id	sid	tid	token	lemma	pos
ejpam-6102	1	1	european	european	PROPN
ejpam-6102	1	2	journal	journal	PROPN
ejpam-6102	1	3	of	of	ADP
ejpam-6102	1	4	pure	pure	ADJ
ejpam-6102	1	5	and	and	CCONJ
ejpam-6102	1	6	applied	applied	ADJ
ejpam-6102	1	7	mathematics	mathematic	NOUN
ejpam-6102	1	8	2025	2025	NUM
ejpam-6102	1	9	,	,	PUNCT
ejpam-6102	1	10	vol	vol	NOUN
ejpam-6102	1	11	.	.	PROPN
ejpam-6102	1	12	18	18	NUM
ejpam-6102	1	13	,	,	PUNCT
ejpam-6102	1	14	issue	issue	NOUN
ejpam-6102	1	15	2	2	NUM
ejpam-6102	1	16	,	,	PUNCT
ejpam-6102	1	17	article	article	NOUN
ejpam-6102	1	18	number	number	NOUN
ejpam-6102	1	19	6102	6102	NUM
ejpam-6102	1	20	issn	issn	PROPN
ejpam-6102	1	21	1307	1307	NUM
ejpam-6102	1	22	-	-	SYM
ejpam-6102	1	23	5543	5543	NUM
ejpam-6102	1	24	–	–	PUNCT
ejpam-6102	1	25	ejpam.com	ejpam.com	X
ejpam-6102	1	26	published	publish	VERB
ejpam-6102	1	27	by	by	ADP
ejpam-6102	1	28	new	new	PROPN
ejpam-6102	1	29	york	york	PROPN
ejpam-6102	1	30	business	business	PROPN
ejpam-6102	1	31	global	global	ADJ
ejpam-6102	1	32	boundary	boundary	NOUN
ejpam-6102	1	33	blowing	blow	VERB
ejpam-6102	1	34	up	up	ADP
ejpam-6102	1	35	solutions	solution	NOUN
ejpam-6102	1	36	for	for	ADP
ejpam-6102	1	37	an	an	DET
ejpam-6102	1	38	elliptic	elliptic	ADJ
ejpam-6102	1	39	neumann	neumann	PROPN
ejpam-6102	1	40	problem	problem	NOUN
ejpam-6102	1	41	with	with	ADP
ejpam-6102	1	42	nearly	nearly	ADV
ejpam-6102	1	43	critical	critical	ADJ
ejpam-6102	1	44	exponent	exponent	NOUN
ejpam-6102	1	45	rakan	rakan	PROPN
ejpam-6102	1	46	almushahhin1	almushahhin1	PROPN
ejpam-6102	1	47	,	,	PUNCT
ejpam-6102	1	48	mohamed	mohamed	PROPN
ejpam-6102	1	49	ben	ben	PROPN
ejpam-6102	1	50	ayed1,∗	ayed1,∗	PROPN
ejpam-6102	1	51	1	1	NUM
ejpam-6102	1	52	department	department	NOUN
ejpam-6102	1	53	of	of	ADP
ejpam-6102	1	54	mathematics	mathematic	NOUN
ejpam-6102	1	55	,	,	PUNCT
ejpam-6102	1	56	college	college	NOUN
ejpam-6102	1	57	of	of	ADP
ejpam-6102	1	58	science	science	NOUN
ejpam-6102	1	59	,	,	PUNCT
ejpam-6102	1	60	qassim	qassim	PROPN
ejpam-6102	1	61	university	university	PROPN
ejpam-6102	1	62	,	,	PUNCT
ejpam-6102	1	63	buraydah	buraydah	NOUN
ejpam-6102	1	64	51542	51542	NUM
ejpam-6102	1	65	,	,	PUNCT
ejpam-6102	1	66	saudi	saudi	PROPN
ejpam-6102	1	67	arabia	arabia	PROPN
ejpam-6102	1	68	abstract	abstract	NOUN
ejpam-6102	1	69	.	.	PUNCT
ejpam-6102	2	1	in	in	ADP
ejpam-6102	2	2	this	this	DET
ejpam-6102	2	3	paper	paper	NOUN
ejpam-6102	2	4	,	,	PUNCT
ejpam-6102	2	5	we	we	PRON
ejpam-6102	2	6	investigate	investigate	VERB
ejpam-6102	2	7	the	the	DET
ejpam-6102	2	8	nonlinear	nonlinear	ADJ
ejpam-6102	2	9	problem	problem	NOUN
ejpam-6102	2	10	(	(	PUNCT
ejpam-6102	2	11	pε	pε	NOUN
ejpam-6102	2	12	)	)	PUNCT
ejpam-6102	2	13	:	:	PUNCT
ejpam-6102	2	14	−∆u	−∆u	X
ejpam-6102	3	1	+	+	CCONJ
ejpam-6102	3	2	v	v	X
ejpam-6102	3	3	(	(	PUNCT
ejpam-6102	3	4	x)u	x)u	PUNCT
ejpam-6102	3	5	=	=	SYM
ejpam-6102	3	6	fu	fu	PROPN
ejpam-6102	3	7	n+2	n+2	NUM
ejpam-6102	3	8	n−2−ε	n−2−ε	NOUN
ejpam-6102	3	9	,	,	PUNCT
ejpam-6102	3	10	u	u	NOUN
ejpam-6102	3	11	>	>	X
ejpam-6102	3	12	0	0	PUNCT
ejpam-6102	4	1	in	in	ADP
ejpam-6102	4	2	ω	ω	PROPN
ejpam-6102	4	3	and	and	CCONJ
ejpam-6102	4	4	∂u/∂ν	∂u/∂ν	PROPN
ejpam-6102	4	5	=	=	SYM
ejpam-6102	4	6	0	0	NUM
ejpam-6102	4	7	on	on	ADP
ejpam-6102	4	8	∂ω	∂ω	PROPN
ejpam-6102	4	9	,	,	PUNCT
ejpam-6102	4	10	where	where	SCONJ
ejpam-6102	4	11	ω	ω	PROPN
ejpam-6102	4	12	is	be	AUX
ejpam-6102	4	13	a	a	DET
ejpam-6102	4	14	bounded	bounded	ADJ
ejpam-6102	4	15	regular	regular	ADJ
ejpam-6102	4	16	domain	domain	NOUN
ejpam-6102	4	17	in	in	ADP
ejpam-6102	4	18	rn	rn	PROPN
ejpam-6102	4	19	,	,	PUNCT
ejpam-6102	4	20	with	with	ADP
ejpam-6102	4	21	n	n	PRON
ejpam-6102	4	22	≥	≥	NOUN
ejpam-6102	4	23	4	4	NUM
ejpam-6102	4	24	,	,	PUNCT
ejpam-6102	4	25	ε	ε	PROPN
ejpam-6102	4	26	is	be	AUX
ejpam-6102	4	27	a	a	DET
ejpam-6102	4	28	small	small	ADJ
ejpam-6102	4	29	positive	positive	ADJ
ejpam-6102	4	30	parameter	parameter	NOUN
ejpam-6102	4	31	,	,	PUNCT
ejpam-6102	4	32	v	v	NOUN
ejpam-6102	4	33	and	and	CCONJ
ejpam-6102	4	34	f	f	PROPN
ejpam-6102	4	35	are	be	AUX
ejpam-6102	4	36	smooth	smooth	ADJ
ejpam-6102	4	37	positive	positive	ADJ
ejpam-6102	4	38	functions	function	NOUN
ejpam-6102	4	39	on	on	ADP
ejpam-6102	4	40	ω	ω	NOUN
ejpam-6102	4	41	.	.	PUNCT
ejpam-6102	5	1	under	under	ADP
ejpam-6102	5	2	certain	certain	ADJ
ejpam-6102	5	3	conditions	condition	NOUN
ejpam-6102	5	4	involving	involve	VERB
ejpam-6102	5	5	the	the	DET
ejpam-6102	5	6	function	function	NOUN
ejpam-6102	5	7	f	f	NOUN
ejpam-6102	5	8	and	and	CCONJ
ejpam-6102	5	9	the	the	DET
ejpam-6102	5	10	mean	mean	ADJ
ejpam-6102	5	11	curvature	curvature	NOUN
ejpam-6102	5	12	of	of	ADP
ejpam-6102	5	13	the	the	DET
ejpam-6102	5	14	boundary	boundary	NOUN
ejpam-6102	5	15	,	,	PUNCT
ejpam-6102	5	16	we	we	PRON
ejpam-6102	5	17	construct	construct	VERB
ejpam-6102	5	18	boundary	boundary	NOUN
ejpam-6102	5	19	blowing	blow	VERB
ejpam-6102	5	20	up	up	ADP
ejpam-6102	5	21	solutions	solution	NOUN
ejpam-6102	5	22	of	of	ADP
ejpam-6102	5	23	the	the	DET
ejpam-6102	5	24	problem	problem	NOUN
ejpam-6102	5	25	(	(	PUNCT
ejpam-6102	5	26	pε	pε	NOUN
ejpam-6102	5	27	)	)	PUNCT
ejpam-6102	5	28	which	which	PRON
ejpam-6102	5	29	converge	converge	VERB
ejpam-6102	5	30	weakly	weakly	ADV
ejpam-6102	5	31	to	to	ADP
ejpam-6102	5	32	0	0	NUM
ejpam-6102	5	33	and	and	CCONJ
ejpam-6102	5	34	blow	blow	VERB
ejpam-6102	5	35	up	up	ADP
ejpam-6102	5	36	at	at	ADP
ejpam-6102	5	37	some	some	DET
ejpam-6102	5	38	critical	critical	ADJ
ejpam-6102	5	39	points	point	NOUN
ejpam-6102	5	40	of	of	ADP
ejpam-6102	5	41	fb	fb	NOUN
ejpam-6102	5	42	:	:	PUNCT
ejpam-6102	5	43	=	=	SYM
ejpam-6102	5	44	f|∂ω	f|∂ω	PROPN
ejpam-6102	5	45	.	.	PUNCT
ejpam-6102	6	1	this	this	DET
ejpam-6102	6	2	existence	existence	NOUN
ejpam-6102	6	3	of	of	ADP
ejpam-6102	6	4	solutions	solution	NOUN
ejpam-6102	6	5	leads	lead	VERB
ejpam-6102	6	6	to	to	ADP
ejpam-6102	6	7	a	a	DET
ejpam-6102	6	8	multiplicity	multiplicity	NOUN
ejpam-6102	6	9	result	result	NOUN
ejpam-6102	6	10	for	for	ADP
ejpam-6102	6	11	(	(	PUNCT
ejpam-6102	6	12	pε	pε	NOUN
ejpam-6102	6	13	)	)	PUNCT
ejpam-6102	6	14	.	.	PUNCT
ejpam-6102	7	1	the	the	DET
ejpam-6102	7	2	proof	proof	NOUN
ejpam-6102	7	3	of	of	ADP
ejpam-6102	7	4	these	these	DET
ejpam-6102	7	5	results	result	NOUN
ejpam-6102	7	6	involves	involve	VERB
ejpam-6102	7	7	expanding	expand	VERB
ejpam-6102	7	8	the	the	DET
ejpam-6102	7	9	gradient	gradient	NOUN
ejpam-6102	7	10	of	of	ADP
ejpam-6102	7	11	the	the	DET
ejpam-6102	7	12	associated	associated	ADJ
ejpam-6102	7	13	functional	functional	ADJ
ejpam-6102	7	14	and	and	CCONJ
ejpam-6102	7	15	testing	test	VERB
ejpam-6102	7	16	the	the	DET
ejpam-6102	7	17	equation	equation	NOUN
ejpam-6102	7	18	with	with	ADP
ejpam-6102	7	19	suitable	suitable	ADJ
ejpam-6102	7	20	vector	vector	NOUN
ejpam-6102	7	21	fields	field	NOUN
ejpam-6102	7	22	.	.	PUNCT
ejpam-6102	8	1	this	this	DET
ejpam-6102	8	2	process	process	NOUN
ejpam-6102	8	3	imposes	impose	VERB
ejpam-6102	8	4	constraints	constraint	NOUN
ejpam-6102	8	5	on	on	ADP
ejpam-6102	8	6	the	the	DET
ejpam-6102	8	7	concentration	concentration	NOUN
ejpam-6102	8	8	parameters	parameter	NOUN
ejpam-6102	8	9	,	,	PUNCT
ejpam-6102	8	10	and	and	CCONJ
ejpam-6102	8	11	a	a	DET
ejpam-6102	8	12	careful	careful	ADJ
ejpam-6102	8	13	analysis	analysis	NOUN
ejpam-6102	8	14	of	of	ADP
ejpam-6102	8	15	these	these	DET
ejpam-6102	8	16	constraints	constraint	NOUN
ejpam-6102	8	17	leads	lead	VERB
ejpam-6102	8	18	to	to	ADP
ejpam-6102	8	19	the	the	DET
ejpam-6102	8	20	conclusions	conclusion	NOUN
ejpam-6102	8	21	presented	present	VERB
ejpam-6102	8	22	.	.	PUNCT
ejpam-6102	9	1	2020	2020	NUM
ejpam-6102	9	2	mathematics	mathematics	PROPN
ejpam-6102	9	3	subject	subject	NOUN
ejpam-6102	9	4	classifications	classification	NOUN
ejpam-6102	9	5	:	:	PUNCT
ejpam-6102	9	6	35a15	35a15	NUM
ejpam-6102	9	7	,	,	PUNCT
ejpam-6102	9	8	35j20	35j20	NUM
ejpam-6102	9	9	,	,	PUNCT
ejpam-6102	9	10	35j25	35j25	NUM
ejpam-6102	9	11	key	key	ADJ
ejpam-6102	9	12	words	word	NOUN
ejpam-6102	9	13	and	and	CCONJ
ejpam-6102	9	14	phrases	phrase	NOUN
ejpam-6102	9	15	:	:	PUNCT
ejpam-6102	9	16	partial	partial	ADJ
ejpam-6102	9	17	differential	differential	NOUN
ejpam-6102	9	18	equations	equation	NOUN
ejpam-6102	9	19	,	,	PUNCT
ejpam-6102	9	20	neumann	neumann	PROPN
ejpam-6102	9	21	elliptic	elliptic	ADJ
ejpam-6102	9	22	problems	problem	NOUN
ejpam-6102	9	23	,	,	PUNCT
ejpam-6102	9	24	critical	critical	ADJ
ejpam-6102	9	25	sobolev	sobolev	NOUN
ejpam-6102	9	26	exponent	exponent	NOUN
ejpam-6102	9	27	1	1	X
ejpam-6102	9	28	.	.	PUNCT
ejpam-6102	9	29	introduction	introduction	NOUN
ejpam-6102	9	30	in	in	ADP
ejpam-6102	9	31	the	the	DET
ejpam-6102	9	32	last	last	ADJ
ejpam-6102	9	33	decades	decade	NOUN
ejpam-6102	9	34	,	,	PUNCT
ejpam-6102	9	35	there	there	PRON
ejpam-6102	9	36	has	have	AUX
ejpam-6102	9	37	been	be	AUX
ejpam-6102	9	38	a	a	DET
ejpam-6102	9	39	great	great	ADJ
ejpam-6102	9	40	deal	deal	NOUN
ejpam-6102	9	41	of	of	ADP
ejpam-6102	9	42	interest	interest	NOUN
ejpam-6102	9	43	in	in	ADP
ejpam-6102	9	44	studying	study	VERB
ejpam-6102	9	45	the	the	DET
ejpam-6102	9	46	following	follow	VERB
ejpam-6102	9	47	problem	problem	NOUN
ejpam-6102	9	48	(	(	PUNCT
ejpam-6102	9	49	pλ	pλ	NOUN
ejpam-6102	9	50	,	,	PUNCT
ejpam-6102	9	51	q	q	NOUN
ejpam-6102	9	52	)	)	PUNCT
ejpam-6102	9	53	{	{	PUNCT
ejpam-6102	9	54	−∆u+	−∆u+	NOUN
ejpam-6102	9	55	λu	λu	X
ejpam-6102	9	56	=	=	SYM
ejpam-6102	9	57	uq	uq	PROPN
ejpam-6102	9	58	,	,	PUNCT
ejpam-6102	9	59	u	u	NOUN
ejpam-6102	9	60	>	>	X
ejpam-6102	9	61	0	0	PUNCT
ejpam-6102	10	1	in	in	ADP
ejpam-6102	10	2	ω	ω	NUM
ejpam-6102	10	3	,	,	PUNCT
ejpam-6102	10	4	∂u	∂u	PROPN
ejpam-6102	10	5	∂ν	∂ν	X
ejpam-6102	10	6	=	=	PUNCT
ejpam-6102	10	7	0	0	PROPN
ejpam-6102	10	8	,	,	PUNCT
ejpam-6102	10	9	on	on	ADP
ejpam-6102	10	10	∂ω	∂ω	PROPN
ejpam-6102	10	11	,	,	PUNCT
ejpam-6102	10	12	where	where	SCONJ
ejpam-6102	10	13	ω	ω	PROPN
ejpam-6102	10	14	is	be	AUX
ejpam-6102	10	15	a	a	DET
ejpam-6102	10	16	smooth	smooth	ADJ
ejpam-6102	10	17	and	and	CCONJ
ejpam-6102	10	18	bounded	bound	VERB
ejpam-6102	10	19	open	open	ADJ
ejpam-6102	10	20	set	set	NOUN
ejpam-6102	10	21	of	of	ADP
ejpam-6102	10	22	rn	rn	PROPN
ejpam-6102	10	23	with	with	ADP
ejpam-6102	10	24	n	n	PRON
ejpam-6102	10	25	≥	≥	NUM
ejpam-6102	10	26	3	3	NUM
ejpam-6102	10	27	,	,	PUNCT
ejpam-6102	10	28	q	q	ADJ
ejpam-6102	10	29	>	>	X
ejpam-6102	10	30	1	1	NUM
ejpam-6102	10	31	and	and	CCONJ
ejpam-6102	10	32	λ	λ	PROPN
ejpam-6102	10	33	is	be	AUX
ejpam-6102	10	34	a	a	DET
ejpam-6102	10	35	positive	positive	ADJ
ejpam-6102	10	36	real	real	ADJ
ejpam-6102	10	37	number	number	NOUN
ejpam-6102	10	38	.	.	PUNCT
ejpam-6102	11	1	problem	problem	NOUN
ejpam-6102	11	2	(	(	PUNCT
ejpam-6102	11	3	pλ	pλ	NOUN
ejpam-6102	11	4	,	,	PUNCT
ejpam-6102	11	5	q	q	NOUN
ejpam-6102	11	6	)	)	PUNCT
ejpam-6102	11	7	is	be	AUX
ejpam-6102	11	8	a	a	DET
ejpam-6102	11	9	well	well	ADV
ejpam-6102	11	10	-	-	PUNCT
ejpam-6102	11	11	known	know	VERB
ejpam-6102	11	12	example	example	NOUN
ejpam-6102	11	13	encountered	encounter	VERB
ejpam-6102	11	14	in	in	ADP
ejpam-6102	11	15	various	various	ADJ
ejpam-6102	11	16	applied	apply	VERB
ejpam-6102	11	17	sciences	science	NOUN
ejpam-6102	11	18	.	.	PUNCT
ejpam-6102	12	1	for	for	ADP
ejpam-6102	12	2	instance	instance	NOUN
ejpam-6102	12	3	,	,	PUNCT
ejpam-6102	12	4	it	it	PRON
ejpam-6102	12	5	can	can	AUX
ejpam-6102	12	6	be	be	AUX
ejpam-6102	12	7	interpreted	interpret	VERB
ejpam-6102	12	8	as	as	ADP
ejpam-6102	12	9	the	the	DET
ejpam-6102	12	10	stationary	stationary	ADJ
ejpam-6102	12	11	problem	problem	NOUN
ejpam-6102	12	12	arising	arise	VERB
ejpam-6102	12	13	in	in	ADP
ejpam-6102	12	14	a	a	DET
ejpam-6102	12	15	keller	keller	PROPN
ejpam-6102	12	16	-	-	PUNCT
ejpam-6102	12	17	segel	segel	PROPN
ejpam-6102	12	18	chemotaxis	chemotaxis	ADJ
ejpam-6102	12	19	model	model	NOUN
ejpam-6102	12	20	[	[	X
ejpam-6102	12	21	1	1	NUM
ejpam-6102	12	22	,	,	PUNCT
ejpam-6102	12	23	2	2	NUM
ejpam-6102	12	24	]	]	PUNCT
ejpam-6102	12	25	,	,	PUNCT
ejpam-6102	12	26	originally	originally	ADV
ejpam-6102	12	27	developed	develop	VERB
ejpam-6102	12	28	to	to	PART
ejpam-6102	12	29	describe	describe	VERB
ejpam-6102	12	30	cell	cell	NOUN
ejpam-6102	12	31	migration	migration	NOUN
ejpam-6102	12	32	in	in	ADP
ejpam-6102	12	33	response	response	NOUN
ejpam-6102	12	34	to	to	ADP
ejpam-6102	12	35	chemical	chemical	ADJ
ejpam-6102	12	36	cues	cue	NOUN
ejpam-6102	12	37	.	.	PUNCT
ejpam-6102	13	1	over	over	ADP
ejpam-6102	13	2	time	time	NOUN
ejpam-6102	13	3	,	,	PUNCT
ejpam-6102	13	4	this	this	DET
ejpam-6102	13	5	model	model	NOUN
ejpam-6102	13	6	has	have	AUX
ejpam-6102	13	7	found	find	VERB
ejpam-6102	13	8	broad	broad	ADJ
ejpam-6102	13	9	application	application	NOUN
ejpam-6102	13	10	in	in	ADP
ejpam-6102	13	11	engineering	engineering	NOUN
ejpam-6102	13	12	,	,	PUNCT
ejpam-6102	13	13	supporting	support	VERB
ejpam-6102	13	14	advances	advance	NOUN
ejpam-6102	13	15	in	in	ADP
ejpam-6102	13	16	targeted	target	VERB
ejpam-6102	13	17	drug	drug	NOUN
ejpam-6102	13	18	delivery	delivery	NOUN
ejpam-6102	13	19	,	,	PUNCT
ejpam-6102	13	20	tissue	tissue	NOUN
ejpam-6102	13	21	engineering	engineering	NOUN
ejpam-6102	13	22	,	,	PUNCT
ejpam-6102	13	23	microfluidic	microfluidic	ADJ
ejpam-6102	13	24	systems	system	NOUN
ejpam-6102	13	25	,	,	PUNCT
ejpam-6102	13	26	and	and	CCONJ
ejpam-6102	13	27	the	the	DET
ejpam-6102	13	28	design	design	NOUN
ejpam-6102	13	29	of	of	ADP
ejpam-6102	13	30	bio	bio	NOUN
ejpam-6102	13	31	-	-	PUNCT
ejpam-6102	13	32	inspired	inspire	VERB
ejpam-6102	13	33	robots	robot	NOUN
ejpam-6102	13	34	guided	guide	VERB
ejpam-6102	13	35	by	by	ADP
ejpam-6102	13	36	chemotactic	chemotactic	ADJ
ejpam-6102	13	37	behavior	behavior	NOUN
ejpam-6102	14	1	[	[	X
ejpam-6102	14	2	3–5	3–5	NOUN
ejpam-6102	14	3	]	]	PUNCT
ejpam-6102	14	4	.	.	PUNCT
ejpam-6102	15	1	∗corresponding	∗corresponde	VERB
ejpam-6102	15	2	author	author	NOUN
ejpam-6102	15	3	.	.	PUNCT
ejpam-6102	16	1	doi	doi	NOUN
ejpam-6102	16	2	:	:	PUNCT
ejpam-6102	16	3	https://doi.org/10.29020/nybg.ejpam.v18i2.6102	https://doi.org/10.29020/nybg.ejpam.v18i2.6102	PUNCT
ejpam-6102	16	4	email	email	NOUN
ejpam-6102	16	5	addresses	address	NOUN
ejpam-6102	16	6	:	:	PUNCT
ejpam-6102	16	7	441112378@qu.edu.sa	441112378@qu.edu.sa	PROPN
ejpam-6102	16	8	(	(	PUNCT
ejpam-6102	16	9	r.	r.	PROPN
ejpam-6102	16	10	almushahhin	almushahhin	PROPN
ejpam-6102	16	11	)	)	PUNCT
ejpam-6102	16	12	,	,	PUNCT
ejpam-6102	16	13	m.benayed@qu.edu.sa	m.benayed@qu.edu.sa	PROPN
ejpam-6102	16	14	(	(	PUNCT
ejpam-6102	16	15	m.	m.	NOUN
ejpam-6102	16	16	ben	ben	PROPN
ejpam-6102	16	17	ayed	aye	VERB
ejpam-6102	16	18	)	)	PUNCT
ejpam-6102	16	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6102	17	1	1	1	NUM
ejpam-6102	17	2	copyright	copyright	NOUN
ejpam-6102	17	3	:	:	PUNCT
ejpam-6102	17	4	©	©	PROPN
ejpam-6102	17	5	2025	2025	NUM
ejpam-6102	17	6	the	the	DET
ejpam-6102	17	7	author(s	author(s	NOUN
ejpam-6102	17	8	)	)	PUNCT
ejpam-6102	17	9	.	.	PUNCT
ejpam-6102	18	1	(	(	PUNCT
ejpam-6102	18	2	cc	cc	NOUN
ejpam-6102	18	3	by	by	ADP
ejpam-6102	18	4	-	-	PUNCT
ejpam-6102	18	5	nc	nc	PROPN
ejpam-6102	18	6	4.0	4.0	NUM
ejpam-6102	18	7	)	)	PUNCT
ejpam-6102	18	8	r.	r.	PROPN
ejpam-6102	18	9	almushahhin	almushahhin	PROPN
ejpam-6102	18	10	,	,	PUNCT
ejpam-6102	18	11	m.	m.	PROPN
ejpam-6102	18	12	ben	ben	PROPN
ejpam-6102	18	13	ayed	aye	VERB
ejpam-6102	18	14	/	/	SYM
ejpam-6102	18	15	eur	eur	PROPN
ejpam-6102	18	16	.	.	PUNCT
ejpam-6102	19	1	j.	j.	PROPN
ejpam-6102	19	2	pure	pure	PROPN
ejpam-6102	19	3	appl	appl	PROPN
ejpam-6102	19	4	.	.	PROPN
ejpam-6102	19	5	math	math	PROPN
ejpam-6102	19	6	,	,	PUNCT
ejpam-6102	19	7	18	18	NUM
ejpam-6102	19	8	(	(	PUNCT
ejpam-6102	19	9	2	2	NUM
ejpam-6102	19	10	)	)	PUNCT
ejpam-6102	19	11	(	(	PUNCT
ejpam-6102	19	12	2025	2025	NUM
ejpam-6102	19	13	)	)	PUNCT
ejpam-6102	19	14	,	,	PUNCT
ejpam-6102	19	15	6102	6102	NUM
ejpam-6102	19	16	2	2	NUM
ejpam-6102	19	17	of	of	ADP
ejpam-6102	19	18	31	31	NUM
ejpam-6102	19	19	from	from	ADP
ejpam-6102	19	20	a	a	DET
ejpam-6102	19	21	mathematical	mathematical	ADJ
ejpam-6102	19	22	standpoint	standpoint	NOUN
ejpam-6102	19	23	,	,	PUNCT
ejpam-6102	19	24	problem	problem	NOUN
ejpam-6102	19	25	(	(	PUNCT
ejpam-6102	19	26	pλ	pλ	NOUN
ejpam-6102	19	27	,	,	PUNCT
ejpam-6102	19	28	q	q	NOUN
ejpam-6102	19	29	)	)	PUNCT
ejpam-6102	19	30	is	be	AUX
ejpam-6102	19	31	an	an	DET
ejpam-6102	19	32	interesting	interesting	ADJ
ejpam-6102	19	33	model	model	NOUN
ejpam-6102	19	34	due	due	ADP
ejpam-6102	19	35	to	to	ADP
ejpam-6102	19	36	its	its	PRON
ejpam-6102	19	37	solutions	solution	NOUN
ejpam-6102	19	38	often	often	ADV
ejpam-6102	19	39	exhibiting	exhibit	VERB
ejpam-6102	19	40	the	the	DET
ejpam-6102	19	41	bubbling	bubble	VERB
ejpam-6102	19	42	phenomenon	phenomenon	NOUN
ejpam-6102	19	43	,	,	PUNCT
ejpam-6102	19	44	with	with	ADP
ejpam-6102	19	45	the	the	DET
ejpam-6102	19	46	center	center	NOUN
ejpam-6102	19	47	of	of	ADP
ejpam-6102	19	48	the	the	DET
ejpam-6102	19	49	bubble	bubble	NOUN
ejpam-6102	19	50	located	locate	VERB
ejpam-6102	19	51	on	on	ADP
ejpam-6102	19	52	the	the	DET
ejpam-6102	19	53	boundary	boundary	NOUN
ejpam-6102	19	54	.	.	PUNCT
ejpam-6102	20	1	this	this	DET
ejpam-6102	20	2	boundary	boundary	ADJ
ejpam-6102	20	3	bubbling	bubble	VERB
ejpam-6102	20	4	highlights	highlight	NOUN
ejpam-6102	20	5	a	a	DET
ejpam-6102	20	6	strong	strong	ADJ
ejpam-6102	20	7	interaction	interaction	NOUN
ejpam-6102	20	8	between	between	ADP
ejpam-6102	20	9	the	the	DET
ejpam-6102	20	10	geometry	geometry	NOUN
ejpam-6102	20	11	of	of	ADP
ejpam-6102	20	12	the	the	DET
ejpam-6102	20	13	boundary	boundary	NOUN
ejpam-6102	20	14	and	and	CCONJ
ejpam-6102	20	15	the	the	DET
ejpam-6102	20	16	solutions	solution	NOUN
ejpam-6102	20	17	of	of	ADP
ejpam-6102	20	18	(	(	PUNCT
ejpam-6102	20	19	pλ	pλ	PROPN
ejpam-6102	20	20	,	,	PUNCT
ejpam-6102	20	21	q	q	NOUN
ejpam-6102	20	22	)	)	PUNCT
ejpam-6102	20	23	.	.	PUNCT
ejpam-6102	21	1	a	a	DET
ejpam-6102	21	2	large	large	ADJ
ejpam-6102	21	3	body	body	NOUN
ejpam-6102	21	4	of	of	ADP
ejpam-6102	21	5	research	research	NOUN
ejpam-6102	21	6	has	have	AUX
ejpam-6102	21	7	explored	explore	VERB
ejpam-6102	21	8	problem	problem	NOUN
ejpam-6102	21	9	(	(	PUNCT
ejpam-6102	21	10	pλ	pλ	NOUN
ejpam-6102	21	11	,	,	PUNCT
ejpam-6102	21	12	q	q	NOUN
ejpam-6102	21	13	)	)	PUNCT
ejpam-6102	21	14	when	when	SCONJ
ejpam-6102	21	15	the	the	DET
ejpam-6102	21	16	exponent	exponent	NOUN
ejpam-6102	21	17	q	q	NOUN
ejpam-6102	21	18	is	be	AUX
ejpam-6102	21	19	fixed	fix	VERB
ejpam-6102	21	20	and	and	CCONJ
ejpam-6102	21	21	λ	λ	NOUN
ejpam-6102	21	22	is	be	AUX
ejpam-6102	21	23	treated	treat	VERB
ejpam-6102	21	24	as	as	ADP
ejpam-6102	21	25	the	the	DET
ejpam-6102	21	26	parameter	parameter	NOUN
ejpam-6102	21	27	.	.	PUNCT
ejpam-6102	22	1	a	a	DET
ejpam-6102	22	2	noteworthy	noteworthy	ADJ
ejpam-6102	22	3	aspect	aspect	NOUN
ejpam-6102	22	4	of	of	ADP
ejpam-6102	22	5	the	the	DET
ejpam-6102	22	6	problem	problem	NOUN
ejpam-6102	22	7	(	(	PUNCT
ejpam-6102	22	8	pλ	pλ	NOUN
ejpam-6102	22	9	,	,	PUNCT
ejpam-6102	22	10	q	q	NOUN
ejpam-6102	22	11	)	)	PUNCT
ejpam-6102	22	12	is	be	AUX
ejpam-6102	22	13	the	the	DET
ejpam-6102	22	14	existence	existence	NOUN
ejpam-6102	22	15	of	of	ADP
ejpam-6102	22	16	solution	solution	NOUN
ejpam-6102	22	17	families	family	NOUN
ejpam-6102	22	18	,	,	PUNCT
ejpam-6102	22	19	denoted	denote	VERB
ejpam-6102	22	20	uλ	uλ	ADP
ejpam-6102	22	21	,	,	PUNCT
ejpam-6102	22	22	q	q	NOUN
ejpam-6102	22	23	,	,	PUNCT
ejpam-6102	22	24	that	that	PRON
ejpam-6102	22	25	exhibit	exhibit	AUX
ejpam-6102	22	26	blow	blow	VERB
ejpam-6102	22	27	up	up	ADP
ejpam-6102	22	28	phenomena	phenomenon	NOUN
ejpam-6102	22	29	as	as	ADP
ejpam-6102	22	30	λ	λ	NOUN
ejpam-6102	22	31	changes	change	NOUN
ejpam-6102	22	32	.	.	PUNCT
ejpam-6102	23	1	more	more	ADV
ejpam-6102	23	2	precisely	precisely	ADV
ejpam-6102	23	3	,	,	PUNCT
ejpam-6102	23	4	these	these	DET
ejpam-6102	23	5	solutions	solution	NOUN
ejpam-6102	23	6	blow	blow	VERB
ejpam-6102	23	7	up	up	ADP
ejpam-6102	23	8	around	around	ADP
ejpam-6102	23	9	certain	certain	ADJ
ejpam-6102	23	10	points	point	NOUN
ejpam-6102	23	11	within	within	ADP
ejpam-6102	23	12	ω	ω	PROPN
ejpam-6102	23	13	or	or	CCONJ
ejpam-6102	23	14	on	on	ADP
ejpam-6102	23	15	its	its	PRON
ejpam-6102	23	16	boundary	boundary	ADJ
ejpam-6102	23	17	∂ω	∂ω	PROPN
ejpam-6102	23	18	,	,	PUNCT
ejpam-6102	23	19	while	while	SCONJ
ejpam-6102	23	20	remaining	remain	VERB
ejpam-6102	23	21	negligibly	negligibly	ADV
ejpam-6102	23	22	small	small	ADJ
ejpam-6102	23	23	elsewhere	elsewhere	ADV
ejpam-6102	23	24	.	.	PUNCT
ejpam-6102	24	1	for	for	ADP
ejpam-6102	24	2	the	the	DET
ejpam-6102	24	3	subcritical	subcritical	ADJ
ejpam-6102	24	4	case	case	NOUN
ejpam-6102	24	5	,	,	PUNCT
ejpam-6102	24	6	where	where	SCONJ
ejpam-6102	24	7	1	1	NUM
ejpam-6102	24	8	<	<	X
ejpam-6102	24	9	q	q	X
ejpam-6102	24	10	<	<	X
ejpam-6102	24	11	(	(	PUNCT
ejpam-6102	24	12	n	n	PROPN
ejpam-6102	24	13	+	+	CCONJ
ejpam-6102	24	14	2)/(n	2)/(n	NUM
ejpam-6102	24	15	−	−	NOUN
ejpam-6102	24	16	2	2	NUM
ejpam-6102	24	17	)	)	PUNCT
ejpam-6102	24	18	,	,	PUNCT
ejpam-6102	24	19	the	the	DET
ejpam-6102	24	20	only	only	ADJ
ejpam-6102	24	21	solution	solution	NOUN
ejpam-6102	24	22	to	to	ADP
ejpam-6102	24	23	(	(	PUNCT
ejpam-6102	24	24	pλ	pλ	NOUN
ejpam-6102	24	25	,	,	PUNCT
ejpam-6102	24	26	q	q	NOUN
ejpam-6102	24	27	)	)	PUNCT
ejpam-6102	24	28	for	for	ADP
ejpam-6102	24	29	small	small	ADJ
ejpam-6102	24	30	λ	λ	PROPN
ejpam-6102	24	31	is	be	AUX
ejpam-6102	24	32	the	the	DET
ejpam-6102	24	33	constant	constant	ADJ
ejpam-6102	24	34	one	one	NUM
ejpam-6102	24	35	.	.	PUNCT
ejpam-6102	25	1	however	however	ADV
ejpam-6102	25	2	,	,	PUNCT
ejpam-6102	25	3	as	as	SCONJ
ejpam-6102	25	4	λ	λ	PROPN
ejpam-6102	25	5	grows	grow	VERB
ejpam-6102	25	6	larger	large	ADJ
ejpam-6102	25	7	,	,	PUNCT
ejpam-6102	25	8	non	non	ADJ
ejpam-6102	25	9	-	-	ADJ
ejpam-6102	25	10	constant	constant	ADJ
ejpam-6102	25	11	solutions	solution	NOUN
ejpam-6102	25	12	arise	arise	VERB
ejpam-6102	25	13	,	,	PUNCT
ejpam-6102	25	14	which	which	PRON
ejpam-6102	25	15	blow	blow	VERB
ejpam-6102	25	16	up	up	ADP
ejpam-6102	25	17	at	at	ADP
ejpam-6102	25	18	one	one	NUM
ejpam-6102	25	19	or	or	CCONJ
ejpam-6102	25	20	more	more	ADJ
ejpam-6102	25	21	points	point	NOUN
ejpam-6102	25	22	as	as	ADP
ejpam-6102	25	23	λ→	λ→	NUM
ejpam-6102	25	24	∞	∞	PROPN
ejpam-6102	26	1	[	[	X
ejpam-6102	26	2	6	6	NUM
ejpam-6102	26	3	]	]	PUNCT
ejpam-6102	26	4	.	.	PUNCT
ejpam-6102	27	1	the	the	DET
ejpam-6102	27	2	least	least	ADJ
ejpam-6102	27	3	energy	energy	NOUN
ejpam-6102	27	4	solution	solution	NOUN
ejpam-6102	27	5	experiences	experience	NOUN
ejpam-6102	27	6	,	,	PUNCT
ejpam-6102	27	7	for	for	ADP
ejpam-6102	27	8	large	large	ADJ
ejpam-6102	27	9	λ	λ	NOUN
ejpam-6102	27	10	,	,	PUNCT
ejpam-6102	27	11	a	a	DET
ejpam-6102	27	12	blow	blow	NOUN
ejpam-6102	27	13	-	-	PUNCT
ejpam-6102	27	14	up	up	NOUN
ejpam-6102	27	15	at	at	ADP
ejpam-6102	27	16	a	a	DET
ejpam-6102	27	17	boundary	boundary	ADJ
ejpam-6102	27	18	point	point	NOUN
ejpam-6102	27	19	where	where	SCONJ
ejpam-6102	27	20	the	the	DET
ejpam-6102	27	21	mean	mean	ADJ
ejpam-6102	27	22	curvature	curvature	NOUN
ejpam-6102	27	23	of	of	ADP
ejpam-6102	27	24	the	the	DET
ejpam-6102	27	25	boundary	boundary	NOUN
ejpam-6102	27	26	is	be	AUX
ejpam-6102	27	27	maximized	maximize	VERB
ejpam-6102	27	28	[	[	X
ejpam-6102	27	29	6–9	6–9	NOUN
ejpam-6102	27	30	]	]	PUNCT
ejpam-6102	27	31	.	.	PUNCT
ejpam-6102	28	1	numerous	numerous	ADJ
ejpam-6102	28	2	works	work	NOUN
ejpam-6102	28	3	,	,	PUNCT
ejpam-6102	28	4	such	such	ADJ
ejpam-6102	28	5	as	as	ADP
ejpam-6102	28	6	[	[	X
ejpam-6102	28	7	6	6	NUM
ejpam-6102	28	8	,	,	PUNCT
ejpam-6102	28	9	10–13	10–13	NUM
ejpam-6102	28	10	]	]	PUNCT
ejpam-6102	28	11	,	,	PUNCT
ejpam-6102	28	12	have	have	AUX
ejpam-6102	28	13	analyzed	analyze	VERB
ejpam-6102	28	14	higher	high	ADJ
ejpam-6102	28	15	-	-	PUNCT
ejpam-6102	28	16	energy	energy	NOUN
ejpam-6102	28	17	solutions	solution	NOUN
ejpam-6102	28	18	of	of	ADP
ejpam-6102	28	19	(	(	PUNCT
ejpam-6102	28	20	pλ	pλ	PROPN
ejpam-6102	28	21	,	,	PUNCT
ejpam-6102	28	22	q	q	NOUN
ejpam-6102	28	23	)	)	PUNCT
ejpam-6102	28	24	that	that	PRON
ejpam-6102	28	25	exhibit	exhibit	VERB
ejpam-6102	28	26	this	this	DET
ejpam-6102	28	27	asymptotic	asymptotic	ADJ
ejpam-6102	28	28	profile	profile	NOUN
ejpam-6102	28	29	,	,	PUNCT
ejpam-6102	28	30	whether	whether	SCONJ
ejpam-6102	28	31	blow	blow	VERB
ejpam-6102	28	32	up	up	ADP
ejpam-6102	28	33	at	at	ADP
ejpam-6102	28	34	boundary	boundary	ADJ
ejpam-6102	28	35	or	or	CCONJ
ejpam-6102	28	36	interior	interior	ADJ
ejpam-6102	28	37	points	point	NOUN
ejpam-6102	28	38	,	,	PUNCT
ejpam-6102	28	39	as	as	ADP
ejpam-6102	28	40	λ	λ	PROPN
ejpam-6102	28	41	→	→	SYM
ejpam-6102	28	42	∞.	∞.	PROPN
ejpam-6102	28	43	in	in	ADP
ejpam-6102	28	44	particular	particular	ADJ
ejpam-6102	28	45	,	,	PUNCT
ejpam-6102	28	46	solutions	solution	NOUN
ejpam-6102	28	47	with	with	ADP
ejpam-6102	28	48	any	any	DET
ejpam-6102	28	49	desired	desire	VERB
ejpam-6102	28	50	number	number	NOUN
ejpam-6102	28	51	of	of	ADP
ejpam-6102	28	52	blow	blow	NOUN
ejpam-6102	28	53	up	up	ADP
ejpam-6102	28	54	points	point	NOUN
ejpam-6102	28	55	,	,	PUNCT
ejpam-6102	28	56	both	both	CCONJ
ejpam-6102	28	57	interior	interior	ADJ
ejpam-6102	28	58	and	and	CCONJ
ejpam-6102	28	59	boundary	boundary	ADJ
ejpam-6102	28	60	,	,	PUNCT
ejpam-6102	28	61	have	have	AUX
ejpam-6102	28	62	been	be	AUX
ejpam-6102	28	63	shown	show	VERB
ejpam-6102	28	64	to	to	PART
ejpam-6102	28	65	exist	exist	VERB
ejpam-6102	28	66	.	.	PUNCT
ejpam-6102	29	1	the	the	DET
ejpam-6102	29	2	case	case	NOUN
ejpam-6102	29	3	when	when	SCONJ
ejpam-6102	29	4	q	q	PROPN
ejpam-6102	29	5	=	=	PUNCT
ejpam-6102	29	6	(	(	PUNCT
ejpam-6102	29	7	n	n	PROPN
ejpam-6102	29	8	+	+	CCONJ
ejpam-6102	29	9	2)/(n	2)/(n	NUM
ejpam-6102	29	10	−	−	NOUN
ejpam-6102	29	11	2	2	NUM
ejpam-6102	29	12	)	)	PUNCT
ejpam-6102	29	13	,	,	PUNCT
ejpam-6102	29	14	the	the	DET
ejpam-6102	29	15	critical	critical	ADJ
ejpam-6102	29	16	exponent	exponent	NOUN
ejpam-6102	29	17	,	,	PUNCT
ejpam-6102	29	18	differs	differ	VERB
ejpam-6102	29	19	significantly	significantly	ADV
ejpam-6102	29	20	.	.	PUNCT
ejpam-6102	30	1	for	for	ADP
ejpam-6102	30	2	n	n	PRON
ejpam-6102	30	3	∈	∈	PROPN
ejpam-6102	30	4	{	{	PUNCT
ejpam-6102	30	5	4	4	NUM
ejpam-6102	30	6	,	,	PUNCT
ejpam-6102	30	7	5	5	NUM
ejpam-6102	30	8	,	,	PUNCT
ejpam-6102	30	9	6	6	NUM
ejpam-6102	30	10	}	}	PUNCT
ejpam-6102	30	11	and	and	CCONJ
ejpam-6102	30	12	small	small	ADJ
ejpam-6102	30	13	λ	λ	PROPN
ejpam-6102	30	14	,	,	PUNCT
ejpam-6102	30	15	(	(	PUNCT
ejpam-6102	30	16	pλ	pλ	NOUN
ejpam-6102	30	17	,	,	PUNCT
ejpam-6102	30	18	q	q	NOUN
ejpam-6102	30	19	)	)	PUNCT
ejpam-6102	30	20	admits	admit	VERB
ejpam-6102	30	21	non	non	ADJ
ejpam-6102	30	22	-	-	ADJ
ejpam-6102	30	23	constant	constant	ADJ
ejpam-6102	30	24	solutions	solution	NOUN
ejpam-6102	30	25	[	[	X
ejpam-6102	30	26	14–16	14–16	NUM
ejpam-6102	30	27	]	]	PUNCT
ejpam-6102	30	28	.	.	PUNCT
ejpam-6102	31	1	on	on	ADP
ejpam-6102	31	2	the	the	DET
ejpam-6102	31	3	other	other	ADJ
ejpam-6102	31	4	hand	hand	NOUN
ejpam-6102	31	5	,	,	PUNCT
ejpam-6102	31	6	the	the	DET
ejpam-6102	31	7	limiting	limit	VERB
ejpam-6102	31	8	equation	equation	NOUN
ejpam-6102	31	9	of	of	ADP
ejpam-6102	31	10	problem	problem	NOUN
ejpam-6102	31	11	(	(	PUNCT
ejpam-6102	31	12	pλ	pλ	NOUN
ejpam-6102	31	13	,	,	PUNCT
ejpam-6102	31	14	q	q	NOUN
ejpam-6102	31	15	)	)	PUNCT
ejpam-6102	31	16	,	,	PUNCT
ejpam-6102	31	17	which	which	PRON
ejpam-6102	31	18	arises	arise	VERB
ejpam-6102	31	19	when	when	SCONJ
ejpam-6102	31	20	studying	study	VERB
ejpam-6102	31	21	the	the	DET
ejpam-6102	31	22	asymptotic	asymptotic	ADJ
ejpam-6102	31	23	behavior	behavior	NOUN
ejpam-6102	31	24	of	of	ADP
ejpam-6102	31	25	the	the	DET
ejpam-6102	31	26	least	least	ADJ
ejpam-6102	31	27	-	-	PUNCT
ejpam-6102	31	28	energy	energy	NOUN
ejpam-6102	31	29	solution	solution	NOUN
ejpam-6102	31	30	as	as	ADP
ejpam-6102	31	31	λ→	λ→	PROPN
ejpam-6102	31	32	∞	∞	PROPN
ejpam-6102	31	33	,	,	PUNCT
ejpam-6102	31	34	does	do	AUX
ejpam-6102	31	35	not	not	PART
ejpam-6102	31	36	have	have	VERB
ejpam-6102	31	37	any	any	DET
ejpam-6102	31	38	solutions	solution	NOUN
ejpam-6102	31	39	.	.	PUNCT
ejpam-6102	32	1	nevertheless	nevertheless	ADV
ejpam-6102	32	2	,	,	PUNCT
ejpam-6102	32	3	least	least	ADJ
ejpam-6102	32	4	-	-	PUNCT
ejpam-6102	32	5	energy	energy	NOUN
ejpam-6102	32	6	solutions	solution	NOUN
ejpam-6102	32	7	uλ	uλ	ADP
ejpam-6102	32	8	,	,	PUNCT
ejpam-6102	32	9	q	q	PROPN
ejpam-6102	32	10	still	still	ADV
ejpam-6102	32	11	exist	exist	VERB
ejpam-6102	32	12	for	for	ADP
ejpam-6102	32	13	large	large	ADJ
ejpam-6102	32	14	λ	λ	NOUN
ejpam-6102	32	15	,	,	PUNCT
ejpam-6102	32	16	and	and	CCONJ
ejpam-6102	32	17	concentration	concentration	NOUN
ejpam-6102	32	18	appears	appear	VERB
ejpam-6102	32	19	in	in	ADP
ejpam-6102	32	20	the	the	DET
ejpam-6102	32	21	form	form	NOUN
ejpam-6102	32	22	[	[	X
ejpam-6102	32	23	17	17	NUM
ejpam-6102	32	24	,	,	PUNCT
ejpam-6102	32	25	18	18	NUM
ejpam-6102	32	26	]	]	PUNCT
ejpam-6102	32	27	ωaλ,µλ	ωaλ,µλ	NUM
ejpam-6102	32	28	(	(	PUNCT
ejpam-6102	32	29	x	x	X
ejpam-6102	32	30	)	)	PUNCT
ejpam-6102	32	31	,	,	PUNCT
ejpam-6102	32	32	where	where	SCONJ
ejpam-6102	32	33	aλ	aλ	AUX
ejpam-6102	32	34	∈	∈	PROPN
ejpam-6102	32	35	∂ω	∂ω	PROPN
ejpam-6102	32	36	behaves	behave	VERB
ejpam-6102	32	37	as	as	ADP
ejpam-6102	32	38	in	in	ADP
ejpam-6102	32	39	the	the	DET
ejpam-6102	32	40	subcritical	subcritical	ADJ
ejpam-6102	32	41	case	case	NOUN
ejpam-6102	32	42	,	,	PUNCT
ejpam-6102	32	43	converging	converge	VERB
ejpam-6102	32	44	to	to	ADP
ejpam-6102	32	45	the	the	DET
ejpam-6102	32	46	point	point	NOUN
ejpam-6102	32	47	that	that	PRON
ejpam-6102	32	48	maximizes	maximize	VERB
ejpam-6102	32	49	the	the	DET
ejpam-6102	32	50	mean	mean	ADJ
ejpam-6102	32	51	curvature	curvature	NOUN
ejpam-6102	32	52	of	of	ADP
ejpam-6102	32	53	the	the	DET
ejpam-6102	32	54	boundary	boundary	NOUN
ejpam-6102	32	55	.	.	PUNCT
ejpam-6102	33	1	in	in	ADP
ejpam-6102	33	2	this	this	DET
ejpam-6102	33	3	context	context	NOUN
ejpam-6102	33	4	,	,	PUNCT
ejpam-6102	33	5	for	for	ADP
ejpam-6102	33	6	any	any	DET
ejpam-6102	33	7	a	a	DET
ejpam-6102	33	8	∈	∈	PROPN
ejpam-6102	33	9	rn	rn	NOUN
ejpam-6102	33	10	and	and	CCONJ
ejpam-6102	33	11	µ	µ	PROPN
ejpam-6102	33	12	∈	∈	PROPN
ejpam-6102	33	13	(	(	PUNCT
ejpam-6102	33	14	0,∞	0,∞	NOUN
ejpam-6102	33	15	)	)	PUNCT
ejpam-6102	33	16	,	,	PUNCT
ejpam-6102	33	17	the	the	DET
ejpam-6102	33	18	function	function	NOUN
ejpam-6102	33	19	ωa,µ	ωa,µ	PUNCT
ejpam-6102	33	20	represents	represent	VERB
ejpam-6102	33	21	the	the	DET
ejpam-6102	33	22	standard	standard	ADJ
ejpam-6102	33	23	bubble	bubble	NOUN
ejpam-6102	33	24	defined	define	VERB
ejpam-6102	33	25	by	by	ADP
ejpam-6102	33	26	ωa,µ(x	ωa,µ(x	NOUN
ejpam-6102	33	27	)	)	PUNCT
ejpam-6102	33	28	:	:	PUNCT
ejpam-6102	33	29	=	=	X
ejpam-6102	33	30	β0	β0	PROPN
ejpam-6102	33	31	µ(n−2)/2	µ(n−2)/2	PROPN
ejpam-6102	33	32	(	(	PUNCT
ejpam-6102	33	33	1	1	NUM
ejpam-6102	33	34	+	+	CCONJ
ejpam-6102	33	35	µ2|x−	µ2|x−	NOUN
ejpam-6102	33	36	a|2)(n−2)/2	a|2)(n−2)/2	NOUN
ejpam-6102	33	37	,	,	PUNCT
ejpam-6102	33	38	where	where	SCONJ
ejpam-6102	33	39	β0	β0	NOUN
ejpam-6102	33	40	:	:	PUNCT
ejpam-6102	33	41	=	=	PUNCT
ejpam-6102	34	1	[	[	X
ejpam-6102	34	2	n(n−	n(n−	NUM
ejpam-6102	34	3	2)](n−2)/4	2)](n−2)/4	NUM
ejpam-6102	34	4	(	(	PUNCT
ejpam-6102	34	5	1	1	NUM
ejpam-6102	34	6	)	)	PUNCT
ejpam-6102	34	7	which	which	PRON
ejpam-6102	34	8	are	be	AUX
ejpam-6102	34	9	the	the	DET
ejpam-6102	34	10	only	only	ADJ
ejpam-6102	34	11	solutions	solution	NOUN
ejpam-6102	34	12	[	[	X
ejpam-6102	34	13	19	19	NUM
ejpam-6102	34	14	]	]	PUNCT
ejpam-6102	34	15	of	of	ADP
ejpam-6102	34	16	−∆u	−∆u	PRON
ejpam-6102	34	17	=	=	PUNCT
ejpam-6102	34	18	u	u	PROPN
ejpam-6102	34	19	n+2	n+2	PROPN
ejpam-6102	34	20	n−2	n−2	PROPN
ejpam-6102	34	21	,	,	PUNCT
ejpam-6102	34	22	u	u	NOUN
ejpam-6102	34	23	>	>	X
ejpam-6102	34	24	0	0	PUNCT
ejpam-6102	34	25	in	in	ADP
ejpam-6102	34	26	rn	rn	PROPN
ejpam-6102	34	27	.	.	PROPN
ejpam-6102	34	28	higher	high	ADJ
ejpam-6102	34	29	-	-	PUNCT
ejpam-6102	34	30	energy	energy	NOUN
ejpam-6102	34	31	solutions	solution	NOUN
ejpam-6102	34	32	of	of	ADP
ejpam-6102	34	33	(	(	PUNCT
ejpam-6102	34	34	pλ	pλ	PROPN
ejpam-6102	34	35	,	,	PUNCT
ejpam-6102	34	36	q	q	NOUN
ejpam-6102	34	37	)	)	PUNCT
ejpam-6102	34	38	with	with	ADP
ejpam-6102	34	39	concentration	concentration	NOUN
ejpam-6102	34	40	on	on	ADP
ejpam-6102	34	41	the	the	DET
ejpam-6102	34	42	boundary	boundary	NOUN
ejpam-6102	34	43	as	as	SCONJ
ejpam-6102	34	44	λ→	λ→	NOUN
ejpam-6102	34	45	∞	∞	PROPN
ejpam-6102	34	46	have	have	AUX
ejpam-6102	34	47	been	be	AUX
ejpam-6102	34	48	constructed	construct	VERB
ejpam-6102	34	49	in	in	ADP
ejpam-6102	34	50	several	several	ADJ
ejpam-6102	34	51	studies	study	NOUN
ejpam-6102	34	52	,	,	PUNCT
ejpam-6102	34	53	such	such	ADJ
ejpam-6102	34	54	as	as	ADP
ejpam-6102	34	55	[	[	X
ejpam-6102	34	56	17	17	NUM
ejpam-6102	34	57	,	,	PUNCT
ejpam-6102	34	58	18	18	NUM
ejpam-6102	34	59	,	,	PUNCT
ejpam-6102	34	60	20–27	20–27	NUM
ejpam-6102	34	61	]	]	PUNCT
ejpam-6102	34	62	and	and	CCONJ
ejpam-6102	34	63	the	the	DET
ejpam-6102	34	64	references	reference	NOUN
ejpam-6102	34	65	therein	therein	ADV
ejpam-6102	34	66	.	.	PUNCT
ejpam-6102	35	1	unlike	unlike	ADP
ejpam-6102	35	2	the	the	DET
ejpam-6102	35	3	subcritical	subcritical	ADJ
ejpam-6102	35	4	scenario	scenario	NOUN
ejpam-6102	35	5	,	,	PUNCT
ejpam-6102	35	6	at	at	ADP
ejpam-6102	35	7	least	least	ADV
ejpam-6102	35	8	one	one	NUM
ejpam-6102	35	9	blow	blow	NOUN
ejpam-6102	35	10	up	up	ADP
ejpam-6102	35	11	point	point	NOUN
ejpam-6102	35	12	must	must	AUX
ejpam-6102	35	13	lie	lie	VERB
ejpam-6102	35	14	on	on	ADP
ejpam-6102	35	15	the	the	DET
ejpam-6102	35	16	boundary	boundary	NOUN
ejpam-6102	35	17	[	[	X
ejpam-6102	35	18	28	28	NUM
ejpam-6102	35	19	]	]	PUNCT
ejpam-6102	35	20	.	.	PUNCT
ejpam-6102	36	1	another	another	DET
ejpam-6102	36	2	interesting	interesting	ADJ
ejpam-6102	36	3	avenue	avenue	NOUN
ejpam-6102	36	4	of	of	ADP
ejpam-6102	36	5	research	research	NOUN
ejpam-6102	36	6	for	for	ADP
ejpam-6102	36	7	problem	problem	NOUN
ejpam-6102	36	8	(	(	PUNCT
ejpam-6102	36	9	pλ	pλ	NOUN
ejpam-6102	36	10	,	,	PUNCT
ejpam-6102	36	11	q	q	NOUN
ejpam-6102	36	12	)	)	PUNCT
ejpam-6102	36	13	involves	involve	VERB
ejpam-6102	36	14	studying	study	VERB
ejpam-6102	36	15	blow	blow	VERB
ejpam-6102	36	16	up	up	ADP
ejpam-6102	36	17	phenomena	phenomenon	NOUN
ejpam-6102	36	18	by	by	ADP
ejpam-6102	36	19	fixing	fix	VERB
ejpam-6102	36	20	λ	λ	PROPN
ejpam-6102	36	21	while	while	SCONJ
ejpam-6102	36	22	letting	let	VERB
ejpam-6102	36	23	the	the	DET
ejpam-6102	36	24	exponent	exponent	NOUN
ejpam-6102	36	25	q	q	PROPN
ejpam-6102	36	26	approaches	approach	VERB
ejpam-6102	36	27	the	the	DET
ejpam-6102	36	28	critical	critical	ADJ
ejpam-6102	36	29	exponent	exponent	NOUN
ejpam-6102	36	30	,	,	PUNCT
ejpam-6102	36	31	i.e.	i.e.	X
ejpam-6102	36	32	,	,	PUNCT
ejpam-6102	36	33	q	q	X
ejpam-6102	36	34	=	=	PUNCT
ejpam-6102	36	35	n+2	n+2	NUM
ejpam-6102	36	36	n−2	n−2	PROPN
ejpam-6102	36	37	±	±	NUM
ejpam-6102	36	38	ε	ε	PROPN
ejpam-6102	36	39	,	,	PUNCT
ejpam-6102	36	40	where	where	SCONJ
ejpam-6102	36	41	ε	ε	PROPN
ejpam-6102	36	42	is	be	AUX
ejpam-6102	36	43	a	a	DET
ejpam-6102	36	44	small	small	ADJ
ejpam-6102	36	45	positive	positive	ADJ
ejpam-6102	36	46	parameter	parameter	NOUN
ejpam-6102	36	47	.	.	PUNCT
ejpam-6102	37	1	this	this	PRON
ejpam-6102	37	2	was	be	AUX
ejpam-6102	37	3	first	first	ADV
ejpam-6102	37	4	explored	explore	VERB
ejpam-6102	37	5	by	by	ADP
ejpam-6102	37	6	rey	rey	PROPN
ejpam-6102	37	7	and	and	CCONJ
ejpam-6102	37	8	wei	wei	PROPN
ejpam-6102	37	9	.	.	PROPN
ejpam-6102	37	10	for	for	ADP
ejpam-6102	37	11	n	n	PROPN
ejpam-6102	37	12	≥	≥	NOUN
ejpam-6102	37	13	4	4	NUM
ejpam-6102	37	14	and	and	CCONJ
ejpam-6102	37	15	q	q	NOUN
ejpam-6102	37	16	=	=	PUNCT
ejpam-6102	37	17	n+2	n+2	NUM
ejpam-6102	37	18	n−2	n−2	PROPN
ejpam-6102	37	19	+	+	CCONJ
ejpam-6102	37	20	ε	ε	PROPN
ejpam-6102	37	21	,	,	PUNCT
ejpam-6102	37	22	they	they	PRON
ejpam-6102	37	23	demonstrated	demonstrate	VERB
ejpam-6102	37	24	the	the	DET
ejpam-6102	37	25	existence	existence	NOUN
ejpam-6102	37	26	of	of	ADP
ejpam-6102	37	27	a	a	DET
ejpam-6102	37	28	solution	solution	NOUN
ejpam-6102	37	29	that	that	PRON
ejpam-6102	37	30	blows	blow	VERB
ejpam-6102	37	31	up	up	ADP
ejpam-6102	37	32	at	at	ADP
ejpam-6102	37	33	a	a	DET
ejpam-6102	37	34	boundary	boundary	ADJ
ejpam-6102	37	35	point	point	NOUN
ejpam-6102	37	36	where	where	SCONJ
ejpam-6102	37	37	the	the	DET
ejpam-6102	37	38	mean	mean	ADJ
ejpam-6102	37	39	curvature	curvature	NOUN
ejpam-6102	37	40	is	be	AUX
ejpam-6102	37	41	maximized	maximize	VERB
ejpam-6102	37	42	[	[	X
ejpam-6102	37	43	29	29	NUM
ejpam-6102	37	44	]	]	PUNCT
ejpam-6102	37	45	.	.	PUNCT
ejpam-6102	38	1	they	they	PRON
ejpam-6102	38	2	also	also	ADV
ejpam-6102	38	3	showed	show	VERB
ejpam-6102	38	4	r.	r.	PROPN
ejpam-6102	38	5	almushahhin	almushahhin	PROPN
ejpam-6102	38	6	,	,	PUNCT
ejpam-6102	38	7	m.	m.	PROPN
ejpam-6102	38	8	ben	ben	PROPN
ejpam-6102	38	9	ayed	aye	VERB
ejpam-6102	38	10	/	/	SYM
ejpam-6102	38	11	eur	eur	PROPN
ejpam-6102	38	12	.	.	PUNCT
ejpam-6102	39	1	j.	j.	PROPN
ejpam-6102	39	2	pure	pure	PROPN
ejpam-6102	39	3	appl	appl	PROPN
ejpam-6102	39	4	.	.	PROPN
ejpam-6102	39	5	math	math	PROPN
ejpam-6102	39	6	,	,	PUNCT
ejpam-6102	39	7	18	18	NUM
ejpam-6102	39	8	(	(	PUNCT
ejpam-6102	39	9	2	2	NUM
ejpam-6102	39	10	)	)	PUNCT
ejpam-6102	39	11	(	(	PUNCT
ejpam-6102	39	12	2025	2025	NUM
ejpam-6102	39	13	)	)	PUNCT
ejpam-6102	39	14	,	,	PUNCT
ejpam-6102	39	15	6102	6102	NUM
ejpam-6102	39	16	3	3	NUM
ejpam-6102	39	17	of	of	ADP
ejpam-6102	39	18	31	31	NUM
ejpam-6102	39	19	the	the	DET
ejpam-6102	39	20	existence	existence	NOUN
ejpam-6102	39	21	of	of	ADP
ejpam-6102	39	22	a	a	DET
ejpam-6102	39	23	solution	solution	NOUN
ejpam-6102	39	24	that	that	PRON
ejpam-6102	39	25	blows	blow	VERB
ejpam-6102	39	26	up	up	ADP
ejpam-6102	39	27	at	at	ADP
ejpam-6102	39	28	a	a	DET
ejpam-6102	39	29	boundary	boundary	ADJ
ejpam-6102	39	30	point	point	NOUN
ejpam-6102	39	31	where	where	SCONJ
ejpam-6102	39	32	the	the	DET
ejpam-6102	39	33	mean	mean	ADJ
ejpam-6102	39	34	curvature	curvature	NOUN
ejpam-6102	39	35	is	be	AUX
ejpam-6102	39	36	minimized	minimize	VERB
ejpam-6102	39	37	when	when	SCONJ
ejpam-6102	39	38	q	q	PROPN
ejpam-6102	39	39	=	=	SYM
ejpam-6102	39	40	n+2	n+2	NUM
ejpam-6102	39	41	n−2	n−2	PROPN
ejpam-6102	39	42	−	−	PROPN
ejpam-6102	39	43	ε	ε	PROPN
ejpam-6102	39	44	and	and	CCONJ
ejpam-6102	39	45	ω	ω	PROPN
ejpam-6102	39	46	is	be	AUX
ejpam-6102	39	47	not	not	PART
ejpam-6102	39	48	convex	convex	ADJ
ejpam-6102	39	49	[	[	PUNCT
ejpam-6102	39	50	29	29	NUM
ejpam-6102	39	51	]	]	PUNCT
ejpam-6102	39	52	.	.	PUNCT
ejpam-6102	40	1	in	in	ADP
ejpam-6102	40	2	dimension	dimension	NOUN
ejpam-6102	40	3	3	3	NUM
ejpam-6102	40	4	,	,	PUNCT
ejpam-6102	40	5	they	they	PRON
ejpam-6102	40	6	found	find	VERB
ejpam-6102	40	7	a	a	DET
ejpam-6102	40	8	solution	solution	NOUN
ejpam-6102	40	9	with	with	ADP
ejpam-6102	40	10	single	single	ADJ
ejpam-6102	40	11	interior	interior	ADJ
ejpam-6102	40	12	blow	blow	NOUN
ejpam-6102	40	13	-	-	PUNCT
ejpam-6102	40	14	up	up	ADP
ejpam-6102	40	15	point	point	NOUN
ejpam-6102	40	16	[	[	X
ejpam-6102	40	17	30	30	NUM
ejpam-6102	40	18	]	]	PUNCT
ejpam-6102	40	19	.	.	PUNCT
ejpam-6102	41	1	more	more	ADV
ejpam-6102	41	2	recently	recently	ADV
ejpam-6102	41	3	,	,	PUNCT
ejpam-6102	41	4	it	it	PRON
ejpam-6102	41	5	was	be	AUX
ejpam-6102	41	6	shown	show	VERB
ejpam-6102	41	7	that	that	SCONJ
ejpam-6102	41	8	for	for	ADP
ejpam-6102	41	9	n	n	PRON
ejpam-6102	41	10	≥	≥	NOUN
ejpam-6102	41	11	4	4	NUM
ejpam-6102	41	12	and	and	CCONJ
ejpam-6102	41	13	q	q	NOUN
ejpam-6102	41	14	=	=	PUNCT
ejpam-6102	41	15	n+2	n+2	NUM
ejpam-6102	41	16	n−2	n−2	PROPN
ejpam-6102	41	17	+	+	CCONJ
ejpam-6102	41	18	ε	ε	PROPN
ejpam-6102	41	19	,	,	PUNCT
ejpam-6102	41	20	there	there	PRON
ejpam-6102	41	21	are	be	VERB
ejpam-6102	41	22	no	no	DET
ejpam-6102	41	23	solutions	solution	NOUN
ejpam-6102	41	24	that	that	PRON
ejpam-6102	41	25	exhibit	exhibit	VERB
ejpam-6102	41	26	blow	blow	NOUN
ejpam-6102	41	27	-	-	PUNCT
ejpam-6102	41	28	up	up	NOUN
ejpam-6102	41	29	exclusively	exclusively	ADV
ejpam-6102	41	30	at	at	ADP
ejpam-6102	41	31	interior	interior	ADJ
ejpam-6102	41	32	points	point	NOUN
ejpam-6102	41	33	when	when	SCONJ
ejpam-6102	41	34	ε	ε	PROPN
ejpam-6102	41	35	is	be	AUX
ejpam-6102	41	36	a	a	DET
ejpam-6102	41	37	small	small	ADJ
ejpam-6102	41	38	positive	positive	ADJ
ejpam-6102	41	39	number	number	NOUN
ejpam-6102	41	40	[	[	X
ejpam-6102	41	41	31	31	NUM
ejpam-6102	41	42	]	]	PUNCT
ejpam-6102	41	43	.	.	PUNCT
ejpam-6102	42	1	furthermore	furthermore	ADV
ejpam-6102	42	2	,	,	PUNCT
ejpam-6102	42	3	in	in	ADP
ejpam-6102	42	4	[	[	PUNCT
ejpam-6102	42	5	32	32	NUM
ejpam-6102	42	6	]	]	PUNCT
ejpam-6102	42	7	,	,	PUNCT
ejpam-6102	42	8	the	the	DET
ejpam-6102	42	9	authors	author	NOUN
ejpam-6102	42	10	extended	extend	VERB
ejpam-6102	42	11	the	the	DET
ejpam-6102	42	12	problem	problem	NOUN
ejpam-6102	42	13	by	by	ADP
ejpam-6102	42	14	replacing	replace	VERB
ejpam-6102	42	15	the	the	DET
ejpam-6102	42	16	constant	constant	ADJ
ejpam-6102	42	17	λ	λ	NOUN
ejpam-6102	42	18	with	with	ADP
ejpam-6102	42	19	a	a	DET
ejpam-6102	42	20	function	function	NOUN
ejpam-6102	42	21	v	v	NOUN
ejpam-6102	42	22	and	and	CCONJ
ejpam-6102	42	23	studied	study	VERB
ejpam-6102	42	24	the	the	DET
ejpam-6102	42	25	problem	problem	NOUN
ejpam-6102	42	26	(	(	PUNCT
ejpam-6102	42	27	pv	pv	INTJ
ejpam-6102	42	28	,	,	PUNCT
ejpam-6102	42	29	ε	ε	PROPN
ejpam-6102	42	30	)	)	PUNCT
ejpam-6102	42	31	{	{	PUNCT
ejpam-6102	43	1	−∆u+	−∆u+	NOUN
ejpam-6102	43	2	v	v	X
ejpam-6102	43	3	u	u	NOUN
ejpam-6102	43	4	=	=	SYM
ejpam-6102	43	5	u	u	PROPN
ejpam-6102	43	6	n+2	n+2	PROPN
ejpam-6102	43	7	n−2	n−2	PROPN
ejpam-6102	43	8	−ε	−ε	PROPN
ejpam-6102	43	9	,	,	PUNCT
ejpam-6102	43	10	u	u	NOUN
ejpam-6102	43	11	>	>	X
ejpam-6102	43	12	0	0	PUNCT
ejpam-6102	43	13	in	in	ADP
ejpam-6102	43	14	ω	ω	NUM
ejpam-6102	43	15	,	,	PUNCT
ejpam-6102	43	16	∂u	∂u	PROPN
ejpam-6102	43	17	∂ν	∂ν	X
ejpam-6102	44	1	=	=	PUNCT
ejpam-6102	44	2	0	0	PROPN
ejpam-6102	44	3	,	,	PUNCT
ejpam-6102	44	4	on	on	ADP
ejpam-6102	44	5	∂ω	∂ω	PROPN
ejpam-6102	44	6	,	,	PUNCT
ejpam-6102	44	7	where	where	SCONJ
ejpam-6102	44	8	ω	ω	PROPN
ejpam-6102	44	9	is	be	AUX
ejpam-6102	44	10	a	a	DET
ejpam-6102	44	11	smooth	smooth	ADJ
ejpam-6102	44	12	,	,	PUNCT
ejpam-6102	44	13	bounded	bounded	ADJ
ejpam-6102	44	14	subset	subset	NOUN
ejpam-6102	44	15	of	of	ADP
ejpam-6102	44	16	rn	rn	PROPN
ejpam-6102	44	17	,	,	PUNCT
ejpam-6102	44	18	n	n	PRON
ejpam-6102	44	19	≥	≥	NUM
ejpam-6102	44	20	6	6	NUM
ejpam-6102	44	21	,	,	PUNCT
ejpam-6102	44	22	v	v	NOUN
ejpam-6102	44	23	is	be	AUX
ejpam-6102	44	24	a	a	DET
ejpam-6102	44	25	positive	positive	ADJ
ejpam-6102	44	26	c2	c2	PROPN
ejpam-6102	44	27	-	-	PUNCT
ejpam-6102	44	28	function	function	NOUN
ejpam-6102	44	29	on	on	ADP
ejpam-6102	44	30	ω	ω	NUM
ejpam-6102	44	31	,	,	PUNCT
ejpam-6102	44	32	and	and	CCONJ
ejpam-6102	44	33	ε	ε	PROPN
ejpam-6102	44	34	is	be	AUX
ejpam-6102	44	35	a	a	DET
ejpam-6102	44	36	small	small	ADJ
ejpam-6102	44	37	positive	positive	ADJ
ejpam-6102	44	38	parameter	parameter	NOUN
ejpam-6102	44	39	.	.	PUNCT
ejpam-6102	45	1	they	they	PRON
ejpam-6102	45	2	constructed	construct	VERB
ejpam-6102	45	3	interior	interior	ADJ
ejpam-6102	45	4	bubbling	bubbling	NOUN
ejpam-6102	45	5	solutions	solution	NOUN
ejpam-6102	45	6	,	,	PUNCT
ejpam-6102	45	7	where	where	SCONJ
ejpam-6102	45	8	the	the	DET
ejpam-6102	45	9	interior	interior	ADJ
ejpam-6102	45	10	blow	blow	NOUN
ejpam-6102	45	11	-	-	PUNCT
ejpam-6102	45	12	up	up	ADP
ejpam-6102	45	13	points	point	NOUN
ejpam-6102	45	14	of	of	ADP
ejpam-6102	45	15	these	these	DET
ejpam-6102	45	16	solutions	solution	NOUN
ejpam-6102	45	17	converge	converge	VERB
ejpam-6102	45	18	,	,	PUNCT
ejpam-6102	45	19	as	as	ADP
ejpam-6102	45	20	ε	ε	PROPN
ejpam-6102	45	21	→	→	SYM
ejpam-6102	45	22	0	0	NUM
ejpam-6102	45	23	,	,	PUNCT
ejpam-6102	45	24	to	to	ADP
ejpam-6102	45	25	the	the	DET
ejpam-6102	45	26	critical	critical	ADJ
ejpam-6102	45	27	points	point	NOUN
ejpam-6102	45	28	of	of	ADP
ejpam-6102	45	29	the	the	DET
ejpam-6102	45	30	function	function	NOUN
ejpam-6102	45	31	v	v	NOUN
ejpam-6102	45	32	.	.	PUNCT
ejpam-6102	46	1	more	more	ADV
ejpam-6102	46	2	recently	recently	ADV
ejpam-6102	46	3	,	,	PUNCT
ejpam-6102	46	4	in	in	ADP
ejpam-6102	46	5	[	[	PUNCT
ejpam-6102	46	6	33	33	NUM
ejpam-6102	46	7	]	]	PUNCT
ejpam-6102	46	8	,	,	PUNCT
ejpam-6102	46	9	the	the	DET
ejpam-6102	46	10	authors	author	NOUN
ejpam-6102	46	11	studied	study	VERB
ejpam-6102	46	12	the	the	DET
ejpam-6102	46	13	case	case	NOUN
ejpam-6102	46	14	where	where	SCONJ
ejpam-6102	46	15	a	a	DET
ejpam-6102	46	16	function	function	NOUN
ejpam-6102	46	17	f	f	PROPN
ejpam-6102	46	18	is	be	AUX
ejpam-6102	46	19	introduced	introduce	VERB
ejpam-6102	46	20	in	in	ADP
ejpam-6102	46	21	front	front	NOUN
ejpam-6102	46	22	of	of	ADP
ejpam-6102	46	23	the	the	DET
ejpam-6102	46	24	nonlinear	nonlinear	ADJ
ejpam-6102	46	25	term	term	NOUN
ejpam-6102	46	26	.	.	PUNCT
ejpam-6102	47	1	more	more	ADV
ejpam-6102	47	2	precisely	precisely	ADV
ejpam-6102	47	3	,	,	PUNCT
ejpam-6102	47	4	they	they	PRON
ejpam-6102	47	5	considered	consider	VERB
ejpam-6102	47	6	the	the	DET
ejpam-6102	47	7	following	follow	VERB
ejpam-6102	47	8	problem	problem	NOUN
ejpam-6102	47	9	(	(	PUNCT
ejpam-6102	47	10	pε	pε	NOUN
ejpam-6102	47	11	)	)	PUNCT
ejpam-6102	47	12	{	{	PUNCT
ejpam-6102	48	1	−∆u+	−∆u+	NOUN
ejpam-6102	48	2	v	v	X
ejpam-6102	48	3	u	u	X
ejpam-6102	48	4	=	=	PROPN
ejpam-6102	48	5	fup−ε	fup−ε	PROPN
ejpam-6102	48	6	,	,	PUNCT
ejpam-6102	48	7	u	u	NOUN
ejpam-6102	48	8	>	>	X
ejpam-6102	48	9	0	0	PUNCT
ejpam-6102	48	10	in	in	ADP
ejpam-6102	48	11	ω	ω	NUM
ejpam-6102	48	12	,	,	PUNCT
ejpam-6102	48	13	∂u	∂u	PROPN
ejpam-6102	48	14	∂ν	∂ν	X
ejpam-6102	49	1	=	=	PUNCT
ejpam-6102	49	2	0	0	NUM
ejpam-6102	49	3	on	on	ADP
ejpam-6102	49	4	∂ω	∂ω	PROPN
ejpam-6102	49	5	,	,	PUNCT
ejpam-6102	49	6	where	where	SCONJ
ejpam-6102	49	7	ω	ω	PROPN
ejpam-6102	49	8	is	be	AUX
ejpam-6102	49	9	a	a	DET
ejpam-6102	49	10	smooth	smooth	ADJ
ejpam-6102	49	11	bounded	bounded	ADJ
ejpam-6102	49	12	domain	domain	NOUN
ejpam-6102	49	13	of	of	ADP
ejpam-6102	49	14	rn	rn	PROPN
ejpam-6102	49	15	,	,	PUNCT
ejpam-6102	49	16	n	n	CCONJ
ejpam-6102	49	17	⩾	⩾	NOUN
ejpam-6102	49	18	4	4	NUM
ejpam-6102	49	19	,	,	PUNCT
ejpam-6102	49	20	v	v	NOUN
ejpam-6102	49	21	and	and	CCONJ
ejpam-6102	49	22	f	f	PROPN
ejpam-6102	49	23	are	be	AUX
ejpam-6102	49	24	positive	positive	ADJ
ejpam-6102	49	25	c2	c2	PROPN
ejpam-6102	49	26	-	-	PUNCT
ejpam-6102	49	27	functions	function	NOUN
ejpam-6102	49	28	on	on	ADP
ejpam-6102	49	29	ω	ω	PROPN
ejpam-6102	49	30	,	,	PUNCT
ejpam-6102	49	31	ε	ε	PROPN
ejpam-6102	49	32	is	be	AUX
ejpam-6102	49	33	a	a	DET
ejpam-6102	49	34	small	small	ADJ
ejpam-6102	49	35	positive	positive	ADJ
ejpam-6102	49	36	parameter	parameter	NOUN
ejpam-6102	49	37	and	and	CCONJ
ejpam-6102	49	38	p+1	p+1	NOUN
ejpam-6102	49	39	=	=	PUNCT
ejpam-6102	49	40	(	(	PUNCT
ejpam-6102	49	41	2n)/(n−2	2n)/(n−2	NUM
ejpam-6102	49	42	)	)	PUNCT
ejpam-6102	50	1	is	be	AUX
ejpam-6102	50	2	the	the	DET
ejpam-6102	50	3	critical	critical	ADJ
ejpam-6102	50	4	sobolev	sobolev	NOUN
ejpam-6102	50	5	exponent	exponent	NOUN
ejpam-6102	50	6	for	for	ADP
ejpam-6102	50	7	the	the	DET
ejpam-6102	50	8	embedding	embed	VERB
ejpam-6102	50	9	h1(ω	h1(ω	NOUN
ejpam-6102	50	10	)	)	PUNCT
ejpam-6102	50	11	↪	↪	PROPN
ejpam-6102	50	12	→	→	SYM
ejpam-6102	50	13	lq(ω	lq(ω	NOUN
ejpam-6102	50	14	)	)	PUNCT
ejpam-6102	50	15	.	.	PUNCT
ejpam-6102	51	1	they	they	PRON
ejpam-6102	51	2	constructed	construct	VERB
ejpam-6102	51	3	solutions	solution	NOUN
ejpam-6102	51	4	of	of	ADP
ejpam-6102	51	5	(	(	PUNCT
ejpam-6102	51	6	pε	pε	NOUN
ejpam-6102	51	7	)	)	PUNCT
ejpam-6102	51	8	with	with	ADP
ejpam-6102	51	9	multi	multi	ADJ
ejpam-6102	51	10	-	-	ADJ
ejpam-6102	51	11	blow	blow	VERB
ejpam-6102	51	12	up	up	ADP
ejpam-6102	51	13	points	point	NOUN
ejpam-6102	51	14	located	locate	VERB
ejpam-6102	51	15	in	in	ADP
ejpam-6102	51	16	the	the	DET
ejpam-6102	51	17	interior	interior	NOUN
ejpam-6102	51	18	.	.	PUNCT
ejpam-6102	52	1	a	a	DET
ejpam-6102	52	2	natural	natural	ADJ
ejpam-6102	52	3	question	question	NOUN
ejpam-6102	52	4	arises	arise	VERB
ejpam-6102	52	5	:	:	PUNCT
ejpam-6102	52	6	is	be	AUX
ejpam-6102	52	7	it	it	PRON
ejpam-6102	52	8	possible	possible	ADJ
ejpam-6102	52	9	to	to	PART
ejpam-6102	52	10	construct	construct	VERB
ejpam-6102	52	11	solutions	solution	NOUN
ejpam-6102	52	12	with	with	ADP
ejpam-6102	52	13	boundary	boundary	ADJ
ejpam-6102	52	14	blow	blow	NOUN
ejpam-6102	52	15	-	-	PUNCT
ejpam-6102	52	16	up	up	ADP
ejpam-6102	52	17	points	point	NOUN
ejpam-6102	52	18	?	?	PUNCT
ejpam-6102	53	1	as	as	SCONJ
ejpam-6102	53	2	mentioned	mention	VERB
ejpam-6102	53	3	earlier	early	ADV
ejpam-6102	53	4	,	,	PUNCT
ejpam-6102	53	5	this	this	DET
ejpam-6102	53	6	question	question	NOUN
ejpam-6102	53	7	was	be	AUX
ejpam-6102	53	8	partially	partially	ADV
ejpam-6102	53	9	addressed	address	VERB
ejpam-6102	53	10	by	by	ADP
ejpam-6102	53	11	rey	rey	PROPN
ejpam-6102	53	12	and	and	CCONJ
ejpam-6102	53	13	wei	wei	PROPN
ejpam-6102	54	1	[	[	X
ejpam-6102	54	2	29	29	NUM
ejpam-6102	54	3	]	]	PUNCT
ejpam-6102	54	4	,	,	PUNCT
ejpam-6102	54	5	who	who	PRON
ejpam-6102	54	6	constructed	construct	VERB
ejpam-6102	54	7	a	a	DET
ejpam-6102	54	8	solution	solution	NOUN
ejpam-6102	54	9	with	with	ADP
ejpam-6102	54	10	a	a	DET
ejpam-6102	54	11	single	single	ADJ
ejpam-6102	54	12	boundary	boundary	ADJ
ejpam-6102	54	13	blow	blow	NOUN
ejpam-6102	54	14	-	-	PUNCT
ejpam-6102	54	15	up	up	ADP
ejpam-6102	54	16	point	point	NOUN
ejpam-6102	54	17	when	when	SCONJ
ejpam-6102	54	18	ω	ω	PROPN
ejpam-6102	54	19	is	be	AUX
ejpam-6102	54	20	non	non	ADJ
ejpam-6102	54	21	-	-	ADJ
ejpam-6102	54	22	convex	convex	ADJ
ejpam-6102	54	23	and	and	CCONJ
ejpam-6102	54	24	the	the	DET
ejpam-6102	54	25	function	function	NOUN
ejpam-6102	54	26	f	f	PROPN
ejpam-6102	54	27	is	be	AUX
ejpam-6102	54	28	equal	equal	ADJ
ejpam-6102	54	29	to	to	ADP
ejpam-6102	54	30	1	1	NUM
ejpam-6102	54	31	.	.	PUNCT
ejpam-6102	55	1	in	in	ADP
ejpam-6102	55	2	this	this	DET
ejpam-6102	55	3	paper	paper	NOUN
ejpam-6102	55	4	,	,	PUNCT
ejpam-6102	55	5	our	our	PRON
ejpam-6102	55	6	objective	objective	NOUN
ejpam-6102	55	7	is	be	AUX
ejpam-6102	55	8	to	to	PART
ejpam-6102	55	9	construct	construct	VERB
ejpam-6102	55	10	solutions	solution	NOUN
ejpam-6102	55	11	to	to	ADP
ejpam-6102	55	12	(	(	PUNCT
ejpam-6102	55	13	pε	pε	NOUN
ejpam-6102	55	14	)	)	PUNCT
ejpam-6102	55	15	with	with	ADP
ejpam-6102	55	16	multiple	multiple	ADJ
ejpam-6102	55	17	boundary	boundary	ADJ
ejpam-6102	55	18	blow	blow	NOUN
ejpam-6102	55	19	-	-	PUNCT
ejpam-6102	55	20	up	up	ADP
ejpam-6102	55	21	points	point	NOUN
ejpam-6102	55	22	and	and	CCONJ
ejpam-6102	55	23	to	to	PART
ejpam-6102	55	24	present	present	VERB
ejpam-6102	55	25	a	a	DET
ejpam-6102	55	26	multiplicity	multiplicity	NOUN
ejpam-6102	55	27	result	result	NOUN
ejpam-6102	55	28	for	for	ADP
ejpam-6102	55	29	this	this	DET
ejpam-6102	55	30	problem	problem	NOUN
ejpam-6102	55	31	.	.	PUNCT
ejpam-6102	56	1	more	more	ADV
ejpam-6102	56	2	precisely	precisely	ADV
ejpam-6102	56	3	,	,	PUNCT
ejpam-6102	56	4	the	the	DET
ejpam-6102	56	5	main	main	ADJ
ejpam-6102	56	6	results	result	NOUN
ejpam-6102	56	7	of	of	ADP
ejpam-6102	56	8	our	our	PRON
ejpam-6102	56	9	work	work	NOUN
ejpam-6102	56	10	are	be	AUX
ejpam-6102	56	11	stated	state	VERB
ejpam-6102	56	12	as	as	ADP
ejpam-6102	56	13	follow	follow	NOUN
ejpam-6102	56	14	:	:	PUNCT
ejpam-6102	56	15	theorem	theorem	NOUN
ejpam-6102	56	16	1	1	NUM
ejpam-6102	56	17	.	.	PUNCT
ejpam-6102	57	1	let	let	VERB
ejpam-6102	57	2	n	n	PRON
ejpam-6102	57	3	≥	≥	X
ejpam-6102	57	4	4	4	NUM
ejpam-6102	57	5	and	and	CCONJ
ejpam-6102	57	6	b1	b1	NOUN
ejpam-6102	57	7	,	,	PUNCT
ejpam-6102	57	8	·	·	PUNCT
ejpam-6102	57	9	·	·	PUNCT
ejpam-6102	57	10	·	·	PUNCT
ejpam-6102	57	11	,	,	PUNCT
ejpam-6102	57	12	bn	bn	INTJ
ejpam-6102	57	13	be	be	AUX
ejpam-6102	57	14	n	n	PRON
ejpam-6102	57	15	non	non	ADJ
ejpam-6102	57	16	-	-	ADJ
ejpam-6102	57	17	degenerate	degenerate	ADJ
ejpam-6102	57	18	critical	critical	ADJ
ejpam-6102	57	19	points	point	NOUN
ejpam-6102	57	20	of	of	ADP
ejpam-6102	57	21	f1	f1	NOUN
ejpam-6102	58	1	:	:	PUNCT
ejpam-6102	58	2	=	=	SYM
ejpam-6102	58	3	f|∂ω	f|∂ω	NOUN
ejpam-6102	58	4	.	.	PUNCT
ejpam-6102	59	1	we	we	PRON
ejpam-6102	59	2	assume	assume	VERB
ejpam-6102	59	3	that	that	SCONJ
ejpam-6102	59	4	c5	c5	PROPN
ejpam-6102	59	5	f(bk	f(bk	PROPN
ejpam-6102	59	6	)	)	PUNCT
ejpam-6102	60	1	∂f	∂f	PROPN
ejpam-6102	60	2	∂ν	∂ν	NOUN
ejpam-6102	60	3	(	(	PUNCT
ejpam-6102	60	4	bk)−	bk)−	PROPN
ejpam-6102	60	5	(	(	PUNCT
ejpam-6102	60	6	c1	c1	NOUN
ejpam-6102	60	7	2	2	NUM
ejpam-6102	60	8	−	−	PROPN
ejpam-6102	60	9	c4	c4	NOUN
ejpam-6102	60	10	)	)	PUNCT
ejpam-6102	60	11	h(bk	h(bk	PROPN
ejpam-6102	60	12	)	)	PUNCT
ejpam-6102	60	13	>	>	X
ejpam-6102	60	14	0	0	NUM
ejpam-6102	60	15	∀	∀	PUNCT
ejpam-6102	60	16	k	k	X
ejpam-6102	60	17	∈	∈	PROPN
ejpam-6102	60	18	{	{	PUNCT
ejpam-6102	60	19	1	1	NUM
ejpam-6102	60	20	,	,	PUNCT
ejpam-6102	60	21	·	·	PUNCT
ejpam-6102	60	22	·	·	PUNCT
ejpam-6102	60	23	·	·	PUNCT
ejpam-6102	60	24	,	,	PUNCT
ejpam-6102	60	25	n	n	CCONJ
ejpam-6102	60	26	}	}	PUNCT
ejpam-6102	60	27	,	,	PUNCT
ejpam-6102	60	28	(	(	PUNCT
ejpam-6102	60	29	2	2	X
ejpam-6102	60	30	)	)	PUNCT
ejpam-6102	60	31	where	where	SCONJ
ejpam-6102	60	32	h	h	NOUN
ejpam-6102	60	33	is	be	AUX
ejpam-6102	60	34	the	the	DET
ejpam-6102	60	35	mean	mean	ADJ
ejpam-6102	60	36	curvature	curvature	NOUN
ejpam-6102	60	37	of	of	ADP
ejpam-6102	60	38	the	the	DET
ejpam-6102	60	39	boundary	boundary	ADJ
ejpam-6102	60	40	∂ω	∂ω	PROPN
ejpam-6102	60	41	and	and	CCONJ
ejpam-6102	60	42	c1	c1	PROPN
ejpam-6102	60	43	,	,	PUNCT
ejpam-6102	60	44	c4	c4	NOUN
ejpam-6102	60	45	and	and	CCONJ
ejpam-6102	60	46	c5	c5	PROPN
ejpam-6102	60	47	are	be	AUX
ejpam-6102	60	48	defined	define	VERB
ejpam-6102	60	49	in	in	ADP
ejpam-6102	60	50	lemmas	lemmas	PROPN
ejpam-6102	60	51	4	4	NUM
ejpam-6102	60	52	,	,	PUNCT
ejpam-6102	60	53	6	6	NUM
ejpam-6102	60	54	and	and	CCONJ
ejpam-6102	60	55	8	8	NUM
ejpam-6102	60	56	respectively	respectively	ADV
ejpam-6102	60	57	.	.	PUNCT
ejpam-6102	61	1	then	then	ADV
ejpam-6102	61	2	,	,	PUNCT
ejpam-6102	61	3	there	there	PRON
ejpam-6102	61	4	exists	exist	VERB
ejpam-6102	61	5	ε0	ε0	PROPN
ejpam-6102	61	6	>	>	X
ejpam-6102	61	7	0	0	NUM
ejpam-6102	61	8	such	such	ADJ
ejpam-6102	61	9	that	that	SCONJ
ejpam-6102	61	10	,	,	PUNCT
ejpam-6102	61	11	for	for	ADP
ejpam-6102	61	12	any	any	DET
ejpam-6102	61	13	ε	ε	PROPN
ejpam-6102	61	14	∈	∈	PROPN
ejpam-6102	61	15	(	(	PUNCT
ejpam-6102	61	16	0	0	NUM
ejpam-6102	61	17	,	,	PUNCT
ejpam-6102	61	18	ε0	ε0	PROPN
ejpam-6102	61	19	)	)	PUNCT
ejpam-6102	61	20	and	and	CCONJ
ejpam-6102	61	21	for	for	ADP
ejpam-6102	61	22	any	any	DET
ejpam-6102	61	23	subset	subset	NOUN
ejpam-6102	61	24	{	{	PUNCT
ejpam-6102	61	25	bi1	bi1	NOUN
ejpam-6102	61	26	,	,	PUNCT
ejpam-6102	61	27	·	·	PUNCT
ejpam-6102	61	28	·	·	PUNCT
ejpam-6102	61	29	·	·	PUNCT
ejpam-6102	61	30	,	,	PUNCT
ejpam-6102	61	31	biℓ	biℓ	ADJ
ejpam-6102	61	32	}	}	PUNCT
ejpam-6102	61	33	⊂	⊂	PRON
ejpam-6102	61	34	{	{	PUNCT
ejpam-6102	61	35	b1	b1	PROPN
ejpam-6102	61	36	,	,	PUNCT
ejpam-6102	61	37	·	·	PUNCT
ejpam-6102	61	38	·	·	PUNCT
ejpam-6102	61	39	·	·	PUNCT
ejpam-6102	61	40	,	,	PUNCT
ejpam-6102	61	41	bn	bn	X
ejpam-6102	61	42	}	}	PUNCT
ejpam-6102	61	43	,	,	PUNCT
ejpam-6102	61	44	problem	problem	NOUN
ejpam-6102	61	45	(	(	PUNCT
ejpam-6102	61	46	pε	pε	NOUN
ejpam-6102	61	47	)	)	PUNCT
ejpam-6102	61	48	has	have	VERB
ejpam-6102	61	49	a	a	DET
ejpam-6102	61	50	solution	solution	NOUN
ejpam-6102	61	51	uε	uε	ADP
ejpam-6102	61	52	which	which	PRON
ejpam-6102	61	53	converges	converge	VERB
ejpam-6102	61	54	weakly	weakly	ADJ
ejpam-6102	61	55	to	to	ADP
ejpam-6102	61	56	zero	zero	NUM
ejpam-6102	61	57	and	and	CCONJ
ejpam-6102	61	58	blows	blow	VERB
ejpam-6102	61	59	up	up	ADP
ejpam-6102	61	60	at	at	ADP
ejpam-6102	61	61	the	the	DET
ejpam-6102	61	62	points	point	NOUN
ejpam-6102	61	63	bij	bij	NOUN
ejpam-6102	61	64	’s	’s	ADJ
ejpam-6102	61	65	with	with	ADP
ejpam-6102	61	66	the	the	DET
ejpam-6102	61	67	following	follow	VERB
ejpam-6102	61	68	properties	property	NOUN
ejpam-6102	61	69	lim	lim	PROPN
ejpam-6102	61	70	ρ→0	ρ→0	ADP
ejpam-6102	61	71	lim	lim	PROPN
ejpam-6102	61	72	ε→0	ε→0	PROPN
ejpam-6102	61	73	∫	∫	PROPN
ejpam-6102	61	74	ω∩b(bij	ω∩b(bij	PROPN
ejpam-6102	61	75	,	,	PUNCT
ejpam-6102	61	76	ρ	ρ	PROPN
ejpam-6102	61	77	)	)	PUNCT
ejpam-6102	61	78	fu2n/(n−2	fu2n/(n−2	NOUN
ejpam-6102	61	79	)	)	PUNCT
ejpam-6102	61	80	ε	ε	PROPN
ejpam-6102	61	81	=	=	PRON
ejpam-6102	61	82	f(bij	f(bij	PROPN
ejpam-6102	61	83	)	)	PUNCT
ejpam-6102	61	84	sn	sn	PROPN
ejpam-6102	61	85	for	for	ADP
ejpam-6102	61	86	each	each	DET
ejpam-6102	61	87	j	j	PROPN
ejpam-6102	61	88	∈	∈	PROPN
ejpam-6102	61	89	{	{	PUNCT
ejpam-6102	61	90	1	1	NUM
ejpam-6102	61	91	,	,	PUNCT
ejpam-6102	61	92	·	·	PUNCT
ejpam-6102	61	93	·	·	PUNCT
ejpam-6102	61	94	·	·	PUNCT
ejpam-6102	61	95	,	,	PUNCT
ejpam-6102	61	96	ℓ	ℓ	X
ejpam-6102	61	97	}	}	PUNCT
ejpam-6102	61	98	,	,	PUNCT
ejpam-6102	61	99	r.	r.	PROPN
ejpam-6102	61	100	almushahhin	almushahhin	PROPN
ejpam-6102	61	101	,	,	PUNCT
ejpam-6102	61	102	m.	m.	PROPN
ejpam-6102	61	103	ben	ben	PROPN
ejpam-6102	61	104	ayed	aye	VERB
ejpam-6102	61	105	/	/	SYM
ejpam-6102	61	106	eur	eur	PROPN
ejpam-6102	61	107	.	.	PUNCT
ejpam-6102	62	1	j.	j.	PROPN
ejpam-6102	62	2	pure	pure	PROPN
ejpam-6102	62	3	appl	appl	PROPN
ejpam-6102	62	4	.	.	PROPN
ejpam-6102	62	5	math	math	PROPN
ejpam-6102	62	6	,	,	PUNCT
ejpam-6102	62	7	18	18	NUM
ejpam-6102	62	8	(	(	PUNCT
ejpam-6102	62	9	2	2	NUM
ejpam-6102	62	10	)	)	PUNCT
ejpam-6102	62	11	(	(	PUNCT
ejpam-6102	62	12	2025	2025	NUM
ejpam-6102	62	13	)	)	PUNCT
ejpam-6102	62	14	,	,	PUNCT
ejpam-6102	62	15	6102	6102	NUM
ejpam-6102	62	16	4	4	NUM
ejpam-6102	62	17	of	of	ADP
ejpam-6102	62	18	31	31	NUM
ejpam-6102	62	19	where	where	SCONJ
ejpam-6102	62	20	sn	sn	PROPN
ejpam-6102	62	21	is	be	AUX
ejpam-6102	62	22	an	an	DET
ejpam-6102	62	23	universal	universal	ADJ
ejpam-6102	62	24	constant	constant	NOUN
ejpam-6102	62	25	defined	define	VERB
ejpam-6102	62	26	in	in	ADP
ejpam-6102	62	27	(	(	PUNCT
ejpam-6102	62	28	22	22	NUM
ejpam-6102	62	29	)	)	PUNCT
ejpam-6102	62	30	.	.	PUNCT
ejpam-6102	63	1	more	more	ADV
ejpam-6102	63	2	precisely	precisely	ADV
ejpam-6102	63	3	,	,	PUNCT
ejpam-6102	63	4	for	for	ADP
ejpam-6102	63	5	any	any	DET
ejpam-6102	63	6	ℓ	ℓ	NOUN
ejpam-6102	63	7	≤	≤	NOUN
ejpam-6102	63	8	n	n	CCONJ
ejpam-6102	63	9	,	,	PUNCT
ejpam-6102	63	10	there	there	PRON
ejpam-6102	63	11	exist	exist	VERB
ejpam-6102	63	12	µ1,ε	µ1,ε	NOUN
ejpam-6102	63	13	,	,	PUNCT
ejpam-6102	63	14	...	...	PUNCT
ejpam-6102	63	15	,	,	PUNCT
ejpam-6102	63	16	µℓ,ε	µℓ,ε	X
ejpam-6102	63	17	having	have	VERB
ejpam-6102	63	18	the	the	DET
ejpam-6102	63	19	same	same	ADJ
ejpam-6102	63	20	order	order	NOUN
ejpam-6102	63	21	as	as	ADP
ejpam-6102	63	22	ε−1/2	ε−1/2	PROPN
ejpam-6102	63	23	for	for	ADP
ejpam-6102	63	24	n	n	X
ejpam-6102	63	25	≥	≥	NUM
ejpam-6102	63	26	5	5	NUM
ejpam-6102	63	27	,	,	PUNCT
ejpam-6102	63	28	and	and	CCONJ
ejpam-6102	63	29	as	as	ADP
ejpam-6102	63	30	ε−1/2|	ε−1/2|	X
ejpam-6102	63	31	ln	ln	ADJ
ejpam-6102	63	32	ε|1/2	ε|1/2	NOUN
ejpam-6102	63	33	for	for	ADP
ejpam-6102	63	34	n	n	NOUN
ejpam-6102	63	35	=	=	SYM
ejpam-6102	63	36	4	4	NUM
ejpam-6102	63	37	and	and	CCONJ
ejpam-6102	63	38	ℓ	ℓ	PROPN
ejpam-6102	63	39	points	point	NOUN
ejpam-6102	63	40	aj	aj	PROPN
ejpam-6102	63	41	,	,	PUNCT
ejpam-6102	63	42	ε	ε	PROPN
ejpam-6102	63	43	→	→	SYM
ejpam-6102	63	44	bij	bij	VERB
ejpam-6102	63	45	for	for	ADP
ejpam-6102	63	46	all	all	DET
ejpam-6102	63	47	j	j	NOUN
ejpam-6102	63	48	such	such	ADJ
ejpam-6102	63	49	that	that	SCONJ
ejpam-6102	63	50	∣∣∣∣∣∣∣∣uε	∣∣∣∣∣∣∣∣uε	ADJ
ejpam-6102	63	51	−	−	PROPN
ejpam-6102	63	52	ℓ∑	ℓ∑	PROPN
ejpam-6102	63	53	j=1	j=1	PROPN
ejpam-6102	63	54	ωaj	ωaj	PROPN
ejpam-6102	63	55	,	,	PUNCT
ejpam-6102	63	56	ε,µj	ε,µj	PROPN
ejpam-6102	63	57	,	,	PUNCT
ejpam-6102	63	58	ε	ε	PROPN
ejpam-6102	63	59	∣∣∣∣∣∣∣∣	∣∣∣∣∣∣∣∣	PROPN
ejpam-6102	63	60	h1(ω	h1(ω	PROPN
ejpam-6102	63	61	)	)	PUNCT
ejpam-6102	63	62	→	→	SYM
ejpam-6102	63	63	0	0	NUM
ejpam-6102	63	64	,	,	PUNCT
ejpam-6102	63	65	as	as	ADP
ejpam-6102	63	66	ε→	ε→	X
ejpam-6102	63	67	0	0	NUM
ejpam-6102	63	68	where	where	SCONJ
ejpam-6102	63	69	the	the	DET
ejpam-6102	63	70	function	function	NOUN
ejpam-6102	63	71	ωa,µ	ωa,µ	PUNCT
ejpam-6102	63	72	is	be	AUX
ejpam-6102	63	73	defined	define	VERB
ejpam-6102	63	74	in	in	ADP
ejpam-6102	63	75	(	(	PUNCT
ejpam-6102	63	76	1	1	NUM
ejpam-6102	63	77	)	)	PUNCT
ejpam-6102	63	78	.	.	PUNCT
ejpam-6102	64	1	theorem	theorem	NOUN
ejpam-6102	64	2	1	1	NUM
ejpam-6102	64	3	allows	allow	VERB
ejpam-6102	64	4	us	we	PRON
ejpam-6102	64	5	to	to	PART
ejpam-6102	64	6	obtain	obtain	VERB
ejpam-6102	64	7	the	the	DET
ejpam-6102	64	8	following	follow	VERB
ejpam-6102	64	9	multiplicity	multiplicity	NOUN
ejpam-6102	64	10	result	result	NOUN
ejpam-6102	64	11	for	for	ADP
ejpam-6102	64	12	problem	problem	NOUN
ejpam-6102	64	13	(	(	PUNCT
ejpam-6102	64	14	pε	pε	NOUN
ejpam-6102	64	15	)	)	PUNCT
ejpam-6102	64	16	in	in	ADP
ejpam-6102	64	17	relation	relation	NOUN
ejpam-6102	64	18	to	to	ADP
ejpam-6102	64	19	the	the	DET
ejpam-6102	64	20	number	number	NOUN
ejpam-6102	64	21	of	of	ADP
ejpam-6102	64	22	non	non	ADJ
ejpam-6102	64	23	-	-	ADJ
ejpam-6102	64	24	degenerate	degenerate	ADJ
ejpam-6102	64	25	critical	critical	ADJ
ejpam-6102	64	26	points	point	NOUN
ejpam-6102	64	27	of	of	ADP
ejpam-6102	64	28	the	the	DET
ejpam-6102	64	29	restriction	restriction	NOUN
ejpam-6102	64	30	of	of	ADP
ejpam-6102	64	31	the	the	DET
ejpam-6102	64	32	function	function	NOUN
ejpam-6102	64	33	f	f	PROPN
ejpam-6102	64	34	on	on	ADP
ejpam-6102	64	35	the	the	DET
ejpam-6102	64	36	boundary	boundary	NOUN
ejpam-6102	64	37	of	of	ADP
ejpam-6102	64	38	ω	ω	PROPN
ejpam-6102	64	39	.	.	PUNCT
ejpam-6102	64	40	theorem	theorem	PROPN
ejpam-6102	64	41	2	2	NUM
ejpam-6102	64	42	.	.	PUNCT
ejpam-6102	65	1	let	let	VERB
ejpam-6102	65	2	n	n	PRON
ejpam-6102	65	3	≥	≥	X
ejpam-6102	65	4	4	4	NUM
ejpam-6102	65	5	and	and	CCONJ
ejpam-6102	65	6	assume	assume	VERB
ejpam-6102	65	7	that	that	SCONJ
ejpam-6102	65	8	the	the	DET
ejpam-6102	65	9	restriction	restriction	NOUN
ejpam-6102	65	10	of	of	ADP
ejpam-6102	65	11	f	f	PROPN
ejpam-6102	65	12	to	to	ADP
ejpam-6102	65	13	the	the	DET
ejpam-6102	65	14	boundary	boundary	NOUN
ejpam-6102	65	15	has	have	VERB
ejpam-6102	65	16	n	n	NUM
ejpam-6102	65	17	nondegenerate	nondegenerate	ADJ
ejpam-6102	65	18	critical	critical	ADJ
ejpam-6102	65	19	points	point	NOUN
ejpam-6102	65	20	b1	b1	PROPN
ejpam-6102	65	21	,	,	PUNCT
ejpam-6102	65	22	·	·	PUNCT
ejpam-6102	65	23	·	·	PUNCT
ejpam-6102	65	24	·	·	PUNCT
ejpam-6102	66	1	,	,	PUNCT
ejpam-6102	66	2	bn	bn	ADP
ejpam-6102	66	3	satisfying	satisfy	VERB
ejpam-6102	66	4	assumption	assumption	NOUN
ejpam-6102	66	5	(	(	PUNCT
ejpam-6102	66	6	2	2	NUM
ejpam-6102	66	7	)	)	PUNCT
ejpam-6102	66	8	.	.	PUNCT
ejpam-6102	67	1	then	then	ADV
ejpam-6102	67	2	,	,	PUNCT
ejpam-6102	67	3	for	for	ADP
ejpam-6102	67	4	small	small	ADJ
ejpam-6102	67	5	positive	positive	ADJ
ejpam-6102	67	6	ε	ε	PROPN
ejpam-6102	67	7	,	,	PUNCT
ejpam-6102	67	8	the	the	DET
ejpam-6102	67	9	number	number	NOUN
ejpam-6102	67	10	of	of	ADP
ejpam-6102	67	11	solutions	solution	NOUN
ejpam-6102	67	12	to	to	ADP
ejpam-6102	67	13	(	(	PUNCT
ejpam-6102	67	14	pε	pε	NOUN
ejpam-6102	67	15	)	)	PUNCT
ejpam-6102	67	16	that	that	PRON
ejpam-6102	67	17	blow	blow	VERB
ejpam-6102	67	18	up	up	ADP
ejpam-6102	67	19	on	on	ADP
ejpam-6102	67	20	the	the	DET
ejpam-6102	67	21	boundary	boundary	NOUN
ejpam-6102	67	22	is	be	AUX
ejpam-6102	67	23	at	at	ADP
ejpam-6102	67	24	least	least	ADJ
ejpam-6102	67	25	2n	2n	NUM
ejpam-6102	67	26	−	−	ADP
ejpam-6102	67	27	1	1	X
ejpam-6102	67	28	.	.	PUNCT
ejpam-6102	67	29	remark	remark	NOUN
ejpam-6102	67	30	1	1	NUM
ejpam-6102	67	31	.	.	PUNCT
ejpam-6102	68	1	as	as	ADP
ejpam-6102	68	2	examples	example	NOUN
ejpam-6102	68	3	of	of	ADP
ejpam-6102	68	4	functions	function	NOUN
ejpam-6102	68	5	satisfying	satisfy	VERB
ejpam-6102	68	6	the	the	DET
ejpam-6102	68	7	assumption	assumption	NOUN
ejpam-6102	68	8	(	(	PUNCT
ejpam-6102	68	9	2	2	NUM
ejpam-6102	68	10	)	)	PUNCT
ejpam-6102	68	11	,	,	PUNCT
ejpam-6102	68	12	let	let	VERB
ejpam-6102	68	13	ω	ω	PRON
ejpam-6102	68	14	:	:	PUNCT
ejpam-6102	68	15	=	=	SYM
ejpam-6102	68	16	b(0	b(0	PROPN
ejpam-6102	68	17	,	,	PUNCT
ejpam-6102	68	18	1	1	NUM
ejpam-6102	68	19	)	)	PUNCT
ejpam-6102	68	20	and	and	CCONJ
ejpam-6102	68	21	g	g	PROPN
ejpam-6102	68	22	be	be	AUX
ejpam-6102	68	23	a	a	DET
ejpam-6102	68	24	positive	positive	ADJ
ejpam-6102	68	25	c2	c2	PROPN
ejpam-6102	68	26	-	-	PUNCT
ejpam-6102	68	27	function	function	NOUN
ejpam-6102	68	28	on	on	ADP
ejpam-6102	68	29	ω	ω	NUM
ejpam-6102	68	30	such	such	ADJ
ejpam-6102	68	31	that	that	SCONJ
ejpam-6102	68	32	g|∂ω	g|∂ω	NOUN
ejpam-6102	68	33	has	have	VERB
ejpam-6102	68	34	only	only	ADV
ejpam-6102	68	35	non	non	ADJ
ejpam-6102	68	36	-	-	ADJ
ejpam-6102	68	37	degenerate	degenerate	ADJ
ejpam-6102	68	38	critical	critical	ADJ
ejpam-6102	68	39	points	point	NOUN
ejpam-6102	68	40	.	.	PUNCT
ejpam-6102	69	1	let	let	VERB
ejpam-6102	69	2	f(x	f(x	PROPN
ejpam-6102	69	3	)	)	PUNCT
ejpam-6102	69	4	:	:	PUNCT
ejpam-6102	70	1	=	=	PUNCT
ejpam-6102	70	2	g(x	g(x	NOUN
ejpam-6102	70	3	)	)	PUNCT
ejpam-6102	71	1	+	+	CCONJ
ejpam-6102	71	2	γ|x|2	γ|x|2	ADJ
ejpam-6102	71	3	.	.	PUNCT
ejpam-6102	72	1	it	it	PRON
ejpam-6102	72	2	easy	easy	ADJ
ejpam-6102	72	3	to	to	PART
ejpam-6102	72	4	see	see	VERB
ejpam-6102	72	5	that	that	SCONJ
ejpam-6102	72	6	∂f	∂f	PROPN
ejpam-6102	72	7	∂ν	∂ν	PROPN
ejpam-6102	72	8	(	(	PUNCT
ejpam-6102	72	9	y	y	NOUN
ejpam-6102	72	10	)	)	PUNCT
ejpam-6102	73	1	=	=	SYM
ejpam-6102	74	1	∂g	∂g	PROPN
ejpam-6102	74	2	∂ν	∂ν	X
ejpam-6102	74	3	(	(	PUNCT
ejpam-6102	74	4	y	y	PROPN
ejpam-6102	74	5	)	)	PUNCT
ejpam-6102	74	6	+	+	CCONJ
ejpam-6102	74	7	2γ	2γ	X
ejpam-6102	74	8	∀y	∀y	PROPN
ejpam-6102	74	9	∈	∈	PROPN
ejpam-6102	74	10	∂ω	∂ω	PROPN
ejpam-6102	74	11	and	and	CCONJ
ejpam-6102	74	12	f|∂ω	f|∂ω	PROPN
ejpam-6102	74	13	=	=	SYM
ejpam-6102	74	14	g|∂ω	g|∂ω	PROPN
ejpam-6102	74	15	+	+	CCONJ
ejpam-6102	74	16	γ	γ	X
ejpam-6102	74	17	.	.	PROPN
ejpam-6102	75	1	since	since	SCONJ
ejpam-6102	75	2	the	the	DET
ejpam-6102	75	3	function	function	NOUN
ejpam-6102	75	4	h	h	NOUN
ejpam-6102	75	5	is	be	AUX
ejpam-6102	75	6	constant	constant	ADJ
ejpam-6102	75	7	on	on	ADP
ejpam-6102	75	8	∂ω	∂ω	PROPN
ejpam-6102	75	9	,	,	PUNCT
ejpam-6102	75	10	it	it	PRON
ejpam-6102	75	11	follows	follow	VERB
ejpam-6102	75	12	that	that	SCONJ
ejpam-6102	75	13	,	,	PUNCT
ejpam-6102	75	14	for	for	ADP
ejpam-6102	75	15	γ	γ	X
ejpam-6102	75	16	large	large	ADJ
ejpam-6102	75	17	,	,	PUNCT
ejpam-6102	75	18	the	the	DET
ejpam-6102	75	19	function	function	NOUN
ejpam-6102	75	20	f	f	PROPN
ejpam-6102	75	21	satisfies	satisfy	VERB
ejpam-6102	75	22	the	the	DET
ejpam-6102	75	23	assumption	assumption	NOUN
ejpam-6102	75	24	(	(	PUNCT
ejpam-6102	75	25	2	2	NUM
ejpam-6102	75	26	)	)	PUNCT
ejpam-6102	75	27	.	.	PUNCT
ejpam-6102	76	1	the	the	DET
ejpam-6102	76	2	proof	proof	NOUN
ejpam-6102	76	3	of	of	ADP
ejpam-6102	76	4	our	our	PRON
ejpam-6102	76	5	results	result	NOUN
ejpam-6102	76	6	relies	rely	VERB
ejpam-6102	76	7	on	on	ADP
ejpam-6102	76	8	certain	certain	ADJ
ejpam-6102	76	9	balancing	balancing	NOUN
ejpam-6102	76	10	conditions	condition	NOUN
ejpam-6102	76	11	satisfied	satisfy	VERB
ejpam-6102	76	12	by	by	ADP
ejpam-6102	76	13	the	the	DET
ejpam-6102	76	14	concentration	concentration	NOUN
ejpam-6102	76	15	parameters	parameter	NOUN
ejpam-6102	76	16	,	,	PUNCT
ejpam-6102	76	17	which	which	PRON
ejpam-6102	76	18	are	be	AUX
ejpam-6102	76	19	relationships	relationship	NOUN
ejpam-6102	76	20	that	that	PRON
ejpam-6102	76	21	ensure	ensure	VERB
ejpam-6102	76	22	equilibrium	equilibrium	NOUN
ejpam-6102	76	23	between	between	ADP
ejpam-6102	76	24	the	the	DET
ejpam-6102	76	25	various	various	ADJ
ejpam-6102	76	26	factors	factor	NOUN
ejpam-6102	76	27	influencing	influence	VERB
ejpam-6102	76	28	the	the	DET
ejpam-6102	76	29	blow	blow	VERB
ejpam-6102	76	30	-	-	PUNCT
ejpam-6102	76	31	up	up	ADP
ejpam-6102	76	32	behavior	behavior	NOUN
ejpam-6102	76	33	of	of	ADP
ejpam-6102	76	34	the	the	DET
ejpam-6102	76	35	solutions	solution	NOUN
ejpam-6102	76	36	.	.	PUNCT
ejpam-6102	77	1	these	these	DET
ejpam-6102	77	2	conditions	condition	NOUN
ejpam-6102	77	3	are	be	AUX
ejpam-6102	77	4	derived	derive	VERB
ejpam-6102	77	5	by	by	ADP
ejpam-6102	77	6	performing	perform	VERB
ejpam-6102	77	7	an	an	DET
ejpam-6102	77	8	asymptotic	asymptotic	ADJ
ejpam-6102	77	9	expansion	expansion	NOUN
ejpam-6102	77	10	of	of	ADP
ejpam-6102	77	11	the	the	DET
ejpam-6102	77	12	gradient	gradient	NOUN
ejpam-6102	77	13	of	of	ADP
ejpam-6102	77	14	the	the	DET
ejpam-6102	77	15	euler	euler	NOUN
ejpam-6102	77	16	-	-	PUNCT
ejpam-6102	77	17	lagrange	lagrange	NOUN
ejpam-6102	77	18	functional	functional	NOUN
ejpam-6102	77	19	associated	associate	VERB
ejpam-6102	77	20	with	with	ADP
ejpam-6102	77	21	the	the	DET
ejpam-6102	77	22	problem	problem	NOUN
ejpam-6102	77	23	and	and	CCONJ
ejpam-6102	77	24	testing	test	VERB
ejpam-6102	77	25	the	the	DET
ejpam-6102	77	26	equation	equation	NOUN
ejpam-6102	77	27	with	with	ADP
ejpam-6102	77	28	appropriate	appropriate	ADJ
ejpam-6102	77	29	vector	vector	NOUN
ejpam-6102	77	30	fields	field	NOUN
ejpam-6102	77	31	.	.	PUNCT
ejpam-6102	78	1	this	this	DET
ejpam-6102	78	2	process	process	NOUN
ejpam-6102	78	3	leads	lead	VERB
ejpam-6102	78	4	to	to	ADP
ejpam-6102	78	5	constraints	constraint	NOUN
ejpam-6102	78	6	on	on	ADP
ejpam-6102	78	7	both	both	CCONJ
ejpam-6102	78	8	the	the	DET
ejpam-6102	78	9	concentration	concentration	NOUN
ejpam-6102	78	10	points	point	NOUN
ejpam-6102	78	11	and	and	CCONJ
ejpam-6102	78	12	the	the	DET
ejpam-6102	78	13	corresponding	corresponding	ADJ
ejpam-6102	78	14	blowup	blowup	ADJ
ejpam-6102	78	15	rates	rate	NOUN
ejpam-6102	78	16	of	of	ADP
ejpam-6102	78	17	the	the	DET
ejpam-6102	78	18	solution	solution	NOUN
ejpam-6102	78	19	.	.	PUNCT
ejpam-6102	79	1	through	through	ADP
ejpam-6102	79	2	a	a	DET
ejpam-6102	79	3	careful	careful	ADJ
ejpam-6102	79	4	analysis	analysis	NOUN
ejpam-6102	79	5	of	of	ADP
ejpam-6102	79	6	these	these	DET
ejpam-6102	79	7	conditions	condition	NOUN
ejpam-6102	79	8	,	,	PUNCT
ejpam-6102	79	9	we	we	PRON
ejpam-6102	79	10	derive	derive	VERB
ejpam-6102	79	11	our	our	PRON
ejpam-6102	79	12	results	result	NOUN
ejpam-6102	79	13	.	.	PUNCT
ejpam-6102	80	1	note	note	VERB
ejpam-6102	80	2	that	that	SCONJ
ejpam-6102	80	3	traditional	traditional	ADJ
ejpam-6102	80	4	blow	blow	NOUN
ejpam-6102	80	5	-	-	PUNCT
ejpam-6102	80	6	up	up	ADP
ejpam-6102	80	7	analysis	analysis	NOUN
ejpam-6102	80	8	methods	method	NOUN
ejpam-6102	80	9	depend	depend	VERB
ejpam-6102	80	10	on	on	ADP
ejpam-6102	80	11	precise	precise	ADJ
ejpam-6102	80	12	point	point	NOUN
ejpam-6102	80	13	-	-	PUNCT
ejpam-6102	80	14	wise	wise	ADJ
ejpam-6102	80	15	c0estimates	c0estimate	NOUN
ejpam-6102	80	16	and	and	CCONJ
ejpam-6102	80	17	the	the	DET
ejpam-6102	80	18	use	use	NOUN
ejpam-6102	80	19	of	of	ADP
ejpam-6102	80	20	pohozaev	pohozaev	NOUN
ejpam-6102	80	21	identities	identity	NOUN
ejpam-6102	80	22	.	.	PUNCT
ejpam-6102	81	1	in	in	ADP
ejpam-6102	81	2	contrast	contrast	NOUN
ejpam-6102	81	3	,	,	PUNCT
ejpam-6102	81	4	our	our	PRON
ejpam-6102	81	5	method	method	NOUN
ejpam-6102	81	6	,	,	PUNCT
ejpam-6102	81	7	used	use	VERB
ejpam-6102	81	8	in	in	ADP
ejpam-6102	81	9	this	this	DET
ejpam-6102	81	10	paper	paper	NOUN
ejpam-6102	81	11	,	,	PUNCT
ejpam-6102	81	12	deviates	deviate	VERB
ejpam-6102	81	13	from	from	ADP
ejpam-6102	81	14	these	these	DET
ejpam-6102	81	15	techniques	technique	NOUN
ejpam-6102	81	16	.	.	PUNCT
ejpam-6102	82	1	bypassing	bypass	VERB
ejpam-6102	82	2	the	the	DET
ejpam-6102	82	3	need	need	NOUN
ejpam-6102	82	4	for	for	ADP
ejpam-6102	82	5	point	point	NOUN
ejpam-6102	82	6	-	-	PUNCT
ejpam-6102	82	7	wise	wise	ADJ
ejpam-6102	82	8	estimates	estimate	NOUN
ejpam-6102	82	9	and	and	CCONJ
ejpam-6102	82	10	pohozaev	pohozaev	NOUN
ejpam-6102	82	11	identities	identity	NOUN
ejpam-6102	82	12	,	,	PUNCT
ejpam-6102	82	13	our	our	PRON
ejpam-6102	82	14	method	method	NOUN
ejpam-6102	82	15	holds	hold	VERB
ejpam-6102	82	16	significant	significant	ADJ
ejpam-6102	82	17	promise	promise	NOUN
ejpam-6102	82	18	for	for	ADP
ejpam-6102	82	19	handling	handle	VERB
ejpam-6102	82	20	non	non	ADJ
ejpam-6102	82	21	-	-	ADJ
ejpam-6102	82	22	compact	compact	ADJ
ejpam-6102	82	23	variational	variational	ADJ
ejpam-6102	82	24	problems	problem	NOUN
ejpam-6102	82	25	that	that	PRON
ejpam-6102	82	26	involve	involve	VERB
ejpam-6102	82	27	more	more	ADJ
ejpam-6102	82	28	intricate	intricate	ADJ
ejpam-6102	82	29	blow	blow	NOUN
ejpam-6102	82	30	-	-	PUNCT
ejpam-6102	82	31	up	up	ADP
ejpam-6102	82	32	behaviors	behavior	NOUN
ejpam-6102	82	33	,	,	PUNCT
ejpam-6102	82	34	as	as	ADP
ejpam-6102	82	35	the	the	DET
ejpam-6102	82	36	existence	existence	NOUN
ejpam-6102	82	37	of	of	ADP
ejpam-6102	82	38	non	non	ADJ
ejpam-6102	82	39	-	-	ADJ
ejpam-6102	82	40	simple	simple	ADJ
ejpam-6102	82	41	blow	blow	NOUN
ejpam-6102	82	42	-	-	PUNCT
ejpam-6102	82	43	up	up	ADP
ejpam-6102	82	44	points	point	NOUN
ejpam-6102	82	45	.	.	PUNCT
ejpam-6102	83	1	moreover	moreover	ADV
ejpam-6102	83	2	,	,	PUNCT
ejpam-6102	83	3	the	the	DET
ejpam-6102	83	4	method	method	NOUN
ejpam-6102	83	5	developed	develop	VERB
ejpam-6102	83	6	in	in	ADP
ejpam-6102	83	7	this	this	DET
ejpam-6102	83	8	paper	paper	NOUN
ejpam-6102	83	9	is	be	AUX
ejpam-6102	83	10	specifically	specifically	ADV
ejpam-6102	83	11	tailored	tailor	VERB
ejpam-6102	83	12	to	to	ADP
ejpam-6102	83	13	the	the	DET
ejpam-6102	83	14	variational	variational	ADJ
ejpam-6102	83	15	problem	problem	NOUN
ejpam-6102	83	16	and	and	CCONJ
ejpam-6102	83	17	does	do	AUX
ejpam-6102	83	18	not	not	PART
ejpam-6102	83	19	directly	directly	ADV
ejpam-6102	83	20	extend	extend	VERB
ejpam-6102	83	21	to	to	ADP
ejpam-6102	83	22	non	non	ADJ
ejpam-6102	83	23	-	-	ADJ
ejpam-6102	83	24	variational	variational	ADJ
ejpam-6102	83	25	settings	setting	NOUN
ejpam-6102	83	26	.	.	PUNCT
ejpam-6102	84	1	r.	r.	PROPN
ejpam-6102	84	2	almushahhin	almushahhin	PROPN
ejpam-6102	84	3	,	,	PUNCT
ejpam-6102	84	4	m.	m.	PROPN
ejpam-6102	84	5	ben	ben	PROPN
ejpam-6102	84	6	ayed	aye	VERB
ejpam-6102	84	7	/	/	SYM
ejpam-6102	84	8	eur	eur	PROPN
ejpam-6102	84	9	.	.	PUNCT
ejpam-6102	85	1	j.	j.	PROPN
ejpam-6102	85	2	pure	pure	PROPN
ejpam-6102	85	3	appl	appl	PROPN
ejpam-6102	85	4	.	.	PROPN
ejpam-6102	85	5	math	math	PROPN
ejpam-6102	85	6	,	,	PUNCT
ejpam-6102	85	7	18	18	NUM
ejpam-6102	85	8	(	(	PUNCT
ejpam-6102	85	9	2	2	NUM
ejpam-6102	85	10	)	)	PUNCT
ejpam-6102	85	11	(	(	PUNCT
ejpam-6102	85	12	2025	2025	NUM
ejpam-6102	85	13	)	)	PUNCT
ejpam-6102	85	14	,	,	PUNCT
ejpam-6102	85	15	6102	6102	NUM
ejpam-6102	85	16	5	5	NUM
ejpam-6102	85	17	of	of	ADP
ejpam-6102	85	18	31	31	NUM
ejpam-6102	85	19	the	the	DET
ejpam-6102	85	20	paper	paper	NOUN
ejpam-6102	85	21	is	be	AUX
ejpam-6102	85	22	structured	structure	VERB
ejpam-6102	85	23	as	as	SCONJ
ejpam-6102	85	24	follows	follow	VERB
ejpam-6102	85	25	:	:	PUNCT
ejpam-6102	85	26	in	in	ADP
ejpam-6102	85	27	section	section	NOUN
ejpam-6102	85	28	2	2	NUM
ejpam-6102	85	29	,	,	PUNCT
ejpam-6102	85	30	we	we	PRON
ejpam-6102	85	31	introduce	introduce	VERB
ejpam-6102	85	32	the	the	DET
ejpam-6102	85	33	necessary	necessary	ADJ
ejpam-6102	85	34	preliminaries	preliminary	NOUN
ejpam-6102	85	35	for	for	ADP
ejpam-6102	85	36	studying	study	VERB
ejpam-6102	85	37	the	the	DET
ejpam-6102	85	38	problem	problem	NOUN
ejpam-6102	85	39	(	(	PUNCT
ejpam-6102	85	40	pε	pε	NOUN
ejpam-6102	85	41	)	)	PUNCT
ejpam-6102	85	42	.	.	PUNCT
ejpam-6102	86	1	section	section	NOUN
ejpam-6102	86	2	3	3	NUM
ejpam-6102	86	3	focuses	focus	VERB
ejpam-6102	86	4	on	on	ADP
ejpam-6102	86	5	the	the	DET
ejpam-6102	86	6	analysis	analysis	NOUN
ejpam-6102	86	7	of	of	ADP
ejpam-6102	86	8	the	the	DET
ejpam-6102	86	9	infinitedimensional	infinitedimensional	ADJ
ejpam-6102	86	10	part	part	NOUN
ejpam-6102	86	11	of	of	ADP
ejpam-6102	86	12	the	the	DET
ejpam-6102	86	13	solutions	solution	NOUN
ejpam-6102	86	14	.	.	PUNCT
ejpam-6102	87	1	in	in	ADP
ejpam-6102	87	2	section	section	NOUN
ejpam-6102	87	3	4	4	NUM
ejpam-6102	87	4	,	,	PUNCT
ejpam-6102	87	5	we	we	PRON
ejpam-6102	87	6	carry	carry	VERB
ejpam-6102	87	7	out	out	ADP
ejpam-6102	87	8	an	an	DET
ejpam-6102	87	9	asymptotic	asymptotic	ADJ
ejpam-6102	87	10	expansion	expansion	NOUN
ejpam-6102	87	11	of	of	ADP
ejpam-6102	87	12	the	the	DET
ejpam-6102	87	13	gradient	gradient	NOUN
ejpam-6102	87	14	of	of	ADP
ejpam-6102	87	15	the	the	DET
ejpam-6102	87	16	euler	euler	NOUN
ejpam-6102	87	17	-	-	PUNCT
ejpam-6102	87	18	lagrange	lagrange	NOUN
ejpam-6102	87	19	functional	functional	NOUN
ejpam-6102	87	20	associated	associate	VERB
ejpam-6102	87	21	with	with	ADP
ejpam-6102	87	22	(	(	PUNCT
ejpam-6102	87	23	pε	pε	NOUN
ejpam-6102	87	24	)	)	PUNCT
ejpam-6102	87	25	.	.	PUNCT
ejpam-6102	88	1	section	section	NOUN
ejpam-6102	88	2	5	5	NUM
ejpam-6102	88	3	presents	present	VERB
ejpam-6102	88	4	the	the	DET
ejpam-6102	88	5	proof	proof	NOUN
ejpam-6102	88	6	of	of	ADP
ejpam-6102	88	7	our	our	PRON
ejpam-6102	88	8	main	main	ADJ
ejpam-6102	88	9	results	result	NOUN
ejpam-6102	88	10	and	and	CCONJ
ejpam-6102	88	11	section	section	NOUN
ejpam-6102	88	12	6	6	NUM
ejpam-6102	88	13	explores	explore	NOUN
ejpam-6102	88	14	possible	possible	ADJ
ejpam-6102	88	15	avenues	avenue	NOUN
ejpam-6102	88	16	for	for	ADP
ejpam-6102	88	17	future	future	ADJ
ejpam-6102	88	18	research	research	NOUN
ejpam-6102	88	19	.	.	PUNCT
ejpam-6102	89	1	finally	finally	ADV
ejpam-6102	89	2	,	,	PUNCT
ejpam-6102	89	3	the	the	DET
ejpam-6102	89	4	proofs	proof	NOUN
ejpam-6102	89	5	rely	rely	VERB
ejpam-6102	89	6	on	on	ADP
ejpam-6102	89	7	some	some	DET
ejpam-6102	89	8	technical	technical	ADJ
ejpam-6102	89	9	facts	fact	NOUN
ejpam-6102	89	10	,	,	PUNCT
ejpam-6102	89	11	which	which	PRON
ejpam-6102	89	12	are	be	AUX
ejpam-6102	89	13	provided	provide	VERB
ejpam-6102	89	14	in	in	ADP
ejpam-6102	89	15	the	the	DET
ejpam-6102	89	16	appendix	appendix	NOUN
ejpam-6102	89	17	in	in	ADP
ejpam-6102	89	18	section	section	NOUN
ejpam-6102	89	19	7	7	NUM
ejpam-6102	89	20	for	for	ADP
ejpam-6102	89	21	the	the	DET
ejpam-6102	89	22	reader	reader	NOUN
ejpam-6102	89	23	’s	’s	PART
ejpam-6102	89	24	convenience	convenience	NOUN
ejpam-6102	89	25	.	.	PUNCT
ejpam-6102	90	1	2	2	X
ejpam-6102	90	2	.	.	X
ejpam-6102	90	3	preliminaries	preliminary	NOUN
ejpam-6102	90	4	in	in	ADP
ejpam-6102	90	5	this	this	DET
ejpam-6102	90	6	section	section	NOUN
ejpam-6102	90	7	,	,	PUNCT
ejpam-6102	90	8	we	we	PRON
ejpam-6102	90	9	proceed	proceed	VERB
ejpam-6102	90	10	with	with	ADP
ejpam-6102	90	11	the	the	DET
ejpam-6102	90	12	parametrization	parametrization	NOUN
ejpam-6102	90	13	of	of	ADP
ejpam-6102	90	14	the	the	DET
ejpam-6102	90	15	variational	variational	ADJ
ejpam-6102	90	16	problem	problem	NOUN
ejpam-6102	90	17	under	under	ADP
ejpam-6102	90	18	consideration	consideration	NOUN
ejpam-6102	90	19	.	.	PUNCT
ejpam-6102	91	1	indeed	indeed	ADV
ejpam-6102	91	2	,	,	PUNCT
ejpam-6102	91	3	problem	problem	NOUN
ejpam-6102	91	4	(	(	PUNCT
ejpam-6102	91	5	pε	pε	NOUN
ejpam-6102	91	6	)	)	PUNCT
ejpam-6102	91	7	is	be	AUX
ejpam-6102	91	8	a	a	DET
ejpam-6102	91	9	variational	variational	ADJ
ejpam-6102	91	10	one	one	NOUN
ejpam-6102	91	11	and	and	CCONJ
ejpam-6102	91	12	its	its	PRON
ejpam-6102	91	13	solutions	solution	NOUN
ejpam-6102	91	14	are	be	AUX
ejpam-6102	91	15	the	the	DET
ejpam-6102	91	16	positive	positive	ADJ
ejpam-6102	91	17	critical	critical	ADJ
ejpam-6102	91	18	points	point	NOUN
ejpam-6102	91	19	of	of	ADP
ejpam-6102	91	20	the	the	DET
ejpam-6102	91	21	functional	functional	ADJ
ejpam-6102	91	22	jε(u	jε(u	NOUN
ejpam-6102	91	23	)	)	PUNCT
ejpam-6102	91	24	:	:	PUNCT
ejpam-6102	92	1	=	=	SYM
ejpam-6102	92	2	1	1	NUM
ejpam-6102	92	3	2	2	NUM
ejpam-6102	92	4	∫	∫	PROPN
ejpam-6102	92	5	ω	ω	NOUN
ejpam-6102	92	6	|∇u|2	|∇u|2	NOUN
ejpam-6102	92	7	+	+	SYM
ejpam-6102	92	8	1	1	NUM
ejpam-6102	92	9	2	2	NUM
ejpam-6102	92	10	∫	∫	NOUN
ejpam-6102	92	11	ω	ω	NUM
ejpam-6102	92	12	v	v	PROPN
ejpam-6102	92	13	u2	u2	PROPN
ejpam-6102	92	14	−	−	PROPN
ejpam-6102	92	15	n−	n−	NOUN
ejpam-6102	92	16	2	2	NUM
ejpam-6102	92	17	2n−	2n−	PROPN
ejpam-6102	92	18	ε(n−	ε(n−	NOUN
ejpam-6102	92	19	2	2	NUM
ejpam-6102	92	20	)	)	PUNCT
ejpam-6102	92	21	∫	∫	PROPN
ejpam-6102	93	1	ω	ω	PROPN
ejpam-6102	93	2	f	f	PROPN
ejpam-6102	93	3	|u|	|u|	PROPN
ejpam-6102	93	4	2n	2n	NUM
ejpam-6102	93	5	n−2	n−2	PROPN
ejpam-6102	93	6	−ε	−ε	PROPN
ejpam-6102	93	7	,	,	PUNCT
ejpam-6102	93	8	u	u	PROPN
ejpam-6102	93	9	∈	∈	PROPN
ejpam-6102	93	10	h1(ω	h1(ω	PROPN
ejpam-6102	93	11	)	)	PUNCT
ejpam-6102	93	12	.	.	PUNCT
ejpam-6102	94	1	(	(	PUNCT
ejpam-6102	94	2	3	3	X
ejpam-6102	94	3	)	)	PUNCT
ejpam-6102	94	4	the	the	DET
ejpam-6102	94	5	space	space	NOUN
ejpam-6102	94	6	h1(ω	h1(ω	NOUN
ejpam-6102	94	7	)	)	PUNCT
ejpam-6102	94	8	is	be	AUX
ejpam-6102	94	9	equipped	equip	VERB
ejpam-6102	94	10	with	with	ADP
ejpam-6102	94	11	the	the	DET
ejpam-6102	94	12	scalar	scalar	ADJ
ejpam-6102	94	13	product	product	NOUN
ejpam-6102	94	14	and	and	CCONJ
ejpam-6102	94	15	its	its	PRON
ejpam-6102	94	16	corresponding	corresponding	ADJ
ejpam-6102	94	17	norm	norm	NOUN
ejpam-6102	94	18	defined	define	VERB
ejpam-6102	94	19	by	by	ADP
ejpam-6102	94	20	:	:	PUNCT
ejpam-6102	94	21	⟨u1	⟨u1	NOUN
ejpam-6102	94	22	,	,	PUNCT
ejpam-6102	94	23	u2⟩	u2⟩	PRON
ejpam-6102	94	24	:	:	PUNCT
ejpam-6102	95	1	=	=	SYM
ejpam-6102	95	2	∫	∫	PROPN
ejpam-6102	95	3	ω	ω	NUM
ejpam-6102	95	4	∇u1∇u2	∇u1∇u2	PROPN
ejpam-6102	96	1	+	+	CCONJ
ejpam-6102	96	2	∫	∫	PROPN
ejpam-6102	96	3	ω	ω	NUM
ejpam-6102	96	4	v	v	PROPN
ejpam-6102	96	5	u1u2	u1u2	ADP
ejpam-6102	96	6	;	;	PUNCT
ejpam-6102	96	7	∥u∥2	∥u∥2	NOUN
ejpam-6102	96	8	:	:	PUNCT
ejpam-6102	96	9	=	=	SYM
ejpam-6102	96	10	∫	∫	PROPN
ejpam-6102	96	11	ω	ω	PROPN
ejpam-6102	96	12	|∇u|2	|∇u|2	PUNCT
ejpam-6102	96	13	+	+	CCONJ
ejpam-6102	96	14	∫	∫	PROPN
ejpam-6102	96	15	ω	ω	NUM
ejpam-6102	96	16	v	v	PROPN
ejpam-6102	96	17	u2	u2	PROPN
ejpam-6102	96	18	.	.	PUNCT
ejpam-6102	97	1	since	since	SCONJ
ejpam-6102	97	2	v	v	NOUN
ejpam-6102	97	3	is	be	AUX
ejpam-6102	97	4	a	a	DET
ejpam-6102	97	5	bounded	bounded	ADJ
ejpam-6102	97	6	positive	positive	ADJ
ejpam-6102	97	7	continuous	continuous	ADJ
ejpam-6102	97	8	function	function	NOUN
ejpam-6102	97	9	on	on	ADP
ejpam-6102	97	10	ω	ω	NUM
ejpam-6102	97	11	,	,	PUNCT
ejpam-6102	97	12	it	it	PRON
ejpam-6102	97	13	follows	follow	VERB
ejpam-6102	97	14	that	that	SCONJ
ejpam-6102	97	15	this	this	DET
ejpam-6102	97	16	norm	norm	NOUN
ejpam-6102	97	17	is	be	AUX
ejpam-6102	97	18	equivalent	equivalent	ADJ
ejpam-6102	97	19	to	to	ADP
ejpam-6102	97	20	the	the	DET
ejpam-6102	97	21	standard	standard	ADJ
ejpam-6102	97	22	norm	norm	NOUN
ejpam-6102	97	23	of	of	ADP
ejpam-6102	97	24	h1(ω	h1(ω	PROPN
ejpam-6102	97	25	)	)	PUNCT
ejpam-6102	97	26	.	.	PUNCT
ejpam-6102	98	1	observe	observe	VERB
ejpam-6102	98	2	that	that	SCONJ
ejpam-6102	98	3	,	,	PUNCT
ejpam-6102	98	4	if	if	SCONJ
ejpam-6102	98	5	uε	uε	PROPN
ejpam-6102	98	6	is	be	AUX
ejpam-6102	98	7	a	a	DET
ejpam-6102	98	8	solution	solution	NOUN
ejpam-6102	98	9	of	of	ADP
ejpam-6102	98	10	(	(	PUNCT
ejpam-6102	98	11	pε	pε	NOUN
ejpam-6102	98	12	)	)	PUNCT
ejpam-6102	98	13	,	,	PUNCT
ejpam-6102	98	14	satisfying	satisfy	VERB
ejpam-6102	98	15	uε	uε	ADP
ejpam-6102	98	16	⇀	⇀	PROPN
ejpam-6102	98	17	0	0	PUNCT
ejpam-6102	98	18	(	(	PUNCT
ejpam-6102	98	19	converges	converge	VERB
ejpam-6102	98	20	weakly	weakly	ADV
ejpam-6102	98	21	to	to	ADP
ejpam-6102	98	22	zero	zero	NUM
ejpam-6102	98	23	)	)	PUNCT
ejpam-6102	98	24	,	,	PUNCT
ejpam-6102	98	25	by	by	ADP
ejpam-6102	98	26	the	the	DET
ejpam-6102	98	27	concentration	concentration	NOUN
ejpam-6102	98	28	compactness	compactness	NOUN
ejpam-6102	98	29	principle	principle	NOUN
ejpam-6102	98	30	[	[	X
ejpam-6102	98	31	34	34	NUM
ejpam-6102	98	32	]	]	PUNCT
ejpam-6102	98	33	,	,	PUNCT
ejpam-6102	98	34	it	it	PRON
ejpam-6102	98	35	follows	follow	VERB
ejpam-6102	98	36	that	that	SCONJ
ejpam-6102	98	37	uε	uε	PROPN
ejpam-6102	98	38	has	have	VERB
ejpam-6102	98	39	to	to	PART
ejpam-6102	98	40	be	be	AUX
ejpam-6102	98	41	close	close	ADJ
ejpam-6102	98	42	to	to	ADP
ejpam-6102	98	43	some	some	DET
ejpam-6102	98	44	bubbles	bubble	NOUN
ejpam-6102	98	45	as	as	ADP
ejpam-6102	98	46	ε	ε	PROPN
ejpam-6102	98	47	→	→	SYM
ejpam-6102	98	48	0	0	NUM
ejpam-6102	98	49	,	,	PUNCT
ejpam-6102	98	50	that	that	ADV
ejpam-6102	98	51	is	is	ADV
ejpam-6102	98	52	,	,	PUNCT
ejpam-6102	98	53	there	there	PRON
ejpam-6102	98	54	exist	exist	VERB
ejpam-6102	98	55	q	q	PROPN
ejpam-6102	98	56	∈	∈	PROPN
ejpam-6102	98	57	n	n	CCONJ
ejpam-6102	98	58	,	,	PUNCT
ejpam-6102	98	59	µ1	µ1	PROPN
ejpam-6102	98	60	,	,	PUNCT
ejpam-6102	98	61	·	·	PUNCT
ejpam-6102	98	62	·	·	PUNCT
ejpam-6102	98	63	·	·	PUNCT
ejpam-6102	98	64	,	,	PUNCT
ejpam-6102	98	65	µq	µq	VERB
ejpam-6102	98	66	−→	−→	NOUN
ejpam-6102	98	67	∞	∞	PROPN
ejpam-6102	98	68	(	(	PUNCT
ejpam-6102	98	69	as	as	ADP
ejpam-6102	98	70	ε	ε	PROPN
ejpam-6102	98	71	→	→	SYM
ejpam-6102	98	72	0	0	NUM
ejpam-6102	98	73	)	)	PUNCT
ejpam-6102	98	74	and	and	CCONJ
ejpam-6102	98	75	a1	a1	NOUN
ejpam-6102	98	76	,	,	PUNCT
ejpam-6102	98	77	.	.	PUNCT
ejpam-6102	98	78	.	.	PUNCT
ejpam-6102	98	79	.	.	PUNCT
ejpam-6102	99	1	,	,	PUNCT
ejpam-6102	99	2	aq	aq	PROPN
ejpam-6102	99	3	∈	∈	NOUN
ejpam-6102	99	4	ω	ω	NUM
ejpam-6102	99	5	such	such	ADJ
ejpam-6102	99	6	that	that	SCONJ
ejpam-6102	99	7	,	,	PUNCT
ejpam-6102	99	8	as	as	SCONJ
ejpam-6102	99	9	ε→	ε→	PUNCT
ejpam-6102	99	10	0,∥∥∥∥∥uε	0,∥∥∥∥∥uε	VERB
ejpam-6102	100	1	−	−	NOUN
ejpam-6102	100	2	q∑	q∑	PROPN
ejpam-6102	100	3	i=1	i=1	PROPN
ejpam-6102	100	4	f(ai	f(ai	PROPN
ejpam-6102	100	5	)	)	PUNCT
ejpam-6102	100	6	(	(	PUNCT
ejpam-6102	100	7	2−n)/4ωai,µi	2−n)/4ωai,µi	NUM
ejpam-6102	100	8	∥∥∥∥∥→	∥∥∥∥∥→	ADP
ejpam-6102	100	9	0	0	NUM
ejpam-6102	100	10	,	,	PUNCT
ejpam-6102	100	11	and	and	CCONJ
ejpam-6102	100	12	µi	µi	INTJ
ejpam-6102	100	13	µj	µj	PROPN
ejpam-6102	101	1	+	+	NUM
ejpam-6102	101	2	µj	µj	PROPN
ejpam-6102	101	3	µi	µi	X
ejpam-6102	101	4	+	+	NUM
ejpam-6102	101	5	µiµj	µiµj	VERB
ejpam-6102	101	6	|ai	|ai	NUM
ejpam-6102	101	7	−	−	PROPN
ejpam-6102	101	8	aj	aj	PROPN
ejpam-6102	101	9	|2	|2	NUM
ejpam-6102	102	1	−→	−→	NOUN
ejpam-6102	102	2	∞.	∞.	PROPN
ejpam-6102	102	3	in	in	ADP
ejpam-6102	102	4	this	this	DET
ejpam-6102	102	5	paper	paper	NOUN
ejpam-6102	102	6	,	,	PUNCT
ejpam-6102	102	7	we	we	PRON
ejpam-6102	102	8	want	want	VERB
ejpam-6102	102	9	to	to	PART
ejpam-6102	102	10	construct	construct	VERB
ejpam-6102	102	11	some	some	DET
ejpam-6102	102	12	solutions	solution	NOUN
ejpam-6102	102	13	blowing	blow	VERB
ejpam-6102	102	14	up	up	ADP
ejpam-6102	102	15	at	at	ADP
ejpam-6102	102	16	some	some	DET
ejpam-6102	102	17	boundary	boundary	ADJ
ejpam-6102	102	18	points	point	NOUN
ejpam-6102	102	19	.	.	PUNCT
ejpam-6102	103	1	to	to	ADP
ejpam-6102	103	2	this	this	DET
ejpam-6102	103	3	aim	aim	NOUN
ejpam-6102	103	4	,	,	PUNCT
ejpam-6102	103	5	we	we	PRON
ejpam-6102	103	6	introduce	introduce	VERB
ejpam-6102	103	7	the	the	DET
ejpam-6102	103	8	following	follow	VERB
ejpam-6102	103	9	set	set	NOUN
ejpam-6102	103	10	:	:	PUNCT
ejpam-6102	103	11	let	let	VERB
ejpam-6102	103	12	n	n	X
ejpam-6102	103	13	⩾	⩾	NOUN
ejpam-6102	103	14	4	4	NUM
ejpam-6102	103	15	,	,	PUNCT
ejpam-6102	103	16	η0	η0	NOUN
ejpam-6102	103	17	be	be	AUX
ejpam-6102	103	18	a	a	DET
ejpam-6102	103	19	small	small	ADJ
ejpam-6102	103	20	positive	positive	ADJ
ejpam-6102	103	21	real	real	NOUN
ejpam-6102	103	22	,	,	PUNCT
ejpam-6102	103	23	γ0	γ0	NOUN
ejpam-6102	103	24	be	be	VERB
ejpam-6102	103	25	a	a	DET
ejpam-6102	103	26	fixed	fix	VERB
ejpam-6102	103	27	small	small	ADJ
ejpam-6102	103	28	positive	positive	ADJ
ejpam-6102	103	29	constant	constant	ADJ
ejpam-6102	103	30	and	and	CCONJ
ejpam-6102	103	31	q	q	NOUN
ejpam-6102	103	32	∈	∈	PROPN
ejpam-6102	103	33	n	n	CCONJ
ejpam-6102	103	34	,	,	PUNCT
ejpam-6102	103	35	we	we	PRON
ejpam-6102	103	36	define	define	VERB
ejpam-6102	103	37	ϑ	ϑ	X
ejpam-6102	103	38	(	(	PUNCT
ejpam-6102	103	39	q	q	PROPN
ejpam-6102	103	40	,	,	PUNCT
ejpam-6102	103	41	γ0	γ0	NOUN
ejpam-6102	103	42	,	,	PUNCT
ejpam-6102	103	43	η0	η0	NOUN
ejpam-6102	103	44	)	)	PUNCT
ejpam-6102	103	45	:	:	PUNCT
ejpam-6102	103	46	=	=	SYM
ejpam-6102	103	47	{	{	PUNCT
ejpam-6102	103	48	(	(	PUNCT
ejpam-6102	103	49	a	a	PRON
ejpam-6102	103	50	,	,	PUNCT
ejpam-6102	103	51	µ	µ	NOUN
ejpam-6102	103	52	,	,	PUNCT
ejpam-6102	103	53	α	α	NOUN
ejpam-6102	103	54	)	)	PUNCT
ejpam-6102	103	55	∈	∈	PROPN
ejpam-6102	103	56	(	(	PUNCT
ejpam-6102	103	57	∂ω)q×	∂ω)q×	NOUN
ejpam-6102	103	58	(	(	PUNCT
ejpam-6102	103	59	η−1	η−1	PROPN
ejpam-6102	103	60	0	0	NUM
ejpam-6102	103	61	,	,	PUNCT
ejpam-6102	103	62	∞	∞	PROPN
ejpam-6102	103	63	)	)	PUNCT
ejpam-6102	103	64	q	q	PROPN
ejpam-6102	103	65	×	×	NOUN
ejpam-6102	103	66	(	(	PUNCT
ejpam-6102	103	67	0,∞)q	0,∞)q	NOUN
ejpam-6102	103	68	:	:	PUNCT
ejpam-6102	103	69	|ai	|ai	PUNCT
ejpam-6102	103	70	−	−	PROPN
ejpam-6102	103	71	aj	aj	VERB
ejpam-6102	103	72	|	|	ADV
ejpam-6102	103	73	⩾	⩾	PUNCT
ejpam-6102	103	74	γ0	γ0	NOUN
ejpam-6102	103	75	∀i	∀i	NOUN
ejpam-6102	103	76	̸=	̸=	PROPN
ejpam-6102	103	77	j	j	PROPN
ejpam-6102	103	78	,	,	PUNCT
ejpam-6102	103	79	ε	ε	PROPN
ejpam-6102	103	80	lnµi	lnµi	VERB
ejpam-6102	103	81	<	<	X
ejpam-6102	103	82	η0	η0	NOUN
ejpam-6102	103	83	and	and	CCONJ
ejpam-6102	103	84	|1−	|1−	ADJ
ejpam-6102	103	85	αif(ai	αif(ai	NUM
ejpam-6102	103	86	)	)	PUNCT
ejpam-6102	103	87	(	(	PUNCT
ejpam-6102	103	88	n−2)/4|	n−2)/4|	NOUN
ejpam-6102	103	89	⩽	⩽	ADJ
ejpam-6102	103	90	η0	η0	NOUN
ejpam-6102	103	91	∀i	∀i	NOUN
ejpam-6102	103	92	}	}	PUNCT
ejpam-6102	103	93	.	.	PUNCT
ejpam-6102	104	1	furthermore	furthermore	ADV
ejpam-6102	104	2	,	,	PUNCT
ejpam-6102	104	3	for	for	ADP
ejpam-6102	104	4	a	a	DET
ejpam-6102	104	5	∈	∈	PROPN
ejpam-6102	104	6	∂ω	∂ω	PROPN
ejpam-6102	104	7	and	and	CCONJ
ejpam-6102	104	8	µ	µ	ADJ
ejpam-6102	104	9	>	>	X
ejpam-6102	104	10	η−1	η−1	PROPN
ejpam-6102	104	11	0	0	NUM
ejpam-6102	104	12	,	,	PUNCT
ejpam-6102	104	13	we	we	PRON
ejpam-6102	104	14	define	define	VERB
ejpam-6102	104	15	fa,µ	fa,µ	NOUN
ejpam-6102	104	16	:	:	PUNCT
ejpam-6102	104	17	=	=	SYM
ejpam-6102	104	18	{	{	PUNCT
ejpam-6102	104	19	v	v	NUM
ejpam-6102	104	20	∈	∈	PROPN
ejpam-6102	104	21	h1(ω	h1(ω	PROPN
ejpam-6102	104	22	)	)	PUNCT
ejpam-6102	104	23	:	:	PUNCT
ejpam-6102	105	1	∫	∫	PROPN
ejpam-6102	105	2	ω	ω	NUM
ejpam-6102	105	3	∇v∇ωa,µ	∇v∇ωa,µ	PROPN
ejpam-6102	105	4	=	=	SYM
ejpam-6102	105	5	∫	∫	PROPN
ejpam-6102	105	6	ω	ω	NUM
ejpam-6102	105	7	∇v∇∂ωa,µ	∇v∇∂ωa,µ	PROPN
ejpam-6102	105	8	∂µ	∂µ	PROPN
ejpam-6102	105	9	=	=	SYM
ejpam-6102	105	10	∫	∫	PROPN
ejpam-6102	105	11	ω	ω	PROPN
ejpam-6102	105	12	∇v∇∂ωa,µ	∇v∇∂ωa,µ	PROPN
ejpam-6102	106	1	∂τj	∂τj	PROPN
ejpam-6102	106	2	=	=	SYM
ejpam-6102	106	3	0	0	NUM
ejpam-6102	106	4	;	;	PUNCT
ejpam-6102	106	5	1	1	NUM
ejpam-6102	106	6	≤	≤	NUM
ejpam-6102	106	7	j	j	PROPN
ejpam-6102	106	8	≤	≤	ADJ
ejpam-6102	106	9	n−	n−	PROPN
ejpam-6102	106	10	1	1	NUM
ejpam-6102	106	11	}	}	PUNCT
ejpam-6102	106	12	(	(	PUNCT
ejpam-6102	106	13	4	4	X
ejpam-6102	106	14	)	)	PUNCT
ejpam-6102	106	15	r.	r.	PROPN
ejpam-6102	106	16	almushahhin	almushahhin	PROPN
ejpam-6102	106	17	,	,	PUNCT
ejpam-6102	106	18	m.	m.	PROPN
ejpam-6102	106	19	ben	ben	PROPN
ejpam-6102	106	20	ayed	aye	VERB
ejpam-6102	106	21	/	/	SYM
ejpam-6102	106	22	eur	eur	PROPN
ejpam-6102	106	23	.	.	PUNCT
ejpam-6102	107	1	j.	j.	PROPN
ejpam-6102	107	2	pure	pure	PROPN
ejpam-6102	107	3	appl	appl	PROPN
ejpam-6102	107	4	.	.	PROPN
ejpam-6102	107	5	math	math	PROPN
ejpam-6102	107	6	,	,	PUNCT
ejpam-6102	107	7	18	18	NUM
ejpam-6102	107	8	(	(	PUNCT
ejpam-6102	107	9	2	2	NUM
ejpam-6102	107	10	)	)	PUNCT
ejpam-6102	107	11	(	(	PUNCT
ejpam-6102	107	12	2025	2025	NUM
ejpam-6102	107	13	)	)	PUNCT
ejpam-6102	107	14	,	,	PUNCT
ejpam-6102	107	15	6102	6102	NUM
ejpam-6102	107	16	6	6	NUM
ejpam-6102	107	17	of	of	ADP
ejpam-6102	107	18	31	31	NUM
ejpam-6102	107	19	where	where	SCONJ
ejpam-6102	107	20	the	the	DET
ejpam-6102	107	21	τ	τ	PROPN
ejpam-6102	107	22	′js	′js	NOUN
ejpam-6102	107	23	,	,	PUNCT
ejpam-6102	107	24	for	for	ADP
ejpam-6102	107	25	j	j	PROPN
ejpam-6102	107	26	=	=	SYM
ejpam-6102	107	27	1	1	PROPN
ejpam-6102	107	28	,	,	PUNCT
ejpam-6102	107	29	.	.	PUNCT
ejpam-6102	107	30	.	.	PUNCT
ejpam-6102	108	1	.	.	PUNCT
ejpam-6102	109	1	,	,	PUNCT
ejpam-6102	109	2	n	n	CCONJ
ejpam-6102	109	3	−	−	PROPN
ejpam-6102	109	4	1	1	NUM
ejpam-6102	109	5	,	,	PUNCT
ejpam-6102	109	6	build	build	VERB
ejpam-6102	109	7	an	an	DET
ejpam-6102	109	8	orthonormal	orthonormal	ADJ
ejpam-6102	109	9	system	system	NOUN
ejpam-6102	109	10	of	of	ADP
ejpam-6102	109	11	coordinates	coordinate	NOUN
ejpam-6102	109	12	of	of	ADP
ejpam-6102	109	13	the	the	DET
ejpam-6102	109	14	tangent	tangent	ADJ
ejpam-6102	109	15	space	space	NOUN
ejpam-6102	109	16	to	to	ADP
ejpam-6102	109	17	∂ω	∂ω	PROPN
ejpam-6102	109	18	at	at	ADP
ejpam-6102	109	19	the	the	DET
ejpam-6102	109	20	point	point	NOUN
ejpam-6102	109	21	a.	a.	NOUN
ejpam-6102	109	22	in	in	ADP
ejpam-6102	109	23	addition	addition	NOUN
ejpam-6102	109	24	,	,	PUNCT
ejpam-6102	109	25	for	for	ADP
ejpam-6102	109	26	(	(	PUNCT
ejpam-6102	109	27	a	a	PRON
ejpam-6102	109	28	,	,	PUNCT
ejpam-6102	109	29	µ	µ	NOUN
ejpam-6102	109	30	,	,	PUNCT
ejpam-6102	109	31	α	α	NOUN
ejpam-6102	109	32	)	)	PUNCT
ejpam-6102	109	33	∈	∈	PROPN
ejpam-6102	109	34	ϑ	ϑ	X
ejpam-6102	109	35	(	(	PUNCT
ejpam-6102	109	36	q	q	PROPN
ejpam-6102	109	37	,	,	PUNCT
ejpam-6102	109	38	γ0	γ0	NOUN
ejpam-6102	109	39	,	,	PUNCT
ejpam-6102	109	40	η0	η0	NOUN
ejpam-6102	109	41	)	)	PUNCT
ejpam-6102	109	42	,	,	PUNCT
ejpam-6102	109	43	we	we	PRON
ejpam-6102	109	44	introduce	introduce	VERB
ejpam-6102	109	45	fa,µ	fa,µ	PUNCT
ejpam-6102	109	46	:	:	PUNCT
ejpam-6102	109	47	=	=	SYM
ejpam-6102	109	48	⋂	⋂	PROPN
ejpam-6102	109	49	1≤i≤q	1≤i≤q	NUM
ejpam-6102	109	50	fai,µi	fai,µi	NOUN
ejpam-6102	109	51	.	.	PUNCT
ejpam-6102	110	1	(	(	PUNCT
ejpam-6102	110	2	5	5	X
ejpam-6102	110	3	)	)	PUNCT
ejpam-6102	110	4	our	our	PRON
ejpam-6102	110	5	aim	aim	NOUN
ejpam-6102	110	6	is	be	AUX
ejpam-6102	110	7	to	to	PART
ejpam-6102	110	8	construct	construct	VERB
ejpam-6102	110	9	solutions	solution	NOUN
ejpam-6102	110	10	u	u	NOUN
ejpam-6102	110	11	having	have	VERB
ejpam-6102	110	12	the	the	DET
ejpam-6102	110	13	form	form	NOUN
ejpam-6102	110	14	u	u	NOUN
ejpam-6102	110	15	=	=	PROPN
ejpam-6102	110	16	∑q	∑q	PROPN
ejpam-6102	110	17	i=1	i=1	PROPN
ejpam-6102	110	18	αiωai,µi	αiωai,µi	PUNCT
ejpam-6102	111	1	+	+	CCONJ
ejpam-6102	111	2	v	v	ADP
ejpam-6102	111	3	,	,	PUNCT
ejpam-6102	111	4	with	with	ADP
ejpam-6102	111	5	(	(	PUNCT
ejpam-6102	111	6	a	a	PRON
ejpam-6102	111	7	,	,	PUNCT
ejpam-6102	111	8	µ	µ	NOUN
ejpam-6102	111	9	,	,	PUNCT
ejpam-6102	111	10	α	α	NOUN
ejpam-6102	111	11	)	)	PUNCT
ejpam-6102	111	12	∈	∈	PROPN
ejpam-6102	111	13	ϑ	ϑ	X
ejpam-6102	111	14	(	(	PUNCT
ejpam-6102	111	15	q	q	PROPN
ejpam-6102	111	16	,	,	PUNCT
ejpam-6102	111	17	γ0	γ0	NOUN
ejpam-6102	111	18	,	,	PUNCT
ejpam-6102	111	19	η0	η0	NOUN
ejpam-6102	111	20	)	)	PUNCT
ejpam-6102	111	21	and	and	CCONJ
ejpam-6102	111	22	v	v	ADP
ejpam-6102	111	23	∈	∈	NOUN
ejpam-6102	111	24	fa,µ.	fa,µ.	ADP
ejpam-6102	112	1	3	3	X
ejpam-6102	112	2	.	.	X
ejpam-6102	112	3	study	study	NOUN
ejpam-6102	112	4	of	of	ADP
ejpam-6102	112	5	the	the	DET
ejpam-6102	112	6	infinite	infinite	ADJ
ejpam-6102	112	7	-	-	PUNCT
ejpam-6102	112	8	dimensional	dimensional	ADJ
ejpam-6102	112	9	part	part	NOUN
ejpam-6102	112	10	of	of	ADP
ejpam-6102	112	11	the	the	DET
ejpam-6102	112	12	solutions	solution	NOUN
ejpam-6102	112	13	in	in	ADP
ejpam-6102	112	14	this	this	DET
ejpam-6102	112	15	section	section	NOUN
ejpam-6102	112	16	,	,	PUNCT
ejpam-6102	112	17	we	we	PRON
ejpam-6102	112	18	take	take	VERB
ejpam-6102	112	19	(	(	PUNCT
ejpam-6102	112	20	a	a	PRON
ejpam-6102	112	21	,	,	PUNCT
ejpam-6102	112	22	µ	µ	NOUN
ejpam-6102	112	23	,	,	PUNCT
ejpam-6102	112	24	α	α	NOUN
ejpam-6102	112	25	)	)	PUNCT
ejpam-6102	112	26	∈	∈	PROPN
ejpam-6102	112	27	ϑ	ϑ	X
ejpam-6102	112	28	(	(	PUNCT
ejpam-6102	112	29	q	q	PROPN
ejpam-6102	112	30	,	,	PUNCT
ejpam-6102	112	31	γ0	γ0	NOUN
ejpam-6102	112	32	,	,	PUNCT
ejpam-6102	112	33	η0	η0	NOUN
ejpam-6102	112	34	)	)	PUNCT
ejpam-6102	112	35	and	and	CCONJ
ejpam-6102	112	36	we	we	PRON
ejpam-6102	112	37	are	be	AUX
ejpam-6102	112	38	going	go	VERB
ejpam-6102	112	39	to	to	PART
ejpam-6102	112	40	study	study	VERB
ejpam-6102	112	41	the	the	DET
ejpam-6102	112	42	v	v	NOUN
ejpam-6102	112	43	-	-	PUNCT
ejpam-6102	112	44	part	part	NOUN
ejpam-6102	112	45	of	of	ADP
ejpam-6102	112	46	the	the	DET
ejpam-6102	112	47	solution	solution	NOUN
ejpam-6102	112	48	u.	u.	VERB
ejpam-6102	112	49	in	in	ADP
ejpam-6102	112	50	the	the	DET
ejpam-6102	112	51	sequel	sequel	NOUN
ejpam-6102	112	52	,	,	PUNCT
ejpam-6102	112	53	we	we	PRON
ejpam-6102	112	54	denote	denote	VERB
ejpam-6102	112	55	by	by	ADP
ejpam-6102	112	56	ũ	ũ	PROPN
ejpam-6102	112	57	:	:	PUNCT
ejpam-6102	113	1	=	=	PROPN
ejpam-6102	113	2	q∑	q∑	PROPN
ejpam-6102	113	3	i=1	i=1	X
ejpam-6102	113	4	αiωai,µi	αiωai,µi	PROPN
ejpam-6102	113	5	,	,	PUNCT
ejpam-6102	113	6	for	for	ADP
ejpam-6102	113	7	(	(	PUNCT
ejpam-6102	113	8	a	a	PRON
ejpam-6102	113	9	,	,	PUNCT
ejpam-6102	113	10	µ	µ	NOUN
ejpam-6102	113	11	,	,	PUNCT
ejpam-6102	113	12	α	α	NOUN
ejpam-6102	113	13	)	)	PUNCT
ejpam-6102	113	14	∈	∈	PROPN
ejpam-6102	113	15	ϑ	ϑ	X
ejpam-6102	113	16	(	(	PUNCT
ejpam-6102	113	17	q	q	PROPN
ejpam-6102	113	18	,	,	PUNCT
ejpam-6102	113	19	γ0	γ0	NOUN
ejpam-6102	113	20	,	,	PUNCT
ejpam-6102	113	21	η0	η0	NOUN
ejpam-6102	113	22	)	)	PUNCT
ejpam-6102	113	23	.	.	PUNCT
ejpam-6102	114	1	(	(	PUNCT
ejpam-6102	114	2	6	6	X
ejpam-6102	114	3	)	)	PUNCT
ejpam-6102	114	4	furthermore	furthermore	ADV
ejpam-6102	114	5	,	,	PUNCT
ejpam-6102	114	6	for	for	ADP
ejpam-6102	114	7	(	(	PUNCT
ejpam-6102	114	8	a	a	PRON
ejpam-6102	114	9	,	,	PUNCT
ejpam-6102	114	10	µ	µ	NOUN
ejpam-6102	114	11	,	,	PUNCT
ejpam-6102	114	12	α	α	NOUN
ejpam-6102	114	13	)	)	PUNCT
ejpam-6102	114	14	∈	∈	PROPN
ejpam-6102	114	15	ϑ	ϑ	X
ejpam-6102	114	16	(	(	PUNCT
ejpam-6102	114	17	q	q	PROPN
ejpam-6102	114	18	,	,	PUNCT
ejpam-6102	114	19	γ0	γ0	NOUN
ejpam-6102	114	20	,	,	PUNCT
ejpam-6102	114	21	η0	η0	NOUN
ejpam-6102	114	22	)	)	PUNCT
ejpam-6102	114	23	,	,	PUNCT
ejpam-6102	114	24	we	we	PRON
ejpam-6102	114	25	denote	denote	VERB
ejpam-6102	114	26	by	by	ADP
ejpam-6102	114	27	bi	bi	NOUN
ejpam-6102	114	28	:	:	PUNCT
ejpam-6102	114	29	=	=	SYM
ejpam-6102	114	30	b(ai	b(ai	PROPN
ejpam-6102	114	31	,	,	PUNCT
ejpam-6102	114	32	γ0/2	γ0/2	PROPN
ejpam-6102	114	33	)	)	PUNCT
ejpam-6102	114	34	.	.	PUNCT
ejpam-6102	115	1	it	it	PRON
ejpam-6102	115	2	follows	follow	VERB
ejpam-6102	115	3	that	that	SCONJ
ejpam-6102	115	4	ωai,µi	ωai,µi	PRON
ejpam-6102	115	5	≤	≤	PROPN
ejpam-6102	115	6	c	c	PROPN
ejpam-6102	115	7	µ	µ	X
ejpam-6102	115	8	(	(	PUNCT
ejpam-6102	115	9	n−2)/2	n−2)/2	ADP
ejpam-6102	115	10	i	i	PRON
ejpam-6102	115	11	in	in	ADP
ejpam-6102	115	12	ω	ω	NUM
ejpam-6102	115	13	\bi	\bi	PROPN
ejpam-6102	115	14	and	and	CCONJ
ejpam-6102	115	15	ũ	ũ	PROPN
ejpam-6102	115	16	=	=	SYM
ejpam-6102	115	17	αiωai,µi	αiωai,µi	PUNCT
ejpam-6102	116	1	+	+	ADJ
ejpam-6102	116	2	o	o	X
ejpam-6102	116	3	(	(	PUNCT
ejpam-6102	116	4	∑	∑	PUNCT
ejpam-6102	116	5	j	j	PROPN
ejpam-6102	116	6	̸=i	̸=i	PROPN
ejpam-6102	116	7	c	c	PROPN
ejpam-6102	116	8	µ	µ	X
ejpam-6102	116	9	(	(	PUNCT
ejpam-6102	116	10	n−2)/2	n−2)/2	NOUN
ejpam-6102	116	11	j	j	PROPN
ejpam-6102	116	12	)	)	PUNCT
ejpam-6102	116	13	in	in	ADP
ejpam-6102	116	14	bi	bi	PROPN
ejpam-6102	116	15	.	.	PUNCT
ejpam-6102	117	1	(	(	PUNCT
ejpam-6102	117	2	7	7	NUM
ejpam-6102	117	3	)	)	PUNCT
ejpam-6102	117	4	in	in	ADP
ejpam-6102	117	5	the	the	DET
ejpam-6102	117	6	following	following	NOUN
ejpam-6102	117	7	,	,	PUNCT
ejpam-6102	117	8	we	we	PRON
ejpam-6102	117	9	will	will	AUX
ejpam-6102	117	10	use	use	VERB
ejpam-6102	117	11	the	the	DET
ejpam-6102	117	12	estimate	estimate	NOUN
ejpam-6102	117	13	given	give	VERB
ejpam-6102	117	14	below	below	ADP
ejpam-6102	117	15	,	,	PUNCT
ejpam-6102	117	16	the	the	DET
ejpam-6102	117	17	proof	proof	NOUN
ejpam-6102	117	18	of	of	ADP
ejpam-6102	117	19	which	which	PRON
ejpam-6102	117	20	is	be	AUX
ejpam-6102	117	21	derived	derive	VERB
ejpam-6102	117	22	by	by	ADP
ejpam-6102	117	23	applying	apply	VERB
ejpam-6102	117	24	taylor	taylor	PROPN
ejpam-6102	117	25	’s	’s	PART
ejpam-6102	117	26	expansion	expansion	NOUN
ejpam-6102	117	27	.	.	PUNCT
ejpam-6102	118	1	for	for	ADP
ejpam-6102	118	2	t1	t1	NOUN
ejpam-6102	118	3	,	,	PUNCT
ejpam-6102	118	4	t2	t2	PROPN
ejpam-6102	118	5	∈	∈	PROPN
ejpam-6102	118	6	r	r	NOUN
ejpam-6102	118	7	and	and	CCONJ
ejpam-6102	118	8	γ	γ	NOUN
ejpam-6102	118	9	≥	≥	NUM
ejpam-6102	118	10	2	2	NUM
ejpam-6102	118	11	,	,	PUNCT
ejpam-6102	118	12	we	we	PRON
ejpam-6102	118	13	have	have	VERB
ejpam-6102	118	14	|t1	|t1	NOUN
ejpam-6102	118	15	+	+	NOUN
ejpam-6102	118	16	t2|γ	t2|γ	NOUN
ejpam-6102	118	17	=	=	SYM
ejpam-6102	118	18	|t1|γ	|t1|γ	NOUN
ejpam-6102	118	19	+	+	CCONJ
ejpam-6102	118	20	γ	γ	X
ejpam-6102	118	21	|t1|γ−2	|t1|γ−2	NUM
ejpam-6102	119	1	t1t2	t1t2	ADP
ejpam-6102	119	2	+	+	NOUN
ejpam-6102	119	3	1	1	NUM
ejpam-6102	119	4	2	2	NUM
ejpam-6102	119	5	γ(γ	γ(γ	PROPN
ejpam-6102	119	6	−	−	PROPN
ejpam-6102	119	7	1	1	X
ejpam-6102	119	8	)	)	PUNCT
ejpam-6102	119	9	|t1|γ−2	|t1|γ−2	NUM
ejpam-6102	119	10	t22	t22	NOUN
ejpam-6102	119	11	+	+	CCONJ
ejpam-6102	119	12	{	{	PUNCT
ejpam-6102	119	13	o	o	X
ejpam-6102	119	14	(	(	PUNCT
ejpam-6102	119	15	|t1|γ−3	|t1|γ−3	NOUN
ejpam-6102	119	16	|t2|3	|t2|3	PRON
ejpam-6102	119	17	+	+	NUM
ejpam-6102	119	18	|t2|γ	|t2|γ	NOUN
ejpam-6102	119	19	)	)	PUNCT
ejpam-6102	119	20	if	if	SCONJ
ejpam-6102	119	21	γ	γ	X
ejpam-6102	119	22	>	>	X
ejpam-6102	119	23	3	3	NUM
ejpam-6102	119	24	,	,	PUNCT
ejpam-6102	119	25	o	o	X
ejpam-6102	119	26	(	(	PUNCT
ejpam-6102	119	27	|t2|γ	|t2|γ	NOUN
ejpam-6102	119	28	)	)	PUNCT
ejpam-6102	119	29	if	if	SCONJ
ejpam-6102	119	30	γ	γ	X
ejpam-6102	119	31	⩽	⩽	NOUN
ejpam-6102	119	32	3	3	NUM
ejpam-6102	119	33	.	.	PUNCT
ejpam-6102	119	34	(	(	PUNCT
ejpam-6102	119	35	8)	8)	NUM
ejpam-6102	119	36	thus	thus	ADV
ejpam-6102	119	37	,	,	PUNCT
ejpam-6102	119	38	for	for	ADP
ejpam-6102	119	39	u	u	NOUN
ejpam-6102	119	40	=	=	NOUN
ejpam-6102	119	41	ũ+v	ũ+v	ADV
ejpam-6102	119	42	with	with	ADP
ejpam-6102	119	43	v	v	NOUN
ejpam-6102	119	44	∈	∈	PROPN
ejpam-6102	119	45	fa,µ	fa,µ	NOUN
ejpam-6102	119	46	,	,	PUNCT
ejpam-6102	119	47	using	use	VERB
ejpam-6102	119	48	eq	eq	X
ejpam-6102	119	49	.	.	PUNCT
ejpam-6102	119	50	(	(	PUNCT
ejpam-6102	119	51	8)	8)	NUM
ejpam-6102	119	52	,	,	PUNCT
ejpam-6102	119	53	,	,	PUNCT
ejpam-6102	119	54	the	the	DET
ejpam-6102	119	55	expansion	expansion	NOUN
ejpam-6102	119	56	of	of	ADP
ejpam-6102	119	57	jε	jε	PROPN
ejpam-6102	119	58	,	,	PUNCT
ejpam-6102	119	59	defined	define	VERB
ejpam-6102	119	60	by	by	ADP
ejpam-6102	119	61	(	(	PUNCT
ejpam-6102	119	62	3	3	NUM
ejpam-6102	119	63	)	)	PUNCT
ejpam-6102	119	64	,	,	PUNCT
ejpam-6102	119	65	is	be	AUX
ejpam-6102	119	66	as	as	SCONJ
ejpam-6102	119	67	follows	follow	VERB
ejpam-6102	119	68	jε(u	jε(u	PRON
ejpam-6102	119	69	)	)	PUNCT
ejpam-6102	119	70	=	=	SYM
ejpam-6102	119	71	jε(ũ)−	jε(ũ)−	NOUN
ejpam-6102	119	72	lε(v	lε(v	PUNCT
ejpam-6102	119	73	)	)	PUNCT
ejpam-6102	119	74	+	+	CCONJ
ejpam-6102	119	75	1	1	NUM
ejpam-6102	119	76	2	2	NUM
ejpam-6102	119	77	qε(v	qε(v	NOUN
ejpam-6102	119	78	)	)	PUNCT
ejpam-6102	119	79	+	+	NOUN
ejpam-6102	119	80	rε(v	rε(v	NOUN
ejpam-6102	119	81	)	)	PUNCT
ejpam-6102	119	82	,	,	PUNCT
ejpam-6102	119	83	with	with	ADP
ejpam-6102	119	84	(	(	PUNCT
ejpam-6102	119	85	9	9	NUM
ejpam-6102	119	86	)	)	PUNCT
ejpam-6102	119	87	qε(v	qε(v	NOUN
ejpam-6102	119	88	)	)	PUNCT
ejpam-6102	119	89	:	:	PUNCT
ejpam-6102	119	90	=	=	NOUN
ejpam-6102	119	91	∥v∥2	∥v∥2	NUM
ejpam-6102	119	92	−	−	X
ejpam-6102	119	93	(	(	PUNCT
ejpam-6102	119	94	p−	p−	NOUN
ejpam-6102	119	95	ε	ε	PROPN
ejpam-6102	119	96	)	)	PUNCT
ejpam-6102	119	97	∫	∫	PROPN
ejpam-6102	120	1	ω	ω	PROPN
ejpam-6102	120	2	fũp−ε−1v2	fũp−ε−1v2	PROPN
ejpam-6102	120	3	,	,	PUNCT
ejpam-6102	120	4	(	(	PUNCT
ejpam-6102	120	5	10	10	NUM
ejpam-6102	120	6	)	)	PUNCT
ejpam-6102	120	7	lε(v	lε(v	NOUN
ejpam-6102	120	8	)	)	PUNCT
ejpam-6102	120	9	:	:	PUNCT
ejpam-6102	121	1	=	=	SYM
ejpam-6102	121	2	∫	∫	PROPN
ejpam-6102	121	3	ω	ω	NUM
ejpam-6102	121	4	fũp−εv	fũp−εv	PROPN
ejpam-6102	121	5	,	,	PUNCT
ejpam-6102	121	6	(	(	PUNCT
ejpam-6102	121	7	11	11	NUM
ejpam-6102	121	8	)	)	PUNCT
ejpam-6102	121	9	rε(v	rε(v	NOUN
ejpam-6102	121	10	)	)	PUNCT
ejpam-6102	122	1	=	=	SYM
ejpam-6102	122	2	o	o	X
ejpam-6102	122	3	(	(	PUNCT
ejpam-6102	122	4	∥v∥2	∥v∥2	PROPN
ejpam-6102	122	5	)	)	PUNCT
ejpam-6102	122	6	,	,	PUNCT
ejpam-6102	122	7	r′	r′	PROPN
ejpam-6102	122	8	ε(v	ε(v	NOUN
ejpam-6102	122	9	)	)	PUNCT
ejpam-6102	122	10	=	=	SYM
ejpam-6102	122	11	o(∥v∥	o(∥v∥	PROPN
ejpam-6102	122	12	)	)	PUNCT
ejpam-6102	122	13	and	and	CCONJ
ejpam-6102	122	14	r′′	r′′	VERB
ejpam-6102	122	15	ε	ε	PROPN
ejpam-6102	122	16	(	(	PUNCT
ejpam-6102	122	17	v	v	NOUN
ejpam-6102	122	18	)	)	PUNCT
ejpam-6102	122	19	=	=	SYM
ejpam-6102	122	20	o(1	o(1	NOUN
ejpam-6102	122	21	)	)	PUNCT
ejpam-6102	122	22	.	.	PUNCT
ejpam-6102	123	1	next	next	ADV
ejpam-6102	123	2	,	,	PUNCT
ejpam-6102	123	3	we	we	PRON
ejpam-6102	123	4	will	will	AUX
ejpam-6102	123	5	prove	prove	VERB
ejpam-6102	123	6	the	the	DET
ejpam-6102	123	7	coercivity	coercivity	NOUN
ejpam-6102	123	8	of	of	ADP
ejpam-6102	123	9	the	the	DET
ejpam-6102	123	10	form	form	NOUN
ejpam-6102	123	11	qε	qε	X
ejpam-6102	123	12	.	.	PUNCT
ejpam-6102	124	1	more	more	ADV
ejpam-6102	124	2	precisely	precisely	ADV
ejpam-6102	124	3	,	,	PUNCT
ejpam-6102	124	4	we	we	PRON
ejpam-6102	124	5	have	have	VERB
ejpam-6102	124	6	:	:	PUNCT
ejpam-6102	124	7	lemma	lemma	PROPN
ejpam-6102	124	8	1	1	X
ejpam-6102	124	9	.	.	PUNCT
ejpam-6102	125	1	let	let	VERB
ejpam-6102	125	2	(	(	PUNCT
ejpam-6102	125	3	a	a	PRON
ejpam-6102	125	4	,	,	PUNCT
ejpam-6102	125	5	µ	µ	NOUN
ejpam-6102	125	6	,	,	PUNCT
ejpam-6102	125	7	α	α	NOUN
ejpam-6102	125	8	)	)	PUNCT
ejpam-6102	125	9	∈	∈	PROPN
ejpam-6102	125	10	ϑ	ϑ	X
ejpam-6102	125	11	(	(	PUNCT
ejpam-6102	125	12	q	q	PROPN
ejpam-6102	125	13	,	,	PUNCT
ejpam-6102	125	14	γ0	γ0	NOUN
ejpam-6102	125	15	,	,	PUNCT
ejpam-6102	125	16	η0	η0	NOUN
ejpam-6102	125	17	)	)	PUNCT
ejpam-6102	125	18	.	.	PUNCT
ejpam-6102	126	1	then	then	ADV
ejpam-6102	126	2	the	the	DET
ejpam-6102	126	3	following	follow	VERB
ejpam-6102	126	4	fact	fact	NOUN
ejpam-6102	126	5	holds	hold	VERB
ejpam-6102	126	6	qε(v	qε(v	NOUN
ejpam-6102	126	7	)	)	PUNCT
ejpam-6102	126	8	=	=	SYM
ejpam-6102	126	9	q(v	q(v	NOUN
ejpam-6102	126	10	)	)	PUNCT
ejpam-6102	127	1	+	+	NUM
ejpam-6102	127	2	o	o	X
ejpam-6102	127	3	(	(	PUNCT
ejpam-6102	127	4	∥∥v2∥∥	∥∥v2∥∥	NOUN
ejpam-6102	127	5	)	)	PUNCT
ejpam-6102	127	6	where	where	SCONJ
ejpam-6102	127	7	q(v	q(v	NOUN
ejpam-6102	127	8	)	)	PUNCT
ejpam-6102	127	9	:	:	PUNCT
ejpam-6102	128	1	=	=	NOUN
ejpam-6102	128	2	∥v∥2	∥v∥2	ADJ
ejpam-6102	128	3	−	−	X
ejpam-6102	128	4	n+	n+	ADP
ejpam-6102	128	5	2	2	NUM
ejpam-6102	128	6	n−	n−	NOUN
ejpam-6102	128	7	2	2	NUM
ejpam-6102	128	8	q∑	q∑	NOUN
ejpam-6102	128	9	i=1	i=1	PROPN
ejpam-6102	128	10	∫	∫	PROPN
ejpam-6102	128	11	ω	ω	PROPN
ejpam-6102	128	12	ω	ω	PROPN
ejpam-6102	128	13	4	4	NUM
ejpam-6102	128	14	n−2	n−2	PROPN
ejpam-6102	128	15	ai,µiv	ai,µiv	PROPN
ejpam-6102	128	16	2	2	NUM
ejpam-6102	128	17	.	.	PUNCT
ejpam-6102	128	18	proof	proof	NOUN
ejpam-6102	128	19	.	.	PUNCT
ejpam-6102	129	1	by	by	ADP
ejpam-6102	129	2	using	use	VERB
ejpam-6102	129	3	the	the	DET
ejpam-6102	129	4	following	follow	VERB
ejpam-6102	129	5	formula	formula	NOUN
ejpam-6102	129	6	derived	derive	VERB
ejpam-6102	129	7	from	from	ADP
ejpam-6102	129	8	taylor	taylor	PROPN
ejpam-6102	129	9	’s	’s	PART
ejpam-6102	129	10	expansion	expansion	NOUN
ejpam-6102	129	11	∣∣∣∑	∣∣∣∑	PROPN
ejpam-6102	129	12	ti	ti	NOUN
ejpam-6102	129	13	∣∣∣γ	∣∣∣γ	PROPN
ejpam-6102	129	14	=	=	SYM
ejpam-6102	129	15	∑	∑	PUNCT
ejpam-6102	129	16	|ti|γ	|ti|γ	ADJ
ejpam-6102	129	17	+	+	PROPN
ejpam-6102	129	18	o	o	X
ejpam-6102	129	19	∑	∑	NOUN
ejpam-6102	129	20	j	j	NOUN
ejpam-6102	129	21	̸=i	̸=i	PROPN
ejpam-6102	129	22	|titj	|titj	VERB
ejpam-6102	129	23	|γ/2	|γ/2	NUM
ejpam-6102	129	24			PROPN
ejpam-6102	129	25	∀ti	∀ti	PROPN
ejpam-6102	129	26	∈	∈	PROPN
ejpam-6102	129	27	r	r	PROPN
ejpam-6102	129	28	,	,	PUNCT
ejpam-6102	129	29	∀γ	∀γ	PROPN
ejpam-6102	129	30	∈	∈	PROPN
ejpam-6102	129	31	(	(	PUNCT
ejpam-6102	129	32	0	0	NUM
ejpam-6102	129	33	,	,	PUNCT
ejpam-6102	129	34	2	2	NUM
ejpam-6102	129	35	]	]	PUNCT
ejpam-6102	129	36	,	,	PUNCT
ejpam-6102	129	37	r.	r.	PROPN
ejpam-6102	129	38	almushahhin	almushahhin	PROPN
ejpam-6102	129	39	,	,	PUNCT
ejpam-6102	129	40	m.	m.	PROPN
ejpam-6102	129	41	ben	ben	PROPN
ejpam-6102	129	42	ayed	aye	VERB
ejpam-6102	129	43	/	/	SYM
ejpam-6102	129	44	eur	eur	PROPN
ejpam-6102	129	45	.	.	PUNCT
ejpam-6102	130	1	j.	j.	PROPN
ejpam-6102	130	2	pure	pure	PROPN
ejpam-6102	130	3	appl	appl	PROPN
ejpam-6102	130	4	.	.	PROPN
ejpam-6102	130	5	math	math	PROPN
ejpam-6102	130	6	,	,	PUNCT
ejpam-6102	130	7	18	18	NUM
ejpam-6102	130	8	(	(	PUNCT
ejpam-6102	130	9	2	2	NUM
ejpam-6102	130	10	)	)	PUNCT
ejpam-6102	130	11	(	(	PUNCT
ejpam-6102	130	12	2025	2025	NUM
ejpam-6102	130	13	)	)	PUNCT
ejpam-6102	130	14	,	,	PUNCT
ejpam-6102	130	15	6102	6102	NUM
ejpam-6102	130	16	7	7	NUM
ejpam-6102	130	17	of	of	ADP
ejpam-6102	130	18	31	31	NUM
ejpam-6102	130	19	we	we	PRON
ejpam-6102	130	20	derive	derive	VERB
ejpam-6102	131	1	that∫	that∫	PROPN
ejpam-6102	131	2	ω	ω	NOUN
ejpam-6102	131	3	fũp−ε−1v2	fũp−ε−1v2	PROPN
ejpam-6102	132	1	=	=	SYM
ejpam-6102	132	2	q∑	q∑	PROPN
ejpam-6102	132	3	i=1	i=1	PRON
ejpam-6102	132	4	αp−ε−1	αp−ε−1	NUM
ejpam-6102	133	1	i	i	PRON
ejpam-6102	133	2	∫	∫	PROPN
ejpam-6102	133	3	ω	ω	PROPN
ejpam-6102	133	4	fω	fω	PROPN
ejpam-6102	133	5	4	4	NUM
ejpam-6102	133	6	n−2−ε	n−2−ε	NOUN
ejpam-6102	133	7	ai,µi	ai,µi	ADJ
ejpam-6102	133	8	v2	v2	PROPN
ejpam-6102	134	1	+	+	CCONJ
ejpam-6102	134	2	∑	∑	PROPN
ejpam-6102	134	3	j	j	PROPN
ejpam-6102	134	4	̸=i	̸=i	PROPN
ejpam-6102	134	5	o	o	PROPN
ejpam-6102	134	6	(	(	PUNCT
ejpam-6102	134	7	∫	∫	PROPN
ejpam-6102	134	8	ω	ω	PROPN
ejpam-6102	134	9	(	(	PUNCT
ejpam-6102	134	10	ωai,µi	ωai,µi	PROPN
ejpam-6102	134	11	ωaj	ωaj	PROPN
ejpam-6102	134	12	,	,	PUNCT
ejpam-6102	134	13	µj	µj	PROPN
ejpam-6102	134	14	)	)	PUNCT
ejpam-6102	134	15	2	2	NUM
ejpam-6102	134	16	n−2	n−2	PROPN
ejpam-6102	134	17	v2	v2	PROPN
ejpam-6102	134	18	)	)	PUNCT
ejpam-6102	134	19	.	.	PUNCT
ejpam-6102	135	1	expanding	expand	VERB
ejpam-6102	135	2	f	f	PROPN
ejpam-6102	135	3	around	around	ADP
ejpam-6102	135	4	ai	ai	VERB
ejpam-6102	135	5	,	,	PUNCT
ejpam-6102	135	6	we	we	PRON
ejpam-6102	135	7	obtain∫	obtain∫	VERB
ejpam-6102	135	8	ω	ω	NUM
ejpam-6102	135	9	fω	fω	PROPN
ejpam-6102	135	10	4	4	NUM
ejpam-6102	135	11	n−2−ε	n−2−ε	NOUN
ejpam-6102	135	12	ai,µi	ai,µi	NOUN
ejpam-6102	135	13	v2	v2	PROPN
ejpam-6102	135	14	=	=	SYM
ejpam-6102	135	15	f	f	PROPN
ejpam-6102	135	16	(	(	PUNCT
ejpam-6102	135	17	ai	ai	PROPN
ejpam-6102	135	18	)	)	PUNCT
ejpam-6102	135	19	∫	∫	PROPN
ejpam-6102	136	1	ω	ω	PROPN
ejpam-6102	136	2	ω	ω	PROPN
ejpam-6102	136	3	4	4	NUM
ejpam-6102	136	4	n−2−ε	n−2−ε	NOUN
ejpam-6102	136	5	ai,µi	ai,µi	NOUN
ejpam-6102	136	6	v2	v2	PROPN
ejpam-6102	137	1	+	+	PROPN
ejpam-6102	137	2	o	o	PROPN
ejpam-6102	137	3	(	(	PUNCT
ejpam-6102	137	4	∫	∫	PROPN
ejpam-6102	137	5	ω	ω	PROPN
ejpam-6102	137	6	|x−	|x−	PROPN
ejpam-6102	137	7	ai|ω	ai|ω	PROPN
ejpam-6102	137	8	4	4	NUM
ejpam-6102	137	9	n−2−ε	n−2−ε	NOUN
ejpam-6102	137	10	ai,µi	ai,µi	ADJ
ejpam-6102	137	11	v2	v2	PROPN
ejpam-6102	137	12	)	)	PUNCT
ejpam-6102	138	1	=	=	SYM
ejpam-6102	138	2	f	f	PROPN
ejpam-6102	138	3	(	(	PUNCT
ejpam-6102	138	4	ai	ai	PROPN
ejpam-6102	138	5	)	)	PUNCT
ejpam-6102	138	6	∫	∫	PROPN
ejpam-6102	139	1	ω	ω	PROPN
ejpam-6102	139	2	ω	ω	PROPN
ejpam-6102	139	3	4	4	NUM
ejpam-6102	139	4	n−2−ε	n−2−ε	NOUN
ejpam-6102	139	5	ai,µi	ai,µi	NOUN
ejpam-6102	139	6	v2	v2	PROPN
ejpam-6102	140	1	+	+	CCONJ
ejpam-6102	140	2	o	o	X
ejpam-6102	140	3	(	(	PUNCT
ejpam-6102	140	4	∥v∥2	∥v∥2	PROPN
ejpam-6102	140	5	)	)	PUNCT
ejpam-6102	140	6	.	.	PUNCT
ejpam-6102	141	1	furthermore	furthermore	ADV
ejpam-6102	141	2	,	,	PUNCT
ejpam-6102	141	3	since	since	SCONJ
ejpam-6102	141	4	ε	ε	PROPN
ejpam-6102	141	5	lnµi	lnµi	PROPN
ejpam-6102	141	6	is	be	AUX
ejpam-6102	141	7	small	small	ADJ
ejpam-6102	141	8	,	,	PUNCT
ejpam-6102	141	9	we	we	PRON
ejpam-6102	141	10	have	have	VERB
ejpam-6102	141	11	ω−ε	ω−ε	NUM
ejpam-6102	141	12	ai,µi	ai,µi	ADJ
ejpam-6102	141	13	=	=	PUNCT
ejpam-6102	141	14	β−ε	β−ε	PROPN
ejpam-6102	141	15	0	0	NUM
ejpam-6102	141	16	µ	µ	X
ejpam-6102	141	17	−εn−2	−εn−2	ADP
ejpam-6102	141	18	2	2	NUM
ejpam-6102	141	19	i	i	NOUN
ejpam-6102	141	20	(	(	PUNCT
ejpam-6102	141	21	1	1	X
ejpam-6102	141	22	+	+	NUM
ejpam-6102	141	23	n−	n−	NOUN
ejpam-6102	141	24	2	2	NUM
ejpam-6102	141	25	2	2	NUM
ejpam-6102	141	26	ε	ε	X
ejpam-6102	141	27	ln	ln	NOUN
ejpam-6102	141	28	(	(	PUNCT
ejpam-6102	141	29	1	1	NUM
ejpam-6102	141	30	+	+	CCONJ
ejpam-6102	141	31	µ2	µ2	PROPN
ejpam-6102	141	32	i	i	PRON
ejpam-6102	141	33	|x−	|x−	PROPN
ejpam-6102	141	34	ai|2	ai|2	PROPN
ejpam-6102	141	35	)	)	PUNCT
ejpam-6102	141	36	)	)	PUNCT
ejpam-6102	142	1	+	+	NOUN
ejpam-6102	142	2	o	o	X
ejpam-6102	142	3	(	(	PUNCT
ejpam-6102	142	4	ε2	ε2	ADV
ejpam-6102	142	5	ln2	ln2	NOUN
ejpam-6102	142	6	(	(	PUNCT
ejpam-6102	142	7	1	1	NUM
ejpam-6102	142	8	+	+	CCONJ
ejpam-6102	142	9	µ2	µ2	PROPN
ejpam-6102	142	10	i	i	PRON
ejpam-6102	142	11	|x−	|x−	PROPN
ejpam-6102	142	12	ai|2	ai|2	PROPN
ejpam-6102	142	13	)	)	PUNCT
ejpam-6102	142	14	)	)	PUNCT
ejpam-6102	142	15	(	(	PUNCT
ejpam-6102	142	16	12	12	NUM
ejpam-6102	142	17	)	)	PUNCT
ejpam-6102	142	18	=	=	SYM
ejpam-6102	142	19	1	1	NUM
ejpam-6102	142	20	+	+	NUM
ejpam-6102	142	21	o(1	o(1	NOUN
ejpam-6102	142	22	)	)	PUNCT
ejpam-6102	142	23	.	.	PUNCT
ejpam-6102	143	1	(	(	PUNCT
ejpam-6102	143	2	13	13	NUM
ejpam-6102	143	3	)	)	PUNCT
ejpam-6102	143	4	thus	thus	ADV
ejpam-6102	143	5	,	,	PUNCT
ejpam-6102	143	6	since	since	SCONJ
ejpam-6102	143	7	∣∣∣1−	∣∣∣1−	NUM
ejpam-6102	143	8	αif	αif	NOUN
ejpam-6102	143	9	(	(	PUNCT
ejpam-6102	143	10	ai	ai	NOUN
ejpam-6102	143	11	)	)	PUNCT
ejpam-6102	143	12	(	(	PUNCT
ejpam-6102	143	13	n−2)/4	n−2)/4	NOUN
ejpam-6102	143	14	∣∣∣	∣∣∣	NOUN
ejpam-6102	143	15	is	be	AUX
ejpam-6102	143	16	small	small	ADJ
ejpam-6102	143	17	,	,	PUNCT
ejpam-6102	143	18	we	we	PRON
ejpam-6102	143	19	get	get	VERB
ejpam-6102	143	20	α	α	PRON
ejpam-6102	143	21	4	4	NUM
ejpam-6102	143	22	n−2−ε	n−2−ε	NOUN
ejpam-6102	144	1	i	i	PRON
ejpam-6102	144	2	∫	∫	PROPN
ejpam-6102	144	3	ω	ω	PROPN
ejpam-6102	144	4	fω	fω	PROPN
ejpam-6102	144	5	4	4	NUM
ejpam-6102	144	6	n−2−ε	n−2−ε	NOUN
ejpam-6102	144	7	ai,µi	ai,µi	NOUN
ejpam-6102	144	8	v2	v2	PROPN
ejpam-6102	144	9	=	=	NOUN
ejpam-6102	144	10	α	α	PROPN
ejpam-6102	144	11	4	4	NUM
ejpam-6102	144	12	n−2	n−2	PROPN
ejpam-6102	145	1	i	i	PRON
ejpam-6102	145	2	f	f	X
ejpam-6102	145	3	(	(	PUNCT
ejpam-6102	145	4	ai	ai	PROPN
ejpam-6102	145	5	)	)	PUNCT
ejpam-6102	145	6	∫	∫	PROPN
ejpam-6102	146	1	ω	ω	PROPN
ejpam-6102	146	2	ω	ω	PROPN
ejpam-6102	146	3	4	4	NUM
ejpam-6102	146	4	n−2	n−2	PROPN
ejpam-6102	146	5	ai,µiv	ai,µiv	PROPN
ejpam-6102	146	6	2	2	NUM
ejpam-6102	146	7	+	+	NUM
ejpam-6102	146	8	o	o	NOUN
ejpam-6102	146	9	(	(	PUNCT
ejpam-6102	146	10	∥v∥2	∥v∥2	X
ejpam-6102	146	11	)	)	PUNCT
ejpam-6102	147	1	=	=	SYM
ejpam-6102	147	2	∫	∫	PROPN
ejpam-6102	148	1	ω	ω	PROPN
ejpam-6102	148	2	ω	ω	PROPN
ejpam-6102	148	3	4	4	NUM
ejpam-6102	148	4	n−2	n−2	PROPN
ejpam-6102	148	5	ai,µiv	ai,µiv	PROPN
ejpam-6102	148	6	2	2	NUM
ejpam-6102	148	7	+	+	NUM
ejpam-6102	148	8	o	o	NOUN
ejpam-6102	148	9	(	(	PUNCT
ejpam-6102	148	10	∥v∥2	∥v∥2	PROPN
ejpam-6102	148	11	)	)	PUNCT
ejpam-6102	148	12	.	.	PUNCT
ejpam-6102	149	1	this	this	PRON
ejpam-6102	149	2	completes	complete	VERB
ejpam-6102	149	3	the	the	DET
ejpam-6102	149	4	proof	proof	NOUN
ejpam-6102	149	5	of	of	ADP
ejpam-6102	149	6	lemma	lemma	PROPN
ejpam-6102	149	7	1	1	NUM
ejpam-6102	149	8	.	.	PUNCT
ejpam-6102	150	1	at	at	ADP
ejpam-6102	150	2	this	this	DET
ejpam-6102	150	3	point	point	NOUN
ejpam-6102	150	4	,	,	PUNCT
ejpam-6102	150	5	we	we	PRON
ejpam-6102	150	6	require	require	VERB
ejpam-6102	150	7	the	the	DET
ejpam-6102	150	8	following	follow	VERB
ejpam-6102	150	9	important	important	ADJ
ejpam-6102	150	10	result	result	NOUN
ejpam-6102	150	11	regarding	regard	VERB
ejpam-6102	150	12	the	the	DET
ejpam-6102	150	13	uniform	uniform	ADJ
ejpam-6102	150	14	coercivity	coercivity	NOUN
ejpam-6102	150	15	of	of	ADP
ejpam-6102	150	16	the	the	DET
ejpam-6102	150	17	quadratic	quadratic	ADJ
ejpam-6102	150	18	form	form	NOUN
ejpam-6102	150	19	q.	q.	NOUN
ejpam-6102	150	20	proposition	proposition	NOUN
ejpam-6102	150	21	1	1	NUM
ejpam-6102	150	22	.	.	PUNCT
ejpam-6102	151	1	let	let	VERB
ejpam-6102	151	2	(	(	PUNCT
ejpam-6102	151	3	a	a	PRON
ejpam-6102	151	4	,	,	PUNCT
ejpam-6102	151	5	µ	µ	NOUN
ejpam-6102	151	6	,	,	PUNCT
ejpam-6102	151	7	α	α	NOUN
ejpam-6102	151	8	)	)	PUNCT
ejpam-6102	151	9	∈	∈	PROPN
ejpam-6102	151	10	ϑ	ϑ	X
ejpam-6102	151	11	(	(	PUNCT
ejpam-6102	151	12	q	q	PROPN
ejpam-6102	151	13	,	,	PUNCT
ejpam-6102	151	14	γ0	γ0	NOUN
ejpam-6102	151	15	,	,	PUNCT
ejpam-6102	151	16	η0	η0	NOUN
ejpam-6102	151	17	)	)	PUNCT
ejpam-6102	151	18	.	.	PUNCT
ejpam-6102	152	1	there	there	PRON
ejpam-6102	152	2	exists	exist	VERB
ejpam-6102	152	3	β3	β3	ADJ
ejpam-6102	152	4	>	>	X
ejpam-6102	152	5	0	0	PUNCT
ejpam-6102	153	1	(	(	PUNCT
ejpam-6102	153	2	independent	independent	ADJ
ejpam-6102	153	3	of	of	ADP
ejpam-6102	153	4	α	α	PROPN
ejpam-6102	153	5	,	,	PUNCT
ejpam-6102	153	6	µ	µ	NOUN
ejpam-6102	153	7	and	and	CCONJ
ejpam-6102	153	8	a	a	X
ejpam-6102	153	9	)	)	PUNCT
ejpam-6102	153	10	such	such	ADJ
ejpam-6102	153	11	that	that	DET
ejpam-6102	153	12	q(v	q(v	NOUN
ejpam-6102	153	13	)	)	PUNCT
ejpam-6102	153	14	⩾	⩾	PUNCT
ejpam-6102	153	15	β3∥v∥2	β3∥v∥2	X
ejpam-6102	154	1	∀v	∀v	PROPN
ejpam-6102	154	2	∈	∈	PROPN
ejpam-6102	154	3	fa,µ.	fa,µ.	NOUN
ejpam-6102	154	4	the	the	DET
ejpam-6102	154	5	proof	proof	NOUN
ejpam-6102	154	6	of	of	ADP
ejpam-6102	154	7	this	this	DET
ejpam-6102	154	8	proposition	proposition	NOUN
ejpam-6102	154	9	will	will	AUX
ejpam-6102	154	10	be	be	AUX
ejpam-6102	154	11	presented	present	VERB
ejpam-6102	154	12	in	in	ADP
ejpam-6102	154	13	subsection	subsection	NOUN
ejpam-6102	154	14	7.2	7.2	NUM
ejpam-6102	154	15	.	.	PUNCT
ejpam-6102	154	16	combining	combine	VERB
ejpam-6102	154	17	lemma	lemma	PROPN
ejpam-6102	154	18	1	1	NUM
ejpam-6102	154	19	and	and	CCONJ
ejpam-6102	154	20	proposition	proposition	NOUN
ejpam-6102	154	21	1	1	NUM
ejpam-6102	154	22	,	,	PUNCT
ejpam-6102	154	23	we	we	PRON
ejpam-6102	154	24	deduce	deduce	VERB
ejpam-6102	154	25	that	that	SCONJ
ejpam-6102	154	26	the	the	DET
ejpam-6102	154	27	quadratic	quadratic	ADJ
ejpam-6102	154	28	form	form	NOUN
ejpam-6102	154	29	qε	qε	INTJ
ejpam-6102	154	30	is	be	AUX
ejpam-6102	154	31	coercive	coercive	ADJ
ejpam-6102	154	32	,	,	PUNCT
ejpam-6102	154	33	that	that	PRON
ejpam-6102	154	34	is	is	ADV
ejpam-6102	154	35	qε(v	qε(v	NOUN
ejpam-6102	154	36	)	)	PUNCT
ejpam-6102	154	37	⩾	⩾	NOUN
ejpam-6102	154	38	1	1	NUM
ejpam-6102	154	39	2	2	NUM
ejpam-6102	154	40	β3∥v∥2	β3∥v∥2	X
ejpam-6102	154	41	∀v	∀v	PROPN
ejpam-6102	154	42	∈	∈	PROPN
ejpam-6102	154	43	fa,µ.	fa,µ.	SYM
ejpam-6102	154	44	(	(	PUNCT
ejpam-6102	154	45	14	14	NUM
ejpam-6102	154	46	)	)	PUNCT
ejpam-6102	154	47	now	now	ADV
ejpam-6102	154	48	,	,	PUNCT
ejpam-6102	154	49	we	we	PRON
ejpam-6102	154	50	need	need	VERB
ejpam-6102	154	51	to	to	PART
ejpam-6102	154	52	estimate	estimate	VERB
ejpam-6102	154	53	the	the	DET
ejpam-6102	154	54	norm	norm	NOUN
ejpam-6102	154	55	of	of	ADP
ejpam-6102	154	56	the	the	DET
ejpam-6102	154	57	linear	linear	ADJ
ejpam-6102	154	58	form	form	NOUN
ejpam-6102	154	59	lε	lε	VERB
ejpam-6102	154	60	.	.	PUNCT
ejpam-6102	155	1	more	more	ADV
ejpam-6102	155	2	precisely	precisely	ADV
ejpam-6102	155	3	,	,	PUNCT
ejpam-6102	155	4	we	we	PRON
ejpam-6102	155	5	have	have	AUX
ejpam-6102	155	6	:	:	PUNCT
ejpam-6102	155	7	lemma	lemma	PROPN
ejpam-6102	155	8	2	2	X
ejpam-6102	155	9	.	.	PUNCT
ejpam-6102	155	10	let	let	VERB
ejpam-6102	155	11	a	a	DET
ejpam-6102	155	12	∈	∈	PROPN
ejpam-6102	155	13	∂ω	∂ω	PROPN
ejpam-6102	155	14	,	,	PUNCT
ejpam-6102	155	15	µ	µ	X
ejpam-6102	155	16	be	be	VERB
ejpam-6102	155	17	a	a	DET
ejpam-6102	155	18	large	large	ADJ
ejpam-6102	155	19	real	real	ADJ
ejpam-6102	155	20	satisfying	satisfying	NOUN
ejpam-6102	155	21	ε	ε	PROPN
ejpam-6102	155	22	lnµ	lnµ	NOUN
ejpam-6102	155	23	is	be	AUX
ejpam-6102	155	24	small	small	ADJ
ejpam-6102	155	25	.	.	PUNCT
ejpam-6102	156	1	then	then	ADV
ejpam-6102	156	2	,	,	PUNCT
ejpam-6102	156	3	for	for	ADP
ejpam-6102	156	4	ψ	ψ	NOUN
ejpam-6102	156	5	and	and	CCONJ
ejpam-6102	156	6	v	v	AUX
ejpam-6102	156	7	satisfying	satisfy	VERB
ejpam-6102	156	8	ψ	ψ	X
ejpam-6102	156	9	∈	∈	PROPN
ejpam-6102	156	10	{	{	PUNCT
ejpam-6102	156	11	ωa,µ	ωa,µ	ADP
ejpam-6102	156	12	,	,	PUNCT
ejpam-6102	156	13	µ	µ	PRON
ejpam-6102	156	14	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	156	15	∂µ	∂µ	PROPN
ejpam-6102	156	16	,	,	PUNCT
ejpam-6102	156	17	1	1	NUM
ejpam-6102	156	18	µ	µ	PRON
ejpam-6102	156	19	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	156	20	∂a	∂a	NOUN
ejpam-6102	156	21	}	}	PUNCT
ejpam-6102	156	22	,	,	PUNCT
ejpam-6102	156	23	v	v	X
ejpam-6102	156	24	∈	∈	PROPN
ejpam-6102	156	25	h1(ω	h1(ω	PROPN
ejpam-6102	156	26	)	)	PUNCT
ejpam-6102	156	27	with	with	ADP
ejpam-6102	156	28	∫	∫	PROPN
ejpam-6102	156	29	ω	ω	NUM
ejpam-6102	156	30	∇v	∇v	PROPN
ejpam-6102	156	31	·	·	PUNCT
ejpam-6102	157	1	∇ψ	∇ψ	NOUN
ejpam-6102	157	2	=	=	SYM
ejpam-6102	157	3	0	0	NUM
ejpam-6102	157	4	,	,	PUNCT
ejpam-6102	157	5	(	(	PUNCT
ejpam-6102	157	6	15	15	X
ejpam-6102	157	7	)	)	PUNCT
ejpam-6102	157	8	we	we	PRON
ejpam-6102	157	9	have	have	VERB
ejpam-6102	157	10	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-6102	157	11	ω	ω	NUM
ejpam-6102	157	12	fω	fω	PROPN
ejpam-6102	157	13	4	4	NUM
ejpam-6102	157	14	n−2−ε	n−2−ε	NOUN
ejpam-6102	157	15	a,µ	a,µ	ADV
ejpam-6102	157	16	ψv	ψv	ADP
ejpam-6102	157	17	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	157	18	⩽	⩽	PROPN
ejpam-6102	157	19	c∥v∥	c∥v∥	PROPN
ejpam-6102	157	20	(	(	PUNCT
ejpam-6102	157	21	ε+	ε+	X
ejpam-6102	157	22	1	1	NUM
ejpam-6102	157	23	µ	µ	NOUN
ejpam-6102	157	24	)	)	PUNCT
ejpam-6102	157	25	.	.	PUNCT
ejpam-6102	158	1	r.	r.	PROPN
ejpam-6102	158	2	almushahhin	almushahhin	PROPN
ejpam-6102	158	3	,	,	PUNCT
ejpam-6102	158	4	m.	m.	PROPN
ejpam-6102	158	5	ben	ben	PROPN
ejpam-6102	158	6	ayed	aye	VERB
ejpam-6102	158	7	/	/	SYM
ejpam-6102	158	8	eur	eur	PROPN
ejpam-6102	158	9	.	.	PUNCT
ejpam-6102	159	1	j.	j.	PROPN
ejpam-6102	159	2	pure	pure	PROPN
ejpam-6102	159	3	appl	appl	PROPN
ejpam-6102	159	4	.	.	PROPN
ejpam-6102	159	5	math	math	PROPN
ejpam-6102	159	6	,	,	PUNCT
ejpam-6102	159	7	18	18	NUM
ejpam-6102	159	8	(	(	PUNCT
ejpam-6102	159	9	2	2	NUM
ejpam-6102	159	10	)	)	PUNCT
ejpam-6102	159	11	(	(	PUNCT
ejpam-6102	159	12	2025	2025	NUM
ejpam-6102	159	13	)	)	PUNCT
ejpam-6102	159	14	,	,	PUNCT
ejpam-6102	159	15	6102	6102	NUM
ejpam-6102	159	16	8	8	NUM
ejpam-6102	159	17	of	of	ADP
ejpam-6102	159	18	31	31	NUM
ejpam-6102	159	19	proof	proof	NOUN
ejpam-6102	159	20	.	.	PUNCT
ejpam-6102	160	1	observe	observe	VERB
ejpam-6102	160	2	that	that	SCONJ
ejpam-6102	160	3	,	,	PUNCT
ejpam-6102	160	4	since	since	SCONJ
ejpam-6102	160	5	ε	ε	PROPN
ejpam-6102	160	6	lnµ	lnµ	NOUN
ejpam-6102	160	7	is	be	AUX
ejpam-6102	160	8	small	small	ADJ
ejpam-6102	160	9	,	,	PUNCT
ejpam-6102	160	10	then	then	ADV
ejpam-6102	160	11	equation	equation	NOUN
ejpam-6102	160	12	(	(	PUNCT
ejpam-6102	160	13	13	13	NUM
ejpam-6102	160	14	)	)	PUNCT
ejpam-6102	160	15	holds	hold	VERB
ejpam-6102	160	16	true	true	ADJ
ejpam-6102	160	17	.	.	PUNCT
ejpam-6102	161	1	therefore	therefore	ADV
ejpam-6102	161	2	,	,	PUNCT
ejpam-6102	161	3	using	use	VERB
ejpam-6102	161	4	the	the	DET
ejpam-6102	161	5	fact	fact	NOUN
ejpam-6102	161	6	that	that	SCONJ
ejpam-6102	161	7	|ψ|	|ψ|	PROPN
ejpam-6102	161	8	⩽	⩽	PROPN
ejpam-6102	161	9	cωa,µ	cωa,µ	PROPN
ejpam-6102	161	10	,	,	PUNCT
ejpam-6102	161	11	we	we	PRON
ejpam-6102	161	12	get∫	get∫	VERB
ejpam-6102	161	13	ω	ω	PROPN
ejpam-6102	161	14	fω	fω	PROPN
ejpam-6102	161	15	4	4	NUM
ejpam-6102	161	16	n−2−ε	n−2−ε	NOUN
ejpam-6102	161	17	a,µ	a,µ	ADV
ejpam-6102	161	18	ψv	ψv	PROPN
ejpam-6102	161	19	=	=	SYM
ejpam-6102	161	20	f(a	f(a	PROPN
ejpam-6102	161	21	)	)	PUNCT
ejpam-6102	161	22	∫	∫	PROPN
ejpam-6102	161	23	ω	ω	PROPN
ejpam-6102	161	24	ω	ω	PROPN
ejpam-6102	161	25	4	4	NUM
ejpam-6102	161	26	n−2−ε	n−2−ε	NOUN
ejpam-6102	161	27	a,µ	a,µ	ADP
ejpam-6102	161	28	ψv	ψv	ADV
ejpam-6102	161	29	+	+	PROPN
ejpam-6102	161	30	o	o	X
ejpam-6102	161	31	(	(	PUNCT
ejpam-6102	161	32	∫	∫	PROPN
ejpam-6102	161	33	ω	ω	PROPN
ejpam-6102	161	34	|x−	|x−	PROPN
ejpam-6102	161	35	a|ω	a|ω	VERB
ejpam-6102	161	36	n+2	n+2	NUM
ejpam-6102	161	37	n−2	n−2	PROPN
ejpam-6102	161	38	a,µ	a,µ	ADP
ejpam-6102	161	39	|v|	|v|	INTJ
ejpam-6102	161	40	)	)	PUNCT
ejpam-6102	161	41	=	=	PUNCT
ejpam-6102	161	42	β−ε	β−ε	PROPN
ejpam-6102	161	43	0	0	NUM
ejpam-6102	161	44	µ−εn−2	µ−εn−2	PROPN
ejpam-6102	161	45	2	2	NUM
ejpam-6102	161	46	f(a	f(a	NOUN
ejpam-6102	161	47	)	)	PUNCT
ejpam-6102	161	48	∫	∫	PROPN
ejpam-6102	162	1	ω	ω	PROPN
ejpam-6102	162	2	ω	ω	PROPN
ejpam-6102	162	3	4	4	NUM
ejpam-6102	162	4	n−2ψv	n−2ψv	NOUN
ejpam-6102	162	5	+	+	NOUN
ejpam-6102	162	6	o	o	X
ejpam-6102	162	7	(	(	PUNCT
ejpam-6102	162	8	ε	ε	PROPN
ejpam-6102	162	9	∫	∫	PROPN
ejpam-6102	162	10	ω	ω	PROPN
ejpam-6102	162	11	ω	ω	PROPN
ejpam-6102	162	12	n+2	n+2	PROPN
ejpam-6102	162	13	n−2	n−2	PROPN
ejpam-6102	162	14	a,µ	a,µ	ADP
ejpam-6102	162	15	ln	ln	ADV
ejpam-6102	162	16	(	(	PUNCT
ejpam-6102	162	17	1	1	NUM
ejpam-6102	162	18	+	+	NUM
ejpam-6102	162	19	µ2|x−	µ2|x−	PROPN
ejpam-6102	162	20	a|2	a|2	PROPN
ejpam-6102	162	21	)	)	PUNCT
ejpam-6102	163	1	|v|+	|v|+	PRON
ejpam-6102	163	2	∥v∥	∥v∥	VERB
ejpam-6102	163	3	µ	µ	NOUN
ejpam-6102	163	4	)	)	PUNCT
ejpam-6102	163	5	.	.	PUNCT
ejpam-6102	164	1	(	(	PUNCT
ejpam-6102	164	2	16	16	NUM
ejpam-6102	164	3	)	)	PUNCT
ejpam-6102	164	4	easy	easy	ADJ
ejpam-6102	164	5	computation	computation	NOUN
ejpam-6102	164	6	leads	lead	VERB
ejpam-6102	164	7	to∫	to∫	PROPN
ejpam-6102	164	8	ω	ω	PROPN
ejpam-6102	164	9	ω	ω	PROPN
ejpam-6102	164	10	2n	2n	NUM
ejpam-6102	165	1	n−2	n−2	PROPN
ejpam-6102	165	2	a,µ	a,µ	ADV
ejpam-6102	165	3	(	(	PUNCT
ejpam-6102	165	4	ln	ln	X
ejpam-6102	165	5	(	(	PUNCT
ejpam-6102	165	6	1	1	NUM
ejpam-6102	165	7	+	+	NUM
ejpam-6102	165	8	µ2|x−	µ2|x−	PROPN
ejpam-6102	165	9	a|2	a|2	PROPN
ejpam-6102	165	10	)	)	PUNCT
ejpam-6102	165	11	)	)	PUNCT
ejpam-6102	165	12	γ	γ	PROPN
ejpam-6102	165	13	≤	≤	PROPN
ejpam-6102	165	14	c	c	NOUN
ejpam-6102	165	15	∀	∀	X
ejpam-6102	165	16	γ	γ	X
ejpam-6102	165	17	>	>	X
ejpam-6102	165	18	0	0	PUNCT
ejpam-6102	165	19	(	(	PUNCT
ejpam-6102	165	20	17	17	NUM
ejpam-6102	165	21	)	)	PUNCT
ejpam-6102	165	22	which	which	PRON
ejpam-6102	165	23	implies	imply	VERB
ejpam-6102	165	24	that	that	SCONJ
ejpam-6102	165	25	ε	ε	PROPN
ejpam-6102	165	26	∫	∫	PROPN
ejpam-6102	165	27	ω	ω	PROPN
ejpam-6102	165	28	ω	ω	PROPN
ejpam-6102	165	29	n+2	n+2	PROPN
ejpam-6102	165	30	n−2	n−2	PROPN
ejpam-6102	165	31	a,µ	a,µ	ADP
ejpam-6102	165	32	ln	ln	ADV
ejpam-6102	165	33	(	(	PUNCT
ejpam-6102	165	34	1	1	NUM
ejpam-6102	165	35	+	+	NUM
ejpam-6102	165	36	µ2|x−	µ2|x−	PROPN
ejpam-6102	165	37	a|2	a|2	PROPN
ejpam-6102	165	38	)	)	PUNCT
ejpam-6102	165	39	|v|	|v|	PROPN
ejpam-6102	165	40	≤	≤	NOUN
ejpam-6102	165	41	cε∥v∥.	cε∥v∥.	X
ejpam-6102	165	42	(	(	PUNCT
ejpam-6102	165	43	18	18	NUM
ejpam-6102	165	44	)	)	PUNCT
ejpam-6102	165	45	to	to	PART
ejpam-6102	165	46	estimate	estimate	VERB
ejpam-6102	165	47	the	the	DET
ejpam-6102	165	48	first	first	ADJ
ejpam-6102	165	49	integral	integral	NOUN
ejpam-6102	165	50	in	in	ADP
ejpam-6102	165	51	the	the	DET
ejpam-6102	165	52	right	right	ADJ
ejpam-6102	165	53	hand	hand	NOUN
ejpam-6102	165	54	side	side	NOUN
ejpam-6102	165	55	of	of	ADP
ejpam-6102	165	56	(	(	PUNCT
ejpam-6102	165	57	16	16	NUM
ejpam-6102	165	58	)	)	PUNCT
ejpam-6102	165	59	,	,	PUNCT
ejpam-6102	165	60	we	we	PRON
ejpam-6102	165	61	distinguish	distinguish	VERB
ejpam-6102	165	62	three	three	NUM
ejpam-6102	165	63	cases	case	NOUN
ejpam-6102	165	64	:	:	PUNCT
ejpam-6102	165	65	•	•	NUM
ejpam-6102	165	66	case	case	NOUN
ejpam-6102	165	67	1	1	X
ejpam-6102	165	68	.	.	PUNCT
ejpam-6102	166	1	if	if	SCONJ
ejpam-6102	166	2	ψ	ψ	NOUN
ejpam-6102	166	3	=	=	PUNCT
ejpam-6102	166	4	ωa,µ	ωa,µ	ADP
ejpam-6102	166	5	,	,	PUNCT
ejpam-6102	166	6	using	use	VERB
ejpam-6102	166	7	(	(	PUNCT
ejpam-6102	166	8	15	15	NUM
ejpam-6102	166	9	)	)	PUNCT
ejpam-6102	166	10	,	,	PUNCT
ejpam-6102	166	11	holder	holder	NOUN
ejpam-6102	166	12	’s	’s	PART
ejpam-6102	166	13	inequality	inequality	NOUN
ejpam-6102	166	14	,	,	PUNCT
ejpam-6102	166	15	lemma	lemma	PROPN
ejpam-6102	166	16	7	7	NUM
ejpam-6102	166	17	and	and	CCONJ
ejpam-6102	166	18	the	the	DET
ejpam-6102	166	19	continuity	continuity	NOUN
ejpam-6102	166	20	of	of	ADP
ejpam-6102	166	21	the	the	DET
ejpam-6102	166	22	embedding	embed	VERB
ejpam-6102	166	23	h1(ω	h1(ω	NOUN
ejpam-6102	166	24	)	)	PUNCT
ejpam-6102	166	25	↪	↪	PROPN
ejpam-6102	166	26	→	→	SYM
ejpam-6102	166	27	l	l	NOUN
ejpam-6102	166	28	2n−2	2n−2	PROPN
ejpam-6102	166	29	n−2	n−2	PROPN
ejpam-6102	166	30	(	(	PUNCT
ejpam-6102	166	31	∂ω	∂ω	PROPN
ejpam-6102	166	32	)	)	PUNCT
ejpam-6102	166	33	,	,	PUNCT
ejpam-6102	167	1	we	we	PRON
ejpam-6102	167	2	get∫	get∫	PROPN
ejpam-6102	167	3	ω	ω	PROPN
ejpam-6102	167	4	ω	ω	PROPN
ejpam-6102	167	5	4	4	NUM
ejpam-6102	167	6	n−2	n−2	PROPN
ejpam-6102	167	7	a,µ	a,µ	ADV
ejpam-6102	167	8	ψv	ψv	ADV
ejpam-6102	167	9	=	=	SYM
ejpam-6102	167	10	∫	∫	PROPN
ejpam-6102	168	1	ω	ω	PROPN
ejpam-6102	168	2	ω	ω	PROPN
ejpam-6102	168	3	n+2	n+2	PROPN
ejpam-6102	168	4	n−2	n−2	PROPN
ejpam-6102	168	5	a,µ	a,µ	ADP
ejpam-6102	168	6	v	v	NOUN
ejpam-6102	168	7	=	=	SYM
ejpam-6102	168	8	∫	∫	PROPN
ejpam-6102	168	9	ω	ω	NUM
ejpam-6102	168	10	−∆ωa,µv	−∆ωa,µv	NOUN
ejpam-6102	169	1	=	=	PUNCT
ejpam-6102	169	2	∫	∫	PROPN
ejpam-6102	169	3	ω	ω	NUM
ejpam-6102	169	4	∇ωa,µ∇v	∇ωa,µ∇v	PROPN
ejpam-6102	169	5	−	−	NUM
ejpam-6102	169	6	∫	∫	INTJ
ejpam-6102	170	1	∂ω	∂ω	ADJ
ejpam-6102	170	2	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	170	3	∂ν	∂ν	NOUN
ejpam-6102	170	4	v	v	NOUN
ejpam-6102	170	5	=	=	SYM
ejpam-6102	170	6	o	o	X
ejpam-6102	170	7	[∫	[∫	X
ejpam-6102	171	1	∂ω	∂ω	PROPN
ejpam-6102	171	2	|v|	|v|	PROPN
ejpam-6102	171	3	2n−2	2n−2	NUM
ejpam-6102	171	4	n−2	n−2	PROPN
ejpam-6102	171	5	]	]	PUNCT
ejpam-6102	172	1	n−2	n−2	PROPN
ejpam-6102	172	2	2n−2	2n−2	PROPN
ejpam-6102	173	1	[	[	X
ejpam-6102	173	2	∫	∫	X
ejpam-6102	173	3	∂ω	∂ω	ADJ
ejpam-6102	173	4	∣∣∣∣∂ωa,µ	∣∣∣∣∂ωa,µ	NOUN
ejpam-6102	173	5	∂ν	∂ν	PROPN
ejpam-6102	173	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	173	7	2n−2	2n−2	NUM
ejpam-6102	173	8	n	n	NOUN
ejpam-6102	173	9	]	]	PUNCT
ejpam-6102	173	10	n	n	CCONJ
ejpam-6102	173	11	2n−2	2n−2	NUM
ejpam-6102	173	12			PROPN
ejpam-6102	173	13	=	=	SYM
ejpam-6102	173	14	o	o	PROPN
ejpam-6102	173	15	(	(	PUNCT
ejpam-6102	173	16	∥v∥	∥v∥	PROPN
ejpam-6102	173	17	µ	µ	NOUN
ejpam-6102	173	18	)	)	PUNCT
ejpam-6102	173	19	.	.	PUNCT
ejpam-6102	174	1	(	(	PUNCT
ejpam-6102	174	2	19	19	NUM
ejpam-6102	174	3	)	)	PUNCT
ejpam-6102	174	4	combining	combine	VERB
ejpam-6102	174	5	eqs	eqs	PROPN
ejpam-6102	174	6	.	.	PUNCT
ejpam-6102	175	1	(	(	PUNCT
ejpam-6102	175	2	16	16	NUM
ejpam-6102	175	3	)	)	PUNCT
ejpam-6102	175	4	,	,	PUNCT
ejpam-6102	175	5	(	(	PUNCT
ejpam-6102	175	6	18	18	NUM
ejpam-6102	175	7	)	)	PUNCT
ejpam-6102	175	8	and	and	CCONJ
ejpam-6102	175	9	(	(	PUNCT
ejpam-6102	175	10	19	19	NUM
ejpam-6102	175	11	)	)	PUNCT
ejpam-6102	175	12	,	,	PUNCT
ejpam-6102	175	13	the	the	DET
ejpam-6102	175	14	proof	proof	NOUN
ejpam-6102	175	15	of	of	ADP
ejpam-6102	175	16	the	the	DET
ejpam-6102	175	17	lemma	lemma	PROPN
ejpam-6102	175	18	is	be	AUX
ejpam-6102	175	19	completed	complete	VERB
ejpam-6102	175	20	in	in	ADP
ejpam-6102	175	21	the	the	DET
ejpam-6102	175	22	case	case	NOUN
ejpam-6102	175	23	where	where	SCONJ
ejpam-6102	175	24	ψ	ψ	NOUN
ejpam-6102	175	25	=	=	SYM
ejpam-6102	175	26	ωa,µ.	ωa,µ.	NUM
ejpam-6102	175	27	•	•	NUM
ejpam-6102	175	28	case	case	NOUN
ejpam-6102	175	29	2	2	NUM
ejpam-6102	175	30	.	.	PUNCT
ejpam-6102	176	1	if	if	SCONJ
ejpam-6102	176	2	ψ	ψ	X
ejpam-6102	176	3	=	=	SYM
ejpam-6102	176	4	µ	µ	X
ejpam-6102	176	5	(	(	PUNCT
ejpam-6102	176	6	∂ωa,µ/∂µ	∂ωa,µ/∂µ	NOUN
ejpam-6102	176	7	)	)	PUNCT
ejpam-6102	176	8	,	,	PUNCT
ejpam-6102	177	1	it	it	PRON
ejpam-6102	177	2	holds:∫	holds:∫	NOUN
ejpam-6102	177	3	ω	ω	PROPN
ejpam-6102	177	4	ω	ω	PROPN
ejpam-6102	177	5	4	4	NUM
ejpam-6102	177	6	n−2	n−2	PROPN
ejpam-6102	177	7	a,µ	a,µ	ADV
ejpam-6102	177	8	ψv	ψv	ADJ
ejpam-6102	177	9	=	=	PUNCT
ejpam-6102	177	10	n−	n−	NOUN
ejpam-6102	177	11	2	2	NUM
ejpam-6102	177	12	n+	n+	NUM
ejpam-6102	177	13	2	2	NUM
ejpam-6102	177	14	∫	∫	NOUN
ejpam-6102	177	15	ω	ω	NUM
ejpam-6102	177	16	−∆	−∆	PROPN
ejpam-6102	177	17	(	(	PUNCT
ejpam-6102	177	18	µ	µ	X
ejpam-6102	177	19	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	177	20	∂µ	∂µ	PROPN
ejpam-6102	177	21	)	)	PUNCT
ejpam-6102	177	22	v	v	NOUN
ejpam-6102	177	23	=	=	PUNCT
ejpam-6102	177	24	n−	n−	NOUN
ejpam-6102	177	25	2	2	NUM
ejpam-6102	177	26	n+	n+	SYM
ejpam-6102	177	27	2	2	NUM
ejpam-6102	177	28	(	(	PUNCT
ejpam-6102	177	29	∫	∫	PROPN
ejpam-6102	177	30	ω	ω	NUM
ejpam-6102	177	31	∇	∇	X
ejpam-6102	177	32	(	(	PUNCT
ejpam-6102	177	33	µ	µ	X
ejpam-6102	177	34	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	177	35	∂µ	∂µ	PROPN
ejpam-6102	177	36	)	)	PUNCT
ejpam-6102	177	37	∇v	∇v	ADV
ejpam-6102	177	38	−	−	ADP
ejpam-6102	177	39	∫	∫	PROPN
ejpam-6102	178	1	∂ω	∂ω	PROPN
ejpam-6102	178	2	∂	∂	NOUN
ejpam-6102	178	3	∂ν	∂ν	X
ejpam-6102	178	4	(	(	PUNCT
ejpam-6102	178	5	µ	µ	X
ejpam-6102	178	6	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	178	7	∂µ	∂µ	PROPN
ejpam-6102	178	8	)	)	PUNCT
ejpam-6102	178	9	v	v	NOUN
ejpam-6102	178	10	)	)	PUNCT
ejpam-6102	179	1	=	=	SYM
ejpam-6102	180	1	o	o	X
ejpam-6102	180	2	[∫	[∫	PROPN
ejpam-6102	181	1	∂ω	∂ω	PROPN
ejpam-6102	181	2	|v|	|v|	PROPN
ejpam-6102	181	3	2n−2	2n−2	NUM
ejpam-6102	181	4	n−2	n−2	PROPN
ejpam-6102	181	5	]	]	PUNCT
ejpam-6102	181	6	n−2	n−2	PROPN
ejpam-6102	181	7	2n−2	2n−2	PROPN
ejpam-6102	182	1	[	[	X
ejpam-6102	182	2	∫	∫	X
ejpam-6102	182	3	∂ω	∂ω	ADJ
ejpam-6102	182	4	∣∣∣∣µ∂2ωa,µ	∣∣∣∣µ∂2ωa,µ	NOUN
ejpam-6102	182	5	∂ν∂µ	∂ν∂µ	ADJ
ejpam-6102	182	6	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	182	7	2n−2	2n−2	NUM
ejpam-6102	182	8	n	n	NOUN
ejpam-6102	182	9	]	]	PUNCT
ejpam-6102	182	10	n	n	CCONJ
ejpam-6102	182	11	2n−2	2n−2	NUM
ejpam-6102	182	12			PROPN
ejpam-6102	182	13	=	=	SYM
ejpam-6102	182	14	o	o	PROPN
ejpam-6102	182	15	(	(	PUNCT
ejpam-6102	182	16	∥v∥	∥v∥	PROPN
ejpam-6102	182	17	µ	µ	NOUN
ejpam-6102	182	18	)	)	PUNCT
ejpam-6102	182	19	,	,	PUNCT
ejpam-6102	182	20	by	by	ADP
ejpam-6102	182	21	using	use	VERB
ejpam-6102	182	22	claims	claim	NOUN
ejpam-6102	182	23	(	(	PUNCT
ejpam-6102	182	24	i	i	NOUN
ejpam-6102	182	25	)	)	PUNCT
ejpam-6102	182	26	and	and	CCONJ
ejpam-6102	182	27	(	(	PUNCT
ejpam-6102	182	28	ii	ii	NOUN
ejpam-6102	182	29	)	)	PUNCT
ejpam-6102	182	30	of	of	ADP
ejpam-6102	182	31	lemma	lemma	PROPN
ejpam-6102	182	32	7	7	NUM
ejpam-6102	182	33	.	.	PUNCT
ejpam-6102	183	1	this	this	PRON
ejpam-6102	183	2	completes	complete	VERB
ejpam-6102	183	3	the	the	DET
ejpam-6102	183	4	proof	proof	NOUN
ejpam-6102	183	5	of	of	ADP
ejpam-6102	183	6	of	of	ADP
ejpam-6102	183	7	the	the	DET
ejpam-6102	183	8	lemma	lemma	PROPN
ejpam-6102	183	9	in	in	ADP
ejpam-6102	183	10	the	the	DET
ejpam-6102	183	11	case	case	NOUN
ejpam-6102	183	12	where	where	SCONJ
ejpam-6102	183	13	ψ	ψ	ADP
ejpam-6102	183	14	=	=	SYM
ejpam-6102	183	15	µ	µ	X
ejpam-6102	183	16	(	(	PUNCT
ejpam-6102	183	17	∂ωa,µ/∂µ	∂ωa,µ/∂µ	NOUN
ejpam-6102	183	18	)	)	PUNCT
ejpam-6102	183	19	.	.	PUNCT
ejpam-6102	184	1	•	•	NUM
ejpam-6102	184	2	case	case	NOUN
ejpam-6102	184	3	3	3	X
ejpam-6102	184	4	.	.	PUNCT
ejpam-6102	185	1	if	if	SCONJ
ejpam-6102	185	2	ψ	ψ	X
ejpam-6102	185	3	=	=	X
ejpam-6102	185	4	µ−1	µ−1	PROPN
ejpam-6102	185	5	(	(	PUNCT
ejpam-6102	185	6	∂ωa,µ/∂aj	∂ωa,µ/∂aj	NOUN
ejpam-6102	185	7	)	)	PUNCT
ejpam-6102	185	8	,	,	PUNCT
ejpam-6102	185	9	the	the	DET
ejpam-6102	185	10	proof	proof	NOUN
ejpam-6102	185	11	can	can	AUX
ejpam-6102	185	12	be	be	AUX
ejpam-6102	185	13	done	do	VERB
ejpam-6102	185	14	in	in	ADP
ejpam-6102	185	15	the	the	DET
ejpam-6102	185	16	same	same	ADJ
ejpam-6102	185	17	way	way	NOUN
ejpam-6102	185	18	.	.	PUNCT
ejpam-6102	186	1	hence	hence	ADV
ejpam-6102	186	2	,	,	PUNCT
ejpam-6102	186	3	we	we	PRON
ejpam-6102	186	4	omit	omit	VERB
ejpam-6102	186	5	it	it	PRON
ejpam-6102	186	6	.	.	PUNCT
ejpam-6102	187	1	the	the	DET
ejpam-6102	187	2	proof	proof	NOUN
ejpam-6102	187	3	of	of	ADP
ejpam-6102	187	4	lemma	lemma	PROPN
ejpam-6102	187	5	2	2	NUM
ejpam-6102	187	6	is	be	AUX
ejpam-6102	187	7	thereby	thereby	ADV
ejpam-6102	187	8	completed	complete	VERB
ejpam-6102	187	9	.	.	PUNCT
ejpam-6102	188	1	now	now	ADV
ejpam-6102	188	2	,	,	PUNCT
ejpam-6102	188	3	we	we	PRON
ejpam-6102	188	4	are	be	AUX
ejpam-6102	188	5	ready	ready	ADJ
ejpam-6102	188	6	to	to	PART
ejpam-6102	188	7	present	present	VERB
ejpam-6102	188	8	the	the	DET
ejpam-6102	188	9	estimate	estimate	NOUN
ejpam-6102	188	10	of	of	ADP
ejpam-6102	188	11	the	the	DET
ejpam-6102	188	12	linear	linear	ADJ
ejpam-6102	188	13	form	form	NOUN
ejpam-6102	188	14	lε	lε	AUX
ejpam-6102	188	15	defined	define	VERB
ejpam-6102	188	16	in	in	ADP
ejpam-6102	188	17	(	(	PUNCT
ejpam-6102	188	18	11	11	NUM
ejpam-6102	188	19	)	)	PUNCT
ejpam-6102	188	20	.	.	PUNCT
ejpam-6102	189	1	proposition	proposition	NOUN
ejpam-6102	189	2	2	2	NUM
ejpam-6102	189	3	.	.	PUNCT
ejpam-6102	190	1	let	let	VERB
ejpam-6102	190	2	(	(	PUNCT
ejpam-6102	190	3	a	a	PRON
ejpam-6102	190	4	,	,	PUNCT
ejpam-6102	190	5	µ	µ	NOUN
ejpam-6102	190	6	,	,	PUNCT
ejpam-6102	190	7	α	α	NOUN
ejpam-6102	190	8	)	)	PUNCT
ejpam-6102	190	9	∈	∈	PROPN
ejpam-6102	190	10	ϑ	ϑ	X
ejpam-6102	190	11	(	(	PUNCT
ejpam-6102	190	12	q	q	PROPN
ejpam-6102	190	13	,	,	PUNCT
ejpam-6102	190	14	γ0	γ0	NOUN
ejpam-6102	190	15	,	,	PUNCT
ejpam-6102	190	16	η0	η0	NOUN
ejpam-6102	190	17	)	)	PUNCT
ejpam-6102	190	18	.	.	PUNCT
ejpam-6102	191	1	then	then	ADV
ejpam-6102	191	2	,	,	PUNCT
ejpam-6102	191	3	we	we	PRON
ejpam-6102	191	4	have	have	VERB
ejpam-6102	191	5	|lε(v)|	|lε(v)|	NOUN
ejpam-6102	191	6	:	:	PUNCT
ejpam-6102	191	7	=	=	SYM
ejpam-6102	191	8	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-6102	191	9	ω	ω	NUM
ejpam-6102	191	10	fũp−εv	fũp−εv	PROPN
ejpam-6102	191	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	191	12	⩽	⩽	PROPN
ejpam-6102	191	13	c∥v∥	c∥v∥	PROPN
ejpam-6102	191	14	(	(	PUNCT
ejpam-6102	191	15	ε+	ε+	NOUN
ejpam-6102	191	16	∑	∑	SYM
ejpam-6102	191	17	1	1	NUM
ejpam-6102	191	18	µi	µi	ADV
ejpam-6102	191	19	)	)	PUNCT
ejpam-6102	191	20	∀v	∀v	PROPN
ejpam-6102	191	21	∈	∈	PROPN
ejpam-6102	191	22	fa,µ.	fa,µ.	ADJ
ejpam-6102	191	23	r.	r.	PROPN
ejpam-6102	191	24	almushahhin	almushahhin	PROPN
ejpam-6102	191	25	,	,	PUNCT
ejpam-6102	191	26	m.	m.	PROPN
ejpam-6102	191	27	ben	ben	PROPN
ejpam-6102	191	28	ayed	aye	VERB
ejpam-6102	191	29	/	/	SYM
ejpam-6102	191	30	eur	eur	PROPN
ejpam-6102	191	31	.	.	PUNCT
ejpam-6102	192	1	j.	j.	PROPN
ejpam-6102	192	2	pure	pure	PROPN
ejpam-6102	192	3	appl	appl	PROPN
ejpam-6102	192	4	.	.	PROPN
ejpam-6102	192	5	math	math	PROPN
ejpam-6102	192	6	,	,	PUNCT
ejpam-6102	192	7	18	18	NUM
ejpam-6102	192	8	(	(	PUNCT
ejpam-6102	192	9	2	2	NUM
ejpam-6102	192	10	)	)	PUNCT
ejpam-6102	192	11	(	(	PUNCT
ejpam-6102	192	12	2025	2025	NUM
ejpam-6102	192	13	)	)	PUNCT
ejpam-6102	192	14	,	,	PUNCT
ejpam-6102	192	15	6102	6102	NUM
ejpam-6102	192	16	9	9	NUM
ejpam-6102	192	17	of	of	ADP
ejpam-6102	192	18	31	31	NUM
ejpam-6102	192	19	proof	proof	NOUN
ejpam-6102	192	20	.	.	PUNCT
ejpam-6102	193	1	we	we	PRON
ejpam-6102	193	2	will	will	AUX
ejpam-6102	193	3	use	use	VERB
ejpam-6102	193	4	the	the	DET
ejpam-6102	193	5	following	follow	VERB
ejpam-6102	193	6	formula	formula	NOUN
ejpam-6102	193	7	,	,	PUNCT
ejpam-6102	193	8	the	the	DET
ejpam-6102	193	9	proof	proof	NOUN
ejpam-6102	193	10	of	of	ADP
ejpam-6102	193	11	which	which	PRON
ejpam-6102	193	12	follows	follow	VERB
ejpam-6102	193	13	from	from	ADP
ejpam-6102	193	14	taylor	taylor	PROPN
ejpam-6102	193	15	expansion	expansion	NOUN
ejpam-6102	193	16	.	.	PUNCT
ejpam-6102	194	1	for	for	ADP
ejpam-6102	194	2	tj	tj	PROPN
ejpam-6102	194	3	>	>	X
ejpam-6102	194	4	0	0	NUM
ejpam-6102	194	5	,	,	PUNCT
ejpam-6102	194	6	(	(	PUNCT
ejpam-6102	194	7	∑	∑	PART
ejpam-6102	194	8	tj	tj	NOUN
ejpam-6102	194	9	)	)	PUNCT
ejpam-6102	194	10	γ	γ	X
ejpam-6102	194	11	=	=	SYM
ejpam-6102	194	12	∑	∑	PUNCT
ejpam-6102	194	13	tγj	tγj	NOUN
ejpam-6102	194	14	+	+	CCONJ
ejpam-6102	194	15	∑	∑	PROPN
ejpam-6102	194	16	i	i	PRON
ejpam-6102	194	17	̸=j	̸=j	X
ejpam-6102	194	18	o	o	X
ejpam-6102	194	19	(	(	PUNCT
ejpam-6102	194	20	(	(	PUNCT
ejpam-6102	194	21	titj	titj	NOUN
ejpam-6102	194	22	)	)	PUNCT
ejpam-6102	194	23	γ/2	γ/2	PUNCT
ejpam-6102	194	24	)	)	PUNCT
ejpam-6102	194	25	if	if	SCONJ
ejpam-6102	194	26	γ	γ	X
ejpam-6102	194	27	⩽	⩽	PROPN
ejpam-6102	194	28	2	2	NUM
ejpam-6102	194	29	,	,	PUNCT
ejpam-6102	194	30	o	o	X
ejpam-6102	194	31	(	(	PUNCT
ejpam-6102	194	32	tγ−1	tγ−1	NOUN
ejpam-6102	194	33	i	i	NOUN
ejpam-6102	194	34	tj	tj	NOUN
ejpam-6102	194	35	)	)	PUNCT
ejpam-6102	194	36	if	if	SCONJ
ejpam-6102	194	37	γ	γ	X
ejpam-6102	194	38	>	>	X
ejpam-6102	194	39	2	2	NUM
ejpam-6102	194	40	.	.	PUNCT
ejpam-6102	194	41	(	(	PUNCT
ejpam-6102	194	42	20	20	X
ejpam-6102	194	43	)	)	PUNCT
ejpam-6102	194	44	observe	observe	VERB
ejpam-6102	194	45	that	that	SCONJ
ejpam-6102	194	46	,	,	PUNCT
ejpam-6102	194	47	if	if	SCONJ
ejpam-6102	194	48	n	n	CCONJ
ejpam-6102	194	49	⩾	⩾	NOUN
ejpam-6102	194	50	6	6	NUM
ejpam-6102	194	51	,	,	PUNCT
ejpam-6102	194	52	it	it	PRON
ejpam-6102	194	53	follows	follow	VERB
ejpam-6102	194	54	that	that	SCONJ
ejpam-6102	194	55	p	p	X
ejpam-6102	194	56	:	:	PUNCT
ejpam-6102	194	57	=	=	SYM
ejpam-6102	194	58	(	(	PUNCT
ejpam-6102	194	59	n+2	n+2	NUM
ejpam-6102	194	60	)	)	PUNCT
ejpam-6102	194	61	(	(	PUNCT
ejpam-6102	194	62	n−2	n−2	PROPN
ejpam-6102	194	63	)	)	PUNCT
ejpam-6102	194	64	⩽	⩽	NOUN
ejpam-6102	194	65	2	2	NUM
ejpam-6102	194	66	,	,	PUNCT
ejpam-6102	194	67	and	and	CCONJ
ejpam-6102	194	68	therefore	therefore	ADV
ejpam-6102	194	69	,	,	PUNCT
ejpam-6102	194	70	using	use	VERB
ejpam-6102	194	71	(	(	PUNCT
ejpam-6102	194	72	20	20	NUM
ejpam-6102	194	73	)	)	PUNCT
ejpam-6102	194	74	and	and	CCONJ
ejpam-6102	194	75	(	(	PUNCT
ejpam-6102	194	76	13	13	NUM
ejpam-6102	194	77	)	)	PUNCT
ejpam-6102	194	78	,	,	PUNCT
ejpam-6102	194	79	we	we	PRON
ejpam-6102	194	80	deduce	deduce	VERB
ejpam-6102	194	81	that	that	PRON
ejpam-6102	194	82	lε(v	lε(v	NOUN
ejpam-6102	194	83	)	)	PUNCT
ejpam-6102	195	1	=	=	SYM
ejpam-6102	196	1	q∑	q∑	PROPN
ejpam-6102	197	1	i=1	i=1	PROPN
ejpam-6102	197	2	αp−ε	αp−ε	PROPN
ejpam-6102	198	1	i	i	PRON
ejpam-6102	198	2	∫	∫	PROPN
ejpam-6102	198	3	ω	ω	NUM
ejpam-6102	198	4	fωp−ε	fωp−ε	PROPN
ejpam-6102	198	5	ai,µi	ai,µi	NOUN
ejpam-6102	198	6	v	v	ADP
ejpam-6102	198	7	+	+	CCONJ
ejpam-6102	198	8	∑	∑	PROPN
ejpam-6102	198	9	i	i	PRON
ejpam-6102	198	10	̸=j	̸=j	X
ejpam-6102	198	11	o	o	X
ejpam-6102	198	12	(	(	PUNCT
ejpam-6102	198	13	∫	∫	PROPN
ejpam-6102	198	14	ω	ω	PROPN
ejpam-6102	198	15	(	(	PUNCT
ejpam-6102	198	16	ωai,µiωaj	ωai,µiωaj	PROPN
ejpam-6102	198	17	,	,	PUNCT
ejpam-6102	198	18	µj	µj	NOUN
ejpam-6102	198	19	)	)	PUNCT
ejpam-6102	198	20	p/2	p/2	NOUN
ejpam-6102	198	21	|v|	|v|	NOUN
ejpam-6102	198	22	)	)	PUNCT
ejpam-6102	198	23	.	.	PUNCT
ejpam-6102	199	1	thus	thus	ADV
ejpam-6102	199	2	,	,	PUNCT
ejpam-6102	199	3	using	use	VERB
ejpam-6102	199	4	lemma	lemma	PROPN
ejpam-6102	199	5	2	2	NUM
ejpam-6102	199	6	and	and	CCONJ
ejpam-6102	199	7	holder	holder	NOUN
ejpam-6102	199	8	’s	’s	PART
ejpam-6102	199	9	inequality	inequality	NOUN
ejpam-6102	199	10	,	,	PUNCT
ejpam-6102	199	11	we	we	PRON
ejpam-6102	199	12	get	get	VERB
ejpam-6102	199	13	|lε(v)|	|lε(v)|	NOUN
ejpam-6102	199	14	⩽	⩽	ADJ
ejpam-6102	199	15	c∥v∥	c∥v∥	PROPN
ejpam-6102	199	16	(	(	PUNCT
ejpam-6102	199	17	ε+	ε+	NOUN
ejpam-6102	199	18	∑	∑	SYM
ejpam-6102	199	19	1	1	NUM
ejpam-6102	199	20	µi	µi	PROPN
ejpam-6102	199	21	)	)	PUNCT
ejpam-6102	200	1	+	+	CCONJ
ejpam-6102	200	2	c∥v∥	c∥v∥	PROPN
ejpam-6102	200	3	(	(	PUNCT
ejpam-6102	200	4	∫	∫	PROPN
ejpam-6102	200	5	ω	ω	PROPN
ejpam-6102	200	6	ω	ω	PROPN
ejpam-6102	200	7	n	n	PROPN
ejpam-6102	200	8	n−2	n−2	PROPN
ejpam-6102	200	9	ai,µiω	ai,µiω	PROPN
ejpam-6102	200	10	n	n	PRON
ejpam-6102	200	11	n−2	n−2	PROPN
ejpam-6102	200	12	aj	aj	PROPN
ejpam-6102	200	13	,	,	PUNCT
ejpam-6102	200	14	µj	µj	PROPN
ejpam-6102	200	15	)	)	PUNCT
ejpam-6102	200	16	n+2	n+2	NUM
ejpam-6102	200	17	2n	2n	NUM
ejpam-6102	200	18	.	.	PUNCT
ejpam-6102	201	1	but	but	CCONJ
ejpam-6102	201	2	,	,	PUNCT
ejpam-6102	201	3	since	since	SCONJ
ejpam-6102	201	4	|ai	|ai	NUM
ejpam-6102	201	5	−	−	PROPN
ejpam-6102	201	6	aj	aj	PROPN
ejpam-6102	201	7	|	|	ADV
ejpam-6102	201	8	⩾	⩾	PROPN
ejpam-6102	201	9	γ0	γ0	PROPN
ejpam-6102	201	10	,	,	PUNCT
ejpam-6102	201	11	let	let	VERB
ejpam-6102	201	12	bk	bk	NOUN
ejpam-6102	201	13	=	=	SYM
ejpam-6102	201	14	b	b	PROPN
ejpam-6102	201	15	(	(	PUNCT
ejpam-6102	201	16	ak	ak	PROPN
ejpam-6102	201	17	,	,	PUNCT
ejpam-6102	201	18	γ0/2	γ0/2	PROPN
ejpam-6102	201	19	)	)	PUNCT
ejpam-6102	201	20	,	,	PUNCT
ejpam-6102	201	21	using	use	VERB
ejpam-6102	201	22	(	(	PUNCT
ejpam-6102	201	23	7	7	NUM
ejpam-6102	201	24	)	)	PUNCT
ejpam-6102	201	25	,	,	PUNCT
ejpam-6102	201	26	it	it	PRON
ejpam-6102	201	27	follows	follow	VERB
ejpam-6102	201	28	that∫	that∫	PROPN
ejpam-6102	201	29	ω	ω	PROPN
ejpam-6102	201	30	ω	ω	PROPN
ejpam-6102	201	31	n	n	PROPN
ejpam-6102	201	32	n−2	n−2	PROPN
ejpam-6102	201	33	ai,µiω	ai,µiω	PROPN
ejpam-6102	201	34	n	n	PRON
ejpam-6102	201	35	n−2	n−2	PROPN
ejpam-6102	201	36	aj	aj	PROPN
ejpam-6102	201	37	,	,	PUNCT
ejpam-6102	201	38	µj	µj	PROPN
ejpam-6102	201	39	⩽	⩽	PROPN
ejpam-6102	201	40	c	c	PROPN
ejpam-6102	201	41	µ	µ	PROPN
ejpam-6102	201	42	n	n	PRON
ejpam-6102	201	43	2	2	NUM
ejpam-6102	201	44	j	j	NOUN
ejpam-6102	201	45	∫	∫	PROPN
ejpam-6102	201	46	bi	bi	PROPN
ejpam-6102	201	47	ω	ω	PROPN
ejpam-6102	201	48	n	n	PROPN
ejpam-6102	201	49	n−2	n−2	PROPN
ejpam-6102	201	50	ai,µi	ai,µi	NOUN
ejpam-6102	201	51	+	+	CCONJ
ejpam-6102	201	52	c	c	PROPN
ejpam-6102	201	53	µ	µ	X
ejpam-6102	201	54	n	n	PRON
ejpam-6102	201	55	2	2	NUM
ejpam-6102	202	1	i	i	PRON
ejpam-6102	202	2	∫	∫	VERB
ejpam-6102	202	3	bj	bj	VERB
ejpam-6102	202	4	ω	ω	PROPN
ejpam-6102	202	5	n	n	PROPN
ejpam-6102	202	6	n−2	n−2	PROPN
ejpam-6102	202	7	aj	aj	PROPN
ejpam-6102	202	8	,	,	PUNCT
ejpam-6102	202	9	µj	µj	PROPN
ejpam-6102	203	1	+	+	NUM
ejpam-6102	203	2	c	c	X
ejpam-6102	203	3	(	(	PUNCT
ejpam-6102	203	4	µiµj	µiµj	NOUN
ejpam-6102	203	5	)	)	PUNCT
ejpam-6102	203	6	n	n	PRON
ejpam-6102	203	7	2	2	NUM
ejpam-6102	203	8	∫	∫	NOUN
ejpam-6102	203	9	ω\(bi∪bj	ω\(bi∪bj	PROPN
ejpam-6102	203	10	)	)	PUNCT
ejpam-6102	203	11	dx	dx	PROPN
ejpam-6102	204	1	⩽	⩽	PROPN
ejpam-6102	204	2	c	c	PROPN
ejpam-6102	204	3	ln	ln	X
ejpam-6102	204	4	(	(	PUNCT
ejpam-6102	204	5	µiµj	µiµj	NOUN
ejpam-6102	204	6	)	)	PUNCT
ejpam-6102	204	7	(	(	PUNCT
ejpam-6102	204	8	µiµj	µiµj	NOUN
ejpam-6102	204	9	)	)	PUNCT
ejpam-6102	204	10	n	n	PRON
ejpam-6102	204	11	2	2	NUM
ejpam-6102	204	12	.	.	PUNCT
ejpam-6102	205	1	this	this	PRON
ejpam-6102	205	2	completes	complete	VERB
ejpam-6102	205	3	the	the	DET
ejpam-6102	205	4	proof	proof	NOUN
ejpam-6102	205	5	for	for	ADP
ejpam-6102	205	6	n	n	NOUN
ejpam-6102	205	7	⩾	⩾	NOUN
ejpam-6102	205	8	6	6	NUM
ejpam-6102	205	9	.	.	PUNCT
ejpam-6102	206	1	however	however	ADV
ejpam-6102	206	2	,	,	PUNCT
ejpam-6102	206	3	for	for	ADP
ejpam-6102	206	4	n	n	CCONJ
ejpam-6102	206	5	⩽	⩽	NOUN
ejpam-6102	206	6	5	5	NUM
ejpam-6102	206	7	,	,	PUNCT
ejpam-6102	206	8	we	we	PRON
ejpam-6102	206	9	need	need	VERB
ejpam-6102	206	10	to	to	PART
ejpam-6102	206	11	estimate∫	estimate∫	VERB
ejpam-6102	206	12	ω	ω	PROPN
ejpam-6102	206	13	ω	ω	PROPN
ejpam-6102	206	14	4	4	NUM
ejpam-6102	206	15	n−2	n−2	PROPN
ejpam-6102	206	16	ai,µiωaj	ai,µiωaj	PROPN
ejpam-6102	206	17	,	,	PUNCT
ejpam-6102	206	18	µj	µj	PROPN
ejpam-6102	206	19	|v|	|v|	NUM
ejpam-6102	206	20	⩽	⩽	ADJ
ejpam-6102	206	21	c∥v∥	c∥v∥	PROPN
ejpam-6102	206	22	(	(	PUNCT
ejpam-6102	206	23	∫	∫	PROPN
ejpam-6102	206	24	ω	ω	PROPN
ejpam-6102	206	25	ω	ω	PROPN
ejpam-6102	206	26	8n	8n	NOUN
ejpam-6102	206	27	(	(	PUNCT
ejpam-6102	206	28	n−2)(n+2	n−2)(n+2	NOUN
ejpam-6102	206	29	)	)	PUNCT
ejpam-6102	206	30	ai,µi	ai,µi	NOUN
ejpam-6102	206	31	ω	ω	PROPN
ejpam-6102	206	32	2n	2n	PROPN
ejpam-6102	207	1	n+2	n+2	NUM
ejpam-6102	207	2	aj	aj	PROPN
ejpam-6102	207	3	,	,	PUNCT
ejpam-6102	207	4	µj	µj	PROPN
ejpam-6102	207	5	)	)	PUNCT
ejpam-6102	207	6	n+2	n+2	NUM
ejpam-6102	207	7	2n	2n	NUM
ejpam-6102	207	8	.	.	PUNCT
ejpam-6102	208	1	but	but	CCONJ
ejpam-6102	208	2	,	,	PUNCT
ejpam-6102	208	3	since	since	SCONJ
ejpam-6102	208	4	|ai	|ai	NUM
ejpam-6102	208	5	−	−	PROPN
ejpam-6102	208	6	aj	aj	PROPN
ejpam-6102	208	7	|	|	ADV
ejpam-6102	208	8	⩾	⩾	PROPN
ejpam-6102	208	9	γ0	γ0	PROPN
ejpam-6102	208	10	,	,	PUNCT
ejpam-6102	208	11	using	use	VERB
ejpam-6102	208	12	(	(	PUNCT
ejpam-6102	208	13	7	7	NUM
ejpam-6102	208	14	)	)	PUNCT
ejpam-6102	208	15	,	,	PUNCT
ejpam-6102	208	16	we	we	PRON
ejpam-6102	208	17	get∫	get∫	PROPN
ejpam-6102	208	18	ω	ω	PROPN
ejpam-6102	208	19	ω	ω	PROPN
ejpam-6102	208	20	8n	8n	NOUN
ejpam-6102	208	21	(	(	PUNCT
ejpam-6102	208	22	n−2)(n+2	n−2)(n+2	NOUN
ejpam-6102	208	23	)	)	PUNCT
ejpam-6102	208	24	ai,µi	ai,µi	NOUN
ejpam-6102	208	25	ω	ω	PROPN
ejpam-6102	208	26	2n	2n	PROPN
ejpam-6102	209	1	n+2	n+2	NUM
ejpam-6102	209	2	aj	aj	PROPN
ejpam-6102	209	3	,	,	PUNCT
ejpam-6102	209	4	µj	µj	PROPN
ejpam-6102	209	5	⩽	⩽	PROPN
ejpam-6102	209	6	c	c	PROPN
ejpam-6102	209	7	µ	µ	X
ejpam-6102	209	8	n(n−2	n(n−2	PROPN
ejpam-6102	209	9	)	)	PUNCT
ejpam-6102	209	10	n+2	n+2	NUM
ejpam-6102	210	1	j	j	NOUN
ejpam-6102	210	2	∫	∫	PROPN
ejpam-6102	210	3	bi	bi	PROPN
ejpam-6102	210	4	ω	ω	PROPN
ejpam-6102	210	5	8n	8n	NOUN
ejpam-6102	210	6	(	(	PUNCT
ejpam-6102	210	7	n−2)(n+2	n−2)(n+2	NOUN
ejpam-6102	210	8	)	)	PUNCT
ejpam-6102	210	9	ai,µi	ai,µi	NOUN
ejpam-6102	210	10	+	+	CCONJ
ejpam-6102	210	11	c	c	X
ejpam-6102	210	12	µ	µ	X
ejpam-6102	210	13	4n	4n	NOUN
ejpam-6102	210	14	n+2	n+2	X
ejpam-6102	211	1	i	i	PRON
ejpam-6102	211	2	∫	∫	VERB
ejpam-6102	211	3	bj	bj	VERB
ejpam-6102	211	4	ω	ω	NUM
ejpam-6102	211	5	2n	2n	NUM
ejpam-6102	211	6	n+2	n+2	NUM
ejpam-6102	211	7	aj	aj	PROPN
ejpam-6102	211	8	,	,	PUNCT
ejpam-6102	211	9	µj	µj	PROPN
ejpam-6102	212	1	+	+	CCONJ
ejpam-6102	212	2	c	c	X
ejpam-6102	212	3	µ	µ	X
ejpam-6102	212	4	4n	4n	NOUN
ejpam-6102	212	5	n+2	n+2	PUNCT
ejpam-6102	212	6	i	i	PRON
ejpam-6102	212	7	µ	µ	PROPN
ejpam-6102	212	8	n(n−2	n(n−2	ADP
ejpam-6102	212	9	)	)	PUNCT
ejpam-6102	212	10	(	(	PUNCT
ejpam-6102	212	11	n+2	n+2	NUM
ejpam-6102	212	12	)	)	PUNCT
ejpam-6102	212	13	j	j	PROPN
ejpam-6102	212	14	⩽	⩽	PROPN
ejpam-6102	212	15	c	c	PROPN
ejpam-6102	212	16	(	(	PUNCT
ejpam-6102	212	17	µiµj	µiµj	NOUN
ejpam-6102	212	18	)	)	PUNCT
ejpam-6102	212	19	n(n−2	n(n−2	PROPN
ejpam-6102	212	20	)	)	PUNCT
ejpam-6102	212	21	(	(	PUNCT
ejpam-6102	212	22	n+2	n+2	NUM
ejpam-6102	212	23	)	)	PUNCT
ejpam-6102	212	24	.	.	PUNCT
ejpam-6102	213	1	this	this	PRON
ejpam-6102	213	2	completes	complete	VERB
ejpam-6102	213	3	the	the	DET
ejpam-6102	213	4	proof	proof	NOUN
ejpam-6102	213	5	of	of	ADP
ejpam-6102	213	6	the	the	DET
ejpam-6102	213	7	proposition	proposition	NOUN
ejpam-6102	213	8	.	.	PUNCT
ejpam-6102	214	1	proposition	proposition	NOUN
ejpam-6102	214	2	3	3	X
ejpam-6102	214	3	.	.	PUNCT
ejpam-6102	215	1	let	let	VERB
ejpam-6102	215	2	(	(	PUNCT
ejpam-6102	215	3	a	a	PRON
ejpam-6102	215	4	,	,	PUNCT
ejpam-6102	215	5	µ	µ	NOUN
ejpam-6102	215	6	,	,	PUNCT
ejpam-6102	215	7	α	α	NOUN
ejpam-6102	215	8	)	)	PUNCT
ejpam-6102	215	9	∈	∈	PROPN
ejpam-6102	215	10	ϑ	ϑ	X
ejpam-6102	215	11	(	(	PUNCT
ejpam-6102	215	12	q	q	PROPN
ejpam-6102	215	13	,	,	PUNCT
ejpam-6102	215	14	γ0	γ0	NOUN
ejpam-6102	215	15	,	,	PUNCT
ejpam-6102	215	16	η0	η0	NOUN
ejpam-6102	215	17	)	)	PUNCT
ejpam-6102	215	18	.	.	PUNCT
ejpam-6102	216	1	then	then	ADV
ejpam-6102	216	2	,	,	PUNCT
ejpam-6102	216	3	for	for	ADP
ejpam-6102	216	4	ε	ε	PROPN
ejpam-6102	216	5	small	small	PROPN
ejpam-6102	216	6	,	,	PUNCT
ejpam-6102	216	7	there	there	PRON
ejpam-6102	216	8	exists	exist	VERB
ejpam-6102	216	9	a	a	DET
ejpam-6102	216	10	unique	unique	ADJ
ejpam-6102	216	11	v	v	NOUN
ejpam-6102	216	12	∈	∈	NOUN
ejpam-6102	216	13	fa,µ	fa,µ	NOUN
ejpam-6102	216	14	verifying	verify	VERB
ejpam-6102	216	15	⟨∇jε(ũ+	⟨∇jε(ũ+	PROPN
ejpam-6102	216	16	v	v	NOUN
ejpam-6102	216	17	)	)	PUNCT
ejpam-6102	216	18	,	,	PUNCT
ejpam-6102	216	19	v⟩	v⟩	NOUN
ejpam-6102	216	20	=	=	SYM
ejpam-6102	216	21	0	0	NUM
ejpam-6102	216	22	∀v	∀v	NOUN
ejpam-6102	216	23	∈	∈	PROPN
ejpam-6102	216	24	fa,µ.	fa,µ.	PROPN
ejpam-6102	216	25	and	and	CCONJ
ejpam-6102	216	26	∥v∥	∥v∥	ADJ
ejpam-6102	216	27	⩽	⩽	NOUN
ejpam-6102	216	28	c	c	PROPN
ejpam-6102	216	29	(	(	PUNCT
ejpam-6102	216	30	ε+	ε+	X
ejpam-6102	216	31	∑	∑	SYM
ejpam-6102	216	32	1	1	NUM
ejpam-6102	216	33	µi	µi	PROPN
ejpam-6102	216	34	)	)	PUNCT
ejpam-6102	216	35	.	.	PUNCT
ejpam-6102	217	1	proof	proof	NOUN
ejpam-6102	217	2	.	.	PUNCT
ejpam-6102	218	1	the	the	DET
ejpam-6102	218	2	proof	proof	NOUN
ejpam-6102	218	3	follows	follow	VERB
ejpam-6102	218	4	from	from	ADP
ejpam-6102	218	5	(	(	PUNCT
ejpam-6102	218	6	9	9	NUM
ejpam-6102	218	7	)	)	PUNCT
ejpam-6102	218	8	,	,	PUNCT
ejpam-6102	218	9	(	(	PUNCT
ejpam-6102	218	10	14	14	NUM
ejpam-6102	218	11	)	)	PUNCT
ejpam-6102	218	12	and	and	CCONJ
ejpam-6102	218	13	proposition	proposition	NOUN
ejpam-6102	218	14	2	2	NUM
ejpam-6102	218	15	by	by	ADP
ejpam-6102	218	16	using	use	VERB
ejpam-6102	218	17	the	the	DET
ejpam-6102	218	18	implicit	implicit	ADJ
ejpam-6102	218	19	function	function	NOUN
ejpam-6102	218	20	theorem	theorem	VERB
ejpam-6102	218	21	.	.	PROPN
ejpam-6102	219	1	4	4	X
ejpam-6102	219	2	.	.	PUNCT
ejpam-6102	219	3	asymptotic	asymptotic	ADJ
ejpam-6102	219	4	expansion	expansion	NOUN
ejpam-6102	219	5	of	of	ADP
ejpam-6102	219	6	the	the	DET
ejpam-6102	219	7	gradient	gradient	NOUN
ejpam-6102	219	8	in	in	ADP
ejpam-6102	219	9	the	the	DET
ejpam-6102	219	10	potential	potential	ADJ
ejpam-6102	219	11	sets	set	NOUN
ejpam-6102	219	12	this	this	DET
ejpam-6102	219	13	section	section	NOUN
ejpam-6102	219	14	is	be	AUX
ejpam-6102	219	15	devoted	devote	VERB
ejpam-6102	219	16	to	to	ADP
ejpam-6102	219	17	the	the	DET
ejpam-6102	219	18	asymptotic	asymptotic	ADJ
ejpam-6102	219	19	expansion	expansion	NOUN
ejpam-6102	219	20	of	of	ADP
ejpam-6102	219	21	the	the	DET
ejpam-6102	219	22	gradient	gradient	NOUN
ejpam-6102	219	23	of	of	ADP
ejpam-6102	219	24	the	the	DET
ejpam-6102	219	25	functional	functional	ADJ
ejpam-6102	219	26	jε	jε	NOUN
ejpam-6102	219	27	defined	define	VERB
ejpam-6102	219	28	in	in	ADP
ejpam-6102	219	29	(	(	PUNCT
ejpam-6102	219	30	3	3	NUM
ejpam-6102	219	31	)	)	PUNCT
ejpam-6102	219	32	.	.	PUNCT
ejpam-6102	220	1	to	to	ADP
ejpam-6102	220	2	this	this	DET
ejpam-6102	220	3	aim	aim	NOUN
ejpam-6102	220	4	,	,	PUNCT
ejpam-6102	220	5	by	by	ADP
ejpam-6102	220	6	easy	easy	ADJ
ejpam-6102	220	7	computation	computation	NOUN
ejpam-6102	220	8	,	,	PUNCT
ejpam-6102	220	9	we	we	PRON
ejpam-6102	220	10	see	see	VERB
ejpam-6102	220	11	that	that	PRON
ejpam-6102	220	12	⟨∇jε(u	⟨∇jε(u	PROPN
ejpam-6102	220	13	)	)	PUNCT
ejpam-6102	220	14	,	,	PUNCT
ejpam-6102	220	15	g⟩	g⟩	VERB
ejpam-6102	220	16	=	=	SYM
ejpam-6102	220	17	⟨u	⟨u	NOUN
ejpam-6102	220	18	,	,	PUNCT
ejpam-6102	220	19	g⟩	g⟩	VERB
ejpam-6102	220	20	−	−	PROPN
ejpam-6102	220	21	∫	∫	PROPN
ejpam-6102	220	22	ω	ω	PROPN
ejpam-6102	220	23	f	f	PROPN
ejpam-6102	220	24	|u|p−ε−1ug	|u|p−ε−1ug	PROPN
ejpam-6102	220	25	∀u	∀u	NOUN
ejpam-6102	220	26	,	,	PUNCT
ejpam-6102	220	27	g	g	PROPN
ejpam-6102	220	28	∈	∈	PROPN
ejpam-6102	220	29	h1(ω	h1(ω	PROPN
ejpam-6102	220	30	)	)	PUNCT
ejpam-6102	220	31	.	.	PUNCT
ejpam-6102	221	1	(	(	PUNCT
ejpam-6102	221	2	21	21	NUM
ejpam-6102	221	3	)	)	PUNCT
ejpam-6102	221	4	we	we	PRON
ejpam-6102	221	5	start	start	VERB
ejpam-6102	221	6	by	by	ADP
ejpam-6102	221	7	the	the	DET
ejpam-6102	221	8	expansion	expansion	NOUN
ejpam-6102	221	9	with	with	ADP
ejpam-6102	221	10	respect	respect	NOUN
ejpam-6102	221	11	to	to	ADP
ejpam-6102	221	12	the	the	DET
ejpam-6102	221	13	variable	variable	ADJ
ejpam-6102	221	14	α	α	NOUN
ejpam-6102	221	15	.	.	PUNCT
ejpam-6102	222	1	r.	r.	PROPN
ejpam-6102	222	2	almushahhin	almushahhin	PROPN
ejpam-6102	222	3	,	,	PUNCT
ejpam-6102	222	4	m.	m.	PROPN
ejpam-6102	222	5	ben	ben	PROPN
ejpam-6102	222	6	ayed	aye	VERB
ejpam-6102	222	7	/	/	SYM
ejpam-6102	222	8	eur	eur	PROPN
ejpam-6102	222	9	.	.	PUNCT
ejpam-6102	223	1	j.	j.	PROPN
ejpam-6102	223	2	pure	pure	PROPN
ejpam-6102	223	3	appl	appl	PROPN
ejpam-6102	223	4	.	.	PROPN
ejpam-6102	223	5	math	math	PROPN
ejpam-6102	223	6	,	,	PUNCT
ejpam-6102	223	7	18	18	NUM
ejpam-6102	223	8	(	(	PUNCT
ejpam-6102	223	9	2	2	NUM
ejpam-6102	223	10	)	)	PUNCT
ejpam-6102	223	11	(	(	PUNCT
ejpam-6102	223	12	2025	2025	NUM
ejpam-6102	223	13	)	)	PUNCT
ejpam-6102	223	14	,	,	PUNCT
ejpam-6102	223	15	6102	6102	NUM
ejpam-6102	223	16	10	10	NUM
ejpam-6102	223	17	of	of	ADP
ejpam-6102	223	18	31	31	NUM
ejpam-6102	223	19	proposition	proposition	NOUN
ejpam-6102	223	20	4	4	NUM
ejpam-6102	223	21	.	.	PUNCT
ejpam-6102	224	1	let	let	VERB
ejpam-6102	224	2	(	(	PUNCT
ejpam-6102	224	3	a	a	PRON
ejpam-6102	224	4	,	,	PUNCT
ejpam-6102	224	5	µ	µ	NOUN
ejpam-6102	224	6	,	,	PUNCT
ejpam-6102	224	7	α	α	NOUN
ejpam-6102	224	8	)	)	PUNCT
ejpam-6102	224	9	∈	∈	PROPN
ejpam-6102	224	10	ϑ	ϑ	X
ejpam-6102	224	11	(	(	PUNCT
ejpam-6102	224	12	q	q	PROPN
ejpam-6102	224	13	,	,	PUNCT
ejpam-6102	224	14	γ0	γ0	NOUN
ejpam-6102	224	15	,	,	PUNCT
ejpam-6102	224	16	η0	η0	NOUN
ejpam-6102	224	17	)	)	PUNCT
ejpam-6102	224	18	,	,	PUNCT
ejpam-6102	224	19	ũ	ũ	PROPN
ejpam-6102	224	20	be	be	AUX
ejpam-6102	224	21	defined	define	VERB
ejpam-6102	224	22	in	in	ADP
ejpam-6102	224	23	(	(	PUNCT
ejpam-6102	224	24	6	6	NUM
ejpam-6102	224	25	)	)	PUNCT
ejpam-6102	224	26	and	and	CCONJ
ejpam-6102	224	27	v	v	NOUN
ejpam-6102	224	28	∈	∈	NOUN
ejpam-6102	224	29	fa,µ	fa,µ	NOUN
ejpam-6102	224	30	where	where	SCONJ
ejpam-6102	224	31	fa,µ	fa,µ	ADJ
ejpam-6102	224	32	is	be	AUX
ejpam-6102	224	33	defined	define	VERB
ejpam-6102	224	34	in	in	ADP
ejpam-6102	224	35	(	(	PUNCT
ejpam-6102	224	36	5	5	NUM
ejpam-6102	224	37	)	)	PUNCT
ejpam-6102	224	38	.	.	PUNCT
ejpam-6102	225	1	then	then	ADV
ejpam-6102	225	2	,	,	PUNCT
ejpam-6102	225	3	for	for	ADP
ejpam-6102	225	4	ε	ε	PROPN
ejpam-6102	225	5	small	small	NOUN
ejpam-6102	225	6	and	and	CCONJ
ejpam-6102	225	7	i	i	PRON
ejpam-6102	225	8	∈	∈	PROPN
ejpam-6102	225	9	{	{	PUNCT
ejpam-6102	225	10	1	1	NUM
ejpam-6102	225	11	,	,	PUNCT
ejpam-6102	225	12	.	.	PUNCT
ejpam-6102	225	13	.	.	PUNCT
ejpam-6102	225	14	.	.	PUNCT
ejpam-6102	226	1	,	,	PUNCT
ejpam-6102	226	2	q	q	X
ejpam-6102	226	3	}	}	PUNCT
ejpam-6102	226	4	,	,	PUNCT
ejpam-6102	226	5	it	it	PRON
ejpam-6102	226	6	holds	hold	VERB
ejpam-6102	226	7	⟨∇jε(ũ+	⟨∇jε(ũ+	PROPN
ejpam-6102	226	8	v	v	NOUN
ejpam-6102	226	9	)	)	PUNCT
ejpam-6102	226	10	,	,	PUNCT
ejpam-6102	226	11	ωai,µi	ωai,µi	NOUN
ejpam-6102	226	12	⟩	⟩	NOUN
ejpam-6102	226	13	=	=	SYM
ejpam-6102	227	1	αisn	αisn	PROPN
ejpam-6102	227	2	(	(	PUNCT
ejpam-6102	227	3	1−	1−	NUM
ejpam-6102	227	4	µ	µ	X
ejpam-6102	227	5	−εn−2	−εn−2	ADP
ejpam-6102	227	6	2	2	NUM
ejpam-6102	227	7	i	i	PRON
ejpam-6102	227	8	αp−ε−1	αp−ε−1	NUM
ejpam-6102	228	1	i	i	PRON
ejpam-6102	228	2	f	f	X
ejpam-6102	228	3	(	(	PUNCT
ejpam-6102	228	4	ai	ai	PROPN
ejpam-6102	228	5	)	)	PUNCT
ejpam-6102	228	6	)	)	PUNCT
ejpam-6102	229	1	+	+	ADP
ejpam-6102	229	2	o	o	NOUN
ejpam-6102	229	3	(	(	PUNCT
ejpam-6102	229	4	∥v∥2	∥v∥2	ADJ
ejpam-6102	229	5	+	+	CCONJ
ejpam-6102	229	6	1	1	NUM
ejpam-6102	229	7	µi	µi	PROPN
ejpam-6102	229	8	+	+	CCONJ
ejpam-6102	229	9	ε	ε	PROPN
ejpam-6102	229	10	)	)	PUNCT
ejpam-6102	229	11	,	,	PUNCT
ejpam-6102	229	12	with	with	ADP
ejpam-6102	229	13	sn	sn	PROPN
ejpam-6102	229	14	:	:	PUNCT
ejpam-6102	229	15	=	=	SYM
ejpam-6102	229	16	1	1	NUM
ejpam-6102	229	17	2	2	NUM
ejpam-6102	229	18	[	[	X
ejpam-6102	229	19	n(n−	n(n−	NOUN
ejpam-6102	229	20	2)]n/2	2)]n/2	ADJ
ejpam-6102	229	21	∫	∫	PROPN
ejpam-6102	229	22	rn	rn	PROPN
ejpam-6102	229	23	1	1	NUM
ejpam-6102	229	24	(	(	PUNCT
ejpam-6102	229	25	1	1	NUM
ejpam-6102	229	26	+	+	CCONJ
ejpam-6102	229	27	|x|2)n	|x|2)n	ADJ
ejpam-6102	229	28	dx	dx	PROPN
ejpam-6102	229	29	.	.	PUNCT
ejpam-6102	230	1	(	(	PUNCT
ejpam-6102	230	2	22	22	NUM
ejpam-6102	230	3	)	)	PUNCT
ejpam-6102	230	4	proof	proof	NOUN
ejpam-6102	230	5	.	.	PUNCT
ejpam-6102	231	1	since	since	SCONJ
ejpam-6102	231	2	v	v	NUM
ejpam-6102	231	3	∈	∈	PROPN
ejpam-6102	231	4	fa,µ	fa,µ	NOUN
ejpam-6102	231	5	,	,	PUNCT
ejpam-6102	231	6	using	use	VERB
ejpam-6102	231	7	lemmas	lemmas	PROPN
ejpam-6102	231	8	4	4	NUM
ejpam-6102	231	9	and	and	CCONJ
ejpam-6102	231	10	5	5	NUM
ejpam-6102	231	11	,	,	PUNCT
ejpam-6102	231	12	it	it	PRON
ejpam-6102	231	13	follows	follow	VERB
ejpam-6102	231	14	that	that	SCONJ
ejpam-6102	231	15	⟨ũ+	⟨ũ+	PROPN
ejpam-6102	231	16	v	v	NOUN
ejpam-6102	231	17	,	,	PUNCT
ejpam-6102	231	18	ωai,µi	ωai,µi	NOUN
ejpam-6102	231	19	⟩	⟩	NOUN
ejpam-6102	231	20	=	=	SYM
ejpam-6102	231	21	q∑	q∑	PROPN
ejpam-6102	231	22	j=1	j=1	NOUN
ejpam-6102	231	23	αj	αj	PROPN
ejpam-6102	231	24	〈	〈	PROPN
ejpam-6102	231	25	ωaj	ωaj	PROPN
ejpam-6102	231	26	,	,	PUNCT
ejpam-6102	231	27	µj	µj	PROPN
ejpam-6102	231	28	ωai,µi	ωai,µi	NUM
ejpam-6102	231	29	〉	〉	NOUN
ejpam-6102	231	30	=	=	PUNCT
ejpam-6102	231	31	αi	αi	VERB
ejpam-6102	231	32	(	(	PUNCT
ejpam-6102	231	33	sn	sn	PROPN
ejpam-6102	232	1	+	+	NOUN
ejpam-6102	232	2	o	o	X
ejpam-6102	232	3	(	(	PUNCT
ejpam-6102	232	4	1	1	NUM
ejpam-6102	232	5	µi	µi	PROPN
ejpam-6102	232	6	)	)	PUNCT
ejpam-6102	232	7	)	)	PUNCT
ejpam-6102	233	1	+	+	CCONJ
ejpam-6102	234	1	q∑	q∑	INTJ
ejpam-6102	234	2	j	j	X
ejpam-6102	235	1	̸=i	̸=i	PROPN
ejpam-6102	235	2	o	o	PROPN
ejpam-6102	235	3	(	(	PUNCT
ejpam-6102	235	4	1	1	NUM
ejpam-6102	235	5	(	(	PUNCT
ejpam-6102	235	6	µiµj	µiµj	NOUN
ejpam-6102	235	7	)	)	PUNCT
ejpam-6102	235	8	(	(	PUNCT
ejpam-6102	235	9	n−2)/2	n−2)/2	NOUN
ejpam-6102	235	10	)	)	PUNCT
ejpam-6102	235	11	.	.	PUNCT
ejpam-6102	236	1	(	(	PUNCT
ejpam-6102	236	2	23	23	NUM
ejpam-6102	236	3	)	)	PUNCT
ejpam-6102	236	4	now	now	ADV
ejpam-6102	236	5	,	,	PUNCT
ejpam-6102	236	6	observe	observe	VERB
ejpam-6102	236	7	that	that	SCONJ
ejpam-6102	236	8	|s+	|s+	PROPN
ejpam-6102	236	9	t|γ(s+	t|γ(s+	PROPN
ejpam-6102	236	10	t)z	t)z	NOUN
ejpam-6102	236	11	=	=	SYM
ejpam-6102	236	12	|s|γsz	|s|γsz	PART
ejpam-6102	236	13	+	+	X
ejpam-6102	236	14	(	(	PUNCT
ejpam-6102	236	15	γ	γ	X
ejpam-6102	236	16	+	+	NOUN
ejpam-6102	236	17	1)|s|γtz	1)|s|γtz	NUM
ejpam-6102	236	18	+	+	NOUN
ejpam-6102	236	19	o(|s|γt2	o(|s|γt2	ADV
ejpam-6102	236	20	+	+	SYM
ejpam-6102	236	21	|t|γ+2	|t|γ+2	NOUN
ejpam-6102	236	22	)	)	PUNCT
ejpam-6102	236	23	∀	∀	PUNCT
ejpam-6102	236	24	s	s	X
ejpam-6102	236	25	,	,	PUNCT
ejpam-6102	236	26	t	t	PROPN
ejpam-6102	236	27	∈	∈	PROPN
ejpam-6102	236	28	r	r	NOUN
ejpam-6102	236	29	,	,	PUNCT
ejpam-6102	236	30	|z|	|z|	VERB
ejpam-6102	236	31	≤	≤	NUM
ejpam-6102	236	32	|s|	|s|	NOUN
ejpam-6102	236	33	and	and	CCONJ
ejpam-6102	236	34	γ	γ	X
ejpam-6102	236	35	>	>	X
ejpam-6102	236	36	0	0	NUM
ejpam-6102	236	37	.	.	PUNCT
ejpam-6102	237	1	thus	thus	ADV
ejpam-6102	237	2	,	,	PUNCT
ejpam-6102	237	3	for	for	ADP
ejpam-6102	237	4	each	each	DET
ejpam-6102	237	5	ψi	ψi	ADP
ejpam-6102	237	6	satisfying	satisfy	VERB
ejpam-6102	237	7	|ψi|	|ψi|	PROPN
ejpam-6102	237	8	⩽	⩽	PROPN
ejpam-6102	237	9	cωai,µi	cωai,µi	NOUN
ejpam-6102	237	10	,	,	PUNCT
ejpam-6102	237	11	in	in	ADP
ejpam-6102	237	12	bi	bi	NOUN
ejpam-6102	237	13	:	:	PUNCT
ejpam-6102	237	14	=	=	SYM
ejpam-6102	237	15	b	b	X
ejpam-6102	237	16	(	(	PUNCT
ejpam-6102	237	17	ai	ai	PROPN
ejpam-6102	237	18	,	,	PUNCT
ejpam-6102	237	19	γ0/2	γ0/2	PROPN
ejpam-6102	237	20	)	)	PUNCT
ejpam-6102	237	21	∩	∩	PROPN
ejpam-6102	237	22	ω	ω	PROPN
ejpam-6102	237	23	,	,	PUNCT
ejpam-6102	237	24	using	use	VERB
ejpam-6102	237	25	(	(	PUNCT
ejpam-6102	237	26	7	7	NUM
ejpam-6102	237	27	)	)	PUNCT
ejpam-6102	237	28	and	and	CCONJ
ejpam-6102	237	29	(	(	PUNCT
ejpam-6102	237	30	13	13	NUM
ejpam-6102	237	31	)	)	PUNCT
ejpam-6102	237	32	,	,	PUNCT
ejpam-6102	237	33	it	it	PRON
ejpam-6102	237	34	holds	hold	VERB
ejpam-6102	237	35	|ũ+	|ũ+	NUM
ejpam-6102	237	36	v|p−ε−1(ũ+	v|p−ε−1(ũ+	NOUN
ejpam-6102	237	37	v)ψi	v)ψi	PROPN
ejpam-6102	237	38	=	=	NOUN
ejpam-6102	237	39	αp−ε	αp−ε	PROPN
ejpam-6102	237	40	i	i	PRON
ejpam-6102	237	41	ωp−ε	ωp−ε	PROPN
ejpam-6102	237	42	ai,µi	ai,µi	VERB
ejpam-6102	237	43	ψi	ψi	ADP
ejpam-6102	237	44	+	+	CCONJ
ejpam-6102	237	45	(	(	PUNCT
ejpam-6102	237	46	p−	p−	NOUN
ejpam-6102	237	47	ε	ε	PROPN
ejpam-6102	237	48	)	)	PUNCT
ejpam-6102	237	49	(	(	PUNCT
ejpam-6102	237	50	αiωai,µi	αiωai,µi	X
ejpam-6102	237	51	)	)	PUNCT
ejpam-6102	238	1	p−ε−1	p−ε−1	PROPN
ejpam-6102	238	2	∑	∑	NOUN
ejpam-6102	238	3	j	j	NOUN
ejpam-6102	238	4	̸=i	̸=i	PROPN
ejpam-6102	238	5	αjωaj	αjωaj	ADV
ejpam-6102	238	6	,	,	PUNCT
ejpam-6102	238	7	µj	µj	PROPN
ejpam-6102	239	1	+	+	CCONJ
ejpam-6102	239	2	v	v	NOUN
ejpam-6102	239	3	ψi	ψi	PUNCT
ejpam-6102	240	1	+	+	NOUN
ejpam-6102	240	2	o	o	X
ejpam-6102	240	3	(	(	PUNCT
ejpam-6102	240	4	ωp−1	ωp−1	NOUN
ejpam-6102	240	5	ai,µi	ai,µi	NOUN
ejpam-6102	240	6	[	[	X
ejpam-6102	240	7	∑	∑	PROPN
ejpam-6102	240	8	1	1	NUM
ejpam-6102	240	9	µn−2	µn−2	PROPN
ejpam-6102	240	10	j	j	PROPN
ejpam-6102	240	11	+	+	PROPN
ejpam-6102	240	12	|v|2	|v|2	PROPN
ejpam-6102	240	13	]	]	PUNCT
ejpam-6102	241	1	+	+	CCONJ
ejpam-6102	241	2	∑	∑	SYM
ejpam-6102	241	3	1	1	NUM
ejpam-6102	241	4	µn	µn	PROPN
ejpam-6102	241	5	j	j	PROPN
ejpam-6102	241	6	+	+	CCONJ
ejpam-6102	241	7	|v|p+1−ε	|v|p+1−ε	PROPN
ejpam-6102	241	8	)	)	PUNCT
ejpam-6102	241	9	in	in	ADP
ejpam-6102	241	10	bi	bi	PROPN
ejpam-6102	241	11	.	.	PUNCT
ejpam-6102	242	1	(	(	PUNCT
ejpam-6102	242	2	24	24	NUM
ejpam-6102	242	3	)	)	PUNCT
ejpam-6102	242	4	but	but	CCONJ
ejpam-6102	242	5	,	,	PUNCT
ejpam-6102	242	6	in	in	ADP
ejpam-6102	242	7	ω\bi	ω\bi	PROPN
ejpam-6102	242	8	,	,	PUNCT
ejpam-6102	242	9	we	we	PRON
ejpam-6102	242	10	have	have	VERB
ejpam-6102	242	11	|ũ+	|ũ+	NUM
ejpam-6102	242	12	v|p−ε	v|p−ε	PROPN
ejpam-6102	242	13	|ψi|	|ψi|	NOUN
ejpam-6102	242	14	⩽	⩽	NOUN
ejpam-6102	242	15	c	c	PROPN
ejpam-6102	242	16	(	(	PUNCT
ejpam-6102	242	17	|v|p−ε	|v|p−ε	PROPN
ejpam-6102	242	18	+	+	CCONJ
ejpam-6102	242	19	∑	∑	PROPN
ejpam-6102	242	20	ωp	ωp	PROPN
ejpam-6102	242	21	aj	aj	PROPN
ejpam-6102	242	22	,	,	PUNCT
ejpam-6102	242	23	µj	µj	PROPN
ejpam-6102	242	24	)	)	PUNCT
ejpam-6102	242	25	|ψi|	|ψi|	PROPN
ejpam-6102	242	26	in	in	ADP
ejpam-6102	242	27	ω\bi	ω\bi	PROPN
ejpam-6102	242	28	.	.	PUNCT
ejpam-6102	243	1	(	(	PUNCT
ejpam-6102	243	2	25	25	NUM
ejpam-6102	243	3	)	)	PUNCT
ejpam-6102	243	4	thus	thus	ADV
ejpam-6102	243	5	,	,	PUNCT
ejpam-6102	243	6	the	the	DET
ejpam-6102	243	7	integral	integral	NOUN
ejpam-6102	243	8	in	in	ADP
ejpam-6102	243	9	eq	eq	PROPN
ejpam-6102	243	10	.	.	PUNCT
ejpam-6102	244	1	(	(	PUNCT
ejpam-6102	244	2	21	21	NUM
ejpam-6102	244	3	)	)	PUNCT
ejpam-6102	244	4	becomes∫	becomes∫	VERB
ejpam-6102	244	5	ω	ω	NUM
ejpam-6102	244	6	f	f	PROPN
ejpam-6102	244	7	|ũ+	|ũ+	NUM
ejpam-6102	244	8	v|p−ε−1(ũ+	v|p−ε−1(ũ+	NOUN
ejpam-6102	244	9	v)ωai,µi	v)ωai,µi	NOUN
ejpam-6102	244	10	=	=	PUNCT
ejpam-6102	244	11	αp−ε	αp−ε	PROPN
ejpam-6102	245	1	i	i	PRON
ejpam-6102	245	2	∫	∫	VERB
ejpam-6102	245	3	bi	bi	PROPN
ejpam-6102	245	4	fωp+1−ε	fωp+1−ε	PROPN
ejpam-6102	245	5	ai,µi	ai,µi	NOUN
ejpam-6102	246	1	+	+	CCONJ
ejpam-6102	246	2	(	(	PUNCT
ejpam-6102	246	3	p−	p−	NOUN
ejpam-6102	246	4	ε)αp−ε−1	ε)αp−ε−1	NOUN
ejpam-6102	246	5	i	i	PRON
ejpam-6102	246	6	[	[	X
ejpam-6102	246	7	∑	∑	X
ejpam-6102	246	8	j	j	PROPN
ejpam-6102	246	9	̸=i	̸=i	NOUN
ejpam-6102	246	10	αj	αj	PROPN
ejpam-6102	246	11	∫	∫	PROPN
ejpam-6102	246	12	bi	bi	PROPN
ejpam-6102	246	13	fωp−ε	fωp−ε	PROPN
ejpam-6102	246	14	ai,µi	ai,µi	NOUN
ejpam-6102	246	15	ωaj	ωaj	PROPN
ejpam-6102	246	16	,	,	PUNCT
ejpam-6102	246	17	µj	µj	PROPN
ejpam-6102	247	1	+	+	NUM
ejpam-6102	247	2	∫	∫	PROPN
ejpam-6102	247	3	bi	bi	ADJ
ejpam-6102	247	4	fωp−ε	fωp−ε	PROPN
ejpam-6102	247	5	ai,µi	ai,µi	NOUN
ejpam-6102	247	6	v	v	ADP
ejpam-6102	247	7	]	]	X
ejpam-6102	248	1	+	+	NOUN
ejpam-6102	248	2	o	o	X
ejpam-6102	248	3	(	(	PUNCT
ejpam-6102	248	4	∥v∥2	∥v∥2	VERB
ejpam-6102	248	5	+	+	CCONJ
ejpam-6102	248	6	∑	∑	SYM
ejpam-6102	248	7	1	1	NUM
ejpam-6102	248	8	µn	µn	PROPN
ejpam-6102	248	9	j	j	PROPN
ejpam-6102	248	10	+	+	CCONJ
ejpam-6102	248	11	∑	∑	PROPN
ejpam-6102	248	12	1	1	NUM
ejpam-6102	248	13	µn−2	µn−2	PROPN
ejpam-6102	248	14	j	j	PROPN
ejpam-6102	248	15	∫	∫	PROPN
ejpam-6102	248	16	bi	bi	PROPN
ejpam-6102	248	17	ωp−1	ωp−1	PROPN
ejpam-6102	248	18	ai,µi	ai,µi	NOUN
ejpam-6102	248	19	+	+	CCONJ
ejpam-6102	248	20	∥v∥p−ε	∥v∥p−ε	X
ejpam-6102	248	21	µ	µ	X
ejpam-6102	248	22	n−2	n−2	PROPN
ejpam-6102	248	23	2	2	NUM
ejpam-6102	249	1	i	i	NOUN
ejpam-6102	249	2	+	+	NOUN
ejpam-6102	249	3	1	1	NUM
ejpam-6102	249	4	µ	µ	X
ejpam-6102	249	5	n−2	n−2	PROPN
ejpam-6102	249	6	2	2	NUM
ejpam-6102	249	7	i	i	NOUN
ejpam-6102	249	8	∑∫	∑∫	PROPN
ejpam-6102	249	9	ω\bi	ω\bi	NOUN
ejpam-6102	249	10	ωp	ωp	NOUN
ejpam-6102	249	11	aj	aj	PROPN
ejpam-6102	249	12	,	,	PUNCT
ejpam-6102	249	13	µj	µj	PROPN
ejpam-6102	249	14	)	)	PUNCT
ejpam-6102	249	15	.	.	PUNCT
ejpam-6102	250	1	(	(	PUNCT
ejpam-6102	250	2	26	26	NUM
ejpam-6102	250	3	)	)	PUNCT
ejpam-6102	250	4	using	use	VERB
ejpam-6102	250	5	(	(	PUNCT
ejpam-6102	250	6	13	13	NUM
ejpam-6102	250	7	)	)	PUNCT
ejpam-6102	250	8	and	and	CCONJ
ejpam-6102	250	9	lemma	lemma	PROPN
ejpam-6102	250	10	5	5	NUM
ejpam-6102	250	11	,	,	PUNCT
ejpam-6102	250	12	we	we	PRON
ejpam-6102	250	13	get∫	get∫	VERB
ejpam-6102	250	14	bi	bi	PROPN
ejpam-6102	250	15	ωp−ε	ωp−ε	PROPN
ejpam-6102	250	16	ai,µi	ai,µi	PROPN
ejpam-6102	250	17	ωaj	ωaj	PROPN
ejpam-6102	250	18	,	,	PUNCT
ejpam-6102	250	19	µj	µj	PROPN
ejpam-6102	250	20	⩽	⩽	PROPN
ejpam-6102	250	21	c	c	PROPN
ejpam-6102	250	22	∫	∫	PROPN
ejpam-6102	251	1	bi	bi	PROPN
ejpam-6102	251	2	ωp	ωp	PROPN
ejpam-6102	251	3	ai,µi	ai,µi	PROPN
ejpam-6102	251	4	ωaj	ωaj	PROPN
ejpam-6102	251	5	,	,	PUNCT
ejpam-6102	251	6	µj	µj	PROPN
ejpam-6102	251	7	⩽	⩽	PROPN
ejpam-6102	251	8	c	c	PROPN
ejpam-6102	251	9	(	(	PUNCT
ejpam-6102	251	10	µiµj	µiµj	NOUN
ejpam-6102	251	11	)	)	PUNCT
ejpam-6102	251	12	(	(	PUNCT
ejpam-6102	251	13	n−2)/2	n−2)/2	ADJ
ejpam-6102	251	14	.	.	PUNCT
ejpam-6102	252	1	(	(	PUNCT
ejpam-6102	252	2	27	27	NUM
ejpam-6102	252	3	)	)	PUNCT
ejpam-6102	252	4	in	in	ADP
ejpam-6102	252	5	addition	addition	NOUN
ejpam-6102	252	6	,	,	PUNCT
ejpam-6102	252	7	using	use	VERB
ejpam-6102	252	8	(	(	PUNCT
ejpam-6102	252	9	13	13	NUM
ejpam-6102	252	10	)	)	PUNCT
ejpam-6102	252	11	,	,	PUNCT
ejpam-6102	252	12	(	(	PUNCT
ejpam-6102	252	13	17	17	NUM
ejpam-6102	252	14	)	)	PUNCT
ejpam-6102	252	15	and	and	CCONJ
ejpam-6102	252	16	lemma	lemma	PROPN
ejpam-6102	252	17	6	6	NUM
ejpam-6102	252	18	,	,	PUNCT
ejpam-6102	252	19	we	we	PRON
ejpam-6102	252	20	get∫	get∫	VERB
ejpam-6102	252	21	bi	bi	ADJ
ejpam-6102	252	22	fωp+1−ε	fωp+1−ε	PROPN
ejpam-6102	252	23	ai,µi	ai,µi	NOUN
ejpam-6102	253	1	=	=	PUNCT
ejpam-6102	253	2	β−ε	β−ε	PROPN
ejpam-6102	253	3	0	0	NUM
ejpam-6102	253	4	µ	µ	PROPN
ejpam-6102	253	5	−ε(n−2)/2	−ε(n−2)/2	PROPN
ejpam-6102	253	6	i	i	PRON
ejpam-6102	253	7	f(ai	f(ai	PROPN
ejpam-6102	253	8	)	)	PUNCT
ejpam-6102	253	9	∫	∫	PROPN
ejpam-6102	253	10	ω	ω	NUM
ejpam-6102	253	11	ωp+1	ωp+1	PROPN
ejpam-6102	253	12	ai,µi	ai,µi	NOUN
ejpam-6102	253	13	+	+	PROPN
ejpam-6102	253	14	o	o	PROPN
ejpam-6102	253	15	(	(	PUNCT
ejpam-6102	253	16	∫	∫	PROPN
ejpam-6102	253	17	ω\bi	ω\bi	PROPN
ejpam-6102	253	18	ωp+1	ωp+1	PROPN
ejpam-6102	253	19	ai,µi	ai,µi	NOUN
ejpam-6102	253	20	+	+	CCONJ
ejpam-6102	253	21	ε	ε	PROPN
ejpam-6102	253	22	∫	∫	PROPN
ejpam-6102	253	23	ω	ω	PROPN
ejpam-6102	253	24	ωp+1	ωp+1	PROPN
ejpam-6102	253	25	ai,µi	ai,µi	NOUN
ejpam-6102	253	26	ln	ln	NOUN
ejpam-6102	253	27	(	(	PUNCT
ejpam-6102	253	28	1	1	NUM
ejpam-6102	253	29	+	+	CCONJ
ejpam-6102	253	30	µ2	µ2	PROPN
ejpam-6102	253	31	i	i	PRON
ejpam-6102	253	32	|x−	|x−	PROPN
ejpam-6102	253	33	ai|2	ai|2	PROPN
ejpam-6102	253	34	)	)	PUNCT
ejpam-6102	254	1	+	+	CCONJ
ejpam-6102	254	2	∫	∫	PROPN
ejpam-6102	254	3	bi	bi	PROPN
ejpam-6102	254	4	|x−	|x−	PROPN
ejpam-6102	254	5	ai|ωp+1	ai|ωp+1	PROPN
ejpam-6102	254	6	ai,µi	ai,µi	PROPN
ejpam-6102	254	7	)	)	PUNCT
ejpam-6102	254	8	r.	r.	PROPN
ejpam-6102	254	9	almushahhin	almushahhin	PROPN
ejpam-6102	254	10	,	,	PUNCT
ejpam-6102	254	11	m.	m.	PROPN
ejpam-6102	254	12	ben	ben	PROPN
ejpam-6102	254	13	ayed	aye	VERB
ejpam-6102	254	14	/	/	SYM
ejpam-6102	254	15	eur	eur	PROPN
ejpam-6102	254	16	.	.	PUNCT
ejpam-6102	255	1	j.	j.	PROPN
ejpam-6102	255	2	pure	pure	PROPN
ejpam-6102	255	3	appl	appl	PROPN
ejpam-6102	255	4	.	.	PROPN
ejpam-6102	255	5	math	math	PROPN
ejpam-6102	255	6	,	,	PUNCT
ejpam-6102	255	7	18	18	NUM
ejpam-6102	255	8	(	(	PUNCT
ejpam-6102	255	9	2	2	NUM
ejpam-6102	255	10	)	)	PUNCT
ejpam-6102	255	11	(	(	PUNCT
ejpam-6102	255	12	2025	2025	NUM
ejpam-6102	255	13	)	)	PUNCT
ejpam-6102	255	14	,	,	PUNCT
ejpam-6102	255	15	6102	6102	NUM
ejpam-6102	255	16	11	11	NUM
ejpam-6102	255	17	of	of	ADP
ejpam-6102	255	18	31	31	NUM
ejpam-6102	255	19	=	=	SYM
ejpam-6102	255	20	β−ε	β−ε	PROPN
ejpam-6102	255	21	0	0	NUM
ejpam-6102	255	22	µ	µ	PROPN
ejpam-6102	255	23	−ε(n−2)/2	−ε(n−2)/2	NOUN
ejpam-6102	255	24	i	i	PRON
ejpam-6102	255	25	f(ai)sn	f(ai)sn	VERB
ejpam-6102	255	26	+	+	ADP
ejpam-6102	255	27	o	o	X
ejpam-6102	255	28	(	(	PUNCT
ejpam-6102	255	29	1	1	NUM
ejpam-6102	255	30	µi	µi	PROPN
ejpam-6102	255	31	+	+	CCONJ
ejpam-6102	255	32	ε	ε	PROPN
ejpam-6102	255	33	)	)	PUNCT
ejpam-6102	255	34	.	.	PUNCT
ejpam-6102	256	1	(	(	PUNCT
ejpam-6102	256	2	28	28	NUM
ejpam-6102	256	3	)	)	PUNCT
ejpam-6102	256	4	furthermore	furthermore	ADV
ejpam-6102	256	5	,	,	PUNCT
ejpam-6102	256	6	taking	take	VERB
ejpam-6102	256	7	ψ	ψ	X
ejpam-6102	256	8	=	=	PUNCT
ejpam-6102	256	9	ωa,µ	ωa,µ	PUNCT
ejpam-6102	256	10	in	in	ADP
ejpam-6102	256	11	lemma	lemma	PROPN
ejpam-6102	256	12	2	2	NUM
ejpam-6102	256	13	and	and	CCONJ
ejpam-6102	256	14	using	use	VERB
ejpam-6102	256	15	(	(	PUNCT
ejpam-6102	256	16	7	7	NUM
ejpam-6102	256	17	)	)	PUNCT
ejpam-6102	256	18	,	,	PUNCT
ejpam-6102	256	19	we	we	PRON
ejpam-6102	256	20	deduce	deduce	VERB
ejpam-6102	256	21	that∫	that∫	NOUN
ejpam-6102	256	22	bi	bi	ADJ
ejpam-6102	256	23	fωp−ε	fωp−ε	NOUN
ejpam-6102	256	24	ai,µi	ai,µi	NOUN
ejpam-6102	256	25	v	v	ADP
ejpam-6102	256	26	=	=	SYM
ejpam-6102	256	27	∫	∫	PROPN
ejpam-6102	256	28	ω	ω	NUM
ejpam-6102	256	29	fωp−ε	fωp−ε	NOUN
ejpam-6102	256	30	ai,µi	ai,µi	NOUN
ejpam-6102	256	31	v	v	ADP
ejpam-6102	256	32	+	+	PROPN
ejpam-6102	256	33	o	o	X
ejpam-6102	256	34	(	(	PUNCT
ejpam-6102	256	35	∫	∫	PROPN
ejpam-6102	256	36	ω\bi	ω\bi	PROPN
ejpam-6102	256	37	ωp	ωp	NOUN
ejpam-6102	256	38	ai,µi	ai,µi	NOUN
ejpam-6102	256	39	|v|	|v|	PROPN
ejpam-6102	256	40	)	)	PUNCT
ejpam-6102	257	1	=	=	SYM
ejpam-6102	257	2	o	o	NOUN
ejpam-6102	257	3	(	(	PUNCT
ejpam-6102	257	4	∥v∥	∥v∥	PROPN
ejpam-6102	257	5	[	[	PUNCT
ejpam-6102	257	6	ε+	ε+	X
ejpam-6102	257	7	1	1	NUM
ejpam-6102	257	8	µi	µi	PROPN
ejpam-6102	257	9	]	]	PUNCT
ejpam-6102	257	10	)	)	PUNCT
ejpam-6102	258	1	+	+	NOUN
ejpam-6102	258	2	o	o	NOUN
ejpam-6102	258	3	(	(	PUNCT
ejpam-6102	258	4	∥v∥	∥v∥	PROPN
ejpam-6102	258	5	µ	µ	X
ejpam-6102	258	6	(	(	PUNCT
ejpam-6102	258	7	n+2)/2	n+2)/2	NOUN
ejpam-6102	258	8	i	i	NOUN
ejpam-6102	258	9	)	)	PUNCT
ejpam-6102	259	1	=	=	PUNCT
ejpam-6102	259	2	o	o	NOUN
ejpam-6102	259	3	(	(	PUNCT
ejpam-6102	259	4	∥v∥	∥v∥	PROPN
ejpam-6102	259	5	[	[	PUNCT
ejpam-6102	259	6	ε+	ε+	X
ejpam-6102	259	7	1	1	NUM
ejpam-6102	259	8	µi	µi	PROPN
ejpam-6102	259	9	]	]	X
ejpam-6102	259	10	)	)	PUNCT
ejpam-6102	259	11	.	.	PUNCT
ejpam-6102	260	1	(	(	PUNCT
ejpam-6102	260	2	29	29	X
ejpam-6102	260	3	)	)	PUNCT
ejpam-6102	260	4	combining	combine	VERB
ejpam-6102	260	5	(	(	PUNCT
ejpam-6102	260	6	29	29	NUM
ejpam-6102	260	7	)	)	PUNCT
ejpam-6102	260	8	,	,	PUNCT
ejpam-6102	260	9	(	(	PUNCT
ejpam-6102	260	10	28	28	NUM
ejpam-6102	260	11	)	)	PUNCT
ejpam-6102	260	12	and	and	CCONJ
ejpam-6102	260	13	(	(	PUNCT
ejpam-6102	260	14	27	27	NUM
ejpam-6102	260	15	)	)	PUNCT
ejpam-6102	260	16	,	,	PUNCT
ejpam-6102	260	17	the	the	DET
ejpam-6102	260	18	equation	equation	NOUN
ejpam-6102	260	19	(	(	PUNCT
ejpam-6102	260	20	26	26	NUM
ejpam-6102	260	21	)	)	PUNCT
ejpam-6102	260	22	becomes∫	becomes∫	VERB
ejpam-6102	260	23	bi	bi	PROPN
ejpam-6102	260	24	f	f	PROPN
ejpam-6102	260	25	|ũ+	|ũ+	NUM
ejpam-6102	260	26	v|p−ε−1(ũ+	v|p−ε−1(ũ+	PROPN
ejpam-6102	260	27	v)ωai,µi	v)ωai,µi	NOUN
ejpam-6102	260	28	=	=	PUNCT
ejpam-6102	260	29	µ	µ	X
ejpam-6102	260	30	−ε(n−2)/2	−ε(n−2)/2	NOUN
ejpam-6102	260	31	i	i	PRON
ejpam-6102	260	32	αp−ε	αp−ε	VERB
ejpam-6102	260	33	i	i	PRON
ejpam-6102	260	34	f	f	X
ejpam-6102	260	35	(	(	PUNCT
ejpam-6102	260	36	ai)sn	ai)sn	X
ejpam-6102	261	1	+	+	NOUN
ejpam-6102	261	2	o	o	X
ejpam-6102	261	3	(	(	PUNCT
ejpam-6102	261	4	1	1	NUM
ejpam-6102	261	5	µi	µi	ADP
ejpam-6102	261	6	+	+	NUM
ejpam-6102	261	7	ε+	ε+	NOUN
ejpam-6102	261	8	∥v∥2	∥v∥2	X
ejpam-6102	261	9	)	)	PUNCT
ejpam-6102	261	10	.	.	PUNCT
ejpam-6102	262	1	(	(	PUNCT
ejpam-6102	262	2	30	30	X
ejpam-6102	262	3	)	)	PUNCT
ejpam-6102	262	4	combining	combine	VERB
ejpam-6102	262	5	(	(	PUNCT
ejpam-6102	262	6	23	23	NUM
ejpam-6102	262	7	)	)	PUNCT
ejpam-6102	262	8	and	and	CCONJ
ejpam-6102	262	9	(	(	PUNCT
ejpam-6102	262	10	30	30	NUM
ejpam-6102	262	11	)	)	PUNCT
ejpam-6102	262	12	,	,	PUNCT
ejpam-6102	262	13	the	the	DET
ejpam-6102	262	14	proof	proof	NOUN
ejpam-6102	262	15	of	of	ADP
ejpam-6102	262	16	proposition	proposition	NOUN
ejpam-6102	262	17	4	4	NUM
ejpam-6102	262	18	follows	follow	VERB
ejpam-6102	262	19	.	.	PUNCT
ejpam-6102	263	1	next	next	ADV
ejpam-6102	263	2	,	,	PUNCT
ejpam-6102	263	3	we	we	PRON
ejpam-6102	263	4	deal	deal	VERB
ejpam-6102	263	5	with	with	ADP
ejpam-6102	263	6	the	the	DET
ejpam-6102	263	7	expansion	expansion	NOUN
ejpam-6102	263	8	with	with	ADP
ejpam-6102	263	9	respect	respect	NOUN
ejpam-6102	263	10	to	to	ADP
ejpam-6102	263	11	µ.	µ.	NOUN
ejpam-6102	263	12	proposition	proposition	NOUN
ejpam-6102	263	13	5	5	NUM
ejpam-6102	263	14	.	.	PUNCT
ejpam-6102	264	1	let	let	VERB
ejpam-6102	264	2	(	(	PUNCT
ejpam-6102	264	3	a	a	PRON
ejpam-6102	264	4	,	,	PUNCT
ejpam-6102	264	5	µ	µ	NOUN
ejpam-6102	264	6	,	,	PUNCT
ejpam-6102	264	7	α	α	NOUN
ejpam-6102	264	8	)	)	PUNCT
ejpam-6102	264	9	∈	∈	PROPN
ejpam-6102	264	10	ϑ	ϑ	X
ejpam-6102	264	11	(	(	PUNCT
ejpam-6102	264	12	q	q	PROPN
ejpam-6102	264	13	,	,	PUNCT
ejpam-6102	264	14	γ0	γ0	NOUN
ejpam-6102	264	15	,	,	PUNCT
ejpam-6102	264	16	η0	η0	NOUN
ejpam-6102	264	17	)	)	PUNCT
ejpam-6102	264	18	and	and	CCONJ
ejpam-6102	264	19	v	v	ADP
ejpam-6102	264	20	∈	∈	PROPN
ejpam-6102	264	21	fa,µ.	fa,µ.	PROPN
ejpam-6102	264	22	for	for	ADP
ejpam-6102	264	23	ε	ε	PROPN
ejpam-6102	264	24	small	small	PROPN
ejpam-6102	264	25	and	and	CCONJ
ejpam-6102	264	26	i	i	PRON
ejpam-6102	264	27	⩽	⩽	NOUN
ejpam-6102	265	1	q	q	X
ejpam-6102	265	2	,	,	PUNCT
ejpam-6102	265	3	we	we	PRON
ejpam-6102	265	4	have	have	VERB
ejpam-6102	265	5	〈	〈	PROPN
ejpam-6102	265	6	∇jε(ũ+	∇jε(ũ+	PROPN
ejpam-6102	265	7	v),µi	v),µi	PROPN
ejpam-6102	265	8	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	265	9	∂µi	∂µi	PROPN
ejpam-6102	265	10	〉	〉	NOUN
ejpam-6102	265	11	=	=	PUNCT
ejpam-6102	265	12	n−	n−	NOUN
ejpam-6102	265	13	2	2	NUM
ejpam-6102	265	14	4	4	NUM
ejpam-6102	265	15	c6µ	c6µ	NOUN
ejpam-6102	265	16	−εn−2	−εn−2	ADP
ejpam-6102	265	17	2	2	NUM
ejpam-6102	265	18	i	i	PRON
ejpam-6102	265	19	αp−ε	αp−ε	VERB
ejpam-6102	266	1	i	i	PRON
ejpam-6102	266	2	f	f	X
ejpam-6102	266	3	(	(	PUNCT
ejpam-6102	266	4	ai	ai	PROPN
ejpam-6102	266	5	)	)	PUNCT
ejpam-6102	266	6	ε+	ε+	NOUN
ejpam-6102	266	7	αi	αi	PART
ejpam-6102	266	8	h	h	NOUN
ejpam-6102	266	9	(	(	PUNCT
ejpam-6102	266	10	ai	ai	PROPN
ejpam-6102	266	11	)	)	PUNCT
ejpam-6102	266	12	µi	µi	PROPN
ejpam-6102	266	13	(	(	PUNCT
ejpam-6102	266	14	c1	c1	PROPN
ejpam-6102	266	15	2	2	NUM
ejpam-6102	266	16	−	−	NOUN
ejpam-6102	266	17	µ−ε	µ−ε	NOUN
ejpam-6102	267	1	i	i	PRON
ejpam-6102	267	2	n−2	n−2	PROPN
ejpam-6102	267	3	2	2	NUM
ejpam-6102	267	4	αp−ε−1	αp−ε−1	NUM
ejpam-6102	267	5	i	i	PRON
ejpam-6102	267	6	f	f	X
ejpam-6102	267	7	(	(	PUNCT
ejpam-6102	267	8	ai	ai	PROPN
ejpam-6102	267	9	)	)	PUNCT
ejpam-6102	267	10	c4	c4	NOUN
ejpam-6102	267	11	)	)	PUNCT
ejpam-6102	267	12	−	−	PROPN
ejpam-6102	268	1	c5	c5	PROPN
ejpam-6102	268	2	µi	µi	PROPN
ejpam-6102	268	3	∂f	∂f	PROPN
ejpam-6102	268	4	∂ν	∂ν	PROPN
ejpam-6102	268	5	(	(	PUNCT
ejpam-6102	268	6	ai)µ	ai)µ	PROPN
ejpam-6102	268	7	−ε	−ε	NOUN
ejpam-6102	268	8	i	i	PRON
ejpam-6102	268	9	n−2	n−2	PROPN
ejpam-6102	268	10	2	2	NUM
ejpam-6102	268	11	αp−ε	αp−ε	VERB
ejpam-6102	268	12	i	i	PRON
ejpam-6102	268	13	+	+	NOUN
ejpam-6102	268	14	o	o	X
ejpam-6102	268	15	(	(	PUNCT
ejpam-6102	268	16	n=4	n=4	NOUN
ejpam-6102	268	17	)	)	PUNCT
ejpam-6102	268	18	(	(	PUNCT
ejpam-6102	268	19	lnµi	lnµi	NOUN
ejpam-6102	268	20	µ2	µ2	VERB
ejpam-6102	268	21	i	i	PRON
ejpam-6102	268	22	)	)	PUNCT
ejpam-6102	269	1	+	+	NOUN
ejpam-6102	269	2	o	o	NOUN
ejpam-6102	269	3	(	(	PUNCT
ejpam-6102	269	4	∥v∥2	∥v∥2	ADJ
ejpam-6102	269	5	+	+	CCONJ
ejpam-6102	269	6	ε2	ε2	ADJ
ejpam-6102	269	7	+	+	CCONJ
ejpam-6102	269	8	1	1	NUM
ejpam-6102	269	9	µ2	µ2	NOUN
ejpam-6102	269	10	i	i	NOUN
ejpam-6102	270	1	+	+	CCONJ
ejpam-6102	270	2	∑	∑	PROPN
ejpam-6102	270	3	1	1	NUM
ejpam-6102	270	4	µn−2	µn−2	PROPN
ejpam-6102	270	5	j	j	PROPN
ejpam-6102	270	6	)	)	PUNCT
ejpam-6102	270	7	,	,	PUNCT
ejpam-6102	270	8	where	where	SCONJ
ejpam-6102	270	9	o	o	X
ejpam-6102	270	10	(	(	PUNCT
ejpam-6102	270	11	n=4	n=4	NOUN
ejpam-6102	270	12	)	)	PUNCT
ejpam-6102	270	13	appears	appear	VERB
ejpam-6102	270	14	only	only	ADV
ejpam-6102	270	15	if	if	SCONJ
ejpam-6102	270	16	n	n	NOUN
ejpam-6102	270	17	=	=	SYM
ejpam-6102	270	18	4	4	NUM
ejpam-6102	270	19	and	and	CCONJ
ejpam-6102	270	20	the	the	DET
ejpam-6102	270	21	constants	constant	NOUN
ejpam-6102	270	22	c1	c1	PROPN
ejpam-6102	270	23	,	,	PUNCT
ejpam-6102	270	24	c4	c4	NOUN
ejpam-6102	270	25	,	,	PUNCT
ejpam-6102	270	26	c5	c5	PROPN
ejpam-6102	270	27	and	and	CCONJ
ejpam-6102	270	28	c6	c6	PROPN
ejpam-6102	270	29	are	be	AUX
ejpam-6102	270	30	defined	define	VERB
ejpam-6102	270	31	in	in	ADP
ejpam-6102	270	32	(	(	PUNCT
ejpam-6102	270	33	55	55	NUM
ejpam-6102	270	34	)	)	PUNCT
ejpam-6102	270	35	,	,	PUNCT
ejpam-6102	270	36	(	(	PUNCT
ejpam-6102	270	37	56	56	NUM
ejpam-6102	270	38	)	)	PUNCT
ejpam-6102	270	39	,	,	PUNCT
ejpam-6102	270	40	(	(	PUNCT
ejpam-6102	270	41	57	57	NUM
ejpam-6102	270	42	)	)	PUNCT
ejpam-6102	270	43	,	,	PUNCT
ejpam-6102	270	44	(	(	PUNCT
ejpam-6102	270	45	58	58	NUM
ejpam-6102	270	46	)	)	PUNCT
ejpam-6102	270	47	respectively	respectively	ADV
ejpam-6102	270	48	.	.	PUNCT
ejpam-6102	271	1	proof	proof	NOUN
ejpam-6102	271	2	.	.	PUNCT
ejpam-6102	272	1	observe	observe	VERB
ejpam-6102	272	2	that	that	SCONJ
ejpam-6102	272	3	,	,	PUNCT
ejpam-6102	272	4	using	use	VERB
ejpam-6102	272	5	lemmas	lemmas	PROPN
ejpam-6102	272	6	4	4	NUM
ejpam-6102	272	7	,	,	PUNCT
ejpam-6102	272	8	5	5	NUM
ejpam-6102	272	9	,	,	PUNCT
ejpam-6102	272	10	9	9	NUM
ejpam-6102	272	11	and	and	CCONJ
ejpam-6102	272	12	the	the	DET
ejpam-6102	272	13	fact	fact	NOUN
ejpam-6102	272	14	that	that	SCONJ
ejpam-6102	272	15	v	v	X
ejpam-6102	272	16	∈	∈	PROPN
ejpam-6102	272	17	fa,µ	fa,µ	NOUN
ejpam-6102	272	18	,	,	PUNCT
ejpam-6102	272	19	we	we	PRON
ejpam-6102	272	20	obtain	obtain	VERB
ejpam-6102	272	21	〈	〈	PROPN
ejpam-6102	272	22	ũ+	ũ+	NUM
ejpam-6102	272	23	v	v	NOUN
ejpam-6102	272	24	,	,	PUNCT
ejpam-6102	272	25	µi	µi	PROPN
ejpam-6102	272	26	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	272	27	∂µi	∂µi	PROPN
ejpam-6102	272	28	〉	〉	NOUN
ejpam-6102	272	29	=	=	SYM
ejpam-6102	273	1	q∑	q∑	NOUN
ejpam-6102	273	2	j=1	j=1	NOUN
ejpam-6102	273	3	αj	αj	PROPN
ejpam-6102	273	4	〈	〈	PROPN
ejpam-6102	273	5	ωaj	ωaj	PROPN
ejpam-6102	273	6	,	,	PUNCT
ejpam-6102	273	7	µj	µj	INTJ
ejpam-6102	273	8	,	,	PUNCT
ejpam-6102	273	9	µi	µi	PROPN
ejpam-6102	273	10	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	273	11	∂µi	∂µi	PROPN
ejpam-6102	273	12	〉	〉	NOUN
ejpam-6102	273	13	=	=	SYM
ejpam-6102	273	14	c1	c1	NOUN
ejpam-6102	273	15	2	2	NUM
ejpam-6102	273	16	αi	αi	NOUN
ejpam-6102	273	17	h	h	NOUN
ejpam-6102	273	18	(	(	PUNCT
ejpam-6102	273	19	ai	ai	PROPN
ejpam-6102	273	20	)	)	PUNCT
ejpam-6102	273	21	µi	µi	PROPN
ejpam-6102	274	1	+	+	PROPN
ejpam-6102	274	2	o	o	X
ejpam-6102	274	3	(	(	PUNCT
ejpam-6102	274	4	1	1	NUM
ejpam-6102	274	5	µ2	µ2	NOUN
ejpam-6102	274	6	i	i	PRON
ejpam-6102	274	7	+	+	CCONJ
ejpam-6102	274	8	∑	∑	PROPN
ejpam-6102	274	9	1	1	NUM
ejpam-6102	274	10	µn−2	µn−2	PROPN
ejpam-6102	274	11	k	k	PROPN
ejpam-6102	274	12	)	)	PUNCT
ejpam-6102	275	1	+	+	NUM
ejpam-6102	275	2	o	o	X
ejpam-6102	275	3	(	(	PUNCT
ejpam-6102	275	4	n=4	n=4	NOUN
ejpam-6102	275	5	)	)	PUNCT
ejpam-6102	275	6	(	(	PUNCT
ejpam-6102	275	7	lnµi	lnµi	NOUN
ejpam-6102	275	8	µ2	µ2	NOUN
ejpam-6102	275	9	i	i	PRON
ejpam-6102	275	10	)	)	PUNCT
ejpam-6102	275	11	.	.	PUNCT
ejpam-6102	276	1	(	(	PUNCT
ejpam-6102	276	2	31	31	NUM
ejpam-6102	276	3	)	)	PUNCT
ejpam-6102	276	4	in	in	ADP
ejpam-6102	276	5	addition	addition	NOUN
ejpam-6102	276	6	,	,	PUNCT
ejpam-6102	276	7	using	use	VERB
ejpam-6102	276	8	(	(	PUNCT
ejpam-6102	276	9	24	24	NUM
ejpam-6102	276	10	)	)	PUNCT
ejpam-6102	276	11	and	and	CCONJ
ejpam-6102	276	12	(	(	PUNCT
ejpam-6102	276	13	25	25	NUM
ejpam-6102	276	14	)	)	PUNCT
ejpam-6102	276	15	,	,	PUNCT
ejpam-6102	276	16	we	we	PRON
ejpam-6102	276	17	get∫	get∫	VERB
ejpam-6102	276	18	ω	ω	NUM
ejpam-6102	276	19	f	f	PROPN
ejpam-6102	276	20	|ũ+	|ũ+	NUM
ejpam-6102	276	21	v|p−ε−1(ũ+	v|p−ε−1(ũ+	NOUN
ejpam-6102	276	22	v)µi	v)µi	PROPN
ejpam-6102	276	23	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	276	24	∂µi	∂µi	PROPN
ejpam-6102	276	25	=	=	PUNCT
ejpam-6102	276	26	αp−ε	αp−ε	PROPN
ejpam-6102	276	27	i	i	PRON
ejpam-6102	276	28	∫	∫	VERB
ejpam-6102	276	29	bi	bi	ADJ
ejpam-6102	276	30	fωp−ε	fωp−ε	PROPN
ejpam-6102	276	31	ai,µi	ai,µi	NOUN
ejpam-6102	276	32	µi	µi	PROPN
ejpam-6102	276	33	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	276	34	∂µi	∂µi	PROPN
ejpam-6102	276	35	+	+	CCONJ
ejpam-6102	276	36	(	(	PUNCT
ejpam-6102	276	37	p−	p−	NOUN
ejpam-6102	276	38	ε)αp−ε−1	ε)αp−ε−1	PROPN
ejpam-6102	276	39	i	i	PRON
ejpam-6102	276	40	∫	∫	PROPN
ejpam-6102	276	41	bi	bi	PROPN
ejpam-6102	276	42	fωp−ε−1	fωp−ε−1	PROPN
ejpam-6102	276	43	ai,µi	ai,µi	PROPN
ejpam-6102	276	44	vµi	vµi	NOUN
ejpam-6102	276	45	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	276	46	∂µi	∂µi	PROPN
ejpam-6102	277	1	+	+	PROPN
ejpam-6102	277	2	o	o	X
ejpam-6102	277	3	(	(	PUNCT
ejpam-6102	277	4	∑	∑	PUNCT
ejpam-6102	277	5	j	j	PROPN
ejpam-6102	277	6	̸=i	̸=i	PROPN
ejpam-6102	277	7	1	1	NUM
ejpam-6102	277	8	µ	µ	X
ejpam-6102	277	9	(	(	PUNCT
ejpam-6102	277	10	n−2)/2	n−2)/2	PROPN
ejpam-6102	277	11	j	j	PROPN
ejpam-6102	277	12	∫	∫	PROPN
ejpam-6102	277	13	bi	bi	PROPN
ejpam-6102	277	14	ωp	ωp	PROPN
ejpam-6102	277	15	ai,µi	ai,µi	NOUN
ejpam-6102	278	1	+	+	CCONJ
ejpam-6102	278	2	∑	∑	PROPN
ejpam-6102	278	3	j	j	PROPN
ejpam-6102	278	4	̸=i	̸=i	PROPN
ejpam-6102	278	5	1	1	NUM
ejpam-6102	278	6	µn−2	µn−2	PROPN
ejpam-6102	278	7	j	j	PROPN
ejpam-6102	278	8	∫	∫	PROPN
ejpam-6102	278	9	bi	bi	PROPN
ejpam-6102	278	10	ωp−1	ωp−1	PROPN
ejpam-6102	278	11	ai,µi	ai,µi	NOUN
ejpam-6102	279	1	+	+	CCONJ
ejpam-6102	279	2	∑	∑	PROPN
ejpam-6102	279	3	1	1	NUM
ejpam-6102	279	4	µn	µn	PROPN
ejpam-6102	279	5	j	j	PROPN
ejpam-6102	279	6	+	+	CCONJ
ejpam-6102	279	7	∥v∥2	∥v∥2	ADJ
ejpam-6102	279	8	+	+	CCONJ
ejpam-6102	279	9	1	1	NUM
ejpam-6102	279	10	µ	µ	X
ejpam-6102	279	11	(	(	PUNCT
ejpam-6102	279	12	n−2)/2	n−2)/2	NOUN
ejpam-6102	279	13	i	i	PRON
ejpam-6102	279	14	(	(	PUNCT
ejpam-6102	279	15	∥v∥p−ε	∥v∥p−ε	X
ejpam-6102	279	16	+	+	CCONJ
ejpam-6102	279	17	∑∫	∑∫	PROPN
ejpam-6102	279	18	ω	ω	PROPN
ejpam-6102	279	19	ωp	ωp	NOUN
ejpam-6102	279	20	aj	aj	PROPN
ejpam-6102	279	21	,	,	PUNCT
ejpam-6102	279	22	µj	µj	PROPN
ejpam-6102	279	23	)	)	PUNCT
ejpam-6102	279	24	)	)	PUNCT
ejpam-6102	279	25	.	.	PUNCT
ejpam-6102	280	1	(	(	PUNCT
ejpam-6102	280	2	32	32	NUM
ejpam-6102	280	3	)	)	PUNCT
ejpam-6102	280	4	notice	notice	VERB
ejpam-6102	280	5	that	that	SCONJ
ejpam-6102	280	6	,	,	PUNCT
ejpam-6102	280	7	the	the	DET
ejpam-6102	280	8	remainder	remainder	NOUN
ejpam-6102	280	9	term	term	NOUN
ejpam-6102	280	10	can	can	AUX
ejpam-6102	280	11	be	be	AUX
ejpam-6102	280	12	estimated	estimate	VERB
ejpam-6102	280	13	as	as	ADP
ejpam-6102	280	14	o	o	PROPN
ejpam-6102	280	15	(	(	PUNCT
ejpam-6102	280	16	q∑	q∑	NOUN
ejpam-6102	280	17	j=1	j=1	NOUN
ejpam-6102	280	18	1	1	NUM
ejpam-6102	280	19	µn−2	µn−2	PROPN
ejpam-6102	280	20	j	j	PROPN
ejpam-6102	280	21	+	+	CCONJ
ejpam-6102	280	22	∥v∥2	∥v∥2	ADJ
ejpam-6102	280	23	)	)	PUNCT
ejpam-6102	280	24	.	.	PUNCT
ejpam-6102	281	1	r.	r.	PROPN
ejpam-6102	281	2	almushahhin	almushahhin	PROPN
ejpam-6102	281	3	,	,	PUNCT
ejpam-6102	281	4	m.	m.	PROPN
ejpam-6102	281	5	ben	ben	PROPN
ejpam-6102	281	6	ayed	aye	VERB
ejpam-6102	281	7	/	/	SYM
ejpam-6102	281	8	eur	eur	PROPN
ejpam-6102	281	9	.	.	PUNCT
ejpam-6102	282	1	j.	j.	PROPN
ejpam-6102	282	2	pure	pure	PROPN
ejpam-6102	282	3	appl	appl	PROPN
ejpam-6102	282	4	.	.	PROPN
ejpam-6102	282	5	math	math	PROPN
ejpam-6102	282	6	,	,	PUNCT
ejpam-6102	282	7	18	18	NUM
ejpam-6102	282	8	(	(	PUNCT
ejpam-6102	282	9	2	2	NUM
ejpam-6102	282	10	)	)	PUNCT
ejpam-6102	282	11	(	(	PUNCT
ejpam-6102	282	12	2025	2025	NUM
ejpam-6102	282	13	)	)	PUNCT
ejpam-6102	282	14	,	,	PUNCT
ejpam-6102	282	15	6102	6102	NUM
ejpam-6102	282	16	12	12	NUM
ejpam-6102	282	17	of	of	ADP
ejpam-6102	282	18	31	31	NUM
ejpam-6102	282	19	furthermore	furthermore	ADV
ejpam-6102	282	20	,	,	PUNCT
ejpam-6102	282	21	taking	take	VERB
ejpam-6102	282	22	ψ	ψ	X
ejpam-6102	282	23	=	=	PUNCT
ejpam-6102	282	24	µ∂ωa,µ/∂µ	µ∂ωa,µ/∂µ	NOUN
ejpam-6102	282	25	in	in	ADP
ejpam-6102	282	26	lemma	lemma	PROPN
ejpam-6102	282	27	2	2	NUM
ejpam-6102	282	28	and	and	CCONJ
ejpam-6102	282	29	using	use	VERB
ejpam-6102	282	30	(	(	PUNCT
ejpam-6102	282	31	7	7	NUM
ejpam-6102	282	32	)	)	PUNCT
ejpam-6102	282	33	,	,	PUNCT
ejpam-6102	282	34	we	we	PRON
ejpam-6102	282	35	get∫	get∫	VERB
ejpam-6102	282	36	bi	bi	ADJ
ejpam-6102	282	37	fωp−ε−1	fωp−ε−1	PROPN
ejpam-6102	282	38	ai,µi	ai,µi	PROPN
ejpam-6102	282	39	vµi	vµi	NOUN
ejpam-6102	282	40	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	282	41	∂µi	∂µi	PROPN
ejpam-6102	282	42	=	=	SYM
ejpam-6102	282	43	∫	∫	PROPN
ejpam-6102	282	44	ω	ω	NUM
ejpam-6102	282	45	fωp−ε−1	fωp−ε−1	NOUN
ejpam-6102	282	46	ai,µi	ai,µi	ADJ
ejpam-6102	282	47	vµi	vµi	NOUN
ejpam-6102	282	48	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	282	49	∂µi	∂µi	PROPN
ejpam-6102	283	1	+	+	PROPN
ejpam-6102	283	2	o	o	PROPN
ejpam-6102	283	3	(	(	PUNCT
ejpam-6102	283	4	∫	∫	PROPN
ejpam-6102	283	5	ω\bi	ω\bi	PROPN
ejpam-6102	283	6	ωp	ωp	NOUN
ejpam-6102	283	7	ai,µi	ai,µi	NOUN
ejpam-6102	283	8	|v|	|v|	PROPN
ejpam-6102	283	9	)	)	PUNCT
ejpam-6102	284	1	=	=	SYM
ejpam-6102	284	2	o	o	NOUN
ejpam-6102	284	3	(	(	PUNCT
ejpam-6102	284	4	∥v∥	∥v∥	PROPN
ejpam-6102	284	5	[	[	PUNCT
ejpam-6102	284	6	ε+	ε+	X
ejpam-6102	284	7	1	1	NUM
ejpam-6102	284	8	µi	µi	PROPN
ejpam-6102	284	9	]	]	PUNCT
ejpam-6102	284	10	)	)	PUNCT
ejpam-6102	285	1	+	+	NOUN
ejpam-6102	285	2	o	o	NOUN
ejpam-6102	285	3	(	(	PUNCT
ejpam-6102	285	4	∥v∥	∥v∥	PROPN
ejpam-6102	285	5	µ	µ	X
ejpam-6102	285	6	(	(	PUNCT
ejpam-6102	285	7	n+2)/2	n+2)/2	NOUN
ejpam-6102	285	8	i	i	NOUN
ejpam-6102	285	9	)	)	PUNCT
ejpam-6102	286	1	=	=	PUNCT
ejpam-6102	286	2	o	o	NOUN
ejpam-6102	286	3	(	(	PUNCT
ejpam-6102	286	4	∥v∥	∥v∥	PROPN
ejpam-6102	286	5	[	[	PUNCT
ejpam-6102	286	6	ε+	ε+	X
ejpam-6102	286	7	1	1	NUM
ejpam-6102	286	8	µi	µi	PROPN
ejpam-6102	286	9	]	]	X
ejpam-6102	286	10	)	)	PUNCT
ejpam-6102	286	11	.	.	PUNCT
ejpam-6102	287	1	(	(	PUNCT
ejpam-6102	287	2	33	33	NUM
ejpam-6102	287	3	)	)	PUNCT
ejpam-6102	287	4	to	to	PART
ejpam-6102	287	5	complete	complete	VERB
ejpam-6102	287	6	the	the	DET
ejpam-6102	287	7	estimate	estimate	NOUN
ejpam-6102	287	8	of	of	ADP
ejpam-6102	287	9	(	(	PUNCT
ejpam-6102	287	10	32	32	NUM
ejpam-6102	287	11	)	)	PUNCT
ejpam-6102	287	12	,	,	PUNCT
ejpam-6102	287	13	using	use	VERB
ejpam-6102	287	14	(	(	PUNCT
ejpam-6102	287	15	12	12	NUM
ejpam-6102	287	16	)	)	PUNCT
ejpam-6102	287	17	,	,	PUNCT
ejpam-6102	287	18	we	we	PRON
ejpam-6102	287	19	write∫	write∫	VERB
ejpam-6102	287	20	bi	bi	ADJ
ejpam-6102	287	21	fωp−ε	fωp−ε	PROPN
ejpam-6102	287	22	ai,µi	ai,µi	NOUN
ejpam-6102	287	23	µi	µi	PROPN
ejpam-6102	287	24	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	287	25	∂µi	∂µi	PROPN
ejpam-6102	287	26	=	=	PUNCT
ejpam-6102	287	27	β−ε	β−ε	PROPN
ejpam-6102	287	28	0	0	NUM
ejpam-6102	287	29	µ	µ	X
ejpam-6102	287	30	−εn−2	−εn−2	ADP
ejpam-6102	287	31	2	2	NUM
ejpam-6102	287	32	i	i	PRON
ejpam-6102	288	1	[	[	X
ejpam-6102	288	2	∫	∫	X
ejpam-6102	288	3	bi	bi	ADJ
ejpam-6102	288	4	fωp	fωp	PROPN
ejpam-6102	288	5	ai,µi	ai,µi	NOUN
ejpam-6102	288	6	µi	µi	PROPN
ejpam-6102	288	7	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	288	8	∂µi	∂µi	PROPN
ejpam-6102	289	1	+	+	CCONJ
ejpam-6102	289	2	n−	n−	NOUN
ejpam-6102	289	3	2	2	NUM
ejpam-6102	289	4	2	2	NUM
ejpam-6102	289	5	ε×	ε×	NOUN
ejpam-6102	289	6	×	×	NOUN
ejpam-6102	289	7	∫	∫	PROPN
ejpam-6102	289	8	bi	bi	PROPN
ejpam-6102	289	9	fωp	fωp	PROPN
ejpam-6102	289	10	ai,µi	ai,µi	NOUN
ejpam-6102	289	11	µi	µi	PROPN
ejpam-6102	289	12	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	289	13	∂µi	∂µi	PROPN
ejpam-6102	289	14	ln	ln	ADV
ejpam-6102	290	1	(	(	PUNCT
ejpam-6102	290	2	1	1	NUM
ejpam-6102	290	3	+	+	CCONJ
ejpam-6102	290	4	µ2	µ2	PROPN
ejpam-6102	290	5	i	i	PRON
ejpam-6102	290	6	|x−	|x−	PROPN
ejpam-6102	290	7	ai|2	ai|2	PROPN
ejpam-6102	290	8	)	)	PUNCT
ejpam-6102	290	9	]	]	PUNCT
ejpam-6102	291	1	+	+	PUNCT
ejpam-6102	291	2	o	o	X
ejpam-6102	291	3	(	(	PUNCT
ejpam-6102	291	4	ε2	ε2	PROPN
ejpam-6102	291	5	∫	∫	PROPN
ejpam-6102	291	6	bi	bi	PROPN
ejpam-6102	291	7	ωp+1	ωp+1	PROPN
ejpam-6102	291	8	ai,µi	ai,µi	NOUN
ejpam-6102	291	9	ln2	ln2	NOUN
ejpam-6102	291	10	(	(	PUNCT
ejpam-6102	291	11	1	1	NUM
ejpam-6102	291	12	+	+	CCONJ
ejpam-6102	291	13	µ2	µ2	PROPN
ejpam-6102	291	14	i	i	PRON
ejpam-6102	291	15	|x−	|x−	PROPN
ejpam-6102	291	16	ai|2	ai|2	PROPN
ejpam-6102	291	17	)	)	PUNCT
ejpam-6102	291	18	)	)	PUNCT
ejpam-6102	291	19	.	.	PUNCT
ejpam-6102	292	1	(	(	PUNCT
ejpam-6102	292	2	34	34	NUM
ejpam-6102	292	3	)	)	PUNCT
ejpam-6102	292	4	expanding	expand	VERB
ejpam-6102	292	5	f	f	PROPN
ejpam-6102	292	6	around	around	ADP
ejpam-6102	292	7	ai	ai	ADP
ejpam-6102	292	8	and	and	CCONJ
ejpam-6102	292	9	using	use	VERB
ejpam-6102	292	10	lemmas	lemmas	PROPN
ejpam-6102	292	11	6	6	NUM
ejpam-6102	292	12	and	and	CCONJ
ejpam-6102	292	13	8	8	NUM
ejpam-6102	292	14	,	,	PUNCT
ejpam-6102	292	15	we	we	PRON
ejpam-6102	292	16	obtain∫	obtain∫	VERB
ejpam-6102	292	17	bi	bi	ADJ
ejpam-6102	292	18	fωp	fωp	NOUN
ejpam-6102	292	19	ai,µi	ai,µi	NOUN
ejpam-6102	292	20	µi	µi	PROPN
ejpam-6102	292	21	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	292	22	∂µi	∂µi	PROPN
ejpam-6102	292	23	=	=	SYM
ejpam-6102	292	24	f(ai	f(ai	PROPN
ejpam-6102	292	25	)	)	PUNCT
ejpam-6102	292	26	∫	∫	PROPN
ejpam-6102	292	27	bi	bi	PROPN
ejpam-6102	292	28	ωp	ωp	PROPN
ejpam-6102	292	29	ai,µi	ai,µi	NOUN
ejpam-6102	292	30	µi	µi	PROPN
ejpam-6102	292	31	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	292	32	∂µi	∂µi	PROPN
ejpam-6102	293	1	+	+	PROPN
ejpam-6102	293	2	∇f	∇f	PROPN
ejpam-6102	293	3	(	(	PUNCT
ejpam-6102	293	4	ai	ai	PROPN
ejpam-6102	293	5	)	)	PUNCT
ejpam-6102	293	6	∫	∫	PROPN
ejpam-6102	293	7	bi	bi	PROPN
ejpam-6102	293	8	(	(	PUNCT
ejpam-6102	293	9	x−	x−	PROPN
ejpam-6102	293	10	ai)ω	ai)ω	PROPN
ejpam-6102	293	11	p	p	PROPN
ejpam-6102	293	12	ai,µi	ai,µi	NOUN
ejpam-6102	293	13	µi	µi	PROPN
ejpam-6102	293	14	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	293	15	∂µi	∂µi	PROPN
ejpam-6102	294	1	+	+	PROPN
ejpam-6102	294	2	o	o	PROPN
ejpam-6102	294	3	(	(	PUNCT
ejpam-6102	294	4	∫	∫	PROPN
ejpam-6102	294	5	bi	bi	PROPN
ejpam-6102	294	6	|x−	|x−	PROPN
ejpam-6102	294	7	ai|2	ai|2	PROPN
ejpam-6102	294	8	ωp	ωp	PRON
ejpam-6102	294	9	ai,µi	ai,µi	NOUN
ejpam-6102	294	10	)	)	PUNCT
ejpam-6102	295	1	=	=	SYM
ejpam-6102	295	2	f	f	X
ejpam-6102	295	3	(	(	PUNCT
ejpam-6102	295	4	ai	ai	PROPN
ejpam-6102	295	5	)	)	PUNCT
ejpam-6102	295	6	(	(	PUNCT
ejpam-6102	295	7	c4	c4	NOUN
ejpam-6102	295	8	h	h	NOUN
ejpam-6102	295	9	(	(	PUNCT
ejpam-6102	295	10	ai	ai	PROPN
ejpam-6102	295	11	)	)	PUNCT
ejpam-6102	295	12	µi	µi	PROPN
ejpam-6102	296	1	+	+	PROPN
ejpam-6102	296	2	o	o	X
ejpam-6102	296	3	(	(	PUNCT
ejpam-6102	296	4	1	1	NUM
ejpam-6102	296	5	µ2	µ2	NOUN
ejpam-6102	296	6	i	i	PROPN
ejpam-6102	296	7	)	)	PUNCT
ejpam-6102	296	8	)	)	PUNCT
ejpam-6102	297	1	+	+	CCONJ
ejpam-6102	298	1	∂f	∂f	PROPN
ejpam-6102	298	2	∂ν	∂ν	NOUN
ejpam-6102	298	3	(	(	PUNCT
ejpam-6102	298	4	ai	ai	PROPN
ejpam-6102	298	5	)	)	PUNCT
ejpam-6102	298	6	(	(	PUNCT
ejpam-6102	298	7	c5	c5	PROPN
ejpam-6102	298	8	µi	µi	PROPN
ejpam-6102	299	1	+	+	PROPN
ejpam-6102	299	2	o	o	X
ejpam-6102	299	3	(	(	PUNCT
ejpam-6102	299	4	1	1	NUM
ejpam-6102	299	5	µ2	µ2	NOUN
ejpam-6102	299	6	i	i	PRON
ejpam-6102	299	7	)	)	PUNCT
ejpam-6102	299	8	)	)	PUNCT
ejpam-6102	300	1	+	+	ADP
ejpam-6102	300	2	o	o	X
ejpam-6102	300	3	(	(	PUNCT
ejpam-6102	300	4	1	1	NUM
ejpam-6102	300	5	µ2	µ2	NOUN
ejpam-6102	300	6	i	i	PROPN
ejpam-6102	300	7	)	)	PUNCT
ejpam-6102	300	8	.	.	PUNCT
ejpam-6102	301	1	for	for	ADP
ejpam-6102	301	2	the	the	DET
ejpam-6102	301	3	second	second	ADJ
ejpam-6102	301	4	integral	integral	NOUN
ejpam-6102	301	5	in	in	ADP
ejpam-6102	301	6	the	the	DET
ejpam-6102	301	7	right	right	ADJ
ejpam-6102	301	8	hand	hand	NOUN
ejpam-6102	301	9	side	side	NOUN
ejpam-6102	301	10	of	of	ADP
ejpam-6102	301	11	(	(	PUNCT
ejpam-6102	301	12	34	34	NUM
ejpam-6102	301	13	)	)	PUNCT
ejpam-6102	301	14	,	,	PUNCT
ejpam-6102	301	15	expanding	expand	VERB
ejpam-6102	301	16	f	f	PROPN
ejpam-6102	301	17	around	around	ADP
ejpam-6102	301	18	ai	ai	ADP
ejpam-6102	301	19	and	and	CCONJ
ejpam-6102	301	20	using	use	VERB
ejpam-6102	301	21	lemma	lemma	PROPN
ejpam-6102	301	22	8	8	NUM
ejpam-6102	301	23	,	,	PUNCT
ejpam-6102	301	24	we	we	PRON
ejpam-6102	301	25	get	get	VERB
ejpam-6102	301	26	∫	∫	PROPN
ejpam-6102	301	27	bi	bi	ADJ
ejpam-6102	301	28	fωp	fωp	PROPN
ejpam-6102	301	29	ai,µi	ai,µi	NOUN
ejpam-6102	301	30	µi	µi	PROPN
ejpam-6102	301	31	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	302	1	∂µi	∂µi	PROPN
ejpam-6102	302	2	ln	ln	ADV
ejpam-6102	302	3	(	(	PUNCT
ejpam-6102	302	4	1	1	NUM
ejpam-6102	302	5	+	+	CCONJ
ejpam-6102	302	6	µ2	µ2	PROPN
ejpam-6102	302	7	i	i	PRON
ejpam-6102	302	8	|x−	|x−	PROPN
ejpam-6102	302	9	ai|2	ai|2	PROPN
ejpam-6102	302	10	)	)	PUNCT
ejpam-6102	303	1	=	=	SYM
ejpam-6102	303	2	f	f	PROPN
ejpam-6102	303	3	(	(	PUNCT
ejpam-6102	303	4	ai	ai	PROPN
ejpam-6102	303	5	)	)	PUNCT
ejpam-6102	303	6	(	(	PUNCT
ejpam-6102	303	7	−c6	−c6	SYM
ejpam-6102	303	8	2	2	NUM
ejpam-6102	303	9	+	+	NOUN
ejpam-6102	303	10	o	o	X
ejpam-6102	303	11	(	(	PUNCT
ejpam-6102	303	12	1	1	NUM
ejpam-6102	303	13	µi	µi	NOUN
ejpam-6102	303	14	)	)	PUNCT
ejpam-6102	303	15	)	)	PUNCT
ejpam-6102	304	1	+	+	ADP
ejpam-6102	304	2	o	o	NOUN
ejpam-6102	304	3	(	(	PUNCT
ejpam-6102	304	4	1	1	NUM
ejpam-6102	304	5	µi	µi	ADV
ejpam-6102	304	6	)	)	PUNCT
ejpam-6102	304	7	.	.	PUNCT
ejpam-6102	305	1	thus	thus	ADV
ejpam-6102	305	2	,	,	PUNCT
ejpam-6102	305	3	using	use	VERB
ejpam-6102	305	4	(	(	PUNCT
ejpam-6102	305	5	17	17	NUM
ejpam-6102	305	6	)	)	PUNCT
ejpam-6102	305	7	,	,	PUNCT
ejpam-6102	305	8	(	(	PUNCT
ejpam-6102	305	9	34	34	NUM
ejpam-6102	305	10	)	)	PUNCT
ejpam-6102	305	11	becomes∫	becomes∫	VERB
ejpam-6102	305	12	bi	bi	ADJ
ejpam-6102	305	13	fωp−ε	fωp−ε	PROPN
ejpam-6102	305	14	ai,µi	ai,µi	NOUN
ejpam-6102	305	15	µi	µi	PROPN
ejpam-6102	305	16	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	305	17	∂µi	∂µi	PROPN
ejpam-6102	305	18	=	=	PRON
ejpam-6102	305	19	β−ε	β−ε	PROPN
ejpam-6102	305	20	0	0	NUM
ejpam-6102	305	21	µ	µ	X
ejpam-6102	305	22	−εn−2	−εn−2	ADP
ejpam-6102	305	23	2	2	NUM
ejpam-6102	305	24	i	i	PROPN
ejpam-6102	305	25	[	[	PUNCT
ejpam-6102	305	26	c4f(ai	c4f(ai	PROPN
ejpam-6102	305	27	)	)	PUNCT
ejpam-6102	305	28	h	h	NOUN
ejpam-6102	305	29	(	(	PUNCT
ejpam-6102	305	30	ai	ai	PROPN
ejpam-6102	305	31	)	)	PUNCT
ejpam-6102	305	32	µi	µi	PROPN
ejpam-6102	306	1	+	+	CCONJ
ejpam-6102	306	2	c5	c5	PROPN
ejpam-6102	306	3	µi	µi	PROPN
ejpam-6102	306	4	∂f	∂f	PROPN
ejpam-6102	306	5	∂ν	∂ν	PROPN
ejpam-6102	306	6	(	(	PUNCT
ejpam-6102	306	7	ai)−	ai)−	NOUN
ejpam-6102	306	8	n−	n−	NOUN
ejpam-6102	306	9	2	2	NUM
ejpam-6102	306	10	4	4	NUM
ejpam-6102	306	11	c6f	c6f	ADJ
ejpam-6102	306	12	(	(	PUNCT
ejpam-6102	306	13	ai	ai	NOUN
ejpam-6102	306	14	)	)	PUNCT
ejpam-6102	306	15	ε	ε	PROPN
ejpam-6102	306	16	]	]	PUNCT
ejpam-6102	307	1	+	+	PUNCT
ejpam-6102	307	2	o	o	X
ejpam-6102	307	3	(	(	PUNCT
ejpam-6102	307	4	ε2	ε2	ADJ
ejpam-6102	307	5	+	+	CCONJ
ejpam-6102	307	6	1	1	NUM
ejpam-6102	307	7	µ2	µ2	NOUN
ejpam-6102	307	8	i	i	PROPN
ejpam-6102	307	9	)	)	PUNCT
ejpam-6102	307	10	.	.	PUNCT
ejpam-6102	308	1	(	(	PUNCT
ejpam-6102	308	2	35	35	NUM
ejpam-6102	308	3	)	)	PUNCT
ejpam-6102	308	4	this	this	PRON
ejpam-6102	308	5	completes	complete	VERB
ejpam-6102	308	6	the	the	DET
ejpam-6102	308	7	proof	proof	NOUN
ejpam-6102	308	8	of	of	ADP
ejpam-6102	308	9	(	(	PUNCT
ejpam-6102	308	10	32	32	NUM
ejpam-6102	308	11	)	)	PUNCT
ejpam-6102	308	12	and	and	CCONJ
ejpam-6102	308	13	we	we	PRON
ejpam-6102	308	14	get	get	VERB
ejpam-6102	308	15	(	(	PUNCT
ejpam-6102	308	16	by	by	ADP
ejpam-6102	308	17	combining	combine	VERB
ejpam-6102	308	18	(	(	PUNCT
ejpam-6102	308	19	35	35	NUM
ejpam-6102	308	20	)	)	PUNCT
ejpam-6102	308	21	and	and	CCONJ
ejpam-6102	308	22	(	(	PUNCT
ejpam-6102	308	23	33))∫	33))∫	PROPN
ejpam-6102	308	24	ω	ω	NUM
ejpam-6102	308	25	f	f	PROPN
ejpam-6102	308	26	|ũ+	|ũ+	NUM
ejpam-6102	308	27	v|p−ε−1(ũ+	v|p−ε−1(ũ+	NOUN
ejpam-6102	308	28	v)µi	v)µi	PROPN
ejpam-6102	308	29	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	308	30	∂µi	∂µi	PROPN
ejpam-6102	308	31	=	=	PUNCT
ejpam-6102	308	32	β−ε	β−ε	PROPN
ejpam-6102	308	33	0	0	NUM
ejpam-6102	308	34	µ	µ	X
ejpam-6102	308	35	−εn−2	−εn−2	ADP
ejpam-6102	308	36	2	2	NUM
ejpam-6102	308	37	i	i	NOUN
ejpam-6102	308	38	[	[	PUNCT
ejpam-6102	308	39	c4f	c4f	X
ejpam-6102	308	40	(	(	PUNCT
ejpam-6102	308	41	ai	ai	NOUN
ejpam-6102	308	42	)	)	PUNCT
ejpam-6102	308	43	h	h	NOUN
ejpam-6102	308	44	(	(	PUNCT
ejpam-6102	308	45	ai	ai	PROPN
ejpam-6102	308	46	)	)	PUNCT
ejpam-6102	308	47	µi	µi	PROPN
ejpam-6102	309	1	+	+	CCONJ
ejpam-6102	309	2	c5	c5	PROPN
ejpam-6102	309	3	µi	µi	PROPN
ejpam-6102	309	4	∂f	∂f	PROPN
ejpam-6102	309	5	∂ν	∂ν	X
ejpam-6102	309	6	(	(	PUNCT
ejpam-6102	309	7	ai	ai	NOUN
ejpam-6102	309	8	)	)	PUNCT
ejpam-6102	309	9	−n−	−n−	NOUN
ejpam-6102	309	10	2	2	NUM
ejpam-6102	309	11	4	4	NUM
ejpam-6102	309	12	c6f	c6f	ADJ
ejpam-6102	309	13	(	(	PUNCT
ejpam-6102	309	14	ai	ai	NOUN
ejpam-6102	309	15	)	)	PUNCT
ejpam-6102	309	16	ε	ε	PROPN
ejpam-6102	309	17	]	]	PUNCT
ejpam-6102	310	1	+	+	NOUN
ejpam-6102	310	2	o	o	X
ejpam-6102	310	3	(	(	PUNCT
ejpam-6102	310	4	∥v∥2	∥v∥2	ADJ
ejpam-6102	310	5	+	+	CCONJ
ejpam-6102	310	6	ε2	ε2	ADJ
ejpam-6102	310	7	+	+	CCONJ
ejpam-6102	310	8	1	1	NUM
ejpam-6102	310	9	µi	µi	ADP
ejpam-6102	310	10	2	2	NUM
ejpam-6102	310	11	+	+	CCONJ
ejpam-6102	310	12	∑	∑	PROPN
ejpam-6102	310	13	1	1	NUM
ejpam-6102	310	14	µn−2	µn−2	PROPN
ejpam-6102	310	15	j	j	PROPN
ejpam-6102	310	16	)	)	PUNCT
ejpam-6102	310	17	.	.	PUNCT
ejpam-6102	311	1	(	(	PUNCT
ejpam-6102	311	2	36	36	NUM
ejpam-6102	311	3	)	)	PUNCT
ejpam-6102	311	4	thus	thus	ADV
ejpam-6102	311	5	,	,	PUNCT
ejpam-6102	311	6	combining	combine	VERB
ejpam-6102	311	7	(	(	PUNCT
ejpam-6102	311	8	36	36	NUM
ejpam-6102	311	9	)	)	PUNCT
ejpam-6102	311	10	and	and	CCONJ
ejpam-6102	311	11	(	(	PUNCT
ejpam-6102	311	12	31	31	NUM
ejpam-6102	311	13	)	)	PUNCT
ejpam-6102	311	14	,	,	PUNCT
ejpam-6102	311	15	the	the	DET
ejpam-6102	311	16	proof	proof	NOUN
ejpam-6102	311	17	of	of	ADP
ejpam-6102	311	18	proposition	proposition	NOUN
ejpam-6102	311	19	5	5	NUM
ejpam-6102	311	20	follows	follow	VERB
ejpam-6102	311	21	.	.	PUNCT
ejpam-6102	312	1	we	we	PRON
ejpam-6102	312	2	end	end	VERB
ejpam-6102	312	3	this	this	DET
ejpam-6102	312	4	section	section	NOUN
ejpam-6102	312	5	by	by	ADP
ejpam-6102	312	6	expanding	expand	VERB
ejpam-6102	312	7	the	the	DET
ejpam-6102	312	8	gradient	gradient	NOUN
ejpam-6102	312	9	of	of	ADP
ejpam-6102	312	10	jε	jε	ADP
ejpam-6102	312	11	with	with	ADP
ejpam-6102	312	12	respect	respect	NOUN
ejpam-6102	312	13	to	to	ADP
ejpam-6102	312	14	the	the	DET
ejpam-6102	312	15	concentration	concentration	NOUN
ejpam-6102	312	16	point	point	NOUN
ejpam-6102	312	17	a.	a.	PROPN
ejpam-6102	312	18	r.	r.	PROPN
ejpam-6102	312	19	almushahhin	almushahhin	PROPN
ejpam-6102	312	20	,	,	PUNCT
ejpam-6102	312	21	m.	m.	PROPN
ejpam-6102	312	22	ben	ben	PROPN
ejpam-6102	312	23	ayed	aye	VERB
ejpam-6102	312	24	/	/	SYM
ejpam-6102	312	25	eur	eur	PROPN
ejpam-6102	312	26	.	.	PUNCT
ejpam-6102	313	1	j.	j.	PROPN
ejpam-6102	313	2	pure	pure	PROPN
ejpam-6102	313	3	appl	appl	PROPN
ejpam-6102	313	4	.	.	PROPN
ejpam-6102	313	5	math	math	PROPN
ejpam-6102	313	6	,	,	PUNCT
ejpam-6102	313	7	18	18	NUM
ejpam-6102	313	8	(	(	PUNCT
ejpam-6102	313	9	2	2	NUM
ejpam-6102	313	10	)	)	PUNCT
ejpam-6102	313	11	(	(	PUNCT
ejpam-6102	313	12	2025	2025	NUM
ejpam-6102	313	13	)	)	PUNCT
ejpam-6102	313	14	,	,	PUNCT
ejpam-6102	313	15	6102	6102	NUM
ejpam-6102	313	16	13	13	NUM
ejpam-6102	313	17	of	of	ADP
ejpam-6102	313	18	31	31	NUM
ejpam-6102	313	19	proposition	proposition	NOUN
ejpam-6102	313	20	6	6	NUM
ejpam-6102	313	21	.	.	PUNCT
ejpam-6102	314	1	let	let	VERB
ejpam-6102	314	2	(	(	PUNCT
ejpam-6102	314	3	a	a	PRON
ejpam-6102	314	4	,	,	PUNCT
ejpam-6102	314	5	µ	µ	NOUN
ejpam-6102	314	6	,	,	PUNCT
ejpam-6102	314	7	α	α	NOUN
ejpam-6102	314	8	)	)	PUNCT
ejpam-6102	314	9	∈	∈	PROPN
ejpam-6102	314	10	ϑ	ϑ	X
ejpam-6102	314	11	(	(	PUNCT
ejpam-6102	314	12	q	q	PROPN
ejpam-6102	314	13	,	,	PUNCT
ejpam-6102	314	14	γ0	γ0	NOUN
ejpam-6102	314	15	,	,	PUNCT
ejpam-6102	314	16	η0	η0	NOUN
ejpam-6102	314	17	)	)	PUNCT
ejpam-6102	314	18	and	and	CCONJ
ejpam-6102	314	19	v	v	ADP
ejpam-6102	314	20	∈	∈	PRON
ejpam-6102	315	1	fa,µ.	fa,µ.	ADJ
ejpam-6102	315	2	let	let	VERB
ejpam-6102	315	3	i	i	PRON
ejpam-6102	315	4	∈	∈	PROPN
ejpam-6102	315	5	{	{	PUNCT
ejpam-6102	315	6	1	1	NUM
ejpam-6102	315	7	,	,	PUNCT
ejpam-6102	315	8	.	.	PUNCT
ejpam-6102	315	9	.	.	PUNCT
ejpam-6102	316	1	.	.	PUNCT
ejpam-6102	317	1	,	,	PUNCT
ejpam-6102	317	2	q	q	X
ejpam-6102	317	3	}	}	PUNCT
ejpam-6102	317	4	,	,	PUNCT
ejpam-6102	317	5	we	we	PRON
ejpam-6102	317	6	denote	denote	VERB
ejpam-6102	317	7	by	by	ADP
ejpam-6102	317	8	(	(	PUNCT
ejpam-6102	317	9	σk	σk	INTJ
ejpam-6102	317	10	i	i	PROPN
ejpam-6102	317	11	)	)	PUNCT
ejpam-6102	317	12	,	,	PUNCT
ejpam-6102	317	13	where	where	SCONJ
ejpam-6102	317	14	1	1	NUM
ejpam-6102	317	15	⩽	⩽	NOUN
ejpam-6102	317	16	k	k	PROPN
ejpam-6102	317	17	⩽	⩽	PROPN
ejpam-6102	317	18	n−	n−	PROPN
ejpam-6102	317	19	1	1	NUM
ejpam-6102	317	20	,	,	PUNCT
ejpam-6102	317	21	an	an	DET
ejpam-6102	317	22	orthonormal	orthonormal	ADJ
ejpam-6102	317	23	system	system	NOUN
ejpam-6102	317	24	of	of	ADP
ejpam-6102	317	25	coordinates	coordinate	NOUN
ejpam-6102	317	26	on	on	ADP
ejpam-6102	317	27	the	the	DET
ejpam-6102	317	28	tangent	tangent	ADJ
ejpam-6102	317	29	space	space	NOUN
ejpam-6102	317	30	to	to	ADP
ejpam-6102	317	31	the	the	DET
ejpam-6102	317	32	boundary	boundary	ADJ
ejpam-6102	317	33	∂ω	∂ω	PROPN
ejpam-6102	317	34	at	at	ADP
ejpam-6102	317	35	ai	ai	NOUN
ejpam-6102	317	36	.	.	PUNCT
ejpam-6102	318	1	it	it	PRON
ejpam-6102	318	2	holds	hold	VERB
ejpam-6102	318	3	〈	〈	PROPN
ejpam-6102	318	4	∇jε(ũ+	∇jε(ũ+	PROPN
ejpam-6102	318	5	v	v	NOUN
ejpam-6102	318	6	)	)	PUNCT
ejpam-6102	318	7	,	,	PUNCT
ejpam-6102	318	8	1	1	NUM
ejpam-6102	318	9	µi	µi	ADP
ejpam-6102	318	10	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	319	1	∂σk	∂σk	ADV
ejpam-6102	320	1	i	i	PRON
ejpam-6102	320	2	〉	〉	NOUN
ejpam-6102	320	3	=	=	SYM
ejpam-6102	320	4	−c7µ	−c7µ	PROPN
ejpam-6102	320	5	−εn−2	−εn−2	ADP
ejpam-6102	320	6	2	2	NUM
ejpam-6102	320	7	i	i	PRON
ejpam-6102	320	8	αp−ε	αp−ε	VERB
ejpam-6102	320	9	i	i	PRON
ejpam-6102	320	10	1	1	X
ejpam-6102	320	11	µi	µi	ADP
ejpam-6102	320	12	∂f	∂f	PROPN
ejpam-6102	321	1	∂σk	∂σk	NOUN
ejpam-6102	321	2	i	i	PRON
ejpam-6102	321	3	(	(	PUNCT
ejpam-6102	321	4	ai	ai	NOUN
ejpam-6102	321	5	)	)	PUNCT
ejpam-6102	322	1	+	+	NOUN
ejpam-6102	322	2	o	o	X
ejpam-6102	322	3	(	(	PUNCT
ejpam-6102	322	4	ε2	ε2	ADJ
ejpam-6102	322	5	+	+	CCONJ
ejpam-6102	322	6	1	1	NUM
ejpam-6102	322	7	µ2	µ2	NOUN
ejpam-6102	322	8	i	i	NOUN
ejpam-6102	322	9	+	+	CCONJ
ejpam-6102	322	10	∑	∑	PROPN
ejpam-6102	322	11	1	1	NUM
ejpam-6102	322	12	µn−2	µn−2	PROPN
ejpam-6102	322	13	j	j	PROPN
ejpam-6102	322	14	+	+	CCONJ
ejpam-6102	322	15	∥v∥2	∥v∥2	PROPN
ejpam-6102	322	16	)	)	PUNCT
ejpam-6102	322	17	where	where	SCONJ
ejpam-6102	322	18	c7	c7	PROPN
ejpam-6102	322	19	is	be	AUX
ejpam-6102	322	20	defined	define	VERB
ejpam-6102	322	21	in	in	ADP
ejpam-6102	322	22	(	(	PUNCT
ejpam-6102	322	23	59	59	NUM
ejpam-6102	322	24	)	)	PUNCT
ejpam-6102	322	25	.	.	PUNCT
ejpam-6102	323	1	proof	proof	NOUN
ejpam-6102	323	2	.	.	PUNCT
ejpam-6102	324	1	to	to	PART
ejpam-6102	324	2	simply	simply	ADV
ejpam-6102	324	3	the	the	DET
ejpam-6102	324	4	presentation	presentation	NOUN
ejpam-6102	324	5	,	,	PUNCT
ejpam-6102	324	6	without	without	ADP
ejpam-6102	324	7	loss	loss	NOUN
ejpam-6102	324	8	of	of	ADP
ejpam-6102	324	9	generality	generality	NOUN
ejpam-6102	324	10	,	,	PUNCT
ejpam-6102	324	11	we	we	PRON
ejpam-6102	324	12	will	will	AUX
ejpam-6102	324	13	assume	assume	VERB
ejpam-6102	324	14	that	that	SCONJ
ejpam-6102	324	15	ai	ai	VERB
ejpam-6102	324	16	=	=	SYM
ejpam-6102	324	17	0	0	NUM
ejpam-6102	324	18	and	and	CCONJ
ejpam-6102	324	19	the	the	DET
ejpam-6102	324	20	normal	normal	ADJ
ejpam-6102	324	21	exterior	exterior	ADJ
ejpam-6102	324	22	vector	vector	NOUN
ejpam-6102	324	23	νai	νai	NOUN
ejpam-6102	325	1	=	=	SYM
ejpam-6102	325	2	−en	−en	PROPN
ejpam-6102	325	3	.	.	PUNCT
ejpam-6102	325	4	by	by	ADP
ejpam-6102	325	5	this	this	DET
ejpam-6102	325	6	choose	choose	NOUN
ejpam-6102	325	7	,	,	PUNCT
ejpam-6102	325	8	we	we	PRON
ejpam-6102	325	9	deduce	deduce	VERB
ejpam-6102	325	10	that	that	SCONJ
ejpam-6102	325	11	the	the	DET
ejpam-6102	325	12	tangent	tangent	ADJ
ejpam-6102	325	13	space	space	NOUN
ejpam-6102	325	14	to	to	ADP
ejpam-6102	325	15	the	the	DET
ejpam-6102	325	16	boundary	boundary	ADJ
ejpam-6102	325	17	∂ω	∂ω	PROPN
ejpam-6102	325	18	at	at	ADP
ejpam-6102	325	19	the	the	DET
ejpam-6102	325	20	point	point	NOUN
ejpam-6102	325	21	ai	ai	VERB
ejpam-6102	325	22	=	=	SYM
ejpam-6102	325	23	0	0	NUM
ejpam-6102	325	24	is	be	AUX
ejpam-6102	325	25	rn−1	rn−1	PROPN
ejpam-6102	325	26	×	×	NOUN
ejpam-6102	325	27	{	{	PUNCT
ejpam-6102	325	28	0	0	NUM
ejpam-6102	325	29	}	}	PUNCT
ejpam-6102	325	30	.	.	PUNCT
ejpam-6102	326	1	let	let	VERB
ejpam-6102	326	2	k	k	PROPN
ejpam-6102	326	3	∈	∈	PROPN
ejpam-6102	326	4	{	{	PUNCT
ejpam-6102	326	5	1	1	NUM
ejpam-6102	326	6	,	,	PUNCT
ejpam-6102	326	7	·	·	PUNCT
ejpam-6102	326	8	·	·	PUNCT
ejpam-6102	326	9	·	·	PUNCT
ejpam-6102	326	10	,	,	PUNCT
ejpam-6102	326	11	n−	n−	NOUN
ejpam-6102	326	12	1	1	NUM
ejpam-6102	326	13	}	}	PUNCT
ejpam-6102	326	14	,	,	PUNCT
ejpam-6102	326	15	using	use	VERB
ejpam-6102	326	16	lemmas	lemmas	PROPN
ejpam-6102	326	17	4	4	NUM
ejpam-6102	326	18	,	,	PUNCT
ejpam-6102	326	19	5	5	NUM
ejpam-6102	326	20	,	,	PUNCT
ejpam-6102	326	21	the	the	DET
ejpam-6102	326	22	proof	proof	NOUN
ejpam-6102	326	23	is	be	AUX
ejpam-6102	326	24	similar	similar	ADJ
ejpam-6102	326	25	to	to	ADP
ejpam-6102	326	26	the	the	DET
ejpam-6102	326	27	proof	proof	NOUN
ejpam-6102	326	28	of	of	ADP
ejpam-6102	326	29	proposition	proposition	NOUN
ejpam-6102	326	30	5	5	NUM
ejpam-6102	326	31	.	.	PUNCT
ejpam-6102	327	1	here	here	ADV
ejpam-6102	327	2	,	,	PUNCT
ejpam-6102	327	3	we	we	PRON
ejpam-6102	327	4	will	will	AUX
ejpam-6102	327	5	give	give	VERB
ejpam-6102	327	6	a	a	DET
ejpam-6102	327	7	sketch	sketch	NOUN
ejpam-6102	327	8	and	and	CCONJ
ejpam-6102	327	9	precise	precise	ADJ
ejpam-6102	327	10	the	the	DET
ejpam-6102	327	11	argument	argument	NOUN
ejpam-6102	327	12	of	of	ADP
ejpam-6102	327	13	the	the	DET
ejpam-6102	327	14	estimate	estimate	NOUN
ejpam-6102	327	15	of	of	ADP
ejpam-6102	327	16	some	some	DET
ejpam-6102	327	17	integrals	integral	NOUN
ejpam-6102	327	18	.	.	PUNCT
ejpam-6102	328	1	using	use	VERB
ejpam-6102	328	2	lemma	lemma	PROPN
ejpam-6102	328	3	9	9	NUM
ejpam-6102	328	4	and	and	CCONJ
ejpam-6102	328	5	the	the	DET
ejpam-6102	328	6	fact	fact	NOUN
ejpam-6102	328	7	that	that	SCONJ
ejpam-6102	328	8	v	v	X
ejpam-6102	328	9	∈	∈	PROPN
ejpam-6102	328	10	fa,µ	fa,µ	NOUN
ejpam-6102	328	11	,	,	PUNCT
ejpam-6102	328	12	we	we	PRON
ejpam-6102	328	13	deduce	deduce	VERB
ejpam-6102	328	14	that	that	SCONJ
ejpam-6102	328	15	〈	〈	PROPN
ejpam-6102	328	16	ũ+	ũ+	NUM
ejpam-6102	328	17	v	v	NOUN
ejpam-6102	328	18	,	,	PUNCT
ejpam-6102	328	19	1	1	NUM
ejpam-6102	328	20	µi	µi	ADP
ejpam-6102	328	21	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	328	22	∂ai	∂ai	PROPN
ejpam-6102	328	23	,	,	PUNCT
ejpam-6102	328	24	k	k	X
ejpam-6102	328	25	〉	〉	NOUN
ejpam-6102	328	26	=	=	SYM
ejpam-6102	329	1	q∑	q∑	NOUN
ejpam-6102	329	2	j=1	j=1	NOUN
ejpam-6102	329	3	αj	αj	PROPN
ejpam-6102	329	4	〈	〈	PROPN
ejpam-6102	329	5	ωaj	ωaj	PROPN
ejpam-6102	329	6	,	,	PUNCT
ejpam-6102	329	7	µj	µj	INTJ
ejpam-6102	329	8	,	,	PUNCT
ejpam-6102	329	9	1	1	NUM
ejpam-6102	329	10	µi	µi	ADP
ejpam-6102	329	11	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	329	12	∂ai	∂ai	PROPN
ejpam-6102	329	13	,	,	PUNCT
ejpam-6102	329	14	k	k	X
ejpam-6102	329	15	〉	〉	NOUN
ejpam-6102	329	16	=	=	PUNCT
ejpam-6102	329	17	o	o	X
ejpam-6102	329	18	(	(	PUNCT
ejpam-6102	329	19	1	1	NUM
ejpam-6102	329	20	µ2	µ2	NOUN
ejpam-6102	329	21	i	i	PRON
ejpam-6102	329	22	+	+	CCONJ
ejpam-6102	329	23	∑	∑	PROPN
ejpam-6102	329	24	1	1	NUM
ejpam-6102	329	25	µn−1	µn−1	PROPN
ejpam-6102	329	26	j	j	PROPN
ejpam-6102	329	27	)	)	PUNCT
ejpam-6102	329	28	.	.	PUNCT
ejpam-6102	330	1	for	for	ADP
ejpam-6102	330	2	the	the	DET
ejpam-6102	330	3	other	other	ADJ
ejpam-6102	330	4	part	part	NOUN
ejpam-6102	330	5	of	of	ADP
ejpam-6102	330	6	the	the	DET
ejpam-6102	330	7	gradient	gradient	NOUN
ejpam-6102	330	8	,	,	PUNCT
ejpam-6102	330	9	using	use	VERB
ejpam-6102	330	10	(	(	PUNCT
ejpam-6102	330	11	24	24	NUM
ejpam-6102	330	12	)	)	PUNCT
ejpam-6102	330	13	and	and	CCONJ
ejpam-6102	330	14	(	(	PUNCT
ejpam-6102	330	15	25	25	NUM
ejpam-6102	330	16	)	)	PUNCT
ejpam-6102	330	17	,	,	PUNCT
ejpam-6102	330	18	we	we	PRON
ejpam-6102	330	19	deduce	deduce	VERB
ejpam-6102	330	20	that	that	SCONJ
ejpam-6102	330	21	(	(	PUNCT
ejpam-6102	330	22	32	32	NUM
ejpam-6102	330	23	)	)	PUNCT
ejpam-6102	330	24	,	,	PUNCT
ejpam-6102	330	25	(	(	PUNCT
ejpam-6102	330	26	33	33	NUM
ejpam-6102	330	27	)	)	PUNCT
ejpam-6102	330	28	and	and	CCONJ
ejpam-6102	330	29	(	(	PUNCT
ejpam-6102	330	30	34	34	NUM
ejpam-6102	330	31	)	)	PUNCT
ejpam-6102	330	32	hold	hold	VERB
ejpam-6102	330	33	true	true	ADJ
ejpam-6102	330	34	by	by	ADP
ejpam-6102	330	35	taking	take	VERB
ejpam-6102	330	36	1	1	NUM
ejpam-6102	330	37	µi	µi	PROPN
ejpam-6102	330	38	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	330	39	∂ai	∂ai	PROPN
ejpam-6102	330	40	,	,	PUNCT
ejpam-6102	330	41	k	k	PROPN
ejpam-6102	330	42	instead	instead	ADV
ejpam-6102	330	43	of	of	ADP
ejpam-6102	330	44	µi	µi	PROPN
ejpam-6102	330	45	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	330	46	∂µi	∂µi	PROPN
ejpam-6102	330	47	.	.	PUNCT
ejpam-6102	331	1	now	now	ADV
ejpam-6102	331	2	,	,	PUNCT
ejpam-6102	331	3	using	use	VERB
ejpam-6102	331	4	lemmas	lemmas	PROPN
ejpam-6102	331	5	6	6	NUM
ejpam-6102	331	6	and	and	CCONJ
ejpam-6102	331	7	8	8	NUM
ejpam-6102	331	8	,	,	PUNCT
ejpam-6102	331	9	it	it	PRON
ejpam-6102	331	10	holds∫	holds∫	VERB
ejpam-6102	331	11	bi	bi	ADJ
ejpam-6102	331	12	fωp	fωp	NOUN
ejpam-6102	331	13	ai,µi	ai,µi	NOUN
ejpam-6102	331	14	1	1	NUM
ejpam-6102	332	1	µi	µi	ADP
ejpam-6102	332	2	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	332	3	∂ai	∂ai	PROPN
ejpam-6102	332	4	,	,	PUNCT
ejpam-6102	333	1	k	k	PROPN
ejpam-6102	333	2	=	=	SYM
ejpam-6102	333	3	f	f	PROPN
ejpam-6102	333	4	(	(	PUNCT
ejpam-6102	333	5	ai	ai	PROPN
ejpam-6102	333	6	)	)	PUNCT
ejpam-6102	333	7	∫	∫	PROPN
ejpam-6102	334	1	bi	bi	PROPN
ejpam-6102	334	2	ωp	ωp	PROPN
ejpam-6102	334	3	ai,µi	ai,µi	NOUN
ejpam-6102	334	4	1	1	NUM
ejpam-6102	334	5	µi	µi	ADP
ejpam-6102	334	6	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	334	7	∂ai	∂ai	PROPN
ejpam-6102	334	8	,	,	PUNCT
ejpam-6102	334	9	k	k	PROPN
ejpam-6102	334	10	+	+	PROPN
ejpam-6102	334	11	∇f	∇f	PROPN
ejpam-6102	334	12	(	(	PUNCT
ejpam-6102	334	13	ai	ai	PROPN
ejpam-6102	334	14	)	)	PUNCT
ejpam-6102	334	15	∫	∫	PROPN
ejpam-6102	335	1	bi	bi	PROPN
ejpam-6102	335	2	(	(	PUNCT
ejpam-6102	335	3	x−	x−	PROPN
ejpam-6102	335	4	ai)ω	ai)ω	PROPN
ejpam-6102	335	5	p	p	PROPN
ejpam-6102	335	6	ai,µi	ai,µi	NOUN
ejpam-6102	335	7	1	1	NUM
ejpam-6102	335	8	µi	µi	PROPN
ejpam-6102	335	9	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	335	10	∂ai	∂ai	PROPN
ejpam-6102	335	11	,	,	PUNCT
ejpam-6102	335	12	k	k	PROPN
ejpam-6102	336	1	+	+	PROPN
ejpam-6102	336	2	o	o	PROPN
ejpam-6102	336	3	(	(	PUNCT
ejpam-6102	336	4	∫	∫	PROPN
ejpam-6102	336	5	bi	bi	PROPN
ejpam-6102	336	6	|x−	|x−	PROPN
ejpam-6102	336	7	ai|2ωp+1	ai|2ωp+1	NOUN
ejpam-6102	336	8	ai,µi	ai,µi	ADJ
ejpam-6102	336	9	)	)	PUNCT
ejpam-6102	337	1	=	=	SYM
ejpam-6102	337	2	c7	c7	PROPN
ejpam-6102	337	3	µi	µi	PROPN
ejpam-6102	337	4	∂f	∂f	PROPN
ejpam-6102	337	5	∂xi	∂xi	NOUN
ejpam-6102	337	6	(	(	PUNCT
ejpam-6102	337	7	ai	ai	NOUN
ejpam-6102	337	8	)	)	PUNCT
ejpam-6102	338	1	+	+	NOUN
ejpam-6102	338	2	o	o	NOUN
ejpam-6102	338	3	(	(	PUNCT
ejpam-6102	338	4	1	1	NUM
ejpam-6102	338	5	µ2	µ2	NOUN
ejpam-6102	338	6	i	i	PROPN
ejpam-6102	338	7	)	)	PUNCT
ejpam-6102	338	8	,	,	PUNCT
ejpam-6102	338	9	∫	∫	PROPN
ejpam-6102	338	10	bi	bi	PROPN
ejpam-6102	338	11	fωp	fωp	PROPN
ejpam-6102	338	12	ai,µi	ai,µi	NOUN
ejpam-6102	338	13	1	1	NUM
ejpam-6102	338	14	µi	µi	ADP
ejpam-6102	338	15	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	338	16	∂ai	∂ai	PROPN
ejpam-6102	338	17	,	,	PUNCT
ejpam-6102	338	18	k	k	PROPN
ejpam-6102	338	19	ln	ln	X
ejpam-6102	339	1	(	(	PUNCT
ejpam-6102	339	2	1	1	NUM
ejpam-6102	339	3	+	+	CCONJ
ejpam-6102	339	4	µ2	µ2	PROPN
ejpam-6102	339	5	i	i	PRON
ejpam-6102	339	6	|x−	|x−	PROPN
ejpam-6102	339	7	ai|2	ai|2	PROPN
ejpam-6102	339	8	)	)	PUNCT
ejpam-6102	340	1	=	=	PUNCT
ejpam-6102	340	2	o	o	NOUN
ejpam-6102	340	3	(	(	PUNCT
ejpam-6102	340	4	1	1	NUM
ejpam-6102	340	5	µi	µi	ADV
ejpam-6102	340	6	)	)	PUNCT
ejpam-6102	340	7	,	,	PUNCT
ejpam-6102	340	8	by	by	ADP
ejpam-6102	340	9	expanding	expand	VERB
ejpam-6102	340	10	f	f	PROPN
ejpam-6102	340	11	around	around	ADP
ejpam-6102	340	12	ai	ai	PROPN
ejpam-6102	340	13	.	.	PUNCT
ejpam-6102	341	1	hence	hence	ADV
ejpam-6102	341	2	,	,	PUNCT
ejpam-6102	341	3	we	we	PRON
ejpam-6102	341	4	obtain∫	obtain∫	VERB
ejpam-6102	341	5	bi	bi	ADJ
ejpam-6102	341	6	fωp−ε	fωp−ε	NOUN
ejpam-6102	341	7	ai,µi	ai,µi	NOUN
ejpam-6102	341	8	1	1	NUM
ejpam-6102	342	1	µi	µi	ADP
ejpam-6102	342	2	∂ωai,µi	∂ωai,µi	PROPN
ejpam-6102	342	3	∂ai	∂ai	PROPN
ejpam-6102	342	4	,	,	PUNCT
ejpam-6102	342	5	k	k	PROPN
ejpam-6102	342	6	=	=	PUNCT
ejpam-6102	342	7	β−ε	β−ε	PROPN
ejpam-6102	342	8	0	0	NUM
ejpam-6102	342	9	µ	µ	PRON
ejpam-6102	342	10	−ε(n−2)/2	−ε(n−2)/2	X
ejpam-6102	342	11	i	i	PRON
ejpam-6102	342	12	c7	c7	PROPN
ejpam-6102	342	13	µi	µi	PROPN
ejpam-6102	342	14	∂f	∂f	PROPN
ejpam-6102	342	15	∂xk	∂xk	PROPN
ejpam-6102	342	16	(	(	PUNCT
ejpam-6102	342	17	ai	ai	NOUN
ejpam-6102	342	18	)	)	PUNCT
ejpam-6102	343	1	+	+	NOUN
ejpam-6102	343	2	o	o	NOUN
ejpam-6102	343	3	(	(	PUNCT
ejpam-6102	343	4	1	1	NUM
ejpam-6102	343	5	µ2	µ2	NOUN
ejpam-6102	343	6	i	i	PRON
ejpam-6102	343	7	)	)	PUNCT
ejpam-6102	344	1	+	+	NOUN
ejpam-6102	344	2	o	o	X
ejpam-6102	344	3	(	(	PUNCT
ejpam-6102	344	4	ε2	ε2	PROPN
ejpam-6102	344	5	)	)	PUNCT
ejpam-6102	344	6	.	.	PUNCT
ejpam-6102	345	1	this	this	PRON
ejpam-6102	345	2	completes	complete	VERB
ejpam-6102	345	3	the	the	DET
ejpam-6102	345	4	proof	proof	NOUN
ejpam-6102	345	5	of	of	ADP
ejpam-6102	345	6	proposition	proposition	NOUN
ejpam-6102	345	7	6	6	NUM
ejpam-6102	345	8	.	.	NOUN
ejpam-6102	345	9	5	5	NUM
ejpam-6102	345	10	.	.	X
ejpam-6102	345	11	proof	proof	NOUN
ejpam-6102	345	12	of	of	ADP
ejpam-6102	345	13	theorems	theorem	NOUN
ejpam-6102	345	14	1	1	NUM
ejpam-6102	345	15	and	and	CCONJ
ejpam-6102	345	16	2	2	NUM
ejpam-6102	345	17	since	since	SCONJ
ejpam-6102	345	18	theorem	theorem	VERB
ejpam-6102	345	19	2	2	NUM
ejpam-6102	345	20	is	be	AUX
ejpam-6102	345	21	a	a	DET
ejpam-6102	345	22	direct	direct	ADJ
ejpam-6102	345	23	consequence	consequence	NOUN
ejpam-6102	345	24	of	of	ADP
ejpam-6102	345	25	theorem	theorem	NOUN
ejpam-6102	345	26	1	1	NUM
ejpam-6102	345	27	,	,	PUNCT
ejpam-6102	345	28	it	it	PRON
ejpam-6102	345	29	is	be	AUX
ejpam-6102	345	30	sufficient	sufficient	ADJ
ejpam-6102	345	31	to	to	PART
ejpam-6102	345	32	prove	prove	VERB
ejpam-6102	345	33	the	the	DET
ejpam-6102	345	34	latter	latter	ADJ
ejpam-6102	345	35	.	.	PUNCT
ejpam-6102	346	1	adopting	adopt	VERB
ejpam-6102	346	2	the	the	DET
ejpam-6102	346	3	proof	proof	ADJ
ejpam-6102	346	4	strategy	strategy	NOUN
ejpam-6102	346	5	from	from	ADP
ejpam-6102	346	6	[	[	X
ejpam-6102	346	7	35	35	NUM
ejpam-6102	346	8	]	]	PUNCT
ejpam-6102	346	9	,	,	PUNCT
ejpam-6102	346	10	let	let	VERB
ejpam-6102	346	11	n	n	PRON
ejpam-6102	346	12	∈	∈	PROPN
ejpam-6102	346	13	n	n	CCONJ
ejpam-6102	346	14	,	,	PUNCT
ejpam-6102	346	15	b1	b1	NOUN
ejpam-6102	346	16	,	,	PUNCT
ejpam-6102	346	17	.	.	PUNCT
ejpam-6102	346	18	.	.	PUNCT
ejpam-6102	347	1	.	.	PUNCT
ejpam-6102	348	1	,	,	PUNCT
ejpam-6102	348	2	bn	bn	INTJ
ejpam-6102	348	3	be	be	AUX
ejpam-6102	348	4	as	as	ADV
ejpam-6102	348	5	defined	define	VERB
ejpam-6102	348	6	in	in	ADP
ejpam-6102	348	7	theorem	theorem	NOUN
ejpam-6102	348	8	1	1	NUM
ejpam-6102	348	9	and	and	CCONJ
ejpam-6102	348	10	ε	ε	PROPN
ejpam-6102	348	11	>	>	X
ejpam-6102	348	12	0	0	PUNCT
ejpam-6102	348	13	be	be	AUX
ejpam-6102	348	14	small	small	ADJ
ejpam-6102	348	15	.	.	PUNCT
ejpam-6102	349	1	we	we	PRON
ejpam-6102	349	2	consider	consider	VERB
ejpam-6102	349	3	the	the	DET
ejpam-6102	349	4	set	set	NOUN
ejpam-6102	349	5	dε	dε	NOUN
ejpam-6102	349	6	,	,	PUNCT
ejpam-6102	349	7	n	n	PROPN
ejpam-6102	349	8	:	:	PUNCT
ejpam-6102	349	9	=	=	SYM
ejpam-6102	349	10	{	{	PUNCT
ejpam-6102	349	11	(	(	PUNCT
ejpam-6102	349	12	a	a	PRON
ejpam-6102	349	13	,	,	PUNCT
ejpam-6102	349	14	µ	µ	NOUN
ejpam-6102	349	15	,	,	PUNCT
ejpam-6102	349	16	α	α	NOUN
ejpam-6102	349	17	,	,	PUNCT
ejpam-6102	349	18	v	v	NOUN
ejpam-6102	349	19	)	)	PUNCT
ejpam-6102	349	20	∈	∈	PROPN
ejpam-6102	349	21	(	(	PUNCT
ejpam-6102	349	22	∂ω)n	∂ω)n	NOUN
ejpam-6102	349	23	×	×	PROPN
ejpam-6102	349	24	(	(	PUNCT
ejpam-6102	349	25	0,∞)n	0,∞)n	NUM
ejpam-6102	349	26	×	×	NOUN
ejpam-6102	349	27	(	(	PUNCT
ejpam-6102	349	28	0,∞)n	0,∞)n	NUM
ejpam-6102	349	29	×h1(ω	×h1(ω	NOUN
ejpam-6102	349	30	)	)	PUNCT
ejpam-6102	349	31	:	:	PUNCT
ejpam-6102	349	32	|ai	|ai	PUNCT
ejpam-6102	349	33	−	−	PROPN
ejpam-6102	349	34	bi|	bi|	NOUN
ejpam-6102	349	35	<	<	X
ejpam-6102	349	36	√	√	PROPN
ejpam-6102	349	37	ε	ε	PROPN
ejpam-6102	349	38	;	;	PUNCT
ejpam-6102	349	39	m−1	m−1	PROPN
ejpam-6102	349	40	1	1	NUM
ejpam-6102	349	41	⩽	⩽	PROPN
ejpam-6102	349	42	µiε	µiε	PROPN
ejpam-6102	349	43	⩽m1	⩽m1	PROPN
ejpam-6102	349	44	;	;	PUNCT
ejpam-6102	349	45	∣∣∣1−	∣∣∣1−	NUM
ejpam-6102	349	46	αif	αif	NOUN
ejpam-6102	349	47	(	(	PUNCT
ejpam-6102	349	48	ai	ai	NOUN
ejpam-6102	349	49	)	)	PUNCT
ejpam-6102	349	50	(	(	PUNCT
ejpam-6102	349	51	n−2)/4	n−2)/4	NOUN
ejpam-6102	349	52	∣∣∣	∣∣∣	X
ejpam-6102	349	53	<	<	X
ejpam-6102	349	54	ε	ε	PROPN
ejpam-6102	349	55	ln2	ln2	PROPN
ejpam-6102	349	56	ε	ε	PROPN
ejpam-6102	349	57	,	,	PUNCT
ejpam-6102	349	58	v	v	NOUN
ejpam-6102	349	59	∈	∈	NOUN
ejpam-6102	349	60	fa,µ	fa,µ	NOUN
ejpam-6102	349	61	and	and	CCONJ
ejpam-6102	349	62	∥v∥	∥v∥	VERB
ejpam-6102	349	63	<	<	X
ejpam-6102	349	64	√	√	PROPN
ejpam-6102	349	65	ε	ε	PROPN
ejpam-6102	349	66	}	}	PUNCT
ejpam-6102	349	67	where	where	SCONJ
ejpam-6102	349	68	m1	m1	PROPN
ejpam-6102	349	69	is	be	AUX
ejpam-6102	349	70	a	a	DET
ejpam-6102	349	71	fixed	fix	VERB
ejpam-6102	349	72	large	large	ADJ
ejpam-6102	349	73	constant	constant	ADJ
ejpam-6102	349	74	.	.	PUNCT
ejpam-6102	350	1	let	let	VERB
ejpam-6102	350	2	j̃ε	j̃ε	PRON
ejpam-6102	350	3	be	be	AUX
ejpam-6102	350	4	the	the	DET
ejpam-6102	350	5	function	function	NOUN
ejpam-6102	350	6	defined	define	VERB
ejpam-6102	350	7	by	by	ADP
ejpam-6102	350	8	j̃ε	j̃ε	PRON
ejpam-6102	350	9	:	:	PUNCT
ejpam-6102	350	10	dε	dε	NOUN
ejpam-6102	350	11	,	,	PUNCT
ejpam-6102	350	12	n	n	PRON
ejpam-6102	350	13	−→	−→	NOUN
ejpam-6102	350	14	r	r	NOUN
ejpam-6102	350	15	;	;	PUNCT
ejpam-6102	350	16	λ	λ	X
ejpam-6102	350	17	:	:	PUNCT
ejpam-6102	350	18	=	=	SYM
ejpam-6102	350	19	(	(	PUNCT
ejpam-6102	350	20	a	a	PRON
ejpam-6102	350	21	,	,	PUNCT
ejpam-6102	350	22	µ	µ	NOUN
ejpam-6102	350	23	,	,	PUNCT
ejpam-6102	350	24	α	α	NOUN
ejpam-6102	350	25	,	,	PUNCT
ejpam-6102	350	26	v	v	NOUN
ejpam-6102	350	27	)	)	PUNCT
ejpam-6102	350	28	7−→	7−→	PROPN
ejpam-6102	350	29	j̃ε(λ	j̃ε(λ	NOUN
ejpam-6102	350	30	)	)	PUNCT
ejpam-6102	350	31	:	:	PUNCT
ejpam-6102	351	1	=	=	SYM
ejpam-6102	351	2	jε	jε	X
ejpam-6102	351	3	(	(	PUNCT
ejpam-6102	351	4	n∑	n∑	NOUN
ejpam-6102	351	5	i=1	i=1	PROPN
ejpam-6102	351	6	αiwai,µi	αiwai,µi	PROPN
ejpam-6102	352	1	+	+	CCONJ
ejpam-6102	352	2	v	v	NOUN
ejpam-6102	352	3	)	)	PUNCT
ejpam-6102	352	4	.	.	PUNCT
ejpam-6102	353	1	r.	r.	PROPN
ejpam-6102	353	2	almushahhin	almushahhin	PROPN
ejpam-6102	353	3	,	,	PUNCT
ejpam-6102	353	4	m.	m.	PROPN
ejpam-6102	353	5	ben	ben	PROPN
ejpam-6102	353	6	ayed	aye	VERB
ejpam-6102	353	7	/	/	SYM
ejpam-6102	353	8	eur	eur	PROPN
ejpam-6102	353	9	.	.	PUNCT
ejpam-6102	354	1	j.	j.	PROPN
ejpam-6102	354	2	pure	pure	PROPN
ejpam-6102	354	3	appl	appl	PROPN
ejpam-6102	354	4	.	.	PROPN
ejpam-6102	354	5	math	math	PROPN
ejpam-6102	354	6	,	,	PUNCT
ejpam-6102	354	7	18	18	NUM
ejpam-6102	354	8	(	(	PUNCT
ejpam-6102	354	9	2	2	NUM
ejpam-6102	354	10	)	)	PUNCT
ejpam-6102	354	11	(	(	PUNCT
ejpam-6102	354	12	2025	2025	NUM
ejpam-6102	354	13	)	)	PUNCT
ejpam-6102	354	14	,	,	PUNCT
ejpam-6102	354	15	6102	6102	NUM
ejpam-6102	354	16	14	14	NUM
ejpam-6102	354	17	of	of	ADP
ejpam-6102	354	18	31	31	NUM
ejpam-6102	354	19	there	there	PRON
ejpam-6102	354	20	exists	exist	VERB
ejpam-6102	354	21	a	a	DET
ejpam-6102	354	22	biunivoque	biunivoque	ADJ
ejpam-6102	354	23	relation	relation	NOUN
ejpam-6102	354	24	between	between	ADP
ejpam-6102	354	25	the	the	DET
ejpam-6102	354	26	critical	critical	ADJ
ejpam-6102	354	27	points	point	NOUN
ejpam-6102	354	28	of	of	ADP
ejpam-6102	354	29	j̃ε	j̃ε	NUM
ejpam-6102	354	30	and	and	CCONJ
ejpam-6102	354	31	the	the	DET
ejpam-6102	354	32	ones	one	NOUN
ejpam-6102	354	33	of	of	ADP
ejpam-6102	354	34	jε	jε	PROPN
ejpam-6102	354	35	.	.	PROPN
ejpam-6102	354	36	proposition	proposition	NOUN
ejpam-6102	354	37	7	7	NUM
ejpam-6102	354	38	.	.	PUNCT
ejpam-6102	355	1	let	let	VERB
ejpam-6102	355	2	λ	λ	X
ejpam-6102	355	3	:	:	PUNCT
ejpam-6102	355	4	=	=	SYM
ejpam-6102	355	5	(	(	PUNCT
ejpam-6102	355	6	a	a	DET
ejpam-6102	355	7	,	,	PUNCT
ejpam-6102	355	8	µ	µ	NOUN
ejpam-6102	355	9	,	,	PUNCT
ejpam-6102	355	10	α	α	NOUN
ejpam-6102	355	11	,	,	PUNCT
ejpam-6102	355	12	v	v	NOUN
ejpam-6102	355	13	)	)	PUNCT
ejpam-6102	355	14	∈	∈	PROPN
ejpam-6102	355	15	dε	dε	NOUN
ejpam-6102	355	16	,	,	PUNCT
ejpam-6102	355	17	n	n	NOUN
ejpam-6102	355	18	.	.	PUNCT
ejpam-6102	356	1	u	u	NOUN
ejpam-6102	357	1	=	=	PUNCT
ejpam-6102	357	2	∑n	∑n	PROPN
ejpam-6102	357	3	i=1	i=1	X
ejpam-6102	357	4	αiwai,µi	αiwai,µi	PUNCT
ejpam-6102	358	1	+	+	CCONJ
ejpam-6102	358	2	v	v	NOUN
ejpam-6102	358	3	is	be	AUX
ejpam-6102	358	4	a	a	DET
ejpam-6102	358	5	critical	critical	ADJ
ejpam-6102	358	6	point	point	NOUN
ejpam-6102	358	7	of	of	ADP
ejpam-6102	358	8	jε	jε	NOUN
ejpam-6102	358	9	if	if	SCONJ
ejpam-6102	358	10	and	and	CCONJ
ejpam-6102	358	11	only	only	ADV
ejpam-6102	358	12	if	if	SCONJ
ejpam-6102	358	13	λ	λ	NOUN
ejpam-6102	358	14	is	be	AUX
ejpam-6102	358	15	a	a	DET
ejpam-6102	358	16	critical	critical	ADJ
ejpam-6102	358	17	point	point	NOUN
ejpam-6102	358	18	of	of	ADP
ejpam-6102	358	19	j̃ε	j̃ε	PROPN
ejpam-6102	358	20	,	,	PUNCT
ejpam-6102	358	21	i.	i.	NOUN
ejpam-6102	358	22	,e	,e	PROPN
ejpam-6102	358	23	.	.	PUNCT
ejpam-6102	358	24	,	,	PUNCT
ejpam-6102	358	25	there	there	PRON
ejpam-6102	358	26	exists	exist	VERB
ejpam-6102	358	27	(	(	PUNCT
ejpam-6102	358	28	γ	γ	X
ejpam-6102	358	29	,	,	PUNCT
ejpam-6102	358	30	η	η	PROPN
ejpam-6102	358	31	,	,	PUNCT
ejpam-6102	358	32	σ	σ	PROPN
ejpam-6102	358	33	)	)	PUNCT
ejpam-6102	358	34	∈	∈	PROPN
ejpam-6102	358	35	(	(	PUNCT
ejpam-6102	358	36	rn−1	rn−1	PROPN
ejpam-6102	358	37	)	)	PUNCT
ejpam-6102	358	38	n	n	CCONJ
ejpam-6102	358	39	×	×	PROPN
ejpam-6102	358	40	rn	rn	PROPN
ejpam-6102	358	41	×	×	PROPN
ejpam-6102	358	42	rn	rn	PROPN
ejpam-6102	358	43	such	such	ADJ
ejpam-6102	358	44	that	that	SCONJ
ejpam-6102	358	45	the	the	DET
ejpam-6102	358	46	following	follow	VERB
ejpam-6102	358	47	system	system	NOUN
ejpam-6102	358	48	is	be	AUX
ejpam-6102	358	49	satisfied	satisfied	ADJ
ejpam-6102	358	50	:	:	PUNCT
ejpam-6102	358	51	(	(	PUNCT
ejpam-6102	358	52	ak	ak	PROPN
ejpam-6102	358	53	)	)	PUNCT
ejpam-6102	358	54	∂j̃ε	∂j̃ε	PROPN
ejpam-6102	359	1	∂αk	∂αk	PROPN
ejpam-6102	359	2	(	(	PUNCT
ejpam-6102	359	3	λ	λ	NOUN
ejpam-6102	359	4	)	)	PUNCT
ejpam-6102	359	5	=	=	SYM
ejpam-6102	359	6	0	0	NUM
ejpam-6102	359	7	∀	∀	NOUN
ejpam-6102	359	8	k	k	X
ejpam-6102	359	9	,	,	PUNCT
ejpam-6102	359	10	(	(	PUNCT
ejpam-6102	359	11	v	v	NOUN
ejpam-6102	359	12	)	)	PUNCT
ejpam-6102	359	13	∂j̃ε	∂j̃ε	PROPN
ejpam-6102	360	1	∂v	∂v	PROPN
ejpam-6102	360	2	(	(	PUNCT
ejpam-6102	360	3	λ	λ	X
ejpam-6102	360	4	)	)	PUNCT
ejpam-6102	360	5	=	=	SYM
ejpam-6102	361	1	∑n	∑n	NOUN
ejpam-6102	362	1	k=1	k=1	NOUN
ejpam-6102	362	2	(	(	PUNCT
ejpam-6102	362	3	ηk	ηk	PROPN
ejpam-6102	362	4	∂g1,k	∂g1,k	PROPN
ejpam-6102	362	5	∂v	∂v	PROPN
ejpam-6102	362	6	(	(	PUNCT
ejpam-6102	362	7	λ	λ	X
ejpam-6102	362	8	)	)	PUNCT
ejpam-6102	363	1	+	+	CCONJ
ejpam-6102	363	2	σk	σk	CCONJ
ejpam-6102	363	3	∂g2,k	∂g2,k	NOUN
ejpam-6102	363	4	∂v	∂v	PROPN
ejpam-6102	363	5	(	(	PUNCT
ejpam-6102	363	6	λ	λ	X
ejpam-6102	363	7	)	)	PUNCT
ejpam-6102	363	8	+	+	CCONJ
ejpam-6102	363	9	∑n−1	∑n−1	ADJ
ejpam-6102	363	10	j=1	j=1	PROPN
ejpam-6102	363	11	γk	γk	PROPN
ejpam-6102	363	12	,	,	PUNCT
ejpam-6102	363	13	j	j	PROPN
ejpam-6102	363	14	∂g3,k	∂g3,k	PROPN
ejpam-6102	363	15	,	,	PUNCT
ejpam-6102	363	16	j	j	PROPN
ejpam-6102	363	17	∂v	∂v	PROPN
ejpam-6102	363	18	(	(	PUNCT
ejpam-6102	363	19	λ	λ	NOUN
ejpam-6102	363	20	)	)	PUNCT
ejpam-6102	363	21	)	)	PUNCT
ejpam-6102	363	22	,	,	PUNCT
ejpam-6102	363	23	(	(	PUNCT
ejpam-6102	363	24	mk	mk	X
ejpam-6102	363	25	)	)	PUNCT
ejpam-6102	363	26	∂j̃ε	∂j̃ε	NUM
ejpam-6102	363	27	∂µk	∂µk	PROPN
ejpam-6102	363	28	(	(	PUNCT
ejpam-6102	363	29	λ	λ	NOUN
ejpam-6102	363	30	)	)	PUNCT
ejpam-6102	363	31	=	=	PUNCT
ejpam-6102	364	1	σk	σk	PROPN
ejpam-6102	364	2	∫	∫	PROPN
ejpam-6102	364	3	ω	ω	PROPN
ejpam-6102	364	4	∇v	∇v	PROPN
ejpam-6102	364	5	·	·	PUNCT
ejpam-6102	364	6	∇	∇	X
ejpam-6102	364	7	(	(	PUNCT
ejpam-6102	364	8	µk	µk	PROPN
ejpam-6102	364	9	∂2wak,µk	∂2wak,µk	PROPN
ejpam-6102	364	10	∂µ2	∂µ2	PROPN
ejpam-6102	364	11	k	k	PROPN
ejpam-6102	364	12	)	)	PUNCT
ejpam-6102	365	1	+	+	CCONJ
ejpam-6102	365	2	∑n−1	∑n−1	ADJ
ejpam-6102	365	3	j=1	j=1	PROPN
ejpam-6102	365	4	γk	γk	PROPN
ejpam-6102	365	5	,	,	PUNCT
ejpam-6102	365	6	j	j	PROPN
ejpam-6102	365	7	∫	∫	PROPN
ejpam-6102	365	8	ω	ω	PROPN
ejpam-6102	365	9	∇v	∇v	PROPN
ejpam-6102	365	10	·	·	PUNCT
ejpam-6102	365	11	∇	∇	X
ejpam-6102	365	12	(	(	PUNCT
ejpam-6102	365	13	1	1	NUM
ejpam-6102	365	14	µk	µk	NOUN
ejpam-6102	365	15	∂2wak,µk	∂2wak,µk	PROPN
ejpam-6102	365	16	∂µk∂τk	∂µk∂τk	PROPN
ejpam-6102	365	17	,	,	PUNCT
ejpam-6102	365	18	j	j	PROPN
ejpam-6102	365	19	)	)	PUNCT
ejpam-6102	365	20	,	,	PUNCT
ejpam-6102	365	21	∀	∀	X
ejpam-6102	365	22	k	k	X
ejpam-6102	365	23	,	,	PUNCT
ejpam-6102	365	24	(	(	PUNCT
ejpam-6102	365	25	tk	tk	PROPN
ejpam-6102	365	26	)	)	PUNCT
ejpam-6102	365	27	∂j̃ε	∂j̃ε	PROPN
ejpam-6102	366	1	∂τk	∂τk	PROPN
ejpam-6102	366	2	,	,	PUNCT
ejpam-6102	366	3	l	l	NOUN
ejpam-6102	366	4	(	(	PUNCT
ejpam-6102	366	5	λ	λ	NOUN
ejpam-6102	366	6	)	)	PUNCT
ejpam-6102	366	7	=	=	PRON
ejpam-6102	367	1	σk	σk	PROPN
ejpam-6102	367	2	∫	∫	PROPN
ejpam-6102	367	3	ω	ω	PROPN
ejpam-6102	367	4	∇v	∇v	PROPN
ejpam-6102	367	5	·	·	PUNCT
ejpam-6102	367	6	∇	∇	X
ejpam-6102	367	7	(	(	PUNCT
ejpam-6102	367	8	µk	µk	NOUN
ejpam-6102	367	9	∂2wak,µk	∂2wak,µk	PROPN
ejpam-6102	367	10	∂µk∂τk	∂µk∂τk	NOUN
ejpam-6102	367	11	,	,	PUNCT
ejpam-6102	367	12	l	l	NOUN
ejpam-6102	367	13	)	)	PUNCT
ejpam-6102	368	1	+	+	CCONJ
ejpam-6102	368	2	∑n−1	∑n−1	ADP
ejpam-6102	368	3	j=1	j=1	PROPN
ejpam-6102	368	4	γk	γk	PROPN
ejpam-6102	368	5	,	,	PUNCT
ejpam-6102	368	6	j	j	PROPN
ejpam-6102	368	7	∫	∫	PROPN
ejpam-6102	368	8	ω	ω	PROPN
ejpam-6102	368	9	∇v	∇v	PROPN
ejpam-6102	368	10	·	·	PUNCT
ejpam-6102	368	11	∇	∇	X
ejpam-6102	368	12	(	(	PUNCT
ejpam-6102	368	13	1	1	NUM
ejpam-6102	368	14	µk	µk	PRON
ejpam-6102	368	15	∂2wak,µk	∂2wak,µk	PROPN
ejpam-6102	368	16	∂τk	∂τk	PROPN
ejpam-6102	368	17	,	,	PUNCT
ejpam-6102	368	18	j∂τk	j∂τk	NOUN
ejpam-6102	368	19	,	,	PUNCT
ejpam-6102	368	20	l	l	NOUN
ejpam-6102	368	21	)	)	PUNCT
ejpam-6102	368	22	,	,	PUNCT
ejpam-6102	368	23	∀	∀	X
ejpam-6102	368	24	k	k	X
ejpam-6102	368	25	,	,	PUNCT
ejpam-6102	368	26	∀	∀	X
ejpam-6102	368	27	l.	l.	NOUN
ejpam-6102	368	28	(	(	PUNCT
ejpam-6102	368	29	37	37	NUM
ejpam-6102	368	30	)	)	PUNCT
ejpam-6102	368	31	proof	proof	NOUN
ejpam-6102	368	32	.	.	PUNCT
ejpam-6102	369	1	observe	observe	VERB
ejpam-6102	369	2	that	that	SCONJ
ejpam-6102	369	3	dε	dε	NOUN
ejpam-6102	369	4	,	,	PUNCT
ejpam-6102	369	5	n	n	PRON
ejpam-6102	369	6	is	be	AUX
ejpam-6102	369	7	not	not	PART
ejpam-6102	369	8	an	an	DET
ejpam-6102	369	9	open	open	ADJ
ejpam-6102	369	10	set	set	NOUN
ejpam-6102	369	11	in	in	ADP
ejpam-6102	369	12	(	(	PUNCT
ejpam-6102	369	13	∂ω)n	∂ω)n	INTJ
ejpam-6102	369	14	×	×	PROPN
ejpam-6102	369	15	(	(	PUNCT
ejpam-6102	369	16	0,∞)n	0,∞)n	NUM
ejpam-6102	369	17	×	×	NOUN
ejpam-6102	369	18	(	(	PUNCT
ejpam-6102	369	19	0,∞)n	0,∞)n	NUM
ejpam-6102	369	20	×h1(ω	×h1(ω	NOUN
ejpam-6102	369	21	)	)	PUNCT
ejpam-6102	369	22	since	since	SCONJ
ejpam-6102	369	23	the	the	DET
ejpam-6102	369	24	elements	element	NOUN
ejpam-6102	369	25	λ	λ	PROPN
ejpam-6102	369	26	of	of	ADP
ejpam-6102	369	27	dε	dε	PROPN
ejpam-6102	369	28	,	,	PUNCT
ejpam-6102	369	29	n	n	PRON
ejpam-6102	369	30	have	have	VERB
ejpam-6102	369	31	to	to	PART
ejpam-6102	369	32	satisfy	satisfy	VERB
ejpam-6102	369	33	the	the	DET
ejpam-6102	369	34	following	follow	VERB
ejpam-6102	369	35	orthogonality	orthogonality	NOUN
ejpam-6102	369	36	constraints	constraint	NOUN
ejpam-6102	369	37	:	:	PUNCT
ejpam-6102	369	38	g1,k(λ	g1,k(λ	X
ejpam-6102	369	39	)	)	PUNCT
ejpam-6102	369	40	:	:	PUNCT
ejpam-6102	370	1	=	=	SYM
ejpam-6102	370	2	∫	∫	PROPN
ejpam-6102	371	1	ω	ω	X
ejpam-6102	371	2	∇v	∇v	PROPN
ejpam-6102	371	3	·	·	PUNCT
ejpam-6102	371	4	∇wak,µk	∇wak,µk	NOUN
ejpam-6102	371	5	=	=	SYM
ejpam-6102	371	6	0	0	NUM
ejpam-6102	371	7	,	,	PUNCT
ejpam-6102	371	8	k	k	PROPN
ejpam-6102	371	9	∈	∈	PROPN
ejpam-6102	371	10	{	{	PUNCT
ejpam-6102	371	11	1	1	NUM
ejpam-6102	371	12	,	,	PUNCT
ejpam-6102	371	13	·	·	PUNCT
ejpam-6102	371	14	·	·	PUNCT
ejpam-6102	371	15	·	·	PUNCT
ejpam-6102	371	16	,	,	PUNCT
ejpam-6102	371	17	n	n	CCONJ
ejpam-6102	371	18	}	}	PUNCT
ejpam-6102	371	19	,	,	PUNCT
ejpam-6102	371	20	g2,k(λ	g2,k(λ	NOUN
ejpam-6102	371	21	)	)	PUNCT
ejpam-6102	371	22	:	:	PUNCT
ejpam-6102	371	23	=	=	SYM
ejpam-6102	371	24	∫	∫	PROPN
ejpam-6102	371	25	ω	ω	X
ejpam-6102	371	26	∇v	∇v	PROPN
ejpam-6102	371	27	·	·	PUNCT
ejpam-6102	371	28	∇	∇	X
ejpam-6102	371	29	(	(	PUNCT
ejpam-6102	371	30	µk	µk	PRON
ejpam-6102	371	31	∂wak,µk	∂wak,µk	PROPN
ejpam-6102	371	32	∂µk	∂µk	PROPN
ejpam-6102	371	33	)	)	PUNCT
ejpam-6102	371	34	=	=	SYM
ejpam-6102	371	35	0	0	NUM
ejpam-6102	371	36	,	,	PUNCT
ejpam-6102	371	37	k	k	PROPN
ejpam-6102	371	38	∈	∈	PROPN
ejpam-6102	371	39	{	{	PUNCT
ejpam-6102	371	40	1	1	NUM
ejpam-6102	371	41	,	,	PUNCT
ejpam-6102	371	42	.	.	PUNCT
ejpam-6102	371	43	.	.	PUNCT
ejpam-6102	371	44	.	.	PUNCT
ejpam-6102	371	45	,	,	PUNCT
ejpam-6102	371	46	n	n	CCONJ
ejpam-6102	371	47	}	}	PUNCT
ejpam-6102	371	48	,	,	PUNCT
ejpam-6102	371	49	g3,k	g3,k	PROPN
ejpam-6102	371	50	,	,	PUNCT
ejpam-6102	371	51	j(λ	j(λ	PROPN
ejpam-6102	371	52	)	)	PUNCT
ejpam-6102	371	53	:	:	PUNCT
ejpam-6102	372	1	=	=	SYM
ejpam-6102	372	2	∫	∫	PROPN
ejpam-6102	373	1	ω	ω	X
ejpam-6102	373	2	∇v	∇v	PROPN
ejpam-6102	373	3	·	·	PUNCT
ejpam-6102	373	4	∇	∇	X
ejpam-6102	373	5	(	(	PUNCT
ejpam-6102	373	6	1	1	NUM
ejpam-6102	373	7	µk	µk	PRON
ejpam-6102	373	8	∂wak,µk	∂wak,µk	PROPN
ejpam-6102	373	9	∂τk	∂τk	PROPN
ejpam-6102	373	10	,	,	PUNCT
ejpam-6102	373	11	j	j	PROPN
ejpam-6102	373	12	)	)	PUNCT
ejpam-6102	373	13	=	=	SYM
ejpam-6102	373	14	0	0	NUM
ejpam-6102	373	15	,	,	PUNCT
ejpam-6102	373	16	k	k	PROPN
ejpam-6102	373	17	∈	∈	PROPN
ejpam-6102	373	18	{	{	PUNCT
ejpam-6102	373	19	1	1	NUM
ejpam-6102	373	20	,	,	PUNCT
ejpam-6102	373	21	.	.	PUNCT
ejpam-6102	373	22	.	.	PUNCT
ejpam-6102	373	23	.	.	PUNCT
ejpam-6102	373	24	,	,	PUNCT
ejpam-6102	373	25	n	n	CCONJ
ejpam-6102	373	26	}	}	PUNCT
ejpam-6102	373	27	,	,	PUNCT
ejpam-6102	373	28	j	j	PROPN
ejpam-6102	373	29	∈	∈	PROPN
ejpam-6102	373	30	{	{	PUNCT
ejpam-6102	373	31	1	1	NUM
ejpam-6102	373	32	,	,	PUNCT
ejpam-6102	373	33	.	.	PUNCT
ejpam-6102	373	34	.	.	PUNCT
ejpam-6102	373	35	.	.	PUNCT
ejpam-6102	374	1	,	,	PUNCT
ejpam-6102	374	2	n−	n−	NOUN
ejpam-6102	374	3	1	1	NUM
ejpam-6102	374	4	}	}	PUNCT
ejpam-6102	374	5	.	.	PUNCT
ejpam-6102	375	1	therefore	therefore	ADV
ejpam-6102	375	2	,	,	PUNCT
ejpam-6102	375	3	it	it	PRON
ejpam-6102	375	4	follows	follow	VERB
ejpam-6102	375	5	from	from	ADP
ejpam-6102	375	6	the	the	DET
ejpam-6102	375	7	multiplier	multipli	ADJ
ejpam-6102	375	8	lagrange	lagrange	NOUN
ejpam-6102	375	9	theorem	theorem	VERB
ejpam-6102	375	10	that	that	SCONJ
ejpam-6102	375	11	λ	λ	PROPN
ejpam-6102	375	12	is	be	AUX
ejpam-6102	375	13	a	a	DET
ejpam-6102	375	14	critical	critical	ADJ
ejpam-6102	375	15	point	point	NOUN
ejpam-6102	375	16	of	of	ADP
ejpam-6102	375	17	j̃ε	j̃ε	NOUN
ejpam-6102	375	18	in	in	ADP
ejpam-6102	375	19	dε	dε	NOUN
ejpam-6102	375	20	,	,	PUNCT
ejpam-6102	375	21	n	n	CCONJ
ejpam-6102	375	22	if	if	SCONJ
ejpam-6102	376	1	and	and	CCONJ
ejpam-6102	376	2	only	only	ADV
ejpam-6102	376	3	if	if	SCONJ
ejpam-6102	376	4	there	there	PRON
ejpam-6102	376	5	exist	exist	VERB
ejpam-6102	376	6	some	some	DET
ejpam-6102	376	7	constants	constant	NOUN
ejpam-6102	376	8	γ	γ	X
ejpam-6102	376	9	∈	∈	PROPN
ejpam-6102	376	10	(	(	PUNCT
ejpam-6102	376	11	rn−1	rn−1	PROPN
ejpam-6102	376	12	)	)	PUNCT
ejpam-6102	376	13	n	n	CCONJ
ejpam-6102	376	14	,	,	PUNCT
ejpam-6102	376	15	η	η	PROPN
ejpam-6102	376	16	∈	∈	PROPN
ejpam-6102	376	17	rn	rn	PROPN
ejpam-6102	376	18	and	and	CCONJ
ejpam-6102	376	19	σ	σ	PROPN
ejpam-6102	376	20	∈	∈	PROPN
ejpam-6102	376	21	rn	rn	PROPN
ejpam-6102	376	22	such	such	ADJ
ejpam-6102	376	23	that	that	SCONJ
ejpam-6102	376	24	∇j̃ε(λ	∇j̃ε(λ	NOUN
ejpam-6102	376	25	)	)	PUNCT
ejpam-6102	376	26	=	=	SYM
ejpam-6102	377	1	n∑	n∑	NOUN
ejpam-6102	377	2	k=1	k=1	PROPN
ejpam-6102	377	3	(	(	PUNCT
ejpam-6102	377	4	ηk∇g1,k(λ	ηk∇g1,k(λ	PROPN
ejpam-6102	377	5	)	)	PUNCT
ejpam-6102	378	1	+	+	CCONJ
ejpam-6102	378	2	σk∇g2,k(λ	σk∇g2,k(λ	NOUN
ejpam-6102	378	3	)	)	PUNCT
ejpam-6102	378	4	+	+	CCONJ
ejpam-6102	378	5	∑	∑	PROPN
ejpam-6102	378	6	1≤j≤n−1	1≤j≤n−1	NUM
ejpam-6102	378	7	γk	γk	PROPN
ejpam-6102	378	8	,	,	PUNCT
ejpam-6102	378	9	j∇g3,k	j∇g3,k	PROPN
ejpam-6102	378	10	,	,	PUNCT
ejpam-6102	378	11	j(λ	j(λ	NOUN
ejpam-6102	378	12	)	)	PUNCT
ejpam-6102	378	13	)	)	PUNCT
ejpam-6102	378	14	.	.	PUNCT
ejpam-6102	379	1	(	(	PUNCT
ejpam-6102	379	2	38	38	NUM
ejpam-6102	379	3	)	)	PUNCT
ejpam-6102	379	4	notice	notice	NOUN
ejpam-6102	379	5	that	that	SCONJ
ejpam-6102	379	6	∇j̃ε(λ	∇j̃ε(λ	NOUN
ejpam-6102	379	7	)	)	PUNCT
ejpam-6102	379	8	=	=	SYM
ejpam-6102	380	1	(	(	PUNCT
ejpam-6102	380	2	(	(	PUNCT
ejpam-6102	380	3	∂j̃ε(λ	∂j̃ε(λ	NOUN
ejpam-6102	380	4	)	)	PUNCT
ejpam-6102	380	5	∂τk,1	∂τk,1	NOUN
ejpam-6102	380	6	)	)	PUNCT
ejpam-6102	380	7	k≤n	k≤n	PROPN
ejpam-6102	380	8	,	,	PUNCT
ejpam-6102	380	9	·	·	PUNCT
ejpam-6102	380	10	·	·	PUNCT
ejpam-6102	380	11	·	·	PUNCT
ejpam-6102	380	12	,	,	PUNCT
ejpam-6102	380	13	(	(	PUNCT
ejpam-6102	380	14	∂j̃ε(λ	∂j̃ε(λ	NOUN
ejpam-6102	380	15	)	)	PUNCT
ejpam-6102	380	16	∂τk	∂τk	PROPN
ejpam-6102	380	17	,	,	PUNCT
ejpam-6102	380	18	n−1	n−1	PROPN
ejpam-6102	380	19	)	)	PUNCT
ejpam-6102	380	20	k≤n	k≤n	PROPN
ejpam-6102	380	21	,	,	PUNCT
ejpam-6102	380	22	(	(	PUNCT
ejpam-6102	380	23	∂j̃ε(λ	∂j̃ε(λ	NOUN
ejpam-6102	380	24	)	)	PUNCT
ejpam-6102	380	25	∂µk	∂µk	PROPN
ejpam-6102	380	26	)	)	PUNCT
ejpam-6102	380	27	k≤n	k≤n	PROPN
ejpam-6102	380	28	,	,	PUNCT
ejpam-6102	380	29	(	(	PUNCT
ejpam-6102	380	30	∂j̃ε(λ	∂j̃ε(λ	NOUN
ejpam-6102	380	31	)	)	PUNCT
ejpam-6102	380	32	∂αk	∂αk	PROPN
ejpam-6102	380	33	)	)	PUNCT
ejpam-6102	380	34	k≤n	k≤n	PROPN
ejpam-6102	380	35	,	,	PUNCT
ejpam-6102	380	36	∂j̃ε(λ	∂j̃ε(λ	NUM
ejpam-6102	380	37	)	)	PUNCT
ejpam-6102	380	38	∂v	∂v	PROPN
ejpam-6102	380	39	)	)	PUNCT
ejpam-6102	380	40	.	.	PUNCT
ejpam-6102	381	1	(	(	PUNCT
ejpam-6102	381	2	39	39	NUM
ejpam-6102	381	3	)	)	PUNCT
ejpam-6102	381	4	combining	combine	VERB
ejpam-6102	381	5	(	(	PUNCT
ejpam-6102	381	6	38	38	NUM
ejpam-6102	381	7	)	)	PUNCT
ejpam-6102	381	8	,	,	PUNCT
ejpam-6102	381	9	(	(	PUNCT
ejpam-6102	381	10	39	39	NUM
ejpam-6102	381	11	)	)	PUNCT
ejpam-6102	381	12	and	and	CCONJ
ejpam-6102	381	13	the	the	DET
ejpam-6102	381	14	fact	fact	NOUN
ejpam-6102	381	15	that	that	SCONJ
ejpam-6102	381	16	the	the	DET
ejpam-6102	381	17	functions	function	NOUN
ejpam-6102	381	18	g1,k	g1,k	PROPN
ejpam-6102	381	19	,	,	PUNCT
ejpam-6102	381	20	g2,k	g2,k	PROPN
ejpam-6102	381	21	and	and	CCONJ
ejpam-6102	381	22	g3,k	g3,k	PROPN
ejpam-6102	381	23	are	be	AUX
ejpam-6102	381	24	independent	independent	ADJ
ejpam-6102	381	25	of	of	ADP
ejpam-6102	381	26	the	the	DET
ejpam-6102	381	27	variable	variable	ADJ
ejpam-6102	381	28	α	α	NOUN
ejpam-6102	381	29	,	,	PUNCT
ejpam-6102	381	30	we	we	PRON
ejpam-6102	381	31	easily	easily	ADV
ejpam-6102	381	32	derive	derive	VERB
ejpam-6102	381	33	the	the	DET
ejpam-6102	381	34	result	result	NOUN
ejpam-6102	381	35	.	.	PUNCT
ejpam-6102	382	1	to	to	PART
ejpam-6102	382	2	prove	prove	VERB
ejpam-6102	382	3	theorem	theorem	VERB
ejpam-6102	382	4	1	1	NUM
ejpam-6102	382	5	,	,	PUNCT
ejpam-6102	382	6	we	we	PRON
ejpam-6102	382	7	observe	observe	VERB
ejpam-6102	382	8	that	that	SCONJ
ejpam-6102	382	9	proposition	proposition	NOUN
ejpam-6102	382	10	7	7	NUM
ejpam-6102	382	11	implies	imply	VERB
ejpam-6102	382	12	that	that	SCONJ
ejpam-6102	382	13	it	it	PRON
ejpam-6102	382	14	is	be	AUX
ejpam-6102	382	15	sufficient	sufficient	ADJ
ejpam-6102	382	16	to	to	PART
ejpam-6102	382	17	study	study	VERB
ejpam-6102	382	18	the	the	DET
ejpam-6102	382	19	system	system	NOUN
ejpam-6102	382	20	(	(	PUNCT
ejpam-6102	382	21	37	37	NUM
ejpam-6102	382	22	)	)	PUNCT
ejpam-6102	382	23	and	and	CCONJ
ejpam-6102	382	24	demonstrate	demonstrate	VERB
ejpam-6102	382	25	that	that	SCONJ
ejpam-6102	382	26	(	(	PUNCT
ejpam-6102	382	27	37	37	NUM
ejpam-6102	382	28	)	)	PUNCT
ejpam-6102	382	29	has	have	VERB
ejpam-6102	382	30	a	a	DET
ejpam-6102	382	31	solution	solution	NOUN
ejpam-6102	382	32	.	.	PUNCT
ejpam-6102	383	1	first	first	ADV
ejpam-6102	383	2	,	,	PUNCT
ejpam-6102	383	3	for	for	ADP
ejpam-6102	383	4	λ	λ	PROPN
ejpam-6102	383	5	∈	∈	PROPN
ejpam-6102	383	6	dε	dε	NOUN
ejpam-6102	383	7	,	,	PUNCT
ejpam-6102	383	8	n	n	CCONJ
ejpam-6102	383	9	,	,	PUNCT
ejpam-6102	383	10	let	let	VERB
ejpam-6102	383	11	u	u	PRON
ejpam-6102	383	12	=	=	PUNCT
ejpam-6102	383	13	∑n	∑n	PROPN
ejpam-6102	383	14	i=1	i=1	PROPN
ejpam-6102	383	15	αiwaiµi	αiwaiµi	PROPN
ejpam-6102	384	1	+	+	PROPN
ejpam-6102	384	2	v	v	NOUN
ejpam-6102	384	3	,	,	PUNCT
ejpam-6102	384	4	the	the	DET
ejpam-6102	384	5	definition	definition	NOUN
ejpam-6102	384	6	of	of	ADP
ejpam-6102	384	7	j̃ε	j̃ε	PRON
ejpam-6102	384	8	implies	imply	VERB
ejpam-6102	384	9	that	that	SCONJ
ejpam-6102	384	10	,	,	PUNCT
ejpam-6102	384	11	for	for	ADP
ejpam-6102	384	12	each	each	DET
ejpam-6102	384	13	k	k	PROPN
ejpam-6102	384	14	∈	∈	PROPN
ejpam-6102	384	15	{	{	PUNCT
ejpam-6102	384	16	1	1	NUM
ejpam-6102	384	17	,	,	PUNCT
ejpam-6102	384	18	.	.	PUNCT
ejpam-6102	384	19	.	.	PUNCT
ejpam-6102	385	1	.	.	PUNCT
ejpam-6102	386	1	,	,	PUNCT
ejpam-6102	386	2	n	n	CCONJ
ejpam-6102	386	3	}	}	PUNCT
ejpam-6102	386	4	,	,	PUNCT
ejpam-6102	386	5	∂j̃ε	∂j̃ε	PROPN
ejpam-6102	386	6	∂v	∂v	PROPN
ejpam-6102	386	7	(	(	PUNCT
ejpam-6102	386	8	λ	λ	NOUN
ejpam-6102	386	9	)	)	PUNCT
ejpam-6102	386	10	=	=	SYM
ejpam-6102	386	11	∇jε(u	∇jε(u	NOUN
ejpam-6102	386	12	)	)	PUNCT
ejpam-6102	386	13	,	,	PUNCT
ejpam-6102	386	14	∂j̃ε	∂j̃ε	PROPN
ejpam-6102	386	15	∂µk	∂µk	PROPN
ejpam-6102	386	16	(	(	PUNCT
ejpam-6102	386	17	λ	λ	NOUN
ejpam-6102	386	18	)	)	PUNCT
ejpam-6102	386	19	=	=	SYM
ejpam-6102	386	20	〈	〈	NOUN
ejpam-6102	386	21	∇jε(u	∇jε(u	NOUN
ejpam-6102	386	22	)	)	PUNCT
ejpam-6102	386	23	,	,	PUNCT
ejpam-6102	386	24	αk	αk	ADP
ejpam-6102	386	25	∂wak,µk	∂wak,µk	PROPN
ejpam-6102	386	26	∂µk	∂µk	VERB
ejpam-6102	386	27	〉	〉	NOUN
ejpam-6102	386	28	,	,	PUNCT
ejpam-6102	386	29	∂j̃ε	∂j̃ε	PROPN
ejpam-6102	386	30	∂αk	∂αk	PROPN
ejpam-6102	386	31	(	(	PUNCT
ejpam-6102	386	32	λ	λ	NOUN
ejpam-6102	386	33	)	)	PUNCT
ejpam-6102	386	34	=	=	SYM
ejpam-6102	386	35	⟨∇jε(u	⟨∇jε(u	NOUN
ejpam-6102	386	36	)	)	PUNCT
ejpam-6102	386	37	,	,	PUNCT
ejpam-6102	386	38	wak,µk	wak,µk	PROPN
ejpam-6102	386	39	⟩	⟩	NOUN
ejpam-6102	386	40	,	,	PUNCT
ejpam-6102	386	41	∂j̃	∂j̃	VERB
ejpam-6102	386	42	∂τk	∂τk	PROPN
ejpam-6102	386	43	,	,	PUNCT
ejpam-6102	386	44	j	j	PROPN
ejpam-6102	386	45	(	(	PUNCT
ejpam-6102	386	46	λ	λ	PROPN
ejpam-6102	386	47	)	)	PUNCT
ejpam-6102	386	48	=	=	SYM
ejpam-6102	386	49	〈	〈	NOUN
ejpam-6102	386	50	∇jε(u	∇jε(u	NOUN
ejpam-6102	386	51	)	)	PUNCT
ejpam-6102	386	52	,	,	PUNCT
ejpam-6102	386	53	αk	αk	ADP
ejpam-6102	386	54	∂wak,µk	∂wak,µk	PROPN
ejpam-6102	386	55	∂τk	∂τk	PROPN
ejpam-6102	386	56	,	,	PUNCT
ejpam-6102	386	57	j	j	PROPN
ejpam-6102	386	58	〉	〉	NOUN
ejpam-6102	386	59	,	,	PUNCT
ejpam-6102	386	60	1	1	NUM
ejpam-6102	386	61	≤	≤	NUM
ejpam-6102	386	62	j	j	PROPN
ejpam-6102	386	63	≤	≤	PROPN
ejpam-6102	386	64	n−	n−	PROPN
ejpam-6102	386	65	1	1	NUM
ejpam-6102	386	66	.	.	PUNCT
ejpam-6102	387	1	(	(	PUNCT
ejpam-6102	387	2	40	40	NUM
ejpam-6102	387	3	)	)	PUNCT
ejpam-6102	387	4	second	second	ADV
ejpam-6102	387	5	,	,	PUNCT
ejpam-6102	387	6	using	use	VERB
ejpam-6102	387	7	proposition	proposition	NOUN
ejpam-6102	387	8	3	3	NUM
ejpam-6102	387	9	,	,	PUNCT
ejpam-6102	387	10	for	for	ADP
ejpam-6102	387	11	each	each	DET
ejpam-6102	387	12	(	(	PUNCT
ejpam-6102	387	13	a	a	PRON
ejpam-6102	387	14	,	,	PUNCT
ejpam-6102	387	15	µ	µ	NOUN
ejpam-6102	387	16	,	,	PUNCT
ejpam-6102	387	17	α	α	NOUN
ejpam-6102	387	18	,	,	PUNCT
ejpam-6102	387	19	0	0	NUM
ejpam-6102	387	20	)	)	PUNCT
ejpam-6102	387	21	∈	∈	PROPN
ejpam-6102	387	22	dε	dε	NOUN
ejpam-6102	387	23	,	,	PUNCT
ejpam-6102	387	24	n	n	CCONJ
ejpam-6102	387	25	,	,	PUNCT
ejpam-6102	387	26	there	there	PRON
ejpam-6102	387	27	exists	exist	VERB
ejpam-6102	387	28	v	v	ADP
ejpam-6102	387	29	:	:	PUNCT
ejpam-6102	387	30	=	=	SYM
ejpam-6102	387	31	v̄ε	v̄ε	NOUN
ejpam-6102	387	32	,	,	PUNCT
ejpam-6102	387	33	a,µ,α	a,µ,α	PROPN
ejpam-6102	387	34	∈	∈	NOUN
ejpam-6102	387	35	fa,µ	fa,µ	NOUN
ejpam-6102	387	36	such	such	ADJ
ejpam-6102	387	37	that	that	SCONJ
ejpam-6102	387	38	〈	〈	PROPN
ejpam-6102	387	39	∇jε	∇jε	NOUN
ejpam-6102	387	40	(	(	PUNCT
ejpam-6102	387	41	n∑	n∑	NOUN
ejpam-6102	387	42	i=1	i=1	PROPN
ejpam-6102	387	43	αiwaiµi	αiwaiµi	PROPN
ejpam-6102	387	44	+	+	CCONJ
ejpam-6102	387	45	v	v	NOUN
ejpam-6102	387	46	)	)	PUNCT
ejpam-6102	387	47	,	,	PUNCT
ejpam-6102	387	48	h	h	NOUN
ejpam-6102	387	49	〉	〉	NOUN
ejpam-6102	387	50	=	=	SYM
ejpam-6102	387	51	0	0	NUM
ejpam-6102	387	52	∀h	∀h	PROPN
ejpam-6102	387	53	∈	∈	PROPN
ejpam-6102	387	54	fa,µ	fa,µ	NOUN
ejpam-6102	387	55	and	and	CCONJ
ejpam-6102	387	56	∥v∥	∥v∥	ADJ
ejpam-6102	387	57	⩽	⩽	NOUN
ejpam-6102	387	58	c	c	PROPN
ejpam-6102	387	59	(	(	PUNCT
ejpam-6102	387	60	ε+	ε+	X
ejpam-6102	387	61	∑	∑	SYM
ejpam-6102	387	62	1	1	NUM
ejpam-6102	387	63	µi	µi	PROPN
ejpam-6102	387	64	)	)	PUNCT
ejpam-6102	387	65	.	.	PUNCT
ejpam-6102	388	1	(	(	PUNCT
ejpam-6102	388	2	41	41	NUM
ejpam-6102	388	3	)	)	PUNCT
ejpam-6102	388	4	r.	r.	PROPN
ejpam-6102	388	5	almushahhin	almushahhin	PROPN
ejpam-6102	388	6	,	,	PUNCT
ejpam-6102	388	7	m.	m.	PROPN
ejpam-6102	388	8	ben	ben	PROPN
ejpam-6102	388	9	ayed	aye	VERB
ejpam-6102	388	10	/	/	SYM
ejpam-6102	388	11	eur	eur	PROPN
ejpam-6102	388	12	.	.	PUNCT
ejpam-6102	389	1	j.	j.	PROPN
ejpam-6102	389	2	pure	pure	PROPN
ejpam-6102	389	3	appl	appl	PROPN
ejpam-6102	389	4	.	.	PROPN
ejpam-6102	389	5	math	math	PROPN
ejpam-6102	389	6	,	,	PUNCT
ejpam-6102	389	7	18	18	NUM
ejpam-6102	389	8	(	(	PUNCT
ejpam-6102	389	9	2	2	NUM
ejpam-6102	389	10	)	)	PUNCT
ejpam-6102	389	11	(	(	PUNCT
ejpam-6102	389	12	2025	2025	NUM
ejpam-6102	389	13	)	)	PUNCT
ejpam-6102	389	14	,	,	PUNCT
ejpam-6102	389	15	6102	6102	NUM
ejpam-6102	389	16	15	15	NUM
ejpam-6102	389	17	of	of	ADP
ejpam-6102	389	18	31	31	NUM
ejpam-6102	389	19	therefore	therefore	ADV
ejpam-6102	389	20	,	,	PUNCT
ejpam-6102	389	21	eqs	eqs	X
ejpam-6102	389	22	.	.	PUNCT
ejpam-6102	390	1	(	(	PUNCT
ejpam-6102	390	2	40	40	NUM
ejpam-6102	390	3	)	)	PUNCT
ejpam-6102	390	4	and	and	CCONJ
ejpam-6102	390	5	(	(	PUNCT
ejpam-6102	390	6	41	41	NUM
ejpam-6102	390	7	)	)	PUNCT
ejpam-6102	390	8	imply	imply	VERB
ejpam-6102	390	9	the	the	DET
ejpam-6102	390	10	existence	existence	NOUN
ejpam-6102	390	11	of	of	ADP
ejpam-6102	390	12	η	η	PROPN
ejpam-6102	390	13	∈	∈	PROPN
ejpam-6102	390	14	rn	rn	PROPN
ejpam-6102	390	15	,	,	PUNCT
ejpam-6102	390	16	σ	σ	PROPN
ejpam-6102	390	17	∈	∈	PROPN
ejpam-6102	390	18	rn	rn	PROPN
ejpam-6102	390	19	and	and	CCONJ
ejpam-6102	390	20	γ	γ	PROPN
ejpam-6102	390	21	∈	∈	PROPN
ejpam-6102	390	22	(	(	PUNCT
ejpam-6102	390	23	rn−1	rn−1	PROPN
ejpam-6102	390	24	)	)	PUNCT
ejpam-6102	390	25	n	n	NOUN
ejpam-6102	390	26	such	such	ADJ
ejpam-6102	390	27	that	that	SCONJ
ejpam-6102	390	28	∇jε(ū	∇jε(ū	PROPN
ejpam-6102	390	29	)	)	PUNCT
ejpam-6102	390	30	=	=	SYM
ejpam-6102	390	31	∇j̃ε(λ̄	∇j̃ε(λ̄	ADJ
ejpam-6102	390	32	)	)	PUNCT
ejpam-6102	391	1	=	=	SYM
ejpam-6102	391	2	n∑	n∑	NOUN
ejpam-6102	391	3	k=1	k=1	PUNCT
ejpam-6102	391	4	ηkwak,µk	ηkwak,µk	PROPN
ejpam-6102	392	1	+	+	PROPN
ejpam-6102	392	2	σkµk	σkµk	PROPN
ejpam-6102	392	3	∂wak,µk	∂wak,µk	PROPN
ejpam-6102	392	4	∂µk	∂µk	PROPN
ejpam-6102	392	5	+	+	CCONJ
ejpam-6102	392	6	n−1∑	n−1∑	PROPN
ejpam-6102	392	7	j=1	j=1	PROPN
ejpam-6102	392	8	γk	γk	PROPN
ejpam-6102	392	9	,	,	PUNCT
ejpam-6102	392	10	j	j	PROPN
ejpam-6102	392	11	1	1	NUM
ejpam-6102	392	12	µk	µk	ADP
ejpam-6102	392	13	∂wak,µk	∂wak,µk	PROPN
ejpam-6102	392	14	∂τk	∂τk	PROPN
ejpam-6102	392	15	,	,	PUNCT
ejpam-6102	392	16	j	j	PROPN
ejpam-6102	392	17			PROPN
ejpam-6102	392	18	(	(	PUNCT
ejpam-6102	392	19	42	42	NUM
ejpam-6102	392	20	)	)	PUNCT
ejpam-6102	392	21	where	where	SCONJ
ejpam-6102	392	22	λ̄	λ̄	VERB
ejpam-6102	392	23	=	=	SYM
ejpam-6102	392	24	(	(	PUNCT
ejpam-6102	392	25	a	a	PRON
ejpam-6102	392	26	,	,	PUNCT
ejpam-6102	392	27	µ	µ	NOUN
ejpam-6102	392	28	,	,	PUNCT
ejpam-6102	392	29	α	α	NOUN
ejpam-6102	392	30	,	,	PUNCT
ejpam-6102	392	31	v̄	v̄	NOUN
ejpam-6102	392	32	)	)	PUNCT
ejpam-6102	392	33	and	and	CCONJ
ejpam-6102	392	34	ū	ū	NOUN
ejpam-6102	393	1	=	=	PUNCT
ejpam-6102	393	2	∑n	∑n	PROPN
ejpam-6102	393	3	i=1	i=1	X
ejpam-6102	393	4	αiwai,µi	αiwai,µi	PROPN
ejpam-6102	394	1	+	+	CCONJ
ejpam-6102	394	2	v̄.	v̄.	PUNCT
ejpam-6102	394	3	thus	thus	ADV
ejpam-6102	394	4	,	,	PUNCT
ejpam-6102	394	5	(	(	PUNCT
ejpam-6102	394	6	42	42	NUM
ejpam-6102	394	7	)	)	PUNCT
ejpam-6102	394	8	implies	imply	VERB
ejpam-6102	394	9	that	that	SCONJ
ejpam-6102	394	10	the	the	DET
ejpam-6102	394	11	second	second	ADJ
ejpam-6102	394	12	equation	equation	NOUN
ejpam-6102	394	13	of	of	ADP
ejpam-6102	394	14	(	(	PUNCT
ejpam-6102	394	15	37	37	NUM
ejpam-6102	394	16	)	)	PUNCT
ejpam-6102	394	17	is	be	AUX
ejpam-6102	394	18	satisfied	satisfied	ADJ
ejpam-6102	394	19	for	for	ADP
ejpam-6102	394	20	each	each	PRON
ejpam-6102	394	21	(	(	PUNCT
ejpam-6102	394	22	a	a	PRON
ejpam-6102	394	23	,	,	PUNCT
ejpam-6102	394	24	µ	µ	NOUN
ejpam-6102	394	25	,	,	PUNCT
ejpam-6102	394	26	α	α	NOUN
ejpam-6102	394	27	,	,	PUNCT
ejpam-6102	394	28	v̄	v̄	NOUN
ejpam-6102	394	29	)	)	PUNCT
ejpam-6102	394	30	∈	∈	PROPN
ejpam-6102	394	31	dε	dε	NOUN
ejpam-6102	394	32	,	,	PUNCT
ejpam-6102	394	33	n	n	NOUN
ejpam-6102	394	34	.	.	PUNCT
ejpam-6102	395	1	hence	hence	ADV
ejpam-6102	395	2	,	,	PUNCT
ejpam-6102	395	3	it	it	PRON
ejpam-6102	395	4	remains	remain	VERB
ejpam-6102	395	5	to	to	PART
ejpam-6102	395	6	solve	solve	VERB
ejpam-6102	395	7	the	the	DET
ejpam-6102	395	8	three	three	NUM
ejpam-6102	395	9	other	other	ADJ
ejpam-6102	395	10	equations	equation	NOUN
ejpam-6102	395	11	.	.	PUNCT
ejpam-6102	396	1	to	to	PART
ejpam-6102	396	2	do	do	VERB
ejpam-6102	396	3	so	so	ADV
ejpam-6102	396	4	,	,	PUNCT
ejpam-6102	396	5	we	we	PRON
ejpam-6102	396	6	start	start	VERB
ejpam-6102	396	7	by	by	ADP
ejpam-6102	396	8	giving	give	VERB
ejpam-6102	396	9	the	the	DET
ejpam-6102	396	10	estimate	estimate	NOUN
ejpam-6102	396	11	of	of	ADP
ejpam-6102	396	12	the	the	DET
ejpam-6102	396	13	multiplier	multipli	ADJ
ejpam-6102	396	14	lagrange	lagrange	NOUN
ejpam-6102	396	15	coefficients	coefficient	NOUN
ejpam-6102	396	16	(	(	PUNCT
ejpam-6102	396	17	η	η	PROPN
ejpam-6102	396	18	,	,	PUNCT
ejpam-6102	396	19	σ	σ	PROPN
ejpam-6102	396	20	,	,	PUNCT
ejpam-6102	396	21	γ	γ	PROPN
ejpam-6102	396	22	)	)	PUNCT
ejpam-6102	396	23	.	.	PUNCT
ejpam-6102	397	1	lemma	lemma	PROPN
ejpam-6102	397	2	3	3	X
ejpam-6102	397	3	.	.	PUNCT
ejpam-6102	398	1	the	the	DET
ejpam-6102	398	2	multiplier	multipli	ADJ
ejpam-6102	398	3	lagrange	lagrange	PROPN
ejpam-6102	398	4	coefficients	coefficient	NOUN
ejpam-6102	398	5	(	(	PUNCT
ejpam-6102	398	6	η	η	PROPN
ejpam-6102	398	7	,	,	PUNCT
ejpam-6102	398	8	σ	σ	PROPN
ejpam-6102	398	9	,	,	PUNCT
ejpam-6102	398	10	γ	γ	PROPN
ejpam-6102	398	11	)	)	PUNCT
ejpam-6102	398	12	found	find	VERB
ejpam-6102	398	13	in	in	ADP
ejpam-6102	398	14	(	(	PUNCT
ejpam-6102	398	15	42	42	NUM
ejpam-6102	398	16	)	)	PUNCT
ejpam-6102	398	17	satisfy	satisfy	NOUN
ejpam-6102	398	18	:	:	PUNCT
ejpam-6102	398	19	|ηk|	|ηk|	PROPN
ejpam-6102	398	20	⩽	⩽	NOUN
ejpam-6102	398	21	cε	cε	PUNCT
ejpam-6102	398	22	ln2	ln2	PROPN
ejpam-6102	398	23	ε	ε	PROPN
ejpam-6102	398	24	;	;	PUNCT
ejpam-6102	398	25	|σk|	|σk|	ADJ
ejpam-6102	398	26	⩽	⩽	PROPN
ejpam-6102	398	27	cε	cε	VERB
ejpam-6102	398	28	;	;	PUNCT
ejpam-6102	398	29	|γk	|γk	PUNCT
ejpam-6102	398	30	,	,	PUNCT
ejpam-6102	398	31	j	j	PROPN
ejpam-6102	398	32	|	|	ADV
ejpam-6102	398	33	⩽	⩽	PROPN
ejpam-6102	398	34	cε3/2	cε3/2	PROPN
ejpam-6102	398	35	,	,	PUNCT
ejpam-6102	398	36	for	for	ADP
ejpam-6102	398	37	each	each	DET
ejpam-6102	398	38	k	k	PROPN
ejpam-6102	398	39	∈	∈	PROPN
ejpam-6102	398	40	{	{	PUNCT
ejpam-6102	398	41	1	1	NUM
ejpam-6102	398	42	,	,	PUNCT
ejpam-6102	398	43	.	.	PUNCT
ejpam-6102	398	44	.	.	PUNCT
ejpam-6102	399	1	.	.	PUNCT
ejpam-6102	400	1	,	,	PUNCT
ejpam-6102	400	2	n	n	CCONJ
ejpam-6102	400	3	}	}	PUNCT
ejpam-6102	400	4	and	and	CCONJ
ejpam-6102	400	5	each	each	DET
ejpam-6102	400	6	j	j	PROPN
ejpam-6102	400	7	∈	∈	PROPN
ejpam-6102	400	8	{	{	PUNCT
ejpam-6102	400	9	1	1	NUM
ejpam-6102	400	10	,	,	PUNCT
ejpam-6102	400	11	.	.	PUNCT
ejpam-6102	400	12	.	.	PUNCT
ejpam-6102	401	1	.	.	PUNCT
ejpam-6102	402	1	,	,	PUNCT
ejpam-6102	402	2	n−	n−	NOUN
ejpam-6102	402	3	1	1	NUM
ejpam-6102	402	4	}	}	PUNCT
ejpam-6102	402	5	.	.	PUNCT
ejpam-6102	403	1	proof	proof	NOUN
ejpam-6102	403	2	.	.	PUNCT
ejpam-6102	404	1	using	use	VERB
ejpam-6102	404	2	λ̄	λ̄	NOUN
ejpam-6102	404	3	:	:	PUNCT
ejpam-6102	404	4	=	=	SYM
ejpam-6102	404	5	(	(	PUNCT
ejpam-6102	404	6	a	a	PRON
ejpam-6102	404	7	,	,	PUNCT
ejpam-6102	404	8	µ	µ	NOUN
ejpam-6102	404	9	,	,	PUNCT
ejpam-6102	404	10	α	α	NOUN
ejpam-6102	404	11	,	,	PUNCT
ejpam-6102	404	12	v̄	v̄	NOUN
ejpam-6102	404	13	)	)	PUNCT
ejpam-6102	404	14	∈	∈	PROPN
ejpam-6102	404	15	dε	dε	NOUN
ejpam-6102	404	16	,	,	PUNCT
ejpam-6102	404	17	n	n	NOUN
ejpam-6102	404	18	and	and	CCONJ
ejpam-6102	404	19	propositions	proposition	NOUN
ejpam-6102	404	20	4	4	NUM
ejpam-6102	404	21	,	,	PUNCT
ejpam-6102	404	22	5	5	NUM
ejpam-6102	404	23	and	and	CCONJ
ejpam-6102	404	24	6	6	NUM
ejpam-6102	404	25	,	,	PUNCT
ejpam-6102	404	26	it	it	PRON
ejpam-6102	404	27	follows	follow	VERB
ejpam-6102	404	28	that	that	PRON
ejpam-6102	404	29	⟨∇jε(ū	⟨∇jε(ū	PROPN
ejpam-6102	404	30	)	)	PUNCT
ejpam-6102	404	31	,	,	PUNCT
ejpam-6102	404	32	wak,µk	wak,µk	PROPN
ejpam-6102	404	33	⟩	⟩	NOUN
ejpam-6102	404	34	=	=	SYM
ejpam-6102	404	35	o	o	X
ejpam-6102	404	36	(	(	PUNCT
ejpam-6102	404	37	ε+	ε+	X
ejpam-6102	404	38	∣∣∣1−	∣∣∣1−	NUM
ejpam-6102	404	39	α	α	PROPN
ejpam-6102	404	40	4/(n−2	4/(n−2	NUM
ejpam-6102	404	41	)	)	PUNCT
ejpam-6102	405	1	i	i	PRON
ejpam-6102	405	2	f	f	X
ejpam-6102	405	3	(	(	PUNCT
ejpam-6102	405	4	ai	ai	PROPN
ejpam-6102	405	5	)	)	PUNCT
ejpam-6102	405	6	∣∣∣+	∣∣∣+	PROPN
ejpam-6102	405	7	ε	ε	PROPN
ejpam-6102	405	8	|ln	|ln	PUNCT
ejpam-6102	405	9	ε|	ε|	ADV
ejpam-6102	405	10	)	)	PUNCT
ejpam-6102	406	1	=	=	PUNCT
ejpam-6102	406	2	o	o	X
ejpam-6102	406	3	(	(	PUNCT
ejpam-6102	406	4	ε|	ε|	PROPN
ejpam-6102	406	5	ln	ln	PROPN
ejpam-6102	406	6	ε|2	ε|2	PROPN
ejpam-6102	406	7	)	)	PUNCT
ejpam-6102	406	8	,	,	PUNCT
ejpam-6102	406	9	〈	〈	PROPN
ejpam-6102	406	10	∇jε(ū	∇jε(ū	PROPN
ejpam-6102	406	11	)	)	PUNCT
ejpam-6102	406	12	,	,	PUNCT
ejpam-6102	406	13	µk	µk	DET
ejpam-6102	406	14	∂wak,µk	∂wak,µk	PROPN
ejpam-6102	406	15	∂µk	∂µk	VERB
ejpam-6102	406	16	〉	〉	NOUN
ejpam-6102	406	17	=	=	SYM
ejpam-6102	406	18	o(ε	o(ε	PROPN
ejpam-6102	406	19	)	)	PUNCT
ejpam-6102	406	20	,	,	PUNCT
ejpam-6102	406	21	〈	〈	PROPN
ejpam-6102	406	22	∇jε(ū	∇jε(ū	PROPN
ejpam-6102	406	23	)	)	PUNCT
ejpam-6102	406	24	,	,	PUNCT
ejpam-6102	406	25	1	1	NUM
ejpam-6102	406	26	µk	µk	PRON
ejpam-6102	406	27	∂wak,µk	∂wak,µk	PROPN
ejpam-6102	406	28	∂τk	∂τk	PROPN
ejpam-6102	406	29	,	,	PUNCT
ejpam-6102	406	30	j	j	PROPN
ejpam-6102	406	31	〉	〉	NOUN
ejpam-6102	406	32	=	=	PUNCT
ejpam-6102	407	1	o	o	X
ejpam-6102	407	2	(	(	PUNCT
ejpam-6102	407	3	ε	ε	PROPN
ejpam-6102	407	4	|ak	|ak	NUM
ejpam-6102	407	5	−	−	NOUN
ejpam-6102	407	6	bk|+	bk|+	PROPN
ejpam-6102	407	7	ε2	ε2	ADV
ejpam-6102	407	8	)	)	PUNCT
ejpam-6102	408	1	=	=	SYM
ejpam-6102	408	2	o	o	X
ejpam-6102	408	3	(	(	PUNCT
ejpam-6102	408	4	ε3/2	ε3/2	NOUN
ejpam-6102	408	5	)	)	PUNCT
ejpam-6102	408	6	.	.	PUNCT
ejpam-6102	409	1	furthermore	furthermore	ADV
ejpam-6102	409	2	,	,	PUNCT
ejpam-6102	409	3	for	for	ADP
ejpam-6102	409	4	ψk	ψk	NOUN
ejpam-6102	409	5	,	,	PUNCT
ejpam-6102	409	6	ψl	ψl	ADP
ejpam-6102	409	7	∈	∈	PROPN
ejpam-6102	409	8	n⋃	n⋃	VERB
ejpam-6102	409	9	i=1	i=1	PRON
ejpam-6102	409	10	{	{	PUNCT
ejpam-6102	409	11	wai,µi	wai,µi	NOUN
ejpam-6102	409	12	,	,	PUNCT
ejpam-6102	409	13	µi	µi	PROPN
ejpam-6102	409	14	∂wai,µi	∂wai,µi	PROPN
ejpam-6102	409	15	∂µi	∂µi	PROPN
ejpam-6102	409	16	,	,	PUNCT
ejpam-6102	409	17	1	1	NUM
ejpam-6102	409	18	µi	µi	PROPN
ejpam-6102	409	19	∂wai,µi	∂wai,µi	PROPN
ejpam-6102	409	20	∂τi	∂τi	PROPN
ejpam-6102	409	21	,	,	PUNCT
ejpam-6102	409	22	j	j	PROPN
ejpam-6102	409	23	,	,	PUNCT
ejpam-6102	409	24	j	j	PROPN
ejpam-6102	409	25	∈	∈	PROPN
ejpam-6102	409	26	{	{	PUNCT
ejpam-6102	409	27	1	1	NUM
ejpam-6102	409	28	,	,	PUNCT
ejpam-6102	409	29	.	.	PUNCT
ejpam-6102	409	30	.	.	PUNCT
ejpam-6102	409	31	.	.	PUNCT
ejpam-6102	410	1	,	,	PUNCT
ejpam-6102	410	2	n−	n−	NOUN
ejpam-6102	410	3	1	1	NUM
ejpam-6102	410	4	}	}	PUNCT
ejpam-6102	410	5	}	}	PUNCT
ejpam-6102	410	6	,	,	PUNCT
ejpam-6102	410	7	using	use	VERB
ejpam-6102	410	8	lemmas	lemmas	PROPN
ejpam-6102	410	9	4	4	NUM
ejpam-6102	410	10	,	,	PUNCT
ejpam-6102	410	11	5	5	NUM
ejpam-6102	410	12	and	and	CCONJ
ejpam-6102	410	13	9	9	NUM
ejpam-6102	410	14	,	,	PUNCT
ejpam-6102	410	15	we	we	PRON
ejpam-6102	410	16	deduce	deduce	VERB
ejpam-6102	410	17	that	that	DET
ejpam-6102	410	18	⟨ψk	⟨ψk	NOUN
ejpam-6102	410	19	,	,	PUNCT
ejpam-6102	410	20	ψl⟩	ψl⟩	PUNCT
ejpam-6102	410	21	=	=	SYM
ejpam-6102	410	22	{	{	PUNCT
ejpam-6102	410	23	c+o(ε	c+o(ε	PROPN
ejpam-6102	410	24	)	)	PUNCT
ejpam-6102	410	25	if	if	SCONJ
ejpam-6102	410	26	k	k	PROPN
ejpam-6102	410	27	=	=	SYM
ejpam-6102	410	28	l	l	PROPN
ejpam-6102	410	29	,	,	PUNCT
ejpam-6102	410	30	o(ε	o(ε	PROPN
ejpam-6102	410	31	)	)	PUNCT
ejpam-6102	410	32	if	if	SCONJ
ejpam-6102	410	33	k	k	PROPN
ejpam-6102	410	34	̸=	̸=	PROPN
ejpam-6102	410	35	l	l	NOUN
ejpam-6102	410	36	,	,	PUNCT
ejpam-6102	410	37	for	for	ADP
ejpam-6102	410	38	some	some	DET
ejpam-6102	410	39	positive	positive	ADJ
ejpam-6102	410	40	constant	constant	ADJ
ejpam-6102	410	41	c.	c.	NOUN
ejpam-6102	410	42	thus	thus	ADV
ejpam-6102	410	43	,	,	PUNCT
ejpam-6102	410	44	the	the	DET
ejpam-6102	410	45	scalar	scalar	ADJ
ejpam-6102	410	46	products	product	NOUN
ejpam-6102	410	47	of	of	ADP
ejpam-6102	410	48	(	(	PUNCT
ejpam-6102	410	49	42	42	NUM
ejpam-6102	410	50	)	)	PUNCT
ejpam-6102	410	51	with	with	ADP
ejpam-6102	410	52	wai,µi	wai,µi	NOUN
ejpam-6102	410	53	,	,	PUNCT
ejpam-6102	410	54	µi	µi	PROPN
ejpam-6102	410	55	∂wai,µi	∂wai,µi	PROPN
ejpam-6102	410	56	∂µi	∂µi	PROPN
ejpam-6102	410	57	and	and	CCONJ
ejpam-6102	410	58	1	1	NUM
ejpam-6102	410	59	µi	µi	PROPN
ejpam-6102	410	60	∂wai,µi	∂wai,µi	PROPN
ejpam-6102	410	61	∂τi	∂τi	PROPN
ejpam-6102	410	62	,	,	PUNCT
ejpam-6102	410	63	j	j	PROPN
ejpam-6102	410	64	,	,	PUNCT
ejpam-6102	410	65	respectively	respectively	ADV
ejpam-6102	410	66	,	,	PUNCT
ejpam-6102	410	67	give	give	VERB
ejpam-6102	410	68	the	the	DET
ejpam-6102	410	69	following	follow	VERB
ejpam-6102	410	70	quasi	quasi	ADJ
ejpam-6102	410	71	-	-	ADJ
ejpam-6102	410	72	diagonal	diagonal	ADJ
ejpam-6102	410	73	system	system	NOUN
ejpam-6102	410	74	:	:	PUNCT
ejpam-6102	410	75	cηi	cηi	VERB
ejpam-6102	411	1	+	+	CCONJ
ejpam-6102	411	2	∑	∑	PROPN
ejpam-6102	411	3	k	k	PROPN
ejpam-6102	411	4	o	o	PROPN
ejpam-6102	411	5	(	(	PUNCT
ejpam-6102	411	6	ε	ε	PROPN
ejpam-6102	411	7	(	(	PUNCT
ejpam-6102	411	8	|γk|+	|γk|+	VERB
ejpam-6102	411	9	|σk|+	|σk|+	PROPN
ejpam-6102	411	10	|ηk|	|ηk|	PROPN
ejpam-6102	411	11	)	)	PUNCT
ejpam-6102	411	12	)	)	PUNCT
ejpam-6102	412	1	=	=	PUNCT
ejpam-6102	412	2	o	o	NOUN
ejpam-6102	412	3	(	(	PUNCT
ejpam-6102	412	4	ε	ε	PROPN
ejpam-6102	412	5	ln2	ln2	PROPN
ejpam-6102	412	6	ε	ε	PROPN
ejpam-6102	412	7	)	)	PUNCT
ejpam-6102	412	8	,	,	PUNCT
ejpam-6102	412	9	cσi	cσi	PROPN
ejpam-6102	413	1	+	+	CCONJ
ejpam-6102	413	2	∑	∑	PROPN
ejpam-6102	413	3	k	k	PROPN
ejpam-6102	413	4	o	o	PROPN
ejpam-6102	413	5	(	(	PUNCT
ejpam-6102	413	6	ε	ε	PROPN
ejpam-6102	413	7	(	(	PUNCT
ejpam-6102	413	8	|γk|+	|γk|+	VERB
ejpam-6102	413	9	|σk|+	|σk|+	PROPN
ejpam-6102	413	10	|ηk|	|ηk|	PROPN
ejpam-6102	413	11	)	)	PUNCT
ejpam-6102	413	12	)	)	PUNCT
ejpam-6102	414	1	=	=	SYM
ejpam-6102	414	2	o(ε	o(ε	PROPN
ejpam-6102	414	3	)	)	PUNCT
ejpam-6102	414	4	,	,	PUNCT
ejpam-6102	414	5	cγij	cγij	NOUN
ejpam-6102	414	6	+	+	NOUN
ejpam-6102	414	7	o	o	X
ejpam-6102	414	8	(	(	PUNCT
ejpam-6102	414	9	ε	ε	PROPN
ejpam-6102	414	10	(	(	PUNCT
ejpam-6102	414	11	|γk|+	|γk|+	VERB
ejpam-6102	414	12	|σk|+	|σk|+	PROPN
ejpam-6102	414	13	|ηk|	|ηk|	PROPN
ejpam-6102	414	14	)	)	PUNCT
ejpam-6102	414	15	)	)	PUNCT
ejpam-6102	415	1	=	=	PUNCT
ejpam-6102	415	2	o	o	NOUN
ejpam-6102	415	3	(	(	PUNCT
ejpam-6102	415	4	ε3/2	ε3/2	NOUN
ejpam-6102	415	5	)	)	PUNCT
ejpam-6102	415	6	,	,	PUNCT
ejpam-6102	415	7	which	which	PRON
ejpam-6102	415	8	implies	imply	VERB
ejpam-6102	415	9	the	the	DET
ejpam-6102	415	10	result	result	NOUN
ejpam-6102	415	11	.	.	PUNCT
ejpam-6102	416	1	now	now	ADV
ejpam-6102	416	2	,	,	PUNCT
ejpam-6102	416	3	we	we	PRON
ejpam-6102	416	4	are	be	AUX
ejpam-6102	416	5	ready	ready	ADJ
ejpam-6102	416	6	to	to	PART
ejpam-6102	416	7	solve	solve	VERB
ejpam-6102	416	8	the	the	DET
ejpam-6102	416	9	equations	equation	NOUN
ejpam-6102	416	10	(	(	PUNCT
ejpam-6102	416	11	ak	ak	PROPN
ejpam-6102	416	12	,	,	PUNCT
ejpam-6102	416	13	mk	mk	PROPN
ejpam-6102	416	14	,	,	PUNCT
ejpam-6102	416	15	tk	tk	PROPN
ejpam-6102	416	16	)	)	PUNCT
ejpam-6102	416	17	for	for	ADP
ejpam-6102	416	18	k	k	PROPN
ejpam-6102	416	19	∈	∈	PROPN
ejpam-6102	416	20	{	{	PUNCT
ejpam-6102	416	21	1	1	NUM
ejpam-6102	416	22	,	,	PUNCT
ejpam-6102	416	23	.	.	PUNCT
ejpam-6102	416	24	.	.	PUNCT
ejpam-6102	417	1	.	.	PUNCT
ejpam-6102	418	1	,	,	PUNCT
ejpam-6102	418	2	n	n	CCONJ
ejpam-6102	418	3	}	}	PUNCT
ejpam-6102	418	4	defined	define	VERB
ejpam-6102	418	5	in	in	ADP
ejpam-6102	418	6	proposition	proposition	NOUN
ejpam-6102	418	7	7	7	NUM
ejpam-6102	418	8	.	.	PUNCT
ejpam-6102	418	9	r.	r.	PROPN
ejpam-6102	418	10	almushahhin	almushahhin	PROPN
ejpam-6102	418	11	,	,	PUNCT
ejpam-6102	418	12	m.	m.	PROPN
ejpam-6102	418	13	ben	ben	PROPN
ejpam-6102	418	14	ayed	aye	VERB
ejpam-6102	418	15	/	/	SYM
ejpam-6102	418	16	eur	eur	PROPN
ejpam-6102	418	17	.	.	PUNCT
ejpam-6102	419	1	j.	j.	PROPN
ejpam-6102	419	2	pure	pure	PROPN
ejpam-6102	419	3	appl	appl	PROPN
ejpam-6102	419	4	.	.	PROPN
ejpam-6102	419	5	math	math	PROPN
ejpam-6102	419	6	,	,	PUNCT
ejpam-6102	419	7	18	18	NUM
ejpam-6102	419	8	(	(	PUNCT
ejpam-6102	419	9	2	2	NUM
ejpam-6102	419	10	)	)	PUNCT
ejpam-6102	419	11	(	(	PUNCT
ejpam-6102	419	12	2025	2025	NUM
ejpam-6102	419	13	)	)	PUNCT
ejpam-6102	419	14	,	,	PUNCT
ejpam-6102	419	15	6102	6102	NUM
ejpam-6102	419	16	16	16	NUM
ejpam-6102	419	17	of	of	ADP
ejpam-6102	419	18	31	31	NUM
ejpam-6102	419	19	first	first	ADJ
ejpam-6102	419	20	,	,	PUNCT
ejpam-6102	419	21	using	use	VERB
ejpam-6102	419	22	lemma	lemma	PROPN
ejpam-6102	419	23	3	3	NUM
ejpam-6102	419	24	and	and	CCONJ
ejpam-6102	419	25	eq	eq	NOUN
ejpam-6102	419	26	.	.	PUNCT
ejpam-6102	420	1	(	(	PUNCT
ejpam-6102	420	2	41	41	NUM
ejpam-6102	420	3	)	)	PUNCT
ejpam-6102	420	4	,	,	PUNCT
ejpam-6102	420	5	for	for	ADP
ejpam-6102	420	6	λ̄	λ̄	NUM
ejpam-6102	420	7	=	=	SYM
ejpam-6102	420	8	(	(	PUNCT
ejpam-6102	420	9	a	a	PRON
ejpam-6102	420	10	,	,	PUNCT
ejpam-6102	420	11	µ	µ	NOUN
ejpam-6102	420	12	,	,	PUNCT
ejpam-6102	420	13	α	α	NOUN
ejpam-6102	420	14	,	,	PUNCT
ejpam-6102	420	15	v̄	v̄	NOUN
ejpam-6102	420	16	)	)	PUNCT
ejpam-6102	420	17	,	,	PUNCT
ejpam-6102	420	18	the	the	DET
ejpam-6102	420	19	equations	equation	NOUN
ejpam-6102	420	20	(	(	PUNCT
ejpam-6102	420	21	ak	ak	PROPN
ejpam-6102	420	22	,	,	PUNCT
ejpam-6102	420	23	mk	mk	PROPN
ejpam-6102	420	24	,	,	PUNCT
ejpam-6102	420	25	tk	tk	PROPN
ejpam-6102	420	26	)	)	PUNCT
ejpam-6102	420	27	in	in	ADP
ejpam-6102	420	28	the	the	DET
ejpam-6102	420	29	system	system	NOUN
ejpam-6102	420	30	(	(	PUNCT
ejpam-6102	420	31	37	37	NUM
ejpam-6102	420	32	)	)	PUNCT
ejpam-6102	420	33	are	be	AUX
ejpam-6102	420	34	equivalent	equivalent	ADJ
ejpam-6102	420	35	to	to	ADP
ejpam-6102	420	36	:	:	PUNCT
ejpam-6102	420	37	∂j̃ε	∂j̃ε	PROPN
ejpam-6102	420	38	∂αk	∂αk	PROPN
ejpam-6102	420	39	(	(	PUNCT
ejpam-6102	420	40	λ̄	λ̄	ADJ
ejpam-6102	420	41	)	)	PUNCT
ejpam-6102	420	42	=	=	SYM
ejpam-6102	420	43	0	0	NUM
ejpam-6102	420	44	,	,	PUNCT
ejpam-6102	420	45	∀k	∀k	NOUN
ejpam-6102	420	46	∈	∈	PROPN
ejpam-6102	420	47	{	{	PUNCT
ejpam-6102	420	48	1	1	NUM
ejpam-6102	420	49	,	,	PUNCT
ejpam-6102	420	50	.	.	PUNCT
ejpam-6102	420	51	.	.	PUNCT
ejpam-6102	421	1	.	.	PUNCT
ejpam-6102	422	1	,	,	PUNCT
ejpam-6102	423	1	n	n	CCONJ
ejpam-6102	423	2	}	}	PUNCT
ejpam-6102	423	3	,	,	PUNCT
ejpam-6102	423	4	µk	µk	PRON
ejpam-6102	423	5	∂j̃ε	∂j̃ε	NUM
ejpam-6102	423	6	∂µk	∂µk	PROPN
ejpam-6102	423	7	(	(	PUNCT
ejpam-6102	423	8	λ̄	λ̄	ADJ
ejpam-6102	423	9	)	)	PUNCT
ejpam-6102	424	1	=	=	SYM
ejpam-6102	424	2	o	o	X
ejpam-6102	424	3	(	(	PUNCT
ejpam-6102	424	4	(	(	PUNCT
ejpam-6102	424	5	|σk|+	|σk|+	VERB
ejpam-6102	424	6	∑	∑	PUNCT
ejpam-6102	424	7	|γk	|γk	PROPN
ejpam-6102	424	8	,	,	PUNCT
ejpam-6102	424	9	j	j	PROPN
ejpam-6102	424	10	|	|	ADV
ejpam-6102	424	11	)	)	PUNCT
ejpam-6102	424	12	∥v̄∥	∥v̄∥	PUNCT
ejpam-6102	424	13	)	)	PUNCT
ejpam-6102	425	1	=	=	PUNCT
ejpam-6102	425	2	o	o	X
ejpam-6102	425	3	(	(	PUNCT
ejpam-6102	425	4	ε2	ε2	PROPN
ejpam-6102	425	5	)	)	PUNCT
ejpam-6102	425	6	,	,	PUNCT
ejpam-6102	425	7	∀k	∀k	X
ejpam-6102	425	8	∈	∈	PROPN
ejpam-6102	425	9	{	{	PUNCT
ejpam-6102	425	10	1	1	NUM
ejpam-6102	425	11	,	,	PUNCT
ejpam-6102	425	12	.	.	PUNCT
ejpam-6102	425	13	.	.	PUNCT
ejpam-6102	425	14	.	.	PUNCT
ejpam-6102	426	1	;	;	PUNCT
ejpam-6102	426	2	n	n	CCONJ
ejpam-6102	426	3	}	}	PUNCT
ejpam-6102	426	4	,	,	PUNCT
ejpam-6102	426	5	(	(	PUNCT
ejpam-6102	426	6	43	43	NUM
ejpam-6102	426	7	)	)	PUNCT
ejpam-6102	426	8	1	1	NUM
ejpam-6102	426	9	µk	µk	NOUN
ejpam-6102	426	10	∂j̃ε	∂j̃ε	PROPN
ejpam-6102	426	11	∂τk	∂τk	PROPN
ejpam-6102	426	12	,	,	PUNCT
ejpam-6102	426	13	j	j	PROPN
ejpam-6102	426	14	(	(	PUNCT
ejpam-6102	426	15	λ̄	λ̄	ADP
ejpam-6102	426	16	)	)	PUNCT
ejpam-6102	427	1	=	=	SYM
ejpam-6102	427	2	o	o	X
ejpam-6102	427	3	(	(	PUNCT
ejpam-6102	427	4	(	(	PUNCT
ejpam-6102	427	5	|σk|+	|σk|+	VERB
ejpam-6102	427	6	∑	∑	PUNCT
ejpam-6102	427	7	|γk	|γk	PROPN
ejpam-6102	427	8	,	,	PUNCT
ejpam-6102	427	9	j	j	PROPN
ejpam-6102	427	10	|	|	ADV
ejpam-6102	427	11	)	)	PUNCT
ejpam-6102	427	12	∥v̄∥	∥v̄∥	PUNCT
ejpam-6102	427	13	)	)	PUNCT
ejpam-6102	428	1	=	=	PUNCT
ejpam-6102	428	2	o	o	X
ejpam-6102	428	3	(	(	PUNCT
ejpam-6102	428	4	ε2	ε2	PROPN
ejpam-6102	428	5	)	)	PUNCT
ejpam-6102	428	6	,	,	PUNCT
ejpam-6102	428	7	∀k	∀k	X
ejpam-6102	428	8	∈	∈	PROPN
ejpam-6102	428	9	{	{	PUNCT
ejpam-6102	428	10	1	1	NUM
ejpam-6102	428	11	,	,	PUNCT
ejpam-6102	428	12	.	.	PUNCT
ejpam-6102	428	13	.	.	PUNCT
ejpam-6102	428	14	.	.	PUNCT
ejpam-6102	429	1	,	,	PUNCT
ejpam-6102	429	2	n},∀j	n},∀j	PROPN
ejpam-6102	429	3	∈	∈	PROPN
ejpam-6102	429	4	{	{	PUNCT
ejpam-6102	429	5	1	1	NUM
ejpam-6102	429	6	,	,	PUNCT
ejpam-6102	429	7	.	.	PUNCT
ejpam-6102	429	8	.	.	PUNCT
ejpam-6102	430	1	.	.	PUNCT
ejpam-6102	431	1	,	,	PUNCT
ejpam-6102	431	2	n−	n−	NOUN
ejpam-6102	431	3	1	1	NUM
ejpam-6102	431	4	}	}	PUNCT
ejpam-6102	431	5	.	.	PUNCT
ejpam-6102	432	1	second	second	ADJ
ejpam-6102	432	2	,	,	PUNCT
ejpam-6102	432	3	using	use	VERB
ejpam-6102	432	4	(	(	PUNCT
ejpam-6102	432	5	41	41	NUM
ejpam-6102	432	6	)	)	PUNCT
ejpam-6102	432	7	and	and	CCONJ
ejpam-6102	432	8	propositions	proposition	NOUN
ejpam-6102	432	9	4	4	NUM
ejpam-6102	432	10	,	,	PUNCT
ejpam-6102	432	11	5	5	NUM
ejpam-6102	432	12	and	and	CCONJ
ejpam-6102	432	13	6	6	NUM
ejpam-6102	432	14	,	,	PUNCT
ejpam-6102	432	15	we	we	PRON
ejpam-6102	432	16	derive	derive	VERB
ejpam-6102	432	17	that	that	SCONJ
ejpam-6102	432	18	the	the	DET
ejpam-6102	432	19	system	system	NOUN
ejpam-6102	432	20	(	(	PUNCT
ejpam-6102	432	21	43	43	NUM
ejpam-6102	432	22	)	)	PUNCT
ejpam-6102	432	23	is	be	AUX
ejpam-6102	432	24	equivalent	equivalent	ADJ
ejpam-6102	432	25	to	to	ADP
ejpam-6102	432	26	1−	1−	NUM
ejpam-6102	432	27	µ	µ	PROPN
ejpam-6102	432	28	−ε(n−2)/2	−ε(n−2)/2	PROPN
ejpam-6102	432	29	k	k	PROPN
ejpam-6102	432	30	αp−1−ε	αp−1−ε	PROPN
ejpam-6102	432	31	k	k	PROPN
ejpam-6102	432	32	f	f	X
ejpam-6102	432	33	(	(	PUNCT
ejpam-6102	432	34	ak	ak	PROPN
ejpam-6102	432	35	)	)	PUNCT
ejpam-6102	432	36	=	=	SYM
ejpam-6102	432	37	o(ε	o(ε	PROPN
ejpam-6102	432	38	)	)	PUNCT
ejpam-6102	432	39	,	,	PUNCT
ejpam-6102	432	40	∀k	∀k	NOUN
ejpam-6102	432	41	,	,	PUNCT
ejpam-6102	432	42	n−	n−	NOUN
ejpam-6102	432	43	2	2	NUM
ejpam-6102	432	44	4	4	NUM
ejpam-6102	432	45	c6ε+	c6ε+	NOUN
ejpam-6102	433	1	(	(	PUNCT
ejpam-6102	433	2	c1	c1	NOUN
ejpam-6102	433	3	2	2	NUM
ejpam-6102	433	4	−	−	PROPN
ejpam-6102	433	5	c4	c4	NOUN
ejpam-6102	433	6	)	)	PUNCT
ejpam-6102	433	7	h	h	PROPN
ejpam-6102	433	8	(	(	PUNCT
ejpam-6102	433	9	ak	ak	PROPN
ejpam-6102	433	10	)	)	PUNCT
ejpam-6102	433	11	µk	µk	NOUN
ejpam-6102	433	12	−	−	PROPN
ejpam-6102	433	13	c5	c5	PROPN
ejpam-6102	433	14	µk	µk	VERB
ejpam-6102	433	15	1	1	NUM
ejpam-6102	433	16	f	f	PROPN
ejpam-6102	433	17	(	(	PUNCT
ejpam-6102	433	18	ak	ak	PROPN
ejpam-6102	433	19	)	)	PUNCT
ejpam-6102	433	20	∂f	∂f	PROPN
ejpam-6102	433	21	∂ν	∂ν	PROPN
ejpam-6102	433	22	(	(	PUNCT
ejpam-6102	433	23	ak	ak	PROPN
ejpam-6102	433	24	)	)	PUNCT
ejpam-6102	433	25	=	=	PRON
ejpam-6102	433	26	{	{	PUNCT
ejpam-6102	433	27	o	o	X
ejpam-6102	433	28	(	(	PUNCT
ejpam-6102	433	29	ε2	ε2	ADV
ejpam-6102	433	30	)	)	PUNCT
ejpam-6102	433	31	if	if	SCONJ
ejpam-6102	433	32	n	n	CCONJ
ejpam-6102	433	33	⩾	⩾	NOUN
ejpam-6102	433	34	5	5	NUM
ejpam-6102	433	35	,	,	PUNCT
ejpam-6102	433	36	o	o	NOUN
ejpam-6102	433	37	(	(	PUNCT
ejpam-6102	433	38	ε2|	ε2|	X
ejpam-6102	433	39	ln	ln	PROPN
ejpam-6102	433	40	ε|	ε|	PROPN
ejpam-6102	433	41	)	)	PUNCT
ejpam-6102	434	1	if	if	SCONJ
ejpam-6102	434	2	n	n	NOUN
ejpam-6102	434	3	=	=	SYM
ejpam-6102	434	4	4	4	NUM
ejpam-6102	434	5	,	,	PUNCT
ejpam-6102	434	6	∀k	∀k	NOUN
ejpam-6102	434	7	,	,	PUNCT
ejpam-6102	434	8	1	1	NUM
ejpam-6102	434	9	µk	µk	NOUN
ejpam-6102	434	10	∇f1	∇f1	PROPN
ejpam-6102	434	11	(	(	PUNCT
ejpam-6102	434	12	ak	ak	PROPN
ejpam-6102	434	13	)	)	PUNCT
ejpam-6102	435	1	=	=	SYM
ejpam-6102	435	2	o	o	X
ejpam-6102	435	3	(	(	PUNCT
ejpam-6102	435	4	ε2	ε2	PROPN
ejpam-6102	435	5	)	)	PUNCT
ejpam-6102	435	6	,	,	PUNCT
ejpam-6102	435	7	∀k	∀k	X
ejpam-6102	435	8	.	.	PUNCT
ejpam-6102	436	1	(	(	PUNCT
ejpam-6102	436	2	44	44	NUM
ejpam-6102	436	3	)	)	PUNCT
ejpam-6102	436	4	at	at	ADP
ejpam-6102	436	5	this	this	DET
ejpam-6102	436	6	step	step	NOUN
ejpam-6102	436	7	,	,	PUNCT
ejpam-6102	436	8	to	to	PART
ejpam-6102	436	9	solve	solve	VERB
ejpam-6102	436	10	the	the	DET
ejpam-6102	436	11	system	system	NOUN
ejpam-6102	436	12	(	(	PUNCT
ejpam-6102	436	13	44	44	NUM
ejpam-6102	436	14	)	)	PUNCT
ejpam-6102	436	15	,	,	PUNCT
ejpam-6102	436	16	it	it	PRON
ejpam-6102	436	17	is	be	AUX
ejpam-6102	436	18	better	well	ADJ
ejpam-6102	436	19	to	to	PART
ejpam-6102	436	20	take	take	VERB
ejpam-6102	436	21	a	a	DET
ejpam-6102	436	22	change	change	NOUN
ejpam-6102	436	23	of	of	ADP
ejpam-6102	436	24	variables	variable	NOUN
ejpam-6102	436	25	to	to	PART
ejpam-6102	436	26	obtain	obtain	VERB
ejpam-6102	436	27	an	an	DET
ejpam-6102	436	28	easier	easy	ADJ
ejpam-6102	436	29	system	system	NOUN
ejpam-6102	436	30	to	to	PART
ejpam-6102	436	31	solve	solve	VERB
ejpam-6102	436	32	.	.	PUNCT
ejpam-6102	437	1	notice	notice	VERB
ejpam-6102	437	2	that	that	SCONJ
ejpam-6102	437	3	αk	αk	AUX
ejpam-6102	437	4	∈	∈	PROPN
ejpam-6102	437	5	(	(	PUNCT
ejpam-6102	437	6	0,∞	0,∞	NOUN
ejpam-6102	437	7	)	)	PUNCT
ejpam-6102	437	8	and	and	CCONJ
ejpam-6102	437	9	µk	µk	DET
ejpam-6102	437	10	∈	∈	PROPN
ejpam-6102	437	11	(	(	PUNCT
ejpam-6102	437	12	0,∞	0,∞	NOUN
ejpam-6102	437	13	)	)	PUNCT
ejpam-6102	437	14	,	,	PUNCT
ejpam-6102	437	15	however	however	SCONJ
ejpam-6102	437	16	ak	ak	PROPN
ejpam-6102	437	17	∈	∈	PROPN
ejpam-6102	437	18	∂ω	∂ω	PROPN
ejpam-6102	437	19	and	and	CCONJ
ejpam-6102	437	20	therefore	therefore	ADV
ejpam-6102	437	21	,	,	PUNCT
ejpam-6102	437	22	we	we	PRON
ejpam-6102	437	23	need	need	VERB
ejpam-6102	437	24	to	to	PART
ejpam-6102	437	25	be	be	AUX
ejpam-6102	437	26	move	move	VERB
ejpam-6102	437	27	careful	careful	ADJ
ejpam-6102	437	28	in	in	ADP
ejpam-6102	437	29	the	the	DET
ejpam-6102	437	30	change	change	NOUN
ejpam-6102	437	31	of	of	ADP
ejpam-6102	437	32	variables	variable	NOUN
ejpam-6102	437	33	for	for	SCONJ
ejpam-6102	437	34	ak	ak	PROPN
ejpam-6102	437	35	.	.	PROPN
ejpam-6102	437	36	to	to	PART
ejpam-6102	437	37	be	be	AUX
ejpam-6102	437	38	more	more	ADV
ejpam-6102	437	39	precise	precise	ADJ
ejpam-6102	437	40	,	,	PUNCT
ejpam-6102	437	41	let	let	VERB
ejpam-6102	437	42	y	y	PRON
ejpam-6102	437	43	∈	∈	PROPN
ejpam-6102	437	44	∂ω	∂ω	PROPN
ejpam-6102	437	45	and	and	CCONJ
ejpam-6102	437	46	(	(	PUNCT
ejpam-6102	437	47	e′1	e′1	NOUN
ejpam-6102	437	48	,	,	PUNCT
ejpam-6102	437	49	.	.	PUNCT
ejpam-6102	437	50	.	.	PUNCT
ejpam-6102	437	51	.	.	PUNCT
ejpam-6102	438	1	,	,	PUNCT
ejpam-6102	438	2	e	e	X
ejpam-6102	438	3	′	′	NOUN
ejpam-6102	438	4	n−1,−νy	n−1,−νy	NUM
ejpam-6102	438	5	)	)	PUNCT
ejpam-6102	438	6	be	be	AUX
ejpam-6102	438	7	an	an	DET
ejpam-6102	438	8	orthonormal	orthonormal	ADJ
ejpam-6102	438	9	basis	basis	NOUN
ejpam-6102	438	10	of	of	ADP
ejpam-6102	438	11	rn	rn	PROPN
ejpam-6102	438	12	.	.	PUNCT
ejpam-6102	439	1	in	in	ADP
ejpam-6102	439	2	this	this	DET
ejpam-6102	439	3	basis	basis	NOUN
ejpam-6102	439	4	,	,	PUNCT
ejpam-6102	439	5	the	the	DET
ejpam-6102	439	6	tangent	tangent	ADJ
ejpam-6102	439	7	space	space	NOUN
ejpam-6102	439	8	to	to	ADP
ejpam-6102	439	9	∂ω	∂ω	PROPN
ejpam-6102	439	10	at	at	ADP
ejpam-6102	439	11	y	y	PROPN
ejpam-6102	439	12	is	be	AUX
ejpam-6102	439	13	rn−1	rn−1	PROPN
ejpam-6102	439	14	×	×	NOUN
ejpam-6102	439	15	{	{	PUNCT
ejpam-6102	439	16	0	0	NUM
ejpam-6102	439	17	}	}	PUNCT
ejpam-6102	439	18	.	.	PUNCT
ejpam-6102	440	1	written	write	VERB
ejpam-6102	440	2	y	y	PROPN
ejpam-6102	440	3	=	=	PUNCT
ejpam-6102	440	4	(	(	PUNCT
ejpam-6102	440	5	y′	y′	PROPN
ejpam-6102	440	6	,	,	PUNCT
ejpam-6102	440	7	yn	yn	NOUN
ejpam-6102	440	8	)	)	PUNCT
ejpam-6102	440	9	∈	∈	PROPN
ejpam-6102	440	10	rn−1	rn−1	PROPN
ejpam-6102	440	11	×	×	NOUN
ejpam-6102	440	12	r	r	NOUN
ejpam-6102	440	13	,	,	PUNCT
ejpam-6102	440	14	since	since	SCONJ
ejpam-6102	440	15	ω	ω	PROPN
ejpam-6102	440	16	is	be	AUX
ejpam-6102	440	17	a	a	DET
ejpam-6102	440	18	c2	c2	PROPN
ejpam-6102	440	19	-	-	PUNCT
ejpam-6102	440	20	domain	domain	NOUN
ejpam-6102	440	21	,	,	PUNCT
ejpam-6102	440	22	there	there	PRON
ejpam-6102	440	23	exist	exist	VERB
ejpam-6102	440	24	ρ	ρ	PROPN
ejpam-6102	440	25	>	>	X
ejpam-6102	440	26	0	0	PUNCT
ejpam-6102	441	1	(	(	PUNCT
ejpam-6102	441	2	small	small	ADJ
ejpam-6102	441	3	)	)	PUNCT
ejpam-6102	441	4	and	and	CCONJ
ejpam-6102	441	5	a	a	DET
ejpam-6102	441	6	c2	c2	PROPN
ejpam-6102	441	7	-	-	PUNCT
ejpam-6102	441	8	function	function	NOUN
ejpam-6102	441	9	g	g	NOUN
ejpam-6102	441	10	:	:	PUNCT
ejpam-6102	441	11	bn−1(0	bn−1(0	PROPN
ejpam-6102	441	12	,	,	PUNCT
ejpam-6102	441	13	ρ	ρ	PROPN
ejpam-6102	441	14	)	)	PUNCT
ejpam-6102	441	15	⊂	⊂	PROPN
ejpam-6102	441	16	rn−1	rn−1	PROPN
ejpam-6102	441	17	→	→	SYM
ejpam-6102	442	1	r	r	NOUN
ejpam-6102	442	2	such	such	ADJ
ejpam-6102	442	3	that	that	PRON
ejpam-6102	442	4	:	:	PUNCT
ejpam-6102	442	5	•	•	NUM
ejpam-6102	442	6	g(0	g(0	NOUN
ejpam-6102	442	7	)	)	PUNCT
ejpam-6102	442	8	=	=	SYM
ejpam-6102	442	9	0	0	NUM
ejpam-6102	442	10	,	,	PUNCT
ejpam-6102	442	11	∇g(0	∇g(0	NOUN
ejpam-6102	442	12	)	)	PUNCT
ejpam-6102	442	13	=	=	SYM
ejpam-6102	442	14	0	0	PUNCT
ejpam-6102	442	15	and	and	CCONJ
ejpam-6102	442	16	therefore	therefore	ADV
ejpam-6102	442	17	|g	|g	X
ejpam-6102	442	18	(	(	PUNCT
ejpam-6102	442	19	z′)|	z′)|	NUM
ejpam-6102	442	20	⩽	⩽	PROPN
ejpam-6102	442	21	c	c	PROPN
ejpam-6102	442	22	|z′|2	|z′|2	PROPN
ejpam-6102	442	23	∀z′	∀z′	PROPN
ejpam-6102	442	24	,	,	PUNCT
ejpam-6102	442	25	•	•	PROPN
ejpam-6102	442	26	ω	ω	PROPN
ejpam-6102	442	27	∩bn	∩bn	PROPN
ejpam-6102	442	28	(	(	PUNCT
ejpam-6102	442	29	y	y	PROPN
ejpam-6102	442	30	,	,	PUNCT
ejpam-6102	442	31	ρ	ρ	PROPN
ejpam-6102	442	32	)	)	PUNCT
ejpam-6102	442	33	=	=	PRON
ejpam-6102	442	34	{	{	PUNCT
ejpam-6102	442	35	(	(	PUNCT
ejpam-6102	442	36	y′	y′	X
ejpam-6102	442	37	+	+	CCONJ
ejpam-6102	442	38	z′	z′	NOUN
ejpam-6102	442	39	,	,	PUNCT
ejpam-6102	442	40	yn	yn	PROPN
ejpam-6102	442	41	+	+	PROPN
ejpam-6102	442	42	zn	zn	X
ejpam-6102	442	43	)	)	PUNCT
ejpam-6102	442	44	∈	∈	PROPN
ejpam-6102	443	1	rn−1	rn−1	PROPN
ejpam-6102	443	2	×	×	NOUN
ejpam-6102	443	3	r	r	NOUN
ejpam-6102	443	4	:	:	PUNCT
ejpam-6102	443	5	|(z′	|(z′	NOUN
ejpam-6102	443	6	,	,	PUNCT
ejpam-6102	443	7	zn)|	zn)|	PROPN
ejpam-6102	443	8	<	<	X
ejpam-6102	443	9	ρ	ρ	PROPN
ejpam-6102	443	10	and	and	CCONJ
ejpam-6102	443	11	zn	zn	NUM
ejpam-6102	443	12	>	>	X
ejpam-6102	443	13	g	g	PROPN
ejpam-6102	443	14	(	(	PUNCT
ejpam-6102	443	15	z′	z′	PROPN
ejpam-6102	443	16	)	)	PUNCT
ejpam-6102	443	17	}	}	PUNCT
ejpam-6102	443	18	,	,	PUNCT
ejpam-6102	443	19	•	•	NUM
ejpam-6102	443	20	∂ω	∂ω	ADJ
ejpam-6102	443	21	∩bn	∩bn	NOUN
ejpam-6102	443	22	(	(	PUNCT
ejpam-6102	443	23	y	y	PROPN
ejpam-6102	443	24	,	,	PUNCT
ejpam-6102	443	25	ρ	ρ	PROPN
ejpam-6102	443	26	)	)	PUNCT
ejpam-6102	443	27	=	=	PRON
ejpam-6102	443	28	{	{	PUNCT
ejpam-6102	443	29	(	(	PUNCT
ejpam-6102	443	30	y′	y′	X
ejpam-6102	443	31	+	+	CCONJ
ejpam-6102	443	32	z′	z′	NOUN
ejpam-6102	443	33	,	,	PUNCT
ejpam-6102	443	34	yn	yn	PROPN
ejpam-6102	443	35	+	+	PROPN
ejpam-6102	443	36	zn	zn	X
ejpam-6102	443	37	)	)	PUNCT
ejpam-6102	443	38	∈	∈	PROPN
ejpam-6102	443	39	rn−1	rn−1	PROPN
ejpam-6102	443	40	×	×	NOUN
ejpam-6102	443	41	r	r	NOUN
ejpam-6102	443	42	:	:	PUNCT
ejpam-6102	443	43	|(z′	|(z′	NOUN
ejpam-6102	443	44	,	,	PUNCT
ejpam-6102	443	45	zn)|	zn)|	PROPN
ejpam-6102	443	46	<	<	X
ejpam-6102	443	47	ρ	ρ	PROPN
ejpam-6102	443	48	and	and	CCONJ
ejpam-6102	443	49	zn	zn	PROPN
ejpam-6102	443	50	=	=	SYM
ejpam-6102	443	51	g	g	PROPN
ejpam-6102	443	52	(	(	PUNCT
ejpam-6102	443	53	z′	z′	PROPN
ejpam-6102	443	54	)	)	PUNCT
ejpam-6102	443	55	}	}	PUNCT
ejpam-6102	443	56	.	.	PUNCT
ejpam-6102	444	1	furthermore	furthermore	ADV
ejpam-6102	444	2	,	,	PUNCT
ejpam-6102	444	3	assume	assume	VERB
ejpam-6102	444	4	that	that	SCONJ
ejpam-6102	444	5	y	y	PROPN
ejpam-6102	444	6	is	be	AUX
ejpam-6102	444	7	a	a	DET
ejpam-6102	444	8	critical	critical	ADJ
ejpam-6102	444	9	point	point	NOUN
ejpam-6102	444	10	of	of	ADP
ejpam-6102	444	11	f1	f1	NOUN
ejpam-6102	444	12	:	:	PUNCT
ejpam-6102	444	13	=	=	SYM
ejpam-6102	444	14	f|∂ω	f|∂ω	NOUN
ejpam-6102	444	15	(	(	PUNCT
ejpam-6102	444	16	the	the	DET
ejpam-6102	444	17	restriction	restriction	NOUN
ejpam-6102	444	18	of	of	ADP
ejpam-6102	444	19	f	f	PROPN
ejpam-6102	444	20	on	on	ADP
ejpam-6102	444	21	the	the	DET
ejpam-6102	444	22	boundary	boundary	NOUN
ejpam-6102	444	23	)	)	PUNCT
ejpam-6102	444	24	,	,	PUNCT
ejpam-6102	444	25	for	for	ADP
ejpam-6102	444	26	a	a	DET
ejpam-6102	444	27	∈	∈	PROPN
ejpam-6102	444	28	∂ω	∂ω	PROPN
ejpam-6102	444	29	∩b(y	∩b(y	ADJ
ejpam-6102	444	30	,	,	PUNCT
ejpam-6102	444	31	ρ	ρ	NOUN
ejpam-6102	444	32	)	)	PUNCT
ejpam-6102	444	33	,	,	PUNCT
ejpam-6102	444	34	written	write	VERB
ejpam-6102	444	35	a	a	PRON
ejpam-6102	444	36	as	as	ADP
ejpam-6102	444	37	a	a	PRON
ejpam-6102	444	38	:	:	PUNCT
ejpam-6102	444	39	=	=	SYM
ejpam-6102	444	40	(	(	PUNCT
ejpam-6102	444	41	a′	a′	PROPN
ejpam-6102	444	42	,	,	PUNCT
ejpam-6102	444	43	an	an	PRON
ejpam-6102	444	44	)	)	PUNCT
ejpam-6102	444	45	=	=	PUNCT
ejpam-6102	444	46	(	(	PUNCT
ejpam-6102	444	47	y′	y′	X
ejpam-6102	444	48	+	+	CCONJ
ejpam-6102	444	49	z′	z′	NOUN
ejpam-6102	444	50	,	,	PUNCT
ejpam-6102	444	51	yn	yn	PROPN
ejpam-6102	444	52	+	+	CCONJ
ejpam-6102	444	53	g	g	PROPN
ejpam-6102	444	54	(	(	PUNCT
ejpam-6102	444	55	z′	z′	NUM
ejpam-6102	444	56	)	)	PUNCT
ejpam-6102	444	57	)	)	PUNCT
ejpam-6102	444	58	with	with	ADP
ejpam-6102	444	59	z′	z′	NUM
ejpam-6102	444	60	∈	∈	PROPN
ejpam-6102	444	61	bn−1(0	bn−1(0	PROPN
ejpam-6102	444	62	,	,	PUNCT
ejpam-6102	444	63	ρ	ρ	PROPN
ejpam-6102	444	64	)	)	PUNCT
ejpam-6102	444	65	,	,	PUNCT
ejpam-6102	444	66	(	(	PUNCT
ejpam-6102	444	67	45	45	NUM
ejpam-6102	444	68	)	)	PUNCT
ejpam-6102	444	69	then	then	ADV
ejpam-6102	444	70	it	it	PRON
ejpam-6102	444	71	holds	hold	VERB
ejpam-6102	444	72	that	that	DET
ejpam-6102	444	73	∇t	∇t	PROPN
ejpam-6102	444	74	f(a	f(a	NOUN
ejpam-6102	444	75	)	)	PUNCT
ejpam-6102	444	76	=	=	SYM
ejpam-6102	445	1	∇f1(a	∇f1(a	NUM
ejpam-6102	445	2	)	)	PUNCT
ejpam-6102	445	3	=	=	SYM
ejpam-6102	445	4	d2f1(y	d2f1(y	PROPN
ejpam-6102	445	5	)	)	PUNCT
ejpam-6102	445	6	(	(	PUNCT
ejpam-6102	445	7	(	(	PUNCT
ejpam-6102	445	8	z	z	NOUN
ejpam-6102	445	9	′	′	NUM
ejpam-6102	445	10	,	,	PUNCT
ejpam-6102	445	11	0	0	NUM
ejpam-6102	445	12	)	)	PUNCT
ejpam-6102	445	13	,	,	PUNCT
ejpam-6102	445	14	·	·	PUNCT
ejpam-6102	445	15	)	)	PUNCT
ejpam-6102	446	1	+	+	NOUN
ejpam-6102	446	2	o	o	X
ejpam-6102	446	3	(	(	PUNCT
ejpam-6102	446	4	|z′|2	|z′|2	PROPN
ejpam-6102	446	5	)	)	PUNCT
ejpam-6102	446	6	.	.	PUNCT
ejpam-6102	447	1	(	(	PUNCT
ejpam-6102	447	2	46	46	X
ejpam-6102	447	3	)	)	PUNCT
ejpam-6102	447	4	recall	recall	VERB
ejpam-6102	447	5	that	that	DET
ejpam-6102	447	6	(	(	PUNCT
ejpam-6102	447	7	a	a	PRON
ejpam-6102	447	8	,	,	PUNCT
ejpam-6102	447	9	µ	µ	NOUN
ejpam-6102	447	10	,	,	PUNCT
ejpam-6102	447	11	α	α	NOUN
ejpam-6102	447	12	,	,	PUNCT
ejpam-6102	447	13	0	0	NUM
ejpam-6102	447	14	)	)	PUNCT
ejpam-6102	447	15	∈	∈	PROPN
ejpam-6102	447	16	dε	dε	NOUN
ejpam-6102	447	17	,	,	PUNCT
ejpam-6102	447	18	n	n	PRON
ejpam-6102	447	19	which	which	PRON
ejpam-6102	447	20	implies	imply	VERB
ejpam-6102	447	21	that	that	SCONJ
ejpam-6102	447	22	ak	ak	PROPN
ejpam-6102	447	23	is	be	AUX
ejpam-6102	447	24	close	close	ADJ
ejpam-6102	447	25	to	to	ADP
ejpam-6102	447	26	bk	bk	PROPN
ejpam-6102	447	27	(	(	PUNCT
ejpam-6102	447	28	which	which	PRON
ejpam-6102	447	29	is	be	AUX
ejpam-6102	447	30	a	a	DET
ejpam-6102	447	31	critical	critical	ADJ
ejpam-6102	447	32	point	point	NOUN
ejpam-6102	447	33	of	of	ADP
ejpam-6102	447	34	f1	f1	NOUN
ejpam-6102	447	35	)	)	PUNCT
ejpam-6102	447	36	and	and	CCONJ
ejpam-6102	447	37	αkf	αkf	NUM
ejpam-6102	447	38	(	(	PUNCT
ejpam-6102	447	39	ak	ak	PROPN
ejpam-6102	447	40	)	)	PUNCT
ejpam-6102	447	41	n−2/4	n−2/4	PROPN
ejpam-6102	447	42	is	be	AUX
ejpam-6102	447	43	close	close	ADJ
ejpam-6102	447	44	to	to	ADP
ejpam-6102	447	45	1	1	NUM
ejpam-6102	447	46	for	for	ADP
ejpam-6102	447	47	each	each	DET
ejpam-6102	447	48	k.	k.	PROPN
ejpam-6102	447	49	hence	hence	ADV
ejpam-6102	447	50	,	,	PUNCT
ejpam-6102	447	51	let	let	VERB
ejpam-6102	447	52	us	we	PRON
ejpam-6102	447	53	consider	consider	VERB
ejpam-6102	447	54	the	the	DET
ejpam-6102	447	55	following	follow	VERB
ejpam-6102	447	56	change	change	NOUN
ejpam-6102	447	57	of	of	ADP
ejpam-6102	447	58	variables	variable	NOUN
ejpam-6102	447	59	:	:	PUNCT
ejpam-6102	447	60	ρk	ρk	ADP
ejpam-6102	447	61	:	:	PUNCT
ejpam-6102	448	1	=	=	SYM
ejpam-6102	448	2	1−	1−	NUM
ejpam-6102	448	3	αkf	αkf	NOUN
ejpam-6102	448	4	(	(	PUNCT
ejpam-6102	448	5	bk	bk	NOUN
ejpam-6102	448	6	)	)	PUNCT
ejpam-6102	448	7	n−2/4	n−2/4	NOUN
ejpam-6102	448	8	,	,	PUNCT
ejpam-6102	448	9	k	k	PROPN
ejpam-6102	448	10	∈	∈	PROPN
ejpam-6102	448	11	{	{	PUNCT
ejpam-6102	448	12	1	1	NUM
ejpam-6102	448	13	,	,	PUNCT
ejpam-6102	448	14	.	.	PUNCT
ejpam-6102	448	15	.	.	PUNCT
ejpam-6102	448	16	.	.	PUNCT
ejpam-6102	448	17	,	,	PUNCT
ejpam-6102	448	18	n	n	CCONJ
ejpam-6102	448	19	}	}	PUNCT
ejpam-6102	448	20	,	,	PUNCT
ejpam-6102	448	21	(	(	PUNCT
ejpam-6102	448	22	47	47	NUM
ejpam-6102	448	23	)	)	PUNCT
ejpam-6102	448	24	1	1	NUM
ejpam-6102	448	25	µk	µk	NOUN
ejpam-6102	448	26	:	:	PUNCT
ejpam-6102	448	27	=	=	SYM
ejpam-6102	448	28	[	[	PUNCT
ejpam-6102	448	29	c5	c5	PROPN
ejpam-6102	448	30	f	f	PROPN
ejpam-6102	448	31	(	(	PUNCT
ejpam-6102	448	32	bk	bk	INTJ
ejpam-6102	448	33	)	)	PUNCT
ejpam-6102	448	34	∂f	∂f	PROPN
ejpam-6102	448	35	∂ν	∂ν	NOUN
ejpam-6102	448	36	(	(	PUNCT
ejpam-6102	448	37	bk)−	bk)−	PROPN
ejpam-6102	448	38	(	(	PUNCT
ejpam-6102	448	39	c1	c1	NOUN
ejpam-6102	448	40	2	2	NUM
ejpam-6102	448	41	−	−	PROPN
ejpam-6102	448	42	c4	c4	NOUN
ejpam-6102	448	43	)	)	PUNCT
ejpam-6102	448	44	h	h	NOUN
ejpam-6102	448	45	(	(	PUNCT
ejpam-6102	448	46	bk	bk	PROPN
ejpam-6102	448	47	)	)	PUNCT
ejpam-6102	448	48	]	]	SYM
ejpam-6102	448	49	−1	−1	NOUN
ejpam-6102	448	50	n−	n−	NOUN
ejpam-6102	448	51	2	2	NUM
ejpam-6102	448	52	4	4	NUM
ejpam-6102	448	53	c6ε	c6ε	NOUN
ejpam-6102	448	54	(	(	PUNCT
ejpam-6102	448	55	1	1	NUM
ejpam-6102	448	56	+	+	NUM
ejpam-6102	448	57	λk	λk	X
ejpam-6102	448	58	)	)	PUNCT
ejpam-6102	448	59	,	,	PUNCT
ejpam-6102	448	60	(	(	PUNCT
ejpam-6102	448	61	48	48	NUM
ejpam-6102	448	62	)	)	PUNCT
ejpam-6102	448	63	ak	ak	NOUN
ejpam-6102	448	64	:	:	PUNCT
ejpam-6102	448	65	=	=	SYM
ejpam-6102	448	66	(	(	PUNCT
ejpam-6102	448	67	b′k	b′k	NOUN
ejpam-6102	448	68	+	+	CCONJ
ejpam-6102	448	69	z′k	z′k	PROPN
ejpam-6102	448	70	,	,	PUNCT
ejpam-6102	448	71	(	(	PUNCT
ejpam-6102	448	72	bk)n	bk)n	PROPN
ejpam-6102	448	73	+	+	NUM
ejpam-6102	448	74	g	g	PROPN
ejpam-6102	448	75	(	(	PUNCT
ejpam-6102	448	76	z′k	z′k	NOUN
ejpam-6102	448	77	)	)	PUNCT
ejpam-6102	448	78	)	)	PUNCT
ejpam-6102	448	79	,	,	PUNCT
ejpam-6102	448	80	k	k	PROPN
ejpam-6102	448	81	∈	∈	PROPN
ejpam-6102	448	82	{	{	PUNCT
ejpam-6102	448	83	1	1	NUM
ejpam-6102	448	84	,	,	PUNCT
ejpam-6102	448	85	.	.	PUNCT
ejpam-6102	448	86	.	.	PUNCT
ejpam-6102	448	87	.	.	PUNCT
ejpam-6102	448	88	,	,	PUNCT
ejpam-6102	448	89	n	n	CCONJ
ejpam-6102	448	90	}	}	PUNCT
ejpam-6102	448	91	,	,	PUNCT
ejpam-6102	448	92	(	(	PUNCT
ejpam-6102	448	93	49	49	NUM
ejpam-6102	448	94	)	)	PUNCT
ejpam-6102	448	95	by	by	ADP
ejpam-6102	448	96	using	use	VERB
ejpam-6102	448	97	the	the	DET
ejpam-6102	448	98	notation	notation	NOUN
ejpam-6102	448	99	of	of	ADP
ejpam-6102	448	100	(	(	PUNCT
ejpam-6102	448	101	45	45	NUM
ejpam-6102	448	102	)	)	PUNCT
ejpam-6102	448	103	.	.	PUNCT
ejpam-6102	449	1	using	use	VERB
ejpam-6102	449	2	this	this	DET
ejpam-6102	449	3	change	change	NOUN
ejpam-6102	449	4	of	of	ADP
ejpam-6102	449	5	variables	variable	NOUN
ejpam-6102	449	6	,	,	PUNCT
ejpam-6102	449	7	we	we	PRON
ejpam-6102	449	8	get	get	VERB
ejpam-6102	449	9	:	:	PUNCT
ejpam-6102	449	10	f	f	PROPN
ejpam-6102	449	11	(	(	PUNCT
ejpam-6102	449	12	ak	ak	PROPN
ejpam-6102	449	13	)	)	PUNCT
ejpam-6102	449	14	=	=	SYM
ejpam-6102	449	15	f1	f1	PROPN
ejpam-6102	449	16	(	(	PUNCT
ejpam-6102	449	17	ak	ak	PROPN
ejpam-6102	449	18	)	)	PUNCT
ejpam-6102	449	19	=	=	SYM
ejpam-6102	449	20	f1	f1	NOUN
ejpam-6102	449	21	(	(	PUNCT
ejpam-6102	449	22	bk	bk	NOUN
ejpam-6102	449	23	)	)	PUNCT
ejpam-6102	450	1	+	+	NOUN
ejpam-6102	450	2	o	o	X
ejpam-6102	450	3	(	(	PUNCT
ejpam-6102	450	4	|ak	|ak	X
ejpam-6102	450	5	−	−	NOUN
ejpam-6102	450	6	bk|2	bk|2	NOUN
ejpam-6102	450	7	)	)	PUNCT
ejpam-6102	450	8	=	=	SYM
ejpam-6102	450	9	f1	f1	NOUN
ejpam-6102	450	10	(	(	PUNCT
ejpam-6102	450	11	bk	bk	NOUN
ejpam-6102	450	12	)	)	PUNCT
ejpam-6102	450	13	+	+	NOUN
ejpam-6102	450	14	o	o	NOUN
ejpam-6102	450	15	(	(	PUNCT
ejpam-6102	450	16	|z′k|	|z′k|	NOUN
ejpam-6102	450	17	2	2	NUM
ejpam-6102	450	18	)	)	PUNCT
ejpam-6102	450	19	,	,	PUNCT
ejpam-6102	450	20	r.	r.	PROPN
ejpam-6102	450	21	almushahhin	almushahhin	PROPN
ejpam-6102	450	22	,	,	PUNCT
ejpam-6102	450	23	m.	m.	PROPN
ejpam-6102	450	24	ben	ben	PROPN
ejpam-6102	450	25	ayed	aye	VERB
ejpam-6102	450	26	/	/	SYM
ejpam-6102	450	27	eur	eur	PROPN
ejpam-6102	450	28	.	.	PUNCT
ejpam-6102	451	1	j.	j.	PROPN
ejpam-6102	451	2	pure	pure	PROPN
ejpam-6102	451	3	appl	appl	PROPN
ejpam-6102	451	4	.	.	PROPN
ejpam-6102	451	5	math	math	PROPN
ejpam-6102	451	6	,	,	PUNCT
ejpam-6102	451	7	18	18	NUM
ejpam-6102	451	8	(	(	PUNCT
ejpam-6102	451	9	2	2	NUM
ejpam-6102	451	10	)	)	PUNCT
ejpam-6102	451	11	(	(	PUNCT
ejpam-6102	451	12	2025	2025	NUM
ejpam-6102	451	13	)	)	PUNCT
ejpam-6102	451	14	,	,	PUNCT
ejpam-6102	451	15	6102	6102	NUM
ejpam-6102	451	16	17	17	NUM
ejpam-6102	451	17	of	of	ADP
ejpam-6102	451	18	31	31	NUM
ejpam-6102	451	19	h	h	NOUN
ejpam-6102	451	20	(	(	PUNCT
ejpam-6102	451	21	ak	ak	PROPN
ejpam-6102	451	22	)	)	PUNCT
ejpam-6102	451	23	=	=	SYM
ejpam-6102	451	24	h	h	NOUN
ejpam-6102	451	25	(	(	PUNCT
ejpam-6102	451	26	bk	bk	NOUN
ejpam-6102	451	27	)	)	PUNCT
ejpam-6102	452	1	+	+	NOUN
ejpam-6102	452	2	o	o	NOUN
ejpam-6102	452	3	(	(	PUNCT
ejpam-6102	452	4	|z′k|	|z′k|	NOUN
ejpam-6102	452	5	)	)	PUNCT
ejpam-6102	452	6	,	,	PUNCT
ejpam-6102	452	7	1	1	NUM
ejpam-6102	452	8	f(ak	f(ak	NOUN
ejpam-6102	452	9	)	)	PUNCT
ejpam-6102	452	10	∂f	∂f	PROPN
ejpam-6102	452	11	∂ν	∂ν	PROPN
ejpam-6102	452	12	(	(	PUNCT
ejpam-6102	452	13	ak	ak	PROPN
ejpam-6102	452	14	)	)	PUNCT
ejpam-6102	452	15	=	=	SYM
ejpam-6102	452	16	1	1	NUM
ejpam-6102	452	17	f	f	X
ejpam-6102	452	18	(	(	PUNCT
ejpam-6102	452	19	bk	bk	NOUN
ejpam-6102	452	20	)	)	PUNCT
ejpam-6102	452	21	∂f	∂f	PROPN
ejpam-6102	452	22	∂ν	∂ν	PROPN
ejpam-6102	452	23	(	(	PUNCT
ejpam-6102	452	24	bk	bk	NOUN
ejpam-6102	452	25	)	)	PUNCT
ejpam-6102	453	1	+	+	NOUN
ejpam-6102	453	2	o	o	NOUN
ejpam-6102	453	3	(	(	PUNCT
ejpam-6102	453	4	|z′k|	|z′k|	NOUN
ejpam-6102	453	5	)	)	PUNCT
ejpam-6102	453	6	,	,	PUNCT
ejpam-6102	453	7	1−	1−	NUM
ejpam-6102	453	8	µ	µ	PROPN
ejpam-6102	453	9	−ε(n−2)/2	−ε(n−2)/2	PROPN
ejpam-6102	453	10	k	k	PROPN
ejpam-6102	453	11	α	α	PROPN
ejpam-6102	453	12	4	4	NUM
ejpam-6102	453	13	n−2−ε	n−2−ε	PROPN
ejpam-6102	453	14	k	k	PROPN
ejpam-6102	453	15	f	f	PROPN
ejpam-6102	453	16	(	(	PUNCT
ejpam-6102	453	17	ak	ak	PROPN
ejpam-6102	453	18	)	)	PUNCT
ejpam-6102	453	19	=	=	SYM
ejpam-6102	454	1	1−	1−	NUM
ejpam-6102	454	2	α	α	SYM
ejpam-6102	454	3	4	4	NUM
ejpam-6102	454	4	n−2	n−2	PROPN
ejpam-6102	454	5	k	k	PROPN
ejpam-6102	454	6	f1	f1	PROPN
ejpam-6102	454	7	(	(	PUNCT
ejpam-6102	454	8	bk	bk	NOUN
ejpam-6102	454	9	)	)	PUNCT
ejpam-6102	455	1	+	+	NOUN
ejpam-6102	455	2	o	o	X
ejpam-6102	455	3	(	(	PUNCT
ejpam-6102	455	4	|z′|2	|z′|2	PROPN
ejpam-6102	455	5	+	+	CCONJ
ejpam-6102	455	6	ε	ε	PROPN
ejpam-6102	455	7	|ln	|ln	PUNCT
ejpam-6102	455	8	ε|	ε|	ADV
ejpam-6102	455	9	)	)	PUNCT
ejpam-6102	455	10	=	=	SYM
ejpam-6102	455	11	4	4	NUM
ejpam-6102	455	12	n−	n−	NOUN
ejpam-6102	455	13	2	2	NUM
ejpam-6102	455	14	ρk	ρk	ADP
ejpam-6102	455	15	+	+	ADJ
ejpam-6102	455	16	o	o	X
ejpam-6102	455	17	(	(	PUNCT
ejpam-6102	455	18	ρ2k	ρ2k	PROPN
ejpam-6102	455	19	+	+	CCONJ
ejpam-6102	455	20	|z′|2	|z′|2	PROPN
ejpam-6102	455	21	+	+	CCONJ
ejpam-6102	455	22	ε	ε	PROPN
ejpam-6102	455	23	|ln	|ln	PUNCT
ejpam-6102	455	24	ε|	ε|	PROPN
ejpam-6102	455	25	)	)	PUNCT
ejpam-6102	455	26	,	,	PUNCT
ejpam-6102	455	27	(	(	PUNCT
ejpam-6102	455	28	50	50	X
ejpam-6102	455	29	)	)	PUNCT
ejpam-6102	455	30	n−	n−	NOUN
ejpam-6102	455	31	2	2	NUM
ejpam-6102	455	32	4	4	NUM
ejpam-6102	455	33	c6ε+	c6ε+	NOUN
ejpam-6102	455	34	1	1	NUM
ejpam-6102	455	35	µk	µk	NOUN
ejpam-6102	455	36	[	[	X
ejpam-6102	455	37	(	(	PUNCT
ejpam-6102	455	38	c1	c1	NOUN
ejpam-6102	455	39	2	2	NUM
ejpam-6102	455	40	−	−	PROPN
ejpam-6102	455	41	c4	c4	NOUN
ejpam-6102	455	42	)	)	PUNCT
ejpam-6102	455	43	h	h	NOUN
ejpam-6102	455	44	(	(	PUNCT
ejpam-6102	455	45	ak)−	ak)−	PROPN
ejpam-6102	455	46	c5	c5	PROPN
ejpam-6102	455	47	f	f	PROPN
ejpam-6102	455	48	(	(	PUNCT
ejpam-6102	455	49	ak	ak	PROPN
ejpam-6102	455	50	)	)	PUNCT
ejpam-6102	455	51	∂f	∂f	PROPN
ejpam-6102	455	52	∂ν	∂ν	PROPN
ejpam-6102	455	53	(	(	PUNCT
ejpam-6102	455	54	ak	ak	PROPN
ejpam-6102	455	55	)	)	PUNCT
ejpam-6102	455	56	]	]	PUNCT
ejpam-6102	456	1	=	=	PUNCT
ejpam-6102	456	2	n−	n−	NOUN
ejpam-6102	456	3	2	2	NUM
ejpam-6102	456	4	4	4	NUM
ejpam-6102	456	5	c6ε−	c6ε−	NOUN
ejpam-6102	456	6	1	1	NUM
ejpam-6102	456	7	µk	µk	NOUN
ejpam-6102	456	8	[	[	PUNCT
ejpam-6102	456	9	c5	c5	PROPN
ejpam-6102	456	10	f	f	PROPN
ejpam-6102	456	11	(	(	PUNCT
ejpam-6102	456	12	bk	bk	INTJ
ejpam-6102	456	13	)	)	PUNCT
ejpam-6102	456	14	∂f	∂f	PROPN
ejpam-6102	456	15	∂ν	∂ν	NOUN
ejpam-6102	456	16	(	(	PUNCT
ejpam-6102	456	17	bk)−	bk)−	PROPN
ejpam-6102	456	18	(	(	PUNCT
ejpam-6102	456	19	c1	c1	NOUN
ejpam-6102	456	20	2	2	NUM
ejpam-6102	456	21	−	−	PROPN
ejpam-6102	456	22	c4	c4	NOUN
ejpam-6102	456	23	)	)	PUNCT
ejpam-6102	456	24	h	h	NOUN
ejpam-6102	456	25	(	(	PUNCT
ejpam-6102	456	26	bk	bk	PROPN
ejpam-6102	456	27	)	)	PUNCT
ejpam-6102	456	28	]	]	PUNCT
ejpam-6102	457	1	+	+	PUNCT
ejpam-6102	457	2	o	o	X
ejpam-6102	457	3	(	(	PUNCT
ejpam-6102	457	4	1	1	NUM
ejpam-6102	457	5	µk	µk	PRON
ejpam-6102	457	6	|z′|	|z′|	NOUN
ejpam-6102	457	7	)	)	PUNCT
ejpam-6102	457	8	=	=	SYM
ejpam-6102	457	9	−n−	−n−	NOUN
ejpam-6102	457	10	2	2	NUM
ejpam-6102	457	11	4	4	NUM
ejpam-6102	457	12	c6ελk	c6ελk	PROPN
ejpam-6102	458	1	+	+	NOUN
ejpam-6102	458	2	o	o	X
ejpam-6102	458	3	(	(	PUNCT
ejpam-6102	458	4	ε	ε	PROPN
ejpam-6102	458	5	|z′|	|z′|	PROPN
ejpam-6102	458	6	)	)	PUNCT
ejpam-6102	458	7	.	.	PUNCT
ejpam-6102	459	1	(	(	PUNCT
ejpam-6102	459	2	51	51	NUM
ejpam-6102	459	3	)	)	PUNCT
ejpam-6102	459	4	thus	thus	ADV
ejpam-6102	459	5	,	,	PUNCT
ejpam-6102	459	6	using	use	VERB
ejpam-6102	459	7	(	(	PUNCT
ejpam-6102	459	8	46	46	NUM
ejpam-6102	459	9	)	)	PUNCT
ejpam-6102	459	10	,	,	PUNCT
ejpam-6102	459	11	(	(	PUNCT
ejpam-6102	459	12	50	50	NUM
ejpam-6102	459	13	)	)	PUNCT
ejpam-6102	459	14	and	and	CCONJ
ejpam-6102	459	15	(	(	PUNCT
ejpam-6102	459	16	51	51	NUM
ejpam-6102	459	17	)	)	PUNCT
ejpam-6102	459	18	,	,	PUNCT
ejpam-6102	459	19	the	the	DET
ejpam-6102	459	20	system	system	NOUN
ejpam-6102	459	21	(	(	PUNCT
ejpam-6102	459	22	44	44	NUM
ejpam-6102	459	23	)	)	PUNCT
ejpam-6102	459	24	becomes	become	VERB
ejpam-6102	459	25	equivalent	equivalent	ADJ
ejpam-6102	459	26	to	to	ADP
ejpam-6102	459	27	:	:	PUNCT
ejpam-6102	459	28	ρk	ρk	ADP
ejpam-6102	459	29	=	=	SYM
ejpam-6102	459	30	o	o	PROPN
ejpam-6102	459	31	(	(	PUNCT
ejpam-6102	459	32	ρ2k	ρ2k	PROPN
ejpam-6102	459	33	+	+	CCONJ
ejpam-6102	459	34	|z′|2	|z′|2	PROPN
ejpam-6102	459	35	+	+	CCONJ
ejpam-6102	459	36	ε	ε	PROPN
ejpam-6102	459	37	|ln	|ln	PUNCT
ejpam-6102	459	38	ε|	ε|	PROPN
ejpam-6102	459	39	)	)	PUNCT
ejpam-6102	459	40	,	,	PUNCT
ejpam-6102	459	41	k	k	PROPN
ejpam-6102	459	42	∈	∈	PROPN
ejpam-6102	459	43	{	{	PUNCT
ejpam-6102	459	44	1	1	NUM
ejpam-6102	459	45	,	,	PUNCT
ejpam-6102	459	46	.	.	PUNCT
ejpam-6102	459	47	.	.	PUNCT
ejpam-6102	459	48	.	.	PUNCT
ejpam-6102	459	49	,	,	PUNCT
ejpam-6102	459	50	n	n	CCONJ
ejpam-6102	459	51	}	}	PUNCT
ejpam-6102	459	52	,	,	PUNCT
ejpam-6102	459	53	λk	λk	X
ejpam-6102	459	54	=	=	PUNCT
ejpam-6102	459	55	o	o	X
ejpam-6102	459	56	(	(	PUNCT
ejpam-6102	459	57	|z′|+	|z′|+	PROPN
ejpam-6102	459	58	(	(	PUNCT
ejpam-6102	459	59	if	if	SCONJ
ejpam-6102	459	60	n	n	CCONJ
ejpam-6102	459	61	⩾	⩾	NOUN
ejpam-6102	459	62	5	5	NUM
ejpam-6102	459	63	)	)	PUNCT
ejpam-6102	459	64	ε+	ε+	X
ejpam-6102	459	65	(	(	PUNCT
ejpam-6102	459	66	if	if	SCONJ
ejpam-6102	459	67	n	n	X
ejpam-6102	459	68	=	=	SYM
ejpam-6102	459	69	4	4	X
ejpam-6102	459	70	)	)	PUNCT
ejpam-6102	459	71	ε	ε	PROPN
ejpam-6102	459	72	|ln	|ln	PUNCT
ejpam-6102	459	73	ε|	ε|	ADV
ejpam-6102	459	74	)	)	PUNCT
ejpam-6102	459	75	d2f1	d2f1	VERB
ejpam-6102	459	76	(	(	PUNCT
ejpam-6102	459	77	bk	bk	NOUN
ejpam-6102	459	78	)	)	PUNCT
ejpam-6102	459	79	(	(	PUNCT
ejpam-6102	459	80	(	(	PUNCT
ejpam-6102	459	81	z	z	NOUN
ejpam-6102	459	82	′	′	NUM
ejpam-6102	459	83	,	,	PUNCT
ejpam-6102	459	84	0	0	NUM
ejpam-6102	459	85	)	)	PUNCT
ejpam-6102	459	86	,	,	PUNCT
ejpam-6102	459	87	·	·	PUNCT
ejpam-6102	459	88	)	)	PUNCT
ejpam-6102	460	1	=	=	SYM
ejpam-6102	460	2	o	o	X
ejpam-6102	460	3	(	(	PUNCT
ejpam-6102	460	4	ε+	ε+	X
ejpam-6102	460	5	|z′|2	|z′|2	NOUN
ejpam-6102	460	6	)	)	PUNCT
ejpam-6102	460	7	,	,	PUNCT
ejpam-6102	460	8	k	k	PROPN
ejpam-6102	460	9	∈	∈	PROPN
ejpam-6102	460	10	{	{	PUNCT
ejpam-6102	460	11	1	1	NUM
ejpam-6102	460	12	,	,	PUNCT
ejpam-6102	460	13	.	.	PUNCT
ejpam-6102	460	14	.	.	PUNCT
ejpam-6102	460	15	.	.	PUNCT
ejpam-6102	460	16	,	,	PUNCT
ejpam-6102	460	17	n	n	CCONJ
ejpam-6102	460	18	}	}	PUNCT
ejpam-6102	460	19	.	.	PUNCT
ejpam-6102	461	1	(	(	PUNCT
ejpam-6102	461	2	52	52	NUM
ejpam-6102	461	3	)	)	PUNCT
ejpam-6102	461	4	since	since	SCONJ
ejpam-6102	461	5	d2f1	d2f1	PROPN
ejpam-6102	461	6	(	(	PUNCT
ejpam-6102	461	7	bk	bk	NOUN
ejpam-6102	461	8	)	)	PUNCT
ejpam-6102	461	9	is	be	AUX
ejpam-6102	461	10	assumed	assume	VERB
ejpam-6102	461	11	to	to	PART
ejpam-6102	461	12	be	be	AUX
ejpam-6102	461	13	non	non	ADJ
ejpam-6102	461	14	-	-	ADJ
ejpam-6102	461	15	degenerate	degenerate	ADJ
ejpam-6102	461	16	,	,	PUNCT
ejpam-6102	461	17	the	the	DET
ejpam-6102	461	18	last	last	ADJ
ejpam-6102	461	19	equation	equation	NOUN
ejpam-6102	461	20	in	in	ADP
ejpam-6102	461	21	(	(	PUNCT
ejpam-6102	461	22	52	52	NUM
ejpam-6102	461	23	)	)	PUNCT
ejpam-6102	461	24	implies	imply	VERB
ejpam-6102	461	25	that	that	SCONJ
ejpam-6102	461	26	|z′|	|z′|	PROPN
ejpam-6102	461	27	⩽	⩽	PROPN
ejpam-6102	461	28	c	c	PROPN
ejpam-6102	461	29	(	(	PUNCT
ejpam-6102	461	30	ε+	ε+	X
ejpam-6102	461	31	|z′|2	|z′|2	NOUN
ejpam-6102	461	32	)	)	PUNCT
ejpam-6102	461	33	,	,	PUNCT
ejpam-6102	461	34	and	and	CCONJ
ejpam-6102	461	35	therefore	therefore	ADV
ejpam-6102	461	36	,	,	PUNCT
ejpam-6102	461	37	the	the	DET
ejpam-6102	461	38	system	system	NOUN
ejpam-6102	461	39	(	(	PUNCT
ejpam-6102	461	40	52	52	NUM
ejpam-6102	461	41	)	)	PUNCT
ejpam-6102	461	42	can	can	AUX
ejpam-6102	461	43	be	be	AUX
ejpam-6102	461	44	rewritten	rewrite	VERB
ejpam-6102	461	45	as	as	ADP
ejpam-6102	461	46	ρk	ρk	ADP
ejpam-6102	461	47	=	=	PROPN
ejpam-6102	461	48	o	o	PROPN
ejpam-6102	461	49	(	(	PUNCT
ejpam-6102	461	50	ρ2k	ρ2k	PROPN
ejpam-6102	461	51	+	+	CCONJ
ejpam-6102	461	52	|z′|2	|z′|2	PROPN
ejpam-6102	461	53	+	+	CCONJ
ejpam-6102	461	54	ε	ε	PROPN
ejpam-6102	461	55	|ln	|ln	PUNCT
ejpam-6102	461	56	ε|	ε|	PROPN
ejpam-6102	461	57	)	)	PUNCT
ejpam-6102	461	58	,	,	PUNCT
ejpam-6102	461	59	k	k	PROPN
ejpam-6102	461	60	∈	∈	PROPN
ejpam-6102	461	61	{	{	PUNCT
ejpam-6102	461	62	1	1	NUM
ejpam-6102	461	63	,	,	PUNCT
ejpam-6102	461	64	.	.	PUNCT
ejpam-6102	461	65	.	.	PUNCT
ejpam-6102	461	66	.	.	PUNCT
ejpam-6102	461	67	,	,	PUNCT
ejpam-6102	461	68	n	n	CCONJ
ejpam-6102	461	69	}	}	PUNCT
ejpam-6102	461	70	,	,	PUNCT
ejpam-6102	461	71	λk	λk	X
ejpam-6102	461	72	=	=	PUNCT
ejpam-6102	461	73	o	o	X
ejpam-6102	461	74	(	(	PUNCT
ejpam-6102	461	75	|z′|2	|z′|2	PROPN
ejpam-6102	461	76	+	+	CCONJ
ejpam-6102	461	77	(	(	PUNCT
ejpam-6102	461	78	if	if	SCONJ
ejpam-6102	461	79	n	n	CCONJ
ejpam-6102	461	80	⩾	⩾	NOUN
ejpam-6102	461	81	5	5	NUM
ejpam-6102	461	82	)	)	PUNCT
ejpam-6102	461	83	ε+	ε+	X
ejpam-6102	461	84	(	(	PUNCT
ejpam-6102	461	85	if	if	SCONJ
ejpam-6102	461	86	n	n	X
ejpam-6102	461	87	=	=	SYM
ejpam-6102	461	88	4	4	X
ejpam-6102	461	89	)	)	PUNCT
ejpam-6102	461	90	|ε	|ε	NOUN
ejpam-6102	461	91	ln	ln	ADJ
ejpam-6102	461	92	ε|	ε|	PROPN
ejpam-6102	461	93	)	)	PUNCT
ejpam-6102	461	94	,	,	PUNCT
ejpam-6102	461	95	d2f1	d2f1	PROPN
ejpam-6102	461	96	(	(	PUNCT
ejpam-6102	461	97	bk	bk	NOUN
ejpam-6102	461	98	)	)	PUNCT
ejpam-6102	461	99	=	=	SYM
ejpam-6102	461	100	o	o	X
ejpam-6102	461	101	(	(	PUNCT
ejpam-6102	461	102	ε+	ε+	X
ejpam-6102	461	103	|z′|2	|z′|2	NOUN
ejpam-6102	461	104	)	)	PUNCT
ejpam-6102	461	105	,	,	PUNCT
ejpam-6102	461	106	k	k	PROPN
ejpam-6102	461	107	∈	∈	PROPN
ejpam-6102	461	108	{	{	PUNCT
ejpam-6102	461	109	1	1	NUM
ejpam-6102	461	110	,	,	PUNCT
ejpam-6102	461	111	.	.	PUNCT
ejpam-6102	461	112	.	.	PUNCT
ejpam-6102	462	1	.	.	PUNCT
ejpam-6102	462	2	,	,	PUNCT
ejpam-6102	462	3	n	n	CCONJ
ejpam-6102	462	4	}	}	PUNCT
ejpam-6102	462	5	.	.	PUNCT
ejpam-6102	463	1	(	(	PUNCT
ejpam-6102	463	2	53	53	NUM
ejpam-6102	463	3	)	)	PUNCT
ejpam-6102	463	4	since	since	SCONJ
ejpam-6102	463	5	,	,	PUNCT
ejpam-6102	463	6	d2f1	d2f1	PROPN
ejpam-6102	463	7	(	(	PUNCT
ejpam-6102	463	8	bk	bk	NOUN
ejpam-6102	463	9	)	)	PUNCT
ejpam-6102	463	10	is	be	AUX
ejpam-6102	463	11	non	non	ADJ
ejpam-6102	463	12	-	-	ADJ
ejpam-6102	463	13	degenerate	degenerate	ADJ
ejpam-6102	463	14	,	,	PUNCT
ejpam-6102	463	15	using	use	VERB
ejpam-6102	463	16	brouwer	brouwer	PROPN
ejpam-6102	463	17	’s	’s	PART
ejpam-6102	463	18	fixed	fix	VERB
ejpam-6102	463	19	point	point	NOUN
ejpam-6102	463	20	theorem	theorem	VERB
ejpam-6102	463	21	,	,	PUNCT
ejpam-6102	463	22	we	we	PRON
ejpam-6102	463	23	deduce	deduce	VERB
ejpam-6102	463	24	that	that	SCONJ
ejpam-6102	463	25	(	(	PUNCT
ejpam-6102	463	26	53	53	NUM
ejpam-6102	463	27	)	)	PUNCT
ejpam-6102	463	28	has	have	VERB
ejpam-6102	463	29	a	a	DET
ejpam-6102	463	30	solution	solution	NOUN
ejpam-6102	463	31	(	(	PUNCT
ejpam-6102	463	32	ρε	ρε	PROPN
ejpam-6102	463	33	,	,	PUNCT
ejpam-6102	463	34	λε	λε	INTJ
ejpam-6102	463	35	,	,	PUNCT
ejpam-6102	463	36	(	(	PUNCT
ejpam-6102	463	37	z′	z′	NOUN
ejpam-6102	463	38	)	)	PUNCT
ejpam-6102	463	39	ε	ε	PROPN
ejpam-6102	463	40	)	)	PUNCT
ejpam-6102	463	41	.	.	PUNCT
ejpam-6102	464	1	furthermore	furthermore	ADV
ejpam-6102	464	2	,	,	PUNCT
ejpam-6102	464	3	it	it	PRON
ejpam-6102	464	4	holds	hold	VERB
ejpam-6102	464	5	,	,	PUNCT
ejpam-6102	464	6	for	for	ADP
ejpam-6102	464	7	each	each	DET
ejpam-6102	464	8	k	k	PROPN
ejpam-6102	464	9	∈	∈	PROPN
ejpam-6102	464	10	{	{	PUNCT
ejpam-6102	464	11	1	1	NUM
ejpam-6102	464	12	,	,	PUNCT
ejpam-6102	464	13	.	.	PUNCT
ejpam-6102	464	14	.	.	PUNCT
ejpam-6102	465	1	.	.	PUNCT
ejpam-6102	465	2	,	,	PUNCT
ejpam-6102	466	1	n	n	CCONJ
ejpam-6102	466	2	}	}	PUNCT
ejpam-6102	466	3	,	,	PUNCT
ejpam-6102	466	4	ρεk	ρεk	NOUN
ejpam-6102	466	5	=	=	SYM
ejpam-6102	466	6	o	o	X
ejpam-6102	466	7	(	(	PUNCT
ejpam-6102	466	8	ε	ε	PROPN
ejpam-6102	466	9	|ln	|ln	X
ejpam-6102	466	10	ε|	ε|	PROPN
ejpam-6102	466	11	)	)	PUNCT
ejpam-6102	466	12	;	;	PUNCT
ejpam-6102	466	13	λεk	λεk	NOUN
ejpam-6102	466	14	=	=	PUNCT
ejpam-6102	466	15	o	o	X
ejpam-6102	466	16	(	(	PUNCT
ejpam-6102	466	17	(	(	PUNCT
ejpam-6102	466	18	if	if	SCONJ
ejpam-6102	466	19	n	n	CCONJ
ejpam-6102	466	20	⩾	⩾	NOUN
ejpam-6102	466	21	5	5	NUM
ejpam-6102	466	22	)	)	PUNCT
ejpam-6102	466	23	ε+	ε+	X
ejpam-6102	466	24	(	(	PUNCT
ejpam-6102	466	25	if	if	SCONJ
ejpam-6102	466	26	n	n	X
ejpam-6102	466	27	=	=	SYM
ejpam-6102	466	28	4	4	X
ejpam-6102	466	29	)	)	PUNCT
ejpam-6102	466	30	|ε	|ε	NOUN
ejpam-6102	466	31	ln	ln	ADJ
ejpam-6102	466	32	ε|	ε|	PROPN
ejpam-6102	466	33	)	)	PUNCT
ejpam-6102	466	34	;	;	PUNCT
ejpam-6102	466	35	(	(	PUNCT
ejpam-6102	466	36	z′k	z′k	NOUN
ejpam-6102	466	37	)	)	PUNCT
ejpam-6102	466	38	ε	ε	PROPN
ejpam-6102	466	39	=	=	SYM
ejpam-6102	466	40	o(ε	o(ε	PROPN
ejpam-6102	466	41	)	)	PUNCT
ejpam-6102	466	42	.	.	PUNCT
ejpam-6102	467	1	taking	take	VERB
ejpam-6102	467	2	αε	αε	ADP
ejpam-6102	467	3	k	k	PROPN
ejpam-6102	467	4	,	,	PUNCT
ejpam-6102	467	5	µ	µ	X
ejpam-6102	467	6	ε	ε	PROPN
ejpam-6102	467	7	k	k	PROPN
ejpam-6102	467	8	and	and	CCONJ
ejpam-6102	467	9	aεk	aεk	VERB
ejpam-6102	467	10	by	by	ADP
ejpam-6102	467	11	using	use	VERB
ejpam-6102	467	12	the	the	DET
ejpam-6102	467	13	equations	equation	NOUN
ejpam-6102	467	14	(	(	PUNCT
ejpam-6102	467	15	47	47	NUM
ejpam-6102	467	16	)	)	PUNCT
ejpam-6102	467	17	,	,	PUNCT
ejpam-6102	467	18	(	(	PUNCT
ejpam-6102	467	19	48	48	NUM
ejpam-6102	467	20	)	)	PUNCT
ejpam-6102	467	21	and	and	CCONJ
ejpam-6102	467	22	(	(	PUNCT
ejpam-6102	467	23	49	49	NUM
ejpam-6102	467	24	)	)	PUNCT
ejpam-6102	467	25	and	and	CCONJ
ejpam-6102	467	26	taking	take	VERB
ejpam-6102	467	27	uε	uε	X
ejpam-6102	468	1	=	=	PUNCT
ejpam-6102	468	2	∑n	∑n	NOUN
ejpam-6102	469	1	k=1	k=1	NOUN
ejpam-6102	469	2	α	α	NOUN
ejpam-6102	469	3	ε	ε	PROPN
ejpam-6102	469	4	kwaε	kwaε	PROPN
ejpam-6102	469	5	k,µ	k,µ	PROPN
ejpam-6102	469	6	ε	ε	PROPN
ejpam-6102	469	7	k	k	PROPN
ejpam-6102	470	1	+	+	CCONJ
ejpam-6102	470	2	v̄ε	v̄ε	NOUN
ejpam-6102	470	3	,	,	PUNCT
ejpam-6102	470	4	we	we	PRON
ejpam-6102	470	5	deduce	deduce	VERB
ejpam-6102	470	6	that	that	SCONJ
ejpam-6102	470	7	uε	uε	PROPN
ejpam-6102	470	8	is	be	AUX
ejpam-6102	470	9	a	a	DET
ejpam-6102	470	10	critical	critical	ADJ
ejpam-6102	470	11	point	point	NOUN
ejpam-6102	470	12	of	of	ADP
ejpam-6102	470	13	iε	iε	NOUN
ejpam-6102	470	14	and	and	CCONJ
ejpam-6102	470	15	therefore	therefore	ADV
ejpam-6102	470	16	it	it	PRON
ejpam-6102	470	17	satisfies	satisfy	VERB
ejpam-6102	470	18	{	{	PUNCT
ejpam-6102	470	19	(	(	PUNCT
ejpam-6102	470	20	−∆+	−∆+	NOUN
ejpam-6102	470	21	v	v	NOUN
ejpam-6102	470	22	)	)	PUNCT
ejpam-6102	470	23	uε	uε	NOUN
ejpam-6102	471	1	=	=	SYM
ejpam-6102	471	2	f	f	PROPN
ejpam-6102	471	3	|uε|	|uε|	VERB
ejpam-6102	471	4	4	4	NUM
ejpam-6102	471	5	n−2−εuε	n−2−εuε	NOUN
ejpam-6102	471	6	in	in	ADP
ejpam-6102	471	7	ω	ω	NUM
ejpam-6102	471	8	,	,	PUNCT
ejpam-6102	471	9	∂uε/∂ν	∂uε/∂ν	X
ejpam-6102	472	1	=	=	SYM
ejpam-6102	472	2	0	0	NUM
ejpam-6102	472	3	on	on	ADP
ejpam-6102	472	4	∂ω	∂ω	PROPN
ejpam-6102	472	5	.	.	PUNCT
ejpam-6102	473	1	finally	finally	ADV
ejpam-6102	473	2	,	,	PUNCT
ejpam-6102	473	3	we	we	PRON
ejpam-6102	473	4	have	have	VERB
ejpam-6102	473	5	to	to	PART
ejpam-6102	473	6	prove	prove	VERB
ejpam-6102	473	7	that	that	SCONJ
ejpam-6102	473	8	uε	uε	PROPN
ejpam-6102	473	9	>	>	X
ejpam-6102	473	10	0	0	X
ejpam-6102	473	11	.	.	PUNCT
ejpam-6102	474	1	to	to	ADP
ejpam-6102	474	2	this	this	DET
ejpam-6102	474	3	aim	aim	NOUN
ejpam-6102	474	4	,	,	PUNCT
ejpam-6102	474	5	let	let	VERB
ejpam-6102	474	6	u−ε	u−ε	NOUN
ejpam-6102	474	7	:	:	PUNCT
ejpam-6102	474	8	=	=	SYM
ejpam-6102	474	9	max(0,−uε	max(0,−uε	X
ejpam-6102	474	10	)	)	PUNCT
ejpam-6102	474	11	,	,	PUNCT
ejpam-6102	474	12	it	it	PRON
ejpam-6102	474	13	follows	follow	VERB
ejpam-6102	474	14	that	that	SCONJ
ejpam-6102	474	15	0	0	NUM
ejpam-6102	474	16	≤	≤	NUM
ejpam-6102	474	17	u−ε	u−ε	ADJ
ejpam-6102	474	18	≤	≤	ADJ
ejpam-6102	474	19	|vε|	|vε|	NOUN
ejpam-6102	474	20	.	.	PUNCT
ejpam-6102	475	1	furthermore	furthermore	ADV
ejpam-6102	475	2	,	,	PUNCT
ejpam-6102	475	3	multiplying	multiply	VERB
ejpam-6102	475	4	the	the	DET
ejpam-6102	475	5	previous	previous	ADJ
ejpam-6102	475	6	equation	equation	NOUN
ejpam-6102	475	7	by	by	ADP
ejpam-6102	475	8	u−ε	u−ε	PROPN
ejpam-6102	475	9	and	and	CCONJ
ejpam-6102	475	10	integrating	integrate	VERB
ejpam-6102	475	11	over	over	ADP
ejpam-6102	475	12	ω	ω	PROPN
ejpam-6102	475	13	,	,	PUNCT
ejpam-6102	475	14	we	we	PRON
ejpam-6102	475	15	obtain	obtain	VERB
ejpam-6102	475	16	∥u−ε	∥u−ε	ADJ
ejpam-6102	475	17	∥2	∥2	PUNCT
ejpam-6102	476	1	=	=	SYM
ejpam-6102	477	1	∫	∫	PROPN
ejpam-6102	478	1	ω	ω	NUM
ejpam-6102	479	1	∇uε∇u−ε	∇uε∇u−ε	PROPN
ejpam-6102	480	1	+	+	NUM
ejpam-6102	481	1	∫	∫	PROPN
ejpam-6102	482	1	ω	ω	NUM
ejpam-6102	482	2	v	v	NOUN
ejpam-6102	482	3	uεu	uεu	NOUN
ejpam-6102	482	4	−	−	PROPN
ejpam-6102	482	5	ε	ε	PROPN
ejpam-6102	482	6	r.	r.	PROPN
ejpam-6102	482	7	almushahhin	almushahhin	PROPN
ejpam-6102	482	8	,	,	PUNCT
ejpam-6102	482	9	m.	m.	PROPN
ejpam-6102	482	10	ben	ben	PROPN
ejpam-6102	482	11	ayed	aye	VERB
ejpam-6102	482	12	/	/	SYM
ejpam-6102	482	13	eur	eur	PROPN
ejpam-6102	482	14	.	.	PUNCT
ejpam-6102	483	1	j.	j.	PROPN
ejpam-6102	483	2	pure	pure	PROPN
ejpam-6102	483	3	appl	appl	PROPN
ejpam-6102	483	4	.	.	PROPN
ejpam-6102	483	5	math	math	PROPN
ejpam-6102	483	6	,	,	PUNCT
ejpam-6102	483	7	18	18	NUM
ejpam-6102	483	8	(	(	PUNCT
ejpam-6102	483	9	2	2	NUM
ejpam-6102	483	10	)	)	PUNCT
ejpam-6102	483	11	(	(	PUNCT
ejpam-6102	483	12	2025	2025	NUM
ejpam-6102	483	13	)	)	PUNCT
ejpam-6102	483	14	,	,	PUNCT
ejpam-6102	483	15	6102	6102	NUM
ejpam-6102	483	16	18	18	NUM
ejpam-6102	483	17	of	of	ADP
ejpam-6102	483	18	31	31	NUM
ejpam-6102	483	19	=	=	SYM
ejpam-6102	483	20	∫	∫	PROPN
ejpam-6102	483	21	ω	ω	PROPN
ejpam-6102	483	22	(	(	PUNCT
ejpam-6102	483	23	−∆+	−∆+	NOUN
ejpam-6102	483	24	v	v	NOUN
ejpam-6102	483	25	)	)	PUNCT
ejpam-6102	483	26	uεu	uεu	PROPN
ejpam-6102	484	1	−	−	PROPN
ejpam-6102	484	2	ε	ε	PROPN
ejpam-6102	484	3	=	=	SYM
ejpam-6102	484	4	∫	∫	PROPN
ejpam-6102	484	5	ω	ω	PROPN
ejpam-6102	484	6	f	f	PROPN
ejpam-6102	484	7	|uε|p−ε−1uεu	|uε|p−ε−1uεu	PROPN
ejpam-6102	485	1	−	−	PROPN
ejpam-6102	485	2	ε	ε	PROPN
ejpam-6102	485	3	=	=	SYM
ejpam-6102	485	4	∫	∫	PROPN
ejpam-6102	485	5	ω	ω	PROPN
ejpam-6102	485	6	f(u−ε	f(u−ε	PROPN
ejpam-6102	485	7	)	)	PUNCT
ejpam-6102	485	8	p−ε+1	p−ε+1	PROPN
ejpam-6102	485	9	(	(	PUNCT
ejpam-6102	485	10	54	54	NUM
ejpam-6102	485	11	)	)	PUNCT
ejpam-6102	485	12	which	which	PRON
ejpam-6102	485	13	implies	imply	VERB
ejpam-6102	485	14	that	that	SCONJ
ejpam-6102	485	15	∥u−ε	∥u−ε	ADJ
ejpam-6102	485	16	∥2	∥2	NOUN
ejpam-6102	485	17	=	=	SYM
ejpam-6102	485	18	o(1	o(1	PROPN
ejpam-6102	485	19	)	)	PUNCT
ejpam-6102	485	20	(	(	PUNCT
ejpam-6102	485	21	since	since	SCONJ
ejpam-6102	485	22	0	0	NUM
ejpam-6102	485	23	≤	≤	NUM
ejpam-6102	485	24	u−ε	u−ε	PROPN
ejpam-6102	485	25	≤	≤	ADJ
ejpam-6102	485	26	|vε|	|vε|	NOUN
ejpam-6102	485	27	)	)	PUNCT
ejpam-6102	485	28	.	.	PUNCT
ejpam-6102	486	1	now	now	ADV
ejpam-6102	486	2	,	,	PUNCT
ejpam-6102	486	3	using	use	VERB
ejpam-6102	486	4	the	the	DET
ejpam-6102	486	5	holder	holder	NOUN
ejpam-6102	486	6	’s	’s	PART
ejpam-6102	486	7	inequality	inequality	NOUN
ejpam-6102	486	8	,	,	PUNCT
ejpam-6102	486	9	we	we	PRON
ejpam-6102	486	10	obtain	obtain	VERB
ejpam-6102	486	11	∥u−ε	∥u−ε	PROPN
ejpam-6102	486	12	∥2	∥2	NOUN
ejpam-6102	486	13	≤	≤	NUM
ejpam-6102	486	14	c∥u−ε	c∥u−ε	PROPN
ejpam-6102	486	15	∥p+1−ε	∥p+1−ε	PROPN
ejpam-6102	486	16	.	.	PUNCT
ejpam-6102	487	1	thus	thus	ADV
ejpam-6102	487	2	,	,	PUNCT
ejpam-6102	487	3	u−ε	u−ε	PROPN
ejpam-6102	487	4	has	have	VERB
ejpam-6102	487	5	to	to	PART
ejpam-6102	487	6	be	be	AUX
ejpam-6102	487	7	zero	zero	NUM
ejpam-6102	487	8	and	and	CCONJ
ejpam-6102	487	9	therefore	therefore	ADV
ejpam-6102	487	10	,	,	PUNCT
ejpam-6102	487	11	by	by	ADP
ejpam-6102	487	12	the	the	DET
ejpam-6102	487	13	maximum	maximum	PROPN
ejpam-6102	487	14	principle	principle	NOUN
ejpam-6102	487	15	,	,	PUNCT
ejpam-6102	487	16	we	we	PRON
ejpam-6102	487	17	derive	derive	VERB
ejpam-6102	487	18	that	that	SCONJ
ejpam-6102	487	19	uε	uε	PROPN
ejpam-6102	487	20	>	>	X
ejpam-6102	487	21	0	0	PUNCT
ejpam-6102	487	22	in	in	ADP
ejpam-6102	487	23	ω	ω	PROPN
ejpam-6102	487	24	.	.	PUNCT
ejpam-6102	488	1	hence	hence	ADV
ejpam-6102	488	2	uε	uε	PROPN
ejpam-6102	488	3	is	be	AUX
ejpam-6102	488	4	a	a	DET
ejpam-6102	488	5	solution	solution	NOUN
ejpam-6102	488	6	of	of	ADP
ejpam-6102	488	7	problem	problem	NOUN
ejpam-6102	488	8	(	(	PUNCT
ejpam-6102	488	9	pε	pε	NOUN
ejpam-6102	488	10	)	)	PUNCT
ejpam-6102	488	11	.	.	PUNCT
ejpam-6102	489	1	this	this	PRON
ejpam-6102	489	2	completes	complete	VERB
ejpam-6102	489	3	the	the	DET
ejpam-6102	489	4	proof	proof	NOUN
ejpam-6102	489	5	of	of	ADP
ejpam-6102	489	6	theorem	theorem	NOUN
ejpam-6102	489	7	1	1	NUM
ejpam-6102	489	8	.	.	NOUN
ejpam-6102	489	9	6	6	NUM
ejpam-6102	489	10	.	.	X
ejpam-6102	489	11	conclusion	conclusion	NOUN
ejpam-6102	489	12	by	by	ADP
ejpam-6102	489	13	expanding	expand	VERB
ejpam-6102	489	14	the	the	DET
ejpam-6102	489	15	gradient	gradient	NOUN
ejpam-6102	489	16	of	of	ADP
ejpam-6102	489	17	the	the	DET
ejpam-6102	489	18	associated	associated	ADJ
ejpam-6102	489	19	functional	functional	ADJ
ejpam-6102	489	20	and	and	CCONJ
ejpam-6102	489	21	testing	test	VERB
ejpam-6102	489	22	the	the	DET
ejpam-6102	489	23	equation	equation	NOUN
ejpam-6102	489	24	with	with	ADP
ejpam-6102	489	25	appropriate	appropriate	ADJ
ejpam-6102	489	26	vector	vector	NOUN
ejpam-6102	489	27	fields	field	NOUN
ejpam-6102	489	28	,	,	PUNCT
ejpam-6102	489	29	we	we	PRON
ejpam-6102	489	30	were	be	AUX
ejpam-6102	489	31	able	able	ADJ
ejpam-6102	489	32	to	to	PART
ejpam-6102	489	33	construct	construct	VERB
ejpam-6102	489	34	boundary	boundary	ADJ
ejpam-6102	489	35	blow	blow	NOUN
ejpam-6102	489	36	-	-	PUNCT
ejpam-6102	489	37	up	up	ADP
ejpam-6102	489	38	solutions	solution	NOUN
ejpam-6102	489	39	for	for	ADP
ejpam-6102	489	40	the	the	DET
ejpam-6102	489	41	problem	problem	NOUN
ejpam-6102	489	42	(	(	PUNCT
ejpam-6102	489	43	pε	pε	NOUN
ejpam-6102	489	44	)	)	PUNCT
ejpam-6102	489	45	,	,	PUNCT
ejpam-6102	489	46	which	which	PRON
ejpam-6102	489	47	exhibit	exhibit	VERB
ejpam-6102	489	48	isolated	isolated	ADJ
ejpam-6102	489	49	bubbles	bubble	NOUN
ejpam-6102	489	50	.	.	PUNCT
ejpam-6102	490	1	this	this	DET
ejpam-6102	490	2	construction	construction	NOUN
ejpam-6102	490	3	exploits	exploit	VERB
ejpam-6102	490	4	the	the	DET
ejpam-6102	490	5	structure	structure	NOUN
ejpam-6102	490	6	of	of	ADP
ejpam-6102	490	7	the	the	DET
ejpam-6102	490	8	problem	problem	NOUN
ejpam-6102	490	9	,	,	PUNCT
ejpam-6102	490	10	using	use	VERB
ejpam-6102	490	11	asymptotic	asymptotic	ADJ
ejpam-6102	490	12	analysis	analysis	NOUN
ejpam-6102	490	13	to	to	PART
ejpam-6102	490	14	capture	capture	VERB
ejpam-6102	490	15	the	the	DET
ejpam-6102	490	16	intricate	intricate	ADJ
ejpam-6102	490	17	behavior	behavior	NOUN
ejpam-6102	490	18	of	of	ADP
ejpam-6102	490	19	the	the	DET
ejpam-6102	490	20	concentration	concentration	NOUN
ejpam-6102	490	21	points	point	NOUN
ejpam-6102	490	22	and	and	CCONJ
ejpam-6102	490	23	the	the	DET
ejpam-6102	490	24	corresponding	correspond	VERB
ejpam-6102	490	25	blow	blow	NOUN
ejpam-6102	490	26	-	-	PUNCT
ejpam-6102	490	27	up	up	ADP
ejpam-6102	490	28	rates	rate	NOUN
ejpam-6102	490	29	of	of	ADP
ejpam-6102	490	30	the	the	DET
ejpam-6102	490	31	solution	solution	NOUN
ejpam-6102	490	32	as	as	ADP
ejpam-6102	490	33	the	the	DET
ejpam-6102	490	34	perturbation	perturbation	NOUN
ejpam-6102	490	35	parameter	parameter	NOUN
ejpam-6102	490	36	ε	ε	PROPN
ejpam-6102	490	37	approaches	approach	VERB
ejpam-6102	490	38	zero	zero	NUM
ejpam-6102	490	39	.	.	PUNCT
ejpam-6102	491	1	by	by	ADP
ejpam-6102	491	2	carefully	carefully	ADV
ejpam-6102	491	3	analyzing	analyze	VERB
ejpam-6102	491	4	the	the	DET
ejpam-6102	491	5	interaction	interaction	NOUN
ejpam-6102	491	6	between	between	ADP
ejpam-6102	491	7	the	the	DET
ejpam-6102	491	8	nonlinearities	nonlinearitie	NOUN
ejpam-6102	491	9	of	of	ADP
ejpam-6102	491	10	the	the	DET
ejpam-6102	491	11	equation	equation	NOUN
ejpam-6102	491	12	and	and	CCONJ
ejpam-6102	491	13	the	the	DET
ejpam-6102	491	14	boundary	boundary	ADJ
ejpam-6102	491	15	conditions	condition	NOUN
ejpam-6102	491	16	,	,	PUNCT
ejpam-6102	491	17	we	we	PRON
ejpam-6102	491	18	establish	establish	VERB
ejpam-6102	491	19	a	a	DET
ejpam-6102	491	20	connection	connection	NOUN
ejpam-6102	491	21	between	between	ADP
ejpam-6102	491	22	the	the	DET
ejpam-6102	491	23	number	number	NOUN
ejpam-6102	491	24	of	of	ADP
ejpam-6102	491	25	isolated	isolated	ADJ
ejpam-6102	491	26	bubbles	bubble	NOUN
ejpam-6102	491	27	and	and	CCONJ
ejpam-6102	491	28	the	the	DET
ejpam-6102	491	29	topology	topology	NOUN
ejpam-6102	491	30	of	of	ADP
ejpam-6102	491	31	the	the	DET
ejpam-6102	491	32	problem	problem	NOUN
ejpam-6102	491	33	.	.	PUNCT
ejpam-6102	492	1	this	this	DET
ejpam-6102	492	2	approach	approach	NOUN
ejpam-6102	492	3	ultimately	ultimately	ADV
ejpam-6102	492	4	leads	lead	VERB
ejpam-6102	492	5	to	to	ADP
ejpam-6102	492	6	a	a	DET
ejpam-6102	492	7	multiplicity	multiplicity	NOUN
ejpam-6102	492	8	result	result	NOUN
ejpam-6102	492	9	,	,	PUNCT
ejpam-6102	492	10	demonstrating	demonstrate	VERB
ejpam-6102	492	11	that	that	SCONJ
ejpam-6102	492	12	the	the	DET
ejpam-6102	492	13	number	number	NOUN
ejpam-6102	492	14	of	of	ADP
ejpam-6102	492	15	boundary	boundary	ADJ
ejpam-6102	492	16	blow	blow	NOUN
ejpam-6102	492	17	-	-	PUNCT
ejpam-6102	492	18	up	up	ADP
ejpam-6102	492	19	solutions	solution	NOUN
ejpam-6102	492	20	is	be	AUX
ejpam-6102	492	21	closely	closely	ADV
ejpam-6102	492	22	related	relate	VERB
ejpam-6102	492	23	to	to	ADP
ejpam-6102	492	24	the	the	DET
ejpam-6102	492	25	number	number	NOUN
ejpam-6102	492	26	of	of	ADP
ejpam-6102	492	27	non	non	ADJ
ejpam-6102	492	28	-	-	ADJ
ejpam-6102	492	29	degenerate	degenerate	ADJ
ejpam-6102	492	30	critical	critical	ADJ
ejpam-6102	492	31	points	point	NOUN
ejpam-6102	492	32	of	of	ADP
ejpam-6102	492	33	the	the	DET
ejpam-6102	492	34	restriction	restriction	NOUN
ejpam-6102	492	35	of	of	ADP
ejpam-6102	492	36	the	the	DET
ejpam-6102	492	37	function	function	NOUN
ejpam-6102	492	38	f	f	PROPN
ejpam-6102	492	39	on	on	ADP
ejpam-6102	492	40	the	the	DET
ejpam-6102	492	41	boundary	boundary	NOUN
ejpam-6102	492	42	of	of	ADP
ejpam-6102	492	43	the	the	DET
ejpam-6102	492	44	domain	domain	NOUN
ejpam-6102	492	45	ω	ω	NOUN
ejpam-6102	492	46	.	.	PUNCT
ejpam-6102	493	1	this	this	DET
ejpam-6102	493	2	result	result	NOUN
ejpam-6102	493	3	provides	provide	VERB
ejpam-6102	493	4	a	a	DET
ejpam-6102	493	5	deeper	deep	ADJ
ejpam-6102	493	6	understanding	understanding	NOUN
ejpam-6102	493	7	of	of	ADP
ejpam-6102	493	8	the	the	DET
ejpam-6102	493	9	solution	solution	NOUN
ejpam-6102	493	10	structure	structure	NOUN
ejpam-6102	493	11	,	,	PUNCT
ejpam-6102	493	12	offering	offer	VERB
ejpam-6102	493	13	insights	insight	NOUN
ejpam-6102	493	14	into	into	ADP
ejpam-6102	493	15	bifurcation	bifurcation	NOUN
ejpam-6102	493	16	behavior	behavior	NOUN
ejpam-6102	493	17	and	and	CCONJ
ejpam-6102	493	18	the	the	DET
ejpam-6102	493	19	stability	stability	NOUN
ejpam-6102	493	20	of	of	ADP
ejpam-6102	493	21	solutions	solution	NOUN
ejpam-6102	493	22	as	as	ADP
ejpam-6102	493	23	the	the	DET
ejpam-6102	493	24	boundary	boundary	ADJ
ejpam-6102	493	25	conditions	condition	NOUN
ejpam-6102	493	26	are	be	AUX
ejpam-6102	493	27	varied	varied	ADJ
ejpam-6102	493	28	.	.	PUNCT
ejpam-6102	494	1	nevertheless	nevertheless	ADV
ejpam-6102	494	2	,	,	PUNCT
ejpam-6102	494	3	several	several	ADJ
ejpam-6102	494	4	promising	promising	ADJ
ejpam-6102	494	5	avenues	avenue	NOUN
ejpam-6102	494	6	for	for	ADP
ejpam-6102	494	7	further	further	ADJ
ejpam-6102	494	8	research	research	NOUN
ejpam-6102	494	9	and	and	CCONJ
ejpam-6102	494	10	open	open	ADJ
ejpam-6102	494	11	questions	question	NOUN
ejpam-6102	494	12	remain	remain	VERB
ejpam-6102	494	13	:	:	PUNCT
ejpam-6102	494	14	(	(	PUNCT
ejpam-6102	494	15	i	i	NOUN
ejpam-6102	494	16	)	)	PUNCT
ejpam-6102	494	17	do	do	AUX
ejpam-6102	494	18	boundary	boundary	ADJ
ejpam-6102	494	19	clustered	clustered	ADJ
ejpam-6102	494	20	bubble	bubble	NOUN
ejpam-6102	494	21	solutions	solution	NOUN
ejpam-6102	494	22	exist	exist	VERB
ejpam-6102	494	23	for	for	ADP
ejpam-6102	494	24	the	the	DET
ejpam-6102	494	25	problem	problem	NOUN
ejpam-6102	494	26	?	?	PUNCT
ejpam-6102	495	1	(	(	PUNCT
ejpam-6102	495	2	ii	ii	NOUN
ejpam-6102	495	3	)	)	PUNCT
ejpam-6102	495	4	can	can	AUX
ejpam-6102	495	5	we	we	PRON
ejpam-6102	495	6	provide	provide	VERB
ejpam-6102	495	7	a	a	DET
ejpam-6102	495	8	complete	complete	ADJ
ejpam-6102	495	9	description	description	NOUN
ejpam-6102	495	10	of	of	ADP
ejpam-6102	495	11	the	the	DET
ejpam-6102	495	12	asymptotic	asymptotic	ADJ
ejpam-6102	495	13	profile	profile	NOUN
ejpam-6102	495	14	of	of	ADP
ejpam-6102	495	15	the	the	DET
ejpam-6102	495	16	boundary	boundary	NOUN
ejpam-6102	495	17	blowing	blow	VERB
ejpam-6102	495	18	up	up	ADP
ejpam-6102	495	19	solutions	solution	NOUN
ejpam-6102	495	20	?	?	PUNCT
ejpam-6102	496	1	(	(	PUNCT
ejpam-6102	496	2	iii	iii	X
ejpam-6102	496	3	)	)	PUNCT
ejpam-6102	496	4	what	what	PRON
ejpam-6102	496	5	occurs	occur	VERB
ejpam-6102	496	6	if	if	SCONJ
ejpam-6102	496	7	the	the	DET
ejpam-6102	496	8	critical	critical	ADJ
ejpam-6102	496	9	points	point	NOUN
ejpam-6102	496	10	of	of	ADP
ejpam-6102	496	11	the	the	DET
ejpam-6102	496	12	restriction	restriction	NOUN
ejpam-6102	496	13	f1	f1	NOUN
ejpam-6102	496	14	of	of	ADP
ejpam-6102	496	15	the	the	DET
ejpam-6102	496	16	function	function	NOUN
ejpam-6102	496	17	f	f	PROPN
ejpam-6102	496	18	on	on	ADP
ejpam-6102	496	19	the	the	DET
ejpam-6102	496	20	boundary	boundary	NOUN
ejpam-6102	496	21	are	be	AUX
ejpam-6102	496	22	degenerate	degenerate	ADJ
ejpam-6102	496	23	?	?	PUNCT
ejpam-6102	497	1	in	in	ADP
ejpam-6102	497	2	particular	particular	ADJ
ejpam-6102	497	3	,	,	PUNCT
ejpam-6102	497	4	what	what	PRON
ejpam-6102	497	5	occurs	occur	VERB
ejpam-6102	497	6	when	when	SCONJ
ejpam-6102	497	7	f1	f1	ADJ
ejpam-6102	497	8	satisfies	satisfy	VERB
ejpam-6102	497	9	certain	certain	ADJ
ejpam-6102	497	10	flatness	flatness	NOUN
ejpam-6102	497	11	conditions	condition	NOUN
ejpam-6102	497	12	?	?	PUNCT
ejpam-6102	498	1	(	(	PUNCT
ejpam-6102	498	2	iv	iv	X
ejpam-6102	498	3	)	)	PUNCT
ejpam-6102	498	4	is	be	AUX
ejpam-6102	498	5	it	it	PRON
ejpam-6102	498	6	possible	possible	ADJ
ejpam-6102	498	7	to	to	PART
ejpam-6102	498	8	get	get	VERB
ejpam-6102	498	9	the	the	DET
ejpam-6102	498	10	same	same	ADJ
ejpam-6102	498	11	results	result	NOUN
ejpam-6102	498	12	presented	present	VERB
ejpam-6102	498	13	in	in	ADP
ejpam-6102	498	14	this	this	DET
ejpam-6102	498	15	paper	paper	NOUN
ejpam-6102	498	16	when	when	SCONJ
ejpam-6102	498	17	the	the	DET
ejpam-6102	498	18	solutions	solution	NOUN
ejpam-6102	498	19	do	do	AUX
ejpam-6102	498	20	not	not	PART
ejpam-6102	498	21	converge	converge	VERB
ejpam-6102	498	22	weakly	weakly	ADV
ejpam-6102	498	23	to	to	ADP
ejpam-6102	498	24	zero	zero	NUM
ejpam-6102	498	25	?	?	PUNCT
ejpam-6102	499	1	7	7	X
ejpam-6102	499	2	.	.	X
ejpam-6102	499	3	appendix	appendix	NOUN
ejpam-6102	499	4	in	in	ADP
ejpam-6102	499	5	this	this	DET
ejpam-6102	499	6	section	section	NOUN
ejpam-6102	499	7	,	,	PUNCT
ejpam-6102	499	8	we	we	PRON
ejpam-6102	499	9	gather	gather	VERB
ejpam-6102	499	10	estimates	estimate	NOUN
ejpam-6102	499	11	for	for	ADP
ejpam-6102	499	12	several	several	ADJ
ejpam-6102	499	13	integrals	integral	NOUN
ejpam-6102	499	14	,	,	PUNCT
ejpam-6102	499	15	which	which	PRON
ejpam-6102	499	16	are	be	AUX
ejpam-6102	499	17	crucial	crucial	ADJ
ejpam-6102	499	18	for	for	ADP
ejpam-6102	499	19	refining	refine	VERB
ejpam-6102	499	20	the	the	DET
ejpam-6102	499	21	expansion	expansion	NOUN
ejpam-6102	499	22	of	of	ADP
ejpam-6102	499	23	the	the	DET
ejpam-6102	499	24	gradient	gradient	NOUN
ejpam-6102	499	25	of	of	ADP
ejpam-6102	499	26	the	the	DET
ejpam-6102	499	27	euler	euler	NOUN
ejpam-6102	499	28	-	-	PUNCT
ejpam-6102	499	29	lagrange	lagrange	NOUN
ejpam-6102	499	30	functional	functional	ADJ
ejpam-6102	499	31	jε	jε	NOUN
ejpam-6102	499	32	.	.	PROPN
ejpam-6102	499	33	additionally	additionally	ADV
ejpam-6102	499	34	,	,	PUNCT
ejpam-6102	499	35	we	we	PRON
ejpam-6102	499	36	prove	prove	VERB
ejpam-6102	499	37	the	the	DET
ejpam-6102	499	38	coercivity	coercivity	NOUN
ejpam-6102	499	39	of	of	ADP
ejpam-6102	499	40	the	the	DET
ejpam-6102	499	41	quadratic	quadratic	ADJ
ejpam-6102	499	42	form	form	NOUN
ejpam-6102	499	43	defined	define	VERB
ejpam-6102	499	44	by	by	ADP
ejpam-6102	499	45	(	(	PUNCT
ejpam-6102	499	46	10	10	NUM
ejpam-6102	499	47	)	)	PUNCT
ejpam-6102	499	48	.	.	PUNCT
ejpam-6102	500	1	7.1	7.1	NUM
ejpam-6102	500	2	.	.	PUNCT
ejpam-6102	501	1	useful	useful	ADJ
ejpam-6102	501	2	estimates	estimate	NOUN
ejpam-6102	501	3	of	of	ADP
ejpam-6102	501	4	some	some	DET
ejpam-6102	501	5	integrals	integral	NOUN
ejpam-6102	501	6	we	we	PRON
ejpam-6102	501	7	start	start	VERB
ejpam-6102	501	8	by	by	ADP
ejpam-6102	501	9	the	the	DET
ejpam-6102	501	10	following	follow	VERB
ejpam-6102	501	11	lemma	lemma	PROPN
ejpam-6102	501	12	which	which	PRON
ejpam-6102	501	13	is	be	AUX
ejpam-6102	501	14	extracted	extract	VERB
ejpam-6102	501	15	from	from	ADP
ejpam-6102	501	16	[	[	X
ejpam-6102	501	17	27	27	NUM
ejpam-6102	501	18	]	]	PUNCT
ejpam-6102	501	19	(	(	PUNCT
ejpam-6102	501	20	see	see	VERB
ejpam-6102	501	21	equations	equation	NOUN
ejpam-6102	501	22	(	(	PUNCT
ejpam-6102	501	23	d.6	d.6	NOUN
ejpam-6102	501	24	)	)	PUNCT
ejpam-6102	501	25	,	,	PUNCT
ejpam-6102	501	26	(	(	PUNCT
ejpam-6102	501	27	d.7	d.7	NUM
ejpam-6102	501	28	)	)	PUNCT
ejpam-6102	501	29	and	and	CCONJ
ejpam-6102	501	30	(	(	PUNCT
ejpam-6102	501	31	d.8	d.8	NOUN
ejpam-6102	501	32	)	)	PUNCT
ejpam-6102	501	33	)	)	PUNCT
ejpam-6102	501	34	.	.	PUNCT
ejpam-6102	502	1	lemma	lemma	PROPN
ejpam-6102	502	2	4	4	NUM
ejpam-6102	502	3	.	.	PUNCT
ejpam-6102	503	1	[	[	X
ejpam-6102	503	2	27	27	NUM
ejpam-6102	503	3	]	]	X
ejpam-6102	503	4	let	let	VERB
ejpam-6102	503	5	n	n	INTJ
ejpam-6102	503	6	⩾	⩾	NOUN
ejpam-6102	503	7	3	3	NUM
ejpam-6102	503	8	,	,	PUNCT
ejpam-6102	503	9	a	a	DET
ejpam-6102	503	10	∈	∈	PROPN
ejpam-6102	503	11	∂ω	∂ω	PROPN
ejpam-6102	503	12	and	and	CCONJ
ejpam-6102	503	13	µ	µ	PRON
ejpam-6102	503	14	be	be	AUX
ejpam-6102	503	15	a	a	DET
ejpam-6102	503	16	large	large	ADJ
ejpam-6102	503	17	real	real	NOUN
ejpam-6102	503	18	.	.	PUNCT
ejpam-6102	504	1	we	we	PRON
ejpam-6102	504	2	have	have	VERB
ejpam-6102	504	3	(	(	PUNCT
ejpam-6102	504	4	i	i	NOUN
ejpam-6102	504	5	)	)	PUNCT
ejpam-6102	504	6	∫	∫	PROPN
ejpam-6102	505	1	ω	ω	X
ejpam-6102	505	2	|∇ωa,µ|2	|∇ωa,µ|2	PROPN
ejpam-6102	505	3	=	=	SYM
ejpam-6102	505	4	sn	sn	PROPN
ejpam-6102	505	5	−	−	PROPN
ejpam-6102	505	6	c1	c1	PROPN
ejpam-6102	505	7	h(a	h(a	PROPN
ejpam-6102	505	8	)	)	PUNCT
ejpam-6102	505	9	µ	µ	PRON
ejpam-6102	505	10	+	+	PROPN
ejpam-6102	505	11	o	o	X
ejpam-6102	505	12	(	(	PUNCT
ejpam-6102	505	13	1	1	NUM
ejpam-6102	505	14	µ2	µ2	PROPN
ejpam-6102	505	15	)	)	PUNCT
ejpam-6102	505	16	,	,	PUNCT
ejpam-6102	505	17	r.	r.	PROPN
ejpam-6102	505	18	almushahhin	almushahhin	PROPN
ejpam-6102	505	19	,	,	PUNCT
ejpam-6102	505	20	m.	m.	PROPN
ejpam-6102	505	21	ben	ben	PROPN
ejpam-6102	505	22	ayed	aye	VERB
ejpam-6102	505	23	/	/	SYM
ejpam-6102	505	24	eur	eur	PROPN
ejpam-6102	505	25	.	.	PUNCT
ejpam-6102	506	1	j.	j.	PROPN
ejpam-6102	506	2	pure	pure	PROPN
ejpam-6102	506	3	appl	appl	PROPN
ejpam-6102	506	4	.	.	PROPN
ejpam-6102	506	5	math	math	PROPN
ejpam-6102	506	6	,	,	PUNCT
ejpam-6102	506	7	18	18	NUM
ejpam-6102	506	8	(	(	PUNCT
ejpam-6102	506	9	2	2	NUM
ejpam-6102	506	10	)	)	PUNCT
ejpam-6102	506	11	(	(	PUNCT
ejpam-6102	506	12	2025	2025	NUM
ejpam-6102	506	13	)	)	PUNCT
ejpam-6102	506	14	,	,	PUNCT
ejpam-6102	506	15	6102	6102	NUM
ejpam-6102	506	16	19	19	NUM
ejpam-6102	506	17	of	of	ADP
ejpam-6102	506	18	31	31	NUM
ejpam-6102	506	19	(	(	PUNCT
ejpam-6102	506	20	ii	ii	NOUN
ejpam-6102	506	21	)	)	PUNCT
ejpam-6102	506	22	∫	∫	PROPN
ejpam-6102	507	1	ω	ω	NUM
ejpam-6102	507	2	∇ωa,µ∇	∇ωa,µ∇	PROPN
ejpam-6102	507	3	(	(	PUNCT
ejpam-6102	507	4	µ	µ	X
ejpam-6102	507	5	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	507	6	∂µ	∂µ	PROPN
ejpam-6102	507	7	)	)	PUNCT
ejpam-6102	507	8	=	=	PROPN
ejpam-6102	507	9	c1	c1	PROPN
ejpam-6102	507	10	2	2	NUM
ejpam-6102	507	11	h(a	h(a	PROPN
ejpam-6102	507	12	)	)	PUNCT
ejpam-6102	507	13	µ	µ	PRON
ejpam-6102	508	1	+	+	PROPN
ejpam-6102	508	2	o	o	X
ejpam-6102	508	3	(	(	PUNCT
ejpam-6102	508	4	1	1	NUM
ejpam-6102	508	5	µ2	µ2	NOUN
ejpam-6102	508	6	)	)	PUNCT
ejpam-6102	508	7	,	,	PUNCT
ejpam-6102	508	8	(	(	PUNCT
ejpam-6102	508	9	iii	iii	X
ejpam-6102	508	10	)	)	PUNCT
ejpam-6102	508	11	∫	∫	PROPN
ejpam-6102	509	1	ω	ω	NUM
ejpam-6102	509	2	∇ωa,µ∇	∇ωa,µ∇	PROPN
ejpam-6102	509	3	(	(	PUNCT
ejpam-6102	509	4	1	1	NUM
ejpam-6102	509	5	µ	µ	PRON
ejpam-6102	509	6	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	509	7	∂τj	∂τj	PROPN
ejpam-6102	509	8	)	)	PUNCT
ejpam-6102	510	1	=	=	SYM
ejpam-6102	510	2	o	o	NOUN
ejpam-6102	510	3	(	(	PUNCT
ejpam-6102	510	4	1	1	NUM
ejpam-6102	510	5	µ2	µ2	NOUN
ejpam-6102	510	6	)	)	PUNCT
ejpam-6102	510	7	∀j	∀j	PROPN
ejpam-6102	510	8	∈	∈	PROPN
ejpam-6102	510	9	{	{	PUNCT
ejpam-6102	510	10	1	1	NUM
ejpam-6102	510	11	,	,	PUNCT
ejpam-6102	510	12	.	.	PUNCT
ejpam-6102	510	13	.	.	PUNCT
ejpam-6102	510	14	.	.	PUNCT
ejpam-6102	511	1	,	,	PUNCT
ejpam-6102	511	2	n−	n−	NOUN
ejpam-6102	511	3	1	1	NUM
ejpam-6102	511	4	}	}	PUNCT
ejpam-6102	511	5	,	,	PUNCT
ejpam-6102	511	6	where	where	SCONJ
ejpam-6102	511	7	τ	τ	PROPN
ejpam-6102	511	8	′js	′js	NOUN
ejpam-6102	511	9	,	,	PUNCT
ejpam-6102	511	10	for	for	ADP
ejpam-6102	511	11	j	j	PROPN
ejpam-6102	511	12	=	=	SYM
ejpam-6102	511	13	1	1	PROPN
ejpam-6102	511	14	,	,	PUNCT
ejpam-6102	511	15	.	.	PUNCT
ejpam-6102	511	16	.	.	PUNCT
ejpam-6102	512	1	.	.	PUNCT
ejpam-6102	513	1	,	,	PUNCT
ejpam-6102	513	2	n	n	CCONJ
ejpam-6102	513	3	−	−	PROPN
ejpam-6102	513	4	1	1	NUM
ejpam-6102	513	5	,	,	PUNCT
ejpam-6102	513	6	build	build	VERB
ejpam-6102	513	7	an	an	DET
ejpam-6102	513	8	orthonormal	orthonormal	ADJ
ejpam-6102	513	9	system	system	NOUN
ejpam-6102	513	10	of	of	ADP
ejpam-6102	513	11	coordinates	coordinate	NOUN
ejpam-6102	513	12	on	on	ADP
ejpam-6102	513	13	the	the	DET
ejpam-6102	513	14	tangent	tangent	ADJ
ejpam-6102	513	15	space	space	NOUN
ejpam-6102	513	16	to	to	ADP
ejpam-6102	513	17	∂ω	∂ω	PROPN
ejpam-6102	513	18	at	at	ADP
ejpam-6102	513	19	the	the	DET
ejpam-6102	513	20	point	point	NOUN
ejpam-6102	513	21	a	a	DET
ejpam-6102	513	22	∈	∈	PROPN
ejpam-6102	513	23	∂ω	∂ω	PROPN
ejpam-6102	513	24	,	,	PUNCT
ejpam-6102	513	25	the	the	DET
ejpam-6102	513	26	constant	constant	ADJ
ejpam-6102	513	27	sn	sn	PROPN
ejpam-6102	513	28	is	be	AUX
ejpam-6102	513	29	defined	define	VERB
ejpam-6102	513	30	in	in	ADP
ejpam-6102	513	31	(	(	PUNCT
ejpam-6102	513	32	22	22	NUM
ejpam-6102	513	33	)	)	PUNCT
ejpam-6102	513	34	and	and	CCONJ
ejpam-6102	513	35	the	the	DET
ejpam-6102	513	36	constant	constant	ADJ
ejpam-6102	513	37	c1	c1	NOUN
ejpam-6102	513	38	is	be	AUX
ejpam-6102	513	39	defined	define	VERB
ejpam-6102	513	40	by	by	ADP
ejpam-6102	513	41	c1	c1	PROPN
ejpam-6102	513	42	:	:	PUNCT
ejpam-6102	513	43	=	=	PUNCT
ejpam-6102	514	1	[	[	X
ejpam-6102	514	2	n(n−	n(n−	NOUN
ejpam-6102	514	3	2	2	NUM
ejpam-6102	514	4	)	)	PUNCT
ejpam-6102	514	5	]	]	PUNCT
ejpam-6102	514	6	(	(	PUNCT
ejpam-6102	514	7	n−2)/2	n−2)/2	X
ejpam-6102	514	8	(	(	PUNCT
ejpam-6102	514	9	n−	n−	NOUN
ejpam-6102	514	10	2)2	2)2	NUM
ejpam-6102	514	11	4	4	NUM
ejpam-6102	514	12	meas	mea	NOUN
ejpam-6102	514	13	(	(	PUNCT
ejpam-6102	514	14	sn−2	sn−2	ADV
ejpam-6102	514	15	)	)	PUNCT
ejpam-6102	514	16	γ	γ	PROPN
ejpam-6102	514	17	(	(	PUNCT
ejpam-6102	514	18	n+3	n+3	PROPN
ejpam-6102	514	19	2	2	NUM
ejpam-6102	514	20	)	)	PUNCT
ejpam-6102	514	21	γ	γ	PROPN
ejpam-6102	514	22	(	(	PUNCT
ejpam-6102	514	23	n−3	n−3	PROPN
ejpam-6102	514	24	2	2	NUM
ejpam-6102	514	25	)	)	PUNCT
ejpam-6102	514	26	γ(n	γ(n	PROPN
ejpam-6102	514	27	)	)	PUNCT
ejpam-6102	514	28	.	.	PUNCT
ejpam-6102	515	1	(	(	PUNCT
ejpam-6102	515	2	55	55	NUM
ejpam-6102	515	3	)	)	PUNCT
ejpam-6102	515	4	we	we	PRON
ejpam-6102	515	5	notice	notice	VERB
ejpam-6102	515	6	that	that	SCONJ
ejpam-6102	515	7	,	,	PUNCT
ejpam-6102	515	8	in	in	ADP
ejpam-6102	515	9	this	this	DET
ejpam-6102	515	10	paper	paper	NOUN
ejpam-6102	515	11	we	we	PRON
ejpam-6102	515	12	use	use	VERB
ejpam-6102	515	13	ωa,µ	ωa,µ	X
ejpam-6102	515	14	=	=	PUNCT
ejpam-6102	515	15	β0ua,µ	β0ua,µ	X
ejpam-6102	515	16	where	where	SCONJ
ejpam-6102	515	17	β0	β0	NOUN
ejpam-6102	516	1	=	=	PUNCT
ejpam-6102	517	1	[	[	X
ejpam-6102	517	2	n(n	n(n	NOUN
ejpam-6102	517	3	−	−	PROPN
ejpam-6102	517	4	2)](n−2)/4	2)](n−2)/4	NUM
ejpam-6102	517	5	and	and	CCONJ
ejpam-6102	517	6	ua,µ	ua,µ	PUNCT
ejpam-6102	517	7	is	be	AUX
ejpam-6102	517	8	the	the	DET
ejpam-6102	517	9	function	function	NOUN
ejpam-6102	517	10	used	use	VERB
ejpam-6102	517	11	in	in	ADP
ejpam-6102	517	12	[	[	X
ejpam-6102	517	13	27	27	NUM
ejpam-6102	517	14	]	]	PUNCT
ejpam-6102	517	15	.	.	PUNCT
ejpam-6102	518	1	for	for	ADP
ejpam-6102	518	2	this	this	DET
ejpam-6102	518	3	reason	reason	NOUN
ejpam-6102	518	4	,	,	PUNCT
ejpam-6102	518	5	there	there	PRON
ejpam-6102	518	6	is	be	VERB
ejpam-6102	518	7	some	some	DET
ejpam-6102	518	8	changes	change	NOUN
ejpam-6102	518	9	in	in	ADP
ejpam-6102	518	10	the	the	DET
ejpam-6102	518	11	constants	constant	NOUN
ejpam-6102	518	12	found	find	VERB
ejpam-6102	518	13	in	in	ADP
ejpam-6102	518	14	lemma	lemma	PROPN
ejpam-6102	518	15	4	4	NUM
ejpam-6102	518	16	and	and	CCONJ
ejpam-6102	518	17	the	the	DET
ejpam-6102	518	18	following	follow	VERB
ejpam-6102	518	19	lemmas	lemma	VERB
ejpam-6102	518	20	with	with	ADP
ejpam-6102	518	21	the	the	DET
ejpam-6102	518	22	corresponding	corresponding	ADJ
ejpam-6102	518	23	results	result	NOUN
ejpam-6102	518	24	in	in	ADP
ejpam-6102	518	25	[	[	X
ejpam-6102	518	26	27	27	NUM
ejpam-6102	518	27	]	]	PUNCT
ejpam-6102	518	28	.	.	PUNCT
ejpam-6102	519	1	the	the	DET
ejpam-6102	519	2	second	second	ADJ
ejpam-6102	519	3	lemma	lemma	PROPN
ejpam-6102	519	4	deals	deal	NOUN
ejpam-6102	519	5	with	with	ADP
ejpam-6102	519	6	some	some	DET
ejpam-6102	519	7	integrals	integral	NOUN
ejpam-6102	519	8	involving	involve	VERB
ejpam-6102	519	9	the	the	DET
ejpam-6102	519	10	bubbles	bubble	NOUN
ejpam-6102	519	11	.	.	PUNCT
ejpam-6102	520	1	lemma	lemma	PROPN
ejpam-6102	520	2	5	5	X
ejpam-6102	520	3	.	.	PUNCT
ejpam-6102	521	1	let	let	VERB
ejpam-6102	521	2	n	n	CCONJ
ejpam-6102	521	3	⩾	⩾	NOUN
ejpam-6102	521	4	4	4	NUM
ejpam-6102	521	5	,	,	PUNCT
ejpam-6102	521	6	a	a	DET
ejpam-6102	521	7	∈	∈	PROPN
ejpam-6102	521	8	∂ω	∂ω	PROPN
ejpam-6102	521	9	and	and	CCONJ
ejpam-6102	521	10	µ	µ	PRON
ejpam-6102	521	11	be	be	AUX
ejpam-6102	521	12	a	a	DET
ejpam-6102	521	13	large	large	ADJ
ejpam-6102	521	14	real	real	NOUN
ejpam-6102	521	15	.	.	PUNCT
ejpam-6102	522	1	it	it	PRON
ejpam-6102	522	2	holds	hold	VERB
ejpam-6102	522	3	:	:	PUNCT
ejpam-6102	522	4	(	(	PUNCT
ejpam-6102	522	5	i	i	NOUN
ejpam-6102	522	6	)	)	PUNCT
ejpam-6102	522	7	∫	∫	PROPN
ejpam-6102	523	1	ω	ω	NUM
ejpam-6102	523	2	ω2	ω2	ADP
ejpam-6102	523	3	a,µ	a,µ	ADP
ejpam-6102	523	4	⩽	⩽	PROPN
ejpam-6102	523	5	c	c	PROPN
ejpam-6102	523	6	{	{	PUNCT
ejpam-6102	523	7	µ−2	µ−2	VERB
ejpam-6102	523	8	if	if	SCONJ
ejpam-6102	523	9	n	n	PRON
ejpam-6102	523	10	⩾	⩾	NOUN
ejpam-6102	523	11	5	5	NUM
ejpam-6102	523	12	,	,	PUNCT
ejpam-6102	523	13	µ−2	µ−2	NOUN
ejpam-6102	523	14	lnµ	lnµ	NOUN
ejpam-6102	523	15	if	if	SCONJ
ejpam-6102	523	16	n	n	NOUN
ejpam-6102	523	17	=	=	SYM
ejpam-6102	523	18	4	4	NUM
ejpam-6102	523	19	,	,	PUNCT
ejpam-6102	523	20	(	(	PUNCT
ejpam-6102	523	21	ii	ii	NOUN
ejpam-6102	523	22	)	)	PUNCT
ejpam-6102	523	23	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6102	523	24	ω	ω	PROPN
ejpam-6102	523	25	ωa,µµ	ωa,µµ	PROPN
ejpam-6102	523	26	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	523	27	∂µ	∂µ	PROPN
ejpam-6102	523	28	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	523	29	⩽	⩽	PROPN
ejpam-6102	523	30	c	c	PROPN
ejpam-6102	523	31	{	{	PUNCT
ejpam-6102	523	32	µ−2	µ−2	VERB
ejpam-6102	523	33	if	if	SCONJ
ejpam-6102	523	34	n	n	PRON
ejpam-6102	523	35	⩾	⩾	NOUN
ejpam-6102	523	36	5	5	NUM
ejpam-6102	523	37	,	,	PUNCT
ejpam-6102	523	38	µ−2	µ−2	NOUN
ejpam-6102	523	39	lnµ	lnµ	NOUN
ejpam-6102	523	40	if	if	SCONJ
ejpam-6102	523	41	n	n	NOUN
ejpam-6102	523	42	=	=	SYM
ejpam-6102	523	43	4	4	NUM
ejpam-6102	523	44	,	,	PUNCT
ejpam-6102	523	45	(	(	PUNCT
ejpam-6102	523	46	iii	iii	X
ejpam-6102	523	47	)	)	PUNCT
ejpam-6102	523	48	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-6102	523	49	ω	ω	NOUN
ejpam-6102	523	50	ωa,µ	ωa,µ	X
ejpam-6102	523	51	1	1	NUM
ejpam-6102	523	52	µ	µ	PRON
ejpam-6102	523	53	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	523	54	∂a	∂a	NOUN
ejpam-6102	523	55	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	523	56	⩽	⩽	PROPN
ejpam-6102	523	57	c	c	PROPN
ejpam-6102	523	58	µ3	µ3	NOUN
ejpam-6102	523	59	.	.	PUNCT
ejpam-6102	524	1	proof	proof	NOUN
ejpam-6102	524	2	.	.	PUNCT
ejpam-6102	525	1	notice	notice	VERB
ejpam-6102	525	2	that	that	SCONJ
ejpam-6102	525	3	,	,	PUNCT
ejpam-6102	525	4	since	since	SCONJ
ejpam-6102	525	5	ω	ω	PROPN
ejpam-6102	525	6	is	be	AUX
ejpam-6102	525	7	bounded	bound	VERB
ejpam-6102	525	8	,	,	PUNCT
ejpam-6102	525	9	there	there	PRON
ejpam-6102	525	10	exists	exist	VERB
ejpam-6102	525	11	r	r	NOUN
ejpam-6102	525	12	>	>	X
ejpam-6102	525	13	0	0	NUM
ejpam-6102	525	14	such	such	ADJ
ejpam-6102	525	15	that	that	SCONJ
ejpam-6102	525	16	ω	ω	PROPN
ejpam-6102	525	17	⊂	⊂	PROPN
ejpam-6102	525	18	b(a	b(a	NOUN
ejpam-6102	525	19	,	,	PUNCT
ejpam-6102	525	20	r	r	NOUN
ejpam-6102	525	21	)	)	PUNCT
ejpam-6102	525	22	.	.	PUNCT
ejpam-6102	526	1	claim	claim	NOUN
ejpam-6102	526	2	(	(	PUNCT
ejpam-6102	526	3	i	i	NOUN
ejpam-6102	526	4	)	)	PUNCT
ejpam-6102	526	5	follows	follow	VERB
ejpam-6102	526	6	by	by	ADP
ejpam-6102	526	7	standard	standard	ADJ
ejpam-6102	526	8	computations	computation	NOUN
ejpam-6102	526	9	.	.	PUNCT
ejpam-6102	527	1	concerning	concern	VERB
ejpam-6102	527	2	claim	claim	NOUN
ejpam-6102	527	3	(	(	PUNCT
ejpam-6102	527	4	ii	ii	NOUN
ejpam-6102	527	5	)	)	PUNCT
ejpam-6102	527	6	,	,	PUNCT
ejpam-6102	527	7	it	it	PRON
ejpam-6102	527	8	follows	follow	VERB
ejpam-6102	527	9	from	from	ADP
ejpam-6102	527	10	the	the	DET
ejpam-6102	527	11	first	first	ADJ
ejpam-6102	527	12	one	one	NUM
ejpam-6102	527	13	and	and	CCONJ
ejpam-6102	527	14	the	the	DET
ejpam-6102	527	15	fact	fact	NOUN
ejpam-6102	527	16	that	that	SCONJ
ejpam-6102	527	17	µ	µ	X
ejpam-6102	527	18	∣∣∣∂ωa,µ	∣∣∣∂ωa,µ	PROPN
ejpam-6102	527	19	∂µ	∂µ	PROPN
ejpam-6102	527	20	∣∣∣	∣∣∣	ADJ
ejpam-6102	527	21	⩽	⩽	PROPN
ejpam-6102	527	22	cωa,µ.	cωa,µ.	PROPN
ejpam-6102	527	23	finally	finally	ADV
ejpam-6102	527	24	,	,	PUNCT
ejpam-6102	527	25	for	for	ADP
ejpam-6102	527	26	claim	claim	NOUN
ejpam-6102	527	27	(	(	PUNCT
ejpam-6102	527	28	iii	iii	NOUN
ejpam-6102	527	29	)	)	PUNCT
ejpam-6102	527	30	,	,	PUNCT
ejpam-6102	527	31	observe	observe	VERB
ejpam-6102	527	32	that	that	SCONJ
ejpam-6102	527	33	1	1	NUM
ejpam-6102	527	34	µ	µ	NOUN
ejpam-6102	527	35	∣∣∣∣∂ωa,µ	∣∣∣∣∂ωa,µ	NOUN
ejpam-6102	527	36	∂a	∂a	PROPN
ejpam-6102	527	37	∣∣∣∣	∣∣∣∣	NOUN
ejpam-6102	527	38	⩽	⩽	NOUN
ejpam-6102	527	39	1	1	NUM
ejpam-6102	527	40	µ|x−	µ|x−	ADP
ejpam-6102	527	41	a|	a|	PROPN
ejpam-6102	527	42	ωa,µ.	ωa,µ.	NUM
ejpam-6102	527	43	hence	hence	ADV
ejpam-6102	527	44	,	,	PUNCT
ejpam-6102	527	45	the	the	DET
ejpam-6102	527	46	result	result	NOUN
ejpam-6102	527	47	follows	follow	VERB
ejpam-6102	527	48	by	by	ADP
ejpam-6102	527	49	standard	standard	ADJ
ejpam-6102	527	50	computations	computation	NOUN
ejpam-6102	527	51	.	.	PUNCT
ejpam-6102	528	1	the	the	DET
ejpam-6102	528	2	next	next	ADJ
ejpam-6102	528	3	lemma	lemma	PROPN
ejpam-6102	528	4	is	be	AUX
ejpam-6102	528	5	extracted	extract	VERB
ejpam-6102	528	6	from	from	ADP
ejpam-6102	528	7	[	[	X
ejpam-6102	528	8	27	27	NUM
ejpam-6102	528	9	]	]	PUNCT
ejpam-6102	528	10	(	(	PUNCT
ejpam-6102	528	11	see	see	VERB
ejpam-6102	528	12	the	the	DET
ejpam-6102	528	13	equations	equation	NOUN
ejpam-6102	528	14	(	(	PUNCT
ejpam-6102	528	15	d.17	d.17	NOUN
ejpam-6102	528	16	)	)	PUNCT
ejpam-6102	528	17	,	,	PUNCT
ejpam-6102	528	18	(	(	PUNCT
ejpam-6102	528	19	d.18	d.18	NOUN
ejpam-6102	528	20	)	)	PUNCT
ejpam-6102	528	21	and	and	CCONJ
ejpam-6102	528	22	(	(	PUNCT
ejpam-6102	528	23	d.19	d.19	PROPN
ejpam-6102	528	24	)	)	PUNCT
ejpam-6102	528	25	)	)	PUNCT
ejpam-6102	528	26	.	.	PUNCT
ejpam-6102	529	1	lemma	lemma	PROPN
ejpam-6102	529	2	6	6	NUM
ejpam-6102	529	3	.	.	PUNCT
ejpam-6102	530	1	[	[	X
ejpam-6102	530	2	27	27	NUM
ejpam-6102	530	3	]	]	PUNCT
ejpam-6102	530	4	let	let	VERB
ejpam-6102	530	5	n	n	NOUN
ejpam-6102	530	6	⩾	⩾	NOUN
ejpam-6102	530	7	4	4	NUM
ejpam-6102	530	8	,	,	PUNCT
ejpam-6102	530	9	a	a	DET
ejpam-6102	530	10	∈	∈	PROPN
ejpam-6102	530	11	∂ω	∂ω	PROPN
ejpam-6102	530	12	and	and	CCONJ
ejpam-6102	530	13	µ	µ	PRON
ejpam-6102	530	14	be	be	AUX
ejpam-6102	530	15	a	a	DET
ejpam-6102	530	16	large	large	ADJ
ejpam-6102	530	17	real	real	NOUN
ejpam-6102	530	18	.	.	PUNCT
ejpam-6102	531	1	there	there	PRON
ejpam-6102	531	2	hold	hold	VERB
ejpam-6102	531	3	:	:	PUNCT
ejpam-6102	531	4	(	(	PUNCT
ejpam-6102	531	5	i	i	NOUN
ejpam-6102	531	6	)	)	PUNCT
ejpam-6102	531	7	∫	∫	PROPN
ejpam-6102	532	1	ω	ω	PROPN
ejpam-6102	532	2	ω	ω	PROPN
ejpam-6102	532	3	2n	2n	NUM
ejpam-6102	533	1	n−2	n−2	PROPN
ejpam-6102	533	2	a,µ	a,µ	ADV
ejpam-6102	533	3	=	=	SYM
ejpam-6102	533	4	sn	sn	PROPN
ejpam-6102	533	5	−	−	PROPN
ejpam-6102	533	6	2n	2n	NUM
ejpam-6102	533	7	n−	n−	PROPN
ejpam-6102	533	8	2	2	NUM
ejpam-6102	533	9	c4	c4	NOUN
ejpam-6102	533	10	h(a	h(a	PROPN
ejpam-6102	533	11	)	)	PUNCT
ejpam-6102	533	12	µ	µ	PRON
ejpam-6102	533	13	+	+	PROPN
ejpam-6102	533	14	o	o	X
ejpam-6102	533	15	(	(	PUNCT
ejpam-6102	533	16	1	1	NUM
ejpam-6102	533	17	µ2	µ2	NOUN
ejpam-6102	533	18	)	)	PUNCT
ejpam-6102	533	19	,	,	PUNCT
ejpam-6102	533	20	(	(	PUNCT
ejpam-6102	533	21	ii	ii	NOUN
ejpam-6102	533	22	)	)	PUNCT
ejpam-6102	533	23	∫	∫	PROPN
ejpam-6102	534	1	ω	ω	PROPN
ejpam-6102	534	2	ω	ω	PROPN
ejpam-6102	535	1	n+2	n+2	PROPN
ejpam-6102	535	2	n−2	n−2	PROPN
ejpam-6102	535	3	a,µ	a,µ	ADP
ejpam-6102	535	4	µ	µ	DET
ejpam-6102	535	5	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	535	6	∂µ	∂µ	PROPN
ejpam-6102	535	7	=	=	PUNCT
ejpam-6102	535	8	c4	c4	PROPN
ejpam-6102	535	9	h(a	h(a	PROPN
ejpam-6102	535	10	)	)	PUNCT
ejpam-6102	535	11	µ	µ	PRON
ejpam-6102	536	1	+	+	PROPN
ejpam-6102	536	2	o	o	X
ejpam-6102	536	3	(	(	PUNCT
ejpam-6102	536	4	1	1	NUM
ejpam-6102	536	5	µ2	µ2	NOUN
ejpam-6102	536	6	)	)	PUNCT
ejpam-6102	536	7	,	,	PUNCT
ejpam-6102	536	8	(	(	PUNCT
ejpam-6102	536	9	iii	iii	X
ejpam-6102	536	10	)	)	PUNCT
ejpam-6102	536	11	∫	∫	PROPN
ejpam-6102	537	1	ω	ω	PROPN
ejpam-6102	537	2	ω	ω	PROPN
ejpam-6102	538	1	n+2	n+2	PROPN
ejpam-6102	538	2	n−2	n−2	PROPN
ejpam-6102	538	3	a,µ	a,µ	ADP
ejpam-6102	538	4	1	1	NUM
ejpam-6102	538	5	µ	µ	PRON
ejpam-6102	538	6	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	538	7	∂τj	∂τj	PROPN
ejpam-6102	538	8	=	=	SYM
ejpam-6102	538	9	o	o	X
ejpam-6102	538	10	(	(	PUNCT
ejpam-6102	538	11	1	1	NUM
ejpam-6102	538	12	µ2	µ2	NOUN
ejpam-6102	538	13	)	)	PUNCT
ejpam-6102	538	14	∀j	∀j	PROPN
ejpam-6102	538	15	∈	∈	PROPN
ejpam-6102	538	16	{	{	PUNCT
ejpam-6102	538	17	1	1	NUM
ejpam-6102	538	18	,	,	PUNCT
ejpam-6102	538	19	.	.	PUNCT
ejpam-6102	538	20	.	.	PUNCT
ejpam-6102	539	1	.	.	PUNCT
ejpam-6102	540	1	,	,	PUNCT
ejpam-6102	540	2	n−	n−	NOUN
ejpam-6102	540	3	1	1	NUM
ejpam-6102	540	4	}	}	PUNCT
ejpam-6102	540	5	,	,	PUNCT
ejpam-6102	540	6	where	where	SCONJ
ejpam-6102	540	7	c4	c4	NOUN
ejpam-6102	540	8	:	:	PUNCT
ejpam-6102	540	9	=	=	PUNCT
ejpam-6102	540	10	n−	n−	NOUN
ejpam-6102	540	11	2	2	NUM
ejpam-6102	540	12	2n	2n	NUM
ejpam-6102	540	13	[	[	X
ejpam-6102	540	14	n(n−	n(n−	NOUN
ejpam-6102	540	15	2	2	NUM
ejpam-6102	540	16	)	)	PUNCT
ejpam-6102	540	17	]	]	PUNCT
ejpam-6102	540	18	n/2	n/2	PRON
ejpam-6102	540	19	1	1	NUM
ejpam-6102	540	20	4	4	NUM
ejpam-6102	540	21	meas	mea	NOUN
ejpam-6102	540	22	(	(	PUNCT
ejpam-6102	540	23	sn−2	sn−2	ADV
ejpam-6102	540	24	)	)	PUNCT
ejpam-6102	540	25	γ	γ	PROPN
ejpam-6102	540	26	(	(	PUNCT
ejpam-6102	540	27	n+1	n+1	PROPN
ejpam-6102	540	28	2	2	X
ejpam-6102	540	29	)	)	PUNCT
ejpam-6102	540	30	γ	γ	PROPN
ejpam-6102	540	31	(	(	PUNCT
ejpam-6102	540	32	n−1	n−1	PROPN
ejpam-6102	540	33	2	2	NUM
ejpam-6102	540	34	)	)	PUNCT
ejpam-6102	540	35	γ(n	γ(n	PROPN
ejpam-6102	540	36	)	)	PUNCT
ejpam-6102	540	37	.	.	PUNCT
ejpam-6102	541	1	(	(	PUNCT
ejpam-6102	541	2	56	56	X
ejpam-6102	541	3	)	)	PUNCT
ejpam-6102	541	4	r.	r.	PROPN
ejpam-6102	541	5	almushahhin	almushahhin	PROPN
ejpam-6102	541	6	,	,	PUNCT
ejpam-6102	541	7	m.	m.	PROPN
ejpam-6102	541	8	ben	ben	PROPN
ejpam-6102	541	9	ayed	aye	VERB
ejpam-6102	541	10	/	/	SYM
ejpam-6102	541	11	eur	eur	PROPN
ejpam-6102	541	12	.	.	PUNCT
ejpam-6102	542	1	j.	j.	PROPN
ejpam-6102	542	2	pure	pure	PROPN
ejpam-6102	542	3	appl	appl	PROPN
ejpam-6102	542	4	.	.	PROPN
ejpam-6102	542	5	math	math	PROPN
ejpam-6102	542	6	,	,	PUNCT
ejpam-6102	542	7	18	18	NUM
ejpam-6102	542	8	(	(	PUNCT
ejpam-6102	542	9	2	2	NUM
ejpam-6102	542	10	)	)	PUNCT
ejpam-6102	542	11	(	(	PUNCT
ejpam-6102	542	12	2025	2025	NUM
ejpam-6102	542	13	)	)	PUNCT
ejpam-6102	542	14	,	,	PUNCT
ejpam-6102	542	15	6102	6102	NUM
ejpam-6102	542	16	20	20	NUM
ejpam-6102	542	17	of	of	ADP
ejpam-6102	542	18	31	31	NUM
ejpam-6102	542	19	we	we	PRON
ejpam-6102	542	20	also	also	ADV
ejpam-6102	542	21	have	have	VERB
ejpam-6102	542	22	the	the	DET
ejpam-6102	542	23	following	follow	VERB
ejpam-6102	542	24	estimates	estimate	NOUN
ejpam-6102	542	25	:	:	PUNCT
ejpam-6102	542	26	lemma	lemma	PROPN
ejpam-6102	542	27	7	7	X
ejpam-6102	542	28	.	.	PUNCT
ejpam-6102	542	29	let	let	VERB
ejpam-6102	542	30	a	a	DET
ejpam-6102	542	31	∈	∈	PROPN
ejpam-6102	542	32	∂ω	∂ω	PROPN
ejpam-6102	542	33	and	and	CCONJ
ejpam-6102	542	34	µ	µ	PRON
ejpam-6102	542	35	be	be	AUX
ejpam-6102	542	36	a	a	DET
ejpam-6102	542	37	large	large	ADJ
ejpam-6102	542	38	real	real	NOUN
ejpam-6102	542	39	.	.	PUNCT
ejpam-6102	543	1	it	it	PRON
ejpam-6102	543	2	holds	hold	VERB
ejpam-6102	543	3	:	:	PUNCT
ejpam-6102	543	4	(	(	PUNCT
ejpam-6102	543	5	i	i	NOUN
ejpam-6102	543	6	)	)	PUNCT
ejpam-6102	543	7	µ	µ	PRON
ejpam-6102	543	8	∣∣∣∣∂2ωa,µ	∣∣∣∣∂2ωa,µ	PROPN
ejpam-6102	543	9	∂ν∂µ	∂ν∂µ	PROPN
ejpam-6102	543	10	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	543	11	⩽	⩽	PROPN
ejpam-6102	543	12	c	c	PROPN
ejpam-6102	543	13	∣∣∣∣∂ωa,µ	∣∣∣∣∂ωa,µ	PROPN
ejpam-6102	543	14	∂ν	∂ν	PROPN
ejpam-6102	543	15	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	543	16	,	,	PUNCT
ejpam-6102	543	17	(	(	PUNCT
ejpam-6102	543	18	ii	ii	NOUN
ejpam-6102	543	19	)	)	PUNCT
ejpam-6102	543	20	(	(	PUNCT
ejpam-6102	543	21	∫	∫	PROPN
ejpam-6102	544	1	∂ω	∂ω	ADJ
ejpam-6102	544	2	∣∣∣∂ωa,µ	∣∣∣∂ωa,µ	PROPN
ejpam-6102	544	3	∂ν	∂ν	PROPN
ejpam-6102	544	4	∣∣∣(2n−2)/n)n/(2n−2	∣∣∣(2n−2)/n)n/(2n−2	PROPN
ejpam-6102	544	5	)	)	PUNCT
ejpam-6102	544	6	≤	≤	NUM
ejpam-6102	544	7	c	c	NOUN
ejpam-6102	544	8	µ	µ	X
ejpam-6102	544	9	,	,	PUNCT
ejpam-6102	544	10	(	(	PUNCT
ejpam-6102	544	11	iii	iii	NOUN
ejpam-6102	544	12	)	)	PUNCT
ejpam-6102	544	13	(	(	PUNCT
ejpam-6102	544	14	∫	∫	PROPN
ejpam-6102	544	15	∂ω	∂ω	PROPN
ejpam-6102	544	16	∣∣∣∂2ωa,µ	∣∣∣∂2ωa,µ	PROPN
ejpam-6102	544	17	∂ν∂a	∂ν∂a	PROPN
ejpam-6102	544	18	∣∣∣(2n−2)/n)n/(2n−2	∣∣∣(2n−2)/n)n/(2n−2	PROPN
ejpam-6102	544	19	)	)	PUNCT
ejpam-6102	544	20	⩽	⩽	ADJ
ejpam-6102	544	21	c.	c.	PROPN
ejpam-6102	544	22	proof	proof	NOUN
ejpam-6102	544	23	.	.	PUNCT
ejpam-6102	545	1	claims	claim	NOUN
ejpam-6102	545	2	(	(	PUNCT
ejpam-6102	545	3	ii	ii	NOUN
ejpam-6102	545	4	)	)	PUNCT
ejpam-6102	545	5	and	and	CCONJ
ejpam-6102	545	6	(	(	PUNCT
ejpam-6102	545	7	iii	iii	X
ejpam-6102	545	8	)	)	PUNCT
ejpam-6102	545	9	are	be	AUX
ejpam-6102	545	10	extracted	extract	VERB
ejpam-6102	545	11	from	from	ADP
ejpam-6102	545	12	[	[	X
ejpam-6102	545	13	27	27	NUM
ejpam-6102	545	14	]	]	PUNCT
ejpam-6102	545	15	(	(	PUNCT
ejpam-6102	545	16	see	see	VERB
ejpam-6102	545	17	the	the	DET
ejpam-6102	545	18	equations	equation	NOUN
ejpam-6102	545	19	(	(	PUNCT
ejpam-6102	545	20	d.49	d.49	X
ejpam-6102	545	21	)	)	PUNCT
ejpam-6102	545	22	and	and	CCONJ
ejpam-6102	545	23	(	(	PUNCT
ejpam-6102	545	24	d.50	d.50	NOUN
ejpam-6102	545	25	)	)	PUNCT
ejpam-6102	545	26	)	)	PUNCT
ejpam-6102	545	27	.	.	PUNCT
ejpam-6102	546	1	concerning	concern	VERB
ejpam-6102	546	2	claim	claim	NOUN
ejpam-6102	546	3	(	(	PUNCT
ejpam-6102	546	4	i	i	NOUN
ejpam-6102	546	5	)	)	PUNCT
ejpam-6102	546	6	,	,	PUNCT
ejpam-6102	546	7	it	it	PRON
ejpam-6102	546	8	follows	follow	VERB
ejpam-6102	546	9	easily	easily	ADV
ejpam-6102	546	10	.	.	PUNCT
ejpam-6102	547	1	we	we	PRON
ejpam-6102	547	2	end	end	VERB
ejpam-6102	547	3	this	this	DET
ejpam-6102	547	4	subsection	subsection	NOUN
ejpam-6102	547	5	by	by	ADP
ejpam-6102	547	6	the	the	DET
ejpam-6102	547	7	following	follow	VERB
ejpam-6102	547	8	two	two	NUM
ejpam-6102	547	9	lemmas	lemma	NOUN
ejpam-6102	547	10	:	:	PUNCT
ejpam-6102	547	11	lemma	lemma	PROPN
ejpam-6102	547	12	8	8	NUM
ejpam-6102	547	13	.	.	PUNCT
ejpam-6102	548	1	let	let	VERB
ejpam-6102	548	2	a	a	DET
ejpam-6102	548	3	∈	∈	PROPN
ejpam-6102	548	4	∂ω	∂ω	PROPN
ejpam-6102	548	5	and	and	CCONJ
ejpam-6102	548	6	µ	µ	PRON
ejpam-6102	548	7	be	be	AUX
ejpam-6102	548	8	a	a	DET
ejpam-6102	548	9	large	large	ADJ
ejpam-6102	548	10	real	real	NOUN
ejpam-6102	548	11	.	.	PUNCT
ejpam-6102	549	1	it	it	PRON
ejpam-6102	549	2	holds	hold	VERB
ejpam-6102	549	3	:	:	PUNCT
ejpam-6102	549	4	(	(	PUNCT
ejpam-6102	549	5	i	i	NOUN
ejpam-6102	549	6	)	)	PUNCT
ejpam-6102	549	7	∫	∫	PROPN
ejpam-6102	550	1	ω	ω	PROPN
ejpam-6102	550	2	(	(	PUNCT
ejpam-6102	550	3	x−	x−	PROPN
ejpam-6102	550	4	a	a	PROPN
ejpam-6102	550	5	)	)	PUNCT
ejpam-6102	550	6	·	·	PUNCT
ejpam-6102	550	7	τjω	τjω	VERB
ejpam-6102	550	8	n+2	n+2	PRON
ejpam-6102	550	9	n−2	n−2	PROPN
ejpam-6102	550	10	a,µ	a,µ	ADP
ejpam-6102	550	11	µ	µ	PRON
ejpam-6102	550	12	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	550	13	∂µ	∂µ	PROPN
ejpam-6102	550	14	=	=	SYM
ejpam-6102	550	15	o	o	PROPN
ejpam-6102	550	16	(	(	PUNCT
ejpam-6102	550	17	1	1	NUM
ejpam-6102	550	18	µ2	µ2	NOUN
ejpam-6102	550	19	)	)	PUNCT
ejpam-6102	550	20	∀j	∀j	PROPN
ejpam-6102	550	21	∈	∈	PROPN
ejpam-6102	550	22	{	{	PUNCT
ejpam-6102	550	23	1	1	NUM
ejpam-6102	550	24	,	,	PUNCT
ejpam-6102	550	25	.	.	PUNCT
ejpam-6102	550	26	.	.	PUNCT
ejpam-6102	551	1	.	.	PUNCT
ejpam-6102	552	1	,	,	PUNCT
ejpam-6102	552	2	n−	n−	NOUN
ejpam-6102	552	3	1	1	NUM
ejpam-6102	552	4	}	}	PUNCT
ejpam-6102	552	5	,	,	PUNCT
ejpam-6102	552	6	(	(	PUNCT
ejpam-6102	552	7	ii	ii	NOUN
ejpam-6102	552	8	)	)	PUNCT
ejpam-6102	552	9	∫	∫	PROPN
ejpam-6102	553	1	ω	ω	PROPN
ejpam-6102	553	2	(	(	PUNCT
ejpam-6102	553	3	x−	x−	PROPN
ejpam-6102	553	4	a	a	PROPN
ejpam-6102	553	5	)	)	PUNCT
ejpam-6102	553	6	·	·	PUNCT
ejpam-6102	553	7	νaω	νaω	VERB
ejpam-6102	553	8	n+2	n+2	NUM
ejpam-6102	553	9	n−2	n−2	PROPN
ejpam-6102	553	10	a,µ	a,µ	ADP
ejpam-6102	553	11	µ	µ	PRON
ejpam-6102	553	12	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	553	13	∂µ	∂µ	PROPN
ejpam-6102	553	14	=	=	SYM
ejpam-6102	553	15	c5	c5	PROPN
ejpam-6102	553	16	µ	µ	PROPN
ejpam-6102	553	17	+	+	PROPN
ejpam-6102	553	18	o	o	X
ejpam-6102	553	19	(	(	PUNCT
ejpam-6102	553	20	1	1	NUM
ejpam-6102	553	21	µ2	µ2	NOUN
ejpam-6102	553	22	)	)	PUNCT
ejpam-6102	553	23	,	,	PUNCT
ejpam-6102	553	24	(	(	PUNCT
ejpam-6102	553	25	iii	iii	X
ejpam-6102	553	26	)	)	PUNCT
ejpam-6102	553	27	∫	∫	PROPN
ejpam-6102	554	1	ω	ω	PROPN
ejpam-6102	554	2	ω	ω	PROPN
ejpam-6102	555	1	n+2	n+2	PROPN
ejpam-6102	555	2	n−2	n−2	PROPN
ejpam-6102	555	3	a,µ	a,µ	ADP
ejpam-6102	555	4	µ	µ	DET
ejpam-6102	555	5	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	555	6	∂µ	∂µ	PROPN
ejpam-6102	555	7	ln	ln	NOUN
ejpam-6102	555	8	(	(	PUNCT
ejpam-6102	555	9	1	1	NUM
ejpam-6102	555	10	+	+	CCONJ
ejpam-6102	555	11	µ2	µ2	PROPN
ejpam-6102	555	12	|x−	|x−	PROPN
ejpam-6102	555	13	a|2	a|2	PROPN
ejpam-6102	555	14	)	)	PUNCT
ejpam-6102	556	1	=	=	PUNCT
ejpam-6102	556	2	−c6	−c6	ADP
ejpam-6102	556	3	2	2	NUM
ejpam-6102	557	1	+	+	NOUN
ejpam-6102	557	2	o	o	NOUN
ejpam-6102	557	3	(	(	PUNCT
ejpam-6102	557	4	1	1	NUM
ejpam-6102	557	5	µ	µ	NOUN
ejpam-6102	557	6	)	)	PUNCT
ejpam-6102	557	7	,	,	PUNCT
ejpam-6102	557	8	(	(	PUNCT
ejpam-6102	557	9	iv	iv	X
ejpam-6102	557	10	)	)	PUNCT
ejpam-6102	557	11	∫	∫	PROPN
ejpam-6102	557	12	ω	ω	PROPN
ejpam-6102	557	13	(	(	PUNCT
ejpam-6102	557	14	x−	x−	PROPN
ejpam-6102	557	15	a	a	PROPN
ejpam-6102	557	16	)	)	PUNCT
ejpam-6102	557	17	·	·	PUNCT
ejpam-6102	557	18	τkω	τkω	VERB
ejpam-6102	557	19	n+2	n+2	NUM
ejpam-6102	558	1	n−2	n−2	PROPN
ejpam-6102	558	2	a,µ	a,µ	ADP
ejpam-6102	558	3	1	1	NUM
ejpam-6102	558	4	µ	µ	PRON
ejpam-6102	558	5	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	558	6	∂τj	∂τj	PROPN
ejpam-6102	558	7	=	=	PUNCT
ejpam-6102	558	8	{	{	PUNCT
ejpam-6102	558	9	o	o	X
ejpam-6102	558	10	(	(	PUNCT
ejpam-6102	558	11	µ−2	µ−2	PROPN
ejpam-6102	558	12	)	)	PUNCT
ejpam-6102	558	13	if	if	SCONJ
ejpam-6102	558	14	k	k	PROPN
ejpam-6102	558	15	̸=	̸=	PROPN
ejpam-6102	558	16	j	j	PROPN
ejpam-6102	558	17	,	,	PUNCT
ejpam-6102	558	18	c7	c7	PROPN
ejpam-6102	558	19	µ	µ	PROPN
ejpam-6102	558	20	+	+	PROPN
ejpam-6102	558	21	o	o	X
ejpam-6102	558	22	(	(	PUNCT
ejpam-6102	558	23	1	1	NUM
ejpam-6102	558	24	µ2	µ2	NOUN
ejpam-6102	558	25	)	)	PUNCT
ejpam-6102	558	26	if	if	SCONJ
ejpam-6102	558	27	k	k	PROPN
ejpam-6102	558	28	=	=	SYM
ejpam-6102	558	29	j	j	PROPN
ejpam-6102	558	30	,	,	PUNCT
ejpam-6102	558	31	for	for	ADP
ejpam-6102	558	32	each	each	DET
ejpam-6102	558	33	j	j	PROPN
ejpam-6102	558	34	∈	∈	PROPN
ejpam-6102	558	35	{	{	PUNCT
ejpam-6102	558	36	1	1	NUM
ejpam-6102	558	37	,	,	PUNCT
ejpam-6102	558	38	.	.	PUNCT
ejpam-6102	558	39	.	.	PUNCT
ejpam-6102	558	40	.	.	PUNCT
ejpam-6102	559	1	,	,	PUNCT
ejpam-6102	559	2	n−	n−	NOUN
ejpam-6102	559	3	1	1	NUM
ejpam-6102	559	4	}	}	PUNCT
ejpam-6102	559	5	and	and	CCONJ
ejpam-6102	559	6	k	k	PROPN
ejpam-6102	559	7	∈	∈	PROPN
ejpam-6102	559	8	{	{	PUNCT
ejpam-6102	559	9	1	1	NUM
ejpam-6102	559	10	,	,	PUNCT
ejpam-6102	559	11	.	.	PUNCT
ejpam-6102	559	12	.	.	PUNCT
ejpam-6102	559	13	.	.	PUNCT
ejpam-6102	559	14	,	,	PUNCT
ejpam-6102	559	15	n	n	CCONJ
ejpam-6102	559	16	}	}	PUNCT
ejpam-6102	559	17	,	,	PUNCT
ejpam-6102	559	18	(	(	PUNCT
ejpam-6102	559	19	v	v	NOUN
ejpam-6102	559	20	)	)	PUNCT
ejpam-6102	559	21	∫	∫	PROPN
ejpam-6102	560	1	ω	ω	PROPN
ejpam-6102	560	2	ω	ω	PROPN
ejpam-6102	561	1	n+2	n+2	PROPN
ejpam-6102	561	2	n−2	n−2	PROPN
ejpam-6102	561	3	a,µ	a,µ	ADP
ejpam-6102	561	4	1	1	NUM
ejpam-6102	561	5	µ	µ	PRON
ejpam-6102	561	6	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	561	7	∂τj	∂τj	PROPN
ejpam-6102	561	8	ln	ln	NOUN
ejpam-6102	561	9	(	(	PUNCT
ejpam-6102	561	10	1	1	NUM
ejpam-6102	561	11	+	+	CCONJ
ejpam-6102	561	12	µ2	µ2	PROPN
ejpam-6102	561	13	|x−	|x−	PROPN
ejpam-6102	561	14	a|2	a|2	PROPN
ejpam-6102	561	15	)	)	PUNCT
ejpam-6102	562	1	=	=	SYM
ejpam-6102	562	2	o	o	NOUN
ejpam-6102	562	3	(	(	PUNCT
ejpam-6102	562	4	1	1	NUM
ejpam-6102	562	5	µ2	µ2	NOUN
ejpam-6102	562	6	)	)	PUNCT
ejpam-6102	562	7	∀j	∀j	PROPN
ejpam-6102	562	8	∈	∈	PROPN
ejpam-6102	562	9	{	{	PUNCT
ejpam-6102	562	10	1	1	NUM
ejpam-6102	562	11	,	,	PUNCT
ejpam-6102	562	12	.	.	PUNCT
ejpam-6102	562	13	.	.	PUNCT
ejpam-6102	562	14	.	.	PUNCT
ejpam-6102	563	1	,	,	PUNCT
ejpam-6102	563	2	n−	n−	NOUN
ejpam-6102	563	3	1	1	NUM
ejpam-6102	563	4	}	}	PUNCT
ejpam-6102	563	5	,	,	PUNCT
ejpam-6102	563	6	where	where	SCONJ
ejpam-6102	563	7	c5	c5	PROPN
ejpam-6102	563	8	:	:	PUNCT
ejpam-6102	563	9	=	=	PUNCT
ejpam-6102	564	1	[	[	X
ejpam-6102	564	2	n(n−	n(n−	NOUN
ejpam-6102	564	3	2	2	NUM
ejpam-6102	564	4	]	]	PUNCT
ejpam-6102	564	5	n/2	n/2	NUM
ejpam-6102	564	6	n−	n−	NOUN
ejpam-6102	564	7	2	2	NUM
ejpam-6102	564	8	2	2	NUM
ejpam-6102	564	9	∫	∫	NOUN
ejpam-6102	564	10	rn	rn	PROPN
ejpam-6102	564	11	+	+	PROPN
ejpam-6102	564	12	xn	xn	PROPN
ejpam-6102	564	13	|x|2	|x|2	PROPN
ejpam-6102	564	14	−	−	PROPN
ejpam-6102	564	15	1	1	NUM
ejpam-6102	564	16	(	(	PUNCT
ejpam-6102	564	17	1	1	NUM
ejpam-6102	564	18	+	+	NUM
ejpam-6102	564	19	|x|2)n+1	|x|2)n+1	NUM
ejpam-6102	564	20	dx	dx	PROPN
ejpam-6102	564	21	>	>	X
ejpam-6102	564	22	0	0	PROPN
ejpam-6102	564	23	,	,	PUNCT
ejpam-6102	564	24	(	(	PUNCT
ejpam-6102	564	25	57	57	NUM
ejpam-6102	564	26	)	)	PUNCT
ejpam-6102	564	27	c6	c6	NOUN
ejpam-6102	564	28	:	:	PUNCT
ejpam-6102	565	1	=	=	SYM
ejpam-6102	565	2	n−	n−	NOUN
ejpam-6102	565	3	2	2	NUM
ejpam-6102	565	4	2	2	NUM
ejpam-6102	565	5	[	[	X
ejpam-6102	565	6	n(n−	n(n−	NOUN
ejpam-6102	565	7	2)]n/2	2)]n/2	ADJ
ejpam-6102	565	8	∫	∫	PROPN
ejpam-6102	565	9	rn	rn	PROPN
ejpam-6102	565	10	|x|2	|x|2	PROPN
ejpam-6102	565	11	−	−	PROPN
ejpam-6102	565	12	1	1	NUM
ejpam-6102	565	13	(	(	PUNCT
ejpam-6102	565	14	1	1	NUM
ejpam-6102	565	15	+	+	CCONJ
ejpam-6102	565	16	|x|2)n+1	|x|2)n+1	SYM
ejpam-6102	565	17	ln	ln	X
ejpam-6102	565	18	(	(	PUNCT
ejpam-6102	565	19	1	1	NUM
ejpam-6102	565	20	+	+	CCONJ
ejpam-6102	565	21	|x|2	|x|2	PROPN
ejpam-6102	565	22	)	)	PUNCT
ejpam-6102	565	23	dx	dx	PROPN
ejpam-6102	565	24	>	>	X
ejpam-6102	565	25	0	0	NUM
ejpam-6102	565	26	,	,	PUNCT
ejpam-6102	565	27	(	(	PUNCT
ejpam-6102	565	28	58	58	X
ejpam-6102	565	29	)	)	PUNCT
ejpam-6102	565	30	c7	c7	NOUN
ejpam-6102	565	31	:	:	PUNCT
ejpam-6102	566	1	=	=	PUNCT
ejpam-6102	566	2	n−	n−	NOUN
ejpam-6102	566	3	2	2	NUM
ejpam-6102	566	4	2n	2n	NUM
ejpam-6102	566	5	[	[	X
ejpam-6102	566	6	n(n−	n(n−	PROPN
ejpam-6102	566	7	2)]n/2	2)]n/2	ADJ
ejpam-6102	566	8	∫	∫	PROPN
ejpam-6102	566	9	rn	rn	PROPN
ejpam-6102	566	10	|x|2	|x|2	PROPN
ejpam-6102	566	11	(	(	PUNCT
ejpam-6102	566	12	1	1	NUM
ejpam-6102	566	13	+	+	NUM
ejpam-6102	566	14	|x|2)n+1	|x|2)n+1	NUM
ejpam-6102	566	15	dx	dx	PROPN
ejpam-6102	566	16	.	.	PUNCT
ejpam-6102	567	1	(	(	PUNCT
ejpam-6102	567	2	59	59	NUM
ejpam-6102	567	3	)	)	PUNCT
ejpam-6102	567	4	proof	proof	NOUN
ejpam-6102	567	5	.	.	PUNCT
ejpam-6102	568	1	without	without	ADP
ejpam-6102	568	2	loss	loss	NOUN
ejpam-6102	568	3	of	of	ADP
ejpam-6102	568	4	generality	generality	NOUN
ejpam-6102	568	5	,	,	PUNCT
ejpam-6102	568	6	we	we	PRON
ejpam-6102	568	7	can	can	AUX
ejpam-6102	568	8	assume	assume	VERB
ejpam-6102	568	9	that	that	SCONJ
ejpam-6102	568	10	a	a	DET
ejpam-6102	568	11	=	=	SYM
ejpam-6102	568	12	0	0	NUM
ejpam-6102	568	13	and	and	CCONJ
ejpam-6102	568	14	νa	νa	VERB
ejpam-6102	568	15	=	=	PROPN
ejpam-6102	568	16	−en	−en	PROPN
ejpam-6102	568	17	.	.	PUNCT
ejpam-6102	569	1	(	(	PUNCT
ejpam-6102	569	2	60	60	NUM
ejpam-6102	569	3	)	)	PUNCT
ejpam-6102	569	4	since	since	SCONJ
ejpam-6102	569	5	we	we	PRON
ejpam-6102	569	6	assumed	assume	VERB
ejpam-6102	569	7	that	that	SCONJ
ejpam-6102	569	8	ω	ω	PROPN
ejpam-6102	569	9	is	be	AUX
ejpam-6102	569	10	smooth	smooth	ADJ
ejpam-6102	569	11	,	,	PUNCT
ejpam-6102	569	12	there	there	ADV
ejpam-6102	569	13	exit	exit	NOUN
ejpam-6102	569	14	ρ	ρ	PROPN
ejpam-6102	569	15	>	>	X
ejpam-6102	569	16	0	0	PUNCT
ejpam-6102	570	1	(	(	PUNCT
ejpam-6102	570	2	we	we	PRON
ejpam-6102	570	3	take	take	VERB
ejpam-6102	570	4	it	it	PRON
ejpam-6102	570	5	small	small	ADJ
ejpam-6102	570	6	)	)	PUNCT
ejpam-6102	570	7	and	and	CCONJ
ejpam-6102	570	8	a	a	DET
ejpam-6102	570	9	function	function	NOUN
ejpam-6102	570	10	φ	φ	NOUN
ejpam-6102	570	11	:	:	PUNCT
ejpam-6102	570	12	bn−1(0	bn−1(0	PROPN
ejpam-6102	570	13	,	,	PUNCT
ejpam-6102	570	14	ρ	ρ	PROPN
ejpam-6102	570	15	)	)	PUNCT
ejpam-6102	570	16	⊂	⊂	PROPN
ejpam-6102	570	17	rn−1	rn−1	VERB
ejpam-6102	570	18	−→	−→	ADJ
ejpam-6102	570	19	r	r	NOUN
ejpam-6102	570	20	such	such	ADJ
ejpam-6102	570	21	that	that	DET
ejpam-6102	570	22	φ(0	φ(0	ADJ
ejpam-6102	570	23	)	)	PUNCT
ejpam-6102	570	24	=	=	SYM
ejpam-6102	570	25	0	0	NUM
ejpam-6102	570	26	,	,	PUNCT
ejpam-6102	570	27	φ′(0	φ′(0	X
ejpam-6102	570	28	)	)	PUNCT
ejpam-6102	570	29	=	=	SYM
ejpam-6102	570	30	0	0	NUM
ejpam-6102	570	31	and	and	CCONJ
ejpam-6102	570	32	ω	ω	NUM
ejpam-6102	570	33	∩bn(0	∩bn(0	PROPN
ejpam-6102	570	34	,	,	PUNCT
ejpam-6102	570	35	ρ	ρ	NOUN
ejpam-6102	570	36	)	)	PUNCT
ejpam-6102	570	37	=	=	PRON
ejpam-6102	570	38	{	{	PUNCT
ejpam-6102	570	39	x	x	SYM
ejpam-6102	570	40	=	=	X
ejpam-6102	570	41	(	(	PUNCT
ejpam-6102	570	42	x′	x′	PROPN
ejpam-6102	570	43	,	,	PUNCT
ejpam-6102	570	44	xn	xn	X
ejpam-6102	570	45	)	)	PUNCT
ejpam-6102	570	46	∈	∈	PROPN
ejpam-6102	570	47	bn−1(0	bn−1(0	PROPN
ejpam-6102	570	48	,	,	PUNCT
ejpam-6102	570	49	ρ)×	ρ)×	X
ejpam-6102	570	50	r	r	NOUN
ejpam-6102	570	51	:	:	PUNCT
ejpam-6102	570	52	xn	xn	PROPN
ejpam-6102	570	53	>	>	X
ejpam-6102	570	54	φ	φ	PROPN
ejpam-6102	570	55	(	(	PUNCT
ejpam-6102	570	56	x′	x′	NUM
ejpam-6102	570	57	)	)	PUNCT
ejpam-6102	570	58	}	}	PUNCT
ejpam-6102	570	59	.	.	PUNCT
ejpam-6102	571	1	r.	r.	PROPN
ejpam-6102	571	2	almushahhin	almushahhin	PROPN
ejpam-6102	571	3	,	,	PUNCT
ejpam-6102	571	4	m.	m.	PROPN
ejpam-6102	571	5	ben	ben	PROPN
ejpam-6102	571	6	ayed	aye	VERB
ejpam-6102	571	7	/	/	SYM
ejpam-6102	571	8	eur	eur	PROPN
ejpam-6102	571	9	.	.	PUNCT
ejpam-6102	572	1	j.	j.	PROPN
ejpam-6102	572	2	pure	pure	PROPN
ejpam-6102	572	3	appl	appl	PROPN
ejpam-6102	572	4	.	.	PROPN
ejpam-6102	572	5	math	math	PROPN
ejpam-6102	572	6	,	,	PUNCT
ejpam-6102	572	7	18	18	NUM
ejpam-6102	572	8	(	(	PUNCT
ejpam-6102	572	9	2	2	NUM
ejpam-6102	572	10	)	)	PUNCT
ejpam-6102	572	11	(	(	PUNCT
ejpam-6102	572	12	2025	2025	NUM
ejpam-6102	572	13	)	)	PUNCT
ejpam-6102	572	14	,	,	PUNCT
ejpam-6102	572	15	6102	6102	NUM
ejpam-6102	572	16	21	21	NUM
ejpam-6102	572	17	of	of	ADP
ejpam-6102	572	18	31	31	NUM
ejpam-6102	572	19	since	since	SCONJ
ejpam-6102	572	20	φ′(0	φ′(0	NOUN
ejpam-6102	572	21	)	)	PUNCT
ejpam-6102	572	22	=	=	SYM
ejpam-6102	572	23	0	0	NUM
ejpam-6102	572	24	,	,	PUNCT
ejpam-6102	572	25	it	it	PRON
ejpam-6102	572	26	is	be	AUX
ejpam-6102	572	27	easy	easy	ADJ
ejpam-6102	572	28	to	to	PART
ejpam-6102	572	29	see	see	VERB
ejpam-6102	572	30	that	that	SCONJ
ejpam-6102	572	31	φ	φ	PROPN
ejpam-6102	572	32	(	(	PUNCT
ejpam-6102	572	33	x′	x′	NUM
ejpam-6102	572	34	)	)	PUNCT
ejpam-6102	573	1	=	=	SYM
ejpam-6102	573	2	o	o	NOUN
ejpam-6102	573	3	(	(	PUNCT
ejpam-6102	573	4	|x′|2	|x′|2	NOUN
ejpam-6102	573	5	)	)	PUNCT
ejpam-6102	573	6	∀x′	∀x′	PUNCT
ejpam-6102	573	7	∈	∈	PROPN
ejpam-6102	573	8	bn−1(0	bn−1(0	PROPN
ejpam-6102	573	9	,	,	PUNCT
ejpam-6102	573	10	ρ	ρ	PROPN
ejpam-6102	573	11	)	)	PUNCT
ejpam-6102	573	12	.	.	PUNCT
ejpam-6102	574	1	(	(	PUNCT
ejpam-6102	574	2	61	61	NUM
ejpam-6102	574	3	)	)	PUNCT
ejpam-6102	574	4	observe	observe	VERB
ejpam-6102	574	5	that	that	SCONJ
ejpam-6102	574	6	∫	∫	PROPN
ejpam-6102	574	7	ω\b(0,ρ	ω\b(0,ρ	NUM
ejpam-6102	574	8	)	)	PUNCT
ejpam-6102	574	9	|x|ω	|x|ω	PROPN
ejpam-6102	574	10	2n	2n	NUM
ejpam-6102	574	11	n−2	n−2	PROPN
ejpam-6102	574	12	0,µ	0,µ	PROPN
ejpam-6102	574	13	⩽	⩽	PROPN
ejpam-6102	574	14	∫	∫	PROPN
ejpam-6102	574	15	ω\b(0,ρ	ω\b(0,ρ	NUM
ejpam-6102	574	16	)	)	PUNCT
ejpam-6102	575	1	|x|	|x|	PROPN
ejpam-6102	575	2	µn|x|2n	µn|x|2n	NOUN
ejpam-6102	575	3	dx	dx	PROPN
ejpam-6102	575	4	⩽	⩽	PROPN
ejpam-6102	575	5	c	c	PROPN
ejpam-6102	575	6	µn	µn	PROPN
ejpam-6102	575	7	.	.	PUNCT
ejpam-6102	576	1	(	(	PUNCT
ejpam-6102	576	2	62	62	NUM
ejpam-6102	576	3	)	)	PUNCT
ejpam-6102	576	4	to	to	PART
ejpam-6102	576	5	estimate	estimate	VERB
ejpam-6102	576	6	the	the	DET
ejpam-6102	576	7	integral	integral	ADJ
ejpam-6102	576	8	over	over	ADP
ejpam-6102	576	9	ω	ω	PROPN
ejpam-6102	576	10	∩b(0	∩b(0	PROPN
ejpam-6102	576	11	,	,	PUNCT
ejpam-6102	576	12	ρ	ρ	PROPN
ejpam-6102	576	13	)	)	PUNCT
ejpam-6102	576	14	,	,	PUNCT
ejpam-6102	576	15	we	we	PRON
ejpam-6102	576	16	introduce	introduce	VERB
ejpam-6102	576	17	the	the	DET
ejpam-6102	576	18	following	follow	VERB
ejpam-6102	576	19	sets	set	NOUN
ejpam-6102	576	20	b+(0	b+(0	PROPN
ejpam-6102	576	21	,	,	PUNCT
ejpam-6102	576	22	ρ	ρ	PROPN
ejpam-6102	576	23	)	)	PUNCT
ejpam-6102	576	24	:	:	PUNCT
ejpam-6102	576	25	=	=	SYM
ejpam-6102	576	26	{	{	PUNCT
ejpam-6102	576	27	x	x	SYM
ejpam-6102	576	28	=	=	X
ejpam-6102	576	29	(	(	PUNCT
ejpam-6102	576	30	x′	x′	PROPN
ejpam-6102	576	31	,	,	PUNCT
ejpam-6102	576	32	xn	xn	X
ejpam-6102	576	33	)	)	PUNCT
ejpam-6102	576	34	∈	∈	PROPN
ejpam-6102	576	35	b(0	b(0	NOUN
ejpam-6102	576	36	,	,	PUNCT
ejpam-6102	576	37	ρ	ρ	NOUN
ejpam-6102	576	38	)	)	PUNCT
ejpam-6102	576	39	:	:	PUNCT
ejpam-6102	577	1	xn	xn	PUNCT
ejpam-6102	577	2	>	>	PUNCT
ejpam-6102	577	3	0	0	NUM
ejpam-6102	577	4	}	}	PUNCT
ejpam-6102	577	5	,	,	PUNCT
ejpam-6102	577	6	ω1	ω1	PROPN
ejpam-6102	577	7	:	:	PUNCT
ejpam-6102	577	8	=	=	SYM
ejpam-6102	577	9	{	{	PUNCT
ejpam-6102	577	10	x	x	SYM
ejpam-6102	577	11	=	=	X
ejpam-6102	577	12	(	(	PUNCT
ejpam-6102	577	13	x′	x′	PROPN
ejpam-6102	577	14	,	,	PUNCT
ejpam-6102	577	15	xn	xn	X
ejpam-6102	577	16	)	)	PUNCT
ejpam-6102	577	17	∈	∈	PROPN
ejpam-6102	577	18	b(0	b(0	NOUN
ejpam-6102	577	19	,	,	PUNCT
ejpam-6102	577	20	ρ	ρ	NOUN
ejpam-6102	577	21	)	)	PUNCT
ejpam-6102	577	22	:	:	PUNCT
ejpam-6102	577	23	0	0	PUNCT
ejpam-6102	578	1	<	<	X
ejpam-6102	578	2	xn	xn	X
ejpam-6102	578	3	<	<	X
ejpam-6102	578	4	φ	φ	PROPN
ejpam-6102	578	5	(	(	PUNCT
ejpam-6102	578	6	x′	x′	NUM
ejpam-6102	578	7	)	)	PUNCT
ejpam-6102	578	8	}	}	PUNCT
ejpam-6102	578	9	,	,	PUNCT
ejpam-6102	578	10	ω2	ω2	ADV
ejpam-6102	578	11	:	:	PUNCT
ejpam-6102	578	12	=	=	SYM
ejpam-6102	578	13	{	{	PUNCT
ejpam-6102	578	14	x	x	SYM
ejpam-6102	578	15	=	=	X
ejpam-6102	578	16	(	(	PUNCT
ejpam-6102	578	17	x′	x′	PROPN
ejpam-6102	578	18	,	,	PUNCT
ejpam-6102	578	19	xn	xn	X
ejpam-6102	578	20	)	)	PUNCT
ejpam-6102	578	21	∈	∈	PROPN
ejpam-6102	578	22	b(0	b(0	NOUN
ejpam-6102	578	23	,	,	PUNCT
ejpam-6102	578	24	ρ	ρ	PROPN
ejpam-6102	578	25	)	)	PUNCT
ejpam-6102	578	26	:	:	PUNCT
ejpam-6102	578	27	φ	φ	PROPN
ejpam-6102	578	28	(	(	PUNCT
ejpam-6102	578	29	x′	x′	NUM
ejpam-6102	578	30	)	)	PUNCT
ejpam-6102	578	31	<	<	X
ejpam-6102	578	32	xn	xn	X
ejpam-6102	578	33	<	<	X
ejpam-6102	578	34	0	0	NUM
ejpam-6102	578	35	}	}	PUNCT
ejpam-6102	578	36	,	,	PUNCT
ejpam-6102	578	37	and	and	CCONJ
ejpam-6102	578	38	we	we	PRON
ejpam-6102	578	39	have	have	VERB
ejpam-6102	578	40	∫	∫	PROPN
ejpam-6102	578	41	ω∩b(0,ρ	ω∩b(0,ρ	ADP
ejpam-6102	578	42	)	)	PUNCT
ejpam-6102	578	43	.	.	PUNCT
ejpam-6102	578	44	.	.	PUNCT
ejpam-6102	578	45	.	.	PUNCT
ejpam-6102	579	1	=	=	PRON
ejpam-6102	579	2	∫	∫	PROPN
ejpam-6102	579	3	b+(0,ρ	b+(0,ρ	PROPN
ejpam-6102	579	4	)	)	PUNCT
ejpam-6102	579	5	.	.	PUNCT
ejpam-6102	579	6	.	.	PUNCT
ejpam-6102	580	1	.−	.−	PUNCT
ejpam-6102	581	1	∫	∫	PROPN
ejpam-6102	581	2	ω1	ω1	PROPN
ejpam-6102	581	3	.	.	PUNCT
ejpam-6102	581	4	.	.	PUNCT
ejpam-6102	582	1	.+	.+	NOUN
ejpam-6102	582	2	∫	∫	PROPN
ejpam-6102	583	1	ω2	ω2	ADJ
ejpam-6102	583	2	.	.	PUNCT
ejpam-6102	583	3	.	.	PUNCT
ejpam-6102	583	4	.	.	PUNCT
ejpam-6102	583	5	.	.	PUNCT
ejpam-6102	584	1	(	(	PUNCT
ejpam-6102	584	2	63	63	NUM
ejpam-6102	584	3	)	)	PUNCT
ejpam-6102	584	4	proof	proof	NOUN
ejpam-6102	584	5	of	of	ADP
ejpam-6102	584	6	(	(	PUNCT
ejpam-6102	584	7	i	i	NOUN
ejpam-6102	584	8	):	):	PUNCT
ejpam-6102	584	9	let	let	VERB
ejpam-6102	584	10	j	j	PROPN
ejpam-6102	584	11	∈	∈	PROPN
ejpam-6102	584	12	{	{	PUNCT
ejpam-6102	584	13	1	1	NUM
ejpam-6102	584	14	,	,	PUNCT
ejpam-6102	584	15	·	·	PUNCT
ejpam-6102	584	16	·	·	PUNCT
ejpam-6102	584	17	·	·	PUNCT
ejpam-6102	584	18	,	,	PUNCT
ejpam-6102	584	19	n−	n−	NOUN
ejpam-6102	584	20	1	1	NUM
ejpam-6102	584	21	}	}	PUNCT
ejpam-6102	584	22	.	.	PUNCT
ejpam-6102	585	1	by	by	ADP
ejpam-6102	585	2	(	(	PUNCT
ejpam-6102	585	3	60	60	NUM
ejpam-6102	585	4	)	)	PUNCT
ejpam-6102	585	5	,	,	PUNCT
ejpam-6102	585	6	it	it	PRON
ejpam-6102	585	7	follows	follow	VERB
ejpam-6102	585	8	that	that	SCONJ
ejpam-6102	585	9	(	(	PUNCT
ejpam-6102	585	10	x−	x−	PROPN
ejpam-6102	585	11	a	a	PROPN
ejpam-6102	585	12	)	)	PUNCT
ejpam-6102	585	13	·	·	PUNCT
ejpam-6102	585	14	τj	τj	ADP
ejpam-6102	585	15	=	=	PROPN
ejpam-6102	585	16	xj	xj	PROPN
ejpam-6102	585	17	.	.	PUNCT
ejpam-6102	586	1	by	by	ADP
ejpam-6102	586	2	oddness	oddness	NOUN
ejpam-6102	586	3	of	of	ADP
ejpam-6102	586	4	the	the	DET
ejpam-6102	586	5	function	function	NOUN
ejpam-6102	586	6	,	,	PUNCT
ejpam-6102	586	7	it	it	PRON
ejpam-6102	586	8	is	be	AUX
ejpam-6102	586	9	easy	easy	ADJ
ejpam-6102	586	10	to	to	PART
ejpam-6102	586	11	get	get	VERB
ejpam-6102	586	12	that	that	SCONJ
ejpam-6102	586	13	the	the	DET
ejpam-6102	586	14	first	first	ADJ
ejpam-6102	586	15	integral	integral	NOUN
ejpam-6102	586	16	is	be	AUX
ejpam-6102	586	17	zero	zero	NUM
ejpam-6102	586	18	.	.	PUNCT
ejpam-6102	587	1	concerning	concern	VERB
ejpam-6102	587	2	the	the	DET
ejpam-6102	587	3	other	other	ADJ
ejpam-6102	587	4	ones	one	NOUN
ejpam-6102	587	5	,	,	PUNCT
ejpam-6102	587	6	using	use	VERB
ejpam-6102	587	7	(	(	PUNCT
ejpam-6102	587	8	61	61	NUM
ejpam-6102	587	9	)	)	PUNCT
ejpam-6102	587	10	,	,	PUNCT
ejpam-6102	587	11	we	we	PRON
ejpam-6102	587	12	derive	derive	VERB
ejpam-6102	587	13	that	that	SCONJ
ejpam-6102	587	14	|xn|	|xn|	PROPN
ejpam-6102	587	15	⩽	⩽	PROPN
ejpam-6102	587	16	φ	φ	PROPN
ejpam-6102	587	17	(	(	PUNCT
ejpam-6102	587	18	x′	x′	NUM
ejpam-6102	587	19	)	)	PUNCT
ejpam-6102	588	1	=	=	SYM
ejpam-6102	588	2	o	o	X
ejpam-6102	588	3	(	(	PUNCT
ejpam-6102	588	4	|x′|2	|x′|2	NOUN
ejpam-6102	588	5	)	)	PUNCT
ejpam-6102	588	6	∀	∀	X
ejpam-6102	588	7	(	(	PUNCT
ejpam-6102	588	8	x′	x′	NUM
ejpam-6102	588	9	,	,	PUNCT
ejpam-6102	588	10	xn	xn	X
ejpam-6102	588	11	)	)	PUNCT
ejpam-6102	588	12	∈	∈	PROPN
ejpam-6102	588	13	ωi	ωi	PROPN
ejpam-6102	588	14	,	,	PUNCT
ejpam-6102	588	15	i	i	NOUN
ejpam-6102	588	16	=	=	NOUN
ejpam-6102	588	17	1	1	NUM
ejpam-6102	588	18	,	,	PUNCT
ejpam-6102	588	19	2	2	NUM
ejpam-6102	588	20	.	.	PUNCT
ejpam-6102	588	21	(	(	PUNCT
ejpam-6102	588	22	64	64	NUM
ejpam-6102	588	23	)	)	PUNCT
ejpam-6102	588	24	furthermore	furthermore	ADV
ejpam-6102	588	25	,	,	PUNCT
ejpam-6102	588	26	it	it	PRON
ejpam-6102	588	27	is	be	AUX
ejpam-6102	588	28	easy	easy	ADJ
ejpam-6102	588	29	to	to	PART
ejpam-6102	588	30	see	see	VERB
ejpam-6102	588	31	that	that	SCONJ
ejpam-6102	588	32	1	1	NUM
ejpam-6102	588	33	+	+	CCONJ
ejpam-6102	588	34	µ2|x|2	µ2|x|2	PROPN
ejpam-6102	588	35	⩾	⩾	ADJ
ejpam-6102	588	36	1	1	NUM
ejpam-6102	588	37	+	+	CCONJ
ejpam-6102	588	38	µ2	µ2	PROPN
ejpam-6102	588	39	|x′|2	|x′|2	PROPN
ejpam-6102	588	40	.	.	PUNCT
ejpam-6102	589	1	thus	thus	ADV
ejpam-6102	589	2	,	,	PUNCT
ejpam-6102	589	3	we	we	PRON
ejpam-6102	589	4	obtain	obtain	VERB
ejpam-6102	589	5	,	,	PUNCT
ejpam-6102	589	6	for	for	ADP
ejpam-6102	589	7	i	i	PRON
ejpam-6102	589	8	∈	∈	PROPN
ejpam-6102	589	9	{	{	PUNCT
ejpam-6102	589	10	1	1	NUM
ejpam-6102	589	11	,	,	PUNCT
ejpam-6102	589	12	2},∣∣∣∣∫	2},∣∣∣∣∫	NUM
ejpam-6102	589	13	ωi	ωi	NUM
ejpam-6102	589	14	.	.	PUNCT
ejpam-6102	589	15	.	.	PUNCT
ejpam-6102	589	16	.	.	PUNCT
ejpam-6102	590	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	590	2	⩽	⩽	PROPN
ejpam-6102	590	3	∫	∫	PROPN
ejpam-6102	590	4	ωi	ωi	PROPN
ejpam-6102	590	5	|x′|ω	|x′|ω	PROPN
ejpam-6102	590	6	2n	2n	NUM
ejpam-6102	590	7	n−2	n−2	PROPN
ejpam-6102	590	8	a,µ	a,µ	ADP
ejpam-6102	590	9	⩽	⩽	PROPN
ejpam-6102	590	10	c	c	PROPN
ejpam-6102	590	11	∫	∫	PROPN
ejpam-6102	590	12	ωi	ωi	PROPN
ejpam-6102	590	13	µn	µn	PROPN
ejpam-6102	590	14	|x′|	|x′|	PROPN
ejpam-6102	590	15	(	(	PUNCT
ejpam-6102	590	16	1	1	NUM
ejpam-6102	590	17	+	+	CCONJ
ejpam-6102	590	18	µ2|x′|2	µ2|x′|2	NUM
ejpam-6102	590	19	dx′dxn	dx′dxn	VERB
ejpam-6102	590	20	⩽	⩽	PROPN
ejpam-6102	590	21	c	c	PROPN
ejpam-6102	590	22	∫	∫	PROPN
ejpam-6102	590	23	bn−1(0,ρ	bn−1(0,ρ	NOUN
ejpam-6102	590	24	)	)	PUNCT
ejpam-6102	590	25	µn	µn	PROPN
ejpam-6102	590	26	|x′|3	|x′|3	NOUN
ejpam-6102	590	27	(	(	PUNCT
ejpam-6102	590	28	1	1	NUM
ejpam-6102	590	29	+	+	CCONJ
ejpam-6102	590	30	µ2	µ2	PROPN
ejpam-6102	590	31	|x′|2	|x′|2	PROPN
ejpam-6102	590	32	)	)	PUNCT
ejpam-6102	590	33	n	n	PRON
ejpam-6102	590	34	dx′	dx′	ADJ
ejpam-6102	590	35	⩽	⩽	NOUN
ejpam-6102	590	36	c	c	PROPN
ejpam-6102	590	37	µ2	µ2	PROPN
ejpam-6102	590	38	·	·	PUNCT
ejpam-6102	590	39	(	(	PUNCT
ejpam-6102	590	40	65	65	NUM
ejpam-6102	590	41	)	)	PUNCT
ejpam-6102	590	42	hence	hence	ADV
ejpam-6102	590	43	,	,	PUNCT
ejpam-6102	590	44	eqs	eqs	X
ejpam-6102	590	45	.	.	PUNCT
ejpam-6102	591	1	(	(	PUNCT
ejpam-6102	591	2	62	62	NUM
ejpam-6102	591	3	)	)	PUNCT
ejpam-6102	591	4	,	,	PUNCT
ejpam-6102	591	5	(	(	PUNCT
ejpam-6102	591	6	63	63	NUM
ejpam-6102	591	7	)	)	PUNCT
ejpam-6102	591	8	and	and	CCONJ
ejpam-6102	591	9	(	(	PUNCT
ejpam-6102	591	10	65	65	NUM
ejpam-6102	591	11	)	)	PUNCT
ejpam-6102	591	12	end	end	VERB
ejpam-6102	591	13	the	the	DET
ejpam-6102	591	14	proof	proof	NOUN
ejpam-6102	591	15	of	of	ADP
ejpam-6102	591	16	claim	claim	NOUN
ejpam-6102	591	17	(	(	PUNCT
ejpam-6102	591	18	i	i	NOUN
ejpam-6102	591	19	)	)	PUNCT
ejpam-6102	591	20	.	.	PUNCT
ejpam-6102	592	1	proof	proof	NOUN
ejpam-6102	592	2	of	of	ADP
ejpam-6102	592	3	(	(	PUNCT
ejpam-6102	592	4	ii	ii	PROPN
ejpam-6102	592	5	):	):	PUNCT
ejpam-6102	592	6	from	from	ADP
ejpam-6102	592	7	(	(	PUNCT
ejpam-6102	592	8	60	60	NUM
ejpam-6102	592	9	)	)	PUNCT
ejpam-6102	592	10	,	,	PUNCT
ejpam-6102	592	11	we	we	PRON
ejpam-6102	592	12	deduce	deduce	VERB
ejpam-6102	592	13	that	that	PRON
ejpam-6102	592	14	(	(	PUNCT
ejpam-6102	592	15	x−	x−	PROPN
ejpam-6102	592	16	a	a	PROPN
ejpam-6102	592	17	)	)	PUNCT
ejpam-6102	592	18	·	·	PUNCT
ejpam-6102	592	19	νa	νa	NOUN
ejpam-6102	592	20	=	=	ADJ
ejpam-6102	592	21	−xn	−xn	NOUN
ejpam-6102	592	22	.	.	PUNCT
ejpam-6102	593	1	as	as	ADP
ejpam-6102	593	2	in	in	ADP
ejpam-6102	593	3	the	the	DET
ejpam-6102	593	4	proof	proof	NOUN
ejpam-6102	593	5	of	of	ADP
ejpam-6102	593	6	claim	claim	NOUN
ejpam-6102	593	7	(	(	PUNCT
ejpam-6102	593	8	i	i	NOUN
ejpam-6102	593	9	)	)	PUNCT
ejpam-6102	593	10	,	,	PUNCT
ejpam-6102	593	11	for	for	ADP
ejpam-6102	593	12	i	i	PRON
ejpam-6102	593	13	∈	∈	PROPN
ejpam-6102	593	14	{	{	PUNCT
ejpam-6102	593	15	1	1	NUM
ejpam-6102	593	16	,	,	PUNCT
ejpam-6102	593	17	2	2	NUM
ejpam-6102	593	18	}	}	PUNCT
ejpam-6102	593	19	,	,	PUNCT
ejpam-6102	593	20	we	we	PRON
ejpam-6102	593	21	have	have	AUX
ejpam-6102	593	22	(	(	PUNCT
ejpam-6102	593	23	using	use	VERB
ejpam-6102	593	24	(	(	PUNCT
ejpam-6102	593	25	64))∣∣∣∣∫	64))∣∣∣∣∫	NOUN
ejpam-6102	593	26	ωi	ωi	NOUN
ejpam-6102	593	27	xnω	xnω	NOUN
ejpam-6102	593	28	n+2	n+2	PRON
ejpam-6102	593	29	n−2	n−2	PROPN
ejpam-6102	593	30	a,µ	a,µ	ADP
ejpam-6102	593	31	µ	µ	PRON
ejpam-6102	593	32	∂ωa,µ	∂ωa,µ	NOUN
ejpam-6102	593	33	∂µ	∂µ	PROPN
ejpam-6102	593	34	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	593	35	⩽	⩽	PROPN
ejpam-6102	593	36	c	c	PROPN
ejpam-6102	593	37	∫	∫	PROPN
ejpam-6102	593	38	ωi	ωi	X
ejpam-6102	593	39	µn|xn|	µn|xn|	PROPN
ejpam-6102	593	40	(	(	PUNCT
ejpam-6102	593	41	1	1	NUM
ejpam-6102	593	42	+	+	CCONJ
ejpam-6102	593	43	µ2	µ2	PROPN
ejpam-6102	593	44	|x′|2	|x′|2	PROPN
ejpam-6102	593	45	)	)	PUNCT
ejpam-6102	593	46	n	n	CCONJ
ejpam-6102	593	47	dx′dxn	dx′dxn	VERB
ejpam-6102	593	48	⩽	⩽	PROPN
ejpam-6102	593	49	c	c	PROPN
ejpam-6102	593	50	∫	∫	PROPN
ejpam-6102	593	51	bn−1(0,ρ	bn−1(0,ρ	NOUN
ejpam-6102	593	52	)	)	PUNCT
ejpam-6102	593	53	µn	µn	PROPN
ejpam-6102	593	54	|x′|4	|x′|4	NOUN
ejpam-6102	593	55	(	(	PUNCT
ejpam-6102	593	56	1	1	NUM
ejpam-6102	593	57	+	+	CCONJ
ejpam-6102	593	58	µ2	µ2	PROPN
ejpam-6102	593	59	|x′|2	|x′|2	PROPN
ejpam-6102	593	60	)	)	PUNCT
ejpam-6102	593	61	n	n	PRON
ejpam-6102	593	62	dx′	dx′	ADJ
ejpam-6102	593	63	⩽	⩽	NOUN
ejpam-6102	593	64	c	c	PROPN
ejpam-6102	593	65	µ3	µ3	PROPN
ejpam-6102	593	66	.	.	PUNCT
ejpam-6102	594	1	(	(	PUNCT
ejpam-6102	594	2	66	66	NUM
ejpam-6102	594	3	)	)	PUNCT
ejpam-6102	594	4	for	for	ADP
ejpam-6102	594	5	the	the	DET
ejpam-6102	594	6	integral	integral	ADJ
ejpam-6102	594	7	over	over	ADP
ejpam-6102	594	8	b+(0	b+(0	PROPN
ejpam-6102	594	9	,	,	PUNCT
ejpam-6102	594	10	ρ	ρ	PROPN
ejpam-6102	594	11	)	)	PUNCT
ejpam-6102	594	12	,	,	PUNCT
ejpam-6102	594	13	it	it	PRON
ejpam-6102	594	14	holds∫	holds∫	VERB
ejpam-6102	594	15	b+(0,ρ	b+(0,ρ	NOUN
ejpam-6102	594	16	)	)	PUNCT
ejpam-6102	594	17	−xnω	−xnω	NOUN
ejpam-6102	595	1	n+2	n+2	NUM
ejpam-6102	596	1	n−2	n−2	PROPN
ejpam-6102	596	2	0,µ	0,µ	PROPN
ejpam-6102	596	3	µ	µ	PRON
ejpam-6102	596	4	∂ω0,µ	∂ω0,µ	NOUN
ejpam-6102	596	5	∂µ	∂µ	PROPN
ejpam-6102	596	6	=	=	SYM
ejpam-6102	596	7	∫	∫	PROPN
ejpam-6102	596	8	b+(0,ρ	b+(0,ρ	PROPN
ejpam-6102	596	9	)	)	PUNCT
ejpam-6102	596	10	−xn	−xn	NOUN
ejpam-6102	596	11	(	(	PUNCT
ejpam-6102	596	12	n−	n−	NOUN
ejpam-6102	596	13	2	2	NUM
ejpam-6102	596	14	2	2	NUM
ejpam-6102	596	15	)	)	PUNCT
ejpam-6102	596	16	ω	ω	NUM
ejpam-6102	596	17	2n	2n	NUM
ejpam-6102	597	1	n−2	n−2	PROPN
ejpam-6102	597	2	0,µ	0,µ	PROPN
ejpam-6102	597	3	1−	1−	NUM
ejpam-6102	598	1	µ2|x|2	µ2|x|2	PROPN
ejpam-6102	598	2	1	1	NUM
ejpam-6102	599	1	+	+	CCONJ
ejpam-6102	599	2	µ2|x|2	µ2|x|2	PROPN
ejpam-6102	599	3	dx	dx	PROPN
ejpam-6102	599	4	=	=	SYM
ejpam-6102	599	5	−β	−β	PROPN
ejpam-6102	599	6	2n	2n	NUM
ejpam-6102	599	7	n−2	n−2	PROPN
ejpam-6102	599	8	0	0	NUM
ejpam-6102	599	9	n−	n−	NOUN
ejpam-6102	599	10	2	2	NUM
ejpam-6102	599	11	2	2	NUM
ejpam-6102	599	12	∫	∫	NOUN
ejpam-6102	599	13	b+(0,ρ	b+(0,ρ	NOUN
ejpam-6102	599	14	)	)	PUNCT
ejpam-6102	599	15	µnxn	µnxn	VERB
ejpam-6102	599	16	1−	1−	NUM
ejpam-6102	599	17	µ2|x|2	µ2|x|2	PROPN
ejpam-6102	599	18	(	(	PUNCT
ejpam-6102	599	19	1	1	NUM
ejpam-6102	599	20	+	+	NUM
ejpam-6102	599	21	µ2|x|2)n+1	µ2|x|2)n+1	PROPN
ejpam-6102	599	22	dx	dx	PROPN
ejpam-6102	599	23	=	=	SYM
ejpam-6102	599	24	−β	−β	PROPN
ejpam-6102	599	25	2n	2n	NUM
ejpam-6102	600	1	n−2	n−2	PROPN
ejpam-6102	600	2	0	0	NUM
ejpam-6102	600	3	n−	n−	NOUN
ejpam-6102	600	4	2	2	NUM
ejpam-6102	600	5	2	2	NUM
ejpam-6102	600	6	1	1	NUM
ejpam-6102	600	7	µ	µ	PRON
ejpam-6102	600	8	∫	∫	PROPN
ejpam-6102	600	9	rn	rn	PROPN
ejpam-6102	600	10	+	+	PROPN
ejpam-6102	600	11	xn	xn	PROPN
ejpam-6102	600	12	1−	1−	NUM
ejpam-6102	600	13	|x|2	|x|2	NOUN
ejpam-6102	600	14	(	(	PUNCT
ejpam-6102	600	15	1	1	NUM
ejpam-6102	600	16	+	+	NUM
ejpam-6102	600	17	|x|2)n+1	|x|2)n+1	X
ejpam-6102	600	18	dx+o	dx+o	NOUN
ejpam-6102	600	19	(	(	PUNCT
ejpam-6102	600	20	1	1	NUM
ejpam-6102	600	21	µn	µn	NOUN
ejpam-6102	600	22	)	)	PUNCT
ejpam-6102	600	23	.	.	PUNCT
ejpam-6102	601	1	(	(	PUNCT
ejpam-6102	601	2	67	67	X
ejpam-6102	601	3	)	)	PUNCT
ejpam-6102	601	4	combining	combine	VERB
ejpam-6102	601	5	eqs	eqs	PROPN
ejpam-6102	601	6	.	.	PUNCT
ejpam-6102	602	1	(	(	PUNCT
ejpam-6102	602	2	62	62	NUM
ejpam-6102	602	3	)	)	PUNCT
ejpam-6102	602	4	,	,	PUNCT
ejpam-6102	602	5	(	(	PUNCT
ejpam-6102	602	6	66	66	NUM
ejpam-6102	602	7	)	)	PUNCT
ejpam-6102	602	8	and	and	CCONJ
ejpam-6102	602	9	(	(	PUNCT
ejpam-6102	602	10	67	67	NUM
ejpam-6102	602	11	)	)	PUNCT
ejpam-6102	602	12	,	,	PUNCT
ejpam-6102	602	13	the	the	DET
ejpam-6102	602	14	proof	proof	NOUN
ejpam-6102	602	15	of	of	ADP
ejpam-6102	602	16	claim	claim	NOUN
ejpam-6102	602	17	(	(	PUNCT
ejpam-6102	602	18	ii	ii	NOUN
ejpam-6102	602	19	)	)	PUNCT
ejpam-6102	602	20	follows	follow	VERB
ejpam-6102	602	21	.	.	PUNCT
ejpam-6102	603	1	proof	proof	NOUN
ejpam-6102	603	2	of	of	ADP
ejpam-6102	603	3	(	(	PUNCT
ejpam-6102	603	4	iii	iii	NOUN
ejpam-6102	603	5	):	):	PUNCT
ejpam-6102	603	6	following	follow	VERB
ejpam-6102	603	7	the	the	DET
ejpam-6102	603	8	proof	proof	NOUN
ejpam-6102	603	9	of	of	ADP
ejpam-6102	603	10	the	the	DET
ejpam-6102	603	11	previous	previous	ADJ
ejpam-6102	603	12	claims	claim	NOUN
ejpam-6102	603	13	,	,	PUNCT
ejpam-6102	603	14	we	we	PRON
ejpam-6102	603	15	need	need	VERB
ejpam-6102	603	16	to	to	ADP
ejpam-6102	603	17	estimate:∣∣∣∣∣	estimate:∣∣∣∣∣	PROPN
ejpam-6102	603	18	∫	∫	PROPN
ejpam-6102	603	19	ω\b(0,ρ	ω\b(0,ρ	NUM
ejpam-6102	603	20	)	)	PUNCT
ejpam-6102	603	21	.	.	PUNCT
ejpam-6102	603	22	.	.	PUNCT
ejpam-6102	603	23	.	.	PUNCT
ejpam-6102	604	1	∣∣∣∣∣	∣∣∣∣∣	ADJ
ejpam-6102	604	2	⩽	⩽	ADJ
ejpam-6102	604	3	∫	∫	PROPN
ejpam-6102	604	4	ω\b(0,ρ	ω\b(0,ρ	NUM
ejpam-6102	604	5	)	)	PUNCT
ejpam-6102	604	6	ω	ω	NUM
ejpam-6102	604	7	2n	2n	NUM
ejpam-6102	605	1	n−2	n−2	PROPN
ejpam-6102	605	2	a,µ	a,µ	ADP
ejpam-6102	605	3	ln	ln	ADV
ejpam-6102	605	4	(	(	PUNCT
ejpam-6102	605	5	1	1	NUM
ejpam-6102	605	6	+	+	CCONJ
ejpam-6102	605	7	µ2	µ2	PROPN
ejpam-6102	605	8	|x−	|x−	PROPN
ejpam-6102	605	9	a|2	a|2	PROPN
ejpam-6102	605	10	)	)	PUNCT
ejpam-6102	605	11	⩽	⩽	PROPN
ejpam-6102	605	12	c	c	PROPN
ejpam-6102	605	13	lnµ	lnµ	NOUN
ejpam-6102	605	14	µn	µn	PROPN
ejpam-6102	605	15	,	,	PUNCT
ejpam-6102	605	16	(	(	PUNCT
ejpam-6102	605	17	68	68	NUM
ejpam-6102	605	18	)	)	PUNCT
ejpam-6102	605	19	r.	r.	PROPN
ejpam-6102	605	20	almushahhin	almushahhin	PROPN
ejpam-6102	605	21	,	,	PUNCT
ejpam-6102	605	22	m.	m.	PROPN
ejpam-6102	605	23	ben	ben	PROPN
ejpam-6102	605	24	ayed	aye	VERB
ejpam-6102	605	25	/	/	SYM
ejpam-6102	605	26	eur	eur	PROPN
ejpam-6102	605	27	.	.	PUNCT
ejpam-6102	606	1	j.	j.	PROPN
ejpam-6102	606	2	pure	pure	PROPN
ejpam-6102	606	3	appl	appl	PROPN
ejpam-6102	606	4	.	.	PROPN
ejpam-6102	606	5	math	math	PROPN
ejpam-6102	606	6	,	,	PUNCT
ejpam-6102	606	7	18	18	NUM
ejpam-6102	606	8	(	(	PUNCT
ejpam-6102	606	9	2	2	NUM
ejpam-6102	606	10	)	)	PUNCT
ejpam-6102	606	11	(	(	PUNCT
ejpam-6102	606	12	2025	2025	NUM
ejpam-6102	606	13	)	)	PUNCT
ejpam-6102	606	14	,	,	PUNCT
ejpam-6102	606	15	6102	6102	NUM
ejpam-6102	606	16	22	22	NUM
ejpam-6102	606	17	of	of	ADP
ejpam-6102	606	18	31∫	31∫	NUM
ejpam-6102	606	19	b+(0,ρ	b+(0,ρ	ADP
ejpam-6102	606	20	)	)	PUNCT
ejpam-6102	606	21	.	.	PUNCT
ejpam-6102	606	22	.	.	PUNCT
ejpam-6102	606	23	.	.	PUNCT
ejpam-6102	607	1	=	=	PUNCT
ejpam-6102	607	2	β	β	X
ejpam-6102	607	3	2n	2n	NUM
ejpam-6102	607	4	n−2	n−2	PROPN
ejpam-6102	607	5	0	0	NUM
ejpam-6102	607	6	n−	n−	NOUN
ejpam-6102	607	7	2	2	NUM
ejpam-6102	607	8	2	2	NUM
ejpam-6102	607	9	∫	∫	NOUN
ejpam-6102	607	10	b+(0,ρ	b+(0,ρ	NOUN
ejpam-6102	607	11	)	)	PUNCT
ejpam-6102	607	12	µn	µn	PROPN
ejpam-6102	607	13	(	(	PUNCT
ejpam-6102	607	14	1−	1−	NUM
ejpam-6102	607	15	µ2|x|2	µ2|x|2	PROPN
ejpam-6102	607	16	)	)	PUNCT
ejpam-6102	607	17	(	(	PUNCT
ejpam-6102	607	18	1	1	NUM
ejpam-6102	607	19	+	+	NUM
ejpam-6102	607	20	µ2|x|2)n+1	µ2|x|2)n+1	ADJ
ejpam-6102	607	21	ln	ln	ADJ
ejpam-6102	607	22	(	(	PUNCT
ejpam-6102	607	23	1	1	NUM
ejpam-6102	607	24	+	+	CCONJ
ejpam-6102	607	25	µ2|x|2	µ2|x|2	PROPN
ejpam-6102	607	26	)	)	PUNCT
ejpam-6102	607	27	dx	dx	PROPN
ejpam-6102	608	1	=	=	PUNCT
ejpam-6102	608	2	β	β	X
ejpam-6102	608	3	2n	2n	NUM
ejpam-6102	608	4	n−2	n−2	PROPN
ejpam-6102	608	5	0	0	NUM
ejpam-6102	608	6	n−	n−	NOUN
ejpam-6102	608	7	2	2	NUM
ejpam-6102	608	8	2	2	NUM
ejpam-6102	608	9	∫	∫	NOUN
ejpam-6102	608	10	(	(	PUNCT
ejpam-6102	608	11	b+(0,λρ	b+(0,λρ	NOUN
ejpam-6102	608	12	)	)	PUNCT
ejpam-6102	608	13	1−	1−	NUM
ejpam-6102	608	14	|x|2	|x|2	NOUN
ejpam-6102	608	15	(	(	PUNCT
ejpam-6102	608	16	1	1	NUM
ejpam-6102	608	17	+	+	NUM
ejpam-6102	608	18	|x|2)n+1	|x|2)n+1	SYM
ejpam-6102	608	19	ln	ln	X
ejpam-6102	608	20	(	(	PUNCT
ejpam-6102	608	21	1	1	NUM
ejpam-6102	608	22	+	+	CCONJ
ejpam-6102	608	23	|x|2	|x|2	NOUN
ejpam-6102	608	24	)	)	PUNCT
ejpam-6102	608	25	dx	dx	PROPN
ejpam-6102	609	1	=	=	SYM
ejpam-6102	609	2	−1	−1	NOUN
ejpam-6102	609	3	2	2	NUM
ejpam-6102	609	4	β	β	X
ejpam-6102	609	5	2n	2n	NUM
ejpam-6102	609	6	n−2	n−2	PROPN
ejpam-6102	609	7	0	0	NUM
ejpam-6102	609	8	n−	n−	NOUN
ejpam-6102	609	9	2	2	NUM
ejpam-6102	609	10	2	2	NUM
ejpam-6102	609	11	∫	∫	PROPN
ejpam-6102	609	12	rn	rn	PROPN
ejpam-6102	609	13	|x|2	|x|2	PROPN
ejpam-6102	609	14	−	−	PROPN
ejpam-6102	609	15	1	1	NUM
ejpam-6102	609	16	(	(	PUNCT
ejpam-6102	609	17	1	1	NUM
ejpam-6102	609	18	+	+	CCONJ
ejpam-6102	609	19	|x|2)n+1	|x|2)n+1	SYM
ejpam-6102	609	20	ln	ln	X
ejpam-6102	609	21	(	(	PUNCT
ejpam-6102	609	22	1	1	NUM
ejpam-6102	609	23	+	+	CCONJ
ejpam-6102	609	24	|x|2	|x|2	NOUN
ejpam-6102	609	25	)	)	PUNCT
ejpam-6102	610	1	dx+o	dx+o	PROPN
ejpam-6102	610	2	(	(	PUNCT
ejpam-6102	610	3	lnµ	lnµ	NOUN
ejpam-6102	610	4	µn	µn	PROPN
ejpam-6102	610	5	)	)	PUNCT
ejpam-6102	610	6	.	.	PUNCT
ejpam-6102	611	1	(	(	PUNCT
ejpam-6102	611	2	69	69	NUM
ejpam-6102	611	3	)	)	PUNCT
ejpam-6102	611	4	for	for	ADP
ejpam-6102	611	5	the	the	DET
ejpam-6102	611	6	integrals	integral	NOUN
ejpam-6102	611	7	over	over	ADP
ejpam-6102	611	8	ωi	ωi	PROPN
ejpam-6102	611	9	,	,	PUNCT
ejpam-6102	611	10	i	i	NOUN
ejpam-6102	611	11	=	=	NOUN
ejpam-6102	611	12	1	1	NUM
ejpam-6102	611	13	,	,	PUNCT
ejpam-6102	611	14	2	2	NUM
ejpam-6102	611	15	,	,	PUNCT
ejpam-6102	611	16	note	note	VERB
ejpam-6102	611	17	that	that	SCONJ
ejpam-6102	611	18	,	,	PUNCT
ejpam-6102	611	19	using	use	VERB
ejpam-6102	611	20	eq	eq	ADP
ejpam-6102	611	21	.	.	PUNCT
ejpam-6102	612	1	(	(	PUNCT
ejpam-6102	612	2	64	64	NUM
ejpam-6102	612	3	)	)	PUNCT
ejpam-6102	612	4	,	,	PUNCT
ejpam-6102	612	5	we	we	PRON
ejpam-6102	612	6	have	have	VERB
ejpam-6102	612	7	|xn|	|xn|	VERB
ejpam-6102	612	8	≤	≤	NUM
ejpam-6102	612	9	c	c	PROPN
ejpam-6102	612	10	|x′|2	|x′|2	PROPN
ejpam-6102	612	11	,	,	PUNCT
ejpam-6102	612	12	which	which	PRON
ejpam-6102	612	13	implies	imply	VERB
ejpam-6102	612	14	that	that	SCONJ
ejpam-6102	612	15	1	1	NUM
ejpam-6102	612	16	+	+	NUM
ejpam-6102	612	17	µ2|x|2	µ2|x|2	PROPN
ejpam-6102	612	18	=	=	SYM
ejpam-6102	612	19	1	1	NUM
ejpam-6102	613	1	+	+	CCONJ
ejpam-6102	613	2	µ2	µ2	PROPN
ejpam-6102	613	3	|x′|2	|x′|2	NOUN
ejpam-6102	613	4	+	+	CCONJ
ejpam-6102	613	5	µ2x2n	µ2x2n	SYM
ejpam-6102	613	6	⩽	⩽	ADJ
ejpam-6102	613	7	1	1	NUM
ejpam-6102	614	1	+	+	CCONJ
ejpam-6102	615	1	µ2	µ2	PROPN
ejpam-6102	615	2	|x′|2	|x′|2	NOUN
ejpam-6102	615	3	(	(	PUNCT
ejpam-6102	615	4	1	1	NUM
ejpam-6102	615	5	+	+	CCONJ
ejpam-6102	615	6	c	c	NOUN
ejpam-6102	615	7	|x′|2	|x′|2	NOUN
ejpam-6102	615	8	)	)	PUNCT
ejpam-6102	615	9	⩽	⩽	ADV
ejpam-6102	615	10	2(1	2(1	NUM
ejpam-6102	615	11	+	+	CCONJ
ejpam-6102	615	12	µ2	µ2	PROPN
ejpam-6102	615	13	|x′|2	|x′|2	PROPN
ejpam-6102	615	14	)	)	PUNCT
ejpam-6102	615	15	,	,	PUNCT
ejpam-6102	615	16	(	(	PUNCT
ejpam-6102	615	17	70	70	NUM
ejpam-6102	615	18	)	)	PUNCT
ejpam-6102	615	19	since	since	SCONJ
ejpam-6102	615	20	|x′|	|x′|	PROPN
ejpam-6102	615	21	<	<	X
ejpam-6102	615	22	ρ	ρ	PRON
ejpam-6102	615	23	which	which	PRON
ejpam-6102	615	24	is	be	AUX
ejpam-6102	615	25	small	small	ADJ
ejpam-6102	615	26	.	.	PUNCT
ejpam-6102	616	1	thus	thus	ADV
ejpam-6102	616	2	we	we	PRON
ejpam-6102	616	3	obtain	obtain	VERB
ejpam-6102	616	4	∣∣∣∣∫	∣∣∣∣∫	PRON
ejpam-6102	616	5	ωi	ωi	PROPN
ejpam-6102	616	6	.	.	PUNCT
ejpam-6102	616	7	.	.	PUNCT
ejpam-6102	616	8	.	.	PUNCT
ejpam-6102	617	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	617	2	⩽	⩽	PROPN
ejpam-6102	617	3	c	c	PROPN
ejpam-6102	617	4	∫	∫	PROPN
ejpam-6102	617	5	ωi	ωi	PROPN
ejpam-6102	617	6	µn	µn	PROPN
ejpam-6102	617	7	ln	ln	NOUN
ejpam-6102	617	8	(	(	PUNCT
ejpam-6102	617	9	1	1	NUM
ejpam-6102	617	10	+	+	CCONJ
ejpam-6102	617	11	µ2|x|2	µ2|x|2	PROPN
ejpam-6102	617	12	)	)	PUNCT
ejpam-6102	617	13	(	(	PUNCT
ejpam-6102	617	14	1	1	NUM
ejpam-6102	617	15	+	+	SYM
ejpam-6102	618	1	µ2|x|2)n	µ2|x|2)n	NUM
ejpam-6102	618	2	dx	dx	PROPN
ejpam-6102	618	3	≤	≤	PROPN
ejpam-6102	618	4	c	c	PROPN
ejpam-6102	618	5	∫	∫	PROPN
ejpam-6102	618	6	bn−1(0,ρ	bn−1(0,ρ	NOUN
ejpam-6102	618	7	)	)	PUNCT
ejpam-6102	618	8	µn	µn	PROPN
ejpam-6102	618	9	|x′|2	|x′|2	NOUN
ejpam-6102	618	10	ln	ln	NOUN
ejpam-6102	618	11	(	(	PUNCT
ejpam-6102	618	12	1	1	NUM
ejpam-6102	618	13	+	+	CCONJ
ejpam-6102	618	14	µ2	µ2	PROPN
ejpam-6102	618	15	|x′|2	|x′|2	PROPN
ejpam-6102	618	16	)	)	PUNCT
ejpam-6102	618	17	(	(	PUNCT
ejpam-6102	618	18	1	1	X
ejpam-6102	618	19	+	+	CCONJ
ejpam-6102	618	20	µ2	µ2	PROPN
ejpam-6102	618	21	|x′|2	|x′|2	PROPN
ejpam-6102	618	22	)	)	PUNCT
ejpam-6102	618	23	n	n	PRON
ejpam-6102	619	1	dx′	dx′	VERB
ejpam-6102	619	2	⩽	⩽	PROPN
ejpam-6102	619	3	c	c	PROPN
ejpam-6102	619	4	µ	µ	X
ejpam-6102	619	5	∫	∫	PROPN
ejpam-6102	619	6	rn−1	rn−1	PROPN
ejpam-6102	619	7	|x′|2	|x′|2	PROPN
ejpam-6102	619	8	ln	ln	NOUN
ejpam-6102	619	9	(	(	PUNCT
ejpam-6102	619	10	1	1	NUM
ejpam-6102	619	11	+	+	X
ejpam-6102	619	12	|x′|2	|x′|2	NOUN
ejpam-6102	619	13	)	)	PUNCT
ejpam-6102	619	14	(	(	PUNCT
ejpam-6102	619	15	1	1	NUM
ejpam-6102	619	16	+	+	X
ejpam-6102	619	17	|x′|2	|x′|2	NOUN
ejpam-6102	619	18	)	)	PUNCT
ejpam-6102	619	19	n	n	PRON
ejpam-6102	619	20	dx′	dx′	VERB
ejpam-6102	619	21	⩽	⩽	NOUN
ejpam-6102	619	22	c	c	PROPN
ejpam-6102	619	23	µ	µ	X
ejpam-6102	619	24	.	.	PUNCT
ejpam-6102	620	1	(	(	PUNCT
ejpam-6102	620	2	71	71	NUM
ejpam-6102	620	3	)	)	PUNCT
ejpam-6102	620	4	hence	hence	ADV
ejpam-6102	620	5	,	,	PUNCT
ejpam-6102	620	6	(	(	PUNCT
ejpam-6102	620	7	68	68	NUM
ejpam-6102	620	8	)	)	PUNCT
ejpam-6102	620	9	,	,	PUNCT
ejpam-6102	620	10	(	(	PUNCT
ejpam-6102	620	11	69	69	NUM
ejpam-6102	620	12	)	)	PUNCT
ejpam-6102	620	13	and	and	CCONJ
ejpam-6102	620	14	(	(	PUNCT
ejpam-6102	620	15	71	71	NUM
ejpam-6102	620	16	)	)	PUNCT
ejpam-6102	620	17	imply	imply	VERB
ejpam-6102	620	18	the	the	DET
ejpam-6102	620	19	proof	proof	NOUN
ejpam-6102	620	20	of	of	ADP
ejpam-6102	620	21	cham	cham	PROPN
ejpam-6102	620	22	(	(	PUNCT
ejpam-6102	620	23	iii	iii	NOUN
ejpam-6102	620	24	)	)	PUNCT
ejpam-6102	620	25	.	.	PUNCT
ejpam-6102	621	1	proof	proof	NOUN
ejpam-6102	621	2	of	of	ADP
ejpam-6102	621	3	(	(	PUNCT
ejpam-6102	621	4	iv	iv	NUM
ejpam-6102	621	5	):	):	PUNCT
ejpam-6102	621	6	note	note	VERB
ejpam-6102	621	7	that	that	SCONJ
ejpam-6102	621	8	,	,	PUNCT
ejpam-6102	621	9	by	by	ADP
ejpam-6102	621	10	(	(	PUNCT
ejpam-6102	621	11	60	60	NUM
ejpam-6102	621	12	)	)	PUNCT
ejpam-6102	621	13	,	,	PUNCT
ejpam-6102	621	14	it	it	PRON
ejpam-6102	621	15	follows	follow	VERB
ejpam-6102	621	16	that	that	SCONJ
ejpam-6102	621	17	(	(	PUNCT
ejpam-6102	621	18	x−	x−	PROPN
ejpam-6102	621	19	a	a	PROPN
ejpam-6102	621	20	)	)	PUNCT
ejpam-6102	621	21	·	·	PUNCT
ejpam-6102	621	22	τk	τk	ADP
ejpam-6102	621	23	=	=	PUNCT
ejpam-6102	621	24	xk	xk	PROPN
ejpam-6102	621	25	and	and	CCONJ
ejpam-6102	621	26	∂ωa,µ	∂ωa,µ	PROPN
ejpam-6102	621	27	∂τj	∂τj	PROPN
ejpam-6102	621	28	=	=	PUNCT
ejpam-6102	621	29	∂ωa,µ	∂ωa,µ	PROPN
ejpam-6102	621	30	∂aj	∂aj	PROPN
ejpam-6102	621	31	.	.	PUNCT
ejpam-6102	622	1	as	as	ADP
ejpam-6102	622	2	before	before	ADV
ejpam-6102	622	3	,	,	PUNCT
ejpam-6102	622	4	we	we	PRON
ejpam-6102	622	5	compute	compute	VERB
ejpam-6102	622	6	:	:	PUNCT
ejpam-6102	623	1	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-6102	623	2	∫	∫	PROPN
ejpam-6102	623	3	ω\b(0,ρ	ω\b(0,ρ	NUM
ejpam-6102	623	4	)	)	PUNCT
ejpam-6102	623	5	.	.	PUNCT
ejpam-6102	623	6	.	.	PUNCT
ejpam-6102	623	7	.	.	PUNCT
ejpam-6102	624	1	∣∣∣∣∣	∣∣∣∣∣	ADJ
ejpam-6102	624	2	⩽	⩽	ADJ
ejpam-6102	624	3	∫	∫	PROPN
ejpam-6102	624	4	ω\b(0,ρ	ω\b(0,ρ	NUM
ejpam-6102	624	5	)	)	PUNCT
ejpam-6102	624	6	|x|	|x|	PROPN
ejpam-6102	624	7	1	1	NUM
ejpam-6102	624	8	µ|x|	µ|x|	NOUN
ejpam-6102	624	9	ω	ω	NUM
ejpam-6102	624	10	2n	2n	NUM
ejpam-6102	625	1	n−2	n−2	PROPN
ejpam-6102	625	2	0,µ	0,µ	PROPN
ejpam-6102	625	3	⩽	⩽	PROPN
ejpam-6102	625	4	c	c	PROPN
ejpam-6102	625	5	µn+1	µn+1	PRON
ejpam-6102	625	6	,	,	PUNCT
ejpam-6102	625	7	(	(	PUNCT
ejpam-6102	625	8	72	72	NUM
ejpam-6102	625	9	)	)	PUNCT
ejpam-6102	625	10	where	where	SCONJ
ejpam-6102	625	11	we	we	PRON
ejpam-6102	625	12	have	have	AUX
ejpam-6102	625	13	uses	use	VERB
ejpam-6102	625	14	the	the	DET
ejpam-6102	625	15	fact	fact	NOUN
ejpam-6102	625	16	that	that	SCONJ
ejpam-6102	625	17	∣∣∣∂ωa,µ	∣∣∣∂ωa,µ	PROPN
ejpam-6102	626	1	∂a	∂a	ADP
ejpam-6102	626	2	∣∣∣	∣∣∣	ADJ
ejpam-6102	626	3	⩽	⩽	PROPN
ejpam-6102	626	4	c	c	NOUN
ejpam-6102	626	5	ωa,µ	ωa,µ	NOUN
ejpam-6102	626	6	|x−a|	|x−a|	PUNCT
ejpam-6102	626	7	.	.	PUNCT
ejpam-6102	627	1	concerning	concern	VERB
ejpam-6102	627	2	the	the	DET
ejpam-6102	627	3	integral	integral	ADJ
ejpam-6102	627	4	over	over	ADP
ejpam-6102	627	5	ω	ω	PROPN
ejpam-6102	627	6	∩b(0	∩b(0	PROPN
ejpam-6102	627	7	,	,	PUNCT
ejpam-6102	627	8	ρ	ρ	PROPN
ejpam-6102	627	9	)	)	PUNCT
ejpam-6102	627	10	,	,	PUNCT
ejpam-6102	627	11	using	use	VERB
ejpam-6102	627	12	(	(	PUNCT
ejpam-6102	627	13	63	63	NUM
ejpam-6102	627	14	)	)	PUNCT
ejpam-6102	627	15	,	,	PUNCT
ejpam-6102	627	16	we	we	PRON
ejpam-6102	627	17	need	need	VERB
ejpam-6102	627	18	to	to	PART
ejpam-6102	627	19	compute:∫	compute:∫	VERB
ejpam-6102	627	20	b+(0,ρ	b+(0,ρ	X
ejpam-6102	627	21	)	)	PUNCT
ejpam-6102	627	22	·	·	PUNCT
ejpam-6102	627	23	·	·	PUNCT
ejpam-6102	627	24	·	·	PUNCT
ejpam-6102	628	1	=	=	PUNCT
ejpam-6102	628	2	(	(	PUNCT
ejpam-6102	628	3	n−	n−	NOUN
ejpam-6102	628	4	2)β	2)β	NOUN
ejpam-6102	628	5	2n	2n	NUM
ejpam-6102	629	1	n−2	n−2	PROPN
ejpam-6102	629	2	0	0	NUM
ejpam-6102	629	3	∫	∫	PROPN
ejpam-6102	629	4	b+(0,ρ	b+(0,ρ	PROPN
ejpam-6102	629	5	)	)	PUNCT
ejpam-6102	629	6	xk	xk	PROPN
ejpam-6102	629	7	µn+1xj	µn+1xj	PROPN
ejpam-6102	629	8	(	(	PUNCT
ejpam-6102	629	9	1	1	NUM
ejpam-6102	629	10	+	+	NUM
ejpam-6102	629	11	µ2|x|2)n+1	µ2|x|2)n+1	PROPN
ejpam-6102	629	12	dx	dx	PROPN
ejpam-6102	629	13	=	=	SYM
ejpam-6102	629	14	0	0	PROPN
ejpam-6102	629	15	,	,	PUNCT
ejpam-6102	629	16	k	k	PROPN
ejpam-6102	629	17	̸=	̸=	PROPN
ejpam-6102	629	18	j	j	PROPN
ejpam-6102	629	19	,	,	PUNCT
ejpam-6102	629	20	(	(	PUNCT
ejpam-6102	629	21	73	73	NUM
ejpam-6102	629	22	)	)	PUNCT
ejpam-6102	629	23	(	(	PUNCT
ejpam-6102	629	24	by	by	ADP
ejpam-6102	629	25	oddness	oddness	NOUN
ejpam-6102	629	26	with	with	ADP
ejpam-6102	629	27	respect	respect	NOUN
ejpam-6102	629	28	to	to	ADP
ejpam-6102	629	29	the	the	DET
ejpam-6102	629	30	variable	variable	NOUN
ejpam-6102	629	31	xj	xj	PROPN
ejpam-6102	629	32	)	)	PUNCT
ejpam-6102	629	33	.	.	PUNCT
ejpam-6102	630	1	however	however	ADV
ejpam-6102	630	2	,	,	PUNCT
ejpam-6102	630	3	if	if	SCONJ
ejpam-6102	630	4	k	k	PROPN
ejpam-6102	630	5	=	=	SYM
ejpam-6102	630	6	j	j	PROPN
ejpam-6102	630	7	,	,	PUNCT
ejpam-6102	630	8	we	we	PRON
ejpam-6102	630	9	obtain∫	obtain∫	VERB
ejpam-6102	630	10	b+(0,ρ	b+(0,ρ	ADP
ejpam-6102	630	11	)	)	PUNCT
ejpam-6102	630	12	·	·	PUNCT
ejpam-6102	630	13	·	·	PUNCT
ejpam-6102	630	14	·	·	PUNCT
ejpam-6102	631	1	=	=	PUNCT
ejpam-6102	631	2	(	(	PUNCT
ejpam-6102	631	3	n−	n−	NOUN
ejpam-6102	631	4	2)β	2)β	NOUN
ejpam-6102	631	5	2n	2n	NUM
ejpam-6102	632	1	n−2	n−2	PROPN
ejpam-6102	632	2	0	0	NUM
ejpam-6102	632	3	∫	∫	PROPN
ejpam-6102	632	4	b+(0,ρ	b+(0,ρ	PROPN
ejpam-6102	632	5	)	)	PUNCT
ejpam-6102	632	6	µn+1x2j	µn+1x2j	NOUN
ejpam-6102	632	7	(	(	PUNCT
ejpam-6102	632	8	1	1	NUM
ejpam-6102	632	9	+	+	NUM
ejpam-6102	632	10	µ2|x|2)n+1	µ2|x|2)n+1	PROPN
ejpam-6102	632	11	dx	dx	PROPN
ejpam-6102	632	12	=	=	SYM
ejpam-6102	632	13	1	1	NUM
ejpam-6102	632	14	2	2	NUM
ejpam-6102	632	15	n−	n−	NOUN
ejpam-6102	632	16	2	2	NUM
ejpam-6102	632	17	µ	µ	PRON
ejpam-6102	632	18	β	β	X
ejpam-6102	632	19	2n	2n	NUM
ejpam-6102	632	20	n−2	n−2	PROPN
ejpam-6102	632	21	∫	∫	PROPN
ejpam-6102	632	22	b(0,µρ	b(0,µρ	PROPN
ejpam-6102	632	23	)	)	PUNCT
ejpam-6102	632	24	x2j	x2j	PUNCT
ejpam-6102	633	1	(	(	PUNCT
ejpam-6102	633	2	1	1	NUM
ejpam-6102	633	3	+	+	NUM
ejpam-6102	633	4	|x|2)n+1	|x|2)n+1	NUM
ejpam-6102	633	5	dx	dx	NOUN
ejpam-6102	633	6	=	=	SYM
ejpam-6102	633	7	1	1	NUM
ejpam-6102	633	8	2µ	2µ	NUM
ejpam-6102	633	9	n−	n−	NOUN
ejpam-6102	633	10	2	2	NUM
ejpam-6102	633	11	n	n	PROPN
ejpam-6102	633	12	β	β	X
ejpam-6102	633	13	2n	2n	NUM
ejpam-6102	633	14	n−2	n−2	PROPN
ejpam-6102	633	15	0	0	NUM
ejpam-6102	633	16	∫	∫	PROPN
ejpam-6102	633	17	b(0,µρ	b(0,µρ	PROPN
ejpam-6102	633	18	)	)	PUNCT
ejpam-6102	633	19	|x|2	|x|2	NOUN
ejpam-6102	633	20	(	(	PUNCT
ejpam-6102	633	21	1	1	NUM
ejpam-6102	633	22	+	+	NUM
ejpam-6102	633	23	|x|2)n+1	|x|2)n+1	NUM
ejpam-6102	633	24	dx	dx	NOUN
ejpam-6102	634	1	=	=	SYM
ejpam-6102	634	2	c7	c7	PROPN
ejpam-6102	634	3	µ	µ	PROPN
ejpam-6102	634	4	+	+	PROPN
ejpam-6102	634	5	o	o	X
ejpam-6102	634	6	(	(	PUNCT
ejpam-6102	634	7	1	1	NUM
ejpam-6102	634	8	µn+1	µn+1	NUM
ejpam-6102	634	9	)	)	PUNCT
ejpam-6102	634	10	.	.	PUNCT
ejpam-6102	635	1	(	(	PUNCT
ejpam-6102	635	2	74	74	X
ejpam-6102	635	3	)	)	PUNCT
ejpam-6102	635	4	it	it	PRON
ejpam-6102	635	5	remains	remain	VERB
ejpam-6102	635	6	the	the	DET
ejpam-6102	635	7	integrals	integral	NOUN
ejpam-6102	635	8	over	over	ADP
ejpam-6102	635	9	ωi	ωi	PROPN
ejpam-6102	635	10	,	,	PUNCT
ejpam-6102	635	11	i	i	NOUN
ejpam-6102	635	12	=	=	NOUN
ejpam-6102	635	13	1	1	NUM
ejpam-6102	635	14	,	,	PUNCT
ejpam-6102	635	15	2	2	NUM
ejpam-6102	635	16	.	.	X
ejpam-6102	635	17	using	use	VERB
ejpam-6102	635	18	(	(	PUNCT
ejpam-6102	635	19	70	70	NUM
ejpam-6102	635	20	)	)	PUNCT
ejpam-6102	635	21	,	,	PUNCT
ejpam-6102	635	22	it	it	PRON
ejpam-6102	635	23	holds∣∣∣∣∫	holds∣∣∣∣∫	VERB
ejpam-6102	635	24	ωi	ωi	X
ejpam-6102	635	25	.	.	PUNCT
ejpam-6102	635	26	.	.	PUNCT
ejpam-6102	635	27	.	.	PUNCT
ejpam-6102	636	1	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	636	2	⩽	⩽	PROPN
ejpam-6102	636	3	c	c	PROPN
ejpam-6102	636	4	∫	∫	PROPN
ejpam-6102	636	5	ωi	ωi	X
ejpam-6102	636	6	|xk|	|xk|	PROPN
ejpam-6102	636	7	1	1	NUM
ejpam-6102	636	8	µ|x|	µ|x|	PROPN
ejpam-6102	636	9	ω	ω	NUM
ejpam-6102	636	10	2n	2n	NUM
ejpam-6102	637	1	n−2	n−2	PROPN
ejpam-6102	637	2	a,µ	a,µ	ADP
ejpam-6102	637	3	⩽	⩽	PROPN
ejpam-6102	637	4	c	c	PROPN
ejpam-6102	637	5	∫	∫	PROPN
ejpam-6102	637	6	ωi	ωi	X
ejpam-6102	638	1	µn−1	µn−1	PROPN
ejpam-6102	638	2	(	(	PUNCT
ejpam-6102	638	3	1	1	NUM
ejpam-6102	638	4	+	+	NUM
ejpam-6102	638	5	µ2|x′|2)n	µ2|x′|2)n	PROPN
ejpam-6102	638	6	dx′dxn	dx′dxn	PROPN
ejpam-6102	638	7	r.	r.	PROPN
ejpam-6102	638	8	almushahhin	almushahhin	PROPN
ejpam-6102	638	9	,	,	PUNCT
ejpam-6102	638	10	m.	m.	PROPN
ejpam-6102	638	11	ben	ben	PROPN
ejpam-6102	638	12	ayed	aye	VERB
ejpam-6102	638	13	/	/	SYM
ejpam-6102	638	14	eur	eur	PROPN
ejpam-6102	638	15	.	.	PUNCT
ejpam-6102	639	1	j.	j.	PROPN
ejpam-6102	639	2	pure	pure	PROPN
ejpam-6102	639	3	appl	appl	PROPN
ejpam-6102	639	4	.	.	PROPN
ejpam-6102	639	5	math	math	PROPN
ejpam-6102	639	6	,	,	PUNCT
ejpam-6102	639	7	18	18	NUM
ejpam-6102	639	8	(	(	PUNCT
ejpam-6102	639	9	2	2	NUM
ejpam-6102	639	10	)	)	PUNCT
ejpam-6102	639	11	(	(	PUNCT
ejpam-6102	639	12	2025	2025	NUM
ejpam-6102	639	13	)	)	PUNCT
ejpam-6102	639	14	,	,	PUNCT
ejpam-6102	639	15	6102	6102	NUM
ejpam-6102	639	16	23	23	NUM
ejpam-6102	639	17	of	of	ADP
ejpam-6102	639	18	31	31	NUM
ejpam-6102	639	19	⩽	⩽	PROPN
ejpam-6102	639	20	c	c	PROPN
ejpam-6102	639	21	∫	∫	PROPN
ejpam-6102	639	22	bn−1(0,ρ	bn−1(0,ρ	ADP
ejpam-6102	639	23	)	)	PUNCT
ejpam-6102	639	24	µn−1	µn−1	ADP
ejpam-6102	639	25	|x′|2	|x′|2	PROPN
ejpam-6102	639	26	(	(	PUNCT
ejpam-6102	639	27	1	1	NUM
ejpam-6102	639	28	+	+	CCONJ
ejpam-6102	639	29	µ2	µ2	PROPN
ejpam-6102	639	30	|x′|2	|x′|2	PROPN
ejpam-6102	639	31	)	)	PUNCT
ejpam-6102	639	32	n	n	X
ejpam-6102	639	33	⩽	⩽	NOUN
ejpam-6102	639	34	c	c	PROPN
ejpam-6102	639	35	µ2	µ2	PROPN
ejpam-6102	639	36	.	.	PUNCT
ejpam-6102	640	1	(	(	PUNCT
ejpam-6102	640	2	75	75	NUM
ejpam-6102	640	3	)	)	PUNCT
ejpam-6102	640	4	thus	thus	ADV
ejpam-6102	640	5	,	,	PUNCT
ejpam-6102	640	6	combining	combine	VERB
ejpam-6102	640	7	(	(	PUNCT
ejpam-6102	640	8	72	72	NUM
ejpam-6102	640	9	)	)	PUNCT
ejpam-6102	640	10	(	(	PUNCT
ejpam-6102	640	11	75	75	NUM
ejpam-6102	640	12	)	)	PUNCT
ejpam-6102	640	13	,	,	PUNCT
ejpam-6102	640	14	the	the	DET
ejpam-6102	640	15	proof	proof	NOUN
ejpam-6102	640	16	of	of	ADP
ejpam-6102	640	17	claim	claim	NOUN
ejpam-6102	640	18	(	(	PUNCT
ejpam-6102	640	19	iv	iv	X
ejpam-6102	640	20	)	)	PUNCT
ejpam-6102	640	21	follows	follow	VERB
ejpam-6102	640	22	.	.	PUNCT
ejpam-6102	641	1	proof	proof	NOUN
ejpam-6102	641	2	of	of	ADP
ejpam-6102	641	3	(	(	PUNCT
ejpam-6102	641	4	v	v	NOUN
ejpam-6102	641	5	):	):	PUNCT
ejpam-6102	641	6	it	it	PRON
ejpam-6102	641	7	can	can	AUX
ejpam-6102	641	8	be	be	AUX
ejpam-6102	641	9	done	do	VERB
ejpam-6102	641	10	in	in	ADP
ejpam-6102	641	11	the	the	DET
ejpam-6102	641	12	same	same	ADJ
ejpam-6102	641	13	way	way	NOUN
ejpam-6102	641	14	than	than	ADP
ejpam-6102	641	15	the	the	DET
ejpam-6102	641	16	proof	proof	NOUN
ejpam-6102	641	17	of	of	ADP
ejpam-6102	641	18	claims	claim	NOUN
ejpam-6102	641	19	(	(	PUNCT
ejpam-6102	641	20	iii	iii	NOUN
ejpam-6102	641	21	)	)	PUNCT
ejpam-6102	641	22	and	and	CCONJ
ejpam-6102	641	23	(	(	PUNCT
ejpam-6102	641	24	iv	iv	X
ejpam-6102	641	25	)	)	PUNCT
ejpam-6102	641	26	.	.	PUNCT
ejpam-6102	642	1	hence	hence	ADV
ejpam-6102	642	2	,	,	PUNCT
ejpam-6102	642	3	we	we	PRON
ejpam-6102	642	4	omit	omit	VERB
ejpam-6102	642	5	it	it	PRON
ejpam-6102	642	6	.	.	PUNCT
ejpam-6102	643	1	lemma	lemma	PROPN
ejpam-6102	643	2	9	9	NUM
ejpam-6102	643	3	.	.	PUNCT
ejpam-6102	644	1	let	let	VERB
ejpam-6102	644	2	a1	a1	NOUN
ejpam-6102	644	3	,	,	PUNCT
ejpam-6102	644	4	a2	a2	NOUN
ejpam-6102	644	5	∈	∈	NOUN
ejpam-6102	644	6	∂ω	∂ω	PROPN
ejpam-6102	644	7	with	with	ADP
ejpam-6102	644	8	|a1	|a1	NOUN
ejpam-6102	644	9	−	−	PROPN
ejpam-6102	645	1	a2|	a2|	ADV
ejpam-6102	645	2	⩾	⩾	PROPN
ejpam-6102	646	1	c	c	NOUN
ejpam-6102	646	2	>	>	PUNCT
ejpam-6102	646	3	0	0	NUM
ejpam-6102	646	4	and	and	CCONJ
ejpam-6102	646	5	µ1	µ1	PROPN
ejpam-6102	646	6	,	,	PUNCT
ejpam-6102	646	7	µ2	µ2	PROPN
ejpam-6102	646	8	be	be	AUX
ejpam-6102	646	9	large	large	ADJ
ejpam-6102	646	10	reals	real	NOUN
ejpam-6102	646	11	.	.	PUNCT
ejpam-6102	647	1	we	we	PRON
ejpam-6102	647	2	have	have	VERB
ejpam-6102	647	3	:	:	PUNCT
ejpam-6102	647	4	(	(	PUNCT
ejpam-6102	647	5	i	i	NOUN
ejpam-6102	647	6	)	)	PUNCT
ejpam-6102	647	7	∫	∫	PROPN
ejpam-6102	648	1	ω	ω	NUM
ejpam-6102	648	2	|∇ωa1,µ1	|∇ωa1,µ1	NOUN
ejpam-6102	648	3	|	|	ADV
ejpam-6102	648	4	|∇ωa2,µ2	|∇ωa2,µ2	NOUN
ejpam-6102	648	5	|	|	ADV
ejpam-6102	648	6	⩽	⩽	PROPN
ejpam-6102	648	7	c	c	PROPN
ejpam-6102	648	8	(	(	PUNCT
ejpam-6102	648	9	µ1µ2)(n−2)/2	µ1µ2)(n−2)/2	PROPN
ejpam-6102	648	10	⩽	⩽	PROPN
ejpam-6102	648	11	c	c	PROPN
ejpam-6102	648	12	µn−2	µn−2	PROPN
ejpam-6102	648	13	1	1	NUM
ejpam-6102	648	14	+	+	CCONJ
ejpam-6102	648	15	c	c	PROPN
ejpam-6102	648	16	µn−2	µn−2	PROPN
ejpam-6102	648	17	2	2	NUM
ejpam-6102	648	18	,	,	PUNCT
ejpam-6102	648	19	(	(	PUNCT
ejpam-6102	648	20	ii	ii	NOUN
ejpam-6102	648	21	)	)	PUNCT
ejpam-6102	648	22	∫	∫	PROPN
ejpam-6102	649	1	ω	ω	PROPN
ejpam-6102	649	2	|∇ωa1,µ1	|∇ωa1,µ1	NOUN
ejpam-6102	649	3	|	|	ADP
ejpam-6102	649	4	∣∣∣∣∇(µ2	∣∣∣∣∇(µ2	PROPN
ejpam-6102	649	5	∂ωa2,µ2	∂ωa2,µ2	NOUN
ejpam-6102	649	6	∂µ2	∂µ2	PROPN
ejpam-6102	649	7	)	)	PUNCT
ejpam-6102	649	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	649	9	⩽	⩽	PROPN
ejpam-6102	649	10	c	c	PROPN
ejpam-6102	649	11	(	(	PUNCT
ejpam-6102	649	12	µ1µ2)(n−2)/2	µ1µ2)(n−2)/2	PROPN
ejpam-6102	649	13	⩽	⩽	PROPN
ejpam-6102	649	14	c	c	PROPN
ejpam-6102	649	15	µn−2	µn−2	PROPN
ejpam-6102	649	16	1	1	NUM
ejpam-6102	649	17	+	+	CCONJ
ejpam-6102	649	18	c	c	PROPN
ejpam-6102	649	19	µn−2	µn−2	PROPN
ejpam-6102	649	20	2	2	NUM
ejpam-6102	649	21	,	,	PUNCT
ejpam-6102	649	22	(	(	PUNCT
ejpam-6102	649	23	iii	iii	NOUN
ejpam-6102	649	24	)	)	PUNCT
ejpam-6102	649	25	∫	∫	PROPN
ejpam-6102	650	1	ω	ω	PROPN
ejpam-6102	650	2	|∇ωa1,µ1	|∇ωa1,µ1	PROPN
ejpam-6102	650	3	|	|	ADV
ejpam-6102	650	4	∣∣∣∣∇	∣∣∣∣∇	PROPN
ejpam-6102	650	5	(	(	PUNCT
ejpam-6102	650	6	1	1	NUM
ejpam-6102	650	7	µ2	µ2	PROPN
ejpam-6102	650	8	∂ωa2,µ2	∂ωa2,µ2	PROPN
ejpam-6102	650	9	∂a2	∂a2	PROPN
ejpam-6102	650	10	)	)	PUNCT
ejpam-6102	650	11	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	650	12	⩽	⩽	PROPN
ejpam-6102	650	13	c	c	PROPN
ejpam-6102	650	14	µ	µ	X
ejpam-6102	650	15	(	(	PUNCT
ejpam-6102	650	16	n−2)/2	n−2)/2	NOUN
ejpam-6102	650	17	1	1	NUM
ejpam-6102	650	18	lnµ2	lnµ2	NOUN
ejpam-6102	650	19	µ	µ	PROPN
ejpam-6102	650	20	n/2	n/2	PRON
ejpam-6102	650	21	2	2	NUM
ejpam-6102	650	22	,	,	PUNCT
ejpam-6102	650	23	(	(	PUNCT
ejpam-6102	650	24	iv	iv	X
ejpam-6102	650	25	)	)	PUNCT
ejpam-6102	650	26	∫	∫	PROPN
ejpam-6102	650	27	ω	ω	NUM
ejpam-6102	651	1	ωa1,µ1ωa2,µ2	ωa1,µ1ωa2,µ2	PROPN
ejpam-6102	651	2	⩽	⩽	PROPN
ejpam-6102	651	3	c	c	PROPN
ejpam-6102	651	4	(	(	PUNCT
ejpam-6102	651	5	µ1µ2)(n−2)/2	µ1µ2)(n−2)/2	PROPN
ejpam-6102	651	6	⩽	⩽	PROPN
ejpam-6102	651	7	c	c	PROPN
ejpam-6102	651	8	µn−2	µn−2	PROPN
ejpam-6102	651	9	1	1	NUM
ejpam-6102	651	10	+	+	CCONJ
ejpam-6102	651	11	c	c	PROPN
ejpam-6102	651	12	µn−2	µn−2	PROPN
ejpam-6102	651	13	2	2	NUM
ejpam-6102	651	14	,	,	PUNCT
ejpam-6102	651	15	(	(	PUNCT
ejpam-6102	651	16	v	v	NOUN
ejpam-6102	651	17	)	)	PUNCT
ejpam-6102	651	18	∫	∫	PROPN
ejpam-6102	651	19	ω	ω	NUM
ejpam-6102	651	20	ωa1,µ1	ωa1,µ1	PROPN
ejpam-6102	651	21	∣∣∣∣µ2	∣∣∣∣µ2	PROPN
ejpam-6102	651	22	∂ωa2,µ2	∂ωa2,µ2	NOUN
ejpam-6102	651	23	∂µ2	∂µ2	PROPN
ejpam-6102	651	24	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	651	25	⩽	⩽	PROPN
ejpam-6102	651	26	c	c	PROPN
ejpam-6102	651	27	(	(	PUNCT
ejpam-6102	651	28	µ1µ2)(n−2)/2	µ1µ2)(n−2)/2	PROPN
ejpam-6102	651	29	⩽	⩽	PROPN
ejpam-6102	651	30	c	c	PROPN
ejpam-6102	651	31	µn−2	µn−2	PROPN
ejpam-6102	651	32	1	1	NUM
ejpam-6102	651	33	+	+	CCONJ
ejpam-6102	651	34	c	c	PROPN
ejpam-6102	651	35	µn−2	µn−2	PROPN
ejpam-6102	651	36	2	2	NUM
ejpam-6102	651	37	,	,	PUNCT
ejpam-6102	651	38	(	(	PUNCT
ejpam-6102	651	39	vi	vi	NOUN
ejpam-6102	651	40	)	)	PUNCT
ejpam-6102	651	41	∫	∫	PROPN
ejpam-6102	652	1	ω	ω	NUM
ejpam-6102	652	2	ωa1,µ1	ωa1,µ1	PROPN
ejpam-6102	652	3	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	652	4	1µ2	1µ2	NUM
ejpam-6102	652	5	∂ωa2,µ2	∂ωa2,µ2	PROPN
ejpam-6102	652	6	∂a2	∂a2	PROPN
ejpam-6102	652	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	652	8	⩽	⩽	PROPN
ejpam-6102	652	9	c	c	PROPN
ejpam-6102	652	10	µ	µ	X
ejpam-6102	652	11	(	(	PUNCT
ejpam-6102	652	12	n−2)/2	n−2)/2	PROPN
ejpam-6102	652	13	1	1	NUM
ejpam-6102	652	14	µ	µ	NOUN
ejpam-6102	652	15	n/2	n/2	PRON
ejpam-6102	652	16	2	2	NUM
ejpam-6102	652	17	⩽	⩽	NOUN
ejpam-6102	652	18	c	c	NOUN
ejpam-6102	652	19	µn−1	µn−1	PROPN
ejpam-6102	652	20	1	1	NUM
ejpam-6102	652	21	+	+	CCONJ
ejpam-6102	652	22	c	c	NOUN
ejpam-6102	652	23	µn−1	µn−1	ADP
ejpam-6102	652	24	2	2	NUM
ejpam-6102	652	25	,	,	PUNCT
ejpam-6102	652	26	(	(	PUNCT
ejpam-6102	652	27	vii	vii	PROPN
ejpam-6102	652	28	)	)	PUNCT
ejpam-6102	652	29	∫	∫	PROPN
ejpam-6102	653	1	ω	ω	PROPN
ejpam-6102	653	2	ω	ω	PROPN
ejpam-6102	654	1	n+2	n+2	NUM
ejpam-6102	655	1	n−2	n−2	PROPN
ejpam-6102	655	2	a1,µ1ωa2,µ2	a1,µ1ωa2,µ2	VERB
ejpam-6102	655	3	⩽	⩽	PROPN
ejpam-6102	655	4	c	c	PROPN
ejpam-6102	655	5	(	(	PUNCT
ejpam-6102	655	6	µ1µ2)(n−2)/2	µ1µ2)(n−2)/2	PROPN
ejpam-6102	655	7	⩽	⩽	PROPN
ejpam-6102	655	8	c	c	PROPN
ejpam-6102	655	9	µn−2	µn−2	PROPN
ejpam-6102	655	10	1	1	NUM
ejpam-6102	655	11	+	+	CCONJ
ejpam-6102	655	12	c	c	PROPN
ejpam-6102	655	13	µn−2	µn−2	PROPN
ejpam-6102	655	14	2	2	NUM
ejpam-6102	655	15	,	,	PUNCT
ejpam-6102	655	16	(	(	PUNCT
ejpam-6102	655	17	viii	viii	NOUN
ejpam-6102	655	18	)	)	PUNCT
ejpam-6102	655	19	∫	∫	PROPN
ejpam-6102	656	1	ω	ω	PROPN
ejpam-6102	656	2	ω	ω	PROPN
ejpam-6102	656	3	n+2	n+2	PROPN
ejpam-6102	657	1	n−2	n−2	PROPN
ejpam-6102	657	2	a1,µ1µ2	a1,µ1µ2	VERB
ejpam-6102	657	3	∣∣∣∣∂ωa2,µ2	∣∣∣∣∂ωa2,µ2	PROPN
ejpam-6102	657	4	∂µ2	∂µ2	PROPN
ejpam-6102	657	5	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	657	6	⩽	⩽	PROPN
ejpam-6102	657	7	c	c	PROPN
ejpam-6102	657	8	(	(	PUNCT
ejpam-6102	657	9	µ1µ2)(n−2)/2	µ1µ2)(n−2)/2	PROPN
ejpam-6102	657	10	⩽	⩽	PROPN
ejpam-6102	657	11	c	c	PROPN
ejpam-6102	657	12	µn−2	µn−2	PROPN
ejpam-6102	657	13	1	1	NUM
ejpam-6102	657	14	+	+	CCONJ
ejpam-6102	657	15	c	c	PROPN
ejpam-6102	657	16	µn−2	µn−2	PROPN
ejpam-6102	657	17	2	2	NUM
ejpam-6102	657	18	,	,	PUNCT
ejpam-6102	657	19	(	(	PUNCT
ejpam-6102	657	20	ix	ix	PROPN
ejpam-6102	657	21	)	)	PUNCT
ejpam-6102	657	22	∫	∫	PROPN
ejpam-6102	658	1	ω	ω	PROPN
ejpam-6102	658	2	ω	ω	PROPN
ejpam-6102	659	1	n+2	n+2	NUM
ejpam-6102	659	2	n−2	n−2	PROPN
ejpam-6102	659	3	a1,µ1	a1,µ1	ADP
ejpam-6102	659	4	1	1	NUM
ejpam-6102	659	5	µ2	µ2	PROPN
ejpam-6102	659	6	∣∣∣∣∂ωa2,µ2	∣∣∣∣∂ωa2,µ2	PROPN
ejpam-6102	659	7	∂a2	∂a2	PROPN
ejpam-6102	659	8	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	659	9	⩽	⩽	PROPN
ejpam-6102	659	10	c	c	PROPN
ejpam-6102	659	11	µ	µ	X
ejpam-6102	659	12	(	(	PUNCT
ejpam-6102	659	13	n−2)/2	n−2)/2	PROPN
ejpam-6102	659	14	1	1	NUM
ejpam-6102	659	15	µ	µ	NOUN
ejpam-6102	659	16	n/2	n/2	PRON
ejpam-6102	659	17	2	2	NUM
ejpam-6102	659	18	⩽	⩽	NOUN
ejpam-6102	659	19	c	c	NOUN
ejpam-6102	659	20	µn−1	µn−1	PROPN
ejpam-6102	659	21	1	1	NUM
ejpam-6102	659	22	+	+	CCONJ
ejpam-6102	659	23	c	c	NOUN
ejpam-6102	659	24	µn−1	µn−1	ADP
ejpam-6102	659	25	2	2	NUM
ejpam-6102	659	26	.	.	PUNCT
ejpam-6102	660	1	proof	proof	NOUN
ejpam-6102	660	2	.	.	PUNCT
ejpam-6102	661	1	we	we	PRON
ejpam-6102	661	2	will	will	AUX
ejpam-6102	661	3	focus	focus	VERB
ejpam-6102	661	4	on	on	ADP
ejpam-6102	661	5	the	the	DET
ejpam-6102	661	6	proof	proof	NOUN
ejpam-6102	661	7	of	of	ADP
ejpam-6102	661	8	the	the	DET
ejpam-6102	661	9	first	first	ADJ
ejpam-6102	661	10	one	one	NUM
ejpam-6102	661	11	and	and	CCONJ
ejpam-6102	661	12	the	the	DET
ejpam-6102	661	13	other	other	ADJ
ejpam-6102	661	14	proofs	proof	NOUN
ejpam-6102	661	15	can	can	AUX
ejpam-6102	661	16	be	be	AUX
ejpam-6102	661	17	done	do	VERB
ejpam-6102	661	18	in	in	ADP
ejpam-6102	661	19	the	the	DET
ejpam-6102	661	20	same	same	ADJ
ejpam-6102	661	21	way	way	NOUN
ejpam-6102	661	22	.	.	PUNCT
ejpam-6102	662	1	note	note	VERB
ejpam-6102	662	2	that	that	SCONJ
ejpam-6102	662	3	∣∣∇ωai,µi|	∣∣∇ωai,µi|	PROPN
ejpam-6102	662	4	∣∣	∣∣	PUNCT
ejpam-6102	663	1	⩽	⩽	PROPN
ejpam-6102	663	2	c	c	PROPN
ejpam-6102	663	3	µ	µ	PROPN
ejpam-6102	663	4	n+2	n+2	NUM
ejpam-6102	663	5	2	2	NUM
ejpam-6102	663	6	|x−	|x−	NOUN
ejpam-6102	663	7	ai|	ai|	NOUN
ejpam-6102	663	8	(	(	PUNCT
ejpam-6102	663	9	1	1	NUM
ejpam-6102	663	10	+	+	CCONJ
ejpam-6102	663	11	µ2	µ2	PROPN
ejpam-6102	663	12	i	i	PRON
ejpam-6102	663	13	|x−	|x−	PROPN
ejpam-6102	663	14	ai|2	ai|2	PROPN
ejpam-6102	663	15	)	)	PUNCT
ejpam-6102	663	16	n/2	n/2	PROPN
ejpam-6102	664	1	⩽	⩽	NOUN
ejpam-6102	664	2	c	c	PROPN
ejpam-6102	664	3	µ	µ	X
ejpam-6102	664	4	(	(	PUNCT
ejpam-6102	664	5	n−2)/2	n−2)/2	ADP
ejpam-6102	664	6	i	i	PRON
ejpam-6102	664	7	|x−	|x−	PROPN
ejpam-6102	664	8	ai|n−1	ai|n−1	PROPN
ejpam-6102	664	9	.	.	PUNCT
ejpam-6102	665	1	thus	thus	ADV
ejpam-6102	665	2	,	,	PUNCT
ejpam-6102	665	3	let	let	VERB
ejpam-6102	665	4	ρ	ρ	NOUN
ejpam-6102	665	5	:	:	PUNCT
ejpam-6102	665	6	=	=	PRON
ejpam-6102	665	7	|a1	|a1	NOUN
ejpam-6102	665	8	−	−	PROPN
ejpam-6102	666	1	a2|	a2|	PROPN
ejpam-6102	666	2	/2	/2	PUNCT
ejpam-6102	666	3	,	,	PUNCT
ejpam-6102	666	4	it	it	PRON
ejpam-6102	666	5	holds	hold	VERB
ejpam-6102	666	6	:	:	PUNCT
ejpam-6102	666	7	∫	∫	PROPN
ejpam-6102	666	8	ω	ω	PROPN
ejpam-6102	666	9	|∇ωa1,µ1	|∇ωa1,µ1	NOUN
ejpam-6102	666	10	|	|	ADV
ejpam-6102	666	11	|∇ωa2,µ2	|∇ωa2,µ2	NOUN
ejpam-6102	666	12	|	|	ADV
ejpam-6102	666	13	⩽	⩽	PROPN
ejpam-6102	666	14	1	1	NUM
ejpam-6102	666	15	µ	µ	X
ejpam-6102	666	16	(	(	PUNCT
ejpam-6102	666	17	n−2)/2	n−2)/2	PROPN
ejpam-6102	666	18	1	1	NUM
ejpam-6102	666	19	µ	µ	X
ejpam-6102	666	20	(	(	PUNCT
ejpam-6102	666	21	n−2)/2	n−2)/2	ADJ
ejpam-6102	666	22	2	2	NUM
ejpam-6102	666	23	∑	∑	NOUN
ejpam-6102	666	24	i=1,2	i=1,2	ADJ
ejpam-6102	666	25	∫	∫	NOUN
ejpam-6102	666	26	b(ai	b(ai	PROPN
ejpam-6102	666	27	,	,	PUNCT
ejpam-6102	666	28	ρ	ρ	PROPN
ejpam-6102	666	29	)	)	PUNCT
ejpam-6102	666	30	dx	dx	PROPN
ejpam-6102	666	31	|x−	|x−	PROPN
ejpam-6102	666	32	ai|n−1	ai|n−1	PROPN
ejpam-6102	667	1	+	+	CCONJ
ejpam-6102	667	2	∫	∫	PROPN
ejpam-6102	667	3	ω\∪b(ai	ω\∪b(ai	PROPN
ejpam-6102	667	4	,	,	PUNCT
ejpam-6102	667	5	ρ	ρ	NOUN
ejpam-6102	667	6	)	)	PUNCT
ejpam-6102	667	7	1dx	1dx	NOUN
ejpam-6102	668	1			PROPN
ejpam-6102	668	2	.	.	PUNCT
ejpam-6102	669	1	⩽	⩽	PROPN
ejpam-6102	669	2	c	c	PROPN
ejpam-6102	669	3	(	(	PUNCT
ejpam-6102	669	4	µ1µ2	µ1µ2	NOUN
ejpam-6102	669	5	)	)	PUNCT
ejpam-6102	669	6	(	(	PUNCT
ejpam-6102	669	7	n−2)/2	n−2)/2	ADJ
ejpam-6102	669	8	⩽	⩽	PROPN
ejpam-6102	669	9	c	c	PROPN
ejpam-6102	669	10	(	(	PUNCT
ejpam-6102	669	11	1	1	NUM
ejpam-6102	669	12	µn−2	µn−2	PROPN
ejpam-6102	669	13	1	1	NUM
ejpam-6102	669	14	+	+	SYM
ejpam-6102	669	15	1	1	NUM
ejpam-6102	669	16	µn−2	µn−2	PROPN
ejpam-6102	669	17	2	2	NUM
ejpam-6102	669	18	)	)	PUNCT
ejpam-6102	669	19	.	.	PUNCT
ejpam-6102	670	1	hence	hence	ADV
ejpam-6102	670	2	,	,	PUNCT
ejpam-6102	670	3	the	the	DET
ejpam-6102	670	4	proof	proof	NOUN
ejpam-6102	670	5	of	of	ADP
ejpam-6102	670	6	claim	claim	NOUN
ejpam-6102	670	7	(	(	PUNCT
ejpam-6102	670	8	i	i	NOUN
ejpam-6102	670	9	)	)	PUNCT
ejpam-6102	670	10	is	be	AUX
ejpam-6102	670	11	completed	complete	VERB
ejpam-6102	670	12	.	.	PUNCT
ejpam-6102	671	1	r.	r.	PROPN
ejpam-6102	671	2	almushahhin	almushahhin	PROPN
ejpam-6102	671	3	,	,	PUNCT
ejpam-6102	671	4	m.	m.	PROPN
ejpam-6102	671	5	ben	ben	PROPN
ejpam-6102	671	6	ayed	aye	VERB
ejpam-6102	671	7	/	/	SYM
ejpam-6102	671	8	eur	eur	PROPN
ejpam-6102	671	9	.	.	PUNCT
ejpam-6102	672	1	j.	j.	PROPN
ejpam-6102	672	2	pure	pure	PROPN
ejpam-6102	672	3	appl	appl	PROPN
ejpam-6102	672	4	.	.	PROPN
ejpam-6102	672	5	math	math	PROPN
ejpam-6102	672	6	,	,	PUNCT
ejpam-6102	672	7	18	18	NUM
ejpam-6102	672	8	(	(	PUNCT
ejpam-6102	672	9	2	2	NUM
ejpam-6102	672	10	)	)	PUNCT
ejpam-6102	672	11	(	(	PUNCT
ejpam-6102	672	12	2025	2025	NUM
ejpam-6102	672	13	)	)	PUNCT
ejpam-6102	672	14	,	,	PUNCT
ejpam-6102	672	15	6102	6102	NUM
ejpam-6102	672	16	24	24	NUM
ejpam-6102	672	17	of	of	ADP
ejpam-6102	672	18	31	31	NUM
ejpam-6102	672	19	7.2	7.2	NUM
ejpam-6102	672	20	.	.	PUNCT
ejpam-6102	673	1	coercivity	coercivity	NOUN
ejpam-6102	673	2	of	of	ADP
ejpam-6102	673	3	the	the	DET
ejpam-6102	673	4	quadratic	quadratic	ADJ
ejpam-6102	673	5	form	form	NOUN
ejpam-6102	673	6	the	the	DET
ejpam-6102	673	7	goal	goal	NOUN
ejpam-6102	673	8	of	of	ADP
ejpam-6102	673	9	this	this	DET
ejpam-6102	673	10	subsection	subsection	NOUN
ejpam-6102	673	11	is	be	AUX
ejpam-6102	673	12	to	to	PART
ejpam-6102	673	13	prove	prove	VERB
ejpam-6102	673	14	proposition	proposition	NOUN
ejpam-6102	673	15	1	1	NUM
ejpam-6102	673	16	.	.	PUNCT
ejpam-6102	673	17	to	to	ADP
ejpam-6102	673	18	this	this	DET
ejpam-6102	673	19	aim	aim	NOUN
ejpam-6102	673	20	,	,	PUNCT
ejpam-6102	673	21	for	for	ADP
ejpam-6102	673	22	µ	µ	NOUN
ejpam-6102	673	23	>	>	SYM
ejpam-6102	673	24	0	0	PUNCT
ejpam-6102	674	1	and	and	CCONJ
ejpam-6102	674	2	x	x	SYM
ejpam-6102	674	3	=	=	SYM
ejpam-6102	674	4	(	(	PUNCT
ejpam-6102	674	5	x1	x1	PROPN
ejpam-6102	674	6	,	,	PUNCT
ejpam-6102	674	7	.	.	PUNCT
ejpam-6102	674	8	.	.	PUNCT
ejpam-6102	674	9	.	.	PUNCT
ejpam-6102	675	1	,	,	PUNCT
ejpam-6102	675	2	xn	xn	X
ejpam-6102	675	3	)	)	PUNCT
ejpam-6102	675	4	∈	∈	PROPN
ejpam-6102	675	5	rn	rn	PROPN
ejpam-6102	675	6	,	,	PUNCT
ejpam-6102	675	7	we	we	PRON
ejpam-6102	675	8	denote	denote	VERB
ejpam-6102	675	9	by	by	ADP
ejpam-6102	675	10	ψ1(x	ψ1(x	PROPN
ejpam-6102	675	11	)	)	PUNCT
ejpam-6102	675	12	:	:	PUNCT
ejpam-6102	676	1	=	=	PUNCT
ejpam-6102	676	2	ω0,µ(x	ω0,µ(x	NOUN
ejpam-6102	676	3	)	)	PUNCT
ejpam-6102	676	4	:	:	PUNCT
ejpam-6102	677	1	=	=	X
ejpam-6102	677	2	β0	β0	PROPN
ejpam-6102	677	3	µ(n−2)/2	µ(n−2)/2	PROPN
ejpam-6102	677	4	(	(	PUNCT
ejpam-6102	677	5	1	1	NUM
ejpam-6102	677	6	+	+	CCONJ
ejpam-6102	677	7	µ2|x|2)(n−2)/2	µ2|x|2)(n−2)/2	NOUN
ejpam-6102	677	8	,	,	PUNCT
ejpam-6102	677	9	ψ2(x	ψ2(x	PROPN
ejpam-6102	677	10	)	)	PUNCT
ejpam-6102	677	11	:	:	PUNCT
ejpam-6102	677	12	=	=	PUNCT
ejpam-6102	678	1	µ	µ	X
ejpam-6102	678	2	∂ω0,µ	∂ω0,µ	ADJ
ejpam-6102	678	3	∂µ	∂µ	PROPN
ejpam-6102	678	4	(	(	PUNCT
ejpam-6102	678	5	x	x	X
ejpam-6102	678	6	)	)	PUNCT
ejpam-6102	678	7	=	=	PUNCT
ejpam-6102	678	8	n−	n−	NOUN
ejpam-6102	678	9	2	2	NUM
ejpam-6102	678	10	2	2	NUM
ejpam-6102	678	11	β0	β0	NOUN
ejpam-6102	678	12	µ(n−2)/2	µ(n−2)/2	PROPN
ejpam-6102	678	13	(	(	PUNCT
ejpam-6102	678	14	1−	1−	NUM
ejpam-6102	678	15	µ2|x|2	µ2|x|2	PROPN
ejpam-6102	678	16	)	)	PUNCT
ejpam-6102	678	17	(	(	PUNCT
ejpam-6102	678	18	1	1	NUM
ejpam-6102	678	19	+	+	NUM
ejpam-6102	678	20	µ2|x|2)n/2	µ2|x|2)n/2	NOUN
ejpam-6102	678	21	,	,	PUNCT
ejpam-6102	678	22	ψj(x	ψj(x	PUNCT
ejpam-6102	678	23	)	)	PUNCT
ejpam-6102	678	24	:	:	PUNCT
ejpam-6102	678	25	=	=	SYM
ejpam-6102	678	26	(	(	PUNCT
ejpam-6102	678	27	n−	n−	NOUN
ejpam-6102	678	28	2)β0	2)β0	ADJ
ejpam-6102	678	29	µn/2xj−2	µn/2xj−2	NOUN
ejpam-6102	678	30	(	(	PUNCT
ejpam-6102	678	31	1	1	NUM
ejpam-6102	678	32	+	+	NUM
ejpam-6102	678	33	µ2|x|2)n/2	µ2|x|2)n/2	NOUN
ejpam-6102	678	34	,	,	PUNCT
ejpam-6102	678	35	for	for	ADP
ejpam-6102	678	36	j	j	PROPN
ejpam-6102	678	37	∈	∈	PROPN
ejpam-6102	678	38	{	{	PUNCT
ejpam-6102	678	39	3	3	NUM
ejpam-6102	678	40	,	,	PUNCT
ejpam-6102	678	41	·	·	PUNCT
ejpam-6102	678	42	·	·	PUNCT
ejpam-6102	678	43	·	·	PUNCT
ejpam-6102	678	44	,	,	PUNCT
ejpam-6102	678	45	n+	n+	ADP
ejpam-6102	678	46	2	2	NUM
ejpam-6102	678	47	}	}	PUNCT
ejpam-6102	678	48	.	.	PUNCT
ejpam-6102	679	1	(	(	PUNCT
ejpam-6102	679	2	76	76	NUM
ejpam-6102	679	3	)	)	PUNCT
ejpam-6102	679	4	we	we	PRON
ejpam-6102	679	5	begin	begin	VERB
ejpam-6102	679	6	by	by	ADP
ejpam-6102	679	7	the	the	DET
ejpam-6102	679	8	following	follow	VERB
ejpam-6102	679	9	lemma	lemma	PROPN
ejpam-6102	679	10	:	:	PUNCT
ejpam-6102	679	11	lemma	lemma	PROPN
ejpam-6102	679	12	10	10	NUM
ejpam-6102	679	13	.	.	PUNCT
ejpam-6102	680	1	let	let	VERB
ejpam-6102	680	2	ρ	ρ	PROPN
ejpam-6102	680	3	>	>	X
ejpam-6102	680	4	0	0	PUNCT
ejpam-6102	680	5	be	be	AUX
ejpam-6102	680	6	a	a	DET
ejpam-6102	680	7	small	small	ADJ
ejpam-6102	680	8	radius	radius	NOUN
ejpam-6102	680	9	and	and	CCONJ
ejpam-6102	680	10	b+	b+	ADP
ejpam-6102	680	11	ρ	ρ	NOUN
ejpam-6102	680	12	:	:	PUNCT
ejpam-6102	680	13	=	=	X
ejpam-6102	680	14	{	{	PUNCT
ejpam-6102	680	15	x	x	X
ejpam-6102	680	16	:	:	PUNCT
ejpam-6102	680	17	=	=	SYM
ejpam-6102	680	18	(	(	PUNCT
ejpam-6102	680	19	x′	x′	PROPN
ejpam-6102	680	20	,	,	PUNCT
ejpam-6102	680	21	xn	xn	X
ejpam-6102	680	22	)	)	PUNCT
ejpam-6102	680	23	∈	∈	PROPN
ejpam-6102	680	24	rn−1	rn−1	PROPN
ejpam-6102	680	25	×	×	NOUN
ejpam-6102	680	26	r	r	NOUN
ejpam-6102	680	27	:	:	PUNCT
ejpam-6102	680	28	|x|	|x|	PROPN
ejpam-6102	680	29	<	<	X
ejpam-6102	680	30	ρ	ρ	PROPN
ejpam-6102	680	31	and	and	CCONJ
ejpam-6102	680	32	xn	xn	PROPN
ejpam-6102	680	33	>	>	X
ejpam-6102	680	34	0	0	NUM
ejpam-6102	680	35	}	}	PUNCT
ejpam-6102	680	36	.	.	PUNCT
ejpam-6102	681	1	for	for	ADP
ejpam-6102	681	2	µ	µ	X
ejpam-6102	681	3	large	large	ADJ
ejpam-6102	681	4	and	and	CCONJ
ejpam-6102	681	5	γ̄	γ̄	PROPN
ejpam-6102	681	6	>	>	X
ejpam-6102	681	7	0	0	PROPN
ejpam-6102	681	8	,	,	PUNCT
ejpam-6102	681	9	let	let	VERB
ejpam-6102	681	10	us	we	PRON
ejpam-6102	681	11	define	define	VERB
ejpam-6102	681	12	q+(v	q+(v	NOUN
ejpam-6102	681	13	)	)	PUNCT
ejpam-6102	681	14	:	:	PUNCT
ejpam-6102	682	1	=	=	SYM
ejpam-6102	682	2	∫	∫	PROPN
ejpam-6102	682	3	b+	b+	X
ejpam-6102	682	4	ρ	ρ	X
ejpam-6102	682	5	|∇v|2	|∇v|2	X
ejpam-6102	682	6	+	+	CCONJ
ejpam-6102	682	7	γ̄	γ̄	PROPN
ejpam-6102	682	8	∫	∫	PROPN
ejpam-6102	682	9	b+	b+	PUNCT
ejpam-6102	682	10	ρ	ρ	PROPN
ejpam-6102	682	11	v2	v2	PROPN
ejpam-6102	682	12	−	−	PROPN
ejpam-6102	682	13	n+	n+	NOUN
ejpam-6102	682	14	2	2	NUM
ejpam-6102	682	15	n−	n−	NOUN
ejpam-6102	682	16	2	2	NUM
ejpam-6102	682	17	∫	∫	NOUN
ejpam-6102	682	18	b+	b+	X
ejpam-6102	682	19	ρ	ρ	PROPN
ejpam-6102	682	20	ω	ω	PROPN
ejpam-6102	682	21	4	4	NUM
ejpam-6102	682	22	n−2	n−2	PROPN
ejpam-6102	682	23	0,µ	0,µ	PROPN
ejpam-6102	682	24	v2	v2	NOUN
ejpam-6102	682	25	then	then	ADV
ejpam-6102	682	26	there	there	PRON
ejpam-6102	682	27	exists	exist	VERB
ejpam-6102	682	28	a	a	DET
ejpam-6102	682	29	constant	constant	ADJ
ejpam-6102	682	30	β1	β1	NOUN
ejpam-6102	682	31	>	>	X
ejpam-6102	682	32	0	0	NUM
ejpam-6102	683	1	such	such	ADJ
ejpam-6102	683	2	that	that	SCONJ
ejpam-6102	683	3	q+(v	q+(v	NOUN
ejpam-6102	683	4	)	)	PUNCT
ejpam-6102	683	5	⩾	⩾	NOUN
ejpam-6102	683	6	β1	β1	PROPN
ejpam-6102	683	7	(	(	PUNCT
ejpam-6102	683	8	∫	∫	PROPN
ejpam-6102	683	9	b+	b+	X
ejpam-6102	683	10	ρ	ρ	X
ejpam-6102	683	11	|∇v|2	|∇v|2	X
ejpam-6102	684	1	+	+	CCONJ
ejpam-6102	684	2	γ̄	γ̄	PROPN
ejpam-6102	684	3	∫	∫	PROPN
ejpam-6102	684	4	b+	b+	VERB
ejpam-6102	684	5	ρ	ρ	PROPN
ejpam-6102	684	6	v2	v2	PROPN
ejpam-6102	684	7	)	)	PUNCT
ejpam-6102	684	8	∀v	∀v	PROPN
ejpam-6102	684	9	∈	∈	PROPN
ejpam-6102	684	10	e+	e+	VERB
ejpam-6102	684	11	µ	µ	NOUN
ejpam-6102	684	12	,	,	PUNCT
ejpam-6102	684	13	where	where	SCONJ
ejpam-6102	684	14	e+	e+	VERB
ejpam-6102	684	15	µ	µ	X
ejpam-6102	684	16	:	:	PUNCT
ejpam-6102	684	17	=	=	SYM
ejpam-6102	684	18	{	{	PUNCT
ejpam-6102	684	19	v	v	NUM
ejpam-6102	684	20	∈	∈	PROPN
ejpam-6102	684	21	h1	h1	NOUN
ejpam-6102	684	22	(	(	PUNCT
ejpam-6102	684	23	b+	b+	ADP
ejpam-6102	684	24	ρ	ρ	PROPN
ejpam-6102	684	25	)	)	PUNCT
ejpam-6102	684	26	:	:	PUNCT
ejpam-6102	685	1	∫	∫	PROPN
ejpam-6102	685	2	b+	b+	X
ejpam-6102	685	3	ρ	ρ	PROPN
ejpam-6102	685	4	∇v	∇v	PROPN
ejpam-6102	685	5	·	·	PUNCT
ejpam-6102	685	6	∇ψj	∇ψj	ADJ
ejpam-6102	685	7	=	=	NOUN
ejpam-6102	685	8	0	0	NUM
ejpam-6102	685	9	∀j	∀j	PROPN
ejpam-6102	685	10	∈	∈	PROPN
ejpam-6102	685	11	{	{	PUNCT
ejpam-6102	685	12	1	1	NUM
ejpam-6102	685	13	,	,	PUNCT
ejpam-6102	685	14	.	.	PUNCT
ejpam-6102	685	15	.	.	PUNCT
ejpam-6102	685	16	.	.	PUNCT
ejpam-6102	686	1	,	,	PUNCT
ejpam-6102	686	2	n+	n+	ADP
ejpam-6102	686	3	1	1	X
ejpam-6102	686	4	}	}	PUNCT
ejpam-6102	686	5	}	}	PUNCT
ejpam-6102	686	6	.	.	PUNCT
ejpam-6102	687	1	proof	proof	NOUN
ejpam-6102	687	2	.	.	PUNCT
ejpam-6102	688	1	let	let	VERB
ejpam-6102	688	2	us	we	PRON
ejpam-6102	688	3	introduce	introduce	VERB
ejpam-6102	688	4	the	the	DET
ejpam-6102	688	5	function	function	NOUN
ejpam-6102	688	6	ṽ	ṽ	PROPN
ejpam-6102	688	7	defined	define	VERB
ejpam-6102	688	8	on	on	ADP
ejpam-6102	688	9	b(0	b(0	PROPN
ejpam-6102	688	10	,	,	PUNCT
ejpam-6102	688	11	ρ	ρ	NOUN
ejpam-6102	688	12	)	)	PUNCT
ejpam-6102	688	13	by	by	ADP
ejpam-6102	688	14	for	for	ADP
ejpam-6102	688	15	y	y	PROPN
ejpam-6102	688	16	:	:	PUNCT
ejpam-6102	688	17	=	=	SYM
ejpam-6102	688	18	(	(	PUNCT
ejpam-6102	688	19	y′	y′	NUM
ejpam-6102	688	20	,	,	PUNCT
ejpam-6102	688	21	yn	yn	NOUN
ejpam-6102	688	22	)	)	PUNCT
ejpam-6102	688	23	∈	∈	PROPN
ejpam-6102	688	24	b(0	b(0	PROPN
ejpam-6102	688	25	,	,	PUNCT
ejpam-6102	688	26	ρ	ρ	NOUN
ejpam-6102	688	27	)	)	PUNCT
ejpam-6102	688	28	,	,	PUNCT
ejpam-6102	688	29	ṽ(y	ṽ(y	PROPN
ejpam-6102	688	30	)	)	PUNCT
ejpam-6102	688	31	:	:	PUNCT
ejpam-6102	689	1	=	=	PRON
ejpam-6102	689	2	{	{	PUNCT
ejpam-6102	689	3	v(y	v(y	PROPN
ejpam-6102	689	4	)	)	PUNCT
ejpam-6102	689	5	if	if	SCONJ
ejpam-6102	689	6	yn	yn	PROPN
ejpam-6102	689	7	>	>	X
ejpam-6102	689	8	0	0	PROPN
ejpam-6102	689	9	,	,	PUNCT
ejpam-6102	689	10	v	v	NOUN
ejpam-6102	689	11	(	(	PUNCT
ejpam-6102	689	12	y′,−yn	y′,−yn	NOUN
ejpam-6102	689	13	)	)	PUNCT
ejpam-6102	689	14	if	if	SCONJ
ejpam-6102	689	15	yn	yn	PRON
ejpam-6102	689	16	<	<	X
ejpam-6102	689	17	0	0	X
ejpam-6102	689	18	.	.	PUNCT
ejpam-6102	689	19	easy	easy	ADJ
ejpam-6102	689	20	computations	computation	NOUN
ejpam-6102	689	21	imply	imply	VERB
ejpam-6102	689	22	that	that	SCONJ
ejpam-6102	689	23	ṽ	ṽ	PROPN
ejpam-6102	689	24	∈	∈	PROPN
ejpam-6102	689	25	h1	h1	NOUN
ejpam-6102	689	26	(	(	PUNCT
ejpam-6102	689	27	b(0	b(0	PROPN
ejpam-6102	689	28	,	,	PUNCT
ejpam-6102	689	29	ρ	ρ	NOUN
ejpam-6102	689	30	)	)	PUNCT
ejpam-6102	689	31	)	)	PUNCT
ejpam-6102	689	32	,	,	PUNCT
ejpam-6102	689	33	2q+(v	2q+(v	NUM
ejpam-6102	689	34	)	)	PUNCT
ejpam-6102	689	35	=	=	SYM
ejpam-6102	689	36	q̃+(ṽ	q̃+(ṽ	PROPN
ejpam-6102	689	37	)	)	PUNCT
ejpam-6102	689	38	:	:	PUNCT
ejpam-6102	689	39	=	=	SYM
ejpam-6102	689	40	∫	∫	PROPN
ejpam-6102	689	41	b(0,ρ	b(0,ρ	NUM
ejpam-6102	689	42	)	)	PUNCT
ejpam-6102	689	43	|∇ṽ|2	|∇ṽ|2	PROPN
ejpam-6102	690	1	+	+	CCONJ
ejpam-6102	690	2	γ̄	γ̄	PROPN
ejpam-6102	690	3	∫	∫	PROPN
ejpam-6102	690	4	b(0,ρ	b(0,ρ	PROPN
ejpam-6102	690	5	)	)	PUNCT
ejpam-6102	690	6	(	(	PUNCT
ejpam-6102	690	7	ṽ)2	ṽ)2	ADV
ejpam-6102	690	8	−	−	NOUN
ejpam-6102	690	9	n+	n+	NOUN
ejpam-6102	690	10	2	2	NUM
ejpam-6102	690	11	n−	n−	NOUN
ejpam-6102	690	12	2	2	NUM
ejpam-6102	690	13	∫	∫	NOUN
ejpam-6102	690	14	b(0,ρ	b(0,ρ	PROPN
ejpam-6102	690	15	)	)	PUNCT
ejpam-6102	690	16	ω	ω	PROPN
ejpam-6102	690	17	4	4	NUM
ejpam-6102	690	18	n−2	n−2	PROPN
ejpam-6102	690	19	0,µ	0,µ	PROPN
ejpam-6102	690	20	ṽ2	ṽ2	PROPN
ejpam-6102	690	21	.	.	PUNCT
ejpam-6102	691	1	(	(	PUNCT
ejpam-6102	691	2	77	77	NUM
ejpam-6102	691	3	)	)	PUNCT
ejpam-6102	691	4	notice	notice	VERB
ejpam-6102	691	5	that	that	SCONJ
ejpam-6102	691	6	the	the	DET
ejpam-6102	691	7	function	function	NOUN
ejpam-6102	691	8	q̃+	q̃+	PROPN
ejpam-6102	691	9	is	be	AUX
ejpam-6102	691	10	a	a	DET
ejpam-6102	691	11	positive	positive	ADJ
ejpam-6102	691	12	definite	definite	ADJ
ejpam-6102	691	13	quadratic	quadratic	ADJ
ejpam-6102	691	14	form	form	NOUN
ejpam-6102	691	15	on	on	ADP
ejpam-6102	691	16	the	the	DET
ejpam-6102	691	17	space	space	NOUN
ejpam-6102	691	18	e0,µ	e0,µ	PROPN
ejpam-6102	691	19	:	:	PUNCT
ejpam-6102	691	20	=	=	SYM
ejpam-6102	691	21	{	{	PUNCT
ejpam-6102	691	22	v	v	NUM
ejpam-6102	691	23	∈	∈	PROPN
ejpam-6102	691	24	h1	h1	NOUN
ejpam-6102	691	25	(	(	PUNCT
ejpam-6102	691	26	b(0	b(0	PROPN
ejpam-6102	691	27	,	,	PUNCT
ejpam-6102	691	28	ρ	ρ	NOUN
ejpam-6102	691	29	)	)	PUNCT
ejpam-6102	691	30	)	)	PUNCT
ejpam-6102	691	31	:	:	PUNCT
ejpam-6102	691	32	∫	∫	PROPN
ejpam-6102	691	33	b(0,ρ	b(0,ρ	SYM
ejpam-6102	691	34	)	)	PUNCT
ejpam-6102	692	1	∇v∇ψj	∇v∇ψj	NOUN
ejpam-6102	692	2	=	=	SYM
ejpam-6102	692	3	0	0	NUM
ejpam-6102	692	4	∀j	∀j	NOUN
ejpam-6102	692	5	=	=	SYM
ejpam-6102	692	6	1	1	NUM
ejpam-6102	692	7	,	,	PUNCT
ejpam-6102	692	8	.	.	PUNCT
ejpam-6102	692	9	.	.	PUNCT
ejpam-6102	692	10	.	.	PUNCT
ejpam-6102	693	1	,	,	PUNCT
ejpam-6102	693	2	n+	n+	ADP
ejpam-6102	693	3	2	2	X
ejpam-6102	693	4	}	}	PUNCT
ejpam-6102	693	5	,	,	PUNCT
ejpam-6102	693	6	(	(	PUNCT
ejpam-6102	693	7	see	see	VERB
ejpam-6102	693	8	proposition	proposition	NOUN
ejpam-6102	693	9	1	1	NUM
ejpam-6102	693	10	of	of	ADP
ejpam-6102	693	11	[	[	X
ejpam-6102	693	12	32	32	NUM
ejpam-6102	693	13	]	]	PUNCT
ejpam-6102	693	14	and	and	CCONJ
ejpam-6102	693	15	equation	equation	NOUN
ejpam-6102	693	16	(	(	PUNCT
ejpam-6102	693	17	19	19	NUM
ejpam-6102	693	18	)	)	PUNCT
ejpam-6102	693	19	by	by	ADP
ejpam-6102	693	20	taking	take	VERB
ejpam-6102	693	21	ω	ω	PROPN
ejpam-6102	693	22	=	=	SYM
ejpam-6102	693	23	b	b	PROPN
ejpam-6102	693	24	(	(	PUNCT
ejpam-6102	693	25	0	0	NUM
ejpam-6102	693	26	,	,	PUNCT
ejpam-6102	693	27	1	1	NUM
ejpam-6102	693	28	)	)	PUNCT
ejpam-6102	693	29	,	,	PUNCT
ejpam-6102	694	1	k	k	PROPN
ejpam-6102	694	2	=	=	PUNCT
ejpam-6102	694	3	γ̄	γ̄	PROPN
ejpam-6102	694	4	and	and	CCONJ
ejpam-6102	694	5	n	n	CCONJ
ejpam-6102	694	6	=	=	NOUN
ejpam-6102	694	7	1	1	NUM
ejpam-6102	694	8	)	)	PUNCT
ejpam-6102	694	9	.	.	PUNCT
ejpam-6102	695	1	this	this	PRON
ejpam-6102	695	2	implies	imply	VERB
ejpam-6102	695	3	that	that	SCONJ
ejpam-6102	695	4	there	there	PRON
ejpam-6102	695	5	exists	exist	VERB
ejpam-6102	695	6	a	a	DET
ejpam-6102	695	7	constant	constant	ADJ
ejpam-6102	695	8	β0	β0	NOUN
ejpam-6102	695	9	>	>	X
ejpam-6102	695	10	0	0	NUM
ejpam-6102	695	11	such	such	ADJ
ejpam-6102	695	12	that	that	DET
ejpam-6102	695	13	q̃+(w	q̃+(w	X
ejpam-6102	695	14	)	)	PUNCT
ejpam-6102	695	15	⩾	⩾	PROPN
ejpam-6102	695	16	β0∥w∥h1(b(0,ρ	β0∥w∥h1(b(0,ρ	PROPN
ejpam-6102	695	17	)	)	PUNCT
ejpam-6102	695	18	)	)	PUNCT
ejpam-6102	695	19	∀w	∀w	X
ejpam-6102	695	20	∈	∈	PROPN
ejpam-6102	695	21	e0,µ.	e0,µ.	NOUN
ejpam-6102	695	22	(	(	PUNCT
ejpam-6102	695	23	78	78	NUM
ejpam-6102	695	24	)	)	PUNCT
ejpam-6102	695	25	r.	r.	PROPN
ejpam-6102	695	26	almushahhin	almushahhin	PROPN
ejpam-6102	695	27	,	,	PUNCT
ejpam-6102	695	28	m.	m.	PROPN
ejpam-6102	695	29	ben	ben	PROPN
ejpam-6102	695	30	ayed	aye	VERB
ejpam-6102	695	31	/	/	SYM
ejpam-6102	695	32	eur	eur	PROPN
ejpam-6102	695	33	.	.	PUNCT
ejpam-6102	696	1	j.	j.	PROPN
ejpam-6102	696	2	pure	pure	PROPN
ejpam-6102	696	3	appl	appl	PROPN
ejpam-6102	696	4	.	.	PROPN
ejpam-6102	696	5	math	math	PROPN
ejpam-6102	696	6	,	,	PUNCT
ejpam-6102	696	7	18	18	NUM
ejpam-6102	696	8	(	(	PUNCT
ejpam-6102	696	9	2	2	NUM
ejpam-6102	696	10	)	)	PUNCT
ejpam-6102	696	11	(	(	PUNCT
ejpam-6102	696	12	2025	2025	NUM
ejpam-6102	696	13	)	)	PUNCT
ejpam-6102	696	14	,	,	PUNCT
ejpam-6102	696	15	6102	6102	NUM
ejpam-6102	696	16	25	25	NUM
ejpam-6102	696	17	of	of	ADP
ejpam-6102	696	18	31	31	NUM
ejpam-6102	696	19	in	in	ADP
ejpam-6102	696	20	the	the	DET
ejpam-6102	696	21	following	following	NOUN
ejpam-6102	696	22	,	,	PUNCT
ejpam-6102	696	23	we	we	PRON
ejpam-6102	696	24	will	will	AUX
ejpam-6102	696	25	prove	prove	VERB
ejpam-6102	696	26	that	that	SCONJ
ejpam-6102	696	27	ṽ	ṽ	PROPN
ejpam-6102	696	28	∈	∈	PROPN
ejpam-6102	696	29	e0,µ.	e0,µ.	NOUN
ejpam-6102	696	30	for	for	ADP
ejpam-6102	696	31	this	this	DET
ejpam-6102	696	32	aim	aim	NOUN
ejpam-6102	696	33	,	,	PUNCT
ejpam-6102	696	34	for	for	ADP
ejpam-6102	696	35	1	1	NUM
ejpam-6102	696	36	⩽	⩽	PROPN
ejpam-6102	696	37	j	j	PROPN
ejpam-6102	696	38	⩽	⩽	PROPN
ejpam-6102	696	39	n+	n+	PUNCT
ejpam-6102	696	40	1	1	NUM
ejpam-6102	696	41	,	,	PUNCT
ejpam-6102	696	42	we	we	PRON
ejpam-6102	696	43	compute∫	compute∫	VERB
ejpam-6102	696	44	b(0,ρ	b(0,ρ	NOUN
ejpam-6102	696	45	)	)	PUNCT
ejpam-6102	696	46	∇ṽ∇ψj	∇ṽ∇ψj	NOUN
ejpam-6102	696	47	=	=	SYM
ejpam-6102	696	48	2	2	NUM
ejpam-6102	696	49	∫	∫	NOUN
ejpam-6102	696	50	b+	b+	X
ejpam-6102	696	51	ρ	ρ	X
ejpam-6102	696	52	∇v∇ψj	∇v∇ψj	NOUN
ejpam-6102	696	53	=	=	SYM
ejpam-6102	696	54	0	0	NUM
ejpam-6102	696	55	,	,	PUNCT
ejpam-6102	696	56	since	since	SCONJ
ejpam-6102	696	57	v	v	NUM
ejpam-6102	696	58	∈	∈	PROPN
ejpam-6102	696	59	e+	e+	PUNCT
ejpam-6102	696	60	µ	µ	NOUN
ejpam-6102	696	61	.	.	PUNCT
ejpam-6102	697	1	now	now	ADV
ejpam-6102	697	2	,	,	PUNCT
ejpam-6102	697	3	for	for	ADP
ejpam-6102	697	4	j	j	PROPN
ejpam-6102	697	5	=	=	SYM
ejpam-6102	697	6	n+	n+	NUM
ejpam-6102	697	7	2	2	NUM
ejpam-6102	697	8	,	,	PUNCT
ejpam-6102	697	9	observe	observe	VERB
ejpam-6102	697	10	that	that	SCONJ
ejpam-6102	697	11	(	(	PUNCT
ejpam-6102	697	12	by	by	ADP
ejpam-6102	697	13	easy	easy	ADJ
ejpam-6102	697	14	computations	computation	NOUN
ejpam-6102	697	15	)	)	PUNCT
ejpam-6102	697	16	−∆ψn+2	−∆ψn+2	NUM
ejpam-6102	697	17	=	=	SYM
ejpam-6102	698	1	n+	n+	NUM
ejpam-6102	698	2	2	2	NUM
ejpam-6102	698	3	n−	n−	NOUN
ejpam-6102	698	4	2	2	NUM
ejpam-6102	698	5	ω0,µψn+2	ω0,µψn+2	NUM
ejpam-6102	698	6	in	in	ADP
ejpam-6102	698	7	b(0	b(0	PROPN
ejpam-6102	698	8	,	,	PUNCT
ejpam-6102	698	9	ρ	ρ	NOUN
ejpam-6102	698	10	)	)	PUNCT
ejpam-6102	698	11	;	;	PUNCT
ejpam-6102	699	1	∂ψn+2	∂ψn+2	NOUN
ejpam-6102	699	2	∂ν	∂ν	X
ejpam-6102	699	3	=	=	SYM
ejpam-6102	699	4	c(ρ	c(ρ	PROPN
ejpam-6102	699	5	,	,	PUNCT
ejpam-6102	699	6	µ)xn	µ)xn	PROPN
ejpam-6102	699	7	on	on	ADP
ejpam-6102	699	8	∂b(0	∂b(0	PROPN
ejpam-6102	699	9	,	,	PUNCT
ejpam-6102	699	10	ρ	ρ	PROPN
ejpam-6102	699	11	)	)	PUNCT
ejpam-6102	699	12	.	.	PUNCT
ejpam-6102	700	1	thus	thus	ADV
ejpam-6102	700	2	,	,	PUNCT
ejpam-6102	700	3	by	by	ADP
ejpam-6102	700	4	oddness	oddness	NOUN
ejpam-6102	700	5	(	(	PUNCT
ejpam-6102	700	6	with	with	ADP
ejpam-6102	700	7	respect	respect	VERB
ejpam-6102	700	8	the	the	DET
ejpam-6102	700	9	variable	variable	NOUN
ejpam-6102	700	10	xn	xn	PROPN
ejpam-6102	700	11	)	)	PUNCT
ejpam-6102	700	12	,	,	PUNCT
ejpam-6102	700	13	we	we	PRON
ejpam-6102	700	14	obtain∫	obtain∫	VERB
ejpam-6102	700	15	b(0,ρ	b(0,ρ	PROPN
ejpam-6102	700	16	)	)	PUNCT
ejpam-6102	700	17	∇ṽ∇ψn+2	∇ṽ∇ψn+2	PROPN
ejpam-6102	700	18	=	=	PUNCT
ejpam-6102	700	19	∫	∫	PROPN
ejpam-6102	700	20	b(0,ρ	b(0,ρ	NUM
ejpam-6102	700	21	)	)	PUNCT
ejpam-6102	700	22	−∆ψn+2ṽ	−∆ψn+2ṽ	NOUN
ejpam-6102	700	23	+	+	CCONJ
ejpam-6102	700	24	∫	∫	PROPN
ejpam-6102	700	25	∂b(0,ρ	∂b(0,ρ	NOUN
ejpam-6102	700	26	)	)	PUNCT
ejpam-6102	700	27	∂ψn+2	∂ψn+2	NOUN
ejpam-6102	700	28	∂ν	∂ν	PROPN
ejpam-6102	701	1	ṽ	ṽ	PROPN
ejpam-6102	701	2	=	=	SYM
ejpam-6102	701	3	0	0	NUM
ejpam-6102	701	4	,	,	PUNCT
ejpam-6102	701	5	hence	hence	ADV
ejpam-6102	701	6	,	,	PUNCT
ejpam-6102	701	7	v	v	PROPN
ejpam-6102	701	8	∈	∈	PROPN
ejpam-6102	701	9	e0,µ	e0,µ	PROPN
ejpam-6102	701	10	and	and	CCONJ
ejpam-6102	701	11	the	the	DET
ejpam-6102	701	12	assumptions	assumption	NOUN
ejpam-6102	701	13	of	of	ADP
ejpam-6102	701	14	proposition	proposition	NOUN
ejpam-6102	701	15	1	1	NUM
ejpam-6102	701	16	of	of	ADP
ejpam-6102	701	17	[	[	X
ejpam-6102	701	18	32	32	NUM
ejpam-6102	701	19	]	]	PUNCT
ejpam-6102	701	20	are	be	AUX
ejpam-6102	701	21	satisfied	satisfied	ADJ
ejpam-6102	701	22	.	.	PUNCT
ejpam-6102	702	1	combining	combine	VERB
ejpam-6102	702	2	(	(	PUNCT
ejpam-6102	702	3	77	77	NUM
ejpam-6102	702	4	)	)	PUNCT
ejpam-6102	702	5	and	and	CCONJ
ejpam-6102	702	6	(	(	PUNCT
ejpam-6102	702	7	78	78	NUM
ejpam-6102	702	8	)	)	PUNCT
ejpam-6102	702	9	(	(	PUNCT
ejpam-6102	702	10	by	by	ADP
ejpam-6102	702	11	taking	take	VERB
ejpam-6102	702	12	w	w	PROPN
ejpam-6102	702	13	=	=	SYM
ejpam-6102	702	14	ṽ	ṽ	PROPN
ejpam-6102	702	15	)	)	PUNCT
ejpam-6102	702	16	,	,	PUNCT
ejpam-6102	702	17	we	we	PRON
ejpam-6102	702	18	get	get	VERB
ejpam-6102	702	19	q+(v	q+(v	NOUN
ejpam-6102	702	20	)	)	PUNCT
ejpam-6102	702	21	⩾	⩾	NOUN
ejpam-6102	702	22	(	(	PUNCT
ejpam-6102	702	23	β0/2	β0/2	NOUN
ejpam-6102	702	24	)	)	PUNCT
ejpam-6102	702	25	∥ṽ∥2h1(b(0,ρ	∥ṽ∥2h1(b(0,ρ	NUM
ejpam-6102	702	26	)	)	PUNCT
ejpam-6102	702	27	)	)	PUNCT
ejpam-6102	703	1	⩾	⩾	PROPN
ejpam-6102	703	2	β0∥v∥2h1(b+	β0∥v∥2h1(b+	NUM
ejpam-6102	704	1	ρ	ρ	NOUN
ejpam-6102	704	2	)	)	PUNCT
ejpam-6102	704	3	.	.	PUNCT
ejpam-6102	705	1	we	we	PRON
ejpam-6102	705	2	remark	remark	VERB
ejpam-6102	705	3	that∫	that∫	NOUN
ejpam-6102	705	4	b+	b+	X
ejpam-6102	705	5	ρ	ρ	X
ejpam-6102	705	6	|∇v|2	|∇v|2	X
ejpam-6102	706	1	+	+	CCONJ
ejpam-6102	706	2	γ̄	γ̄	PROPN
ejpam-6102	706	3	∫	∫	PROPN
ejpam-6102	706	4	b+	b+	PUNCT
ejpam-6102	706	5	ρ	ρ	PROPN
ejpam-6102	706	6	v2	v2	PROPN
ejpam-6102	706	7	⩽	⩽	PROPN
ejpam-6102	706	8	∥v∥2	∥v∥2	NOUN
ejpam-6102	706	9	h1(b+	h1(b+	PROPN
ejpam-6102	706	10	ρ	ρ	PROPN
ejpam-6102	706	11	)	)	PUNCT
ejpam-6102	706	12	⩽	⩽	NOUN
ejpam-6102	706	13	1	1	NUM
ejpam-6102	706	14	γ̄	γ̄	PROPN
ejpam-6102	706	15	(	(	PUNCT
ejpam-6102	706	16	∫	∫	PROPN
ejpam-6102	706	17	b+	b+	X
ejpam-6102	706	18	ρ	ρ	X
ejpam-6102	706	19	|∇v|2	|∇v|2	X
ejpam-6102	707	1	+	+	CCONJ
ejpam-6102	707	2	γ̄	γ̄	PROPN
ejpam-6102	707	3	∫	∫	PROPN
ejpam-6102	707	4	b+	b+	VERB
ejpam-6102	707	5	ρ	ρ	PROPN
ejpam-6102	707	6	v2	v2	PROPN
ejpam-6102	707	7	)	)	PUNCT
ejpam-6102	707	8	if	if	SCONJ
ejpam-6102	707	9	γ̄	γ̄	PROPN
ejpam-6102	707	10	⩽	⩽	PROPN
ejpam-6102	707	11	1	1	NUM
ejpam-6102	707	12	,	,	PUNCT
ejpam-6102	707	13	1	1	NUM
ejpam-6102	707	14	γ̄	γ̄	X
ejpam-6102	707	15	(	(	PUNCT
ejpam-6102	707	16	∫	∫	PROPN
ejpam-6102	707	17	b+	b+	X
ejpam-6102	707	18	ρ	ρ	X
ejpam-6102	707	19	|∇v|2	|∇v|2	X
ejpam-6102	707	20	+	+	PUNCT
ejpam-6102	708	1	γ̃	γ̃	PROPN
ejpam-6102	708	2	∫	∫	NOUN
ejpam-6102	708	3	b+	b+	X
ejpam-6102	708	4	ρ	ρ	PROPN
ejpam-6102	708	5	v2	v2	PROPN
ejpam-6102	708	6	)	)	PUNCT
ejpam-6102	708	7	⩽	⩽	ADJ
ejpam-6102	708	8	∥v∥2	∥v∥2	NOUN
ejpam-6102	708	9	h1(b+	h1(b+	PROPN
ejpam-6102	708	10	ρ	ρ	PROPN
ejpam-6102	708	11	)	)	PUNCT
ejpam-6102	708	12	⩽	⩽	PROPN
ejpam-6102	708	13	∫	∫	PROPN
ejpam-6102	708	14	b+	b+	X
ejpam-6102	708	15	ρ	ρ	X
ejpam-6102	708	16	|∇v|2	|∇v|2	X
ejpam-6102	709	1	+	+	CCONJ
ejpam-6102	709	2	γ̄	γ̄	PROPN
ejpam-6102	709	3	∫	∫	PROPN
ejpam-6102	709	4	b+	b+	VERB
ejpam-6102	709	5	ρ	ρ	PROPN
ejpam-6102	709	6	v2	v2	PROPN
ejpam-6102	709	7	if	if	SCONJ
ejpam-6102	709	8	γ̄	γ̄	PROPN
ejpam-6102	709	9	>	>	X
ejpam-6102	709	10	1	1	X
ejpam-6102	709	11	.	.	PUNCT
ejpam-6102	710	1	(	(	PUNCT
ejpam-6102	710	2	79	79	NUM
ejpam-6102	710	3	)	)	PUNCT
ejpam-6102	710	4	the	the	DET
ejpam-6102	710	5	proof	proof	NOUN
ejpam-6102	710	6	of	of	ADP
ejpam-6102	710	7	the	the	DET
ejpam-6102	710	8	lemma	lemma	PROPN
ejpam-6102	710	9	is	be	AUX
ejpam-6102	710	10	thereby	thereby	ADV
ejpam-6102	710	11	completed	complete	VERB
ejpam-6102	710	12	.	.	PUNCT
ejpam-6102	711	1	notice	notice	VERB
ejpam-6102	711	2	that	that	SCONJ
ejpam-6102	711	3	,	,	PUNCT
ejpam-6102	711	4	for	for	ADP
ejpam-6102	711	5	a	a	DET
ejpam-6102	711	6	∈	∈	PROPN
ejpam-6102	711	7	∂ω	∂ω	PROPN
ejpam-6102	711	8	,	,	PUNCT
ejpam-6102	711	9	a	a	DET
ejpam-6102	711	10	neighborhood	neighborhood	NOUN
ejpam-6102	711	11	of	of	ADP
ejpam-6102	711	12	a	a	PRON
ejpam-6102	711	13	in	in	ADP
ejpam-6102	711	14	ω	ω	PROPN
ejpam-6102	711	15	is	be	AUX
ejpam-6102	711	16	not	not	PART
ejpam-6102	711	17	necessary	necessary	ADJ
ejpam-6102	711	18	a	a	DET
ejpam-6102	711	19	half	half	NOUN
ejpam-6102	711	20	ball	ball	NOUN
ejpam-6102	711	21	.	.	PUNCT
ejpam-6102	712	1	for	for	ADP
ejpam-6102	712	2	this	this	DET
ejpam-6102	712	3	reason	reason	NOUN
ejpam-6102	712	4	,	,	PUNCT
ejpam-6102	712	5	we	we	PRON
ejpam-6102	712	6	need	need	VERB
ejpam-6102	712	7	to	to	PART
ejpam-6102	712	8	take	take	VERB
ejpam-6102	712	9	a	a	DET
ejpam-6102	712	10	general	general	ADJ
ejpam-6102	712	11	case	case	NOUN
ejpam-6102	712	12	.	.	PUNCT
ejpam-6102	713	1	lemma	lemma	PROPN
ejpam-6102	713	2	11	11	NUM
ejpam-6102	713	3	.	.	PUNCT
ejpam-6102	714	1	let	let	VERB
ejpam-6102	714	2	a	a	DET
ejpam-6102	714	3	∈	∈	PROPN
ejpam-6102	714	4	∂ω	∂ω	PROPN
ejpam-6102	714	5	,	,	PUNCT
ejpam-6102	714	6	µ	µ	X
ejpam-6102	714	7	be	be	VERB
ejpam-6102	714	8	a	a	DET
ejpam-6102	714	9	large	large	ADJ
ejpam-6102	714	10	real	real	NOUN
ejpam-6102	714	11	and	and	CCONJ
ejpam-6102	714	12	ρ	ρ	NOUN
ejpam-6102	714	13	be	be	AUX
ejpam-6102	714	14	a	a	DET
ejpam-6102	714	15	small	small	ADJ
ejpam-6102	714	16	radius	radius	NOUN
ejpam-6102	714	17	.	.	PUNCT
ejpam-6102	715	1	let	let	VERB
ejpam-6102	715	2	qa	qa	PROPN
ejpam-6102	715	3	,	,	PUNCT
ejpam-6102	715	4	ρ(v	ρ(v	PROPN
ejpam-6102	715	5	)	)	PUNCT
ejpam-6102	715	6	:	:	PUNCT
ejpam-6102	716	1	=	=	SYM
ejpam-6102	716	2	∫	∫	PROPN
ejpam-6102	716	3	b(a	b(a	PROPN
ejpam-6102	716	4	,	,	PUNCT
ejpam-6102	716	5	ρ)∩ω	ρ)∩ω	PROPN
ejpam-6102	716	6	|∇v|2	|∇v|2	X
ejpam-6102	717	1	+	+	CCONJ
ejpam-6102	717	2	γ̄	γ̄	PROPN
ejpam-6102	717	3	∫	∫	PROPN
ejpam-6102	717	4	b(a	b(a	PROPN
ejpam-6102	717	5	,	,	PUNCT
ejpam-6102	717	6	ρ)∩ω	ρ)∩ω	PROPN
ejpam-6102	717	7	v2	v2	PROPN
ejpam-6102	717	8	−	−	NUM
ejpam-6102	717	9	n+	n+	NOUN
ejpam-6102	717	10	2	2	NUM
ejpam-6102	717	11	n−	n−	NOUN
ejpam-6102	717	12	2	2	NUM
ejpam-6102	717	13	∫	∫	PROPN
ejpam-6102	717	14	b(a	b(a	PROPN
ejpam-6102	717	15	,	,	PUNCT
ejpam-6102	717	16	ρ)∩ω	ρ)∩ω	PROPN
ejpam-6102	717	17	ω	ω	PROPN
ejpam-6102	717	18	4	4	NUM
ejpam-6102	717	19	n−2	n−2	PROPN
ejpam-6102	717	20	a,µ	a,µ	ADP
ejpam-6102	717	21	v2	v2	PROPN
ejpam-6102	717	22	.	.	PUNCT
ejpam-6102	718	1	then	then	ADV
ejpam-6102	718	2	,	,	PUNCT
ejpam-6102	718	3	there	there	PRON
ejpam-6102	718	4	exists	exist	VERB
ejpam-6102	718	5	a	a	DET
ejpam-6102	718	6	constant	constant	ADJ
ejpam-6102	718	7	β2	β2	NOUN
ejpam-6102	718	8	>	>	X
ejpam-6102	718	9	0	0	NUM
ejpam-6102	719	1	such	such	ADJ
ejpam-6102	719	2	that	that	SCONJ
ejpam-6102	719	3	qa	qa	PROPN
ejpam-6102	719	4	,	,	PUNCT
ejpam-6102	719	5	ρ(v	ρ(v	PROPN
ejpam-6102	719	6	)	)	PUNCT
ejpam-6102	719	7	⩾	⩾	PROPN
ejpam-6102	719	8	β2	β2	NOUN
ejpam-6102	719	9	(	(	PUNCT
ejpam-6102	719	10	∫	∫	PROPN
ejpam-6102	719	11	b(a	b(a	PROPN
ejpam-6102	719	12	,	,	PUNCT
ejpam-6102	719	13	ρ)∩ω	ρ)∩ω	PROPN
ejpam-6102	719	14	|∇v|2	|∇v|2	X
ejpam-6102	720	1	+	+	CCONJ
ejpam-6102	720	2	γ̄	γ̄	PROPN
ejpam-6102	720	3	∫	∫	PROPN
ejpam-6102	720	4	b(a	b(a	PROPN
ejpam-6102	720	5	,	,	PUNCT
ejpam-6102	720	6	ρ)∩ω	ρ)∩ω	PROPN
ejpam-6102	720	7	v2	v2	PROPN
ejpam-6102	720	8	)	)	PUNCT
ejpam-6102	721	1	+	+	CCONJ
ejpam-6102	721	2	o	o	X
ejpam-6102	721	3	(	(	PUNCT
ejpam-6102	721	4	∥v∥2h1(ω	∥v∥2h1(ω	NOUN
ejpam-6102	721	5	)	)	PUNCT
ejpam-6102	721	6	)	)	PUNCT
ejpam-6102	722	1	∀v	∀v	PROPN
ejpam-6102	722	2	∈	∈	PROPN
ejpam-6102	722	3	fa,µ	fa,µ	NOUN
ejpam-6102	722	4	,	,	PUNCT
ejpam-6102	722	5	where	where	SCONJ
ejpam-6102	722	6	fa,µ	fa,µ	NOUN
ejpam-6102	722	7	is	be	AUX
ejpam-6102	722	8	defined	define	VERB
ejpam-6102	722	9	in	in	ADP
ejpam-6102	722	10	(	(	PUNCT
ejpam-6102	722	11	4	4	NUM
ejpam-6102	722	12	)	)	PUNCT
ejpam-6102	722	13	.	.	PUNCT
ejpam-6102	723	1	proof	proof	NOUN
ejpam-6102	723	2	.	.	PUNCT
ejpam-6102	724	1	let	let	VERB
ejpam-6102	724	2	(	(	PUNCT
ejpam-6102	724	3	e1	e1	VERB
ejpam-6102	724	4	,	,	PUNCT
ejpam-6102	724	5	.	.	PUNCT
ejpam-6102	724	6	.	.	PUNCT
ejpam-6102	724	7	.	.	PUNCT
ejpam-6102	725	1	,	,	PUNCT
ejpam-6102	725	2	en	en	AUX
ejpam-6102	725	3	)	)	PUNCT
ejpam-6102	725	4	be	be	VERB
ejpam-6102	725	5	the	the	DET
ejpam-6102	725	6	canonical	canonical	ADJ
ejpam-6102	725	7	basis	basis	NOUN
ejpam-6102	725	8	of	of	ADP
ejpam-6102	725	9	rn	rn	PROPN
ejpam-6102	725	10	.	.	PROPN
ejpam-6102	725	11	without	without	ADP
ejpam-6102	725	12	loss	loss	NOUN
ejpam-6102	725	13	of	of	ADP
ejpam-6102	725	14	generality	generality	NOUN
ejpam-6102	725	15	,	,	PUNCT
ejpam-6102	725	16	we	we	PRON
ejpam-6102	725	17	can	can	AUX
ejpam-6102	725	18	assume	assume	VERB
ejpam-6102	725	19	that	that	SCONJ
ejpam-6102	725	20	a	a	DET
ejpam-6102	725	21	=	=	SYM
ejpam-6102	725	22	0	0	NUM
ejpam-6102	725	23	and	and	CCONJ
ejpam-6102	725	24	νa	νa	VERB
ejpam-6102	725	25	=	=	SYM
ejpam-6102	725	26	−en	−en	X
ejpam-6102	725	27	(	(	PUNCT
ejpam-6102	725	28	which	which	PRON
ejpam-6102	725	29	implies	imply	VERB
ejpam-6102	725	30	that	that	SCONJ
ejpam-6102	725	31	the	the	DET
ejpam-6102	725	32	tangent	tangent	ADJ
ejpam-6102	725	33	space	space	NOUN
ejpam-6102	725	34	to	to	ADP
ejpam-6102	725	35	∂ω	∂ω	PROPN
ejpam-6102	725	36	at	at	ADP
ejpam-6102	725	37	a	a	DET
ejpam-6102	725	38	=	=	SYM
ejpam-6102	725	39	0	0	NUM
ejpam-6102	725	40	is	be	AUX
ejpam-6102	725	41	rn−1	rn−1	PROPN
ejpam-6102	725	42	×	×	NOUN
ejpam-6102	725	43	{	{	PUNCT
ejpam-6102	725	44	0	0	NUM
ejpam-6102	725	45	}	}	PUNCT
ejpam-6102	725	46	and	and	CCONJ
ejpam-6102	725	47	a	a	DET
ejpam-6102	725	48	basis	basis	NOUN
ejpam-6102	725	49	of	of	ADP
ejpam-6102	725	50	this	this	DET
ejpam-6102	725	51	tangent	tangent	NOUN
ejpam-6102	725	52	space	space	NOUN
ejpam-6102	725	53	is	be	AUX
ejpam-6102	725	54	(	(	PUNCT
ejpam-6102	725	55	e1	e1	NOUN
ejpam-6102	725	56	,	,	PUNCT
ejpam-6102	725	57	.	.	PUNCT
ejpam-6102	725	58	.	.	PUNCT
ejpam-6102	726	1	.	.	PUNCT
ejpam-6102	727	1	,	,	PUNCT
ejpam-6102	727	2	en−1	en−1	PROPN
ejpam-6102	727	3	)	)	PUNCT
ejpam-6102	727	4	)	)	PUNCT
ejpam-6102	727	5	.	.	PUNCT
ejpam-6102	728	1	since	since	SCONJ
ejpam-6102	728	2	ρ	ρ	PROPN
ejpam-6102	728	3	is	be	AUX
ejpam-6102	728	4	small	small	ADJ
ejpam-6102	728	5	and	and	CCONJ
ejpam-6102	728	6	ω	ω	PROPN
ejpam-6102	728	7	is	be	AUX
ejpam-6102	728	8	a	a	DET
ejpam-6102	728	9	regular	regular	ADJ
ejpam-6102	728	10	domain	domain	NOUN
ejpam-6102	728	11	,	,	PUNCT
ejpam-6102	728	12	there	there	PRON
ejpam-6102	728	13	exists	exist	VERB
ejpam-6102	728	14	a	a	DET
ejpam-6102	728	15	smooth	smooth	ADJ
ejpam-6102	728	16	function	function	NOUN
ejpam-6102	728	17	f	f	NOUN
ejpam-6102	728	18	:	:	PUNCT
ejpam-6102	728	19	rn−1	rn−1	VERB
ejpam-6102	728	20	−→	−→	ADJ
ejpam-6102	728	21	r	r	NOUN
ejpam-6102	728	22	,	,	PUNCT
ejpam-6102	728	23	satisfying	satisfy	VERB
ejpam-6102	728	24	f(0	f(0	NOUN
ejpam-6102	728	25	)	)	PUNCT
ejpam-6102	728	26	=	=	SYM
ejpam-6102	728	27	0	0	NUM
ejpam-6102	728	28	,	,	PUNCT
ejpam-6102	728	29	∇f(0	∇f(0	NOUN
ejpam-6102	728	30	)	)	PUNCT
ejpam-6102	728	31	=	=	SYM
ejpam-6102	728	32	0	0	NUM
ejpam-6102	728	33	and	and	CCONJ
ejpam-6102	728	34	ω	ω	NUM
ejpam-6102	728	35	∩b(0	∩b(0	PROPN
ejpam-6102	728	36	,	,	PUNCT
ejpam-6102	728	37	ρ	ρ	NOUN
ejpam-6102	728	38	)	)	PUNCT
ejpam-6102	728	39	=	=	PRON
ejpam-6102	728	40	{	{	PUNCT
ejpam-6102	728	41	x	x	X
ejpam-6102	728	42	:	:	PUNCT
ejpam-6102	728	43	=	=	SYM
ejpam-6102	728	44	(	(	PUNCT
ejpam-6102	728	45	x′	x′	PROPN
ejpam-6102	728	46	,	,	PUNCT
ejpam-6102	728	47	xn	xn	X
ejpam-6102	728	48	)	)	PUNCT
ejpam-6102	728	49	∈	∈	PROPN
ejpam-6102	729	1	rn−1	rn−1	PROPN
ejpam-6102	729	2	×	×	NOUN
ejpam-6102	729	3	r	r	NOUN
ejpam-6102	729	4	:	:	PUNCT
ejpam-6102	729	5	|x|	|x|	PROPN
ejpam-6102	729	6	<	<	X
ejpam-6102	729	7	ρ	ρ	PROPN
ejpam-6102	729	8	,	,	PUNCT
ejpam-6102	729	9	xn	xn	PROPN
ejpam-6102	729	10	>	>	X
ejpam-6102	729	11	f	f	PROPN
ejpam-6102	729	12	(	(	PUNCT
ejpam-6102	729	13	x′	x′	NUM
ejpam-6102	729	14	)	)	PUNCT
ejpam-6102	729	15	}	}	PUNCT
ejpam-6102	729	16	.	.	PUNCT
ejpam-6102	730	1	r.	r.	PROPN
ejpam-6102	730	2	almushahhin	almushahhin	PROPN
ejpam-6102	730	3	,	,	PUNCT
ejpam-6102	730	4	m.	m.	PROPN
ejpam-6102	730	5	ben	ben	PROPN
ejpam-6102	730	6	ayed	aye	VERB
ejpam-6102	730	7	/	/	SYM
ejpam-6102	730	8	eur	eur	PROPN
ejpam-6102	730	9	.	.	PUNCT
ejpam-6102	731	1	j.	j.	PROPN
ejpam-6102	731	2	pure	pure	PROPN
ejpam-6102	731	3	appl	appl	PROPN
ejpam-6102	731	4	.	.	PROPN
ejpam-6102	731	5	math	math	PROPN
ejpam-6102	731	6	,	,	PUNCT
ejpam-6102	731	7	18	18	NUM
ejpam-6102	731	8	(	(	PUNCT
ejpam-6102	731	9	2	2	NUM
ejpam-6102	731	10	)	)	PUNCT
ejpam-6102	731	11	(	(	PUNCT
ejpam-6102	731	12	2025	2025	NUM
ejpam-6102	731	13	)	)	PUNCT
ejpam-6102	731	14	,	,	PUNCT
ejpam-6102	731	15	6102	6102	NUM
ejpam-6102	731	16	26	26	NUM
ejpam-6102	731	17	of	of	ADP
ejpam-6102	731	18	31	31	NUM
ejpam-6102	731	19	now	now	ADV
ejpam-6102	731	20	,	,	PUNCT
ejpam-6102	731	21	we	we	PRON
ejpam-6102	731	22	define	define	VERB
ejpam-6102	731	23	φ	φ	PROPN
ejpam-6102	731	24	:	:	PUNCT
ejpam-6102	731	25	ω	ω	PROPN
ejpam-6102	731	26	∩b(0	∩b(0	PROPN
ejpam-6102	731	27	,	,	PUNCT
ejpam-6102	731	28	ρ	ρ	NOUN
ejpam-6102	731	29	)	)	PUNCT
ejpam-6102	731	30	−→	−→	NOUN
ejpam-6102	731	31	rn−1	rn−1	PROPN
ejpam-6102	731	32	×	×	NOUN
ejpam-6102	731	33	r	r	NOUN
ejpam-6102	731	34	,	,	PUNCT
ejpam-6102	731	35	φ	φ	PROPN
ejpam-6102	731	36	(	(	PUNCT
ejpam-6102	731	37	x′	x′	PROPN
ejpam-6102	731	38	,	,	PUNCT
ejpam-6102	731	39	xn	xn	PROPN
ejpam-6102	731	40	)	)	PUNCT
ejpam-6102	731	41	=	=	SYM
ejpam-6102	732	1	(	(	PUNCT
ejpam-6102	732	2	x′	x′	PROPN
ejpam-6102	732	3	,	,	PUNCT
ejpam-6102	732	4	xn	xn	PROPN
ejpam-6102	733	1	−	−	PROPN
ejpam-6102	733	2	f	f	PROPN
ejpam-6102	733	3	(	(	PUNCT
ejpam-6102	733	4	x′	x′	NUM
ejpam-6102	733	5	)	)	PUNCT
ejpam-6102	733	6	)	)	PUNCT
ejpam-6102	733	7	.	.	PUNCT
ejpam-6102	734	1	(	(	PUNCT
ejpam-6102	734	2	80	80	NUM
ejpam-6102	734	3	)	)	PUNCT
ejpam-6102	734	4	from	from	ADP
ejpam-6102	734	5	(	(	PUNCT
ejpam-6102	734	6	80	80	NUM
ejpam-6102	734	7	)	)	PUNCT
ejpam-6102	734	8	,	,	PUNCT
ejpam-6102	734	9	we	we	PRON
ejpam-6102	734	10	remark	remark	VERB
ejpam-6102	734	11	that	that	SCONJ
ejpam-6102	734	12	there	there	PRON
ejpam-6102	734	13	exists	exist	VERB
ejpam-6102	734	14	a	a	DET
ejpam-6102	734	15	neighborhood	neighborhood	NOUN
ejpam-6102	734	16	v	v	NOUN
ejpam-6102	734	17	of	of	ADP
ejpam-6102	734	18	0	0	NUM
ejpam-6102	734	19	in	in	ADP
ejpam-6102	734	20	b	b	PROPN
ejpam-6102	734	21	(	(	PUNCT
ejpam-6102	734	22	0	0	NUM
ejpam-6102	734	23	,	,	PUNCT
ejpam-6102	734	24	ρ	ρ	NOUN
ejpam-6102	734	25	)	)	PUNCT
ejpam-6102	734	26	such	such	ADJ
ejpam-6102	734	27	that	that	SCONJ
ejpam-6102	734	28	φ	φ	PROPN
ejpam-6102	734	29	induces	induce	VERB
ejpam-6102	734	30	a	a	DET
ejpam-6102	734	31	diffeomorphism	diffeomorphism	NOUN
ejpam-6102	734	32	between	between	ADP
ejpam-6102	734	33	v	v	NOUN
ejpam-6102	734	34	∩	∩	ADJ
ejpam-6102	734	35	ω	ω	NOUN
ejpam-6102	734	36	and	and	CCONJ
ejpam-6102	734	37	b+	b+	NOUN
ejpam-6102	734	38	:	:	PUNCT
ejpam-6102	734	39	=	=	SYM
ejpam-6102	734	40	{	{	PUNCT
ejpam-6102	734	41	x	x	SYM
ejpam-6102	734	42	=	=	X
ejpam-6102	734	43	(	(	PUNCT
ejpam-6102	734	44	x′	x′	PROPN
ejpam-6102	734	45	,	,	PUNCT
ejpam-6102	734	46	xn	xn	PROPN
ejpam-6102	734	47	)	)	PUNCT
ejpam-6102	734	48	∈	∈	PROPN
ejpam-6102	734	49	b	b	PROPN
ejpam-6102	734	50	(	(	PUNCT
ejpam-6102	734	51	0	0	NUM
ejpam-6102	734	52	,	,	PUNCT
ejpam-6102	734	53	ρ/2	ρ/2	NUM
ejpam-6102	734	54	)	)	PUNCT
ejpam-6102	734	55	:	:	PUNCT
ejpam-6102	734	56	xn	xn	PUNCT
ejpam-6102	734	57	>	>	X
ejpam-6102	734	58	0	0	NUM
ejpam-6102	734	59	}	}	PUNCT
ejpam-6102	734	60	,	,	PUNCT
ejpam-6102	734	61	that	that	PRON
ejpam-6102	734	62	is	be	AUX
ejpam-6102	734	63	φ(v	φ(v	PROPN
ejpam-6102	734	64	∩	∩	ADJ
ejpam-6102	734	65	ω	ω	NOUN
ejpam-6102	734	66	)	)	PUNCT
ejpam-6102	734	67	=	=	PUNCT
ejpam-6102	734	68	b+	b+	X
ejpam-6102	734	69	.	.	PUNCT
ejpam-6102	735	1	(	(	PUNCT
ejpam-6102	735	2	81	81	NUM
ejpam-6102	735	3	)	)	PUNCT
ejpam-6102	735	4	in	in	ADP
ejpam-6102	735	5	addition	addition	NOUN
ejpam-6102	735	6	,	,	PUNCT
ejpam-6102	735	7	we	we	PRON
ejpam-6102	735	8	have	have	VERB
ejpam-6102	735	9	b	b	NUM
ejpam-6102	735	10	(	(	PUNCT
ejpam-6102	735	11	0	0	NUM
ejpam-6102	735	12	,	,	PUNCT
ejpam-6102	735	13	ρ/4	ρ/4	NUM
ejpam-6102	735	14	)	)	PUNCT
ejpam-6102	736	1	⊂	⊂	PROPN
ejpam-6102	736	2	v.	v.	CCONJ
ejpam-6102	736	3	furthermore	furthermore	ADV
ejpam-6102	736	4	,	,	PUNCT
ejpam-6102	736	5	from	from	ADP
ejpam-6102	736	6	the	the	DET
ejpam-6102	736	7	definition	definition	NOUN
ejpam-6102	736	8	of	of	ADP
ejpam-6102	736	9	φ	φ	PROPN
ejpam-6102	736	10	in	in	ADP
ejpam-6102	736	11	(	(	PUNCT
ejpam-6102	736	12	80	80	NUM
ejpam-6102	736	13	)	)	PUNCT
ejpam-6102	736	14	,	,	PUNCT
ejpam-6102	736	15	we	we	PRON
ejpam-6102	736	16	deduce	deduce	VERB
ejpam-6102	736	17	that	that	SCONJ
ejpam-6102	736	18	∂φ	∂φ	PROPN
ejpam-6102	736	19	∂xi	∂xi	PROPN
ejpam-6102	736	20	(	(	PUNCT
ejpam-6102	736	21	x	x	NOUN
ejpam-6102	736	22	)	)	PUNCT
ejpam-6102	736	23	=	=	SYM
ejpam-6102	737	1	ei	ei	ADP
ejpam-6102	737	2	−	−	NOUN
ejpam-6102	738	1	∂f	∂f	PROPN
ejpam-6102	738	2	∂xi	∂xi	PROPN
ejpam-6102	738	3	(	(	PUNCT
ejpam-6102	738	4	x′	x′	NUM
ejpam-6102	738	5	)	)	PUNCT
ejpam-6102	738	6	en	en	ADP
ejpam-6102	738	7	for	for	ADP
ejpam-6102	738	8	1	1	NUM
ejpam-6102	738	9	⩽	⩽	NOUN
ejpam-6102	738	10	i	i	PRON
ejpam-6102	738	11	⩽	⩽	ADJ
ejpam-6102	738	12	n−	n−	NOUN
ejpam-6102	738	13	1	1	NUM
ejpam-6102	738	14	and	and	CCONJ
ejpam-6102	738	15	∂φ	∂φ	PROPN
ejpam-6102	738	16	∂xn	∂xn	NOUN
ejpam-6102	738	17	(	(	PUNCT
ejpam-6102	738	18	x	x	NOUN
ejpam-6102	738	19	)	)	PUNCT
ejpam-6102	738	20	=	=	SYM
ejpam-6102	738	21	en	en	X
ejpam-6102	738	22	,	,	PUNCT
ejpam-6102	738	23	(	(	PUNCT
ejpam-6102	738	24	82	82	NUM
ejpam-6102	738	25	)	)	PUNCT
ejpam-6102	738	26	which	which	PRON
ejpam-6102	738	27	implies	imply	VERB
ejpam-6102	738	28	that	that	SCONJ
ejpam-6102	738	29	the	the	DET
ejpam-6102	738	30	jacobian	jacobian	NOUN
ejpam-6102	738	31	of	of	ADP
ejpam-6102	738	32	φ	φ	PROPN
ejpam-6102	738	33	at	at	ADP
ejpam-6102	738	34	each	each	DET
ejpam-6102	738	35	point	point	NOUN
ejpam-6102	738	36	x	x	PUNCT
ejpam-6102	738	37	is	be	AUX
ejpam-6102	738	38	1	1	NUM
ejpam-6102	738	39	(	(	PUNCT
ejpam-6102	738	40	|jacφ|	|jacφ|	NOUN
ejpam-6102	738	41	=	=	SYM
ejpam-6102	738	42	1	1	NUM
ejpam-6102	738	43	)	)	PUNCT
ejpam-6102	738	44	.	.	PUNCT
ejpam-6102	739	1	now	now	ADV
ejpam-6102	739	2	,	,	PUNCT
ejpam-6102	739	3	let	let	VERB
ejpam-6102	739	4	us	we	PRON
ejpam-6102	739	5	define	define	VERB
ejpam-6102	739	6	the	the	DET
ejpam-6102	739	7	function	function	NOUN
ejpam-6102	739	8	v1	v1	NOUN
ejpam-6102	739	9	by	by	ADP
ejpam-6102	739	10	v1	v1	PROPN
ejpam-6102	739	11	:	:	PUNCT
ejpam-6102	739	12	b+	b+	X
ejpam-6102	739	13	−→	−→	NOUN
ejpam-6102	739	14	r	r	NOUN
ejpam-6102	739	15	,	,	PUNCT
ejpam-6102	739	16	v1	v1	NOUN
ejpam-6102	739	17	:	:	PUNCT
ejpam-6102	739	18	=	=	SYM
ejpam-6102	739	19	v	v	PART
ejpam-6102	739	20	◦	◦	NOUN
ejpam-6102	739	21	φ−1	φ−1	PROPN
ejpam-6102	739	22	.	.	PUNCT
ejpam-6102	740	1	(	(	PUNCT
ejpam-6102	740	2	83	83	NUM
ejpam-6102	740	3	)	)	PUNCT
ejpam-6102	740	4	using	use	VERB
ejpam-6102	740	5	(	(	PUNCT
ejpam-6102	740	6	82	82	NUM
ejpam-6102	740	7	)	)	PUNCT
ejpam-6102	740	8	,	,	PUNCT
ejpam-6102	740	9	easy	easy	ADJ
ejpam-6102	740	10	computations	computation	NOUN
ejpam-6102	740	11	imply	imply	VERB
ejpam-6102	740	12	that	that	SCONJ
ejpam-6102	740	13	|∇v(x)|2	|∇v(x)|2	AUX
ejpam-6102	740	14	=	=	SYM
ejpam-6102	740	15	|(∇v1	|(∇v1	NUM
ejpam-6102	740	16	)	)	PUNCT
ejpam-6102	740	17	(	(	PUNCT
ejpam-6102	740	18	φ(x))|2	φ(x))|2	X
ejpam-6102	740	19	+	+	NOUN
ejpam-6102	740	20	o	o	X
ejpam-6102	740	21	(	(	PUNCT
ejpam-6102	740	22	ρ	ρ	PROPN
ejpam-6102	740	23	|(∇v1	|(∇v1	PROPN
ejpam-6102	740	24	)	)	PUNCT
ejpam-6102	740	25	(	(	PUNCT
ejpam-6102	740	26	φ(x))|2	φ(x))|2	NOUN
ejpam-6102	740	27	)	)	PUNCT
ejpam-6102	740	28	,	,	PUNCT
ejpam-6102	740	29	which	which	PRON
ejpam-6102	740	30	implies	imply	VERB
ejpam-6102	740	31	that	that	SCONJ
ejpam-6102	740	32	,	,	PUNCT
ejpam-6102	740	33	by	by	ADP
ejpam-6102	740	34	using	use	VERB
ejpam-6102	740	35	(	(	PUNCT
ejpam-6102	740	36	81),∫	81),∫	NUM
ejpam-6102	740	37	v∩ω	v∩ω	PROPN
ejpam-6102	740	38	|∇v(x)|2	|∇v(x)|2	NOUN
ejpam-6102	740	39	dx	dx	PROPN
ejpam-6102	740	40	=	=	SYM
ejpam-6102	740	41	∫	∫	PROPN
ejpam-6102	740	42	b+	b+	X
ejpam-6102	740	43	|∇v1(z)|2	|∇v1(z)|2	PRON
ejpam-6102	740	44	dz	dz	X
ejpam-6102	740	45	+	+	PROPN
ejpam-6102	740	46	o	o	X
ejpam-6102	740	47	(	(	PUNCT
ejpam-6102	740	48	ρ	ρ	PROPN
ejpam-6102	740	49	∫	∫	PROPN
ejpam-6102	740	50	b+	b+	X
ejpam-6102	740	51	|∇v1(z)|2	|∇v1(z)|2	X
ejpam-6102	740	52	dz	dz	NOUN
ejpam-6102	740	53	)	)	PUNCT
ejpam-6102	740	54	,	,	PUNCT
ejpam-6102	740	55	and	and	CCONJ
ejpam-6102	740	56	therefore∫	therefore∫	ADP
ejpam-6102	740	57	v∩ω	v∩ω	PROPN
ejpam-6102	740	58	|∇v|2	|∇v|2	X
ejpam-6102	741	1	+	+	CCONJ
ejpam-6102	741	2	γ̄	γ̄	PROPN
ejpam-6102	741	3	∫	∫	PROPN
ejpam-6102	741	4	v∩ω	v∩ω	PROPN
ejpam-6102	741	5	|v|2	|v|2	PROPN
ejpam-6102	741	6	=	=	SYM
ejpam-6102	741	7	∫	∫	PROPN
ejpam-6102	741	8	b+	b+	X
ejpam-6102	741	9	|∇v1|2	|∇v1|2	X
ejpam-6102	742	1	+	+	CCONJ
ejpam-6102	742	2	γ̄	γ̄	PROPN
ejpam-6102	742	3	∫	∫	PROPN
ejpam-6102	742	4	b+	b+	X
ejpam-6102	742	5	(	(	PUNCT
ejpam-6102	742	6	v1	v1	NOUN
ejpam-6102	742	7	)	)	PUNCT
ejpam-6102	742	8	2	2	NUM
ejpam-6102	743	1	+	+	NOUN
ejpam-6102	743	2	o	o	X
ejpam-6102	743	3	(	(	PUNCT
ejpam-6102	743	4	ρ	ρ	PROPN
ejpam-6102	743	5	∫	∫	PROPN
ejpam-6102	743	6	b+	b+	X
ejpam-6102	743	7	|∇v1|2	|∇v1|2	X
ejpam-6102	743	8	)	)	PUNCT
ejpam-6102	743	9	.	.	PUNCT
ejpam-6102	744	1	(	(	PUNCT
ejpam-6102	744	2	84	84	NUM
ejpam-6102	744	3	)	)	PUNCT
ejpam-6102	744	4	concerning	concern	VERB
ejpam-6102	744	5	the	the	DET
ejpam-6102	744	6	last	last	ADJ
ejpam-6102	744	7	integral	integral	NOUN
ejpam-6102	744	8	in	in	ADP
ejpam-6102	744	9	the	the	DET
ejpam-6102	744	10	definition	definition	NOUN
ejpam-6102	744	11	of	of	ADP
ejpam-6102	744	12	qa	qa	PROPN
ejpam-6102	744	13	,	,	PUNCT
ejpam-6102	744	14	ρ	ρ	PROPN
ejpam-6102	744	15	,	,	PUNCT
ejpam-6102	744	16	we	we	PRON
ejpam-6102	744	17	have∫	have∫	VERB
ejpam-6102	744	18	v∩ω	v∩ω	PROPN
ejpam-6102	744	19	ω	ω	PROPN
ejpam-6102	744	20	4	4	NUM
ejpam-6102	744	21	n−2	n−2	PROPN
ejpam-6102	744	22	0,µ	0,µ	NOUN
ejpam-6102	744	23	(	(	PUNCT
ejpam-6102	744	24	x)v2(x)dx	x)v2(x)dx	VERB
ejpam-6102	744	25	=	=	SYM
ejpam-6102	744	26	∫	∫	PROPN
ejpam-6102	744	27	v∩ω	v∩ω	PROPN
ejpam-6102	744	28	ω	ω	PROPN
ejpam-6102	744	29	4	4	NUM
ejpam-6102	744	30	n−2	n−2	PROPN
ejpam-6102	744	31	a,µ	a,µ	ADV
ejpam-6102	744	32	(	(	PUNCT
ejpam-6102	744	33	x)v21(φ(x))dx	x)v21(φ(x))dx	PROPN
ejpam-6102	744	34	=	=	SYM
ejpam-6102	744	35	∫	∫	PROPN
ejpam-6102	744	36	b+	b+	X
ejpam-6102	744	37	ω	ω	X
ejpam-6102	744	38	4	4	NUM
ejpam-6102	744	39	n−2	n−2	PROPN
ejpam-6102	744	40	0,µ	0,µ	PROPN
ejpam-6102	744	41	(	(	PUNCT
ejpam-6102	744	42	φ−1(z	φ−1(z	PROPN
ejpam-6102	744	43	)	)	PUNCT
ejpam-6102	744	44	)	)	PUNCT
ejpam-6102	745	1	v21(z)dz	v21(z)dz	PROPN
ejpam-6102	745	2	.	.	PUNCT
ejpam-6102	746	1	(	(	PUNCT
ejpam-6102	746	2	85	85	NUM
ejpam-6102	746	3	)	)	PUNCT
ejpam-6102	746	4	observe	observe	VERB
ejpam-6102	746	5	that	that	SCONJ
ejpam-6102	746	6	equation	equation	NOUN
ejpam-6102	746	7	(	(	PUNCT
ejpam-6102	746	8	c.	c.	NOUN
ejpam-6102	746	9	25	25	NUM
ejpam-6102	746	10	)	)	PUNCT
ejpam-6102	746	11	of	of	ADP
ejpam-6102	746	12	[	[	X
ejpam-6102	746	13	27	27	NUM
ejpam-6102	746	14	]	]	PUNCT
ejpam-6102	746	15	gives	give	VERB
ejpam-6102	746	16	us	we	PRON
ejpam-6102	746	17	(	(	PUNCT
ejpam-6102	746	18	1	1	NUM
ejpam-6102	746	19	+	+	CCONJ
ejpam-6102	746	20	µ2|x|2	µ2|x|2	PROPN
ejpam-6102	746	21	)	)	PUNCT
ejpam-6102	746	22	γ	γ	X
ejpam-6102	746	23	=	=	SYM
ejpam-6102	746	24	(	(	PUNCT
ejpam-6102	746	25	1	1	NUM
ejpam-6102	746	26	+	+	CCONJ
ejpam-6102	746	27	µ2	µ2	PROPN
ejpam-6102	746	28	∣∣φ−1(z	∣∣φ−1(z	PROPN
ejpam-6102	746	29	)	)	PUNCT
ejpam-6102	746	30	∣∣2)γ	∣∣2)γ	NOUN
ejpam-6102	746	31	=	=	PUNCT
ejpam-6102	746	32	(	(	PUNCT
ejpam-6102	746	33	1	1	NUM
ejpam-6102	746	34	+	+	CCONJ
ejpam-6102	746	35	µ2|z|2	µ2|z|2	PROPN
ejpam-6102	746	36	)	)	PUNCT
ejpam-6102	747	1	γ	γ	PROPN
ejpam-6102	747	2	+	+	PROPN
ejpam-6102	747	3	o	o	X
ejpam-6102	747	4	(	(	PUNCT
ejpam-6102	747	5	(	(	PUNCT
ejpam-6102	747	6	1	1	NUM
ejpam-6102	747	7	+	+	CCONJ
ejpam-6102	747	8	µ2|z|2	µ2|z|2	PROPN
ejpam-6102	747	9	)	)	PUNCT
ejpam-6102	747	10	γ−1	γ−1	ADJ
ejpam-6102	747	11	µ2|z|2ρ	µ2|z|2ρ	NOUN
ejpam-6102	747	12	)	)	PUNCT
ejpam-6102	748	1	=	=	PUNCT
ejpam-6102	748	2	(	(	PUNCT
ejpam-6102	748	3	1	1	NUM
ejpam-6102	748	4	+	+	CCONJ
ejpam-6102	748	5	µ2|z|2	µ2|z|2	PROPN
ejpam-6102	748	6	)	)	PUNCT
ejpam-6102	748	7	γ	γ	PROPN
ejpam-6102	749	1	+	+	PROPN
ejpam-6102	749	2	o	o	X
ejpam-6102	749	3	(	(	PUNCT
ejpam-6102	749	4	(	(	PUNCT
ejpam-6102	749	5	1	1	NUM
ejpam-6102	749	6	+	+	CCONJ
ejpam-6102	749	7	µ2|z|2	µ2|z|2	PROPN
ejpam-6102	749	8	)	)	PUNCT
ejpam-6102	749	9	γ	γ	PROPN
ejpam-6102	749	10	ρ	ρ	PROPN
ejpam-6102	749	11	)	)	PUNCT
ejpam-6102	749	12	.	.	PUNCT
ejpam-6102	750	1	(	(	PUNCT
ejpam-6102	750	2	86	86	NUM
ejpam-6102	750	3	)	)	PUNCT
ejpam-6102	750	4	hence	hence	ADV
ejpam-6102	750	5	we	we	PRON
ejpam-6102	750	6	obtain∫	obtain∫	VERB
ejpam-6102	750	7	b+	b+	ADJ
ejpam-6102	750	8	ω	ω	X
ejpam-6102	750	9	4	4	NUM
ejpam-6102	750	10	n−2	n−2	PROPN
ejpam-6102	750	11	0,µ	0,µ	PROPN
ejpam-6102	750	12	(	(	PUNCT
ejpam-6102	750	13	φ−1(z	φ−1(z	PROPN
ejpam-6102	750	14	)	)	PUNCT
ejpam-6102	750	15	)	)	PUNCT
ejpam-6102	751	1	v21(z)dz	v21(z)dz	PROPN
ejpam-6102	752	1	=	=	SYM
ejpam-6102	752	2	∫	∫	PROPN
ejpam-6102	752	3	b+	b+	X
ejpam-6102	752	4	ω	ω	X
ejpam-6102	752	5	4	4	NUM
ejpam-6102	752	6	n−2	n−2	PROPN
ejpam-6102	752	7	0,µ	0,µ	NOUN
ejpam-6102	752	8	v21(z)dz	v21(z)dz	PROPN
ejpam-6102	753	1	+	+	PROPN
ejpam-6102	753	2	o	o	X
ejpam-6102	753	3	(	(	PUNCT
ejpam-6102	753	4	ρ	ρ	PROPN
ejpam-6102	753	5	∫	∫	PROPN
ejpam-6102	753	6	b+	b+	X
ejpam-6102	753	7	ω	ω	PROPN
ejpam-6102	753	8	4	4	NUM
ejpam-6102	753	9	n−2	n−2	PROPN
ejpam-6102	753	10	0,µ	0,µ	NOUN
ejpam-6102	753	11	v21(z)dz	v21(z)dz	PROPN
ejpam-6102	753	12	)	)	PUNCT
ejpam-6102	754	1	=	=	SYM
ejpam-6102	754	2	∫	∫	PROPN
ejpam-6102	754	3	b+	b+	X
ejpam-6102	754	4	ω	ω	X
ejpam-6102	754	5	4	4	NUM
ejpam-6102	754	6	n−2	n−2	PROPN
ejpam-6102	754	7	0,µ	0,µ	NOUN
ejpam-6102	754	8	v21(z)dz	v21(z)dz	PROPN
ejpam-6102	755	1	+	+	PROPN
ejpam-6102	755	2	o	o	X
ejpam-6102	755	3	(	(	PUNCT
ejpam-6102	755	4	ρ	ρ	PROPN
ejpam-6102	755	5	∥v1∥2l2n/(n−2)(b+	∥v1∥2l2n/(n−2)(b+	PROPN
ejpam-6102	755	6	)	)	PUNCT
ejpam-6102	755	7	)	)	PUNCT
ejpam-6102	755	8	.	.	PUNCT
ejpam-6102	756	1	(	(	PUNCT
ejpam-6102	756	2	87	87	X
ejpam-6102	756	3	)	)	PUNCT
ejpam-6102	756	4	combining	combine	VERB
ejpam-6102	756	5	(	(	PUNCT
ejpam-6102	756	6	84	84	NUM
ejpam-6102	756	7	)	)	PUNCT
ejpam-6102	756	8	,	,	PUNCT
ejpam-6102	756	9	(	(	PUNCT
ejpam-6102	756	10	85	85	NUM
ejpam-6102	756	11	)	)	PUNCT
ejpam-6102	756	12	and	and	CCONJ
ejpam-6102	756	13	(	(	PUNCT
ejpam-6102	756	14	87	87	NUM
ejpam-6102	756	15	)	)	PUNCT
ejpam-6102	756	16	,	,	PUNCT
ejpam-6102	756	17	we	we	PRON
ejpam-6102	756	18	get	get	VERB
ejpam-6102	756	19	qa	qa	PROPN
ejpam-6102	756	20	,	,	PUNCT
ejpam-6102	756	21	ρ(v	ρ(v	PROPN
ejpam-6102	756	22	)	)	PUNCT
ejpam-6102	757	1	=	=	SYM
ejpam-6102	757	2	∫	∫	PROPN
ejpam-6102	757	3	(	(	PUNCT
ejpam-6102	757	4	b(0,ρ)∩ω)\v	b(0,ρ)∩ω)\v	NUM
ejpam-6102	757	5	(	(	PUNCT
ejpam-6102	757	6	|∇v|2	|∇v|2	X
ejpam-6102	757	7	+	+	X
ejpam-6102	757	8	γ̄v2	γ̄v2	X
ejpam-6102	757	9	)	)	PUNCT
ejpam-6102	758	1	−	−	PROPN
ejpam-6102	759	1	n+	n+	NUM
ejpam-6102	759	2	2	2	NUM
ejpam-6102	759	3	n−	n−	NOUN
ejpam-6102	759	4	2	2	NUM
ejpam-6102	759	5	∫	∫	NOUN
ejpam-6102	759	6	(	(	PUNCT
ejpam-6102	759	7	b(0,ρ)∩ω)\v	b(0,ρ)∩ω)\v	PROPN
ejpam-6102	759	8	ω	ω	PROPN
ejpam-6102	759	9	4	4	NUM
ejpam-6102	759	10	n−2	n−2	PROPN
ejpam-6102	759	11	0,µ	0,µ	PROPN
ejpam-6102	759	12	v2	v2	PROPN
ejpam-6102	759	13	r.	r.	PROPN
ejpam-6102	759	14	almushahhin	almushahhin	PROPN
ejpam-6102	759	15	,	,	PUNCT
ejpam-6102	759	16	m.	m.	PROPN
ejpam-6102	759	17	ben	ben	PROPN
ejpam-6102	759	18	ayed	aye	VERB
ejpam-6102	759	19	/	/	SYM
ejpam-6102	759	20	eur	eur	PROPN
ejpam-6102	759	21	.	.	PUNCT
ejpam-6102	760	1	j.	j.	PROPN
ejpam-6102	760	2	pure	pure	PROPN
ejpam-6102	760	3	appl	appl	PROPN
ejpam-6102	760	4	.	.	PROPN
ejpam-6102	760	5	math	math	PROPN
ejpam-6102	760	6	,	,	PUNCT
ejpam-6102	760	7	18	18	NUM
ejpam-6102	760	8	(	(	PUNCT
ejpam-6102	760	9	2	2	NUM
ejpam-6102	760	10	)	)	PUNCT
ejpam-6102	760	11	(	(	PUNCT
ejpam-6102	760	12	2025	2025	NUM
ejpam-6102	760	13	)	)	PUNCT
ejpam-6102	760	14	,	,	PUNCT
ejpam-6102	760	15	6102	6102	NUM
ejpam-6102	760	16	27	27	NUM
ejpam-6102	760	17	of	of	ADP
ejpam-6102	760	18	31	31	NUM
ejpam-6102	760	19	+	+	CCONJ
ejpam-6102	760	20	∫	∫	PROPN
ejpam-6102	760	21	b+	b+	X
ejpam-6102	760	22	|∇v1|2	|∇v1|2	X
ejpam-6102	760	23	+	+	CCONJ
ejpam-6102	760	24	γ̄	γ̄	PROPN
ejpam-6102	760	25	∫	∫	PROPN
ejpam-6102	760	26	b+	b+	X
ejpam-6102	760	27	(	(	PUNCT
ejpam-6102	760	28	v1	v1	NOUN
ejpam-6102	760	29	)	)	PUNCT
ejpam-6102	760	30	2	2	NUM
ejpam-6102	760	31	−	−	NOUN
ejpam-6102	760	32	n+	n+	ADP
ejpam-6102	760	33	2	2	NUM
ejpam-6102	760	34	n−	n−	NOUN
ejpam-6102	760	35	2	2	NUM
ejpam-6102	760	36	∫	∫	NOUN
ejpam-6102	760	37	b+	b+	X
ejpam-6102	760	38	ω	ω	PROPN
ejpam-6102	760	39	4	4	NUM
ejpam-6102	760	40	n−2	n−2	PROPN
ejpam-6102	760	41	0,µ	0,µ	NOUN
ejpam-6102	760	42	v21	v21	NOUN
ejpam-6102	761	1	+	+	NOUN
ejpam-6102	761	2	o	o	X
ejpam-6102	761	3	(	(	PUNCT
ejpam-6102	761	4	ρ	ρ	PROPN
ejpam-6102	761	5	∥v1∥h1(b+	∥v1∥h1(b+	PROPN
ejpam-6102	761	6	)	)	PUNCT
ejpam-6102	761	7	)	)	PUNCT
ejpam-6102	761	8	,	,	PUNCT
ejpam-6102	761	9	(	(	PUNCT
ejpam-6102	761	10	88	88	X
ejpam-6102	761	11	)	)	PUNCT
ejpam-6102	761	12	observe	observe	VERB
ejpam-6102	761	13	that	that	SCONJ
ejpam-6102	761	14	,	,	PUNCT
ejpam-6102	761	15	since	since	SCONJ
ejpam-6102	761	16	b(0	b(0	NOUN
ejpam-6102	761	17	,	,	PUNCT
ejpam-6102	761	18	ρ/4	ρ/4	NUM
ejpam-6102	761	19	)	)	PUNCT
ejpam-6102	762	1	⊂	⊂	PROPN
ejpam-6102	762	2	v	v	ADP
ejpam-6102	762	3	,	,	PUNCT
ejpam-6102	762	4	we	we	PRON
ejpam-6102	762	5	deduce	deduce	VERB
ejpam-6102	762	6	that∫	that∫	NOUN
ejpam-6102	762	7	(	(	PUNCT
ejpam-6102	762	8	b(0,ρ)∩ω\v	b(0,ρ)∩ω\v	PROPN
ejpam-6102	762	9	)	)	PUNCT
ejpam-6102	762	10	ω	ω	PROPN
ejpam-6102	762	11	4	4	NUM
ejpam-6102	762	12	n−2	n−2	PROPN
ejpam-6102	762	13	0,µ	0,µ	PROPN
ejpam-6102	762	14	v2	v2	PROPN
ejpam-6102	762	15	⩽	⩽	PROPN
ejpam-6102	762	16	c∥v∥2l2(b(0,ρ	c∥v∥2l2(b(0,ρ	PROPN
ejpam-6102	762	17	)	)	PUNCT
ejpam-6102	762	18	)	)	PUNCT
ejpam-6102	763	1	(	(	PUNCT
ejpam-6102	763	2	∫	∫	PROPN
ejpam-6102	763	3	rn\b(0,ρ/4	rn\b(0,ρ/4	PROPN
ejpam-6102	763	4	)	)	PUNCT
ejpam-6102	763	5	ω	ω	NUM
ejpam-6102	763	6	2n	2n	NUM
ejpam-6102	764	1	n−2	n−2	PROPN
ejpam-6102	764	2	0,µ	0,µ	PROPN
ejpam-6102	764	3	)	)	PUNCT
ejpam-6102	764	4	2	2	NUM
ejpam-6102	764	5	/	/	SYM
ejpam-6102	764	6	n	n	CCONJ
ejpam-6102	764	7	⩽	⩽	NOUN
ejpam-6102	764	8	c	c	PROPN
ejpam-6102	764	9	(	(	PUNCT
ejpam-6102	764	10	µρ)2	µρ)2	PROPN
ejpam-6102	764	11	∥v∥2l2(b(0,r)∩ω	∥v∥2l2(b(0,r)∩ω	PROPN
ejpam-6102	764	12	)	)	PUNCT
ejpam-6102	764	13	.	.	PUNCT
ejpam-6102	765	1	thus	thus	ADV
ejpam-6102	765	2	(	(	PUNCT
ejpam-6102	765	3	88	88	NUM
ejpam-6102	765	4	)	)	PUNCT
ejpam-6102	765	5	becomes	become	VERB
ejpam-6102	765	6	qa	qa	PROPN
ejpam-6102	765	7	,	,	PUNCT
ejpam-6102	765	8	ρ(v	ρ(v	PROPN
ejpam-6102	765	9	)	)	PUNCT
ejpam-6102	765	10	=	=	SYM
ejpam-6102	765	11	∫	∫	PROPN
ejpam-6102	765	12	(	(	PUNCT
ejpam-6102	765	13	b(0,ρ)∩ω)\v	b(0,ρ)∩ω)\v	NUM
ejpam-6102	765	14	(	(	PUNCT
ejpam-6102	765	15	|∇v|2	|∇v|2	X
ejpam-6102	765	16	+	+	X
ejpam-6102	765	17	γ̄v2	γ̄v2	X
ejpam-6102	765	18	)	)	PUNCT
ejpam-6102	766	1	+	+	ADJ
ejpam-6102	766	2	q+	q+	ADV
ejpam-6102	766	3	(	(	PUNCT
ejpam-6102	766	4	v1	v1	NOUN
ejpam-6102	766	5	)	)	PUNCT
ejpam-6102	767	1	+	+	NOUN
ejpam-6102	767	2	o	o	X
ejpam-6102	767	3	(	(	PUNCT
ejpam-6102	767	4	ρ∥v∥h1(b(0,ρ)∩ω	ρ∥v∥h1(b(0,ρ)∩ω	NUM
ejpam-6102	767	5	)	)	PUNCT
ejpam-6102	767	6	)	)	PUNCT
ejpam-6102	767	7	.	.	PUNCT
ejpam-6102	768	1	(	(	PUNCT
ejpam-6102	768	2	89	89	NUM
ejpam-6102	768	3	)	)	PUNCT
ejpam-6102	768	4	at	at	ADP
ejpam-6102	768	5	this	this	DET
ejpam-6102	768	6	step	step	NOUN
ejpam-6102	768	7	,	,	PUNCT
ejpam-6102	768	8	we	we	PRON
ejpam-6102	768	9	need	need	VERB
ejpam-6102	768	10	to	to	PART
ejpam-6102	768	11	apply	apply	VERB
ejpam-6102	768	12	lemma	lemma	PROPN
ejpam-6102	768	13	10	10	NUM
ejpam-6102	768	14	to	to	ADP
ejpam-6102	768	15	the	the	DET
ejpam-6102	768	16	function	function	NOUN
ejpam-6102	768	17	v1	v1	NOUN
ejpam-6102	768	18	,	,	PUNCT
ejpam-6102	768	19	defined	define	VERB
ejpam-6102	768	20	by	by	ADP
ejpam-6102	768	21	(	(	PUNCT
ejpam-6102	768	22	83	83	NUM
ejpam-6102	768	23	)	)	PUNCT
ejpam-6102	768	24	,	,	PUNCT
ejpam-6102	768	25	but	but	CCONJ
ejpam-6102	768	26	v1	v1	PROPN
ejpam-6102	768	27	/∈	/∈	PUNCT
ejpam-6102	768	28	e+	e+	ADJ
ejpam-6102	768	29	µ	µ	NOUN
ejpam-6102	768	30	.	.	PUNCT
ejpam-6102	769	1	for	for	ADP
ejpam-6102	769	2	this	this	DET
ejpam-6102	769	3	reason	reason	NOUN
ejpam-6102	769	4	,	,	PUNCT
ejpam-6102	769	5	we	we	PRON
ejpam-6102	769	6	decompose	decompose	VERB
ejpam-6102	769	7	v1	v1	NOUN
ejpam-6102	769	8	as	as	SCONJ
ejpam-6102	769	9	follows	follow	VERB
ejpam-6102	769	10	:	:	PUNCT
ejpam-6102	769	11	v1	v1	PROPN
ejpam-6102	769	12	=	=	SYM
ejpam-6102	769	13	n+1∑	n+1∑	PROPN
ejpam-6102	769	14	j=1	j=1	PROPN
ejpam-6102	769	15	σjψj	σjψj	PROPN
ejpam-6102	770	1	+	+	CCONJ
ejpam-6102	770	2	v⊥1	v⊥1	PUNCT
ejpam-6102	770	3	with	with	ADP
ejpam-6102	770	4	v⊥1	v⊥1	SYM
ejpam-6102	770	5	∈	∈	PROPN
ejpam-6102	770	6	e+	e+	VERB
ejpam-6102	770	7	µ	µ	NOUN
ejpam-6102	770	8	,	,	PUNCT
ejpam-6102	770	9	where	where	SCONJ
ejpam-6102	770	10	the	the	DET
ejpam-6102	770	11	ψj	ψj	ADV
ejpam-6102	770	12	’s	’s	ADJ
ejpam-6102	770	13	are	be	AUX
ejpam-6102	770	14	defined	define	VERB
ejpam-6102	770	15	in	in	ADP
ejpam-6102	770	16	(	(	PUNCT
ejpam-6102	770	17	76	76	NUM
ejpam-6102	770	18	)	)	PUNCT
ejpam-6102	770	19	.	.	PUNCT
ejpam-6102	771	1	now	now	ADV
ejpam-6102	771	2	,	,	PUNCT
ejpam-6102	771	3	we	we	PRON
ejpam-6102	771	4	need	need	VERB
ejpam-6102	771	5	to	to	PART
ejpam-6102	771	6	estimate	estimate	VERB
ejpam-6102	771	7	the	the	DET
ejpam-6102	771	8	parameters	parameter	NOUN
ejpam-6102	771	9	σj	σj	VERB
ejpam-6102	771	10	’	'	PUNCT
ejpam-6102	771	11	s.	s.	PROPN
ejpam-6102	771	12	observe	observe	VERB
ejpam-6102	771	13	that	that	SCONJ
ejpam-6102	771	14	,	,	PUNCT
ejpam-6102	771	15	on	on	ADP
ejpam-6102	771	16	one	one	NUM
ejpam-6102	771	17	hand	hand	NOUN
ejpam-6102	771	18	we	we	PRON
ejpam-6102	771	19	have:∫	have:∫	VERB
ejpam-6102	771	20	b+	b+	X
ejpam-6102	771	21	∇v1∇ψ1	∇v1∇ψ1	NOUN
ejpam-6102	771	22	=	=	SYM
ejpam-6102	771	23	σ1	σ1	PROPN
ejpam-6102	771	24	∫	∫	NOUN
ejpam-6102	771	25	b+	b+	PUNCT
ejpam-6102	771	26	|∇ψ1|2	|∇ψ1|2	PROPN
ejpam-6102	771	27	+	+	CCONJ
ejpam-6102	771	28	∑	∑	PROPN
ejpam-6102	771	29	j	j	PROPN
ejpam-6102	771	30	̸=1	̸=1	NOUN
ejpam-6102	771	31	∫	∫	PROPN
ejpam-6102	771	32	b+	b+	X
ejpam-6102	771	33	∇ψ1∇ψj	∇ψ1∇ψj	NOUN
ejpam-6102	771	34	=	=	SYM
ejpam-6102	771	35	cσ1	cσ1	NOUN
ejpam-6102	771	36	+	+	CCONJ
ejpam-6102	771	37	o	o	X
ejpam-6102	771	38	(	(	PUNCT
ejpam-6102	771	39	∑	∑	PROPN
ejpam-6102	771	40	|σj	|σj	PRON
ejpam-6102	771	41	|	|	ADV
ejpam-6102	771	42	)	)	PUNCT
ejpam-6102	771	43	.	.	PUNCT
ejpam-6102	772	1	(	(	PUNCT
ejpam-6102	772	2	90	90	NUM
ejpam-6102	772	3	)	)	PUNCT
ejpam-6102	772	4	on	on	ADP
ejpam-6102	772	5	the	the	DET
ejpam-6102	772	6	other	other	ADJ
ejpam-6102	772	7	hand	hand	NOUN
ejpam-6102	772	8	,	,	PUNCT
ejpam-6102	772	9	we	we	PRON
ejpam-6102	772	10	have	have	VERB
ejpam-6102	772	11	:	:	PUNCT
ejpam-6102	772	12	∫	∫	PROPN
ejpam-6102	772	13	b+	b+	X
ejpam-6102	772	14	∇v1∇ψ1	∇v1∇ψ1	X
ejpam-6102	772	15	=	=	SYM
ejpam-6102	772	16	∫	∫	X
ejpam-6102	772	17	b+	b+	X
ejpam-6102	772	18	∇v1∇ω0,µ	∇v1∇ω0,µ	NOUN
ejpam-6102	772	19	=	=	SYM
ejpam-6102	772	20	∫	∫	X
ejpam-6102	772	21	b+	b+	X
ejpam-6102	772	22	(	(	PUNCT
ejpam-6102	772	23	−∆ω0,µ	−∆ω0,µ	NOUN
ejpam-6102	772	24	)	)	PUNCT
ejpam-6102	772	25	v1	v1	PROPN
ejpam-6102	772	26	+	+	CCONJ
ejpam-6102	772	27	∫	∫	PROPN
ejpam-6102	772	28	∂b+	∂b+	PROPN
ejpam-6102	772	29	(	(	PUNCT
ejpam-6102	772	30	∂	∂	NUM
ejpam-6102	772	31	∂ν	∂ν	PROPN
ejpam-6102	772	32	ω0,µ	ω0,µ	PROPN
ejpam-6102	772	33	)	)	PUNCT
ejpam-6102	772	34	v1	v1	PROPN
ejpam-6102	772	35	=	=	SYM
ejpam-6102	772	36	∫	∫	PROPN
ejpam-6102	772	37	b+	b+	X
ejpam-6102	773	1	ω	ω	PROPN
ejpam-6102	773	2	n+2	n+2	NUM
ejpam-6102	773	3	n−2	n−2	PROPN
ejpam-6102	773	4	0,µ	0,µ	PROPN
ejpam-6102	773	5	v1	v1	NOUN
ejpam-6102	773	6	+	+	CCONJ
ejpam-6102	773	7	∫	∫	PROPN
ejpam-6102	773	8	∂b+	∂b+	PROPN
ejpam-6102	773	9	(	(	PUNCT
ejpam-6102	773	10	∂	∂	NUM
ejpam-6102	773	11	∂ν	∂ν	PROPN
ejpam-6102	773	12	ω0,µ	ω0,µ	PROPN
ejpam-6102	773	13	)	)	PUNCT
ejpam-6102	773	14	v1	v1	NOUN
ejpam-6102	773	15	.	.	PUNCT
ejpam-6102	774	1	(	(	PUNCT
ejpam-6102	774	2	91	91	NUM
ejpam-6102	774	3	)	)	PUNCT
ejpam-6102	774	4	let	let	VERB
ejpam-6102	774	5	γ1	γ1	NOUN
ejpam-6102	774	6	:	:	PUNCT
ejpam-6102	774	7	=	=	SYM
ejpam-6102	774	8	{	{	PUNCT
ejpam-6102	774	9	x	x	SYM
ejpam-6102	774	10	=	=	X
ejpam-6102	774	11	(	(	PUNCT
ejpam-6102	774	12	x′	x′	PROPN
ejpam-6102	774	13	,	,	PUNCT
ejpam-6102	774	14	xn	xn	PROPN
ejpam-6102	774	15	)	)	PUNCT
ejpam-6102	774	16	:	:	PUNCT
ejpam-6102	775	1	|x|	|x|	PROPN
ejpam-6102	775	2	=	=	SYM
ejpam-6102	775	3	ρ	ρ	PROPN
ejpam-6102	775	4	and	and	CCONJ
ejpam-6102	775	5	xn	xn	NUM
ejpam-6102	775	6	⩾	⩾	PROPN
ejpam-6102	775	7	0	0	NUM
ejpam-6102	775	8	}	}	PUNCT
ejpam-6102	775	9	and	and	CCONJ
ejpam-6102	775	10	γ2	γ2	ADJ
ejpam-6102	775	11	:	:	PUNCT
ejpam-6102	775	12	=	=	SYM
ejpam-6102	775	13	{	{	PUNCT
ejpam-6102	775	14	x	x	SYM
ejpam-6102	775	15	=	=	SYM
ejpam-6102	775	16	(	(	PUNCT
ejpam-6102	775	17	x	x	X
ejpam-6102	775	18	,	,	PUNCT
ejpam-6102	775	19	0	0	NUM
ejpam-6102	775	20	)	)	PUNCT
ejpam-6102	775	21	:	:	PUNCT
ejpam-6102	776	1	|x|	|x|	PROPN
ejpam-6102	776	2	⩽	⩽	PROPN
ejpam-6102	776	3	ρ	ρ	PROPN
ejpam-6102	776	4	}	}	PUNCT
ejpam-6102	776	5	.	.	PUNCT
ejpam-6102	777	1	it	it	PRON
ejpam-6102	777	2	is	be	AUX
ejpam-6102	777	3	easy	easy	ADJ
ejpam-6102	777	4	to	to	PART
ejpam-6102	777	5	see	see	VERB
ejpam-6102	777	6	that	that	DET
ejpam-6102	777	7	∂b+	∂b+	NOUN
ejpam-6102	777	8	=	=	SYM
ejpam-6102	777	9	γ1uγ2	γ1uγ2	NOUN
ejpam-6102	777	10	,	,	PUNCT
ejpam-6102	777	11	∂	∂	NUM
ejpam-6102	777	12	∂ν	∂ν	PROPN
ejpam-6102	778	1	ω0,µ	ω0,µ	PROPN
ejpam-6102	778	2	=	=	NOUN
ejpam-6102	778	3	0	0	PROPN
ejpam-6102	778	4	on	on	ADP
ejpam-6102	778	5	γ2	γ2	PROPN
ejpam-6102	778	6	and	and	CCONJ
ejpam-6102	778	7	∂	∂	NUM
ejpam-6102	778	8	∂ν	∂ν	X
ejpam-6102	779	1	ω0,µ	ω0,µ	PROPN
ejpam-6102	779	2	=	=	SYM
ejpam-6102	779	3	o	o	PROPN
ejpam-6102	779	4	(	(	PUNCT
ejpam-6102	779	5	1	1	NUM
ejpam-6102	779	6	µ(n−2)/2	µ(n−2)/2	PROPN
ejpam-6102	779	7	)	)	PUNCT
ejpam-6102	779	8	on	on	ADP
ejpam-6102	779	9	γ1	γ1	PROPN
ejpam-6102	779	10	.	.	PUNCT
ejpam-6102	780	1	thus	thus	ADV
ejpam-6102	780	2	∣∣∣∣∫	∣∣∣∣∫	NUM
ejpam-6102	780	3	∂b+	∂b+	PROPN
ejpam-6102	780	4	(	(	PUNCT
ejpam-6102	780	5	∂	∂	NUM
ejpam-6102	780	6	∂ν	∂ν	PROPN
ejpam-6102	780	7	ω0,µ	ω0,µ	PROPN
ejpam-6102	780	8	)	)	PUNCT
ejpam-6102	780	9	v1	v1	PROPN
ejpam-6102	780	10	∣∣∣∣	∣∣∣∣	PROPN
ejpam-6102	780	11	⩽	⩽	NOUN
ejpam-6102	780	12	c	c	PROPN
ejpam-6102	780	13	µ(n−2)/2	µ(n−2)/2	PROPN
ejpam-6102	780	14	∫	∫	PROPN
ejpam-6102	780	15	γ1	γ1	PROPN
ejpam-6102	780	16	|v1|	|v1|	PROPN
ejpam-6102	780	17	⩽	⩽	PROPN
ejpam-6102	780	18	c	c	PROPN
ejpam-6102	780	19	µ(n−2)/2	µ(n−2)/2	PROPN
ejpam-6102	780	20	∥v1∥h1(b+	∥v1∥h1(b+	PROPN
ejpam-6102	780	21	)	)	PUNCT
ejpam-6102	780	22	.	.	PUNCT
ejpam-6102	781	1	(	(	PUNCT
ejpam-6102	781	2	92	92	NUM
ejpam-6102	781	3	)	)	PUNCT
ejpam-6102	781	4	for	for	ADP
ejpam-6102	781	5	the	the	DET
ejpam-6102	781	6	other	other	ADJ
ejpam-6102	781	7	integral	integral	ADJ
ejpam-6102	781	8	,	,	PUNCT
ejpam-6102	781	9	we	we	PRON
ejpam-6102	781	10	get∫	get∫	X
ejpam-6102	781	11	b+	b+	ADV
ejpam-6102	781	12	ω	ω	PROPN
ejpam-6102	781	13	n+2	n+2	NUM
ejpam-6102	781	14	n−2	n−2	PROPN
ejpam-6102	781	15	0,µ	0,µ	PROPN
ejpam-6102	781	16	v1	v1	NOUN
ejpam-6102	781	17	=	=	SYM
ejpam-6102	781	18	∫	∫	PROPN
ejpam-6102	781	19	b+	b+	X
ejpam-6102	782	1	ω	ω	PROPN
ejpam-6102	782	2	n+2	n+2	NUM
ejpam-6102	782	3	n−2	n−2	PROPN
ejpam-6102	782	4	0,µ	0,µ	PROPN
ejpam-6102	782	5	(	(	PUNCT
ejpam-6102	782	6	z)v	z)v	X
ejpam-6102	782	7	(	(	PUNCT
ejpam-6102	782	8	φ−1(z	φ−1(z	PROPN
ejpam-6102	782	9	)	)	PUNCT
ejpam-6102	782	10	)	)	PUNCT
ejpam-6102	783	1	dz	dz	PROPN
ejpam-6102	783	2	=	=	PUNCT
ejpam-6102	783	3	∫	∫	PROPN
ejpam-6102	783	4	v	v	NUM
ejpam-6102	783	5	∩ω	∩ω	PROPN
ejpam-6102	783	6	ω	ω	PROPN
ejpam-6102	784	1	n+2	n+2	NUM
ejpam-6102	784	2	n−2	n−2	PROPN
ejpam-6102	784	3	0,µ	0,µ	PROPN
ejpam-6102	784	4	(	(	PUNCT
ejpam-6102	784	5	φ(x))v(x)dx	φ(x))v(x)dx	PROPN
ejpam-6102	784	6	.	.	PUNCT
ejpam-6102	785	1	(	(	PUNCT
ejpam-6102	785	2	93	93	NUM
ejpam-6102	785	3	)	)	PUNCT
ejpam-6102	785	4	using	use	VERB
ejpam-6102	785	5	(	(	PUNCT
ejpam-6102	785	6	86	86	NUM
ejpam-6102	785	7	)	)	PUNCT
ejpam-6102	785	8	,	,	PUNCT
ejpam-6102	785	9	(	(	PUNCT
ejpam-6102	785	10	93	93	NUM
ejpam-6102	785	11	)	)	PUNCT
ejpam-6102	785	12	becomes∫	becomes∫	NOUN
ejpam-6102	785	13	b+	b+	VERB
ejpam-6102	785	14	ω	ω	PROPN
ejpam-6102	785	15	n+2	n+2	NUM
ejpam-6102	785	16	n−2	n−2	PROPN
ejpam-6102	785	17	0,µ	0,µ	PROPN
ejpam-6102	785	18	v1	v1	NOUN
ejpam-6102	785	19	=	=	SYM
ejpam-6102	785	20	∫	∫	PROPN
ejpam-6102	785	21	v∩ω	v∩ω	PROPN
ejpam-6102	785	22	ω	ω	PROPN
ejpam-6102	786	1	n+2	n+2	PROPN
ejpam-6102	786	2	n−2	n−2	PROPN
ejpam-6102	786	3	0,µ	0,µ	PROPN
ejpam-6102	786	4	(	(	PUNCT
ejpam-6102	786	5	x)v(x)dx+o	x)v(x)dx+o	PROPN
ejpam-6102	786	6	(	(	PUNCT
ejpam-6102	786	7	ρ	ρ	PROPN
ejpam-6102	786	8	∫	∫	PROPN
ejpam-6102	786	9	v∩ω	v∩ω	PROPN
ejpam-6102	786	10	ω	ω	PROPN
ejpam-6102	786	11	n+2	n+2	PROPN
ejpam-6102	786	12	n−2	n−2	PROPN
ejpam-6102	786	13	0,µ	0,µ	PROPN
ejpam-6102	786	14	(	(	PUNCT
ejpam-6102	786	15	x	x	X
ejpam-6102	786	16	)	)	PUNCT
ejpam-6102	786	17	|v(x)|	|v(x)|	PROPN
ejpam-6102	786	18	dx	dx	PROPN
ejpam-6102	786	19	)	)	PUNCT
ejpam-6102	787	1	=	=	SYM
ejpam-6102	788	1	∫	∫	PROPN
ejpam-6102	789	1	ω	ω	PROPN
ejpam-6102	789	2	ω	ω	PROPN
ejpam-6102	790	1	n+2	n+2	NUM
ejpam-6102	791	1	n−2	n−2	PROPN
ejpam-6102	791	2	0,µ	0,µ	NOUN
ejpam-6102	791	3	v	v	ADP
ejpam-6102	791	4	−	−	PROPN
ejpam-6102	791	5	∫	∫	PROPN
ejpam-6102	791	6	ω\v	ω\v	PROPN
ejpam-6102	791	7	ω	ω	PROPN
ejpam-6102	792	1	n+2	n+2	PROPN
ejpam-6102	792	2	n−2	n−2	PROPN
ejpam-6102	792	3	0,µ	0,µ	NOUN
ejpam-6102	792	4	v	v	ADP
ejpam-6102	792	5	+	+	NOUN
ejpam-6102	792	6	o	o	X
ejpam-6102	792	7	(	(	PUNCT
ejpam-6102	792	8	ρ∥v∥l2n	ρ∥v∥l2n	PROPN
ejpam-6102	792	9	/	/	SYM
ejpam-6102	792	10	n−2(v	n−2(v	NOUN
ejpam-6102	792	11	∩ω	∩ω	NOUN
ejpam-6102	792	12	)	)	PUNCT
ejpam-6102	792	13	)	)	PUNCT
ejpam-6102	793	1	=	=	SYM
ejpam-6102	793	2	∫	∫	PROPN
ejpam-6102	793	3	ω	ω	NUM
ejpam-6102	793	4	∇ω0,µ∇v	∇ω0,µ∇v	NOUN
ejpam-6102	793	5	−	−	PROPN
ejpam-6102	793	6	∫	∫	PROPN
ejpam-6102	793	7	∂ω	∂ω	PROPN
ejpam-6102	793	8	(	(	PUNCT
ejpam-6102	793	9	∂	∂	NUM
ejpam-6102	793	10	∂ν	∂ν	PROPN
ejpam-6102	793	11	ω0,µ	ω0,µ	PROPN
ejpam-6102	793	12	)	)	PUNCT
ejpam-6102	793	13	v	v	ADP
ejpam-6102	793	14	+	+	PROPN
ejpam-6102	793	15	o	o	X
ejpam-6102	793	16	(	(	PUNCT
ejpam-6102	793	17	∥v∥l2n	∥v∥l2n	X
ejpam-6102	793	18	/	/	SYM
ejpam-6102	793	19	n−2(ω	n−2(ω	NOUN
ejpam-6102	793	20	)	)	PUNCT
ejpam-6102	793	21	[	[	PUNCT
ejpam-6102	793	22	ρ+	ρ+	NUM
ejpam-6102	793	23	1	1	NUM
ejpam-6102	793	24	(	(	PUNCT
ejpam-6102	793	25	µρ)(n+2)/2	µρ)(n+2)/2	X
ejpam-6102	793	26	]	]	PUNCT
ejpam-6102	793	27	)	)	PUNCT
ejpam-6102	793	28	.	.	PUNCT
ejpam-6102	794	1	r.	r.	PROPN
ejpam-6102	794	2	almushahhin	almushahhin	PROPN
ejpam-6102	794	3	,	,	PUNCT
ejpam-6102	794	4	m.	m.	PROPN
ejpam-6102	794	5	ben	ben	PROPN
ejpam-6102	794	6	ayed	aye	VERB
ejpam-6102	794	7	/	/	SYM
ejpam-6102	794	8	eur	eur	PROPN
ejpam-6102	794	9	.	.	PUNCT
ejpam-6102	795	1	j.	j.	PROPN
ejpam-6102	795	2	pure	pure	PROPN
ejpam-6102	795	3	appl	appl	PROPN
ejpam-6102	795	4	.	.	PROPN
ejpam-6102	795	5	math	math	PROPN
ejpam-6102	795	6	,	,	PUNCT
ejpam-6102	795	7	18	18	NUM
ejpam-6102	795	8	(	(	PUNCT
ejpam-6102	795	9	2	2	NUM
ejpam-6102	795	10	)	)	PUNCT
ejpam-6102	795	11	(	(	PUNCT
ejpam-6102	795	12	2025	2025	NUM
ejpam-6102	795	13	)	)	PUNCT
ejpam-6102	795	14	,	,	PUNCT
ejpam-6102	795	15	6102	6102	NUM
ejpam-6102	795	16	28	28	NUM
ejpam-6102	795	17	of	of	ADP
ejpam-6102	795	18	31	31	NUM
ejpam-6102	795	19	using	use	VERB
ejpam-6102	795	20	the	the	DET
ejpam-6102	795	21	fact	fact	NOUN
ejpam-6102	795	22	that	that	SCONJ
ejpam-6102	795	23	v	v	NUM
ejpam-6102	795	24	∈	∈	NOUN
ejpam-6102	795	25	fa,µ	fa,µ	NOUN
ejpam-6102	795	26	and	and	CCONJ
ejpam-6102	795	27	equation	equation	NOUN
ejpam-6102	795	28	(	(	PUNCT
ejpam-6102	795	29	19	19	NUM
ejpam-6102	795	30	)	)	PUNCT
ejpam-6102	795	31	,	,	PUNCT
ejpam-6102	795	32	we	we	PRON
ejpam-6102	795	33	obtain∫	obtain∫	VERB
ejpam-6102	795	34	b+	b+	ADJ
ejpam-6102	795	35	ω	ω	PROPN
ejpam-6102	795	36	n+2	n+2	NUM
ejpam-6102	796	1	n−2	n−2	PROPN
ejpam-6102	796	2	0,µ	0,µ	NOUN
ejpam-6102	796	3	v1	v1	NOUN
ejpam-6102	796	4	=	=	SYM
ejpam-6102	796	5	o	o	X
ejpam-6102	796	6	(	(	PUNCT
ejpam-6102	796	7	∥v∥l2n	∥v∥l2n	X
ejpam-6102	796	8	/	/	SYM
ejpam-6102	796	9	n−2(ω	n−2(ω	NOUN
ejpam-6102	796	10	)	)	PUNCT
ejpam-6102	796	11	[	[	PUNCT
ejpam-6102	796	12	1	1	NUM
ejpam-6102	796	13	µ	µ	X
ejpam-6102	796	14	+	+	NUM
ejpam-6102	796	15	ρ+	ρ+	NUM
ejpam-6102	796	16	1	1	NUM
ejpam-6102	796	17	(	(	PUNCT
ejpam-6102	796	18	µρ)(n+2)/2	µρ)(n+2)/2	X
ejpam-6102	796	19	]	]	PUNCT
ejpam-6102	796	20	)	)	PUNCT
ejpam-6102	797	1	=	=	SYM
ejpam-6102	797	2	o	o	X
ejpam-6102	797	3	(	(	PUNCT
ejpam-6102	797	4	∥v∥l2n/(n−2)(ω	∥v∥l2n/(n−2)(ω	NOUN
ejpam-6102	797	5	)	)	PUNCT
ejpam-6102	797	6	)	)	PUNCT
ejpam-6102	797	7	.	.	PUNCT
ejpam-6102	798	1	(	(	PUNCT
ejpam-6102	798	2	94	94	X
ejpam-6102	798	3	)	)	PUNCT
ejpam-6102	798	4	combining	combine	VERB
ejpam-6102	798	5	(	(	PUNCT
ejpam-6102	798	6	90	90	NUM
ejpam-6102	798	7	)	)	PUNCT
ejpam-6102	798	8	,	,	PUNCT
ejpam-6102	798	9	(	(	PUNCT
ejpam-6102	798	10	91	91	NUM
ejpam-6102	798	11	)	)	PUNCT
ejpam-6102	798	12	,	,	PUNCT
ejpam-6102	798	13	(	(	PUNCT
ejpam-6102	798	14	92	92	NUM
ejpam-6102	798	15	)	)	PUNCT
ejpam-6102	798	16	and	and	CCONJ
ejpam-6102	798	17	(	(	PUNCT
ejpam-6102	798	18	94	94	NUM
ejpam-6102	798	19	)	)	PUNCT
ejpam-6102	798	20	,	,	PUNCT
ejpam-6102	798	21	we	we	PRON
ejpam-6102	798	22	get	get	VERB
ejpam-6102	798	23	σ1	σ1	NOUN
ejpam-6102	798	24	=	=	PUNCT
ejpam-6102	799	1	o	o	X
ejpam-6102	799	2	(	(	PUNCT
ejpam-6102	799	3	∑	∑	PROPN
ejpam-6102	799	4	|σj	|σj	PRON
ejpam-6102	799	5	|	|	ADV
ejpam-6102	799	6	)	)	PUNCT
ejpam-6102	800	1	+	+	CCONJ
ejpam-6102	800	2	o	o	X
ejpam-6102	800	3	(	(	PUNCT
ejpam-6102	800	4	∥v∥h1(ω	∥v∥h1(ω	NOUN
ejpam-6102	800	5	)	)	PUNCT
ejpam-6102	800	6	)	)	PUNCT
ejpam-6102	800	7	.	.	PUNCT
ejpam-6102	801	1	in	in	ADP
ejpam-6102	801	2	the	the	DET
ejpam-6102	801	3	same	same	ADJ
ejpam-6102	801	4	way	way	NOUN
ejpam-6102	801	5	,	,	PUNCT
ejpam-6102	801	6	we	we	PRON
ejpam-6102	801	7	get	get	VERB
ejpam-6102	801	8	the	the	DET
ejpam-6102	801	9	estimate	estimate	NOUN
ejpam-6102	801	10	of	of	ADP
ejpam-6102	801	11	σi	σi	PRON
ejpam-6102	801	12	for	for	ADP
ejpam-6102	801	13	i	i	PRON
ejpam-6102	801	14	⩾	⩾	NOUN
ejpam-6102	801	15	2	2	NUM
ejpam-6102	801	16	and	and	CCONJ
ejpam-6102	801	17	therefore	therefore	ADV
ejpam-6102	801	18	we	we	PRON
ejpam-6102	801	19	obtain	obtain	VERB
ejpam-6102	801	20	σi	σi	NOUN
ejpam-6102	802	1	=	=	NOUN
ejpam-6102	802	2	o	o	X
ejpam-6102	802	3	(	(	PUNCT
ejpam-6102	802	4	∑	∑	PROPN
ejpam-6102	802	5	|σj	|σj	PRON
ejpam-6102	802	6	|	|	ADV
ejpam-6102	802	7	)	)	PUNCT
ejpam-6102	803	1	+	+	CCONJ
ejpam-6102	803	2	o	o	X
ejpam-6102	803	3	(	(	PUNCT
ejpam-6102	803	4	∥v∥h1(ω	∥v∥h1(ω	NOUN
ejpam-6102	803	5	)	)	PUNCT
ejpam-6102	803	6	)	)	PUNCT
ejpam-6102	803	7	∀i	∀i	NOUN
ejpam-6102	803	8	=	=	SYM
ejpam-6102	803	9	1	1	NUM
ejpam-6102	803	10	,	,	PUNCT
ejpam-6102	803	11	.	.	PUNCT
ejpam-6102	803	12	.	.	PUNCT
ejpam-6102	804	1	.	.	PUNCT
ejpam-6102	805	1	,	,	PUNCT
ejpam-6102	805	2	n+	n+	ADP
ejpam-6102	805	3	1	1	NUM
ejpam-6102	805	4	,	,	PUNCT
ejpam-6102	805	5	which	which	PRON
ejpam-6102	805	6	implies	imply	VERB
ejpam-6102	805	7	that	that	SCONJ
ejpam-6102	806	1	σi	σi	NOUN
ejpam-6102	806	2	=	=	NOUN
ejpam-6102	806	3	o	o	X
ejpam-6102	806	4	(	(	PUNCT
ejpam-6102	806	5	∥v∥h1(ω	∥v∥h1(ω	NOUN
ejpam-6102	806	6	)	)	PUNCT
ejpam-6102	806	7	)	)	PUNCT
ejpam-6102	806	8	∀i	∀i	NOUN
ejpam-6102	806	9	=	=	SYM
ejpam-6102	806	10	1	1	NUM
ejpam-6102	806	11	,	,	PUNCT
ejpam-6102	806	12	.	.	PUNCT
ejpam-6102	806	13	.	.	PUNCT
ejpam-6102	806	14	.	.	PUNCT
ejpam-6102	807	1	,	,	PUNCT
ejpam-6102	807	2	n+	n+	PUNCT
ejpam-6102	807	3	1	1	X
ejpam-6102	807	4	.	.	PUNCT
ejpam-6102	807	5	hence	hence	ADV
ejpam-6102	807	6	we	we	PRON
ejpam-6102	807	7	deduce	deduce	VERB
ejpam-6102	807	8	that	that	DET
ejpam-6102	807	9	v1	v1	NOUN
ejpam-6102	807	10	−	−	NOUN
ejpam-6102	807	11	v⊥1	v⊥1	PUNCT
ejpam-6102	808	1	=	=	SYM
ejpam-6102	808	2	o	o	X
ejpam-6102	808	3	(	(	PUNCT
ejpam-6102	808	4	∥v∥ω0,µ	∥v∥ω0,µ	NOUN
ejpam-6102	808	5	)	)	PUNCT
ejpam-6102	808	6	and	and	CCONJ
ejpam-6102	808	7	∇	∇	X
ejpam-6102	808	8	(	(	PUNCT
ejpam-6102	808	9	v1	v1	VERB
ejpam-6102	808	10	−	−	NOUN
ejpam-6102	808	11	v⊥1	v⊥1	PUNCT
ejpam-6102	808	12	)	)	PUNCT
ejpam-6102	809	1	=	=	SYM
ejpam-6102	809	2	o	o	NOUN
ejpam-6102	809	3	(	(	PUNCT
ejpam-6102	809	4	∥v∥	∥v∥	PROPN
ejpam-6102	809	5	∑	∑	PROPN
ejpam-6102	809	6	|∇ψj	|∇ψj	PROPN
ejpam-6102	809	7	|	|	ADV
ejpam-6102	809	8	)	)	PUNCT
ejpam-6102	809	9	.	.	PUNCT
ejpam-6102	810	1	(	(	PUNCT
ejpam-6102	810	2	95	95	NUM
ejpam-6102	810	3	)	)	PUNCT
ejpam-6102	810	4	this	this	PRON
ejpam-6102	810	5	implies	imply	VERB
ejpam-6102	810	6	that	that	SCONJ
ejpam-6102	810	7	(	(	PUNCT
ejpam-6102	810	8	by	by	ADP
ejpam-6102	810	9	using	use	VERB
ejpam-6102	810	10	v⊥2	v⊥2	PROPN
ejpam-6102	810	11	∈	∈	PROPN
ejpam-6102	810	12	e+	e+	PUNCT
ejpam-6102	810	13	µ	µ	NOUN
ejpam-6102	810	14	)	)	PUNCT
ejpam-6102	810	15	q+	q+	ADV
ejpam-6102	810	16	(	(	PUNCT
ejpam-6102	810	17	v1	v1	NOUN
ejpam-6102	810	18	)	)	PUNCT
ejpam-6102	810	19	=	=	SYM
ejpam-6102	810	20	∫	∫	X
ejpam-6102	810	21	b+	b+	X
ejpam-6102	810	22	|∇v1|2	|∇v1|2	X
ejpam-6102	810	23	+	+	CCONJ
ejpam-6102	810	24	γ̄	γ̄	PROPN
ejpam-6102	810	25	∫	∫	PROPN
ejpam-6102	810	26	b+	b+	X
ejpam-6102	810	27	v21	v21	PROPN
ejpam-6102	810	28	−	−	PROPN
ejpam-6102	810	29	n+	n+	NOUN
ejpam-6102	810	30	2	2	NUM
ejpam-6102	810	31	n−	n−	NOUN
ejpam-6102	810	32	2	2	NUM
ejpam-6102	810	33	∫	∫	NOUN
ejpam-6102	810	34	b+	b+	X
ejpam-6102	810	35	ω	ω	PROPN
ejpam-6102	810	36	4	4	NUM
ejpam-6102	810	37	n−2	n−2	PROPN
ejpam-6102	810	38	0,µ	0,µ	NOUN
ejpam-6102	810	39	v21	v21	NOUN
ejpam-6102	810	40	=	=	SYM
ejpam-6102	810	41	∫	∫	X
ejpam-6102	810	42	b+	b+	X
ejpam-6102	810	43	∣∣∇v⊥1	∣∣∇v⊥1	PROPN
ejpam-6102	810	44	∣∣2	∣∣2	PROPN
ejpam-6102	810	45	+	+	CCONJ
ejpam-6102	810	46	∫	∫	PROPN
ejpam-6102	810	47	b+	b+	X
ejpam-6102	810	48	∣∣∇	∣∣∇	PROPN
ejpam-6102	810	49	(	(	PUNCT
ejpam-6102	810	50	v1	v1	VERB
ejpam-6102	810	51	−	−	NOUN
ejpam-6102	810	52	v⊥1	v⊥1	PUNCT
ejpam-6102	810	53	)	)	PUNCT
ejpam-6102	810	54	∣∣2	∣∣2	PROPN
ejpam-6102	810	55	+	+	NUM
ejpam-6102	810	56	γ̄	γ̄	PROPN
ejpam-6102	810	57	∫	∫	PROPN
ejpam-6102	810	58	b+	b+	X
ejpam-6102	810	59	(	(	PUNCT
ejpam-6102	810	60	v⊥1	v⊥1	ADJ
ejpam-6102	810	61	)	)	PUNCT
ejpam-6102	810	62	2	2	NUM
ejpam-6102	810	63	+	+	SYM
ejpam-6102	810	64	2γ̄	2γ̄	NUM
ejpam-6102	810	65	∫	∫	NOUN
ejpam-6102	810	66	b+	b+	X
ejpam-6102	810	67	(	(	PUNCT
ejpam-6102	810	68	v⊥1	v⊥1	X
ejpam-6102	810	69	)	)	PUNCT
ejpam-6102	810	70	(	(	PUNCT
ejpam-6102	810	71	v1	v1	VERB
ejpam-6102	810	72	−	−	NOUN
ejpam-6102	810	73	v⊥1	v⊥1	PUNCT
ejpam-6102	810	74	)	)	PUNCT
ejpam-6102	811	1	+	+	CCONJ
ejpam-6102	811	2	γ̄	γ̄	PROPN
ejpam-6102	811	3	∫	∫	PROPN
ejpam-6102	811	4	b+	b+	X
ejpam-6102	811	5	(	(	PUNCT
ejpam-6102	811	6	v1	v1	VERB
ejpam-6102	811	7	−	−	NOUN
ejpam-6102	811	8	v⊥1	v⊥1	PUNCT
ejpam-6102	811	9	)	)	PUNCT
ejpam-6102	811	10	2	2	NUM
ejpam-6102	811	11	−	−	NOUN
ejpam-6102	811	12	n+	n+	ADP
ejpam-6102	811	13	2	2	NUM
ejpam-6102	811	14	n−	n−	NOUN
ejpam-6102	811	15	2	2	NUM
ejpam-6102	811	16	∫	∫	NOUN
ejpam-6102	811	17	b+	b+	X
ejpam-6102	811	18	ω	ω	X
ejpam-6102	811	19	4	4	NUM
ejpam-6102	811	20	n−2	n−2	PROPN
ejpam-6102	811	21	0,µ	0,µ	NOUN
ejpam-6102	811	22	[	[	X
ejpam-6102	811	23	(	(	PUNCT
ejpam-6102	811	24	v⊥1	v⊥1	ADJ
ejpam-6102	811	25	)	)	PUNCT
ejpam-6102	811	26	2	2	NUM
ejpam-6102	812	1	+	+	NUM
ejpam-6102	812	2	2v⊥1	2v⊥1	NUM
ejpam-6102	812	3	(	(	PUNCT
ejpam-6102	812	4	v1	v1	NOUN
ejpam-6102	812	5	−	−	NOUN
ejpam-6102	812	6	v⊥1	v⊥1	PUNCT
ejpam-6102	812	7	)	)	PUNCT
ejpam-6102	813	1	+	+	CCONJ
ejpam-6102	813	2	(	(	PUNCT
ejpam-6102	813	3	v1	v1	VERB
ejpam-6102	813	4	−	−	NOUN
ejpam-6102	813	5	v⊥1	v⊥1	PUNCT
ejpam-6102	813	6	)	)	PUNCT
ejpam-6102	813	7	2	2	X
ejpam-6102	813	8	]	]	PUNCT
ejpam-6102	813	9	=	=	SYM
ejpam-6102	813	10	q+	q+	X
ejpam-6102	813	11	(	(	PUNCT
ejpam-6102	813	12	v⊥1	v⊥1	PUNCT
ejpam-6102	813	13	)	)	PUNCT
ejpam-6102	814	1	+	+	CCONJ
ejpam-6102	815	1	o	o	NOUN
ejpam-6102	815	2	(	(	PUNCT
ejpam-6102	815	3	∥v⊥1	∥v⊥1	NOUN
ejpam-6102	815	4	∥2	∥2	NOUN
ejpam-6102	815	5	+	+	CCONJ
ejpam-6102	815	6	∥v∥2	∥v∥2	ADJ
ejpam-6102	815	7	)	)	PUNCT
ejpam-6102	815	8	⩾	⩾	NOUN
ejpam-6102	815	9	1	1	NUM
ejpam-6102	815	10	2	2	NUM
ejpam-6102	815	11	β1	β1	NOUN
ejpam-6102	815	12	(	(	PUNCT
ejpam-6102	815	13	∫	∫	PROPN
ejpam-6102	815	14	b+	b+	X
ejpam-6102	815	15	∣∣∇v⊥1	∣∣∇v⊥1	PROPN
ejpam-6102	815	16	∣∣2	∣∣2	PROPN
ejpam-6102	815	17	+	+	CCONJ
ejpam-6102	815	18	γ̄	γ̄	PROPN
ejpam-6102	815	19	∫	∫	PROPN
ejpam-6102	815	20	b+	b+	X
ejpam-6102	815	21	(	(	PUNCT
ejpam-6102	815	22	v⊥1	v⊥1	ADJ
ejpam-6102	815	23	)	)	PUNCT
ejpam-6102	815	24	2	2	X
ejpam-6102	815	25	)	)	PUNCT
ejpam-6102	816	1	+	+	NUM
ejpam-6102	816	2	o	o	X
ejpam-6102	816	3	(	(	PUNCT
ejpam-6102	816	4	∥v∥2	∥v∥2	PROPN
ejpam-6102	816	5	)	)	PUNCT
ejpam-6102	816	6	,	,	PUNCT
ejpam-6102	816	7	(	(	PUNCT
ejpam-6102	816	8	96	96	NUM
ejpam-6102	816	9	)	)	PUNCT
ejpam-6102	816	10	by	by	ADP
ejpam-6102	816	11	using	use	VERB
ejpam-6102	816	12	lemma	lemma	PROPN
ejpam-6102	816	13	10	10	NUM
ejpam-6102	816	14	,	,	PUNCT
ejpam-6102	816	15	eq	eq	NOUN
ejpam-6102	816	16	.	.	PUNCT
ejpam-6102	816	17	(	(	PUNCT
ejpam-6102	816	18	79	79	NUM
ejpam-6102	816	19	)	)	PUNCT
ejpam-6102	816	20	and	and	CCONJ
ejpam-6102	816	21	the	the	DET
ejpam-6102	816	22	fact	fact	NOUN
ejpam-6102	816	23	that	that	SCONJ
ejpam-6102	816	24	v⊥1	v⊥1	PRON
ejpam-6102	816	25	∈	∈	PROPN
ejpam-6102	816	26	e+	e+	VERB
ejpam-6102	816	27	µ	µ	X
ejpam-6102	816	28	.	.	PUNCT
ejpam-6102	817	1	combining	combine	VERB
ejpam-6102	817	2	(	(	PUNCT
ejpam-6102	817	3	96	96	NUM
ejpam-6102	817	4	)	)	PUNCT
ejpam-6102	817	5	,	,	PUNCT
ejpam-6102	817	6	(	(	PUNCT
ejpam-6102	817	7	95	95	NUM
ejpam-6102	817	8	)	)	PUNCT
ejpam-6102	817	9	,	,	PUNCT
ejpam-6102	817	10	(	(	PUNCT
ejpam-6102	817	11	89	89	NUM
ejpam-6102	817	12	)	)	PUNCT
ejpam-6102	817	13	and	and	CCONJ
ejpam-6102	817	14	(	(	PUNCT
ejpam-6102	817	15	84	84	NUM
ejpam-6102	817	16	)	)	PUNCT
ejpam-6102	817	17	,	,	PUNCT
ejpam-6102	817	18	the	the	DET
ejpam-6102	817	19	proof	proof	NOUN
ejpam-6102	817	20	of	of	ADP
ejpam-6102	817	21	lemma	lemma	PROPN
ejpam-6102	817	22	11	11	NUM
ejpam-6102	817	23	follows	follow	VERB
ejpam-6102	817	24	.	.	PUNCT
ejpam-6102	818	1	now	now	ADV
ejpam-6102	818	2	,	,	PUNCT
ejpam-6102	818	3	we	we	PRON
ejpam-6102	818	4	are	be	AUX
ejpam-6102	818	5	ready	ready	ADJ
ejpam-6102	818	6	to	to	PART
ejpam-6102	818	7	prove	prove	VERB
ejpam-6102	818	8	proposition	proposition	NOUN
ejpam-6102	818	9	1	1	NUM
ejpam-6102	818	10	.	.	PUNCT
ejpam-6102	818	11	proof	proof	NOUN
ejpam-6102	818	12	of	of	ADP
ejpam-6102	818	13	proposition	proposition	NOUN
ejpam-6102	818	14	1	1	NUM
ejpam-6102	818	15	let	let	VERB
ejpam-6102	818	16	ρ	ρ	NOUN
ejpam-6102	818	17	be	be	AUX
ejpam-6102	818	18	a	a	DET
ejpam-6102	818	19	small	small	ADJ
ejpam-6102	818	20	radius	radius	NOUN
ejpam-6102	818	21	and	and	CCONJ
ejpam-6102	818	22	let	let	VERB
ejpam-6102	818	23	bi	bi	NOUN
ejpam-6102	818	24	:	:	PUNCT
ejpam-6102	818	25	=	=	SYM
ejpam-6102	818	26	b	b	X
ejpam-6102	818	27	(	(	PUNCT
ejpam-6102	818	28	ai	ai	NOUN
ejpam-6102	818	29	,	,	PUNCT
ejpam-6102	818	30	ρ)∩ω	ρ)∩ω	PROPN
ejpam-6102	818	31	.	.	PUNCT
ejpam-6102	819	1	since	since	SCONJ
ejpam-6102	819	2	|ai	|ai	NUM
ejpam-6102	819	3	−	−	PROPN
ejpam-6102	819	4	aj	aj	VERB
ejpam-6102	819	5	|	|	ADV
ejpam-6102	819	6	⩾	⩾	PROPN
ejpam-6102	819	7	c	c	NOUN
ejpam-6102	819	8	>	>	PUNCT
ejpam-6102	819	9	0	0	PUNCT
ejpam-6102	820	1	for	for	ADP
ejpam-6102	820	2	i	i	PROPN
ejpam-6102	820	3	̸=	̸=	PROPN
ejpam-6102	820	4	j	j	PROPN
ejpam-6102	820	5	,	,	PUNCT
ejpam-6102	820	6	it	it	PRON
ejpam-6102	820	7	follows	follow	VERB
ejpam-6102	820	8	that	that	SCONJ
ejpam-6102	820	9	bi	bi	NOUN
ejpam-6102	820	10	∩bj	∩bj	NOUN
ejpam-6102	820	11	=	=	NOUN
ejpam-6102	820	12	∅	∅	NOUN
ejpam-6102	820	13	for	for	ADP
ejpam-6102	820	14	each	each	DET
ejpam-6102	820	15	i	i	PRON
ejpam-6102	820	16	̸=	̸=	PROPN
ejpam-6102	820	17	j.	j.	PROPN
ejpam-6102	820	18	thus	thus	ADV
ejpam-6102	820	19	we	we	PRON
ejpam-6102	820	20	get	get	VERB
ejpam-6102	820	21	q(v	q(v	ADJ
ejpam-6102	820	22	)	)	PUNCT
ejpam-6102	821	1	=	=	PUNCT
ejpam-6102	822	1	q∑	q∑	PROPN
ejpam-6102	822	2	i=1	i=1	PROPN
ejpam-6102	823	1	(	(	PUNCT
ejpam-6102	823	2	∫	∫	PROPN
ejpam-6102	823	3	bi	bi	PROPN
ejpam-6102	823	4	|∇v|2	|∇v|2	PROPN
ejpam-6102	824	1	+	+	CCONJ
ejpam-6102	824	2	∫	∫	PROPN
ejpam-6102	824	3	bi	bi	NOUN
ejpam-6102	824	4	v	v	X
ejpam-6102	824	5	v2	v2	PROPN
ejpam-6102	824	6	−	−	PROPN
ejpam-6102	824	7	n+	n+	NOUN
ejpam-6102	824	8	2	2	NUM
ejpam-6102	824	9	n−	n−	NOUN
ejpam-6102	824	10	2	2	NUM
ejpam-6102	824	11	∫	∫	PROPN
ejpam-6102	824	12	bi	bi	PROPN
ejpam-6102	824	13	ω	ω	PROPN
ejpam-6102	824	14	4	4	NUM
ejpam-6102	824	15	n−2	n−2	PROPN
ejpam-6102	824	16	ai,µiv	ai,µiv	PROPN
ejpam-6102	824	17	2	2	NUM
ejpam-6102	824	18	)	)	PUNCT
ejpam-6102	824	19	+	+	CCONJ
ejpam-6102	824	20	∫	∫	PROPN
ejpam-6102	824	21	ω\(ubi	ω\(ubi	NUM
ejpam-6102	824	22	)	)	PUNCT
ejpam-6102	824	23	|∇v|2	|∇v|2	VERB
ejpam-6102	824	24	+	+	CCONJ
ejpam-6102	824	25	∫	∫	PROPN
ejpam-6102	824	26	ω\(ubi	ω\(ubi	NUM
ejpam-6102	824	27	)	)	PUNCT
ejpam-6102	824	28	v	v	ADP
ejpam-6102	824	29	v2	v2	PROPN
ejpam-6102	824	30	−	−	PUNCT
ejpam-6102	824	31	n+	n+	NOUN
ejpam-6102	824	32	2	2	NUM
ejpam-6102	824	33	n−	n−	NOUN
ejpam-6102	824	34	2	2	NUM
ejpam-6102	824	35	q∑	q∑	PROPN
ejpam-6102	824	36	i=1	i=1	PROPN
ejpam-6102	824	37	∫	∫	PROPN
ejpam-6102	824	38	ω\bi	ω\bi	PROPN
ejpam-6102	824	39	ω	ω	PROPN
ejpam-6102	824	40	4	4	NUM
ejpam-6102	824	41	n−2	n−2	PROPN
ejpam-6102	824	42	ai,µiv	ai,µiv	PROPN
ejpam-6102	824	43	2	2	NUM
ejpam-6102	824	44	.	.	X
ejpam-6102	825	1	observe	observe	VERB
ejpam-6102	825	2	that	that	SCONJ
ejpam-6102	825	3	,	,	PUNCT
ejpam-6102	825	4	for	for	ADP
ejpam-6102	825	5	each	each	DET
ejpam-6102	825	6	i	i	PRON
ejpam-6102	825	7	∈	∈	PROPN
ejpam-6102	825	8	{	{	PUNCT
ejpam-6102	825	9	1	1	NUM
ejpam-6102	825	10	,	,	PUNCT
ejpam-6102	825	11	.	.	PUNCT
ejpam-6102	825	12	.	.	PUNCT
ejpam-6102	826	1	.	.	PUNCT
ejpam-6102	827	1	,	,	PUNCT
ejpam-6102	827	2	q	q	X
ejpam-6102	827	3	}	}	PUNCT
ejpam-6102	827	4	,	,	PUNCT
ejpam-6102	827	5	we	we	PRON
ejpam-6102	827	6	have	have	VERB
ejpam-6102	827	7	∫	∫	PROPN
ejpam-6102	827	8	ω\bi	ω\bi	PROPN
ejpam-6102	827	9	ω	ω	PROPN
ejpam-6102	827	10	4	4	NUM
ejpam-6102	827	11	n−2	n−2	PROPN
ejpam-6102	827	12	ai,µiv	ai,µiv	PROPN
ejpam-6102	827	13	2	2	NUM
ejpam-6102	827	14	⩽	⩽	NOUN
ejpam-6102	827	15	(	(	PUNCT
ejpam-6102	827	16	∫	∫	PROPN
ejpam-6102	827	17	ω\bi	ω\bi	PROPN
ejpam-6102	827	18	v	v	PROPN
ejpam-6102	827	19	2n	2n	NUM
ejpam-6102	827	20	n−2	n−2	PROPN
ejpam-6102	827	21	)	)	PUNCT
ejpam-6102	828	1	n−2	n−2	PROPN
ejpam-6102	828	2	n	n	PROPN
ejpam-6102	828	3	(	(	PUNCT
ejpam-6102	828	4	∫	∫	PROPN
ejpam-6102	828	5	ω\bi	ω\bi	PROPN
ejpam-6102	828	6	ω	ω	PROPN
ejpam-6102	828	7	2n	2n	NUM
ejpam-6102	828	8	n−2	n−2	PROPN
ejpam-6102	828	9	ai,µi	ai,µi	NOUN
ejpam-6102	828	10	)	)	PUNCT
ejpam-6102	828	11	2	2	NUM
ejpam-6102	828	12	/	/	SYM
ejpam-6102	828	13	n	n	CCONJ
ejpam-6102	828	14	⩽	⩽	NOUN
ejpam-6102	828	15	c	c	PROPN
ejpam-6102	828	16	(	(	PUNCT
ejpam-6102	828	17	µiρ	µiρ	PROPN
ejpam-6102	828	18	)	)	PUNCT
ejpam-6102	828	19	2	2	NUM
ejpam-6102	828	20	∥v∥	∥v∥	NOUN
ejpam-6102	828	21	2	2	NUM
ejpam-6102	828	22	h1(ω	h1(ω	NOUN
ejpam-6102	828	23	)	)	PUNCT
ejpam-6102	828	24	.	.	PUNCT
ejpam-6102	829	1	(	(	PUNCT
ejpam-6102	829	2	97	97	NUM
ejpam-6102	829	3	)	)	PUNCT
ejpam-6102	829	4	r.	r.	PROPN
ejpam-6102	829	5	almushahhin	almushahhin	PROPN
ejpam-6102	829	6	,	,	PUNCT
ejpam-6102	829	7	m.	m.	PROPN
ejpam-6102	829	8	ben	ben	PROPN
ejpam-6102	829	9	ayed	aye	VERB
ejpam-6102	829	10	/	/	SYM
ejpam-6102	829	11	eur	eur	PROPN
ejpam-6102	829	12	.	.	PUNCT
ejpam-6102	830	1	j.	j.	PROPN
ejpam-6102	830	2	pure	pure	PROPN
ejpam-6102	830	3	appl	appl	PROPN
ejpam-6102	830	4	.	.	PROPN
ejpam-6102	830	5	math	math	PROPN
ejpam-6102	830	6	,	,	PUNCT
ejpam-6102	830	7	18	18	NUM
ejpam-6102	830	8	(	(	PUNCT
ejpam-6102	830	9	2	2	NUM
ejpam-6102	830	10	)	)	PUNCT
ejpam-6102	830	11	(	(	PUNCT
ejpam-6102	830	12	2025	2025	NUM
ejpam-6102	830	13	)	)	PUNCT
ejpam-6102	830	14	,	,	PUNCT
ejpam-6102	830	15	6102	6102	NUM
ejpam-6102	830	16	29	29	NUM
ejpam-6102	830	17	of	of	ADP
ejpam-6102	830	18	31	31	NUM
ejpam-6102	830	19	in	in	ADP
ejpam-6102	830	20	addition	addition	NOUN
ejpam-6102	830	21	,	,	PUNCT
ejpam-6102	830	22	let	let	VERB
ejpam-6102	830	23	γ̄	γ̄	PROPN
ejpam-6102	830	24	=	=	PRON
ejpam-6102	830	25	minv	minv	PROPN
ejpam-6102	830	26	>	>	X
ejpam-6102	830	27	0	0	NUM
ejpam-6102	830	28	,	,	PUNCT
ejpam-6102	830	29	using	use	VERB
ejpam-6102	830	30	(	(	PUNCT
ejpam-6102	830	31	97	97	NUM
ejpam-6102	830	32	)	)	PUNCT
ejpam-6102	830	33	and	and	CCONJ
ejpam-6102	830	34	lemma	lemma	PROPN
ejpam-6102	830	35	11	11	NUM
ejpam-6102	830	36	,	,	PUNCT
ejpam-6102	830	37	we	we	PRON
ejpam-6102	830	38	derive	derive	VERB
ejpam-6102	830	39	that	that	SCONJ
ejpam-6102	830	40	q(v	q(v	NOUN
ejpam-6102	830	41	)	)	PUNCT
ejpam-6102	831	1	⩾	⩾	PROPN
ejpam-6102	832	1	q∑	q∑	PROPN
ejpam-6102	832	2	i=1	i=1	PROPN
ejpam-6102	832	3	qai	qai	PROPN
ejpam-6102	832	4	,	,	PUNCT
ejpam-6102	832	5	ρ(v	ρ(v	PROPN
ejpam-6102	832	6	)	)	PUNCT
ejpam-6102	832	7	+	+	CCONJ
ejpam-6102	832	8	∫	∫	PROPN
ejpam-6102	832	9	ω\(∪bi	ω\(∪bi	NUM
ejpam-6102	832	10	)	)	PUNCT
ejpam-6102	832	11	|∇v|2	|∇v|2	VERB
ejpam-6102	833	1	+	+	CCONJ
ejpam-6102	833	2	∫	∫	PROPN
ejpam-6102	833	3	ω\(∪bi	ω\(∪bi	NUM
ejpam-6102	833	4	)	)	PUNCT
ejpam-6102	833	5	v	v	ADP
ejpam-6102	833	6	v2	v2	PROPN
ejpam-6102	834	1	+	+	CCONJ
ejpam-6102	834	2	∑	∑	PROPN
ejpam-6102	834	3	o	o	X
ejpam-6102	834	4	(	(	PUNCT
ejpam-6102	834	5	∥v∥2	∥v∥2	X
ejpam-6102	834	6	(	(	PUNCT
ejpam-6102	834	7	µiρ	µiρ	NOUN
ejpam-6102	834	8	)	)	PUNCT
ejpam-6102	834	9	2	2	NUM
ejpam-6102	834	10	)	)	PUNCT
ejpam-6102	835	1	⩾	⩾	INTJ
ejpam-6102	835	2	q∑	q∑	PROPN
ejpam-6102	836	1	i=1	i=1	PROPN
ejpam-6102	836	2	β2	β2	PROPN
ejpam-6102	836	3	(	(	PUNCT
ejpam-6102	836	4	∫	∫	PROPN
ejpam-6102	836	5	bi	bi	PROPN
ejpam-6102	836	6	|∇v|2	|∇v|2	PROPN
ejpam-6102	837	1	+	+	CCONJ
ejpam-6102	837	2	γ̄	γ̄	PROPN
ejpam-6102	837	3	∫	∫	PROPN
ejpam-6102	837	4	bi	bi	PROPN
ejpam-6102	837	5	v2	v2	PROPN
ejpam-6102	837	6	)	)	PUNCT
ejpam-6102	838	1	+	+	CCONJ
ejpam-6102	838	2	∫	∫	X
ejpam-6102	838	3	ω\∪bi	ω\∪bi	NOUN
ejpam-6102	838	4	|∇v|2	|∇v|2	X
ejpam-6102	838	5	+	+	CCONJ
ejpam-6102	838	6	∫	∫	X
ejpam-6102	838	7	ω\∪bi	ω\∪bi	NOUN
ejpam-6102	838	8	v	v	ADP
ejpam-6102	838	9	v2	v2	PROPN
ejpam-6102	839	1	+	+	CCONJ
ejpam-6102	839	2	∑	∑	PROPN
ejpam-6102	839	3	o	o	X
ejpam-6102	839	4	(	(	PUNCT
ejpam-6102	839	5	∥v∥2	∥v∥2	X
ejpam-6102	839	6	(	(	PUNCT
ejpam-6102	839	7	µiρ	µiρ	NOUN
ejpam-6102	839	8	)	)	PUNCT
ejpam-6102	839	9	2	2	NUM
ejpam-6102	839	10	)	)	PUNCT
ejpam-6102	839	11	⩾	⩾	PUNCT
ejpam-6102	840	1	β3∥v∥2	β3∥v∥2	NOUN
ejpam-6102	840	2	,	,	PUNCT
ejpam-6102	840	3	for	for	ADP
ejpam-6102	840	4	some	some	DET
ejpam-6102	840	5	positive	positive	ADJ
ejpam-6102	840	6	constant	constant	ADJ
ejpam-6102	840	7	β3	β3	NOUN
ejpam-6102	840	8	(	(	PUNCT
ejpam-6102	840	9	since	since	SCONJ
ejpam-6102	840	10	ρ	ρ	PROPN
ejpam-6102	840	11	is	be	AUX
ejpam-6102	840	12	fixed	fix	VERB
ejpam-6102	840	13	and	and	CCONJ
ejpam-6102	840	14	the	the	DET
ejpam-6102	840	15	µi	µi	PROPN
ejpam-6102	840	16	’s	’s	PART
ejpam-6102	840	17	are	be	AUX
ejpam-6102	840	18	large	large	ADJ
ejpam-6102	840	19	)	)	PUNCT
ejpam-6102	840	20	.	.	PUNCT
ejpam-6102	841	1	this	this	PRON
ejpam-6102	841	2	completes	complete	VERB
ejpam-6102	841	3	the	the	DET
ejpam-6102	841	4	proof	proof	NOUN
ejpam-6102	841	5	.	.	PUNCT
ejpam-6102	842	1	acknowledgements	acknowledgement	NOUN
ejpam-6102	842	2	the	the	DET
ejpam-6102	842	3	authors	author	NOUN
ejpam-6102	842	4	gratefully	gratefully	ADV
ejpam-6102	842	5	acknowledge	acknowledge	VERB
ejpam-6102	842	6	qassim	qassim	PROPN
ejpam-6102	842	7	university	university	PROPN
ejpam-6102	842	8	,	,	PUNCT
ejpam-6102	842	9	represented	represent	VERB
ejpam-6102	842	10	by	by	ADP
ejpam-6102	842	11	the	the	DET
ejpam-6102	842	12	deanship	deanship	NOUN
ejpam-6102	842	13	of	of	ADP
ejpam-6102	842	14	graduate	graduate	NOUN
ejpam-6102	842	15	studies	study	NOUN
ejpam-6102	842	16	and	and	CCONJ
ejpam-6102	842	17	scientific	scientific	ADJ
ejpam-6102	842	18	research	research	NOUN
ejpam-6102	842	19	,	,	PUNCT
ejpam-6102	842	20	on	on	ADP
ejpam-6102	842	21	the	the	DET
ejpam-6102	842	22	financial	financial	ADJ
ejpam-6102	842	23	support	support	NOUN
ejpam-6102	842	24	for	for	ADP
ejpam-6102	842	25	this	this	DET
ejpam-6102	842	26	research	research	NOUN
ejpam-6102	842	27	under	under	ADP
ejpam-6102	842	28	the	the	DET
ejpam-6102	842	29	number	number	NOUN
ejpam-6102	842	30	(	(	PUNCT
ejpam-6102	842	31	qu	qu	PROPN
ejpam-6102	842	32	-	-	PROPN
ejpam-6102	842	33	j	j	NOUN
ejpam-6102	842	34	-	-	PUNCT
ejpam-6102	842	35	pg-2	pg-2	NOUN
ejpam-6102	842	36	-	-	PUNCT
ejpam-6102	842	37	2025	2025	NUM
ejpam-6102	842	38	-	-	SYM
ejpam-6102	842	39	53906	53906	NUM
ejpam-6102	842	40	)	)	PUNCT
ejpam-6102	842	41	during	during	ADP
ejpam-6102	842	42	the	the	DET
ejpam-6102	842	43	academic	academic	ADJ
ejpam-6102	842	44	year	year	NOUN
ejpam-6102	842	45	1446	1446	NUM
ejpam-6102	842	46	ah	ah	INTJ
ejpam-6102	842	47	/	/	SYM
ejpam-6102	842	48	2024	2024	NUM
ejpam-6102	842	49	ad	ad	NOUN
ejpam-6102	842	50	.	.	PUNCT
ejpam-6102	843	1	author	author	NOUN
ejpam-6102	843	2	contributions	contribution	NOUN
ejpam-6102	843	3	:	:	PUNCT
ejpam-6102	844	1	r.a	r.a	NOUN
ejpam-6102	844	2	and	and	CCONJ
ejpam-6102	844	3	m.b.a	m.b.a	NOUN
ejpam-6102	844	4	.	.	PUNCT
ejpam-6102	844	5	:	:	PUNCT
ejpam-6102	845	1	conceptualization	conceptualization	NOUN
ejpam-6102	845	2	,	,	PUNCT
ejpam-6102	845	3	methodology	methodology	NOUN
ejpam-6102	845	4	,	,	PUNCT
ejpam-6102	845	5	investigation	investigation	NOUN
ejpam-6102	845	6	,	,	PUNCT
ejpam-6102	845	7	writing	write	VERB
ejpam-6102	845	8	original	original	ADJ
ejpam-6102	845	9	draft	draft	NOUN
ejpam-6102	845	10	,	,	PUNCT
ejpam-6102	845	11	writing	writing	NOUN
ejpam-6102	845	12	-	-	PUNCT
ejpam-6102	845	13	review	review	NOUN
ejpam-6102	845	14	and	and	CCONJ
ejpam-6102	845	15	editing	editing	NOUN
ejpam-6102	845	16	.	.	PUNCT
ejpam-6102	846	1	all	all	DET
ejpam-6102	846	2	authors	author	NOUN
ejpam-6102	846	3	have	have	AUX
ejpam-6102	846	4	read	read	VERB
ejpam-6102	846	5	and	and	CCONJ
ejpam-6102	846	6	agreed	agree	VERB
ejpam-6102	846	7	to	to	ADP
ejpam-6102	846	8	the	the	DET
ejpam-6102	846	9	published	publish	VERB
ejpam-6102	846	10	version	version	NOUN
ejpam-6102	846	11	of	of	ADP
ejpam-6102	846	12	the	the	DET
ejpam-6102	846	13	manuscript	manuscript	NOUN
ejpam-6102	846	14	.	.	PUNCT
ejpam-6102	847	1	funding	funding	NOUN
ejpam-6102	847	2	:	:	PUNCT
ejpam-6102	847	3	this	this	DET
ejpam-6102	847	4	research	research	NOUN
ejpam-6102	847	5	was	be	AUX
ejpam-6102	847	6	funded	fund	VERB
ejpam-6102	847	7	by	by	ADP
ejpam-6102	847	8	the	the	DET
ejpam-6102	847	9	deanship	deanship	NOUN
ejpam-6102	847	10	of	of	ADP
ejpam-6102	847	11	scientific	scientific	ADJ
ejpam-6102	847	12	research	research	NOUN
ejpam-6102	847	13	,	,	PUNCT
ejpam-6102	847	14	qassim	qassim	PROPN
ejpam-6102	847	15	university	university	NOUN
ejpam-6102	847	16	,	,	PUNCT
ejpam-6102	847	17	grant	grant	VERB
ejpam-6102	847	18	number	number	NOUN
ejpam-6102	847	19	project	project	NOUN
ejpam-6102	847	20	qu	qu	PROPN
ejpam-6102	847	21	-	-	PROPN
ejpam-6102	847	22	j	j	PROPN
ejpam-6102	847	23	-	-	PUNCT
ejpam-6102	847	24	pg-2	pg-2	NOUN
ejpam-6102	847	25	-	-	PUNCT
ejpam-6102	847	26	2025	2025	NUM
ejpam-6102	847	27	-	-	PUNCT
ejpam-6102	847	28	53906	53906	NUM
ejpam-6102	847	29	.	.	PUNCT
ejpam-6102	848	1	data	datum	NOUN
ejpam-6102	848	2	availability	availability	NOUN
ejpam-6102	848	3	statement	statement	NOUN
ejpam-6102	848	4	:	:	PUNCT
ejpam-6102	848	5	no	no	DET
ejpam-6102	848	6	data	datum	NOUN
ejpam-6102	848	7	to	to	PART
ejpam-6102	848	8	report	report	VERB
ejpam-6102	848	9	in	in	ADP
ejpam-6102	848	10	this	this	DET
ejpam-6102	848	11	manuscript	manuscript	NOUN
ejpam-6102	848	12	.	.	PUNCT
ejpam-6102	849	1	conflicts	conflict	NOUN
ejpam-6102	849	2	of	of	ADP
ejpam-6102	849	3	interest	interest	NOUN
ejpam-6102	849	4	:	:	PUNCT
ejpam-6102	849	5	the	the	DET
ejpam-6102	849	6	authors	author	NOUN
ejpam-6102	849	7	declare	declare	VERB
ejpam-6102	849	8	no	no	DET
ejpam-6102	849	9	conflict	conflict	NOUN
ejpam-6102	849	10	of	of	ADP
ejpam-6102	849	11	interest	interest	NOUN
ejpam-6102	849	12	.	.	PUNCT
ejpam-6102	850	1	references	reference	NOUN
ejpam-6102	850	2	[	[	X
ejpam-6102	850	3	1	1	NUM
ejpam-6102	850	4	]	]	X
ejpam-6102	850	5	e.f	e.f	PROPN
ejpam-6102	850	6	.	.	PROPN
ejpam-6102	850	7	keller	keller	PROPN
ejpam-6102	850	8	and	and	CCONJ
ejpam-6102	850	9	l.a	l.a	PROPN
ejpam-6102	850	10	.	.	PROPN
ejpam-6102	850	11	segel	segel	PROPN
ejpam-6102	850	12	.	.	PUNCT
ejpam-6102	851	1	initiation	initiation	NOUN
ejpam-6102	851	2	of	of	ADP
ejpam-6102	851	3	slime	slime	NOUN
ejpam-6102	851	4	mold	mold	NOUN
ejpam-6102	851	5	aggregation	aggregation	NOUN
ejpam-6102	851	6	viewed	view	VERB
ejpam-6102	851	7	as	as	ADP
ejpam-6102	851	8	an	an	DET
ejpam-6102	851	9	instability	instability	NOUN
ejpam-6102	851	10	.	.	PUNCT
ejpam-6102	852	1	j.	j.	PROPN
ejpam-6102	852	2	theor	theor	PROPN
ejpam-6102	852	3	.	.	PUNCT
ejpam-6102	853	1	biol	biol	PROPN
ejpam-6102	853	2	.	.	PUNCT
ejpam-6102	853	3	,	,	PUNCT
ejpam-6102	853	4	26:399–415	26:399–415	NUM
ejpam-6102	853	5	,	,	PUNCT
ejpam-6102	853	6	1970	1970	NUM
ejpam-6102	853	7	.	.	PUNCT
ejpam-6102	854	1	[	[	X
ejpam-6102	854	2	2	2	NUM
ejpam-6102	854	3	]	]	PUNCT
ejpam-6102	854	4	r.	r.	PROPN
ejpam-6102	854	5	schaaf	schaaf	PROPN
ejpam-6102	854	6	.	.	PUNCT
ejpam-6102	855	1	stationary	stationary	ADJ
ejpam-6102	855	2	solutions	solution	NOUN
ejpam-6102	855	3	of	of	ADP
ejpam-6102	855	4	chemotaxis	chemotaxis	ADJ
ejpam-6102	855	5	systems	system	NOUN
ejpam-6102	855	6	.	.	PUNCT
ejpam-6102	856	1	trans	trans	PROPN
ejpam-6102	856	2	.	.	PUNCT
ejpam-6102	857	1	amer	amer	PROPN
ejpam-6102	857	2	.	.	PUNCT
ejpam-6102	857	3	math	math	PROPN
ejpam-6102	857	4	.	.	PUNCT
ejpam-6102	858	1	soc	soc	PROPN
ejpam-6102	858	2	.	.	PUNCT
ejpam-6102	858	3	,	,	PUNCT
ejpam-6102	858	4	292:531–556	292:531–556	NUM
ejpam-6102	858	5	,	,	PUNCT
ejpam-6102	858	6	1985	1985	NUM
ejpam-6102	858	7	.	.	PUNCT
ejpam-6102	859	1	[	[	X
ejpam-6102	859	2	3	3	X
ejpam-6102	859	3	]	]	PUNCT
ejpam-6102	859	4	t.	t.	NOUN
ejpam-6102	859	5	hillen	hillen	PROPN
ejpam-6102	859	6	and	and	CCONJ
ejpam-6102	859	7	k.j	k.j	PROPN
ejpam-6102	859	8	.	.	PROPN
ejpam-6102	859	9	painter	painter	PROPN
ejpam-6102	859	10	.	.	PUNCT
ejpam-6102	860	1	a	a	DET
ejpam-6102	860	2	user	user	NOUN
ejpam-6102	860	3	’s	’s	PART
ejpam-6102	860	4	guide	guide	NOUN
ejpam-6102	860	5	to	to	ADP
ejpam-6102	860	6	pde	pde	NOUN
ejpam-6102	860	7	models	model	NOUN
ejpam-6102	860	8	for	for	ADP
ejpam-6102	860	9	chemotaxis	chemotaxis	NOUN
ejpam-6102	860	10	.	.	PUNCT
ejpam-6102	861	1	j.	j.	PROPN
ejpam-6102	861	2	math	math	PROPN
ejpam-6102	861	3	.	.	PUNCT
ejpam-6102	862	1	biol	biol	PROPN
ejpam-6102	862	2	.	.	PUNCT
ejpam-6102	862	3	,	,	PUNCT
ejpam-6102	862	4	58:183–217	58:183–217	NOUN
ejpam-6102	862	5	,	,	PUNCT
ejpam-6102	862	6	2009	2009	NUM
ejpam-6102	862	7	.	.	PUNCT
ejpam-6102	863	1	[	[	X
ejpam-6102	863	2	4	4	X
ejpam-6102	863	3	]	]	PUNCT
ejpam-6102	863	4	m.	m.	PROPN
ejpam-6102	863	5	bezerra	bezerra	PROPN
ejpam-6102	863	6	,	,	PUNCT
ejpam-6102	863	7	c.	c.	PROPN
ejpam-6102	863	8	cuevas	cuevas	PROPN
ejpam-6102	863	9	,	,	PUNCT
ejpam-6102	863	10	c.	c.	PROPN
ejpam-6102	863	11	silva	silva	PROPN
ejpam-6102	863	12	,	,	PUNCT
ejpam-6102	863	13	and	and	CCONJ
ejpam-6102	863	14	h.	h.	PROPN
ejpam-6102	863	15	soto	soto	PROPN
ejpam-6102	863	16	.	.	PUNCT
ejpam-6102	864	1	on	on	ADP
ejpam-6102	864	2	the	the	DET
ejpam-6102	864	3	fractional	fractional	ADJ
ejpam-6102	864	4	doubly	doubly	ADV
ejpam-6102	864	5	parabolic	parabolic	ADJ
ejpam-6102	864	6	keller	keller	PROPN
ejpam-6102	864	7	-	-	PUNCT
ejpam-6102	864	8	segel	segel	PROPN
ejpam-6102	864	9	system	system	NOUN
ejpam-6102	864	10	modelling	model	VERB
ejpam-6102	864	11	chemotaxis	chemotaxis	ADJ
ejpam-6102	864	12	.	.	PUNCT
ejpam-6102	865	1	science	science	PROPN
ejpam-6102	865	2	china	china	PROPN
ejpam-6102	865	3	mathematics	mathematics	PROPN
ejpam-6102	865	4	,	,	PUNCT
ejpam-6102	865	5	65:1827–1874	65:1827–1874	NUM
ejpam-6102	865	6	,	,	PUNCT
ejpam-6102	865	7	2022	2022	NUM
ejpam-6102	865	8	.	.	PUNCT
ejpam-6102	866	1	[	[	X
ejpam-6102	866	2	5	5	X
ejpam-6102	866	3	]	]	PUNCT
ejpam-6102	866	4	l.	l.	PROPN
ejpam-6102	866	5	almeida	almeida	PROPN
ejpam-6102	866	6	,	,	PUNCT
ejpam-6102	866	7	f.	f.	PROPN
ejpam-6102	866	8	bubba	bubba	PROPN
ejpam-6102	866	9	,	,	PUNCT
ejpam-6102	866	10	b.	b.	PROPN
ejpam-6102	866	11	perthame	perthame	PROPN
ejpam-6102	866	12	,	,	PUNCT
ejpam-6102	866	13	and	and	CCONJ
ejpam-6102	866	14	c.	c.	PROPN
ejpam-6102	866	15	pouchol	pouchol	PROPN
ejpam-6102	866	16	.	.	PUNCT
ejpam-6102	867	1	energy	energy	NOUN
ejpam-6102	867	2	and	and	CCONJ
ejpam-6102	867	3	implicit	implicit	ADJ
ejpam-6102	867	4	discretization	discretization	NOUN
ejpam-6102	867	5	of	of	ADP
ejpam-6102	867	6	the	the	DET
ejpam-6102	867	7	fokker	fokker	NOUN
ejpam-6102	867	8	-	-	PUNCT
ejpam-6102	867	9	planck	planck	NOUN
ejpam-6102	867	10	and	and	CCONJ
ejpam-6102	867	11	keller	keller	PROPN
ejpam-6102	867	12	-	-	PUNCT
ejpam-6102	867	13	segel	segel	PROPN
ejpam-6102	867	14	type	type	NOUN
ejpam-6102	867	15	equations	equation	NOUN
ejpam-6102	867	16	.	.	PUNCT
ejpam-6102	868	1	networks	network	NOUN
ejpam-6102	868	2	and	and	CCONJ
ejpam-6102	868	3	heterogeneous	heterogeneous	ADJ
ejpam-6102	868	4	media	medium	NOUN
ejpam-6102	868	5	,	,	PUNCT
ejpam-6102	868	6	14:23–41	14:23–41	NUM
ejpam-6102	868	7	,	,	PUNCT
ejpam-6102	868	8	2019	2019	NUM
ejpam-6102	868	9	.	.	PUNCT
ejpam-6102	869	1	[	[	X
ejpam-6102	869	2	6	6	NUM
ejpam-6102	869	3	]	]	X
ejpam-6102	869	4	c.s	c.s	PROPN
ejpam-6102	869	5	.	.	PROPN
ejpam-6102	869	6	lin	lin	PROPN
ejpam-6102	869	7	,	,	PUNCT
ejpam-6102	869	8	w.m	w.m	PROPN
ejpam-6102	869	9	.	.	PROPN
ejpam-6102	869	10	ni	ni	PROPN
ejpam-6102	869	11	,	,	PUNCT
ejpam-6102	869	12	and	and	CCONJ
ejpam-6102	869	13	i.	i.	PROPN
ejpam-6102	869	14	takagi	takagi	PROPN
ejpam-6102	869	15	.	.	PUNCT
ejpam-6102	870	1	large	large	ADJ
ejpam-6102	870	2	amplitude	amplitude	NOUN
ejpam-6102	870	3	stationary	stationary	ADJ
ejpam-6102	870	4	solutions	solution	NOUN
ejpam-6102	870	5	to	to	ADP
ejpam-6102	870	6	a	a	DET
ejpam-6102	870	7	chemotaxis	chemotaxis	ADJ
ejpam-6102	870	8	system	system	NOUN
ejpam-6102	870	9	.	.	PUNCT
ejpam-6102	871	1	j.	j.	PROPN
ejpam-6102	871	2	differential	differential	PROPN
ejpam-6102	871	3	equations	equations	PROPN
ejpam-6102	871	4	,	,	PUNCT
ejpam-6102	871	5	72:1–27	72:1–27	NUM
ejpam-6102	871	6	,	,	PUNCT
ejpam-6102	871	7	1988	1988	NUM
ejpam-6102	871	8	.	.	PUNCT
ejpam-6102	872	1	[	[	X
ejpam-6102	872	2	7	7	X
ejpam-6102	872	3	]	]	X
ejpam-6102	872	4	w.m	w.m	PROPN
ejpam-6102	872	5	.	.	PROPN
ejpam-6102	872	6	ni	ni	PROPN
ejpam-6102	872	7	and	and	CCONJ
ejpam-6102	872	8	i.	i.	PROPN
ejpam-6102	872	9	takagi	takagi	PROPN
ejpam-6102	872	10	.	.	PUNCT
ejpam-6102	873	1	on	on	ADP
ejpam-6102	873	2	the	the	DET
ejpam-6102	873	3	shape	shape	NOUN
ejpam-6102	873	4	of	of	ADP
ejpam-6102	873	5	least	least	ADJ
ejpam-6102	873	6	-	-	PUNCT
ejpam-6102	873	7	energy	energy	NOUN
ejpam-6102	873	8	solutions	solution	NOUN
ejpam-6102	873	9	to	to	ADP
ejpam-6102	873	10	a	a	DET
ejpam-6102	873	11	semi	semi	ADJ
ejpam-6102	873	12	-	-	ADJ
ejpam-6102	873	13	linear	linear	ADJ
ejpam-6102	873	14	neumann	neumann	PROPN
ejpam-6102	873	15	problem	problem	NOUN
ejpam-6102	873	16	.	.	PUNCT
ejpam-6102	874	1	comm	comm	NOUN
ejpam-6102	874	2	.	.	PUNCT
ejpam-6102	875	1	pure	pure	ADJ
ejpam-6102	875	2	appl	appl	PROPN
ejpam-6102	875	3	.	.	PUNCT
ejpam-6102	875	4	math	math	PROPN
ejpam-6102	875	5	.	.	PUNCT
ejpam-6102	875	6	,	,	PUNCT
ejpam-6102	876	1	44:819–851	44:819–851	PROPN
ejpam-6102	876	2	,	,	PUNCT
ejpam-6102	876	3	1991	1991	NUM
ejpam-6102	876	4	.	.	PUNCT
ejpam-6102	877	1	[	[	X
ejpam-6102	877	2	8	8	NUM
ejpam-6102	877	3	]	]	X
ejpam-6102	877	4	w.m	w.m	PROPN
ejpam-6102	877	5	.	.	PROPN
ejpam-6102	877	6	ni	ni	PROPN
ejpam-6102	877	7	and	and	CCONJ
ejpam-6102	877	8	i.	i.	PROPN
ejpam-6102	877	9	takagi	takagi	PROPN
ejpam-6102	877	10	.	.	PUNCT
ejpam-6102	878	1	locating	locate	VERB
ejpam-6102	878	2	the	the	DET
ejpam-6102	878	3	peaks	peak	NOUN
ejpam-6102	878	4	of	of	ADP
ejpam-6102	878	5	least	least	ADJ
ejpam-6102	878	6	-	-	PUNCT
ejpam-6102	878	7	energy	energy	NOUN
ejpam-6102	878	8	solutions	solution	NOUN
ejpam-6102	878	9	to	to	ADP
ejpam-6102	878	10	a	a	DET
ejpam-6102	878	11	semi	semi	ADJ
ejpam-6102	878	12	-	-	ADJ
ejpam-6102	878	13	linear	linear	ADJ
ejpam-6102	878	14	neumann	neumann	PROPN
ejpam-6102	878	15	problem	problem	NOUN
ejpam-6102	878	16	.	.	PUNCT
ejpam-6102	879	1	duke	duke	PROPN
ejpam-6102	879	2	math	math	PROPN
ejpam-6102	879	3	.	.	PUNCT
ejpam-6102	880	1	j.	j.	PROPN
ejpam-6102	880	2	,	,	PUNCT
ejpam-6102	880	3	70:247–281	70:247–281	PROPN
ejpam-6102	880	4	,	,	PUNCT
ejpam-6102	880	5	1993	1993	NUM
ejpam-6102	880	6	.	.	PUNCT
ejpam-6102	881	1	r.	r.	PROPN
ejpam-6102	881	2	almushahhin	almushahhin	PROPN
ejpam-6102	881	3	,	,	PUNCT
ejpam-6102	881	4	m.	m.	PROPN
ejpam-6102	881	5	ben	ben	PROPN
ejpam-6102	881	6	ayed	aye	VERB
ejpam-6102	881	7	/	/	SYM
ejpam-6102	881	8	eur	eur	PROPN
ejpam-6102	881	9	.	.	PUNCT
ejpam-6102	882	1	j.	j.	PROPN
ejpam-6102	882	2	pure	pure	PROPN
ejpam-6102	882	3	appl	appl	PROPN
ejpam-6102	882	4	.	.	PROPN
ejpam-6102	882	5	math	math	PROPN
ejpam-6102	882	6	,	,	PUNCT
ejpam-6102	882	7	18	18	NUM
ejpam-6102	882	8	(	(	PUNCT
ejpam-6102	882	9	2	2	NUM
ejpam-6102	882	10	)	)	PUNCT
ejpam-6102	882	11	(	(	PUNCT
ejpam-6102	882	12	2025	2025	NUM
ejpam-6102	882	13	)	)	PUNCT
ejpam-6102	882	14	,	,	PUNCT
ejpam-6102	882	15	6102	6102	NUM
ejpam-6102	882	16	30	30	NUM
ejpam-6102	882	17	of	of	ADP
ejpam-6102	882	18	31	31	NUM
ejpam-6102	882	19	[	[	X
ejpam-6102	882	20	9	9	NUM
ejpam-6102	882	21	]	]	PUNCT
ejpam-6102	882	22	m.	m.	NOUN
ejpam-6102	882	23	del	del	PROPN
ejpam-6102	882	24	pino	pino	PROPN
ejpam-6102	882	25	and	and	CCONJ
ejpam-6102	882	26	p.	p.	PROPN
ejpam-6102	882	27	felmer	felmer	NOUN
ejpam-6102	882	28	.	.	PUNCT
ejpam-6102	883	1	spike	spike	NOUN
ejpam-6102	883	2	-	-	PUNCT
ejpam-6102	883	3	layered	layer	VERB
ejpam-6102	883	4	solutions	solution	NOUN
ejpam-6102	883	5	of	of	ADP
ejpam-6102	883	6	singularly	singularly	ADV
ejpam-6102	883	7	perturbed	perturb	VERB
ejpam-6102	883	8	elliptic	elliptic	ADJ
ejpam-6102	883	9	problems	problem	NOUN
ejpam-6102	883	10	in	in	ADP
ejpam-6102	883	11	a	a	DET
ejpam-6102	883	12	degenerate	degenerate	ADJ
ejpam-6102	883	13	setting	setting	NOUN
ejpam-6102	883	14	.	.	PUNCT
ejpam-6102	884	1	indiana	indiana	PROPN
ejpam-6102	884	2	univ	univ	PROPN
ejpam-6102	884	3	.	.	PUNCT
ejpam-6102	885	1	math	math	PROPN
ejpam-6102	885	2	.	.	PUNCT
ejpam-6102	886	1	j.	j.	PROPN
ejpam-6102	886	2	,	,	PUNCT
ejpam-6102	886	3	48:883–898	48:883–898	PROPN
ejpam-6102	886	4	,	,	PUNCT
ejpam-6102	886	5	1999	1999	NUM
ejpam-6102	886	6	.	.	PUNCT
ejpam-6102	887	1	[	[	X
ejpam-6102	887	2	10	10	NUM
ejpam-6102	887	3	]	]	X
ejpam-6102	887	4	e.	e.	PROPN
ejpam-6102	887	5	n.	n.	PROPN
ejpam-6102	887	6	dancer	dancer	NOUN
ejpam-6102	887	7	and	and	CCONJ
ejpam-6102	887	8	s.	s.	PROPN
ejpam-6102	887	9	yan	yan	PROPN
ejpam-6102	887	10	.	.	PUNCT
ejpam-6102	888	1	multipeak	multipeak	PROPN
ejpam-6102	888	2	solutions	solution	NOUN
ejpam-6102	888	3	for	for	ADP
ejpam-6102	888	4	a	a	DET
ejpam-6102	888	5	singularly	singularly	ADV
ejpam-6102	888	6	perturbed	perturb	VERB
ejpam-6102	888	7	neumann	neumann	PROPN
ejpam-6102	888	8	problem	problem	PROPN
ejpam-6102	888	9	.	.	PUNCT
ejpam-6102	889	1	pacific	pacific	PROPN
ejpam-6102	889	2	j.	j.	PROPN
ejpam-6102	889	3	math	math	PROPN
ejpam-6102	889	4	.	.	PUNCT
ejpam-6102	889	5	,	,	PUNCT
ejpam-6102	889	6	189(2):241–262	189(2):241–262	NUM
ejpam-6102	889	7	,	,	PUNCT
ejpam-6102	889	8	1999	1999	NUM
ejpam-6102	889	9	.	.	PUNCT
ejpam-6102	890	1	[	[	X
ejpam-6102	890	2	11	11	NUM
ejpam-6102	890	3	]	]	PUNCT
ejpam-6102	890	4	m.	m.	NOUN
ejpam-6102	890	5	del	del	PROPN
ejpam-6102	890	6	pino	pino	PROPN
ejpam-6102	890	7	,	,	PUNCT
ejpam-6102	890	8	p.	p.	NOUN
ejpam-6102	890	9	felmer	felmer	NOUN
ejpam-6102	890	10	,	,	PUNCT
ejpam-6102	890	11	and	and	CCONJ
ejpam-6102	890	12	j.	j.	PROPN
ejpam-6102	890	13	wei	wei	PROPN
ejpam-6102	890	14	.	.	PUNCT
ejpam-6102	891	1	on	on	ADP
ejpam-6102	891	2	the	the	DET
ejpam-6102	891	3	role	role	NOUN
ejpam-6102	891	4	of	of	ADP
ejpam-6102	891	5	mean	mean	ADJ
ejpam-6102	891	6	curvature	curvature	NOUN
ejpam-6102	891	7	in	in	ADP
ejpam-6102	891	8	some	some	DET
ejpam-6102	891	9	singularly	singularly	ADV
ejpam-6102	891	10	perturbed	perturb	VERB
ejpam-6102	891	11	neumann	neumann	PROPN
ejpam-6102	891	12	problems	problem	NOUN
ejpam-6102	891	13	.	.	PUNCT
ejpam-6102	892	1	siam	siam	PROPN
ejpam-6102	892	2	j.	j.	PROPN
ejpam-6102	892	3	math	math	PROPN
ejpam-6102	892	4	.	.	PUNCT
ejpam-6102	893	1	anal	anal	PROPN
ejpam-6102	893	2	.	.	PROPN
ejpam-6102	893	3	,	,	PUNCT
ejpam-6102	893	4	31:63–79	31:63–79	NUM
ejpam-6102	893	5	,	,	PUNCT
ejpam-6102	893	6	2000	2000	NUM
ejpam-6102	893	7	.	.	PUNCT
ejpam-6102	894	1	[	[	X
ejpam-6102	894	2	12	12	NUM
ejpam-6102	894	3	]	]	PUNCT
ejpam-6102	894	4	m.	m.	NOUN
ejpam-6102	894	5	grossi	grossi	PROPN
ejpam-6102	894	6	,	,	PUNCT
ejpam-6102	894	7	a.	a.	PROPN
ejpam-6102	894	8	pistoia	pistoia	PROPN
ejpam-6102	894	9	,	,	PUNCT
ejpam-6102	894	10	and	and	CCONJ
ejpam-6102	894	11	j.	j.	PROPN
ejpam-6102	894	12	wei	wei	PROPN
ejpam-6102	894	13	.	.	PUNCT
ejpam-6102	894	14	existence	existence	NOUN
ejpam-6102	894	15	of	of	ADP
ejpam-6102	894	16	multipeak	multipeak	NOUN
ejpam-6102	894	17	solutions	solution	NOUN
ejpam-6102	894	18	for	for	ADP
ejpam-6102	894	19	a	a	DET
ejpam-6102	894	20	semilinear	semilinear	PROPN
ejpam-6102	894	21	neumann	neumann	PROPN
ejpam-6102	894	22	problem	problem	NOUN
ejpam-6102	894	23	via	via	ADP
ejpam-6102	894	24	nonsmooth	nonsmooth	ADJ
ejpam-6102	894	25	critical	critical	ADJ
ejpam-6102	894	26	point	point	NOUN
ejpam-6102	894	27	theory	theory	NOUN
ejpam-6102	894	28	.	.	PUNCT
ejpam-6102	895	1	calc	calc	PROPN
ejpam-6102	895	2	.	.	PUNCT
ejpam-6102	896	1	var	var	PROPN
ejpam-6102	896	2	.	.	PUNCT
ejpam-6102	897	1	pde	pde	NOUN
ejpam-6102	897	2	,	,	PUNCT
ejpam-6102	897	3	11(2):143–175	11(2):143–175	PROPN
ejpam-6102	897	4	,	,	PUNCT
ejpam-6102	897	5	2000	2000	NUM
ejpam-6102	897	6	.	.	PUNCT
ejpam-6102	898	1	[	[	X
ejpam-6102	898	2	13	13	NUM
ejpam-6102	898	3	]	]	X
ejpam-6102	898	4	c.	c.	PROPN
ejpam-6102	898	5	gui	gui	PROPN
ejpam-6102	898	6	and	and	CCONJ
ejpam-6102	898	7	j.	j.	PROPN
ejpam-6102	898	8	wei	wei	PROPN
ejpam-6102	898	9	.	.	PUNCT
ejpam-6102	899	1	multiple	multiple	ADJ
ejpam-6102	899	2	interior	interior	ADJ
ejpam-6102	899	3	peak	peak	NOUN
ejpam-6102	899	4	solutions	solution	NOUN
ejpam-6102	899	5	for	for	ADP
ejpam-6102	899	6	some	some	DET
ejpam-6102	899	7	singularly	singularly	ADV
ejpam-6102	899	8	perturbed	perturb	VERB
ejpam-6102	899	9	neumann	neumann	PROPN
ejpam-6102	899	10	problems	problem	NOUN
ejpam-6102	899	11	.	.	PUNCT
ejpam-6102	900	1	j.	j.	PROPN
ejpam-6102	900	2	differential	differential	PROPN
ejpam-6102	900	3	equations	equations	PROPN
ejpam-6102	900	4	,	,	PUNCT
ejpam-6102	900	5	158:1–27	158:1–27	NUM
ejpam-6102	900	6	,	,	PUNCT
ejpam-6102	900	7	1999	1999	NUM
ejpam-6102	900	8	.	.	PUNCT
ejpam-6102	901	1	[	[	X
ejpam-6102	901	2	14	14	NUM
ejpam-6102	901	3	]	]	X
ejpam-6102	901	4	j.	j.	PROPN
ejpam-6102	901	5	wei	wei	PROPN
ejpam-6102	901	6	,	,	PUNCT
ejpam-6102	901	7	b.	b.	PROPN
ejpam-6102	901	8	xu	xu	PROPN
ejpam-6102	901	9	,	,	PUNCT
ejpam-6102	901	10	and	and	CCONJ
ejpam-6102	901	11	w.	w.	PROPN
ejpam-6102	901	12	yang	yang	PROPN
ejpam-6102	901	13	.	.	PUNCT
ejpam-6102	902	1	on	on	ADP
ejpam-6102	902	2	lin	lin	PROPN
ejpam-6102	902	3	-	-	PUNCT
ejpam-6102	902	4	ni	ni	PROPN
ejpam-6102	902	5	’s	’s	PART
ejpam-6102	902	6	conjecture	conjecture	NOUN
ejpam-6102	902	7	in	in	ADP
ejpam-6102	902	8	dimensions	dimension	NOUN
ejpam-6102	902	9	four	four	NUM
ejpam-6102	902	10	and	and	CCONJ
ejpam-6102	902	11	six	six	NUM
ejpam-6102	902	12	.	.	PUNCT
ejpam-6102	903	1	science	science	NOUN
ejpam-6102	903	2	in	in	ADP
ejpam-6102	903	3	china	china	PROPN
ejpam-6102	903	4	:	:	PUNCT
ejpam-6102	903	5	mathematics	mathematic	NOUN
ejpam-6102	903	6	,	,	PUNCT
ejpam-6102	903	7	49(2):281–306	49(2):281–306	PROPN
ejpam-6102	903	8	,	,	PUNCT
ejpam-6102	903	9	2019	2019	NUM
ejpam-6102	903	10	.	.	PUNCT
ejpam-6102	904	1	[	[	X
ejpam-6102	904	2	15	15	NUM
ejpam-6102	904	3	]	]	X
ejpam-6102	904	4	adimurthi	adimurthi	PROPN
ejpam-6102	904	5	and	and	CCONJ
ejpam-6102	904	6	s.l	s.l	PROPN
ejpam-6102	904	7	.	.	PROPN
ejpam-6102	904	8	yadava	yadava	PROPN
ejpam-6102	904	9	.	.	PUNCT
ejpam-6102	905	1	existence	existence	NOUN
ejpam-6102	905	2	and	and	CCONJ
ejpam-6102	905	3	nonexistence	nonexistence	NOUN
ejpam-6102	905	4	of	of	ADP
ejpam-6102	905	5	positive	positive	ADJ
ejpam-6102	905	6	radial	radial	ADJ
ejpam-6102	905	7	solutions	solution	NOUN
ejpam-6102	905	8	of	of	ADP
ejpam-6102	905	9	neumann	neumann	PROPN
ejpam-6102	905	10	problems	problem	NOUN
ejpam-6102	905	11	with	with	ADP
ejpam-6102	905	12	critical	critical	ADJ
ejpam-6102	905	13	sobolev	sobolev	NOUN
ejpam-6102	905	14	exponents	exponent	NOUN
ejpam-6102	905	15	.	.	PUNCT
ejpam-6102	906	1	arch	arch	NOUN
ejpam-6102	906	2	.	.	PUNCT
ejpam-6102	907	1	rat	rat	NOUN
ejpam-6102	907	2	.	.	PROPN
ejpam-6102	907	3	mech	mech	PROPN
ejpam-6102	907	4	.	.	PUNCT
ejpam-6102	908	1	anal	anal	PROPN
ejpam-6102	908	2	.	.	PROPN
ejpam-6102	908	3	,	,	PUNCT
ejpam-6102	908	4	115:275–296	115:275–296	NUM
ejpam-6102	908	5	,	,	PUNCT
ejpam-6102	908	6	1991	1991	NUM
ejpam-6102	908	7	.	.	PUNCT
ejpam-6102	909	1	[	[	X
ejpam-6102	909	2	16	16	NUM
ejpam-6102	909	3	]	]	X
ejpam-6102	909	4	o.	o.	PROPN
ejpam-6102	909	5	rey	rey	PROPN
ejpam-6102	909	6	and	and	CCONJ
ejpam-6102	909	7	j.	j.	PROPN
ejpam-6102	909	8	wei	wei	PROPN
ejpam-6102	909	9	.	.	PUNCT
ejpam-6102	910	1	arbitrary	arbitrary	ADJ
ejpam-6102	910	2	number	number	NOUN
ejpam-6102	910	3	of	of	ADP
ejpam-6102	910	4	positive	positive	ADJ
ejpam-6102	910	5	solutions	solution	NOUN
ejpam-6102	910	6	for	for	ADP
ejpam-6102	910	7	elliptic	elliptic	ADJ
ejpam-6102	910	8	problem	problem	NOUN
ejpam-6102	910	9	with	with	ADP
ejpam-6102	910	10	critical	critical	ADJ
ejpam-6102	910	11	nonlinearity	nonlinearity	NOUN
ejpam-6102	910	12	.	.	PUNCT
ejpam-6102	911	1	j.	j.	PROPN
ejpam-6102	911	2	eur	eur	PROPN
ejpam-6102	911	3	.	.	PUNCT
ejpam-6102	911	4	math	math	PROPN
ejpam-6102	911	5	.	.	PUNCT
ejpam-6102	912	1	soc	soc	PROPN
ejpam-6102	912	2	.	.	PUNCT
ejpam-6102	912	3	,	,	PUNCT
ejpam-6102	912	4	7:449–476	7:449–476	NOUN
ejpam-6102	912	5	,	,	PUNCT
ejpam-6102	912	6	2005	2005	NUM
ejpam-6102	912	7	.	.	PUNCT
ejpam-6102	913	1	[	[	X
ejpam-6102	913	2	17	17	NUM
ejpam-6102	913	3	]	]	X
ejpam-6102	913	4	adimurthi	adimurthi	PROPN
ejpam-6102	913	5	,	,	PUNCT
ejpam-6102	913	6	f.	f.	PROPN
ejpam-6102	913	7	pacella	pacella	PROPN
ejpam-6102	913	8	,	,	PUNCT
ejpam-6102	913	9	and	and	CCONJ
ejpam-6102	913	10	s.l	s.l	PROPN
ejpam-6102	913	11	.	.	PROPN
ejpam-6102	913	12	yadava	yadava	PROPN
ejpam-6102	913	13	.	.	PUNCT
ejpam-6102	914	1	interaction	interaction	NOUN
ejpam-6102	914	2	between	between	ADP
ejpam-6102	914	3	the	the	DET
ejpam-6102	914	4	geometry	geometry	NOUN
ejpam-6102	914	5	of	of	ADP
ejpam-6102	914	6	the	the	DET
ejpam-6102	914	7	boundary	boundary	ADJ
ejpam-6102	914	8	and	and	CCONJ
ejpam-6102	914	9	positive	positive	ADJ
ejpam-6102	914	10	solutions	solution	NOUN
ejpam-6102	914	11	of	of	ADP
ejpam-6102	914	12	a	a	DET
ejpam-6102	914	13	semilinear	semilinear	PROPN
ejpam-6102	914	14	neumann	neumann	PROPN
ejpam-6102	914	15	problem	problem	NOUN
ejpam-6102	914	16	with	with	ADP
ejpam-6102	914	17	critical	critical	ADJ
ejpam-6102	914	18	nonlinearity	nonlinearity	NOUN
ejpam-6102	914	19	.	.	PUNCT
ejpam-6102	915	1	j.	j.	PROPN
ejpam-6102	915	2	funct	funct	PROPN
ejpam-6102	915	3	.	.	PUNCT
ejpam-6102	916	1	anal	anal	PROPN
ejpam-6102	916	2	.	.	PROPN
ejpam-6102	916	3	,	,	PUNCT
ejpam-6102	916	4	113:318–350	113:318–350	NUM
ejpam-6102	916	5	,	,	PUNCT
ejpam-6102	916	6	1993	1993	NUM
ejpam-6102	916	7	.	.	PUNCT
ejpam-6102	917	1	[	[	X
ejpam-6102	917	2	18	18	NUM
ejpam-6102	917	3	]	]	X
ejpam-6102	917	4	w.m	w.m	PROPN
ejpam-6102	917	5	.	.	PROPN
ejpam-6102	917	6	ni	ni	PROPN
ejpam-6102	917	7	,	,	PUNCT
ejpam-6102	917	8	x.b	x.b	PROPN
ejpam-6102	917	9	.	.	PROPN
ejpam-6102	917	10	pan	pan	PROPN
ejpam-6102	917	11	,	,	PUNCT
ejpam-6102	917	12	and	and	CCONJ
ejpam-6102	917	13	i.	i.	PROPN
ejpam-6102	917	14	takagi	takagi	PROPN
ejpam-6102	917	15	.	.	PUNCT
ejpam-6102	918	1	singular	singular	PROPN
ejpam-6102	918	2	behavior	behavior	NOUN
ejpam-6102	918	3	of	of	ADP
ejpam-6102	918	4	least	least	ADJ
ejpam-6102	918	5	-	-	PUNCT
ejpam-6102	918	6	energy	energy	NOUN
ejpam-6102	918	7	solutions	solution	NOUN
ejpam-6102	918	8	of	of	ADP
ejpam-6102	918	9	a	a	DET
ejpam-6102	918	10	semi	semi	ADJ
ejpam-6102	918	11	-	-	ADJ
ejpam-6102	918	12	linear	linear	ADJ
ejpam-6102	918	13	neumann	neumann	PROPN
ejpam-6102	918	14	problem	problem	NOUN
ejpam-6102	918	15	involving	involve	VERB
ejpam-6102	918	16	critical	critical	ADJ
ejpam-6102	918	17	sobolev	sobolev	NOUN
ejpam-6102	918	18	exponents	exponent	NOUN
ejpam-6102	918	19	.	.	PUNCT
ejpam-6102	919	1	duke	duke	PROPN
ejpam-6102	919	2	math	math	PROPN
ejpam-6102	919	3	.	.	PUNCT
ejpam-6102	920	1	j.	j.	PROPN
ejpam-6102	920	2	,	,	PUNCT
ejpam-6102	920	3	67:1–20	67:1–20	NUM
ejpam-6102	920	4	,	,	PUNCT
ejpam-6102	920	5	1992	1992	NUM
ejpam-6102	920	6	.	.	PUNCT
ejpam-6102	921	1	[	[	X
ejpam-6102	921	2	19	19	NUM
ejpam-6102	921	3	]	]	X
ejpam-6102	921	4	l.	l.	PROPN
ejpam-6102	921	5	caffarelli	caffarelli	PROPN
ejpam-6102	921	6	,	,	PUNCT
ejpam-6102	921	7	b.	b.	PROPN
ejpam-6102	921	8	gidas	gidas	PROPN
ejpam-6102	921	9	,	,	PUNCT
ejpam-6102	921	10	and	and	CCONJ
ejpam-6102	921	11	j.	j.	PROPN
ejpam-6102	921	12	spruck	spruck	PROPN
ejpam-6102	921	13	.	.	PUNCT
ejpam-6102	922	1	asymptotic	asymptotic	ADJ
ejpam-6102	922	2	symmetry	symmetry	NOUN
ejpam-6102	922	3	and	and	CCONJ
ejpam-6102	922	4	local	local	ADJ
ejpam-6102	922	5	behavior	behavior	NOUN
ejpam-6102	922	6	of	of	ADP
ejpam-6102	922	7	semilinear	semilinear	PROPN
ejpam-6102	922	8	elliptic	elliptic	ADJ
ejpam-6102	922	9	equations	equation	NOUN
ejpam-6102	922	10	with	with	ADP
ejpam-6102	922	11	critical	critical	ADJ
ejpam-6102	922	12	sobolev	sobolev	NOUN
ejpam-6102	922	13	growth	growth	NOUN
ejpam-6102	922	14	.	.	PUNCT
ejpam-6102	923	1	comm	comm	NOUN
ejpam-6102	923	2	.	.	PUNCT
ejpam-6102	924	1	pure	pure	ADJ
ejpam-6102	924	2	appl	appl	PROPN
ejpam-6102	924	3	.	.	PUNCT
ejpam-6102	924	4	math	math	PROPN
ejpam-6102	924	5	.	.	PUNCT
ejpam-6102	924	6	,	,	PUNCT
ejpam-6102	924	7	42:271–297	42:271–297	PROPN
ejpam-6102	924	8	,	,	PUNCT
ejpam-6102	924	9	1989	1989	NUM
ejpam-6102	924	10	.	.	PUNCT
ejpam-6102	925	1	[	[	X
ejpam-6102	925	2	20	20	NUM
ejpam-6102	925	3	]	]	X
ejpam-6102	925	4	adimurthi	adimurthi	PROPN
ejpam-6102	925	5	and	and	CCONJ
ejpam-6102	925	6	g.	g.	PROPN
ejpam-6102	925	7	mancini	mancini	PROPN
ejpam-6102	925	8	.	.	PUNCT
ejpam-6102	926	1	the	the	DET
ejpam-6102	926	2	neumann	neumann	PROPN
ejpam-6102	926	3	problem	problem	NOUN
ejpam-6102	926	4	for	for	ADP
ejpam-6102	926	5	elliptic	elliptic	ADJ
ejpam-6102	926	6	equations	equation	NOUN
ejpam-6102	926	7	with	with	ADP
ejpam-6102	926	8	critical	critical	ADJ
ejpam-6102	926	9	nonlinearity	nonlinearity	NOUN
ejpam-6102	926	10	.	.	PUNCT
ejpam-6102	927	1	in	in	ADP
ejpam-6102	927	2	a	a	DET
ejpam-6102	927	3	tribute	tribute	NOUN
ejpam-6102	927	4	in	in	ADP
ejpam-6102	927	5	honour	honour	NOUN
ejpam-6102	927	6	of	of	ADP
ejpam-6102	927	7	g.	g.	PROPN
ejpam-6102	927	8	prodi	prodi	PROPN
ejpam-6102	927	9	,	,	PUNCT
ejpam-6102	927	10	pages	page	NOUN
ejpam-6102	927	11	9–25	9–25	PROPN
ejpam-6102	927	12	.	.	PUNCT
ejpam-6102	927	13	scuola	scuola	NOUN
ejpam-6102	927	14	norm	norm	NOUN
ejpam-6102	927	15	.	.	PUNCT
ejpam-6102	928	1	sup	sup	NOUN
ejpam-6102	928	2	.	.	PUNCT
ejpam-6102	929	1	pisa	pisa	PROPN
ejpam-6102	929	2	,	,	PUNCT
ejpam-6102	929	3	1991	1991	NUM
ejpam-6102	929	4	.	.	PUNCT
ejpam-6102	930	1	[	[	X
ejpam-6102	930	2	21	21	NUM
ejpam-6102	930	3	]	]	X
ejpam-6102	930	4	o.	o.	PROPN
ejpam-6102	930	5	druet	druet	PROPN
ejpam-6102	930	6	,	,	PUNCT
ejpam-6102	930	7	f.	f.	PROPN
ejpam-6102	930	8	robert	robert	PROPN
ejpam-6102	930	9	,	,	PUNCT
ejpam-6102	930	10	and	and	CCONJ
ejpam-6102	930	11	j.	j.	PROPN
ejpam-6102	930	12	wei	wei	PROPN
ejpam-6102	930	13	.	.	PUNCT
ejpam-6102	931	1	the	the	DET
ejpam-6102	931	2	lin	lin	PROPN
ejpam-6102	931	3	-	-	PUNCT
ejpam-6102	931	4	nis	nis	PROPN
ejpam-6102	931	5	problem	problem	NOUN
ejpam-6102	931	6	for	for	ADP
ejpam-6102	931	7	mean	mean	ADJ
ejpam-6102	931	8	convex	convex	NOUN
ejpam-6102	931	9	domains	domain	NOUN
ejpam-6102	931	10	.	.	PUNCT
ejpam-6102	932	1	mem	mem	PROPN
ejpam-6102	932	2	.	.	PUNCT
ejpam-6102	933	1	amer	amer	PROPN
ejpam-6102	933	2	.	.	PUNCT
ejpam-6102	933	3	math	math	PROPN
ejpam-6102	933	4	.	.	PUNCT
ejpam-6102	934	1	soc	soc	PROPN
ejpam-6102	934	2	.	.	PROPN
ejpam-6102	934	3	,	,	PUNCT
ejpam-6102	934	4	218(1027	218(1027	NUM
ejpam-6102	934	5	)	)	PUNCT
ejpam-6102	934	6	,	,	PUNCT
ejpam-6102	934	7	2012	2012	NUM
ejpam-6102	934	8	.	.	PUNCT
ejpam-6102	935	1	[	[	X
ejpam-6102	935	2	22	22	NUM
ejpam-6102	935	3	]	]	X
ejpam-6102	935	4	n.	n.	NOUN
ejpam-6102	935	5	ghoussoub	ghoussoub	PROPN
ejpam-6102	935	6	and	and	CCONJ
ejpam-6102	935	7	c.	c.	PROPN
ejpam-6102	935	8	gui	gui	PROPN
ejpam-6102	935	9	.	.	PUNCT
ejpam-6102	936	1	multi	multi	ADJ
ejpam-6102	936	2	-	-	ADJ
ejpam-6102	936	3	peak	peak	ADJ
ejpam-6102	936	4	solutions	solution	NOUN
ejpam-6102	936	5	for	for	ADP
ejpam-6102	936	6	a	a	DET
ejpam-6102	936	7	semilinear	semilinear	PROPN
ejpam-6102	936	8	neumann	neumann	PROPN
ejpam-6102	936	9	problem	problem	NOUN
ejpam-6102	936	10	involving	involve	VERB
ejpam-6102	936	11	the	the	DET
ejpam-6102	936	12	critical	critical	ADJ
ejpam-6102	936	13	sobolev	sobolev	NOUN
ejpam-6102	936	14	exponent	exponent	NOUN
ejpam-6102	936	15	.	.	PUNCT
ejpam-6102	937	1	math	math	PROPN
ejpam-6102	937	2	.	.	PUNCT
ejpam-6102	938	1	z.	z.	PROPN
ejpam-6102	938	2	,	,	PUNCT
ejpam-6102	938	3	229:443–474	229:443–474	PROPN
ejpam-6102	938	4	,	,	PUNCT
ejpam-6102	938	5	1998	1998	NUM
ejpam-6102	938	6	.	.	PUNCT
ejpam-6102	939	1	[	[	X
ejpam-6102	939	2	23	23	NUM
ejpam-6102	939	3	]	]	X
ejpam-6102	939	4	c.	c.	PROPN
ejpam-6102	939	5	gui	gui	PROPN
ejpam-6102	939	6	and	and	CCONJ
ejpam-6102	939	7	c.-s	c.-	NOUN
ejpam-6102	939	8	.	.	PUNCT
ejpam-6102	940	1	lin	lin	PROPN
ejpam-6102	940	2	.	.	PUNCT
ejpam-6102	940	3	estimates	estimate	NOUN
ejpam-6102	940	4	for	for	ADP
ejpam-6102	940	5	boundary	boundary	NOUN
ejpam-6102	940	6	-	-	PUNCT
ejpam-6102	940	7	bubbling	bubble	VERB
ejpam-6102	940	8	solutions	solution	NOUN
ejpam-6102	940	9	to	to	ADP
ejpam-6102	940	10	an	an	DET
ejpam-6102	940	11	elliptic	elliptic	ADJ
ejpam-6102	940	12	neumann	neumann	PROPN
ejpam-6102	940	13	problem	problem	NOUN
ejpam-6102	940	14	.	.	PUNCT
ejpam-6102	941	1	j.	j.	PROPN
ejpam-6102	941	2	reine	reine	PROPN
ejpam-6102	941	3	angew	angew	PROPN
ejpam-6102	941	4	.	.	PUNCT
ejpam-6102	942	1	math	math	NOUN
ejpam-6102	942	2	.	.	PUNCT
ejpam-6102	942	3	,	,	PUNCT
ejpam-6102	942	4	546:201–235	546:201–235	NUM
ejpam-6102	942	5	,	,	PUNCT
ejpam-6102	942	6	2002	2002	NUM
ejpam-6102	942	7	.	.	PUNCT
ejpam-6102	943	1	[	[	X
ejpam-6102	943	2	24	24	NUM
ejpam-6102	943	3	]	]	PUNCT
ejpam-6102	943	4	l.	l.	PROPN
ejpam-6102	943	5	wang	wang	PROPN
ejpam-6102	943	6	,	,	PUNCT
ejpam-6102	943	7	j.	j.	PROPN
ejpam-6102	943	8	wei	wei	PROPN
ejpam-6102	943	9	,	,	PUNCT
ejpam-6102	943	10	and	and	CCONJ
ejpam-6102	943	11	s.	s.	PROPN
ejpam-6102	943	12	yan	yan	PROPN
ejpam-6102	943	13	.	.	PUNCT
ejpam-6102	944	1	a	a	DET
ejpam-6102	944	2	neumann	neumann	PROPN
ejpam-6102	944	3	problem	problem	NOUN
ejpam-6102	944	4	with	with	ADP
ejpam-6102	944	5	critical	critical	ADJ
ejpam-6102	944	6	exponent	exponent	NOUN
ejpam-6102	944	7	in	in	ADP
ejpam-6102	944	8	nonconvex	nonconvex	NOUN
ejpam-6102	944	9	domains	domain	NOUN
ejpam-6102	944	10	and	and	CCONJ
ejpam-6102	944	11	lin	lin	PROPN
ejpam-6102	944	12	-	-	PUNCT
ejpam-6102	944	13	ni	ni	PROPN
ejpam-6102	944	14	’s	’s	PART
ejpam-6102	944	15	conjecture	conjecture	NOUN
ejpam-6102	944	16	.	.	PUNCT
ejpam-6102	945	1	trans	trans	PROPN
ejpam-6102	945	2	.	.	PUNCT
ejpam-6102	946	1	amer	amer	PROPN
ejpam-6102	946	2	.	.	PUNCT
ejpam-6102	946	3	math	math	PROPN
ejpam-6102	946	4	.	.	PUNCT
ejpam-6102	947	1	soc	soc	PROPN
ejpam-6102	947	2	.	.	PUNCT
ejpam-6102	947	3	,	,	PUNCT
ejpam-6102	947	4	362(9):4581–4615	362(9):4581–4615	NUM
ejpam-6102	947	5	,	,	PUNCT
ejpam-6102	947	6	2010	2010	NUM
ejpam-6102	947	7	.	.	PUNCT
ejpam-6102	948	1	[	[	X
ejpam-6102	948	2	25	25	NUM
ejpam-6102	948	3	]	]	PUNCT
ejpam-6102	948	4	z.-q	z.-q	PROPN
ejpam-6102	948	5	.	.	PUNCT
ejpam-6102	948	6	wang	wang	PROPN
ejpam-6102	948	7	.	.	PUNCT
ejpam-6102	949	1	construction	construction	NOUN
ejpam-6102	949	2	of	of	ADP
ejpam-6102	949	3	multi	multi	ADJ
ejpam-6102	949	4	-	-	ADJ
ejpam-6102	949	5	peaked	peaked	ADJ
ejpam-6102	949	6	solutions	solution	NOUN
ejpam-6102	949	7	for	for	ADP
ejpam-6102	949	8	a	a	DET
ejpam-6102	949	9	nonlinear	nonlinear	ADJ
ejpam-6102	949	10	neumann	neumann	PROPN
ejpam-6102	949	11	problem	problem	NOUN
ejpam-6102	949	12	with	with	ADP
ejpam-6102	949	13	critical	critical	ADJ
ejpam-6102	949	14	exponent	exponent	NOUN
ejpam-6102	949	15	in	in	ADP
ejpam-6102	949	16	symmetric	symmetric	ADJ
ejpam-6102	949	17	domains	domain	NOUN
ejpam-6102	949	18	.	.	PUNCT
ejpam-6102	950	1	nonlinear	nonlinear	ADJ
ejpam-6102	950	2	anal	anal	PROPN
ejpam-6102	950	3	.	.	PUNCT
ejpam-6102	950	4	,	,	PUNCT
ejpam-6102	950	5	27(11):1281–1306	27(11):1281–1306	PROPN
ejpam-6102	950	6	,	,	PUNCT
ejpam-6102	950	7	1996	1996	NUM
ejpam-6102	950	8	.	.	PUNCT
ejpam-6102	951	1	[	[	X
ejpam-6102	951	2	26	26	NUM
ejpam-6102	951	3	]	]	PUNCT
ejpam-6102	951	4	j.	j.	PROPN
ejpam-6102	951	5	wei	wei	PROPN
ejpam-6102	951	6	and	and	CCONJ
ejpam-6102	951	7	s.	s.	PROPN
ejpam-6102	951	8	yan	yan	PROPN
ejpam-6102	951	9	.	.	PUNCT
ejpam-6102	952	1	arbitrary	arbitrary	ADJ
ejpam-6102	952	2	many	many	ADJ
ejpam-6102	952	3	boundary	boundary	ADJ
ejpam-6102	952	4	peak	peak	NOUN
ejpam-6102	952	5	solutions	solution	NOUN
ejpam-6102	952	6	for	for	ADP
ejpam-6102	952	7	an	an	DET
ejpam-6102	952	8	elliptic	elliptic	ADJ
ejpam-6102	952	9	neumann	neumann	PROPN
ejpam-6102	952	10	problem	problem	NOUN
ejpam-6102	952	11	with	with	ADP
ejpam-6102	952	12	critical	critical	ADJ
ejpam-6102	952	13	growth	growth	NOUN
ejpam-6102	952	14	.	.	PUNCT
ejpam-6102	953	1	j.	j.	PROPN
ejpam-6102	953	2	math	math	PROPN
ejpam-6102	953	3	.	.	PUNCT
ejpam-6102	954	1	pures	pure	NOUN
ejpam-6102	954	2	appl	appl	PROPN
ejpam-6102	954	3	.	.	PUNCT
ejpam-6102	955	1	(	(	PUNCT
ejpam-6102	955	2	9	9	NUM
ejpam-6102	955	3	)	)	PUNCT
ejpam-6102	955	4	,	,	PUNCT
ejpam-6102	955	5	88(4):350–378	88(4):350–378	PROPN
ejpam-6102	955	6	,	,	PUNCT
ejpam-6102	955	7	2007	2007	NUM
ejpam-6102	955	8	.	.	PUNCT
ejpam-6102	956	1	[	[	X
ejpam-6102	956	2	27	27	NUM
ejpam-6102	956	3	]	]	X
ejpam-6102	956	4	o.	o.	PROPN
ejpam-6102	956	5	rey	rey	PROPN
ejpam-6102	956	6	.	.	PUNCT
ejpam-6102	957	1	boundary	boundary	ADJ
ejpam-6102	957	2	effect	effect	NOUN
ejpam-6102	957	3	for	for	ADP
ejpam-6102	957	4	an	an	DET
ejpam-6102	957	5	elliptic	elliptic	ADJ
ejpam-6102	957	6	neumann	neumann	PROPN
ejpam-6102	957	7	problem	problem	NOUN
ejpam-6102	957	8	with	with	ADP
ejpam-6102	957	9	critical	critical	ADJ
ejpam-6102	957	10	nonlinearity	nonlinearity	NOUN
ejpam-6102	957	11	.	.	PUNCT
ejpam-6102	958	1	comm	comm	NOUN
ejpam-6102	958	2	.	.	PUNCT
ejpam-6102	959	1	partial	partial	ADJ
ejpam-6102	959	2	differential	differential	NOUN
ejpam-6102	959	3	equations	equation	NOUN
ejpam-6102	959	4	,	,	PUNCT
ejpam-6102	959	5	22:1055–1139	22:1055–1139	NUM
ejpam-6102	959	6	,	,	PUNCT
ejpam-6102	959	7	1997	1997	NUM
ejpam-6102	959	8	.	.	PUNCT
ejpam-6102	960	1	[	[	X
ejpam-6102	960	2	28	28	NUM
ejpam-6102	960	3	]	]	X
ejpam-6102	960	4	o.	o.	PROPN
ejpam-6102	960	5	rey	rey	PROPN
ejpam-6102	960	6	.	.	PUNCT
ejpam-6102	961	1	the	the	DET
ejpam-6102	961	2	question	question	NOUN
ejpam-6102	961	3	of	of	ADP
ejpam-6102	961	4	interior	interior	ADJ
ejpam-6102	961	5	blow	blow	NOUN
ejpam-6102	961	6	-	-	PUNCT
ejpam-6102	961	7	up	up	ADP
ejpam-6102	961	8	points	point	NOUN
ejpam-6102	961	9	for	for	ADP
ejpam-6102	961	10	an	an	DET
ejpam-6102	961	11	elliptic	elliptic	ADJ
ejpam-6102	961	12	neumann	neumann	PROPN
ejpam-6102	961	13	problem	problem	NOUN
ejpam-6102	961	14	:	:	PUNCT
ejpam-6102	961	15	the	the	DET
ejpam-6102	961	16	critical	critical	ADJ
ejpam-6102	961	17	case	case	NOUN
ejpam-6102	961	18	.	.	PUNCT
ejpam-6102	962	1	j.	j.	PROPN
ejpam-6102	962	2	math	math	PROPN
ejpam-6102	962	3	.	.	PUNCT
ejpam-6102	963	1	pures	pure	NOUN
ejpam-6102	963	2	appl	appl	PROPN
ejpam-6102	963	3	.	.	PROPN
ejpam-6102	963	4	,	,	PUNCT
ejpam-6102	963	5	81:655–696	81:655–696	NUM
ejpam-6102	963	6	,	,	PUNCT
ejpam-6102	963	7	2002	2002	NUM
ejpam-6102	963	8	.	.	PUNCT
ejpam-6102	964	1	[	[	X
ejpam-6102	964	2	29	29	NUM
ejpam-6102	964	3	]	]	X
ejpam-6102	964	4	o.	o.	PROPN
ejpam-6102	964	5	rey	rey	PROPN
ejpam-6102	964	6	and	and	CCONJ
ejpam-6102	964	7	j.	j.	PROPN
ejpam-6102	964	8	wei	wei	PROPN
ejpam-6102	964	9	.	.	PUNCT
ejpam-6102	965	1	blow	blow	VERB
ejpam-6102	965	2	-	-	PUNCT
ejpam-6102	965	3	up	up	ADP
ejpam-6102	965	4	solutions	solution	NOUN
ejpam-6102	965	5	for	for	ADP
ejpam-6102	965	6	an	an	DET
ejpam-6102	965	7	elliptic	elliptic	ADJ
ejpam-6102	965	8	neumann	neumann	PROPN
ejpam-6102	965	9	problem	problem	NOUN
ejpam-6102	965	10	with	with	ADP
ejpam-6102	965	11	subor	subor	NOUN
ejpam-6102	965	12	supercritical	supercritical	ADJ
ejpam-6102	965	13	nonlinearity	nonlinearity	NOUN
ejpam-6102	965	14	,	,	PUNCT
ejpam-6102	965	15	ii	ii	PROPN
ejpam-6102	965	16	:	:	PUNCT
ejpam-6102	965	17	n	n	PRON
ejpam-6102	965	18	≥	≥	NOUN
ejpam-6102	965	19	4	4	NUM
ejpam-6102	965	20	.	.	PUNCT
ejpam-6102	965	21	ann	ann	PROPN
ejpam-6102	965	22	.	.	PROPN
ejpam-6102	965	23	inst	inst	PROPN
ejpam-6102	965	24	.	.	PUNCT
ejpam-6102	966	1	h.	h.	PROPN
ejpam-6102	966	2	poincaré	poincaré	ADJ
ejpam-6102	966	3	,	,	PUNCT
ejpam-6102	966	4	anal	anal	PROPN
ejpam-6102	966	5	.	.	PUNCT
ejpam-6102	967	1	non	non	PROPN
ejpam-6102	967	2	-	-	ADJ
ejpam-6102	967	3	lin	lin	PROPN
ejpam-6102	967	4	,	,	PUNCT
ejpam-6102	967	5	22(4):459–484	22(4):459–484	PROPN
ejpam-6102	967	6	,	,	PUNCT
ejpam-6102	967	7	2005	2005	NUM
ejpam-6102	967	8	.	.	PUNCT
ejpam-6102	968	1	[	[	X
ejpam-6102	968	2	30	30	NUM
ejpam-6102	968	3	]	]	X
ejpam-6102	968	4	o.	o.	PROPN
ejpam-6102	968	5	rey	rey	PROPN
ejpam-6102	968	6	and	and	CCONJ
ejpam-6102	968	7	j.	j.	PROPN
ejpam-6102	968	8	wei	wei	PROPN
ejpam-6102	968	9	.	.	PUNCT
ejpam-6102	969	1	blow	blow	VERB
ejpam-6102	969	2	-	-	PUNCT
ejpam-6102	969	3	up	up	ADP
ejpam-6102	969	4	solutions	solution	NOUN
ejpam-6102	969	5	for	for	ADP
ejpam-6102	969	6	an	an	DET
ejpam-6102	969	7	elliptic	elliptic	ADJ
ejpam-6102	969	8	neumann	neumann	PROPN
ejpam-6102	969	9	problem	problem	NOUN
ejpam-6102	969	10	with	with	ADP
ejpam-6102	969	11	subor	subor	NOUN
ejpam-6102	969	12	supercritical	supercritical	ADJ
ejpam-6102	969	13	nonlinearity	nonlinearity	NOUN
ejpam-6102	969	14	,	,	PUNCT
ejpam-6102	969	15	i	i	PRON
ejpam-6102	969	16	:	:	PUNCT
ejpam-6102	969	17	n	n	PROPN
ejpam-6102	969	18	=	=	SYM
ejpam-6102	969	19	3	3	X
ejpam-6102	969	20	.	.	PUNCT
ejpam-6102	969	21	j.	j.	PROPN
ejpam-6102	969	22	funct	funct	PROPN
ejpam-6102	969	23	.	.	PUNCT
ejpam-6102	970	1	anal	anal	PROPN
ejpam-6102	970	2	.	.	PROPN
ejpam-6102	970	3	,	,	PUNCT
ejpam-6102	970	4	212:472–499	212:472–499	NUM
ejpam-6102	970	5	,	,	PUNCT
ejpam-6102	970	6	2004	2004	NUM
ejpam-6102	970	7	.	.	PUNCT
ejpam-6102	971	1	[	[	X
ejpam-6102	971	2	31	31	NUM
ejpam-6102	971	3	]	]	PUNCT
ejpam-6102	971	4	m.	m.	NOUN
ejpam-6102	971	5	ben	ben	PROPN
ejpam-6102	971	6	ayed	aye	VERB
ejpam-6102	971	7	and	and	CCONJ
ejpam-6102	971	8	k.	k.	PROPN
ejpam-6102	971	9	el	el	PROPN
ejpam-6102	971	10	mehdi	mehdi	PROPN
ejpam-6102	971	11	.	.	PUNCT
ejpam-6102	972	1	non	non	ADJ
ejpam-6102	973	1	-	-	NOUN
ejpam-6102	974	1	existence	existence	NOUN
ejpam-6102	974	2	of	of	ADP
ejpam-6102	974	3	interior	interior	ADJ
ejpam-6102	974	4	bubbling	bubble	VERB
ejpam-6102	974	5	solutions	solution	NOUN
ejpam-6102	974	6	for	for	ADP
ejpam-6102	974	7	slightly	slightly	ADV
ejpam-6102	974	8	supercritical	supercritical	ADJ
ejpam-6102	974	9	elliptic	elliptic	ADJ
ejpam-6102	974	10	problems	problem	NOUN
ejpam-6102	974	11	.	.	PUNCT
ejpam-6102	975	1	boundary	boundary	ADJ
ejpam-6102	975	2	value	value	NOUN
ejpam-6102	975	3	problems	problem	NOUN
ejpam-6102	975	4	,	,	PUNCT
ejpam-6102	975	5	2023(90	2023(90	NUM
ejpam-6102	975	6	)	)	PUNCT
ejpam-6102	975	7	,	,	PUNCT
ejpam-6102	975	8	2023	2023	NUM
ejpam-6102	975	9	.	.	PUNCT
ejpam-6102	976	1	[	[	X
ejpam-6102	976	2	32	32	NUM
ejpam-6102	976	3	]	]	PUNCT
ejpam-6102	976	4	k.	k.	PROPN
ejpam-6102	976	5	el	el	PROPN
ejpam-6102	976	6	mehdi	mehdi	PROPN
ejpam-6102	976	7	and	and	CCONJ
ejpam-6102	976	8	f.	f.	PROPN
ejpam-6102	976	9	mohamed	mohamed	PROPN
ejpam-6102	976	10	salem	salem	PROPN
ejpam-6102	976	11	.	.	PUNCT
ejpam-6102	977	1	interior	interior	ADJ
ejpam-6102	977	2	bubbling	bubble	VERB
ejpam-6102	977	3	solutions	solution	NOUN
ejpam-6102	977	4	for	for	ADP
ejpam-6102	977	5	an	an	DET
ejpam-6102	977	6	elliptic	elliptic	ADJ
ejpam-6102	977	7	equation	equation	NOUN
ejpam-6102	977	8	with	with	ADP
ejpam-6102	977	9	r.	r.	PROPN
ejpam-6102	977	10	almushahhin	almushahhin	PROPN
ejpam-6102	977	11	,	,	PUNCT
ejpam-6102	977	12	m.	m.	PROPN
ejpam-6102	977	13	ben	ben	PROPN
ejpam-6102	977	14	ayed	aye	VERB
ejpam-6102	977	15	/	/	SYM
ejpam-6102	977	16	eur	eur	PROPN
ejpam-6102	977	17	.	.	PUNCT
ejpam-6102	978	1	j.	j.	PROPN
ejpam-6102	978	2	pure	pure	PROPN
ejpam-6102	978	3	appl	appl	PROPN
ejpam-6102	978	4	.	.	PROPN
ejpam-6102	978	5	math	math	PROPN
ejpam-6102	978	6	,	,	PUNCT
ejpam-6102	978	7	18	18	NUM
ejpam-6102	978	8	(	(	PUNCT
ejpam-6102	978	9	2	2	NUM
ejpam-6102	978	10	)	)	PUNCT
ejpam-6102	978	11	(	(	PUNCT
ejpam-6102	978	12	2025	2025	NUM
ejpam-6102	978	13	)	)	PUNCT
ejpam-6102	978	14	,	,	PUNCT
ejpam-6102	978	15	6102	6102	NUM
ejpam-6102	978	16	31	31	NUM
ejpam-6102	978	17	of	of	ADP
ejpam-6102	978	18	31	31	NUM
ejpam-6102	978	19	slightly	slightly	ADV
ejpam-6102	978	20	subcritical	subcritical	ADJ
ejpam-6102	978	21	nonlinearity	nonlinearity	NOUN
ejpam-6102	978	22	.	.	PUNCT
ejpam-6102	979	1	mathematics	mathematic	NOUN
ejpam-6102	979	2	,	,	PUNCT
ejpam-6102	979	3	11(6):1471	11(6):1471	NUM
ejpam-6102	979	4	,	,	PUNCT
ejpam-6102	979	5	2023	2023	NUM
ejpam-6102	979	6	.	.	PUNCT
ejpam-6102	980	1	[	[	X
ejpam-6102	980	2	33	33	NUM
ejpam-6102	980	3	]	]	PUNCT
ejpam-6102	980	4	m.	m.	NOUN
ejpam-6102	980	5	ben	ben	PROPN
ejpam-6102	980	6	ayed	aye	VERB
ejpam-6102	980	7	,	,	PUNCT
ejpam-6102	980	8	k.	k.	PROPN
ejpam-6102	980	9	el	el	PROPN
ejpam-6102	980	10	mehdi	mehdi	PROPN
ejpam-6102	980	11	,	,	PUNCT
ejpam-6102	980	12	and	and	CCONJ
ejpam-6102	980	13	f.	f.	PROPN
ejpam-6102	980	14	mohamed	mohamed	PROPN
ejpam-6102	980	15	salem	salem	PROPN
ejpam-6102	980	16	.	.	PUNCT
ejpam-6102	981	1	interior	interior	ADJ
ejpam-6102	981	2	multi	multi	ADJ
ejpam-6102	981	3	-	-	ADJ
ejpam-6102	981	4	peak	peak	ADJ
ejpam-6102	981	5	solution	solution	NOUN
ejpam-6102	981	6	for	for	ADP
ejpam-6102	981	7	a	a	DET
ejpam-6102	981	8	slightly	slightly	ADV
ejpam-6102	981	9	subcritical	subcritical	ADJ
ejpam-6102	981	10	nonlinear	nonlinear	PROPN
ejpam-6102	981	11	neumann	neumann	PROPN
ejpam-6102	981	12	equation	equation	PROPN
ejpam-6102	981	13	.	.	PUNCT
ejpam-6102	982	1	symmetry	symmetry	NOUN
ejpam-6102	982	2	,	,	PUNCT
ejpam-6102	982	3	16(291	16(291	NUM
ejpam-6102	982	4	)	)	PUNCT
ejpam-6102	982	5	,	,	PUNCT
ejpam-6102	982	6	2024	2024	NUM
ejpam-6102	982	7	.	.	PUNCT
ejpam-6102	983	1	[	[	X
ejpam-6102	983	2	34	34	NUM
ejpam-6102	983	3	]	]	PUNCT
ejpam-6102	983	4	m.	m.	NOUN
ejpam-6102	983	5	struwe	struwe	PROPN
ejpam-6102	983	6	.	.	PUNCT
ejpam-6102	984	1	a	a	DET
ejpam-6102	984	2	global	global	ADJ
ejpam-6102	984	3	compactness	compactness	NOUN
ejpam-6102	984	4	result	result	NOUN
ejpam-6102	984	5	for	for	ADP
ejpam-6102	984	6	elliptic	elliptic	ADJ
ejpam-6102	984	7	boundary	boundary	ADJ
ejpam-6102	984	8	value	value	NOUN
ejpam-6102	984	9	problems	problem	NOUN
ejpam-6102	984	10	involving	involve	VERB
ejpam-6102	984	11	limiting	limit	VERB
ejpam-6102	984	12	nonlinearities	nonlinearitie	NOUN
ejpam-6102	984	13	.	.	PUNCT
ejpam-6102	985	1	math	math	NOUN
ejpam-6102	985	2	.	.	PUNCT
ejpam-6102	986	1	z.	z.	PROPN
ejpam-6102	986	2	,	,	PUNCT
ejpam-6102	986	3	187:511–517	187:511–517	NUM
ejpam-6102	986	4	,	,	PUNCT
ejpam-6102	986	5	1984	1984	NUM
ejpam-6102	986	6	.	.	PUNCT
ejpam-6102	987	1	[	[	X
ejpam-6102	987	2	35	35	NUM
ejpam-6102	987	3	]	]	PUNCT
ejpam-6102	987	4	a.	a.	NOUN
ejpam-6102	987	5	bahri	bahri	PROPN
ejpam-6102	987	6	,	,	PUNCT
ejpam-6102	987	7	y.y	y.y	PROPN
ejpam-6102	987	8	.	.	PROPN
ejpam-6102	987	9	li	li	PROPN
ejpam-6102	987	10	,	,	PUNCT
ejpam-6102	987	11	and	and	CCONJ
ejpam-6102	987	12	o.	o.	PROPN
ejpam-6102	987	13	rey	rey	PROPN
ejpam-6102	987	14	.	.	PUNCT
ejpam-6102	988	1	on	on	ADP
ejpam-6102	988	2	a	a	DET
ejpam-6102	988	3	variational	variational	ADJ
ejpam-6102	988	4	problem	problem	NOUN
ejpam-6102	988	5	with	with	ADP
ejpam-6102	988	6	lack	lack	NOUN
ejpam-6102	988	7	of	of	ADP
ejpam-6102	988	8	compactness	compactness	NOUN
ejpam-6102	988	9	:	:	PUNCT
ejpam-6102	988	10	the	the	DET
ejpam-6102	988	11	topological	topological	ADJ
ejpam-6102	988	12	effect	effect	NOUN
ejpam-6102	988	13	of	of	ADP
ejpam-6102	988	14	the	the	DET
ejpam-6102	988	15	critical	critical	ADJ
ejpam-6102	988	16	points	point	NOUN
ejpam-6102	988	17	at	at	ADP
ejpam-6102	988	18	infinity	infinity	NOUN
ejpam-6102	988	19	.	.	PUNCT
ejpam-6102	989	1	calculus	calculus	NOUN
ejpam-6102	989	2	of	of	ADP
ejpam-6102	989	3	variations	variation	NOUN
ejpam-6102	989	4	and	and	CCONJ
ejpam-6102	989	5	partial	partial	ADJ
ejpam-6102	989	6	differential	differential	NOUN
ejpam-6102	989	7	equations	equation	NOUN
ejpam-6102	989	8	,	,	PUNCT
ejpam-6102	989	9	3:67–94	3:67–94	NUM
ejpam-6102	989	10	,	,	PUNCT
ejpam-6102	989	11	1995	1995	NUM
ejpam-6102	989	12	.	.	PUNCT