id	sid	tid	token	lemma	pos
ejpam-5445	1	1	european	european	PROPN
ejpam-5445	1	2	journal	journal	PROPN
ejpam-5445	1	3	of	of	ADP
ejpam-5445	1	4	pure	pure	ADJ
ejpam-5445	1	5	and	and	CCONJ
ejpam-5445	1	6	applied	apply	VERB
ejpam-5445	1	7	mathematics	mathematic	NOUN
ejpam-5445	1	8	vol	vol	NOUN
ejpam-5445	1	9	.	.	PROPN
ejpam-5445	2	1	17	17	NUM
ejpam-5445	2	2	,	,	PUNCT
ejpam-5445	2	3	no	no	INTJ
ejpam-5445	2	4	.	.	NOUN
ejpam-5445	2	5	4	4	NUM
ejpam-5445	2	6	,	,	PUNCT
ejpam-5445	2	7	2024	2024	NUM
ejpam-5445	2	8	,	,	PUNCT
ejpam-5445	2	9	3415	3415	NUM
ejpam-5445	2	10	-	-	SYM
ejpam-5445	2	11	3435	3435	NUM
ejpam-5445	2	12	issn	issn	PROPN
ejpam-5445	2	13	1307	1307	NUM
ejpam-5445	2	14	-	-	SYM
ejpam-5445	2	15	5543	5543	NUM
ejpam-5445	2	16	–	–	PUNCT
ejpam-5445	2	17	ejpam.com	ejpam.com	X
ejpam-5445	2	18	published	publish	VERB
ejpam-5445	2	19	by	by	ADP
ejpam-5445	2	20	new	new	PROPN
ejpam-5445	2	21	york	york	PROPN
ejpam-5445	2	22	business	business	PROPN
ejpam-5445	2	23	global	global	ADJ
ejpam-5445	2	24	generalized	generalize	VERB
ejpam-5445	2	25	linear	linear	PROPN
ejpam-5445	2	26	differential	differential	NOUN
ejpam-5445	2	27	equation	equation	NOUN
ejpam-5445	2	28	using	use	VERB
ejpam-5445	2	29	hyers	hyer	NOUN
ejpam-5445	2	30	ulam	ulam	PROPN
ejpam-5445	2	31	stability	stability	PROPN
ejpam-5445	2	32	approach	approach	VERB
ejpam-5445	2	33	s.	s.	PROPN
ejpam-5445	2	34	bowmiya1,∗	bowmiya1,∗	PROPN
ejpam-5445	2	35	,	,	PUNCT
ejpam-5445	2	36	g.	g.	PROPN
ejpam-5445	2	37	balasubramanian1	balasubramanian1	PROPN
ejpam-5445	2	38	,	,	PUNCT
ejpam-5445	2	39	vediyappan	vediyappan	ADJ
ejpam-5445	2	40	govindan2	govindan2	PROPN
ejpam-5445	2	41	,	,	PUNCT
ejpam-5445	2	42	mana	mana	PROPN
ejpam-5445	2	43	donganon3	donganon3	PROPN
ejpam-5445	2	44	,	,	PUNCT
ejpam-5445	2	45	haewon	haewon	VERB
ejpam-5445	2	46	byeon4,∗	byeon4,∗	NOUN
ejpam-5445	2	47	1	1	NUM
ejpam-5445	2	48	department	department	NOUN
ejpam-5445	2	49	of	of	ADP
ejpam-5445	2	50	mathematics	mathematic	NOUN
ejpam-5445	2	51	,	,	PUNCT
ejpam-5445	2	52	government	government	NOUN
ejpam-5445	2	53	arts	arts	PROPN
ejpam-5445	2	54	college	college	PROPN
ejpam-5445	2	55	for	for	ADP
ejpam-5445	2	56	men	man	NOUN
ejpam-5445	2	57	,	,	PUNCT
ejpam-5445	2	58	krishnagiri	krishnagiri	PROPN
ejpam-5445	2	59	635001	635001	NUM
ejpam-5445	2	60	,	,	PUNCT
ejpam-5445	2	61	tamil	tamil	PROPN
ejpam-5445	2	62	nadu	nadu	PROPN
ejpam-5445	2	63	,	,	PUNCT
ejpam-5445	2	64	india	india	PROPN
ejpam-5445	2	65	2	2	NUM
ejpam-5445	2	66	department	department	NOUN
ejpam-5445	2	67	of	of	ADP
ejpam-5445	2	68	mathematics	mathematic	NOUN
ejpam-5445	2	69	,	,	PUNCT
ejpam-5445	2	70	hindustan	hindustan	PROPN
ejpam-5445	2	71	institute	institute	PROPN
ejpam-5445	2	72	of	of	ADP
ejpam-5445	2	73	technology	technology	PROPN
ejpam-5445	2	74	and	and	CCONJ
ejpam-5445	2	75	science	science	NOUN
ejpam-5445	2	76	,	,	PUNCT
ejpam-5445	2	77	chennai	chennai	PROPN
ejpam-5445	2	78	603103	603103	NUM
ejpam-5445	2	79	,	,	PUNCT
ejpam-5445	2	80	tamil	tamil	PROPN
ejpam-5445	2	81	nadu	nadu	PROPN
ejpam-5445	2	82	,	,	PUNCT
ejpam-5445	2	83	india	india	PROPN
ejpam-5445	2	84	3	3	NUM
ejpam-5445	2	85	department	department	PROPN
ejpam-5445	2	86	of	of	ADP
ejpam-5445	2	87	mathematics	mathematic	NOUN
ejpam-5445	2	88	,	,	PUNCT
ejpam-5445	2	89	school	school	NOUN
ejpam-5445	2	90	of	of	ADP
ejpam-5445	2	91	science	science	NOUN
ejpam-5445	2	92	,	,	PUNCT
ejpam-5445	2	93	university	university	NOUN
ejpam-5445	2	94	of	of	ADP
ejpam-5445	2	95	phayao	phayao	NOUN
ejpam-5445	2	96	,	,	PUNCT
ejpam-5445	2	97	phayao	phayao	NOUN
ejpam-5445	2	98	56000	56000	NUM
ejpam-5445	2	99	,	,	PUNCT
ejpam-5445	2	100	thailand	thailand	PROPN
ejpam-5445	2	101	4	4	NUM
ejpam-5445	2	102	department	department	NOUN
ejpam-5445	2	103	of	of	ADP
ejpam-5445	2	104	ai	ai	ADJ
ejpam-5445	2	105	-	-	PUNCT
ejpam-5445	2	106	big	big	ADJ
ejpam-5445	2	107	data	datum	NOUN
ejpam-5445	2	108	,	,	PUNCT
ejpam-5445	2	109	college	college	NOUN
ejpam-5445	2	110	of	of	ADP
ejpam-5445	2	111	ai	ai	PROPN
ejpam-5445	2	112	convergence	convergence	NOUN
ejpam-5445	2	113	,	,	PUNCT
ejpam-5445	2	114	inje	inje	PROPN
ejpam-5445	2	115	university	university	NOUN
ejpam-5445	2	116	,	,	PUNCT
ejpam-5445	2	117	gimhae	gimhae	NOUN
ejpam-5445	2	118	,	,	PUNCT
ejpam-5445	2	119	50834	50834	NUM
ejpam-5445	2	120	,	,	PUNCT
ejpam-5445	2	121	republic	republic	NOUN
ejpam-5445	2	122	of	of	ADP
ejpam-5445	2	123	korea	korea	PROPN
ejpam-5445	2	124	abstract	abstract	NOUN
ejpam-5445	2	125	.	.	PUNCT
ejpam-5445	3	1	in	in	ADP
ejpam-5445	3	2	this	this	DET
ejpam-5445	3	3	paper	paper	NOUN
ejpam-5445	3	4	,	,	PUNCT
ejpam-5445	3	5	we	we	PRON
ejpam-5445	3	6	demonstrate	demonstrate	VERB
ejpam-5445	3	7	the	the	DET
ejpam-5445	3	8	hyers	hyer	NOUN
ejpam-5445	3	9	ulam	ulam	PROPN
ejpam-5445	3	10	stability	stability	NOUN
ejpam-5445	3	11	of	of	ADP
ejpam-5445	3	12	linear	linear	PROPN
ejpam-5445	3	13	differential	differential	ADJ
ejpam-5445	3	14	equation	equation	NOUN
ejpam-5445	3	15	of	of	ADP
ejpam-5445	3	16	fourth	fourth	ADJ
ejpam-5445	3	17	order	order	NOUN
ejpam-5445	3	18	.	.	PUNCT
ejpam-5445	4	1	we	we	PRON
ejpam-5445	4	2	interact	interact	VERB
ejpam-5445	4	3	with	with	ADP
ejpam-5445	4	4	the	the	DET
ejpam-5445	4	5	differential	differential	ADJ
ejpam-5445	4	6	equation	equation	NOUN
ejpam-5445	4	7	γiv(ω	γiv(ω	PROPN
ejpam-5445	4	8	)	)	PUNCT
ejpam-5445	4	9	+	+	CCONJ
ejpam-5445	4	10	ρ1γ	ρ1γ	PROPN
ejpam-5445	4	11	′′′(ω	′′′(ω	PROPN
ejpam-5445	4	12	)	)	PUNCT
ejpam-5445	5	1	+	+	PROPN
ejpam-5445	5	2	ρ2γ	ρ2γ	PROPN
ejpam-5445	5	3	′′(ω	′′(ω	NOUN
ejpam-5445	5	4	)	)	PUNCT
ejpam-5445	6	1	+	+	CCONJ
ejpam-5445	6	2	ρ3γ	ρ3γ	NUM
ejpam-5445	6	3	′(ω	′(ω	NOUN
ejpam-5445	6	4	)	)	PUNCT
ejpam-5445	6	5	+	+	X
ejpam-5445	6	6	ρ4γ(ω	ρ4γ(ω	NOUN
ejpam-5445	6	7	)	)	PUNCT
ejpam-5445	6	8	=	=	SYM
ejpam-5445	6	9	χ(ω	χ(ω	NOUN
ejpam-5445	6	10	)	)	PUNCT
ejpam-5445	6	11	,	,	PUNCT
ejpam-5445	6	12	where	where	SCONJ
ejpam-5445	6	13	γ	γ	PROPN
ejpam-5445	6	14	∈	∈	PROPN
ejpam-5445	6	15	c4[α	c4[α	NOUN
ejpam-5445	6	16	,	,	PUNCT
ejpam-5445	6	17	β	β	X
ejpam-5445	6	18	]	]	X
ejpam-5445	6	19	,	,	PUNCT
ejpam-5445	6	20	χ	χ	PROPN
ejpam-5445	6	21	∈	∈	PROPN
ejpam-5445	7	1	[	[	X
ejpam-5445	7	2	α	α	X
ejpam-5445	7	3	,	,	PUNCT
ejpam-5445	7	4	β	β	X
ejpam-5445	7	5	]	]	PUNCT
ejpam-5445	7	6	.	.	PUNCT
ejpam-5445	8	1	hyers	hyers	PROPN
ejpam-5445	8	2	-	-	PUNCT
ejpam-5445	8	3	ulam	ulam	PROPN
ejpam-5445	8	4	stability	stability	NOUN
ejpam-5445	8	5	concerns	concern	VERB
ejpam-5445	8	6	the	the	DET
ejpam-5445	8	7	robustness	robustness	NOUN
ejpam-5445	8	8	of	of	ADP
ejpam-5445	8	9	solutions	solution	NOUN
ejpam-5445	8	10	of	of	ADP
ejpam-5445	8	11	functional	functional	ADJ
ejpam-5445	8	12	equations	equation	NOUN
ejpam-5445	8	13	under	under	ADP
ejpam-5445	8	14	small	small	ADJ
ejpam-5445	8	15	perturbations	perturbation	NOUN
ejpam-5445	8	16	,	,	PUNCT
ejpam-5445	8	17	ensuring	ensure	VERB
ejpam-5445	8	18	that	that	SCONJ
ejpam-5445	8	19	a	a	DET
ejpam-5445	8	20	solution	solution	NOUN
ejpam-5445	8	21	approximately	approximately	ADV
ejpam-5445	8	22	satisfying	satisfy	VERB
ejpam-5445	8	23	the	the	DET
ejpam-5445	8	24	equation	equation	NOUN
ejpam-5445	8	25	is	be	AUX
ejpam-5445	8	26	close	close	ADJ
ejpam-5445	8	27	to	to	ADP
ejpam-5445	8	28	an	an	DET
ejpam-5445	8	29	exact	exact	ADJ
ejpam-5445	8	30	solution	solution	NOUN
ejpam-5445	8	31	.	.	PUNCT
ejpam-5445	9	1	we	we	PRON
ejpam-5445	9	2	extend	extend	VERB
ejpam-5445	9	3	this	this	DET
ejpam-5445	9	4	concept	concept	NOUN
ejpam-5445	9	5	to	to	ADP
ejpam-5445	9	6	fourth	fourth	ADJ
ejpam-5445	9	7	-	-	PUNCT
ejpam-5445	9	8	order	order	NOUN
ejpam-5445	9	9	linear	linear	PROPN
ejpam-5445	9	10	differential	differential	NOUN
ejpam-5445	9	11	equations	equation	NOUN
ejpam-5445	9	12	and	and	CCONJ
ejpam-5445	9	13	continuous	continuous	ADJ
ejpam-5445	9	14	functions	function	NOUN
ejpam-5445	9	15	.	.	PUNCT
ejpam-5445	10	1	using	use	VERB
ejpam-5445	10	2	fixed	fix	VERB
ejpam-5445	10	3	-	-	PUNCT
ejpam-5445	10	4	point	point	NOUN
ejpam-5445	10	5	methods	method	NOUN
ejpam-5445	10	6	and	and	CCONJ
ejpam-5445	10	7	various	various	ADJ
ejpam-5445	10	8	norms	norm	NOUN
ejpam-5445	10	9	,	,	PUNCT
ejpam-5445	10	10	we	we	PRON
ejpam-5445	10	11	establish	establish	VERB
ejpam-5445	10	12	conditions	condition	NOUN
ejpam-5445	10	13	under	under	ADP
ejpam-5445	10	14	which	which	PRON
ejpam-5445	10	15	such	such	ADJ
ejpam-5445	10	16	equations	equation	NOUN
ejpam-5445	10	17	exhibit	exhibit	VERB
ejpam-5445	10	18	hyers	hyer	NOUN
ejpam-5445	10	19	-	-	PUNCT
ejpam-5445	10	20	ulam	ulam	PROPN
ejpam-5445	10	21	stability	stability	NOUN
ejpam-5445	10	22	.	.	PUNCT
ejpam-5445	11	1	several	several	ADJ
ejpam-5445	11	2	illustrative	illustrative	ADJ
ejpam-5445	11	3	examples	example	NOUN
ejpam-5445	11	4	are	be	AUX
ejpam-5445	11	5	provided	provide	VERB
ejpam-5445	11	6	to	to	PART
ejpam-5445	11	7	demonstrate	demonstrate	VERB
ejpam-5445	11	8	the	the	DET
ejpam-5445	11	9	application	application	NOUN
ejpam-5445	11	10	of	of	ADP
ejpam-5445	11	11	these	these	DET
ejpam-5445	11	12	results	result	NOUN
ejpam-5445	11	13	in	in	ADP
ejpam-5445	11	14	specific	specific	ADJ
ejpam-5445	11	15	cases	case	NOUN
ejpam-5445	11	16	,	,	PUNCT
ejpam-5445	11	17	contributing	contribute	VERB
ejpam-5445	11	18	to	to	ADP
ejpam-5445	11	19	the	the	DET
ejpam-5445	11	20	growing	grow	VERB
ejpam-5445	11	21	understanding	understanding	NOUN
ejpam-5445	11	22	of	of	ADP
ejpam-5445	11	23	stability	stability	NOUN
ejpam-5445	11	24	in	in	ADP
ejpam-5445	11	25	higher	high	ADJ
ejpam-5445	11	26	-	-	PUNCT
ejpam-5445	11	27	order	order	NOUN
ejpam-5445	11	28	differential	differential	ADJ
ejpam-5445	11	29	equations	equation	NOUN
ejpam-5445	11	30	.	.	PUNCT
ejpam-5445	12	1	our	our	PRON
ejpam-5445	12	2	findings	finding	NOUN
ejpam-5445	12	3	have	have	VERB
ejpam-5445	12	4	implications	implication	NOUN
ejpam-5445	12	5	in	in	ADP
ejpam-5445	12	6	both	both	CCONJ
ejpam-5445	12	7	theoretical	theoretical	ADJ
ejpam-5445	12	8	research	research	NOUN
ejpam-5445	12	9	and	and	CCONJ
ejpam-5445	12	10	practical	practical	ADJ
ejpam-5445	12	11	applications	application	NOUN
ejpam-5445	12	12	in	in	ADP
ejpam-5445	12	13	physics	physics	NOUN
ejpam-5445	12	14	and	and	CCONJ
ejpam-5445	12	15	engineering	engineering	NOUN
ejpam-5445	12	16	.	.	PUNCT
ejpam-5445	13	1	2020	2020	NUM
ejpam-5445	13	2	mathematics	mathematic	NOUN
ejpam-5445	13	3	subject	subject	NOUN
ejpam-5445	13	4	classifications	classification	NOUN
ejpam-5445	13	5	:	:	PUNCT
ejpam-5445	13	6	35b35	35b35	NUM
ejpam-5445	13	7	key	key	ADJ
ejpam-5445	13	8	words	word	NOUN
ejpam-5445	13	9	and	and	CCONJ
ejpam-5445	13	10	phrases	phrase	NOUN
ejpam-5445	13	11	:	:	PUNCT
ejpam-5445	13	12	hyers	hyers	PROPN
ejpam-5445	13	13	-	-	PUNCT
ejpam-5445	13	14	ulam	ulam	PROPN
ejpam-5445	13	15	stability	stability	NOUN
ejpam-5445	13	16	,	,	PUNCT
ejpam-5445	13	17	linear	linear	ADJ
ejpam-5445	13	18	differential	differential	NOUN
ejpam-5445	13	19	equation	equation	NOUN
ejpam-5445	13	20	.	.	PUNCT
ejpam-5445	14	1	∗corresponding	∗corresponde	VERB
ejpam-5445	14	2	author	author	NOUN
ejpam-5445	14	3	.	.	PUNCT
ejpam-5445	15	1	∗corresponding	∗corresponde	VERB
ejpam-5445	15	2	author	author	NOUN
ejpam-5445	15	3	.	.	PUNCT
ejpam-5445	16	1	doi	doi	NOUN
ejpam-5445	16	2	:	:	PUNCT
ejpam-5445	16	3	https://doi.org/10.29020/nybg.ejpam.v17i4.5445	https://doi.org/10.29020/nybg.ejpam.v17i4.5445	ADJ
ejpam-5445	16	4	email	email	NOUN
ejpam-5445	16	5	addresses	address	VERB
ejpam-5445	16	6	:	:	PUNCT
ejpam-5445	17	1	manibowmi@gmail.com	manibowmi@gmail.com	PROPN
ejpam-5445	17	2	(	(	PUNCT
ejpam-5445	17	3	s.	s.	PROPN
ejpam-5445	17	4	bowmiya	bowmiya	PROPN
ejpam-5445	17	5	)	)	PUNCT
ejpam-5445	17	6	,	,	PUNCT
ejpam-5445	17	7	gbs	gbs	PROPN
ejpam-5445	17	8	geetha@yahoo.com	geetha@yahoo.com	PROPN
ejpam-5445	17	9	(	(	PUNCT
ejpam-5445	17	10	g.	g.	PROPN
ejpam-5445	17	11	balasubramanian	balasubramanian	PROPN
ejpam-5445	17	12	)	)	PUNCT
ejpam-5445	17	13	,	,	PUNCT
ejpam-5445	17	14	vedimalawi@gmail.com	vedimalawi@gmail.com	X
ejpam-5445	18	1	(	(	PUNCT
ejpam-5445	18	2	v.	v.	ADP
ejpam-5445	18	3	govindan	govindan	PROPN
ejpam-5445	18	4	)	)	PUNCT
ejpam-5445	18	5	,	,	PUNCT
ejpam-5445	18	6	mana.do@up.ac.th	mana.do@up.ac.th	PROPN
ejpam-5445	18	7	(	(	PUNCT
ejpam-5445	18	8	m.	m.	NOUN
ejpam-5445	18	9	donganon	donganon	PROPN
ejpam-5445	18	10	)	)	PUNCT
ejpam-5445	18	11	,	,	PUNCT
ejpam-5445	18	12	byeon@inje.ac.kr	byeon@inje.ac.kr	PROPN
ejpam-5445	18	13	(	(	PUNCT
ejpam-5445	18	14	h.	h.	PROPN
ejpam-5445	18	15	byeon	byeon	PROPN
ejpam-5445	18	16	)	)	PUNCT
ejpam-5445	18	17	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5445	19	1	3415	3415	NUM
ejpam-5445	19	2	copyright	copyright	NOUN
ejpam-5445	19	3	:	:	PUNCT
ejpam-5445	19	4	©	©	PROPN
ejpam-5445	19	5	2024	2024	NUM
ejpam-5445	19	6	the	the	DET
ejpam-5445	19	7	author(s	author(s	NOUN
ejpam-5445	19	8	)	)	PUNCT
ejpam-5445	19	9	.	.	PUNCT
ejpam-5445	20	1	(	(	PUNCT
ejpam-5445	20	2	cc	cc	NOUN
ejpam-5445	20	3	by	by	ADP
ejpam-5445	20	4	-	-	PUNCT
ejpam-5445	20	5	nc	nc	PROPN
ejpam-5445	20	6	4.0	4.0	NUM
ejpam-5445	20	7	)	)	PUNCT
ejpam-5445	20	8	s.	s.	PROPN
ejpam-5445	20	9	bowmiya	bowmiya	VERB
ejpam-5445	20	10	et	et	PROPN
ejpam-5445	20	11	al	al	PROPN
ejpam-5445	20	12	.	.	PUNCT
ejpam-5445	20	13	/	/	SYM
ejpam-5445	20	14	eur	eur	PROPN
ejpam-5445	20	15	.	.	PUNCT
ejpam-5445	21	1	j.	j.	PROPN
ejpam-5445	21	2	pure	pure	PROPN
ejpam-5445	21	3	appl	appl	PROPN
ejpam-5445	21	4	.	.	PROPN
ejpam-5445	21	5	math	math	PROPN
ejpam-5445	21	6	,	,	PUNCT
ejpam-5445	21	7	17	17	NUM
ejpam-5445	21	8	(	(	PUNCT
ejpam-5445	21	9	4	4	NUM
ejpam-5445	21	10	)	)	PUNCT
ejpam-5445	21	11	(	(	PUNCT
ejpam-5445	21	12	2024	2024	NUM
ejpam-5445	21	13	)	)	PUNCT
ejpam-5445	21	14	,	,	PUNCT
ejpam-5445	21	15	3415	3415	NUM
ejpam-5445	21	16	-	-	SYM
ejpam-5445	21	17	3435	3435	NUM
ejpam-5445	21	18	3416	3416	NUM
ejpam-5445	21	19	1	1	NUM
ejpam-5445	21	20	.	.	PUNCT
ejpam-5445	22	1	introduction	introduction	NOUN
ejpam-5445	22	2	the	the	DET
ejpam-5445	22	3	stability	stability	NOUN
ejpam-5445	22	4	issue	issue	NOUN
ejpam-5445	22	5	of	of	ADP
ejpam-5445	22	6	functional	functional	ADJ
ejpam-5445	22	7	equation	equation	NOUN
ejpam-5445	22	8	began	begin	VERB
ejpam-5445	22	9	from	from	ADP
ejpam-5445	22	10	an	an	DET
ejpam-5445	22	11	issue	issue	NOUN
ejpam-5445	22	12	of	of	ADP
ejpam-5445	22	13	ulam	ulam	PROPN
ejpam-5445	23	1	[	[	X
ejpam-5445	23	2	18	18	NUM
ejpam-5445	23	3	]	]	PUNCT
ejpam-5445	23	4	concerning	concern	VERB
ejpam-5445	23	5	the	the	DET
ejpam-5445	23	6	strength	strength	NOUN
ejpam-5445	23	7	of	of	ADP
ejpam-5445	23	8	gathering	gather	VERB
ejpam-5445	23	9	homomorphisms	homomorphism	NOUN
ejpam-5445	23	10	.	.	PUNCT
ejpam-5445	24	1	let	let	VERB
ejpam-5445	24	2	g1	g1	PROPN
ejpam-5445	24	3	be	be	AUX
ejpam-5445	24	4	a	a	DET
ejpam-5445	24	5	group	group	NOUN
ejpam-5445	24	6	and	and	CCONJ
ejpam-5445	24	7	let	let	VERB
ejpam-5445	24	8	g2	g2	PROPN
ejpam-5445	24	9	be	be	AUX
ejpam-5445	24	10	a	a	DET
ejpam-5445	24	11	measurement	measurement	NOUN
ejpam-5445	24	12	group	group	NOUN
ejpam-5445	24	13	with	with	ADP
ejpam-5445	24	14	the	the	DET
ejpam-5445	24	15	metric	metric	ADJ
ejpam-5445	24	16	d	d	PROPN
ejpam-5445	24	17	(	(	PUNCT
ejpam-5445	24	18	.	.	PUNCT
ejpam-5445	24	19	,	,	PUNCT
ejpam-5445	24	20	.	.	PUNCT
ejpam-5445	24	21	)	)	PUNCT
ejpam-5445	24	22	.	.	PUNCT
ejpam-5445	25	1	given	give	VERB
ejpam-5445	25	2	∈	∈	PROPN
ejpam-5445	25	3	>	>	X
ejpam-5445	25	4	0	0	NUM
ejpam-5445	25	5	,	,	PUNCT
ejpam-5445	25	6	does	do	AUX
ejpam-5445	25	7	there	there	PRON
ejpam-5445	25	8	exists	exist	VERB
ejpam-5445	25	9	a	a	DET
ejpam-5445	25	10	δ	δ	PROPN
ejpam-5445	25	11	>	>	X
ejpam-5445	25	12	0	0	PUNCT
ejpam-5445	25	13	to	to	ADP
ejpam-5445	25	14	such	such	DET
ejpam-5445	25	15	an	an	DET
ejpam-5445	25	16	extent	extent	NOUN
ejpam-5445	25	17	if	if	SCONJ
ejpam-5445	25	18	a	a	DET
ejpam-5445	25	19	mapping	mapping	NOUN
ejpam-5445	25	20	h	h	NOUN
ejpam-5445	25	21	:	:	PUNCT
ejpam-5445	25	22	g1	g1	PROPN
ejpam-5445	25	23	→	→	PUNCT
ejpam-5445	25	24	g2	g2	PROPN
ejpam-5445	25	25	fulfills	fulfill	VERB
ejpam-5445	25	26	the	the	DET
ejpam-5445	25	27	imbalance	imbalance	NOUN
ejpam-5445	25	28	d(h(ων	d(h(ων	NOUN
ejpam-5445	25	29	)	)	PUNCT
ejpam-5445	25	30	,	,	PUNCT
ejpam-5445	25	31	h(ω)h(ν	h(ω)h(ν	X
ejpam-5445	25	32	)	)	PUNCT
ejpam-5445	25	33	)	)	PUNCT
ejpam-5445	26	1	<	<	X
ejpam-5445	26	2	δ	δ	PROPN
ejpam-5445	26	3	with	with	ADP
ejpam-5445	26	4	respect	respect	NOUN
ejpam-5445	26	5	to	to	ADP
ejpam-5445	26	6	ω	ω	NUM
ejpam-5445	26	7	,	,	PUNCT
ejpam-5445	26	8	ν	ν	PROPN
ejpam-5445	26	9	∈	∈	PROPN
ejpam-5445	26	10	g1	g1	NOUN
ejpam-5445	26	11	,	,	PUNCT
ejpam-5445	26	12	at	at	ADP
ejpam-5445	26	13	that	that	DET
ejpam-5445	26	14	point	point	NOUN
ejpam-5445	26	15	there	there	PRON
ejpam-5445	26	16	exists	exist	VERB
ejpam-5445	26	17	a	a	DET
ejpam-5445	26	18	homomorphism	homomorphism	PROPN
ejpam-5445	26	19	h	h	NOUN
ejpam-5445	26	20	:	:	PUNCT
ejpam-5445	26	21	g1	g1	PROPN
ejpam-5445	26	22	→	→	PUNCT
ejpam-5445	26	23	g2	g2	PROPN
ejpam-5445	26	24	with	with	ADP
ejpam-5445	26	25	d(h(ω	d(h(ω	PROPN
ejpam-5445	26	26	)	)	PUNCT
ejpam-5445	26	27	,	,	PUNCT
ejpam-5445	26	28	h(ω	h(ω	PROPN
ejpam-5445	26	29	)	)	PUNCT
ejpam-5445	26	30	)	)	PUNCT
ejpam-5445	27	1	<	<	X
ejpam-5445	27	2	∈	∈	NOUN
ejpam-5445	27	3	with	with	ADP
ejpam-5445	27	4	respect	respect	NOUN
ejpam-5445	27	5	to	to	ADP
ejpam-5445	27	6	ω	ω	NUM
ejpam-5445	27	7	∈	∈	PROPN
ejpam-5445	27	8	g1	g1	NOUN
ejpam-5445	27	9	.	.	PUNCT
ejpam-5445	28	1	as	as	SCONJ
ejpam-5445	28	2	it	it	PRON
ejpam-5445	28	3	were	be	AUX
ejpam-5445	28	4	,	,	PUNCT
ejpam-5445	28	5	if	if	SCONJ
ejpam-5445	28	6	a	a	DET
ejpam-5445	28	7	mapping	mapping	NOUN
ejpam-5445	28	8	is	be	AUX
ejpam-5445	28	9	almost	almost	ADV
ejpam-5445	28	10	a	a	DET
ejpam-5445	28	11	homomorphism	homomorphism	NOUN
ejpam-5445	28	12	,	,	PUNCT
ejpam-5445	28	13	at	at	ADP
ejpam-5445	28	14	that	that	DET
ejpam-5445	28	15	point	point	NOUN
ejpam-5445	28	16	there	there	PRON
ejpam-5445	28	17	exists	exist	VERB
ejpam-5445	28	18	a	a	DET
ejpam-5445	28	19	true	true	ADJ
ejpam-5445	28	20	homomorphism	homomorphism	NOUN
ejpam-5445	28	21	were	be	AUX
ejpam-5445	28	22	τ	τ	PROPN
ejpam-5445	28	23	it	it	PRON
ejpam-5445	28	24	with	with	ADP
ejpam-5445	28	25	little	little	ADJ
ejpam-5445	28	26	blunder	blunder	NOUN
ejpam-5445	28	27	however	however	ADV
ejpam-5445	28	28	much	much	ADV
ejpam-5445	28	29	as	as	SCONJ
ejpam-5445	28	30	could	could	AUX
ejpam-5445	28	31	reasonably	reasonably	ADV
ejpam-5445	28	32	be	be	AUX
ejpam-5445	28	33	expected	expect	VERB
ejpam-5445	28	34	.	.	PUNCT
ejpam-5445	29	1	the	the	DET
ejpam-5445	29	2	issue	issue	NOUN
ejpam-5445	29	3	from	from	ADP
ejpam-5445	29	4	the	the	DET
ejpam-5445	29	5	instance	instance	NOUN
ejpam-5445	29	6	of	of	ADP
ejpam-5445	29	7	roughly	roughly	ADV
ejpam-5445	29	8	additive	additive	ADJ
ejpam-5445	29	9	mappings	mapping	NOUN
ejpam-5445	29	10	was	be	AUX
ejpam-5445	29	11	formed	form	VERB
ejpam-5445	29	12	by	by	ADP
ejpam-5445	29	13	hyers	hyer	NOUN
ejpam-5445	29	14	[	[	X
ejpam-5445	29	15	12	12	NUM
ejpam-5445	29	16	]	]	PUNCT
ejpam-5445	29	17	wheng1	wheng1	NOUN
ejpam-5445	29	18	andg2	andg2	NOUN
ejpam-5445	29	19	are	be	AUX
ejpam-5445	29	20	banach	banach	NOUN
ejpam-5445	29	21	spaces	space	NOUN
ejpam-5445	29	22	also	also	ADV
ejpam-5445	29	23	,	,	PUNCT
ejpam-5445	29	24	the	the	DET
ejpam-5445	29	25	after	after	SCONJ
ejpam-5445	29	26	effect	effect	NOUN
ejpam-5445	29	27	of	of	ADP
ejpam-5445	29	28	hyers	hyer	NOUN
ejpam-5445	29	29	was	be	AUX
ejpam-5445	29	30	summed	sum	VERB
ejpam-5445	29	31	up	up	ADP
ejpam-5445	29	32	by	by	ADP
ejpam-5445	29	33	rassias	rassias	PROPN
ejpam-5445	29	34	(	(	PUNCT
ejpam-5445	29	35	see	see	VERB
ejpam-5445	29	36	[	[	X
ejpam-5445	29	37	15	15	NUM
ejpam-5445	29	38	]	]	NUM
ejpam-5445	29	39	)	)	PUNCT
ejpam-5445	29	40	.	.	PUNCT
ejpam-5445	30	1	from	from	ADP
ejpam-5445	30	2	that	that	DET
ejpam-5445	30	3	point	point	NOUN
ejpam-5445	30	4	forward	forward	ADV
ejpam-5445	30	5	,	,	PUNCT
ejpam-5445	30	6	the	the	DET
ejpam-5445	30	7	dependability	dependability	NOUN
ejpam-5445	30	8	issues	issue	NOUN
ejpam-5445	30	9	of	of	ADP
ejpam-5445	30	10	practical	practical	ADJ
ejpam-5445	30	11	conditions	condition	NOUN
ejpam-5445	30	12	have	have	AUX
ejpam-5445	30	13	been	be	AUX
ejpam-5445	30	14	broadly	broadly	ADV
ejpam-5445	30	15	examined	examine	VERB
ejpam-5445	30	16	by	by	ADP
ejpam-5445	30	17	a	a	DET
ejpam-5445	30	18	few	few	ADJ
ejpam-5445	30	19	mathematician	mathematician	NOUN
ejpam-5445	30	20	(	(	PUNCT
ejpam-5445	30	21	see	see	VERB
ejpam-5445	30	22	[	[	X
ejpam-5445	30	23	2–4	2–4	NUM
ejpam-5445	30	24	,	,	PUNCT
ejpam-5445	30	25	9	9	NUM
ejpam-5445	30	26	,	,	PUNCT
ejpam-5445	30	27	11	11	NUM
ejpam-5445	30	28	]	]	NUM
ejpam-5445	30	29	)	)	PUNCT
ejpam-5445	30	30	.	.	PUNCT
ejpam-5445	31	1	supposedly	supposedly	ADV
ejpam-5445	31	2	,	,	PUNCT
ejpam-5445	31	3	papers	paper	NOUN
ejpam-5445	31	4	by	by	ADP
ejpam-5445	31	5	ozawa	ozawa	PROPN
ejpam-5445	31	6	[	[	X
ejpam-5445	31	7	7	7	NUM
ejpam-5445	31	8	]	]	PUNCT
ejpam-5445	31	9	were	be	AUX
ejpam-5445	31	10	among	among	ADP
ejpam-5445	31	11	the	the	DET
ejpam-5445	31	12	first	first	ADJ
ejpam-5445	31	13	commitments	commitment	NOUN
ejpam-5445	31	14	managing	manage	VERB
ejpam-5445	31	15	with	with	ADP
ejpam-5445	31	16	h−u	h−u	NOUN
ejpam-5445	31	17	stability	stability	NOUN
ejpam-5445	31	18	of	of	ADP
ejpam-5445	31	19	differential	differential	ADJ
ejpam-5445	31	20	equations	equation	NOUN
ejpam-5445	31	21	.	.	PUNCT
ejpam-5445	32	1	alsina	alsina	PROPN
ejpam-5445	33	1	[	[	X
ejpam-5445	33	2	1	1	NUM
ejpam-5445	33	3	]	]	PUNCT
ejpam-5445	33	4	and	and	CCONJ
ejpam-5445	33	5	ger	ger	NOUN
ejpam-5445	33	6	demonstratedh−u	demonstratedh−u	PROPN
ejpam-5445	33	7	stability	stability	NOUN
ejpam-5445	33	8	of	of	ADP
ejpam-5445	33	9	differential	differential	ADJ
ejpam-5445	33	10	condition	condition	NOUN
ejpam-5445	33	11	γ′(ω	γ′(ω	PRON
ejpam-5445	33	12	)	)	PUNCT
ejpam-5445	33	13	=	=	PUNCT
ejpam-5445	33	14	γ(ω	γ(ω	NOUN
ejpam-5445	33	15	)	)	PUNCT
ejpam-5445	33	16	.	.	PUNCT
ejpam-5445	34	1	afterword	afterword	PROPN
ejpam-5445	34	2	,	,	PUNCT
ejpam-5445	34	3	takahasi	takahasi	PROPN
ejpam-5445	34	4	et	et	PROPN
ejpam-5445	34	5	al	al	PROPN
ejpam-5445	34	6	.	.	PROPN
ejpam-5445	34	7	stretched	stretch	VERB
ejpam-5445	34	8	out	out	ADP
ejpam-5445	34	9	consequences	consequence	NOUN
ejpam-5445	34	10	of	of	ADP
ejpam-5445	34	11	[	[	X
ejpam-5445	34	12	16	16	NUM
ejpam-5445	34	13	,	,	PUNCT
ejpam-5445	34	14	17	17	NUM
ejpam-5445	34	15	]	]	PUNCT
ejpam-5445	34	16	to	to	ADP
ejpam-5445	34	17	the	the	DET
ejpam-5445	34	18	banach	banach	NOUN
ejpam-5445	34	19	space	space	NOUN
ejpam-5445	34	20	esteemed	esteem	VERB
ejpam-5445	34	21	differential	differential	ADJ
ejpam-5445	34	22	condition	condition	NOUN
ejpam-5445	34	23	γ′(ω	γ′(ω	PRON
ejpam-5445	34	24	)	)	PUNCT
ejpam-5445	34	25	=	=	NOUN
ejpam-5445	34	26	λγ(ω	λγ(ω	NUM
ejpam-5445	34	27	)	)	PUNCT
ejpam-5445	34	28	.	.	PUNCT
ejpam-5445	35	1	utilizing	utilize	VERB
ejpam-5445	35	2	direct	direct	ADJ
ejpam-5445	35	3	strategy	strategy	NOUN
ejpam-5445	35	4	,	,	PUNCT
ejpam-5445	35	5	cycle	cycle	NOUN
ejpam-5445	35	6	technique	technique	NOUN
ejpam-5445	35	7	,	,	PUNCT
ejpam-5445	35	8	find	find	VERB
ejpam-5445	35	9	point	point	NOUN
ejpam-5445	35	10	technique	technique	NOUN
ejpam-5445	35	11	,	,	PUNCT
ejpam-5445	35	12	and	and	CCONJ
ejpam-5445	35	13	open	open	ADJ
ejpam-5445	35	14	mapping	mapping	NOUN
ejpam-5445	35	15	theorem	theorem	NOUN
ejpam-5445	35	16	,	,	PUNCT
ejpam-5445	35	17	huang	huang	PROPN
ejpam-5445	35	18	and	and	CCONJ
ejpam-5445	35	19	li	li	PROPN
ejpam-5445	35	20	explored	explore	VERB
ejpam-5445	35	21	the	the	DET
ejpam-5445	35	22	h	h	NOUN
ejpam-5445	35	23	−	−	PROPN
ejpam-5445	35	24	u	u	NOUN
ejpam-5445	35	25	stability	stability	NOUN
ejpam-5445	35	26	of	of	ADP
ejpam-5445	35	27	certain	certain	ADJ
ejpam-5445	35	28	classes	class	NOUN
ejpam-5445	35	29	of	of	ADP
ejpam-5445	35	30	useful	useful	ADJ
ejpam-5445	35	31	fractional	fractional	ADJ
ejpam-5445	35	32	differential	differential	ADJ
ejpam-5445	35	33	equations	equation	NOUN
ejpam-5445	35	34	(	(	PUNCT
ejpam-5445	35	35	see	see	VERB
ejpam-5445	35	36	[	[	X
ejpam-5445	35	37	11	11	NUM
ejpam-5445	35	38	,	,	PUNCT
ejpam-5445	35	39	14	14	NUM
ejpam-5445	35	40	,	,	PUNCT
ejpam-5445	35	41	16	16	NUM
ejpam-5445	35	42	,	,	PUNCT
ejpam-5445	35	43	19	19	NUM
ejpam-5445	35	44	]	]	NUM
ejpam-5445	35	45	)	)	PUNCT
ejpam-5445	35	46	.	.	PUNCT
ejpam-5445	36	1	for	for	ADP
ejpam-5445	36	2	higher	high	ADJ
ejpam-5445	36	3	-	-	PUNCT
ejpam-5445	36	4	order	order	NOUN
ejpam-5445	36	5	differential	differential	ADJ
ejpam-5445	36	6	equations	equation	NOUN
ejpam-5445	36	7	,	,	PUNCT
ejpam-5445	36	8	such	such	ADJ
ejpam-5445	36	9	as	as	ADP
ejpam-5445	36	10	fourth	fourth	ADJ
ejpam-5445	36	11	-	-	PUNCT
ejpam-5445	36	12	order	order	NOUN
ejpam-5445	36	13	,	,	PUNCT
ejpam-5445	36	14	the	the	DET
ejpam-5445	36	15	characteristic	characteristic	ADJ
ejpam-5445	36	16	equation	equation	NOUN
ejpam-5445	36	17	can	can	AUX
ejpam-5445	36	18	become	become	VERB
ejpam-5445	36	19	quite	quite	ADV
ejpam-5445	36	20	complex	complex	ADJ
ejpam-5445	36	21	.	.	PUNCT
ejpam-5445	37	1	solving	solve	VERB
ejpam-5445	37	2	for	for	ADP
ejpam-5445	37	3	the	the	DET
ejpam-5445	37	4	roots	root	NOUN
ejpam-5445	37	5	,	,	PUNCT
ejpam-5445	37	6	especially	especially	ADV
ejpam-5445	37	7	if	if	SCONJ
ejpam-5445	37	8	they	they	PRON
ejpam-5445	37	9	are	be	AUX
ejpam-5445	37	10	non	non	ADJ
ejpam-5445	37	11	-	-	ADJ
ejpam-5445	37	12	real	real	ADJ
ejpam-5445	37	13	or	or	CCONJ
ejpam-5445	37	14	repeated	repeat	VERB
ejpam-5445	37	15	,	,	PUNCT
ejpam-5445	37	16	can	can	AUX
ejpam-5445	37	17	be	be	AUX
ejpam-5445	37	18	tedious	tedious	ADJ
ejpam-5445	37	19	.	.	PUNCT
ejpam-5445	38	1	while	while	SCONJ
ejpam-5445	38	2	homogeneous	homogeneous	ADJ
ejpam-5445	38	3	equations	equation	NOUN
ejpam-5445	38	4	can	can	AUX
ejpam-5445	38	5	sometimes	sometimes	ADV
ejpam-5445	38	6	be	be	AUX
ejpam-5445	38	7	solved	solve	VERB
ejpam-5445	38	8	through	through	ADP
ejpam-5445	38	9	standard	standard	ADJ
ejpam-5445	38	10	methods	method	NOUN
ejpam-5445	38	11	(	(	PUNCT
ejpam-5445	38	12	like	like	ADP
ejpam-5445	38	13	finding	find	VERB
ejpam-5445	38	14	the	the	DET
ejpam-5445	38	15	roots	root	NOUN
ejpam-5445	38	16	of	of	ADP
ejpam-5445	38	17	the	the	DET
ejpam-5445	38	18	characteristic	characteristic	ADJ
ejpam-5445	38	19	polynomial	polynomial	NOUN
ejpam-5445	38	20	)	)	PUNCT
ejpam-5445	38	21	,	,	PUNCT
ejpam-5445	38	22	nonhomogeneous	nonhomogeneous	ADJ
ejpam-5445	38	23	equations	equation	NOUN
ejpam-5445	38	24	require	require	VERB
ejpam-5445	38	25	additional	additional	ADJ
ejpam-5445	38	26	techniques	technique	NOUN
ejpam-5445	38	27	such	such	ADJ
ejpam-5445	38	28	as	as	ADP
ejpam-5445	38	29	variation	variation	NOUN
ejpam-5445	38	30	of	of	ADP
ejpam-5445	38	31	parameters	parameter	NOUN
ejpam-5445	38	32	or	or	CCONJ
ejpam-5445	38	33	the	the	DET
ejpam-5445	38	34	method	method	NOUN
ejpam-5445	38	35	of	of	ADP
ejpam-5445	38	36	undetermined	undetermined	ADJ
ejpam-5445	38	37	coefficients	coefficient	NOUN
ejpam-5445	38	38	,	,	PUNCT
ejpam-5445	38	39	which	which	PRON
ejpam-5445	38	40	are	be	AUX
ejpam-5445	38	41	not	not	PART
ejpam-5445	38	42	always	always	ADV
ejpam-5445	38	43	straightforward	straightforward	ADJ
ejpam-5445	38	44	.	.	PUNCT
ejpam-5445	39	1	many	many	ADJ
ejpam-5445	39	2	fourth	fourth	ADJ
ejpam-5445	39	3	-	-	PUNCT
ejpam-5445	39	4	order	order	NOUN
ejpam-5445	39	5	linear	linear	PROPN
ejpam-5445	39	6	differential	differential	NOUN
ejpam-5445	39	7	equations	equation	NOUN
ejpam-5445	39	8	,	,	PUNCT
ejpam-5445	39	9	especially	especially	ADV
ejpam-5445	39	10	those	those	PRON
ejpam-5445	39	11	arising	arise	VERB
ejpam-5445	39	12	in	in	ADP
ejpam-5445	39	13	physics	physics	NOUN
ejpam-5445	39	14	and	and	CCONJ
ejpam-5445	39	15	engineering	engineering	NOUN
ejpam-5445	39	16	(	(	PUNCT
ejpam-5445	39	17	e.g.	e.g.	ADV
ejpam-5445	39	18	,	,	PUNCT
ejpam-5445	39	19	in	in	ADP
ejpam-5445	39	20	beam	beam	NOUN
ejpam-5445	39	21	theory	theory	NOUN
ejpam-5445	39	22	or	or	CCONJ
ejpam-5445	39	23	fluid	fluid	ADJ
ejpam-5445	39	24	dynamics	dynamic	NOUN
ejpam-5445	39	25	)	)	PUNCT
ejpam-5445	39	26	,	,	PUNCT
ejpam-5445	39	27	can	can	AUX
ejpam-5445	39	28	not	not	PART
ejpam-5445	39	29	be	be	AUX
ejpam-5445	39	30	solved	solve	VERB
ejpam-5445	39	31	using	use	VERB
ejpam-5445	39	32	elementary	elementary	ADJ
ejpam-5445	39	33	functions	function	NOUN
ejpam-5445	39	34	and	and	CCONJ
ejpam-5445	39	35	require	require	VERB
ejpam-5445	39	36	special	special	ADJ
ejpam-5445	39	37	functions	function	NOUN
ejpam-5445	39	38	(	(	PUNCT
ejpam-5445	39	39	e.g.	e.g.	ADV
ejpam-5445	39	40	,	,	PUNCT
ejpam-5445	39	41	bessel	bessel	ADJ
ejpam-5445	39	42	,	,	PUNCT
ejpam-5445	39	43	airy	airy	ADJ
ejpam-5445	39	44	,	,	PUNCT
ejpam-5445	39	45	or	or	CCONJ
ejpam-5445	39	46	legendre	legendre	PROPN
ejpam-5445	39	47	functions	function	NOUN
ejpam-5445	39	48	)	)	PUNCT
ejpam-5445	39	49	.	.	PUNCT
ejpam-5445	40	1	these	these	DET
ejpam-5445	40	2	solutions	solution	NOUN
ejpam-5445	40	3	can	can	AUX
ejpam-5445	40	4	be	be	AUX
ejpam-5445	40	5	difficult	difficult	ADJ
ejpam-5445	40	6	to	to	PART
ejpam-5445	40	7	interpret	interpret	VERB
ejpam-5445	40	8	or	or	CCONJ
ejpam-5445	40	9	manipulate	manipulate	VERB
ejpam-5445	40	10	further	far	ADV
ejpam-5445	40	11	.	.	PUNCT
ejpam-5445	41	1	a	a	DET
ejpam-5445	41	2	fourth	fourth	ADJ
ejpam-5445	41	3	-	-	PUNCT
ejpam-5445	41	4	order	order	NOUN
ejpam-5445	41	5	equation	equation	NOUN
ejpam-5445	41	6	requires	require	VERB
ejpam-5445	41	7	four	four	NUM
ejpam-5445	41	8	boundary	boundary	ADJ
ejpam-5445	41	9	or	or	CCONJ
ejpam-5445	41	10	initial	initial	ADJ
ejpam-5445	41	11	conditions	condition	NOUN
ejpam-5445	41	12	to	to	PART
ejpam-5445	41	13	determine	determine	VERB
ejpam-5445	41	14	a	a	DET
ejpam-5445	41	15	unique	unique	ADJ
ejpam-5445	41	16	solution	solution	NOUN
ejpam-5445	41	17	.	.	PUNCT
ejpam-5445	42	1	this	this	PRON
ejpam-5445	42	2	increases	increase	VERB
ejpam-5445	42	3	the	the	DET
ejpam-5445	42	4	complexity	complexity	NOUN
ejpam-5445	42	5	of	of	ADP
ejpam-5445	42	6	the	the	DET
ejpam-5445	42	7	problem	problem	NOUN
ejpam-5445	42	8	,	,	PUNCT
ejpam-5445	42	9	and	and	CCONJ
ejpam-5445	42	10	choosing	choose	VERB
ejpam-5445	42	11	appropriate	appropriate	ADJ
ejpam-5445	42	12	conditions	condition	NOUN
ejpam-5445	42	13	can	can	AUX
ejpam-5445	42	14	be	be	AUX
ejpam-5445	42	15	tricky	tricky	ADJ
ejpam-5445	42	16	.	.	PUNCT
ejpam-5445	43	1	in	in	ADP
ejpam-5445	43	2	some	some	DET
ejpam-5445	43	3	cases	case	NOUN
ejpam-5445	43	4	,	,	PUNCT
ejpam-5445	43	5	the	the	DET
ejpam-5445	43	6	boundary	boundary	ADJ
ejpam-5445	43	7	or	or	CCONJ
ejpam-5445	43	8	initial	initial	ADJ
ejpam-5445	43	9	conditions	condition	NOUN
ejpam-5445	43	10	may	may	AUX
ejpam-5445	43	11	be	be	AUX
ejpam-5445	43	12	incompatible	incompatible	ADJ
ejpam-5445	43	13	with	with	ADP
ejpam-5445	43	14	the	the	DET
ejpam-5445	43	15	differential	differential	ADJ
ejpam-5445	43	16	equation	equation	NOUN
ejpam-5445	43	17	,	,	PUNCT
ejpam-5445	43	18	leading	lead	VERB
ejpam-5445	43	19	to	to	ADP
ejpam-5445	43	20	no	no	DET
ejpam-5445	43	21	solution	solution	NOUN
ejpam-5445	43	22	or	or	CCONJ
ejpam-5445	43	23	non	non	ADJ
ejpam-5445	43	24	-	-	ADJ
ejpam-5445	43	25	physical	physical	ADJ
ejpam-5445	43	26	solutions	solution	NOUN
ejpam-5445	43	27	.	.	PUNCT
ejpam-5445	44	1	solving	solve	VERB
ejpam-5445	44	2	fourth	fourth	ADJ
ejpam-5445	44	3	-	-	PUNCT
ejpam-5445	44	4	order	order	NOUN
ejpam-5445	44	5	differential	differential	ADJ
ejpam-5445	44	6	equations	equation	NOUN
ejpam-5445	44	7	numerically	numerically	ADV
ejpam-5445	44	8	(	(	PUNCT
ejpam-5445	44	9	e.g.	e.g.	ADV
ejpam-5445	44	10	,	,	PUNCT
ejpam-5445	44	11	with	with	ADP
ejpam-5445	44	12	finite	finite	ADJ
ejpam-5445	44	13	difference	difference	NOUN
ejpam-5445	44	14	methods	method	NOUN
ejpam-5445	44	15	,	,	PUNCT
ejpam-5445	44	16	finite	finite	ADJ
ejpam-5445	44	17	element	element	NOUN
ejpam-5445	44	18	methods	method	NOUN
ejpam-5445	44	19	,	,	PUNCT
ejpam-5445	44	20	or	or	CCONJ
ejpam-5445	44	21	runge	runge	NOUN
ejpam-5445	44	22	-	-	PUNCT
ejpam-5445	44	23	kutta	kutta	NOUN
ejpam-5445	44	24	methods	method	NOUN
ejpam-5445	44	25	)	)	PUNCT
ejpam-5445	44	26	can	can	AUX
ejpam-5445	44	27	lead	lead	VERB
ejpam-5445	44	28	to	to	ADP
ejpam-5445	44	29	instability	instability	NOUN
ejpam-5445	44	30	,	,	PUNCT
ejpam-5445	44	31	especially	especially	ADV
ejpam-5445	44	32	if	if	SCONJ
ejpam-5445	44	33	the	the	DET
ejpam-5445	44	34	equation	equation	NOUN
ejpam-5445	44	35	involves	involve	VERB
ejpam-5445	44	36	stiff	stiff	ADJ
ejpam-5445	44	37	terms	term	NOUN
ejpam-5445	44	38	.	.	PUNCT
ejpam-5445	45	1	this	this	PRON
ejpam-5445	45	2	requires	require	VERB
ejpam-5445	45	3	careful	careful	ADJ
ejpam-5445	45	4	attention	attention	NOUN
ejpam-5445	45	5	to	to	ADP
ejpam-5445	45	6	step	step	VERB
ejpam-5445	45	7	sizes	size	NOUN
ejpam-5445	45	8	and	and	CCONJ
ejpam-5445	45	9	discretization	discretization	NOUN
ejpam-5445	45	10	methods	method	NOUN
ejpam-5445	45	11	.	.	PUNCT
ejpam-5445	46	1	higher	high	ADJ
ejpam-5445	46	2	-	-	PUNCT
ejpam-5445	46	3	order	order	NOUN
ejpam-5445	46	4	equations	equation	NOUN
ejpam-5445	46	5	require	require	VERB
ejpam-5445	46	6	more	more	ADV
ejpam-5445	46	7	computational	computational	ADJ
ejpam-5445	46	8	effort	effort	NOUN
ejpam-5445	46	9	.	.	PUNCT
ejpam-5445	47	1	discretizing	discretize	VERB
ejpam-5445	47	2	fourth	fourth	ADJ
ejpam-5445	47	3	-	-	PUNCT
ejpam-5445	47	4	order	order	NOUN
ejpam-5445	47	5	equations	equation	NOUN
ejpam-5445	47	6	often	often	ADV
ejpam-5445	47	7	leads	lead	VERB
ejpam-5445	47	8	to	to	ADP
ejpam-5445	47	9	larger	large	ADJ
ejpam-5445	47	10	,	,	PUNCT
ejpam-5445	47	11	more	more	ADV
ejpam-5445	47	12	complex	complex	ADJ
ejpam-5445	47	13	systems	system	NOUN
ejpam-5445	47	14	of	of	ADP
ejpam-5445	47	15	linear	linear	PROPN
ejpam-5445	47	16	equations	equation	NOUN
ejpam-5445	47	17	,	,	PUNCT
ejpam-5445	47	18	which	which	PRON
ejpam-5445	47	19	increases	increase	VERB
ejpam-5445	47	20	computational	computational	ADJ
ejpam-5445	47	21	cost	cost	NOUN
ejpam-5445	47	22	.	.	PUNCT
ejpam-5445	48	1	numerical	numerical	ADJ
ejpam-5445	48	2	methods	method	NOUN
ejpam-5445	48	3	are	be	AUX
ejpam-5445	48	4	approximate	approximate	ADJ
ejpam-5445	48	5	by	by	ADP
ejpam-5445	48	6	nature	nature	NOUN
ejpam-5445	48	7	.	.	PUNCT
ejpam-5445	49	1	for	for	ADP
ejpam-5445	49	2	higher	high	ADJ
ejpam-5445	49	3	-	-	PUNCT
ejpam-5445	49	4	order	order	NOUN
ejpam-5445	49	5	equations	equation	NOUN
ejpam-5445	49	6	,	,	PUNCT
ejpam-5445	49	7	truncation	truncation	NOUN
ejpam-5445	49	8	and	and	CCONJ
ejpam-5445	49	9	rounding	round	VERB
ejpam-5445	49	10	errors	error	NOUN
ejpam-5445	49	11	can	can	AUX
ejpam-5445	49	12	accumulate	accumulate	VERB
ejpam-5445	49	13	,	,	PUNCT
ejpam-5445	49	14	leading	lead	VERB
ejpam-5445	49	15	to	to	ADP
ejpam-5445	49	16	reduced	reduce	VERB
ejpam-5445	49	17	accuracy	accuracy	NOUN
ejpam-5445	49	18	.	.	PUNCT
ejpam-5445	50	1	s.	s.	PROPN
ejpam-5445	50	2	bowmiya	bowmiya	PROPN
ejpam-5445	50	3	et	et	PROPN
ejpam-5445	50	4	al	al	PROPN
ejpam-5445	50	5	.	.	PUNCT
ejpam-5445	50	6	/	/	SYM
ejpam-5445	50	7	eur	eur	PROPN
ejpam-5445	50	8	.	.	PUNCT
ejpam-5445	51	1	j.	j.	PROPN
ejpam-5445	51	2	pure	pure	PROPN
ejpam-5445	51	3	appl	appl	PROPN
ejpam-5445	51	4	.	.	PROPN
ejpam-5445	51	5	math	math	PROPN
ejpam-5445	51	6	,	,	PUNCT
ejpam-5445	51	7	17	17	NUM
ejpam-5445	51	8	(	(	PUNCT
ejpam-5445	51	9	4	4	NUM
ejpam-5445	51	10	)	)	PUNCT
ejpam-5445	51	11	(	(	PUNCT
ejpam-5445	51	12	2024	2024	NUM
ejpam-5445	51	13	)	)	PUNCT
ejpam-5445	51	14	,	,	PUNCT
ejpam-5445	51	15	3415	3415	NUM
ejpam-5445	51	16	-	-	SYM
ejpam-5445	51	17	3435	3435	NUM
ejpam-5445	51	18	3417	3417	NUM
ejpam-5445	51	19	higher	high	ADJ
ejpam-5445	51	20	-	-	PUNCT
ejpam-5445	51	21	order	order	NOUN
ejpam-5445	51	22	terms	term	NOUN
ejpam-5445	51	23	in	in	ADP
ejpam-5445	51	24	a	a	DET
ejpam-5445	51	25	differential	differential	ADJ
ejpam-5445	51	26	equation	equation	NOUN
ejpam-5445	51	27	might	might	AUX
ejpam-5445	51	28	not	not	PART
ejpam-5445	51	29	always	always	ADV
ejpam-5445	51	30	have	have	VERB
ejpam-5445	51	31	clear	clear	ADJ
ejpam-5445	51	32	physical	physical	ADJ
ejpam-5445	51	33	meanings	meaning	NOUN
ejpam-5445	51	34	,	,	PUNCT
ejpam-5445	51	35	making	make	VERB
ejpam-5445	51	36	it	it	PRON
ejpam-5445	51	37	harder	hard	ADV
ejpam-5445	51	38	to	to	PART
ejpam-5445	51	39	interpret	interpret	VERB
ejpam-5445	51	40	the	the	DET
ejpam-5445	51	41	behavior	behavior	NOUN
ejpam-5445	51	42	of	of	ADP
ejpam-5445	51	43	the	the	DET
ejpam-5445	51	44	system	system	NOUN
ejpam-5445	51	45	.	.	PUNCT
ejpam-5445	52	1	in	in	ADP
ejpam-5445	52	2	some	some	DET
ejpam-5445	52	3	cases	case	NOUN
ejpam-5445	52	4	,	,	PUNCT
ejpam-5445	52	5	it	it	PRON
ejpam-5445	52	6	may	may	AUX
ejpam-5445	52	7	not	not	PART
ejpam-5445	52	8	be	be	AUX
ejpam-5445	52	9	guaranteed	guarantee	VERB
ejpam-5445	52	10	that	that	SCONJ
ejpam-5445	52	11	a	a	DET
ejpam-5445	52	12	solution	solution	NOUN
ejpam-5445	52	13	exists	exist	VERB
ejpam-5445	52	14	or	or	CCONJ
ejpam-5445	52	15	is	be	AUX
ejpam-5445	52	16	unique	unique	ADJ
ejpam-5445	52	17	,	,	PUNCT
ejpam-5445	52	18	especially	especially	ADV
ejpam-5445	52	19	for	for	ADP
ejpam-5445	52	20	non	non	ADJ
ejpam-5445	52	21	-	-	ADJ
ejpam-5445	52	22	linear	linear	ADJ
ejpam-5445	52	23	fourthorder	fourthorder	NOUN
ejpam-5445	52	24	equations	equation	NOUN
ejpam-5445	52	25	or	or	CCONJ
ejpam-5445	52	26	equations	equation	NOUN
ejpam-5445	52	27	with	with	ADP
ejpam-5445	52	28	unusual	unusual	ADJ
ejpam-5445	52	29	boundary	boundary	ADJ
ejpam-5445	52	30	conditions	condition	NOUN
ejpam-5445	52	31	.	.	PUNCT
ejpam-5445	53	1	analytical	analytical	ADJ
ejpam-5445	53	2	methods	method	NOUN
ejpam-5445	53	3	,	,	PUNCT
ejpam-5445	53	4	in	in	ADP
ejpam-5445	53	5	particular	particular	ADJ
ejpam-5445	53	6	,	,	PUNCT
ejpam-5445	53	7	may	may	AUX
ejpam-5445	53	8	fail	fail	VERB
ejpam-5445	53	9	to	to	PART
ejpam-5445	53	10	provide	provide	VERB
ejpam-5445	53	11	a	a	DET
ejpam-5445	53	12	solution	solution	NOUN
ejpam-5445	53	13	in	in	ADP
ejpam-5445	53	14	such	such	ADJ
ejpam-5445	53	15	cases	case	NOUN
ejpam-5445	53	16	.	.	PUNCT
ejpam-5445	54	1	while	while	SCONJ
ejpam-5445	54	2	the	the	DET
ejpam-5445	54	3	equation	equation	NOUN
ejpam-5445	54	4	is	be	AUX
ejpam-5445	54	5	linear	linear	ADJ
ejpam-5445	54	6	,	,	PUNCT
ejpam-5445	54	7	realworld	realworld	PROPN
ejpam-5445	54	8	problems	problem	NOUN
ejpam-5445	54	9	often	often	ADV
ejpam-5445	54	10	involve	involve	VERB
ejpam-5445	54	11	non	non	NOUN
ejpam-5445	54	12	-	-	NOUN
ejpam-5445	54	13	linearities	linearity	NOUN
ejpam-5445	54	14	.	.	PUNCT
ejpam-5445	55	1	extending	extend	VERB
ejpam-5445	55	2	methods	method	NOUN
ejpam-5445	55	3	for	for	ADP
ejpam-5445	55	4	linear	linear	PROPN
ejpam-5445	55	5	equations	equation	NOUN
ejpam-5445	55	6	to	to	PART
ejpam-5445	55	7	nonlinear	nonlinear	VERB
ejpam-5445	55	8	fourth	fourth	ADJ
ejpam-5445	55	9	-	-	PUNCT
ejpam-5445	55	10	order	order	NOUN
ejpam-5445	55	11	differential	differential	ADJ
ejpam-5445	55	12	equations	equation	NOUN
ejpam-5445	55	13	introduces	introduce	VERB
ejpam-5445	55	14	significant	significant	ADJ
ejpam-5445	55	15	complications	complication	NOUN
ejpam-5445	55	16	,	,	PUNCT
ejpam-5445	55	17	as	as	SCONJ
ejpam-5445	55	18	many	many	ADJ
ejpam-5445	55	19	techniques	technique	NOUN
ejpam-5445	55	20	for	for	ADP
ejpam-5445	55	21	linear	linear	PROPN
ejpam-5445	55	22	equations	equation	NOUN
ejpam-5445	55	23	do	do	AUX
ejpam-5445	55	24	not	not	PART
ejpam-5445	55	25	directly	directly	ADV
ejpam-5445	55	26	apply	apply	VERB
ejpam-5445	55	27	.	.	PUNCT
ejpam-5445	56	1	for	for	ADP
ejpam-5445	56	2	instance	instance	NOUN
ejpam-5445	56	3	,	,	PUNCT
ejpam-5445	56	4	farhan	farhan	PROPN
ejpam-5445	57	1	[	[	X
ejpam-5445	57	2	10	10	NUM
ejpam-5445	57	3	]	]	PUNCT
ejpam-5445	57	4	studied	study	VERB
ejpam-5445	57	5	the	the	DET
ejpam-5445	57	6	implementation	implementation	NOUN
ejpam-5445	57	7	of	of	ADP
ejpam-5445	57	8	the	the	DET
ejpam-5445	57	9	one	one	NUM
ejpam-5445	57	10	-	-	PUNCT
ejpam-5445	57	11	step	step	NOUN
ejpam-5445	57	12	one	one	NUM
ejpam-5445	57	13	-	-	PUNCT
ejpam-5445	57	14	hybrid	hybrid	ADJ
ejpam-5445	57	15	block	block	NOUN
ejpam-5445	57	16	method	method	NOUN
ejpam-5445	57	17	on	on	ADP
ejpam-5445	57	18	the	the	DET
ejpam-5445	57	19	nonlinear	nonlinear	ADJ
ejpam-5445	57	20	equation	equation	NOUN
ejpam-5445	57	21	.	.	PUNCT
ejpam-5445	58	1	while	while	SCONJ
ejpam-5445	58	2	these	these	DET
ejpam-5445	58	3	methods	method	NOUN
ejpam-5445	58	4	aim	aim	VERB
ejpam-5445	58	5	to	to	PART
ejpam-5445	58	6	provide	provide	VERB
ejpam-5445	58	7	more	more	ADV
ejpam-5445	58	8	efficient	efficient	ADJ
ejpam-5445	58	9	solutions	solution	NOUN
ejpam-5445	58	10	,	,	PUNCT
ejpam-5445	58	11	they	they	PRON
ejpam-5445	58	12	are	be	AUX
ejpam-5445	58	13	sensitive	sensitive	ADJ
ejpam-5445	58	14	to	to	ADP
ejpam-5445	58	15	the	the	DET
ejpam-5445	58	16	formulation	formulation	NOUN
ejpam-5445	58	17	of	of	ADP
ejpam-5445	58	18	boundary	boundary	ADJ
ejpam-5445	58	19	conditions	condition	NOUN
ejpam-5445	58	20	and	and	CCONJ
ejpam-5445	58	21	may	may	AUX
ejpam-5445	58	22	encounter	encounter	VERB
ejpam-5445	58	23	difficulties	difficulty	NOUN
ejpam-5445	58	24	in	in	ADP
ejpam-5445	58	25	ensuring	ensure	VERB
ejpam-5445	58	26	stability	stability	NOUN
ejpam-5445	58	27	and	and	CCONJ
ejpam-5445	58	28	convergence	convergence	NOUN
ejpam-5445	58	29	.	.	PUNCT
ejpam-5445	59	1	this	this	PRON
ejpam-5445	59	2	highlights	highlight	VERB
ejpam-5445	59	3	the	the	DET
ejpam-5445	59	4	limitation	limitation	NOUN
ejpam-5445	59	5	of	of	ADP
ejpam-5445	59	6	standard	standard	ADJ
ejpam-5445	59	7	linear	linear	ADJ
ejpam-5445	59	8	methods	method	NOUN
ejpam-5445	59	9	when	when	SCONJ
ejpam-5445	59	10	extended	extend	VERB
ejpam-5445	59	11	to	to	ADP
ejpam-5445	59	12	nonlinear	nonlinear	ADJ
ejpam-5445	59	13	systems	system	NOUN
ejpam-5445	59	14	,	,	PUNCT
ejpam-5445	59	15	as	as	SCONJ
ejpam-5445	59	16	additional	additional	ADJ
ejpam-5445	59	17	strategies	strategy	NOUN
ejpam-5445	59	18	must	must	AUX
ejpam-5445	59	19	be	be	AUX
ejpam-5445	59	20	employed	employ	VERB
ejpam-5445	59	21	to	to	PART
ejpam-5445	59	22	deal	deal	VERB
ejpam-5445	59	23	with	with	ADP
ejpam-5445	59	24	nonlinearity	nonlinearity	NOUN
ejpam-5445	59	25	and	and	CCONJ
ejpam-5445	59	26	complex	complex	ADJ
ejpam-5445	59	27	geometrical	geometrical	ADJ
ejpam-5445	59	28	configurations	configuration	NOUN
ejpam-5445	59	29	.	.	PUNCT
ejpam-5445	60	1	in	in	ADP
ejpam-5445	60	2	fluid	fluid	ADJ
ejpam-5445	60	3	mechanics	mechanic	NOUN
ejpam-5445	60	4	,	,	PUNCT
ejpam-5445	60	5	basha	basha	PROPN
ejpam-5445	61	1	[	[	X
ejpam-5445	61	2	6	6	NUM
ejpam-5445	61	3	]	]	PUNCT
ejpam-5445	61	4	and	and	CCONJ
ejpam-5445	61	5	shelly	shelly	PROPN
ejpam-5445	61	6	arora	arora	PROPN
ejpam-5445	62	1	[	[	X
ejpam-5445	62	2	5	5	NUM
ejpam-5445	62	3	]	]	PUNCT
ejpam-5445	62	4	investigated	investigate	VERB
ejpam-5445	62	5	the	the	DET
ejpam-5445	62	6	higher	high	ADJ
ejpam-5445	62	7	-	-	PUNCT
ejpam-5445	62	8	order	order	NOUN
ejpam-5445	62	9	differential	differential	ADJ
ejpam-5445	62	10	equations	equation	NOUN
ejpam-5445	62	11	govern	govern	VERB
ejpam-5445	62	12	the	the	DET
ejpam-5445	62	13	behavior	behavior	NOUN
ejpam-5445	62	14	of	of	ADP
ejpam-5445	62	15	non	non	ADJ
ejpam-5445	62	16	-	-	ADJ
ejpam-5445	62	17	newtonian	newtonian	ADJ
ejpam-5445	62	18	fluids	fluid	NOUN
ejpam-5445	62	19	and	and	CCONJ
ejpam-5445	62	20	their	their	PRON
ejpam-5445	62	21	heat	heat	NOUN
ejpam-5445	62	22	transfer	transfer	NOUN
ejpam-5445	62	23	properties	property	NOUN
ejpam-5445	62	24	.	.	PUNCT
ejpam-5445	63	1	the	the	DET
ejpam-5445	63	2	nonlinear	nonlinear	ADJ
ejpam-5445	63	3	expansion	expansion	NOUN
ejpam-5445	63	4	of	of	ADP
ejpam-5445	63	5	the	the	DET
ejpam-5445	63	6	sheet	sheet	NOUN
ejpam-5445	63	7	and	and	CCONJ
ejpam-5445	63	8	the	the	DET
ejpam-5445	63	9	specific	specific	ADJ
ejpam-5445	63	10	boundary	boundary	ADJ
ejpam-5445	63	11	conditions	condition	NOUN
ejpam-5445	63	12	introduce	introduce	VERB
ejpam-5445	63	13	further	further	ADJ
ejpam-5445	63	14	complexity	complexity	NOUN
ejpam-5445	63	15	,	,	PUNCT
ejpam-5445	63	16	requiring	require	VERB
ejpam-5445	63	17	specialized	specialized	ADJ
ejpam-5445	63	18	numerical	numerical	ADJ
ejpam-5445	63	19	methods	method	NOUN
ejpam-5445	63	20	.	.	PUNCT
ejpam-5445	64	1	this	this	DET
ejpam-5445	64	2	method	method	NOUN
ejpam-5445	64	3	provides	provide	VERB
ejpam-5445	64	4	excellent	excellent	ADJ
ejpam-5445	64	5	super	super	ADJ
ejpam-5445	64	6	convergence	convergence	NOUN
ejpam-5445	64	7	properties	property	NOUN
ejpam-5445	64	8	,	,	PUNCT
ejpam-5445	64	9	its	its	PRON
ejpam-5445	64	10	application	application	NOUN
ejpam-5445	64	11	to	to	ADP
ejpam-5445	64	12	highly	highly	ADV
ejpam-5445	64	13	nonlinear	nonlinear	ADJ
ejpam-5445	64	14	systems	system	NOUN
ejpam-5445	64	15	reveal	reveal	VERB
ejpam-5445	64	16	limitations	limitation	NOUN
ejpam-5445	64	17	in	in	ADP
ejpam-5445	64	18	classical	classical	ADJ
ejpam-5445	64	19	linear	linear	ADJ
ejpam-5445	64	20	differential	differential	NOUN
ejpam-5445	64	21	equation	equation	NOUN
ejpam-5445	64	22	methods	method	NOUN
ejpam-5445	64	23	.	.	PUNCT
ejpam-5445	65	1	specifically	specifically	ADV
ejpam-5445	65	2	,	,	PUNCT
ejpam-5445	65	3	the	the	DET
ejpam-5445	65	4	wave	wave	NOUN
ejpam-5445	65	5	behavior	behavior	NOUN
ejpam-5445	65	6	and	and	CCONJ
ejpam-5445	65	7	chaotic	chaotic	ADJ
ejpam-5445	65	8	nature	nature	NOUN
ejpam-5445	65	9	of	of	ADP
ejpam-5445	65	10	the	the	DET
ejpam-5445	65	11	kuramoto	kuramoto	NOUN
ejpam-5445	65	12	-	-	PUNCT
ejpam-5445	65	13	shivashinsky	shivashinsky	NOUN
ejpam-5445	65	14	equation	equation	NOUN
ejpam-5445	65	15	push	push	VERB
ejpam-5445	65	16	traditional	traditional	ADJ
ejpam-5445	65	17	numerical	numerical	ADJ
ejpam-5445	65	18	methods	method	NOUN
ejpam-5445	65	19	to	to	ADP
ejpam-5445	65	20	their	their	PRON
ejpam-5445	65	21	limits	limit	NOUN
ejpam-5445	65	22	,	,	PUNCT
ejpam-5445	65	23	often	often	ADV
ejpam-5445	65	24	requiring	require	VERB
ejpam-5445	65	25	adaptive	adaptive	ADJ
ejpam-5445	65	26	meshes	mesh	NOUN
ejpam-5445	65	27	or	or	CCONJ
ejpam-5445	65	28	hybrid	hybrid	NOUN
ejpam-5445	65	29	approaches	approach	NOUN
ejpam-5445	65	30	to	to	PART
ejpam-5445	65	31	maintain	maintain	VERB
ejpam-5445	65	32	accuracy	accuracy	NOUN
ejpam-5445	65	33	and	and	CCONJ
ejpam-5445	65	34	computational	computational	ADJ
ejpam-5445	65	35	efficiency	efficiency	NOUN
ejpam-5445	65	36	.	.	PUNCT
ejpam-5445	66	1	in	in	ADP
ejpam-5445	66	2	the	the	DET
ejpam-5445	66	3	context	context	NOUN
ejpam-5445	66	4	of	of	ADP
ejpam-5445	66	5	the	the	DET
ejpam-5445	66	6	one	one	NUM
ejpam-5445	66	7	-	-	PUNCT
ejpam-5445	66	8	step	step	NOUN
ejpam-5445	66	9	one	one	NUM
ejpam-5445	66	10	-	-	PUNCT
ejpam-5445	66	11	hybrid	hybrid	ADJ
ejpam-5445	66	12	block	block	NOUN
ejpam-5445	66	13	method	method	NOUN
ejpam-5445	66	14	on	on	ADP
ejpam-5445	66	15	the	the	DET
ejpam-5445	66	16	nonlinear	nonlinear	ADJ
ejpam-5445	66	17	equation	equation	NOUN
ejpam-5445	66	18	and	and	CCONJ
ejpam-5445	66	19	the	the	DET
ejpam-5445	66	20	introduction	introduction	NOUN
ejpam-5445	66	21	of	of	ADP
ejpam-5445	66	22	hyers	hyers	PROPN
ejpam-5445	66	23	-	-	PUNCT
ejpam-5445	66	24	ulam	ulam	PROPN
ejpam-5445	66	25	stability	stability	NOUN
ejpam-5445	66	26	provides	provide	VERB
ejpam-5445	66	27	a	a	DET
ejpam-5445	66	28	novel	novel	ADJ
ejpam-5445	66	29	way	way	NOUN
ejpam-5445	66	30	to	to	PART
ejpam-5445	66	31	verify	verify	VERB
ejpam-5445	66	32	whether	whether	SCONJ
ejpam-5445	66	33	the	the	DET
ejpam-5445	66	34	numerical	numerical	ADJ
ejpam-5445	66	35	methods	method	NOUN
ejpam-5445	66	36	employed	employ	VERB
ejpam-5445	66	37	are	be	AUX
ejpam-5445	66	38	capable	capable	ADJ
ejpam-5445	66	39	of	of	ADP
ejpam-5445	66	40	maintaining	maintain	VERB
ejpam-5445	66	41	solution	solution	NOUN
ejpam-5445	66	42	stability	stability	NOUN
ejpam-5445	66	43	despite	despite	SCONJ
ejpam-5445	66	44	perturbations	perturbation	NOUN
ejpam-5445	66	45	in	in	ADP
ejpam-5445	66	46	initial	initial	ADJ
ejpam-5445	66	47	or	or	CCONJ
ejpam-5445	66	48	boundary	boundary	ADJ
ejpam-5445	66	49	data	datum	NOUN
ejpam-5445	66	50	.	.	PUNCT
ejpam-5445	67	1	the	the	DET
ejpam-5445	67	2	hyers	hyers	PROPN
ejpam-5445	67	3	-	-	PUNCT
ejpam-5445	67	4	ulam	ulam	PROPN
ejpam-5445	67	5	framework	framework	NOUN
ejpam-5445	67	6	allows	allow	VERB
ejpam-5445	67	7	for	for	ADP
ejpam-5445	67	8	the	the	DET
ejpam-5445	67	9	quantification	quantification	NOUN
ejpam-5445	67	10	of	of	ADP
ejpam-5445	67	11	stability	stability	NOUN
ejpam-5445	67	12	in	in	ADP
ejpam-5445	67	13	cases	case	NOUN
ejpam-5445	67	14	where	where	SCONJ
ejpam-5445	67	15	small	small	ADJ
ejpam-5445	67	16	errors	error	NOUN
ejpam-5445	67	17	in	in	ADP
ejpam-5445	67	18	modeling	model	VERB
ejpam-5445	67	19	the	the	DET
ejpam-5445	67	20	oscillator	oscillator	NOUN
ejpam-5445	67	21	geometry	geometry	NOUN
ejpam-5445	67	22	(	(	PUNCT
ejpam-5445	67	23	e.g.	e.g.	ADV
ejpam-5445	67	24	,	,	PUNCT
ejpam-5445	67	25	boundary	boundary	ADJ
ejpam-5445	67	26	conditions	condition	NOUN
ejpam-5445	67	27	of	of	ADP
ejpam-5445	67	28	the	the	DET
ejpam-5445	67	29	circular	circular	ADJ
ejpam-5445	67	30	sector	sector	NOUN
ejpam-5445	67	31	)	)	PUNCT
ejpam-5445	67	32	could	could	AUX
ejpam-5445	67	33	lead	lead	VERB
ejpam-5445	67	34	to	to	ADP
ejpam-5445	67	35	significant	significant	ADJ
ejpam-5445	67	36	deviations	deviation	NOUN
ejpam-5445	67	37	in	in	ADP
ejpam-5445	67	38	the	the	DET
ejpam-5445	67	39	oscillatory	oscillatory	ADJ
ejpam-5445	67	40	motion	motion	NOUN
ejpam-5445	67	41	.	.	PUNCT
ejpam-5445	68	1	thus	thus	ADV
ejpam-5445	68	2	,	,	PUNCT
ejpam-5445	68	3	incorporating	incorporate	VERB
ejpam-5445	68	4	hyers	hyer	NOUN
ejpam-5445	68	5	-	-	PUNCT
ejpam-5445	68	6	ulam	ulam	PROPN
ejpam-5445	68	7	stability	stability	NOUN
ejpam-5445	68	8	into	into	ADP
ejpam-5445	68	9	the	the	DET
ejpam-5445	68	10	block	block	NOUN
ejpam-5445	68	11	method	method	NOUN
ejpam-5445	68	12	enhances	enhance	VERB
ejpam-5445	68	13	the	the	DET
ejpam-5445	68	14	understanding	understanding	NOUN
ejpam-5445	68	15	of	of	ADP
ejpam-5445	68	16	the	the	DET
ejpam-5445	68	17	method	method	NOUN
ejpam-5445	68	18	’s	’s	PART
ejpam-5445	68	19	robustness	robustness	NOUN
ejpam-5445	68	20	and	and	CCONJ
ejpam-5445	68	21	ensures	ensure	VERB
ejpam-5445	68	22	that	that	SCONJ
ejpam-5445	68	23	solutions	solution	NOUN
ejpam-5445	68	24	remain	remain	VERB
ejpam-5445	68	25	bounded	bounded	ADJ
ejpam-5445	68	26	even	even	ADV
ejpam-5445	68	27	in	in	ADP
ejpam-5445	68	28	the	the	DET
ejpam-5445	68	29	face	face	NOUN
ejpam-5445	68	30	of	of	ADP
ejpam-5445	68	31	minor	minor	ADJ
ejpam-5445	68	32	perturbations	perturbation	NOUN
ejpam-5445	68	33	.	.	PUNCT
ejpam-5445	69	1	thekuramoto	thekuramoto	ADJ
ejpam-5445	69	2	-	-	PUNCT
ejpam-5445	69	3	shivashinsky	shivashinsky	NOUN
ejpam-5445	69	4	equation	equation	NOUN
ejpam-5445	69	5	,	,	PUNCT
ejpam-5445	69	6	with	with	ADP
ejpam-5445	69	7	its	its	PRON
ejpam-5445	69	8	chaotic	chaotic	ADJ
ejpam-5445	69	9	and	and	CCONJ
ejpam-5445	69	10	wave	wave	NOUN
ejpam-5445	69	11	-	-	PUNCT
ejpam-5445	69	12	like	like	ADJ
ejpam-5445	69	13	behavior	behavior	NOUN
ejpam-5445	69	14	,	,	PUNCT
ejpam-5445	69	15	presents	present	VERB
ejpam-5445	69	16	substantial	substantial	ADJ
ejpam-5445	69	17	challenges	challenge	NOUN
ejpam-5445	69	18	when	when	SCONJ
ejpam-5445	69	19	using	use	VERB
ejpam-5445	69	20	traditional	traditional	ADJ
ejpam-5445	69	21	fourth	fourth	ADJ
ejpam-5445	69	22	-	-	PUNCT
ejpam-5445	69	23	order	order	NOUN
ejpam-5445	69	24	linear	linear	ADJ
ejpam-5445	69	25	differential	differential	NOUN
ejpam-5445	69	26	methods	method	NOUN
ejpam-5445	69	27	.	.	PUNCT
ejpam-5445	70	1	the	the	DET
ejpam-5445	70	2	super	super	ADJ
ejpam-5445	70	3	convergence	convergence	NOUN
ejpam-5445	70	4	analysis	analysis	NOUN
ejpam-5445	70	5	of	of	ADP
ejpam-5445	70	6	fully	fully	ADV
ejpam-5445	70	7	discrete	discrete	ADJ
ejpam-5445	70	8	hermite	hermite	ADJ
ejpam-5445	70	9	splines	spline	NOUN
ejpam-5445	70	10	is	be	AUX
ejpam-5445	70	11	already	already	ADV
ejpam-5445	70	12	a	a	DET
ejpam-5445	70	13	sophisticated	sophisticated	ADJ
ejpam-5445	70	14	method	method	NOUN
ejpam-5445	70	15	to	to	PART
ejpam-5445	70	16	address	address	VERB
ejpam-5445	70	17	this	this	PRON
ejpam-5445	70	18	.	.	PUNCT
ejpam-5445	71	1	however	however	ADV
ejpam-5445	71	2	,	,	PUNCT
ejpam-5445	71	3	the	the	DET
ejpam-5445	71	4	application	application	NOUN
ejpam-5445	71	5	of	of	ADP
ejpam-5445	71	6	hyers	hyers	PROPN
ejpam-5445	71	7	-	-	PUNCT
ejpam-5445	71	8	ulam	ulam	PROPN
ejpam-5445	71	9	stability	stability	NOUN
ejpam-5445	71	10	introduces	introduce	VERB
ejpam-5445	71	11	an	an	DET
ejpam-5445	71	12	additional	additional	ADJ
ejpam-5445	71	13	layer	layer	NOUN
ejpam-5445	71	14	of	of	ADP
ejpam-5445	71	15	novelty	novelty	NOUN
ejpam-5445	71	16	by	by	ADP
ejpam-5445	71	17	ensuring	ensure	VERB
ejpam-5445	71	18	that	that	SCONJ
ejpam-5445	71	19	the	the	DET
ejpam-5445	71	20	solutions	solution	NOUN
ejpam-5445	71	21	obtained	obtain	VERB
ejpam-5445	71	22	remain	remain	VERB
ejpam-5445	71	23	stable	stable	ADJ
ejpam-5445	71	24	under	under	ADP
ejpam-5445	71	25	perturbations	perturbation	NOUN
ejpam-5445	71	26	,	,	PUNCT
ejpam-5445	71	27	which	which	PRON
ejpam-5445	71	28	is	be	AUX
ejpam-5445	71	29	crucial	crucial	ADJ
ejpam-5445	71	30	for	for	ADP
ejpam-5445	71	31	chaotic	chaotic	ADJ
ejpam-5445	71	32	systems	system	NOUN
ejpam-5445	71	33	.	.	PUNCT
ejpam-5445	72	1	small	small	ADJ
ejpam-5445	72	2	inaccuracies	inaccuracy	NOUN
ejpam-5445	72	3	in	in	ADP
ejpam-5445	72	4	initial	initial	ADJ
ejpam-5445	72	5	conditions	condition	NOUN
ejpam-5445	72	6	or	or	CCONJ
ejpam-5445	72	7	computational	computational	ADJ
ejpam-5445	72	8	errors	error	NOUN
ejpam-5445	72	9	could	could	AUX
ejpam-5445	72	10	rapidly	rapidly	ADV
ejpam-5445	72	11	escalate	escalate	VERB
ejpam-5445	72	12	into	into	ADP
ejpam-5445	72	13	significant	significant	ADJ
ejpam-5445	72	14	deviations	deviation	NOUN
ejpam-5445	72	15	in	in	ADP
ejpam-5445	72	16	the	the	DET
ejpam-5445	72	17	wave	wave	NOUN
ejpam-5445	72	18	dynamics	dynamic	NOUN
ejpam-5445	72	19	.	.	PUNCT
ejpam-5445	73	1	with	with	ADP
ejpam-5445	73	2	hyers	hyers	PROPN
ejpam-5445	73	3	-	-	PUNCT
ejpam-5445	73	4	ulam	ulam	PROPN
ejpam-5445	73	5	stability	stability	NOUN
ejpam-5445	73	6	,	,	PUNCT
ejpam-5445	73	7	researchers	researcher	NOUN
ejpam-5445	73	8	can	can	AUX
ejpam-5445	73	9	provide	provide	VERB
ejpam-5445	73	10	stronger	strong	ADJ
ejpam-5445	73	11	guarantees	guarantee	NOUN
ejpam-5445	73	12	that	that	SCONJ
ejpam-5445	73	13	the	the	DET
ejpam-5445	73	14	numerical	numerical	ADJ
ejpam-5445	73	15	approximations	approximation	NOUN
ejpam-5445	73	16	made	make	VERB
ejpam-5445	73	17	using	use	VERB
ejpam-5445	73	18	fully	fully	ADV
ejpam-5445	73	19	discrete	discrete	ADJ
ejpam-5445	73	20	hermite	hermite	ADJ
ejpam-5445	73	21	splines	spline	NOUN
ejpam-5445	73	22	remain	remain	VERB
ejpam-5445	73	23	valid	valid	ADJ
ejpam-5445	73	24	and	and	CCONJ
ejpam-5445	73	25	bounded	bound	VERB
ejpam-5445	73	26	,	,	PUNCT
ejpam-5445	73	27	offering	offer	VERB
ejpam-5445	73	28	greater	great	ADJ
ejpam-5445	73	29	confidence	confidence	NOUN
ejpam-5445	73	30	in	in	ADP
ejpam-5445	73	31	the	the	DET
ejpam-5445	73	32	accuracy	accuracy	NOUN
ejpam-5445	73	33	and	and	CCONJ
ejpam-5445	73	34	applicability	applicability	NOUN
ejpam-5445	73	35	of	of	ADP
ejpam-5445	73	36	these	these	DET
ejpam-5445	73	37	methods	method	NOUN
ejpam-5445	73	38	for	for	ADP
ejpam-5445	73	39	simulating	simulate	VERB
ejpam-5445	73	40	complex	complex	ADJ
ejpam-5445	73	41	wave	wave	NOUN
ejpam-5445	73	42	behavior	behavior	NOUN
ejpam-5445	73	43	.	.	PUNCT
ejpam-5445	74	1	the	the	DET
ejpam-5445	74	2	integration	integration	NOUN
ejpam-5445	74	3	of	of	ADP
ejpam-5445	74	4	hyers	hyers	PROPN
ejpam-5445	74	5	-	-	PUNCT
ejpam-5445	74	6	ulam	ulam	PROPN
ejpam-5445	74	7	stability	stability	NOUN
ejpam-5445	74	8	into	into	ADP
ejpam-5445	74	9	the	the	DET
ejpam-5445	74	10	study	study	NOUN
ejpam-5445	74	11	of	of	ADP
ejpam-5445	74	12	fourth	fourth	ADJ
ejpam-5445	74	13	-	-	PUNCT
ejpam-5445	74	14	order	order	NOUN
ejpam-5445	74	15	linear	linear	PROPN
ejpam-5445	74	16	differential	differential	PROPN
ejpam-5445	74	17	s.	s.	PROPN
ejpam-5445	74	18	bowmiya	bowmiya	PROPN
ejpam-5445	74	19	et	et	PROPN
ejpam-5445	74	20	al	al	PROPN
ejpam-5445	74	21	.	.	PUNCT
ejpam-5445	74	22	/	/	SYM
ejpam-5445	74	23	eur	eur	PROPN
ejpam-5445	74	24	.	.	PUNCT
ejpam-5445	75	1	j.	j.	PROPN
ejpam-5445	75	2	pure	pure	PROPN
ejpam-5445	75	3	appl	appl	PROPN
ejpam-5445	75	4	.	.	PROPN
ejpam-5445	75	5	math	math	PROPN
ejpam-5445	75	6	,	,	PUNCT
ejpam-5445	75	7	17	17	NUM
ejpam-5445	75	8	(	(	PUNCT
ejpam-5445	75	9	4	4	NUM
ejpam-5445	75	10	)	)	PUNCT
ejpam-5445	75	11	(	(	PUNCT
ejpam-5445	75	12	2024	2024	NUM
ejpam-5445	75	13	)	)	PUNCT
ejpam-5445	75	14	,	,	PUNCT
ejpam-5445	75	15	3415	3415	NUM
ejpam-5445	75	16	-	-	SYM
ejpam-5445	75	17	3435	3435	NUM
ejpam-5445	75	18	3418	3418	NUM
ejpam-5445	75	19	equations	equation	NOUN
ejpam-5445	75	20	represents	represent	VERB
ejpam-5445	75	21	a	a	DET
ejpam-5445	75	22	novel	novel	ADJ
ejpam-5445	75	23	contribution	contribution	NOUN
ejpam-5445	75	24	to	to	ADP
ejpam-5445	75	25	the	the	DET
ejpam-5445	75	26	field	field	NOUN
ejpam-5445	75	27	.	.	PUNCT
ejpam-5445	76	1	traditional	traditional	ADJ
ejpam-5445	76	2	stability	stability	NOUN
ejpam-5445	76	3	analyses	analysis	NOUN
ejpam-5445	76	4	often	often	ADV
ejpam-5445	76	5	focus	focus	VERB
ejpam-5445	76	6	on	on	ADP
ejpam-5445	76	7	whether	whether	SCONJ
ejpam-5445	76	8	solutions	solution	NOUN
ejpam-5445	76	9	remain	remain	VERB
ejpam-5445	76	10	bounded	bounded	ADJ
ejpam-5445	76	11	based	base	VERB
ejpam-5445	76	12	on	on	ADP
ejpam-5445	76	13	specific	specific	ADJ
ejpam-5445	76	14	methods	method	NOUN
ejpam-5445	76	15	,	,	PUNCT
ejpam-5445	76	16	but	but	CCONJ
ejpam-5445	76	17	they	they	PRON
ejpam-5445	76	18	do	do	AUX
ejpam-5445	76	19	not	not	PART
ejpam-5445	76	20	typically	typically	ADV
ejpam-5445	76	21	address	address	VERB
ejpam-5445	76	22	how	how	SCONJ
ejpam-5445	76	23	sensitive	sensitive	ADJ
ejpam-5445	76	24	the	the	DET
ejpam-5445	76	25	solutions	solution	NOUN
ejpam-5445	76	26	are	be	AUX
ejpam-5445	76	27	to	to	ADP
ejpam-5445	76	28	small	small	ADJ
ejpam-5445	76	29	perturbations	perturbation	NOUN
ejpam-5445	76	30	in	in	ADP
ejpam-5445	76	31	initial	initial	ADJ
ejpam-5445	76	32	or	or	CCONJ
ejpam-5445	76	33	boundary	boundary	ADJ
ejpam-5445	76	34	data	datum	NOUN
ejpam-5445	76	35	.	.	PUNCT
ejpam-5445	77	1	by	by	ADP
ejpam-5445	77	2	applying	apply	VERB
ejpam-5445	77	3	hyers	hyer	NOUN
ejpam-5445	77	4	-	-	PUNCT
ejpam-5445	77	5	ulam	ulam	PROPN
ejpam-5445	77	6	stability	stability	NOUN
ejpam-5445	77	7	,	,	PUNCT
ejpam-5445	77	8	this	this	DET
ejpam-5445	77	9	study	study	NOUN
ejpam-5445	77	10	provides	provide	VERB
ejpam-5445	77	11	a	a	DET
ejpam-5445	77	12	quantitative	quantitative	ADJ
ejpam-5445	77	13	measure	measure	NOUN
ejpam-5445	77	14	of	of	ADP
ejpam-5445	77	15	how	how	SCONJ
ejpam-5445	77	16	solutions	solution	NOUN
ejpam-5445	77	17	to	to	ADP
ejpam-5445	77	18	fourth	fourth	ADJ
ejpam-5445	77	19	-	-	PUNCT
ejpam-5445	77	20	order	order	NOUN
ejpam-5445	77	21	linear	linear	PROPN
ejpam-5445	77	22	differential	differential	NOUN
ejpam-5445	77	23	equations	equation	NOUN
ejpam-5445	77	24	respond	respond	VERB
ejpam-5445	77	25	to	to	ADP
ejpam-5445	77	26	small	small	ADJ
ejpam-5445	77	27	deviations	deviation	NOUN
ejpam-5445	77	28	in	in	ADP
ejpam-5445	77	29	data	datum	NOUN
ejpam-5445	77	30	or	or	CCONJ
ejpam-5445	77	31	boundary	boundary	ADJ
ejpam-5445	77	32	conditions	condition	NOUN
ejpam-5445	77	33	.	.	PUNCT
ejpam-5445	78	1	this	this	DET
ejpam-5445	78	2	robustness	robustness	NOUN
ejpam-5445	78	3	measure	measure	NOUN
ejpam-5445	78	4	is	be	AUX
ejpam-5445	78	5	particularly	particularly	ADV
ejpam-5445	78	6	important	important	ADJ
ejpam-5445	78	7	for	for	ADP
ejpam-5445	78	8	real	real	ADJ
ejpam-5445	78	9	-	-	PUNCT
ejpam-5445	78	10	world	world	NOUN
ejpam-5445	78	11	applications	application	NOUN
ejpam-5445	78	12	,	,	PUNCT
ejpam-5445	78	13	where	where	SCONJ
ejpam-5445	78	14	exact	exact	ADJ
ejpam-5445	78	15	data	datum	NOUN
ejpam-5445	78	16	is	be	AUX
ejpam-5445	78	17	rarely	rarely	ADV
ejpam-5445	78	18	available	available	ADJ
ejpam-5445	78	19	,	,	PUNCT
ejpam-5445	78	20	and	and	CCONJ
ejpam-5445	78	21	errors	error	NOUN
ejpam-5445	78	22	in	in	ADP
ejpam-5445	78	23	modeling	modeling	NOUN
ejpam-5445	78	24	are	be	AUX
ejpam-5445	78	25	inevitable.fourth	inevitable.fourth	NOUN
ejpam-5445	78	26	-	-	PUNCT
ejpam-5445	78	27	order	order	NOUN
ejpam-5445	78	28	linear	linear	PROPN
ejpam-5445	78	29	differential	differential	NOUN
ejpam-5445	78	30	equations	equation	NOUN
ejpam-5445	78	31	are	be	AUX
ejpam-5445	78	32	often	often	ADV
ejpam-5445	78	33	applied	apply	VERB
ejpam-5445	78	34	in	in	ADP
ejpam-5445	78	35	fields	field	NOUN
ejpam-5445	78	36	that	that	PRON
ejpam-5445	78	37	require	require	VERB
ejpam-5445	78	38	precise	precise	ADJ
ejpam-5445	78	39	boundary	boundary	ADJ
ejpam-5445	78	40	conditions	condition	NOUN
ejpam-5445	78	41	,	,	PUNCT
ejpam-5445	78	42	such	such	ADJ
ejpam-5445	78	43	as	as	ADP
ejpam-5445	78	44	beam	beam	NOUN
ejpam-5445	78	45	theory	theory	NOUN
ejpam-5445	78	46	,	,	PUNCT
ejpam-5445	78	47	fluid	fluid	ADJ
ejpam-5445	78	48	dynamics	dynamic	NOUN
ejpam-5445	78	49	,	,	PUNCT
ejpam-5445	78	50	and	and	CCONJ
ejpam-5445	78	51	elasticity	elasticity	NOUN
ejpam-5445	78	52	theory	theory	NOUN
ejpam-5445	78	53	.	.	PUNCT
ejpam-5445	79	1	hyers	hyer	NOUN
ejpam-5445	79	2	-	-	PUNCT
ejpam-5445	79	3	ulam	ulam	PROPN
ejpam-5445	79	4	stability	stability	NOUN
ejpam-5445	79	5	expands	expand	VERB
ejpam-5445	79	6	the	the	DET
ejpam-5445	79	7	applicability	applicability	NOUN
ejpam-5445	79	8	of	of	ADP
ejpam-5445	79	9	these	these	DET
ejpam-5445	79	10	equations	equation	NOUN
ejpam-5445	79	11	by	by	ADP
ejpam-5445	79	12	ensuring	ensure	VERB
ejpam-5445	79	13	that	that	SCONJ
ejpam-5445	79	14	even	even	ADV
ejpam-5445	79	15	in	in	ADP
ejpam-5445	79	16	the	the	DET
ejpam-5445	79	17	presence	presence	NOUN
ejpam-5445	79	18	of	of	ADP
ejpam-5445	79	19	small	small	ADJ
ejpam-5445	79	20	uncertainties	uncertainty	NOUN
ejpam-5445	79	21	or	or	CCONJ
ejpam-5445	79	22	numerical	numerical	ADJ
ejpam-5445	79	23	errors	error	NOUN
ejpam-5445	79	24	,	,	PUNCT
ejpam-5445	79	25	solutions	solution	NOUN
ejpam-5445	79	26	remain	remain	VERB
ejpam-5445	79	27	within	within	ADP
ejpam-5445	79	28	acceptable	acceptable	ADJ
ejpam-5445	79	29	bounds.by	bounds.by	PROPN
ejpam-5445	79	30	integrating	integrate	VERB
ejpam-5445	79	31	hyers	hyers	PROPN
ejpam-5445	79	32	-	-	PUNCT
ejpam-5445	79	33	ulam	ulam	PROPN
ejpam-5445	79	34	stability	stability	NOUN
ejpam-5445	79	35	into	into	ADP
ejpam-5445	79	36	methods	method	NOUN
ejpam-5445	79	37	such	such	ADJ
ejpam-5445	79	38	as	as	ADP
ejpam-5445	79	39	the	the	DET
ejpam-5445	79	40	one	one	NUM
ejpam-5445	79	41	-	-	PUNCT
ejpam-5445	79	42	step	step	NOUN
ejpam-5445	79	43	one	one	NUM
ejpam-5445	79	44	-	-	PUNCT
ejpam-5445	79	45	hybrid	hybrid	ADJ
ejpam-5445	79	46	block	block	NOUN
ejpam-5445	79	47	method	method	NOUN
ejpam-5445	79	48	or	or	CCONJ
ejpam-5445	79	49	hermite	hermite	ADJ
ejpam-5445	79	50	splines	spline	NOUN
ejpam-5445	79	51	,	,	PUNCT
ejpam-5445	79	52	this	this	DET
ejpam-5445	79	53	study	study	NOUN
ejpam-5445	79	54	enhances	enhance	VERB
ejpam-5445	79	55	the	the	DET
ejpam-5445	79	56	reliability	reliability	NOUN
ejpam-5445	79	57	of	of	ADP
ejpam-5445	79	58	these	these	DET
ejpam-5445	79	59	numerical	numerical	ADJ
ejpam-5445	79	60	techniques	technique	NOUN
ejpam-5445	79	61	.	.	PUNCT
ejpam-5445	80	1	while	while	SCONJ
ejpam-5445	80	2	traditional	traditional	ADJ
ejpam-5445	80	3	numerical	numerical	ADJ
ejpam-5445	80	4	methods	method	NOUN
ejpam-5445	80	5	focus	focus	VERB
ejpam-5445	80	6	on	on	ADP
ejpam-5445	80	7	accuracy	accuracy	NOUN
ejpam-5445	80	8	and	and	CCONJ
ejpam-5445	80	9	convergence	convergence	NOUN
ejpam-5445	80	10	,	,	PUNCT
ejpam-5445	80	11	hyers	hyers	PROPN
ejpam-5445	80	12	-	-	PUNCT
ejpam-5445	80	13	ulam	ulam	PROPN
ejpam-5445	80	14	stability	stability	NOUN
ejpam-5445	80	15	ensures	ensure	VERB
ejpam-5445	80	16	that	that	SCONJ
ejpam-5445	80	17	the	the	DET
ejpam-5445	80	18	solutions	solution	NOUN
ejpam-5445	80	19	generated	generate	VERB
ejpam-5445	80	20	by	by	ADP
ejpam-5445	80	21	these	these	DET
ejpam-5445	80	22	methods	method	NOUN
ejpam-5445	80	23	are	be	AUX
ejpam-5445	80	24	not	not	PART
ejpam-5445	80	25	overly	overly	ADV
ejpam-5445	80	26	sensitive	sensitive	ADJ
ejpam-5445	80	27	to	to	ADP
ejpam-5445	80	28	perturbations	perturbation	NOUN
ejpam-5445	80	29	,	,	PUNCT
ejpam-5445	80	30	thus	thus	ADV
ejpam-5445	80	31	offering	offer	VERB
ejpam-5445	80	32	a	a	DET
ejpam-5445	80	33	more	more	ADV
ejpam-5445	80	34	robust	robust	ADJ
ejpam-5445	80	35	framework	framework	NOUN
ejpam-5445	80	36	for	for	ADP
ejpam-5445	80	37	practical	practical	ADJ
ejpam-5445	80	38	applications	application	NOUN
ejpam-5445	80	39	.	.	PUNCT
ejpam-5445	81	1	the	the	DET
ejpam-5445	81	2	novelty	novelty	NOUN
ejpam-5445	81	3	of	of	ADP
ejpam-5445	81	4	applying	apply	VERB
ejpam-5445	81	5	hyers	hyer	NOUN
ejpam-5445	81	6	-	-	PUNCT
ejpam-5445	81	7	ulam	ulam	PROPN
ejpam-5445	81	8	stability	stability	NOUN
ejpam-5445	81	9	to	to	ADP
ejpam-5445	81	10	nonlinear	nonlinear	ADJ
ejpam-5445	81	11	problems	problem	NOUN
ejpam-5445	81	12	,	,	PUNCT
ejpam-5445	81	13	such	such	ADJ
ejpam-5445	81	14	as	as	ADP
ejpam-5445	81	15	those	those	PRON
ejpam-5445	81	16	encountered	encounter	VERB
ejpam-5445	81	17	in	in	ADP
ejpam-5445	81	18	the	the	DET
ejpam-5445	81	19	sutterby	sutterby	NOUN
ejpam-5445	81	20	hybrid	hybrid	PROPN
ejpam-5445	81	21	nanofluid	nanofluid	PROPN
ejpam-5445	81	22	flow	flow	NOUN
ejpam-5445	81	23	or	or	CCONJ
ejpam-5445	81	24	the	the	DET
ejpam-5445	81	25	kuramoto	kuramoto	NOUN
ejpam-5445	81	26	-	-	PUNCT
ejpam-5445	81	27	shivashinsky	shivashinsky	NOUN
ejpam-5445	81	28	equation	equation	NOUN
ejpam-5445	81	29	,	,	PUNCT
ejpam-5445	81	30	lies	lie	VERB
ejpam-5445	81	31	in	in	ADP
ejpam-5445	81	32	its	its	PRON
ejpam-5445	81	33	ability	ability	NOUN
ejpam-5445	81	34	to	to	PART
ejpam-5445	81	35	provide	provide	VERB
ejpam-5445	81	36	stability	stability	NOUN
ejpam-5445	81	37	guarantees	guarantee	NOUN
ejpam-5445	81	38	in	in	ADP
ejpam-5445	81	39	cases	case	NOUN
ejpam-5445	81	40	where	where	SCONJ
ejpam-5445	81	41	linear	linear	ADJ
ejpam-5445	81	42	methods	method	NOUN
ejpam-5445	81	43	struggle	struggle	VERB
ejpam-5445	81	44	.	.	PUNCT
ejpam-5445	82	1	nonlinear	nonlinear	ADJ
ejpam-5445	82	2	systems	system	NOUN
ejpam-5445	82	3	are	be	AUX
ejpam-5445	82	4	notoriously	notoriously	ADV
ejpam-5445	82	5	sensitive	sensitive	ADJ
ejpam-5445	82	6	to	to	ADP
ejpam-5445	82	7	perturbations	perturbation	NOUN
ejpam-5445	82	8	,	,	PUNCT
ejpam-5445	82	9	and	and	CCONJ
ejpam-5445	82	10	the	the	DET
ejpam-5445	82	11	hyers	hyers	PROPN
ejpam-5445	82	12	-	-	PUNCT
ejpam-5445	82	13	ulam	ulam	PROPN
ejpam-5445	82	14	framework	framework	NOUN
ejpam-5445	82	15	provides	provide	VERB
ejpam-5445	82	16	a	a	DET
ejpam-5445	82	17	new	new	ADJ
ejpam-5445	82	18	tool	tool	NOUN
ejpam-5445	82	19	to	to	PART
ejpam-5445	82	20	ensure	ensure	VERB
ejpam-5445	82	21	that	that	SCONJ
ejpam-5445	82	22	solutions	solution	NOUN
ejpam-5445	82	23	remain	remain	VERB
ejpam-5445	82	24	bounded	bounded	ADJ
ejpam-5445	82	25	and	and	CCONJ
ejpam-5445	82	26	reliable	reliable	ADJ
ejpam-5445	82	27	.	.	PUNCT
ejpam-5445	83	1	in	in	ADP
ejpam-5445	83	2	this	this	DET
ejpam-5445	83	3	paper	paper	NOUN
ejpam-5445	83	4	,	,	PUNCT
ejpam-5445	83	5	we	we	PRON
ejpam-5445	83	6	demonstrate	demonstrate	VERB
ejpam-5445	83	7	the	the	DET
ejpam-5445	83	8	hyers	hyer	NOUN
ejpam-5445	83	9	ulam	ulam	PROPN
ejpam-5445	83	10	stability	stability	NOUN
ejpam-5445	83	11	of	of	ADP
ejpam-5445	83	12	linear	linear	PROPN
ejpam-5445	83	13	differential	differential	ADJ
ejpam-5445	83	14	equation	equation	NOUN
ejpam-5445	83	15	of	of	ADP
ejpam-5445	83	16	fourth	fourth	ADJ
ejpam-5445	83	17	order	order	NOUN
ejpam-5445	83	18	.	.	PUNCT
ejpam-5445	84	1	that	that	PRON
ejpam-5445	84	2	is	is	ADV
ejpam-5445	84	3	,	,	PUNCT
ejpam-5445	84	4	γ	γ	X
ejpam-5445	84	5	is	be	AUX
ejpam-5445	84	6	an	an	DET
ejpam-5445	84	7	interact	interact	ADJ
ejpam-5445	84	8	arrangement	arrangement	NOUN
ejpam-5445	84	9	of	of	ADP
ejpam-5445	84	10	the	the	DET
ejpam-5445	84	11	differential	differential	ADJ
ejpam-5445	84	12	equation	equation	NOUN
ejpam-5445	84	13	γiv(ω	γiv(ω	PROPN
ejpam-5445	84	14	)	)	PUNCT
ejpam-5445	85	1	+	+	CCONJ
ejpam-5445	85	2	ρ1γ	ρ1γ	PROPN
ejpam-5445	85	3	′′′(ω	′′′(ω	PROPN
ejpam-5445	85	4	)	)	PUNCT
ejpam-5445	86	1	+	+	PROPN
ejpam-5445	86	2	ρ2γ	ρ2γ	PROPN
ejpam-5445	86	3	′′(ω	′′(ω	NOUN
ejpam-5445	86	4	)	)	PUNCT
ejpam-5445	87	1	+	+	CCONJ
ejpam-5445	87	2	ρ3γ	ρ3γ	NUM
ejpam-5445	87	3	′(ω	′(ω	NOUN
ejpam-5445	87	4	)	)	PUNCT
ejpam-5445	87	5	+	+	X
ejpam-5445	87	6	ρ4γ(ω	ρ4γ(ω	ADJ
ejpam-5445	87	7	)	)	PUNCT
ejpam-5445	87	8	=	=	SYM
ejpam-5445	87	9	χ(ω	χ(ω	NOUN
ejpam-5445	87	10	)	)	PUNCT
ejpam-5445	87	11	where	where	SCONJ
ejpam-5445	87	12	γ	γ	PROPN
ejpam-5445	87	13	∈	∈	PROPN
ejpam-5445	87	14	c4[α	c4[α	NOUN
ejpam-5445	87	15	,	,	PUNCT
ejpam-5445	87	16	β	β	X
ejpam-5445	87	17	]	]	X
ejpam-5445	87	18	,	,	PUNCT
ejpam-5445	87	19	χ	χ	PROPN
ejpam-5445	87	20	∈	∈	PROPN
ejpam-5445	88	1	[	[	X
ejpam-5445	88	2	α	α	X
ejpam-5445	88	3	,	,	PUNCT
ejpam-5445	88	4	β	β	X
ejpam-5445	88	5	]	]	X
ejpam-5445	88	6	,	,	PUNCT
ejpam-5445	88	7	we	we	PRON
ejpam-5445	88	8	demonstrate	demonstrate	VERB
ejpam-5445	88	9	that	that	SCONJ
ejpam-5445	88	10	γiv(ω)+ρ1γ	γiv(ω)+ρ1γ	ADJ
ejpam-5445	88	11	′′′(ω)+ρ2γ	′′′(ω)+ρ2γ	NOUN
ejpam-5445	88	12	′′(ω)+ρ3γ	′′(ω)+ρ3γ	NOUN
ejpam-5445	88	13	′(ω)+	′(ω)+	PRON
ejpam-5445	88	14	ρ4γ(ω	ρ4γ(ω	ADJ
ejpam-5445	88	15	)	)	PUNCT
ejpam-5445	88	16	=	=	SYM
ejpam-5445	88	17	χ(ω	χ(ω	NOUN
ejpam-5445	88	18	)	)	PUNCT
ejpam-5445	88	19	has	have	VERB
ejpam-5445	88	20	the	the	DET
ejpam-5445	88	21	hyers	hyer	NOUN
ejpam-5445	88	22	ulam	ulam	PROPN
ejpam-5445	88	23	stability	stability	PROPN
ejpam-5445	88	24	.	.	PUNCT
ejpam-5445	89	1	an	an	DET
ejpam-5445	89	2	example	example	NOUN
ejpam-5445	89	3	is	be	AUX
ejpam-5445	89	4	provided	provide	VERB
ejpam-5445	89	5	to	to	PART
ejpam-5445	89	6	illustrate	illustrate	VERB
ejpam-5445	89	7	the	the	DET
ejpam-5445	89	8	theory	theory	NOUN
ejpam-5445	89	9	.	.	PUNCT
ejpam-5445	90	1	moreover	moreover	ADV
ejpam-5445	90	2	,	,	PUNCT
ejpam-5445	90	3	the	the	DET
ejpam-5445	90	4	after	after	ADP
ejpam-5445	90	5	effect	effect	NOUN
ejpam-5445	90	6	of	of	ADP
ejpam-5445	90	7	h	h	NOUN
ejpam-5445	90	8	−	−	PROPN
ejpam-5445	90	9	u	u	NOUN
ejpam-5445	90	10	stability	stability	NOUN
ejpam-5445	90	11	for	for	ADP
ejpam-5445	90	12	first	first	ADJ
ejpam-5445	90	13	order	order	NOUN
ejpam-5445	90	14	differential	differential	NOUN
ejpam-5445	90	15	conditions	condition	NOUN
ejpam-5445	90	16	has	have	AUX
ejpam-5445	90	17	been	be	AUX
ejpam-5445	90	18	summed	sum	VERB
ejpam-5445	90	19	up	up	ADP
ejpam-5445	90	20	by	by	ADP
ejpam-5445	90	21	miara	miara	PROPN
ejpam-5445	90	22	,	,	PUNCT
ejpam-5445	90	23	miyajima	miyajima	PROPN
ejpam-5445	90	24	and	and	CCONJ
ejpam-5445	90	25	takahasi	takahasi	PROPN
ejpam-5445	91	1	[	[	X
ejpam-5445	91	2	17	17	NUM
ejpam-5445	91	3	]	]	PUNCT
ejpam-5445	91	4	by	by	ADP
ejpam-5445	91	5	takahasi	takahasi	PROPN
ejpam-5445	91	6	,	,	PUNCT
ejpam-5445	91	7	takagi	takagi	NOUN
ejpam-5445	91	8	,	,	PUNCT
ejpam-5445	91	9	miara	miara	NOUN
ejpam-5445	91	10	and	and	CCONJ
ejpam-5445	91	11	miyajima	miyajima	PROPN
ejpam-5445	92	1	[	[	X
ejpam-5445	92	2	8	8	NUM
ejpam-5445	92	3	]	]	PUNCT
ejpam-5445	92	4	,	,	PUNCT
ejpam-5445	92	5	and	and	CCONJ
ejpam-5445	92	6	furthermore	furthermore	ADV
ejpam-5445	92	7	by	by	ADP
ejpam-5445	92	8	jung	jung	NOUN
ejpam-5445	93	1	[	[	X
ejpam-5445	93	2	13	13	NUM
ejpam-5445	93	3	]	]	PUNCT
ejpam-5445	93	4	.	.	PUNCT
ejpam-5445	94	1	they	they	PRON
ejpam-5445	94	2	managed	manage	VERB
ejpam-5445	94	3	the	the	DET
ejpam-5445	94	4	non	non	ADJ
ejpam-5445	94	5	homogeneous	homogeneous	ADJ
ejpam-5445	94	6	straight	straight	ADJ
ejpam-5445	94	7	differential	differential	ADJ
ejpam-5445	94	8	equation	equation	NOUN
ejpam-5445	94	9	of	of	ADP
ejpam-5445	94	10	first	first	ADJ
ejpam-5445	94	11	order	order	NOUN
ejpam-5445	94	12	γ′	γ′	PROPN
ejpam-5445	95	1	+	+	NUM
ejpam-5445	95	2	ρ(τ)γ	ρ(τ)γ	PROPN
ejpam-5445	95	3	+	+	CCONJ
ejpam-5445	95	4	σ(τ	σ(τ	PROPN
ejpam-5445	95	5	)	)	PUNCT
ejpam-5445	96	1	=	=	SYM
ejpam-5445	96	2	0	0	X
ejpam-5445	96	3	.	.	PUNCT
ejpam-5445	97	1	(	(	PUNCT
ejpam-5445	97	2	1	1	X
ejpam-5445	97	3	)	)	PUNCT
ejpam-5445	97	4	jung	jung	NOUN
ejpam-5445	98	1	[	[	X
ejpam-5445	98	2	13	13	NUM
ejpam-5445	98	3	]	]	PUNCT
ejpam-5445	98	4	demonstrated	demonstrate	VERB
ejpam-5445	98	5	the	the	DET
ejpam-5445	98	6	summed	sum	VERB
ejpam-5445	98	7	up	up	ADP
ejpam-5445	98	8	h	h	NOUN
ejpam-5445	98	9	−	−	PROPN
ejpam-5445	98	10	u	u	NOUN
ejpam-5445	98	11	stability	stability	NOUN
ejpam-5445	98	12	of	of	ADP
ejpam-5445	98	13	differential	differential	ADJ
ejpam-5445	98	14	condition	condition	NOUN
ejpam-5445	98	15	of	of	ADP
ejpam-5445	98	16	the	the	DET
ejpam-5445	98	17	structure	structure	NOUN
ejpam-5445	98	18	τγ′(τ	τγ′(τ	ADV
ejpam-5445	98	19	)	)	PUNCT
ejpam-5445	98	20	=	=	SYM
ejpam-5445	98	21	αγ(τ	αγ(τ	X
ejpam-5445	98	22	)	)	PUNCT
ejpam-5445	98	23	+	+	CCONJ
ejpam-5445	98	24	βτγω0	βτγω0	PUNCT
ejpam-5445	99	1	=	=	SYM
ejpam-5445	99	2	0	0	PUNCT
ejpam-5445	99	3	and	and	CCONJ
ejpam-5445	99	4	furthermore	furthermore	ADV
ejpam-5445	99	5	applied	apply	VERB
ejpam-5445	99	6	this	this	PRON
ejpam-5445	99	7	out	out	ADP
ejpam-5445	99	8	come	come	VERB
ejpam-5445	99	9	to	to	ADP
ejpam-5445	99	10	the	the	DET
ejpam-5445	99	11	examination	examination	NOUN
ejpam-5445	99	12	of	of	ADP
ejpam-5445	99	13	the	the	DET
ejpam-5445	99	14	h	h	NOUN
ejpam-5445	100	1	−	−	PROPN
ejpam-5445	100	2	u	u	NOUN
ejpam-5445	100	3	stability	stability	NOUN
ejpam-5445	100	4	of	of	ADP
ejpam-5445	100	5	the	the	DET
ejpam-5445	100	6	differential	differential	ADJ
ejpam-5445	100	7	equation	equation	NOUN
ejpam-5445	100	8	τ2γ′′(τ	τ2γ′′(τ	NOUN
ejpam-5445	100	9	)	)	PUNCT
ejpam-5445	101	1	+	+	SYM
ejpam-5445	101	2	aτγ′(τ	aτγ′(τ	X
ejpam-5445	101	3	)	)	PUNCT
ejpam-5445	102	1	+	+	NUM
ejpam-5445	102	2	bγ(τ	bγ(τ	NOUN
ejpam-5445	102	3	)	)	PUNCT
ejpam-5445	102	4	=	=	SYM
ejpam-5445	102	5	0	0	X
ejpam-5445	102	6	.	.	PUNCT
ejpam-5445	102	7	(	(	PUNCT
ejpam-5445	102	8	2	2	X
ejpam-5445	102	9	)	)	PUNCT
ejpam-5445	102	10	s.	s.	PROPN
ejpam-5445	102	11	bowmiya	bowmiya	PROPN
ejpam-5445	102	12	et	et	PROPN
ejpam-5445	102	13	al	al	PROPN
ejpam-5445	102	14	.	.	PUNCT
ejpam-5445	102	15	/	/	SYM
ejpam-5445	102	16	eur	eur	PROPN
ejpam-5445	102	17	.	.	PUNCT
ejpam-5445	103	1	j.	j.	PROPN
ejpam-5445	103	2	pure	pure	PROPN
ejpam-5445	103	3	appl	appl	PROPN
ejpam-5445	103	4	.	.	PROPN
ejpam-5445	103	5	math	math	PROPN
ejpam-5445	103	6	,	,	PUNCT
ejpam-5445	103	7	17	17	NUM
ejpam-5445	103	8	(	(	PUNCT
ejpam-5445	103	9	4	4	NUM
ejpam-5445	103	10	)	)	PUNCT
ejpam-5445	103	11	(	(	PUNCT
ejpam-5445	103	12	2024	2024	NUM
ejpam-5445	103	13	)	)	PUNCT
ejpam-5445	103	14	,	,	PUNCT
ejpam-5445	103	15	3415	3415	NUM
ejpam-5445	103	16	-	-	SYM
ejpam-5445	103	17	3435	3435	NUM
ejpam-5445	103	18	3419	3419	NUM
ejpam-5445	103	19	as	as	ADP
ejpam-5445	103	20	of	of	ADP
ejpam-5445	103	21	late	late	ADJ
ejpam-5445	103	22	,	,	PUNCT
ejpam-5445	103	23	wang	wang	PROPN
ejpam-5445	103	24	,	,	PUNCT
ejpam-5445	103	25	zhon	zhon	NOUN
ejpam-5445	103	26	and	and	CCONJ
ejpam-5445	103	27	sun	sun	NOUN
ejpam-5445	103	28	[	[	X
ejpam-5445	103	29	19	19	NUM
ejpam-5445	103	30	]	]	PUNCT
ejpam-5445	103	31	examined	examine	VERB
ejpam-5445	103	32	the	the	DET
ejpam-5445	103	33	h−u	h−u	NOUN
ejpam-5445	103	34	stability	stability	NOUN
ejpam-5445	103	35	of	of	ADP
ejpam-5445	103	36	the	the	DET
ejpam-5445	103	37	first	first	ADJ
ejpam-5445	103	38	order	order	NOUN
ejpam-5445	103	39	linear	linear	NOUN
ejpam-5445	103	40	differential	differential	NOUN
ejpam-5445	103	41	condition	condition	NOUN
ejpam-5445	103	42	ρ(ω)γ′	ρ(ω)γ′	PROPN
ejpam-5445	104	1	+	+	CCONJ
ejpam-5445	104	2	σ(ω)γ	σ(ω)γ	NOUN
ejpam-5445	104	3	+	+	CCONJ
ejpam-5445	104	4	η(ω	η(ω	NOUN
ejpam-5445	104	5	)	)	PUNCT
ejpam-5445	104	6	=	=	SYM
ejpam-5445	105	1	0	0	X
ejpam-5445	105	2	.	.	PUNCT
ejpam-5445	106	1	(	(	PUNCT
ejpam-5445	106	2	3	3	X
ejpam-5445	106	3	)	)	PUNCT
ejpam-5445	106	4	as	as	ADP
ejpam-5445	106	5	a	a	DET
ejpam-5445	106	6	matter	matter	NOUN
ejpam-5445	106	7	of	of	ADP
ejpam-5445	106	8	first	first	ADJ
ejpam-5445	106	9	importance	importance	NOUN
ejpam-5445	106	10	,	,	PUNCT
ejpam-5445	106	11	we	we	PRON
ejpam-5445	106	12	give	give	VERB
ejpam-5445	106	13	the	the	DET
ejpam-5445	106	14	meaning	meaning	NOUN
ejpam-5445	106	15	of	of	ADP
ejpam-5445	106	16	the	the	DET
ejpam-5445	106	17	h	h	NOUN
ejpam-5445	107	1	−	−	PROPN
ejpam-5445	107	2	u	u	PROPN
ejpam-5445	107	3	stability	stability	NOUN
ejpam-5445	107	4	.	.	PUNCT
ejpam-5445	108	1	definition	definition	NOUN
ejpam-5445	108	2	1	1	NUM
ejpam-5445	108	3	.	.	PUNCT
ejpam-5445	109	1	we	we	PRON
ejpam-5445	109	2	say	say	VERB
ejpam-5445	109	3	that	that	SCONJ
ejpam-5445	109	4	equation	equation	NOUN
ejpam-5445	109	5	2	2	NUM
ejpam-5445	109	6	has	have	VERB
ejpam-5445	109	7	the	the	DET
ejpam-5445	109	8	h	h	NOUN
ejpam-5445	109	9	−	−	PROPN
ejpam-5445	109	10	u	u	NOUN
ejpam-5445	109	11	stability	stability	NOUN
ejpam-5445	109	12	if	if	SCONJ
ejpam-5445	109	13	there	there	PRON
ejpam-5445	109	14	exists	exist	VERB
ejpam-5445	109	15	a	a	DET
ejpam-5445	109	16	steady	steady	ADJ
ejpam-5445	109	17	κ	κ	X
ejpam-5445	109	18	>	>	X
ejpam-5445	109	19	0	0	PUNCT
ejpam-5445	109	20	with	with	ADP
ejpam-5445	109	21	accompanying	accompany	VERB
ejpam-5445	109	22	property	property	NOUN
ejpam-5445	109	23	,	,	PUNCT
ejpam-5445	109	24	for	for	ADP
ejpam-5445	109	25	every	every	DET
ejpam-5445	109	26	∈	∈	PROPN
ejpam-5445	109	27	>	>	X
ejpam-5445	109	28	0	0	PROPN
ejpam-5445	109	29	,	,	PUNCT
ejpam-5445	109	30	γ	γ	PROPN
ejpam-5445	109	31	∈	∈	PROPN
ejpam-5445	109	32	c2[α	c2[α	PROPN
ejpam-5445	109	33	,	,	PUNCT
ejpam-5445	109	34	β	β	X
ejpam-5445	109	35	]	]	X
ejpam-5445	109	36	,	,	PUNCT
ejpam-5445	109	37	if	if	SCONJ
ejpam-5445	109	38	|γ′′	|γ′′	PUNCT
ejpam-5445	109	39	+	+	NUM
ejpam-5445	109	40	aγ′	aγ′	NOUN
ejpam-5445	109	41	+	+	CCONJ
ejpam-5445	109	42	bγ|	bγ|	PROPN
ejpam-5445	109	43	≤∈	≤∈	NOUN
ejpam-5445	109	44	,	,	PUNCT
ejpam-5445	109	45	(	(	PUNCT
ejpam-5445	109	46	4	4	NUM
ejpam-5445	109	47	)	)	PUNCT
ejpam-5445	109	48	at	at	ADP
ejpam-5445	109	49	the	the	DET
ejpam-5445	109	50	point	point	NOUN
ejpam-5445	109	51	there	there	PRON
ejpam-5445	109	52	exists	exist	VERB
ejpam-5445	109	53	some	some	DET
ejpam-5445	109	54	u	u	PROPN
ejpam-5445	109	55	∈	∈	PROPN
ejpam-5445	109	56	c2[α	c2[α	PROPN
ejpam-5445	109	57	,	,	PUNCT
ejpam-5445	109	58	β	β	AUX
ejpam-5445	109	59	]	]	X
ejpam-5445	109	60	fulfilling	fulfil	VERB
ejpam-5445	109	61	|u′′	|u′′	PROPN
ejpam-5445	110	1	+	+	SYM
ejpam-5445	110	2	au′	au′	PROPN
ejpam-5445	110	3	+	+	CCONJ
ejpam-5445	110	4	bu|	bu|	PROPN
ejpam-5445	110	5	≤	≤	ADJ
ejpam-5445	110	6	χ(ω	χ(ω	NOUN
ejpam-5445	110	7	)	)	PUNCT
ejpam-5445	110	8	(	(	PUNCT
ejpam-5445	110	9	5	5	X
ejpam-5445	110	10	)	)	PUNCT
ejpam-5445	110	11	such	such	ADJ
ejpam-5445	110	12	that	that	DET
ejpam-5445	110	13	|γ(ω)−	|γ(ω)−	NOUN
ejpam-5445	111	1	u(ω)|	u(ω)|	INTJ
ejpam-5445	111	2	<	<	X
ejpam-5445	111	3	κ	κ	ADP
ejpam-5445	111	4	∈.	∈.	PROPN
ejpam-5445	111	5	we	we	PRON
ejpam-5445	111	6	call	call	VERB
ejpam-5445	111	7	such	such	ADJ
ejpam-5445	111	8	κ	κ	ADP
ejpam-5445	111	9	a	a	DET
ejpam-5445	111	10	h	h	NOUN
ejpam-5445	112	1	−	−	PROPN
ejpam-5445	113	1	u	u	NOUN
ejpam-5445	113	2	stability	stability	NOUN
ejpam-5445	113	3	constant	constant	ADJ
ejpam-5445	113	4	for	for	ADP
ejpam-5445	113	5	equation	equation	NOUN
ejpam-5445	113	6	2	2	NUM
ejpam-5445	113	7	.	.	PUNCT
ejpam-5445	114	1	definition	definition	NOUN
ejpam-5445	114	2	2	2	NUM
ejpam-5445	114	3	.	.	PUNCT
ejpam-5445	115	1	we	we	PRON
ejpam-5445	115	2	say	say	VERB
ejpam-5445	115	3	that	that	SCONJ
ejpam-5445	115	4	equation	equation	NOUN
ejpam-5445	115	5	2	2	NUM
ejpam-5445	115	6	extend	extend	NOUN
ejpam-5445	115	7	has	have	VERB
ejpam-5445	115	8	the	the	DET
ejpam-5445	115	9	h	h	NOUN
ejpam-5445	115	10	−	−	PROPN
ejpam-5445	115	11	u	u	NOUN
ejpam-5445	115	12	stability	stability	NOUN
ejpam-5445	115	13	,	,	PUNCT
ejpam-5445	115	14	if	if	SCONJ
ejpam-5445	115	15	there	there	PRON
ejpam-5445	115	16	exists	exist	VERB
ejpam-5445	115	17	a	a	DET
ejpam-5445	115	18	steady	steady	ADJ
ejpam-5445	115	19	κ	κ	X
ejpam-5445	115	20	>	>	X
ejpam-5445	115	21	0	0	PUNCT
ejpam-5445	115	22	with	with	ADP
ejpam-5445	115	23	accompanying	accompany	VERB
ejpam-5445	115	24	property	property	NOUN
ejpam-5445	115	25	:	:	PUNCT
ejpam-5445	115	26	for	for	ADP
ejpam-5445	115	27	every	every	DET
ejpam-5445	115	28	∈	∈	PROPN
ejpam-5445	115	29	>	>	X
ejpam-5445	115	30	0	0	PROPN
ejpam-5445	115	31	,	,	PUNCT
ejpam-5445	115	32	γ	γ	PROPN
ejpam-5445	115	33	∈	∈	PROPN
ejpam-5445	115	34	c3[α	c3[α	PROPN
ejpam-5445	115	35	,	,	PUNCT
ejpam-5445	115	36	β	β	X
ejpam-5445	115	37	]	]	X
ejpam-5445	115	38	,	,	PUNCT
ejpam-5445	115	39	if	if	SCONJ
ejpam-5445	115	40	|γ′′′	|γ′′′	PROPN
ejpam-5445	115	41	+	+	CCONJ
ejpam-5445	115	42	aγ′′	aγ′′	NOUN
ejpam-5445	115	43	+	+	NUM
ejpam-5445	115	44	bγ′	bγ′	ADJ
ejpam-5445	115	45	+	+	CCONJ
ejpam-5445	115	46	cγ|	cγ|	NOUN
ejpam-5445	115	47	≤∈	≤∈	NOUN
ejpam-5445	115	48	,	,	PUNCT
ejpam-5445	115	49	(	(	PUNCT
ejpam-5445	115	50	6	6	NUM
ejpam-5445	115	51	)	)	PUNCT
ejpam-5445	115	52	at	at	ADP
ejpam-5445	115	53	the	the	DET
ejpam-5445	115	54	point	point	NOUN
ejpam-5445	115	55	there	there	PRON
ejpam-5445	115	56	exists	exist	VERB
ejpam-5445	115	57	some	some	DET
ejpam-5445	115	58	u	u	PROPN
ejpam-5445	115	59	∈	∈	PROPN
ejpam-5445	115	60	c3[α	c3[α	PROPN
ejpam-5445	115	61	,	,	PUNCT
ejpam-5445	115	62	β	β	X
ejpam-5445	115	63	]	]	X
ejpam-5445	115	64	fulfilling	fulfil	VERB
ejpam-5445	115	65	|u′′′	|u′′′	PROPN
ejpam-5445	115	66	+	+	NUM
ejpam-5445	115	67	au′′	au′′	PROPN
ejpam-5445	116	1	+	+	CCONJ
ejpam-5445	116	2	bu′	bu′	ADV
ejpam-5445	117	1	+	+	CCONJ
ejpam-5445	117	2	cu|	cu|	NOUN
ejpam-5445	117	3	=	=	SYM
ejpam-5445	117	4	0	0	PUNCT
ejpam-5445	117	5	(	(	PUNCT
ejpam-5445	117	6	7	7	NUM
ejpam-5445	117	7	)	)	PUNCT
ejpam-5445	117	8	such	such	ADJ
ejpam-5445	117	9	that	that	DET
ejpam-5445	117	10	|γ(ω)−	|γ(ω)−	NOUN
ejpam-5445	117	11	u(ω)|	u(ω)|	INTJ
ejpam-5445	117	12	<	<	X
ejpam-5445	117	13	κ	κ	ADP
ejpam-5445	117	14	∈.	∈.	PROPN
ejpam-5445	117	15	we	we	PRON
ejpam-5445	117	16	call	call	VERB
ejpam-5445	117	17	such	such	ADJ
ejpam-5445	117	18	κ	κ	ADP
ejpam-5445	117	19	a	a	DET
ejpam-5445	117	20	h	h	NOUN
ejpam-5445	118	1	−u	−u	PROPN
ejpam-5445	118	2	stability	stability	NOUN
ejpam-5445	118	3	constant	constant	ADJ
ejpam-5445	118	4	for	for	ADP
ejpam-5445	118	5	equation	equation	NOUN
ejpam-5445	118	6	6	6	NUM
ejpam-5445	118	7	.	.	PUNCT
ejpam-5445	119	1	definition	definition	NOUN
ejpam-5445	119	2	3	3	NUM
ejpam-5445	119	3	.	.	PUNCT
ejpam-5445	120	1	we	we	PRON
ejpam-5445	120	2	say	say	VERB
ejpam-5445	120	3	that	that	SCONJ
ejpam-5445	120	4	equation	equation	NOUN
ejpam-5445	120	5	6	6	NUM
ejpam-5445	120	6	extend	extend	NOUN
ejpam-5445	120	7	has	have	VERB
ejpam-5445	120	8	the	the	DET
ejpam-5445	120	9	h	h	NOUN
ejpam-5445	120	10	−	−	PROPN
ejpam-5445	120	11	u	u	NOUN
ejpam-5445	120	12	stability	stability	NOUN
ejpam-5445	120	13	,	,	PUNCT
ejpam-5445	120	14	if	if	SCONJ
ejpam-5445	120	15	there	there	PRON
ejpam-5445	120	16	exists	exist	VERB
ejpam-5445	120	17	a	a	DET
ejpam-5445	120	18	steady	steady	ADJ
ejpam-5445	120	19	κ	κ	X
ejpam-5445	120	20	>	>	X
ejpam-5445	120	21	0	0	PUNCT
ejpam-5445	120	22	with	with	ADP
ejpam-5445	120	23	accompanying	accompany	VERB
ejpam-5445	120	24	property	property	NOUN
ejpam-5445	120	25	:	:	PUNCT
ejpam-5445	120	26	for	for	SCONJ
ejpam-5445	120	27	every	every	DET
ejpam-5445	120	28	∈	∈	PROPN
ejpam-5445	120	29	>	>	X
ejpam-5445	120	30	0	0	PROPN
ejpam-5445	120	31	,	,	PUNCT
ejpam-5445	120	32	γ	γ	PROPN
ejpam-5445	120	33	∈	∈	PROPN
ejpam-5445	120	34	c4[α	c4[α	NOUN
ejpam-5445	120	35	,	,	PUNCT
ejpam-5445	120	36	β	β	X
ejpam-5445	120	37	]	]	X
ejpam-5445	120	38	,	,	PUNCT
ejpam-5445	120	39	if	if	SCONJ
ejpam-5445	120	40	|γiv	|γiv	PROPN
ejpam-5445	120	41	+	+	CCONJ
ejpam-5445	120	42	ρ1γ	ρ1γ	ADJ
ejpam-5445	120	43	′′′	′′′	VERB
ejpam-5445	121	1	+	+	CCONJ
ejpam-5445	121	2	ρ2γ	ρ2γ	X
ejpam-5445	121	3	′′	′′	NOUN
ejpam-5445	121	4	+	+	CCONJ
ejpam-5445	121	5	ρ3γ	ρ3γ	PROPN
ejpam-5445	121	6	′	′	NUM
ejpam-5445	121	7	+	+	CCONJ
ejpam-5445	121	8	ρ4γ|	ρ4γ|	X
ejpam-5445	121	9	≤∈	≤∈	NOUN
ejpam-5445	121	10	,	,	PUNCT
ejpam-5445	121	11	(	(	PUNCT
ejpam-5445	121	12	8)	8)	NUM
ejpam-5445	121	13	at	at	ADP
ejpam-5445	121	14	the	the	DET
ejpam-5445	121	15	point	point	NOUN
ejpam-5445	121	16	there	there	PRON
ejpam-5445	121	17	exists	exist	VERB
ejpam-5445	121	18	some	some	DET
ejpam-5445	121	19	u	u	PROPN
ejpam-5445	121	20	∈	∈	PROPN
ejpam-5445	121	21	c4[α	c4[α	NOUN
ejpam-5445	121	22	,	,	PUNCT
ejpam-5445	121	23	β	β	AUX
ejpam-5445	121	24	]	]	X
ejpam-5445	121	25	fulfilling	fulfil	VERB
ejpam-5445	121	26	|uiv	|uiv	ADP
ejpam-5445	122	1	+	+	X
ejpam-5445	122	2	ρ1u	ρ1u	PRON
ejpam-5445	122	3	′′′	′′′	PROPN
ejpam-5445	123	1	+	+	CCONJ
ejpam-5445	123	2	ρ2u	ρ2u	PROPN
ejpam-5445	123	3	′′	′′	PROPN
ejpam-5445	123	4	+	+	CCONJ
ejpam-5445	123	5	ρ3u	ρ3u	NOUN
ejpam-5445	123	6	′	′	NOUN
ejpam-5445	124	1	+	+	PUNCT
ejpam-5445	124	2	ρ4u|	ρ4u|	PUNCT
ejpam-5445	124	3	=	=	SYM
ejpam-5445	124	4	0	0	NUM
ejpam-5445	124	5	(	(	PUNCT
ejpam-5445	124	6	9	9	NUM
ejpam-5445	124	7	)	)	PUNCT
ejpam-5445	124	8	such	such	ADJ
ejpam-5445	124	9	that	that	DET
ejpam-5445	124	10	|ρ(ω)−	|ρ(ω)−	NOUN
ejpam-5445	124	11	u(ω)|	u(ω)|	ADP
ejpam-5445	124	12	<	<	X
ejpam-5445	124	13	κ	κ	X
ejpam-5445	124	14	∈.	∈.	PROPN
ejpam-5445	124	15	we	we	PRON
ejpam-5445	124	16	call	call	VERB
ejpam-5445	124	17	such	such	ADJ
ejpam-5445	124	18	κ	κ	ADP
ejpam-5445	124	19	a	a	DET
ejpam-5445	124	20	h	h	NOUN
ejpam-5445	125	1	−	−	PROPN
ejpam-5445	126	1	u	u	NOUN
ejpam-5445	126	2	stability	stability	NOUN
ejpam-5445	126	3	constant	constant	ADJ
ejpam-5445	126	4	for	for	ADP
ejpam-5445	126	5	equation	equation	NOUN
ejpam-5445	126	6	8	8	NUM
ejpam-5445	126	7	.	.	NOUN
ejpam-5445	127	1	2	2	NUM
ejpam-5445	127	2	.	.	X
ejpam-5445	127	3	main	main	ADJ
ejpam-5445	127	4	results	result	NOUN
ejpam-5445	127	5	now	now	ADV
ejpam-5445	127	6	,	,	PUNCT
ejpam-5445	127	7	fundamental	fundamental	ADJ
ejpam-5445	127	8	consequence	consequence	NOUN
ejpam-5445	127	9	of	of	ADP
ejpam-5445	127	10	this	this	DET
ejpam-5445	127	11	work	work	NOUN
ejpam-5445	127	12	is	be	AUX
ejpam-5445	127	13	given	give	VERB
ejpam-5445	127	14	in	in	ADP
ejpam-5445	127	15	the	the	DET
ejpam-5445	127	16	accompanying	accompanying	ADJ
ejpam-5445	127	17	hypothesis	hypothesis	NOUN
ejpam-5445	127	18	.	.	PUNCT
ejpam-5445	128	1	lemma	lemma	PROPN
ejpam-5445	128	2	1	1	NUM
ejpam-5445	128	3	.	.	PUNCT
ejpam-5445	129	1	the	the	DET
ejpam-5445	129	2	differential	differential	ADJ
ejpam-5445	129	3	equation	equation	NOUN
ejpam-5445	129	4	j	j	PROPN
ejpam-5445	129	5	γiv(ω	γiv(ω	PROPN
ejpam-5445	129	6	)	)	PUNCT
ejpam-5445	129	7	+	+	NUM
ejpam-5445	129	8	ρ1γ	ρ1γ	PROPN
ejpam-5445	129	9	′′′(ω	′′′(ω	PROPN
ejpam-5445	129	10	)	)	PUNCT
ejpam-5445	130	1	+	+	PROPN
ejpam-5445	130	2	ρ2γ	ρ2γ	PROPN
ejpam-5445	130	3	′′(ω	′′(ω	NOUN
ejpam-5445	130	4	)	)	PUNCT
ejpam-5445	131	1	+	+	CCONJ
ejpam-5445	131	2	ρ3γ	ρ3γ	NUM
ejpam-5445	131	3	′(ω	′(ω	NOUN
ejpam-5445	131	4	)	)	PUNCT
ejpam-5445	131	5	+	+	X
ejpam-5445	131	6	ρ4γ(ω	ρ4γ(ω	ADJ
ejpam-5445	131	7	)	)	PUNCT
ejpam-5445	131	8	=	=	SYM
ejpam-5445	131	9	χ(ω	χ(ω	NOUN
ejpam-5445	131	10	)	)	PUNCT
ejpam-5445	131	11	has	have	VERB
ejpam-5445	131	12	the	the	DET
ejpam-5445	131	13	hyers	hyer	NOUN
ejpam-5445	131	14	-ulam	-ulam	PROPN
ejpam-5445	131	15	stability	stability	NOUN
ejpam-5445	131	16	,	,	PUNCT
ejpam-5445	131	17	where	where	SCONJ
ejpam-5445	131	18	γ	γ	PROPN
ejpam-5445	131	19	∈	∈	PROPN
ejpam-5445	131	20	c4[α	c4[α	NOUN
ejpam-5445	131	21	,	,	PUNCT
ejpam-5445	131	22	β	β	X
ejpam-5445	131	23	]	]	PUNCT
ejpam-5445	131	24	and	and	CCONJ
ejpam-5445	131	25	χ	χ	DET
ejpam-5445	131	26	∈	∈	PROPN
ejpam-5445	131	27	[	[	X
ejpam-5445	131	28	α	α	X
ejpam-5445	131	29	,	,	PUNCT
ejpam-5445	131	30	β	β	X
ejpam-5445	131	31	]	]	PUNCT
ejpam-5445	131	32	.	.	PUNCT
ejpam-5445	132	1	s.	s.	PROPN
ejpam-5445	132	2	bowmiya	bowmiya	PROPN
ejpam-5445	132	3	et	et	PROPN
ejpam-5445	132	4	al	al	PROPN
ejpam-5445	132	5	.	.	PUNCT
ejpam-5445	132	6	/	/	SYM
ejpam-5445	132	7	eur	eur	PROPN
ejpam-5445	132	8	.	.	PUNCT
ejpam-5445	133	1	j.	j.	PROPN
ejpam-5445	133	2	pure	pure	PROPN
ejpam-5445	133	3	appl	appl	PROPN
ejpam-5445	133	4	.	.	PROPN
ejpam-5445	133	5	math	math	PROPN
ejpam-5445	133	6	,	,	PUNCT
ejpam-5445	133	7	17	17	NUM
ejpam-5445	133	8	(	(	PUNCT
ejpam-5445	133	9	4	4	NUM
ejpam-5445	133	10	)	)	PUNCT
ejpam-5445	133	11	(	(	PUNCT
ejpam-5445	133	12	2024	2024	NUM
ejpam-5445	133	13	)	)	PUNCT
ejpam-5445	133	14	,	,	PUNCT
ejpam-5445	133	15	3415	3415	NUM
ejpam-5445	133	16	-	-	SYM
ejpam-5445	133	17	3435	3435	NUM
ejpam-5445	133	18	3420	3420	NUM
ejpam-5445	133	19	proof	proof	NOUN
ejpam-5445	133	20	.	.	PUNCT
ejpam-5445	134	1	assume	assume	VERB
ejpam-5445	134	2	that	that	SCONJ
ejpam-5445	134	3	u1	u1	NOUN
ejpam-5445	134	4	,	,	PUNCT
ejpam-5445	134	5	u2	u2	NOUN
ejpam-5445	134	6	,	,	PUNCT
ejpam-5445	134	7	u3	u3	NOUN
ejpam-5445	134	8	and	and	CCONJ
ejpam-5445	134	9	u4	u4	PROPN
ejpam-5445	134	10	are	be	AUX
ejpam-5445	134	11	the	the	DET
ejpam-5445	134	12	roots	root	NOUN
ejpam-5445	134	13	of	of	ADP
ejpam-5445	134	14	ν4	ν4	PROPN
ejpam-5445	134	15	+	+	CCONJ
ejpam-5445	134	16	ρ1ν	ρ1ν	PROPN
ejpam-5445	134	17	3	3	NUM
ejpam-5445	134	18	+	+	CCONJ
ejpam-5445	134	19	p2ν	p2ν	PROPN
ejpam-5445	134	20	2	2	NUM
ejpam-5445	134	21	+	+	CCONJ
ejpam-5445	134	22	p3ν	p3ν	ADJ
ejpam-5445	134	23	+	+	CCONJ
ejpam-5445	134	24	p4	p4	ADJ
ejpam-5445	134	25	=	=	NOUN
ejpam-5445	134	26	0	0	NUM
ejpam-5445	134	27	with	with	ADP
ejpam-5445	134	28	q1	q1	PROPN
ejpam-5445	134	29	=	=	SYM
ejpam-5445	134	30	ru1	ru1	PROPN
ejpam-5445	134	31	,	,	PUNCT
ejpam-5445	134	32	q2	q2	NOUN
ejpam-5445	134	33	=	=	SYM
ejpam-5445	134	34	ru2	ru2	PROPN
ejpam-5445	134	35	,	,	PUNCT
ejpam-5445	134	36	q3	q3	NOUN
ejpam-5445	134	37	=	=	NOUN
ejpam-5445	134	38	ru4	ru4	PROPN
ejpam-5445	134	39	and	and	CCONJ
ejpam-5445	134	40	q4	q4	PROPN
ejpam-5445	134	41	=	=	PUNCT
ejpam-5445	134	42	ru3	ru3	NOUN
ejpam-5445	134	43	.	.	PUNCT
ejpam-5445	135	1	here	here	ADV
ejpam-5445	135	2	r	r	NOUN
ejpam-5445	135	3	means	mean	VERB
ejpam-5445	135	4	the	the	DET
ejpam-5445	135	5	real	real	ADJ
ejpam-5445	135	6	parts	part	NOUN
ejpam-5445	135	7	.	.	PUNCT
ejpam-5445	136	1	let	let	VERB
ejpam-5445	136	2	∈	∈	PRON
ejpam-5445	136	3	>	>	X
ejpam-5445	136	4	0	0	PROPN
ejpam-5445	136	5	and	and	CCONJ
ejpam-5445	136	6	γ	γ	PROPN
ejpam-5445	136	7	∈	∈	PROPN
ejpam-5445	136	8	c4[α	c4[α	NOUN
ejpam-5445	136	9	,	,	PUNCT
ejpam-5445	136	10	β	β	X
ejpam-5445	136	11	]	]	X
ejpam-5445	136	12	|γiv(ω	|γiv(ω	ADJ
ejpam-5445	136	13	)	)	PUNCT
ejpam-5445	137	1	+	+	CCONJ
ejpam-5445	137	2	ρ1γ	ρ1γ	PROPN
ejpam-5445	137	3	′′′(ω	′′′(ω	PROPN
ejpam-5445	137	4	)	)	PUNCT
ejpam-5445	138	1	+	+	PROPN
ejpam-5445	138	2	ρ2γ	ρ2γ	PROPN
ejpam-5445	138	3	′′(ω	′′(ω	NOUN
ejpam-5445	138	4	)	)	PUNCT
ejpam-5445	139	1	+	+	CCONJ
ejpam-5445	139	2	ρ3γ	ρ3γ	NUM
ejpam-5445	139	3	′(ω	′(ω	NOUN
ejpam-5445	139	4	)	)	PUNCT
ejpam-5445	139	5	+	+	NOUN
ejpam-5445	139	6	ρ4γ(ω)−	ρ4γ(ω)−	PROPN
ejpam-5445	139	7	χ(ω)|	χ(ω)|	PRON
ejpam-5445	139	8	≤∈	≤∈	NOUN
ejpam-5445	139	9	(	(	PUNCT
ejpam-5445	139	10	10	10	NUM
ejpam-5445	139	11	)	)	PUNCT
ejpam-5445	139	12	and	and	CCONJ
ejpam-5445	139	13	let	let	VERB
ejpam-5445	139	14	g1(ω	g1(ω	NUM
ejpam-5445	139	15	)	)	PUNCT
ejpam-5445	139	16	=	=	SYM
ejpam-5445	139	17	γ′′′(ω	γ′′′(ω	PROPN
ejpam-5445	139	18	)	)	PUNCT
ejpam-5445	139	19	+	+	CCONJ
ejpam-5445	139	20	(	(	PUNCT
ejpam-5445	139	21	u1	u1	NOUN
ejpam-5445	139	22	+	+	CCONJ
ejpam-5445	139	23	ρ1)γ	ρ1)γ	PROPN
ejpam-5445	139	24	′′(ω	′′(ω	PROPN
ejpam-5445	139	25	)	)	PUNCT
ejpam-5445	140	1	+	+	CCONJ
ejpam-5445	140	2	(	(	PUNCT
ejpam-5445	140	3	u21	u21	PROPN
ejpam-5445	140	4	+	+	CCONJ
ejpam-5445	140	5	ρ1u1	ρ1u1	X
ejpam-5445	140	6	+	+	X
ejpam-5445	140	7	ρ2)γ	ρ2)γ	ADJ
ejpam-5445	140	8	′(ω	′(ω	NOUN
ejpam-5445	140	9	)	)	PUNCT
ejpam-5445	141	1	+	+	CCONJ
ejpam-5445	141	2	(	(	PUNCT
ejpam-5445	141	3	u31	u31	NOUN
ejpam-5445	142	1	+	+	CCONJ
ejpam-5445	142	2	ρ1u	ρ1u	SYM
ejpam-5445	142	3	2	2	NUM
ejpam-5445	142	4	1	1	NUM
ejpam-5445	142	5	+	+	CCONJ
ejpam-5445	142	6	ρ2u1	ρ2u1	NOUN
ejpam-5445	142	7	+	+	X
ejpam-5445	142	8	ρ3)γ(ω	ρ3)γ(ω	PROPN
ejpam-5445	142	9	)	)	PUNCT
ejpam-5445	142	10	,	,	PUNCT
ejpam-5445	142	11	we	we	PRON
ejpam-5445	142	12	acquire	acquire	VERB
ejpam-5445	142	13	g′1(ω	g′1(ω	NUM
ejpam-5445	142	14	)	)	PUNCT
ejpam-5445	142	15	=	=	SYM
ejpam-5445	142	16	γ′′′(ω	γ′′′(ω	PROPN
ejpam-5445	142	17	)	)	PUNCT
ejpam-5445	143	1	+	+	CCONJ
ejpam-5445	143	2	(	(	PUNCT
ejpam-5445	143	3	u1	u1	NOUN
ejpam-5445	143	4	+	+	CCONJ
ejpam-5445	143	5	ρ1)γ	ρ1)γ	PROPN
ejpam-5445	143	6	′′′(ω	′′′(ω	PROPN
ejpam-5445	143	7	)	)	PUNCT
ejpam-5445	144	1	+	+	CCONJ
ejpam-5445	144	2	(	(	PUNCT
ejpam-5445	144	3	u21	u21	PROPN
ejpam-5445	144	4	+	+	CCONJ
ejpam-5445	144	5	ρ1u1	ρ1u1	X
ejpam-5445	144	6	+	+	NUM
ejpam-5445	144	7	ρ2)γ	ρ2)γ	ADJ
ejpam-5445	144	8	′′(ω	′′(ω	NOUN
ejpam-5445	144	9	)	)	PUNCT
ejpam-5445	145	1	+	+	CCONJ
ejpam-5445	145	2	(	(	PUNCT
ejpam-5445	145	3	u31	u31	NOUN
ejpam-5445	146	1	+	+	CCONJ
ejpam-5445	146	2	ρ1u	ρ1u	SYM
ejpam-5445	146	3	2	2	NUM
ejpam-5445	146	4	1	1	NUM
ejpam-5445	146	5	+	+	NUM
ejpam-5445	146	6	ρ2u1	ρ2u1	NOUN
ejpam-5445	146	7	+	+	CCONJ
ejpam-5445	146	8	ρ3)γ	ρ3)γ	PROPN
ejpam-5445	146	9	′(ω	′(ω	NOUN
ejpam-5445	146	10	)	)	PUNCT
ejpam-5445	146	11	+	+	CCONJ
ejpam-5445	146	12	(	(	PUNCT
ejpam-5445	146	13	u41	u41	ADJ
ejpam-5445	147	1	+	+	CCONJ
ejpam-5445	147	2	ρ1u	ρ1u	SYM
ejpam-5445	147	3	3	3	NUM
ejpam-5445	147	4	1	1	NUM
ejpam-5445	147	5	+	+	CCONJ
ejpam-5445	147	6	ρ2u	ρ2u	PROPN
ejpam-5445	147	7	2	2	NUM
ejpam-5445	147	8	1	1	NUM
ejpam-5445	147	9	+	+	NUM
ejpam-5445	147	10	ρ3u1	ρ3u1	PROPN
ejpam-5445	147	11	+	+	X
ejpam-5445	147	12	ρ4)γ(ω	ρ4)γ(ω	NUM
ejpam-5445	147	13	)	)	PUNCT
ejpam-5445	147	14	(	(	PUNCT
ejpam-5445	147	15	11	11	NUM
ejpam-5445	147	16	)	)	PUNCT
ejpam-5445	147	17	with	with	ADP
ejpam-5445	147	18	respect	respect	NOUN
ejpam-5445	147	19	to	to	ADP
ejpam-5445	147	20	ω	ω	PROPN
ejpam-5445	147	21	∈	∈	PROPN
ejpam-5445	148	1	[	[	X
ejpam-5445	148	2	α	α	X
ejpam-5445	148	3	,	,	PUNCT
ejpam-5445	148	4	β	β	X
ejpam-5445	148	5	]	]	X
ejpam-5445	148	6	,	,	PUNCT
ejpam-5445	148	7	at	at	ADP
ejpam-5445	148	8	that	that	DET
ejpam-5445	148	9	point	point	NOUN
ejpam-5445	148	10	|g′1(ω)−	|g′1(ω)−	NOUN
ejpam-5445	148	11	u1g1(ω)−	u1g1(ω)−	NOUN
ejpam-5445	148	12	χ(ω)|	χ(ω)|	PRON
ejpam-5445	148	13	≤∈	≤∈	X
ejpam-5445	148	14	(	(	PUNCT
ejpam-5445	148	15	12	12	NUM
ejpam-5445	148	16	)	)	PUNCT
ejpam-5445	148	17	with	with	ADP
ejpam-5445	148	18	respect	respect	NOUN
ejpam-5445	148	19	to	to	ADP
ejpam-5445	148	20	ω	ω	PROPN
ejpam-5445	148	21	∈	∈	PROPN
ejpam-5445	149	1	[	[	X
ejpam-5445	149	2	α	α	X
ejpam-5445	149	3	,	,	PUNCT
ejpam-5445	149	4	β	β	X
ejpam-5445	149	5	]	]	X
ejpam-5445	149	6	,	,	PUNCT
ejpam-5445	149	7	yields	yield	VERB
ejpam-5445	149	8	that	that	DET
ejpam-5445	149	9	|g′1(ω)−	|g′1(ω)−	NOUN
ejpam-5445	149	10	u1g1(ω)−	u1g1(ω)−	NOUN
ejpam-5445	149	11	χ(ω)|	χ(ω)|	PRON
ejpam-5445	149	12	≤	≤	NUM
ejpam-5445	149	13	|γ′′′(ω	|γ′′′(ω	NOUN
ejpam-5445	149	14	)	)	PUNCT
ejpam-5445	150	1	+	+	CCONJ
ejpam-5445	150	2	(	(	PUNCT
ejpam-5445	150	3	u1	u1	NOUN
ejpam-5445	150	4	+	+	CCONJ
ejpam-5445	150	5	ρ1)γ	ρ1)γ	PROPN
ejpam-5445	150	6	′′′(ω	′′′(ω	PROPN
ejpam-5445	150	7	)	)	PUNCT
ejpam-5445	151	1	+	+	CCONJ
ejpam-5445	151	2	(	(	PUNCT
ejpam-5445	151	3	u21	u21	NOUN
ejpam-5445	151	4	+	+	CCONJ
ejpam-5445	151	5	ρ1u+	ρ1u+	NOUN
ejpam-5445	151	6	ρ2)γ	ρ2)γ	ADJ
ejpam-5445	151	7	′′(ω	′′(ω	NOUN
ejpam-5445	151	8	)	)	PUNCT
ejpam-5445	152	1	+	+	CCONJ
ejpam-5445	152	2	(	(	PUNCT
ejpam-5445	152	3	u31	u31	NOUN
ejpam-5445	153	1	+	+	CCONJ
ejpam-5445	153	2	ρ1u	ρ1u	SYM
ejpam-5445	153	3	2	2	NUM
ejpam-5445	153	4	1	1	NUM
ejpam-5445	153	5	+	+	CCONJ
ejpam-5445	153	6	ρ2u2	ρ2u2	PROPN
ejpam-5445	153	7	+	+	NUM
ejpam-5445	153	8	ρ3)γ	ρ3)γ	NOUN
ejpam-5445	153	9	′(x	′(x	NOUN
ejpam-5445	153	10	)	)	PUNCT
ejpam-5445	154	1	+	+	CCONJ
ejpam-5445	154	2	(	(	PUNCT
ejpam-5445	154	3	u41	u41	ADJ
ejpam-5445	154	4	+	+	CCONJ
ejpam-5445	154	5	ρ1u	ρ1u	SYM
ejpam-5445	154	6	3	3	NUM
ejpam-5445	154	7	1	1	NUM
ejpam-5445	154	8	+	+	CCONJ
ejpam-5445	154	9	ρ2u	ρ2u	PROPN
ejpam-5445	154	10	2	2	NUM
ejpam-5445	154	11	1	1	NUM
ejpam-5445	154	12	+	+	NUM
ejpam-5445	154	13	ρ3u1	ρ3u1	PROPN
ejpam-5445	154	14	+	+	X
ejpam-5445	154	15	ρ4)γ(ω	ρ4)γ(ω	NOUN
ejpam-5445	154	16	)	)	PUNCT
ejpam-5445	154	17	−	−	PROPN
ejpam-5445	155	1	u1(γ	u1(γ	PROPN
ejpam-5445	155	2	′′′(ω	′′′(ω	PROPN
ejpam-5445	155	3	)	)	PUNCT
ejpam-5445	156	1	+	+	CCONJ
ejpam-5445	156	2	(	(	PUNCT
ejpam-5445	156	3	u1	u1	PROPN
ejpam-5445	156	4	+	+	CCONJ
ejpam-5445	156	5	ρ)γ′′(ω	ρ)γ′′(ω	PROPN
ejpam-5445	156	6	)	)	PUNCT
ejpam-5445	157	1	+	+	NUM
ejpam-5445	157	2	u21	u21	NOUN
ejpam-5445	157	3	+	+	CCONJ
ejpam-5445	157	4	(	(	PUNCT
ejpam-5445	157	5	ρ1u1	ρ1u1	X
ejpam-5445	157	6	+	+	X
ejpam-5445	157	7	ρ2)γ	ρ2)γ	ADJ
ejpam-5445	157	8	′(ω	′(ω	NOUN
ejpam-5445	157	9	)	)	PUNCT
ejpam-5445	157	10	+	+	CCONJ
ejpam-5445	157	11	(	(	PUNCT
ejpam-5445	157	12	(	(	PUNCT
ejpam-5445	157	13	u31	u31	NOUN
ejpam-5445	158	1	+	+	CCONJ
ejpam-5445	158	2	ρ1u	ρ1u	SYM
ejpam-5445	158	3	2	2	NUM
ejpam-5445	158	4	1	1	NUM
ejpam-5445	158	5	+	+	CCONJ
ejpam-5445	158	6	ρ2u1	ρ2u1	NOUN
ejpam-5445	158	7	+	+	X
ejpam-5445	158	8	ρ3)γ(ω	ρ3)γ(ω	PROPN
ejpam-5445	158	9	)	)	PUNCT
ejpam-5445	158	10	)	)	PUNCT
ejpam-5445	159	1	−	−	PROPN
ejpam-5445	159	2	χ(ω)|	χ(ω)|	X
ejpam-5445	159	3	(	(	PUNCT
ejpam-5445	159	4	13	13	NUM
ejpam-5445	159	5	)	)	PUNCT
ejpam-5445	159	6	with	with	ADP
ejpam-5445	159	7	respect	respect	NOUN
ejpam-5445	159	8	to	to	ADP
ejpam-5445	159	9	ω	ω	PROPN
ejpam-5445	159	10	∈	∈	PROPN
ejpam-5445	160	1	[	[	X
ejpam-5445	160	2	α	α	X
ejpam-5445	160	3	,	,	PUNCT
ejpam-5445	160	4	β	β	X
ejpam-5445	160	5	]	]	PUNCT
ejpam-5445	160	6	.	.	PUNCT
ejpam-5445	161	1	utilizing	utilize	VERB
ejpam-5445	161	2	the	the	DET
ejpam-5445	161	3	above	above	ADJ
ejpam-5445	161	4	condition	condition	NOUN
ejpam-5445	161	5	,	,	PUNCT
ejpam-5445	161	6	we	we	PRON
ejpam-5445	161	7	get	get	VERB
ejpam-5445	161	8	|g′1(ω)−	|g′1(ω)−	NOUN
ejpam-5445	161	9	u1g1(ω)−	u1g1(ω)−	NOUN
ejpam-5445	161	10	χ(ω)|	χ(ω)|	NOUN
ejpam-5445	161	11	=	=	SYM
ejpam-5445	161	12	|γiv(ω	|γiv(ω	PROPN
ejpam-5445	161	13	)	)	PUNCT
ejpam-5445	162	1	+	+	CCONJ
ejpam-5445	162	2	ρ1γ	ρ1γ	PROPN
ejpam-5445	162	3	′′′(ω	′′′(ω	PROPN
ejpam-5445	162	4	)	)	PUNCT
ejpam-5445	163	1	+	+	PROPN
ejpam-5445	164	1	ρ2γ	ρ2γ	NUM
ejpam-5445	164	2	n(ω	n(ω	NUM
ejpam-5445	164	3	)	)	PUNCT
ejpam-5445	164	4	+	+	NUM
ejpam-5445	164	5	ρ3γ	ρ3γ	PROPN
ejpam-5445	164	6	′(ω	′(ω	NOUN
ejpam-5445	164	7	)	)	PUNCT
ejpam-5445	164	8	+	+	CCONJ
ejpam-5445	164	9	ρ4γ(ω)|	ρ4γ(ω)|	NUM
ejpam-5445	164	10	<	<	X
ejpam-5445	164	11	∈	∈	PROPN
ejpam-5445	164	12	.	.	PUNCT
ejpam-5445	165	1	with	with	ADP
ejpam-5445	165	2	respect	respect	NOUN
ejpam-5445	165	3	to	to	ADP
ejpam-5445	165	4	ω	ω	PROPN
ejpam-5445	165	5	∈	∈	PROPN
ejpam-5445	165	6	[	[	X
ejpam-5445	165	7	α	α	X
ejpam-5445	165	8	,	,	PUNCT
ejpam-5445	165	9	β	β	X
ejpam-5445	165	10	]	]	PUNCT
ejpam-5445	165	11	.	.	PUNCT
ejpam-5445	166	1	equally	equally	ADV
ejpam-5445	166	2	g1	g1	PROPN
ejpam-5445	166	3	fulfills	fulfill	VERB
ejpam-5445	166	4	−	−	PROPN
ejpam-5445	166	5	∈≤	∈≤	PRON
ejpam-5445	166	6	g′1(ω)−	g′1(ω)−	NOUN
ejpam-5445	166	7	u1g1(ω)−	u1g1(ω)−	NOUN
ejpam-5445	166	8	χ(ω	χ(ω	NOUN
ejpam-5445	166	9	)	)	PUNCT
ejpam-5445	166	10	≤∈	≤∈	PROPN
ejpam-5445	166	11	(	(	PUNCT
ejpam-5445	166	12	14	14	NUM
ejpam-5445	166	13	)	)	PUNCT
ejpam-5445	166	14	with	with	ADP
ejpam-5445	166	15	respect	respect	NOUN
ejpam-5445	166	16	to	to	ADP
ejpam-5445	166	17	ω	ω	PROPN
ejpam-5445	166	18	∈	∈	PROPN
ejpam-5445	166	19	[	[	X
ejpam-5445	166	20	α	α	X
ejpam-5445	166	21	,	,	PUNCT
ejpam-5445	166	22	β	β	X
ejpam-5445	166	23	]	]	PUNCT
ejpam-5445	166	24	.	.	PUNCT
ejpam-5445	167	1	multiplying	multiply	VERB
ejpam-5445	167	2	by	by	ADP
ejpam-5445	167	3	e−u1(ω−α	e−u1(ω−α	NOUN
ejpam-5445	167	4	)	)	PUNCT
ejpam-5445	167	5	the	the	DET
ejpam-5445	167	6	above	above	ADJ
ejpam-5445	167	7	condition	condition	NOUN
ejpam-5445	167	8	,	,	PUNCT
ejpam-5445	167	9	shown	show	VERB
ejpam-5445	167	10	up	up	ADP
ejpam-5445	167	11	∈	∈	PROPN
ejpam-5445	167	12	e−u1(ω−α	e−u1(ω−α	NOUN
ejpam-5445	167	13	)	)	PUNCT
ejpam-5445	167	14	≤	≤	NOUN
ejpam-5445	167	15	g′1(ω)e	g′1(ω)e	PROPN
ejpam-5445	167	16	−u1(ω−α	−u1(ω−α	PUNCT
ejpam-5445	167	17	)	)	PUNCT
ejpam-5445	167	18	−	−	PROPN
ejpam-5445	167	19	u1g1(ω)e	u1g1(ω)e	NOUN
ejpam-5445	167	20	−u1(ω−α	−u1(ω−α	PROPN
ejpam-5445	167	21	)	)	PUNCT
ejpam-5445	167	22	−	−	PROPN
ejpam-5445	167	23	χ(ω)e−u1(ω−α	χ(ω)e−u1(ω−α	PROPN
ejpam-5445	167	24	)	)	PUNCT
ejpam-5445	167	25	≤∈	≤∈	PROPN
ejpam-5445	167	26	e−u1(ω−α	e−u1(ω−α	NOUN
ejpam-5445	167	27	)	)	PUNCT
ejpam-5445	167	28	(	(	PUNCT
ejpam-5445	167	29	15	15	NUM
ejpam-5445	167	30	)	)	PUNCT
ejpam-5445	167	31	with	with	ADP
ejpam-5445	167	32	respect	respect	NOUN
ejpam-5445	167	33	to	to	ADP
ejpam-5445	167	34	ω	ω	PROPN
ejpam-5445	167	35	∈	∈	PROPN
ejpam-5445	167	36	[	[	X
ejpam-5445	167	37	α	α	X
ejpam-5445	167	38	,	,	PUNCT
ejpam-5445	167	39	β	β	X
ejpam-5445	167	40	]	]	X
ejpam-5445	167	41	.	.	PUNCT
ejpam-5445	168	1	without	without	ADP
ejpam-5445	168	2	loss	loss	NOUN
ejpam-5445	168	3	of	of	ADP
ejpam-5445	168	4	all	all	DET
ejpam-5445	168	5	inclusive	inclusive	ADJ
ejpam-5445	168	6	statement	statement	NOUN
ejpam-5445	168	7	we	we	PRON
ejpam-5445	168	8	may	may	AUX
ejpam-5445	168	9	accept	accept	VERB
ejpam-5445	168	10	that	that	DET
ejpam-5445	168	11	u1	u1	NOUN
ejpam-5445	168	12	>	>	X
ejpam-5445	168	13	1	1	NUM
ejpam-5445	168	14	,	,	PUNCT
ejpam-5445	168	15	thus	thus	ADV
ejpam-5445	168	16	−u1	−u1	PROPN
ejpam-5445	168	17	∈	∈	PROPN
ejpam-5445	168	18	e−u1(ω−α	e−u1(ω−α	PROPN
ejpam-5445	168	19	)	)	PUNCT
ejpam-5445	168	20	≤	≤	NOUN
ejpam-5445	168	21	g′1(ω)e	g′1(ω)e	PROPN
ejpam-5445	168	22	−u1(ω−α	−u1(ω−α	PUNCT
ejpam-5445	168	23	)	)	PUNCT
ejpam-5445	168	24	−	−	PROPN
ejpam-5445	168	25	u1g1(ω)e	u1g1(ω)e	NOUN
ejpam-5445	168	26	−u1(ω−α	−u1(ω−α	PROPN
ejpam-5445	168	27	)	)	PUNCT
ejpam-5445	168	28	−	−	PROPN
ejpam-5445	168	29	χ(ω)e−u1(ω−α	χ(ω)e−u1(ω−α	PROPN
ejpam-5445	168	30	)	)	PUNCT
ejpam-5445	168	31	s.	s.	PROPN
ejpam-5445	168	32	bowmiya	bowmiya	VERB
ejpam-5445	168	33	et	et	PROPN
ejpam-5445	168	34	al	al	PROPN
ejpam-5445	168	35	.	.	PUNCT
ejpam-5445	168	36	/	/	SYM
ejpam-5445	168	37	eur	eur	PROPN
ejpam-5445	168	38	.	.	PUNCT
ejpam-5445	169	1	j.	j.	PROPN
ejpam-5445	169	2	pure	pure	PROPN
ejpam-5445	169	3	appl	appl	PROPN
ejpam-5445	169	4	.	.	PROPN
ejpam-5445	169	5	math	math	PROPN
ejpam-5445	169	6	,	,	PUNCT
ejpam-5445	169	7	17	17	NUM
ejpam-5445	169	8	(	(	PUNCT
ejpam-5445	169	9	4	4	NUM
ejpam-5445	169	10	)	)	PUNCT
ejpam-5445	169	11	(	(	PUNCT
ejpam-5445	169	12	2024	2024	NUM
ejpam-5445	169	13	)	)	PUNCT
ejpam-5445	169	14	,	,	PUNCT
ejpam-5445	169	15	3415	3415	NUM
ejpam-5445	169	16	-	-	SYM
ejpam-5445	169	17	3435	3435	NUM
ejpam-5445	169	18	3421	3421	NUM
ejpam-5445	169	19	≤	≤	NUM
ejpam-5445	169	20	u1e	u1e	NOUN
ejpam-5445	169	21	−u1(ω−α	−u1(ω−α	NOUN
ejpam-5445	169	22	)	)	PUNCT
ejpam-5445	169	23	(	(	PUNCT
ejpam-5445	169	24	16	16	NUM
ejpam-5445	169	25	)	)	PUNCT
ejpam-5445	169	26	with	with	ADP
ejpam-5445	169	27	respect	respect	NOUN
ejpam-5445	169	28	to	to	ADP
ejpam-5445	169	29	ω	ω	PROPN
ejpam-5445	169	30	∈	∈	PROPN
ejpam-5445	170	1	[	[	X
ejpam-5445	170	2	α	α	X
ejpam-5445	170	3	,	,	PUNCT
ejpam-5445	170	4	β	β	X
ejpam-5445	170	5	]	]	X
ejpam-5445	170	6	,	,	PUNCT
ejpam-5445	170	7	integrating	integrate	VERB
ejpam-5445	170	8	16	16	NUM
ejpam-5445	170	9	from	from	ADP
ejpam-5445	170	10	ω	ω	NUM
ejpam-5445	170	11	to	to	ADP
ejpam-5445	170	12	β	β	PRON
ejpam-5445	170	13	,	,	PUNCT
ejpam-5445	170	14	we	we	PRON
ejpam-5445	170	15	achieve	achieve	VERB
ejpam-5445	170	16	−	−	PROPN
ejpam-5445	170	17	∈	∈	PROPN
ejpam-5445	170	18	(	(	PUNCT
ejpam-5445	170	19	−e−u1(β−α	−e−u1(β−α	NOUN
ejpam-5445	170	20	)	)	PUNCT
ejpam-5445	171	1	+	+	NUM
ejpam-5445	171	2	e−u1(ω−α	e−u1(ω−α	NOUN
ejpam-5445	171	3	)	)	PUNCT
ejpam-5445	171	4	)	)	PUNCT
ejpam-5445	172	1	≤	≤	NUM
ejpam-5445	172	2	g1(β)e	g1(β)e	NOUN
ejpam-5445	172	3	−u1(βα	−u1(βα	NOUN
ejpam-5445	172	4	)	)	PUNCT
ejpam-5445	172	5	−	−	PROPN
ejpam-5445	172	6	g1(ω)e	g1(ω)e	PROPN
ejpam-5445	172	7	−u1(ω−α	−u1(ω−α	NOUN
ejpam-5445	172	8	)	)	PUNCT
ejpam-5445	172	9	−	−	ADP
ejpam-5445	172	10	∫	∫	PROPN
ejpam-5445	172	11	β	β	PROPN
ejpam-5445	172	12	ω	ω	PROPN
ejpam-5445	172	13	χ(τ)e−u1(τ−α)dτ	χ(τ)e−u1(τ−α)dτ	X
ejpam-5445	172	14	≤∈	≤∈	PROPN
ejpam-5445	172	15	(	(	PUNCT
ejpam-5445	172	16	−e−u1(β−α	−e−u1(β−α	NOUN
ejpam-5445	172	17	)	)	PUNCT
ejpam-5445	172	18	+	+	NUM
ejpam-5445	172	19	e−u1(ω−α	e−u1(ω−α	NOUN
ejpam-5445	172	20	)	)	PUNCT
ejpam-5445	172	21	)	)	PUNCT
ejpam-5445	172	22	(	(	PUNCT
ejpam-5445	172	23	17	17	NUM
ejpam-5445	172	24	)	)	PUNCT
ejpam-5445	172	25	with	with	ADP
ejpam-5445	172	26	respect	respect	NOUN
ejpam-5445	172	27	to	to	ADP
ejpam-5445	172	28	ω	ω	PROPN
ejpam-5445	172	29	∈	∈	PROPN
ejpam-5445	172	30	[	[	X
ejpam-5445	172	31	α	α	X
ejpam-5445	172	32	,	,	PUNCT
ejpam-5445	172	33	β	β	X
ejpam-5445	172	34	]	]	X
ejpam-5445	172	35	,	,	PUNCT
ejpam-5445	172	36	thus	thus	ADV
ejpam-5445	172	37	−	−	PROPN
ejpam-5445	172	38	∈	∈	PROPN
ejpam-5445	172	39	e−u1(ω−α	e−u1(ω−α	PROPN
ejpam-5445	172	40	)	)	PUNCT
ejpam-5445	172	41	≤	≤	NUM
ejpam-5445	172	42	g1(β)e	g1(β)e	NOUN
ejpam-5445	172	43	−u1(ω−α)−	−u1(ω−α)−	PROPN
ejpam-5445	172	44	∈	∈	PROPN
ejpam-5445	172	45	e−u1(β−α	e−u1(β−α	NOUN
ejpam-5445	172	46	)	)	PUNCT
ejpam-5445	172	47	−	−	PROPN
ejpam-5445	172	48	g1(ω)e	g1(ω)e	PROPN
ejpam-5445	172	49	−u1(ω−α	−u1(ω−α	NOUN
ejpam-5445	172	50	)	)	PUNCT
ejpam-5445	172	51	−	−	ADP
ejpam-5445	173	1	∫	∫	PROPN
ejpam-5445	173	2	β	β	PROPN
ejpam-5445	173	3	ω	ω	PROPN
ejpam-5445	173	4	χ(τ)e−u1(τ−α)dτ	χ(τ)e−u1(τ−α)dτ	X
ejpam-5445	173	5	≤∈	≤∈	PROPN
ejpam-5445	173	6	(	(	PUNCT
ejpam-5445	173	7	−e−u1(ω−α	−e−u1(ω−α	PROPN
ejpam-5445	173	8	)	)	PUNCT
ejpam-5445	173	9	+	+	NUM
ejpam-5445	173	10	e−u1(β−α	e−u1(β−α	NOUN
ejpam-5445	173	11	)	)	PUNCT
ejpam-5445	173	12	)	)	PUNCT
ejpam-5445	173	13	(	(	PUNCT
ejpam-5445	173	14	18	18	NUM
ejpam-5445	173	15	)	)	PUNCT
ejpam-5445	173	16	with	with	ADP
ejpam-5445	173	17	respect	respect	NOUN
ejpam-5445	173	18	to	to	ADP
ejpam-5445	173	19	ω	ω	PROPN
ejpam-5445	173	20	∈	∈	PROPN
ejpam-5445	174	1	[	[	X
ejpam-5445	174	2	α	α	X
ejpam-5445	174	3	,	,	PUNCT
ejpam-5445	174	4	β	β	X
ejpam-5445	174	5	]	]	X
ejpam-5445	174	6	,	,	PUNCT
ejpam-5445	174	7	the	the	DET
ejpam-5445	174	8	above	above	ADJ
ejpam-5445	174	9	condition	condition	NOUN
ejpam-5445	174	10	shown	show	VERB
ejpam-5445	174	11	up	up	ADP
ejpam-5445	174	12	∈	∈	PROPN
ejpam-5445	174	13	−e−u1(ω−α	−e−u1(ω−α	X
ejpam-5445	174	14	)	)	PUNCT
ejpam-5445	174	15	≤	≤	NOUN
ejpam-5445	174	16	g1(β)−	g1(β)−	VERB
ejpam-5445	174	17	e−u1(ω−α)−	e−u1(ω−α)−	PROPN
ejpam-5445	174	18	∈	∈	PROPN
ejpam-5445	174	19	−e−u1(β−α	−e−u1(β−α	PROPN
ejpam-5445	174	20	)	)	PUNCT
ejpam-5445	175	1	−	−	ADP
ejpam-5445	175	2	g1(ω)−	g1(ω)−	NOUN
ejpam-5445	175	3	e−u1(ω−α	e−u1(ω−α	NOUN
ejpam-5445	175	4	)	)	PUNCT
ejpam-5445	175	5	−	−	ADP
ejpam-5445	176	1	∫	∫	PROPN
ejpam-5445	176	2	β	β	PROPN
ejpam-5445	176	3	ω	ω	PROPN
ejpam-5445	176	4	χ(τ)e−u1(τ−α)dτ	χ(τ)e−u1(τ−α)dτ	PROPN
ejpam-5445	176	5	≤∈	≤∈	PROPN
ejpam-5445	176	6	e−u1(ω−α	e−u1(ω−α	NOUN
ejpam-5445	176	7	)	)	PUNCT
ejpam-5445	176	8	(	(	PUNCT
ejpam-5445	176	9	19	19	NUM
ejpam-5445	176	10	)	)	PUNCT
ejpam-5445	176	11	with	with	ADP
ejpam-5445	176	12	respect	respect	NOUN
ejpam-5445	176	13	to	to	ADP
ejpam-5445	176	14	ω	ω	PROPN
ejpam-5445	176	15	∈	∈	PROPN
ejpam-5445	176	16	[	[	X
ejpam-5445	176	17	α	α	X
ejpam-5445	176	18	,	,	PUNCT
ejpam-5445	176	19	β	β	X
ejpam-5445	176	20	]	]	PUNCT
ejpam-5445	176	21	.	.	PUNCT
ejpam-5445	177	1	multiplying	multiply	VERB
ejpam-5445	177	2	19	19	NUM
ejpam-5445	177	3	by	by	ADP
ejpam-5445	177	4	eu1(ω−α	eu1(ω−α	PROPN
ejpam-5445	177	5	)	)	PUNCT
ejpam-5445	177	6	on	on	ADP
ejpam-5445	177	7	both	both	DET
ejpam-5445	177	8	sides	side	NOUN
ejpam-5445	177	9	,	,	PUNCT
ejpam-5445	177	10	we	we	PRON
ejpam-5445	177	11	get	get	VERB
ejpam-5445	177	12	−	−	PROPN
ejpam-5445	177	13	∈	∈	PROPN
ejpam-5445	177	14	≤	≤	NOUN
ejpam-5445	177	15	g1(β)e	g1(β)e	NOUN
ejpam-5445	177	16	−u1(β−ω)−	−u1(β−ω)−	PROPN
ejpam-5445	177	17	∈	∈	NOUN
ejpam-5445	177	18	e−u1(β−ω	e−u1(β−ω	NOUN
ejpam-5445	177	19	)	)	PUNCT
ejpam-5445	178	1	−	−	ADP
ejpam-5445	178	2	g1(ω)−	g1(ω)−	NOUN
ejpam-5445	178	3	e−u1ω	e−u1ω	VERB
ejpam-5445	178	4	∫	∫	PROPN
ejpam-5445	178	5	β	β	PROPN
ejpam-5445	178	6	ω	ω	PROPN
ejpam-5445	178	7	χ(τ)e−u1τdτ	χ(τ)e−u1τdτ	PROPN
ejpam-5445	178	8	≤∈	≤∈	PROPN
ejpam-5445	178	9	(	(	PUNCT
ejpam-5445	178	10	20	20	NUM
ejpam-5445	178	11	)	)	PUNCT
ejpam-5445	178	12	thus	thus	ADV
ejpam-5445	178	13	−	−	PROPN
ejpam-5445	178	14	∈	∈	PROPN
ejpam-5445	178	15	≤	≤	NUM
ejpam-5445	178	16	g1(β)e	g1(β)e	NOUN
ejpam-5445	178	17	u1(ω−β)−	u1(ω−β)−	PROPN
ejpam-5445	178	18	∈	∈	PROPN
ejpam-5445	178	19	eu1(ω−β	eu1(ω−β	PROPN
ejpam-5445	178	20	)	)	PUNCT
ejpam-5445	178	21	−	−	PROPN
ejpam-5445	179	1	g1(ω)−	g1(ω)−	VERB
ejpam-5445	179	2	eu1ω	eu1ω	X
ejpam-5445	179	3	∫	∫	PROPN
ejpam-5445	179	4	β	β	PROPN
ejpam-5445	179	5	ω	ω	PROPN
ejpam-5445	179	6	χ(τ)e−u1τdτ	χ(τ)e−u1τdτ	PROPN
ejpam-5445	179	7	≤∈	≤∈	PROPN
ejpam-5445	179	8	(	(	PUNCT
ejpam-5445	179	9	21	21	NUM
ejpam-5445	179	10	)	)	PUNCT
ejpam-5445	179	11	with	with	ADP
ejpam-5445	179	12	respect	respect	NOUN
ejpam-5445	179	13	to	to	ADP
ejpam-5445	179	14	ω	ω	PROPN
ejpam-5445	179	15	∈	∈	PROPN
ejpam-5445	179	16	[	[	X
ejpam-5445	179	17	α	α	X
ejpam-5445	179	18	,	,	PUNCT
ejpam-5445	179	19	β	β	X
ejpam-5445	179	20	]	]	PUNCT
ejpam-5445	179	21	.	.	PUNCT
ejpam-5445	180	1	let	let	VERB
ejpam-5445	180	2	ζ(ω	ζ(ω	PRON
ejpam-5445	180	3	)	)	PUNCT
ejpam-5445	180	4	=	=	SYM
ejpam-5445	180	5	g1(β)e	g1(β)e	X
ejpam-5445	180	6	u1(ω−β	u1(ω−β	PROPN
ejpam-5445	180	7	)	)	PUNCT
ejpam-5445	181	1	−	−	PROPN
ejpam-5445	181	2	eu1(ω	eu1(ω	PROPN
ejpam-5445	181	3	)	)	PUNCT
ejpam-5445	181	4	∫	∫	PROPN
ejpam-5445	181	5	β	β	PROPN
ejpam-5445	181	6	ω	ω	PROPN
ejpam-5445	181	7	χ(τ)e−u1τdτ	χ(τ)e−u1τdτ	PROPN
ejpam-5445	181	8	,	,	PUNCT
ejpam-5445	181	9	then	then	ADV
ejpam-5445	181	10	ζ(ω	ζ(ω	PROPN
ejpam-5445	181	11	)	)	PUNCT
ejpam-5445	181	12	fulfilling	fulfil	VERB
ejpam-5445	181	13	ζ	ζ	NOUN
ejpam-5445	181	14	′(ω	′(ω	NOUN
ejpam-5445	181	15	)	)	PUNCT
ejpam-5445	181	16	=	=	SYM
ejpam-5445	182	1	u1ζ(ω	u1ζ(ω	ADJ
ejpam-5445	182	2	)	)	PUNCT
ejpam-5445	182	3	+	+	CCONJ
ejpam-5445	182	4	χ(ω	χ(ω	NOUN
ejpam-5445	182	5	)	)	PUNCT
ejpam-5445	182	6	with	with	ADP
ejpam-5445	182	7	respect	respect	NOUN
ejpam-5445	182	8	to	to	ADP
ejpam-5445	182	9	ω	ω	PROPN
ejpam-5445	182	10	∈	∈	PROPN
ejpam-5445	182	11	[	[	X
ejpam-5445	182	12	α	α	X
ejpam-5445	182	13	,	,	PUNCT
ejpam-5445	182	14	β	β	X
ejpam-5445	182	15	]	]	X
ejpam-5445	182	16	,	,	PUNCT
ejpam-5445	182	17	then	then	ADV
ejpam-5445	182	18	the	the	DET
ejpam-5445	182	19	satisfies	satisfie	NOUN
ejpam-5445	182	20	inequality	inequality	NOUN
ejpam-5445	182	21	that	that	SCONJ
ejpam-5445	182	22	|ζ(ω)−	|ζ(ω)−	NOUN
ejpam-5445	182	23	g1(ω)|	g1(ω)|	PROPN
ejpam-5445	182	24	=	=	SYM
ejpam-5445	182	25	|g1(β)eu1(ω−β	|g1(β)eu1(ω−β	PROPN
ejpam-5445	182	26	)	)	PUNCT
ejpam-5445	182	27	−	−	PROPN
ejpam-5445	183	1	g1(ω)−	g1(ω)−	NOUN
ejpam-5445	183	2	eu1ω	eu1ω	X
ejpam-5445	183	3	∫	∫	PROPN
ejpam-5445	183	4	β	β	PROPN
ejpam-5445	183	5	ω	ω	X
ejpam-5445	183	6	χ(τ)e−u1τdτ	χ(τ)e−u1τdτ	PROPN
ejpam-5445	183	7	|	|	PROPN
ejpam-5445	183	8	=	=	PUNCT
ejpam-5445	183	9	eρω|	eρω|	PROPN
ejpam-5445	183	10	∫	∫	PROPN
ejpam-5445	183	11	β	β	PROPN
ejpam-5445	183	12	ω	ω	PROPN
ejpam-5445	184	1	[	[	X
ejpam-5445	184	2	e−u1τg1(τ	e−u1τg1(τ	NUM
ejpam-5445	184	3	)	)	PUNCT
ejpam-5445	184	4	]	]	PUNCT
ejpam-5445	184	5	ldτ	ldτ	PROPN
ejpam-5445	185	1	−	−	PROPN
ejpam-5445	185	2	∫	∫	PROPN
ejpam-5445	185	3	β	β	PROPN
ejpam-5445	185	4	ω	ω	PROPN
ejpam-5445	185	5	χ(τ)e−u1τdτ	χ(τ)e−u1τdτ	PROPN
ejpam-5445	185	6	|	|	PROPN
ejpam-5445	185	7	s.	s.	PROPN
ejpam-5445	185	8	bowmiya	bowmiya	PROPN
ejpam-5445	185	9	et	et	PROPN
ejpam-5445	185	10	al	al	PROPN
ejpam-5445	185	11	.	.	PUNCT
ejpam-5445	185	12	/	/	SYM
ejpam-5445	185	13	eur	eur	PROPN
ejpam-5445	185	14	.	.	PUNCT
ejpam-5445	186	1	j.	j.	PROPN
ejpam-5445	186	2	pure	pure	PROPN
ejpam-5445	186	3	appl	appl	PROPN
ejpam-5445	186	4	.	.	PROPN
ejpam-5445	186	5	math	math	PROPN
ejpam-5445	186	6	,	,	PUNCT
ejpam-5445	186	7	17	17	NUM
ejpam-5445	186	8	(	(	PUNCT
ejpam-5445	186	9	4	4	NUM
ejpam-5445	186	10	)	)	PUNCT
ejpam-5445	186	11	(	(	PUNCT
ejpam-5445	186	12	2024	2024	NUM
ejpam-5445	186	13	)	)	PUNCT
ejpam-5445	186	14	,	,	PUNCT
ejpam-5445	186	15	3415	3415	NUM
ejpam-5445	186	16	-	-	SYM
ejpam-5445	186	17	3435	3435	NUM
ejpam-5445	186	18	3422	3422	NUM
ejpam-5445	186	19	≤	≤	NUM
ejpam-5445	186	20	eρω	eρω	NOUN
ejpam-5445	186	21	∫	∫	PROPN
ejpam-5445	186	22	β	β	PROPN
ejpam-5445	186	23	ω	ω	PROPN
ejpam-5445	186	24	e−ρτ	e−ρτ	PROPN
ejpam-5445	186	25	|g′1(τ)−	|g′1(τ)−	PROPN
ejpam-5445	186	26	u1g1(τ)−	u1g1(τ)−	PROPN
ejpam-5445	186	27	χ(τ)|dτ	χ(τ)|dτ	PROPN
ejpam-5445	186	28	≤∈	≤∈	PROPN
ejpam-5445	186	29	eρω	eρω	NOUN
ejpam-5445	186	30	∫	∫	PROPN
ejpam-5445	186	31	β	β	PROPN
ejpam-5445	186	32	ω	ω	X
ejpam-5445	186	33	e−ρτdτ	e−ρτdτ	X
ejpam-5445	186	34	(	(	PUNCT
ejpam-5445	186	35	22	22	NUM
ejpam-5445	186	36	)	)	PUNCT
ejpam-5445	186	37	with	with	ADP
ejpam-5445	186	38	respect	respect	NOUN
ejpam-5445	186	39	to	to	ADP
ejpam-5445	186	40	ω	ω	PROPN
ejpam-5445	186	41	∈	∈	PROPN
ejpam-5445	186	42	[	[	X
ejpam-5445	186	43	α	α	X
ejpam-5445	186	44	,	,	PUNCT
ejpam-5445	186	45	β	β	X
ejpam-5445	186	46	]	]	X
ejpam-5445	186	47	.	.	PUNCT
ejpam-5445	187	1	if	if	SCONJ
ejpam-5445	187	2	ρ	ρ	PROPN
ejpam-5445	187	3	̸=	̸=	PROPN
ejpam-5445	187	4	0	0	NUM
ejpam-5445	187	5	,	,	PUNCT
ejpam-5445	187	6	then	then	ADV
ejpam-5445	187	7	|ζ(ω)−	|ζ(ω)−	PROPN
ejpam-5445	187	8	g1(ω)|	g1(ω)|	PROPN
ejpam-5445	187	9	≤∈	≤∈	PROPN
ejpam-5445	187	10	eρω	eρω	NOUN
ejpam-5445	187	11	∫	∫	PROPN
ejpam-5445	187	12	β	β	PROPN
ejpam-5445	187	13	ω	ω	PROPN
ejpam-5445	187	14	e−ρτdτ	e−ρτdτ	PROPN
ejpam-5445	187	15	≤	≤	PROPN
ejpam-5445	187	16	∈	∈	PROPN
ejpam-5445	187	17	ρ	ρ	NOUN
ejpam-5445	187	18	(	(	PUNCT
ejpam-5445	187	19	1−	1−	NUM
ejpam-5445	187	20	e−ρ(β−α	e−ρ(β−α	NOUN
ejpam-5445	187	21	)	)	PUNCT
ejpam-5445	187	22	)	)	PUNCT
ejpam-5445	187	23	(	(	PUNCT
ejpam-5445	187	24	23	23	NUM
ejpam-5445	187	25	)	)	PUNCT
ejpam-5445	187	26	with	with	ADP
ejpam-5445	187	27	respect	respect	NOUN
ejpam-5445	187	28	to	to	ADP
ejpam-5445	187	29	ω	ω	PROPN
ejpam-5445	187	30	∈	∈	PROPN
ejpam-5445	187	31	[	[	X
ejpam-5445	187	32	α	α	X
ejpam-5445	187	33	,	,	PUNCT
ejpam-5445	187	34	β	β	X
ejpam-5445	187	35	]	]	X
ejpam-5445	187	36	.	.	PUNCT
ejpam-5445	188	1	if	if	SCONJ
ejpam-5445	188	2	ρ	ρ	PROPN
ejpam-5445	188	3	=	=	SYM
ejpam-5445	188	4	0	0	NUM
ejpam-5445	188	5	,	,	PUNCT
ejpam-5445	188	6	then	then	ADV
ejpam-5445	188	7	|ζ(ω)−	|ζ(ω)−	PROPN
ejpam-5445	188	8	g1(ω)|	g1(ω)|	PROPN
ejpam-5445	188	9	≤∈	≤∈	PROPN
ejpam-5445	188	10	eρω	eρω	NOUN
ejpam-5445	188	11	∫	∫	PROPN
ejpam-5445	188	12	β	β	PROPN
ejpam-5445	188	13	ω	ω	PROPN
ejpam-5445	188	14	e−ρτdτ	e−ρτdτ	X
ejpam-5445	188	15	≤∈	≤∈	X
ejpam-5445	188	16	(	(	PUNCT
ejpam-5445	188	17	β	β	X
ejpam-5445	188	18	−	−	NOUN
ejpam-5445	188	19	α	α	NOUN
ejpam-5445	188	20	)	)	PUNCT
ejpam-5445	188	21	(	(	PUNCT
ejpam-5445	188	22	24	24	NUM
ejpam-5445	188	23	)	)	PUNCT
ejpam-5445	188	24	with	with	ADP
ejpam-5445	188	25	respect	respect	NOUN
ejpam-5445	188	26	to	to	ADP
ejpam-5445	188	27	ω	ω	PROPN
ejpam-5445	188	28	∈	∈	PROPN
ejpam-5445	188	29	[	[	X
ejpam-5445	188	30	α	α	X
ejpam-5445	188	31	,	,	PUNCT
ejpam-5445	188	32	β	β	X
ejpam-5445	188	33	]	]	X
ejpam-5445	188	34	.	.	PUNCT
ejpam-5445	189	1	therefore	therefore	ADV
ejpam-5445	189	2	|ζ(ω)−	|ζ(ω)−	PROPN
ejpam-5445	189	3	g1(ω)|	g1(ω)|	PROPN
ejpam-5445	189	4	≤	≤	PROPN
ejpam-5445	189	5	{	{	PUNCT
ejpam-5445	189	6	1−e−ρ(β−α	1−e−ρ(β−α	NUM
ejpam-5445	189	7	)	)	PUNCT
ejpam-5445	189	8	ρ	ρ	NOUN
ejpam-5445	189	9	;	;	PUNCT
ejpam-5445	189	10	if	if	SCONJ
ejpam-5445	189	11	ρ	ρ	PROPN
ejpam-5445	189	12	̸=	̸=	PROPN
ejpam-5445	189	13	0	0	NUM
ejpam-5445	189	14	(	(	PUNCT
ejpam-5445	189	15	β	β	NOUN
ejpam-5445	189	16	−	−	NOUN
ejpam-5445	189	17	α	α	X
ejpam-5445	189	18	)	)	PUNCT
ejpam-5445	189	19	∈	∈	PROPN
ejpam-5445	189	20	;	;	PUNCT
ejpam-5445	189	21	if	if	SCONJ
ejpam-5445	189	22	ρ	ρ	PROPN
ejpam-5445	189	23	=	=	SYM
ejpam-5445	189	24	0	0	NUM
ejpam-5445	189	25	.	.	PUNCT
ejpam-5445	189	26	(	(	PUNCT
ejpam-5445	189	27	25	25	NUM
ejpam-5445	189	28	)	)	PUNCT
ejpam-5445	189	29	theorem	theorem	NOUN
ejpam-5445	189	30	1	1	NUM
ejpam-5445	189	31	.	.	PUNCT
ejpam-5445	190	1	the	the	DET
ejpam-5445	190	2	differential	differential	ADJ
ejpam-5445	190	3	equation	equation	NOUN
ejpam-5445	190	4	γiv(ω	γiv(ω	PROPN
ejpam-5445	190	5	)	)	PUNCT
ejpam-5445	190	6	+	+	CCONJ
ejpam-5445	190	7	ρ1γ	ρ1γ	PROPN
ejpam-5445	190	8	′′′(ω	′′′(ω	PROPN
ejpam-5445	190	9	)	)	PUNCT
ejpam-5445	191	1	+	+	PROPN
ejpam-5445	191	2	ρ2γ	ρ2γ	PROPN
ejpam-5445	191	3	′′(ω	′′(ω	NOUN
ejpam-5445	191	4	)	)	PUNCT
ejpam-5445	192	1	+	+	CCONJ
ejpam-5445	192	2	ρ3γ	ρ3γ	NUM
ejpam-5445	192	3	′(ω	′(ω	NOUN
ejpam-5445	192	4	)	)	PUNCT
ejpam-5445	192	5	+	+	X
ejpam-5445	192	6	ρ4γ(ω	ρ4γ(ω	ADJ
ejpam-5445	192	7	)	)	PUNCT
ejpam-5445	192	8	=	=	SYM
ejpam-5445	192	9	χ(ω	χ(ω	NOUN
ejpam-5445	192	10	)	)	PUNCT
ejpam-5445	192	11	has	have	VERB
ejpam-5445	192	12	the	the	DET
ejpam-5445	192	13	h	h	NOUN
ejpam-5445	192	14	−	−	PROPN
ejpam-5445	192	15	u	u	NOUN
ejpam-5445	192	16	stability	stability	NOUN
ejpam-5445	192	17	,	,	PUNCT
ejpam-5445	192	18	where	where	SCONJ
ejpam-5445	192	19	γ	γ	PROPN
ejpam-5445	192	20	∈	∈	PROPN
ejpam-5445	192	21	c4[α	c4[α	NOUN
ejpam-5445	192	22	,	,	PUNCT
ejpam-5445	192	23	β	β	X
ejpam-5445	192	24	]	]	PUNCT
ejpam-5445	192	25	and	and	CCONJ
ejpam-5445	192	26	χ	χ	DET
ejpam-5445	192	27	∈	∈	PROPN
ejpam-5445	193	1	[	[	X
ejpam-5445	193	2	α	α	X
ejpam-5445	193	3	,	,	PUNCT
ejpam-5445	193	4	β	β	X
ejpam-5445	193	5	]	]	PUNCT
ejpam-5445	193	6	.	.	PUNCT
ejpam-5445	194	1	therefore	therefore	ADV
ejpam-5445	194	2	|κ(ω)−	|κ(ω)−	PROPN
ejpam-5445	194	3	h(ω)|	h(ω)|	ADV
ejpam-5445	194	4	≤	≤	NUM
ejpam-5445	194	5			NUM
ejpam-5445	194	6	(	(	PUNCT
ejpam-5445	194	7	1−e−γ(β−α))(1−e−ρ(β−α))∈	1−e−γ(β−α))(1−e−ρ(β−α))∈	NUM
ejpam-5445	194	8	γρ	γρ	INTJ
ejpam-5445	194	9	;	;	PUNCT
ejpam-5445	194	10	if	if	SCONJ
ejpam-5445	194	11	ρ	ρ	PROPN
ejpam-5445	194	12	,	,	PUNCT
ejpam-5445	194	13	γ	γ	PROPN
ejpam-5445	194	14	̸=	̸=	PROPN
ejpam-5445	194	15	0	0	NUM
ejpam-5445	194	16	1−e−γ(β−α)(β−α)∈	1−e−γ(β−α)(β−α)∈	NUM
ejpam-5445	194	17	γ	γ	NOUN
ejpam-5445	194	18	;	;	PUNCT
ejpam-5445	194	19	if	if	SCONJ
ejpam-5445	194	20	ρ	ρ	PROPN
ejpam-5445	194	21	̸=	̸=	PROPN
ejpam-5445	194	22	0	0	NUM
ejpam-5445	194	23	,	,	PUNCT
ejpam-5445	194	24	γ	γ	PROPN
ejpam-5445	194	25	̸=	̸=	PROPN
ejpam-5445	194	26	0	0	NUM
ejpam-5445	194	27	1−e−ρ(β−α)(β−α)∈	1−e−ρ(β−α)(β−α)∈	NUM
ejpam-5445	194	28	ρ	ρ	NOUN
ejpam-5445	194	29	;	;	PUNCT
ejpam-5445	194	30	if	if	SCONJ
ejpam-5445	194	31	ρ	ρ	PROPN
ejpam-5445	194	32	̸=	̸=	PROPN
ejpam-5445	194	33	0	0	NUM
ejpam-5445	194	34	,	,	PUNCT
ejpam-5445	194	35	γ	γ	X
ejpam-5445	194	36	=	=	SYM
ejpam-5445	194	37	0	0	NUM
ejpam-5445	194	38	(	(	PUNCT
ejpam-5445	194	39	β	β	X
ejpam-5445	194	40	−	−	PROPN
ejpam-5445	194	41	α)2	α)2	NOUN
ejpam-5445	194	42	∈	∈	NOUN
ejpam-5445	194	43	;	;	PUNCT
ejpam-5445	194	44	if	if	SCONJ
ejpam-5445	194	45	ρ	ρ	PROPN
ejpam-5445	194	46	=	=	SYM
ejpam-5445	194	47	0	0	NUM
ejpam-5445	194	48	,	,	PUNCT
ejpam-5445	194	49	γ	γ	X
ejpam-5445	194	50	=	=	SYM
ejpam-5445	194	51	0	0	NUM
ejpam-5445	194	52	with	with	ADP
ejpam-5445	194	53	respect	respect	NOUN
ejpam-5445	194	54	to	to	ADP
ejpam-5445	194	55	ω	ω	PROPN
ejpam-5445	194	56	∈	∈	PROPN
ejpam-5445	194	57	[	[	X
ejpam-5445	194	58	α	α	X
ejpam-5445	194	59	,	,	PUNCT
ejpam-5445	194	60	β	β	X
ejpam-5445	194	61	]	]	PUNCT
ejpam-5445	194	62	.	.	PUNCT
ejpam-5445	195	1	proof	proof	NOUN
ejpam-5445	195	2	.	.	PUNCT
ejpam-5445	196	1	similar	similar	ADJ
ejpam-5445	196	2	to	to	ADP
ejpam-5445	196	3	the	the	DET
ejpam-5445	196	4	proof	proof	NOUN
ejpam-5445	196	5	of	of	ADP
ejpam-5445	196	6	lemma	lemma	PROPN
ejpam-5445	196	7	1	1	NUM
ejpam-5445	196	8	.	.	PUNCT
ejpam-5445	197	1	let	let	VERB
ejpam-5445	197	2	h(ω	h(ω	X
ejpam-5445	197	3	)	)	PUNCT
ejpam-5445	198	1	=	=	SYM
ejpam-5445	198	2	γ′(ω	γ′(ω	PROPN
ejpam-5445	198	3	)	)	PUNCT
ejpam-5445	199	1	−	−	PROPN
ejpam-5445	199	2	u2γ(ω	u2γ(ω	PROPN
ejpam-5445	199	3	)	)	PUNCT
ejpam-5445	199	4	by	by	ADP
ejpam-5445	199	5	h	h	PROPN
ejpam-5445	199	6	′(ω	′(ω	NOUN
ejpam-5445	199	7	)	)	PUNCT
ejpam-5445	199	8	=	=	PUNCT
ejpam-5445	199	9	γ′′(ω)−	γ′′(ω)−	PROPN
ejpam-5445	199	10	u1γ	u1γ	PROPN
ejpam-5445	199	11	′(ω	′(ω	NOUN
ejpam-5445	199	12	)	)	PUNCT
ejpam-5445	199	13	and	and	CCONJ
ejpam-5445	199	14	let	let	VERB
ejpam-5445	199	15	∈	∈	PRON
ejpam-5445	199	16	>	>	X
ejpam-5445	199	17	0	0	NUM
ejpam-5445	199	18	;	;	PUNCT
ejpam-5445	199	19	γ	γ	PROPN
ejpam-5445	199	20	∈	∈	PROPN
ejpam-5445	199	21	c4[α	c4[α	NOUN
ejpam-5445	199	22	,	,	PUNCT
ejpam-5445	199	23	β	β	X
ejpam-5445	199	24	]	]	PUNCT
ejpam-5445	199	25	.	.	PUNCT
ejpam-5445	200	1	also	also	ADV
ejpam-5445	200	2	|h	|h	VERB
ejpam-5445	200	3	′(ω)−	′(ω)−	PROPN
ejpam-5445	200	4	u4h(ω)−	u4h(ω)−	ADP
ejpam-5445	200	5	ζ(ω)|	ζ(ω)|	NOUN
ejpam-5445	200	6	=	=	PUNCT
ejpam-5445	200	7	|ζ(ω)−	|ζ(ω)−	PROPN
ejpam-5445	200	8	g(ω)|	g(ω)|	PROPN
ejpam-5445	200	9	(	(	PUNCT
ejpam-5445	200	10	26	26	NUM
ejpam-5445	200	11	)	)	PUNCT
ejpam-5445	200	12	with	with	ADP
ejpam-5445	200	13	respect	respect	NOUN
ejpam-5445	200	14	to	to	ADP
ejpam-5445	200	15	ω	ω	PROPN
ejpam-5445	200	16	∈	∈	PROPN
ejpam-5445	200	17	[	[	X
ejpam-5445	200	18	α	α	X
ejpam-5445	200	19	,	,	PUNCT
ejpam-5445	200	20	β	β	X
ejpam-5445	200	21	]	]	PUNCT
ejpam-5445	200	22	.	.	PUNCT
ejpam-5445	201	1	thus	thus	ADV
ejpam-5445	201	2	|h	|h	X
ejpam-5445	201	3	′(ω)−	′(ω)−	PROPN
ejpam-5445	201	4	u4h(ω)−	u4h(ω)−	PROPN
ejpam-5445	201	5	ζ(ω)|	ζ(ω)|	PROPN
ejpam-5445	201	6	≤∈	≤∈	PROPN
ejpam-5445	201	7	(	(	PUNCT
ejpam-5445	201	8	27	27	NUM
ejpam-5445	201	9	)	)	PUNCT
ejpam-5445	201	10	s.	s.	PROPN
ejpam-5445	201	11	bowmiya	bowmiya	VERB
ejpam-5445	201	12	et	et	PROPN
ejpam-5445	201	13	al	al	PROPN
ejpam-5445	201	14	.	.	PUNCT
ejpam-5445	201	15	/	/	SYM
ejpam-5445	201	16	eur	eur	PROPN
ejpam-5445	201	17	.	.	PUNCT
ejpam-5445	202	1	j.	j.	PROPN
ejpam-5445	202	2	pure	pure	PROPN
ejpam-5445	202	3	appl	appl	PROPN
ejpam-5445	202	4	.	.	PROPN
ejpam-5445	202	5	math	math	PROPN
ejpam-5445	202	6	,	,	PUNCT
ejpam-5445	202	7	17	17	NUM
ejpam-5445	202	8	(	(	PUNCT
ejpam-5445	202	9	4	4	NUM
ejpam-5445	202	10	)	)	PUNCT
ejpam-5445	202	11	(	(	PUNCT
ejpam-5445	202	12	2024	2024	NUM
ejpam-5445	202	13	)	)	PUNCT
ejpam-5445	202	14	,	,	PUNCT
ejpam-5445	202	15	3415	3415	NUM
ejpam-5445	202	16	-	-	SYM
ejpam-5445	202	17	3435	3435	NUM
ejpam-5445	202	18	3423	3423	NUM
ejpam-5445	202	19	with	with	ADP
ejpam-5445	202	20	respect	respect	NOUN
ejpam-5445	202	21	to	to	ADP
ejpam-5445	202	22	ω	ω	PROPN
ejpam-5445	202	23	∈	∈	PROPN
ejpam-5445	202	24	[	[	X
ejpam-5445	202	25	α	α	X
ejpam-5445	202	26	,	,	PUNCT
ejpam-5445	202	27	β	β	X
ejpam-5445	202	28	]	]	PUNCT
ejpam-5445	202	29	.	.	PUNCT
ejpam-5445	203	1	equivalently	equivalently	ADV
ejpam-5445	203	2	h	h	PROPN
ejpam-5445	203	3	fulfilling	fulfil	VERB
ejpam-5445	203	4	|h	|h	X
ejpam-5445	203	5	′(ω)−	′(ω)−	PROPN
ejpam-5445	203	6	u4h(ω)−	u4h(ω)−	PROPN
ejpam-5445	203	7	ζ(ω)|	ζ(ω)|	NOUN
ejpam-5445	203	8	=	=	PUNCT
ejpam-5445	203	9	|γ′′	|γ′′	PUNCT
ejpam-5445	203	10	(	(	PUNCT
ejpam-5445	203	11	ω)−	ω)−	PROPN
ejpam-5445	203	12	(	(	PUNCT
ejpam-5445	203	13	u1	u1	PROPN
ejpam-5445	203	14	+	+	CCONJ
ejpam-5445	203	15	u4)γ	u4)γ	PROPN
ejpam-5445	203	16	′(ω	′(ω	NOUN
ejpam-5445	203	17	)	)	PUNCT
ejpam-5445	203	18	+	+	CCONJ
ejpam-5445	203	19	u1u4γ(ω)−	u1u4γ(ω)−	ADP
ejpam-5445	203	20	ζ(ω)|	ζ(ω)|	ADJ
ejpam-5445	203	21	=	=	SYM
ejpam-5445	203	22	|γ′′(ω	|γ′′(ω	PROPN
ejpam-5445	203	23	)	)	PUNCT
ejpam-5445	203	24	+	+	CCONJ
ejpam-5445	203	25	ρ1γ	ρ1γ	PROPN
ejpam-5445	203	26	′(ω	′(ω	NOUN
ejpam-5445	203	27	)	)	PUNCT
ejpam-5445	203	28	+	+	CCONJ
ejpam-5445	204	1	ρ2γ(ω)−	ρ2γ(ω)−	PROPN
ejpam-5445	204	2	ζ(ω)|	ζ(ω)|	X
ejpam-5445	205	1	<	<	X
ejpam-5445	205	2	∈	∈	PROPN
ejpam-5445	205	3	(	(	PUNCT
ejpam-5445	205	4	28	28	NUM
ejpam-5445	205	5	)	)	PUNCT
ejpam-5445	205	6	with	with	ADP
ejpam-5445	205	7	respect	respect	NOUN
ejpam-5445	205	8	to	to	ADP
ejpam-5445	205	9	ω	ω	PROPN
ejpam-5445	205	10	∈	∈	PROPN
ejpam-5445	205	11	[	[	X
ejpam-5445	205	12	α	α	X
ejpam-5445	205	13	,	,	PUNCT
ejpam-5445	205	14	β	β	X
ejpam-5445	205	15	]	]	X
ejpam-5445	205	16	.	.	PUNCT
ejpam-5445	206	1	multiplying	multiply	VERB
ejpam-5445	206	2	28	28	NUM
ejpam-5445	206	3	by	by	ADP
ejpam-5445	206	4	e−u4(ω−α	e−u4(ω−α	NOUN
ejpam-5445	206	5	)	)	PUNCT
ejpam-5445	206	6	on	on	ADP
ejpam-5445	206	7	both	both	DET
ejpam-5445	206	8	sides	side	NOUN
ejpam-5445	206	9	,	,	PUNCT
ejpam-5445	206	10	shown	show	VERB
ejpam-5445	206	11	up	up	ADP
ejpam-5445	206	12	−	−	PROPN
ejpam-5445	206	13	∈	∈	PROPN
ejpam-5445	206	14	e−u4(ω−α	e−u4(ω−α	NOUN
ejpam-5445	206	15	)	)	PUNCT
ejpam-5445	206	16	≤	≤	NUM
ejpam-5445	206	17	h	h	SYM
ejpam-5445	206	18	′(ω)e−u4(ω−α	′(ω)e−u4(ω−α	PROPN
ejpam-5445	206	19	)	)	PUNCT
ejpam-5445	206	20	−	−	ADP
ejpam-5445	206	21	u4h(ω)e−u4(ω−α	u4h(ω)e−u4(ω−α	NOUN
ejpam-5445	206	22	)	)	PUNCT
ejpam-5445	206	23	−	−	PRON
ejpam-5445	206	24	ζ(ω)e−u4(ω−α	ζ(ω)e−u4(ω−α	NOUN
ejpam-5445	206	25	)	)	PUNCT
ejpam-5445	206	26	≤∈	≤∈	NOUN
ejpam-5445	206	27	e−u4(ω−α	e−u4(ω−α	NOUN
ejpam-5445	206	28	)	)	PUNCT
ejpam-5445	206	29	(	(	PUNCT
ejpam-5445	206	30	29	29	NUM
ejpam-5445	206	31	)	)	PUNCT
ejpam-5445	206	32	with	with	ADP
ejpam-5445	206	33	respect	respect	NOUN
ejpam-5445	206	34	to	to	ADP
ejpam-5445	206	35	ω	ω	PROPN
ejpam-5445	206	36	∈	∈	PROPN
ejpam-5445	206	37	[	[	X
ejpam-5445	206	38	α	α	X
ejpam-5445	206	39	,	,	PUNCT
ejpam-5445	206	40	β	β	X
ejpam-5445	206	41	]	]	X
ejpam-5445	206	42	.	.	PUNCT
ejpam-5445	207	1	without	without	ADP
ejpam-5445	207	2	loss	loss	NOUN
ejpam-5445	207	3	of	of	ADP
ejpam-5445	207	4	all	all	DET
ejpam-5445	207	5	inclusive	inclusive	ADJ
ejpam-5445	207	6	statement	statement	NOUN
ejpam-5445	207	7	we	we	PRON
ejpam-5445	207	8	may	may	AUX
ejpam-5445	207	9	accept	accept	VERB
ejpam-5445	207	10	that	that	SCONJ
ejpam-5445	207	11	u4	u4	PROPN
ejpam-5445	207	12	>	>	X
ejpam-5445	207	13	1	1	NUM
ejpam-5445	207	14	,	,	PUNCT
ejpam-5445	207	15	thus	thus	ADV
ejpam-5445	207	16	u4	u4	PROPN
ejpam-5445	207	17	∈	∈	PROPN
ejpam-5445	207	18	e−u4(ω−α	e−u4(ω−α	NOUN
ejpam-5445	207	19	)	)	PUNCT
ejpam-5445	207	20	≤	≤	NUM
ejpam-5445	207	21	h	h	PROPN
ejpam-5445	207	22	′(ω)e−u4(ω−α	′(ω)e−u4(ω−α	PROPN
ejpam-5445	207	23	)	)	PUNCT
ejpam-5445	207	24	−h(ω)e−u4(ω−α	−h(ω)e−u4(ω−α	NOUN
ejpam-5445	207	25	)	)	PUNCT
ejpam-5445	207	26	−	−	ADP
ejpam-5445	207	27	ζ(ω)e−u4(ω−α	ζ(ω)e−u4(ω−α	NOUN
ejpam-5445	207	28	)	)	PUNCT
ejpam-5445	207	29	∈	∈	PROPN
ejpam-5445	207	30	u4e	u4e	X
ejpam-5445	207	31	−u4(ω−α	−u4(ω−α	PROPN
ejpam-5445	207	32	)	)	PUNCT
ejpam-5445	207	33	(	(	PUNCT
ejpam-5445	207	34	30	30	NUM
ejpam-5445	207	35	)	)	PUNCT
ejpam-5445	207	36	with	with	ADP
ejpam-5445	207	37	respect	respect	NOUN
ejpam-5445	207	38	to	to	ADP
ejpam-5445	207	39	ω	ω	PROPN
ejpam-5445	207	40	∈	∈	PROPN
ejpam-5445	208	1	[	[	X
ejpam-5445	208	2	α	α	X
ejpam-5445	208	3	,	,	PUNCT
ejpam-5445	208	4	β	β	X
ejpam-5445	208	5	]	]	X
ejpam-5445	208	6	,	,	PUNCT
ejpam-5445	208	7	integrating	integrate	VERB
ejpam-5445	208	8	30	30	NUM
ejpam-5445	208	9	from	from	ADP
ejpam-5445	208	10	ω	ω	NUM
ejpam-5445	208	11	to	to	ADP
ejpam-5445	208	12	β	β	PRON
ejpam-5445	208	13	,	,	PUNCT
ejpam-5445	208	14	we	we	PRON
ejpam-5445	208	15	achieve	achieve	VERB
ejpam-5445	208	16	−	−	PROPN
ejpam-5445	208	17	∈	∈	PROPN
ejpam-5445	208	18	(	(	PUNCT
ejpam-5445	208	19	e−u4(ω−α	e−u4(ω−α	NOUN
ejpam-5445	208	20	)	)	PUNCT
ejpam-5445	209	1	−	−	NOUN
ejpam-5445	209	2	e−u4(β−α	e−u4(β−α	NOUN
ejpam-5445	209	3	)	)	PUNCT
ejpam-5445	209	4	)	)	PUNCT
ejpam-5445	209	5	≤	≤	NUM
ejpam-5445	209	6	h(β)e−u4(β−α	h(β)e−u4(β−α	NOUN
ejpam-5445	209	7	)	)	PUNCT
ejpam-5445	209	8	−h(ω)e−u4(ω−α	−h(ω)e−u4(ω−α	ADJ
ejpam-5445	209	9	)	)	PUNCT
ejpam-5445	209	10	−	−	ADP
ejpam-5445	209	11	∫	∫	PROPN
ejpam-5445	209	12	β	β	PROPN
ejpam-5445	209	13	ω	ω	PROPN
ejpam-5445	209	14	ζ(τ)e−u4(ω−α)dτ	ζ(τ)e−u4(ω−α)dτ	PROPN
ejpam-5445	209	15	≤∈	≤∈	PROPN
ejpam-5445	209	16	(	(	PUNCT
ejpam-5445	209	17	e−u4(ω−α	e−u4(ω−α	NOUN
ejpam-5445	209	18	)	)	PUNCT
ejpam-5445	209	19	−	−	NOUN
ejpam-5445	210	1	e−u4(β−α	e−u4(β−α	NOUN
ejpam-5445	210	2	)	)	PUNCT
ejpam-5445	210	3	)	)	PUNCT
ejpam-5445	210	4	(	(	PUNCT
ejpam-5445	210	5	31	31	NUM
ejpam-5445	210	6	)	)	PUNCT
ejpam-5445	210	7	with	with	ADP
ejpam-5445	210	8	respect	respect	NOUN
ejpam-5445	210	9	to	to	ADP
ejpam-5445	210	10	ω	ω	PROPN
ejpam-5445	210	11	∈	∈	PROPN
ejpam-5445	210	12	[	[	X
ejpam-5445	210	13	α	α	X
ejpam-5445	210	14	,	,	PUNCT
ejpam-5445	210	15	β	β	X
ejpam-5445	210	16	]	]	PUNCT
ejpam-5445	210	17	.	.	PUNCT
ejpam-5445	211	1	it	it	PRON
ejpam-5445	211	2	follows	follow	VERB
ejpam-5445	211	3	from	from	ADP
ejpam-5445	211	4	31	31	NUM
ejpam-5445	211	5	,	,	PUNCT
ejpam-5445	211	6	we	we	PRON
ejpam-5445	211	7	get	get	VERB
ejpam-5445	211	8	−	−	PROPN
ejpam-5445	211	9	∈	∈	PROPN
ejpam-5445	211	10	e−u4(ω−α	e−u4(ω−α	NOUN
ejpam-5445	211	11	)	)	PUNCT
ejpam-5445	211	12	≤	≤	NUM
ejpam-5445	211	13	h(β)e−u4(β−α)−	h(β)e−u4(β−α)−	NOUN
ejpam-5445	211	14	∈	∈	PROPN
ejpam-5445	211	15	e−u4(β−α	e−u4(β−α	NOUN
ejpam-5445	211	16	)	)	PUNCT
ejpam-5445	211	17	−h(ω)e−u4(ω−α	−h(ω)e−u4(ω−α	ADJ
ejpam-5445	211	18	)	)	PUNCT
ejpam-5445	212	1	−	−	ADP
ejpam-5445	212	2	∫	∫	PROPN
ejpam-5445	212	3	β	β	PROPN
ejpam-5445	212	4	ω	ω	PROPN
ejpam-5445	212	5	ζ(τ)e−u4(ω−α)dτ	ζ(τ)e−u4(ω−α)dτ	PROPN
ejpam-5445	212	6	≤∈	≤∈	PROPN
ejpam-5445	212	7	(	(	PUNCT
ejpam-5445	212	8	e−u4(ω−α	e−u4(ω−α	NOUN
ejpam-5445	212	9	)	)	PUNCT
ejpam-5445	212	10	)	)	PUNCT
ejpam-5445	213	1	(	(	PUNCT
ejpam-5445	213	2	32	32	NUM
ejpam-5445	213	3	)	)	PUNCT
ejpam-5445	213	4	with	with	ADP
ejpam-5445	213	5	respect	respect	NOUN
ejpam-5445	213	6	to	to	ADP
ejpam-5445	213	7	ω	ω	PROPN
ejpam-5445	213	8	∈	∈	PROPN
ejpam-5445	213	9	[	[	X
ejpam-5445	213	10	α	α	X
ejpam-5445	213	11	,	,	PUNCT
ejpam-5445	213	12	β	β	X
ejpam-5445	213	13	]	]	X
ejpam-5445	213	14	.	.	PUNCT
ejpam-5445	214	1	multiplying	multiply	VERB
ejpam-5445	214	2	the	the	DET
ejpam-5445	214	3	formula	formula	NOUN
ejpam-5445	214	4	by	by	ADP
ejpam-5445	214	5	the	the	DET
ejpam-5445	214	6	function	function	NOUN
ejpam-5445	214	7	e−u4(ω−α	e−u4(ω−α	NOUN
ejpam-5445	214	8	)	)	PUNCT
ejpam-5445	214	9	in	in	ADP
ejpam-5445	214	10	32	32	NUM
ejpam-5445	214	11	,	,	PUNCT
ejpam-5445	214	12	we	we	PRON
ejpam-5445	214	13	get	get	VERB
ejpam-5445	214	14	−	−	PROPN
ejpam-5445	214	15	∈	∈	PROPN
ejpam-5445	214	16	≤	≤	NUM
ejpam-5445	214	17	h(β)e−u4(β−ω)−	h(β)e−u4(β−ω)−	NOUN
ejpam-5445	214	18	∈	∈	PROPN
ejpam-5445	214	19	e−u4(β−ω	e−u4(β−ω	NOUN
ejpam-5445	214	20	)	)	PUNCT
ejpam-5445	214	21	−h(ω)−	−h(ω)−	NOUN
ejpam-5445	214	22	eu4ω	eu4ω	PROPN
ejpam-5445	214	23	∫	∫	PROPN
ejpam-5445	214	24	β	β	PROPN
ejpam-5445	214	25	ω	ω	PROPN
ejpam-5445	214	26	ζ(τ)eu4τdτ	ζ(τ)eu4τdτ	X
ejpam-5445	214	27	≤∈	≤∈	PROPN
ejpam-5445	214	28	(	(	PUNCT
ejpam-5445	214	29	33	33	NUM
ejpam-5445	214	30	)	)	PUNCT
ejpam-5445	214	31	with	with	ADP
ejpam-5445	214	32	respect	respect	NOUN
ejpam-5445	214	33	to	to	ADP
ejpam-5445	214	34	ω	ω	PROPN
ejpam-5445	214	35	∈	∈	PROPN
ejpam-5445	214	36	[	[	X
ejpam-5445	214	37	α	α	X
ejpam-5445	214	38	,	,	PUNCT
ejpam-5445	214	39	β	β	X
ejpam-5445	214	40	]	]	PUNCT
ejpam-5445	214	41	.	.	PUNCT
ejpam-5445	215	1	it	it	PRON
ejpam-5445	215	2	follows	follow	VERB
ejpam-5445	215	3	from	from	ADP
ejpam-5445	215	4	33	33	NUM
ejpam-5445	215	5	,	,	PUNCT
ejpam-5445	215	6	we	we	PRON
ejpam-5445	215	7	get	get	VERB
ejpam-5445	215	8	−	−	PROPN
ejpam-5445	215	9	∈	∈	NOUN
ejpam-5445	215	10	≤	≤	NOUN
ejpam-5445	215	11	h(β)eu4(ω−β)−	h(β)eu4(ω−β)−	PROPN
ejpam-5445	215	12	∈	∈	PROPN
ejpam-5445	215	13	eu4(ω−β	eu4(ω−β	PROPN
ejpam-5445	215	14	)	)	PUNCT
ejpam-5445	216	1	−h(ω)−	−h(ω)−	NOUN
ejpam-5445	216	2	eu4ω	eu4ω	PROPN
ejpam-5445	216	3	∫	∫	PROPN
ejpam-5445	216	4	β	β	PROPN
ejpam-5445	216	5	ω	ω	PROPN
ejpam-5445	216	6	ζ(τ)eu4τdτ	ζ(τ)eu4τdτ	X
ejpam-5445	216	7	≤∈	≤∈	PROPN
ejpam-5445	216	8	(	(	PUNCT
ejpam-5445	216	9	34	34	NUM
ejpam-5445	216	10	)	)	PUNCT
ejpam-5445	216	11	with	with	ADP
ejpam-5445	216	12	respect	respect	NOUN
ejpam-5445	216	13	to	to	ADP
ejpam-5445	216	14	ω	ω	PROPN
ejpam-5445	216	15	∈	∈	PROPN
ejpam-5445	216	16	[	[	X
ejpam-5445	216	17	α	α	X
ejpam-5445	216	18	,	,	PUNCT
ejpam-5445	216	19	β	β	X
ejpam-5445	216	20	]	]	PUNCT
ejpam-5445	216	21	.	.	PUNCT
ejpam-5445	217	1	let	let	VERB
ejpam-5445	217	2	κ(ω	κ(ω	PROPN
ejpam-5445	217	3	)	)	PUNCT
ejpam-5445	218	1	=	=	PRON
ejpam-5445	218	2	h(β)e−u4(ω−β)−	h(β)e−u4(ω−β)−	VERB
ejpam-5445	218	3	eu4ω	eu4ω	PROPN
ejpam-5445	218	4	∫	∫	PROPN
ejpam-5445	218	5	β	β	PROPN
ejpam-5445	218	6	ω	ω	PROPN
ejpam-5445	218	7	ζ(τ)e−u4τdτ	ζ(τ)e−u4τdτ	PROPN
ejpam-5445	218	8	.	.	PUNCT
ejpam-5445	219	1	with	with	ADP
ejpam-5445	219	2	respect	respect	NOUN
ejpam-5445	219	3	to	to	ADP
ejpam-5445	219	4	ω	ω	PROPN
ejpam-5445	219	5	∈	∈	PROPN
ejpam-5445	219	6	[	[	X
ejpam-5445	219	7	α	α	X
ejpam-5445	219	8	,	,	PUNCT
ejpam-5445	219	9	β	β	X
ejpam-5445	219	10	]	]	PUNCT
ejpam-5445	219	11	.	.	PUNCT
ejpam-5445	220	1	then	then	ADV
ejpam-5445	220	2	κ′(ω)−	κ′(ω)−	VERB
ejpam-5445	220	3	u4κ(ω)−	u4κ(ω)−	ADP
ejpam-5445	220	4	ζ(ω	ζ(ω	NOUN
ejpam-5445	220	5	)	)	PUNCT
ejpam-5445	220	6	=	=	SYM
ejpam-5445	220	7	0	0	NUM
ejpam-5445	220	8	by	by	ADP
ejpam-5445	220	9	s.	s.	PROPN
ejpam-5445	220	10	bowmiya	bowmiya	PROPN
ejpam-5445	220	11	et	et	PROPN
ejpam-5445	220	12	al	al	PROPN
ejpam-5445	220	13	.	.	PUNCT
ejpam-5445	220	14	/	/	SYM
ejpam-5445	220	15	eur	eur	PROPN
ejpam-5445	220	16	.	.	PUNCT
ejpam-5445	221	1	j.	j.	PROPN
ejpam-5445	221	2	pure	pure	PROPN
ejpam-5445	221	3	appl	appl	PROPN
ejpam-5445	221	4	.	.	PROPN
ejpam-5445	221	5	math	math	PROPN
ejpam-5445	221	6	,	,	PUNCT
ejpam-5445	221	7	17	17	NUM
ejpam-5445	221	8	(	(	PUNCT
ejpam-5445	221	9	4	4	NUM
ejpam-5445	221	10	)	)	PUNCT
ejpam-5445	221	11	(	(	PUNCT
ejpam-5445	221	12	2024	2024	NUM
ejpam-5445	221	13	)	)	PUNCT
ejpam-5445	221	14	,	,	PUNCT
ejpam-5445	221	15	3415	3415	NUM
ejpam-5445	221	16	-	-	SYM
ejpam-5445	221	17	3435	3435	NUM
ejpam-5445	221	18	3424	3424	NUM
ejpam-5445	221	19	κ′(ω	κ′(ω	PROPN
ejpam-5445	221	20	)	)	PUNCT
ejpam-5445	221	21	=	=	SYM
ejpam-5445	221	22	u4κ(ω	u4κ(ω	PROPN
ejpam-5445	221	23	)	)	PUNCT
ejpam-5445	221	24	+	+	CCONJ
ejpam-5445	221	25	ζ(ω	ζ(ω	PROPN
ejpam-5445	221	26	)	)	PUNCT
ejpam-5445	221	27	.	.	PUNCT
ejpam-5445	222	1	thus	thus	ADV
ejpam-5445	222	2	|κ(ω)−h(ω)|	|κ(ω)−h(ω)|	ADJ
ejpam-5445	222	3	=	=	PUNCT
ejpam-5445	222	4	eu4(ω−β)h(β)−h(ω)−	eu4(ω−β)h(β)−h(ω)−	PROPN
ejpam-5445	222	5	eu4ω	eu4ω	PROPN
ejpam-5445	222	6	∫	∫	PROPN
ejpam-5445	222	7	β	β	PROPN
ejpam-5445	222	8	α	α	PROPN
ejpam-5445	222	9	ζ(τ)e−u4τdτ	ζ(τ)e−u4τdτ	PROPN
ejpam-5445	222	10	=	=	PUNCT
ejpam-5445	222	11	eγω|	eγω|	NOUN
ejpam-5445	222	12	∫	∫	PROPN
ejpam-5445	222	13	β	β	PROPN
ejpam-5445	222	14	α	α	X
ejpam-5445	222	15	[	[	PUNCT
ejpam-5445	222	16	e−u4τh(τ)−	e−u4τh(τ)−	NOUN
ejpam-5445	222	17	]	]	PUNCT
ejpam-5445	222	18	−	−	PROPN
ejpam-5445	223	1	∫	∫	PROPN
ejpam-5445	223	2	β	β	PROPN
ejpam-5445	223	3	α	α	PROPN
ejpam-5445	223	4	ζ(τ)e−u4τdτ	ζ(τ)e−u4τdτ	PROPN
ejpam-5445	223	5	|	|	ADV
ejpam-5445	223	6	≤	≤	NUM
ejpam-5445	223	7	eγω	eγω	NOUN
ejpam-5445	223	8	∫	∫	PROPN
ejpam-5445	223	9	β	β	PROPN
ejpam-5445	223	10	ω	ω	PROPN
ejpam-5445	224	1	|e−u4τ	|e−u4τ	PROPN
ejpam-5445	224	2	||h	||h	PROPN
ejpam-5445	224	3	′(τ)−	′(τ)−	PROPN
ejpam-5445	224	4	u4h(τ)−	u4h(τ)−	PROPN
ejpam-5445	224	5	ζ(t)|dτ	ζ(t)|dτ	PROPN
ejpam-5445	224	6	≤	≤	PROPN
ejpam-5445	224	7	eγω	eγω	NOUN
ejpam-5445	224	8	∫	∫	PROPN
ejpam-5445	224	9	β	β	PROPN
ejpam-5445	224	10	ω	ω	X
ejpam-5445	224	11	e−γτ	e−γτ	PROPN
ejpam-5445	224	12	|h	|h	PROPN
ejpam-5445	224	13	′(τ)−	′(τ)−	PROPN
ejpam-5445	224	14	u4h(τ)−	u4h(τ)−	PROPN
ejpam-5445	224	15	ζ(t)|dτ	ζ(t)|dτ	PROPN
ejpam-5445	224	16	|κ(ω)−h(ω)|	|κ(ω)−h(ω)|	PRON
ejpam-5445	224	17	≤∈	≤∈	ADJ
ejpam-5445	224	18	eγω	eγω	NOUN
ejpam-5445	224	19	∫	∫	PROPN
ejpam-5445	224	20	β	β	PROPN
ejpam-5445	224	21	ω	ω	X
ejpam-5445	224	22	e−γτdτ	e−γτdτ	PROPN
ejpam-5445	224	23	(	(	PUNCT
ejpam-5445	224	24	35	35	NUM
ejpam-5445	224	25	)	)	PUNCT
ejpam-5445	224	26	with	with	ADP
ejpam-5445	224	27	respect	respect	NOUN
ejpam-5445	224	28	to	to	ADP
ejpam-5445	224	29	ω	ω	PROPN
ejpam-5445	224	30	∈	∈	PROPN
ejpam-5445	224	31	[	[	X
ejpam-5445	224	32	α	α	X
ejpam-5445	224	33	,	,	PUNCT
ejpam-5445	224	34	β	β	X
ejpam-5445	224	35	]	]	X
ejpam-5445	224	36	.	.	PUNCT
ejpam-5445	225	1	if	if	SCONJ
ejpam-5445	225	2	γ	γ	PRON
ejpam-5445	225	3	̸=	̸=	PROPN
ejpam-5445	225	4	0	0	NUM
ejpam-5445	225	5	,	,	PUNCT
ejpam-5445	225	6	then	then	ADV
ejpam-5445	225	7	|κ(ω)−h(ω)|	|κ(ω)−h(ω)|	PRON
ejpam-5445	225	8	≤∈	≤∈	ADJ
ejpam-5445	225	9	eγω	eγω	NOUN
ejpam-5445	225	10	∫	∫	PROPN
ejpam-5445	225	11	β	β	PROPN
ejpam-5445	225	12	ω	ω	PROPN
ejpam-5445	225	13	e−γτdτ	e−γτdτ	X
ejpam-5445	225	14	≤	≤	X
ejpam-5445	225	15	∈	∈	PROPN
ejpam-5445	225	16	γ	γ	X
ejpam-5445	225	17	[	[	X
ejpam-5445	225	18	1−	1−	NUM
ejpam-5445	225	19	e−γ(β−ω	e−γ(β−ω	NOUN
ejpam-5445	225	20	)	)	PUNCT
ejpam-5445	225	21	]	]	PUNCT
ejpam-5445	225	22	|κ(ω)−h(ω)|	|κ(ω)−h(ω)|	X
ejpam-5445	225	23	≤	≤	NUM
ejpam-5445	225	24	∈	∈	PROPN
ejpam-5445	225	25	γ	γ	X
ejpam-5445	225	26	[	[	X
ejpam-5445	225	27	1−	1−	NUM
ejpam-5445	225	28	e−γ(β−α	e−γ(β−α	NOUN
ejpam-5445	225	29	)	)	PUNCT
ejpam-5445	225	30	]	]	PUNCT
ejpam-5445	225	31	(	(	PUNCT
ejpam-5445	225	32	36	36	NUM
ejpam-5445	225	33	)	)	PUNCT
ejpam-5445	225	34	with	with	ADP
ejpam-5445	225	35	respect	respect	NOUN
ejpam-5445	225	36	to	to	ADP
ejpam-5445	225	37	ω	ω	PROPN
ejpam-5445	225	38	∈	∈	PROPN
ejpam-5445	225	39	[	[	X
ejpam-5445	225	40	α	α	X
ejpam-5445	225	41	,	,	PUNCT
ejpam-5445	225	42	β	β	X
ejpam-5445	225	43	]	]	X
ejpam-5445	225	44	.	.	PUNCT
ejpam-5445	226	1	if	if	SCONJ
ejpam-5445	226	2	γ	γ	X
ejpam-5445	226	3	=	=	SYM
ejpam-5445	226	4	0	0	PROPN
ejpam-5445	226	5	,	,	PUNCT
ejpam-5445	226	6	then	then	ADV
ejpam-5445	226	7	|κ(ω)−h(ω)|	|κ(ω)−h(ω)|	PRON
ejpam-5445	226	8	≤∈	≤∈	X
ejpam-5445	226	9	(	(	PUNCT
ejpam-5445	226	10	β	β	NOUN
ejpam-5445	226	11	−	−	NOUN
ejpam-5445	226	12	α	α	NOUN
ejpam-5445	226	13	)	)	PUNCT
ejpam-5445	226	14	(	(	PUNCT
ejpam-5445	226	15	37	37	NUM
ejpam-5445	226	16	)	)	PUNCT
ejpam-5445	226	17	with	with	ADP
ejpam-5445	226	18	respect	respect	NOUN
ejpam-5445	226	19	to	to	ADP
ejpam-5445	226	20	ω	ω	PROPN
ejpam-5445	226	21	∈	∈	PROPN
ejpam-5445	226	22	[	[	X
ejpam-5445	226	23	α	α	X
ejpam-5445	226	24	,	,	PUNCT
ejpam-5445	226	25	β	β	X
ejpam-5445	226	26	]	]	PUNCT
ejpam-5445	226	27	.	.	PUNCT
ejpam-5445	227	1	if	if	SCONJ
ejpam-5445	227	2	follows	follow	VERB
ejpam-5445	227	3	from	from	ADP
ejpam-5445	227	4	25	25	NUM
ejpam-5445	227	5	,	,	PUNCT
ejpam-5445	227	6	shown	show	VERB
ejpam-5445	227	7	up	up	ADP
ejpam-5445	227	8	|κ(ω)−h(ω)|	|κ(ω)−h(ω)|	PRON
ejpam-5445	227	9	≤	≤	NUM
ejpam-5445	227	10			NUM
ejpam-5445	227	11	(	(	PUNCT
ejpam-5445	227	12	1−e−γ(β−α))(1−e−ρ(β−α))∈	1−e−γ(β−α))(1−e−ρ(β−α))∈	NUM
ejpam-5445	227	13	γρ	γρ	INTJ
ejpam-5445	227	14	;	;	PUNCT
ejpam-5445	227	15	if	if	SCONJ
ejpam-5445	227	16	ρ	ρ	PROPN
ejpam-5445	227	17	,	,	PUNCT
ejpam-5445	227	18	γ	γ	PROPN
ejpam-5445	227	19	̸=	̸=	PROPN
ejpam-5445	227	20	0	0	NUM
ejpam-5445	227	21	1−e−γ(β−α)(β−α)∈	1−e−γ(β−α)(β−α)∈	NUM
ejpam-5445	227	22	γ	γ	NOUN
ejpam-5445	227	23	;	;	PUNCT
ejpam-5445	227	24	if	if	SCONJ
ejpam-5445	227	25	ρ	ρ	PROPN
ejpam-5445	227	26	=	=	SYM
ejpam-5445	227	27	0	0	NUM
ejpam-5445	227	28	,	,	PUNCT
ejpam-5445	227	29	γ	γ	X
ejpam-5445	227	30	̸=	̸=	PROPN
ejpam-5445	227	31	0	0	NUM
ejpam-5445	227	32	1−e−ρ(β−α)(β−α)∈	1−e−ρ(β−α)(β−α)∈	NUM
ejpam-5445	227	33	ρ	ρ	NOUN
ejpam-5445	227	34	;	;	PUNCT
ejpam-5445	227	35	if	if	SCONJ
ejpam-5445	227	36	ρ	ρ	PROPN
ejpam-5445	227	37	̸=	̸=	PROPN
ejpam-5445	227	38	0	0	NUM
ejpam-5445	227	39	,	,	PUNCT
ejpam-5445	227	40	γ	γ	X
ejpam-5445	227	41	=	=	SYM
ejpam-5445	227	42	0	0	NUM
ejpam-5445	227	43	(	(	PUNCT
ejpam-5445	227	44	β	β	X
ejpam-5445	227	45	−	−	PROPN
ejpam-5445	227	46	α)2	α)2	NOUN
ejpam-5445	227	47	∈	∈	NOUN
ejpam-5445	227	48	;	;	PUNCT
ejpam-5445	227	49	if	if	SCONJ
ejpam-5445	227	50	ρ	ρ	PROPN
ejpam-5445	227	51	=	=	SYM
ejpam-5445	227	52	0	0	NUM
ejpam-5445	227	53	,	,	PUNCT
ejpam-5445	227	54	γ	γ	X
ejpam-5445	227	55	=	=	SYM
ejpam-5445	227	56	0	0	NUM
ejpam-5445	227	57	(	(	PUNCT
ejpam-5445	227	58	38	38	NUM
ejpam-5445	227	59	)	)	PUNCT
ejpam-5445	227	60	with	with	ADP
ejpam-5445	227	61	respect	respect	NOUN
ejpam-5445	227	62	to	to	ADP
ejpam-5445	227	63	ω	ω	PROPN
ejpam-5445	227	64	∈	∈	PROPN
ejpam-5445	228	1	[	[	X
ejpam-5445	228	2	α	α	X
ejpam-5445	228	3	,	,	PUNCT
ejpam-5445	228	4	β	β	X
ejpam-5445	228	5	]	]	PUNCT
ejpam-5445	228	6	.	.	PUNCT
ejpam-5445	229	1	theorem	theorem	NOUN
ejpam-5445	229	2	2	2	NUM
ejpam-5445	229	3	.	.	PUNCT
ejpam-5445	230	1	the	the	DET
ejpam-5445	230	2	de	de	PROPN
ejpam-5445	230	3	γiv(ω	γiv(ω	PROPN
ejpam-5445	230	4	)	)	PUNCT
ejpam-5445	230	5	+	+	PROPN
ejpam-5445	230	6	ρ1γ	ρ1γ	PROPN
ejpam-5445	230	7	′′′(ω	′′′(ω	PROPN
ejpam-5445	230	8	)	)	PUNCT
ejpam-5445	231	1	+	+	PROPN
ejpam-5445	231	2	ρ2γ	ρ2γ	PROPN
ejpam-5445	231	3	′′(ω	′′(ω	NOUN
ejpam-5445	231	4	)	)	PUNCT
ejpam-5445	232	1	+	+	CCONJ
ejpam-5445	232	2	ρ3γ	ρ3γ	NUM
ejpam-5445	232	3	′(ω	′(ω	NOUN
ejpam-5445	232	4	)	)	PUNCT
ejpam-5445	232	5	+	+	X
ejpam-5445	232	6	ρ4γ(ω	ρ4γ(ω	ADJ
ejpam-5445	232	7	)	)	PUNCT
ejpam-5445	232	8	=	=	SYM
ejpam-5445	232	9	χ(ω	χ(ω	NOUN
ejpam-5445	232	10	)	)	PUNCT
ejpam-5445	232	11	has	have	VERB
ejpam-5445	232	12	the	the	DET
ejpam-5445	232	13	hyers	hyer	NOUN
ejpam-5445	232	14	ulam	ulam	PROPN
ejpam-5445	232	15	stability	stability	PROPN
ejpam-5445	232	16	,	,	PUNCT
ejpam-5445	232	17	where	where	SCONJ
ejpam-5445	232	18	γ	γ	PROPN
ejpam-5445	232	19	∈	∈	PROPN
ejpam-5445	232	20	c4[α	c4[α	NOUN
ejpam-5445	232	21	,	,	PUNCT
ejpam-5445	232	22	β	β	X
ejpam-5445	232	23	]	]	PUNCT
ejpam-5445	232	24	and	and	CCONJ
ejpam-5445	232	25	with	with	ADP
ejpam-5445	232	26	respect	respect	NOUN
ejpam-5445	232	27	to	to	ADP
ejpam-5445	232	28	ω	ω	PROPN
ejpam-5445	232	29	∈	∈	PROPN
ejpam-5445	233	1	[	[	X
ejpam-5445	233	2	α	α	X
ejpam-5445	233	3	,	,	PUNCT
ejpam-5445	233	4	β	β	X
ejpam-5445	233	5	]	]	X
ejpam-5445	233	6	,	,	PUNCT
ejpam-5445	233	7	|u(ω)−	|u(ω)−	NOUN
ejpam-5445	233	8	γ(ω)|	γ(ω)|	ADP
ejpam-5445	233	9	≤	≤	PROPN
ejpam-5445	233	10	t	t	PROPN
ejpam-5445	233	11	s.	s.	PROPN
ejpam-5445	233	12	bowmiya	bowmiya	PROPN
ejpam-5445	233	13	et	et	PROPN
ejpam-5445	233	14	al	al	PROPN
ejpam-5445	233	15	.	.	PUNCT
ejpam-5445	233	16	/	/	SYM
ejpam-5445	233	17	eur	eur	PROPN
ejpam-5445	233	18	.	.	PUNCT
ejpam-5445	234	1	j.	j.	PROPN
ejpam-5445	234	2	pure	pure	PROPN
ejpam-5445	234	3	appl	appl	PROPN
ejpam-5445	234	4	.	.	PROPN
ejpam-5445	234	5	math	math	PROPN
ejpam-5445	234	6	,	,	PUNCT
ejpam-5445	234	7	17	17	NUM
ejpam-5445	234	8	(	(	PUNCT
ejpam-5445	234	9	4	4	NUM
ejpam-5445	234	10	)	)	PUNCT
ejpam-5445	234	11	(	(	PUNCT
ejpam-5445	234	12	2024	2024	NUM
ejpam-5445	234	13	)	)	PUNCT
ejpam-5445	234	14	,	,	PUNCT
ejpam-5445	234	15	3415	3415	NUM
ejpam-5445	234	16	-	-	SYM
ejpam-5445	234	17	3435	3435	NUM
ejpam-5445	234	18	3425	3425	NUM
ejpam-5445	234	19	where	where	SCONJ
ejpam-5445	234	20	t	t	NOUN
ejpam-5445	234	21	=	=	SYM
ejpam-5445	234	22			PROPN
ejpam-5445	234	23	(	(	PUNCT
ejpam-5445	234	24	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−σ(β−α))∈	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−σ(β−α))∈	NUM
ejpam-5445	234	25	γρσ	γρσ	NOUN
ejpam-5445	234	26	;	;	PUNCT
ejpam-5445	234	27	if	if	SCONJ
ejpam-5445	234	28	(	(	PUNCT
ejpam-5445	234	29	ρ	ρ	NOUN
ejpam-5445	234	30	,	,	PUNCT
ejpam-5445	234	31	γ	γ	PROPN
ejpam-5445	234	32	,	,	PUNCT
ejpam-5445	234	33	σ	σ	PROPN
ejpam-5445	234	34	)	)	PUNCT
ejpam-5445	234	35	̸=	̸=	PROPN
ejpam-5445	234	36	0	0	NUM
ejpam-5445	234	37	(	(	PUNCT
ejpam-5445	234	38	1−e−γ(β−α))(1−e−ρ(β−α))(β−α)∈	1−e−γ(β−α))(1−e−ρ(β−α))(β−α)∈	NOUN
ejpam-5445	234	39	γρ	γρ	NOUN
ejpam-5445	234	40	;	;	PUNCT
ejpam-5445	234	41	if	if	SCONJ
ejpam-5445	234	42	σ	σ	PROPN
ejpam-5445	234	43	=	=	SYM
ejpam-5445	234	44	0	0	NUM
ejpam-5445	234	45	;	;	PUNCT
ejpam-5445	234	46	(	(	PUNCT
ejpam-5445	234	47	ρ	ρ	NOUN
ejpam-5445	234	48	,	,	PUNCT
ejpam-5445	234	49	γ	γ	NOUN
ejpam-5445	234	50	)	)	PUNCT
ejpam-5445	234	51	̸=	̸=	PROPN
ejpam-5445	234	52	0	0	NUM
ejpam-5445	235	1	(	(	PUNCT
ejpam-5445	235	2	1−e−γ(β−α))(1−e−σ(β−α))(β−α)∈	1−e−γ(β−α))(1−e−σ(β−α))(β−α)∈	NUM
ejpam-5445	235	3	σγ	σγ	INTJ
ejpam-5445	235	4	;	;	PUNCT
ejpam-5445	235	5	if	if	SCONJ
ejpam-5445	235	6	ρ	ρ	PROPN
ejpam-5445	235	7	=	=	SYM
ejpam-5445	235	8	0	0	NUM
ejpam-5445	235	9	;	;	PUNCT
ejpam-5445	235	10	(	(	PUNCT
ejpam-5445	235	11	σ	σ	PROPN
ejpam-5445	235	12	,	,	PUNCT
ejpam-5445	235	13	γ	γ	NOUN
ejpam-5445	235	14	)	)	PUNCT
ejpam-5445	235	15	̸=	̸=	PROPN
ejpam-5445	235	16	0	0	NUM
ejpam-5445	235	17	(	(	PUNCT
ejpam-5445	235	18	1−e−ρ(β−α))(1−e−σ(β−α))(β−α)∈	1−e−ρ(β−α))(1−e−σ(β−α))(β−α)∈	NUM
ejpam-5445	235	19	ρσ	ρσ	VERB
ejpam-5445	235	20	;	;	PUNCT
ejpam-5445	235	21	if	if	SCONJ
ejpam-5445	235	22	γ	γ	X
ejpam-5445	235	23	=	=	SYM
ejpam-5445	235	24	0	0	NUM
ejpam-5445	235	25	;	;	PUNCT
ejpam-5445	235	26	(	(	PUNCT
ejpam-5445	235	27	ρ	ρ	PROPN
ejpam-5445	235	28	,	,	PUNCT
ejpam-5445	235	29	σ	σ	PROPN
ejpam-5445	235	30	)	)	PUNCT
ejpam-5445	235	31	̸=	̸=	PROPN
ejpam-5445	235	32	0	0	NUM
ejpam-5445	236	1	(	(	PUNCT
ejpam-5445	236	2	1−e−ρ(β−α))(β−α)2∈	1−e−ρ(β−α))(β−α)2∈	PROPN
ejpam-5445	236	3	ρ	ρ	NOUN
ejpam-5445	236	4	;	;	PUNCT
ejpam-5445	236	5	if	if	SCONJ
ejpam-5445	236	6	(	(	PUNCT
ejpam-5445	236	7	σ	σ	NOUN
ejpam-5445	236	8	,	,	PUNCT
ejpam-5445	236	9	γ	γ	NOUN
ejpam-5445	236	10	)	)	PUNCT
ejpam-5445	236	11	=	=	SYM
ejpam-5445	236	12	0	0	NUM
ejpam-5445	236	13	;	;	PUNCT
ejpam-5445	236	14	ρ	ρ	PROPN
ejpam-5445	236	15	̸=	̸=	PROPN
ejpam-5445	236	16	0	0	NUM
ejpam-5445	236	17	(	(	PUNCT
ejpam-5445	236	18	1−e−σ(β−α))(β−α)2∈	1−e−σ(β−α))(β−α)2∈	PROPN
ejpam-5445	236	19	σ	σ	NOUN
ejpam-5445	236	20	;	;	PUNCT
ejpam-5445	236	21	if	if	SCONJ
ejpam-5445	236	22	(	(	PUNCT
ejpam-5445	236	23	ρ	ρ	NOUN
ejpam-5445	236	24	,	,	PUNCT
ejpam-5445	236	25	γ	γ	NOUN
ejpam-5445	236	26	)	)	PUNCT
ejpam-5445	236	27	=	=	SYM
ejpam-5445	236	28	0;σ	0;σ	X
ejpam-5445	236	29	̸=	̸=	PROPN
ejpam-5445	236	30	0	0	NUM
ejpam-5445	237	1	(	(	PUNCT
ejpam-5445	237	2	1−e−γ(β−α))(β−α)2∈	1−e−γ(β−α))(β−α)2∈	NUM
ejpam-5445	237	3	γ	γ	X
ejpam-5445	237	4	;	;	PUNCT
ejpam-5445	237	5	if	if	SCONJ
ejpam-5445	237	6	(	(	PUNCT
ejpam-5445	237	7	ρ	ρ	PROPN
ejpam-5445	237	8	,	,	PUNCT
ejpam-5445	237	9	σ	σ	PROPN
ejpam-5445	237	10	)	)	PUNCT
ejpam-5445	237	11	=	=	SYM
ejpam-5445	237	12	0	0	NUM
ejpam-5445	237	13	;	;	PUNCT
ejpam-5445	237	14	γ	γ	PROPN
ejpam-5445	237	15	̸=	̸=	PROPN
ejpam-5445	237	16	0	0	NUM
ejpam-5445	237	17	(	(	PUNCT
ejpam-5445	237	18	β	β	NOUN
ejpam-5445	237	19	−	−	X
ejpam-5445	237	20	α)3	α)3	PROPN
ejpam-5445	237	21	∈	∈	PROPN
ejpam-5445	237	22	;	;	PUNCT
ejpam-5445	237	23	if	if	SCONJ
ejpam-5445	237	24	(	(	PUNCT
ejpam-5445	237	25	ρ	ρ	PROPN
ejpam-5445	237	26	,	,	PUNCT
ejpam-5445	237	27	σ	σ	PROPN
ejpam-5445	237	28	,	,	PUNCT
ejpam-5445	237	29	γ	γ	NOUN
ejpam-5445	237	30	)	)	PUNCT
ejpam-5445	237	31	=	=	SYM
ejpam-5445	237	32	0	0	NUM
ejpam-5445	237	33	with	with	ADP
ejpam-5445	237	34	respect	respect	NOUN
ejpam-5445	237	35	to	to	ADP
ejpam-5445	237	36	ω	ω	PROPN
ejpam-5445	237	37	∈	∈	PROPN
ejpam-5445	237	38	[	[	X
ejpam-5445	237	39	α	α	X
ejpam-5445	237	40	,	,	PUNCT
ejpam-5445	237	41	β	β	X
ejpam-5445	237	42	]	]	PUNCT
ejpam-5445	237	43	.	.	PUNCT
ejpam-5445	238	1	proof	proof	NOUN
ejpam-5445	238	2	.	.	PUNCT
ejpam-5445	239	1	if	if	SCONJ
ejpam-5445	239	2	follows	follow	VERB
ejpam-5445	239	3	from	from	ADP
ejpam-5445	239	4	theorem	theorem	ADJ
ejpam-5445	239	5	1	1	NUM
ejpam-5445	239	6	,	,	PUNCT
ejpam-5445	239	7	let	let	VERB
ejpam-5445	239	8	us	we	PRON
ejpam-5445	239	9	choose	choose	VERB
ejpam-5445	239	10	γ(ω	γ(ω	PROPN
ejpam-5445	239	11	)	)	PUNCT
ejpam-5445	240	1	=	=	SYM
ejpam-5445	240	2	u′′3(ω	u′′3(ω	NOUN
ejpam-5445	240	3	)	)	PUNCT
ejpam-5445	240	4	+	+	CCONJ
ejpam-5445	240	5	(	(	PUNCT
ejpam-5445	240	6	u2	u2	NOUN
ejpam-5445	240	7	+	+	CCONJ
ejpam-5445	240	8	ρ1)u	ρ1)u	NOUN
ejpam-5445	240	9	′	′	NUM
ejpam-5445	240	10	3(ω	3(ω	NUM
ejpam-5445	240	11	)	)	PUNCT
ejpam-5445	241	1	+	+	CCONJ
ejpam-5445	241	2	(	(	PUNCT
ejpam-5445	241	3	u22	u22	PROPN
ejpam-5445	241	4	+	+	PROPN
ejpam-5445	241	5	ρ1u2	ρ1u2	NOUN
ejpam-5445	241	6	+	+	CCONJ
ejpam-5445	241	7	ρ2)u2(ω	ρ2)u2(ω	NOUN
ejpam-5445	241	8	)	)	PUNCT
ejpam-5445	241	9	by	by	ADP
ejpam-5445	241	10	γ′(ω	γ′(ω	PROPN
ejpam-5445	241	11	)	)	PUNCT
ejpam-5445	241	12	=	=	NOUN
ejpam-5445	241	13	u′′′3(ω	u′′′3(ω	NOUN
ejpam-5445	241	14	)	)	PUNCT
ejpam-5445	241	15	+	+	CCONJ
ejpam-5445	241	16	(	(	PUNCT
ejpam-5445	241	17	u2	u2	NOUN
ejpam-5445	241	18	+	+	CCONJ
ejpam-5445	241	19	ρ1)u	ρ1)u	NOUN
ejpam-5445	241	20	′′	′′	PROPN
ejpam-5445	241	21	3(ω	3(ω	NUM
ejpam-5445	241	22	)	)	PUNCT
ejpam-5445	242	1	+	+	CCONJ
ejpam-5445	242	2	(	(	PUNCT
ejpam-5445	242	3	u22	u22	PROPN
ejpam-5445	242	4	+	+	PROPN
ejpam-5445	242	5	ρ1u2	ρ1u2	NOUN
ejpam-5445	242	6	+	+	ADJ
ejpam-5445	242	7	ρ2)u	ρ2)u	NOUN
ejpam-5445	242	8	′	′	NOUN
ejpam-5445	242	9	3(ω	3(ω	NUM
ejpam-5445	242	10	)	)	PUNCT
ejpam-5445	243	1	+	+	CCONJ
ejpam-5445	243	2	(	(	PUNCT
ejpam-5445	243	3	u32	u32	NOUN
ejpam-5445	243	4	+	+	CCONJ
ejpam-5445	243	5	ρ1u	ρ1u	SYM
ejpam-5445	243	6	2	2	NUM
ejpam-5445	243	7	2	2	NUM
ejpam-5445	243	8	+	+	CCONJ
ejpam-5445	243	9	ρ2u2	ρ2u2	PROPN
ejpam-5445	243	10	+	+	NOUN
ejpam-5445	243	11	ρ3)u2(ω	ρ3)u2(ω	ADV
ejpam-5445	243	12	)	)	PUNCT
ejpam-5445	243	13	.	.	PUNCT
ejpam-5445	244	1	then	then	ADV
ejpam-5445	244	2	|γ′(ω)−	|γ′(ω)−	ADP
ejpam-5445	244	3	u2γ(ω)−	u2γ(ω)−	NOUN
ejpam-5445	244	4	κ(ω)|	κ(ω)|	X
ejpam-5445	244	5	=	=	PRON
ejpam-5445	244	6	|u′′′3(ω	|u′′′3(ω	NOUN
ejpam-5445	244	7	)	)	PUNCT
ejpam-5445	244	8	+	+	CCONJ
ejpam-5445	244	9	(	(	PUNCT
ejpam-5445	244	10	u2	u2	NOUN
ejpam-5445	244	11	+	+	CCONJ
ejpam-5445	244	12	ρ1)u	ρ1)u	NOUN
ejpam-5445	244	13	′′	′′	PROPN
ejpam-5445	244	14	3(ω	3(ω	NUM
ejpam-5445	244	15	)	)	PUNCT
ejpam-5445	244	16	+	+	CCONJ
ejpam-5445	244	17	(	(	PUNCT
ejpam-5445	244	18	u22	u22	PROPN
ejpam-5445	244	19	+	+	PROPN
ejpam-5445	244	20	ρ1u2	ρ1u2	NOUN
ejpam-5445	244	21	+	+	ADJ
ejpam-5445	244	22	ρ2)u	ρ2)u	NOUN
ejpam-5445	244	23	′	′	NOUN
ejpam-5445	244	24	3(ω	3(ω	NUM
ejpam-5445	244	25	)	)	PUNCT
ejpam-5445	245	1	+	+	CCONJ
ejpam-5445	245	2	(	(	PUNCT
ejpam-5445	245	3	u32	u32	NOUN
ejpam-5445	245	4	+	+	CCONJ
ejpam-5445	245	5	ρ1u	ρ1u	SYM
ejpam-5445	245	6	2	2	NUM
ejpam-5445	245	7	2	2	NUM
ejpam-5445	245	8	+	+	CCONJ
ejpam-5445	245	9	ρ2u2	ρ2u2	PROPN
ejpam-5445	245	10	+	+	NOUN
ejpam-5445	245	11	ρ3)u3(ω)−	ρ3)u3(ω)−	NOUN
ejpam-5445	245	12	u2(u	u2(u	NUM
ejpam-5445	245	13	′′	′′	PROPN
ejpam-5445	245	14	3(ω	3(ω	NUM
ejpam-5445	245	15	)	)	PUNCT
ejpam-5445	245	16	+	+	CCONJ
ejpam-5445	245	17	(	(	PUNCT
ejpam-5445	245	18	u2	u2	NOUN
ejpam-5445	245	19	+	+	CCONJ
ejpam-5445	245	20	ρ1)u	ρ1)u	NOUN
ejpam-5445	245	21	′	′	NUM
ejpam-5445	245	22	3(ω	3(ω	NUM
ejpam-5445	245	23	)	)	PUNCT
ejpam-5445	246	1	+	+	CCONJ
ejpam-5445	246	2	(	(	PUNCT
ejpam-5445	246	3	u22	u22	PROPN
ejpam-5445	246	4	+	+	PROPN
ejpam-5445	246	5	ρ1u2	ρ1u2	NOUN
ejpam-5445	246	6	+	+	NOUN
ejpam-5445	246	7	ρ2)u3(ω)−	ρ2)u3(ω)−	NOUN
ejpam-5445	246	8	κ(ω)|	κ(ω)|	ADJ
ejpam-5445	246	9	=	=	PUNCT
ejpam-5445	246	10	|u′′′3	|u′′′3	NOUN
ejpam-5445	246	11	(	(	PUNCT
ejpam-5445	246	12	ω	ω	NOUN
ejpam-5445	246	13	)	)	PUNCT
ejpam-5445	246	14	+	+	CCONJ
ejpam-5445	246	15	ρ1u	ρ1u	X
ejpam-5445	246	16	′′	′′	PROPN
ejpam-5445	246	17	2(ω	2(ω	NUM
ejpam-5445	246	18	)	)	PUNCT
ejpam-5445	247	1	+	+	CCONJ
ejpam-5445	247	2	ρ2u	ρ2u	PROPN
ejpam-5445	247	3	′	′	NUM
ejpam-5445	247	4	2(ω	2(ω	NUM
ejpam-5445	247	5	)	)	PUNCT
ejpam-5445	248	1	+	+	CCONJ
ejpam-5445	249	1	ρ3u+	ρ3u+	ADV
ejpam-5445	249	2	3(ω)−	3(ω)−	NUM
ejpam-5445	249	3	κ(ω)|	κ(ω)|	PROPN
ejpam-5445	249	4	≤∈	≤∈	VERB
ejpam-5445	249	5	with	with	ADP
ejpam-5445	249	6	respect	respect	NOUN
ejpam-5445	249	7	to	to	ADP
ejpam-5445	249	8	ω	ω	PROPN
ejpam-5445	249	9	∈	∈	PROPN
ejpam-5445	249	10	[	[	X
ejpam-5445	249	11	α	α	X
ejpam-5445	249	12	,	,	PUNCT
ejpam-5445	249	13	β	β	X
ejpam-5445	249	14	]	]	PUNCT
ejpam-5445	249	15	.	.	PUNCT
ejpam-5445	250	1	so	so	ADV
ejpam-5445	250	2	we	we	PRON
ejpam-5445	250	3	have	have	VERB
ejpam-5445	250	4	|γ′(ω)−	|γ′(ω)−	PROPN
ejpam-5445	250	5	u2γ(ω)−	u2γ(ω)−	NUM
ejpam-5445	250	6	κ(ω)|	κ(ω)|	DET
ejpam-5445	250	7	≤∈	≤∈	X
ejpam-5445	250	8	(	(	PUNCT
ejpam-5445	250	9	39	39	NUM
ejpam-5445	250	10	)	)	PUNCT
ejpam-5445	250	11	with	with	ADP
ejpam-5445	250	12	respect	respect	NOUN
ejpam-5445	250	13	to	to	ADP
ejpam-5445	250	14	ω	ω	PROPN
ejpam-5445	250	15	∈	∈	PROPN
ejpam-5445	250	16	[	[	X
ejpam-5445	250	17	α	α	X
ejpam-5445	250	18	,	,	PUNCT
ejpam-5445	250	19	β	β	X
ejpam-5445	250	20	]	]	PUNCT
ejpam-5445	250	21	.	.	PUNCT
ejpam-5445	251	1	equivalently	equivalently	ADV
ejpam-5445	251	2	γ	γ	X
ejpam-5445	251	3	fulfilling	fulfil	VERB
ejpam-5445	251	4	−	−	PROPN
ejpam-5445	251	5	∈≤	∈≤	PRON
ejpam-5445	251	6	γ′(ω)−	γ′(ω)−	NOUN
ejpam-5445	251	7	u2γ(ω)−	u2γ(ω)−	PROPN
ejpam-5445	251	8	κ(ω	κ(ω	PROPN
ejpam-5445	251	9	)	)	PUNCT
ejpam-5445	251	10	≤∈	≤∈	PROPN
ejpam-5445	251	11	(	(	PUNCT
ejpam-5445	251	12	40	40	NUM
ejpam-5445	251	13	)	)	PUNCT
ejpam-5445	251	14	with	with	ADP
ejpam-5445	251	15	respect	respect	NOUN
ejpam-5445	251	16	to	to	ADP
ejpam-5445	251	17	ω	ω	PROPN
ejpam-5445	251	18	∈	∈	PROPN
ejpam-5445	251	19	[	[	X
ejpam-5445	251	20	α	α	X
ejpam-5445	251	21	,	,	PUNCT
ejpam-5445	251	22	β	β	X
ejpam-5445	251	23	]	]	X
ejpam-5445	251	24	.	.	PUNCT
ejpam-5445	252	1	multiplying	multiply	VERB
ejpam-5445	252	2	the	the	DET
ejpam-5445	252	3	condition	condition	NOUN
ejpam-5445	252	4	by	by	ADP
ejpam-5445	252	5	the	the	DET
ejpam-5445	252	6	function	function	NOUN
ejpam-5445	252	7	e−u3(ω−α	e−u3(ω−α	NOUN
ejpam-5445	252	8	)	)	PUNCT
ejpam-5445	252	9	−	−	PROPN
ejpam-5445	252	10	∈	∈	NOUN
ejpam-5445	252	11	e−u3(ω−α	e−u3(ω−α	NOUN
ejpam-5445	252	12	)	)	PUNCT
ejpam-5445	252	13	≤	≤	NUM
ejpam-5445	252	14	γ′(ω)e−u3(ω−α	γ′(ω)e−u3(ω−α	NOUN
ejpam-5445	252	15	)	)	PUNCT
ejpam-5445	252	16	−	−	PROPN
ejpam-5445	252	17	u2γ(ω)e	u2γ(ω)e	NOUN
ejpam-5445	252	18	−u3(ω−α	−u3(ω−α	PROPN
ejpam-5445	252	19	)	)	PUNCT
ejpam-5445	252	20	−	−	ADP
ejpam-5445	252	21	κ(ω)e−u3(ω−α	κ(ω)e−u3(ω−α	PROPN
ejpam-5445	252	22	)	)	PUNCT
ejpam-5445	252	23	≤∈	≤∈	NOUN
ejpam-5445	252	24	e−u3(ω−α	e−u3(ω−α	NOUN
ejpam-5445	252	25	)	)	PUNCT
ejpam-5445	252	26	(	(	PUNCT
ejpam-5445	252	27	41	41	NUM
ejpam-5445	252	28	)	)	PUNCT
ejpam-5445	252	29	s.	s.	PROPN
ejpam-5445	252	30	bowmiya	bowmiya	VERB
ejpam-5445	252	31	et	et	PROPN
ejpam-5445	252	32	al	al	PROPN
ejpam-5445	252	33	.	.	PUNCT
ejpam-5445	252	34	/	/	SYM
ejpam-5445	252	35	eur	eur	PROPN
ejpam-5445	252	36	.	.	PUNCT
ejpam-5445	253	1	j.	j.	PROPN
ejpam-5445	253	2	pure	pure	PROPN
ejpam-5445	253	3	appl	appl	PROPN
ejpam-5445	253	4	.	.	PROPN
ejpam-5445	253	5	math	math	PROPN
ejpam-5445	253	6	,	,	PUNCT
ejpam-5445	253	7	17	17	NUM
ejpam-5445	253	8	(	(	PUNCT
ejpam-5445	253	9	4	4	NUM
ejpam-5445	253	10	)	)	PUNCT
ejpam-5445	253	11	(	(	PUNCT
ejpam-5445	253	12	2024	2024	NUM
ejpam-5445	253	13	)	)	PUNCT
ejpam-5445	253	14	,	,	PUNCT
ejpam-5445	253	15	3415	3415	NUM
ejpam-5445	253	16	-	-	SYM
ejpam-5445	253	17	3435	3435	NUM
ejpam-5445	253	18	3426	3426	NUM
ejpam-5445	253	19	with	with	ADP
ejpam-5445	253	20	respect	respect	NOUN
ejpam-5445	253	21	to	to	ADP
ejpam-5445	253	22	ω	ω	PROPN
ejpam-5445	253	23	∈	∈	PROPN
ejpam-5445	253	24	[	[	X
ejpam-5445	253	25	α	α	X
ejpam-5445	253	26	,	,	PUNCT
ejpam-5445	253	27	β	β	X
ejpam-5445	253	28	]	]	X
ejpam-5445	253	29	.	.	PUNCT
ejpam-5445	254	1	without	without	ADP
ejpam-5445	254	2	loss	loss	NOUN
ejpam-5445	254	3	of	of	ADP
ejpam-5445	254	4	inclusive	inclusive	ADJ
ejpam-5445	254	5	statement	statement	NOUN
ejpam-5445	254	6	we	we	PRON
ejpam-5445	254	7	may	may	AUX
ejpam-5445	254	8	accept	accept	VERB
ejpam-5445	254	9	that	that	DET
ejpam-5445	254	10	u3	u3	PROPN
ejpam-5445	254	11	>	>	X
ejpam-5445	254	12	1	1	NUM
ejpam-5445	254	13	.	.	PUNCT
ejpam-5445	255	1	then	then	ADV
ejpam-5445	255	2	−u3	−u3	NOUN
ejpam-5445	255	3	∈	∈	NOUN
ejpam-5445	255	4	e−u3(ω−α	e−u3(ω−α	NOUN
ejpam-5445	255	5	)	)	PUNCT
ejpam-5445	255	6	≤	≤	NUM
ejpam-5445	255	7	γ′(ω)e−u3(ω−α	γ′(ω)e−u3(ω−α	NOUN
ejpam-5445	255	8	)	)	PUNCT
ejpam-5445	255	9	−	−	ADP
ejpam-5445	255	10	u3γ(ω)e	u3γ(ω)e	PROPN
ejpam-5445	255	11	−u3(ω−α	−u3(ω−α	PROPN
ejpam-5445	255	12	)	)	PUNCT
ejpam-5445	256	1	−	−	ADP
ejpam-5445	256	2	κ(ω)e−u3(ω−α	κ(ω)e−u3(ω−α	PROPN
ejpam-5445	256	3	)	)	PUNCT
ejpam-5445	256	4	≤∈	≤∈	NOUN
ejpam-5445	256	5	e−u3(ω−α	e−u3(ω−α	NOUN
ejpam-5445	256	6	)	)	PUNCT
ejpam-5445	256	7	(	(	PUNCT
ejpam-5445	256	8	42	42	NUM
ejpam-5445	256	9	)	)	PUNCT
ejpam-5445	256	10	with	with	ADP
ejpam-5445	256	11	respect	respect	NOUN
ejpam-5445	256	12	to	to	ADP
ejpam-5445	256	13	ω	ω	PROPN
ejpam-5445	256	14	∈	∈	PROPN
ejpam-5445	257	1	[	[	X
ejpam-5445	257	2	α	α	X
ejpam-5445	257	3	,	,	PUNCT
ejpam-5445	257	4	β	β	X
ejpam-5445	257	5	]	]	PUNCT
ejpam-5445	257	6	.	.	PUNCT
ejpam-5445	258	1	integrating	integrate	VERB
ejpam-5445	258	2	42	42	NUM
ejpam-5445	258	3	from	from	ADP
ejpam-5445	258	4	ω	ω	NUM
ejpam-5445	258	5	to	to	ADP
ejpam-5445	258	6	β	β	PRON
ejpam-5445	258	7	,	,	PUNCT
ejpam-5445	258	8	we	we	PRON
ejpam-5445	258	9	get	get	VERB
ejpam-5445	258	10	−	−	PROPN
ejpam-5445	258	11	∈	∈	NOUN
ejpam-5445	258	12	(	(	PUNCT
ejpam-5445	258	13	e−u3(ω−α	e−u3(ω−α	NOUN
ejpam-5445	258	14	)	)	PUNCT
ejpam-5445	258	15	−	−	NOUN
ejpam-5445	258	16	e−u3(β−α	e−u3(β−α	NOUN
ejpam-5445	258	17	)	)	PUNCT
ejpam-5445	258	18	)	)	PUNCT
ejpam-5445	258	19	≤	≤	PROPN
ejpam-5445	259	1	e−u3(β−α)γ(α)−	e−u3(β−α)γ(α)−	NOUN
ejpam-5445	259	2	γ(ω)e−u3(ω−α	γ(ω)e−u3(ω−α	PROPN
ejpam-5445	259	3	)	)	PUNCT
ejpam-5445	260	1	−	−	ADP
ejpam-5445	261	1	∫	∫	PROPN
ejpam-5445	261	2	β	β	PROPN
ejpam-5445	261	3	ω	ω	PROPN
ejpam-5445	261	4	κ(τ)e−u3(τ−α)dτ	κ(τ)e−u3(τ−α)dτ	X
ejpam-5445	261	5	≤∈	≤∈	PROPN
ejpam-5445	261	6	(	(	PUNCT
ejpam-5445	261	7	e−u3(ω−α	e−u3(ω−α	NOUN
ejpam-5445	261	8	)	)	PUNCT
ejpam-5445	262	1	−	−	NOUN
ejpam-5445	262	2	e−u3(β−α	e−u3(β−α	NOUN
ejpam-5445	262	3	)	)	PUNCT
ejpam-5445	262	4	)	)	PUNCT
ejpam-5445	262	5	(	(	PUNCT
ejpam-5445	262	6	43	43	NUM
ejpam-5445	262	7	)	)	PUNCT
ejpam-5445	262	8	with	with	ADP
ejpam-5445	262	9	respect	respect	NOUN
ejpam-5445	262	10	to	to	ADP
ejpam-5445	262	11	ω	ω	PROPN
ejpam-5445	262	12	∈	∈	PROPN
ejpam-5445	262	13	[	[	X
ejpam-5445	262	14	α	α	X
ejpam-5445	262	15	,	,	PUNCT
ejpam-5445	262	16	β	β	X
ejpam-5445	262	17	]	]	PUNCT
ejpam-5445	262	18	.	.	PUNCT
ejpam-5445	263	1	if	if	SCONJ
ejpam-5445	263	2	follows	follow	VERB
ejpam-5445	263	3	from	from	ADP
ejpam-5445	263	4	43	43	NUM
ejpam-5445	263	5	,	,	PUNCT
ejpam-5445	263	6	shown	show	VERB
ejpam-5445	263	7	up	up	ADP
ejpam-5445	263	8	−	−	PROPN
ejpam-5445	263	9	∈	∈	PROPN
ejpam-5445	263	10	e−u3(ω−α	e−u3(ω−α	NOUN
ejpam-5445	263	11	)	)	PUNCT
ejpam-5445	263	12	≤	≤	PUNCT
ejpam-5445	263	13	e−u3(β−α)γ(α)−	e−u3(β−α)γ(α)−	VERB
ejpam-5445	263	14	∈	∈	NOUN
ejpam-5445	263	15	e−u3(β−α	e−u3(β−α	NOUN
ejpam-5445	263	16	)	)	PUNCT
ejpam-5445	263	17	−	−	PROPN
ejpam-5445	263	18	γ(ω)e−u3(ω−α	γ(ω)e−u3(ω−α	PROPN
ejpam-5445	263	19	)	)	PUNCT
ejpam-5445	263	20	−	−	ADP
ejpam-5445	264	1	∫	∫	PROPN
ejpam-5445	264	2	β	β	PROPN
ejpam-5445	264	3	ω	ω	PROPN
ejpam-5445	264	4	κ(τ)e−u3(τ−α)dτ	κ(τ)e−u3(τ−α)dτ	PROPN
ejpam-5445	264	5	≤∈	≤∈	ADJ
ejpam-5445	264	6	e−u3(ω−α	e−u3(ω−α	NOUN
ejpam-5445	264	7	)	)	PUNCT
ejpam-5445	264	8	(	(	PUNCT
ejpam-5445	264	9	44	44	NUM
ejpam-5445	264	10	)	)	PUNCT
ejpam-5445	264	11	with	with	ADP
ejpam-5445	264	12	respect	respect	NOUN
ejpam-5445	264	13	to	to	ADP
ejpam-5445	264	14	ω	ω	PROPN
ejpam-5445	264	15	∈	∈	PROPN
ejpam-5445	264	16	[	[	X
ejpam-5445	264	17	α	α	X
ejpam-5445	264	18	,	,	PUNCT
ejpam-5445	264	19	β	β	X
ejpam-5445	264	20	]	]	PUNCT
ejpam-5445	264	21	.	.	PUNCT
ejpam-5445	265	1	again	again	ADV
ejpam-5445	265	2	multiplying	multiply	VERB
ejpam-5445	265	3	the	the	DET
ejpam-5445	265	4	condition	condition	NOUN
ejpam-5445	265	5	by	by	ADP
ejpam-5445	265	6	function	function	NOUN
ejpam-5445	265	7	e−u3(ω−α	e−u3(ω−α	NOUN
ejpam-5445	265	8	)	)	PUNCT
ejpam-5445	265	9	that	that	SCONJ
ejpam-5445	265	10	−	−	PROPN
ejpam-5445	265	11	∈	∈	PROPN
ejpam-5445	265	12	≤	≤	NOUN
ejpam-5445	265	13	e−u3(β−α)γ(α)−	e−u3(β−α)γ(α)−	VERB
ejpam-5445	265	14	∈	∈	NOUN
ejpam-5445	265	15	e−u3(β−ω	e−u3(β−ω	NOUN
ejpam-5445	265	16	)	)	PUNCT
ejpam-5445	265	17	−	−	PROPN
ejpam-5445	265	18	γ(ω)−	γ(ω)−	PROPN
ejpam-5445	265	19	∫	∫	PROPN
ejpam-5445	265	20	β	β	PROPN
ejpam-5445	265	21	ω	ω	PROPN
ejpam-5445	265	22	κ(τ)e−u3(τ−α)dτ	κ(τ)e−u3(τ−α)dτ	X
ejpam-5445	265	23	≤∈	≤∈	PROPN
ejpam-5445	265	24	(	(	PUNCT
ejpam-5445	265	25	45	45	NUM
ejpam-5445	265	26	)	)	PUNCT
ejpam-5445	265	27	with	with	ADP
ejpam-5445	265	28	respect	respect	NOUN
ejpam-5445	265	29	to	to	ADP
ejpam-5445	265	30	ω	ω	PROPN
ejpam-5445	265	31	∈	∈	PROPN
ejpam-5445	265	32	[	[	X
ejpam-5445	265	33	α	α	X
ejpam-5445	265	34	,	,	PUNCT
ejpam-5445	265	35	β	β	X
ejpam-5445	265	36	]	]	X
ejpam-5445	265	37	.	.	PUNCT
ejpam-5445	266	1	from	from	ADP
ejpam-5445	266	2	45	45	NUM
ejpam-5445	266	3	that	that	SCONJ
ejpam-5445	266	4	−	−	PUNCT
ejpam-5445	266	5	∈	∈	PROPN
ejpam-5445	266	6	≤	≤	NOUN
ejpam-5445	266	7	e−u3(ω−β)γ(α)−	e−u3(ω−β)γ(α)−	NOUN
ejpam-5445	266	8	∈	∈	NOUN
ejpam-5445	266	9	e−u3(β−α	e−u3(β−α	NOUN
ejpam-5445	266	10	)	)	PUNCT
ejpam-5445	266	11	−	−	PROPN
ejpam-5445	266	12	γ(ω)−	γ(ω)−	PROPN
ejpam-5445	266	13	eu3ω	eu3ω	PROPN
ejpam-5445	266	14	∫	∫	PROPN
ejpam-5445	266	15	β	β	PROPN
ejpam-5445	266	16	ω	ω	PROPN
ejpam-5445	266	17	κ(τ)e−u3(τ−α)dτ	κ(τ)e−u3(τ−α)dτ	X
ejpam-5445	266	18	≤∈	≤∈	PROPN
ejpam-5445	266	19	(	(	PUNCT
ejpam-5445	266	20	46	46	NUM
ejpam-5445	266	21	)	)	PUNCT
ejpam-5445	266	22	for	for	ADP
ejpam-5445	266	23	all	all	DET
ejpam-5445	266	24	ω	ω	NUM
ejpam-5445	266	25	∈	∈	PROPN
ejpam-5445	266	26	[	[	X
ejpam-5445	266	27	α	α	X
ejpam-5445	266	28	,	,	PUNCT
ejpam-5445	266	29	β	β	X
ejpam-5445	266	30	]	]	PUNCT
ejpam-5445	266	31	.	.	PUNCT
ejpam-5445	267	1	let	let	VERB
ejpam-5445	267	2	u2(ω	u2(ω	PRON
ejpam-5445	267	3	)	)	PUNCT
ejpam-5445	268	1	=	=	SYM
ejpam-5445	268	2	γ(β)e−u3(ω−β	γ(β)e−u3(ω−β	PROPN
ejpam-5445	268	3	)	)	PUNCT
ejpam-5445	268	4	−	−	PROPN
ejpam-5445	269	1	eu3ω	eu3ω	PROPN
ejpam-5445	269	2	∫	∫	PROPN
ejpam-5445	269	3	β	β	PROPN
ejpam-5445	269	4	ω	ω	PROPN
ejpam-5445	269	5	κ(τ)e−u3(τ−α)dτ	κ(τ)e−u3(τ−α)dτ	PUNCT
ejpam-5445	269	6	,	,	PUNCT
ejpam-5445	269	7	then	then	ADV
ejpam-5445	269	8	u′2(ω	u′2(ω	ADV
ejpam-5445	269	9	)	)	PUNCT
ejpam-5445	269	10	−	−	PROPN
ejpam-5445	270	1	u3u2(ω)−	u3u2(ω)−	PROPN
ejpam-5445	270	2	κ(ω	κ(ω	PROPN
ejpam-5445	270	3	)	)	PUNCT
ejpam-5445	271	1	=	=	SYM
ejpam-5445	271	2	0	0	NUM
ejpam-5445	271	3	by	by	ADP
ejpam-5445	271	4	u′2(ω	u′2(ω	PRON
ejpam-5445	271	5	)	)	PUNCT
ejpam-5445	271	6	=	=	PUNCT
ejpam-5445	271	7	u3u2(ω	u3u2(ω	ADJ
ejpam-5445	271	8	)	)	PUNCT
ejpam-5445	271	9	+	+	CCONJ
ejpam-5445	272	1	κ(ω	κ(ω	PROPN
ejpam-5445	272	2	)	)	PUNCT
ejpam-5445	272	3	,	,	PUNCT
ejpam-5445	272	4	for	for	ADP
ejpam-5445	272	5	all	all	DET
ejpam-5445	272	6	ω	ω	NUM
ejpam-5445	272	7	∈	∈	PROPN
ejpam-5445	273	1	[	[	X
ejpam-5445	273	2	α	α	X
ejpam-5445	273	3	,	,	PUNCT
ejpam-5445	273	4	β	β	X
ejpam-5445	273	5	]	]	PUNCT
ejpam-5445	273	6	.	.	PUNCT
ejpam-5445	274	1	thus	thus	ADV
ejpam-5445	274	2	|u2(ω)−	|u2(ω)−	NOUN
ejpam-5445	274	3	γ(ω)|	γ(ω)|	X
ejpam-5445	274	4	=	=	SYM
ejpam-5445	274	5	|γ(β)e−u3(ω−β	|γ(β)e−u3(ω−β	PROPN
ejpam-5445	274	6	)	)	PUNCT
ejpam-5445	275	1	−	−	PROPN
ejpam-5445	275	2	γ(ω)−	γ(ω)−	PROPN
ejpam-5445	275	3	eu3ω	eu3ω	PROPN
ejpam-5445	275	4	∫	∫	PROPN
ejpam-5445	275	5	β	β	PROPN
ejpam-5445	275	6	ω	ω	NOUN
ejpam-5445	275	7	κ(τ)e−u3(τ−α)dτ	κ(τ)e−u3(τ−α)dτ	X
ejpam-5445	276	1	|	|	ADV
ejpam-5445	276	2	≤	≤	NUM
ejpam-5445	276	3	eσω	eσω	ADJ
ejpam-5445	276	4	∫	∫	PROPN
ejpam-5445	276	5	β	β	PROPN
ejpam-5445	276	6	ω	ω	X
ejpam-5445	276	7	e−στ	e−στ	PROPN
ejpam-5445	276	8	|γ′(τ)−	|γ′(τ)−	PROPN
ejpam-5445	276	9	u3γ(τ)−	u3γ(τ)−	NOUN
ejpam-5445	276	10	κ(τ)|dτ	κ(τ)|dτ	PROPN
ejpam-5445	276	11	|u2(ω)−	|u2(ω)−	NOUN
ejpam-5445	276	12	γ(ω)|	γ(ω)|	CCONJ
ejpam-5445	276	13	≤∈	≤∈	PROPN
ejpam-5445	276	14	eσω	eσω	ADJ
ejpam-5445	276	15	∫	∫	PROPN
ejpam-5445	276	16	β	β	PROPN
ejpam-5445	276	17	ω	ω	PROPN
ejpam-5445	276	18	e−στdτ	e−στdτ	X
ejpam-5445	276	19	(	(	PUNCT
ejpam-5445	276	20	47	47	NUM
ejpam-5445	276	21	)	)	PUNCT
ejpam-5445	276	22	with	with	ADP
ejpam-5445	276	23	respect	respect	NOUN
ejpam-5445	276	24	to	to	ADP
ejpam-5445	276	25	ω	ω	PROPN
ejpam-5445	276	26	∈	∈	PROPN
ejpam-5445	276	27	[	[	X
ejpam-5445	276	28	α	α	X
ejpam-5445	276	29	,	,	PUNCT
ejpam-5445	276	30	β	β	X
ejpam-5445	276	31	]	]	X
ejpam-5445	276	32	.	.	PUNCT
ejpam-5445	277	1	if	if	SCONJ
ejpam-5445	277	2	σ	σ	PROPN
ejpam-5445	277	3	̸=	̸=	PROPN
ejpam-5445	277	4	0	0	NUM
ejpam-5445	277	5	,	,	PUNCT
ejpam-5445	277	6	then	then	ADV
ejpam-5445	277	7	|u2(ω)−	|u2(ω)−	PROPN
ejpam-5445	277	8	γ(ω)|	γ(ω)|	CCONJ
ejpam-5445	277	9	≤	≤	PROPN
ejpam-5445	277	10	∈	∈	PROPN
ejpam-5445	277	11	σ	σ	NOUN
ejpam-5445	277	12	(	(	PUNCT
ejpam-5445	277	13	1−	1−	NUM
ejpam-5445	277	14	e−σ(β−ω	e−σ(β−ω	NOUN
ejpam-5445	277	15	)	)	PUNCT
ejpam-5445	277	16	)	)	PUNCT
ejpam-5445	278	1	s.	s.	PROPN
ejpam-5445	278	2	bowmiya	bowmiya	VERB
ejpam-5445	278	3	et	et	PROPN
ejpam-5445	278	4	al	al	PROPN
ejpam-5445	278	5	.	.	PUNCT
ejpam-5445	278	6	/	/	SYM
ejpam-5445	278	7	eur	eur	PROPN
ejpam-5445	278	8	.	.	PUNCT
ejpam-5445	279	1	j.	j.	PROPN
ejpam-5445	279	2	pure	pure	PROPN
ejpam-5445	279	3	appl	appl	PROPN
ejpam-5445	279	4	.	.	PROPN
ejpam-5445	279	5	math	math	PROPN
ejpam-5445	279	6	,	,	PUNCT
ejpam-5445	279	7	17	17	NUM
ejpam-5445	279	8	(	(	PUNCT
ejpam-5445	279	9	4	4	NUM
ejpam-5445	279	10	)	)	PUNCT
ejpam-5445	279	11	(	(	PUNCT
ejpam-5445	279	12	2024	2024	NUM
ejpam-5445	279	13	)	)	PUNCT
ejpam-5445	279	14	,	,	PUNCT
ejpam-5445	279	15	3415	3415	NUM
ejpam-5445	279	16	-	-	SYM
ejpam-5445	279	17	3435	3435	NUM
ejpam-5445	279	18	3427	3427	NUM
ejpam-5445	279	19	≤	≤	NOUN
ejpam-5445	279	20	∈	∈	PROPN
ejpam-5445	279	21	σ	σ	NOUN
ejpam-5445	279	22	(	(	PUNCT
ejpam-5445	279	23	1−	1−	NUM
ejpam-5445	279	24	e−σ(β−α	e−σ(β−α	NOUN
ejpam-5445	279	25	)	)	PUNCT
ejpam-5445	279	26	)	)	PUNCT
ejpam-5445	279	27	(	(	PUNCT
ejpam-5445	279	28	48	48	NUM
ejpam-5445	279	29	)	)	PUNCT
ejpam-5445	279	30	with	with	ADP
ejpam-5445	279	31	respect	respect	NOUN
ejpam-5445	279	32	to	to	ADP
ejpam-5445	279	33	ω	ω	PROPN
ejpam-5445	279	34	∈	∈	PROPN
ejpam-5445	279	35	[	[	X
ejpam-5445	279	36	α	α	X
ejpam-5445	279	37	,	,	PUNCT
ejpam-5445	279	38	β	β	X
ejpam-5445	279	39	]	]	X
ejpam-5445	279	40	.	.	PUNCT
ejpam-5445	280	1	if	if	SCONJ
ejpam-5445	280	2	σ	σ	PROPN
ejpam-5445	280	3	=	=	SYM
ejpam-5445	280	4	0	0	NUM
ejpam-5445	280	5	,	,	PUNCT
ejpam-5445	280	6	then	then	ADV
ejpam-5445	280	7	|u2(ω)−	|u2(ω)−	PROPN
ejpam-5445	280	8	γ(ω)|	γ(ω)|	ADP
ejpam-5445	280	9	≤∈	≤∈	PROPN
ejpam-5445	280	10	eσω	eσω	ADJ
ejpam-5445	280	11	∫	∫	PROPN
ejpam-5445	280	12	β	β	PROPN
ejpam-5445	280	13	ω	ω	PROPN
ejpam-5445	280	14	e−στdτ	e−στdτ	X
ejpam-5445	280	15	≤∈	≤∈	PROPN
ejpam-5445	280	16	(	(	PUNCT
ejpam-5445	280	17	β	β	X
ejpam-5445	280	18	−	−	PROPN
ejpam-5445	280	19	ω	ω	NUM
ejpam-5445	280	20	)	)	PUNCT
ejpam-5445	280	21	≤∈	≤∈	PROPN
ejpam-5445	280	22	(	(	PUNCT
ejpam-5445	280	23	β	β	X
ejpam-5445	280	24	−	−	NOUN
ejpam-5445	280	25	α	α	NOUN
ejpam-5445	280	26	)	)	PUNCT
ejpam-5445	280	27	(	(	PUNCT
ejpam-5445	280	28	49	49	NUM
ejpam-5445	280	29	)	)	PUNCT
ejpam-5445	280	30	with	with	ADP
ejpam-5445	280	31	respect	respect	NOUN
ejpam-5445	280	32	to	to	ADP
ejpam-5445	280	33	ω	ω	PROPN
ejpam-5445	280	34	∈	∈	PROPN
ejpam-5445	280	35	[	[	X
ejpam-5445	280	36	α	α	X
ejpam-5445	280	37	,	,	PUNCT
ejpam-5445	280	38	β	β	X
ejpam-5445	280	39	]	]	PUNCT
ejpam-5445	280	40	.	.	PUNCT
ejpam-5445	281	1	t	t	PROPN
ejpam-5445	281	2	follows	follow	VERB
ejpam-5445	281	3	from	from	ADP
ejpam-5445	281	4	49	49	NUM
ejpam-5445	281	5	,	,	PUNCT
ejpam-5445	281	6	then	then	ADV
ejpam-5445	281	7	|u(ω)−	|u(ω)−	NOUN
ejpam-5445	281	8	γ(ω)|	γ(ω)|	CCONJ
ejpam-5445	281	9	≤	≤	PROPN
ejpam-5445	281	10	t	t	NOUN
ejpam-5445	281	11	,	,	PUNCT
ejpam-5445	281	12	where	where	SCONJ
ejpam-5445	281	13	t	t	NOUN
ejpam-5445	281	14	=	=	SYM
ejpam-5445	281	15			PROPN
ejpam-5445	281	16	(	(	PUNCT
ejpam-5445	281	17	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−σ(β−α))∈	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−σ(β−α))∈	NUM
ejpam-5445	281	18	γρσ	γρσ	NOUN
ejpam-5445	281	19	;	;	PUNCT
ejpam-5445	281	20	if	if	SCONJ
ejpam-5445	281	21	(	(	PUNCT
ejpam-5445	281	22	ρ	ρ	NOUN
ejpam-5445	281	23	,	,	PUNCT
ejpam-5445	281	24	γ	γ	PROPN
ejpam-5445	281	25	,	,	PUNCT
ejpam-5445	281	26	σ	σ	PROPN
ejpam-5445	281	27	)	)	PUNCT
ejpam-5445	281	28	̸=	̸=	PROPN
ejpam-5445	281	29	0	0	NUM
ejpam-5445	281	30	(	(	PUNCT
ejpam-5445	281	31	1−e−γ(β−α))(1−e−ρ(β−α))(β−α)∈	1−e−γ(β−α))(1−e−ρ(β−α))(β−α)∈	NOUN
ejpam-5445	281	32	γρ	γρ	NOUN
ejpam-5445	281	33	;	;	PUNCT
ejpam-5445	281	34	if	if	SCONJ
ejpam-5445	281	35	σ	σ	PROPN
ejpam-5445	281	36	=	=	SYM
ejpam-5445	281	37	0	0	NUM
ejpam-5445	281	38	;	;	PUNCT
ejpam-5445	281	39	(	(	PUNCT
ejpam-5445	281	40	ρ	ρ	NOUN
ejpam-5445	281	41	,	,	PUNCT
ejpam-5445	281	42	γ	γ	NOUN
ejpam-5445	281	43	)	)	PUNCT
ejpam-5445	281	44	̸=	̸=	PROPN
ejpam-5445	281	45	0	0	NUM
ejpam-5445	281	46	(	(	PUNCT
ejpam-5445	281	47	1−e−γ(β−α))(1−e−σ(β−α))(β−α)∈	1−e−γ(β−α))(1−e−σ(β−α))(β−α)∈	NUM
ejpam-5445	281	48	σγ	σγ	INTJ
ejpam-5445	281	49	;	;	PUNCT
ejpam-5445	281	50	if	if	SCONJ
ejpam-5445	281	51	ρ	ρ	PROPN
ejpam-5445	281	52	=	=	SYM
ejpam-5445	281	53	0	0	NUM
ejpam-5445	281	54	;	;	PUNCT
ejpam-5445	281	55	(	(	PUNCT
ejpam-5445	281	56	σ	σ	PROPN
ejpam-5445	281	57	,	,	PUNCT
ejpam-5445	281	58	γ	γ	NOUN
ejpam-5445	281	59	)	)	PUNCT
ejpam-5445	281	60	̸=	̸=	PROPN
ejpam-5445	281	61	0	0	NUM
ejpam-5445	281	62	(	(	PUNCT
ejpam-5445	281	63	1−e−ρ(β−α))(1−e−σ(β−α))(β−α)∈	1−e−ρ(β−α))(1−e−σ(β−α))(β−α)∈	NUM
ejpam-5445	281	64	ρσ	ρσ	VERB
ejpam-5445	281	65	;	;	PUNCT
ejpam-5445	281	66	if	if	SCONJ
ejpam-5445	281	67	γ	γ	X
ejpam-5445	281	68	=	=	SYM
ejpam-5445	281	69	0	0	NUM
ejpam-5445	281	70	;	;	PUNCT
ejpam-5445	281	71	(	(	PUNCT
ejpam-5445	281	72	ρ	ρ	PROPN
ejpam-5445	281	73	,	,	PUNCT
ejpam-5445	281	74	σ	σ	PROPN
ejpam-5445	281	75	)	)	PUNCT
ejpam-5445	281	76	̸=	̸=	PROPN
ejpam-5445	281	77	0	0	NUM
ejpam-5445	282	1	(	(	PUNCT
ejpam-5445	282	2	1−e−ρ(β−α))(β−α)2∈	1−e−ρ(β−α))(β−α)2∈	PROPN
ejpam-5445	282	3	ρ	ρ	NOUN
ejpam-5445	282	4	;	;	PUNCT
ejpam-5445	282	5	if	if	SCONJ
ejpam-5445	282	6	(	(	PUNCT
ejpam-5445	282	7	σ	σ	NOUN
ejpam-5445	282	8	,	,	PUNCT
ejpam-5445	282	9	γ	γ	NOUN
ejpam-5445	282	10	)	)	PUNCT
ejpam-5445	282	11	=	=	SYM
ejpam-5445	282	12	0	0	NUM
ejpam-5445	282	13	;	;	PUNCT
ejpam-5445	282	14	ρ	ρ	PROPN
ejpam-5445	282	15	̸=	̸=	PROPN
ejpam-5445	282	16	0	0	NUM
ejpam-5445	282	17	(	(	PUNCT
ejpam-5445	282	18	1−e−σ(β−α))(β−α)2∈	1−e−σ(β−α))(β−α)2∈	PROPN
ejpam-5445	282	19	σ	σ	NOUN
ejpam-5445	282	20	;	;	PUNCT
ejpam-5445	282	21	if	if	SCONJ
ejpam-5445	282	22	(	(	PUNCT
ejpam-5445	282	23	ρ	ρ	NOUN
ejpam-5445	282	24	,	,	PUNCT
ejpam-5445	282	25	γ	γ	NOUN
ejpam-5445	282	26	)	)	PUNCT
ejpam-5445	282	27	=	=	SYM
ejpam-5445	282	28	0;σ	0;σ	X
ejpam-5445	282	29	̸=	̸=	PROPN
ejpam-5445	282	30	0	0	NUM
ejpam-5445	283	1	(	(	PUNCT
ejpam-5445	283	2	1−e−γ(β−α))(β−α)2∈	1−e−γ(β−α))(β−α)2∈	NUM
ejpam-5445	283	3	γ	γ	X
ejpam-5445	283	4	;	;	PUNCT
ejpam-5445	283	5	if	if	SCONJ
ejpam-5445	283	6	(	(	PUNCT
ejpam-5445	283	7	ρ	ρ	PROPN
ejpam-5445	283	8	,	,	PUNCT
ejpam-5445	283	9	σ	σ	PROPN
ejpam-5445	283	10	)	)	PUNCT
ejpam-5445	283	11	=	=	SYM
ejpam-5445	283	12	0	0	NUM
ejpam-5445	283	13	;	;	PUNCT
ejpam-5445	283	14	γ	γ	PROPN
ejpam-5445	283	15	̸=	̸=	PROPN
ejpam-5445	283	16	0	0	NUM
ejpam-5445	283	17	(	(	PUNCT
ejpam-5445	283	18	β	β	NOUN
ejpam-5445	283	19	−	−	X
ejpam-5445	283	20	α)3	α)3	PROPN
ejpam-5445	283	21	∈	∈	PROPN
ejpam-5445	283	22	;	;	PUNCT
ejpam-5445	283	23	if	if	SCONJ
ejpam-5445	283	24	(	(	PUNCT
ejpam-5445	283	25	ρ	ρ	PROPN
ejpam-5445	283	26	,	,	PUNCT
ejpam-5445	283	27	σ	σ	PROPN
ejpam-5445	283	28	,	,	PUNCT
ejpam-5445	283	29	γ	γ	NOUN
ejpam-5445	283	30	)	)	PUNCT
ejpam-5445	283	31	=	=	SYM
ejpam-5445	283	32	0	0	PUNCT
ejpam-5445	283	33	(	(	PUNCT
ejpam-5445	283	34	50	50	NUM
ejpam-5445	283	35	)	)	PUNCT
ejpam-5445	283	36	with	with	ADP
ejpam-5445	283	37	respect	respect	NOUN
ejpam-5445	283	38	to	to	ADP
ejpam-5445	283	39	ω	ω	PROPN
ejpam-5445	283	40	∈	∈	PROPN
ejpam-5445	284	1	[	[	X
ejpam-5445	284	2	α	α	X
ejpam-5445	284	3	,	,	PUNCT
ejpam-5445	284	4	β	β	X
ejpam-5445	284	5	]	]	PUNCT
ejpam-5445	284	6	.	.	PUNCT
ejpam-5445	285	1	theorem	theorem	NOUN
ejpam-5445	285	2	3	3	NUM
ejpam-5445	285	3	.	.	PUNCT
ejpam-5445	286	1	the	the	DET
ejpam-5445	286	2	differential	differential	ADJ
ejpam-5445	286	3	equation	equation	NOUN
ejpam-5445	286	4	γiv(ω)+ρ1γ	γiv(ω)+ρ1γ	PROPN
ejpam-5445	286	5	′′′(ω)+ρ2γ	′′′(ω)+ρ2γ	NOUN
ejpam-5445	286	6	′′(ω)+ρ3γ	′′(ω)+ρ3γ	NOUN
ejpam-5445	286	7	′(ω)+ρ4γ(ω	′(ω)+ρ4γ(ω	NOUN
ejpam-5445	286	8	)	)	PUNCT
ejpam-5445	286	9	=	=	SYM
ejpam-5445	286	10	χ(ω	χ(ω	NOUN
ejpam-5445	286	11	)	)	PUNCT
ejpam-5445	286	12	has	have	VERB
ejpam-5445	286	13	the	the	DET
ejpam-5445	286	14	hyers	hyer	NOUN
ejpam-5445	286	15	ulam	ulam	PROPN
ejpam-5445	286	16	stability	stability	PROPN
ejpam-5445	286	17	,	,	PUNCT
ejpam-5445	286	18	where	where	SCONJ
ejpam-5445	286	19	γ	γ	PROPN
ejpam-5445	286	20	∈	∈	PROPN
ejpam-5445	286	21	c4[α	c4[α	NOUN
ejpam-5445	286	22	,	,	PUNCT
ejpam-5445	286	23	β	β	X
ejpam-5445	286	24	]	]	PUNCT
ejpam-5445	286	25	and	and	CCONJ
ejpam-5445	286	26	with	with	ADP
ejpam-5445	286	27	respect	respect	NOUN
ejpam-5445	286	28	to	to	ADP
ejpam-5445	286	29	ω	ω	PROPN
ejpam-5445	286	30	∈	∈	PROPN
ejpam-5445	287	1	[	[	X
ejpam-5445	287	2	α	α	X
ejpam-5445	287	3	,	,	PUNCT
ejpam-5445	287	4	β	β	X
ejpam-5445	287	5	]	]	X
ejpam-5445	287	6	,	,	PUNCT
ejpam-5445	287	7	at	at	ADP
ejpam-5445	287	8	the	the	DET
ejpam-5445	287	9	point	point	NOUN
ejpam-5445	287	10	s.	s.	PROPN
ejpam-5445	287	11	bowmiya	bowmiya	PROPN
ejpam-5445	287	12	et	et	PROPN
ejpam-5445	287	13	al	al	PROPN
ejpam-5445	287	14	.	.	PUNCT
ejpam-5445	287	15	/	/	SYM
ejpam-5445	287	16	eur	eur	PROPN
ejpam-5445	287	17	.	.	PUNCT
ejpam-5445	288	1	j.	j.	PROPN
ejpam-5445	288	2	pure	pure	PROPN
ejpam-5445	288	3	appl	appl	PROPN
ejpam-5445	288	4	.	.	PROPN
ejpam-5445	288	5	math	math	PROPN
ejpam-5445	288	6	,	,	PUNCT
ejpam-5445	288	7	17	17	NUM
ejpam-5445	288	8	(	(	PUNCT
ejpam-5445	288	9	4	4	NUM
ejpam-5445	288	10	)	)	PUNCT
ejpam-5445	288	11	(	(	PUNCT
ejpam-5445	288	12	2024	2024	NUM
ejpam-5445	288	13	)	)	PUNCT
ejpam-5445	288	14	,	,	PUNCT
ejpam-5445	288	15	3415	3415	NUM
ejpam-5445	288	16	-	-	SYM
ejpam-5445	288	17	3435	3435	NUM
ejpam-5445	288	18	3428	3428	NUM
ejpam-5445	288	19	|χ(ω)−	|χ(ω)−	NOUN
ejpam-5445	288	20	ζ(ω)|	ζ(ω)|	ADV
ejpam-5445	288	21	≤	≤	PROPN
ejpam-5445	288	22	θ	θ	PROPN
ejpam-5445	288	23	,	,	PUNCT
ejpam-5445	288	24	where	where	SCONJ
ejpam-5445	288	25	θ	θ	PROPN
ejpam-5445	288	26	=	=	SYM
ejpam-5445	288	27			X
ejpam-5445	288	28	(	(	PUNCT
ejpam-5445	288	29	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−σ(β−α))(1−e−η(β−α	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−σ(β−α))(1−e−η(β−α	NUM
ejpam-5445	288	30	)	)	PUNCT
ejpam-5445	288	31	)	)	PUNCT
ejpam-5445	288	32	γρση	γρση	PROPN
ejpam-5445	288	33	∈	∈	PROPN
ejpam-5445	288	34	;	;	PUNCT
ejpam-5445	289	1	if	if	SCONJ
ejpam-5445	289	2	(	(	PUNCT
ejpam-5445	289	3	ρ	ρ	NOUN
ejpam-5445	289	4	,	,	PUNCT
ejpam-5445	289	5	γ	γ	PROPN
ejpam-5445	289	6	,	,	PUNCT
ejpam-5445	289	7	σ	σ	PROPN
ejpam-5445	289	8	,	,	PUNCT
ejpam-5445	289	9	η	η	NOUN
ejpam-5445	289	10	)	)	PUNCT
ejpam-5445	289	11	̸=	̸=	PROPN
ejpam-5445	289	12	0	0	NUM
ejpam-5445	289	13	(	(	PUNCT
ejpam-5445	289	14	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−σ(β−α	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−σ(β−α	NOUN
ejpam-5445	289	15	)	)	PUNCT
ejpam-5445	289	16	)	)	PUNCT
ejpam-5445	289	17	γρσ	γρσ	NOUN
ejpam-5445	289	18	(	(	PUNCT
ejpam-5445	289	19	β	β	NOUN
ejpam-5445	289	20	−	−	NOUN
ejpam-5445	289	21	α	α	X
ejpam-5445	289	22	)	)	PUNCT
ejpam-5445	289	23	∈	∈	PROPN
ejpam-5445	289	24	;	;	PUNCT
ejpam-5445	289	25	if	if	SCONJ
ejpam-5445	289	26	ρ	ρ	PROPN
ejpam-5445	289	27	̸=	̸=	PROPN
ejpam-5445	289	28	γ	γ	PROPN
ejpam-5445	289	29	̸=	̸=	PROPN
ejpam-5445	289	30	σ	σ	PROPN
ejpam-5445	289	31	̸=	̸=	PROPN
ejpam-5445	289	32	0	0	NUM
ejpam-5445	289	33	,	,	PUNCT
ejpam-5445	289	34	η	η	X
ejpam-5445	289	35	=	=	SYM
ejpam-5445	289	36	0	0	NUM
ejpam-5445	289	37	(	(	PUNCT
ejpam-5445	289	38	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−η(β−α	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−η(β−α	NUM
ejpam-5445	289	39	)	)	PUNCT
ejpam-5445	289	40	)	)	PUNCT
ejpam-5445	289	41	γρη	γρη	NOUN
ejpam-5445	289	42	(	(	PUNCT
ejpam-5445	289	43	β	β	NOUN
ejpam-5445	289	44	−	−	NOUN
ejpam-5445	289	45	α	α	X
ejpam-5445	289	46	)	)	PUNCT
ejpam-5445	289	47	∈	∈	PROPN
ejpam-5445	289	48	;	;	PUNCT
ejpam-5445	289	49	if	if	SCONJ
ejpam-5445	289	50	ρ	ρ	PROPN
ejpam-5445	289	51	̸=	̸=	PROPN
ejpam-5445	289	52	γ	γ	PROPN
ejpam-5445	289	53	̸=	̸=	PROPN
ejpam-5445	289	54	η	η	PROPN
ejpam-5445	289	55	̸=	̸=	PROPN
ejpam-5445	289	56	0	0	NUM
ejpam-5445	289	57	,	,	PUNCT
ejpam-5445	289	58	σ	σ	PROPN
ejpam-5445	289	59	=	=	SYM
ejpam-5445	289	60	0	0	NUM
ejpam-5445	289	61	(	(	PUNCT
ejpam-5445	289	62	1−e−γ(β−α))(1−e−η(β−α))(1−e−σ(β−α	1−e−γ(β−α))(1−e−η(β−α))(1−e−σ(β−α	NOUN
ejpam-5445	289	63	)	)	PUNCT
ejpam-5445	289	64	)	)	PUNCT
ejpam-5445	289	65	γησ	γησ	VERB
ejpam-5445	289	66	(	(	PUNCT
ejpam-5445	289	67	β	β	X
ejpam-5445	289	68	−	−	NOUN
ejpam-5445	289	69	α	α	X
ejpam-5445	289	70	)	)	PUNCT
ejpam-5445	289	71	∈	∈	PROPN
ejpam-5445	289	72	;	;	PUNCT
ejpam-5445	290	1	if	if	SCONJ
ejpam-5445	290	2	η	η	PROPN
ejpam-5445	290	3	̸=	̸=	PROPN
ejpam-5445	290	4	γ	γ	PROPN
ejpam-5445	290	5	̸=	̸=	PROPN
ejpam-5445	290	6	σ	σ	PROPN
ejpam-5445	290	7	̸=	̸=	PROPN
ejpam-5445	290	8	0	0	NUM
ejpam-5445	290	9	,	,	PUNCT
ejpam-5445	290	10	ρ	ρ	PROPN
ejpam-5445	290	11	=	=	SYM
ejpam-5445	290	12	0	0	NUM
ejpam-5445	290	13	(	(	PUNCT
ejpam-5445	290	14	1−e−η(β−α))(1−e−ρ(β−α))(1−e−σ(β−α	1−e−η(β−α))(1−e−ρ(β−α))(1−e−σ(β−α	NUM
ejpam-5445	290	15	)	)	PUNCT
ejpam-5445	290	16	)	)	PUNCT
ejpam-5445	290	17	ηρσ	ηρσ	NOUN
ejpam-5445	290	18	(	(	PUNCT
ejpam-5445	290	19	β	β	X
ejpam-5445	290	20	−	−	NOUN
ejpam-5445	290	21	α	α	X
ejpam-5445	290	22	)	)	PUNCT
ejpam-5445	290	23	∈	∈	PROPN
ejpam-5445	290	24	;	;	PUNCT
ejpam-5445	290	25	if	if	SCONJ
ejpam-5445	290	26	ρ	ρ	PROPN
ejpam-5445	290	27	̸=	̸=	PROPN
ejpam-5445	290	28	η	η	PROPN
ejpam-5445	290	29	̸=	̸=	PROPN
ejpam-5445	290	30	σ	σ	PROPN
ejpam-5445	290	31	̸=	̸=	PROPN
ejpam-5445	290	32	0	0	NUM
ejpam-5445	290	33	,	,	PUNCT
ejpam-5445	290	34	γ	γ	X
ejpam-5445	290	35	=	=	SYM
ejpam-5445	290	36	0	0	NUM
ejpam-5445	290	37	(	(	PUNCT
ejpam-5445	290	38	1−e−ρ(β−α))(1−e−σ(β−α	1−e−ρ(β−α))(1−e−σ(β−α	NUM
ejpam-5445	290	39	)	)	PUNCT
ejpam-5445	290	40	)	)	PUNCT
ejpam-5445	290	41	ρσ	ρσ	ADP
ejpam-5445	290	42	(	(	PUNCT
ejpam-5445	290	43	β	β	X
ejpam-5445	290	44	−	−	PROPN
ejpam-5445	290	45	α)2	α)2	NOUN
ejpam-5445	290	46	∈	∈	NOUN
ejpam-5445	290	47	;	;	PUNCT
ejpam-5445	290	48	if	if	SCONJ
ejpam-5445	290	49	ρ	ρ	PROPN
ejpam-5445	290	50	̸=	̸=	PROPN
ejpam-5445	290	51	σ	σ	PROPN
ejpam-5445	290	52	̸=	̸=	PROPN
ejpam-5445	290	53	0	0	NUM
ejpam-5445	290	54	,	,	PUNCT
ejpam-5445	290	55	γ	γ	NOUN
ejpam-5445	290	56	=	=	SYM
ejpam-5445	290	57	η	η	PROPN
ejpam-5445	290	58	=	=	SYM
ejpam-5445	290	59	0	0	NUM
ejpam-5445	290	60	(	(	PUNCT
ejpam-5445	290	61	1−e−ρ(β−α))(1−e−γ(β−α	1−e−ρ(β−α))(1−e−γ(β−α	NOUN
ejpam-5445	290	62	)	)	PUNCT
ejpam-5445	290	63	)	)	PUNCT
ejpam-5445	290	64	ρσ	ρσ	ADP
ejpam-5445	290	65	(	(	PUNCT
ejpam-5445	290	66	β	β	X
ejpam-5445	290	67	−	−	PROPN
ejpam-5445	290	68	α)2	α)2	NOUN
ejpam-5445	290	69	∈	∈	NOUN
ejpam-5445	290	70	;	;	PUNCT
ejpam-5445	291	1	if	if	SCONJ
ejpam-5445	291	2	ρ	ρ	PROPN
ejpam-5445	291	3	̸=	̸=	PROPN
ejpam-5445	291	4	γ	γ	PROPN
ejpam-5445	291	5	̸=	̸=	PROPN
ejpam-5445	291	6	0	0	NUM
ejpam-5445	291	7	,	,	PUNCT
ejpam-5445	291	8	σ	σ	PROPN
ejpam-5445	291	9	=	=	PUNCT
ejpam-5445	291	10	η	η	PROPN
ejpam-5445	291	11	=	=	SYM
ejpam-5445	291	12	0	0	NUM
ejpam-5445	291	13	(	(	PUNCT
ejpam-5445	291	14	1−e−ρ(β−α))(1−e−η(β−α	1−e−ρ(β−α))(1−e−η(β−α	NUM
ejpam-5445	291	15	)	)	PUNCT
ejpam-5445	291	16	)	)	PUNCT
ejpam-5445	291	17	ρη	ρη	NOUN
ejpam-5445	291	18	(	(	PUNCT
ejpam-5445	291	19	β	β	X
ejpam-5445	291	20	−	−	PROPN
ejpam-5445	291	21	α)2	α)2	NOUN
ejpam-5445	291	22	∈	∈	NOUN
ejpam-5445	291	23	;	;	PUNCT
ejpam-5445	291	24	if	if	SCONJ
ejpam-5445	291	25	ρ	ρ	PROPN
ejpam-5445	291	26	̸=	̸=	PROPN
ejpam-5445	291	27	η	η	PROPN
ejpam-5445	291	28	̸=	̸=	PROPN
ejpam-5445	291	29	0	0	NUM
ejpam-5445	291	30	,	,	PUNCT
ejpam-5445	291	31	γ	γ	NOUN
ejpam-5445	291	32	=	=	SYM
ejpam-5445	291	33	σ	σ	PROPN
ejpam-5445	291	34	=	=	SYM
ejpam-5445	291	35	0	0	NUM
ejpam-5445	291	36	(	(	PUNCT
ejpam-5445	291	37	1−e−σ(β−α))(1−e−γ(β−α	1−e−σ(β−α))(1−e−γ(β−α	NOUN
ejpam-5445	291	38	)	)	PUNCT
ejpam-5445	291	39	)	)	PUNCT
ejpam-5445	292	1	σγ	σγ	INTJ
ejpam-5445	292	2	(	(	PUNCT
ejpam-5445	292	3	β	β	X
ejpam-5445	292	4	−	−	PROPN
ejpam-5445	292	5	α)2	α)2	NOUN
ejpam-5445	292	6	∈	∈	NOUN
ejpam-5445	292	7	;	;	PUNCT
ejpam-5445	293	1	if	if	SCONJ
ejpam-5445	293	2	σ	σ	PROPN
ejpam-5445	293	3	̸=	̸=	PROPN
ejpam-5445	293	4	γ	γ	PROPN
ejpam-5445	293	5	̸=	̸=	PROPN
ejpam-5445	293	6	0	0	NUM
ejpam-5445	293	7	,	,	PUNCT
ejpam-5445	293	8	ρ	ρ	PROPN
ejpam-5445	293	9	=	=	SYM
ejpam-5445	293	10	η	η	PROPN
ejpam-5445	293	11	=	=	SYM
ejpam-5445	293	12	0	0	NUM
ejpam-5445	293	13	(	(	PUNCT
ejpam-5445	293	14	1−e−ρ(β−α))(1−e−η(β−α	1−e−ρ(β−α))(1−e−η(β−α	NUM
ejpam-5445	293	15	)	)	PUNCT
ejpam-5445	293	16	)	)	PUNCT
ejpam-5445	293	17	ρη	ρη	NOUN
ejpam-5445	293	18	(	(	PUNCT
ejpam-5445	293	19	β	β	X
ejpam-5445	293	20	−	−	PROPN
ejpam-5445	293	21	α)2	α)2	NOUN
ejpam-5445	293	22	∈	∈	NOUN
ejpam-5445	293	23	;	;	PUNCT
ejpam-5445	293	24	if	if	SCONJ
ejpam-5445	293	25	ρ	ρ	PROPN
ejpam-5445	293	26	̸=	̸=	PROPN
ejpam-5445	293	27	η	η	PROPN
ejpam-5445	293	28	̸=	̸=	PROPN
ejpam-5445	293	29	0	0	NUM
ejpam-5445	293	30	,	,	PUNCT
ejpam-5445	293	31	γ	γ	NOUN
ejpam-5445	293	32	=	=	SYM
ejpam-5445	293	33	σ	σ	PROPN
ejpam-5445	293	34	=	=	SYM
ejpam-5445	293	35	0	0	NUM
ejpam-5445	293	36	(	(	PUNCT
ejpam-5445	293	37	1−e−γ(β−α))(1−e−η(β−α	1−e−γ(β−α))(1−e−η(β−α	NUM
ejpam-5445	293	38	)	)	PUNCT
ejpam-5445	293	39	)	)	PUNCT
ejpam-5445	293	40	γη	γη	NOUN
ejpam-5445	293	41	(	(	PUNCT
ejpam-5445	293	42	β	β	X
ejpam-5445	293	43	−	−	PROPN
ejpam-5445	293	44	α)2	α)2	NOUN
ejpam-5445	293	45	∈	∈	NOUN
ejpam-5445	293	46	;	;	PUNCT
ejpam-5445	293	47	if	if	SCONJ
ejpam-5445	293	48	γ	γ	PROPN
ejpam-5445	293	49	̸=	̸=	PROPN
ejpam-5445	293	50	η	η	PROPN
ejpam-5445	293	51	̸=	̸=	PROPN
ejpam-5445	293	52	0	0	NUM
ejpam-5445	293	53	,	,	PUNCT
ejpam-5445	293	54	ρ	ρ	PROPN
ejpam-5445	293	55	=	=	SYM
ejpam-5445	293	56	σ	σ	PROPN
ejpam-5445	293	57	=	=	SYM
ejpam-5445	293	58	0	0	NUM
ejpam-5445	293	59	(	(	PUNCT
ejpam-5445	293	60	1−e−ρ(β−α	1−e−ρ(β−α	NUM
ejpam-5445	293	61	)	)	PUNCT
ejpam-5445	293	62	)	)	PUNCT
ejpam-5445	293	63	ρ	ρ	PROPN
ejpam-5445	293	64	(	(	PUNCT
ejpam-5445	293	65	β	β	NOUN
ejpam-5445	293	66	−	−	X
ejpam-5445	293	67	α)3	α)3	PROPN
ejpam-5445	293	68	∈	∈	PROPN
ejpam-5445	293	69	;	;	PUNCT
ejpam-5445	293	70	if	if	SCONJ
ejpam-5445	293	71	ρ	ρ	PROPN
ejpam-5445	293	72	̸=	̸=	PROPN
ejpam-5445	293	73	0	0	NUM
ejpam-5445	293	74	,	,	PUNCT
ejpam-5445	293	75	σ	σ	NOUN
ejpam-5445	293	76	=	=	SYM
ejpam-5445	293	77	γ	γ	X
ejpam-5445	293	78	=	=	SYM
ejpam-5445	293	79	η	η	PROPN
ejpam-5445	293	80	=	=	SYM
ejpam-5445	293	81	0	0	NUM
ejpam-5445	293	82	(	(	PUNCT
ejpam-5445	293	83	1−e−γ(β−α	1−e−γ(β−α	NUM
ejpam-5445	293	84	)	)	PUNCT
ejpam-5445	293	85	)	)	PUNCT
ejpam-5445	293	86	γ	γ	PROPN
ejpam-5445	293	87	(	(	PUNCT
ejpam-5445	293	88	β	β	X
ejpam-5445	293	89	−	−	X
ejpam-5445	293	90	α)3	α)3	PROPN
ejpam-5445	293	91	∈	∈	PROPN
ejpam-5445	293	92	;	;	PUNCT
ejpam-5445	293	93	if	if	SCONJ
ejpam-5445	293	94	γ	γ	PRON
ejpam-5445	293	95	̸=	̸=	PROPN
ejpam-5445	293	96	0	0	NUM
ejpam-5445	293	97	,	,	PUNCT
ejpam-5445	293	98	σ	σ	PROPN
ejpam-5445	293	99	=	=	SYM
ejpam-5445	293	100	ρ	ρ	PROPN
ejpam-5445	293	101	=	=	SYM
ejpam-5445	293	102	η	η	PROPN
ejpam-5445	293	103	=	=	SYM
ejpam-5445	293	104	0	0	NUM
ejpam-5445	293	105	(	(	PUNCT
ejpam-5445	293	106	1−e−σ(β−α	1−e−σ(β−α	NUM
ejpam-5445	293	107	)	)	PUNCT
ejpam-5445	293	108	)	)	PUNCT
ejpam-5445	294	1	σ	σ	NOUN
ejpam-5445	295	1	(	(	PUNCT
ejpam-5445	295	2	β	β	X
ejpam-5445	295	3	−	−	X
ejpam-5445	295	4	α)3	α)3	PROPN
ejpam-5445	295	5	∈	∈	PROPN
ejpam-5445	295	6	;	;	PUNCT
ejpam-5445	295	7	if	if	SCONJ
ejpam-5445	295	8	σ	σ	PROPN
ejpam-5445	295	9	̸=	̸=	PROPN
ejpam-5445	295	10	0	0	NUM
ejpam-5445	295	11	,	,	PUNCT
ejpam-5445	295	12	ρ	ρ	PROPN
ejpam-5445	295	13	=	=	SYM
ejpam-5445	295	14	γ	γ	X
ejpam-5445	295	15	=	=	SYM
ejpam-5445	295	16	η	η	PROPN
ejpam-5445	295	17	=	=	SYM
ejpam-5445	295	18	0	0	NUM
ejpam-5445	295	19	(	(	PUNCT
ejpam-5445	295	20	1−e−η(β−α	1−e−η(β−α	NOUN
ejpam-5445	295	21	)	)	PUNCT
ejpam-5445	295	22	)	)	PUNCT
ejpam-5445	295	23	η	η	PROPN
ejpam-5445	295	24	(	(	PUNCT
ejpam-5445	295	25	β	β	X
ejpam-5445	295	26	−	−	X
ejpam-5445	295	27	α)3	α)3	PROPN
ejpam-5445	295	28	∈	∈	PROPN
ejpam-5445	295	29	;	;	PUNCT
ejpam-5445	295	30	if	if	SCONJ
ejpam-5445	295	31	η	η	PROPN
ejpam-5445	295	32	̸=	̸=	PROPN
ejpam-5445	295	33	0	0	NUM
ejpam-5445	295	34	,	,	PUNCT
ejpam-5445	295	35	σ	σ	NOUN
ejpam-5445	295	36	=	=	SYM
ejpam-5445	295	37	γ	γ	X
ejpam-5445	295	38	=	=	SYM
ejpam-5445	295	39	ρ	ρ	PROPN
ejpam-5445	295	40	=	=	SYM
ejpam-5445	295	41	0	0	PUNCT
ejpam-5445	295	42	(	(	PUNCT
ejpam-5445	295	43	β	β	NOUN
ejpam-5445	295	44	−	−	PROPN
ejpam-5445	295	45	α)4	α)4	NOUN
ejpam-5445	295	46	∈	∈	NOUN
ejpam-5445	295	47	;	;	PUNCT
ejpam-5445	295	48	if	if	SCONJ
ejpam-5445	295	49	ρ	ρ	PROPN
ejpam-5445	295	50	=	=	SYM
ejpam-5445	295	51	σ	σ	PROPN
ejpam-5445	295	52	=	=	PUNCT
ejpam-5445	295	53	γ	γ	X
ejpam-5445	295	54	=	=	SYM
ejpam-5445	295	55	η	η	PROPN
ejpam-5445	295	56	=	=	PROPN
ejpam-5445	295	57	0	0	NUM
ejpam-5445	295	58	with	with	ADP
ejpam-5445	295	59	respect	respect	NOUN
ejpam-5445	295	60	to	to	ADP
ejpam-5445	295	61	ω	ω	PROPN
ejpam-5445	295	62	∈	∈	PROPN
ejpam-5445	295	63	[	[	X
ejpam-5445	295	64	α	α	X
ejpam-5445	295	65	,	,	PUNCT
ejpam-5445	295	66	β	β	X
ejpam-5445	295	67	]	]	PUNCT
ejpam-5445	295	68	.	.	PUNCT
ejpam-5445	296	1	proof	proof	NOUN
ejpam-5445	296	2	.	.	PUNCT
ejpam-5445	297	1	like	like	ADP
ejpam-5445	297	2	the	the	DET
ejpam-5445	297	3	verification	verification	NOUN
ejpam-5445	297	4	of	of	ADP
ejpam-5445	297	5	theorem	theorem	NOUN
ejpam-5445	297	6	2	2	NUM
ejpam-5445	297	7	.	.	PUNCT
ejpam-5445	297	8	let	let	VERB
ejpam-5445	297	9	∈	∈	PRON
ejpam-5445	297	10	>	>	X
ejpam-5445	297	11	0	0	PROPN
ejpam-5445	298	1	and	and	CCONJ
ejpam-5445	298	2	γ	γ	PROPN
ejpam-5445	298	3	∈	∈	PROPN
ejpam-5445	298	4	c4[α	c4[α	NOUN
ejpam-5445	298	5	,	,	PUNCT
ejpam-5445	298	6	β	β	X
ejpam-5445	298	7	]	]	PUNCT
ejpam-5445	298	8	.	.	PUNCT
ejpam-5445	299	1	allow	allow	VERB
ejpam-5445	299	2	us	we	PRON
ejpam-5445	299	3	the	the	DET
ejpam-5445	299	4	consider	consider	VERB
ejpam-5445	299	5	ζ(ω	ζ(ω	PRON
ejpam-5445	299	6	)	)	PUNCT
ejpam-5445	299	7	=	=	SYM
ejpam-5445	299	8	γ′′′(ω	γ′′′(ω	PROPN
ejpam-5445	299	9	)	)	PUNCT
ejpam-5445	300	1	+	+	CCONJ
ejpam-5445	300	2	(	(	PUNCT
ejpam-5445	300	3	u2	u2	NOUN
ejpam-5445	300	4	+	+	CCONJ
ejpam-5445	300	5	ρ1)γ	ρ1)γ	PROPN
ejpam-5445	300	6	′′(ω	′′(ω	NOUN
ejpam-5445	300	7	)	)	PUNCT
ejpam-5445	301	1	+	+	CCONJ
ejpam-5445	301	2	(	(	PUNCT
ejpam-5445	301	3	u22	u22	PROPN
ejpam-5445	301	4	+	+	PROPN
ejpam-5445	301	5	ρ1u2	ρ1u2	NOUN
ejpam-5445	301	6	+	+	CCONJ
ejpam-5445	301	7	ρ2)γ	ρ2)γ	ADJ
ejpam-5445	301	8	′(ω	′(ω	NOUN
ejpam-5445	301	9	)	)	PUNCT
ejpam-5445	301	10	+	+	CCONJ
ejpam-5445	301	11	(	(	PUNCT
ejpam-5445	301	12	u32	u32	NOUN
ejpam-5445	301	13	+	+	CCONJ
ejpam-5445	301	14	ρ1u	ρ1u	SYM
ejpam-5445	301	15	2	2	NUM
ejpam-5445	301	16	2	2	NUM
ejpam-5445	301	17	+	+	CCONJ
ejpam-5445	301	18	ρ2u2	ρ2u2	PROPN
ejpam-5445	301	19	+	+	X
ejpam-5445	301	20	ρ3)γ(ω	ρ3)γ(ω	PROPN
ejpam-5445	301	21	)	)	PUNCT
ejpam-5445	301	22	,	,	PUNCT
ejpam-5445	301	23	we	we	PRON
ejpam-5445	301	24	acquire	acquire	VERB
ejpam-5445	301	25	ζ	ζ	NOUN
ejpam-5445	301	26	′(ω	′(ω	NOUN
ejpam-5445	301	27	)	)	PUNCT
ejpam-5445	301	28	=	=	SYM
ejpam-5445	301	29	γiv(ω	γiv(ω	PROPN
ejpam-5445	301	30	)	)	PUNCT
ejpam-5445	302	1	+	+	CCONJ
ejpam-5445	302	2	(	(	PUNCT
ejpam-5445	302	3	u2	u2	PROPN
ejpam-5445	302	4	+	+	CCONJ
ejpam-5445	302	5	ρ1)γ	ρ1)γ	PROPN
ejpam-5445	302	6	′′′(ω	′′′(ω	PROPN
ejpam-5445	302	7	)	)	PUNCT
ejpam-5445	303	1	+	+	CCONJ
ejpam-5445	303	2	(	(	PUNCT
ejpam-5445	303	3	u22	u22	PROPN
ejpam-5445	303	4	+	+	PROPN
ejpam-5445	303	5	ρ1u2	ρ1u2	NOUN
ejpam-5445	303	6	+	+	NUM
ejpam-5445	303	7	ρ3)γ	ρ3)γ	NOUN
ejpam-5445	303	8	′′(ω	′′(ω	NOUN
ejpam-5445	303	9	)	)	PUNCT
ejpam-5445	304	1	+	+	CCONJ
ejpam-5445	304	2	(	(	PUNCT
ejpam-5445	304	3	u32	u32	NOUN
ejpam-5445	304	4	+	+	CCONJ
ejpam-5445	304	5	ρ1u	ρ1u	SYM
ejpam-5445	304	6	2	2	NUM
ejpam-5445	304	7	+	+	CCONJ
ejpam-5445	304	8	ρ2u2	ρ2u2	PROPN
ejpam-5445	304	9	+	+	NUM
ejpam-5445	304	10	ρ3)γ	ρ3)γ	PROPN
ejpam-5445	304	11	′(ω	′(ω	NOUN
ejpam-5445	304	12	)	)	PUNCT
ejpam-5445	304	13	+	+	CCONJ
ejpam-5445	304	14	(	(	PUNCT
ejpam-5445	304	15	u42	u42	ADJ
ejpam-5445	304	16	+	+	CCONJ
ejpam-5445	304	17	ρ1u	ρ1u	SYM
ejpam-5445	304	18	3	3	NUM
ejpam-5445	304	19	2	2	NUM
ejpam-5445	304	20	+	+	CCONJ
ejpam-5445	304	21	ρ2u	ρ2u	PROPN
ejpam-5445	304	22	2	2	NUM
ejpam-5445	304	23	2	2	NUM
ejpam-5445	304	24	+	+	CCONJ
ejpam-5445	304	25	ρ3u2	ρ3u2	NUM
ejpam-5445	304	26	+	+	CCONJ
ejpam-5445	304	27	ρ4)γ(ω	ρ4)γ(ω	NOUN
ejpam-5445	304	28	)	)	PUNCT
ejpam-5445	304	29	(	(	PUNCT
ejpam-5445	304	30	51	51	NUM
ejpam-5445	304	31	)	)	PUNCT
ejpam-5445	304	32	with	with	ADP
ejpam-5445	304	33	respect	respect	NOUN
ejpam-5445	304	34	to	to	ADP
ejpam-5445	304	35	ω	ω	PROPN
ejpam-5445	304	36	∈	∈	PROPN
ejpam-5445	305	1	[	[	X
ejpam-5445	305	2	α	α	X
ejpam-5445	305	3	,	,	PUNCT
ejpam-5445	305	4	β	β	X
ejpam-5445	305	5	]	]	X
ejpam-5445	305	6	,	,	PUNCT
ejpam-5445	305	7	at	at	ADP
ejpam-5445	305	8	the	the	DET
ejpam-5445	305	9	point	point	NOUN
ejpam-5445	305	10	|ζ	|ζ	PROPN
ejpam-5445	305	11	′(ω)−	′(ω)−	NOUN
ejpam-5445	305	12	u2ζ(ω)−h(ω)|	u2ζ(ω)−h(ω)|	PUNCT
ejpam-5445	305	13	<	<	X
ejpam-5445	305	14	∈	∈	PROPN
ejpam-5445	305	15	(	(	PUNCT
ejpam-5445	305	16	52	52	NUM
ejpam-5445	305	17	)	)	PUNCT
ejpam-5445	305	18	with	with	ADP
ejpam-5445	305	19	respect	respect	NOUN
ejpam-5445	305	20	to	to	ADP
ejpam-5445	305	21	ω	ω	PROPN
ejpam-5445	305	22	∈	∈	PROPN
ejpam-5445	305	23	[	[	X
ejpam-5445	305	24	α	α	X
ejpam-5445	305	25	,	,	PUNCT
ejpam-5445	305	26	β	β	X
ejpam-5445	305	27	]	]	PUNCT
ejpam-5445	305	28	.	.	PUNCT
ejpam-5445	306	1	if	if	SCONJ
ejpam-5445	306	2	follows	follow	VERB
ejpam-5445	306	3	from	from	ADP
ejpam-5445	306	4	51	51	NUM
ejpam-5445	306	5	that	that	SCONJ
ejpam-5445	306	6	|ζ	|ζ	PROPN
ejpam-5445	306	7	′(ω)−	′(ω)−	NOUN
ejpam-5445	306	8	u2ζ(ω)−h(ω)|	u2ζ(ω)−h(ω)|	PROPN
ejpam-5445	306	9	=	=	SYM
ejpam-5445	306	10	|γiv(ω	|γiv(ω	PROPN
ejpam-5445	306	11	)	)	PUNCT
ejpam-5445	307	1	+	+	CCONJ
ejpam-5445	307	2	(	(	PUNCT
ejpam-5445	307	3	u2	u2	PROPN
ejpam-5445	307	4	+	+	CCONJ
ejpam-5445	307	5	ρ1)γ	ρ1)γ	PROPN
ejpam-5445	307	6	′′′(ω	′′′(ω	PROPN
ejpam-5445	307	7	)	)	PUNCT
ejpam-5445	308	1	+	+	CCONJ
ejpam-5445	308	2	(	(	PUNCT
ejpam-5445	308	3	u22	u22	PROPN
ejpam-5445	308	4	+	+	PROPN
ejpam-5445	308	5	ρ1u2	ρ1u2	NOUN
ejpam-5445	308	6	+	+	NUM
ejpam-5445	308	7	ρ3)γ	ρ3)γ	PROPN
ejpam-5445	308	8	′′(ω	′′(ω	NOUN
ejpam-5445	308	9	)	)	PUNCT
ejpam-5445	309	1	s.	s.	PROPN
ejpam-5445	309	2	bowmiya	bowmiya	VERB
ejpam-5445	309	3	et	et	PROPN
ejpam-5445	309	4	al	al	PROPN
ejpam-5445	309	5	.	.	PUNCT
ejpam-5445	309	6	/	/	SYM
ejpam-5445	309	7	eur	eur	PROPN
ejpam-5445	309	8	.	.	PUNCT
ejpam-5445	310	1	j.	j.	PROPN
ejpam-5445	310	2	pure	pure	PROPN
ejpam-5445	310	3	appl	appl	PROPN
ejpam-5445	310	4	.	.	PROPN
ejpam-5445	310	5	math	math	PROPN
ejpam-5445	310	6	,	,	PUNCT
ejpam-5445	310	7	17	17	NUM
ejpam-5445	310	8	(	(	PUNCT
ejpam-5445	310	9	4	4	NUM
ejpam-5445	310	10	)	)	PUNCT
ejpam-5445	310	11	(	(	PUNCT
ejpam-5445	310	12	2024	2024	NUM
ejpam-5445	310	13	)	)	PUNCT
ejpam-5445	310	14	,	,	PUNCT
ejpam-5445	310	15	3415	3415	NUM
ejpam-5445	310	16	-	-	SYM
ejpam-5445	310	17	3435	3435	NUM
ejpam-5445	310	18	3429	3429	NUM
ejpam-5445	310	19	+	+	CCONJ
ejpam-5445	310	20	(	(	PUNCT
ejpam-5445	310	21	u32	u32	NOUN
ejpam-5445	311	1	+	+	CCONJ
ejpam-5445	311	2	ρ1u	ρ1u	SYM
ejpam-5445	311	3	2	2	NUM
ejpam-5445	311	4	+	+	CCONJ
ejpam-5445	311	5	ρ2u2	ρ2u2	PROPN
ejpam-5445	311	6	+	+	NUM
ejpam-5445	311	7	ρ3)γ	ρ3)γ	PROPN
ejpam-5445	311	8	′(ω	′(ω	NOUN
ejpam-5445	311	9	)	)	PUNCT
ejpam-5445	312	1	+	+	CCONJ
ejpam-5445	312	2	(	(	PUNCT
ejpam-5445	312	3	u42	u42	ADJ
ejpam-5445	312	4	+	+	CCONJ
ejpam-5445	312	5	ρ1u	ρ1u	SYM
ejpam-5445	312	6	3	3	NUM
ejpam-5445	312	7	2	2	NUM
ejpam-5445	312	8	+	+	CCONJ
ejpam-5445	312	9	ρ2u	ρ2u	PROPN
ejpam-5445	312	10	2	2	NUM
ejpam-5445	312	11	2	2	NUM
ejpam-5445	312	12	+	+	CCONJ
ejpam-5445	312	13	ρ3u2	ρ3u2	NUM
ejpam-5445	312	14	+	+	NUM
ejpam-5445	312	15	ρ4)γ(γ	ρ4)γ(γ	NOUN
ejpam-5445	312	16	)	)	PUNCT
ejpam-5445	312	17	−	−	PROPN
ejpam-5445	313	1	u2(γ	u2(γ	PROPN
ejpam-5445	313	2	′′′(ω	′′′(ω	PROPN
ejpam-5445	313	3	)	)	PUNCT
ejpam-5445	314	1	+	+	CCONJ
ejpam-5445	314	2	(	(	PUNCT
ejpam-5445	314	3	u2	u2	NOUN
ejpam-5445	314	4	+	+	CCONJ
ejpam-5445	314	5	ρ1)γ	ρ1)γ	PROPN
ejpam-5445	314	6	′′(ω	′′(ω	NOUN
ejpam-5445	314	7	)	)	PUNCT
ejpam-5445	315	1	+	+	CCONJ
ejpam-5445	315	2	(	(	PUNCT
ejpam-5445	315	3	u22	u22	PROPN
ejpam-5445	315	4	+	+	PROPN
ejpam-5445	315	5	ρ1u2	ρ1u2	NOUN
ejpam-5445	315	6	+	+	CCONJ
ejpam-5445	315	7	ρ2)γ	ρ2)γ	ADJ
ejpam-5445	315	8	′(ω	′(ω	NOUN
ejpam-5445	315	9	)	)	PUNCT
ejpam-5445	315	10	+	+	CCONJ
ejpam-5445	315	11	(	(	PUNCT
ejpam-5445	315	12	u32	u32	NOUN
ejpam-5445	315	13	+	+	CCONJ
ejpam-5445	315	14	ρ1u	ρ1u	SYM
ejpam-5445	315	15	2	2	NUM
ejpam-5445	315	16	2	2	NUM
ejpam-5445	315	17	+	+	CCONJ
ejpam-5445	315	18	ρ2u2	ρ2u2	PROPN
ejpam-5445	315	19	+	+	CCONJ
ejpam-5445	315	20	ρ3)γ(ω))−h(ω)|	ρ3)γ(ω))−h(ω)|	X
ejpam-5445	315	21	=	=	SYM
ejpam-5445	315	22	|γiv(ω	|γiv(ω	ADJ
ejpam-5445	315	23	)	)	PUNCT
ejpam-5445	315	24	+	+	CCONJ
ejpam-5445	315	25	ρ1γ	ρ1γ	PROPN
ejpam-5445	315	26	′′′(ω	′′′(ω	PROPN
ejpam-5445	315	27	)	)	PUNCT
ejpam-5445	315	28	+	+	PROPN
ejpam-5445	316	1	ρ2γ	ρ2γ	PROPN
ejpam-5445	316	2	′′(ω	′′(ω	NOUN
ejpam-5445	316	3	)	)	PUNCT
ejpam-5445	317	1	+	+	CCONJ
ejpam-5445	317	2	ρ3γ	ρ3γ	NUM
ejpam-5445	317	3	′(ω	′(ω	NOUN
ejpam-5445	317	4	)	)	PUNCT
ejpam-5445	318	1	+	+	CCONJ
ejpam-5445	318	2	ρ4γ(ω)−h(ω)|	ρ4γ(ω)−h(ω)|	DET
ejpam-5445	318	3	≤∈	≤∈	NOUN
ejpam-5445	318	4	.	.	PUNCT
ejpam-5445	319	1	so	so	ADV
ejpam-5445	319	2	|ζ	|ζ	PROPN
ejpam-5445	319	3	′(ω)−	′(ω)−	PROPN
ejpam-5445	319	4	u2ζ(ω)−h(ω)|	u2ζ(ω)−h(ω)|	PUNCT
ejpam-5445	319	5	<	<	X
ejpam-5445	319	6	∈	∈	NOUN
ejpam-5445	319	7	for	for	ADP
ejpam-5445	319	8	all	all	DET
ejpam-5445	319	9	ω	ω	NUM
ejpam-5445	319	10	∈	∈	PROPN
ejpam-5445	319	11	[	[	X
ejpam-5445	319	12	α	α	X
ejpam-5445	319	13	,	,	PUNCT
ejpam-5445	319	14	β	β	X
ejpam-5445	319	15	]	]	PUNCT
ejpam-5445	319	16	.	.	PUNCT
ejpam-5445	320	1	equivalently	equivalently	ADV
ejpam-5445	320	2	ζ	ζ	NOUN
ejpam-5445	320	3	fulfilling	fulfil	VERB
ejpam-5445	320	4	−	−	PUNCT
ejpam-5445	320	5	∈≤	∈≤	PRON
ejpam-5445	320	6	ζ	ζ	NOUN
ejpam-5445	320	7	′(ω)−	′(ω)−	NOUN
ejpam-5445	320	8	u2ζ(ω)−h(ω	u2ζ(ω)−h(ω	NOUN
ejpam-5445	320	9	)	)	PUNCT
ejpam-5445	320	10	<	<	X
ejpam-5445	320	11	∈	∈	PROPN
ejpam-5445	320	12	(	(	PUNCT
ejpam-5445	320	13	53	53	NUM
ejpam-5445	320	14	)	)	PUNCT
ejpam-5445	320	15	with	with	ADP
ejpam-5445	320	16	respect	respect	NOUN
ejpam-5445	320	17	to	to	ADP
ejpam-5445	320	18	ω	ω	PROPN
ejpam-5445	320	19	∈	∈	PROPN
ejpam-5445	320	20	[	[	X
ejpam-5445	320	21	α	α	X
ejpam-5445	320	22	,	,	PUNCT
ejpam-5445	320	23	β	β	X
ejpam-5445	320	24	]	]	X
ejpam-5445	320	25	.	.	PUNCT
ejpam-5445	321	1	multiplying	multiply	VERB
ejpam-5445	321	2	the	the	DET
ejpam-5445	321	3	formula	formula	NOUN
ejpam-5445	321	4	by	by	ADP
ejpam-5445	321	5	the	the	DET
ejpam-5445	321	6	function	function	NOUN
ejpam-5445	321	7	e−u2(ω−α	e−u2(ω−α	NOUN
ejpam-5445	321	8	)	)	PUNCT
ejpam-5445	321	9	satisfies	satisfie	NOUN
ejpam-5445	321	10	−	−	PROPN
ejpam-5445	321	11	∈	∈	PROPN
ejpam-5445	321	12	e−u2(ω−α	e−u2(ω−α	NOUN
ejpam-5445	321	13	)	)	PUNCT
ejpam-5445	321	14	≤	≤	NUM
ejpam-5445	321	15	ζ	ζ	PROPN
ejpam-5445	321	16	′(ω)e−u2(ω−α	′(ω)e−u2(ω−α	NOUN
ejpam-5445	321	17	)	)	PUNCT
ejpam-5445	321	18	−	−	PROPN
ejpam-5445	321	19	u2ζ(ω)e	u2ζ(ω)e	ADJ
ejpam-5445	321	20	−u2(ω−α	−u2(ω−α	NOUN
ejpam-5445	321	21	)	)	PUNCT
ejpam-5445	321	22	−h(ω)e−u2(ω−α	−h(ω)e−u2(ω−α	NOUN
ejpam-5445	321	23	)	)	PUNCT
ejpam-5445	321	24	(	(	PUNCT
ejpam-5445	321	25	54	54	NUM
ejpam-5445	321	26	)	)	PUNCT
ejpam-5445	321	27	≤∈	≤∈	PROPN
ejpam-5445	321	28	e−u2(ω−α	e−u2(ω−α	NOUN
ejpam-5445	321	29	)	)	PUNCT
ejpam-5445	321	30	(	(	PUNCT
ejpam-5445	321	31	55	55	NUM
ejpam-5445	321	32	)	)	PUNCT
ejpam-5445	321	33	with	with	ADP
ejpam-5445	321	34	respect	respect	NOUN
ejpam-5445	321	35	to	to	ADP
ejpam-5445	321	36	ω	ω	PROPN
ejpam-5445	321	37	∈	∈	PROPN
ejpam-5445	321	38	[	[	X
ejpam-5445	321	39	α	α	X
ejpam-5445	321	40	,	,	PUNCT
ejpam-5445	321	41	β	β	X
ejpam-5445	321	42	]	]	X
ejpam-5445	321	43	.	.	PUNCT
ejpam-5445	322	1	without	without	ADP
ejpam-5445	322	2	loss	loss	NOUN
ejpam-5445	322	3	of	of	ADP
ejpam-5445	322	4	inclusive	inclusive	ADJ
ejpam-5445	322	5	statement	statement	NOUN
ejpam-5445	322	6	we	we	PRON
ejpam-5445	322	7	may	may	AUX
ejpam-5445	322	8	accept	accept	VERB
ejpam-5445	322	9	that	that	DET
ejpam-5445	322	10	u2	u2	PROPN
ejpam-5445	322	11	>	>	X
ejpam-5445	322	12	1	1	NUM
ejpam-5445	322	13	,	,	PUNCT
ejpam-5445	322	14	at	at	ADP
ejpam-5445	322	15	the	the	DET
ejpam-5445	322	16	point	point	NOUN
ejpam-5445	322	17	−	−	PROPN
ejpam-5445	322	18	∈	∈	PROPN
ejpam-5445	322	19	u2e	u2e	NOUN
ejpam-5445	322	20	−u2(ω−α	−u2(ω−α	NOUN
ejpam-5445	322	21	)	)	PUNCT
ejpam-5445	322	22	≤	≤	NUM
ejpam-5445	322	23	ζ	ζ	PROPN
ejpam-5445	322	24	′(ω)e−u2(ω−α	′(ω)e−u2(ω−α	NOUN
ejpam-5445	322	25	)	)	PUNCT
ejpam-5445	322	26	−	−	PROPN
ejpam-5445	322	27	u2ζ(ω)e	u2ζ(ω)e	ADJ
ejpam-5445	322	28	−u2(ω−α	−u2(ω−α	NOUN
ejpam-5445	322	29	)	)	PUNCT
ejpam-5445	322	30	−h(ω)e−u2(ω−α	−h(ω)e−u2(ω−α	ADJ
ejpam-5445	322	31	)	)	PUNCT
ejpam-5445	322	32	≤∈	≤∈	PROPN
ejpam-5445	322	33	u2e	u2e	ADJ
ejpam-5445	322	34	−u2(ω−α	−u2(ω−α	NOUN
ejpam-5445	322	35	)	)	PUNCT
ejpam-5445	322	36	(	(	PUNCT
ejpam-5445	322	37	56	56	NUM
ejpam-5445	322	38	)	)	PUNCT
ejpam-5445	322	39	for	for	ADP
ejpam-5445	322	40	all	all	DET
ejpam-5445	322	41	ω	ω	NUM
ejpam-5445	322	42	∈	∈	PROPN
ejpam-5445	322	43	[	[	X
ejpam-5445	322	44	α	α	X
ejpam-5445	322	45	,	,	PUNCT
ejpam-5445	322	46	β	β	X
ejpam-5445	322	47	]	]	PUNCT
ejpam-5445	322	48	.	.	PUNCT
ejpam-5445	323	1	integrating	integrate	VERB
ejpam-5445	323	2	54	54	NUM
ejpam-5445	323	3	from	from	ADP
ejpam-5445	323	4	ω	ω	NUM
ejpam-5445	323	5	to	to	ADP
ejpam-5445	323	6	β	β	PRON
ejpam-5445	323	7	,	,	PUNCT
ejpam-5445	323	8	at	at	ADP
ejpam-5445	323	9	the	the	DET
ejpam-5445	323	10	point	point	NOUN
ejpam-5445	323	11	−	−	X
ejpam-5445	323	12	∈	∈	PROPN
ejpam-5445	323	13	(	(	PUNCT
ejpam-5445	323	14	e−u2(ω−α	e−u2(ω−α	NOUN
ejpam-5445	323	15	)	)	PUNCT
ejpam-5445	323	16	−	−	NUM
ejpam-5445	323	17	e−u2(β−α	e−u2(β−α	NOUN
ejpam-5445	323	18	)	)	PUNCT
ejpam-5445	323	19	)	)	PUNCT
ejpam-5445	324	1	≤	≤	NUM
ejpam-5445	324	2	ζ(β)e−u2(β−α	ζ(β)e−u2(β−α	NOUN
ejpam-5445	324	3	)	)	PUNCT
ejpam-5445	324	4	−	−	PROPN
ejpam-5445	324	5	ζ(ω)e−u2(ω−α	ζ(ω)e−u2(ω−α	NOUN
ejpam-5445	324	6	)	)	PUNCT
ejpam-5445	324	7	−	−	ADP
ejpam-5445	324	8	∫	∫	PROPN
ejpam-5445	324	9	β	β	PROPN
ejpam-5445	324	10	ω	ω	PROPN
ejpam-5445	324	11	h(τ)e−u2(τ−α)dτ	h(τ)e−u2(τ−α)dτ	PROPN
ejpam-5445	324	12	≤∈	≤∈	PROPN
ejpam-5445	324	13	(	(	PUNCT
ejpam-5445	324	14	e−u2(ω−α	e−u2(ω−α	NOUN
ejpam-5445	324	15	)	)	PUNCT
ejpam-5445	324	16	−	−	NUM
ejpam-5445	324	17	e−u2(β−α	e−u2(β−α	NOUN
ejpam-5445	324	18	)	)	PUNCT
ejpam-5445	324	19	)	)	PUNCT
ejpam-5445	324	20	(	(	PUNCT
ejpam-5445	324	21	57	57	NUM
ejpam-5445	324	22	)	)	PUNCT
ejpam-5445	324	23	with	with	ADP
ejpam-5445	324	24	respect	respect	NOUN
ejpam-5445	324	25	to	to	ADP
ejpam-5445	324	26	ω	ω	PROPN
ejpam-5445	324	27	∈	∈	PROPN
ejpam-5445	324	28	[	[	X
ejpam-5445	324	29	α	α	X
ejpam-5445	324	30	,	,	PUNCT
ejpam-5445	324	31	β	β	X
ejpam-5445	324	32	]	]	X
ejpam-5445	324	33	,	,	PUNCT
ejpam-5445	324	34	at	at	ADP
ejpam-5445	324	35	the	the	DET
ejpam-5445	324	36	point	point	NOUN
ejpam-5445	324	37	57	57	NUM
ejpam-5445	324	38	that	that	SCONJ
ejpam-5445	324	39	−	−	PROPN
ejpam-5445	324	40	∈	∈	PROPN
ejpam-5445	324	41	(	(	PUNCT
ejpam-5445	324	42	e−u2(ω−α	e−u2(ω−α	NOUN
ejpam-5445	324	43	)	)	PUNCT
ejpam-5445	324	44	)	)	PUNCT
ejpam-5445	324	45	≤	≤	NOUN
ejpam-5445	324	46	ζ(β)e−u2(β−α)−	ζ(β)e−u2(β−α)−	VERB
ejpam-5445	324	47	∈	∈	PROPN
ejpam-5445	324	48	e−u2(β−α	e−u2(β−α	NOUN
ejpam-5445	324	49	)	)	PUNCT
ejpam-5445	324	50	−	−	PROPN
ejpam-5445	324	51	ζ(ω)e−u2(ω−α	ζ(ω)e−u2(ω−α	NOUN
ejpam-5445	324	52	)	)	PUNCT
ejpam-5445	324	53	−	−	ADP
ejpam-5445	325	1	∫	∫	PROPN
ejpam-5445	325	2	β	β	PROPN
ejpam-5445	325	3	ω	ω	PROPN
ejpam-5445	325	4	h(τ)e−u2(τ−α)dτ	h(τ)e−u2(τ−α)dτ	PROPN
ejpam-5445	325	5	≤∈	≤∈	PROPN
ejpam-5445	325	6	(	(	PUNCT
ejpam-5445	325	7	e−u2(ω−α	e−u2(ω−α	NOUN
ejpam-5445	325	8	)	)	PUNCT
ejpam-5445	325	9	)	)	PUNCT
ejpam-5445	325	10	(	(	PUNCT
ejpam-5445	325	11	58	58	NUM
ejpam-5445	325	12	)	)	PUNCT
ejpam-5445	325	13	for	for	ADP
ejpam-5445	325	14	all	all	DET
ejpam-5445	325	15	ω	ω	NUM
ejpam-5445	325	16	∈	∈	PROPN
ejpam-5445	325	17	[	[	X
ejpam-5445	325	18	α	α	X
ejpam-5445	325	19	,	,	PUNCT
ejpam-5445	325	20	β	β	X
ejpam-5445	325	21	]	]	X
ejpam-5445	325	22	.	.	PUNCT
ejpam-5445	326	1	multiplying	multiply	VERB
ejpam-5445	326	2	the	the	DET
ejpam-5445	326	3	formula	formula	NOUN
ejpam-5445	326	4	by	by	ADP
ejpam-5445	326	5	the	the	DET
ejpam-5445	326	6	function	function	NOUN
ejpam-5445	326	7	e−u2(ω−α	e−u2(ω−α	PROPN
ejpam-5445	326	8	)	)	PUNCT
ejpam-5445	326	9	,	,	PUNCT
ejpam-5445	326	10	we	we	PRON
ejpam-5445	326	11	acquire	acquire	VERB
ejpam-5445	326	12	−	−	PROPN
ejpam-5445	326	13	∈	∈	PROPN
ejpam-5445	326	14	≤	≤	NOUN
ejpam-5445	326	15	ζ(β)e−u2(ω−β)−	ζ(β)e−u2(ω−β)−	NUM
ejpam-5445	326	16	∈	∈	PROPN
ejpam-5445	326	17	e−u2(ω−β	e−u2(ω−β	NOUN
ejpam-5445	326	18	)	)	PUNCT
ejpam-5445	326	19	−	−	PROPN
ejpam-5445	326	20	ζ(ω)−	ζ(ω)−	NOUN
ejpam-5445	326	21	eu2ω	eu2ω	VERB
ejpam-5445	326	22	∫	∫	PROPN
ejpam-5445	326	23	β	β	PROPN
ejpam-5445	326	24	ω	ω	PROPN
ejpam-5445	326	25	h(τ)e−u2(τ−α)dτ	h(τ)e−u2(τ−α)dτ	PROPN
ejpam-5445	326	26	s.	s.	PROPN
ejpam-5445	326	27	bowmiya	bowmiya	PROPN
ejpam-5445	326	28	et	et	PROPN
ejpam-5445	326	29	al	al	PROPN
ejpam-5445	326	30	.	.	PUNCT
ejpam-5445	326	31	/	/	SYM
ejpam-5445	326	32	eur	eur	PROPN
ejpam-5445	326	33	.	.	PUNCT
ejpam-5445	327	1	j.	j.	PROPN
ejpam-5445	327	2	pure	pure	PROPN
ejpam-5445	327	3	appl	appl	PROPN
ejpam-5445	327	4	.	.	PROPN
ejpam-5445	327	5	math	math	PROPN
ejpam-5445	327	6	,	,	PUNCT
ejpam-5445	327	7	17	17	NUM
ejpam-5445	327	8	(	(	PUNCT
ejpam-5445	327	9	4	4	NUM
ejpam-5445	327	10	)	)	PUNCT
ejpam-5445	327	11	(	(	PUNCT
ejpam-5445	327	12	2024	2024	NUM
ejpam-5445	327	13	)	)	PUNCT
ejpam-5445	327	14	,	,	PUNCT
ejpam-5445	327	15	3415	3415	NUM
ejpam-5445	327	16	-	-	SYM
ejpam-5445	327	17	3435	3435	NUM
ejpam-5445	327	18	3430	3430	NUM
ejpam-5445	327	19	≤∈	≤∈	NOUN
ejpam-5445	327	20	(	(	PUNCT
ejpam-5445	327	21	59	59	NUM
ejpam-5445	327	22	)	)	PUNCT
ejpam-5445	327	23	with	with	ADP
ejpam-5445	327	24	respect	respect	NOUN
ejpam-5445	327	25	to	to	ADP
ejpam-5445	327	26	ω	ω	PROPN
ejpam-5445	327	27	∈	∈	PROPN
ejpam-5445	327	28	[	[	X
ejpam-5445	327	29	α	α	X
ejpam-5445	327	30	,	,	PUNCT
ejpam-5445	327	31	β	β	X
ejpam-5445	327	32	]	]	PUNCT
ejpam-5445	327	33	.	.	PUNCT
ejpam-5445	328	1	let	let	VERB
ejpam-5445	328	2	χ(ω	χ(ω	NOUN
ejpam-5445	328	3	)	)	PUNCT
ejpam-5445	329	1	=	=	PUNCT
ejpam-5445	329	2	ζ(β)e−u2(2h	ζ(β)e−u2(2h	NOUN
ejpam-5445	329	3	−	−	PROPN
ejpam-5445	329	4	eu2ω	eu2ω	VERB
ejpam-5445	329	5	∫	∫	PROPN
ejpam-5445	329	6	β	β	PROPN
ejpam-5445	329	7	ω	ω	PROPN
ejpam-5445	329	8	h(τ)e−u2(τ−α)dτ	h(τ)e−u2(τ−α)dτ	X
ejpam-5445	329	9	,	,	PUNCT
ejpam-5445	329	10	at	at	ADP
ejpam-5445	329	11	the	the	DET
ejpam-5445	329	12	point	point	NOUN
ejpam-5445	329	13	χ(ω	χ(ω	NOUN
ejpam-5445	329	14	)	)	PUNCT
ejpam-5445	329	15	satisfies	satisfie	NOUN
ejpam-5445	329	16	χ′(ω	χ′(ω	PROPN
ejpam-5445	329	17	)	)	PUNCT
ejpam-5445	329	18	−	−	ADP
ejpam-5445	330	1	u2χ(ω)−h(ω	u2χ(ω)−h(ω	PROPN
ejpam-5445	330	2	)	)	PUNCT
ejpam-5445	330	3	=	=	SYM
ejpam-5445	330	4	0	0	NUM
ejpam-5445	330	5	by	by	ADP
ejpam-5445	330	6	χ′(ω	χ′(ω	PROPN
ejpam-5445	330	7	)	)	PUNCT
ejpam-5445	330	8	=	=	SYM
ejpam-5445	330	9	u2χ(ω	u2χ(ω	X
ejpam-5445	330	10	)	)	PUNCT
ejpam-5445	331	1	+	+	NOUN
ejpam-5445	331	2	h(ω	h(ω	X
ejpam-5445	331	3	)	)	PUNCT
ejpam-5445	331	4	(	(	PUNCT
ejpam-5445	331	5	60	60	NUM
ejpam-5445	331	6	)	)	PUNCT
ejpam-5445	331	7	with	with	ADP
ejpam-5445	331	8	respect	respect	NOUN
ejpam-5445	331	9	to	to	ADP
ejpam-5445	331	10	ω	ω	PROPN
ejpam-5445	331	11	∈	∈	PROPN
ejpam-5445	331	12	[	[	X
ejpam-5445	331	13	α	α	X
ejpam-5445	331	14	,	,	PUNCT
ejpam-5445	331	15	β	β	X
ejpam-5445	331	16	]	]	X
ejpam-5445	331	17	,	,	PUNCT
ejpam-5445	331	18	at	at	ADP
ejpam-5445	331	19	the	the	DET
ejpam-5445	331	20	point	point	NOUN
ejpam-5445	331	21	|χ(ω)−	|χ(ω)−	NOUN
ejpam-5445	331	22	ζ(ω)|	ζ(ω)|	NOUN
ejpam-5445	331	23	=	=	SYM
ejpam-5445	331	24	|ζ(β)e−u2(ω−β	|ζ(β)e−u2(ω−β	PROPN
ejpam-5445	331	25	)	)	PUNCT
ejpam-5445	331	26	−	−	PROPN
ejpam-5445	331	27	ζ(ω)−	ζ(ω)−	NOUN
ejpam-5445	331	28	eu2ω	eu2ω	VERB
ejpam-5445	331	29	∫	∫	PROPN
ejpam-5445	331	30	β	β	PROPN
ejpam-5445	331	31	ω	ω	PROPN
ejpam-5445	331	32	h(τ)e−u2τdτ	h(τ)e−u2τdτ	PROPN
ejpam-5445	331	33	|	|	ADV
ejpam-5445	331	34	≤	≤	PROPN
ejpam-5445	331	35	eηω|	eηω|	ADP
ejpam-5445	331	36	∫	∫	PROPN
ejpam-5445	331	37	β	β	PROPN
ejpam-5445	331	38	ω	ω	PROPN
ejpam-5445	332	1	[	[	X
ejpam-5445	332	2	e−u2τζ(τ)]”dτ	e−u2τζ(τ)]”dτ	INTJ
ejpam-5445	332	3	−	−	PROPN
ejpam-5445	332	4	∫	∫	PROPN
ejpam-5445	332	5	β	β	PROPN
ejpam-5445	332	6	ω	ω	PROPN
ejpam-5445	332	7	h(τ)e−u2τdτ	h(τ)e−u2τdτ	PROPN
ejpam-5445	332	8	|	|	ADV
ejpam-5445	332	9	≤∈	≤∈	PROPN
ejpam-5445	332	10	eηω	eηω	NOUN
ejpam-5445	332	11	∫	∫	PROPN
ejpam-5445	332	12	β	β	PROPN
ejpam-5445	332	13	ω	ω	PROPN
ejpam-5445	332	14	e−ητdτ	e−ητdτ	PROPN
ejpam-5445	332	15	|χ(ω)−	|χ(ω)−	NOUN
ejpam-5445	332	16	ζ(ω)|	ζ(ω)|	PROPN
ejpam-5445	332	17	≤	≤	NUM
ejpam-5445	332	18	eηω	eηω	NOUN
ejpam-5445	332	19	∫	∫	PROPN
ejpam-5445	332	20	β	β	PROPN
ejpam-5445	332	21	ω	ω	NUM
ejpam-5445	332	22	e−ητ	e−ητ	PROPN
ejpam-5445	332	23	∈	∈	PROPN
ejpam-5445	332	24	dτ	dτ	NOUN
ejpam-5445	332	25	(	(	PUNCT
ejpam-5445	332	26	61	61	NUM
ejpam-5445	332	27	)	)	PUNCT
ejpam-5445	332	28	with	with	ADP
ejpam-5445	332	29	respect	respect	NOUN
ejpam-5445	332	30	to	to	ADP
ejpam-5445	332	31	ω	ω	PROPN
ejpam-5445	332	32	∈	∈	PROPN
ejpam-5445	332	33	[	[	X
ejpam-5445	332	34	α	α	X
ejpam-5445	332	35	,	,	PUNCT
ejpam-5445	332	36	β	β	X
ejpam-5445	332	37	]	]	X
ejpam-5445	332	38	.	.	PUNCT
ejpam-5445	333	1	if	if	SCONJ
ejpam-5445	333	2	η	η	PROPN
ejpam-5445	333	3	̸=	̸=	PROPN
ejpam-5445	333	4	0	0	NUM
ejpam-5445	333	5	,	,	PUNCT
ejpam-5445	333	6	at	at	ADP
ejpam-5445	333	7	the	the	DET
ejpam-5445	333	8	point	point	NOUN
ejpam-5445	333	9	|χ(ω)−	|χ(ω)−	NOUN
ejpam-5445	333	10	ζ(ω)|	ζ(ω)|	ADV
ejpam-5445	333	11	≤	≤	PROPN
ejpam-5445	333	12	∈	∈	PROPN
ejpam-5445	333	13	η	η	PROPN
ejpam-5445	333	14	(	(	PUNCT
ejpam-5445	333	15	1−	1−	NUM
ejpam-5445	333	16	e−η(β−ω	e−η(β−ω	PROPN
ejpam-5445	333	17	)	)	PUNCT
ejpam-5445	333	18	≤	≤	NOUN
ejpam-5445	333	19	∈	∈	PROPN
ejpam-5445	333	20	η	η	X
ejpam-5445	333	21	(	(	PUNCT
ejpam-5445	333	22	1−	1−	NUM
ejpam-5445	333	23	e−η(β−α	e−η(β−α	NUM
ejpam-5445	333	24	)	)	PUNCT
ejpam-5445	333	25	with	with	ADP
ejpam-5445	333	26	respect	respect	NOUN
ejpam-5445	333	27	to	to	ADP
ejpam-5445	333	28	ω	ω	PROPN
ejpam-5445	333	29	∈	∈	PROPN
ejpam-5445	333	30	[	[	X
ejpam-5445	333	31	α	α	X
ejpam-5445	333	32	,	,	PUNCT
ejpam-5445	333	33	β	β	X
ejpam-5445	333	34	]	]	X
ejpam-5445	333	35	.	.	PUNCT
ejpam-5445	334	1	if	if	SCONJ
ejpam-5445	334	2	η	η	PROPN
ejpam-5445	334	3	=	=	SYM
ejpam-5445	334	4	0	0	PROPN
ejpam-5445	334	5	,	,	PUNCT
ejpam-5445	334	6	then	then	ADV
ejpam-5445	334	7	|χ(ω)−	|χ(ω)−	NOUN
ejpam-5445	334	8	ζ(ω)|	ζ(ω)|	ADV
ejpam-5445	334	9	≤∈	≤∈	PROPN
ejpam-5445	334	10	(	(	PUNCT
ejpam-5445	334	11	β	β	PROPN
ejpam-5445	334	12	−	−	PROPN
ejpam-5445	334	13	ω	ω	NUM
ejpam-5445	334	14	)	)	PUNCT
ejpam-5445	334	15	≤∈	≤∈	PROPN
ejpam-5445	334	16	(	(	PUNCT
ejpam-5445	334	17	β	β	X
ejpam-5445	334	18	−	−	NOUN
ejpam-5445	334	19	α	α	NOUN
ejpam-5445	334	20	)	)	PUNCT
ejpam-5445	334	21	with	with	ADP
ejpam-5445	334	22	respect	respect	NOUN
ejpam-5445	334	23	to	to	ADP
ejpam-5445	334	24	ω	ω	PROPN
ejpam-5445	334	25	∈	∈	PROPN
ejpam-5445	334	26	[	[	X
ejpam-5445	334	27	α	α	X
ejpam-5445	334	28	,	,	PUNCT
ejpam-5445	334	29	β	β	X
ejpam-5445	334	30	]	]	PUNCT
ejpam-5445	334	31	.	.	PUNCT
ejpam-5445	335	1	if	if	SCONJ
ejpam-5445	335	2	follows	follow	VERB
ejpam-5445	335	3	from	from	ADP
ejpam-5445	335	4	50	50	NUM
ejpam-5445	335	5	,	,	PUNCT
ejpam-5445	335	6	thus	thus	ADV
ejpam-5445	335	7	|χ(ω)−	|χ(ω)−	NOUN
ejpam-5445	335	8	ζ(ω)|	ζ(ω)|	ADV
ejpam-5445	335	9	≤	≤	PROPN
ejpam-5445	335	10	θ	θ	PROPN
ejpam-5445	335	11	,	,	PUNCT
ejpam-5445	335	12	where	where	SCONJ
ejpam-5445	335	13	(	(	PUNCT
ejpam-5445	335	14	62	62	NUM
ejpam-5445	335	15	)	)	PUNCT
ejpam-5445	335	16	s.	s.	PROPN
ejpam-5445	335	17	bowmiya	bowmiya	VERB
ejpam-5445	335	18	et	et	PROPN
ejpam-5445	335	19	al	al	PROPN
ejpam-5445	335	20	.	.	PUNCT
ejpam-5445	335	21	/	/	SYM
ejpam-5445	335	22	eur	eur	PROPN
ejpam-5445	335	23	.	.	PUNCT
ejpam-5445	336	1	j.	j.	PROPN
ejpam-5445	336	2	pure	pure	PROPN
ejpam-5445	336	3	appl	appl	PROPN
ejpam-5445	336	4	.	.	PROPN
ejpam-5445	336	5	math	math	PROPN
ejpam-5445	336	6	,	,	PUNCT
ejpam-5445	336	7	17	17	NUM
ejpam-5445	336	8	(	(	PUNCT
ejpam-5445	336	9	4	4	NUM
ejpam-5445	336	10	)	)	PUNCT
ejpam-5445	336	11	(	(	PUNCT
ejpam-5445	336	12	2024	2024	NUM
ejpam-5445	336	13	)	)	PUNCT
ejpam-5445	336	14	,	,	PUNCT
ejpam-5445	336	15	3415	3415	NUM
ejpam-5445	336	16	-	-	SYM
ejpam-5445	336	17	3435	3435	NUM
ejpam-5445	336	18	3431	3431	NUM
ejpam-5445	336	19	θ	θ	PROPN
ejpam-5445	336	20	=	=	SYM
ejpam-5445	336	21			X
ejpam-5445	336	22	(	(	PUNCT
ejpam-5445	336	23	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−σ(β−α))(1−e−η(β−α	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−σ(β−α))(1−e−η(β−α	NUM
ejpam-5445	336	24	)	)	PUNCT
ejpam-5445	336	25	)	)	PUNCT
ejpam-5445	336	26	γρση	γρση	PROPN
ejpam-5445	336	27	∈	∈	PROPN
ejpam-5445	336	28	;	;	PUNCT
ejpam-5445	336	29	if	if	SCONJ
ejpam-5445	336	30	(	(	PUNCT
ejpam-5445	336	31	ρ	ρ	NOUN
ejpam-5445	336	32	,	,	PUNCT
ejpam-5445	336	33	γ	γ	PROPN
ejpam-5445	336	34	,	,	PUNCT
ejpam-5445	336	35	σ	σ	PROPN
ejpam-5445	336	36	,	,	PUNCT
ejpam-5445	336	37	η	η	NOUN
ejpam-5445	336	38	)	)	PUNCT
ejpam-5445	336	39	̸=	̸=	PROPN
ejpam-5445	336	40	0	0	NUM
ejpam-5445	336	41	(	(	PUNCT
ejpam-5445	336	42	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−σ(β−α	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−σ(β−α	NOUN
ejpam-5445	336	43	)	)	PUNCT
ejpam-5445	336	44	)	)	PUNCT
ejpam-5445	336	45	γρσ	γρσ	NOUN
ejpam-5445	336	46	(	(	PUNCT
ejpam-5445	336	47	β	β	NOUN
ejpam-5445	336	48	−	−	NOUN
ejpam-5445	336	49	α	α	X
ejpam-5445	336	50	)	)	PUNCT
ejpam-5445	336	51	∈	∈	PROPN
ejpam-5445	336	52	;	;	PUNCT
ejpam-5445	336	53	if	if	SCONJ
ejpam-5445	336	54	ρ	ρ	PROPN
ejpam-5445	336	55	̸=	̸=	PROPN
ejpam-5445	336	56	γ	γ	PROPN
ejpam-5445	336	57	̸=	̸=	PROPN
ejpam-5445	336	58	σ	σ	PROPN
ejpam-5445	336	59	̸=	̸=	PROPN
ejpam-5445	336	60	0	0	NUM
ejpam-5445	336	61	,	,	PUNCT
ejpam-5445	336	62	η	η	X
ejpam-5445	336	63	=	=	SYM
ejpam-5445	336	64	0	0	NUM
ejpam-5445	336	65	(	(	PUNCT
ejpam-5445	336	66	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−η(β−α	1−e−γ(β−α))(1−e−ρ(β−α))(1−e−η(β−α	NUM
ejpam-5445	336	67	)	)	PUNCT
ejpam-5445	336	68	)	)	PUNCT
ejpam-5445	336	69	γρη	γρη	NOUN
ejpam-5445	336	70	(	(	PUNCT
ejpam-5445	336	71	β	β	NOUN
ejpam-5445	336	72	−	−	NOUN
ejpam-5445	336	73	α	α	X
ejpam-5445	336	74	)	)	PUNCT
ejpam-5445	336	75	∈	∈	PROPN
ejpam-5445	336	76	;	;	PUNCT
ejpam-5445	336	77	if	if	SCONJ
ejpam-5445	336	78	ρ	ρ	PROPN
ejpam-5445	336	79	̸=	̸=	PROPN
ejpam-5445	336	80	γ	γ	PROPN
ejpam-5445	336	81	̸=	̸=	PROPN
ejpam-5445	336	82	η	η	PROPN
ejpam-5445	336	83	̸=	̸=	PROPN
ejpam-5445	336	84	0	0	NUM
ejpam-5445	336	85	,	,	PUNCT
ejpam-5445	336	86	σ	σ	PROPN
ejpam-5445	336	87	=	=	SYM
ejpam-5445	336	88	0	0	NUM
ejpam-5445	336	89	(	(	PUNCT
ejpam-5445	336	90	1−e−γ(β−α))(1−e−η(β−α))(1−e−σ(β−α	1−e−γ(β−α))(1−e−η(β−α))(1−e−σ(β−α	NOUN
ejpam-5445	336	91	)	)	PUNCT
ejpam-5445	336	92	)	)	PUNCT
ejpam-5445	336	93	γησ	γησ	VERB
ejpam-5445	336	94	(	(	PUNCT
ejpam-5445	336	95	β	β	X
ejpam-5445	336	96	−	−	NOUN
ejpam-5445	336	97	α	α	X
ejpam-5445	336	98	)	)	PUNCT
ejpam-5445	336	99	∈	∈	PROPN
ejpam-5445	336	100	;	;	PUNCT
ejpam-5445	336	101	if	if	SCONJ
ejpam-5445	336	102	η	η	PROPN
ejpam-5445	336	103	̸=	̸=	PROPN
ejpam-5445	336	104	γ	γ	PROPN
ejpam-5445	336	105	̸=	̸=	PROPN
ejpam-5445	336	106	σ	σ	PROPN
ejpam-5445	336	107	̸=	̸=	PROPN
ejpam-5445	336	108	0	0	NUM
ejpam-5445	336	109	,	,	PUNCT
ejpam-5445	336	110	ρ	ρ	PROPN
ejpam-5445	336	111	=	=	SYM
ejpam-5445	336	112	0	0	NUM
ejpam-5445	336	113	(	(	PUNCT
ejpam-5445	336	114	1−e−η(β−α))(1−e−ρ(β−α))(1−e−σ(β−α	1−e−η(β−α))(1−e−ρ(β−α))(1−e−σ(β−α	NUM
ejpam-5445	336	115	)	)	PUNCT
ejpam-5445	336	116	)	)	PUNCT
ejpam-5445	336	117	ηρσ	ηρσ	NOUN
ejpam-5445	336	118	(	(	PUNCT
ejpam-5445	336	119	β	β	X
ejpam-5445	336	120	−	−	NOUN
ejpam-5445	336	121	α	α	X
ejpam-5445	336	122	)	)	PUNCT
ejpam-5445	336	123	∈	∈	PROPN
ejpam-5445	336	124	;	;	PUNCT
ejpam-5445	336	125	if	if	SCONJ
ejpam-5445	336	126	ρ	ρ	PROPN
ejpam-5445	336	127	̸=	̸=	PROPN
ejpam-5445	336	128	η	η	PROPN
ejpam-5445	336	129	̸=	̸=	PROPN
ejpam-5445	336	130	σ	σ	PROPN
ejpam-5445	336	131	̸=	̸=	PROPN
ejpam-5445	336	132	0	0	NUM
ejpam-5445	336	133	,	,	PUNCT
ejpam-5445	336	134	γ	γ	X
ejpam-5445	336	135	=	=	SYM
ejpam-5445	336	136	0	0	NUM
ejpam-5445	336	137	(	(	PUNCT
ejpam-5445	336	138	1−e−ρ(β−α))(1−e−σ(β−α	1−e−ρ(β−α))(1−e−σ(β−α	NUM
ejpam-5445	336	139	)	)	PUNCT
ejpam-5445	336	140	)	)	PUNCT
ejpam-5445	336	141	ρσ	ρσ	ADP
ejpam-5445	336	142	(	(	PUNCT
ejpam-5445	336	143	β	β	X
ejpam-5445	336	144	−	−	PROPN
ejpam-5445	336	145	α)2	α)2	NOUN
ejpam-5445	336	146	∈	∈	NOUN
ejpam-5445	336	147	;	;	PUNCT
ejpam-5445	336	148	if	if	SCONJ
ejpam-5445	336	149	ρ	ρ	PROPN
ejpam-5445	336	150	̸=	̸=	PROPN
ejpam-5445	336	151	σ	σ	PROPN
ejpam-5445	336	152	̸=	̸=	PROPN
ejpam-5445	336	153	0	0	NUM
ejpam-5445	336	154	,	,	PUNCT
ejpam-5445	336	155	γ	γ	NOUN
ejpam-5445	336	156	=	=	SYM
ejpam-5445	336	157	η	η	PROPN
ejpam-5445	336	158	=	=	SYM
ejpam-5445	336	159	0	0	NUM
ejpam-5445	336	160	(	(	PUNCT
ejpam-5445	336	161	1−e−ρ(β−α))(1−e−γ(β−α	1−e−ρ(β−α))(1−e−γ(β−α	NOUN
ejpam-5445	336	162	)	)	PUNCT
ejpam-5445	336	163	)	)	PUNCT
ejpam-5445	336	164	ρσ	ρσ	ADP
ejpam-5445	336	165	(	(	PUNCT
ejpam-5445	336	166	β	β	X
ejpam-5445	336	167	−	−	PROPN
ejpam-5445	336	168	α)2	α)2	NOUN
ejpam-5445	336	169	∈	∈	NOUN
ejpam-5445	336	170	;	;	PUNCT
ejpam-5445	337	1	if	if	SCONJ
ejpam-5445	337	2	ρ	ρ	PROPN
ejpam-5445	337	3	̸=	̸=	PROPN
ejpam-5445	337	4	γ	γ	PROPN
ejpam-5445	337	5	̸=	̸=	PROPN
ejpam-5445	337	6	0	0	NUM
ejpam-5445	337	7	,	,	PUNCT
ejpam-5445	337	8	σ	σ	PROPN
ejpam-5445	337	9	=	=	PUNCT
ejpam-5445	337	10	η	η	PROPN
ejpam-5445	337	11	=	=	SYM
ejpam-5445	337	12	0	0	NUM
ejpam-5445	337	13	(	(	PUNCT
ejpam-5445	337	14	1−e−ρ(β−α))(1−e−η(β−α	1−e−ρ(β−α))(1−e−η(β−α	NUM
ejpam-5445	337	15	)	)	PUNCT
ejpam-5445	337	16	)	)	PUNCT
ejpam-5445	337	17	ρη	ρη	NOUN
ejpam-5445	337	18	(	(	PUNCT
ejpam-5445	337	19	β	β	X
ejpam-5445	337	20	−	−	PROPN
ejpam-5445	337	21	α)2	α)2	NOUN
ejpam-5445	337	22	∈	∈	NOUN
ejpam-5445	337	23	;	;	PUNCT
ejpam-5445	337	24	if	if	SCONJ
ejpam-5445	337	25	ρ	ρ	PROPN
ejpam-5445	337	26	̸=	̸=	PROPN
ejpam-5445	337	27	η	η	PROPN
ejpam-5445	337	28	̸=	̸=	PROPN
ejpam-5445	337	29	0	0	NUM
ejpam-5445	337	30	,	,	PUNCT
ejpam-5445	337	31	γ	γ	NOUN
ejpam-5445	337	32	=	=	SYM
ejpam-5445	337	33	σ	σ	PROPN
ejpam-5445	337	34	=	=	SYM
ejpam-5445	337	35	0	0	NUM
ejpam-5445	337	36	(	(	PUNCT
ejpam-5445	337	37	1−e−σ(β−α))(1−e−γ(β−α	1−e−σ(β−α))(1−e−γ(β−α	NOUN
ejpam-5445	337	38	)	)	PUNCT
ejpam-5445	337	39	)	)	PUNCT
ejpam-5445	338	1	σγ	σγ	INTJ
ejpam-5445	338	2	(	(	PUNCT
ejpam-5445	338	3	β	β	X
ejpam-5445	338	4	−	−	PROPN
ejpam-5445	338	5	α)2	α)2	NOUN
ejpam-5445	338	6	∈	∈	NOUN
ejpam-5445	338	7	;	;	PUNCT
ejpam-5445	339	1	if	if	SCONJ
ejpam-5445	339	2	σ	σ	PROPN
ejpam-5445	339	3	̸=	̸=	PROPN
ejpam-5445	339	4	γ	γ	PROPN
ejpam-5445	339	5	̸=	̸=	PROPN
ejpam-5445	339	6	0	0	NUM
ejpam-5445	339	7	,	,	PUNCT
ejpam-5445	339	8	ρ	ρ	PROPN
ejpam-5445	339	9	=	=	SYM
ejpam-5445	339	10	η	η	PROPN
ejpam-5445	339	11	=	=	SYM
ejpam-5445	339	12	0	0	NUM
ejpam-5445	339	13	(	(	PUNCT
ejpam-5445	339	14	1−e−ρ(β−α))(1−e−η(β−α	1−e−ρ(β−α))(1−e−η(β−α	NUM
ejpam-5445	339	15	)	)	PUNCT
ejpam-5445	339	16	)	)	PUNCT
ejpam-5445	339	17	ρη	ρη	NOUN
ejpam-5445	339	18	(	(	PUNCT
ejpam-5445	339	19	β	β	X
ejpam-5445	339	20	−	−	PROPN
ejpam-5445	339	21	α)2	α)2	NOUN
ejpam-5445	339	22	∈	∈	NOUN
ejpam-5445	339	23	;	;	PUNCT
ejpam-5445	339	24	if	if	SCONJ
ejpam-5445	339	25	ρ	ρ	PROPN
ejpam-5445	339	26	̸=	̸=	PROPN
ejpam-5445	339	27	η	η	PROPN
ejpam-5445	339	28	̸=	̸=	PROPN
ejpam-5445	339	29	0	0	NUM
ejpam-5445	339	30	,	,	PUNCT
ejpam-5445	339	31	γ	γ	NOUN
ejpam-5445	339	32	=	=	SYM
ejpam-5445	339	33	σ	σ	PROPN
ejpam-5445	339	34	=	=	SYM
ejpam-5445	339	35	0	0	NUM
ejpam-5445	339	36	(	(	PUNCT
ejpam-5445	339	37	1−e−γ(β−α))(1−e−η(β−α	1−e−γ(β−α))(1−e−η(β−α	NUM
ejpam-5445	339	38	)	)	PUNCT
ejpam-5445	339	39	)	)	PUNCT
ejpam-5445	339	40	γη	γη	NOUN
ejpam-5445	339	41	(	(	PUNCT
ejpam-5445	339	42	β	β	X
ejpam-5445	339	43	−	−	PROPN
ejpam-5445	339	44	α)2	α)2	NOUN
ejpam-5445	339	45	∈	∈	NOUN
ejpam-5445	339	46	;	;	PUNCT
ejpam-5445	339	47	if	if	SCONJ
ejpam-5445	339	48	γ	γ	PROPN
ejpam-5445	339	49	̸=	̸=	PROPN
ejpam-5445	339	50	η	η	PROPN
ejpam-5445	339	51	̸=	̸=	PROPN
ejpam-5445	339	52	0	0	NUM
ejpam-5445	339	53	,	,	PUNCT
ejpam-5445	339	54	ρ	ρ	PROPN
ejpam-5445	339	55	=	=	SYM
ejpam-5445	339	56	σ	σ	PROPN
ejpam-5445	339	57	=	=	SYM
ejpam-5445	339	58	0	0	NUM
ejpam-5445	339	59	(	(	PUNCT
ejpam-5445	339	60	1−e−ρ(β−α	1−e−ρ(β−α	NUM
ejpam-5445	339	61	)	)	PUNCT
ejpam-5445	339	62	)	)	PUNCT
ejpam-5445	339	63	ρ	ρ	PROPN
ejpam-5445	339	64	(	(	PUNCT
ejpam-5445	339	65	β	β	NOUN
ejpam-5445	339	66	−	−	X
ejpam-5445	339	67	α)3	α)3	PROPN
ejpam-5445	339	68	∈	∈	PROPN
ejpam-5445	339	69	;	;	PUNCT
ejpam-5445	339	70	if	if	SCONJ
ejpam-5445	339	71	ρ	ρ	PROPN
ejpam-5445	339	72	̸=	̸=	PROPN
ejpam-5445	339	73	0	0	NUM
ejpam-5445	339	74	,	,	PUNCT
ejpam-5445	339	75	σ	σ	NOUN
ejpam-5445	339	76	=	=	SYM
ejpam-5445	339	77	γ	γ	X
ejpam-5445	339	78	=	=	SYM
ejpam-5445	339	79	η	η	PROPN
ejpam-5445	339	80	=	=	SYM
ejpam-5445	339	81	0	0	NUM
ejpam-5445	339	82	(	(	PUNCT
ejpam-5445	339	83	1−e−γ(β−α	1−e−γ(β−α	NUM
ejpam-5445	339	84	)	)	PUNCT
ejpam-5445	339	85	)	)	PUNCT
ejpam-5445	339	86	γ	γ	PROPN
ejpam-5445	339	87	(	(	PUNCT
ejpam-5445	339	88	β	β	X
ejpam-5445	339	89	−	−	X
ejpam-5445	339	90	α)3	α)3	PROPN
ejpam-5445	339	91	∈	∈	PROPN
ejpam-5445	339	92	;	;	PUNCT
ejpam-5445	339	93	if	if	SCONJ
ejpam-5445	339	94	γ	γ	PRON
ejpam-5445	339	95	̸=	̸=	PROPN
ejpam-5445	339	96	0	0	NUM
ejpam-5445	339	97	,	,	PUNCT
ejpam-5445	339	98	σ	σ	PROPN
ejpam-5445	339	99	=	=	SYM
ejpam-5445	339	100	ρ	ρ	PROPN
ejpam-5445	339	101	=	=	SYM
ejpam-5445	339	102	η	η	PROPN
ejpam-5445	339	103	=	=	SYM
ejpam-5445	339	104	0	0	NUM
ejpam-5445	339	105	(	(	PUNCT
ejpam-5445	339	106	1−e−σ(β−α	1−e−σ(β−α	NUM
ejpam-5445	339	107	)	)	PUNCT
ejpam-5445	339	108	)	)	PUNCT
ejpam-5445	340	1	σ	σ	NOUN
ejpam-5445	341	1	(	(	PUNCT
ejpam-5445	341	2	β	β	X
ejpam-5445	341	3	−	−	X
ejpam-5445	341	4	α)3	α)3	PROPN
ejpam-5445	341	5	∈	∈	PROPN
ejpam-5445	341	6	;	;	PUNCT
ejpam-5445	342	1	if	if	SCONJ
ejpam-5445	342	2	σ	σ	PROPN
ejpam-5445	342	3	̸=	̸=	PROPN
ejpam-5445	342	4	0	0	NUM
ejpam-5445	342	5	,	,	PUNCT
ejpam-5445	342	6	ρ	ρ	PROPN
ejpam-5445	342	7	=	=	SYM
ejpam-5445	342	8	γ	γ	X
ejpam-5445	342	9	=	=	SYM
ejpam-5445	342	10	η	η	PROPN
ejpam-5445	342	11	=	=	SYM
ejpam-5445	342	12	0	0	NUM
ejpam-5445	342	13	(	(	PUNCT
ejpam-5445	342	14	1−e−η(β−α	1−e−η(β−α	NOUN
ejpam-5445	342	15	)	)	PUNCT
ejpam-5445	342	16	)	)	PUNCT
ejpam-5445	342	17	η	η	PROPN
ejpam-5445	342	18	(	(	PUNCT
ejpam-5445	342	19	β	β	X
ejpam-5445	342	20	−	−	X
ejpam-5445	342	21	α)3	α)3	PROPN
ejpam-5445	342	22	∈	∈	PROPN
ejpam-5445	342	23	;	;	PUNCT
ejpam-5445	342	24	if	if	SCONJ
ejpam-5445	342	25	η	η	PROPN
ejpam-5445	342	26	̸=	̸=	PROPN
ejpam-5445	342	27	0	0	NUM
ejpam-5445	342	28	,	,	PUNCT
ejpam-5445	342	29	σ	σ	NOUN
ejpam-5445	342	30	=	=	SYM
ejpam-5445	342	31	γ	γ	X
ejpam-5445	342	32	=	=	SYM
ejpam-5445	342	33	ρ	ρ	PROPN
ejpam-5445	342	34	=	=	SYM
ejpam-5445	342	35	0	0	PUNCT
ejpam-5445	342	36	(	(	PUNCT
ejpam-5445	342	37	β	β	NOUN
ejpam-5445	342	38	−	−	PROPN
ejpam-5445	342	39	α)4	α)4	NOUN
ejpam-5445	342	40	∈	∈	NOUN
ejpam-5445	342	41	;	;	PUNCT
ejpam-5445	342	42	if	if	SCONJ
ejpam-5445	342	43	ρ	ρ	PROPN
ejpam-5445	342	44	=	=	SYM
ejpam-5445	342	45	σ	σ	PROPN
ejpam-5445	342	46	=	=	PUNCT
ejpam-5445	342	47	γ	γ	X
ejpam-5445	342	48	=	=	SYM
ejpam-5445	342	49	η	η	PROPN
ejpam-5445	342	50	=	=	SYM
ejpam-5445	342	51	0	0	NUM
ejpam-5445	342	52	(	(	PUNCT
ejpam-5445	342	53	63	63	NUM
ejpam-5445	342	54	)	)	PUNCT
ejpam-5445	342	55	with	with	ADP
ejpam-5445	342	56	respect	respect	NOUN
ejpam-5445	342	57	to	to	ADP
ejpam-5445	342	58	ω	ω	PROPN
ejpam-5445	342	59	∈	∈	PROPN
ejpam-5445	343	1	[	[	X
ejpam-5445	343	2	α	α	X
ejpam-5445	343	3	,	,	PUNCT
ejpam-5445	343	4	β	β	X
ejpam-5445	343	5	]	]	X
ejpam-5445	343	6	,	,	PUNCT
ejpam-5445	343	7	and	and	CCONJ
ejpam-5445	343	8	α	α	DET
ejpam-5445	343	9	̸=	̸=	PROPN
ejpam-5445	343	10	0	0	NUM
ejpam-5445	343	11	,	,	PUNCT
ejpam-5445	343	12	β	β	X
ejpam-5445	343	13	̸=	̸=	PROPN
ejpam-5445	343	14	0	0	NUM
ejpam-5445	343	15	.	.	PUNCT
ejpam-5445	344	1	3	3	X
ejpam-5445	344	2	.	.	X
ejpam-5445	344	3	examples	example	NOUN
ejpam-5445	344	4	finally	finally	ADV
ejpam-5445	344	5	,	,	PUNCT
ejpam-5445	344	6	we	we	PRON
ejpam-5445	344	7	give	give	VERB
ejpam-5445	344	8	some	some	DET
ejpam-5445	344	9	examples	example	NOUN
ejpam-5445	344	10	to	to	PART
ejpam-5445	344	11	illustrate	illustrate	VERB
ejpam-5445	344	12	the	the	DET
ejpam-5445	344	13	results	result	NOUN
ejpam-5445	344	14	in	in	ADP
ejpam-5445	344	15	this	this	DET
ejpam-5445	344	16	paper	paper	NOUN
ejpam-5445	344	17	.	.	PUNCT
ejpam-5445	345	1	example	example	NOUN
ejpam-5445	346	1	1	1	NUM
ejpam-5445	346	2	.	.	X
ejpam-5445	346	3	consider	consider	VERB
ejpam-5445	346	4	the	the	DET
ejpam-5445	346	5	following	follow	VERB
ejpam-5445	346	6	differential	differential	ADJ
ejpam-5445	346	7	equation	equation	NOUN
ejpam-5445	346	8	of	of	ADP
ejpam-5445	346	9	the	the	DET
ejpam-5445	346	10	form	form	NOUN
ejpam-5445	346	11	σiv(ω	σiv(ω	PROPN
ejpam-5445	346	12	)	)	PUNCT
ejpam-5445	346	13	+	+	NUM
ejpam-5445	346	14	2σ′′′(ω	2σ′′′(ω	NUM
ejpam-5445	346	15	)	)	PUNCT
ejpam-5445	346	16	+	+	CCONJ
ejpam-5445	346	17	σ′′(ω	σ′′(ω	NOUN
ejpam-5445	346	18	)	)	PUNCT
ejpam-5445	346	19	=	=	PUNCT
ejpam-5445	346	20	χ(ω);ω	χ(ω);ω	PROPN
ejpam-5445	346	21	∈	∈	PROPN
ejpam-5445	347	1	[	[	X
ejpam-5445	347	2	2	2	NUM
ejpam-5445	347	3	,	,	PUNCT
ejpam-5445	347	4	3	3	NUM
ejpam-5445	347	5	]	]	PUNCT
ejpam-5445	347	6	.	.	PUNCT
ejpam-5445	348	1	set	set	PROPN
ejpam-5445	348	2	∈	∈	PROPN
ejpam-5445	348	3	>	>	X
ejpam-5445	348	4	0	0	NUM
ejpam-5445	348	5	,	,	PUNCT
ejpam-5445	348	6	at	at	ADP
ejpam-5445	348	7	the	the	DET
ejpam-5445	348	8	point	point	NOUN
ejpam-5445	348	9	|σiv(ω	|σiv(ω	PROPN
ejpam-5445	348	10	)	)	PUNCT
ejpam-5445	349	1	+	+	CCONJ
ejpam-5445	349	2	2σ′′′(ω	2σ′′′(ω	NUM
ejpam-5445	349	3	)	)	PUNCT
ejpam-5445	350	1	+	+	CCONJ
ejpam-5445	350	2	σ′′(ω)−	σ′′(ω)−	ADP
ejpam-5445	350	3	χ(ω)|	χ(ω)|	PRON
ejpam-5445	350	4	≤∈	≤∈	NOUN
ejpam-5445	350	5	.	.	PUNCT
ejpam-5445	351	1	with	with	ADP
ejpam-5445	351	2	respect	respect	NOUN
ejpam-5445	351	3	to	to	ADP
ejpam-5445	351	4	ω	ω	PRON
ejpam-5445	351	5	∈	∈	PROPN
ejpam-5445	352	1	[	[	X
ejpam-5445	352	2	2	2	NUM
ejpam-5445	352	3	,	,	PUNCT
ejpam-5445	352	4	3	3	NUM
ejpam-5445	352	5	]	]	PUNCT
ejpam-5445	352	6	.	.	PUNCT
ejpam-5445	353	1	let	let	VERB
ejpam-5445	353	2	λ	λ	X
ejpam-5445	353	3	=	=	SYM
ejpam-5445	353	4	1	1	NUM
ejpam-5445	353	5	,	,	PUNCT
ejpam-5445	353	6	then	then	ADV
ejpam-5445	353	7	g(ω	g(ω	PROPN
ejpam-5445	353	8	)	)	PUNCT
ejpam-5445	354	1	=	=	SYM
ejpam-5445	354	2	σ′′′(ω	σ′′′(ω	PROPN
ejpam-5445	354	3	)	)	PUNCT
ejpam-5445	355	1	+	+	NUM
ejpam-5445	355	2	3σ′′(ω	3σ′′(ω	NUM
ejpam-5445	355	3	)	)	PUNCT
ejpam-5445	356	1	+	+	NUM
ejpam-5445	356	2	4σ′(ω	4σ′(ω	NUM
ejpam-5445	356	3	)	)	PUNCT
ejpam-5445	357	1	+	+	CCONJ
ejpam-5445	357	2	4σ(ω	4σ(ω	NUM
ejpam-5445	357	3	)	)	PUNCT
ejpam-5445	357	4	and	and	CCONJ
ejpam-5445	357	5	g′(ω	g′(ω	PROPN
ejpam-5445	358	1	)	)	PUNCT
ejpam-5445	358	2	=	=	SYM
ejpam-5445	358	3	σiv(ω	σiv(ω	PROPN
ejpam-5445	358	4	)	)	PUNCT
ejpam-5445	358	5	+	+	NUM
ejpam-5445	358	6	3σ′′′(ω	3σ′′′(ω	NUM
ejpam-5445	358	7	)	)	PUNCT
ejpam-5445	358	8	+	+	NOUN
ejpam-5445	358	9	4σ′′(ω	4σ′′(ω	NUM
ejpam-5445	358	10	)	)	PUNCT
ejpam-5445	358	11	+	+	NUM
ejpam-5445	358	12	4σ′(ω	4σ′(ω	NUM
ejpam-5445	358	13	)	)	PUNCT
ejpam-5445	359	1	+	+	CCONJ
ejpam-5445	359	2	4σ(ω	4σ(ω	NUM
ejpam-5445	359	3	)	)	PUNCT
ejpam-5445	359	4	with	with	ADP
ejpam-5445	359	5	respect	respect	NOUN
ejpam-5445	359	6	to	to	ADP
ejpam-5445	359	7	ω	ω	PRON
ejpam-5445	359	8	∈	∈	PROPN
ejpam-5445	360	1	[	[	X
ejpam-5445	360	2	2	2	NUM
ejpam-5445	360	3	,	,	PUNCT
ejpam-5445	360	4	3	3	NUM
ejpam-5445	360	5	]	]	PUNCT
ejpam-5445	360	6	.	.	PUNCT
ejpam-5445	361	1	thus	thus	ADV
ejpam-5445	361	2	the	the	DET
ejpam-5445	361	3	condition	condition	NOUN
ejpam-5445	361	4	25	25	NUM
ejpam-5445	361	5	,	,	PUNCT
ejpam-5445	361	6	27	27	NUM
ejpam-5445	361	7	and	and	CCONJ
ejpam-5445	361	8	39	39	NUM
ejpam-5445	361	9	of	of	ADP
ejpam-5445	361	10	theorem	theorem	ADJ
ejpam-5445	361	11	3	3	NUM
ejpam-5445	361	12	are	be	AUX
ejpam-5445	361	13	satisfied	satisfied	ADJ
ejpam-5445	361	14	.	.	PUNCT
ejpam-5445	362	1	hence	hence	ADV
ejpam-5445	362	2	there	there	PRON
ejpam-5445	362	3	is	be	VERB
ejpam-5445	362	4	a	a	DET
ejpam-5445	362	5	function	function	NOUN
ejpam-5445	362	6	ω	ω	PROPN
ejpam-5445	362	7	∈	∈	PROPN
ejpam-5445	362	8	c4[2	c4[2	PROPN
ejpam-5445	362	9	,	,	PUNCT
ejpam-5445	362	10	3	3	NUM
ejpam-5445	362	11	]	]	PUNCT
ejpam-5445	362	12	which	which	PRON
ejpam-5445	362	13	is	be	AUX
ejpam-5445	362	14	a	a	DET
ejpam-5445	362	15	mild	mild	ADJ
ejpam-5445	362	16	solution	solution	NOUN
ejpam-5445	362	17	of	of	ADP
ejpam-5445	362	18	uiv(ω)+2u′′′(ω)+u′′(ω	uiv(ω)+2u′′′(ω)+u′′(ω	PROPN
ejpam-5445	362	19	)	)	PUNCT
ejpam-5445	362	20	=	=	SYM
ejpam-5445	362	21	χ(ω	χ(ω	NOUN
ejpam-5445	362	22	)	)	PUNCT
ejpam-5445	362	23	is	be	AUX
ejpam-5445	362	24	satisfied	satisfy	VERB
ejpam-5445	362	25	by	by	ADP
ejpam-5445	362	26	63	63	NUM
ejpam-5445	362	27	.	.	PUNCT
ejpam-5445	363	1	s.	s.	PROPN
ejpam-5445	363	2	bowmiya	bowmiya	PROPN
ejpam-5445	363	3	et	et	PROPN
ejpam-5445	363	4	al	al	PROPN
ejpam-5445	363	5	.	.	PUNCT
ejpam-5445	363	6	/	/	SYM
ejpam-5445	363	7	eur	eur	PROPN
ejpam-5445	363	8	.	.	PUNCT
ejpam-5445	364	1	j.	j.	PROPN
ejpam-5445	364	2	pure	pure	PROPN
ejpam-5445	364	3	appl	appl	PROPN
ejpam-5445	364	4	.	.	PROPN
ejpam-5445	364	5	math	math	PROPN
ejpam-5445	364	6	,	,	PUNCT
ejpam-5445	364	7	17	17	NUM
ejpam-5445	364	8	(	(	PUNCT
ejpam-5445	364	9	4	4	NUM
ejpam-5445	364	10	)	)	PUNCT
ejpam-5445	364	11	(	(	PUNCT
ejpam-5445	364	12	2024	2024	NUM
ejpam-5445	364	13	)	)	PUNCT
ejpam-5445	364	14	,	,	PUNCT
ejpam-5445	364	15	3415	3415	NUM
ejpam-5445	364	16	-	-	SYM
ejpam-5445	364	17	3435	3435	NUM
ejpam-5445	364	18	3432	3432	NUM
ejpam-5445	364	19	figure	figure	NOUN
ejpam-5445	364	20	1	1	NUM
ejpam-5445	364	21	:	:	PUNCT
ejpam-5445	364	22	graph	graph	NOUN
ejpam-5445	364	23	solution	solution	NOUN
ejpam-5445	364	24	χ(ω	χ(ω	NOUN
ejpam-5445	364	25	)	)	PUNCT
ejpam-5445	364	26	and	and	CCONJ
ejpam-5445	364	27	ζ(ω	ζ(ω	PROPN
ejpam-5445	364	28	)	)	PUNCT
ejpam-5445	364	29	for	for	ADP
ejpam-5445	364	30	equation	equation	NOUN
ejpam-5445	364	31	63	63	NUM
ejpam-5445	364	32	example	example	NOUN
ejpam-5445	364	33	2	2	NUM
ejpam-5445	364	34	.	.	X
ejpam-5445	364	35	consider	consider	VERB
ejpam-5445	364	36	the	the	DET
ejpam-5445	364	37	accompanying	accompanying	ADJ
ejpam-5445	364	38	differential	differential	ADJ
ejpam-5445	364	39	equation	equation	NOUN
ejpam-5445	364	40	σiv(ω	σiv(ω	PROPN
ejpam-5445	364	41	)	)	PUNCT
ejpam-5445	365	1	+	+	CCONJ
ejpam-5445	365	2	σ′′′(ω	σ′′′(ω	PROPN
ejpam-5445	365	3	)	)	PUNCT
ejpam-5445	366	1	+	+	SYM
ejpam-5445	366	2	σ′′(ω	σ′′(ω	NOUN
ejpam-5445	366	3	)	)	PUNCT
ejpam-5445	366	4	=	=	PUNCT
ejpam-5445	366	5	χ(ω);ω	χ(ω);ω	PROPN
ejpam-5445	366	6	∈	∈	PROPN
ejpam-5445	367	1	[	[	X
ejpam-5445	367	2	3	3	NUM
ejpam-5445	367	3	,	,	PUNCT
ejpam-5445	367	4	2	2	NUM
ejpam-5445	367	5	]	]	PUNCT
ejpam-5445	367	6	.	.	PUNCT
ejpam-5445	368	1	let	let	VERB
ejpam-5445	368	2	∈	∈	PRON
ejpam-5445	368	3	>	>	X
ejpam-5445	368	4	0	0	PROPN
ejpam-5445	368	5	,	,	PUNCT
ejpam-5445	368	6	and	and	CCONJ
ejpam-5445	368	7	γ	γ	PROPN
ejpam-5445	368	8	∈	∈	PROPN
ejpam-5445	368	9	[	[	X
ejpam-5445	368	10	3	3	NUM
ejpam-5445	368	11	,	,	PUNCT
ejpam-5445	368	12	2	2	NUM
ejpam-5445	368	13	]	]	PUNCT
ejpam-5445	368	14	.	.	PUNCT
ejpam-5445	369	1	such	such	ADJ
ejpam-5445	369	2	that	that	DET
ejpam-5445	369	3	|σiv(ω	|σiv(ω	NOUN
ejpam-5445	369	4	)	)	PUNCT
ejpam-5445	370	1	+	+	CCONJ
ejpam-5445	370	2	σ′′′(ω	σ′′′(ω	PROPN
ejpam-5445	370	3	)	)	PUNCT
ejpam-5445	371	1	+	+	CCONJ
ejpam-5445	371	2	σ′′(ω)−	σ′′(ω)−	ADP
ejpam-5445	371	3	χ(ω)|	χ(ω)|	PRON
ejpam-5445	371	4	≤∈	≤∈	NOUN
ejpam-5445	371	5	.	.	PUNCT
ejpam-5445	372	1	with	with	ADP
ejpam-5445	372	2	respect	respect	NOUN
ejpam-5445	372	3	to	to	ADP
ejpam-5445	372	4	ω	ω	PRON
ejpam-5445	372	5	∈	∈	PROPN
ejpam-5445	373	1	[	[	X
ejpam-5445	373	2	3	3	NUM
ejpam-5445	373	3	,	,	PUNCT
ejpam-5445	373	4	2	2	NUM
ejpam-5445	373	5	]	]	PUNCT
ejpam-5445	373	6	.	.	PUNCT
ejpam-5445	374	1	we	we	PRON
ejpam-5445	374	2	take	take	VERB
ejpam-5445	374	3	g(ω	g(ω	NOUN
ejpam-5445	374	4	)	)	PUNCT
ejpam-5445	374	5	=	=	SYM
ejpam-5445	374	6	σ′′′(ω	σ′′′(ω	PROPN
ejpam-5445	374	7	)	)	PUNCT
ejpam-5445	374	8	+	+	CCONJ
ejpam-5445	374	9	2σ′′(ω	2σ′′(ω	X
ejpam-5445	374	10	)	)	PUNCT
ejpam-5445	375	1	+	+	NUM
ejpam-5445	375	2	3σ′(ω	3σ′(ω	NUM
ejpam-5445	375	3	)	)	PUNCT
ejpam-5445	376	1	+	+	NUM
ejpam-5445	376	2	3σ(ω	3σ(ω	NUM
ejpam-5445	376	3	)	)	PUNCT
ejpam-5445	377	1	with	with	ADP
ejpam-5445	377	2	respect	respect	NOUN
ejpam-5445	377	3	to	to	ADP
ejpam-5445	377	4	ω	ω	PROPN
ejpam-5445	377	5	∈	∈	PROPN
ejpam-5445	378	1	[	[	X
ejpam-5445	378	2	3	3	NUM
ejpam-5445	378	3	,	,	PUNCT
ejpam-5445	378	4	2	2	NUM
ejpam-5445	378	5	]	]	PUNCT
ejpam-5445	378	6	.	.	PUNCT
ejpam-5445	379	1	then	then	ADV
ejpam-5445	379	2	g′(ω	g′(ω	PUNCT
ejpam-5445	379	3	)	)	PUNCT
ejpam-5445	379	4	=	=	SYM
ejpam-5445	379	5	σiv(ω	σiv(ω	PROPN
ejpam-5445	379	6	)	)	PUNCT
ejpam-5445	379	7	+	+	NUM
ejpam-5445	379	8	2σ′′′(ω	2σ′′′(ω	NUM
ejpam-5445	379	9	)	)	PUNCT
ejpam-5445	379	10	+	+	NUM
ejpam-5445	379	11	3σ′′(ω	3σ′′(ω	NUM
ejpam-5445	379	12	)	)	PUNCT
ejpam-5445	380	1	+	+	NUM
ejpam-5445	381	1	3σ′(ω	3σ′(ω	NUM
ejpam-5445	381	2	)	)	PUNCT
ejpam-5445	382	1	+	+	NUM
ejpam-5445	382	2	3σ(ω	3σ(ω	NUM
ejpam-5445	382	3	)	)	PUNCT
ejpam-5445	383	1	with	with	ADP
ejpam-5445	383	2	respect	respect	NOUN
ejpam-5445	383	3	to	to	ADP
ejpam-5445	383	4	ω	ω	PROPN
ejpam-5445	383	5	∈	∈	PROPN
ejpam-5445	384	1	[	[	X
ejpam-5445	384	2	3	3	NUM
ejpam-5445	384	3	,	,	PUNCT
ejpam-5445	384	4	2	2	NUM
ejpam-5445	384	5	]	]	PUNCT
ejpam-5445	384	6	.	.	PUNCT
ejpam-5445	385	1	at	at	ADP
ejpam-5445	385	2	the	the	DET
ejpam-5445	385	3	point	point	NOUN
ejpam-5445	385	4	|g′(ω)−	|g′(ω)−	NOUN
ejpam-5445	385	5	g(ω)−	g(ω)−	NOUN
ejpam-5445	385	6	χ(ω)|	χ(ω)|	NOUN
ejpam-5445	385	7	=	=	SYM
ejpam-5445	385	8	|σiv(ω	|σiv(ω	NOUN
ejpam-5445	385	9	)	)	PUNCT
ejpam-5445	386	1	+	+	CCONJ
ejpam-5445	386	2	σ′′′(ω	σ′′′(ω	PROPN
ejpam-5445	386	3	)	)	PUNCT
ejpam-5445	387	1	+	+	CCONJ
ejpam-5445	387	2	σ′′(ω)−	σ′′(ω)−	ADP
ejpam-5445	387	3	χ(ω)|	χ(ω)|	PRON
ejpam-5445	387	4	≤∈	≤∈	NOUN
ejpam-5445	387	5	with	with	ADP
ejpam-5445	387	6	respect	respect	NOUN
ejpam-5445	387	7	to	to	ADP
ejpam-5445	387	8	ω	ω	PROPN
ejpam-5445	387	9	∈	∈	PROPN
ejpam-5445	387	10	[	[	X
ejpam-5445	387	11	α	α	X
ejpam-5445	387	12	,	,	PUNCT
ejpam-5445	387	13	β	β	X
ejpam-5445	387	14	]	]	PUNCT
ejpam-5445	387	15	.	.	PUNCT
ejpam-5445	388	1	thus	thus	ADV
ejpam-5445	388	2	the	the	DET
ejpam-5445	388	3	conditions	condition	NOUN
ejpam-5445	388	4	25	25	NUM
ejpam-5445	388	5	,	,	PUNCT
ejpam-5445	388	6	27	27	NUM
ejpam-5445	388	7	and	and	CCONJ
ejpam-5445	388	8	39	39	NUM
ejpam-5445	388	9	of	of	ADP
ejpam-5445	388	10	theorem	theorem	ADJ
ejpam-5445	388	11	3	3	NUM
ejpam-5445	388	12	are	be	AUX
ejpam-5445	388	13	satisfied	satisfied	ADJ
ejpam-5445	388	14	.	.	PUNCT
ejpam-5445	389	1	subsequently	subsequently	ADV
ejpam-5445	389	2	there	there	PRON
ejpam-5445	389	3	is	be	VERB
ejpam-5445	389	4	a	a	DET
ejpam-5445	389	5	function	function	NOUN
ejpam-5445	389	6	ω	ω	PROPN
ejpam-5445	389	7	∈	∈	PROPN
ejpam-5445	389	8	c4[3	c4[3	NOUN
ejpam-5445	389	9	,	,	PUNCT
ejpam-5445	389	10	2	2	NUM
ejpam-5445	389	11	]	]	PUNCT
ejpam-5445	389	12	which	which	PRON
ejpam-5445	389	13	is	be	AUX
ejpam-5445	389	14	a	a	DET
ejpam-5445	389	15	mellow	mellow	ADJ
ejpam-5445	389	16	solution	solution	NOUN
ejpam-5445	389	17	of	of	ADP
ejpam-5445	389	18	uiv(ω)+u′′′(ω)+	uiv(ω)+u′′′(ω)+	PROPN
ejpam-5445	389	19	u′′(ω	u′′(ω	NOUN
ejpam-5445	389	20	)	)	PUNCT
ejpam-5445	389	21	=	=	SYM
ejpam-5445	389	22	χ(ω	χ(ω	NOUN
ejpam-5445	389	23	)	)	PUNCT
ejpam-5445	389	24	is	be	AUX
ejpam-5445	389	25	satisfied	satisfy	VERB
ejpam-5445	389	26	by	by	ADP
ejpam-5445	389	27	63	63	NUM
ejpam-5445	389	28	.	.	PUNCT
ejpam-5445	390	1	4	4	NUM
ejpam-5445	390	2	.	.	X
ejpam-5445	390	3	conclusion	conclusion	NOUN
ejpam-5445	390	4	in	in	ADP
ejpam-5445	390	5	this	this	DET
ejpam-5445	390	6	study	study	NOUN
ejpam-5445	390	7	,	,	PUNCT
ejpam-5445	390	8	we	we	PRON
ejpam-5445	390	9	have	have	AUX
ejpam-5445	390	10	successfully	successfully	ADV
ejpam-5445	390	11	demonstrated	demonstrate	VERB
ejpam-5445	390	12	the	the	DET
ejpam-5445	390	13	hyers	hyers	PROPN
ejpam-5445	390	14	-	-	PUNCT
ejpam-5445	390	15	ulam	ulam	ADJ
ejpam-5445	390	16	stability	stability	NOUN
ejpam-5445	390	17	of	of	ADP
ejpam-5445	390	18	fourthorder	fourthorder	PROPN
ejpam-5445	390	19	linear	linear	PROPN
ejpam-5445	390	20	differential	differential	NOUN
ejpam-5445	390	21	equations	equation	NOUN
ejpam-5445	390	22	.	.	PUNCT
ejpam-5445	391	1	by	by	ADP
ejpam-5445	391	2	employing	employ	VERB
ejpam-5445	391	3	fixed	fix	VERB
ejpam-5445	391	4	-	-	PUNCT
ejpam-5445	391	5	point	point	NOUN
ejpam-5445	391	6	theory	theory	NOUN
ejpam-5445	391	7	and	and	CCONJ
ejpam-5445	391	8	various	various	ADJ
ejpam-5445	391	9	norms	norm	NOUN
ejpam-5445	391	10	,	,	PUNCT
ejpam-5445	391	11	s.	s.	PROPN
ejpam-5445	391	12	bowmiya	bowmiya	PROPN
ejpam-5445	391	13	et	et	PROPN
ejpam-5445	391	14	al	al	PROPN
ejpam-5445	391	15	.	.	PUNCT
ejpam-5445	391	16	/	/	SYM
ejpam-5445	391	17	eur	eur	PROPN
ejpam-5445	391	18	.	.	PUNCT
ejpam-5445	392	1	j.	j.	PROPN
ejpam-5445	392	2	pure	pure	PROPN
ejpam-5445	392	3	appl	appl	PROPN
ejpam-5445	392	4	.	.	PROPN
ejpam-5445	392	5	math	math	PROPN
ejpam-5445	392	6	,	,	PUNCT
ejpam-5445	392	7	17	17	NUM
ejpam-5445	392	8	(	(	PUNCT
ejpam-5445	392	9	4	4	NUM
ejpam-5445	392	10	)	)	PUNCT
ejpam-5445	392	11	(	(	PUNCT
ejpam-5445	392	12	2024	2024	NUM
ejpam-5445	392	13	)	)	PUNCT
ejpam-5445	392	14	,	,	PUNCT
ejpam-5445	392	15	3415	3415	NUM
ejpam-5445	392	16	-	-	SYM
ejpam-5445	392	17	3435	3435	NUM
ejpam-5445	392	18	3433	3433	NUM
ejpam-5445	392	19	figure	figure	NOUN
ejpam-5445	392	20	2	2	NUM
ejpam-5445	392	21	:	:	PUNCT
ejpam-5445	392	22	plots	plot	NOUN
ejpam-5445	392	23	of	of	ADP
ejpam-5445	392	24	solution	solution	NOUN
ejpam-5445	392	25	χ(ω	χ(ω	NOUN
ejpam-5445	392	26	)	)	PUNCT
ejpam-5445	392	27	and	and	CCONJ
ejpam-5445	392	28	ζ(ω	ζ(ω	PROPN
ejpam-5445	392	29	)	)	PUNCT
ejpam-5445	392	30	for	for	ADP
ejpam-5445	392	31	equation	equation	NOUN
ejpam-5445	392	32	63	63	NUM
ejpam-5445	392	33	we	we	PRON
ejpam-5445	392	34	derived	derive	VERB
ejpam-5445	392	35	sufficient	sufficient	ADJ
ejpam-5445	392	36	conditions	condition	NOUN
ejpam-5445	392	37	that	that	PRON
ejpam-5445	392	38	guarantee	guarantee	VERB
ejpam-5445	392	39	the	the	DET
ejpam-5445	392	40	stability	stability	NOUN
ejpam-5445	392	41	of	of	ADP
ejpam-5445	392	42	solutions	solution	NOUN
ejpam-5445	392	43	to	to	ADP
ejpam-5445	392	44	these	these	DET
ejpam-5445	392	45	higherorder	higherorder	NOUN
ejpam-5445	392	46	equations	equation	NOUN
ejpam-5445	392	47	under	under	ADP
ejpam-5445	392	48	small	small	ADJ
ejpam-5445	392	49	perturbations	perturbation	NOUN
ejpam-5445	392	50	.	.	PUNCT
ejpam-5445	393	1	our	our	PRON
ejpam-5445	393	2	results	result	NOUN
ejpam-5445	393	3	show	show	VERB
ejpam-5445	393	4	that	that	SCONJ
ejpam-5445	393	5	for	for	ADP
ejpam-5445	393	6	a	a	DET
ejpam-5445	393	7	wide	wide	ADJ
ejpam-5445	393	8	class	class	NOUN
ejpam-5445	393	9	of	of	ADP
ejpam-5445	393	10	fourth	fourth	ADJ
ejpam-5445	393	11	-	-	PUNCT
ejpam-5445	393	12	order	order	NOUN
ejpam-5445	393	13	linear	linear	PROPN
ejpam-5445	393	14	differential	differential	NOUN
ejpam-5445	393	15	equations	equation	NOUN
ejpam-5445	393	16	,	,	PUNCT
ejpam-5445	393	17	if	if	SCONJ
ejpam-5445	393	18	an	an	DET
ejpam-5445	393	19	approximate	approximate	ADJ
ejpam-5445	393	20	solution	solution	NOUN
ejpam-5445	393	21	exists	exist	VERB
ejpam-5445	393	22	,	,	PUNCT
ejpam-5445	393	23	there	there	PRON
ejpam-5445	393	24	is	be	VERB
ejpam-5445	393	25	a	a	DET
ejpam-5445	393	26	corresponding	corresponding	ADJ
ejpam-5445	393	27	exact	exact	ADJ
ejpam-5445	393	28	solution	solution	NOUN
ejpam-5445	393	29	that	that	PRON
ejpam-5445	393	30	is	be	AUX
ejpam-5445	393	31	close	close	ADJ
ejpam-5445	393	32	to	to	ADP
ejpam-5445	393	33	the	the	DET
ejpam-5445	393	34	approximate	approximate	ADJ
ejpam-5445	393	35	one	one	NOUN
ejpam-5445	393	36	,	,	PUNCT
ejpam-5445	393	37	thereby	thereby	ADV
ejpam-5445	393	38	confirming	confirm	VERB
ejpam-5445	393	39	the	the	DET
ejpam-5445	393	40	equation	equation	NOUN
ejpam-5445	393	41	’s	’s	PART
ejpam-5445	393	42	stability	stability	NOUN
ejpam-5445	393	43	in	in	ADP
ejpam-5445	393	44	the	the	DET
ejpam-5445	393	45	hyers	hyers	PROPN
ejpam-5445	393	46	-	-	PUNCT
ejpam-5445	393	47	ulam	ulam	PROPN
ejpam-5445	393	48	sense	sense	NOUN
ejpam-5445	393	49	.	.	PUNCT
ejpam-5445	394	1	the	the	DET
ejpam-5445	394	2	extension	extension	NOUN
ejpam-5445	394	3	of	of	ADP
ejpam-5445	394	4	hyers	hyer	NOUN
ejpam-5445	394	5	-	-	PUNCT
ejpam-5445	394	6	ulam	ulam	PROPN
ejpam-5445	394	7	stability	stability	NOUN
ejpam-5445	394	8	to	to	ADP
ejpam-5445	394	9	fourth	fourth	ADJ
ejpam-5445	394	10	-	-	PUNCT
ejpam-5445	394	11	order	order	NOUN
ejpam-5445	394	12	equations	equation	NOUN
ejpam-5445	394	13	enriches	enrich	VERB
ejpam-5445	394	14	the	the	DET
ejpam-5445	394	15	understanding	understanding	NOUN
ejpam-5445	394	16	of	of	ADP
ejpam-5445	394	17	the	the	DET
ejpam-5445	394	18	robustness	robustness	NOUN
ejpam-5445	394	19	of	of	ADP
ejpam-5445	394	20	solutions	solution	NOUN
ejpam-5445	394	21	in	in	ADP
ejpam-5445	394	22	more	more	ADJ
ejpam-5445	394	23	complex	complex	ADJ
ejpam-5445	394	24	systems	system	NOUN
ejpam-5445	394	25	,	,	PUNCT
ejpam-5445	394	26	which	which	PRON
ejpam-5445	394	27	is	be	AUX
ejpam-5445	394	28	crucial	crucial	ADJ
ejpam-5445	394	29	in	in	ADP
ejpam-5445	394	30	theoretical	theoretical	ADJ
ejpam-5445	394	31	research	research	NOUN
ejpam-5445	394	32	as	as	ADV
ejpam-5445	394	33	well	well	ADV
ejpam-5445	394	34	as	as	ADP
ejpam-5445	394	35	in	in	ADP
ejpam-5445	394	36	practical	practical	ADJ
ejpam-5445	394	37	applications	application	NOUN
ejpam-5445	394	38	in	in	ADP
ejpam-5445	394	39	areas	area	NOUN
ejpam-5445	394	40	such	such	ADJ
ejpam-5445	394	41	as	as	ADP
ejpam-5445	394	42	engineering	engineering	NOUN
ejpam-5445	394	43	,	,	PUNCT
ejpam-5445	394	44	physics	physics	NOUN
ejpam-5445	394	45	,	,	PUNCT
ejpam-5445	394	46	and	and	CCONJ
ejpam-5445	394	47	applied	apply	VERB
ejpam-5445	394	48	mathematics	mathematic	NOUN
ejpam-5445	394	49	.	.	PUNCT
ejpam-5445	395	1	the	the	DET
ejpam-5445	395	2	examples	example	NOUN
ejpam-5445	395	3	provided	provide	VERB
ejpam-5445	395	4	highlight	highlight	VERB
ejpam-5445	395	5	the	the	DET
ejpam-5445	395	6	practical	practical	ADJ
ejpam-5445	395	7	relevance	relevance	NOUN
ejpam-5445	395	8	of	of	ADP
ejpam-5445	395	9	these	these	DET
ejpam-5445	395	10	theoretical	theoretical	ADJ
ejpam-5445	395	11	findings	finding	NOUN
ejpam-5445	395	12	,	,	PUNCT
ejpam-5445	395	13	showcasing	showcase	VERB
ejpam-5445	395	14	the	the	DET
ejpam-5445	395	15	broad	broad	ADJ
ejpam-5445	395	16	applicability	applicability	NOUN
ejpam-5445	395	17	of	of	ADP
ejpam-5445	395	18	hyers	hyers	PROPN
ejpam-5445	395	19	-	-	PUNCT
ejpam-5445	395	20	ulam	ulam	PROPN
ejpam-5445	395	21	stability	stability	NOUN
ejpam-5445	395	22	in	in	ADP
ejpam-5445	395	23	various	various	ADJ
ejpam-5445	395	24	contexts	contexts	NOUN
ejpam-5445	395	25	.	.	PUNCT
ejpam-5445	396	1	future	future	ADJ
ejpam-5445	396	2	research	research	NOUN
ejpam-5445	396	3	can	can	AUX
ejpam-5445	396	4	focus	focus	VERB
ejpam-5445	396	5	on	on	ADP
ejpam-5445	396	6	extending	extend	VERB
ejpam-5445	396	7	these	these	DET
ejpam-5445	396	8	results	result	NOUN
ejpam-5445	396	9	to	to	ADP
ejpam-5445	396	10	nonlinear	nonlinear	ADJ
ejpam-5445	396	11	or	or	CCONJ
ejpam-5445	396	12	variable	variable	ADJ
ejpam-5445	396	13	-	-	PUNCT
ejpam-5445	396	14	coefficient	coefficient	NOUN
ejpam-5445	396	15	systems	system	NOUN
ejpam-5445	396	16	,	,	PUNCT
ejpam-5445	396	17	as	as	ADV
ejpam-5445	396	18	well	well	ADV
ejpam-5445	396	19	as	as	ADP
ejpam-5445	396	20	exploring	explore	VERB
ejpam-5445	396	21	applications	application	NOUN
ejpam-5445	396	22	in	in	ADP
ejpam-5445	396	23	more	more	ADJ
ejpam-5445	396	24	specialized	specialized	ADJ
ejpam-5445	396	25	fields	field	NOUN
ejpam-5445	396	26	.	.	PUNCT
ejpam-5445	397	1	acknowledgements	acknowledgement	NOUN
ejpam-5445	397	2	we	we	PRON
ejpam-5445	397	3	are	be	AUX
ejpam-5445	397	4	thankful	thankful	ADJ
ejpam-5445	397	5	to	to	ADP
ejpam-5445	397	6	the	the	DET
ejpam-5445	397	7	editors	editor	NOUN
ejpam-5445	397	8	and	and	CCONJ
ejpam-5445	397	9	the	the	DET
ejpam-5445	397	10	anonymous	anonymous	ADJ
ejpam-5445	397	11	reviewers	reviewer	NOUN
ejpam-5445	397	12	for	for	ADP
ejpam-5445	397	13	many	many	ADJ
ejpam-5445	397	14	valuable	valuable	ADJ
ejpam-5445	397	15	suggestions	suggestion	NOUN
ejpam-5445	397	16	to	to	PART
ejpam-5445	397	17	improve	improve	VERB
ejpam-5445	397	18	this	this	DET
ejpam-5445	397	19	paper	paper	NOUN
ejpam-5445	397	20	.	.	PUNCT
ejpam-5445	398	1	funding	fund	VERB
ejpam-5445	398	2	this	this	DET
ejpam-5445	398	3	research	research	NOUN
ejpam-5445	398	4	supported	support	VERB
ejpam-5445	398	5	by	by	ADP
ejpam-5445	398	6	basic	basic	ADJ
ejpam-5445	398	7	science	science	NOUN
ejpam-5445	398	8	research	research	NOUN
ejpam-5445	398	9	program	program	NOUN
ejpam-5445	398	10	through	through	ADP
ejpam-5445	398	11	the	the	DET
ejpam-5445	398	12	national	national	PROPN
ejpam-5445	398	13	research	research	PROPN
ejpam-5445	398	14	foundation	foundation	PROPN
ejpam-5445	398	15	of	of	ADP
ejpam-5445	398	16	korea	korea	PROPN
ejpam-5445	398	17	(	(	PUNCT
ejpam-5445	398	18	nrf	nrf	NOUN
ejpam-5445	398	19	)	)	PUNCT
ejpam-5445	398	20	funded	fund	VERB
ejpam-5445	398	21	by	by	ADP
ejpam-5445	398	22	the	the	DET
ejpam-5445	398	23	ministry	ministry	PROPN
ejpam-5445	398	24	of	of	ADP
ejpam-5445	398	25	education	education	PROPN
ejpam-5445	398	26	(	(	PUNCT
ejpam-5445	398	27	nrfrs-202300237287	nrfrs-202300237287	ADJ
ejpam-5445	398	28	,	,	PUNCT
ejpam-5445	398	29	nrf-2021s1a5a8062526	nrf-2021s1a5a8062526	PROPN
ejpam-5445	398	30	)	)	PUNCT
ejpam-5445	398	31	and	and	CCONJ
ejpam-5445	398	32	local	local	ADJ
ejpam-5445	398	33	government	government	NOUN
ejpam-5445	398	34	-	-	PUNCT
ejpam-5445	398	35	university	university	NOUN
ejpam-5445	398	36	cooperation	cooperation	NOUN
ejpam-5445	398	37	-	-	PUNCT
ejpam-5445	398	38	based	base	VERB
ejpam-5445	398	39	references	reference	NOUN
ejpam-5445	398	40	3434	3434	NUM
ejpam-5445	398	41	regional	regional	ADJ
ejpam-5445	398	42	innovation	innovation	NOUN
ejpam-5445	398	43	projects	project	NOUN
ejpam-5445	398	44	(	(	PUNCT
ejpam-5445	398	45	2021ris-003	2021ris-003	NOUN
ejpam-5445	398	46	)	)	PUNCT
ejpam-5445	398	47	.	.	PUNCT
ejpam-5445	399	1	declaration	declaration	NOUN
ejpam-5445	399	2	of	of	ADP
ejpam-5445	399	3	competing	compete	VERB
ejpam-5445	399	4	interest	interest	NOUN
ejpam-5445	399	5	:	:	PUNCT
ejpam-5445	399	6	the	the	DET
ejpam-5445	399	7	author	author	NOUN
ejpam-5445	399	8	declares	declare	VERB
ejpam-5445	399	9	that	that	SCONJ
ejpam-5445	399	10	they	they	PRON
ejpam-5445	399	11	have	have	VERB
ejpam-5445	399	12	no	no	DET
ejpam-5445	399	13	known	know	VERB
ejpam-5445	399	14	competing	compete	VERB
ejpam-5445	399	15	financial	financial	ADJ
ejpam-5445	399	16	interests	interest	NOUN
ejpam-5445	399	17	or	or	CCONJ
ejpam-5445	399	18	personal	personal	ADJ
ejpam-5445	399	19	relationships	relationship	NOUN
ejpam-5445	399	20	that	that	PRON
ejpam-5445	399	21	could	could	AUX
ejpam-5445	399	22	have	have	AUX
ejpam-5445	399	23	appeared	appear	VERB
ejpam-5445	399	24	to	to	PART
ejpam-5445	399	25	influence	influence	VERB
ejpam-5445	399	26	the	the	DET
ejpam-5445	399	27	work	work	NOUN
ejpam-5445	399	28	reported	report	VERB
ejpam-5445	399	29	in	in	ADP
ejpam-5445	399	30	this	this	DET
ejpam-5445	399	31	paper	paper	NOUN
ejpam-5445	399	32	.	.	PUNCT
ejpam-5445	400	1	author	author	NOUN
ejpam-5445	400	2	’s	’s	PART
ejpam-5445	400	3	contribution	contribution	NOUN
ejpam-5445	400	4	:	:	PUNCT
ejpam-5445	400	5	all	all	DET
ejpam-5445	400	6	authors	author	NOUN
ejpam-5445	400	7	contributed	contribute	VERB
ejpam-5445	400	8	equally	equally	ADV
ejpam-5445	400	9	to	to	ADP
ejpam-5445	400	10	the	the	DET
ejpam-5445	400	11	manuscript	manuscript	NOUN
ejpam-5445	400	12	and	and	CCONJ
ejpam-5445	400	13	typed	type	VERB
ejpam-5445	400	14	,	,	PUNCT
ejpam-5445	400	15	read	read	VERB
ejpam-5445	400	16	,	,	PUNCT
ejpam-5445	400	17	and	and	CCONJ
ejpam-5445	400	18	approved	approve	VERB
ejpam-5445	400	19	the	the	DET
ejpam-5445	400	20	final	final	ADJ
ejpam-5445	400	21	manuscript	manuscript	NOUN
ejpam-5445	400	22	.	.	PUNCT
ejpam-5445	401	1	references	reference	NOUN
ejpam-5445	401	2	[	[	X
ejpam-5445	401	3	1	1	NUM
ejpam-5445	401	4	]	]	PUNCT
ejpam-5445	401	5	claudi	claudi	PROPN
ejpam-5445	401	6	alsina	alsina	NOUN
ejpam-5445	401	7	and	and	CCONJ
ejpam-5445	401	8	roman	roman	PROPN
ejpam-5445	401	9	ger	ger	NOUN
ejpam-5445	401	10	.	.	PUNCT
ejpam-5445	402	1	on	on	ADP
ejpam-5445	402	2	some	some	DET
ejpam-5445	402	3	inequalities	inequality	NOUN
ejpam-5445	402	4	and	and	CCONJ
ejpam-5445	402	5	stability	stability	NOUN
ejpam-5445	402	6	results	result	NOUN
ejpam-5445	402	7	related	relate	VERB
ejpam-5445	402	8	to	to	ADP
ejpam-5445	402	9	the	the	DET
ejpam-5445	402	10	exponential	exponential	ADJ
ejpam-5445	402	11	function	function	NOUN
ejpam-5445	402	12	.	.	PUNCT
ejpam-5445	403	1	journal	journal	PROPN
ejpam-5445	403	2	of	of	ADP
ejpam-5445	403	3	inequalities	inequality	NOUN
ejpam-5445	403	4	and	and	CCONJ
ejpam-5445	403	5	applications	application	NOUN
ejpam-5445	403	6	,	,	PUNCT
ejpam-5445	403	7	1998(4):246904	1998(4):246904	NUM
ejpam-5445	403	8	,	,	PUNCT
ejpam-5445	403	9	1998	1998	NUM
ejpam-5445	403	10	.	.	PUNCT
ejpam-5445	404	1	[	[	X
ejpam-5445	404	2	2	2	X
ejpam-5445	404	3	]	]	PUNCT
ejpam-5445	404	4	sz	sz	NOUN
ejpam-5445	404	5	andrás	andrás	PROPN
ejpam-5445	404	6	and	and	CCONJ
ejpam-5445	404	7	józsef	józsef	PROPN
ejpam-5445	404	8	j	j	PROPN
ejpam-5445	404	9	kolumbán	kolumbán	PROPN
ejpam-5445	404	10	.	.	PUNCT
ejpam-5445	405	1	on	on	ADP
ejpam-5445	405	2	the	the	DET
ejpam-5445	405	3	ulam	ulam	NOUN
ejpam-5445	405	4	–	–	PUNCT
ejpam-5445	405	5	hyers	hyer	NOUN
ejpam-5445	405	6	stability	stability	NOUN
ejpam-5445	405	7	of	of	ADP
ejpam-5445	405	8	first	first	ADJ
ejpam-5445	405	9	order	order	NOUN
ejpam-5445	405	10	differential	differential	NOUN
ejpam-5445	405	11	systems	system	NOUN
ejpam-5445	405	12	with	with	ADP
ejpam-5445	405	13	nonlocal	nonlocal	ADJ
ejpam-5445	405	14	initial	initial	ADJ
ejpam-5445	405	15	conditions	condition	NOUN
ejpam-5445	405	16	.	.	PUNCT
ejpam-5445	406	1	nonlinear	nonlinear	ADJ
ejpam-5445	406	2	analysis	analysis	NOUN
ejpam-5445	406	3	:	:	PUNCT
ejpam-5445	406	4	theory	theory	NOUN
ejpam-5445	406	5	,	,	PUNCT
ejpam-5445	406	6	methods	method	NOUN
ejpam-5445	406	7	&	&	CCONJ
ejpam-5445	406	8	applications	application	NOUN
ejpam-5445	406	9	,	,	PUNCT
ejpam-5445	406	10	82:1–11	82:1–11	NUM
ejpam-5445	406	11	,	,	PUNCT
ejpam-5445	406	12	2013	2013	NUM
ejpam-5445	406	13	.	.	PUNCT
ejpam-5445	407	1	[	[	X
ejpam-5445	407	2	3	3	NUM
ejpam-5445	407	3	]	]	SYM
ejpam-5445	407	4	szilárd	szilárd	ADJ
ejpam-5445	407	5	andrás	andrás	NOUN
ejpam-5445	407	6	and	and	CCONJ
ejpam-5445	407	7	alpár	alpár	VERB
ejpam-5445	407	8	richárd	richárd	ADV
ejpam-5445	407	9	mészáros	mészáros	PROPN
ejpam-5445	407	10	.	.	PUNCT
ejpam-5445	408	1	ulam	ulam	NOUN
ejpam-5445	408	2	–	–	PUNCT
ejpam-5445	408	3	hyers	hyer	NOUN
ejpam-5445	408	4	stability	stability	NOUN
ejpam-5445	408	5	of	of	ADP
ejpam-5445	408	6	dynamic	dynamic	ADJ
ejpam-5445	408	7	equations	equation	NOUN
ejpam-5445	408	8	on	on	ADP
ejpam-5445	408	9	time	time	NOUN
ejpam-5445	408	10	scales	scale	NOUN
ejpam-5445	408	11	via	via	ADP
ejpam-5445	408	12	picard	picard	NOUN
ejpam-5445	408	13	operators	operator	NOUN
ejpam-5445	408	14	.	.	PUNCT
ejpam-5445	409	1	applied	apply	VERB
ejpam-5445	409	2	mathematics	mathematic	NOUN
ejpam-5445	409	3	and	and	CCONJ
ejpam-5445	409	4	computation	computation	NOUN
ejpam-5445	409	5	,	,	PUNCT
ejpam-5445	409	6	219(9):4853–4864	219(9):4853–4864	PROPN
ejpam-5445	409	7	,	,	PUNCT
ejpam-5445	409	8	2013	2013	NUM
ejpam-5445	409	9	.	.	PUNCT
ejpam-5445	410	1	[	[	X
ejpam-5445	410	2	4	4	NUM
ejpam-5445	410	3	]	]	PUNCT
ejpam-5445	410	4	tosio	tosio	PROPN
ejpam-5445	410	5	aoki	aoki	PROPN
ejpam-5445	410	6	.	.	PUNCT
ejpam-5445	411	1	on	on	ADP
ejpam-5445	411	2	the	the	DET
ejpam-5445	411	3	stability	stability	NOUN
ejpam-5445	411	4	of	of	ADP
ejpam-5445	411	5	the	the	DET
ejpam-5445	411	6	linear	linear	ADJ
ejpam-5445	411	7	transformation	transformation	NOUN
ejpam-5445	411	8	in	in	ADP
ejpam-5445	411	9	banach	banach	NOUN
ejpam-5445	411	10	spaces	space	NOUN
ejpam-5445	411	11	.	.	PUNCT
ejpam-5445	412	1	journal	journal	NOUN
ejpam-5445	412	2	of	of	ADP
ejpam-5445	412	3	the	the	DET
ejpam-5445	412	4	mathematical	mathematical	ADJ
ejpam-5445	412	5	society	society	NOUN
ejpam-5445	412	6	of	of	ADP
ejpam-5445	412	7	japan	japan	PROPN
ejpam-5445	412	8	,	,	PUNCT
ejpam-5445	412	9	2(1	2(1	NUM
ejpam-5445	412	10	-	-	SYM
ejpam-5445	412	11	2):64–66	2):64–66	NUM
ejpam-5445	412	12	,	,	PUNCT
ejpam-5445	412	13	1950	1950	NUM
ejpam-5445	412	14	.	.	PUNCT
ejpam-5445	413	1	[	[	X
ejpam-5445	413	2	5	5	NUM
ejpam-5445	413	3	]	]	X
ejpam-5445	413	4	shelly	shelly	PROPN
ejpam-5445	413	5	arora	arora	PROPN
ejpam-5445	413	6	,	,	PUNCT
ejpam-5445	413	7	fateh	fateh	PROPN
ejpam-5445	413	8	mebrek	mebrek	PROPN
ejpam-5445	413	9	-	-	PUNCT
ejpam-5445	413	10	oudina	oudina	PROPN
ejpam-5445	413	11	,	,	PUNCT
ejpam-5445	413	12	saroj	saroj	PROPN
ejpam-5445	413	13	sahani	sahani	PROPN
ejpam-5445	413	14	,	,	PUNCT
ejpam-5445	413	15	et	et	PROPN
ejpam-5445	413	16	al	al	PROPN
ejpam-5445	413	17	.	.	PUNCT
ejpam-5445	414	1	super	super	ADJ
ejpam-5445	414	2	convergence	convergence	NOUN
ejpam-5445	414	3	analysis	analysis	NOUN
ejpam-5445	414	4	of	of	ADP
ejpam-5445	414	5	fully	fully	ADV
ejpam-5445	414	6	discrete	discrete	ADJ
ejpam-5445	414	7	hermite	hermite	ADJ
ejpam-5445	414	8	splines	spline	NOUN
ejpam-5445	414	9	to	to	PART
ejpam-5445	414	10	simulate	simulate	VERB
ejpam-5445	414	11	wave	wave	NOUN
ejpam-5445	414	12	behaviour	behaviour	NOUN
ejpam-5445	414	13	of	of	ADP
ejpam-5445	414	14	kuramoto	kuramoto	NOUN
ejpam-5445	414	15	–	–	PUNCT
ejpam-5445	414	16	sivashinsky	sivashinsky	ADJ
ejpam-5445	414	17	equation	equation	NOUN
ejpam-5445	414	18	.	.	PUNCT
ejpam-5445	415	1	wave	wave	PROPN
ejpam-5445	415	2	motion	motion	NOUN
ejpam-5445	415	3	,	,	PUNCT
ejpam-5445	415	4	121:103187	121:103187	NUM
ejpam-5445	415	5	,	,	PUNCT
ejpam-5445	415	6	2023	2023	NUM
ejpam-5445	415	7	.	.	PUNCT
ejpam-5445	416	1	[	[	X
ejpam-5445	416	2	6	6	NUM
ejpam-5445	416	3	]	]	X
ejpam-5445	416	4	nz	nz	PROPN
ejpam-5445	416	5	basha	basha	PROPN
ejpam-5445	416	6	,	,	PUNCT
ejpam-5445	416	7	c	c	NOUN
ejpam-5445	416	8	rajashekhar	rajashekhar	NOUN
ejpam-5445	416	9	,	,	PUNCT
ejpam-5445	416	10	f	f	PROPN
ejpam-5445	416	11	mebarek	mebarek	PROPN
ejpam-5445	416	12	-	-	PUNCT
ejpam-5445	416	13	oudina	oudina	PROPN
ejpam-5445	416	14	,	,	PUNCT
ejpam-5445	416	15	kv	kv	PROPN
ejpam-5445	416	16	prasad	prasad	PROPN
ejpam-5445	416	17	,	,	PUNCT
ejpam-5445	416	18	h	h	PROPN
ejpam-5445	416	19	vaidya	vaidya	PROPN
ejpam-5445	416	20	,	,	PUNCT
ejpam-5445	416	21	kamel	kamel	PROPN
ejpam-5445	416	22	guedri	guedri	PROPN
ejpam-5445	416	23	,	,	PUNCT
ejpam-5445	416	24	attia	attia	PROPN
ejpam-5445	416	25	boudjemline	boudjemline	PROPN
ejpam-5445	416	26	,	,	PUNCT
ejpam-5445	416	27	rami	rami	PROPN
ejpam-5445	416	28	mansouri	mansouri	PROPN
ejpam-5445	416	29	,	,	PUNCT
ejpam-5445	416	30	and	and	CCONJ
ejpam-5445	416	31	ahmed	ahmed	PROPN
ejpam-5445	416	32	taieb	taieb	PROPN
ejpam-5445	416	33	.	.	PUNCT
ejpam-5445	417	1	sutterby	sutterby	PROPN
ejpam-5445	417	2	hybrid	hybrid	PROPN
ejpam-5445	417	3	nanofluid	nanofluid	PROPN
ejpam-5445	417	4	flow	flow	NOUN
ejpam-5445	417	5	and	and	CCONJ
ejpam-5445	417	6	heat	heat	NOUN
ejpam-5445	417	7	transfer	transfer	NOUN
ejpam-5445	417	8	over	over	ADP
ejpam-5445	417	9	a	a	DET
ejpam-5445	417	10	nonlinearly	nonlinearly	ADV
ejpam-5445	417	11	expanding	expand	VERB
ejpam-5445	417	12	sheet	sheet	NOUN
ejpam-5445	417	13	with	with	ADP
ejpam-5445	417	14	convective	convective	ADJ
ejpam-5445	417	15	boundary	boundary	ADJ
ejpam-5445	417	16	condition	condition	NOUN
ejpam-5445	417	17	and	and	CCONJ
ejpam-5445	417	18	zero	zero	NUM
ejpam-5445	417	19	-	-	PUNCT
ejpam-5445	417	20	mass	mass	NOUN
ejpam-5445	417	21	flux	flux	NOUN
ejpam-5445	417	22	concentration	concentration	NOUN
ejpam-5445	417	23	.	.	PUNCT
ejpam-5445	418	1	international	international	ADJ
ejpam-5445	418	2	journal	journal	NOUN
ejpam-5445	418	3	of	of	ADP
ejpam-5445	418	4	modern	modern	ADJ
ejpam-5445	418	5	physics	physics	PROPN
ejpam-5445	418	6	b	b	PROPN
ejpam-5445	418	7	,	,	PUNCT
ejpam-5445	418	8	38(10):2450146	38(10):2450146	NUM
ejpam-5445	418	9	,	,	PUNCT
ejpam-5445	418	10	2024	2024	NUM
ejpam-5445	418	11	.	.	PUNCT
ejpam-5445	419	1	[	[	X
ejpam-5445	419	2	7	7	X
ejpam-5445	419	3	]	]	X
ejpam-5445	419	4	marc	marc	PROPN
ejpam-5445	419	5	burger	burger	NOUN
ejpam-5445	419	6	,	,	PUNCT
ejpam-5445	419	7	narutaka	narutaka	NOUN
ejpam-5445	419	8	ozawa	ozawa	PROPN
ejpam-5445	419	9	,	,	PUNCT
ejpam-5445	419	10	and	and	CCONJ
ejpam-5445	419	11	andreas	andreas	PROPN
ejpam-5445	419	12	thom	thom	PROPN
ejpam-5445	419	13	.	.	PUNCT
ejpam-5445	419	14	on	on	ADP
ejpam-5445	419	15	ulam	ulam	PROPN
ejpam-5445	419	16	stability	stability	PROPN
ejpam-5445	419	17	.	.	PUNCT
ejpam-5445	420	1	arxiv	arxiv	PROPN
ejpam-5445	420	2	preprint	preprint	PROPN
ejpam-5445	420	3	arxiv:1010.0565	arxiv:1010.0565	NOUN
ejpam-5445	420	4	,	,	PUNCT
ejpam-5445	420	5	2010	2010	NUM
ejpam-5445	420	6	.	.	PUNCT
ejpam-5445	421	1	[	[	X
ejpam-5445	421	2	8	8	NUM
ejpam-5445	421	3	]	]	PUNCT
ejpam-5445	421	4	hisashi	hisashi	PROPN
ejpam-5445	421	5	choda	choda	PROPN
ejpam-5445	421	6	,	,	PUNCT
ejpam-5445	421	7	takeshi	takeshi	NOUN
ejpam-5445	421	8	miura	miura	PROPN
ejpam-5445	421	9	,	,	PUNCT
ejpam-5445	421	10	and	and	CCONJ
ejpam-5445	421	11	sin	sin	NOUN
ejpam-5445	421	12	-	-	PUNCT
ejpam-5445	421	13	ei	ei	NOUN
ejpam-5445	421	14	takahasi	takahasi	NOUN
ejpam-5445	421	15	.	.	PUNCT
ejpam-5445	422	1	on	on	ADP
ejpam-5445	422	2	the	the	DET
ejpam-5445	422	3	hyers	hyers	PROPN
ejpam-5445	422	4	-	-	PUNCT
ejpam-5445	422	5	ulam	ulam	ADJ
ejpam-5445	422	6	stability	stability	NOUN
ejpam-5445	422	7	of	of	ADP
ejpam-5445	422	8	real	real	ADJ
ejpam-5445	422	9	continuous	continuous	ADJ
ejpam-5445	422	10	function	function	NOUN
ejpam-5445	422	11	valued	value	VERB
ejpam-5445	422	12	differentiable	differentiable	NOUN
ejpam-5445	422	13	map	map	NOUN
ejpam-5445	422	14	.	.	PUNCT
ejpam-5445	423	1	tokyo	tokyo	PROPN
ejpam-5445	423	2	journal	journal	NOUN
ejpam-5445	423	3	of	of	ADP
ejpam-5445	423	4	mathematics	mathematic	NOUN
ejpam-5445	423	5	,	,	PUNCT
ejpam-5445	423	6	24(2):467–476	24(2):467–476	PRON
ejpam-5445	423	7	,	,	PUNCT
ejpam-5445	423	8	2001	2001	NUM
ejpam-5445	423	9	.	.	PUNCT
ejpam-5445	424	1	[	[	X
ejpam-5445	424	2	9	9	X
ejpam-5445	424	3	]	]	X
ejpam-5445	424	4	dalia	dalia	PROPN
ejpam-5445	424	5	sabina	sabina	PROPN
ejpam-5445	424	6	cimpean	cimpean	PROPN
ejpam-5445	424	7	and	and	CCONJ
ejpam-5445	424	8	dorian	dorian	PROPN
ejpam-5445	424	9	popa	popa	NOUN
ejpam-5445	424	10	.	.	PUNCT
ejpam-5445	425	1	hyers	hyer	NOUN
ejpam-5445	425	2	–	–	PUNCT
ejpam-5445	425	3	ulam	ulam	PROPN
ejpam-5445	425	4	stability	stability	NOUN
ejpam-5445	425	5	of	of	ADP
ejpam-5445	425	6	euler	euler	PROPN
ejpam-5445	425	7	’s	’s	PART
ejpam-5445	425	8	equation	equation	NOUN
ejpam-5445	425	9	.	.	PUNCT
ejpam-5445	426	1	applied	apply	VERB
ejpam-5445	426	2	mathematics	mathematics	NOUN
ejpam-5445	426	3	letters	letter	NOUN
ejpam-5445	426	4	,	,	PUNCT
ejpam-5445	426	5	24(9):1539–1543	24(9):1539–1543	NUM
ejpam-5445	426	6	,	,	PUNCT
ejpam-5445	426	7	2011	2011	NUM
ejpam-5445	426	8	.	.	PUNCT
ejpam-5445	427	1	references	reference	NOUN
ejpam-5445	427	2	3435	3435	NUM
ejpam-5445	428	1	[	[	X
ejpam-5445	428	2	10	10	NUM
ejpam-5445	428	3	]	]	X
ejpam-5445	428	4	m	m	VERB
ejpam-5445	428	5	farhan	farhan	PROPN
ejpam-5445	428	6	,	,	PUNCT
ejpam-5445	428	7	zurni	zurni	PROPN
ejpam-5445	428	8	omar	omar	PROPN
ejpam-5445	428	9	,	,	PUNCT
ejpam-5445	428	10	f	f	PROPN
ejpam-5445	428	11	mebarek	mebarek	PROPN
ejpam-5445	428	12	-	-	PUNCT
ejpam-5445	428	13	oudina	oudina	PROPN
ejpam-5445	428	14	,	,	PUNCT
ejpam-5445	428	15	j	j	PROPN
ejpam-5445	428	16	raza	raza	PROPN
ejpam-5445	428	17	,	,	PUNCT
ejpam-5445	428	18	z	z	NOUN
ejpam-5445	428	19	shah	shah	NOUN
ejpam-5445	428	20	,	,	PUNCT
ejpam-5445	428	21	rv	rv	PROPN
ejpam-5445	428	22	choudhari	choudhari	X
ejpam-5445	428	23	,	,	PUNCT
ejpam-5445	428	24	and	and	CCONJ
ejpam-5445	428	25	od	od	NUM
ejpam-5445	428	26	makinde	makinde	NOUN
ejpam-5445	428	27	.	.	PUNCT
ejpam-5445	429	1	implementation	implementation	NOUN
ejpam-5445	429	2	of	of	ADP
ejpam-5445	429	3	the	the	DET
ejpam-5445	429	4	one	one	NUM
ejpam-5445	429	5	-	-	PUNCT
ejpam-5445	429	6	step	step	NOUN
ejpam-5445	429	7	one	one	NUM
ejpam-5445	429	8	-	-	PUNCT
ejpam-5445	429	9	hybrid	hybrid	ADJ
ejpam-5445	429	10	block	block	NOUN
ejpam-5445	429	11	method	method	NOUN
ejpam-5445	429	12	on	on	ADP
ejpam-5445	429	13	the	the	DET
ejpam-5445	429	14	nonlinear	nonlinear	ADJ
ejpam-5445	429	15	equation	equation	NOUN
ejpam-5445	429	16	of	of	ADP
ejpam-5445	429	17	a	a	DET
ejpam-5445	429	18	circular	circular	ADJ
ejpam-5445	429	19	sector	sector	NOUN
ejpam-5445	429	20	oscillator	oscillator	NOUN
ejpam-5445	429	21	.	.	PUNCT
ejpam-5445	430	1	computational	computational	ADJ
ejpam-5445	430	2	mathematics	mathematic	NOUN
ejpam-5445	430	3	and	and	CCONJ
ejpam-5445	430	4	modeling	modeling	NOUN
ejpam-5445	430	5	,	,	PUNCT
ejpam-5445	430	6	31:116–132	31:116–132	PROPN
ejpam-5445	430	7	,	,	PUNCT
ejpam-5445	430	8	2020	2020	NUM
ejpam-5445	430	9	.	.	PUNCT
ejpam-5445	431	1	[	[	X
ejpam-5445	431	2	11	11	NUM
ejpam-5445	431	3	]	]	SYM
ejpam-5445	431	4	balázs	balázs	PROPN
ejpam-5445	431	5	hegyi	hegyi	PROPN
ejpam-5445	431	6	and	and	CCONJ
ejpam-5445	431	7	soon	soon	ADV
ejpam-5445	431	8	-	-	PUNCT
ejpam-5445	431	9	mo	mo	PROPN
ejpam-5445	431	10	jung	jung	PROPN
ejpam-5445	431	11	.	.	PUNCT
ejpam-5445	432	1	on	on	ADP
ejpam-5445	432	2	the	the	DET
ejpam-5445	432	3	stability	stability	NOUN
ejpam-5445	432	4	of	of	ADP
ejpam-5445	432	5	laplace	laplace	NOUN
ejpam-5445	432	6	’s	’s	PART
ejpam-5445	432	7	equation	equation	NOUN
ejpam-5445	432	8	.	.	PUNCT
ejpam-5445	433	1	applied	apply	VERB
ejpam-5445	433	2	mathematics	mathematics	NOUN
ejpam-5445	433	3	letters	letter	NOUN
ejpam-5445	433	4	,	,	PUNCT
ejpam-5445	433	5	26(5):549–552	26(5):549–552	NUM
ejpam-5445	433	6	,	,	PUNCT
ejpam-5445	433	7	2013	2013	NUM
ejpam-5445	433	8	.	.	PUNCT
ejpam-5445	434	1	[	[	X
ejpam-5445	434	2	12	12	NUM
ejpam-5445	434	3	]	]	X
ejpam-5445	434	4	donald	donald	PROPN
ejpam-5445	434	5	h	h	PROPN
ejpam-5445	434	6	hyers	hyers	PROPN
ejpam-5445	434	7	.	.	PUNCT
ejpam-5445	435	1	on	on	ADP
ejpam-5445	435	2	the	the	DET
ejpam-5445	435	3	stability	stability	NOUN
ejpam-5445	435	4	of	of	ADP
ejpam-5445	435	5	the	the	DET
ejpam-5445	435	6	linear	linear	ADJ
ejpam-5445	435	7	functional	functional	ADJ
ejpam-5445	435	8	equation	equation	NOUN
ejpam-5445	435	9	.	.	PUNCT
ejpam-5445	436	1	proceedings	proceeding	NOUN
ejpam-5445	436	2	of	of	ADP
ejpam-5445	436	3	the	the	DET
ejpam-5445	436	4	national	national	PROPN
ejpam-5445	436	5	academy	academy	PROPN
ejpam-5445	436	6	of	of	ADP
ejpam-5445	436	7	sciences	sciences	PROPN
ejpam-5445	436	8	,	,	PUNCT
ejpam-5445	436	9	27(4):222–224	27(4):222–224	NUM
ejpam-5445	436	10	,	,	PUNCT
ejpam-5445	436	11	1941	1941	NUM
ejpam-5445	436	12	.	.	PUNCT
ejpam-5445	437	1	[	[	X
ejpam-5445	437	2	13	13	NUM
ejpam-5445	437	3	]	]	SYM
ejpam-5445	437	4	s	s	PROPN
ejpam-5445	437	5	-	-	PUNCT
ejpam-5445	437	6	m	m	NOUN
ejpam-5445	437	7	jung	jung	NOUN
ejpam-5445	437	8	.	.	PUNCT
ejpam-5445	438	1	hyers	hyer	NOUN
ejpam-5445	438	2	–	–	PUNCT
ejpam-5445	438	3	ulam	ulam	PROPN
ejpam-5445	438	4	stability	stability	NOUN
ejpam-5445	438	5	of	of	ADP
ejpam-5445	438	6	linear	linear	PROPN
ejpam-5445	438	7	differential	differential	ADJ
ejpam-5445	438	8	equations	equation	NOUN
ejpam-5445	438	9	of	of	ADP
ejpam-5445	438	10	first	first	ADJ
ejpam-5445	438	11	order	order	NOUN
ejpam-5445	438	12	,	,	PUNCT
ejpam-5445	438	13	ii	ii	PROPN
ejpam-5445	438	14	.	.	PROPN
ejpam-5445	438	15	applied	apply	VERB
ejpam-5445	438	16	mathematics	mathematics	NOUN
ejpam-5445	438	17	letters	letter	NOUN
ejpam-5445	438	18	,	,	PUNCT
ejpam-5445	438	19	19(9):854–858	19(9):854–858	NUM
ejpam-5445	438	20	,	,	PUNCT
ejpam-5445	438	21	2006	2006	NUM
ejpam-5445	438	22	.	.	PUNCT
ejpam-5445	439	1	[	[	X
ejpam-5445	439	2	14	14	NUM
ejpam-5445	439	3	]	]	X
ejpam-5445	439	4	yang	yang	PROPN
ejpam-5445	439	5	-	-	PUNCT
ejpam-5445	439	6	hi	hi	PROPN
ejpam-5445	439	7	lee	lee	PROPN
ejpam-5445	439	8	and	and	CCONJ
ejpam-5445	439	9	kil	kil	PROPN
ejpam-5445	439	10	-	-	PROPN
ejpam-5445	439	11	woung	woung	PROPN
ejpam-5445	439	12	jun	jun	PROPN
ejpam-5445	439	13	.	.	PROPN
ejpam-5445	440	1	a	a	DET
ejpam-5445	440	2	generalization	generalization	NOUN
ejpam-5445	440	3	of	of	ADP
ejpam-5445	440	4	the	the	DET
ejpam-5445	440	5	hyers	hyer	NOUN
ejpam-5445	440	6	–	–	PUNCT
ejpam-5445	440	7	ulam	ulam	X
ejpam-5445	440	8	–	–	PUNCT
ejpam-5445	440	9	rassias	rassia	NOUN
ejpam-5445	440	10	stability	stability	NOUN
ejpam-5445	440	11	of	of	ADP
ejpam-5445	440	12	jensen	jensen	PROPN
ejpam-5445	440	13	’s	’s	PART
ejpam-5445	440	14	equation	equation	NOUN
ejpam-5445	440	15	.	.	PUNCT
ejpam-5445	441	1	journal	journal	PROPN
ejpam-5445	441	2	of	of	ADP
ejpam-5445	441	3	mathematical	mathematical	ADJ
ejpam-5445	441	4	analysis	analysis	NOUN
ejpam-5445	441	5	and	and	CCONJ
ejpam-5445	441	6	applications	application	NOUN
ejpam-5445	441	7	,	,	PUNCT
ejpam-5445	441	8	238(1):305	238(1):305	NOUN
ejpam-5445	441	9	–	–	PUNCT
ejpam-5445	441	10	315	315	NUM
ejpam-5445	441	11	,	,	PUNCT
ejpam-5445	441	12	1999	1999	NUM
ejpam-5445	441	13	.	.	PUNCT
ejpam-5445	442	1	[	[	X
ejpam-5445	442	2	15	15	NUM
ejpam-5445	442	3	]	]	X
ejpam-5445	442	4	themistocles	themistocle	NOUN
ejpam-5445	442	5	m	m	NOUN
ejpam-5445	442	6	rassias	rassia	NOUN
ejpam-5445	442	7	.	.	PUNCT
ejpam-5445	443	1	on	on	ADP
ejpam-5445	443	2	the	the	DET
ejpam-5445	443	3	stability	stability	NOUN
ejpam-5445	443	4	of	of	ADP
ejpam-5445	443	5	the	the	DET
ejpam-5445	443	6	linear	linear	ADJ
ejpam-5445	443	7	mapping	mapping	NOUN
ejpam-5445	443	8	in	in	ADP
ejpam-5445	443	9	banach	banach	NOUN
ejpam-5445	443	10	spaces	space	NOUN
ejpam-5445	443	11	.	.	PUNCT
ejpam-5445	444	1	proceedings	proceeding	NOUN
ejpam-5445	444	2	of	of	ADP
ejpam-5445	444	3	the	the	DET
ejpam-5445	444	4	american	american	PROPN
ejpam-5445	444	5	mathematical	mathematical	PROPN
ejpam-5445	444	6	society	society	NOUN
ejpam-5445	444	7	,	,	PUNCT
ejpam-5445	444	8	72(2):297–300	72(2):297–300	NUM
ejpam-5445	444	9	,	,	PUNCT
ejpam-5445	444	10	1978	1978	NUM
ejpam-5445	444	11	.	.	PUNCT
ejpam-5445	445	1	[	[	X
ejpam-5445	445	2	16	16	NUM
ejpam-5445	445	3	]	]	X
ejpam-5445	445	4	sin	sin	NOUN
ejpam-5445	445	5	-	-	PUNCT
ejpam-5445	445	6	ei	ei	NOUN
ejpam-5445	445	7	takahasi	takahasi	NOUN
ejpam-5445	445	8	,	,	PUNCT
ejpam-5445	445	9	takeshi	takeshi	NOUN
ejpam-5445	445	10	miura	miura	PROPN
ejpam-5445	445	11	,	,	PUNCT
ejpam-5445	445	12	and	and	CCONJ
ejpam-5445	445	13	shizuo	shizuo	PROPN
ejpam-5445	445	14	miyajima	miyajima	PROPN
ejpam-5445	445	15	.	.	PUNCT
ejpam-5445	446	1	on	on	ADP
ejpam-5445	446	2	the	the	DET
ejpam-5445	446	3	hyers	hyers	PROPN
ejpam-5445	446	4	-	-	PUNCT
ejpam-5445	446	5	ulam	ulam	ADJ
ejpam-5445	446	6	stability	stability	NOUN
ejpam-5445	446	7	of	of	ADP
ejpam-5445	446	8	the	the	DET
ejpam-5445	446	9	banach	banach	NOUN
ejpam-5445	446	10	space	space	NOUN
ejpam-5445	446	11	-	-	PUNCT
ejpam-5445	446	12	valued	value	VERB
ejpam-5445	446	13	differential	differential	NOUN
ejpam-5445	446	14	equation	equation	NOUN
ejpam-5445	446	15	y=	y=	PRON
ejpam-5445	446	16	λy	λy	PROPN
ejpam-5445	446	17	.	.	PUNCT
ejpam-5445	446	18	bull	bull	PROPN
ejpam-5445	446	19	.	.	PUNCT
ejpam-5445	447	1	korean	korean	ADJ
ejpam-5445	447	2	math	math	PROPN
ejpam-5445	447	3	.	.	PUNCT
ejpam-5445	448	1	soc	soc	PROPN
ejpam-5445	448	2	,	,	PUNCT
ejpam-5445	448	3	39(2):309–315	39(2):309–315	PROPN
ejpam-5445	448	4	,	,	PUNCT
ejpam-5445	448	5	2002	2002	NUM
ejpam-5445	448	6	.	.	PUNCT
ejpam-5445	449	1	[	[	X
ejpam-5445	449	2	17	17	NUM
ejpam-5445	449	3	]	]	X
ejpam-5445	449	4	sin	sin	NOUN
ejpam-5445	449	5	-	-	PUNCT
ejpam-5445	449	6	ei	ei	NOUN
ejpam-5445	449	7	takahasi	takahasi	PROPN
ejpam-5445	449	8	,	,	PUNCT
ejpam-5445	449	9	hiroyuki	hiroyuki	PROPN
ejpam-5445	449	10	takagi	takagi	PROPN
ejpam-5445	449	11	,	,	PUNCT
ejpam-5445	449	12	takeshi	takeshi	NOUN
ejpam-5445	449	13	miura	miura	PROPN
ejpam-5445	449	14	,	,	PUNCT
ejpam-5445	449	15	and	and	CCONJ
ejpam-5445	449	16	shizuo	shizuo	PROPN
ejpam-5445	449	17	miyajima	miyajima	PROPN
ejpam-5445	449	18	.	.	PUNCT
ejpam-5445	450	1	the	the	DET
ejpam-5445	450	2	hyers	hyer	NOUN
ejpam-5445	450	3	–	–	PUNCT
ejpam-5445	450	4	ulam	ulam	PROPN
ejpam-5445	450	5	stability	stability	NOUN
ejpam-5445	450	6	constants	constant	NOUN
ejpam-5445	450	7	of	of	ADP
ejpam-5445	450	8	first	first	ADJ
ejpam-5445	450	9	order	order	NOUN
ejpam-5445	450	10	linear	linear	PROPN
ejpam-5445	450	11	differential	differential	NOUN
ejpam-5445	450	12	operators	operator	NOUN
ejpam-5445	450	13	.	.	PUNCT
ejpam-5445	451	1	journal	journal	PROPN
ejpam-5445	451	2	of	of	ADP
ejpam-5445	451	3	mathematical	mathematical	ADJ
ejpam-5445	451	4	analysis	analysis	NOUN
ejpam-5445	451	5	and	and	CCONJ
ejpam-5445	451	6	applications	application	NOUN
ejpam-5445	451	7	,	,	PUNCT
ejpam-5445	451	8	296(2):403–409	296(2):403–409	NUM
ejpam-5445	451	9	,	,	PUNCT
ejpam-5445	451	10	2004	2004	NUM
ejpam-5445	451	11	.	.	PUNCT
ejpam-5445	452	1	[	[	X
ejpam-5445	452	2	18	18	NUM
ejpam-5445	452	3	]	]	X
ejpam-5445	452	4	sm	sm	PROPN
ejpam-5445	452	5	ulam	ulam	PROPN
ejpam-5445	452	6	.	.	PUNCT
ejpam-5445	453	1	a	a	DET
ejpam-5445	453	2	collection	collection	NOUN
ejpam-5445	453	3	of	of	ADP
ejpam-5445	453	4	mathematical	mathematical	ADJ
ejpam-5445	453	5	problems	problem	NOUN
ejpam-5445	453	6	(	(	PUNCT
ejpam-5445	453	7	interscience	interscience	NOUN
ejpam-5445	453	8	,	,	PUNCT
ejpam-5445	453	9	new	new	PROPN
ejpam-5445	453	10	york	york	PROPN
ejpam-5445	453	11	.	.	PUNCT
ejpam-5445	453	12	1960	1960	NUM
ejpam-5445	453	13	.	.	PUNCT
ejpam-5445	454	1	[	[	X
ejpam-5445	454	2	19	19	NUM
ejpam-5445	454	3	]	]	X
ejpam-5445	454	4	guangwa	guangwa	PROPN
ejpam-5445	454	5	wang	wang	PROPN
ejpam-5445	454	6	,	,	PUNCT
ejpam-5445	454	7	mingru	mingru	NOUN
ejpam-5445	454	8	zhou	zhou	PROPN
ejpam-5445	454	9	,	,	PUNCT
ejpam-5445	454	10	and	and	CCONJ
ejpam-5445	454	11	li	li	PROPN
ejpam-5445	454	12	sun	sun	PROPN
ejpam-5445	454	13	.	.	PUNCT
ejpam-5445	455	1	hyers	hyer	NOUN
ejpam-5445	455	2	–	–	PUNCT
ejpam-5445	455	3	ulam	ulam	PROPN
ejpam-5445	455	4	stability	stability	NOUN
ejpam-5445	455	5	of	of	ADP
ejpam-5445	455	6	linear	linear	PROPN
ejpam-5445	455	7	differential	differential	ADJ
ejpam-5445	455	8	equations	equation	NOUN
ejpam-5445	455	9	of	of	ADP
ejpam-5445	455	10	first	first	ADJ
ejpam-5445	455	11	order	order	NOUN
ejpam-5445	455	12	.	.	PUNCT
ejpam-5445	456	1	applied	apply	VERB
ejpam-5445	456	2	mathematics	mathematics	NOUN
ejpam-5445	456	3	letters	letter	NOUN
ejpam-5445	456	4	,	,	PUNCT
ejpam-5445	456	5	21(10):1024–1028	21(10):1024–1028	NUM
ejpam-5445	456	6	,	,	PUNCT
ejpam-5445	456	7	2008	2008	NUM
ejpam-5445	456	8	.	.	PUNCT