id	sid	tid	token	lemma	pos
ejpam-3070	1	1	european	european	PROPN
ejpam-3070	1	2	journal	journal	PROPN
ejpam-3070	1	3	of	of	ADP
ejpam-3070	1	4	pure	pure	ADJ
ejpam-3070	1	5	and	and	CCONJ
ejpam-3070	1	6	applied	apply	VERB
ejpam-3070	1	7	mathematics	mathematic	NOUN
ejpam-3070	1	8	vol	vol	NOUN
ejpam-3070	1	9	.	.	PROPN
ejpam-3070	2	1	10	10	NUM
ejpam-3070	2	2	,	,	PUNCT
ejpam-3070	2	3	no	no	INTJ
ejpam-3070	2	4	.	.	NOUN
ejpam-3070	2	5	4	4	NUM
ejpam-3070	2	6	,	,	PUNCT
ejpam-3070	2	7	2017	2017	NUM
ejpam-3070	2	8	,	,	PUNCT
ejpam-3070	2	9	645	645	NUM
ejpam-3070	2	10	-	-	SYM
ejpam-3070	2	11	654	654	NUM
ejpam-3070	2	12	issn	issn	PROPN
ejpam-3070	2	13	1307	1307	NUM
ejpam-3070	2	14	-	-	SYM
ejpam-3070	2	15	5543	5543	NUM
ejpam-3070	2	16	–	–	PUNCT
ejpam-3070	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3070	2	18	published	publish	VERB
ejpam-3070	2	19	by	by	ADP
ejpam-3070	2	20	new	new	PROPN
ejpam-3070	2	21	york	york	PROPN
ejpam-3070	2	22	business	business	PROPN
ejpam-3070	2	23	global	global	ADJ
ejpam-3070	2	24	stability	stability	NOUN
ejpam-3070	2	25	results	result	VERB
ejpam-3070	2	26	in	in	ADP
ejpam-3070	2	27	terms	term	NOUN
ejpam-3070	2	28	of	of	ADP
ejpam-3070	2	29	two	two	NUM
ejpam-3070	2	30	measures	measure	NOUN
ejpam-3070	2	31	for	for	ADP
ejpam-3070	2	32	set	set	VERB
ejpam-3070	2	33	differential	differential	ADJ
ejpam-3070	2	34	equations	equation	NOUN
ejpam-3070	2	35	involving	involve	VERB
ejpam-3070	2	36	causal	causal	PROPN
ejpam-3070	2	37	operators	operator	NOUN
ejpam-3070	2	38	ch	ch	PROPN
ejpam-3070	2	39	.	.	PUNCT
ejpam-3070	2	40	appala	appala	PROPN
ejpam-3070	2	41	naidu1,∗	naidu1,∗	PROPN
ejpam-3070	2	42	,	,	PUNCT
ejpam-3070	2	43	d.	d.	PROPN
ejpam-3070	2	44	b.	b.	PROPN
ejpam-3070	2	45	dhaigude2	dhaigude2	PROPN
ejpam-3070	2	46	,	,	PUNCT
ejpam-3070	2	47	j.	j.	PROPN
ejpam-3070	2	48	vasundhara	vasundhara	PROPN
ejpam-3070	2	49	devi1	devi1	PROPN
ejpam-3070	2	50	1	1	NUM
ejpam-3070	2	51	gvp	gvp	NOUN
ejpam-3070	2	52	prof	prof	NOUN
ejpam-3070	2	53	.	.	PUNCT
ejpam-3070	3	1	v.	v.	PROPN
ejpam-3070	3	2	lakshmikantham	lakshmikantham	PROPN
ejpam-3070	3	3	institute	institute	PROPN
ejpam-3070	3	4	for	for	ADP
ejpam-3070	3	5	advanced	advanced	ADJ
ejpam-3070	3	6	studies	study	NOUN
ejpam-3070	3	7	,	,	PUNCT
ejpam-3070	3	8	department	department	NOUN
ejpam-3070	3	9	of	of	ADP
ejpam-3070	3	10	mathematics	mathematic	NOUN
ejpam-3070	3	11	,	,	PUNCT
ejpam-3070	3	12	gvp	gvp	PROPN
ejpam-3070	3	13	college	college	PROPN
ejpam-3070	3	14	of	of	ADP
ejpam-3070	3	15	engineering(a	engineering(a	PROPN
ejpam-3070	3	16	)	)	PUNCT
ejpam-3070	3	17	,	,	PUNCT
ejpam-3070	3	18	andhra	andhra	PROPN
ejpam-3070	3	19	pradesh	pradesh	PROPN
ejpam-3070	3	20	,	,	PUNCT
ejpam-3070	3	21	india	india	PROPN
ejpam-3070	3	22	2	2	NUM
ejpam-3070	3	23	department	department	NOUN
ejpam-3070	3	24	of	of	ADP
ejpam-3070	3	25	mathematics	mathematics	PROPN
ejpam-3070	3	26	,	,	PUNCT
ejpam-3070	3	27	dr	dr	PROPN
ejpam-3070	3	28	.	.	PROPN
ejpam-3070	3	29	babasaheb	babasaheb	PROPN
ejpam-3070	3	30	ambedkar	ambedkar	PROPN
ejpam-3070	3	31	marathwada	marathwada	PROPN
ejpam-3070	3	32	university	university	PROPN
ejpam-3070	3	33	,	,	PUNCT
ejpam-3070	3	34	maharashtra	maharashtra	PROPN
ejpam-3070	3	35	,	,	PUNCT
ejpam-3070	3	36	india	india	PROPN
ejpam-3070	3	37	abstract	abstract	PROPN
ejpam-3070	3	38	.	.	PUNCT
ejpam-3070	4	1	differential	differential	ADJ
ejpam-3070	4	2	equations	equation	NOUN
ejpam-3070	4	3	involving	involve	VERB
ejpam-3070	4	4	causal	causal	ADJ
ejpam-3070	4	5	operators	operator	NOUN
ejpam-3070	4	6	is	be	AUX
ejpam-3070	4	7	an	an	DET
ejpam-3070	4	8	area	area	NOUN
ejpam-3070	4	9	of	of	ADP
ejpam-3070	4	10	research	research	NOUN
ejpam-3070	4	11	that	that	PRON
ejpam-3070	4	12	unifies	unify	VERB
ejpam-3070	4	13	many	many	ADJ
ejpam-3070	4	14	types	type	NOUN
ejpam-3070	4	15	of	of	ADP
ejpam-3070	4	16	mathematical	mathematical	ADJ
ejpam-3070	4	17	models	model	NOUN
ejpam-3070	4	18	such	such	ADJ
ejpam-3070	4	19	as	as	ADP
ejpam-3070	4	20	ordinary	ordinary	ADJ
ejpam-3070	4	21	differential	differential	ADJ
ejpam-3070	4	22	equations	equation	NOUN
ejpam-3070	4	23	,	,	PUNCT
ejpam-3070	4	24	integro	integro	PROPN
ejpam-3070	4	25	differential	differential	NOUN
ejpam-3070	4	26	equations	equation	NOUN
ejpam-3070	4	27	,	,	PUNCT
ejpam-3070	4	28	delay	delay	VERB
ejpam-3070	4	29	differential	differential	ADJ
ejpam-3070	4	30	equations	equation	NOUN
ejpam-3070	4	31	and	and	CCONJ
ejpam-3070	4	32	so	so	ADV
ejpam-3070	4	33	on	on	ADV
ejpam-3070	4	34	.	.	PUNCT
ejpam-3070	5	1	also	also	ADV
ejpam-3070	5	2	,	,	PUNCT
ejpam-3070	5	3	stability	stability	NOUN
ejpam-3070	5	4	in	in	ADP
ejpam-3070	5	5	terms	term	NOUN
ejpam-3070	5	6	of	of	ADP
ejpam-3070	5	7	two	two	NUM
ejpam-3070	5	8	measures	measure	NOUN
ejpam-3070	5	9	is	be	AUX
ejpam-3070	5	10	another	another	DET
ejpam-3070	5	11	concept	concept	NOUN
ejpam-3070	5	12	that	that	PRON
ejpam-3070	5	13	unifies	unify	VERB
ejpam-3070	5	14	various	various	ADJ
ejpam-3070	5	15	types	type	NOUN
ejpam-3070	5	16	of	of	ADP
ejpam-3070	5	17	stability	stability	NOUN
ejpam-3070	5	18	.	.	PUNCT
ejpam-3070	6	1	it	it	PRON
ejpam-3070	6	2	has	have	AUX
ejpam-3070	6	3	been	be	AUX
ejpam-3070	6	4	observed	observe	VERB
ejpam-3070	6	5	that	that	SCONJ
ejpam-3070	6	6	set	set	VERB
ejpam-3070	6	7	differential	differential	ADJ
ejpam-3070	6	8	equations	equation	NOUN
ejpam-3070	6	9	generalizes	generalize	VERB
ejpam-3070	6	10	ordinary	ordinary	ADJ
ejpam-3070	6	11	differential	differential	ADJ
ejpam-3070	6	12	equations	equation	NOUN
ejpam-3070	6	13	(	(	PUNCT
ejpam-3070	6	14	odes	ode	NOUN
ejpam-3070	6	15	)	)	PUNCT
ejpam-3070	6	16	and	and	CCONJ
ejpam-3070	6	17	the	the	DET
ejpam-3070	6	18	study	study	NOUN
ejpam-3070	6	19	of	of	ADP
ejpam-3070	6	20	odes	ode	NOUN
ejpam-3070	6	21	can	can	AUX
ejpam-3070	6	22	be	be	AUX
ejpam-3070	6	23	done	do	VERB
ejpam-3070	6	24	in	in	ADP
ejpam-3070	6	25	semilinear	semilinear	ADJ
ejpam-3070	6	26	metric	metric	ADJ
ejpam-3070	6	27	space	space	NOUN
ejpam-3070	6	28	.	.	PUNCT
ejpam-3070	7	1	in	in	ADP
ejpam-3070	7	2	this	this	DET
ejpam-3070	7	3	paper	paper	NOUN
ejpam-3070	7	4	,	,	PUNCT
ejpam-3070	7	5	combining	combine	VERB
ejpam-3070	7	6	all	all	DET
ejpam-3070	7	7	the	the	DET
ejpam-3070	7	8	fore	fore	NOUN
ejpam-3070	7	9	mentioned	mention	VERB
ejpam-3070	7	10	notions	notion	NOUN
ejpam-3070	7	11	an	an	DET
ejpam-3070	7	12	attempt	attempt	NOUN
ejpam-3070	7	13	is	be	AUX
ejpam-3070	7	14	made	make	VERB
ejpam-3070	7	15	to	to	PART
ejpam-3070	7	16	obtain	obtain	VERB
ejpam-3070	7	17	stability	stability	NOUN
ejpam-3070	7	18	results	result	NOUN
ejpam-3070	7	19	in	in	ADP
ejpam-3070	7	20	terms	term	NOUN
ejpam-3070	7	21	of	of	ADP
ejpam-3070	7	22	two	two	NUM
ejpam-3070	7	23	measures	measure	NOUN
ejpam-3070	7	24	for	for	ADP
ejpam-3070	7	25	set	set	VERB
ejpam-3070	7	26	differential	differential	ADJ
ejpam-3070	7	27	equations	equation	NOUN
ejpam-3070	7	28	involving	involve	VERB
ejpam-3070	7	29	causal	causal	ADJ
ejpam-3070	7	30	operators	operator	NOUN
ejpam-3070	7	31	.	.	PUNCT
ejpam-3070	8	1	2010	2010	NUM
ejpam-3070	8	2	mathematics	mathematic	NOUN
ejpam-3070	8	3	subject	subject	NOUN
ejpam-3070	8	4	classifications	classification	NOUN
ejpam-3070	8	5	:	:	PUNCT
ejpam-3070	8	6	34d20	34d20	NUM
ejpam-3070	8	7	,	,	PUNCT
ejpam-3070	8	8	34g20	34g20	NUM
ejpam-3070	8	9	key	key	ADJ
ejpam-3070	8	10	words	word	NOUN
ejpam-3070	8	11	and	and	CCONJ
ejpam-3070	8	12	phrases	phrase	NOUN
ejpam-3070	8	13	:	:	PUNCT
ejpam-3070	8	14	hukuhara	hukuhara	ADV
ejpam-3070	8	15	difference	difference	NOUN
ejpam-3070	8	16	,	,	PUNCT
ejpam-3070	8	17	(	(	PUNCT
ejpam-3070	8	18	h0	h0	PROPN
ejpam-3070	8	19	,	,	PUNCT
ejpam-3070	8	20	h)-equi	h)-equi	NOUN
ejpam-3070	8	21	stable	stable	ADJ
ejpam-3070	8	22	,	,	PUNCT
ejpam-3070	8	23	(	(	PUNCT
ejpam-3070	8	24	h0	h0	PROPN
ejpam-3070	8	25	,	,	PUNCT
ejpam-3070	8	26	h)-uniformly	h)-uniformly	ADV
ejpam-3070	8	27	stable	stable	ADJ
ejpam-3070	8	28	,	,	PUNCT
ejpam-3070	8	29	(	(	PUNCT
ejpam-3070	8	30	h0	h0	PROPN
ejpam-3070	8	31	,	,	PUNCT
ejpam-3070	8	32	h)-equi	h)-equi	NOUN
ejpam-3070	8	33	attractive	attractive	ADJ
ejpam-3070	8	34	,	,	PUNCT
ejpam-3070	8	35	(	(	PUNCT
ejpam-3070	8	36	h0	h0	PROPN
ejpam-3070	8	37	,	,	PUNCT
ejpam-3070	8	38	h)-equi	h)-equi	PUNCT
ejpam-3070	8	39	asymptotically	asymptotically	ADV
ejpam-3070	8	40	stable	stable	ADJ
ejpam-3070	8	41	,	,	PUNCT
ejpam-3070	8	42	(	(	PUNCT
ejpam-3070	8	43	h0	h0	PROPN
ejpam-3070	8	44	,	,	PUNCT
ejpam-3070	8	45	h)-uniformly	h)-uniformly	ADV
ejpam-3070	8	46	asymptotically	asymptotically	ADV
ejpam-3070	8	47	stable	stable	ADJ
ejpam-3070	8	48	1	1	NUM
ejpam-3070	8	49	.	.	PUNCT
ejpam-3070	8	50	introduction	introduction	NOUN
ejpam-3070	8	51	during	during	ADP
ejpam-3070	8	52	the	the	DET
ejpam-3070	8	53	past	past	ADJ
ejpam-3070	8	54	couple	couple	NOUN
ejpam-3070	8	55	of	of	ADP
ejpam-3070	8	56	decades	decade	NOUN
ejpam-3070	8	57	the	the	DET
ejpam-3070	8	58	theory	theory	NOUN
ejpam-3070	8	59	of	of	ADP
ejpam-3070	8	60	set	set	VERB
ejpam-3070	8	61	differential	differential	ADJ
ejpam-3070	8	62	equations	equation	NOUN
ejpam-3070	8	63	attracted	attract	VERB
ejpam-3070	8	64	the	the	DET
ejpam-3070	8	65	attention	attention	NOUN
ejpam-3070	8	66	of	of	ADP
ejpam-3070	8	67	many	many	ADJ
ejpam-3070	8	68	researchers	researcher	NOUN
ejpam-3070	8	69	and	and	CCONJ
ejpam-3070	8	70	much	much	ADJ
ejpam-3070	8	71	of	of	ADP
ejpam-3070	8	72	the	the	DET
ejpam-3070	8	73	basic	basic	ADJ
ejpam-3070	8	74	theory	theory	NOUN
ejpam-3070	8	75	is	be	AUX
ejpam-3070	8	76	given	give	VERB
ejpam-3070	8	77	in	in	ADP
ejpam-3070	8	78	[	[	PUNCT
ejpam-3070	8	79	9	9	NUM
ejpam-3070	8	80	]	]	PUNCT
ejpam-3070	8	81	.	.	PUNCT
ejpam-3070	9	1	some	some	PRON
ejpam-3070	9	2	of	of	ADP
ejpam-3070	9	3	the	the	DET
ejpam-3070	9	4	papers	paper	NOUN
ejpam-3070	9	5	dealing	deal	VERB
ejpam-3070	9	6	with	with	ADP
ejpam-3070	9	7	stability	stability	NOUN
ejpam-3070	9	8	of	of	ADP
ejpam-3070	9	9	set	set	VERB
ejpam-3070	9	10	differential	differential	ADJ
ejpam-3070	9	11	equations	equation	NOUN
ejpam-3070	9	12	are	be	AUX
ejpam-3070	9	13	[	[	PUNCT
ejpam-3070	9	14	7	7	NUM
ejpam-3070	9	15	,	,	PUNCT
ejpam-3070	9	16	5	5	NUM
ejpam-3070	9	17	]	]	PUNCT
ejpam-3070	9	18	.	.	PUNCT
ejpam-3070	10	1	the	the	DET
ejpam-3070	10	2	reason	reason	NOUN
ejpam-3070	10	3	for	for	ADP
ejpam-3070	10	4	the	the	DET
ejpam-3070	10	5	continued	continue	VERB
ejpam-3070	10	6	interest	interest	NOUN
ejpam-3070	10	7	in	in	ADP
ejpam-3070	10	8	this	this	DET
ejpam-3070	10	9	area	area	NOUN
ejpam-3070	10	10	of	of	ADP
ejpam-3070	10	11	research	research	NOUN
ejpam-3070	10	12	is	be	AUX
ejpam-3070	10	13	that	that	SCONJ
ejpam-3070	10	14	studying	study	VERB
ejpam-3070	10	15	differential	differential	ADJ
ejpam-3070	10	16	equations	equation	NOUN
ejpam-3070	10	17	in	in	ADP
ejpam-3070	10	18	metric	metric	ADJ
ejpam-3070	10	19	space	space	NOUN
ejpam-3070	10	20	is	be	AUX
ejpam-3070	10	21	gaining	gain	VERB
ejpam-3070	10	22	attention	attention	NOUN
ejpam-3070	10	23	and	and	CCONJ
ejpam-3070	10	24	also	also	ADV
ejpam-3070	10	25	for	for	ADP
ejpam-3070	10	26	the	the	DET
ejpam-3070	10	27	following	follow	VERB
ejpam-3070	10	28	reasons	reason	NOUN
ejpam-3070	10	29	:	:	PUNCT
ejpam-3070	10	30	the	the	DET
ejpam-3070	10	31	base	base	NOUN
ejpam-3070	10	32	space	space	NOUN
ejpam-3070	10	33	kc(rn	kc(rn	PROPN
ejpam-3070	10	34	)	)	PUNCT
ejpam-3070	10	35	,	,	PUNCT
ejpam-3070	10	36	consisting	consist	VERB
ejpam-3070	10	37	of	of	ADP
ejpam-3070	10	38	all	all	DET
ejpam-3070	10	39	compact	compact	ADJ
ejpam-3070	10	40	convex	convex	NOUN
ejpam-3070	10	41	subsets	subset	NOUN
ejpam-3070	10	42	of	of	ADP
ejpam-3070	10	43	rn	rn	PROPN
ejpam-3070	10	44	endowed	endow	VERB
ejpam-3070	10	45	with	with	ADP
ejpam-3070	10	46	hausdorff	hausdorff	PROPN
ejpam-3070	10	47	metric	metric	PROPN
ejpam-3070	10	48	,	,	PUNCT
ejpam-3070	10	49	is	be	AUX
ejpam-3070	10	50	a	a	DET
ejpam-3070	10	51	semi	semi	ADJ
ejpam-3070	10	52	linear	linear	ADJ
ejpam-3070	10	53	metric	metric	ADJ
ejpam-3070	10	54	space	space	NOUN
ejpam-3070	10	55	.	.	PUNCT
ejpam-3070	11	1	if	if	SCONJ
ejpam-3070	11	2	the	the	DET
ejpam-3070	11	3	hukuhara	hukuhara	ADJ
ejpam-3070	11	4	derivative	derivative	NOUN
ejpam-3070	11	5	and	and	CCONJ
ejpam-3070	11	6	the	the	DET
ejpam-3070	11	7	hukuhara	hukuhara	ADJ
ejpam-3070	11	8	integral	integral	ADJ
ejpam-3070	11	9	are	be	AUX
ejpam-3070	11	10	restricted	restrict	VERB
ejpam-3070	11	11	to	to	ADP
ejpam-3070	11	12	r	r	NOUN
ejpam-3070	11	13	they	they	PRON
ejpam-3070	11	14	become	become	VERB
ejpam-3070	11	15	the	the	DET
ejpam-3070	11	16	conventional	conventional	ADJ
ejpam-3070	11	17	derivative	derivative	ADJ
ejpam-3070	11	18	and	and	CCONJ
ejpam-3070	11	19	integral	integral	ADJ
ejpam-3070	11	20	and	and	CCONJ
ejpam-3070	11	21	one	one	PRON
ejpam-3070	11	22	can	can	AUX
ejpam-3070	11	23	observe	observe	VERB
ejpam-3070	11	24	that	that	SCONJ
ejpam-3070	11	25	the	the	DET
ejpam-3070	11	26	theory	theory	NOUN
ejpam-3070	11	27	of	of	ADP
ejpam-3070	11	28	ordinary	ordinary	ADJ
ejpam-3070	11	29	differential	differential	ADJ
ejpam-3070	11	30	equations	equation	NOUN
ejpam-3070	11	31	(	(	PUNCT
ejpam-3070	11	32	ode	ode	PROPN
ejpam-3070	11	33	’s	’s	PART
ejpam-3070	11	34	)	)	PUNCT
ejpam-3070	11	35	can	can	AUX
ejpam-3070	11	36	be	be	AUX
ejpam-3070	11	37	developed	develop	VERB
ejpam-3070	11	38	in	in	ADP
ejpam-3070	11	39	a	a	DET
ejpam-3070	11	40	semi	semi	ADJ
ejpam-3070	11	41	linear	linear	ADJ
ejpam-3070	11	42	metric	metric	ADJ
ejpam-3070	11	43	space	space	NOUN
ejpam-3070	11	44	.	.	PUNCT
ejpam-3070	12	1	similarly	similarly	ADV
ejpam-3070	12	2	when	when	SCONJ
ejpam-3070	12	3	we	we	PRON
ejpam-3070	12	4	restrict	restrict	VERB
ejpam-3070	12	5	to	to	ADP
ejpam-3070	12	6	rn	rn	PROPN
ejpam-3070	12	7	,	,	PUNCT
ejpam-3070	12	8	then	then	ADV
ejpam-3070	12	9	the	the	DET
ejpam-3070	12	10	theory	theory	NOUN
ejpam-3070	12	11	of	of	ADP
ejpam-3070	12	12	vector	vector	NOUN
ejpam-3070	12	13	differential	differential	NOUN
ejpam-3070	12	14	equations	equation	NOUN
ejpam-3070	12	15	can	can	AUX
ejpam-3070	12	16	∗corresponding	∗corresponde	VERB
ejpam-3070	12	17	author	author	NOUN
ejpam-3070	12	18	.	.	PUNCT
ejpam-3070	13	1	email	email	NOUN
ejpam-3070	13	2	addresses	address	NOUN
ejpam-3070	13	3	:	:	PUNCT
ejpam-3070	13	4	appalanaidu7@gmail.com	appalanaidu7@gmail.com	X
ejpam-3070	13	5	(	(	PUNCT
ejpam-3070	13	6	ch.a.naidu	ch.a.naidu	NOUN
ejpam-3070	13	7	)	)	PUNCT
ejpam-3070	13	8	,	,	PUNCT
ejpam-3070	13	9	dnyanraja@gmail.com	dnyanraja@gmail.com	X
ejpam-3070	13	10	(	(	PUNCT
ejpam-3070	13	11	d.b	d.b	PROPN
ejpam-3070	13	12	.	.	NOUN
ejpam-3070	13	13	dhaigude	dhaigude	NOUN
ejpam-3070	13	14	)	)	PUNCT
ejpam-3070	13	15	,	,	PUNCT
ejpam-3070	13	16	jvdevi@gmail.com	jvdevi@gmail.com	X
ejpam-3070	13	17	(	(	PUNCT
ejpam-3070	13	18	j.	j.	PROPN
ejpam-3070	13	19	vasundhara	vasundhara	PROPN
ejpam-3070	13	20	devi	devi	PROPN
ejpam-3070	13	21	)	)	PUNCT
ejpam-3070	13	22	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3070	14	1	645	645	NUM
ejpam-3070	14	2	c	c	X
ejpam-3070	14	3	©	©	PROPN
ejpam-3070	14	4	2017	2017	NUM
ejpam-3070	14	5	ejpam	ejpam	NOUN
ejpam-3070	14	6	all	all	DET
ejpam-3070	14	7	rights	right	NOUN
ejpam-3070	14	8	reserved	reserve	VERB
ejpam-3070	14	9	.	.	PUNCT
ejpam-3070	15	1	ch	ch	NOUN
ejpam-3070	15	2	.	.	PUNCT
ejpam-3070	15	3	a.	a.	PROPN
ejpam-3070	15	4	naidu,̧	naidu,̧	PROPN
ejpam-3070	15	5	d.	d.	PROPN
ejpam-3070	15	6	b.	b.	PROPN
ejpam-3070	15	7	dhaigude	dhaigude	PROPN
ejpam-3070	15	8	,	,	PUNCT
ejpam-3070	15	9	j.	j.	PROPN
ejpam-3070	15	10	v.	v.	PROPN
ejpam-3070	15	11	devi	devi	PROPN
ejpam-3070	15	12	/	/	SYM
ejpam-3070	15	13	eur	eur	PROPN
ejpam-3070	15	14	.	.	PUNCT
ejpam-3070	16	1	j.	j.	PROPN
ejpam-3070	16	2	pure	pure	PROPN
ejpam-3070	16	3	appl	appl	PROPN
ejpam-3070	16	4	.	.	PROPN
ejpam-3070	16	5	math	math	PROPN
ejpam-3070	16	6	,	,	PUNCT
ejpam-3070	16	7	10	10	NUM
ejpam-3070	16	8	(	(	PUNCT
ejpam-3070	16	9	4	4	NUM
ejpam-3070	16	10	)	)	PUNCT
ejpam-3070	16	11	(	(	PUNCT
ejpam-3070	16	12	2017	2017	NUM
ejpam-3070	16	13	)	)	PUNCT
ejpam-3070	16	14	,	,	PUNCT
ejpam-3070	16	15	645	645	NUM
ejpam-3070	16	16	-	-	SYM
ejpam-3070	16	17	654	654	NUM
ejpam-3070	16	18	646	646	NUM
ejpam-3070	16	19	be	be	AUX
ejpam-3070	16	20	studied	study	VERB
ejpam-3070	16	21	in	in	ADP
ejpam-3070	16	22	a	a	DET
ejpam-3070	16	23	semi	semi	ADJ
ejpam-3070	16	24	linear	linear	ADJ
ejpam-3070	16	25	space	space	NOUN
ejpam-3070	16	26	.	.	PUNCT
ejpam-3070	17	1	further	far	ADV
ejpam-3070	17	2	,	,	PUNCT
ejpam-3070	17	3	it	it	PRON
ejpam-3070	17	4	is	be	AUX
ejpam-3070	17	5	useful	useful	ADJ
ejpam-3070	17	6	in	in	ADP
ejpam-3070	17	7	studying	study	VERB
ejpam-3070	17	8	multi	multi	NOUN
ejpam-3070	17	9	valued	value	VERB
ejpam-3070	17	10	inclusions	inclusion	NOUN
ejpam-3070	17	11	and	and	CCONJ
ejpam-3070	17	12	also	also	ADV
ejpam-3070	17	13	is	be	AUX
ejpam-3070	17	14	related	relate	VERB
ejpam-3070	17	15	to	to	ADP
ejpam-3070	17	16	fuzzy	fuzzy	ADJ
ejpam-3070	17	17	differential	differential	ADJ
ejpam-3070	17	18	equations	equation	NOUN
ejpam-3070	17	19	.	.	PUNCT
ejpam-3070	18	1	also	also	ADV
ejpam-3070	18	2	,	,	PUNCT
ejpam-3070	18	3	one	one	PRON
ejpam-3070	18	4	can	can	AUX
ejpam-3070	18	5	observe	observe	VERB
ejpam-3070	18	6	that	that	SCONJ
ejpam-3070	18	7	the	the	DET
ejpam-3070	18	8	solution	solution	NOUN
ejpam-3070	18	9	u(t	u(t	NOUN
ejpam-3070	18	10	)	)	PUNCT
ejpam-3070	18	11	of	of	ADP
ejpam-3070	18	12	the	the	DET
ejpam-3070	18	13	set	set	VERB
ejpam-3070	18	14	differential	differential	NOUN
ejpam-3070	18	15	equation	equation	NOUN
ejpam-3070	18	16	has	have	VERB
ejpam-3070	18	17	the	the	DET
ejpam-3070	18	18	interesting	interesting	ADJ
ejpam-3070	18	19	nature	nature	NOUN
ejpam-3070	18	20	that	that	PRON
ejpam-3070	18	21	as	as	ADP
ejpam-3070	18	22	time	time	NOUN
ejpam-3070	18	23	increases	increase	VERB
ejpam-3070	18	24	the	the	DET
ejpam-3070	18	25	diameter	diameter	NOUN
ejpam-3070	18	26	of	of	ADP
ejpam-3070	18	27	u(t	u(t	NOUN
ejpam-3070	18	28	)	)	PUNCT
ejpam-3070	18	29	is	be	AUX
ejpam-3070	18	30	non	non	ADJ
ejpam-3070	18	31	decreasing	decrease	VERB
ejpam-3070	18	32	.	.	PUNCT
ejpam-3070	19	1	it	it	PRON
ejpam-3070	19	2	has	have	AUX
ejpam-3070	19	3	been	be	AUX
ejpam-3070	19	4	observed	observe	VERB
ejpam-3070	19	5	that	that	SCONJ
ejpam-3070	19	6	this	this	PRON
ejpam-3070	19	7	is	be	AUX
ejpam-3070	19	8	due	due	ADJ
ejpam-3070	19	9	to	to	ADP
ejpam-3070	19	10	the	the	DET
ejpam-3070	19	11	fact	fact	NOUN
ejpam-3070	19	12	that	that	SCONJ
ejpam-3070	19	13	,	,	PUNCT
ejpam-3070	19	14	in	in	ADP
ejpam-3070	19	15	the	the	DET
ejpam-3070	19	16	generation	generation	NOUN
ejpam-3070	19	17	of	of	ADP
ejpam-3070	19	18	the	the	DET
ejpam-3070	19	19	set	set	VERB
ejpam-3070	19	20	differential	differential	ADJ
ejpam-3070	19	21	equation	equation	NOUN
ejpam-3070	19	22	(	(	PUNCT
ejpam-3070	19	23	sde	sde	PROPN
ejpam-3070	19	24	)	)	PUNCT
ejpam-3070	19	25	from	from	ADP
ejpam-3070	19	26	an	an	DET
ejpam-3070	19	27	ode	ode	ADJ
ejpam-3070	19	28	,	,	PUNCT
ejpam-3070	19	29	certain	certain	ADJ
ejpam-3070	19	30	undesirable	undesirable	ADJ
ejpam-3070	19	31	elements	element	NOUN
ejpam-3070	19	32	may	may	AUX
ejpam-3070	19	33	enter	enter	VERB
ejpam-3070	19	34	the	the	DET
ejpam-3070	19	35	solution	solution	NOUN
ejpam-3070	19	36	u(t	u(t	NOUN
ejpam-3070	19	37	)	)	PUNCT
ejpam-3070	19	38	and	and	CCONJ
ejpam-3070	19	39	hence	hence	ADV
ejpam-3070	19	40	the	the	DET
ejpam-3070	19	41	norm	norm	NOUN
ejpam-3070	19	42	used	use	VERB
ejpam-3070	19	43	may	may	AUX
ejpam-3070	19	44	not	not	PART
ejpam-3070	19	45	be	be	AUX
ejpam-3070	19	46	suitable	suitable	ADJ
ejpam-3070	19	47	to	to	PART
ejpam-3070	19	48	develop	develop	VERB
ejpam-3070	19	49	stability	stability	NOUN
ejpam-3070	19	50	without	without	ADP
ejpam-3070	19	51	some	some	DET
ejpam-3070	19	52	adjustment	adjustment	NOUN
ejpam-3070	19	53	.	.	PUNCT
ejpam-3070	20	1	therefore	therefore	ADV
ejpam-3070	20	2	while	while	SCONJ
ejpam-3070	20	3	studying	study	VERB
ejpam-3070	20	4	the	the	DET
ejpam-3070	20	5	stability	stability	NOUN
ejpam-3070	20	6	theory	theory	NOUN
ejpam-3070	20	7	for	for	ADP
ejpam-3070	20	8	sde	sde	PROPN
ejpam-3070	20	9	’s	’s	PART
ejpam-3070	20	10	the	the	DET
ejpam-3070	20	11	concept	concept	NOUN
ejpam-3070	20	12	of	of	ADP
ejpam-3070	20	13	hukuhara	hukuhara	ADJ
ejpam-3070	20	14	difference	difference	NOUN
ejpam-3070	20	15	in	in	ADP
ejpam-3070	20	16	the	the	DET
ejpam-3070	20	17	initial	initial	ADJ
ejpam-3070	20	18	values	value	NOUN
ejpam-3070	20	19	was	be	AUX
ejpam-3070	20	20	introduced	introduce	VERB
ejpam-3070	20	21	in	in	ADP
ejpam-3070	20	22	[	[	PUNCT
ejpam-3070	20	23	11	11	NUM
ejpam-3070	20	24	]	]	PUNCT
ejpam-3070	20	25	so	so	SCONJ
ejpam-3070	20	26	as	as	SCONJ
ejpam-3070	20	27	to	to	PART
ejpam-3070	20	28	see	see	VERB
ejpam-3070	20	29	that	that	SCONJ
ejpam-3070	20	30	the	the	DET
ejpam-3070	20	31	properties	property	NOUN
ejpam-3070	20	32	of	of	ADP
ejpam-3070	20	33	the	the	DET
ejpam-3070	20	34	solutions	solution	NOUN
ejpam-3070	20	35	of	of	ADP
ejpam-3070	20	36	the	the	DET
ejpam-3070	20	37	ode	ode	PROPN
ejpam-3070	20	38	’s	’s	PART
ejpam-3070	20	39	are	be	AUX
ejpam-3070	20	40	preserved	preserve	VERB
ejpam-3070	20	41	to	to	ADP
ejpam-3070	20	42	a	a	DET
ejpam-3070	20	43	certain	certain	ADJ
ejpam-3070	20	44	extent	extent	NOUN
ejpam-3070	20	45	in	in	ADP
ejpam-3070	20	46	the	the	DET
ejpam-3070	20	47	sde	sde	PROPN
ejpam-3070	20	48	.	.	PUNCT
ejpam-3070	21	1	for	for	ADP
ejpam-3070	21	2	a	a	DET
ejpam-3070	21	3	detailed	detailed	ADJ
ejpam-3070	21	4	description	description	NOUN
ejpam-3070	21	5	through	through	ADP
ejpam-3070	21	6	an	an	DET
ejpam-3070	21	7	example	example	NOUN
ejpam-3070	21	8	see	see	VERB
ejpam-3070	21	9	[	[	PUNCT
ejpam-3070	21	10	11	11	NUM
ejpam-3070	21	11	]	]	PUNCT
ejpam-3070	21	12	.	.	PUNCT
ejpam-3070	22	1	the	the	DET
ejpam-3070	22	2	stability	stability	NOUN
ejpam-3070	22	3	theory	theory	NOUN
ejpam-3070	22	4	via	via	ADP
ejpam-3070	22	5	the	the	DET
ejpam-3070	22	6	lyapunov	lyapunov	ADJ
ejpam-3070	22	7	function	function	NOUN
ejpam-3070	22	8	has	have	AUX
ejpam-3070	22	9	been	be	AUX
ejpam-3070	22	10	extensively	extensively	ADV
ejpam-3070	22	11	studied	study	VERB
ejpam-3070	22	12	and	and	CCONJ
ejpam-3070	22	13	is	be	AUX
ejpam-3070	22	14	applied	apply	VERB
ejpam-3070	22	15	in	in	ADP
ejpam-3070	22	16	various	various	ADJ
ejpam-3070	22	17	models	model	NOUN
ejpam-3070	22	18	due	due	ADP
ejpam-3070	22	19	to	to	ADP
ejpam-3070	22	20	the	the	DET
ejpam-3070	22	21	fact	fact	NOUN
ejpam-3070	22	22	that	that	SCONJ
ejpam-3070	22	23	the	the	DET
ejpam-3070	22	24	lyapunov	lyapunov	ADJ
ejpam-3070	22	25	function	function	NOUN
ejpam-3070	22	26	helps	help	VERB
ejpam-3070	22	27	to	to	PART
ejpam-3070	22	28	study	study	VERB
ejpam-3070	22	29	the	the	DET
ejpam-3070	22	30	qualitative	qualitative	ADJ
ejpam-3070	22	31	behavior	behavior	NOUN
ejpam-3070	22	32	of	of	ADP
ejpam-3070	22	33	the	the	DET
ejpam-3070	22	34	solution	solution	NOUN
ejpam-3070	22	35	without	without	ADP
ejpam-3070	22	36	knowing	know	VERB
ejpam-3070	22	37	the	the	DET
ejpam-3070	22	38	solution	solution	NOUN
ejpam-3070	22	39	.	.	PUNCT
ejpam-3070	23	1	of	of	ADP
ejpam-3070	23	2	late	late	ADV
ejpam-3070	23	3	it	it	PRON
ejpam-3070	23	4	has	have	AUX
ejpam-3070	23	5	been	be	AUX
ejpam-3070	23	6	observed	observe	VERB
ejpam-3070	23	7	that	that	SCONJ
ejpam-3070	23	8	the	the	DET
ejpam-3070	23	9	lyapunov	lyapunov	ADJ
ejpam-3070	23	10	function	function	NOUN
ejpam-3070	23	11	can	can	AUX
ejpam-3070	23	12	be	be	AUX
ejpam-3070	23	13	utilized	utilize	VERB
ejpam-3070	23	14	to	to	PART
ejpam-3070	23	15	construct	construct	VERB
ejpam-3070	23	16	simpler	simple	ADJ
ejpam-3070	23	17	scalar	scalar	ADJ
ejpam-3070	23	18	differential	differential	ADJ
ejpam-3070	23	19	equations	equation	NOUN
ejpam-3070	23	20	to	to	PART
ejpam-3070	23	21	study	study	VERB
ejpam-3070	23	22	complex	complex	ADJ
ejpam-3070	23	23	systems	system	NOUN
ejpam-3070	23	24	.	.	PUNCT
ejpam-3070	24	1	also	also	ADV
ejpam-3070	24	2	,	,	PUNCT
ejpam-3070	24	3	lyapunov	lyapunov	NOUN
ejpam-3070	24	4	function	function	NOUN
ejpam-3070	24	5	can	can	AUX
ejpam-3070	24	6	be	be	AUX
ejpam-3070	24	7	used	use	VERB
ejpam-3070	24	8	as	as	ADP
ejpam-3070	24	9	a	a	DET
ejpam-3070	24	10	generalized	generalized	ADJ
ejpam-3070	24	11	distance	distance	NOUN
ejpam-3070	24	12	and	and	CCONJ
ejpam-3070	24	13	can	can	AUX
ejpam-3070	24	14	be	be	AUX
ejpam-3070	24	15	utilized	utilize	VERB
ejpam-3070	24	16	to	to	PART
ejpam-3070	24	17	study	study	VERB
ejpam-3070	24	18	the	the	DET
ejpam-3070	24	19	qualitative	qualitative	ADJ
ejpam-3070	24	20	and	and	CCONJ
ejpam-3070	24	21	quantitative	quantitative	ADJ
ejpam-3070	24	22	behavior	behavior	NOUN
ejpam-3070	24	23	of	of	ADP
ejpam-3070	24	24	solutions	solution	NOUN
ejpam-3070	24	25	of	of	ADP
ejpam-3070	24	26	differential	differential	ADJ
ejpam-3070	24	27	equations	equation	NOUN
ejpam-3070	24	28	.	.	PUNCT
ejpam-3070	25	1	owing	owe	VERB
ejpam-3070	25	2	to	to	ADP
ejpam-3070	25	3	the	the	DET
ejpam-3070	25	4	developments	development	NOUN
ejpam-3070	25	5	in	in	ADP
ejpam-3070	25	6	the	the	DET
ejpam-3070	25	7	study	study	NOUN
ejpam-3070	25	8	of	of	ADP
ejpam-3070	25	9	many	many	ADJ
ejpam-3070	25	10	physical	physical	ADJ
ejpam-3070	25	11	phenomena	phenomenon	NOUN
ejpam-3070	25	12	,	,	PUNCT
ejpam-3070	25	13	new	new	ADJ
ejpam-3070	25	14	concepts	concept	NOUN
ejpam-3070	25	15	of	of	ADP
ejpam-3070	25	16	stability	stability	NOUN
ejpam-3070	25	17	such	such	ADJ
ejpam-3070	25	18	as	as	ADP
ejpam-3070	25	19	partial	partial	ADJ
ejpam-3070	25	20	stability	stability	NOUN
ejpam-3070	25	21	,	,	PUNCT
ejpam-3070	25	22	practical	practical	ADJ
ejpam-3070	25	23	stability	stability	NOUN
ejpam-3070	25	24	,	,	PUNCT
ejpam-3070	25	25	eventual	eventual	ADJ
ejpam-3070	25	26	stability	stability	NOUN
ejpam-3070	25	27	have	have	AUX
ejpam-3070	25	28	been	be	AUX
ejpam-3070	25	29	introduced	introduce	VERB
ejpam-3070	25	30	.	.	PUNCT
ejpam-3070	26	1	all	all	DET
ejpam-3070	26	2	these	these	DET
ejpam-3070	26	3	developments	development	NOUN
ejpam-3070	26	4	posed	pose	VERB
ejpam-3070	26	5	the	the	DET
ejpam-3070	26	6	question	question	NOUN
ejpam-3070	26	7	of	of	ADP
ejpam-3070	26	8	unifying	unify	VERB
ejpam-3070	26	9	all	all	DET
ejpam-3070	26	10	the	the	DET
ejpam-3070	26	11	definitions	definition	NOUN
ejpam-3070	26	12	under	under	ADP
ejpam-3070	26	13	one	one	NUM
ejpam-3070	26	14	set	set	VERB
ejpam-3070	26	15	up	up	ADP
ejpam-3070	26	16	.	.	PUNCT
ejpam-3070	27	1	this	this	DET
ejpam-3070	27	2	lead	lead	NOUN
ejpam-3070	27	3	to	to	ADP
ejpam-3070	27	4	the	the	DET
ejpam-3070	27	5	introduction	introduction	NOUN
ejpam-3070	27	6	of	of	ADP
ejpam-3070	27	7	stability	stability	NOUN
ejpam-3070	27	8	theory	theory	NOUN
ejpam-3070	27	9	in	in	ADP
ejpam-3070	27	10	terms	term	NOUN
ejpam-3070	27	11	of	of	ADP
ejpam-3070	27	12	two	two	NUM
ejpam-3070	27	13	measures	measure	NOUN
ejpam-3070	27	14	[	[	PUNCT
ejpam-3070	27	15	10	10	NUM
ejpam-3070	27	16	]	]	PUNCT
ejpam-3070	27	17	.	.	PUNCT
ejpam-3070	28	1	the	the	DET
ejpam-3070	28	2	notion	notion	NOUN
ejpam-3070	28	3	of	of	ADP
ejpam-3070	28	4	causal	causal	ADJ
ejpam-3070	28	5	operators	operator	NOUN
ejpam-3070	28	6	has	have	AUX
ejpam-3070	28	7	been	be	AUX
ejpam-3070	28	8	introduced	introduce	VERB
ejpam-3070	28	9	by	by	ADP
ejpam-3070	28	10	tonneli	tonneli	NOUN
ejpam-3070	28	11	[	[	PUNCT
ejpam-3070	28	12	1	1	NUM
ejpam-3070	28	13	]	]	PUNCT
ejpam-3070	28	14	.	.	PUNCT
ejpam-3070	29	1	a	a	DET
ejpam-3070	29	2	causal	causal	ADJ
ejpam-3070	29	3	operator	operator	NOUN
ejpam-3070	29	4	or	or	CCONJ
ejpam-3070	29	5	a	a	DET
ejpam-3070	29	6	non	non	X
ejpam-3070	29	7	anticipative	anticipative	NOUN
ejpam-3070	29	8	operator	operator	NOUN
ejpam-3070	29	9	is	be	AUX
ejpam-3070	29	10	an	an	DET
ejpam-3070	29	11	operator	operator	NOUN
ejpam-3070	29	12	whose	whose	DET
ejpam-3070	29	13	prior	prior	ADJ
ejpam-3070	29	14	information	information	NOUN
ejpam-3070	29	15	or	or	CCONJ
ejpam-3070	29	16	memory	memory	NOUN
ejpam-3070	29	17	is	be	AUX
ejpam-3070	29	18	known	know	VERB
ejpam-3070	29	19	till	till	SCONJ
ejpam-3070	29	20	the	the	DET
ejpam-3070	29	21	present	present	ADJ
ejpam-3070	29	22	time	time	NOUN
ejpam-3070	29	23	’	'	PUNCT
ejpam-3070	29	24	t	t	PROPN
ejpam-3070	29	25	’	'	PUNCT
ejpam-3070	29	26	.	.	PUNCT
ejpam-3070	30	1	ordinary	ordinary	ADJ
ejpam-3070	30	2	differential	differential	ADJ
ejpam-3070	30	3	equations	equation	NOUN
ejpam-3070	30	4	,	,	PUNCT
ejpam-3070	30	5	delay	delay	VERB
ejpam-3070	30	6	differential	differential	ADJ
ejpam-3070	30	7	equations	equation	NOUN
ejpam-3070	30	8	,	,	PUNCT
ejpam-3070	30	9	integro	integro	PROPN
ejpam-3070	30	10	differential	differential	NOUN
ejpam-3070	30	11	equations	equation	NOUN
ejpam-3070	30	12	,	,	PUNCT
ejpam-3070	30	13	impulsive	impulsive	ADJ
ejpam-3070	30	14	differential	differential	ADJ
ejpam-3070	30	15	equations	equation	NOUN
ejpam-3070	30	16	etc	etc	X
ejpam-3070	30	17	.	.	X
ejpam-3070	30	18	are	be	AUX
ejpam-3070	30	19	some	some	PRON
ejpam-3070	30	20	of	of	ADP
ejpam-3070	30	21	the	the	DET
ejpam-3070	30	22	differential	differential	ADJ
ejpam-3070	30	23	equations	equation	NOUN
ejpam-3070	30	24	involving	involve	VERB
ejpam-3070	30	25	causal	causal	ADJ
ejpam-3070	30	26	operators	operator	NOUN
ejpam-3070	30	27	.	.	PUNCT
ejpam-3070	31	1	the	the	DET
ejpam-3070	31	2	unifying	unifying	ADJ
ejpam-3070	31	3	character	character	NOUN
ejpam-3070	31	4	of	of	ADP
ejpam-3070	31	5	the	the	DET
ejpam-3070	31	6	causal	causal	ADJ
ejpam-3070	31	7	operator	operator	NOUN
ejpam-3070	31	8	makes	make	VERB
ejpam-3070	31	9	it	it	PRON
ejpam-3070	31	10	an	an	DET
ejpam-3070	31	11	interesting	interesting	ADJ
ejpam-3070	31	12	topic	topic	NOUN
ejpam-3070	31	13	of	of	ADP
ejpam-3070	31	14	study	study	NOUN
ejpam-3070	31	15	.	.	PUNCT
ejpam-3070	32	1	in	in	ADP
ejpam-3070	32	2	[	[	PUNCT
ejpam-3070	32	3	2	2	NUM
ejpam-3070	32	4	,	,	PUNCT
ejpam-3070	32	5	3	3	NUM
ejpam-3070	32	6	,	,	PUNCT
ejpam-3070	32	7	4	4	NUM
ejpam-3070	32	8	]	]	PUNCT
ejpam-3070	32	9	the	the	DET
ejpam-3070	32	10	mathematical	mathematical	ADJ
ejpam-3070	32	11	model	model	NOUN
ejpam-3070	32	12	of	of	ADP
ejpam-3070	32	13	sde	sde	PROPN
ejpam-3070	32	14	involving	involve	VERB
ejpam-3070	32	15	causal	causal	ADJ
ejpam-3070	32	16	operator	operator	NOUN
ejpam-3070	32	17	with	with	ADP
ejpam-3070	32	18	memory	memory	NOUN
ejpam-3070	32	19	was	be	AUX
ejpam-3070	32	20	introduced	introduce	VERB
ejpam-3070	32	21	.	.	PUNCT
ejpam-3070	33	1	the	the	DET
ejpam-3070	33	2	existence	existence	NOUN
ejpam-3070	33	3	and	and	CCONJ
ejpam-3070	33	4	uniqueness	uniqueness	NOUN
ejpam-3070	33	5	results	result	NOUN
ejpam-3070	33	6	,	,	PUNCT
ejpam-3070	33	7	comparison	comparison	NOUN
ejpam-3070	33	8	theorems	theorem	NOUN
ejpam-3070	33	9	and	and	CCONJ
ejpam-3070	33	10	stability	stability	NOUN
ejpam-3070	33	11	results	result	NOUN
ejpam-3070	33	12	has	have	AUX
ejpam-3070	33	13	been	be	AUX
ejpam-3070	33	14	studied	study	VERB
ejpam-3070	33	15	.	.	PUNCT
ejpam-3070	34	1	much	much	ADJ
ejpam-3070	34	2	of	of	ADP
ejpam-3070	34	3	the	the	DET
ejpam-3070	34	4	basic	basic	ADJ
ejpam-3070	34	5	theory	theory	NOUN
ejpam-3070	34	6	has	have	AUX
ejpam-3070	34	7	been	be	AUX
ejpam-3070	34	8	established	establish	VERB
ejpam-3070	34	9	in	in	ADP
ejpam-3070	34	10	[	[	PUNCT
ejpam-3070	34	11	8	8	NUM
ejpam-3070	34	12	]	]	PUNCT
ejpam-3070	34	13	.	.	PUNCT
ejpam-3070	35	1	in	in	ADP
ejpam-3070	35	2	this	this	DET
ejpam-3070	35	3	paper	paper	NOUN
ejpam-3070	35	4	an	an	DET
ejpam-3070	35	5	attempt	attempt	NOUN
ejpam-3070	35	6	has	have	AUX
ejpam-3070	35	7	been	be	AUX
ejpam-3070	35	8	made	make	VERB
ejpam-3070	35	9	to	to	PART
ejpam-3070	35	10	combine	combine	VERB
ejpam-3070	35	11	all	all	DET
ejpam-3070	35	12	the	the	PRON
ejpam-3070	35	13	above	above	ADJ
ejpam-3070	35	14	set	set	VERB
ejpam-3070	35	15	ups	up	NOUN
ejpam-3070	35	16	and	and	CCONJ
ejpam-3070	35	17	develop	develop	VERB
ejpam-3070	35	18	some	some	DET
ejpam-3070	35	19	stability	stability	NOUN
ejpam-3070	35	20	results	result	NOUN
ejpam-3070	35	21	in	in	ADP
ejpam-3070	35	22	two	two	NUM
ejpam-3070	35	23	measures	measure	NOUN
ejpam-3070	35	24	for	for	ADP
ejpam-3070	35	25	set	set	VERB
ejpam-3070	35	26	differential	differential	ADJ
ejpam-3070	35	27	equations	equation	NOUN
ejpam-3070	35	28	involving	involve	VERB
ejpam-3070	35	29	causal	causal	ADJ
ejpam-3070	35	30	operators	operator	NOUN
ejpam-3070	35	31	.	.	PUNCT
ejpam-3070	36	1	2	2	X
ejpam-3070	36	2	.	.	X
ejpam-3070	36	3	preliminaries	preliminary	NOUN
ejpam-3070	36	4	in	in	ADP
ejpam-3070	36	5	this	this	DET
ejpam-3070	36	6	section	section	NOUN
ejpam-3070	36	7	,	,	PUNCT
ejpam-3070	36	8	we	we	PRON
ejpam-3070	36	9	begin	begin	VERB
ejpam-3070	36	10	with	with	ADP
ejpam-3070	36	11	the	the	DET
ejpam-3070	36	12	definition	definition	NOUN
ejpam-3070	36	13	of	of	ADP
ejpam-3070	36	14	hausdorff	hausdorff	PROPN
ejpam-3070	36	15	metric	metric	PROPN
ejpam-3070	36	16	,	,	PUNCT
ejpam-3070	36	17	hukuhara	hukuhara	ADV
ejpam-3070	36	18	difference	difference	NOUN
ejpam-3070	36	19	and	and	CCONJ
ejpam-3070	36	20	proceed	proceed	VERB
ejpam-3070	36	21	to	to	PART
ejpam-3070	36	22	define	define	VERB
ejpam-3070	36	23	the	the	DET
ejpam-3070	36	24	semi	semi	ADJ
ejpam-3070	36	25	metric	metric	ADJ
ejpam-3070	36	26	space	space	NOUN
ejpam-3070	36	27	kc(rn	kc(rn	PROPN
ejpam-3070	36	28	)	)	PUNCT
ejpam-3070	36	29	.	.	PUNCT
ejpam-3070	37	1	next	next	ADV
ejpam-3070	37	2	we	we	PRON
ejpam-3070	37	3	proceed	proceed	VERB
ejpam-3070	37	4	to	to	PART
ejpam-3070	37	5	define	define	VERB
ejpam-3070	37	6	the	the	DET
ejpam-3070	37	7	hukuhara	hukuhara	ADJ
ejpam-3070	37	8	derivative	derivative	NOUN
ejpam-3070	37	9	,	,	PUNCT
ejpam-3070	37	10	hukuhara	hukuhara	ADV
ejpam-3070	37	11	integral	integral	ADJ
ejpam-3070	37	12	and	and	CCONJ
ejpam-3070	37	13	a	a	DET
ejpam-3070	37	14	partial	partial	ADJ
ejpam-3070	37	15	order	order	NOUN
ejpam-3070	37	16	in	in	ADP
ejpam-3070	37	17	kc(rn	kc(rn	PROPN
ejpam-3070	37	18	)	)	PUNCT
ejpam-3070	38	1	[	[	PUNCT
ejpam-3070	38	2	9	9	NUM
ejpam-3070	38	3	]	]	PUNCT
ejpam-3070	38	4	.	.	PUNCT
ejpam-3070	39	1	further	far	ADV
ejpam-3070	39	2	,	,	PUNCT
ejpam-3070	39	3	we	we	PRON
ejpam-3070	39	4	state	state	VERB
ejpam-3070	39	5	some	some	DET
ejpam-3070	39	6	important	important	ADJ
ejpam-3070	39	7	properties	property	NOUN
ejpam-3070	39	8	that	that	PRON
ejpam-3070	39	9	are	be	AUX
ejpam-3070	39	10	useful	useful	ADJ
ejpam-3070	39	11	tools	tool	NOUN
ejpam-3070	39	12	in	in	ADP
ejpam-3070	39	13	establishing	establish	VERB
ejpam-3070	39	14	our	our	PRON
ejpam-3070	39	15	main	main	ADJ
ejpam-3070	39	16	results	result	NOUN
ejpam-3070	39	17	.	.	PUNCT
ejpam-3070	40	1	let	let	VERB
ejpam-3070	40	2	kc(rn	kc(rn	PROPN
ejpam-3070	40	3	)	)	PUNCT
ejpam-3070	41	1	denote	denote	VERB
ejpam-3070	41	2	the	the	DET
ejpam-3070	41	3	collection	collection	NOUN
ejpam-3070	41	4	of	of	ADP
ejpam-3070	41	5	all	all	DET
ejpam-3070	41	6	nonempty	nonempty	ADJ
ejpam-3070	41	7	,	,	PUNCT
ejpam-3070	41	8	compact	compact	ADJ
ejpam-3070	41	9	and	and	CCONJ
ejpam-3070	41	10	convex	convex	ADJ
ejpam-3070	41	11	subsets	subset	NOUN
ejpam-3070	41	12	of	of	ADP
ejpam-3070	41	13	rn	rn	PROPN
ejpam-3070	41	14	.	.	PUNCT
ejpam-3070	42	1	ch	ch	PROPN
ejpam-3070	42	2	.	.	PUNCT
ejpam-3070	42	3	a.	a.	PROPN
ejpam-3070	42	4	naidu,̧	naidu,̧	PROPN
ejpam-3070	42	5	d.	d.	PROPN
ejpam-3070	42	6	b.	b.	PROPN
ejpam-3070	42	7	dhaigude	dhaigude	PROPN
ejpam-3070	42	8	,	,	PUNCT
ejpam-3070	42	9	j.	j.	PROPN
ejpam-3070	42	10	v.	v.	PROPN
ejpam-3070	42	11	devi	devi	PROPN
ejpam-3070	42	12	/	/	SYM
ejpam-3070	42	13	eur	eur	PROPN
ejpam-3070	42	14	.	.	PUNCT
ejpam-3070	43	1	j.	j.	PROPN
ejpam-3070	43	2	pure	pure	PROPN
ejpam-3070	43	3	appl	appl	PROPN
ejpam-3070	43	4	.	.	PROPN
ejpam-3070	43	5	math	math	PROPN
ejpam-3070	43	6	,	,	PUNCT
ejpam-3070	43	7	10	10	NUM
ejpam-3070	43	8	(	(	PUNCT
ejpam-3070	43	9	4	4	NUM
ejpam-3070	43	10	)	)	PUNCT
ejpam-3070	43	11	(	(	PUNCT
ejpam-3070	43	12	2017	2017	NUM
ejpam-3070	43	13	)	)	PUNCT
ejpam-3070	43	14	,	,	PUNCT
ejpam-3070	43	15	645	645	NUM
ejpam-3070	43	16	-	-	SYM
ejpam-3070	43	17	654	654	NUM
ejpam-3070	43	18	647	647	NUM
ejpam-3070	43	19	we	we	PRON
ejpam-3070	43	20	define	define	VERB
ejpam-3070	43	21	the	the	DET
ejpam-3070	43	22	hausdorff	hausdorff	NOUN
ejpam-3070	43	23	metric	metric	ADJ
ejpam-3070	43	24	by	by	ADP
ejpam-3070	43	25	d[a	d[a	PROPN
ejpam-3070	43	26	,	,	PUNCT
ejpam-3070	43	27	b	b	NOUN
ejpam-3070	43	28	]	]	X
ejpam-3070	43	29	=	=	SYM
ejpam-3070	43	30	max	max	PROPN
ejpam-3070	43	31	[	[	PUNCT
ejpam-3070	43	32	sup	sup	NOUN
ejpam-3070	43	33	x∈b	x∈b	ADJ
ejpam-3070	43	34	d(x	d(x	PROPN
ejpam-3070	43	35	,	,	PUNCT
ejpam-3070	43	36	a	a	PRON
ejpam-3070	43	37	)	)	PUNCT
ejpam-3070	43	38	,	,	PUNCT
ejpam-3070	43	39	sup	sup	NOUN
ejpam-3070	43	40	y∈a	y∈a	NOUN
ejpam-3070	43	41	d(y	d(y	PROPN
ejpam-3070	43	42	,	,	PUNCT
ejpam-3070	43	43	b	b	NOUN
ejpam-3070	43	44	)	)	PUNCT
ejpam-3070	43	45	]	]	PUNCT
ejpam-3070	43	46	,	,	PUNCT
ejpam-3070	43	47	(	(	PUNCT
ejpam-3070	43	48	1	1	X
ejpam-3070	43	49	)	)	PUNCT
ejpam-3070	43	50	where	where	SCONJ
ejpam-3070	43	51	d(x	d(x	PROPN
ejpam-3070	43	52	,	,	PUNCT
ejpam-3070	43	53	a	a	PRON
ejpam-3070	43	54	)	)	PUNCT
ejpam-3070	43	55	=	=	SYM
ejpam-3070	43	56	inf[d(x	inf[d(x	PROPN
ejpam-3070	43	57	,	,	PUNCT
ejpam-3070	43	58	y	y	NOUN
ejpam-3070	43	59	)	)	PUNCT
ejpam-3070	43	60	:	:	PUNCT
ejpam-3070	44	1	y	y	PROPN
ejpam-3070	44	2	∈	∈	PROPN
ejpam-3070	44	3	a	a	X
ejpam-3070	44	4	]	]	X
ejpam-3070	44	5	,	,	PUNCT
ejpam-3070	44	6	a	a	PRON
ejpam-3070	44	7	and	and	CCONJ
ejpam-3070	44	8	b	b	NOUN
ejpam-3070	44	9	are	be	AUX
ejpam-3070	44	10	bounded	bound	VERB
ejpam-3070	44	11	sets	set	NOUN
ejpam-3070	44	12	in	in	ADP
ejpam-3070	44	13	rn	rn	PROPN
ejpam-3070	44	14	.	.	PUNCT
ejpam-3070	45	1	we	we	PRON
ejpam-3070	45	2	note	note	VERB
ejpam-3070	45	3	that	that	SCONJ
ejpam-3070	45	4	kc(rn	kc(rn	PROPN
ejpam-3070	45	5	)	)	PUNCT
ejpam-3070	45	6	with	with	ADP
ejpam-3070	45	7	this	this	DET
ejpam-3070	45	8	metric	metric	NOUN
ejpam-3070	45	9	is	be	AUX
ejpam-3070	45	10	a	a	DET
ejpam-3070	45	11	complete	complete	ADJ
ejpam-3070	45	12	metric	metric	ADJ
ejpam-3070	45	13	space	space	NOUN
ejpam-3070	45	14	.	.	PUNCT
ejpam-3070	46	1	it	it	PRON
ejpam-3070	46	2	is	be	AUX
ejpam-3070	46	3	known	know	VERB
ejpam-3070	46	4	that	that	SCONJ
ejpam-3070	46	5	if	if	SCONJ
ejpam-3070	46	6	the	the	DET
ejpam-3070	46	7	space	space	NOUN
ejpam-3070	46	8	kc(rn	kc(rn	PROPN
ejpam-3070	46	9	)	)	PUNCT
ejpam-3070	46	10	is	be	AUX
ejpam-3070	46	11	equipped	equip	VERB
ejpam-3070	46	12	with	with	ADP
ejpam-3070	46	13	the	the	DET
ejpam-3070	46	14	natural	natural	ADJ
ejpam-3070	46	15	algebraic	algebraic	ADJ
ejpam-3070	46	16	operations	operation	NOUN
ejpam-3070	46	17	of	of	ADP
ejpam-3070	46	18	addition	addition	NOUN
ejpam-3070	46	19	and	and	CCONJ
ejpam-3070	46	20	non	non	ADJ
ejpam-3070	46	21	-	-	ADJ
ejpam-3070	46	22	negative	negative	ADJ
ejpam-3070	46	23	scalar	scalar	ADJ
ejpam-3070	46	24	multiplication	multiplication	NOUN
ejpam-3070	46	25	,	,	PUNCT
ejpam-3070	46	26	then	then	ADV
ejpam-3070	46	27	kc(rn	kc(rn	PROPN
ejpam-3070	46	28	)	)	PUNCT
ejpam-3070	46	29	becomes	become	VERB
ejpam-3070	46	30	a	a	DET
ejpam-3070	46	31	semi	semi	ADJ
ejpam-3070	46	32	linear	linear	ADJ
ejpam-3070	46	33	metric	metric	ADJ
ejpam-3070	46	34	space	space	NOUN
ejpam-3070	46	35	which	which	PRON
ejpam-3070	46	36	can	can	AUX
ejpam-3070	46	37	be	be	AUX
ejpam-3070	46	38	embedded	embed	VERB
ejpam-3070	46	39	as	as	ADP
ejpam-3070	46	40	a	a	DET
ejpam-3070	46	41	complete	complete	ADJ
ejpam-3070	46	42	cone	cone	NOUN
ejpam-3070	46	43	into	into	ADP
ejpam-3070	46	44	a	a	DET
ejpam-3070	46	45	corresponding	corresponding	ADJ
ejpam-3070	46	46	banach	banach	NOUN
ejpam-3070	46	47	space	space	NOUN
ejpam-3070	46	48	.	.	PUNCT
ejpam-3070	47	1	the	the	DET
ejpam-3070	47	2	hausdorff	hausdorff	PROPN
ejpam-3070	47	3	metric	metric	NOUN
ejpam-3070	47	4	(	(	PUNCT
ejpam-3070	47	5	1	1	NUM
ejpam-3070	47	6	)	)	PUNCT
ejpam-3070	47	7	satisfies	satisfy	VERB
ejpam-3070	47	8	the	the	DET
ejpam-3070	47	9	following	follow	VERB
ejpam-3070	47	10	properties	property	NOUN
ejpam-3070	47	11	:	:	PUNCT
ejpam-3070	48	1	d[a+	d[a+	NOUN
ejpam-3070	48	2	c	c	X
ejpam-3070	48	3	,	,	PUNCT
ejpam-3070	48	4	b	b	PROPN
ejpam-3070	49	1	+	+	CCONJ
ejpam-3070	49	2	c	c	NOUN
ejpam-3070	49	3	]	]	X
ejpam-3070	49	4	=	=	SYM
ejpam-3070	49	5	d[a	d[a	PROPN
ejpam-3070	49	6	,	,	PUNCT
ejpam-3070	49	7	b	b	NOUN
ejpam-3070	49	8	]	]	PUNCT
ejpam-3070	49	9	and	and	CCONJ
ejpam-3070	49	10	d[a	d[a	ADJ
ejpam-3070	49	11	,	,	PUNCT
ejpam-3070	49	12	b	b	NOUN
ejpam-3070	49	13	]	]	X
ejpam-3070	49	14	=	=	SYM
ejpam-3070	49	15	d[b	d[b	PROPN
ejpam-3070	49	16	,	,	PUNCT
ejpam-3070	49	17	a	a	PRON
ejpam-3070	49	18	]	]	X
ejpam-3070	49	19	,	,	PUNCT
ejpam-3070	49	20	(	(	PUNCT
ejpam-3070	49	21	2	2	X
ejpam-3070	49	22	)	)	PUNCT
ejpam-3070	49	23	d[λa	d[λa	PROPN
ejpam-3070	49	24	,	,	PUNCT
ejpam-3070	49	25	λb	λb	ADP
ejpam-3070	49	26	]	]	X
ejpam-3070	49	27	=	=	SYM
ejpam-3070	49	28	λd[a	λd[a	PROPN
ejpam-3070	49	29	,	,	PUNCT
ejpam-3070	49	30	b	b	NOUN
ejpam-3070	49	31	]	]	X
ejpam-3070	49	32	,	,	PUNCT
ejpam-3070	49	33	(	(	PUNCT
ejpam-3070	49	34	3	3	X
ejpam-3070	49	35	)	)	PUNCT
ejpam-3070	49	36	d[a	d[a	ADJ
ejpam-3070	49	37	,	,	PUNCT
ejpam-3070	49	38	b	b	NOUN
ejpam-3070	49	39	]	]	PUNCT
ejpam-3070	49	40	≤	≤	NUM
ejpam-3070	49	41	d[a	d[a	PROPN
ejpam-3070	49	42	,	,	PUNCT
ejpam-3070	49	43	c	c	X
ejpam-3070	49	44	]	]	X
ejpam-3070	50	1	+	+	ADJ
ejpam-3070	50	2	d[c	d[c	ADJ
ejpam-3070	50	3	,	,	PUNCT
ejpam-3070	50	4	b	b	NOUN
ejpam-3070	50	5	]	]	X
ejpam-3070	50	6	,	,	PUNCT
ejpam-3070	50	7	(	(	PUNCT
ejpam-3070	50	8	4	4	X
ejpam-3070	50	9	)	)	PUNCT
ejpam-3070	50	10	for	for	ADP
ejpam-3070	50	11	all	all	DET
ejpam-3070	50	12	a	a	DET
ejpam-3070	50	13	,	,	PUNCT
ejpam-3070	50	14	b	b	NOUN
ejpam-3070	50	15	,	,	PUNCT
ejpam-3070	50	16	c	c	PROPN
ejpam-3070	50	17	∈	∈	PROPN
ejpam-3070	50	18	kc(rn	kc(rn	PROPN
ejpam-3070	50	19	)	)	PUNCT
ejpam-3070	50	20	and	and	CCONJ
ejpam-3070	50	21	λ	λ	PROPN
ejpam-3070	50	22	∈	∈	PROPN
ejpam-3070	50	23	r+	r+	X
ejpam-3070	50	24	.	.	PUNCT
ejpam-3070	51	1	let	let	VERB
ejpam-3070	51	2	a	a	DET
ejpam-3070	51	3	,	,	PUNCT
ejpam-3070	51	4	b	b	PROPN
ejpam-3070	51	5	∈	∈	PROPN
ejpam-3070	51	6	kc(rn	kc(rn	PROPN
ejpam-3070	51	7	)	)	PUNCT
ejpam-3070	51	8	.	.	PUNCT
ejpam-3070	52	1	the	the	DET
ejpam-3070	52	2	set	set	NOUN
ejpam-3070	52	3	c	c	PROPN
ejpam-3070	52	4	∈	∈	PROPN
ejpam-3070	52	5	kc(rn	kc(rn	PROPN
ejpam-3070	52	6	)	)	PUNCT
ejpam-3070	52	7	satisfying	satisfy	VERB
ejpam-3070	52	8	a	a	DET
ejpam-3070	52	9	=	=	SYM
ejpam-3070	52	10	b	b	PROPN
ejpam-3070	53	1	+	+	CCONJ
ejpam-3070	53	2	c	c	NOUN
ejpam-3070	53	3	is	be	AUX
ejpam-3070	53	4	known	know	VERB
ejpam-3070	53	5	as	as	ADP
ejpam-3070	53	6	the	the	DET
ejpam-3070	53	7	hukuhara	hukuhara	ADJ
ejpam-3070	53	8	difference	difference	NOUN
ejpam-3070	53	9	of	of	ADP
ejpam-3070	53	10	the	the	DET
ejpam-3070	53	11	sets	set	NOUN
ejpam-3070	53	12	a	a	PRON
ejpam-3070	53	13	and	and	CCONJ
ejpam-3070	53	14	b	b	NOUN
ejpam-3070	53	15	and	and	CCONJ
ejpam-3070	53	16	is	be	AUX
ejpam-3070	53	17	denoted	denote	VERB
ejpam-3070	53	18	by	by	ADP
ejpam-3070	53	19	the	the	DET
ejpam-3070	53	20	symbol	symbol	NOUN
ejpam-3070	53	21	a	a	DET
ejpam-3070	53	22	−	−	PROPN
ejpam-3070	53	23	b.	b.	NOUN
ejpam-3070	54	1	we	we	PRON
ejpam-3070	54	2	say	say	VERB
ejpam-3070	54	3	that	that	SCONJ
ejpam-3070	54	4	the	the	DET
ejpam-3070	54	5	mapping	mapping	NOUN
ejpam-3070	54	6	f	f	X
ejpam-3070	54	7	:	:	PUNCT
ejpam-3070	55	1	i	i	PROPN
ejpam-3070	55	2	→	→	SYM
ejpam-3070	55	3	kc(rn	kc(rn	PROPN
ejpam-3070	55	4	)	)	PUNCT
ejpam-3070	55	5	has	have	VERB
ejpam-3070	55	6	a	a	DET
ejpam-3070	55	7	hukuhara	hukuhara	ADJ
ejpam-3070	55	8	derivative	derivative	ADJ
ejpam-3070	55	9	dhf	dhf	NOUN
ejpam-3070	55	10	(	(	PUNCT
ejpam-3070	55	11	t0	t0	PROPN
ejpam-3070	55	12	)	)	PUNCT
ejpam-3070	55	13	at	at	ADP
ejpam-3070	55	14	a	a	DET
ejpam-3070	55	15	point	point	NOUN
ejpam-3070	56	1	t0	t0	X
ejpam-3070	57	1	∈	∈	PROPN
ejpam-3070	58	1	i	i	PRON
ejpam-3070	58	2	,	,	PUNCT
ejpam-3070	58	3	if	if	SCONJ
ejpam-3070	58	4	lim	lim	PROPN
ejpam-3070	58	5	h→0	h→0	PROPN
ejpam-3070	58	6	+	+	PROPN
ejpam-3070	58	7	f	f	X
ejpam-3070	58	8	(	(	PUNCT
ejpam-3070	58	9	t0	t0	NOUN
ejpam-3070	58	10	+	+	CCONJ
ejpam-3070	59	1	h)−	h)−	PROPN
ejpam-3070	59	2	f	f	PROPN
ejpam-3070	59	3	(	(	PUNCT
ejpam-3070	59	4	t0	t0	PROPN
ejpam-3070	59	5	)	)	PUNCT
ejpam-3070	59	6	h	h	PROPN
ejpam-3070	59	7	and	and	CCONJ
ejpam-3070	59	8	lim	lim	PROPN
ejpam-3070	60	1	h→0	h→0	PROPN
ejpam-3070	61	1	+	+	NUM
ejpam-3070	61	2	f	f	X
ejpam-3070	61	3	(	(	PUNCT
ejpam-3070	61	4	t0)−	t0)−	INTJ
ejpam-3070	61	5	f	f	X
ejpam-3070	61	6	(	(	PUNCT
ejpam-3070	61	7	t0	t0	NOUN
ejpam-3070	61	8	−	−	PROPN
ejpam-3070	61	9	h	h	NOUN
ejpam-3070	61	10	)	)	PUNCT
ejpam-3070	61	11	h	h	NOUN
ejpam-3070	61	12	exist	exist	VERB
ejpam-3070	61	13	in	in	ADP
ejpam-3070	61	14	the	the	DET
ejpam-3070	61	15	topology	topology	NOUN
ejpam-3070	61	16	of	of	ADP
ejpam-3070	61	17	kc(rn	kc(rn	PROPN
ejpam-3070	61	18	)	)	PUNCT
ejpam-3070	61	19	and	and	CCONJ
ejpam-3070	61	20	are	be	AUX
ejpam-3070	61	21	equal	equal	ADJ
ejpam-3070	61	22	to	to	PART
ejpam-3070	61	23	dhf	dhf	VERB
ejpam-3070	61	24	(	(	PUNCT
ejpam-3070	61	25	t0	t0	PROPN
ejpam-3070	61	26	)	)	PUNCT
ejpam-3070	61	27	.	.	PUNCT
ejpam-3070	62	1	here	here	ADV
ejpam-3070	62	2	i	i	PRON
ejpam-3070	62	3	is	be	AUX
ejpam-3070	62	4	any	any	DET
ejpam-3070	62	5	interval	interval	NOUN
ejpam-3070	62	6	in	in	ADP
ejpam-3070	62	7	r.	r.	PROPN
ejpam-3070	62	8	with	with	ADP
ejpam-3070	62	9	these	these	DET
ejpam-3070	62	10	preliminaries	preliminary	NOUN
ejpam-3070	62	11	,	,	PUNCT
ejpam-3070	62	12	we	we	PRON
ejpam-3070	62	13	consider	consider	VERB
ejpam-3070	62	14	the	the	DET
ejpam-3070	62	15	ivp	ivp	NOUN
ejpam-3070	62	16	for	for	ADP
ejpam-3070	62	17	set	set	VERB
ejpam-3070	62	18	differential	differential	ADJ
ejpam-3070	62	19	equation	equation	NOUN
ejpam-3070	62	20	dhu	dhu	NOUN
ejpam-3070	62	21	=	=	SYM
ejpam-3070	62	22	f	f	PROPN
ejpam-3070	62	23	(	(	PUNCT
ejpam-3070	62	24	t	t	PROPN
ejpam-3070	62	25	,	,	PUNCT
ejpam-3070	62	26	u	u	NOUN
ejpam-3070	62	27	)	)	PUNCT
ejpam-3070	62	28	,	,	PUNCT
ejpam-3070	62	29	u(t0	u(t0	NOUN
ejpam-3070	62	30	)	)	PUNCT
ejpam-3070	62	31	=	=	PUNCT
ejpam-3070	62	32	u0	u0	PROPN
ejpam-3070	62	33	∈	∈	PROPN
ejpam-3070	62	34	kc(rn	kc(rn	PROPN
ejpam-3070	62	35	)	)	PUNCT
ejpam-3070	62	36	,	,	PUNCT
ejpam-3070	62	37	t0	t0	PROPN
ejpam-3070	62	38	≥	≥	NUM
ejpam-3070	62	39	0	0	NUM
ejpam-3070	62	40	,	,	PUNCT
ejpam-3070	62	41	(	(	PUNCT
ejpam-3070	62	42	5	5	NUM
ejpam-3070	62	43	)	)	PUNCT
ejpam-3070	62	44	where	where	SCONJ
ejpam-3070	62	45	f	f	PROPN
ejpam-3070	62	46	∈	∈	PROPN
ejpam-3070	62	47	c[r+	c[r+	NOUN
ejpam-3070	62	48	×kc(rn),kc(rn	×kc(rn),kc(rn	PROPN
ejpam-3070	62	49	)	)	PUNCT
ejpam-3070	62	50	]	]	PUNCT
ejpam-3070	62	51	.	.	PUNCT
ejpam-3070	63	1	the	the	DET
ejpam-3070	63	2	mapping	mapping	NOUN
ejpam-3070	63	3	u	u	NOUN
ejpam-3070	63	4	∈	∈	PROPN
ejpam-3070	63	5	c1[j	c1[j	NOUN
ejpam-3070	63	6	,	,	PUNCT
ejpam-3070	63	7	kc(rn	kc(rn	PROPN
ejpam-3070	63	8	)	)	PUNCT
ejpam-3070	63	9	]	]	PUNCT
ejpam-3070	63	10	,	,	PUNCT
ejpam-3070	63	11	j	j	X
ejpam-3070	63	12	=	=	PUNCT
ejpam-3070	64	1	[	[	X
ejpam-3070	64	2	t0	t0	PROPN
ejpam-3070	64	3	,	,	PUNCT
ejpam-3070	64	4	t0	t0	PROPN
ejpam-3070	64	5	+	+	CCONJ
ejpam-3070	64	6	a	a	PRON
ejpam-3070	64	7	]	]	X
ejpam-3070	64	8	is	be	AUX
ejpam-3070	64	9	said	say	VERB
ejpam-3070	64	10	to	to	PART
ejpam-3070	64	11	be	be	AUX
ejpam-3070	64	12	a	a	DET
ejpam-3070	64	13	solution	solution	NOUN
ejpam-3070	64	14	of	of	ADP
ejpam-3070	64	15	ivp	ivp	PROPN
ejpam-3070	64	16	(	(	PUNCT
ejpam-3070	64	17	5	5	NUM
ejpam-3070	64	18	)	)	PUNCT
ejpam-3070	64	19	on	on	ADP
ejpam-3070	64	20	j	j	PROPN
ejpam-3070	64	21	if	if	SCONJ
ejpam-3070	64	22	it	it	PRON
ejpam-3070	64	23	satisfies	satisfy	VERB
ejpam-3070	64	24	(	(	PUNCT
ejpam-3070	64	25	5	5	NUM
ejpam-3070	64	26	)	)	PUNCT
ejpam-3070	64	27	on	on	ADP
ejpam-3070	64	28	j	j	PROPN
ejpam-3070	64	29	.	.	PUNCT
ejpam-3070	65	1	since	since	SCONJ
ejpam-3070	65	2	u(t	u(t	NOUN
ejpam-3070	65	3	)	)	PUNCT
ejpam-3070	65	4	is	be	AUX
ejpam-3070	65	5	continuously	continuously	ADV
ejpam-3070	65	6	differentiable	differentiable	ADJ
ejpam-3070	65	7	,	,	PUNCT
ejpam-3070	65	8	we	we	PRON
ejpam-3070	65	9	have	have	VERB
ejpam-3070	65	10	u(t	u(t	NOUN
ejpam-3070	65	11	)	)	PUNCT
ejpam-3070	65	12	=	=	PUNCT
ejpam-3070	66	1	u0	u0	PROPN
ejpam-3070	67	1	+	+	X
ejpam-3070	67	2	∫	∫	PROPN
ejpam-3070	67	3	t	t	PROPN
ejpam-3070	67	4	t0	t0	PROPN
ejpam-3070	67	5	dhu(s)ds	dhu(s)d	VERB
ejpam-3070	67	6	,	,	PUNCT
ejpam-3070	67	7	t	t	PROPN
ejpam-3070	67	8	∈	∈	PROPN
ejpam-3070	67	9	j.	j.	PROPN
ejpam-3070	67	10	(	(	PUNCT
ejpam-3070	67	11	6	6	NUM
ejpam-3070	67	12	)	)	PUNCT
ejpam-3070	67	13	hence	hence	ADV
ejpam-3070	67	14	,	,	PUNCT
ejpam-3070	67	15	we	we	PRON
ejpam-3070	67	16	can	can	AUX
ejpam-3070	67	17	associate	associate	VERB
ejpam-3070	67	18	with	with	ADP
ejpam-3070	67	19	the	the	DET
ejpam-3070	67	20	ivp	ivp	NOUN
ejpam-3070	67	21	(	(	PUNCT
ejpam-3070	67	22	5	5	NUM
ejpam-3070	67	23	)	)	PUNCT
ejpam-3070	67	24	the	the	DET
ejpam-3070	67	25	hukuhara	hukuhara	ADV
ejpam-3070	67	26	integral	integral	ADJ
ejpam-3070	67	27	u(t	u(t	NOUN
ejpam-3070	67	28	)	)	PUNCT
ejpam-3070	67	29	=	=	PUNCT
ejpam-3070	68	1	u0	u0	PROPN
ejpam-3070	69	1	+	+	X
ejpam-3070	69	2	∫	∫	PROPN
ejpam-3070	69	3	t	t	PROPN
ejpam-3070	69	4	t0	t0	PROPN
ejpam-3070	69	5	f	f	PROPN
ejpam-3070	69	6	(	(	PUNCT
ejpam-3070	69	7	s	s	PROPN
ejpam-3070	69	8	,	,	PUNCT
ejpam-3070	69	9	u(s))ds	u(s))ds	PROPN
ejpam-3070	69	10	,	,	PUNCT
ejpam-3070	69	11	t	t	PROPN
ejpam-3070	69	12	∈	∈	PROPN
ejpam-3070	69	13	j.	j.	PROPN
ejpam-3070	69	14	(	(	PUNCT
ejpam-3070	69	15	7	7	NUM
ejpam-3070	69	16	)	)	PUNCT
ejpam-3070	69	17	where	where	SCONJ
ejpam-3070	69	18	the	the	DET
ejpam-3070	69	19	integral	integral	ADJ
ejpam-3070	69	20	is	be	AUX
ejpam-3070	69	21	the	the	DET
ejpam-3070	69	22	hukuhara	hukuhara	ADV
ejpam-3070	69	23	integral	integral	ADJ
ejpam-3070	69	24	which	which	PRON
ejpam-3070	69	25	is	be	AUX
ejpam-3070	69	26	defined	define	VERB
ejpam-3070	69	27	as,∫	as,∫	X
ejpam-3070	69	28	f	f	X
ejpam-3070	69	29	(	(	PUNCT
ejpam-3070	69	30	s)ds	s)ds	PROPN
ejpam-3070	69	31	=	=	SYM
ejpam-3070	69	32	{	{	PUNCT
ejpam-3070	69	33	∫	∫	PROPN
ejpam-3070	69	34	f(s)ds	f(s)ds	PROPN
ejpam-3070	69	35	:	:	PUNCT
ejpam-3070	69	36	f	f	PROPN
ejpam-3070	69	37	is	be	AUX
ejpam-3070	69	38	any	any	DET
ejpam-3070	69	39	continuous	continuous	ADJ
ejpam-3070	69	40	selector	selector	NOUN
ejpam-3070	69	41	of	of	ADP
ejpam-3070	69	42	f	f	PROPN
ejpam-3070	69	43	}	}	PUNCT
ejpam-3070	69	44	ch	ch	NOUN
ejpam-3070	69	45	.	.	PUNCT
ejpam-3070	69	46	a.	a.	PROPN
ejpam-3070	69	47	naidu,̧	naidu,̧	PROPN
ejpam-3070	69	48	d.	d.	PROPN
ejpam-3070	69	49	b.	b.	PROPN
ejpam-3070	69	50	dhaigude	dhaigude	PROPN
ejpam-3070	69	51	,	,	PUNCT
ejpam-3070	69	52	j.	j.	PROPN
ejpam-3070	69	53	v.	v.	PROPN
ejpam-3070	69	54	devi	devi	PROPN
ejpam-3070	69	55	/	/	SYM
ejpam-3070	69	56	eur	eur	PROPN
ejpam-3070	69	57	.	.	PUNCT
ejpam-3070	70	1	j.	j.	PROPN
ejpam-3070	70	2	pure	pure	PROPN
ejpam-3070	70	3	appl	appl	PROPN
ejpam-3070	70	4	.	.	PROPN
ejpam-3070	70	5	math	math	PROPN
ejpam-3070	70	6	,	,	PUNCT
ejpam-3070	70	7	10	10	NUM
ejpam-3070	70	8	(	(	PUNCT
ejpam-3070	70	9	4	4	NUM
ejpam-3070	70	10	)	)	PUNCT
ejpam-3070	70	11	(	(	PUNCT
ejpam-3070	70	12	2017	2017	NUM
ejpam-3070	70	13	)	)	PUNCT
ejpam-3070	70	14	,	,	PUNCT
ejpam-3070	70	15	645	645	NUM
ejpam-3070	70	16	-	-	SYM
ejpam-3070	70	17	654	654	NUM
ejpam-3070	70	18	648	648	NUM
ejpam-3070	70	19	observe	observe	VERB
ejpam-3070	70	20	also	also	ADV
ejpam-3070	70	21	that	that	SCONJ
ejpam-3070	70	22	u(t	u(t	NOUN
ejpam-3070	70	23	)	)	PUNCT
ejpam-3070	70	24	is	be	AUX
ejpam-3070	70	25	a	a	DET
ejpam-3070	70	26	solution	solution	NOUN
ejpam-3070	70	27	of	of	ADP
ejpam-3070	70	28	ivp	ivp	PROPN
ejpam-3070	70	29	(	(	PUNCT
ejpam-3070	70	30	5	5	NUM
ejpam-3070	70	31	)	)	PUNCT
ejpam-3070	70	32	on	on	ADP
ejpam-3070	70	33	j	j	PROPN
ejpam-3070	70	34	iff	iff	PROPN
ejpam-3070	70	35	it	it	PRON
ejpam-3070	70	36	satisfies	satisfy	VERB
ejpam-3070	70	37	(	(	PUNCT
ejpam-3070	70	38	7	7	NUM
ejpam-3070	70	39	)	)	PUNCT
ejpam-3070	70	40	on	on	ADP
ejpam-3070	70	41	j.	j.	PROPN
ejpam-3070	70	42	we	we	PRON
ejpam-3070	70	43	now	now	ADV
ejpam-3070	70	44	proceed	proceed	VERB
ejpam-3070	70	45	to	to	PART
ejpam-3070	70	46	define	define	VERB
ejpam-3070	70	47	a	a	DET
ejpam-3070	70	48	partial	partial	ADJ
ejpam-3070	70	49	order	order	NOUN
ejpam-3070	70	50	in	in	ADP
ejpam-3070	70	51	the	the	DET
ejpam-3070	70	52	metric	metric	ADJ
ejpam-3070	70	53	space	space	NOUN
ejpam-3070	70	54	(	(	PUNCT
ejpam-3070	70	55	kc(rn	kc(rn	PROPN
ejpam-3070	70	56	)	)	PUNCT
ejpam-3070	70	57	,	,	PUNCT
ejpam-3070	70	58	d	d	NOUN
ejpam-3070	70	59	)	)	PUNCT
ejpam-3070	70	60	.	.	PUNCT
ejpam-3070	71	1	we	we	PRON
ejpam-3070	71	2	begin	begin	VERB
ejpam-3070	71	3	with	with	ADP
ejpam-3070	71	4	the	the	DET
ejpam-3070	71	5	definition	definition	NOUN
ejpam-3070	71	6	of	of	ADP
ejpam-3070	71	7	a	a	DET
ejpam-3070	71	8	cone	cone	NOUN
ejpam-3070	71	9	in	in	ADP
ejpam-3070	71	10	this	this	DET
ejpam-3070	71	11	set	set	VERB
ejpam-3070	71	12	up	up	ADP
ejpam-3070	71	13	.	.	PUNCT
ejpam-3070	72	1	let	let	VERB
ejpam-3070	72	2	k(ko	k(ko	NOUN
ejpam-3070	72	3	)	)	PUNCT
ejpam-3070	72	4	be	be	AUX
ejpam-3070	72	5	the	the	DET
ejpam-3070	72	6	subfamily	subfamily	NOUN
ejpam-3070	72	7	of	of	ADP
ejpam-3070	72	8	kc(rn	kc(rn	PROPN
ejpam-3070	72	9	)	)	PUNCT
ejpam-3070	73	1	consisting	consist	VERB
ejpam-3070	73	2	of	of	ADP
ejpam-3070	73	3	set	set	NOUN
ejpam-3070	73	4	u	u	PROPN
ejpam-3070	73	5	∈	∈	PROPN
ejpam-3070	73	6	kc(rn	kc(rn	PROPN
ejpam-3070	73	7	)	)	PUNCT
ejpam-3070	73	8	such	such	ADJ
ejpam-3070	73	9	that	that	SCONJ
ejpam-3070	73	10	any	any	DET
ejpam-3070	73	11	u	u	PROPN
ejpam-3070	73	12	∈	∈	PROPN
ejpam-3070	73	13	u	u	NOUN
ejpam-3070	73	14	is	be	AUX
ejpam-3070	73	15	a	a	DET
ejpam-3070	73	16	non	non	ADJ
ejpam-3070	73	17	-	-	ADJ
ejpam-3070	73	18	negative	negative	ADJ
ejpam-3070	73	19	(	(	PUNCT
ejpam-3070	73	20	positive	positive	ADJ
ejpam-3070	73	21	)	)	PUNCT
ejpam-3070	73	22	vector	vector	NOUN
ejpam-3070	73	23	of	of	ADP
ejpam-3070	73	24	n	n	DET
ejpam-3070	73	25	components	component	NOUN
ejpam-3070	73	26	satisfying	satisfy	VERB
ejpam-3070	73	27	ui	ui	PROPN
ejpam-3070	73	28	≥	≥	NOUN
ejpam-3070	73	29	0	0	NUM
ejpam-3070	74	1	(	(	PUNCT
ejpam-3070	74	2	ui	ui	NOUN
ejpam-3070	74	3	>	>	X
ejpam-3070	74	4	0	0	NUM
ejpam-3070	74	5	)	)	PUNCT
ejpam-3070	74	6	for	for	ADP
ejpam-3070	74	7	i=1	i=1	X
ejpam-3070	74	8	...	...	PUNCT
ejpam-3070	74	9	n.	n.	NOUN
ejpam-3070	74	10	then	then	ADV
ejpam-3070	74	11	k	k	PROPN
ejpam-3070	74	12	is	be	AUX
ejpam-3070	74	13	a	a	DET
ejpam-3070	74	14	cone	cone	NOUN
ejpam-3070	74	15	in	in	ADP
ejpam-3070	74	16	kc(rn	kc(rn	PROPN
ejpam-3070	74	17	)	)	PUNCT
ejpam-3070	74	18	and	and	CCONJ
ejpam-3070	74	19	k0	k0	PROPN
ejpam-3070	74	20	is	be	AUX
ejpam-3070	74	21	the	the	DET
ejpam-3070	74	22	nonempty	nonempty	ADJ
ejpam-3070	74	23	interior	interior	NOUN
ejpam-3070	74	24	of	of	ADP
ejpam-3070	74	25	k.	k.	PROPN
ejpam-3070	74	26	definition	definition	PROPN
ejpam-3070	74	27	1	1	NUM
ejpam-3070	74	28	.	.	PUNCT
ejpam-3070	75	1	for	for	ADP
ejpam-3070	75	2	any	any	DET
ejpam-3070	75	3	u	u	NOUN
ejpam-3070	75	4	and	and	CCONJ
ejpam-3070	75	5	v	v	ADP
ejpam-3070	75	6	∈	∈	PROPN
ejpam-3070	75	7	kc(rn	kc(rn	PROPN
ejpam-3070	75	8	)	)	PUNCT
ejpam-3070	75	9	,	,	PUNCT
ejpam-3070	75	10	if	if	SCONJ
ejpam-3070	75	11	there	there	PRON
ejpam-3070	75	12	exists	exist	VERB
ejpam-3070	75	13	z	z	PROPN
ejpam-3070	75	14	∈	∈	PROPN
ejpam-3070	75	15	kc(rn	kc(rn	PROPN
ejpam-3070	75	16	)	)	PUNCT
ejpam-3070	75	17	such	such	ADJ
ejpam-3070	75	18	that	that	SCONJ
ejpam-3070	75	19	z	z	PROPN
ejpam-3070	75	20	∈	∈	PROPN
ejpam-3070	75	21	k(k0	k(k0	NOUN
ejpam-3070	75	22	)	)	PUNCT
ejpam-3070	75	23	and	and	CCONJ
ejpam-3070	75	24	u	u	X
ejpam-3070	75	25	=	=	NOUN
ejpam-3070	75	26	v	v	PROPN
ejpam-3070	75	27	+	+	NOUN
ejpam-3070	75	28	z	z	NOUN
ejpam-3070	75	29	then	then	ADV
ejpam-3070	75	30	we	we	PRON
ejpam-3070	75	31	say	say	VERB
ejpam-3070	75	32	that	that	SCONJ
ejpam-3070	75	33	u	u	PROPN
ejpam-3070	75	34	≥	≥	NUM
ejpam-3070	75	35	v	v	NOUN
ejpam-3070	75	36	(	(	PUNCT
ejpam-3070	75	37	u	u	NOUN
ejpam-3070	75	38	>	>	X
ejpam-3070	75	39	v	v	NOUN
ejpam-3070	75	40	)	)	PUNCT
ejpam-3070	75	41	.	.	PUNCT
ejpam-3070	76	1	similarly	similarly	ADV
ejpam-3070	76	2	we	we	PRON
ejpam-3070	76	3	can	can	AUX
ejpam-3070	76	4	define	define	VERB
ejpam-3070	76	5	u	u	NOUN
ejpam-3070	76	6	≤	≤	X
ejpam-3070	76	7	v	v	NOUN
ejpam-3070	76	8	(	(	PUNCT
ejpam-3070	76	9	u	u	NOUN
ejpam-3070	76	10	<	<	X
ejpam-3070	76	11	v	v	NOUN
ejpam-3070	76	12	)	)	PUNCT
ejpam-3070	76	13	.	.	PUNCT
ejpam-3070	77	1	to	to	PART
ejpam-3070	77	2	introduce	introduce	VERB
ejpam-3070	77	3	the	the	DET
ejpam-3070	77	4	causal	causal	ADJ
ejpam-3070	77	5	operator	operator	NOUN
ejpam-3070	77	6	[	[	PUNCT
ejpam-3070	77	7	9	9	NUM
ejpam-3070	77	8	,	,	PUNCT
ejpam-3070	77	9	10	10	NUM
ejpam-3070	77	10	,	,	PUNCT
ejpam-3070	77	11	8	8	NUM
ejpam-3070	77	12	]	]	PUNCT
ejpam-3070	77	13	which	which	PRON
ejpam-3070	77	14	is	be	AUX
ejpam-3070	77	15	also	also	ADV
ejpam-3070	77	16	known	know	VERB
ejpam-3070	77	17	as	as	ADP
ejpam-3070	77	18	a	a	DET
ejpam-3070	77	19	non	non	X
ejpam-3070	77	20	anticipative	anticipative	NOUN
ejpam-3070	77	21	operator	operator	NOUN
ejpam-3070	77	22	we	we	PRON
ejpam-3070	77	23	first	first	ADV
ejpam-3070	77	24	introduce	introduce	VERB
ejpam-3070	77	25	the	the	DET
ejpam-3070	77	26	following	following	ADJ
ejpam-3070	77	27	notation	notation	NOUN
ejpam-3070	77	28	and	and	CCONJ
ejpam-3070	77	29	notion	notion	NOUN
ejpam-3070	77	30	.	.	PUNCT
ejpam-3070	78	1	let	let	VERB
ejpam-3070	78	2	e	e	NOUN
ejpam-3070	78	3	=	=	SYM
ejpam-3070	78	4	c[[t0	c[[t0	PROPN
ejpam-3070	78	5	,	,	PUNCT
ejpam-3070	78	6	t	t	X
ejpam-3070	78	7	]	]	PUNCT
ejpam-3070	78	8	,	,	PUNCT
ejpam-3070	78	9	kc(rn	kc(rn	PROPN
ejpam-3070	78	10	)	)	PUNCT
ejpam-3070	78	11	]	]	PUNCT
ejpam-3070	78	12	,	,	PUNCT
ejpam-3070	78	13	we	we	PRON
ejpam-3070	78	14	define	define	VERB
ejpam-3070	78	15	a	a	DET
ejpam-3070	78	16	norm	norm	NOUN
ejpam-3070	78	17	d0	d0	NOUN
ejpam-3070	78	18	:	:	PUNCT
ejpam-3070	78	19	e	e	X
ejpam-3070	78	20	×e	×e	X
ejpam-3070	78	21	→	→	SYM
ejpam-3070	78	22	r+	r+	NOUN
ejpam-3070	78	23	as	as	SCONJ
ejpam-3070	78	24	follows	follow	VERB
ejpam-3070	78	25	:	:	PUNCT
ejpam-3070	78	26	for	for	ADP
ejpam-3070	78	27	u	u	NOUN
ejpam-3070	78	28	,	,	PUNCT
ejpam-3070	78	29	v	v	NOUN
ejpam-3070	78	30	∈	∈	NOUN
ejpam-3070	78	31	e	e	NOUN
ejpam-3070	78	32	,	,	PUNCT
ejpam-3070	78	33	d0[u	d0[u	PROPN
ejpam-3070	78	34	,	,	PUNCT
ejpam-3070	78	35	v	v	NOUN
ejpam-3070	78	36	]	]	X
ejpam-3070	78	37	=	=	PUNCT
ejpam-3070	78	38	sup	sup	NOUN
ejpam-3070	78	39	t0≤t≤t	t0≤t≤t	PROPN
ejpam-3070	78	40	d[u(t	d[u(t	PROPN
ejpam-3070	78	41	)	)	PUNCT
ejpam-3070	78	42	,	,	PUNCT
ejpam-3070	78	43	v	v	X
ejpam-3070	78	44	(	(	PUNCT
ejpam-3070	78	45	t	t	PROPN
ejpam-3070	78	46	)	)	PUNCT
ejpam-3070	78	47	]	]	PUNCT
ejpam-3070	79	1	(	(	PUNCT
ejpam-3070	79	2	8)	8)	NUM
ejpam-3070	79	3	where	where	SCONJ
ejpam-3070	79	4	d	d	NOUN
ejpam-3070	79	5	is	be	AUX
ejpam-3070	79	6	the	the	DET
ejpam-3070	79	7	hausdorff	hausdorff	PROPN
ejpam-3070	79	8	metric	metric	NOUN
ejpam-3070	79	9	.	.	PUNCT
ejpam-3070	80	1	definition	definition	NOUN
ejpam-3070	80	2	2	2	NUM
ejpam-3070	80	3	.	.	PUNCT
ejpam-3070	80	4	by	by	ADP
ejpam-3070	80	5	a	a	DET
ejpam-3070	80	6	causal	causal	ADJ
ejpam-3070	80	7	operator	operator	NOUN
ejpam-3070	80	8	or	or	CCONJ
ejpam-3070	80	9	a	a	DET
ejpam-3070	80	10	volterra	volterra	NOUN
ejpam-3070	80	11	operator	operator	NOUN
ejpam-3070	80	12	or	or	CCONJ
ejpam-3070	80	13	a	a	DET
ejpam-3070	80	14	nonanticipative	nonanticipative	ADJ
ejpam-3070	80	15	operator	operator	NOUN
ejpam-3070	80	16	we	we	PRON
ejpam-3070	80	17	mean	mean	VERB
ejpam-3070	80	18	a	a	DET
ejpam-3070	80	19	mapping	mapping	NOUN
ejpam-3070	80	20	q	q	NOUN
ejpam-3070	80	21	:	:	PUNCT
ejpam-3070	80	22	e	e	X
ejpam-3070	80	23	→	→	SYM
ejpam-3070	80	24	e	e	X
ejpam-3070	80	25	satisfying	satisfy	VERB
ejpam-3070	80	26	the	the	DET
ejpam-3070	80	27	property	property	NOUN
ejpam-3070	81	1	that	that	PRON
ejpam-3070	81	2	if	if	SCONJ
ejpam-3070	81	3	u(s	u(s	ADJ
ejpam-3070	81	4	)	)	PUNCT
ejpam-3070	81	5	=	=	SYM
ejpam-3070	81	6	v	v	X
ejpam-3070	81	7	(	(	PUNCT
ejpam-3070	81	8	s	s	NOUN
ejpam-3070	81	9	)	)	PUNCT
ejpam-3070	81	10	,	,	PUNCT
ejpam-3070	81	11	t0	t0	PROPN
ejpam-3070	81	12	≤	≤	PROPN
ejpam-3070	81	13	s	s	PART
ejpam-3070	81	14	≤	≤	NOUN
ejpam-3070	81	15	t	t	PROPN
ejpam-3070	81	16	<	<	X
ejpam-3070	81	17	t	t	PROPN
ejpam-3070	81	18	then	then	ADV
ejpam-3070	81	19	(	(	PUNCT
ejpam-3070	81	20	qu)(s	qu)(s	PROPN
ejpam-3070	81	21	)	)	PUNCT
ejpam-3070	81	22	=	=	PUNCT
ejpam-3070	82	1	(	(	PUNCT
ejpam-3070	82	2	qv	qv	INTJ
ejpam-3070	82	3	)	)	PUNCT
ejpam-3070	82	4	(	(	PUNCT
ejpam-3070	82	5	s	s	NOUN
ejpam-3070	82	6	)	)	PUNCT
ejpam-3070	82	7	,	,	PUNCT
ejpam-3070	82	8	t0	t0	PROPN
ejpam-3070	82	9	≤	≤	PROPN
ejpam-3070	82	10	s	s	PART
ejpam-3070	82	11	≤	≤	NOUN
ejpam-3070	82	12	t	t	NOUN
ejpam-3070	82	13	<	<	X
ejpam-3070	82	14	t.	t.	X
ejpam-3070	82	15	to	to	PART
ejpam-3070	82	16	develop	develop	VERB
ejpam-3070	82	17	the	the	DET
ejpam-3070	82	18	stability	stability	NOUN
ejpam-3070	82	19	results	result	NOUN
ejpam-3070	82	20	in	in	ADP
ejpam-3070	82	21	terms	term	NOUN
ejpam-3070	82	22	of	of	ADP
ejpam-3070	82	23	two	two	NUM
ejpam-3070	82	24	measures	measure	NOUN
ejpam-3070	82	25	we	we	PRON
ejpam-3070	82	26	need	need	VERB
ejpam-3070	82	27	new	new	ADJ
ejpam-3070	82	28	concepts	concept	NOUN
ejpam-3070	82	29	that	that	PRON
ejpam-3070	82	30	are	be	AUX
ejpam-3070	82	31	introduced	introduce	VERB
ejpam-3070	82	32	in	in	ADP
ejpam-3070	82	33	[	[	PUNCT
ejpam-3070	82	34	5	5	NUM
ejpam-3070	82	35	]	]	PUNCT
ejpam-3070	82	36	,	,	PUNCT
ejpam-3070	82	37	which	which	PRON
ejpam-3070	82	38	we	we	PRON
ejpam-3070	82	39	present	present	VERB
ejpam-3070	82	40	below	below	ADV
ejpam-3070	82	41	.	.	PUNCT
ejpam-3070	83	1	k	k	X
ejpam-3070	84	1	=	=	PRON
ejpam-3070	84	2	{	{	PUNCT
ejpam-3070	84	3	a	a	DET
ejpam-3070	84	4	∈	∈	PROPN
ejpam-3070	84	5	c[r+,r+	c[r+,r+	NOUN
ejpam-3070	84	6	]	]	PUNCT
ejpam-3070	84	7	:	:	PUNCT
ejpam-3070	84	8	a(u	a(u	X
ejpam-3070	84	9	)	)	PUNCT
ejpam-3070	84	10	is	be	AUX
ejpam-3070	84	11	strictly	strictly	ADV
ejpam-3070	84	12	increasing	increase	VERB
ejpam-3070	84	13	in	in	ADP
ejpam-3070	84	14	u	u	NOUN
ejpam-3070	84	15	and	and	CCONJ
ejpam-3070	84	16	a(0	a(0	PROPN
ejpam-3070	84	17	)	)	PUNCT
ejpam-3070	84	18	=	=	SYM
ejpam-3070	84	19	0	0	X
ejpam-3070	84	20	}	}	PUNCT
ejpam-3070	84	21	l	l	NOUN
ejpam-3070	84	22	=	=	SYM
ejpam-3070	84	23	{	{	PUNCT
ejpam-3070	84	24	σ	σ	PROPN
ejpam-3070	84	25	∈	∈	PROPN
ejpam-3070	84	26	c[r+,r+	c[r+,r+	PROPN
ejpam-3070	84	27	]	]	PUNCT
ejpam-3070	84	28	,	,	PUNCT
ejpam-3070	84	29	σ(u	σ(u	PROPN
ejpam-3070	84	30	)	)	PUNCT
ejpam-3070	84	31	is	be	AUX
ejpam-3070	84	32	strictly	strictly	ADV
ejpam-3070	84	33	decresing	decrese	VERB
ejpam-3070	84	34	in	in	ADP
ejpam-3070	84	35	u	u	NOUN
ejpam-3070	84	36	and	and	CCONJ
ejpam-3070	84	37	limu→∞	limu→∞	PROPN
ejpam-3070	84	38	σ(u	σ(u	NOUN
ejpam-3070	84	39	)	)	PUNCT
ejpam-3070	84	40	=	=	SYM
ejpam-3070	84	41	0	0	X
ejpam-3070	84	42	}	}	PUNCT
ejpam-3070	84	43	ck	ck	NOUN
ejpam-3070	84	44	=	=	PUNCT
ejpam-3070	84	45	{	{	PUNCT
ejpam-3070	84	46	a	a	DET
ejpam-3070	84	47	∈	∈	PROPN
ejpam-3070	84	48	c[r2	c[r2	NOUN
ejpam-3070	85	1	+	+	NOUN
ejpam-3070	85	2	,	,	PUNCT
ejpam-3070	85	3	r+	r+	X
ejpam-3070	85	4	]	]	PUNCT
ejpam-3070	85	5	,	,	PUNCT
ejpam-3070	85	6	a(t	a(t	PROPN
ejpam-3070	85	7	,	,	PUNCT
ejpam-3070	85	8	s	s	X
ejpam-3070	85	9	)	)	PUNCT
ejpam-3070	85	10	∈	∈	PROPN
ejpam-3070	85	11	k	k	PROPN
ejpam-3070	85	12	for	for	ADP
ejpam-3070	85	13	each	each	DET
ejpam-3070	85	14	t	t	NOUN
ejpam-3070	85	15	and	and	CCONJ
ejpam-3070	85	16	a(t	a(t	PROPN
ejpam-3070	85	17	,	,	PUNCT
ejpam-3070	85	18	s	s	PART
ejpam-3070	85	19	)	)	PUNCT
ejpam-3070	85	20	is	be	AUX
ejpam-3070	85	21	continious	continious	ADJ
ejpam-3070	85	22	for	for	SCONJ
ejpam-3070	85	23	each	each	DET
ejpam-3070	85	24	s	s	NOUN
ejpam-3070	85	25	}	}	PUNCT
ejpam-3070	85	26	γ	γ	X
ejpam-3070	85	27	=	=	SYM
ejpam-3070	85	28	{	{	PUNCT
ejpam-3070	85	29	h	h	NOUN
ejpam-3070	85	30	∈	∈	PROPN
ejpam-3070	85	31	c[r+	c[r+	NOUN
ejpam-3070	85	32	×kc(rn),r+	×kc(rn),r+	VERB
ejpam-3070	85	33	]	]	X
ejpam-3070	85	34	:	:	PUNCT
ejpam-3070	85	35	inf	inf	PROPN
ejpam-3070	85	36	(	(	PUNCT
ejpam-3070	85	37	t	t	PROPN
ejpam-3070	85	38	,	,	PUNCT
ejpam-3070	85	39	u	u	NOUN
ejpam-3070	85	40	)	)	PUNCT
ejpam-3070	85	41	h(t	h(t	PROPN
ejpam-3070	85	42	,	,	PUNCT
ejpam-3070	85	43	u	u	NOUN
ejpam-3070	85	44	)	)	PUNCT
ejpam-3070	85	45	=	=	SYM
ejpam-3070	85	46	0	0	NUM
ejpam-3070	85	47	}	}	PUNCT
ejpam-3070	85	48	γ0	γ0	NOUN
ejpam-3070	85	49	=	=	SYM
ejpam-3070	85	50	{	{	PUNCT
ejpam-3070	85	51	h	h	NOUN
ejpam-3070	85	52	∈	∈	PROPN
ejpam-3070	85	53	γ	γ	X
ejpam-3070	85	54	:	:	PUNCT
ejpam-3070	85	55	inf	inf	PROPN
ejpam-3070	85	56	u	u	PROPN
ejpam-3070	85	57	h(t	h(t	PROPN
ejpam-3070	85	58	,	,	PUNCT
ejpam-3070	85	59	u	u	NOUN
ejpam-3070	85	60	)	)	PUNCT
ejpam-3070	85	61	=	=	SYM
ejpam-3070	85	62	0	0	NUM
ejpam-3070	85	63	,	,	PUNCT
ejpam-3070	85	64	for	for	ADP
ejpam-3070	85	65	each	each	DET
ejpam-3070	85	66	t	t	PROPN
ejpam-3070	85	67	∈	∈	PROPN
ejpam-3070	85	68	r+	r+	PUNCT
ejpam-3070	85	69	}	}	PUNCT
ejpam-3070	85	70	we	we	PRON
ejpam-3070	85	71	next	next	ADV
ejpam-3070	85	72	give	give	VERB
ejpam-3070	85	73	the	the	DET
ejpam-3070	85	74	definitions	definition	NOUN
ejpam-3070	85	75	that	that	PRON
ejpam-3070	85	76	must	must	AUX
ejpam-3070	85	77	be	be	AUX
ejpam-3070	85	78	satisfied	satisfy	VERB
ejpam-3070	85	79	by	by	ADP
ejpam-3070	85	80	a	a	DET
ejpam-3070	85	81	function	function	NOUN
ejpam-3070	85	82	v	v	ADP
ejpam-3070	85	83	when	when	SCONJ
ejpam-3070	85	84	the	the	DET
ejpam-3070	85	85	notion	notion	NOUN
ejpam-3070	85	86	of	of	ADP
ejpam-3070	85	87	two	two	NUM
ejpam-3070	85	88	measures	measure	NOUN
ejpam-3070	85	89	is	be	AUX
ejpam-3070	85	90	involved	involve	VERB
ejpam-3070	85	91	,	,	PUNCT
ejpam-3070	85	92	thus	thus	ADV
ejpam-3070	85	93	introducing	introduce	VERB
ejpam-3070	85	94	a	a	DET
ejpam-3070	85	95	lyapunov	lyapunov	NOUN
ejpam-3070	85	96	like	like	ADP
ejpam-3070	85	97	function	function	NOUN
ejpam-3070	85	98	.	.	PUNCT
ejpam-3070	86	1	let	let	VERB
ejpam-3070	86	2	v	v	NUM
ejpam-3070	86	3	∈	∈	PROPN
ejpam-3070	86	4	c[r+	c[r+	NOUN
ejpam-3070	86	5	×	×	PROPN
ejpam-3070	86	6	kc(rn	kc(rn	PROPN
ejpam-3070	86	7	)	)	PUNCT
ejpam-3070	86	8	,	,	PUNCT
ejpam-3070	86	9	r+	r+	X
ejpam-3070	86	10	]	]	PUNCT
ejpam-3070	86	11	,	,	PUNCT
ejpam-3070	86	12	then	then	ADV
ejpam-3070	86	13	v	v	NOUN
ejpam-3070	86	14	is	be	AUX
ejpam-3070	86	15	said	say	VERB
ejpam-3070	86	16	to	to	PART
ejpam-3070	86	17	be	be	AUX
ejpam-3070	86	18	definition	definition	NOUN
ejpam-3070	86	19	3	3	NUM
ejpam-3070	86	20	.	.	PUNCT
ejpam-3070	86	21	h	h	NOUN
ejpam-3070	86	22	-	-	PUNCT
ejpam-3070	86	23	positive	positive	ADJ
ejpam-3070	86	24	definite	definite	ADJ
ejpam-3070	86	25	if	if	SCONJ
ejpam-3070	86	26	there	there	PRON
ejpam-3070	86	27	exists	exist	VERB
ejpam-3070	86	28	a	a	DET
ejpam-3070	86	29	ρ	ρ	PROPN
ejpam-3070	86	30	>	>	X
ejpam-3070	86	31	0	0	PROPN
ejpam-3070	86	32	and	and	CCONJ
ejpam-3070	86	33	a	a	DET
ejpam-3070	86	34	function	function	NOUN
ejpam-3070	86	35	b	b	NOUN
ejpam-3070	86	36	∈	∈	PROPN
ejpam-3070	86	37	k	k	ADP
ejpam-3070	87	1	such	such	ADJ
ejpam-3070	87	2	that	that	SCONJ
ejpam-3070	87	3	b(h(t	b(h(t	PROPN
ejpam-3070	87	4	,	,	PUNCT
ejpam-3070	87	5	u	u	NOUN
ejpam-3070	87	6	)	)	PUNCT
ejpam-3070	87	7	)	)	PUNCT
ejpam-3070	87	8	≤	≤	NUM
ejpam-3070	87	9	v	v	X
ejpam-3070	87	10	(	(	PUNCT
ejpam-3070	87	11	t	t	PROPN
ejpam-3070	87	12	,	,	PUNCT
ejpam-3070	87	13	u	u	NOUN
ejpam-3070	87	14	)	)	PUNCT
ejpam-3070	87	15	,	,	PUNCT
ejpam-3070	87	16	whenever	whenever	SCONJ
ejpam-3070	87	17	h(t	h(t	PROPN
ejpam-3070	87	18	,	,	PUNCT
ejpam-3070	87	19	u	u	NOUN
ejpam-3070	87	20	)	)	PUNCT
ejpam-3070	87	21	<	<	X
ejpam-3070	87	22	ρ	ρ	PROPN
ejpam-3070	87	23	.	.	PUNCT
ejpam-3070	87	24	ch	ch	NOUN
ejpam-3070	87	25	.	.	PUNCT
ejpam-3070	87	26	a.	a.	PROPN
ejpam-3070	87	27	naidu,̧	naidu,̧	PROPN
ejpam-3070	87	28	d.	d.	PROPN
ejpam-3070	87	29	b.	b.	PROPN
ejpam-3070	87	30	dhaigude	dhaigude	PROPN
ejpam-3070	87	31	,	,	PUNCT
ejpam-3070	87	32	j.	j.	PROPN
ejpam-3070	87	33	v.	v.	PROPN
ejpam-3070	87	34	devi	devi	PROPN
ejpam-3070	87	35	/	/	SYM
ejpam-3070	87	36	eur	eur	PROPN
ejpam-3070	87	37	.	.	PUNCT
ejpam-3070	88	1	j.	j.	PROPN
ejpam-3070	88	2	pure	pure	PROPN
ejpam-3070	88	3	appl	appl	PROPN
ejpam-3070	88	4	.	.	PROPN
ejpam-3070	88	5	math	math	PROPN
ejpam-3070	88	6	,	,	PUNCT
ejpam-3070	88	7	10	10	NUM
ejpam-3070	88	8	(	(	PUNCT
ejpam-3070	88	9	4	4	NUM
ejpam-3070	88	10	)	)	PUNCT
ejpam-3070	88	11	(	(	PUNCT
ejpam-3070	88	12	2017	2017	NUM
ejpam-3070	88	13	)	)	PUNCT
ejpam-3070	88	14	,	,	PUNCT
ejpam-3070	88	15	645	645	NUM
ejpam-3070	88	16	-	-	SYM
ejpam-3070	88	17	654	654	NUM
ejpam-3070	88	18	649	649	NUM
ejpam-3070	88	19	definition	definition	NOUN
ejpam-3070	88	20	4	4	NUM
ejpam-3070	88	21	.	.	PUNCT
ejpam-3070	89	1	h	h	NOUN
ejpam-3070	89	2	-	-	PUNCT
ejpam-3070	89	3	decrescent	decrescent	NOUN
ejpam-3070	89	4	if	if	SCONJ
ejpam-3070	89	5	there	there	PRON
ejpam-3070	89	6	exists	exist	VERB
ejpam-3070	89	7	a	a	DET
ejpam-3070	89	8	ρ	ρ	PROPN
ejpam-3070	89	9	>	>	X
ejpam-3070	89	10	0	0	PROPN
ejpam-3070	89	11	and	and	CCONJ
ejpam-3070	89	12	a	a	DET
ejpam-3070	89	13	function	function	NOUN
ejpam-3070	89	14	a	a	DET
ejpam-3070	89	15	∈	∈	NOUN
ejpam-3070	90	1	k	k	ADP
ejpam-3070	90	2	such	such	ADJ
ejpam-3070	90	3	that	that	PRON
ejpam-3070	90	4	v	v	NOUN
ejpam-3070	90	5	(	(	PUNCT
ejpam-3070	90	6	t	t	PROPN
ejpam-3070	90	7	,	,	PUNCT
ejpam-3070	90	8	u	u	NOUN
ejpam-3070	90	9	)	)	PUNCT
ejpam-3070	90	10	≤	≤	NOUN
ejpam-3070	90	11	a(h(t	a(h(t	PROPN
ejpam-3070	90	12	,	,	PUNCT
ejpam-3070	90	13	u	u	NOUN
ejpam-3070	90	14	)	)	PUNCT
ejpam-3070	90	15	)	)	PUNCT
ejpam-3070	90	16	,	,	PUNCT
ejpam-3070	91	1	whenever	whenever	SCONJ
ejpam-3070	91	2	h(t	h(t	PROPN
ejpam-3070	91	3	,	,	PUNCT
ejpam-3070	91	4	u	u	NOUN
ejpam-3070	91	5	)	)	PUNCT
ejpam-3070	91	6	<	<	X
ejpam-3070	91	7	ρ	ρ	PROPN
ejpam-3070	91	8	.	.	PUNCT
ejpam-3070	91	9	definition	definition	NOUN
ejpam-3070	91	10	5	5	NUM
ejpam-3070	91	11	.	.	PUNCT
ejpam-3070	91	12	hweakly	hweakly	ADJ
ejpam-3070	91	13	decrescent	decrescent	NOUN
ejpam-3070	91	14	if	if	SCONJ
ejpam-3070	91	15	there	there	PRON
ejpam-3070	91	16	exists	exist	VERB
ejpam-3070	91	17	a	a	DET
ejpam-3070	91	18	ρ	ρ	PROPN
ejpam-3070	91	19	>	>	X
ejpam-3070	91	20	0	0	PROPN
ejpam-3070	91	21	and	and	CCONJ
ejpam-3070	91	22	a	a	DET
ejpam-3070	91	23	function	function	NOUN
ejpam-3070	91	24	a	a	DET
ejpam-3070	91	25	∈	∈	NOUN
ejpam-3070	91	26	ck	ck	INTJ
ejpam-3070	91	27	such	such	ADJ
ejpam-3070	91	28	that	that	DET
ejpam-3070	91	29	v	v	NOUN
ejpam-3070	91	30	(	(	PUNCT
ejpam-3070	91	31	t	t	PROPN
ejpam-3070	91	32	,	,	PUNCT
ejpam-3070	91	33	u	u	NOUN
ejpam-3070	91	34	)	)	PUNCT
ejpam-3070	91	35	≤	≤	NOUN
ejpam-3070	91	36	a(t	a(t	PROPN
ejpam-3070	91	37	,	,	PUNCT
ejpam-3070	91	38	h(t	h(t	PROPN
ejpam-3070	91	39	,	,	PUNCT
ejpam-3070	91	40	u	u	NOUN
ejpam-3070	91	41	)	)	PUNCT
ejpam-3070	91	42	)	)	PUNCT
ejpam-3070	91	43	,	,	PUNCT
ejpam-3070	91	44	whenever	whenever	SCONJ
ejpam-3070	91	45	h(t	h(t	PROPN
ejpam-3070	91	46	,	,	PUNCT
ejpam-3070	91	47	u	u	NOUN
ejpam-3070	91	48	)	)	PUNCT
ejpam-3070	91	49	<	<	X
ejpam-3070	91	50	ρ	ρ	PROPN
ejpam-3070	91	51	.	.	PUNCT
ejpam-3070	92	1	let	let	PROPN
ejpam-3070	92	2	h0	h0	PROPN
ejpam-3070	92	3	,	,	PUNCT
ejpam-3070	92	4	h	h	NOUN
ejpam-3070	92	5	∈	∈	PROPN
ejpam-3070	92	6	γ	γ	PROPN
ejpam-3070	92	7	,	,	PUNCT
ejpam-3070	92	8	then	then	ADV
ejpam-3070	92	9	we	we	PRON
ejpam-3070	92	10	say	say	VERB
ejpam-3070	92	11	that	that	SCONJ
ejpam-3070	92	12	definition	definition	NOUN
ejpam-3070	92	13	6	6	NUM
ejpam-3070	92	14	.	.	PUNCT
ejpam-3070	93	1	h0	h0	PROPN
ejpam-3070	93	2	is	be	AUX
ejpam-3070	93	3	finer	fine	ADJ
ejpam-3070	93	4	than	than	ADP
ejpam-3070	93	5	h	h	NOUN
ejpam-3070	93	6	if	if	SCONJ
ejpam-3070	93	7	there	there	PRON
ejpam-3070	93	8	exists	exist	VERB
ejpam-3070	93	9	a	a	DET
ejpam-3070	93	10	ρ	ρ	PROPN
ejpam-3070	93	11	>	>	X
ejpam-3070	93	12	0	0	PROPN
ejpam-3070	93	13	and	and	CCONJ
ejpam-3070	93	14	a	a	DET
ejpam-3070	93	15	function	function	NOUN
ejpam-3070	93	16	φ	φ	PROPN
ejpam-3070	93	17	∈	∈	PROPN
ejpam-3070	94	1	ck	ck	INTJ
ejpam-3070	94	2	such	such	ADJ
ejpam-3070	94	3	that	that	SCONJ
ejpam-3070	94	4	h0(t	h0(t	PROPN
ejpam-3070	94	5	,	,	PUNCT
ejpam-3070	94	6	u	u	NOUN
ejpam-3070	94	7	)	)	PUNCT
ejpam-3070	94	8	≤	≤	NUM
ejpam-3070	94	9	ρ	ρ	NOUN
ejpam-3070	94	10	implies	imply	VERB
ejpam-3070	94	11	h(t	h(t	PROPN
ejpam-3070	94	12	,	,	PUNCT
ejpam-3070	94	13	u	u	NOUN
ejpam-3070	94	14	)	)	PUNCT
ejpam-3070	94	15	≤	≤	NOUN
ejpam-3070	94	16	φ(t	φ(t	PROPN
ejpam-3070	94	17	,	,	PUNCT
ejpam-3070	94	18	h0(t	h0(t	PROPN
ejpam-3070	94	19	,	,	PUNCT
ejpam-3070	94	20	u	u	NOUN
ejpam-3070	94	21	)	)	PUNCT
ejpam-3070	94	22	)	)	PUNCT
ejpam-3070	94	23	.	.	PUNCT
ejpam-3070	95	1	definition	definition	NOUN
ejpam-3070	95	2	7	7	NUM
ejpam-3070	95	3	.	.	PUNCT
ejpam-3070	96	1	h0	h0	PROPN
ejpam-3070	96	2	is	be	AUX
ejpam-3070	96	3	uniformly	uniformly	ADV
ejpam-3070	96	4	finer	fine	ADJ
ejpam-3070	96	5	than	than	ADP
ejpam-3070	96	6	h	h	NOUN
ejpam-3070	96	7	if	if	SCONJ
ejpam-3070	96	8	φ	φ	PROPN
ejpam-3070	96	9	is	be	AUX
ejpam-3070	96	10	independent	independent	ADJ
ejpam-3070	96	11	of	of	ADP
ejpam-3070	96	12	t	t	PROPN
ejpam-3070	96	13	in	in	ADP
ejpam-3070	96	14	the	the	DET
ejpam-3070	96	15	above	above	ADJ
ejpam-3070	96	16	definition	definition	NOUN
ejpam-3070	96	17	.	.	PUNCT
ejpam-3070	97	1	3	3	X
ejpam-3070	97	2	.	.	X
ejpam-3070	97	3	stability	stability	NOUN
ejpam-3070	97	4	results	result	VERB
ejpam-3070	97	5	in	in	ADP
ejpam-3070	97	6	this	this	DET
ejpam-3070	97	7	section	section	NOUN
ejpam-3070	97	8	,	,	PUNCT
ejpam-3070	97	9	we	we	PRON
ejpam-3070	97	10	develop	develop	VERB
ejpam-3070	97	11	the	the	DET
ejpam-3070	97	12	stability	stability	NOUN
ejpam-3070	97	13	results	result	NOUN
ejpam-3070	97	14	for	for	ADP
ejpam-3070	97	15	set	set	VERB
ejpam-3070	97	16	differential	differential	ADJ
ejpam-3070	97	17	equations	equation	NOUN
ejpam-3070	97	18	involving	involve	VERB
ejpam-3070	97	19	causal	causal	ADJ
ejpam-3070	97	20	operators	operator	NOUN
ejpam-3070	97	21	given	give	VERB
ejpam-3070	97	22	by	by	ADP
ejpam-3070	97	23	dhu	dhu	PROPN
ejpam-3070	97	24	=	=	SYM
ejpam-3070	97	25	(	(	PUNCT
ejpam-3070	97	26	qu)(t	qu)(t	PROPN
ejpam-3070	97	27	)	)	PUNCT
ejpam-3070	97	28	u(t0	u(t0	NOUN
ejpam-3070	97	29	)	)	PUNCT
ejpam-3070	98	1	=	=	SYM
ejpam-3070	98	2	u0	u0	ADJ
ejpam-3070	98	3	,	,	PUNCT
ejpam-3070	98	4	(	(	PUNCT
ejpam-3070	98	5	9	9	X
ejpam-3070	98	6	)	)	PUNCT
ejpam-3070	98	7	where	where	SCONJ
ejpam-3070	98	8	q	q	PROPN
ejpam-3070	98	9	∈	∈	PROPN
ejpam-3070	98	10	c[e	c[e	NOUN
ejpam-3070	98	11	,	,	PUNCT
ejpam-3070	98	12	e	e	NOUN
ejpam-3070	98	13	]	]	X
ejpam-3070	98	14	is	be	AUX
ejpam-3070	98	15	a	a	DET
ejpam-3070	98	16	causal	causal	ADJ
ejpam-3070	98	17	operator	operator	NOUN
ejpam-3070	98	18	e	e	NOUN
ejpam-3070	98	19	=	=	SYM
ejpam-3070	98	20	c[j	c[j	PROPN
ejpam-3070	98	21	,	,	PUNCT
ejpam-3070	98	22	kc(rn	kc(rn	PROPN
ejpam-3070	98	23	)	)	PUNCT
ejpam-3070	98	24	]	]	PUNCT
ejpam-3070	98	25	,	,	PUNCT
ejpam-3070	98	26	and	and	CCONJ
ejpam-3070	98	27	j=[0,t	j=[0,t	PROPN
ejpam-3070	98	28	]	]	X
ejpam-3070	98	29	.	.	PUNCT
ejpam-3070	99	1	we	we	PRON
ejpam-3070	99	2	assume	assume	VERB
ejpam-3070	99	3	that	that	SCONJ
ejpam-3070	99	4	the	the	DET
ejpam-3070	99	5	operator	operator	NOUN
ejpam-3070	99	6	q	q	NOUN
ejpam-3070	99	7	is	be	AUX
ejpam-3070	99	8	smooth	smooth	ADJ
ejpam-3070	99	9	enough	enough	ADV
ejpam-3070	99	10	to	to	PART
ejpam-3070	99	11	gaurantee	gaurantee	NOUN
ejpam-3070	99	12	existence	existence	NOUN
ejpam-3070	99	13	,	,	PUNCT
ejpam-3070	99	14	uniqueness	uniqueness	NOUN
ejpam-3070	99	15	of	of	ADP
ejpam-3070	99	16	solutions	solution	NOUN
ejpam-3070	99	17	and	and	CCONJ
ejpam-3070	99	18	continuous	continuous	ADJ
ejpam-3070	99	19	dependence	dependence	NOUN
ejpam-3070	99	20	of	of	ADP
ejpam-3070	99	21	solutions	solution	NOUN
ejpam-3070	99	22	u(t	u(t	NOUN
ejpam-3070	99	23	)	)	PUNCT
ejpam-3070	99	24	=	=	SYM
ejpam-3070	99	25	u(t	u(t	NOUN
ejpam-3070	99	26	,	,	PUNCT
ejpam-3070	99	27	t0	t0	PROPN
ejpam-3070	99	28	,	,	PUNCT
ejpam-3070	99	29	u0	u0	ADJ
ejpam-3070	99	30	)	)	PUNCT
ejpam-3070	99	31	of	of	ADP
ejpam-3070	99	32	(	(	PUNCT
ejpam-3070	99	33	9	9	NUM
ejpam-3070	99	34	)	)	PUNCT
ejpam-3070	99	35	with	with	ADP
ejpam-3070	99	36	respect	respect	NOUN
ejpam-3070	99	37	to	to	ADP
ejpam-3070	99	38	the	the	DET
ejpam-3070	99	39	initial	initial	ADJ
ejpam-3070	99	40	values	value	NOUN
ejpam-3070	99	41	.	.	PUNCT
ejpam-3070	100	1	now	now	ADV
ejpam-3070	100	2	we	we	PRON
ejpam-3070	100	3	state	state	VERB
ejpam-3070	100	4	from	from	ADP
ejpam-3070	100	5	[	[	PUNCT
ejpam-3070	100	6	10	10	NUM
ejpam-3070	100	7	]	]	PUNCT
ejpam-3070	100	8	the	the	DET
ejpam-3070	100	9	various	various	ADJ
ejpam-3070	100	10	stability	stability	NOUN
ejpam-3070	100	11	concepts	concept	NOUN
ejpam-3070	100	12	for	for	ADP
ejpam-3070	100	13	the	the	DET
ejpam-3070	100	14	system	system	NOUN
ejpam-3070	100	15	(	(	PUNCT
ejpam-3070	100	16	9	9	NUM
ejpam-3070	100	17	)	)	PUNCT
ejpam-3070	100	18	in	in	ADP
ejpam-3070	100	19	terms	term	NOUN
ejpam-3070	100	20	of	of	ADP
ejpam-3070	100	21	two	two	NUM
ejpam-3070	100	22	measures	measure	NOUN
ejpam-3070	100	23	h0	h0	PROPN
ejpam-3070	100	24	,	,	PUNCT
ejpam-3070	100	25	h	h	NOUN
ejpam-3070	100	26	∈	∈	PROPN
ejpam-3070	100	27	γ	γ	PROPN
ejpam-3070	100	28	.	.	PROPN
ejpam-3070	100	29	assume	assume	VERB
ejpam-3070	100	30	that	that	SCONJ
ejpam-3070	100	31	the	the	DET
ejpam-3070	100	32	system	system	NOUN
ejpam-3070	100	33	(	(	PUNCT
ejpam-3070	100	34	9	9	X
ejpam-3070	100	35	)	)	PUNCT
ejpam-3070	100	36	admits	admit	VERB
ejpam-3070	100	37	the	the	DET
ejpam-3070	100	38	trivial	trivial	ADJ
ejpam-3070	100	39	solution	solution	NOUN
ejpam-3070	100	40	u(t	u(t	NOUN
ejpam-3070	100	41	)	)	PUNCT
ejpam-3070	100	42	=	=	SYM
ejpam-3070	100	43	θ	θ	NOUN
ejpam-3070	100	44	through	through	ADP
ejpam-3070	100	45	(	(	PUNCT
ejpam-3070	100	46	t0	t0	PROPN
ejpam-3070	100	47	,	,	PUNCT
ejpam-3070	100	48	θ	θ	PROPN
ejpam-3070	100	49	)	)	PUNCT
ejpam-3070	100	50	,	,	PUNCT
ejpam-3070	100	51	then	then	ADV
ejpam-3070	100	52	the	the	DET
ejpam-3070	100	53	differential	differential	ADJ
ejpam-3070	100	54	system	system	NOUN
ejpam-3070	100	55	(	(	PUNCT
ejpam-3070	100	56	9	9	NUM
ejpam-3070	100	57	)	)	PUNCT
ejpam-3070	100	58	is	be	AUX
ejpam-3070	100	59	definition	definition	NOUN
ejpam-3070	100	60	8	8	NUM
ejpam-3070	100	61	.	.	PUNCT
ejpam-3070	101	1	(	(	PUNCT
ejpam-3070	101	2	h0	h0	PROPN
ejpam-3070	101	3	,	,	PUNCT
ejpam-3070	101	4	h)−equi	h)−equi	VERB
ejpam-3070	101	5	stable	stable	ADJ
ejpam-3070	101	6	if	if	SCONJ
ejpam-3070	101	7	for	for	ADP
ejpam-3070	101	8	each	each	DET
ejpam-3070	101	9	ε	ε	PROPN
ejpam-3070	101	10	>	>	X
ejpam-3070	101	11	0	0	PROPN
ejpam-3070	101	12	,	,	PUNCT
ejpam-3070	101	13	t0	t0	PROPN
ejpam-3070	101	14	∈	∈	PROPN
ejpam-3070	101	15	r+	r+	ADV
ejpam-3070	101	16	,	,	PUNCT
ejpam-3070	101	17	there	there	PRON
ejpam-3070	101	18	exists	exist	VERB
ejpam-3070	101	19	a	a	DET
ejpam-3070	101	20	positive	positive	ADJ
ejpam-3070	101	21	function	function	NOUN
ejpam-3070	101	22	δ	δ	PROPN
ejpam-3070	101	23	=	=	SYM
ejpam-3070	101	24	δ(t0	δ(t0	PROPN
ejpam-3070	101	25	,	,	PUNCT
ejpam-3070	101	26	ε	ε	PROPN
ejpam-3070	101	27	)	)	PUNCT
ejpam-3070	101	28	that	that	PRON
ejpam-3070	101	29	is	be	AUX
ejpam-3070	101	30	continuous	continuous	ADJ
ejpam-3070	101	31	in	in	ADP
ejpam-3070	101	32	t0	t0	PROPN
ejpam-3070	101	33	for	for	ADP
ejpam-3070	101	34	each	each	DET
ejpam-3070	101	35	ε	ε	PROPN
ejpam-3070	101	36	such	such	ADJ
ejpam-3070	101	37	that	that	DET
ejpam-3070	101	38	h0(t0	h0(t0	NOUN
ejpam-3070	101	39	,	,	PUNCT
ejpam-3070	101	40	u0	u0	ADJ
ejpam-3070	101	41	)	)	PUNCT
ejpam-3070	101	42	<	<	X
ejpam-3070	101	43	δ	δ	PROPN
ejpam-3070	101	44	⇒	⇒	VERB
ejpam-3070	101	45	h(t	h(t	PROPN
ejpam-3070	101	46	,	,	PUNCT
ejpam-3070	101	47	u(t	u(t	NOUN
ejpam-3070	101	48	)	)	PUNCT
ejpam-3070	101	49	)	)	PUNCT
ejpam-3070	101	50	≤	≤	NUM
ejpam-3070	101	51	ε	ε	PROPN
ejpam-3070	101	52	,	,	PUNCT
ejpam-3070	101	53	t	t	PROPN
ejpam-3070	101	54	≥	≥	PROPN
ejpam-3070	101	55	t0	t0	PROPN
ejpam-3070	101	56	,	,	PUNCT
ejpam-3070	101	57	where	where	SCONJ
ejpam-3070	101	58	u(t	u(t	NOUN
ejpam-3070	101	59	,	,	PUNCT
ejpam-3070	101	60	t0	t0	PROPN
ejpam-3070	101	61	,	,	PUNCT
ejpam-3070	101	62	u0	u0	ADJ
ejpam-3070	101	63	)	)	PUNCT
ejpam-3070	101	64	is	be	AUX
ejpam-3070	101	65	any	any	DET
ejpam-3070	101	66	solution	solution	NOUN
ejpam-3070	101	67	of	of	ADP
ejpam-3070	101	68	(	(	PUNCT
ejpam-3070	101	69	9	9	NUM
ejpam-3070	101	70	)	)	PUNCT
ejpam-3070	101	71	.	.	PUNCT
ejpam-3070	102	1	definition	definition	NOUN
ejpam-3070	102	2	9	9	NUM
ejpam-3070	102	3	.	.	PUNCT
ejpam-3070	103	1	(	(	PUNCT
ejpam-3070	103	2	h0	h0	PROPN
ejpam-3070	103	3	,	,	PUNCT
ejpam-3070	103	4	h)−	h)−	PROPN
ejpam-3070	103	5	uniformly	uniformly	ADV
ejpam-3070	103	6	stable	stable	ADJ
ejpam-3070	103	7	if	if	SCONJ
ejpam-3070	103	8	the	the	DET
ejpam-3070	103	9	δ	δ	PROPN
ejpam-3070	103	10	in	in	ADP
ejpam-3070	103	11	definition	definition	NOUN
ejpam-3070	103	12	8	8	NUM
ejpam-3070	103	13	is	be	AUX
ejpam-3070	103	14	independent	independent	ADJ
ejpam-3070	103	15	of	of	ADP
ejpam-3070	103	16	t0	t0	PROPN
ejpam-3070	103	17	.	.	PUNCT
ejpam-3070	104	1	definition	definition	NOUN
ejpam-3070	104	2	10	10	NUM
ejpam-3070	104	3	.	.	PUNCT
ejpam-3070	105	1	(	(	PUNCT
ejpam-3070	105	2	h0	h0	PROPN
ejpam-3070	105	3	,	,	PUNCT
ejpam-3070	105	4	h)−	h)−	PROPN
ejpam-3070	105	5	equi	equi	NOUN
ejpam-3070	105	6	attractive	attractive	ADJ
ejpam-3070	105	7	,	,	PUNCT
ejpam-3070	105	8	if	if	SCONJ
ejpam-3070	105	9	for	for	ADP
ejpam-3070	105	10	each	each	DET
ejpam-3070	105	11	ε	ε	PROPN
ejpam-3070	105	12	>	>	X
ejpam-3070	105	13	0	0	PROPN
ejpam-3070	105	14	,	,	PUNCT
ejpam-3070	105	15	t0	t0	PROPN
ejpam-3070	105	16	∈	∈	PROPN
ejpam-3070	105	17	r+	r+	ADV
ejpam-3070	105	18	,	,	PUNCT
ejpam-3070	105	19	there	there	PRON
ejpam-3070	105	20	exists	exist	VERB
ejpam-3070	105	21	a	a	DET
ejpam-3070	105	22	positive	positive	ADJ
ejpam-3070	105	23	constant	constant	ADJ
ejpam-3070	105	24	δ0	δ0	NOUN
ejpam-3070	105	25	=	=	SYM
ejpam-3070	105	26	δ(t0	δ(t0	NOUN
ejpam-3070	105	27	)	)	PUNCT
ejpam-3070	105	28	and	and	CCONJ
ejpam-3070	105	29	t	t	PROPN
ejpam-3070	105	30	=	=	SYM
ejpam-3070	105	31	t	t	PROPN
ejpam-3070	105	32	(	(	PUNCT
ejpam-3070	105	33	t0	t0	PROPN
ejpam-3070	105	34	,	,	PUNCT
ejpam-3070	105	35	ε	ε	PROPN
ejpam-3070	105	36	)	)	PUNCT
ejpam-3070	105	37	such	such	ADJ
ejpam-3070	105	38	that	that	DET
ejpam-3070	105	39	h0(t0	h0(t0	NOUN
ejpam-3070	105	40	,	,	PUNCT
ejpam-3070	105	41	u0	u0	ADJ
ejpam-3070	105	42	)	)	PUNCT
ejpam-3070	105	43	<	<	X
ejpam-3070	105	44	δ0	δ0	NOUN
ejpam-3070	105	45	⇒	⇒	VERB
ejpam-3070	105	46	h(t	h(t	PROPN
ejpam-3070	105	47	,	,	PUNCT
ejpam-3070	105	48	u(t	u(t	NOUN
ejpam-3070	105	49	)	)	PUNCT
ejpam-3070	105	50	)	)	PUNCT
ejpam-3070	105	51	<	<	X
ejpam-3070	105	52	ε	ε	PROPN
ejpam-3070	105	53	,	,	PUNCT
ejpam-3070	105	54	t	t	PROPN
ejpam-3070	105	55	≥	≥	PROPN
ejpam-3070	105	56	t0	t0	NOUN
ejpam-3070	105	57	+	+	CCONJ
ejpam-3070	105	58	t.	t.	PROPN
ejpam-3070	105	59	.	.	PUNCT
ejpam-3070	106	1	definition	definition	NOUN
ejpam-3070	106	2	11	11	NUM
ejpam-3070	106	3	.	.	PUNCT
ejpam-3070	107	1	(	(	PUNCT
ejpam-3070	107	2	h0	h0	PROPN
ejpam-3070	107	3	,	,	PUNCT
ejpam-3070	107	4	h)−	h)−	PROPN
ejpam-3070	107	5	uniformly	uniformly	ADV
ejpam-3070	107	6	attractive	attractive	ADJ
ejpam-3070	107	7	,	,	PUNCT
ejpam-3070	107	8	if	if	SCONJ
ejpam-3070	107	9	definition	definition	NOUN
ejpam-3070	107	10	10	10	NUM
ejpam-3070	107	11	holds	hold	VERB
ejpam-3070	107	12	with	with	ADP
ejpam-3070	107	13	δ0	δ0	NOUN
ejpam-3070	107	14	and	and	CCONJ
ejpam-3070	107	15	t	t	NOUN
ejpam-3070	107	16	being	be	AUX
ejpam-3070	107	17	independent	independent	ADJ
ejpam-3070	107	18	of	of	ADP
ejpam-3070	107	19	t0	t0	PROPN
ejpam-3070	107	20	.	.	PUNCT
ejpam-3070	108	1	ch	ch	NOUN
ejpam-3070	108	2	.	.	PUNCT
ejpam-3070	108	3	a.	a.	PROPN
ejpam-3070	108	4	naidu,̧	naidu,̧	PROPN
ejpam-3070	108	5	d.	d.	PROPN
ejpam-3070	108	6	b.	b.	PROPN
ejpam-3070	108	7	dhaigude	dhaigude	PROPN
ejpam-3070	108	8	,	,	PUNCT
ejpam-3070	108	9	j.	j.	PROPN
ejpam-3070	108	10	v.	v.	PROPN
ejpam-3070	108	11	devi	devi	PROPN
ejpam-3070	108	12	/	/	SYM
ejpam-3070	108	13	eur	eur	PROPN
ejpam-3070	108	14	.	.	PUNCT
ejpam-3070	109	1	j.	j.	PROPN
ejpam-3070	109	2	pure	pure	PROPN
ejpam-3070	109	3	appl	appl	PROPN
ejpam-3070	109	4	.	.	PROPN
ejpam-3070	109	5	math	math	PROPN
ejpam-3070	109	6	,	,	PUNCT
ejpam-3070	109	7	10	10	NUM
ejpam-3070	109	8	(	(	PUNCT
ejpam-3070	109	9	4	4	NUM
ejpam-3070	109	10	)	)	PUNCT
ejpam-3070	109	11	(	(	PUNCT
ejpam-3070	109	12	2017	2017	NUM
ejpam-3070	109	13	)	)	PUNCT
ejpam-3070	109	14	,	,	PUNCT
ejpam-3070	109	15	645	645	NUM
ejpam-3070	109	16	-	-	SYM
ejpam-3070	109	17	654	654	NUM
ejpam-3070	109	18	650	650	NUM
ejpam-3070	109	19	definition	definition	NOUN
ejpam-3070	109	20	12	12	NUM
ejpam-3070	109	21	.	.	PUNCT
ejpam-3070	110	1	(	(	PUNCT
ejpam-3070	110	2	h0	h0	PROPN
ejpam-3070	110	3	,	,	PUNCT
ejpam-3070	110	4	h)−	h)−	PROPN
ejpam-3070	110	5	equi	equi	NOUN
ejpam-3070	110	6	asymptotically	asymptotically	ADV
ejpam-3070	110	7	stable	stable	ADJ
ejpam-3070	110	8	if	if	SCONJ
ejpam-3070	110	9	the	the	DET
ejpam-3070	110	10	definition	definition	NOUN
ejpam-3070	110	11	8	8	NUM
ejpam-3070	110	12	and	and	CCONJ
ejpam-3070	110	13	definition	definition	NOUN
ejpam-3070	110	14	10	10	NUM
ejpam-3070	110	15	hold	hold	VERB
ejpam-3070	110	16	simultaneously	simultaneously	ADV
ejpam-3070	110	17	.	.	PUNCT
ejpam-3070	111	1	definition	definition	NOUN
ejpam-3070	111	2	13	13	NUM
ejpam-3070	111	3	.	.	PUNCT
ejpam-3070	112	1	(	(	PUNCT
ejpam-3070	112	2	h0	h0	PROPN
ejpam-3070	112	3	,	,	PUNCT
ejpam-3070	112	4	h)−	h)−	PROPN
ejpam-3070	112	5	uniformly	uniformly	ADV
ejpam-3070	112	6	asymptotically	asymptotically	ADV
ejpam-3070	112	7	stable	stable	ADJ
ejpam-3070	112	8	if	if	SCONJ
ejpam-3070	112	9	the	the	DET
ejpam-3070	112	10	definition	definition	NOUN
ejpam-3070	112	11	9	9	NUM
ejpam-3070	112	12	and	and	CCONJ
ejpam-3070	112	13	definition	definition	NOUN
ejpam-3070	112	14	11	11	NUM
ejpam-3070	112	15	hold	hold	VERB
ejpam-3070	112	16	simultaneously	simultaneously	ADV
ejpam-3070	112	17	.	.	PUNCT
ejpam-3070	113	1	in	in	ADP
ejpam-3070	113	2	order	order	NOUN
ejpam-3070	113	3	to	to	PART
ejpam-3070	113	4	use	use	VERB
ejpam-3070	113	5	the	the	DET
ejpam-3070	113	6	method	method	NOUN
ejpam-3070	113	7	of	of	ADP
ejpam-3070	113	8	lyapunov	lyapunov	ADJ
ejpam-3070	113	9	function	function	NOUN
ejpam-3070	113	10	,	,	PUNCT
ejpam-3070	113	11	it	it	PRON
ejpam-3070	113	12	is	be	AUX
ejpam-3070	113	13	necessary	necessary	ADJ
ejpam-3070	113	14	to	to	PART
ejpam-3070	113	15	select	select	VERB
ejpam-3070	113	16	minimal	minimal	ADJ
ejpam-3070	113	17	subset	subset	NOUN
ejpam-3070	113	18	of	of	ADP
ejpam-3070	113	19	e	e	PROPN
ejpam-3070	113	20	over	over	ADP
ejpam-3070	113	21	which	which	PRON
ejpam-3070	113	22	the	the	DET
ejpam-3070	113	23	derivative	derivative	NOUN
ejpam-3070	113	24	of	of	ADP
ejpam-3070	113	25	the	the	DET
ejpam-3070	113	26	lyapunov	lyapunov	ADJ
ejpam-3070	113	27	function	function	NOUN
ejpam-3070	113	28	can	can	AUX
ejpam-3070	113	29	be	be	AUX
ejpam-3070	113	30	conveniently	conveniently	ADV
ejpam-3070	113	31	estimated	estimate	VERB
ejpam-3070	113	32	.	.	PUNCT
ejpam-3070	114	1	to	to	PART
ejpam-3070	114	2	define	define	VERB
ejpam-3070	114	3	this	this	DET
ejpam-3070	114	4	set	set	NOUN
ejpam-3070	114	5	,	,	PUNCT
ejpam-3070	114	6	we	we	PRON
ejpam-3070	114	7	consider	consider	VERB
ejpam-3070	114	8	v	v	ADP
ejpam-3070	114	9	∈	∈	PROPN
ejpam-3070	114	10	c[r+	c[r+	NOUN
ejpam-3070	114	11	×bb	×bb	NOUN
ejpam-3070	114	12	,	,	PUNCT
ejpam-3070	114	13	r+	r+	X
ejpam-3070	114	14	]	]	PUNCT
ejpam-3070	114	15	,	,	PUNCT
ejpam-3070	114	16	where	where	SCONJ
ejpam-3070	114	17	bb	bb	NOUN
ejpam-3070	114	18	=	=	SYM
ejpam-3070	114	19	b(θ	b(θ	PROPN
ejpam-3070	114	20	,	,	PUNCT
ejpam-3070	114	21	b	b	X
ejpam-3070	114	22	)	)	PUNCT
ejpam-3070	114	23	=	=	SYM
ejpam-3070	114	24	{	{	PUNCT
ejpam-3070	114	25	u	u	NOUN
ejpam-3070	114	26	∈	∈	PROPN
ejpam-3070	114	27	kc(rn	kc(rn	PROPN
ejpam-3070	114	28	)	)	PUNCT
ejpam-3070	114	29	:	:	PUNCT
ejpam-3070	115	1	d[u	d[u	PROPN
ejpam-3070	115	2	,	,	PUNCT
ejpam-3070	115	3	θ	θ	PROPN
ejpam-3070	115	4	]	]	PUNCT
ejpam-3070	115	5	≤	≤	ADJ
ejpam-3070	115	6	b	b	X
ejpam-3070	115	7	}	}	PUNCT
ejpam-3070	115	8	e1	e1	NOUN
ejpam-3070	115	9	=	=	SYM
ejpam-3070	115	10	{	{	PUNCT
ejpam-3070	115	11	u	u	NOUN
ejpam-3070	115	12	∈	∈	PROPN
ejpam-3070	115	13	e;v	e;v	PROPN
ejpam-3070	115	14	(	(	PUNCT
ejpam-3070	115	15	s	s	X
ejpam-3070	115	16	,	,	PUNCT
ejpam-3070	115	17	u(s	u(s	ADJ
ejpam-3070	115	18	)	)	PUNCT
ejpam-3070	115	19	)	)	PUNCT
ejpam-3070	115	20	≤	≤	NUM
ejpam-3070	116	1	v	v	X
ejpam-3070	116	2	(	(	PUNCT
ejpam-3070	116	3	t	t	PROPN
ejpam-3070	116	4	,	,	PUNCT
ejpam-3070	116	5	u(t	u(t	NOUN
ejpam-3070	116	6	)	)	PUNCT
ejpam-3070	116	7	)	)	PUNCT
ejpam-3070	116	8	,	,	PUNCT
ejpam-3070	116	9	t0	t0	PROPN
ejpam-3070	116	10	≤	≤	PROPN
ejpam-3070	116	11	s	s	PART
ejpam-3070	116	12	≤	≤	NUM
ejpam-3070	116	13	t	t	PROPN
ejpam-3070	116	14	}	}	PUNCT
ejpam-3070	116	15	,	,	PUNCT
ejpam-3070	116	16	where	where	SCONJ
ejpam-3070	116	17	v	v	X
ejpam-3070	116	18	∈	∈	PROPN
ejpam-3070	116	19	c[r+	c[r+	NOUN
ejpam-3070	116	20	×kc(rn	×kc(rn	PROPN
ejpam-3070	116	21	)	)	PUNCT
ejpam-3070	116	22	,	,	PUNCT
ejpam-3070	116	23	r+	r+	X
ejpam-3070	116	24	]	]	PUNCT
ejpam-3070	116	25	is	be	AUX
ejpam-3070	116	26	a	a	DET
ejpam-3070	116	27	lyapunov	lyapunov	ADJ
ejpam-3070	116	28	function	function	NOUN
ejpam-3070	116	29	.	.	PUNCT
ejpam-3070	117	1	in	in	ADP
ejpam-3070	117	2	order	order	NOUN
ejpam-3070	117	3	to	to	PART
ejpam-3070	117	4	discuss	discuss	VERB
ejpam-3070	117	5	the	the	DET
ejpam-3070	117	6	stability	stability	NOUN
ejpam-3070	117	7	properties	property	NOUN
ejpam-3070	117	8	of	of	ADP
ejpam-3070	117	9	(	(	PUNCT
ejpam-3070	117	10	9	9	X
ejpam-3070	117	11	)	)	PUNCT
ejpam-3070	117	12	let	let	VERB
ejpam-3070	117	13	us	we	PRON
ejpam-3070	117	14	assume	assume	VERB
ejpam-3070	117	15	that	that	SCONJ
ejpam-3070	117	16	the	the	DET
ejpam-3070	117	17	solutions	solution	NOUN
ejpam-3070	117	18	of	of	ADP
ejpam-3070	117	19	(	(	PUNCT
ejpam-3070	117	20	9	9	X
ejpam-3070	117	21	)	)	PUNCT
ejpam-3070	117	22	exist	exist	VERB
ejpam-3070	117	23	and	and	CCONJ
ejpam-3070	117	24	are	be	AUX
ejpam-3070	117	25	unique	unique	ADJ
ejpam-3070	117	26	for	for	ADP
ejpam-3070	117	27	all	all	DET
ejpam-3070	117	28	t	t	PROPN
ejpam-3070	117	29	≥	≥	PROPN
ejpam-3070	117	30	t0	t0	PROPN
ejpam-3070	117	31	.	.	PUNCT
ejpam-3070	118	1	in	in	ADP
ejpam-3070	118	2	addition	addition	NOUN
ejpam-3070	118	3	,	,	PUNCT
ejpam-3070	118	4	in	in	ADP
ejpam-3070	118	5	order	order	NOUN
ejpam-3070	118	6	to	to	PART
ejpam-3070	118	7	match	match	VERB
ejpam-3070	118	8	the	the	DET
ejpam-3070	118	9	behavior	behavior	NOUN
ejpam-3070	118	10	of	of	ADP
ejpam-3070	118	11	solutions	solution	NOUN
ejpam-3070	118	12	of	of	ADP
ejpam-3070	118	13	(	(	PUNCT
ejpam-3070	118	14	9	9	NUM
ejpam-3070	118	15	)	)	PUNCT
ejpam-3070	118	16	with	with	ADP
ejpam-3070	118	17	those	those	PRON
ejpam-3070	118	18	of	of	ADP
ejpam-3070	118	19	the	the	DET
ejpam-3070	118	20	corresponding	corresponding	ADJ
ejpam-3070	118	21	ordinary	ordinary	ADJ
ejpam-3070	118	22	differential	differential	ADJ
ejpam-3070	118	23	equations	equation	NOUN
ejpam-3070	118	24	with	with	ADP
ejpam-3070	118	25	causal	causal	NOUN
ejpam-3070	118	26	map	map	NOUN
ejpam-3070	118	27	,	,	PUNCT
ejpam-3070	118	28	we	we	PRON
ejpam-3070	118	29	assume	assume	VERB
ejpam-3070	118	30	that	that	SCONJ
ejpam-3070	118	31	u0	u0	ADJ
ejpam-3070	118	32	=	=	PUNCT
ejpam-3070	118	33	v0+w0	v0+w0	NOUN
ejpam-3070	118	34	so	so	SCONJ
ejpam-3070	118	35	that	that	PRON
ejpam-3070	118	36	hukuhara	hukuhara	ADV
ejpam-3070	118	37	difference	difference	VERB
ejpam-3070	118	38	u0−v0	u0−v0	PROPN
ejpam-3070	118	39	=	=	SYM
ejpam-3070	118	40	w0	w0	PROPN
ejpam-3070	118	41	exists	exist	VERB
ejpam-3070	118	42	.	.	PUNCT
ejpam-3070	119	1	consequently	consequently	ADV
ejpam-3070	119	2	,	,	PUNCT
ejpam-3070	119	3	in	in	ADP
ejpam-3070	119	4	what	what	PRON
ejpam-3070	119	5	follows	follow	VERB
ejpam-3070	119	6	,	,	PUNCT
ejpam-3070	119	7	we	we	PRON
ejpam-3070	119	8	consider	consider	VERB
ejpam-3070	119	9	the	the	DET
ejpam-3070	119	10	solutions	solution	NOUN
ejpam-3070	119	11	u(t	u(t	NOUN
ejpam-3070	119	12	)	)	PUNCT
ejpam-3070	119	13	=	=	SYM
ejpam-3070	119	14	u(t	u(t	NOUN
ejpam-3070	119	15	,	,	PUNCT
ejpam-3070	119	16	t0	t0	PROPN
ejpam-3070	119	17	,	,	PUNCT
ejpam-3070	119	18	u0	u0	ADJ
ejpam-3070	119	19	−	−	PROPN
ejpam-3070	119	20	v0	v0	NOUN
ejpam-3070	119	21	)	)	PUNCT
ejpam-3070	119	22	=	=	SYM
ejpam-3070	119	23	u(t	u(t	NOUN
ejpam-3070	119	24	,	,	PUNCT
ejpam-3070	119	25	t0,w0	t0,w0	PROPN
ejpam-3070	119	26	)	)	PUNCT
ejpam-3070	119	27	.	.	PUNCT
ejpam-3070	120	1	hence	hence	ADV
ejpam-3070	120	2	we	we	PRON
ejpam-3070	120	3	have	have	VERB
ejpam-3070	120	4	the	the	DET
ejpam-3070	120	5	initial	initial	ADJ
ejpam-3070	120	6	value	value	NOUN
ejpam-3070	120	7	problem	problem	NOUN
ejpam-3070	120	8	.	.	PUNCT
ejpam-3070	121	1	dhu	dhu	NOUN
ejpam-3070	121	2	=	=	PRON
ejpam-3070	121	3	(	(	PUNCT
ejpam-3070	121	4	qu)(t	qu)(t	PROPN
ejpam-3070	121	5	)	)	PUNCT
ejpam-3070	121	6	u(t0	u(t0	NOUN
ejpam-3070	121	7	)	)	PUNCT
ejpam-3070	121	8	=	=	SYM
ejpam-3070	121	9	w0	w0	PROPN
ejpam-3070	121	10	,	,	PUNCT
ejpam-3070	121	11	where	where	SCONJ
ejpam-3070	121	12	u0	u0	ADJ
ejpam-3070	121	13	=	=	PROPN
ejpam-3070	121	14	v0	v0	PROPN
ejpam-3070	121	15	+	+	PROPN
ejpam-3070	121	16	w0	w0	PROPN
ejpam-3070	121	17	(	(	PUNCT
ejpam-3070	121	18	10	10	NUM
ejpam-3070	121	19	)	)	PUNCT
ejpam-3070	121	20	this	this	DET
ejpam-3070	121	21	idea	idea	NOUN
ejpam-3070	121	22	is	be	AUX
ejpam-3070	121	23	clearly	clearly	ADV
ejpam-3070	121	24	explained	explain	VERB
ejpam-3070	121	25	with	with	ADP
ejpam-3070	121	26	example	example	NOUN
ejpam-3070	121	27	in	in	ADP
ejpam-3070	121	28	the	the	DET
ejpam-3070	121	29	paper	paper	NOUN
ejpam-3070	121	30	[	[	PUNCT
ejpam-3070	121	31	7	7	NUM
ejpam-3070	121	32	]	]	PUNCT
ejpam-3070	121	33	.	.	PUNCT
ejpam-3070	122	1	now	now	ADV
ejpam-3070	122	2	we	we	PRON
ejpam-3070	122	3	will	will	AUX
ejpam-3070	122	4	state	state	VERB
ejpam-3070	122	5	the	the	DET
ejpam-3070	122	6	comparison	comparison	NOUN
ejpam-3070	122	7	result	result	NOUN
ejpam-3070	122	8	,	,	PUNCT
ejpam-3070	122	9	which	which	PRON
ejpam-3070	122	10	is	be	AUX
ejpam-3070	122	11	analogous	analogous	ADJ
ejpam-3070	122	12	to	to	ADP
ejpam-3070	122	13	the	the	DET
ejpam-3070	122	14	comparison	comparison	NOUN
ejpam-3070	122	15	result	result	VERB
ejpam-3070	122	16	in	in	ADP
ejpam-3070	122	17	[	[	PUNCT
ejpam-3070	122	18	6	6	NUM
ejpam-3070	122	19	]	]	PUNCT
ejpam-3070	122	20	.	.	PUNCT
ejpam-3070	123	1	theorem	theorem	NOUN
ejpam-3070	123	2	1	1	NUM
ejpam-3070	123	3	.	.	PUNCT
ejpam-3070	123	4	suppose	suppose	VERB
ejpam-3070	123	5	that	that	SCONJ
ejpam-3070	123	6	the	the	DET
ejpam-3070	123	7	following	follow	VERB
ejpam-3070	123	8	hypotheses	hypothesis	NOUN
ejpam-3070	123	9	hold	hold	VERB
ejpam-3070	123	10	(	(	PUNCT
ejpam-3070	123	11	i	i	NOUN
ejpam-3070	123	12	)	)	PUNCT
ejpam-3070	123	13	v	v	ADP
ejpam-3070	123	14	∈	∈	PROPN
ejpam-3070	123	15	c[r+	c[r+	NOUN
ejpam-3070	123	16	×kc(rn),r+	×kc(rn),r+	PROPN
ejpam-3070	123	17	]	]	X
ejpam-3070	123	18	,	,	PUNCT
ejpam-3070	123	19	v(t	v(t	PROPN
ejpam-3070	123	20	,	,	PUNCT
ejpam-3070	123	21	u	u	NOUN
ejpam-3070	123	22	)	)	PUNCT
ejpam-3070	123	23	is	be	AUX
ejpam-3070	123	24	locally	locally	ADV
ejpam-3070	123	25	lipschitzian	lipschitzian	ADJ
ejpam-3070	123	26	in	in	ADP
ejpam-3070	123	27	u	u	NOUN
ejpam-3070	123	28	,	,	PUNCT
ejpam-3070	123	29	(	(	PUNCT
ejpam-3070	123	30	ii	ii	NOUN
ejpam-3070	123	31	)	)	PUNCT
ejpam-3070	123	32	for	for	ADP
ejpam-3070	123	33	t	t	PROPN
ejpam-3070	124	1	≥	≥	NOUN
ejpam-3070	124	2	t0	t0	PROPN
ejpam-3070	124	3	and	and	CCONJ
ejpam-3070	124	4	u	u	PROPN
ejpam-3070	124	5	∈	∈	PROPN
ejpam-3070	124	6	e1	e1	NOUN
ejpam-3070	124	7	,	,	PUNCT
ejpam-3070	124	8	d+v	d+v	PROPN
ejpam-3070	124	9	(	(	PUNCT
ejpam-3070	124	10	t	t	NOUN
ejpam-3070	124	11	,	,	PUNCT
ejpam-3070	124	12	u(t	u(t	NOUN
ejpam-3070	124	13	)	)	PUNCT
ejpam-3070	124	14	)	)	PUNCT
ejpam-3070	125	1	≤	≤	NUM
ejpam-3070	125	2	g(t	g(t	PROPN
ejpam-3070	125	3	,	,	PUNCT
ejpam-3070	125	4	v	v	PROPN
ejpam-3070	125	5	(	(	PUNCT
ejpam-3070	125	6	t	t	NOUN
ejpam-3070	125	7	,	,	PUNCT
ejpam-3070	125	8	u(t	u(t	NOUN
ejpam-3070	125	9	)	)	PUNCT
ejpam-3070	125	10	)	)	PUNCT
ejpam-3070	126	1	where	where	SCONJ
ejpam-3070	126	2	d+v	d+v	PROPN
ejpam-3070	126	3	(	(	PUNCT
ejpam-3070	126	4	t	t	PROPN
ejpam-3070	126	5	,	,	PUNCT
ejpam-3070	126	6	u(t	u(t	NOUN
ejpam-3070	126	7	)	)	PUNCT
ejpam-3070	126	8	)	)	PUNCT
ejpam-3070	127	1	=	=	SYM
ejpam-3070	127	2	lim	lim	PROPN
ejpam-3070	127	3	sup	sup	VERB
ejpam-3070	127	4	h→0	h→0	ADV
ejpam-3070	127	5	+	+	SYM
ejpam-3070	127	6	1	1	NUM
ejpam-3070	127	7	h	h	NOUN
ejpam-3070	128	1	[	[	X
ejpam-3070	128	2	v	v	X
ejpam-3070	128	3	(	(	PUNCT
ejpam-3070	128	4	t+	t+	NOUN
ejpam-3070	128	5	h	h	NOUN
ejpam-3070	128	6	,	,	PUNCT
ejpam-3070	128	7	u(t	u(t	NOUN
ejpam-3070	128	8	)	)	PUNCT
ejpam-3070	129	1	+	+	CCONJ
ejpam-3070	130	1	h(qu)(t))−	h(qu)(t))−	NOUN
ejpam-3070	130	2	v	v	ADP
ejpam-3070	130	3	(	(	PUNCT
ejpam-3070	130	4	t	t	PROPN
ejpam-3070	130	5	,	,	PUNCT
ejpam-3070	130	6	u(t	u(t	NOUN
ejpam-3070	130	7	)	)	PUNCT
ejpam-3070	130	8	)	)	PUNCT
ejpam-3070	130	9	]	]	PUNCT
ejpam-3070	130	10	(	(	PUNCT
ejpam-3070	130	11	iii	iii	X
ejpam-3070	130	12	)	)	PUNCT
ejpam-3070	130	13	r(t	r(t	NOUN
ejpam-3070	130	14	)	)	PUNCT
ejpam-3070	130	15	=	=	SYM
ejpam-3070	130	16	r(t	r(t	NOUN
ejpam-3070	130	17	,	,	PUNCT
ejpam-3070	130	18	t0	t0	PROPN
ejpam-3070	130	19	,	,	PUNCT
ejpam-3070	130	20	u0	u0	ADJ
ejpam-3070	130	21	)	)	PUNCT
ejpam-3070	130	22	is	be	AUX
ejpam-3070	130	23	the	the	DET
ejpam-3070	130	24	maximal	maximal	ADJ
ejpam-3070	130	25	solution	solution	NOUN
ejpam-3070	130	26	of	of	ADP
ejpam-3070	130	27	the	the	DET
ejpam-3070	130	28	scalar	scalar	ADJ
ejpam-3070	130	29	differential	differential	NOUN
ejpam-3070	130	30	equation	equation	NOUN
ejpam-3070	130	31	u′	u′	PROPN
ejpam-3070	130	32	=	=	SYM
ejpam-3070	130	33	g(t	g(t	PROPN
ejpam-3070	130	34	,	,	PUNCT
ejpam-3070	130	35	u	u	NOUN
ejpam-3070	130	36	)	)	PUNCT
ejpam-3070	130	37	,	,	PUNCT
ejpam-3070	130	38	u(t0	u(t0	NOUN
ejpam-3070	130	39	)	)	PUNCT
ejpam-3070	130	40	=	=	PUNCT
ejpam-3070	130	41	u0	u0	ADJ
ejpam-3070	130	42	≥	≥	NOUN
ejpam-3070	130	43	0	0	NUM
ejpam-3070	130	44	where	where	SCONJ
ejpam-3070	130	45	g	g	PROPN
ejpam-3070	130	46	∈	∈	PROPN
ejpam-3070	130	47	c[r2	c[r2	NOUN
ejpam-3070	131	1	+	+	ADJ
ejpam-3070	131	2	,	,	PUNCT
ejpam-3070	131	3	r+	r+	X
ejpam-3070	131	4	]	]	PUNCT
ejpam-3070	131	5	existing	exist	VERB
ejpam-3070	131	6	on	on	ADP
ejpam-3070	131	7	[	[	X
ejpam-3070	131	8	t0,∞	t0,∞	NUM
ejpam-3070	131	9	)	)	PUNCT
ejpam-3070	131	10	then	then	ADV
ejpam-3070	131	11	if	if	SCONJ
ejpam-3070	131	12	u(t	u(t	NOUN
ejpam-3070	131	13	;	;	PUNCT
ejpam-3070	131	14	t0	t0	NUM
ejpam-3070	131	15	,	,	PUNCT
ejpam-3070	131	16	u0	u0	ADJ
ejpam-3070	131	17	)	)	PUNCT
ejpam-3070	131	18	is	be	AUX
ejpam-3070	131	19	any	any	DET
ejpam-3070	131	20	solution	solution	NOUN
ejpam-3070	131	21	of	of	ADP
ejpam-3070	131	22	ivp	ivp	PROPN
ejpam-3070	131	23	(	(	PUNCT
ejpam-3070	131	24	9	9	X
ejpam-3070	131	25	)	)	PUNCT
ejpam-3070	131	26	existing	exist	VERB
ejpam-3070	131	27	on	on	ADP
ejpam-3070	131	28	[	[	X
ejpam-3070	131	29	t0,∞	t0,∞	NUM
ejpam-3070	131	30	)	)	PUNCT
ejpam-3070	131	31	,	,	PUNCT
ejpam-3070	131	32	v	v	X
ejpam-3070	131	33	(	(	PUNCT
ejpam-3070	131	34	t0	t0	PROPN
ejpam-3070	131	35	,	,	PUNCT
ejpam-3070	131	36	u0	u0	ADJ
ejpam-3070	131	37	)	)	PUNCT
ejpam-3070	131	38	≤	≤	NOUN
ejpam-3070	131	39	u0	u0	PROPN
ejpam-3070	131	40	implies	imply	VERB
ejpam-3070	131	41	v	v	NUM
ejpam-3070	131	42	(	(	PUNCT
ejpam-3070	131	43	t	t	NOUN
ejpam-3070	131	44	,	,	PUNCT
ejpam-3070	131	45	u(t	u(t	NOUN
ejpam-3070	131	46	)	)	PUNCT
ejpam-3070	131	47	)	)	PUNCT
ejpam-3070	131	48	≤	≤	NUM
ejpam-3070	131	49	r(t	r(t	NOUN
ejpam-3070	131	50	)	)	PUNCT
ejpam-3070	131	51	,	,	PUNCT
ejpam-3070	131	52	t	t	PROPN
ejpam-3070	131	53	≥	≥	PROPN
ejpam-3070	131	54	t0	t0	PROPN
ejpam-3070	131	55	.	.	PUNCT
ejpam-3070	132	1	corollary	corollary	ADJ
ejpam-3070	132	2	1	1	NUM
ejpam-3070	132	3	.	.	PUNCT
ejpam-3070	133	1	if	if	SCONJ
ejpam-3070	133	2	,	,	PUNCT
ejpam-3070	133	3	in	in	ADP
ejpam-3070	133	4	addition	addition	NOUN
ejpam-3070	133	5	to	to	ADP
ejpam-3070	133	6	the	the	DET
ejpam-3070	133	7	assumptions	assumption	NOUN
ejpam-3070	133	8	of	of	ADP
ejpam-3070	133	9	theorem	theorem	NOUN
ejpam-3070	133	10	1	1	NUM
ejpam-3070	133	11	with	with	ADP
ejpam-3070	133	12	g(t	g(t	PROPN
ejpam-3070	133	13	,	,	PUNCT
ejpam-3070	133	14	u)=0	u)=0	ADJ
ejpam-3070	133	15	and	and	CCONJ
ejpam-3070	133	16	u(t	u(t	NOUN
ejpam-3070	133	17	)	)	PUNCT
ejpam-3070	133	18	∈	∈	PROPN
ejpam-3070	133	19	e1	e1	NOUN
ejpam-3070	133	20	then	then	ADV
ejpam-3070	133	21	v	v	X
ejpam-3070	133	22	(	(	PUNCT
ejpam-3070	133	23	t	t	PROPN
ejpam-3070	133	24	,	,	PUNCT
ejpam-3070	133	25	u(t	u(t	NOUN
ejpam-3070	133	26	)	)	PUNCT
ejpam-3070	133	27	)	)	PUNCT
ejpam-3070	133	28	≤	≤	NUM
ejpam-3070	133	29	v	v	X
ejpam-3070	133	30	(	(	PUNCT
ejpam-3070	133	31	t0	t0	PROPN
ejpam-3070	133	32	,	,	PUNCT
ejpam-3070	133	33	u0	u0	ADJ
ejpam-3070	133	34	)	)	PUNCT
ejpam-3070	133	35	,	,	PUNCT
ejpam-3070	133	36	t	t	PROPN
ejpam-3070	133	37	≥	≥	PROPN
ejpam-3070	133	38	t0	t0	PROPN
ejpam-3070	133	39	,	,	PUNCT
ejpam-3070	133	40	where	where	SCONJ
ejpam-3070	133	41	u(t	u(t	NOUN
ejpam-3070	133	42	)	)	PUNCT
ejpam-3070	133	43	is	be	AUX
ejpam-3070	133	44	any	any	DET
ejpam-3070	133	45	solution	solution	NOUN
ejpam-3070	133	46	of	of	ADP
ejpam-3070	133	47	ivp	ivp	NOUN
ejpam-3070	133	48	(	(	PUNCT
ejpam-3070	133	49	9	9	NUM
ejpam-3070	133	50	)	)	PUNCT
ejpam-3070	133	51	.	.	PUNCT
ejpam-3070	134	1	ch	ch	NOUN
ejpam-3070	134	2	.	.	PUNCT
ejpam-3070	134	3	a.	a.	PROPN
ejpam-3070	134	4	naidu,̧	naidu,̧	PROPN
ejpam-3070	134	5	d.	d.	PROPN
ejpam-3070	134	6	b.	b.	PROPN
ejpam-3070	134	7	dhaigude	dhaigude	PROPN
ejpam-3070	134	8	,	,	PUNCT
ejpam-3070	134	9	j.	j.	PROPN
ejpam-3070	134	10	v.	v.	PROPN
ejpam-3070	134	11	devi	devi	PROPN
ejpam-3070	134	12	/	/	SYM
ejpam-3070	134	13	eur	eur	PROPN
ejpam-3070	134	14	.	.	PUNCT
ejpam-3070	135	1	j.	j.	PROPN
ejpam-3070	135	2	pure	pure	PROPN
ejpam-3070	135	3	appl	appl	PROPN
ejpam-3070	135	4	.	.	PROPN
ejpam-3070	135	5	math	math	PROPN
ejpam-3070	135	6	,	,	PUNCT
ejpam-3070	135	7	10	10	NUM
ejpam-3070	135	8	(	(	PUNCT
ejpam-3070	135	9	4	4	NUM
ejpam-3070	135	10	)	)	PUNCT
ejpam-3070	135	11	(	(	PUNCT
ejpam-3070	135	12	2017	2017	NUM
ejpam-3070	135	13	)	)	PUNCT
ejpam-3070	135	14	,	,	PUNCT
ejpam-3070	135	15	645	645	NUM
ejpam-3070	135	16	-	-	SYM
ejpam-3070	135	17	654	654	NUM
ejpam-3070	135	18	651	651	NUM
ejpam-3070	135	19	now	now	ADV
ejpam-3070	135	20	we	we	PRON
ejpam-3070	135	21	prove	prove	VERB
ejpam-3070	135	22	the	the	DET
ejpam-3070	135	23	main	main	ADJ
ejpam-3070	135	24	stability	stability	NOUN
ejpam-3070	135	25	results	result	VERB
ejpam-3070	135	26	for	for	ADP
ejpam-3070	135	27	the	the	DET
ejpam-3070	135	28	system	system	NOUN
ejpam-3070	135	29	(	(	PUNCT
ejpam-3070	135	30	9	9	NUM
ejpam-3070	135	31	)	)	PUNCT
ejpam-3070	135	32	theorem	theorem	NOUN
ejpam-3070	135	33	2	2	NUM
ejpam-3070	135	34	.	.	PUNCT
ejpam-3070	135	35	suppose	suppose	VERB
ejpam-3070	135	36	that	that	SCONJ
ejpam-3070	135	37	the	the	DET
ejpam-3070	135	38	following	follow	VERB
ejpam-3070	135	39	hypothesis	hypothesis	NOUN
ejpam-3070	135	40	hold	hold	NOUN
ejpam-3070	135	41	(	(	PUNCT
ejpam-3070	135	42	i	i	NOUN
ejpam-3070	135	43	)	)	PUNCT
ejpam-3070	135	44	v	v	ADP
ejpam-3070	135	45	∈	∈	PROPN
ejpam-3070	135	46	c[r+	c[r+	NOUN
ejpam-3070	135	47	×kc(rn	×kc(rn	PROPN
ejpam-3070	135	48	)	)	PUNCT
ejpam-3070	135	49	,	,	PUNCT
ejpam-3070	135	50	r+	r+	X
ejpam-3070	135	51	]	]	PUNCT
ejpam-3070	135	52	,	,	PUNCT
ejpam-3070	135	53	h	h	PROPN
ejpam-3070	135	54	∈	∈	PROPN
ejpam-3070	135	55	γ	γ	X
ejpam-3070	135	56	,	,	PUNCT
ejpam-3070	135	57	v(t	v(t	PROPN
ejpam-3070	135	58	,	,	PUNCT
ejpam-3070	135	59	u	u	NOUN
ejpam-3070	135	60	)	)	PUNCT
ejpam-3070	135	61	is	be	AUX
ejpam-3070	135	62	locally	locally	ADV
ejpam-3070	135	63	lipschitzian	lipschitzian	ADJ
ejpam-3070	135	64	in	in	ADP
ejpam-3070	135	65	u	u	NOUN
ejpam-3070	135	66	and	and	CCONJ
ejpam-3070	135	67	h	h	NOUN
ejpam-3070	135	68	-	-	PUNCT
ejpam-3070	135	69	positive	positive	ADJ
ejpam-3070	135	70	definite	definite	ADJ
ejpam-3070	135	71	,	,	PUNCT
ejpam-3070	135	72	(	(	PUNCT
ejpam-3070	135	73	ii	ii	NOUN
ejpam-3070	135	74	)	)	PUNCT
ejpam-3070	135	75	d+v	d+v	PROPN
ejpam-3070	135	76	(	(	PUNCT
ejpam-3070	135	77	t	t	NOUN
ejpam-3070	135	78	,	,	PUNCT
ejpam-3070	135	79	u(t	u(t	NOUN
ejpam-3070	135	80	)	)	PUNCT
ejpam-3070	135	81	)	)	PUNCT
ejpam-3070	135	82	≤	≤	NUM
ejpam-3070	135	83	0	0	NUM
ejpam-3070	136	1	for	for	ADP
ejpam-3070	136	2	(	(	PUNCT
ejpam-3070	136	3	t	t	PROPN
ejpam-3070	136	4	,	,	PUNCT
ejpam-3070	136	5	u	u	NOUN
ejpam-3070	136	6	)	)	PUNCT
ejpam-3070	136	7	∈	∈	PROPN
ejpam-3070	136	8	s(h	s(h	PROPN
ejpam-3070	136	9	,	,	PUNCT
ejpam-3070	136	10	ρ	ρ	NOUN
ejpam-3070	136	11	)	)	PUNCT
ejpam-3070	136	12	where	where	SCONJ
ejpam-3070	136	13	s(h	s(h	PROPN
ejpam-3070	136	14	,	,	PUNCT
ejpam-3070	136	15	ρ	ρ	NOUN
ejpam-3070	136	16	)	)	PUNCT
ejpam-3070	136	17	=	=	PRON
ejpam-3070	136	18	{	{	PUNCT
ejpam-3070	136	19	(	(	PUNCT
ejpam-3070	136	20	t	t	PROPN
ejpam-3070	136	21	,	,	PUNCT
ejpam-3070	136	22	u	u	NOUN
ejpam-3070	136	23	)	)	PUNCT
ejpam-3070	136	24	∈	∈	PROPN
ejpam-3070	136	25	r+	r+	PUNCT
ejpam-3070	136	26	×kc(rn	×kc(rn	PROPN
ejpam-3070	136	27	)	)	PUNCT
ejpam-3070	136	28	,	,	PUNCT
ejpam-3070	136	29	h(t	h(t	PROPN
ejpam-3070	136	30	,	,	PUNCT
ejpam-3070	136	31	u	u	NOUN
ejpam-3070	136	32	)	)	PUNCT
ejpam-3070	136	33	<	<	X
ejpam-3070	136	34	ρ	ρ	PROPN
ejpam-3070	136	35	,	,	PUNCT
ejpam-3070	136	36	ρ	ρ	PROPN
ejpam-3070	136	37	>	>	X
ejpam-3070	136	38	0	0	NUM
ejpam-3070	136	39	}	}	PUNCT
ejpam-3070	136	40	and	and	CCONJ
ejpam-3070	136	41	u	u	PROPN
ejpam-3070	136	42	∈	∈	PROPN
ejpam-3070	136	43	e1	e1	NOUN
ejpam-3070	136	44	then	then	ADV
ejpam-3070	136	45	(	(	PUNCT
ejpam-3070	136	46	a	a	X
ejpam-3070	136	47	)	)	PUNCT
ejpam-3070	136	48	if	if	SCONJ
ejpam-3070	136	49	,	,	PUNCT
ejpam-3070	136	50	in	in	ADP
ejpam-3070	136	51	addition	addition	NOUN
ejpam-3070	136	52	,	,	PUNCT
ejpam-3070	136	53	h0	h0	PROPN
ejpam-3070	136	54	∈	∈	PROPN
ejpam-3070	136	55	γ	γ	PROPN
ejpam-3070	136	56	,	,	PUNCT
ejpam-3070	136	57	h0	h0	PROPN
ejpam-3070	136	58	is	be	AUX
ejpam-3070	136	59	finer	fine	ADJ
ejpam-3070	136	60	than	than	ADP
ejpam-3070	136	61	h	h	NOUN
ejpam-3070	136	62	and	and	CCONJ
ejpam-3070	136	63	v(t	v(t	PROPN
ejpam-3070	136	64	,	,	PUNCT
ejpam-3070	136	65	u	u	NOUN
ejpam-3070	136	66	)	)	PUNCT
ejpam-3070	136	67	is	be	AUX
ejpam-3070	136	68	h0	h0	ADJ
ejpam-3070	136	69	-	-	PUNCT
ejpam-3070	136	70	weakly	weakly	ADJ
ejpam-3070	136	71	decrescent	decrescent	NOUN
ejpam-3070	136	72	,	,	PUNCT
ejpam-3070	136	73	then	then	ADV
ejpam-3070	136	74	the	the	DET
ejpam-3070	136	75	system	system	NOUN
ejpam-3070	136	76	(	(	PUNCT
ejpam-3070	136	77	9	9	NUM
ejpam-3070	136	78	)	)	PUNCT
ejpam-3070	136	79	is	be	AUX
ejpam-3070	136	80	(	(	PUNCT
ejpam-3070	136	81	h0	h0	NOUN
ejpam-3070	136	82	,	,	PUNCT
ejpam-3070	136	83	h)equistable	h)equistable	ADJ
ejpam-3070	136	84	.	.	PUNCT
ejpam-3070	137	1	(	(	PUNCT
ejpam-3070	137	2	b	b	X
ejpam-3070	137	3	)	)	PUNCT
ejpam-3070	137	4	if	if	SCONJ
ejpam-3070	137	5	,	,	PUNCT
ejpam-3070	137	6	in	in	ADP
ejpam-3070	137	7	addition	addition	NOUN
ejpam-3070	137	8	,	,	PUNCT
ejpam-3070	137	9	h0	h0	PROPN
ejpam-3070	137	10	∈	∈	PROPN
ejpam-3070	137	11	γ	γ	PROPN
ejpam-3070	137	12	,	,	PUNCT
ejpam-3070	137	13	h0	h0	PROPN
ejpam-3070	137	14	is	be	AUX
ejpam-3070	137	15	uniformly	uniformly	ADV
ejpam-3070	137	16	finer	fine	ADJ
ejpam-3070	137	17	than	than	ADP
ejpam-3070	137	18	h	h	NOUN
ejpam-3070	137	19	and	and	CCONJ
ejpam-3070	137	20	v(t	v(t	PROPN
ejpam-3070	137	21	,	,	PUNCT
ejpam-3070	137	22	u	u	NOUN
ejpam-3070	137	23	)	)	PUNCT
ejpam-3070	137	24	is	be	AUX
ejpam-3070	137	25	h0decrescent	h0decrescent	ADJ
ejpam-3070	137	26	,	,	PUNCT
ejpam-3070	137	27	then	then	ADV
ejpam-3070	137	28	the	the	DET
ejpam-3070	137	29	system	system	NOUN
ejpam-3070	137	30	(	(	PUNCT
ejpam-3070	137	31	9	9	NUM
ejpam-3070	137	32	)	)	PUNCT
ejpam-3070	137	33	is	be	AUX
ejpam-3070	137	34	(	(	PUNCT
ejpam-3070	137	35	h0	h0	PROPN
ejpam-3070	137	36	,	,	PUNCT
ejpam-3070	137	37	h)-uniformly	h)-uniformly	ADV
ejpam-3070	137	38	stable	stable	ADJ
ejpam-3070	137	39	.	.	PUNCT
ejpam-3070	138	1	proof	proof	NOUN
ejpam-3070	138	2	.	.	PUNCT
ejpam-3070	139	1	given	give	VERB
ejpam-3070	139	2	that	that	SCONJ
ejpam-3070	139	3	v(t	v(t	NOUN
ejpam-3070	139	4	,	,	PUNCT
ejpam-3070	139	5	u	u	NOUN
ejpam-3070	139	6	)	)	PUNCT
ejpam-3070	139	7	is	be	AUX
ejpam-3070	139	8	h0	h0	VERB
ejpam-3070	139	9	-weakly	-weakly	NOUN
ejpam-3070	139	10	decrescent	decrescent	NOUN
ejpam-3070	139	11	,	,	PUNCT
ejpam-3070	139	12	then	then	ADV
ejpam-3070	139	13	by	by	ADP
ejpam-3070	139	14	the	the	DET
ejpam-3070	139	15	definition	definition	NOUN
ejpam-3070	139	16	for	for	ADP
ejpam-3070	139	17	t0	t0	PROPN
ejpam-3070	139	18	∈	∈	PROPN
ejpam-3070	139	19	r+	r+	X
ejpam-3070	139	20	,	,	PUNCT
ejpam-3070	139	21	w0	w0	PROPN
ejpam-3070	139	22	∈	∈	PROPN
ejpam-3070	139	23	kc(rn	kc(rn	PROPN
ejpam-3070	139	24	)	)	PUNCT
ejpam-3070	139	25	,	,	PUNCT
ejpam-3070	139	26	there	there	PRON
ejpam-3070	139	27	exist	exist	VERB
ejpam-3070	139	28	constsnt	constsnt	NOUN
ejpam-3070	139	29	δ0	δ0	NOUN
ejpam-3070	139	30	=	=	NOUN
ejpam-3070	139	31	δ0(t0	δ0(t0	PROPN
ejpam-3070	139	32	)	)	PUNCT
ejpam-3070	139	33	>	>	X
ejpam-3070	139	34	0	0	PUNCT
ejpam-3070	139	35	and	and	CCONJ
ejpam-3070	139	36	a	a	DET
ejpam-3070	139	37	function	function	NOUN
ejpam-3070	139	38	a	a	DET
ejpam-3070	139	39	∈	∈	NOUN
ejpam-3070	139	40	ck	ck	INTJ
ejpam-3070	139	41	such	such	ADJ
ejpam-3070	139	42	that	that	DET
ejpam-3070	139	43	v	v	NOUN
ejpam-3070	139	44	(	(	PUNCT
ejpam-3070	139	45	t0,w0	t0,w0	PROPN
ejpam-3070	139	46	)	)	PUNCT
ejpam-3070	139	47	≤	≤	NOUN
ejpam-3070	139	48	a(t0	a(t0	NOUN
ejpam-3070	139	49	,	,	PUNCT
ejpam-3070	139	50	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	139	51	)	)	PUNCT
ejpam-3070	139	52	)	)	PUNCT
ejpam-3070	139	53	(	(	PUNCT
ejpam-3070	139	54	11	11	NUM
ejpam-3070	139	55	)	)	PUNCT
ejpam-3070	139	56	provided	provide	VERB
ejpam-3070	139	57	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	139	58	)	)	PUNCT
ejpam-3070	139	59	<	<	X
ejpam-3070	139	60	δ0	δ0	NOUN
ejpam-3070	139	61	and	and	CCONJ
ejpam-3070	139	62	w0	w0	PROPN
ejpam-3070	139	63	=	=	PROPN
ejpam-3070	139	64	u0	u0	PROPN
ejpam-3070	139	65	−	−	PROPN
ejpam-3070	139	66	v0	v0	NOUN
ejpam-3070	139	67	.	.	PUNCT
ejpam-3070	140	1	also	also	ADV
ejpam-3070	140	2	from	from	ADP
ejpam-3070	140	3	hypothesis	hypothesis	NOUN
ejpam-3070	140	4	v(t	v(t	PROPN
ejpam-3070	140	5	,	,	PUNCT
ejpam-3070	140	6	u	u	NOUN
ejpam-3070	140	7	)	)	PUNCT
ejpam-3070	140	8	is	be	AUX
ejpam-3070	140	9	h	h	ADJ
ejpam-3070	140	10	-	-	PUNCT
ejpam-3070	140	11	positive	positive	ADJ
ejpam-3070	140	12	definite	definite	ADJ
ejpam-3070	140	13	,	,	PUNCT
ejpam-3070	140	14	implies	imply	VERB
ejpam-3070	140	15	that	that	SCONJ
ejpam-3070	140	16	there	there	PRON
ejpam-3070	140	17	exist	exist	VERB
ejpam-3070	140	18	constant	constant	ADJ
ejpam-3070	140	19	ρ0	ρ0	PROPN
ejpam-3070	140	20	∈	∈	PROPN
ejpam-3070	140	21	(	(	PUNCT
ejpam-3070	140	22	0	0	NUM
ejpam-3070	140	23	,	,	PUNCT
ejpam-3070	140	24	ρ	ρ	NOUN
ejpam-3070	140	25	)	)	PUNCT
ejpam-3070	140	26	and	and	CCONJ
ejpam-3070	140	27	a	a	DET
ejpam-3070	140	28	function	function	NOUN
ejpam-3070	140	29	b	b	NOUN
ejpam-3070	140	30	∈	∈	PROPN
ejpam-3070	140	31	k	k	ADP
ejpam-3070	140	32	such	such	ADJ
ejpam-3070	140	33	that	that	SCONJ
ejpam-3070	140	34	b(h(t	b(h(t	PROPN
ejpam-3070	140	35	,	,	PUNCT
ejpam-3070	140	36	u	u	NOUN
ejpam-3070	140	37	)	)	PUNCT
ejpam-3070	140	38	)	)	PUNCT
ejpam-3070	141	1	≤	≤	NUM
ejpam-3070	141	2	v	v	X
ejpam-3070	141	3	(	(	PUNCT
ejpam-3070	141	4	t	t	PROPN
ejpam-3070	141	5	,	,	PUNCT
ejpam-3070	141	6	u	u	NOUN
ejpam-3070	141	7	)	)	PUNCT
ejpam-3070	141	8	whenever	whenever	SCONJ
ejpam-3070	141	9	h(t	h(t	PROPN
ejpam-3070	141	10	,	,	PUNCT
ejpam-3070	141	11	u	u	NOUN
ejpam-3070	141	12	)	)	PUNCT
ejpam-3070	141	13	≤	≤	NOUN
ejpam-3070	141	14	ρ0	ρ0	PROPN
ejpam-3070	141	15	(	(	PUNCT
ejpam-3070	141	16	12	12	NUM
ejpam-3070	141	17	)	)	PUNCT
ejpam-3070	141	18	and	and	CCONJ
ejpam-3070	141	19	by	by	ADP
ejpam-3070	141	20	the	the	DET
ejpam-3070	141	21	assumption	assumption	NOUN
ejpam-3070	141	22	that	that	SCONJ
ejpam-3070	141	23	h0	h0	PROPN
ejpam-3070	141	24	is	be	AUX
ejpam-3070	141	25	finer	fine	ADJ
ejpam-3070	141	26	than	than	ADP
ejpam-3070	141	27	h	h	NOUN
ejpam-3070	141	28	,	,	PUNCT
ejpam-3070	141	29	there	there	PRON
ejpam-3070	141	30	exists	exist	VERB
ejpam-3070	141	31	a	a	DET
ejpam-3070	141	32	constant	constant	ADJ
ejpam-3070	141	33	δ1	δ1	NOUN
ejpam-3070	141	34	=	=	SYM
ejpam-3070	141	35	δ1(t0	δ1(t0	PROPN
ejpam-3070	141	36	)	)	PUNCT
ejpam-3070	141	37	>	>	X
ejpam-3070	141	38	0	0	PUNCT
ejpam-3070	142	1	and	and	CCONJ
ejpam-3070	142	2	function	function	VERB
ejpam-3070	142	3	φ	φ	PROPN
ejpam-3070	142	4	∈	∈	PROPN
ejpam-3070	142	5	ck	ck	INTJ
ejpam-3070	142	6	such	such	ADJ
ejpam-3070	142	7	that	that	DET
ejpam-3070	142	8	h(t0,w0	h(t0,w0	NOUN
ejpam-3070	142	9	)	)	PUNCT
ejpam-3070	142	10	≤	≤	NOUN
ejpam-3070	142	11	φ(t0	φ(t0	NOUN
ejpam-3070	142	12	,	,	PUNCT
ejpam-3070	142	13	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	142	14	)	)	PUNCT
ejpam-3070	142	15	)	)	PUNCT
ejpam-3070	143	1	if	if	SCONJ
ejpam-3070	143	2	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	143	3	)	)	PUNCT
ejpam-3070	143	4	<	<	X
ejpam-3070	143	5	δ1	δ1	NOUN
ejpam-3070	143	6	,	,	PUNCT
ejpam-3070	143	7	(	(	PUNCT
ejpam-3070	143	8	13	13	NUM
ejpam-3070	143	9	)	)	PUNCT
ejpam-3070	143	10	where	where	SCONJ
ejpam-3070	143	11	δ1	δ1	NOUN
ejpam-3070	143	12	is	be	AUX
ejpam-3070	143	13	chosen	choose	VERB
ejpam-3070	143	14	so	so	SCONJ
ejpam-3070	143	15	that	that	SCONJ
ejpam-3070	143	16	φ(t0	φ(t0	NOUN
ejpam-3070	143	17	,	,	PUNCT
ejpam-3070	143	18	δ1	δ1	NOUN
ejpam-3070	143	19	)	)	PUNCT
ejpam-3070	143	20	<	<	X
ejpam-3070	143	21	ρ0	ρ0	PROPN
ejpam-3070	143	22	.	.	PUNCT
ejpam-3070	144	1	let	let	AUX
ejpam-3070	144	2	ε	ε	PROPN
ejpam-3070	144	3	∈	∈	PROPN
ejpam-3070	144	4	(	(	PUNCT
ejpam-3070	144	5	0	0	NUM
ejpam-3070	144	6	,	,	PUNCT
ejpam-3070	144	7	ρ0	ρ0	PROPN
ejpam-3070	144	8	)	)	PUNCT
ejpam-3070	144	9	and	and	CCONJ
ejpam-3070	144	10	t0	t0	PROPN
ejpam-3070	144	11	∈	∈	PROPN
ejpam-3070	144	12	r+	r+	PUNCT
ejpam-3070	144	13	be	be	AUX
ejpam-3070	144	14	given	give	VERB
ejpam-3070	144	15	,	,	PUNCT
ejpam-3070	144	16	then	then	ADV
ejpam-3070	144	17	by	by	ADP
ejpam-3070	144	18	the	the	DET
ejpam-3070	144	19	assumption	assumption	NOUN
ejpam-3070	144	20	on	on	ADP
ejpam-3070	144	21	’	'	PUNCT
ejpam-3070	144	22	a	a	PRON
ejpam-3070	144	23	’	'	PUNCT
ejpam-3070	144	24	,	,	PUNCT
ejpam-3070	144	25	there	there	PRON
ejpam-3070	144	26	exists	exist	VERB
ejpam-3070	144	27	a	a	DET
ejpam-3070	144	28	δ2	δ2	VERB
ejpam-3070	144	29	=	=	SYM
ejpam-3070	144	30	δ2(t0	δ2(t0	NOUN
ejpam-3070	144	31	,	,	PUNCT
ejpam-3070	144	32	ε	ε	PROPN
ejpam-3070	144	33	)	)	PUNCT
ejpam-3070	144	34	>	>	X
ejpam-3070	144	35	0	0	PUNCT
ejpam-3070	145	1	that	that	PRON
ejpam-3070	145	2	is	be	AUX
ejpam-3070	145	3	continuous	continuous	ADJ
ejpam-3070	145	4	in	in	ADP
ejpam-3070	145	5	t0	t0	PROPN
ejpam-3070	145	6	such	such	ADJ
ejpam-3070	145	7	that	that	PRON
ejpam-3070	145	8	a(t0	a(t0	NOUN
ejpam-3070	145	9	,	,	PUNCT
ejpam-3070	145	10	δ2	δ2	ADJ
ejpam-3070	145	11	)	)	PUNCT
ejpam-3070	145	12	<	<	X
ejpam-3070	145	13	b(ε	b(ε	PROPN
ejpam-3070	145	14	)	)	PUNCT
ejpam-3070	145	15	.	.	PUNCT
ejpam-3070	146	1	(	(	PUNCT
ejpam-3070	146	2	14	14	NUM
ejpam-3070	146	3	)	)	PUNCT
ejpam-3070	146	4	now	now	ADV
ejpam-3070	146	5	choose	choose	VERB
ejpam-3070	146	6	δ(t0	δ(t0	NOUN
ejpam-3070	146	7	)	)	PUNCT
ejpam-3070	147	1	=	=	SYM
ejpam-3070	147	2	min{δ0	min{δ0	NOUN
ejpam-3070	147	3	,	,	PUNCT
ejpam-3070	147	4	δ1	δ1	NOUN
ejpam-3070	147	5	,	,	PUNCT
ejpam-3070	147	6	δ2	δ2	VERB
ejpam-3070	147	7	}	}	PUNCT
ejpam-3070	147	8	then	then	ADV
ejpam-3070	147	9	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	147	10	)	)	PUNCT
ejpam-3070	147	11	<	<	X
ejpam-3070	147	12	δ	δ	PROPN
ejpam-3070	147	13	,	,	PUNCT
ejpam-3070	147	14	where	where	SCONJ
ejpam-3070	147	15	w0	w0	PROPN
ejpam-3070	147	16	=	=	PROPN
ejpam-3070	147	17	u0	u0	PROPN
ejpam-3070	147	18	−	−	PROPN
ejpam-3070	147	19	v0	v0	NOUN
ejpam-3070	147	20	.	.	PUNCT
ejpam-3070	148	1	b(h(t0,w0	b(h(t0,w0	NOUN
ejpam-3070	148	2	)	)	PUNCT
ejpam-3070	148	3	)	)	PUNCT
ejpam-3070	149	1	≤	≤	NUM
ejpam-3070	149	2	v	v	X
ejpam-3070	149	3	(	(	PUNCT
ejpam-3070	149	4	t0,w0	t0,w0	PROPN
ejpam-3070	149	5	)	)	PUNCT
ejpam-3070	149	6	≤	≤	NOUN
ejpam-3070	149	7	a(t0	a(t0	NOUN
ejpam-3070	149	8	,	,	PUNCT
ejpam-3070	149	9	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	149	10	)	)	PUNCT
ejpam-3070	149	11	)	)	PUNCT
ejpam-3070	149	12	<	<	X
ejpam-3070	149	13	b(ε	b(ε	X
ejpam-3070	149	14	)	)	PUNCT
ejpam-3070	149	15	hence	hence	ADV
ejpam-3070	149	16	h(t0,w0	h(t0,w0	NOUN
ejpam-3070	149	17	)	)	PUNCT
ejpam-3070	149	18	<	<	X
ejpam-3070	149	19	ε	ε	PROPN
ejpam-3070	149	20	.	.	PUNCT
ejpam-3070	150	1	now	now	ADV
ejpam-3070	150	2	we	we	PRON
ejpam-3070	150	3	claim	claim	VERB
ejpam-3070	150	4	that	that	SCONJ
ejpam-3070	150	5	for	for	ADP
ejpam-3070	150	6	every	every	DET
ejpam-3070	150	7	solution	solution	NOUN
ejpam-3070	150	8	u(t	u(t	NOUN
ejpam-3070	150	9	)	)	PUNCT
ejpam-3070	150	10	=	=	SYM
ejpam-3070	150	11	u(t	u(t	NOUN
ejpam-3070	150	12	,	,	PUNCT
ejpam-3070	150	13	t0,w0	t0,w0	NUM
ejpam-3070	150	14	)	)	PUNCT
ejpam-3070	150	15	=	=	SYM
ejpam-3070	150	16	u(t	u(t	NOUN
ejpam-3070	150	17	,	,	PUNCT
ejpam-3070	150	18	t0	t0	PROPN
ejpam-3070	150	19	,	,	PUNCT
ejpam-3070	150	20	u0	u0	ADJ
ejpam-3070	150	21	−	−	PROPN
ejpam-3070	150	22	v0	v0	NOUN
ejpam-3070	150	23	)	)	PUNCT
ejpam-3070	150	24	of	of	ADP
ejpam-3070	150	25	(	(	PUNCT
ejpam-3070	150	26	10	10	NUM
ejpam-3070	150	27	)	)	PUNCT
ejpam-3070	150	28	with	with	ADP
ejpam-3070	150	29	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	150	30	)	)	PUNCT
ejpam-3070	150	31	<	<	X
ejpam-3070	150	32	δ	δ	PROPN
ejpam-3070	150	33	implise	implise	VERB
ejpam-3070	150	34	h(t	h(t	PROPN
ejpam-3070	150	35	,	,	PUNCT
ejpam-3070	150	36	u(t	u(t	NOUN
ejpam-3070	150	37	)	)	PUNCT
ejpam-3070	150	38	)	)	PUNCT
ejpam-3070	150	39	<	<	X
ejpam-3070	150	40	ε	ε	PROPN
ejpam-3070	150	41	,	,	PUNCT
ejpam-3070	150	42	t	t	PROPN
ejpam-3070	150	43	≥	≥	PROPN
ejpam-3070	150	44	t0	t0	PROPN
ejpam-3070	150	45	,	,	PUNCT
ejpam-3070	150	46	(	(	PUNCT
ejpam-3070	150	47	15	15	X
ejpam-3070	150	48	)	)	PUNCT
ejpam-3070	150	49	suppose	suppose	VERB
ejpam-3070	150	50	(	(	PUNCT
ejpam-3070	150	51	15	15	NUM
ejpam-3070	150	52	)	)	PUNCT
ejpam-3070	150	53	is	be	AUX
ejpam-3070	150	54	not	not	PART
ejpam-3070	150	55	true	true	ADJ
ejpam-3070	150	56	,	,	PUNCT
ejpam-3070	150	57	then	then	ADV
ejpam-3070	150	58	there	there	PRON
ejpam-3070	150	59	would	would	AUX
ejpam-3070	150	60	exists	exist	VERB
ejpam-3070	150	61	a	a	DET
ejpam-3070	150	62	t1	t1	NOUN
ejpam-3070	150	63	>	>	X
ejpam-3070	151	1	t0	t0	NOUN
ejpam-3070	151	2	such	such	ADJ
ejpam-3070	151	3	that	that	DET
ejpam-3070	151	4	h(t1	h(t1	NOUN
ejpam-3070	151	5	,	,	PUNCT
ejpam-3070	151	6	u(t1	u(t1	NOUN
ejpam-3070	151	7	)	)	PUNCT
ejpam-3070	151	8	)	)	PUNCT
ejpam-3070	152	1	=	=	PUNCT
ejpam-3070	152	2	ε	ε	PROPN
ejpam-3070	152	3	,	,	PUNCT
ejpam-3070	152	4	and	and	CCONJ
ejpam-3070	152	5	h(t	h(t	PROPN
ejpam-3070	152	6	,	,	PUNCT
ejpam-3070	152	7	u(t	u(t	NOUN
ejpam-3070	152	8	)	)	PUNCT
ejpam-3070	152	9	)	)	PUNCT
ejpam-3070	152	10	<	<	X
ejpam-3070	152	11	ε	ε	PROPN
ejpam-3070	152	12	for	for	ADP
ejpam-3070	152	13	t	t	PROPN
ejpam-3070	152	14	∈	∈	PROPN
ejpam-3070	152	15	[	[	X
ejpam-3070	152	16	t0	t0	PROPN
ejpam-3070	152	17	,	,	PUNCT
ejpam-3070	152	18	t1	t1	NOUN
ejpam-3070	152	19	)	)	PUNCT
ejpam-3070	152	20	ch	ch	NOUN
ejpam-3070	152	21	.	.	PUNCT
ejpam-3070	152	22	a.	a.	PROPN
ejpam-3070	152	23	naidu,̧	naidu,̧	PROPN
ejpam-3070	152	24	d.	d.	PROPN
ejpam-3070	152	25	b.	b.	PROPN
ejpam-3070	152	26	dhaigude	dhaigude	PROPN
ejpam-3070	152	27	,	,	PUNCT
ejpam-3070	152	28	j.	j.	PROPN
ejpam-3070	152	29	v.	v.	PROPN
ejpam-3070	152	30	devi	devi	PROPN
ejpam-3070	152	31	/	/	SYM
ejpam-3070	152	32	eur	eur	PROPN
ejpam-3070	152	33	.	.	PUNCT
ejpam-3070	153	1	j.	j.	PROPN
ejpam-3070	153	2	pure	pure	PROPN
ejpam-3070	153	3	appl	appl	PROPN
ejpam-3070	153	4	.	.	PROPN
ejpam-3070	153	5	math	math	PROPN
ejpam-3070	153	6	,	,	PUNCT
ejpam-3070	153	7	10	10	NUM
ejpam-3070	153	8	(	(	PUNCT
ejpam-3070	153	9	4	4	NUM
ejpam-3070	153	10	)	)	PUNCT
ejpam-3070	153	11	(	(	PUNCT
ejpam-3070	153	12	2017	2017	NUM
ejpam-3070	153	13	)	)	PUNCT
ejpam-3070	153	14	,	,	PUNCT
ejpam-3070	153	15	645	645	NUM
ejpam-3070	153	16	-	-	SYM
ejpam-3070	153	17	654	654	NUM
ejpam-3070	153	18	652	652	NUM
ejpam-3070	153	19	for	for	ADP
ejpam-3070	153	20	some	some	DET
ejpam-3070	153	21	u(t	u(t	NOUN
ejpam-3070	153	22	)	)	PUNCT
ejpam-3070	153	23	=	=	SYM
ejpam-3070	153	24	u(t	u(t	NOUN
ejpam-3070	153	25	,	,	PUNCT
ejpam-3070	153	26	t0,w0	t0,w0	PROPN
ejpam-3070	153	27	)	)	PUNCT
ejpam-3070	153	28	of	of	ADP
ejpam-3070	153	29	(	(	PUNCT
ejpam-3070	153	30	10	10	NUM
ejpam-3070	153	31	)	)	PUNCT
ejpam-3070	153	32	.	.	PUNCT
ejpam-3070	154	1	set	set	VERB
ejpam-3070	154	2	m(t	m(t	NOUN
ejpam-3070	154	3	)	)	PUNCT
ejpam-3070	154	4	=	=	SYM
ejpam-3070	154	5	v	v	X
ejpam-3070	154	6	(	(	PUNCT
ejpam-3070	154	7	t	t	PROPN
ejpam-3070	154	8	,	,	PUNCT
ejpam-3070	154	9	u(t	u(t	NOUN
ejpam-3070	154	10	)	)	PUNCT
ejpam-3070	154	11	)	)	PUNCT
ejpam-3070	154	12	for	for	ADP
ejpam-3070	154	13	t	t	PROPN
ejpam-3070	154	14	∈	∈	PROPN
ejpam-3070	154	15	[	[	X
ejpam-3070	154	16	t0	t0	NOUN
ejpam-3070	154	17	,	,	PUNCT
ejpam-3070	154	18	t1	t1	PROPN
ejpam-3070	154	19	]	]	X
ejpam-3070	154	20	.	.	PUNCT
ejpam-3070	155	1	since	since	SCONJ
ejpam-3070	155	2	v(t	v(t	PROPN
ejpam-3070	155	3	,	,	PUNCT
ejpam-3070	155	4	u	u	NOUN
ejpam-3070	155	5	)	)	PUNCT
ejpam-3070	155	6	is	be	AUX
ejpam-3070	155	7	locally	locally	ADV
ejpam-3070	155	8	lipschitzian	lipschitzian	ADJ
ejpam-3070	155	9	in	in	ADP
ejpam-3070	155	10	u	u	NOUN
ejpam-3070	155	11	,	,	PUNCT
ejpam-3070	155	12	it	it	PRON
ejpam-3070	155	13	follows	follow	VERB
ejpam-3070	155	14	from	from	ADP
ejpam-3070	155	15	corollory	corollory	ADJ
ejpam-3070	155	16	1	1	NUM
ejpam-3070	155	17	that	that	SCONJ
ejpam-3070	155	18	m(t	m(t	NOUN
ejpam-3070	155	19	)	)	PUNCT
ejpam-3070	155	20	is	be	AUX
ejpam-3070	155	21	non	non	PRON
ejpam-3070	155	22	increasing	increase	VERB
ejpam-3070	155	23	in	in	ADP
ejpam-3070	155	24	[	[	X
ejpam-3070	155	25	t0	t0	NOUN
ejpam-3070	155	26	,	,	PUNCT
ejpam-3070	155	27	t1	t1	NOUN
ejpam-3070	155	28	]	]	PUNCT
ejpam-3070	155	29	and	and	CCONJ
ejpam-3070	155	30	v	v	X
ejpam-3070	155	31	(	(	PUNCT
ejpam-3070	155	32	t	t	NOUN
ejpam-3070	155	33	,	,	PUNCT
ejpam-3070	155	34	u(t	u(t	NOUN
ejpam-3070	155	35	)	)	PUNCT
ejpam-3070	155	36	)	)	PUNCT
ejpam-3070	155	37	≤	≤	NUM
ejpam-3070	155	38	v	v	X
ejpam-3070	155	39	(	(	PUNCT
ejpam-3070	155	40	t0,w0	t0,w0	PROPN
ejpam-3070	155	41	)	)	PUNCT
ejpam-3070	155	42	,	,	PUNCT
ejpam-3070	155	43	δ	δ	PROPN
ejpam-3070	155	44	≤	≤	PROPN
ejpam-3070	155	45	t	t	PROPN
ejpam-3070	155	46	≤	≤	NUM
ejpam-3070	155	47	t1	t1	PROPN
ejpam-3070	155	48	.	.	PUNCT
ejpam-3070	156	1	thus	thus	ADV
ejpam-3070	156	2	it	it	PRON
ejpam-3070	156	3	follows	follow	VERB
ejpam-3070	156	4	that	that	SCONJ
ejpam-3070	156	5	b(ε	b(ε	X
ejpam-3070	156	6	)	)	PUNCT
ejpam-3070	156	7	=	=	SYM
ejpam-3070	156	8	b(h(t1	b(h(t1	NOUN
ejpam-3070	156	9	,	,	PUNCT
ejpam-3070	156	10	u(t1	u(t1	NOUN
ejpam-3070	156	11	)	)	PUNCT
ejpam-3070	156	12	)	)	PUNCT
ejpam-3070	156	13	≤	≤	NUM
ejpam-3070	156	14	v	v	X
ejpam-3070	156	15	(	(	PUNCT
ejpam-3070	156	16	t1	t1	NOUN
ejpam-3070	156	17	,	,	PUNCT
ejpam-3070	156	18	u(t1	u(t1	NOUN
ejpam-3070	156	19	)	)	PUNCT
ejpam-3070	156	20	)	)	PUNCT
ejpam-3070	156	21	≤	≤	NUM
ejpam-3070	156	22	v	v	X
ejpam-3070	156	23	(	(	PUNCT
ejpam-3070	156	24	t0,w0	t0,w0	PROPN
ejpam-3070	156	25	)	)	PUNCT
ejpam-3070	156	26	<	<	X
ejpam-3070	156	27	b(ε	b(ε	PROPN
ejpam-3070	156	28	)	)	PUNCT
ejpam-3070	156	29	,	,	PUNCT
ejpam-3070	156	30	which	which	PRON
ejpam-3070	156	31	is	be	AUX
ejpam-3070	156	32	a	a	DET
ejpam-3070	156	33	contraduction	contraduction	NOUN
ejpam-3070	156	34	to	to	ADP
ejpam-3070	156	35	(	(	PUNCT
ejpam-3070	156	36	15	15	NUM
ejpam-3070	156	37	)	)	PUNCT
ejpam-3070	156	38	and	and	CCONJ
ejpam-3070	156	39	hence	hence	ADV
ejpam-3070	156	40	the	the	DET
ejpam-3070	156	41	system	system	NOUN
ejpam-3070	156	42	(	(	PUNCT
ejpam-3070	156	43	10	10	NUM
ejpam-3070	156	44	)	)	PUNCT
ejpam-3070	156	45	is	be	AUX
ejpam-3070	156	46	(	(	PUNCT
ejpam-3070	156	47	h0	h0	NOUN
ejpam-3070	156	48	,	,	PUNCT
ejpam-3070	156	49	h)-equistable	h)-equistable	ADJ
ejpam-3070	156	50	.	.	PUNCT
ejpam-3070	157	1	now	now	ADV
ejpam-3070	157	2	we	we	PRON
ejpam-3070	157	3	prove	prove	VERB
ejpam-3070	157	4	the	the	DET
ejpam-3070	157	5	second	second	ADJ
ejpam-3070	157	6	part	part	NOUN
ejpam-3070	157	7	of	of	ADP
ejpam-3070	157	8	the	the	DET
ejpam-3070	157	9	theorem	theorem	NOUN
ejpam-3070	157	10	.	.	PUNCT
ejpam-3070	158	1	since	since	SCONJ
ejpam-3070	158	2	v	v	PROPN
ejpam-3070	158	3	(	(	PUNCT
ejpam-3070	158	4	t	t	PROPN
ejpam-3070	158	5	,	,	PUNCT
ejpam-3070	158	6	u	u	NOUN
ejpam-3070	158	7	)	)	PUNCT
ejpam-3070	158	8	is	be	AUX
ejpam-3070	158	9	hpositive	hpositive	ADJ
ejpam-3070	158	10	definite	definite	ADJ
ejpam-3070	158	11	,	,	PUNCT
ejpam-3070	158	12	there	there	PRON
ejpam-3070	158	13	exists	exist	VERB
ejpam-3070	158	14	a	a	DET
ejpam-3070	158	15	constant	constant	ADJ
ejpam-3070	158	16	0	0	NUM
ejpam-3070	158	17	<	<	X
ejpam-3070	158	18	ρ0	ρ0	PROPN
ejpam-3070	158	19	≤	≤	PROPN
ejpam-3070	158	20	ρ	ρ	PROPN
ejpam-3070	158	21	,	,	PUNCT
ejpam-3070	158	22	0	0	PUNCT
ejpam-3070	158	23	<	<	X
ejpam-3070	158	24	δ0	δ0	NOUN
ejpam-3070	158	25	and	and	CCONJ
ejpam-3070	158	26	a	a	DET
ejpam-3070	158	27	function	function	NOUN
ejpam-3070	158	28	a	a	DET
ejpam-3070	158	29	∈	∈	NOUN
ejpam-3070	158	30	k	k	ADP
ejpam-3070	158	31	such	such	ADJ
ejpam-3070	158	32	that	that	SCONJ
ejpam-3070	158	33	b(h(t	b(h(t	PROPN
ejpam-3070	158	34	,	,	PUNCT
ejpam-3070	158	35	u	u	NOUN
ejpam-3070	158	36	)	)	PUNCT
ejpam-3070	158	37	)	)	PUNCT
ejpam-3070	158	38	≤	≤	NUM
ejpam-3070	158	39	v	v	X
ejpam-3070	158	40	(	(	PUNCT
ejpam-3070	158	41	t	t	PROPN
ejpam-3070	158	42	,	,	PUNCT
ejpam-3070	158	43	u	u	NOUN
ejpam-3070	158	44	)	)	PUNCT
ejpam-3070	158	45	,	,	PUNCT
ejpam-3070	158	46	(	(	PUNCT
ejpam-3070	158	47	t	t	PROPN
ejpam-3070	158	48	,	,	PUNCT
ejpam-3070	158	49	u	u	NOUN
ejpam-3070	158	50	)	)	PUNCT
ejpam-3070	158	51	∈	∈	PROPN
ejpam-3070	158	52	s(h	s(h	PROPN
ejpam-3070	158	53	,	,	PUNCT
ejpam-3070	158	54	ρ0	ρ0	PROPN
ejpam-3070	158	55	)	)	PUNCT
ejpam-3070	158	56	(	(	PUNCT
ejpam-3070	158	57	16	16	NUM
ejpam-3070	158	58	)	)	PUNCT
ejpam-3070	158	59	and	and	CCONJ
ejpam-3070	158	60	since	since	SCONJ
ejpam-3070	158	61	v(t	v(t	PROPN
ejpam-3070	158	62	,	,	PUNCT
ejpam-3070	158	63	u	u	NOUN
ejpam-3070	158	64	)	)	PUNCT
ejpam-3070	158	65	is	be	AUX
ejpam-3070	158	66	h0	h0	NOUN
ejpam-3070	158	67	-	-	PUNCT
ejpam-3070	158	68	decrescent	decrescent	NOUN
ejpam-3070	158	69	,	,	PUNCT
ejpam-3070	158	70	there	there	PRON
ejpam-3070	158	71	exist	exist	VERB
ejpam-3070	158	72	constants	constant	NOUN
ejpam-3070	158	73	0	0	PUNCT
ejpam-3070	159	1	<	<	X
ejpam-3070	159	2	ρ0	ρ0	PROPN
ejpam-3070	159	3	≤	≤	PROPN
ejpam-3070	159	4	ρ	ρ	PROPN
ejpam-3070	159	5	,	,	PUNCT
ejpam-3070	159	6	δ0	δ0	NOUN
ejpam-3070	159	7	>	>	X
ejpam-3070	159	8	0	0	PUNCT
ejpam-3070	159	9	and	and	CCONJ
ejpam-3070	159	10	b	b	PROPN
ejpam-3070	159	11	∈	∈	PROPN
ejpam-3070	159	12	k	k	NOUN
ejpam-3070	159	13	,	,	PUNCT
ejpam-3070	159	14	such	such	ADJ
ejpam-3070	159	15	that	that	PRON
ejpam-3070	159	16	v	v	NOUN
ejpam-3070	159	17	(	(	PUNCT
ejpam-3070	159	18	t	t	PROPN
ejpam-3070	159	19	,	,	PUNCT
ejpam-3070	159	20	u	u	NOUN
ejpam-3070	159	21	)	)	PUNCT
ejpam-3070	159	22	≤	≤	PUNCT
ejpam-3070	159	23	a(h0(t	a(h0(t	PROPN
ejpam-3070	159	24	,	,	PUNCT
ejpam-3070	159	25	u	u	NOUN
ejpam-3070	159	26	)	)	PUNCT
ejpam-3070	159	27	)	)	PUNCT
ejpam-3070	159	28	,	,	PUNCT
ejpam-3070	159	29	if	if	SCONJ
ejpam-3070	159	30	h0(t	h0(t	X
ejpam-3070	159	31	,	,	PUNCT
ejpam-3070	159	32	u	u	NOUN
ejpam-3070	159	33	)	)	PUNCT
ejpam-3070	159	34	<	<	X
ejpam-3070	159	35	δ0	δ0	NOUN
ejpam-3070	159	36	.	.	PUNCT
ejpam-3070	160	1	(	(	PUNCT
ejpam-3070	160	2	17	17	NUM
ejpam-3070	160	3	)	)	PUNCT
ejpam-3070	160	4	also	also	ADV
ejpam-3070	160	5	we	we	PRON
ejpam-3070	160	6	have	have	AUX
ejpam-3070	160	7	h0	h0	NOUN
ejpam-3070	160	8	is	be	AUX
ejpam-3070	160	9	uniformly	uniformly	ADV
ejpam-3070	160	10	finer	fine	ADJ
ejpam-3070	160	11	than	than	ADP
ejpam-3070	160	12	h	h	NOUN
ejpam-3070	160	13	,	,	PUNCT
ejpam-3070	160	14	there	there	PRON
ejpam-3070	160	15	exists	exist	VERB
ejpam-3070	160	16	a	a	DET
ejpam-3070	160	17	constant	constant	ADJ
ejpam-3070	160	18	δ1	δ1	NOUN
ejpam-3070	160	19	>	>	X
ejpam-3070	160	20	0	0	PROPN
ejpam-3070	160	21	,	,	PUNCT
ejpam-3070	160	22	independent	independent	ADJ
ejpam-3070	160	23	of	of	ADP
ejpam-3070	160	24	’	'	PUNCT
ejpam-3070	160	25	t	t	PROPN
ejpam-3070	160	26	’	'	PUNCT
ejpam-3070	160	27	and	and	CCONJ
ejpam-3070	160	28	a	a	DET
ejpam-3070	160	29	function	function	NOUN
ejpam-3070	160	30	φ	φ	PROPN
ejpam-3070	160	31	∈	∈	PROPN
ejpam-3070	160	32	ck	ck	INTJ
ejpam-3070	160	33	such	such	ADJ
ejpam-3070	160	34	that	that	DET
ejpam-3070	160	35	h(t0,w0	h(t0,w0	NOUN
ejpam-3070	160	36	)	)	PUNCT
ejpam-3070	160	37	≤	≤	NOUN
ejpam-3070	160	38	φ(t0	φ(t0	NOUN
ejpam-3070	160	39	,	,	PUNCT
ejpam-3070	160	40	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	160	41	)	)	PUNCT
ejpam-3070	160	42	)	)	PUNCT
ejpam-3070	160	43	if	if	SCONJ
ejpam-3070	160	44	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	160	45	)	)	PUNCT
ejpam-3070	160	46	<	<	X
ejpam-3070	160	47	δ1	δ1	NOUN
ejpam-3070	160	48	,	,	PUNCT
ejpam-3070	160	49	(	(	PUNCT
ejpam-3070	160	50	18	18	NUM
ejpam-3070	160	51	)	)	PUNCT
ejpam-3070	160	52	where	where	SCONJ
ejpam-3070	160	53	δ1	δ1	NOUN
ejpam-3070	160	54	chosen	choose	VERB
ejpam-3070	160	55	so	so	SCONJ
ejpam-3070	160	56	that	that	SCONJ
ejpam-3070	160	57	φ(t0	φ(t0	NOUN
ejpam-3070	160	58	,	,	PUNCT
ejpam-3070	160	59	δ1	δ1	NOUN
ejpam-3070	160	60	)	)	PUNCT
ejpam-3070	160	61	<	<	X
ejpam-3070	160	62	ρ0	ρ0	PROPN
ejpam-3070	160	63	.	.	PUNCT
ejpam-3070	161	1	let	let	VERB
ejpam-3070	161	2	ε	ε	PROPN
ejpam-3070	161	3	∈	∈	PROPN
ejpam-3070	161	4	(	(	PUNCT
ejpam-3070	161	5	0	0	NUM
ejpam-3070	161	6	,	,	PUNCT
ejpam-3070	161	7	ρ0	ρ0	PROPN
ejpam-3070	161	8	)	)	PUNCT
ejpam-3070	161	9	and	and	CCONJ
ejpam-3070	161	10	t0	t0	PROPN
ejpam-3070	161	11	∈	∈	PROPN
ejpam-3070	161	12	r+	r+	PUNCT
ejpam-3070	161	13	be	be	AUX
ejpam-3070	161	14	given	give	VERB
ejpam-3070	161	15	.	.	PUNCT
ejpam-3070	162	1	by	by	ADP
ejpam-3070	162	2	the	the	DET
ejpam-3070	162	3	assumption	assumption	NOUN
ejpam-3070	162	4	on	on	ADP
ejpam-3070	162	5	’	'	PUNCT
ejpam-3070	162	6	a	a	PRON
ejpam-3070	162	7	’	'	PUNCT
ejpam-3070	162	8	there	there	PRON
ejpam-3070	162	9	exists	exist	VERB
ejpam-3070	162	10	a	a	DET
ejpam-3070	162	11	δ2	δ2	VERB
ejpam-3070	162	12	=	=	SYM
ejpam-3070	162	13	δ2(ε	δ2(ε	PROPN
ejpam-3070	162	14	)	)	PUNCT
ejpam-3070	162	15	>	>	X
ejpam-3070	163	1	0	0	PUNCT
ejpam-3070	164	1	such	such	ADJ
ejpam-3070	164	2	that	that	ADV
ejpam-3070	164	3	a(δ2	a(δ2	ADJ
ejpam-3070	164	4	)	)	PUNCT
ejpam-3070	164	5	<	<	X
ejpam-3070	164	6	b(ε	b(ε	X
ejpam-3070	164	7	)	)	PUNCT
ejpam-3070	164	8	.	.	PUNCT
ejpam-3070	165	1	choose	choose	VERB
ejpam-3070	165	2	δ	δ	X
ejpam-3070	165	3	=	=	NOUN
ejpam-3070	165	4	min{δ0	min{δ0	NOUN
ejpam-3070	165	5	,	,	PUNCT
ejpam-3070	165	6	δ1	δ1	NOUN
ejpam-3070	165	7	,	,	PUNCT
ejpam-3070	165	8	δ2	δ2	VERB
ejpam-3070	165	9	}	}	PUNCT
ejpam-3070	165	10	then	then	ADV
ejpam-3070	165	11	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	165	12	)	)	PUNCT
ejpam-3070	165	13	<	<	X
ejpam-3070	165	14	δ	δ	PROPN
ejpam-3070	165	15	,	,	PUNCT
ejpam-3070	165	16	where	where	SCONJ
ejpam-3070	165	17	w0	w0	PROPN
ejpam-3070	165	18	=	=	PROPN
ejpam-3070	165	19	u0	u0	PROPN
ejpam-3070	165	20	−	−	PROPN
ejpam-3070	165	21	v0	v0	NOUN
ejpam-3070	165	22	.	.	PUNCT
ejpam-3070	166	1	(	(	PUNCT
ejpam-3070	166	2	19	19	NUM
ejpam-3070	166	3	)	)	PUNCT
ejpam-3070	166	4	we	we	PRON
ejpam-3070	166	5	claim	claim	VERB
ejpam-3070	166	6	that	that	SCONJ
ejpam-3070	166	7	for	for	ADP
ejpam-3070	166	8	every	every	DET
ejpam-3070	166	9	solution	solution	NOUN
ejpam-3070	166	10	u(t	u(t	NOUN
ejpam-3070	166	11	)	)	PUNCT
ejpam-3070	166	12	=	=	SYM
ejpam-3070	166	13	u(t	u(t	NOUN
ejpam-3070	166	14	,	,	PUNCT
ejpam-3070	166	15	t0,w0	t0,w0	NUM
ejpam-3070	166	16	)	)	PUNCT
ejpam-3070	167	1	=	=	SYM
ejpam-3070	167	2	w	w	PROPN
ejpam-3070	167	3	(	(	PUNCT
ejpam-3070	167	4	t	t	PROPN
ejpam-3070	167	5	,	,	PUNCT
ejpam-3070	167	6	t0	t0	PROPN
ejpam-3070	167	7	,	,	PUNCT
ejpam-3070	167	8	u0	u0	ADJ
ejpam-3070	167	9	−	−	PROPN
ejpam-3070	167	10	v0	v0	NOUN
ejpam-3070	167	11	)	)	PUNCT
ejpam-3070	167	12	of	of	ADP
ejpam-3070	167	13	(	(	PUNCT
ejpam-3070	167	14	10	10	NUM
ejpam-3070	167	15	)	)	PUNCT
ejpam-3070	167	16	with	with	ADP
ejpam-3070	167	17	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	167	18	)	)	PUNCT
ejpam-3070	167	19	<	<	X
ejpam-3070	167	20	δ	δ	PROPN
ejpam-3070	167	21	=	=	AUX
ejpam-3070	167	22	⇒	⇒	VERB
ejpam-3070	167	23	h(t	h(t	PROPN
ejpam-3070	167	24	,	,	PUNCT
ejpam-3070	167	25	u(t	u(t	NOUN
ejpam-3070	167	26	)	)	PUNCT
ejpam-3070	167	27	)	)	PUNCT
ejpam-3070	167	28	<	<	X
ejpam-3070	167	29	ε	ε	PROPN
ejpam-3070	167	30	,	,	PUNCT
ejpam-3070	167	31	t	t	PROPN
ejpam-3070	167	32	≥	≥	PROPN
ejpam-3070	167	33	t0	t0	PROPN
ejpam-3070	167	34	.	.	PUNCT
ejpam-3070	168	1	(	(	PUNCT
ejpam-3070	168	2	20	20	X
ejpam-3070	168	3	)	)	PUNCT
ejpam-3070	168	4	suppose	suppose	VERB
ejpam-3070	168	5	it	it	PRON
ejpam-3070	168	6	is	be	AUX
ejpam-3070	168	7	not	not	PART
ejpam-3070	168	8	true	true	ADJ
ejpam-3070	168	9	,	,	PUNCT
ejpam-3070	168	10	then	then	ADV
ejpam-3070	168	11	there	there	PRON
ejpam-3070	168	12	would	would	AUX
ejpam-3070	168	13	exists	exist	VERB
ejpam-3070	168	14	a	a	DET
ejpam-3070	168	15	t1	t1	NOUN
ejpam-3070	168	16	>	>	X
ejpam-3070	168	17	t0	t0	NOUN
ejpam-3070	168	18	such	such	ADJ
ejpam-3070	168	19	that	that	DET
ejpam-3070	168	20	h(t1	h(t1	NOUN
ejpam-3070	168	21	,	,	PUNCT
ejpam-3070	168	22	u(t1	u(t1	NOUN
ejpam-3070	168	23	)	)	PUNCT
ejpam-3070	168	24	)	)	PUNCT
ejpam-3070	169	1	=	=	SYM
ejpam-3070	169	2	ε	ε	PROPN
ejpam-3070	169	3	and	and	CCONJ
ejpam-3070	169	4	h(t	h(t	PROPN
ejpam-3070	169	5	,	,	PUNCT
ejpam-3070	169	6	u(t	u(t	NOUN
ejpam-3070	169	7	)	)	PUNCT
ejpam-3070	169	8	)	)	PUNCT
ejpam-3070	169	9	<	<	X
ejpam-3070	169	10	ε	ε	PROPN
ejpam-3070	169	11	for	for	ADP
ejpam-3070	169	12	t	t	PROPN
ejpam-3070	169	13	∈	∈	PROPN
ejpam-3070	169	14	[	[	X
ejpam-3070	169	15	t0	t0	PROPN
ejpam-3070	169	16	,	,	PUNCT
ejpam-3070	169	17	t1	t1	PROPN
ejpam-3070	169	18	)	)	PUNCT
ejpam-3070	169	19	for	for	ADP
ejpam-3070	169	20	some	some	DET
ejpam-3070	169	21	u(t	u(t	NOUN
ejpam-3070	169	22	)	)	PUNCT
ejpam-3070	169	23	=	=	SYM
ejpam-3070	169	24	u(t	u(t	NOUN
ejpam-3070	169	25	,	,	PUNCT
ejpam-3070	169	26	t0,w0	t0,w0	PROPN
ejpam-3070	169	27	)	)	PUNCT
ejpam-3070	169	28	of	of	ADP
ejpam-3070	169	29	(	(	PUNCT
ejpam-3070	169	30	10	10	NUM
ejpam-3070	169	31	)	)	PUNCT
ejpam-3070	169	32	.	.	PUNCT
ejpam-3070	170	1	set	set	VERB
ejpam-3070	170	2	m(t	m(t	NOUN
ejpam-3070	170	3	)	)	PUNCT
ejpam-3070	170	4	=	=	SYM
ejpam-3070	170	5	v	v	X
ejpam-3070	170	6	(	(	PUNCT
ejpam-3070	170	7	t	t	PROPN
ejpam-3070	170	8	,	,	PUNCT
ejpam-3070	170	9	u(t	u(t	NOUN
ejpam-3070	170	10	)	)	PUNCT
ejpam-3070	170	11	)	)	PUNCT
ejpam-3070	170	12	for	for	ADP
ejpam-3070	170	13	t	t	PROPN
ejpam-3070	170	14	∈	∈	PROPN
ejpam-3070	170	15	[	[	X
ejpam-3070	170	16	t0	t0	PROPN
ejpam-3070	170	17	,	,	PUNCT
ejpam-3070	170	18	t1	t1	NOUN
ejpam-3070	170	19	)	)	PUNCT
ejpam-3070	170	20	.	.	PUNCT
ejpam-3070	171	1	since	since	SCONJ
ejpam-3070	171	2	v(t	v(t	PROPN
ejpam-3070	171	3	,	,	PUNCT
ejpam-3070	171	4	u	u	NOUN
ejpam-3070	171	5	)	)	PUNCT
ejpam-3070	171	6	is	be	AUX
ejpam-3070	171	7	locally	locally	ADV
ejpam-3070	171	8	lipschitzian	lipschitzian	ADJ
ejpam-3070	171	9	in	in	ADP
ejpam-3070	171	10	u	u	NOUN
ejpam-3070	171	11	,	,	PUNCT
ejpam-3070	171	12	it	it	PRON
ejpam-3070	171	13	follows	follow	VERB
ejpam-3070	171	14	from	from	ADP
ejpam-3070	171	15	corollary	corollary	ADJ
ejpam-3070	171	16	1	1	NUM
ejpam-3070	171	17	that	that	SCONJ
ejpam-3070	171	18	m(t	m(t	NOUN
ejpam-3070	171	19	)	)	PUNCT
ejpam-3070	171	20	is	be	AUX
ejpam-3070	171	21	non	non	PRON
ejpam-3070	171	22	increasing	increase	VERB
ejpam-3070	171	23	in	in	ADP
ejpam-3070	171	24	[	[	X
ejpam-3070	171	25	t0	t0	NOUN
ejpam-3070	171	26	,	,	PUNCT
ejpam-3070	171	27	t1	t1	NOUN
ejpam-3070	171	28	]	]	PUNCT
ejpam-3070	171	29	and	and	CCONJ
ejpam-3070	171	30	it	it	PRON
ejpam-3070	171	31	follows	follow	VERB
ejpam-3070	171	32	that	that	SCONJ
ejpam-3070	171	33	b(ε	b(ε	X
ejpam-3070	171	34	)	)	PUNCT
ejpam-3070	171	35	=	=	SYM
ejpam-3070	171	36	b(h(t1	b(h(t1	NOUN
ejpam-3070	171	37	,	,	PUNCT
ejpam-3070	171	38	u(t1	u(t1	NOUN
ejpam-3070	171	39	)	)	PUNCT
ejpam-3070	171	40	)	)	PUNCT
ejpam-3070	172	1	≤	≤	NUM
ejpam-3070	172	2	v	v	X
ejpam-3070	172	3	(	(	PUNCT
ejpam-3070	172	4	t1	t1	NOUN
ejpam-3070	172	5	,	,	PUNCT
ejpam-3070	172	6	u(t1	u(t1	NOUN
ejpam-3070	172	7	)	)	PUNCT
ejpam-3070	172	8	)	)	PUNCT
ejpam-3070	172	9	≤	≤	NUM
ejpam-3070	172	10	v	v	X
ejpam-3070	172	11	(	(	PUNCT
ejpam-3070	172	12	t0,w0	t0,w0	PROPN
ejpam-3070	172	13	)	)	PUNCT
ejpam-3070	172	14	<	<	X
ejpam-3070	172	15	b(ε	b(ε	PROPN
ejpam-3070	172	16	)	)	PUNCT
ejpam-3070	172	17	,	,	PUNCT
ejpam-3070	172	18	which	which	PRON
ejpam-3070	172	19	is	be	AUX
ejpam-3070	172	20	a	a	DET
ejpam-3070	172	21	contraduction	contraduction	NOUN
ejpam-3070	172	22	to	to	ADP
ejpam-3070	172	23	(	(	PUNCT
ejpam-3070	172	24	15	15	NUM
ejpam-3070	172	25	)	)	PUNCT
ejpam-3070	172	26	hence	hence	ADV
ejpam-3070	172	27	the	the	DET
ejpam-3070	172	28	system	system	NOUN
ejpam-3070	172	29	(	(	PUNCT
ejpam-3070	172	30	10	10	NUM
ejpam-3070	172	31	)	)	PUNCT
ejpam-3070	172	32	is	be	AUX
ejpam-3070	172	33	(	(	PUNCT
ejpam-3070	172	34	h0	h0	PROPN
ejpam-3070	172	35	,	,	PUNCT
ejpam-3070	172	36	h)-uniformly	h)-uniformly	ADV
ejpam-3070	172	37	stable	stable	ADJ
ejpam-3070	172	38	.	.	PUNCT
ejpam-3070	173	1	now	now	ADV
ejpam-3070	173	2	we	we	PRON
ejpam-3070	173	3	will	will	AUX
ejpam-3070	173	4	prove	prove	VERB
ejpam-3070	173	5	uniform	uniform	ADJ
ejpam-3070	173	6	asymptotic	asymptotic	ADJ
ejpam-3070	173	7	stability	stability	NOUN
ejpam-3070	173	8	result	result	NOUN
ejpam-3070	173	9	.	.	PUNCT
ejpam-3070	174	1	ch	ch	NOUN
ejpam-3070	174	2	.	.	PUNCT
ejpam-3070	174	3	a.	a.	PROPN
ejpam-3070	174	4	naidu,̧	naidu,̧	PROPN
ejpam-3070	174	5	d.	d.	PROPN
ejpam-3070	174	6	b.	b.	PROPN
ejpam-3070	174	7	dhaigude	dhaigude	PROPN
ejpam-3070	174	8	,	,	PUNCT
ejpam-3070	174	9	j.	j.	PROPN
ejpam-3070	174	10	v.	v.	PROPN
ejpam-3070	174	11	devi	devi	PROPN
ejpam-3070	174	12	/	/	SYM
ejpam-3070	174	13	eur	eur	PROPN
ejpam-3070	174	14	.	.	PUNCT
ejpam-3070	175	1	j.	j.	PROPN
ejpam-3070	175	2	pure	pure	PROPN
ejpam-3070	175	3	appl	appl	PROPN
ejpam-3070	175	4	.	.	PROPN
ejpam-3070	175	5	math	math	PROPN
ejpam-3070	175	6	,	,	PUNCT
ejpam-3070	175	7	10	10	NUM
ejpam-3070	175	8	(	(	PUNCT
ejpam-3070	175	9	4	4	NUM
ejpam-3070	175	10	)	)	PUNCT
ejpam-3070	175	11	(	(	PUNCT
ejpam-3070	175	12	2017	2017	NUM
ejpam-3070	175	13	)	)	PUNCT
ejpam-3070	175	14	,	,	PUNCT
ejpam-3070	175	15	645	645	NUM
ejpam-3070	175	16	-	-	SYM
ejpam-3070	175	17	654	654	NUM
ejpam-3070	175	18	653	653	NUM
ejpam-3070	175	19	theorem	theorem	NOUN
ejpam-3070	175	20	3	3	NUM
ejpam-3070	175	21	.	.	PUNCT
ejpam-3070	175	22	suppose	suppose	VERB
ejpam-3070	175	23	that	that	SCONJ
ejpam-3070	175	24	(	(	PUNCT
ejpam-3070	175	25	i	i	NOUN
ejpam-3070	175	26	)	)	PUNCT
ejpam-3070	175	27	h0	h0	PROPN
ejpam-3070	175	28	,	,	PUNCT
ejpam-3070	175	29	h	h	NOUN
ejpam-3070	175	30	∈	∈	PROPN
ejpam-3070	175	31	γ	γ	X
ejpam-3070	175	32	and	and	CCONJ
ejpam-3070	175	33	h0	h0	PROPN
ejpam-3070	175	34	is	be	AUX
ejpam-3070	175	35	uniformly	uniformly	ADV
ejpam-3070	175	36	finer	fine	ADJ
ejpam-3070	175	37	than	than	ADP
ejpam-3070	175	38	h	h	NOUN
ejpam-3070	175	39	;	;	PUNCT
ejpam-3070	175	40	(	(	PUNCT
ejpam-3070	175	41	ii	ii	NOUN
ejpam-3070	175	42	)	)	PUNCT
ejpam-3070	175	43	v	v	PROPN
ejpam-3070	175	44	∈	∈	PROPN
ejpam-3070	175	45	c[r+	c[r+	NOUN
ejpam-3070	175	46	×	×	PROPN
ejpam-3070	175	47	kc(rn	kc(rn	PROPN
ejpam-3070	175	48	)	)	PUNCT
ejpam-3070	175	49	,	,	PUNCT
ejpam-3070	175	50	r+	r+	X
ejpam-3070	175	51	]	]	PUNCT
ejpam-3070	175	52	,	,	PUNCT
ejpam-3070	175	53	h	h	PROPN
ejpam-3070	175	54	∈	∈	PROPN
ejpam-3070	175	55	γ	γ	X
ejpam-3070	175	56	,	,	PUNCT
ejpam-3070	175	57	v(t	v(t	PROPN
ejpam-3070	175	58	,	,	PUNCT
ejpam-3070	175	59	u	u	NOUN
ejpam-3070	175	60	)	)	PUNCT
ejpam-3070	175	61	is	be	AUX
ejpam-3070	175	62	locally	locally	ADV
ejpam-3070	175	63	lipschitzian	lipschitzian	ADJ
ejpam-3070	175	64	in	in	ADP
ejpam-3070	175	65	u	u	NOUN
ejpam-3070	175	66	and	and	CCONJ
ejpam-3070	175	67	h	h	NOUN
ejpam-3070	175	68	-	-	PUNCT
ejpam-3070	175	69	positive	positive	ADJ
ejpam-3070	175	70	definite	definite	ADJ
ejpam-3070	175	71	,	,	PUNCT
ejpam-3070	175	72	h0	h0	NOUN
ejpam-3070	175	73	-	-	PUNCT
ejpam-3070	175	74	decrescent	decrescent	PROPN
ejpam-3070	175	75	and	and	CCONJ
ejpam-3070	175	76	d+v	d+v	PROPN
ejpam-3070	175	77	(	(	PUNCT
ejpam-3070	175	78	t	t	NOUN
ejpam-3070	175	79	,	,	PUNCT
ejpam-3070	175	80	u(t	u(t	NOUN
ejpam-3070	175	81	)	)	PUNCT
ejpam-3070	175	82	)	)	PUNCT
ejpam-3070	176	1	≤	≤	NUM
ejpam-3070	176	2	−c(h0(t	−c(h0(t	PROPN
ejpam-3070	176	3	,	,	PUNCT
ejpam-3070	176	4	u	u	NOUN
ejpam-3070	176	5	)	)	PUNCT
ejpam-3070	176	6	)	)	PUNCT
ejpam-3070	176	7	for	for	ADP
ejpam-3070	176	8	(	(	PUNCT
ejpam-3070	176	9	t	t	PROPN
ejpam-3070	176	10	,	,	PUNCT
ejpam-3070	176	11	u	u	NOUN
ejpam-3070	176	12	)	)	PUNCT
ejpam-3070	176	13	∈	∈	PROPN
ejpam-3070	176	14	s(h	s(h	PROPN
ejpam-3070	176	15	,	,	PUNCT
ejpam-3070	176	16	ρ	ρ	PROPN
ejpam-3070	176	17	)	)	PUNCT
ejpam-3070	177	1	where	where	SCONJ
ejpam-3070	177	2	c	c	PROPN
ejpam-3070	177	3	∈	∈	PROPN
ejpam-3070	177	4	k	k	X
ejpam-3070	177	5	s(h	s(h	PROPN
ejpam-3070	177	6	,	,	PUNCT
ejpam-3070	177	7	ρ	ρ	NOUN
ejpam-3070	177	8	)	)	PUNCT
ejpam-3070	177	9	=	=	PRON
ejpam-3070	177	10	{	{	PUNCT
ejpam-3070	177	11	(	(	PUNCT
ejpam-3070	177	12	t	t	PROPN
ejpam-3070	177	13	,	,	PUNCT
ejpam-3070	177	14	u	u	NOUN
ejpam-3070	177	15	)	)	PUNCT
ejpam-3070	177	16	∈	∈	PROPN
ejpam-3070	177	17	r+	r+	PUNCT
ejpam-3070	177	18	×kc(rn	×kc(rn	PROPN
ejpam-3070	177	19	)	)	PUNCT
ejpam-3070	177	20	,	,	PUNCT
ejpam-3070	177	21	h(t	h(t	PROPN
ejpam-3070	177	22	,	,	PUNCT
ejpam-3070	177	23	u	u	NOUN
ejpam-3070	177	24	)	)	PUNCT
ejpam-3070	177	25	<	<	X
ejpam-3070	177	26	ρ	ρ	PROPN
ejpam-3070	177	27	,	,	PUNCT
ejpam-3070	177	28	ρ	ρ	PROPN
ejpam-3070	177	29	>	>	X
ejpam-3070	177	30	0	0	NUM
ejpam-3070	177	31	}	}	PUNCT
ejpam-3070	177	32	and	and	CCONJ
ejpam-3070	177	33	u	u	PROPN
ejpam-3070	177	34	∈	∈	PROPN
ejpam-3070	177	35	e1	e1	NOUN
ejpam-3070	177	36	then	then	ADV
ejpam-3070	177	37	the	the	DET
ejpam-3070	177	38	system	system	NOUN
ejpam-3070	177	39	(	(	PUNCT
ejpam-3070	177	40	10	10	NUM
ejpam-3070	177	41	)	)	PUNCT
ejpam-3070	177	42	is	be	AUX
ejpam-3070	177	43	(	(	PUNCT
ejpam-3070	177	44	h0	h0	PROPN
ejpam-3070	177	45	,	,	PUNCT
ejpam-3070	177	46	h)-uniformly	h)-uniformly	ADV
ejpam-3070	177	47	asymptotically	asymptotically	ADV
ejpam-3070	177	48	stable	stable	ADJ
ejpam-3070	177	49	.	.	PUNCT
ejpam-3070	178	1	proof	proof	NOUN
ejpam-3070	178	2	.	.	PUNCT
ejpam-3070	179	1	since	since	SCONJ
ejpam-3070	179	2	v	v	NUM
ejpam-3070	179	3	(	(	PUNCT
ejpam-3070	179	4	t	t	PROPN
ejpam-3070	179	5	,	,	PUNCT
ejpam-3070	179	6	u	u	NOUN
ejpam-3070	179	7	)	)	PUNCT
ejpam-3070	179	8	is	be	AUX
ejpam-3070	179	9	h	h	ADJ
ejpam-3070	179	10	-	-	PUNCT
ejpam-3070	179	11	positive	positive	ADJ
ejpam-3070	179	12	definite	definite	ADJ
ejpam-3070	179	13	and	and	CCONJ
ejpam-3070	179	14	h0	h0	ADJ
ejpam-3070	179	15	decrescent	decrescent	NOUN
ejpam-3070	179	16	,	,	PUNCT
ejpam-3070	179	17	there	there	PRON
ejpam-3070	179	18	exists	exist	VERB
ejpam-3070	179	19	a	a	DET
ejpam-3070	179	20	constant	constant	ADJ
ejpam-3070	179	21	0	0	NUM
ejpam-3070	179	22	<	<	X
ejpam-3070	179	23	ρ0	ρ0	PROPN
ejpam-3070	179	24	≤	≤	PROPN
ejpam-3070	179	25	ρ	ρ	PROPN
ejpam-3070	179	26	,	,	PUNCT
ejpam-3070	179	27	and	and	CCONJ
ejpam-3070	179	28	functions	function	VERB
ejpam-3070	179	29	a	a	PRON
ejpam-3070	179	30	,	,	PUNCT
ejpam-3070	179	31	b	b	X
ejpam-3070	179	32	∈	∈	PROPN
ejpam-3070	179	33	k	k	ADP
ejpam-3070	179	34	such	such	ADJ
ejpam-3070	179	35	that	that	SCONJ
ejpam-3070	179	36	b(h(t	b(h(t	PROPN
ejpam-3070	179	37	,	,	PUNCT
ejpam-3070	179	38	u	u	NOUN
ejpam-3070	179	39	)	)	PUNCT
ejpam-3070	179	40	)	)	PUNCT
ejpam-3070	180	1	≤	≤	NUM
ejpam-3070	180	2	v	v	X
ejpam-3070	180	3	(	(	PUNCT
ejpam-3070	180	4	t	t	PROPN
ejpam-3070	180	5	,	,	PUNCT
ejpam-3070	180	6	u	u	NOUN
ejpam-3070	180	7	)	)	PUNCT
ejpam-3070	180	8	,	,	PUNCT
ejpam-3070	180	9	(	(	PUNCT
ejpam-3070	180	10	t	t	PROPN
ejpam-3070	180	11	,	,	PUNCT
ejpam-3070	180	12	u	u	NOUN
ejpam-3070	180	13	)	)	PUNCT
ejpam-3070	180	14	∈	∈	PROPN
ejpam-3070	180	15	s(h	s(h	PROPN
ejpam-3070	180	16	,	,	PUNCT
ejpam-3070	180	17	ρ0	ρ0	PROPN
ejpam-3070	180	18	)	)	PUNCT
ejpam-3070	180	19	,	,	PUNCT
ejpam-3070	180	20	(	(	PUNCT
ejpam-3070	180	21	21	21	NUM
ejpam-3070	180	22	)	)	PUNCT
ejpam-3070	180	23	and	and	CCONJ
ejpam-3070	180	24	v	v	X
ejpam-3070	180	25	(	(	PUNCT
ejpam-3070	180	26	t	t	PROPN
ejpam-3070	180	27	,	,	PUNCT
ejpam-3070	180	28	u	u	NOUN
ejpam-3070	180	29	)	)	PUNCT
ejpam-3070	180	30	≤	≤	PUNCT
ejpam-3070	180	31	a(h0(t	a(h0(t	PROPN
ejpam-3070	180	32	,	,	PUNCT
ejpam-3070	180	33	u	u	NOUN
ejpam-3070	180	34	)	)	PUNCT
ejpam-3070	180	35	)	)	PUNCT
ejpam-3070	180	36	,	,	PUNCT
ejpam-3070	180	37	if	if	SCONJ
ejpam-3070	180	38	h0(t	h0(t	X
ejpam-3070	180	39	,	,	PUNCT
ejpam-3070	180	40	u	u	NOUN
ejpam-3070	180	41	)	)	PUNCT
ejpam-3070	180	42	≤	≤	NUM
ejpam-3070	180	43	δ0	δ0	NOUN
ejpam-3070	180	44	,	,	PUNCT
ejpam-3070	180	45	(	(	PUNCT
ejpam-3070	180	46	22	22	NUM
ejpam-3070	180	47	)	)	PUNCT
ejpam-3070	180	48	then	then	ADV
ejpam-3070	180	49	by	by	ADP
ejpam-3070	180	50	the	the	DET
ejpam-3070	180	51	theorem	theorem	ADJ
ejpam-3070	180	52	2	2	NUM
ejpam-3070	180	53	the	the	DET
ejpam-3070	180	54	system	system	NOUN
ejpam-3070	180	55	(	(	PUNCT
ejpam-3070	180	56	10	10	NUM
ejpam-3070	180	57	)	)	PUNCT
ejpam-3070	180	58	is	be	AUX
ejpam-3070	180	59	(	(	PUNCT
ejpam-3070	180	60	h0.h)uniformly	h0.h)uniformly	ADV
ejpam-3070	180	61	stable	stable	ADJ
ejpam-3070	180	62	.	.	PUNCT
ejpam-3070	181	1	now	now	ADV
ejpam-3070	181	2	we	we	PRON
ejpam-3070	181	3	will	will	AUX
ejpam-3070	181	4	prove	prove	VERB
ejpam-3070	181	5	asymptotic	asymptotic	ADJ
ejpam-3070	181	6	stability	stability	NOUN
ejpam-3070	181	7	.	.	PUNCT
ejpam-3070	182	1	let	let	VERB
ejpam-3070	182	2	ε	ε	PROPN
ejpam-3070	182	3	=	=	SYM
ejpam-3070	182	4	ρ0	ρ0	PROPN
ejpam-3070	182	5	then	then	ADV
ejpam-3070	182	6	there	there	PRON
ejpam-3070	182	7	exists	exist	VERB
ejpam-3070	182	8	δ1	δ1	NOUN
ejpam-3070	182	9	=	=	SYM
ejpam-3070	182	10	δ1(ρ	δ1(ρ	PROPN
ejpam-3070	182	11	)	)	PUNCT
ejpam-3070	182	12	>	>	X
ejpam-3070	182	13	0	0	NUM
ejpam-3070	183	1	such	such	ADJ
ejpam-3070	183	2	that	that	SCONJ
ejpam-3070	183	3	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	183	4	)	)	PUNCT
ejpam-3070	183	5	<	<	X
ejpam-3070	183	6	δ1	δ1	NOUN
ejpam-3070	183	7	⇒	⇒	NOUN
ejpam-3070	183	8	h(t	h(t	PROPN
ejpam-3070	183	9	,	,	PUNCT
ejpam-3070	183	10	u(t	u(t	NOUN
ejpam-3070	183	11	)	)	PUNCT
ejpam-3070	183	12	)	)	PUNCT
ejpam-3070	184	1	<	<	X
ejpam-3070	184	2	ρ0	ρ0	PROPN
ejpam-3070	184	3	,	,	PUNCT
ejpam-3070	184	4	t	t	PROPN
ejpam-3070	184	5	≥	≥	PROPN
ejpam-3070	184	6	t0	t0	PROPN
ejpam-3070	184	7	,	,	PUNCT
ejpam-3070	184	8	(	(	PUNCT
ejpam-3070	184	9	23	23	NUM
ejpam-3070	184	10	)	)	PUNCT
ejpam-3070	184	11	where	where	SCONJ
ejpam-3070	184	12	u(t	u(t	NOUN
ejpam-3070	184	13	)	)	PUNCT
ejpam-3070	184	14	=	=	SYM
ejpam-3070	184	15	u(t	u(t	NOUN
ejpam-3070	184	16	,	,	PUNCT
ejpam-3070	184	17	t0,w0	t0,w0	PROPN
ejpam-3070	184	18	)	)	PUNCT
ejpam-3070	184	19	is	be	AUX
ejpam-3070	184	20	any	any	DET
ejpam-3070	184	21	solution	solution	NOUN
ejpam-3070	184	22	of	of	ADP
ejpam-3070	184	23	(	(	PUNCT
ejpam-3070	184	24	10	10	NUM
ejpam-3070	184	25	)	)	PUNCT
ejpam-3070	184	26	.	.	PUNCT
ejpam-3070	185	1	let	let	VERB
ejpam-3070	185	2	0	0	NUM
ejpam-3070	185	3	<	<	X
ejpam-3070	185	4	ε	ε	PROPN
ejpam-3070	185	5	<	<	X
ejpam-3070	185	6	ρ0	ρ0	PROPN
ejpam-3070	185	7	and	and	CCONJ
ejpam-3070	185	8	δ	δ	PROPN
ejpam-3070	185	9	=	=	PUNCT
ejpam-3070	185	10	δ(ε	δ(ε	PROPN
ejpam-3070	185	11	)	)	PUNCT
ejpam-3070	185	12	be	be	VERB
ejpam-3070	185	13	the	the	DET
ejpam-3070	185	14	same	same	ADJ
ejpam-3070	185	15	δ	δ	NOUN
ejpam-3070	185	16	as	as	ADP
ejpam-3070	185	17	in	in	ADP
ejpam-3070	185	18	the	the	DET
ejpam-3070	185	19	definition	definition	NOUN
ejpam-3070	185	20	of	of	ADP
ejpam-3070	185	21	(	(	PUNCT
ejpam-3070	185	22	h0	h0	PROPN
ejpam-3070	185	23	,	,	PUNCT
ejpam-3070	185	24	h)uniform	h)uniform	NOUN
ejpam-3070	185	25	stability	stability	NOUN
ejpam-3070	185	26	.	.	PUNCT
ejpam-3070	186	1	assume	assume	VERB
ejpam-3070	186	2	that	that	SCONJ
ejpam-3070	186	3	h0(t0	h0(t0	NOUN
ejpam-3070	186	4	,	,	PUNCT
ejpam-3070	186	5	u0	u0	ADJ
ejpam-3070	186	6	)	)	PUNCT
ejpam-3070	186	7	<	<	X
ejpam-3070	186	8	δ∗	δ∗	PROPN
ejpam-3070	186	9	=	=	PUNCT
ejpam-3070	186	10	min{δ0	min{δ0	NOUN
ejpam-3070	186	11	,	,	PUNCT
ejpam-3070	186	12	δ1	δ1	NOUN
ejpam-3070	186	13	}	}	PUNCT
ejpam-3070	186	14	and	and	CCONJ
ejpam-3070	186	15	set	set	VERB
ejpam-3070	186	16	t	t	PROPN
ejpam-3070	186	17	=	=	SYM
ejpam-3070	186	18	t	t	PROPN
ejpam-3070	186	19	(	(	PUNCT
ejpam-3070	186	20	ε	ε	PROPN
ejpam-3070	186	21	)	)	PUNCT
ejpam-3070	186	22	=	=	SYM
ejpam-3070	186	23	a(δ∗	a(δ∗	NOUN
ejpam-3070	186	24	)	)	PUNCT
ejpam-3070	186	25	c(δ	c(δ	PROPN
ejpam-3070	186	26	)	)	PUNCT
ejpam-3070	186	27	+	+	CCONJ
ejpam-3070	186	28	1	1	NUM
ejpam-3070	186	29	to	to	PART
ejpam-3070	186	30	prove	prove	VERB
ejpam-3070	186	31	(	(	PUNCT
ejpam-3070	186	32	h0	h0	NOUN
ejpam-3070	186	33	,	,	PUNCT
ejpam-3070	186	34	h)uniform	h)uniform	NOUN
ejpam-3070	187	1	asymptotic	asymptotic	ADJ
ejpam-3070	187	2	stability	stability	NOUN
ejpam-3070	187	3	,	,	PUNCT
ejpam-3070	187	4	it	it	PRON
ejpam-3070	187	5	is	be	AUX
ejpam-3070	187	6	enough	enough	ADJ
ejpam-3070	187	7	to	to	PART
ejpam-3070	187	8	show	show	VERB
ejpam-3070	187	9	that	that	SCONJ
ejpam-3070	187	10	there	there	PRON
ejpam-3070	187	11	exists	exist	VERB
ejpam-3070	187	12	a	a	DET
ejpam-3070	187	13	t∗	t∗	NOUN
ejpam-3070	187	14	∈	∈	PROPN
ejpam-3070	187	15	[	[	X
ejpam-3070	187	16	t0	t0	NOUN
ejpam-3070	187	17	,	,	PUNCT
ejpam-3070	187	18	t0	t0	PROPN
ejpam-3070	187	19	+	+	CCONJ
ejpam-3070	187	20	t	t	X
ejpam-3070	187	21	]	]	PUNCT
ejpam-3070	187	22	such	such	ADJ
ejpam-3070	187	23	that	that	SCONJ
ejpam-3070	187	24	h0(t	h0(t	PROPN
ejpam-3070	187	25	∗	∗	NOUN
ejpam-3070	187	26	,	,	PUNCT
ejpam-3070	187	27	u(t∗	u(t∗	NOUN
ejpam-3070	187	28	)	)	PUNCT
ejpam-3070	187	29	)	)	PUNCT
ejpam-3070	187	30	<	<	X
ejpam-3070	187	31	δ	δ	PROPN
ejpam-3070	187	32	,	,	PUNCT
ejpam-3070	187	33	(	(	PUNCT
ejpam-3070	187	34	24	24	NUM
ejpam-3070	187	35	)	)	PUNCT
ejpam-3070	187	36	suppose	suppose	VERB
ejpam-3070	187	37	(	(	PUNCT
ejpam-3070	187	38	24	24	NUM
ejpam-3070	187	39	)	)	PUNCT
ejpam-3070	187	40	is	be	AUX
ejpam-3070	187	41	not	not	PART
ejpam-3070	187	42	true	true	ADJ
ejpam-3070	187	43	,	,	PUNCT
ejpam-3070	187	44	then	then	ADV
ejpam-3070	187	45	there	there	PRON
ejpam-3070	187	46	exists	exist	VERB
ejpam-3070	187	47	a	a	DET
ejpam-3070	187	48	solution	solution	NOUN
ejpam-3070	187	49	u(t	u(t	NOUN
ejpam-3070	187	50	)	)	PUNCT
ejpam-3070	187	51	=	=	SYM
ejpam-3070	187	52	u(t	u(t	NOUN
ejpam-3070	187	53	,	,	PUNCT
ejpam-3070	187	54	t0,w0	t0,w0	PROPN
ejpam-3070	187	55	)	)	PUNCT
ejpam-3070	187	56	of	of	ADP
ejpam-3070	187	57	(	(	PUNCT
ejpam-3070	187	58	10	10	NUM
ejpam-3070	187	59	)	)	PUNCT
ejpam-3070	187	60	with	with	ADP
ejpam-3070	187	61	h0(t0,w0	h0(t0,w0	NOUN
ejpam-3070	187	62	)	)	PUNCT
ejpam-3070	187	63	<	<	X
ejpam-3070	187	64	δ∗	δ∗	NOUN
ejpam-3070	187	65	such	such	ADJ
ejpam-3070	187	66	that	that	SCONJ
ejpam-3070	187	67	h0(t	h0(t	PROPN
ejpam-3070	187	68	,	,	PUNCT
ejpam-3070	187	69	u(t	u(t	NOUN
ejpam-3070	187	70	)	)	PUNCT
ejpam-3070	187	71	)	)	PUNCT
ejpam-3070	187	72	≥	≥	PROPN
ejpam-3070	187	73	δ	δ	PROPN
ejpam-3070	187	74	,	,	PUNCT
ejpam-3070	187	75	t	t	PROPN
ejpam-3070	187	76	∈	∈	PROPN
ejpam-3070	188	1	[	[	X
ejpam-3070	188	2	t0	t0	PROPN
ejpam-3070	188	3	,	,	PUNCT
ejpam-3070	188	4	t0	t0	PROPN
ejpam-3070	188	5	+	+	X
ejpam-3070	188	6	t	t	X
ejpam-3070	188	7	]	]	PUNCT
ejpam-3070	188	8	.	.	PUNCT
ejpam-3070	189	1	(	(	PUNCT
ejpam-3070	189	2	25	25	NUM
ejpam-3070	189	3	)	)	PUNCT
ejpam-3070	189	4	let	let	VERB
ejpam-3070	189	5	m(t	m(t	NOUN
ejpam-3070	189	6	)	)	PUNCT
ejpam-3070	190	1	=	=	SYM
ejpam-3070	190	2	v	v	X
ejpam-3070	190	3	(	(	PUNCT
ejpam-3070	190	4	t	t	PROPN
ejpam-3070	190	5	,	,	PUNCT
ejpam-3070	190	6	u(t	u(t	NOUN
ejpam-3070	190	7	)	)	PUNCT
ejpam-3070	190	8	)	)	PUNCT
ejpam-3070	190	9	,	,	PUNCT
ejpam-3070	190	10	then	then	ADV
ejpam-3070	190	11	it	it	PRON
ejpam-3070	190	12	follows	follow	VERB
ejpam-3070	190	13	from	from	ADP
ejpam-3070	190	14	hypothesis	hypothesis	NOUN
ejpam-3070	190	15	(	(	PUNCT
ejpam-3070	190	16	ii	ii	NOUN
ejpam-3070	190	17	)	)	PUNCT
ejpam-3070	191	1	that	that	DET
ejpam-3070	191	2	d+m(t	d+m(t	NOUN
ejpam-3070	191	3	)	)	PUNCT
ejpam-3070	191	4	≤	≤	NOUN
ejpam-3070	191	5	−c(h0(t	−c(h0(t	PROPN
ejpam-3070	191	6	,	,	PUNCT
ejpam-3070	191	7	u(t	u(t	NOUN
ejpam-3070	191	8	)	)	PUNCT
ejpam-3070	191	9	)	)	PUNCT
ejpam-3070	191	10	,	,	PUNCT
ejpam-3070	191	11	t	t	PROPN
ejpam-3070	191	12	≥	≥	PROPN
ejpam-3070	191	13	t0	t0	PROPN
ejpam-3070	191	14	.	.	PUNCT
ejpam-3070	192	1	(	(	PUNCT
ejpam-3070	192	2	26	26	NUM
ejpam-3070	192	3	)	)	PUNCT
ejpam-3070	192	4	then	then	ADV
ejpam-3070	192	5	from	from	ADP
ejpam-3070	192	6	the	the	DET
ejpam-3070	192	7	equation	equation	NOUN
ejpam-3070	192	8	(	(	PUNCT
ejpam-3070	192	9	22	22	NUM
ejpam-3070	192	10	)	)	PUNCT
ejpam-3070	192	11	we	we	PRON
ejpam-3070	192	12	get,∫	get,∫	PUNCT
ejpam-3070	192	13	t0+t	t0+t	VERB
ejpam-3070	192	14	t0	t0	PROPN
ejpam-3070	192	15	c(h0(s	c(h0(s	PROPN
ejpam-3070	192	16	,	,	PUNCT
ejpam-3070	192	17	u(s))ds	u(s))ds	PROPN
ejpam-3070	192	18	≤	≤	PROPN
ejpam-3070	192	19	m(t0	m(t0	PROPN
ejpam-3070	192	20	)	)	PUNCT
ejpam-3070	192	21	≤	≤	NUM
ejpam-3070	192	22	a(δ∗	a(δ∗	NOUN
ejpam-3070	192	23	)	)	PUNCT
ejpam-3070	192	24	,	,	PUNCT
ejpam-3070	192	25	also	also	ADV
ejpam-3070	192	26	from	from	ADP
ejpam-3070	192	27	(	(	PUNCT
ejpam-3070	192	28	25	25	NUM
ejpam-3070	192	29	)	)	PUNCT
ejpam-3070	192	30	we	we	PRON
ejpam-3070	192	31	have	have	AUX
ejpam-3070	192	32	∫	∫	PROPN
ejpam-3070	192	33	t0+t	t0+t	PROPN
ejpam-3070	192	34	t0	t0	PROPN
ejpam-3070	192	35	c(h0(s	c(h0(s	PROPN
ejpam-3070	192	36	,	,	PUNCT
ejpam-3070	192	37	u(s))ds	u(s))ds	PROPN
ejpam-3070	192	38	≥	≥	X
ejpam-3070	192	39	c(δ)t	c(δ)t	X
ejpam-3070	192	40	>	>	X
ejpam-3070	192	41	a(δ∗	a(δ∗	PROPN
ejpam-3070	192	42	)	)	PUNCT
ejpam-3070	192	43	which	which	PRON
ejpam-3070	192	44	is	be	AUX
ejpam-3070	192	45	a	a	DET
ejpam-3070	192	46	contraduction	contraduction	NOUN
ejpam-3070	192	47	.	.	PUNCT
ejpam-3070	193	1	hence	hence	ADV
ejpam-3070	193	2	proof	proof	NOUN
ejpam-3070	193	3	of	of	ADP
ejpam-3070	193	4	the	the	DET
ejpam-3070	193	5	theorem	theorem	NOUN
ejpam-3070	193	6	is	be	AUX
ejpam-3070	193	7	complete	complete	ADJ
ejpam-3070	193	8	.	.	PUNCT
ejpam-3070	194	1	references	reference	NOUN
ejpam-3070	194	2	654	654	NUM
ejpam-3070	194	3	references	reference	NOUN
ejpam-3070	194	4	[	[	X
ejpam-3070	194	5	1	1	NUM
ejpam-3070	194	6	]	]	PUNCT
ejpam-3070	194	7	c.corduneanu	c.corduneanu	NOUN
ejpam-3070	194	8	,	,	PUNCT
ejpam-3070	194	9	functional	functional	ADJ
ejpam-3070	194	10	equations	equation	NOUN
ejpam-3070	194	11	with	with	ADP
ejpam-3070	194	12	causal	causal	ADJ
ejpam-3070	194	13	operators	operator	NOUN
ejpam-3070	194	14	,	,	PUNCT
ejpam-3070	194	15	taylor	taylor	PROPN
ejpam-3070	194	16	and	and	CCONJ
ejpam-3070	194	17	francis	francis	PROPN
ejpam-3070	194	18	,	,	PUNCT
ejpam-3070	194	19	new	new	PROPN
ejpam-3070	194	20	york	york	PROPN
ejpam-3070	194	21	,	,	PUNCT
ejpam-3070	194	22	2003	2003	NUM
ejpam-3070	194	23	.	.	PUNCT
ejpam-3070	195	1	[	[	X
ejpam-3070	195	2	2	2	NUM
ejpam-3070	195	3	]	]	PUNCT
ejpam-3070	195	4	j.vasundhara	j.vasundhara	X
ejpam-3070	195	5	devi	devi	PROPN
ejpam-3070	195	6	,	,	PUNCT
ejpam-3070	195	7	ch	ch	PROPN
ejpam-3070	195	8	.	.	PROPN
ejpam-3070	195	9	appala	appala	PROPN
ejpam-3070	195	10	naidu	naidu	PROPN
ejpam-3070	195	11	,	,	PUNCT
ejpam-3070	195	12	stability	stability	NOUN
ejpam-3070	195	13	results	result	VERB
ejpam-3070	195	14	for	for	ADP
ejpam-3070	195	15	impulsive	impulsive	ADJ
ejpam-3070	195	16	set	set	VERB
ejpam-3070	195	17	differential	differential	ADJ
ejpam-3070	195	18	equations	equation	NOUN
ejpam-3070	195	19	involving	involve	VERB
ejpam-3070	195	20	causal	causal	ADJ
ejpam-3070	195	21	operators	operator	NOUN
ejpam-3070	195	22	with	with	ADP
ejpam-3070	195	23	memory	memory	NOUN
ejpam-3070	195	24	,	,	PUNCT
ejpam-3070	195	25	gjms	gjms	ADJ
ejpam-3070	195	26	,	,	PUNCT
ejpam-3070	195	27	vol	vol	NOUN
ejpam-3070	195	28	2.2	2.2	NUM
ejpam-3070	195	29	,	,	PUNCT
ejpam-3070	195	30	49	49	NUM
ejpam-3070	195	31	-	-	SYM
ejpam-3070	195	32	53	53	NUM
ejpam-3070	195	33	.	.	PUNCT
ejpam-3070	196	1	[	[	X
ejpam-3070	196	2	3	3	NUM
ejpam-3070	196	3	]	]	PUNCT
ejpam-3070	196	4	j.vasundhara	j.vasundhara	X
ejpam-3070	196	5	devi	devi	PROPN
ejpam-3070	196	6	,	,	PUNCT
ejpam-3070	196	7	comparison	comparison	NOUN
ejpam-3070	196	8	theorems	theorem	NOUN
ejpam-3070	196	9	and	and	CCONJ
ejpam-3070	196	10	existence	existence	NOUN
ejpam-3070	196	11	results	result	VERB
ejpam-3070	196	12	for	for	ADP
ejpam-3070	196	13	set	set	VERB
ejpam-3070	196	14	differential	differential	ADJ
ejpam-3070	196	15	equations	equation	NOUN
ejpam-3070	196	16	involving	involve	VERB
ejpam-3070	196	17	causal	causal	ADJ
ejpam-3070	196	18	operators	operator	NOUN
ejpam-3070	196	19	with	with	ADP
ejpam-3070	196	20	memory	memory	NOUN
ejpam-3070	196	21	,	,	PUNCT
ejpam-3070	196	22	nonlinear	nonlinear	ADJ
ejpam-3070	196	23	studies	study	NOUN
ejpam-3070	196	24	,	,	PUNCT
ejpam-3070	196	25	vol	vol	NOUN
ejpam-3070	196	26	.	.	PROPN
ejpam-3070	196	27	18	18	NUM
ejpam-3070	196	28	,	,	PUNCT
ejpam-3070	196	29	no	no	INTJ
ejpam-3070	196	30	.	.	NOUN
ejpam-3070	196	31	4	4	NUM
ejpam-3070	196	32	,	,	PUNCT
ejpam-3070	196	33	603	603	NUM
ejpam-3070	196	34	-	-	SYM
ejpam-3070	196	35	610	610	NUM
ejpam-3070	196	36	,	,	PUNCT
ejpam-3070	196	37	2011	2011	NUM
ejpam-3070	196	38	.	.	PUNCT
ejpam-3070	197	1	[	[	X
ejpam-3070	197	2	4	4	NUM
ejpam-3070	197	3	]	]	PUNCT
ejpam-3070	197	4	j.vasundhara	j.vasundhara	X
ejpam-3070	197	5	devi	devi	PROPN
ejpam-3070	197	6	,	,	PUNCT
ejpam-3070	197	7	existence	existence	NOUN
ejpam-3070	197	8	and	and	CCONJ
ejpam-3070	197	9	uniqueness	uniqueness	NOUN
ejpam-3070	197	10	of	of	ADP
ejpam-3070	197	11	solutions	solution	NOUN
ejpam-3070	197	12	for	for	ADP
ejpam-3070	197	13	set	set	ADJ
ejpam-3070	197	14	differential	differential	ADJ
ejpam-3070	197	15	equations	equation	NOUN
ejpam-3070	197	16	involving	involve	VERB
ejpam-3070	197	17	causal	causal	ADJ
ejpam-3070	197	18	operators	operator	NOUN
ejpam-3070	197	19	with	with	ADP
ejpam-3070	197	20	memory	memory	NOUN
ejpam-3070	197	21	,	,	PUNCT
ejpam-3070	197	22	ejpam	ejpam	NOUN
ejpam-3070	197	23	,	,	PUNCT
ejpam-3070	197	24	vol	vol	NOUN
ejpam-3070	197	25	3	3	NUM
ejpam-3070	197	26	,	,	PUNCT
ejpam-3070	197	27	n0	n0	PROPN
ejpam-3070	197	28	.	.	PROPN
ejpam-3070	197	29	4	4	NUM
ejpam-3070	197	30	,	,	PUNCT
ejpam-3070	197	31	2010	2010	NUM
ejpam-3070	197	32	,	,	PUNCT
ejpam-3070	197	33	737	737	NUM
ejpam-3070	197	34	-	-	SYM
ejpam-3070	197	35	747	747	NUM
ejpam-3070	197	36	.	.	PUNCT
ejpam-3070	198	1	[	[	X
ejpam-3070	198	2	5	5	X
ejpam-3070	198	3	]	]	PUNCT
ejpam-3070	198	4	t.gnana	t.gnana	NOUN
ejpam-3070	198	5	bhasker	bhasker	NOUN
ejpam-3070	198	6	,	,	PUNCT
ejpam-3070	198	7	j.vasundhara	j.vasundhara	X
ejpam-3070	198	8	devi	devi	PROPN
ejpam-3070	198	9	,	,	PUNCT
ejpam-3070	198	10	stability	stability	NOUN
ejpam-3070	198	11	criteria	criterion	NOUN
ejpam-3070	198	12	for	for	ADP
ejpam-3070	198	13	set	set	VERB
ejpam-3070	198	14	differential	differential	ADJ
ejpam-3070	198	15	equations	equation	NOUN
ejpam-3070	198	16	,	,	PUNCT
ejpam-3070	198	17	mathematical	mathematical	ADJ
ejpam-3070	198	18	and	and	CCONJ
ejpam-3070	198	19	computer	computer	NOUN
ejpam-3070	198	20	modelling	modelling	NOUN
ejpam-3070	198	21	,	,	PUNCT
ejpam-3070	198	22	41	41	NUM
ejpam-3070	198	23	(	(	PUNCT
ejpam-3070	198	24	2005	2005	NUM
ejpam-3070	198	25	)	)	PUNCT
ejpam-3070	198	26	,	,	PUNCT
ejpam-3070	198	27	1371	1371	NUM
ejpam-3070	198	28	-	-	SYM
ejpam-3070	198	29	1378	1378	NUM
ejpam-3070	198	30	.	.	PUNCT
ejpam-3070	199	1	[	[	X
ejpam-3070	199	2	6	6	NUM
ejpam-3070	199	3	]	]	PUNCT
ejpam-3070	199	4	v.	v.	ADP
ejpam-3070	199	5	lakshmikantham	lakshmikantham	ADJ
ejpam-3070	199	6	,	,	PUNCT
ejpam-3070	199	7	s.leela	s.leela	PRON
ejpam-3070	199	8	,	,	PUNCT
ejpam-3070	199	9	differential	differential	ADJ
ejpam-3070	199	10	and	and	CCONJ
ejpam-3070	199	11	integral	integral	ADJ
ejpam-3070	199	12	inequalities	inequality	NOUN
ejpam-3070	199	13	,	,	PUNCT
ejpam-3070	199	14	vol	vol	NOUN
ejpam-3070	199	15	.	.	PUNCT
ejpam-3070	200	1	i	i	PRON
ejpam-3070	200	2	,	,	PUNCT
ejpam-3070	200	3	academic	academic	ADJ
ejpam-3070	200	4	press	press	NOUN
ejpam-3070	200	5	,	,	PUNCT
ejpam-3070	200	6	new	new	PROPN
ejpam-3070	200	7	york	york	PROPN
ejpam-3070	200	8	,	,	PUNCT
ejpam-3070	200	9	1969	1969	NUM
ejpam-3070	200	10	.	.	PUNCT
ejpam-3070	201	1	[	[	X
ejpam-3070	201	2	7	7	X
ejpam-3070	201	3	]	]	SYM
ejpam-3070	201	4	v.lakshmikantham	v.lakshmikantham	PROPN
ejpam-3070	201	5	,	,	PUNCT
ejpam-3070	201	6	s.leela	s.leela	PRON
ejpam-3070	201	7	,	,	PUNCT
ejpam-3070	201	8	j.vasundhara	j.vasundhara	X
ejpam-3070	201	9	devi	devi	PROPN
ejpam-3070	201	10	,	,	PUNCT
ejpam-3070	201	11	stability	stability	NOUN
ejpam-3070	201	12	theory	theory	NOUN
ejpam-3070	201	13	for	for	ADP
ejpam-3070	201	14	set	set	VERB
ejpam-3070	201	15	differential	differential	ADJ
ejpam-3070	201	16	equations	equation	NOUN
ejpam-3070	201	17	,	,	PUNCT
ejpam-3070	201	18	dynamics	dynamic	NOUN
ejpam-3070	201	19	of	of	ADP
ejpam-3070	201	20	continuous	continuous	ADJ
ejpam-3070	201	21	discrete	discrete	ADJ
ejpam-3070	201	22	and	and	CCONJ
ejpam-3070	201	23	impulsive	impulsive	ADJ
ejpam-3070	201	24	systems	system	NOUN
ejpam-3070	201	25	,	,	PUNCT
ejpam-3070	201	26	series	series	NOUN
ejpam-3070	201	27	a	a	NOUN
ejpam-3070	201	28	,	,	PUNCT
ejpam-3070	201	29	181	181	NUM
ejpam-3070	201	30	-	-	SYM
ejpam-3070	201	31	190	190	NUM
ejpam-3070	201	32	,	,	PUNCT
ejpam-3070	201	33	(	(	PUNCT
ejpam-3070	201	34	2004	2004	NUM
ejpam-3070	201	35	)	)	PUNCT
ejpam-3070	201	36	.	.	PUNCT
ejpam-3070	202	1	[	[	X
ejpam-3070	202	2	8	8	NUM
ejpam-3070	202	3	]	]	X
ejpam-3070	202	4	v.	v.	CCONJ
ejpam-3070	202	5	lakshmikantham	lakshmikantham	ADJ
ejpam-3070	202	6	,	,	PUNCT
ejpam-3070	202	7	s.leela	s.leela	PROPN
ejpam-3070	202	8	,	,	PUNCT
ejpam-3070	202	9	z.	z.	PROPN
ejpam-3070	202	10	drici	drici	PROPN
ejpam-3070	202	11	and	and	CCONJ
ejpam-3070	202	12	mcrae	mcrae	PROPN
ejpam-3070	202	13	f.a	f.a	PROPN
ejpam-3070	202	14	,	,	PUNCT
ejpam-3070	202	15	theory	theory	NOUN
ejpam-3070	202	16	of	of	ADP
ejpam-3070	202	17	causal	causal	ADJ
ejpam-3070	202	18	differential	differential	ADJ
ejpam-3070	202	19	equations	equation	NOUN
ejpam-3070	202	20	,	,	PUNCT
ejpam-3070	202	21	atlantis	atlantis	PROPN
ejpam-3070	202	22	press	press	PROPN
ejpam-3070	202	23	and	and	CCONJ
ejpam-3070	202	24	world	world	NOUN
ejpam-3070	202	25	scientific	scientific	ADJ
ejpam-3070	202	26	,	,	PUNCT
ejpam-3070	202	27	2009	2009	NUM
ejpam-3070	202	28	.	.	PUNCT
ejpam-3070	203	1	[	[	X
ejpam-3070	203	2	9	9	NUM
ejpam-3070	203	3	]	]	SYM
ejpam-3070	203	4	v.lakshmikantham	v.lakshmikantham	PROPN
ejpam-3070	203	5	,	,	PUNCT
ejpam-3070	203	6	t.gnana	t.gnana	NOUN
ejpam-3070	203	7	bhasker	bhasker	NOUN
ejpam-3070	203	8	,	,	PUNCT
ejpam-3070	203	9	j.vasundhara	j.vasundhara	X
ejpam-3070	203	10	devi	devi	PROPN
ejpam-3070	203	11	,	,	PUNCT
ejpam-3070	203	12	theory	theory	NOUN
ejpam-3070	203	13	of	of	ADP
ejpam-3070	203	14	set	set	VERB
ejpam-3070	203	15	differential	differential	ADJ
ejpam-3070	203	16	equations	equation	NOUN
ejpam-3070	203	17	in	in	ADP
ejpam-3070	203	18	metric	metric	ADJ
ejpam-3070	203	19	spaces	space	NOUN
ejpam-3070	203	20	,	,	PUNCT
ejpam-3070	203	21	cambridge	cambridge	NOUN
ejpam-3070	203	22	scientific	scientific	ADJ
ejpam-3070	203	23	publishers	publisher	NOUN
ejpam-3070	203	24	,	,	PUNCT
ejpam-3070	203	25	cottenham	cottenham	NOUN
ejpam-3070	203	26	,	,	PUNCT
ejpam-3070	203	27	uk	uk	PROPN
ejpam-3070	203	28	,	,	PUNCT
ejpam-3070	203	29	2006	2006	NUM
ejpam-3070	203	30	.	.	PUNCT
ejpam-3070	204	1	[	[	X
ejpam-3070	204	2	10	10	NUM
ejpam-3070	204	3	]	]	X
ejpam-3070	204	4	v.	v.	ADP
ejpam-3070	204	5	lakshmikantham	lakshmikantham	ADJ
ejpam-3070	204	6	,	,	PUNCT
ejpam-3070	204	7	x.z.liu	x.z.liu	PROPN
ejpam-3070	204	8	,	,	PUNCT
ejpam-3070	204	9	stability	stability	NOUN
ejpam-3070	204	10	analysis	analysis	NOUN
ejpam-3070	204	11	in	in	ADP
ejpam-3070	204	12	terms	term	NOUN
ejpam-3070	204	13	of	of	ADP
ejpam-3070	204	14	two	two	NUM
ejpam-3070	204	15	measures	measure	NOUN
ejpam-3070	204	16	,	,	PUNCT
ejpam-3070	204	17	world	world	NOUN
ejpam-3070	204	18	scientific	scientific	NOUN
ejpam-3070	204	19	,	,	PUNCT
ejpam-3070	204	20	1993	1993	NUM
ejpam-3070	204	21	.	.	PUNCT
ejpam-3070	205	1	[	[	X
ejpam-3070	205	2	11	11	NUM
ejpam-3070	205	3	]	]	PUNCT
ejpam-3070	205	4	z.drici	z.drici	NOUN
ejpam-3070	205	5	,	,	PUNCT
ejpam-3070	205	6	mc	mc	PROPN
ejpam-3070	205	7	rae	rae	PROPN
ejpam-3070	205	8	f.a	f.a	PROPN
ejpam-3070	205	9	.	.	PROPN
ejpam-3070	205	10	,	,	PUNCT
ejpam-3070	205	11	j.vasundhara	j.vasundhara	X
ejpam-3070	205	12	devi	devi	PROPN
ejpam-3070	205	13	,	,	PUNCT
ejpam-3070	205	14	stability	stability	NOUN
ejpam-3070	205	15	results	result	VERB
ejpam-3070	205	16	for	for	ADP
ejpam-3070	205	17	set	set	VERB
ejpam-3070	205	18	differential	differential	ADJ
ejpam-3070	205	19	equations	equation	NOUN
ejpam-3070	205	20	involving	involve	VERB
ejpam-3070	205	21	causal	causal	ADJ
ejpam-3070	205	22	maps	map	NOUN
ejpam-3070	205	23	,	,	PUNCT
ejpam-3070	205	24	dynamic	dynamic	ADJ
ejpam-3070	205	25	systems	system	NOUN
ejpam-3070	205	26	and	and	CCONJ
ejpam-3070	205	27	applications	application	NOUN
ejpam-3070	205	28	,	,	PUNCT
ejpam-3070	205	29	15	15	NUM
ejpam-3070	205	30	(	(	PUNCT
ejpam-3070	205	31	2006	2006	NUM
ejpam-3070	205	32	)	)	PUNCT
ejpam-3070	205	33	,	,	PUNCT
ejpam-3070	205	34	451	451	NUM
ejpam-3070	205	35	-	-	SYM
ejpam-3070	205	36	464	464	NUM
ejpam-3070	205	37	.	.	PUNCT