id	sid	tid	token	lemma	pos
ejpam-5446	1	1	european	european	PROPN
ejpam-5446	1	2	journal	journal	PROPN
ejpam-5446	1	3	of	of	ADP
ejpam-5446	1	4	pure	pure	ADJ
ejpam-5446	1	5	and	and	CCONJ
ejpam-5446	1	6	applied	apply	VERB
ejpam-5446	1	7	mathematics	mathematic	NOUN
ejpam-5446	1	8	vol	vol	NOUN
ejpam-5446	1	9	.	.	PROPN
ejpam-5446	2	1	17	17	NUM
ejpam-5446	2	2	,	,	PUNCT
ejpam-5446	2	3	no	no	INTJ
ejpam-5446	2	4	.	.	NOUN
ejpam-5446	2	5	4	4	NUM
ejpam-5446	2	6	,	,	PUNCT
ejpam-5446	2	7	2024	2024	NUM
ejpam-5446	2	8	,	,	PUNCT
ejpam-5446	2	9	3585	3585	NUM
ejpam-5446	2	10	-	-	SYM
ejpam-5446	2	11	3609	3609	NUM
ejpam-5446	2	12	issn	issn	PROPN
ejpam-5446	2	13	1307	1307	NUM
ejpam-5446	2	14	-	-	SYM
ejpam-5446	2	15	5543	5543	NUM
ejpam-5446	2	16	–	–	PUNCT
ejpam-5446	2	17	ejpam.com	ejpam.com	X
ejpam-5446	2	18	published	publish	VERB
ejpam-5446	2	19	by	by	ADP
ejpam-5446	2	20	new	new	PROPN
ejpam-5446	2	21	york	york	PROPN
ejpam-5446	2	22	business	business	PROPN
ejpam-5446	2	23	global	global	PROPN
ejpam-5446	2	24	hyers	hyers	PROPN
ejpam-5446	2	25	-	-	PUNCT
ejpam-5446	2	26	ulam	ulam	PROPN
ejpam-5446	2	27	stability	stability	NOUN
ejpam-5446	2	28	of	of	ADP
ejpam-5446	2	29	fifth	fifth	ADJ
ejpam-5446	2	30	order	order	NOUN
ejpam-5446	2	31	linear	linear	PROPN
ejpam-5446	2	32	differential	differential	NOUN
ejpam-5446	2	33	equations	equation	NOUN
ejpam-5446	2	34	s.	s.	PROPN
ejpam-5446	2	35	bowmiya1,∗	bowmiya1,∗	PROPN
ejpam-5446	2	36	,	,	PUNCT
ejpam-5446	2	37	g.	g.	PROPN
ejpam-5446	2	38	balasubramanian1	balasubramanian1	PROPN
ejpam-5446	2	39	,	,	PUNCT
ejpam-5446	2	40	vediyappan	vediyappan	ADJ
ejpam-5446	2	41	govindan2	govindan2	PROPN
ejpam-5446	2	42	,	,	PUNCT
ejpam-5446	2	43	mana	mana	PROPN
ejpam-5446	2	44	donganon3	donganon3	PROPN
ejpam-5446	2	45	,	,	PUNCT
ejpam-5446	3	1	haewon	haewon	VERB
ejpam-5446	3	2	byeon4,∗	byeon4,∗	NOUN
ejpam-5446	3	3	1	1	NUM
ejpam-5446	3	4	department	department	NOUN
ejpam-5446	3	5	of	of	ADP
ejpam-5446	3	6	mathematics	mathematic	NOUN
ejpam-5446	3	7	,	,	PUNCT
ejpam-5446	3	8	government	government	NOUN
ejpam-5446	3	9	arts	arts	PROPN
ejpam-5446	3	10	college	college	PROPN
ejpam-5446	3	11	for	for	ADP
ejpam-5446	3	12	men	man	NOUN
ejpam-5446	3	13	,	,	PUNCT
ejpam-5446	3	14	krishnagiri	krishnagiri	PROPN
ejpam-5446	3	15	635001	635001	NUM
ejpam-5446	3	16	,	,	PUNCT
ejpam-5446	3	17	tamil	tamil	PROPN
ejpam-5446	3	18	nadu	nadu	PROPN
ejpam-5446	3	19	,	,	PUNCT
ejpam-5446	3	20	india	india	PROPN
ejpam-5446	3	21	2	2	NUM
ejpam-5446	3	22	department	department	NOUN
ejpam-5446	3	23	of	of	ADP
ejpam-5446	3	24	mathematics	mathematic	NOUN
ejpam-5446	3	25	,	,	PUNCT
ejpam-5446	3	26	hindustan	hindustan	PROPN
ejpam-5446	3	27	institute	institute	PROPN
ejpam-5446	3	28	of	of	ADP
ejpam-5446	3	29	technology	technology	PROPN
ejpam-5446	3	30	and	and	CCONJ
ejpam-5446	3	31	science	science	NOUN
ejpam-5446	3	32	,	,	PUNCT
ejpam-5446	3	33	chennai	chennai	PROPN
ejpam-5446	3	34	603103	603103	NUM
ejpam-5446	3	35	,	,	PUNCT
ejpam-5446	3	36	tamil	tamil	PROPN
ejpam-5446	3	37	nadu	nadu	PROPN
ejpam-5446	3	38	,	,	PUNCT
ejpam-5446	3	39	india	india	PROPN
ejpam-5446	3	40	3	3	NUM
ejpam-5446	3	41	department	department	PROPN
ejpam-5446	3	42	of	of	ADP
ejpam-5446	3	43	mathematics	mathematic	NOUN
ejpam-5446	3	44	,	,	PUNCT
ejpam-5446	3	45	school	school	NOUN
ejpam-5446	3	46	of	of	ADP
ejpam-5446	3	47	science	science	NOUN
ejpam-5446	3	48	,	,	PUNCT
ejpam-5446	3	49	university	university	NOUN
ejpam-5446	3	50	of	of	ADP
ejpam-5446	3	51	phayao	phayao	NOUN
ejpam-5446	3	52	,	,	PUNCT
ejpam-5446	3	53	phayao	phayao	NOUN
ejpam-5446	3	54	56000	56000	NUM
ejpam-5446	3	55	,	,	PUNCT
ejpam-5446	3	56	thailand	thailand	PROPN
ejpam-5446	3	57	4	4	NUM
ejpam-5446	3	58	department	department	NOUN
ejpam-5446	3	59	of	of	ADP
ejpam-5446	3	60	ai	ai	ADJ
ejpam-5446	3	61	-	-	PUNCT
ejpam-5446	3	62	big	big	ADJ
ejpam-5446	3	63	data	datum	NOUN
ejpam-5446	3	64	,	,	PUNCT
ejpam-5446	3	65	college	college	NOUN
ejpam-5446	3	66	of	of	ADP
ejpam-5446	3	67	ai	ai	PROPN
ejpam-5446	3	68	convergence	convergence	NOUN
ejpam-5446	3	69	,	,	PUNCT
ejpam-5446	3	70	inje	inje	PROPN
ejpam-5446	3	71	university	university	NOUN
ejpam-5446	3	72	,	,	PUNCT
ejpam-5446	3	73	gimhae	gimhae	NOUN
ejpam-5446	3	74	,	,	PUNCT
ejpam-5446	3	75	50834	50834	NUM
ejpam-5446	3	76	,	,	PUNCT
ejpam-5446	3	77	republic	republic	NOUN
ejpam-5446	3	78	of	of	ADP
ejpam-5446	3	79	korea	korea	PROPN
ejpam-5446	3	80	abstract	abstract	NOUN
ejpam-5446	3	81	.	.	PUNCT
ejpam-5446	4	1	in	in	ADP
ejpam-5446	4	2	this	this	DET
ejpam-5446	4	3	paper	paper	NOUN
ejpam-5446	4	4	,	,	PUNCT
ejpam-5446	4	5	we	we	PRON
ejpam-5446	4	6	study	study	VERB
ejpam-5446	4	7	the	the	DET
ejpam-5446	4	8	hyers	hyers	PROPN
ejpam-5446	4	9	-	-	PUNCT
ejpam-5446	4	10	ulam	ulam	PROPN
ejpam-5446	4	11	stability	stability	NOUN
ejpam-5446	4	12	for	for	ADP
ejpam-5446	4	13	the	the	DET
ejpam-5446	4	14	fifth	fifth	ADJ
ejpam-5446	4	15	-	-	PUNCT
ejpam-5446	4	16	order	order	NOUN
ejpam-5446	4	17	linear	linear	ADJ
ejpam-5446	4	18	differential	differential	NOUN
ejpam-5446	4	19	equation	equation	NOUN
ejpam-5446	4	20	.	.	PUNCT
ejpam-5446	5	1	in	in	ADP
ejpam-5446	5	2	particular	particular	ADJ
ejpam-5446	5	3	,	,	PUNCT
ejpam-5446	5	4	we	we	PRON
ejpam-5446	5	5	treat	treat	VERB
ejpam-5446	5	6	ς	ς	PROPN
ejpam-5446	5	7	as	as	ADP
ejpam-5446	5	8	an	an	DET
ejpam-5446	5	9	arrangement	arrangement	NOUN
ejpam-5446	5	10	of	of	ADP
ejpam-5446	5	11	differential	differential	ADJ
ejpam-5446	5	12	equation	equation	NOUN
ejpam-5446	5	13	and	and	CCONJ
ejpam-5446	5	14	in	in	ADP
ejpam-5446	5	15	the	the	DET
ejpam-5446	5	16	form	form	NOUN
ejpam-5446	5	17	ςv(x	ςv(x	NUM
ejpam-5446	5	18	)	)	PUNCT
ejpam-5446	6	1	+	+	CCONJ
ejpam-5446	6	2	η1ς	η1ς	NOUN
ejpam-5446	6	3	iv(x	iv(x	NUM
ejpam-5446	6	4	)	)	PUNCT
ejpam-5446	6	5	+	+	CCONJ
ejpam-5446	6	6	η2ς	η2ς	PROPN
ejpam-5446	6	7	′′′	′′′	PROPN
ejpam-5446	6	8	(	(	PUNCT
ejpam-5446	6	9	x	x	X
ejpam-5446	6	10	)	)	PUNCT
ejpam-5446	6	11	+	+	CCONJ
ejpam-5446	6	12	η3ς	η3ς	PROPN
ejpam-5446	6	13	′′	′′	PROPN
ejpam-5446	6	14	(	(	PUNCT
ejpam-5446	6	15	x	x	X
ejpam-5446	6	16	)	)	PUNCT
ejpam-5446	6	17	+	+	CCONJ
ejpam-5446	6	18	η4ς	η4ς	PROPN
ejpam-5446	6	19	′	′	NUM
ejpam-5446	6	20	(	(	PUNCT
ejpam-5446	6	21	x	x	X
ejpam-5446	6	22	)	)	PUNCT
ejpam-5446	6	23	+	+	CCONJ
ejpam-5446	6	24	η5ς(x	η5ς(x	ADJ
ejpam-5446	6	25	)	)	PUNCT
ejpam-5446	6	26	=	=	SYM
ejpam-5446	6	27	ω(x	ω(x	NOUN
ejpam-5446	6	28	)	)	PUNCT
ejpam-5446	6	29	where	where	SCONJ
ejpam-5446	6	30	ς	ς	PROPN
ejpam-5446	6	31	∈	∈	PROPN
ejpam-5446	6	32	c5[k	c5[k	NOUN
ejpam-5446	6	33	,	,	PUNCT
ejpam-5446	6	34	l	l	NOUN
ejpam-5446	6	35	]	]	X
ejpam-5446	6	36	,	,	PUNCT
ejpam-5446	6	37	ω	ω	PROPN
ejpam-5446	6	38	∈	∈	PROPN
ejpam-5446	6	39	[	[	X
ejpam-5446	6	40	k	k	X
ejpam-5446	6	41	,	,	PUNCT
ejpam-5446	6	42	l	l	NOUN
ejpam-5446	6	43	]	]	X
ejpam-5446	6	44	.	.	PUNCT
ejpam-5446	7	1	we	we	PRON
ejpam-5446	7	2	demonstrate	demonstrate	VERB
ejpam-5446	7	3	that	that	SCONJ
ejpam-5446	7	4	ςv(x)+η1ς	ςv(x)+η1ς	PROPN
ejpam-5446	7	5	iv(x)+η2ς	iv(x)+η2ς	PROPN
ejpam-5446	7	6	′′′	′′′	PROPN
ejpam-5446	7	7	(	(	PUNCT
ejpam-5446	7	8	x)+η3ς	x)+η3ς	PROPN
ejpam-5446	7	9	′′	′′	PROPN
ejpam-5446	7	10	(	(	PUNCT
ejpam-5446	7	11	x)+η4ς	x)+η4ς	PROPN
ejpam-5446	7	12	′	′	NUM
ejpam-5446	7	13	(	(	PUNCT
ejpam-5446	7	14	x)+	x)+	NUM
ejpam-5446	7	15	η5ς(x	η5ς(x	NOUN
ejpam-5446	7	16	)	)	PUNCT
ejpam-5446	7	17	=	=	SYM
ejpam-5446	7	18	ω(x	ω(x	NOUN
ejpam-5446	7	19	)	)	PUNCT
ejpam-5446	7	20	has	have	VERB
ejpam-5446	7	21	the	the	DET
ejpam-5446	7	22	hyers	hyers	PROPN
ejpam-5446	7	23	-	-	PUNCT
ejpam-5446	7	24	ulam	ulam	PROPN
ejpam-5446	7	25	stability	stability	NOUN
ejpam-5446	7	26	.	.	PUNCT
ejpam-5446	8	1	two	two	NUM
ejpam-5446	8	2	illustrative	illustrative	ADJ
ejpam-5446	8	3	examples	example	NOUN
ejpam-5446	8	4	are	be	AUX
ejpam-5446	8	5	given	give	VERB
ejpam-5446	8	6	to	to	PART
ejpam-5446	8	7	represent	represent	VERB
ejpam-5446	8	8	the	the	DET
ejpam-5446	8	9	effectiveness	effectiveness	NOUN
ejpam-5446	8	10	of	of	ADP
ejpam-5446	8	11	the	the	DET
ejpam-5446	8	12	proposed	propose	VERB
ejpam-5446	8	13	method	method	NOUN
ejpam-5446	8	14	.	.	PUNCT
ejpam-5446	9	1	fifth	fifth	ADJ
ejpam-5446	9	2	-	-	PUNCT
ejpam-5446	9	3	order	order	NOUN
ejpam-5446	9	4	linear	linear	PROPN
ejpam-5446	9	5	differential	differential	NOUN
ejpam-5446	9	6	equations	equation	NOUN
ejpam-5446	9	7	find	find	VERB
ejpam-5446	9	8	applications	application	NOUN
ejpam-5446	9	9	in	in	ADP
ejpam-5446	9	10	a	a	DET
ejpam-5446	9	11	wide	wide	ADJ
ejpam-5446	9	12	range	range	NOUN
ejpam-5446	9	13	of	of	ADP
ejpam-5446	9	14	fields	field	NOUN
ejpam-5446	9	15	,	,	PUNCT
ejpam-5446	9	16	from	from	ADP
ejpam-5446	9	17	engineering	engineering	NOUN
ejpam-5446	9	18	and	and	CCONJ
ejpam-5446	9	19	control	control	NOUN
ejpam-5446	9	20	theory	theory	NOUN
ejpam-5446	9	21	to	to	ADP
ejpam-5446	9	22	physics	physics	NOUN
ejpam-5446	9	23	,	,	PUNCT
ejpam-5446	9	24	biology	biology	NOUN
ejpam-5446	9	25	,	,	PUNCT
ejpam-5446	9	26	and	and	CCONJ
ejpam-5446	9	27	beyond	beyond	ADP
ejpam-5446	9	28	.	.	PUNCT
ejpam-5446	10	1	these	these	DET
ejpam-5446	10	2	equations	equation	NOUN
ejpam-5446	10	3	are	be	AUX
ejpam-5446	10	4	powerful	powerful	ADJ
ejpam-5446	10	5	tools	tool	NOUN
ejpam-5446	10	6	for	for	ADP
ejpam-5446	10	7	modeling	model	VERB
ejpam-5446	10	8	systems	system	NOUN
ejpam-5446	10	9	with	with	ADP
ejpam-5446	10	10	complex	complex	ADJ
ejpam-5446	10	11	dynamics	dynamic	NOUN
ejpam-5446	10	12	that	that	PRON
ejpam-5446	10	13	involve	involve	VERB
ejpam-5446	10	14	multiple	multiple	ADJ
ejpam-5446	10	15	interacting	interact	VERB
ejpam-5446	10	16	forces	force	NOUN
ejpam-5446	10	17	or	or	CCONJ
ejpam-5446	10	18	rates	rate	NOUN
ejpam-5446	10	19	of	of	ADP
ejpam-5446	10	20	change	change	NOUN
ejpam-5446	10	21	.	.	PUNCT
ejpam-5446	11	1	understanding	understanding	NOUN
ejpam-5446	11	2	and	and	CCONJ
ejpam-5446	11	3	analyzing	analyze	VERB
ejpam-5446	11	4	their	their	PRON
ejpam-5446	11	5	stability	stability	NOUN
ejpam-5446	11	6	and	and	CCONJ
ejpam-5446	11	7	behavior	behavior	NOUN
ejpam-5446	11	8	can	can	AUX
ejpam-5446	11	9	lead	lead	VERB
ejpam-5446	11	10	to	to	ADP
ejpam-5446	11	11	significant	significant	ADJ
ejpam-5446	11	12	advancements	advancement	NOUN
ejpam-5446	11	13	in	in	ADP
ejpam-5446	11	14	the	the	DET
ejpam-5446	11	15	design	design	NOUN
ejpam-5446	11	16	,	,	PUNCT
ejpam-5446	11	17	control	control	NOUN
ejpam-5446	11	18	,	,	PUNCT
ejpam-5446	11	19	and	and	CCONJ
ejpam-5446	11	20	optimization	optimization	NOUN
ejpam-5446	11	21	of	of	ADP
ejpam-5446	11	22	these	these	DET
ejpam-5446	11	23	systems	system	NOUN
ejpam-5446	11	24	.	.	PUNCT
ejpam-5446	12	1	2020	2020	NUM
ejpam-5446	12	2	mathematics	mathematics	PROPN
ejpam-5446	12	3	subject	subject	NOUN
ejpam-5446	12	4	classifications	classification	NOUN
ejpam-5446	12	5	:	:	PUNCT
ejpam-5446	12	6	35b35	35b35	NUM
ejpam-5446	12	7	key	key	ADJ
ejpam-5446	12	8	words	word	NOUN
ejpam-5446	12	9	and	and	CCONJ
ejpam-5446	12	10	phrases	phrase	NOUN
ejpam-5446	12	11	:	:	PUNCT
ejpam-5446	12	12	hyers	hyers	PROPN
ejpam-5446	12	13	-	-	PUNCT
ejpam-5446	12	14	ulam	ulam	PROPN
ejpam-5446	12	15	stability	stability	NOUN
ejpam-5446	12	16	,	,	PUNCT
ejpam-5446	12	17	linear	linear	ADJ
ejpam-5446	12	18	differential	differential	NOUN
ejpam-5446	12	19	equation	equation	NOUN
ejpam-5446	12	20	.	.	PUNCT
ejpam-5446	13	1	∗corresponding	∗corresponde	VERB
ejpam-5446	13	2	author	author	NOUN
ejpam-5446	13	3	.	.	PUNCT
ejpam-5446	14	1	∗corresponding	∗corresponde	VERB
ejpam-5446	14	2	author	author	NOUN
ejpam-5446	14	3	.	.	PUNCT
ejpam-5446	15	1	doi	doi	NOUN
ejpam-5446	15	2	:	:	PUNCT
ejpam-5446	15	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5446	https://doi.org/10.29020/nybg.ejpam.v17i4.5446	ADJ
ejpam-5446	15	4	email	email	NOUN
ejpam-5446	15	5	addresses	address	NOUN
ejpam-5446	15	6	:	:	PUNCT
ejpam-5446	16	1	manibowmi@gmail.com	manibowmi@gmail.com	PROPN
ejpam-5446	16	2	(	(	PUNCT
ejpam-5446	16	3	s.	s.	PROPN
ejpam-5446	16	4	bowmiya	bowmiya	PROPN
ejpam-5446	16	5	)	)	PUNCT
ejpam-5446	16	6	,	,	PUNCT
ejpam-5446	16	7	gbs	gbs	PROPN
ejpam-5446	16	8	geetha@yahoo.com	geetha@yahoo.com	PROPN
ejpam-5446	16	9	(	(	PUNCT
ejpam-5446	16	10	g.	g.	PROPN
ejpam-5446	16	11	balasubramanian	balasubramanian	PROPN
ejpam-5446	16	12	)	)	PUNCT
ejpam-5446	16	13	,	,	PUNCT
ejpam-5446	16	14	vadimalawi@gmail.com	vadimalawi@gmail.com	X
ejpam-5446	16	15	(	(	PUNCT
ejpam-5446	16	16	v.	v.	ADP
ejpam-5446	16	17	govindan	govindan	PROPN
ejpam-5446	16	18	)	)	PUNCT
ejpam-5446	16	19	,	,	PUNCT
ejpam-5446	16	20	mana.do@up.ac.th	mana.do@up.ac.th	PROPN
ejpam-5446	16	21	(	(	PUNCT
ejpam-5446	16	22	m.	m.	NOUN
ejpam-5446	16	23	donganon	donganon	PROPN
ejpam-5446	16	24	)	)	PUNCT
ejpam-5446	16	25	,	,	PUNCT
ejpam-5446	16	26	byeon@inje.ac.kr	byeon@inje.ac.kr	PROPN
ejpam-5446	16	27	(	(	PUNCT
ejpam-5446	16	28	h.	h.	PROPN
ejpam-5446	16	29	byeon	byeon	PROPN
ejpam-5446	16	30	)	)	PUNCT
ejpam-5446	16	31	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5446	17	1	3585	3585	NUM
ejpam-5446	17	2	copyright	copyright	NOUN
ejpam-5446	17	3	:	:	PUNCT
ejpam-5446	17	4	©	©	PROPN
ejpam-5446	17	5	2024	2024	NUM
ejpam-5446	17	6	the	the	DET
ejpam-5446	17	7	author(s	author(s	NOUN
ejpam-5446	17	8	)	)	PUNCT
ejpam-5446	17	9	.	.	PUNCT
ejpam-5446	18	1	(	(	PUNCT
ejpam-5446	18	2	cc	cc	NOUN
ejpam-5446	18	3	by	by	ADP
ejpam-5446	18	4	-	-	PUNCT
ejpam-5446	18	5	nc	nc	PROPN
ejpam-5446	18	6	4.0	4.0	NUM
ejpam-5446	18	7	)	)	PUNCT
ejpam-5446	18	8	v.	v.	ADP
ejpam-5446	18	9	govindan	govindan	PROPN
ejpam-5446	18	10	et	et	PROPN
ejpam-5446	18	11	al	al	PROPN
ejpam-5446	18	12	.	.	PUNCT
ejpam-5446	18	13	/	/	SYM
ejpam-5446	18	14	eur	eur	PROPN
ejpam-5446	18	15	.	.	PUNCT
ejpam-5446	19	1	j.	j.	PROPN
ejpam-5446	19	2	pure	pure	PROPN
ejpam-5446	19	3	appl	appl	PROPN
ejpam-5446	19	4	.	.	PROPN
ejpam-5446	19	5	math	math	PROPN
ejpam-5446	19	6	,	,	PUNCT
ejpam-5446	19	7	17	17	NUM
ejpam-5446	19	8	(	(	PUNCT
ejpam-5446	19	9	4	4	NUM
ejpam-5446	19	10	)	)	PUNCT
ejpam-5446	19	11	(	(	PUNCT
ejpam-5446	19	12	2024	2024	NUM
ejpam-5446	19	13	)	)	PUNCT
ejpam-5446	19	14	,	,	PUNCT
ejpam-5446	19	15	3585	3585	NUM
ejpam-5446	19	16	-	-	SYM
ejpam-5446	19	17	3609	3609	NUM
ejpam-5446	19	18	3586	3586	NUM
ejpam-5446	19	19	1	1	NUM
ejpam-5446	19	20	.	.	PUNCT
ejpam-5446	20	1	introduction	introduction	NOUN
ejpam-5446	20	2	the	the	DET
ejpam-5446	20	3	hyers	hyers	PROPN
ejpam-5446	20	4	-	-	PUNCT
ejpam-5446	20	5	ulam	ulam	PROPN
ejpam-5446	20	6	stability	stability	NOUN
ejpam-5446	20	7	was	be	AUX
ejpam-5446	20	8	presented	present	VERB
ejpam-5446	20	9	by	by	ADP
ejpam-5446	20	10	s.m	s.m	PROPN
ejpam-5446	20	11	.	.	PROPN
ejpam-5446	20	12	ulam	ulam	PROPN
ejpam-5446	21	1	[	[	X
ejpam-5446	21	2	23	23	NUM
ejpam-5446	21	3	]	]	PUNCT
ejpam-5446	21	4	to	to	PART
ejpam-5446	21	5	bring	bring	VERB
ejpam-5446	21	6	up	up	ADP
ejpam-5446	21	7	the	the	DET
ejpam-5446	21	8	problem	problem	NOUN
ejpam-5446	21	9	,	,	PUNCT
ejpam-5446	21	10	suppose	suppose	VERB
ejpam-5446	21	11	one	one	PRON
ejpam-5446	21	12	has	have	VERB
ejpam-5446	21	13	a	a	DET
ejpam-5446	21	14	function	function	NOUN
ejpam-5446	21	15	ς(t	ς(t	PROPN
ejpam-5446	21	16	)	)	PUNCT
ejpam-5446	21	17	which	which	PRON
ejpam-5446	21	18	is	be	AUX
ejpam-5446	21	19	near	near	ADJ
ejpam-5446	21	20	to	to	PART
ejpam-5446	21	21	solve	solve	VERB
ejpam-5446	21	22	an	an	DET
ejpam-5446	21	23	equation	equation	NOUN
ejpam-5446	21	24	.	.	PUNCT
ejpam-5446	22	1	is	be	AUX
ejpam-5446	22	2	there	there	PRON
ejpam-5446	22	3	a	a	DET
ejpam-5446	22	4	exact	exact	ADJ
ejpam-5446	22	5	solution	solution	NOUN
ejpam-5446	22	6	x(t	x(t	PROPN
ejpam-5446	22	7	)	)	PUNCT
ejpam-5446	22	8	of	of	ADP
ejpam-5446	22	9	the	the	DET
ejpam-5446	22	10	equation	equation	NOUN
ejpam-5446	22	11	which	which	PRON
ejpam-5446	22	12	is	be	AUX
ejpam-5446	22	13	close	close	ADJ
ejpam-5446	22	14	to	to	ADP
ejpam-5446	22	15	ς(t	ς(t	NUM
ejpam-5446	22	16	)	)	PUNCT
ejpam-5446	22	17	(	(	PUNCT
ejpam-5446	22	18	see	see	VERB
ejpam-5446	22	19	[	[	X
ejpam-5446	22	20	3	3	NUM
ejpam-5446	22	21	,	,	PUNCT
ejpam-5446	22	22	5	5	NUM
ejpam-5446	22	23	,	,	PUNCT
ejpam-5446	22	24	11	11	NUM
ejpam-5446	22	25	]	]	NUM
ejpam-5446	22	26	)	)	PUNCT
ejpam-5446	22	27	.	.	PUNCT
ejpam-5446	23	1	in	in	ADP
ejpam-5446	23	2	1941	1941	NUM
ejpam-5446	23	3	,	,	PUNCT
ejpam-5446	23	4	d.h	d.h	PROPN
ejpam-5446	23	5	.	.	PROPN
ejpam-5446	23	6	hyers	hyer	NOUN
ejpam-5446	24	1	[	[	X
ejpam-5446	24	2	6	6	NUM
ejpam-5446	24	3	]	]	ADJ
ejpam-5446	24	4	response	response	NOUN
ejpam-5446	24	5	to	to	ADP
ejpam-5446	24	6	the	the	DET
ejpam-5446	24	7	condition	condition	NOUN
ejpam-5446	24	8	of	of	ADP
ejpam-5446	24	9	ulam	ulam	PROPN
ejpam-5446	24	10	for	for	ADP
ejpam-5446	24	11	additive	additive	ADJ
ejpam-5446	24	12	cauchy	cauchy	ADJ
ejpam-5446	24	13	equation	equation	NOUN
ejpam-5446	24	14	in	in	ADP
ejpam-5446	24	15	banach	banach	NOUN
ejpam-5446	24	16	space	space	NOUN
ejpam-5446	24	17	.	.	PUNCT
ejpam-5446	25	1	a	a	DET
ejpam-5446	25	2	solution	solution	NOUN
ejpam-5446	25	3	for	for	ADP
ejpam-5446	25	4	ulam	ulam	PROPN
ejpam-5446	25	5	’s	’s	PART
ejpam-5446	25	6	problems	problem	NOUN
ejpam-5446	25	7	for	for	ADP
ejpam-5446	25	8	linear	linear	ADJ
ejpam-5446	25	9	mappings	mapping	NOUN
ejpam-5446	25	10	was	be	AUX
ejpam-5446	25	11	demonstrated	demonstrate	VERB
ejpam-5446	25	12	by	by	ADP
ejpam-5446	25	13	th	th	X
ejpam-5446	25	14	.	.	PUNCT
ejpam-5446	26	1	m.	m.	NOUN
ejpam-5446	26	2	rassias	rassias	PROPN
ejpam-5446	27	1	[	[	X
ejpam-5446	27	2	21	21	NUM
ejpam-5446	27	3	]	]	PUNCT
ejpam-5446	27	4	,	,	PUNCT
ejpam-5446	27	5	thought	think	VERB
ejpam-5446	27	6	about	about	ADP
ejpam-5446	27	7	a	a	DET
ejpam-5446	27	8	mapping	mapping	NOUN
ejpam-5446	27	9	g	g	NOUN
ejpam-5446	27	10	:	:	PUNCT
ejpam-5446	27	11	e1	e1	PROPN
ejpam-5446	27	12	→	→	SYM
ejpam-5446	27	13	e2	e2	PROPN
ejpam-5446	27	14	such	such	ADJ
ejpam-5446	27	15	that	that	SCONJ
ejpam-5446	27	16	t	t	PROPN
ejpam-5446	27	17	→	→	SYM
ejpam-5446	27	18	g(tx	g(tx	X
ejpam-5446	27	19	)	)	PUNCT
ejpam-5446	27	20	is	be	AUX
ejpam-5446	27	21	continuous	continuous	ADJ
ejpam-5446	27	22	in	in	ADP
ejpam-5446	27	23	t	t	PROPN
ejpam-5446	27	24	for	for	ADP
ejpam-5446	27	25	each	each	DET
ejpam-5446	27	26	fixed	fix	VERB
ejpam-5446	27	27	x.	x.	NOUN
ejpam-5446	28	1	if	if	SCONJ
ejpam-5446	28	2	that	that	SCONJ
ejpam-5446	28	3	there	there	PRON
ejpam-5446	28	4	exists	exist	VERB
ejpam-5446	28	5	θ	θ	PROPN
ejpam-5446	28	6	≥	≥	NOUN
ejpam-5446	28	7	0	0	NUM
ejpam-5446	28	8	and	and	CCONJ
ejpam-5446	28	9	0	0	NUM
ejpam-5446	28	10	≤	≤	NOUN
ejpam-5446	28	11	p	p	X
ejpam-5446	28	12	<	<	X
ejpam-5446	28	13	1	1	NUM
ejpam-5446	28	14	such	such	ADJ
ejpam-5446	28	15	that	that	SCONJ
ejpam-5446	28	16	∥g(x+	∥g(x+	ADV
ejpam-5446	28	17	y)−	y)−	PROPN
ejpam-5446	28	18	g(x)−	g(x)−	NOUN
ejpam-5446	28	19	g(y)∥	g(y)∥	NOUN
ejpam-5446	28	20	=	=	SYM
ejpam-5446	28	21	ϑ(∥x∥p	ϑ(∥x∥p	PROPN
ejpam-5446	28	22	+	+	CCONJ
ejpam-5446	28	23	∥ς∥p	∥ς∥p	PROPN
ejpam-5446	28	24	)	)	PUNCT
ejpam-5446	28	25	,	,	PUNCT
ejpam-5446	28	26	∀x	∀x	X
ejpam-5446	28	27	,	,	PUNCT
ejpam-5446	28	28	y	y	PROPN
ejpam-5446	28	29	∈	∈	PROPN
ejpam-5446	28	30	e1	e1	PROPN
ejpam-5446	28	31	.	.	PUNCT
ejpam-5446	29	1	after	after	ADP
ejpam-5446	29	2	that	that	PRON
ejpam-5446	29	3	,	,	PUNCT
ejpam-5446	29	4	numerous	numerous	ADJ
ejpam-5446	29	5	mathematicians	mathematician	NOUN
ejpam-5446	29	6	have	have	AUX
ejpam-5446	29	7	investigate	investigate	VERB
ejpam-5446	29	8	ulam	ulam	PROPN
ejpam-5446	29	9	’s	’s	PART
ejpam-5446	29	10	problem	problem	NOUN
ejpam-5446	29	11	in	in	ADP
ejpam-5446	29	12	different	different	ADJ
ejpam-5446	29	13	ways	way	NOUN
ejpam-5446	29	14	(	(	PUNCT
ejpam-5446	29	15	see	see	VERB
ejpam-5446	29	16	[	[	X
ejpam-5446	29	17	2	2	NUM
ejpam-5446	29	18	,	,	PUNCT
ejpam-5446	29	19	9	9	NUM
ejpam-5446	29	20	,	,	PUNCT
ejpam-5446	29	21	10	10	NUM
ejpam-5446	29	22	,	,	PUNCT
ejpam-5446	29	23	18	18	NUM
ejpam-5446	29	24	,	,	PUNCT
ejpam-5446	29	25	19	19	NUM
ejpam-5446	29	26	,	,	PUNCT
ejpam-5446	29	27	24	24	NUM
ejpam-5446	29	28	]	]	PUNCT
ejpam-5446	29	29	)	)	PUNCT
ejpam-5446	29	30	.	.	PUNCT
ejpam-5446	30	1	a	a	DET
ejpam-5446	30	2	hyers	hyers	PROPN
ejpam-5446	30	3	-	-	PUNCT
ejpam-5446	30	4	ulam	ulam	NOUN
ejpam-5446	30	5	-	-	PUNCT
ejpam-5446	30	6	rassias	rassias	PROPN
ejpam-5446	30	7	problem	problem	NOUN
ejpam-5446	30	8	is	be	AUX
ejpam-5446	30	9	the	the	DET
ejpam-5446	30	10	differential	differential	ADJ
ejpam-5446	30	11	equation	equation	NOUN
ejpam-5446	30	12	φ(g	φ(g	PROPN
ejpam-5446	30	13	,	,	PUNCT
ejpam-5446	30	14	ς	ς	PROPN
ejpam-5446	30	15	,	,	PUNCT
ejpam-5446	30	16	ς	ς	PROPN
ejpam-5446	30	17	′	′	NUM
ejpam-5446	30	18	,	,	PUNCT
ejpam-5446	30	19	ς	ς	PROPN
ejpam-5446	30	20	′′	′′	PROPN
ejpam-5446	30	21	,	,	PUNCT
ejpam-5446	30	22	...	...	PUNCT
ejpam-5446	30	23	,	,	PUNCT
ejpam-5446	30	24	ςn	ςn	X
ejpam-5446	30	25	)	)	PUNCT
ejpam-5446	30	26	=	=	SYM
ejpam-5446	30	27	0	0	PROPN
ejpam-5446	30	28	has	have	VERB
ejpam-5446	30	29	the	the	DET
ejpam-5446	30	30	hyers	hyer	NOUN
ejpam-5446	30	31	-	-	PUNCT
ejpam-5446	30	32	ulam	ulam	ADJ
ejpam-5446	30	33	-	-	PUNCT
ejpam-5446	30	34	rassias	rassias	PROPN
ejpam-5446	30	35	stability	stability	NOUN
ejpam-5446	30	36	with	with	ADP
ejpam-5446	30	37	respect	respect	NOUN
ejpam-5446	30	38	to	to	ADP
ejpam-5446	30	39	ϑ	ϑ	NOUN
ejpam-5446	30	40	if	if	SCONJ
ejpam-5446	30	41	there	there	PRON
ejpam-5446	30	42	exist	exist	VERB
ejpam-5446	30	43	a	a	DET
ejpam-5446	30	44	constant	constant	ADJ
ejpam-5446	30	45	m	m	NOUN
ejpam-5446	30	46	>	>	X
ejpam-5446	30	47	0	0	PUNCT
ejpam-5446	30	48	to	to	ADP
ejpam-5446	30	49	such	such	DET
ejpam-5446	30	50	an	an	DET
ejpam-5446	30	51	extent	extent	NOUN
ejpam-5446	31	1	that	that	SCONJ
ejpam-5446	31	2	for	for	ADP
ejpam-5446	31	3	given	give	VERB
ejpam-5446	31	4	a	a	DET
ejpam-5446	31	5	function	function	NOUN
ejpam-5446	31	6	ς	ς	PROPN
ejpam-5446	31	7	such	such	ADJ
ejpam-5446	31	8	that	that	PRON
ejpam-5446	31	9	|φ(g	|φ(g	PROPN
ejpam-5446	31	10	,	,	PUNCT
ejpam-5446	31	11	ς	ς	PROPN
ejpam-5446	31	12	,	,	PUNCT
ejpam-5446	31	13	ς	ς	PROPN
ejpam-5446	31	14	′	′	NUM
ejpam-5446	31	15	,	,	PUNCT
ejpam-5446	31	16	ς	ς	PROPN
ejpam-5446	31	17	′′	′′	PROPN
ejpam-5446	31	18	,	,	PUNCT
ejpam-5446	31	19	...	...	PUNCT
ejpam-5446	31	20	,	,	PUNCT
ejpam-5446	31	21	ςn)|	ςn)|	PRON
ejpam-5446	31	22	≤	≤	NUM
ejpam-5446	31	23	ϑ(t	ϑ(t	NOUN
ejpam-5446	31	24	)	)	PUNCT
ejpam-5446	31	25	.	.	PUNCT
ejpam-5446	32	1	then	then	ADV
ejpam-5446	32	2	there	there	PRON
ejpam-5446	32	3	exists	exist	VERB
ejpam-5446	32	4	a	a	DET
ejpam-5446	32	5	solution	solution	NOUN
ejpam-5446	32	6	ςc	ςc	INTJ
ejpam-5446	32	7	of	of	ADP
ejpam-5446	32	8	the	the	DET
ejpam-5446	32	9	differential	differential	ADJ
ejpam-5446	32	10	equation	equation	NOUN
ejpam-5446	32	11	such	such	ADJ
ejpam-5446	32	12	that	that	SCONJ
ejpam-5446	32	13	|ς(t)−	|ς(t)−	NOUN
ejpam-5446	32	14	ςc(t)|	ςc(t)|	ADP
ejpam-5446	32	15	≤	≤	NOUN
ejpam-5446	32	16	mϑ(t	mϑ(t	NOUN
ejpam-5446	32	17	)	)	PUNCT
ejpam-5446	32	18	.	.	PUNCT
ejpam-5446	33	1	meaning	meaning	NOUN
ejpam-5446	33	2	of	of	ADP
ejpam-5446	33	3	hyers	hyer	NOUN
ejpam-5446	33	4	-	-	PUNCT
ejpam-5446	33	5	ulam	ulam	ADJ
ejpam-5446	33	6	-	-	PUNCT
ejpam-5446	33	7	rassias	rassias	PROPN
ejpam-5446	33	8	stability	stability	NOUN
ejpam-5446	33	9	importance	importance	NOUN
ejpam-5446	33	10	implies	imply	VERB
ejpam-5446	33	11	that	that	SCONJ
ejpam-5446	33	12	,	,	PUNCT
ejpam-5446	33	13	assuming	assume	VERB
ejpam-5446	33	14	one	one	PRON
ejpam-5446	33	15	is	be	AUX
ejpam-5446	33	16	considering	consider	VERB
ejpam-5446	33	17	a	a	DET
ejpam-5446	33	18	hyers	hyers	PROPN
ejpam-5446	33	19	-	-	PUNCT
ejpam-5446	33	20	ulam	ulam	ADJ
ejpam-5446	33	21	-	-	PUNCT
ejpam-5446	33	22	rassias	rassias	PROPN
ejpam-5446	33	23	stability	stability	NOUN
ejpam-5446	33	24	system	system	NOUN
ejpam-5446	33	25	,	,	PUNCT
ejpam-5446	33	26	one	one	PRON
ejpam-5446	33	27	does	do	AUX
ejpam-5446	33	28	n’t	not	PART
ejpam-5446	33	29	need	need	VERB
ejpam-5446	33	30	to	to	PART
ejpam-5446	33	31	arrive	arrive	VERB
ejpam-5446	33	32	at	at	ADP
ejpam-5446	33	33	the	the	DET
ejpam-5446	33	34	exact	exact	ADJ
ejpam-5446	33	35	solution	solution	NOUN
ejpam-5446	33	36	.	.	PUNCT
ejpam-5446	34	1	this	this	PRON
ejpam-5446	34	2	is	be	AUX
ejpam-5446	34	3	very	very	ADV
ejpam-5446	34	4	useful	useful	ADJ
ejpam-5446	34	5	for	for	ADP
ejpam-5446	34	6	many	many	ADJ
ejpam-5446	34	7	applications	application	NOUN
ejpam-5446	34	8	for	for	ADP
ejpam-5446	34	9	example	example	NOUN
ejpam-5446	34	10	statistical	statistical	ADJ
ejpam-5446	34	11	research	research	NOUN
ejpam-5446	34	12	,	,	PUNCT
ejpam-5446	34	13	optimization	optimization	NOUN
ejpam-5446	34	14	,	,	PUNCT
ejpam-5446	34	15	biology	biology	NOUN
ejpam-5446	34	16	and	and	CCONJ
ejpam-5446	34	17	financial	financial	ADJ
ejpam-5446	34	18	aspects	aspect	NOUN
ejpam-5446	34	19	and	and	CCONJ
ejpam-5446	34	20	so	so	ADV
ejpam-5446	34	21	on	on	ADV
ejpam-5446	34	22	.	.	PUNCT
ejpam-5446	35	1	in	in	ADP
ejpam-5446	35	2	the	the	DET
ejpam-5446	35	3	past	past	ADJ
ejpam-5446	35	4	decades	decade	NOUN
ejpam-5446	35	5	many	many	ADJ
ejpam-5446	35	6	of	of	ADP
ejpam-5446	35	7	the	the	DET
ejpam-5446	35	8	researchers	researcher	NOUN
ejpam-5446	35	9	has	have	AUX
ejpam-5446	35	10	been	be	AUX
ejpam-5446	35	11	concentrated	concentrate	VERB
ejpam-5446	35	12	on	on	ADP
ejpam-5446	35	13	the	the	DET
ejpam-5446	35	14	hyers	hyers	PROPN
ejpam-5446	35	15	-	-	PUNCT
ejpam-5446	35	16	ulam	ulam	ADJ
ejpam-5446	35	17	stability	stability	NOUN
ejpam-5446	35	18	of	of	ADP
ejpam-5446	35	19	linear	linear	PROPN
ejpam-5446	35	20	differential	differential	ADJ
ejpam-5446	35	21	equations	equation	NOUN
ejpam-5446	35	22	(	(	PUNCT
ejpam-5446	35	23	see	see	VERB
ejpam-5446	35	24	[	[	X
ejpam-5446	35	25	7	7	NUM
ejpam-5446	35	26	,	,	PUNCT
ejpam-5446	35	27	8	8	NUM
ejpam-5446	35	28	,	,	PUNCT
ejpam-5446	35	29	25	25	NUM
ejpam-5446	35	30	]	]	PUNCT
ejpam-5446	35	31	)	)	PUNCT
ejpam-5446	35	32	.	.	PUNCT
ejpam-5446	36	1	likewise	likewise	ADV
ejpam-5446	36	2	jung	jung	PROPN
ejpam-5446	36	3	has	have	AUX
ejpam-5446	36	4	demonstrated	demonstrate	VERB
ejpam-5446	36	5	the	the	DET
ejpam-5446	36	6	hyers	hyers	PROPN
ejpam-5446	36	7	-	-	PUNCT
ejpam-5446	36	8	ulam	ulam	ADJ
ejpam-5446	36	9	stability	stability	NOUN
ejpam-5446	36	10	of	of	ADP
ejpam-5446	36	11	linear	linear	PROPN
ejpam-5446	36	12	differential	differential	ADJ
ejpam-5446	36	13	equations	equation	NOUN
ejpam-5446	36	14	by	by	ADP
ejpam-5446	36	15	using	use	VERB
ejpam-5446	36	16	the	the	DET
ejpam-5446	36	17	laplace	laplace	NOUN
ejpam-5446	36	18	transform	transform	NOUN
ejpam-5446	36	19	method	method	NOUN
ejpam-5446	36	20	(	(	PUNCT
ejpam-5446	36	21	see	see	VERB
ejpam-5446	36	22	[	[	X
ejpam-5446	36	23	22	22	NUM
ejpam-5446	36	24	]	]	PUNCT
ejpam-5446	36	25	)	)	PUNCT
ejpam-5446	36	26	and	and	CCONJ
ejpam-5446	36	27	authors	author	NOUN
ejpam-5446	36	28	in	in	ADP
ejpam-5446	36	29	[	[	X
ejpam-5446	36	30	20	20	NUM
ejpam-5446	36	31	]	]	PUNCT
ejpam-5446	36	32	studied	study	VERB
ejpam-5446	36	33	ulam	ulam	PROPN
ejpam-5446	36	34	stability	stability	NOUN
ejpam-5446	36	35	of	of	ADP
ejpam-5446	36	36	linear	linear	PROPN
ejpam-5446	36	37	differential	differential	ADJ
ejpam-5446	36	38	equations	equation	NOUN
ejpam-5446	36	39	using	use	VERB
ejpam-5446	36	40	fourier	fourier	NOUN
ejpam-5446	36	41	transform	transform	NOUN
ejpam-5446	36	42	.	.	PUNCT
ejpam-5446	37	1	recently	recently	ADV
ejpam-5446	37	2	,	,	PUNCT
ejpam-5446	37	3	authors	author	NOUN
ejpam-5446	37	4	in	in	ADP
ejpam-5446	37	5	[	[	X
ejpam-5446	37	6	4	4	NUM
ejpam-5446	37	7	]	]	PUNCT
ejpam-5446	37	8	,	,	PUNCT
ejpam-5446	37	9	researched	research	VERB
ejpam-5446	37	10	hyers	hyers	PROPN
ejpam-5446	37	11	-	-	PUNCT
ejpam-5446	37	12	ulam	ulam	ADJ
ejpam-5446	37	13	stability	stability	NOUN
ejpam-5446	37	14	of	of	ADP
ejpam-5446	37	15	an	an	DET
ejpam-5446	37	16	n	n	CCONJ
ejpam-5446	37	17	-	-	PUNCT
ejpam-5446	37	18	variable	variable	ADJ
ejpam-5446	37	19	quartic	quartic	ADJ
ejpam-5446	37	20	functional	functional	ADJ
ejpam-5446	37	21	equation	equation	NOUN
ejpam-5446	37	22	.	.	PUNCT
ejpam-5446	38	1	to	to	ADP
ejpam-5446	38	2	the	the	DET
ejpam-5446	38	3	best	good	ADJ
ejpam-5446	38	4	of	of	ADP
ejpam-5446	38	5	author	author	NOUN
ejpam-5446	38	6	’s	’s	PART
ejpam-5446	38	7	knowledge	knowledge	NOUN
ejpam-5446	38	8	,	,	PUNCT
ejpam-5446	38	9	hyers	hyers	PROPN
ejpam-5446	38	10	-	-	PUNCT
ejpam-5446	38	11	ulam	ulam	PROPN
ejpam-5446	38	12	stability	stability	PROPN
ejpam-5446	38	13	approaches	approach	VERB
ejpam-5446	38	14	to	to	ADP
ejpam-5446	38	15	linear	linear	VERB
ejpam-5446	38	16	differential	differential	ADJ
ejpam-5446	38	17	equation	equation	NOUN
ejpam-5446	38	18	of	of	ADP
ejpam-5446	38	19	order	order	NOUN
ejpam-5446	38	20	five	five	NUM
ejpam-5446	38	21	has	have	AUX
ejpam-5446	38	22	not	not	PART
ejpam-5446	38	23	been	be	AUX
ejpam-5446	38	24	studied	study	VERB
ejpam-5446	38	25	so	so	ADV
ejpam-5446	38	26	far	far	ADV
ejpam-5446	38	27	,	,	PUNCT
ejpam-5446	38	28	which	which	PRON
ejpam-5446	38	29	motivates	motivate	VERB
ejpam-5446	38	30	the	the	DET
ejpam-5446	38	31	present	present	ADJ
ejpam-5446	38	32	study	study	NOUN
ejpam-5446	38	33	.	.	PUNCT
ejpam-5446	39	1	linear	linear	ADJ
ejpam-5446	39	2	differential	differential	ADJ
ejpam-5446	39	3	equations	equation	NOUN
ejpam-5446	39	4	have	have	AUX
ejpam-5446	39	5	been	be	AUX
ejpam-5446	39	6	studied	study	VERB
ejpam-5446	39	7	extensively	extensively	ADV
ejpam-5446	39	8	across	across	ADP
ejpam-5446	39	9	various	various	ADJ
ejpam-5446	39	10	fields	field	NOUN
ejpam-5446	39	11	like	like	ADP
ejpam-5446	39	12	physics	physics	NOUN
ejpam-5446	39	13	,	,	PUNCT
ejpam-5446	39	14	engineering	engineering	NOUN
ejpam-5446	39	15	,	,	PUNCT
ejpam-5446	39	16	and	and	CCONJ
ejpam-5446	39	17	applied	applied	ADJ
ejpam-5446	39	18	mathematics	mathematic	NOUN
ejpam-5446	39	19	.	.	PUNCT
ejpam-5446	40	1	early	early	ADJ
ejpam-5446	40	2	research	research	NOUN
ejpam-5446	40	3	primarily	primarily	ADV
ejpam-5446	40	4	focused	focus	VERB
ejpam-5446	40	5	on	on	ADP
ejpam-5446	40	6	firstand	firstand	NOUN
ejpam-5446	40	7	second	second	ADJ
ejpam-5446	40	8	-	-	PUNCT
ejpam-5446	40	9	order	order	NOUN
ejpam-5446	40	10	differential	differential	ADJ
ejpam-5446	40	11	equations	equation	NOUN
ejpam-5446	40	12	,	,	PUNCT
ejpam-5446	40	13	which	which	PRON
ejpam-5446	40	14	are	be	AUX
ejpam-5446	40	15	simpler	simple	ADJ
ejpam-5446	40	16	to	to	PART
ejpam-5446	40	17	analyze	analyze	VERB
ejpam-5446	40	18	both	both	PRON
ejpam-5446	40	19	analytically	analytically	ADV
ejpam-5446	40	20	and	and	CCONJ
ejpam-5446	40	21	numerically	numerically	ADV
ejpam-5446	40	22	.	.	PUNCT
ejpam-5446	41	1	fifth	fifth	ADJ
ejpam-5446	41	2	-	-	PUNCT
ejpam-5446	41	3	order	order	NOUN
ejpam-5446	41	4	differential	differential	ADJ
ejpam-5446	41	5	equations	equation	NOUN
ejpam-5446	41	6	frequently	frequently	ADV
ejpam-5446	41	7	arise	arise	VERB
ejpam-5446	41	8	in	in	ADP
ejpam-5446	41	9	models	model	NOUN
ejpam-5446	41	10	related	relate	VERB
ejpam-5446	41	11	to	to	ADP
ejpam-5446	41	12	advanced	advanced	ADJ
ejpam-5446	41	13	mechanical	mechanical	ADJ
ejpam-5446	41	14	systems	system	NOUN
ejpam-5446	41	15	,	,	PUNCT
ejpam-5446	41	16	fluid	fluid	ADJ
ejpam-5446	41	17	dynamics	dynamic	NOUN
ejpam-5446	41	18	,	,	PUNCT
ejpam-5446	41	19	or	or	CCONJ
ejpam-5446	41	20	even	even	ADV
ejpam-5446	41	21	quantum	quantum	ADJ
ejpam-5446	41	22	mechanics	mechanic	NOUN
ejpam-5446	41	23	.	.	PUNCT
ejpam-5446	42	1	they	they	PRON
ejpam-5446	42	2	are	be	AUX
ejpam-5446	42	3	often	often	ADV
ejpam-5446	42	4	used	use	VERB
ejpam-5446	42	5	in	in	ADP
ejpam-5446	42	6	beam	beam	NOUN
ejpam-5446	42	7	theory	theory	NOUN
ejpam-5446	42	8	(	(	PUNCT
ejpam-5446	42	9	e.g.	e.g.	ADV
ejpam-5446	42	10	,	,	PUNCT
ejpam-5446	42	11	the	the	DET
ejpam-5446	42	12	bending	bending	NOUN
ejpam-5446	42	13	of	of	ADP
ejpam-5446	42	14	beams	beam	NOUN
ejpam-5446	42	15	)	)	PUNCT
ejpam-5446	42	16	,	,	PUNCT
ejpam-5446	42	17	electromagnetic	electromagnetic	ADJ
ejpam-5446	42	18	theory	theory	NOUN
ejpam-5446	42	19	,	,	PUNCT
ejpam-5446	42	20	and	and	CCONJ
ejpam-5446	42	21	more	more	ADV
ejpam-5446	42	22	complex	complex	ADJ
ejpam-5446	42	23	vibrational	vibrational	ADJ
ejpam-5446	42	24	systems	system	NOUN
ejpam-5446	42	25	.	.	PUNCT
ejpam-5446	43	1	in	in	ADP
ejpam-5446	43	2	control	control	NOUN
ejpam-5446	43	3	theory	theory	NOUN
ejpam-5446	43	4	and	and	CCONJ
ejpam-5446	43	5	signal	signal	NOUN
ejpam-5446	43	6	processing	processing	NOUN
ejpam-5446	43	7	,	,	PUNCT
ejpam-5446	43	8	fifth	fifth	ADJ
ejpam-5446	43	9	-	-	PUNCT
ejpam-5446	43	10	order	order	NOUN
ejpam-5446	43	11	differential	differential	ADJ
ejpam-5446	43	12	equations	equation	NOUN
ejpam-5446	43	13	can	can	AUX
ejpam-5446	43	14	model	model	VERB
ejpam-5446	43	15	systems	system	NOUN
ejpam-5446	43	16	with	with	ADP
ejpam-5446	43	17	higher	high	ADJ
ejpam-5446	43	18	-	-	PUNCT
ejpam-5446	43	19	order	order	NOUN
ejpam-5446	43	20	dynamics	dynamic	NOUN
ejpam-5446	43	21	,	,	PUNCT
ejpam-5446	43	22	particularly	particularly	ADV
ejpam-5446	43	23	in	in	ADP
ejpam-5446	43	24	cases	case	NOUN
ejpam-5446	43	25	involving	involve	VERB
ejpam-5446	43	26	feedback	feedback	NOUN
ejpam-5446	43	27	systems	system	NOUN
ejpam-5446	43	28	or	or	CCONJ
ejpam-5446	43	29	circuits	circuit	NOUN
ejpam-5446	43	30	.	.	PUNCT
ejpam-5446	44	1	stability	stability	NOUN
ejpam-5446	44	2	in	in	ADP
ejpam-5446	44	3	the	the	DET
ejpam-5446	44	4	context	context	NOUN
ejpam-5446	44	5	of	of	ADP
ejpam-5446	44	6	differential	differential	ADJ
ejpam-5446	44	7	equations	equation	NOUN
ejpam-5446	44	8	refers	refer	VERB
ejpam-5446	44	9	to	to	ADP
ejpam-5446	44	10	the	the	DET
ejpam-5446	44	11	behavior	behavior	NOUN
ejpam-5446	44	12	of	of	ADP
ejpam-5446	44	13	solutions	solution	NOUN
ejpam-5446	44	14	as	as	SCONJ
ejpam-5446	44	15	they	they	PRON
ejpam-5446	44	16	respond	respond	VERB
ejpam-5446	44	17	to	to	ADP
ejpam-5446	44	18	small	small	ADJ
ejpam-5446	44	19	changes	change	NOUN
ejpam-5446	44	20	in	in	ADP
ejpam-5446	44	21	initial	initial	ADJ
ejpam-5446	44	22	conditions	condition	NOUN
ejpam-5446	44	23	or	or	CCONJ
ejpam-5446	44	24	v.	v.	ADP
ejpam-5446	44	25	govindan	govindan	PROPN
ejpam-5446	45	1	et	et	PROPN
ejpam-5446	45	2	al	al	PROPN
ejpam-5446	45	3	.	.	PUNCT
ejpam-5446	45	4	/	/	SYM
ejpam-5446	45	5	eur	eur	PROPN
ejpam-5446	45	6	.	.	PUNCT
ejpam-5446	46	1	j.	j.	PROPN
ejpam-5446	46	2	pure	pure	PROPN
ejpam-5446	46	3	appl	appl	PROPN
ejpam-5446	46	4	.	.	PROPN
ejpam-5446	46	5	math	math	PROPN
ejpam-5446	46	6	,	,	PUNCT
ejpam-5446	46	7	17	17	NUM
ejpam-5446	46	8	(	(	PUNCT
ejpam-5446	46	9	4	4	NUM
ejpam-5446	46	10	)	)	PUNCT
ejpam-5446	46	11	(	(	PUNCT
ejpam-5446	46	12	2024	2024	NUM
ejpam-5446	46	13	)	)	PUNCT
ejpam-5446	46	14	,	,	PUNCT
ejpam-5446	46	15	3585	3585	NUM
ejpam-5446	46	16	-	-	SYM
ejpam-5446	46	17	3609	3609	NUM
ejpam-5446	46	18	3587	3587	NUM
ejpam-5446	46	19	the	the	DET
ejpam-5446	46	20	forcing	force	VERB
ejpam-5446	46	21	function	function	NOUN
ejpam-5446	46	22	.	.	PUNCT
ejpam-5446	47	1	in	in	ADP
ejpam-5446	47	2	simpler	simple	ADJ
ejpam-5446	47	3	terms	term	NOUN
ejpam-5446	47	4	,	,	PUNCT
ejpam-5446	47	5	stability	stability	NOUN
ejpam-5446	47	6	determines	determine	VERB
ejpam-5446	47	7	whether	whether	SCONJ
ejpam-5446	47	8	a	a	DET
ejpam-5446	47	9	small	small	ADJ
ejpam-5446	47	10	perturbation	perturbation	NOUN
ejpam-5446	47	11	will	will	AUX
ejpam-5446	47	12	grow	grow	VERB
ejpam-5446	47	13	or	or	CCONJ
ejpam-5446	47	14	decay	decay	VERB
ejpam-5446	47	15	over	over	ADP
ejpam-5446	47	16	time	time	NOUN
ejpam-5446	47	17	.	.	PUNCT
ejpam-5446	48	1	the	the	DET
ejpam-5446	48	2	literature	literature	NOUN
ejpam-5446	48	3	on	on	ADP
ejpam-5446	48	4	stability	stability	NOUN
ejpam-5446	48	5	analysis	analysis	NOUN
ejpam-5446	48	6	for	for	ADP
ejpam-5446	48	7	differential	differential	ADJ
ejpam-5446	48	8	equations	equation	NOUN
ejpam-5446	48	9	has	have	AUX
ejpam-5446	48	10	traditionally	traditionally	ADV
ejpam-5446	48	11	focused	focus	VERB
ejpam-5446	48	12	on	on	ADP
ejpam-5446	48	13	lower	low	ADJ
ejpam-5446	48	14	-	-	PUNCT
ejpam-5446	48	15	order	order	NOUN
ejpam-5446	48	16	systems	system	NOUN
ejpam-5446	48	17	(	(	PUNCT
ejpam-5446	48	18	especially	especially	ADV
ejpam-5446	48	19	second	second	ADJ
ejpam-5446	48	20	-	-	PUNCT
ejpam-5446	48	21	order	order	NOUN
ejpam-5446	48	22	)	)	PUNCT
ejpam-5446	48	23	.	.	PUNCT
ejpam-5446	49	1	however	however	ADV
ejpam-5446	49	2	,	,	PUNCT
ejpam-5446	49	3	the	the	DET
ejpam-5446	49	4	theory	theory	NOUN
ejpam-5446	49	5	has	have	AUX
ejpam-5446	49	6	been	be	AUX
ejpam-5446	49	7	extended	extend	VERB
ejpam-5446	49	8	to	to	ADP
ejpam-5446	49	9	higher	high	ADJ
ejpam-5446	49	10	-	-	PUNCT
ejpam-5446	49	11	order	order	NOUN
ejpam-5446	49	12	systems	system	NOUN
ejpam-5446	49	13	,	,	PUNCT
ejpam-5446	49	14	including	include	VERB
ejpam-5446	49	15	fifth	fifth	ADJ
ejpam-5446	49	16	-	-	PUNCT
ejpam-5446	49	17	order	order	NOUN
ejpam-5446	49	18	equations	equation	NOUN
ejpam-5446	49	19	,	,	PUNCT
ejpam-5446	49	20	particularly	particularly	ADV
ejpam-5446	49	21	in	in	ADP
ejpam-5446	49	22	the	the	DET
ejpam-5446	49	23	study	study	NOUN
ejpam-5446	49	24	of	of	ADP
ejpam-5446	49	25	physical	physical	ADJ
ejpam-5446	49	26	systems	system	NOUN
ejpam-5446	49	27	with	with	ADP
ejpam-5446	49	28	complex	complex	ADJ
ejpam-5446	49	29	dynamics.the	dynamics.the	DET
ejpam-5446	49	30	concept	concept	NOUN
ejpam-5446	49	31	of	of	ADP
ejpam-5446	49	32	hyers	hyers	PROPN
ejpam-5446	49	33	-	-	PUNCT
ejpam-5446	49	34	ulam	ulam	PROPN
ejpam-5446	49	35	stability	stability	NOUN
ejpam-5446	49	36	examines	examine	VERB
ejpam-5446	49	37	whether	whether	SCONJ
ejpam-5446	49	38	a	a	DET
ejpam-5446	49	39	differential	differential	ADJ
ejpam-5446	49	40	equation	equation	NOUN
ejpam-5446	49	41	exhibits	exhibit	VERB
ejpam-5446	49	42	stability	stability	NOUN
ejpam-5446	49	43	when	when	SCONJ
ejpam-5446	49	44	subjected	subject	VERB
ejpam-5446	49	45	to	to	ADP
ejpam-5446	49	46	small	small	ADJ
ejpam-5446	49	47	perturbations	perturbation	NOUN
ejpam-5446	49	48	in	in	ADP
ejpam-5446	49	49	the	the	DET
ejpam-5446	49	50	functional	functional	ADJ
ejpam-5446	49	51	form	form	NOUN
ejpam-5446	49	52	.	.	PUNCT
ejpam-5446	50	1	specifically	specifically	ADV
ejpam-5446	50	2	,	,	PUNCT
ejpam-5446	50	3	it	it	PRON
ejpam-5446	50	4	asks	ask	VERB
ejpam-5446	50	5	whether	whether	SCONJ
ejpam-5446	50	6	the	the	DET
ejpam-5446	50	7	approximate	approximate	ADJ
ejpam-5446	50	8	solution	solution	NOUN
ejpam-5446	50	9	remains	remain	VERB
ejpam-5446	50	10	close	close	ADJ
ejpam-5446	50	11	to	to	ADP
ejpam-5446	50	12	the	the	DET
ejpam-5446	50	13	exact	exact	ADJ
ejpam-5446	50	14	solution.much	solution.much	PROPN
ejpam-5446	50	15	of	of	ADP
ejpam-5446	50	16	the	the	DET
ejpam-5446	50	17	early	early	ADJ
ejpam-5446	50	18	work	work	NOUN
ejpam-5446	50	19	on	on	ADP
ejpam-5446	50	20	hyers	hyers	PROPN
ejpam-5446	50	21	-	-	PUNCT
ejpam-5446	50	22	ulam	ulam	PROPN
ejpam-5446	50	23	stability	stability	NOUN
ejpam-5446	50	24	focused	focus	VERB
ejpam-5446	50	25	on	on	ADP
ejpam-5446	50	26	firstand	firstand	NOUN
ejpam-5446	50	27	secondorder	secondorder	NOUN
ejpam-5446	50	28	linear	linear	PROPN
ejpam-5446	50	29	differential	differential	NOUN
ejpam-5446	50	30	equations	equation	NOUN
ejpam-5446	50	31	,	,	PUNCT
ejpam-5446	50	32	but	but	CCONJ
ejpam-5446	50	33	more	more	ADV
ejpam-5446	50	34	recent	recent	ADJ
ejpam-5446	50	35	studies	study	NOUN
ejpam-5446	50	36	have	have	AUX
ejpam-5446	50	37	extended	extend	VERB
ejpam-5446	50	38	this	this	DET
ejpam-5446	50	39	analysis	analysis	NOUN
ejpam-5446	50	40	to	to	ADP
ejpam-5446	50	41	higher	high	ADJ
ejpam-5446	50	42	-	-	PUNCT
ejpam-5446	50	43	order	order	NOUN
ejpam-5446	50	44	equations	equation	NOUN
ejpam-5446	50	45	,	,	PUNCT
ejpam-5446	50	46	including	include	VERB
ejpam-5446	50	47	fifth	fifth	ADJ
ejpam-5446	50	48	-	-	PUNCT
ejpam-5446	50	49	order	order	NOUN
ejpam-5446	50	50	systems	system	NOUN
ejpam-5446	50	51	.	.	PUNCT
ejpam-5446	51	1	these	these	DET
ejpam-5446	51	2	studies	study	NOUN
ejpam-5446	51	3	are	be	AUX
ejpam-5446	51	4	particularly	particularly	ADV
ejpam-5446	51	5	important	important	ADJ
ejpam-5446	51	6	because	because	SCONJ
ejpam-5446	51	7	higher	high	ADJ
ejpam-5446	51	8	-	-	PUNCT
ejpam-5446	51	9	order	order	NOUN
ejpam-5446	51	10	systems	system	NOUN
ejpam-5446	51	11	are	be	AUX
ejpam-5446	51	12	more	more	ADV
ejpam-5446	51	13	sensitive	sensitive	ADJ
ejpam-5446	51	14	to	to	ADP
ejpam-5446	51	15	perturbations	perturbation	NOUN
ejpam-5446	51	16	,	,	PUNCT
ejpam-5446	51	17	making	make	VERB
ejpam-5446	51	18	the	the	DET
ejpam-5446	51	19	stability	stability	NOUN
ejpam-5446	51	20	analysis	analysis	NOUN
ejpam-5446	51	21	more	more	ADV
ejpam-5446	51	22	complex	complex	ADJ
ejpam-5446	51	23	.	.	PUNCT
ejpam-5446	52	1	recent	recent	ADJ
ejpam-5446	52	2	works	work	NOUN
ejpam-5446	52	3	in	in	ADP
ejpam-5446	52	4	the	the	DET
ejpam-5446	52	5	field	field	NOUN
ejpam-5446	52	6	have	have	AUX
ejpam-5446	52	7	explored	explore	VERB
ejpam-5446	52	8	conditions	condition	NOUN
ejpam-5446	52	9	under	under	ADP
ejpam-5446	52	10	which	which	PRON
ejpam-5446	52	11	fifth	fifth	ADJ
ejpam-5446	52	12	-	-	PUNCT
ejpam-5446	52	13	order	order	NOUN
ejpam-5446	52	14	differential	differential	ADJ
ejpam-5446	52	15	equations	equation	NOUN
ejpam-5446	52	16	admit	admit	VERB
ejpam-5446	52	17	unique	unique	ADJ
ejpam-5446	52	18	solutions	solution	NOUN
ejpam-5446	52	19	.	.	PUNCT
ejpam-5446	53	1	these	these	DET
ejpam-5446	53	2	results	result	NOUN
ejpam-5446	53	3	typically	typically	ADV
ejpam-5446	53	4	depend	depend	VERB
ejpam-5446	53	5	on	on	ADP
ejpam-5446	53	6	the	the	DET
ejpam-5446	53	7	properties	property	NOUN
ejpam-5446	53	8	of	of	ADP
ejpam-5446	53	9	the	the	DET
ejpam-5446	53	10	coefficients	coefficient	NOUN
ejpam-5446	53	11	and	and	CCONJ
ejpam-5446	53	12	boundary	boundary	ADJ
ejpam-5446	53	13	conditions	condition	NOUN
ejpam-5446	53	14	.	.	PUNCT
ejpam-5446	54	1	with	with	ADP
ejpam-5446	54	2	increasing	increase	VERB
ejpam-5446	54	3	computational	computational	ADJ
ejpam-5446	54	4	power	power	NOUN
ejpam-5446	54	5	,	,	PUNCT
ejpam-5446	54	6	researchers	researcher	NOUN
ejpam-5446	54	7	have	have	AUX
ejpam-5446	54	8	developed	develop	VERB
ejpam-5446	54	9	sophisticated	sophisticated	ADJ
ejpam-5446	54	10	numerical	numerical	ADJ
ejpam-5446	54	11	techniques	technique	NOUN
ejpam-5446	54	12	to	to	PART
ejpam-5446	54	13	approximate	approximate	VERB
ejpam-5446	54	14	solutions	solution	NOUN
ejpam-5446	54	15	of	of	ADP
ejpam-5446	54	16	fifth	fifth	ADJ
ejpam-5446	54	17	-	-	PUNCT
ejpam-5446	54	18	order	order	NOUN
ejpam-5446	54	19	equations	equation	NOUN
ejpam-5446	54	20	.	.	PUNCT
ejpam-5446	55	1	finite	finite	PROPN
ejpam-5446	55	2	element	element	NOUN
ejpam-5446	55	3	methods	method	NOUN
ejpam-5446	55	4	and	and	CCONJ
ejpam-5446	55	5	spectral	spectral	ADJ
ejpam-5446	55	6	methods	method	NOUN
ejpam-5446	55	7	have	have	AUX
ejpam-5446	55	8	become	become	VERB
ejpam-5446	55	9	popular	popular	ADJ
ejpam-5446	55	10	in	in	ADP
ejpam-5446	55	11	this	this	DET
ejpam-5446	55	12	regard	regard	NOUN
ejpam-5446	55	13	.	.	PUNCT
ejpam-5446	56	1	current	current	ADJ
ejpam-5446	56	2	research	research	NOUN
ejpam-5446	56	3	extends	extend	VERB
ejpam-5446	56	4	classical	classical	ADJ
ejpam-5446	56	5	stability	stability	NOUN
ejpam-5446	56	6	theorems	theorem	NOUN
ejpam-5446	56	7	,	,	PUNCT
ejpam-5446	56	8	such	such	ADJ
ejpam-5446	56	9	as	as	ADP
ejpam-5446	56	10	lyapunov	lyapunov	ADJ
ejpam-5446	56	11	stability	stability	NOUN
ejpam-5446	56	12	,	,	PUNCT
ejpam-5446	56	13	to	to	ADP
ejpam-5446	56	14	fifth	fifth	ADJ
ejpam-5446	56	15	-	-	PUNCT
ejpam-5446	56	16	order	order	NOUN
ejpam-5446	56	17	systems	system	NOUN
ejpam-5446	56	18	.	.	PUNCT
ejpam-5446	57	1	this	this	PRON
ejpam-5446	57	2	often	often	ADV
ejpam-5446	57	3	involves	involve	VERB
ejpam-5446	57	4	formulating	formulate	VERB
ejpam-5446	57	5	and	and	CCONJ
ejpam-5446	57	6	solving	solve	VERB
ejpam-5446	57	7	lyapunov	lyapunov	NOUN
ejpam-5446	57	8	functions	function	NOUN
ejpam-5446	57	9	for	for	ADP
ejpam-5446	57	10	these	these	DET
ejpam-5446	57	11	complex	complex	ADJ
ejpam-5446	57	12	systems	system	NOUN
ejpam-5446	57	13	to	to	PART
ejpam-5446	57	14	determine	determine	VERB
ejpam-5446	57	15	conditions	condition	NOUN
ejpam-5446	57	16	under	under	ADP
ejpam-5446	57	17	which	which	PRON
ejpam-5446	57	18	solutions	solution	NOUN
ejpam-5446	57	19	are	be	AUX
ejpam-5446	57	20	stable	stable	ADJ
ejpam-5446	57	21	.	.	PUNCT
ejpam-5446	58	1	several	several	ADJ
ejpam-5446	58	2	recent	recent	ADJ
ejpam-5446	58	3	studies	study	NOUN
ejpam-5446	58	4	have	have	AUX
ejpam-5446	58	5	focused	focus	VERB
ejpam-5446	58	6	on	on	ADP
ejpam-5446	58	7	extending	extend	VERB
ejpam-5446	58	8	hyers	hyer	NOUN
ejpam-5446	58	9	-	-	PUNCT
ejpam-5446	58	10	ulam	ulam	PROPN
ejpam-5446	58	11	stability	stability	NOUN
ejpam-5446	58	12	to	to	ADP
ejpam-5446	58	13	fifth	fifth	ADJ
ejpam-5446	58	14	-	-	PUNCT
ejpam-5446	58	15	order	order	NOUN
ejpam-5446	58	16	differential	differential	ADJ
ejpam-5446	58	17	equations	equation	NOUN
ejpam-5446	58	18	.	.	PUNCT
ejpam-5446	59	1	these	these	DET
ejpam-5446	59	2	works	work	NOUN
ejpam-5446	59	3	build	build	VERB
ejpam-5446	59	4	on	on	ADP
ejpam-5446	59	5	classical	classical	ADJ
ejpam-5446	59	6	stability	stability	NOUN
ejpam-5446	59	7	results	result	NOUN
ejpam-5446	59	8	but	but	CCONJ
ejpam-5446	59	9	adapt	adapt	VERB
ejpam-5446	59	10	them	they	PRON
ejpam-5446	59	11	to	to	ADP
ejpam-5446	59	12	the	the	DET
ejpam-5446	59	13	unique	unique	ADJ
ejpam-5446	59	14	challenges	challenge	NOUN
ejpam-5446	59	15	posed	pose	VERB
ejpam-5446	59	16	by	by	ADP
ejpam-5446	59	17	higher	high	ADJ
ejpam-5446	59	18	-	-	PUNCT
ejpam-5446	59	19	order	order	NOUN
ejpam-5446	59	20	systems	system	NOUN
ejpam-5446	59	21	.	.	PUNCT
ejpam-5446	60	1	the	the	DET
ejpam-5446	60	2	key	key	ADJ
ejpam-5446	60	3	focus	focus	NOUN
ejpam-5446	60	4	of	of	ADP
ejpam-5446	60	5	this	this	DET
ejpam-5446	60	6	research	research	NOUN
ejpam-5446	60	7	has	have	AUX
ejpam-5446	60	8	been	be	AUX
ejpam-5446	60	9	to	to	PART
ejpam-5446	60	10	identify	identify	VERB
ejpam-5446	60	11	conditions	condition	NOUN
ejpam-5446	60	12	under	under	ADP
ejpam-5446	60	13	which	which	PRON
ejpam-5446	60	14	small	small	ADJ
ejpam-5446	60	15	deviations	deviation	NOUN
ejpam-5446	60	16	in	in	ADP
ejpam-5446	60	17	the	the	DET
ejpam-5446	60	18	approximate	approximate	ADJ
ejpam-5446	60	19	solution	solution	NOUN
ejpam-5446	60	20	lead	lead	VERB
ejpam-5446	60	21	to	to	ADP
ejpam-5446	60	22	bounded	bound	VERB
ejpam-5446	60	23	deviations	deviation	NOUN
ejpam-5446	60	24	in	in	ADP
ejpam-5446	60	25	the	the	DET
ejpam-5446	60	26	actual	actual	ADJ
ejpam-5446	60	27	solution	solution	NOUN
ejpam-5446	60	28	,	,	PUNCT
ejpam-5446	60	29	thus	thus	ADV
ejpam-5446	60	30	extending	extend	VERB
ejpam-5446	60	31	hyers	hyer	NOUN
ejpam-5446	60	32	-	-	PUNCT
ejpam-5446	60	33	ulam	ulam	PROPN
ejpam-5446	60	34	’s	’s	PART
ejpam-5446	60	35	classical	classical	ADJ
ejpam-5446	60	36	framework	framework	NOUN
ejpam-5446	60	37	to	to	ADP
ejpam-5446	60	38	a	a	DET
ejpam-5446	60	39	more	more	ADV
ejpam-5446	60	40	complex	complex	ADJ
ejpam-5446	60	41	domain	domain	NOUN
ejpam-5446	60	42	.	.	PUNCT
ejpam-5446	61	1	the	the	DET
ejpam-5446	61	2	study	study	NOUN
ejpam-5446	61	3	of	of	ADP
ejpam-5446	61	4	fifth	fifth	ADJ
ejpam-5446	61	5	-	-	PUNCT
ejpam-5446	61	6	order	order	NOUN
ejpam-5446	61	7	linear	linear	PROPN
ejpam-5446	61	8	differential	differential	NOUN
ejpam-5446	61	9	equations	equation	NOUN
ejpam-5446	61	10	is	be	AUX
ejpam-5446	61	11	motivated	motivate	VERB
ejpam-5446	61	12	by	by	ADP
ejpam-5446	61	13	both	both	CCONJ
ejpam-5446	61	14	practical	practical	ADJ
ejpam-5446	61	15	and	and	CCONJ
ejpam-5446	61	16	theoretical	theoretical	ADJ
ejpam-5446	61	17	needs	need	NOUN
ejpam-5446	61	18	.	.	PUNCT
ejpam-5446	62	1	from	from	ADP
ejpam-5446	62	2	a	a	DET
ejpam-5446	62	3	practical	practical	ADJ
ejpam-5446	62	4	standpoint	standpoint	NOUN
ejpam-5446	62	5	,	,	PUNCT
ejpam-5446	62	6	these	these	DET
ejpam-5446	62	7	equations	equation	NOUN
ejpam-5446	62	8	model	model	VERB
ejpam-5446	62	9	complex	complex	ADJ
ejpam-5446	62	10	real	real	ADJ
ejpam-5446	62	11	-	-	PUNCT
ejpam-5446	62	12	world	world	NOUN
ejpam-5446	62	13	systems	system	NOUN
ejpam-5446	62	14	that	that	PRON
ejpam-5446	62	15	involve	involve	VERB
ejpam-5446	62	16	higher	high	ADJ
ejpam-5446	62	17	-	-	PUNCT
ejpam-5446	62	18	order	order	NOUN
ejpam-5446	62	19	dynamics	dynamic	NOUN
ejpam-5446	62	20	and	and	CCONJ
ejpam-5446	62	21	feedback	feedback	NOUN
ejpam-5446	62	22	loops	loop	NOUN
ejpam-5446	62	23	,	,	PUNCT
ejpam-5446	62	24	such	such	ADJ
ejpam-5446	62	25	as	as	ADP
ejpam-5446	62	26	in	in	ADP
ejpam-5446	62	27	engineering	engineering	NOUN
ejpam-5446	62	28	,	,	PUNCT
ejpam-5446	62	29	physics	physics	NOUN
ejpam-5446	62	30	,	,	PUNCT
ejpam-5446	62	31	and	and	CCONJ
ejpam-5446	62	32	control	control	NOUN
ejpam-5446	62	33	theory	theory	NOUN
ejpam-5446	62	34	.	.	PUNCT
ejpam-5446	63	1	from	from	ADP
ejpam-5446	63	2	a	a	DET
ejpam-5446	63	3	theoretical	theoretical	ADJ
ejpam-5446	63	4	perspective	perspective	NOUN
ejpam-5446	63	5	,	,	PUNCT
ejpam-5446	63	6	studying	study	VERB
ejpam-5446	63	7	fifth	fifth	ADJ
ejpam-5446	63	8	-	-	PUNCT
ejpam-5446	63	9	order	order	NOUN
ejpam-5446	63	10	equations	equation	NOUN
ejpam-5446	63	11	enhances	enhance	VERB
ejpam-5446	63	12	understanding	understanding	NOUN
ejpam-5446	63	13	of	of	ADP
ejpam-5446	63	14	stability	stability	NOUN
ejpam-5446	63	15	,	,	PUNCT
ejpam-5446	63	16	existence	existence	NOUN
ejpam-5446	63	17	,	,	PUNCT
ejpam-5446	63	18	uniqueness	uniqueness	NOUN
ejpam-5446	63	19	,	,	PUNCT
ejpam-5446	63	20	and	and	CCONJ
ejpam-5446	63	21	the	the	DET
ejpam-5446	63	22	development	development	NOUN
ejpam-5446	63	23	of	of	ADP
ejpam-5446	63	24	more	more	ADV
ejpam-5446	63	25	sophisticated	sophisticated	ADJ
ejpam-5446	63	26	numerical	numerical	ADJ
ejpam-5446	63	27	methods	method	NOUN
ejpam-5446	63	28	.	.	PUNCT
ejpam-5446	64	1	as	as	SCONJ
ejpam-5446	64	2	these	these	DET
ejpam-5446	64	3	equations	equation	NOUN
ejpam-5446	64	4	play	play	VERB
ejpam-5446	64	5	a	a	DET
ejpam-5446	64	6	crucial	crucial	ADJ
ejpam-5446	64	7	role	role	NOUN
ejpam-5446	64	8	in	in	ADP
ejpam-5446	64	9	accurately	accurately	ADV
ejpam-5446	64	10	describing	describe	VERB
ejpam-5446	64	11	advanced	advanced	ADJ
ejpam-5446	64	12	systems	system	NOUN
ejpam-5446	64	13	,	,	PUNCT
ejpam-5446	64	14	their	their	PRON
ejpam-5446	64	15	study	study	NOUN
ejpam-5446	64	16	not	not	PART
ejpam-5446	64	17	only	only	ADV
ejpam-5446	64	18	fills	fill	VERB
ejpam-5446	64	19	important	important	ADJ
ejpam-5446	64	20	gaps	gap	NOUN
ejpam-5446	64	21	in	in	ADP
ejpam-5446	64	22	the	the	DET
ejpam-5446	64	23	literature	literature	NOUN
ejpam-5446	64	24	but	but	CCONJ
ejpam-5446	64	25	also	also	ADV
ejpam-5446	64	26	leads	lead	VERB
ejpam-5446	64	27	to	to	ADP
ejpam-5446	64	28	advancements	advancement	NOUN
ejpam-5446	64	29	in	in	ADP
ejpam-5446	64	30	applied	apply	VERB
ejpam-5446	64	31	mathematics	mathematic	NOUN
ejpam-5446	64	32	and	and	CCONJ
ejpam-5446	64	33	various	various	ADJ
ejpam-5446	64	34	scientific	scientific	ADJ
ejpam-5446	64	35	fields	field	NOUN
ejpam-5446	64	36	.	.	PUNCT
ejpam-5446	65	1	before	before	ADP
ejpam-5446	65	2	diving	diving	NOUN
ejpam-5446	65	3	into	into	ADP
ejpam-5446	65	4	the	the	DET
ejpam-5446	65	5	mathematical	mathematical	ADJ
ejpam-5446	65	6	derivations	derivation	NOUN
ejpam-5446	65	7	,	,	PUNCT
ejpam-5446	65	8	offer	offer	VERB
ejpam-5446	65	9	a	a	DET
ejpam-5446	65	10	brief	brief	ADJ
ejpam-5446	65	11	overview	overview	NOUN
ejpam-5446	65	12	of	of	ADP
ejpam-5446	65	13	the	the	DET
ejpam-5446	65	14	problem	problem	NOUN
ejpam-5446	65	15	being	be	AUX
ejpam-5446	65	16	solved	solve	VERB
ejpam-5446	65	17	and	and	CCONJ
ejpam-5446	65	18	the	the	DET
ejpam-5446	65	19	key	key	ADJ
ejpam-5446	65	20	assumptions	assumption	NOUN
ejpam-5446	65	21	made	make	VERB
ejpam-5446	65	22	.	.	PUNCT
ejpam-5446	66	1	for	for	ADP
ejpam-5446	66	2	example	example	NOUN
ejpam-5446	66	3	,	,	PUNCT
ejpam-5446	66	4	if	if	SCONJ
ejpam-5446	66	5	you	you	PRON
ejpam-5446	66	6	’re	’re	AUX
ejpam-5446	66	7	proving	prove	VERB
ejpam-5446	66	8	stability	stability	NOUN
ejpam-5446	66	9	for	for	ADP
ejpam-5446	66	10	a	a	DET
ejpam-5446	66	11	specific	specific	ADJ
ejpam-5446	66	12	class	class	NOUN
ejpam-5446	66	13	of	of	ADP
ejpam-5446	66	14	fifth	fifth	ADJ
ejpam-5446	66	15	-	-	PUNCT
ejpam-5446	66	16	order	order	NOUN
ejpam-5446	66	17	linear	linear	PROPN
ejpam-5446	66	18	differential	differential	NOUN
ejpam-5446	66	19	equations	equation	NOUN
ejpam-5446	66	20	,	,	PUNCT
ejpam-5446	66	21	start	start	VERB
ejpam-5446	66	22	by	by	ADP
ejpam-5446	66	23	clearly	clearly	ADV
ejpam-5446	66	24	stating	state	VERB
ejpam-5446	66	25	.	.	PUNCT
ejpam-5446	67	1	the	the	DET
ejpam-5446	67	2	general	general	ADJ
ejpam-5446	67	3	form	form	NOUN
ejpam-5446	67	4	of	of	ADP
ejpam-5446	67	5	the	the	DET
ejpam-5446	67	6	fifth	fifth	ADJ
ejpam-5446	67	7	-	-	PUNCT
ejpam-5446	67	8	order	order	NOUN
ejpam-5446	67	9	equation	equation	NOUN
ejpam-5446	67	10	you	you	PRON
ejpam-5446	67	11	’re	’re	AUX
ejpam-5446	67	12	focusing	focus	VERB
ejpam-5446	67	13	on	on	ADP
ejpam-5446	67	14	(	(	PUNCT
ejpam-5446	67	15	e.g.	e.g.	ADV
ejpam-5446	67	16	,	,	PUNCT
ejpam-5446	67	17	constant	constant	ADJ
ejpam-5446	67	18	coefficients	coefficient	NOUN
ejpam-5446	67	19	or	or	CCONJ
ejpam-5446	67	20	variable	variable	ADJ
ejpam-5446	67	21	coefficients).the	coefficients).the	NOUN
ejpam-5446	67	22	conditions	condition	NOUN
ejpam-5446	67	23	under	under	ADP
ejpam-5446	67	24	which	which	PRON
ejpam-5446	67	25	the	the	DET
ejpam-5446	67	26	stability	stability	NOUN
ejpam-5446	67	27	analysis	analysis	NOUN
ejpam-5446	67	28	is	be	AUX
ejpam-5446	67	29	conducted	conduct	VERB
ejpam-5446	67	30	,	,	PUNCT
ejpam-5446	67	31	such	such	ADJ
ejpam-5446	67	32	as	as	ADP
ejpam-5446	67	33	the	the	DET
ejpam-5446	67	34	smoothness	smoothness	NOUN
ejpam-5446	67	35	of	of	ADP
ejpam-5446	67	36	the	the	DET
ejpam-5446	67	37	solution	solution	NOUN
ejpam-5446	67	38	or	or	CCONJ
ejpam-5446	67	39	boundary	boundary	ADJ
ejpam-5446	67	40	conditions	condition	NOUN
ejpam-5446	67	41	.	.	PUNCT
ejpam-5446	68	1	we	we	PRON
ejpam-5446	68	2	consider	consider	VERB
ejpam-5446	68	3	a	a	DET
ejpam-5446	68	4	fifth	fifth	ADJ
ejpam-5446	68	5	-	-	PUNCT
ejpam-5446	68	6	order	order	NOUN
ejpam-5446	68	7	linear	linear	ADJ
ejpam-5446	68	8	differential	differential	NOUN
ejpam-5446	68	9	equation	equation	NOUN
ejpam-5446	68	10	with	with	ADP
ejpam-5446	68	11	constant	constant	ADJ
ejpam-5446	68	12	coefficients	coefficient	NOUN
ejpam-5446	68	13	,	,	PUNCT
ejpam-5446	68	14	where	where	SCONJ
ejpam-5446	68	15	we	we	PRON
ejpam-5446	68	16	assume	assume	VERB
ejpam-5446	68	17	that	that	SCONJ
ejpam-5446	68	18	the	the	DET
ejpam-5446	68	19	solutions	solution	NOUN
ejpam-5446	68	20	are	be	AUX
ejpam-5446	68	21	continuous	continuous	ADJ
ejpam-5446	68	22	and	and	CCONJ
ejpam-5446	68	23	differentiable	differentiable	VERB
ejpam-5446	68	24	up	up	ADP
ejpam-5446	68	25	to	to	ADP
ejpam-5446	68	26	the	the	DET
ejpam-5446	68	27	fifth	fifth	ADJ
ejpam-5446	68	28	derivative	derivative	NOUN
ejpam-5446	68	29	.	.	PUNCT
ejpam-5446	69	1	these	these	DET
ejpam-5446	69	2	assumptions	assumption	NOUN
ejpam-5446	69	3	are	be	AUX
ejpam-5446	69	4	essential	essential	ADJ
ejpam-5446	69	5	for	for	ADP
ejpam-5446	69	6	v.	v.	ADP
ejpam-5446	69	7	govindan	govindan	PROPN
ejpam-5446	70	1	et	et	PROPN
ejpam-5446	70	2	al	al	PROPN
ejpam-5446	70	3	.	.	PUNCT
ejpam-5446	70	4	/	/	SYM
ejpam-5446	70	5	eur	eur	PROPN
ejpam-5446	70	6	.	.	PUNCT
ejpam-5446	71	1	j.	j.	PROPN
ejpam-5446	71	2	pure	pure	PROPN
ejpam-5446	71	3	appl	appl	PROPN
ejpam-5446	71	4	.	.	PROPN
ejpam-5446	71	5	math	math	PROPN
ejpam-5446	71	6	,	,	PUNCT
ejpam-5446	71	7	17	17	NUM
ejpam-5446	71	8	(	(	PUNCT
ejpam-5446	71	9	4	4	NUM
ejpam-5446	71	10	)	)	PUNCT
ejpam-5446	71	11	(	(	PUNCT
ejpam-5446	71	12	2024	2024	NUM
ejpam-5446	71	13	)	)	PUNCT
ejpam-5446	71	14	,	,	PUNCT
ejpam-5446	71	15	3585	3585	NUM
ejpam-5446	71	16	-	-	SYM
ejpam-5446	71	17	3609	3609	NUM
ejpam-5446	71	18	3588	3588	NUM
ejpam-5446	71	19	ensuring	ensure	VERB
ejpam-5446	71	20	that	that	SCONJ
ejpam-5446	71	21	the	the	DET
ejpam-5446	71	22	equation	equation	NOUN
ejpam-5446	71	23	can	can	AUX
ejpam-5446	71	24	be	be	AUX
ejpam-5446	71	25	analyzed	analyze	VERB
ejpam-5446	71	26	within	within	ADP
ejpam-5446	71	27	the	the	DET
ejpam-5446	71	28	framework	framework	NOUN
ejpam-5446	71	29	of	of	ADP
ejpam-5446	71	30	hyers	hyer	NOUN
ejpam-5446	71	31	-	-	PUNCT
ejpam-5446	71	32	ulam	ulam	PROPN
ejpam-5446	71	33	stability	stability	NOUN
ejpam-5446	71	34	.	.	PUNCT
ejpam-5446	72	1	in	in	ADP
ejpam-5446	72	2	practical	practical	ADJ
ejpam-5446	72	3	applications	application	NOUN
ejpam-5446	72	4	,	,	PUNCT
ejpam-5446	72	5	stability	stability	NOUN
ejpam-5446	72	6	often	often	ADV
ejpam-5446	72	7	refers	refer	VERB
ejpam-5446	72	8	to	to	ADP
ejpam-5446	72	9	the	the	DET
ejpam-5446	72	10	system	system	NOUN
ejpam-5446	72	11	’s	’s	PART
ejpam-5446	72	12	ability	ability	NOUN
ejpam-5446	72	13	to	to	PART
ejpam-5446	72	14	resist	resist	VERB
ejpam-5446	72	15	or	or	CCONJ
ejpam-5446	72	16	dampen	dampen	VERB
ejpam-5446	72	17	perturbations	perturbation	NOUN
ejpam-5446	72	18	.	.	PUNCT
ejpam-5446	73	1	when	when	SCONJ
ejpam-5446	73	2	you	you	PRON
ejpam-5446	73	3	discuss	discuss	VERB
ejpam-5446	73	4	an	an	DET
ejpam-5446	73	5	example	example	NOUN
ejpam-5446	73	6	showing	show	VERB
ejpam-5446	73	7	hyers	hyer	NOUN
ejpam-5446	73	8	-	-	PUNCT
ejpam-5446	73	9	ulam	ulam	PROPN
ejpam-5446	73	10	stability	stability	PROPN
ejpam-5446	73	11	,	,	PUNCT
ejpam-5446	73	12	interpret	interpret	VERB
ejpam-5446	73	13	it	it	PRON
ejpam-5446	73	14	by	by	ADP
ejpam-5446	73	15	explaining	explain	VERB
ejpam-5446	73	16	how	how	SCONJ
ejpam-5446	73	17	small	small	ADJ
ejpam-5446	73	18	deviations	deviation	NOUN
ejpam-5446	73	19	in	in	ADP
ejpam-5446	73	20	the	the	DET
ejpam-5446	73	21	inputs	input	NOUN
ejpam-5446	73	22	(	(	PUNCT
ejpam-5446	73	23	such	such	ADJ
ejpam-5446	73	24	as	as	ADP
ejpam-5446	73	25	initial	initial	ADJ
ejpam-5446	73	26	conditions	condition	NOUN
ejpam-5446	73	27	or	or	CCONJ
ejpam-5446	73	28	external	external	ADJ
ejpam-5446	73	29	forces	force	NOUN
ejpam-5446	73	30	)	)	PUNCT
ejpam-5446	73	31	do	do	AUX
ejpam-5446	73	32	not	not	PART
ejpam-5446	73	33	lead	lead	VERB
ejpam-5446	73	34	to	to	ADP
ejpam-5446	73	35	exponential	exponential	ADJ
ejpam-5446	73	36	or	or	CCONJ
ejpam-5446	73	37	uncontrolled	uncontrolled	ADJ
ejpam-5446	73	38	growth	growth	NOUN
ejpam-5446	73	39	in	in	ADP
ejpam-5446	73	40	the	the	DET
ejpam-5446	73	41	system	system	NOUN
ejpam-5446	73	42	’s	’s	PART
ejpam-5446	73	43	response	response	NOUN
ejpam-5446	73	44	.	.	PUNCT
ejpam-5446	74	1	in	in	ADP
ejpam-5446	74	2	this	this	DET
ejpam-5446	74	3	example	example	NOUN
ejpam-5446	74	4	,	,	PUNCT
ejpam-5446	74	5	the	the	DET
ejpam-5446	74	6	fifth	fifth	ADJ
ejpam-5446	74	7	-	-	PUNCT
ejpam-5446	74	8	order	order	NOUN
ejpam-5446	74	9	differential	differential	NOUN
ejpam-5446	74	10	equation	equation	NOUN
ejpam-5446	74	11	models	model	VERB
ejpam-5446	74	12	the	the	DET
ejpam-5446	74	13	motion	motion	NOUN
ejpam-5446	74	14	of	of	ADP
ejpam-5446	74	15	a	a	DET
ejpam-5446	74	16	mechanical	mechanical	ADJ
ejpam-5446	74	17	system	system	NOUN
ejpam-5446	74	18	with	with	ADP
ejpam-5446	74	19	multiple	multiple	ADJ
ejpam-5446	74	20	feedback	feedback	NOUN
ejpam-5446	74	21	loops	loop	NOUN
ejpam-5446	74	22	.	.	PUNCT
ejpam-5446	75	1	the	the	DET
ejpam-5446	75	2	stability	stability	NOUN
ejpam-5446	75	3	results	result	NOUN
ejpam-5446	75	4	demonstrate	demonstrate	VERB
ejpam-5446	75	5	that	that	SCONJ
ejpam-5446	75	6	even	even	ADV
ejpam-5446	75	7	with	with	ADP
ejpam-5446	75	8	slight	slight	ADJ
ejpam-5446	75	9	variations	variation	NOUN
ejpam-5446	75	10	in	in	ADP
ejpam-5446	75	11	the	the	DET
ejpam-5446	75	12	input	input	NOUN
ejpam-5446	75	13	forces	force	NOUN
ejpam-5446	75	14	or	or	CCONJ
ejpam-5446	75	15	initial	initial	ADJ
ejpam-5446	75	16	velocities	velocity	NOUN
ejpam-5446	75	17	,	,	PUNCT
ejpam-5446	75	18	the	the	DET
ejpam-5446	75	19	motion	motion	NOUN
ejpam-5446	75	20	remains	remain	VERB
ejpam-5446	75	21	bounded	bound	VERB
ejpam-5446	75	22	.	.	PUNCT
ejpam-5446	76	1	this	this	PRON
ejpam-5446	76	2	is	be	AUX
ejpam-5446	76	3	particularly	particularly	ADV
ejpam-5446	76	4	important	important	ADJ
ejpam-5446	76	5	in	in	ADP
ejpam-5446	76	6	control	control	NOUN
ejpam-5446	76	7	systems	system	NOUN
ejpam-5446	76	8	,	,	PUNCT
ejpam-5446	76	9	where	where	SCONJ
ejpam-5446	76	10	small	small	ADJ
ejpam-5446	76	11	inaccuracies	inaccuracy	NOUN
ejpam-5446	76	12	in	in	ADP
ejpam-5446	76	13	the	the	DET
ejpam-5446	76	14	measurement	measurement	NOUN
ejpam-5446	76	15	or	or	CCONJ
ejpam-5446	76	16	control	control	NOUN
ejpam-5446	76	17	signals	signal	NOUN
ejpam-5446	76	18	can	can	AUX
ejpam-5446	76	19	lead	lead	VERB
ejpam-5446	76	20	to	to	ADP
ejpam-5446	76	21	significant	significant	ADJ
ejpam-5446	76	22	errors	error	NOUN
ejpam-5446	76	23	in	in	ADP
ejpam-5446	76	24	the	the	DET
ejpam-5446	76	25	system	system	NOUN
ejpam-5446	76	26	’s	’s	PART
ejpam-5446	76	27	behavior	behavior	NOUN
ejpam-5446	76	28	.	.	PUNCT
ejpam-5446	77	1	by	by	ADP
ejpam-5446	77	2	ensuring	ensure	VERB
ejpam-5446	77	3	hyers	hyer	NOUN
ejpam-5446	77	4	-	-	PUNCT
ejpam-5446	77	5	ulam	ulam	PROPN
ejpam-5446	77	6	stability	stability	NOUN
ejpam-5446	77	7	,	,	PUNCT
ejpam-5446	77	8	we	we	PRON
ejpam-5446	77	9	know	know	VERB
ejpam-5446	77	10	that	that	SCONJ
ejpam-5446	77	11	such	such	ADJ
ejpam-5446	77	12	small	small	ADJ
ejpam-5446	77	13	deviations	deviation	NOUN
ejpam-5446	77	14	will	will	AUX
ejpam-5446	77	15	not	not	PART
ejpam-5446	77	16	cause	cause	VERB
ejpam-5446	77	17	instability	instability	NOUN
ejpam-5446	77	18	,	,	PUNCT
ejpam-5446	77	19	ensuring	ensure	VERB
ejpam-5446	77	20	the	the	DET
ejpam-5446	77	21	system	system	NOUN
ejpam-5446	77	22	operates	operate	VERB
ejpam-5446	77	23	predictably	predictably	ADV
ejpam-5446	77	24	.	.	PUNCT
ejpam-5446	78	1	“	"	PUNCT
ejpam-5446	78	2	many	many	ADJ
ejpam-5446	78	3	physical	physical	ADJ
ejpam-5446	78	4	systems	system	NOUN
ejpam-5446	78	5	governed	govern	VERB
ejpam-5446	78	6	by	by	ADP
ejpam-5446	78	7	fifth	fifth	ADJ
ejpam-5446	78	8	-	-	PUNCT
ejpam-5446	78	9	order	order	NOUN
ejpam-5446	78	10	differential	differential	ADJ
ejpam-5446	78	11	equations	equation	NOUN
ejpam-5446	78	12	,	,	PUNCT
ejpam-5446	78	13	such	such	ADJ
ejpam-5446	78	14	as	as	ADP
ejpam-5446	78	15	beam	beam	NOUN
ejpam-5446	78	16	vibrations	vibration	NOUN
ejpam-5446	78	17	or	or	CCONJ
ejpam-5446	78	18	wave	wave	NOUN
ejpam-5446	78	19	propagation	propagation	NOUN
ejpam-5446	78	20	,	,	PUNCT
ejpam-5446	78	21	rely	rely	VERB
ejpam-5446	78	22	on	on	ADP
ejpam-5446	78	23	stability	stability	NOUN
ejpam-5446	78	24	for	for	ADP
ejpam-5446	78	25	consistent	consistent	ADJ
ejpam-5446	78	26	performance	performance	NOUN
ejpam-5446	78	27	.	.	PUNCT
ejpam-5446	79	1	when	when	SCONJ
ejpam-5446	79	2	interpreting	interpret	VERB
ejpam-5446	79	3	examples	example	NOUN
ejpam-5446	79	4	,	,	PUNCT
ejpam-5446	79	5	explain	explain	VERB
ejpam-5446	79	6	how	how	SCONJ
ejpam-5446	79	7	the	the	DET
ejpam-5446	79	8	stability	stability	NOUN
ejpam-5446	79	9	results	result	VERB
ejpam-5446	79	10	ensure	ensure	VERB
ejpam-5446	79	11	that	that	SCONJ
ejpam-5446	79	12	the	the	DET
ejpam-5446	79	13	system	system	NOUN
ejpam-5446	79	14	remains	remain	VERB
ejpam-5446	79	15	predictable	predictable	ADJ
ejpam-5446	79	16	and	and	CCONJ
ejpam-5446	79	17	controllable	controllable	ADJ
ejpam-5446	79	18	,	,	PUNCT
ejpam-5446	79	19	even	even	ADV
ejpam-5446	79	20	when	when	SCONJ
ejpam-5446	79	21	exposed	expose	VERB
ejpam-5446	79	22	to	to	ADP
ejpam-5446	79	23	small	small	ADJ
ejpam-5446	79	24	disturbances	disturbance	NOUN
ejpam-5446	79	25	.	.	PUNCT
ejpam-5446	80	1	in	in	ADP
ejpam-5446	80	2	the	the	DET
ejpam-5446	80	3	case	case	NOUN
ejpam-5446	80	4	of	of	ADP
ejpam-5446	80	5	wave	wave	NOUN
ejpam-5446	80	6	propagation	propagation	NOUN
ejpam-5446	80	7	,	,	PUNCT
ejpam-5446	80	8	the	the	DET
ejpam-5446	80	9	stability	stability	NOUN
ejpam-5446	80	10	result	result	NOUN
ejpam-5446	80	11	indicates	indicate	VERB
ejpam-5446	80	12	that	that	SCONJ
ejpam-5446	80	13	small	small	ADJ
ejpam-5446	80	14	perturbations	perturbation	NOUN
ejpam-5446	80	15	in	in	ADP
ejpam-5446	80	16	the	the	DET
ejpam-5446	80	17	medium	medium	NOUN
ejpam-5446	80	18	(	(	PUNCT
ejpam-5446	80	19	such	such	ADJ
ejpam-5446	80	20	as	as	ADP
ejpam-5446	80	21	density	density	NOUN
ejpam-5446	80	22	or	or	CCONJ
ejpam-5446	80	23	pressure	pressure	NOUN
ejpam-5446	80	24	)	)	PUNCT
ejpam-5446	80	25	will	will	AUX
ejpam-5446	80	26	not	not	PART
ejpam-5446	80	27	cause	cause	VERB
ejpam-5446	80	28	the	the	DET
ejpam-5446	80	29	wave	wave	NOUN
ejpam-5446	80	30	to	to	PART
ejpam-5446	80	31	grow	grow	VERB
ejpam-5446	80	32	uncontrollably	uncontrollably	ADV
ejpam-5446	80	33	in	in	ADP
ejpam-5446	80	34	amplitude	amplitude	NOUN
ejpam-5446	80	35	.	.	PUNCT
ejpam-5446	81	1	this	this	DET
ejpam-5446	81	2	property	property	NOUN
ejpam-5446	81	3	is	be	AUX
ejpam-5446	81	4	crucial	crucial	ADJ
ejpam-5446	81	5	for	for	ADP
ejpam-5446	81	6	the	the	DET
ejpam-5446	81	7	design	design	NOUN
ejpam-5446	81	8	of	of	ADP
ejpam-5446	81	9	wave	wave	NOUN
ejpam-5446	81	10	guides	guide	NOUN
ejpam-5446	81	11	or	or	CCONJ
ejpam-5446	81	12	telecommunications	telecommunication	NOUN
ejpam-5446	81	13	systems	system	NOUN
ejpam-5446	81	14	,	,	PUNCT
ejpam-5446	81	15	where	where	SCONJ
ejpam-5446	81	16	small	small	ADJ
ejpam-5446	81	17	variations	variation	NOUN
ejpam-5446	81	18	in	in	ADP
ejpam-5446	81	19	the	the	DET
ejpam-5446	81	20	physical	physical	ADJ
ejpam-5446	81	21	properties	property	NOUN
ejpam-5446	81	22	of	of	ADP
ejpam-5446	81	23	the	the	DET
ejpam-5446	81	24	medium	medium	NOUN
ejpam-5446	81	25	can	can	AUX
ejpam-5446	81	26	lead	lead	VERB
ejpam-5446	81	27	to	to	ADP
ejpam-5446	81	28	large	large	ADJ
ejpam-5446	81	29	-	-	PUNCT
ejpam-5446	81	30	scale	scale	NOUN
ejpam-5446	81	31	disruptions	disruption	NOUN
ejpam-5446	81	32	if	if	SCONJ
ejpam-5446	81	33	the	the	DET
ejpam-5446	81	34	system	system	NOUN
ejpam-5446	81	35	is	be	AUX
ejpam-5446	81	36	unstable	unstable	ADJ
ejpam-5446	81	37	.	.	PUNCT
ejpam-5446	81	38	”	"	PUNCT
ejpam-5446	82	1	one	one	NUM
ejpam-5446	82	2	of	of	ADP
ejpam-5446	82	3	the	the	DET
ejpam-5446	82	4	most	most	ADV
ejpam-5446	82	5	natural	natural	ADJ
ejpam-5446	82	6	future	future	ADJ
ejpam-5446	82	7	directions	direction	NOUN
ejpam-5446	82	8	is	be	AUX
ejpam-5446	82	9	extending	extend	VERB
ejpam-5446	82	10	the	the	DET
ejpam-5446	82	11	methods	method	NOUN
ejpam-5446	82	12	and	and	CCONJ
ejpam-5446	82	13	stability	stability	NOUN
ejpam-5446	82	14	results	result	NOUN
ejpam-5446	82	15	developed	develop	VERB
ejpam-5446	82	16	for	for	ADP
ejpam-5446	82	17	linear	linear	ADJ
ejpam-5446	82	18	fifth	fifth	ADJ
ejpam-5446	82	19	-	-	PUNCT
ejpam-5446	82	20	order	order	NOUN
ejpam-5446	82	21	differential	differential	ADJ
ejpam-5446	82	22	equations	equation	NOUN
ejpam-5446	82	23	to	to	ADP
ejpam-5446	82	24	nonlinear	nonlinear	ADJ
ejpam-5446	82	25	systems	system	NOUN
ejpam-5446	82	26	.	.	PUNCT
ejpam-5446	83	1	in	in	ADP
ejpam-5446	83	2	practical	practical	ADJ
ejpam-5446	83	3	applications	application	NOUN
ejpam-5446	83	4	,	,	PUNCT
ejpam-5446	83	5	many	many	ADJ
ejpam-5446	83	6	systems	system	NOUN
ejpam-5446	83	7	exhibit	exhibit	VERB
ejpam-5446	83	8	nonlinear	nonlinear	ADJ
ejpam-5446	83	9	behavior	behavior	NOUN
ejpam-5446	83	10	,	,	PUNCT
ejpam-5446	83	11	especially	especially	ADV
ejpam-5446	83	12	when	when	SCONJ
ejpam-5446	83	13	dealing	deal	VERB
ejpam-5446	83	14	with	with	ADP
ejpam-5446	83	15	large	large	ADJ
ejpam-5446	83	16	deviations	deviation	NOUN
ejpam-5446	83	17	from	from	ADP
ejpam-5446	83	18	equilibrium	equilibrium	NOUN
ejpam-5446	83	19	or	or	CCONJ
ejpam-5446	83	20	complex	complex	ADJ
ejpam-5446	83	21	feedback	feedback	NOUN
ejpam-5446	83	22	mechanisms	mechanism	NOUN
ejpam-5446	83	23	.	.	PUNCT
ejpam-5446	84	1	for	for	ADP
ejpam-5446	84	2	instance	instance	NOUN
ejpam-5446	84	3	,	,	PUNCT
ejpam-5446	84	4	in	in	ADP
ejpam-5446	84	5	engineering	engineering	NOUN
ejpam-5446	84	6	or	or	CCONJ
ejpam-5446	84	7	physics	physics	NOUN
ejpam-5446	84	8	,	,	PUNCT
ejpam-5446	84	9	systems	system	NOUN
ejpam-5446	84	10	often	often	ADV
ejpam-5446	84	11	become	become	VERB
ejpam-5446	84	12	nonlinear	nonlinear	ADJ
ejpam-5446	84	13	when	when	SCONJ
ejpam-5446	84	14	subjected	subject	VERB
ejpam-5446	84	15	to	to	ADP
ejpam-5446	84	16	strong	strong	ADJ
ejpam-5446	84	17	external	external	ADJ
ejpam-5446	84	18	forces	force	NOUN
ejpam-5446	84	19	or	or	CCONJ
ejpam-5446	84	20	interactions	interaction	NOUN
ejpam-5446	84	21	between	between	ADP
ejpam-5446	84	22	components	component	NOUN
ejpam-5446	84	23	.	.	PUNCT
ejpam-5446	85	1	boundary	boundary	ADJ
ejpam-5446	85	2	value	value	NOUN
ejpam-5446	85	3	problems	problem	NOUN
ejpam-5446	85	4	for	for	ADP
ejpam-5446	85	5	fifth	fifth	ADJ
ejpam-5446	85	6	-	-	PUNCT
ejpam-5446	85	7	order	order	NOUN
ejpam-5446	85	8	systems	system	NOUN
ejpam-5446	85	9	often	often	ADV
ejpam-5446	85	10	arise	arise	VERB
ejpam-5446	85	11	in	in	ADP
ejpam-5446	85	12	the	the	DET
ejpam-5446	85	13	study	study	NOUN
ejpam-5446	85	14	of	of	ADP
ejpam-5446	85	15	elastic	elastic	ADJ
ejpam-5446	85	16	structures	structure	NOUN
ejpam-5446	85	17	and	and	CCONJ
ejpam-5446	85	18	fluid	fluid	ADJ
ejpam-5446	85	19	dynamics	dynamic	NOUN
ejpam-5446	85	20	.	.	PUNCT
ejpam-5446	86	1	investigating	investigate	VERB
ejpam-5446	86	2	how	how	SCONJ
ejpam-5446	86	3	the	the	DET
ejpam-5446	86	4	stability	stability	NOUN
ejpam-5446	86	5	results	result	VERB
ejpam-5446	86	6	extend	extend	VERB
ejpam-5446	86	7	to	to	ADP
ejpam-5446	86	8	these	these	DET
ejpam-5446	86	9	problems	problem	NOUN
ejpam-5446	86	10	would	would	AUX
ejpam-5446	86	11	be	be	AUX
ejpam-5446	86	12	essential	essential	ADJ
ejpam-5446	86	13	for	for	ADP
ejpam-5446	86	14	expanding	expand	VERB
ejpam-5446	86	15	the	the	DET
ejpam-5446	86	16	applicability	applicability	NOUN
ejpam-5446	86	17	of	of	ADP
ejpam-5446	86	18	the	the	DET
ejpam-5446	86	19	current	current	ADJ
ejpam-5446	86	20	results	result	NOUN
ejpam-5446	86	21	.	.	PUNCT
ejpam-5446	87	1	boundary	boundary	ADJ
ejpam-5446	87	2	conditions	condition	NOUN
ejpam-5446	87	3	can	can	AUX
ejpam-5446	87	4	introduce	introduce	VERB
ejpam-5446	87	5	additional	additional	ADJ
ejpam-5446	87	6	constraints	constraint	NOUN
ejpam-5446	87	7	or	or	CCONJ
ejpam-5446	87	8	complexities	complexity	NOUN
ejpam-5446	87	9	that	that	PRON
ejpam-5446	87	10	affect	affect	VERB
ejpam-5446	87	11	the	the	DET
ejpam-5446	87	12	stability	stability	NOUN
ejpam-5446	87	13	behavior	behavior	NOUN
ejpam-5446	87	14	.	.	PUNCT
ejpam-5446	88	1	the	the	DET
ejpam-5446	88	2	stability	stability	NOUN
ejpam-5446	88	3	of	of	ADP
ejpam-5446	88	4	fifth	fifth	ADJ
ejpam-5446	88	5	-	-	PUNCT
ejpam-5446	88	6	order	order	NOUN
ejpam-5446	88	7	linear	linear	PROPN
ejpam-5446	88	8	differential	differential	NOUN
ejpam-5446	88	9	equations	equation	NOUN
ejpam-5446	88	10	opens	open	VERB
ejpam-5446	88	11	several	several	ADJ
ejpam-5446	88	12	exciting	exciting	ADJ
ejpam-5446	88	13	future	future	ADJ
ejpam-5446	88	14	research	research	NOUN
ejpam-5446	88	15	directions	direction	NOUN
ejpam-5446	88	16	.	.	PUNCT
ejpam-5446	89	1	potential	potential	ADJ
ejpam-5446	89	2	extensions	extension	NOUN
ejpam-5446	89	3	include	include	VERB
ejpam-5446	89	4	generalizing	generalize	VERB
ejpam-5446	89	5	the	the	DET
ejpam-5446	89	6	results	result	NOUN
ejpam-5446	89	7	to	to	PART
ejpam-5446	89	8	nonlinear	nonlinear	ADJ
ejpam-5446	89	9	and	and	CCONJ
ejpam-5446	89	10	fractional	fractional	ADJ
ejpam-5446	89	11	differential	differential	ADJ
ejpam-5446	89	12	equations	equation	NOUN
ejpam-5446	89	13	,	,	PUNCT
ejpam-5446	89	14	handling	handle	VERB
ejpam-5446	89	15	systems	system	NOUN
ejpam-5446	89	16	with	with	ADP
ejpam-5446	89	17	variable	variable	ADJ
ejpam-5446	89	18	coefficients	coefficient	NOUN
ejpam-5446	89	19	,	,	PUNCT
ejpam-5446	89	20	investigating	investigate	VERB
ejpam-5446	89	21	boundary	boundary	ADJ
ejpam-5446	89	22	value	value	NOUN
ejpam-5446	89	23	problems	problem	NOUN
ejpam-5446	89	24	,	,	PUNCT
ejpam-5446	89	25	and	and	CCONJ
ejpam-5446	89	26	exploring	explore	VERB
ejpam-5446	89	27	applications	application	NOUN
ejpam-5446	89	28	in	in	ADP
ejpam-5446	89	29	control	control	NOUN
ejpam-5446	89	30	theory	theory	NOUN
ejpam-5446	89	31	.	.	PUNCT
ejpam-5446	90	1	additionally	additionally	ADV
ejpam-5446	90	2	,	,	PUNCT
ejpam-5446	90	3	addressing	address	VERB
ejpam-5446	90	4	the	the	DET
ejpam-5446	90	5	challenges	challenge	NOUN
ejpam-5446	90	6	of	of	ADP
ejpam-5446	90	7	non	non	ADJ
ejpam-5446	90	8	-	-	ADJ
ejpam-5446	90	9	classical	classical	ADJ
ejpam-5446	90	10	solutions	solution	NOUN
ejpam-5446	90	11	and	and	CCONJ
ejpam-5446	90	12	weak	weak	ADJ
ejpam-5446	90	13	forms	form	NOUN
ejpam-5446	90	14	provides	provide	VERB
ejpam-5446	90	15	a	a	DET
ejpam-5446	90	16	pathway	pathway	NOUN
ejpam-5446	90	17	for	for	ADP
ejpam-5446	90	18	further	further	ADJ
ejpam-5446	90	19	theoretical	theoretical	ADJ
ejpam-5446	90	20	development	development	NOUN
ejpam-5446	90	21	.	.	PUNCT
ejpam-5446	91	1	these	these	DET
ejpam-5446	91	2	future	future	ADJ
ejpam-5446	91	3	directions	direction	NOUN
ejpam-5446	91	4	not	not	PART
ejpam-5446	91	5	only	only	ADV
ejpam-5446	91	6	deepen	deepen	VERB
ejpam-5446	91	7	the	the	DET
ejpam-5446	91	8	understanding	understanding	NOUN
ejpam-5446	91	9	of	of	ADP
ejpam-5446	91	10	stability	stability	NOUN
ejpam-5446	91	11	in	in	ADP
ejpam-5446	91	12	complex	complex	ADJ
ejpam-5446	91	13	systems	system	NOUN
ejpam-5446	91	14	but	but	CCONJ
ejpam-5446	91	15	also	also	ADV
ejpam-5446	91	16	offer	offer	VERB
ejpam-5446	91	17	practical	practical	ADJ
ejpam-5446	91	18	tools	tool	NOUN
ejpam-5446	91	19	for	for	ADP
ejpam-5446	91	20	tackling	tackle	VERB
ejpam-5446	91	21	real	real	ADJ
ejpam-5446	91	22	-	-	PUNCT
ejpam-5446	91	23	world	world	NOUN
ejpam-5446	91	24	problems	problem	NOUN
ejpam-5446	91	25	in	in	ADP
ejpam-5446	91	26	various	various	ADJ
ejpam-5446	91	27	scientific	scientific	ADJ
ejpam-5446	91	28	and	and	CCONJ
ejpam-5446	91	29	engineering	engineering	NOUN
ejpam-5446	91	30	fields	field	NOUN
ejpam-5446	91	31	.	.	PUNCT
ejpam-5446	92	1	the	the	DET
ejpam-5446	92	2	paper	paper	NOUN
ejpam-5446	92	3	concludes	conclude	VERB
ejpam-5446	92	4	by	by	ADP
ejpam-5446	92	5	summarizing	summarize	VERB
ejpam-5446	92	6	the	the	DET
ejpam-5446	92	7	key	key	ADJ
ejpam-5446	92	8	findings	finding	NOUN
ejpam-5446	92	9	and	and	CCONJ
ejpam-5446	92	10	contributions	contribution	NOUN
ejpam-5446	92	11	.	.	PUNCT
ejpam-5446	93	1	we	we	PRON
ejpam-5446	93	2	discuss	discuss	VERB
ejpam-5446	93	3	the	the	DET
ejpam-5446	93	4	significance	significance	NOUN
ejpam-5446	93	5	of	of	ADP
ejpam-5446	93	6	extending	extend	VERB
ejpam-5446	93	7	hyers	hyer	NOUN
ejpam-5446	93	8	-	-	PUNCT
ejpam-5446	93	9	ulam	ulam	PROPN
ejpam-5446	93	10	stability	stability	NOUN
ejpam-5446	93	11	to	to	ADP
ejpam-5446	93	12	fifth	fifth	ADJ
ejpam-5446	93	13	-	-	PUNCT
ejpam-5446	93	14	order	order	NOUN
ejpam-5446	93	15	equations	equation	NOUN
ejpam-5446	93	16	and	and	CCONJ
ejpam-5446	93	17	suggest	suggest	VERB
ejpam-5446	93	18	potential	potential	ADJ
ejpam-5446	93	19	directions	direction	NOUN
ejpam-5446	93	20	for	for	ADP
ejpam-5446	93	21	future	future	ADJ
ejpam-5446	93	22	research	research	NOUN
ejpam-5446	93	23	,	,	PUNCT
ejpam-5446	93	24	including	include	VERB
ejpam-5446	93	25	the	the	DET
ejpam-5446	93	26	extension	extension	NOUN
ejpam-5446	93	27	of	of	ADP
ejpam-5446	93	28	these	these	DET
ejpam-5446	93	29	results	result	NOUN
ejpam-5446	93	30	to	to	ADP
ejpam-5446	93	31	nonlinear	nonlinear	ADJ
ejpam-5446	93	32	equations	equation	NOUN
ejpam-5446	93	33	and	and	CCONJ
ejpam-5446	93	34	other	other	ADJ
ejpam-5446	93	35	higher	high	ADJ
ejpam-5446	93	36	-	-	PUNCT
ejpam-5446	93	37	order	order	NOUN
ejpam-5446	93	38	systems	system	NOUN
ejpam-5446	93	39	.	.	PUNCT
ejpam-5446	94	1	let	let	VERB
ejpam-5446	94	2	x	x	PRON
ejpam-5446	94	3	be	be	AUX
ejpam-5446	94	4	a	a	DET
ejpam-5446	94	5	normed	normed	ADJ
ejpam-5446	94	6	space	space	NOUN
ejpam-5446	94	7	over	over	ADP
ejpam-5446	94	8	a	a	DET
ejpam-5446	94	9	scalar	scalar	ADJ
ejpam-5446	94	10	field	field	NOUN
ejpam-5446	94	11	k	k	PROPN
ejpam-5446	94	12	and	and	CCONJ
ejpam-5446	94	13	let	let	VERB
ejpam-5446	94	14	i	i	PRON
ejpam-5446	94	15	be	be	AUX
ejpam-5446	94	16	an	an	DET
ejpam-5446	94	17	open	open	ADJ
ejpam-5446	94	18	span	span	NOUN
ejpam-5446	94	19	.	.	PUNCT
ejpam-5446	95	1	expect	expect	VERB
ejpam-5446	95	2	that	that	PRON
ejpam-5446	95	3	v.	v.	INTJ
ejpam-5446	95	4	govindan	govindan	PROPN
ejpam-5446	95	5	et	et	PROPN
ejpam-5446	95	6	al	al	PROPN
ejpam-5446	95	7	.	.	PUNCT
ejpam-5446	95	8	/	/	SYM
ejpam-5446	95	9	eur	eur	PROPN
ejpam-5446	95	10	.	.	PUNCT
ejpam-5446	96	1	j.	j.	PROPN
ejpam-5446	96	2	pure	pure	PROPN
ejpam-5446	96	3	appl	appl	PROPN
ejpam-5446	96	4	.	.	PROPN
ejpam-5446	96	5	math	math	PROPN
ejpam-5446	96	6	,	,	PUNCT
ejpam-5446	96	7	17	17	NUM
ejpam-5446	96	8	(	(	PUNCT
ejpam-5446	96	9	4	4	NUM
ejpam-5446	96	10	)	)	PUNCT
ejpam-5446	96	11	(	(	PUNCT
ejpam-5446	96	12	2024	2024	NUM
ejpam-5446	96	13	)	)	PUNCT
ejpam-5446	96	14	,	,	PUNCT
ejpam-5446	96	15	3585	3585	NUM
ejpam-5446	96	16	-	-	SYM
ejpam-5446	96	17	3609	3609	NUM
ejpam-5446	96	18	3589	3589	NUM
ejpam-5446	96	19	c0	c0	NOUN
ejpam-5446	96	20	,	,	PUNCT
ejpam-5446	96	21	c1	c1	PROPN
ejpam-5446	96	22	,	,	PUNCT
ejpam-5446	96	23	...	...	PUNCT
ejpam-5446	96	24	,	,	PUNCT
ejpam-5446	96	25	cn	cn	PROPN
ejpam-5446	96	26	are	be	AUX
ejpam-5446	96	27	fixed	fix	VERB
ejpam-5446	96	28	components	component	NOUN
ejpam-5446	96	29	of	of	ADP
ejpam-5446	96	30	k.	k.	PROPN
ejpam-5446	97	1	we	we	PRON
ejpam-5446	97	2	say	say	VERB
ejpam-5446	97	3	that	that	SCONJ
ejpam-5446	97	4	the	the	DET
ejpam-5446	97	5	differential	differential	ADJ
ejpam-5446	97	6	equation	equation	NOUN
ejpam-5446	97	7	cn(t)ς	cn(t)ς	PROPN
ejpam-5446	97	8	(	(	PUNCT
ejpam-5446	97	9	n)(t	n)(t	X
ejpam-5446	97	10	)	)	PUNCT
ejpam-5446	97	11	+	+	CCONJ
ejpam-5446	98	1	cn−1(t)ς	cn−1(t)ς	ADV
ejpam-5446	98	2	(	(	PUNCT
ejpam-5446	98	3	n−1)(t	n−1)(t	PROPN
ejpam-5446	98	4	)	)	PUNCT
ejpam-5446	98	5	+	+	CCONJ
ejpam-5446	98	6	....	....	PUNCT
ejpam-5446	99	1	+	+	CCONJ
ejpam-5446	99	2	c1(t)ς	c1(t)ς	ADJ
ejpam-5446	99	3	′(t	′(t	NOUN
ejpam-5446	99	4	)	)	PUNCT
ejpam-5446	100	1	+	+	SYM
ejpam-5446	100	2	c0ς(t	c0ς(t	PROPN
ejpam-5446	100	3	)	)	PUNCT
ejpam-5446	101	1	+	+	CCONJ
ejpam-5446	101	2	h(t	h(t	NUM
ejpam-5446	101	3	)	)	PUNCT
ejpam-5446	101	4	=	=	SYM
ejpam-5446	101	5	0	0	PUNCT
ejpam-5446	101	6	(	(	PUNCT
ejpam-5446	101	7	1.1	1.1	NUM
ejpam-5446	101	8	)	)	PUNCT
ejpam-5446	101	9	has	have	VERB
ejpam-5446	101	10	the	the	DET
ejpam-5446	101	11	hyers	hyer	NOUN
ejpam-5446	101	12	–	–	PUNCT
ejpam-5446	101	13	ulam	ulam	X
ejpam-5446	101	14	stability	stability	NOUN
ejpam-5446	101	15	,	,	PUNCT
ejpam-5446	101	16	if	if	SCONJ
ejpam-5446	101	17	for	for	ADP
ejpam-5446	101	18	any	any	DET
ejpam-5446	101	19	function	function	NOUN
ejpam-5446	101	20	g	g	NOUN
ejpam-5446	101	21	:	:	PUNCT
ejpam-5446	101	22	i	i	PRON
ejpam-5446	101	23	→	→	PUNCT
ejpam-5446	101	24	x	x	PART
ejpam-5446	101	25	satisfies	satisfy	VERB
ejpam-5446	101	26	the	the	DET
ejpam-5446	101	27	differential	differential	ADJ
ejpam-5446	101	28	inequality	inequality	NOUN
ejpam-5446	101	29	∥cn(t)ς(n)(t	∥cn(t)ς(n)(t	PROPN
ejpam-5446	101	30	)	)	PUNCT
ejpam-5446	102	1	+	+	X
ejpam-5446	102	2	cn−1(t)ς	cn−1(t)ς	ADV
ejpam-5446	102	3	(	(	PUNCT
ejpam-5446	102	4	n−1)(t	n−1)(t	ADJ
ejpam-5446	102	5	)	)	PUNCT
ejpam-5446	103	1	+	+	CCONJ
ejpam-5446	103	2	+	+	CCONJ
ejpam-5446	103	3	c1(t)ς	c1(t)ς	ADJ
ejpam-5446	103	4	′(t	′(t	NOUN
ejpam-5446	103	5	)	)	PUNCT
ejpam-5446	104	1	+	+	SYM
ejpam-5446	104	2	c0ς(t	c0ς(t	PROPN
ejpam-5446	104	3	)	)	PUNCT
ejpam-5446	105	1	+	+	CCONJ
ejpam-5446	105	2	h(t)∥	h(t)∥	NOUN
ejpam-5446	105	3	≤	≤	NUM
ejpam-5446	105	4	ϵ	ϵ	ADP
ejpam-5446	105	5	,	,	PUNCT
ejpam-5446	105	6	for	for	ADP
ejpam-5446	105	7	all	all	DET
ejpam-5446	105	8	t	t	NOUN
ejpam-5446	105	9	∈	∈	PRON
ejpam-5446	106	1	i	i	PRON
ejpam-5446	106	2	and	and	CCONJ
ejpam-5446	106	3	for	for	ADP
ejpam-5446	106	4	some	some	DET
ejpam-5446	106	5	ϵ	ϵ	PRON
ejpam-5446	106	6	≥	≥	NOUN
ejpam-5446	106	7	0	0	NUM
ejpam-5446	106	8	.	.	PUNCT
ejpam-5446	107	1	then	then	ADV
ejpam-5446	107	2	there	there	PRON
ejpam-5446	107	3	exists	exist	VERB
ejpam-5446	107	4	a	a	DET
ejpam-5446	107	5	solution	solution	NOUN
ejpam-5446	107	6	f	f	X
ejpam-5446	107	7	:	:	PUNCT
ejpam-5446	107	8	i	i	PRON
ejpam-5446	107	9	→	→	PUNCT
ejpam-5446	107	10	x	x	X
ejpam-5446	107	11	of	of	ADP
ejpam-5446	107	12	(	(	PUNCT
ejpam-5446	107	13	1.1	1.1	NUM
ejpam-5446	107	14	)	)	PUNCT
ejpam-5446	107	15	such	such	ADJ
ejpam-5446	107	16	that	that	SCONJ
ejpam-5446	107	17	∥g(t)−	∥g(t)−	PROPN
ejpam-5446	107	18	f(t)∥	f(t)∥	ADV
ejpam-5446	107	19	≤	≤	ADJ
ejpam-5446	107	20	k(ϵ	k(ϵ	PROPN
ejpam-5446	107	21	)	)	PUNCT
ejpam-5446	107	22	,	,	PUNCT
ejpam-5446	107	23	for	for	ADP
ejpam-5446	107	24	any	any	DET
ejpam-5446	107	25	t	t	NOUN
ejpam-5446	107	26	∈	∈	PROPN
ejpam-5446	108	1	i	i	PRON
ejpam-5446	108	2	,	,	PUNCT
ejpam-5446	108	3	where	where	SCONJ
ejpam-5446	108	4	k(ϵ	k(ϵ	PROPN
ejpam-5446	108	5	)	)	PUNCT
ejpam-5446	108	6	is	be	AUX
ejpam-5446	108	7	an	an	DET
ejpam-5446	108	8	articulation	articulation	NOUN
ejpam-5446	108	9	for	for	ADP
ejpam-5446	108	10	ϵ	ϵ	X
ejpam-5446	108	11	as	as	SCONJ
ejpam-5446	108	12	it	it	PRON
ejpam-5446	108	13	were	be	AUX
ejpam-5446	108	14	.	.	PUNCT
ejpam-5446	109	1	the	the	DET
ejpam-5446	109	2	stability	stability	NOUN
ejpam-5446	109	3	of	of	ADP
ejpam-5446	109	4	differential	differential	ADJ
ejpam-5446	109	5	equation	equation	NOUN
ejpam-5446	109	6	explored	explore	VERB
ejpam-5446	109	7	by	by	ADP
ejpam-5446	109	8	[	[	X
ejpam-5446	109	9	1	1	X
ejpam-5446	109	10	]	]	PUNCT
ejpam-5446	109	11	if	if	SCONJ
ejpam-5446	109	12	ϵ	ϵ	PROPN
ejpam-5446	109	13	>	>	X
ejpam-5446	109	14	0	0	PROPN
ejpam-5446	109	15	,	,	PUNCT
ejpam-5446	109	16	a	a	DET
ejpam-5446	109	17	differentiable	differentiable	ADJ
ejpam-5446	109	18	function	function	NOUN
ejpam-5446	109	19	g	g	NOUN
ejpam-5446	109	20	:	:	PUNCT
ejpam-5446	109	21	i	i	PRON
ejpam-5446	109	22	→	→	PUNCT
ejpam-5446	109	23	r	r	NOUN
ejpam-5446	109	24	fulfills	fulfill	VERB
ejpam-5446	109	25	the	the	DET
ejpam-5446	109	26	differential	differential	ADJ
ejpam-5446	109	27	disparity	disparity	NOUN
ejpam-5446	109	28	|ς	|ς	PROPN
ejpam-5446	109	29	′(t)−	′(t)−	PROPN
ejpam-5446	109	30	ς(t)|	ς(t)|	VERB
ejpam-5446	109	31	≤	≤	PROPN
ejpam-5446	110	1	ϵ	ϵ	ADP
ejpam-5446	110	2	,	,	PUNCT
ejpam-5446	110	3	where	where	SCONJ
ejpam-5446	110	4	i	i	PRON
ejpam-5446	110	5	is	be	AUX
ejpam-5446	110	6	an	an	DET
ejpam-5446	110	7	open	open	ADJ
ejpam-5446	110	8	subinterval	subinterval	NOUN
ejpam-5446	110	9	of	of	ADP
ejpam-5446	110	10	r	r	NOUN
ejpam-5446	110	11	,	,	PUNCT
ejpam-5446	110	12	at	at	ADP
ejpam-5446	110	13	that	that	DET
ejpam-5446	110	14	point	point	NOUN
ejpam-5446	110	15	there	there	PRON
ejpam-5446	110	16	exists	exist	VERB
ejpam-5446	110	17	a	a	DET
ejpam-5446	110	18	differentiable	differentiable	ADJ
ejpam-5446	110	19	function	function	NOUN
ejpam-5446	110	20	g0	g0	NOUN
ejpam-5446	110	21	:	:	PUNCT
ejpam-5446	110	22	i	i	PRON
ejpam-5446	110	23	→	→	SYM
ejpam-5446	110	24	r	r	NOUN
ejpam-5446	110	25	fulfilling	fulfil	VERB
ejpam-5446	110	26	g′0(t	g′0(t	PROPN
ejpam-5446	110	27	)	)	PUNCT
ejpam-5446	111	1	=	=	SYM
ejpam-5446	111	2	g0(t	g0(t	NOUN
ejpam-5446	111	3	)	)	PUNCT
ejpam-5446	111	4	such	such	ADJ
ejpam-5446	111	5	that	that	SCONJ
ejpam-5446	111	6	|g(t)−	|g(t)−	PROPN
ejpam-5446	111	7	g0(t)|	g0(t)|	VERB
ejpam-5446	111	8	≤	≤	NUM
ejpam-5446	111	9	3ϵ	3ϵ	NOUN
ejpam-5446	111	10	,	,	PUNCT
ejpam-5446	111	11	for	for	ADP
ejpam-5446	111	12	all	all	DET
ejpam-5446	111	13	t	t	PROPN
ejpam-5446	111	14	∈	∈	PROPN
ejpam-5446	111	15	i.	i.	PROPN
ejpam-5446	111	16	li	li	PROPN
ejpam-5446	111	17	and	and	CCONJ
ejpam-5446	111	18	shen	shen	PROPN
ejpam-5446	112	1	[	[	X
ejpam-5446	112	2	12	12	NUM
ejpam-5446	112	3	]	]	PUNCT
ejpam-5446	112	4	have	have	AUX
ejpam-5446	112	5	explored	explore	VERB
ejpam-5446	112	6	the	the	DET
ejpam-5446	112	7	hyers	hyer	NOUN
ejpam-5446	112	8	–	–	PUNCT
ejpam-5446	112	9	ulam	ulam	X
ejpam-5446	112	10	stability	stability	NOUN
ejpam-5446	112	11	of	of	ADP
ejpam-5446	112	12	the	the	DET
ejpam-5446	112	13	linear	linear	PROPN
ejpam-5446	112	14	differential	differential	ADJ
ejpam-5446	112	15	equations	equation	NOUN
ejpam-5446	112	16	of	of	ADP
ejpam-5446	112	17	the	the	DET
ejpam-5446	112	18	second	second	ADJ
ejpam-5446	112	19	order	order	NOUN
ejpam-5446	112	20	ς	ς	PROPN
ejpam-5446	112	21	′′(x	′′(x	NOUN
ejpam-5446	112	22	)	)	PUNCT
ejpam-5446	112	23	+	+	CCONJ
ejpam-5446	112	24	ας	ας	NUM
ejpam-5446	112	25	′(x	′(x	NOUN
ejpam-5446	112	26	)	)	PUNCT
ejpam-5446	112	27	+	+	NUM
ejpam-5446	112	28	βς(x	βς(x	PUNCT
ejpam-5446	112	29	)	)	PUNCT
ejpam-5446	112	30	=	=	SYM
ejpam-5446	112	31	g(x	g(x	NOUN
ejpam-5446	112	32	)	)	PUNCT
ejpam-5446	112	33	,	,	PUNCT
ejpam-5446	112	34	(	(	PUNCT
ejpam-5446	112	35	1.2	1.2	NUM
ejpam-5446	112	36	)	)	PUNCT
ejpam-5446	112	37	where	where	SCONJ
ejpam-5446	112	38	ς	ς	PROPN
ejpam-5446	112	39	∈	∈	PROPN
ejpam-5446	112	40	c2[a	c2[a	NOUN
ejpam-5446	112	41	,	,	PUNCT
ejpam-5446	112	42	b	b	X
ejpam-5446	112	43	]	]	X
ejpam-5446	112	44	,	,	PUNCT
ejpam-5446	112	45	g	g	PROPN
ejpam-5446	112	46	∈	∈	PROPN
ejpam-5446	112	47	c[a	c[a	NOUN
ejpam-5446	112	48	,	,	PUNCT
ejpam-5446	112	49	b	b	X
ejpam-5446	112	50	]	]	PUNCT
ejpam-5446	112	51	and	and	CCONJ
ejpam-5446	112	52	−∞	−∞	X
ejpam-5446	112	53	<	<	X
ejpam-5446	112	54	a	a	DET
ejpam-5446	112	55	<	<	X
ejpam-5446	112	56	b	b	X
ejpam-5446	112	57	<	<	X
ejpam-5446	112	58	∞.	∞.	PROPN
ejpam-5446	112	59	in	in	ADP
ejpam-5446	112	60	fact	fact	NOUN
ejpam-5446	112	61	they	they	PRON
ejpam-5446	112	62	demonstrated	demonstrate	VERB
ejpam-5446	112	63	that	that	SCONJ
ejpam-5446	112	64	if	if	SCONJ
ejpam-5446	112	65	the	the	DET
ejpam-5446	112	66	condition	condition	NOUN
ejpam-5446	112	67	λ2	λ2	VERB
ejpam-5446	112	68	+	+	CCONJ
ejpam-5446	112	69	αλ	αλ	PRON
ejpam-5446	112	70	+	+	X
ejpam-5446	112	71	β	β	X
ejpam-5446	112	72	=	=	SYM
ejpam-5446	112	73	0	0	NUM
ejpam-5446	112	74	has	have	VERB
ejpam-5446	112	75	two	two	NUM
ejpam-5446	112	76	distinctive	distinctive	ADJ
ejpam-5446	112	77	positive	positive	ADJ
ejpam-5446	112	78	roots	root	NOUN
ejpam-5446	112	79	,	,	PUNCT
ejpam-5446	112	80	at	at	ADP
ejpam-5446	112	81	that	that	DET
ejpam-5446	112	82	point	point	NOUN
ejpam-5446	112	83	the	the	DET
ejpam-5446	112	84	condition	condition	NOUN
ejpam-5446	112	85	ς	ς	PROPN
ejpam-5446	112	86	′′(x	′′(x	NOUN
ejpam-5446	112	87	)	)	PUNCT
ejpam-5446	112	88	+	+	CCONJ
ejpam-5446	112	89	ας	ας	NUM
ejpam-5446	112	90	′(x	′(x	NOUN
ejpam-5446	112	91	)	)	PUNCT
ejpam-5446	112	92	+	+	NUM
ejpam-5446	112	93	βς(x	βς(x	PUNCT
ejpam-5446	112	94	)	)	PUNCT
ejpam-5446	112	95	=	=	SYM
ejpam-5446	112	96	g(x	g(x	NOUN
ejpam-5446	112	97	)	)	PUNCT
ejpam-5446	112	98	has	have	VERB
ejpam-5446	112	99	the	the	DET
ejpam-5446	112	100	hyers	hyer	NOUN
ejpam-5446	112	101	–	–	PUNCT
ejpam-5446	112	102	ulam	ulam	X
ejpam-5446	112	103	stability	stability	NOUN
ejpam-5446	112	104	.	.	PUNCT
ejpam-5446	113	1	recently	recently	ADV
ejpam-5446	113	2	,	,	PUNCT
ejpam-5446	113	3	luo	luo	PROPN
ejpam-5446	113	4	[	[	X
ejpam-5446	113	5	13–17	13–17	NUM
ejpam-5446	113	6	,	,	PUNCT
ejpam-5446	113	7	26	26	NUM
ejpam-5446	113	8	]	]	PUNCT
ejpam-5446	113	9	investigated	investigate	VERB
ejpam-5446	113	10	the	the	DET
ejpam-5446	113	11	hyers	hyers	PROPN
ejpam-5446	113	12	-	-	PUNCT
ejpam-5446	113	13	ulam	ulam	PROPN
ejpam-5446	113	14	stability	stability	PROPN
ejpam-5446	113	15	results	result	NOUN
ejpam-5446	113	16	of	of	ADP
ejpam-5446	113	17	differential	differential	ADJ
ejpam-5446	113	18	equations	equation	NOUN
ejpam-5446	113	19	in	in	ADP
ejpam-5446	113	20	fractional	fractional	ADJ
ejpam-5446	113	21	order	order	NOUN
ejpam-5446	113	22	.	.	PUNCT
ejpam-5446	114	1	in	in	ADP
ejpam-5446	114	2	this	this	DET
ejpam-5446	114	3	paper	paper	NOUN
ejpam-5446	114	4	we	we	PRON
ejpam-5446	114	5	will	will	AUX
ejpam-5446	114	6	examine	examine	VERB
ejpam-5446	114	7	the	the	DET
ejpam-5446	114	8	stability	stability	NOUN
ejpam-5446	114	9	of	of	ADP
ejpam-5446	114	10	differential	differential	ADJ
ejpam-5446	114	11	equations	equation	NOUN
ejpam-5446	114	12	of	of	ADP
ejpam-5446	114	13	fifth	fifth	ADJ
ejpam-5446	114	14	order	order	NOUN
ejpam-5446	114	15	.	.	PUNCT
ejpam-5446	115	1	in	in	ADP
ejpam-5446	115	2	section	section	NOUN
ejpam-5446	115	3	2	2	NUM
ejpam-5446	115	4	,	,	PUNCT
ejpam-5446	115	5	we	we	PRON
ejpam-5446	115	6	will	will	AUX
ejpam-5446	115	7	give	give	VERB
ejpam-5446	115	8	a	a	DET
ejpam-5446	115	9	vital	vital	ADJ
ejpam-5446	115	10	and	and	CCONJ
ejpam-5446	115	11	adequate	adequate	ADJ
ejpam-5446	115	12	condition	condition	NOUN
ejpam-5446	115	13	all	all	ADV
ejpam-5446	115	14	together	together	ADV
ejpam-5446	115	15	that	that	SCONJ
ejpam-5446	115	16	the	the	DET
ejpam-5446	115	17	fifth	fifth	ADJ
ejpam-5446	115	18	order	order	NOUN
ejpam-5446	115	19	linear	linear	NOUN
ejpam-5446	115	20	differential	differential	NOUN
ejpam-5446	115	21	equation	equation	NOUN
ejpam-5446	115	22	and	and	CCONJ
ejpam-5446	115	23	established	establish	VERB
ejpam-5446	115	24	hyers	hyers	PROPN
ejpam-5446	115	25	-	-	PUNCT
ejpam-5446	115	26	ulam	ulam	PROPN
ejpam-5446	115	27	stability	stability	NOUN
ejpam-5446	115	28	constant	constant	ADJ
ejpam-5446	115	29	under	under	ADP
ejpam-5446	115	30	those	those	DET
ejpam-5446	115	31	conditions	condition	NOUN
ejpam-5446	115	32	.	.	PUNCT
ejpam-5446	116	1	in	in	ADP
ejpam-5446	116	2	section	section	NOUN
ejpam-5446	116	3	3	3	NUM
ejpam-5446	116	4	,	,	PUNCT
ejpam-5446	116	5	we	we	PRON
ejpam-5446	116	6	will	will	AUX
ejpam-5446	116	7	apply	apply	VERB
ejpam-5446	116	8	this	this	DET
ejpam-5446	116	9	results	result	NOUN
ejpam-5446	116	10	to	to	ADP
ejpam-5446	116	11	fifth	fifth	ADJ
ejpam-5446	116	12	order	order	NOUN
ejpam-5446	116	13	differential	differential	ADJ
ejpam-5446	116	14	equations	equation	NOUN
ejpam-5446	116	15	by	by	ADP
ejpam-5446	116	16	numerical	numerical	ADJ
ejpam-5446	116	17	examples	example	NOUN
ejpam-5446	116	18	.	.	PUNCT
ejpam-5446	117	1	definition:1.1	definition:1.1	NOUN
ejpam-5446	118	1	[	[	X
ejpam-5446	118	2	19	19	NUM
ejpam-5446	118	3	]	]	PUNCT
ejpam-5446	118	4	let	let	VERB
ejpam-5446	118	5	i	i	PRON
ejpam-5446	118	6	be	be	AUX
ejpam-5446	118	7	any	any	DET
ejpam-5446	118	8	interval	interval	NOUN
ejpam-5446	118	9	and	and	CCONJ
ejpam-5446	118	10	let	let	VERB
ejpam-5446	118	11	z	z	NOUN
ejpam-5446	118	12	:	:	PUNCT
ejpam-5446	118	13	i	i	PROPN
ejpam-5446	118	14	→	→	SYM
ejpam-5446	118	15	rn	rn	PROPN
ejpam-5446	118	16	,	,	PUNCT
ejpam-5446	118	17	a	a	PRON
ejpam-5446	118	18	:	:	PUNCT
ejpam-5446	118	19	i	i	PRON
ejpam-5446	118	20	→	→	SYM
ejpam-5446	118	21	rn×n	rn×n	PROPN
ejpam-5446	118	22	,	,	PUNCT
ejpam-5446	118	23	b	b	NOUN
ejpam-5446	118	24	:	:	PUNCT
ejpam-5446	118	25	i	i	PROPN
ejpam-5446	118	26	→	→	SYM
ejpam-5446	118	27	rn	rn	PROPN
ejpam-5446	118	28	at	at	ADP
ejpam-5446	118	29	that	that	DET
ejpam-5446	118	30	point	point	NOUN
ejpam-5446	118	31	z′(t	z′(t	ADP
ejpam-5446	118	32	)	)	PUNCT
ejpam-5446	118	33	+	+	NOUN
ejpam-5446	118	34	a(t)z(t	a(t)z(t	X
ejpam-5446	118	35	)	)	PUNCT
ejpam-5446	118	36	+	+	NUM
ejpam-5446	118	37	b(t	b(t	NOUN
ejpam-5446	118	38	)	)	PUNCT
ejpam-5446	118	39	=	=	SYM
ejpam-5446	118	40	0	0	PUNCT
ejpam-5446	119	1	(	(	PUNCT
ejpam-5446	119	2	1.3	1.3	NUM
ejpam-5446	119	3	)	)	PUNCT
ejpam-5446	119	4	is	be	AUX
ejpam-5446	119	5	hyers	hyer	NOUN
ejpam-5446	119	6	-	-	PUNCT
ejpam-5446	119	7	ulam	ulam	ADJ
ejpam-5446	119	8	-	-	PUNCT
ejpam-5446	119	9	rassias	rassias	NOUN
ejpam-5446	119	10	stable	stable	ADJ
ejpam-5446	119	11	as	as	ADP
ejpam-5446	119	12	for	for	ADP
ejpam-5446	119	13	φ	φ	NOUN
ejpam-5446	119	14	:	:	PUNCT
ejpam-5446	120	1	i	i	PRON
ejpam-5446	120	2	→	→	PUNCT
ejpam-5446	121	1	[	[	X
ejpam-5446	121	2	0,∞	0,∞	NOUN
ejpam-5446	121	3	)	)	PUNCT
ejpam-5446	121	4	with	with	ADP
ejpam-5446	121	5	∥z(t)∥	∥z(t)∥	PROPN
ejpam-5446	121	6	=	=	SYM
ejpam-5446	122	1	∑n	∑n	PROPN
ejpam-5446	122	2	i=1	i=1	PROPN
ejpam-5446	122	3	|zi(t)|	|zi(t)|	PROPN
ejpam-5446	122	4	,	,	PUNCT
ejpam-5446	122	5	if	if	SCONJ
ejpam-5446	122	6	there	there	PRON
ejpam-5446	122	7	exists	exist	VERB
ejpam-5446	122	8	a	a	DET
ejpam-5446	122	9	real	real	ADV
ejpam-5446	122	10	consistent	consistent	ADJ
ejpam-5446	123	1	k	k	PROPN
ejpam-5446	123	2	>	>	X
ejpam-5446	123	3	0	0	PUNCT
ejpam-5446	124	1	with	with	ADP
ejpam-5446	124	2	the	the	DET
ejpam-5446	124	3	end	end	NOUN
ejpam-5446	124	4	goal	goal	NOUN
ejpam-5446	125	1	that	that	SCONJ
ejpam-5446	125	2	for	for	ADP
ejpam-5446	125	3	every	every	DET
ejpam-5446	125	4	arrangement	arrangement	NOUN
ejpam-5446	125	5	s	s	PART
ejpam-5446	125	6	∈	∈	PROPN
ejpam-5446	125	7	c1(i	c1(i	NOUN
ejpam-5446	125	8	,	,	PUNCT
ejpam-5446	125	9	rn	rn	NOUN
ejpam-5446	125	10	)	)	PUNCT
ejpam-5446	125	11	of	of	ADP
ejpam-5446	125	12	the	the	DET
ejpam-5446	125	13	inequality	inequality	NOUN
ejpam-5446	125	14	∥z′(t	∥z′(t	PUNCT
ejpam-5446	125	15	)	)	PUNCT
ejpam-5446	126	1	+	+	NOUN
ejpam-5446	126	2	a(t)z(t	a(t)z(t	X
ejpam-5446	126	3	)	)	PUNCT
ejpam-5446	126	4	+	+	CCONJ
ejpam-5446	126	5	b(t)∥	b(t)∥	VERB
ejpam-5446	126	6	≤	≤	NUM
ejpam-5446	126	7	ψ(t	ψ(t	PROPN
ejpam-5446	126	8	)	)	PUNCT
ejpam-5446	126	9	,	,	PUNCT
ejpam-5446	126	10	there	there	PRON
ejpam-5446	126	11	exists	exist	VERB
ejpam-5446	126	12	an	an	DET
ejpam-5446	126	13	answer	answer	NOUN
ejpam-5446	126	14	z	z	PROPN
ejpam-5446	126	15	∈	∈	PROPN
ejpam-5446	126	16	c1(i	c1(i	PROPN
ejpam-5446	126	17	,	,	PUNCT
ejpam-5446	126	18	rn	rn	NOUN
ejpam-5446	126	19	)	)	PUNCT
ejpam-5446	126	20	of	of	ADP
ejpam-5446	126	21	condition	condition	NOUN
ejpam-5446	126	22	(	(	PUNCT
ejpam-5446	126	23	1.3	1.3	NUM
ejpam-5446	126	24	)	)	PUNCT
ejpam-5446	126	25	with	with	ADP
ejpam-5446	126	26	∥s(t)−	∥s(t)−	PROPN
ejpam-5446	126	27	z(t)∥	z(t)∥	PROPN
ejpam-5446	126	28	≤	≤	NUM
ejpam-5446	126	29	kψ(t	kψ(t	PROPN
ejpam-5446	126	30	)	)	PUNCT
ejpam-5446	126	31	,	,	PUNCT
ejpam-5446	126	32	∀t	∀t	PROPN
ejpam-5446	126	33	∈	∈	PROPN
ejpam-5446	126	34	i.	i.	NOUN
ejpam-5446	126	35	definition:1.2	definition:1.2	PROPN
ejpam-5446	127	1	[	[	X
ejpam-5446	127	2	21	21	NUM
ejpam-5446	127	3	]	]	PUNCT
ejpam-5446	127	4	for	for	ADP
ejpam-5446	127	5	a	a	DET
ejpam-5446	127	6	nonempty	nonempty	ADV
ejpam-5446	127	7	set	set	VERB
ejpam-5446	127	8	x	x	SYM
ejpam-5446	127	9	,	,	PUNCT
ejpam-5446	127	10	a	a	DET
ejpam-5446	127	11	function	function	NOUN
ejpam-5446	127	12	d	d	NOUN
ejpam-5446	127	13	:	:	PUNCT
ejpam-5446	127	14	x	x	SYM
ejpam-5446	127	15	×	×	NOUN
ejpam-5446	127	16	x	x	INTJ
ejpam-5446	127	17	→	→	X
ejpam-5446	128	1	[	[	X
ejpam-5446	128	2	0,∞	0,∞	X
ejpam-5446	128	3	]	]	PUNCT
ejpam-5446	128	4	is	be	AUX
ejpam-5446	128	5	called	call	VERB
ejpam-5446	128	6	a	a	DET
ejpam-5446	128	7	generalized	generalize	VERB
ejpam-5446	128	8	metric	metric	NOUN
ejpam-5446	128	9	on	on	ADP
ejpam-5446	128	10	x	x	SYM
ejpam-5446	128	11	if	if	SCONJ
ejpam-5446	128	12	and	and	CCONJ
ejpam-5446	128	13	only	only	ADV
ejpam-5446	128	14	if	if	SCONJ
ejpam-5446	128	15	d	d	NOUN
ejpam-5446	128	16	satisfies	satisfy	VERB
ejpam-5446	128	17	:	:	PUNCT
ejpam-5446	128	18	v.	v.	CCONJ
ejpam-5446	128	19	govindan	govindan	PROPN
ejpam-5446	128	20	et	et	PROPN
ejpam-5446	128	21	al	al	PROPN
ejpam-5446	128	22	.	.	PUNCT
ejpam-5446	128	23	/	/	SYM
ejpam-5446	128	24	eur	eur	PROPN
ejpam-5446	128	25	.	.	PUNCT
ejpam-5446	129	1	j.	j.	PROPN
ejpam-5446	129	2	pure	pure	PROPN
ejpam-5446	129	3	appl	appl	PROPN
ejpam-5446	129	4	.	.	PROPN
ejpam-5446	129	5	math	math	PROPN
ejpam-5446	129	6	,	,	PUNCT
ejpam-5446	129	7	17	17	NUM
ejpam-5446	129	8	(	(	PUNCT
ejpam-5446	129	9	4	4	NUM
ejpam-5446	129	10	)	)	PUNCT
ejpam-5446	129	11	(	(	PUNCT
ejpam-5446	129	12	2024	2024	NUM
ejpam-5446	129	13	)	)	PUNCT
ejpam-5446	129	14	,	,	PUNCT
ejpam-5446	129	15	3585	3585	NUM
ejpam-5446	129	16	-	-	SYM
ejpam-5446	129	17	3609	3609	NUM
ejpam-5446	129	18	3590	3590	NUM
ejpam-5446	129	19	(	(	PUNCT
ejpam-5446	129	20	i	i	NOUN
ejpam-5446	129	21	)	)	PUNCT
ejpam-5446	129	22	d(x	d(x	PROPN
ejpam-5446	129	23	,	,	PUNCT
ejpam-5446	129	24	y	y	NOUN
ejpam-5446	129	25	)	)	PUNCT
ejpam-5446	129	26	=	=	SYM
ejpam-5446	129	27	0	0	PUNCT
ejpam-5446	130	1	if	if	SCONJ
ejpam-5446	130	2	and	and	CCONJ
ejpam-5446	130	3	only	only	ADV
ejpam-5446	130	4	if	if	SCONJ
ejpam-5446	130	5	x	x	X
ejpam-5446	130	6	=	=	SYM
ejpam-5446	130	7	y	y	PROPN
ejpam-5446	130	8	(	(	PUNCT
ejpam-5446	130	9	ii	ii	NOUN
ejpam-5446	130	10	)	)	PUNCT
ejpam-5446	130	11	d(x	d(x	PROPN
ejpam-5446	130	12	,	,	PUNCT
ejpam-5446	130	13	y	y	NOUN
ejpam-5446	130	14	)	)	PUNCT
ejpam-5446	130	15	=	=	SYM
ejpam-5446	130	16	d(y	d(y	NOUN
ejpam-5446	130	17	,	,	PUNCT
ejpam-5446	130	18	x	x	NOUN
ejpam-5446	130	19	)	)	PUNCT
ejpam-5446	130	20	,	,	PUNCT
ejpam-5446	130	21	for	for	ADP
ejpam-5446	130	22	all	all	DET
ejpam-5446	130	23	x	x	NOUN
ejpam-5446	130	24	,	,	PUNCT
ejpam-5446	130	25	y	y	PROPN
ejpam-5446	130	26	∈	∈	PROPN
ejpam-5446	130	27	x	x	INTJ
ejpam-5446	130	28	(	(	PUNCT
ejpam-5446	130	29	iii	iii	NOUN
ejpam-5446	130	30	)	)	PUNCT
ejpam-5446	130	31	d(x	d(x	PROPN
ejpam-5446	130	32	,	,	PUNCT
ejpam-5446	130	33	z	z	NOUN
ejpam-5446	130	34	)	)	PUNCT
ejpam-5446	130	35	≤	≤	NOUN
ejpam-5446	130	36	d(x	d(x	PROPN
ejpam-5446	130	37	,	,	PUNCT
ejpam-5446	130	38	y	y	NOUN
ejpam-5446	130	39	)	)	PUNCT
ejpam-5446	131	1	+	+	CCONJ
ejpam-5446	131	2	d(y	d(y	NOUN
ejpam-5446	131	3	,	,	PUNCT
ejpam-5446	131	4	z	z	NOUN
ejpam-5446	131	5	)	)	PUNCT
ejpam-5446	131	6	,	,	PUNCT
ejpam-5446	131	7	for	for	ADP
ejpam-5446	131	8	all	all	DET
ejpam-5446	131	9	x	x	NOUN
ejpam-5446	131	10	,	,	PUNCT
ejpam-5446	131	11	y	y	PROPN
ejpam-5446	131	12	,	,	PUNCT
ejpam-5446	131	13	z	z	NOUN
ejpam-5446	131	14	∈	∈	PROPN
ejpam-5446	132	1	x	x	X
ejpam-5446	132	2	.	.	PUNCT
ejpam-5446	133	1	definition:1.3	definition:1.3	PROPN
ejpam-5446	134	1	[	[	X
ejpam-5446	134	2	12	12	NUM
ejpam-5446	134	3	]	]	PUNCT
ejpam-5446	134	4	we	we	PRON
ejpam-5446	134	5	denote	denote	VERB
ejpam-5446	134	6	(	(	PUNCT
ejpam-5446	134	7	1.2	1.2	NUM
ejpam-5446	134	8	)	)	PUNCT
ejpam-5446	134	9	has	have	VERB
ejpam-5446	134	10	the	the	DET
ejpam-5446	134	11	hyers	hyers	PROPN
ejpam-5446	134	12	-	-	PUNCT
ejpam-5446	134	13	ulam	ulam	PROPN
ejpam-5446	134	14	stability	stability	NOUN
ejpam-5446	134	15	if	if	SCONJ
ejpam-5446	134	16	there	there	PRON
ejpam-5446	134	17	exists	exist	VERB
ejpam-5446	134	18	a	a	DET
ejpam-5446	134	19	steady	steady	ADJ
ejpam-5446	134	20	v1	v1	NOUN
ejpam-5446	134	21	>	>	X
ejpam-5446	134	22	0	0	PUNCT
ejpam-5446	134	23	with	with	ADP
ejpam-5446	134	24	the	the	DET
ejpam-5446	134	25	accompanying	accompanying	ADJ
ejpam-5446	134	26	property	property	NOUN
ejpam-5446	134	27	,	,	PUNCT
ejpam-5446	134	28	for	for	ADP
ejpam-5446	134	29	every	every	DET
ejpam-5446	134	30	ε	ε	PROPN
ejpam-5446	134	31	>	>	X
ejpam-5446	134	32	0	0	PROPN
ejpam-5446	134	33	,	,	PUNCT
ejpam-5446	134	34	ς	ς	PROPN
ejpam-5446	134	35	∈	∈	PROPN
ejpam-5446	134	36	c2[k	c2[k	NOUN
ejpam-5446	134	37	,	,	PUNCT
ejpam-5446	134	38	l	l	NOUN
ejpam-5446	134	39	]	]	X
ejpam-5446	134	40	,	,	PUNCT
ejpam-5446	134	41	if	if	SCONJ
ejpam-5446	134	42	|ς	|ς	VERB
ejpam-5446	134	43	′′	′′	PROPN
ejpam-5446	134	44	+	+	CCONJ
ejpam-5446	134	45	aς	aς	VERB
ejpam-5446	134	46	′	′	NOUN
ejpam-5446	134	47	+	+	CCONJ
ejpam-5446	135	1	bς|	bς|	PROPN
ejpam-5446	135	2	≤	≤	PROPN
ejpam-5446	135	3	ε	ε	PROPN
ejpam-5446	135	4	,	,	PUNCT
ejpam-5446	135	5	(	(	PUNCT
ejpam-5446	135	6	1.4	1.4	NUM
ejpam-5446	135	7	)	)	PUNCT
ejpam-5446	135	8	as	as	ADP
ejpam-5446	135	9	such	such	ADJ
ejpam-5446	135	10	,	,	PUNCT
ejpam-5446	135	11	∃	∃	PROPN
ejpam-5446	135	12	u	u	NOUN
ejpam-5446	135	13	∈	∈	PROPN
ejpam-5446	135	14	c2[k	c2[k	NOUN
ejpam-5446	135	15	,	,	PUNCT
ejpam-5446	135	16	l	l	NOUN
ejpam-5446	135	17	]	]	X
ejpam-5446	135	18	that	that	PRON
ejpam-5446	135	19	satisfies	satisfy	VERB
ejpam-5446	135	20	:	:	PUNCT
ejpam-5446	135	21	|u′′	|u′′	PUNCT
ejpam-5446	135	22	+	+	CCONJ
ejpam-5446	135	23	au	au	ADJ
ejpam-5446	135	24	′	′	NOUN
ejpam-5446	135	25	+	+	CCONJ
ejpam-5446	135	26	bu|	bu|	PROPN
ejpam-5446	135	27	=	=	SYM
ejpam-5446	135	28	0	0	PROPN
ejpam-5446	135	29	,	,	PUNCT
ejpam-5446	135	30	(	(	PUNCT
ejpam-5446	135	31	1.5	1.5	NUM
ejpam-5446	135	32	)	)	PUNCT
ejpam-5446	135	33	such	such	ADJ
ejpam-5446	135	34	that	that	SCONJ
ejpam-5446	135	35	|ς(x)−	|ς(x)−	PROPN
ejpam-5446	135	36	u(x)|	u(x)|	NOUN
ejpam-5446	135	37	<	<	X
ejpam-5446	135	38	v1ϵ.	v1ϵ.	ADJ
ejpam-5446	135	39	we	we	PRON
ejpam-5446	135	40	denote	denote	VERB
ejpam-5446	135	41	v1	v1	PROPN
ejpam-5446	135	42	be	be	AUX
ejpam-5446	135	43	a	a	DET
ejpam-5446	135	44	hyers	hyers	PROPN
ejpam-5446	135	45	-	-	PUNCT
ejpam-5446	135	46	ulam	ulam	ADJ
ejpam-5446	135	47	stability	stability	NOUN
ejpam-5446	135	48	constant	constant	ADJ
ejpam-5446	135	49	for	for	ADP
ejpam-5446	135	50	(	(	PUNCT
ejpam-5446	135	51	1.2	1.2	NUM
ejpam-5446	135	52	)	)	PUNCT
ejpam-5446	135	53	.	.	PUNCT
ejpam-5446	136	1	definition:1.4	definition:1.4	NOUN
ejpam-5446	137	1	[	[	X
ejpam-5446	137	2	12	12	NUM
ejpam-5446	137	3	]	]	PUNCT
ejpam-5446	137	4	we	we	PRON
ejpam-5446	137	5	indicate	indicate	VERB
ejpam-5446	137	6	that	that	SCONJ
ejpam-5446	137	7	the	the	DET
ejpam-5446	137	8	augmentation	augmentation	NOUN
ejpam-5446	137	9	of	of	ADP
ejpam-5446	137	10	(	(	PUNCT
ejpam-5446	137	11	1.2	1.2	NUM
ejpam-5446	137	12	)	)	PUNCT
ejpam-5446	137	13	has	have	VERB
ejpam-5446	137	14	the	the	DET
ejpam-5446	137	15	hyers	hyers	PROPN
ejpam-5446	137	16	-	-	PUNCT
ejpam-5446	137	17	ulam	ulam	ADJ
ejpam-5446	137	18	stability	stability	NOUN
ejpam-5446	137	19	,	,	PUNCT
ejpam-5446	137	20	if	if	SCONJ
ejpam-5446	137	21	there	there	PRON
ejpam-5446	137	22	exists	exist	VERB
ejpam-5446	137	23	a	a	DET
ejpam-5446	137	24	consistent	consistent	ADJ
ejpam-5446	137	25	v1	v1	NOUN
ejpam-5446	137	26	>	>	X
ejpam-5446	137	27	0	0	PUNCT
ejpam-5446	137	28	with	with	ADP
ejpam-5446	137	29	the	the	DET
ejpam-5446	137	30	going	go	VERB
ejpam-5446	137	31	with	with	ADP
ejpam-5446	137	32	property	property	NOUN
ejpam-5446	137	33	,	,	PUNCT
ejpam-5446	137	34	for	for	ADP
ejpam-5446	137	35	each	each	DET
ejpam-5446	137	36	ε	ε	PROPN
ejpam-5446	137	37	>	>	X
ejpam-5446	137	38	0	0	PROPN
ejpam-5446	137	39	,	,	PUNCT
ejpam-5446	137	40	ς	ς	PROPN
ejpam-5446	137	41	∈	∈	PROPN
ejpam-5446	137	42	c3[k	c3[k	NOUN
ejpam-5446	137	43	,	,	PUNCT
ejpam-5446	137	44	l	l	NOUN
ejpam-5446	137	45	]	]	X
ejpam-5446	137	46	,	,	PUNCT
ejpam-5446	137	47	if	if	SCONJ
ejpam-5446	137	48	|ς	|ς	PROPN
ejpam-5446	137	49	′′′	′′′	VERB
ejpam-5446	137	50	+	+	NUM
ejpam-5446	137	51	aς	aς	VERB
ejpam-5446	137	52	′′	′′	PROPN
ejpam-5446	137	53	+	+	CCONJ
ejpam-5446	137	54	bς	bς	ADP
ejpam-5446	137	55	′	′	NOUN
ejpam-5446	137	56	+	+	CCONJ
ejpam-5446	138	1	cς|	cς|	ADJ
ejpam-5446	138	2	≤	≤	NUM
ejpam-5446	138	3	ε	ε	PROPN
ejpam-5446	138	4	,	,	PUNCT
ejpam-5446	138	5	(	(	PUNCT
ejpam-5446	138	6	1.6	1.6	NUM
ejpam-5446	138	7	)	)	PUNCT
ejpam-5446	138	8	as	as	ADP
ejpam-5446	138	9	such	such	ADJ
ejpam-5446	138	10	,	,	PUNCT
ejpam-5446	138	11	∃	∃	PROPN
ejpam-5446	138	12	u	u	PROPN
ejpam-5446	138	13	∈	∈	PROPN
ejpam-5446	138	14	c3[k	c3[k	NOUN
ejpam-5446	138	15	,	,	PUNCT
ejpam-5446	138	16	l	l	NOUN
ejpam-5446	138	17	]	]	X
ejpam-5446	138	18	that	that	PRON
ejpam-5446	138	19	satisfies	satisfy	VERB
ejpam-5446	138	20	:	:	PUNCT
ejpam-5446	138	21	|u′′′	|u′′′	VERB
ejpam-5446	138	22	+	+	CCONJ
ejpam-5446	138	23	au	au	X
ejpam-5446	138	24	′′	′′	PROPN
ejpam-5446	138	25	+	+	CCONJ
ejpam-5446	138	26	bu	bu	ADP
ejpam-5446	138	27	′	′	NOUN
ejpam-5446	139	1	+	+	CCONJ
ejpam-5446	140	1	cu|	cu|	NOUN
ejpam-5446	140	2	=	=	PUNCT
ejpam-5446	140	3	0	0	NUM
ejpam-5446	140	4	,	,	PUNCT
ejpam-5446	140	5	(	(	PUNCT
ejpam-5446	140	6	1.7	1.7	NUM
ejpam-5446	140	7	)	)	PUNCT
ejpam-5446	140	8	such	such	ADJ
ejpam-5446	140	9	that	that	SCONJ
ejpam-5446	140	10	|ς(x)−	|ς(x)−	PROPN
ejpam-5446	140	11	u(x)|	u(x)|	PROPN
ejpam-5446	140	12	<	<	X
ejpam-5446	140	13	v1ϵ	v1ϵ	PROPN
ejpam-5446	140	14	,	,	PUNCT
ejpam-5446	140	15	where	where	SCONJ
ejpam-5446	140	16	v1	v1	NOUN
ejpam-5446	140	17	is	be	AUX
ejpam-5446	140	18	a	a	DET
ejpam-5446	140	19	hyers	hyers	PROPN
ejpam-5446	140	20	-	-	PUNCT
ejpam-5446	140	21	ulam	ulam	ADJ
ejpam-5446	140	22	stability	stability	NOUN
ejpam-5446	140	23	constant	constant	ADJ
ejpam-5446	140	24	for	for	ADP
ejpam-5446	140	25	(	(	PUNCT
ejpam-5446	140	26	1.6	1.6	NUM
ejpam-5446	140	27	)	)	PUNCT
ejpam-5446	140	28	.	.	PUNCT
ejpam-5446	141	1	definition:1.5	definition:1.5	PROPN
ejpam-5446	142	1	[	[	X
ejpam-5446	142	2	12	12	NUM
ejpam-5446	142	3	]	]	PUNCT
ejpam-5446	142	4	we	we	PRON
ejpam-5446	142	5	mean	mean	VERB
ejpam-5446	142	6	that	that	SCONJ
ejpam-5446	142	7	the	the	DET
ejpam-5446	142	8	augmentation	augmentation	NOUN
ejpam-5446	142	9	of	of	ADP
ejpam-5446	142	10	(	(	PUNCT
ejpam-5446	142	11	1.6	1.6	NUM
ejpam-5446	142	12	)	)	PUNCT
ejpam-5446	142	13	has	have	VERB
ejpam-5446	142	14	the	the	DET
ejpam-5446	142	15	hyers	hyers	PROPN
ejpam-5446	142	16	-	-	PUNCT
ejpam-5446	142	17	ulam	ulam	ADJ
ejpam-5446	142	18	stability	stability	NOUN
ejpam-5446	142	19	,	,	PUNCT
ejpam-5446	142	20	if	if	SCONJ
ejpam-5446	142	21	there	there	PRON
ejpam-5446	142	22	exists	exist	VERB
ejpam-5446	142	23	a	a	DET
ejpam-5446	142	24	consistent	consistent	ADJ
ejpam-5446	142	25	v1	v1	NOUN
ejpam-5446	142	26	>	>	X
ejpam-5446	142	27	0	0	PUNCT
ejpam-5446	142	28	with	with	ADP
ejpam-5446	142	29	the	the	DET
ejpam-5446	142	30	going	go	VERB
ejpam-5446	142	31	with	with	ADP
ejpam-5446	142	32	property	property	NOUN
ejpam-5446	142	33	,	,	PUNCT
ejpam-5446	142	34	for	for	ADP
ejpam-5446	142	35	each	each	DET
ejpam-5446	142	36	ε	ε	PROPN
ejpam-5446	142	37	>	>	X
ejpam-5446	142	38	0	0	PROPN
ejpam-5446	142	39	,	,	PUNCT
ejpam-5446	142	40	ς	ς	PROPN
ejpam-5446	142	41	∈	∈	PROPN
ejpam-5446	142	42	c4[k	c4[k	NOUN
ejpam-5446	142	43	,	,	PUNCT
ejpam-5446	142	44	l	l	NOUN
ejpam-5446	142	45	]	]	X
ejpam-5446	142	46	,	,	PUNCT
ejpam-5446	142	47	if	if	SCONJ
ejpam-5446	142	48	|ς	|ς	PROPN
ejpam-5446	142	49	iv	iv	X
ejpam-5446	143	1	+	+	CCONJ
ejpam-5446	143	2	η1ς	η1ς	NOUN
ejpam-5446	143	3	′′′	′′′	NOUN
ejpam-5446	144	1	+	+	CCONJ
ejpam-5446	144	2	η2ς	η2ς	PROPN
ejpam-5446	144	3	′′	′′	PROPN
ejpam-5446	144	4	+	+	CCONJ
ejpam-5446	144	5	η3ς	η3ς	VERB
ejpam-5446	144	6	′	′	NOUN
ejpam-5446	145	1	+	+	CCONJ
ejpam-5446	145	2	η4ς|	η4ς|	PROPN
ejpam-5446	145	3	≤	≤	X
ejpam-5446	145	4	ε	ε	PROPN
ejpam-5446	145	5	,	,	PUNCT
ejpam-5446	145	6	(	(	PUNCT
ejpam-5446	145	7	1.8	1.8	NUM
ejpam-5446	145	8	)	)	PUNCT
ejpam-5446	145	9	as	as	ADP
ejpam-5446	145	10	such	such	ADJ
ejpam-5446	145	11	,	,	PUNCT
ejpam-5446	145	12	∃	∃	PROPN
ejpam-5446	145	13	u	u	PROPN
ejpam-5446	145	14	∈	∈	PROPN
ejpam-5446	145	15	c4[k	c4[k	NOUN
ejpam-5446	145	16	,	,	PUNCT
ejpam-5446	145	17	l	l	NOUN
ejpam-5446	145	18	]	]	X
ejpam-5446	145	19	that	that	PRON
ejpam-5446	145	20	satisfies	satisfy	VERB
ejpam-5446	145	21	:	:	PUNCT
ejpam-5446	145	22	|uiv	|uiv	NUM
ejpam-5446	145	23	+	+	PUNCT
ejpam-5446	145	24	η1u	η1u	PROPN
ejpam-5446	145	25	′′′	′′′	PROPN
ejpam-5446	145	26	+	+	CCONJ
ejpam-5446	145	27	η2u	η2u	PUNCT
ejpam-5446	145	28	′′	′′	NOUN
ejpam-5446	145	29	+	+	CCONJ
ejpam-5446	145	30	η3u	η3u	PROPN
ejpam-5446	145	31	′	′	NOUN
ejpam-5446	145	32	+	+	CCONJ
ejpam-5446	145	33	η4u|	η4u|	NOUN
ejpam-5446	145	34	=	=	SYM
ejpam-5446	145	35	0	0	NUM
ejpam-5446	145	36	,	,	PUNCT
ejpam-5446	145	37	(	(	PUNCT
ejpam-5446	145	38	1.9	1.9	NUM
ejpam-5446	145	39	)	)	PUNCT
ejpam-5446	145	40	such	such	ADJ
ejpam-5446	145	41	that	that	SCONJ
ejpam-5446	145	42	|ς(x)−	|ς(x)−	PROPN
ejpam-5446	145	43	u(x)|	u(x)|	PROPN
ejpam-5446	145	44	<	<	X
ejpam-5446	145	45	v1ϵ	v1ϵ	PROPN
ejpam-5446	145	46	,	,	PUNCT
ejpam-5446	145	47	where	where	SCONJ
ejpam-5446	145	48	v1	v1	NOUN
ejpam-5446	145	49	is	be	AUX
ejpam-5446	145	50	a	a	DET
ejpam-5446	145	51	stability	stability	NOUN
ejpam-5446	145	52	constant	constant	ADJ
ejpam-5446	145	53	for	for	ADP
ejpam-5446	145	54	(	(	PUNCT
ejpam-5446	145	55	1.8	1.8	NUM
ejpam-5446	145	56	)	)	PUNCT
ejpam-5446	145	57	.	.	PUNCT
ejpam-5446	146	1	definition:1.6	definition:1.6	NOUN
ejpam-5446	146	2	we	we	PRON
ejpam-5446	146	3	indicate	indicate	VERB
ejpam-5446	146	4	that	that	SCONJ
ejpam-5446	146	5	the	the	DET
ejpam-5446	146	6	augmentation	augmentation	NOUN
ejpam-5446	146	7	of	of	ADP
ejpam-5446	146	8	(	(	PUNCT
ejpam-5446	146	9	1.8	1.8	NUM
ejpam-5446	146	10	)	)	PUNCT
ejpam-5446	146	11	has	have	VERB
ejpam-5446	146	12	the	the	DET
ejpam-5446	146	13	hyers	hyers	PROPN
ejpam-5446	146	14	-	-	PUNCT
ejpam-5446	146	15	ulam	ulam	ADJ
ejpam-5446	146	16	stability	stability	NOUN
ejpam-5446	146	17	,	,	PUNCT
ejpam-5446	146	18	if	if	SCONJ
ejpam-5446	146	19	there	there	PRON
ejpam-5446	146	20	exists	exist	VERB
ejpam-5446	146	21	a	a	DET
ejpam-5446	146	22	consistent	consistent	ADJ
ejpam-5446	146	23	v1	v1	NOUN
ejpam-5446	146	24	>	>	X
ejpam-5446	146	25	0	0	PUNCT
ejpam-5446	146	26	with	with	ADP
ejpam-5446	146	27	the	the	DET
ejpam-5446	146	28	going	go	VERB
ejpam-5446	146	29	with	with	ADP
ejpam-5446	146	30	property	property	NOUN
ejpam-5446	146	31	,	,	PUNCT
ejpam-5446	146	32	for	for	ADP
ejpam-5446	146	33	each	each	DET
ejpam-5446	146	34	ε	ε	PROPN
ejpam-5446	146	35	>	>	X
ejpam-5446	146	36	0	0	PROPN
ejpam-5446	146	37	,	,	PUNCT
ejpam-5446	146	38	ς	ς	PROPN
ejpam-5446	146	39	∈	∈	PROPN
ejpam-5446	146	40	c5[k	c5[k	NOUN
ejpam-5446	146	41	,	,	PUNCT
ejpam-5446	146	42	l	l	NOUN
ejpam-5446	146	43	]	]	X
ejpam-5446	146	44	,	,	PUNCT
ejpam-5446	146	45	if	if	SCONJ
ejpam-5446	146	46	|ςv	|ςv	NOUN
ejpam-5446	146	47	+	+	X
ejpam-5446	146	48	η1ς	η1ς	NOUN
ejpam-5446	146	49	iv	iv	NOUN
ejpam-5446	146	50	+	+	CCONJ
ejpam-5446	146	51	η2ς	η2ς	PROPN
ejpam-5446	146	52	′′′	′′′	NOUN
ejpam-5446	146	53	+	+	PUNCT
ejpam-5446	146	54	η3ς	η3ς	VERB
ejpam-5446	146	55	′′	′′	PROPN
ejpam-5446	146	56	+	+	CCONJ
ejpam-5446	146	57	η4ς	η4ς	PROPN
ejpam-5446	146	58	′	′	VERB
ejpam-5446	147	1	+	+	PUNCT
ejpam-5446	147	2	η5ς|	η5ς|	X
ejpam-5446	147	3	≤	≤	X
ejpam-5446	147	4	ε	ε	PROPN
ejpam-5446	147	5	,	,	PUNCT
ejpam-5446	147	6	(	(	PUNCT
ejpam-5446	147	7	1.10	1.10	NUM
ejpam-5446	147	8	)	)	PUNCT
ejpam-5446	147	9	as	as	ADP
ejpam-5446	147	10	such	such	ADJ
ejpam-5446	147	11	,	,	PUNCT
ejpam-5446	147	12	∃	∃	PROPN
ejpam-5446	147	13	u	u	PROPN
ejpam-5446	147	14	∈	∈	PROPN
ejpam-5446	147	15	c5[k	c5[k	NOUN
ejpam-5446	147	16	,	,	PUNCT
ejpam-5446	147	17	l	l	NOUN
ejpam-5446	147	18	]	]	X
ejpam-5446	147	19	that	that	PRON
ejpam-5446	147	20	satisfies	satisfy	VERB
ejpam-5446	147	21	:	:	PUNCT
ejpam-5446	147	22	|uv	|uv	X
ejpam-5446	147	23	+	+	X
ejpam-5446	147	24	η1u	η1u	X
ejpam-5446	147	25	iv	iv	NUM
ejpam-5446	148	1	+	+	CCONJ
ejpam-5446	148	2	η2u	η2u	PROPN
ejpam-5446	148	3	′′′	′′′	PROPN
ejpam-5446	149	1	+	+	PUNCT
ejpam-5446	149	2	η3u	η3u	NOUN
ejpam-5446	149	3	′′	′′	PROPN
ejpam-5446	149	4	+	+	CCONJ
ejpam-5446	149	5	η4u	η4u	NOUN
ejpam-5446	149	6	′	′	NUM
ejpam-5446	150	1	+	+	CCONJ
ejpam-5446	150	2	η5u|	η5u|	ADJ
ejpam-5446	150	3	=	=	SYM
ejpam-5446	150	4	0	0	NUM
ejpam-5446	150	5	,	,	PUNCT
ejpam-5446	150	6	(	(	PUNCT
ejpam-5446	150	7	1.11	1.11	NUM
ejpam-5446	150	8	)	)	PUNCT
ejpam-5446	150	9	such	such	ADJ
ejpam-5446	150	10	that	that	SCONJ
ejpam-5446	150	11	|ς(x)−	|ς(x)−	PROPN
ejpam-5446	150	12	u(x)|	u(x)|	PROPN
ejpam-5446	150	13	<	<	X
ejpam-5446	150	14	v1ϵ	v1ϵ	PROPN
ejpam-5446	150	15	,	,	PUNCT
ejpam-5446	150	16	where	where	SCONJ
ejpam-5446	150	17	v1	v1	NOUN
ejpam-5446	150	18	is	be	AUX
ejpam-5446	150	19	a	a	DET
ejpam-5446	150	20	constant	constant	ADJ
ejpam-5446	150	21	for	for	ADP
ejpam-5446	150	22	(	(	PUNCT
ejpam-5446	150	23	1.10	1.10	NUM
ejpam-5446	150	24	)	)	PUNCT
ejpam-5446	150	25	.	.	PUNCT
ejpam-5446	151	1	v.	v.	ADP
ejpam-5446	151	2	govindan	govindan	PROPN
ejpam-5446	151	3	et	et	PROPN
ejpam-5446	151	4	al	al	PROPN
ejpam-5446	151	5	.	.	PUNCT
ejpam-5446	151	6	/	/	SYM
ejpam-5446	151	7	eur	eur	PROPN
ejpam-5446	151	8	.	.	PUNCT
ejpam-5446	152	1	j.	j.	PROPN
ejpam-5446	152	2	pure	pure	PROPN
ejpam-5446	152	3	appl	appl	PROPN
ejpam-5446	152	4	.	.	PROPN
ejpam-5446	152	5	math	math	PROPN
ejpam-5446	152	6	,	,	PUNCT
ejpam-5446	152	7	17	17	NUM
ejpam-5446	152	8	(	(	PUNCT
ejpam-5446	152	9	4	4	NUM
ejpam-5446	152	10	)	)	PUNCT
ejpam-5446	152	11	(	(	PUNCT
ejpam-5446	152	12	2024	2024	NUM
ejpam-5446	152	13	)	)	PUNCT
ejpam-5446	152	14	,	,	PUNCT
ejpam-5446	152	15	3585	3585	NUM
ejpam-5446	152	16	-	-	SYM
ejpam-5446	152	17	3609	3609	NUM
ejpam-5446	152	18	3591	3591	NUM
ejpam-5446	152	19	2	2	NUM
ejpam-5446	152	20	.	.	PUNCT
ejpam-5446	152	21	main	main	ADJ
ejpam-5446	152	22	results	result	NOUN
ejpam-5446	152	23	in	in	ADP
ejpam-5446	152	24	this	this	DET
ejpam-5446	152	25	section	section	NOUN
ejpam-5446	153	1	,	,	PUNCT
ejpam-5446	153	2	the	the	DET
ejpam-5446	153	3	authors	author	NOUN
ejpam-5446	153	4	discussed	discuss	VERB
ejpam-5446	153	5	hyers	hyers	PROPN
ejpam-5446	153	6	-	-	PUNCT
ejpam-5446	153	7	ulam	ulam	PROPN
ejpam-5446	153	8	stability	stability	NOUN
ejpam-5446	153	9	of	of	ADP
ejpam-5446	153	10	linear	linear	PROPN
ejpam-5446	153	11	differential	differential	ADJ
ejpam-5446	153	12	equation	equation	NOUN
ejpam-5446	153	13	and	and	CCONJ
ejpam-5446	153	14	also	also	ADV
ejpam-5446	153	15	the	the	DET
ejpam-5446	153	16	critical	critical	ADJ
ejpam-5446	153	17	consequences	consequence	NOUN
ejpam-5446	153	18	of	of	ADP
ejpam-5446	153	19	this	this	DET
ejpam-5446	153	20	investigation	investigation	NOUN
ejpam-5446	153	21	are	be	AUX
ejpam-5446	153	22	given	give	VERB
ejpam-5446	153	23	in	in	ADP
ejpam-5446	153	24	the	the	DET
ejpam-5446	153	25	accompanying	accompanying	ADJ
ejpam-5446	153	26	hypothesis	hypothesis	NOUN
ejpam-5446	153	27	.	.	PUNCT
ejpam-5446	154	1	lemma	lemma	PROPN
ejpam-5446	154	2	2.1.the	2.1.the	DET
ejpam-5446	154	3	differential	differential	ADJ
ejpam-5446	154	4	equation	equation	NOUN
ejpam-5446	154	5	ςv(x	ςv(x	NUM
ejpam-5446	154	6	)	)	PUNCT
ejpam-5446	155	1	+	+	CCONJ
ejpam-5446	155	2	η1ς	η1ς	NOUN
ejpam-5446	155	3	iv(x	iv(x	NUM
ejpam-5446	155	4	)	)	PUNCT
ejpam-5446	155	5	+	+	CCONJ
ejpam-5446	155	6	η2ς	η2ς	PROPN
ejpam-5446	155	7	′′′	′′′	PROPN
ejpam-5446	155	8	(	(	PUNCT
ejpam-5446	155	9	x	x	X
ejpam-5446	155	10	)	)	PUNCT
ejpam-5446	155	11	+	+	CCONJ
ejpam-5446	155	12	η3ς	η3ς	PROPN
ejpam-5446	155	13	′′	′′	PROPN
ejpam-5446	155	14	(	(	PUNCT
ejpam-5446	155	15	x	x	X
ejpam-5446	155	16	)	)	PUNCT
ejpam-5446	155	17	+	+	CCONJ
ejpam-5446	155	18	η4ς	η4ς	PROPN
ejpam-5446	155	19	′	′	NUM
ejpam-5446	155	20	(	(	PUNCT
ejpam-5446	155	21	x	x	X
ejpam-5446	155	22	)	)	PUNCT
ejpam-5446	155	23	+	+	CCONJ
ejpam-5446	155	24	η5ς(x	η5ς(x	ADJ
ejpam-5446	155	25	)	)	PUNCT
ejpam-5446	155	26	=	=	SYM
ejpam-5446	155	27	ω(x	ω(x	NOUN
ejpam-5446	155	28	)	)	PUNCT
ejpam-5446	155	29	has	have	VERB
ejpam-5446	155	30	the	the	DET
ejpam-5446	155	31	hyers	hyer	NOUN
ejpam-5446	155	32	ulam	ulam	PROPN
ejpam-5446	155	33	stability	stability	PROPN
ejpam-5446	155	34	,	,	PUNCT
ejpam-5446	155	35	where	where	SCONJ
ejpam-5446	155	36	ς	ς	PROPN
ejpam-5446	155	37	∈	∈	PROPN
ejpam-5446	155	38	c5[k	c5[k	NOUN
ejpam-5446	155	39	,	,	PUNCT
ejpam-5446	155	40	l	l	NOUN
ejpam-5446	155	41	]	]	PUNCT
ejpam-5446	155	42	and	and	CCONJ
ejpam-5446	155	43	ω	ω	NUM
ejpam-5446	155	44	∈	∈	PROPN
ejpam-5446	155	45	[	[	X
ejpam-5446	155	46	a	a	X
ejpam-5446	155	47	,	,	PUNCT
ejpam-5446	155	48	b	b	NOUN
ejpam-5446	155	49	]	]	PUNCT
ejpam-5446	155	50	.	.	PUNCT
ejpam-5446	156	1	proof	proof	NOUN
ejpam-5446	156	2	:	:	PUNCT
ejpam-5446	156	3	suppose	suppose	VERB
ejpam-5446	156	4	that	that	SCONJ
ejpam-5446	156	5	v1	v1	NOUN
ejpam-5446	156	6	,	,	PUNCT
ejpam-5446	156	7	v2	v2	PROPN
ejpam-5446	156	8	,	,	PUNCT
ejpam-5446	156	9	v3	v3	PROPN
ejpam-5446	156	10	,	,	PUNCT
ejpam-5446	156	11	v4	v4	PROPN
ejpam-5446	156	12	,	,	PUNCT
ejpam-5446	156	13	v5	v5	PROPN
ejpam-5446	156	14	are	be	AUX
ejpam-5446	156	15	the	the	DET
ejpam-5446	156	16	(	(	PUNCT
ejpam-5446	156	17	real	real	ADJ
ejpam-5446	156	18	or	or	CCONJ
ejpam-5446	156	19	complex	complex	ADJ
ejpam-5446	156	20	)	)	PUNCT
ejpam-5446	156	21	roots	root	NOUN
ejpam-5446	156	22	ofm5+η1	ofm5+η1	PROPN
ejpam-5446	156	23	m	m	PROPN
ejpam-5446	156	24	5+η1	5+η1	NUM
ejpam-5446	156	25	m	m	NOUN
ejpam-5446	156	26	4	4	NUM
ejpam-5446	156	27	+	+	NUM
ejpam-5446	156	28	η2	η2	PROPN
ejpam-5446	156	29	m	m	VERB
ejpam-5446	156	30	3	3	NUM
ejpam-5446	156	31	+	+	NUM
ejpam-5446	156	32	η3	η3	NOUN
ejpam-5446	156	33	m	m	VERB
ejpam-5446	156	34	2	2	NUM
ejpam-5446	156	35	+	+	NUM
ejpam-5446	156	36	η4m+	η4m+	PROPN
ejpam-5446	156	37	η5	η5	NOUN
ejpam-5446	156	38	=	=	NOUN
ejpam-5446	156	39	0	0	NUM
ejpam-5446	156	40	with	with	ADP
ejpam-5446	156	41	p1	p1	NOUN
ejpam-5446	156	42	=	=	SYM
ejpam-5446	156	43	ℜv1	ℜv1	NOUN
ejpam-5446	156	44	,	,	PUNCT
ejpam-5446	156	45	p2	p2	PROPN
ejpam-5446	156	46	=	=	PUNCT
ejpam-5446	156	47	ℜv2	ℜv2	NOUN
ejpam-5446	156	48	,	,	PUNCT
ejpam-5446	156	49	p3	p3	PROPN
ejpam-5446	156	50	=	=	PUNCT
ejpam-5446	156	51	ℜv4	ℜv4	ADJ
ejpam-5446	156	52	,	,	PUNCT
ejpam-5446	156	53	p4	p4	ADJ
ejpam-5446	156	54	=	=	NOUN
ejpam-5446	156	55	ℜv3	ℜv3	NOUN
ejpam-5446	156	56	,	,	PUNCT
ejpam-5446	156	57	p5	p5	ADJ
ejpam-5446	156	58	=	=	NOUN
ejpam-5446	156	59	ℜv5	ℜv5	NOUN
ejpam-5446	156	60	.	.	PUNCT
ejpam-5446	157	1	here	here	ADV
ejpam-5446	157	2	ℜ	ℜ	ADJ
ejpam-5446	157	3	denotes	denote	VERB
ejpam-5446	157	4	the	the	DET
ejpam-5446	157	5	real	real	ADJ
ejpam-5446	157	6	part	part	NOUN
ejpam-5446	157	7	.	.	PUNCT
ejpam-5446	158	1	let	let	VERB
ejpam-5446	158	2	ε	ε	PROPN
ejpam-5446	158	3	>	>	X
ejpam-5446	158	4	0	0	PROPN
ejpam-5446	159	1	and	and	CCONJ
ejpam-5446	159	2	ς	ς	PROPN
ejpam-5446	159	3	∈	∈	PROPN
ejpam-5446	159	4	c5[k	c5[k	NOUN
ejpam-5446	159	5	,	,	PUNCT
ejpam-5446	159	6	l	l	NOUN
ejpam-5446	159	7	]	]	PUNCT
ejpam-5446	159	8	with	with	ADP
ejpam-5446	159	9	|ςv(x	|ςv(x	NUM
ejpam-5446	159	10	)	)	PUNCT
ejpam-5446	160	1	+	+	CCONJ
ejpam-5446	160	2	η1ς	η1ς	NOUN
ejpam-5446	160	3	iv(x	iv(x	NUM
ejpam-5446	160	4	)	)	PUNCT
ejpam-5446	160	5	+	+	CCONJ
ejpam-5446	160	6	η2ς	η2ς	PROPN
ejpam-5446	160	7	′′′	′′′	PROPN
ejpam-5446	160	8	(	(	PUNCT
ejpam-5446	160	9	x	x	X
ejpam-5446	160	10	)	)	PUNCT
ejpam-5446	160	11	+	+	CCONJ
ejpam-5446	160	12	η3ς	η3ς	PROPN
ejpam-5446	160	13	′′	′′	PROPN
ejpam-5446	160	14	(	(	PUNCT
ejpam-5446	160	15	x	x	X
ejpam-5446	160	16	)	)	PUNCT
ejpam-5446	160	17	+	+	CCONJ
ejpam-5446	160	18	η4ς	η4ς	PROPN
ejpam-5446	160	19	′	′	NUM
ejpam-5446	160	20	(	(	PUNCT
ejpam-5446	160	21	x	x	X
ejpam-5446	160	22	)	)	PUNCT
ejpam-5446	160	23	+	+	CCONJ
ejpam-5446	160	24	η5ς(x)−	η5ς(x)−	PROPN
ejpam-5446	160	25	ω(x)|	ω(x)|	X
ejpam-5446	160	26	=	=	SYM
ejpam-5446	160	27	0	0	PUNCT
ejpam-5446	160	28	(	(	PUNCT
ejpam-5446	160	29	2.1	2.1	NUM
ejpam-5446	160	30	)	)	PUNCT
ejpam-5446	160	31	and	and	CCONJ
ejpam-5446	160	32	let	let	VERB
ejpam-5446	160	33	g(x	g(x	NOUN
ejpam-5446	160	34	)	)	PUNCT
ejpam-5446	160	35	=	=	SYM
ejpam-5446	160	36	ς	ς	PROPN
ejpam-5446	160	37	iv(x	iv(x	NOUN
ejpam-5446	160	38	)	)	PUNCT
ejpam-5446	160	39	+	+	CCONJ
ejpam-5446	160	40	(	(	PUNCT
ejpam-5446	160	41	v1	v1	VERB
ejpam-5446	160	42	+	+	CCONJ
ejpam-5446	160	43	η1)ς	η1)ς	NOUN
ejpam-5446	160	44	′′′	′′′	PROPN
ejpam-5446	160	45	(	(	PUNCT
ejpam-5446	160	46	x	x	X
ejpam-5446	160	47	)	)	PUNCT
ejpam-5446	160	48	+	+	CCONJ
ejpam-5446	160	49	(	(	PUNCT
ejpam-5446	160	50	v21	v21	X
ejpam-5446	160	51	+	+	CCONJ
ejpam-5446	160	52	η1v1	η1v1	ADJ
ejpam-5446	160	53	+	+	NUM
ejpam-5446	160	54	η2)ς	η2)ς	NOUN
ejpam-5446	160	55	′′	′′	PROPN
ejpam-5446	160	56	(	(	PUNCT
ejpam-5446	160	57	x	x	X
ejpam-5446	160	58	)	)	PUNCT
ejpam-5446	160	59	+	+	ADJ
ejpam-5446	160	60	(	(	PUNCT
ejpam-5446	160	61	v31	v31	PROPN
ejpam-5446	160	62	+	+	CCONJ
ejpam-5446	160	63	η1v	η1v	NOUN
ejpam-5446	160	64	2	2	NUM
ejpam-5446	160	65	1	1	NUM
ejpam-5446	160	66	+	+	NUM
ejpam-5446	160	67	η2v1	η2v1	NOUN
ejpam-5446	160	68	+	+	NUM
ejpam-5446	160	69	η3)ς	η3)ς	NOUN
ejpam-5446	160	70	′	′	NUM
ejpam-5446	160	71	(	(	PUNCT
ejpam-5446	160	72	x)+	x)+	NUM
ejpam-5446	160	73	(	(	PUNCT
ejpam-5446	160	74	v41	v41	NOUN
ejpam-5446	160	75	+	+	CCONJ
ejpam-5446	160	76	η1v	η1v	NOUN
ejpam-5446	160	77	3	3	NUM
ejpam-5446	160	78	1	1	NUM
ejpam-5446	160	79	+	+	CCONJ
ejpam-5446	160	80	η2v	η2v	PROPN
ejpam-5446	160	81	2	2	NUM
ejpam-5446	160	82	1	1	NUM
ejpam-5446	160	83	+	+	CCONJ
ejpam-5446	160	84	η3v1	η3v1	SYM
ejpam-5446	160	85	+	+	NUM
ejpam-5446	160	86	η4)ς(x	η4)ς(x	NUM
ejpam-5446	160	87	)	)	PUNCT
ejpam-5446	160	88	.	.	PUNCT
ejpam-5446	161	1	(	(	PUNCT
ejpam-5446	161	2	2.2	2.2	NUM
ejpam-5446	161	3	)	)	PUNCT
ejpam-5446	161	4	then	then	ADV
ejpam-5446	161	5	we	we	PRON
ejpam-5446	161	6	obtain	obtain	VERB
ejpam-5446	161	7	g′(x	g′(x	NOUN
ejpam-5446	161	8	)	)	PUNCT
ejpam-5446	161	9	=	=	PUNCT
ejpam-5446	162	1	ςv(x	ςv(x	NUM
ejpam-5446	162	2	)	)	PUNCT
ejpam-5446	162	3	+	+	CCONJ
ejpam-5446	162	4	(	(	PUNCT
ejpam-5446	162	5	v1	v1	VERB
ejpam-5446	162	6	+	+	CCONJ
ejpam-5446	162	7	η1)ς	η1)ς	NOUN
ejpam-5446	162	8	iv(x	iv(x	NOUN
ejpam-5446	162	9	)	)	PUNCT
ejpam-5446	163	1	+	+	CCONJ
ejpam-5446	163	2	(	(	PUNCT
ejpam-5446	163	3	v21	v21	X
ejpam-5446	163	4	+	+	CCONJ
ejpam-5446	163	5	η1v1	η1v1	ADJ
ejpam-5446	163	6	+	+	NUM
ejpam-5446	163	7	η2)ς	η2)ς	ADJ
ejpam-5446	163	8	′′′	′′′	PROPN
ejpam-5446	163	9	(	(	PUNCT
ejpam-5446	163	10	x	x	X
ejpam-5446	163	11	)	)	PUNCT
ejpam-5446	163	12	+	+	ADJ
ejpam-5446	163	13	(	(	PUNCT
ejpam-5446	163	14	v31	v31	PROPN
ejpam-5446	163	15	+	+	CCONJ
ejpam-5446	163	16	η1v	η1v	NOUN
ejpam-5446	163	17	2	2	NUM
ejpam-5446	163	18	1	1	NUM
ejpam-5446	164	1	+	+	NUM
ejpam-5446	164	2	η2v1	η2v1	NOUN
ejpam-5446	164	3	+	+	NUM
ejpam-5446	164	4	η3)ς	η3)ς	NOUN
ejpam-5446	164	5	′′	′′	PROPN
ejpam-5446	164	6	(	(	PUNCT
ejpam-5446	164	7	x	x	X
ejpam-5446	164	8	)	)	PUNCT
ejpam-5446	165	1	+	+	CCONJ
ejpam-5446	165	2	(	(	PUNCT
ejpam-5446	165	3	v41	v41	NOUN
ejpam-5446	165	4	+	+	CCONJ
ejpam-5446	165	5	η1v	η1v	NOUN
ejpam-5446	165	6	3	3	NUM
ejpam-5446	165	7	1	1	NUM
ejpam-5446	165	8	+	+	CCONJ
ejpam-5446	165	9	η2v	η2v	PROPN
ejpam-5446	165	10	2	2	NUM
ejpam-5446	165	11	1	1	NUM
ejpam-5446	165	12	+	+	CCONJ
ejpam-5446	165	13	η3v1	η3v1	PUNCT
ejpam-5446	165	14	+	+	CCONJ
ejpam-5446	165	15	η4)ς	η4)ς	ADJ
ejpam-5446	165	16	′	′	NUM
ejpam-5446	165	17	(	(	PUNCT
ejpam-5446	165	18	x	x	X
ejpam-5446	165	19	)	)	PUNCT
ejpam-5446	166	1	+	+	ADJ
ejpam-5446	166	2	(	(	PUNCT
ejpam-5446	166	3	v51	v51	NOUN
ejpam-5446	166	4	+	+	CCONJ
ejpam-5446	166	5	η1v	η1v	NOUN
ejpam-5446	166	6	4	4	NUM
ejpam-5446	166	7	1	1	NUM
ejpam-5446	166	8	+	+	CCONJ
ejpam-5446	166	9	η2v	η2v	PROPN
ejpam-5446	166	10	3	3	NUM
ejpam-5446	166	11	1	1	NUM
ejpam-5446	166	12	+	+	NUM
ejpam-5446	166	13	η3v	η3v	VERB
ejpam-5446	166	14	2	2	NUM
ejpam-5446	166	15	1	1	NUM
ejpam-5446	166	16	+	+	NUM
ejpam-5446	166	17	η4v1	η4v1	NOUN
ejpam-5446	166	18	+	+	CCONJ
ejpam-5446	166	19	η5)ς(x	η5)ς(x	PROPN
ejpam-5446	166	20	)	)	PUNCT
ejpam-5446	166	21	,	,	PUNCT
ejpam-5446	166	22	(	(	PUNCT
ejpam-5446	166	23	2.3	2.3	NUM
ejpam-5446	166	24	)	)	PUNCT
ejpam-5446	166	25	∀	∀	X
ejpam-5446	167	1	x	x	X
ejpam-5446	167	2	∈	∈	PROPN
ejpam-5446	168	1	[	[	X
ejpam-5446	168	2	k	k	X
ejpam-5446	168	3	,	,	PUNCT
ejpam-5446	168	4	l	l	NOUN
ejpam-5446	168	5	]	]	PUNCT
ejpam-5446	168	6	and	and	CCONJ
ejpam-5446	168	7	|g′(x)−	|g′(x)−	PROPN
ejpam-5446	168	8	v1g(x)−	v1g(x)−	PROPN
ejpam-5446	168	9	ω(x)|	ω(x)|	PRON
ejpam-5446	168	10	≤	≤	ADJ
ejpam-5446	168	11	ε	ε	PROPN
ejpam-5446	168	12	(	(	PUNCT
ejpam-5446	168	13	2.4	2.4	NUM
ejpam-5446	168	14	)	)	PUNCT
ejpam-5446	168	15	|g′(x)−	|g′(x)−	NOUN
ejpam-5446	168	16	v1g(x)−	v1g(x)−	PROPN
ejpam-5446	168	17	ω(x)|	ω(x)|	X
ejpam-5446	168	18	=	=	PUNCT
ejpam-5446	168	19	|ςv(x	|ςv(x	X
ejpam-5446	168	20	)	)	PUNCT
ejpam-5446	169	1	+	+	CCONJ
ejpam-5446	169	2	(	(	PUNCT
ejpam-5446	169	3	v1	v1	VERB
ejpam-5446	169	4	+	+	CCONJ
ejpam-5446	169	5	η1)ς	η1)ς	NOUN
ejpam-5446	169	6	iv(x	iv(x	NOUN
ejpam-5446	169	7	)	)	PUNCT
ejpam-5446	170	1	+	+	CCONJ
ejpam-5446	170	2	(	(	PUNCT
ejpam-5446	170	3	v21	v21	X
ejpam-5446	170	4	+	+	CCONJ
ejpam-5446	170	5	η1v1	η1v1	ADJ
ejpam-5446	170	6	+	+	NUM
ejpam-5446	170	7	η2)ς	η2)ς	ADJ
ejpam-5446	170	8	′′′	′′′	PROPN
ejpam-5446	170	9	(	(	PUNCT
ejpam-5446	170	10	x	x	X
ejpam-5446	170	11	)	)	PUNCT
ejpam-5446	170	12	+	+	ADJ
ejpam-5446	170	13	(	(	PUNCT
ejpam-5446	170	14	v31	v31	PROPN
ejpam-5446	170	15	+	+	CCONJ
ejpam-5446	170	16	η1v	η1v	NOUN
ejpam-5446	170	17	2	2	NUM
ejpam-5446	170	18	1	1	NUM
ejpam-5446	171	1	+	+	NUM
ejpam-5446	171	2	η2v1	η2v1	NOUN
ejpam-5446	171	3	+	+	NUM
ejpam-5446	171	4	η3)ς	η3)ς	NOUN
ejpam-5446	171	5	′′	′′	PROPN
ejpam-5446	171	6	(	(	PUNCT
ejpam-5446	171	7	x	x	X
ejpam-5446	171	8	)	)	PUNCT
ejpam-5446	172	1	+	+	CCONJ
ejpam-5446	172	2	(	(	PUNCT
ejpam-5446	172	3	v41	v41	NOUN
ejpam-5446	172	4	+	+	CCONJ
ejpam-5446	172	5	η1v	η1v	NOUN
ejpam-5446	172	6	3	3	NUM
ejpam-5446	172	7	1	1	NUM
ejpam-5446	172	8	+	+	CCONJ
ejpam-5446	172	9	η2v	η2v	PROPN
ejpam-5446	172	10	2	2	NUM
ejpam-5446	172	11	1	1	NUM
ejpam-5446	172	12	+	+	CCONJ
ejpam-5446	172	13	η3v1	η3v1	PUNCT
ejpam-5446	172	14	+	+	CCONJ
ejpam-5446	172	15	η4)ς	η4)ς	ADJ
ejpam-5446	172	16	′	′	NUM
ejpam-5446	172	17	(	(	PUNCT
ejpam-5446	172	18	x	x	X
ejpam-5446	172	19	)	)	PUNCT
ejpam-5446	173	1	+	+	ADJ
ejpam-5446	173	2	(	(	PUNCT
ejpam-5446	173	3	v51	v51	NOUN
ejpam-5446	173	4	+	+	CCONJ
ejpam-5446	173	5	η1v	η1v	NOUN
ejpam-5446	173	6	4	4	NUM
ejpam-5446	173	7	1	1	NUM
ejpam-5446	173	8	+	+	CCONJ
ejpam-5446	173	9	η2v	η2v	PROPN
ejpam-5446	173	10	3	3	NUM
ejpam-5446	173	11	1	1	NUM
ejpam-5446	173	12	+	+	NUM
ejpam-5446	173	13	η3v	η3v	VERB
ejpam-5446	173	14	2	2	NUM
ejpam-5446	173	15	1	1	NUM
ejpam-5446	173	16	+	+	NUM
ejpam-5446	173	17	η4v1	η4v1	NOUN
ejpam-5446	174	1	+	+	NUM
ejpam-5446	174	2	η5)ς(x)−	η5)ς(x)−	PROPN
ejpam-5446	174	3	v1[ς	v1[ς	X
ejpam-5446	174	4	iv(x	iv(x	PUNCT
ejpam-5446	174	5	)	)	PUNCT
ejpam-5446	175	1	+	+	CCONJ
ejpam-5446	175	2	(	(	PUNCT
ejpam-5446	175	3	v1	v1	VERB
ejpam-5446	175	4	+	+	CCONJ
ejpam-5446	175	5	η1)ς	η1)ς	NOUN
ejpam-5446	175	6	′′′	′′′	PROPN
ejpam-5446	175	7	(	(	PUNCT
ejpam-5446	175	8	x	x	X
ejpam-5446	175	9	)	)	PUNCT
ejpam-5446	176	1	+	+	ADJ
ejpam-5446	176	2	(	(	PUNCT
ejpam-5446	176	3	v21	v21	NOUN
ejpam-5446	176	4	+	+	CCONJ
ejpam-5446	176	5	η1v1	η1v1	ADJ
ejpam-5446	176	6	+	+	NUM
ejpam-5446	176	7	η2)ς	η2)ς	NOUN
ejpam-5446	176	8	′′	′′	PROPN
ejpam-5446	176	9	(	(	PUNCT
ejpam-5446	176	10	x	x	X
ejpam-5446	176	11	)	)	PUNCT
ejpam-5446	176	12	+	+	CCONJ
ejpam-5446	176	13	(	(	PUNCT
ejpam-5446	176	14	v31	v31	NOUN
ejpam-5446	176	15	+	+	CCONJ
ejpam-5446	176	16	η1v	η1v	NOUN
ejpam-5446	176	17	2	2	NUM
ejpam-5446	176	18	1	1	NUM
ejpam-5446	176	19	+	+	CCONJ
ejpam-5446	176	20	η2v1	η2v1	NOUN
ejpam-5446	176	21	+	+	CCONJ
ejpam-5446	176	22	η4)ς	η4)ς	VERB
ejpam-5446	176	23	′	′	NUM
ejpam-5446	176	24	(	(	PUNCT
ejpam-5446	176	25	x	x	X
ejpam-5446	176	26	)	)	PUNCT
ejpam-5446	177	1	+	+	ADJ
ejpam-5446	177	2	(	(	PUNCT
ejpam-5446	177	3	v41	v41	NOUN
ejpam-5446	177	4	+	+	CCONJ
ejpam-5446	177	5	η1v	η1v	NOUN
ejpam-5446	177	6	3	3	NUM
ejpam-5446	177	7	1	1	NUM
ejpam-5446	177	8	+	+	CCONJ
ejpam-5446	177	9	η2v	η2v	PROPN
ejpam-5446	177	10	2	2	NUM
ejpam-5446	177	11	1	1	NUM
ejpam-5446	177	12	+	+	CCONJ
ejpam-5446	177	13	η3v1	η3v1	PUNCT
ejpam-5446	177	14	+	+	NUM
ejpam-5446	177	15	η4)ς(x)]−	η4)ς(x)]−	X
ejpam-5446	177	16	ω(x)|	ω(x)|	X
ejpam-5446	177	17	(	(	PUNCT
ejpam-5446	177	18	2.5	2.5	NUM
ejpam-5446	177	19	)	)	PUNCT
ejpam-5446	177	20	|g′(x)−	|g′(x)−	PROPN
ejpam-5446	177	21	v1g(x)−	v1g(x)−	PROPN
ejpam-5446	177	22	ω(x)|	ω(x)|	X
ejpam-5446	177	23	=	=	PUNCT
ejpam-5446	177	24	|ςv(x	|ςv(x	X
ejpam-5446	177	25	)	)	PUNCT
ejpam-5446	178	1	+	+	CCONJ
ejpam-5446	178	2	v1ς	v1ς	NOUN
ejpam-5446	178	3	iv(x	iv(x	NOUN
ejpam-5446	178	4	)	)	PUNCT
ejpam-5446	178	5	+	+	CCONJ
ejpam-5446	178	6	η1ς	η1ς	NOUN
ejpam-5446	178	7	iv(x	iv(x	NUM
ejpam-5446	178	8	)	)	PUNCT
ejpam-5446	178	9	+	+	CCONJ
ejpam-5446	178	10	v21ς	v21ς	ADJ
ejpam-5446	178	11	′′′	′′′	PROPN
ejpam-5446	178	12	(	(	PUNCT
ejpam-5446	178	13	x)+	x)+	PROPN
ejpam-5446	178	14	η1v1ς	η1v1ς	NUM
ejpam-5446	178	15	′′′	′′′	PROPN
ejpam-5446	178	16	(	(	PUNCT
ejpam-5446	178	17	x	x	X
ejpam-5446	178	18	)	)	PUNCT
ejpam-5446	178	19	+	+	CCONJ
ejpam-5446	178	20	η2ς	η2ς	PROPN
ejpam-5446	178	21	′′′	′′′	PROPN
ejpam-5446	178	22	(	(	PUNCT
ejpam-5446	178	23	x	x	X
ejpam-5446	178	24	)	)	PUNCT
ejpam-5446	178	25	+	+	CCONJ
ejpam-5446	178	26	v31ς	v31ς	ADV
ejpam-5446	179	1	′′	′′	PROPN
ejpam-5446	179	2	(	(	PUNCT
ejpam-5446	179	3	x	x	X
ejpam-5446	179	4	)	)	PUNCT
ejpam-5446	179	5	+	+	NUM
ejpam-5446	179	6	η1v	η1v	NOUN
ejpam-5446	179	7	2	2	NUM
ejpam-5446	179	8	1ς	1ς	NOUN
ejpam-5446	179	9	′′	′′	PROPN
ejpam-5446	179	10	(	(	PUNCT
ejpam-5446	179	11	x)+	x)+	NUM
ejpam-5446	179	12	η2v1ς	η2v1ς	PUNCT
ejpam-5446	179	13	′′	′′	PROPN
ejpam-5446	179	14	(	(	PUNCT
ejpam-5446	179	15	x	x	X
ejpam-5446	179	16	)	)	PUNCT
ejpam-5446	179	17	+	+	CCONJ
ejpam-5446	179	18	η3ς	η3ς	PROPN
ejpam-5446	179	19	′′	′′	PROPN
ejpam-5446	179	20	(	(	PUNCT
ejpam-5446	179	21	x	x	X
ejpam-5446	179	22	)	)	PUNCT
ejpam-5446	179	23	+	+	CCONJ
ejpam-5446	179	24	v41ς	v41ς	X
ejpam-5446	180	1	′	′	NUM
ejpam-5446	180	2	(	(	PUNCT
ejpam-5446	180	3	x	x	X
ejpam-5446	180	4	)	)	PUNCT
ejpam-5446	180	5	+	+	NUM
ejpam-5446	180	6	η1v	η1v	NOUN
ejpam-5446	180	7	3	3	NUM
ejpam-5446	180	8	1ς	1ς	NOUN
ejpam-5446	180	9	′	′	NUM
ejpam-5446	180	10	(	(	PUNCT
ejpam-5446	180	11	x	x	X
ejpam-5446	180	12	)	)	PUNCT
ejpam-5446	180	13	+	+	ADJ
ejpam-5446	180	14	η2v	η2v	PROPN
ejpam-5446	180	15	2	2	NUM
ejpam-5446	180	16	1ς	1ς	NOUN
ejpam-5446	180	17	′	′	NUM
ejpam-5446	180	18	(	(	PUNCT
ejpam-5446	180	19	x	x	X
ejpam-5446	180	20	)	)	PUNCT
ejpam-5446	180	21	+	+	NUM
ejpam-5446	180	22	η3v1ς	η3v1ς	NUM
ejpam-5446	180	23	′	′	NUM
ejpam-5446	180	24	(	(	PUNCT
ejpam-5446	180	25	x	x	X
ejpam-5446	180	26	)	)	PUNCT
ejpam-5446	180	27	+	+	CCONJ
ejpam-5446	180	28	η4ς	η4ς	PROPN
ejpam-5446	180	29	′	′	NUM
ejpam-5446	180	30	(	(	PUNCT
ejpam-5446	180	31	x	x	X
ejpam-5446	180	32	)	)	PUNCT
ejpam-5446	180	33	+	+	CCONJ
ejpam-5446	180	34	v51ς(x)+	v51ς(x)+	X
ejpam-5446	180	35	η1v	η1v	NOUN
ejpam-5446	180	36	4	4	NUM
ejpam-5446	180	37	1ς(x	1ς(x	NUM
ejpam-5446	180	38	)	)	PUNCT
ejpam-5446	181	1	+	+	CCONJ
ejpam-5446	181	2	η2v	η2v	PROPN
ejpam-5446	181	3	3	3	NUM
ejpam-5446	181	4	1ς(x	1ς(x	NUM
ejpam-5446	181	5	)	)	PUNCT
ejpam-5446	182	1	+	+	CCONJ
ejpam-5446	182	2	η3v	η3v	VERB
ejpam-5446	182	3	2	2	NUM
ejpam-5446	182	4	1ς(x	1ς(x	NUM
ejpam-5446	182	5	)	)	PUNCT
ejpam-5446	183	1	+	+	NUM
ejpam-5446	183	2	η4v1ς(x)+	η4v1ς(x)+	NOUN
ejpam-5446	183	3	η5ς(x)−	η5ς(x)−	PROPN
ejpam-5446	183	4	v1[ς	v1[ς	ADV
ejpam-5446	183	5	iv(x	iv(x	PRON
ejpam-5446	183	6	)	)	PUNCT
ejpam-5446	184	1	+	+	CCONJ
ejpam-5446	184	2	v1ς	v1ς	PROPN
ejpam-5446	184	3	′′′	′′′	PROPN
ejpam-5446	184	4	(	(	PUNCT
ejpam-5446	184	5	x	x	X
ejpam-5446	184	6	)	)	PUNCT
ejpam-5446	185	1	+	+	CCONJ
ejpam-5446	185	2	η1ς	η1ς	NOUN
ejpam-5446	185	3	′′′	′′′	NOUN
ejpam-5446	185	4	(	(	PUNCT
ejpam-5446	185	5	x	x	X
ejpam-5446	185	6	)	)	PUNCT
ejpam-5446	185	7	+	+	ADJ
ejpam-5446	185	8	v21ς	v21ς	NOUN
ejpam-5446	185	9	′′	′′	PROPN
ejpam-5446	185	10	(	(	PUNCT
ejpam-5446	185	11	x	x	X
ejpam-5446	185	12	)	)	PUNCT
ejpam-5446	185	13	+	+	NUM
ejpam-5446	185	14	η1v1ς	η1v1ς	PUNCT
ejpam-5446	186	1	′′	′′	PROPN
ejpam-5446	186	2	(	(	PUNCT
ejpam-5446	186	3	x	x	X
ejpam-5446	186	4	)	)	PUNCT
ejpam-5446	186	5	+	+	CCONJ
ejpam-5446	186	6	η2ς	η2ς	PROPN
ejpam-5446	186	7	′′	′′	PROPN
ejpam-5446	186	8	(	(	PUNCT
ejpam-5446	186	9	x	x	X
ejpam-5446	186	10	)	)	PUNCT
ejpam-5446	186	11	+	+	CCONJ
ejpam-5446	186	12	v31ς	v31ς	ADP
ejpam-5446	186	13	′	′	NUM
ejpam-5446	186	14	(	(	PUNCT
ejpam-5446	186	15	x)+	x)+	NUM
ejpam-5446	186	16	η1v	η1v	NOUN
ejpam-5446	186	17	2	2	NUM
ejpam-5446	186	18	1ς	1ς	NOUN
ejpam-5446	186	19	′	′	NUM
ejpam-5446	186	20	(	(	PUNCT
ejpam-5446	186	21	x	x	X
ejpam-5446	186	22	)	)	PUNCT
ejpam-5446	186	23	+	+	NUM
ejpam-5446	186	24	η2v1ς	η2v1ς	NUM
ejpam-5446	186	25	′	′	NUM
ejpam-5446	186	26	(	(	PUNCT
ejpam-5446	186	27	x	x	X
ejpam-5446	186	28	)	)	PUNCT
ejpam-5446	186	29	+	+	CCONJ
ejpam-5446	186	30	η3ς	η3ς	NOUN
ejpam-5446	186	31	′	′	NUM
ejpam-5446	186	32	(	(	PUNCT
ejpam-5446	186	33	x	x	X
ejpam-5446	186	34	)	)	PUNCT
ejpam-5446	186	35	+	+	CCONJ
ejpam-5446	186	36	v41ς(x)+	v41ς(x)+	X
ejpam-5446	186	37	η1v	η1v	NOUN
ejpam-5446	186	38	3	3	NUM
ejpam-5446	186	39	1ς(x	1ς(x	NUM
ejpam-5446	186	40	)	)	PUNCT
ejpam-5446	187	1	+	+	CCONJ
ejpam-5446	187	2	η2v	η2v	PROPN
ejpam-5446	187	3	2	2	NUM
ejpam-5446	187	4	1ς(x	1ς(x	NUM
ejpam-5446	187	5	)	)	PUNCT
ejpam-5446	188	1	+	+	PUNCT
ejpam-5446	188	2	η3v1ς(x	η3v1ς(x	X
ejpam-5446	188	3	)	)	PUNCT
ejpam-5446	188	4	+	+	NUM
ejpam-5446	188	5	η4ς(x)]−	η4ς(x)]−	NOUN
ejpam-5446	188	6	ω(x)|	ω(x)|	X
ejpam-5446	188	7	(	(	PUNCT
ejpam-5446	188	8	2.6	2.6	NUM
ejpam-5446	188	9	)	)	PUNCT
ejpam-5446	188	10	v.	v.	ADP
ejpam-5446	188	11	govindan	govindan	PROPN
ejpam-5446	188	12	et	et	PROPN
ejpam-5446	188	13	al	al	PROPN
ejpam-5446	188	14	.	.	PUNCT
ejpam-5446	188	15	/	/	SYM
ejpam-5446	188	16	eur	eur	PROPN
ejpam-5446	188	17	.	.	PUNCT
ejpam-5446	189	1	j.	j.	PROPN
ejpam-5446	189	2	pure	pure	PROPN
ejpam-5446	189	3	appl	appl	PROPN
ejpam-5446	189	4	.	.	PROPN
ejpam-5446	189	5	math	math	PROPN
ejpam-5446	189	6	,	,	PUNCT
ejpam-5446	189	7	17	17	NUM
ejpam-5446	189	8	(	(	PUNCT
ejpam-5446	189	9	4	4	NUM
ejpam-5446	189	10	)	)	PUNCT
ejpam-5446	189	11	(	(	PUNCT
ejpam-5446	189	12	2024	2024	NUM
ejpam-5446	189	13	)	)	PUNCT
ejpam-5446	189	14	,	,	PUNCT
ejpam-5446	189	15	3585	3585	NUM
ejpam-5446	189	16	-	-	SYM
ejpam-5446	189	17	3609	3609	NUM
ejpam-5446	189	18	3592	3592	NUM
ejpam-5446	189	19	|g′(x)−v1g(x)−ω(x)|	|g′(x)−v1g(x)−ω(x)|	PUNCT
ejpam-5446	189	20	=	=	SYM
ejpam-5446	189	21	|ςv(x)+η1ς	|ςv(x)+η1ς	NOUN
ejpam-5446	189	22	iv(x)+η2ς	iv(x)+η2ς	NUM
ejpam-5446	189	23	′′′	′′′	PROPN
ejpam-5446	189	24	(	(	PUNCT
ejpam-5446	189	25	x)+η3ς	x)+η3ς	PROPN
ejpam-5446	189	26	′′	′′	PROPN
ejpam-5446	189	27	(	(	PUNCT
ejpam-5446	189	28	x)+η4ς	x)+η4ς	PROPN
ejpam-5446	189	29	′	′	NUM
ejpam-5446	189	30	(	(	PUNCT
ejpam-5446	189	31	x)+η5ς(x)−ω(x)|	x)+η5ς(x)−ω(x)|	X
ejpam-5446	189	32	≤	≤	X
ejpam-5446	189	33	ε	ε	PROPN
ejpam-5446	189	34	(	(	PUNCT
ejpam-5446	189	35	2.7	2.7	NUM
ejpam-5446	189	36	)	)	PUNCT
ejpam-5446	189	37	|g′(x)−	|g′(x)−	NOUN
ejpam-5446	189	38	v1g(x)−	v1g(x)−	PROPN
ejpam-5446	189	39	ω(x)|	ω(x)|	PRON
ejpam-5446	189	40	≤	≤	NUM
ejpam-5446	189	41	ε	ε	PROPN
ejpam-5446	189	42	.	.	PUNCT
ejpam-5446	190	1	(	(	PUNCT
ejpam-5446	190	2	2.8	2.8	NUM
ejpam-5446	190	3	)	)	PUNCT
ejpam-5446	190	4	equivalently	equivalently	ADV
ejpam-5446	190	5	’	'	PUNCT
ejpam-5446	190	6	g	g	NOUN
ejpam-5446	190	7	’	'	PUNCT
ejpam-5446	190	8	satisfies	satisfie	NOUN
ejpam-5446	190	9	−ε	−ε	PROPN
ejpam-5446	190	10	≤	≤	NOUN
ejpam-5446	190	11	g	g	ADP
ejpam-5446	191	1	′	′	NUM
ejpam-5446	192	1	(	(	PUNCT
ejpam-5446	192	2	x)−	x)−	PROPN
ejpam-5446	192	3	v1g(x)−	v1g(x)−	PROPN
ejpam-5446	192	4	ω(x	ω(x	PROPN
ejpam-5446	192	5	)	)	PUNCT
ejpam-5446	192	6	≤	≤	NUM
ejpam-5446	192	7	ε	ε	PROPN
ejpam-5446	192	8	.	.	PUNCT
ejpam-5446	193	1	(	(	PUNCT
ejpam-5446	193	2	2.9	2.9	NUM
ejpam-5446	193	3	)	)	PUNCT
ejpam-5446	193	4	multiplying	multiply	VERB
ejpam-5446	193	5	the	the	DET
ejpam-5446	193	6	equation	equation	NOUN
ejpam-5446	193	7	by	by	ADP
ejpam-5446	193	8	e−v1(x−k	e−v1(x−k	PROPN
ejpam-5446	193	9	)	)	PUNCT
ejpam-5446	193	10	,	,	PUNCT
ejpam-5446	193	11	we	we	PRON
ejpam-5446	193	12	get	get	VERB
ejpam-5446	193	13	−εe−v1(x−k	−εe−v1(x−k	NOUN
ejpam-5446	193	14	)	)	PUNCT
ejpam-5446	193	15	≤	≤	NOUN
ejpam-5446	193	16	g	g	ADP
ejpam-5446	194	1	′	′	NUM
ejpam-5446	194	2	(	(	PUNCT
ejpam-5446	194	3	x)e−v1(x−k	x)e−v1(x−k	PROPN
ejpam-5446	194	4	)	)	PUNCT
ejpam-5446	194	5	−	−	PROPN
ejpam-5446	194	6	v1g(x)e	v1g(x)e	PROPN
ejpam-5446	194	7	−v1(x−k	−v1(x−k	PROPN
ejpam-5446	194	8	)	)	PUNCT
ejpam-5446	194	9	−	−	PROPN
ejpam-5446	194	10	ω(x)e−v1(x−k	ω(x)e−v1(x−k	SYM
ejpam-5446	194	11	)	)	PUNCT
ejpam-5446	194	12	≤	≤	NUM
ejpam-5446	194	13	εe−v1(x−k	εe−v1(x−k	NOUN
ejpam-5446	194	14	)	)	PUNCT
ejpam-5446	194	15	.	.	PUNCT
ejpam-5446	195	1	(	(	PUNCT
ejpam-5446	195	2	2.10	2.10	NUM
ejpam-5446	195	3	)	)	PUNCT
ejpam-5446	195	4	without	without	ADP
ejpam-5446	195	5	loss	loss	NOUN
ejpam-5446	195	6	of	of	ADP
ejpam-5446	195	7	consensus	consensus	NOUN
ejpam-5446	195	8	,	,	PUNCT
ejpam-5446	195	9	we	we	PRON
ejpam-5446	195	10	may	may	AUX
ejpam-5446	195	11	expect	expect	VERB
ejpam-5446	195	12	to	to	PART
ejpam-5446	195	13	be	be	AUX
ejpam-5446	195	14	that	that	DET
ejpam-5446	195	15	v1	v1	NOUN
ejpam-5446	195	16	>	>	X
ejpam-5446	195	17	1	1	NUM
ejpam-5446	195	18	,	,	PUNCT
ejpam-5446	195	19	thus	thus	ADV
ejpam-5446	195	20	−v1εe−v1(x−k	−v1εe−v1(x−k	NOUN
ejpam-5446	195	21	)	)	PUNCT
ejpam-5446	195	22	≤	≤	NOUN
ejpam-5446	195	23	g	g	ADP
ejpam-5446	195	24	′	′	NUM
ejpam-5446	195	25	(	(	PUNCT
ejpam-5446	195	26	x)e−v1(x−k	x)e−v1(x−k	PROPN
ejpam-5446	195	27	)	)	PUNCT
ejpam-5446	195	28	−	−	PROPN
ejpam-5446	195	29	v1g(x)e	v1g(x)e	PROPN
ejpam-5446	195	30	−v1(x−k	−v1(x−k	PROPN
ejpam-5446	195	31	)	)	PUNCT
ejpam-5446	195	32	−	−	PROPN
ejpam-5446	195	33	ω(x)e−v1(x−k	ω(x)e−v1(x−k	SYM
ejpam-5446	195	34	)	)	PUNCT
ejpam-5446	195	35	≤	≤	NOUN
ejpam-5446	195	36	v1εe	v1εe	PUNCT
ejpam-5446	195	37	−v1(x−k	−v1(x−k	NOUN
ejpam-5446	195	38	)	)	PUNCT
ejpam-5446	195	39	,	,	PUNCT
ejpam-5446	195	40	(	(	PUNCT
ejpam-5446	195	41	2.11	2.11	NUM
ejpam-5446	195	42	)	)	PUNCT
ejpam-5446	195	43	for	for	ADP
ejpam-5446	195	44	any	any	DET
ejpam-5446	195	45	x	x	SYM
ejpam-5446	195	46	∈	∈	PROPN
ejpam-5446	196	1	[	[	X
ejpam-5446	196	2	k	k	X
ejpam-5446	196	3	,	,	PUNCT
ejpam-5446	196	4	l	l	NOUN
ejpam-5446	196	5	]	]	PUNCT
ejpam-5446	196	6	.	.	PUNCT
ejpam-5446	197	1	integrating	integrate	VERB
ejpam-5446	197	2	(	(	PUNCT
ejpam-5446	197	3	2.11	2.11	NUM
ejpam-5446	197	4	)	)	PUNCT
ejpam-5446	197	5	from	from	ADP
ejpam-5446	197	6	x	x	PRON
ejpam-5446	197	7	to	to	ADP
ejpam-5446	197	8	l	l	NOUN
ejpam-5446	197	9	,	,	PUNCT
ejpam-5446	197	10	we	we	PRON
ejpam-5446	197	11	get	get	VERB
ejpam-5446	197	12	−v1ε	−v1ε	NUM
ejpam-5446	197	13	(	(	PUNCT
ejpam-5446	197	14	e−v1(x−k	e−v1(x−k	NOUN
ejpam-5446	197	15	)	)	PUNCT
ejpam-5446	197	16	−v1	−v1	NOUN
ejpam-5446	197	17	)	)	PUNCT
ejpam-5446	198	1	l	l	NOUN
ejpam-5446	198	2	x	x	PUNCT
ejpam-5446	198	3	≤	≤	NUM
ejpam-5446	198	4	g(l)e−v1(l−k	g(l)e−v1(l−k	NOUN
ejpam-5446	198	5	)	)	PUNCT
ejpam-5446	198	6	−	−	PROPN
ejpam-5446	198	7	v1	v1	PROPN
ejpam-5446	198	8	g(x)e−v1(x−k	g(x)e−v1(x−k	PROPN
ejpam-5446	198	9	)	)	PUNCT
ejpam-5446	198	10	v1	v1	NOUN
ejpam-5446	198	11	−	−	PROPN
ejpam-5446	198	12	∫	∫	NOUN
ejpam-5446	198	13	l	l	NOUN
ejpam-5446	198	14	x	x	PUNCT
ejpam-5446	198	15	ω(t)e−v1(t−k)dt	ω(t)e−v1(t−k)dt	PROPN
ejpam-5446	198	16	≤	≤	NUM
ejpam-5446	198	17	v1ε	v1ε	CCONJ
ejpam-5446	198	18	(	(	PUNCT
ejpam-5446	198	19	e−v1(x−k	e−v1(x−k	NOUN
ejpam-5446	198	20	)	)	PUNCT
ejpam-5446	198	21	−v1	−v1	NOUN
ejpam-5446	198	22	)	)	PUNCT
ejpam-5446	199	1	l	l	NOUN
ejpam-5446	199	2	x	x	PUNCT
ejpam-5446	199	3	−ε	−ε	PROPN
ejpam-5446	199	4	(	(	PUNCT
ejpam-5446	199	5	e−v1(l−k	e−v1(l−k	NOUN
ejpam-5446	199	6	)	)	PUNCT
ejpam-5446	199	7	−	−	ADP
ejpam-5446	199	8	e−v1(x−k	e−v1(x−k	NOUN
ejpam-5446	199	9	)	)	PUNCT
ejpam-5446	199	10	−1	−1	NOUN
ejpam-5446	199	11	)	)	PUNCT
ejpam-5446	199	12	≤	≤	NUM
ejpam-5446	199	13	g(l)e−v1(l−k	g(l)e−v1(l−k	NOUN
ejpam-5446	199	14	)	)	PUNCT
ejpam-5446	199	15	−	−	PROPN
ejpam-5446	199	16	g(x)e−v1(x−k	g(x)e−v1(x−k	PROPN
ejpam-5446	199	17	)	)	PUNCT
ejpam-5446	200	1	−	−	ADP
ejpam-5446	201	1	∫	∫	PROPN
ejpam-5446	201	2	l	l	NOUN
ejpam-5446	201	3	x	x	X
ejpam-5446	201	4	ω(t)e−v1(t−k)dt	ω(t)e−v1(t−k)dt	PROPN
ejpam-5446	201	5	≤	≤	NUM
ejpam-5446	201	6	ε	ε	PROPN
ejpam-5446	201	7	(	(	PUNCT
ejpam-5446	201	8	e−v1(l−k	e−v1(l−k	NOUN
ejpam-5446	201	9	)	)	PUNCT
ejpam-5446	201	10	−	−	ADP
ejpam-5446	201	11	e−v1(x−k	e−v1(x−k	NOUN
ejpam-5446	201	12	)	)	PUNCT
ejpam-5446	201	13	−1	−1	NOUN
ejpam-5446	201	14	)	)	PUNCT
ejpam-5446	201	15	−ε	−ε	PROPN
ejpam-5446	201	16	(	(	PUNCT
ejpam-5446	201	17	e−v1(x−k	e−v1(x−k	NOUN
ejpam-5446	201	18	)	)	PUNCT
ejpam-5446	201	19	−	−	ADP
ejpam-5446	201	20	e−v1(l−k	e−v1(l−k	NOUN
ejpam-5446	201	21	)	)	PUNCT
ejpam-5446	201	22	)	)	PUNCT
ejpam-5446	201	23	≤	≤	NUM
ejpam-5446	201	24	g(l)e−v1(l−k	g(l)e−v1(l−k	NOUN
ejpam-5446	201	25	)	)	PUNCT
ejpam-5446	201	26	−	−	PROPN
ejpam-5446	201	27	g(x)e−v1(x−k	g(x)e−v1(x−k	PROPN
ejpam-5446	201	28	)	)	PUNCT
ejpam-5446	201	29	−	−	ADP
ejpam-5446	202	1	∫	∫	PROPN
ejpam-5446	202	2	l	l	NOUN
ejpam-5446	202	3	x	x	X
ejpam-5446	202	4	ω(t)e−v1(t−k)dt	ω(t)e−v1(t−k)dt	PROPN
ejpam-5446	202	5	≤	≤	NUM
ejpam-5446	202	6	ε	ε	PROPN
ejpam-5446	202	7	(	(	PUNCT
ejpam-5446	202	8	e−v1(x−k	e−v1(x−k	PROPN
ejpam-5446	202	9	)	)	PUNCT
ejpam-5446	202	10	−	−	ADP
ejpam-5446	202	11	e−v1(l−k	e−v1(l−k	NOUN
ejpam-5446	202	12	)	)	PUNCT
ejpam-5446	202	13	)	)	PUNCT
ejpam-5446	202	14	(	(	PUNCT
ejpam-5446	202	15	2.12	2.12	NUM
ejpam-5446	202	16	)	)	PUNCT
ejpam-5446	202	17	−εe−v1(x−k	−εe−v1(x−k	NOUN
ejpam-5446	202	18	)	)	PUNCT
ejpam-5446	202	19	≤	≤	NUM
ejpam-5446	202	20	g(l)e−v1(l−k	g(l)e−v1(l−k	NOUN
ejpam-5446	202	21	)	)	PUNCT
ejpam-5446	202	22	−	−	PROPN
ejpam-5446	202	23	εe−v1(l−k	εe−v1(l−k	NUM
ejpam-5446	202	24	)	)	PUNCT
ejpam-5446	202	25	−	−	PROPN
ejpam-5446	202	26	g(x)e−v1(x−k	g(x)e−v1(x−k	PROPN
ejpam-5446	202	27	)	)	PUNCT
ejpam-5446	202	28	−	−	ADP
ejpam-5446	203	1	∫	∫	PROPN
ejpam-5446	203	2	l	l	NOUN
ejpam-5446	203	3	x	x	X
ejpam-5446	203	4	ω(t)e−v1(t−k)dt	ω(t)e−v1(t−k)dt	PROPN
ejpam-5446	203	5	≤	≤	NUM
ejpam-5446	203	6	ε	ε	PROPN
ejpam-5446	203	7	(	(	PUNCT
ejpam-5446	203	8	e−v1(x−k	e−v1(x−k	PROPN
ejpam-5446	203	9	)	)	PUNCT
ejpam-5446	203	10	−	−	ADP
ejpam-5446	203	11	e−v1(l−k	e−v1(l−k	NOUN
ejpam-5446	203	12	)	)	PUNCT
ejpam-5446	203	13	)	)	PUNCT
ejpam-5446	203	14	(	(	PUNCT
ejpam-5446	203	15	2.13	2.13	NUM
ejpam-5446	203	16	)	)	PUNCT
ejpam-5446	203	17	−εe−v1(x−k	−εe−v1(x−k	NOUN
ejpam-5446	203	18	)	)	PUNCT
ejpam-5446	203	19	≤	≤	NUM
ejpam-5446	203	20	g(l)e−v1(l−k	g(l)e−v1(l−k	NOUN
ejpam-5446	203	21	)	)	PUNCT
ejpam-5446	203	22	−	−	PROPN
ejpam-5446	203	23	εe−v1(l−k	εe−v1(l−k	NUM
ejpam-5446	203	24	)	)	PUNCT
ejpam-5446	203	25	−	−	PROPN
ejpam-5446	203	26	g(x)e−v1(x−k	g(x)e−v1(x−k	PROPN
ejpam-5446	203	27	)	)	PUNCT
ejpam-5446	203	28	−	−	ADP
ejpam-5446	204	1	∫	∫	PROPN
ejpam-5446	204	2	l	l	NOUN
ejpam-5446	204	3	x	x	PUNCT
ejpam-5446	204	4	ω(t)e−v1(t−k)dt	ω(t)e−v1(t−k)dt	PROPN
ejpam-5446	204	5	≤	≤	NUM
ejpam-5446	204	6	εe−v1(x−k	εe−v1(x−k	NOUN
ejpam-5446	204	7	)	)	PUNCT
ejpam-5446	204	8	.	.	PUNCT
ejpam-5446	205	1	v.	v.	ADP
ejpam-5446	205	2	govindan	govindan	PROPN
ejpam-5446	205	3	et	et	PROPN
ejpam-5446	205	4	al	al	PROPN
ejpam-5446	205	5	.	.	PUNCT
ejpam-5446	205	6	/	/	SYM
ejpam-5446	205	7	eur	eur	PROPN
ejpam-5446	205	8	.	.	PUNCT
ejpam-5446	206	1	j.	j.	PROPN
ejpam-5446	206	2	pure	pure	PROPN
ejpam-5446	206	3	appl	appl	PROPN
ejpam-5446	206	4	.	.	PROPN
ejpam-5446	206	5	math	math	PROPN
ejpam-5446	206	6	,	,	PUNCT
ejpam-5446	206	7	17	17	NUM
ejpam-5446	206	8	(	(	PUNCT
ejpam-5446	206	9	4	4	NUM
ejpam-5446	206	10	)	)	PUNCT
ejpam-5446	206	11	(	(	PUNCT
ejpam-5446	206	12	2024	2024	NUM
ejpam-5446	206	13	)	)	PUNCT
ejpam-5446	206	14	,	,	PUNCT
ejpam-5446	206	15	3585	3585	NUM
ejpam-5446	206	16	-	-	SYM
ejpam-5446	206	17	3609	3609	NUM
ejpam-5446	206	18	3593	3593	NUM
ejpam-5446	206	19	multiplying	multiply	VERB
ejpam-5446	206	20	the	the	DET
ejpam-5446	206	21	equation	equation	NOUN
ejpam-5446	206	22	by	by	ADP
ejpam-5446	206	23	ev1(x−k	ev1(x−k	NOUN
ejpam-5446	206	24	)	)	PUNCT
ejpam-5446	207	1	,	,	PUNCT
ejpam-5446	207	2	we	we	PRON
ejpam-5446	207	3	get	get	VERB
ejpam-5446	207	4	−εe−v1(x−k)ev1(x−k	−εe−v1(x−k)ev1(x−k	ADV
ejpam-5446	207	5	)	)	PUNCT
ejpam-5446	207	6	≤	≤	NUM
ejpam-5446	207	7	g(l)e−v1(l−k)ev1(x−k	g(l)e−v1(l−k)ev1(x−k	NOUN
ejpam-5446	207	8	)	)	PUNCT
ejpam-5446	208	1	−	−	PROPN
ejpam-5446	208	2	εe−v1(x−k)ev1(x−k	εe−v1(x−k)ev1(x−k	NOUN
ejpam-5446	208	3	)	)	PUNCT
ejpam-5446	208	4	−g(x)e−v1(x−k)ev1(x−k	−g(x)e−v1(x−k)ev1(x−k	ADV
ejpam-5446	208	5	)	)	PUNCT
ejpam-5446	209	1	−	−	NUM
ejpam-5446	209	2	∫	∫	PROPN
ejpam-5446	209	3	l	l	NOUN
ejpam-5446	209	4	x	x	SYM
ejpam-5446	209	5	ω(t)e−v1(t−k)dtev1(x−k	ω(t)e−v1(t−k)dtev1(x−k	PROPN
ejpam-5446	209	6	)	)	PUNCT
ejpam-5446	209	7	≤	≤	NOUN
ejpam-5446	209	8	εe−v1(x−k)ev1(x−k	εe−v1(x−k)ev1(x−k	NOUN
ejpam-5446	209	9	)	)	PUNCT
ejpam-5446	209	10	(	(	PUNCT
ejpam-5446	209	11	2.14	2.14	NUM
ejpam-5446	209	12	)	)	PUNCT
ejpam-5446	209	13	−ε	−ε	PROPN
ejpam-5446	209	14	≤	≤	NOUN
ejpam-5446	209	15	(	(	PUNCT
ejpam-5446	209	16	g(l)−	g(l)−	PROPN
ejpam-5446	209	17	ε)e−v1l+v1k+v1x−v1k	ε)e−v1l+v1k+v1x−v1k	PROPN
ejpam-5446	209	18	−	−	PROPN
ejpam-5446	209	19	g(x)−	g(x)−	PROPN
ejpam-5446	209	20	∫	∫	PROPN
ejpam-5446	209	21	l	l	NOUN
ejpam-5446	209	22	x	x	X
ejpam-5446	209	23	ω(t)e−v1t+v1k+v1x−v1kdt	ω(t)e−v1t+v1k+v1x−v1kdt	PROPN
ejpam-5446	209	24	≤	≤	NUM
ejpam-5446	209	25	ε	ε	PROPN
ejpam-5446	209	26	−ε	−ε	NOUN
ejpam-5446	209	27	≤	≤	PROPN
ejpam-5446	209	28	(	(	PUNCT
ejpam-5446	209	29	g(l)−	g(l)−	PROPN
ejpam-5446	209	30	ε)ev1(x−l	ε)ev1(x−l	PROPN
ejpam-5446	209	31	)	)	PUNCT
ejpam-5446	209	32	−	−	PROPN
ejpam-5446	210	1	g(x)−	g(x)−	PROPN
ejpam-5446	210	2	∫	∫	PROPN
ejpam-5446	210	3	l	l	NOUN
ejpam-5446	210	4	x	x	PUNCT
ejpam-5446	210	5	ω(t)ev1(x−t)dt	ω(t)ev1(x−t)dt	VERB
ejpam-5446	210	6	≤	≤	NUM
ejpam-5446	210	7	ε	ε	PROPN
ejpam-5446	210	8	−ε	−ε	NOUN
ejpam-5446	210	9	≤	≤	ADV
ejpam-5446	210	10	g(l)ev1(x−l	g(l)ev1(x−l	ADV
ejpam-5446	210	11	)	)	PUNCT
ejpam-5446	210	12	−	−	ADP
ejpam-5446	211	1	εev1(x−l	εev1(x−l	ADJ
ejpam-5446	211	2	)	)	PUNCT
ejpam-5446	211	3	−	−	PROPN
ejpam-5446	212	1	g(x)−	g(x)−	PROPN
ejpam-5446	212	2	∫	∫	PROPN
ejpam-5446	212	3	l	l	NOUN
ejpam-5446	212	4	x	x	PUNCT
ejpam-5446	212	5	ω(t)ev1(x−t)dt	ω(t)ev1(x−t)dt	VERB
ejpam-5446	212	6	≤	≤	NUM
ejpam-5446	212	7	ε	ε	PROPN
ejpam-5446	212	8	−ε	−ε	NOUN
ejpam-5446	212	9	≤	≤	ADV
ejpam-5446	212	10	g(l)ev1(x−l	g(l)ev1(x−l	ADV
ejpam-5446	212	11	)	)	PUNCT
ejpam-5446	212	12	−	−	ADP
ejpam-5446	213	1	εev1(x−l	εev1(x−l	ADJ
ejpam-5446	213	2	)	)	PUNCT
ejpam-5446	214	1	−	−	PROPN
ejpam-5446	214	2	g(x)−	g(x)−	PROPN
ejpam-5446	214	3	ev1x	ev1x	PROPN
ejpam-5446	214	4	∫	∫	PROPN
ejpam-5446	214	5	l	l	NOUN
ejpam-5446	214	6	x	x	X
ejpam-5446	214	7	ω(t)e−v1tdt	ω(t)e−v1tdt	PROPN
ejpam-5446	214	8	≤	≤	NUM
ejpam-5446	214	9	ε	ε	PROPN
ejpam-5446	214	10	.	.	PUNCT
ejpam-5446	215	1	(	(	PUNCT
ejpam-5446	215	2	2.15	2.15	NUM
ejpam-5446	215	3	)	)	PUNCT
ejpam-5446	215	4	let	let	VERB
ejpam-5446	215	5	χ(x	χ(x	PRON
ejpam-5446	215	6	)	)	PUNCT
ejpam-5446	216	1	=	=	PUNCT
ejpam-5446	216	2	g(l)ev1(x−l)−ev1x	g(l)ev1(x−l)−ev1x	NOUN
ejpam-5446	216	3	∫	∫	PROPN
ejpam-5446	216	4	l	l	NOUN
ejpam-5446	216	5	xω(t)e	xω(t)e	PUNCT
ejpam-5446	216	6	−v1tdt	−v1tdt	PROPN
ejpam-5446	216	7	.	.	PUNCT
ejpam-5446	217	1	then	then	ADV
ejpam-5446	217	2	χ(x	χ(x	PROPN
ejpam-5446	217	3	)	)	PUNCT
ejpam-5446	217	4	satisfies	satisfy	VERB
ejpam-5446	217	5	χ	χ	X
ejpam-5446	217	6	′	′	NUM
ejpam-5446	217	7	(	(	PUNCT
ejpam-5446	217	8	x)−v1χ(x)−ω(x	x)−v1χ(x)−ω(x	X
ejpam-5446	217	9	)	)	PUNCT
ejpam-5446	217	10	=	=	SYM
ejpam-5446	217	11	0	0	NUM
ejpam-5446	217	12	by	by	ADP
ejpam-5446	217	13	χ	χ	PRON
ejpam-5446	217	14	′	′	NUM
ejpam-5446	217	15	(	(	PUNCT
ejpam-5446	217	16	x	x	X
ejpam-5446	217	17	)	)	PUNCT
ejpam-5446	217	18	=	=	SYM
ejpam-5446	217	19	v1χ(x	v1χ(x	PROPN
ejpam-5446	217	20	)	)	PUNCT
ejpam-5446	218	1	+	+	CCONJ
ejpam-5446	218	2	ω(x	ω(x	NOUN
ejpam-5446	218	3	)	)	PUNCT
ejpam-5446	218	4	,	,	PUNCT
ejpam-5446	218	5	x	x	PUNCT
ejpam-5446	218	6	∈	∈	PROPN
ejpam-5446	219	1	[	[	X
ejpam-5446	219	2	k	k	X
ejpam-5446	219	3	,	,	PUNCT
ejpam-5446	219	4	l	l	NOUN
ejpam-5446	219	5	]	]	X
ejpam-5446	219	6	.	.	PUNCT
ejpam-5446	220	1	|χ(x)−	|χ(x)−	NOUN
ejpam-5446	220	2	g(x)|	g(x)|	NOUN
ejpam-5446	220	3	=	=	PUNCT
ejpam-5446	220	4	|ev1(x−l)g(l)−	|ev1(x−l)g(l)−	PROPN
ejpam-5446	220	5	g(x)−	g(x)−	PROPN
ejpam-5446	220	6	ev1x	ev1x	PROPN
ejpam-5446	220	7	∫	∫	NOUN
ejpam-5446	220	8	l	l	NOUN
ejpam-5446	220	9	x	x	X
ejpam-5446	220	10	ω(t)e−v1tdt|	ω(t)e−v1tdt|	ADJ
ejpam-5446	220	11	|χ(x)−	|χ(x)−	NOUN
ejpam-5446	220	12	g(x)|	g(x)|	NOUN
ejpam-5446	220	13	≤	≤	NUM
ejpam-5446	220	14	ep1x	ep1x	NOUN
ejpam-5446	220	15	∫	∫	PROPN
ejpam-5446	221	1	l	l	NOUN
ejpam-5446	221	2	x	x	X
ejpam-5446	221	3	|e−v1t||g′(t)−	|e−v1t||g′(t)−	PROPN
ejpam-5446	221	4	v1g(t)−	v1g(t)−	PROPN
ejpam-5446	221	5	ω(t)|dt	ω(t)|dt	PROPN
ejpam-5446	221	6	|χ(x)−	|χ(x)−	NOUN
ejpam-5446	221	7	g(x)|	g(x)|	NOUN
ejpam-5446	221	8	≤	≤	NUM
ejpam-5446	221	9	εep1x	εep1x	NOUN
ejpam-5446	221	10	∫	∫	PROPN
ejpam-5446	221	11	l	l	NOUN
ejpam-5446	221	12	x	x	X
ejpam-5446	221	13	e−p1tdt	e−p1tdt	PROPN
ejpam-5446	221	14	.	.	PROPN
ejpam-5446	222	1	(	(	PUNCT
ejpam-5446	222	2	2.16	2.16	NUM
ejpam-5446	222	3	)	)	PUNCT
ejpam-5446	222	4	if	if	SCONJ
ejpam-5446	222	5	p1	p1	PROPN
ejpam-5446	222	6	̸=	̸=	PROPN
ejpam-5446	222	7	0	0	NUM
ejpam-5446	222	8	,	,	PUNCT
ejpam-5446	222	9	then	then	ADV
ejpam-5446	222	10	|χ(x)−	|χ(x)−	NOUN
ejpam-5446	222	11	g(x)|	g(x)|	NOUN
ejpam-5446	222	12	≤	≤	NUM
ejpam-5446	222	13	εep1x	εep1x	NOUN
ejpam-5446	222	14	∫	∫	PROPN
ejpam-5446	222	15	l	l	NOUN
ejpam-5446	223	1	x	x	X
ejpam-5446	224	1	e−p1tdt	e−p1tdt	ADJ
ejpam-5446	224	2	≤	≤	NOUN
ejpam-5446	224	3	εep1x	εep1x	NOUN
ejpam-5446	224	4	[	[	PUNCT
ejpam-5446	224	5	e−p1l	e−p1l	X
ejpam-5446	224	6	−p1	−p1	PRON
ejpam-5446	224	7	−	−	NOUN
ejpam-5446	224	8	e−p1x	e−p1x	VERB
ejpam-5446	224	9	−p1	−p1	X
ejpam-5446	224	10	]	]	PUNCT
ejpam-5446	224	11	≤	≤	NUM
ejpam-5446	224	12	ε	ε	PROPN
ejpam-5446	224	13	−p1	−p1	PROPN
ejpam-5446	224	14	ep1x	ep1x	PROPN
ejpam-5446	224	15	[	[	PUNCT
ejpam-5446	224	16	e−p1l	e−p1l	ADP
ejpam-5446	224	17	−	−	PROPN
ejpam-5446	224	18	e−p1x	e−p1x	X
ejpam-5446	224	19	]	]	PUNCT
ejpam-5446	225	1	≤	≤	NUM
ejpam-5446	225	2	ε	ε	X
ejpam-5446	225	3	−p1	−p1	PROPN
ejpam-5446	226	1	[	[	PUNCT
ejpam-5446	226	2	ep1xe−p1l	ep1xe−p1l	NOUN
ejpam-5446	226	3	−	−	PROPN
ejpam-5446	226	4	ep1xe−p1x	ep1xe−p1x	PROPN
ejpam-5446	226	5	]	]	PUNCT
ejpam-5446	226	6	≤	≤	NUM
ejpam-5446	226	7	ε	ε	X
ejpam-5446	226	8	−p1	−p1	PROPN
ejpam-5446	227	1	[	[	PUNCT
ejpam-5446	227	2	ep1(x−l	ep1(x−l	PROPN
ejpam-5446	227	3	)	)	PUNCT
ejpam-5446	228	1	−	−	PROPN
ejpam-5446	228	2	1	1	NUM
ejpam-5446	228	3	]	]	PUNCT
ejpam-5446	228	4	|χ(x)−	|χ(x)−	NOUN
ejpam-5446	228	5	g(x)|	g(x)|	NOUN
ejpam-5446	228	6	≤	≤	NUM
ejpam-5446	228	7	ε	ε	PROPN
ejpam-5446	228	8	p1	p1	PROPN
ejpam-5446	228	9	[	[	PUNCT
ejpam-5446	228	10	1−	1−	NUM
ejpam-5446	228	11	e−p1(l−x	e−p1(l−x	NUM
ejpam-5446	228	12	)	)	PUNCT
ejpam-5446	228	13	]	]	PUNCT
ejpam-5446	228	14	;	;	PUNCT
ejpam-5446	228	15	x	x	X
ejpam-5446	228	16	∈	∈	PROPN
ejpam-5446	229	1	[	[	X
ejpam-5446	229	2	k	k	X
ejpam-5446	229	3	,	,	PUNCT
ejpam-5446	229	4	l	l	NOUN
ejpam-5446	229	5	]	]	X
ejpam-5446	229	6	.	.	PUNCT
ejpam-5446	230	1	(	(	PUNCT
ejpam-5446	230	2	2.17	2.17	NUM
ejpam-5446	230	3	)	)	PUNCT
ejpam-5446	230	4	v.	v.	ADP
ejpam-5446	230	5	govindan	govindan	PROPN
ejpam-5446	230	6	et	et	PROPN
ejpam-5446	230	7	al	al	PROPN
ejpam-5446	230	8	.	.	PUNCT
ejpam-5446	230	9	/	/	SYM
ejpam-5446	230	10	eur	eur	PROPN
ejpam-5446	230	11	.	.	PUNCT
ejpam-5446	231	1	j.	j.	PROPN
ejpam-5446	231	2	pure	pure	PROPN
ejpam-5446	231	3	appl	appl	PROPN
ejpam-5446	231	4	.	.	PROPN
ejpam-5446	231	5	math	math	PROPN
ejpam-5446	231	6	,	,	PUNCT
ejpam-5446	231	7	17	17	NUM
ejpam-5446	231	8	(	(	PUNCT
ejpam-5446	231	9	4	4	NUM
ejpam-5446	231	10	)	)	PUNCT
ejpam-5446	231	11	(	(	PUNCT
ejpam-5446	231	12	2024	2024	NUM
ejpam-5446	231	13	)	)	PUNCT
ejpam-5446	231	14	,	,	PUNCT
ejpam-5446	231	15	3585	3585	NUM
ejpam-5446	231	16	-	-	SYM
ejpam-5446	231	17	3609	3609	NUM
ejpam-5446	231	18	3594	3594	NUM
ejpam-5446	231	19	if	if	SCONJ
ejpam-5446	231	20	p1	p1	PROPN
ejpam-5446	231	21	=	=	SYM
ejpam-5446	231	22	0	0	PROPN
ejpam-5446	231	23	,	,	PUNCT
ejpam-5446	231	24	then	then	ADV
ejpam-5446	231	25	|χ(x)−	|χ(x)−	NOUN
ejpam-5446	231	26	g(x)|	g(x)|	NOUN
ejpam-5446	231	27	≤	≤	NUM
ejpam-5446	231	28	εep1x	εep1x	NOUN
ejpam-5446	231	29	∫	∫	PROPN
ejpam-5446	231	30	l	l	NOUN
ejpam-5446	232	1	x	x	X
ejpam-5446	233	1	e−p1tdt	e−p1tdt	NOUN
ejpam-5446	233	2	|χ(x)−	|χ(x)−	NOUN
ejpam-5446	233	3	g(x)|	g(x)|	NOUN
ejpam-5446	233	4	≤	≤	NUM
ejpam-5446	233	5	ε	ε	PROPN
ejpam-5446	233	6	∫	∫	PROPN
ejpam-5446	233	7	l	l	NOUN
ejpam-5446	233	8	x	x	X
ejpam-5446	233	9	dt	dt	X
ejpam-5446	233	10	|χ(x)−	|χ(x)−	NOUN
ejpam-5446	233	11	g(x)|	g(x)|	NOUN
ejpam-5446	233	12	≤	≤	PUNCT
ejpam-5446	233	13	ε(l	ε(l	PROPN
ejpam-5446	233	14	−	−	PROPN
ejpam-5446	233	15	x);x	x);x	PROPN
ejpam-5446	233	16	∈	∈	PROPN
ejpam-5446	234	1	[	[	X
ejpam-5446	234	2	k	k	X
ejpam-5446	234	3	,	,	PUNCT
ejpam-5446	234	4	l	l	NOUN
ejpam-5446	234	5	]	]	X
ejpam-5446	234	6	|χ(x)−	|χ(x)−	NOUN
ejpam-5446	234	7	g(x)|	g(x)|	NOUN
ejpam-5446	234	8	≤	≤	PUNCT
ejpam-5446	234	9	ε(l	ε(l	PROPN
ejpam-5446	234	10	−	−	PROPN
ejpam-5446	234	11	k);x	k);x	PROPN
ejpam-5446	234	12	∈	∈	PROPN
ejpam-5446	235	1	[	[	X
ejpam-5446	235	2	k	k	X
ejpam-5446	235	3	,	,	PUNCT
ejpam-5446	235	4	l	l	NOUN
ejpam-5446	235	5	]	]	X
ejpam-5446	235	6	.	.	PUNCT
ejpam-5446	236	1	(	(	PUNCT
ejpam-5446	236	2	2.18	2.18	NUM
ejpam-5446	236	3	)	)	PUNCT
ejpam-5446	236	4	therefore	therefore	ADV
ejpam-5446	236	5	,	,	PUNCT
ejpam-5446	236	6	|χ(x)−	|χ(x)−	NOUN
ejpam-5446	236	7	g(x)|	g(x)|	NOUN
ejpam-5446	236	8	≤	≤	NOUN
ejpam-5446	236	9	{	{	PUNCT
ejpam-5446	237	1	[	[	X
ejpam-5446	237	2	1−e−χ(l−k)]ε	1−e−χ(l−k)]ε	NUM
ejpam-5446	237	3	χ	χ	NOUN
ejpam-5446	237	4	;	;	PUNCT
ejpam-5446	237	5	if	if	SCONJ
ejpam-5446	237	6	χ	χ	DET
ejpam-5446	237	7	̸=	̸=	PROPN
ejpam-5446	237	8	0	0	NUM
ejpam-5446	237	9	(	(	PUNCT
ejpam-5446	237	10	l	l	NOUN
ejpam-5446	237	11	−	−	PROPN
ejpam-5446	237	12	k)ε	k)ε	NOUN
ejpam-5446	237	13	;	;	PUNCT
ejpam-5446	237	14	if	if	SCONJ
ejpam-5446	237	15	χ	χ	ADJ
ejpam-5446	237	16	=	=	SYM
ejpam-5446	237	17	0	0	NUM
ejpam-5446	237	18	,	,	PUNCT
ejpam-5446	237	19	(	(	PUNCT
ejpam-5446	237	20	2.19	2.19	NUM
ejpam-5446	237	21	)	)	PUNCT
ejpam-5446	237	22	∀	∀	X
ejpam-5446	238	1	x	x	X
ejpam-5446	238	2	∈	∈	PROPN
ejpam-5446	239	1	[	[	X
ejpam-5446	239	2	k	k	X
ejpam-5446	239	3	,	,	PUNCT
ejpam-5446	239	4	l	l	NOUN
ejpam-5446	239	5	]	]	PUNCT
ejpam-5446	239	6	.	.	PUNCT
ejpam-5446	240	1	theorem	theorem	VERB
ejpam-5446	240	2	2.2.the	2.2.the	DET
ejpam-5446	240	3	differential	differential	ADJ
ejpam-5446	240	4	equation	equation	NOUN
ejpam-5446	240	5	ςv(x)+η1ς	ςv(x)+η1ς	PROPN
ejpam-5446	240	6	iv(x)+η2ς	iv(x)+η2ς	PROPN
ejpam-5446	240	7	′′′	′′′	PROPN
ejpam-5446	240	8	(	(	PUNCT
ejpam-5446	241	1	x)+η3ς	x)+η3ς	PROPN
ejpam-5446	241	2	′′	′′	PROPN
ejpam-5446	241	3	(	(	PUNCT
ejpam-5446	241	4	x)+η4ς	x)+η4ς	PROPN
ejpam-5446	241	5	′	′	NUM
ejpam-5446	241	6	(	(	PUNCT
ejpam-5446	241	7	x)+η5ς(x	x)+η5ς(x	NOUN
ejpam-5446	241	8	)	)	PUNCT
ejpam-5446	241	9	=	=	SYM
ejpam-5446	241	10	ω(x	ω(x	NOUN
ejpam-5446	241	11	)	)	PUNCT
ejpam-5446	241	12	has	have	VERB
ejpam-5446	241	13	the	the	DET
ejpam-5446	241	14	hyers	hyers	PROPN
ejpam-5446	241	15	-	-	PUNCT
ejpam-5446	241	16	ulam	ulam	PROPN
ejpam-5446	241	17	stability	stability	NOUN
ejpam-5446	241	18	,	,	PUNCT
ejpam-5446	241	19	where	where	SCONJ
ejpam-5446	241	20	ς	ς	PROPN
ejpam-5446	241	21	∈	∈	PROPN
ejpam-5446	241	22	c5[k	c5[k	NOUN
ejpam-5446	241	23	,	,	PUNCT
ejpam-5446	241	24	l	l	NOUN
ejpam-5446	241	25	]	]	PUNCT
ejpam-5446	241	26	and	and	CCONJ
ejpam-5446	241	27	ω	ω	NUM
ejpam-5446	241	28	∈	∈	PROPN
ejpam-5446	242	1	[	[	X
ejpam-5446	242	2	k	k	X
ejpam-5446	242	3	,	,	PUNCT
ejpam-5446	242	4	l	l	NOUN
ejpam-5446	242	5	]	]	PUNCT
ejpam-5446	242	6	.	.	PUNCT
ejpam-5446	243	1	therefore	therefore	ADV
ejpam-5446	243	2	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	243	3	ϕ(x)|	ϕ(x)|	ADV
ejpam-5446	243	4	≤	≤	NUM
ejpam-5446	243	5			PRON
ejpam-5446	244	1	[	[	X
ejpam-5446	244	2	1−e−p2	1−e−p2	NUM
ejpam-5446	244	3	(	(	PUNCT
ejpam-5446	244	4	l−k)][1−e−p1(l−k	l−k)][1−e−p1(l−k	PROPN
ejpam-5446	244	5	)	)	PUNCT
ejpam-5446	244	6	]	]	PUNCT
ejpam-5446	244	7	p2p1	p2p1	NOUN
ejpam-5446	244	8	;	;	PUNCT
ejpam-5446	244	9	if	if	SCONJ
ejpam-5446	244	10	p1	p1	PROPN
ejpam-5446	244	11	,	,	PUNCT
ejpam-5446	244	12	p2	p2	PROPN
ejpam-5446	244	13	̸=	̸=	PROPN
ejpam-5446	244	14	0	0	NUM
ejpam-5446	245	1	[	[	X
ejpam-5446	245	2	1−e−p2	1−e−p2	NUM
ejpam-5446	245	3	(	(	PUNCT
ejpam-5446	245	4	l−k)][l−k]∈	l−k)][l−k]∈	ADV
ejpam-5446	245	5	p2	p2	PROPN
ejpam-5446	245	6	;	;	PUNCT
ejpam-5446	245	7	if	if	SCONJ
ejpam-5446	245	8	p2	p2	PROPN
ejpam-5446	245	9	̸=	̸=	PROPN
ejpam-5446	245	10	0	0	NUM
ejpam-5446	245	11	,	,	PUNCT
ejpam-5446	245	12	p1	p1	NOUN
ejpam-5446	245	13	=	=	NOUN
ejpam-5446	245	14	0	0	PUNCT
ejpam-5446	246	1	[	[	X
ejpam-5446	246	2	1−e−p1	1−e−p1	X
ejpam-5446	246	3	(	(	PUNCT
ejpam-5446	246	4	l−k)][l−k]∈	l−k)][l−k]∈	INTJ
ejpam-5446	246	5	p2	p2	PROPN
ejpam-5446	246	6	;	;	PUNCT
ejpam-5446	246	7	if	if	SCONJ
ejpam-5446	246	8	p2	p2	X
ejpam-5446	246	9	=	=	SYM
ejpam-5446	246	10	0	0	NUM
ejpam-5446	246	11	,	,	PUNCT
ejpam-5446	246	12	p1	p1	NOUN
ejpam-5446	246	13	̸=	̸=	PROPN
ejpam-5446	246	14	0	0	NUM
ejpam-5446	246	15	(	(	PUNCT
ejpam-5446	246	16	l	l	NOUN
ejpam-5446	246	17	−	−	PROPN
ejpam-5446	246	18	k)2	k)2	PROPN
ejpam-5446	246	19	∈	∈	PROPN
ejpam-5446	246	20	ifp2	ifp2	PROPN
ejpam-5446	246	21	,	,	PUNCT
ejpam-5446	246	22	p1	p1	PROPN
ejpam-5446	246	23	=	=	SYM
ejpam-5446	246	24	0	0	NUM
ejpam-5446	246	25	(	(	PUNCT
ejpam-5446	246	26	2.20	2.20	NUM
ejpam-5446	246	27	)	)	PUNCT
ejpam-5446	246	28	with	with	ADP
ejpam-5446	246	29	respect	respect	NOUN
ejpam-5446	246	30	to	to	ADP
ejpam-5446	246	31	x	x	SYM
ejpam-5446	246	32	∈	∈	PROPN
ejpam-5446	247	1	[	[	X
ejpam-5446	247	2	k	k	X
ejpam-5446	247	3	,	,	PUNCT
ejpam-5446	247	4	l	l	NOUN
ejpam-5446	247	5	]	]	PUNCT
ejpam-5446	247	6	.	.	PUNCT
ejpam-5446	248	1	proof	proof	NOUN
ejpam-5446	248	2	:	:	PUNCT
ejpam-5446	248	3	similar	similar	ADJ
ejpam-5446	248	4	to	to	ADP
ejpam-5446	248	5	the	the	DET
ejpam-5446	248	6	proof	proof	NOUN
ejpam-5446	248	7	of	of	ADP
ejpam-5446	248	8	lemma	lemma	PROPN
ejpam-5446	248	9	2.1	2.1	NUM
ejpam-5446	248	10	.	.	PUNCT
ejpam-5446	249	1	let	let	AUX
ejpam-5446	249	2	consider	consider	VERB
ejpam-5446	249	3	ϕ(x	ϕ(x	PRON
ejpam-5446	249	4	)	)	PUNCT
ejpam-5446	249	5	=	=	SYM
ejpam-5446	250	1	ς	ς	PROPN
ejpam-5446	250	2	′(x	′(x	NOUN
ejpam-5446	250	3	)	)	PUNCT
ejpam-5446	251	1	+	+	CCONJ
ejpam-5446	251	2	(	(	PUNCT
ejpam-5446	251	3	v2	v2	NOUN
ejpam-5446	251	4	+	+	SYM
ejpam-5446	251	5	η1)ς(x	η1)ς(x	NOUN
ejpam-5446	251	6	)	)	PUNCT
ejpam-5446	251	7	by	by	ADP
ejpam-5446	251	8	ϕ′(x	ϕ′(x	NOUN
ejpam-5446	251	9	)	)	PUNCT
ejpam-5446	252	1	=	=	SYM
ejpam-5446	252	2	ς	ς	PROPN
ejpam-5446	252	3	′′(x	′′(x	NOUN
ejpam-5446	252	4	)	)	PUNCT
ejpam-5446	253	1	+	+	CCONJ
ejpam-5446	253	2	(	(	PUNCT
ejpam-5446	253	3	v2	v2	VERB
ejpam-5446	253	4	+	+	CCONJ
ejpam-5446	253	5	η1)ς	η1)ς	NOUN
ejpam-5446	253	6	′(x	′(x	NOUN
ejpam-5446	253	7	)	)	PUNCT
ejpam-5446	254	1	+	+	CCONJ
ejpam-5446	254	2	(	(	PUNCT
ejpam-5446	254	3	v22	v22	NOUN
ejpam-5446	254	4	+	+	CCONJ
ejpam-5446	254	5	η1v2	η1v2	X
ejpam-5446	254	6	+	+	CCONJ
ejpam-5446	254	7	η2)ς(x	η2)ς(x	NOUN
ejpam-5446	254	8	)	)	PUNCT
ejpam-5446	254	9	.	.	PUNCT
ejpam-5446	255	1	also	also	ADV
ejpam-5446	255	2	|ϕ′(x)−	|ϕ′(x)−	VERB
ejpam-5446	255	3	v2ϕ(x)−	v2ϕ(x)−	NOUN
ejpam-5446	255	4	χ(x)|	χ(x)|	ADV
ejpam-5446	255	5	=	=	PUNCT
ejpam-5446	255	6	|χ(x)−	|χ(x)−	NOUN
ejpam-5446	255	7	g(x)|	g(x)|	NOUN
ejpam-5446	255	8	.	.	PUNCT
ejpam-5446	256	1	then	then	ADV
ejpam-5446	256	2	,	,	PUNCT
ejpam-5446	256	3	|ϕ′(x)−	|ϕ′(x)−	PROPN
ejpam-5446	256	4	v2ϕ(x)−	v2ϕ(x)−	NOUN
ejpam-5446	256	5	χ(x)|	χ(x)|	VERB
ejpam-5446	256	6	≤	≤	PUNCT
ejpam-5446	257	1	ϵ	ϵ	X
ejpam-5446	257	2	=	=	SYM
ejpam-5446	257	3	|ς	|ς	PROPN
ejpam-5446	257	4	′(x	′(x	NOUN
ejpam-5446	257	5	)	)	PUNCT
ejpam-5446	258	1	+	+	CCONJ
ejpam-5446	258	2	(	(	PUNCT
ejpam-5446	258	3	v2	v2	VERB
ejpam-5446	258	4	+	+	CCONJ
ejpam-5446	258	5	η1)ς	η1)ς	NOUN
ejpam-5446	258	6	′(x	′(x	NOUN
ejpam-5446	258	7	)	)	PUNCT
ejpam-5446	259	1	+	+	CCONJ
ejpam-5446	259	2	(	(	PUNCT
ejpam-5446	259	3	v22	v22	NOUN
ejpam-5446	259	4	+	+	CCONJ
ejpam-5446	259	5	η1v2	η1v2	X
ejpam-5446	259	6	+	+	CCONJ
ejpam-5446	259	7	η2)ς(x)−	η2)ς(x)−	PROPN
ejpam-5446	259	8	v2(ς	v2(ς	NOUN
ejpam-5446	259	9	′(x	′(x	NOUN
ejpam-5446	259	10	)	)	PUNCT
ejpam-5446	260	1	+	+	CCONJ
ejpam-5446	260	2	(	(	PUNCT
ejpam-5446	260	3	v2	v2	PROPN
ejpam-5446	260	4	+	+	NUM
ejpam-5446	260	5	η1)ς(x)−	η1)ς(x)−	NOUN
ejpam-5446	260	6	χ(x)|	χ(x)|	PROPN
ejpam-5446	260	7	=	=	PUNCT
ejpam-5446	260	8	|ς	|ς	PROPN
ejpam-5446	260	9	′(x	′(x	NOUN
ejpam-5446	260	10	)	)	PUNCT
ejpam-5446	261	1	+	+	CCONJ
ejpam-5446	261	2	v2ς	v2ς	PROPN
ejpam-5446	261	3	′(x	′(x	NOUN
ejpam-5446	261	4	)	)	PUNCT
ejpam-5446	262	1	+	+	CCONJ
ejpam-5446	262	2	η1ς	η1ς	ADJ
ejpam-5446	262	3	′(x	′(x	NOUN
ejpam-5446	262	4	)	)	PUNCT
ejpam-5446	263	1	+	+	X
ejpam-5446	264	1	v22ς(x	v22ς(x	PROPN
ejpam-5446	264	2	)	)	PUNCT
ejpam-5446	264	3	+	+	SYM
ejpam-5446	264	4	η1v2ς(x	η1v2ς(x	NOUN
ejpam-5446	264	5	)	)	PUNCT
ejpam-5446	264	6	+	+	CCONJ
ejpam-5446	264	7	η2ς(x)−	η2ς(x)−	PROPN
ejpam-5446	264	8	v2ς	v2ς	PROPN
ejpam-5446	264	9	′(x)−	′(x)−	PROPN
ejpam-5446	264	10	v22ς(x)−	v22ς(x)−	PROPN
ejpam-5446	264	11	η1v2ς(x)−	η1v2ς(x)−	PROPN
ejpam-5446	264	12	χ(x)|	χ(x)|	NOUN
ejpam-5446	264	13	=	=	PUNCT
ejpam-5446	264	14	|ς	|ς	PROPN
ejpam-5446	264	15	′(x	′(x	NOUN
ejpam-5446	264	16	)	)	PUNCT
ejpam-5446	265	1	+	+	CCONJ
ejpam-5446	265	2	η1ς	η1ς	ADJ
ejpam-5446	265	3	′(x	′(x	NOUN
ejpam-5446	265	4	)	)	PUNCT
ejpam-5446	266	1	+	+	CCONJ
ejpam-5446	266	2	η2ς(x)−	η2ς(x)−	PROPN
ejpam-5446	266	3	χ(x)|	χ(x)|	PROPN
ejpam-5446	266	4	(	(	PUNCT
ejpam-5446	266	5	2.21	2.21	NUM
ejpam-5446	266	6	)	)	PUNCT
ejpam-5446	266	7	|ϕ′(x)−	|ϕ′(x)−	NOUN
ejpam-5446	266	8	v2ϕ(x)−	v2ϕ(x)−	NOUN
ejpam-5446	266	9	χ(x)|	χ(x)|	PROPN
ejpam-5446	266	10	=	=	SYM
ejpam-5446	266	11	|ς	|ς	PROPN
ejpam-5446	266	12	′′(x)−	′′(x)−	PROPN
ejpam-5446	266	13	v2ς	v2ς	PROPN
ejpam-5446	266	14	′(x)−	′(x)−	PROPN
ejpam-5446	266	15	v2(ς	v2(ς	ADJ
ejpam-5446	266	16	′(x)−	′(x)−	PROPN
ejpam-5446	266	17	v2ς(x))−	v2ς(x))−	PROPN
ejpam-5446	266	18	χ(x)|	χ(x)|	VERB
ejpam-5446	266	19	|ϕ′(x)−	|ϕ′(x)−	NOUN
ejpam-5446	266	20	v2ϕ(x)−	v2ϕ(x)−	NOUN
ejpam-5446	266	21	χ(x)|	χ(x)|	PROPN
ejpam-5446	266	22	=	=	PUNCT
ejpam-5446	266	23	|ς	|ς	PROPN
ejpam-5446	266	24	′′(x	′′(x	NOUN
ejpam-5446	266	25	)	)	PUNCT
ejpam-5446	266	26	+	+	CCONJ
ejpam-5446	266	27	η1ς	η1ς	ADJ
ejpam-5446	266	28	′(x	′(x	NOUN
ejpam-5446	266	29	)	)	PUNCT
ejpam-5446	266	30	+	+	CCONJ
ejpam-5446	266	31	η2ς(x)−	η2ς(x)−	PROPN
ejpam-5446	266	32	χ(x)|	χ(x)|	PROPN
ejpam-5446	266	33	≤∈	≤∈	VERB
ejpam-5446	266	34	|ϕ′(x)−	|ϕ′(x)−	NOUN
ejpam-5446	266	35	v2ϕ(x)−	v2ϕ(x)−	PROPN
ejpam-5446	266	36	χ(x)|	χ(x)|	PROPN
ejpam-5446	266	37	≤∈	≤∈	ADV
ejpam-5446	266	38	.	.	PUNCT
ejpam-5446	267	1	(	(	PUNCT
ejpam-5446	267	2	2.22	2.22	NUM
ejpam-5446	267	3	)	)	PUNCT
ejpam-5446	267	4	v.	v.	ADP
ejpam-5446	267	5	govindan	govindan	PROPN
ejpam-5446	267	6	et	et	PROPN
ejpam-5446	267	7	al	al	PROPN
ejpam-5446	267	8	.	.	PUNCT
ejpam-5446	267	9	/	/	SYM
ejpam-5446	267	10	eur	eur	PROPN
ejpam-5446	267	11	.	.	PUNCT
ejpam-5446	268	1	j.	j.	PROPN
ejpam-5446	268	2	pure	pure	PROPN
ejpam-5446	268	3	appl	appl	PROPN
ejpam-5446	268	4	.	.	PROPN
ejpam-5446	268	5	math	math	PROPN
ejpam-5446	268	6	,	,	PUNCT
ejpam-5446	268	7	17	17	NUM
ejpam-5446	268	8	(	(	PUNCT
ejpam-5446	268	9	4	4	NUM
ejpam-5446	268	10	)	)	PUNCT
ejpam-5446	268	11	(	(	PUNCT
ejpam-5446	268	12	2024	2024	NUM
ejpam-5446	268	13	)	)	PUNCT
ejpam-5446	268	14	,	,	PUNCT
ejpam-5446	268	15	3585	3585	NUM
ejpam-5446	268	16	-	-	SYM
ejpam-5446	268	17	3609	3609	NUM
ejpam-5446	268	18	3595	3595	NUM
ejpam-5446	268	19	proportionally	proportionally	ADV
ejpam-5446	268	20	′ϕ′	′ϕ′	DET
ejpam-5446	268	21	satisfies	satisfie	NOUN
ejpam-5446	268	22	,	,	PUNCT
ejpam-5446	268	23	−	−	PROPN
ejpam-5446	268	24	∈≤	∈≤	PRON
ejpam-5446	268	25	ϕ′(x)−	ϕ′(x)−	PROPN
ejpam-5446	268	26	v2ϕ(x)−	v2ϕ(x)−	PROPN
ejpam-5446	268	27	χ(x	χ(x	PROPN
ejpam-5446	268	28	)	)	PUNCT
ejpam-5446	268	29	≤∈	≤∈	PROPN
ejpam-5446	268	30	.	.	PUNCT
ejpam-5446	269	1	(	(	PUNCT
ejpam-5446	269	2	2.23	2.23	NUM
ejpam-5446	269	3	)	)	PUNCT
ejpam-5446	269	4	multiplying	multiply	VERB
ejpam-5446	269	5	the	the	DET
ejpam-5446	269	6	equation	equation	NOUN
ejpam-5446	269	7	by	by	ADP
ejpam-5446	269	8	e−v2(x−k	e−v2(x−k	PROPN
ejpam-5446	269	9	)	)	PUNCT
ejpam-5446	269	10	,	,	PUNCT
ejpam-5446	269	11	we	we	PRON
ejpam-5446	269	12	get	get	VERB
ejpam-5446	269	13	−	−	PROPN
ejpam-5446	269	14	∈	∈	PROPN
ejpam-5446	269	15	e−v2(x−k	e−v2(x−k	NOUN
ejpam-5446	269	16	)	)	PUNCT
ejpam-5446	269	17	≤	≤	NUM
ejpam-5446	269	18	ϕ′(x)e−v2(x−k	ϕ′(x)e−v2(x−k	NOUN
ejpam-5446	269	19	)	)	PUNCT
ejpam-5446	269	20	−	−	PROPN
ejpam-5446	269	21	v2ϕ(x)e	v2ϕ(x)e	ADJ
ejpam-5446	269	22	−v2(x−k	−v2(x−k	NOUN
ejpam-5446	269	23	)	)	PUNCT
ejpam-5446	269	24	−	−	PRON
ejpam-5446	269	25	χ(x)e−v2(x−k	χ(x)e−v2(x−k	PROPN
ejpam-5446	269	26	)	)	PUNCT
ejpam-5446	269	27	≤∈	≤∈	PROPN
ejpam-5446	269	28	e−v2(x−k	e−v2(x−k	PROPN
ejpam-5446	269	29	)	)	PUNCT
ejpam-5446	269	30	.	.	PUNCT
ejpam-5446	270	1	(	(	PUNCT
ejpam-5446	270	2	2.24	2.24	NUM
ejpam-5446	270	3	)	)	PUNCT
ejpam-5446	270	4	without	without	ADP
ejpam-5446	270	5	loss	loss	NOUN
ejpam-5446	270	6	of	of	ADP
ejpam-5446	270	7	consensus	consensus	NOUN
ejpam-5446	270	8	,	,	PUNCT
ejpam-5446	270	9	we	we	PRON
ejpam-5446	270	10	may	may	AUX
ejpam-5446	270	11	expect	expect	VERB
ejpam-5446	270	12	to	to	PART
ejpam-5446	270	13	be	be	AUX
ejpam-5446	270	14	that	that	SCONJ
ejpam-5446	270	15	v2	v2	PROPN
ejpam-5446	270	16	>	>	X
ejpam-5446	270	17	1	1	NUM
ejpam-5446	270	18	,	,	PUNCT
ejpam-5446	270	19	thus	thus	ADV
ejpam-5446	270	20	−v2	−v2	PROPN
ejpam-5446	270	21	∈	∈	PROPN
ejpam-5446	270	22	e−v2(x−k	e−v2(x−k	NOUN
ejpam-5446	270	23	)	)	PUNCT
ejpam-5446	270	24	≤	≤	NUM
ejpam-5446	270	25	ϕ′(x)e−v2(x−k	ϕ′(x)e−v2(x−k	NOUN
ejpam-5446	270	26	)	)	PUNCT
ejpam-5446	271	1	−	−	PROPN
ejpam-5446	271	2	v2ϕ(x)e	v2ϕ(x)e	ADJ
ejpam-5446	271	3	−v2(x−k	−v2(x−k	NOUN
ejpam-5446	271	4	)	)	PUNCT
ejpam-5446	271	5	−	−	PRON
ejpam-5446	271	6	χ(x)e−v2(x−k	χ(x)e−v2(x−k	PROPN
ejpam-5446	271	7	)	)	PUNCT
ejpam-5446	271	8	≤∈	≤∈	PROPN
ejpam-5446	271	9	v2e	v2e	PROPN
ejpam-5446	271	10	−v2(x−k	−v2(x−k	NOUN
ejpam-5446	271	11	)	)	PUNCT
ejpam-5446	271	12	,	,	PUNCT
ejpam-5446	271	13	(	(	PUNCT
ejpam-5446	271	14	2.25	2.25	NUM
ejpam-5446	271	15	)	)	PUNCT
ejpam-5446	271	16	∀	∀	X
ejpam-5446	272	1	x	x	X
ejpam-5446	272	2	∈	∈	PROPN
ejpam-5446	273	1	[	[	X
ejpam-5446	273	2	k	k	X
ejpam-5446	273	3	,	,	PUNCT
ejpam-5446	273	4	l	l	NOUN
ejpam-5446	273	5	]	]	PUNCT
ejpam-5446	273	6	.	.	PUNCT
ejpam-5446	274	1	integrating	integrate	VERB
ejpam-5446	274	2	(	(	PUNCT
ejpam-5446	274	3	2.24	2.24	NUM
ejpam-5446	274	4	)	)	PUNCT
ejpam-5446	274	5	from	from	ADP
ejpam-5446	274	6	x	x	X
ejpam-5446	274	7	to	to	ADP
ejpam-5446	274	8	l	l	NOUN
ejpam-5446	274	9	,	,	PUNCT
ejpam-5446	274	10	we	we	PRON
ejpam-5446	274	11	get	get	VERB
ejpam-5446	274	12	−	−	PROPN
ejpam-5446	274	13	∈	∈	NOUN
ejpam-5446	274	14	(	(	PUNCT
ejpam-5446	274	15	e−v2(x−k	e−v2(x−k	NOUN
ejpam-5446	274	16	)	)	PUNCT
ejpam-5446	274	17	−	−	ADP
ejpam-5446	274	18	e−v2(l−k	e−v2(l−k	NOUN
ejpam-5446	274	19	)	)	PUNCT
ejpam-5446	274	20	)	)	PUNCT
ejpam-5446	275	1	≤	≤	PROPN
ejpam-5446	275	2	ϕ(l)e−v2(l−k	ϕ(l)e−v2(l−k	NUM
ejpam-5446	275	3	)	)	PUNCT
ejpam-5446	275	4	−	−	ADP
ejpam-5446	275	5	ϕ(x)e−v2(x−k	ϕ(x)e−v2(x−k	NOUN
ejpam-5446	275	6	)	)	PUNCT
ejpam-5446	275	7	−	−	NUM
ejpam-5446	276	1	∫	∫	NOUN
ejpam-5446	276	2	l	l	NOUN
ejpam-5446	276	3	x	x	X
ejpam-5446	276	4	χ(t)e−v2(t−k)dt	χ(t)e−v2(t−k)dt	PROPN
ejpam-5446	276	5	≤∈	≤∈	PROPN
ejpam-5446	276	6	(	(	PUNCT
ejpam-5446	276	7	e−v2(x−k	e−v2(x−k	NOUN
ejpam-5446	276	8	)	)	PUNCT
ejpam-5446	276	9	−	−	ADP
ejpam-5446	276	10	e−v2(l−k	e−v2(l−k	NOUN
ejpam-5446	276	11	)	)	PUNCT
ejpam-5446	276	12	)	)	PUNCT
ejpam-5446	277	1	−	−	PROPN
ejpam-5446	277	2	∈	∈	PROPN
ejpam-5446	277	3	e−v2(x−k	e−v2(x−k	NOUN
ejpam-5446	277	4	)	)	PUNCT
ejpam-5446	277	5	≤	≤	NOUN
ejpam-5446	277	6	ϕ(l)e−v2(l−k)−	ϕ(l)e−v2(l−k)−	NOUN
ejpam-5446	277	7	∈	∈	PROPN
ejpam-5446	277	8	e−v2(l−k	e−v2(l−k	NOUN
ejpam-5446	277	9	)	)	PUNCT
ejpam-5446	277	10	−	−	ADP
ejpam-5446	277	11	ϕ(x)e−v2(x−k	ϕ(x)e−v2(x−k	NOUN
ejpam-5446	277	12	)	)	PUNCT
ejpam-5446	277	13	−	−	NUM
ejpam-5446	278	1	∫	∫	NOUN
ejpam-5446	278	2	l	l	NOUN
ejpam-5446	278	3	x	x	X
ejpam-5446	278	4	χ(t)e−v2(t−k)dt	χ(t)e−v2(t−k)dt	PROPN
ejpam-5446	278	5	≤∈	≤∈	PROPN
ejpam-5446	278	6	(	(	PUNCT
ejpam-5446	278	7	e−v2(x−k	e−v2(x−k	NOUN
ejpam-5446	278	8	)	)	PUNCT
ejpam-5446	278	9	)	)	PUNCT
ejpam-5446	278	10	.	.	PUNCT
ejpam-5446	279	1	(	(	PUNCT
ejpam-5446	279	2	2.26	2.26	NUM
ejpam-5446	279	3	)	)	PUNCT
ejpam-5446	279	4	multiplying	multiply	VERB
ejpam-5446	279	5	the	the	DET
ejpam-5446	279	6	equation	equation	NOUN
ejpam-5446	279	7	by	by	ADP
ejpam-5446	279	8	ev2(x−k	ev2(x−k	PROPN
ejpam-5446	279	9	)	)	PUNCT
ejpam-5446	279	10	,	,	PUNCT
ejpam-5446	279	11	we	we	PRON
ejpam-5446	279	12	get	get	VERB
ejpam-5446	279	13	−	−	PROPN
ejpam-5446	279	14	∈	∈	NOUN
ejpam-5446	279	15	e−v2(x−k)ev2(x−k	e−v2(x−k)ev2(x−k	NOUN
ejpam-5446	279	16	)	)	PUNCT
ejpam-5446	279	17	≤	≤	NUM
ejpam-5446	279	18	ϕ(l)e−v2(l−k)ev2(x−k)−	ϕ(l)e−v2(l−k)ev2(x−k)−	PROPN
ejpam-5446	279	19	∈	∈	PROPN
ejpam-5446	279	20	e−v2(l−k)ev2(x−k	e−v2(l−k)ev2(x−k	PROPN
ejpam-5446	279	21	)	)	PUNCT
ejpam-5446	279	22	−	−	PROPN
ejpam-5446	279	23	ϕ(x)e−v2(x−k)ev2(x−k	ϕ(x)e−v2(x−k)ev2(x−k	NOUN
ejpam-5446	279	24	)	)	PUNCT
ejpam-5446	280	1	−	−	ADP
ejpam-5446	281	1	∫	∫	PROPN
ejpam-5446	281	2	l	l	NOUN
ejpam-5446	281	3	x	x	X
ejpam-5446	281	4	χ(t)e−v2(t−k)ev2(x−k)dt	χ(t)e−v2(t−k)ev2(x−k)dt	X
ejpam-5446	281	5	≤∈	≤∈	X
ejpam-5446	281	6	(	(	PUNCT
ejpam-5446	281	7	e−v2(x−k)ev2(x−k	e−v2(x−k)ev2(x−k	NOUN
ejpam-5446	281	8	)	)	PUNCT
ejpam-5446	281	9	)	)	PUNCT
ejpam-5446	282	1	−	−	PROPN
ejpam-5446	283	1	∈≤	∈≤	PRON
ejpam-5446	283	2	ϕ(n)e−v2(l−x)−	ϕ(n)e−v2(l−x)−	NOUN
ejpam-5446	283	3	∈	∈	PROPN
ejpam-5446	283	4	e−v2(l−x	e−v2(l−x	NOUN
ejpam-5446	283	5	)	)	PUNCT
ejpam-5446	283	6	−	−	PROPN
ejpam-5446	284	1	ϕ(x)−	ϕ(x)−	PROPN
ejpam-5446	284	2	ev2x	ev2x	VERB
ejpam-5446	284	3	∫	∫	PROPN
ejpam-5446	284	4	l	l	NOUN
ejpam-5446	284	5	x	x	PUNCT
ejpam-5446	285	1	χ(t)e−v2tdt	χ(t)e−v2tdt	PROPN
ejpam-5446	285	2	≤∈	≤∈	PROPN
ejpam-5446	285	3	.	.	PUNCT
ejpam-5446	286	1	(	(	PUNCT
ejpam-5446	286	2	2.27	2.27	NUM
ejpam-5446	286	3	)	)	PUNCT
ejpam-5446	286	4	let	let	VERB
ejpam-5446	286	5	γ(x	γ(x	NOUN
ejpam-5446	286	6	)	)	PUNCT
ejpam-5446	287	1	=	=	SYM
ejpam-5446	287	2	ϕ(l)ev2(x−l	ϕ(l)ev2(x−l	NOUN
ejpam-5446	287	3	)	)	PUNCT
ejpam-5446	288	1	−	−	PUNCT
ejpam-5446	288	2	ev2x	ev2x	VERB
ejpam-5446	288	3	∫	∫	PROPN
ejpam-5446	288	4	l	l	NOUN
ejpam-5446	288	5	x	x	PUNCT
ejpam-5446	288	6	χ(t)e	χ(t)e	ADP
ejpam-5446	288	7	−v2tdt	−v2tdt	PROPN
ejpam-5446	288	8	,	,	PUNCT
ejpam-5446	288	9	for	for	ADP
ejpam-5446	288	10	all	all	DET
ejpam-5446	288	11	x	x	SYM
ejpam-5446	288	12	∈	∈	PROPN
ejpam-5446	289	1	[	[	X
ejpam-5446	289	2	k	k	X
ejpam-5446	289	3	,	,	PUNCT
ejpam-5446	289	4	l	l	NOUN
ejpam-5446	289	5	]	]	PUNCT
ejpam-5446	289	6	.	.	PUNCT
ejpam-5446	290	1	then	then	ADV
ejpam-5446	290	2	γ′(x)−	γ′(x)−	PROPN
ejpam-5446	290	3	v2γ(x)−	v2γ(x)−	PROPN
ejpam-5446	290	4	χ(x	χ(x	PROPN
ejpam-5446	290	5	)	)	PUNCT
ejpam-5446	291	1	=	=	SYM
ejpam-5446	291	2	0	0	NUM
ejpam-5446	291	3	is	be	AUX
ejpam-5446	291	4	defined	define	VERB
ejpam-5446	291	5	by	by	ADP
ejpam-5446	291	6	γ′(x	γ′(x	NOUN
ejpam-5446	291	7	)	)	PUNCT
ejpam-5446	291	8	=	=	SYM
ejpam-5446	291	9	v2γ(x	v2γ(x	PROPN
ejpam-5446	291	10	)	)	PUNCT
ejpam-5446	292	1	+	+	CCONJ
ejpam-5446	292	2	χ(x	χ(x	PROPN
ejpam-5446	292	3	)	)	PUNCT
ejpam-5446	293	1	,	,	PUNCT
ejpam-5446	293	2	x	x	PUNCT
ejpam-5446	293	3	∈	∈	PROPN
ejpam-5446	294	1	[	[	X
ejpam-5446	294	2	k	k	X
ejpam-5446	294	3	,	,	PUNCT
ejpam-5446	294	4	l	l	NOUN
ejpam-5446	294	5	]	]	PUNCT
ejpam-5446	294	6	and	and	CCONJ
ejpam-5446	294	7	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	294	8	ϕ(x)|	ϕ(x)|	X
ejpam-5446	294	9	=	=	SYM
ejpam-5446	294	10	∣∣∣∣ev2(x−l)ϕ(l)−	∣∣∣∣ev2(x−l)ϕ(l)−	PROPN
ejpam-5446	294	11	ϕ(x)−	ϕ(x)−	PROPN
ejpam-5446	294	12	ev2x	ev2x	VERB
ejpam-5446	294	13	∫	∫	PROPN
ejpam-5446	294	14	l	l	NOUN
ejpam-5446	294	15	x	x	X
ejpam-5446	295	1	χ(t)e−v2tdt	χ(t)e−v2tdt	PROPN
ejpam-5446	295	2	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5446	295	3	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	295	4	ϕ(x)|	ϕ(x)|	PROPN
ejpam-5446	295	5	=	=	PUNCT
ejpam-5446	295	6	ep2x	ep2x	PROPN
ejpam-5446	295	7	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-5446	295	8	l	l	NOUN
ejpam-5446	295	9	x	x	PUNCT
ejpam-5446	296	1	[	[	X
ejpam-5446	296	2	e−v2t][ϕ′(t)−	e−v2t][ϕ′(t)−	X
ejpam-5446	296	3	v2ϕ(t)−	v2ϕ(t)−	PROPN
ejpam-5446	296	4	χ(t)]dt	χ(t)]dt	PROPN
ejpam-5446	296	5	∣∣∣∣	∣∣∣∣	NOUN
ejpam-5446	296	6	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	296	7	ϕ(x)|	ϕ(x)|	PROPN
ejpam-5446	296	8	≤∈	≤∈	VERB
ejpam-5446	296	9	ep2x	ep2x	PROPN
ejpam-5446	296	10	∫	∫	PROPN
ejpam-5446	296	11	b	b	X
ejpam-5446	297	1	x	x	PUNCT
ejpam-5446	297	2	e−p2tdt	e−p2tdt	PROPN
ejpam-5446	297	3	.	.	PUNCT
ejpam-5446	298	1	(	(	PUNCT
ejpam-5446	298	2	2.28	2.28	NUM
ejpam-5446	298	3	)	)	PUNCT
ejpam-5446	298	4	v.	v.	ADP
ejpam-5446	298	5	govindan	govindan	PROPN
ejpam-5446	298	6	et	et	PROPN
ejpam-5446	298	7	al	al	PROPN
ejpam-5446	298	8	.	.	PUNCT
ejpam-5446	298	9	/	/	SYM
ejpam-5446	298	10	eur	eur	PROPN
ejpam-5446	298	11	.	.	PUNCT
ejpam-5446	299	1	j.	j.	PROPN
ejpam-5446	299	2	pure	pure	PROPN
ejpam-5446	299	3	appl	appl	PROPN
ejpam-5446	299	4	.	.	PROPN
ejpam-5446	299	5	math	math	PROPN
ejpam-5446	299	6	,	,	PUNCT
ejpam-5446	299	7	17	17	NUM
ejpam-5446	299	8	(	(	PUNCT
ejpam-5446	299	9	4	4	NUM
ejpam-5446	299	10	)	)	PUNCT
ejpam-5446	299	11	(	(	PUNCT
ejpam-5446	299	12	2024	2024	NUM
ejpam-5446	299	13	)	)	PUNCT
ejpam-5446	299	14	,	,	PUNCT
ejpam-5446	299	15	3585	3585	NUM
ejpam-5446	299	16	-	-	SYM
ejpam-5446	299	17	3609	3609	NUM
ejpam-5446	299	18	3596	3596	NUM
ejpam-5446	299	19	if	if	SCONJ
ejpam-5446	299	20	p2	p2	PROPN
ejpam-5446	299	21	̸=	̸=	PROPN
ejpam-5446	299	22	0	0	NUM
ejpam-5446	299	23	,	,	PUNCT
ejpam-5446	299	24	then	then	ADV
ejpam-5446	299	25	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	299	26	ϕ(x)|	ϕ(x)|	PROPN
ejpam-5446	299	27	≤∈	≤∈	VERB
ejpam-5446	299	28	ep2x	ep2x	PROPN
ejpam-5446	299	29	∫	∫	PROPN
ejpam-5446	300	1	l	l	NOUN
ejpam-5446	300	2	x	x	X
ejpam-5446	301	1	e−p2tdt	e−p2tdt	ADJ
ejpam-5446	301	2	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	301	3	ϕ(x)|	ϕ(x)|	VERB
ejpam-5446	301	4	≤	≤	NUM
ejpam-5446	301	5	∈	∈	PROPN
ejpam-5446	301	6	−p2	−p2	PROPN
ejpam-5446	301	7	[	[	X
ejpam-5446	301	8	e−p2(l−x	e−p2(l−x	NOUN
ejpam-5446	301	9	)	)	PUNCT
ejpam-5446	301	10	−	−	PROPN
ejpam-5446	301	11	1	1	NUM
ejpam-5446	301	12	]	]	PUNCT
ejpam-5446	301	13	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	301	14	ϕ(x)|	ϕ(x)|	VERB
ejpam-5446	301	15	≤	≤	NUM
ejpam-5446	301	16	∈	∈	NOUN
ejpam-5446	301	17	p2	p2	X
ejpam-5446	302	1	[	[	X
ejpam-5446	302	2	1−	1−	NUM
ejpam-5446	302	3	e−p2(l−x)];x	e−p2(l−x)];x	X
ejpam-5446	302	4	∈	∈	PROPN
ejpam-5446	302	5	[	[	X
ejpam-5446	302	6	k	k	X
ejpam-5446	302	7	,	,	PUNCT
ejpam-5446	302	8	l	l	NOUN
ejpam-5446	302	9	]	]	X
ejpam-5446	302	10	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	302	11	ϕ(x)|	ϕ(x)|	ADJ
ejpam-5446	302	12	≤	≤	NUM
ejpam-5446	302	13	∈	∈	NOUN
ejpam-5446	302	14	p2	p2	X
ejpam-5446	303	1	[	[	X
ejpam-5446	303	2	1−	1−	NUM
ejpam-5446	303	3	e−p2(l−k)];x	e−p2(l−k)];x	X
ejpam-5446	303	4	∈	∈	PROPN
ejpam-5446	303	5	[	[	X
ejpam-5446	303	6	k	k	X
ejpam-5446	303	7	,	,	PUNCT
ejpam-5446	303	8	l	l	NOUN
ejpam-5446	303	9	]	]	X
ejpam-5446	303	10	.	.	PUNCT
ejpam-5446	304	1	(	(	PUNCT
ejpam-5446	304	2	2.29	2.29	NUM
ejpam-5446	304	3	)	)	PUNCT
ejpam-5446	304	4	if	if	SCONJ
ejpam-5446	304	5	p2	p2	X
ejpam-5446	304	6	=	=	SYM
ejpam-5446	304	7	0	0	NUM
ejpam-5446	304	8	,	,	PUNCT
ejpam-5446	304	9	then	then	ADV
ejpam-5446	304	10	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	304	11	ϕ(x)|	ϕ(x)|	PROPN
ejpam-5446	304	12	≤∈	≤∈	VERB
ejpam-5446	304	13	ep2x	ep2x	PROPN
ejpam-5446	304	14	∫	∫	PROPN
ejpam-5446	305	1	l	l	NOUN
ejpam-5446	305	2	x	x	X
ejpam-5446	306	1	e−p2tdt	e−p2tdt	ADJ
ejpam-5446	306	2	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	306	3	ϕ(x)|	ϕ(x)|	PROPN
ejpam-5446	306	4	≤∈	≤∈	PROPN
ejpam-5446	306	5	e0x	e0x	PROPN
ejpam-5446	306	6	∫	∫	PROPN
ejpam-5446	306	7	l	l	NOUN
ejpam-5446	306	8	x	x	X
ejpam-5446	306	9	e−0tdt	e−0tdt	PROPN
ejpam-5446	306	10	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	306	11	ϕ(x)|	ϕ(x)|	PROPN
ejpam-5446	306	12	≤∈	≤∈	PROPN
ejpam-5446	306	13	∫	∫	PROPN
ejpam-5446	306	14	l	l	NOUN
ejpam-5446	306	15	x	x	X
ejpam-5446	307	1	dt	dt	X
ejpam-5446	307	2	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	307	3	ϕ(x)|	ϕ(x)|	PROPN
ejpam-5446	307	4	≤∈	≤∈	PROPN
ejpam-5446	307	5	(	(	PUNCT
ejpam-5446	307	6	l	l	NOUN
ejpam-5446	307	7	−	−	PROPN
ejpam-5446	307	8	x);x	x);x	PROPN
ejpam-5446	307	9	∈	∈	PROPN
ejpam-5446	308	1	[	[	X
ejpam-5446	308	2	k	k	X
ejpam-5446	308	3	,	,	PUNCT
ejpam-5446	308	4	l	l	NOUN
ejpam-5446	308	5	]	]	X
ejpam-5446	308	6	|γ(x)−	|γ(x)−	PROPN
ejpam-5446	308	7	ϕ(x)|	ϕ(x)|	X
ejpam-5446	308	8	≤∈	≤∈	PROPN
ejpam-5446	308	9	(	(	PUNCT
ejpam-5446	308	10	l	l	NOUN
ejpam-5446	308	11	−	−	PROPN
ejpam-5446	309	1	k);x	k);x	PROPN
ejpam-5446	309	2	∈	∈	PROPN
ejpam-5446	310	1	[	[	X
ejpam-5446	310	2	k	k	X
ejpam-5446	310	3	,	,	PUNCT
ejpam-5446	310	4	l	l	NOUN
ejpam-5446	310	5	]	]	X
ejpam-5446	310	6	.	.	PUNCT
ejpam-5446	311	1	(	(	PUNCT
ejpam-5446	311	2	2.30	2.30	NUM
ejpam-5446	311	3	)	)	PUNCT
ejpam-5446	311	4	it	it	PRON
ejpam-5446	311	5	follows	follow	VERB
ejpam-5446	311	6	from	from	ADP
ejpam-5446	311	7	(	(	PUNCT
ejpam-5446	311	8	2.19	2.19	NUM
ejpam-5446	311	9	)	)	PUNCT
ejpam-5446	311	10	,	,	PUNCT
ejpam-5446	311	11	we	we	PRON
ejpam-5446	311	12	conclude	conclude	VERB
ejpam-5446	311	13	our	our	PRON
ejpam-5446	311	14	result	result	NOUN
ejpam-5446	311	15	(	(	PUNCT
ejpam-5446	311	16	2.20	2.20	NUM
ejpam-5446	311	17	)	)	PUNCT
ejpam-5446	311	18	.	.	PUNCT
ejpam-5446	312	1	theorem.2.3.the	theorem.2.3.the	DET
ejpam-5446	312	2	differential	differential	ADJ
ejpam-5446	312	3	equation	equation	NOUN
ejpam-5446	312	4	ςv(x)+η1ς	ςv(x)+η1ς	PROPN
ejpam-5446	312	5	iv(x)+η2ς	iv(x)+η2ς	PROPN
ejpam-5446	312	6	′′′	′′′	PROPN
ejpam-5446	312	7	(	(	PUNCT
ejpam-5446	312	8	x)+η3ς	x)+η3ς	PROPN
ejpam-5446	312	9	′′	′′	PROPN
ejpam-5446	312	10	(	(	PUNCT
ejpam-5446	312	11	x)+η4ς	x)+η4ς	PROPN
ejpam-5446	312	12	′	′	NUM
ejpam-5446	312	13	(	(	PUNCT
ejpam-5446	312	14	x)+η5ς(x	x)+η5ς(x	NOUN
ejpam-5446	312	15	)	)	PUNCT
ejpam-5446	312	16	=	=	SYM
ejpam-5446	312	17	ω(x	ω(x	NOUN
ejpam-5446	312	18	)	)	PUNCT
ejpam-5446	312	19	has	have	VERB
ejpam-5446	312	20	the	the	DET
ejpam-5446	312	21	hyers	hyers	PROPN
ejpam-5446	312	22	-	-	PUNCT
ejpam-5446	312	23	ulam	ulam	PROPN
ejpam-5446	312	24	stability	stability	NOUN
ejpam-5446	312	25	,	,	PUNCT
ejpam-5446	312	26	where	where	SCONJ
ejpam-5446	312	27	ς	ς	PROPN
ejpam-5446	312	28	∈	∈	PROPN
ejpam-5446	312	29	c5[k	c5[k	NOUN
ejpam-5446	312	30	,	,	PUNCT
ejpam-5446	312	31	l	l	NOUN
ejpam-5446	312	32	]	]	PUNCT
ejpam-5446	312	33	and	and	CCONJ
ejpam-5446	312	34	ω	ω	NUM
ejpam-5446	312	35	∈	∈	PROPN
ejpam-5446	313	1	[	[	X
ejpam-5446	313	2	k	k	X
ejpam-5446	313	3	,	,	PUNCT
ejpam-5446	313	4	l	l	NOUN
ejpam-5446	313	5	]	]	PUNCT
ejpam-5446	313	6	.	.	PUNCT
ejpam-5446	314	1	therefore	therefore	ADV
ejpam-5446	314	2	|u(x)−	|u(x)−	PROPN
ejpam-5446	314	3	ς(x)|	ς(x)|	VERB
ejpam-5446	314	4	≤	≤	NUM
ejpam-5446	314	5			PUNCT
ejpam-5446	315	1	[	[	X
ejpam-5446	315	2	1−e−p3(l−k)][1−e−p1(l−k)][1−e−p2(l−k)]ε	1−e−p3(l−k)][1−e−p1(l−k)][1−e−p2(l−k)]ε	NUM
ejpam-5446	315	3	p3p1p2	p3p1p2	ADV
ejpam-5446	315	4	,	,	PUNCT
ejpam-5446	315	5	if	if	SCONJ
ejpam-5446	315	6	p1	p1	PROPN
ejpam-5446	315	7	,	,	PUNCT
ejpam-5446	315	8	p3	p3	PROPN
ejpam-5446	315	9	,	,	PUNCT
ejpam-5446	315	10	p2	p2	PROPN
ejpam-5446	315	11	̸=	̸=	PROPN
ejpam-5446	315	12	0	0	NUM
ejpam-5446	316	1	[	[	X
ejpam-5446	316	2	1−e−p1(l−k)][1−e−p3(l−k)](l−k)ε	1−e−p1(l−k)][1−e−p3(l−k)](l−k)ε	NUM
ejpam-5446	316	3	p1p3	p1p3	X
ejpam-5446	316	4	,	,	PUNCT
ejpam-5446	316	5	if	if	SCONJ
ejpam-5446	316	6	p1	p1	PROPN
ejpam-5446	316	7	,	,	PUNCT
ejpam-5446	316	8	p3	p3	PROPN
ejpam-5446	316	9	̸=	̸=	PROPN
ejpam-5446	316	10	0	0	NUM
ejpam-5446	316	11	,	,	PUNCT
ejpam-5446	316	12	p2	p2	X
ejpam-5446	316	13	=	=	SYM
ejpam-5446	316	14	0	0	PUNCT
ejpam-5446	317	1	[	[	X
ejpam-5446	317	2	1−e−p1(l−k)][1−e−p2(l−k)](l−k)ε	1−e−p1(l−k)][1−e−p2(l−k)](l−k)ε	NUM
ejpam-5446	317	3	p1p2	p1p2	PROPN
ejpam-5446	317	4	,	,	PUNCT
ejpam-5446	317	5	if	if	SCONJ
ejpam-5446	317	6	p1	p1	PROPN
ejpam-5446	317	7	,	,	PUNCT
ejpam-5446	317	8	p2	p2	PROPN
ejpam-5446	317	9	̸=	̸=	PROPN
ejpam-5446	317	10	0	0	NUM
ejpam-5446	317	11	,	,	PUNCT
ejpam-5446	317	12	p3	p3	PROPN
ejpam-5446	317	13	=	=	X
ejpam-5446	317	14	0	0	PUNCT
ejpam-5446	318	1	[	[	X
ejpam-5446	318	2	1−e−p2(l−k)][1−e−p3(l−k)](l−k)ε	1−e−p2(l−k)][1−e−p3(l−k)](l−k)ε	NUM
ejpam-5446	318	3	p2p3	p2p3	CCONJ
ejpam-5446	318	4	,	,	PUNCT
ejpam-5446	318	5	if	if	SCONJ
ejpam-5446	318	6	p1	p1	PROPN
ejpam-5446	318	7	=	=	SYM
ejpam-5446	318	8	0	0	PROPN
ejpam-5446	318	9	,	,	PUNCT
ejpam-5446	318	10	p3	p3	PROPN
ejpam-5446	318	11	,	,	PUNCT
ejpam-5446	318	12	p2	p2	PROPN
ejpam-5446	318	13	̸=	̸=	PROPN
ejpam-5446	318	14	0	0	NUM
ejpam-5446	319	1	[	[	X
ejpam-5446	319	2	1−e−p1(l−k)](l−k)2ε	1−e−p1(l−k)](l−k)2ε	NUM
ejpam-5446	319	3	p1	p1	NOUN
ejpam-5446	319	4	,	,	PUNCT
ejpam-5446	319	5	if	if	SCONJ
ejpam-5446	319	6	p2	p2	NOUN
ejpam-5446	319	7	,	,	PUNCT
ejpam-5446	319	8	p3	p3	PROPN
ejpam-5446	319	9	=	=	SYM
ejpam-5446	319	10	0	0	NUM
ejpam-5446	319	11	,	,	PUNCT
ejpam-5446	319	12	p1	p1	NOUN
ejpam-5446	319	13	̸=	̸=	PROPN
ejpam-5446	319	14	0	0	NUM
ejpam-5446	320	1	[	[	X
ejpam-5446	320	2	1−e−p2(l−k)](l−k)2ε	1−e−p2(l−k)](l−k)2ε	NUM
ejpam-5446	320	3	p2	p2	PROPN
ejpam-5446	320	4	,	,	PUNCT
ejpam-5446	320	5	if	if	SCONJ
ejpam-5446	320	6	p1	p1	PROPN
ejpam-5446	320	7	,	,	PUNCT
ejpam-5446	320	8	p3	p3	PROPN
ejpam-5446	320	9	=	=	SYM
ejpam-5446	320	10	0	0	NUM
ejpam-5446	320	11	,	,	PUNCT
ejpam-5446	320	12	p2	p2	PROPN
ejpam-5446	320	13	̸=	̸=	PROPN
ejpam-5446	320	14	0	0	NUM
ejpam-5446	321	1	[	[	X
ejpam-5446	321	2	1−e−p3(l−k)](l−k)2ε	1−e−p3(l−k)](l−k)2ε	NUM
ejpam-5446	321	3	p3	p3	PROPN
ejpam-5446	321	4	,	,	PUNCT
ejpam-5446	321	5	if	if	SCONJ
ejpam-5446	321	6	p1	p1	PROPN
ejpam-5446	321	7	,	,	PUNCT
ejpam-5446	321	8	p2	p2	X
ejpam-5446	321	9	=	=	SYM
ejpam-5446	321	10	0	0	NUM
ejpam-5446	321	11	,	,	PUNCT
ejpam-5446	321	12	p3	p3	PROPN
ejpam-5446	321	13	̸=	̸=	PROPN
ejpam-5446	321	14	0	0	NUM
ejpam-5446	321	15	(	(	PUNCT
ejpam-5446	321	16	l	l	NOUN
ejpam-5446	321	17	−	−	PROPN
ejpam-5446	321	18	k)3ε	k)3ε	NOUN
ejpam-5446	321	19	,	,	PUNCT
ejpam-5446	321	20	if	if	SCONJ
ejpam-5446	321	21	p	p	X
ejpam-5446	321	22	,	,	PUNCT
ejpam-5446	321	23	p2	p2	NOUN
ejpam-5446	321	24	,	,	PUNCT
ejpam-5446	321	25	p3	p3	PROPN
ejpam-5446	321	26	=	=	SYM
ejpam-5446	321	27	0	0	PUNCT
ejpam-5446	321	28	(	(	PUNCT
ejpam-5446	321	29	2.31	2.31	NUM
ejpam-5446	321	30	)	)	PUNCT
ejpam-5446	321	31	∀	∀	X
ejpam-5446	322	1	x	x	X
ejpam-5446	322	2	∈	∈	PROPN
ejpam-5446	323	1	[	[	X
ejpam-5446	323	2	k	k	X
ejpam-5446	323	3	,	,	PUNCT
ejpam-5446	323	4	l	l	NOUN
ejpam-5446	323	5	]	]	PUNCT
ejpam-5446	323	6	.	.	PUNCT
ejpam-5446	324	1	proof	proof	NOUN
ejpam-5446	324	2	:	:	PUNCT
ejpam-5446	324	3	let	let	VERB
ejpam-5446	324	4	us	we	PRON
ejpam-5446	324	5	consider	consider	VERB
ejpam-5446	324	6	ς(x	ς(x	NOUN
ejpam-5446	324	7	)	)	PUNCT
ejpam-5446	324	8	=	=	SYM
ejpam-5446	324	9	u′′(x	u′′(x	PROPN
ejpam-5446	324	10	)	)	PUNCT
ejpam-5446	325	1	+	+	CCONJ
ejpam-5446	325	2	(	(	PUNCT
ejpam-5446	325	3	v2	v2	X
ejpam-5446	325	4	+	+	CCONJ
ejpam-5446	325	5	η1)u	η1)u	NOUN
ejpam-5446	325	6	′(x	′(x	NOUN
ejpam-5446	325	7	)	)	PUNCT
ejpam-5446	326	1	+	+	CCONJ
ejpam-5446	326	2	(	(	PUNCT
ejpam-5446	326	3	v22	v22	NOUN
ejpam-5446	326	4	+	+	CCONJ
ejpam-5446	326	5	η1v2	η1v2	X
ejpam-5446	326	6	+	+	CCONJ
ejpam-5446	326	7	η2)u(x	η2)u(x	NOUN
ejpam-5446	326	8	)	)	PUNCT
ejpam-5446	326	9	.	.	PUNCT
ejpam-5446	327	1	then	then	ADV
ejpam-5446	327	2	we	we	PRON
ejpam-5446	327	3	obtain	obtain	VERB
ejpam-5446	327	4	ς	ς	PROPN
ejpam-5446	327	5	′(x	′(x	NOUN
ejpam-5446	327	6	)	)	PUNCT
ejpam-5446	328	1	=	=	SYM
ejpam-5446	328	2	u	u	SYM
ejpam-5446	328	3	′′′	′′′	PROPN
ejpam-5446	328	4	(	(	PUNCT
ejpam-5446	328	5	x	x	X
ejpam-5446	328	6	)	)	PUNCT
ejpam-5446	328	7	+	+	CCONJ
ejpam-5446	328	8	(	(	PUNCT
ejpam-5446	328	9	v2	v2	NOUN
ejpam-5446	328	10	+	+	CCONJ
ejpam-5446	328	11	η1)u	η1)u	NOUN
ejpam-5446	328	12	′′	′′	PROPN
ejpam-5446	328	13	(	(	PUNCT
ejpam-5446	328	14	x	x	X
ejpam-5446	328	15	)	)	PUNCT
ejpam-5446	328	16	+	+	CCONJ
ejpam-5446	328	17	(	(	PUNCT
ejpam-5446	328	18	v22	v22	NOUN
ejpam-5446	328	19	+	+	CCONJ
ejpam-5446	328	20	η1v2	η1v2	X
ejpam-5446	328	21	+	+	CCONJ
ejpam-5446	328	22	η2)u	η2)u	ADJ
ejpam-5446	328	23	′(x	′(x	NOUN
ejpam-5446	328	24	)	)	PUNCT
ejpam-5446	328	25	+	+	CCONJ
ejpam-5446	328	26	(	(	PUNCT
ejpam-5446	328	27	v32	v32	X
ejpam-5446	328	28	+	+	CCONJ
ejpam-5446	328	29	η1v	η1v	NOUN
ejpam-5446	328	30	2	2	NUM
ejpam-5446	328	31	2	2	NUM
ejpam-5446	328	32	+	+	CCONJ
ejpam-5446	328	33	η2v2	η2v2	PUNCT
ejpam-5446	328	34	+	+	X
ejpam-5446	328	35	η3)u(x	η3)u(x	NOUN
ejpam-5446	328	36	)	)	PUNCT
ejpam-5446	328	37	v.	v.	ADP
ejpam-5446	328	38	govindan	govindan	PROPN
ejpam-5446	328	39	et	et	PROPN
ejpam-5446	328	40	al	al	PROPN
ejpam-5446	328	41	.	.	PUNCT
ejpam-5446	328	42	/	/	SYM
ejpam-5446	328	43	eur	eur	PROPN
ejpam-5446	328	44	.	.	PUNCT
ejpam-5446	329	1	j.	j.	PROPN
ejpam-5446	329	2	pure	pure	PROPN
ejpam-5446	329	3	appl	appl	PROPN
ejpam-5446	329	4	.	.	PROPN
ejpam-5446	329	5	math	math	PROPN
ejpam-5446	329	6	,	,	PUNCT
ejpam-5446	329	7	17	17	NUM
ejpam-5446	329	8	(	(	PUNCT
ejpam-5446	329	9	4	4	NUM
ejpam-5446	329	10	)	)	PUNCT
ejpam-5446	329	11	(	(	PUNCT
ejpam-5446	329	12	2024	2024	NUM
ejpam-5446	329	13	)	)	PUNCT
ejpam-5446	329	14	,	,	PUNCT
ejpam-5446	329	15	3585	3585	NUM
ejpam-5446	329	16	-	-	SYM
ejpam-5446	329	17	3609	3609	NUM
ejpam-5446	329	18	3597	3597	NUM
ejpam-5446	329	19	and	and	CCONJ
ejpam-5446	329	20	|ς	|ς	VERB
ejpam-5446	329	21	′(x)−	′(x)−	NOUN
ejpam-5446	329	22	v2ς(x)−	v2ς(x)−	PROPN
ejpam-5446	329	23	γ(x)|	γ(x)|	ADV
ejpam-5446	330	1	=	=	PUNCT
ejpam-5446	330	2	|u′′′	|u′′′	PROPN
ejpam-5446	330	3	(	(	PUNCT
ejpam-5446	330	4	x	x	X
ejpam-5446	330	5	)	)	PUNCT
ejpam-5446	330	6	+	+	CCONJ
ejpam-5446	330	7	(	(	PUNCT
ejpam-5446	330	8	v2	v2	NOUN
ejpam-5446	330	9	+	+	CCONJ
ejpam-5446	330	10	η1)u	η1)u	NOUN
ejpam-5446	330	11	′′	′′	PROPN
ejpam-5446	330	12	(	(	PUNCT
ejpam-5446	330	13	x	x	X
ejpam-5446	330	14	)	)	PUNCT
ejpam-5446	330	15	+	+	CCONJ
ejpam-5446	330	16	(	(	PUNCT
ejpam-5446	330	17	v22	v22	NOUN
ejpam-5446	330	18	+	+	CCONJ
ejpam-5446	330	19	η1v2	η1v2	X
ejpam-5446	330	20	+	+	CCONJ
ejpam-5446	330	21	η2)u	η2)u	ADJ
ejpam-5446	330	22	′(x	′(x	NOUN
ejpam-5446	330	23	)	)	PUNCT
ejpam-5446	331	1	+	+	NOUN
ejpam-5446	331	2	(	(	PUNCT
ejpam-5446	331	3	v32	v32	X
ejpam-5446	331	4	+	+	CCONJ
ejpam-5446	331	5	η1v	η1v	NOUN
ejpam-5446	331	6	2	2	NUM
ejpam-5446	331	7	2	2	NUM
ejpam-5446	331	8	+	+	CCONJ
ejpam-5446	331	9	η2v2	η2v2	PUNCT
ejpam-5446	331	10	+	+	NOUN
ejpam-5446	331	11	η3)u(x)−	η3)u(x)−	PROPN
ejpam-5446	331	12	v2[u	v2[u	PROPN
ejpam-5446	331	13	′′	′′	PROPN
ejpam-5446	331	14	(	(	PUNCT
ejpam-5446	331	15	x	x	X
ejpam-5446	331	16	)	)	PUNCT
ejpam-5446	331	17	+	+	CCONJ
ejpam-5446	331	18	(	(	PUNCT
ejpam-5446	331	19	v2	v2	X
ejpam-5446	331	20	+	+	CCONJ
ejpam-5446	331	21	η1)u	η1)u	NOUN
ejpam-5446	331	22	′(x	′(x	NOUN
ejpam-5446	331	23	)	)	PUNCT
ejpam-5446	332	1	+	+	PROPN
ejpam-5446	332	2	(	(	PUNCT
ejpam-5446	332	3	v22	v22	NOUN
ejpam-5446	332	4	+	+	CCONJ
ejpam-5446	332	5	η1v2	η1v2	X
ejpam-5446	332	6	+	+	NUM
ejpam-5446	332	7	η2)u(x)]−	η2)u(x)]−	PROPN
ejpam-5446	332	8	γ(x)|	γ(x)|	PROPN
ejpam-5446	332	9	|ς	|ς	PROPN
ejpam-5446	332	10	′(x)−	′(x)−	PROPN
ejpam-5446	333	1	v2ς(x)−	v2ς(x)−	X
ejpam-5446	333	2	γ(x)|	γ(x)|	ADV
ejpam-5446	334	1	=	=	PUNCT
ejpam-5446	334	2	|u′′′	|u′′′	PROPN
ejpam-5446	334	3	(	(	PUNCT
ejpam-5446	334	4	x	x	X
ejpam-5446	334	5	)	)	PUNCT
ejpam-5446	334	6	+	+	CCONJ
ejpam-5446	334	7	v2u	v2u	VERB
ejpam-5446	334	8	′′	′′	PROPN
ejpam-5446	334	9	(	(	PUNCT
ejpam-5446	334	10	x	x	X
ejpam-5446	334	11	)	)	PUNCT
ejpam-5446	334	12	+	+	CCONJ
ejpam-5446	334	13	η1u	η1u	PROPN
ejpam-5446	334	14	′′	′′	PROPN
ejpam-5446	334	15	(	(	PUNCT
ejpam-5446	334	16	x	x	X
ejpam-5446	334	17	)	)	PUNCT
ejpam-5446	334	18	+	+	CCONJ
ejpam-5446	334	19	v22u	v22u	NOUN
ejpam-5446	334	20	′(x	′(x	NOUN
ejpam-5446	334	21	)	)	PUNCT
ejpam-5446	334	22	+	+	NOUN
ejpam-5446	334	23	η1v2u	η1v2u	X
ejpam-5446	334	24	′(x	′(x	NOUN
ejpam-5446	334	25	)	)	PUNCT
ejpam-5446	335	1	+	+	CCONJ
ejpam-5446	335	2	η2u	η2u	NOUN
ejpam-5446	335	3	′(x	′(x	NOUN
ejpam-5446	335	4	)	)	PUNCT
ejpam-5446	335	5	+	+	NUM
ejpam-5446	335	6	v32u(x	v32u(x	NOUN
ejpam-5446	335	7	)	)	PUNCT
ejpam-5446	336	1	+	+	NUM
ejpam-5446	336	2	η1v	η1v	NOUN
ejpam-5446	336	3	2	2	NUM
ejpam-5446	336	4	2u(x	2u(x	NUM
ejpam-5446	336	5	)	)	PUNCT
ejpam-5446	337	1	+	+	CCONJ
ejpam-5446	337	2	η2v2u(x	η2v2u(x	NOUN
ejpam-5446	337	3	)	)	PUNCT
ejpam-5446	338	1	+	+	CCONJ
ejpam-5446	338	2	η3u(x	η3u(x	NOUN
ejpam-5446	338	3	)	)	PUNCT
ejpam-5446	338	4	−v2[u	−v2[u	PROPN
ejpam-5446	338	5	′′	′′	PROPN
ejpam-5446	338	6	(	(	PUNCT
ejpam-5446	338	7	x	x	X
ejpam-5446	338	8	)	)	PUNCT
ejpam-5446	338	9	+	+	CCONJ
ejpam-5446	338	10	v2u	v2u	NOUN
ejpam-5446	338	11	′(x	′(x	NOUN
ejpam-5446	338	12	)	)	PUNCT
ejpam-5446	338	13	+	+	CCONJ
ejpam-5446	338	14	η1u	η1u	PROPN
ejpam-5446	338	15	′(x	′(x	NOUN
ejpam-5446	338	16	)	)	PUNCT
ejpam-5446	338	17	+	+	CCONJ
ejpam-5446	338	18	v22u(x	v22u(x	NOUN
ejpam-5446	338	19	)	)	PUNCT
ejpam-5446	338	20	+	+	CCONJ
ejpam-5446	338	21	η1v2u(x	η1v2u(x	NOUN
ejpam-5446	338	22	)	)	PUNCT
ejpam-5446	339	1	+	+	CCONJ
ejpam-5446	340	1	η2u(x)]−	η2u(x)]−	ADP
ejpam-5446	340	2	γ(x)|	γ(x)|	NOUN
ejpam-5446	340	3	|ς	|ς	PROPN
ejpam-5446	340	4	′(x)−	′(x)−	PROPN
ejpam-5446	340	5	v2ς(x)−	v2ς(x)−	X
ejpam-5446	340	6	γ(x)|	γ(x)|	ADV
ejpam-5446	341	1	=	=	PUNCT
ejpam-5446	341	2	|u′′′	|u′′′	PROPN
ejpam-5446	341	3	(	(	PUNCT
ejpam-5446	341	4	x	x	NOUN
ejpam-5446	341	5	)	)	PUNCT
ejpam-5446	341	6	+	+	CCONJ
ejpam-5446	341	7	η1u	η1u	PROPN
ejpam-5446	341	8	′′	′′	PROPN
ejpam-5446	341	9	(	(	PUNCT
ejpam-5446	341	10	x	x	X
ejpam-5446	341	11	)	)	PUNCT
ejpam-5446	341	12	+	+	CCONJ
ejpam-5446	341	13	η2u	η2u	NOUN
ejpam-5446	341	14	′(x	′(x	NOUN
ejpam-5446	341	15	)	)	PUNCT
ejpam-5446	342	1	+	+	CCONJ
ejpam-5446	342	2	η3u(x)−	η3u(x)−	PROPN
ejpam-5446	342	3	γ(x)|	γ(x)|	PROPN
ejpam-5446	342	4	≤∈	≤∈	PROPN
ejpam-5446	342	5	|ς	|ς	PROPN
ejpam-5446	342	6	′(x)−	′(x)−	PROPN
ejpam-5446	342	7	v2ς(x)−	v2ς(x)−	PROPN
ejpam-5446	342	8	γ(x)|	γ(x)|	ADV
ejpam-5446	342	9	≤∈	≤∈	PROPN
ejpam-5446	342	10	.	.	PUNCT
ejpam-5446	343	1	(	(	PUNCT
ejpam-5446	343	2	2.32	2.32	NUM
ejpam-5446	343	3	)	)	PUNCT
ejpam-5446	343	4	proportionally	proportionally	ADV
ejpam-5446	343	5	ς	ς	X
ejpam-5446	343	6	satisfies	satisfie	NOUN
ejpam-5446	343	7	,	,	PUNCT
ejpam-5446	343	8	−ε	−ε	PROPN
ejpam-5446	343	9	≤	≤	PROPN
ejpam-5446	343	10	ς	ς	PROPN
ejpam-5446	343	11	′(x)−	′(x)−	PROPN
ejpam-5446	343	12	v2ς(x)−	v2ς(x)−	PROPN
ejpam-5446	343	13	γ(x	γ(x	PROPN
ejpam-5446	343	14	)	)	PUNCT
ejpam-5446	343	15	≤	≤	NUM
ejpam-5446	344	1	ε	ε	AUX
ejpam-5446	344	2	.	.	PUNCT
ejpam-5446	344	3	(	(	PUNCT
ejpam-5446	344	4	2.33	2.33	NUM
ejpam-5446	344	5	)	)	PUNCT
ejpam-5446	344	6	multiplying	multiply	VERB
ejpam-5446	344	7	the	the	DET
ejpam-5446	344	8	equation	equation	NOUN
ejpam-5446	344	9	by	by	ADP
ejpam-5446	344	10	e−v2(x−k	e−v2(x−k	PROPN
ejpam-5446	344	11	)	)	PUNCT
ejpam-5446	344	12	,	,	PUNCT
ejpam-5446	344	13	we	we	PRON
ejpam-5446	344	14	get	get	VERB
ejpam-5446	344	15	−εe−v2(x−k	−εe−v2(x−k	NOUN
ejpam-5446	344	16	)	)	PUNCT
ejpam-5446	344	17	≤	≤	NOUN
ejpam-5446	345	1	e−v2(x−k)ς	e−v2(x−k)ς	CCONJ
ejpam-5446	345	2	′(x)−	′(x)−	PROPN
ejpam-5446	345	3	v2ς(x)e	v2ς(x)e	ADJ
ejpam-5446	345	4	−v2(x−k	−v2(x−k	NOUN
ejpam-5446	345	5	)	)	PUNCT
ejpam-5446	345	6	−	−	PROPN
ejpam-5446	345	7	γ(x)e−v2(x−k	γ(x)e−v2(x−k	PROPN
ejpam-5446	345	8	)	)	PUNCT
ejpam-5446	345	9	≤	≤	NOUN
ejpam-5446	345	10	.εe−v2(x−k	.εe−v2(x−k	PUNCT
ejpam-5446	345	11	)	)	PUNCT
ejpam-5446	345	12	(	(	PUNCT
ejpam-5446	345	13	2.34	2.34	NUM
ejpam-5446	345	14	)	)	PUNCT
ejpam-5446	345	15	without	without	ADP
ejpam-5446	345	16	loss	loss	NOUN
ejpam-5446	345	17	of	of	ADP
ejpam-5446	345	18	consensus	consensus	NOUN
ejpam-5446	345	19	,	,	PUNCT
ejpam-5446	345	20	we	we	PRON
ejpam-5446	345	21	may	may	AUX
ejpam-5446	345	22	expect	expect	VERB
ejpam-5446	345	23	to	to	PART
ejpam-5446	345	24	be	be	AUX
ejpam-5446	345	25	that	that	SCONJ
ejpam-5446	345	26	v2	v2	PROPN
ejpam-5446	345	27	>	>	X
ejpam-5446	345	28	1	1	NUM
ejpam-5446	345	29	,	,	PUNCT
ejpam-5446	345	30	thus	thus	ADV
ejpam-5446	345	31	−v2εe−v2(x−k	−v2εe−v2(x−k	NOUN
ejpam-5446	345	32	)	)	PUNCT
ejpam-5446	345	33	≤	≤	NOUN
ejpam-5446	346	1	e−v2(x−k)ς	e−v2(x−k)ς	CCONJ
ejpam-5446	346	2	′(x)−	′(x)−	PROPN
ejpam-5446	346	3	v2ς(x)e	v2ς(x)e	ADJ
ejpam-5446	346	4	−v2(x−k	−v2(x−k	NOUN
ejpam-5446	346	5	)	)	PUNCT
ejpam-5446	346	6	−	−	PROPN
ejpam-5446	346	7	γ(x)e−v2(x−k	γ(x)e−v2(x−k	PROPN
ejpam-5446	346	8	)	)	PUNCT
ejpam-5446	346	9	≤	≤	NUM
ejpam-5446	346	10	v2εe	v2εe	X
ejpam-5446	346	11	−v2(x−k	−v2(x−k	NOUN
ejpam-5446	346	12	)	)	PUNCT
ejpam-5446	346	13	,	,	PUNCT
ejpam-5446	346	14	(	(	PUNCT
ejpam-5446	346	15	2.35	2.35	NUM
ejpam-5446	346	16	)	)	PUNCT
ejpam-5446	346	17	for	for	ADP
ejpam-5446	346	18	any	any	DET
ejpam-5446	346	19	x	x	SYM
ejpam-5446	346	20	∈	∈	PROPN
ejpam-5446	346	21	[	[	X
ejpam-5446	346	22	k	k	X
ejpam-5446	346	23	,	,	PUNCT
ejpam-5446	346	24	l	l	NOUN
ejpam-5446	346	25	]	]	PUNCT
ejpam-5446	346	26	.	.	PUNCT
ejpam-5446	347	1	integrating	integrate	VERB
ejpam-5446	347	2	(	(	PUNCT
ejpam-5446	347	3	2.34	2.34	NUM
ejpam-5446	347	4	)	)	PUNCT
ejpam-5446	347	5	from	from	ADP
ejpam-5446	347	6	x	x	PRON
ejpam-5446	347	7	to	to	ADP
ejpam-5446	347	8	l	l	NOUN
ejpam-5446	347	9	,	,	PUNCT
ejpam-5446	347	10	we	we	PRON
ejpam-5446	347	11	obtain	obtain	VERB
ejpam-5446	347	12	−εe−v2(x−k	−εe−v2(x−k	NOUN
ejpam-5446	347	13	)	)	PUNCT
ejpam-5446	347	14	≤	≤	NOUN
ejpam-5446	347	15	ς(n)e−v2(l−k	ς(n)e−v2(l−k	NUM
ejpam-5446	347	16	)	)	PUNCT
ejpam-5446	347	17	−	−	PROPN
ejpam-5446	347	18	εe−v2(l−k	εe−v2(l−k	NOUN
ejpam-5446	347	19	)	)	PUNCT
ejpam-5446	347	20	−	−	PRON
ejpam-5446	347	21	ς(x)e−v2(x−k	ς(x)e−v2(x−k	NOUN
ejpam-5446	347	22	)	)	PUNCT
ejpam-5446	348	1	−	−	NUM
ejpam-5446	348	2	∫	∫	PROPN
ejpam-5446	348	3	l	l	NOUN
ejpam-5446	348	4	x	x	X
ejpam-5446	348	5	γ(t)e−v2(t−a)dt	γ(t)e−v2(t−a)dt	VERB
ejpam-5446	348	6	≤	≤	X
ejpam-5446	348	7	εe−v2(x−k	εe−v2(x−k	ADV
ejpam-5446	348	8	)	)	PUNCT
ejpam-5446	348	9	.	.	PUNCT
ejpam-5446	349	1	(	(	PUNCT
ejpam-5446	349	2	2.36	2.36	NUM
ejpam-5446	349	3	)	)	PUNCT
ejpam-5446	349	4	multiplying	multiply	VERB
ejpam-5446	349	5	the	the	DET
ejpam-5446	349	6	equation	equation	NOUN
ejpam-5446	349	7	by	by	ADP
ejpam-5446	349	8	ev2(x−k	ev2(x−k	PROPN
ejpam-5446	349	9	)	)	PUNCT
ejpam-5446	349	10	,	,	PUNCT
ejpam-5446	349	11	we	we	PRON
ejpam-5446	349	12	get	get	VERB
ejpam-5446	349	13	−εe−v2(x−k)ev2(x−k	−εe−v2(x−k)ev2(x−k	NOUN
ejpam-5446	349	14	)	)	PUNCT
ejpam-5446	349	15	≤	≤	NUM
ejpam-5446	349	16	ς(l)e−v2(l−k)ev2(x−k	ς(l)e−v2(l−k)ev2(x−k	NOUN
ejpam-5446	349	17	)	)	PUNCT
ejpam-5446	349	18	−	−	NOUN
ejpam-5446	349	19	εe−v2(l−k)ev2(x−k	εe−v2(l−k)ev2(x−k	NOUN
ejpam-5446	349	20	)	)	PUNCT
ejpam-5446	349	21	−	−	PROPN
ejpam-5446	349	22	ς(x)e−v2(x−k)ev2(x−k	ς(x)e−v2(x−k)ev2(x−k	NOUN
ejpam-5446	349	23	)	)	PUNCT
ejpam-5446	350	1	−	−	NUM
ejpam-5446	350	2	∫	∫	PROPN
ejpam-5446	350	3	l	l	NOUN
ejpam-5446	350	4	x	x	SYM
ejpam-5446	350	5	γ(t)e−v2(t−k)dtev2(x−k	γ(t)e−v2(t−k)dtev2(x−k	NOUN
ejpam-5446	350	6	)	)	PUNCT
ejpam-5446	350	7	≤	≤	NUM
ejpam-5446	350	8	εe−v2(x−k)ev2(x−k	εe−v2(x−k)ev2(x−k	NOUN
ejpam-5446	350	9	)	)	PUNCT
ejpam-5446	350	10	−ε	−ε	PROPN
ejpam-5446	350	11	≤	≤	PROPN
ejpam-5446	350	12	ς(b)ev2(x−l	ς(b)ev2(x−l	ADV
ejpam-5446	350	13	)	)	PUNCT
ejpam-5446	351	1	−	−	PROPN
ejpam-5446	351	2	εev2(x−l	εev2(x−l	ADV
ejpam-5446	351	3	)	)	PUNCT
ejpam-5446	352	1	−	−	PROPN
ejpam-5446	352	2	ς(x)−	ς(x)−	PROPN
ejpam-5446	352	3	ev2x	ev2x	VERB
ejpam-5446	352	4	∫	∫	PROPN
ejpam-5446	352	5	l	l	NOUN
ejpam-5446	352	6	x	x	PROPN
ejpam-5446	352	7	γ(t)e−v2tdt	γ(t)e−v2tdt	PROPN
ejpam-5446	352	8	≤	≤	NUM
ejpam-5446	352	9	ε	ε	PROPN
ejpam-5446	352	10	.	.	PUNCT
ejpam-5446	352	11	(	(	PUNCT
ejpam-5446	352	12	2.37	2.37	NUM
ejpam-5446	352	13	)	)	PUNCT
ejpam-5446	352	14	let	let	VERB
ejpam-5446	352	15	u(x	u(x	NOUN
ejpam-5446	352	16	)	)	PUNCT
ejpam-5446	352	17	=	=	SYM
ejpam-5446	352	18	ς(l)ev2(x−l	ς(l)ev2(x−l	NOUN
ejpam-5446	352	19	)	)	PUNCT
ejpam-5446	352	20	−	−	PUNCT
ejpam-5446	353	1	ev2x	ev2x	VERB
ejpam-5446	353	2	∫	∫	PROPN
ejpam-5446	353	3	l	l	NOUN
ejpam-5446	353	4	x	x	SYM
ejpam-5446	353	5	γ(t)e	γ(t)e	PROPN
ejpam-5446	353	6	−v2tdt	−v2tdt	PROPN
ejpam-5446	353	7	then	then	ADV
ejpam-5446	353	8	u′(x	u′(x	PROPN
ejpam-5446	353	9	)	)	PUNCT
ejpam-5446	353	10	−	−	PROPN
ejpam-5446	353	11	v2u(x	v2u(x	NOUN
ejpam-5446	353	12	)	)	PUNCT
ejpam-5446	353	13	−	−	PROPN
ejpam-5446	353	14	γ(x	γ(x	NOUN
ejpam-5446	353	15	)	)	PUNCT
ejpam-5446	353	16	=	=	SYM
ejpam-5446	353	17	0	0	NUM
ejpam-5446	353	18	by	by	ADP
ejpam-5446	353	19	u′(x	u′(x	SYM
ejpam-5446	353	20	)	)	PUNCT
ejpam-5446	353	21	=	=	SYM
ejpam-5446	353	22	v2u(x	v2u(x	PROPN
ejpam-5446	353	23	)	)	PUNCT
ejpam-5446	354	1	+	+	NUM
ejpam-5446	355	1	γ(x);x	γ(x);x	PROPN
ejpam-5446	355	2	∈	∈	PROPN
ejpam-5446	356	1	[	[	X
ejpam-5446	356	2	k	k	X
ejpam-5446	356	3	,	,	PUNCT
ejpam-5446	356	4	l	l	NOUN
ejpam-5446	356	5	]	]	X
ejpam-5446	356	6	|u(x)−	|u(x)−	PROPN
ejpam-5446	356	7	ς(x)|	ς(x)|	AUX
ejpam-5446	356	8	=	=	PUNCT
ejpam-5446	356	9	∣∣∣∣ς(l)ev2(x−l	∣∣∣∣ς(l)ev2(x−l	ADJ
ejpam-5446	356	10	)	)	PUNCT
ejpam-5446	357	1	−	−	PROPN
ejpam-5446	357	2	ς(x)−	ς(x)−	PROPN
ejpam-5446	357	3	ev2(x	ev2(x	PROPN
ejpam-5446	357	4	)	)	PUNCT
ejpam-5446	358	1	∫	∫	PROPN
ejpam-5446	359	1	l	l	NOUN
ejpam-5446	359	2	x	x	PROPN
ejpam-5446	359	3	γ(t)e−v2tdt	γ(t)e−v2tdt	PROPN
ejpam-5446	359	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5446	359	5	|u(x)−	|u(x)−	NOUN
ejpam-5446	359	6	ς(x)|	ς(x)|	VERB
ejpam-5446	359	7	=	=	PUNCT
ejpam-5446	359	8	|ev2x|	|ev2x|	X
ejpam-5446	359	9	∣∣∣∣ς(l)e−v2n	∣∣∣∣ς(l)e−v2n	PROPN
ejpam-5446	359	10	−	−	PRON
ejpam-5446	359	11	e−v2xς(x	e−v2xς(x	X
ejpam-5446	359	12	)	)	PUNCT
ejpam-5446	359	13	∫	∫	PROPN
ejpam-5446	360	1	l	l	NOUN
ejpam-5446	360	2	x	x	PROPN
ejpam-5446	360	3	γ(t)e−v2tdt	γ(t)e−v2tdt	PROPN
ejpam-5446	360	4	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5446	360	5	v.	v.	ADP
ejpam-5446	360	6	govindan	govindan	PROPN
ejpam-5446	360	7	et	et	PROPN
ejpam-5446	360	8	al	al	PROPN
ejpam-5446	360	9	.	.	PUNCT
ejpam-5446	360	10	/	/	SYM
ejpam-5446	360	11	eur	eur	PROPN
ejpam-5446	360	12	.	.	PUNCT
ejpam-5446	361	1	j.	j.	PROPN
ejpam-5446	361	2	pure	pure	PROPN
ejpam-5446	361	3	appl	appl	PROPN
ejpam-5446	361	4	.	.	PROPN
ejpam-5446	361	5	math	math	PROPN
ejpam-5446	361	6	,	,	PUNCT
ejpam-5446	361	7	17	17	NUM
ejpam-5446	361	8	(	(	PUNCT
ejpam-5446	361	9	4	4	NUM
ejpam-5446	361	10	)	)	PUNCT
ejpam-5446	361	11	(	(	PUNCT
ejpam-5446	361	12	2024	2024	NUM
ejpam-5446	361	13	)	)	PUNCT
ejpam-5446	361	14	,	,	PUNCT
ejpam-5446	361	15	3585	3585	NUM
ejpam-5446	361	16	-	-	SYM
ejpam-5446	361	17	3609	3609	NUM
ejpam-5446	361	18	3598	3598	NUM
ejpam-5446	361	19	|u(x)−	|u(x)−	PROPN
ejpam-5446	361	20	ς(x)|	ς(x)|	VERB
ejpam-5446	361	21	≤	≤	NUM
ejpam-5446	362	1	ep2x	ep2x	PROPN
ejpam-5446	362	2	∫	∫	PROPN
ejpam-5446	362	3	l	l	NOUN
ejpam-5446	363	1	x	x	X
ejpam-5446	363	2	e−p2tdt	e−p2tdt	PROPN
ejpam-5446	363	3	.	.	PUNCT
ejpam-5446	364	1	(	(	PUNCT
ejpam-5446	364	2	2.38	2.38	NUM
ejpam-5446	364	3	)	)	PUNCT
ejpam-5446	364	4	if	if	SCONJ
ejpam-5446	364	5	p2	p2	PROPN
ejpam-5446	364	6	̸=	̸=	PROPN
ejpam-5446	364	7	0	0	NUM
ejpam-5446	364	8	,	,	PUNCT
ejpam-5446	364	9	then	then	ADV
ejpam-5446	364	10	|u(x)−	|u(x)−	PROPN
ejpam-5446	364	11	ς(x)|	ς(x)|	VERB
ejpam-5446	364	12	≤	≤	NUM
ejpam-5446	364	13	εep2x	εep2x	PROPN
ejpam-5446	364	14	∫	∫	PROPN
ejpam-5446	364	15	l	l	NOUN
ejpam-5446	365	1	x	x	X
ejpam-5446	365	2	e−p2tdt	e−p2tdt	ADJ
ejpam-5446	365	3	|u(x)−	|u(x)−	NOUN
ejpam-5446	365	4	ς(x)|	ς(x)|	VERB
ejpam-5446	365	5	≤	≤	NUM
ejpam-5446	365	6	ε	ε	PROPN
ejpam-5446	365	7	−p2	−p2	PROPN
ejpam-5446	365	8	[	[	PUNCT
ejpam-5446	365	9	e−p2(l−x	e−p2(l−x	NOUN
ejpam-5446	365	10	)	)	PUNCT
ejpam-5446	365	11	−	−	PROPN
ejpam-5446	365	12	1	1	NUM
ejpam-5446	365	13	]	]	PUNCT
ejpam-5446	365	14	;	;	PUNCT
ejpam-5446	365	15	x	x	SYM
ejpam-5446	365	16	∈	∈	PROPN
ejpam-5446	365	17	[	[	X
ejpam-5446	365	18	k	k	X
ejpam-5446	365	19	,	,	PUNCT
ejpam-5446	365	20	l	l	NOUN
ejpam-5446	365	21	]	]	X
ejpam-5446	365	22	|u(x)−	|u(x)−	PROPN
ejpam-5446	365	23	ς(x)|	ς(x)|	VERB
ejpam-5446	365	24	≤	≤	NUM
ejpam-5446	365	25	ε	ε	PROPN
ejpam-5446	365	26	p2	p2	PROPN
ejpam-5446	365	27	[	[	PUNCT
ejpam-5446	365	28	1−	1−	NUM
ejpam-5446	365	29	e−p2(l−x	e−p2(l−x	NOUN
ejpam-5446	365	30	)	)	PUNCT
ejpam-5446	365	31	]	]	PUNCT
ejpam-5446	365	32	;	;	PUNCT
ejpam-5446	365	33	x	x	X
ejpam-5446	365	34	∈	∈	PROPN
ejpam-5446	365	35	[	[	X
ejpam-5446	365	36	k	k	X
ejpam-5446	365	37	,	,	PUNCT
ejpam-5446	365	38	l	l	NOUN
ejpam-5446	365	39	]	]	X
ejpam-5446	365	40	|u(x)−	|u(x)−	PROPN
ejpam-5446	365	41	ς(x)|	ς(x)|	VERB
ejpam-5446	365	42	≤	≤	NUM
ejpam-5446	365	43	ε	ε	PROPN
ejpam-5446	365	44	p2	p2	PROPN
ejpam-5446	365	45	[	[	PUNCT
ejpam-5446	365	46	1−	1−	NUM
ejpam-5446	365	47	e−p2(l−k	e−p2(l−k	NOUN
ejpam-5446	365	48	)	)	PUNCT
ejpam-5446	365	49	]	]	PUNCT
ejpam-5446	365	50	;	;	PUNCT
ejpam-5446	365	51	x	x	X
ejpam-5446	365	52	∈	∈	PROPN
ejpam-5446	366	1	[	[	X
ejpam-5446	366	2	k	k	X
ejpam-5446	366	3	,	,	PUNCT
ejpam-5446	366	4	l	l	NOUN
ejpam-5446	366	5	]	]	X
ejpam-5446	366	6	.	.	PUNCT
ejpam-5446	367	1	(	(	PUNCT
ejpam-5446	367	2	2.39	2.39	NUM
ejpam-5446	367	3	)	)	PUNCT
ejpam-5446	367	4	if	if	SCONJ
ejpam-5446	367	5	p2	p2	X
ejpam-5446	367	6	=	=	SYM
ejpam-5446	367	7	0	0	NUM
ejpam-5446	367	8	,	,	PUNCT
ejpam-5446	367	9	then	then	ADV
ejpam-5446	367	10	|u(x)−	|u(x)−	PROPN
ejpam-5446	367	11	ς(x)|	ς(x)|	VERB
ejpam-5446	367	12	≤	≤	NUM
ejpam-5446	367	13	εep2x	εep2x	PROPN
ejpam-5446	367	14	∫	∫	PROPN
ejpam-5446	367	15	l	l	NOUN
ejpam-5446	368	1	x	x	X
ejpam-5446	368	2	e−p2tdt	e−p2tdt	ADJ
ejpam-5446	368	3	|u(x)−	|u(x)−	NOUN
ejpam-5446	368	4	ς(x)|	ς(x)|	VERB
ejpam-5446	368	5	≤	≤	NUM
ejpam-5446	368	6	ε	ε	PROPN
ejpam-5446	368	7	∫	∫	PROPN
ejpam-5446	369	1	l	l	NOUN
ejpam-5446	370	1	x	x	X
ejpam-5446	370	2	dt	dt	X
ejpam-5446	370	3	|u(x)−	|u(x)−	PROPN
ejpam-5446	370	4	ς(x)|	ς(x)|	VERB
ejpam-5446	370	5	≤	≤	ADJ
ejpam-5446	370	6	ε(l	ε(l	PROPN
ejpam-5446	370	7	−	−	PROPN
ejpam-5446	370	8	x);x	x);x	PROPN
ejpam-5446	370	9	∈	∈	PROPN
ejpam-5446	371	1	[	[	X
ejpam-5446	371	2	k	k	X
ejpam-5446	371	3	,	,	PUNCT
ejpam-5446	371	4	l	l	NOUN
ejpam-5446	371	5	]	]	X
ejpam-5446	371	6	|u(x)−	|u(x)−	PROPN
ejpam-5446	371	7	ς(x)|	ς(x)|	VERB
ejpam-5446	371	8	≤	≤	ADJ
ejpam-5446	371	9	ε(l	ε(l	PROPN
ejpam-5446	371	10	−	−	PROPN
ejpam-5446	372	1	k);x	k);x	PROPN
ejpam-5446	372	2	∈	∈	PROPN
ejpam-5446	373	1	[	[	X
ejpam-5446	373	2	k	k	X
ejpam-5446	373	3	,	,	PUNCT
ejpam-5446	373	4	l	l	NOUN
ejpam-5446	373	5	]	]	X
ejpam-5446	373	6	.	.	PUNCT
ejpam-5446	374	1	(	(	PUNCT
ejpam-5446	374	2	2.40	2.40	NUM
ejpam-5446	374	3	)	)	PUNCT
ejpam-5446	374	4	if	if	SCONJ
ejpam-5446	374	5	follows	follow	VERB
ejpam-5446	374	6	from	from	ADP
ejpam-5446	374	7	(	(	PUNCT
ejpam-5446	374	8	2.20	2.20	NUM
ejpam-5446	374	9	)	)	PUNCT
ejpam-5446	374	10	,	,	PUNCT
ejpam-5446	374	11	we	we	PRON
ejpam-5446	374	12	conclude	conclude	VERB
ejpam-5446	374	13	our	our	PRON
ejpam-5446	374	14	result	result	NOUN
ejpam-5446	374	15	(	(	PUNCT
ejpam-5446	374	16	2.31	2.31	NUM
ejpam-5446	374	17	)	)	PUNCT
ejpam-5446	374	18	,	,	PUNCT
ejpam-5446	374	19	∀	∀	PUNCT
ejpam-5446	375	1	x	x	SYM
ejpam-5446	375	2	∈	∈	PROPN
ejpam-5446	376	1	[	[	X
ejpam-5446	376	2	k	k	X
ejpam-5446	376	3	,	,	PUNCT
ejpam-5446	376	4	l	l	NOUN
ejpam-5446	376	5	]	]	X
ejpam-5446	376	6	.	.	PUNCT
ejpam-5446	377	1	theorem.2.4.the	theorem.2.4.the	DET
ejpam-5446	377	2	differential	differential	ADJ
ejpam-5446	377	3	equation	equation	NOUN
ejpam-5446	377	4	ςv(x)+η1ς	ςv(x)+η1ς	PROPN
ejpam-5446	377	5	iv(x)+η2ς	iv(x)+η2ς	PROPN
ejpam-5446	377	6	′′′	′′′	PROPN
ejpam-5446	377	7	(	(	PUNCT
ejpam-5446	377	8	x)+η3ς	x)+η3ς	PROPN
ejpam-5446	377	9	′′	′′	PROPN
ejpam-5446	377	10	(	(	PUNCT
ejpam-5446	377	11	x)+η4ς	x)+η4ς	PROPN
ejpam-5446	377	12	′	′	NUM
ejpam-5446	377	13	(	(	PUNCT
ejpam-5446	377	14	x)+η5ς(x	x)+η5ς(x	NOUN
ejpam-5446	377	15	)	)	PUNCT
ejpam-5446	377	16	=	=	SYM
ejpam-5446	377	17	ω(x	ω(x	NOUN
ejpam-5446	377	18	)	)	PUNCT
ejpam-5446	377	19	has	have	VERB
ejpam-5446	377	20	the	the	DET
ejpam-5446	377	21	hyers	hyers	PROPN
ejpam-5446	377	22	-	-	PUNCT
ejpam-5446	377	23	ulam	ulam	PROPN
ejpam-5446	377	24	stability	stability	NOUN
ejpam-5446	377	25	,	,	PUNCT
ejpam-5446	377	26	where	where	SCONJ
ejpam-5446	377	27	ς	ς	PROPN
ejpam-5446	377	28	∈	∈	PROPN
ejpam-5446	377	29	c5[k	c5[k	NOUN
ejpam-5446	377	30	,	,	PUNCT
ejpam-5446	377	31	l	l	NOUN
ejpam-5446	377	32	]	]	PUNCT
ejpam-5446	377	33	and	and	CCONJ
ejpam-5446	377	34	ω	ω	NUM
ejpam-5446	377	35	∈	∈	PROPN
ejpam-5446	378	1	[	[	X
ejpam-5446	378	2	k	k	X
ejpam-5446	378	3	,	,	PUNCT
ejpam-5446	378	4	l	l	NOUN
ejpam-5446	378	5	]	]	PUNCT
ejpam-5446	378	6	.	.	PUNCT
ejpam-5446	379	1	then	then	ADV
ejpam-5446	379	2	v.	v.	INTJ
ejpam-5446	379	3	govindan	govindan	PROPN
ejpam-5446	379	4	et	et	PROPN
ejpam-5446	379	5	al	al	PROPN
ejpam-5446	379	6	.	.	PUNCT
ejpam-5446	379	7	/	/	SYM
ejpam-5446	379	8	eur	eur	PROPN
ejpam-5446	379	9	.	.	PUNCT
ejpam-5446	380	1	j.	j.	PROPN
ejpam-5446	380	2	pure	pure	PROPN
ejpam-5446	380	3	appl	appl	PROPN
ejpam-5446	380	4	.	.	PROPN
ejpam-5446	380	5	math	math	PROPN
ejpam-5446	380	6	,	,	PUNCT
ejpam-5446	380	7	17	17	NUM
ejpam-5446	380	8	(	(	PUNCT
ejpam-5446	380	9	4	4	NUM
ejpam-5446	380	10	)	)	PUNCT
ejpam-5446	380	11	(	(	PUNCT
ejpam-5446	380	12	2024	2024	NUM
ejpam-5446	380	13	)	)	PUNCT
ejpam-5446	380	14	,	,	PUNCT
ejpam-5446	380	15	3585	3585	NUM
ejpam-5446	380	16	-	-	SYM
ejpam-5446	380	17	3609	3609	NUM
ejpam-5446	380	18	3599	3599	NUM
ejpam-5446	380	19	|t	|t	PROPN
ejpam-5446	380	20	(	(	PUNCT
ejpam-5446	380	21	x)−	x)−	PROPN
ejpam-5446	380	22	χ(x)|	χ(x)|	PROPN
ejpam-5446	380	23	≤	≤	NUM
ejpam-5446	380	24			PUNCT
ejpam-5446	381	1	[	[	X
ejpam-5446	381	2	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p3(l−k)][1−e−p4(l−k)]ε	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p3(l−k)][1−e−p4(l−k)]ε	NUM
ejpam-5446	381	3	p1p2p3p4	p1p2p3p4	NOUN
ejpam-5446	381	4	,	,	PUNCT
ejpam-5446	381	5	if	if	SCONJ
ejpam-5446	381	6	p1	p1	PROPN
ejpam-5446	381	7	,	,	PUNCT
ejpam-5446	381	8	p2	p2	NOUN
ejpam-5446	381	9	,	,	PUNCT
ejpam-5446	381	10	p3	p3	NOUN
ejpam-5446	381	11	,	,	PUNCT
ejpam-5446	381	12	p4	p4	ADJ
ejpam-5446	381	13	̸=	̸=	PROPN
ejpam-5446	381	14	0	0	NUM
ejpam-5446	382	1	[	[	X
ejpam-5446	382	2	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p3(l−k)](l−k)ε	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p3(l−k)](l−k)ε	NUM
ejpam-5446	382	3	p1p2p3	p1p2p3	NOUN
ejpam-5446	382	4	,	,	PUNCT
ejpam-5446	382	5	if	if	SCONJ
ejpam-5446	382	6	p1	p1	PROPN
ejpam-5446	382	7	,	,	PUNCT
ejpam-5446	382	8	p2	p2	NOUN
ejpam-5446	382	9	,	,	PUNCT
ejpam-5446	382	10	p3	p3	PROPN
ejpam-5446	382	11	̸=	̸=	PROPN
ejpam-5446	382	12	0	0	NUM
ejpam-5446	382	13	,	,	PUNCT
ejpam-5446	382	14	p4	p4	ADJ
ejpam-5446	382	15	=	=	NOUN
ejpam-5446	382	16	0	0	PUNCT
ejpam-5446	383	1	[	[	X
ejpam-5446	383	2	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p4(l−k)](l−k)ε	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p4(l−k)](l−k)ε	NUM
ejpam-5446	383	3	p1p2p4	p1p2p4	NOUN
ejpam-5446	383	4	,	,	PUNCT
ejpam-5446	383	5	if	if	SCONJ
ejpam-5446	383	6	p1	p1	PROPN
ejpam-5446	383	7	,	,	PUNCT
ejpam-5446	383	8	p2	p2	NOUN
ejpam-5446	383	9	,	,	PUNCT
ejpam-5446	383	10	p4	p4	ADJ
ejpam-5446	383	11	̸=	̸=	PROPN
ejpam-5446	383	12	0	0	NUM
ejpam-5446	383	13	,	,	PUNCT
ejpam-5446	383	14	p3	p3	PROPN
ejpam-5446	383	15	=	=	X
ejpam-5446	383	16	0	0	PUNCT
ejpam-5446	384	1	[	[	X
ejpam-5446	384	2	1−e−p1(l−k)][1−e−p3(l−k)][1−e−p4(l−k)](l−k)ε	1−e−p1(l−k)][1−e−p3(l−k)][1−e−p4(l−k)](l−k)ε	NUM
ejpam-5446	384	3	p1p3p4	p1p3p4	NOUN
ejpam-5446	384	4	,	,	PUNCT
ejpam-5446	384	5	if	if	SCONJ
ejpam-5446	384	6	p1	p1	PROPN
ejpam-5446	384	7	,	,	PUNCT
ejpam-5446	384	8	p3	p3	PROPN
ejpam-5446	384	9	,	,	PUNCT
ejpam-5446	384	10	p4	p4	ADJ
ejpam-5446	384	11	̸=	̸=	PROPN
ejpam-5446	384	12	0	0	NUM
ejpam-5446	384	13	,	,	PUNCT
ejpam-5446	384	14	p2	p2	X
ejpam-5446	384	15	=	=	SYM
ejpam-5446	384	16	0	0	PUNCT
ejpam-5446	385	1	[	[	X
ejpam-5446	385	2	1−e−p2(l−k)][1−e−p3(l−k)][1−e−p4(l−k)](l−k)ε	1−e−p2(l−k)][1−e−p3(l−k)][1−e−p4(l−k)](l−k)ε	NUM
ejpam-5446	385	3	p2p3p4	p2p3p4	NOUN
ejpam-5446	385	4	,	,	PUNCT
ejpam-5446	385	5	if	if	SCONJ
ejpam-5446	385	6	p2	p2	NOUN
ejpam-5446	385	7	,	,	PUNCT
ejpam-5446	385	8	p3	p3	NOUN
ejpam-5446	385	9	,	,	PUNCT
ejpam-5446	385	10	p4	p4	ADJ
ejpam-5446	385	11	̸=	̸=	PROPN
ejpam-5446	385	12	0	0	NUM
ejpam-5446	385	13	,	,	PUNCT
ejpam-5446	385	14	p1	p1	NOUN
ejpam-5446	385	15	=	=	NOUN
ejpam-5446	385	16	0	0	PUNCT
ejpam-5446	386	1	[	[	X
ejpam-5446	386	2	1−e−p1(l−k)][1−e−p2(l−k)](l−k)2ε	1−e−p1(l−k)][1−e−p2(l−k)](l−k)2ε	NUM
ejpam-5446	386	3	p1p2	p1p2	NOUN
ejpam-5446	386	4	,	,	PUNCT
ejpam-5446	386	5	if	if	SCONJ
ejpam-5446	386	6	p1	p1	PROPN
ejpam-5446	386	7	,	,	PUNCT
ejpam-5446	386	8	p2	p2	PROPN
ejpam-5446	386	9	̸=	̸=	PROPN
ejpam-5446	386	10	0	0	NUM
ejpam-5446	386	11	,	,	PUNCT
ejpam-5446	386	12	p3	p3	NOUN
ejpam-5446	386	13	,	,	PUNCT
ejpam-5446	386	14	p4	p4	ADJ
ejpam-5446	386	15	=	=	NOUN
ejpam-5446	386	16	0	0	PUNCT
ejpam-5446	387	1	[	[	X
ejpam-5446	387	2	1−e−p1(l−k)][1−e−p3(l−k)](l−k)2ε	1−e−p1(l−k)][1−e−p3(l−k)](l−k)2ε	NUM
ejpam-5446	387	3	p1p3	p1p3	ADP
ejpam-5446	387	4	,	,	PUNCT
ejpam-5446	387	5	if	if	SCONJ
ejpam-5446	387	6	p1	p1	PROPN
ejpam-5446	387	7	,	,	PUNCT
ejpam-5446	387	8	p3	p3	PROPN
ejpam-5446	387	9	̸=	̸=	PROPN
ejpam-5446	387	10	0	0	NUM
ejpam-5446	387	11	,	,	PUNCT
ejpam-5446	387	12	p2	p2	NOUN
ejpam-5446	387	13	,	,	PUNCT
ejpam-5446	387	14	p4	p4	NOUN
ejpam-5446	387	15	=	=	NOUN
ejpam-5446	387	16	0	0	PUNCT
ejpam-5446	388	1	[	[	X
ejpam-5446	388	2	1−e−p1(l−k)][1−e−p4(l−k)](l−k)2ε	1−e−p1(l−k)][1−e−p4(l−k)](l−k)2ε	NUM
ejpam-5446	388	3	p1p4	p1p4	INTJ
ejpam-5446	388	4	,	,	PUNCT
ejpam-5446	388	5	if	if	SCONJ
ejpam-5446	388	6	p1	p1	PROPN
ejpam-5446	388	7	,	,	PUNCT
ejpam-5446	388	8	p4	p4	ADJ
ejpam-5446	388	9	̸=	̸=	PROPN
ejpam-5446	388	10	0	0	NUM
ejpam-5446	388	11	,	,	PUNCT
ejpam-5446	388	12	p2	p2	NOUN
ejpam-5446	388	13	,	,	PUNCT
ejpam-5446	388	14	p3	p3	NOUN
ejpam-5446	388	15	=	=	X
ejpam-5446	388	16	0	0	PUNCT
ejpam-5446	389	1	[	[	X
ejpam-5446	389	2	1−e−p2(l−k)][1−e−p3(l−k)](l−k)2ε	1−e−p2(l−k)][1−e−p3(l−k)](l−k)2ε	X
ejpam-5446	389	3	p2p3	p2p3	CCONJ
ejpam-5446	389	4	,	,	PUNCT
ejpam-5446	389	5	if	if	SCONJ
ejpam-5446	389	6	p2	p2	NOUN
ejpam-5446	389	7	,	,	PUNCT
ejpam-5446	389	8	p3	p3	PROPN
ejpam-5446	389	9	̸=	̸=	PROPN
ejpam-5446	389	10	0	0	NUM
ejpam-5446	389	11	,	,	PUNCT
ejpam-5446	389	12	p1	p1	NOUN
ejpam-5446	389	13	,	,	PUNCT
ejpam-5446	389	14	p4	p4	NOUN
ejpam-5446	389	15	=	=	NOUN
ejpam-5446	389	16	0	0	PUNCT
ejpam-5446	390	1	[	[	X
ejpam-5446	390	2	1−e−p2(l−k)][1−e−p4(l−k)](l−k)2ε	1−e−p2(l−k)][1−e−p4(l−k)](l−k)2ε	X
ejpam-5446	390	3	p2p4	p2p4	ADJ
ejpam-5446	390	4	,	,	PUNCT
ejpam-5446	390	5	if	if	SCONJ
ejpam-5446	390	6	p2	p2	NOUN
ejpam-5446	390	7	,	,	PUNCT
ejpam-5446	390	8	p4	p4	ADJ
ejpam-5446	390	9	̸=	̸=	PROPN
ejpam-5446	390	10	0	0	NUM
ejpam-5446	390	11	,	,	PUNCT
ejpam-5446	390	12	p1	p1	NOUN
ejpam-5446	390	13	,	,	PUNCT
ejpam-5446	390	14	p3	p3	PROPN
ejpam-5446	390	15	=	=	X
ejpam-5446	390	16	0	0	PUNCT
ejpam-5446	391	1	[	[	X
ejpam-5446	391	2	1−e−p3(l−k)][1−e−p4(l−k)](l−k)2ε	1−e−p3(l−k)][1−e−p4(l−k)](l−k)2ε	NUM
ejpam-5446	391	3	p3p4	p3p4	NOUN
ejpam-5446	391	4	,	,	PUNCT
ejpam-5446	391	5	if	if	SCONJ
ejpam-5446	391	6	p3	p3	PROPN
ejpam-5446	391	7	,	,	PUNCT
ejpam-5446	391	8	p4	p4	ADJ
ejpam-5446	391	9	̸=	̸=	PROPN
ejpam-5446	391	10	0	0	NUM
ejpam-5446	391	11	,	,	PUNCT
ejpam-5446	391	12	p1	p1	NOUN
ejpam-5446	391	13	,	,	PUNCT
ejpam-5446	391	14	p2	p2	X
ejpam-5446	391	15	=	=	SYM
ejpam-5446	391	16	0	0	PUNCT
ejpam-5446	392	1	[	[	X
ejpam-5446	392	2	1−e−p1(l−k)](l−k)3ε	1−e−p1(l−k)](l−k)3ε	NUM
ejpam-5446	392	3	p1	p1	NOUN
ejpam-5446	392	4	,	,	PUNCT
ejpam-5446	392	5	if	if	SCONJ
ejpam-5446	392	6	p1	p1	PROPN
ejpam-5446	392	7	̸=	̸=	PROPN
ejpam-5446	392	8	0	0	NUM
ejpam-5446	392	9	,	,	PUNCT
ejpam-5446	392	10	p2	p2	NOUN
ejpam-5446	392	11	,	,	PUNCT
ejpam-5446	392	12	p3	p3	NOUN
ejpam-5446	392	13	,	,	PUNCT
ejpam-5446	392	14	p4	p4	ADJ
ejpam-5446	392	15	=	=	NOUN
ejpam-5446	392	16	0	0	PUNCT
ejpam-5446	393	1	[	[	X
ejpam-5446	393	2	1−e−p2(l−k)](l−k)3ε	1−e−p2(l−k)](l−k)3ε	NUM
ejpam-5446	393	3	p2	p2	NOUN
ejpam-5446	393	4	,	,	PUNCT
ejpam-5446	393	5	if	if	SCONJ
ejpam-5446	393	6	p2	p2	PROPN
ejpam-5446	393	7	̸=	̸=	PROPN
ejpam-5446	393	8	0	0	NUM
ejpam-5446	393	9	,	,	PUNCT
ejpam-5446	393	10	p1	p1	NOUN
ejpam-5446	393	11	,	,	PUNCT
ejpam-5446	393	12	p3	p3	PROPN
ejpam-5446	393	13	,	,	PUNCT
ejpam-5446	393	14	p4	p4	ADJ
ejpam-5446	393	15	=	=	NOUN
ejpam-5446	393	16	0	0	PUNCT
ejpam-5446	394	1	[	[	X
ejpam-5446	394	2	1−e−p3(l−k)](l−k)3ε	1−e−p3(l−k)](l−k)3ε	NUM
ejpam-5446	394	3	p3	p3	NOUN
ejpam-5446	394	4	,	,	PUNCT
ejpam-5446	394	5	if	if	SCONJ
ejpam-5446	394	6	p3	p3	PROPN
ejpam-5446	394	7	̸=	̸=	PROPN
ejpam-5446	394	8	0	0	NUM
ejpam-5446	394	9	,	,	PUNCT
ejpam-5446	394	10	p1	p1	NOUN
ejpam-5446	394	11	,	,	PUNCT
ejpam-5446	394	12	p2	p2	NOUN
ejpam-5446	394	13	,	,	PUNCT
ejpam-5446	394	14	p4	p4	NOUN
ejpam-5446	394	15	=	=	NOUN
ejpam-5446	394	16	0	0	PUNCT
ejpam-5446	395	1	[	[	X
ejpam-5446	395	2	1−e−p4(l−k)](l−k)3ε	1−e−p4(l−k)](l−k)3ε	NUM
ejpam-5446	395	3	p4	p4	NOUN
ejpam-5446	395	4	,	,	PUNCT
ejpam-5446	395	5	if	if	SCONJ
ejpam-5446	395	6	p4	p4	ADJ
ejpam-5446	395	7	̸=	̸=	PROPN
ejpam-5446	395	8	0	0	NUM
ejpam-5446	395	9	,	,	PUNCT
ejpam-5446	395	10	p1	p1	NOUN
ejpam-5446	395	11	,	,	PUNCT
ejpam-5446	395	12	p2	p2	NOUN
ejpam-5446	395	13	,	,	PUNCT
ejpam-5446	395	14	p3	p3	PROPN
ejpam-5446	395	15	=	=	SYM
ejpam-5446	395	16	0	0	PUNCT
ejpam-5446	395	17	(	(	PUNCT
ejpam-5446	395	18	l	l	NOUN
ejpam-5446	395	19	−	−	PROPN
ejpam-5446	395	20	k)4ε	k)4ε	X
ejpam-5446	395	21	,	,	PUNCT
ejpam-5446	395	22	if	if	SCONJ
ejpam-5446	395	23	p1	p1	PROPN
ejpam-5446	395	24	,	,	PUNCT
ejpam-5446	395	25	p2	p2	NOUN
ejpam-5446	395	26	,	,	PUNCT
ejpam-5446	395	27	p3	p3	NOUN
ejpam-5446	395	28	,	,	PUNCT
ejpam-5446	395	29	p4	p4	ADJ
ejpam-5446	395	30	=	=	SYM
ejpam-5446	395	31	0	0	NUM
ejpam-5446	396	1	(	(	PUNCT
ejpam-5446	396	2	2.41	2.41	NUM
ejpam-5446	396	3	)	)	PUNCT
ejpam-5446	396	4	with	with	ADP
ejpam-5446	396	5	respect	respect	NOUN
ejpam-5446	396	6	to	to	ADP
ejpam-5446	396	7	x	x	SYM
ejpam-5446	396	8	∈	∈	PROPN
ejpam-5446	397	1	[	[	X
ejpam-5446	397	2	k	k	X
ejpam-5446	397	3	,	,	PUNCT
ejpam-5446	397	4	l	l	NOUN
ejpam-5446	397	5	]	]	X
ejpam-5446	397	6	proof	proof	NOUN
ejpam-5446	397	7	:	:	PUNCT
ejpam-5446	397	8	similar	similar	ADJ
ejpam-5446	397	9	to	to	ADP
ejpam-5446	397	10	the	the	DET
ejpam-5446	397	11	proof	proof	NOUN
ejpam-5446	397	12	of	of	ADP
ejpam-5446	397	13	theorem	theorem	NOUN
ejpam-5446	397	14	(	(	PUNCT
ejpam-5446	397	15	2.3	2.3	NUM
ejpam-5446	397	16	)	)	PUNCT
ejpam-5446	397	17	,	,	PUNCT
ejpam-5446	397	18	let	let	VERB
ejpam-5446	397	19	∈	∈	PRON
ejpam-5446	397	20	>	>	X
ejpam-5446	397	21	0	0	PROPN
ejpam-5446	397	22	and	and	CCONJ
ejpam-5446	397	23	ω	ω	NUM
ejpam-5446	397	24	∈	∈	PROPN
ejpam-5446	398	1	[	[	X
ejpam-5446	398	2	k	k	X
ejpam-5446	398	3	,	,	PUNCT
ejpam-5446	398	4	l	l	NOUN
ejpam-5446	398	5	]	]	PUNCT
ejpam-5446	398	6	.	.	PUNCT
ejpam-5446	399	1	let	let	VERB
ejpam-5446	399	2	us	we	PRON
ejpam-5446	399	3	consider	consider	VERB
ejpam-5446	399	4	χ(x	χ(x	PRON
ejpam-5446	399	5	)	)	PUNCT
ejpam-5446	400	1	=	=	SYM
ejpam-5446	400	2	ς	ς	PROPN
ejpam-5446	400	3	′′′	′′′	PROPN
ejpam-5446	400	4	(	(	PUNCT
ejpam-5446	400	5	x	x	X
ejpam-5446	400	6	)	)	PUNCT
ejpam-5446	400	7	+	+	CCONJ
ejpam-5446	400	8	(	(	PUNCT
ejpam-5446	400	9	v3	v3	PROPN
ejpam-5446	400	10	+	+	CCONJ
ejpam-5446	400	11	η1)ς	η1)ς	VERB
ejpam-5446	400	12	′′	′′	PROPN
ejpam-5446	400	13	(	(	PUNCT
ejpam-5446	400	14	x	x	X
ejpam-5446	400	15	)	)	PUNCT
ejpam-5446	400	16	+	+	CCONJ
ejpam-5446	400	17	(	(	PUNCT
ejpam-5446	400	18	v23	v23	NOUN
ejpam-5446	400	19	+	+	CCONJ
ejpam-5446	400	20	η1u+	η1u+	PROPN
ejpam-5446	400	21	η2)ς	η2)ς	PROPN
ejpam-5446	400	22	′(x	′(x	PROPN
ejpam-5446	400	23	)	)	PUNCT
ejpam-5446	401	1	+	+	CCONJ
ejpam-5446	401	2	(	(	PUNCT
ejpam-5446	401	3	v33	v33	ADV
ejpam-5446	401	4	+	+	CCONJ
ejpam-5446	401	5	η1u	η1u	X
ejpam-5446	401	6	2	2	NUM
ejpam-5446	401	7	+	+	CCONJ
ejpam-5446	401	8	η2v3	η2v3	ADJ
ejpam-5446	401	9	+	+	ADJ
ejpam-5446	401	10	η3)ς(x	η3)ς(x	NOUN
ejpam-5446	401	11	)	)	PUNCT
ejpam-5446	401	12	,	,	PUNCT
ejpam-5446	401	13	we	we	PRON
ejpam-5446	401	14	obtain	obtain	VERB
ejpam-5446	401	15	χ′(x	χ′(x	NOUN
ejpam-5446	401	16	)	)	PUNCT
ejpam-5446	402	1	=	=	SYM
ejpam-5446	402	2	ς	ς	PROPN
ejpam-5446	402	3	iv(x	iv(x	NOUN
ejpam-5446	402	4	)	)	PUNCT
ejpam-5446	403	1	+	+	CCONJ
ejpam-5446	403	2	(	(	PUNCT
ejpam-5446	403	3	v3	v3	PROPN
ejpam-5446	403	4	+	+	CCONJ
ejpam-5446	403	5	η1)ς	η1)ς	PROPN
ejpam-5446	403	6	′′′	′′′	PROPN
ejpam-5446	403	7	(	(	PUNCT
ejpam-5446	403	8	x	x	X
ejpam-5446	403	9	)	)	PUNCT
ejpam-5446	404	1	+	+	CCONJ
ejpam-5446	404	2	(	(	PUNCT
ejpam-5446	404	3	v23	v23	PROPN
ejpam-5446	404	4	+	+	CCONJ
ejpam-5446	404	5	η1v3	η1v3	NOUN
ejpam-5446	404	6	+	+	CCONJ
ejpam-5446	404	7	η2)ς	η2)ς	NOUN
ejpam-5446	404	8	′′	′′	PROPN
ejpam-5446	404	9	(	(	PUNCT
ejpam-5446	404	10	x	x	X
ejpam-5446	404	11	)	)	PUNCT
ejpam-5446	405	1	+	+	ADJ
ejpam-5446	405	2	(	(	PUNCT
ejpam-5446	405	3	v33	v33	ADJ
ejpam-5446	405	4	+	+	ADJ
ejpam-5446	405	5	η1v	η1v	NOUN
ejpam-5446	405	6	2	2	NUM
ejpam-5446	405	7	3	3	NUM
ejpam-5446	405	8	+	+	CCONJ
ejpam-5446	405	9	η2v3	η2v3	PROPN
ejpam-5446	405	10	+	+	CCONJ
ejpam-5446	405	11	η3)ς	η3)ς	NOUN
ejpam-5446	405	12	′(x	′(x	NOUN
ejpam-5446	405	13	)	)	PUNCT
ejpam-5446	406	1	+	+	CCONJ
ejpam-5446	406	2	(	(	PUNCT
ejpam-5446	406	3	v43	v43	NOUN
ejpam-5446	406	4	+	+	CCONJ
ejpam-5446	406	5	η1v	η1v	NOUN
ejpam-5446	406	6	3	3	NUM
ejpam-5446	406	7	3	3	NUM
ejpam-5446	406	8	+	+	CCONJ
ejpam-5446	406	9	η2v	η2v	PROPN
ejpam-5446	406	10	2	2	NUM
ejpam-5446	406	11	3	3	NUM
ejpam-5446	406	12	+	+	CCONJ
ejpam-5446	406	13	η3v3	η3v3	PROPN
ejpam-5446	406	14	+	+	ADJ
ejpam-5446	406	15	η4)ς(x	η4)ς(x	NUM
ejpam-5446	406	16	)	)	PUNCT
ejpam-5446	406	17	,	,	PUNCT
ejpam-5446	406	18	for	for	ADP
ejpam-5446	406	19	all	all	DET
ejpam-5446	406	20	x	x	SYM
ejpam-5446	406	21	∈	∈	PROPN
ejpam-5446	407	1	[	[	X
ejpam-5446	407	2	k	k	X
ejpam-5446	407	3	,	,	PUNCT
ejpam-5446	407	4	l	l	NOUN
ejpam-5446	407	5	]	]	PUNCT
ejpam-5446	407	6	.	.	PUNCT
ejpam-5446	408	1	then	then	ADV
ejpam-5446	408	2	∣∣χ′(x)−	∣∣χ′(x)−	PROPN
ejpam-5446	408	3	v3(χ(x))−	v3(χ(x))−	PROPN
ejpam-5446	408	4	u(x	u(x	PROPN
ejpam-5446	408	5	)	)	PUNCT
ejpam-5446	409	1	∣∣	∣∣	NUM
ejpam-5446	409	2	≤	≤	PROPN
ejpam-5446	409	3	ε	ε	PROPN
ejpam-5446	409	4	(	(	PUNCT
ejpam-5446	409	5	2.42)∣∣χ′(x)−	2.42)∣∣χ′(x)−	PROPN
ejpam-5446	409	6	v3χ(x)−	v3χ(x)−	PROPN
ejpam-5446	409	7	u(x	u(x	PROPN
ejpam-5446	409	8	)	)	PUNCT
ejpam-5446	409	9	∣∣	∣∣	X
ejpam-5446	409	10	=	=	SYM
ejpam-5446	409	11	|ς	|ς	PROPN
ejpam-5446	409	12	iv(x	iv(x	NOUN
ejpam-5446	409	13	)	)	PUNCT
ejpam-5446	409	14	+	+	CCONJ
ejpam-5446	409	15	(	(	PUNCT
ejpam-5446	409	16	v3	v3	PROPN
ejpam-5446	409	17	+	+	CCONJ
ejpam-5446	409	18	η1)ς	η1)ς	PROPN
ejpam-5446	409	19	′′′	′′′	PROPN
ejpam-5446	409	20	(	(	PUNCT
ejpam-5446	409	21	x	x	X
ejpam-5446	409	22	)	)	PUNCT
ejpam-5446	409	23	+	+	ADJ
ejpam-5446	409	24	(	(	PUNCT
ejpam-5446	409	25	v23	v23	NOUN
ejpam-5446	409	26	+	+	CCONJ
ejpam-5446	409	27	η1v3	η1v3	NOUN
ejpam-5446	409	28	+	+	CCONJ
ejpam-5446	409	29	η2)ς	η2)ς	NOUN
ejpam-5446	409	30	′′	′′	PROPN
ejpam-5446	409	31	(	(	PUNCT
ejpam-5446	409	32	x	x	X
ejpam-5446	409	33	)	)	PUNCT
ejpam-5446	410	1	+	+	ADJ
ejpam-5446	410	2	(	(	PUNCT
ejpam-5446	410	3	v33	v33	ADJ
ejpam-5446	410	4	+	+	ADJ
ejpam-5446	410	5	η1v	η1v	NOUN
ejpam-5446	410	6	2	2	NUM
ejpam-5446	410	7	3	3	NUM
ejpam-5446	410	8	+	+	CCONJ
ejpam-5446	410	9	η2v3	η2v3	PROPN
ejpam-5446	410	10	+	+	CCONJ
ejpam-5446	410	11	η3)ς	η3)ς	NOUN
ejpam-5446	410	12	′(x	′(x	NOUN
ejpam-5446	410	13	)	)	PUNCT
ejpam-5446	411	1	+	+	PROPN
ejpam-5446	411	2	(	(	PUNCT
ejpam-5446	411	3	v43	v43	NOUN
ejpam-5446	411	4	+	+	ADJ
ejpam-5446	411	5	η1v	η1v	NOUN
ejpam-5446	411	6	3	3	NUM
ejpam-5446	411	7	3	3	NUM
ejpam-5446	411	8	+	+	CCONJ
ejpam-5446	411	9	η2v	η2v	PROPN
ejpam-5446	411	10	2	2	NUM
ejpam-5446	411	11	3	3	NUM
ejpam-5446	411	12	+	+	CCONJ
ejpam-5446	411	13	η3v3	η3v3	PUNCT
ejpam-5446	411	14	+	+	ADJ
ejpam-5446	411	15	η4)ς(x	η4)ς(x	NUM
ejpam-5446	411	16	)	)	PUNCT
ejpam-5446	412	1	+	+	NUM
ejpam-5446	412	2	v3[y	v3[y	NOUN
ejpam-5446	412	3	′′′	′′′	PROPN
ejpam-5446	412	4	(	(	PUNCT
ejpam-5446	412	5	x	x	X
ejpam-5446	412	6	)	)	PUNCT
ejpam-5446	412	7	+	+	CCONJ
ejpam-5446	412	8	(	(	PUNCT
ejpam-5446	412	9	v3	v3	PROPN
ejpam-5446	412	10	+	+	CCONJ
ejpam-5446	412	11	η1)ς	η1)ς	VERB
ejpam-5446	412	12	′′	′′	PROPN
ejpam-5446	412	13	(	(	PUNCT
ejpam-5446	412	14	x	x	X
ejpam-5446	412	15	)	)	PUNCT
ejpam-5446	412	16	+	+	ADJ
ejpam-5446	412	17	(	(	PUNCT
ejpam-5446	412	18	v23	v23	NOUN
ejpam-5446	412	19	+	+	CCONJ
ejpam-5446	412	20	η1v3	η1v3	NOUN
ejpam-5446	412	21	+	+	CCONJ
ejpam-5446	412	22	η2)ς	η2)ς	NOUN
ejpam-5446	412	23	′(x	′(x	NOUN
ejpam-5446	412	24	)	)	PUNCT
ejpam-5446	413	1	+	+	CCONJ
ejpam-5446	413	2	v33	v33	ADJ
ejpam-5446	413	3	+	+	ADJ
ejpam-5446	413	4	η1v	η1v	NOUN
ejpam-5446	413	5	2	2	NUM
ejpam-5446	413	6	3	3	NUM
ejpam-5446	413	7	+	+	CCONJ
ejpam-5446	413	8	η2v3	η2v3	PROPN
ejpam-5446	413	9	+	+	ADJ
ejpam-5446	413	10	η3)ς(x)]−	η3)ς(x)]−	PROPN
ejpam-5446	413	11	u(x)|	u(x)|	PROPN
ejpam-5446	413	12	v.	v.	ADP
ejpam-5446	413	13	govindan	govindan	PROPN
ejpam-5446	413	14	et	et	PROPN
ejpam-5446	413	15	al	al	PROPN
ejpam-5446	413	16	.	.	PUNCT
ejpam-5446	413	17	/	/	SYM
ejpam-5446	413	18	eur	eur	PROPN
ejpam-5446	413	19	.	.	PUNCT
ejpam-5446	414	1	j.	j.	PROPN
ejpam-5446	414	2	pure	pure	PROPN
ejpam-5446	414	3	appl	appl	PROPN
ejpam-5446	414	4	.	.	PROPN
ejpam-5446	414	5	math	math	PROPN
ejpam-5446	414	6	,	,	PUNCT
ejpam-5446	414	7	17	17	NUM
ejpam-5446	414	8	(	(	PUNCT
ejpam-5446	414	9	4	4	NUM
ejpam-5446	414	10	)	)	PUNCT
ejpam-5446	414	11	(	(	PUNCT
ejpam-5446	414	12	2024	2024	NUM
ejpam-5446	414	13	)	)	PUNCT
ejpam-5446	414	14	,	,	PUNCT
ejpam-5446	414	15	3585	3585	NUM
ejpam-5446	414	16	-	-	SYM
ejpam-5446	414	17	3609	3609	NUM
ejpam-5446	414	18	3600∣∣χ′(x)−	3600∣∣χ′(x)−	NUM
ejpam-5446	414	19	v3χ(x)−	v3χ(x)−	NOUN
ejpam-5446	414	20	u(x	u(x	PROPN
ejpam-5446	414	21	)	)	PUNCT
ejpam-5446	414	22	∣∣	∣∣	X
ejpam-5446	415	1	=	=	SYM
ejpam-5446	415	2	|ς	|ς	PROPN
ejpam-5446	415	3	iv(x	iv(x	NOUN
ejpam-5446	415	4	)	)	PUNCT
ejpam-5446	416	1	+	+	CCONJ
ejpam-5446	417	1	v3ς	v3ς	PROPN
ejpam-5446	417	2	′′′	′′′	PROPN
ejpam-5446	417	3	(	(	PUNCT
ejpam-5446	417	4	x	x	X
ejpam-5446	417	5	)	)	PUNCT
ejpam-5446	417	6	+	+	CCONJ
ejpam-5446	417	7	η1ς	η1ς	NOUN
ejpam-5446	417	8	′′′	′′′	NOUN
ejpam-5446	417	9	(	(	PUNCT
ejpam-5446	417	10	x	x	X
ejpam-5446	417	11	)	)	PUNCT
ejpam-5446	418	1	+	+	ADJ
ejpam-5446	418	2	v23ς	v23ς	VERB
ejpam-5446	418	3	′′	′′	PROPN
ejpam-5446	418	4	(	(	PUNCT
ejpam-5446	418	5	x	x	X
ejpam-5446	418	6	)	)	PUNCT
ejpam-5446	418	7	+	+	CCONJ
ejpam-5446	418	8	η1v3ς	η1v3ς	X
ejpam-5446	418	9	′′	′′	PROPN
ejpam-5446	418	10	+	+	CCONJ
ejpam-5446	418	11	η2ς	η2ς	PROPN
ejpam-5446	418	12	′′	′′	PROPN
ejpam-5446	418	13	(	(	PUNCT
ejpam-5446	418	14	x	x	X
ejpam-5446	418	15	)	)	PUNCT
ejpam-5446	418	16	+	+	ADJ
ejpam-5446	418	17	v33ς	v33ς	NOUN
ejpam-5446	418	18	′(x	′(x	NOUN
ejpam-5446	418	19	)	)	PUNCT
ejpam-5446	418	20	+	+	NUM
ejpam-5446	418	21	η1v	η1v	NOUN
ejpam-5446	418	22	2	2	NUM
ejpam-5446	418	23	3ς	3ς	NUM
ejpam-5446	418	24	′(x	′(x	NOUN
ejpam-5446	418	25	)	)	PUNCT
ejpam-5446	418	26	+	+	CCONJ
ejpam-5446	418	27	η2v3ς	η2v3ς	NOUN
ejpam-5446	418	28	′(x	′(x	NOUN
ejpam-5446	418	29	)	)	PUNCT
ejpam-5446	418	30	+	+	NUM
ejpam-5446	418	31	η3ς	η3ς	NOUN
ejpam-5446	418	32	′(x	′(x	NOUN
ejpam-5446	418	33	)	)	PUNCT
ejpam-5446	418	34	+	+	X
ejpam-5446	418	35	v43ς(x	v43ς(x	ADJ
ejpam-5446	418	36	)	)	PUNCT
ejpam-5446	418	37	+	+	NUM
ejpam-5446	418	38	η1v	η1v	NOUN
ejpam-5446	418	39	3	3	NUM
ejpam-5446	418	40	3ς(x	3ς(x	NUM
ejpam-5446	418	41	)	)	PUNCT
ejpam-5446	419	1	+	+	ADJ
ejpam-5446	419	2	η2v	η2v	PROPN
ejpam-5446	419	3	2	2	NUM
ejpam-5446	419	4	3ς(x	3ς(x	NUM
ejpam-5446	419	5	)	)	PUNCT
ejpam-5446	420	1	+	+	CCONJ
ejpam-5446	420	2	η3v3ς(x	η3v3ς(x	PROPN
ejpam-5446	420	3	)	)	PUNCT
ejpam-5446	421	1	+	+	CCONJ
ejpam-5446	421	2	η4ς(x)−	η4ς(x)−	PROPN
ejpam-5446	421	3	v3ς	v3ς	PROPN
ejpam-5446	421	4	′′′	′′′	PROPN
ejpam-5446	421	5	(	(	PUNCT
ejpam-5446	421	6	x)−	x)−	PROPN
ejpam-5446	421	7	v23ς	v23ς	VERB
ejpam-5446	421	8	′′	′′	PROPN
ejpam-5446	421	9	−	−	PROPN
ejpam-5446	421	10	η1v3ς	η1v3ς	PUNCT
ejpam-5446	421	11	′′	′′	PROPN
ejpam-5446	421	12	(	(	PUNCT
ejpam-5446	421	13	x	x	X
ejpam-5446	421	14	)	)	PUNCT
ejpam-5446	421	15	−v33ς	−v33ς	PROPN
ejpam-5446	421	16	′(x)−	′(x)−	PROPN
ejpam-5446	421	17	η1v	η1v	VERB
ejpam-5446	421	18	2	2	NUM
ejpam-5446	421	19	3ς	3ς	NUM
ejpam-5446	421	20	′(x)−	′(x)−	PROPN
ejpam-5446	421	21	η2v3ς	η2v3ς	VERB
ejpam-5446	421	22	′(x)−	′(x)−	PROPN
ejpam-5446	421	23	v43ς(x)−	v43ς(x)−	PROPN
ejpam-5446	421	24	η1v	η1v	PROPN
ejpam-5446	421	25	3	3	NUM
ejpam-5446	421	26	3ς(x)−	3ς(x)−	NUM
ejpam-5446	421	27	η2v	η2v	PROPN
ejpam-5446	421	28	2	2	NUM
ejpam-5446	421	29	3ς(x	3ς(x	NUM
ejpam-5446	421	30	)	)	PUNCT
ejpam-5446	422	1	−η3v3ς(x)−	−η3v3ς(x)−	PROPN
ejpam-5446	422	2	u(x)|∣∣χ′(x)−	u(x)|∣∣χ′(x)−	PROPN
ejpam-5446	422	3	v3χ(x)−	v3χ(x)−	PROPN
ejpam-5446	422	4	u(x	u(x	PROPN
ejpam-5446	422	5	)	)	PUNCT
ejpam-5446	422	6	∣∣	∣∣	NUM
ejpam-5446	422	7	=	=	PUNCT
ejpam-5446	422	8	∣∣∣ς	∣∣∣ς	ADJ
ejpam-5446	422	9	iv(x	iv(x	NUM
ejpam-5446	422	10	)	)	PUNCT
ejpam-5446	423	1	+	+	CCONJ
ejpam-5446	423	2	η1ς	η1ς	NOUN
ejpam-5446	423	3	′′′	′′′	NOUN
ejpam-5446	423	4	(	(	PUNCT
ejpam-5446	423	5	x	x	X
ejpam-5446	423	6	)	)	PUNCT
ejpam-5446	424	1	+	+	CCONJ
ejpam-5446	424	2	η2ς	η2ς	PROPN
ejpam-5446	424	3	′′	′′	PROPN
ejpam-5446	424	4	(	(	PUNCT
ejpam-5446	424	5	x	x	X
ejpam-5446	424	6	)	)	PUNCT
ejpam-5446	424	7	+	+	CCONJ
ejpam-5446	424	8	η3ς	η3ς	NOUN
ejpam-5446	424	9	′	′	NUM
ejpam-5446	424	10	(	(	PUNCT
ejpam-5446	424	11	x	x	X
ejpam-5446	424	12	)	)	PUNCT
ejpam-5446	424	13	+	+	CCONJ
ejpam-5446	424	14	η4ς(x)−	η4ς(x)−	PROPN
ejpam-5446	424	15	u(x	u(x	PROPN
ejpam-5446	424	16	)	)	PUNCT
ejpam-5446	424	17	∣∣∣∣∣χ′(x)−	∣∣∣∣∣χ′(x)−	NOUN
ejpam-5446	424	18	v3χ(x)−	v3χ(x)−	PROPN
ejpam-5446	424	19	u(x	u(x	PROPN
ejpam-5446	424	20	)	)	PUNCT
ejpam-5446	424	21	∣∣	∣∣	NUM
ejpam-5446	424	22	≤	≤	PROPN
ejpam-5446	424	23	ε	ε	PROPN
ejpam-5446	424	24	.	.	PUNCT
ejpam-5446	425	1	(	(	PUNCT
ejpam-5446	425	2	2.43	2.43	NUM
ejpam-5446	425	3	)	)	PUNCT
ejpam-5446	425	4	proportionally	proportionally	ADV
ejpam-5446	425	5	χ	χ	DET
ejpam-5446	425	6	satisfies	satisfie	NOUN
ejpam-5446	425	7	,	,	PUNCT
ejpam-5446	425	8	−ε	−ε	PROPN
ejpam-5446	425	9	≤	≤	ADJ
ejpam-5446	425	10	χ′(x)−	χ′(x)−	PROPN
ejpam-5446	425	11	v3χ(x)−	v3χ(x)−	NOUN
ejpam-5446	425	12	u(x	u(x	PROPN
ejpam-5446	425	13	)	)	PUNCT
ejpam-5446	425	14	≤	≤	NUM
ejpam-5446	426	1	ε	ε	PROPN
ejpam-5446	426	2	.	.	PUNCT
ejpam-5446	427	1	(	(	PUNCT
ejpam-5446	427	2	2.44	2.44	NUM
ejpam-5446	427	3	)	)	PUNCT
ejpam-5446	427	4	multiplying	multiply	VERB
ejpam-5446	427	5	the	the	DET
ejpam-5446	427	6	equation	equation	NOUN
ejpam-5446	427	7	by	by	ADP
ejpam-5446	427	8	e−v3(x−k	e−v3(x−k	NOUN
ejpam-5446	427	9	)	)	PUNCT
ejpam-5446	427	10	,	,	PUNCT
ejpam-5446	427	11	we	we	PRON
ejpam-5446	427	12	get	get	VERB
ejpam-5446	427	13	−εe−v3(x−k	−εe−v3(x−k	X
ejpam-5446	427	14	)	)	PUNCT
ejpam-5446	427	15	≤	≤	NUM
ejpam-5446	427	16	χ′(x)e−v3(x−k	χ′(x)e−v3(x−k	NOUN
ejpam-5446	427	17	)	)	PUNCT
ejpam-5446	427	18	−	−	PROPN
ejpam-5446	427	19	v3χ(x)e	v3χ(x)e	ADJ
ejpam-5446	427	20	−v3(x−k	−v3(x−k	NOUN
ejpam-5446	427	21	)	)	PUNCT
ejpam-5446	427	22	−	−	PRON
ejpam-5446	427	23	u(x)e−v3(x−k	u(x)e−v3(x−k	NOUN
ejpam-5446	427	24	)	)	PUNCT
ejpam-5446	427	25	≤	≤	NUM
ejpam-5446	427	26	εe−v3(x−k	εe−v3(x−k	NOUN
ejpam-5446	427	27	)	)	PUNCT
ejpam-5446	427	28	(	(	PUNCT
ejpam-5446	427	29	2.45	2.45	NUM
ejpam-5446	427	30	)	)	PUNCT
ejpam-5446	427	31	without	without	ADP
ejpam-5446	427	32	loss	loss	NOUN
ejpam-5446	427	33	of	of	ADP
ejpam-5446	427	34	consensus	consensus	NOUN
ejpam-5446	427	35	,	,	PUNCT
ejpam-5446	427	36	we	we	PRON
ejpam-5446	427	37	may	may	AUX
ejpam-5446	427	38	expect	expect	VERB
ejpam-5446	427	39	to	to	PART
ejpam-5446	427	40	be	be	AUX
ejpam-5446	427	41	that	that	SCONJ
ejpam-5446	427	42	v3	v3	PROPN
ejpam-5446	427	43	>	>	X
ejpam-5446	427	44	1	1	NUM
ejpam-5446	427	45	,	,	PUNCT
ejpam-5446	427	46	thus	thus	ADV
ejpam-5446	427	47	−εv3e−v3(x−k	−εv3e−v3(x−k	PROPN
ejpam-5446	427	48	)	)	PUNCT
ejpam-5446	427	49	≤	≤	NUM
ejpam-5446	427	50	χ′(x)e−v3(x−k	χ′(x)e−v3(x−k	NOUN
ejpam-5446	427	51	)	)	PUNCT
ejpam-5446	427	52	−	−	PROPN
ejpam-5446	427	53	v3χ(x)e	v3χ(x)e	ADJ
ejpam-5446	427	54	−v3(x−k	−v3(x−k	NOUN
ejpam-5446	427	55	)	)	PUNCT
ejpam-5446	427	56	−	−	PRON
ejpam-5446	427	57	u(x)e−v3(x−k	u(x)e−v3(x−k	NOUN
ejpam-5446	427	58	)	)	PUNCT
ejpam-5446	427	59	≤	≤	NUM
ejpam-5446	427	60	εe−v3(x−k	εe−v3(x−k	NOUN
ejpam-5446	427	61	)	)	PUNCT
ejpam-5446	427	62	,	,	PUNCT
ejpam-5446	427	63	(	(	PUNCT
ejpam-5446	427	64	2.46	2.46	NUM
ejpam-5446	427	65	)	)	PUNCT
ejpam-5446	427	66	for	for	ADP
ejpam-5446	427	67	all	all	DET
ejpam-5446	427	68	x	x	SYM
ejpam-5446	427	69	∈	∈	PROPN
ejpam-5446	428	1	[	[	X
ejpam-5446	428	2	k	k	X
ejpam-5446	428	3	,	,	PUNCT
ejpam-5446	428	4	l	l	NOUN
ejpam-5446	428	5	]	]	PUNCT
ejpam-5446	428	6	.	.	PUNCT
ejpam-5446	429	1	integrating	integrate	VERB
ejpam-5446	429	2	(	(	PUNCT
ejpam-5446	429	3	2.45	2.45	NUM
ejpam-5446	429	4	)	)	PUNCT
ejpam-5446	429	5	from	from	ADP
ejpam-5446	429	6	x	x	X
ejpam-5446	429	7	to	to	ADP
ejpam-5446	429	8	l	l	NOUN
ejpam-5446	429	9	,	,	PUNCT
ejpam-5446	429	10	we	we	PRON
ejpam-5446	429	11	get	get	VERB
ejpam-5446	429	12	−ε(e−v3(x−k	−ε(e−v3(x−k	NOUN
ejpam-5446	429	13	)	)	PUNCT
ejpam-5446	430	1	−	−	ADP
ejpam-5446	430	2	e−v3(l−k	e−v3(l−k	NOUN
ejpam-5446	430	3	)	)	PUNCT
ejpam-5446	430	4	)	)	PUNCT
ejpam-5446	430	5	≤	≤	NUM
ejpam-5446	430	6	χ(l)e−v3(x−k	χ(l)e−v3(x−k	PROPN
ejpam-5446	430	7	)	)	PUNCT
ejpam-5446	430	8	−	−	PROPN
ejpam-5446	430	9	χ(x)e−v3(x−k	χ(x)e−v3(x−k	NOUN
ejpam-5446	430	10	)	)	PUNCT
ejpam-5446	431	1	−	−	NUM
ejpam-5446	431	2	∫	∫	NOUN
ejpam-5446	431	3	l	l	NOUN
ejpam-5446	431	4	x	x	PUNCT
ejpam-5446	431	5	u(t)e−v3(t−k)dt	u(t)e−v3(t−k)dt	PUNCT
ejpam-5446	431	6	≤	≤	NUM
ejpam-5446	431	7	ε(e−v3(x−k	ε(e−v3(x−k	NOUN
ejpam-5446	431	8	)	)	PUNCT
ejpam-5446	431	9	−	−	ADP
ejpam-5446	431	10	e−v3(l−k	e−v3(l−k	NOUN
ejpam-5446	431	11	)	)	PUNCT
ejpam-5446	431	12	)	)	PUNCT
ejpam-5446	432	1	−εe−v3(x−k	−εe−v3(x−k	NOUN
ejpam-5446	432	2	)	)	PUNCT
ejpam-5446	432	3	≤	≤	NUM
ejpam-5446	432	4	χ(l)e−v3(l−k	χ(l)e−v3(l−k	NOUN
ejpam-5446	432	5	)	)	PUNCT
ejpam-5446	432	6	−	−	PROPN
ejpam-5446	432	7	εe−v3(l−k	εe−v3(l−k	NOUN
ejpam-5446	432	8	)	)	PUNCT
ejpam-5446	433	1	−	−	PROPN
ejpam-5446	433	2	χ(x)e−v3(x−k	χ(x)e−v3(x−k	NOUN
ejpam-5446	433	3	)	)	PUNCT
ejpam-5446	434	1	−	−	NUM
ejpam-5446	434	2	∫	∫	NOUN
ejpam-5446	434	3	l	l	NOUN
ejpam-5446	434	4	x	x	PUNCT
ejpam-5446	434	5	u(t)e−v3(t−k)dt	u(t)e−v3(t−k)dt	NOUN
ejpam-5446	434	6	≤	≤	NUM
ejpam-5446	434	7	εe−v3(x−k	εe−v3(x−k	NOUN
ejpam-5446	434	8	)	)	PUNCT
ejpam-5446	434	9	.	.	PUNCT
ejpam-5446	435	1	(	(	PUNCT
ejpam-5446	435	2	2.47	2.47	NUM
ejpam-5446	435	3	)	)	PUNCT
ejpam-5446	435	4	multiplying	multiply	VERB
ejpam-5446	435	5	the	the	DET
ejpam-5446	435	6	equation	equation	NOUN
ejpam-5446	435	7	by	by	ADP
ejpam-5446	435	8	ev3(x−k	ev3(x−k	PROPN
ejpam-5446	435	9	)	)	PUNCT
ejpam-5446	435	10	,	,	PUNCT
ejpam-5446	435	11	we	we	PRON
ejpam-5446	435	12	get	get	VERB
ejpam-5446	435	13	−εe−v3(x−k)ev3(x−k	−εe−v3(x−k)ev3(x−k	NOUN
ejpam-5446	435	14	)	)	PUNCT
ejpam-5446	435	15	≤	≤	NUM
ejpam-5446	435	16	χ(l)e−v3(l−k)ev3(x−k	χ(l)e−v3(l−k)ev3(x−k	NOUN
ejpam-5446	435	17	)	)	PUNCT
ejpam-5446	435	18	−	−	NOUN
ejpam-5446	435	19	εe−v3(l−k)ev3(x−k	εe−v3(l−k)ev3(x−k	NOUN
ejpam-5446	435	20	)	)	PUNCT
ejpam-5446	436	1	−	−	PROPN
ejpam-5446	436	2	χ(x)e−v3(x−k)ev3(x−k	χ(x)e−v3(x−k)ev3(x−k	NOUN
ejpam-5446	436	3	)	)	PUNCT
ejpam-5446	436	4	−	−	NUM
ejpam-5446	437	1	∫	∫	PROPN
ejpam-5446	437	2	l	l	NOUN
ejpam-5446	437	3	x	x	SYM
ejpam-5446	437	4	u(t)e−v3(t−k)dtev3(x−k	u(t)e−v3(t−k)dtev3(x−k	PROPN
ejpam-5446	437	5	)	)	PUNCT
ejpam-5446	437	6	≤	≤	NUM
ejpam-5446	437	7	εe−v3(x−k)ev3(x−k	εe−v3(x−k)ev3(x−k	NOUN
ejpam-5446	437	8	)	)	PUNCT
ejpam-5446	437	9	−ε	−ε	PROPN
ejpam-5446	437	10	≤	≤	PROPN
ejpam-5446	437	11	χ(l)ev3(x−k	χ(l)ev3(x−k	NOUN
ejpam-5446	437	12	)	)	PUNCT
ejpam-5446	437	13	−	−	PROPN
ejpam-5446	437	14	εev3(x−k	εev3(x−k	NOUN
ejpam-5446	437	15	)	)	PUNCT
ejpam-5446	437	16	−	−	PROPN
ejpam-5446	438	1	χ(x)−	χ(x)−	PROPN
ejpam-5446	438	2	ev3x	ev3x	ADJ
ejpam-5446	438	3	∫	∫	PROPN
ejpam-5446	438	4	l	l	NOUN
ejpam-5446	438	5	x	x	X
ejpam-5446	438	6	u(t)e−v3(t)dt	u(t)e−v3(t)dt	PROPN
ejpam-5446	438	7	≤	≤	PROPN
ejpam-5446	438	8	ε	ε	PROPN
ejpam-5446	438	9	.	.	PUNCT
ejpam-5446	439	1	(	(	PUNCT
ejpam-5446	439	2	2.48	2.48	NUM
ejpam-5446	439	3	)	)	PUNCT
ejpam-5446	439	4	let	let	VERB
ejpam-5446	439	5	t	t	PROPN
ejpam-5446	439	6	(	(	PUNCT
ejpam-5446	439	7	x	x	X
ejpam-5446	439	8	)	)	PUNCT
ejpam-5446	439	9	=	=	SYM
ejpam-5446	439	10	χ(l)ev3(x−l	χ(l)ev3(x−l	ADJ
ejpam-5446	439	11	)	)	PUNCT
ejpam-5446	440	1	−	−	PROPN
ejpam-5446	440	2	ev3x	ev3x	ADJ
ejpam-5446	440	3	∫	∫	NOUN
ejpam-5446	440	4	l	l	NOUN
ejpam-5446	440	5	x	x	SYM
ejpam-5446	441	1	ϕ(t)e	ϕ(t)e	PROPN
ejpam-5446	441	2	−v3tdt	−v3tdt	NOUN
ejpam-5446	441	3	and	and	CCONJ
ejpam-5446	441	4	t	t	PROPN
ejpam-5446	441	5	(	(	PUNCT
ejpam-5446	441	6	x	x	X
ejpam-5446	441	7	)	)	PUNCT
ejpam-5446	441	8	satisfies	satisfie	NOUN
ejpam-5446	441	9	t	t	PROPN
ejpam-5446	441	10	′(x)−	′(x)−	PROPN
ejpam-5446	441	11	v3	v3	PROPN
ejpam-5446	441	12	t	t	PROPN
ejpam-5446	441	13	(	(	PUNCT
ejpam-5446	441	14	x)−	x)−	PROPN
ejpam-5446	441	15	u(x	u(x	PROPN
ejpam-5446	441	16	)	)	PUNCT
ejpam-5446	441	17	=	=	SYM
ejpam-5446	441	18	0	0	NUM
ejpam-5446	441	19	by	by	ADP
ejpam-5446	441	20	t	t	NOUN
ejpam-5446	441	21	′(x	′(x	NOUN
ejpam-5446	441	22	)	)	PUNCT
ejpam-5446	442	1	=	=	PUNCT
ejpam-5446	442	2	v3	v3	PROPN
ejpam-5446	442	3	t	t	PROPN
ejpam-5446	442	4	(	(	PUNCT
ejpam-5446	442	5	x	x	X
ejpam-5446	442	6	)	)	PUNCT
ejpam-5446	442	7	+	+	CCONJ
ejpam-5446	442	8	u(x	u(x	NOUN
ejpam-5446	442	9	)	)	PUNCT
ejpam-5446	442	10	.	.	PUNCT
ejpam-5446	443	1	then	then	ADV
ejpam-5446	443	2	|t	|t	PROPN
ejpam-5446	443	3	(	(	PUNCT
ejpam-5446	443	4	x)−	x)−	PROPN
ejpam-5446	443	5	χ(x)|	χ(x)|	NOUN
ejpam-5446	443	6	=	=	PUNCT
ejpam-5446	443	7	∣∣∣∣χ(l)ev3(x−l	∣∣∣∣χ(l)ev3(x−l	PROPN
ejpam-5446	443	8	)	)	PUNCT
ejpam-5446	443	9	−	−	PROPN
ejpam-5446	444	1	χ(x)−	χ(x)−	PROPN
ejpam-5446	444	2	ev3x	ev3x	ADJ
ejpam-5446	444	3	∫	∫	PROPN
ejpam-5446	444	4	l	l	NOUN
ejpam-5446	444	5	x	x	X
ejpam-5446	444	6	u(t)e−v3tdt	u(t)e−v3tdt	PROPN
ejpam-5446	444	7	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5446	444	8	v.	v.	ADP
ejpam-5446	444	9	govindan	govindan	PROPN
ejpam-5446	444	10	et	et	PROPN
ejpam-5446	444	11	al	al	PROPN
ejpam-5446	444	12	.	.	PUNCT
ejpam-5446	444	13	/	/	SYM
ejpam-5446	444	14	eur	eur	PROPN
ejpam-5446	444	15	.	.	PUNCT
ejpam-5446	445	1	j.	j.	PROPN
ejpam-5446	445	2	pure	pure	PROPN
ejpam-5446	445	3	appl	appl	PROPN
ejpam-5446	445	4	.	.	PROPN
ejpam-5446	445	5	math	math	PROPN
ejpam-5446	445	6	,	,	PUNCT
ejpam-5446	445	7	17	17	NUM
ejpam-5446	445	8	(	(	PUNCT
ejpam-5446	445	9	4	4	NUM
ejpam-5446	445	10	)	)	PUNCT
ejpam-5446	445	11	(	(	PUNCT
ejpam-5446	445	12	2024	2024	NUM
ejpam-5446	445	13	)	)	PUNCT
ejpam-5446	445	14	,	,	PUNCT
ejpam-5446	445	15	3585	3585	NUM
ejpam-5446	445	16	-	-	SYM
ejpam-5446	445	17	3609	3609	NUM
ejpam-5446	445	18	3601	3601	NUM
ejpam-5446	445	19	|t	|t	PROPN
ejpam-5446	445	20	(	(	PUNCT
ejpam-5446	445	21	x)−	x)−	PROPN
ejpam-5446	445	22	χ(x)|	χ(x)|	VERB
ejpam-5446	445	23	≤	≤	PUNCT
ejpam-5446	446	1	εep4x	εep4x	CCONJ
ejpam-5446	447	1	∫	∫	PROPN
ejpam-5446	447	2	l	l	NOUN
ejpam-5446	448	1	x	x	X
ejpam-5446	448	2	e−p4tdt	e−p4tdt	PROPN
ejpam-5446	448	3	.	.	PROPN
ejpam-5446	449	1	(	(	PUNCT
ejpam-5446	449	2	2.49	2.49	NUM
ejpam-5446	449	3	)	)	PUNCT
ejpam-5446	449	4	if	if	SCONJ
ejpam-5446	449	5	p4	p4	ADJ
ejpam-5446	449	6	̸=	̸=	PROPN
ejpam-5446	449	7	0	0	NUM
ejpam-5446	449	8	,	,	PUNCT
ejpam-5446	449	9	then	then	ADV
ejpam-5446	449	10	|t	|t	PROPN
ejpam-5446	449	11	(	(	PUNCT
ejpam-5446	449	12	x)−	x)−	PROPN
ejpam-5446	449	13	χ(x)|	χ(x)|	VERB
ejpam-5446	449	14	≤	≤	PUNCT
ejpam-5446	450	1	εep4x	εep4x	CCONJ
ejpam-5446	451	1	∫	∫	PROPN
ejpam-5446	451	2	l	l	NOUN
ejpam-5446	451	3	x	x	X
ejpam-5446	452	1	e−p4tdt	e−p4tdt	PROPN
ejpam-5446	452	2	|t	|t	PROPN
ejpam-5446	452	3	(	(	PUNCT
ejpam-5446	452	4	x)−	x)−	PROPN
ejpam-5446	452	5	χ(x)|	χ(x)|	PROPN
ejpam-5446	452	6	≤	≤	NUM
ejpam-5446	452	7	ε	ε	PROPN
ejpam-5446	452	8	−p4	−p4	PROPN
ejpam-5446	452	9	[	[	PUNCT
ejpam-5446	452	10	e−p4(l−x	e−p4(l−x	X
ejpam-5446	452	11	)	)	PUNCT
ejpam-5446	452	12	−	−	PROPN
ejpam-5446	452	13	1	1	NUM
ejpam-5446	452	14	]	]	PUNCT
ejpam-5446	452	15	;	;	PUNCT
ejpam-5446	452	16	x	x	SYM
ejpam-5446	452	17	∈	∈	PROPN
ejpam-5446	453	1	[	[	X
ejpam-5446	453	2	k	k	X
ejpam-5446	453	3	,	,	PUNCT
ejpam-5446	453	4	l	l	NOUN
ejpam-5446	453	5	]	]	X
ejpam-5446	453	6	|t	|t	PROPN
ejpam-5446	454	1	(	(	PUNCT
ejpam-5446	454	2	x)−	x)−	PROPN
ejpam-5446	454	3	χ(x)|	χ(x)|	PROPN
ejpam-5446	454	4	≤	≤	NUM
ejpam-5446	454	5	ε	ε	PROPN
ejpam-5446	454	6	p4	p4	ADJ
ejpam-5446	454	7	[	[	PUNCT
ejpam-5446	454	8	1−	1−	NUM
ejpam-5446	454	9	e−p4(l−x	e−p4(l−x	NUM
ejpam-5446	454	10	)	)	PUNCT
ejpam-5446	454	11	]	]	PUNCT
ejpam-5446	454	12	;	;	PUNCT
ejpam-5446	454	13	x	x	X
ejpam-5446	454	14	∈	∈	PROPN
ejpam-5446	455	1	[	[	X
ejpam-5446	455	2	k	k	X
ejpam-5446	455	3	,	,	PUNCT
ejpam-5446	455	4	l	l	NOUN
ejpam-5446	455	5	]	]	X
ejpam-5446	455	6	|t	|t	PROPN
ejpam-5446	456	1	(	(	PUNCT
ejpam-5446	456	2	x)−	x)−	PROPN
ejpam-5446	456	3	χ(x)|	χ(x)|	PROPN
ejpam-5446	456	4	≤	≤	NUM
ejpam-5446	456	5	ε	ε	PROPN
ejpam-5446	456	6	p4	p4	ADJ
ejpam-5446	456	7	[	[	PUNCT
ejpam-5446	456	8	1−	1−	NUM
ejpam-5446	456	9	e−p4(l−k	e−p4(l−k	NOUN
ejpam-5446	456	10	)	)	PUNCT
ejpam-5446	456	11	]	]	PUNCT
ejpam-5446	456	12	;	;	PUNCT
ejpam-5446	456	13	x	x	X
ejpam-5446	456	14	∈	∈	PROPN
ejpam-5446	457	1	[	[	X
ejpam-5446	457	2	k	k	X
ejpam-5446	457	3	,	,	PUNCT
ejpam-5446	457	4	l	l	NOUN
ejpam-5446	457	5	]	]	X
ejpam-5446	457	6	.	.	PUNCT
ejpam-5446	458	1	(	(	PUNCT
ejpam-5446	458	2	2.50	2.50	NUM
ejpam-5446	458	3	)	)	PUNCT
ejpam-5446	458	4	if	if	SCONJ
ejpam-5446	458	5	p4	p4	ADJ
ejpam-5446	458	6	=	=	NOUN
ejpam-5446	458	7	0	0	NUM
ejpam-5446	458	8	,	,	PUNCT
ejpam-5446	458	9	then	then	ADV
ejpam-5446	458	10	|t	|t	PROPN
ejpam-5446	458	11	(	(	PUNCT
ejpam-5446	458	12	x)−	x)−	PROPN
ejpam-5446	458	13	χ(x)|	χ(x)|	VERB
ejpam-5446	458	14	≤	≤	PUNCT
ejpam-5446	459	1	εep4x	εep4x	CCONJ
ejpam-5446	460	1	∫	∫	PROPN
ejpam-5446	460	2	l	l	NOUN
ejpam-5446	460	3	x	x	X
ejpam-5446	461	1	e−p4tdt	e−p4tdt	PROPN
ejpam-5446	461	2	|t	|t	PROPN
ejpam-5446	461	3	(	(	PUNCT
ejpam-5446	461	4	x)−	x)−	PROPN
ejpam-5446	461	5	χ(x)|	χ(x)|	PROPN
ejpam-5446	461	6	≤	≤	NUM
ejpam-5446	461	7	ε	ε	PROPN
ejpam-5446	461	8	∫	∫	PROPN
ejpam-5446	461	9	l	l	NOUN
ejpam-5446	461	10	x	x	PUNCT
ejpam-5446	461	11	dt	dt	X
ejpam-5446	461	12	|t	|t	PROPN
ejpam-5446	461	13	(	(	PUNCT
ejpam-5446	461	14	x)−	x)−	PROPN
ejpam-5446	461	15	χ(x)|	χ(x)|	PROPN
ejpam-5446	461	16	≤	≤	ADV
ejpam-5446	461	17	ε(l	ε(l	PROPN
ejpam-5446	461	18	−	−	PROPN
ejpam-5446	461	19	x);x	x);x	PROPN
ejpam-5446	461	20	∈	∈	PROPN
ejpam-5446	462	1	[	[	X
ejpam-5446	462	2	k	k	X
ejpam-5446	462	3	,	,	PUNCT
ejpam-5446	462	4	l	l	NOUN
ejpam-5446	462	5	]	]	X
ejpam-5446	462	6	|t	|t	PROPN
ejpam-5446	463	1	(	(	PUNCT
ejpam-5446	463	2	x)−	x)−	PROPN
ejpam-5446	463	3	χ(x)|	χ(x)|	PROPN
ejpam-5446	463	4	≤	≤	ADV
ejpam-5446	463	5	ε(l	ε(l	PROPN
ejpam-5446	463	6	−	−	PROPN
ejpam-5446	463	7	k);x	k);x	PROPN
ejpam-5446	463	8	∈	∈	PROPN
ejpam-5446	463	9	[	[	X
ejpam-5446	463	10	k	k	X
ejpam-5446	463	11	,	,	PUNCT
ejpam-5446	463	12	l	l	NOUN
ejpam-5446	463	13	]	]	X
ejpam-5446	463	14	.	.	PUNCT
ejpam-5446	464	1	(	(	PUNCT
ejpam-5446	464	2	2.51	2.51	NUM
ejpam-5446	464	3	)	)	PUNCT
ejpam-5446	464	4	it	it	PRON
ejpam-5446	464	5	follows	follow	VERB
ejpam-5446	464	6	from	from	ADP
ejpam-5446	464	7	(	(	PUNCT
ejpam-5446	464	8	2.31	2.31	NUM
ejpam-5446	464	9	)	)	PUNCT
ejpam-5446	464	10	,	,	PUNCT
ejpam-5446	464	11	we	we	PRON
ejpam-5446	464	12	conclude	conclude	VERB
ejpam-5446	464	13	our	our	PRON
ejpam-5446	464	14	result	result	NOUN
ejpam-5446	464	15	(	(	PUNCT
ejpam-5446	464	16	2.41	2.41	NUM
ejpam-5446	464	17	)	)	PUNCT
ejpam-5446	464	18	,	,	PUNCT
ejpam-5446	464	19	for	for	ADP
ejpam-5446	464	20	all	all	DET
ejpam-5446	464	21	x	x	SYM
ejpam-5446	464	22	∈	∈	PROPN
ejpam-5446	465	1	[	[	X
ejpam-5446	465	2	k	k	X
ejpam-5446	465	3	,	,	PUNCT
ejpam-5446	465	4	l	l	NOUN
ejpam-5446	465	5	]	]	PUNCT
ejpam-5446	465	6	.	.	PUNCT
ejpam-5446	466	1	let	let	VERB
ejpam-5446	466	2	∈	∈	PRON
ejpam-5446	466	3	>	>	X
ejpam-5446	466	4	0	0	PROPN
ejpam-5446	467	1	and	and	CCONJ
ejpam-5446	467	2	ς	ς	PROPN
ejpam-5446	467	3	∈	∈	PROPN
ejpam-5446	467	4	c5[k	c5[k	NOUN
ejpam-5446	467	5	,	,	PUNCT
ejpam-5446	467	6	l	l	NOUN
ejpam-5446	467	7	]	]	PUNCT
ejpam-5446	467	8	.	.	PUNCT
ejpam-5446	468	1	theorem.2.5	theorem.2.5	PROPN
ejpam-5446	468	2	the	the	DET
ejpam-5446	468	3	differential	differential	ADJ
ejpam-5446	468	4	equation	equation	NOUN
ejpam-5446	468	5	ςv(x	ςv(x	NUM
ejpam-5446	468	6	)	)	PUNCT
ejpam-5446	469	1	+	+	CCONJ
ejpam-5446	469	2	η1ς	η1ς	NOUN
ejpam-5446	469	3	iv(x	iv(x	NUM
ejpam-5446	469	4	)	)	PUNCT
ejpam-5446	469	5	+	+	CCONJ
ejpam-5446	469	6	η2ς	η2ς	PROPN
ejpam-5446	469	7	′′′	′′′	PROPN
ejpam-5446	469	8	(	(	PUNCT
ejpam-5446	469	9	x	x	X
ejpam-5446	469	10	)	)	PUNCT
ejpam-5446	469	11	+	+	CCONJ
ejpam-5446	469	12	η3ς	η3ς	PROPN
ejpam-5446	469	13	′′	′′	PROPN
ejpam-5446	469	14	(	(	PUNCT
ejpam-5446	469	15	x	x	X
ejpam-5446	469	16	)	)	PUNCT
ejpam-5446	469	17	+	+	CCONJ
ejpam-5446	469	18	η4ς	η4ς	PROPN
ejpam-5446	469	19	′	′	NUM
ejpam-5446	469	20	(	(	PUNCT
ejpam-5446	469	21	x	x	X
ejpam-5446	469	22	)	)	PUNCT
ejpam-5446	469	23	+	+	CCONJ
ejpam-5446	469	24	v.	v.	ADP
ejpam-5446	469	25	govindan	govindan	PROPN
ejpam-5446	469	26	et	et	PROPN
ejpam-5446	469	27	al	al	PROPN
ejpam-5446	469	28	.	.	PUNCT
ejpam-5446	469	29	/	/	SYM
ejpam-5446	469	30	eur	eur	PROPN
ejpam-5446	469	31	.	.	PUNCT
ejpam-5446	470	1	j.	j.	PROPN
ejpam-5446	470	2	pure	pure	PROPN
ejpam-5446	470	3	appl	appl	PROPN
ejpam-5446	470	4	.	.	PROPN
ejpam-5446	470	5	math	math	PROPN
ejpam-5446	470	6	,	,	PUNCT
ejpam-5446	470	7	17	17	NUM
ejpam-5446	470	8	(	(	PUNCT
ejpam-5446	470	9	4	4	NUM
ejpam-5446	470	10	)	)	PUNCT
ejpam-5446	470	11	(	(	PUNCT
ejpam-5446	470	12	2024	2024	NUM
ejpam-5446	470	13	)	)	PUNCT
ejpam-5446	470	14	,	,	PUNCT
ejpam-5446	470	15	3585	3585	NUM
ejpam-5446	470	16	-	-	SYM
ejpam-5446	470	17	3609	3609	NUM
ejpam-5446	470	18	3602	3602	NUM
ejpam-5446	470	19	η5ς(x	η5ς(x	NOUN
ejpam-5446	470	20	)	)	PUNCT
ejpam-5446	470	21	=	=	SYM
ejpam-5446	470	22	ω(x	ω(x	NOUN
ejpam-5446	470	23	)	)	PUNCT
ejpam-5446	470	24	has	have	VERB
ejpam-5446	470	25	the	the	DET
ejpam-5446	470	26	hyers	hyers	PROPN
ejpam-5446	470	27	-	-	PUNCT
ejpam-5446	470	28	ulam	ulam	PROPN
ejpam-5446	470	29	stability	stability	NOUN
ejpam-5446	470	30	,	,	PUNCT
ejpam-5446	470	31	where	where	SCONJ
ejpam-5446	470	32	ς	ς	PROPN
ejpam-5446	470	33	∈	∈	PROPN
ejpam-5446	470	34	c5[k	c5[k	NOUN
ejpam-5446	470	35	,	,	PUNCT
ejpam-5446	470	36	l	l	NOUN
ejpam-5446	470	37	]	]	PUNCT
ejpam-5446	470	38	and	and	CCONJ
ejpam-5446	470	39	ω	ω	NUM
ejpam-5446	470	40	∈	∈	PROPN
ejpam-5446	471	1	[	[	X
ejpam-5446	471	2	k	k	X
ejpam-5446	471	3	,	,	PUNCT
ejpam-5446	471	4	l	l	NOUN
ejpam-5446	471	5	]	]	X
ejpam-5446	471	6	,	,	PUNCT
ejpam-5446	471	7	therefore	therefore	ADV
ejpam-5446	471	8	,	,	PUNCT
ejpam-5446	471	9	|k(x)−	|k(x)−	PROPN
ejpam-5446	471	10	l(x)|	l(x)|	VERB
ejpam-5446	471	11	≤	≤	NUM
ejpam-5446	471	12			NOUN
ejpam-5446	472	1	[	[	X
ejpam-5446	472	2	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p3(l−k)][1−e−p4(l−k)][1−e−p5(l−k)]ε	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p3(l−k)][1−e−p4(l−k)][1−e−p5(l−k)]ε	NUM
ejpam-5446	472	3	p1p2p3p4p5	p1p2p3p4p5	NOUN
ejpam-5446	472	4	if	if	SCONJ
ejpam-5446	472	5	p1	p1	PROPN
ejpam-5446	472	6	,	,	PUNCT
ejpam-5446	472	7	p2	p2	NOUN
ejpam-5446	472	8	,	,	PUNCT
ejpam-5446	472	9	p3	p3	NOUN
ejpam-5446	472	10	,	,	PUNCT
ejpam-5446	472	11	p4	p4	ADJ
ejpam-5446	472	12	,	,	PUNCT
ejpam-5446	472	13	p5	p5	ADJ
ejpam-5446	472	14	̸=	̸=	PROPN
ejpam-5446	472	15	0	0	NUM
ejpam-5446	473	1	[	[	X
ejpam-5446	473	2	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p3(l−k)][1−e−p4(l−k)](l−k)ε	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p3(l−k)][1−e−p4(l−k)](l−k)ε	NUM
ejpam-5446	473	3	p1p2p3p4	p1p2p3p4	NOUN
ejpam-5446	473	4	if	if	SCONJ
ejpam-5446	473	5	p1	p1	PROPN
ejpam-5446	473	6	,	,	PUNCT
ejpam-5446	473	7	p2	p2	NOUN
ejpam-5446	473	8	,	,	PUNCT
ejpam-5446	473	9	p3	p3	NOUN
ejpam-5446	473	10	,	,	PUNCT
ejpam-5446	473	11	p4	p4	ADJ
ejpam-5446	473	12	̸=	̸=	PROPN
ejpam-5446	473	13	0	0	NUM
ejpam-5446	473	14	p5	p5	ADJ
ejpam-5446	473	15	=	=	NOUN
ejpam-5446	473	16	0	0	PUNCT
ejpam-5446	474	1	[	[	X
ejpam-5446	474	2	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p3(l−k)][1−e−p5(l−k)](l−k)ε	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p3(l−k)][1−e−p5(l−k)](l−k)ε	NUM
ejpam-5446	474	3	p1p2p3p5	p1p2p3p5	PROPN
ejpam-5446	474	4	if	if	SCONJ
ejpam-5446	474	5	p1	p1	PROPN
ejpam-5446	474	6	,	,	PUNCT
ejpam-5446	474	7	p2	p2	NOUN
ejpam-5446	474	8	,	,	PUNCT
ejpam-5446	474	9	p3	p3	NOUN
ejpam-5446	474	10	,	,	PUNCT
ejpam-5446	474	11	p5	p5	ADJ
ejpam-5446	474	12	̸=	̸=	PROPN
ejpam-5446	474	13	0	0	NUM
ejpam-5446	474	14	p4	p4	NOUN
ejpam-5446	474	15	=	=	NOUN
ejpam-5446	474	16	0	0	PUNCT
ejpam-5446	475	1	[	[	X
ejpam-5446	475	2	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p4(l−k)][1−e−p5(l−k)](l−k)ε	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p4(l−k)][1−e−p5(l−k)](l−k)ε	X
ejpam-5446	475	3	p1p2p4p5	p1p2p4p5	PROPN
ejpam-5446	475	4	if	if	SCONJ
ejpam-5446	475	5	p1	p1	NOUN
ejpam-5446	475	6	,	,	PUNCT
ejpam-5446	475	7	p2	p2	NOUN
ejpam-5446	475	8	,	,	PUNCT
ejpam-5446	475	9	p4	p4	ADJ
ejpam-5446	475	10	,	,	PUNCT
ejpam-5446	475	11	p5	p5	ADJ
ejpam-5446	475	12	̸=	̸=	PROPN
ejpam-5446	475	13	0	0	NUM
ejpam-5446	475	14	p3	p3	PROPN
ejpam-5446	475	15	=	=	X
ejpam-5446	475	16	0	0	PUNCT
ejpam-5446	476	1	[	[	X
ejpam-5446	476	2	1−e−p1(l−k)][1−e−p3(l−k)][1−e−p4(l−k)][1−e−p5(l−k)](l−k)ε	1−e−p1(l−k)][1−e−p3(l−k)][1−e−p4(l−k)][1−e−p5(l−k)](l−k)ε	NUM
ejpam-5446	476	3	p1p3p4p5	p1p3p4p5	NOUN
ejpam-5446	476	4	if	if	SCONJ
ejpam-5446	476	5	p1	p1	PROPN
ejpam-5446	476	6	,	,	PUNCT
ejpam-5446	476	7	p3	p3	PROPN
ejpam-5446	476	8	,	,	PUNCT
ejpam-5446	476	9	p4	p4	ADJ
ejpam-5446	476	10	,	,	PUNCT
ejpam-5446	476	11	p5	p5	ADJ
ejpam-5446	476	12	̸=	̸=	PROPN
ejpam-5446	476	13	0	0	NUM
ejpam-5446	476	14	p2	p2	PROPN
ejpam-5446	476	15	=	=	NOUN
ejpam-5446	476	16	0	0	PUNCT
ejpam-5446	477	1	[	[	X
ejpam-5446	477	2	1−e−p2(l−k)][1−e−p3(l−k)][1−e−p4(l−k)][1−e−p5(l−k)](l−k)ε	1−e−p2(l−k)][1−e−p3(l−k)][1−e−p4(l−k)][1−e−p5(l−k)](l−k)ε	NUM
ejpam-5446	477	3	p2p3p4p5	p2p3p4p5	NOUN
ejpam-5446	477	4	if	if	SCONJ
ejpam-5446	477	5	p2	p2	NOUN
ejpam-5446	477	6	,	,	PUNCT
ejpam-5446	477	7	p3	p3	NOUN
ejpam-5446	477	8	,	,	PUNCT
ejpam-5446	477	9	p4	p4	ADJ
ejpam-5446	477	10	,	,	PUNCT
ejpam-5446	477	11	p5	p5	ADJ
ejpam-5446	477	12	̸=	̸=	PROPN
ejpam-5446	477	13	0	0	NUM
ejpam-5446	477	14	p1	p1	NOUN
ejpam-5446	477	15	=	=	NOUN
ejpam-5446	477	16	0	0	PUNCT
ejpam-5446	478	1	[	[	X
ejpam-5446	478	2	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p3(l−k)](l−k)2ε	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p3(l−k)](l−k)2ε	NUM
ejpam-5446	478	3	p1p2p3	p1p2p3	NOUN
ejpam-5446	478	4	if	if	SCONJ
ejpam-5446	478	5	p1	p1	NOUN
ejpam-5446	478	6	,	,	PUNCT
ejpam-5446	478	7	p2	p2	NOUN
ejpam-5446	478	8	,	,	PUNCT
ejpam-5446	478	9	p3	p3	PROPN
ejpam-5446	478	10	̸=	̸=	PROPN
ejpam-5446	478	11	0	0	NUM
ejpam-5446	478	12	p4	p4	ADJ
ejpam-5446	478	13	,	,	PUNCT
ejpam-5446	478	14	p5	p5	ADJ
ejpam-5446	478	15	=	=	SYM
ejpam-5446	478	16	0	0	PUNCT
ejpam-5446	479	1	[	[	X
ejpam-5446	479	2	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p4(l−k)](l−k)2ε	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p4(l−k)](l−k)2ε	NUM
ejpam-5446	479	3	p1p2p4	p1p2p4	NOUN
ejpam-5446	479	4	if	if	SCONJ
ejpam-5446	479	5	p1	p1	NOUN
ejpam-5446	479	6	,	,	PUNCT
ejpam-5446	479	7	p2	p2	NOUN
ejpam-5446	479	8	,	,	PUNCT
ejpam-5446	479	9	p4	p4	ADJ
ejpam-5446	479	10	̸=	̸=	PROPN
ejpam-5446	479	11	0	0	NUM
ejpam-5446	479	12	p3	p3	PROPN
ejpam-5446	479	13	,	,	PUNCT
ejpam-5446	479	14	p5	p5	ADJ
ejpam-5446	479	15	=	=	SYM
ejpam-5446	479	16	0	0	PUNCT
ejpam-5446	480	1	[	[	X
ejpam-5446	480	2	1−e−p1(l−k)][1−e−p3(l−k)][1−e−p4(l−k)](l−k)2ε	1−e−p1(l−k)][1−e−p3(l−k)][1−e−p4(l−k)](l−k)2ε	NUM
ejpam-5446	480	3	p1p3p4	p1p3p4	NOUN
ejpam-5446	480	4	if	if	SCONJ
ejpam-5446	480	5	p1p3p4	p1p3p4	VERB
ejpam-5446	480	6	̸=	̸=	PROPN
ejpam-5446	480	7	0	0	NUM
ejpam-5446	480	8	p2	p2	NOUN
ejpam-5446	480	9	,	,	PUNCT
ejpam-5446	480	10	p5	p5	NOUN
ejpam-5446	480	11	=	=	SYM
ejpam-5446	480	12	0	0	PUNCT
ejpam-5446	481	1	[	[	X
ejpam-5446	481	2	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p5(l−k)](l−k)2ε	1−e−p1(l−k)][1−e−p2(l−k)][1−e−p5(l−k)](l−k)2ε	NOUN
ejpam-5446	481	3	p1p2p5	p1p2p5	ADV
ejpam-5446	481	4	if	if	SCONJ
ejpam-5446	481	5	p1	p1	NOUN
ejpam-5446	481	6	,	,	PUNCT
ejpam-5446	481	7	p2	p2	NOUN
ejpam-5446	481	8	,	,	PUNCT
ejpam-5446	481	9	p5	p5	ADJ
ejpam-5446	481	10	̸=	̸=	PROPN
ejpam-5446	481	11	0	0	NUM
ejpam-5446	481	12	p3	p3	PROPN
ejpam-5446	481	13	,	,	PUNCT
ejpam-5446	481	14	p4	p4	ADJ
ejpam-5446	481	15	=	=	NOUN
ejpam-5446	481	16	0	0	PUNCT
ejpam-5446	482	1	[	[	X
ejpam-5446	482	2	1−e−p2(l−k)][1−e−p4(l−k)][1−e−p5(l−k)](l−k)2ε	1−e−p2(l−k)][1−e−p4(l−k)][1−e−p5(l−k)](l−k)2ε	NUM
ejpam-5446	482	3	p2p4p5	p2p4p5	NOUN
ejpam-5446	482	4	if	if	SCONJ
ejpam-5446	482	5	p2	p2	NOUN
ejpam-5446	482	6	,	,	PUNCT
ejpam-5446	482	7	p4	p4	ADJ
ejpam-5446	482	8	,	,	PUNCT
ejpam-5446	482	9	p5	p5	ADJ
ejpam-5446	482	10	̸=	̸=	PROPN
ejpam-5446	482	11	0	0	NUM
ejpam-5446	482	12	p1	p1	PROPN
ejpam-5446	482	13	,	,	PUNCT
ejpam-5446	482	14	p3	p3	PROPN
ejpam-5446	482	15	=	=	X
ejpam-5446	482	16	0	0	PUNCT
ejpam-5446	483	1	[	[	X
ejpam-5446	483	2	1−e−p2(l−k)][1−e−p3(l−k)][1−e−p5(l−k)](l−k)2ε	1−e−p2(l−k)][1−e−p3(l−k)][1−e−p5(l−k)](l−k)2ε	NUM
ejpam-5446	483	3	p2p3p5	p2p3p5	NOUN
ejpam-5446	483	4	if	if	SCONJ
ejpam-5446	483	5	p2	p2	NOUN
ejpam-5446	483	6	,	,	PUNCT
ejpam-5446	483	7	p3	p3	NOUN
ejpam-5446	483	8	,	,	PUNCT
ejpam-5446	483	9	p5	p5	ADJ
ejpam-5446	483	10	̸=	̸=	PROPN
ejpam-5446	483	11	0	0	NUM
ejpam-5446	483	12	p1	p1	PROPN
ejpam-5446	483	13	,	,	PUNCT
ejpam-5446	483	14	p4	p4	NOUN
ejpam-5446	483	15	=	=	NOUN
ejpam-5446	483	16	0	0	PUNCT
ejpam-5446	484	1	[	[	X
ejpam-5446	484	2	1−e−p2(l−k)][1−e−p3(l−k)][1−e−p5(l−k)](l−k)2ε	1−e−p2(l−k)][1−e−p3(l−k)][1−e−p5(l−k)](l−k)2ε	NUM
ejpam-5446	484	3	p2p4p5	p2p4p5	NOUN
ejpam-5446	484	4	if	if	SCONJ
ejpam-5446	484	5	p2	p2	NOUN
ejpam-5446	484	6	,	,	PUNCT
ejpam-5446	484	7	p4	p4	ADJ
ejpam-5446	484	8	,	,	PUNCT
ejpam-5446	484	9	p5	p5	ADJ
ejpam-5446	484	10	̸=	̸=	PROPN
ejpam-5446	484	11	0	0	NUM
ejpam-5446	484	12	p1	p1	PROPN
ejpam-5446	484	13	,	,	PUNCT
ejpam-5446	484	14	p4	p4	NOUN
ejpam-5446	484	15	=	=	NOUN
ejpam-5446	484	16	0	0	PUNCT
ejpam-5446	485	1	[	[	X
ejpam-5446	485	2	1−e−p3(l−k)][1−e−p4(l−k)][1−e−p5(l−k)](l−k)2ε	1−e−p3(l−k)][1−e−p4(l−k)][1−e−p5(l−k)](l−k)2ε	NUM
ejpam-5446	485	3	p3p4p5	p3p4p5	NOUN
ejpam-5446	485	4	if	if	SCONJ
ejpam-5446	485	5	p3	p3	PROPN
ejpam-5446	485	6	,	,	PUNCT
ejpam-5446	485	7	p4	p4	ADJ
ejpam-5446	485	8	,	,	PUNCT
ejpam-5446	485	9	p5	p5	ADJ
ejpam-5446	485	10	̸=	̸=	PROPN
ejpam-5446	485	11	0	0	NUM
ejpam-5446	485	12	p1	p1	NOUN
ejpam-5446	485	13	,	,	PUNCT
ejpam-5446	485	14	p2	p2	X
ejpam-5446	485	15	=	=	SYM
ejpam-5446	485	16	0	0	PUNCT
ejpam-5446	486	1	[	[	X
ejpam-5446	486	2	1−e−p1(l−k)][1−e−p3(l−k)][1−e−p5(l−k)](l−k)2ε	1−e−p1(l−k)][1−e−p3(l−k)][1−e−p5(l−k)](l−k)2ε	NUM
ejpam-5446	486	3	p1p3p5	p1p3p5	NOUN
ejpam-5446	486	4	if	if	SCONJ
ejpam-5446	486	5	p1	p1	PROPN
ejpam-5446	486	6	,	,	PUNCT
ejpam-5446	486	7	p3	p3	PROPN
ejpam-5446	486	8	,	,	PUNCT
ejpam-5446	486	9	p5	p5	ADJ
ejpam-5446	486	10	̸=	̸=	PROPN
ejpam-5446	486	11	0	0	NUM
ejpam-5446	486	12	p2	p2	NOUN
ejpam-5446	486	13	,	,	PUNCT
ejpam-5446	486	14	p4	p4	NOUN
ejpam-5446	486	15	=	=	NOUN
ejpam-5446	486	16	0	0	PUNCT
ejpam-5446	487	1	[	[	X
ejpam-5446	487	2	1−e−p1(l−k)][1−e−p4(l−k)][1−e−p5(l−k)](l−k)2ε	1−e−p1(l−k)][1−e−p4(l−k)][1−e−p5(l−k)](l−k)2ε	NUM
ejpam-5446	487	3	p1p4p5	p1p4p5	NOUN
ejpam-5446	487	4	if	if	SCONJ
ejpam-5446	487	5	p1	p1	PROPN
ejpam-5446	487	6	,	,	PUNCT
ejpam-5446	487	7	p4	p4	ADJ
ejpam-5446	487	8	,	,	PUNCT
ejpam-5446	487	9	p5	p5	ADJ
ejpam-5446	487	10	̸=	̸=	PROPN
ejpam-5446	487	11	0	0	NUM
ejpam-5446	487	12	p2	p2	NOUN
ejpam-5446	487	13	,	,	PUNCT
ejpam-5446	487	14	p3	p3	NOUN
ejpam-5446	487	15	=	=	X
ejpam-5446	487	16	0	0	PUNCT
ejpam-5446	488	1	[	[	X
ejpam-5446	488	2	1−e−p1(l−k)][1−e−p2(l−k)](l−k)3ε	1−e−p1(l−k)][1−e−p2(l−k)](l−k)3ε	NUM
ejpam-5446	488	3	pq	pq	NOUN
ejpam-5446	488	4	if	if	SCONJ
ejpam-5446	488	5	p1	p1	PROPN
ejpam-5446	488	6	,	,	PUNCT
ejpam-5446	488	7	p2	p2	PROPN
ejpam-5446	488	8	̸=	̸=	PROPN
ejpam-5446	488	9	0	0	NUM
ejpam-5446	488	10	p3	p3	PROPN
ejpam-5446	488	11	,	,	PUNCT
ejpam-5446	488	12	p4	p4	ADJ
ejpam-5446	488	13	,	,	PUNCT
ejpam-5446	488	14	p5	p5	ADJ
ejpam-5446	488	15	=	=	SYM
ejpam-5446	488	16	0	0	PUNCT
ejpam-5446	489	1	[	[	X
ejpam-5446	489	2	1−e−p2(l−k)][1−e−p3(l−k)](l−k)3ε	1−e−p2(l−k)][1−e−p3(l−k)](l−k)3ε	NUM
ejpam-5446	489	3	qr	qr	NOUN
ejpam-5446	489	4	if	if	SCONJ
ejpam-5446	489	5	p2	p2	NOUN
ejpam-5446	489	6	,	,	PUNCT
ejpam-5446	489	7	p3	p3	PROPN
ejpam-5446	489	8	̸=	̸=	PROPN
ejpam-5446	489	9	0	0	NUM
ejpam-5446	489	10	p1	p1	PROPN
ejpam-5446	489	11	,	,	PUNCT
ejpam-5446	489	12	p4	p4	ADJ
ejpam-5446	489	13	,	,	PUNCT
ejpam-5446	489	14	p5	p5	ADJ
ejpam-5446	489	15	=	=	SYM
ejpam-5446	489	16	0	0	PUNCT
ejpam-5446	490	1	[	[	X
ejpam-5446	490	2	1−e−p3(l−k)][1−e−p4(l−k)](l−k)3ε	1−e−p3(l−k)][1−e−p4(l−k)](l−k)3ε	NUM
ejpam-5446	490	3	rs	rs	NOUN
ejpam-5446	490	4	if	if	SCONJ
ejpam-5446	490	5	p3	p3	PROPN
ejpam-5446	490	6	,	,	PUNCT
ejpam-5446	490	7	p4	p4	ADJ
ejpam-5446	490	8	̸=	̸=	PROPN
ejpam-5446	490	9	0	0	NUM
ejpam-5446	490	10	p1	p1	PROPN
ejpam-5446	490	11	,	,	PUNCT
ejpam-5446	490	12	p2	p2	NOUN
ejpam-5446	490	13	,	,	PUNCT
ejpam-5446	490	14	p5	p5	NOUN
ejpam-5446	490	15	=	=	SYM
ejpam-5446	490	16	0	0	PUNCT
ejpam-5446	491	1	[	[	X
ejpam-5446	491	2	1−e−p4(l−k)][1−e−p5(l−k)](l−k)3ε	1−e−p4(l−k)][1−e−p5(l−k)](l−k)3ε	NUM
ejpam-5446	491	3	sn	sn	NOUN
ejpam-5446	491	4	if	if	SCONJ
ejpam-5446	491	5	p4	p4	ADJ
ejpam-5446	491	6	,	,	PUNCT
ejpam-5446	491	7	p5	p5	ADJ
ejpam-5446	491	8	̸=	̸=	PROPN
ejpam-5446	491	9	0	0	NUM
ejpam-5446	491	10	p1	p1	PROPN
ejpam-5446	491	11	,	,	PUNCT
ejpam-5446	491	12	p2	p2	NOUN
ejpam-5446	491	13	,	,	PUNCT
ejpam-5446	491	14	p3	p3	NOUN
ejpam-5446	491	15	=	=	X
ejpam-5446	491	16	0	0	PUNCT
ejpam-5446	492	1	[	[	X
ejpam-5446	492	2	1−e−p1(l−k)][1−e−p3(l−k)](l−k)3ε	1−e−p1(l−k)][1−e−p3(l−k)](l−k)3ε	NUM
ejpam-5446	492	3	pr	pr	NOUN
ejpam-5446	492	4	if	if	SCONJ
ejpam-5446	492	5	p1	p1	PROPN
ejpam-5446	492	6	,	,	PUNCT
ejpam-5446	492	7	p3	p3	PROPN
ejpam-5446	492	8	̸=	̸=	PROPN
ejpam-5446	492	9	0	0	NUM
ejpam-5446	492	10	p2	p2	NOUN
ejpam-5446	492	11	,	,	PUNCT
ejpam-5446	492	12	p4	p4	ADJ
ejpam-5446	492	13	,	,	PUNCT
ejpam-5446	492	14	p5	p5	ADJ
ejpam-5446	492	15	=	=	SYM
ejpam-5446	492	16	0	0	PUNCT
ejpam-5446	493	1	[	[	X
ejpam-5446	493	2	1−e−p1(l−k)][1−e−p4(l−k)](l−k)3ε	1−e−p1(l−k)][1−e−p4(l−k)](l−k)3ε	NUM
ejpam-5446	493	3	ps	ps	NOUN
ejpam-5446	493	4	if	if	SCONJ
ejpam-5446	493	5	p1	p1	PROPN
ejpam-5446	493	6	,	,	PUNCT
ejpam-5446	493	7	p4	p4	ADJ
ejpam-5446	493	8	̸=	̸=	PROPN
ejpam-5446	493	9	0	0	NUM
ejpam-5446	493	10	p2	p2	PROPN
ejpam-5446	493	11	,	,	PUNCT
ejpam-5446	493	12	p3	p3	NOUN
ejpam-5446	493	13	,	,	PUNCT
ejpam-5446	493	14	p5	p5	NOUN
ejpam-5446	493	15	=	=	SYM
ejpam-5446	493	16	0	0	PUNCT
ejpam-5446	494	1	[	[	X
ejpam-5446	494	2	1−e−p1(l−k)][1−e−p5(l−k)](l−k)3ε	1−e−p1(l−k)][1−e−p5(l−k)](l−k)3ε	NUM
ejpam-5446	494	3	pn	pn	NOUN
ejpam-5446	494	4	if	if	SCONJ
ejpam-5446	494	5	p1	p1	PROPN
ejpam-5446	494	6	,	,	PUNCT
ejpam-5446	494	7	p5	p5	ADJ
ejpam-5446	494	8	̸=	̸=	PROPN
ejpam-5446	494	9	0	0	NUM
ejpam-5446	494	10	p2	p2	PROPN
ejpam-5446	494	11	,	,	PUNCT
ejpam-5446	494	12	p3	p3	NOUN
ejpam-5446	494	13	,	,	PUNCT
ejpam-5446	494	14	p4	p4	ADJ
ejpam-5446	494	15	=	=	NOUN
ejpam-5446	494	16	0	0	PUNCT
ejpam-5446	495	1	[	[	X
ejpam-5446	495	2	1−e−p2(l−k)][1−e−p4(l−k)](l−k)3ε	1−e−p2(l−k)][1−e−p4(l−k)](l−k)3ε	NUM
ejpam-5446	495	3	qs	qs	NOUN
ejpam-5446	495	4	if	if	SCONJ
ejpam-5446	495	5	p2	p2	NOUN
ejpam-5446	495	6	,	,	PUNCT
ejpam-5446	495	7	p4	p4	ADJ
ejpam-5446	495	8	̸=	̸=	PROPN
ejpam-5446	495	9	0	0	NUM
ejpam-5446	495	10	p1	p1	PROPN
ejpam-5446	495	11	,	,	PUNCT
ejpam-5446	495	12	p3	p3	PROPN
ejpam-5446	495	13	,	,	PUNCT
ejpam-5446	495	14	p5	p5	ADJ
ejpam-5446	495	15	=	=	SYM
ejpam-5446	495	16	0	0	PUNCT
ejpam-5446	496	1	[	[	X
ejpam-5446	496	2	1−e−p2(l−k)][1−e−p5(l−k)](l−k)3ε	1−e−p2(l−k)][1−e−p5(l−k)](l−k)3ε	NUM
ejpam-5446	496	3	qn	qn	NOUN
ejpam-5446	496	4	if	if	SCONJ
ejpam-5446	496	5	p2	p2	NOUN
ejpam-5446	496	6	,	,	PUNCT
ejpam-5446	496	7	p5	p5	ADJ
ejpam-5446	496	8	̸=	̸=	PROPN
ejpam-5446	496	9	0	0	NUM
ejpam-5446	496	10	p1	p1	PROPN
ejpam-5446	496	11	,	,	PUNCT
ejpam-5446	496	12	p3	p3	PROPN
ejpam-5446	496	13	,	,	PUNCT
ejpam-5446	496	14	p4	p4	ADJ
ejpam-5446	496	15	=	=	NOUN
ejpam-5446	496	16	0	0	PUNCT
ejpam-5446	497	1	[	[	X
ejpam-5446	497	2	1−e−p3(l−k)][1−e−p5(l−k)](l−k)3ε	1−e−p3(l−k)][1−e−p5(l−k)](l−k)3ε	NUM
ejpam-5446	497	3	rn	rn	PROPN
ejpam-5446	497	4	if	if	SCONJ
ejpam-5446	497	5	p3	p3	PROPN
ejpam-5446	497	6	,	,	PUNCT
ejpam-5446	497	7	p5	p5	ADJ
ejpam-5446	497	8	̸=	̸=	PROPN
ejpam-5446	497	9	0	0	NUM
ejpam-5446	497	10	p1	p1	PROPN
ejpam-5446	497	11	,	,	PUNCT
ejpam-5446	497	12	p2,=	p2,=	NOUN
ejpam-5446	497	13	0	0	PUNCT
ejpam-5446	498	1	[	[	X
ejpam-5446	498	2	1−e−p1(l−k)](l−k)4ε	1−e−p1(l−k)](l−k)4ε	NUM
ejpam-5446	498	3	p1	p1	NOUN
ejpam-5446	498	4	if	if	SCONJ
ejpam-5446	498	5	p1	p1	PROPN
ejpam-5446	498	6	̸=	̸=	PROPN
ejpam-5446	498	7	0	0	NUM
ejpam-5446	498	8	p2	p2	PROPN
ejpam-5446	498	9	,	,	PUNCT
ejpam-5446	498	10	p3	p3	NOUN
ejpam-5446	498	11	,	,	PUNCT
ejpam-5446	498	12	p4	p4	ADJ
ejpam-5446	498	13	,	,	PUNCT
ejpam-5446	498	14	p5	p5	ADJ
ejpam-5446	498	15	=	=	SYM
ejpam-5446	498	16	0	0	PUNCT
ejpam-5446	499	1	[	[	X
ejpam-5446	499	2	1−e−p2(l−k)](l−k)4ε	1−e−p2(l−k)](l−k)4ε	NUM
ejpam-5446	499	3	p2	p2	NOUN
ejpam-5446	499	4	if	if	SCONJ
ejpam-5446	499	5	p2	p2	PROPN
ejpam-5446	499	6	̸=	̸=	PROPN
ejpam-5446	499	7	0	0	NUM
ejpam-5446	499	8	p1	p1	PROPN
ejpam-5446	499	9	,	,	PUNCT
ejpam-5446	499	10	p3	p3	PROPN
ejpam-5446	499	11	,	,	PUNCT
ejpam-5446	499	12	p4	p4	ADJ
ejpam-5446	499	13	,	,	PUNCT
ejpam-5446	499	14	p5	p5	ADJ
ejpam-5446	499	15	=	=	SYM
ejpam-5446	499	16	0	0	PUNCT
ejpam-5446	500	1	[	[	X
ejpam-5446	500	2	1−e−p3(l−k)](l−k)4ε	1−e−p3(l−k)](l−k)4ε	NUM
ejpam-5446	500	3	p3	p3	NOUN
ejpam-5446	500	4	if	if	SCONJ
ejpam-5446	500	5	p3	p3	PROPN
ejpam-5446	500	6	̸=	̸=	PROPN
ejpam-5446	500	7	0	0	NUM
ejpam-5446	500	8	p1	p1	PROPN
ejpam-5446	500	9	,	,	PUNCT
ejpam-5446	500	10	p2	p2	NOUN
ejpam-5446	500	11	,	,	PUNCT
ejpam-5446	500	12	p4	p4	ADJ
ejpam-5446	500	13	,	,	PUNCT
ejpam-5446	500	14	p5	p5	ADJ
ejpam-5446	500	15	=	=	SYM
ejpam-5446	500	16	0	0	PUNCT
ejpam-5446	501	1	[	[	X
ejpam-5446	501	2	1−e−p4(l−k)](l−k)4ε	1−e−p4(l−k)](l−k)4ε	ADJ
ejpam-5446	501	3	p4	p4	ADJ
ejpam-5446	501	4	if	if	SCONJ
ejpam-5446	501	5	p4	p4	ADJ
ejpam-5446	501	6	̸=	̸=	PROPN
ejpam-5446	501	7	0	0	NUM
ejpam-5446	501	8	p1	p1	PROPN
ejpam-5446	501	9	,	,	PUNCT
ejpam-5446	501	10	p2	p2	NOUN
ejpam-5446	501	11	,	,	PUNCT
ejpam-5446	501	12	p3	p3	NOUN
ejpam-5446	501	13	,	,	PUNCT
ejpam-5446	501	14	p5	p5	NOUN
ejpam-5446	501	15	=	=	SYM
ejpam-5446	501	16	0	0	PUNCT
ejpam-5446	502	1	[	[	X
ejpam-5446	502	2	1−e−p5(l−k)](l−k)4ε	1−e−p5(l−k)](l−k)4ε	ADJ
ejpam-5446	502	3	p5	p5	ADJ
ejpam-5446	502	4	if	if	SCONJ
ejpam-5446	502	5	p5	p5	ADJ
ejpam-5446	502	6	̸=	̸=	PROPN
ejpam-5446	502	7	0	0	NUM
ejpam-5446	502	8	p1	p1	PROPN
ejpam-5446	502	9	,	,	PUNCT
ejpam-5446	502	10	p2	p2	NOUN
ejpam-5446	502	11	,	,	PUNCT
ejpam-5446	502	12	p3	p3	NOUN
ejpam-5446	502	13	,	,	PUNCT
ejpam-5446	502	14	p4	p4	ADJ
ejpam-5446	502	15	=	=	NOUN
ejpam-5446	502	16	0	0	PUNCT
ejpam-5446	503	1	(	(	PUNCT
ejpam-5446	503	2	b−	b−	PROPN
ejpam-5446	503	3	a)5εifp1	a)5εifp1	PROPN
ejpam-5446	503	4	,	,	PUNCT
ejpam-5446	503	5	p2	p2	PROPN
ejpam-5446	503	6	,	,	PUNCT
ejpam-5446	503	7	p3	p3	NOUN
ejpam-5446	503	8	,	,	PUNCT
ejpam-5446	503	9	p4	p4	ADJ
ejpam-5446	503	10	,	,	PUNCT
ejpam-5446	503	11	p5	p5	ADJ
ejpam-5446	503	12	=	=	SYM
ejpam-5446	503	13	0	0	NUM
ejpam-5446	503	14	.	.	PUNCT
ejpam-5446	504	1	(	(	PUNCT
ejpam-5446	504	2	2.52	2.52	NUM
ejpam-5446	504	3	)	)	PUNCT
ejpam-5446	504	4	v.	v.	ADP
ejpam-5446	504	5	govindan	govindan	PROPN
ejpam-5446	504	6	et	et	PROPN
ejpam-5446	504	7	al	al	PROPN
ejpam-5446	504	8	.	.	PUNCT
ejpam-5446	504	9	/	/	SYM
ejpam-5446	504	10	eur	eur	PROPN
ejpam-5446	504	11	.	.	PUNCT
ejpam-5446	505	1	j.	j.	PROPN
ejpam-5446	505	2	pure	pure	PROPN
ejpam-5446	505	3	appl	appl	PROPN
ejpam-5446	505	4	.	.	PROPN
ejpam-5446	505	5	math	math	PROPN
ejpam-5446	505	6	,	,	PUNCT
ejpam-5446	505	7	17	17	NUM
ejpam-5446	505	8	(	(	PUNCT
ejpam-5446	505	9	4	4	NUM
ejpam-5446	505	10	)	)	PUNCT
ejpam-5446	505	11	(	(	PUNCT
ejpam-5446	505	12	2024	2024	NUM
ejpam-5446	505	13	)	)	PUNCT
ejpam-5446	505	14	,	,	PUNCT
ejpam-5446	505	15	3585	3585	NUM
ejpam-5446	505	16	-	-	SYM
ejpam-5446	505	17	3609	3609	NUM
ejpam-5446	505	18	3603	3603	NUM
ejpam-5446	505	19	∀x	∀x	X
ejpam-5446	505	20	∈	∈	PROPN
ejpam-5446	506	1	[	[	X
ejpam-5446	506	2	k	k	X
ejpam-5446	506	3	,	,	PUNCT
ejpam-5446	506	4	l	l	NOUN
ejpam-5446	506	5	]	]	PUNCT
ejpam-5446	506	6	.	.	PUNCT
ejpam-5446	507	1	proof	proof	NOUN
ejpam-5446	507	2	:	:	PUNCT
ejpam-5446	507	3	let	let	VERB
ejpam-5446	507	4	us	we	PRON
ejpam-5446	507	5	consider	consider	VERB
ejpam-5446	507	6	,	,	PUNCT
ejpam-5446	507	7	l(x	l(x	PROPN
ejpam-5446	507	8	)	)	PUNCT
ejpam-5446	507	9	=	=	SYM
ejpam-5446	508	1	ς	ς	PROPN
ejpam-5446	508	2	iv(x	iv(x	NOUN
ejpam-5446	508	3	)	)	PUNCT
ejpam-5446	509	1	+	+	CCONJ
ejpam-5446	509	2	(	(	PUNCT
ejpam-5446	509	3	v5	v5	PROPN
ejpam-5446	509	4	+	+	CCONJ
ejpam-5446	509	5	η1)ς	η1)ς	NOUN
ejpam-5446	509	6	′′′	′′′	PROPN
ejpam-5446	509	7	(	(	PUNCT
ejpam-5446	509	8	x	x	X
ejpam-5446	509	9	)	)	PUNCT
ejpam-5446	509	10	+	+	CCONJ
ejpam-5446	509	11	(	(	PUNCT
ejpam-5446	509	12	v25	v25	NOUN
ejpam-5446	509	13	+	+	CCONJ
ejpam-5446	509	14	η1v5	η1v5	NOUN
ejpam-5446	509	15	+	+	CCONJ
ejpam-5446	509	16	η2)y	η2)y	ADJ
ejpam-5446	509	17	′′	′′	PROPN
ejpam-5446	509	18	(	(	PUNCT
ejpam-5446	509	19	x	x	X
ejpam-5446	509	20	)	)	PUNCT
ejpam-5446	510	1	+	+	CCONJ
ejpam-5446	510	2	(	(	PUNCT
ejpam-5446	510	3	v35	v35	VERB
ejpam-5446	510	4	+	+	NOUN
ejpam-5446	510	5	η1v	η1v	NOUN
ejpam-5446	510	6	2	2	NUM
ejpam-5446	510	7	5	5	NUM
ejpam-5446	510	8	+	+	CCONJ
ejpam-5446	510	9	η2v5	η2v5	NOUN
ejpam-5446	510	10	+	+	CCONJ
ejpam-5446	510	11	η3)ς	η3)ς	NOUN
ejpam-5446	510	12	′(x	′(x	NOUN
ejpam-5446	510	13	)	)	PUNCT
ejpam-5446	511	1	+	+	CCONJ
ejpam-5446	511	2	(	(	PUNCT
ejpam-5446	511	3	v45	v45	PROPN
ejpam-5446	511	4	+	+	NOUN
ejpam-5446	511	5	η1v	η1v	NOUN
ejpam-5446	511	6	3	3	NUM
ejpam-5446	511	7	5	5	NUM
ejpam-5446	511	8	+	+	CCONJ
ejpam-5446	511	9	η2v	η2v	PROPN
ejpam-5446	511	10	2	2	NUM
ejpam-5446	511	11	5	5	NUM
ejpam-5446	511	12	+	+	CCONJ
ejpam-5446	511	13	η3v5	η3v5	PROPN
ejpam-5446	511	14	+	+	CCONJ
ejpam-5446	511	15	η4)ς(x	η4)ς(x	NUM
ejpam-5446	511	16	)	)	PUNCT
ejpam-5446	511	17	,	,	PUNCT
ejpam-5446	511	18	we	we	PRON
ejpam-5446	511	19	obtain	obtain	VERB
ejpam-5446	511	20	l′(x	l′(x	NOUN
ejpam-5446	511	21	)	)	PUNCT
ejpam-5446	511	22	=	=	PUNCT
ejpam-5446	511	23	ςv(x	ςv(x	NUM
ejpam-5446	511	24	)	)	PUNCT
ejpam-5446	512	1	+	+	CCONJ
ejpam-5446	512	2	(	(	PUNCT
ejpam-5446	512	3	v5	v5	PROPN
ejpam-5446	512	4	+	+	CCONJ
ejpam-5446	512	5	η1)ς	η1)ς	NOUN
ejpam-5446	512	6	iv(x	iv(x	NOUN
ejpam-5446	512	7	)	)	PUNCT
ejpam-5446	513	1	+	+	CCONJ
ejpam-5446	513	2	(	(	PUNCT
ejpam-5446	513	3	v25	v25	NOUN
ejpam-5446	513	4	+	+	CCONJ
ejpam-5446	513	5	η1v5	η1v5	PROPN
ejpam-5446	513	6	+	+	NUM
ejpam-5446	513	7	η2)ς	η2)ς	NOUN
ejpam-5446	513	8	′′′	′′′	PROPN
ejpam-5446	513	9	(	(	PUNCT
ejpam-5446	513	10	x	x	X
ejpam-5446	513	11	)	)	PUNCT
ejpam-5446	514	1	+	+	ADJ
ejpam-5446	514	2	(	(	PUNCT
ejpam-5446	514	3	v35	v35	NOUN
ejpam-5446	514	4	+	+	CCONJ
ejpam-5446	514	5	η1v	η1v	NOUN
ejpam-5446	514	6	2	2	NUM
ejpam-5446	514	7	5	5	NUM
ejpam-5446	514	8	+	+	CCONJ
ejpam-5446	514	9	η2v5	η2v5	NOUN
ejpam-5446	514	10	+	+	SYM
ejpam-5446	514	11	η3)ς	η3)ς	NOUN
ejpam-5446	514	12	′′	′′	PROPN
ejpam-5446	514	13	(	(	PUNCT
ejpam-5446	514	14	x	x	X
ejpam-5446	514	15	)	)	PUNCT
ejpam-5446	514	16	+	+	CCONJ
ejpam-5446	514	17	(	(	PUNCT
ejpam-5446	514	18	v45	v45	PROPN
ejpam-5446	514	19	+	+	NOUN
ejpam-5446	514	20	η1v	η1v	NOUN
ejpam-5446	514	21	3	3	NUM
ejpam-5446	514	22	5	5	NUM
ejpam-5446	514	23	+	+	CCONJ
ejpam-5446	514	24	η2v	η2v	PROPN
ejpam-5446	514	25	2	2	NUM
ejpam-5446	514	26	5	5	NUM
ejpam-5446	514	27	+	+	CCONJ
ejpam-5446	514	28	η3v5	η3v5	PROPN
ejpam-5446	514	29	+	+	CCONJ
ejpam-5446	514	30	η4)ς	η4)ς	NOUN
ejpam-5446	514	31	′(x	′(x	NOUN
ejpam-5446	514	32	)	)	PUNCT
ejpam-5446	515	1	+	+	PROPN
ejpam-5446	515	2	(	(	PUNCT
ejpam-5446	515	3	v55	v55	NOUN
ejpam-5446	515	4	+	+	CCONJ
ejpam-5446	515	5	η1v	η1v	NOUN
ejpam-5446	515	6	4	4	NUM
ejpam-5446	515	7	5	5	NUM
ejpam-5446	515	8	+	+	CCONJ
ejpam-5446	515	9	η2v	η2v	PROPN
ejpam-5446	515	10	3	3	NUM
ejpam-5446	515	11	5	5	NUM
ejpam-5446	515	12	+	+	CCONJ
ejpam-5446	515	13	η3v	η3v	VERB
ejpam-5446	515	14	2	2	NUM
ejpam-5446	515	15	5	5	NUM
ejpam-5446	515	16	+	+	CCONJ
ejpam-5446	515	17	η4v5	η4v5	NOUN
ejpam-5446	515	18	+	+	ADJ
ejpam-5446	515	19	η5)ς(x	η5)ς(x	NOUN
ejpam-5446	515	20	)	)	PUNCT
ejpam-5446	515	21	,	,	PUNCT
ejpam-5446	515	22	∀	∀	PUNCT
ejpam-5446	515	23	x	x	SYM
ejpam-5446	516	1	∈	∈	PROPN
ejpam-5446	517	1	[	[	X
ejpam-5446	517	2	k	k	X
ejpam-5446	517	3	,	,	PUNCT
ejpam-5446	517	4	l	l	NOUN
ejpam-5446	517	5	]	]	PUNCT
ejpam-5446	517	6	.	.	PUNCT
ejpam-5446	518	1	then	then	ADV
ejpam-5446	518	2	∣∣l′(x)−	∣∣l′(x)−	PROPN
ejpam-5446	518	3	v5l(x)−	v5l(x)−	PROPN
ejpam-5446	518	4	t	t	PROPN
ejpam-5446	518	5	(	(	PUNCT
ejpam-5446	518	6	x	x	X
ejpam-5446	518	7	)	)	PUNCT
ejpam-5446	518	8	∣∣	∣∣	X
ejpam-5446	518	9	≤	≤	PROPN
ejpam-5446	518	10	ε	ε	PROPN
ejpam-5446	518	11	.	.	PUNCT
ejpam-5446	519	1	(	(	PUNCT
ejpam-5446	519	2	2.53)∣∣l′(x)−	2.53)∣∣l′(x)−	PROPN
ejpam-5446	519	3	v5l(x)−	v5l(x)−	PROPN
ejpam-5446	519	4	t	t	PROPN
ejpam-5446	519	5	(	(	PUNCT
ejpam-5446	519	6	x	x	X
ejpam-5446	519	7	)	)	PUNCT
ejpam-5446	519	8	∣∣	∣∣	X
ejpam-5446	519	9	=	=	SYM
ejpam-5446	519	10	|ςv(x	|ςv(x	X
ejpam-5446	519	11	)	)	PUNCT
ejpam-5446	520	1	+	+	CCONJ
ejpam-5446	520	2	(	(	PUNCT
ejpam-5446	520	3	v5	v5	PROPN
ejpam-5446	520	4	+	+	CCONJ
ejpam-5446	520	5	η1)ς	η1)ς	NOUN
ejpam-5446	520	6	iv(x	iv(x	NOUN
ejpam-5446	520	7	)	)	PUNCT
ejpam-5446	520	8	+	+	CCONJ
ejpam-5446	520	9	(	(	PUNCT
ejpam-5446	520	10	v25	v25	NOUN
ejpam-5446	520	11	+	+	CCONJ
ejpam-5446	520	12	η1v5	η1v5	PROPN
ejpam-5446	520	13	+	+	NUM
ejpam-5446	520	14	η2)ς	η2)ς	NOUN
ejpam-5446	520	15	′′′	′′′	PROPN
ejpam-5446	520	16	(	(	PUNCT
ejpam-5446	520	17	x	x	X
ejpam-5446	520	18	)	)	PUNCT
ejpam-5446	520	19	+	+	ADJ
ejpam-5446	520	20	(	(	PUNCT
ejpam-5446	520	21	v35	v35	NOUN
ejpam-5446	520	22	+	+	CCONJ
ejpam-5446	520	23	η1v	η1v	NOUN
ejpam-5446	520	24	2	2	NUM
ejpam-5446	520	25	5	5	NUM
ejpam-5446	520	26	+	+	CCONJ
ejpam-5446	520	27	η2v5	η2v5	NOUN
ejpam-5446	520	28	+	+	SYM
ejpam-5446	520	29	η3)ς	η3)ς	NOUN
ejpam-5446	520	30	′′	′′	PROPN
ejpam-5446	520	31	(	(	PUNCT
ejpam-5446	520	32	x	x	X
ejpam-5446	520	33	)	)	PUNCT
ejpam-5446	520	34	+	+	PROPN
ejpam-5446	520	35	(	(	PUNCT
ejpam-5446	520	36	v45	v45	PROPN
ejpam-5446	520	37	+	+	NOUN
ejpam-5446	520	38	η1v	η1v	NOUN
ejpam-5446	520	39	3	3	NUM
ejpam-5446	520	40	5	5	NUM
ejpam-5446	520	41	+	+	CCONJ
ejpam-5446	520	42	η2v	η2v	PROPN
ejpam-5446	520	43	2	2	NUM
ejpam-5446	520	44	5	5	NUM
ejpam-5446	520	45	+	+	CCONJ
ejpam-5446	520	46	η3v5	η3v5	PROPN
ejpam-5446	520	47	+	+	CCONJ
ejpam-5446	520	48	η4)ς	η4)ς	NOUN
ejpam-5446	520	49	′(x	′(x	NOUN
ejpam-5446	520	50	)	)	PUNCT
ejpam-5446	521	1	+	+	PROPN
ejpam-5446	521	2	(	(	PUNCT
ejpam-5446	521	3	v55	v55	NOUN
ejpam-5446	521	4	+	+	CCONJ
ejpam-5446	521	5	η1v	η1v	NOUN
ejpam-5446	521	6	4	4	NUM
ejpam-5446	521	7	5	5	NUM
ejpam-5446	521	8	+	+	CCONJ
ejpam-5446	521	9	η2v	η2v	PROPN
ejpam-5446	521	10	3	3	NUM
ejpam-5446	521	11	5	5	NUM
ejpam-5446	521	12	+	+	CCONJ
ejpam-5446	521	13	η3v	η3v	VERB
ejpam-5446	521	14	2	2	NUM
ejpam-5446	521	15	5	5	NUM
ejpam-5446	521	16	+	+	CCONJ
ejpam-5446	521	17	η4v5	η4v5	NOUN
ejpam-5446	521	18	+	+	ADJ
ejpam-5446	521	19	η5)ς(x	η5)ς(x	NOUN
ejpam-5446	521	20	)	)	PUNCT
ejpam-5446	521	21	−v5[ς	−v5[ς	NOUN
ejpam-5446	521	22	iv(x	iv(x	NOUN
ejpam-5446	521	23	)	)	PUNCT
ejpam-5446	522	1	+	+	CCONJ
ejpam-5446	522	2	(	(	PUNCT
ejpam-5446	522	3	v5	v5	PROPN
ejpam-5446	522	4	+	+	CCONJ
ejpam-5446	522	5	η1)y	η1)y	NOUN
ejpam-5446	522	6	′′′	′′′	VERB
ejpam-5446	522	7	(	(	PUNCT
ejpam-5446	522	8	x	x	X
ejpam-5446	522	9	)	)	PUNCT
ejpam-5446	522	10	+	+	CCONJ
ejpam-5446	522	11	(	(	PUNCT
ejpam-5446	522	12	v25	v25	NOUN
ejpam-5446	522	13	+	+	CCONJ
ejpam-5446	522	14	η1v5	η1v5	PROPN
ejpam-5446	522	15	+	+	NUM
ejpam-5446	522	16	η2)ς	η2)ς	NOUN
ejpam-5446	522	17	′′	′′	PROPN
ejpam-5446	522	18	(	(	PUNCT
ejpam-5446	522	19	x	x	X
ejpam-5446	522	20	)	)	PUNCT
ejpam-5446	522	21	+	+	ADJ
ejpam-5446	522	22	(	(	PUNCT
ejpam-5446	522	23	v35	v35	NOUN
ejpam-5446	522	24	+	+	CCONJ
ejpam-5446	522	25	η1v	η1v	NOUN
ejpam-5446	522	26	2	2	NUM
ejpam-5446	522	27	5	5	NUM
ejpam-5446	522	28	+	+	CCONJ
ejpam-5446	522	29	η2v5	η2v5	NOUN
ejpam-5446	522	30	+	+	CCONJ
ejpam-5446	522	31	η3)ς	η3)ς	NOUN
ejpam-5446	522	32	′(x	′(x	NOUN
ejpam-5446	522	33	)	)	PUNCT
ejpam-5446	522	34	+	+	CCONJ
ejpam-5446	522	35	(	(	PUNCT
ejpam-5446	522	36	v45	v45	PROPN
ejpam-5446	522	37	+	+	NOUN
ejpam-5446	522	38	η1v	η1v	NOUN
ejpam-5446	522	39	3	3	NUM
ejpam-5446	522	40	5	5	NUM
ejpam-5446	522	41	+	+	CCONJ
ejpam-5446	522	42	η2v	η2v	PROPN
ejpam-5446	522	43	2	2	NUM
ejpam-5446	522	44	5	5	NUM
ejpam-5446	522	45	+	+	CCONJ
ejpam-5446	522	46	η3v5	η3v5	PROPN
ejpam-5446	522	47	+	+	NUM
ejpam-5446	522	48	η4)ς(x)]−	η4)ς(x)]−	PROPN
ejpam-5446	522	49	t	t	PROPN
ejpam-5446	522	50	(	(	PUNCT
ejpam-5446	522	51	x)|∣∣l′(x)−	x)|∣∣l′(x)−	PROPN
ejpam-5446	522	52	v5l(x)−	v5l(x)−	PROPN
ejpam-5446	522	53	t	t	PROPN
ejpam-5446	522	54	(	(	PUNCT
ejpam-5446	522	55	x	x	X
ejpam-5446	522	56	)	)	PUNCT
ejpam-5446	522	57	∣∣	∣∣	NUM
ejpam-5446	522	58	=	=	SYM
ejpam-5446	522	59	|ς(x	|ς(x	PROPN
ejpam-5446	522	60	)	)	PUNCT
ejpam-5446	522	61	+	+	CCONJ
ejpam-5446	522	62	v5ς	v5ς	PRON
ejpam-5446	522	63	iv(x	iv(x	NOUN
ejpam-5446	522	64	)	)	PUNCT
ejpam-5446	523	1	+	+	CCONJ
ejpam-5446	523	2	η1ς	η1ς	NOUN
ejpam-5446	523	3	iv(x	iv(x	NUM
ejpam-5446	523	4	)	)	PUNCT
ejpam-5446	523	5	+	+	CCONJ
ejpam-5446	523	6	v25ς	v25ς	NOUN
ejpam-5446	523	7	′′′	′′′	PROPN
ejpam-5446	523	8	(	(	PUNCT
ejpam-5446	523	9	x	x	X
ejpam-5446	523	10	)	)	PUNCT
ejpam-5446	523	11	+	+	NUM
ejpam-5446	523	12	η1v5ς	η1v5ς	NUM
ejpam-5446	523	13	′′′	′′′	VERB
ejpam-5446	523	14	(	(	PUNCT
ejpam-5446	523	15	x	x	X
ejpam-5446	523	16	)	)	PUNCT
ejpam-5446	523	17	+	+	CCONJ
ejpam-5446	523	18	η2ς	η2ς	PROPN
ejpam-5446	523	19	′′′	′′′	PROPN
ejpam-5446	523	20	(	(	PUNCT
ejpam-5446	523	21	x	x	X
ejpam-5446	523	22	)	)	PUNCT
ejpam-5446	524	1	+	+	NOUN
ejpam-5446	524	2	v35ς	v35ς	X
ejpam-5446	524	3	′′	′′	PROPN
ejpam-5446	524	4	(	(	PUNCT
ejpam-5446	524	5	x	x	X
ejpam-5446	524	6	)	)	PUNCT
ejpam-5446	524	7	+	+	NUM
ejpam-5446	524	8	η1v	η1v	NOUN
ejpam-5446	524	9	2	2	NUM
ejpam-5446	524	10	5ς	5ς	NOUN
ejpam-5446	524	11	′′	′′	PROPN
ejpam-5446	524	12	(	(	PUNCT
ejpam-5446	524	13	x	x	X
ejpam-5446	524	14	)	)	PUNCT
ejpam-5446	524	15	+	+	NUM
ejpam-5446	524	16	η2v5ς	η2v5ς	NUM
ejpam-5446	525	1	′′	′′	PROPN
ejpam-5446	525	2	(	(	PUNCT
ejpam-5446	525	3	x	x	X
ejpam-5446	525	4	)	)	PUNCT
ejpam-5446	525	5	+	+	CCONJ
ejpam-5446	525	6	η3ς	η3ς	PROPN
ejpam-5446	525	7	′′	′′	PROPN
ejpam-5446	525	8	(	(	PUNCT
ejpam-5446	525	9	x	x	X
ejpam-5446	525	10	)	)	PUNCT
ejpam-5446	525	11	+	+	ADJ
ejpam-5446	525	12	v55ς(x	v55ς(x	NOUN
ejpam-5446	525	13	)	)	PUNCT
ejpam-5446	525	14	+	+	NUM
ejpam-5446	525	15	η1v	η1v	NOUN
ejpam-5446	525	16	4	4	NUM
ejpam-5446	525	17	5ς(x	5ς(x	NUM
ejpam-5446	525	18	)	)	PUNCT
ejpam-5446	525	19	+	+	CCONJ
ejpam-5446	525	20	η2v	η2v	PROPN
ejpam-5446	525	21	3	3	NUM
ejpam-5446	525	22	5ς(x	5ς(x	NUM
ejpam-5446	525	23	)	)	PUNCT
ejpam-5446	525	24	+	+	CCONJ
ejpam-5446	525	25	η3v	η3v	VERB
ejpam-5446	525	26	2	2	NUM
ejpam-5446	525	27	5ς(x	5ς(x	NUM
ejpam-5446	525	28	)	)	PUNCT
ejpam-5446	526	1	+	+	NOUN
ejpam-5446	526	2	η4v5ς(x	η4v5ς(x	NOUN
ejpam-5446	526	3	)	)	PUNCT
ejpam-5446	526	4	+	+	CCONJ
ejpam-5446	526	5	η5ς(x)−	η5ς(x)−	PROPN
ejpam-5446	526	6	v5ς	v5ς	PRON
ejpam-5446	526	7	iv(x)−	iv(x)−	PROPN
ejpam-5446	526	8	v25ς	v25ς	NOUN
ejpam-5446	526	9	′′′	′′′	PROPN
ejpam-5446	526	10	(	(	PUNCT
ejpam-5446	526	11	x)−	x)−	PROPN
ejpam-5446	526	12	v5η1ς	v5η1ς	NUM
ejpam-5446	526	13	′′′	′′′	PROPN
ejpam-5446	526	14	(	(	PUNCT
ejpam-5446	526	15	x	x	X
ejpam-5446	526	16	)	)	PUNCT
ejpam-5446	526	17	−v35ς	−v35ς	NOUN
ejpam-5446	527	1	′′	′′	PROPN
ejpam-5446	527	2	(	(	PUNCT
ejpam-5446	527	3	x)−	x)−	PROPN
ejpam-5446	527	4	η1v	η1v	NOUN
ejpam-5446	527	5	2	2	NUM
ejpam-5446	527	6	5ς	5ς	NOUN
ejpam-5446	527	7	′′	′′	PROPN
ejpam-5446	527	8	(	(	PUNCT
ejpam-5446	527	9	x)−	x)−	PROPN
ejpam-5446	527	10	η2v5ς	η2v5ς	PART
ejpam-5446	527	11	′′	′′	PROPN
ejpam-5446	527	12	(	(	PUNCT
ejpam-5446	527	13	x)−	x)−	PROPN
ejpam-5446	527	14	v45ς	v45ς	PROPN
ejpam-5446	527	15	′(x	′(x	PROPN
ejpam-5446	527	16	)	)	PUNCT
ejpam-5446	528	1	−η1v35ς	−η1v35ς	PROPN
ejpam-5446	528	2	′(x)−	′(x)−	PROPN
ejpam-5446	528	3	η2v	η2v	PROPN
ejpam-5446	528	4	2	2	NUM
ejpam-5446	528	5	5ς	5ς	NUM
ejpam-5446	528	6	′(x)−	′(x)−	PROPN
ejpam-5446	528	7	η3v5ς	η3v5ς	NUM
ejpam-5446	528	8	′(x	′(x	NOUN
ejpam-5446	528	9	)	)	PUNCT
ejpam-5446	528	10	−(v55ς(x)−	−(v55ς(x)−	PROPN
ejpam-5446	528	11	η1v	η1v	VERB
ejpam-5446	528	12	4	4	NUM
ejpam-5446	528	13	5ς(x)−	5ς(x)−	NUM
ejpam-5446	528	14	η2v	η2v	PROPN
ejpam-5446	528	15	3	3	NUM
ejpam-5446	528	16	5ς(x)−	5ς(x)−	NUM
ejpam-5446	528	17	η3v	η3v	VERB
ejpam-5446	528	18	2	2	NUM
ejpam-5446	528	19	5ς(x	5ς(x	NUM
ejpam-5446	528	20	)	)	PUNCT
ejpam-5446	528	21	−η4v5ς(x)−	−η4v5ς(x)−	PROPN
ejpam-5446	528	22	t	t	PROPN
ejpam-5446	529	1	(	(	PUNCT
ejpam-5446	529	2	x)|∣∣l′(x)−	x)|∣∣l′(x)−	PROPN
ejpam-5446	529	3	v5l(x)−	v5l(x)−	PROPN
ejpam-5446	529	4	t	t	PROPN
ejpam-5446	529	5	(	(	PUNCT
ejpam-5446	529	6	x	x	X
ejpam-5446	529	7	)	)	PUNCT
ejpam-5446	529	8	∣∣	∣∣	X
ejpam-5446	530	1	=	=	SYM
ejpam-5446	530	2	∣∣∣ςv	∣∣∣ςv	PROPN
ejpam-5446	530	3	+	+	CCONJ
ejpam-5446	530	4	η1ς	η1ς	NOUN
ejpam-5446	530	5	iv(x	iv(x	NUM
ejpam-5446	530	6	)	)	PUNCT
ejpam-5446	530	7	+	+	CCONJ
ejpam-5446	530	8	η2ς	η2ς	PROPN
ejpam-5446	530	9	′′′	′′′	PROPN
ejpam-5446	530	10	(	(	PUNCT
ejpam-5446	530	11	x	x	X
ejpam-5446	530	12	)	)	PUNCT
ejpam-5446	530	13	+	+	CCONJ
ejpam-5446	530	14	η3ς	η3ς	PROPN
ejpam-5446	530	15	′′	′′	PROPN
ejpam-5446	530	16	(	(	PUNCT
ejpam-5446	530	17	x	x	X
ejpam-5446	530	18	)	)	PUNCT
ejpam-5446	530	19	+	+	CCONJ
ejpam-5446	530	20	η4ς	η4ς	PROPN
ejpam-5446	530	21	′	′	NUM
ejpam-5446	530	22	(	(	PUNCT
ejpam-5446	530	23	x	x	X
ejpam-5446	530	24	)	)	PUNCT
ejpam-5446	530	25	+	+	CCONJ
ejpam-5446	530	26	η5ς(x)−	η5ς(x)−	PROPN
ejpam-5446	530	27	t	t	PROPN
ejpam-5446	530	28	(	(	PUNCT
ejpam-5446	530	29	x	x	NOUN
ejpam-5446	530	30	)	)	PUNCT
ejpam-5446	530	31	∣∣∣	∣∣∣	ADJ
ejpam-5446	530	32	≤	≤	X
ejpam-5446	530	33	ε∣∣l′(x)−	ε∣∣l′(x)−	PROPN
ejpam-5446	530	34	wl(x)−	wl(x)−	PROPN
ejpam-5446	530	35	t	t	PROPN
ejpam-5446	530	36	(	(	PUNCT
ejpam-5446	530	37	x	x	X
ejpam-5446	530	38	)	)	PUNCT
ejpam-5446	530	39	∣∣	∣∣	X
ejpam-5446	530	40	≤	≤	PROPN
ejpam-5446	530	41	ε	ε	PROPN
ejpam-5446	530	42	.	.	PUNCT
ejpam-5446	531	1	(	(	PUNCT
ejpam-5446	531	2	2.54	2.54	NUM
ejpam-5446	531	3	)	)	PUNCT
ejpam-5446	531	4	proportionally	proportionally	ADV
ejpam-5446	531	5	l	l	NOUN
ejpam-5446	531	6	satisfies	satisfie	NOUN
ejpam-5446	531	7	,	,	PUNCT
ejpam-5446	531	8	−ε	−ε	PROPN
ejpam-5446	531	9	≤	≤	X
ejpam-5446	531	10	l′(x)−	l′(x)−	PROPN
ejpam-5446	531	11	v5l(x)−	v5l(x)−	PROPN
ejpam-5446	531	12	t	t	PROPN
ejpam-5446	531	13	(	(	PUNCT
ejpam-5446	531	14	x	x	NOUN
ejpam-5446	531	15	)	)	PUNCT
ejpam-5446	531	16	≤	≤	NUM
ejpam-5446	531	17	ε	ε	PROPN
ejpam-5446	531	18	.	.	PUNCT
ejpam-5446	532	1	(	(	PUNCT
ejpam-5446	532	2	2.55	2.55	NUM
ejpam-5446	532	3	)	)	PUNCT
ejpam-5446	532	4	multiplying	multiply	VERB
ejpam-5446	532	5	the	the	DET
ejpam-5446	532	6	equation	equation	NOUN
ejpam-5446	532	7	by	by	ADP
ejpam-5446	532	8	e−v5(x−k	e−v5(x−k	PROPN
ejpam-5446	532	9	)	)	PUNCT
ejpam-5446	532	10	,	,	PUNCT
ejpam-5446	532	11	we	we	PRON
ejpam-5446	532	12	get	get	VERB
ejpam-5446	532	13	−εe−v5(x−k	−εe−v5(x−k	NOUN
ejpam-5446	532	14	)	)	PUNCT
ejpam-5446	532	15	≤	≤	NOUN
ejpam-5446	532	16	l′(x)e−v5(x−k	l′(x)e−v5(x−k	X
ejpam-5446	532	17	)	)	PUNCT
ejpam-5446	532	18	−	−	PROPN
ejpam-5446	532	19	v5l(x)e	v5l(x)e	NOUN
ejpam-5446	532	20	−v5(x−k	−v5(x−k	PROPN
ejpam-5446	532	21	)	)	PUNCT
ejpam-5446	533	1	−	−	PROPN
ejpam-5446	533	2	t	t	PROPN
ejpam-5446	533	3	(	(	PUNCT
ejpam-5446	533	4	x)e−v5(x−k	x)e−v5(x−k	NOUN
ejpam-5446	533	5	)	)	PUNCT
ejpam-5446	533	6	≤	≤	NUM
ejpam-5446	533	7	εe−v5(x−k	εe−v5(x−k	NOUN
ejpam-5446	533	8	)	)	PUNCT
ejpam-5446	533	9	.	.	PUNCT
ejpam-5446	534	1	(	(	PUNCT
ejpam-5446	534	2	2.56	2.56	NUM
ejpam-5446	534	3	)	)	PUNCT
ejpam-5446	534	4	v.	v.	ADP
ejpam-5446	534	5	govindan	govindan	PROPN
ejpam-5446	534	6	et	et	PROPN
ejpam-5446	534	7	al	al	PROPN
ejpam-5446	534	8	.	.	PUNCT
ejpam-5446	534	9	/	/	SYM
ejpam-5446	534	10	eur	eur	PROPN
ejpam-5446	534	11	.	.	PUNCT
ejpam-5446	535	1	j.	j.	PROPN
ejpam-5446	535	2	pure	pure	PROPN
ejpam-5446	535	3	appl	appl	PROPN
ejpam-5446	535	4	.	.	PROPN
ejpam-5446	535	5	math	math	PROPN
ejpam-5446	535	6	,	,	PUNCT
ejpam-5446	535	7	17	17	NUM
ejpam-5446	535	8	(	(	PUNCT
ejpam-5446	535	9	4	4	NUM
ejpam-5446	535	10	)	)	PUNCT
ejpam-5446	535	11	(	(	PUNCT
ejpam-5446	535	12	2024	2024	NUM
ejpam-5446	535	13	)	)	PUNCT
ejpam-5446	535	14	,	,	PUNCT
ejpam-5446	535	15	3585	3585	NUM
ejpam-5446	535	16	-	-	SYM
ejpam-5446	535	17	3609	3609	NUM
ejpam-5446	535	18	3604	3604	NUM
ejpam-5446	535	19	without	without	ADP
ejpam-5446	535	20	loss	loss	NOUN
ejpam-5446	535	21	of	of	ADP
ejpam-5446	535	22	consensus	consensus	NOUN
ejpam-5446	536	1	,	,	PUNCT
ejpam-5446	536	2	we	we	PRON
ejpam-5446	536	3	may	may	AUX
ejpam-5446	536	4	expect	expect	VERB
ejpam-5446	536	5	to	to	PART
ejpam-5446	536	6	be	be	AUX
ejpam-5446	536	7	that	that	SCONJ
ejpam-5446	536	8	v5	v5	PROPN
ejpam-5446	536	9	>	>	X
ejpam-5446	536	10	1	1	NUM
ejpam-5446	536	11	,	,	PUNCT
ejpam-5446	536	12	thus	thus	ADV
ejpam-5446	536	13	−εe−v5(x−k	−εe−v5(x−k	NOUN
ejpam-5446	536	14	)	)	PUNCT
ejpam-5446	536	15	≤	≤	NOUN
ejpam-5446	536	16	l′(x)e−v5(x−k	l′(x)e−v5(x−k	X
ejpam-5446	536	17	)	)	PUNCT
ejpam-5446	536	18	−	−	PROPN
ejpam-5446	536	19	v5l(x)e	v5l(x)e	ADJ
ejpam-5446	536	20	−v5(x−k	−v5(x−k	PROPN
ejpam-5446	536	21	)	)	PUNCT
ejpam-5446	536	22	−t	−t	NOUN
ejpam-5446	536	23	(	(	PUNCT
ejpam-5446	536	24	x)e−v5(x−k	x)e−v5(x−k	NOUN
ejpam-5446	536	25	)	)	PUNCT
ejpam-5446	536	26	≤	≤	NUM
ejpam-5446	536	27	εe−v5(x−k	εe−v5(x−k	NOUN
ejpam-5446	536	28	)	)	PUNCT
ejpam-5446	536	29	,	,	PUNCT
ejpam-5446	536	30	(	(	PUNCT
ejpam-5446	536	31	2.57	2.57	NUM
ejpam-5446	536	32	)	)	PUNCT
ejpam-5446	536	33	∀	∀	X
ejpam-5446	537	1	x	x	X
ejpam-5446	537	2	∈	∈	PROPN
ejpam-5446	538	1	[	[	X
ejpam-5446	538	2	k	k	X
ejpam-5446	538	3	,	,	PUNCT
ejpam-5446	538	4	l	l	NOUN
ejpam-5446	538	5	]	]	PUNCT
ejpam-5446	538	6	.	.	PUNCT
ejpam-5446	539	1	integrating	integrate	VERB
ejpam-5446	539	2	(	(	PUNCT
ejpam-5446	539	3	2.56	2.56	NUM
ejpam-5446	539	4	)	)	PUNCT
ejpam-5446	539	5	from	from	ADP
ejpam-5446	539	6	x	x	PRON
ejpam-5446	539	7	to	to	ADP
ejpam-5446	539	8	l	l	NOUN
ejpam-5446	539	9	,	,	PUNCT
ejpam-5446	539	10	we	we	PRON
ejpam-5446	539	11	obtain	obtain	VERB
ejpam-5446	539	12	−ε	−ε	PROPN
ejpam-5446	539	13	(	(	PUNCT
ejpam-5446	539	14	e−v5(x−k	e−v5(x−k	NOUN
ejpam-5446	539	15	)	)	PUNCT
ejpam-5446	539	16	−	−	PROPN
ejpam-5446	539	17	e−v5(l−k	e−v5(l−k	NOUN
ejpam-5446	539	18	)	)	PUNCT
ejpam-5446	539	19	)	)	PUNCT
ejpam-5446	540	1	≤	≤	NUM
ejpam-5446	540	2	l(l)e−v5(l−k	l(l)e−v5(l−k	NOUN
ejpam-5446	540	3	)	)	PUNCT
ejpam-5446	540	4	−	−	NUM
ejpam-5446	540	5	l(x)e−v5(x−k	l(x)e−v5(x−k	NOUN
ejpam-5446	540	6	)	)	PUNCT
ejpam-5446	540	7	−	−	NUM
ejpam-5446	541	1	∫	∫	PROPN
ejpam-5446	541	2	l	l	NOUN
ejpam-5446	541	3	x	x	X
ejpam-5446	541	4	t	t	PROPN
ejpam-5446	541	5	(	(	PUNCT
ejpam-5446	541	6	x)e−v5(t−k)dt	x)e−v5(t−k)dt	PROPN
ejpam-5446	541	7	≤	≤	PROPN
ejpam-5446	541	8	ε	ε	PROPN
ejpam-5446	541	9	(	(	PUNCT
ejpam-5446	541	10	e−v5(x−k	e−v5(x−k	NOUN
ejpam-5446	541	11	)	)	PUNCT
ejpam-5446	541	12	−	−	PROPN
ejpam-5446	541	13	e−v5(l−k	e−v5(l−k	NOUN
ejpam-5446	541	14	)	)	PUNCT
ejpam-5446	541	15	)	)	PUNCT
ejpam-5446	542	1	−εe−v5(x−k	−εe−v5(x−k	NOUN
ejpam-5446	542	2	)	)	PUNCT
ejpam-5446	542	3	≤	≤	NUM
ejpam-5446	542	4	l(l)e−v5(l−k	l(l)e−v5(l−k	NOUN
ejpam-5446	542	5	)	)	PUNCT
ejpam-5446	542	6	−	−	NUM
ejpam-5446	542	7	εe−v5(l−k	εe−v5(l−k	NOUN
ejpam-5446	542	8	)	)	PUNCT
ejpam-5446	542	9	−	−	PROPN
ejpam-5446	543	1	l(x)e−v5(x−l	l(x)e−v5(x−l	PROPN
ejpam-5446	543	2	)	)	PUNCT
ejpam-5446	544	1	−	−	NUM
ejpam-5446	545	1	∫	∫	PROPN
ejpam-5446	545	2	l	l	NOUN
ejpam-5446	545	3	x	x	X
ejpam-5446	545	4	t	t	PROPN
ejpam-5446	545	5	(	(	PUNCT
ejpam-5446	545	6	x)e−v5(t−k)dt	x)e−v5(t−k)dt	PROPN
ejpam-5446	545	7	≤	≤	PROPN
ejpam-5446	545	8	εe−v5(x−k	εe−v5(x−k	NOUN
ejpam-5446	545	9	)	)	PUNCT
ejpam-5446	545	10	.	.	PUNCT
ejpam-5446	546	1	(	(	PUNCT
ejpam-5446	546	2	2.58	2.58	NUM
ejpam-5446	546	3	)	)	PUNCT
ejpam-5446	546	4	multiplying	multiply	VERB
ejpam-5446	546	5	the	the	DET
ejpam-5446	546	6	equation	equation	NOUN
ejpam-5446	546	7	by	by	ADP
ejpam-5446	546	8	ev5(x−a	ev5(x−a	PROPN
ejpam-5446	546	9	)	)	PUNCT
ejpam-5446	546	10	,	,	PUNCT
ejpam-5446	546	11	we	we	PRON
ejpam-5446	546	12	get	get	VERB
ejpam-5446	546	13	−εe−v5(x−k)ev5(x−k	−εe−v5(x−k)ev5(x−k	NOUN
ejpam-5446	546	14	)	)	PUNCT
ejpam-5446	546	15	≤	≤	NUM
ejpam-5446	547	1	l(l)e−v5(l−k)ev5(x−k	l(l)e−v5(l−k)ev5(x−k	NOUN
ejpam-5446	547	2	)	)	PUNCT
ejpam-5446	547	3	−	−	NOUN
ejpam-5446	547	4	εe−v5(l−k)ev5(x−k	εe−v5(l−k)ev5(x−k	NOUN
ejpam-5446	547	5	)	)	PUNCT
ejpam-5446	547	6	−l(x)e−v5(x−k)ev5(x−k	−l(x)e−v5(x−k)ev5(x−k	NOUN
ejpam-5446	547	7	)	)	PUNCT
ejpam-5446	548	1	−	−	NUM
ejpam-5446	548	2	∫	∫	PROPN
ejpam-5446	548	3	l	l	NOUN
ejpam-5446	548	4	x	x	X
ejpam-5446	548	5	t	t	PROPN
ejpam-5446	548	6	(	(	PUNCT
ejpam-5446	548	7	x)e−v5(t−k)dtev5(x−k	x)e−v5(t−k)dtev5(x−k	PROPN
ejpam-5446	548	8	)	)	PUNCT
ejpam-5446	548	9	≤	≤	NOUN
ejpam-5446	548	10	εe−v5(x−k)ev5(x−k	εe−v5(x−k)ev5(x−k	NOUN
ejpam-5446	548	11	)	)	PUNCT
ejpam-5446	548	12	−ε	−ε	PROPN
ejpam-5446	548	13	≤	≤	PROPN
ejpam-5446	548	14	l(l)ev5(x−l	l(l)ev5(x−l	PROPN
ejpam-5446	548	15	)	)	PUNCT
ejpam-5446	549	1	−	−	PROPN
ejpam-5446	549	2	εev5(x−l	εev5(x−l	NOUN
ejpam-5446	549	3	)	)	PUNCT
ejpam-5446	550	1	−	−	PROPN
ejpam-5446	551	1	l(x)−	l(x)−	PROPN
ejpam-5446	551	2	ev5x	ev5x	PROPN
ejpam-5446	551	3	∫	∫	NOUN
ejpam-5446	551	4	l	l	NOUN
ejpam-5446	551	5	x	x	X
ejpam-5446	551	6	t	t	PROPN
ejpam-5446	551	7	(	(	PUNCT
ejpam-5446	551	8	t)e−v5tdt	t)e−v5tdt	PROPN
ejpam-5446	551	9	≤	≤	NUM
ejpam-5446	551	10	ε	ε	PROPN
ejpam-5446	551	11	.	.	PUNCT
ejpam-5446	552	1	(	(	PUNCT
ejpam-5446	552	2	2.59	2.59	NUM
ejpam-5446	552	3	)	)	PUNCT
ejpam-5446	552	4	let	let	VERB
ejpam-5446	552	5	k(x	k(x	NOUN
ejpam-5446	552	6	)	)	PUNCT
ejpam-5446	552	7	=	=	SYM
ejpam-5446	552	8	l(l)ev5(x−l	l(l)ev5(x−l	PROPN
ejpam-5446	552	9	)	)	PUNCT
ejpam-5446	553	1	−	−	PROPN
ejpam-5446	554	1	ev5x	ev5x	PROPN
ejpam-5446	554	2	∫	∫	PROPN
ejpam-5446	554	3	l	l	NOUN
ejpam-5446	554	4	x	x	X
ejpam-5446	554	5	t	t	PROPN
ejpam-5446	554	6	(	(	PUNCT
ejpam-5446	554	7	t)e	t)e	NOUN
ejpam-5446	554	8	−v5tdt	−v5tdt	NOUN
ejpam-5446	554	9	.	.	PUNCT
ejpam-5446	555	1	then	then	ADV
ejpam-5446	555	2	|k(x)−	|k(x)−	PROPN
ejpam-5446	555	3	l(x)|	l(x)|	AUX
ejpam-5446	555	4	=	=	SYM
ejpam-5446	555	5	∣∣∣∣l(l)ev5(x−l	∣∣∣∣l(l)ev5(x−l	PROPN
ejpam-5446	555	6	)	)	PUNCT
ejpam-5446	556	1	−	−	PROPN
ejpam-5446	557	1	l(x)−	l(x)−	NOUN
ejpam-5446	557	2	ev5x	ev5x	PROPN
ejpam-5446	557	3	∫	∫	NOUN
ejpam-5446	557	4	l	l	NOUN
ejpam-5446	557	5	x	x	X
ejpam-5446	557	6	t	t	PROPN
ejpam-5446	557	7	(	(	PUNCT
ejpam-5446	557	8	t)e−v5tdt	t)e−v5tdt	PROPN
ejpam-5446	557	9	∣∣∣∣	∣∣∣∣	PROPN
ejpam-5446	557	10	|k(x)−	|k(x)−	NOUN
ejpam-5446	557	11	l(x)|	l(x)|	VERB
ejpam-5446	557	12	≤	≤	NOUN
ejpam-5446	557	13	ep5x	ep5x	ADJ
ejpam-5446	557	14	∫	∫	NOUN
ejpam-5446	557	15	l	l	NOUN
ejpam-5446	557	16	x	x	PUNCT
ejpam-5446	557	17	∣∣e−v5	∣∣e−v5	ADP
ejpam-5446	557	18	t	t	X
ejpam-5446	557	19	∣∣	∣∣	NUM
ejpam-5446	557	20	∣∣l′(t)−	∣∣l′(t)−	PROPN
ejpam-5446	557	21	v5l(t)−	v5l(t)−	PROPN
ejpam-5446	557	22	t	t	PROPN
ejpam-5446	557	23	(	(	PUNCT
ejpam-5446	557	24	t	t	PROPN
ejpam-5446	557	25	)	)	PUNCT
ejpam-5446	557	26	∣∣	∣∣	NUM
ejpam-5446	557	27	dt	dt	NOUN
ejpam-5446	557	28	|k(x)−	|k(x)−	PROPN
ejpam-5446	557	29	l(x)|	l(x)|	VERB
ejpam-5446	557	30	≤	≤	NOUN
ejpam-5446	557	31	ep5x	ep5x	ADJ
ejpam-5446	557	32	∫	∫	NOUN
ejpam-5446	557	33	l	l	NOUN
ejpam-5446	557	34	x	x	PUNCT
ejpam-5446	557	35	e−p5	e−p5	ADP
ejpam-5446	557	36	t	t	PROPN
ejpam-5446	557	37	∣∣l′(t)−	∣∣l′(t)−	PROPN
ejpam-5446	557	38	v5l(t)−	v5l(t)−	PROPN
ejpam-5446	557	39	t	t	PROPN
ejpam-5446	557	40	(	(	PUNCT
ejpam-5446	557	41	t	t	PROPN
ejpam-5446	557	42	)	)	PUNCT
ejpam-5446	557	43	∣∣	∣∣	NUM
ejpam-5446	558	1	dt	dt	NOUN
ejpam-5446	558	2	|k(x)−	|k(x)−	PROPN
ejpam-5446	558	3	l(x)|	l(x)|	VERB
ejpam-5446	558	4	≤	≤	NOUN
ejpam-5446	559	1	εep5x	εep5x	ADJ
ejpam-5446	559	2	∫	∫	PROPN
ejpam-5446	559	3	l	l	NOUN
ejpam-5446	559	4	x	x	X
ejpam-5446	560	1	e−p5tdt	e−p5tdt	ADJ
ejpam-5446	560	2	.	.	PUNCT
ejpam-5446	561	1	(	(	PUNCT
ejpam-5446	561	2	2.60	2.60	NUM
ejpam-5446	561	3	)	)	PUNCT
ejpam-5446	561	4	if	if	SCONJ
ejpam-5446	561	5	p5	p5	ADJ
ejpam-5446	561	6	̸=	̸=	PROPN
ejpam-5446	561	7	0	0	NUM
ejpam-5446	561	8	,	,	PUNCT
ejpam-5446	561	9	then	then	ADV
ejpam-5446	561	10	|k(x)−	|k(x)−	NOUN
ejpam-5446	561	11	l(x)|	l(x)|	VERB
ejpam-5446	561	12	≤	≤	NOUN
ejpam-5446	561	13	εep5x	εep5x	ADJ
ejpam-5446	561	14	∫	∫	NOUN
ejpam-5446	562	1	l	l	NOUN
ejpam-5446	563	1	x	x	X
ejpam-5446	564	1	e−p5tdt	e−p5tdt	ADJ
ejpam-5446	564	2	|k(x)−	|k(x)−	NOUN
ejpam-5446	564	3	l(x)|	l(x)|	VERB
ejpam-5446	564	4	≤	≤	NUM
ejpam-5446	564	5	ε	ε	PROPN
ejpam-5446	564	6	−p5	−p5	PROPN
ejpam-5446	564	7	[	[	PUNCT
ejpam-5446	564	8	e−p5(l−x	e−p5(l−x	NOUN
ejpam-5446	564	9	)	)	PUNCT
ejpam-5446	564	10	−	−	PROPN
ejpam-5446	564	11	1	1	X
ejpam-5446	564	12	]	]	PUNCT
ejpam-5446	564	13	|k(x)−	|k(x)−	NOUN
ejpam-5446	564	14	l(x)|	l(x)|	VERB
ejpam-5446	564	15	≤	≤	NUM
ejpam-5446	564	16	ε	ε	PROPN
ejpam-5446	564	17	p5	p5	PROPN
ejpam-5446	564	18	[	[	PUNCT
ejpam-5446	564	19	1−	1−	NUM
ejpam-5446	564	20	e−p5(l−x	e−p5(l−x	NOUN
ejpam-5446	564	21	)	)	PUNCT
ejpam-5446	564	22	]	]	PUNCT
ejpam-5446	564	23	;	;	PUNCT
ejpam-5446	564	24	x	x	X
ejpam-5446	564	25	∈	∈	PROPN
ejpam-5446	565	1	[	[	X
ejpam-5446	565	2	k	k	X
ejpam-5446	565	3	,	,	PUNCT
ejpam-5446	565	4	l	l	NOUN
ejpam-5446	565	5	]	]	X
ejpam-5446	565	6	v.	v.	ADP
ejpam-5446	565	7	govindan	govindan	PROPN
ejpam-5446	565	8	et	et	PROPN
ejpam-5446	565	9	al	al	PROPN
ejpam-5446	565	10	.	.	PUNCT
ejpam-5446	565	11	/	/	SYM
ejpam-5446	565	12	eur	eur	PROPN
ejpam-5446	565	13	.	.	PUNCT
ejpam-5446	566	1	j.	j.	PROPN
ejpam-5446	566	2	pure	pure	PROPN
ejpam-5446	566	3	appl	appl	PROPN
ejpam-5446	566	4	.	.	PROPN
ejpam-5446	566	5	math	math	PROPN
ejpam-5446	566	6	,	,	PUNCT
ejpam-5446	566	7	17	17	NUM
ejpam-5446	566	8	(	(	PUNCT
ejpam-5446	566	9	4	4	NUM
ejpam-5446	566	10	)	)	PUNCT
ejpam-5446	566	11	(	(	PUNCT
ejpam-5446	566	12	2024	2024	NUM
ejpam-5446	566	13	)	)	PUNCT
ejpam-5446	566	14	,	,	PUNCT
ejpam-5446	566	15	3585	3585	NUM
ejpam-5446	566	16	-	-	SYM
ejpam-5446	566	17	3609	3609	NUM
ejpam-5446	566	18	3605	3605	NUM
ejpam-5446	566	19	|k(x)−	|k(x)−	NOUN
ejpam-5446	566	20	l(x)|	l(x)|	VERB
ejpam-5446	566	21	≤	≤	NUM
ejpam-5446	566	22	ε	ε	PROPN
ejpam-5446	566	23	p5	p5	PROPN
ejpam-5446	566	24	[	[	PUNCT
ejpam-5446	566	25	1−	1−	NUM
ejpam-5446	566	26	e−p5(l−k	e−p5(l−k	NOUN
ejpam-5446	566	27	)	)	PUNCT
ejpam-5446	566	28	]	]	PUNCT
ejpam-5446	567	1	;	;	PUNCT
ejpam-5446	567	2	x	x	X
ejpam-5446	567	3	∈	∈	PROPN
ejpam-5446	568	1	[	[	X
ejpam-5446	568	2	k	k	X
ejpam-5446	568	3	,	,	PUNCT
ejpam-5446	568	4	l	l	NOUN
ejpam-5446	568	5	]	]	X
ejpam-5446	568	6	.	.	PUNCT
ejpam-5446	569	1	(	(	PUNCT
ejpam-5446	569	2	2.61	2.61	NUM
ejpam-5446	569	3	)	)	PUNCT
ejpam-5446	569	4	if	if	SCONJ
ejpam-5446	569	5	p5	p5	ADJ
ejpam-5446	569	6	=	=	SYM
ejpam-5446	569	7	0	0	NUM
ejpam-5446	569	8	,	,	PUNCT
ejpam-5446	569	9	then	then	ADV
ejpam-5446	569	10	|k(x)−	|k(x)−	NOUN
ejpam-5446	569	11	l(x)|	l(x)|	VERB
ejpam-5446	569	12	≤	≤	NOUN
ejpam-5446	569	13	εep5x	εep5x	ADJ
ejpam-5446	569	14	∫	∫	NOUN
ejpam-5446	570	1	l	l	NOUN
ejpam-5446	571	1	x	x	X
ejpam-5446	572	1	e−p5tdt	e−p5tdt	ADJ
ejpam-5446	572	2	|k(x)−	|k(x)−	NOUN
ejpam-5446	572	3	l(x)|	l(x)|	VERB
ejpam-5446	572	4	≤	≤	NUM
ejpam-5446	573	1	ε	ε	PROPN
ejpam-5446	573	2	∫	∫	PROPN
ejpam-5446	573	3	l	l	NOUN
ejpam-5446	573	4	x	x	X
ejpam-5446	574	1	dt	dt	X
ejpam-5446	574	2	|k(x)−	|k(x)−	NOUN
ejpam-5446	574	3	l(x)|	l(x)|	VERB
ejpam-5446	574	4	≤	≤	NOUN
ejpam-5446	574	5	(	(	PUNCT
ejpam-5446	574	6	l	l	NOUN
ejpam-5446	574	7	−	−	PROPN
ejpam-5446	574	8	x);x	x);x	PROPN
ejpam-5446	574	9	∈	∈	PROPN
ejpam-5446	575	1	[	[	X
ejpam-5446	575	2	k	k	X
ejpam-5446	575	3	,	,	PUNCT
ejpam-5446	575	4	l	l	NOUN
ejpam-5446	575	5	]	]	X
ejpam-5446	575	6	|k(x)−	|k(x)−	NOUN
ejpam-5446	575	7	l(x)|	l(x)|	VERB
ejpam-5446	575	8	≤	≤	NOUN
ejpam-5446	575	9	(	(	PUNCT
ejpam-5446	575	10	l	l	NOUN
ejpam-5446	575	11	−	−	PROPN
ejpam-5446	575	12	k);x	k);x	PROPN
ejpam-5446	575	13	∈	∈	PROPN
ejpam-5446	576	1	[	[	X
ejpam-5446	576	2	k	k	X
ejpam-5446	576	3	,	,	PUNCT
ejpam-5446	576	4	l	l	NOUN
ejpam-5446	576	5	]	]	X
ejpam-5446	576	6	.	.	PUNCT
ejpam-5446	577	1	(	(	PUNCT
ejpam-5446	577	2	2.62	2.62	NUM
ejpam-5446	577	3	)	)	PUNCT
ejpam-5446	577	4	it	it	PRON
ejpam-5446	577	5	follow	follow	VERB
ejpam-5446	577	6	from	from	ADP
ejpam-5446	577	7	(	(	PUNCT
ejpam-5446	577	8	2.41	2.41	NUM
ejpam-5446	577	9	)	)	PUNCT
ejpam-5446	577	10	,	,	PUNCT
ejpam-5446	577	11	we	we	PRON
ejpam-5446	577	12	desired	desire	VERB
ejpam-5446	577	13	our	our	PRON
ejpam-5446	577	14	result	result	NOUN
ejpam-5446	577	15	(	(	PUNCT
ejpam-5446	577	16	2.52	2.52	NUM
ejpam-5446	577	17	)	)	PUNCT
ejpam-5446	577	18	,	,	PUNCT
ejpam-5446	577	19	for	for	ADP
ejpam-5446	577	20	all	all	DET
ejpam-5446	577	21	x	x	SYM
ejpam-5446	577	22	∈	∈	PROPN
ejpam-5446	578	1	[	[	X
ejpam-5446	578	2	k	k	X
ejpam-5446	578	3	,	,	PUNCT
ejpam-5446	578	4	l	l	NOUN
ejpam-5446	578	5	]	]	PUNCT
ejpam-5446	578	6	thus	thus	ADV
ejpam-5446	578	7	,	,	PUNCT
ejpam-5446	578	8	the	the	DET
ejpam-5446	578	9	proof	proof	NOUN
ejpam-5446	578	10	is	be	AUX
ejpam-5446	578	11	completed	complete	VERB
ejpam-5446	578	12	.	.	PUNCT
ejpam-5446	579	1	3	3	X
ejpam-5446	579	2	.	.	X
ejpam-5446	579	3	illustrative	illustrative	ADJ
ejpam-5446	579	4	examples	example	NOUN
ejpam-5446	579	5	in	in	ADP
ejpam-5446	579	6	this	this	DET
ejpam-5446	579	7	section	section	NOUN
ejpam-5446	579	8	,	,	PUNCT
ejpam-5446	579	9	the	the	DET
ejpam-5446	579	10	following	follow	VERB
ejpam-5446	579	11	numerical	numerical	ADJ
ejpam-5446	579	12	examples	example	NOUN
ejpam-5446	579	13	are	be	AUX
ejpam-5446	579	14	discussed	discuss	VERB
ejpam-5446	579	15	to	to	PART
ejpam-5446	579	16	prove	prove	VERB
ejpam-5446	579	17	the	the	DET
ejpam-5446	579	18	usefulness	usefulness	NOUN
ejpam-5446	579	19	of	of	ADP
ejpam-5446	579	20	the	the	DET
ejpam-5446	579	21	theortical	theortical	NOUN
ejpam-5446	579	22	in	in	ADP
ejpam-5446	579	23	this	this	DET
ejpam-5446	579	24	paper	paper	NOUN
ejpam-5446	579	25	example	example	NOUN
ejpam-5446	579	26	3.1	3.1	NUM
ejpam-5446	579	27	consider	consider	VERB
ejpam-5446	579	28	the	the	DET
ejpam-5446	579	29	following	follow	VERB
ejpam-5446	579	30	differential	differential	ADJ
ejpam-5446	579	31	equation	equation	NOUN
ejpam-5446	579	32	τv(x	τv(x	PUNCT
ejpam-5446	579	33	)	)	PUNCT
ejpam-5446	580	1	+	+	CCONJ
ejpam-5446	580	2	2τ	2τ	NUM
ejpam-5446	580	3	iv(x	iv(x	PUNCT
ejpam-5446	580	4	)	)	PUNCT
ejpam-5446	581	1	+	+	CCONJ
ejpam-5446	581	2	τ	τ	X
ejpam-5446	581	3	′′′(x	′′′(x	PROPN
ejpam-5446	581	4	)	)	PUNCT
ejpam-5446	582	1	+	+	CCONJ
ejpam-5446	582	2	τ	τ	PROPN
ejpam-5446	582	3	′′(x	′′(x	NOUN
ejpam-5446	582	4	)	)	PUNCT
ejpam-5446	583	1	+	+	NUM
ejpam-5446	583	2	2τ	2τ	NUM
ejpam-5446	583	3	′(x	′(x	NOUN
ejpam-5446	583	4	)	)	PUNCT
ejpam-5446	584	1	+	+	NUM
ejpam-5446	584	2	3τ(x	3τ(x	NUM
ejpam-5446	584	3	)	)	PUNCT
ejpam-5446	585	1	=	=	SYM
ejpam-5446	585	2	ω(x	ω(x	X
ejpam-5446	585	3	)	)	PUNCT
ejpam-5446	585	4	;	;	PUNCT
ejpam-5446	585	5	x	x	X
ejpam-5446	585	6	∈	∈	PROPN
ejpam-5446	586	1	[	[	X
ejpam-5446	586	2	2	2	NUM
ejpam-5446	586	3	,	,	PUNCT
ejpam-5446	586	4	3	3	NUM
ejpam-5446	586	5	]	]	PUNCT
ejpam-5446	586	6	.	.	PUNCT
ejpam-5446	587	1	(	(	PUNCT
ejpam-5446	587	2	3.1	3.1	NUM
ejpam-5446	587	3	)	)	PUNCT
ejpam-5446	587	4	suppose	suppose	VERB
ejpam-5446	587	5	∈	∈	PROPN
ejpam-5446	587	6	>	>	X
ejpam-5446	587	7	0	0	NUM
ejpam-5446	587	8	,	,	PUNCT
ejpam-5446	587	9	as	as	ADP
ejpam-5446	587	10	such	such	ADJ
ejpam-5446	587	11	|τv(x	|τv(x	ADP
ejpam-5446	587	12	)	)	PUNCT
ejpam-5446	588	1	+	+	NUM
ejpam-5446	588	2	2τ	2τ	NUM
ejpam-5446	588	3	iv(x	iv(x	PUNCT
ejpam-5446	588	4	)	)	PUNCT
ejpam-5446	589	1	+	+	CCONJ
ejpam-5446	589	2	τ	τ	X
ejpam-5446	589	3	′′′(x	′′′(x	PROPN
ejpam-5446	589	4	)	)	PUNCT
ejpam-5446	590	1	+	+	CCONJ
ejpam-5446	590	2	τ	τ	PROPN
ejpam-5446	590	3	′′(x	′′(x	NOUN
ejpam-5446	590	4	)	)	PUNCT
ejpam-5446	591	1	+	+	NUM
ejpam-5446	591	2	2τ	2τ	NUM
ejpam-5446	591	3	′(x	′(x	NOUN
ejpam-5446	591	4	)	)	PUNCT
ejpam-5446	592	1	+	+	NUM
ejpam-5446	592	2	3τ(x	3τ(x	NUM
ejpam-5446	592	3	)	)	PUNCT
ejpam-5446	592	4	−	−	NOUN
ejpam-5446	592	5	ω(x	ω(x	NUM
ejpam-5446	592	6	)	)	PUNCT
ejpam-5446	592	7	|	|	ADV
ejpam-5446	592	8	≤∈	≤∈	ADV
ejpam-5446	592	9	.	.	PUNCT
ejpam-5446	593	1	x	x	X
ejpam-5446	593	2	∈	∈	PROPN
ejpam-5446	594	1	[	[	X
ejpam-5446	594	2	2	2	NUM
ejpam-5446	594	3	,	,	PUNCT
ejpam-5446	594	4	3	3	NUM
ejpam-5446	594	5	]	]	PUNCT
ejpam-5446	594	6	.	.	PUNCT
ejpam-5446	595	1	(	(	PUNCT
ejpam-5446	595	2	3.2	3.2	NUM
ejpam-5446	595	3	)	)	PUNCT
ejpam-5446	595	4	suppose	suppose	VERB
ejpam-5446	595	5	v1	v1	NOUN
ejpam-5446	595	6	=	=	SYM
ejpam-5446	595	7	1	1	NUM
ejpam-5446	595	8	,	,	PUNCT
ejpam-5446	595	9	then	then	ADV
ejpam-5446	595	10	g(x	g(x	PROPN
ejpam-5446	595	11	)	)	PUNCT
ejpam-5446	596	1	=	=	PUNCT
ejpam-5446	596	2	τ	τ	PROPN
ejpam-5446	596	3	iv(x	iv(x	X
ejpam-5446	596	4	)	)	PUNCT
ejpam-5446	597	1	+	+	CCONJ
ejpam-5446	597	2	3τ	3τ	NUM
ejpam-5446	597	3	′′′(x	′′′(x	PROPN
ejpam-5446	597	4	)	)	PUNCT
ejpam-5446	597	5	+	+	NUM
ejpam-5446	597	6	4τ	4τ	NUM
ejpam-5446	597	7	′′(x	′′(x	NOUN
ejpam-5446	597	8	)	)	PUNCT
ejpam-5446	598	1	+	+	NUM
ejpam-5446	598	2	5τ	5τ	NUM
ejpam-5446	598	3	′(x	′(x	NOUN
ejpam-5446	598	4	)	)	PUNCT
ejpam-5446	599	1	+	+	CCONJ
ejpam-5446	599	2	7τ(x	7τ(x	NUM
ejpam-5446	599	3	)	)	PUNCT
ejpam-5446	599	4	and	and	CCONJ
ejpam-5446	599	5	g′(x	g′(x	INTJ
ejpam-5446	599	6	)	)	PUNCT
ejpam-5446	600	1	=	=	NOUN
ejpam-5446	600	2	τv(x	τv(x	PUNCT
ejpam-5446	600	3	)	)	PUNCT
ejpam-5446	601	1	+	+	CCONJ
ejpam-5446	601	2	3τ	3τ	NOUN
ejpam-5446	601	3	iv(x	iv(x	PUNCT
ejpam-5446	601	4	)	)	PUNCT
ejpam-5446	602	1	+	+	NUM
ejpam-5446	602	2	4τ	4τ	NUM
ejpam-5446	602	3	′′′(x	′′′(x	PROPN
ejpam-5446	602	4	)	)	PUNCT
ejpam-5446	602	5	+	+	NUM
ejpam-5446	602	6	5τ	5τ	NUM
ejpam-5446	602	7	′′(x	′′(x	NOUN
ejpam-5446	602	8	)	)	PUNCT
ejpam-5446	602	9	+	+	NUM
ejpam-5446	602	10	7τ	7τ	NOUN
ejpam-5446	602	11	′(x	′(x	NOUN
ejpam-5446	602	12	)	)	PUNCT
ejpam-5446	603	1	+	+	CCONJ
ejpam-5446	603	2	7τ(x	7τ(x	NUM
ejpam-5446	603	3	)	)	PUNCT
ejpam-5446	604	1	x	x	X
ejpam-5446	604	2	∈	∈	PROPN
ejpam-5446	605	1	[	[	X
ejpam-5446	605	2	2	2	NUM
ejpam-5446	605	3	,	,	PUNCT
ejpam-5446	605	4	3	3	NUM
ejpam-5446	605	5	]	]	PUNCT
ejpam-5446	605	6	.	.	PUNCT
ejpam-5446	606	1	the	the	DET
ejpam-5446	606	2	conditions	condition	NOUN
ejpam-5446	606	3	(	(	PUNCT
ejpam-5446	606	4	2.16	2.16	NUM
ejpam-5446	606	5	)	)	PUNCT
ejpam-5446	606	6	,	,	PUNCT
ejpam-5446	606	7	(	(	PUNCT
ejpam-5446	606	8	2.29	2.29	NUM
ejpam-5446	606	9	)	)	PUNCT
ejpam-5446	606	10	,	,	PUNCT
ejpam-5446	606	11	(	(	PUNCT
ejpam-5446	606	12	2.42	2.42	NUM
ejpam-5446	606	13	)	)	PUNCT
ejpam-5446	606	14	and	and	CCONJ
ejpam-5446	606	15	(	(	PUNCT
ejpam-5446	606	16	2.53	2.53	NUM
ejpam-5446	606	17	)	)	PUNCT
ejpam-5446	606	18	of	of	ADP
ejpam-5446	606	19	theorem	theorem	ADJ
ejpam-5446	606	20	2.4	2.4	NUM
ejpam-5446	606	21	are	be	AUX
ejpam-5446	606	22	fulfilled	fulfil	VERB
ejpam-5446	606	23	.	.	PUNCT
ejpam-5446	607	1	consequently	consequently	ADV
ejpam-5446	607	2	,	,	PUNCT
ejpam-5446	607	3	there	there	PRON
ejpam-5446	607	4	is	be	VERB
ejpam-5446	607	5	a	a	DET
ejpam-5446	607	6	capacity	capacity	NOUN
ejpam-5446	607	7	x	x	X
ejpam-5446	607	8	∈	∈	PROPN
ejpam-5446	607	9	c5[2	c5[2	PROPN
ejpam-5446	607	10	,	,	PUNCT
ejpam-5446	607	11	3	3	NUM
ejpam-5446	607	12	]	]	PUNCT
ejpam-5446	607	13	,	,	PUNCT
ejpam-5446	607	14	which	which	PRON
ejpam-5446	607	15	is	be	AUX
ejpam-5446	607	16	a	a	DET
ejpam-5446	607	17	gentle	gentle	ADJ
ejpam-5446	607	18	arrangement	arrangement	NOUN
ejpam-5446	607	19	of	of	ADP
ejpam-5446	607	20	uv(x	uv(x	PROPN
ejpam-5446	607	21	)	)	PUNCT
ejpam-5446	607	22	+	+	CCONJ
ejpam-5446	607	23	2uiv(x	2uiv(x	NUM
ejpam-5446	607	24	)	)	PUNCT
ejpam-5446	608	1	+	+	NUM
ejpam-5446	608	2	u′′′(x	u′′′(x	NOUN
ejpam-5446	608	3	)	)	PUNCT
ejpam-5446	609	1	+	+	CCONJ
ejpam-5446	609	2	u′′(x	u′′(x	X
ejpam-5446	609	3	)	)	PUNCT
ejpam-5446	610	1	+	+	CCONJ
ejpam-5446	610	2	2u′(x	2u′(x	NUM
ejpam-5446	610	3	)	)	PUNCT
ejpam-5446	611	1	+	+	CCONJ
ejpam-5446	611	2	3u(x	3u(x	NUM
ejpam-5446	611	3	)	)	PUNCT
ejpam-5446	611	4	=	=	SYM
ejpam-5446	611	5	ω(x	ω(x	X
ejpam-5446	611	6	)	)	PUNCT
ejpam-5446	611	7	that	that	PRON
ejpam-5446	611	8	is	be	AUX
ejpam-5446	611	9	satisfied	satisfied	ADJ
ejpam-5446	611	10	by	by	ADP
ejpam-5446	611	11	equation	equation	NOUN
ejpam-5446	611	12	(	(	PUNCT
ejpam-5446	611	13	3.2	3.2	NUM
ejpam-5446	611	14	)	)	PUNCT
ejpam-5446	611	15	.	.	PUNCT
ejpam-5446	612	1	example	example	NOUN
ejpam-5446	612	2	3.2	3.2	NUM
ejpam-5446	612	3	consider	consider	VERB
ejpam-5446	612	4	the	the	DET
ejpam-5446	612	5	following	follow	VERB
ejpam-5446	612	6	differential	differential	ADJ
ejpam-5446	612	7	equation	equation	NOUN
ejpam-5446	612	8	τv(x	τv(x	PUNCT
ejpam-5446	612	9	)	)	PUNCT
ejpam-5446	613	1	+	+	NUM
ejpam-5446	613	2	4τ	4τ	NOUN
ejpam-5446	613	3	iv(x	iv(x	PUNCT
ejpam-5446	613	4	)	)	PUNCT
ejpam-5446	614	1	+	+	CCONJ
ejpam-5446	614	2	τ	τ	X
ejpam-5446	614	3	′′′(x	′′′(x	PROPN
ejpam-5446	614	4	)	)	PUNCT
ejpam-5446	615	1	+	+	NUM
ejpam-5446	615	2	2τ	2τ	NUM
ejpam-5446	615	3	′′(x	′′(x	NOUN
ejpam-5446	615	4	)	)	PUNCT
ejpam-5446	616	1	+	+	CCONJ
ejpam-5446	616	2	τ	τ	PROPN
ejpam-5446	616	3	′(x	′(x	NOUN
ejpam-5446	616	4	)	)	PUNCT
ejpam-5446	617	1	+	+	NUM
ejpam-5446	617	2	0τ(x	0τ(x	NUM
ejpam-5446	617	3	)	)	PUNCT
ejpam-5446	618	1	=	=	SYM
ejpam-5446	618	2	ω(x	ω(x	X
ejpam-5446	618	3	)	)	PUNCT
ejpam-5446	618	4	;	;	PUNCT
ejpam-5446	618	5	x	x	X
ejpam-5446	618	6	∈	∈	PROPN
ejpam-5446	619	1	[	[	X
ejpam-5446	619	2	3	3	NUM
ejpam-5446	619	3	,	,	PUNCT
ejpam-5446	619	4	2	2	NUM
ejpam-5446	619	5	]	]	PUNCT
ejpam-5446	619	6	.	.	PUNCT
ejpam-5446	620	1	(	(	PUNCT
ejpam-5446	620	2	3.3	3.3	NUM
ejpam-5446	620	3	)	)	PUNCT
ejpam-5446	620	4	suppose	suppose	VERB
ejpam-5446	620	5	∈	∈	PROPN
ejpam-5446	620	6	>	>	X
ejpam-5446	620	7	0	0	NUM
ejpam-5446	621	1	and	and	CCONJ
ejpam-5446	621	2	ω	ω	NUM
ejpam-5446	621	3	∈	∈	PROPN
ejpam-5446	622	1	[	[	X
ejpam-5446	622	2	3	3	NUM
ejpam-5446	622	3	,	,	PUNCT
ejpam-5446	622	4	2	2	NUM
ejpam-5446	622	5	]	]	PUNCT
ejpam-5446	622	6	,	,	PUNCT
ejpam-5446	622	7	such	such	ADJ
ejpam-5446	622	8	that	that	SCONJ
ejpam-5446	622	9	|τv(x	|τv(x	ADP
ejpam-5446	622	10	)	)	PUNCT
ejpam-5446	622	11	+	+	NUM
ejpam-5446	622	12	4τ	4τ	NOUN
ejpam-5446	622	13	iv(x	iv(x	PUNCT
ejpam-5446	622	14	)	)	PUNCT
ejpam-5446	622	15	+	+	CCONJ
ejpam-5446	622	16	τ	τ	X
ejpam-5446	622	17	′′′(x	′′′(x	PROPN
ejpam-5446	622	18	)	)	PUNCT
ejpam-5446	622	19	+	+	NUM
ejpam-5446	622	20	2τ	2τ	NUM
ejpam-5446	622	21	′′(x	′′(x	NOUN
ejpam-5446	622	22	)	)	PUNCT
ejpam-5446	623	1	+	+	CCONJ
ejpam-5446	623	2	τ	τ	PROPN
ejpam-5446	623	3	′(x	′(x	NOUN
ejpam-5446	623	4	)	)	PUNCT
ejpam-5446	624	1	+	+	NUM
ejpam-5446	624	2	0τ(x	0τ(x	NUM
ejpam-5446	624	3	)	)	PUNCT
ejpam-5446	624	4	−	−	NOUN
ejpam-5446	624	5	ω(x	ω(x	NUM
ejpam-5446	624	6	)	)	PUNCT
ejpam-5446	624	7	|	|	ADV
ejpam-5446	624	8	≤∈	≤∈	ADV
ejpam-5446	624	9	.	.	PUNCT
ejpam-5446	625	1	x	x	X
ejpam-5446	625	2	∈	∈	PROPN
ejpam-5446	626	1	[	[	X
ejpam-5446	626	2	3	3	NUM
ejpam-5446	626	3	,	,	PUNCT
ejpam-5446	626	4	2	2	NUM
ejpam-5446	626	5	]	]	PUNCT
ejpam-5446	626	6	.	.	PUNCT
ejpam-5446	627	1	(	(	PUNCT
ejpam-5446	627	2	3.4	3.4	NUM
ejpam-5446	627	3	)	)	PUNCT
ejpam-5446	627	4	v.	v.	ADP
ejpam-5446	627	5	govindan	govindan	PROPN
ejpam-5446	627	6	et	et	PROPN
ejpam-5446	627	7	al	al	PROPN
ejpam-5446	627	8	.	.	PUNCT
ejpam-5446	627	9	/	/	SYM
ejpam-5446	627	10	eur	eur	PROPN
ejpam-5446	627	11	.	.	PUNCT
ejpam-5446	628	1	j.	j.	PROPN
ejpam-5446	628	2	pure	pure	PROPN
ejpam-5446	628	3	appl	appl	PROPN
ejpam-5446	628	4	.	.	PROPN
ejpam-5446	628	5	math	math	PROPN
ejpam-5446	628	6	,	,	PUNCT
ejpam-5446	628	7	17	17	NUM
ejpam-5446	628	8	(	(	PUNCT
ejpam-5446	628	9	4	4	NUM
ejpam-5446	628	10	)	)	PUNCT
ejpam-5446	628	11	(	(	PUNCT
ejpam-5446	628	12	2024	2024	NUM
ejpam-5446	628	13	)	)	PUNCT
ejpam-5446	628	14	,	,	PUNCT
ejpam-5446	628	15	3585	3585	NUM
ejpam-5446	628	16	-	-	SYM
ejpam-5446	628	17	3609	3609	NUM
ejpam-5446	628	18	3606	3606	NUM
ejpam-5446	628	19	figure	figure	NOUN
ejpam-5446	628	20	1	1	NUM
ejpam-5446	628	21	:	:	PUNCT
ejpam-5446	628	22	the	the	DET
ejpam-5446	628	23	solution	solution	NOUN
ejpam-5446	628	24	of	of	ADP
ejpam-5446	628	25	τ(x	τ(x	PUNCT
ejpam-5446	628	26	)	)	PUNCT
ejpam-5446	628	27	by	by	ADP
ejpam-5446	628	28	equation	equation	NOUN
ejpam-5446	628	29	(	(	PUNCT
ejpam-5446	628	30	3.2	3.2	NUM
ejpam-5446	628	31	)	)	PUNCT
ejpam-5446	628	32	we	we	PRON
ejpam-5446	628	33	take	take	VERB
ejpam-5446	628	34	g(x	g(x	NOUN
ejpam-5446	628	35	)	)	PUNCT
ejpam-5446	629	1	=	=	PUNCT
ejpam-5446	629	2	τ	τ	PROPN
ejpam-5446	629	3	iv(x	iv(x	X
ejpam-5446	629	4	)	)	PUNCT
ejpam-5446	630	1	+	+	CCONJ
ejpam-5446	630	2	5τ	5τ	NUM
ejpam-5446	630	3	′′′(x	′′′(x	PROPN
ejpam-5446	630	4	)	)	PUNCT
ejpam-5446	631	1	+	+	NUM
ejpam-5446	631	2	6τ	6τ	NUM
ejpam-5446	631	3	′′(x	′′(x	NOUN
ejpam-5446	631	4	)	)	PUNCT
ejpam-5446	632	1	+	+	CCONJ
ejpam-5446	633	1	8τ	8τ	NUM
ejpam-5446	633	2	′(x	′(x	NOUN
ejpam-5446	633	3	)	)	PUNCT
ejpam-5446	634	1	+	+	CCONJ
ejpam-5446	634	2	7τ(x	7τ(x	NUM
ejpam-5446	634	3	)	)	PUNCT
ejpam-5446	634	4	,	,	PUNCT
ejpam-5446	634	5	x	x	PUNCT
ejpam-5446	634	6	∈	∈	PROPN
ejpam-5446	635	1	[	[	X
ejpam-5446	635	2	3	3	NUM
ejpam-5446	635	3	,	,	PUNCT
ejpam-5446	635	4	2	2	NUM
ejpam-5446	635	5	]	]	PUNCT
ejpam-5446	635	6	.	.	PUNCT
ejpam-5446	636	1	then	then	ADV
ejpam-5446	636	2	,	,	PUNCT
ejpam-5446	636	3	g′(x	g′(x	X
ejpam-5446	636	4	)	)	PUNCT
ejpam-5446	636	5	=	=	NOUN
ejpam-5446	636	6	τv(x	τv(x	PUNCT
ejpam-5446	636	7	)	)	PUNCT
ejpam-5446	636	8	+	+	NUM
ejpam-5446	636	9	5τ	5τ	NOUN
ejpam-5446	636	10	iv(x	iv(x	X
ejpam-5446	636	11	)	)	PUNCT
ejpam-5446	637	1	+	+	CCONJ
ejpam-5446	637	2	6τ	6τ	NUM
ejpam-5446	637	3	′′′(x	′′′(x	PROPN
ejpam-5446	637	4	)	)	PUNCT
ejpam-5446	637	5	+	+	NUM
ejpam-5446	637	6	8τ	8τ	NUM
ejpam-5446	637	7	′′(x	′′(x	NOUN
ejpam-5446	637	8	)	)	PUNCT
ejpam-5446	638	1	+	+	NUM
ejpam-5446	638	2	7τ	7τ	NOUN
ejpam-5446	638	3	′(x	′(x	NOUN
ejpam-5446	638	4	)	)	PUNCT
ejpam-5446	639	1	+	+	CCONJ
ejpam-5446	639	2	7τ(x	7τ(x	NUM
ejpam-5446	639	3	)	)	PUNCT
ejpam-5446	639	4	,	,	PUNCT
ejpam-5446	639	5	x	x	PUNCT
ejpam-5446	639	6	∈	∈	PROPN
ejpam-5446	640	1	[	[	X
ejpam-5446	640	2	3	3	NUM
ejpam-5446	640	3	,	,	PUNCT
ejpam-5446	640	4	2	2	NUM
ejpam-5446	640	5	]	]	PUNCT
ejpam-5446	640	6	.	.	PUNCT
ejpam-5446	641	1	such	such	ADJ
ejpam-5446	641	2	that	that	PRON
ejpam-5446	641	3	,	,	PUNCT
ejpam-5446	641	4	|g′(x	|g′(x	NOUN
ejpam-5446	641	5	)	)	PUNCT
ejpam-5446	641	6	−	−	PROPN
ejpam-5446	641	7	g(x	g(x	NOUN
ejpam-5446	641	8	)	)	PUNCT
ejpam-5446	641	9	−	−	PROPN
ejpam-5446	641	10	ω(x	ω(x	NUM
ejpam-5446	641	11	)	)	PUNCT
ejpam-5446	641	12	|	|	ADV
ejpam-5446	641	13	=	=	SYM
ejpam-5446	641	14	|τv(x	|τv(x	PROPN
ejpam-5446	641	15	)	)	PUNCT
ejpam-5446	641	16	+	+	NUM
ejpam-5446	641	17	4τ	4τ	NOUN
ejpam-5446	641	18	iv(x	iv(x	PUNCT
ejpam-5446	641	19	)	)	PUNCT
ejpam-5446	642	1	+	+	CCONJ
ejpam-5446	642	2	τ	τ	X
ejpam-5446	642	3	′′′(x	′′′(x	PROPN
ejpam-5446	642	4	)	)	PUNCT
ejpam-5446	643	1	+	+	NUM
ejpam-5446	643	2	2τ	2τ	NUM
ejpam-5446	643	3	′′(x	′′(x	NOUN
ejpam-5446	643	4	)	)	PUNCT
ejpam-5446	644	1	+	+	CCONJ
ejpam-5446	644	2	τ	τ	PROPN
ejpam-5446	644	3	′(x	′(x	NOUN
ejpam-5446	644	4	)	)	PUNCT
ejpam-5446	645	1	+	+	NUM
ejpam-5446	645	2	0τ(x	0τ(x	NUM
ejpam-5446	645	3	)	)	PUNCT
ejpam-5446	645	4	−	−	NOUN
ejpam-5446	645	5	ω(x	ω(x	NUM
ejpam-5446	645	6	)	)	PUNCT
ejpam-5446	645	7	|	|	ADV
ejpam-5446	645	8	≤∈	≤∈	NOUN
ejpam-5446	645	9	,	,	PUNCT
ejpam-5446	645	10	for	for	ADP
ejpam-5446	645	11	all	all	DET
ejpam-5446	645	12	x	x	SYM
ejpam-5446	645	13	∈	∈	PROPN
ejpam-5446	646	1	[	[	X
ejpam-5446	646	2	k	k	X
ejpam-5446	646	3	,	,	PUNCT
ejpam-5446	646	4	l	l	NOUN
ejpam-5446	646	5	]	]	X
ejpam-5446	646	6	.	.	PUNCT
ejpam-5446	647	1	the	the	DET
ejpam-5446	647	2	conditions	condition	NOUN
ejpam-5446	647	3	(	(	PUNCT
ejpam-5446	647	4	2.16	2.16	NUM
ejpam-5446	647	5	)	)	PUNCT
ejpam-5446	647	6	,	,	PUNCT
ejpam-5446	647	7	(	(	PUNCT
ejpam-5446	647	8	2.29	2.29	NUM
ejpam-5446	647	9	)	)	PUNCT
ejpam-5446	647	10	,	,	PUNCT
ejpam-5446	647	11	(	(	PUNCT
ejpam-5446	647	12	2.42	2.42	NUM
ejpam-5446	647	13	)	)	PUNCT
ejpam-5446	647	14	and	and	CCONJ
ejpam-5446	647	15	(	(	PUNCT
ejpam-5446	647	16	2.53	2.53	NUM
ejpam-5446	647	17	)	)	PUNCT
ejpam-5446	647	18	of	of	ADP
ejpam-5446	647	19	theorem	theorem	ADJ
ejpam-5446	647	20	2.4	2.4	NUM
ejpam-5446	647	21	are	be	AUX
ejpam-5446	647	22	fulfilled	fulfil	VERB
ejpam-5446	647	23	.	.	PUNCT
ejpam-5446	648	1	consequently	consequently	ADV
ejpam-5446	648	2	,	,	PUNCT
ejpam-5446	648	3	there	there	PRON
ejpam-5446	648	4	is	be	VERB
ejpam-5446	648	5	a	a	DET
ejpam-5446	648	6	capacity	capacity	NOUN
ejpam-5446	648	7	x	x	X
ejpam-5446	648	8	∈	∈	PROPN
ejpam-5446	648	9	c5[2	c5[2	PROPN
ejpam-5446	648	10	,	,	PUNCT
ejpam-5446	648	11	3	3	NUM
ejpam-5446	648	12	]	]	PUNCT
ejpam-5446	648	13	,	,	PUNCT
ejpam-5446	648	14	which	which	PRON
ejpam-5446	648	15	is	be	AUX
ejpam-5446	648	16	a	a	DET
ejpam-5446	648	17	gentle	gentle	ADJ
ejpam-5446	648	18	arrangement	arrangement	NOUN
ejpam-5446	648	19	of	of	ADP
ejpam-5446	648	20	uiv(x	uiv(x	PROPN
ejpam-5446	648	21	)	)	PUNCT
ejpam-5446	649	1	+	+	NUM
ejpam-5446	649	2	u′′′(x	u′′′(x	NOUN
ejpam-5446	649	3	)	)	PUNCT
ejpam-5446	650	1	+	+	CCONJ
ejpam-5446	650	2	u′′(x	u′′(x	X
ejpam-5446	650	3	)	)	PUNCT
ejpam-5446	650	4	=	=	SYM
ejpam-5446	650	5	ψ(x	ψ(x	NOUN
ejpam-5446	650	6	)	)	PUNCT
ejpam-5446	650	7	that	that	PRON
ejpam-5446	650	8	is	be	AUX
ejpam-5446	650	9	satisfied	satisfied	ADJ
ejpam-5446	650	10	by	by	ADP
ejpam-5446	650	11	equation	equation	NOUN
ejpam-5446	650	12	(	(	PUNCT
ejpam-5446	650	13	3.4	3.4	NUM
ejpam-5446	650	14	)	)	PUNCT
ejpam-5446	650	15	.	.	PUNCT
ejpam-5446	651	1	4	4	X
ejpam-5446	651	2	.	.	X
ejpam-5446	651	3	conclusions	conclusion	NOUN
ejpam-5446	651	4	we	we	PRON
ejpam-5446	651	5	have	have	AUX
ejpam-5446	651	6	researched	research	VERB
ejpam-5446	651	7	the	the	DET
ejpam-5446	651	8	hyers	hyers	PROPN
ejpam-5446	651	9	-	-	PUNCT
ejpam-5446	651	10	ulam	ulam	ADJ
ejpam-5446	651	11	stability	stability	NOUN
ejpam-5446	651	12	as	as	ADP
ejpam-5446	651	13	for	for	ADP
ejpam-5446	651	14	the	the	DET
ejpam-5446	651	15	linear	linear	ADJ
ejpam-5446	651	16	differential	differential	ADJ
ejpam-5446	651	17	equation	equation	NOUN
ejpam-5446	651	18	of	of	ADP
ejpam-5446	651	19	fifth	fifth	ADJ
ejpam-5446	651	20	-	-	PUNCT
ejpam-5446	651	21	order	order	NOUN
ejpam-5446	651	22	in	in	ADP
ejpam-5446	651	23	this	this	DET
ejpam-5446	651	24	investigation	investigation	NOUN
ejpam-5446	651	25	.	.	PUNCT
ejpam-5446	652	1	the	the	DET
ejpam-5446	652	2	adequacy	adequacy	NOUN
ejpam-5446	652	3	of	of	ADP
ejpam-5446	652	4	the	the	DET
ejpam-5446	652	5	proposed	propose	VERB
ejpam-5446	652	6	technique	technique	NOUN
ejpam-5446	652	7	has	have	AUX
ejpam-5446	652	8	been	be	AUX
ejpam-5446	652	9	shown	show	VERB
ejpam-5446	652	10	in	in	ADP
ejpam-5446	652	11	the	the	DET
ejpam-5446	652	12	numerical	numerical	ADJ
ejpam-5446	652	13	examples	example	NOUN
ejpam-5446	652	14	.	.	PUNCT
ejpam-5446	653	1	in	in	ADP
ejpam-5446	653	2	future	future	ADJ
ejpam-5446	653	3	work	work	NOUN
ejpam-5446	653	4	,	,	PUNCT
ejpam-5446	653	5	the	the	DET
ejpam-5446	653	6	proposed	propose	VERB
ejpam-5446	653	7	scheme	scheme	NOUN
ejpam-5446	653	8	will	will	AUX
ejpam-5446	653	9	be	be	AUX
ejpam-5446	653	10	taken	take	VERB
ejpam-5446	653	11	into	into	ADP
ejpam-5446	653	12	account	account	NOUN
ejpam-5446	653	13	for	for	ADP
ejpam-5446	653	14	time	time	NOUN
ejpam-5446	653	15	delay	delay	NOUN
ejpam-5446	653	16	with	with	ADP
ejpam-5446	653	17	disturbances	disturbance	NOUN
ejpam-5446	653	18	.	.	PUNCT
ejpam-5446	654	1	references	reference	NOUN
ejpam-5446	654	2	3607	3607	NUM
ejpam-5446	654	3	figure	figure	NOUN
ejpam-5446	654	4	2	2	NUM
ejpam-5446	654	5	:	:	PUNCT
ejpam-5446	654	6	the	the	DET
ejpam-5446	654	7	solution	solution	NOUN
ejpam-5446	654	8	of	of	ADP
ejpam-5446	654	9	τ(x	τ(x	PUNCT
ejpam-5446	654	10	)	)	PUNCT
ejpam-5446	654	11	by	by	ADP
ejpam-5446	654	12	equation	equation	NOUN
ejpam-5446	654	13	(	(	PUNCT
ejpam-5446	654	14	3.4	3.4	NUM
ejpam-5446	654	15	)	)	PUNCT
ejpam-5446	654	16	acknowledgements	acknowledgement	NOUN
ejpam-5446	654	17	we	we	PRON
ejpam-5446	654	18	are	be	AUX
ejpam-5446	654	19	thankful	thankful	ADJ
ejpam-5446	654	20	to	to	ADP
ejpam-5446	654	21	the	the	DET
ejpam-5446	654	22	editors	editor	NOUN
ejpam-5446	654	23	and	and	CCONJ
ejpam-5446	654	24	the	the	DET
ejpam-5446	654	25	anonymous	anonymous	ADJ
ejpam-5446	654	26	reviewers	reviewer	NOUN
ejpam-5446	654	27	for	for	ADP
ejpam-5446	654	28	many	many	ADJ
ejpam-5446	654	29	valuable	valuable	ADJ
ejpam-5446	654	30	suggestions	suggestion	NOUN
ejpam-5446	654	31	to	to	PART
ejpam-5446	654	32	improve	improve	VERB
ejpam-5446	654	33	this	this	DET
ejpam-5446	654	34	paper	paper	NOUN
ejpam-5446	654	35	.	.	PUNCT
ejpam-5446	655	1	funding	fund	VERB
ejpam-5446	655	2	this	this	DET
ejpam-5446	655	3	research	research	NOUN
ejpam-5446	655	4	supported	support	VERB
ejpam-5446	655	5	by	by	ADP
ejpam-5446	655	6	basic	basic	ADJ
ejpam-5446	655	7	science	science	NOUN
ejpam-5446	655	8	research	research	NOUN
ejpam-5446	655	9	program	program	NOUN
ejpam-5446	655	10	through	through	ADP
ejpam-5446	655	11	the	the	DET
ejpam-5446	655	12	national	national	PROPN
ejpam-5446	655	13	research	research	PROPN
ejpam-5446	655	14	foundation	foundation	PROPN
ejpam-5446	655	15	of	of	ADP
ejpam-5446	655	16	korea	korea	PROPN
ejpam-5446	655	17	(	(	PUNCT
ejpam-5446	655	18	nrf	nrf	NOUN
ejpam-5446	655	19	)	)	PUNCT
ejpam-5446	655	20	funded	fund	VERB
ejpam-5446	655	21	by	by	ADP
ejpam-5446	655	22	the	the	DET
ejpam-5446	655	23	ministry	ministry	PROPN
ejpam-5446	655	24	of	of	ADP
ejpam-5446	655	25	education	education	PROPN
ejpam-5446	655	26	(	(	PUNCT
ejpam-5446	655	27	nrfrs-202300237287	nrfrs-202300237287	ADJ
ejpam-5446	655	28	,	,	PUNCT
ejpam-5446	655	29	nrf-2021s1a5a8062526	nrf-2021s1a5a8062526	PROPN
ejpam-5446	655	30	)	)	PUNCT
ejpam-5446	655	31	and	and	CCONJ
ejpam-5446	655	32	local	local	ADJ
ejpam-5446	655	33	government	government	NOUN
ejpam-5446	655	34	-	-	PUNCT
ejpam-5446	655	35	university	university	NOUN
ejpam-5446	655	36	cooperation	cooperation	NOUN
ejpam-5446	655	37	-	-	PUNCT
ejpam-5446	655	38	based	base	VERB
ejpam-5446	655	39	regional	regional	ADJ
ejpam-5446	655	40	innovation	innovation	NOUN
ejpam-5446	655	41	projects	project	NOUN
ejpam-5446	655	42	(	(	PUNCT
ejpam-5446	655	43	2021ris-003	2021ris-003	NOUN
ejpam-5446	655	44	)	)	PUNCT
ejpam-5446	655	45	.	.	PUNCT
ejpam-5446	656	1	declaration	declaration	NOUN
ejpam-5446	656	2	of	of	ADP
ejpam-5446	656	3	competing	compete	VERB
ejpam-5446	656	4	interest	interest	NOUN
ejpam-5446	656	5	:	:	PUNCT
ejpam-5446	656	6	the	the	DET
ejpam-5446	656	7	author	author	NOUN
ejpam-5446	656	8	declares	declare	VERB
ejpam-5446	656	9	that	that	SCONJ
ejpam-5446	656	10	they	they	PRON
ejpam-5446	656	11	have	have	VERB
ejpam-5446	656	12	no	no	DET
ejpam-5446	656	13	known	know	VERB
ejpam-5446	656	14	competing	compete	VERB
ejpam-5446	656	15	financial	financial	ADJ
ejpam-5446	656	16	interests	interest	NOUN
ejpam-5446	656	17	or	or	CCONJ
ejpam-5446	656	18	personal	personal	ADJ
ejpam-5446	656	19	relationships	relationship	NOUN
ejpam-5446	656	20	that	that	PRON
ejpam-5446	656	21	could	could	AUX
ejpam-5446	656	22	have	have	AUX
ejpam-5446	656	23	appeared	appear	VERB
ejpam-5446	656	24	to	to	PART
ejpam-5446	656	25	influence	influence	VERB
ejpam-5446	656	26	the	the	DET
ejpam-5446	656	27	work	work	NOUN
ejpam-5446	656	28	reported	report	VERB
ejpam-5446	656	29	in	in	ADP
ejpam-5446	656	30	this	this	DET
ejpam-5446	656	31	paper	paper	NOUN
ejpam-5446	656	32	.	.	PUNCT
ejpam-5446	657	1	author	author	NOUN
ejpam-5446	657	2	’s	’s	PART
ejpam-5446	657	3	contribution	contribution	NOUN
ejpam-5446	657	4	:	:	PUNCT
ejpam-5446	657	5	all	all	DET
ejpam-5446	657	6	authors	author	NOUN
ejpam-5446	657	7	contributed	contribute	VERB
ejpam-5446	657	8	equally	equally	ADV
ejpam-5446	657	9	to	to	ADP
ejpam-5446	657	10	the	the	DET
ejpam-5446	657	11	manuscript	manuscript	NOUN
ejpam-5446	657	12	and	and	CCONJ
ejpam-5446	657	13	typed	type	VERB
ejpam-5446	657	14	,	,	PUNCT
ejpam-5446	657	15	read	read	VERB
ejpam-5446	657	16	,	,	PUNCT
ejpam-5446	657	17	and	and	CCONJ
ejpam-5446	657	18	approved	approve	VERB
ejpam-5446	657	19	the	the	DET
ejpam-5446	657	20	final	final	ADJ
ejpam-5446	657	21	manuscript	manuscript	NOUN
ejpam-5446	657	22	.	.	PUNCT
ejpam-5446	658	1	references	reference	NOUN
ejpam-5446	658	2	[	[	X
ejpam-5446	658	3	1	1	NUM
ejpam-5446	658	4	]	]	PUNCT
ejpam-5446	658	5	claudi	claudi	PROPN
ejpam-5446	658	6	alsina	alsina	NOUN
ejpam-5446	658	7	and	and	CCONJ
ejpam-5446	658	8	roman	roman	PROPN
ejpam-5446	658	9	ger	ger	NOUN
ejpam-5446	658	10	.	.	PUNCT
ejpam-5446	659	1	on	on	ADP
ejpam-5446	659	2	some	some	DET
ejpam-5446	659	3	inequalities	inequality	NOUN
ejpam-5446	659	4	and	and	CCONJ
ejpam-5446	659	5	stability	stability	NOUN
ejpam-5446	659	6	results	result	NOUN
ejpam-5446	659	7	related	relate	VERB
ejpam-5446	659	8	to	to	ADP
ejpam-5446	659	9	the	the	DET
ejpam-5446	659	10	exponential	exponential	ADJ
ejpam-5446	659	11	function	function	NOUN
ejpam-5446	659	12	.	.	PUNCT
ejpam-5446	660	1	journal	journal	PROPN
ejpam-5446	660	2	of	of	ADP
ejpam-5446	660	3	inequalities	inequality	NOUN
ejpam-5446	660	4	and	and	CCONJ
ejpam-5446	660	5	applications	application	NOUN
ejpam-5446	660	6	,	,	PUNCT
ejpam-5446	660	7	1998(4):246904	1998(4):246904	NUM
ejpam-5446	660	8	,	,	PUNCT
ejpam-5446	660	9	1998	1998	NUM
ejpam-5446	660	10	.	.	PUNCT
ejpam-5446	661	1	references	reference	NOUN
ejpam-5446	661	2	3608	3608	NUM
ejpam-5446	661	3	[	[	X
ejpam-5446	661	4	2	2	NUM
ejpam-5446	661	5	]	]	PUNCT
ejpam-5446	661	6	hisashi	hisashi	PROPN
ejpam-5446	661	7	choda	choda	PROPN
ejpam-5446	661	8	,	,	PUNCT
ejpam-5446	661	9	takeshi	takeshi	NOUN
ejpam-5446	661	10	miura	miura	PROPN
ejpam-5446	661	11	,	,	PUNCT
ejpam-5446	661	12	and	and	CCONJ
ejpam-5446	661	13	sin	sin	NOUN
ejpam-5446	661	14	-	-	PUNCT
ejpam-5446	661	15	ei	ei	NOUN
ejpam-5446	661	16	takahasi	takahasi	NOUN
ejpam-5446	661	17	.	.	PUNCT
ejpam-5446	662	1	on	on	ADP
ejpam-5446	662	2	the	the	DET
ejpam-5446	662	3	hyers	hyers	PROPN
ejpam-5446	662	4	-	-	PUNCT
ejpam-5446	662	5	ulam	ulam	ADJ
ejpam-5446	662	6	stability	stability	NOUN
ejpam-5446	662	7	of	of	ADP
ejpam-5446	662	8	real	real	ADJ
ejpam-5446	662	9	continuous	continuous	ADJ
ejpam-5446	662	10	function	function	NOUN
ejpam-5446	662	11	valued	value	VERB
ejpam-5446	662	12	differentiable	differentiable	NOUN
ejpam-5446	662	13	map	map	NOUN
ejpam-5446	662	14	.	.	PUNCT
ejpam-5446	663	1	tokyo	tokyo	PROPN
ejpam-5446	663	2	journal	journal	NOUN
ejpam-5446	663	3	of	of	ADP
ejpam-5446	663	4	mathematics	mathematic	NOUN
ejpam-5446	663	5	,	,	PUNCT
ejpam-5446	663	6	24(2):467–476	24(2):467–476	PRON
ejpam-5446	663	7	,	,	PUNCT
ejpam-5446	663	8	2001	2001	NUM
ejpam-5446	663	9	.	.	PUNCT
ejpam-5446	664	1	[	[	X
ejpam-5446	664	2	3	3	X
ejpam-5446	664	3	]	]	X
ejpam-5446	664	4	vediyappan	vediyappan	ADJ
ejpam-5446	664	5	govindan	govindan	PROPN
ejpam-5446	664	6	,	,	PUNCT
ejpam-5446	664	7	porpattama	porpattama	NOUN
ejpam-5446	664	8	hammachukiattikul	hammachukiattikul	NOUN
ejpam-5446	664	9	,	,	PUNCT
ejpam-5446	664	10	grienggrai	grienggrai	ADJ
ejpam-5446	664	11	rajchakit	rajchakit	NOUN
ejpam-5446	664	12	,	,	PUNCT
ejpam-5446	664	13	nallappan	nallappan	ADJ
ejpam-5446	664	14	gunasekaran	gunasekaran	NOUN
ejpam-5446	664	15	,	,	PUNCT
ejpam-5446	664	16	and	and	CCONJ
ejpam-5446	664	17	r	r	NOUN
ejpam-5446	664	18	vadivel	vadivel	NOUN
ejpam-5446	664	19	.	.	PUNCT
ejpam-5446	665	1	a	a	DET
ejpam-5446	665	2	new	new	ADJ
ejpam-5446	665	3	approach	approach	NOUN
ejpam-5446	665	4	to	to	ADP
ejpam-5446	665	5	hyers	hyers	PROPN
ejpam-5446	665	6	-	-	PUNCT
ejpam-5446	665	7	ulam	ulam	PROPN
ejpam-5446	665	8	stability	stability	NOUN
ejpam-5446	665	9	of	of	ADP
ejpam-5446	665	10	rvariable	rvariable	ADJ
ejpam-5446	665	11	quadratic	quadratic	ADJ
ejpam-5446	665	12	functional	functional	ADJ
ejpam-5446	665	13	equations	equation	NOUN
ejpam-5446	665	14	.	.	PUNCT
ejpam-5446	666	1	journal	journal	NOUN
ejpam-5446	666	2	of	of	ADP
ejpam-5446	666	3	function	function	NOUN
ejpam-5446	666	4	spaces	space	NOUN
ejpam-5446	666	5	,	,	PUNCT
ejpam-5446	666	6	2021(1):6628733	2021(1):6628733	NUM
ejpam-5446	666	7	,	,	PUNCT
ejpam-5446	666	8	2021	2021	NUM
ejpam-5446	666	9	.	.	PUNCT
ejpam-5446	667	1	[	[	X
ejpam-5446	667	2	4	4	X
ejpam-5446	667	3	]	]	X
ejpam-5446	667	4	vediyappan	vediyappan	ADJ
ejpam-5446	667	5	govindan	govindan	PROPN
ejpam-5446	667	6	,	,	PUNCT
ejpam-5446	667	7	inho	inho	PROPN
ejpam-5446	667	8	hwang	hwang	PROPN
ejpam-5446	667	9	,	,	PUNCT
ejpam-5446	667	10	and	and	CCONJ
ejpam-5446	667	11	choonkil	choonkil	PROPN
ejpam-5446	667	12	park	park	NOUN
ejpam-5446	667	13	.	.	PUNCT
ejpam-5446	668	1	hyers	hyer	NOUN
ejpam-5446	668	2	-	-	PUNCT
ejpam-5446	668	3	ulam	ulam	PROPN
ejpam-5446	668	4	stability	stability	NOUN
ejpam-5446	668	5	of	of	ADP
ejpam-5446	668	6	an	an	DET
ejpam-5446	668	7	n	n	CCONJ
ejpam-5446	668	8	-	-	PUNCT
ejpam-5446	668	9	variable	variable	ADJ
ejpam-5446	668	10	quartic	quartic	ADJ
ejpam-5446	668	11	functional	functional	ADJ
ejpam-5446	668	12	equation	equation	NOUN
ejpam-5446	668	13	.	.	PUNCT
ejpam-5446	669	1	aims	aim	VERB
ejpam-5446	669	2	mathematics	mathematic	NOUN
ejpam-5446	669	3	,	,	PUNCT
ejpam-5446	669	4	6(2	6(2	NUM
ejpam-5446	669	5	)	)	PUNCT
ejpam-5446	669	6	,	,	PUNCT
ejpam-5446	669	7	2021	2021	NUM
ejpam-5446	669	8	.	.	PUNCT
ejpam-5446	670	1	[	[	X
ejpam-5446	670	2	5	5	X
ejpam-5446	670	3	]	]	X
ejpam-5446	670	4	vediyappan	vediyappan	ADJ
ejpam-5446	670	5	govindan	govindan	PROPN
ejpam-5446	670	6	,	,	PUNCT
ejpam-5446	670	7	choonkil	choonkil	PROPN
ejpam-5446	670	8	park	park	PROPN
ejpam-5446	670	9	,	,	PUNCT
ejpam-5446	670	10	sandra	sandra	PROPN
ejpam-5446	670	11	pinelas	pinela	NOUN
ejpam-5446	670	12	,	,	PUNCT
ejpam-5446	670	13	and	and	CCONJ
ejpam-5446	670	14	s	s	VERB
ejpam-5446	670	15	baskaran	baskaran	ADJ
ejpam-5446	670	16	.	.	PUNCT
ejpam-5446	671	1	solution	solution	NOUN
ejpam-5446	671	2	of	of	ADP
ejpam-5446	671	3	a	a	DET
ejpam-5446	671	4	3	3	NUM
ejpam-5446	671	5	-	-	PUNCT
ejpam-5446	671	6	d	d	NOUN
ejpam-5446	671	7	cubic	cubic	ADJ
ejpam-5446	671	8	functional	functional	ADJ
ejpam-5446	671	9	equation	equation	NOUN
ejpam-5446	671	10	and	and	CCONJ
ejpam-5446	671	11	its	its	PRON
ejpam-5446	671	12	stability	stability	NOUN
ejpam-5446	671	13	.	.	PUNCT
ejpam-5446	672	1	aims	aim	VERB
ejpam-5446	672	2	mathematics	mathematic	NOUN
ejpam-5446	672	3	,	,	PUNCT
ejpam-5446	672	4	5(3):1693–1705	5(3):1693–1705	PROPN
ejpam-5446	672	5	,	,	PUNCT
ejpam-5446	672	6	2020	2020	NUM
ejpam-5446	672	7	.	.	PUNCT
ejpam-5446	673	1	[	[	X
ejpam-5446	673	2	6	6	NUM
ejpam-5446	673	3	]	]	X
ejpam-5446	673	4	donald	donald	PROPN
ejpam-5446	673	5	h	h	PROPN
ejpam-5446	673	6	hyers	hyers	PROPN
ejpam-5446	673	7	.	.	PUNCT
ejpam-5446	674	1	on	on	ADP
ejpam-5446	674	2	the	the	DET
ejpam-5446	674	3	stability	stability	NOUN
ejpam-5446	674	4	of	of	ADP
ejpam-5446	674	5	the	the	DET
ejpam-5446	674	6	linear	linear	ADJ
ejpam-5446	674	7	functional	functional	ADJ
ejpam-5446	674	8	equation	equation	NOUN
ejpam-5446	674	9	.	.	PUNCT
ejpam-5446	675	1	proceedings	proceeding	NOUN
ejpam-5446	675	2	of	of	ADP
ejpam-5446	675	3	the	the	DET
ejpam-5446	675	4	national	national	PROPN
ejpam-5446	675	5	academy	academy	PROPN
ejpam-5446	675	6	of	of	ADP
ejpam-5446	675	7	sciences	sciences	PROPN
ejpam-5446	675	8	,	,	PUNCT
ejpam-5446	675	9	27(4):222–224	27(4):222–224	NUM
ejpam-5446	675	10	,	,	PUNCT
ejpam-5446	675	11	1941	1941	NUM
ejpam-5446	675	12	.	.	PUNCT
ejpam-5446	676	1	[	[	X
ejpam-5446	676	2	7	7	NUM
ejpam-5446	676	3	]	]	SYM
ejpam-5446	676	4	s.-m	s.-m	PROPN
ejpam-5446	676	5	.	.	PUNCT
ejpam-5446	676	6	jung	jung	PROPN
ejpam-5446	676	7	.	.	PUNCT
ejpam-5446	677	1	hyers	hyer	NOUN
ejpam-5446	677	2	–	–	PUNCT
ejpam-5446	677	3	ulam	ulam	PROPN
ejpam-5446	677	4	stability	stability	NOUN
ejpam-5446	677	5	of	of	ADP
ejpam-5446	677	6	linear	linear	PROPN
ejpam-5446	677	7	differential	differential	ADJ
ejpam-5446	677	8	equations	equation	NOUN
ejpam-5446	677	9	of	of	ADP
ejpam-5446	677	10	first	first	ADJ
ejpam-5446	677	11	order	order	NOUN
ejpam-5446	677	12	,	,	PUNCT
ejpam-5446	677	13	ii	ii	PROPN
ejpam-5446	677	14	.	.	PROPN
ejpam-5446	677	15	applied	apply	VERB
ejpam-5446	677	16	mathematics	mathematics	NOUN
ejpam-5446	677	17	letters	letter	NOUN
ejpam-5446	677	18	,	,	PUNCT
ejpam-5446	677	19	19(9):854–858	19(9):854–858	NUM
ejpam-5446	677	20	,	,	PUNCT
ejpam-5446	677	21	2006	2006	NUM
ejpam-5446	677	22	.	.	PUNCT
ejpam-5446	678	1	[	[	X
ejpam-5446	678	2	8	8	NUM
ejpam-5446	678	3	]	]	PUNCT
ejpam-5446	678	4	soon	soon	ADV
ejpam-5446	678	5	-	-	PUNCT
ejpam-5446	678	6	mo	mo	PROPN
ejpam-5446	678	7	jung	jung	PROPN
ejpam-5446	678	8	.	.	PUNCT
ejpam-5446	679	1	hyers	hyer	NOUN
ejpam-5446	679	2	–	–	PUNCT
ejpam-5446	679	3	ulam	ulam	PROPN
ejpam-5446	679	4	stability	stability	NOUN
ejpam-5446	679	5	of	of	ADP
ejpam-5446	679	6	linear	linear	PROPN
ejpam-5446	679	7	differential	differential	ADJ
ejpam-5446	679	8	equations	equation	NOUN
ejpam-5446	679	9	of	of	ADP
ejpam-5446	679	10	first	first	ADJ
ejpam-5446	679	11	order	order	NOUN
ejpam-5446	679	12	,	,	PUNCT
ejpam-5446	679	13	iii	iii	PROPN
ejpam-5446	679	14	.	.	PROPN
ejpam-5446	679	15	journal	journal	PROPN
ejpam-5446	679	16	of	of	ADP
ejpam-5446	679	17	mathematical	mathematical	ADJ
ejpam-5446	679	18	analysis	analysis	NOUN
ejpam-5446	679	19	and	and	CCONJ
ejpam-5446	679	20	applications	application	NOUN
ejpam-5446	679	21	,	,	PUNCT
ejpam-5446	679	22	311(1):139–146	311(1):139–146	NUM
ejpam-5446	679	23	,	,	PUNCT
ejpam-5446	679	24	2005	2005	NUM
ejpam-5446	679	25	.	.	PUNCT
ejpam-5446	680	1	[	[	X
ejpam-5446	680	2	9	9	NUM
ejpam-5446	680	3	]	]	PUNCT
ejpam-5446	680	4	soon	soon	ADV
ejpam-5446	680	5	-	-	PUNCT
ejpam-5446	680	6	mo	mo	PROPN
ejpam-5446	680	7	jung	jung	PROPN
ejpam-5446	680	8	.	.	PUNCT
ejpam-5446	681	1	hyers	hyer	NOUN
ejpam-5446	681	2	–	–	PUNCT
ejpam-5446	681	3	ulam	ulam	X
ejpam-5446	681	4	stability	stability	NOUN
ejpam-5446	681	5	of	of	ADP
ejpam-5446	681	6	a	a	DET
ejpam-5446	681	7	system	system	NOUN
ejpam-5446	681	8	of	of	ADP
ejpam-5446	681	9	first	first	ADJ
ejpam-5446	681	10	order	order	NOUN
ejpam-5446	681	11	linear	linear	PROPN
ejpam-5446	681	12	differential	differential	NOUN
ejpam-5446	681	13	equations	equation	NOUN
ejpam-5446	681	14	with	with	ADP
ejpam-5446	681	15	constant	constant	ADJ
ejpam-5446	681	16	coefficients	coefficient	NOUN
ejpam-5446	681	17	.	.	PUNCT
ejpam-5446	682	1	journal	journal	NOUN
ejpam-5446	682	2	of	of	ADP
ejpam-5446	682	3	mathematical	mathematical	ADJ
ejpam-5446	682	4	analysis	analysis	NOUN
ejpam-5446	682	5	and	and	CCONJ
ejpam-5446	682	6	applications	application	NOUN
ejpam-5446	682	7	,	,	PUNCT
ejpam-5446	682	8	320(2):549–561	320(2):549–561	NUM
ejpam-5446	682	9	,	,	PUNCT
ejpam-5446	682	10	2006	2006	NUM
ejpam-5446	682	11	.	.	PUNCT
ejpam-5446	683	1	[	[	X
ejpam-5446	683	2	10	10	NUM
ejpam-5446	683	3	]	]	X
ejpam-5446	683	4	soon	soon	ADV
ejpam-5446	683	5	-	-	PUNCT
ejpam-5446	683	6	mo	mo	NOUN
ejpam-5446	683	7	jung	jung	NOUN
ejpam-5446	683	8	and	and	CCONJ
ejpam-5446	683	9	themistocles	themistocle	NOUN
ejpam-5446	683	10	m	m	NOUN
ejpam-5446	683	11	rassias	rassias	PROPN
ejpam-5446	683	12	.	.	PUNCT
ejpam-5446	684	1	generalized	generalize	VERB
ejpam-5446	684	2	hyers	hyers	PROPN
ejpam-5446	684	3	-	-	PUNCT
ejpam-5446	684	4	ulam	ulam	PROPN
ejpam-5446	684	5	stability	stability	NOUN
ejpam-5446	684	6	of	of	ADP
ejpam-5446	684	7	riccati	riccati	PROPN
ejpam-5446	684	8	differential	differential	PROPN
ejpam-5446	684	9	equation	equation	NOUN
ejpam-5446	684	10	.	.	PUNCT
ejpam-5446	685	1	2008	2008	NUM
ejpam-5446	685	2	.	.	PUNCT
ejpam-5446	686	1	[	[	X
ejpam-5446	686	2	11	11	NUM
ejpam-5446	686	3	]	]	X
ejpam-5446	686	4	yongjin	yongjin	PROPN
ejpam-5446	686	5	li	li	PROPN
ejpam-5446	686	6	and	and	CCONJ
ejpam-5446	686	7	yan	yan	PROPN
ejpam-5446	686	8	shen	shen	PROPN
ejpam-5446	686	9	.	.	PUNCT
ejpam-5446	687	1	hyers	hyers	PROPN
ejpam-5446	687	2	-	-	PUNCT
ejpam-5446	687	3	ulam	ulam	PROPN
ejpam-5446	687	4	stability	stability	NOUN
ejpam-5446	687	5	of	of	ADP
ejpam-5446	687	6	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5446	687	7	linear	linear	PROPN
ejpam-5446	687	8	differential	differential	NOUN
ejpam-5446	687	9	equations	equation	NOUN
ejpam-5446	687	10	of	of	ADP
ejpam-5446	687	11	second	second	ADJ
ejpam-5446	687	12	order	order	NOUN
ejpam-5446	687	13	.	.	PUNCT
ejpam-5446	688	1	international	international	ADJ
ejpam-5446	688	2	journal	journal	PROPN
ejpam-5446	688	3	of	of	ADP
ejpam-5446	688	4	mathematics	mathematics	PROPN
ejpam-5446	688	5	&	&	CCONJ
ejpam-5446	688	6	mathematical	mathematical	PROPN
ejpam-5446	688	7	sciences	sciences	PROPN
ejpam-5446	688	8	,	,	PUNCT
ejpam-5446	688	9	2009	2009	NUM
ejpam-5446	688	10	.	.	PUNCT
ejpam-5446	689	1	[	[	X
ejpam-5446	689	2	12	12	NUM
ejpam-5446	689	3	]	]	X
ejpam-5446	689	4	yongjin	yongjin	PROPN
ejpam-5446	689	5	li	li	PROPN
ejpam-5446	689	6	and	and	CCONJ
ejpam-5446	689	7	yan	yan	PROPN
ejpam-5446	689	8	shen	shen	PROPN
ejpam-5446	689	9	.	.	PUNCT
ejpam-5446	690	1	hyers	hyer	NOUN
ejpam-5446	690	2	–	–	PUNCT
ejpam-5446	690	3	ulam	ulam	PROPN
ejpam-5446	690	4	stability	stability	NOUN
ejpam-5446	690	5	of	of	ADP
ejpam-5446	690	6	linear	linear	PROPN
ejpam-5446	690	7	differential	differential	ADJ
ejpam-5446	690	8	equations	equation	NOUN
ejpam-5446	690	9	of	of	ADP
ejpam-5446	690	10	second	second	ADJ
ejpam-5446	690	11	order	order	NOUN
ejpam-5446	690	12	.	.	PUNCT
ejpam-5446	691	1	applied	apply	VERB
ejpam-5446	691	2	mathematics	mathematics	NOUN
ejpam-5446	691	3	letters	letter	NOUN
ejpam-5446	691	4	,	,	PUNCT
ejpam-5446	691	5	23(3):306–309	23(3):306–309	PROPN
ejpam-5446	691	6	,	,	PUNCT
ejpam-5446	691	7	2010	2010	NUM
ejpam-5446	691	8	.	.	PUNCT
ejpam-5446	692	1	[	[	X
ejpam-5446	692	2	13	13	NUM
ejpam-5446	692	3	]	]	X
ejpam-5446	692	4	danfeng	danfeng	PROPN
ejpam-5446	692	5	luo	luo	PROPN
ejpam-5446	692	6	,	,	PUNCT
ejpam-5446	692	7	thabet	thabet	ADJ
ejpam-5446	692	8	abdeljawad	abdeljawad	NOUN
ejpam-5446	692	9	,	,	PUNCT
ejpam-5446	692	10	and	and	CCONJ
ejpam-5446	692	11	zhiguo	zhiguo	PROPN
ejpam-5446	692	12	luo	luo	PROPN
ejpam-5446	692	13	.	.	PUNCT
ejpam-5446	692	14	ulam	ulam	NOUN
ejpam-5446	692	15	-	-	PUNCT
ejpam-5446	692	16	hyers	hyer	NOUN
ejpam-5446	692	17	stability	stability	NOUN
ejpam-5446	692	18	results	result	VERB
ejpam-5446	692	19	for	for	ADP
ejpam-5446	692	20	a	a	DET
ejpam-5446	692	21	novel	novel	ADJ
ejpam-5446	692	22	nonlinear	nonlinear	ADJ
ejpam-5446	692	23	nabla	nabla	PROPN
ejpam-5446	692	24	caputo	caputo	PROPN
ejpam-5446	692	25	fractional	fractional	ADJ
ejpam-5446	692	26	variable	variable	ADJ
ejpam-5446	692	27	-	-	PUNCT
ejpam-5446	692	28	order	order	NOUN
ejpam-5446	692	29	difference	difference	NOUN
ejpam-5446	692	30	system	system	NOUN
ejpam-5446	692	31	.	.	PUNCT
ejpam-5446	693	1	turkish	turkish	ADJ
ejpam-5446	693	2	journal	journal	NOUN
ejpam-5446	693	3	of	of	ADP
ejpam-5446	693	4	mathematics	mathematic	NOUN
ejpam-5446	693	5	,	,	PUNCT
ejpam-5446	693	6	45(1):456–470	45(1):456–470	PROPN
ejpam-5446	693	7	,	,	PUNCT
ejpam-5446	693	8	2021	2021	NUM
ejpam-5446	693	9	.	.	PUNCT
ejpam-5446	694	1	[	[	X
ejpam-5446	694	2	14	14	NUM
ejpam-5446	694	3	]	]	X
ejpam-5446	694	4	danfeng	danfeng	PROPN
ejpam-5446	694	5	luo	luo	PROPN
ejpam-5446	694	6	and	and	CCONJ
ejpam-5446	694	7	zhiguo	zhiguo	PROPN
ejpam-5446	694	8	luo	luo	PROPN
ejpam-5446	694	9	.	.	PROPN
ejpam-5446	695	1	existence	existence	PROPN
ejpam-5446	695	2	and	and	CCONJ
ejpam-5446	695	3	hyers	hyers	PROPN
ejpam-5446	695	4	-	-	PUNCT
ejpam-5446	695	5	ulam	ulam	PROPN
ejpam-5446	695	6	stability	stability	NOUN
ejpam-5446	695	7	results	result	VERB
ejpam-5446	695	8	for	for	ADP
ejpam-5446	695	9	a	a	DET
ejpam-5446	695	10	class	class	NOUN
ejpam-5446	695	11	of	of	ADP
ejpam-5446	695	12	fractional	fractional	ADJ
ejpam-5446	695	13	order	order	NOUN
ejpam-5446	695	14	delay	delay	NOUN
ejpam-5446	695	15	differential	differential	ADJ
ejpam-5446	695	16	equations	equation	NOUN
ejpam-5446	695	17	with	with	ADP
ejpam-5446	695	18	non	non	ADJ
ejpam-5446	695	19	-	-	ADJ
ejpam-5446	695	20	instantaneous	instantaneous	ADJ
ejpam-5446	695	21	impulses	impulse	NOUN
ejpam-5446	695	22	.	.	PUNCT
ejpam-5446	696	1	mathematica	mathematica	PROPN
ejpam-5446	696	2	slovaca	slovaca	PROPN
ejpam-5446	696	3	,	,	PUNCT
ejpam-5446	696	4	70(5):1231–1248	70(5):1231–1248	NUM
ejpam-5446	696	5	,	,	PUNCT
ejpam-5446	696	6	2020	2020	NUM
ejpam-5446	696	7	.	.	PUNCT
ejpam-5446	697	1	references	reference	NOUN
ejpam-5446	697	2	3609	3609	NUM
ejpam-5446	697	3	[	[	X
ejpam-5446	697	4	15	15	NUM
ejpam-5446	697	5	]	]	X
ejpam-5446	697	6	danfeng	danfeng	PROPN
ejpam-5446	697	7	luo	luo	PROPN
ejpam-5446	697	8	,	,	PUNCT
ejpam-5446	697	9	zhiguo	zhiguo	PROPN
ejpam-5446	697	10	luo	luo	PROPN
ejpam-5446	697	11	,	,	PUNCT
ejpam-5446	697	12	and	and	CCONJ
ejpam-5446	697	13	hongjun	hongjun	PROPN
ejpam-5446	697	14	qiu	qiu	PROPN
ejpam-5446	697	15	.	.	PUNCT
ejpam-5446	698	1	existence	existence	PROPN
ejpam-5446	698	2	and	and	CCONJ
ejpam-5446	698	3	hyers	hyer	NOUN
ejpam-5446	698	4	–	–	PUNCT
ejpam-5446	698	5	ulam	ulam	X
ejpam-5446	698	6	stability	stability	NOUN
ejpam-5446	698	7	of	of	ADP
ejpam-5446	698	8	solutions	solution	NOUN
ejpam-5446	698	9	for	for	ADP
ejpam-5446	698	10	a	a	DET
ejpam-5446	698	11	mixed	mixed	ADJ
ejpam-5446	698	12	fractional	fractional	ADJ
ejpam-5446	698	13	-	-	PUNCT
ejpam-5446	698	14	order	order	NOUN
ejpam-5446	698	15	nonlinear	nonlinear	ADJ
ejpam-5446	698	16	delay	delay	NOUN
ejpam-5446	698	17	difference	difference	NOUN
ejpam-5446	698	18	equation	equation	NOUN
ejpam-5446	698	19	with	with	ADP
ejpam-5446	698	20	parameters	parameter	NOUN
ejpam-5446	698	21	.	.	PUNCT
ejpam-5446	699	1	mathematical	mathematical	ADJ
ejpam-5446	699	2	problems	problem	NOUN
ejpam-5446	699	3	in	in	ADP
ejpam-5446	699	4	engineering	engineering	NOUN
ejpam-5446	699	5	,	,	PUNCT
ejpam-5446	699	6	2020(1):9372406	2020(1):9372406	NUM
ejpam-5446	699	7	,	,	PUNCT
ejpam-5446	699	8	2020	2020	NUM
ejpam-5446	699	9	.	.	PUNCT
ejpam-5446	700	1	[	[	X
ejpam-5446	700	2	16	16	NUM
ejpam-5446	700	3	]	]	X
ejpam-5446	700	4	danfeng	danfeng	PROPN
ejpam-5446	700	5	luo	luo	PROPN
ejpam-5446	700	6	,	,	PUNCT
ejpam-5446	700	7	kamal	kamal	PROPN
ejpam-5446	700	8	shah	shah	PROPN
ejpam-5446	700	9	,	,	PUNCT
ejpam-5446	700	10	and	and	CCONJ
ejpam-5446	700	11	zhiguo	zhiguo	PROPN
ejpam-5446	700	12	luo	luo	PROPN
ejpam-5446	700	13	.	.	PROPN
ejpam-5446	701	1	on	on	ADP
ejpam-5446	701	2	the	the	DET
ejpam-5446	701	3	novel	novel	ADJ
ejpam-5446	701	4	ulam	ulam	X
ejpam-5446	701	5	–	–	PUNCT
ejpam-5446	701	6	hyers	hyer	NOUN
ejpam-5446	701	7	stability	stability	NOUN
ejpam-5446	701	8	for	for	ADP
ejpam-5446	701	9	a	a	DET
ejpam-5446	701	10	class	class	NOUN
ejpam-5446	701	11	of	of	ADP
ejpam-5446	701	12	nonlinear	nonlinear	ADJ
ejpam-5446	701	13	ψ	ψ	NOUN
ejpam-5446	701	14	-	-	ADJ
ejpam-5446	701	15	hilfer	hilfer	NOUN
ejpam-5446	701	16	fractional	fractional	ADJ
ejpam-5446	701	17	differential	differential	NOUN
ejpam-5446	701	18	equation	equation	NOUN
ejpam-5446	701	19	with	with	ADP
ejpam-5446	701	20	time	time	NOUN
ejpam-5446	701	21	-	-	PUNCT
ejpam-5446	701	22	varying	vary	VERB
ejpam-5446	701	23	delays	delay	NOUN
ejpam-5446	701	24	.	.	PUNCT
ejpam-5446	702	1	mediterranean	mediterranean	PROPN
ejpam-5446	702	2	journal	journal	PROPN
ejpam-5446	702	3	of	of	ADP
ejpam-5446	702	4	mathematics	mathematic	NOUN
ejpam-5446	702	5	,	,	PUNCT
ejpam-5446	702	6	16(5):112	16(5):112	PROPN
ejpam-5446	702	7	,	,	PUNCT
ejpam-5446	702	8	2019	2019	NUM
ejpam-5446	702	9	.	.	PUNCT
ejpam-5446	703	1	[	[	X
ejpam-5446	703	2	17	17	NUM
ejpam-5446	703	3	]	]	X
ejpam-5446	703	4	danfeng	danfeng	PROPN
ejpam-5446	703	5	luo	luo	PROPN
ejpam-5446	703	6	,	,	PUNCT
ejpam-5446	703	7	akbar	akbar	PROPN
ejpam-5446	703	8	zada	zada	PROPN
ejpam-5446	703	9	,	,	PUNCT
ejpam-5446	703	10	shaleena	shaleena	ADJ
ejpam-5446	703	11	shaleena	shaleena	NOUN
ejpam-5446	703	12	,	,	PUNCT
ejpam-5446	703	13	and	and	CCONJ
ejpam-5446	703	14	manzoor	manzoor	PROPN
ejpam-5446	703	15	ahmad	ahmad	PROPN
ejpam-5446	703	16	.	.	PUNCT
ejpam-5446	703	17	analysis	analysis	NOUN
ejpam-5446	703	18	of	of	ADP
ejpam-5446	703	19	a	a	DET
ejpam-5446	703	20	coupled	couple	VERB
ejpam-5446	703	21	system	system	NOUN
ejpam-5446	703	22	of	of	ADP
ejpam-5446	703	23	fractional	fractional	ADJ
ejpam-5446	703	24	differential	differential	ADJ
ejpam-5446	703	25	equations	equation	NOUN
ejpam-5446	703	26	with	with	ADP
ejpam-5446	703	27	non	non	ADJ
ejpam-5446	703	28	-	-	ADJ
ejpam-5446	703	29	separated	separate	VERB
ejpam-5446	703	30	boundary	boundary	ADJ
ejpam-5446	703	31	conditions	condition	NOUN
ejpam-5446	703	32	.	.	PUNCT
ejpam-5446	704	1	advances	advance	NOUN
ejpam-5446	704	2	in	in	ADP
ejpam-5446	704	3	difference	difference	NOUN
ejpam-5446	704	4	equations	equation	NOUN
ejpam-5446	704	5	,	,	PUNCT
ejpam-5446	704	6	2020:1–24	2020:1–24	NUM
ejpam-5446	704	7	,	,	PUNCT
ejpam-5446	704	8	2020	2020	NUM
ejpam-5446	704	9	.	.	PUNCT
ejpam-5446	705	1	[	[	X
ejpam-5446	705	2	18	18	NUM
ejpam-5446	705	3	]	]	X
ejpam-5446	705	4	a	a	DET
ejpam-5446	705	5	mohanapriya	mohanapriya	NOUN
ejpam-5446	705	6	,	,	PUNCT
ejpam-5446	705	7	a	a	DET
ejpam-5446	705	8	ganesh	ganesh	NOUN
ejpam-5446	705	9	,	,	PUNCT
ejpam-5446	705	10	g	g	PROPN
ejpam-5446	705	11	rajchakit	rajchakit	NOUN
ejpam-5446	705	12	,	,	PUNCT
ejpam-5446	705	13	sandra	sandra	PROPN
ejpam-5446	705	14	pinelas	pinela	NOUN
ejpam-5446	705	15	,	,	PUNCT
ejpam-5446	705	16	v	v	ADP
ejpam-5446	705	17	govindan	govindan	NOUN
ejpam-5446	705	18	,	,	PUNCT
ejpam-5446	705	19	bundit	bundit	NOUN
ejpam-5446	705	20	unyong	unyong	PROPN
ejpam-5446	705	21	,	,	PUNCT
ejpam-5446	705	22	and	and	CCONJ
ejpam-5446	705	23	nallappan	nallappan	ADJ
ejpam-5446	705	24	gunasekaran	gunasekaran	NOUN
ejpam-5446	705	25	.	.	PUNCT
ejpam-5446	706	1	new	new	ADJ
ejpam-5446	706	2	generalization	generalization	NOUN
ejpam-5446	706	3	of	of	ADP
ejpam-5446	706	4	hermite	hermite	PROPN
ejpam-5446	706	5	-	-	PUNCT
ejpam-5446	706	6	hadamard	hadamard	ADJ
ejpam-5446	706	7	type	type	NOUN
ejpam-5446	706	8	of	of	ADP
ejpam-5446	706	9	inequalities	inequality	NOUN
ejpam-5446	706	10	for	for	ADP
ejpam-5446	706	11	convex	convex	NOUN
ejpam-5446	706	12	functions	function	NOUN
ejpam-5446	706	13	using	use	VERB
ejpam-5446	706	14	fourier	fourier	ADJ
ejpam-5446	706	15	integral	integral	ADJ
ejpam-5446	706	16	transform	transform	NOUN
ejpam-5446	706	17	.	.	PUNCT
ejpam-5446	707	1	thai	thai	PROPN
ejpam-5446	707	2	journal	journal	PROPN
ejpam-5446	707	3	of	of	ADP
ejpam-5446	707	4	mathematics	mathematic	NOUN
ejpam-5446	707	5	,	,	PUNCT
ejpam-5446	707	6	18(3):1051–1061	18(3):1051–1061	NUM
ejpam-5446	707	7	,	,	PUNCT
ejpam-5446	707	8	2020	2020	NUM
ejpam-5446	707	9	.	.	PUNCT
ejpam-5446	708	1	[	[	X
ejpam-5446	708	2	19	19	NUM
ejpam-5446	708	3	]	]	PUNCT
ejpam-5446	708	4	dorian	dorian	PROPN
ejpam-5446	708	5	popa	popa	NOUN
ejpam-5446	708	6	.	.	PUNCT
ejpam-5446	709	1	hyers	hyer	NOUN
ejpam-5446	709	2	–	–	PUNCT
ejpam-5446	709	3	ulam	ulam	X
ejpam-5446	709	4	–	–	PUNCT
ejpam-5446	709	5	rassias	rassia	NOUN
ejpam-5446	709	6	stability	stability	NOUN
ejpam-5446	709	7	of	of	ADP
ejpam-5446	709	8	a	a	DET
ejpam-5446	709	9	linear	linear	ADJ
ejpam-5446	709	10	recurrence	recurrence	NOUN
ejpam-5446	709	11	.	.	PUNCT
ejpam-5446	710	1	journal	journal	NOUN
ejpam-5446	710	2	of	of	ADP
ejpam-5446	710	3	mathematical	mathematical	ADJ
ejpam-5446	710	4	analysis	analysis	NOUN
ejpam-5446	710	5	and	and	CCONJ
ejpam-5446	710	6	applications	application	NOUN
ejpam-5446	710	7	,	,	PUNCT
ejpam-5446	710	8	309(2):591–597	309(2):591–597	NUM
ejpam-5446	710	9	,	,	PUNCT
ejpam-5446	710	10	2005	2005	NUM
ejpam-5446	710	11	.	.	PUNCT
ejpam-5446	711	1	[	[	X
ejpam-5446	711	2	20	20	NUM
ejpam-5446	711	3	]	]	X
ejpam-5446	711	4	murali	murali	PROPN
ejpam-5446	711	5	ramdoss	ramdoss	PROPN
ejpam-5446	711	6	,	,	PUNCT
ejpam-5446	711	7	ponmana	ponmana	ADJ
ejpam-5446	711	8	selvan	selvan	NOUN
ejpam-5446	711	9	-	-	PUNCT
ejpam-5446	711	10	arumugam	arumugam	NOUN
ejpam-5446	711	11	,	,	PUNCT
ejpam-5446	711	12	and	and	CCONJ
ejpam-5446	711	13	choonkil	choonkil	PROPN
ejpam-5446	711	14	park	park	NOUN
ejpam-5446	711	15	.	.	PUNCT
ejpam-5446	712	1	ulam	ulam	PROPN
ejpam-5446	712	2	stability	stability	PROPN
ejpam-5446	712	3	of	of	ADP
ejpam-5446	712	4	linear	linear	PROPN
ejpam-5446	712	5	differential	differential	ADJ
ejpam-5446	712	6	equations	equation	NOUN
ejpam-5446	712	7	using	use	VERB
ejpam-5446	712	8	fourier	fourier	NOUN
ejpam-5446	712	9	transform	transform	NOUN
ejpam-5446	712	10	.	.	PUNCT
ejpam-5446	713	1	aims	aim	VERB
ejpam-5446	713	2	mathematics	mathematic	NOUN
ejpam-5446	713	3	,	,	PUNCT
ejpam-5446	713	4	5(2):766–780	5(2):766–780	NUM
ejpam-5446	713	5	,	,	PUNCT
ejpam-5446	713	6	2020	2020	NUM
ejpam-5446	713	7	.	.	PUNCT
ejpam-5446	714	1	[	[	X
ejpam-5446	714	2	21	21	NUM
ejpam-5446	714	3	]	]	PUNCT
ejpam-5446	714	4	themistocles	themistocle	NOUN
ejpam-5446	714	5	m	m	NOUN
ejpam-5446	714	6	rassias	rassia	NOUN
ejpam-5446	714	7	.	.	PUNCT
ejpam-5446	715	1	on	on	ADP
ejpam-5446	715	2	the	the	DET
ejpam-5446	715	3	stability	stability	NOUN
ejpam-5446	715	4	of	of	ADP
ejpam-5446	715	5	the	the	DET
ejpam-5446	715	6	linear	linear	ADJ
ejpam-5446	715	7	mapping	mapping	NOUN
ejpam-5446	715	8	in	in	ADP
ejpam-5446	715	9	banach	banach	NOUN
ejpam-5446	715	10	spaces	space	NOUN
ejpam-5446	715	11	.	.	PUNCT
ejpam-5446	716	1	proceedings	proceeding	NOUN
ejpam-5446	716	2	of	of	ADP
ejpam-5446	716	3	the	the	DET
ejpam-5446	716	4	american	american	PROPN
ejpam-5446	716	5	mathematical	mathematical	PROPN
ejpam-5446	716	6	society	society	NOUN
ejpam-5446	716	7	,	,	PUNCT
ejpam-5446	716	8	72(2):297–300	72(2):297–300	NUM
ejpam-5446	716	9	,	,	PUNCT
ejpam-5446	716	10	1978	1978	NUM
ejpam-5446	716	11	.	.	PUNCT
ejpam-5446	717	1	[	[	X
ejpam-5446	717	2	22	22	NUM
ejpam-5446	717	3	]	]	X
ejpam-5446	717	4	hamid	hamid	PROPN
ejpam-5446	717	5	rezaei	rezaei	PROPN
ejpam-5446	717	6	,	,	PUNCT
ejpam-5446	717	7	soon	soon	ADV
ejpam-5446	717	8	-	-	PUNCT
ejpam-5446	717	9	mo	mo	NOUN
ejpam-5446	717	10	jung	jung	PROPN
ejpam-5446	717	11	,	,	PUNCT
ejpam-5446	717	12	and	and	CCONJ
ejpam-5446	717	13	themistocles	themistocle	NOUN
ejpam-5446	717	14	m	m	VERB
ejpam-5446	717	15	rassias	rassias	PROPN
ejpam-5446	717	16	.	.	PUNCT
ejpam-5446	718	1	laplace	laplace	NOUN
ejpam-5446	718	2	transform	transform	NOUN
ejpam-5446	718	3	and	and	CCONJ
ejpam-5446	718	4	hyers	hyer	NOUN
ejpam-5446	718	5	–	–	PUNCT
ejpam-5446	718	6	ulam	ulam	X
ejpam-5446	718	7	stability	stability	NOUN
ejpam-5446	718	8	of	of	ADP
ejpam-5446	718	9	linear	linear	PROPN
ejpam-5446	718	10	differential	differential	ADJ
ejpam-5446	718	11	equations	equation	NOUN
ejpam-5446	718	12	.	.	PUNCT
ejpam-5446	719	1	journal	journal	PROPN
ejpam-5446	719	2	of	of	ADP
ejpam-5446	719	3	mathematical	mathematical	ADJ
ejpam-5446	719	4	analysis	analysis	NOUN
ejpam-5446	719	5	and	and	CCONJ
ejpam-5446	719	6	applications	application	NOUN
ejpam-5446	719	7	,	,	PUNCT
ejpam-5446	719	8	403(1):244–251	403(1):244–251	NUM
ejpam-5446	719	9	,	,	PUNCT
ejpam-5446	719	10	2013	2013	NUM
ejpam-5446	719	11	.	.	PUNCT
ejpam-5446	720	1	[	[	X
ejpam-5446	720	2	23	23	NUM
ejpam-5446	720	3	]	]	X
ejpam-5446	720	4	stanislaw	stanislaw	PROPN
ejpam-5446	720	5	m	m	PROPN
ejpam-5446	720	6	ulam	ulam	PROPN
ejpam-5446	720	7	.	.	PUNCT
ejpam-5446	720	8	problems	problem	NOUN
ejpam-5446	720	9	in	in	ADP
ejpam-5446	720	10	modern	modern	ADJ
ejpam-5446	720	11	mathematics	mathematic	NOUN
ejpam-5446	720	12	.	.	PUNCT
ejpam-5446	721	1	courier	courier	NOUN
ejpam-5446	721	2	corporation	corporation	NOUN
ejpam-5446	721	3	,	,	PUNCT
ejpam-5446	721	4	2004	2004	NUM
ejpam-5446	721	5	.	.	PUNCT
ejpam-5446	722	1	[	[	X
ejpam-5446	722	2	24	24	NUM
ejpam-5446	722	3	]	]	PUNCT
ejpam-5446	722	4	bundit	bundit	NOUN
ejpam-5446	722	5	unyong	unyong	PROPN
ejpam-5446	722	6	,	,	PUNCT
ejpam-5446	722	7	vediyappan	vediyappan	ADJ
ejpam-5446	722	8	govindan	govindan	PROPN
ejpam-5446	722	9	,	,	PUNCT
ejpam-5446	722	10	s	s	PART
ejpam-5446	722	11	bowmiya	bowmiya	NOUN
ejpam-5446	722	12	,	,	PUNCT
ejpam-5446	722	13	g	g	PROPN
ejpam-5446	722	14	rajchakit	rajchakit	NOUN
ejpam-5446	722	15	,	,	PUNCT
ejpam-5446	722	16	nallappan	nallappan	ADJ
ejpam-5446	722	17	gunasekaran	gunasekaran	NOUN
ejpam-5446	722	18	,	,	PUNCT
ejpam-5446	722	19	r	r	NOUN
ejpam-5446	722	20	vadivel	vadivel	NOUN
ejpam-5446	722	21	,	,	PUNCT
ejpam-5446	722	22	chee	chee	NOUN
ejpam-5446	722	23	peng	peng	PROPN
ejpam-5446	722	24	lim	lim	PROPN
ejpam-5446	722	25	,	,	PUNCT
ejpam-5446	722	26	and	and	CCONJ
ejpam-5446	722	27	praveen	praveen	PROPN
ejpam-5446	722	28	agarwal	agarwal	PROPN
ejpam-5446	722	29	.	.	PUNCT
ejpam-5446	723	1	generalized	generalized	ADJ
ejpam-5446	723	2	linear	linear	PROPN
ejpam-5446	723	3	differential	differential	NOUN
ejpam-5446	723	4	equation	equation	NOUN
ejpam-5446	723	5	using	use	VERB
ejpam-5446	723	6	hyers	hyers	PROPN
ejpam-5446	723	7	-	-	PUNCT
ejpam-5446	723	8	ulam	ulam	PROPN
ejpam-5446	723	9	stability	stability	PROPN
ejpam-5446	723	10	approach	approach	NOUN
ejpam-5446	723	11	.	.	PUNCT
ejpam-5446	724	1	2021	2021	NUM
ejpam-5446	724	2	.	.	PUNCT
ejpam-5446	725	1	[	[	X
ejpam-5446	725	2	25	25	NUM
ejpam-5446	725	3	]	]	PUNCT
ejpam-5446	725	4	guangwa	guangwa	PROPN
ejpam-5446	725	5	wang	wang	PROPN
ejpam-5446	725	6	,	,	PUNCT
ejpam-5446	725	7	mingru	mingru	NOUN
ejpam-5446	725	8	zhou	zhou	PROPN
ejpam-5446	725	9	,	,	PUNCT
ejpam-5446	725	10	and	and	CCONJ
ejpam-5446	725	11	li	li	PROPN
ejpam-5446	725	12	sun	sun	PROPN
ejpam-5446	725	13	.	.	PUNCT
ejpam-5446	726	1	hyers	hyer	NOUN
ejpam-5446	726	2	–	–	PUNCT
ejpam-5446	726	3	ulam	ulam	PROPN
ejpam-5446	726	4	stability	stability	NOUN
ejpam-5446	726	5	of	of	ADP
ejpam-5446	726	6	linear	linear	PROPN
ejpam-5446	726	7	differential	differential	ADJ
ejpam-5446	726	8	equations	equation	NOUN
ejpam-5446	726	9	of	of	ADP
ejpam-5446	726	10	first	first	ADJ
ejpam-5446	726	11	order	order	NOUN
ejpam-5446	726	12	.	.	PUNCT
ejpam-5446	727	1	applied	apply	VERB
ejpam-5446	727	2	mathematics	mathematics	NOUN
ejpam-5446	727	3	letters	letter	NOUN
ejpam-5446	727	4	,	,	PUNCT
ejpam-5446	727	5	21(10):1024–1028	21(10):1024–1028	NUM
ejpam-5446	727	6	,	,	PUNCT
ejpam-5446	727	7	2008	2008	NUM
ejpam-5446	727	8	.	.	PUNCT
ejpam-5446	728	1	[	[	X
ejpam-5446	728	2	26	26	NUM
ejpam-5446	728	3	]	]	X
ejpam-5446	728	4	xue	xue	PROPN
ejpam-5446	728	5	wang	wang	PROPN
ejpam-5446	728	6	,	,	PUNCT
ejpam-5446	728	7	danfeng	danfeng	PROPN
ejpam-5446	728	8	luo	luo	PROPN
ejpam-5446	728	9	,	,	PUNCT
ejpam-5446	728	10	and	and	CCONJ
ejpam-5446	728	11	quanxin	quanxin	PROPN
ejpam-5446	728	12	zhu	zhu	PROPN
ejpam-5446	728	13	.	.	PUNCT
ejpam-5446	729	1	ulam	ulam	NOUN
ejpam-5446	729	2	-	-	PUNCT
ejpam-5446	729	3	hyers	hyer	NOUN
ejpam-5446	729	4	stability	stability	NOUN
ejpam-5446	729	5	of	of	ADP
ejpam-5446	729	6	caputo	caputo	PROPN
ejpam-5446	729	7	type	type	NOUN
ejpam-5446	729	8	fuzzy	fuzzy	ADJ
ejpam-5446	729	9	fractional	fractional	ADJ
ejpam-5446	729	10	differential	differential	ADJ
ejpam-5446	729	11	equations	equation	NOUN
ejpam-5446	729	12	with	with	ADP
ejpam-5446	729	13	time	time	NOUN
ejpam-5446	729	14	-	-	PUNCT
ejpam-5446	729	15	delays	delay	NOUN
ejpam-5446	729	16	.	.	PUNCT
ejpam-5446	730	1	chaos	chaos	NOUN
ejpam-5446	730	2	,	,	PUNCT
ejpam-5446	730	3	solitons	soliton	NOUN
ejpam-5446	730	4	&	&	CCONJ
ejpam-5446	730	5	fractals	fractal	NOUN
ejpam-5446	730	6	,	,	PUNCT
ejpam-5446	730	7	156:111822	156:111822	NUM
ejpam-5446	730	8	,	,	PUNCT
ejpam-5446	730	9	2022	2022	NUM
ejpam-5446	730	10	.	.	PUNCT