpam-5641	313	6	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	313	7	is	be	AUX
ejpam-5641	313	8	continuous	continuous	ADJ
ejpam-5641	313	9	,	,	PUNCT
ejpam-5641	313	10	one	one	PRON
ejpam-5641	313	11	gets	get	VERB
ejpam-5641	313	12	lim	lim	PROPN
ejpam-5641	313	13	a→∞	a→∞	NOUN
ejpam-5641	313	14	∥φd̂(a	∥φd̂(a	NOUN
ejpam-5641	313	15	)	)	PUNCT
ejpam-5641	314	1	−	−	PROPN
ejpam-5641	314	2	φd̂(0)∥p−qn	φd̂(0)∥p−qn	NOUN
ejpam-5641	315	1	=	=	PROPN
ejpam-5641	315	2	lim	lim	PROPN
ejpam-5641	315	3	a→∞	a→∞	NUM
ejpam-5641	315	4	∥	∥	X
ejpam-5641	315	5	d̂	d̂	X
ejpam-5641	315	6	(	(	PUNCT
ejpam-5641	315	7	a	a	X
ejpam-5641	315	8	)	)	PUNCT
ejpam-5641	315	9	4	4	NUM
ejpam-5641	315	10	−	−	NOUN
ejpam-5641	315	11	d̂(0	d̂(0	NOUN
ejpam-5641	315	12	)	)	PUNCT
ejpam-5641	315	13	5	5	NUM
ejpam-5641	315	14	∥p−qn	∥p−qn	NOUN
ejpam-5641	315	15	=	=	SYM
ejpam-5641	315	16	∥	∥	X
ejpam-5641	315	17	d̂	d̂	X
ejpam-5641	315	18	(	(	PUNCT
ejpam-5641	315	19	0	0	NUM
ejpam-5641	315	20	)	)	PUNCT
ejpam-5641	315	21	20	20	NUM
ejpam-5641	315	22	∥p−qn	∥p−qn	NOUN
ejpam-5641	315	23	>	>	X
ejpam-5641	315	24	0	0	X
ejpam-5641	315	25	.	.	PUNCT
ejpam-5641	316	1	hence	hence	ADV
ejpam-5641	316	2	,	,	PUNCT
ejpam-5641	316	3	φ	φ	PROPN
ejpam-5641	316	4	is	be	AUX
ejpam-5641	316	5	not	not	PART
ejpam-5641	316	6	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	316	7	-	-	PUNCT
ejpam-5641	316	8	seq.c	seq.c	PROPN
ejpam-5641	316	9	at	at	ADP
ejpam-5641	316	10	d̂(0	d̂(0	NOUN
ejpam-5641	316	11	)	)	PUNCT
ejpam-5641	316	12	.	.	PUNCT
ejpam-5641	317	1	therefore	therefore	ADV
ejpam-5641	317	2	,	,	PUNCT
ejpam-5641	317	3	φ	φ	PROPN
ejpam-5641	317	4	is	be	AUX
ejpam-5641	317	5	not	not	PART
ejpam-5641	317	6	continuous	continuous	ADJ
ejpam-5641	317	7	at	at	ADP
ejpam-5641	317	8	d̂(0	d̂(0	NOUN
ejpam-5641	317	9	)	)	PUNCT
ejpam-5641	317	10	.	.	PUNCT
ejpam-5641	318	1	assume	assume	VERB
ejpam-5641	318	2	∥d̂∥2p−qn	∥d̂∥2p−qn	X
ejpam-5641	318	3	=	=	SYM
ejpam-5641	318	4	∑	∑	PUNCT
ejpam-5641	319	1	l∈n	l∈n	VERB
ejpam-5641	319	2			PROPN
ejpam-5641	319	3	ℏ̂	ℏ̂	NUM
ejpam-5641	319	4	(	(	PUNCT
ejpam-5641	319	5	∑l	∑l	PROPN
ejpam-5641	319	6	z=0	z=0	PROPN
ejpam-5641	319	7	d̂z	d̂z	NUM
ejpam-5641	319	8	z+5	z+5	NUM
ejpam-5641	319	9	,	,	PUNCT
ejpam-5641	319	10	0̂	0̂	PROPN
ejpam-5641	319	11	)	)	PUNCT
ejpam-5641	320	1	flfl+1	flfl+1	PROPN
ejpam-5641	320	2			PROPN
ejpam-5641	320	3	2l+3	2l+3	PROPN
ejpam-5641	320	4	l+2	l+2	NOUN
ejpam-5641	320	5	,	,	PUNCT
ejpam-5641	320	6	so	so	SCONJ
ejpam-5641	320	7	that	that	SCONJ
ejpam-5641	320	8	d̂	d̂	ADP
ejpam-5641	320	9	,	,	PUNCT
ejpam-5641	320	10	v̂	v̂	X
ejpam-5641	320	11	∈	∈	PROPN
ejpam-5641	320	12	(	(	PUNCT
ejpam-5641	320	13	γsf	γsf	X
ejpam-5641	320	14	(	(	PUNCT
ejpam-5641	320	15	(	(	PUNCT
ejpam-5641	320	16	1	1	NUM
ejpam-5641	320	17	(	(	PUNCT
ejpam-5641	320	18	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	320	19	)	)	PUNCT
ejpam-5641	320	20	l∈n	l∈n	ADJ
ejpam-5641	320	21	,	,	PUNCT
ejpam-5641	320	22	(	(	PUNCT
ejpam-5641	320	23	2l+3	2l+3	NOUN
ejpam-5641	320	24	l+2	l+2	NOUN
ejpam-5641	320	25	)	)	PUNCT
ejpam-5641	320	26	l∈n	l∈n	ADJ
ejpam-5641	320	27	)	)	PUNCT
ejpam-5641	320	28	)	)	PUNCT
ejpam-5641	320	29	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	320	30	.	.	PUNCT
ejpam-5641	321	1	for	for	ADP
ejpam-5641	321	2	∥d̂∥2p−qn	∥d̂∥2p−qn	PRON
ejpam-5641	321	3	,	,	PUNCT
ejpam-5641	321	4	∥v̂∥2p−qn	∥v̂∥2p−qn	NOUN
ejpam-5641	321	5	∈	∈	PROPN
ejpam-5641	322	1	[	[	X
ejpam-5641	322	2	0	0	NUM
ejpam-5641	322	3	,	,	PUNCT
ejpam-5641	322	4	1	1	NUM
ejpam-5641	322	5	)	)	PUNCT
ejpam-5641	322	6	,	,	PUNCT
ejpam-5641	322	7	one	one	PRON
ejpam-5641	322	8	gets	get	VERB
ejpam-5641	322	9	∥φd̂−	∥φd̂−	ADJ
ejpam-5641	322	10	φv̂∥2p−qn	φv̂∥2p−qn	NOUN
ejpam-5641	322	11	=	=	PUNCT
ejpam-5641	322	12	∥	∥	X
ejpam-5641	322	13	d̂	d̂	PRON
ejpam-5641	322	14	4	4	NUM
ejpam-5641	322	15	−	−	NOUN
ejpam-5641	322	16	v̂	v̂	ADP
ejpam-5641	322	17	4	4	NUM
ejpam-5641	322	18	∥2p−qn	∥2p−qn	SYM
ejpam-5641	322	19	≤	≤	NUM
ejpam-5641	322	20	2√	2√	NUM
ejpam-5641	322	21	27	27	NUM
ejpam-5641	322	22	(	(	PUNCT
ejpam-5641	322	23	∥3d̂	∥3d̂	PROPN
ejpam-5641	322	24	4	4	NUM
ejpam-5641	322	25	∥2p−qn	∥2p−qn	PART
ejpam-5641	322	26	+	+	NUM
ejpam-5641	322	27	∥3v̂	∥3v̂	VERB
ejpam-5641	322	28	4	4	NUM
ejpam-5641	322	29	∥2p−qn	∥2p−qn	NOUN
ejpam-5641	322	30	)	)	PUNCT
ejpam-5641	323	1	+	+	CCONJ
ejpam-5641	323	2	0.05∥d̂−	0.05∥d̂−	NUM
ejpam-5641	323	3	v̂∥2p−qn	v̂∥2p−qn	PROPN
ejpam-5641	323	4	=	=	SYM
ejpam-5641	323	5	2√	2√	PROPN
ejpam-5641	323	6	27	27	NUM
ejpam-5641	323	7	(	(	PUNCT
ejpam-5641	323	8	∥φd̂−	∥φd̂−	ADJ
ejpam-5641	323	9	d̂∥2p−qn	d̂∥2p−qn	VERB
ejpam-5641	323	10	+	+	CCONJ
ejpam-5641	323	11	∥φv̂	∥φv̂	NOUN
ejpam-5641	323	12	−	−	PROPN
ejpam-5641	323	13	v̂∥2p−qn	v̂∥2p−qn	PROPN
ejpam-5641	323	14	)	)	PUNCT
ejpam-5641	324	1	+	+	CCONJ
ejpam-5641	324	2	0.05∥d̂−	0.05∥d̂−	ADJ
ejpam-5641	324	3	v̂∥2p−qn	v̂∥2p−qn	PROPN
ejpam-5641	324	4	.	.	PUNCT
ejpam-5641	325	1	m.	m.	PROPN
ejpam-5641	325	2	m.	m.	PROPN
ejpam-5641	325	3	a	a	PRON
ejpam-5641	325	4	et	et	PROPN
ejpam-5641	325	5	al	al	PROPN
ejpam-5641	325	6	.	.	PUNCT
ejpam-5641	325	7	/	/	SYM
ejpam-5641	325	8	eur	eur	PROPN
ejpam-5641	325	9	.	.	PUNCT
ejpam-5641	326	1	j.	j.	PROPN
ejpam-5641	326	2	pure	pure	PROPN
ejpam-5641	326	3	appl	appl	PROPN
ejpam-5641	326	4	.	.	PROPN
ejpam-5641	326	5	math	math	PROPN
ejpam-5641	326	6	,	,	PUNCT
ejpam-5641	326	7	18	18	NUM
ejpam-5641	326	8	(	(	PUNCT
ejpam-5641	326	9	1	1	NUM
ejpam-5641	326	10	)	)	PUNCT
ejpam-5641	326	11	(	(	PUNCT
ejpam-5641	326	12	2025	2025	NUM
ejpam-5641	326	13	)	)	PUNCT
ejpam-5641	326	14	,	,	PUNCT
ejpam-5641	326	15	5641	5641	NUM
ejpam-5641	326	16	13	13	NUM
ejpam-5641	326	17	of	of	ADP
ejpam-5641	326	18	20	20	NUM
ejpam-5641	326	19	if	if	SCONJ
ejpam-5641	326	20	∥d̂∥2p−qn	∥d̂∥2p−qn	NOUN
ejpam-5641	326	21	,	,	PUNCT
ejpam-5641	326	22	∥v̂∥2p−qn	∥v̂∥2p−qn	NOUN
ejpam-5641	326	23	∈	∈	PROPN
ejpam-5641	327	1	[	[	X
ejpam-5641	327	2	1,∞	1,∞	NUM
ejpam-5641	327	3	)	)	PUNCT
ejpam-5641	327	4	,	,	PUNCT
ejpam-5641	327	5	then	then	ADV
ejpam-5641	327	6	∥φd̂−	∥φd̂−	ADJ
ejpam-5641	327	7	φv̂∥2p−qn	φv̂∥2p−qn	NOUN
ejpam-5641	327	8	=	=	PUNCT
ejpam-5641	327	9	∥	∥	X
ejpam-5641	327	10	d̂	d̂	NOUN
ejpam-5641	327	11	5	5	NUM
ejpam-5641	327	12	−	−	NOUN
ejpam-5641	327	13	v̂	v̂	ADP
ejpam-5641	327	14	5	5	NUM
ejpam-5641	327	15	∥2p−qn	∥2p−qn	SYM
ejpam-5641	327	16	≤	≤	NUM
ejpam-5641	327	17	1	1	NUM
ejpam-5641	327	18	4	4	NUM
ejpam-5641	327	19	(	(	PUNCT
ejpam-5641	327	20	∥4d̂	∥4d̂	ADJ
ejpam-5641	327	21	5	5	NUM
ejpam-5641	327	22	∥2p−qn	∥2p−qn	PART
ejpam-5641	327	23	+	+	NUM
ejpam-5641	327	24	∥4v̂	∥4v̂	PROPN
ejpam-5641	327	25	5	5	NUM
ejpam-5641	327	26	∥2p−qn	∥2p−qn	PUNCT
ejpam-5641	327	27	)	)	PUNCT
ejpam-5641	328	1	+	+	NUM
ejpam-5641	328	2	0.01∥d̂−	0.01∥d̂−	X
ejpam-5641	328	3	v̂∥2p−qn	v̂∥2p−qn	PROPN
ejpam-5641	328	4	=	=	SYM
ejpam-5641	328	5	1	1	NUM
ejpam-5641	328	6	4	4	NUM
ejpam-5641	328	7	(	(	PUNCT
ejpam-5641	328	8	∥φd̂−	∥φd̂−	ADJ
ejpam-5641	328	9	d̂∥2p−qn	d̂∥2p−qn	VERB
ejpam-5641	328	10	+	+	CCONJ
ejpam-5641	328	11	∥φv̂	∥φv̂	NOUN
ejpam-5641	328	12	−	−	PROPN
ejpam-5641	328	13	v̂∥2p−qn	v̂∥2p−qn	PROPN
ejpam-5641	328	14	)	)	PUNCT
ejpam-5641	329	1	+	+	NUM
ejpam-5641	330	1	0.01∥d̂−	0.01∥d̂−	X
ejpam-5641	330	2	v̂∥2p−qn	v̂∥2p−qn	PROPN
ejpam-5641	330	3	.	.	PUNCT
ejpam-5641	331	1	when	when	SCONJ
ejpam-5641	331	2	∥d̂∥2p−qn	∥d̂∥2p−qn	X
ejpam-5641	331	3	∈	∈	PROPN
ejpam-5641	332	1	[	[	X
ejpam-5641	332	2	0	0	NUM
ejpam-5641	332	3	,	,	PUNCT
ejpam-5641	332	4	1	1	NUM
ejpam-5641	332	5	)	)	PUNCT
ejpam-5641	332	6	and	and	CCONJ
ejpam-5641	332	7	∥v̂∥2p−qn	∥v̂∥2p−qn	NOUN
ejpam-5641	332	8	∈	∈	PROPN
ejpam-5641	333	1	[	[	X
ejpam-5641	333	2	1,∞	1,∞	NUM
ejpam-5641	333	3	)	)	PUNCT
ejpam-5641	333	4	,	,	PUNCT
ejpam-5641	333	5	one	one	PRON
ejpam-5641	333	6	obtains	obtain	VERB
ejpam-5641	333	7	∥φd̂−	∥φd̂−	ADJ
ejpam-5641	333	8	φv̂∥2p−qn	φv̂∥2p−qn	NOUN
ejpam-5641	333	9	=	=	PUNCT
ejpam-5641	333	10	∥	∥	X
ejpam-5641	333	11	d̂	d̂	PRON
ejpam-5641	333	12	4	4	NUM
ejpam-5641	333	13	−	−	NOUN
ejpam-5641	333	14	v̂	v̂	ADP
ejpam-5641	333	15	5	5	NUM
ejpam-5641	333	16	∥2p−qn	∥2p−qn	SYM
ejpam-5641	333	17	≤	≤	NUM
ejpam-5641	333	18	2√	2√	NUM
ejpam-5641	333	19	27	27	NUM
ejpam-5641	333	20	∥3d̂	∥3d̂	NOUN
ejpam-5641	333	21	4	4	NUM
ejpam-5641	333	22	∥2p−qn	∥2p−qn	PART
ejpam-5641	333	23	+	+	NUM
ejpam-5641	333	24	1	1	NUM
ejpam-5641	333	25	4	4	NUM
ejpam-5641	333	26	∥4v̂	∥4v̂	PROPN
ejpam-5641	333	27	5	5	NUM
ejpam-5641	333	28	∥2p−qn	∥2p−qn	PART
ejpam-5641	333	29	+	+	NUM
ejpam-5641	333	30	0.01∥d̂−	0.01∥d̂−	NUM
ejpam-5641	333	31	v̂∥2p−qn	v̂∥2p−qn	PROPN
ejpam-5641	333	32	=	=	SYM
ejpam-5641	333	33	2√	2√	PROPN
ejpam-5641	333	34	27	27	NUM
ejpam-5641	333	35	∥φd̂−	∥φd̂−	NOUN
ejpam-5641	333	36	d̂∥2p−qn	d̂∥2p−qn	ADP
ejpam-5641	333	37	+	+	CCONJ
ejpam-5641	333	38	1	1	NUM
ejpam-5641	333	39	4	4	NUM
ejpam-5641	333	40	∥φv̂	∥φv̂	NUM
ejpam-5641	333	41	−	−	PROPN
ejpam-5641	333	42	v̂∥2p−qn	v̂∥2p−qn	PROPN
ejpam-5641	333	43	+	+	CCONJ
ejpam-5641	333	44	0.01∥d̂−	0.01∥d̂−	NUM
ejpam-5641	333	45	v̂∥2p−qn	v̂∥2p−qn	PROPN
ejpam-5641	333	46	.	.	PUNCT
ejpam-5641	334	1	therefore	therefore	ADV
ejpam-5641	334	2	,	,	PUNCT
ejpam-5641	334	3	φ	φ	PROPN
ejpam-5641	334	4	is	be	AUX
ejpam-5641	334	5	ntk-∥.∥2p−qn	ntk-∥.∥2p−qn	NOUN
ejpam-5641	334	6	-	-	PUNCT
ejpam-5641	334	7	c	c	PROPN
ejpam-5641	334	8	and	and	CCONJ
ejpam-5641	334	9	φm(d̂	φm(d̂	NOUN
ejpam-5641	334	10	)	)	PUNCT
ejpam-5641	334	11	=	=	PRON
ejpam-5641	334	12	{	{	PUNCT
ejpam-5641	334	13	d̂	d̂	PROPN
ejpam-5641	334	14	4	4	NUM
ejpam-5641	334	15	m	m	NOUN
ejpam-5641	334	16	,	,	PUNCT
ejpam-5641	334	17	∥d̂∥2p−qn	∥d̂∥2p−qn	NOUN
ejpam-5641	334	18	∈	∈	PROPN
ejpam-5641	335	1	[	[	X
ejpam-5641	335	2	0	0	NUM
ejpam-5641	335	3	,	,	PUNCT
ejpam-5641	335	4	1	1	NUM
ejpam-5641	335	5	)	)	PUNCT
ejpam-5641	335	6	,	,	PUNCT
ejpam-5641	336	1	d̂	d̂	PROPN
ejpam-5641	336	2	5	5	NUM
ejpam-5641	336	3	m	m	NOUN
ejpam-5641	336	4	,	,	PUNCT
ejpam-5641	336	5	∥d̂∥2p−qn	∥d̂∥2p−qn	NOUN
ejpam-5641	336	6	∈	∈	PROPN
ejpam-5641	337	1	[	[	X
ejpam-5641	337	2	1,∞	1,∞	NUM
ejpam-5641	337	3	)	)	PUNCT
ejpam-5641	337	4	.	.	PUNCT
ejpam-5641	338	1	clearly	clearly	ADV
ejpam-5641	338	2	,	,	PUNCT
ejpam-5641	338	3	φ	φ	PROPN
ejpam-5641	338	4	is	be	AUX
ejpam-5641	338	5	∥.∥2p−qn	∥.∥2p−qn	NUM
ejpam-5641	338	6	-	-	PUNCT
ejpam-5641	338	7	seq.c	seq.c	PROPN
ejpam-5641	338	8	at	at	ADP
ejpam-5641	338	9	ϑ̂	ϑ̂	PROPN
ejpam-5641	338	10	∈	∈	PROPN
ejpam-5641	338	11	(	(	PUNCT
ejpam-5641	338	12	γsf	γsf	X
ejpam-5641	338	13	(	(	PUNCT
ejpam-5641	338	14	(	(	PUNCT
ejpam-5641	338	15	1	1	NUM
ejpam-5641	338	16	(	(	PUNCT
ejpam-5641	338	17	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	338	18	)	)	PUNCT
ejpam-5641	338	19	l∈n	l∈n	ADJ
ejpam-5641	338	20	,	,	PUNCT
ejpam-5641	338	21	(	(	PUNCT
ejpam-5641	338	22	2l+3	2l+3	NOUN
ejpam-5641	338	23	l+2	l+2	NOUN
ejpam-5641	338	24	)	)	PUNCT
ejpam-5641	338	25	l∈n	l∈n	ADJ
ejpam-5641	338	26	)	)	PUNCT
ejpam-5641	338	27	)	)	PUNCT
ejpam-5641	338	28	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	338	29	and	and	CCONJ
ejpam-5641	338	30	{	{	PUNCT
ejpam-5641	338	31	φmd̂	φmd̂	PROPN
ejpam-5641	338	32	}	}	PUNCT
ejpam-5641	338	33	includes	include	VERB
ejpam-5641	338	34	a	a	DET
ejpam-5641	338	35	{	{	PUNCT
ejpam-5641	338	36	φmj	φmj	NOUN
ejpam-5641	338	37	d̂	d̂	PROPN
ejpam-5641	338	38	}	}	PUNCT
ejpam-5641	338	39	converges	converge	VERB
ejpam-5641	338	40	to	to	PART
ejpam-5641	338	41	ϑ̂.	ϑ̂.	VERB
ejpam-5641	338	42	according	accord	VERB
ejpam-5641	338	43	theorem	theorem	ADJ
ejpam-5641	338	44	4.5	4.5	NUM
ejpam-5641	338	45	,	,	PUNCT
ejpam-5641	338	46	the	the	DET
ejpam-5641	338	47	element	element	NOUN
ejpam-5641	338	48	ϑ̂	ϑ̂	PROPN
ejpam-5641	338	49	is	be	AUX
ejpam-5641	338	50	the	the	DET
ejpam-5641	338	51	ufp	ufp	NOUN
ejpam-5641	338	52	of	of	ADP
ejpam-5641	338	53	φ	φ	PROPN
ejpam-5641	338	54	.	.	PROPN
ejpam-5641	338	55	example	example	NOUN
ejpam-5641	338	56	4.7	4.7	NUM
ejpam-5641	338	57	.	.	PUNCT
ejpam-5641	339	1	assuming	assume	VERB
ejpam-5641	339	2	that	that	SCONJ
ejpam-5641	339	3	φ	φ	PROPN
ejpam-5641	339	4	:	:	PUNCT
ejpam-5641	339	5	(	(	PUNCT
ejpam-5641	339	6	γsf	γsf	X
ejpam-5641	339	7	(	(	PUNCT
ejpam-5641	339	8	(	(	PUNCT
ejpam-5641	339	9	1	1	NUM
ejpam-5641	339	10	(	(	PUNCT
ejpam-5641	339	11	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	339	12	)	)	PUNCT
ejpam-5641	339	13	l∈n	l∈n	ADJ
ejpam-5641	339	14	,	,	PUNCT
ejpam-5641	339	15	(	(	PUNCT
ejpam-5641	339	16	2l+3	2l+3	NOUN
ejpam-5641	339	17	l+2	l+2	NOUN
ejpam-5641	339	18	)	)	PUNCT
ejpam-5641	339	19	l∈n	l∈n	ADJ
ejpam-5641	339	20	)	)	PUNCT
ejpam-5641	339	21	)	)	PUNCT
ejpam-5641	339	22	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	339	23	→	→	PUNCT
ejpam-5641	339	24	(	(	PUNCT
ejpam-5641	339	25	γsf	γsf	X
ejpam-5641	339	26	(	(	PUNCT
ejpam-5641	339	27	(	(	PUNCT
ejpam-5641	339	28	1	1	NUM
ejpam-5641	339	29	(	(	PUNCT
ejpam-5641	339	30	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	339	31	)	)	PUNCT
ejpam-5641	339	32	l∈n	l∈n	ADJ
ejpam-5641	339	33	,	,	PUNCT
ejpam-5641	339	34	(	(	PUNCT
ejpam-5641	339	35	2l+3	2l+3	NOUN
ejpam-5641	339	36	l+2	l+2	NOUN
ejpam-5641	339	37	)	)	PUNCT
ejpam-5641	339	38	l∈n	l∈n	ADJ
ejpam-5641	339	39	)	)	PUNCT
ejpam-5641	339	40	)	)	PUNCT
ejpam-5641	340	1	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	340	2	,	,	PUNCT
ejpam-5641	340	3	where	where	SCONJ
ejpam-5641	340	4	∥d̂∥2p−qn	∥d̂∥2p−qn	ADV
ejpam-5641	340	5	=	=	SYM
ejpam-5641	340	6	∑	∑	PUNCT
ejpam-5641	340	7	l∈n	l∈n	VERB
ejpam-5641	340	8			PROPN
ejpam-5641	340	9	ℏ̂	ℏ̂	NUM
ejpam-5641	340	10	(	(	PUNCT
ejpam-5641	340	11	∑l	∑l	PROPN
ejpam-5641	340	12	z=0	z=0	PROPN
ejpam-5641	340	13	d̂z	d̂z	NUM
ejpam-5641	340	14	z+5	z+5	NUM
ejpam-5641	340	15	,	,	PUNCT
ejpam-5641	340	16	0̂	0̂	PROPN
ejpam-5641	340	17	)	)	PUNCT
ejpam-5641	341	1	flfl+1	flfl+1	PROPN
ejpam-5641	341	2			PROPN
ejpam-5641	341	3	2l+3	2l+3	PROPN
ejpam-5641	341	4	l+2	l+2	NOUN
ejpam-5641	341	5	,	,	PUNCT
ejpam-5641	342	1	so	so	SCONJ
ejpam-5641	342	2	that	that	SCONJ
ejpam-5641	342	3	d̂	d̂	PRON
ejpam-5641	342	4	∈	∈	PROPN
ejpam-5641	342	5	(	(	PUNCT
ejpam-5641	342	6	γsf	γsf	X
ejpam-5641	342	7	(	(	PUNCT
ejpam-5641	342	8	(	(	PUNCT
ejpam-5641	342	9	1	1	NUM
ejpam-5641	342	10	(	(	PUNCT
ejpam-5641	342	11	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	342	12	)	)	PUNCT
ejpam-5641	342	13	l∈n	l∈n	ADJ
ejpam-5641	342	14	,	,	PUNCT
ejpam-5641	342	15	(	(	PUNCT
ejpam-5641	342	16	2l+3	2l+3	NOUN
ejpam-5641	342	17	l+2	l+2	NOUN
ejpam-5641	342	18	)	)	PUNCT
ejpam-5641	342	19	l∈n	l∈n	ADJ
ejpam-5641	342	20	)	)	PUNCT
ejpam-5641	342	21	)	)	PUNCT
ejpam-5641	342	22	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	342	23	and	and	CCONJ
ejpam-5641	342	24	for	for	ADP
ejpam-5641	342	25	all	all	PRON
ejpam-5641	342	26	t	t	NOUN
ejpam-5641	342	27	∈	∈	PROPN
ejpam-5641	342	28	a	a	PRON
ejpam-5641	342	29	,	,	PUNCT
ejpam-5641	342	30	φ(d̂	φ(d̂	X
ejpam-5641	342	31	)	)	PUNCT
ejpam-5641	342	32	=	=	SYM
ejpam-5641	343	1			NOUN
ejpam-5641	343	2	1	1	NUM
ejpam-5641	343	3	4(ê1	4(ê1	NUM
ejpam-5641	343	4	+	+	NOUN
ejpam-5641	343	5	d̂	d̂	PROPN
ejpam-5641	343	6	)	)	PUNCT
ejpam-5641	343	7	,	,	PUNCT
ejpam-5641	343	8	d̂0(t	d̂0(t	PROPN
ejpam-5641	343	9	)	)	PUNCT
ejpam-5641	343	10	∈	∈	PROPN
ejpam-5641	344	1	[	[	X
ejpam-5641	344	2	0	0	NUM
ejpam-5641	344	3	,	,	PUNCT
ejpam-5641	344	4	13	13	NUM
ejpam-5641	344	5	)	)	PUNCT
ejpam-5641	344	6	,	,	PUNCT
ejpam-5641	344	7	1	1	NUM
ejpam-5641	344	8	3	3	NUM
ejpam-5641	344	9	ê1	ê1	PROPN
ejpam-5641	344	10	,	,	PUNCT
ejpam-5641	344	11	d̂0(t	d̂0(t	PROPN
ejpam-5641	344	12	)	)	PUNCT
ejpam-5641	344	13	=	=	SYM
ejpam-5641	344	14	1	1	NUM
ejpam-5641	344	15	3	3	NUM
ejpam-5641	344	16	,	,	PUNCT
ejpam-5641	344	17	1	1	NUM
ejpam-5641	344	18	4	4	NUM
ejpam-5641	344	19	ê1	ê1	PROPN
ejpam-5641	344	20	,	,	PUNCT
ejpam-5641	344	21	d̂0(t	d̂0(t	PROPN
ejpam-5641	344	22	)	)	PUNCT
ejpam-5641	344	23	∈	∈	PROPN
ejpam-5641	344	24	(	(	PUNCT
ejpam-5641	344	25	13	13	NUM
ejpam-5641	344	26	,	,	PUNCT
ejpam-5641	344	27	1	1	NUM
ejpam-5641	344	28	]	]	PUNCT
ejpam-5641	344	29	.	.	PUNCT
ejpam-5641	345	1	if	if	SCONJ
ejpam-5641	345	2	f̂	f̂	NUM
ejpam-5641	345	3	,	,	PUNCT
ejpam-5641	345	4	ĝ	ĝ	X
ejpam-5641	345	5	∈	∈	PROPN
ejpam-5641	345	6	(	(	PUNCT
ejpam-5641	345	7	γsf	γsf	X
ejpam-5641	345	8	(	(	PUNCT
ejpam-5641	345	9	(	(	PUNCT
ejpam-5641	345	10	1	1	NUM
ejpam-5641	345	11	(	(	PUNCT
ejpam-5641	345	12	l+5)f2l	l+5)f2l	PROPN
ejpam-5641	345	13	)	)	PUNCT
ejpam-5641	345	14	∞	∞	NUM
ejpam-5641	345	15	l=0	l=0	PROPN
ejpam-5641	345	16	,	,	PUNCT
ejpam-5641	345	17	(	(	PUNCT
ejpam-5641	345	18	2l+3	2l+3	NOUN
ejpam-5641	345	19	l+2	l+2	NOUN
ejpam-5641	345	20	)	)	PUNCT
ejpam-5641	345	21	∞	∞	NUM
ejpam-5641	345	22	l=0	l=0	PROPN
ejpam-5641	345	23	)	)	PUNCT
ejpam-5641	345	24	)	)	PUNCT
ejpam-5641	345	25	∥.∥2p−qn	∥.∥2p−qn	PUNCT
ejpam-5641	345	26	with	with	ADP
ejpam-5641	345	27	f̂0(t	f̂0(t	PROPN
ejpam-5641	345	28	)	)	PUNCT
ejpam-5641	345	29	,	,	PUNCT
ejpam-5641	345	30	ĝ0(t	ĝ0(t	PROPN
ejpam-5641	345	31	)	)	PUNCT
ejpam-5641	345	32	∈	∈	PROPN
ejpam-5641	346	1	[	[	X
ejpam-5641	346	2	0	0	NUM
ejpam-5641	346	3	,	,	PUNCT
ejpam-5641	346	4	13	13	NUM
ejpam-5641	346	5	)	)	PUNCT
ejpam-5641	346	6	,	,	PUNCT
ejpam-5641	346	7	then	then	ADV
ejpam-5641	346	8	∥φf̂	∥φf̂	ADJ
ejpam-5641	346	9	−	−	PROPN
ejpam-5641	346	10	φĝ∥2p−qn	φĝ∥2p−qn	PROPN
ejpam-5641	346	11	=	=	PUNCT
ejpam-5641	346	12	∥1	∥1	PRON
ejpam-5641	346	13	4	4	NUM
ejpam-5641	346	14	(	(	PUNCT
ejpam-5641	346	15	f̂0	f̂0	NOUN
ejpam-5641	346	16	−	−	PROPN
ejpam-5641	346	17	ĝ0	ĝ0	NOUN
ejpam-5641	346	18	,	,	PUNCT
ejpam-5641	346	19	f̂1	f̂1	NOUN
ejpam-5641	347	1	−	−	PROPN
ejpam-5641	347	2	ĝ1	ĝ1	NOUN
ejpam-5641	347	3	,	,	PUNCT
ejpam-5641	347	4	f̂2	f̂2	ADJ
ejpam-5641	347	5	−	−	NOUN
ejpam-5641	347	6	ĝ2	ĝ2	NOUN
ejpam-5641	347	7	,	,	PUNCT
ejpam-5641	347	8	.	.	PUNCT
ejpam-5641	347	9	.	.	PUNCT
ejpam-5641	348	1	.)∥2p−qn	.)∥2p−qn	PROPN
ejpam-5641	348	2	≤	≤	NUM
ejpam-5641	349	1	2√	2√	PROPN
ejpam-5641	349	2	27	27	NUM
ejpam-5641	349	3	(	(	PUNCT
ejpam-5641	349	4	∥3f̂	∥3f̂	ADJ
ejpam-5641	349	5	4	4	NUM
ejpam-5641	349	6	∥2p−qn	∥2p−qn	PART
ejpam-5641	349	7	+	+	CCONJ
ejpam-5641	349	8	∥3ĝ	∥3ĝ	ADJ
ejpam-5641	349	9	4	4	NUM
ejpam-5641	349	10	∥2p−qn	∥2p−qn	NUM
ejpam-5641	349	11	)	)	PUNCT
ejpam-5641	350	1	+	+	CCONJ
ejpam-5641	350	2	0.03∥f̂	0.03∥f̂	NOUN
ejpam-5641	350	3	−	−	PROPN
ejpam-5641	351	1	ĝ∥2p−qn	ĝ∥2p−qn	PROPN
ejpam-5641	351	2	≤	≤	PROPN
ejpam-5641	351	3	2√	2√	PROPN
ejpam-5641	351	4	27	27	NUM
ejpam-5641	351	5	(	(	PUNCT
ejpam-5641	351	6	∥φf̂	∥φf̂	ADJ
ejpam-5641	351	7	−	−	PROPN
ejpam-5641	352	1	f̂∥2p−qn	f̂∥2p−qn	PROPN
ejpam-5641	352	2	+	+	CCONJ
ejpam-5641	352	3	∥φĝ	∥φĝ	PROPN
ejpam-5641	352	4	−	−	PROPN
ejpam-5641	352	5	ĝ∥2p−qn	ĝ∥2p−qn	PROPN
ejpam-5641	352	6	)	)	PUNCT
ejpam-5641	353	1	+	+	NUM
ejpam-5641	353	2	0.03∥f̂	0.03∥f̂	NOUN
ejpam-5641	354	1	−	−	PROPN
ejpam-5641	355	1	ĝ∥2p−qn	ĝ∥2p−qn	PROPN
ejpam-5641	355	2	.	.	PUNCT
ejpam-5641	355	3	m.	m.	PROPN
ejpam-5641	355	4	m.	m.	PROPN
ejpam-5641	355	5	a	a	PRON
ejpam-5641	355	6	et	et	PROPN
ejpam-5641	355	7	al	al	PROPN
ejpam-5641	355	8	.	.	PUNCT
ejpam-5641	355	9	/	/	SYM
ejpam-5641	355	10	eur	eur	PROPN
ejpam-5641	355	11	.	.	PUNCT
ejpam-5641	356	1	j.	j.	PROPN
ejpam-5641	356	2	pure	pure	PROPN
ejpam-5641	356	3	appl	appl	PROPN
ejpam-5641	356	4	.	.	PROPN
ejpam-5641	356	5	math	math	PROPN
ejpam-5641	356	6	,	,	PUNCT
ejpam-5641	356	7	18	18	NUM
ejpam-5641	356	8	(	(	PUNCT
ejpam-5641	356	9	1	1	NUM
ejpam-5641	356	10	)	)	PUNCT
ejpam-5641	356	11	(	(	PUNCT
ejpam-5641	356	12	2025	2025	NUM
ejpam-5641	356	13	)	)	PUNCT
ejpam-5641	356	14	,	,	PUNCT
ejpam-5641	356	15	5641	5641	NUM
ejpam-5641	356	16	14	14	NUM
ejpam-5641	356	17	of	of	ADP
ejpam-5641	356	18	20	20	NUM
ejpam-5641	356	19	for	for	ADP
ejpam-5641	356	20	every	every	DET
ejpam-5641	356	21	f̂	f̂	NUM
ejpam-5641	356	22	,	,	PUNCT
ejpam-5641	356	23	ĝ	ĝ	X
ejpam-5641	356	24	∈	∈	PROPN
ejpam-5641	356	25	(	(	PUNCT
ejpam-5641	356	26	γsf	γsf	X
ejpam-5641	356	27	(	(	PUNCT
ejpam-5641	356	28	(	(	PUNCT
ejpam-5641	356	29	1	1	NUM
ejpam-5641	356	30	(	(	PUNCT
ejpam-5641	356	31	l+5)f2l	l+5)f2l	PROPN
ejpam-5641	356	32	)	)	PUNCT
ejpam-5641	356	33	∞	∞	NUM
ejpam-5641	357	1	l=0	l=0	PROPN
ejpam-5641	357	2	,	,	PUNCT
ejpam-5641	357	3	(	(	PUNCT
ejpam-5641	357	4	2l+3	2l+3	NOUN
ejpam-5641	357	5	l+2	l+2	NOUN
ejpam-5641	357	6	)	)	PUNCT
ejpam-5641	357	7	∞	∞	NUM
ejpam-5641	357	8	l=0	l=0	PROPN
ejpam-5641	357	9	)	)	PUNCT
ejpam-5641	357	10	)	)	PUNCT
ejpam-5641	357	11	∥.∥2p−qn	∥.∥2p−qn	X
ejpam-5641	357	12	under	under	ADP
ejpam-5641	357	13	f̂0(t	f̂0(t	PROPN
ejpam-5641	357	14	)	)	PUNCT
ejpam-5641	357	15	,	,	PUNCT
ejpam-5641	357	16	ĝ0(t	ĝ0(t	PROPN
ejpam-5641	357	17	)	)	PUNCT
ejpam-5641	357	18	∈	∈	PROPN
ejpam-5641	357	19	(	(	PUNCT
ejpam-5641	357	20	13	13	NUM
ejpam-5641	357	21	,	,	PUNCT
ejpam-5641	357	22	1	1	NUM
ejpam-5641	357	23	]	]	PUNCT
ejpam-5641	357	24	,	,	PUNCT
ejpam-5641	357	25	hence	hence	ADV
ejpam-5641	357	26	for	for	ADP
ejpam-5641	357	27	all	all	PRON
ejpam-5641	357	28	εi	εi	NOUN
ejpam-5641	357	29	>	>	X
ejpam-5641	357	30	0	0	PUNCT
ejpam-5641	358	1	and	and	CCONJ
ejpam-5641	358	2	i	i	PRON
ejpam-5641	358	3	=	=	NOUN
ejpam-5641	358	4	1	1	NUM
ejpam-5641	358	5	,	,	PUNCT
ejpam-5641	358	6	2	2	NUM
ejpam-5641	358	7	,	,	PUNCT
ejpam-5641	358	8	and	and	CCONJ
ejpam-5641	358	9	3	3	NUM
ejpam-5641	358	10	,	,	PUNCT
ejpam-5641	358	11	we	we	PRON
ejpam-5641	358	12	have	have	VERB
ejpam-5641	358	13	∥φf̂	∥φf̂	ADJ
ejpam-5641	358	14	−	−	PROPN
ejpam-5641	358	15	φĝ∥2p−qn	φĝ∥2p−qn	PROPN
ejpam-5641	358	16	=	=	NOUN
ejpam-5641	358	17	0	0	NUM
ejpam-5641	358	18	≤	≤	NOUN
ejpam-5641	358	19	ε1∥φf̂	ε1∥φf̂	NOUN
ejpam-5641	358	20	−	−	PROPN
ejpam-5641	359	1	f̂∥2p−qn	f̂∥2p−qn	PROPN
ejpam-5641	359	2	+	+	CCONJ
ejpam-5641	359	3	ε2∥φĝ	ε2∥φĝ	ADJ
ejpam-5641	359	4	−	−	PROPN
ejpam-5641	360	1	ĝ∥2p−qn	ĝ∥2p−qn	PROPN
ejpam-5641	360	2	+	+	CCONJ
ejpam-5641	360	3	ε3∥f̂	ε3∥f̂	PROPN
ejpam-5641	360	4	−	−	PROPN
ejpam-5641	360	5	ĝ∥2p−qn	ĝ∥2p−qn	PROPN
ejpam-5641	360	6	.	.	PUNCT
ejpam-5641	361	1	if	if	SCONJ
ejpam-5641	361	2	f̂	f̂	NUM
ejpam-5641	361	3	,	,	PUNCT
ejpam-5641	361	4	ĝ	ĝ	X
ejpam-5641	361	5	∈	∈	PROPN
ejpam-5641	361	6	(	(	PUNCT
ejpam-5641	361	7	γsf	γsf	X
ejpam-5641	361	8	(	(	PUNCT
ejpam-5641	361	9	(	(	PUNCT
ejpam-5641	361	10	1	1	NUM
ejpam-5641	361	11	(	(	PUNCT
ejpam-5641	361	12	l+5)f2l	l+5)f2l	PROPN
ejpam-5641	361	13	)	)	PUNCT
ejpam-5641	361	14	∞	∞	NUM
ejpam-5641	362	1	l=0	l=0	PROPN
ejpam-5641	362	2	,	,	PUNCT
ejpam-5641	362	3	(	(	PUNCT
ejpam-5641	362	4	2l+3	2l+3	NOUN
ejpam-5641	362	5	l+2	l+2	NOUN
ejpam-5641	362	6	)	)	PUNCT
ejpam-5641	362	7	∞	∞	NUM
ejpam-5641	362	8	l=0	l=0	PROPN
ejpam-5641	362	9	)	)	PUNCT
ejpam-5641	362	10	)	)	PUNCT
ejpam-5641	362	11	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	362	12	with	with	ADP
ejpam-5641	362	13	f̂0(t	f̂0(t	PROPN
ejpam-5641	362	14	)	)	PUNCT
ejpam-5641	362	15	∈	∈	PROPN
ejpam-5641	363	1	[	[	X
ejpam-5641	363	2	0	0	NUM
ejpam-5641	363	3	,	,	PUNCT
ejpam-5641	363	4	13	13	NUM
ejpam-5641	363	5	)	)	PUNCT
ejpam-5641	363	6	and	and	CCONJ
ejpam-5641	363	7	ĝ0(t	ĝ0(t	PROPN
ejpam-5641	363	8	)	)	PUNCT
ejpam-5641	363	9	∈	∈	PROPN
ejpam-5641	363	10	(	(	PUNCT
ejpam-5641	363	11	13	13	NUM
ejpam-5641	363	12	,	,	PUNCT
ejpam-5641	363	13	1	1	NUM
ejpam-5641	363	14	]	]	PUNCT
ejpam-5641	363	15	,	,	PUNCT
ejpam-5641	363	16	then	then	ADV
ejpam-5641	363	17	∥φf̂	∥φf̂	ADJ
ejpam-5641	363	18	−	−	PROPN
ejpam-5641	363	19	φĝ∥2p−qn	φĝ∥2p−qn	PROPN
ejpam-5641	363	20	=	=	SYM
ejpam-5641	363	21	∥	∥	X
ejpam-5641	363	22	f̂	f̂	NUM
ejpam-5641	363	23	4	4	NUM
ejpam-5641	363	24	∥2p−qn	∥2p−qn	SYM
ejpam-5641	363	25	≤	≤	NUM
ejpam-5641	363	26	1√	1√	NUM
ejpam-5641	363	27	27	27	NUM
ejpam-5641	363	28	∥3f̂	∥3f̂	ADJ
ejpam-5641	363	29	4	4	NUM
ejpam-5641	363	30	∥2p−qn	∥2p−qn	PART
ejpam-5641	363	31	=	=	SYM
ejpam-5641	363	32	1√	1√	PROPN
ejpam-5641	363	33	27	27	NUM
ejpam-5641	363	34	∥φf̂	∥φf̂	NOUN
ejpam-5641	364	1	−	−	PROPN
ejpam-5641	365	1	f̂∥2p−qn	f̂∥2p−qn	PROPN
ejpam-5641	365	2	+	+	CCONJ
ejpam-5641	365	3	0.2∥f̂	0.2∥f̂	NUM
ejpam-5641	365	4	−	−	PROPN
ejpam-5641	365	5	ĝ∥2p−qn	ĝ∥2p−qn	PROPN
ejpam-5641	365	6	≤	≤	PROPN
ejpam-5641	365	7	1√	1√	PROPN
ejpam-5641	365	8	27	27	NUM
ejpam-5641	365	9	(	(	PUNCT
ejpam-5641	365	10	∥φf̂	∥φf̂	ADJ
ejpam-5641	365	11	−	−	PROPN
ejpam-5641	366	1	f̂∥2p−qn	f̂∥2p−qn	PROPN
ejpam-5641	366	2	+	+	CCONJ
ejpam-5641	366	3	∥φĝ	∥φĝ	PROPN
ejpam-5641	366	4	−	−	PROPN
ejpam-5641	366	5	ĝ∥2p−qn	ĝ∥2p−qn	PROPN
ejpam-5641	366	6	)	)	PUNCT
ejpam-5641	367	1	+	+	NUM
ejpam-5641	367	2	0.2∥f̂	0.2∥f̂	NUM
ejpam-5641	367	3	−	−	PROPN
ejpam-5641	367	4	ĝ∥2p−qn	ĝ∥2p−qn	PROPN
ejpam-5641	367	5	.	.	PUNCT
ejpam-5641	368	1	hence	hence	ADV
ejpam-5641	368	2	,	,	PUNCT
ejpam-5641	368	3	φ	φ	PROPN
ejpam-5641	368	4	is	be	AUX
ejpam-5641	368	5	ntk-∥.∥2p−qn	ntk-∥.∥2p−qn	NOUN
ejpam-5641	368	6	-	-	PUNCT
ejpam-5641	368	7	c	c	PROPN
ejpam-5641	368	8	,	,	PUNCT
ejpam-5641	368	9	∥.∥2p−qn	∥.∥2p−qn	NUM
ejpam-5641	368	10	-	-	SYM
ejpam-5641	368	11	seq.c	seq.c	PROPN
ejpam-5641	368	12	at	at	ADP
ejpam-5641	368	13	1	1	NUM
ejpam-5641	368	14	3	3	NUM
ejpam-5641	368	15	ê1	ê1	PROPN
ejpam-5641	368	16	∈	∈	PROPN
ejpam-5641	368	17	(	(	PUNCT
ejpam-5641	368	18	γsf	γsf	X
ejpam-5641	368	19	(	(	PUNCT
ejpam-5641	368	20	(	(	PUNCT
ejpam-5641	368	21	1	1	NUM
ejpam-5641	368	22	(	(	PUNCT
ejpam-5641	368	23	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	368	24	)	)	PUNCT
ejpam-5641	368	25	l∈n	l∈n	ADJ
ejpam-5641	368	26	,	,	PUNCT
ejpam-5641	368	27	(	(	PUNCT
ejpam-5641	368	28	2l+3	2l+3	NOUN
ejpam-5641	368	29	l+2	l+2	NOUN
ejpam-5641	368	30	)	)	PUNCT
ejpam-5641	368	31	l∈n	l∈n	ADJ
ejpam-5641	368	32	)	)	PUNCT
ejpam-5641	368	33	)	)	PUNCT
ejpam-5641	369	1	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	369	2	,	,	PUNCT
ejpam-5641	369	3	discontinuous	discontinuous	ADJ
ejpam-5641	369	4	at	at	ADP
ejpam-5641	369	5	1	1	NUM
ejpam-5641	369	6	3	3	NUM
ejpam-5641	369	7	ê1	ê1	PROPN
ejpam-5641	369	8	,	,	PUNCT
ejpam-5641	369	9	and	and	CCONJ
ejpam-5641	369	10	we	we	PRON
ejpam-5641	369	11	have	have	VERB
ejpam-5641	369	12	d̂	d̂	VERB
ejpam-5641	369	13	so	so	ADV
ejpam-5641	369	14	that	that	SCONJ
ejpam-5641	369	15	d̂0	d̂0	VERB
ejpam-5641	369	16	∈	∈	PROPN
ejpam-5641	370	1	[	[	X
ejpam-5641	370	2	0	0	NUM
ejpam-5641	370	3	,	,	PUNCT
ejpam-5641	370	4	13	13	NUM
ejpam-5641	370	5	)	)	PUNCT
ejpam-5641	370	6	under	under	ADP
ejpam-5641	370	7	{	{	PUNCT
ejpam-5641	370	8	φ	φ	PROPN
ejpam-5641	370	9	md̂	md̂	PROPN
ejpam-5641	370	10	}	}	PUNCT
ejpam-5641	370	11	=	=	SYM
ejpam-5641	370	12	{	{	PUNCT
ejpam-5641	370	13	∑m	∑m	PROPN
ejpam-5641	370	14	a=1	a=1	X
ejpam-5641	370	15	1	1	NUM
ejpam-5641	370	16	4a	4a	NUM
ejpam-5641	370	17	ê1	ê1	PROPN
ejpam-5641	370	18	+	+	X
ejpam-5641	370	19	1	1	NUM
ejpam-5641	370	20	4	4	NUM
ejpam-5641	370	21	m	m	NOUN
ejpam-5641	370	22	d̂	d̂	PRON
ejpam-5641	370	23	}	}	PUNCT
ejpam-5641	370	24	has	have	VERB
ejpam-5641	370	25	a	a	DET
ejpam-5641	370	26	{	{	PUNCT
ejpam-5641	370	27	φmj	φmj	ADJ
ejpam-5641	370	28	d̂	d̂	PROPN
ejpam-5641	370	29	}	}	PUNCT
ejpam-5641	370	30	=	=	SYM
ejpam-5641	370	31	{	{	PUNCT
ejpam-5641	370	32	∑mj	∑mj	SYM
ejpam-5641	370	33	a=1	a=1	X
ejpam-5641	370	34	1	1	NUM
ejpam-5641	370	35	4a	4a	NUM
ejpam-5641	370	36	ê1	ê1	PROPN
ejpam-5641	370	37	+	+	CCONJ
ejpam-5641	370	38	1	1	NUM
ejpam-5641	370	39	4mj	4mj	NOUN
ejpam-5641	370	40	d̂	d̂	PRON
ejpam-5641	370	41	}	}	PUNCT
ejpam-5641	370	42	converges	converge	VERB
ejpam-5641	370	43	to	to	ADP
ejpam-5641	370	44	1	1	NUM
ejpam-5641	370	45	3	3	NUM
ejpam-5641	370	46	ê1	ê1	NOUN
ejpam-5641	370	47	.	.	PUNCT
ejpam-5641	371	1	by	by	ADP
ejpam-5641	371	2	theorem	theorem	NOUN
ejpam-5641	371	3	4.5	4.5	NUM
ejpam-5641	371	4	,	,	PUNCT
ejpam-5641	371	5	φ	φ	PROPN
ejpam-5641	371	6	has	have	VERB
ejpam-5641	371	7	ufp	ufp	NOUN
ejpam-5641	371	8	at	at	ADP
ejpam-5641	371	9	1	1	NUM
ejpam-5641	371	10	3	3	NUM
ejpam-5641	371	11	ê1	ê1	NOUN
ejpam-5641	371	12	.	.	PUNCT
ejpam-5641	372	1	for	for	ADP
ejpam-5641	372	2	φ	φ	PROPN
ejpam-5641	372	3	:	:	PUNCT
ejpam-5641	372	4	(	(	PUNCT
ejpam-5641	372	5	γsf	γsf	X
ejpam-5641	372	6	(	(	PUNCT
ejpam-5641	372	7	(	(	PUNCT
ejpam-5641	372	8	1	1	NUM
ejpam-5641	372	9	(	(	PUNCT
ejpam-5641	372	10	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	372	11	)	)	PUNCT
ejpam-5641	372	12	l∈n	l∈n	ADJ
ejpam-5641	372	13	,	,	PUNCT
ejpam-5641	372	14	(	(	PUNCT
ejpam-5641	372	15	2l+3	2l+3	NOUN
ejpam-5641	372	16	l+2	l+2	NOUN
ejpam-5641	372	17	)	)	PUNCT
ejpam-5641	372	18	l∈n	l∈n	ADJ
ejpam-5641	372	19	)	)	PUNCT
ejpam-5641	372	20	)	)	PUNCT
ejpam-5641	373	1	∥.∥p−qn	∥.∥p−qn	PRON
ejpam-5641	373	2	→	→	PUNCT
ejpam-5641	373	3	(	(	PUNCT
ejpam-5641	373	4	γsf	γsf	X
ejpam-5641	373	5	(	(	PUNCT
ejpam-5641	373	6	(	(	PUNCT
ejpam-5641	373	7	1	1	NUM
ejpam-5641	373	8	(	(	PUNCT
ejpam-5641	373	9	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	373	10	)	)	PUNCT
ejpam-5641	373	11	l∈n	l∈n	ADJ
ejpam-5641	373	12	,	,	PUNCT
ejpam-5641	373	13	(	(	PUNCT
ejpam-5641	373	14	2l+3	2l+3	NOUN
ejpam-5641	373	15	l+2	l+2	NOUN
ejpam-5641	373	16	)	)	PUNCT
ejpam-5641	373	17	l∈n	l∈n	ADJ
ejpam-5641	373	18	)	)	PUNCT
ejpam-5641	373	19	)	)	PUNCT
ejpam-5641	374	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	374	2	,	,	PUNCT
ejpam-5641	374	3	where	where	SCONJ
ejpam-5641	374	4	∥d̂∥p−qn	∥d̂∥p−qn	NOUN
ejpam-5641	374	5	=	=	NOUN
ejpam-5641	374	6	√√√√√√∑	√√√√√√∑	NOUN
ejpam-5641	374	7	l∈n	l∈n	VERB
ejpam-5641	374	8			PROPN
ejpam-5641	374	9	ℏ̂	ℏ̂	NUM
ejpam-5641	374	10	(	(	PUNCT
ejpam-5641	374	11	∑l	∑l	PROPN
ejpam-5641	374	12	z=0	z=0	PROPN
ejpam-5641	374	13	d̂z	d̂z	NUM
ejpam-5641	374	14	z+5	z+5	NUM
ejpam-5641	374	15	,	,	PUNCT
ejpam-5641	374	16	0̂	0̂	PROPN
ejpam-5641	374	17	)	)	PUNCT
ejpam-5641	375	1	flfl+1	flfl+1	PROPN
ejpam-5641	375	2			PROPN
ejpam-5641	375	3	2l+3	2l+3	PROPN
ejpam-5641	375	4	l+2	l+2	NOUN
ejpam-5641	375	5	,	,	PUNCT
ejpam-5641	375	6	for	for	ADP
ejpam-5641	375	7	all	all	PRON
ejpam-5641	376	1	d̂	d̂	PRON
ejpam-5641	376	2	∈	∈	PROPN
ejpam-5641	376	3	(	(	PUNCT
ejpam-5641	376	4	γsf	γsf	X
ejpam-5641	376	5	(	(	PUNCT
ejpam-5641	376	6	(	(	PUNCT
ejpam-5641	376	7	1	1	NUM
ejpam-5641	376	8	(	(	PUNCT
ejpam-5641	376	9	l+5)f2l	l+5)f2l	NOUN
ejpam-5641	376	10	)	)	PUNCT
ejpam-5641	376	11	l∈n	l∈n	ADJ
ejpam-5641	376	12	,	,	PUNCT
ejpam-5641	376	13	(	(	PUNCT
ejpam-5641	376	14	2l+3	2l+3	NOUN
ejpam-5641	376	15	l+2	l+2	NOUN
ejpam-5641	376	16	)	)	PUNCT
ejpam-5641	376	17	l∈n	l∈n	ADJ
ejpam-5641	376	18	)	)	PUNCT
ejpam-5641	376	19	)	)	PUNCT
ejpam-5641	377	1	∥.∥p−qn	∥.∥p−qn	X
ejpam-5641	377	2	.	.	PUNCT
ejpam-5641	378	1	if	if	SCONJ
ejpam-5641	378	2	f̂	f̂	NUM
ejpam-5641	378	3	,	,	PUNCT
ejpam-5641	378	4	ĝ	ĝ	X
ejpam-5641	378	5	∈	∈	PROPN
ejpam-5641	378	6	(	(	PUNCT
ejpam-5641	378	7	γsf	γsf	X
ejpam-5641	378	8	(	(	PUNCT
ejpam-5641	378	9	(	(	PUNCT
ejpam-5641	378	10	1	1	NUM
ejpam-5641	378	11	(	(	PUNCT
ejpam-5641	378	12	l+5)f2l	l+5)f2l	PROPN
ejpam-5641	378	13	)	)	PUNCT
ejpam-5641	378	14	∞	∞	NUM
ejpam-5641	379	1	l=0	l=0	PROPN
ejpam-5641	379	2	,	,	PUNCT
ejpam-5641	379	3	(	(	PUNCT
ejpam-5641	379	4	2l+3	2l+3	NOUN
ejpam-5641	379	5	l+2	l+2	NOUN
ejpam-5641	379	6	)	)	PUNCT
ejpam-5641	379	7	∞	∞	NUM
ejpam-5641	379	8	l=0	l=0	PROPN
ejpam-5641	379	9	)	)	PUNCT
ejpam-5641	379	10	)	)	PUNCT
ejpam-5641	380	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	380	2	with	with	ADP
ejpam-5641	380	3	f̂0(t	f̂0(t	PROPN
ejpam-5641	380	4	)	)	PUNCT
ejpam-5641	380	5	,	,	PUNCT
ejpam-5641	380	6	ĝ0(t	ĝ0(t	PROPN
ejpam-5641	380	7	)	)	PUNCT
ejpam-5641	380	8	∈	∈	PROPN
ejpam-5641	381	1	[	[	X
ejpam-5641	381	2	0	0	NUM
ejpam-5641	381	3	,	,	PUNCT
ejpam-5641	381	4	13	13	NUM
ejpam-5641	381	5	)	)	PUNCT
ejpam-5641	381	6	,	,	PUNCT
ejpam-5641	381	7	then	then	ADV
ejpam-5641	381	8	∥φf̂	∥φf̂	ADJ
ejpam-5641	381	9	−	−	NOUN
ejpam-5641	381	10	φĝ∥p−qn	φĝ∥p−qn	NOUN
ejpam-5641	381	11	=	=	PUNCT
ejpam-5641	381	12	∥1	∥1	PRON
ejpam-5641	381	13	4	4	NUM
ejpam-5641	381	14	(	(	PUNCT
ejpam-5641	381	15	f̂0	f̂0	NOUN
ejpam-5641	382	1	−	−	PROPN
ejpam-5641	382	2	ĝ0	ĝ0	NOUN
ejpam-5641	382	3	,	,	PUNCT
ejpam-5641	382	4	f̂1	f̂1	NOUN
ejpam-5641	383	1	−	−	PROPN
ejpam-5641	383	2	ĝ1	ĝ1	NOUN
ejpam-5641	383	3	,	,	PUNCT
ejpam-5641	383	4	f̂2	f̂2	ADJ
ejpam-5641	383	5	−	−	NOUN
ejpam-5641	383	6	ĝ2	ĝ2	NOUN
ejpam-5641	383	7	,	,	PUNCT
ejpam-5641	383	8	.	.	PUNCT
ejpam-5641	383	9	.	.	PUNCT
ejpam-5641	384	1	.)∥p−qn	.)∥p−qn	PUNCT
ejpam-5641	385	1	≤	≤	NUM
ejpam-5641	385	2	1	1	NUM
ejpam-5641	385	3	4	4	NUM
ejpam-5641	385	4	√	√	NUM
ejpam-5641	385	5	27	27	NUM
ejpam-5641	385	6	(	(	PUNCT
ejpam-5641	385	7	∥3f̂	∥3f̂	ADJ
ejpam-5641	385	8	4	4	NUM
ejpam-5641	385	9	∥p−qn	∥p−qn	ADJ
ejpam-5641	385	10	+	+	CCONJ
ejpam-5641	385	11	∥3ĝ	∥3ĝ	ADJ
ejpam-5641	385	12	4	4	NUM
ejpam-5641	385	13	∥p−qn	∥p−qn	NOUN
ejpam-5641	385	14	)	)	PUNCT
ejpam-5641	386	1	+	+	CCONJ
ejpam-5641	386	2	0.01∥f̂	0.01∥f̂	NOUN
ejpam-5641	386	3	−	−	PROPN
ejpam-5641	386	4	ĝ∥p−qn	ĝ∥p−qn	PROPN
ejpam-5641	386	5	≤	≤	NUM
ejpam-5641	386	6	1	1	NUM
ejpam-5641	386	7	4	4	NUM
ejpam-5641	386	8	√	√	NUM
ejpam-5641	386	9	27	27	NUM
ejpam-5641	386	10	(	(	PUNCT
ejpam-5641	386	11	∥φf̂	∥φf̂	ADJ
ejpam-5641	386	12	−	−	PROPN
ejpam-5641	387	1	f̂∥p−qn	f̂∥p−qn	PROPN
ejpam-5641	387	2	+	+	CCONJ
ejpam-5641	387	3	∥φĝ	∥φĝ	PROPN
ejpam-5641	387	4	−	−	PROPN
ejpam-5641	387	5	ĝ∥p−qn	ĝ∥p−qn	PROPN
ejpam-5641	387	6	)	)	PUNCT
ejpam-5641	388	1	+	+	NUM
ejpam-5641	388	2	0.01∥f̂	0.01∥f̂	NOUN
ejpam-5641	388	3	−	−	PROPN
ejpam-5641	388	4	ĝ∥p−qn	ĝ∥p−qn	PROPN
ejpam-5641	388	5	.	.	PUNCT
ejpam-5641	388	6	suppose	suppose	VERB
ejpam-5641	388	7	f̂	f̂	PROPN
ejpam-5641	388	8	,	,	PUNCT
ejpam-5641	388	9	ĝ	ĝ	X
ejpam-5641	388	10	∈	∈	PROPN
ejpam-5641	388	11	(	(	PUNCT
ejpam-5641	388	12	γsf	γsf	X
ejpam-5641	388	13	(	(	PUNCT
ejpam-5641	388	14	(	(	PUNCT
ejpam-5641	388	15	1	1	NUM
ejpam-5641	388	16	(	(	PUNCT
ejpam-5641	388	17	l+5)f2l	l+5)f2l	PROPN
ejpam-5641	388	18	)	)	PUNCT
ejpam-5641	388	19	∞	∞	NUM
ejpam-5641	388	20	l=0	l=0	PROPN
ejpam-5641	388	21	,	,	PUNCT
ejpam-5641	388	22	(	(	PUNCT
ejpam-5641	388	23	2l+3	2l+3	NOUN
ejpam-5641	388	24	l+2	l+2	NOUN
ejpam-5641	388	25	)	)	PUNCT
ejpam-5641	388	26	∞	∞	NUM
ejpam-5641	388	27	l=0	l=0	PROPN
ejpam-5641	388	28	)	)	PUNCT
ejpam-5641	388	29	)	)	PUNCT
ejpam-5641	389	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	389	2	with	with	ADP
ejpam-5641	389	3	f̂0(t	f̂0(t	PROPN
ejpam-5641	389	4	)	)	PUNCT
ejpam-5641	389	5	,	,	PUNCT
ejpam-5641	389	6	ĝ0(t	ĝ0(t	PROPN
ejpam-5641	389	7	)	)	PUNCT
ejpam-5641	389	8	∈	∈	PROPN
ejpam-5641	389	9	(	(	PUNCT
ejpam-5641	389	10	13	13	NUM
ejpam-5641	389	11	,	,	PUNCT
ejpam-5641	389	12	1	1	NUM
ejpam-5641	389	13	]	]	PUNCT
ejpam-5641	389	14	,	,	PUNCT
ejpam-5641	389	15	hence	hence	ADV
ejpam-5641	389	16	for	for	ADP
ejpam-5641	389	17	all	all	PRON
ejpam-5641	389	18	εi	εi	NOUN
ejpam-5641	389	19	>	>	X
ejpam-5641	389	20	0	0	PUNCT
ejpam-5641	390	1	and	and	CCONJ
ejpam-5641	390	2	i	i	PRON
ejpam-5641	390	3	=	=	NOUN
ejpam-5641	390	4	1	1	NUM
ejpam-5641	390	5	,	,	PUNCT
ejpam-5641	390	6	2	2	NUM
ejpam-5641	390	7	,	,	PUNCT
ejpam-5641	390	8	and	and	CCONJ
ejpam-5641	390	9	3	3	NUM
ejpam-5641	390	10	,	,	PUNCT
ejpam-5641	390	11	then	then	ADV
ejpam-5641	390	12	∥φf̂	∥φf̂	ADJ
ejpam-5641	390	13	−	−	NOUN
ejpam-5641	390	14	φĝ∥p−qn	φĝ∥p−qn	NOUN
ejpam-5641	390	15	=	=	NOUN
ejpam-5641	390	16	0	0	X
ejpam-5641	390	17	≤	≤	NOUN
ejpam-5641	390	18	ε1∥φf̂	ε1∥φf̂	NOUN
ejpam-5641	390	19	−	−	PROPN
ejpam-5641	391	1	f̂∥p−qn	f̂∥p−qn	PROPN
ejpam-5641	391	2	+	+	CCONJ
ejpam-5641	391	3	ε2∥φĝ	ε2∥φĝ	ADJ
ejpam-5641	391	4	−	−	PROPN
ejpam-5641	391	5	ĝ∥p−qn	ĝ∥p−qn	PROPN
ejpam-5641	391	6	+	+	CCONJ
ejpam-5641	391	7	ε3∥f̂	ε3∥f̂	PROPN
ejpam-5641	391	8	−	−	PROPN
ejpam-5641	391	9	ĝ∥p−qn	ĝ∥p−qn	PROPN
ejpam-5641	391	10	.	.	PUNCT
ejpam-5641	392	1	if	if	SCONJ
ejpam-5641	392	2	f̂	f̂	NUM
ejpam-5641	392	3	,	,	PUNCT
ejpam-5641	392	4	ĝ	ĝ	X
ejpam-5641	392	5	∈	∈	PROPN
ejpam-5641	392	6	(	(	PUNCT
ejpam-5641	392	7	γsf	γsf	X
ejpam-5641	392	8	(	(	PUNCT
ejpam-5641	392	9	(	(	PUNCT
ejpam-5641	392	10	1	1	NUM
ejpam-5641	392	11	(	(	PUNCT
ejpam-5641	392	12	l+5)f2l	l+5)f2l	PROPN
ejpam-5641	392	13	)	)	PUNCT
ejpam-5641	392	14	∞	∞	NUM
ejpam-5641	392	15	l=0	l=0	PROPN
ejpam-5641	392	16	,	,	PUNCT
ejpam-5641	392	17	(	(	PUNCT
ejpam-5641	392	18	2l+3	2l+3	NOUN
ejpam-5641	392	19	l+2	l+2	NOUN
ejpam-5641	392	20	)	)	PUNCT
ejpam-5641	392	21	∞	∞	NUM
ejpam-5641	392	22	l=0	l=0	PROPN
ejpam-5641	392	23	)	)	PUNCT
ejpam-5641	392	24	)	)	PUNCT
ejpam-5641	393	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	393	2	with	with	ADP
ejpam-5641	393	3	f̂0(t	f̂0(t	PROPN
ejpam-5641	393	4	)	)	PUNCT
ejpam-5641	393	5	∈	∈	PROPN
ejpam-5641	394	1	[	[	X
ejpam-5641	394	2	0	0	NUM
ejpam-5641	394	3	,	,	PUNCT
ejpam-5641	394	4	13	13	NUM
ejpam-5641	394	5	)	)	PUNCT
ejpam-5641	394	6	and	and	CCONJ
ejpam-5641	394	7	ĝ0(t	ĝ0(t	PROPN
ejpam-5641	394	8	)	)	PUNCT
ejpam-5641	394	9	∈	∈	PROPN
ejpam-5641	394	10	(	(	PUNCT
ejpam-5641	394	11	13	13	NUM
ejpam-5641	394	12	,	,	PUNCT
ejpam-5641	394	13	1	1	NUM
ejpam-5641	394	14	]	]	PUNCT
ejpam-5641	394	15	,	,	PUNCT
ejpam-5641	394	16	one	one	PRON
ejpam-5641	394	17	obtains	obtain	VERB
ejpam-5641	394	18	∥φf̂	∥φf̂	ADJ
ejpam-5641	394	19	−	−	NOUN
ejpam-5641	394	20	φĝ∥p−qn	φĝ∥p−qn	NOUN
ejpam-5641	394	21	=	=	PUNCT
ejpam-5641	394	22	∥	∥	X
ejpam-5641	394	23	f̂	f̂	NUM
ejpam-5641	394	24	4	4	NUM
ejpam-5641	394	25	∥p−qn	∥p−qn	ADJ
ejpam-5641	394	26	≤	≤	NUM
ejpam-5641	394	27	1	1	NUM
ejpam-5641	394	28	4	4	NUM
ejpam-5641	394	29	√	√	NUM
ejpam-5641	394	30	27	27	NUM
ejpam-5641	394	31	∥3f̂	∥3f̂	ADJ
ejpam-5641	394	32	4	4	NUM
ejpam-5641	394	33	∥p−qn	∥p−qn	NOUN
ejpam-5641	394	34	=	=	SYM
ejpam-5641	394	35	1	1	NUM
ejpam-5641	394	36	4	4	NUM
ejpam-5641	394	37	√	√	NUM
ejpam-5641	394	38	27	27	NUM
ejpam-5641	394	39	∥φf̂	∥φf̂	NOUN
ejpam-5641	394	40	−	−	PROPN
ejpam-5641	394	41	f̂∥p−qn	f̂∥p−qn	PROPN
ejpam-5641	394	42	≤	≤	NOUN
ejpam-5641	394	43	1	1	NUM
ejpam-5641	394	44	4	4	NUM
ejpam-5641	394	45	√	√	NUM
ejpam-5641	394	46	27	27	NUM
ejpam-5641	394	47	(	(	PUNCT
ejpam-5641	394	48	∥φf̂	∥φf̂	ADJ
ejpam-5641	394	49	−	−	PROPN
ejpam-5641	394	50	f̂∥p−qn	f̂∥p−qn	PROPN
ejpam-5641	394	51	+	+	CCONJ
ejpam-5641	395	1	∥φĝ	∥φĝ	PROPN
ejpam-5641	395	2	−	−	PROPN
ejpam-5641	395	3	ĝ∥p−qn	ĝ∥p−qn	PROPN
ejpam-5641	395	4	)	)	PUNCT
ejpam-5641	396	1	+	+	NUM
ejpam-5641	396	2	0.01∥f̂	0.01∥f̂	NOUN
ejpam-5641	396	3	−	−	PROPN
ejpam-5641	396	4	ĝ∥p−qn	ĝ∥p−qn	PROPN
ejpam-5641	396	5	.	.	PUNCT
ejpam-5641	397	1	m.	m.	NOUN
ejpam-5641	397	2	m.	m.	PROPN
ejpam-5641	397	3	a	a	PRON
ejpam-5641	397	4	et	et	PROPN
ejpam-5641	397	5	al	al	PROPN
ejpam-5641	397	6	.	.	PUNCT
ejpam-5641	397	7	/	/	SYM
ejpam-5641	397	8	eur	eur	PROPN
ejpam-5641	397	9	.	.	PUNCT
ejpam-5641	398	1	j.	j.	PROPN
ejpam-5641	398	2	pure	pure	PROPN
ejpam-5641	398	3	appl	appl	PROPN
ejpam-5641	398	4	.	.	PROPN
ejpam-5641	398	5	math	math	PROPN
ejpam-5641	398	6	,	,	PUNCT
ejpam-5641	398	7	18	18	NUM
ejpam-5641	398	8	(	(	PUNCT
ejpam-5641	398	9	1	1	NUM
ejpam-5641	398	10	)	)	PUNCT
ejpam-5641	398	11	(	(	PUNCT
ejpam-5641	398	12	2025	2025	NUM
ejpam-5641	398	13	)	)	PUNCT
ejpam-5641	398	14	,	,	PUNCT
ejpam-5641	398	15	5641	5641	NUM
ejpam-5641	398	16	15	15	NUM
ejpam-5641	398	17	of	of	ADP
ejpam-5641	398	18	20	20	NUM
ejpam-5641	398	19	therefore	therefore	ADV
ejpam-5641	398	20	,	,	PUNCT
ejpam-5641	398	21	φ	φ	PROPN
ejpam-5641	398	22	is	be	AUX
ejpam-5641	398	23	ntk-∥.∥p−qn	ntk-∥.∥p−qn	NOUN
ejpam-5641	398	24	-	-	PUNCT
ejpam-5641	398	25	c.	c.	NOUN
ejpam-5641	398	26	as	as	SCONJ
ejpam-5641	398	27	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	398	28	verifies	verifie	NOUN
ejpam-5641	398	29	the	the	DET
ejpam-5641	398	30	fp	fp	NOUN
ejpam-5641	398	31	.	.	PUNCT
ejpam-5641	399	1	by	by	ADP
ejpam-5641	399	2	theorem	theorem	NOUN
ejpam-5641	399	3	4.3	4.3	NUM
ejpam-5641	399	4	,	,	PUNCT
ejpam-5641	399	5	φ	φ	PROPN
ejpam-5641	399	6	has	have	VERB
ejpam-5641	399	7	a	a	DET
ejpam-5641	399	8	ufp	ufp	NOUN
ejpam-5641	399	9	1	1	NUM
ejpam-5641	399	10	3	3	NUM
ejpam-5641	399	11	ê1	ê1	NOUN
ejpam-5641	399	12	.	.	PUNCT
ejpam-5641	400	1	5	5	X
ejpam-5641	400	2	.	.	PUNCT
ejpam-5641	400	3	applications	application	NOUN
ejpam-5641	400	4	understanding	understand	VERB
ejpam-5641	400	5	economic	economic	ADJ
ejpam-5641	400	6	models	model	NOUN
ejpam-5641	400	7	requires	require	VERB
ejpam-5641	400	8	a	a	DET
ejpam-5641	400	9	firm	firm	ADJ
ejpam-5641	400	10	grasp	grasp	NOUN
ejpam-5641	400	11	of	of	ADP
ejpam-5641	400	12	summable	summable	ADJ
ejpam-5641	400	13	equations	equation	NOUN
ejpam-5641	400	14	,	,	PUNCT
ejpam-5641	400	15	which	which	PRON
ejpam-5641	400	16	offer	offer	VERB
ejpam-5641	400	17	a	a	DET
ejpam-5641	400	18	mathematical	mathematical	ADJ
ejpam-5641	400	19	basis	basis	NOUN
ejpam-5641	400	20	for	for	ADP
ejpam-5641	400	21	investigating	investigate	VERB
ejpam-5641	400	22	issues	issue	NOUN
ejpam-5641	400	23	like	like	ADP
ejpam-5641	400	24	producer	producer	NOUN
ejpam-5641	400	25	and	and	CCONJ
ejpam-5641	400	26	consumer	consumer	NOUN
ejpam-5641	400	27	surplus	surplus	NOUN
ejpam-5641	400	28	,	,	PUNCT
ejpam-5641	400	29	total	total	ADJ
ejpam-5641	400	30	cost	cost	NOUN
ejpam-5641	400	31	computation	computation	NOUN
ejpam-5641	400	32	,	,	PUNCT
ejpam-5641	400	33	and	and	CCONJ
ejpam-5641	400	34	revenue	revenue	NOUN
ejpam-5641	400	35	functions	function	NOUN
ejpam-5641	400	36	,	,	PUNCT
ejpam-5641	400	37	among	among	ADP
ejpam-5641	400	38	others	other	NOUN
ejpam-5641	400	39	.	.	PUNCT
ejpam-5641	401	1	the	the	DET
ejpam-5641	401	2	use	use	NOUN
ejpam-5641	401	3	of	of	ADP
ejpam-5641	401	4	summable	summable	ADJ
ejpam-5641	401	5	equations	equation	NOUN
ejpam-5641	401	6	in	in	ADP
ejpam-5641	401	7	the	the	DET
ejpam-5641	401	8	formulation	formulation	NOUN
ejpam-5641	401	9	and	and	CCONJ
ejpam-5641	401	10	solution	solution	NOUN
ejpam-5641	401	11	of	of	ADP
ejpam-5641	401	12	economic	economic	ADJ
ejpam-5641	401	13	problems	problem	NOUN
ejpam-5641	401	14	has	have	AUX
ejpam-5641	401	15	recently	recently	ADV
ejpam-5641	401	16	expanded	expand	VERB
ejpam-5641	401	17	substantially	substantially	ADV
ejpam-5641	401	18	.	.	PUNCT
ejpam-5641	402	1	take	take	VERB
ejpam-5641	402	2	a	a	DET
ejpam-5641	402	3	look	look	NOUN
ejpam-5641	402	4	at	at	ADP
ejpam-5641	402	5	[	[	X
ejpam-5641	402	6	2	2	NUM
ejpam-5641	402	7	,	,	PUNCT
ejpam-5641	402	8	8	8	NUM
ejpam-5641	402	9	,	,	PUNCT
ejpam-5641	402	10	10	10	NUM
ejpam-5641	402	11	,	,	PUNCT
ejpam-5641	402	12	18	18	NUM
ejpam-5641	402	13	,	,	PUNCT
ejpam-5641	402	14	21	21	NUM
ejpam-5641	402	15	]	]	PUNCT
ejpam-5641	402	16	and	and	CCONJ
ejpam-5641	402	17	the	the	DET
ejpam-5641	402	18	citations	citation	NOUN
ejpam-5641	402	19	that	that	PRON
ejpam-5641	402	20	follow	follow	VERB
ejpam-5641	402	21	.	.	PUNCT
ejpam-5641	403	1	we	we	PRON
ejpam-5641	403	2	present	present	VERB
ejpam-5641	403	3	the	the	DET
ejpam-5641	403	4	existence	existence	NOUN
ejpam-5641	403	5	and	and	CCONJ
ejpam-5641	403	6	uniqueness	uniqueness	NOUN
ejpam-5641	403	7	of	of	ADP
ejpam-5641	403	8	the	the	DET
ejpam-5641	403	9	soft	soft	ADJ
ejpam-5641	403	10	dynamical	dynamical	ADJ
ejpam-5641	403	11	systems	system	NOUN
ejpam-5641	403	12	(	(	PUNCT
ejpam-5641	403	13	1	1	X
ejpam-5641	403	14	)	)	PUNCT
ejpam-5641	403	15	in	in	ADP
ejpam-5641	403	16	(	(	PUNCT
ejpam-5641	403	17	γsf	γsf	X
ejpam-5641	403	18	(	(	PUNCT
ejpam-5641	403	19	q	q	NOUN
ejpam-5641	403	20	,	,	PUNCT
ejpam-5641	403	21	t	t	PROPN
ejpam-5641	403	22	)	)	PUNCT
ejpam-5641	403	23	)	)	PUNCT
ejpam-5641	404	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	404	2	,	,	PUNCT
ejpam-5641	404	3	where	where	SCONJ
ejpam-5641	404	4	the	the	DET
ejpam-5641	404	5	conditions	condition	NOUN
ejpam-5641	404	6	of	of	ADP
ejpam-5641	404	7	theorem	theorem	ADJ
ejpam-5641	404	8	3.3	3.3	NUM
ejpam-5641	404	9	are	be	AUX
ejpam-5641	404	10	confirmed	confirm	VERB
ejpam-5641	404	11	under	under	ADP
ejpam-5641	404	12	the	the	DET
ejpam-5641	404	13	two	two	NUM
ejpam-5641	404	14	equivalent	equivalent	ADJ
ejpam-5641	404	15	p-q.ns	p-q.ns	NOUN
ejpam-5641	404	16	∥ν̂∥p−qn	∥ν̂∥p−qn	NOUN
ejpam-5641	404	17	and	and	CCONJ
ejpam-5641	404	18	∥ν̂∥ℶp−qn	∥ν̂∥ℶp−qn	NUM
ejpam-5641	404	19	,	,	PUNCT
ejpam-5641	404	20	for	for	ADP
ejpam-5641	404	21	any	any	DET
ejpam-5641	404	22	ν̂	ν̂	NUM
ejpam-5641	404	23	∈	∈	PROPN
ejpam-5641	404	24	γsf	γsf	X
ejpam-5641	404	25	(	(	PUNCT
ejpam-5641	404	26	q	q	NOUN
ejpam-5641	404	27	,	,	PUNCT
ejpam-5641	404	28	t	t	PROPN
ejpam-5641	404	29	)	)	PUNCT
ejpam-5641	404	30	.	.	PUNCT
ejpam-5641	405	1	theorem	theorem	VERB
ejpam-5641	405	2	5.1	5.1	NUM
ejpam-5641	405	3	.	.	PUNCT
ejpam-5641	406	1	assume	assume	VERB
ejpam-5641	406	2	that	that	SCONJ
ejpam-5641	406	3	ξ̂	ξ̂	NOUN
ejpam-5641	406	4	:	:	PUNCT
ejpam-5641	406	5	n	n	PROPN
ejpam-5641	406	6	→	→	SYM
ejpam-5641	406	7	r(a	r(a	NUM
ejpam-5641	406	8	)	)	PUNCT
ejpam-5641	406	9	.	.	PUNCT
ejpam-5641	407	1	the	the	DET
ejpam-5641	407	2	dynamical	dynamical	ADJ
ejpam-5641	407	3	systems	system	NOUN
ejpam-5641	407	4	(	(	PUNCT
ejpam-5641	407	5	1	1	X
ejpam-5641	407	6	)	)	PUNCT
ejpam-5641	407	7	have	have	VERB
ejpam-5641	407	8	a	a	DET
ejpam-5641	407	9	unique	unique	ADJ
ejpam-5641	407	10	solution	solution	NOUN
ejpam-5641	407	11	in	in	ADP
ejpam-5641	407	12	(	(	PUNCT
ejpam-5641	407	13	γsf	γsf	X
ejpam-5641	407	14	(	(	PUNCT
ejpam-5641	407	15	q	q	NOUN
ejpam-5641	407	16	,	,	PUNCT
ejpam-5641	407	17	t	t	PROPN
ejpam-5641	407	18	)	)	PUNCT
ejpam-5641	407	19	)	)	PUNCT
ejpam-5641	408	1	∥.∥p−qn	∥.∥p−qn	PRON
ejpam-5641	408	2	whenever	whenever	SCONJ
ejpam-5641	408	3	if	if	SCONJ
ejpam-5641	408	4	there	there	PRON
ejpam-5641	408	5	are	be	VERB
ejpam-5641	408	6	εi	εi	NOUN
ejpam-5641	408	7	∈	∈	NOUN
ejpam-5641	408	8	r	r	NOUN
ejpam-5641	409	1	so	so	SCONJ
ejpam-5641	409	2	that	that	SCONJ
ejpam-5641	409	3	∑3	∑3	PROPN
ejpam-5641	409	4	i=1	i=1	PROPN
ejpam-5641	409	5	supu	supu	PROPN
ejpam-5641	409	6	|εi|	|εi|	PROPN
ejpam-5641	409	7	tu	tu	PROPN
ejpam-5641	409	8	ℶ	ℶ	PROPN
ejpam-5641	409	9	∈	∈	PROPN
ejpam-5641	410	1	[	[	X
ejpam-5641	410	2	0	0	NUM
ejpam-5641	410	3	,	,	PUNCT
ejpam-5641	410	4	1	1	NUM
ejpam-5641	410	5	)	)	PUNCT
ejpam-5641	410	6	and	and	CCONJ
ejpam-5641	410	7	for	for	ADP
ejpam-5641	410	8	every	every	DET
ejpam-5641	410	9	u	u	PROPN
ejpam-5641	410	10	∈	∈	PROPN
ejpam-5641	410	11	n	n	NOUN
ejpam-5641	410	12	,	,	PUNCT
ejpam-5641	410	13	then∣∣∣∣∣	then∣∣∣∣∣	PROPN
ejpam-5641	410	14	u∑	u∑	PROPN
ejpam-5641	410	15	d=0	d=0	PROPN
ejpam-5641	410	16	(	(	PUNCT
ejpam-5641	410	17	∑	∑	INTJ
ejpam-5641	410	18	v∈n	v∈n	VERB
ejpam-5641	410	19	γd	γd	ADP
ejpam-5641	410	20	,	,	PUNCT
ejpam-5641	410	21	v[ψv	v[ψv	X
ejpam-5641	410	22	,	,	PUNCT
ejpam-5641	410	23	ν̂v	ν̂v	PROPN
ejpam-5641	410	24	−ψ	−ψ	NOUN
ejpam-5641	410	25	v	v	NOUN
ejpam-5641	410	26	,	,	PUNCT
ejpam-5641	410	27	ξ̂v	ξ̂v	NOUN
ejpam-5641	410	28	]	]	PUNCT
ejpam-5641	410	29	)	)	PUNCT
ejpam-5641	410	30	f2dqd	f2dqd	VERB
ejpam-5641	411	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5641	411	2	≤̂|ε1|	≤̂|ε1|	PROPN
ejpam-5641	412	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5641	412	2	u∑	u∑	PROPN
ejpam-5641	412	3	d=0	d=0	X
ejpam-5641	412	4	(	(	PUNCT
ejpam-5641	412	5	β̂d	β̂d	NUM
ejpam-5641	412	6	−	−	NOUN
ejpam-5641	412	7	ν̂d	ν̂d	X
ejpam-5641	412	8	+	+	CCONJ
ejpam-5641	412	9	∑	∑	ADP
ejpam-5641	412	10	v∈n	v∈n	NOUN
ejpam-5641	412	11	γd	γd	ADP
ejpam-5641	412	12	,	,	PUNCT
ejpam-5641	412	13	vψv	vψv	ADJ
ejpam-5641	412	14	,	,	PUNCT
ejpam-5641	412	15	ν̂v	ν̂v	PROPN
ejpam-5641	412	16	)	)	PUNCT
ejpam-5641	412	17	f2dqd	f2dqd	VERB
ejpam-5641	413	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5641	414	1	+	+	CCONJ
ejpam-5641	414	2	|ε2|	|ε2|	NOUN
ejpam-5641	414	3	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5641	414	4	u∑	u∑	PROPN
ejpam-5641	414	5	d=0	d=0	X
ejpam-5641	414	6	(	(	PUNCT
ejpam-5641	414	7	β̂d	β̂d	NUM
ejpam-5641	414	8	−	−	NOUN
ejpam-5641	414	9	ξ̂d	ξ̂d	X
ejpam-5641	415	1	+	+	CCONJ
ejpam-5641	415	2	∑	∑	PUNCT
ejpam-5641	415	3	v∈n	v∈n	NOUN
ejpam-5641	415	4	γd	γd	ADP
ejpam-5641	415	5	,	,	PUNCT
ejpam-5641	415	6	vψv	vψv	ADJ
ejpam-5641	415	7	,	,	PUNCT
ejpam-5641	415	8	ξ̂v	ξ̂v	NOUN
ejpam-5641	415	9	)	)	PUNCT
ejpam-5641	415	10	f2dqd	f2dqd	PROPN
ejpam-5641	415	11	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ejpam-5641	415	12	|ε3||	|ε3||	PROPN
ejpam-5641	415	13	u∑	u∑	PROPN
ejpam-5641	415	14	d=0	d=0	X
ejpam-5641	415	15	(	(	PUNCT
ejpam-5641	415	16	ν̂d	ν̂d	X
ejpam-5641	415	17	−	−	PROPN
ejpam-5641	415	18	ξ̂d	ξ̂d	NOUN
ejpam-5641	415	19	)	)	PUNCT
ejpam-5641	416	1	f2dqd|	f2dqd|	NOUN
ejpam-5641	416	2	.	.	PUNCT
ejpam-5641	416	3	proof	proof	NOUN
ejpam-5641	416	4	.	.	PUNCT
ejpam-5641	417	1	let	let	VERB
ejpam-5641	417	2	φ	φ	PROPN
ejpam-5641	417	3	:	:	PUNCT
ejpam-5641	417	4	(	(	PUNCT
ejpam-5641	417	5	γsf	γsf	X
ejpam-5641	417	6	(	(	PUNCT
ejpam-5641	417	7	q	q	NOUN
ejpam-5641	417	8	,	,	PUNCT
ejpam-5641	417	9	t	t	PROPN
ejpam-5641	417	10	)	)	PUNCT
ejpam-5641	417	11	)	)	PUNCT
ejpam-5641	418	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	418	2	→	→	SYM
ejpam-5641	418	3	(	(	PUNCT
ejpam-5641	418	4	γsf	γsf	X
ejpam-5641	418	5	(	(	PUNCT
ejpam-5641	418	6	q	q	NOUN
ejpam-5641	418	7	,	,	PUNCT
ejpam-5641	418	8	t	t	PROPN
ejpam-5641	418	9	)	)	PUNCT
ejpam-5641	418	10	)	)	PUNCT
ejpam-5641	419	1	∥.∥p−qn	∥.∥p−qn	PRON
ejpam-5641	419	2	is	be	AUX
ejpam-5641	419	3	defined	define	VERB
ejpam-5641	419	4	by	by	ADP
ejpam-5641	419	5	equation	equation	NOUN
ejpam-5641	419	6	(	(	PUNCT
ejpam-5641	419	7	2	2	NUM
ejpam-5641	419	8	)	)	PUNCT
ejpam-5641	419	9	.	.	PUNCT
ejpam-5641	420	1	by	by	ADP
ejpam-5641	420	2	theorem	theorem	ADJ
ejpam-5641	420	3	4.3	4.3	NUM
ejpam-5641	420	4	and	and	CCONJ
ejpam-5641	420	5	∥φν̂	∥φν̂	VERB
ejpam-5641	420	6	−	−	PROPN
ejpam-5641	420	7	φξ̂∥p−qn	φξ̂∥p−qn	NOUN
ejpam-5641	420	8	=	=	PUNCT
ejpam-5641	420	9	∑	∑	NOUN
ejpam-5641	420	10	u∈n	u∈n	NOUN
ejpam-5641	420	11			PROPN
ejpam-5641	420	12	ℏ̂	ℏ̂	PUNCT
ejpam-5641	420	13	(	(	PUNCT
ejpam-5641	420	14	∑u	∑u	PROPN
ejpam-5641	420	15	d=0	d=0	X
ejpam-5641	420	16	f	f	PROPN
ejpam-5641	420	17	2	2	NUM
ejpam-5641	420	18	dqd(φν̂d	dqd(φν̂d	NOUN
ejpam-5641	420	19	−	−	PROPN
ejpam-5641	420	20	φξ̂d	φξ̂d	PROPN
ejpam-5641	420	21	)	)	PUNCT
ejpam-5641	420	22	,	,	PUNCT
ejpam-5641	420	23	0̂	0̂	PROPN
ejpam-5641	420	24	)	)	PUNCT
ejpam-5641	421	1	fufu+1	fufu+1	INTJ
ejpam-5641	421	2	tu	tu	ADP
ejpam-5641	421	3			NUM
ejpam-5641	421	4	1	1	NUM
ejpam-5641	421	5	ℶ	ℶ	NOUN
ejpam-5641	421	6	=	=	SYM
ejpam-5641	421	7	∑	∑	NOUN
ejpam-5641	421	8	u∈n	u∈n	NOUN
ejpam-5641	421	9			PROPN
ejpam-5641	421	10	ℏ̂	ℏ̂	PUNCT
ejpam-5641	421	11	(	(	PUNCT
ejpam-5641	421	12	∑u	∑u	PROPN
ejpam-5641	421	13	d=0	d=0	X
ejpam-5641	421	14	(	(	PUNCT
ejpam-5641	421	15	∑	∑	INTJ
ejpam-5641	421	16	v∈n	v∈n	VERB
ejpam-5641	421	17	γd	γd	ADP
ejpam-5641	421	18	,	,	PUNCT
ejpam-5641	421	19	v[ψv	v[ψv	X
ejpam-5641	421	20	,	,	PUNCT
ejpam-5641	421	21	ν̂v	ν̂v	PROPN
ejpam-5641	421	22	−ψ	−ψ	NOUN
ejpam-5641	421	23	v	v	NOUN
ejpam-5641	421	24	,	,	PUNCT
ejpam-5641	421	25	ξ̂v	ξ̂v	NOUN
ejpam-5641	421	26	]	]	PUNCT
ejpam-5641	421	27	)	)	PUNCT
ejpam-5641	422	1	f2dqd	f2dqd	PROPN
ejpam-5641	422	2	,	,	PUNCT
ejpam-5641	422	3	0̂	0̂	PROPN
ejpam-5641	422	4	)	)	PUNCT
ejpam-5641	423	1	fufu+1	fufu+1	INTJ
ejpam-5641	423	2	tu	tu	ADP
ejpam-5641	423	3			NUM
ejpam-5641	423	4	1	1	NUM
ejpam-5641	423	5	ℶ	ℶ	NOUN
ejpam-5641	423	6	m.	m.	NOUN
ejpam-5641	423	7	m.	m.	NOUN
ejpam-5641	423	8	a	a	PRON
ejpam-5641	423	9	et	et	NOUN
ejpam-5641	423	10	al	al	PROPN
ejpam-5641	423	11	.	.	PUNCT
ejpam-5641	423	12	/	/	SYM
ejpam-5641	423	13	eur	eur	PROPN
ejpam-5641	423	14	.	.	PUNCT
ejpam-5641	424	1	j.	j.	PROPN
ejpam-5641	424	2	pure	pure	PROPN
ejpam-5641	424	3	appl	appl	PROPN
ejpam-5641	424	4	.	.	PROPN
ejpam-5641	424	5	math	math	PROPN
ejpam-5641	424	6	,	,	PUNCT
ejpam-5641	424	7	18	18	NUM
ejpam-5641	424	8	(	(	PUNCT
ejpam-5641	424	9	1	1	NUM
ejpam-5641	424	10	)	)	PUNCT
ejpam-5641	424	11	(	(	PUNCT
ejpam-5641	424	12	2025	2025	NUM
ejpam-5641	424	13	)	)	PUNCT
ejpam-5641	424	14	,	,	PUNCT
ejpam-5641	424	15	5641	5641	NUM
ejpam-5641	424	16	16	16	NUM
ejpam-5641	424	17	of	of	ADP
ejpam-5641	424	18	20	20	NUM
ejpam-5641	424	19	≤	≤	NUM
ejpam-5641	424	20	sup	sup	NOUN
ejpam-5641	424	21	u	u	NOUN
ejpam-5641	424	22	|ε1|	|ε1|	NOUN
ejpam-5641	424	23	tu	tu	PROPN
ejpam-5641	424	24	ℶ	ℶ	PROPN
ejpam-5641	424	25	∑	∑	PROPN
ejpam-5641	424	26	u∈n	u∈n	NOUN
ejpam-5641	425	1			PROPN
ejpam-5641	425	2	ℏ̂	ℏ̂	PUNCT
ejpam-5641	425	3	(	(	PUNCT
ejpam-5641	425	4	∑u	∑u	PROPN
ejpam-5641	425	5	d=0	d=0	PROPN
ejpam-5641	425	6	(	(	PUNCT
ejpam-5641	425	7	β̂d	β̂d	NUM
ejpam-5641	425	8	−	−	NOUN
ejpam-5641	425	9	ν̂d	ν̂d	X
ejpam-5641	425	10	+	+	CCONJ
ejpam-5641	425	11	∑	∑	ADP
ejpam-5641	425	12	v∈n	v∈n	NOUN
ejpam-5641	425	13	γd	γd	ADP
ejpam-5641	425	14	,	,	PUNCT
ejpam-5641	425	15	vψv	vψv	ADJ
ejpam-5641	425	16	,	,	PUNCT
ejpam-5641	425	17	ν̂v	ν̂v	PROPN
ejpam-5641	425	18	)	)	PUNCT
ejpam-5641	425	19	f2dqd	f2dqd	ADP
ejpam-5641	425	20	,	,	PUNCT
ejpam-5641	425	21	0̂	0̂	PROPN
ejpam-5641	425	22	)	)	PUNCT
ejpam-5641	426	1	fufu+1	fufu+1	INTJ
ejpam-5641	426	2	tu	tu	ADP
ejpam-5641	426	3			SYM
ejpam-5641	426	4	1	1	NUM
ejpam-5641	426	5	ℶ	ℶ	NOUN
ejpam-5641	426	6	+	+	CCONJ
ejpam-5641	426	7	sup	sup	NOUN
ejpam-5641	426	8	u	u	PROPN
ejpam-5641	426	9	|ε2|	|ε2|	NOUN
ejpam-5641	426	10	tu	tu	PROPN
ejpam-5641	426	11	ℶ	ℶ	PROPN
ejpam-5641	426	12	∑	∑	PROPN
ejpam-5641	426	13	u∈n	u∈n	NOUN
ejpam-5641	426	14			PROPN
ejpam-5641	426	15	ℏ̂	ℏ̂	PUNCT
ejpam-5641	426	16	(	(	PUNCT
ejpam-5641	426	17	∑u	∑u	PROPN
ejpam-5641	426	18	d=0	d=0	PROPN
ejpam-5641	426	19	(	(	PUNCT
ejpam-5641	426	20	β̂d	β̂d	NUM
ejpam-5641	426	21	−	−	NOUN
ejpam-5641	426	22	ξ̂d	ξ̂d	X
ejpam-5641	427	1	+	+	CCONJ
ejpam-5641	427	2	∑	∑	PUNCT
ejpam-5641	427	3	v∈n	v∈n	NOUN
ejpam-5641	427	4	γd	γd	ADP
ejpam-5641	427	5	,	,	PUNCT
ejpam-5641	427	6	vψv	vψv	ADJ
ejpam-5641	427	7	,	,	PUNCT
ejpam-5641	427	8	ξ̂v	ξ̂v	NOUN
ejpam-5641	427	9	)	)	PUNCT
ejpam-5641	427	10	f2dqd	f2dqd	PROPN
ejpam-5641	427	11	,	,	PUNCT
ejpam-5641	427	12	0̂	0̂	PROPN
ejpam-5641	427	13	)	)	PUNCT
ejpam-5641	428	1	fufu+1	fufu+1	INTJ
ejpam-5641	428	2	tu	tu	ADP
ejpam-5641	428	3			SYM
ejpam-5641	428	4	1	1	NUM
ejpam-5641	428	5	ℶ	ℶ	NOUN
ejpam-5641	429	1	+	+	CCONJ
ejpam-5641	429	2	sup	sup	NOUN
ejpam-5641	429	3	u	u	PROPN
ejpam-5641	429	4	|ε3|	|ε3|	ADV
ejpam-5641	429	5	tu	tu	PROPN
ejpam-5641	429	6	ℶ	ℶ	PROPN
ejpam-5641	429	7	∑	∑	PROPN
ejpam-5641	429	8	u∈n	u∈n	NOUN
ejpam-5641	429	9			PROPN
ejpam-5641	429	10	ℏ̂	ℏ̂	PUNCT
ejpam-5641	429	11	(	(	PUNCT
ejpam-5641	429	12	∑u	∑u	PROPN
ejpam-5641	429	13	d=0	d=0	PROPN
ejpam-5641	429	14	(	(	PUNCT
ejpam-5641	429	15	ν̂d	ν̂d	X
ejpam-5641	429	16	−	−	PROPN
ejpam-5641	429	17	ξ̂d	ξ̂d	NOUN
ejpam-5641	429	18	)	)	PUNCT
ejpam-5641	429	19	f2dqd	f2dqd	ADP
ejpam-5641	429	20	,	,	PUNCT
ejpam-5641	429	21	0̂	0̂	PROPN
ejpam-5641	429	22	)	)	PUNCT
ejpam-5641	430	1	fufu+1	fufu+1	INTJ
ejpam-5641	430	2	tu	tu	ADP
ejpam-5641	430	3			SYM
ejpam-5641	430	4	1	1	NUM
ejpam-5641	430	5	ℶ	ℶ	NOUN
ejpam-5641	430	6	=	=	PUNCT
ejpam-5641	430	7	sup	sup	NOUN
ejpam-5641	430	8	u	u	NOUN
ejpam-5641	430	9	|ε1|	|ε1|	NOUN
ejpam-5641	430	10	tu	tu	PROPN
ejpam-5641	430	11	ℶ	ℶ	PROPN
ejpam-5641	430	12	∥φν̂	∥φν̂	VERB
ejpam-5641	430	13	−	−	PROPN
ejpam-5641	430	14	ν̂∥p−qn	ν̂∥p−qn	PROPN
ejpam-5641	430	15	+	+	CCONJ
ejpam-5641	430	16	sup	sup	NOUN
ejpam-5641	430	17	u	u	PROPN
ejpam-5641	430	18	|ε2|	|ε2|	NOUN
ejpam-5641	430	19	tu	tu	PROPN
ejpam-5641	430	20	ℶ	ℶ	PROPN
ejpam-5641	430	21	∥φξ̂	∥φξ̂	VERB
ejpam-5641	430	22	−	−	PROPN
ejpam-5641	430	23	ξ̂∥p−qn	ξ̂∥p−qn	PROPN
ejpam-5641	430	24	+	+	NUM
ejpam-5641	430	25	sup	sup	NOUN
ejpam-5641	430	26	u	u	PROPN
ejpam-5641	430	27	|ε3|	|ε3|	NOUN
ejpam-5641	430	28	tu	tu	PROPN
ejpam-5641	430	29	ℶ	ℶ	PROPN
ejpam-5641	430	30	∥ν̂	∥ν̂	PROPN
ejpam-5641	430	31	−	−	PROPN
ejpam-5641	430	32	ξ̂∥p−qn	ξ̂∥p−qn	PROPN
ejpam-5641	430	33	.	.	PUNCT
ejpam-5641	431	1	we	we	PRON
ejpam-5641	431	2	have	have	VERB
ejpam-5641	431	3	a	a	DET
ejpam-5641	431	4	unique	unique	ADJ
ejpam-5641	431	5	solution	solution	NOUN
ejpam-5641	431	6	of	of	ADP
ejpam-5641	431	7	the	the	DET
ejpam-5641	431	8	dynamical	dynamical	ADJ
ejpam-5641	431	9	systems	system	NOUN
ejpam-5641	431	10	(	(	PUNCT
ejpam-5641	431	11	1	1	X
ejpam-5641	431	12	)	)	PUNCT
ejpam-5641	431	13	in	in	ADP
ejpam-5641	431	14	(	(	PUNCT
ejpam-5641	431	15	γsf	γsf	X
ejpam-5641	431	16	(	(	PUNCT
ejpam-5641	431	17	q	q	NOUN
ejpam-5641	431	18	,	,	PUNCT
ejpam-5641	431	19	t	t	PROPN
ejpam-5641	431	20	)	)	PUNCT
ejpam-5641	431	21	)	)	PUNCT
ejpam-5641	432	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	432	2	.	.	PUNCT
ejpam-5641	432	3	example	example	NOUN
ejpam-5641	432	4	5.2	5.2	NUM
ejpam-5641	432	5	.	.	PUNCT
ejpam-5641	433	1	supposing	suppose	VERB
ejpam-5641	433	2	that	that	PRON
ejpam-5641	433	3	(	(	PUNCT
ejpam-5641	433	4	γsf	γsf	X
ejpam-5641	433	5	(	(	PUNCT
ejpam-5641	433	6	(	(	PUNCT
ejpam-5641	433	7	1	1	NUM
ejpam-5641	433	8	(	(	PUNCT
ejpam-5641	433	9	u+1)f2u	u+1)f2u	NOUN
ejpam-5641	433	10	)	)	PUNCT
ejpam-5641	433	11	u∈n	u∈n	NOUN
ejpam-5641	433	12	,	,	PUNCT
ejpam-5641	433	13	(	(	PUNCT
ejpam-5641	433	14	2u+3	2u+3	NOUN
ejpam-5641	433	15	u+2	u+2	NOUN
ejpam-5641	433	16	)	)	PUNCT
ejpam-5641	433	17	u∈n	u∈n	NOUN
ejpam-5641	433	18	)	)	PUNCT
ejpam-5641	433	19	)	)	PUNCT
ejpam-5641	433	20	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	433	21	,	,	PUNCT
ejpam-5641	433	22	where	where	SCONJ
ejpam-5641	433	23	∥ν̂∥p−qn	∥ν̂∥p−qn	ADJ
ejpam-5641	433	24	=	=	NOUN
ejpam-5641	433	25	√√√√√√∑	√√√√√√∑	NOUN
ejpam-5641	433	26	u∈n	u∈n	NOUN
ejpam-5641	433	27			PROPN
ejpam-5641	433	28	ℏ̂	ℏ̂	PUNCT
ejpam-5641	433	29	(	(	PUNCT
ejpam-5641	433	30	∑u	∑u	PROPN
ejpam-5641	433	31	d=0	d=0	PROPN
ejpam-5641	433	32	ν̂d	ν̂d	X
ejpam-5641	433	33	d+1	d+1	PROPN
ejpam-5641	433	34	,	,	PUNCT
ejpam-5641	433	35	0̂	0̂	PROPN
ejpam-5641	433	36	)	)	PUNCT
ejpam-5641	434	1	fufu+1	fufu+1	NOUN
ejpam-5641	435	1			PROPN
ejpam-5641	435	2	2u+3	2u+3	PROPN
ejpam-5641	435	3	u+2	u+2	PROPN
ejpam-5641	435	4	,	,	PUNCT
ejpam-5641	435	5	for	for	ADP
ejpam-5641	435	6	all	all	DET
ejpam-5641	435	7	ν̂	ν̂	NUM
ejpam-5641	435	8	∈	∈	PROPN
ejpam-5641	435	9	(	(	PUNCT
ejpam-5641	435	10	γsf	γsf	X
ejpam-5641	435	11	(	(	PUNCT
ejpam-5641	435	12	(	(	PUNCT
ejpam-5641	435	13	1	1	NUM
ejpam-5641	435	14	(	(	PUNCT
ejpam-5641	435	15	u+1)f2u	u+1)f2u	NOUN
ejpam-5641	435	16	)	)	PUNCT
ejpam-5641	435	17	u∈n	u∈n	NOUN
ejpam-5641	435	18	,	,	PUNCT
ejpam-5641	435	19	(	(	PUNCT
ejpam-5641	435	20	2u+3	2u+3	NOUN
ejpam-5641	435	21	u+2	u+2	NOUN
ejpam-5641	435	22	)	)	PUNCT
ejpam-5641	435	23	u∈n	u∈n	NOUN
ejpam-5641	435	24	)	)	PUNCT
ejpam-5641	435	25	)	)	PUNCT
ejpam-5641	436	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	436	2	.	.	PUNCT
ejpam-5641	437	1	assume	assume	VERB
ejpam-5641	437	2	that	that	SCONJ
ejpam-5641	437	3	the	the	DET
ejpam-5641	437	4	nldes	nlde	NOUN
ejpam-5641	437	5	:	:	PUNCT
ejpam-5641	437	6	ν̂d	ν̂d	X
ejpam-5641	437	7	=	=	PUNCT
ejpam-5641	437	8	̂log2(d	̂log2(d	ADP
ejpam-5641	437	9	4	4	NUM
ejpam-5641	437	10	+	+	NUM
ejpam-5641	437	11	1	1	NUM
ejpam-5641	437	12	)	)	PUNCT
ejpam-5641	437	13	+	+	CCONJ
ejpam-5641	437	14	∑	∑	PUNCT
ejpam-5641	437	15	v∈n	v∈n	NOUN
ejpam-5641	437	16	cosh	cosh	NOUN
ejpam-5641	437	17	d	d	PROPN
ejpam-5641	437	18	cos2	cos2	PROPN
ejpam-5641	437	19	v	v	PROPN
ejpam-5641	437	20	ν̂xd−2	ν̂xd−2	PROPN
ejpam-5641	437	21	ν̂yd−1	ν̂yd−1	PROPN
ejpam-5641	437	22	+	+	CCONJ
ejpam-5641	437	23	̂tanh(2v	̂tanh(2v	X
ejpam-5641	437	24	+	+	CCONJ
ejpam-5641	437	25	3	3	NUM
ejpam-5641	437	26	)	)	PUNCT
ejpam-5641	437	27	,	,	PUNCT
ejpam-5641	437	28	(	(	PUNCT
ejpam-5641	437	29	4	4	X
ejpam-5641	437	30	)	)	PUNCT
ejpam-5641	437	31	for	for	ADP
ejpam-5641	437	32	every	every	DET
ejpam-5641	437	33	x	x	PROPN
ejpam-5641	437	34	,	,	PUNCT
ejpam-5641	437	35	y	y	PROPN
ejpam-5641	437	36	,	,	PUNCT
ejpam-5641	437	37	ν̂−2(t	ν̂−2(t	PROPN
ejpam-5641	437	38	)	)	PUNCT
ejpam-5641	437	39	,	,	PUNCT
ejpam-5641	437	40	ν̂−1(t	ν̂−1(t	PROPN
ejpam-5641	437	41	)	)	PUNCT
ejpam-5641	437	42	>	>	X
ejpam-5641	437	43	0	0	NUM
ejpam-5641	437	44	,	,	PUNCT
ejpam-5641	437	45	under	under	ADP
ejpam-5641	437	46	t	t	PROPN
ejpam-5641	437	47	∈	∈	NOUN
ejpam-5641	437	48	a.	a.	NOUN
ejpam-5641	437	49	let	let	VERB
ejpam-5641	437	50	the	the	DET
ejpam-5641	437	51	mapping	mapping	NOUN
ejpam-5641	437	52	φ	φ	PROPN
ejpam-5641	437	53	be	be	AUX
ejpam-5641	437	54	defined	define	VERB
ejpam-5641	437	55	as	as	ADP
ejpam-5641	437	56	φ	φ	PROPN
ejpam-5641	437	57	:	:	PUNCT
ejpam-5641	437	58	(	(	PUNCT
ejpam-5641	437	59	γsf	γsf	X
ejpam-5641	437	60	(	(	PUNCT
ejpam-5641	437	61	(	(	PUNCT
ejpam-5641	437	62	1	1	NUM
ejpam-5641	437	63	(	(	PUNCT
ejpam-5641	437	64	u+	u+	NOUN
ejpam-5641	437	65	1)f2u	1)f2u	ADJ
ejpam-5641	437	66	)	)	PUNCT
ejpam-5641	437	67	u∈n	u∈n	NOUN
ejpam-5641	437	68	,	,	PUNCT
ejpam-5641	437	69	(	(	PUNCT
ejpam-5641	437	70	2u+	2u+	NUM
ejpam-5641	437	71	3	3	NUM
ejpam-5641	437	72	u+	u+	SYM
ejpam-5641	437	73	2	2	NUM
ejpam-5641	437	74	)	)	PUNCT
ejpam-5641	437	75	u∈n	u∈n	NOUN
ejpam-5641	437	76	)	)	PUNCT
ejpam-5641	437	77	)	)	PUNCT
ejpam-5641	437	78	∥.∥p−qn	∥.∥p−qn	PRON
ejpam-5641	437	79	→	→	PUNCT
ejpam-5641	437	80	(	(	PUNCT
ejpam-5641	437	81	γsf	γsf	X
ejpam-5641	437	82	(	(	PUNCT
ejpam-5641	437	83	(	(	PUNCT
ejpam-5641	437	84	1	1	NUM
ejpam-5641	437	85	(	(	PUNCT
ejpam-5641	437	86	u+	u+	NOUN
ejpam-5641	437	87	1)f2u	1)f2u	ADJ
ejpam-5641	437	88	)	)	PUNCT
ejpam-5641	437	89	u∈n	u∈n	NOUN
ejpam-5641	437	90	,	,	PUNCT
ejpam-5641	437	91	(	(	PUNCT
ejpam-5641	437	92	2u+	2u+	NUM
ejpam-5641	437	93	3	3	NUM
ejpam-5641	437	94	u+	u+	SYM
ejpam-5641	437	95	2	2	NUM
ejpam-5641	437	96	)	)	PUNCT
ejpam-5641	437	97	u∈n	u∈n	NOUN
ejpam-5641	437	98	)	)	PUNCT
ejpam-5641	437	99	)	)	PUNCT
ejpam-5641	438	1	∥.∥p−qn	∥.∥p−qn	NOUN
ejpam-5641	438	2	,	,	PUNCT
ejpam-5641	438	3	where	where	SCONJ
ejpam-5641	438	4	φ(ν̂d)d∈n	φ(ν̂d)d∈n	NOUN
ejpam-5641	438	5	=	=	X
ejpam-5641	438	6	(	(	PUNCT
ejpam-5641	438	7	̂log2(d	̂log2(d	INTJ
ejpam-5641	438	8	4	4	NUM
ejpam-5641	438	9	+	+	NUM
ejpam-5641	438	10	1	1	NUM
ejpam-5641	438	11	)	)	PUNCT
ejpam-5641	438	12	+	+	CCONJ
ejpam-5641	438	13	∑	∑	PUNCT
ejpam-5641	438	14	v∈n	v∈n	NOUN
ejpam-5641	438	15	cosh	cosh	NOUN
ejpam-5641	438	16	d	d	PROPN
ejpam-5641	438	17	cos2	cos2	PROPN
ejpam-5641	438	18	v	v	PROPN
ejpam-5641	438	19	ν̂xd−2	ν̂xd−2	PROPN
ejpam-5641	438	20	ν̂yd−1	ν̂yd−1	PROPN
ejpam-5641	438	21	+	+	CCONJ
ejpam-5641	438	22	̂tanh(2v	̂tanh(2v	X
ejpam-5641	438	23	+	+	CCONJ
ejpam-5641	438	24	3	3	NUM
ejpam-5641	438	25	)	)	PUNCT
ejpam-5641	438	26	)	)	PUNCT
ejpam-5641	438	27	d∈n	d∈n	NOUN
ejpam-5641	438	28	.	.	PUNCT
ejpam-5641	439	1	(	(	PUNCT
ejpam-5641	439	2	5	5	X
ejpam-5641	439	3	)	)	PUNCT
ejpam-5641	439	4	m.	m.	NOUN
ejpam-5641	439	5	m.	m.	NOUN
ejpam-5641	439	6	a	a	PRON
ejpam-5641	439	7	et	et	PROPN
ejpam-5641	439	8	al	al	PROPN
ejpam-5641	439	9	.	.	PUNCT
ejpam-5641	439	10	/	/	SYM
ejpam-5641	439	11	eur	eur	PROPN
ejpam-5641	439	12	.	.	PUNCT
ejpam-5641	440	1	j.	j.	PROPN
ejpam-5641	440	2	pure	pure	PROPN
ejpam-5641	440	3	appl	appl	PROPN
ejpam-5641	440	4	.	.	PROPN
ejpam-5641	440	5	math	math	PROPN
ejpam-5641	440	6	,	,	PUNCT
ejpam-5641	440	7	18	18	NUM
ejpam-5641	440	8	(	(	PUNCT
ejpam-5641	440	9	1	1	NUM
ejpam-5641	440	10	)	)	PUNCT
ejpam-5641	440	11	(	(	PUNCT
ejpam-5641	440	12	2025	2025	NUM
ejpam-5641	440	13	)	)	PUNCT
ejpam-5641	440	14	,	,	PUNCT
ejpam-5641	440	15	5641	5641	NUM
ejpam-5641	440	16	17	17	NUM
ejpam-5641	440	17	of	of	ADP
ejpam-5641	440	18	20	20	NUM
ejpam-5641	440	19	obviously	obviously	ADV
ejpam-5641	440	20	,	,	PUNCT
ejpam-5641	440	21	we	we	PRON
ejpam-5641	440	22	have	have	AUX
ejpam-5641	440	23	εi	εi	NOUN
ejpam-5641	440	24	∈	∈	NOUN
ejpam-5641	440	25	r	r	NOUN
ejpam-5641	440	26	with	with	ADP
ejpam-5641	440	27	∑3	∑3	PROPN
ejpam-5641	440	28	i=1	i=1	PROPN
ejpam-5641	440	29	supu	supu	ADJ
ejpam-5641	440	30	|εi|	|εi|	VERB
ejpam-5641	440	31	2u+3	2u+3	ADJ
ejpam-5641	440	32	2u+4	2u+4	PROPN
ejpam-5641	440	33	∈	∈	PROPN
ejpam-5641	441	1	[	[	X
ejpam-5641	441	2	0	0	NUM
ejpam-5641	441	3	,	,	PUNCT
ejpam-5641	441	4	1	1	NUM
ejpam-5641	441	5	)	)	PUNCT
ejpam-5641	441	6	and	and	CCONJ
ejpam-5641	441	7	for	for	ADP
ejpam-5641	441	8	any	any	DET
ejpam-5641	441	9	u	u	PROPN
ejpam-5641	441	10	∈	∈	PROPN
ejpam-5641	441	11	n	n	NOUN
ejpam-5641	441	12	,	,	PUNCT
ejpam-5641	441	13	hence∣∣∣∣∣	hence∣∣∣∣∣	PROPN
ejpam-5641	441	14	u∑	u∑	X
ejpam-5641	441	15	d=0	d=0	X
ejpam-5641	441	16	(	(	PUNCT
ejpam-5641	441	17	∑	∑	PART
ejpam-5641	441	18	v∈n	v∈n	VERB
ejpam-5641	441	19	cosh	cosh	PROPN
ejpam-5641	442	1	d	d	PROPN
ejpam-5641	442	2	ν̂xd−2	ν̂xd−2	PROPN
ejpam-5641	442	3	ν̂yd−1	ν̂yd−1	PROPN
ejpam-5641	443	1	+	+	CCONJ
ejpam-5641	443	2	̂tanh(2v	̂tanh(2v	X
ejpam-5641	443	3	+	+	CCONJ
ejpam-5641	443	4	3	3	X
ejpam-5641	443	5	)	)	PUNCT
ejpam-5641	443	6	(	(	PUNCT
ejpam-5641	443	7	cos2	cos2	PROPN
ejpam-5641	443	8	v	v	ADP
ejpam-5641	443	9	−	−	PROPN
ejpam-5641	443	10	cos2	cos2	PROPN
ejpam-5641	443	11	v	v	NOUN
ejpam-5641	443	12	)	)	PUNCT
ejpam-5641	443	13	)	)	PUNCT
ejpam-5641	444	1	f2dqd	f2dqd	VERB
ejpam-5641	444	2	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5641	445	1	≤̂|ε1|	≤̂|ε1|	PROPN
ejpam-5641	445	2	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5641	445	3	u∑	u∑	X
ejpam-5641	445	4	d=0	d=0	X
ejpam-5641	446	1	(	(	PUNCT
ejpam-5641	446	2	̂log2(d	̂log2(d	ADP
ejpam-5641	446	3	4	4	NUM
ejpam-5641	447	1	+	+	SYM
ejpam-5641	447	2	1)−	1)−	NUM
ejpam-5641	447	3	ν̂d	ν̂d	X
ejpam-5641	447	4	+	+	CCONJ
ejpam-5641	447	5	∑	∑	PART
ejpam-5641	447	6	v∈n	v∈n	NOUN
ejpam-5641	447	7	cosh	cosh	NOUN
ejpam-5641	447	8	d	d	PROPN
ejpam-5641	447	9	cos2	cos2	PROPN
ejpam-5641	447	10	v	v	PROPN
ejpam-5641	447	11	ν̂xd−2	ν̂xd−2	PROPN
ejpam-5641	447	12	ν̂yd−1	ν̂yd−1	PROPN
ejpam-5641	448	1	+	+	CCONJ
ejpam-5641	448	2	̂tanh(2v	̂tanh(2v	X
ejpam-5641	448	3	+	+	CCONJ
ejpam-5641	448	4	3	3	NUM
ejpam-5641	448	5	)	)	PUNCT
ejpam-5641	448	6	)	)	PUNCT
ejpam-5641	448	7	f2dqd	f2dqd	VERB
ejpam-5641	448	8	∣∣∣∣∣+	∣∣∣∣∣+	NOUN
ejpam-5641	448	9	|ε2|	|ε2|	NOUN
ejpam-5641	448	10	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5641	448	11	u∑	u∑	PROPN
ejpam-5641	448	12	d=0	d=0	X
ejpam-5641	448	13	(	(	PUNCT
ejpam-5641	448	14	̂log2(d	̂log2(d	ADP
ejpam-5641	448	15	4	4	NUM
ejpam-5641	449	1	+	+	SYM
ejpam-5641	449	2	1)−	1)−	PROPN
ejpam-5641	449	3	η̂d	η̂d	PART
ejpam-5641	449	4	+	+	CCONJ
ejpam-5641	449	5	∑	∑	PART
ejpam-5641	449	6	v∈n	v∈n	NOUN
ejpam-5641	449	7	cosh	cosh	NOUN
ejpam-5641	449	8	d	d	PROPN
ejpam-5641	449	9	cos2	cos2	PROPN
ejpam-5641	449	10	v	v	PROPN
ejpam-5641	449	11	η̂xd−2	η̂xd−2	PROPN
ejpam-5641	449	12	η̂yd−1	η̂yd−1	NOUN
ejpam-5641	449	13	+	+	CCONJ
ejpam-5641	449	14	̂tanh(2v	̂tanh(2v	X
ejpam-5641	449	15	+	+	CCONJ
ejpam-5641	449	16	3	3	NUM
ejpam-5641	449	17	)	)	PUNCT
ejpam-5641	449	18	)	)	PUNCT
ejpam-5641	449	19	f2dqd	f2dqd	VERB
ejpam-5641	449	20	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ejpam-5641	449	21	|ε3||	|ε3||	PROPN
ejpam-5641	449	22	u∑	u∑	PROPN
ejpam-5641	449	23	d=0	d=0	X
ejpam-5641	449	24	(	(	PUNCT
ejpam-5641	449	25	ν̂d	ν̂d	X
ejpam-5641	449	26	−	−	ADV
ejpam-5641	449	27	η̂d	η̂d	NOUN
ejpam-5641	449	28	)	)	PUNCT
ejpam-5641	449	29	f	f	PROPN
ejpam-5641	449	30	2	2	NUM
ejpam-5641	449	31	dqd|	dqd|	NOUN
ejpam-5641	449	32	.	.	PUNCT
ejpam-5641	450	1	by	by	ADP
ejpam-5641	450	2	theorem	theorem	NOUN
ejpam-5641	450	3	5.1	5.1	NUM
ejpam-5641	450	4	,	,	PUNCT
ejpam-5641	450	5	the	the	DET
ejpam-5641	450	6	nldes	nlde	NOUN
ejpam-5641	450	7	(	(	PUNCT
ejpam-5641	450	8	4	4	NUM
ejpam-5641	450	9	)	)	PUNCT
ejpam-5641	450	10	include	include	VERB
ejpam-5641	450	11	a	a	DET
ejpam-5641	450	12	unique	unique	ADJ
ejpam-5641	450	13	solution	solution	NOUN
ejpam-5641	450	14	in	in	ADP
ejpam-5641	450	15	(	(	PUNCT
ejpam-5641	450	16	γsf	γsf	X
ejpam-5641	450	17	(	(	PUNCT
ejpam-5641	450	18	(	(	PUNCT
ejpam-5641	450	19	1	1	NUM
ejpam-5641	450	20	(	(	PUNCT
ejpam-5641	450	21	u+1)f2u	u+1)f2u	NOUN
ejpam-5641	450	22	)	)	PUNCT
ejpam-5641	450	23	u∈n	u∈n	NOUN
ejpam-5641	450	24	,	,	PUNCT
ejpam-5641	450	25	(	(	PUNCT
ejpam-5641	450	26	2u+3	2u+3	NOUN
ejpam-5641	450	27	u+2	u+2	NOUN
ejpam-5641	450	28	)	)	PUNCT
ejpam-5641	450	29	u∈n	u∈n	NOUN
ejpam-5641	450	30	)	)	PUNCT
ejpam-5641	450	31	)	)	PUNCT
ejpam-5641	451	1	∥.∥p−qn	∥.∥p−qn	X
ejpam-5641	451	2	.	.	PUNCT
ejpam-5641	452	1	theorem	theorem	VERB
ejpam-5641	452	2	5.3	5.3	NUM
ejpam-5641	452	3	.	.	PUNCT
ejpam-5641	453	1	assume	assume	VERB
ejpam-5641	453	2	that	that	SCONJ
ejpam-5641	453	3	φ	φ	PROPN
ejpam-5641	453	4	:	:	PUNCT
ejpam-5641	453	5	(	(	PUNCT
ejpam-5641	453	6	γsf	γsf	X
ejpam-5641	453	7	(	(	PUNCT
ejpam-5641	453	8	q	q	NOUN
ejpam-5641	453	9	,	,	PUNCT
ejpam-5641	453	10	t	t	PROPN
ejpam-5641	453	11	)	)	PUNCT
ejpam-5641	453	12	)	)	PUNCT
ejpam-5641	454	1	∥.∥ℶp−qn	∥.∥ℶp−qn	X
ejpam-5641	454	2	→	→	SYM
ejpam-5641	454	3	(	(	PUNCT
ejpam-5641	454	4	γsf	γsf	X
ejpam-5641	454	5	(	(	PUNCT
ejpam-5641	454	6	q	q	NOUN
ejpam-5641	454	7	,	,	PUNCT
ejpam-5641	454	8	t	t	PROPN
ejpam-5641	454	9	)	)	PUNCT
ejpam-5641	454	10	)	)	PUNCT
ejpam-5641	455	1	∥.∥ℶp−qn	∥.∥ℶp−qn	NOUN
ejpam-5641	455	2	is	be	AUX
ejpam-5641	455	3	defined	define	VERB
ejpam-5641	455	4	by	by	ADP
ejpam-5641	455	5	(	(	PUNCT
ejpam-5641	455	6	2	2	NUM
ejpam-5641	455	7	)	)	PUNCT
ejpam-5641	455	8	.	.	PUNCT
ejpam-5641	456	1	the	the	DET
ejpam-5641	456	2	dynamical	dynamical	ADJ
ejpam-5641	456	3	systems	system	NOUN
ejpam-5641	456	4	(	(	PUNCT
ejpam-5641	456	5	1	1	X
ejpam-5641	456	6	)	)	PUNCT
ejpam-5641	456	7	have	have	VERB
ejpam-5641	456	8	a	a	DET
ejpam-5641	456	9	unique	unique	ADJ
ejpam-5641	456	10	solution	solution	NOUN
ejpam-5641	456	11	ẑ	ẑ	X
ejpam-5641	456	12	∈	∈	PROPN
ejpam-5641	456	13	(	(	PUNCT
ejpam-5641	456	14	γsf	γsf	X
ejpam-5641	456	15	(	(	PUNCT
ejpam-5641	456	16	q	q	NOUN
ejpam-5641	456	17	,	,	PUNCT
ejpam-5641	456	18	t	t	PROPN
ejpam-5641	456	19	)	)	PUNCT
ejpam-5641	456	20	)	)	PUNCT
ejpam-5641	457	1	∥.∥ℶp−qn	∥.∥ℶp−qn	NOUN
ejpam-5641	457	2	,	,	PUNCT
ejpam-5641	457	3	when	when	SCONJ
ejpam-5641	457	4	the	the	DET
ejpam-5641	457	5	following	follow	VERB
ejpam-5641	457	6	conditions	condition	NOUN
ejpam-5641	457	7	are	be	AUX
ejpam-5641	457	8	satisfied	satisfied	ADJ
ejpam-5641	457	9	:	:	PUNCT
ejpam-5641	457	10	(	(	PUNCT
ejpam-5641	457	11	k1	k1	NOUN
ejpam-5641	457	12	)	)	PUNCT
ejpam-5641	457	13	suppose	suppose	VERB
ejpam-5641	457	14	γ	γ	NOUN
ejpam-5641	457	15	:	:	PUNCT
ejpam-5641	457	16	n	n	PROPN
ejpam-5641	457	17	2	2	NUM
ejpam-5641	457	18	→	→	SYM
ejpam-5641	457	19	r	r	NOUN
ejpam-5641	457	20	,	,	PUNCT
ejpam-5641	457	21	ψ	ψ	X
ejpam-5641	457	22	:	:	PUNCT
ejpam-5641	457	23	n	n	PRON
ejpam-5641	457	24	×	×	PROPN
ejpam-5641	457	25	r(a	r(a	PROPN
ejpam-5641	457	26	)	)	PUNCT
ejpam-5641	457	27	→	→	SYM
ejpam-5641	457	28	r(a	r(a	NUM
ejpam-5641	457	29	)	)	PUNCT
ejpam-5641	457	30	,	,	PUNCT
ejpam-5641	457	31	ν̂	ν̂	NUM
ejpam-5641	457	32	:	:	PUNCT
ejpam-5641	457	33	n	n	X
ejpam-5641	457	34	→	→	SYM
ejpam-5641	457	35	r(a	r(a	NUM
ejpam-5641	457	36	)	)	PUNCT
ejpam-5641	457	37	,	,	PUNCT
ejpam-5641	457	38	β̂	β̂	X
ejpam-5641	457	39	:	:	PUNCT
ejpam-5641	457	40	n	n	X
ejpam-5641	457	41	→	→	SYM
ejpam-5641	457	42	r(a	r(a	NUM
ejpam-5641	457	43	)	)	PUNCT
ejpam-5641	457	44	,	,	PUNCT
ejpam-5641	457	45	ξ̂	ξ̂	NUM
ejpam-5641	457	46	:	:	PUNCT
ejpam-5641	457	47	n	n	X
ejpam-5641	457	48	→	→	SYM
ejpam-5641	457	49	r(a	r(a	NUM
ejpam-5641	457	50	)	)	PUNCT
ejpam-5641	457	51	,	,	PUNCT
ejpam-5641	457	52	if	if	SCONJ
ejpam-5641	457	53	one	one	PRON
ejpam-5641	457	54	has	have	VERB
ejpam-5641	457	55	εi	εi	VERB
ejpam-5641	457	56	∈	∈	NOUN
ejpam-5641	457	57	r	r	NOUN
ejpam-5641	457	58	under	under	ADP
ejpam-5641	457	59	22ℶ−2	22ℶ−2	NUM
ejpam-5641	457	60	∑3	∑3	PROPN
ejpam-5641	457	61	i=1	i=1	PROPN
ejpam-5641	457	62	supu	supu	ADJ
ejpam-5641	457	63	|εi|tu	|εi|tu	ADJ
ejpam-5641	457	64	∈	∈	PROPN
ejpam-5641	458	1	[	[	X
ejpam-5641	458	2	0	0	NUM
ejpam-5641	458	3	,	,	PUNCT
ejpam-5641	458	4	1	1	NUM
ejpam-5641	458	5	)	)	PUNCT
ejpam-5641	458	6	and	and	CCONJ
ejpam-5641	458	7	for	for	ADP
ejpam-5641	458	8	every	every	DET
ejpam-5641	458	9	u	u	PROPN
ejpam-5641	458	10	∈	∈	PROPN
ejpam-5641	458	11	n	n	NOUN
ejpam-5641	458	12	,	,	PUNCT
ejpam-5641	458	13	one	one	NUM
ejpam-5641	458	14	gets∣∣∣∣∣	gets∣∣∣∣∣	PROPN
ejpam-5641	458	15	u∑	u∑	PROPN
ejpam-5641	458	16	d=0	d=0	PROPN
ejpam-5641	458	17	(	(	PUNCT
ejpam-5641	458	18	∑	∑	INTJ
ejpam-5641	458	19	v∈n	v∈n	VERB
ejpam-5641	458	20	γd	γd	ADP
ejpam-5641	458	21	,	,	PUNCT
ejpam-5641	458	22	v[ψv	v[ψv	X
ejpam-5641	458	23	,	,	PUNCT
ejpam-5641	458	24	ν̂v	ν̂v	PROPN
ejpam-5641	458	25	−ψ	−ψ	NOUN
ejpam-5641	458	26	v	v	NOUN
ejpam-5641	458	27	,	,	PUNCT
ejpam-5641	458	28	ξ̂v	ξ̂v	NOUN
ejpam-5641	458	29	]	]	PUNCT
ejpam-5641	458	30	)	)	PUNCT
ejpam-5641	458	31	f2dqd	f2dqd	VERB
ejpam-5641	458	32	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5641	459	1	≤̂|ε1|	≤̂|ε1|	PROPN
ejpam-5641	459	2	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5641	459	3	u∑	u∑	PROPN
ejpam-5641	459	4	d=0	d=0	X
ejpam-5641	459	5	(	(	PUNCT
ejpam-5641	459	6	β̂d	β̂d	NUM
ejpam-5641	459	7	−	−	NOUN
ejpam-5641	459	8	ν̂d	ν̂d	X
ejpam-5641	459	9	+	+	CCONJ
ejpam-5641	459	10	∑	∑	ADP
ejpam-5641	459	11	v∈n	v∈n	NOUN
ejpam-5641	459	12	γd	γd	ADP
ejpam-5641	459	13	,	,	PUNCT
ejpam-5641	459	14	vψv	vψv	ADJ
ejpam-5641	459	15	,	,	PUNCT
ejpam-5641	459	16	ν̂v	ν̂v	PROPN
ejpam-5641	459	17	)	)	PUNCT
ejpam-5641	459	18	f2dqd	f2dqd	VERB
ejpam-5641	460	1	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5641	461	1	+	+	CCONJ
ejpam-5641	461	2	|ε2|	|ε2|	NOUN
ejpam-5641	461	3	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5641	461	4	u∑	u∑	PROPN
ejpam-5641	461	5	d=0	d=0	X
ejpam-5641	461	6	(	(	PUNCT
ejpam-5641	461	7	β̂d	β̂d	NUM
ejpam-5641	461	8	−	−	NOUN
ejpam-5641	461	9	ξ̂d	ξ̂d	X
ejpam-5641	462	1	+	+	CCONJ
ejpam-5641	462	2	∑	∑	PUNCT
ejpam-5641	462	3	v∈n	v∈n	NOUN
ejpam-5641	462	4	γd	γd	ADP
ejpam-5641	462	5	,	,	PUNCT
ejpam-5641	462	6	vψv	vψv	ADJ
ejpam-5641	462	7	,	,	PUNCT
ejpam-5641	462	8	ξ̂v	ξ̂v	NOUN
ejpam-5641	462	9	)	)	PUNCT
ejpam-5641	462	10	f2dqd	f2dqd	PROPN
ejpam-5641	462	11	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ejpam-5641	462	12	|ε3||	|ε3||	PROPN
ejpam-5641	462	13	u∑	u∑	PROPN
ejpam-5641	462	14	d=0	d=0	X
ejpam-5641	462	15	(	(	PUNCT
ejpam-5641	462	16	ν̂d	ν̂d	X
ejpam-5641	462	17	−	−	PROPN
ejpam-5641	462	18	ξ̂d	ξ̂d	NOUN
ejpam-5641	462	19	)	)	PUNCT
ejpam-5641	463	1	f2dqd|	f2dqd|	PROPN
ejpam-5641	463	2	.	.	PUNCT
ejpam-5641	464	1	(	(	PUNCT
ejpam-5641	464	2	k2	k2	PROPN
ejpam-5641	464	3	)	)	PUNCT
ejpam-5641	464	4	φ	φ	PROPN
ejpam-5641	464	5	is	be	AUX
ejpam-5641	464	6	∥.∥ℶp−qn	∥.∥ℶp−qn	NUM
ejpam-5641	464	7	-	-	PUNCT
ejpam-5641	464	8	seq.c	seq.c	PROPN
ejpam-5641	464	9	at	at	ADP
ejpam-5641	464	10	ẑ	ẑ	PROPN
ejpam-5641	464	11	∈	∈	PROPN
ejpam-5641	464	12	(	(	PUNCT
ejpam-5641	464	13	γsf	γsf	X
ejpam-5641	464	14	(	(	PUNCT
ejpam-5641	464	15	q	q	NOUN
ejpam-5641	464	16	,	,	PUNCT
ejpam-5641	464	17	t	t	PROPN
ejpam-5641	464	18	)	)	PUNCT
ejpam-5641	464	19	)	)	PUNCT
ejpam-5641	465	1	∥.∥ℶp−qn	∥.∥ℶp−qn	X
ejpam-5641	465	2	,	,	PUNCT
ejpam-5641	465	3	(	(	PUNCT
ejpam-5641	465	4	k3	k3	PROPN
ejpam-5641	465	5	)	)	PUNCT
ejpam-5641	465	6	there	there	PRON
ejpam-5641	465	7	is	be	VERB
ejpam-5641	465	8	ŷ	ŷ	NUM
ejpam-5641	465	9	∈	∈	NOUN
ejpam-5641	465	10	(	(	PUNCT
ejpam-5641	465	11	γsf	γsf	X
ejpam-5641	465	12	(	(	PUNCT
ejpam-5641	465	13	q	q	NOUN
ejpam-5641	465	14	,	,	PUNCT
ejpam-5641	465	15	t	t	PROPN
ejpam-5641	465	16	)	)	PUNCT
ejpam-5641	465	17	)	)	PUNCT
ejpam-5641	466	1	∥.∥ℶp−qn	∥.∥ℶp−qn	NOUN
ejpam-5641	466	2	with	with	ADP
ejpam-5641	466	3	{	{	PUNCT
ejpam-5641	466	4	φmŷ	φmŷ	PROPN
ejpam-5641	466	5	}	}	PUNCT
ejpam-5641	466	6	has	have	AUX
ejpam-5641	466	7	{	{	PUNCT
ejpam-5641	466	8	φmj	φmj	NOUN
ejpam-5641	466	9	ŷ	ŷ	NUM
ejpam-5641	466	10	}	}	PUNCT
ejpam-5641	466	11	converging	converge	VERB
ejpam-5641	466	12	to	to	ADP
ejpam-5641	466	13	ẑ.	ẑ.	NOUN
ejpam-5641	466	14	proof	proof	NOUN
ejpam-5641	466	15	.	.	PUNCT
ejpam-5641	467	1	by	by	ADP
ejpam-5641	467	2	theorem	theorem	ADJ
ejpam-5641	467	3	4.5	4.5	NUM
ejpam-5641	467	4	and	and	CCONJ
ejpam-5641	467	5	∥φν̂	∥φν̂	VERB
ejpam-5641	467	6	−	−	NOUN
ejpam-5641	467	7	φξ̂∥ℶp−qn	φξ̂∥ℶp−qn	X
ejpam-5641	467	8	=	=	PUNCT
ejpam-5641	467	9	∑	∑	PUNCT
ejpam-5641	467	10	u∈n	u∈n	PROPN
ejpam-5641	467	11			PROPN
ejpam-5641	467	12	ℏ̂	ℏ̂	PUNCT
ejpam-5641	467	13	(	(	PUNCT
ejpam-5641	467	14	∑u	∑u	PROPN
ejpam-5641	467	15	d=0	d=0	X
ejpam-5641	467	16	f	f	PROPN
ejpam-5641	467	17	2	2	NUM
ejpam-5641	467	18	dqd(φν̂d	dqd(φν̂d	NOUN
ejpam-5641	467	19	−	−	PROPN
ejpam-5641	467	20	φξ̂d	φξ̂d	PROPN
ejpam-5641	467	21	)	)	PUNCT
ejpam-5641	467	22	,	,	PUNCT
ejpam-5641	467	23	0̂	0̂	PROPN
ejpam-5641	467	24	)	)	PUNCT
ejpam-5641	468	1	fufu+1	fufu+1	INTJ
ejpam-5641	468	2	tu	tu	PUNCT
ejpam-5641	468	3	=	=	PUNCT
ejpam-5641	468	4	∑	∑	PUNCT
ejpam-5641	468	5	u∈n	u∈n	PROPN
ejpam-5641	468	6			NOUN
ejpam-5641	468	7	ℏ̂	ℏ̂	PUNCT
ejpam-5641	468	8	(	(	PUNCT
ejpam-5641	468	9	∑u	∑u	PROPN
ejpam-5641	468	10	d=0	d=0	X
ejpam-5641	468	11	(	(	PUNCT
ejpam-5641	468	12	∑	∑	INTJ
ejpam-5641	468	13	v∈n	v∈n	VERB
ejpam-5641	468	14	γd	γd	ADP
ejpam-5641	468	15	,	,	PUNCT
ejpam-5641	468	16	v[ψv	v[ψv	X
ejpam-5641	468	17	,	,	PUNCT
ejpam-5641	468	18	ν̂v	ν̂v	PROPN
ejpam-5641	468	19	−ψ	−ψ	NOUN
ejpam-5641	468	20	v	v	NOUN
ejpam-5641	468	21	,	,	PUNCT
ejpam-5641	468	22	ξ̂v	ξ̂v	NOUN
ejpam-5641	468	23	]	]	PUNCT
ejpam-5641	468	24	)	)	PUNCT
ejpam-5641	468	25	f2dqd	f2dqd	PROPN
ejpam-5641	468	26	,	,	PUNCT
ejpam-5641	468	27	0̂	0̂	PROPN
ejpam-5641	468	28	)	)	PUNCT
ejpam-5641	469	1	fufu+1	fufu+1	NOUN
ejpam-5641	469	2	tu	tu	PUNCT
ejpam-5641	469	3	m.	m.	NOUN
ejpam-5641	469	4	m.	m.	NOUN
ejpam-5641	469	5	a	a	PRON
ejpam-5641	469	6	et	et	NOUN
ejpam-5641	469	7	al	al	PROPN
ejpam-5641	469	8	.	.	PUNCT
ejpam-5641	469	9	/	/	SYM
ejpam-5641	469	10	eur	eur	PROPN
ejpam-5641	469	11	.	.	PUNCT
ejpam-5641	470	1	j.	j.	PROPN
ejpam-5641	470	2	pure	pure	PROPN
ejpam-5641	470	3	appl	appl	PROPN
ejpam-5641	470	4	.	.	PROPN
ejpam-5641	470	5	math	math	PROPN
ejpam-5641	470	6	,	,	PUNCT
ejpam-5641	470	7	18	18	NUM
ejpam-5641	470	8	(	(	PUNCT
ejpam-5641	470	9	1	1	NUM
ejpam-5641	470	10	)	)	PUNCT
ejpam-5641	470	11	(	(	PUNCT
ejpam-5641	470	12	2025	2025	NUM
ejpam-5641	470	13	)	)	PUNCT
ejpam-5641	470	14	,	,	PUNCT
ejpam-5641	470	15	5641	5641	NUM
ejpam-5641	470	16	18	18	NUM
ejpam-5641	470	17	of	of	ADP
ejpam-5641	470	18	20	20	NUM
ejpam-5641	470	19	≤	≤	NUM
ejpam-5641	470	20	22ℶ−2	22ℶ−2	NUM
ejpam-5641	470	21	sup	sup	NOUN
ejpam-5641	470	22	u	u	NOUN
ejpam-5641	470	23	|ε1|tu	|ε1|tu	PROPN
ejpam-5641	470	24	∑	∑	PROPN
ejpam-5641	470	25	u∈n	u∈n	PROPN
ejpam-5641	470	26			PROPN
ejpam-5641	470	27	ℏ̂	ℏ̂	PUNCT
ejpam-5641	470	28	(	(	PUNCT
ejpam-5641	470	29	∑u	∑u	PROPN
ejpam-5641	470	30	d=0	d=0	PROPN
ejpam-5641	470	31	(	(	PUNCT
ejpam-5641	470	32	β̂d	β̂d	NUM
ejpam-5641	470	33	−	−	NOUN
ejpam-5641	470	34	ν̂d	ν̂d	X
ejpam-5641	470	35	+	+	CCONJ
ejpam-5641	470	36	∑	∑	ADP
ejpam-5641	470	37	v∈n	v∈n	NOUN
ejpam-5641	470	38	γd	γd	ADP
ejpam-5641	470	39	,	,	PUNCT
ejpam-5641	470	40	vψv	vψv	ADJ
ejpam-5641	470	41	,	,	PUNCT
ejpam-5641	470	42	ν̂v	ν̂v	PROPN
ejpam-5641	470	43	)	)	PUNCT
ejpam-5641	471	1	f2dqd	f2dqd	ADP
ejpam-5641	471	2	,	,	PUNCT
ejpam-5641	471	3	0̂	0̂	PROPN
ejpam-5641	471	4	)	)	PUNCT
ejpam-5641	472	1	fufu+1	fufu+1	INTJ
ejpam-5641	472	2	tu	tu	ADV
ejpam-5641	473	1	+	+	CCONJ
ejpam-5641	473	2	22ℶ−2	22ℶ−2	NUM
ejpam-5641	473	3	sup	sup	NOUN
ejpam-5641	473	4	u	u	NOUN
ejpam-5641	474	1	|ε2|tu	|ε2|tu	PROPN
ejpam-5641	474	2	∑	∑	PROPN
ejpam-5641	474	3	u∈n	u∈n	PROPN
ejpam-5641	474	4			PROPN
ejpam-5641	474	5	ℏ̂	ℏ̂	PUNCT
ejpam-5641	474	6	(	(	PUNCT
ejpam-5641	474	7	∑u	∑u	PROPN
ejpam-5641	474	8	d=0	d=0	PROPN
ejpam-5641	474	9	(	(	PUNCT
ejpam-5641	474	10	β̂d	β̂d	NUM
ejpam-5641	474	11	−	−	NOUN
ejpam-5641	474	12	ξ̂d	ξ̂d	X
ejpam-5641	475	1	+	+	CCONJ
ejpam-5641	475	2	∑	∑	PUNCT
ejpam-5641	475	3	v∈n	v∈n	NOUN
ejpam-5641	475	4	γd	γd	ADP
ejpam-5641	475	5	,	,	PUNCT
ejpam-5641	475	6	vψv	vψv	ADJ
ejpam-5641	475	7	,	,	PUNCT
ejpam-5641	475	8	ξ̂v	ξ̂v	NOUN
ejpam-5641	475	9	)	)	PUNCT
ejpam-5641	475	10	f2dqd	f2dqd	PROPN
ejpam-5641	475	11	,	,	PUNCT
ejpam-5641	475	12	0̂	0̂	PROPN
ejpam-5641	475	13	)	)	PUNCT
ejpam-5641	476	1	fufu+1	fufu+1	INTJ
ejpam-5641	476	2	tu	tu	ADV
ejpam-5641	476	3	+	+	NUM
ejpam-5641	476	4	2ℶ−1	2ℶ−1	NUM
ejpam-5641	476	5	sup	sup	NOUN
ejpam-5641	476	6	u	u	NOUN
ejpam-5641	476	7	|ε3|tu	|ε3|tu	NOUN
ejpam-5641	476	8	∑	∑	PROPN
ejpam-5641	476	9	u∈n	u∈n	PROPN
ejpam-5641	476	10			PROPN
ejpam-5641	476	11	ℏ̂	ℏ̂	PUNCT
ejpam-5641	476	12	(	(	PUNCT
ejpam-5641	476	13	∑u	∑u	PROPN
ejpam-5641	476	14	d=0	d=0	PROPN
ejpam-5641	476	15	(	(	PUNCT
ejpam-5641	476	16	ν̂d	ν̂d	X
ejpam-5641	476	17	−	−	PROPN
ejpam-5641	476	18	ξ̂d	ξ̂d	NOUN
ejpam-5641	476	19	)	)	PUNCT
ejpam-5641	476	20	f2dqd	f2dqd	ADP
ejpam-5641	476	21	,	,	PUNCT
ejpam-5641	476	22	0̂	0̂	PROPN
ejpam-5641	476	23	)	)	PUNCT
ejpam-5641	477	1	fufu+1	fufu+1	NOUN
ejpam-5641	477	2	tu	tu	NOUN
ejpam-5641	477	3	≤	≤	ADJ
ejpam-5641	477	4	22ℶ−2	22ℶ−2	NUM
ejpam-5641	477	5	(	(	PUNCT
ejpam-5641	477	6	sup	sup	NOUN
ejpam-5641	477	7	u	u	NOUN
ejpam-5641	477	8	|ε1|tu∥φν̂	|ε1|tu∥φν̂	ADJ
ejpam-5641	477	9	−	−	PROPN
ejpam-5641	477	10	ν̂∥ℶp−qn	ν̂∥ℶp−qn	NOUN
ejpam-5641	478	1	+	+	CCONJ
ejpam-5641	478	2	sup	sup	NOUN
ejpam-5641	478	3	u	u	NOUN
ejpam-5641	478	4	|ε2|tu∥φξ̂	|ε2|tu∥φξ̂	ADJ
ejpam-5641	478	5	−	−	PROPN
ejpam-5641	478	6	ξ̂∥ℶp−qn	ξ̂∥ℶp−qn	NOUN
ejpam-5641	478	7	+	+	CCONJ
ejpam-5641	478	8	sup	sup	PROPN
ejpam-5641	478	9	u	u	NOUN
ejpam-5641	478	10	|ε3|tu∥ν̂	|ε3|tu∥ν̂	NOUN
ejpam-5641	478	11	−	−	PROPN
ejpam-5641	478	12	ξ̂∥ℶp−qn	ξ̂∥ℶp−qn	NOUN
ejpam-5641	478	13	)	)	PUNCT
ejpam-5641	478	14	.	.	PUNCT
ejpam-5641	479	1	that	that	PRON
ejpam-5641	479	2	gives	give	VERB
ejpam-5641	479	3	the	the	DET
ejpam-5641	479	4	required	require	VERB
ejpam-5641	479	5	.	.	PUNCT
ejpam-5641	479	6	example	example	NOUN
ejpam-5641	479	7	5.4	5.4	NUM
ejpam-5641	479	8	.	.	PUNCT
ejpam-5641	480	1	supposing	suppose	VERB
ejpam-5641	480	2	that	that	PRON
ejpam-5641	480	3	(	(	PUNCT
ejpam-5641	480	4	γsf	γsf	X
ejpam-5641	480	5	(	(	PUNCT
ejpam-5641	480	6	(	(	PUNCT
ejpam-5641	480	7	1	1	NUM
ejpam-5641	480	8	(	(	PUNCT
ejpam-5641	480	9	u+1)f2u	u+1)f2u	NOUN
ejpam-5641	480	10	)	)	PUNCT
ejpam-5641	480	11	u∈n	u∈n	NOUN
ejpam-5641	480	12	,	,	PUNCT
ejpam-5641	480	13	(	(	PUNCT
ejpam-5641	480	14	2u+3	2u+3	NOUN
ejpam-5641	480	15	u+2	u+2	NOUN
ejpam-5641	480	16	)	)	PUNCT
ejpam-5641	480	17	u∈n	u∈n	NOUN
ejpam-5641	480	18	)	)	PUNCT
ejpam-5641	480	19	)	)	PUNCT
ejpam-5641	480	20	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	480	21	,	,	PUNCT
ejpam-5641	480	22	where	where	SCONJ
ejpam-5641	480	23	∥ν̂∥2p−qn	∥ν̂∥2p−qn	NOUN
ejpam-5641	480	24	=	=	PUNCT
ejpam-5641	480	25	∑	∑	PUNCT
ejpam-5641	480	26	u∈n	u∈n	PROPN
ejpam-5641	480	27			PROPN
ejpam-5641	480	28	ℏ̂	ℏ̂	PUNCT
ejpam-5641	480	29	(	(	PUNCT
ejpam-5641	480	30	∑u	∑u	PROPN
ejpam-5641	480	31	d=0	d=0	PROPN
ejpam-5641	480	32	ν̂d	ν̂d	X
ejpam-5641	480	33	d+1	d+1	PROPN
ejpam-5641	480	34	,	,	PUNCT
ejpam-5641	480	35	0̂	0̂	PROPN
ejpam-5641	480	36	)	)	PUNCT
ejpam-5641	481	1	fufu+1	fufu+1	NOUN
ejpam-5641	482	1			PROPN
ejpam-5641	482	2	2u+3	2u+3	PROPN
ejpam-5641	483	1	u+2	u+2	PROPN
ejpam-5641	483	2	,	,	PUNCT
ejpam-5641	483	3	for	for	ADP
ejpam-5641	483	4	all	all	DET
ejpam-5641	483	5	ν̂	ν̂	NUM
ejpam-5641	483	6	∈	∈	PROPN
ejpam-5641	483	7	(	(	PUNCT
ejpam-5641	483	8	γsf	γsf	X
ejpam-5641	483	9	(	(	PUNCT
ejpam-5641	483	10	(	(	PUNCT
ejpam-5641	483	11	1	1	NUM
ejpam-5641	483	12	(	(	PUNCT
ejpam-5641	483	13	u+1)f2u	u+1)f2u	NOUN
ejpam-5641	483	14	)	)	PUNCT
ejpam-5641	483	15	u∈n	u∈n	NOUN
ejpam-5641	483	16	,	,	PUNCT
ejpam-5641	483	17	(	(	PUNCT
ejpam-5641	483	18	2u+3	2u+3	NOUN
ejpam-5641	483	19	u+2	u+2	NOUN
ejpam-5641	483	20	)	)	PUNCT
ejpam-5641	483	21	u∈n	u∈n	NOUN
ejpam-5641	483	22	)	)	PUNCT
ejpam-5641	483	23	)	)	PUNCT
ejpam-5641	483	24	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	483	25	.	.	PUNCT
ejpam-5641	484	1	consider	consider	VERB
ejpam-5641	484	2	the	the	DET
ejpam-5641	484	3	dynamical	dynamical	ADJ
ejpam-5641	484	4	system	system	NOUN
ejpam-5641	484	5	(	(	PUNCT
ejpam-5641	484	6	4	4	NUM
ejpam-5641	484	7	)	)	PUNCT
ejpam-5641	484	8	and	and	CCONJ
ejpam-5641	484	9	the	the	DET
ejpam-5641	484	10	mapping	mapping	NOUN
ejpam-5641	484	11	φ	φ	NOUN
ejpam-5641	484	12	:	:	PUNCT
ejpam-5641	484	13	(	(	PUNCT
ejpam-5641	484	14	γsf	γsf	X
ejpam-5641	484	15	(	(	PUNCT
ejpam-5641	484	16	(	(	PUNCT
ejpam-5641	484	17	1	1	NUM
ejpam-5641	484	18	(	(	PUNCT
ejpam-5641	484	19	u+1)f2u	u+1)f2u	NOUN
ejpam-5641	484	20	)	)	PUNCT
ejpam-5641	484	21	u∈n	u∈n	NOUN
ejpam-5641	484	22	,	,	PUNCT
ejpam-5641	484	23	(	(	PUNCT
ejpam-5641	484	24	2u+3	2u+3	NOUN
ejpam-5641	484	25	u+2	u+2	NOUN
ejpam-5641	484	26	)	)	PUNCT
ejpam-5641	484	27	u∈n	u∈n	NOUN
ejpam-5641	484	28	)	)	PUNCT
ejpam-5641	484	29	)	)	PUNCT
ejpam-5641	485	1	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	485	2	→	→	PUNCT
ejpam-5641	485	3	(	(	PUNCT
ejpam-5641	485	4	γsf	γsf	X
ejpam-5641	485	5	(	(	PUNCT
ejpam-5641	485	6	(	(	PUNCT
ejpam-5641	485	7	1	1	NUM
ejpam-5641	485	8	(	(	PUNCT
ejpam-5641	485	9	u+1)f2u	u+1)f2u	NOUN
ejpam-5641	485	10	)	)	PUNCT
ejpam-5641	485	11	u∈n	u∈n	NOUN
ejpam-5641	485	12	,	,	PUNCT
ejpam-5641	485	13	(	(	PUNCT
ejpam-5641	485	14	2u+3	2u+3	NOUN
ejpam-5641	485	15	u+2	u+2	NOUN
ejpam-5641	485	16	)	)	PUNCT
ejpam-5641	485	17	u∈n	u∈n	NOUN
ejpam-5641	485	18	)	)	PUNCT
ejpam-5641	485	19	)	)	PUNCT
ejpam-5641	485	20	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	485	21	as	as	SCONJ
ejpam-5641	485	22	defined	define	VERB
ejpam-5641	485	23	by	by	ADP
ejpam-5641	485	24	(	(	PUNCT
ejpam-5641	485	25	5	5	NUM
ejpam-5641	485	26	)	)	PUNCT
ejpam-5641	485	27	.	.	PUNCT
ejpam-5641	486	1	assume	assume	VERB
ejpam-5641	486	2	φ	φ	PROPN
ejpam-5641	486	3	is	be	AUX
ejpam-5641	486	4	∥.∥2p−qn	∥.∥2p−qn	NUM
ejpam-5641	486	5	-	-	PUNCT
ejpam-5641	486	6	seq.c	seq.c	PROPN
ejpam-5641	486	7	at	at	ADP
ejpam-5641	486	8	ẑ	ẑ	PROPN
ejpam-5641	486	9	∈	∈	PROPN
ejpam-5641	486	10	(	(	PUNCT
ejpam-5641	486	11	γsf	γsf	X
ejpam-5641	486	12	(	(	PUNCT
ejpam-5641	486	13	(	(	PUNCT
ejpam-5641	486	14	1	1	NUM
ejpam-5641	486	15	(	(	PUNCT
ejpam-5641	486	16	u+1)f2u	u+1)f2u	NOUN
ejpam-5641	486	17	)	)	PUNCT
ejpam-5641	486	18	u∈n	u∈n	NOUN
ejpam-5641	486	19	,	,	PUNCT
ejpam-5641	486	20	(	(	PUNCT
ejpam-5641	486	21	2u+3	2u+3	NOUN
ejpam-5641	486	22	u+2	u+2	NOUN
ejpam-5641	486	23	)	)	PUNCT
ejpam-5641	486	24	u∈n	u∈n	NOUN
ejpam-5641	486	25	)	)	PUNCT
ejpam-5641	486	26	)	)	PUNCT
ejpam-5641	486	27	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	486	28	,	,	PUNCT
ejpam-5641	486	29	and	and	CCONJ
ejpam-5641	486	30	one	one	NUM
ejpam-5641	486	31	has	have	VERB
ejpam-5641	486	32	ŷ	ŷ	NUM
ejpam-5641	486	33	∈	∈	NOUN
ejpam-5641	486	34	(	(	PUNCT
ejpam-5641	486	35	γsf	γsf	X
ejpam-5641	486	36	(	(	PUNCT
ejpam-5641	486	37	(	(	PUNCT
ejpam-5641	486	38	1	1	NUM
ejpam-5641	486	39	(	(	PUNCT
ejpam-5641	486	40	u+1)f2u	u+1)f2u	NOUN
ejpam-5641	486	41	)	)	PUNCT
ejpam-5641	486	42	u∈n	u∈n	NOUN
ejpam-5641	486	43	,	,	PUNCT
ejpam-5641	486	44	(	(	PUNCT
ejpam-5641	486	45	2u+3	2u+3	NOUN
ejpam-5641	486	46	u+2	u+2	NOUN
ejpam-5641	486	47	)	)	PUNCT
ejpam-5641	486	48	u∈n	u∈n	NOUN
ejpam-5641	486	49	)	)	PUNCT
ejpam-5641	486	50	)	)	PUNCT
ejpam-5641	486	51	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	486	52	with	with	ADP
ejpam-5641	486	53	{	{	PUNCT
ejpam-5641	486	54	φkŷ	φkŷ	NOUN
ejpam-5641	486	55	}	}	PUNCT
ejpam-5641	486	56	has	have	AUX
ejpam-5641	486	57	{	{	PUNCT
ejpam-5641	486	58	φkr	φkr	X
ejpam-5641	486	59	ŷ	ŷ	NUM
ejpam-5641	486	60	}	}	PUNCT
ejpam-5641	486	61	converging	converge	VERB
ejpam-5641	486	62	to	to	ADP
ejpam-5641	486	63	ẑ.	ẑ.	NOUN
ejpam-5641	486	64	clearly	clearly	ADV
ejpam-5641	486	65	,	,	PUNCT
ejpam-5641	486	66	there	there	PRON
ejpam-5641	486	67	are	be	VERB
ejpam-5641	486	68	εi	εi	NOUN
ejpam-5641	486	69	∈	∈	PROPN
ejpam-5641	486	70	r	r	NOUN
ejpam-5641	487	1	such	such	ADJ
ejpam-5641	487	2	that	that	DET
ejpam-5641	487	3	4	4	NUM
ejpam-5641	487	4	∑3	∑3	PROPN
ejpam-5641	487	5	i=1	i=1	PROPN
ejpam-5641	487	6	supu	supu	ADJ
ejpam-5641	487	7	|εi|	|εi|	VERB
ejpam-5641	487	8	2u+3	2u+3	PROPN
ejpam-5641	487	9	u+2	u+2	PROPN
ejpam-5641	487	10	∈	∈	PROPN
ejpam-5641	488	1	[	[	X
ejpam-5641	488	2	0	0	NUM
ejpam-5641	488	3	,	,	PUNCT
ejpam-5641	488	4	1	1	NUM
ejpam-5641	488	5	)	)	PUNCT
ejpam-5641	488	6	and	and	CCONJ
ejpam-5641	488	7	for	for	ADP
ejpam-5641	488	8	any	any	DET
ejpam-5641	488	9	u	u	PROPN
ejpam-5641	488	10	∈	∈	PROPN
ejpam-5641	488	11	n	n	NOUN
ejpam-5641	488	12	,	,	PUNCT
ejpam-5641	488	13	hence∣∣∣∣∣	hence∣∣∣∣∣	PROPN
ejpam-5641	488	14	u∑	u∑	X
ejpam-5641	488	15	d=0	d=0	X
ejpam-5641	488	16	(	(	PUNCT
ejpam-5641	488	17	∑	∑	PART
ejpam-5641	488	18	v∈n	v∈n	VERB
ejpam-5641	488	19	cosh	cosh	PROPN
ejpam-5641	488	20	d	d	PROPN
ejpam-5641	488	21	ν̂xd−2	ν̂xd−2	PROPN
ejpam-5641	488	22	ν̂yd−1	ν̂yd−1	PROPN
ejpam-5641	488	23	+	+	CCONJ
ejpam-5641	488	24	̂tanh(2v	̂tanh(2v	X
ejpam-5641	488	25	+	+	CCONJ
ejpam-5641	488	26	3	3	X
ejpam-5641	488	27	)	)	PUNCT
ejpam-5641	488	28	(	(	PUNCT
ejpam-5641	488	29	cos2	cos2	PROPN
ejpam-5641	488	30	v	v	ADP
ejpam-5641	488	31	−	−	PROPN
ejpam-5641	488	32	cos2	cos2	PROPN
ejpam-5641	488	33	v	v	NOUN
ejpam-5641	488	34	)	)	PUNCT
ejpam-5641	488	35	)	)	PUNCT
ejpam-5641	488	36	f2dqd	f2dqd	VERB
ejpam-5641	488	37	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5641	489	1	≤̂|ε1|	≤̂|ε1|	PROPN
ejpam-5641	489	2	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5641	489	3	u∑	u∑	X
ejpam-5641	489	4	d=0	d=0	X
ejpam-5641	490	1	(	(	PUNCT
ejpam-5641	490	2	̂log2(d	̂log2(d	ADP
ejpam-5641	490	3	4	4	NUM
ejpam-5641	491	1	+	+	SYM
ejpam-5641	491	2	1)−	1)−	NUM
ejpam-5641	491	3	ν̂d	ν̂d	X
ejpam-5641	491	4	+	+	CCONJ
ejpam-5641	491	5	∑	∑	PART
ejpam-5641	491	6	v∈n	v∈n	NOUN
ejpam-5641	491	7	cosh	cosh	NOUN
ejpam-5641	491	8	d	d	PROPN
ejpam-5641	491	9	cos2	cos2	PROPN
ejpam-5641	491	10	v	v	PROPN
ejpam-5641	491	11	ν̂xd−2	ν̂xd−2	PROPN
ejpam-5641	491	12	ν̂yd−1	ν̂yd−1	PROPN
ejpam-5641	492	1	+	+	CCONJ
ejpam-5641	492	2	̂tanh(2v	̂tanh(2v	X
ejpam-5641	492	3	+	+	CCONJ
ejpam-5641	492	4	3	3	NUM
ejpam-5641	492	5	)	)	PUNCT
ejpam-5641	492	6	)	)	PUNCT
ejpam-5641	492	7	f2dqd	f2dqd	VERB
ejpam-5641	492	8	∣∣∣∣∣+	∣∣∣∣∣+	NOUN
ejpam-5641	492	9	|ε2|	|ε2|	NOUN
ejpam-5641	492	10	∣∣∣∣∣	∣∣∣∣∣	ADP
ejpam-5641	492	11	u∑	u∑	PROPN
ejpam-5641	492	12	d=0	d=0	X
ejpam-5641	492	13	(	(	PUNCT
ejpam-5641	492	14	̂log2(d	̂log2(d	ADP
ejpam-5641	492	15	4	4	NUM
ejpam-5641	493	1	+	+	SYM
ejpam-5641	493	2	1)−	1)−	PROPN
ejpam-5641	493	3	η̂d	η̂d	PART
ejpam-5641	493	4	+	+	CCONJ
ejpam-5641	493	5	∑	∑	PART
ejpam-5641	493	6	v∈n	v∈n	NOUN
ejpam-5641	493	7	cosh	cosh	NOUN
ejpam-5641	493	8	d	d	PROPN
ejpam-5641	493	9	cos2	cos2	PROPN
ejpam-5641	493	10	v	v	PROPN
ejpam-5641	493	11	η̂xd−2	η̂xd−2	PROPN
ejpam-5641	493	12	η̂yd−1	η̂yd−1	NOUN
ejpam-5641	493	13	+	+	CCONJ
ejpam-5641	493	14	̂tanh(2v	̂tanh(2v	X
ejpam-5641	493	15	+	+	CCONJ
ejpam-5641	493	16	3	3	NUM
ejpam-5641	493	17	)	)	PUNCT
ejpam-5641	493	18	)	)	PUNCT
ejpam-5641	493	19	f2dqd	f2dqd	VERB
ejpam-5641	493	20	∣∣∣∣∣+	∣∣∣∣∣+	PROPN
ejpam-5641	493	21	|ε3||	|ε3||	PROPN
ejpam-5641	493	22	u∑	u∑	PROPN
ejpam-5641	493	23	d=0	d=0	X
ejpam-5641	493	24	(	(	PUNCT
ejpam-5641	493	25	ν̂d	ν̂d	X
ejpam-5641	493	26	−	−	ADV
ejpam-5641	493	27	η̂d	η̂d	NOUN
ejpam-5641	493	28	)	)	PUNCT
ejpam-5641	493	29	f	f	PROPN
ejpam-5641	493	30	2	2	NUM
ejpam-5641	493	31	dqd|	dqd|	NOUN
ejpam-5641	493	32	.	.	PUNCT
ejpam-5641	494	1	in	in	ADP
ejpam-5641	494	2	view	view	NOUN
ejpam-5641	494	3	of	of	ADP
ejpam-5641	494	4	theorem	theorem	NOUN
ejpam-5641	494	5	5.3	5.3	NUM
ejpam-5641	494	6	,	,	PUNCT
ejpam-5641	494	7	the	the	DET
ejpam-5641	494	8	dynamical	dynamical	ADJ
ejpam-5641	494	9	systems	system	NOUN
ejpam-5641	494	10	(	(	PUNCT
ejpam-5641	494	11	4	4	X
ejpam-5641	494	12	)	)	PUNCT
ejpam-5641	494	13	have	have	VERB
ejpam-5641	494	14	a	a	DET
ejpam-5641	494	15	unique	unique	ADJ
ejpam-5641	494	16	solution	solution	NOUN
ejpam-5641	494	17	ẑ	ẑ	X
ejpam-5641	494	18	∈	∈	PROPN
ejpam-5641	494	19	(	(	PUNCT
ejpam-5641	494	20	γsf	γsf	X
ejpam-5641	494	21	(	(	PUNCT
ejpam-5641	494	22	(	(	PUNCT
ejpam-5641	494	23	1	1	NUM
ejpam-5641	494	24	(	(	PUNCT
ejpam-5641	494	25	u+1)f2u	u+1)f2u	NOUN
ejpam-5641	494	26	)	)	PUNCT
ejpam-5641	494	27	u∈n	u∈n	NOUN
ejpam-5641	494	28	,	,	PUNCT
ejpam-5641	494	29	(	(	PUNCT
ejpam-5641	494	30	2u+3	2u+3	NOUN
ejpam-5641	494	31	u+2	u+2	NOUN
ejpam-5641	494	32	)	)	PUNCT
ejpam-5641	494	33	u∈n	u∈n	NOUN
ejpam-5641	494	34	)	)	PUNCT
ejpam-5641	494	35	)	)	PUNCT
ejpam-5641	494	36	∥.∥2p−qn	∥.∥2p−qn	PRON
ejpam-5641	494	37	.	.	PUNCT
ejpam-5641	495	1	m.	m.	NOUN
ejpam-5641	495	2	m.	m.	PROPN
ejpam-5641	495	3	a	a	PRON
ejpam-5641	495	4	et	et	PROPN
ejpam-5641	495	5	al	al	PROPN
ejpam-5641	495	6	.	.	PUNCT
ejpam-5641	495	7	/	/	SYM
ejpam-5641	495	8	eur	eur	PROPN
ejpam-5641	495	9	.	.	PUNCT
ejpam-5641	496	1	j.	j.	PROPN
ejpam-5641	496	2	pure	pure	PROPN
ejpam-5641	496	3	appl	appl	PROPN
ejpam-5641	496	4	.	.	PROPN
ejpam-5641	496	5	math	math	PROPN
ejpam-5641	496	6	,	,	PUNCT
ejpam-5641	496	7	18	18	NUM
ejpam-5641	496	8	(	(	PUNCT
ejpam-5641	496	9	1	1	NUM
ejpam-5641	496	10	)	)	PUNCT
ejpam-5641	496	11	(	(	PUNCT
ejpam-5641	496	12	2025	2025	NUM
ejpam-5641	496	13	)	)	PUNCT
ejpam-5641	496	14	,	,	PUNCT
ejpam-5641	496	15	5641	5641	NUM
ejpam-5641	496	16	19	19	NUM
ejpam-5641	496	17	of	of	ADP
ejpam-5641	496	18	20	20	NUM
ejpam-5641	496	19	6	6	NUM
ejpam-5641	496	20	.	.	PUNCT
ejpam-5641	497	1	conclusion	conclusion	NOUN
ejpam-5641	497	2	in	in	ADP
ejpam-5641	497	3	this	this	DET
ejpam-5641	497	4	article	article	NOUN
ejpam-5641	498	1	,	,	PUNCT
ejpam-5641	498	2	we	we	PRON
ejpam-5641	498	3	discussed	discuss	VERB
ejpam-5641	498	4	several	several	ADJ
ejpam-5641	498	5	topological	topological	ADJ
ejpam-5641	498	6	and	and	CCONJ
ejpam-5641	498	7	geometric	geometric	ADJ
ejpam-5641	498	8	characteristics	characteristic	NOUN
ejpam-5641	498	9	of	of	ADP
ejpam-5641	498	10	(	(	PUNCT
ejpam-5641	498	11	γsf	γsf	X
ejpam-5641	498	12	(	(	PUNCT
ejpam-5641	498	13	q	q	NOUN
ejpam-5641	498	14	,	,	PUNCT
ejpam-5641	498	15	t	t	PROPN
ejpam-5641	498	16	)	)	PUNCT
ejpam-5641	498	17	)	)	PUNCT
ejpam-5641	499	1	∥.∥p−qn	∥.∥p−qn	PROPN
ejpam-5641	499	2	.	.	PUNCT
ejpam-5641	500	1	analyzed	analyze	VERB
ejpam-5641	500	2	is	be	AUX
ejpam-5641	500	3	the	the	DET
ejpam-5641	500	4	novel	novel	ADJ
ejpam-5641	500	5	kannan	kannan	PROPN
ejpam-5641	500	6	contraction	contraction	NOUN
ejpam-5641	500	7	operator	operator	NOUN
ejpam-5641	500	8	in	in	ADP
ejpam-5641	500	9	this	this	DET
ejpam-5641	500	10	space	space	NOUN
ejpam-5641	500	11	,	,	PUNCT
ejpam-5641	500	12	along	along	ADP
ejpam-5641	500	13	with	with	ADP
ejpam-5641	500	14	the	the	DET
ejpam-5641	500	15	potential	potential	NOUN
ejpam-5641	500	16	for	for	ADP
ejpam-5641	500	17	a	a	DET
ejpam-5641	500	18	fixed	fix	VERB
ejpam-5641	500	19	point	point	NOUN
ejpam-5641	500	20	.	.	PUNCT
ejpam-5641	501	1	we	we	PRON
ejpam-5641	501	2	conducted	conduct	VERB
ejpam-5641	501	3	numerous	numerous	ADJ
ejpam-5641	501	4	numerical	numerical	ADJ
ejpam-5641	501	5	experiments	experiment	NOUN
ejpam-5641	501	6	to	to	PART
ejpam-5641	501	7	validate	validate	VERB
ejpam-5641	501	8	our	our	PRON
ejpam-5641	501	9	theories	theory	NOUN
ejpam-5641	501	10	.	.	PUNCT
ejpam-5641	502	1	investigations	investigation	NOUN
ejpam-5641	502	2	are	be	AUX
ejpam-5641	502	3	conducted	conduct	VERB
ejpam-5641	502	4	on	on	ADP
ejpam-5641	502	5	soft	soft	ADJ
ejpam-5641	502	6	functions	function	NOUN
ejpam-5641	502	7	with	with	ADP
ejpam-5641	502	8	non	non	ADJ
ejpam-5641	502	9	-	-	ADJ
ejpam-5641	502	10	linear	linear	ADJ
ejpam-5641	502	11	uncertainty	uncertainty	NOUN
ejpam-5641	502	12	equation	equation	NOUN
ejpam-5641	502	13	implementations	implementation	NOUN
ejpam-5641	502	14	.	.	PUNCT
ejpam-5641	503	1	future	future	ADJ
ejpam-5641	503	2	work	work	NOUN
ejpam-5641	503	3	uses	use	VERB
ejpam-5641	503	4	the	the	DET
ejpam-5641	503	5	innovative	innovative	ADJ
ejpam-5641	503	6	soft	soft	ADJ
ejpam-5641	503	7	function	function	NOUN
ejpam-5641	503	8	space	space	NOUN
ejpam-5641	503	9	to	to	PART
ejpam-5641	503	10	analyze	analyze	VERB
ejpam-5641	503	11	the	the	DET
ejpam-5641	503	12	fixed	fix	VERB
ejpam-5641	503	13	points	point	NOUN
ejpam-5641	503	14	of	of	ADP
ejpam-5641	503	15	the	the	DET
ejpam-5641	503	16	new	new	ADJ
ejpam-5641	503	17	type	type	NOUN
ejpam-5641	503	18	of	of	ADP
ejpam-5641	503	19	kannan	kannan	PROPN
ejpam-5641	503	20	contraction	contraction	NOUN
ejpam-5641	503	21	operator	operator	NOUN
ejpam-5641	503	22	,	,	PUNCT
ejpam-5641	503	23	providing	provide	VERB
ejpam-5641	503	24	a	a	DET
ejpam-5641	503	25	new	new	ADJ
ejpam-5641	503	26	universal	universal	ADJ
ejpam-5641	503	27	solution	solution	NOUN
ejpam-5641	503	28	space	space	NOUN
ejpam-5641	503	29	for	for	ADP
ejpam-5641	503	30	a	a	DET
ejpam-5641	503	31	variety	variety	NOUN
ejpam-5641	503	32	of	of	ADP
ejpam-5641	503	33	stochastic	stochastic	ADJ
ejpam-5641	503	34	non	non	ADJ
ejpam-5641	503	35	-	-	ADJ
ejpam-5641	503	36	linear	linear	ADJ
ejpam-5641	503	37	dynamical	dynamical	ADJ
ejpam-5641	503	38	systems	system	NOUN
ejpam-5641	503	39	.	.	PUNCT
ejpam-5641	504	1	acknowledgements	acknowledgement	NOUN
ejpam-5641	504	2	this	this	DET
ejpam-5641	504	3	work	work	NOUN
ejpam-5641	504	4	was	be	AUX
ejpam-5641	504	5	funded	fund	VERB
ejpam-5641	504	6	by	by	ADP
ejpam-5641	504	7	the	the	DET
ejpam-5641	504	8	university	university	PROPN
ejpam-5641	504	9	of	of	ADP
ejpam-5641	504	10	jeddah	jeddah	PROPN
ejpam-5641	504	11	,	,	PUNCT
ejpam-5641	504	12	jeddah	jeddah	PROPN
ejpam-5641	504	13	,	,	PUNCT
ejpam-5641	504	14	saudi	saudi	PROPN
ejpam-5641	504	15	arabia	arabia	PROPN
ejpam-5641	504	16	,	,	PUNCT
ejpam-5641	504	17	under	under	ADP
ejpam-5641	504	18	grant	grant	NOUN
ejpam-5641	504	19	no	no	NOUN
ejpam-5641	504	20	.	.	PUNCT
ejpam-5641	505	1	(	(	PUNCT
ejpam-5641	505	2	uj-23	uj-23	NOUN
ejpam-5641	505	3	-	-	PUNCT
ejpam-5641	505	4	dr-33	dr-33	NUM
ejpam-5641	505	5	)	)	PUNCT
ejpam-5641	505	6	.	.	PUNCT
ejpam-5641	506	1	therefore	therefore	ADV
ejpam-5641	506	2	,	,	PUNCT
ejpam-5641	506	3	the	the	DET
ejpam-5641	506	4	authors	author	NOUN
ejpam-5641	506	5	thank	thank	VERB
ejpam-5641	506	6	the	the	DET
ejpam-5641	506	7	university	university	NOUN
ejpam-5641	506	8	of	of	ADP
ejpam-5641	506	9	jeddah	jeddah	PROPN
ejpam-5641	506	10	for	for	ADP
ejpam-5641	506	11	its	its	PRON
ejpam-5641	506	12	technical	technical	ADJ
ejpam-5641	506	13	and	and	CCONJ
ejpam-5641	506	14	financial	financial	ADJ
ejpam-5641	506	15	support	support	NOUN
ejpam-5641	506	16	.	.	PUNCT
ejpam-5641	507	1	references	reference	NOUN
ejpam-5641	507	2	[	[	X
ejpam-5641	507	3	1	1	NUM
ejpam-5641	507	4	]	]	PUNCT
ejpam-5641	507	5	h.	h.	PROPN
ejpam-5641	507	6	ahmad	ahmad	PROPN
ejpam-5641	507	7	,	,	PUNCT
ejpam-5641	507	8	m.	m.	NOUN
ejpam-5641	507	9	younis	younis	PROPN
ejpam-5641	507	10	,	,	PUNCT
ejpam-5641	507	11	and	and	CCONJ
ejpam-5641	507	12	m.e	m.e	PROPN
ejpam-5641	507	13	.	.	PROPN
ejpam-5641	507	14	koksal	koksal	PROPN
ejpam-5641	507	15	.	.	PUNCT
ejpam-5641	508	1	double	double	PROPN
ejpam-5641	508	2	controlled	control	VERB
ejpam-5641	508	3	partial	partial	ADJ
ejpam-5641	508	4	metric	metric	ADJ
ejpam-5641	508	5	type	type	NOUN
ejpam-5641	508	6	spaces	space	NOUN
ejpam-5641	508	7	and	and	CCONJ
ejpam-5641	508	8	convergence	convergence	NOUN
ejpam-5641	508	9	results	result	NOUN
ejpam-5641	508	10	.	.	PUNCT
ejpam-5641	509	1	journal	journal	NOUN
ejpam-5641	509	2	of	of	ADP
ejpam-5641	509	3	mathematics	mathematic	NOUN
ejpam-5641	509	4	,	,	PUNCT
ejpam-5641	509	5	2021	2021	NUM
ejpam-5641	509	6	.	.	PUNCT
ejpam-5641	510	1	[	[	X
ejpam-5641	510	2	2	2	NUM
ejpam-5641	510	3	]	]	X
ejpam-5641	510	4	s.h	s.h	PROPN
ejpam-5641	510	5	.	.	PROPN
ejpam-5641	510	6	et	et	PROPN
ejpam-5641	510	7	al	al	PROPN
ejpam-5641	510	8	.	.	PROPN
ejpam-5641	510	9	alshabhi	alshabhi	PROPN
ejpam-5641	510	10	.	.	PUNCT
ejpam-5641	511	1	decision	decision	NOUN
ejpam-5641	511	2	-	-	PUNCT
ejpam-5641	511	3	making	making	NOUN
ejpam-5641	511	4	of	of	ADP
ejpam-5641	511	5	fredholm	fredholm	NOUN
ejpam-5641	511	6	operator	operator	NOUN
ejpam-5641	511	7	on	on	ADP
ejpam-5641	511	8	a	a	DET
ejpam-5641	511	9	new	new	ADJ
ejpam-5641	511	10	variable	variable	ADJ
ejpam-5641	511	11	exponents	exponent	NOUN
ejpam-5641	511	12	sequence	sequence	NOUN
ejpam-5641	511	13	space	space	NOUN
ejpam-5641	511	14	of	of	ADP
ejpam-5641	511	15	supply	supply	NOUN
ejpam-5641	511	16	fuzzy	fuzzy	ADJ
ejpam-5641	511	17	functions	function	NOUN
ejpam-5641	511	18	defined	define	VERB
ejpam-5641	511	19	by	by	ADP
ejpam-5641	511	20	leonardo	leonardo	PROPN
ejpam-5641	511	21	numbers	number	NOUN
ejpam-5641	511	22	.	.	PUNCT
ejpam-5641	512	1	contemporary	contemporary	ADJ
ejpam-5641	512	2	mathematics	mathematic	NOUN
ejpam-5641	512	3	,	,	PUNCT
ejpam-5641	512	4	2024	2024	NUM
ejpam-5641	512	5	.	.	PUNCT
ejpam-5641	513	1	[	[	X
ejpam-5641	513	2	3	3	X
ejpam-5641	513	3	]	]	X
ejpam-5641	513	4	meshayil	meshayil	PROPN
ejpam-5641	513	5	m.	m.	PROPN
ejpam-5641	513	6	alsolmi	alsolmi	PROPN
ejpam-5641	513	7	,	,	PUNCT
ejpam-5641	513	8	arafa	arafa	PROPN
ejpam-5641	513	9	o.	o.	PROPN
ejpam-5641	513	10	mustafa	mustafa	PROPN
ejpam-5641	513	11	,	,	PUNCT
ejpam-5641	513	12	om	om	PROPN
ejpam-5641	513	13	kalthum	kalthum	PROPN
ejpam-5641	513	14	s.	s.	PROPN
ejpam-5641	513	15	k.	k.	PROPN
ejpam-5641	513	16	mohamed	mohamed	PROPN
ejpam-5641	513	17	,	,	PUNCT
ejpam-5641	513	18	and	and	CCONJ
ejpam-5641	513	19	awad	awad	PROPN
ejpam-5641	513	20	a.	a.	PROPN
ejpam-5641	513	21	bakery	bakery	PROPN
ejpam-5641	513	22	.	.	PUNCT
ejpam-5641	514	1	prequasiideal	prequasiideal	NOUN
ejpam-5641	514	2	of	of	ADP
ejpam-5641	514	3	the	the	DET
ejpam-5641	514	4	type	type	NOUN
ejpam-5641	514	5	weighted	weight	VERB
ejpam-5641	514	6	binomial	binomial	ADJ
ejpam-5641	514	7	matrices	matrix	NOUN
ejpam-5641	514	8	in	in	ADP
ejpam-5641	514	9	the	the	DET
ejpam-5641	514	10	nakano	nakano	NOUN
ejpam-5641	514	11	sequence	sequence	NOUN
ejpam-5641	514	12	space	space	NOUN
ejpam-5641	514	13	of	of	ADP
ejpam-5641	514	14	soft	soft	ADJ
ejpam-5641	514	15	functions	function	NOUN
ejpam-5641	514	16	with	with	ADP
ejpam-5641	514	17	some	some	DET
ejpam-5641	514	18	applications	application	NOUN
ejpam-5641	514	19	.	.	PUNCT
ejpam-5641	515	1	journal	journal	PROPN
ejpam-5641	515	2	of	of	ADP
ejpam-5641	515	3	inequalities	inequality	NOUN
ejpam-5641	515	4	and	and	CCONJ
ejpam-5641	515	5	applications	application	NOUN
ejpam-5641	515	6	,	,	PUNCT
ejpam-5641	515	7	2022:152	2022:152	NUM
ejpam-5641	515	8	,	,	PUNCT
ejpam-5641	515	9	2022	2022	NUM
ejpam-5641	515	10	.	.	PUNCT
ejpam-5641	516	1	[	[	X
ejpam-5641	516	2	4	4	NUM
ejpam-5641	516	3	]	]	X
ejpam-5641	516	4	m.m	m.m	PROPN
ejpam-5641	516	5	.	.	PROPN
ejpam-5641	516	6	alsolmi	alsolmi	PROPN
ejpam-5641	516	7	and	and	CCONJ
ejpam-5641	516	8	a.a	a.a	PROPN
ejpam-5641	516	9	.	.	PROPN
ejpam-5641	516	10	bakery	bakery	PROPN
ejpam-5641	516	11	.	.	PUNCT
ejpam-5641	517	1	decision	decision	NOUN
ejpam-5641	517	2	-	-	PUNCT
ejpam-5641	517	3	making	making	NOUN
ejpam-5641	517	4	on	on	ADP
ejpam-5641	517	5	the	the	DET
ejpam-5641	517	6	solution	solution	NOUN
ejpam-5641	517	7	of	of	ADP
ejpam-5641	517	8	a	a	DET
ejpam-5641	517	9	stochastic	stochastic	ADJ
ejpam-5641	517	10	nonlinear	nonlinear	ADJ
ejpam-5641	517	11	dynamical	dynamical	ADJ
ejpam-5641	517	12	system	system	NOUN
ejpam-5641	517	13	of	of	ADP
ejpam-5641	517	14	kannan	kannan	PROPN
ejpam-5641	517	15	-	-	PUNCT
ejpam-5641	517	16	type	type	NOUN
ejpam-5641	517	17	in	in	ADP
ejpam-5641	517	18	new	new	ADJ
ejpam-5641	517	19	sequence	sequence	NOUN
ejpam-5641	517	20	space	space	NOUN
ejpam-5641	517	21	of	of	ADP
ejpam-5641	517	22	soft	soft	ADJ
ejpam-5641	517	23	functions	function	NOUN
ejpam-5641	517	24	.	.	PUNCT
ejpam-5641	518	1	j.	j.	PROPN
ejpam-5641	518	2	funct	funct	PROPN
ejpam-5641	518	3	.	.	PUNCT
ejpam-5641	519	1	spaces	space	NOUN
ejpam-5641	519	2	,	,	PUNCT
ejpam-5641	519	3	2022	2022	NUM
ejpam-5641	519	4	.	.	PUNCT
ejpam-5641	520	1	[	[	X
ejpam-5641	520	2	5	5	X
ejpam-5641	520	3	]	]	PUNCT
ejpam-5641	520	4	b.	b.	NOUN
ejpam-5641	520	5	altay	altay	NOUN
ejpam-5641	520	6	and	and	CCONJ
ejpam-5641	520	7	f.	f.	PROPN
ejpam-5641	520	8	başar	başar	PROPN
ejpam-5641	520	9	.	.	PUNCT
ejpam-5641	521	1	generalization	generalization	NOUN
ejpam-5641	521	2	of	of	ADP
ejpam-5641	521	3	the	the	DET
ejpam-5641	521	4	sequence	sequence	NOUN
ejpam-5641	521	5	space	space	NOUN
ejpam-5641	521	6	ℓ(p	ℓ(p	NOUN
ejpam-5641	521	7	)	)	PUNCT
ejpam-5641	521	8	derived	derive	VERB
ejpam-5641	521	9	by	by	ADP
ejpam-5641	521	10	weighted	weight	VERB
ejpam-5641	521	11	means	mean	NOUN
ejpam-5641	521	12	.	.	PUNCT
ejpam-5641	522	1	j.	j.	PROPN
ejpam-5641	522	2	math	math	PROPN
ejpam-5641	522	3	.	.	PUNCT
ejpam-5641	523	1	anal	anal	PROPN
ejpam-5641	523	2	.	.	PUNCT
ejpam-5641	523	3	appl	appl	PROPN
ejpam-5641	523	4	.	.	PROPN
ejpam-5641	523	5	,	,	PUNCT
ejpam-5641	524	1	330(1):147–185	330(1):147–185	NUM
ejpam-5641	524	2	,	,	PUNCT
ejpam-5641	524	3	2007	2007	NUM
ejpam-5641	524	4	.	.	PUNCT
ejpam-5641	525	1	[	[	X
ejpam-5641	525	2	6	6	NUM
ejpam-5641	525	3	]	]	PUNCT
ejpam-5641	525	4	s.	s.	PROPN
ejpam-5641	525	5	das	das	PROPN
ejpam-5641	525	6	and	and	CCONJ
ejpam-5641	525	7	s.k	s.k	PROPN
ejpam-5641	525	8	.	.	PROPN
ejpam-5641	525	9	samanta	samanta	PROPN
ejpam-5641	525	10	.	.	PUNCT
ejpam-5641	525	11	soft	soft	ADJ
ejpam-5641	525	12	metric	metric	NOUN
ejpam-5641	525	13	.	.	PUNCT
ejpam-5641	526	1	ann	ann	PROPN
ejpam-5641	526	2	.	.	PUNCT
ejpam-5641	526	3	fuzzy	fuzzy	ADJ
ejpam-5641	526	4	math	math	NOUN
ejpam-5641	526	5	.	.	PUNCT
ejpam-5641	527	1	inform	inform	NOUN
ejpam-5641	527	2	.	.	PUNCT
ejpam-5641	527	3	,	,	PUNCT
ejpam-5641	527	4	6:77–94	6:77–94	NUM
ejpam-5641	527	5	,	,	PUNCT
ejpam-5641	527	6	2013	2013	NUM
ejpam-5641	527	7	.	.	PUNCT
ejpam-5641	528	1	[	[	X
ejpam-5641	528	2	7	7	X
ejpam-5641	528	3	]	]	X
ejpam-5641	528	4	l.	l.	PROPN
ejpam-5641	528	5	diening	diening	PROPN
ejpam-5641	528	6	,	,	PUNCT
ejpam-5641	528	7	p.	p.	PROPN
ejpam-5641	528	8	harjulehto	harjulehto	PROPN
ejpam-5641	528	9	,	,	PUNCT
ejpam-5641	528	10	p.	p.	NOUN
ejpam-5641	528	11	hästö	hästö	PROPN
ejpam-5641	528	12	,	,	PUNCT
ejpam-5641	528	13	and	and	CCONJ
ejpam-5641	528	14	m.	m.	NOUN
ejpam-5641	528	15	ruẑiĉka	ruẑiĉka	PROPN
ejpam-5641	528	16	.	.	PROPN
ejpam-5641	529	1	lebesgue	lebesgue	PROPN
ejpam-5641	529	2	and	and	CCONJ
ejpam-5641	529	3	sobolev	sobolev	NOUN
ejpam-5641	529	4	spaces	space	NOUN
ejpam-5641	529	5	with	with	ADP
ejpam-5641	529	6	variable	variable	ADJ
ejpam-5641	529	7	exponents	exponent	NOUN
ejpam-5641	529	8	.	.	PUNCT
ejpam-5641	530	1	springer	springer	NOUN
ejpam-5641	530	2	,	,	PUNCT
ejpam-5641	530	3	berlin	berlin	PROPN
ejpam-5641	530	4	,	,	PUNCT
ejpam-5641	530	5	2011	2011	NUM
ejpam-5641	530	6	.	.	PUNCT
ejpam-5641	531	1	[	[	X
ejpam-5641	531	2	8	8	NUM
ejpam-5641	531	3	]	]	X
ejpam-5641	531	4	mutti	mutti	PROPN
ejpam-5641	531	5	-	-	PUNCT
ejpam-5641	531	6	ur	ur	PROPN
ejpam-5641	531	7	rehman	rehman	PROPN
ejpam-5641	531	8	et	et	PROPN
ejpam-5641	531	9	al	al	PROPN
ejpam-5641	531	10	.	.	PROPN
ejpam-5641	531	11	spectrum	spectrum	PROPN
ejpam-5641	531	12	and	and	CCONJ
ejpam-5641	531	13	pseudspectrum	pseudspectrum	NOUN
ejpam-5641	531	14	of	of	ADP
ejpam-5641	531	15	d	d	ADJ
ejpam-5641	531	16	-	-	ADJ
ejpam-5641	531	17	stable	stable	ADJ
ejpam-5641	531	18	matrices	matrix	NOUN
ejpam-5641	531	19	of	of	ADP
ejpam-5641	531	20	economy	economy	NOUN
ejpam-5641	531	21	models	model	NOUN
ejpam-5641	531	22	.	.	PUNCT
ejpam-5641	532	1	j.	j.	PROPN
ejpam-5641	532	2	math	math	PROPN
ejpam-5641	532	3	.	.	PUNCT
ejpam-5641	533	1	computer	computer	PROPN
ejpam-5641	533	2	sci	sci	PROPN
ejpam-5641	533	3	.	.	PROPN
ejpam-5641	533	4	,	,	PUNCT
ejpam-5641	533	5	38:298–312	38:298–312	NUM
ejpam-5641	533	6	,	,	PUNCT
ejpam-5641	533	7	2025	2025	NUM
ejpam-5641	533	8	.	.	PUNCT
ejpam-5641	534	1	[	[	X
ejpam-5641	534	2	9	9	NUM
ejpam-5641	534	3	]	]	PUNCT
ejpam-5641	534	4	l.	l.	PROPN
ejpam-5641	534	5	guo	guo	PROPN
ejpam-5641	534	6	and	and	CCONJ
ejpam-5641	534	7	q.	q.	PROPN
ejpam-5641	534	8	zhu	zhu	PROPN
ejpam-5641	534	9	.	.	PUNCT
ejpam-5641	535	1	stability	stability	NOUN
ejpam-5641	535	2	analysis	analysis	NOUN
ejpam-5641	535	3	for	for	ADP
ejpam-5641	535	4	stochastic	stochastic	ADJ
ejpam-5641	535	5	volterra	volterra	NOUN
ejpam-5641	535	6	–	–	PUNCT
ejpam-5641	535	7	levin	levin	PROPN
ejpam-5641	535	8	equations	equation	NOUN
ejpam-5641	535	9	with	with	ADP
ejpam-5641	535	10	poisson	poisson	PROPN
ejpam-5641	535	11	jumps	jump	VERB
ejpam-5641	535	12	:	:	PUNCT
ejpam-5641	535	13	fixed	fix	VERB
ejpam-5641	535	14	point	point	NOUN
ejpam-5641	535	15	approach	approach	NOUN
ejpam-5641	535	16	.	.	PUNCT
ejpam-5641	536	1	journal	journal	PROPN
ejpam-5641	536	2	of	of	ADP
ejpam-5641	536	3	mathematical	mathematical	ADJ
ejpam-5641	536	4	physics	physics	NOUN
ejpam-5641	536	5	,	,	PUNCT
ejpam-5641	536	6	52:042702	52:042702	NUM
ejpam-5641	536	7	,	,	PUNCT
ejpam-5641	536	8	2011	2011	NUM
ejpam-5641	536	9	.	.	PUNCT
ejpam-5641	537	1	[	[	X
ejpam-5641	537	2	10	10	NUM
ejpam-5641	537	3	]	]	X
ejpam-5641	537	4	m.b	m.b	PROPN
ejpam-5641	537	5	.	.	PROPN
ejpam-5641	537	6	kadirovich	kadirovich	PROPN
ejpam-5641	537	7	and	and	CCONJ
ejpam-5641	537	8	m.a.z	m.a.z	PROPN
ejpam-5641	537	9	.	.	PROPN
ejpam-5641	538	1	kudratovich	kudratovich	PROPN
ejpam-5641	538	2	.	.	PUNCT
ejpam-5641	539	1	integral	integral	ADJ
ejpam-5641	539	2	and	and	CCONJ
ejpam-5641	539	3	its	its	PRON
ejpam-5641	539	4	applications	application	NOUN
ejpam-5641	539	5	.	.	PUNCT
ejpam-5641	540	1	international	international	ADJ
ejpam-5641	540	2	journal	journal	PROPN
ejpam-5641	540	3	of	of	ADP
ejpam-5641	540	4	artificial	artificial	ADJ
ejpam-5641	540	5	intelligence	intelligence	NOUN
ejpam-5641	540	6	,	,	PUNCT
ejpam-5641	540	7	4(10):299–304	4(10):299–304	NUM
ejpam-5641	540	8	,	,	PUNCT
ejpam-5641	540	9	2024	2024	NUM
ejpam-5641	540	10	.	.	PUNCT
ejpam-5641	541	1	m.	m.	NOUN
ejpam-5641	541	2	m.	m.	NOUN
ejpam-5641	541	3	a	a	PRON
ejpam-5641	541	4	et	et	PROPN
ejpam-5641	541	5	al	al	PROPN
ejpam-5641	541	6	.	.	PUNCT
ejpam-5641	541	7	/	/	SYM
ejpam-5641	541	8	eur	eur	PROPN
ejpam-5641	541	9	.	.	PUNCT
ejpam-5641	542	1	j.	j.	PROPN
ejpam-5641	542	2	pure	pure	PROPN
ejpam-5641	542	3	appl	appl	PROPN
ejpam-5641	542	4	.	.	PROPN
ejpam-5641	542	5	math	math	PROPN
ejpam-5641	542	6	,	,	PUNCT
ejpam-5641	542	7	18	18	NUM
ejpam-5641	542	8	(	(	PUNCT
ejpam-5641	542	9	1	1	NUM
ejpam-5641	542	10	)	)	PUNCT
ejpam-5641	542	11	(	(	PUNCT
ejpam-5641	542	12	2025	2025	NUM
ejpam-5641	542	13	)	)	PUNCT
ejpam-5641	542	14	,	,	PUNCT
ejpam-5641	542	15	5641	5641	NUM
ejpam-5641	542	16	20	20	NUM
ejpam-5641	542	17	of	of	ADP
ejpam-5641	542	18	20	20	NUM
ejpam-5641	543	1	[	[	SYM
ejpam-5641	543	2	11	11	NUM
ejpam-5641	543	3	]	]	X
ejpam-5641	543	4	e.e	e.e	PROPN
ejpam-5641	543	5	.	.	PROPN
ejpam-5641	543	6	kara	kara	PROPN
ejpam-5641	543	7	and	and	CCONJ
ejpam-5641	543	8	m.	m.	PROPN
ejpam-5641	543	9	başarı	başarı	PROPN
ejpam-5641	543	10	r.	r.	VERB
ejpam-5641	543	11	an	an	DET
ejpam-5641	543	12	application	application	NOUN
ejpam-5641	543	13	of	of	ADP
ejpam-5641	543	14	fibonacci	fibonacci	NOUN
ejpam-5641	543	15	numbers	number	NOUN
ejpam-5641	543	16	into	into	ADP
ejpam-5641	543	17	infinite	infinite	ADJ
ejpam-5641	543	18	toeplitz	toeplitz	NOUN
ejpam-5641	543	19	matrices	matrix	NOUN
ejpam-5641	543	20	.	.	PUNCT
ejpam-5641	544	1	caspian	caspian	PROPN
ejpam-5641	544	2	j.	j.	PROPN
ejpam-5641	544	3	math	math	PROPN
ejpam-5641	544	4	.	.	PUNCT
ejpam-5641	544	5	,	,	PUNCT
ejpam-5641	544	6	1(1):43–47	1(1):43–47	NUM
ejpam-5641	544	7	,	,	PUNCT
ejpam-5641	544	8	2012	2012	NUM
ejpam-5641	544	9	.	.	PUNCT
ejpam-5641	545	1	[	[	X
ejpam-5641	545	2	12	12	NUM
ejpam-5641	545	3	]	]	X
ejpam-5641	545	4	t.	t.	PROPN
ejpam-5641	545	5	koshy	koshy	PROPN
ejpam-5641	545	6	.	.	PUNCT
ejpam-5641	546	1	fibonacci	fibonacci	PROPN
ejpam-5641	546	2	and	and	CCONJ
ejpam-5641	546	3	lucas	lucas	PROPN
ejpam-5641	546	4	numbers	number	NOUN
ejpam-5641	546	5	with	with	ADP
ejpam-5641	546	6	applications	application	NOUN
ejpam-5641	546	7	.	.	PUNCT
ejpam-5641	547	1	wiley	wiley	PROPN
ejpam-5641	547	2	,	,	PUNCT
ejpam-5641	547	3	new	new	PROPN
ejpam-5641	547	4	york	york	PROPN
ejpam-5641	547	5	,	,	PUNCT
ejpam-5641	547	6	2001	2001	NUM
ejpam-5641	547	7	.	.	PUNCT
ejpam-5641	548	1	[	[	X
ejpam-5641	548	2	13	13	NUM
ejpam-5641	548	3	]	]	X
ejpam-5641	548	4	w.	w.	PROPN
ejpam-5641	548	5	mao	mao	PROPN
ejpam-5641	548	6	,	,	PUNCT
ejpam-5641	548	7	q.	q.	PROPN
ejpam-5641	548	8	zhu	zhu	PROPN
ejpam-5641	548	9	,	,	PUNCT
ejpam-5641	548	10	and	and	CCONJ
ejpam-5641	548	11	x.	x.	PROPN
ejpam-5641	548	12	mao	mao	PROPN
ejpam-5641	548	13	.	.	PUNCT
ejpam-5641	549	1	existence	existence	NOUN
ejpam-5641	549	2	,	,	PUNCT
ejpam-5641	549	3	uniqueness	uniqueness	NOUN
ejpam-5641	549	4	and	and	CCONJ
ejpam-5641	549	5	almost	almost	ADV
ejpam-5641	549	6	surely	surely	ADV
ejpam-5641	549	7	asymptotic	asymptotic	ADJ
ejpam-5641	549	8	estimations	estimation	NOUN
ejpam-5641	549	9	of	of	ADP
ejpam-5641	549	10	the	the	DET
ejpam-5641	549	11	solutions	solution	NOUN
ejpam-5641	549	12	to	to	ADP
ejpam-5641	549	13	neutral	neutral	ADJ
ejpam-5641	549	14	stochastic	stochastic	ADJ
ejpam-5641	549	15	functional	functional	ADJ
ejpam-5641	549	16	differential	differential	ADJ
ejpam-5641	549	17	equations	equation	NOUN
ejpam-5641	549	18	driven	drive	VERB
ejpam-5641	549	19	by	by	ADP
ejpam-5641	549	20	pure	pure	ADJ
ejpam-5641	549	21	jumps	jump	NOUN
ejpam-5641	549	22	.	.	PUNCT
ejpam-5641	550	1	applied	apply	VERB
ejpam-5641	550	2	mathematics	mathematic	NOUN
ejpam-5641	550	3	and	and	CCONJ
ejpam-5641	550	4	computation	computation	NOUN
ejpam-5641	550	5	,	,	PUNCT
ejpam-5641	550	6	254:252–265	254:252–265	NUM
ejpam-5641	550	7	,	,	PUNCT
ejpam-5641	550	8	2015	2015	NUM
ejpam-5641	550	9	.	.	PUNCT
ejpam-5641	551	1	[	[	X
ejpam-5641	551	2	14	14	NUM
ejpam-5641	551	3	]	]	X
ejpam-5641	551	4	e.a.e	e.a.e	PROPN
ejpam-5641	551	5	.	.	PUNCT
ejpam-5641	552	1	mohamed	mohamed	PROPN
ejpam-5641	552	2	and	and	CCONJ
ejpam-5641	552	3	a.a	a.a	PROPN
ejpam-5641	552	4	.	.	PROPN
ejpam-5641	552	5	bakery	bakery	PROPN
ejpam-5641	552	6	.	.	PUNCT
ejpam-5641	553	1	the	the	DET
ejpam-5641	553	2	uniqueness	uniqueness	NOUN
ejpam-5641	553	3	and	and	CCONJ
ejpam-5641	553	4	existence	existence	NOUN
ejpam-5641	553	5	of	of	ADP
ejpam-5641	553	6	solutions	solution	NOUN
ejpam-5641	553	7	in	in	ADP
ejpam-5641	553	8	a	a	DET
ejpam-5641	553	9	new	new	ADJ
ejpam-5641	553	10	complex	complex	ADJ
ejpam-5641	553	11	function	function	NOUN
ejpam-5641	553	12	space	space	NOUN
ejpam-5641	553	13	for	for	ADP
ejpam-5641	553	14	kannan	kannan	PROPN
ejpam-5641	553	15	nonlinear	nonlinear	ADJ
ejpam-5641	553	16	dynamical	dynamical	ADJ
ejpam-5641	553	17	systems	system	NOUN
ejpam-5641	553	18	.	.	PUNCT
ejpam-5641	554	1	j.	j.	PROPN
ejpam-5641	554	2	math	math	PROPN
ejpam-5641	554	3	.	.	PUNCT
ejpam-5641	555	1	computer	computer	NOUN
ejpam-5641	555	2	sci	sci	PROPN
ejpam-5641	555	3	.	.	PROPN
ejpam-5641	555	4	,	,	PUNCT
ejpam-5641	555	5	35:270–290	35:270–290	NUM
ejpam-5641	555	6	,	,	PUNCT
ejpam-5641	555	7	2024	2024	NUM
ejpam-5641	555	8	.	.	PUNCT
ejpam-5641	556	1	[	[	X
ejpam-5641	556	2	15	15	NUM
ejpam-5641	556	3	]	]	X
ejpam-5641	556	4	m.	m.	NOUN
ejpam-5641	556	5	mursaleen	mursaleen	PROPN
ejpam-5641	556	6	and	and	CCONJ
ejpam-5641	556	7	f.	f.	PROPN
ejpam-5641	556	8	başar	başar	PROPN
ejpam-5641	556	9	.	.	PUNCT
ejpam-5641	557	1	domain	domain	NOUN
ejpam-5641	557	2	of	of	ADP
ejpam-5641	557	3	cesàro	cesàro	PROPN
ejpam-5641	557	4	mean	mean	NOUN
ejpam-5641	557	5	of	of	ADP
ejpam-5641	557	6	order	order	NOUN
ejpam-5641	557	7	one	one	NUM
ejpam-5641	557	8	in	in	ADP
ejpam-5641	557	9	some	some	DET
ejpam-5641	557	10	spaces	space	NOUN
ejpam-5641	557	11	of	of	ADP
ejpam-5641	557	12	double	double	ADJ
ejpam-5641	557	13	sequences	sequence	NOUN
ejpam-5641	557	14	.	.	PUNCT
ejpam-5641	558	1	studia	studia	PROPN
ejpam-5641	558	2	sci	sci	PROPN
ejpam-5641	558	3	.	.	PUNCT
ejpam-5641	558	4	math	math	PROPN
ejpam-5641	558	5	.	.	PUNCT
ejpam-5641	559	1	hung	hung	PROPN
ejpam-5641	559	2	.	.	PROPN
ejpam-5641	559	3	,	,	PUNCT
ejpam-5641	559	4	51(3):335–356	51(3):335–356	NUM
ejpam-5641	559	5	,	,	PUNCT
ejpam-5641	559	6	2014	2014	NUM
ejpam-5641	559	7	.	.	PUNCT
ejpam-5641	560	1	[	[	X
ejpam-5641	560	2	16	16	NUM
ejpam-5641	560	3	]	]	PUNCT
ejpam-5641	560	4	m.	m.	NOUN
ejpam-5641	560	5	mursaleen	mursaleen	PROPN
ejpam-5641	560	6	and	and	CCONJ
ejpam-5641	560	7	f.	f.	PROPN
ejpam-5641	560	8	başar	başar	PROPN
ejpam-5641	560	9	.	.	PUNCT
ejpam-5641	561	1	sequence	sequence	NOUN
ejpam-5641	561	2	spaces	space	VERB
ejpam-5641	561	3	:	:	PUNCT
ejpam-5641	561	4	topics	topic	NOUN
ejpam-5641	561	5	in	in	ADP
ejpam-5641	561	6	modern	modern	ADJ
ejpam-5641	561	7	summability	summability	NOUN
ejpam-5641	561	8	theory	theory	NOUN
ejpam-5641	561	9	.	.	PUNCT
ejpam-5641	562	1	mathematics	mathematic	NOUN
ejpam-5641	562	2	and	and	CCONJ
ejpam-5641	562	3	its	its	PRON
ejpam-5641	562	4	applications	application	NOUN
ejpam-5641	562	5	.	.	PUNCT
ejpam-5641	563	1	crc	crc	PROPN
ejpam-5641	563	2	press	press	PROPN
ejpam-5641	563	3	/	/	SYM
ejpam-5641	563	4	taylor	taylor	PROPN
ejpam-5641	563	5	&	&	CCONJ
ejpam-5641	563	6	francis	francis	PROPN
ejpam-5641	563	7	group	group	PROPN
ejpam-5641	563	8	,	,	PUNCT
ejpam-5641	563	9	boca	boca	PROPN
ejpam-5641	563	10	raton	raton	PROPN
ejpam-5641	563	11	,	,	PUNCT
ejpam-5641	563	12	london	london	PROPN
ejpam-5641	563	13	,	,	PUNCT
ejpam-5641	563	14	new	new	PROPN
ejpam-5641	563	15	york	york	PROPN
ejpam-5641	563	16	,	,	PUNCT
ejpam-5641	563	17	2020	2020	NUM
ejpam-5641	563	18	.	.	PUNCT
ejpam-5641	564	1	[	[	X
ejpam-5641	564	2	17	17	NUM
ejpam-5641	564	3	]	]	PUNCT
ejpam-5641	564	4	m.	m.	NOUN
ejpam-5641	564	5	mursaleen	mursaleen	PROPN
ejpam-5641	564	6	and	and	CCONJ
ejpam-5641	564	7	a.	a.	PROPN
ejpam-5641	564	8	k.	k.	PROPN
ejpam-5641	564	9	noman	noman	PROPN
ejpam-5641	564	10	.	.	PUNCT
ejpam-5641	565	1	on	on	ADP
ejpam-5641	565	2	some	some	DET
ejpam-5641	565	3	new	new	ADJ
ejpam-5641	565	4	sequence	sequence	NOUN
ejpam-5641	565	5	spaces	space	NOUN
ejpam-5641	565	6	of	of	ADP
ejpam-5641	565	7	non	non	ADJ
ejpam-5641	565	8	-	-	ADJ
ejpam-5641	565	9	absolute	absolute	ADJ
ejpam-5641	565	10	type	type	NOUN
ejpam-5641	565	11	related	relate	VERB
ejpam-5641	565	12	to	to	ADP
ejpam-5641	565	13	the	the	DET
ejpam-5641	565	14	spaces	space	NOUN
ejpam-5641	565	15	ℓp	ℓp	NOUN
ejpam-5641	565	16	and	and	CCONJ
ejpam-5641	565	17	ℓ∞	ℓ∞	PROPN
ejpam-5641	565	18	i.	i.	NOUN
ejpam-5641	565	19	filomat	filomat	PROPN
ejpam-5641	565	20	,	,	PUNCT
ejpam-5641	565	21	25:33–51	25:33–51	NUM
ejpam-5641	565	22	,	,	PUNCT
ejpam-5641	565	23	2011	2011	NUM
ejpam-5641	565	24	.	.	PUNCT
ejpam-5641	566	1	[	[	X
ejpam-5641	566	2	18	18	NUM
ejpam-5641	566	3	]	]	X
ejpam-5641	566	4	d.i	d.i	PROPN
ejpam-5641	566	5	.	.	PROPN
ejpam-5641	566	6	ostonaqulov	ostonaqulov	PROPN
ejpam-5641	566	7	.	.	PUNCT
ejpam-5641	567	1	integration	integration	NOUN
ejpam-5641	567	2	and	and	CCONJ
ejpam-5641	567	3	applications	application	NOUN
ejpam-5641	567	4	in	in	ADP
ejpam-5641	567	5	economic	economic	ADJ
ejpam-5641	567	6	dynamics	dynamic	NOUN
ejpam-5641	567	7	.	.	PUNCT
ejpam-5641	568	1	open	open	ADJ
ejpam-5641	568	2	herald	herald	PROPN
ejpam-5641	568	3	:	:	PUNCT
ejpam-5641	569	1	periodical	periodical	ADJ
ejpam-5641	569	2	of	of	ADP
ejpam-5641	569	3	methodical	methodical	ADJ
ejpam-5641	569	4	research	research	NOUN
ejpam-5641	569	5	,	,	PUNCT
ejpam-5641	569	6	1(4):9–14	1(4):9–14	PROPN
ejpam-5641	569	7	,	,	PUNCT
ejpam-5641	569	8	2023	2023	NUM
ejpam-5641	569	9	.	.	PUNCT
ejpam-5641	570	1	[	[	X
ejpam-5641	570	2	19	19	NUM
ejpam-5641	570	3	]	]	PUNCT
ejpam-5641	570	4	a.	a.	NOUN
ejpam-5641	570	5	pietsch	pietsch	PROPN
ejpam-5641	570	6	.	.	PUNCT
ejpam-5641	571	1	operator	operator	NOUN
ejpam-5641	571	2	ideals	ideal	NOUN
ejpam-5641	571	3	.	.	PUNCT
ejpam-5641	572	1	veb	veb	PROPN
ejpam-5641	572	2	deutscher	deutscher	PROPN
ejpam-5641	572	3	verlag	verlag	PROPN
ejpam-5641	572	4	der	der	PROPN
ejpam-5641	572	5	wissenschaften	wissenschaften	NOUN
ejpam-5641	572	6	,	,	PUNCT
ejpam-5641	572	7	berlin	berlin	PROPN
ejpam-5641	572	8	,	,	PUNCT
ejpam-5641	572	9	1978	1978	NUM
ejpam-5641	572	10	.	.	PUNCT
ejpam-5641	573	1	[	[	X
ejpam-5641	573	2	20	20	NUM
ejpam-5641	573	3	]	]	PUNCT
ejpam-5641	573	4	m.	m.	NOUN
ejpam-5641	573	5	ruẑiĉka	ruẑiĉka	PROPN
ejpam-5641	573	6	.	.	PROPN
ejpam-5641	573	7	electrorheological	electrorheological	ADJ
ejpam-5641	573	8	fluids	fluid	NOUN
ejpam-5641	573	9	:	:	PUNCT
ejpam-5641	573	10	modeling	modeling	NOUN
ejpam-5641	573	11	and	and	CCONJ
ejpam-5641	573	12	mathematical	mathematical	ADJ
ejpam-5641	573	13	theory	theory	NOUN
ejpam-5641	573	14	,	,	PUNCT
ejpam-5641	573	15	volume	volume	NOUN
ejpam-5641	573	16	1748	1748	NUM
ejpam-5641	573	17	of	of	ADP
ejpam-5641	573	18	lecture	lecture	NOUN
ejpam-5641	573	19	notes	note	NOUN
ejpam-5641	573	20	in	in	ADP
ejpam-5641	573	21	mathematics	mathematic	NOUN
ejpam-5641	573	22	.	.	PUNCT
ejpam-5641	574	1	springer	springer	PROPN
ejpam-5641	574	2	,	,	PUNCT
ejpam-5641	574	3	berlin	berlin	PROPN
ejpam-5641	574	4	,	,	PUNCT
ejpam-5641	574	5	germany	germany	PROPN
ejpam-5641	574	6	,	,	PUNCT
ejpam-5641	574	7	2000	2000	NUM
ejpam-5641	574	8	.	.	PUNCT
ejpam-5641	575	1	[	[	X
ejpam-5641	575	2	21	21	NUM
ejpam-5641	575	3	]	]	X
ejpam-5641	575	4	v.e	v.e	PROPN
ejpam-5641	575	5	.	.	PROPN
ejpam-5641	575	6	tarasov	tarasov	PROPN
ejpam-5641	575	7	.	.	PUNCT
ejpam-5641	576	1	on	on	ADP
ejpam-5641	576	2	history	history	NOUN
ejpam-5641	576	3	of	of	ADP
ejpam-5641	576	4	mathematical	mathematical	ADJ
ejpam-5641	576	5	economics	economic	NOUN
ejpam-5641	576	6	:	:	PUNCT
ejpam-5641	576	7	application	application	NOUN
ejpam-5641	576	8	of	of	ADP
ejpam-5641	576	9	fractional	fractional	ADJ
ejpam-5641	576	10	calculus	calculus	NOUN
ejpam-5641	576	11	.	.	PUNCT
ejpam-5641	577	1	mathematics	mathematic	NOUN
ejpam-5641	577	2	,	,	PUNCT
ejpam-5641	577	3	7(6):509	7(6):509	NUM
ejpam-5641	577	4	,	,	PUNCT
ejpam-5641	577	5	2019	2019	NUM
ejpam-5641	577	6	.	.	PUNCT