id	sid	tid	token	lemma	pos
ejpam-1600	1	1	8_devi.dvi	8_devi.dvi	NUM
ejpam-1600	1	2	european	european	ADJ
ejpam-1600	1	3	journal	journal	NOUN
ejpam-1600	1	4	of	of	ADP
ejpam-1600	1	5	pure	pure	ADJ
ejpam-1600	1	6	and	and	CCONJ
ejpam-1600	1	7	applied	apply	VERB
ejpam-1600	1	8	mathematics	mathematic	NOUN
ejpam-1600	1	9	vol	vol	NOUN
ejpam-1600	1	10	.	.	PROPN
ejpam-1600	2	1	5	5	NUM
ejpam-1600	2	2	,	,	PUNCT
ejpam-1600	2	3	no	no	INTJ
ejpam-1600	2	4	.	.	NOUN
ejpam-1600	2	5	2	2	NUM
ejpam-1600	2	6	,	,	PUNCT
ejpam-1600	2	7	2012	2012	NUM
ejpam-1600	2	8	,	,	PUNCT
ejpam-1600	2	9	187	187	NUM
ejpam-1600	2	10	-	-	SYM
ejpam-1600	2	11	196	196	NUM
ejpam-1600	2	12	issn	issn	PROPN
ejpam-1600	2	13	1307	1307	NUM
ejpam-1600	2	14	-	-	SYM
ejpam-1600	2	15	5543	5543	NUM
ejpam-1600	2	16	–	–	PUNCT
ejpam-1600	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-1600	2	18	stability	stability	NOUN
ejpam-1600	2	19	results	result	VERB
ejpam-1600	2	20	for	for	ADP
ejpam-1600	2	21	set	set	VERB
ejpam-1600	2	22	differential	differential	ADJ
ejpam-1600	2	23	equations	equation	NOUN
ejpam-1600	2	24	involving	involve	VERB
ejpam-1600	2	25	causal	causal	ADJ
ejpam-1600	2	26	operators	operator	NOUN
ejpam-1600	2	27	with	with	ADP
ejpam-1600	2	28	memory	memory	NOUN
ejpam-1600	2	29	j.	j.	PROPN
ejpam-1600	2	30	vasundhara	vasundhara	PROPN
ejpam-1600	2	31	devi∗	devi∗	PROPN
ejpam-1600	2	32	,	,	PUNCT
ejpam-1600	2	33	ch	ch	NOUN
ejpam-1600	2	34	.	.	PROPN
ejpam-1600	2	35	appala	appala	PROPN
ejpam-1600	2	36	naidu	naidu	PROPN
ejpam-1600	2	37	gvp	gvp	PROPN
ejpam-1600	2	38	–	–	PUNCT
ejpam-1600	2	39	prof	prof	NOUN
ejpam-1600	2	40	.	.	PUNCT
ejpam-1600	3	1	v.	v.	ADP
ejpam-1600	3	2	lakshmikantham	lakshmikantham	PROPN
ejpam-1600	3	3	,	,	PUNCT
ejpam-1600	3	4	department	department	NOUN
ejpam-1600	3	5	of	of	ADP
ejpam-1600	3	6	mathematics	mathematics	PROPN
ejpam-1600	3	7	,	,	PUNCT
ejpam-1600	3	8	institute	institute	NOUN
ejpam-1600	3	9	for	for	ADP
ejpam-1600	3	10	advanced	advanced	ADJ
ejpam-1600	3	11	studies	study	NOUN
ejpam-1600	3	12	,	,	PUNCT
ejpam-1600	3	13	gvp	gvp	PROPN
ejpam-1600	3	14	college	college	PROPN
ejpam-1600	3	15	of	of	ADP
ejpam-1600	3	16	engineering	engineering	PROPN
ejpam-1600	3	17	,	,	PUNCT
ejpam-1600	3	18	visakhapatnam	visakhapatnam	PROPN
ejpam-1600	3	19	,	,	PUNCT
ejpam-1600	3	20	andhra	andhra	PROPN
ejpam-1600	3	21	pradesh	pradesh	PROPN
ejpam-1600	3	22	,	,	PUNCT
ejpam-1600	3	23	india	india	PROPN
ejpam-1600	3	24	abstract	abstract	NOUN
ejpam-1600	3	25	.	.	PUNCT
ejpam-1600	4	1	in	in	ADP
ejpam-1600	4	2	this	this	DET
ejpam-1600	4	3	paper	paper	NOUN
ejpam-1600	4	4	we	we	PRON
ejpam-1600	4	5	study	study	VERB
ejpam-1600	4	6	the	the	DET
ejpam-1600	4	7	stability	stability	NOUN
ejpam-1600	4	8	concepts	concept	NOUN
ejpam-1600	4	9	for	for	ADP
ejpam-1600	4	10	set	set	VERB
ejpam-1600	4	11	differential	differential	ADJ
ejpam-1600	4	12	equations	equation	NOUN
ejpam-1600	4	13	involving	involve	VERB
ejpam-1600	4	14	causal	causal	ADJ
ejpam-1600	4	15	operators	operator	NOUN
ejpam-1600	4	16	with	with	ADP
ejpam-1600	4	17	memory	memory	NOUN
ejpam-1600	4	18	by	by	ADP
ejpam-1600	4	19	considering	consider	VERB
ejpam-1600	4	20	initial	initial	ADJ
ejpam-1600	4	21	functions	function	NOUN
ejpam-1600	4	22	as	as	ADP
ejpam-1600	4	23	a	a	DET
ejpam-1600	4	24	hukuhara	hukuhara	ADJ
ejpam-1600	4	25	difference	difference	NOUN
ejpam-1600	4	26	of	of	ADP
ejpam-1600	4	27	two	two	NUM
ejpam-1600	4	28	functions	function	NOUN
ejpam-1600	4	29	.	.	PUNCT
ejpam-1600	5	1	this	this	PRON
ejpam-1600	5	2	will	will	AUX
ejpam-1600	5	3	enable	enable	VERB
ejpam-1600	5	4	to	to	PART
ejpam-1600	5	5	obtain	obtain	VERB
ejpam-1600	5	6	results	result	NOUN
ejpam-1600	5	7	parallel	parallel	ADJ
ejpam-1600	5	8	to	to	ADP
ejpam-1600	5	9	ordinary	ordinary	ADJ
ejpam-1600	5	10	differential	differential	ADJ
ejpam-1600	5	11	equations	equation	NOUN
ejpam-1600	5	12	with	with	ADP
ejpam-1600	5	13	delay	delay	NOUN
ejpam-1600	5	14	.	.	PUNCT
ejpam-1600	6	1	2010	2010	NUM
ejpam-1600	6	2	mathematics	mathematic	NOUN
ejpam-1600	6	3	subject	subject	NOUN
ejpam-1600	6	4	classifications	classification	NOUN
ejpam-1600	6	5	:	:	PUNCT
ejpam-1600	6	6	34a12	34a12	NUM
ejpam-1600	6	7	key	key	ADJ
ejpam-1600	6	8	words	word	NOUN
ejpam-1600	6	9	and	and	CCONJ
ejpam-1600	6	10	phrases	phrase	NOUN
ejpam-1600	6	11	:	:	PUNCT
ejpam-1600	6	12	set	set	VERB
ejpam-1600	6	13	differential	differential	ADJ
ejpam-1600	6	14	equations	equation	NOUN
ejpam-1600	6	15	,	,	PUNCT
ejpam-1600	6	16	causal	causal	ADJ
ejpam-1600	6	17	operators	operator	NOUN
ejpam-1600	6	18	,	,	PUNCT
ejpam-1600	6	19	causal	causal	ADJ
ejpam-1600	6	20	operator	operator	NOUN
ejpam-1600	6	21	with	with	ADP
ejpam-1600	6	22	memory	memory	NOUN
ejpam-1600	6	23	,	,	PUNCT
ejpam-1600	6	24	delay	delay	NOUN
ejpam-1600	6	25	,	,	PUNCT
ejpam-1600	6	26	stability	stability	NOUN
ejpam-1600	6	27	,	,	PUNCT
ejpam-1600	6	28	asymptotic	asymptotic	ADJ
ejpam-1600	6	29	stablility	stablility	NOUN
ejpam-1600	6	30	.	.	PUNCT
ejpam-1600	7	1	1	1	X
ejpam-1600	7	2	.	.	X
ejpam-1600	7	3	introduction	introduction	NOUN
ejpam-1600	7	4	it	it	PRON
ejpam-1600	7	5	is	be	AUX
ejpam-1600	7	6	well	well	ADV
ejpam-1600	7	7	recognized	recognize	VERB
ejpam-1600	7	8	and	and	CCONJ
ejpam-1600	7	9	accepted	accept	VERB
ejpam-1600	7	10	that	that	SCONJ
ejpam-1600	7	11	set	set	VERB
ejpam-1600	7	12	differential	differential	ADJ
ejpam-1600	7	13	equations	equation	NOUN
ejpam-1600	7	14	are	be	AUX
ejpam-1600	7	15	a	a	DET
ejpam-1600	7	16	generalization	generalization	NOUN
ejpam-1600	7	17	of	of	ADP
ejpam-1600	7	18	ordinary	ordinary	ADJ
ejpam-1600	7	19	differential	differential	ADJ
ejpam-1600	7	20	equations	equation	NOUN
ejpam-1600	7	21	and	and	CCONJ
ejpam-1600	7	22	vector	vector	NOUN
ejpam-1600	7	23	differential	differential	NOUN
ejpam-1600	7	24	equations	equation	NOUN
ejpam-1600	7	25	in	in	ADP
ejpam-1600	7	26	a	a	DET
ejpam-1600	7	27	semilinear	semilinear	ADJ
ejpam-1600	7	28	metric	metric	ADJ
ejpam-1600	7	29	space	space	NOUN
ejpam-1600	7	30	and	and	CCONJ
ejpam-1600	7	31	that	that	SCONJ
ejpam-1600	7	32	they	they	PRON
ejpam-1600	7	33	are	be	AUX
ejpam-1600	7	34	useful	useful	ADJ
ejpam-1600	7	35	in	in	ADP
ejpam-1600	7	36	studying	study	VERB
ejpam-1600	7	37	multivalued	multivalued	ADJ
ejpam-1600	7	38	differential	differential	ADJ
ejpam-1600	7	39	inclusions	inclusion	NOUN
ejpam-1600	7	40	or	or	CCONJ
ejpam-1600	7	41	multivalued	multivalue	VERB
ejpam-1600	7	42	differential	differential	ADJ
ejpam-1600	7	43	equations	equation	NOUN
ejpam-1600	7	44	.	.	PUNCT
ejpam-1600	8	1	also	also	ADV
ejpam-1600	8	2	causal	causal	PROPN
ejpam-1600	8	3	operators	operator	NOUN
ejpam-1600	8	4	or	or	CCONJ
ejpam-1600	8	5	volterra	volterra	NOUN
ejpam-1600	8	6	operators	operator	NOUN
ejpam-1600	8	7	or	or	CCONJ
ejpam-1600	8	8	non	non	ADJ
ejpam-1600	8	9	anticipative	anticipative	PROPN
ejpam-1600	8	10	operators	operator	NOUN
ejpam-1600	8	11	encompass	encompass	VERB
ejpam-1600	8	12	a	a	DET
ejpam-1600	8	13	wide	wide	ADJ
ejpam-1600	8	14	range	range	NOUN
ejpam-1600	8	15	of	of	ADP
ejpam-1600	8	16	equations	equation	NOUN
ejpam-1600	8	17	such	such	ADJ
ejpam-1600	8	18	as	as	ADP
ejpam-1600	8	19	ordinary	ordinary	ADJ
ejpam-1600	8	20	differential	differential	ADJ
ejpam-1600	8	21	equations	equation	NOUN
ejpam-1600	8	22	,	,	PUNCT
ejpam-1600	8	23	integral	integral	ADJ
ejpam-1600	8	24	equations	equation	NOUN
ejpam-1600	8	25	,	,	PUNCT
ejpam-1600	8	26	integro	integro	PROPN
ejpam-1600	8	27	differential	differential	NOUN
ejpam-1600	8	28	equations	equation	NOUN
ejpam-1600	8	29	,	,	PUNCT
ejpam-1600	8	30	to	to	PART
ejpam-1600	8	31	name	name	VERB
ejpam-1600	8	32	a	a	DET
ejpam-1600	8	33	few	few	ADJ
ejpam-1600	8	34	.	.	PUNCT
ejpam-1600	9	1	thus	thus	ADV
ejpam-1600	9	2	set	set	VERB
ejpam-1600	9	3	differential	differential	ADJ
ejpam-1600	9	4	equations	equation	NOUN
ejpam-1600	9	5	involving	involve	VERB
ejpam-1600	9	6	causal	causal	ADJ
ejpam-1600	9	7	operators	operator	NOUN
ejpam-1600	9	8	with	with	ADP
ejpam-1600	9	9	memory	memory	NOUN
ejpam-1600	9	10	include	include	VERB
ejpam-1600	9	11	the	the	DET
ejpam-1600	9	12	above	above	ADJ
ejpam-1600	9	13	said	say	VERB
ejpam-1600	9	14	special	special	ADJ
ejpam-1600	9	15	cases	case	NOUN
ejpam-1600	9	16	for	for	ADP
ejpam-1600	9	17	various	various	ADJ
ejpam-1600	9	18	types	type	NOUN
ejpam-1600	9	19	of	of	ADP
ejpam-1600	9	20	equations	equation	NOUN
ejpam-1600	9	21	and	and	CCONJ
ejpam-1600	9	22	such	such	DET
ejpam-1600	9	23	a	a	DET
ejpam-1600	9	24	generalization	generalization	NOUN
ejpam-1600	9	25	is	be	AUX
ejpam-1600	9	26	interesting	interesting	ADJ
ejpam-1600	9	27	as	as	SCONJ
ejpam-1600	9	28	it	it	PRON
ejpam-1600	9	29	gives	give	VERB
ejpam-1600	9	30	a	a	DET
ejpam-1600	9	31	comprehensive	comprehensive	ADJ
ejpam-1600	9	32	view	view	NOUN
ejpam-1600	9	33	of	of	ADP
ejpam-1600	9	34	different	different	ADJ
ejpam-1600	9	35	types	type	NOUN
ejpam-1600	9	36	of	of	ADP
ejpam-1600	9	37	differential	differential	ADJ
ejpam-1600	9	38	equations	equation	NOUN
ejpam-1600	9	39	.	.	PUNCT
ejpam-1600	10	1	also	also	ADV
ejpam-1600	10	2	it	it	PRON
ejpam-1600	10	3	is	be	AUX
ejpam-1600	10	4	observed	observe	VERB
ejpam-1600	10	5	in	in	ADP
ejpam-1600	10	6	[	[	X
ejpam-1600	10	7	1	1	X
ejpam-1600	10	8	]	]	PUNCT
ejpam-1600	10	9	that	that	PRON
ejpam-1600	10	10	solutions	solution	NOUN
ejpam-1600	10	11	for	for	ADP
ejpam-1600	10	12	set	set	ADJ
ejpam-1600	10	13	differential	differential	ADJ
ejpam-1600	10	14	equations	equation	NOUN
ejpam-1600	10	15	contain	contain	VERB
ejpam-1600	10	16	a	a	DET
ejpam-1600	10	17	lot	lot	NOUN
ejpam-1600	10	18	of	of	ADP
ejpam-1600	10	19	undesirable	undesirable	ADJ
ejpam-1600	10	20	information	information	NOUN
ejpam-1600	10	21	that	that	PRON
ejpam-1600	10	22	needs	need	VERB
ejpam-1600	10	23	to	to	PART
ejpam-1600	10	24	be	be	AUX
ejpam-1600	10	25	seperated	seperate	VERB
ejpam-1600	10	26	,	,	PUNCT
ejpam-1600	10	27	so	so	SCONJ
ejpam-1600	10	28	that	that	SCONJ
ejpam-1600	10	29	the	the	DET
ejpam-1600	10	30	equations	equation	NOUN
ejpam-1600	10	31	in	in	ADP
ejpam-1600	10	32	this	this	DET
ejpam-1600	10	33	setup	setup	NOUN
ejpam-1600	10	34	satisfy	satisfy	VERB
ejpam-1600	10	35	the	the	DET
ejpam-1600	10	36	stability	stability	NOUN
ejpam-1600	10	37	behaviour	behaviour	NOUN
ejpam-1600	10	38	similar	similar	ADJ
ejpam-1600	10	39	to	to	ADP
ejpam-1600	10	40	that	that	PRON
ejpam-1600	10	41	of	of	ADP
ejpam-1600	10	42	scalar	scalar	ADJ
ejpam-1600	10	43	or	or	CCONJ
ejpam-1600	10	44	vector	vector	NOUN
ejpam-1600	10	45	equations	equation	NOUN
ejpam-1600	10	46	.	.	PUNCT
ejpam-1600	11	1	in	in	ADP
ejpam-1600	11	2	order	order	NOUN
ejpam-1600	11	3	to	to	PART
ejpam-1600	11	4	take	take	VERB
ejpam-1600	11	5	care	care	NOUN
ejpam-1600	11	6	of	of	ADP
ejpam-1600	11	7	this	this	DET
ejpam-1600	11	8	situation	situation	NOUN
ejpam-1600	11	9	,	,	PUNCT
ejpam-1600	11	10	the	the	DET
ejpam-1600	11	11	hukuhara	hukuhara	ADJ
ejpam-1600	11	12	difference	difference	NOUN
ejpam-1600	11	13	in	in	ADP
ejpam-1600	11	14	initial	initial	ADJ
ejpam-1600	11	15	values	value	NOUN
ejpam-1600	11	16	is	be	AUX
ejpam-1600	11	17	introduced	introduce	VERB
ejpam-1600	11	18	.	.	PUNCT
ejpam-1600	12	1	in	in	ADP
ejpam-1600	12	2	this	this	DET
ejpam-1600	12	3	paper	paper	NOUN
ejpam-1600	12	4	we	we	PRON
ejpam-1600	12	5	extend	extend	VERB
ejpam-1600	12	6	results	result	NOUN
ejpam-1600	12	7	in	in	ADP
ejpam-1600	12	8	[	[	X
ejpam-1600	12	9	1	1	NUM
ejpam-1600	12	10	]	]	PUNCT
ejpam-1600	12	11	to	to	PART
ejpam-1600	12	12	set	set	VERB
ejpam-1600	12	13	differential	differential	ADJ
ejpam-1600	12	14	equations	equation	NOUN
ejpam-1600	12	15	involving	involve	VERB
ejpam-1600	12	16	causal	causal	ADJ
ejpam-1600	12	17	operators	operator	NOUN
ejpam-1600	12	18	with	with	ADP
ejpam-1600	12	19	memory	memory	NOUN
ejpam-1600	12	20	by	by	ADP
ejpam-1600	12	21	considering	consider	VERB
ejpam-1600	12	22	the	the	DET
ejpam-1600	12	23	hukuhara	hukuhara	ADJ
ejpam-1600	12	24	difference	difference	NOUN
ejpam-1600	12	25	of	of	ADP
ejpam-1600	12	26	initial	initial	ADJ
ejpam-1600	12	27	functions	function	NOUN
ejpam-1600	12	28	.	.	PUNCT
ejpam-1600	13	1	we	we	PRON
ejpam-1600	13	2	obtain	obtain	VERB
ejpam-1600	13	3	stability	stability	NOUN
ejpam-1600	13	4	results	result	NOUN
ejpam-1600	13	5	using	use	VERB
ejpam-1600	13	6	lyapunov	lyapunov	NOUN
ejpam-1600	13	7	-	-	PUNCT
ejpam-1600	13	8	like	like	ADJ
ejpam-1600	13	9	functions	function	NOUN
ejpam-1600	13	10	and	and	CCONJ
ejpam-1600	13	11	the	the	DET
ejpam-1600	13	12	concept	concept	NOUN
ejpam-1600	13	13	of	of	ADP
ejpam-1600	13	14	minimal	minimal	ADJ
ejpam-1600	13	15	classes	class	NOUN
ejpam-1600	13	16	.	.	PUNCT
ejpam-1600	14	1	∗corresponding	∗corresponde	VERB
ejpam-1600	14	2	author	author	NOUN
ejpam-1600	14	3	.	.	PUNCT
ejpam-1600	15	1	email	email	NOUN
ejpam-1600	15	2	address	address	PROPN
ejpam-1600	15	3	:	:	PUNCT
ejpam-1600	15	4	jvdevi	jvdevi	ADJ
ejpam-1600	15	5	�	�	PROPN
ejpam-1600	15	6	gmail	gmail	NOUN
ejpam-1600	15	7	.	.	PUNCT
ejpam-1600	16	1	om	om	PROPN
ejpam-1600	16	2	(	(	PUNCT
ejpam-1600	16	3	j.	j.	PROPN
ejpam-1600	16	4	devi	devi	PROPN
ejpam-1600	16	5	)	)	PUNCT
ejpam-1600	16	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1600	17	1	187	187	NUM
ejpam-1600	17	2	c	c	X
ejpam-1600	17	3	©	©	PROPN
ejpam-1600	17	4	2012	2012	NUM
ejpam-1600	17	5	ejpam	ejpam	VERB
ejpam-1600	17	6	all	all	DET
ejpam-1600	17	7	rights	right	NOUN
ejpam-1600	17	8	reserved	reserve	VERB
ejpam-1600	17	9	.	.	PUNCT
ejpam-1600	18	1	j.	j.	PROPN
ejpam-1600	18	2	devi	devi	PROPN
ejpam-1600	18	3	,	,	PUNCT
ejpam-1600	18	4	ch	ch	PROPN
ejpam-1600	18	5	.	.	PUNCT
ejpam-1600	18	6	naidu	naidu	PROPN
ejpam-1600	18	7	/	/	SYM
ejpam-1600	18	8	eur	eur	PROPN
ejpam-1600	18	9	.	.	PUNCT
ejpam-1600	19	1	j.	j.	PROPN
ejpam-1600	19	2	pure	pure	PROPN
ejpam-1600	19	3	appl	appl	PROPN
ejpam-1600	19	4	.	.	PROPN
ejpam-1600	19	5	math	math	PROPN
ejpam-1600	19	6	,	,	PUNCT
ejpam-1600	19	7	5	5	NUM
ejpam-1600	19	8	(	(	PUNCT
ejpam-1600	19	9	2012	2012	NUM
ejpam-1600	19	10	)	)	PUNCT
ejpam-1600	19	11	,	,	PUNCT
ejpam-1600	19	12	187	187	NUM
ejpam-1600	19	13	-	-	SYM
ejpam-1600	19	14	196	196	NUM
ejpam-1600	19	15	188	188	NUM
ejpam-1600	19	16	2	2	NUM
ejpam-1600	19	17	.	.	PUNCT
ejpam-1600	19	18	preliminaries	preliminary	NOUN
ejpam-1600	19	19	we	we	PRON
ejpam-1600	19	20	begin	begin	VERB
ejpam-1600	19	21	with	with	ADP
ejpam-1600	19	22	the	the	DET
ejpam-1600	19	23	definitions	definition	NOUN
ejpam-1600	19	24	of	of	ADP
ejpam-1600	19	25	kc(r	kc(r	NOUN
ejpam-1600	19	26	n	n	CCONJ
ejpam-1600	19	27	)	)	PUNCT
ejpam-1600	19	28	,	,	PUNCT
ejpam-1600	19	29	the	the	DET
ejpam-1600	19	30	semilinear	semilinear	ADJ
ejpam-1600	19	31	space	space	NOUN
ejpam-1600	19	32	in	in	ADP
ejpam-1600	19	33	which	which	PRON
ejpam-1600	19	34	we	we	PRON
ejpam-1600	19	35	work	work	VERB
ejpam-1600	19	36	.	.	PUNCT
ejpam-1600	20	1	we	we	PRON
ejpam-1600	20	2	next	next	ADV
ejpam-1600	20	3	define	define	VERB
ejpam-1600	20	4	the	the	DET
ejpam-1600	20	5	hausdorff	hausdorff	NOUN
ejpam-1600	20	6	metric	metric	NOUN
ejpam-1600	20	7	,	,	PUNCT
ejpam-1600	20	8	the	the	DET
ejpam-1600	20	9	hukuhara	hukuhara	ADJ
ejpam-1600	20	10	difference	difference	NOUN
ejpam-1600	20	11	,	,	PUNCT
ejpam-1600	20	12	the	the	DET
ejpam-1600	20	13	hukuhara	hukuhara	ADV
ejpam-1600	20	14	derivative	derivative	NOUN
ejpam-1600	20	15	and	and	CCONJ
ejpam-1600	20	16	the	the	DET
ejpam-1600	20	17	hukuhara	hukuhara	ADV
ejpam-1600	20	18	integral	integral	ADJ
ejpam-1600	20	19	.	.	PUNCT
ejpam-1600	21	1	we	we	PRON
ejpam-1600	21	2	also	also	ADV
ejpam-1600	21	3	state	state	VERB
ejpam-1600	21	4	all	all	DET
ejpam-1600	21	5	the	the	DET
ejpam-1600	21	6	important	important	ADJ
ejpam-1600	21	7	properties	property	NOUN
ejpam-1600	21	8	that	that	PRON
ejpam-1600	21	9	are	be	AUX
ejpam-1600	21	10	useful	useful	ADJ
ejpam-1600	21	11	in	in	ADP
ejpam-1600	21	12	this	this	DET
ejpam-1600	21	13	paper	paper	NOUN
ejpam-1600	21	14	.	.	PUNCT
ejpam-1600	22	1	we	we	PRON
ejpam-1600	22	2	further	far	ADV
ejpam-1600	22	3	define	define	VERB
ejpam-1600	22	4	a	a	DET
ejpam-1600	22	5	partial	partial	ADJ
ejpam-1600	22	6	order	order	NOUN
ejpam-1600	22	7	in	in	ADP
ejpam-1600	22	8	kc(r	kc(r	NOUN
ejpam-1600	22	9	n	n	CCONJ
ejpam-1600	22	10	)	)	PUNCT
ejpam-1600	22	11	.	.	PUNCT
ejpam-1600	23	1	we	we	PRON
ejpam-1600	23	2	also	also	ADV
ejpam-1600	23	3	state	state	VERB
ejpam-1600	23	4	all	all	DET
ejpam-1600	23	5	the	the	DET
ejpam-1600	23	6	required	require	VERB
ejpam-1600	23	7	results	result	NOUN
ejpam-1600	23	8	developed	develop	VERB
ejpam-1600	23	9	in	in	ADP
ejpam-1600	23	10	[	[	X
ejpam-1600	23	11	4	4	X
ejpam-1600	23	12	]	]	PUNCT
ejpam-1600	23	13	that	that	PRON
ejpam-1600	23	14	will	will	AUX
ejpam-1600	23	15	be	be	AUX
ejpam-1600	23	16	used	use	VERB
ejpam-1600	23	17	in	in	ADP
ejpam-1600	23	18	this	this	DET
ejpam-1600	23	19	paper	paper	NOUN
ejpam-1600	23	20	.	.	PUNCT
ejpam-1600	24	1	let	let	VERB
ejpam-1600	24	2	kc(r	kc(r	NOUN
ejpam-1600	24	3	n	n	CCONJ
ejpam-1600	24	4	)	)	PUNCT
ejpam-1600	24	5	denote	denote	VERB
ejpam-1600	24	6	the	the	DET
ejpam-1600	24	7	collection	collection	NOUN
ejpam-1600	24	8	of	of	ADP
ejpam-1600	24	9	all	all	DET
ejpam-1600	24	10	nonempty	nonempty	ADJ
ejpam-1600	24	11	,	,	PUNCT
ejpam-1600	24	12	compact	compact	ADJ
ejpam-1600	24	13	and	and	CCONJ
ejpam-1600	24	14	convex	convex	ADJ
ejpam-1600	24	15	subsets	subset	NOUN
ejpam-1600	24	16	of	of	ADP
ejpam-1600	24	17	rn	rn	PROPN
ejpam-1600	24	18	.	.	PROPN
ejpam-1600	24	19	define	define	VERB
ejpam-1600	24	20	the	the	DET
ejpam-1600	24	21	hausdorff	hausdorff	NOUN
ejpam-1600	24	22	metric	metric	ADJ
ejpam-1600	24	23	by	by	ADP
ejpam-1600	24	24	d[a	d[a	PROPN
ejpam-1600	24	25	,	,	PUNCT
ejpam-1600	24	26	b	b	X
ejpam-1600	24	27	]	]	X
ejpam-1600	24	28	=	=	NOUN
ejpam-1600	24	29	max[sup	max[sup	NOUN
ejpam-1600	24	30	x∈b	x∈b	NOUN
ejpam-1600	24	31	d(x	d(x	PROPN
ejpam-1600	24	32	,	,	PUNCT
ejpam-1600	24	33	a	a	X
ejpam-1600	24	34	)	)	PUNCT
ejpam-1600	24	35	,	,	PUNCT
ejpam-1600	24	36	sup	sup	NOUN
ejpam-1600	24	37	y∈a	y∈a	NOUN
ejpam-1600	24	38	d(y	d(y	PROPN
ejpam-1600	24	39	,	,	PUNCT
ejpam-1600	24	40	b	b	NOUN
ejpam-1600	24	41	)	)	PUNCT
ejpam-1600	24	42	]	]	PUNCT
ejpam-1600	24	43	,	,	PUNCT
ejpam-1600	24	44	(	(	PUNCT
ejpam-1600	24	45	1	1	X
ejpam-1600	24	46	)	)	PUNCT
ejpam-1600	25	1	where	where	SCONJ
ejpam-1600	25	2	d(x	d(x	NOUN
ejpam-1600	25	3	,	,	PUNCT
ejpam-1600	25	4	a	a	X
ejpam-1600	25	5	)	)	PUNCT
ejpam-1600	25	6	=	=	SYM
ejpam-1600	25	7	inf[d(x	inf[d(x	ADP
ejpam-1600	25	8	,	,	PUNCT
ejpam-1600	25	9	y	y	PROPN
ejpam-1600	25	10	)	)	PUNCT
ejpam-1600	25	11	:	:	PUNCT
ejpam-1600	25	12	y	y	PROPN
ejpam-1600	25	13	∈	∈	PROPN
ejpam-1600	25	14	a	a	X
ejpam-1600	25	15	]	]	X
ejpam-1600	25	16	,	,	PUNCT
ejpam-1600	25	17	a	a	DET
ejpam-1600	25	18	,	,	PUNCT
ejpam-1600	25	19	b	b	PROPN
ejpam-1600	25	20	are	be	AUX
ejpam-1600	25	21	bounded	bound	VERB
ejpam-1600	25	22	sets	set	NOUN
ejpam-1600	25	23	in	in	ADP
ejpam-1600	25	24	rn	rn	PROPN
ejpam-1600	25	25	.	.	PUNCT
ejpam-1600	26	1	we	we	PRON
ejpam-1600	26	2	note	note	VERB
ejpam-1600	26	3	that	that	SCONJ
ejpam-1600	26	4	kc(r	kc(r	NOUN
ejpam-1600	26	5	n	n	CCONJ
ejpam-1600	26	6	)	)	PUNCT
ejpam-1600	26	7	with	with	ADP
ejpam-1600	26	8	this	this	DET
ejpam-1600	26	9	metric	metric	NOUN
ejpam-1600	26	10	is	be	AUX
ejpam-1600	26	11	a	a	DET
ejpam-1600	26	12	complete	complete	ADJ
ejpam-1600	26	13	metric	metric	ADJ
ejpam-1600	26	14	space	space	NOUN
ejpam-1600	26	15	.	.	PUNCT
ejpam-1600	27	1	it	it	PRON
ejpam-1600	27	2	is	be	AUX
ejpam-1600	27	3	known	know	VERB
ejpam-1600	27	4	that	that	SCONJ
ejpam-1600	27	5	if	if	SCONJ
ejpam-1600	27	6	the	the	DET
ejpam-1600	27	7	space	space	NOUN
ejpam-1600	27	8	kc(r	kc(r	X
ejpam-1600	27	9	n	n	CCONJ
ejpam-1600	27	10	)	)	PUNCT
ejpam-1600	27	11	is	be	AUX
ejpam-1600	27	12	equipped	equip	VERB
ejpam-1600	27	13	with	with	ADP
ejpam-1600	27	14	the	the	DET
ejpam-1600	27	15	natural	natural	ADJ
ejpam-1600	27	16	algebraic	algebraic	ADJ
ejpam-1600	27	17	operations	operation	NOUN
ejpam-1600	27	18	of	of	ADP
ejpam-1600	27	19	addition	addition	NOUN
ejpam-1600	27	20	and	and	CCONJ
ejpam-1600	27	21	non	non	ADJ
ejpam-1600	27	22	-	-	ADJ
ejpam-1600	27	23	negative	negative	ADJ
ejpam-1600	27	24	scalar	scalar	ADJ
ejpam-1600	27	25	multiplication	multiplication	NOUN
ejpam-1600	27	26	,	,	PUNCT
ejpam-1600	27	27	then	then	ADV
ejpam-1600	27	28	kc(r	kc(r	NOUN
ejpam-1600	27	29	n	n	CCONJ
ejpam-1600	27	30	)	)	PUNCT
ejpam-1600	27	31	becomes	become	VERB
ejpam-1600	27	32	a	a	DET
ejpam-1600	27	33	semilinear	semilinear	ADJ
ejpam-1600	27	34	metric	metric	ADJ
ejpam-1600	27	35	space	space	NOUN
ejpam-1600	27	36	which	which	PRON
ejpam-1600	27	37	can	can	AUX
ejpam-1600	27	38	be	be	AUX
ejpam-1600	27	39	embedded	embed	VERB
ejpam-1600	27	40	as	as	ADP
ejpam-1600	27	41	a	a	DET
ejpam-1600	27	42	complete	complete	ADJ
ejpam-1600	27	43	cone	cone	NOUN
ejpam-1600	27	44	into	into	ADP
ejpam-1600	27	45	a	a	DET
ejpam-1600	27	46	corresponding	corresponding	ADJ
ejpam-1600	27	47	banach	banach	NOUN
ejpam-1600	27	48	space	space	NOUN
ejpam-1600	27	49	.	.	PUNCT
ejpam-1600	28	1	the	the	DET
ejpam-1600	28	2	hausdorff	hausdorff	PROPN
ejpam-1600	28	3	metric	metric	NOUN
ejpam-1600	28	4	(	(	PUNCT
ejpam-1600	28	5	1	1	NUM
ejpam-1600	28	6	)	)	PUNCT
ejpam-1600	28	7	satisfies	satisfy	VERB
ejpam-1600	28	8	the	the	DET
ejpam-1600	28	9	following	follow	VERB
ejpam-1600	28	10	properties	property	NOUN
ejpam-1600	28	11	:	:	PUNCT
ejpam-1600	28	12	d[a+	d[a+	PROPN
ejpam-1600	28	13	c	c	NOUN
ejpam-1600	28	14	,	,	PUNCT
ejpam-1600	28	15	b+	b+	X
ejpam-1600	28	16	c	c	X
ejpam-1600	28	17	]	]	X
ejpam-1600	28	18	=	=	SYM
ejpam-1600	28	19	d[a	d[a	ADJ
ejpam-1600	28	20	,	,	PUNCT
ejpam-1600	28	21	b	b	NOUN
ejpam-1600	28	22	]	]	PUNCT
ejpam-1600	28	23	and	and	CCONJ
ejpam-1600	28	24	d[a	d[a	ADJ
ejpam-1600	28	25	,	,	PUNCT
ejpam-1600	28	26	b	b	X
ejpam-1600	28	27	]	]	X
ejpam-1600	28	28	=	=	SYM
ejpam-1600	28	29	d[b	d[b	PROPN
ejpam-1600	28	30	,	,	PUNCT
ejpam-1600	28	31	a	a	PRON
ejpam-1600	28	32	]	]	X
ejpam-1600	28	33	,	,	PUNCT
ejpam-1600	28	34	(	(	PUNCT
ejpam-1600	28	35	2	2	X
ejpam-1600	28	36	)	)	PUNCT
ejpam-1600	28	37	d[λa	d[λa	NOUN
ejpam-1600	28	38	,	,	PUNCT
ejpam-1600	28	39	λb	λb	ADP
ejpam-1600	28	40	]	]	X
ejpam-1600	29	1	=	=	SYM
ejpam-1600	29	2	λd[a	λd[a	PROPN
ejpam-1600	29	3	,	,	PUNCT
ejpam-1600	29	4	b	b	NOUN
ejpam-1600	29	5	]	]	X
ejpam-1600	29	6	,	,	PUNCT
ejpam-1600	29	7	(	(	PUNCT
ejpam-1600	29	8	3	3	X
ejpam-1600	29	9	)	)	PUNCT
ejpam-1600	29	10	d[a	d[a	ADJ
ejpam-1600	29	11	,	,	PUNCT
ejpam-1600	29	12	b	b	X
ejpam-1600	29	13	]	]	PUNCT
ejpam-1600	29	14	≤	≤	NUM
ejpam-1600	29	15	d[a	d[a	PROPN
ejpam-1600	29	16	,	,	PUNCT
ejpam-1600	29	17	c	c	X
ejpam-1600	29	18	]	]	X
ejpam-1600	30	1	+	+	CCONJ
ejpam-1600	30	2	d[c	d[c	ADJ
ejpam-1600	30	3	,	,	PUNCT
ejpam-1600	30	4	b	b	NOUN
ejpam-1600	30	5	]	]	X
ejpam-1600	30	6	,	,	PUNCT
ejpam-1600	30	7	(	(	PUNCT
ejpam-1600	30	8	4	4	X
ejpam-1600	30	9	)	)	PUNCT
ejpam-1600	30	10	for	for	ADP
ejpam-1600	30	11	all	all	DET
ejpam-1600	30	12	a	a	DET
ejpam-1600	30	13	,	,	PUNCT
ejpam-1600	30	14	b	b	NOUN
ejpam-1600	30	15	,	,	PUNCT
ejpam-1600	30	16	c	c	PROPN
ejpam-1600	30	17	∈	∈	PROPN
ejpam-1600	30	18	kc(r	kc(r	X
ejpam-1600	30	19	n	n	CCONJ
ejpam-1600	30	20	)	)	PUNCT
ejpam-1600	30	21	and	and	CCONJ
ejpam-1600	30	22	λ	λ	PROPN
ejpam-1600	30	23	∈	∈	PROPN
ejpam-1600	30	24	r+	r+	X
ejpam-1600	30	25	.	.	PUNCT
ejpam-1600	31	1	let	let	VERB
ejpam-1600	31	2	a	a	DET
ejpam-1600	31	3	,	,	PUNCT
ejpam-1600	31	4	b	b	PROPN
ejpam-1600	31	5	∈	∈	PROPN
ejpam-1600	31	6	kc(r	kc(r	NOUN
ejpam-1600	31	7	n	n	CCONJ
ejpam-1600	31	8	)	)	PUNCT
ejpam-1600	31	9	.	.	PUNCT
ejpam-1600	32	1	the	the	DET
ejpam-1600	32	2	set	set	NOUN
ejpam-1600	32	3	c	c	PROPN
ejpam-1600	32	4	∈	∈	PROPN
ejpam-1600	32	5	kc(r	kc(r	X
ejpam-1600	32	6	n	n	CCONJ
ejpam-1600	32	7	)	)	PUNCT
ejpam-1600	32	8	satisfying	satisfy	VERB
ejpam-1600	32	9	a	a	DET
ejpam-1600	32	10	=	=	SYM
ejpam-1600	32	11	b	b	PROPN
ejpam-1600	32	12	+	+	CCONJ
ejpam-1600	32	13	c	c	NOUN
ejpam-1600	32	14	is	be	AUX
ejpam-1600	32	15	known	know	VERB
ejpam-1600	32	16	as	as	ADP
ejpam-1600	32	17	the	the	DET
ejpam-1600	32	18	hukuhara	hukuhara	ADJ
ejpam-1600	32	19	difference	difference	NOUN
ejpam-1600	32	20	of	of	ADP
ejpam-1600	32	21	the	the	DET
ejpam-1600	32	22	sets	set	NOUN
ejpam-1600	32	23	a	a	PRON
ejpam-1600	32	24	and	and	CCONJ
ejpam-1600	32	25	b	b	NOUN
ejpam-1600	32	26	and	and	CCONJ
ejpam-1600	32	27	is	be	AUX
ejpam-1600	32	28	denoted	denote	VERB
ejpam-1600	32	29	by	by	ADP
ejpam-1600	32	30	the	the	DET
ejpam-1600	32	31	symbol	symbol	NOUN
ejpam-1600	32	32	a−	a−	PROPN
ejpam-1600	32	33	b.	b.	PROPN
ejpam-1600	33	1	we	we	PRON
ejpam-1600	33	2	say	say	VERB
ejpam-1600	33	3	that	that	SCONJ
ejpam-1600	33	4	the	the	DET
ejpam-1600	33	5	mapping	mapping	NOUN
ejpam-1600	33	6	f	f	X
ejpam-1600	33	7	:	:	PUNCT
ejpam-1600	33	8	i	i	PROPN
ejpam-1600	33	9	→	→	SYM
ejpam-1600	33	10	kc(r	kc(r	X
ejpam-1600	33	11	n	n	CCONJ
ejpam-1600	33	12	)	)	PUNCT
ejpam-1600	33	13	has	have	VERB
ejpam-1600	33	14	a	a	DET
ejpam-1600	33	15	hukuhara	hukuhara	ADJ
ejpam-1600	33	16	derivative	derivative	ADJ
ejpam-1600	33	17	dh	dh	NOUN
ejpam-1600	33	18	f(t0	f(t0	NOUN
ejpam-1600	33	19	)	)	PUNCT
ejpam-1600	33	20	at	at	ADP
ejpam-1600	33	21	a	a	DET
ejpam-1600	33	22	point	point	NOUN
ejpam-1600	33	23	t0	t0	X
ejpam-1600	33	24	∈	∈	PROPN
ejpam-1600	34	1	i	i	PRON
ejpam-1600	34	2	,	,	PUNCT
ejpam-1600	34	3	if	if	SCONJ
ejpam-1600	34	4	lim	lim	PROPN
ejpam-1600	34	5	h→0	h→0	NOUN
ejpam-1600	34	6	+	+	NUM
ejpam-1600	34	7	f(t0	f(t0	NOUN
ejpam-1600	34	8	+	+	CCONJ
ejpam-1600	34	9	h)−	h)−	PROPN
ejpam-1600	34	10	f(t0	f(t0	NOUN
ejpam-1600	34	11	)	)	PUNCT
ejpam-1600	34	12	h	h	NOUN
ejpam-1600	34	13	and	and	CCONJ
ejpam-1600	34	14	lim	lim	PROPN
ejpam-1600	34	15	h→0	h→0	PROPN
ejpam-1600	34	16	+	+	CCONJ
ejpam-1600	34	17	f(t0)−	f(t0)−	PROPN
ejpam-1600	34	18	f(t0	f(t0	NOUN
ejpam-1600	34	19	−	−	PROPN
ejpam-1600	34	20	h	h	NOUN
ejpam-1600	34	21	)	)	PUNCT
ejpam-1600	34	22	h	h	NOUN
ejpam-1600	34	23	exist	exist	VERB
ejpam-1600	34	24	in	in	ADP
ejpam-1600	34	25	the	the	DET
ejpam-1600	34	26	topology	topology	NOUN
ejpam-1600	34	27	of	of	ADP
ejpam-1600	34	28	kc(r	kc(r	NOUN
ejpam-1600	34	29	n	n	CCONJ
ejpam-1600	34	30	)	)	PUNCT
ejpam-1600	34	31	and	and	CCONJ
ejpam-1600	34	32	are	be	AUX
ejpam-1600	34	33	equal	equal	ADJ
ejpam-1600	34	34	to	to	ADP
ejpam-1600	34	35	dh	dh	PROPN
ejpam-1600	34	36	f(t0	f(t0	NOUN
ejpam-1600	34	37	)	)	PUNCT
ejpam-1600	34	38	.	.	PUNCT
ejpam-1600	35	1	here	here	ADV
ejpam-1600	35	2	i	i	PRON
ejpam-1600	35	3	is	be	AUX
ejpam-1600	35	4	any	any	DET
ejpam-1600	35	5	interval	interval	NOUN
ejpam-1600	35	6	in	in	ADP
ejpam-1600	35	7	r.	r.	PROPN
ejpam-1600	35	8	with	with	ADP
ejpam-1600	35	9	these	these	DET
ejpam-1600	35	10	preliminaries	preliminary	NOUN
ejpam-1600	35	11	,	,	PUNCT
ejpam-1600	35	12	we	we	PRON
ejpam-1600	35	13	consider	consider	VERB
ejpam-1600	35	14	the	the	DET
ejpam-1600	35	15	set	set	ADJ
ejpam-1600	35	16	differential	differential	ADJ
ejpam-1600	35	17	equation	equation	NOUN
ejpam-1600	35	18	dh	dh	PROPN
ejpam-1600	35	19	u	u	PROPN
ejpam-1600	35	20	=	=	PROPN
ejpam-1600	35	21	f(t	f(t	NOUN
ejpam-1600	35	22	,	,	PUNCT
ejpam-1600	35	23	u	u	NOUN
ejpam-1600	35	24	)	)	PUNCT
ejpam-1600	35	25	,	,	PUNCT
ejpam-1600	35	26	u(t0	u(t0	NOUN
ejpam-1600	35	27	)	)	PUNCT
ejpam-1600	35	28	=	=	PUNCT
ejpam-1600	35	29	u0	u0	PROPN
ejpam-1600	35	30	∈	∈	PROPN
ejpam-1600	35	31	kc(r	kc(r	NOUN
ejpam-1600	35	32	n	n	CCONJ
ejpam-1600	35	33	)	)	PUNCT
ejpam-1600	35	34	,	,	PUNCT
ejpam-1600	35	35	t0	t0	PROPN
ejpam-1600	35	36	≥	≥	NUM
ejpam-1600	35	37	0	0	NUM
ejpam-1600	35	38	,	,	PUNCT
ejpam-1600	35	39	(	(	PUNCT
ejpam-1600	35	40	5	5	NUM
ejpam-1600	35	41	)	)	PUNCT
ejpam-1600	35	42	where	where	SCONJ
ejpam-1600	35	43	f	f	PROPN
ejpam-1600	35	44	∈	∈	PROPN
ejpam-1600	35	45	c[r+	c[r+	NOUN
ejpam-1600	35	46	×	×	NOUN
ejpam-1600	35	47	kc(r	kc(r	X
ejpam-1600	35	48	n	n	CCONJ
ejpam-1600	35	49	)	)	PUNCT
ejpam-1600	35	50	,	,	PUNCT
ejpam-1600	35	51	kc(r	kc(r	NOUN
ejpam-1600	35	52	n	n	CCONJ
ejpam-1600	35	53	)	)	PUNCT
ejpam-1600	35	54	]	]	PUNCT
ejpam-1600	35	55	.	.	PUNCT
ejpam-1600	36	1	the	the	DET
ejpam-1600	36	2	mapping	mapping	NOUN
ejpam-1600	36	3	u	u	NOUN
ejpam-1600	36	4	∈	∈	PROPN
ejpam-1600	36	5	c1[j	c1[j	NOUN
ejpam-1600	36	6	,	,	PUNCT
ejpam-1600	36	7	kc(r	kc(r	NOUN
ejpam-1600	36	8	n	n	CCONJ
ejpam-1600	36	9	)	)	PUNCT
ejpam-1600	36	10	]	]	PUNCT
ejpam-1600	36	11	,	,	PUNCT
ejpam-1600	36	12	j	j	X
ejpam-1600	36	13	=	=	PUNCT
ejpam-1600	37	1	[	[	X
ejpam-1600	37	2	t0	t0	PROPN
ejpam-1600	37	3	,	,	PUNCT
ejpam-1600	37	4	t0	t0	PROPN
ejpam-1600	37	5	+	+	CCONJ
ejpam-1600	37	6	a	a	PRON
ejpam-1600	37	7	]	]	X
ejpam-1600	37	8	is	be	AUX
ejpam-1600	37	9	said	say	VERB
ejpam-1600	37	10	to	to	PART
ejpam-1600	37	11	be	be	AUX
ejpam-1600	37	12	a	a	DET
ejpam-1600	37	13	solution	solution	NOUN
ejpam-1600	37	14	of	of	ADP
ejpam-1600	37	15	(	(	PUNCT
ejpam-1600	37	16	5	5	NUM
ejpam-1600	37	17	)	)	PUNCT
ejpam-1600	37	18	on	on	ADP
ejpam-1600	37	19	j	j	PROPN
ejpam-1600	37	20	if	if	SCONJ
ejpam-1600	37	21	it	it	PRON
ejpam-1600	37	22	satisfies	satisfy	VERB
ejpam-1600	37	23	(	(	PUNCT
ejpam-1600	37	24	5	5	NUM
ejpam-1600	37	25	)	)	PUNCT
ejpam-1600	37	26	on	on	ADP
ejpam-1600	37	27	j	j	PROPN
ejpam-1600	37	28	.	.	PUNCT
ejpam-1600	38	1	since	since	SCONJ
ejpam-1600	38	2	u(t	u(t	NOUN
ejpam-1600	38	3	)	)	PUNCT
ejpam-1600	38	4	is	be	AUX
ejpam-1600	38	5	continuously	continuously	ADV
ejpam-1600	38	6	differentiable	differentiable	ADJ
ejpam-1600	38	7	,	,	PUNCT
ejpam-1600	38	8	we	we	PRON
ejpam-1600	38	9	have	have	VERB
ejpam-1600	38	10	u(t	u(t	NOUN
ejpam-1600	38	11	)	)	PUNCT
ejpam-1600	38	12	=	=	PUNCT
ejpam-1600	39	1	u0	u0	PROPN
ejpam-1600	40	1	+	+	X
ejpam-1600	40	2	∫	∫	PROPN
ejpam-1600	40	3	t	t	PROPN
ejpam-1600	40	4	t0	t0	PROPN
ejpam-1600	40	5	dh	dh	PROPN
ejpam-1600	40	6	u(s)ds	u(s)ds	PROPN
ejpam-1600	40	7	,	,	PUNCT
ejpam-1600	40	8	t	t	PROPN
ejpam-1600	40	9	∈	∈	PROPN
ejpam-1600	40	10	j	j	PROPN
ejpam-1600	40	11	.	.	PUNCT
ejpam-1600	41	1	(	(	PUNCT
ejpam-1600	41	2	6	6	NUM
ejpam-1600	41	3	)	)	PUNCT
ejpam-1600	41	4	j.	j.	PROPN
ejpam-1600	41	5	devi	devi	PROPN
ejpam-1600	41	6	,	,	PUNCT
ejpam-1600	41	7	ch	ch	PROPN
ejpam-1600	41	8	.	.	PUNCT
ejpam-1600	41	9	naidu	naidu	PROPN
ejpam-1600	41	10	/	/	SYM
ejpam-1600	41	11	eur	eur	PROPN
ejpam-1600	41	12	.	.	PUNCT
ejpam-1600	42	1	j.	j.	PROPN
ejpam-1600	42	2	pure	pure	PROPN
ejpam-1600	42	3	appl	appl	PROPN
ejpam-1600	42	4	.	.	PROPN
ejpam-1600	42	5	math	math	PROPN
ejpam-1600	42	6	,	,	PUNCT
ejpam-1600	42	7	5	5	NUM
ejpam-1600	42	8	(	(	PUNCT
ejpam-1600	42	9	2012	2012	NUM
ejpam-1600	42	10	)	)	PUNCT
ejpam-1600	42	11	,	,	PUNCT
ejpam-1600	42	12	187	187	NUM
ejpam-1600	42	13	-	-	SYM
ejpam-1600	42	14	196	196	NUM
ejpam-1600	42	15	189	189	NUM
ejpam-1600	42	16	hence	hence	ADV
ejpam-1600	42	17	,	,	PUNCT
ejpam-1600	42	18	we	we	PRON
ejpam-1600	42	19	can	can	AUX
ejpam-1600	42	20	associate	associate	VERB
ejpam-1600	42	21	with	with	ADP
ejpam-1600	42	22	the	the	DET
ejpam-1600	42	23	ivp	ivp	NOUN
ejpam-1600	42	24	(	(	PUNCT
ejpam-1600	42	25	5	5	NUM
ejpam-1600	42	26	)	)	PUNCT
ejpam-1600	42	27	the	the	DET
ejpam-1600	42	28	hukuhara	hukuhara	ADV
ejpam-1600	42	29	integral	integral	ADJ
ejpam-1600	42	30	u(t	u(t	NOUN
ejpam-1600	42	31	)	)	PUNCT
ejpam-1600	42	32	=	=	PUNCT
ejpam-1600	43	1	u0	u0	PROPN
ejpam-1600	44	1	+	+	X
ejpam-1600	44	2	∫	∫	PROPN
ejpam-1600	44	3	t	t	PROPN
ejpam-1600	44	4	t0	t0	PROPN
ejpam-1600	44	5	f(s	f(s	PROPN
ejpam-1600	44	6	,	,	PUNCT
ejpam-1600	44	7	u(s))ds	u(s))ds	PROPN
ejpam-1600	44	8	,	,	PUNCT
ejpam-1600	44	9	t	t	PROPN
ejpam-1600	44	10	∈	∈	PROPN
ejpam-1600	44	11	j	j	PROPN
ejpam-1600	44	12	.	.	PUNCT
ejpam-1600	45	1	(	(	PUNCT
ejpam-1600	45	2	7	7	X
ejpam-1600	45	3	)	)	PUNCT
ejpam-1600	45	4	where	where	SCONJ
ejpam-1600	45	5	the	the	DET
ejpam-1600	45	6	integral	integral	ADJ
ejpam-1600	45	7	is	be	AUX
ejpam-1600	45	8	the	the	DET
ejpam-1600	45	9	hukuhara	hukuhara	ADV
ejpam-1600	45	10	integral	integral	ADJ
ejpam-1600	45	11	which	which	PRON
ejpam-1600	45	12	is	be	AUX
ejpam-1600	45	13	defined	define	VERB
ejpam-1600	45	14	as	as	ADP
ejpam-1600	45	15	,	,	PUNCT
ejpam-1600	45	16	∫	∫	PROPN
ejpam-1600	45	17	f(s)ds	f(s)ds	PROPN
ejpam-1600	45	18	=	=	PRON
ejpam-1600	45	19	{	{	PUNCT
ejpam-1600	46	1	∫	∫	PROPN
ejpam-1600	46	2	f	f	X
ejpam-1600	46	3	(	(	PUNCT
ejpam-1600	46	4	s)ds	s)ds	PROPN
ejpam-1600	46	5	:	:	PUNCT
ejpam-1600	46	6	f	f	PROPN
ejpam-1600	46	7	is	be	AUX
ejpam-1600	46	8	any	any	DET
ejpam-1600	46	9	continuous	continuous	ADJ
ejpam-1600	46	10	selector	selector	NOUN
ejpam-1600	46	11	o	o	NOUN
ejpam-1600	46	12	f	f	X
ejpam-1600	46	13	f	f	AUX
ejpam-1600	46	14	}	}	PUNCT
ejpam-1600	46	15	observe	observe	VERB
ejpam-1600	46	16	also	also	ADV
ejpam-1600	46	17	that	that	SCONJ
ejpam-1600	46	18	u(t	u(t	NOUN
ejpam-1600	46	19	)	)	PUNCT
ejpam-1600	46	20	is	be	AUX
ejpam-1600	46	21	a	a	DET
ejpam-1600	46	22	solution	solution	NOUN
ejpam-1600	46	23	of	of	ADP
ejpam-1600	46	24	(	(	PUNCT
ejpam-1600	46	25	5	5	NUM
ejpam-1600	46	26	)	)	PUNCT
ejpam-1600	46	27	on	on	ADP
ejpam-1600	46	28	j	j	PROPN
ejpam-1600	46	29	iff	iff	PROPN
ejpam-1600	46	30	it	it	PRON
ejpam-1600	46	31	satisfies	satisfy	VERB
ejpam-1600	46	32	(	(	PUNCT
ejpam-1600	46	33	7	7	NUM
ejpam-1600	46	34	)	)	PUNCT
ejpam-1600	46	35	on	on	ADP
ejpam-1600	46	36	j	j	PROPN
ejpam-1600	46	37	.	.	PUNCT
ejpam-1600	47	1	we	we	PRON
ejpam-1600	47	2	now	now	ADV
ejpam-1600	47	3	proceed	proceed	VERB
ejpam-1600	47	4	to	to	PART
ejpam-1600	47	5	define	define	VERB
ejpam-1600	47	6	a	a	DET
ejpam-1600	47	7	partial	partial	ADJ
ejpam-1600	47	8	order	order	NOUN
ejpam-1600	47	9	in	in	ADP
ejpam-1600	47	10	the	the	DET
ejpam-1600	47	11	metric	metric	ADJ
ejpam-1600	47	12	space	space	NOUN
ejpam-1600	47	13	(	(	PUNCT
ejpam-1600	47	14	kc(r	kc(r	X
ejpam-1600	47	15	n	n	CCONJ
ejpam-1600	47	16	)	)	PUNCT
ejpam-1600	47	17	,	,	PUNCT
ejpam-1600	47	18	d	d	NOUN
ejpam-1600	47	19	)	)	PUNCT
ejpam-1600	47	20	.	.	PUNCT
ejpam-1600	48	1	we	we	PRON
ejpam-1600	48	2	begin	begin	VERB
ejpam-1600	48	3	with	with	ADP
ejpam-1600	48	4	the	the	DET
ejpam-1600	48	5	definition	definition	NOUN
ejpam-1600	48	6	of	of	ADP
ejpam-1600	48	7	a	a	DET
ejpam-1600	48	8	cone	cone	NOUN
ejpam-1600	48	9	in	in	ADP
ejpam-1600	48	10	this	this	DET
ejpam-1600	48	11	set	set	VERB
ejpam-1600	48	12	up	up	ADP
ejpam-1600	48	13	.	.	PUNCT
ejpam-1600	49	1	let	let	VERB
ejpam-1600	49	2	k(ko	k(ko	NOUN
ejpam-1600	49	3	)	)	PUNCT
ejpam-1600	49	4	be	be	AUX
ejpam-1600	49	5	the	the	DET
ejpam-1600	49	6	subfamily	subfamily	NOUN
ejpam-1600	49	7	of	of	ADP
ejpam-1600	49	8	kc(r	kc(r	NOUN
ejpam-1600	49	9	n	n	CCONJ
ejpam-1600	49	10	)	)	PUNCT
ejpam-1600	50	1	consisting	consist	VERB
ejpam-1600	50	2	of	of	ADP
ejpam-1600	50	3	set	set	NOUN
ejpam-1600	50	4	u	u	PROPN
ejpam-1600	50	5	∈	∈	PROPN
ejpam-1600	50	6	kc(r	kc(r	X
ejpam-1600	50	7	n	n	CCONJ
ejpam-1600	50	8	)	)	PUNCT
ejpam-1600	50	9	such	such	ADJ
ejpam-1600	50	10	that	that	SCONJ
ejpam-1600	50	11	any	any	DET
ejpam-1600	50	12	u	u	PROPN
ejpam-1600	50	13	∈	∈	PROPN
ejpam-1600	50	14	u	u	NOUN
ejpam-1600	50	15	is	be	AUX
ejpam-1600	50	16	a	a	DET
ejpam-1600	50	17	non	non	ADJ
ejpam-1600	50	18	-	-	ADJ
ejpam-1600	50	19	negative(positive	negative(positive	ADJ
ejpam-1600	50	20	)	)	PUNCT
ejpam-1600	50	21	vector	vector	NOUN
ejpam-1600	50	22	of	of	ADP
ejpam-1600	50	23	n	n	DET
ejpam-1600	50	24	components	component	NOUN
ejpam-1600	50	25	satisfying	satisfy	VERB
ejpam-1600	50	26	ui	ui	PROPN
ejpam-1600	50	27	≥	≥	NOUN
ejpam-1600	50	28	0	0	NUM
ejpam-1600	51	1	(	(	PUNCT
ejpam-1600	51	2	ui	ui	NOUN
ejpam-1600	51	3	>	>	X
ejpam-1600	51	4	0	0	NUM
ejpam-1600	51	5	)	)	PUNCT
ejpam-1600	52	1	for	for	ADP
ejpam-1600	52	2	i	i	PRON
ejpam-1600	52	3	=	=	NOUN
ejpam-1600	52	4	1	1	NUM
ejpam-1600	52	5	.	.	PUNCT
ejpam-1600	52	6	.	.	PUNCT
ejpam-1600	52	7	.	.	PUNCT
ejpam-1600	53	1	n.	n.	NOUN
ejpam-1600	53	2	then	then	ADV
ejpam-1600	53	3	k	k	PROPN
ejpam-1600	53	4	is	be	AUX
ejpam-1600	53	5	a	a	DET
ejpam-1600	53	6	cone	cone	NOUN
ejpam-1600	53	7	in	in	ADP
ejpam-1600	53	8	kc(r	kc(r	NOUN
ejpam-1600	53	9	n	n	CCONJ
ejpam-1600	53	10	)	)	PUNCT
ejpam-1600	53	11	and	and	CCONJ
ejpam-1600	53	12	k0	k0	PROPN
ejpam-1600	53	13	is	be	AUX
ejpam-1600	53	14	the	the	DET
ejpam-1600	53	15	nonempty	nonempty	ADJ
ejpam-1600	53	16	interior	interior	NOUN
ejpam-1600	53	17	of	of	ADP
ejpam-1600	53	18	k	k	PROPN
ejpam-1600	53	19	.	.	PUNCT
ejpam-1600	54	1	definition	definition	NOUN
ejpam-1600	54	2	1	1	NUM
ejpam-1600	54	3	.	.	PUNCT
ejpam-1600	55	1	for	for	ADP
ejpam-1600	55	2	any	any	DET
ejpam-1600	55	3	u	u	NOUN
ejpam-1600	55	4	and	and	CCONJ
ejpam-1600	55	5	v	v	NOUN
ejpam-1600	55	6	∈	∈	PROPN
ejpam-1600	55	7	kc(r	kc(r	NOUN
ejpam-1600	55	8	n	n	CCONJ
ejpam-1600	55	9	)	)	PUNCT
ejpam-1600	55	10	,	,	PUNCT
ejpam-1600	55	11	if	if	SCONJ
ejpam-1600	55	12	there	there	PRON
ejpam-1600	55	13	exists	exist	VERB
ejpam-1600	55	14	z	z	PROPN
ejpam-1600	55	15	∈	∈	PROPN
ejpam-1600	55	16	kc(r	kc(r	X
ejpam-1600	55	17	n	n	CCONJ
ejpam-1600	55	18	)	)	PUNCT
ejpam-1600	55	19	such	such	ADJ
ejpam-1600	55	20	that	that	SCONJ
ejpam-1600	55	21	z	z	PROPN
ejpam-1600	55	22	∈	∈	PROPN
ejpam-1600	55	23	k(k0	k(k0	NOUN
ejpam-1600	55	24	)	)	PUNCT
ejpam-1600	55	25	and	and	CCONJ
ejpam-1600	55	26	u	u	X
ejpam-1600	55	27	=	=	NOUN
ejpam-1600	55	28	v	v	PROPN
ejpam-1600	55	29	+	+	NOUN
ejpam-1600	55	30	z	z	NOUN
ejpam-1600	55	31	then	then	ADV
ejpam-1600	55	32	we	we	PRON
ejpam-1600	55	33	say	say	VERB
ejpam-1600	55	34	that	that	SCONJ
ejpam-1600	55	35	u	u	PROPN
ejpam-1600	55	36	≥	≥	NUM
ejpam-1600	55	37	v	v	NOUN
ejpam-1600	55	38	(	(	PUNCT
ejpam-1600	55	39	u	u	NOUN
ejpam-1600	55	40	>	>	X
ejpam-1600	55	41	v	v	NOUN
ejpam-1600	55	42	)	)	PUNCT
ejpam-1600	55	43	.	.	PUNCT
ejpam-1600	56	1	similarly	similarly	ADV
ejpam-1600	56	2	we	we	PRON
ejpam-1600	56	3	can	can	AUX
ejpam-1600	56	4	define	define	VERB
ejpam-1600	56	5	u	u	NOUN
ejpam-1600	56	6	≤	≤	X
ejpam-1600	56	7	v	v	NOUN
ejpam-1600	56	8	(	(	PUNCT
ejpam-1600	56	9	u	u	NOUN
ejpam-1600	56	10	<	<	X
ejpam-1600	56	11	v	v	NOUN
ejpam-1600	56	12	)	)	PUNCT
ejpam-1600	56	13	.	.	PUNCT
ejpam-1600	57	1	to	to	PART
ejpam-1600	57	2	define	define	VERB
ejpam-1600	57	3	the	the	DET
ejpam-1600	57	4	causal	causal	ADJ
ejpam-1600	57	5	operator	operator	NOUN
ejpam-1600	57	6	we	we	PRON
ejpam-1600	57	7	introduce	introduce	VERB
ejpam-1600	57	8	the	the	DET
ejpam-1600	57	9	following	following	ADJ
ejpam-1600	57	10	notation	notation	NOUN
ejpam-1600	57	11	.	.	PUNCT
ejpam-1600	58	1	let	let	VERB
ejpam-1600	58	2	e	e	NOUN
ejpam-1600	58	3	=	=	SYM
ejpam-1600	58	4	c[[t0	c[[t0	PROPN
ejpam-1600	58	5	,	,	PUNCT
ejpam-1600	58	6	t	t	PROPN
ejpam-1600	58	7	]	]	PUNCT
ejpam-1600	58	8	,	,	PUNCT
ejpam-1600	58	9	kc(r	kc(r	NOUN
ejpam-1600	58	10	n	n	CCONJ
ejpam-1600	58	11	)	)	PUNCT
ejpam-1600	58	12	]	]	PUNCT
ejpam-1600	58	13	and	and	CCONJ
ejpam-1600	59	1	e0	e0	PROPN
ejpam-1600	59	2	=	=	SYM
ejpam-1600	59	3	c[[t0	c[[t0	PROPN
ejpam-1600	59	4	−	−	PROPN
ejpam-1600	59	5	h1	h1	PROPN
ejpam-1600	59	6	,	,	PUNCT
ejpam-1600	59	7	t	t	PROPN
ejpam-1600	59	8	]	]	PUNCT
ejpam-1600	59	9	,	,	PUNCT
ejpam-1600	59	10	kc(r	kc(r	NOUN
ejpam-1600	59	11	n	n	CCONJ
ejpam-1600	59	12	)	)	PUNCT
ejpam-1600	59	13	]	]	PUNCT
ejpam-1600	59	14	,	,	PUNCT
ejpam-1600	59	15	where	where	SCONJ
ejpam-1600	59	16	u	u	PROPN
ejpam-1600	59	17	∈	∈	PROPN
ejpam-1600	59	18	e0	e0	PROPN
ejpam-1600	59	19	implies	imply	VERB
ejpam-1600	59	20	u(t	u(t	NOUN
ejpam-1600	59	21	)	)	PUNCT
ejpam-1600	59	22	=	=	PUNCT
ejpam-1600	59	23	φ0(t	φ0(t	PROPN
ejpam-1600	59	24	)	)	PUNCT
ejpam-1600	59	25	,	,	PUNCT
ejpam-1600	59	26	t0	t0	PROPN
ejpam-1600	59	27	−	−	PROPN
ejpam-1600	59	28	h1	h1	VERB
ejpam-1600	59	29	≤	≤	PROPN
ejpam-1600	59	30	t	t	NOUN
ejpam-1600	59	31	≤	≤	NUM
ejpam-1600	59	32	t0	t0	PROPN
ejpam-1600	59	33	and	and	CCONJ
ejpam-1600	59	34	u(t	u(t	NOUN
ejpam-1600	59	35	)	)	PUNCT
ejpam-1600	59	36	is	be	AUX
ejpam-1600	59	37	any	any	DET
ejpam-1600	59	38	arbitrarily	arbitrarily	ADV
ejpam-1600	59	39	continuous	continuous	ADJ
ejpam-1600	59	40	function	function	NOUN
ejpam-1600	59	41	on	on	ADP
ejpam-1600	59	42	[	[	X
ejpam-1600	59	43	t0	t0	PROPN
ejpam-1600	59	44	,	,	PUNCT
ejpam-1600	59	45	t	t	PROPN
ejpam-1600	59	46	]	]	PUNCT
ejpam-1600	59	47	.	.	PUNCT
ejpam-1600	60	1	we	we	PRON
ejpam-1600	60	2	define	define	VERB
ejpam-1600	60	3	a	a	DET
ejpam-1600	60	4	norm	norm	NOUN
ejpam-1600	60	5	on	on	ADP
ejpam-1600	60	6	e	e	PROPN
ejpam-1600	60	7	as	as	SCONJ
ejpam-1600	60	8	follows	follow	VERB
ejpam-1600	60	9	:	:	PUNCT
ejpam-1600	60	10	for	for	ADP
ejpam-1600	60	11	u	u	PROPN
ejpam-1600	60	12	,	,	PUNCT
ejpam-1600	60	13	v	v	NOUN
ejpam-1600	60	14	∈	∈	PROPN
ejpam-1600	60	15	e	e	NOUN
ejpam-1600	60	16	d0[u	d0[u	NOUN
ejpam-1600	60	17	,	,	PUNCT
ejpam-1600	60	18	v	v	X
ejpam-1600	60	19	]	]	X
ejpam-1600	60	20	=	=	SYM
ejpam-1600	60	21	supt0≤t≤t	supt0≤t≤t	NUM
ejpam-1600	60	22	d[u(t	d[u(t	NOUN
ejpam-1600	60	23	)	)	PUNCT
ejpam-1600	60	24	,	,	PUNCT
ejpam-1600	60	25	v	v	X
ejpam-1600	60	26	(	(	PUNCT
ejpam-1600	60	27	t	t	PROPN
ejpam-1600	60	28	)	)	PUNCT
ejpam-1600	60	29	]	]	PUNCT
ejpam-1600	60	30	where	where	SCONJ
ejpam-1600	60	31	d	d	PROPN
ejpam-1600	60	32	denotes	denote	VERB
ejpam-1600	60	33	the	the	DET
ejpam-1600	60	34	hausdorff	hausdorff	PROPN
ejpam-1600	60	35	metric	metric	PROPN
ejpam-1600	60	36	.	.	PUNCT
ejpam-1600	61	1	definition	definition	NOUN
ejpam-1600	61	2	2	2	NUM
ejpam-1600	61	3	.	.	PUNCT
ejpam-1600	61	4	by	by	ADP
ejpam-1600	61	5	a	a	DET
ejpam-1600	61	6	causal	causal	ADJ
ejpam-1600	61	7	operator	operator	NOUN
ejpam-1600	61	8	or	or	CCONJ
ejpam-1600	61	9	a	a	DET
ejpam-1600	61	10	volterra	volterra	NOUN
ejpam-1600	61	11	operator	operator	NOUN
ejpam-1600	61	12	or	or	CCONJ
ejpam-1600	61	13	a	a	DET
ejpam-1600	61	14	nonanticipative	nonanticipative	ADJ
ejpam-1600	61	15	operator	operator	NOUN
ejpam-1600	61	16	we	we	PRON
ejpam-1600	61	17	mean	mean	VERB
ejpam-1600	61	18	a	a	DET
ejpam-1600	61	19	mappling	mappling	NOUN
ejpam-1600	61	20	q	q	NOUN
ejpam-1600	61	21	:	:	PUNCT
ejpam-1600	61	22	e	e	X
ejpam-1600	61	23	→	→	SYM
ejpam-1600	61	24	e	e	X
ejpam-1600	61	25	satisfying	satisfy	VERB
ejpam-1600	61	26	the	the	DET
ejpam-1600	61	27	property	property	NOUN
ejpam-1600	62	1	that	that	PRON
ejpam-1600	62	2	if	if	SCONJ
ejpam-1600	62	3	u(s	u(s	ADJ
ejpam-1600	62	4	)	)	PUNCT
ejpam-1600	62	5	=	=	SYM
ejpam-1600	62	6	v	v	X
ejpam-1600	62	7	(	(	PUNCT
ejpam-1600	62	8	s	s	NOUN
ejpam-1600	62	9	)	)	PUNCT
ejpam-1600	62	10	,	,	PUNCT
ejpam-1600	62	11	t0	t0	PROPN
ejpam-1600	62	12	≤	≤	PROPN
ejpam-1600	62	13	s	s	PART
ejpam-1600	62	14	≤	≤	NOUN
ejpam-1600	62	15	t	t	PROPN
ejpam-1600	62	16	<	<	X
ejpam-1600	62	17	t	t	PROPN
ejpam-1600	62	18	then	then	ADV
ejpam-1600	62	19	(	(	PUNCT
ejpam-1600	62	20	qu)(s	qu)(s	PROPN
ejpam-1600	62	21	)	)	PUNCT
ejpam-1600	62	22	=	=	PUNCT
ejpam-1600	63	1	(	(	PUNCT
ejpam-1600	63	2	qv	qv	INTJ
ejpam-1600	63	3	)	)	PUNCT
ejpam-1600	63	4	(	(	PUNCT
ejpam-1600	63	5	s	s	NOUN
ejpam-1600	63	6	)	)	PUNCT
ejpam-1600	63	7	,	,	PUNCT
ejpam-1600	63	8	t0	t0	PROPN
ejpam-1600	63	9	≤	≤	PROPN
ejpam-1600	63	10	s	s	PART
ejpam-1600	63	11	≤	≤	NOUN
ejpam-1600	63	12	t	t	NOUN
ejpam-1600	63	13	<	<	X
ejpam-1600	63	14	t.	t.	NOUN
ejpam-1600	63	15	by	by	ADP
ejpam-1600	63	16	a	a	DET
ejpam-1600	63	17	causal	causal	ADJ
ejpam-1600	63	18	operator	operator	NOUN
ejpam-1600	63	19	with	with	ADP
ejpam-1600	63	20	memory	memory	NOUN
ejpam-1600	63	21	we	we	PRON
ejpam-1600	63	22	mean	mean	VERB
ejpam-1600	63	23	a	a	DET
ejpam-1600	63	24	mapping	mapping	NOUN
ejpam-1600	63	25	q	q	NOUN
ejpam-1600	63	26	:	:	PUNCT
ejpam-1600	63	27	e0→	e0→	X
ejpam-1600	63	28	e	e	X
ejpam-1600	63	29	such	such	ADJ
ejpam-1600	63	30	that	that	PRON
ejpam-1600	63	31	for	for	ADP
ejpam-1600	63	32	u(s	u(s	PROPN
ejpam-1600	63	33	)	)	PUNCT
ejpam-1600	63	34	=	=	SYM
ejpam-1600	63	35	v	v	X
ejpam-1600	63	36	(	(	PUNCT
ejpam-1600	63	37	s	s	NOUN
ejpam-1600	63	38	)	)	PUNCT
ejpam-1600	63	39	,	,	PUNCT
ejpam-1600	63	40	t0	t0	PROPN
ejpam-1600	63	41	≤	≤	PROPN
ejpam-1600	63	42	s	s	PART
ejpam-1600	63	43	≤	≤	PROPN
ejpam-1600	63	44	t	t	PROPN
ejpam-1600	63	45	<	<	X
ejpam-1600	63	46	t	t	PROPN
ejpam-1600	63	47	,	,	PUNCT
ejpam-1600	63	48	then	then	ADV
ejpam-1600	63	49	q(u	q(u	NOUN
ejpam-1600	63	50	,	,	PUNCT
ejpam-1600	63	51	φ0)(s	φ0)(s	PROPN
ejpam-1600	63	52	)	)	PUNCT
ejpam-1600	63	53	=	=	SYM
ejpam-1600	64	1	q(v	q(v	NOUN
ejpam-1600	64	2	,	,	PUNCT
ejpam-1600	64	3	φ0)(s	φ0)(s	PROPN
ejpam-1600	64	4	)	)	PUNCT
ejpam-1600	64	5	,	,	PUNCT
ejpam-1600	64	6	t0	t0	PROPN
ejpam-1600	64	7	≤	≤	PROPN
ejpam-1600	64	8	s	s	PART
ejpam-1600	64	9	≤	≤	NOUN
ejpam-1600	64	10	t	t	PROPN
ejpam-1600	64	11	<	<	X
ejpam-1600	64	12	t	t	PROPN
ejpam-1600	64	13	and	and	CCONJ
ejpam-1600	64	14	φ0	φ0	PROPN
ejpam-1600	64	15	∈	∈	PROPN
ejpam-1600	64	16	c1	c1	NOUN
ejpam-1600	65	1	=	=	PROPN
ejpam-1600	65	2	c[[t0	c[[t0	PROPN
ejpam-1600	65	3	−	−	PROPN
ejpam-1600	65	4	h1	h1	PROPN
ejpam-1600	65	5	,	,	PUNCT
ejpam-1600	65	6	t0	t0	PROPN
ejpam-1600	65	7	]	]	PUNCT
ejpam-1600	65	8	,	,	PUNCT
ejpam-1600	65	9	kc(r	kc(r	NOUN
ejpam-1600	65	10	n	n	CCONJ
ejpam-1600	65	11	)	)	PUNCT
ejpam-1600	65	12	]	]	PUNCT
ejpam-1600	66	1	3	3	X
ejpam-1600	66	2	.	.	X
ejpam-1600	66	3	comparison	comparison	NOUN
ejpam-1600	66	4	theorems	theorem	NOUN
ejpam-1600	66	5	in	in	ADP
ejpam-1600	66	6	this	this	DET
ejpam-1600	66	7	section	section	NOUN
ejpam-1600	66	8	we	we	PRON
ejpam-1600	66	9	give	give	VERB
ejpam-1600	66	10	the	the	DET
ejpam-1600	66	11	necessary	necessary	ADJ
ejpam-1600	66	12	notations	notation	NOUN
ejpam-1600	66	13	and	and	CCONJ
ejpam-1600	66	14	the	the	DET
ejpam-1600	66	15	comparison	comparison	NOUN
ejpam-1600	66	16	theorems	theorem	NOUN
ejpam-1600	66	17	required	require	VERB
ejpam-1600	66	18	to	to	PART
ejpam-1600	66	19	prove	prove	VERB
ejpam-1600	66	20	the	the	DET
ejpam-1600	66	21	stability	stability	NOUN
ejpam-1600	66	22	theorems	theorem	VERB
ejpam-1600	66	23	.	.	PUNCT
ejpam-1600	67	1	consider	consider	VERB
ejpam-1600	67	2	the	the	DET
ejpam-1600	67	3	ivp	ivp	NOUN
ejpam-1600	67	4	for	for	ADP
ejpam-1600	67	5	set	set	ADJ
ejpam-1600	67	6	differential	differential	ADJ
ejpam-1600	67	7	equation	equation	NOUN
ejpam-1600	67	8	involving	involve	VERB
ejpam-1600	67	9	causal	causal	ADJ
ejpam-1600	67	10	operators	operator	NOUN
ejpam-1600	67	11	with	with	ADP
ejpam-1600	67	12	memory	memory	NOUN
ejpam-1600	67	13	given	give	VERB
ejpam-1600	67	14	by	by	ADP
ejpam-1600	67	15	dh	dh	NOUN
ejpam-1600	67	16	u(t	u(t	PROPN
ejpam-1600	67	17	)	)	PUNCT
ejpam-1600	68	1	=	=	PRON
ejpam-1600	68	2	(	(	PUNCT
ejpam-1600	68	3	qu)(t	qu)(t	PROPN
ejpam-1600	68	4	)	)	PUNCT
ejpam-1600	68	5	,	,	PUNCT
ejpam-1600	68	6	ut0	ut0	VERB
ejpam-1600	68	7	=	=	NOUN
ejpam-1600	69	1	φ0	φ0	PROPN
ejpam-1600	69	2	∈	∈	PROPN
ejpam-1600	69	3	c1	c1	NOUN
ejpam-1600	69	4	(	(	PUNCT
ejpam-1600	69	5	8)	8)	PROPN
ejpam-1600	69	6	j.	j.	PROPN
ejpam-1600	69	7	devi	devi	PROPN
ejpam-1600	69	8	,	,	PUNCT
ejpam-1600	69	9	ch	ch	PROPN
ejpam-1600	69	10	.	.	PUNCT
ejpam-1600	69	11	naidu	naidu	PROPN
ejpam-1600	69	12	/	/	SYM
ejpam-1600	69	13	eur	eur	PROPN
ejpam-1600	69	14	.	.	PUNCT
ejpam-1600	70	1	j.	j.	PROPN
ejpam-1600	70	2	pure	pure	PROPN
ejpam-1600	70	3	appl	appl	PROPN
ejpam-1600	70	4	.	.	PROPN
ejpam-1600	70	5	math	math	PROPN
ejpam-1600	70	6	,	,	PUNCT
ejpam-1600	70	7	5	5	NUM
ejpam-1600	70	8	(	(	PUNCT
ejpam-1600	70	9	2012	2012	NUM
ejpam-1600	70	10	)	)	PUNCT
ejpam-1600	70	11	,	,	PUNCT
ejpam-1600	70	12	187	187	NUM
ejpam-1600	70	13	-	-	SYM
ejpam-1600	70	14	196	196	NUM
ejpam-1600	70	15	190	190	NUM
ejpam-1600	70	16	where	where	SCONJ
ejpam-1600	70	17	c1	c1	PROPN
ejpam-1600	70	18	=	=	PROPN
ejpam-1600	71	1	c[[t0	c[[t0	PROPN
ejpam-1600	71	2	−	−	PROPN
ejpam-1600	71	3	h1	h1	PROPN
ejpam-1600	71	4	,	,	PUNCT
ejpam-1600	71	5	t0	t0	PROPN
ejpam-1600	71	6	]	]	PUNCT
ejpam-1600	71	7	,	,	PUNCT
ejpam-1600	71	8	kc(r	kc(r	NOUN
ejpam-1600	71	9	n	n	CCONJ
ejpam-1600	71	10	)	)	PUNCT
ejpam-1600	71	11	]	]	PUNCT
ejpam-1600	71	12	with	with	ADP
ejpam-1600	71	13	metric	metric	ADJ
ejpam-1600	71	14	d1[φ0,ψ0	d1[φ0,ψ0	NOUN
ejpam-1600	71	15	]	]	X
ejpam-1600	71	16	=	=	PUNCT
ejpam-1600	71	17	sup	sup	NOUN
ejpam-1600	71	18	t0−h1≤s≤t0	t0−h1≤s≤t0	PROPN
ejpam-1600	71	19	d[φ0(s),ψ0(s	d[φ0(s),ψ0(s	PROPN
ejpam-1600	71	20	)	)	PUNCT
ejpam-1600	71	21	]	]	PUNCT
ejpam-1600	71	22	,	,	PUNCT
ejpam-1600	71	23	φ0,ψ0	φ0,ψ0	PROPN
ejpam-1600	71	24	∈	∈	PROPN
ejpam-1600	71	25	c1	c1	NOUN
ejpam-1600	71	26	let	let	VERB
ejpam-1600	71	27	ẽ	ẽ	PROPN
ejpam-1600	71	28	=	=	SYM
ejpam-1600	71	29	c[[t0	c[[t0	PROPN
ejpam-1600	71	30	−	−	PROPN
ejpam-1600	71	31	h1,∞	h1,∞	NUM
ejpam-1600	71	32	)	)	PUNCT
ejpam-1600	71	33	,	,	PUNCT
ejpam-1600	71	34	kc(r	kc(r	NOUN
ejpam-1600	71	35	n	n	CCONJ
ejpam-1600	71	36	)	)	PUNCT
ejpam-1600	71	37	]	]	PUNCT
ejpam-1600	71	38	with	with	ADP
ejpam-1600	71	39	norm	norm	NOUN
ejpam-1600	71	40	d̃[u	d̃[u	PROPN
ejpam-1600	71	41	,	,	PUNCT
ejpam-1600	71	42	θ	θ	PROPN
ejpam-1600	71	43	]	]	X
ejpam-1600	71	44	=	=	PUNCT
ejpam-1600	71	45	sup	sup	NOUN
ejpam-1600	71	46	t0−h1≤t<∞	t0−h1≤t<∞	NOUN
ejpam-1600	71	47	d[u(t),θ	d[u(t),θ	NOUN
ejpam-1600	71	48	]	]	X
ejpam-1600	71	49	h(t	h(t	PROPN
ejpam-1600	71	50	)	)	PUNCT
ejpam-1600	71	51	where	where	SCONJ
ejpam-1600	71	52	θ	θ	PROPN
ejpam-1600	71	53	is	be	AUX
ejpam-1600	71	54	the	the	DET
ejpam-1600	71	55	zero	zero	NUM
ejpam-1600	71	56	element	element	NOUN
ejpam-1600	71	57	in	in	ADP
ejpam-1600	71	58	rn	rn	PROPN
ejpam-1600	71	59	,	,	PUNCT
ejpam-1600	71	60	which	which	PRON
ejpam-1600	71	61	is	be	AUX
ejpam-1600	71	62	regarded	regard	VERB
ejpam-1600	71	63	as	as	ADP
ejpam-1600	71	64	a	a	DET
ejpam-1600	71	65	point	point	NOUN
ejpam-1600	71	66	set	set	VERB
ejpam-1600	71	67	and	and	CCONJ
ejpam-1600	71	68	h	h	NOUN
ejpam-1600	71	69	:	:	PUNCT
ejpam-1600	72	1	[	[	X
ejpam-1600	72	2	t0,∞)→	t0,∞)→	ADJ
ejpam-1600	72	3	r+	r+	NOUN
ejpam-1600	72	4	is	be	AUX
ejpam-1600	72	5	a	a	DET
ejpam-1600	72	6	continuous	continuous	ADJ
ejpam-1600	72	7	map	map	NOUN
ejpam-1600	72	8	and	and	CCONJ
ejpam-1600	72	9	(	(	PUNCT
ejpam-1600	72	10	ẽ	ẽ	PROPN
ejpam-1600	72	11	,	,	PUNCT
ejpam-1600	72	12	d̃	d̃	PROPN
ejpam-1600	72	13	)	)	PUNCT
ejpam-1600	72	14	is	be	AUX
ejpam-1600	72	15	a	a	DET
ejpam-1600	72	16	banach	banach	NOUN
ejpam-1600	72	17	space	space	NOUN
ejpam-1600	72	18	.	.	PUNCT
ejpam-1600	73	1	in	in	ADP
ejpam-1600	73	2	this	this	DET
ejpam-1600	73	3	paper	paper	NOUN
ejpam-1600	73	4	we	we	PRON
ejpam-1600	73	5	consider	consider	VERB
ejpam-1600	73	6	the	the	DET
ejpam-1600	73	7	causal	causal	ADJ
ejpam-1600	73	8	operator	operator	NOUN
ejpam-1600	73	9	with	with	ADP
ejpam-1600	73	10	memory	memory	NOUN
ejpam-1600	73	11	as	as	ADP
ejpam-1600	73	12	q	q	PROPN
ejpam-1600	73	13	∈	∈	PROPN
ejpam-1600	73	14	c[ẽ	c[ẽ	NOUN
ejpam-1600	73	15	,	,	PUNCT
ejpam-1600	73	16	ẽ	ẽ	PROPN
ejpam-1600	73	17	]	]	PUNCT
ejpam-1600	73	18	such	such	ADJ
ejpam-1600	73	19	that	that	PRON
ejpam-1600	73	20	q	q	NOUN
ejpam-1600	73	21	:	:	PUNCT
ejpam-1600	73	22	ẽ	ẽ	PROPN
ejpam-1600	73	23	→	→	SYM
ejpam-1600	73	24	ẽ	ẽ	PROPN
ejpam-1600	73	25	and	and	CCONJ
ejpam-1600	73	26	u(s	u(s	NUM
ejpam-1600	73	27	)	)	PUNCT
ejpam-1600	73	28	=	=	SYM
ejpam-1600	73	29	v	v	X
ejpam-1600	73	30	(	(	PUNCT
ejpam-1600	73	31	s	s	NOUN
ejpam-1600	73	32	)	)	PUNCT
ejpam-1600	73	33	for	for	ADP
ejpam-1600	73	34	t0	t0	PROPN
ejpam-1600	73	35	−	−	PROPN
ejpam-1600	73	36	h1	h1	VERB
ejpam-1600	73	37	≤	≤	PROPN
ejpam-1600	73	38	s	s	PART
ejpam-1600	73	39	≤	≤	NUM
ejpam-1600	73	40	t	t	PROPN
ejpam-1600	73	41	implies	imply	VERB
ejpam-1600	73	42	(	(	PUNCT
ejpam-1600	73	43	qu)(s	qu)(s	PROPN
ejpam-1600	73	44	)	)	PUNCT
ejpam-1600	73	45	=	=	PUNCT
ejpam-1600	74	1	(	(	PUNCT
ejpam-1600	74	2	qv	qv	INTJ
ejpam-1600	74	3	)	)	PUNCT
ejpam-1600	74	4	(	(	PUNCT
ejpam-1600	74	5	s	s	NOUN
ejpam-1600	74	6	)	)	PUNCT
ejpam-1600	74	7	for	for	ADP
ejpam-1600	74	8	t0	t0	PROPN
ejpam-1600	74	9	−	−	PROPN
ejpam-1600	74	10	h1	h1	VERB
ejpam-1600	74	11	≤	≤	PROPN
ejpam-1600	74	12	s	s	PART
ejpam-1600	74	13	≤	≤	ADJ
ejpam-1600	74	14	t.	t.	NOUN
ejpam-1600	74	15	in	in	ADP
ejpam-1600	74	16	order	order	NOUN
ejpam-1600	74	17	to	to	PART
ejpam-1600	74	18	develop	develop	VERB
ejpam-1600	74	19	the	the	DET
ejpam-1600	74	20	comparison	comparison	NOUN
ejpam-1600	74	21	theorems	theorem	NOUN
ejpam-1600	74	22	using	use	VERB
ejpam-1600	74	23	lyapunov	lyapunov	NOUN
ejpam-1600	74	24	-	-	PUNCT
ejpam-1600	74	25	like	like	ADJ
ejpam-1600	74	26	functions	function	NOUN
ejpam-1600	74	27	it	it	PRON
ejpam-1600	74	28	is	be	AUX
ejpam-1600	74	29	useful	useful	ADJ
ejpam-1600	74	30	to	to	PART
ejpam-1600	74	31	select	select	VERB
ejpam-1600	74	32	some	some	DET
ejpam-1600	74	33	class	class	NOUN
ejpam-1600	74	34	of	of	ADP
ejpam-1600	74	35	functions	function	NOUN
ejpam-1600	74	36	in	in	ADP
ejpam-1600	74	37	kc(r	kc(r	NOUN
ejpam-1600	74	38	n	n	CCONJ
ejpam-1600	74	39	)	)	PUNCT
ejpam-1600	74	40	or	or	CCONJ
ejpam-1600	74	41	elements	element	NOUN
ejpam-1600	74	42	in	in	ADP
ejpam-1600	74	43	ẽ	ẽ	PROPN
ejpam-1600	74	44	such	such	ADJ
ejpam-1600	74	45	that	that	SCONJ
ejpam-1600	74	46	the	the	DET
ejpam-1600	74	47	generalized	generalized	ADJ
ejpam-1600	74	48	derivative	derivative	NOUN
ejpam-1600	74	49	of	of	ADP
ejpam-1600	74	50	the	the	DET
ejpam-1600	74	51	lyapunov	lyapunov	ADJ
ejpam-1600	74	52	function	function	NOUN
ejpam-1600	74	53	satisfies	satisfy	VERB
ejpam-1600	74	54	certain	certain	ADJ
ejpam-1600	74	55	conditions	condition	NOUN
ejpam-1600	74	56	on	on	ADP
ejpam-1600	74	57	these	these	DET
ejpam-1600	74	58	classes	class	NOUN
ejpam-1600	74	59	.	.	PUNCT
ejpam-1600	75	1	we	we	PRON
ejpam-1600	75	2	begin	begin	VERB
ejpam-1600	75	3	by	by	ADP
ejpam-1600	75	4	defining	define	VERB
ejpam-1600	75	5	the	the	DET
ejpam-1600	75	6	following	follow	VERB
ejpam-1600	75	7	sets	set	NOUN
ejpam-1600	75	8	.	.	PUNCT
ejpam-1600	76	1	e0	e0	PROPN
ejpam-1600	76	2	=	=	PUNCT
ejpam-1600	76	3	{	{	PUNCT
ejpam-1600	76	4	u	u	NOUN
ejpam-1600	76	5	∈	∈	PROPN
ejpam-1600	76	6	ẽ	ẽ	PROPN
ejpam-1600	76	7	:	:	PUNCT
ejpam-1600	77	1	l(s	l(s	PROPN
ejpam-1600	77	2	,	,	PUNCT
ejpam-1600	77	3	u(s	u(s	PROPN
ejpam-1600	77	4	)	)	PUNCT
ejpam-1600	77	5	)	)	PUNCT
ejpam-1600	78	1	≤	≤	NUM
ejpam-1600	78	2	f	f	X
ejpam-1600	78	3	(	(	PUNCT
ejpam-1600	78	4	l(t	l(t	PROPN
ejpam-1600	78	5	,	,	PUNCT
ejpam-1600	78	6	u(t	u(t	NOUN
ejpam-1600	78	7	)	)	PUNCT
ejpam-1600	78	8	)	)	PUNCT
ejpam-1600	78	9	;	;	PUNCT
ejpam-1600	78	10	t1	t1	PROPN
ejpam-1600	78	11	≤	≤	NUM
ejpam-1600	78	12	s	s	PART
ejpam-1600	78	13	≤	≤	PROPN
ejpam-1600	78	14	t	t	PROPN
ejpam-1600	78	15	,	,	PUNCT
ejpam-1600	78	16	t1	t1	PROPN
ejpam-1600	78	17	≥	≥	NUM
ejpam-1600	78	18	t0	t0	PROPN
ejpam-1600	78	19	}	}	PUNCT
ejpam-1600	78	20	;	;	PUNCT
ejpam-1600	78	21	e1	e1	PROPN
ejpam-1600	78	22	=	=	SYM
ejpam-1600	78	23	{	{	PUNCT
ejpam-1600	78	24	u	u	NOUN
ejpam-1600	78	25	∈	∈	PROPN
ejpam-1600	78	26	ẽ	ẽ	PROPN
ejpam-1600	78	27	:	:	PUNCT
ejpam-1600	78	28	l(s	l(s	PROPN
ejpam-1600	78	29	,	,	PUNCT
ejpam-1600	78	30	u(s	u(s	PROPN
ejpam-1600	78	31	)	)	PUNCT
ejpam-1600	78	32	)	)	PUNCT
ejpam-1600	78	33	≤	≤	NUM
ejpam-1600	78	34	l(t	l(t	NOUN
ejpam-1600	78	35	,	,	PUNCT
ejpam-1600	78	36	u(t	u(t	NOUN
ejpam-1600	78	37	)	)	PUNCT
ejpam-1600	78	38	)	)	PUNCT
ejpam-1600	78	39	;	;	PUNCT
ejpam-1600	78	40	t0	t0	PROPN
ejpam-1600	78	41	≤	≤	PROPN
ejpam-1600	78	42	s	s	PART
ejpam-1600	78	43	≤	≤	NUM
ejpam-1600	78	44	t	t	PROPN
ejpam-1600	78	45	}	}	PUNCT
ejpam-1600	78	46	;	;	PUNCT
ejpam-1600	78	47	eα	eα	X
ejpam-1600	78	48	=	=	PUNCT
ejpam-1600	78	49	{	{	PUNCT
ejpam-1600	78	50	u	u	NOUN
ejpam-1600	78	51	∈	∈	PROPN
ejpam-1600	78	52	ẽ	ẽ	PROPN
ejpam-1600	78	53	:	:	PUNCT
ejpam-1600	78	54	l(s	l(s	PROPN
ejpam-1600	78	55	,	,	PUNCT
ejpam-1600	78	56	u(s))α(s	u(s))α(s	NOUN
ejpam-1600	78	57	)	)	PUNCT
ejpam-1600	78	58	≤	≤	NUM
ejpam-1600	78	59	l(t	l(t	NOUN
ejpam-1600	78	60	,	,	PUNCT
ejpam-1600	78	61	u(t))α(t	u(t))α(t	NOUN
ejpam-1600	78	62	)	)	PUNCT
ejpam-1600	78	63	;	;	PUNCT
ejpam-1600	78	64	t0	t0	PROPN
ejpam-1600	78	65	≤	≤	PROPN
ejpam-1600	78	66	s	s	PART
ejpam-1600	78	67	≤	≤	NUM
ejpam-1600	78	68	t	t	PROPN
ejpam-1600	78	69	}	}	PUNCT
ejpam-1600	78	70	;	;	PUNCT
ejpam-1600	78	71	where	where	SCONJ
ejpam-1600	78	72	(	(	PUNCT
ejpam-1600	78	73	i	i	NOUN
ejpam-1600	78	74	)	)	PUNCT
ejpam-1600	78	75	α(t	α(t	PROPN
ejpam-1600	78	76	)	)	PUNCT
ejpam-1600	78	77	≥	≥	X
ejpam-1600	78	78	0	0	NUM
ejpam-1600	78	79	is	be	AUX
ejpam-1600	78	80	a	a	DET
ejpam-1600	78	81	continuous	continuous	ADJ
ejpam-1600	78	82	function	function	NOUN
ejpam-1600	78	83	on	on	ADP
ejpam-1600	78	84	r+	r+	X
ejpam-1600	78	85	,	,	PUNCT
ejpam-1600	78	86	(	(	PUNCT
ejpam-1600	78	87	ii	ii	NOUN
ejpam-1600	78	88	)	)	PUNCT
ejpam-1600	78	89	f	f	NOUN
ejpam-1600	78	90	(	(	PUNCT
ejpam-1600	78	91	r	r	NOUN
ejpam-1600	78	92	)	)	PUNCT
ejpam-1600	78	93	is	be	AUX
ejpam-1600	78	94	continuous	continuous	ADJ
ejpam-1600	78	95	on	on	ADP
ejpam-1600	78	96	r+	r+	NOUN
ejpam-1600	78	97	,	,	PUNCT
ejpam-1600	78	98	non	non	X
ejpam-1600	78	99	decreasing	decrease	VERB
ejpam-1600	78	100	in	in	ADP
ejpam-1600	78	101	r	r	NOUN
ejpam-1600	78	102	and	and	CCONJ
ejpam-1600	78	103	f	f	PROPN
ejpam-1600	78	104	(	(	PUNCT
ejpam-1600	78	105	r)≥	r)≥	NOUN
ejpam-1600	78	106	r	r	NOUN
ejpam-1600	78	107	for	for	ADP
ejpam-1600	78	108	r	r	NOUN
ejpam-1600	78	109	≥	≥	NOUN
ejpam-1600	78	110	0	0	NUM
ejpam-1600	78	111	.	.	PUNCT
ejpam-1600	79	1	now	now	ADV
ejpam-1600	79	2	we	we	PRON
ejpam-1600	79	3	proceed	proceed	VERB
ejpam-1600	79	4	to	to	PART
ejpam-1600	79	5	state	state	VERB
ejpam-1600	79	6	the	the	DET
ejpam-1600	79	7	comparison	comparison	NOUN
ejpam-1600	79	8	theorems	theorem	NOUN
ejpam-1600	79	9	using	use	VERB
ejpam-1600	79	10	the	the	DET
ejpam-1600	79	11	lyapunov	lyapunov	ADJ
ejpam-1600	79	12	-	-	PUNCT
ejpam-1600	79	13	like	like	ADJ
ejpam-1600	79	14	functions	function	NOUN
ejpam-1600	79	15	.	.	PUNCT
ejpam-1600	80	1	as	as	SCONJ
ejpam-1600	80	2	the	the	DET
ejpam-1600	80	3	proofs	proof	NOUN
ejpam-1600	80	4	are	be	AUX
ejpam-1600	80	5	similar	similar	ADJ
ejpam-1600	80	6	to	to	ADP
ejpam-1600	80	7	that	that	PRON
ejpam-1600	80	8	in	in	ADP
ejpam-1600	80	9	[	[	X
ejpam-1600	80	10	1	1	X
ejpam-1600	80	11	]	]	PUNCT
ejpam-1600	80	12	we	we	PRON
ejpam-1600	80	13	omit	omit	VERB
ejpam-1600	80	14	them	they	PRON
ejpam-1600	80	15	.	.	PUNCT
ejpam-1600	81	1	theorem	theorem	NOUN
ejpam-1600	81	2	1	1	NUM
ejpam-1600	81	3	.	.	PUNCT
ejpam-1600	82	1	let	let	VERB
ejpam-1600	82	2	l	l	PROPN
ejpam-1600	82	3	∈	∈	PROPN
ejpam-1600	82	4	c[r+	c[r+	NOUN
ejpam-1600	82	5	×	×	PROPN
ejpam-1600	82	6	b	b	PROPN
ejpam-1600	82	7	,	,	PUNCT
ejpam-1600	82	8	r+	r+	X
ejpam-1600	82	9	]	]	PUNCT
ejpam-1600	82	10	,	,	PUNCT
ejpam-1600	82	11	b	b	X
ejpam-1600	82	12	=	=	PRON
ejpam-1600	82	13	{	{	PUNCT
ejpam-1600	82	14	u	u	NOUN
ejpam-1600	82	15	∈	∈	PROPN
ejpam-1600	82	16	kc(r	kc(r	X
ejpam-1600	82	17	n	n	CCONJ
ejpam-1600	82	18	)	)	PUNCT
ejpam-1600	82	19	:	:	PUNCT
ejpam-1600	83	1	d[u	d[u	PROPN
ejpam-1600	83	2	,	,	PUNCT
ejpam-1600	83	3	θ	θ	PROPN
ejpam-1600	83	4	]	]	X
ejpam-1600	83	5	≤	≤	NUM
ejpam-1600	83	6	ρ	ρ	NOUN
ejpam-1600	83	7	}	}	PUNCT
ejpam-1600	83	8	=	=	PUNCT
ejpam-1600	84	1	b(θ	b(θ	ADV
ejpam-1600	84	2	,	,	PUNCT
ejpam-1600	84	3	ρ	ρ	PROPN
ejpam-1600	84	4	)	)	PUNCT
ejpam-1600	84	5	and	and	CCONJ
ejpam-1600	84	6	let	let	VERB
ejpam-1600	84	7	l(t	l(t	PROPN
ejpam-1600	84	8	,	,	PUNCT
ejpam-1600	84	9	u	u	NOUN
ejpam-1600	84	10	)	)	PUNCT
ejpam-1600	84	11	be	be	VERB
ejpam-1600	84	12	locally	locally	ADV
ejpam-1600	84	13	lipschitzian	lipschitzian	ADJ
ejpam-1600	84	14	in	in	ADP
ejpam-1600	84	15	u	u	PROPN
ejpam-1600	84	16	(	(	PUNCT
ejpam-1600	84	17	i.e	i.e	PROPN
ejpam-1600	84	18	)	)	PUNCT
ejpam-1600	84	19	for	for	ADP
ejpam-1600	84	20	u	u	PROPN
ejpam-1600	84	21	,	,	PUNCT
ejpam-1600	84	22	v	v	PROPN
ejpam-1600	84	23	∈	∈	PROPN
ejpam-1600	84	24	b	b	PROPN
ejpam-1600	84	25	,	,	PUNCT
ejpam-1600	84	26	t	t	PROPN
ejpam-1600	84	27	∈	∈	PROPN
ejpam-1600	84	28	r+	r+	NOUN
ejpam-1600	84	29	and	and	CCONJ
ejpam-1600	84	30	k	k	X
ejpam-1600	84	31	>	>	X
ejpam-1600	84	32	0	0	PROPN
ejpam-1600	84	33	,	,	PUNCT
ejpam-1600	84	34	|l(t	|l(t	PROPN
ejpam-1600	84	35	,	,	PUNCT
ejpam-1600	84	36	u)−	u)−	PROPN
ejpam-1600	84	37	l(t	l(t	PROPN
ejpam-1600	84	38	,	,	PUNCT
ejpam-1600	84	39	v	v	NOUN
ejpam-1600	84	40	)	)	PUNCT
ejpam-1600	84	41	|	|	ADV
ejpam-1600	84	42	≤	≤	NUM
ejpam-1600	84	43	kd̃[u	kd̃[u	NOUN
ejpam-1600	84	44	,	,	PUNCT
ejpam-1600	84	45	v	v	NOUN
ejpam-1600	84	46	]	]	PUNCT
ejpam-1600	84	47	(	(	PUNCT
ejpam-1600	84	48	9	9	NUM
ejpam-1600	84	49	)	)	PUNCT
ejpam-1600	84	50	(	(	PUNCT
ejpam-1600	84	51	i	i	NOUN
ejpam-1600	84	52	)	)	PUNCT
ejpam-1600	84	53	assume	assume	VERB
ejpam-1600	84	54	that	that	SCONJ
ejpam-1600	84	55	for	for	ADP
ejpam-1600	84	56	t	t	PROPN
ejpam-1600	84	57	≥	≥	NOUN
ejpam-1600	84	58	t0	t0	PROPN
ejpam-1600	84	59	and	and	CCONJ
ejpam-1600	84	60	u	u	PROPN
ejpam-1600	84	61	∈	∈	PROPN
ejpam-1600	84	62	e1	e1	NOUN
ejpam-1600	84	63	d−l(t	d−l(t	NOUN
ejpam-1600	84	64	,	,	PUNCT
ejpam-1600	84	65	u(t	u(t	NOUN
ejpam-1600	84	66	)	)	PUNCT
ejpam-1600	84	67	)	)	PUNCT
ejpam-1600	85	1	≤	≤	NUM
ejpam-1600	85	2	g(t	g(t	PROPN
ejpam-1600	85	3	,	,	PUNCT
ejpam-1600	85	4	l(t	l(t	PROPN
ejpam-1600	85	5	,	,	PUNCT
ejpam-1600	85	6	u(t	u(t	NOUN
ejpam-1600	85	7	)	)	PUNCT
ejpam-1600	85	8	)	)	PUNCT
ejpam-1600	85	9	)	)	PUNCT
ejpam-1600	85	10	(	(	PUNCT
ejpam-1600	85	11	10	10	NUM
ejpam-1600	85	12	)	)	PUNCT
ejpam-1600	86	1	where	where	SCONJ
ejpam-1600	86	2	d−l(t	d−l(t	NOUN
ejpam-1600	86	3	,	,	PUNCT
ejpam-1600	86	4	u(t	u(t	NOUN
ejpam-1600	86	5	)	)	PUNCT
ejpam-1600	86	6	)	)	PUNCT
ejpam-1600	86	7	=	=	SYM
ejpam-1600	86	8	lim	lim	PROPN
ejpam-1600	86	9	inf	inf	PROPN
ejpam-1600	86	10	h→0−	h→0−	PROPN
ejpam-1600	86	11	1	1	NUM
ejpam-1600	86	12	h	h	NOUN
ejpam-1600	87	1	[	[	X
ejpam-1600	87	2	l(t	l(t	X
ejpam-1600	87	3	+	+	CCONJ
ejpam-1600	87	4	h	h	NOUN
ejpam-1600	87	5	,	,	PUNCT
ejpam-1600	87	6	u(t	u(t	NOUN
ejpam-1600	87	7	)	)	PUNCT
ejpam-1600	88	1	+	+	CCONJ
ejpam-1600	88	2	h(qu)(t))−	h(qu)(t))−	ADJ
ejpam-1600	88	3	l(t	l(t	NOUN
ejpam-1600	88	4	,	,	PUNCT
ejpam-1600	88	5	u(t	u(t	NOUN
ejpam-1600	88	6	)	)	PUNCT
ejpam-1600	88	7	]	]	PUNCT
ejpam-1600	88	8	and	and	CCONJ
ejpam-1600	88	9	g	g	PROPN
ejpam-1600	88	10	∈	∈	PROPN
ejpam-1600	88	11	c[r+	c[r+	NOUN
ejpam-1600	88	12	×r+,r+	×r+,r+	X
ejpam-1600	88	13	]	]	X
ejpam-1600	88	14	j.	j.	PROPN
ejpam-1600	88	15	devi	devi	PROPN
ejpam-1600	88	16	,	,	PUNCT
ejpam-1600	88	17	ch	ch	PROPN
ejpam-1600	88	18	.	.	PUNCT
ejpam-1600	88	19	naidu	naidu	PROPN
ejpam-1600	88	20	/	/	SYM
ejpam-1600	88	21	eur	eur	PROPN
ejpam-1600	88	22	.	.	PUNCT
ejpam-1600	89	1	j.	j.	PROPN
ejpam-1600	89	2	pure	pure	PROPN
ejpam-1600	89	3	appl	appl	PROPN
ejpam-1600	89	4	.	.	PROPN
ejpam-1600	89	5	math	math	PROPN
ejpam-1600	89	6	,	,	PUNCT
ejpam-1600	89	7	5	5	NUM
ejpam-1600	89	8	(	(	PUNCT
ejpam-1600	89	9	2012	2012	NUM
ejpam-1600	89	10	)	)	PUNCT
ejpam-1600	89	11	,	,	PUNCT
ejpam-1600	89	12	187	187	NUM
ejpam-1600	89	13	-	-	SYM
ejpam-1600	89	14	196	196	NUM
ejpam-1600	89	15	191	191	NUM
ejpam-1600	89	16	(	(	PUNCT
ejpam-1600	89	17	ii	ii	NOUN
ejpam-1600	89	18	)	)	PUNCT
ejpam-1600	89	19	let	let	VERB
ejpam-1600	89	20	r(t	r(t	NOUN
ejpam-1600	89	21	)	)	PUNCT
ejpam-1600	89	22	=	=	SYM
ejpam-1600	89	23	r(t	r(t	NOUN
ejpam-1600	89	24	,	,	PUNCT
ejpam-1600	89	25	t0,w0	t0,w0	PROPN
ejpam-1600	89	26	)	)	PUNCT
ejpam-1600	89	27	be	be	VERB
ejpam-1600	89	28	the	the	DET
ejpam-1600	89	29	maximal	maximal	ADJ
ejpam-1600	89	30	solution	solution	NOUN
ejpam-1600	89	31	of	of	ADP
ejpam-1600	89	32	scalar	scalar	ADJ
ejpam-1600	89	33	ordinary	ordinary	ADJ
ejpam-1600	89	34	differential	differential	ADJ
ejpam-1600	89	35	equation	equation	NOUN
ejpam-1600	89	36	w′	w′	NOUN
ejpam-1600	89	37	=	=	SYM
ejpam-1600	89	38	g(t	g(t	PROPN
ejpam-1600	89	39	,	,	PUNCT
ejpam-1600	89	40	w	w	NOUN
ejpam-1600	89	41	)	)	PUNCT
ejpam-1600	89	42	,	,	PUNCT
ejpam-1600	89	43	w(t0	w(t0	NOUN
ejpam-1600	89	44	)	)	PUNCT
ejpam-1600	90	1	=	=	PUNCT
ejpam-1600	90	2	w0	w0	PROPN
ejpam-1600	90	3	≥	≥	NOUN
ejpam-1600	90	4	0	0	NUM
ejpam-1600	90	5	(	(	PUNCT
ejpam-1600	90	6	11	11	NUM
ejpam-1600	90	7	)	)	PUNCT
ejpam-1600	90	8	existing	exist	VERB
ejpam-1600	90	9	on	on	ADP
ejpam-1600	90	10	t0	t0	PROPN
ejpam-1600	90	11	≤	≤	PROPN
ejpam-1600	90	12	t	t	PROPN
ejpam-1600	90	13	<	<	AUX
ejpam-1600	90	14	∞.	∞.	PROPN
ejpam-1600	90	15	let	let	VERB
ejpam-1600	90	16	u(t	u(t	NOUN
ejpam-1600	90	17	,	,	PUNCT
ejpam-1600	90	18	t0,φ0(t0	t0,φ0(t0	NOUN
ejpam-1600	90	19	)	)	PUNCT
ejpam-1600	90	20	)	)	PUNCT
ejpam-1600	90	21	be	be	AUX
ejpam-1600	90	22	any	any	DET
ejpam-1600	90	23	solution	solution	NOUN
ejpam-1600	90	24	of	of	ADP
ejpam-1600	90	25	the	the	DET
ejpam-1600	90	26	system	system	NOUN
ejpam-1600	90	27	(	(	PUNCT
ejpam-1600	90	28	8)	8)	NUM
ejpam-1600	90	29	such	such	ADJ
ejpam-1600	90	30	that	that	SCONJ
ejpam-1600	90	31	u(t	u(t	NOUN
ejpam-1600	90	32	,	,	PUNCT
ejpam-1600	90	33	t0,φ0(t0	t0,φ0(t0	NOUN
ejpam-1600	90	34	)	)	PUNCT
ejpam-1600	90	35	)	)	PUNCT
ejpam-1600	91	1	∈	∈	PROPN
ejpam-1600	91	2	b	b	PROPN
ejpam-1600	91	3	for	for	ADP
ejpam-1600	91	4	t	t	PROPN
ejpam-1600	91	5	∈	∈	PROPN
ejpam-1600	91	6	[	[	X
ejpam-1600	91	7	t0	t0	NOUN
ejpam-1600	91	8	,	,	PUNCT
ejpam-1600	91	9	t1	t1	NOUN
ejpam-1600	91	10	]	]	PUNCT
ejpam-1600	91	11	and	and	CCONJ
ejpam-1600	91	12	let	let	VERB
ejpam-1600	91	13	l(t0,φ0(t0))≤	l(t0,φ0(t0))≤	PROPN
ejpam-1600	91	14	w0	w0	VERB
ejpam-1600	91	15	then	then	ADV
ejpam-1600	91	16	l(t	l(t	NOUN
ejpam-1600	91	17	,	,	PUNCT
ejpam-1600	91	18	u(t	u(t	NOUN
ejpam-1600	91	19	,	,	PUNCT
ejpam-1600	91	20	t0	t0	PROPN
ejpam-1600	91	21	,	,	PUNCT
ejpam-1600	91	22	φ0(t0))≤	φ0(t0))≤	CCONJ
ejpam-1600	91	23	r(t	r(t	NOUN
ejpam-1600	91	24	)	)	PUNCT
ejpam-1600	91	25	,	,	PUNCT
ejpam-1600	91	26	∀t	∀t	PROPN
ejpam-1600	91	27	∈	∈	PROPN
ejpam-1600	91	28	[	[	X
ejpam-1600	91	29	t0	t0	NOUN
ejpam-1600	91	30	,	,	PUNCT
ejpam-1600	91	31	t1	t1	PROPN
ejpam-1600	91	32	]	]	X
ejpam-1600	91	33	,	,	PUNCT
ejpam-1600	91	34	t	t	PROPN
ejpam-1600	91	35	≥	≥	PROPN
ejpam-1600	91	36	t0	t0	PROPN
ejpam-1600	91	37	.	.	PUNCT
ejpam-1600	92	1	theorem	theorem	NOUN
ejpam-1600	92	2	2	2	NUM
ejpam-1600	93	1	.	.	X
ejpam-1600	93	2	assume	assume	VERB
ejpam-1600	93	3	that	that	SCONJ
ejpam-1600	93	4	the	the	DET
ejpam-1600	93	5	hypothesis	hypothesis	NOUN
ejpam-1600	93	6	of	of	ADP
ejpam-1600	93	7	theorem	theorem	ADJ
ejpam-1600	93	8	1	1	NUM
ejpam-1600	93	9	holds	hold	NOUN
ejpam-1600	93	10	,	,	PUNCT
ejpam-1600	93	11	except	except	SCONJ
ejpam-1600	93	12	for	for	ADP
ejpam-1600	93	13	inequality	inequality	NOUN
ejpam-1600	93	14	(	(	PUNCT
ejpam-1600	93	15	10	10	NUM
ejpam-1600	93	16	)	)	PUNCT
ejpam-1600	93	17	which	which	PRON
ejpam-1600	93	18	is	be	AUX
ejpam-1600	93	19	replaced	replace	VERB
ejpam-1600	93	20	by	by	ADP
ejpam-1600	93	21	α(t)d−l(t	α(t)d−l(t	NOUN
ejpam-1600	93	22	,	,	PUNCT
ejpam-1600	93	23	u(t	u(t	NOUN
ejpam-1600	93	24	)	)	PUNCT
ejpam-1600	93	25	)	)	PUNCT
ejpam-1600	94	1	+	+	CCONJ
ejpam-1600	94	2	l(t	l(t	NOUN
ejpam-1600	94	3	,	,	PUNCT
ejpam-1600	94	4	u(t))d−α(t	u(t))d−α(t	PROPN
ejpam-1600	94	5	)	)	PUNCT
ejpam-1600	94	6	≤	≤	NUM
ejpam-1600	94	7	w(t	w(t	PROPN
ejpam-1600	94	8	,	,	PUNCT
ejpam-1600	94	9	l(t	l(t	PROPN
ejpam-1600	94	10	,	,	PUNCT
ejpam-1600	94	11	u(t))α(t	u(t))α(t	NOUN
ejpam-1600	94	12	)	)	PUNCT
ejpam-1600	94	13	)	)	PUNCT
ejpam-1600	94	14	,	,	PUNCT
ejpam-1600	94	15	(	(	PUNCT
ejpam-1600	94	16	12	12	NUM
ejpam-1600	94	17	)	)	PUNCT
ejpam-1600	94	18	for	for	ADP
ejpam-1600	94	19	t	t	PROPN
ejpam-1600	94	20	>	>	X
ejpam-1600	94	21	t0	t0	PROPN
ejpam-1600	94	22	,	,	PUNCT
ejpam-1600	94	23	u	u	PROPN
ejpam-1600	94	24	∈	∈	PROPN
ejpam-1600	94	25	eα	eα	NOUN
ejpam-1600	94	26	,	,	PUNCT
ejpam-1600	94	27	where	where	SCONJ
ejpam-1600	94	28	α(t	α(t	VERB
ejpam-1600	94	29	)	)	PUNCT
ejpam-1600	94	30	>	>	X
ejpam-1600	94	31	0	0	PUNCT
ejpam-1600	94	32	is	be	AUX
ejpam-1600	94	33	continuous	continuous	ADJ
ejpam-1600	94	34	on	on	ADP
ejpam-1600	94	35	r+	r+	NOUN
ejpam-1600	94	36	and	and	CCONJ
ejpam-1600	94	37	d−α(t	d−α(t	VERB
ejpam-1600	94	38	)	)	PUNCT
ejpam-1600	94	39	=	=	PROPN
ejpam-1600	94	40	lim	lim	PROPN
ejpam-1600	94	41	inf	inf	PROPN
ejpam-1600	94	42	h→o−	h→o−	X
ejpam-1600	94	43	α(t	α(t	PROPN
ejpam-1600	94	44	+	+	CCONJ
ejpam-1600	94	45	h)−α(t	h)−α(t	X
ejpam-1600	94	46	)	)	PUNCT
ejpam-1600	94	47	h	h	NOUN
ejpam-1600	94	48	then	then	ADV
ejpam-1600	94	49	α(t0)l(t0,φ0)≤	α(t0)l(t0,φ0)≤	NUM
ejpam-1600	94	50	w0	w0	PROPN
ejpam-1600	94	51	implies	imply	VERB
ejpam-1600	94	52	α(t)l(t	α(t)l(t	NOUN
ejpam-1600	94	53	,	,	PUNCT
ejpam-1600	94	54	u(t	u(t	NOUN
ejpam-1600	94	55	)	)	PUNCT
ejpam-1600	94	56	)	)	PUNCT
ejpam-1600	94	57	≤	≤	NUM
ejpam-1600	94	58	r(t	r(t	NOUN
ejpam-1600	94	59	)	)	PUNCT
ejpam-1600	94	60	,	,	PUNCT
ejpam-1600	94	61	t	t	PROPN
ejpam-1600	94	62	≥	≥	PROPN
ejpam-1600	94	63	t0	t0	PROPN
ejpam-1600	94	64	.	.	PUNCT
ejpam-1600	95	1	theorem	theorem	NOUN
ejpam-1600	95	2	3	3	NUM
ejpam-1600	96	1	.	.	PUNCT
ejpam-1600	96	2	assume	assume	VERB
ejpam-1600	96	3	that	that	SCONJ
ejpam-1600	96	4	(	(	PUNCT
ejpam-1600	96	5	i	i	NOUN
ejpam-1600	96	6	)	)	PUNCT
ejpam-1600	96	7	l	l	PROPN
ejpam-1600	96	8	∈	∈	PROPN
ejpam-1600	96	9	c[r+	c[r+	NOUN
ejpam-1600	96	10	×	×	PROPN
ejpam-1600	96	11	b	b	PROPN
ejpam-1600	96	12	,	,	PUNCT
ejpam-1600	96	13	r+	r+	X
ejpam-1600	96	14	]	]	PUNCT
ejpam-1600	96	15	and	and	CCONJ
ejpam-1600	96	16	l(t	l(t	PROPN
ejpam-1600	96	17	,	,	PUNCT
ejpam-1600	96	18	u	u	NOUN
ejpam-1600	96	19	)	)	PUNCT
ejpam-1600	96	20	be	be	VERB
ejpam-1600	96	21	locally	locally	ADV
ejpam-1600	96	22	lipschitzian	lipschitzian	ADJ
ejpam-1600	96	23	in	in	ADP
ejpam-1600	96	24	u.	u.	PROPN
ejpam-1600	96	25	(	(	PUNCT
ejpam-1600	96	26	ii	ii	PROPN
ejpam-1600	96	27	)	)	PUNCT
ejpam-1600	96	28	g0	g0	PROPN
ejpam-1600	96	29	,	,	PUNCT
ejpam-1600	96	30	g	g	PROPN
ejpam-1600	96	31	∈	∈	PROPN
ejpam-1600	96	32	c[r2	c[r2	NOUN
ejpam-1600	97	1	+	+	ADJ
ejpam-1600	97	2	,	,	PUNCT
ejpam-1600	97	3	r	r	X
ejpam-1600	97	4	]	]	PUNCT
ejpam-1600	97	5	such	such	ADJ
ejpam-1600	97	6	that	that	SCONJ
ejpam-1600	97	7	g0(t	g0(t	PROPN
ejpam-1600	97	8	,	,	PUNCT
ejpam-1600	97	9	w	w	NOUN
ejpam-1600	97	10	)	)	PUNCT
ejpam-1600	97	11	≤	≤	NUM
ejpam-1600	97	12	g(t	g(t	PROPN
ejpam-1600	97	13	,	,	PUNCT
ejpam-1600	97	14	w	w	NOUN
ejpam-1600	97	15	)	)	PUNCT
ejpam-1600	97	16	,	,	PUNCT
ejpam-1600	97	17	(	(	PUNCT
ejpam-1600	97	18	t	t	PROPN
ejpam-1600	97	19	,	,	PUNCT
ejpam-1600	97	20	w	w	NOUN
ejpam-1600	97	21	)	)	PUNCT
ejpam-1600	97	22	∈	∈	PROPN
ejpam-1600	97	23	r+	r+	PUNCT
ejpam-1600	97	24	2	2	NUM
ejpam-1600	97	25	,	,	PUNCT
ejpam-1600	97	26	and	and	CCONJ
ejpam-1600	97	27	η(t	η(t	NOUN
ejpam-1600	97	28	,	,	PUNCT
ejpam-1600	97	29	t0	t0	PROPN
ejpam-1600	97	30	,	,	PUNCT
ejpam-1600	97	31	v0	v0	PROPN
ejpam-1600	97	32	)	)	PUNCT
ejpam-1600	97	33	is	be	AUX
ejpam-1600	97	34	the	the	DET
ejpam-1600	97	35	left	left	ADJ
ejpam-1600	97	36	maximal	maximal	ADJ
ejpam-1600	97	37	solution	solution	NOUN
ejpam-1600	97	38	of	of	ADP
ejpam-1600	97	39	v′	v′	PROPN
ejpam-1600	97	40	=	=	SYM
ejpam-1600	97	41	g0(t	g0(t	PROPN
ejpam-1600	97	42	,	,	PUNCT
ejpam-1600	97	43	v	v	NOUN
ejpam-1600	97	44	)	)	PUNCT
ejpam-1600	97	45	,	,	PUNCT
ejpam-1600	97	46	v(t0	v(t0	NOUN
ejpam-1600	97	47	)	)	PUNCT
ejpam-1600	97	48	=	=	SYM
ejpam-1600	97	49	v0	v0	NOUN
ejpam-1600	97	50	(	(	PUNCT
ejpam-1600	97	51	13	13	NUM
ejpam-1600	97	52	)	)	PUNCT
ejpam-1600	97	53	existing	exist	VERB
ejpam-1600	97	54	on	on	ADP
ejpam-1600	97	55	t0	t0	PROPN
ejpam-1600	97	56	≤	≤	PROPN
ejpam-1600	97	57	t	t	PROPN
ejpam-1600	97	58	≤	≤	NUM
ejpam-1600	97	59	t0	t0	PROPN
ejpam-1600	97	60	and	and	CCONJ
ejpam-1600	97	61	r(t	r(t	PROPN
ejpam-1600	97	62	,	,	PUNCT
ejpam-1600	97	63	t0	t0	PROPN
ejpam-1600	97	64	,	,	PUNCT
ejpam-1600	97	65	w0	w0	PROPN
ejpam-1600	97	66	)	)	PUNCT
ejpam-1600	97	67	is	be	AUX
ejpam-1600	97	68	the	the	DET
ejpam-1600	97	69	right	right	ADJ
ejpam-1600	97	70	maximal	maximal	ADJ
ejpam-1600	97	71	solution	solution	NOUN
ejpam-1600	97	72	of	of	ADP
ejpam-1600	97	73	w′	w′	PROPN
ejpam-1600	97	74	=	=	SYM
ejpam-1600	97	75	g(t	g(t	PROPN
ejpam-1600	97	76	,	,	PUNCT
ejpam-1600	97	77	w	w	NOUN
ejpam-1600	97	78	)	)	PUNCT
ejpam-1600	97	79	,	,	PUNCT
ejpam-1600	97	80	w(t0	w(t0	NOUN
ejpam-1600	97	81	)	)	PUNCT
ejpam-1600	98	1	=	=	SYM
ejpam-1600	98	2	w0	w0	PROPN
ejpam-1600	98	3	(	(	PUNCT
ejpam-1600	98	4	14	14	NUM
ejpam-1600	98	5	)	)	PUNCT
ejpam-1600	98	6	existing	exist	VERB
ejpam-1600	98	7	on	on	ADP
ejpam-1600	98	8	[	[	X
ejpam-1600	98	9	t0,∞	t0,∞	NUM
ejpam-1600	98	10	)	)	PUNCT
ejpam-1600	98	11	(	(	PUNCT
ejpam-1600	98	12	iii	iii	X
ejpam-1600	98	13	)	)	PUNCT
ejpam-1600	98	14	d−l(t	d−l(t	NOUN
ejpam-1600	98	15	,	,	PUNCT
ejpam-1600	98	16	u(t	u(t	NOUN
ejpam-1600	98	17	)	)	PUNCT
ejpam-1600	98	18	)	)	PUNCT
ejpam-1600	99	1	≤	≤	NUM
ejpam-1600	99	2	g(t	g(t	PROPN
ejpam-1600	99	3	,	,	PUNCT
ejpam-1600	99	4	l(t	l(t	PROPN
ejpam-1600	99	5	,	,	PUNCT
ejpam-1600	99	6	u(t	u(t	NOUN
ejpam-1600	99	7	)	)	PUNCT
ejpam-1600	99	8	)	)	PUNCT
ejpam-1600	99	9	)	)	PUNCT
ejpam-1600	99	10	(	(	PUNCT
ejpam-1600	99	11	15	15	NUM
ejpam-1600	99	12	)	)	PUNCT
ejpam-1600	99	13	on	on	ADP
ejpam-1600	99	14	ω	ω	NUM
ejpam-1600	99	15	where	where	SCONJ
ejpam-1600	99	16	ω	ω	NOUN
ejpam-1600	99	17	=	=	SYM
ejpam-1600	99	18	{	{	PUNCT
ejpam-1600	99	19	u	u	NOUN
ejpam-1600	99	20	∈	∈	PROPN
ejpam-1600	99	21	ẽ	ẽ	PROPN
ejpam-1600	99	22	:	:	PUNCT
ejpam-1600	99	23	l(s	l(s	PROPN
ejpam-1600	99	24	,	,	PUNCT
ejpam-1600	99	25	u(s	u(s	PROPN
ejpam-1600	99	26	)	)	PUNCT
ejpam-1600	99	27	)	)	PUNCT
ejpam-1600	99	28	≤	≤	NUM
ejpam-1600	100	1	η(s	η(s	PROPN
ejpam-1600	100	2	,	,	PUNCT
ejpam-1600	100	3	t	t	PROPN
ejpam-1600	100	4	,	,	PUNCT
ejpam-1600	100	5	l(t	l(t	PROPN
ejpam-1600	100	6	,	,	PUNCT
ejpam-1600	100	7	u(t	u(t	NOUN
ejpam-1600	100	8	)	)	PUNCT
ejpam-1600	100	9	)	)	PUNCT
ejpam-1600	100	10	)	)	PUNCT
ejpam-1600	100	11	,	,	PUNCT
ejpam-1600	100	12	t0	t0	PROPN
ejpam-1600	100	13	≤	≤	PROPN
ejpam-1600	100	14	s	s	PART
ejpam-1600	100	15	≤	≤	NUM
ejpam-1600	100	16	t	t	PROPN
ejpam-1600	100	17	}	}	PUNCT
ejpam-1600	100	18	then	then	ADV
ejpam-1600	100	19	we	we	PRON
ejpam-1600	100	20	have	have	VERB
ejpam-1600	100	21	l(t	l(t	NOUN
ejpam-1600	100	22	,	,	PUNCT
ejpam-1600	100	23	u(t	u(t	NOUN
ejpam-1600	100	24	,	,	PUNCT
ejpam-1600	100	25	t0	t0	PROPN
ejpam-1600	100	26	,	,	PUNCT
ejpam-1600	100	27	φ0(t0))≤	φ0(t0))≤	CCONJ
ejpam-1600	100	28	r(t	r(t	NOUN
ejpam-1600	100	29	,	,	PUNCT
ejpam-1600	100	30	t0	t0	PROPN
ejpam-1600	100	31	,	,	PUNCT
ejpam-1600	100	32	w0	w0	PROPN
ejpam-1600	100	33	)	)	PUNCT
ejpam-1600	100	34	,	,	PUNCT
ejpam-1600	100	35	t	t	PROPN
ejpam-1600	100	36	≥	≥	NUM
ejpam-1600	100	37	t0	t0	PROPN
ejpam-1600	100	38	whenever	whenever	SCONJ
ejpam-1600	100	39	l(t0,φ0(t0))≤	l(t0,φ0(t0))≤	VERB
ejpam-1600	100	40	w0	w0	PROPN
ejpam-1600	100	41	.	.	PUNCT
ejpam-1600	101	1	in	in	ADP
ejpam-1600	101	2	the	the	DET
ejpam-1600	101	3	proof	proof	NOUN
ejpam-1600	101	4	of	of	ADP
ejpam-1600	101	5	theorem	theorem	NOUN
ejpam-1600	101	6	3	3	NUM
ejpam-1600	101	7	we	we	PRON
ejpam-1600	101	8	use	use	VERB
ejpam-1600	101	9	the	the	DET
ejpam-1600	101	10	lemma	lemma	PROPN
ejpam-1600	101	11	1.4.1	1.4.1	NUM
ejpam-1600	101	12	in	in	ADP
ejpam-1600	101	13	[	[	X
ejpam-1600	101	14	2	2	NUM
ejpam-1600	101	15	]	]	PUNCT
ejpam-1600	101	16	.	.	PUNCT
ejpam-1600	102	1	j.	j.	PROPN
ejpam-1600	102	2	devi	devi	PROPN
ejpam-1600	102	3	,	,	PUNCT
ejpam-1600	102	4	ch	ch	PROPN
ejpam-1600	102	5	.	.	PUNCT
ejpam-1600	102	6	naidu	naidu	PROPN
ejpam-1600	102	7	/	/	SYM
ejpam-1600	102	8	eur	eur	PROPN
ejpam-1600	102	9	.	.	PUNCT
ejpam-1600	103	1	j.	j.	PROPN
ejpam-1600	103	2	pure	pure	PROPN
ejpam-1600	103	3	appl	appl	PROPN
ejpam-1600	103	4	.	.	PROPN
ejpam-1600	103	5	math	math	PROPN
ejpam-1600	103	6	,	,	PUNCT
ejpam-1600	103	7	5	5	NUM
ejpam-1600	103	8	(	(	PUNCT
ejpam-1600	103	9	2012	2012	NUM
ejpam-1600	103	10	)	)	PUNCT
ejpam-1600	103	11	,	,	PUNCT
ejpam-1600	103	12	187	187	NUM
ejpam-1600	103	13	-	-	SYM
ejpam-1600	103	14	196	196	NUM
ejpam-1600	103	15	192	192	NUM
ejpam-1600	103	16	4	4	NUM
ejpam-1600	103	17	.	.	PUNCT
ejpam-1600	104	1	stability	stability	NOUN
ejpam-1600	104	2	results	result	NOUN
ejpam-1600	104	3	in	in	ADP
ejpam-1600	104	4	this	this	DET
ejpam-1600	104	5	section	section	NOUN
ejpam-1600	104	6	we	we	PRON
ejpam-1600	104	7	study	study	VERB
ejpam-1600	104	8	the	the	DET
ejpam-1600	104	9	stability	stability	NOUN
ejpam-1600	104	10	properties	property	NOUN
ejpam-1600	104	11	of	of	ADP
ejpam-1600	104	12	the	the	DET
ejpam-1600	104	13	solution	solution	NOUN
ejpam-1600	104	14	of	of	ADP
ejpam-1600	104	15	(	(	PUNCT
ejpam-1600	104	16	8)	8)	NUM
ejpam-1600	104	17	in	in	ADP
ejpam-1600	104	18	order	order	NOUN
ejpam-1600	104	19	to	to	PART
ejpam-1600	104	20	do	do	AUX
ejpam-1600	104	21	so	so	ADV
ejpam-1600	104	22	,	,	PUNCT
ejpam-1600	104	23	we	we	PRON
ejpam-1600	104	24	assume	assume	VERB
ejpam-1600	104	25	that	that	SCONJ
ejpam-1600	104	26	the	the	DET
ejpam-1600	104	27	solutions	solution	NOUN
ejpam-1600	104	28	of	of	ADP
ejpam-1600	104	29	(	(	PUNCT
ejpam-1600	104	30	8)	8)	NUM
ejpam-1600	104	31	exist	exist	VERB
ejpam-1600	104	32	for	for	ADP
ejpam-1600	104	33	t	t	PROPN
ejpam-1600	104	34	≥	≥	NOUN
ejpam-1600	104	35	t0	t0	PROPN
ejpam-1600	104	36	and	and	CCONJ
ejpam-1600	104	37	are	be	AUX
ejpam-1600	104	38	unique	unique	ADJ
ejpam-1600	104	39	.	.	PUNCT
ejpam-1600	105	1	it	it	PRON
ejpam-1600	105	2	is	be	AUX
ejpam-1600	105	3	to	to	PART
ejpam-1600	105	4	be	be	AUX
ejpam-1600	105	5	noted	note	VERB
ejpam-1600	105	6	that	that	SCONJ
ejpam-1600	105	7	if	if	SCONJ
ejpam-1600	105	8	we	we	PRON
ejpam-1600	105	9	have	have	VERB
ejpam-1600	105	10	to	to	PART
ejpam-1600	105	11	study	study	VERB
ejpam-1600	105	12	the	the	DET
ejpam-1600	105	13	stability	stability	NOUN
ejpam-1600	105	14	properties	property	NOUN
ejpam-1600	105	15	of	of	ADP
ejpam-1600	105	16	any	any	DET
ejpam-1600	105	17	solution	solution	NOUN
ejpam-1600	105	18	u(t	u(t	NOUN
ejpam-1600	105	19	,	,	PUNCT
ejpam-1600	105	20	t0,φ0	t0,φ0	PROPN
ejpam-1600	105	21	)	)	PUNCT
ejpam-1600	105	22	of	of	ADP
ejpam-1600	105	23	(	(	PUNCT
ejpam-1600	105	24	8)	8)	NUM
ejpam-1600	105	25	.	.	PUNCT
ejpam-1600	106	1	then	then	ADV
ejpam-1600	106	2	we	we	PRON
ejpam-1600	106	3	have	have	VERB
ejpam-1600	106	4	to	to	PART
ejpam-1600	106	5	find	find	VERB
ejpam-1600	106	6	two	two	NUM
ejpam-1600	106	7	functions	function	NOUN
ejpam-1600	106	8	z	z	NOUN
ejpam-1600	106	9	and	and	CCONJ
ejpam-1600	106	10	v	v	ADP
ejpam-1600	106	11	such	such	ADJ
ejpam-1600	106	12	that	that	SCONJ
ejpam-1600	106	13	the	the	DET
ejpam-1600	106	14	hukuhara	hukuhara	ADJ
ejpam-1600	106	15	difference	difference	NOUN
ejpam-1600	106	16	z	z	NOUN
ejpam-1600	106	17	=	=	SYM
ejpam-1600	106	18	u	u	NOUN
ejpam-1600	106	19	−	−	PROPN
ejpam-1600	106	20	v	v	NOUN
ejpam-1600	106	21	exists	exist	VERB
ejpam-1600	106	22	and	and	CCONJ
ejpam-1600	106	23	dh	dh	NOUN
ejpam-1600	106	24	z	z	PROPN
ejpam-1600	106	25	=	=	SYM
ejpam-1600	106	26	dh	dh	NOUN
ejpam-1600	106	27	u	u	NOUN
ejpam-1600	106	28	−	−	PROPN
ejpam-1600	106	29	dh	dh	NOUN
ejpam-1600	106	30	v	v	NOUN
ejpam-1600	106	31	exists	exist	VERB
ejpam-1600	106	32	and	and	CCONJ
ejpam-1600	106	33	further	further	ADJ
ejpam-1600	106	34	q(0)(t	q(0)(t	NOUN
ejpam-1600	106	35	)	)	PUNCT
ejpam-1600	106	36	≡	≡	PROPN
ejpam-1600	106	37	0	0	PUNCT
ejpam-1600	107	1	for	for	ADP
ejpam-1600	107	2	all	all	DET
ejpam-1600	107	3	t.	t.	NOUN
ejpam-1600	107	4	thus	thus	ADV
ejpam-1600	107	5	if	if	SCONJ
ejpam-1600	107	6	all	all	DET
ejpam-1600	107	7	the	the	DET
ejpam-1600	107	8	above	above	ADJ
ejpam-1600	107	9	conditions	condition	NOUN
ejpam-1600	107	10	are	be	AUX
ejpam-1600	107	11	satisfied	satisfied	ADJ
ejpam-1600	107	12	then	then	ADV
ejpam-1600	107	13	studying	study	VERB
ejpam-1600	107	14	the	the	DET
ejpam-1600	107	15	stability	stability	NOUN
ejpam-1600	107	16	properties	property	NOUN
ejpam-1600	107	17	of	of	ADP
ejpam-1600	107	18	any	any	DET
ejpam-1600	107	19	solution	solution	NOUN
ejpam-1600	107	20	u(t	u(t	NOUN
ejpam-1600	107	21	,	,	PUNCT
ejpam-1600	107	22	t0,φ0	t0,φ0	PROPN
ejpam-1600	107	23	)	)	PUNCT
ejpam-1600	107	24	of	of	ADP
ejpam-1600	107	25	(	(	PUNCT
ejpam-1600	107	26	8)	8)	NUM
ejpam-1600	107	27	reduces	reduce	VERB
ejpam-1600	107	28	to	to	ADP
ejpam-1600	107	29	the	the	DET
ejpam-1600	107	30	study	study	NOUN
ejpam-1600	107	31	of	of	ADP
ejpam-1600	107	32	zero	zero	NUM
ejpam-1600	107	33	solution	solution	NOUN
ejpam-1600	107	34	of	of	ADP
ejpam-1600	107	35	(	(	PUNCT
ejpam-1600	107	36	8)	8)	NUM
ejpam-1600	107	37	.	.	PUNCT
ejpam-1600	108	1	we	we	PRON
ejpam-1600	108	2	observe	observe	VERB
ejpam-1600	108	3	that	that	SCONJ
ejpam-1600	108	4	in	in	ADP
ejpam-1600	108	5	the	the	DET
ejpam-1600	108	6	generation	generation	NOUN
ejpam-1600	108	7	of	of	ADP
ejpam-1600	108	8	set	set	ADJ
ejpam-1600	108	9	differential	differential	ADJ
ejpam-1600	108	10	equation	equation	NOUN
ejpam-1600	108	11	involving	involve	VERB
ejpam-1600	108	12	causal	causal	ADJ
ejpam-1600	108	13	operators	operator	NOUN
ejpam-1600	108	14	with	with	ADP
ejpam-1600	108	15	memory	memory	NOUN
ejpam-1600	108	16	from	from	ADP
ejpam-1600	108	17	ordinary	ordinary	ADJ
ejpam-1600	108	18	differential	differential	ADJ
ejpam-1600	108	19	equations	equation	NOUN
ejpam-1600	108	20	involving	involve	VERB
ejpam-1600	108	21	causal	causal	ADJ
ejpam-1600	108	22	operators	operator	NOUN
ejpam-1600	108	23	with	with	ADP
ejpam-1600	108	24	memory	memory	NOUN
ejpam-1600	108	25	,	,	PUNCT
ejpam-1600	108	26	certain	certain	ADJ
ejpam-1600	108	27	undesirable	undesirable	ADJ
ejpam-1600	108	28	elements	element	NOUN
ejpam-1600	108	29	may	may	AUX
ejpam-1600	108	30	enter	enter	VERB
ejpam-1600	108	31	the	the	DET
ejpam-1600	108	32	solution	solution	NOUN
ejpam-1600	108	33	u(t	u(t	NOUN
ejpam-1600	108	34	)	)	PUNCT
ejpam-1600	108	35	of	of	ADP
ejpam-1600	108	36	(	(	PUNCT
ejpam-1600	108	37	8)	8)	NUM
ejpam-1600	108	38	.	.	PUNCT
ejpam-1600	109	1	in	in	ADP
ejpam-1600	109	2	order	order	NOUN
ejpam-1600	109	3	that	that	SCONJ
ejpam-1600	109	4	the	the	DET
ejpam-1600	109	5	solutions	solution	NOUN
ejpam-1600	109	6	of	of	ADP
ejpam-1600	109	7	(	(	PUNCT
ejpam-1600	109	8	8)	8)	NUM
ejpam-1600	109	9	project	project	NOUN
ejpam-1600	109	10	the	the	DET
ejpam-1600	109	11	behaviour	behaviour	NOUN
ejpam-1600	109	12	of	of	ADP
ejpam-1600	109	13	ordinary	ordinary	ADJ
ejpam-1600	109	14	differential	differential	ADJ
ejpam-1600	109	15	equations	equation	NOUN
ejpam-1600	109	16	involving	involve	VERB
ejpam-1600	109	17	causal	causal	ADJ
ejpam-1600	109	18	operator	operator	NOUN
ejpam-1600	109	19	with	with	ADP
ejpam-1600	109	20	memory	memory	NOUN
ejpam-1600	109	21	,	,	PUNCT
ejpam-1600	109	22	from	from	ADP
ejpam-1600	109	23	which	which	PRON
ejpam-1600	109	24	they	they	PRON
ejpam-1600	109	25	can	can	AUX
ejpam-1600	109	26	be	be	AUX
ejpam-1600	109	27	generated	generate	VERB
ejpam-1600	109	28	,	,	PUNCT
ejpam-1600	109	29	we	we	PRON
ejpam-1600	109	30	introduce	introduce	VERB
ejpam-1600	109	31	the	the	DET
ejpam-1600	109	32	concept	concept	NOUN
ejpam-1600	109	33	of	of	ADP
ejpam-1600	109	34	hukuhara	hukuhara	ADJ
ejpam-1600	109	35	difference	difference	NOUN
ejpam-1600	109	36	in	in	ADP
ejpam-1600	109	37	initial	initial	ADJ
ejpam-1600	109	38	functions	function	NOUN
ejpam-1600	109	39	.	.	PUNCT
ejpam-1600	110	1	before	before	SCONJ
ejpam-1600	110	2	we	we	PRON
ejpam-1600	110	3	introduce	introduce	VERB
ejpam-1600	110	4	the	the	DET
ejpam-1600	110	5	theory	theory	NOUN
ejpam-1600	110	6	,	,	PUNCT
ejpam-1600	110	7	we	we	PRON
ejpam-1600	110	8	consider	consider	VERB
ejpam-1600	110	9	the	the	DET
ejpam-1600	110	10	following	follow	VERB
ejpam-1600	110	11	example	example	NOUN
ejpam-1600	110	12	.	.	PUNCT
ejpam-1600	111	1	example	example	NOUN
ejpam-1600	112	1	1	1	NUM
ejpam-1600	112	2	.	.	X
ejpam-1600	112	3	consider	consider	VERB
ejpam-1600	112	4	the	the	DET
ejpam-1600	112	5	set	set	ADJ
ejpam-1600	112	6	differential	differential	ADJ
ejpam-1600	112	7	equation	equation	NOUN
ejpam-1600	112	8	with	with	ADP
ejpam-1600	112	9	delay	delay	NOUN
ejpam-1600	112	10	on	on	ADP
ejpam-1600	112	11	r.	r.	PROPN
ejpam-1600	112	12	dh	dh	PROPN
ejpam-1600	112	13	u	u	PROPN
ejpam-1600	112	14	=	=	NOUN
ejpam-1600	112	15	−u(t	−u(t	ADJ
ejpam-1600	112	16	−τ	−τ	NOUN
ejpam-1600	112	17	)	)	PUNCT
ejpam-1600	112	18	,	,	PUNCT
ejpam-1600	112	19	u0	u0	NOUN
ejpam-1600	112	20	=	=	PUNCT
ejpam-1600	113	1	[	[	X
ejpam-1600	113	2	φ1,φ2	φ1,φ2	X
ejpam-1600	113	3	]	]	X
ejpam-1600	113	4	(	(	PUNCT
ejpam-1600	113	5	16	16	NUM
ejpam-1600	113	6	)	)	PUNCT
ejpam-1600	113	7	where	where	SCONJ
ejpam-1600	113	8	φ1,φ2	φ1,φ2	PROPN
ejpam-1600	113	9	are	be	AUX
ejpam-1600	113	10	real	real	ADV
ejpam-1600	113	11	valued	value	VERB
ejpam-1600	113	12	functions	function	NOUN
ejpam-1600	113	13	and	and	CCONJ
ejpam-1600	113	14	u(t	u(t	NOUN
ejpam-1600	113	15	)	)	PUNCT
ejpam-1600	113	16	=	=	PUNCT
ejpam-1600	114	1	[	[	X
ejpam-1600	114	2	u1(t),u2(t	u1(t),u2(t	NOUN
ejpam-1600	114	3	)	)	PUNCT
ejpam-1600	114	4	]	]	PUNCT
ejpam-1600	114	5	u	u	PRON
ejpam-1600	114	6	′(t	′(t	NOUN
ejpam-1600	114	7	)	)	PUNCT
ejpam-1600	114	8	=[	=[	NOUN
ejpam-1600	114	9	u′1(t),u	u′1(t),u	ADJ
ejpam-1600	114	10	′	′	NUM
ejpam-1600	114	11	2(t	2(t	NUM
ejpam-1600	114	12	)	)	PUNCT
ejpam-1600	114	13	]	]	PUNCT
ejpam-1600	115	1	=	=	PUNCT
ejpam-1600	115	2	−	−	NOUN
ejpam-1600	115	3	u(t	u(t	PROPN
ejpam-1600	115	4	−τ	−τ	NOUN
ejpam-1600	115	5	)	)	PUNCT
ejpam-1600	116	1	=	=	SYM
ejpam-1600	116	2	−	−	X
ejpam-1600	117	1	[	[	X
ejpam-1600	117	2	u1(t	u1(t	ADP
ejpam-1600	117	3	−τ),u2(t	−τ),u2(t	NOUN
ejpam-1600	117	4	−τ	−τ	NOUN
ejpam-1600	117	5	)	)	PUNCT
ejpam-1600	117	6	]	]	PUNCT
ejpam-1600	118	1	=	=	PUNCT
ejpam-1600	119	1	[	[	X
ejpam-1600	119	2	−u2(t	−u2(t	NOUN
ejpam-1600	119	3	−τ),−u1(t	−τ),−u1(t	VERB
ejpam-1600	119	4	−τ	−τ	ADJ
ejpam-1600	119	5	)	)	PUNCT
ejpam-1600	119	6	]	]	PUNCT
ejpam-1600	119	7	therefore	therefore	ADV
ejpam-1600	119	8	u′1	u′1	VERB
ejpam-1600	119	9	=	=	PUNCT
ejpam-1600	119	10	−u2(t	−u2(t	NOUN
ejpam-1600	119	11	−τ	−τ	NOUN
ejpam-1600	119	12	)	)	PUNCT
ejpam-1600	119	13	and	and	CCONJ
ejpam-1600	119	14	u′2	u′2	X
ejpam-1600	119	15	=	=	NOUN
ejpam-1600	119	16	−u1(t	−u1(t	ADJ
ejpam-1600	119	17	−τ	−τ	NOUN
ejpam-1600	119	18	)	)	PUNCT
ejpam-1600	119	19	(	(	PUNCT
ejpam-1600	119	20	17	17	NUM
ejpam-1600	119	21	)	)	PUNCT
ejpam-1600	119	22	where	where	SCONJ
ejpam-1600	119	23	u1(0	u1(0	NOUN
ejpam-1600	119	24	)	)	PUNCT
ejpam-1600	119	25	=	=	SYM
ejpam-1600	119	26	φ1(0	φ1(0	PROPN
ejpam-1600	119	27	)	)	PUNCT
ejpam-1600	119	28	,	,	PUNCT
ejpam-1600	119	29	u2(0	u2(0	NOUN
ejpam-1600	119	30	)	)	PUNCT
ejpam-1600	119	31	=	=	SYM
ejpam-1600	119	32	φ2(0	φ2(0	ADV
ejpam-1600	119	33	)	)	PUNCT
ejpam-1600	119	34	u′′1	u′′1	NOUN
ejpam-1600	119	35	=	=	NOUN
ejpam-1600	120	1	u1(t	u1(t	ADP
ejpam-1600	120	2	−	−	PROPN
ejpam-1600	120	3	2τ	2τ	NUM
ejpam-1600	120	4	)	)	PUNCT
ejpam-1600	121	1	and	and	CCONJ
ejpam-1600	121	2	u′′2	u′′2	PUNCT
ejpam-1600	122	1	=	=	SYM
ejpam-1600	122	2	u2(t	u2(t	NOUN
ejpam-1600	123	1	−	−	NOUN
ejpam-1600	123	2	2τ),−2τ≤	2τ),−2τ≤	PROPN
ejpam-1600	123	3	t	t	PROPN
ejpam-1600	123	4	≤	≤	NOUN
ejpam-1600	123	5	0	0	NUM
ejpam-1600	123	6	.	.	PUNCT
ejpam-1600	124	1	(	(	PUNCT
ejpam-1600	124	2	18	18	NUM
ejpam-1600	124	3	)	)	PUNCT
ejpam-1600	124	4	suppose	suppose	VERB
ejpam-1600	124	5	eλ1	eλ1	PROPN
ejpam-1600	124	6	t	t	PROPN
ejpam-1600	124	7	and	and	CCONJ
ejpam-1600	124	8	e−λ2	e−λ2	PROPN
ejpam-1600	124	9	t	t	PROPN
ejpam-1600	124	10	are	be	AUX
ejpam-1600	124	11	solutions	solution	NOUN
ejpam-1600	124	12	of	of	ADP
ejpam-1600	124	13	the	the	DET
ejpam-1600	124	14	system	system	NOUN
ejpam-1600	124	15	(	(	PUNCT
ejpam-1600	124	16	18	18	NUM
ejpam-1600	124	17	)	)	PUNCT
ejpam-1600	124	18	.	.	PUNCT
ejpam-1600	125	1	let	let	VERB
ejpam-1600	125	2	u1(t	u1(t	PRON
ejpam-1600	125	3	)	)	PUNCT
ejpam-1600	125	4	=	=	PUNCT
ejpam-1600	125	5	eλ1	eλ1	NOUN
ejpam-1600	125	6	t	t	NOUN
ejpam-1600	125	7	and	and	CCONJ
ejpam-1600	125	8	u2(t	u2(t	NOUN
ejpam-1600	125	9	)	)	PUNCT
ejpam-1600	125	10	=	=	PUNCT
ejpam-1600	125	11	e−λ2	e−λ2	NOUN
ejpam-1600	125	12	t	t	PROPN
ejpam-1600	125	13	u′1(t	u′1(t	PROPN
ejpam-1600	125	14	)	)	PUNCT
ejpam-1600	126	1	=	=	PUNCT
ejpam-1600	126	2	λ1eλ1	λ1eλ1	PROPN
ejpam-1600	126	3	t	t	NOUN
ejpam-1600	126	4	u′2(t	u′2(t	NOUN
ejpam-1600	126	5	)	)	PUNCT
ejpam-1600	127	1	=	=	PUNCT
ejpam-1600	127	2	−λ2e−λ2	−λ2e−λ2	PROPN
ejpam-1600	127	3	t	t	PROPN
ejpam-1600	127	4	u′′1	u′′1	PROPN
ejpam-1600	127	5	(	(	PUNCT
ejpam-1600	127	6	t	t	NOUN
ejpam-1600	127	7	)	)	PUNCT
ejpam-1600	127	8	=	=	SYM
ejpam-1600	128	1	λ	λ	X
ejpam-1600	128	2	2	2	NUM
ejpam-1600	128	3	1eλ1	1eλ1	NUM
ejpam-1600	128	4	t	t	NOUN
ejpam-1600	128	5	u′′2	u′′2	CCONJ
ejpam-1600	128	6	(	(	PUNCT
ejpam-1600	128	7	t	t	NOUN
ejpam-1600	128	8	)	)	PUNCT
ejpam-1600	128	9	=	=	SYM
ejpam-1600	129	1	λ	λ	X
ejpam-1600	129	2	2	2	NUM
ejpam-1600	129	3	2e−λ2	2e−λ2	NUM
ejpam-1600	129	4	t	t	NOUN
ejpam-1600	129	5	u1(t	u1(t	ADP
ejpam-1600	129	6	−	−	PROPN
ejpam-1600	129	7	2τ	2τ	NUM
ejpam-1600	129	8	)	)	PUNCT
ejpam-1600	129	9	=	=	SYM
ejpam-1600	129	10	eλ1(t−2τ	eλ1(t−2τ	NOUN
ejpam-1600	129	11	)	)	PUNCT
ejpam-1600	129	12	u2(t	u2(t	NOUN
ejpam-1600	129	13	−	−	NOUN
ejpam-1600	129	14	2τ	2τ	NOUN
ejpam-1600	129	15	)	)	PUNCT
ejpam-1600	129	16	=	=	SYM
ejpam-1600	129	17	e−λ2(t−2τ	e−λ2(t−2τ	PROPN
ejpam-1600	129	18	)	)	PUNCT
ejpam-1600	129	19	since	since	SCONJ
ejpam-1600	129	20	u1(t	u1(t	ADV
ejpam-1600	129	21	)	)	PUNCT
ejpam-1600	129	22	and	and	CCONJ
ejpam-1600	129	23	u2(t	u2(t	NOUN
ejpam-1600	129	24	)	)	PUNCT
ejpam-1600	129	25	are	be	AUX
ejpam-1600	129	26	solutions	solution	NOUN
ejpam-1600	129	27	of	of	ADP
ejpam-1600	129	28	the	the	DET
ejpam-1600	129	29	system	system	NOUN
ejpam-1600	129	30	(	(	PUNCT
ejpam-1600	129	31	18	18	NUM
ejpam-1600	129	32	)	)	PUNCT
ejpam-1600	129	33	we	we	PRON
ejpam-1600	129	34	have	have	VERB
ejpam-1600	129	35	to	to	PART
ejpam-1600	129	36	choose	choose	VERB
ejpam-1600	129	37	λ1,λ2	λ1,λ2	PROPN
ejpam-1600	129	38	>	>	X
ejpam-1600	129	39	0	0	NUM
ejpam-1600	129	40	such	such	ADJ
ejpam-1600	129	41	that	that	DET
ejpam-1600	129	42	λ2	λ2	NOUN
ejpam-1600	129	43	1	1	NUM
ejpam-1600	129	44	=	=	SYM
ejpam-1600	129	45	e−2λ1τ	e−2λ1τ	NOUN
ejpam-1600	129	46	,	,	PUNCT
ejpam-1600	129	47	λ2	λ2	NOUN
ejpam-1600	129	48	2	2	NUM
ejpam-1600	129	49	=	=	SYM
ejpam-1600	129	50	e2λ2τ	e2λ2τ	PRON
ejpam-1600	129	51	,	,	PUNCT
ejpam-1600	129	52	then	then	ADV
ejpam-1600	129	53	u1(t	u1(t	ADP
ejpam-1600	129	54	)	)	PUNCT
ejpam-1600	129	55	=	=	SYM
ejpam-1600	129	56	eλ1	eλ1	NOUN
ejpam-1600	129	57	t	t	NOUN
ejpam-1600	129	58	and	and	CCONJ
ejpam-1600	129	59	u2(t	u2(t	NOUN
ejpam-1600	129	60	)	)	PUNCT
ejpam-1600	129	61	=	=	PUNCT
ejpam-1600	129	62	e−λ2	e−λ2	NOUN
ejpam-1600	129	63	t	t	PROPN
ejpam-1600	129	64	are	be	AUX
ejpam-1600	129	65	solutions	solution	NOUN
ejpam-1600	129	66	of	of	ADP
ejpam-1600	129	67	the	the	DET
ejpam-1600	129	68	system	system	NOUN
ejpam-1600	129	69	(	(	PUNCT
ejpam-1600	129	70	18	18	NUM
ejpam-1600	129	71	)	)	PUNCT
ejpam-1600	129	72	.	.	PUNCT
ejpam-1600	130	1	as	as	ADP
ejpam-1600	130	2	a	a	DET
ejpam-1600	130	3	result	result	NOUN
ejpam-1600	130	4	we	we	PRON
ejpam-1600	130	5	have	have	VERB
ejpam-1600	130	6	u1(t	u1(t	NOUN
ejpam-1600	130	7	)	)	PUNCT
ejpam-1600	130	8	=	=	SYM
ejpam-1600	130	9	c1eλ1	c1eλ1	ADP
ejpam-1600	130	10	t	t	PROPN
ejpam-1600	130	11	+	+	NUM
ejpam-1600	130	12	c2e−λ2	c2e−λ2	PROPN
ejpam-1600	130	13	t	t	NOUN
ejpam-1600	130	14	and	and	CCONJ
ejpam-1600	130	15	u2(t	u2(t	NOUN
ejpam-1600	130	16	)	)	PUNCT
ejpam-1600	131	1	=	=	PUNCT
ejpam-1600	131	2	c3eλ1	c3eλ1	ADP
ejpam-1600	131	3	t	t	PROPN
ejpam-1600	131	4	+	+	NUM
ejpam-1600	131	5	c4e−λ2	c4e−λ2	PROPN
ejpam-1600	131	6	t	t	NOUN
ejpam-1600	131	7	.	.	PUNCT
ejpam-1600	132	1	(	(	PUNCT
ejpam-1600	132	2	19	19	NUM
ejpam-1600	132	3	)	)	PUNCT
ejpam-1600	132	4	j.	j.	PROPN
ejpam-1600	132	5	devi	devi	PROPN
ejpam-1600	132	6	,	,	PUNCT
ejpam-1600	132	7	ch	ch	PROPN
ejpam-1600	132	8	.	.	PUNCT
ejpam-1600	132	9	naidu	naidu	PROPN
ejpam-1600	132	10	/	/	SYM
ejpam-1600	132	11	eur	eur	PROPN
ejpam-1600	132	12	.	.	PUNCT
ejpam-1600	133	1	j.	j.	PROPN
ejpam-1600	133	2	pure	pure	PROPN
ejpam-1600	133	3	appl	appl	PROPN
ejpam-1600	133	4	.	.	PROPN
ejpam-1600	133	5	math	math	PROPN
ejpam-1600	133	6	,	,	PUNCT
ejpam-1600	133	7	5	5	NUM
ejpam-1600	133	8	(	(	PUNCT
ejpam-1600	133	9	2012	2012	NUM
ejpam-1600	133	10	)	)	PUNCT
ejpam-1600	133	11	,	,	PUNCT
ejpam-1600	133	12	187	187	NUM
ejpam-1600	133	13	-	-	SYM
ejpam-1600	133	14	196	196	NUM
ejpam-1600	133	15	193	193	NUM
ejpam-1600	133	16	suppose	suppose	VERB
ejpam-1600	133	17	the	the	DET
ejpam-1600	133	18	initial	initial	ADJ
ejpam-1600	133	19	functions	function	NOUN
ejpam-1600	133	20	are	be	AUX
ejpam-1600	133	21	given	give	VERB
ejpam-1600	133	22	by	by	ADP
ejpam-1600	133	23	φ1(s	φ1(	NOUN
ejpam-1600	133	24	)	)	PUNCT
ejpam-1600	133	25	=	=	SYM
ejpam-1600	133	26	1	1	NUM
ejpam-1600	133	27	2	2	NUM
ejpam-1600	133	28	[	[	SYM
ejpam-1600	133	29	u10	u10	NOUN
ejpam-1600	133	30	−	−	PROPN
ejpam-1600	133	31	u20]e	u20]e	PROPN
ejpam-1600	133	32	λ1s	λ1s	NOUN
ejpam-1600	134	1	+	+	CCONJ
ejpam-1600	134	2	1	1	NUM
ejpam-1600	134	3	2	2	NUM
ejpam-1600	134	4	[	[	X
ejpam-1600	134	5	u10	u10	NOUN
ejpam-1600	134	6	+	+	CCONJ
ejpam-1600	134	7	u20]e	u20]e	NOUN
ejpam-1600	134	8	−λ2s	−λ2s	NUM
ejpam-1600	134	9	(	(	PUNCT
ejpam-1600	134	10	20	20	NUM
ejpam-1600	134	11	)	)	PUNCT
ejpam-1600	134	12	φ2(s	φ2(s	NOUN
ejpam-1600	134	13	)	)	PUNCT
ejpam-1600	134	14	=	=	SYM
ejpam-1600	134	15	1	1	NUM
ejpam-1600	134	16	2	2	NUM
ejpam-1600	134	17	[	[	X
ejpam-1600	134	18	u20	u20	NUM
ejpam-1600	134	19	−	−	PROPN
ejpam-1600	134	20	u10]e	u10]e	PROPN
ejpam-1600	134	21	λ1s	λ1s	NOUN
ejpam-1600	134	22	+	+	CCONJ
ejpam-1600	134	23	1	1	NUM
ejpam-1600	134	24	2	2	NUM
ejpam-1600	134	25	[	[	X
ejpam-1600	134	26	u10	u10	NOUN
ejpam-1600	134	27	+	+	CCONJ
ejpam-1600	134	28	u20]e	u20]e	NOUN
ejpam-1600	134	29	−λ2s	−λ2s	NUM
ejpam-1600	134	30	(	(	PUNCT
ejpam-1600	134	31	21	21	NUM
ejpam-1600	134	32	)	)	PUNCT
ejpam-1600	134	33	for	for	ADP
ejpam-1600	134	34	−2τ	−2τ	PROPN
ejpam-1600	134	35	≤	≤	NUM
ejpam-1600	134	36	s	s	PART
ejpam-1600	134	37	≤	≤	NOUN
ejpam-1600	134	38	0	0	NUM
ejpam-1600	134	39	.	.	PUNCT
ejpam-1600	135	1	by	by	ADP
ejpam-1600	135	2	using	use	VERB
ejpam-1600	135	3	the	the	DET
ejpam-1600	135	4	relations	relation	NOUN
ejpam-1600	135	5	(	(	PUNCT
ejpam-1600	135	6	17	17	NUM
ejpam-1600	135	7	)	)	PUNCT
ejpam-1600	135	8	,	,	PUNCT
ejpam-1600	135	9	(	(	PUNCT
ejpam-1600	135	10	19	19	NUM
ejpam-1600	135	11	)	)	PUNCT
ejpam-1600	135	12	,	,	PUNCT
ejpam-1600	135	13	and	and	CCONJ
ejpam-1600	135	14	(	(	PUNCT
ejpam-1600	135	15	20	20	X
ejpam-1600	135	16	)	)	PUNCT
ejpam-1600	135	17	we	we	PRON
ejpam-1600	135	18	have	have	VERB
ejpam-1600	135	19	to	to	PART
ejpam-1600	135	20	compute	compute	VERB
ejpam-1600	135	21	the	the	DET
ejpam-1600	135	22	values	value	NOUN
ejpam-1600	135	23	c1	c1	PROPN
ejpam-1600	135	24	,	,	PUNCT
ejpam-1600	135	25	c2	c2	PROPN
ejpam-1600	135	26	,	,	PUNCT
ejpam-1600	135	27	c3	c3	PROPN
ejpam-1600	135	28	and	and	CCONJ
ejpam-1600	135	29	c4	c4	NOUN
ejpam-1600	135	30	.	.	PUNCT
ejpam-1600	136	1	taking	take	VERB
ejpam-1600	136	2	t	t	NOUN
ejpam-1600	136	3	=	=	SYM
ejpam-1600	136	4	0	0	NUM
ejpam-1600	136	5	and	and	CCONJ
ejpam-1600	136	6	t	t	PROPN
ejpam-1600	137	1	=	=	PUNCT
ejpam-1600	137	2	τ	τ	PROPN
ejpam-1600	137	3	we	we	PRON
ejpam-1600	137	4	get	get	VERB
ejpam-1600	137	5	c1	c1	NOUN
ejpam-1600	137	6	=	=	NOUN
ejpam-1600	137	7	1	1	NUM
ejpam-1600	137	8	2	2	NUM
ejpam-1600	137	9	[	[	PUNCT
ejpam-1600	137	10	u10	u10	PROPN
ejpam-1600	137	11	−	−	PROPN
ejpam-1600	137	12	u20	u20	PROPN
ejpam-1600	137	13	]	]	PUNCT
ejpam-1600	137	14	,	,	PUNCT
ejpam-1600	137	15	c2	c2	PROPN
ejpam-1600	137	16	=	=	SYM
ejpam-1600	137	17	1	1	NUM
ejpam-1600	137	18	2	2	NUM
ejpam-1600	137	19	[	[	X
ejpam-1600	137	20	u10	u10	X
ejpam-1600	137	21	+	+	CCONJ
ejpam-1600	137	22	u20	u20	PROPN
ejpam-1600	137	23	]	]	PUNCT
ejpam-1600	137	24	,	,	PUNCT
ejpam-1600	137	25	c3	c3	PROPN
ejpam-1600	137	26	=	=	PUNCT
ejpam-1600	137	27	1	1	NUM
ejpam-1600	137	28	2	2	NUM
ejpam-1600	137	29	[	[	X
ejpam-1600	137	30	u20	u20	PROPN
ejpam-1600	137	31	−	−	PROPN
ejpam-1600	137	32	u10	u10	PROPN
ejpam-1600	137	33	]	]	PUNCT
ejpam-1600	137	34	,	,	PUNCT
ejpam-1600	137	35	c4	c4	NOUN
ejpam-1600	137	36	=	=	NOUN
ejpam-1600	137	37	1	1	NUM
ejpam-1600	137	38	2	2	NUM
ejpam-1600	137	39	[	[	X
ejpam-1600	137	40	u10	u10	X
ejpam-1600	137	41	+	+	CCONJ
ejpam-1600	137	42	u20	u20	PROPN
ejpam-1600	137	43	]	]	PUNCT
ejpam-1600	137	44	.	.	PUNCT
ejpam-1600	138	1	therefore	therefore	ADV
ejpam-1600	138	2	u(t	u(t	NOUN
ejpam-1600	138	3	)	)	PUNCT
ejpam-1600	138	4	=	=	PUNCT
ejpam-1600	139	1	[	[	X
ejpam-1600	139	2	−	−	NOUN
ejpam-1600	139	3	1	1	NUM
ejpam-1600	139	4	2	2	NUM
ejpam-1600	139	5	[	[	X
ejpam-1600	139	6	u20	u20	PROPN
ejpam-1600	139	7	−	−	PROPN
ejpam-1600	139	8	u10	u10	PROPN
ejpam-1600	139	9	]	]	X
ejpam-1600	139	10	,	,	PUNCT
ejpam-1600	139	11	1	1	NUM
ejpam-1600	139	12	2	2	NUM
ejpam-1600	139	13	[	[	X
ejpam-1600	139	14	u20	u20	NUM
ejpam-1600	139	15	−	−	PROPN
ejpam-1600	139	16	u10]]e	u10]]e	PROPN
ejpam-1600	139	17	λ1	λ1	PROPN
ejpam-1600	139	18	t	t	PROPN
ejpam-1600	139	19	+	+	CCONJ
ejpam-1600	139	20	[	[	PUNCT
ejpam-1600	139	21	1	1	NUM
ejpam-1600	139	22	2	2	NUM
ejpam-1600	139	23	[	[	X
ejpam-1600	139	24	u10	u10	X
ejpam-1600	139	25	+	+	CCONJ
ejpam-1600	139	26	u20	u20	PROPN
ejpam-1600	139	27	]	]	PUNCT
ejpam-1600	139	28	,	,	PUNCT
ejpam-1600	139	29	1	1	NUM
ejpam-1600	139	30	2	2	NUM
ejpam-1600	139	31	[	[	X
ejpam-1600	139	32	u10	u10	X
ejpam-1600	139	33	+	+	CCONJ
ejpam-1600	139	34	u20]]e	u20]]e	NOUN
ejpam-1600	139	35	−λ2	−λ2	PROPN
ejpam-1600	139	36	t	t	PROPN
ejpam-1600	139	37	choose	choose	VERB
ejpam-1600	139	38	ψ0	ψ0	ADV
ejpam-1600	139	39	=	=	PUNCT
ejpam-1600	140	1	[	[	X
ejpam-1600	140	2	−	−	NUM
ejpam-1600	140	3	1	1	NUM
ejpam-1600	140	4	2	2	NUM
ejpam-1600	140	5	[	[	X
ejpam-1600	140	6	u20	u20	PROPN
ejpam-1600	140	7	−	−	PROPN
ejpam-1600	140	8	u10	u10	PROPN
ejpam-1600	140	9	]	]	X
ejpam-1600	140	10	,	,	PUNCT
ejpam-1600	140	11	1	1	NUM
ejpam-1600	140	12	2	2	NUM
ejpam-1600	140	13	[	[	X
ejpam-1600	140	14	u20	u20	NUM
ejpam-1600	140	15	+	+	CCONJ
ejpam-1600	140	16	u10]]e	u10]]e	PROPN
ejpam-1600	140	17	λ1s	λ1s	PROPN
ejpam-1600	140	18	and	and	CCONJ
ejpam-1600	140	19	χ0	χ0	PROPN
ejpam-1600	140	20	=	=	PUNCT
ejpam-1600	141	1	[	[	PUNCT
ejpam-1600	141	2	1	1	NUM
ejpam-1600	141	3	2	2	NUM
ejpam-1600	141	4	[	[	X
ejpam-1600	141	5	u10	u10	X
ejpam-1600	141	6	+	+	CCONJ
ejpam-1600	141	7	u20	u20	PROPN
ejpam-1600	141	8	]	]	PUNCT
ejpam-1600	141	9	,	,	PUNCT
ejpam-1600	141	10	1	1	NUM
ejpam-1600	141	11	2	2	NUM
ejpam-1600	141	12	[	[	X
ejpam-1600	141	13	u10	u10	X
ejpam-1600	141	14	+	+	CCONJ
ejpam-1600	141	15	u20]]e	u20]]e	NOUN
ejpam-1600	141	16	−λ2s	−λ2s	PUNCT
ejpam-1600	141	17	for	for	ADP
ejpam-1600	141	18	φ0	φ0	PROPN
ejpam-1600	141	19	=	=	PUNCT
ejpam-1600	142	1	[	[	X
ejpam-1600	142	2	φ1,φ2	φ1,φ2	X
ejpam-1600	142	3	]	]	X
ejpam-1600	142	4	=	=	SYM
ejpam-1600	142	5	ψ0	ψ0	PROPN
ejpam-1600	142	6	+	+	X
ejpam-1600	142	7	χ0	χ0	PROPN
ejpam-1600	142	8	.	.	PUNCT
ejpam-1600	143	1	then	then	ADV
ejpam-1600	143	2	u(t	u(t	PROPN
ejpam-1600	143	3	,	,	PUNCT
ejpam-1600	143	4	t0,χ0	t0,χ0	PROPN
ejpam-1600	143	5	)	)	PUNCT
ejpam-1600	144	1	=	=	PUNCT
ejpam-1600	144	2	[	[	PUNCT
ejpam-1600	144	3	1	1	NUM
ejpam-1600	144	4	2	2	NUM
ejpam-1600	144	5	[	[	X
ejpam-1600	144	6	u10	u10	X
ejpam-1600	144	7	+	+	CCONJ
ejpam-1600	144	8	u20	u20	PROPN
ejpam-1600	144	9	]	]	PUNCT
ejpam-1600	144	10	,	,	PUNCT
ejpam-1600	144	11	1	1	NUM
ejpam-1600	144	12	2	2	NUM
ejpam-1600	144	13	[	[	X
ejpam-1600	144	14	u10	u10	X
ejpam-1600	144	15	+	+	CCONJ
ejpam-1600	144	16	u20]]e	u20]]e	NOUN
ejpam-1600	144	17	−λ2s	−λ2s	NUM
ejpam-1600	144	18	which	which	PRON
ejpam-1600	144	19	implies	imply	VERB
ejpam-1600	144	20	the	the	DET
ejpam-1600	144	21	stability	stability	NOUN
ejpam-1600	144	22	of	of	ADP
ejpam-1600	144	23	the	the	DET
ejpam-1600	144	24	trivial	trivial	ADJ
ejpam-1600	144	25	solution	solution	NOUN
ejpam-1600	144	26	of	of	ADP
ejpam-1600	144	27	the	the	DET
ejpam-1600	144	28	equation	equation	NOUN
ejpam-1600	144	29	(	(	PUNCT
ejpam-1600	144	30	16	16	NUM
ejpam-1600	144	31	)	)	PUNCT
ejpam-1600	144	32	.	.	PUNCT
ejpam-1600	145	1	we	we	PRON
ejpam-1600	145	2	suppose	suppose	VERB
ejpam-1600	145	3	that	that	SCONJ
ejpam-1600	145	4	given	give	VERB
ejpam-1600	145	5	any	any	DET
ejpam-1600	145	6	solution	solution	NOUN
ejpam-1600	145	7	u(t	u(t	NOUN
ejpam-1600	145	8	,	,	PUNCT
ejpam-1600	145	9	t0,φ0	t0,φ0	PROPN
ejpam-1600	145	10	)	)	PUNCT
ejpam-1600	145	11	of	of	ADP
ejpam-1600	145	12	(	(	PUNCT
ejpam-1600	145	13	8)	8)	NUM
ejpam-1600	145	14	,	,	PUNCT
ejpam-1600	145	15	we	we	PRON
ejpam-1600	145	16	can	can	AUX
ejpam-1600	145	17	find	find	VERB
ejpam-1600	145	18	a	a	DET
ejpam-1600	145	19	function	function	NOUN
ejpam-1600	145	20	v	v	ADP
ejpam-1600	145	21	such	such	ADJ
ejpam-1600	145	22	that	that	SCONJ
ejpam-1600	145	23	the	the	DET
ejpam-1600	145	24	hukuhara	hukuhara	ADJ
ejpam-1600	145	25	difference	difference	NOUN
ejpam-1600	145	26	u	u	PROPN
ejpam-1600	145	27	−	−	PROPN
ejpam-1600	145	28	v	v	NOUN
ejpam-1600	145	29	exists	exist	VERB
ejpam-1600	145	30	,	,	PUNCT
ejpam-1600	145	31	satisfies	satisfy	VERB
ejpam-1600	145	32	the	the	DET
ejpam-1600	145	33	properties	property	NOUN
ejpam-1600	145	34	mentioned	mention	VERB
ejpam-1600	145	35	earlier	early	ADV
ejpam-1600	145	36	in	in	ADP
ejpam-1600	145	37	this	this	DET
ejpam-1600	145	38	context	context	NOUN
ejpam-1600	145	39	so	so	SCONJ
ejpam-1600	145	40	that	that	SCONJ
ejpam-1600	145	41	it	it	PRON
ejpam-1600	145	42	is	be	AUX
ejpam-1600	145	43	sufficient	sufficient	ADJ
ejpam-1600	145	44	to	to	PART
ejpam-1600	145	45	study	study	VERB
ejpam-1600	145	46	the	the	DET
ejpam-1600	145	47	stability	stability	NOUN
ejpam-1600	145	48	properties	property	NOUN
ejpam-1600	145	49	of	of	ADP
ejpam-1600	145	50	the	the	DET
ejpam-1600	145	51	trivial	trivial	ADJ
ejpam-1600	145	52	solution	solution	NOUN
ejpam-1600	145	53	.	.	PUNCT
ejpam-1600	146	1	other	other	ADJ
ejpam-1600	146	2	notations	notation	NOUN
ejpam-1600	146	3	of	of	ADP
ejpam-1600	146	4	lyapunov	lyapunov	ADJ
ejpam-1600	146	5	stability	stability	NOUN
ejpam-1600	146	6	can	can	AUX
ejpam-1600	146	7	be	be	AUX
ejpam-1600	146	8	formulated	formulate	VERB
ejpam-1600	146	9	in	in	ADP
ejpam-1600	146	10	a	a	DET
ejpam-1600	146	11	similar	similar	ADJ
ejpam-1600	146	12	way	way	NOUN
ejpam-1600	146	13	following	follow	VERB
ejpam-1600	146	14	the	the	DET
ejpam-1600	146	15	standard	standard	ADJ
ejpam-1600	146	16	stability	stability	NOUN
ejpam-1600	146	17	definitions	definition	VERB
ejpam-1600	146	18	in	in	ADP
ejpam-1600	146	19	[	[	X
ejpam-1600	146	20	3	3	NUM
ejpam-1600	146	21	]	]	PUNCT
ejpam-1600	146	22	.	.	PUNCT
ejpam-1600	147	1	we	we	PRON
ejpam-1600	147	2	now	now	ADV
ejpam-1600	147	3	present	present	VERB
ejpam-1600	147	4	the	the	DET
ejpam-1600	147	5	stability	stability	NOUN
ejpam-1600	147	6	theorems	theorem	VERB
ejpam-1600	147	7	in	in	ADP
ejpam-1600	147	8	this	this	DET
ejpam-1600	147	9	context	context	NOUN
ejpam-1600	147	10	.	.	PUNCT
ejpam-1600	148	1	theorem	theorem	ADJ
ejpam-1600	148	2	4	4	NUM
ejpam-1600	148	3	.	.	PUNCT
ejpam-1600	148	4	assume	assume	VERB
ejpam-1600	148	5	that	that	SCONJ
ejpam-1600	148	6	there	there	PRON
ejpam-1600	148	7	exist	exist	VERB
ejpam-1600	148	8	functions	function	NOUN
ejpam-1600	148	9	l(t	l(t	NOUN
ejpam-1600	148	10	,	,	PUNCT
ejpam-1600	148	11	u(t	u(t	NOUN
ejpam-1600	148	12	)	)	PUNCT
ejpam-1600	148	13	)	)	PUNCT
ejpam-1600	148	14	and	and	CCONJ
ejpam-1600	148	15	g(t	g(t	PROPN
ejpam-1600	148	16	,	,	PUNCT
ejpam-1600	148	17	w	w	NOUN
ejpam-1600	148	18	)	)	PUNCT
ejpam-1600	148	19	satisfying	satisfy	VERB
ejpam-1600	148	20	the	the	DET
ejpam-1600	148	21	following	follow	VERB
ejpam-1600	148	22	conditions	condition	NOUN
ejpam-1600	148	23	(	(	PUNCT
ejpam-1600	148	24	i	i	NOUN
ejpam-1600	148	25	)	)	PUNCT
ejpam-1600	148	26	g	g	PROPN
ejpam-1600	148	27	∈	∈	PROPN
ejpam-1600	148	28	c[r+×r+,r+	c[r+×r+,r+	NOUN
ejpam-1600	148	29	]	]	PUNCT
ejpam-1600	148	30	and	and	CCONJ
ejpam-1600	148	31	g(t	g(t	PROPN
ejpam-1600	148	32	,	,	PUNCT
ejpam-1600	148	33	0	0	NUM
ejpam-1600	148	34	)	)	PUNCT
ejpam-1600	148	35	≡	≡	PROPN
ejpam-1600	148	36	0	0	NUM
ejpam-1600	148	37	;	;	PUNCT
ejpam-1600	148	38	(	(	PUNCT
ejpam-1600	148	39	ii	ii	NOUN
ejpam-1600	148	40	)	)	PUNCT
ejpam-1600	148	41	l	l	NOUN
ejpam-1600	148	42	∈	∈	PROPN
ejpam-1600	148	43	c[r+	c[r+	NOUN
ejpam-1600	148	44	×	×	PROPN
ejpam-1600	148	45	b	b	PROPN
ejpam-1600	148	46	,	,	PUNCT
ejpam-1600	148	47	r+	r+	X
ejpam-1600	148	48	]	]	PUNCT
ejpam-1600	148	49	where	where	SCONJ
ejpam-1600	148	50	b	b	X
ejpam-1600	148	51	=	=	SYM
ejpam-1600	148	52	b(θ	b(θ	PROPN
ejpam-1600	148	53	,	,	PUNCT
ejpam-1600	148	54	ρ	ρ	PROPN
ejpam-1600	148	55	)	)	PUNCT
ejpam-1600	148	56	=	=	PRON
ejpam-1600	148	57	{	{	PUNCT
ejpam-1600	148	58	u	u	NOUN
ejpam-1600	148	59	∈	∈	PROPN
ejpam-1600	148	60	kc(r	kc(r	X
ejpam-1600	148	61	n	n	CCONJ
ejpam-1600	148	62	)	)	PUNCT
ejpam-1600	148	63	:	:	PUNCT
ejpam-1600	149	1	d[u	d[u	PROPN
ejpam-1600	149	2	,	,	PUNCT
ejpam-1600	149	3	θ	θ	PROPN
ejpam-1600	149	4	]	]	X
ejpam-1600	149	5	≤	≤	NUM
ejpam-1600	149	6	ρ	ρ	PROPN
ejpam-1600	149	7	}	}	PUNCT
ejpam-1600	149	8	;	;	PUNCT
ejpam-1600	149	9	l(t	l(t	PROPN
ejpam-1600	149	10	,	,	PUNCT
ejpam-1600	149	11	θ	θ	NOUN
ejpam-1600	149	12	)	)	PUNCT
ejpam-1600	149	13	≡	≡	PROPN
ejpam-1600	149	14	0	0	NUM
ejpam-1600	149	15	and	and	CCONJ
ejpam-1600	149	16	l(t	l(t	PROPN
ejpam-1600	149	17	,	,	PUNCT
ejpam-1600	149	18	u	u	NOUN
ejpam-1600	149	19	)	)	PUNCT
ejpam-1600	149	20	is	be	AUX
ejpam-1600	149	21	positive	positive	ADJ
ejpam-1600	149	22	definite	definite	ADJ
ejpam-1600	149	23	and	and	CCONJ
ejpam-1600	149	24	locally	locally	ADV
ejpam-1600	149	25	lipschitzian	lipschitzian	ADJ
ejpam-1600	149	26	in	in	ADP
ejpam-1600	149	27	u	u	NOUN
ejpam-1600	149	28	;	;	PUNCT
ejpam-1600	149	29	(	(	PUNCT
ejpam-1600	149	30	iii	iii	NOUN
ejpam-1600	149	31	)	)	PUNCT
ejpam-1600	149	32	for	for	ADP
ejpam-1600	149	33	t	t	PROPN
ejpam-1600	149	34	>	>	X
ejpam-1600	149	35	t0	t0	PROPN
ejpam-1600	149	36	and	and	CCONJ
ejpam-1600	149	37	u	u	PROPN
ejpam-1600	149	38	∈	∈	PROPN
ejpam-1600	149	39	e1	e1	NOUN
ejpam-1600	149	40	d−l(t	d−l(t	NOUN
ejpam-1600	149	41	,	,	PUNCT
ejpam-1600	149	42	u(t	u(t	NOUN
ejpam-1600	149	43	)	)	PUNCT
ejpam-1600	149	44	)	)	PUNCT
ejpam-1600	150	1	≤	≤	NUM
ejpam-1600	150	2	g(t	g(t	PROPN
ejpam-1600	150	3	,	,	PUNCT
ejpam-1600	150	4	l(t	l(t	PROPN
ejpam-1600	150	5	,	,	PUNCT
ejpam-1600	150	6	u(t	u(t	NOUN
ejpam-1600	150	7	)	)	PUNCT
ejpam-1600	150	8	)	)	PUNCT
ejpam-1600	150	9	)	)	PUNCT
ejpam-1600	150	10	j.	j.	PROPN
ejpam-1600	150	11	devi	devi	PROPN
ejpam-1600	150	12	,	,	PUNCT
ejpam-1600	150	13	ch	ch	PROPN
ejpam-1600	150	14	.	.	PUNCT
ejpam-1600	150	15	naidu	naidu	PROPN
ejpam-1600	150	16	/	/	SYM
ejpam-1600	150	17	eur	eur	PROPN
ejpam-1600	150	18	.	.	PUNCT
ejpam-1600	151	1	j.	j.	PROPN
ejpam-1600	151	2	pure	pure	PROPN
ejpam-1600	151	3	appl	appl	PROPN
ejpam-1600	151	4	.	.	PROPN
ejpam-1600	151	5	math	math	PROPN
ejpam-1600	151	6	,	,	PUNCT
ejpam-1600	151	7	5	5	NUM
ejpam-1600	151	8	(	(	PUNCT
ejpam-1600	151	9	2012	2012	NUM
ejpam-1600	151	10	)	)	PUNCT
ejpam-1600	151	11	,	,	PUNCT
ejpam-1600	151	12	187	187	NUM
ejpam-1600	151	13	-	-	SYM
ejpam-1600	151	14	196	196	NUM
ejpam-1600	151	15	194	194	NUM
ejpam-1600	151	16	then	then	ADV
ejpam-1600	151	17	the	the	DET
ejpam-1600	151	18	stability	stability	NOUN
ejpam-1600	151	19	of	of	ADP
ejpam-1600	151	20	the	the	DET
ejpam-1600	151	21	zero	zero	NUM
ejpam-1600	151	22	solution	solution	NOUN
ejpam-1600	151	23	of	of	ADP
ejpam-1600	151	24	w′	w′	PROPN
ejpam-1600	151	25	=	=	SYM
ejpam-1600	151	26	g(t	g(t	PROPN
ejpam-1600	151	27	,	,	PUNCT
ejpam-1600	151	28	w	w	NOUN
ejpam-1600	151	29	)	)	PUNCT
ejpam-1600	151	30	w(t0	w(t0	NOUN
ejpam-1600	151	31	)	)	PUNCT
ejpam-1600	152	1	=	=	SYM
ejpam-1600	152	2	w0	w0	PROPN
ejpam-1600	152	3	(	(	PUNCT
ejpam-1600	152	4	22	22	NUM
ejpam-1600	152	5	)	)	PUNCT
ejpam-1600	152	6	implies	imply	VERB
ejpam-1600	152	7	the	the	DET
ejpam-1600	152	8	stability	stability	NOUN
ejpam-1600	152	9	of	of	ADP
ejpam-1600	152	10	the	the	DET
ejpam-1600	152	11	zero	zero	NUM
ejpam-1600	152	12	solution	solution	NOUN
ejpam-1600	152	13	of	of	ADP
ejpam-1600	152	14	dh	dh	NOUN
ejpam-1600	152	15	u(t	u(t	PROPN
ejpam-1600	152	16	)	)	PUNCT
ejpam-1600	153	1	=	=	SYM
ejpam-1600	153	2	(	(	PUNCT
ejpam-1600	153	3	qu)(t	qu)(t	PROPN
ejpam-1600	153	4	)	)	PUNCT
ejpam-1600	153	5	ut0	ut0	PROPN
ejpam-1600	153	6	=	=	PROPN
ejpam-1600	153	7	χ0	χ0	PROPN
ejpam-1600	153	8	(	(	PUNCT
ejpam-1600	153	9	23	23	NUM
ejpam-1600	153	10	)	)	PUNCT
ejpam-1600	153	11	where	where	SCONJ
ejpam-1600	153	12	φo	φo	ADP
ejpam-1600	153	13	=	=	NOUN
ejpam-1600	153	14	ψ0	ψ0	ADJ
ejpam-1600	153	15	+	+	ADJ
ejpam-1600	153	16	χ0	χ0	PROPN
ejpam-1600	153	17	.	.	PUNCT
ejpam-1600	154	1	proof	proof	NOUN
ejpam-1600	154	2	.	.	PUNCT
ejpam-1600	155	1	let	let	VERB
ejpam-1600	155	2	0	0	NUM
ejpam-1600	155	3	<	<	X
ejpam-1600	155	4	ε	ε	PROPN
ejpam-1600	155	5	<	<	X
ejpam-1600	155	6	ρ	ρ	PROPN
ejpam-1600	155	7	and	and	CCONJ
ejpam-1600	155	8	t0	t0	PROPN
ejpam-1600	155	9	∈	∈	PROPN
ejpam-1600	155	10	r+	r+	PUNCT
ejpam-1600	155	11	be	be	AUX
ejpam-1600	155	12	given	give	VERB
ejpam-1600	155	13	.	.	PUNCT
ejpam-1600	156	1	since	since	SCONJ
ejpam-1600	156	2	l(t	l(t	PROPN
ejpam-1600	156	3	,	,	PUNCT
ejpam-1600	156	4	u	u	NOUN
ejpam-1600	156	5	)	)	PUNCT
ejpam-1600	156	6	is	be	AUX
ejpam-1600	156	7	positive	positive	ADJ
ejpam-1600	156	8	definite	definite	ADJ
ejpam-1600	156	9	,	,	PUNCT
ejpam-1600	156	10	it	it	PRON
ejpam-1600	156	11	follows	follow	VERB
ejpam-1600	156	12	that	that	SCONJ
ejpam-1600	156	13	there	there	PRON
ejpam-1600	156	14	exists	exist	VERB
ejpam-1600	156	15	a	a	DET
ejpam-1600	156	16	function	function	NOUN
ejpam-1600	156	17	b	b	NOUN
ejpam-1600	156	18	∈	∈	PROPN
ejpam-1600	156	19	k	k	ADP
ejpam-1600	156	20	such	such	ADJ
ejpam-1600	156	21	that	that	SCONJ
ejpam-1600	156	22	b(d̃[u	b(d̃[u	NOUN
ejpam-1600	156	23	,	,	PUNCT
ejpam-1600	156	24	θ	θ	NOUN
ejpam-1600	156	25	]	]	X
ejpam-1600	156	26	)	)	PUNCT
ejpam-1600	156	27	≤	≤	NUM
ejpam-1600	156	28	l(t	l(t	PROPN
ejpam-1600	156	29	,	,	PUNCT
ejpam-1600	156	30	u	u	NOUN
ejpam-1600	156	31	)	)	PUNCT
ejpam-1600	156	32	for	for	ADP
ejpam-1600	156	33	(	(	PUNCT
ejpam-1600	156	34	t	t	PROPN
ejpam-1600	156	35	,	,	PUNCT
ejpam-1600	156	36	u	u	NOUN
ejpam-1600	156	37	)	)	PUNCT
ejpam-1600	156	38	∈	∈	PROPN
ejpam-1600	156	39	r+×	r+×	PROPN
ejpam-1600	156	40	b	b	PROPN
ejpam-1600	156	41	(	(	PUNCT
ejpam-1600	156	42	24	24	NUM
ejpam-1600	156	43	)	)	PUNCT
ejpam-1600	156	44	suppose	suppose	VERB
ejpam-1600	156	45	that	that	SCONJ
ejpam-1600	156	46	the	the	DET
ejpam-1600	156	47	solution	solution	NOUN
ejpam-1600	156	48	of	of	ADP
ejpam-1600	156	49	the	the	DET
ejpam-1600	156	50	system	system	NOUN
ejpam-1600	156	51	(	(	PUNCT
ejpam-1600	156	52	22	22	NUM
ejpam-1600	156	53	)	)	PUNCT
ejpam-1600	156	54	is	be	AUX
ejpam-1600	156	55	stable	stable	ADJ
ejpam-1600	156	56	.	.	PUNCT
ejpam-1600	157	1	then	then	ADV
ejpam-1600	157	2	,	,	PUNCT
ejpam-1600	157	3	given	give	VERB
ejpam-1600	157	4	b(ε	b(ε	PROPN
ejpam-1600	157	5	)	)	PUNCT
ejpam-1600	157	6	>	>	X
ejpam-1600	157	7	0	0	NUM
ejpam-1600	157	8	,	,	PUNCT
ejpam-1600	157	9	t0	t0	PROPN
ejpam-1600	157	10	∈	∈	PROPN
ejpam-1600	157	11	r+	r+	ADV
ejpam-1600	157	12	,	,	PUNCT
ejpam-1600	157	13	there	there	PRON
ejpam-1600	157	14	exists	exist	VERB
ejpam-1600	157	15	a	a	DET
ejpam-1600	157	16	δ	δ	NOUN
ejpam-1600	157	17	=	=	SYM
ejpam-1600	157	18	δ(t0,ε	δ(t0,ε	PROPN
ejpam-1600	157	19	)	)	PUNCT
ejpam-1600	157	20	>	>	X
ejpam-1600	157	21	0	0	NUM
ejpam-1600	158	1	such	such	ADJ
ejpam-1600	158	2	that	that	SCONJ
ejpam-1600	158	3	when	when	SCONJ
ejpam-1600	158	4	ever	ever	ADV
ejpam-1600	158	5	w0	w0	PROPN
ejpam-1600	158	6	<	<	X
ejpam-1600	158	7	δ	δ	PROPN
ejpam-1600	158	8	,	,	PUNCT
ejpam-1600	158	9	we	we	PRON
ejpam-1600	158	10	have	have	VERB
ejpam-1600	158	11	w(t	w(t	PROPN
ejpam-1600	158	12	,	,	PUNCT
ejpam-1600	158	13	t0	t0	PROPN
ejpam-1600	158	14	,	,	PUNCT
ejpam-1600	158	15	w0	w0	PROPN
ejpam-1600	158	16	)	)	PUNCT
ejpam-1600	158	17	<	<	X
ejpam-1600	158	18	b(ε	b(ε	PROPN
ejpam-1600	158	19	)	)	PUNCT
ejpam-1600	158	20	,	,	PUNCT
ejpam-1600	158	21	t	t	PROPN
ejpam-1600	158	22	≥	≥	PROPN
ejpam-1600	158	23	t0	t0	PROPN
ejpam-1600	158	24	,	,	PUNCT
ejpam-1600	158	25	where	where	SCONJ
ejpam-1600	158	26	w(t	w(t	PROPN
ejpam-1600	158	27	,	,	PUNCT
ejpam-1600	158	28	t0	t0	PROPN
ejpam-1600	158	29	,	,	PUNCT
ejpam-1600	158	30	w0	w0	PROPN
ejpam-1600	158	31	)	)	PUNCT
ejpam-1600	158	32	is	be	AUX
ejpam-1600	158	33	any	any	DET
ejpam-1600	158	34	solution	solution	NOUN
ejpam-1600	158	35	of	of	ADP
ejpam-1600	158	36	the	the	DET
ejpam-1600	158	37	system	system	NOUN
ejpam-1600	158	38	(	(	PUNCT
ejpam-1600	158	39	22	22	NUM
ejpam-1600	158	40	)	)	PUNCT
ejpam-1600	158	41	.	.	PUNCT
ejpam-1600	159	1	choose	choose	VERB
ejpam-1600	159	2	w0	w0	PROPN
ejpam-1600	159	3	=	=	PUNCT
ejpam-1600	159	4	l(t0,χ0	l(t0,χ0	NOUN
ejpam-1600	159	5	)	)	PUNCT
ejpam-1600	159	6	.	.	PUNCT
ejpam-1600	160	1	sincel(t	sincel(t	PROPN
ejpam-1600	160	2	,	,	PUNCT
ejpam-1600	160	3	u	u	NOUN
ejpam-1600	160	4	)	)	PUNCT
ejpam-1600	160	5	is	be	AUX
ejpam-1600	160	6	continuous	continuous	ADJ
ejpam-1600	160	7	and	and	CCONJ
ejpam-1600	160	8	l(t	l(t	NOUN
ejpam-1600	160	9	,	,	PUNCT
ejpam-1600	160	10	θ	θ	NOUN
ejpam-1600	160	11	)	)	PUNCT
ejpam-1600	160	12	≡	≡	PROPN
ejpam-1600	160	13	0	0	NUM
ejpam-1600	160	14	,	,	PUNCT
ejpam-1600	160	15	there	there	PRON
ejpam-1600	160	16	exist	exist	VERB
ejpam-1600	160	17	function	function	NOUN
ejpam-1600	160	18	δ1	δ1	NOUN
ejpam-1600	160	19	=	=	SYM
ejpam-1600	160	20	δ1(t0,ε	δ1(t0,ε	NOUN
ejpam-1600	160	21	)	)	PUNCT
ejpam-1600	160	22	>	>	X
ejpam-1600	160	23	0	0	NUM
ejpam-1600	161	1	such	such	ADJ
ejpam-1600	161	2	that	that	SCONJ
ejpam-1600	161	3	d1[χ0,θ	d1[χ0,θ	NOUN
ejpam-1600	161	4	]	]	X
ejpam-1600	161	5	≤	≤	NUM
ejpam-1600	161	6	δ1	δ1	NOUN
ejpam-1600	161	7	and	and	CCONJ
ejpam-1600	161	8	l(t0,χ0)≤	l(t0,χ0)≤	ADV
ejpam-1600	161	9	δ	δ	PROPN
ejpam-1600	161	10	holds	hold	VERB
ejpam-1600	161	11	simultaneously	simultaneously	ADV
ejpam-1600	161	12	.	.	PUNCT
ejpam-1600	162	1	we	we	PRON
ejpam-1600	162	2	claim	claim	VERB
ejpam-1600	162	3	that	that	SCONJ
ejpam-1600	162	4	if	if	SCONJ
ejpam-1600	162	5	d1[χ0,θ	d1[χ0,θ	X
ejpam-1600	162	6	]	]	X
ejpam-1600	162	7	≤	≤	NUM
ejpam-1600	162	8	δ1	δ1	NOUN
ejpam-1600	162	9	,	,	PUNCT
ejpam-1600	162	10	then	then	ADV
ejpam-1600	162	11	d̃[u(t),θ	d̃[u(t),θ	PROPN
ejpam-1600	162	12	]	]	PUNCT
ejpam-1600	162	13	<	<	X
ejpam-1600	162	14	ε	ε	PROPN
ejpam-1600	162	15	for	for	ADP
ejpam-1600	162	16	all	all	DET
ejpam-1600	162	17	t	t	PROPN
ejpam-1600	162	18	≥	≥	PROPN
ejpam-1600	162	19	t0	t0	PROPN
ejpam-1600	162	20	.	.	PUNCT
ejpam-1600	163	1	suppose	suppose	VERB
ejpam-1600	163	2	this	this	PRON
ejpam-1600	163	3	is	be	AUX
ejpam-1600	163	4	not	not	PART
ejpam-1600	163	5	true	true	ADJ
ejpam-1600	163	6	.	.	PUNCT
ejpam-1600	164	1	then	then	ADV
ejpam-1600	164	2	there	there	PRON
ejpam-1600	164	3	exists	exist	VERB
ejpam-1600	164	4	a	a	DET
ejpam-1600	164	5	solution	solution	NOUN
ejpam-1600	164	6	u(t	u(t	NOUN
ejpam-1600	164	7	)	)	PUNCT
ejpam-1600	164	8	=	=	SYM
ejpam-1600	164	9	u(t	u(t	NOUN
ejpam-1600	164	10	,	,	PUNCT
ejpam-1600	164	11	t0,χ0	t0,χ0	PROPN
ejpam-1600	164	12	)	)	PUNCT
ejpam-1600	164	13	of	of	ADP
ejpam-1600	164	14	the	the	DET
ejpam-1600	164	15	system	system	NOUN
ejpam-1600	164	16	(	(	PUNCT
ejpam-1600	164	17	23	23	NUM
ejpam-1600	164	18	)	)	PUNCT
ejpam-1600	164	19	satisfying	satisfy	VERB
ejpam-1600	164	20	the	the	DET
ejpam-1600	164	21	properties	property	NOUN
ejpam-1600	164	22	d̃[u(t2),θ	d̃[u(t2),θ	NOUN
ejpam-1600	164	23	]	]	X
ejpam-1600	164	24	=	=	SYM
ejpam-1600	164	25	ε	ε	PROPN
ejpam-1600	164	26	and	and	CCONJ
ejpam-1600	164	27	d̃[u(t),θ	d̃[u(t),θ	PROPN
ejpam-1600	164	28	]	]	PUNCT
ejpam-1600	164	29	<	<	X
ejpam-1600	164	30	ε	ε	PROPN
ejpam-1600	164	31	for	for	ADP
ejpam-1600	164	32	t0	t0	PROPN
ejpam-1600	164	33	<	<	X
ejpam-1600	164	34	t	t	X
ejpam-1600	164	35	<	<	X
ejpam-1600	164	36	t2	t2	PROPN
ejpam-1600	164	37	<	<	X
ejpam-1600	164	38	∞.	∞.	PROPN
ejpam-1600	164	39	from	from	ADP
ejpam-1600	164	40	(	(	PUNCT
ejpam-1600	164	41	24	24	NUM
ejpam-1600	164	42	)	)	PUNCT
ejpam-1600	164	43	b(ε)≤	b(ε)≤	ADJ
ejpam-1600	164	44	l(t2	l(t2	NOUN
ejpam-1600	164	45	,	,	PUNCT
ejpam-1600	164	46	u(t2	u(t2	NOUN
ejpam-1600	164	47	)	)	PUNCT
ejpam-1600	164	48	)	)	PUNCT
ejpam-1600	164	49	(	(	PUNCT
ejpam-1600	164	50	25	25	NUM
ejpam-1600	164	51	)	)	PUNCT
ejpam-1600	164	52	furthermore	furthermore	ADV
ejpam-1600	164	53	,	,	PUNCT
ejpam-1600	164	54	u(t	u(t	NOUN
ejpam-1600	164	55	)	)	PUNCT
ejpam-1600	164	56	∈	∈	PROPN
ejpam-1600	164	57	b	b	PROPN
ejpam-1600	164	58	for	for	ADP
ejpam-1600	164	59	t	t	PROPN
ejpam-1600	164	60	∈	∈	PROPN
ejpam-1600	164	61	[	[	X
ejpam-1600	164	62	t0	t0	PROPN
ejpam-1600	164	63	,	,	PUNCT
ejpam-1600	164	64	t2	t2	NOUN
ejpam-1600	164	65	]	]	PUNCT
ejpam-1600	164	66	.	.	PUNCT
ejpam-1600	165	1	hence	hence	ADV
ejpam-1600	165	2	,	,	PUNCT
ejpam-1600	165	3	the	the	DET
ejpam-1600	165	4	choice	choice	NOUN
ejpam-1600	165	5	of	of	ADP
ejpam-1600	165	6	w0	w0	PROPN
ejpam-1600	165	7	=	=	SYM
ejpam-1600	165	8	l(t0,χ0	l(t0,χ0	NOUN
ejpam-1600	165	9	)	)	PUNCT
ejpam-1600	165	10	and	and	CCONJ
ejpam-1600	165	11	condition	condition	NOUN
ejpam-1600	165	12	(	(	PUNCT
ejpam-1600	165	13	iii	iii	NOUN
ejpam-1600	165	14	)	)	PUNCT
ejpam-1600	165	15	gives	give	VERB
ejpam-1600	165	16	,	,	PUNCT
ejpam-1600	165	17	as	as	ADP
ejpam-1600	165	18	a	a	DET
ejpam-1600	165	19	consequence	consequence	NOUN
ejpam-1600	165	20	of	of	ADP
ejpam-1600	165	21	theorem	theorem	NOUN
ejpam-1600	165	22	1	1	NUM
ejpam-1600	165	23	,	,	PUNCT
ejpam-1600	165	24	the	the	DET
ejpam-1600	165	25	estimate	estimate	NOUN
ejpam-1600	165	26	l(t	l(t	NOUN
ejpam-1600	165	27	,	,	PUNCT
ejpam-1600	165	28	u(t	u(t	NOUN
ejpam-1600	165	29	)	)	PUNCT
ejpam-1600	165	30	)	)	PUNCT
ejpam-1600	165	31	≤	≤	NUM
ejpam-1600	165	32	r(t	r(t	NOUN
ejpam-1600	165	33	)	)	PUNCT
ejpam-1600	165	34	,	,	PUNCT
ejpam-1600	165	35	t	t	PROPN
ejpam-1600	165	36	∈	∈	PROPN
ejpam-1600	165	37	[	[	X
ejpam-1600	165	38	t0	t0	PROPN
ejpam-1600	165	39	,	,	PUNCT
ejpam-1600	165	40	t2	t2	NOUN
ejpam-1600	165	41	]	]	PUNCT
ejpam-1600	165	42	,	,	PUNCT
ejpam-1600	165	43	(	(	PUNCT
ejpam-1600	165	44	26	26	NUM
ejpam-1600	165	45	)	)	PUNCT
ejpam-1600	165	46	where	where	SCONJ
ejpam-1600	165	47	r(t	r(t	NOUN
ejpam-1600	165	48	)	)	PUNCT
ejpam-1600	166	1	=	=	SYM
ejpam-1600	166	2	r(t	r(t	NOUN
ejpam-1600	166	3	,	,	PUNCT
ejpam-1600	166	4	t0	t0	PROPN
ejpam-1600	166	5	,	,	PUNCT
ejpam-1600	166	6	w0	w0	PROPN
ejpam-1600	166	7	)	)	PUNCT
ejpam-1600	166	8	is	be	AUX
ejpam-1600	166	9	the	the	DET
ejpam-1600	166	10	maximal	maximal	ADJ
ejpam-1600	166	11	solution	solution	NOUN
ejpam-1600	166	12	of	of	ADP
ejpam-1600	166	13	the	the	DET
ejpam-1600	166	14	comparison	comparison	NOUN
ejpam-1600	166	15	equation	equation	NOUN
ejpam-1600	166	16	(	(	PUNCT
ejpam-1600	166	17	22	22	NUM
ejpam-1600	166	18	)	)	PUNCT
ejpam-1600	166	19	.	.	PUNCT
ejpam-1600	167	1	now	now	ADV
ejpam-1600	167	2	from	from	ADP
ejpam-1600	167	3	equation	equation	NOUN
ejpam-1600	167	4	(	(	PUNCT
ejpam-1600	167	5	25	25	NUM
ejpam-1600	167	6	)	)	PUNCT
ejpam-1600	167	7	b(ε)≤	b(ε)≤	ADJ
ejpam-1600	167	8	l(t2	l(t2	VERB
ejpam-1600	167	9	,	,	PUNCT
ejpam-1600	167	10	u(t2))≤	u(t2))≤	ADJ
ejpam-1600	167	11	r(t2	r(t2	NOUN
ejpam-1600	167	12	)	)	PUNCT
ejpam-1600	167	13	<	<	X
ejpam-1600	167	14	b(ε	b(ε	X
ejpam-1600	167	15	)	)	PUNCT
ejpam-1600	167	16	,	,	PUNCT
ejpam-1600	167	17	which	which	PRON
ejpam-1600	167	18	is	be	AUX
ejpam-1600	167	19	a	a	DET
ejpam-1600	167	20	contradiction	contradiction	NOUN
ejpam-1600	167	21	.	.	PUNCT
ejpam-1600	168	1	hence	hence	ADV
ejpam-1600	168	2	the	the	DET
ejpam-1600	168	3	zero	zero	NUM
ejpam-1600	168	4	solution	solution	NOUN
ejpam-1600	168	5	of	of	ADP
ejpam-1600	168	6	the	the	DET
ejpam-1600	168	7	system	system	NOUN
ejpam-1600	168	8	(	(	PUNCT
ejpam-1600	168	9	23	23	NUM
ejpam-1600	168	10	)	)	PUNCT
ejpam-1600	168	11	is	be	AUX
ejpam-1600	168	12	stable	stable	ADJ
ejpam-1600	168	13	.	.	PUNCT
ejpam-1600	169	1	the	the	DET
ejpam-1600	169	2	following	follow	VERB
ejpam-1600	169	3	theorem	theorem	NOUN
ejpam-1600	169	4	provides	provide	VERB
ejpam-1600	169	5	sufficient	sufficient	ADJ
ejpam-1600	169	6	conditions	condition	NOUN
ejpam-1600	169	7	for	for	ADP
ejpam-1600	169	8	asymptotic	asymptotic	ADJ
ejpam-1600	169	9	stability	stability	NOUN
ejpam-1600	169	10	of	of	ADP
ejpam-1600	169	11	the	the	DET
ejpam-1600	169	12	system	system	NOUN
ejpam-1600	169	13	(	(	PUNCT
ejpam-1600	169	14	23	23	NUM
ejpam-1600	169	15	)	)	PUNCT
ejpam-1600	169	16	.	.	PUNCT
ejpam-1600	170	1	theorem	theorem	ADJ
ejpam-1600	170	2	5	5	NUM
ejpam-1600	170	3	.	.	PUNCT
ejpam-1600	170	4	assume	assume	VERB
ejpam-1600	170	5	that	that	SCONJ
ejpam-1600	170	6	(	(	PUNCT
ejpam-1600	170	7	i	i	NOUN
ejpam-1600	170	8	)	)	PUNCT
ejpam-1600	170	9	there	there	PRON
ejpam-1600	170	10	exist	exist	VERB
ejpam-1600	170	11	functions	function	NOUN
ejpam-1600	170	12	l(t	l(t	PROPN
ejpam-1600	170	13	,	,	PUNCT
ejpam-1600	170	14	u	u	NOUN
ejpam-1600	170	15	)	)	PUNCT
ejpam-1600	170	16	,	,	PUNCT
ejpam-1600	170	17	g(t	g(t	PROPN
ejpam-1600	170	18	,	,	PUNCT
ejpam-1600	170	19	w	w	NOUN
ejpam-1600	170	20	)	)	PUNCT
ejpam-1600	170	21	satisfying	satisfy	VERB
ejpam-1600	170	22	the	the	DET
ejpam-1600	170	23	conditions	condition	NOUN
ejpam-1600	170	24	of	of	ADP
ejpam-1600	170	25	theorem	theorem	NOUN
ejpam-1600	170	26	4	4	NUM
ejpam-1600	170	27	;	;	PUNCT
ejpam-1600	170	28	(	(	PUNCT
ejpam-1600	170	29	ii	ii	NOUN
ejpam-1600	170	30	)	)	PUNCT
ejpam-1600	170	31	there	there	PRON
ejpam-1600	170	32	exists	exist	VERB
ejpam-1600	170	33	a	a	DET
ejpam-1600	170	34	function	function	NOUN
ejpam-1600	170	35	α(t	α(t	NOUN
ejpam-1600	170	36	)	)	PUNCT
ejpam-1600	171	1	such	such	ADJ
ejpam-1600	171	2	that	that	PRON
ejpam-1600	171	3	α(t	α(t	PROPN
ejpam-1600	171	4	)	)	PUNCT
ejpam-1600	171	5	>	>	X
ejpam-1600	171	6	0	0	PUNCT
ejpam-1600	171	7	is	be	AUX
ejpam-1600	171	8	continuous	continuous	ADJ
ejpam-1600	171	9	for	for	ADP
ejpam-1600	171	10	t	t	PROPN
ejpam-1600	171	11	∈	∈	PROPN
ejpam-1600	171	12	r+	r+	NOUN
ejpam-1600	171	13	and	and	CCONJ
ejpam-1600	171	14	α(t	α(t	NOUN
ejpam-1600	171	15	)	)	PUNCT
ejpam-1600	171	16	−→∞	−→∞	PROPN
ejpam-1600	171	17	as	as	ADP
ejpam-1600	171	18	t	t	PROPN
ejpam-1600	171	19	−→∞.	−→∞.	PUNCT
ejpam-1600	172	1	further	far	ADV
ejpam-1600	172	2	assume	assume	VERB
ejpam-1600	172	3	that	that	SCONJ
ejpam-1600	172	4	the	the	DET
ejpam-1600	172	5	relation	relation	NOUN
ejpam-1600	172	6	α(t)d−l(t	α(t)d−l(t	NOUN
ejpam-1600	172	7	,	,	PUNCT
ejpam-1600	172	8	u(t	u(t	NOUN
ejpam-1600	172	9	)	)	PUNCT
ejpam-1600	172	10	)	)	PUNCT
ejpam-1600	173	1	+	+	CCONJ
ejpam-1600	173	2	l(t	l(t	NOUN
ejpam-1600	173	3	,	,	PUNCT
ejpam-1600	173	4	u(t))d−α(t	u(t))d−α(t	PROPN
ejpam-1600	173	5	)	)	PUNCT
ejpam-1600	173	6	≤	≤	NUM
ejpam-1600	173	7	w(t	w(t	PROPN
ejpam-1600	173	8	,	,	PUNCT
ejpam-1600	173	9	l(t	l(t	PROPN
ejpam-1600	173	10	,	,	PUNCT
ejpam-1600	173	11	u(t))α(t	u(t))α(t	NOUN
ejpam-1600	173	12	)	)	PUNCT
ejpam-1600	173	13	)	)	PUNCT
ejpam-1600	173	14	j.	j.	PROPN
ejpam-1600	173	15	devi	devi	PROPN
ejpam-1600	173	16	,	,	PUNCT
ejpam-1600	173	17	ch	ch	PROPN
ejpam-1600	173	18	.	.	PUNCT
ejpam-1600	173	19	naidu	naidu	PROPN
ejpam-1600	173	20	/	/	SYM
ejpam-1600	173	21	eur	eur	PROPN
ejpam-1600	173	22	.	.	PUNCT
ejpam-1600	174	1	j.	j.	PROPN
ejpam-1600	174	2	pure	pure	PROPN
ejpam-1600	174	3	appl	appl	PROPN
ejpam-1600	174	4	.	.	PROPN
ejpam-1600	174	5	math	math	PROPN
ejpam-1600	174	6	,	,	PUNCT
ejpam-1600	174	7	5	5	NUM
ejpam-1600	174	8	(	(	PUNCT
ejpam-1600	174	9	2012	2012	NUM
ejpam-1600	174	10	)	)	PUNCT
ejpam-1600	174	11	,	,	PUNCT
ejpam-1600	174	12	187	187	NUM
ejpam-1600	174	13	-	-	SYM
ejpam-1600	174	14	196	196	NUM
ejpam-1600	174	15	195	195	NUM
ejpam-1600	174	16	for	for	ADP
ejpam-1600	174	17	t	t	PROPN
ejpam-1600	174	18	≥	≥	PROPN
ejpam-1600	174	19	t0	t0	PROPN
ejpam-1600	174	20	,	,	PUNCT
ejpam-1600	174	21	u	u	PROPN
ejpam-1600	174	22	∈	∈	PROPN
ejpam-1600	174	23	eα	eα	VERB
ejpam-1600	174	24	then	then	ADV
ejpam-1600	174	25	,	,	PUNCT
ejpam-1600	174	26	if	if	SCONJ
ejpam-1600	174	27	the	the	DET
ejpam-1600	174	28	zero	zero	NUM
ejpam-1600	174	29	solution	solution	NOUN
ejpam-1600	174	30	of	of	ADP
ejpam-1600	174	31	the	the	DET
ejpam-1600	174	32	system	system	NOUN
ejpam-1600	174	33	(	(	PUNCT
ejpam-1600	174	34	22	22	NUM
ejpam-1600	174	35	)	)	PUNCT
ejpam-1600	174	36	is	be	AUX
ejpam-1600	174	37	stable	stable	ADJ
ejpam-1600	174	38	then	then	ADV
ejpam-1600	174	39	the	the	DET
ejpam-1600	174	40	zero	zero	NUM
ejpam-1600	174	41	solution	solution	NOUN
ejpam-1600	174	42	of	of	ADP
ejpam-1600	174	43	the	the	DET
ejpam-1600	174	44	system	system	NOUN
ejpam-1600	174	45	(	(	PUNCT
ejpam-1600	174	46	23	23	NUM
ejpam-1600	174	47	)	)	PUNCT
ejpam-1600	174	48	is	be	AUX
ejpam-1600	174	49	asymptotically	asymptotically	ADV
ejpam-1600	174	50	stable	stable	ADJ
ejpam-1600	174	51	.	.	PUNCT
ejpam-1600	175	1	proof	proof	NOUN
ejpam-1600	175	2	.	.	PUNCT
ejpam-1600	176	1	let	let	VERB
ejpam-1600	176	2	0	0	NUM
ejpam-1600	176	3	<	<	X
ejpam-1600	176	4	ε	ε	PROPN
ejpam-1600	176	5	<	<	X
ejpam-1600	176	6	ρ	ρ	PROPN
ejpam-1600	176	7	and	and	CCONJ
ejpam-1600	176	8	t0	t0	PROPN
ejpam-1600	176	9	∈	∈	PROPN
ejpam-1600	176	10	r+	r+	PUNCT
ejpam-1600	176	11	be	be	AUX
ejpam-1600	176	12	given.set	given.set	NOUN
ejpam-1600	176	13	α0	α0	ADJ
ejpam-1600	176	14	=	=	SYM
ejpam-1600	176	15	mint∈r+α(t	mint∈r+α(t	PROPN
ejpam-1600	176	16	)	)	PUNCT
ejpam-1600	176	17	,	,	PUNCT
ejpam-1600	176	18	then	then	ADV
ejpam-1600	176	19	α0	α0	ADJ
ejpam-1600	176	20	>	>	X
ejpam-1600	176	21	0	0	NUM
ejpam-1600	176	22	follows	follow	VERB
ejpam-1600	176	23	from	from	ADP
ejpam-1600	176	24	the	the	DET
ejpam-1600	176	25	assumption	assumption	NOUN
ejpam-1600	176	26	(	(	PUNCT
ejpam-1600	176	27	ii	ii	NOUN
ejpam-1600	176	28	)	)	PUNCT
ejpam-1600	176	29	.	.	PUNCT
ejpam-1600	177	1	since	since	SCONJ
ejpam-1600	177	2	l(t	l(t	PROPN
ejpam-1600	177	3	,	,	PUNCT
ejpam-1600	177	4	u	u	NOUN
ejpam-1600	177	5	)	)	PUNCT
ejpam-1600	177	6	is	be	AUX
ejpam-1600	177	7	positive	positive	ADJ
ejpam-1600	177	8	definite	definite	ADJ
ejpam-1600	177	9	,	,	PUNCT
ejpam-1600	177	10	there	there	PRON
ejpam-1600	177	11	exists	exist	VERB
ejpam-1600	177	12	b	b	PROPN
ejpam-1600	177	13	∈	∈	PROPN
ejpam-1600	177	14	k	k	ADP
ejpam-1600	177	15	such	such	ADJ
ejpam-1600	177	16	that	that	DET
ejpam-1600	177	17	equation	equation	NOUN
ejpam-1600	177	18	(	(	PUNCT
ejpam-1600	177	19	24	24	NUM
ejpam-1600	177	20	)	)	PUNCT
ejpam-1600	177	21	holds	hold	VERB
ejpam-1600	177	22	.	.	PUNCT
ejpam-1600	178	1	ε1	ε1	PROPN
ejpam-1600	178	2	=	=	SYM
ejpam-1600	178	3	α0	α0	ADJ
ejpam-1600	178	4	b(ε	b(ε	NUM
ejpam-1600	178	5	)	)	PUNCT
ejpam-1600	178	6	,	,	PUNCT
ejpam-1600	178	7	(	(	PUNCT
ejpam-1600	178	8	27	27	NUM
ejpam-1600	178	9	)	)	PUNCT
ejpam-1600	178	10	where	where	SCONJ
ejpam-1600	178	11	ε	ε	PROPN
ejpam-1600	178	12	>	>	X
ejpam-1600	178	13	0	0	PROPN
ejpam-1600	178	14	.	.	PUNCT
ejpam-1600	179	1	then	then	ADV
ejpam-1600	179	2	the	the	DET
ejpam-1600	179	3	stability	stability	NOUN
ejpam-1600	179	4	of	of	ADP
ejpam-1600	179	5	the	the	DET
ejpam-1600	179	6	zero	zero	NUM
ejpam-1600	179	7	solution	solution	NOUN
ejpam-1600	179	8	(	(	PUNCT
ejpam-1600	179	9	22	22	NUM
ejpam-1600	179	10	)	)	PUNCT
ejpam-1600	179	11	implies	imply	VERB
ejpam-1600	179	12	that	that	SCONJ
ejpam-1600	179	13	,	,	PUNCT
ejpam-1600	179	14	given	give	VERB
ejpam-1600	179	15	ε1	ε1	PROPN
ejpam-1600	179	16	>	>	X
ejpam-1600	179	17	0	0	PUNCT
ejpam-1600	179	18	and	and	CCONJ
ejpam-1600	179	19	t0	t0	PROPN
ejpam-1600	179	20	∈	∈	PROPN
ejpam-1600	179	21	r+	r+	PUNCT
ejpam-1600	179	22	there	there	PRON
ejpam-1600	179	23	exists	exist	VERB
ejpam-1600	179	24	δ	δ	PROPN
ejpam-1600	179	25	=	=	SYM
ejpam-1600	179	26	δ(ε1	δ(ε1	PROPN
ejpam-1600	179	27	,	,	PUNCT
ejpam-1600	179	28	t0	t0	PROPN
ejpam-1600	179	29	)	)	PUNCT
ejpam-1600	179	30	such	such	ADJ
ejpam-1600	179	31	that	that	SCONJ
ejpam-1600	179	32	w0	w0	PROPN
ejpam-1600	179	33	<	<	X
ejpam-1600	179	34	δ	δ	PROPN
ejpam-1600	179	35	=	=	NOUN
ejpam-1600	179	36	⇒	⇒	PROPN
ejpam-1600	179	37	w(t	w(t	PROPN
ejpam-1600	179	38	,	,	PUNCT
ejpam-1600	179	39	t0	t0	PROPN
ejpam-1600	179	40	,	,	PUNCT
ejpam-1600	179	41	w0	w0	PROPN
ejpam-1600	179	42	)	)	PUNCT
ejpam-1600	179	43	<	<	X
ejpam-1600	179	44	ε1	ε1	PROPN
ejpam-1600	179	45	,	,	PUNCT
ejpam-1600	179	46	t	t	PROPN
ejpam-1600	179	47	≥	≥	PROPN
ejpam-1600	179	48	t0	t0	PROPN
ejpam-1600	179	49	,	,	PUNCT
ejpam-1600	179	50	where	where	SCONJ
ejpam-1600	179	51	w(t	w(t	PROPN
ejpam-1600	179	52	,	,	PUNCT
ejpam-1600	179	53	t0	t0	PROPN
ejpam-1600	179	54	,	,	PUNCT
ejpam-1600	179	55	w0	w0	PROPN
ejpam-1600	179	56	)	)	PUNCT
ejpam-1600	179	57	is	be	AUX
ejpam-1600	179	58	any	any	DET
ejpam-1600	179	59	solution	solution	NOUN
ejpam-1600	179	60	of	of	ADP
ejpam-1600	179	61	(	(	PUNCT
ejpam-1600	179	62	23	23	NUM
ejpam-1600	179	63	)	)	PUNCT
ejpam-1600	179	64	.	.	PUNCT
ejpam-1600	180	1	choose	choose	VERB
ejpam-1600	180	2	w0	w0	PROPN
ejpam-1600	180	3	=	=	PUNCT
ejpam-1600	180	4	l(t0,χ0	l(t0,χ0	NOUN
ejpam-1600	180	5	)	)	PUNCT
ejpam-1600	180	6	,	,	PUNCT
ejpam-1600	180	7	then	then	ADV
ejpam-1600	180	8	proceeding	proceed	VERB
ejpam-1600	180	9	as	as	ADP
ejpam-1600	180	10	in	in	ADP
ejpam-1600	180	11	the	the	DET
ejpam-1600	180	12	theorem	theorem	NOUN
ejpam-1600	180	13	4	4	NUM
ejpam-1600	180	14	with	with	ADP
ejpam-1600	180	15	ε1	ε1	PROPN
ejpam-1600	180	16	insted	inste	VERB
ejpam-1600	180	17	of	of	ADP
ejpam-1600	180	18	b(ε	b(ε	PROPN
ejpam-1600	180	19	)	)	PUNCT
ejpam-1600	180	20	,	,	PUNCT
ejpam-1600	180	21	we	we	PRON
ejpam-1600	180	22	can	can	AUX
ejpam-1600	180	23	prove	prove	VERB
ejpam-1600	180	24	that	that	SCONJ
ejpam-1600	180	25	the	the	DET
ejpam-1600	180	26	zero	zero	NUM
ejpam-1600	180	27	solution	solution	NOUN
ejpam-1600	180	28	of	of	ADP
ejpam-1600	180	29	(	(	PUNCT
ejpam-1600	180	30	23	23	NUM
ejpam-1600	180	31	)	)	PUNCT
ejpam-1600	180	32	is	be	AUX
ejpam-1600	180	33	stable	stable	ADJ
ejpam-1600	180	34	.	.	PUNCT
ejpam-1600	181	1	let	let	VERB
ejpam-1600	181	2	u(t	u(t	NOUN
ejpam-1600	181	3	,	,	PUNCT
ejpam-1600	181	4	t0,χ0	t0,χ0	PROPN
ejpam-1600	181	5	)	)	PUNCT
ejpam-1600	181	6	be	be	VERB
ejpam-1600	181	7	any	any	DET
ejpam-1600	181	8	solution	solution	NOUN
ejpam-1600	181	9	of	of	ADP
ejpam-1600	181	10	the	the	DET
ejpam-1600	181	11	system	system	NOUN
ejpam-1600	181	12	(	(	PUNCT
ejpam-1600	181	13	23	23	NUM
ejpam-1600	181	14	)	)	PUNCT
ejpam-1600	181	15	such	such	ADJ
ejpam-1600	181	16	that	that	SCONJ
ejpam-1600	181	17	d1[χ0,θ	d1[χ0,θ	NOUN
ejpam-1600	181	18	]	]	X
ejpam-1600	181	19	≤	≤	NUM
ejpam-1600	181	20	δ0	δ0	NOUN
ejpam-1600	181	21	where	where	SCONJ
ejpam-1600	181	22	δ0	δ0	NOUN
ejpam-1600	181	23	=	=	SYM
ejpam-1600	181	24	δ(t0	δ(t0	NOUN
ejpam-1600	181	25	,	,	PUNCT
ejpam-1600	181	26	1	1	NUM
ejpam-1600	181	27	2	2	NUM
ejpam-1600	181	28	ρ	ρ	NOUN
ejpam-1600	181	29	)	)	PUNCT
ejpam-1600	181	30	.	.	PUNCT
ejpam-1600	182	1	since	since	SCONJ
ejpam-1600	182	2	the	the	DET
ejpam-1600	182	3	zero	zero	NUM
ejpam-1600	182	4	solution	solution	NOUN
ejpam-1600	182	5	of	of	ADP
ejpam-1600	182	6	the	the	DET
ejpam-1600	182	7	system	system	NOUN
ejpam-1600	182	8	(	(	PUNCT
ejpam-1600	182	9	23	23	NUM
ejpam-1600	182	10	)	)	PUNCT
ejpam-1600	182	11	is	be	AUX
ejpam-1600	182	12	stable	stable	ADJ
ejpam-1600	182	13	,	,	PUNCT
ejpam-1600	182	14	it	it	PRON
ejpam-1600	182	15	follows	follow	VERB
ejpam-1600	182	16	that	that	SCONJ
ejpam-1600	182	17	d̃[u(t),θ	d̃[u(t),θ	NOUN
ejpam-1600	182	18	]	]	PUNCT
ejpam-1600	182	19	<	<	X
ejpam-1600	182	20	1	1	NUM
ejpam-1600	182	21	2	2	NUM
ejpam-1600	182	22	ρ	ρ	NOUN
ejpam-1600	182	23	,	,	PUNCT
ejpam-1600	182	24	t	t	PROPN
ejpam-1600	182	25	≥	≥	PROPN
ejpam-1600	182	26	t0	t0	PROPN
ejpam-1600	182	27	.	.	PUNCT
ejpam-1600	183	1	since	since	SCONJ
ejpam-1600	183	2	α(t	α(t	NOUN
ejpam-1600	183	3	)	)	PUNCT
ejpam-1600	183	4	−→∞	−→∞	PROPN
ejpam-1600	183	5	as	as	ADP
ejpam-1600	183	6	t	t	PROPN
ejpam-1600	183	7	−→∞	−→∞	PROPN
ejpam-1600	183	8	,	,	PUNCT
ejpam-1600	183	9	there	there	PRON
ejpam-1600	183	10	exists	exist	VERB
ejpam-1600	183	11	a	a	DET
ejpam-1600	183	12	number	number	NOUN
ejpam-1600	183	13	t	t	NOUN
ejpam-1600	183	14	=	=	SYM
ejpam-1600	183	15	t	t	PROPN
ejpam-1600	183	16	(	(	PUNCT
ejpam-1600	183	17	t0,ε	t0,ε	PROPN
ejpam-1600	183	18	)	)	PUNCT
ejpam-1600	183	19	>	>	X
ejpam-1600	183	20	0	0	PUNCT
ejpam-1600	183	21	such	such	ADJ
ejpam-1600	183	22	that	that	PRON
ejpam-1600	183	23	b(ε)α(t	b(ε)α(t	VERB
ejpam-1600	183	24	)	)	PUNCT
ejpam-1600	183	25	>	>	X
ejpam-1600	183	26	ε1	ε1	PROPN
ejpam-1600	183	27	,	,	PUNCT
ejpam-1600	183	28	t	t	PROPN
ejpam-1600	183	29	≥	≥	PROPN
ejpam-1600	183	30	t0	t0	PROPN
ejpam-1600	183	31	+	+	PROPN
ejpam-1600	183	32	t	t	PROPN
ejpam-1600	183	33	(	(	PUNCT
ejpam-1600	183	34	28	28	NUM
ejpam-1600	183	35	)	)	PUNCT
ejpam-1600	183	36	now	now	ADV
ejpam-1600	183	37	from	from	ADP
ejpam-1600	183	38	the	the	DET
ejpam-1600	183	39	theorem	theorem	ADJ
ejpam-1600	183	40	2	2	NUM
ejpam-1600	183	41	and	and	CCONJ
ejpam-1600	183	42	the	the	DET
ejpam-1600	183	43	relation	relation	NOUN
ejpam-1600	183	44	(	(	PUNCT
ejpam-1600	183	45	24	24	NUM
ejpam-1600	183	46	)	)	PUNCT
ejpam-1600	183	47	,	,	PUNCT
ejpam-1600	183	48	we	we	PRON
ejpam-1600	183	49	get	get	VERB
ejpam-1600	183	50	α(t)b(d̃[u	α(t)b(d̃[u	X
ejpam-1600	183	51	,	,	PUNCT
ejpam-1600	183	52	θ	θ	NOUN
ejpam-1600	183	53	]	]	X
ejpam-1600	183	54	)	)	PUNCT
ejpam-1600	183	55	≤	≤	NUM
ejpam-1600	183	56	α(t)l(t	α(t)l(t	NOUN
ejpam-1600	183	57	,	,	PUNCT
ejpam-1600	183	58	u	u	NOUN
ejpam-1600	183	59	)	)	PUNCT
ejpam-1600	183	60	≤	≤	NOUN
ejpam-1600	183	61	r(t	r(t	NOUN
ejpam-1600	183	62	)	)	PUNCT
ejpam-1600	183	63	,	,	PUNCT
ejpam-1600	183	64	t	t	PROPN
ejpam-1600	183	65	≥	≥	NUM
ejpam-1600	183	66	t0	t0	NUM
ejpam-1600	183	67	where	where	SCONJ
ejpam-1600	183	68	u(t	u(t	NOUN
ejpam-1600	183	69	)	)	PUNCT
ejpam-1600	183	70	=	=	SYM
ejpam-1600	183	71	u(t	u(t	NOUN
ejpam-1600	183	72	,	,	PUNCT
ejpam-1600	183	73	t0,χ0	t0,χ0	PROPN
ejpam-1600	183	74	)	)	PUNCT
ejpam-1600	183	75	is	be	AUX
ejpam-1600	183	76	any	any	DET
ejpam-1600	183	77	solution	solution	NOUN
ejpam-1600	183	78	of	of	ADP
ejpam-1600	183	79	(	(	PUNCT
ejpam-1600	183	80	23	23	NUM
ejpam-1600	183	81	)	)	PUNCT
ejpam-1600	183	82	such	such	ADJ
ejpam-1600	183	83	that	that	SCONJ
ejpam-1600	183	84	d1[χ0,θ	d1[χ0,θ	PROPN
ejpam-1600	183	85	]	]	X
ejpam-1600	183	86	≤	≤	NUM
ejpam-1600	183	87	δ0	δ0	NOUN
ejpam-1600	183	88	.	.	PUNCT
ejpam-1600	184	1	if	if	SCONJ
ejpam-1600	184	2	the	the	DET
ejpam-1600	184	3	zero	zero	NUM
ejpam-1600	184	4	solution	solution	NOUN
ejpam-1600	184	5	of	of	ADP
ejpam-1600	184	6	the	the	DET
ejpam-1600	184	7	system	system	NOUN
ejpam-1600	184	8	(	(	PUNCT
ejpam-1600	184	9	23	23	NUM
ejpam-1600	184	10	)	)	PUNCT
ejpam-1600	184	11	is	be	AUX
ejpam-1600	184	12	not	not	PART
ejpam-1600	184	13	asymptotically	asymptotically	ADV
ejpam-1600	184	14	stable	stable	ADJ
ejpam-1600	184	15	,	,	PUNCT
ejpam-1600	184	16	then	then	ADV
ejpam-1600	184	17	there	there	PRON
ejpam-1600	184	18	exists	exist	VERB
ejpam-1600	184	19	a	a	DET
ejpam-1600	184	20	sequence	sequence	NOUN
ejpam-1600	184	21	{	{	PUNCT
ejpam-1600	184	22	tk	tk	PROPN
ejpam-1600	184	23	}	}	PUNCT
ejpam-1600	184	24	,	,	PUNCT
ejpam-1600	184	25	tk	tk	PROPN
ejpam-1600	184	26	≥	≥	PROPN
ejpam-1600	184	27	t0	t0	PROPN
ejpam-1600	184	28	+	+	CCONJ
ejpam-1600	184	29	t	t	PROPN
ejpam-1600	184	30	and	and	CCONJ
ejpam-1600	184	31	tk	tk	PROPN
ejpam-1600	184	32	−→	−→	NOUN
ejpam-1600	184	33	∞	∞	PROPN
ejpam-1600	184	34	as	as	ADP
ejpam-1600	184	35	k	k	PROPN
ejpam-1600	184	36	→	→	SYM
ejpam-1600	184	37	∞	∞	PROPN
ejpam-1600	184	38	such	such	ADJ
ejpam-1600	184	39	that	that	SCONJ
ejpam-1600	184	40	d̃[u(tk),θ	d̃[u(tk),θ	NOUN
ejpam-1600	184	41	]	]	PUNCT
ejpam-1600	184	42	≥	≥	X
ejpam-1600	184	43	ε	ε	PROPN
ejpam-1600	184	44	for	for	ADP
ejpam-1600	184	45	some	some	DET
ejpam-1600	184	46	solution	solution	NOUN
ejpam-1600	184	47	u(t	u(t	NOUN
ejpam-1600	184	48	)	)	PUNCT
ejpam-1600	184	49	satisfying	satisfy	VERB
ejpam-1600	184	50	d1[χ0,θ	d1[χ0,θ	PROPN
ejpam-1600	184	51	]	]	X
ejpam-1600	184	52	≤	≤	NUM
ejpam-1600	184	53	δ0	δ0	NOUN
ejpam-1600	184	54	.	.	PUNCT
ejpam-1600	185	1	now	now	ADV
ejpam-1600	185	2	b(ε)α(t	b(ε)α(t	VERB
ejpam-1600	185	3	)	)	PUNCT
ejpam-1600	185	4	≤b(d̃[u(tk),θ])α(t	≤b(d̃[u(tk),θ])α(t	VERB
ejpam-1600	185	5	)	)	PUNCT
ejpam-1600	185	6	≤α(tk)l(tk	≤α(tk)l(tk	NOUN
ejpam-1600	185	7	,	,	PUNCT
ejpam-1600	185	8	u(tk	u(tk	NOUN
ejpam-1600	185	9	)	)	PUNCT
ejpam-1600	185	10	)	)	PUNCT
ejpam-1600	185	11	≤r(tk	≤r(tk	NOUN
ejpam-1600	185	12	)	)	PUNCT
ejpam-1600	186	1	<	<	X
ejpam-1600	186	2	ε1	ε1	VERB
ejpam-1600	186	3	for	for	ADP
ejpam-1600	186	4	tk	tk	PROPN
ejpam-1600	186	5	≥	≥	PROPN
ejpam-1600	186	6	t0	t0	PROPN
ejpam-1600	186	7	+	+	CCONJ
ejpam-1600	186	8	t	t	PROPN
ejpam-1600	186	9	which	which	PRON
ejpam-1600	186	10	is	be	AUX
ejpam-1600	186	11	a	a	DET
ejpam-1600	186	12	contraduction	contraduction	NOUN
ejpam-1600	186	13	.	.	PUNCT
ejpam-1600	187	1	hence	hence	ADV
ejpam-1600	187	2	the	the	DET
ejpam-1600	187	3	solution	solution	NOUN
ejpam-1600	187	4	of	of	ADP
ejpam-1600	187	5	ivp	ivp	PROPN
ejpam-1600	187	6	(	(	PUNCT
ejpam-1600	187	7	23	23	NUM
ejpam-1600	187	8	)	)	PUNCT
ejpam-1600	187	9	is	be	AUX
ejpam-1600	187	10	asymptotically	asymptotically	ADV
ejpam-1600	187	11	stable	stable	ADJ
ejpam-1600	187	12	and	and	CCONJ
ejpam-1600	187	13	the	the	DET
ejpam-1600	187	14	proof	proof	NOUN
ejpam-1600	187	15	is	be	AUX
ejpam-1600	187	16	complete	complete	ADJ
ejpam-1600	187	17	.	.	PUNCT
ejpam-1600	188	1	the	the	DET
ejpam-1600	188	2	next	next	ADJ
ejpam-1600	188	3	theorem	theorem	NOUN
ejpam-1600	188	4	gives	give	VERB
ejpam-1600	188	5	sufficient	sufficient	ADJ
ejpam-1600	188	6	conditions	condition	NOUN
ejpam-1600	188	7	for	for	ADP
ejpam-1600	188	8	the	the	DET
ejpam-1600	188	9	uniformly	uniformly	ADV
ejpam-1600	188	10	asymptotic	asymptotic	ADJ
ejpam-1600	188	11	stablity	stablity	NOUN
ejpam-1600	188	12	of	of	ADP
ejpam-1600	188	13	ivp	ivp	PROPN
ejpam-1600	188	14	(	(	PUNCT
ejpam-1600	188	15	23	23	NUM
ejpam-1600	188	16	)	)	PUNCT
ejpam-1600	188	17	.	.	PUNCT
ejpam-1600	189	1	as	as	SCONJ
ejpam-1600	189	2	the	the	DET
ejpam-1600	189	3	proofs	proof	NOUN
ejpam-1600	189	4	are	be	AUX
ejpam-1600	189	5	similar	similar	ADJ
ejpam-1600	189	6	to	to	ADP
ejpam-1600	189	7	that	that	PRON
ejpam-1600	189	8	in	in	ADP
ejpam-1600	189	9	[	[	X
ejpam-1600	189	10	1	1	X
ejpam-1600	189	11	]	]	PUNCT
ejpam-1600	189	12	we	we	PRON
ejpam-1600	189	13	omit	omit	VERB
ejpam-1600	189	14	them	they	PRON
ejpam-1600	189	15	.	.	PUNCT
ejpam-1600	190	1	references	reference	NOUN
ejpam-1600	190	2	196	196	NUM
ejpam-1600	190	3	theorem	theorem	NOUN
ejpam-1600	190	4	6	6	NUM
ejpam-1600	190	5	.	.	PUNCT
ejpam-1600	190	6	assume	assume	VERB
ejpam-1600	190	7	that	that	SCONJ
ejpam-1600	190	8	there	there	PRON
ejpam-1600	190	9	exists	exist	VERB
ejpam-1600	190	10	a	a	DET
ejpam-1600	190	11	function	function	NOUN
ejpam-1600	190	12	l(t	l(t	NOUN
ejpam-1600	190	13	,	,	PUNCT
ejpam-1600	190	14	u	u	NOUN
ejpam-1600	190	15	)	)	PUNCT
ejpam-1600	190	16	satisfies	satisfy	VERB
ejpam-1600	190	17	the	the	DET
ejpam-1600	190	18	following	follow	VERB
ejpam-1600	190	19	properties	property	NOUN
ejpam-1600	190	20	(	(	PUNCT
ejpam-1600	190	21	i	i	NOUN
ejpam-1600	190	22	)	)	PUNCT
ejpam-1600	190	23	l	l	PROPN
ejpam-1600	190	24	∈	∈	PROPN
ejpam-1600	190	25	c[r+	c[r+	NOUN
ejpam-1600	190	26	×	×	PROPN
ejpam-1600	190	27	b	b	PROPN
ejpam-1600	190	28	,	,	PUNCT
ejpam-1600	190	29	r+	r+	X
ejpam-1600	190	30	]	]	PUNCT
ejpam-1600	190	31	where	where	SCONJ
ejpam-1600	190	32	b	b	X
ejpam-1600	190	33	=	=	SYM
ejpam-1600	190	34	b(θ	b(θ	PROPN
ejpam-1600	190	35	,	,	PUNCT
ejpam-1600	190	36	ρ	ρ	PROPN
ejpam-1600	190	37	)	)	PUNCT
ejpam-1600	190	38	,	,	PUNCT
ejpam-1600	190	39	l(t	l(t	PROPN
ejpam-1600	190	40	,	,	PUNCT
ejpam-1600	190	41	u	u	NOUN
ejpam-1600	190	42	)	)	PUNCT
ejpam-1600	190	43	is	be	AUX
ejpam-1600	190	44	positive	positive	ADJ
ejpam-1600	190	45	definite	definite	ADJ
ejpam-1600	190	46	,	,	PUNCT
ejpam-1600	190	47	decrescent	decrescent	ADJ
ejpam-1600	190	48	and	and	CCONJ
ejpam-1600	190	49	locally	locally	ADV
ejpam-1600	190	50	lipschitzian	lipschitzian	ADJ
ejpam-1600	190	51	in	in	ADP
ejpam-1600	190	52	u	u	NOUN
ejpam-1600	190	53	,	,	PUNCT
ejpam-1600	190	54	(	(	PUNCT
ejpam-1600	190	55	ii	ii	NOUN
ejpam-1600	190	56	)	)	PUNCT
ejpam-1600	190	57	d−l(t	d−l(t	NOUN
ejpam-1600	190	58	,	,	PUNCT
ejpam-1600	190	59	u(t	u(t	NOUN
ejpam-1600	190	60	)	)	PUNCT
ejpam-1600	190	61	)	)	PUNCT
ejpam-1600	190	62	<	<	X
ejpam-1600	190	63	−c(d̃[u(t),θ	−c(d̃[u(t),θ	NUM
ejpam-1600	190	64	]	]	SYM
ejpam-1600	190	65	)	)	PUNCT
ejpam-1600	190	66	(	(	PUNCT
ejpam-1600	190	67	29	29	NUM
ejpam-1600	190	68	)	)	PUNCT
ejpam-1600	190	69	for	for	ADP
ejpam-1600	190	70	t	t	PROPN
ejpam-1600	190	71	≥	≥	PROPN
ejpam-1600	190	72	t0	t0	PROPN
ejpam-1600	190	73	,	,	PUNCT
ejpam-1600	190	74	u	u	PROPN
ejpam-1600	190	75	∈	∈	PROPN
ejpam-1600	190	76	e0	e0	PROPN
ejpam-1600	190	77	and	and	CCONJ
ejpam-1600	190	78	c	c	NOUN
ejpam-1600	190	79	∈	∈	PROPN
ejpam-1600	191	1	k	k	NOUN
ejpam-1600	191	2	then	then	ADV
ejpam-1600	191	3	the	the	DET
ejpam-1600	191	4	zero	zero	NUM
ejpam-1600	191	5	solution	solution	NOUN
ejpam-1600	191	6	of	of	ADP
ejpam-1600	191	7	(	(	PUNCT
ejpam-1600	191	8	23	23	NUM
ejpam-1600	191	9	)	)	PUNCT
ejpam-1600	191	10	is	be	AUX
ejpam-1600	191	11	uniformly	uniformly	ADV
ejpam-1600	191	12	assymptotically	assymptotically	ADV
ejpam-1600	191	13	stable	stable	ADJ
ejpam-1600	191	14	.	.	PUNCT
ejpam-1600	192	1	our	our	PRON
ejpam-1600	192	2	final	final	ADJ
ejpam-1600	192	3	stability	stability	NOUN
ejpam-1600	192	4	result	result	NOUN
ejpam-1600	192	5	is	be	AUX
ejpam-1600	192	6	a	a	DET
ejpam-1600	192	7	general	general	ADJ
ejpam-1600	192	8	result	result	NOUN
ejpam-1600	192	9	which	which	PRON
ejpam-1600	192	10	offers	offer	VERB
ejpam-1600	192	11	various	various	ADJ
ejpam-1600	192	12	stability	stability	NOUN
ejpam-1600	192	13	criteria	criterion	NOUN
ejpam-1600	192	14	in	in	ADP
ejpam-1600	192	15	a	a	DET
ejpam-1600	192	16	single	single	ADJ
ejpam-1600	192	17	setup	setup	NOUN
ejpam-1600	192	18	.	.	PUNCT
ejpam-1600	193	1	the	the	DET
ejpam-1600	193	2	proof	proof	NOUN
ejpam-1600	193	3	of	of	ADP
ejpam-1600	193	4	this	this	DET
ejpam-1600	193	5	theorem	theorem	NOUN
ejpam-1600	193	6	,	,	PUNCT
ejpam-1600	193	7	which	which	PRON
ejpam-1600	193	8	can	can	AUX
ejpam-1600	193	9	be	be	AUX
ejpam-1600	193	10	obtained	obtain	VERB
ejpam-1600	193	11	using	use	VERB
ejpam-1600	193	12	the	the	DET
ejpam-1600	193	13	comparison	comparison	NOUN
ejpam-1600	193	14	results	result	NOUN
ejpam-1600	193	15	given	give	VERB
ejpam-1600	193	16	in	in	ADP
ejpam-1600	193	17	theorem	theorem	ADJ
ejpam-1600	193	18	3	3	NUM
ejpam-1600	193	19	,	,	PUNCT
ejpam-1600	193	20	is	be	AUX
ejpam-1600	193	21	omitted	omit	VERB
ejpam-1600	193	22	.	.	PUNCT
ejpam-1600	194	1	theorem	theorem	ADJ
ejpam-1600	194	2	7	7	NUM
ejpam-1600	194	3	.	.	PUNCT
ejpam-1600	194	4	assume	assume	VERB
ejpam-1600	194	5	that	that	SCONJ
ejpam-1600	194	6	there	there	PRON
ejpam-1600	194	7	exists	exist	VERB
ejpam-1600	194	8	a	a	DET
ejpam-1600	194	9	function	function	NOUN
ejpam-1600	194	10	l(t	l(t	NOUN
ejpam-1600	194	11	,	,	PUNCT
ejpam-1600	194	12	u	u	NOUN
ejpam-1600	194	13	)	)	PUNCT
ejpam-1600	194	14	satisfying	satisfy	VERB
ejpam-1600	194	15	properties	property	NOUN
ejpam-1600	194	16	(	(	PUNCT
ejpam-1600	194	17	i	i	NOUN
ejpam-1600	194	18	)	)	PUNCT
ejpam-1600	194	19	,	,	PUNCT
ejpam-1600	194	20	(	(	PUNCT
ejpam-1600	194	21	ii	ii	NOUN
ejpam-1600	194	22	)	)	PUNCT
ejpam-1600	194	23	and	and	CCONJ
ejpam-1600	194	24	(	(	PUNCT
ejpam-1600	194	25	iii	iii	NOUN
ejpam-1600	194	26	)	)	PUNCT
ejpam-1600	194	27	of	of	ADP
ejpam-1600	194	28	the	the	DET
ejpam-1600	194	29	theorem	theorem	NOUN
ejpam-1600	194	30	3	3	NUM
ejpam-1600	194	31	then	then	ADV
ejpam-1600	194	32	the	the	DET
ejpam-1600	194	33	stability	stability	NOUN
ejpam-1600	194	34	properties	property	NOUN
ejpam-1600	194	35	of	of	ADP
ejpam-1600	194	36	the	the	DET
ejpam-1600	194	37	zero	zero	NUM
ejpam-1600	194	38	solution	solution	NOUN
ejpam-1600	194	39	of	of	ADP
ejpam-1600	194	40	ivp	ivp	PROPN
ejpam-1600	194	41	(	(	PUNCT
ejpam-1600	194	42	22	22	NUM
ejpam-1600	194	43	)	)	PUNCT
ejpam-1600	194	44	implies	imply	VERB
ejpam-1600	194	45	the	the	DET
ejpam-1600	194	46	corresponding	correspond	VERB
ejpam-1600	194	47	properties	property	NOUN
ejpam-1600	194	48	of	of	ADP
ejpam-1600	194	49	the	the	DET
ejpam-1600	194	50	zero	zero	NUM
ejpam-1600	194	51	solution	solution	NOUN
ejpam-1600	194	52	of	of	ADP
ejpam-1600	194	53	ivp	ivp	PROPN
ejpam-1600	194	54	(	(	PUNCT
ejpam-1600	194	55	23	23	NUM
ejpam-1600	194	56	)	)	PUNCT
ejpam-1600	194	57	.	.	PUNCT
ejpam-1600	195	1	acknowledgements	acknowledgement	NOUN
ejpam-1600	195	2	this	this	DET
ejpam-1600	195	3	work	work	NOUN
ejpam-1600	195	4	has	have	AUX
ejpam-1600	195	5	been	be	AUX
ejpam-1600	195	6	done	do	VERB
ejpam-1600	195	7	under	under	ADP
ejpam-1600	195	8	the	the	DET
ejpam-1600	195	9	project	project	NOUN
ejpam-1600	195	10	no	no	INTJ
ejpam-1600	195	11	.	.	PUNCT
ejpam-1600	196	1	sr	sr	PROPN
ejpam-1600	196	2	/	/	SYM
ejpam-1600	196	3	s4	s4	PROPN
ejpam-1600	196	4	/	/	SYM
ejpam-1600	196	5	ms	ms	NOUN
ejpam-1600	196	6	:	:	PUNCT
ejpam-1600	196	7	491/07	491/07	NUM
ejpam-1600	196	8	sanctioned	sanction	VERB
ejpam-1600	196	9	by	by	ADP
ejpam-1600	196	10	department	department	PROPN
ejpam-1600	196	11	of	of	ADP
ejpam-1600	196	12	science	science	NOUN
ejpam-1600	196	13	and	and	CCONJ
ejpam-1600	196	14	technology	technology	NOUN
ejpam-1600	196	15	,	,	PUNCT
ejpam-1600	196	16	government	government	NOUN
ejpam-1600	196	17	of	of	ADP
ejpam-1600	196	18	india	india	PROPN
ejpam-1600	196	19	.	.	PUNCT
ejpam-1600	197	1	the	the	DET
ejpam-1600	197	2	authors	author	NOUN
ejpam-1600	197	3	acknowledge	acknowledge	VERB
ejpam-1600	197	4	their	their	PRON
ejpam-1600	197	5	support	support	NOUN
ejpam-1600	197	6	.	.	PUNCT
ejpam-1600	198	1	references	reference	NOUN
ejpam-1600	198	2	[	[	X
ejpam-1600	198	3	1	1	NUM
ejpam-1600	198	4	]	]	PUNCT
ejpam-1600	198	5	z	z	NOUN
ejpam-1600	198	6	drici	drici	NOUN
ejpam-1600	198	7	,	,	PUNCT
ejpam-1600	198	8	f	f	PROPN
ejpam-1600	198	9	mcrae	mcrae	PROPN
ejpam-1600	198	10	,	,	PUNCT
ejpam-1600	198	11	j	j	PROPN
ejpam-1600	198	12	devi	devi	PROPN
ejpam-1600	198	13	.	.	PUNCT
ejpam-1600	199	1	stability	stability	NOUN
ejpam-1600	199	2	results	result	VERB
ejpam-1600	199	3	for	for	ADP
ejpam-1600	199	4	set	set	VERB
ejpam-1600	199	5	differential	differential	ADJ
ejpam-1600	199	6	equations	equation	NOUN
ejpam-1600	199	7	with	with	ADP
ejpam-1600	199	8	causal	causal	ADJ
ejpam-1600	199	9	maps	map	NOUN
ejpam-1600	199	10	,	,	PUNCT
ejpam-1600	199	11	dynamic	dynamic	ADJ
ejpam-1600	199	12	systems	system	NOUN
ejpam-1600	199	13	and	and	CCONJ
ejpam-1600	199	14	applications	application	NOUN
ejpam-1600	199	15	1s	1s	NUM
ejpam-1600	199	16	.	.	PUNCT
ejpam-1600	200	1	451	451	NUM
ejpam-1600	200	2	-	-	SYM
ejpam-1600	200	3	464	464	NUM
ejpam-1600	200	4	.	.	PUNCT
ejpam-1600	201	1	2006	2006	NUM
ejpam-1600	201	2	.	.	PUNCT
ejpam-1600	202	1	[	[	X
ejpam-1600	202	2	2	2	NUM
ejpam-1600	202	3	]	]	PUNCT
ejpam-1600	202	4	v	v	NOUN
ejpam-1600	202	5	lakshmikantham	lakshmikantham	NOUN
ejpam-1600	202	6	and	and	CCONJ
ejpam-1600	202	7	r	r	NOUN
ejpam-1600	202	8	mohan	mohan	PROPN
ejpam-1600	202	9	.	.	PUNCT
ejpam-1600	203	1	theory	theory	NOUN
ejpam-1600	203	2	of	of	ADP
ejpam-1600	203	3	integro	integro	PROPN
ejpam-1600	203	4	differential	differential	ADJ
ejpam-1600	203	5	equations	equation	NOUN
ejpam-1600	203	6	,	,	PUNCT
ejpam-1600	203	7	gordan	gordan	PROPN
ejpam-1600	203	8	and	and	CCONJ
ejpam-1600	203	9	breach	breach	VERB
ejpam-1600	203	10	science	science	NOUN
ejpam-1600	203	11	publishers	publisher	NOUN
ejpam-1600	203	12	,	,	PUNCT
ejpam-1600	203	13	amsterdam	amsterdam	NOUN
ejpam-1600	203	14	,	,	PUNCT
ejpam-1600	203	15	1995	1995	NUM
ejpam-1600	203	16	.	.	PUNCT
ejpam-1600	204	1	[	[	X
ejpam-1600	204	2	3	3	X
ejpam-1600	204	3	]	]	X
ejpam-1600	204	4	m	m	VERB
ejpam-1600	204	5	lakshmikantham	lakshmikantham	ADJ
ejpam-1600	204	6	and	and	CCONJ
ejpam-1600	204	7	s	s	VERB
ejpam-1600	204	8	leela	leela	PROPN
ejpam-1600	204	9	.	.	PUNCT
ejpam-1600	205	1	differential	differential	PROPN
ejpam-1600	205	2	and	and	CCONJ
ejpam-1600	205	3	integral	integral	ADJ
ejpam-1600	205	4	inequalities	inequality	NOUN
ejpam-1600	205	5	,	,	PUNCT
ejpam-1600	205	6	vol.i	vol.i	PROPN
ejpam-1600	205	7	and	and	CCONJ
ejpam-1600	205	8	ii	ii	PROPN
ejpam-1600	205	9	,	,	PUNCT
ejpam-1600	205	10	academic	academic	ADJ
ejpam-1600	205	11	press	press	NOUN
ejpam-1600	205	12	,	,	PUNCT
ejpam-1600	205	13	newyork	newyork	NOUN
ejpam-1600	205	14	,	,	PUNCT
ejpam-1600	205	15	1969	1969	NUM
ejpam-1600	205	16	.	.	PUNCT
ejpam-1600	206	1	[	[	X
ejpam-1600	206	2	4	4	X
ejpam-1600	206	3	]	]	SYM
ejpam-1600	206	4	v	v	ADP
ejpam-1600	206	5	lakshmikantham	lakshmikantham	NOUN
ejpam-1600	206	6	,	,	PUNCT
ejpam-1600	206	7	t	t	NOUN
ejpam-1600	206	8	gnanabhaskar	gnanabhaskar	NOUN
ejpam-1600	206	9	and	and	CCONJ
ejpam-1600	206	10	j	j	PROPN
ejpam-1600	206	11	devi	devi	PROPN
ejpam-1600	206	12	.	.	PUNCT
ejpam-1600	206	13	theory	theory	NOUN
ejpam-1600	206	14	of	of	ADP
ejpam-1600	206	15	set	set	VERB
ejpam-1600	206	16	differential	differential	ADJ
ejpam-1600	206	17	equations	equation	NOUN
ejpam-1600	206	18	in	in	ADP
ejpam-1600	206	19	metric	metric	ADJ
ejpam-1600	206	20	spaces	space	NOUN
ejpam-1600	206	21	,	,	PUNCT
ejpam-1600	206	22	cambridge	cambridge	NOUN
ejpam-1600	206	23	scientific	scientific	ADJ
ejpam-1600	206	24	publishers	publisher	NOUN
ejpam-1600	206	25	,	,	PUNCT
ejpam-1600	206	26	2006	2006	NUM
ejpam-1600	206	27	.	.	PUNCT