id	sid	tid	token	lemma	pos
ejpam-1478	1	1	4_269611_hristova.dvi	4_269611_hristova.dvi	PROPN
ejpam-1478	1	2	european	european	PROPN
ejpam-1478	1	3	journal	journal	PROPN
ejpam-1478	1	4	of	of	ADP
ejpam-1478	1	5	pure	pure	ADJ
ejpam-1478	1	6	and	and	CCONJ
ejpam-1478	1	7	applied	apply	VERB
ejpam-1478	1	8	mathematics	mathematic	NOUN
ejpam-1478	1	9	vol	vol	NOUN
ejpam-1478	1	10	.	.	PROPN
ejpam-1478	1	11	5	5	NUM
ejpam-1478	1	12	,	,	PUNCT
ejpam-1478	1	13	no	no	INTJ
ejpam-1478	1	14	.	.	NOUN
ejpam-1478	1	15	1	1	NUM
ejpam-1478	1	16	,	,	PUNCT
ejpam-1478	1	17	2012	2012	NUM
ejpam-1478	1	18	,	,	PUNCT
ejpam-1478	1	19	30	30	NUM
ejpam-1478	1	20	-	-	SYM
ejpam-1478	1	21	44	44	NUM
ejpam-1478	1	22	issn	issn	PROPN
ejpam-1478	1	23	1307	1307	NUM
ejpam-1478	1	24	-	-	SYM
ejpam-1478	1	25	5543	5543	NUM
ejpam-1478	1	26	–	–	PUNCT
ejpam-1478	1	27	www.ejpam.com	www.ejpam.com	X
ejpam-1478	1	28	special	special	ADJ
ejpam-1478	1	29	issue	issue	NOUN
ejpam-1478	1	30	for	for	ADP
ejpam-1478	1	31	the	the	DET
ejpam-1478	1	32	international	international	ADJ
ejpam-1478	1	33	conference	conference	NOUN
ejpam-1478	1	34	on	on	ADP
ejpam-1478	1	35	applied	apply	VERB
ejpam-1478	1	36	analysis	analysis	NOUN
ejpam-1478	1	37	and	and	CCONJ
ejpam-1478	1	38	algebra	algebra	NOUN
ejpam-1478	1	39	29	29	NUM
ejpam-1478	1	40	june	june	PROPN
ejpam-1478	1	41	02	02	NUM
ejpam-1478	1	42	july	july	PROPN
ejpam-1478	1	43	2011	2011	NUM
ejpam-1478	1	44	,	,	PUNCT
ejpam-1478	1	45	istanbul	istanbul	PROPN
ejpam-1478	1	46	turkey	turkey	PROPN
ejpam-1478	1	47	practical	practical	ADJ
ejpam-1478	1	48	stability	stability	NOUN
ejpam-1478	1	49	of	of	ADP
ejpam-1478	1	50	impulsive	impulsive	ADJ
ejpam-1478	1	51	differential	differential	ADJ
ejpam-1478	1	52	equations	equation	NOUN
ejpam-1478	1	53	with	with	ADP
ejpam-1478	1	54	“	"	PUNCT
ejpam-1478	1	55	supremum	supremum	ADJ
ejpam-1478	1	56	”	"	PUNCT
ejpam-1478	1	57	by	by	ADP
ejpam-1478	1	58	integral	integral	ADJ
ejpam-1478	1	59	inequalities	inequality	NOUN
ejpam-1478	1	60	snezhana	snezhana	VERB
ejpam-1478	1	61	hristova	hristova	PROPN
ejpam-1478	1	62	1∗	1∗	NUM
ejpam-1478	1	63	,	,	PUNCT
ejpam-1478	1	64	kremena	kremena	X
ejpam-1478	1	65	stefanova	stefanova	PROPN
ejpam-1478	1	66	2	2	NUM
ejpam-1478	1	67	1	1	NUM
ejpam-1478	1	68	department	department	NOUN
ejpam-1478	1	69	of	of	ADP
ejpam-1478	1	70	applied	apply	VERB
ejpam-1478	1	71	mathematics	mathematic	NOUN
ejpam-1478	1	72	and	and	CCONJ
ejpam-1478	1	73	modeling	modeling	NOUN
ejpam-1478	1	74	,	,	PUNCT
ejpam-1478	1	75	faculty	faculty	NOUN
ejpam-1478	1	76	of	of	ADP
ejpam-1478	1	77	mathematics	mathematic	NOUN
ejpam-1478	1	78	and	and	CCONJ
ejpam-1478	1	79	informatics	informatic	NOUN
ejpam-1478	1	80	,	,	PUNCT
ejpam-1478	1	81	plovdiv	plovdiv	PROPN
ejpam-1478	1	82	university	university	PROPN
ejpam-1478	1	83	,	,	PUNCT
ejpam-1478	1	84	plovdiv	plovdiv	PROPN
ejpam-1478	1	85	,	,	PUNCT
ejpam-1478	1	86	bulgaria	bulgaria	PROPN
ejpam-1478	1	87	2	2	NUM
ejpam-1478	1	88	department	department	NOUN
ejpam-1478	1	89	of	of	ADP
ejpam-1478	1	90	computer	computer	NOUN
ejpam-1478	1	91	technologies	technology	NOUN
ejpam-1478	1	92	,	,	PUNCT
ejpam-1478	1	93	faculty	faculty	NOUN
ejpam-1478	1	94	of	of	ADP
ejpam-1478	1	95	mathematics	mathematic	NOUN
ejpam-1478	1	96	and	and	CCONJ
ejpam-1478	1	97	informatics	informatic	NOUN
ejpam-1478	1	98	,	,	PUNCT
ejpam-1478	1	99	plovdiv	plovdiv	PROPN
ejpam-1478	1	100	university	university	PROPN
ejpam-1478	1	101	,	,	PUNCT
ejpam-1478	1	102	plovdiv	plovdiv	PROPN
ejpam-1478	1	103	,	,	PUNCT
ejpam-1478	1	104	bulgaria	bulgaria	PROPN
ejpam-1478	1	105	abstract	abstract	NOUN
ejpam-1478	1	106	.	.	PUNCT
ejpam-1478	2	1	the	the	DET
ejpam-1478	2	2	paper	paper	NOUN
ejpam-1478	2	3	deals	deal	VERB
ejpam-1478	2	4	with	with	ADP
ejpam-1478	2	5	some	some	DET
ejpam-1478	2	6	stability	stability	NOUN
ejpam-1478	2	7	properties	property	NOUN
ejpam-1478	2	8	of	of	ADP
ejpam-1478	2	9	the	the	DET
ejpam-1478	2	10	solutions	solution	NOUN
ejpam-1478	2	11	of	of	ADP
ejpam-1478	2	12	impulsive	impulsive	ADJ
ejpam-1478	2	13	differential	differential	ADJ
ejpam-1478	2	14	equations	equation	NOUN
ejpam-1478	2	15	with	with	ADP
ejpam-1478	2	16	“	"	PUNCT
ejpam-1478	2	17	supremum	supremum	ADJ
ejpam-1478	2	18	”	"	PUNCT
ejpam-1478	2	19	.	.	PUNCT
ejpam-1478	3	1	initially	initially	ADV
ejpam-1478	3	2	several	several	ADJ
ejpam-1478	3	3	integro	integro	ADJ
ejpam-1478	3	4	-	-	PUNCT
ejpam-1478	3	5	summation	summation	NOUN
ejpam-1478	3	6	inequalities	inequality	NOUN
ejpam-1478	3	7	for	for	ADP
ejpam-1478	3	8	piecewise	piecewise	NOUN
ejpam-1478	3	9	continuous	continuous	ADJ
ejpam-1478	3	10	functions	function	NOUN
ejpam-1478	3	11	are	be	AUX
ejpam-1478	3	12	solved	solve	VERB
ejpam-1478	3	13	.	.	PUNCT
ejpam-1478	4	1	the	the	DET
ejpam-1478	4	2	main	main	ADJ
ejpam-1478	4	3	characteristic	characteristic	NOUN
ejpam-1478	4	4	of	of	ADP
ejpam-1478	4	5	the	the	DET
ejpam-1478	4	6	considered	consider	VERB
ejpam-1478	4	7	inequalities	inequality	NOUN
ejpam-1478	4	8	is	be	AUX
ejpam-1478	4	9	the	the	DET
ejpam-1478	4	10	presence	presence	NOUN
ejpam-1478	4	11	of	of	ADP
ejpam-1478	4	12	the	the	DET
ejpam-1478	4	13	supremum	supremum	NOUN
ejpam-1478	4	14	of	of	ADP
ejpam-1478	4	15	the	the	DET
ejpam-1478	4	16	unknown	unknown	ADJ
ejpam-1478	4	17	function	function	NOUN
ejpam-1478	4	18	over	over	ADP
ejpam-1478	4	19	a	a	DET
ejpam-1478	4	20	past	past	ADJ
ejpam-1478	4	21	time	time	NOUN
ejpam-1478	4	22	interval	interval	NOUN
ejpam-1478	4	23	.	.	PUNCT
ejpam-1478	5	1	these	these	DET
ejpam-1478	5	2	inequalities	inequality	NOUN
ejpam-1478	5	3	are	be	AUX
ejpam-1478	5	4	generalizations	generalization	NOUN
ejpam-1478	5	5	of	of	ADP
ejpam-1478	5	6	bihari	bihari	PROPN
ejpam-1478	5	7	’s	’s	PART
ejpam-1478	5	8	integral	integral	ADJ
ejpam-1478	5	9	inequality	inequality	NOUN
ejpam-1478	5	10	.	.	PUNCT
ejpam-1478	6	1	they	they	PRON
ejpam-1478	6	2	are	be	AUX
ejpam-1478	6	3	base	base	NOUN
ejpam-1478	6	4	of	of	ADP
ejpam-1478	6	5	studying	study	VERB
ejpam-1478	6	6	the	the	DET
ejpam-1478	6	7	practical	practical	ADJ
ejpam-1478	6	8	stability	stability	NOUN
ejpam-1478	6	9	as	as	ADV
ejpam-1478	6	10	well	well	ADV
ejpam-1478	6	11	as	as	ADP
ejpam-1478	6	12	the	the	DET
ejpam-1478	6	13	uniform	uniform	ADJ
ejpam-1478	6	14	practical	practical	ADJ
ejpam-1478	6	15	stability	stability	NOUN
ejpam-1478	6	16	of	of	ADP
ejpam-1478	6	17	the	the	DET
ejpam-1478	6	18	solutions	solution	NOUN
ejpam-1478	6	19	of	of	ADP
ejpam-1478	6	20	nonlinear	nonlinear	ADJ
ejpam-1478	6	21	impulsive	impulsive	ADJ
ejpam-1478	6	22	differential	differential	ADJ
ejpam-1478	6	23	equations	equation	NOUN
ejpam-1478	6	24	with	with	ADP
ejpam-1478	6	25	“	"	PUNCT
ejpam-1478	6	26	supremum	supremum	ADJ
ejpam-1478	6	27	”	"	PUNCT
ejpam-1478	6	28	.	.	PUNCT
ejpam-1478	7	1	2000	2000	NUM
ejpam-1478	7	2	mathematics	mathematic	NOUN
ejpam-1478	7	3	subject	subject	NOUN
ejpam-1478	7	4	classifications	classification	NOUN
ejpam-1478	7	5	:	:	PUNCT
ejpam-1478	7	6	26d99	26d99	NUM
ejpam-1478	7	7	,	,	PUNCT
ejpam-1478	7	8	34a37	34a37	NUM
ejpam-1478	7	9	,	,	PUNCT
ejpam-1478	7	10	34d99	34d99	NUM
ejpam-1478	7	11	key	key	ADJ
ejpam-1478	7	12	words	word	NOUN
ejpam-1478	7	13	and	and	CCONJ
ejpam-1478	7	14	phrases	phrase	NOUN
ejpam-1478	7	15	:	:	PUNCT
ejpam-1478	7	16	integral	integral	ADJ
ejpam-1478	7	17	inequality	inequality	NOUN
ejpam-1478	7	18	,	,	PUNCT
ejpam-1478	7	19	supremum	supremum	ADJ
ejpam-1478	7	20	,	,	PUNCT
ejpam-1478	7	21	practical	practical	ADJ
ejpam-1478	7	22	stability	stability	NOUN
ejpam-1478	7	23	,	,	PUNCT
ejpam-1478	7	24	impulses	impulse	VERB
ejpam-1478	7	25	1	1	NUM
ejpam-1478	7	26	.	.	PUNCT
ejpam-1478	8	1	introduction	introduction	NOUN
ejpam-1478	8	2	in	in	ADP
ejpam-1478	8	3	the	the	DET
ejpam-1478	8	4	last	last	ADJ
ejpam-1478	8	5	few	few	ADJ
ejpam-1478	8	6	decades	decade	NOUN
ejpam-1478	8	7	great	great	ADJ
ejpam-1478	8	8	attention	attention	NOUN
ejpam-1478	8	9	has	have	AUX
ejpam-1478	8	10	been	be	AUX
ejpam-1478	8	11	paid	pay	VERB
ejpam-1478	8	12	to	to	ADP
ejpam-1478	8	13	automatic	automatic	ADJ
ejpam-1478	8	14	control	control	NOUN
ejpam-1478	8	15	systems	system	NOUN
ejpam-1478	8	16	and	and	CCONJ
ejpam-1478	8	17	their	their	PRON
ejpam-1478	8	18	applications	application	NOUN
ejpam-1478	8	19	to	to	ADP
ejpam-1478	8	20	computational	computational	ADJ
ejpam-1478	8	21	mathematics	mathematic	NOUN
ejpam-1478	8	22	and	and	CCONJ
ejpam-1478	8	23	modeling	modeling	NOUN
ejpam-1478	8	24	.	.	PUNCT
ejpam-1478	9	1	many	many	ADJ
ejpam-1478	9	2	problems	problem	NOUN
ejpam-1478	9	3	in	in	ADP
ejpam-1478	9	4	the	the	DET
ejpam-1478	9	5	control	control	NOUN
ejpam-1478	9	6	theory	theory	NOUN
ejpam-1478	9	7	correspond	correspond	VERB
ejpam-1478	9	8	to	to	ADP
ejpam-1478	9	9	the	the	DET
ejpam-1478	9	10	maximal	maximal	ADJ
ejpam-1478	9	11	deviation	deviation	NOUN
ejpam-1478	9	12	of	of	ADP
ejpam-1478	9	13	the	the	DET
ejpam-1478	9	14	regulated	regulated	ADJ
ejpam-1478	9	15	quantity	quantity	NOUN
ejpam-1478	9	16	.	.	PUNCT
ejpam-1478	10	1	such	such	ADJ
ejpam-1478	10	2	kind	kind	NOUN
ejpam-1478	10	3	of	of	ADP
ejpam-1478	10	4	real	real	ADJ
ejpam-1478	10	5	world	world	NOUN
ejpam-1478	10	6	problems	problem	NOUN
ejpam-1478	10	7	are	be	AUX
ejpam-1478	10	8	adequately	adequately	ADV
ejpam-1478	10	9	modeled	model	VERB
ejpam-1478	10	10	by	by	ADP
ejpam-1478	10	11	differential	differential	ADJ
ejpam-1478	10	12	equations	equation	NOUN
ejpam-1478	10	13	with	with	ADP
ejpam-1478	10	14	“	"	PUNCT
ejpam-1478	10	15	maxima	maxima	NOUN
ejpam-1478	10	16	”	"	PUNCT
ejpam-1478	11	1	[	[	X
ejpam-1478	11	2	16	16	NUM
ejpam-1478	11	3	]	]	PUNCT
ejpam-1478	11	4	.	.	PUNCT
ejpam-1478	12	1	in	in	ADP
ejpam-1478	12	2	connection	connection	NOUN
ejpam-1478	12	3	with	with	ADP
ejpam-1478	12	4	many	many	ADJ
ejpam-1478	12	5	possible	possible	ADJ
ejpam-1478	12	6	applications	application	NOUN
ejpam-1478	12	7	it	it	PRON
ejpam-1478	12	8	is	be	AUX
ejpam-1478	12	9	absolutely	absolutely	ADV
ejpam-1478	12	10	necessary	necessary	ADJ
ejpam-1478	12	11	to	to	PART
ejpam-1478	12	12	be	be	AUX
ejpam-1478	12	13	developed	develop	VERB
ejpam-1478	12	14	qualitative	qualitative	ADJ
ejpam-1478	12	15	theory	theory	NOUN
ejpam-1478	12	16	of	of	ADP
ejpam-1478	12	17	differential	differential	ADJ
ejpam-1478	12	18	equations	equation	NOUN
ejpam-1478	12	19	with	with	ADP
ejpam-1478	12	20	“	"	PUNCT
ejpam-1478	12	21	maxima	maxima	NOUN
ejpam-1478	12	22	”	"	PUNCT
ejpam-1478	12	23	(	(	PUNCT
ejpam-1478	12	24	see	see	VERB
ejpam-1478	12	25	the	the	DET
ejpam-1478	12	26	monograph	monograph	NOUN
ejpam-1478	13	1	[	[	X
ejpam-1478	13	2	3	3	NUM
ejpam-1478	13	3	]	]	PUNCT
ejpam-1478	13	4	and	and	CCONJ
ejpam-1478	13	5	papers	paper	NOUN
ejpam-1478	13	6	[	[	X
ejpam-1478	13	7	2	2	NUM
ejpam-1478	13	8	,	,	PUNCT
ejpam-1478	13	9	4	4	NUM
ejpam-1478	13	10	,	,	PUNCT
ejpam-1478	13	11	5	5	NUM
ejpam-1478	13	12	,	,	PUNCT
ejpam-1478	13	13	6	6	NUM
ejpam-1478	13	14	,	,	PUNCT
ejpam-1478	13	15	10	10	NUM
ejpam-1478	13	16	,	,	PUNCT
ejpam-1478	13	17	11	11	NUM
ejpam-1478	13	18	]	]	NUM
ejpam-1478	13	19	)	)	PUNCT
ejpam-1478	13	20	.	.	PUNCT
ejpam-1478	14	1	one	one	NUM
ejpam-1478	14	2	of	of	ADP
ejpam-1478	14	3	the	the	DET
ejpam-1478	14	4	main	main	ADJ
ejpam-1478	14	5	mathematical	mathematical	ADJ
ejpam-1478	14	6	tools	tool	NOUN
ejpam-1478	14	7	,	,	PUNCT
ejpam-1478	14	8	employed	employ	VERB
ejpam-1478	14	9	successfully	successfully	ADV
ejpam-1478	14	10	for	for	ADP
ejpam-1478	14	11	studying	study	VERB
ejpam-1478	14	12	existence	existence	NOUN
ejpam-1478	14	13	,	,	PUNCT
ejpam-1478	14	14	uniqueness	uniqueness	NOUN
ejpam-1478	14	15	,	,	PUNCT
ejpam-1478	14	16	continuous	continuous	ADJ
ejpam-1478	14	17	dependence	dependence	NOUN
ejpam-1478	14	18	,	,	PUNCT
ejpam-1478	14	19	comparison	comparison	NOUN
ejpam-1478	14	20	results	result	NOUN
ejpam-1478	14	21	,	,	PUNCT
ejpam-1478	14	22	perturbations	perturbation	NOUN
ejpam-1478	14	23	,	,	PUNCT
ejpam-1478	14	24	boundedness	boundedness	NOUN
ejpam-1478	14	25	,	,	PUNCT
ejpam-1478	14	26	and	and	CCONJ
ejpam-1478	14	27	stability	stability	NOUN
ejpam-1478	14	28	of	of	ADP
ejpam-1478	14	29	solutions	solution	NOUN
ejpam-1478	14	30	of	of	ADP
ejpam-1478	14	31	differential	differential	ADJ
ejpam-1478	14	32	and	and	CCONJ
ejpam-1478	14	33	integral	integral	ADJ
ejpam-1478	14	34	equations	equation	NOUN
ejpam-1478	14	35	is	be	AUX
ejpam-1478	14	36	the	the	DET
ejpam-1478	14	37	method	method	NOUN
ejpam-1478	14	38	of	of	ADP
ejpam-1478	14	39	integral	integral	ADJ
ejpam-1478	14	40	∗corresponding	∗corresponding	NOUN
ejpam-1478	14	41	author	author	NOUN
ejpam-1478	14	42	.	.	PUNCT
ejpam-1478	15	1	email	email	NOUN
ejpam-1478	15	2	addresses	address	NOUN
ejpam-1478	15	3	:	:	PUNCT
ejpam-1478	15	4	snehri�uni-plovdiv.bg	snehri�uni-plovdiv.bg	PROPN
ejpam-1478	15	5	(	(	PUNCT
ejpam-1478	15	6	s.	s.	PROPN
ejpam-1478	15	7	hristova	hristova	PROPN
ejpam-1478	15	8	)	)	PUNCT
ejpam-1478	15	9	,	,	PUNCT
ejpam-1478	15	10	kstefanova�uni-plovdiv.bg	kstefanova�uni-plovdiv.bg	PROPN
ejpam-1478	15	11	(	(	PUNCT
ejpam-1478	15	12	k.	k.	PROPN
ejpam-1478	15	13	stefanova	stefanova	PROPN
ejpam-1478	15	14	)	)	PUNCT
ejpam-1478	15	15	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-1478	16	1	30	30	NUM
ejpam-1478	16	2	c	c	X
ejpam-1478	16	3	©	©	PROPN
ejpam-1478	16	4	2012	2012	NUM
ejpam-1478	16	5	ejpam	ejpam	VERB
ejpam-1478	16	6	all	all	DET
ejpam-1478	16	7	rights	right	NOUN
ejpam-1478	16	8	reserved	reserve	VERB
ejpam-1478	16	9	.	.	PUNCT
ejpam-1478	17	1	s.	s.	PROPN
ejpam-1478	17	2	hristova	hristova	PROPN
ejpam-1478	17	3	,	,	PUNCT
ejpam-1478	17	4	k.	k.	PROPN
ejpam-1478	17	5	stefanova	stefanova	PROPN
ejpam-1478	17	6	/	/	SYM
ejpam-1478	17	7	eur	eur	PROPN
ejpam-1478	17	8	.	.	PUNCT
ejpam-1478	18	1	j.	j.	PROPN
ejpam-1478	18	2	pure	pure	PROPN
ejpam-1478	18	3	appl	appl	PROPN
ejpam-1478	18	4	.	.	PROPN
ejpam-1478	18	5	math	math	PROPN
ejpam-1478	18	6	,	,	PUNCT
ejpam-1478	18	7	5	5	NUM
ejpam-1478	18	8	(	(	PUNCT
ejpam-1478	18	9	2012	2012	NUM
ejpam-1478	18	10	)	)	PUNCT
ejpam-1478	18	11	,	,	PUNCT
ejpam-1478	18	12	30	30	NUM
ejpam-1478	18	13	-	-	SYM
ejpam-1478	18	14	44	44	NUM
ejpam-1478	18	15	31	31	NUM
ejpam-1478	18	16	inequalities	inequality	NOUN
ejpam-1478	18	17	.	.	PUNCT
ejpam-1478	19	1	various	various	ADJ
ejpam-1478	19	2	types	type	NOUN
ejpam-1478	19	3	of	of	ADP
ejpam-1478	19	4	integral	integral	ADJ
ejpam-1478	19	5	inequalities	inequality	NOUN
ejpam-1478	19	6	are	be	AUX
ejpam-1478	19	7	solved	solve	VERB
ejpam-1478	19	8	in	in	ADP
ejpam-1478	19	9	the	the	DET
ejpam-1478	19	10	papers	paper	NOUN
ejpam-1478	19	11	[	[	X
ejpam-1478	19	12	1	1	NUM
ejpam-1478	19	13	,	,	PUNCT
ejpam-1478	19	14	7	7	NUM
ejpam-1478	19	15	,	,	PUNCT
ejpam-1478	19	16	9	9	NUM
ejpam-1478	19	17	,	,	PUNCT
ejpam-1478	19	18	13	13	NUM
ejpam-1478	19	19	,	,	PUNCT
ejpam-1478	19	20	15	15	NUM
ejpam-1478	19	21	,	,	PUNCT
ejpam-1478	19	22	17	17	NUM
ejpam-1478	19	23	,	,	PUNCT
ejpam-1478	19	24	20	20	NUM
ejpam-1478	19	25	,	,	PUNCT
ejpam-1478	19	26	21	21	NUM
ejpam-1478	19	27	,	,	PUNCT
ejpam-1478	19	28	22	22	NUM
ejpam-1478	19	29	]	]	PUNCT
ejpam-1478	19	30	.	.	PUNCT
ejpam-1478	20	1	the	the	DET
ejpam-1478	20	2	involvement	involvement	NOUN
ejpam-1478	20	3	of	of	ADP
ejpam-1478	20	4	maximum	maximum	ADJ
ejpam-1478	20	5	function	function	NOUN
ejpam-1478	20	6	in	in	ADP
ejpam-1478	20	7	the	the	DET
ejpam-1478	20	8	equation	equation	NOUN
ejpam-1478	20	9	requires	require	VERB
ejpam-1478	20	10	application	application	NOUN
ejpam-1478	20	11	of	of	ADP
ejpam-1478	20	12	a	a	DET
ejpam-1478	20	13	new	new	ADJ
ejpam-1478	20	14	type	type	NOUN
ejpam-1478	20	15	of	of	ADP
ejpam-1478	20	16	integral	integral	ADJ
ejpam-1478	20	17	inequalities	inequality	NOUN
ejpam-1478	20	18	.	.	PUNCT
ejpam-1478	21	1	additionally	additionally	ADV
ejpam-1478	21	2	,	,	PUNCT
ejpam-1478	21	3	if	if	SCONJ
ejpam-1478	21	4	the	the	DET
ejpam-1478	21	5	unknown	unknown	ADJ
ejpam-1478	21	6	function	function	NOUN
ejpam-1478	21	7	is	be	AUX
ejpam-1478	21	8	piecewise	piecewise	NOUN
ejpam-1478	21	9	continuous	continuous	ADJ
ejpam-1478	21	10	then	then	ADV
ejpam-1478	21	11	so	so	ADV
ejpam-1478	21	12	called	call	VERB
ejpam-1478	21	13	integro	integro	ADJ
ejpam-1478	21	14	-	-	PUNCT
ejpam-1478	21	15	summation	summation	NOUN
ejpam-1478	21	16	inequalities	inequality	NOUN
ejpam-1478	21	17	with	with	ADP
ejpam-1478	21	18	supremum	supremum	ADJ
ejpam-1478	21	19	have	have	VERB
ejpam-1478	21	20	to	to	PART
ejpam-1478	21	21	be	be	AUX
ejpam-1478	21	22	applied	apply	VERB
ejpam-1478	21	23	.	.	PUNCT
ejpam-1478	22	1	the	the	DET
ejpam-1478	22	2	purpose	purpose	NOUN
ejpam-1478	22	3	of	of	ADP
ejpam-1478	22	4	the	the	DET
ejpam-1478	22	5	paper	paper	NOUN
ejpam-1478	22	6	is	be	AUX
ejpam-1478	22	7	studying	study	VERB
ejpam-1478	22	8	some	some	DET
ejpam-1478	22	9	stability	stability	NOUN
ejpam-1478	22	10	properties	property	NOUN
ejpam-1478	22	11	of	of	ADP
ejpam-1478	22	12	the	the	DET
ejpam-1478	22	13	solutions	solution	NOUN
ejpam-1478	22	14	of	of	ADP
ejpam-1478	22	15	impulsive	impulsive	ADJ
ejpam-1478	22	16	differential	differential	ADJ
ejpam-1478	22	17	equations	equation	NOUN
ejpam-1478	22	18	with	with	ADP
ejpam-1478	22	19	“	"	PUNCT
ejpam-1478	22	20	supremum	supremum	ADJ
ejpam-1478	22	21	”	"	PUNCT
ejpam-1478	22	22	.	.	PUNCT
ejpam-1478	23	1	the	the	DET
ejpam-1478	23	2	main	main	ADJ
ejpam-1478	23	3	apparatus	apparatus	NOUN
ejpam-1478	23	4	of	of	ADP
ejpam-1478	23	5	investigation	investigation	NOUN
ejpam-1478	23	6	are	be	AUX
ejpam-1478	23	7	integral	integral	ADJ
ejpam-1478	23	8	inequalities	inequality	NOUN
ejpam-1478	23	9	which	which	PRON
ejpam-1478	23	10	contain	contain	VERB
ejpam-1478	23	11	the	the	DET
ejpam-1478	23	12	supremum	supremum	NOUN
ejpam-1478	23	13	of	of	ADP
ejpam-1478	23	14	the	the	DET
ejpam-1478	23	15	unknown	unknown	ADJ
ejpam-1478	23	16	scalar	scalar	ADJ
ejpam-1478	23	17	piecewise	piecewise	NOUN
ejpam-1478	23	18	continuous	continuous	ADJ
ejpam-1478	23	19	function	function	NOUN
ejpam-1478	23	20	over	over	ADP
ejpam-1478	23	21	a	a	DET
ejpam-1478	23	22	past	past	ADJ
ejpam-1478	23	23	time	time	NOUN
ejpam-1478	23	24	interval	interval	NOUN
ejpam-1478	23	25	.	.	PUNCT
ejpam-1478	24	1	some	some	DET
ejpam-1478	24	2	nonlinear	nonlinear	ADJ
ejpam-1478	24	3	inequalities	inequality	NOUN
ejpam-1478	24	4	are	be	AUX
ejpam-1478	24	5	solved	solve	VERB
ejpam-1478	24	6	and	and	CCONJ
ejpam-1478	24	7	applied	apply	VERB
ejpam-1478	24	8	to	to	PART
ejpam-1478	24	9	investigate	investigate	VERB
ejpam-1478	24	10	some	some	DET
ejpam-1478	24	11	properties	property	NOUN
ejpam-1478	24	12	of	of	ADP
ejpam-1478	24	13	the	the	DET
ejpam-1478	24	14	solutions	solution	NOUN
ejpam-1478	24	15	of	of	ADP
ejpam-1478	24	16	the	the	DET
ejpam-1478	24	17	considered	consider	VERB
ejpam-1478	24	18	equation	equation	NOUN
ejpam-1478	24	19	.	.	PUNCT
ejpam-1478	25	1	2	2	X
ejpam-1478	25	2	.	.	X
ejpam-1478	25	3	mathematical	mathematical	ADJ
ejpam-1478	25	4	model	model	NOUN
ejpam-1478	25	5	let	let	VERB
ejpam-1478	25	6	{	{	PUNCT
ejpam-1478	25	7	t	t	PROPN
ejpam-1478	25	8	i}∞1	i}∞1	AUX
ejpam-1478	25	9	be	be	AUX
ejpam-1478	25	10	a	a	DET
ejpam-1478	25	11	given	give	VERB
ejpam-1478	25	12	sequence	sequence	NOUN
ejpam-1478	25	13	of	of	ADP
ejpam-1478	25	14	points	point	NOUN
ejpam-1478	25	15	such	such	ADJ
ejpam-1478	25	16	that	that	SCONJ
ejpam-1478	25	17	t	t	NOUN
ejpam-1478	26	1	i	i	PRON
ejpam-1478	26	2	<	<	X
ejpam-1478	26	3	t	t	PROPN
ejpam-1478	26	4	i+1	i+1	NOUN
ejpam-1478	26	5	,	,	PUNCT
ejpam-1478	26	6	lim	lim	PROPN
ejpam-1478	26	7	i→∞	i→∞	VERB
ejpam-1478	26	8	t	t	PROPN
ejpam-1478	27	1	i	i	PRON
ejpam-1478	27	2	=	=	NOUN
ejpam-1478	27	3	∞.	∞.	PROPN
ejpam-1478	27	4	let	let	VERB
ejpam-1478	27	5	the	the	DET
ejpam-1478	27	6	points	point	NOUN
ejpam-1478	27	7	t0	t0	PROPN
ejpam-1478	27	8	,	,	PUNCT
ejpam-1478	27	9	t	t	PROPN
ejpam-1478	27	10	be	be	AUX
ejpam-1478	27	11	fixed	fix	VERB
ejpam-1478	27	12	,	,	PUNCT
ejpam-1478	27	13	0≤	0≤	NUM
ejpam-1478	27	14	t0	t0	NOUN
ejpam-1478	27	15	<	<	X
ejpam-1478	27	16	t	t	PROPN
ejpam-1478	27	17	≤∞	≤∞	PROPN
ejpam-1478	27	18	,	,	PUNCT
ejpam-1478	27	19	and	and	CCONJ
ejpam-1478	27	20	the	the	DET
ejpam-1478	27	21	following	follow	VERB
ejpam-1478	27	22	condition	condition	NOUN
ejpam-1478	27	23	be	be	AUX
ejpam-1478	27	24	satisfied	satisfied	ADJ
ejpam-1478	27	25	:	:	PUNCT
ejpam-1478	27	26	h1	h1	VERB
ejpam-1478	27	27	the	the	DET
ejpam-1478	27	28	functions	function	NOUN
ejpam-1478	27	29	σ	σ	PROPN
ejpam-1478	27	30	,	,	PUNCT
ejpam-1478	27	31	τ	τ	PROPN
ejpam-1478	27	32	∈	∈	PROPN
ejpam-1478	27	33	c1([t0	c1([t0	NOUN
ejpam-1478	27	34	,	,	PUNCT
ejpam-1478	27	35	t	t	PROPN
ejpam-1478	27	36	)	)	PUNCT
ejpam-1478	27	37	,	,	PUNCT
ejpam-1478	27	38	r+	r+	X
ejpam-1478	27	39	)	)	PUNCT
ejpam-1478	27	40	are	be	AUX
ejpam-1478	27	41	nondecreasing	nondecrease	VERB
ejpam-1478	27	42	,	,	PUNCT
ejpam-1478	27	43	τ(t	τ(t	NOUN
ejpam-1478	27	44	)	)	PUNCT
ejpam-1478	27	45	≤	≤	NOUN
ejpam-1478	27	46	t	t	PROPN
ejpam-1478	27	47	for	for	ADP
ejpam-1478	27	48	t	t	PROPN
ejpam-1478	27	49	∈	∈	PROPN
ejpam-1478	27	50	[	[	X
ejpam-1478	27	51	t0	t0	PROPN
ejpam-1478	27	52	,	,	PUNCT
ejpam-1478	27	53	t	t	PROPN
ejpam-1478	27	54	)	)	PUNCT
ejpam-1478	27	55	and	and	CCONJ
ejpam-1478	27	56	there	there	PRON
ejpam-1478	27	57	exists	exist	VERB
ejpam-1478	27	58	a	a	DET
ejpam-1478	27	59	nonnegative	nonnegative	ADJ
ejpam-1478	27	60	constant	constant	ADJ
ejpam-1478	27	61	h	h	NOUN
ejpam-1478	28	1	such	such	ADJ
ejpam-1478	28	2	that	that	SCONJ
ejpam-1478	28	3	the	the	DET
ejpam-1478	28	4	inequalities	inequality	NOUN
ejpam-1478	28	5	0	0	NUM
ejpam-1478	28	6	≤	≤	NUM
ejpam-1478	28	7	τ(t	τ(t	NOUN
ejpam-1478	28	8	)	)	PUNCT
ejpam-1478	28	9	−	−	PRON
ejpam-1478	28	10	σ(t	σ(t	NOUN
ejpam-1478	28	11	)	)	PUNCT
ejpam-1478	28	12	≤	≤	NUM
ejpam-1478	28	13	h	h	NOUN
ejpam-1478	28	14	hold	hold	VERB
ejpam-1478	28	15	for	for	ADP
ejpam-1478	28	16	t	t	PROPN
ejpam-1478	28	17	∈	∈	PROPN
ejpam-1478	28	18	[	[	X
ejpam-1478	28	19	t0	t0	PROPN
ejpam-1478	28	20	,	,	PUNCT
ejpam-1478	28	21	t	t	PROPN
ejpam-1478	28	22	)	)	PUNCT
ejpam-1478	28	23	.	.	PUNCT
ejpam-1478	29	1	denote	denote	VERB
ejpam-1478	29	2	by	by	ADP
ejpam-1478	29	3	z(t0	z(t0	PROPN
ejpam-1478	29	4	,	,	PUNCT
ejpam-1478	29	5	t	t	PROPN
ejpam-1478	29	6	)	)	PUNCT
ejpam-1478	29	7	the	the	DET
ejpam-1478	29	8	set	set	NOUN
ejpam-1478	29	9	of	of	ADP
ejpam-1478	29	10	all	all	DET
ejpam-1478	29	11	natural	natural	ADJ
ejpam-1478	29	12	numbers	number	NOUN
ejpam-1478	29	13	k	k	X
ejpam-1478	29	14	such	such	ADJ
ejpam-1478	29	15	that	that	SCONJ
ejpam-1478	29	16	tk	tk	PROPN
ejpam-1478	29	17	∈	∈	PROPN
ejpam-1478	29	18	(	(	PUNCT
ejpam-1478	29	19	t0	t0	PROPN
ejpam-1478	29	20	,	,	PUNCT
ejpam-1478	29	21	t	t	PROPN
ejpam-1478	29	22	)	)	PUNCT
ejpam-1478	29	23	.	.	PUNCT
ejpam-1478	30	1	consider	consider	VERB
ejpam-1478	30	2	the	the	DET
ejpam-1478	30	3	following	follow	VERB
ejpam-1478	30	4	impulsive	impulsive	ADJ
ejpam-1478	30	5	differential	differential	ADJ
ejpam-1478	30	6	equation	equation	NOUN
ejpam-1478	30	7	with	with	ADP
ejpam-1478	30	8	“	"	PUNCT
ejpam-1478	30	9	supremum	supremum	ADJ
ejpam-1478	30	10	”	"	PUNCT
ejpam-1478	30	11	x	x	SYM
ejpam-1478	30	12	′	′	NUM
ejpam-1478	30	13	=	=	SYM
ejpam-1478	30	14	f	f	PROPN
ejpam-1478	30	15	�	�	PROPN
ejpam-1478	30	16	t	t	PROPN
ejpam-1478	30	17	,	,	PUNCT
ejpam-1478	30	18	x(t	x(t	PROPN
ejpam-1478	30	19	)	)	PUNCT
ejpam-1478	30	20	,	,	PUNCT
ejpam-1478	30	21	sup	sup	NOUN
ejpam-1478	30	22	s∈[σ(t),τ(t	s∈[σ(t),τ(t	PROPN
ejpam-1478	30	23	)	)	PUNCT
ejpam-1478	30	24	]	]	PUNCT
ejpam-1478	30	25	x(s	x(s	PROPN
ejpam-1478	30	26	)	)	PUNCT
ejpam-1478	30	27	�	�	PROPN
ejpam-1478	30	28	,	,	PUNCT
ejpam-1478	30	29	for	for	ADP
ejpam-1478	30	30	t	t	PROPN
ejpam-1478	30	31	∈	∈	PROPN
ejpam-1478	30	32	[	[	X
ejpam-1478	30	33	t0	t0	PROPN
ejpam-1478	30	34	,	,	PUNCT
ejpam-1478	30	35	t	t	PROPN
ejpam-1478	30	36	)	)	PUNCT
ejpam-1478	30	37	,	,	PUNCT
ejpam-1478	30	38	t	t	PROPN
ejpam-1478	30	39	6=	6=	PROPN
ejpam-1478	30	40	t	t	PROPN
ejpam-1478	31	1	i	i	PRON
ejpam-1478	31	2	,	,	PUNCT
ejpam-1478	31	3	(	(	PUNCT
ejpam-1478	31	4	1	1	X
ejpam-1478	31	5	)	)	PUNCT
ejpam-1478	31	6	∆x	∆x	PROPN
ejpam-1478	31	7	�	�	PROPN
ejpam-1478	31	8	�	�	PROPN
ejpam-1478	31	9	t	t	PROPN
ejpam-1478	31	10	=	=	SYM
ejpam-1478	31	11	ti	ti	NOUN
ejpam-1478	31	12	=	=	SYM
ejpam-1478	31	13	ii	ii	PROPN
ejpam-1478	31	14	�	�	PROPN
ejpam-1478	31	15	x(t	x(t	PROPN
ejpam-1478	31	16	i	i	PRON
ejpam-1478	31	17	)	)	PUNCT
ejpam-1478	31	18	�	�	PROPN
ejpam-1478	31	19	,	,	PUNCT
ejpam-1478	31	20	for	for	ADP
ejpam-1478	31	21	i	i	PROPN
ejpam-1478	31	22	∈	∈	PROPN
ejpam-1478	31	23	z(t0	z(t0	NOUN
ejpam-1478	31	24	,	,	PUNCT
ejpam-1478	31	25	t	t	PROPN
ejpam-1478	31	26	)	)	PUNCT
ejpam-1478	31	27	,	,	PUNCT
ejpam-1478	31	28	(	(	PUNCT
ejpam-1478	31	29	2	2	X
ejpam-1478	31	30	)	)	PUNCT
ejpam-1478	31	31	with	with	ADP
ejpam-1478	31	32	initial	initial	ADJ
ejpam-1478	31	33	condition	condition	NOUN
ejpam-1478	31	34	x(t	x(t	PROPN
ejpam-1478	31	35	)	)	PUNCT
ejpam-1478	31	36	=	=	SYM
ejpam-1478	31	37	φ(t	φ(t	PROPN
ejpam-1478	31	38	)	)	PUNCT
ejpam-1478	31	39	,	,	PUNCT
ejpam-1478	31	40	t	t	PROPN
ejpam-1478	31	41	∈	∈	PROPN
ejpam-1478	32	1	[	[	X
ejpam-1478	32	2	τ(t0)−	τ(t0)−	X
ejpam-1478	32	3	h	h	PROPN
ejpam-1478	32	4	,	,	PUNCT
ejpam-1478	32	5	t0	t0	PROPN
ejpam-1478	32	6	]	]	PUNCT
ejpam-1478	32	7	(	(	PUNCT
ejpam-1478	32	8	3	3	X
ejpam-1478	32	9	)	)	PUNCT
ejpam-1478	32	10	where	where	SCONJ
ejpam-1478	32	11	x	x	SYM
ejpam-1478	32	12	∈	∈	PROPN
ejpam-1478	32	13	r	r	PROPN
ejpam-1478	32	14	,	,	PUNCT
ejpam-1478	32	15	∆x	∆x	PROPN
ejpam-1478	32	16	�	�	PROPN
ejpam-1478	32	17	�	�	PROPN
ejpam-1478	32	18	t	t	PROPN
ejpam-1478	32	19	=	=	SYM
ejpam-1478	32	20	ti	ti	X
ejpam-1478	32	21	=	=	PUNCT
ejpam-1478	32	22	x(t	x(t	PROPN
ejpam-1478	32	23	i	i	PRON
ejpam-1478	32	24	+	+	PROPN
ejpam-1478	32	25	0)−	0)−	PUNCT
ejpam-1478	32	26	x(t	x(t	PROPN
ejpam-1478	32	27	i	i	PRON
ejpam-1478	32	28	−	−	NOUN
ejpam-1478	32	29	0	0	NUM
ejpam-1478	32	30	)	)	PUNCT
ejpam-1478	32	31	for	for	ADP
ejpam-1478	32	32	i	i	PROPN
ejpam-1478	32	33	∈	∈	PROPN
ejpam-1478	32	34	z(t0	z(t0	NOUN
ejpam-1478	32	35	,	,	PUNCT
ejpam-1478	32	36	t	t	PROPN
ejpam-1478	32	37	)	)	PUNCT
ejpam-1478	32	38	.	.	PUNCT
ejpam-1478	33	1	let	let	VERB
ejpam-1478	33	2	pc(ω	pc(ω	PRON
ejpam-1478	33	3	,	,	PUNCT
ejpam-1478	33	4	r	r	NOUN
ejpam-1478	33	5	)	)	PUNCT
ejpam-1478	33	6	,	,	PUNCT
ejpam-1478	33	7	ω⊂	ω⊂	PROPN
ejpam-1478	33	8	r	r	NOUN
ejpam-1478	33	9	,	,	PUNCT
ejpam-1478	33	10	be	be	AUX
ejpam-1478	33	11	the	the	DET
ejpam-1478	33	12	set	set	NOUN
ejpam-1478	33	13	of	of	ADP
ejpam-1478	33	14	all	all	DET
ejpam-1478	33	15	functions	function	NOUN
ejpam-1478	33	16	u	u	NOUN
ejpam-1478	33	17	:	:	PUNCT
ejpam-1478	33	18	ω→	ω→	PUNCT
ejpam-1478	33	19	r	r	NOUN
ejpam-1478	33	20	which	which	PRON
ejpam-1478	33	21	are	be	AUX
ejpam-1478	33	22	piecewise	piecewise	NOUN
ejpam-1478	33	23	continuous	continuous	ADJ
ejpam-1478	33	24	in	in	ADP
ejpam-1478	33	25	ω	ω	PROPN
ejpam-1478	33	26	,	,	PUNCT
ejpam-1478	33	27	i.e.	i.e.	X
ejpam-1478	33	28	there	there	PRON
ejpam-1478	33	29	exist	exist	VERB
ejpam-1478	33	30	limits	limit	NOUN
ejpam-1478	33	31	lim	lim	PROPN
ejpam-1478	33	32	t↓tk	t↓tk	PROPN
ejpam-1478	33	33	u(t	u(t	PROPN
ejpam-1478	33	34	)	)	PUNCT
ejpam-1478	34	1	=	=	SYM
ejpam-1478	34	2	u(tk	u(tk	NOUN
ejpam-1478	34	3	+	+	CCONJ
ejpam-1478	34	4	0)<∞	0)<∞	NOUN
ejpam-1478	34	5	and	and	CCONJ
ejpam-1478	34	6	lim	lim	PROPN
ejpam-1478	34	7	t↑tk	t↑tk	VERB
ejpam-1478	34	8	u(t	u(t	NOUN
ejpam-1478	34	9	)	)	PUNCT
ejpam-1478	34	10	=	=	PUNCT
ejpam-1478	34	11	u(tk	u(tk	NOUN
ejpam-1478	34	12	−	−	NOUN
ejpam-1478	34	13	0	0	NUM
ejpam-1478	34	14	)	)	PUNCT
ejpam-1478	34	15	=	=	SYM
ejpam-1478	35	1	u(tk)<∞	u(tk)<∞	PROPN
ejpam-1478	35	2	,	,	PUNCT
ejpam-1478	35	3	tk	tk	PROPN
ejpam-1478	35	4	∈	∈	PROPN
ejpam-1478	35	5	ω	ω	PROPN
ejpam-1478	35	6	.	.	PROPN
ejpam-1478	35	7	denote	denote	VERB
ejpam-1478	35	8	by	by	ADP
ejpam-1478	35	9	x(t	x(t	PROPN
ejpam-1478	35	10	;	;	PUNCT
ejpam-1478	35	11	t0,φ	t0,φ	NOUN
ejpam-1478	35	12	)	)	PUNCT
ejpam-1478	35	13	the	the	DET
ejpam-1478	35	14	solution	solution	NOUN
ejpam-1478	35	15	of	of	ADP
ejpam-1478	35	16	the	the	DET
ejpam-1478	35	17	initial	initial	ADJ
ejpam-1478	35	18	value	value	NOUN
ejpam-1478	35	19	problem	problem	NOUN
ejpam-1478	35	20	(	(	PUNCT
ejpam-1478	35	21	1)–(3	1)–(3	NUM
ejpam-1478	35	22	)	)	PUNCT
ejpam-1478	35	23	and	and	CCONJ
ejpam-1478	35	24	|φ|0	|φ|0	PROPN
ejpam-1478	35	25	=	=	SYM
ejpam-1478	35	26	max	max	PROPN
ejpam-1478	35	27	s∈[τ(t0)−h	s∈[τ(t0)−h	PROPN
ejpam-1478	35	28	,	,	PUNCT
ejpam-1478	35	29	t0	t0	PROPN
ejpam-1478	35	30	]	]	PUNCT
ejpam-1478	36	1	|φ(s)|	|φ(s)|	PROPN
ejpam-1478	36	2	.	.	PUNCT
ejpam-1478	36	3	let	let	VERB
ejpam-1478	36	4	the	the	DET
ejpam-1478	36	5	following	follow	VERB
ejpam-1478	36	6	conditions	condition	NOUN
ejpam-1478	36	7	be	be	AUX
ejpam-1478	36	8	satisfied	satisfied	ADJ
ejpam-1478	36	9	:	:	PUNCT
ejpam-1478	36	10	h2	h2	VERB
ejpam-1478	36	11	the	the	DET
ejpam-1478	36	12	function	function	NOUN
ejpam-1478	36	13	f	f	PROPN
ejpam-1478	36	14	∈	∈	PROPN
ejpam-1478	36	15	c(r+×r×r	c(r+×r×r	PROPN
ejpam-1478	36	16	,	,	PUNCT
ejpam-1478	36	17	r	r	NOUN
ejpam-1478	36	18	)	)	PUNCT
ejpam-1478	36	19	,	,	PUNCT
ejpam-1478	36	20	f	f	PROPN
ejpam-1478	36	21	(	(	PUNCT
ejpam-1478	36	22	t	t	PROPN
ejpam-1478	36	23	,	,	PUNCT
ejpam-1478	36	24	0,0	0,0	NUM
ejpam-1478	36	25	)	)	PUNCT
ejpam-1478	36	26	=	=	SYM
ejpam-1478	36	27	0	0	NUM
ejpam-1478	36	28	and	and	CCONJ
ejpam-1478	36	29	the	the	DET
ejpam-1478	36	30	inequality	inequality	NOUN
ejpam-1478	37	1	|	|	ADV
ejpam-1478	37	2	f	f	PROPN
ejpam-1478	37	3	(	(	PUNCT
ejpam-1478	37	4	t	t	PROPN
ejpam-1478	37	5	,	,	PUNCT
ejpam-1478	37	6	x	x	X
ejpam-1478	37	7	,	,	PUNCT
ejpam-1478	37	8	y)|	y)|	PROPN
ejpam-1478	37	9	≤	≤	NOUN
ejpam-1478	38	1	a(t)|x	a(t)|x	PROPN
ejpam-1478	38	2	|p+	|p+	PROPN
ejpam-1478	38	3	b(t)|y|p	b(t)|y|p	VERB
ejpam-1478	38	4	for	for	ADP
ejpam-1478	38	5	x	x	X
ejpam-1478	38	6	,	,	PUNCT
ejpam-1478	38	7	y	y	PROPN
ejpam-1478	38	8	∈	∈	PROPN
ejpam-1478	38	9	r	r	NOUN
ejpam-1478	38	10	holds	hold	NOUN
ejpam-1478	38	11	,	,	PUNCT
ejpam-1478	38	12	where	where	SCONJ
ejpam-1478	38	13	the	the	DET
ejpam-1478	38	14	functions	function	NOUN
ejpam-1478	38	15	a	a	PRON
ejpam-1478	38	16	,	,	PUNCT
ejpam-1478	38	17	b	b	PROPN
ejpam-1478	38	18	∈	∈	PROPN
ejpam-1478	38	19	c(r+,r+	c(r+,r+	PROPN
ejpam-1478	38	20	)	)	PUNCT
ejpam-1478	38	21	and	and	CCONJ
ejpam-1478	38	22	p	p	NOUN
ejpam-1478	38	23	=	=	NOUN
ejpam-1478	38	24	const	const	X
ejpam-1478	38	25	>	>	X
ejpam-1478	38	26	0	0	X
ejpam-1478	38	27	.	.	PUNCT
ejpam-1478	39	1	s.	s.	PROPN
ejpam-1478	39	2	hristova	hristova	PROPN
ejpam-1478	39	3	,	,	PUNCT
ejpam-1478	39	4	k.	k.	PROPN
ejpam-1478	39	5	stefanova	stefanova	PROPN
ejpam-1478	39	6	/	/	SYM
ejpam-1478	39	7	eur	eur	PROPN
ejpam-1478	39	8	.	.	PUNCT
ejpam-1478	40	1	j.	j.	PROPN
ejpam-1478	40	2	pure	pure	PROPN
ejpam-1478	40	3	appl	appl	PROPN
ejpam-1478	40	4	.	.	PROPN
ejpam-1478	40	5	math	math	PROPN
ejpam-1478	40	6	,	,	PUNCT
ejpam-1478	40	7	5	5	NUM
ejpam-1478	40	8	(	(	PUNCT
ejpam-1478	40	9	2012	2012	NUM
ejpam-1478	40	10	)	)	PUNCT
ejpam-1478	40	11	,	,	PUNCT
ejpam-1478	40	12	30	30	NUM
ejpam-1478	40	13	-	-	SYM
ejpam-1478	40	14	44	44	NUM
ejpam-1478	40	15	32	32	NUM
ejpam-1478	40	16	h3	h3	NOUN
ejpam-1478	40	17	the	the	DET
ejpam-1478	40	18	functions	function	NOUN
ejpam-1478	40	19	ii	ii	NOUN
ejpam-1478	40	20	:	:	PUNCT
ejpam-1478	40	21	r→	r→	PROPN
ejpam-1478	40	22	r	r	PROPN
ejpam-1478	40	23	,	,	PUNCT
ejpam-1478	40	24	ii(0	ii(0	NOUN
ejpam-1478	40	25	)	)	PUNCT
ejpam-1478	40	26	=	=	SYM
ejpam-1478	40	27	0	0	NUM
ejpam-1478	40	28	and	and	CCONJ
ejpam-1478	40	29	the	the	DET
ejpam-1478	40	30	inequalities	inequality	NOUN
ejpam-1478	40	31	|ii(x)|	|ii(x)|	VERB
ejpam-1478	40	32	≤	≤	NUM
ejpam-1478	40	33	βi|x	βi|x	PUNCT
ejpam-1478	41	1	|p	|p	PROPN
ejpam-1478	41	2	for	for	ADP
ejpam-1478	41	3	x	x	PROPN
ejpam-1478	41	4	∈	∈	PROPN
ejpam-1478	41	5	r	r	NOUN
ejpam-1478	41	6	,	,	PUNCT
ejpam-1478	41	7	hold	hold	VERB
ejpam-1478	41	8	,	,	PUNCT
ejpam-1478	41	9	where	where	SCONJ
ejpam-1478	41	10	βi	βi	ADV
ejpam-1478	41	11	=	=	SYM
ejpam-1478	41	12	const	const	X
ejpam-1478	41	13	>	>	X
ejpam-1478	41	14	0	0	PUNCT
ejpam-1478	41	15	for	for	ADP
ejpam-1478	41	16	i	i	PROPN
ejpam-1478	41	17	∈	∈	PROPN
ejpam-1478	41	18	z(0,∞	z(0,∞	NUM
ejpam-1478	41	19	)	)	PUNCT
ejpam-1478	41	20	.	.	PUNCT
ejpam-1478	42	1	h4	h4	NOUN
ejpam-1478	42	2	for	for	ADP
ejpam-1478	42	3	any	any	DET
ejpam-1478	42	4	point	point	NOUN
ejpam-1478	42	5	t0	t0	PROPN
ejpam-1478	42	6	∈	∈	PROPN
ejpam-1478	42	7	r+	r+	NOUN
ejpam-1478	42	8	and	and	CCONJ
ejpam-1478	42	9	any	any	DET
ejpam-1478	42	10	initial	initial	ADJ
ejpam-1478	42	11	function	function	NOUN
ejpam-1478	42	12	φ	φ	PROPN
ejpam-1478	42	13	∈	∈	PROPN
ejpam-1478	42	14	c([τ(t0)−	c([τ(t0)−	NOUN
ejpam-1478	42	15	h	h	NOUN
ejpam-1478	42	16	,	,	PUNCT
ejpam-1478	42	17	t0],r	t0],r	PROPN
ejpam-1478	42	18	)	)	PUNCT
ejpam-1478	42	19	the	the	DET
ejpam-1478	42	20	initial	initial	ADJ
ejpam-1478	42	21	value	value	NOUN
ejpam-1478	42	22	problem	problem	NOUN
ejpam-1478	42	23	(	(	PUNCT
ejpam-1478	42	24	1)–(3	1)–(3	NUM
ejpam-1478	42	25	)	)	PUNCT
ejpam-1478	42	26	has	have	VERB
ejpam-1478	42	27	a	a	DET
ejpam-1478	42	28	solution	solution	NOUN
ejpam-1478	42	29	x(t	x(t	PROPN
ejpam-1478	42	30	;	;	PUNCT
ejpam-1478	42	31	t0,φ	t0,φ	PROPN
ejpam-1478	42	32	)	)	PUNCT
ejpam-1478	42	33	∈	∈	PROPN
ejpam-1478	42	34	pc([τ(t0)−	pc([τ(t0)−	X
ejpam-1478	42	35	h,∞),r	h,∞),r	PROPN
ejpam-1478	42	36	)	)	PUNCT
ejpam-1478	42	37	.	.	PUNCT
ejpam-1478	43	1	the	the	DET
ejpam-1478	43	2	solution	solution	NOUN
ejpam-1478	43	3	x(t	x(t	PROPN
ejpam-1478	43	4	)	)	PUNCT
ejpam-1478	43	5	=	=	SYM
ejpam-1478	43	6	x(t	x(t	PROPN
ejpam-1478	43	7	;	;	PUNCT
ejpam-1478	43	8	t0,φ	t0,φ	PROPN
ejpam-1478	43	9	)	)	PUNCT
ejpam-1478	43	10	of	of	ADP
ejpam-1478	43	11	the	the	DET
ejpam-1478	43	12	initial	initial	ADJ
ejpam-1478	43	13	value	value	NOUN
ejpam-1478	43	14	problem	problem	NOUN
ejpam-1478	43	15	(	(	PUNCT
ejpam-1478	43	16	1)–(3	1)–(3	X
ejpam-1478	43	17	)	)	PUNCT
ejpam-1478	43	18	satisfies	satisfy	VERB
ejpam-1478	43	19	the	the	DET
ejpam-1478	43	20	following	follow	VERB
ejpam-1478	43	21	integral	integral	ADJ
ejpam-1478	43	22	equation	equation	NOUN
ejpam-1478	43	23	x(t	x(t	PROPN
ejpam-1478	43	24	)	)	PUNCT
ejpam-1478	43	25	=	=	SYM
ejpam-1478	43	26	φ(t0	φ(t0	NOUN
ejpam-1478	43	27	)	)	PUNCT
ejpam-1478	44	1	+	+	CCONJ
ejpam-1478	44	2	∑	∑	PUNCT
ejpam-1478	44	3	t0	t0	PROPN
ejpam-1478	44	4	<	<	X
ejpam-1478	44	5	ti	ti	X
ejpam-1478	44	6	<	<	PROPN
ejpam-1478	44	7	t	t	PROPN
ejpam-1478	44	8	ii	ii	PROPN
ejpam-1478	44	9	�	�	PROPN
ejpam-1478	44	10	x(t	x(t	PROPN
ejpam-1478	44	11	i	i	PRON
ejpam-1478	44	12	)	)	PUNCT
ejpam-1478	44	13	�	�	PROPN
ejpam-1478	44	14	+	+	CCONJ
ejpam-1478	44	15	∫	∫	PROPN
ejpam-1478	44	16	t	t	PROPN
ejpam-1478	44	17	t0	t0	PROPN
ejpam-1478	44	18	f	f	PROPN
ejpam-1478	44	19	�	�	PROPN
ejpam-1478	44	20	s	s	PROPN
ejpam-1478	44	21	,	,	PUNCT
ejpam-1478	44	22	x(s	x(s	PROPN
ejpam-1478	44	23	)	)	PUNCT
ejpam-1478	44	24	,	,	PUNCT
ejpam-1478	44	25	sup	sup	NOUN
ejpam-1478	44	26	ξ∈[σ(s),τ(s	ξ∈[σ(s),τ(s	NOUN
ejpam-1478	44	27	)	)	PUNCT
ejpam-1478	44	28	]	]	PUNCT
ejpam-1478	45	1	x(ξ	x(ξ	PROPN
ejpam-1478	45	2	)	)	PUNCT
ejpam-1478	45	3	�	�	PROPN
ejpam-1478	45	4	ds	ds	PROPN
ejpam-1478	45	5	,	,	PUNCT
ejpam-1478	45	6	t	t	PROPN
ejpam-1478	45	7	∈	∈	PROPN
ejpam-1478	46	1	[	[	X
ejpam-1478	46	2	t0	t0	PROPN
ejpam-1478	46	3	,	,	PUNCT
ejpam-1478	46	4	t	t	PROPN
ejpam-1478	46	5	)	)	PUNCT
ejpam-1478	46	6	.	.	PUNCT
ejpam-1478	47	1	(	(	PUNCT
ejpam-1478	47	2	4	4	X
ejpam-1478	47	3	)	)	SYM
ejpam-1478	47	4	3	3	NUM
ejpam-1478	47	5	.	.	X
ejpam-1478	47	6	integro	integro	ADJ
ejpam-1478	47	7	-	-	PUNCT
ejpam-1478	47	8	summation	summation	NOUN
ejpam-1478	47	9	inequalities	inequality	NOUN
ejpam-1478	47	10	with	with	ADP
ejpam-1478	47	11	“	"	PUNCT
ejpam-1478	47	12	supremum	supremum	ADJ
ejpam-1478	47	13	”	"	PUNCT
ejpam-1478	47	14	we	we	PRON
ejpam-1478	47	15	will	will	AUX
ejpam-1478	47	16	solve	solve	VERB
ejpam-1478	47	17	some	some	DET
ejpam-1478	47	18	nonlinear	nonlinear	ADJ
ejpam-1478	47	19	integro	integro	ADJ
ejpam-1478	47	20	-	-	PUNCT
ejpam-1478	47	21	summation	summation	NOUN
ejpam-1478	47	22	inequalities	inequality	NOUN
ejpam-1478	47	23	which	which	PRON
ejpam-1478	47	24	contain	contain	VERB
ejpam-1478	47	25	the	the	DET
ejpam-1478	47	26	supremum	supremum	NOUN
ejpam-1478	47	27	of	of	ADP
ejpam-1478	47	28	the	the	DET
ejpam-1478	47	29	unknown	unknown	ADJ
ejpam-1478	47	30	scalar	scalar	ADJ
ejpam-1478	47	31	nonnegative	nonnegative	ADJ
ejpam-1478	47	32	piecewise	piecewise	NOUN
ejpam-1478	47	33	continuous	continuous	ADJ
ejpam-1478	47	34	function	function	NOUN
ejpam-1478	47	35	over	over	ADP
ejpam-1478	47	36	a	a	DET
ejpam-1478	47	37	past	past	ADJ
ejpam-1478	47	38	time	time	NOUN
ejpam-1478	47	39	interval	interval	NOUN
ejpam-1478	47	40	.	.	PUNCT
ejpam-1478	48	1	in	in	ADP
ejpam-1478	48	2	the	the	DET
ejpam-1478	48	3	proof	proof	NOUN
ejpam-1478	48	4	of	of	ADP
ejpam-1478	48	5	the	the	DET
ejpam-1478	48	6	main	main	ADJ
ejpam-1478	48	7	results	result	NOUN
ejpam-1478	48	8	we	we	PRON
ejpam-1478	48	9	will	will	AUX
ejpam-1478	48	10	use	use	VERB
ejpam-1478	48	11	the	the	DET
ejpam-1478	48	12	following	follow	VERB
ejpam-1478	48	13	results	result	NOUN
ejpam-1478	48	14	:	:	PUNCT
ejpam-1478	48	15	lemma	lemma	PROPN
ejpam-1478	48	16	1	1	NUM
ejpam-1478	48	17	(	(	PUNCT
ejpam-1478	48	18	[	[	X
ejpam-1478	48	19	9	9	NUM
ejpam-1478	48	20	,	,	PUNCT
ejpam-1478	48	21	corollary	corollary	ADJ
ejpam-1478	48	22	1	1	NUM
ejpam-1478	48	23	,	,	PUNCT
ejpam-1478	48	24	p.16	p.16	NOUN
ejpam-1478	48	25	]	]	PUNCT
ejpam-1478	48	26	)	)	PUNCT
ejpam-1478	48	27	.	.	PUNCT
ejpam-1478	49	1	let	let	VERB
ejpam-1478	49	2	the	the	DET
ejpam-1478	49	3	following	follow	VERB
ejpam-1478	49	4	conditions	condition	NOUN
ejpam-1478	49	5	be	be	AUX
ejpam-1478	49	6	satisfied	satisfied	ADJ
ejpam-1478	49	7	:	:	PUNCT
ejpam-1478	50	1	1	1	X
ejpam-1478	50	2	.	.	X
ejpam-1478	51	1	the	the	DET
ejpam-1478	51	2	function	function	NOUN
ejpam-1478	51	3	v(t	v(t	NOUN
ejpam-1478	51	4	)	)	PUNCT
ejpam-1478	51	5	∈	∈	PROPN
ejpam-1478	51	6	pc([0,∞	pc([0,∞	NOUN
ejpam-1478	51	7	)	)	PUNCT
ejpam-1478	51	8	,	,	PUNCT
ejpam-1478	52	1	[	[	X
ejpam-1478	52	2	0,∞	0,∞	NOUN
ejpam-1478	52	3	)	)	PUNCT
ejpam-1478	52	4	)	)	PUNCT
ejpam-1478	52	5	.	.	PUNCT
ejpam-1478	53	1	2	2	X
ejpam-1478	53	2	.	.	X
ejpam-1478	53	3	the	the	DET
ejpam-1478	53	4	function	function	NOUN
ejpam-1478	53	5	u(t	u(t	NOUN
ejpam-1478	53	6	)	)	PUNCT
ejpam-1478	53	7	∈	∈	PROPN
ejpam-1478	53	8	pc([0,∞	pc([0,∞	NOUN
ejpam-1478	53	9	)	)	PUNCT
ejpam-1478	53	10	,	,	PUNCT
ejpam-1478	53	11	[	[	X
ejpam-1478	53	12	0,∞	0,∞	NOUN
ejpam-1478	53	13	)	)	PUNCT
ejpam-1478	53	14	)	)	PUNCT
ejpam-1478	53	15	satisfies	satisfy	VERB
ejpam-1478	53	16	the	the	DET
ejpam-1478	53	17	inequality	inequality	NOUN
ejpam-1478	53	18	u(t	u(t	NOUN
ejpam-1478	53	19	)	)	PUNCT
ejpam-1478	53	20	≤	≤	PUNCT
ejpam-1478	53	21	c	c	NOUN
ejpam-1478	53	22	+	+	CCONJ
ejpam-1478	53	23	∑	∑	PROPN
ejpam-1478	53	24	0	0	NUM
ejpam-1478	53	25	<	<	X
ejpam-1478	53	26	ti	ti	X
ejpam-1478	53	27	<	<	X
ejpam-1478	53	28	t	t	X
ejpam-1478	53	29	βiu(t	βiu(t	NUM
ejpam-1478	53	30	i	i	NOUN
ejpam-1478	53	31	)	)	PUNCT
ejpam-1478	54	1	+	+	CCONJ
ejpam-1478	54	2	∫	∫	PROPN
ejpam-1478	54	3	t	t	PROPN
ejpam-1478	54	4	0	0	NUM
ejpam-1478	54	5	v(s)u(s)ds	v(s)u(s)d	NOUN
ejpam-1478	54	6	,	,	PUNCT
ejpam-1478	54	7	where	where	SCONJ
ejpam-1478	54	8	c	c	PROPN
ejpam-1478	54	9	≥	≥	PROPN
ejpam-1478	54	10	0	0	NUM
ejpam-1478	54	11	,	,	PUNCT
ejpam-1478	54	12	βi	βi	PRON
ejpam-1478	54	13	≥	≥	NOUN
ejpam-1478	54	14	0	0	NUM
ejpam-1478	54	15	,	,	PUNCT
ejpam-1478	54	16	(	(	PUNCT
ejpam-1478	54	17	i	i	NOUN
ejpam-1478	54	18	=	=	SYM
ejpam-1478	54	19	1,2	1,2	NUM
ejpam-1478	54	20	,	,	PUNCT
ejpam-1478	54	21	.	.	PUNCT
ejpam-1478	54	22	.	.	PUNCT
ejpam-1478	54	23	.	.	PUNCT
ejpam-1478	54	24	)	)	PUNCT
ejpam-1478	54	25	are	be	AUX
ejpam-1478	54	26	constants	constant	NOUN
ejpam-1478	54	27	.	.	PUNCT
ejpam-1478	55	1	then	then	ADV
ejpam-1478	55	2	for	for	ADP
ejpam-1478	55	3	t	t	PROPN
ejpam-1478	55	4	≥	≥	NOUN
ejpam-1478	55	5	0	0	NUM
ejpam-1478	55	6	the	the	DET
ejpam-1478	55	7	inequality	inequality	NOUN
ejpam-1478	55	8	u(t	u(t	NOUN
ejpam-1478	55	9	)	)	PUNCT
ejpam-1478	55	10	≤	≤	NUM
ejpam-1478	55	11	c	c	X
ejpam-1478	55	12	�	�	PROPN
ejpam-1478	55	13	∏	∏	PROPN
ejpam-1478	55	14	0	0	NUM
ejpam-1478	55	15	<	<	X
ejpam-1478	55	16	ti	ti	X
ejpam-1478	55	17	<	<	X
ejpam-1478	55	18	t	t	X
ejpam-1478	55	19	(	(	PUNCT
ejpam-1478	55	20	1	1	NUM
ejpam-1478	55	21	+	+	NUM
ejpam-1478	55	22	βi	βi	X
ejpam-1478	55	23	)	)	PUNCT
ejpam-1478	55	24	�	�	PROPN
ejpam-1478	55	25	exp	exp	NOUN
ejpam-1478	55	26	�	�	PROPN
ejpam-1478	55	27	∫	∫	PROPN
ejpam-1478	55	28	t	t	PROPN
ejpam-1478	55	29	0	0	NUM
ejpam-1478	55	30	v(s)ds	v(s)ds	NUM
ejpam-1478	55	31	�	�	PROPN
ejpam-1478	55	32	holds	hold	VERB
ejpam-1478	55	33	.	.	PUNCT
ejpam-1478	56	1	lemma	lemma	PROPN
ejpam-1478	56	2	2	2	NUM
ejpam-1478	56	3	(	(	PUNCT
ejpam-1478	56	4	[	[	NOUN
ejpam-1478	56	5	8	8	NUM
ejpam-1478	56	6	,	,	PUNCT
ejpam-1478	56	7	corollary	corollary	ADJ
ejpam-1478	56	8	2.2	2.2	NUM
ejpam-1478	56	9	.	.	PUNCT
ejpam-1478	56	10	]	]	PUNCT
ejpam-1478	56	11	)	)	PUNCT
ejpam-1478	56	12	.	.	PUNCT
ejpam-1478	57	1	let	let	VERB
ejpam-1478	57	2	the	the	DET
ejpam-1478	57	3	nonnegative	nonnegative	ADJ
ejpam-1478	57	4	piecewise	piecewise	NOUN
ejpam-1478	57	5	continuous	continuous	ADJ
ejpam-1478	57	6	function	function	NOUN
ejpam-1478	57	7	v	v	NOUN
ejpam-1478	57	8	(	(	PUNCT
ejpam-1478	57	9	t	t	NOUN
ejpam-1478	57	10	)	)	PUNCT
ejpam-1478	57	11	at	at	ADP
ejpam-1478	57	12	t	t	PROPN
ejpam-1478	57	13	≥	≥	NOUN
ejpam-1478	57	14	t0	t0	PROPN
ejpam-1478	57	15	≥	≥	NUM
ejpam-1478	57	16	0	0	NUM
ejpam-1478	57	17	,	,	PUNCT
ejpam-1478	57	18	with	with	ADP
ejpam-1478	57	19	discontinuities	discontinuity	NOUN
ejpam-1478	57	20	of	of	ADP
ejpam-1478	57	21	the	the	DET
ejpam-1478	57	22	first	first	ADJ
ejpam-1478	57	23	kind	kind	NOUN
ejpam-1478	57	24	in	in	ADP
ejpam-1478	57	25	the	the	DET
ejpam-1478	57	26	points	point	NOUN
ejpam-1478	57	27	tk	tk	PROPN
ejpam-1478	57	28	(	(	PUNCT
ejpam-1478	57	29	t0	t0	X
ejpam-1478	57	30	<	<	X
ejpam-1478	57	31	t1	t1	NOUN
ejpam-1478	57	32	<	<	X
ejpam-1478	57	33	t2	t2	PROPN
ejpam-1478	57	34	<	<	X
ejpam-1478	57	35	·	·	PUNCT
ejpam-1478	57	36	·	·	PUNCT
ejpam-1478	57	37	·	·	PUNCT
ejpam-1478	58	1	<	<	X
ejpam-1478	58	2	lim	lim	PROPN
ejpam-1478	58	3	i→∞	i→∞	VERB
ejpam-1478	58	4	t	t	PROPN
ejpam-1478	59	1	i	i	X
ejpam-1478	59	2	=	=	NOUN
ejpam-1478	59	3	∞	∞	NOUN
ejpam-1478	59	4	)	)	PUNCT
ejpam-1478	59	5	satisfies	satisfy	VERB
ejpam-1478	59	6	the	the	DET
ejpam-1478	59	7	inequality	inequality	NOUN
ejpam-1478	59	8	v	v	ADP
ejpam-1478	59	9	(	(	PUNCT
ejpam-1478	59	10	t	t	NOUN
ejpam-1478	59	11	)	)	PUNCT
ejpam-1478	59	12	≤	≤	PUNCT
ejpam-1478	60	1	c	c	ADP
ejpam-1478	60	2	+	+	CCONJ
ejpam-1478	60	3	∑	∑	PROPN
ejpam-1478	60	4	t0	t0	PROPN
ejpam-1478	60	5	<	<	X
ejpam-1478	60	6	ti	ti	X
ejpam-1478	60	7	<	<	X
ejpam-1478	60	8	t	t	X
ejpam-1478	60	9	aiv	aiv	NOUN
ejpam-1478	60	10	m(t	m(t	PROPN
ejpam-1478	60	11	i	i	PRON
ejpam-1478	60	12	−	−	PROPN
ejpam-1478	60	13	0	0	NUM
ejpam-1478	60	14	)	)	PUNCT
ejpam-1478	61	1	+	+	CCONJ
ejpam-1478	61	2	∫	∫	PROPN
ejpam-1478	61	3	t	t	PROPN
ejpam-1478	61	4	t0	t0	PROPN
ejpam-1478	61	5	q(s)v	q(s)v	PROPN
ejpam-1478	61	6	m(s)ds	m(s)ds	PROPN
ejpam-1478	61	7	,	,	PUNCT
ejpam-1478	61	8	where	where	SCONJ
ejpam-1478	61	9	q(s	q(s	NOUN
ejpam-1478	61	10	)	)	PUNCT
ejpam-1478	61	11	∈	∈	PROPN
ejpam-1478	61	12	c([t0,∞),r+	c([t0,∞),r+	PROPN
ejpam-1478	61	13	)	)	PUNCT
ejpam-1478	61	14	and	and	CCONJ
ejpam-1478	61	15	m	m	PROPN
ejpam-1478	61	16	is	be	AUX
ejpam-1478	61	17	a	a	DET
ejpam-1478	61	18	positive	positive	ADJ
ejpam-1478	61	19	constant	constant	NOUN
ejpam-1478	61	20	.	.	PUNCT
ejpam-1478	62	1	then	then	ADV
ejpam-1478	62	2	for	for	ADP
ejpam-1478	62	3	t	t	PROPN
ejpam-1478	62	4	≥	≥	NOUN
ejpam-1478	62	5	t0	t0	PROPN
ejpam-1478	62	6	the	the	DET
ejpam-1478	62	7	following	follow	VERB
ejpam-1478	62	8	estimates	estimate	NOUN
ejpam-1478	62	9	hold	hold	VERB
ejpam-1478	62	10	:	:	PUNCT
ejpam-1478	62	11	s.	s.	PROPN
ejpam-1478	62	12	hristova	hristova	PROPN
ejpam-1478	62	13	,	,	PUNCT
ejpam-1478	62	14	k.	k.	PROPN
ejpam-1478	62	15	stefanova	stefanova	PROPN
ejpam-1478	62	16	/	/	SYM
ejpam-1478	62	17	eur	eur	PROPN
ejpam-1478	62	18	.	.	PUNCT
ejpam-1478	63	1	j.	j.	PROPN
ejpam-1478	63	2	pure	pure	PROPN
ejpam-1478	63	3	appl	appl	PROPN
ejpam-1478	63	4	.	.	PROPN
ejpam-1478	63	5	math	math	PROPN
ejpam-1478	63	6	,	,	PUNCT
ejpam-1478	63	7	5	5	NUM
ejpam-1478	63	8	(	(	PUNCT
ejpam-1478	63	9	2012	2012	NUM
ejpam-1478	63	10	)	)	PUNCT
ejpam-1478	63	11	,	,	PUNCT
ejpam-1478	63	12	30	30	NUM
ejpam-1478	63	13	-	-	SYM
ejpam-1478	63	14	44	44	NUM
ejpam-1478	63	15	33	33	NUM
ejpam-1478	63	16	(	(	PUNCT
ejpam-1478	63	17	i	i	NOUN
ejpam-1478	63	18	)	)	PUNCT
ejpam-1478	63	19	for	for	ADP
ejpam-1478	63	20	m	m	PROPN
ejpam-1478	63	21	∈	∈	PROPN
ejpam-1478	63	22	(	(	PUNCT
ejpam-1478	63	23	0,1	0,1	NUM
ejpam-1478	63	24	)	)	PUNCT
ejpam-1478	63	25	v	v	NOUN
ejpam-1478	63	26	(	(	PUNCT
ejpam-1478	63	27	t	t	NOUN
ejpam-1478	63	28	)	)	PUNCT
ejpam-1478	63	29	≤	≤	NOUN
ejpam-1478	63	30	∏	∏	PROPN
ejpam-1478	63	31	t0	t0	PROPN
ejpam-1478	63	32	<	<	X
ejpam-1478	63	33	ti	ti	X
ejpam-1478	63	34	<	<	X
ejpam-1478	63	35	t	t	X
ejpam-1478	63	36	(	(	PUNCT
ejpam-1478	63	37	1	1	NUM
ejpam-1478	63	38	+	+	CCONJ
ejpam-1478	63	39	aic	aic	PROPN
ejpam-1478	63	40	m−1	m−1	PROPN
ejpam-1478	63	41	)	)	PUNCT
ejpam-1478	63	42	�	�	PROPN
ejpam-1478	63	43	c1−m	c1−m	VERB
ejpam-1478	63	44	+	+	CCONJ
ejpam-1478	63	45	(	(	PUNCT
ejpam-1478	63	46	1−m	1−m	NUM
ejpam-1478	63	47	)	)	PUNCT
ejpam-1478	63	48	∫	∫	PROPN
ejpam-1478	63	49	t	t	PROPN
ejpam-1478	63	50	t0	t0	PROPN
ejpam-1478	63	51	q(τ)dτ	q(τ)dτ	PROPN
ejpam-1478	63	52	�	�	PROPN
ejpam-1478	63	53	1	1	NUM
ejpam-1478	63	54	1−m	1−m	NUM
ejpam-1478	63	55	;	;	PUNCT
ejpam-1478	63	56	(	(	PUNCT
ejpam-1478	63	57	5	5	NUM
ejpam-1478	63	58	)	)	PUNCT
ejpam-1478	63	59	(	(	PUNCT
ejpam-1478	63	60	ii	ii	NOUN
ejpam-1478	63	61	)	)	PUNCT
ejpam-1478	63	62	for	for	ADP
ejpam-1478	63	63	m	m	PROPN
ejpam-1478	63	64	>	>	X
ejpam-1478	63	65	1	1	NUM
ejpam-1478	63	66	v	v	NOUN
ejpam-1478	63	67	(	(	PUNCT
ejpam-1478	63	68	t	t	NOUN
ejpam-1478	63	69	)	)	PUNCT
ejpam-1478	63	70	≤	≤	NUM
ejpam-1478	64	1	c	c	X
ejpam-1478	64	2	∏	∏	PROPN
ejpam-1478	64	3	t0	t0	PROPN
ejpam-1478	64	4	<	<	X
ejpam-1478	64	5	ti	ti	X
ejpam-1478	64	6	<	<	X
ejpam-1478	64	7	t	t	X
ejpam-1478	64	8	(	(	PUNCT
ejpam-1478	64	9	1+aimcm−1)×	1+aimcm−1)×	PROPN
ejpam-1478	64	10	�	�	PROPN
ejpam-1478	64	11	1−(m−1	1−(m−1	NUM
ejpam-1478	64	12	)	)	PUNCT
ejpam-1478	64	13	�	�	PROPN
ejpam-1478	64	14	c	c	PROPN
ejpam-1478	64	15	∏	∏	PROPN
ejpam-1478	64	16	t0	t0	PROPN
ejpam-1478	64	17	<	<	X
ejpam-1478	64	18	ti	ti	X
ejpam-1478	64	19	<	<	X
ejpam-1478	64	20	t	t	X
ejpam-1478	64	21	(	(	PUNCT
ejpam-1478	64	22	1+aimcm−1	1+aimcm−1	NUM
ejpam-1478	64	23	)	)	PUNCT
ejpam-1478	64	24	�	�	PROPN
ejpam-1478	65	1	m−1	m−1	PROPN
ejpam-1478	65	2	∫	∫	PROPN
ejpam-1478	65	3	t	t	PROPN
ejpam-1478	65	4	t0	t0	PROPN
ejpam-1478	65	5	q(τ)dτ	q(τ)dτ	PROPN
ejpam-1478	65	6	�	�	PROPN
ejpam-1478	65	7	−	−	NOUN
ejpam-1478	65	8	1	1	NUM
ejpam-1478	65	9	m−1	m−1	PROPN
ejpam-1478	65	10	,	,	PUNCT
ejpam-1478	65	11	(	(	PUNCT
ejpam-1478	65	12	6	6	NUM
ejpam-1478	65	13	)	)	PUNCT
ejpam-1478	65	14	where	where	SCONJ
ejpam-1478	65	15	∫	∫	PROPN
ejpam-1478	65	16	t	t	PROPN
ejpam-1478	65	17	t0	t0	PROPN
ejpam-1478	65	18	q(τ)dτ≤	q(τ)dτ≤	PROPN
ejpam-1478	65	19	c1−m	c1−m	PROPN
ejpam-1478	65	20	m	m	PROPN
ejpam-1478	65	21	,	,	PUNCT
ejpam-1478	65	22	and	and	CCONJ
ejpam-1478	65	23	∏	∏	NUM
ejpam-1478	65	24	t0	t0	PROPN
ejpam-1478	65	25	<	<	X
ejpam-1478	65	26	ti	ti	X
ejpam-1478	65	27	<	<	X
ejpam-1478	65	28	t	t	X
ejpam-1478	65	29	(	(	PUNCT
ejpam-1478	65	30	1	1	NUM
ejpam-1478	65	31	+	+	NUM
ejpam-1478	65	32	aimcm−1	aimcm−1	NUM
ejpam-1478	65	33	)	)	PUNCT
ejpam-1478	65	34	<	<	X
ejpam-1478	65	35	�	�	PROPN
ejpam-1478	65	36	m	m	PROPN
ejpam-1478	65	37	m−	m−	PROPN
ejpam-1478	65	38	1	1	NUM
ejpam-1478	65	39	�	�	PROPN
ejpam-1478	65	40	1	1	NUM
ejpam-1478	65	41	m−1	m−1	PROPN
ejpam-1478	65	42	.	.	PUNCT
ejpam-1478	66	1	in	in	ADP
ejpam-1478	66	2	the	the	DET
ejpam-1478	66	3	case	case	NOUN
ejpam-1478	66	4	when	when	SCONJ
ejpam-1478	66	5	the	the	DET
ejpam-1478	66	6	supremum	supremum	NOUN
ejpam-1478	66	7	of	of	ADP
ejpam-1478	66	8	the	the	DET
ejpam-1478	66	9	unknown	unknown	ADJ
ejpam-1478	66	10	nonnegative	nonnegative	ADJ
ejpam-1478	66	11	scalar	scalar	ADJ
ejpam-1478	66	12	piecewise	piecewise	NOUN
ejpam-1478	66	13	continuous	continuous	ADJ
ejpam-1478	66	14	function	function	NOUN
ejpam-1478	66	15	is	be	AUX
ejpam-1478	66	16	involved	involve	VERB
ejpam-1478	66	17	in	in	ADP
ejpam-1478	66	18	the	the	DET
ejpam-1478	66	19	integrals	integral	NOUN
ejpam-1478	66	20	we	we	PRON
ejpam-1478	66	21	obtain	obtain	VERB
ejpam-1478	66	22	the	the	DET
ejpam-1478	66	23	following	following	ADJ
ejpam-1478	66	24	result	result	NOUN
ejpam-1478	66	25	:	:	PUNCT
ejpam-1478	66	26	theorem	theorem	NOUN
ejpam-1478	66	27	1	1	X
ejpam-1478	66	28	.	.	PUNCT
ejpam-1478	67	1	let	let	VERB
ejpam-1478	67	2	the	the	DET
ejpam-1478	67	3	following	follow	VERB
ejpam-1478	67	4	conditions	condition	NOUN
ejpam-1478	67	5	be	be	AUX
ejpam-1478	67	6	fulfilled	fulfil	VERB
ejpam-1478	67	7	:	:	PUNCT
ejpam-1478	68	1	1	1	X
ejpam-1478	68	2	.	.	PUNCT
ejpam-1478	69	1	the	the	DET
ejpam-1478	69	2	function	function	NOUN
ejpam-1478	69	3	α	α	PROPN
ejpam-1478	69	4	∈	∈	PROPN
ejpam-1478	69	5	c1([t0	c1([t0	NOUN
ejpam-1478	69	6	,	,	PUNCT
ejpam-1478	69	7	t	t	PROPN
ejpam-1478	69	8	)	)	PUNCT
ejpam-1478	69	9	,	,	PUNCT
ejpam-1478	69	10	r+	r+	X
ejpam-1478	69	11	)	)	PUNCT
ejpam-1478	69	12	is	be	AUX
ejpam-1478	69	13	a	a	DET
ejpam-1478	69	14	nondecreasing	nondecrease	VERB
ejpam-1478	69	15	function	function	NOUN
ejpam-1478	69	16	and	and	CCONJ
ejpam-1478	69	17	α(t	α(t	NOUN
ejpam-1478	69	18	)	)	PUNCT
ejpam-1478	69	19	≤	≤	NOUN
ejpam-1478	69	20	t	t	PROPN
ejpam-1478	69	21	for	for	ADP
ejpam-1478	69	22	t	t	PROPN
ejpam-1478	69	23	∈	∈	PROPN
ejpam-1478	69	24	[	[	X
ejpam-1478	69	25	t0	t0	PROPN
ejpam-1478	69	26	,	,	PUNCT
ejpam-1478	69	27	t	t	PROPN
ejpam-1478	69	28	)	)	PUNCT
ejpam-1478	69	29	.	.	PUNCT
ejpam-1478	70	1	2	2	X
ejpam-1478	70	2	.	.	X
ejpam-1478	70	3	the	the	DET
ejpam-1478	70	4	functions	function	NOUN
ejpam-1478	70	5	a	a	PRON
ejpam-1478	70	6	,	,	PUNCT
ejpam-1478	70	7	b	b	PROPN
ejpam-1478	70	8	∈	∈	PROPN
ejpam-1478	70	9	c([α(t0	c([α(t0	NOUN
ejpam-1478	70	10	)	)	PUNCT
ejpam-1478	70	11	,	,	PUNCT
ejpam-1478	70	12	t	t	PROPN
ejpam-1478	70	13	)	)	PUNCT
ejpam-1478	70	14	,	,	PUNCT
ejpam-1478	70	15	r+	r+	X
ejpam-1478	70	16	)	)	PUNCT
ejpam-1478	70	17	.	.	PUNCT
ejpam-1478	71	1	3	3	X
ejpam-1478	71	2	.	.	X
ejpam-1478	71	3	the	the	DET
ejpam-1478	71	4	function	function	NOUN
ejpam-1478	71	5	φ	φ	PROPN
ejpam-1478	71	6	∈	∈	PROPN
ejpam-1478	71	7	c([α(t0)−	c([α(t0)−	PROPN
ejpam-1478	71	8	h	h	NOUN
ejpam-1478	71	9	,	,	PUNCT
ejpam-1478	71	10	t0],r+	t0],r+	NOUN
ejpam-1478	71	11	)	)	PUNCT
ejpam-1478	71	12	,	,	PUNCT
ejpam-1478	71	13	where	where	SCONJ
ejpam-1478	71	14	h=	h=	PROPN
ejpam-1478	71	15	const	const	X
ejpam-1478	71	16	≥	≥	PROPN
ejpam-1478	71	17	0	0	NUM
ejpam-1478	71	18	.	.	PROPN
ejpam-1478	71	19	4	4	NUM
ejpam-1478	71	20	.	.	X
ejpam-1478	72	1	the	the	DET
ejpam-1478	72	2	function	function	NOUN
ejpam-1478	72	3	u	u	PROPN
ejpam-1478	72	4	∈	∈	PROPN
ejpam-1478	72	5	pc([α(t0)−	pc([α(t0)−	SYM
ejpam-1478	72	6	h	h	PROPN
ejpam-1478	72	7	,	,	PUNCT
ejpam-1478	72	8	t	t	PROPN
ejpam-1478	72	9	)	)	PUNCT
ejpam-1478	72	10	,	,	PUNCT
ejpam-1478	72	11	r+	r+	X
ejpam-1478	72	12	)	)	PUNCT
ejpam-1478	72	13	satisfies	satisfy	VERB
ejpam-1478	72	14	the	the	DET
ejpam-1478	72	15	following	follow	VERB
ejpam-1478	72	16	inequalities	inequality	NOUN
ejpam-1478	72	17	u(t	u(t	NOUN
ejpam-1478	72	18	)	)	PUNCT
ejpam-1478	72	19	≤	≤	NOUN
ejpam-1478	72	20	γ+	γ+	PUNCT
ejpam-1478	72	21	∑	∑	PROPN
ejpam-1478	72	22	t0	t0	X
ejpam-1478	72	23	<	<	X
ejpam-1478	72	24	ti	ti	X
ejpam-1478	72	25	<	<	X
ejpam-1478	72	26	t	t	NOUN
ejpam-1478	72	27	βiu	βiu	NOUN
ejpam-1478	72	28	p(t	p(t	PROPN
ejpam-1478	72	29	i)+	i)+	PROPN
ejpam-1478	72	30	∫	∫	PROPN
ejpam-1478	72	31	α(t	α(t	PROPN
ejpam-1478	72	32	)	)	PUNCT
ejpam-1478	72	33	α(t0	α(t0	NOUN
ejpam-1478	72	34	)	)	PUNCT
ejpam-1478	72	35	�	�	PROPN
ejpam-1478	72	36	a(s	a(s	PROPN
ejpam-1478	72	37	)	)	PUNCT
ejpam-1478	72	38	�	�	PROPN
ejpam-1478	72	39	u(s	u(s	PROPN
ejpam-1478	72	40	)	)	PUNCT
ejpam-1478	72	41	�	�	PROPN
ejpam-1478	72	42	p	p	NOUN
ejpam-1478	72	43	+	+	NOUN
ejpam-1478	72	44	b(s	b(	NOUN
ejpam-1478	72	45	)	)	PUNCT
ejpam-1478	72	46	�	�	PROPN
ejpam-1478	72	47	sup	sup	PROPN
ejpam-1478	72	48	ξ∈[s−h	ξ∈[s−h	NOUN
ejpam-1478	72	49	,	,	PUNCT
ejpam-1478	72	50	s	s	PART
ejpam-1478	72	51	]	]	X
ejpam-1478	72	52	u(ξ	u(ξ	NOUN
ejpam-1478	72	53	)	)	PUNCT
ejpam-1478	72	54	�	�	PROPN
ejpam-1478	72	55	p	p	NOUN
ejpam-1478	72	56	�	�	PROPN
ejpam-1478	72	57	ds	ds	NOUN
ejpam-1478	72	58	for	for	ADP
ejpam-1478	72	59	t	t	PROPN
ejpam-1478	72	60	∈	∈	PROPN
ejpam-1478	72	61	[	[	X
ejpam-1478	72	62	t0	t0	PROPN
ejpam-1478	72	63	,	,	PUNCT
ejpam-1478	72	64	t	t	PROPN
ejpam-1478	72	65	)	)	PUNCT
ejpam-1478	72	66	,	,	PUNCT
ejpam-1478	72	67	(	(	PUNCT
ejpam-1478	72	68	7	7	X
ejpam-1478	72	69	)	)	PUNCT
ejpam-1478	72	70	u(t	u(t	NOUN
ejpam-1478	72	71	)	)	PUNCT
ejpam-1478	72	72	≤	≤	NOUN
ejpam-1478	72	73	φ(t	φ(t	PROPN
ejpam-1478	72	74	)	)	PUNCT
ejpam-1478	72	75	for	for	ADP
ejpam-1478	72	76	t	t	PROPN
ejpam-1478	72	77	∈	∈	PROPN
ejpam-1478	73	1	[	[	X
ejpam-1478	73	2	α(t0)−	α(t0)−	NUM
ejpam-1478	73	3	h	h	NOUN
ejpam-1478	73	4	,	,	PUNCT
ejpam-1478	73	5	t0	t0	PROPN
ejpam-1478	73	6	]	]	PUNCT
ejpam-1478	73	7	,	,	PUNCT
ejpam-1478	73	8	(	(	PUNCT
ejpam-1478	73	9	8)	8)	NUM
ejpam-1478	73	10	where	where	SCONJ
ejpam-1478	73	11	the	the	DET
ejpam-1478	73	12	constants	constant	NOUN
ejpam-1478	73	13	p	p	X
ejpam-1478	73	14	>	>	X
ejpam-1478	73	15	0	0	NUM
ejpam-1478	73	16	,	,	PUNCT
ejpam-1478	73	17	βi	βi	PRON
ejpam-1478	73	18	≥	≥	NOUN
ejpam-1478	73	19	0	0	NUM
ejpam-1478	73	20	for	for	ADP
ejpam-1478	73	21	i	i	PROPN
ejpam-1478	73	22	∈	∈	PROPN
ejpam-1478	73	23	z(t0	z(t0	NOUN
ejpam-1478	73	24	,	,	PUNCT
ejpam-1478	73	25	t	t	PROPN
ejpam-1478	73	26	)	)	PUNCT
ejpam-1478	73	27	and	and	CCONJ
ejpam-1478	73	28	γ≤	γ≤	NUM
ejpam-1478	73	29	max	max	PROPN
ejpam-1478	73	30	s∈[α(t0)−h	s∈[α(t0)−h	PROPN
ejpam-1478	73	31	,	,	PUNCT
ejpam-1478	73	32	t0	t0	NOUN
ejpam-1478	73	33	]	]	PUNCT
ejpam-1478	73	34	φ(s	φ(s	NOUN
ejpam-1478	73	35	)	)	PUNCT
ejpam-1478	73	36	=	=	VERB
ejpam-1478	73	37	m.	m.	NOUN
ejpam-1478	73	38	then	then	ADV
ejpam-1478	73	39	for	for	ADP
ejpam-1478	73	40	t	t	PROPN
ejpam-1478	73	41	∈	∈	PROPN
ejpam-1478	73	42	[	[	X
ejpam-1478	73	43	t0	t0	PROPN
ejpam-1478	73	44	,	,	PUNCT
ejpam-1478	73	45	t	t	PROPN
ejpam-1478	73	46	)	)	PUNCT
ejpam-1478	73	47	the	the	DET
ejpam-1478	73	48	following	follow	VERB
ejpam-1478	73	49	inequalities	inequality	NOUN
ejpam-1478	73	50	are	be	AUX
ejpam-1478	73	51	fulfilled	fulfil	VERB
ejpam-1478	73	52	:	:	PUNCT
ejpam-1478	73	53	(	(	PUNCT
ejpam-1478	73	54	i	i	NOUN
ejpam-1478	73	55	)	)	PUNCT
ejpam-1478	73	56	for	for	ADP
ejpam-1478	73	57	p	p	NOUN
ejpam-1478	73	58	=	=	SYM
ejpam-1478	73	59	1	1	NUM
ejpam-1478	73	60	u(t	u(t	NOUN
ejpam-1478	73	61	)	)	PUNCT
ejpam-1478	73	62	≤	≤	NUM
ejpam-1478	73	63	m	m	VERB
ejpam-1478	73	64	�	�	PROPN
ejpam-1478	73	65	∏	∏	PROPN
ejpam-1478	73	66	t0	t0	PROPN
ejpam-1478	73	67	<	<	X
ejpam-1478	73	68	ti	ti	X
ejpam-1478	73	69	<	<	X
ejpam-1478	73	70	t	t	X
ejpam-1478	73	71	�	�	PROPN
ejpam-1478	74	1	1	1	NUM
ejpam-1478	74	2	+	+	NUM
ejpam-1478	74	3	βi	βi	PROPN
ejpam-1478	74	4	�	�	PROPN
ejpam-1478	74	5	�	�	PROPN
ejpam-1478	74	6	exp	exp	NOUN
ejpam-1478	74	7	�	�	PROPN
ejpam-1478	74	8	q(t	q(t	PROPN
ejpam-1478	74	9	)	)	PUNCT
ejpam-1478	74	10	�	�	PROPN
ejpam-1478	74	11	,	,	PUNCT
ejpam-1478	74	12	(	(	PUNCT
ejpam-1478	74	13	9	9	X
ejpam-1478	74	14	)	)	PUNCT
ejpam-1478	74	15	where	where	SCONJ
ejpam-1478	74	16	q(t	q(t	X
ejpam-1478	74	17	)	)	PUNCT
ejpam-1478	74	18	=	=	SYM
ejpam-1478	74	19	∫	∫	PROPN
ejpam-1478	74	20	α(t	α(t	PROPN
ejpam-1478	74	21	)	)	PUNCT
ejpam-1478	74	22	α(t0	α(t0	NOUN
ejpam-1478	74	23	)	)	PUNCT
ejpam-1478	74	24	h	h	NOUN
ejpam-1478	74	25	a(s	a(s	PROPN
ejpam-1478	74	26	)	)	PUNCT
ejpam-1478	75	1	+	+	NUM
ejpam-1478	75	2	b(s	b(	NOUN
ejpam-1478	75	3	)	)	PUNCT
ejpam-1478	75	4	i	i	PRON
ejpam-1478	75	5	ds	ds	VERB
ejpam-1478	75	6	;	;	PUNCT
ejpam-1478	75	7	(	(	PUNCT
ejpam-1478	75	8	10	10	NUM
ejpam-1478	75	9	)	)	PUNCT
ejpam-1478	75	10	s.	s.	PROPN
ejpam-1478	75	11	hristova	hristova	PROPN
ejpam-1478	75	12	,	,	PUNCT
ejpam-1478	75	13	k.	k.	PROPN
ejpam-1478	75	14	stefanova	stefanova	PROPN
ejpam-1478	75	15	/	/	SYM
ejpam-1478	75	16	eur	eur	PROPN
ejpam-1478	75	17	.	.	PUNCT
ejpam-1478	76	1	j.	j.	PROPN
ejpam-1478	76	2	pure	pure	PROPN
ejpam-1478	76	3	appl	appl	PROPN
ejpam-1478	76	4	.	.	PROPN
ejpam-1478	76	5	math	math	PROPN
ejpam-1478	76	6	,	,	PUNCT
ejpam-1478	76	7	5	5	NUM
ejpam-1478	76	8	(	(	PUNCT
ejpam-1478	76	9	2012	2012	NUM
ejpam-1478	76	10	)	)	PUNCT
ejpam-1478	76	11	,	,	PUNCT
ejpam-1478	76	12	30	30	NUM
ejpam-1478	76	13	-	-	SYM
ejpam-1478	76	14	44	44	NUM
ejpam-1478	76	15	34	34	NUM
ejpam-1478	76	16	(	(	PUNCT
ejpam-1478	76	17	ii	ii	NOUN
ejpam-1478	76	18	)	)	PUNCT
ejpam-1478	76	19	for	for	ADP
ejpam-1478	76	20	p	p	PROPN
ejpam-1478	76	21	∈	∈	PROPN
ejpam-1478	76	22	(	(	PUNCT
ejpam-1478	76	23	0,1	0,1	NOUN
ejpam-1478	76	24	)	)	PUNCT
ejpam-1478	76	25	u(t	u(t	NOUN
ejpam-1478	76	26	)	)	PUNCT
ejpam-1478	76	27	≤	≤	NUM
ejpam-1478	76	28	�	�	PROPN
ejpam-1478	76	29	∏	∏	PROPN
ejpam-1478	76	30	t0	t0	PROPN
ejpam-1478	76	31	<	<	X
ejpam-1478	76	32	ti	ti	X
ejpam-1478	76	33	<	<	X
ejpam-1478	76	34	t	t	X
ejpam-1478	76	35	�	�	PROPN
ejpam-1478	76	36	1	1	NUM
ejpam-1478	76	37	+	+	NUM
ejpam-1478	76	38	βi	βi	PROPN
ejpam-1478	76	39	m	m	NOUN
ejpam-1478	77	1	p−1	p−1	PROPN
ejpam-1478	77	2	�	�	PROPN
ejpam-1478	77	3	�	�	PROPN
ejpam-1478	77	4	h	h	NOUN
ejpam-1478	77	5	m1−p	m1−p	PROPN
ejpam-1478	77	6	+	+	CCONJ
ejpam-1478	77	7	(	(	PUNCT
ejpam-1478	77	8	1−	1−	NUM
ejpam-1478	77	9	p)q(t	p)q(t	NOUN
ejpam-1478	77	10	)	)	PUNCT
ejpam-1478	77	11	i	i	PROPN
ejpam-1478	77	12	1	1	NUM
ejpam-1478	77	13	1−p	1−p	NUM
ejpam-1478	77	14	;	;	PUNCT
ejpam-1478	77	15	(	(	PUNCT
ejpam-1478	77	16	11	11	NUM
ejpam-1478	77	17	)	)	PUNCT
ejpam-1478	77	18	(	(	PUNCT
ejpam-1478	77	19	iii	iii	NOUN
ejpam-1478	77	20	)	)	PUNCT
ejpam-1478	77	21	for	for	ADP
ejpam-1478	77	22	p	p	PROPN
ejpam-1478	77	23	>	>	SYM
ejpam-1478	77	24	1	1	NUM
ejpam-1478	77	25	u(t	u(t	NOUN
ejpam-1478	77	26	)	)	PUNCT
ejpam-1478	77	27	≤	≤	NUM
ejpam-1478	77	28	m	m	VERB
ejpam-1478	77	29	�	�	PROPN
ejpam-1478	77	30	∏	∏	PROPN
ejpam-1478	77	31	t0	t0	PROPN
ejpam-1478	77	32	<	<	X
ejpam-1478	77	33	ti	ti	X
ejpam-1478	77	34	<	<	X
ejpam-1478	77	35	t	t	PROPN
ejpam-1478	77	36	�	�	PROPN
ejpam-1478	77	37	1+pβi	1+pβi	NUM
ejpam-1478	77	38	m	m	PROPN
ejpam-1478	77	39	p−1	p−1	PROPN
ejpam-1478	77	40	�	�	PROPN
ejpam-1478	77	41	�	�	PROPN
ejpam-1478	77	42	×	×	PROPN
ejpam-1478	77	43	�	�	PROPN
ejpam-1478	77	44	1−(p−1	1−(p−1	NUM
ejpam-1478	77	45	)	)	PUNCT
ejpam-1478	77	46	�	�	PROPN
ejpam-1478	77	47	m	m	PROPN
ejpam-1478	77	48	�	�	PROPN
ejpam-1478	77	49	∏	∏	PROPN
ejpam-1478	77	50	t0	t0	PROPN
ejpam-1478	77	51	<	<	X
ejpam-1478	77	52	ti	ti	X
ejpam-1478	77	53	<	<	X
ejpam-1478	77	54	t	t	PROPN
ejpam-1478	77	55	�	�	PROPN
ejpam-1478	77	56	1+pβi	1+pβi	NUM
ejpam-1478	77	57	m	m	PROPN
ejpam-1478	78	1	p−1	p−1	PROPN
ejpam-1478	78	2	�	�	PROPN
ejpam-1478	78	3	�	�	PROPN
ejpam-1478	78	4	�	�	PROPN
ejpam-1478	78	5	p−1	p−1	PROPN
ejpam-1478	78	6	q(t	q(t	PROPN
ejpam-1478	78	7	)	)	PUNCT
ejpam-1478	78	8	�	�	PROPN
ejpam-1478	78	9	1	1	NUM
ejpam-1478	78	10	p−1	p−1	PROPN
ejpam-1478	78	11	,	,	PUNCT
ejpam-1478	78	12	(	(	PUNCT
ejpam-1478	78	13	12	12	NUM
ejpam-1478	78	14	)	)	PUNCT
ejpam-1478	78	15	where	where	SCONJ
ejpam-1478	78	16	q(t)≤	q(t)≤	NOUN
ejpam-1478	78	17	m1−p	m1−p	PROPN
ejpam-1478	78	18	p	p	NOUN
ejpam-1478	78	19	,	,	PUNCT
ejpam-1478	78	20	(	(	PUNCT
ejpam-1478	78	21	13	13	NUM
ejpam-1478	78	22	)	)	PUNCT
ejpam-1478	78	23	∏	∏	PROPN
ejpam-1478	78	24	t0	t0	PROPN
ejpam-1478	78	25	<	<	X
ejpam-1478	78	26	ti	ti	X
ejpam-1478	78	27	<	<	X
ejpam-1478	78	28	t	t	X
ejpam-1478	78	29	�	�	PROPN
ejpam-1478	78	30	1	1	NUM
ejpam-1478	78	31	+	+	CCONJ
ejpam-1478	78	32	pβi	pβi	PROPN
ejpam-1478	78	33	m	m	VERB
ejpam-1478	78	34	p−1	p−1	PROPN
ejpam-1478	78	35	�	�	PROPN
ejpam-1478	78	36	<	<	X
ejpam-1478	78	37	�	�	PROPN
ejpam-1478	78	38	p	p	NOUN
ejpam-1478	78	39	p−	p−	NOUN
ejpam-1478	78	40	1	1	NUM
ejpam-1478	78	41	�	�	PROPN
ejpam-1478	78	42	1	1	NUM
ejpam-1478	78	43	p−1	p−1	PROPN
ejpam-1478	78	44	.	.	PUNCT
ejpam-1478	79	1	(	(	PUNCT
ejpam-1478	79	2	14	14	NUM
ejpam-1478	79	3	)	)	PUNCT
ejpam-1478	79	4	proof	proof	NOUN
ejpam-1478	79	5	.	.	PUNCT
ejpam-1478	80	1	define	define	VERB
ejpam-1478	80	2	a	a	DET
ejpam-1478	80	3	function	function	NOUN
ejpam-1478	80	4	z	z	NOUN
ejpam-1478	80	5	:	:	PUNCT
ejpam-1478	81	1	[	[	X
ejpam-1478	81	2	α(t0)−	α(t0)−	NOUN
ejpam-1478	81	3	h	h	NOUN
ejpam-1478	81	4	,	,	PUNCT
ejpam-1478	81	5	t	t	NOUN
ejpam-1478	81	6	)	)	PUNCT
ejpam-1478	81	7	→	→	PUNCT
ejpam-1478	82	1	[	[	X
ejpam-1478	82	2	m	m	X
ejpam-1478	82	3	,	,	PUNCT
ejpam-1478	82	4	∞	∞	PROPN
ejpam-1478	82	5	)	)	PUNCT
ejpam-1478	82	6	by	by	ADP
ejpam-1478	82	7	the	the	DET
ejpam-1478	82	8	equalities	equality	NOUN
ejpam-1478	82	9	z(t	z(t	NOUN
ejpam-1478	82	10	)	)	PUNCT
ejpam-1478	82	11	=	=	SYM
ejpam-1478	82	12			PROPN
ejpam-1478	82	13			VERB
ejpam-1478	82	14			PRON
ejpam-1478	82	15			ADJ
ejpam-1478	82	16			PROPN
ejpam-1478	82	17	m	m	PROPN
ejpam-1478	82	18	+	+	PROPN
ejpam-1478	82	19	∑	∑	PROPN
ejpam-1478	82	20	t0	t0	PROPN
ejpam-1478	82	21	<	<	X
ejpam-1478	82	22	ti	ti	X
ejpam-1478	82	23	<	<	X
ejpam-1478	82	24	t	t	NOUN
ejpam-1478	82	25	βiu	βiu	NOUN
ejpam-1478	82	26	p(t	p(t	PROPN
ejpam-1478	82	27	i	i	PRON
ejpam-1478	82	28	)	)	PUNCT
ejpam-1478	83	1	+	+	CCONJ
ejpam-1478	83	2	∫	∫	PROPN
ejpam-1478	83	3	α(t	α(t	PROPN
ejpam-1478	83	4	)	)	PUNCT
ejpam-1478	83	5	α(t0	α(t0	NOUN
ejpam-1478	83	6	)	)	PUNCT
ejpam-1478	83	7	�	�	PROPN
ejpam-1478	83	8	a(s	a(s	PROPN
ejpam-1478	83	9	)	)	PUNCT
ejpam-1478	83	10	�	�	PROPN
ejpam-1478	83	11	u(s	u(s	PROPN
ejpam-1478	83	12	)	)	PUNCT
ejpam-1478	83	13	�	�	PROPN
ejpam-1478	83	14	p	p	NOUN
ejpam-1478	83	15	+	+	PROPN
ejpam-1478	83	16	b(s	b(	NOUN
ejpam-1478	83	17	)	)	PUNCT
ejpam-1478	83	18	�	�	PROPN
ejpam-1478	83	19	supξ∈[s−h	supξ∈[s−h	PROPN
ejpam-1478	83	20	,	,	PUNCT
ejpam-1478	83	21	s	s	X
ejpam-1478	83	22	]	]	X
ejpam-1478	83	23	u(ξ	u(ξ	NOUN
ejpam-1478	83	24	)	)	PUNCT
ejpam-1478	83	25	�	�	PROPN
ejpam-1478	83	26	p	p	NOUN
ejpam-1478	83	27	�	�	PROPN
ejpam-1478	83	28	ds	ds	PROPN
ejpam-1478	83	29	t	t	PROPN
ejpam-1478	83	30	∈	∈	PROPN
ejpam-1478	84	1	[	[	X
ejpam-1478	84	2	t0	t0	PROPN
ejpam-1478	84	3	,	,	PUNCT
ejpam-1478	84	4	t	t	PROPN
ejpam-1478	84	5	)	)	PUNCT
ejpam-1478	85	1	m	m	VERB
ejpam-1478	85	2	t	t	NOUN
ejpam-1478	85	3	∈	∈	PROPN
ejpam-1478	86	1	[	[	X
ejpam-1478	86	2	α(t0)−	α(t0)−	NOUN
ejpam-1478	86	3	h	h	NOUN
ejpam-1478	86	4	,	,	PUNCT
ejpam-1478	86	5	t0	t0	PROPN
ejpam-1478	86	6	]	]	PUNCT
ejpam-1478	86	7	from	from	ADP
ejpam-1478	86	8	the	the	DET
ejpam-1478	86	9	definition	definition	NOUN
ejpam-1478	86	10	of	of	ADP
ejpam-1478	86	11	the	the	DET
ejpam-1478	86	12	function	function	NOUN
ejpam-1478	86	13	z(t	z(t	NOUN
ejpam-1478	86	14	)	)	PUNCT
ejpam-1478	86	15	and	and	CCONJ
ejpam-1478	86	16	the	the	DET
ejpam-1478	86	17	choice	choice	NOUN
ejpam-1478	86	18	of	of	ADP
ejpam-1478	86	19	the	the	DET
ejpam-1478	86	20	constant	constant	ADJ
ejpam-1478	86	21	m	m	NOUN
ejpam-1478	86	22	it	it	PRON
ejpam-1478	86	23	follows	follow	VERB
ejpam-1478	86	24	the	the	DET
ejpam-1478	86	25	validity	validity	NOUN
ejpam-1478	86	26	of	of	ADP
ejpam-1478	86	27	the	the	DET
ejpam-1478	86	28	inequalities	inequality	NOUN
ejpam-1478	86	29	u(t	u(t	NOUN
ejpam-1478	86	30	)	)	PUNCT
ejpam-1478	86	31	≤	≤	NOUN
ejpam-1478	86	32	z(t	z(t	NOUN
ejpam-1478	86	33	)	)	PUNCT
ejpam-1478	86	34	,	,	PUNCT
ejpam-1478	86	35	t	t	PROPN
ejpam-1478	86	36	∈	∈	PROPN
ejpam-1478	87	1	[	[	X
ejpam-1478	87	2	α(t0)−	α(t0)−	NOUN
ejpam-1478	87	3	h	h	NOUN
ejpam-1478	87	4	,	,	PUNCT
ejpam-1478	87	5	t	t	PROPN
ejpam-1478	87	6	)	)	PUNCT
ejpam-1478	87	7	(	(	PUNCT
ejpam-1478	87	8	15	15	NUM
ejpam-1478	87	9	)	)	PUNCT
ejpam-1478	87	10	sup	sup	NOUN
ejpam-1478	87	11	ξ∈[s−h	ξ∈[s−h	NOUN
ejpam-1478	87	12	,	,	PUNCT
ejpam-1478	87	13	s	s	PART
ejpam-1478	87	14	]	]	X
ejpam-1478	87	15	u(ξ)≤	u(ξ)≤	ADJ
ejpam-1478	87	16	sup	sup	NOUN
ejpam-1478	87	17	ξ∈[s−h	ξ∈[s−h	NOUN
ejpam-1478	87	18	,	,	PUNCT
ejpam-1478	87	19	s	s	PART
ejpam-1478	87	20	]	]	X
ejpam-1478	87	21	z(ξ	z(ξ	NOUN
ejpam-1478	87	22	)	)	PUNCT
ejpam-1478	87	23	=	=	SYM
ejpam-1478	87	24	z(s	z(s	PROPN
ejpam-1478	87	25	)	)	PUNCT
ejpam-1478	87	26	,	,	PUNCT
ejpam-1478	87	27	s	s	VERB
ejpam-1478	87	28	∈	∈	PROPN
ejpam-1478	88	1	[	[	X
ejpam-1478	88	2	α(t0	α(t0	NOUN
ejpam-1478	88	3	)	)	PUNCT
ejpam-1478	88	4	,	,	PUNCT
ejpam-1478	88	5	t	t	NOUN
ejpam-1478	88	6	)	)	PUNCT
ejpam-1478	88	7	.	.	PUNCT
ejpam-1478	89	1	(	(	PUNCT
ejpam-1478	89	2	16	16	NUM
ejpam-1478	89	3	)	)	PUNCT
ejpam-1478	89	4	then	then	ADV
ejpam-1478	89	5	from	from	ADP
ejpam-1478	89	6	(	(	PUNCT
ejpam-1478	89	7	7	7	NUM
ejpam-1478	89	8	)	)	PUNCT
ejpam-1478	89	9	,	,	PUNCT
ejpam-1478	89	10	(	(	PUNCT
ejpam-1478	89	11	15	15	NUM
ejpam-1478	89	12	)	)	PUNCT
ejpam-1478	89	13	,	,	PUNCT
ejpam-1478	89	14	(	(	PUNCT
ejpam-1478	89	15	16	16	NUM
ejpam-1478	89	16	)	)	PUNCT
ejpam-1478	89	17	and	and	CCONJ
ejpam-1478	89	18	the	the	DET
ejpam-1478	89	19	definition	definition	NOUN
ejpam-1478	89	20	of	of	ADP
ejpam-1478	89	21	the	the	DET
ejpam-1478	89	22	function	function	NOUN
ejpam-1478	89	23	z(t	z(t	NOUN
ejpam-1478	89	24	)	)	PUNCT
ejpam-1478	89	25	we	we	PRON
ejpam-1478	89	26	get	get	VERB
ejpam-1478	89	27	z(t	z(t	NOUN
ejpam-1478	89	28	)	)	PUNCT
ejpam-1478	89	29	≤	≤	NUM
ejpam-1478	90	1	m	m	VERB
ejpam-1478	90	2	+	+	NUM
ejpam-1478	90	3	∑	∑	PROPN
ejpam-1478	90	4	t0	t0	PROPN
ejpam-1478	90	5	<	<	X
ejpam-1478	90	6	ti	ti	X
ejpam-1478	90	7	<	<	X
ejpam-1478	90	8	t	t	NOUN
ejpam-1478	90	9	βiz	βiz	NOUN
ejpam-1478	90	10	p(t	p(t	NOUN
ejpam-1478	90	11	i	i	PRON
ejpam-1478	90	12	)	)	PUNCT
ejpam-1478	91	1	+	+	CCONJ
ejpam-1478	91	2	∫	∫	PROPN
ejpam-1478	91	3	α(t	α(t	PROPN
ejpam-1478	91	4	)	)	PUNCT
ejpam-1478	91	5	α(t0	α(t0	NOUN
ejpam-1478	91	6	)	)	PUNCT
ejpam-1478	91	7	h	h	NOUN
ejpam-1478	91	8	a(s	a(s	PROPN
ejpam-1478	91	9	)	)	PUNCT
ejpam-1478	92	1	+	+	NUM
ejpam-1478	92	2	b(s	b(	NOUN
ejpam-1478	92	3	)	)	PUNCT
ejpam-1478	93	1	i	i	PRON
ejpam-1478	93	2	�	�	PROPN
ejpam-1478	93	3	z(s	z(s	PROPN
ejpam-1478	93	4	)	)	PUNCT
ejpam-1478	93	5	�	�	PROPN
ejpam-1478	93	6	p	p	NOUN
ejpam-1478	93	7	ds	ds	PROPN
ejpam-1478	93	8	,	,	PUNCT
ejpam-1478	93	9	t	t	PROPN
ejpam-1478	93	10	∈	∈	PROPN
ejpam-1478	94	1	[	[	X
ejpam-1478	94	2	t0	t0	PROPN
ejpam-1478	94	3	,	,	PUNCT
ejpam-1478	94	4	t	t	PROPN
ejpam-1478	94	5	)	)	PUNCT
ejpam-1478	94	6	.	.	PUNCT
ejpam-1478	95	1	(	(	PUNCT
ejpam-1478	95	2	17	17	NUM
ejpam-1478	95	3	)	)	PUNCT
ejpam-1478	95	4	consider	consider	VERB
ejpam-1478	95	5	the	the	DET
ejpam-1478	95	6	following	follow	VERB
ejpam-1478	95	7	three	three	NUM
ejpam-1478	95	8	cases	case	NOUN
ejpam-1478	95	9	:	:	PUNCT
ejpam-1478	95	10	case	case	NOUN
ejpam-1478	95	11	(	(	PUNCT
ejpam-1478	95	12	i	i	NOUN
ejpam-1478	95	13	):	):	PUNCT
ejpam-1478	95	14	let	let	VERB
ejpam-1478	95	15	p	p	NOUN
ejpam-1478	95	16	=	=	NOUN
ejpam-1478	95	17	1	1	X
ejpam-1478	95	18	.	.	PUNCT
ejpam-1478	95	19	then	then	ADV
ejpam-1478	95	20	inequality	inequality	NOUN
ejpam-1478	95	21	(	(	PUNCT
ejpam-1478	95	22	17	17	NUM
ejpam-1478	95	23	)	)	PUNCT
ejpam-1478	95	24	reduces	reduce	VERB
ejpam-1478	95	25	to	to	ADP
ejpam-1478	95	26	the	the	DET
ejpam-1478	95	27	following	follow	VERB
ejpam-1478	95	28	inequality	inequality	NOUN
ejpam-1478	95	29	z(t	z(t	NOUN
ejpam-1478	95	30	)	)	PUNCT
ejpam-1478	95	31	≤	≤	NUM
ejpam-1478	96	1	m	m	VERB
ejpam-1478	96	2	+	+	NUM
ejpam-1478	96	3	∑	∑	PROPN
ejpam-1478	96	4	t0	t0	PROPN
ejpam-1478	96	5	<	<	X
ejpam-1478	96	6	ti	ti	X
ejpam-1478	96	7	<	<	X
ejpam-1478	96	8	t	t	PROPN
ejpam-1478	96	9	βiz(t	βiz(t	PROPN
ejpam-1478	96	10	i	i	NOUN
ejpam-1478	96	11	)	)	PUNCT
ejpam-1478	97	1	+	+	CCONJ
ejpam-1478	97	2	∫	∫	PROPN
ejpam-1478	97	3	α(t	α(t	PROPN
ejpam-1478	97	4	)	)	PUNCT
ejpam-1478	97	5	α(t0	α(t0	NOUN
ejpam-1478	97	6	)	)	PUNCT
ejpam-1478	97	7	h	h	NOUN
ejpam-1478	97	8	a(s	a(s	PROPN
ejpam-1478	97	9	)	)	PUNCT
ejpam-1478	98	1	+	+	NUM
ejpam-1478	98	2	b(s	b(	NOUN
ejpam-1478	98	3	)	)	PUNCT
ejpam-1478	99	1	i	i	PRON
ejpam-1478	99	2	z(s)ds	z(s)ds	VERB
ejpam-1478	99	3	,	,	PUNCT
ejpam-1478	99	4	t	t	PROPN
ejpam-1478	99	5	∈	∈	PROPN
ejpam-1478	100	1	[	[	X
ejpam-1478	100	2	t0	t0	PROPN
ejpam-1478	100	3	,	,	PUNCT
ejpam-1478	100	4	t	t	PROPN
ejpam-1478	100	5	)	)	PUNCT
ejpam-1478	100	6	.	.	PUNCT
ejpam-1478	101	1	(	(	PUNCT
ejpam-1478	101	2	18	18	NUM
ejpam-1478	101	3	)	)	PUNCT
ejpam-1478	101	4	from	from	ADP
ejpam-1478	101	5	inequality	inequality	NOUN
ejpam-1478	101	6	(	(	PUNCT
ejpam-1478	101	7	18	18	NUM
ejpam-1478	101	8	)	)	PUNCT
ejpam-1478	101	9	according	accord	VERB
ejpam-1478	101	10	to	to	ADP
ejpam-1478	101	11	lemma	lemma	PROPN
ejpam-1478	101	12	1	1	NUM
ejpam-1478	101	13	it	it	PRON
ejpam-1478	101	14	follows	follow	VERB
ejpam-1478	101	15	z(t	z(t	NOUN
ejpam-1478	101	16	)	)	PUNCT
ejpam-1478	101	17	≤	≤	NUM
ejpam-1478	101	18	m	m	VERB
ejpam-1478	101	19	�	�	PROPN
ejpam-1478	101	20	∏	∏	PROPN
ejpam-1478	101	21	t0	t0	PROPN
ejpam-1478	101	22	<	<	X
ejpam-1478	101	23	ti	ti	X
ejpam-1478	101	24	<	<	X
ejpam-1478	101	25	t	t	X
ejpam-1478	101	26	�	�	PROPN
ejpam-1478	101	27	1	1	NUM
ejpam-1478	101	28	+	+	NUM
ejpam-1478	101	29	βi	βi	PROPN
ejpam-1478	101	30	�	�	PROPN
ejpam-1478	101	31	�	�	PROPN
ejpam-1478	101	32	exp	exp	NOUN
ejpam-1478	101	33	�	�	PROPN
ejpam-1478	101	34	∫	∫	PROPN
ejpam-1478	101	35	α(t	α(t	PROPN
ejpam-1478	101	36	)	)	PUNCT
ejpam-1478	101	37	α(t0	α(t0	NOUN
ejpam-1478	101	38	)	)	PUNCT
ejpam-1478	101	39	h	h	NOUN
ejpam-1478	101	40	a(s	a(s	PROPN
ejpam-1478	101	41	)	)	PUNCT
ejpam-1478	102	1	+	+	NUM
ejpam-1478	102	2	b(s	b(	NOUN
ejpam-1478	102	3	)	)	PUNCT
ejpam-1478	103	1	i	i	PRON
ejpam-1478	103	2	�	�	PROPN
ejpam-1478	103	3	,	,	PUNCT
ejpam-1478	103	4	t	t	PROPN
ejpam-1478	103	5	∈	∈	PROPN
ejpam-1478	104	1	[	[	X
ejpam-1478	104	2	t0	t0	PROPN
ejpam-1478	104	3	,	,	PUNCT
ejpam-1478	104	4	t	t	PROPN
ejpam-1478	104	5	)	)	PUNCT
ejpam-1478	104	6	.	.	PUNCT
ejpam-1478	105	1	(	(	PUNCT
ejpam-1478	105	2	19	19	NUM
ejpam-1478	105	3	)	)	PUNCT
ejpam-1478	105	4	inequalities	inequality	NOUN
ejpam-1478	105	5	(	(	PUNCT
ejpam-1478	105	6	19	19	NUM
ejpam-1478	105	7	)	)	PUNCT
ejpam-1478	105	8	and	and	CCONJ
ejpam-1478	105	9	(	(	PUNCT
ejpam-1478	105	10	15	15	X
ejpam-1478	105	11	)	)	PUNCT
ejpam-1478	105	12	imply	imply	VERB
ejpam-1478	105	13	the	the	DET
ejpam-1478	105	14	validity	validity	NOUN
ejpam-1478	105	15	of	of	ADP
ejpam-1478	105	16	the	the	DET
ejpam-1478	105	17	required	required	ADJ
ejpam-1478	105	18	inequality	inequality	NOUN
ejpam-1478	105	19	(	(	PUNCT
ejpam-1478	105	20	9	9	NUM
ejpam-1478	105	21	)	)	PUNCT
ejpam-1478	105	22	.	.	PUNCT
ejpam-1478	106	1	s.	s.	PROPN
ejpam-1478	106	2	hristova	hristova	PROPN
ejpam-1478	106	3	,	,	PUNCT
ejpam-1478	106	4	k.	k.	PROPN
ejpam-1478	106	5	stefanova	stefanova	PROPN
ejpam-1478	106	6	/	/	SYM
ejpam-1478	106	7	eur	eur	PROPN
ejpam-1478	106	8	.	.	PUNCT
ejpam-1478	107	1	j.	j.	PROPN
ejpam-1478	107	2	pure	pure	PROPN
ejpam-1478	107	3	appl	appl	PROPN
ejpam-1478	107	4	.	.	PROPN
ejpam-1478	107	5	math	math	PROPN
ejpam-1478	107	6	,	,	PUNCT
ejpam-1478	107	7	5	5	NUM
ejpam-1478	107	8	(	(	PUNCT
ejpam-1478	107	9	2012	2012	NUM
ejpam-1478	107	10	)	)	PUNCT
ejpam-1478	107	11	,	,	PUNCT
ejpam-1478	107	12	30	30	NUM
ejpam-1478	107	13	-	-	SYM
ejpam-1478	107	14	44	44	NUM
ejpam-1478	107	15	35	35	NUM
ejpam-1478	107	16	case	case	NOUN
ejpam-1478	107	17	(	(	PUNCT
ejpam-1478	107	18	ii	ii	NOUN
ejpam-1478	107	19	):	):	PUNCT
ejpam-1478	107	20	let	let	VERB
ejpam-1478	107	21	p	p	X
ejpam-1478	107	22	∈	∈	PROPN
ejpam-1478	107	23	(	(	PUNCT
ejpam-1478	107	24	0,1	0,1	NUM
ejpam-1478	107	25	)	)	PUNCT
ejpam-1478	107	26	.	.	PUNCT
ejpam-1478	108	1	from	from	ADP
ejpam-1478	108	2	inequality	inequality	NOUN
ejpam-1478	108	3	(	(	PUNCT
ejpam-1478	108	4	17	17	NUM
ejpam-1478	108	5	)	)	PUNCT
ejpam-1478	108	6	according	accord	VERB
ejpam-1478	108	7	to	to	ADP
ejpam-1478	108	8	lemma	lemma	PROPN
ejpam-1478	108	9	2	2	NUM
ejpam-1478	108	10	we	we	PRON
ejpam-1478	108	11	obtain	obtain	VERB
ejpam-1478	108	12	for	for	ADP
ejpam-1478	108	13	t	t	PROPN
ejpam-1478	108	14	∈	∈	PROPN
ejpam-1478	108	15	[	[	X
ejpam-1478	108	16	t0	t0	PROPN
ejpam-1478	108	17	,	,	PUNCT
ejpam-1478	108	18	t	t	PROPN
ejpam-1478	108	19	)	)	PUNCT
ejpam-1478	108	20	z(t	z(t	NOUN
ejpam-1478	108	21	)	)	PUNCT
ejpam-1478	108	22	≤	≤	NUM
ejpam-1478	108	23	�	�	PROPN
ejpam-1478	108	24	∏	∏	PROPN
ejpam-1478	108	25	t0	t0	PROPN
ejpam-1478	108	26	<	<	X
ejpam-1478	108	27	ti	ti	X
ejpam-1478	108	28	<	<	X
ejpam-1478	108	29	t	t	X
ejpam-1478	108	30	�	�	PROPN
ejpam-1478	108	31	1	1	NUM
ejpam-1478	108	32	+	+	NUM
ejpam-1478	108	33	βi	βi	PROPN
ejpam-1478	108	34	m	m	NOUN
ejpam-1478	109	1	p−1	p−1	PROPN
ejpam-1478	109	2	�	�	PROPN
ejpam-1478	109	3	�	�	PROPN
ejpam-1478	109	4	h	h	NOUN
ejpam-1478	109	5	m1−p	m1−p	PROPN
ejpam-1478	109	6	+	+	CCONJ
ejpam-1478	109	7	(	(	PUNCT
ejpam-1478	109	8	1−	1−	NUM
ejpam-1478	109	9	p)q(t	p)q(t	NOUN
ejpam-1478	109	10	)	)	PUNCT
ejpam-1478	109	11	i	i	PROPN
ejpam-1478	109	12	1	1	NUM
ejpam-1478	109	13	1−p	1−p	NUM
ejpam-1478	109	14	,	,	PUNCT
ejpam-1478	109	15	(	(	PUNCT
ejpam-1478	109	16	20	20	NUM
ejpam-1478	109	17	)	)	PUNCT
ejpam-1478	109	18	where	where	SCONJ
ejpam-1478	109	19	the	the	DET
ejpam-1478	109	20	function	function	NOUN
ejpam-1478	109	21	q(t	q(t	PROPN
ejpam-1478	109	22	)	)	PUNCT
ejpam-1478	109	23	is	be	AUX
ejpam-1478	109	24	defined	define	VERB
ejpam-1478	109	25	by	by	ADP
ejpam-1478	109	26	equality	equality	NOUN
ejpam-1478	109	27	(	(	PUNCT
ejpam-1478	109	28	10	10	NUM
ejpam-1478	109	29	)	)	PUNCT
ejpam-1478	109	30	.	.	PUNCT
ejpam-1478	110	1	substitute	substitute	VERB
ejpam-1478	110	2	the	the	DET
ejpam-1478	110	3	bound	bound	ADJ
ejpam-1478	110	4	(	(	PUNCT
ejpam-1478	110	5	20	20	NUM
ejpam-1478	110	6	)	)	PUNCT
ejpam-1478	110	7	for	for	ADP
ejpam-1478	110	8	the	the	DET
ejpam-1478	110	9	function	function	NOUN
ejpam-1478	110	10	z(t	z(t	NOUN
ejpam-1478	110	11	)	)	PUNCT
ejpam-1478	110	12	into	into	ADP
ejpam-1478	110	13	the	the	DET
ejpam-1478	110	14	right	right	ADJ
ejpam-1478	110	15	hand	hand	NOUN
ejpam-1478	110	16	-	-	PUNCT
ejpam-1478	110	17	side	side	NOUN
ejpam-1478	110	18	of	of	ADP
ejpam-1478	110	19	(	(	PUNCT
ejpam-1478	110	20	15	15	NUM
ejpam-1478	110	21	)	)	PUNCT
ejpam-1478	110	22	and	and	CCONJ
ejpam-1478	110	23	get	get	VERB
ejpam-1478	110	24	the	the	DET
ejpam-1478	110	25	required	require	VERB
ejpam-1478	110	26	inequality	inequality	NOUN
ejpam-1478	110	27	(	(	PUNCT
ejpam-1478	110	28	11	11	NUM
ejpam-1478	110	29	)	)	PUNCT
ejpam-1478	110	30	.	.	PUNCT
ejpam-1478	111	1	case	case	NOUN
ejpam-1478	111	2	(	(	PUNCT
ejpam-1478	111	3	iii	iii	NOUN
ejpam-1478	111	4	):	):	PUNCT
ejpam-1478	111	5	let	let	VERB
ejpam-1478	111	6	p	p	PRON
ejpam-1478	111	7	>	>	X
ejpam-1478	111	8	1	1	NUM
ejpam-1478	111	9	.	.	PUNCT
ejpam-1478	112	1	as	as	ADP
ejpam-1478	112	2	in	in	ADP
ejpam-1478	112	3	the	the	DET
ejpam-1478	112	4	case	case	NOUN
ejpam-1478	112	5	(	(	PUNCT
ejpam-1478	112	6	ii	ii	NOUN
ejpam-1478	112	7	)	)	PUNCT
ejpam-1478	112	8	from	from	ADP
ejpam-1478	112	9	inequality	inequality	NOUN
ejpam-1478	112	10	(	(	PUNCT
ejpam-1478	112	11	17	17	NUM
ejpam-1478	112	12	)	)	PUNCT
ejpam-1478	112	13	according	accord	VERB
ejpam-1478	112	14	to	to	ADP
ejpam-1478	112	15	lemma	lemma	PROPN
ejpam-1478	112	16	2	2	NUM
ejpam-1478	112	17	we	we	PRON
ejpam-1478	112	18	obtain	obtain	VERB
ejpam-1478	112	19	for	for	ADP
ejpam-1478	112	20	t	t	PROPN
ejpam-1478	112	21	∈	∈	PROPN
ejpam-1478	112	22	[	[	X
ejpam-1478	112	23	t0	t0	PROPN
ejpam-1478	112	24	,	,	PUNCT
ejpam-1478	112	25	t	t	PROPN
ejpam-1478	112	26	)	)	PUNCT
ejpam-1478	112	27	z(t	z(t	NOUN
ejpam-1478	112	28	)	)	PUNCT
ejpam-1478	113	1	≤	≤	NUM
ejpam-1478	113	2	m	m	VERB
ejpam-1478	113	3	�	�	PROPN
ejpam-1478	113	4	∏	∏	PROPN
ejpam-1478	113	5	t0	t0	PROPN
ejpam-1478	113	6	<	<	X
ejpam-1478	113	7	ti	ti	X
ejpam-1478	113	8	<	<	X
ejpam-1478	113	9	t	t	X
ejpam-1478	113	10	�	�	PROPN
ejpam-1478	113	11	1	1	NUM
ejpam-1478	113	12	+	+	CCONJ
ejpam-1478	113	13	pβi	pβi	PROPN
ejpam-1478	113	14	m	m	VERB
ejpam-1478	113	15	p−1	p−1	PROPN
ejpam-1478	113	16	�	�	PROPN
ejpam-1478	113	17	�	�	PROPN
ejpam-1478	113	18	×	×	PROPN
ejpam-1478	113	19	×	×	PROPN
ejpam-1478	113	20	�	�	PROPN
ejpam-1478	113	21	1−	1−	NUM
ejpam-1478	113	22	(	(	PUNCT
ejpam-1478	113	23	p−	p−	NOUN
ejpam-1478	113	24	1	1	NUM
ejpam-1478	113	25	)	)	PUNCT
ejpam-1478	113	26	�	�	PROPN
ejpam-1478	113	27	m	m	PROPN
ejpam-1478	113	28	�	�	PROPN
ejpam-1478	113	29	∏	∏	PROPN
ejpam-1478	113	30	t0	t0	PROPN
ejpam-1478	113	31	<	<	X
ejpam-1478	113	32	ti	ti	X
ejpam-1478	113	33	<	<	X
ejpam-1478	113	34	t	t	X
ejpam-1478	113	35	�	�	PROPN
ejpam-1478	113	36	1	1	NUM
ejpam-1478	113	37	+	+	CCONJ
ejpam-1478	113	38	pβi	pβi	PROPN
ejpam-1478	113	39	m	m	VERB
ejpam-1478	113	40	p−1	p−1	PROPN
ejpam-1478	113	41	�	�	PROPN
ejpam-1478	113	42	�	�	PROPN
ejpam-1478	113	43	�	�	PROPN
ejpam-1478	113	44	p−1	p−1	PROPN
ejpam-1478	113	45	q(t	q(t	PROPN
ejpam-1478	113	46	)	)	PUNCT
ejpam-1478	113	47	�	�	PROPN
ejpam-1478	113	48	1	1	NUM
ejpam-1478	113	49	p−1	p−1	PROPN
ejpam-1478	113	50	,	,	PUNCT
ejpam-1478	113	51	(	(	PUNCT
ejpam-1478	113	52	21	21	NUM
ejpam-1478	113	53	)	)	PUNCT
ejpam-1478	113	54	where	where	SCONJ
ejpam-1478	113	55	the	the	DET
ejpam-1478	113	56	function	function	NOUN
ejpam-1478	113	57	q(t	q(t	PROPN
ejpam-1478	113	58	)	)	PUNCT
ejpam-1478	113	59	is	be	AUX
ejpam-1478	113	60	defined	define	VERB
ejpam-1478	113	61	by	by	ADP
ejpam-1478	113	62	equality	equality	NOUN
ejpam-1478	113	63	(	(	PUNCT
ejpam-1478	113	64	10	10	NUM
ejpam-1478	113	65	)	)	PUNCT
ejpam-1478	113	66	and	and	CCONJ
ejpam-1478	113	67	inequalities	inequality	NOUN
ejpam-1478	113	68	(	(	PUNCT
ejpam-1478	113	69	13	13	NUM
ejpam-1478	113	70	)	)	PUNCT
ejpam-1478	113	71	and	and	CCONJ
ejpam-1478	113	72	(	(	PUNCT
ejpam-1478	113	73	14	14	NUM
ejpam-1478	113	74	)	)	PUNCT
ejpam-1478	113	75	hold	hold	NOUN
ejpam-1478	113	76	.	.	PUNCT
ejpam-1478	114	1	substitute	substitute	VERB
ejpam-1478	114	2	the	the	DET
ejpam-1478	114	3	bound	bound	ADJ
ejpam-1478	114	4	(	(	PUNCT
ejpam-1478	114	5	21	21	NUM
ejpam-1478	114	6	)	)	PUNCT
ejpam-1478	114	7	for	for	ADP
ejpam-1478	114	8	the	the	DET
ejpam-1478	114	9	function	function	NOUN
ejpam-1478	114	10	z(t	z(t	NOUN
ejpam-1478	114	11	)	)	PUNCT
ejpam-1478	114	12	into	into	ADP
ejpam-1478	114	13	the	the	DET
ejpam-1478	114	14	right	right	ADJ
ejpam-1478	114	15	hand	hand	NOUN
ejpam-1478	114	16	-	-	PUNCT
ejpam-1478	114	17	side	side	NOUN
ejpam-1478	114	18	of	of	ADP
ejpam-1478	114	19	(	(	PUNCT
ejpam-1478	114	20	15	15	NUM
ejpam-1478	114	21	)	)	PUNCT
ejpam-1478	114	22	and	and	CCONJ
ejpam-1478	114	23	get	get	VERB
ejpam-1478	114	24	the	the	DET
ejpam-1478	114	25	required	require	VERB
ejpam-1478	114	26	inequality	inequality	NOUN
ejpam-1478	114	27	(	(	PUNCT
ejpam-1478	114	28	12	12	NUM
ejpam-1478	114	29	)	)	PUNCT
ejpam-1478	114	30	.	.	PUNCT
ejpam-1478	115	1	similarly	similarly	ADV
ejpam-1478	115	2	to	to	ADP
ejpam-1478	115	3	the	the	DET
ejpam-1478	115	4	proof	proof	NOUN
ejpam-1478	115	5	of	of	ADP
ejpam-1478	115	6	theorem	theorem	NOUN
ejpam-1478	115	7	1	1	NUM
ejpam-1478	115	8	we	we	PRON
ejpam-1478	115	9	can	can	AUX
ejpam-1478	115	10	obtain	obtain	VERB
ejpam-1478	115	11	the	the	DET
ejpam-1478	115	12	following	follow	VERB
ejpam-1478	115	13	result	result	NOUN
ejpam-1478	115	14	:	:	PUNCT
ejpam-1478	115	15	theorem	theorem	NOUN
ejpam-1478	115	16	2	2	NUM
ejpam-1478	115	17	.	.	PUNCT
ejpam-1478	116	1	let	let	VERB
ejpam-1478	116	2	the	the	DET
ejpam-1478	116	3	following	follow	VERB
ejpam-1478	116	4	conditions	condition	NOUN
ejpam-1478	116	5	be	be	AUX
ejpam-1478	116	6	fulfilled	fulfil	VERB
ejpam-1478	116	7	:	:	PUNCT
ejpam-1478	116	8	1	1	X
ejpam-1478	116	9	.	.	X
ejpam-1478	116	10	the	the	DET
ejpam-1478	116	11	functions	function	NOUN
ejpam-1478	116	12	α	α	X
ejpam-1478	116	13	j	j	PROPN
ejpam-1478	116	14	∈	∈	PROPN
ejpam-1478	116	15	c1([t0	c1([t0	PROPN
ejpam-1478	116	16	,	,	PUNCT
ejpam-1478	116	17	t	t	PROPN
ejpam-1478	116	18	)	)	PUNCT
ejpam-1478	116	19	,	,	PUNCT
ejpam-1478	116	20	r+	r+	X
ejpam-1478	116	21	)	)	PUNCT
ejpam-1478	116	22	are	be	AUX
ejpam-1478	116	23	nondecreasing	nondecrease	VERB
ejpam-1478	116	24	and	and	CCONJ
ejpam-1478	116	25	the	the	DET
ejpam-1478	116	26	inequalities	inequality	NOUN
ejpam-1478	116	27	α	α	PROPN
ejpam-1478	116	28	j(t	j(t	PROPN
ejpam-1478	116	29	)	)	PUNCT
ejpam-1478	116	30	≤	≤	PUNCT
ejpam-1478	117	1	t	t	PROPN
ejpam-1478	117	2	hold	hold	VERB
ejpam-1478	117	3	for	for	ADP
ejpam-1478	117	4	t	t	PROPN
ejpam-1478	117	5	∈	∈	PROPN
ejpam-1478	117	6	[	[	X
ejpam-1478	117	7	t0	t0	PROPN
ejpam-1478	117	8	,	,	PUNCT
ejpam-1478	117	9	t	t	PROPN
ejpam-1478	117	10	)	)	PUNCT
ejpam-1478	117	11	,	,	PUNCT
ejpam-1478	117	12	j	j	PROPN
ejpam-1478	118	1	=	=	SYM
ejpam-1478	118	2	1,2	1,2	NUM
ejpam-1478	118	3	,	,	PUNCT
ejpam-1478	118	4	.	.	PUNCT
ejpam-1478	118	5	.	.	PUNCT
ejpam-1478	119	1	.	.	PUNCT
ejpam-1478	120	1	,	,	PUNCT
ejpam-1478	120	2	m.	m.	NOUN
ejpam-1478	120	3	2	2	NUM
ejpam-1478	120	4	.	.	PUNCT
ejpam-1478	121	1	the	the	DET
ejpam-1478	121	2	functions	function	NOUN
ejpam-1478	121	3	a	a	DET
ejpam-1478	121	4	j	j	PROPN
ejpam-1478	121	5	,	,	PUNCT
ejpam-1478	121	6	b	b	PROPN
ejpam-1478	121	7	j	j	PROPN
ejpam-1478	121	8	∈	∈	PROPN
ejpam-1478	121	9	c([a	c([a	PROPN
ejpam-1478	121	10	,	,	PUNCT
ejpam-1478	121	11	t	t	PROPN
ejpam-1478	121	12	)	)	PUNCT
ejpam-1478	121	13	,	,	PUNCT
ejpam-1478	121	14	r+	r+	X
ejpam-1478	121	15	)	)	PUNCT
ejpam-1478	121	16	for	for	ADP
ejpam-1478	121	17	j	j	PROPN
ejpam-1478	121	18	=	=	SYM
ejpam-1478	121	19	1,2	1,2	NUM
ejpam-1478	121	20	,	,	PUNCT
ejpam-1478	121	21	.	.	PUNCT
ejpam-1478	121	22	.	.	PUNCT
ejpam-1478	122	1	.	.	PUNCT
ejpam-1478	123	1	,	,	PUNCT
ejpam-1478	123	2	m	m	PROPN
ejpam-1478	123	3	,	,	PUNCT
ejpam-1478	123	4	where	where	SCONJ
ejpam-1478	123	5	a=	a=	PROPN
ejpam-1478	123	6	min	min	PROPN
ejpam-1478	123	7	1≤	1≤	PROPN
ejpam-1478	123	8	j≤n	j≤n	PROPN
ejpam-1478	123	9	α	α	PROPN
ejpam-1478	123	10	j(t0	j(t0	NOUN
ejpam-1478	123	11	)	)	PUNCT
ejpam-1478	123	12	.	.	PUNCT
ejpam-1478	124	1	3	3	X
ejpam-1478	124	2	.	.	X
ejpam-1478	124	3	the	the	DET
ejpam-1478	124	4	function	function	NOUN
ejpam-1478	124	5	φ	φ	PROPN
ejpam-1478	124	6	∈	∈	PROPN
ejpam-1478	124	7	c([a−	c([a−	PROPN
ejpam-1478	124	8	h	h	NOUN
ejpam-1478	124	9	,	,	PUNCT
ejpam-1478	124	10	t0],r+	t0],r+	NOUN
ejpam-1478	124	11	)	)	PUNCT
ejpam-1478	124	12	,	,	PUNCT
ejpam-1478	124	13	where	where	SCONJ
ejpam-1478	124	14	h=	h=	PROPN
ejpam-1478	124	15	const	const	X
ejpam-1478	124	16	≥	≥	PROPN
ejpam-1478	124	17	0	0	NUM
ejpam-1478	124	18	.	.	PROPN
ejpam-1478	124	19	4	4	NUM
ejpam-1478	124	20	.	.	X
ejpam-1478	125	1	the	the	DET
ejpam-1478	125	2	function	function	NOUN
ejpam-1478	125	3	u	u	PROPN
ejpam-1478	125	4	∈	∈	PROPN
ejpam-1478	125	5	pc([a−	pc([a−	NOUN
ejpam-1478	125	6	h	h	PROPN
ejpam-1478	125	7	,	,	PUNCT
ejpam-1478	125	8	t	t	PROPN
ejpam-1478	125	9	)	)	PUNCT
ejpam-1478	125	10	,	,	PUNCT
ejpam-1478	125	11	r+	r+	X
ejpam-1478	125	12	)	)	PUNCT
ejpam-1478	125	13	satisfies	satisfy	VERB
ejpam-1478	125	14	the	the	DET
ejpam-1478	125	15	following	follow	VERB
ejpam-1478	125	16	inequalities	inequality	NOUN
ejpam-1478	125	17	u(t	u(t	NOUN
ejpam-1478	125	18	)	)	PUNCT
ejpam-1478	125	19	≤	≤	NOUN
ejpam-1478	125	20	γ+	γ+	PUNCT
ejpam-1478	125	21	∑	∑	PROPN
ejpam-1478	125	22	t0	t0	X
ejpam-1478	125	23	<	<	X
ejpam-1478	125	24	ti	ti	X
ejpam-1478	125	25	<	<	X
ejpam-1478	125	26	t	t	NOUN
ejpam-1478	125	27	βiu	βiu	NOUN
ejpam-1478	125	28	p(t	p(t	PROPN
ejpam-1478	125	29	i)+	i)+	PUNCT
ejpam-1478	125	30	m	m	VERB
ejpam-1478	125	31	∑	∑	PUNCT
ejpam-1478	125	32	j=1	j=1	ADJ
ejpam-1478	125	33	∫	∫	PROPN
ejpam-1478	125	34	α	α	PROPN
ejpam-1478	125	35	j(t	j(t	PROPN
ejpam-1478	125	36	)	)	PUNCT
ejpam-1478	125	37	α	α	PROPN
ejpam-1478	125	38	j(t0	j(t0	NOUN
ejpam-1478	125	39	)	)	PUNCT
ejpam-1478	125	40	�	�	PROPN
ejpam-1478	125	41	a	a	DET
ejpam-1478	125	42	j(s	j(s	NOUN
ejpam-1478	125	43	)	)	PUNCT
ejpam-1478	125	44	�	�	PROPN
ejpam-1478	125	45	u(s	u(s	PROPN
ejpam-1478	125	46	)	)	PUNCT
ejpam-1478	125	47	�	�	PROPN
ejpam-1478	125	48	p	p	NOUN
ejpam-1478	126	1	+	+	PROPN
ejpam-1478	126	2	b	b	PROPN
ejpam-1478	126	3	j(s	j(s	NOUN
ejpam-1478	126	4	)	)	PUNCT
ejpam-1478	126	5	�	�	PROPN
ejpam-1478	126	6	sup	sup	PROPN
ejpam-1478	126	7	ξ∈[s−h	ξ∈[s−h	NOUN
ejpam-1478	126	8	,	,	PUNCT
ejpam-1478	126	9	s	s	PART
ejpam-1478	126	10	]	]	X
ejpam-1478	126	11	u(ξ	u(ξ	NOUN
ejpam-1478	126	12	)	)	PUNCT
ejpam-1478	126	13	�	�	PROPN
ejpam-1478	126	14	p	p	NOUN
ejpam-1478	126	15	�	�	PROPN
ejpam-1478	126	16	ds	ds	PROPN
ejpam-1478	126	17	,	,	PUNCT
ejpam-1478	126	18	t	t	PROPN
ejpam-1478	126	19	∈	∈	PROPN
ejpam-1478	127	1	[	[	X
ejpam-1478	127	2	t0	t0	PROPN
ejpam-1478	127	3	,	,	PUNCT
ejpam-1478	127	4	t	t	PROPN
ejpam-1478	127	5	)	)	PUNCT
ejpam-1478	127	6	,	,	PUNCT
ejpam-1478	127	7	(	(	PUNCT
ejpam-1478	127	8	22	22	NUM
ejpam-1478	127	9	)	)	PUNCT
ejpam-1478	127	10	u(t	u(t	NOUN
ejpam-1478	127	11	)	)	PUNCT
ejpam-1478	127	12	≤	≤	NOUN
ejpam-1478	127	13	φ(t	φ(t	PROPN
ejpam-1478	127	14	)	)	PUNCT
ejpam-1478	127	15	,	,	PUNCT
ejpam-1478	127	16	t	t	PROPN
ejpam-1478	127	17	∈	∈	PROPN
ejpam-1478	128	1	[	[	X
ejpam-1478	128	2	a−	a−	PROPN
ejpam-1478	128	3	h	h	NOUN
ejpam-1478	128	4	,	,	PUNCT
ejpam-1478	128	5	t0	t0	PROPN
ejpam-1478	128	6	]	]	PUNCT
ejpam-1478	128	7	,	,	PUNCT
ejpam-1478	128	8	(	(	PUNCT
ejpam-1478	128	9	23	23	NUM
ejpam-1478	128	10	)	)	PUNCT
ejpam-1478	128	11	where	where	SCONJ
ejpam-1478	128	12	the	the	DET
ejpam-1478	128	13	constants	constant	NOUN
ejpam-1478	128	14	p	p	X
ejpam-1478	128	15	>	>	X
ejpam-1478	128	16	0	0	NUM
ejpam-1478	128	17	,	,	PUNCT
ejpam-1478	128	18	βi	βi	PRON
ejpam-1478	128	19	≥	≥	NOUN
ejpam-1478	128	20	0	0	NUM
ejpam-1478	128	21	for	for	ADP
ejpam-1478	128	22	i	i	PROPN
ejpam-1478	128	23	∈	∈	PROPN
ejpam-1478	128	24	z(t0	z(t0	NOUN
ejpam-1478	128	25	,	,	PUNCT
ejpam-1478	128	26	t	t	PROPN
ejpam-1478	128	27	)	)	PUNCT
ejpam-1478	128	28	and	and	CCONJ
ejpam-1478	128	29	γ	γ	PROPN
ejpam-1478	128	30	≤	≤	NUM
ejpam-1478	128	31	max	max	PROPN
ejpam-1478	128	32	s∈[a−h	s∈[a−h	NOUN
ejpam-1478	128	33	,	,	PUNCT
ejpam-1478	128	34	t0	t0	NOUN
ejpam-1478	128	35	]	]	PUNCT
ejpam-1478	128	36	φ(s	φ(s	NOUN
ejpam-1478	128	37	)	)	PUNCT
ejpam-1478	128	38	=	=	SYM
ejpam-1478	128	39	m̃	m̃	PROPN
ejpam-1478	128	40	.	.	PUNCT
ejpam-1478	129	1	then	then	ADV
ejpam-1478	129	2	for	for	ADP
ejpam-1478	129	3	t	t	PROPN
ejpam-1478	129	4	∈	∈	PROPN
ejpam-1478	129	5	[	[	X
ejpam-1478	129	6	t0	t0	PROPN
ejpam-1478	129	7	,	,	PUNCT
ejpam-1478	129	8	t	t	PROPN
ejpam-1478	129	9	)	)	PUNCT
ejpam-1478	129	10	the	the	DET
ejpam-1478	129	11	following	follow	VERB
ejpam-1478	129	12	inequalities	inequality	NOUN
ejpam-1478	129	13	are	be	AUX
ejpam-1478	129	14	fulfilled	fulfil	VERB
ejpam-1478	129	15	:	:	PUNCT
ejpam-1478	129	16	s.	s.	PROPN
ejpam-1478	129	17	hristova	hristova	PROPN
ejpam-1478	129	18	,	,	PUNCT
ejpam-1478	129	19	k.	k.	PROPN
ejpam-1478	129	20	stefanova	stefanova	PROPN
ejpam-1478	129	21	/	/	SYM
ejpam-1478	129	22	eur	eur	PROPN
ejpam-1478	129	23	.	.	PUNCT
ejpam-1478	130	1	j.	j.	PROPN
ejpam-1478	130	2	pure	pure	PROPN
ejpam-1478	130	3	appl	appl	PROPN
ejpam-1478	130	4	.	.	PROPN
ejpam-1478	130	5	math	math	PROPN
ejpam-1478	130	6	,	,	PUNCT
ejpam-1478	130	7	5	5	NUM
ejpam-1478	130	8	(	(	PUNCT
ejpam-1478	130	9	2012	2012	NUM
ejpam-1478	130	10	)	)	PUNCT
ejpam-1478	130	11	,	,	PUNCT
ejpam-1478	130	12	30	30	NUM
ejpam-1478	130	13	-	-	SYM
ejpam-1478	130	14	44	44	NUM
ejpam-1478	130	15	36	36	NUM
ejpam-1478	130	16	(	(	PUNCT
ejpam-1478	130	17	i	i	NOUN
ejpam-1478	130	18	)	)	PUNCT
ejpam-1478	130	19	for	for	ADP
ejpam-1478	130	20	p	p	NOUN
ejpam-1478	130	21	=	=	SYM
ejpam-1478	130	22	1	1	NUM
ejpam-1478	130	23	u(t	u(t	NOUN
ejpam-1478	130	24	)	)	PUNCT
ejpam-1478	130	25	≤	≤	PUNCT
ejpam-1478	130	26	m̃	m̃	PROPN
ejpam-1478	130	27	�	�	PROPN
ejpam-1478	130	28	∏	∏	PROPN
ejpam-1478	130	29	t0	t0	PROPN
ejpam-1478	130	30	<	<	X
ejpam-1478	130	31	ti	ti	X
ejpam-1478	130	32	<	<	X
ejpam-1478	130	33	t	t	X
ejpam-1478	130	34	�	�	PROPN
ejpam-1478	131	1	1	1	NUM
ejpam-1478	131	2	+	+	NUM
ejpam-1478	131	3	βi	βi	PROPN
ejpam-1478	131	4	�	�	PROPN
ejpam-1478	131	5	�	�	PROPN
ejpam-1478	131	6	exp	exp	NOUN
ejpam-1478	131	7	�	�	PROPN
ejpam-1478	131	8	q̃(t	q̃(t	PROPN
ejpam-1478	131	9	)	)	PUNCT
ejpam-1478	131	10	�	�	PROPN
ejpam-1478	131	11	,	,	PUNCT
ejpam-1478	131	12	(	(	PUNCT
ejpam-1478	131	13	24	24	NUM
ejpam-1478	131	14	)	)	PUNCT
ejpam-1478	131	15	where	where	SCONJ
ejpam-1478	131	16	q̃(t	q̃(t	NOUN
ejpam-1478	131	17	)	)	PUNCT
ejpam-1478	132	1	=	=	PUNCT
ejpam-1478	132	2	m	m	VERB
ejpam-1478	132	3	∑	∑	VERB
ejpam-1478	132	4	j=1	j=1	ADJ
ejpam-1478	132	5	∫	∫	PROPN
ejpam-1478	132	6	α	α	PROPN
ejpam-1478	132	7	j(t	j(t	PROPN
ejpam-1478	132	8	)	)	PUNCT
ejpam-1478	132	9	α	α	PROPN
ejpam-1478	132	10	j(t0	j(t0	NOUN
ejpam-1478	132	11	)	)	PUNCT
ejpam-1478	132	12	h	h	NOUN
ejpam-1478	132	13	a	a	DET
ejpam-1478	132	14	j(s	j(s	NOUN
ejpam-1478	132	15	)	)	PUNCT
ejpam-1478	133	1	+	+	CCONJ
ejpam-1478	133	2	b	b	X
ejpam-1478	133	3	j(s	j(s	NOUN
ejpam-1478	133	4	)	)	PUNCT
ejpam-1478	134	1	i	i	PRON
ejpam-1478	134	2	ds	ds	VERB
ejpam-1478	134	3	;	;	PUNCT
ejpam-1478	134	4	(	(	PUNCT
ejpam-1478	134	5	25	25	NUM
ejpam-1478	134	6	)	)	PUNCT
ejpam-1478	134	7	(	(	PUNCT
ejpam-1478	134	8	ii	ii	NOUN
ejpam-1478	134	9	)	)	PUNCT
ejpam-1478	134	10	for	for	ADP
ejpam-1478	134	11	p	p	PROPN
ejpam-1478	134	12	∈	∈	PROPN
ejpam-1478	134	13	(	(	PUNCT
ejpam-1478	134	14	0,1	0,1	NOUN
ejpam-1478	134	15	)	)	PUNCT
ejpam-1478	134	16	u(t	u(t	NOUN
ejpam-1478	134	17	)	)	PUNCT
ejpam-1478	134	18	≤	≤	NUM
ejpam-1478	134	19	�	�	PROPN
ejpam-1478	134	20	∏	∏	PROPN
ejpam-1478	134	21	t0	t0	PROPN
ejpam-1478	134	22	<	<	X
ejpam-1478	134	23	ti	ti	X
ejpam-1478	134	24	<	<	X
ejpam-1478	134	25	t	t	X
ejpam-1478	134	26	�	�	PROPN
ejpam-1478	134	27	1	1	NUM
ejpam-1478	134	28	+	+	CCONJ
ejpam-1478	134	29	βi	βi	PROPN
ejpam-1478	134	30	m̃	m̃	PROPN
ejpam-1478	134	31	p−1	p−1	PROPN
ejpam-1478	134	32	�	�	PROPN
ejpam-1478	134	33	�	�	PROPN
ejpam-1478	134	34	h	h	NOUN
ejpam-1478	134	35	m̃1−p	m̃1−p	VERB
ejpam-1478	134	36	+	+	PUNCT
ejpam-1478	134	37	(	(	PUNCT
ejpam-1478	134	38	1−	1−	NUM
ejpam-1478	134	39	p)q̃(t	p)q̃(t	NOUN
ejpam-1478	134	40	)	)	PUNCT
ejpam-1478	134	41	i	i	PROPN
ejpam-1478	134	42	1	1	NUM
ejpam-1478	134	43	1−p	1−p	NUM
ejpam-1478	134	44	;	;	PUNCT
ejpam-1478	134	45	(	(	PUNCT
ejpam-1478	134	46	26	26	NUM
ejpam-1478	134	47	)	)	PUNCT
ejpam-1478	134	48	(	(	PUNCT
ejpam-1478	134	49	iii	iii	NOUN
ejpam-1478	134	50	)	)	PUNCT
ejpam-1478	134	51	for	for	ADP
ejpam-1478	134	52	p	p	PROPN
ejpam-1478	134	53	>	>	SYM
ejpam-1478	134	54	1	1	NUM
ejpam-1478	134	55	u(t	u(t	NOUN
ejpam-1478	134	56	)	)	PUNCT
ejpam-1478	134	57	≤	≤	PUNCT
ejpam-1478	134	58	m̃	m̃	PROPN
ejpam-1478	134	59	�	�	PROPN
ejpam-1478	134	60	∏	∏	PROPN
ejpam-1478	134	61	t0	t0	PROPN
ejpam-1478	134	62	<	<	X
ejpam-1478	134	63	ti	ti	X
ejpam-1478	134	64	<	<	X
ejpam-1478	134	65	t	t	PROPN
ejpam-1478	134	66	�	�	PROPN
ejpam-1478	134	67	1+pβi	1+pβi	PROPN
ejpam-1478	134	68	m̃	m̃	PROPN
ejpam-1478	134	69	p−1	p−1	PROPN
ejpam-1478	134	70	�	�	PROPN
ejpam-1478	134	71	×	×	PROPN
ejpam-1478	134	72	�	�	PROPN
ejpam-1478	134	73	1−(p−1	1−(p−1	NUM
ejpam-1478	134	74	)	)	PUNCT
ejpam-1478	134	75	�	�	PROPN
ejpam-1478	134	76	m̃	m̃	PROPN
ejpam-1478	134	77	�	�	PROPN
ejpam-1478	134	78	∏	∏	PROPN
ejpam-1478	134	79	t0	t0	PROPN
ejpam-1478	134	80	<	<	X
ejpam-1478	134	81	ti	ti	X
ejpam-1478	134	82	<	<	X
ejpam-1478	134	83	t	t	PROPN
ejpam-1478	134	84	�	�	PROPN
ejpam-1478	134	85	1+pβi	1+pβi	PROPN
ejpam-1478	134	86	m̃	m̃	PROPN
ejpam-1478	134	87	p−1	p−1	PROPN
ejpam-1478	134	88	�	�	PROPN
ejpam-1478	134	89	�	�	PROPN
ejpam-1478	134	90	�	�	PROPN
ejpam-1478	134	91	p−1	p−1	PROPN
ejpam-1478	134	92	q̃(t	q̃(t	PROPN
ejpam-1478	134	93	)	)	PUNCT
ejpam-1478	134	94	�	�	PROPN
ejpam-1478	134	95	1	1	NUM
ejpam-1478	134	96	p−1	p−1	PROPN
ejpam-1478	134	97	,	,	PUNCT
ejpam-1478	134	98	(	(	PUNCT
ejpam-1478	134	99	27	27	NUM
ejpam-1478	134	100	)	)	PUNCT
ejpam-1478	134	101	where	where	SCONJ
ejpam-1478	134	102	q̃(t)≤	q̃(t)≤	PROPN
ejpam-1478	134	103	m̃1−p	m̃1−p	VERB
ejpam-1478	134	104	p	p	X
ejpam-1478	134	105	,	,	PUNCT
ejpam-1478	134	106	(	(	PUNCT
ejpam-1478	134	107	28	28	NUM
ejpam-1478	134	108	)	)	PUNCT
ejpam-1478	134	109	∏	∏	PROPN
ejpam-1478	134	110	t0	t0	PROPN
ejpam-1478	134	111	<	<	X
ejpam-1478	134	112	ti	ti	X
ejpam-1478	134	113	<	<	X
ejpam-1478	134	114	t	t	X
ejpam-1478	134	115	�	�	PROPN
ejpam-1478	134	116	1	1	NUM
ejpam-1478	134	117	+	+	CCONJ
ejpam-1478	134	118	pβi	pβi	PROPN
ejpam-1478	134	119	m̃	m̃	PROPN
ejpam-1478	134	120	p−1	p−1	PROPN
ejpam-1478	134	121	�	�	PROPN
ejpam-1478	134	122	<	<	X
ejpam-1478	134	123	�	�	PROPN
ejpam-1478	134	124	p	p	NOUN
ejpam-1478	134	125	p−	p−	NOUN
ejpam-1478	134	126	1	1	NUM
ejpam-1478	134	127	�	�	PROPN
ejpam-1478	134	128	1	1	NUM
ejpam-1478	134	129	p−1	p−1	PROPN
ejpam-1478	134	130	.	.	PUNCT
ejpam-1478	135	1	(	(	PUNCT
ejpam-1478	135	2	29	29	NUM
ejpam-1478	135	3	)	)	SYM
ejpam-1478	135	4	4	4	NUM
ejpam-1478	135	5	.	.	X
ejpam-1478	135	6	practical	practical	ADJ
ejpam-1478	135	7	stability	stability	NOUN
ejpam-1478	135	8	now	now	ADV
ejpam-1478	135	9	we	we	PRON
ejpam-1478	135	10	will	will	AUX
ejpam-1478	135	11	use	use	VERB
ejpam-1478	135	12	the	the	DET
ejpam-1478	135	13	solved	solve	VERB
ejpam-1478	135	14	above	above	ADP
ejpam-1478	135	15	inequalities	inequality	NOUN
ejpam-1478	135	16	to	to	PART
ejpam-1478	135	17	investigate	investigate	VERB
ejpam-1478	135	18	some	some	DET
ejpam-1478	135	19	stability	stability	NOUN
ejpam-1478	135	20	properties	property	NOUN
ejpam-1478	135	21	of	of	ADP
ejpam-1478	135	22	the	the	DET
ejpam-1478	135	23	solutions	solution	NOUN
ejpam-1478	135	24	of	of	ADP
ejpam-1478	135	25	impulsive	impulsive	ADJ
ejpam-1478	135	26	differential	differential	ADJ
ejpam-1478	135	27	equation	equation	NOUN
ejpam-1478	135	28	with	with	ADP
ejpam-1478	135	29	“	"	PUNCT
ejpam-1478	135	30	supremum	supremum	ADJ
ejpam-1478	135	31	”	"	PUNCT
ejpam-1478	135	32	(	(	PUNCT
ejpam-1478	135	33	1	1	NUM
ejpam-1478	135	34	)	)	PUNCT
ejpam-1478	135	35	,	,	PUNCT
ejpam-1478	135	36	(	(	PUNCT
ejpam-1478	135	37	2	2	NUM
ejpam-1478	135	38	)	)	PUNCT
ejpam-1478	135	39	.	.	PUNCT
ejpam-1478	136	1	note	note	VERB
ejpam-1478	136	2	that	that	SCONJ
ejpam-1478	136	3	stability	stability	NOUN
ejpam-1478	136	4	properties	property	NOUN
ejpam-1478	136	5	of	of	ADP
ejpam-1478	136	6	solutions	solution	NOUN
ejpam-1478	136	7	of	of	ADP
ejpam-1478	136	8	various	various	ADJ
ejpam-1478	136	9	types	type	NOUN
ejpam-1478	136	10	of	of	ADP
ejpam-1478	136	11	differential	differential	ADJ
ejpam-1478	136	12	equations	equation	NOUN
ejpam-1478	136	13	are	be	AUX
ejpam-1478	136	14	very	very	ADV
ejpam-1478	136	15	intensively	intensively	ADV
ejpam-1478	136	16	studied	study	VERB
ejpam-1478	136	17	because	because	SCONJ
ejpam-1478	136	18	of	of	ADP
ejpam-1478	136	19	its	its	PRON
ejpam-1478	136	20	applications	application	NOUN
ejpam-1478	136	21	to	to	ADP
ejpam-1478	136	22	many	many	ADJ
ejpam-1478	136	23	models	model	NOUN
ejpam-1478	136	24	of	of	ADP
ejpam-1478	136	25	real	real	ADJ
ejpam-1478	136	26	world	world	NOUN
ejpam-1478	136	27	problems	problem	NOUN
ejpam-1478	136	28	[	[	X
ejpam-1478	136	29	14	14	NUM
ejpam-1478	136	30	,	,	PUNCT
ejpam-1478	136	31	18	18	NUM
ejpam-1478	136	32	,	,	PUNCT
ejpam-1478	136	33	19	19	NUM
ejpam-1478	136	34	]	]	PUNCT
ejpam-1478	136	35	.	.	PUNCT
ejpam-1478	137	1	the	the	DET
ejpam-1478	137	2	main	main	ADJ
ejpam-1478	137	3	object	object	NOUN
ejpam-1478	137	4	of	of	ADP
ejpam-1478	137	5	the	the	DET
ejpam-1478	137	6	paper	paper	NOUN
ejpam-1478	137	7	is	be	AUX
ejpam-1478	137	8	practical	practical	ADJ
ejpam-1478	137	9	stability	stability	NOUN
ejpam-1478	137	10	.	.	PUNCT
ejpam-1478	138	1	we	we	PRON
ejpam-1478	138	2	will	will	AUX
ejpam-1478	138	3	extend	extend	VERB
ejpam-1478	138	4	the	the	DET
ejpam-1478	138	5	concept	concept	NOUN
ejpam-1478	138	6	of	of	ADP
ejpam-1478	138	7	boundedness	boundedness	NOUN
ejpam-1478	138	8	as	as	ADV
ejpam-1478	138	9	well	well	ADV
ejpam-1478	138	10	as	as	ADP
ejpam-1478	138	11	practical	practical	ADJ
ejpam-1478	138	12	stability	stability	NOUN
ejpam-1478	138	13	to	to	ADP
ejpam-1478	138	14	the	the	DET
ejpam-1478	138	15	considered	consider	VERB
ejpam-1478	138	16	nonlinear	nonlinear	ADJ
ejpam-1478	138	17	system	system	NOUN
ejpam-1478	138	18	of	of	ADP
ejpam-1478	138	19	impulsive	impulsive	ADJ
ejpam-1478	138	20	differential	differential	ADJ
ejpam-1478	138	21	equation	equation	NOUN
ejpam-1478	138	22	with	with	ADP
ejpam-1478	138	23	“	"	PUNCT
ejpam-1478	138	24	supremum	supremum	ADJ
ejpam-1478	138	25	”	"	PUNCT
ejpam-1478	138	26	(	(	PUNCT
ejpam-1478	138	27	1	1	NUM
ejpam-1478	138	28	)	)	PUNCT
ejpam-1478	138	29	,	,	PUNCT
ejpam-1478	138	30	(	(	PUNCT
ejpam-1478	138	31	2	2	NUM
ejpam-1478	138	32	)	)	PUNCT
ejpam-1478	138	33	,	,	PUNCT
ejpam-1478	138	34	based	base	VERB
ejpam-1478	138	35	on	on	ADP
ejpam-1478	138	36	the	the	DET
ejpam-1478	138	37	definitions	definition	NOUN
ejpam-1478	138	38	for	for	ADP
ejpam-1478	138	39	ordinary	ordinary	ADJ
ejpam-1478	138	40	differential	differential	ADJ
ejpam-1478	138	41	equations	equation	NOUN
ejpam-1478	138	42	given	give	VERB
ejpam-1478	138	43	in	in	ADP
ejpam-1478	138	44	[	[	NOUN
ejpam-1478	138	45	14	14	NUM
ejpam-1478	138	46	]	]	PUNCT
ejpam-1478	138	47	.	.	PUNCT
ejpam-1478	139	1	definition	definition	NOUN
ejpam-1478	139	2	1	1	NUM
ejpam-1478	139	3	.	.	PUNCT
ejpam-1478	140	1	we	we	PRON
ejpam-1478	140	2	will	will	AUX
ejpam-1478	140	3	say	say	VERB
ejpam-1478	140	4	that	that	SCONJ
ejpam-1478	140	5	the	the	DET
ejpam-1478	140	6	solution	solution	NOUN
ejpam-1478	140	7	x(t	x(t	PROPN
ejpam-1478	140	8	;	;	PUNCT
ejpam-1478	140	9	t0,φ	t0,φ	PROPN
ejpam-1478	140	10	)	)	PUNCT
ejpam-1478	140	11	of	of	ADP
ejpam-1478	140	12	the	the	DET
ejpam-1478	140	13	initial	initial	ADJ
ejpam-1478	140	14	value	value	NOUN
ejpam-1478	140	15	problem	problem	NOUN
ejpam-1478	140	16	(	(	PUNCT
ejpam-1478	140	17	1	1	NUM
ejpam-1478	140	18	)	)	PUNCT
ejpam-1478	140	19	,	,	PUNCT
ejpam-1478	140	20	(	(	PUNCT
ejpam-1478	140	21	2	2	NUM
ejpam-1478	140	22	)	)	PUNCT
ejpam-1478	140	23	,	,	PUNCT
ejpam-1478	140	24	(	(	PUNCT
ejpam-1478	140	25	3	3	X
ejpam-1478	140	26	)	)	PUNCT
ejpam-1478	140	27	is	be	AUX
ejpam-1478	140	28	bounded	bound	VERB
ejpam-1478	140	29	if	if	SCONJ
ejpam-1478	140	30	for	for	ADP
ejpam-1478	140	31	any	any	DET
ejpam-1478	140	32	number	number	NOUN
ejpam-1478	140	33	α	α	NOUN
ejpam-1478	140	34	>	>	X
ejpam-1478	140	35	0	0	PUNCT
ejpam-1478	141	1	there	there	PRON
ejpam-1478	141	2	exists	exist	VERB
ejpam-1478	141	3	β	β	X
ejpam-1478	141	4	=	=	SYM
ejpam-1478	141	5	β(α	β(α	PROPN
ejpam-1478	141	6	,	,	PUNCT
ejpam-1478	141	7	t0	t0	PROPN
ejpam-1478	141	8	)	)	PUNCT
ejpam-1478	141	9	>	>	X
ejpam-1478	141	10	0	0	PUNCT
ejpam-1478	142	1	such	such	ADJ
ejpam-1478	142	2	that	that	DET
ejpam-1478	142	3	inequality	inequality	NOUN
ejpam-1478	142	4	|φ|0	|φ|0	VERB
ejpam-1478	142	5	<	<	X
ejpam-1478	142	6	α	α	PROPN
ejpam-1478	142	7	implies	imply	VERB
ejpam-1478	142	8	|x(t	|x(t	PROPN
ejpam-1478	142	9	;	;	PUNCT
ejpam-1478	142	10	t0,φ)|	t0,φ)|	X
ejpam-1478	142	11	<	<	X
ejpam-1478	142	12	β	β	X
ejpam-1478	142	13	,	,	PUNCT
ejpam-1478	142	14	t	t	PROPN
ejpam-1478	142	15	≥	≥	PROPN
ejpam-1478	142	16	t0	t0	PROPN
ejpam-1478	142	17	,	,	PUNCT
ejpam-1478	142	18	where	where	SCONJ
ejpam-1478	142	19	φ	φ	PROPN
ejpam-1478	142	20	∈	∈	PROPN
ejpam-1478	142	21	c([τ(t0)−	c([τ(t0)−	X
ejpam-1478	142	22	h	h	NOUN
ejpam-1478	142	23	,	,	PUNCT
ejpam-1478	142	24	t0],r	t0],r	PROPN
ejpam-1478	142	25	)	)	PUNCT
ejpam-1478	142	26	.	.	PUNCT
ejpam-1478	143	1	definition	definition	NOUN
ejpam-1478	143	2	2	2	NUM
ejpam-1478	143	3	.	.	PUNCT
ejpam-1478	144	1	we	we	PRON
ejpam-1478	144	2	will	will	AUX
ejpam-1478	144	3	say	say	VERB
ejpam-1478	144	4	that	that	SCONJ
ejpam-1478	144	5	the	the	DET
ejpam-1478	144	6	solutions	solution	NOUN
ejpam-1478	144	7	of	of	ADP
ejpam-1478	144	8	the	the	DET
ejpam-1478	144	9	initial	initial	ADJ
ejpam-1478	144	10	value	value	NOUN
ejpam-1478	144	11	problem	problem	NOUN
ejpam-1478	144	12	(	(	PUNCT
ejpam-1478	144	13	1	1	NUM
ejpam-1478	144	14	)	)	PUNCT
ejpam-1478	144	15	,	,	PUNCT
ejpam-1478	144	16	(	(	PUNCT
ejpam-1478	144	17	2	2	NUM
ejpam-1478	144	18	)	)	PUNCT
ejpam-1478	144	19	,	,	PUNCT
ejpam-1478	144	20	(	(	PUNCT
ejpam-1478	144	21	3	3	X
ejpam-1478	144	22	)	)	PUNCT
ejpam-1478	144	23	are	be	AUX
ejpam-1478	144	24	uniformly	uniformly	ADV
ejpam-1478	144	25	bounded	bound	VERB
ejpam-1478	144	26	if	if	SCONJ
ejpam-1478	144	27	for	for	ADP
ejpam-1478	144	28	any	any	DET
ejpam-1478	144	29	number	number	NOUN
ejpam-1478	144	30	α	α	NOUN
ejpam-1478	144	31	>	>	X
ejpam-1478	144	32	0	0	PUNCT
ejpam-1478	145	1	there	there	PRON
ejpam-1478	145	2	exists	exist	VERB
ejpam-1478	145	3	β	β	X
ejpam-1478	145	4	=	=	SYM
ejpam-1478	145	5	β(α	β(α	ADJ
ejpam-1478	145	6	)	)	PUNCT
ejpam-1478	145	7	>	>	X
ejpam-1478	145	8	0	0	NUM
ejpam-1478	146	1	such	such	ADJ
ejpam-1478	146	2	that	that	DET
ejpam-1478	146	3	inequality	inequality	NOUN
ejpam-1478	146	4	|φ|0	|φ|0	VERB
ejpam-1478	146	5	<	<	X
ejpam-1478	146	6	α	α	PROPN
ejpam-1478	146	7	implies	imply	VERB
ejpam-1478	146	8	|x(t	|x(t	PROPN
ejpam-1478	146	9	;	;	PUNCT
ejpam-1478	146	10	t0,φ)|	t0,φ)|	X
ejpam-1478	146	11	<	<	X
ejpam-1478	146	12	β	β	X
ejpam-1478	146	13	,	,	PUNCT
ejpam-1478	146	14	t	t	PROPN
ejpam-1478	146	15	≥	≥	NOUN
ejpam-1478	146	16	t0	t0	NOUN
ejpam-1478	146	17	for	for	ADP
ejpam-1478	146	18	all	all	DET
ejpam-1478	146	19	t0	t0	PROPN
ejpam-1478	146	20	∈	∈	PROPN
ejpam-1478	146	21	r+	r+	NOUN
ejpam-1478	146	22	,	,	PUNCT
ejpam-1478	146	23	where	where	SCONJ
ejpam-1478	146	24	φ	φ	PROPN
ejpam-1478	146	25	∈	∈	PROPN
ejpam-1478	146	26	c([τ(t0)−	c([τ(t0)−	X
ejpam-1478	146	27	h	h	NOUN
ejpam-1478	146	28	,	,	PUNCT
ejpam-1478	146	29	t0],r	t0],r	PROPN
ejpam-1478	146	30	)	)	PUNCT
ejpam-1478	146	31	.	.	PUNCT
ejpam-1478	147	1	s.	s.	PROPN
ejpam-1478	147	2	hristova	hristova	PROPN
ejpam-1478	147	3	,	,	PUNCT
ejpam-1478	147	4	k.	k.	PROPN
ejpam-1478	147	5	stefanova	stefanova	PROPN
ejpam-1478	147	6	/	/	SYM
ejpam-1478	147	7	eur	eur	PROPN
ejpam-1478	147	8	.	.	PUNCT
ejpam-1478	148	1	j.	j.	PROPN
ejpam-1478	148	2	pure	pure	PROPN
ejpam-1478	148	3	appl	appl	PROPN
ejpam-1478	148	4	.	.	PROPN
ejpam-1478	148	5	math	math	PROPN
ejpam-1478	148	6	,	,	PUNCT
ejpam-1478	148	7	5	5	NUM
ejpam-1478	148	8	(	(	PUNCT
ejpam-1478	148	9	2012	2012	NUM
ejpam-1478	148	10	)	)	PUNCT
ejpam-1478	148	11	,	,	PUNCT
ejpam-1478	148	12	30	30	NUM
ejpam-1478	148	13	-	-	SYM
ejpam-1478	148	14	44	44	NUM
ejpam-1478	148	15	37	37	NUM
ejpam-1478	148	16	let	let	VERB
ejpam-1478	148	17	the	the	DET
ejpam-1478	148	18	constants	constant	NOUN
ejpam-1478	148	19	λ	λ	PROPN
ejpam-1478	148	20	,	,	PUNCT
ejpam-1478	148	21	λ	λ	X
ejpam-1478	148	22	:	:	PUNCT
ejpam-1478	148	23	0	0	PUNCT
ejpam-1478	148	24	<	<	X
ejpam-1478	148	25	λ	λ	X
ejpam-1478	148	26	<	<	X
ejpam-1478	148	27	λ	λ	X
ejpam-1478	148	28	be	be	AUX
ejpam-1478	148	29	given	give	VERB
ejpam-1478	148	30	.	.	PUNCT
ejpam-1478	149	1	definition	definition	NOUN
ejpam-1478	149	2	3	3	NUM
ejpam-1478	149	3	.	.	PUNCT
ejpam-1478	150	1	we	we	PRON
ejpam-1478	150	2	will	will	AUX
ejpam-1478	150	3	say	say	VERB
ejpam-1478	150	4	that	that	SCONJ
ejpam-1478	150	5	the	the	DET
ejpam-1478	150	6	system	system	NOUN
ejpam-1478	150	7	of	of	ADP
ejpam-1478	150	8	impulsive	impulsive	ADJ
ejpam-1478	150	9	differential	differential	ADJ
ejpam-1478	150	10	equation	equation	NOUN
ejpam-1478	150	11	with	with	ADP
ejpam-1478	150	12	“	"	PUNCT
ejpam-1478	150	13	supremum	supremum	ADJ
ejpam-1478	150	14	”	"	PUNCT
ejpam-1478	150	15	(	(	PUNCT
ejpam-1478	150	16	1	1	NUM
ejpam-1478	150	17	)	)	PUNCT
ejpam-1478	150	18	,	,	PUNCT
ejpam-1478	150	19	(	(	PUNCT
ejpam-1478	150	20	2	2	X
ejpam-1478	150	21	)	)	PUNCT
ejpam-1478	150	22	is	be	AUX
ejpam-1478	150	23	practically	practically	ADV
ejpam-1478	150	24	stable	stable	ADJ
ejpam-1478	150	25	with	with	ADP
ejpam-1478	150	26	respect	respect	NOUN
ejpam-1478	150	27	to	to	ADP
ejpam-1478	150	28	(	(	PUNCT
ejpam-1478	150	29	λ	λ	X
ejpam-1478	150	30	,	,	PUNCT
ejpam-1478	150	31	λ	λ	NOUN
ejpam-1478	150	32	)	)	PUNCT
ejpam-1478	150	33	if	if	SCONJ
ejpam-1478	150	34	the	the	DET
ejpam-1478	150	35	inequality	inequality	NOUN
ejpam-1478	150	36	|φ|0	|φ|0	VERB
ejpam-1478	150	37	<	<	X
ejpam-1478	150	38	λ	λ	PROPN
ejpam-1478	150	39	implies	imply	VERB
ejpam-1478	150	40	|x(t	|x(t	PROPN
ejpam-1478	150	41	;	;	PUNCT
ejpam-1478	150	42	t0,φ)|	t0,φ)|	X
ejpam-1478	150	43	<	<	X
ejpam-1478	150	44	λ	λ	PROPN
ejpam-1478	150	45	,	,	PUNCT
ejpam-1478	150	46	t	t	PROPN
ejpam-1478	150	47	≥	≥	NOUN
ejpam-1478	150	48	t0	t0	NOUN
ejpam-1478	150	49	for	for	ADP
ejpam-1478	150	50	some	some	DET
ejpam-1478	150	51	t0	t0	PROPN
ejpam-1478	150	52	∈	∈	PROPN
ejpam-1478	150	53	r+	r+	NOUN
ejpam-1478	150	54	,	,	PUNCT
ejpam-1478	150	55	where	where	SCONJ
ejpam-1478	150	56	φ	φ	PROPN
ejpam-1478	150	57	∈	∈	PROPN
ejpam-1478	150	58	c([τ(t0)−	c([τ(t0)−	X
ejpam-1478	150	59	h	h	NOUN
ejpam-1478	150	60	,	,	PUNCT
ejpam-1478	150	61	t0],r	t0],r	PROPN
ejpam-1478	150	62	)	)	PUNCT
ejpam-1478	150	63	;	;	PUNCT
ejpam-1478	150	64	uniformly	uniformly	ADV
ejpam-1478	150	65	practically	practically	ADV
ejpam-1478	150	66	stable	stable	ADJ
ejpam-1478	150	67	with	with	ADP
ejpam-1478	150	68	respect	respect	NOUN
ejpam-1478	150	69	to	to	ADP
ejpam-1478	150	70	(	(	PUNCT
ejpam-1478	150	71	λ	λ	X
ejpam-1478	150	72	,	,	PUNCT
ejpam-1478	150	73	λ	λ	NOUN
ejpam-1478	150	74	)	)	PUNCT
ejpam-1478	150	75	if	if	SCONJ
ejpam-1478	150	76	the	the	DET
ejpam-1478	150	77	inequality	inequality	NOUN
ejpam-1478	150	78	|φ|0	|φ|0	VERB
ejpam-1478	150	79	<	<	X
ejpam-1478	150	80	λ	λ	PROPN
ejpam-1478	150	81	implies	imply	VERB
ejpam-1478	150	82	|x(t	|x(t	PROPN
ejpam-1478	150	83	;	;	PUNCT
ejpam-1478	150	84	t0,φ)|	t0,φ)|	X
ejpam-1478	150	85	<	<	X
ejpam-1478	150	86	λ	λ	PROPN
ejpam-1478	150	87	,	,	PUNCT
ejpam-1478	150	88	t	t	PROPN
ejpam-1478	150	89	≥	≥	NOUN
ejpam-1478	150	90	t0	t0	NOUN
ejpam-1478	150	91	for	for	ADP
ejpam-1478	150	92	all	all	DET
ejpam-1478	150	93	t0	t0	PROPN
ejpam-1478	150	94	∈	∈	PROPN
ejpam-1478	150	95	r+	r+	NOUN
ejpam-1478	150	96	,	,	PUNCT
ejpam-1478	150	97	where	where	SCONJ
ejpam-1478	150	98	φ	φ	PROPN
ejpam-1478	150	99	∈	∈	PROPN
ejpam-1478	150	100	c([τ(t0)−	c([τ(t0)−	X
ejpam-1478	150	101	h	h	NOUN
ejpam-1478	150	102	,	,	PUNCT
ejpam-1478	150	103	t0],r	t0],r	PROPN
ejpam-1478	150	104	)	)	PUNCT
ejpam-1478	150	105	.	.	PUNCT
ejpam-1478	151	1	now	now	ADV
ejpam-1478	151	2	will	will	AUX
ejpam-1478	151	3	obtain	obtain	VERB
ejpam-1478	151	4	some	some	DET
ejpam-1478	151	5	stability	stability	NOUN
ejpam-1478	151	6	properties	property	NOUN
ejpam-1478	151	7	of	of	ADP
ejpam-1478	151	8	the	the	DET
ejpam-1478	151	9	solutions	solution	NOUN
ejpam-1478	151	10	of	of	ADP
ejpam-1478	151	11	the	the	DET
ejpam-1478	151	12	impulsive	impulsive	ADJ
ejpam-1478	151	13	differential	differential	ADJ
ejpam-1478	151	14	equation	equation	NOUN
ejpam-1478	151	15	with	with	ADP
ejpam-1478	151	16	“	"	PUNCT
ejpam-1478	151	17	supremum	supremum	ADJ
ejpam-1478	151	18	”	"	PUNCT
ejpam-1478	151	19	(	(	PUNCT
ejpam-1478	151	20	1	1	NUM
ejpam-1478	151	21	)	)	PUNCT
ejpam-1478	151	22	,	,	PUNCT
ejpam-1478	151	23	(	(	PUNCT
ejpam-1478	151	24	2	2	NUM
ejpam-1478	151	25	)	)	PUNCT
ejpam-1478	151	26	.	.	PUNCT
ejpam-1478	152	1	we	we	PRON
ejpam-1478	152	2	will	will	AUX
ejpam-1478	152	3	consider	consider	VERB
ejpam-1478	152	4	the	the	DET
ejpam-1478	152	5	case	case	NOUN
ejpam-1478	152	6	when	when	SCONJ
ejpam-1478	152	7	the	the	DET
ejpam-1478	152	8	right	right	ADJ
ejpam-1478	152	9	part	part	NOUN
ejpam-1478	152	10	of	of	ADP
ejpam-1478	152	11	the	the	DET
ejpam-1478	152	12	equations	equation	NOUN
ejpam-1478	152	13	satisfy	satisfy	VERB
ejpam-1478	152	14	the	the	DET
ejpam-1478	152	15	conditions	condition	NOUN
ejpam-1478	152	16	h2	h2	NOUN
ejpam-1478	152	17	and	and	CCONJ
ejpam-1478	152	18	h3	h3	NOUN
ejpam-1478	152	19	for	for	ADP
ejpam-1478	152	20	different	different	ADJ
ejpam-1478	152	21	values	value	NOUN
ejpam-1478	152	22	of	of	ADP
ejpam-1478	152	23	the	the	DET
ejpam-1478	152	24	power	power	NOUN
ejpam-1478	152	25	p.	p.	NOUN
ejpam-1478	152	26	theorem	theorem	NOUN
ejpam-1478	152	27	3	3	X
ejpam-1478	152	28	.	.	PUNCT
ejpam-1478	153	1	let	let	VERB
ejpam-1478	153	2	the	the	DET
ejpam-1478	153	3	following	follow	VERB
ejpam-1478	153	4	conditions	condition	NOUN
ejpam-1478	153	5	be	be	AUX
ejpam-1478	153	6	fulfilled	fulfil	VERB
ejpam-1478	153	7	:	:	PUNCT
ejpam-1478	154	1	1	1	X
ejpam-1478	154	2	.	.	PUNCT
ejpam-1478	155	1	the	the	DET
ejpam-1478	155	2	conditions	condition	NOUN
ejpam-1478	155	3	h1	h1	PROPN
ejpam-1478	155	4	–	–	PUNCT
ejpam-1478	155	5	h4	h4	NOUN
ejpam-1478	155	6	are	be	AUX
ejpam-1478	155	7	satisfied	satisfied	ADJ
ejpam-1478	155	8	for	for	ADP
ejpam-1478	155	9	p	p	NOUN
ejpam-1478	155	10	=	=	NOUN
ejpam-1478	155	11	1	1	NUM
ejpam-1478	155	12	.	.	NOUN
ejpam-1478	155	13	2	2	NUM
ejpam-1478	155	14	.	.	X
ejpam-1478	156	1	for	for	ADP
ejpam-1478	156	2	any	any	DET
ejpam-1478	156	3	t0	t0	PROPN
ejpam-1478	156	4	∈	∈	PROPN
ejpam-1478	156	5	r+	r+	PUNCT
ejpam-1478	156	6	there	there	PRON
ejpam-1478	156	7	exist	exist	VERB
ejpam-1478	156	8	lim	lim	PROPN
ejpam-1478	156	9	t→∞ψ(t0	t→∞ψ(t0	PROPN
ejpam-1478	156	10	,	,	PUNCT
ejpam-1478	156	11	t	t	PROPN
ejpam-1478	156	12	)	)	PUNCT
ejpam-1478	156	13	=	=	SYM
ejpam-1478	156	14	η1(t0	η1(t0	PROPN
ejpam-1478	156	15	)	)	PUNCT
ejpam-1478	156	16	and	and	CCONJ
ejpam-1478	156	17	lim	lim	PROPN
ejpam-1478	156	18	t→∞φ(t0	t→∞φ(t0	PROPN
ejpam-1478	156	19	,	,	PUNCT
ejpam-1478	156	20	t	t	PROPN
ejpam-1478	156	21	)	)	PUNCT
ejpam-1478	156	22	=	=	SYM
ejpam-1478	156	23	η2(t0	η2(t0	NOUN
ejpam-1478	156	24	)	)	PUNCT
ejpam-1478	156	25	where	where	SCONJ
ejpam-1478	156	26	the	the	DET
ejpam-1478	156	27	functions	function	NOUN
ejpam-1478	156	28	ψ(t0	ψ(t0	PROPN
ejpam-1478	156	29	,	,	PUNCT
ejpam-1478	156	30	t	t	PROPN
ejpam-1478	156	31	)	)	PUNCT
ejpam-1478	156	32	and	and	CCONJ
ejpam-1478	156	33	φ(t0	φ(t0	PROPN
ejpam-1478	156	34	,	,	PUNCT
ejpam-1478	156	35	t	t	PROPN
ejpam-1478	156	36	)	)	PUNCT
ejpam-1478	156	37	are	be	AUX
ejpam-1478	156	38	defined	define	VERB
ejpam-1478	156	39	by	by	ADP
ejpam-1478	156	40	the	the	DET
ejpam-1478	156	41	equalities	equality	NOUN
ejpam-1478	156	42	ψ(t0	ψ(t0	PROPN
ejpam-1478	156	43	,	,	PUNCT
ejpam-1478	156	44	t	t	PROPN
ejpam-1478	156	45	)	)	PUNCT
ejpam-1478	157	1	=	=	SYM
ejpam-1478	157	2	∏	∏	PROPN
ejpam-1478	157	3	t0	t0	PROPN
ejpam-1478	157	4	<	<	X
ejpam-1478	157	5	ti	ti	X
ejpam-1478	157	6	<	<	X
ejpam-1478	157	7	t	t	X
ejpam-1478	157	8	�	�	PROPN
ejpam-1478	157	9	1	1	NUM
ejpam-1478	157	10	+	+	NUM
ejpam-1478	157	11	βi	βi	PROPN
ejpam-1478	157	12	�	�	PROPN
ejpam-1478	157	13	,	,	PUNCT
ejpam-1478	157	14	(	(	PUNCT
ejpam-1478	157	15	30	30	NUM
ejpam-1478	157	16	)	)	PUNCT
ejpam-1478	157	17	φ(t0	φ(t0	NOUN
ejpam-1478	157	18	,	,	PUNCT
ejpam-1478	157	19	t	t	PROPN
ejpam-1478	157	20	)	)	PUNCT
ejpam-1478	157	21	=	=	SYM
ejpam-1478	158	1	∫	∫	PROPN
ejpam-1478	158	2	t	t	PROPN
ejpam-1478	158	3	t0	t0	PROPN
ejpam-1478	158	4	h	h	PROPN
ejpam-1478	158	5	a(s	a(s	PROPN
ejpam-1478	158	6	)	)	PUNCT
ejpam-1478	159	1	+	+	NUM
ejpam-1478	159	2	b(s	b(	NOUN
ejpam-1478	159	3	)	)	PUNCT
ejpam-1478	159	4	i	i	PRON
ejpam-1478	159	5	ds	ds	VERB
ejpam-1478	159	6	,	,	PUNCT
ejpam-1478	159	7	(	(	PUNCT
ejpam-1478	159	8	31	31	NUM
ejpam-1478	159	9	)	)	PUNCT
ejpam-1478	159	10	and	and	CCONJ
ejpam-1478	159	11	the	the	DET
ejpam-1478	159	12	functions	function	NOUN
ejpam-1478	159	13	η1,η2	η1,η2	PROPN
ejpam-1478	159	14	∈	∈	PROPN
ejpam-1478	159	15	c(r+,r+	c(r+,r+	PROPN
ejpam-1478	159	16	)	)	PUNCT
ejpam-1478	159	17	.	.	PUNCT
ejpam-1478	160	1	then	then	ADV
ejpam-1478	160	2	:	:	PUNCT
ejpam-1478	160	3	(	(	PUNCT
ejpam-1478	160	4	i	i	NOUN
ejpam-1478	160	5	)	)	PUNCT
ejpam-1478	160	6	any	any	DET
ejpam-1478	160	7	solution	solution	NOUN
ejpam-1478	160	8	of	of	ADP
ejpam-1478	160	9	the	the	DET
ejpam-1478	160	10	impulsive	impulsive	ADJ
ejpam-1478	160	11	differential	differential	ADJ
ejpam-1478	160	12	equation	equation	NOUN
ejpam-1478	160	13	with	with	ADP
ejpam-1478	160	14	“	"	PUNCT
ejpam-1478	160	15	supremum	supremum	ADJ
ejpam-1478	160	16	”	"	PUNCT
ejpam-1478	160	17	(	(	PUNCT
ejpam-1478	160	18	1	1	NUM
ejpam-1478	160	19	)	)	PUNCT
ejpam-1478	160	20	,	,	PUNCT
ejpam-1478	160	21	(	(	PUNCT
ejpam-1478	160	22	2	2	X
ejpam-1478	160	23	)	)	PUNCT
ejpam-1478	160	24	is	be	AUX
ejpam-1478	160	25	bounded	bound	VERB
ejpam-1478	160	26	;	;	PUNCT
ejpam-1478	160	27	(	(	PUNCT
ejpam-1478	160	28	ii	ii	NOUN
ejpam-1478	160	29	)	)	PUNCT
ejpam-1478	160	30	if	if	SCONJ
ejpam-1478	160	31	the	the	DET
ejpam-1478	160	32	functions	function	NOUN
ejpam-1478	160	33	η1(t	η1(t	PRON
ejpam-1478	160	34	)	)	PUNCT
ejpam-1478	160	35	and	and	CCONJ
ejpam-1478	160	36	η2(t	η2(t	PROPN
ejpam-1478	160	37	)	)	PUNCT
ejpam-1478	160	38	are	be	AUX
ejpam-1478	160	39	bounded	bound	VERB
ejpam-1478	160	40	,	,	PUNCT
ejpam-1478	160	41	i.e.	i.e.	X
ejpam-1478	160	42	there	there	PRON
ejpam-1478	160	43	exist	exist	VERB
ejpam-1478	160	44	constants	constant	NOUN
ejpam-1478	160	45	µ1,µ2	µ1,µ2	PROPN
ejpam-1478	160	46	>	>	X
ejpam-1478	160	47	0	0	PUNCT
ejpam-1478	161	1	such	such	ADJ
ejpam-1478	161	2	that	that	SCONJ
ejpam-1478	161	3	ηk(t	ηk(t	NOUN
ejpam-1478	161	4	)	)	PUNCT
ejpam-1478	161	5	≤	≤	NUM
ejpam-1478	161	6	µk	µk	ADP
ejpam-1478	161	7	,	,	PUNCT
ejpam-1478	161	8	(	(	PUNCT
ejpam-1478	161	9	k	k	NOUN
ejpam-1478	161	10	=	=	SYM
ejpam-1478	161	11	1,2	1,2	NUM
ejpam-1478	161	12	)	)	PUNCT
ejpam-1478	161	13	for	for	ADP
ejpam-1478	161	14	t	t	PROPN
ejpam-1478	161	15	∈	∈	PROPN
ejpam-1478	161	16	r+	r+	X
ejpam-1478	161	17	,	,	PUNCT
ejpam-1478	161	18	then	then	ADV
ejpam-1478	161	19	all	all	DET
ejpam-1478	161	20	solutions	solution	NOUN
ejpam-1478	161	21	of	of	ADP
ejpam-1478	161	22	the	the	DET
ejpam-1478	161	23	impulsive	impulsive	ADJ
ejpam-1478	161	24	differential	differential	ADJ
ejpam-1478	161	25	equation	equation	NOUN
ejpam-1478	161	26	with	with	ADP
ejpam-1478	161	27	“	"	PUNCT
ejpam-1478	161	28	supremum	supremum	ADJ
ejpam-1478	161	29	”	"	PUNCT
ejpam-1478	161	30	(	(	PUNCT
ejpam-1478	161	31	1	1	NUM
ejpam-1478	161	32	)	)	PUNCT
ejpam-1478	161	33	,	,	PUNCT
ejpam-1478	161	34	(	(	PUNCT
ejpam-1478	161	35	2	2	X
ejpam-1478	161	36	)	)	PUNCT
ejpam-1478	161	37	are	be	AUX
ejpam-1478	161	38	uniformly	uniformly	ADV
ejpam-1478	161	39	bounded	bound	VERB
ejpam-1478	161	40	;	;	PUNCT
ejpam-1478	161	41	(	(	PUNCT
ejpam-1478	161	42	iii	iii	X
ejpam-1478	161	43	)	)	PUNCT
ejpam-1478	161	44	if	if	SCONJ
ejpam-1478	161	45	for	for	ADP
ejpam-1478	161	46	the	the	DET
ejpam-1478	161	47	given	give	VERB
ejpam-1478	161	48	constants	constant	NOUN
ejpam-1478	161	49	0	0	NUM
ejpam-1478	161	50	<	<	X
ejpam-1478	161	51	λ	λ	X
ejpam-1478	161	52	<	<	X
ejpam-1478	161	53	λ	λ	X
ejpam-1478	161	54	there	there	PRON
ejpam-1478	161	55	exists	exist	VERB
ejpam-1478	161	56	a	a	DET
ejpam-1478	161	57	point	point	NOUN
ejpam-1478	161	58	t0	t0	PROPN
ejpam-1478	161	59	∈	∈	PROPN
ejpam-1478	161	60	r+	r+	NOUN
ejpam-1478	161	61	such	such	ADJ
ejpam-1478	161	62	that	that	SCONJ
ejpam-1478	161	63	λη1(t0)e	λη1(t0)e	PROPN
ejpam-1478	161	64	η2(t0	η2(t0	NOUN
ejpam-1478	161	65	)	)	PUNCT
ejpam-1478	161	66	<	<	X
ejpam-1478	162	1	λ	λ	PROPN
ejpam-1478	162	2	,	,	PUNCT
ejpam-1478	162	3	(	(	PUNCT
ejpam-1478	162	4	32	32	NUM
ejpam-1478	162	5	)	)	PUNCT
ejpam-1478	162	6	then	then	ADV
ejpam-1478	162	7	the	the	DET
ejpam-1478	162	8	trivial	trivial	ADJ
ejpam-1478	162	9	solution	solution	NOUN
ejpam-1478	162	10	of	of	ADP
ejpam-1478	162	11	the	the	DET
ejpam-1478	162	12	impulsive	impulsive	ADJ
ejpam-1478	162	13	differential	differential	ADJ
ejpam-1478	162	14	equation	equation	NOUN
ejpam-1478	162	15	with	with	ADP
ejpam-1478	162	16	“	"	PUNCT
ejpam-1478	162	17	supremum	supremum	ADJ
ejpam-1478	162	18	”	"	PUNCT
ejpam-1478	162	19	(	(	PUNCT
ejpam-1478	162	20	1	1	NUM
ejpam-1478	162	21	)	)	PUNCT
ejpam-1478	162	22	,	,	PUNCT
ejpam-1478	162	23	(	(	PUNCT
ejpam-1478	162	24	2	2	X
ejpam-1478	162	25	)	)	PUNCT
ejpam-1478	162	26	is	be	AUX
ejpam-1478	162	27	practically	practically	ADV
ejpam-1478	162	28	stable	stable	ADJ
ejpam-1478	162	29	with	with	ADP
ejpam-1478	162	30	respect	respect	NOUN
ejpam-1478	162	31	to	to	ADP
ejpam-1478	162	32	(	(	PUNCT
ejpam-1478	162	33	λ	λ	X
ejpam-1478	162	34	,	,	PUNCT
ejpam-1478	162	35	λ	λ	PROPN
ejpam-1478	162	36	)	)	PUNCT
ejpam-1478	162	37	;	;	PUNCT
ejpam-1478	162	38	(	(	PUNCT
ejpam-1478	162	39	iv	iv	X
ejpam-1478	162	40	)	)	PUNCT
ejpam-1478	162	41	if	if	SCONJ
ejpam-1478	162	42	the	the	DET
ejpam-1478	162	43	functions	function	NOUN
ejpam-1478	162	44	η1(t	η1(t	PRON
ejpam-1478	162	45	)	)	PUNCT
ejpam-1478	162	46	and	and	CCONJ
ejpam-1478	162	47	η2(t	η2(t	PROPN
ejpam-1478	162	48	)	)	PUNCT
ejpam-1478	162	49	are	be	AUX
ejpam-1478	162	50	bounded	bound	VERB
ejpam-1478	162	51	,	,	PUNCT
ejpam-1478	162	52	i.e.	i.e.	X
ejpam-1478	162	53	there	there	PRON
ejpam-1478	162	54	exist	exist	VERB
ejpam-1478	162	55	constants	constant	NOUN
ejpam-1478	162	56	µ1,µ2	µ1,µ2	PROPN
ejpam-1478	162	57	>	>	X
ejpam-1478	162	58	0	0	PUNCT
ejpam-1478	162	59	such	such	ADJ
ejpam-1478	162	60	that	that	SCONJ
ejpam-1478	162	61	ηk(t	ηk(t	NOUN
ejpam-1478	162	62	)	)	PUNCT
ejpam-1478	162	63	≤	≤	NUM
ejpam-1478	162	64	µk	µk	ADP
ejpam-1478	162	65	,	,	PUNCT
ejpam-1478	162	66	(	(	PUNCT
ejpam-1478	162	67	k	k	NOUN
ejpam-1478	162	68	=	=	SYM
ejpam-1478	162	69	1,2	1,2	NUM
ejpam-1478	162	70	)	)	PUNCT
ejpam-1478	162	71	for	for	ADP
ejpam-1478	162	72	t	t	PROPN
ejpam-1478	162	73	∈	∈	PROPN
ejpam-1478	162	74	r+	r+	NOUN
ejpam-1478	162	75	,	,	PUNCT
ejpam-1478	162	76	and	and	CCONJ
ejpam-1478	162	77	λµ1eµ2	λµ1eµ2	X
ejpam-1478	162	78	<	<	X
ejpam-1478	162	79	λ	λ	PROPN
ejpam-1478	162	80	,	,	PUNCT
ejpam-1478	162	81	(	(	PUNCT
ejpam-1478	162	82	33	33	NUM
ejpam-1478	162	83	)	)	PUNCT
ejpam-1478	162	84	then	then	ADV
ejpam-1478	162	85	the	the	DET
ejpam-1478	162	86	impulsive	impulsive	ADJ
ejpam-1478	162	87	differential	differential	ADJ
ejpam-1478	162	88	equation	equation	NOUN
ejpam-1478	162	89	with	with	ADP
ejpam-1478	162	90	“	"	PUNCT
ejpam-1478	162	91	supremum	supremum	ADJ
ejpam-1478	162	92	”	"	PUNCT
ejpam-1478	162	93	(	(	PUNCT
ejpam-1478	162	94	1	1	NUM
ejpam-1478	162	95	)	)	PUNCT
ejpam-1478	162	96	,	,	PUNCT
ejpam-1478	162	97	(	(	PUNCT
ejpam-1478	162	98	2	2	X
ejpam-1478	162	99	)	)	PUNCT
ejpam-1478	162	100	is	be	AUX
ejpam-1478	162	101	uniformly	uniformly	ADV
ejpam-1478	162	102	practically	practically	ADV
ejpam-1478	162	103	stable	stable	ADJ
ejpam-1478	162	104	with	with	ADP
ejpam-1478	162	105	respect	respect	NOUN
ejpam-1478	162	106	to	to	ADP
ejpam-1478	162	107	(	(	PUNCT
ejpam-1478	162	108	λ	λ	X
ejpam-1478	162	109	,	,	PUNCT
ejpam-1478	162	110	λ	λ	NOUN
ejpam-1478	162	111	)	)	PUNCT
ejpam-1478	162	112	.	.	PUNCT
ejpam-1478	163	1	s.	s.	PROPN
ejpam-1478	163	2	hristova	hristova	PROPN
ejpam-1478	163	3	,	,	PUNCT
ejpam-1478	163	4	k.	k.	PROPN
ejpam-1478	163	5	stefanova	stefanova	PROPN
ejpam-1478	163	6	/	/	SYM
ejpam-1478	163	7	eur	eur	PROPN
ejpam-1478	163	8	.	.	PUNCT
ejpam-1478	164	1	j.	j.	PROPN
ejpam-1478	164	2	pure	pure	PROPN
ejpam-1478	164	3	appl	appl	PROPN
ejpam-1478	164	4	.	.	PROPN
ejpam-1478	164	5	math	math	PROPN
ejpam-1478	164	6	,	,	PUNCT
ejpam-1478	164	7	5	5	NUM
ejpam-1478	164	8	(	(	PUNCT
ejpam-1478	164	9	2012	2012	NUM
ejpam-1478	164	10	)	)	PUNCT
ejpam-1478	164	11	,	,	PUNCT
ejpam-1478	164	12	30	30	NUM
ejpam-1478	164	13	-	-	SYM
ejpam-1478	164	14	44	44	NUM
ejpam-1478	164	15	38	38	NUM
ejpam-1478	164	16	proof	proof	NOUN
ejpam-1478	164	17	.	.	PUNCT
ejpam-1478	165	1	according	accord	VERB
ejpam-1478	165	2	to	to	ADP
ejpam-1478	165	3	conditions	condition	NOUN
ejpam-1478	165	4	h1	h1	PROPN
ejpam-1478	165	5	–	–	PUNCT
ejpam-1478	165	6	h4	h4	PROPN
ejpam-1478	165	7	from	from	ADP
ejpam-1478	165	8	integral	integral	ADJ
ejpam-1478	165	9	equation	equation	NOUN
ejpam-1478	165	10	(	(	PUNCT
ejpam-1478	165	11	4	4	X
ejpam-1478	165	12	)	)	PUNCT
ejpam-1478	165	13	we	we	PRON
ejpam-1478	165	14	get	get	VERB
ejpam-1478	165	15	|x(t)|	|x(t)|	PROPN
ejpam-1478	165	16	≤|φ|0	≤|φ|0	PROPN
ejpam-1478	165	17	+	+	CCONJ
ejpam-1478	165	18	∑	∑	PROPN
ejpam-1478	165	19	t0	t0	PROPN
ejpam-1478	165	20	<	<	X
ejpam-1478	165	21	ti	ti	X
ejpam-1478	165	22	<	<	X
ejpam-1478	165	23	t	t	PROPN
ejpam-1478	165	24	�	�	PROPN
ejpam-1478	165	25	�	�	PROPN
ejpam-1478	165	26	ii	ii	PROPN
ejpam-1478	165	27	�	�	PROPN
ejpam-1478	165	28	x(t	x(t	PROPN
ejpam-1478	165	29	i	i	PRON
ejpam-1478	165	30	)	)	PUNCT
ejpam-1478	165	31	�	�	PROPN
ejpam-1478	165	32	�	�	PROPN
ejpam-1478	165	33	�	�	PROPN
ejpam-1478	165	34	+	+	CCONJ
ejpam-1478	165	35	∫	∫	PROPN
ejpam-1478	165	36	t	t	PROPN
ejpam-1478	165	37	t0	t0	PROPN
ejpam-1478	165	38	�	�	PROPN
ejpam-1478	165	39	a(s)|x(s)|p+	a(s)|x(s)|p+	PROPN
ejpam-1478	165	40	b(s	b(s	PROPN
ejpam-1478	165	41	)	)	PUNCT
ejpam-1478	165	42	�	�	PROPN
ejpam-1478	165	43	�	�	PROPN
ejpam-1478	165	44	�	�	PROPN
ejpam-1478	165	45	sup	sup	PROPN
ejpam-1478	165	46	ξ∈[σ(s),τ(s	ξ∈[σ(s),τ(s	NOUN
ejpam-1478	165	47	)	)	PUNCT
ejpam-1478	165	48	]	]	PUNCT
ejpam-1478	166	1	x(ξ	x(ξ	PROPN
ejpam-1478	166	2	)	)	PUNCT
ejpam-1478	166	3	�	�	PROPN
ejpam-1478	166	4	�	�	PROPN
ejpam-1478	166	5	�	�	PROPN
ejpam-1478	166	6	p	p	PROPN
ejpam-1478	166	7	�	�	PROPN
ejpam-1478	166	8	ds	ds	PROPN
ejpam-1478	166	9	≤|φ|0	≤|φ|0	VERB
ejpam-1478	166	10	+	+	CCONJ
ejpam-1478	166	11	∑	∑	PROPN
ejpam-1478	166	12	t0	t0	PROPN
ejpam-1478	166	13	<	<	X
ejpam-1478	166	14	ti	ti	X
ejpam-1478	166	15	<	<	X
ejpam-1478	166	16	t	t	NOUN
ejpam-1478	166	17	βi|x(t	βi|x(t	PUNCT
ejpam-1478	166	18	i)|p	i)|p	PROPN
ejpam-1478	166	19	+	+	CCONJ
ejpam-1478	166	20	∫	∫	PROPN
ejpam-1478	166	21	t	t	PROPN
ejpam-1478	166	22	t0	t0	PROPN
ejpam-1478	166	23	a(s)|x(s)|pds	a(s)|x(s)|pds	PROPN
ejpam-1478	166	24	+	+	CCONJ
ejpam-1478	166	25	∫	∫	PROPN
ejpam-1478	166	26	τ(t	τ(t	NOUN
ejpam-1478	166	27	)	)	PUNCT
ejpam-1478	166	28	τ(t0	τ(t0	NOUN
ejpam-1478	166	29	)	)	PUNCT
ejpam-1478	166	30	b(τ−1(η))(τ−1(η))′	b(τ−1(η))(τ−1(η))′	PROPN
ejpam-1478	167	1	sup	sup	PROPN
ejpam-1478	167	2	ξ∈[η−h	ξ∈[η−h	NUM
ejpam-1478	167	3	,	,	PUNCT
ejpam-1478	167	4	η	η	NOUN
ejpam-1478	167	5	]	]	X
ejpam-1478	167	6	�	�	PROPN
ejpam-1478	167	7	�	�	PROPN
ejpam-1478	167	8	x(ξ	x(ξ	PROPN
ejpam-1478	167	9	)	)	PUNCT
ejpam-1478	167	10	�	�	PROPN
ejpam-1478	167	11	�	�	PROPN
ejpam-1478	167	12	p	p	PROPN
ejpam-1478	167	13	dη	dη	PROPN
ejpam-1478	167	14	,	,	PUNCT
ejpam-1478	167	15	t	t	PROPN
ejpam-1478	167	16	∈	∈	PROPN
ejpam-1478	168	1	[	[	X
ejpam-1478	168	2	t0	t0	PROPN
ejpam-1478	168	3	,	,	PUNCT
ejpam-1478	168	4	t	t	PROPN
ejpam-1478	168	5	)	)	PUNCT
ejpam-1478	168	6	(	(	PUNCT
ejpam-1478	168	7	34	34	NUM
ejpam-1478	168	8	)	)	PUNCT
ejpam-1478	168	9	|x(t)|	|x(t)|	PROPN
ejpam-1478	168	10	≤	≤	ADJ
ejpam-1478	168	11	|φ|0	|φ|0	PROPN
ejpam-1478	168	12	,	,	PUNCT
ejpam-1478	168	13	t	t	PROPN
ejpam-1478	168	14	∈	∈	PROPN
ejpam-1478	169	1	[	[	X
ejpam-1478	169	2	τ(t0)−	τ(t0)−	X
ejpam-1478	169	3	h	h	PROPN
ejpam-1478	169	4	,	,	PUNCT
ejpam-1478	169	5	t0	t0	PROPN
ejpam-1478	169	6	]	]	PUNCT
ejpam-1478	169	7	,	,	PUNCT
ejpam-1478	169	8	(	(	PUNCT
ejpam-1478	169	9	35	35	NUM
ejpam-1478	169	10	)	)	PUNCT
ejpam-1478	169	11	where	where	SCONJ
ejpam-1478	169	12	x(t	x(t	PROPN
ejpam-1478	169	13	)	)	PUNCT
ejpam-1478	169	14	=	=	SYM
ejpam-1478	169	15	x(t	x(t	PROPN
ejpam-1478	169	16	;	;	PUNCT
ejpam-1478	169	17	t0,φ	t0,φ	PROPN
ejpam-1478	169	18	)	)	PUNCT
ejpam-1478	169	19	.	.	PUNCT
ejpam-1478	170	1	from	from	ADP
ejpam-1478	170	2	inequalities	inequality	NOUN
ejpam-1478	170	3	(	(	PUNCT
ejpam-1478	170	4	34	34	NUM
ejpam-1478	170	5	)	)	PUNCT
ejpam-1478	170	6	,	,	PUNCT
ejpam-1478	170	7	(	(	PUNCT
ejpam-1478	170	8	35	35	NUM
ejpam-1478	170	9	)	)	PUNCT
ejpam-1478	170	10	according	accord	VERB
ejpam-1478	170	11	to	to	ADP
ejpam-1478	170	12	theorem	theorem	NOUN
ejpam-1478	170	13	2	2	NUM
ejpam-1478	170	14	for	for	ADP
ejpam-1478	170	15	m	m	PROPN
ejpam-1478	170	16	=	=	SYM
ejpam-1478	170	17	2	2	NUM
ejpam-1478	170	18	,	,	PUNCT
ejpam-1478	170	19	α1(t	α1(t	NUM
ejpam-1478	170	20	)	)	PUNCT
ejpam-1478	170	21	≡	≡	PROPN
ejpam-1478	170	22	t	t	PROPN
ejpam-1478	170	23	,	,	PUNCT
ejpam-1478	170	24	α2(t	α2(t	NUM
ejpam-1478	170	25	)	)	PUNCT
ejpam-1478	170	26	≡	≡	PROPN
ejpam-1478	170	27	τ(t	τ(t	NOUN
ejpam-1478	170	28	)	)	PUNCT
ejpam-1478	170	29	,	,	PUNCT
ejpam-1478	170	30	u(t	u(t	NOUN
ejpam-1478	170	31	)	)	PUNCT
ejpam-1478	170	32	=	=	PUNCT
ejpam-1478	171	1	|x(t)|	|x(t)|	ADJ
ejpam-1478	171	2	,	,	PUNCT
ejpam-1478	171	3	m̃	m̃	PROPN
ejpam-1478	171	4	=	=	SYM
ejpam-1478	171	5	|φ|0	|φ|0	PROPN
ejpam-1478	171	6	,	,	PUNCT
ejpam-1478	171	7	a1(t	a1(t	ADJ
ejpam-1478	171	8	)	)	PUNCT
ejpam-1478	171	9	≡	≡	PROPN
ejpam-1478	171	10	a(t	a(t	PROPN
ejpam-1478	171	11	)	)	PUNCT
ejpam-1478	171	12	,	,	PUNCT
ejpam-1478	171	13	a2(t	a2(t	X
ejpam-1478	171	14	)	)	PUNCT
ejpam-1478	171	15	≡	≡	PROPN
ejpam-1478	171	16	0	0	NUM
ejpam-1478	171	17	,	,	PUNCT
ejpam-1478	171	18	b1(t	b1(t	NUM
ejpam-1478	171	19	)	)	PUNCT
ejpam-1478	171	20	≡	≡	PROPN
ejpam-1478	171	21	0	0	NUM
ejpam-1478	171	22	,	,	PUNCT
ejpam-1478	171	23	b2(t	b2(t	PROPN
ejpam-1478	171	24	)	)	PUNCT
ejpam-1478	171	25	≡	≡	PROPN
ejpam-1478	171	26	b(τ−1(η))(τ−1(η	b(τ−1(η))(τ−1(η	PROPN
ejpam-1478	171	27	)	)	PUNCT
ejpam-1478	171	28	)	)	PUNCT
ejpam-1478	171	29	′	′	VERB
ejpam-1478	171	30	for	for	ADP
ejpam-1478	171	31	t	t	PROPN
ejpam-1478	171	32	∈	∈	PROPN
ejpam-1478	172	1	[	[	X
ejpam-1478	172	2	τ(t0	τ(t0	NOUN
ejpam-1478	172	3	)	)	PUNCT
ejpam-1478	172	4	,	,	PUNCT
ejpam-1478	172	5	t	t	NOUN
ejpam-1478	172	6	)	)	PUNCT
ejpam-1478	172	7	,	,	PUNCT
ejpam-1478	172	8	p	p	NOUN
ejpam-1478	172	9	=	=	NOUN
ejpam-1478	172	10	1	1	NUM
ejpam-1478	172	11	and	and	CCONJ
ejpam-1478	172	12	t	t	NOUN
ejpam-1478	172	13	∈	∈	PROPN
ejpam-1478	173	1	[	[	X
ejpam-1478	173	2	t0	t0	PROPN
ejpam-1478	173	3	,	,	PUNCT
ejpam-1478	173	4	t	t	PROPN
ejpam-1478	173	5	)	)	PUNCT
ejpam-1478	174	1	we	we	PRON
ejpam-1478	174	2	obtain	obtain	VERB
ejpam-1478	174	3	|x(t)|	|x(t)|	PROPN
ejpam-1478	174	4	≤	≤	ADV
ejpam-1478	174	5	|φ|0	|φ|0	PROPN
ejpam-1478	174	6	�	�	PROPN
ejpam-1478	174	7	∏	∏	PROPN
ejpam-1478	174	8	t0	t0	PROPN
ejpam-1478	174	9	<	<	X
ejpam-1478	174	10	ti	ti	X
ejpam-1478	174	11	<	<	X
ejpam-1478	174	12	t	t	X
ejpam-1478	174	13	�	�	PROPN
ejpam-1478	174	14	1	1	NUM
ejpam-1478	174	15	+	+	NUM
ejpam-1478	174	16	βi	βi	PROPN
ejpam-1478	174	17	�	�	PROPN
ejpam-1478	174	18	�	�	PROPN
ejpam-1478	174	19	exp	exp	NOUN
ejpam-1478	174	20	�	�	PROPN
ejpam-1478	174	21	∫	∫	PROPN
ejpam-1478	174	22	t	t	PROPN
ejpam-1478	174	23	t0	t0	PROPN
ejpam-1478	174	24	h	h	PROPN
ejpam-1478	174	25	a(s	a(s	PROPN
ejpam-1478	174	26	)	)	PUNCT
ejpam-1478	175	1	+	+	NUM
ejpam-1478	175	2	b(s	b(	NOUN
ejpam-1478	175	3	)	)	PUNCT
ejpam-1478	176	1	i	i	PRON
ejpam-1478	176	2	ds	ds	VERB
ejpam-1478	176	3	�	�	PROPN
ejpam-1478	176	4	=	=	SYM
ejpam-1478	176	5	|φ|0ψ(t0	|φ|0ψ(t0	PROPN
ejpam-1478	176	6	,	,	PUNCT
ejpam-1478	176	7	t)eφ(t0	t)eφ(t0	NOUN
ejpam-1478	176	8	,	,	PUNCT
ejpam-1478	176	9	t	t	PROPN
ejpam-1478	176	10	)	)	PUNCT
ejpam-1478	176	11	.	.	PUNCT
ejpam-1478	177	1	(	(	PUNCT
ejpam-1478	177	2	36	36	NUM
ejpam-1478	177	3	)	)	PUNCT
ejpam-1478	177	4	since	since	SCONJ
ejpam-1478	177	5	the	the	DET
ejpam-1478	177	6	functions	function	NOUN
ejpam-1478	177	7	ψ(t0	ψ(t0	PROPN
ejpam-1478	177	8	,	,	PUNCT
ejpam-1478	177	9	t	t	PROPN
ejpam-1478	177	10	)	)	PUNCT
ejpam-1478	177	11	and	and	CCONJ
ejpam-1478	177	12	φ(t0	φ(t0	PROPN
ejpam-1478	177	13	,	,	PUNCT
ejpam-1478	177	14	t	t	PROPN
ejpam-1478	177	15	)	)	PUNCT
ejpam-1478	177	16	are	be	AUX
ejpam-1478	177	17	nondecreasing	nondecrease	VERB
ejpam-1478	177	18	in	in	ADP
ejpam-1478	177	19	their	their	PRON
ejpam-1478	177	20	second	second	ADJ
ejpam-1478	177	21	arguments	argument	NOUN
ejpam-1478	177	22	,	,	PUNCT
ejpam-1478	177	23	from	from	ADP
ejpam-1478	177	24	inequality	inequality	NOUN
ejpam-1478	177	25	(	(	PUNCT
ejpam-1478	177	26	36	36	NUM
ejpam-1478	177	27	)	)	PUNCT
ejpam-1478	177	28	and	and	CCONJ
ejpam-1478	177	29	condition	condition	NOUN
ejpam-1478	177	30	2	2	NUM
ejpam-1478	177	31	of	of	ADP
ejpam-1478	177	32	theorem	theorem	NOUN
ejpam-1478	177	33	3	3	NUM
ejpam-1478	177	34	it	it	PRON
ejpam-1478	177	35	follows	follow	VERB
ejpam-1478	177	36	|x(t)|	|x(t)|	PROPN
ejpam-1478	177	37	≤	≤	PROPN
ejpam-1478	177	38	|φ|0η1(t0)e	|φ|0η1(t0)e	NOUN
ejpam-1478	177	39	η2(t0	η2(t0	NOUN
ejpam-1478	177	40	)	)	PUNCT
ejpam-1478	177	41	.	.	PUNCT
ejpam-1478	178	1	(	(	PUNCT
ejpam-1478	178	2	37	37	NUM
ejpam-1478	178	3	)	)	PUNCT
ejpam-1478	178	4	the	the	DET
ejpam-1478	178	5	inequality	inequality	NOUN
ejpam-1478	178	6	(	(	PUNCT
ejpam-1478	178	7	37	37	NUM
ejpam-1478	178	8	)	)	PUNCT
ejpam-1478	178	9	proves	prove	VERB
ejpam-1478	178	10	the	the	DET
ejpam-1478	178	11	claim	claim	NOUN
ejpam-1478	178	12	of	of	ADP
ejpam-1478	178	13	theorem	theorem	ADJ
ejpam-1478	178	14	3	3	NUM
ejpam-1478	178	15	.	.	NOUN
ejpam-1478	178	16	remark	remark	NOUN
ejpam-1478	178	17	1	1	NUM
ejpam-1478	178	18	.	.	PUNCT
ejpam-1478	179	1	if	if	SCONJ
ejpam-1478	179	2	the	the	DET
ejpam-1478	179	3	conditions	condition	NOUN
ejpam-1478	179	4	1	1	NUM
ejpam-1478	179	5	and	and	CCONJ
ejpam-1478	179	6	2	2	NUM
ejpam-1478	179	7	of	of	ADP
ejpam-1478	179	8	theorem	theorem	ADJ
ejpam-1478	179	9	3	3	NUM
ejpam-1478	179	10	are	be	AUX
ejpam-1478	179	11	satisfied	satisfied	ADJ
ejpam-1478	179	12	,	,	PUNCT
ejpam-1478	179	13	then	then	ADV
ejpam-1478	179	14	the	the	DET
ejpam-1478	179	15	trivial	trivial	ADJ
ejpam-1478	179	16	solution	solution	NOUN
ejpam-1478	179	17	of	of	ADP
ejpam-1478	179	18	the	the	DET
ejpam-1478	179	19	impulsive	impulsive	ADJ
ejpam-1478	179	20	differential	differential	ADJ
ejpam-1478	179	21	equation	equation	NOUN
ejpam-1478	179	22	with	with	ADP
ejpam-1478	179	23	“	"	PUNCT
ejpam-1478	179	24	supremum	supremum	ADJ
ejpam-1478	179	25	”	"	PUNCT
ejpam-1478	179	26	(	(	PUNCT
ejpam-1478	179	27	1	1	NUM
ejpam-1478	179	28	)	)	PUNCT
ejpam-1478	179	29	,	,	PUNCT
ejpam-1478	179	30	(	(	PUNCT
ejpam-1478	179	31	2	2	X
ejpam-1478	179	32	)	)	PUNCT
ejpam-1478	179	33	is	be	AUX
ejpam-1478	179	34	stable	stable	ADJ
ejpam-1478	179	35	in	in	ADP
ejpam-1478	179	36	the	the	DET
ejpam-1478	179	37	sense	sense	NOUN
ejpam-1478	179	38	of	of	ADP
ejpam-1478	179	39	lyapunov	lyapunov	PROPN
ejpam-1478	179	40	.	.	PUNCT
ejpam-1478	180	1	theorem	theorem	VERB
ejpam-1478	180	2	4	4	NUM
ejpam-1478	180	3	.	.	PUNCT
ejpam-1478	181	1	let	let	VERB
ejpam-1478	181	2	the	the	DET
ejpam-1478	181	3	following	follow	VERB
ejpam-1478	181	4	conditions	condition	NOUN
ejpam-1478	181	5	be	be	AUX
ejpam-1478	181	6	fulfilled	fulfil	VERB
ejpam-1478	181	7	:	:	PUNCT
ejpam-1478	182	1	1	1	X
ejpam-1478	182	2	.	.	PUNCT
ejpam-1478	183	1	the	the	DET
ejpam-1478	183	2	conditions	condition	NOUN
ejpam-1478	183	3	h1	h1	PROPN
ejpam-1478	183	4	–	–	PUNCT
ejpam-1478	183	5	h4	h4	NOUN
ejpam-1478	183	6	are	be	AUX
ejpam-1478	183	7	satisfied	satisfied	ADJ
ejpam-1478	183	8	for	for	ADP
ejpam-1478	183	9	p	p	PROPN
ejpam-1478	183	10	∈	∈	PROPN
ejpam-1478	183	11	(	(	PUNCT
ejpam-1478	183	12	0,1	0,1	NUM
ejpam-1478	183	13	)	)	PUNCT
ejpam-1478	183	14	.	.	PUNCT
ejpam-1478	184	1	2	2	X
ejpam-1478	184	2	.	.	X
ejpam-1478	184	3	for	for	ADP
ejpam-1478	184	4	any	any	DET
ejpam-1478	184	5	t0	t0	PROPN
ejpam-1478	184	6	∈	∈	PROPN
ejpam-1478	184	7	r+	r+	PUNCT
ejpam-1478	184	8	there	there	PRON
ejpam-1478	184	9	exist	exist	VERB
ejpam-1478	184	10	lim	lim	PROPN
ejpam-1478	184	11	t→∞ψ(t0	t→∞ψ(t0	PROPN
ejpam-1478	184	12	,	,	PUNCT
ejpam-1478	184	13	t	t	PROPN
ejpam-1478	184	14	)	)	PUNCT
ejpam-1478	184	15	=	=	SYM
ejpam-1478	184	16	η1(t0	η1(t0	PROPN
ejpam-1478	184	17	)	)	PUNCT
ejpam-1478	184	18	and	and	CCONJ
ejpam-1478	184	19	lim	lim	PROPN
ejpam-1478	184	20	t→∞φ(t0	t→∞φ(t0	PROPN
ejpam-1478	184	21	,	,	PUNCT
ejpam-1478	184	22	t	t	PROPN
ejpam-1478	184	23	)	)	PUNCT
ejpam-1478	184	24	=	=	SYM
ejpam-1478	184	25	η2(t0	η2(t0	NOUN
ejpam-1478	184	26	)	)	PUNCT
ejpam-1478	184	27	where	where	SCONJ
ejpam-1478	184	28	the	the	DET
ejpam-1478	184	29	functions	function	NOUN
ejpam-1478	184	30	ψ(t0	ψ(t0	PROPN
ejpam-1478	184	31	,	,	PUNCT
ejpam-1478	184	32	t	t	PROPN
ejpam-1478	184	33	)	)	PUNCT
ejpam-1478	184	34	and	and	CCONJ
ejpam-1478	184	35	φ(t0	φ(t0	PROPN
ejpam-1478	184	36	,	,	PUNCT
ejpam-1478	184	37	t	t	PROPN
ejpam-1478	184	38	)	)	PUNCT
ejpam-1478	184	39	are	be	AUX
ejpam-1478	184	40	defined	define	VERB
ejpam-1478	184	41	by	by	ADP
ejpam-1478	184	42	(	(	PUNCT
ejpam-1478	184	43	30	30	NUM
ejpam-1478	184	44	)	)	PUNCT
ejpam-1478	184	45	and	and	CCONJ
ejpam-1478	184	46	(	(	PUNCT
ejpam-1478	184	47	31	31	NUM
ejpam-1478	184	48	)	)	PUNCT
ejpam-1478	184	49	,	,	PUNCT
ejpam-1478	184	50	correspondingly	correspondingly	ADV
ejpam-1478	184	51	,	,	PUNCT
ejpam-1478	184	52	and	and	CCONJ
ejpam-1478	184	53	the	the	DET
ejpam-1478	184	54	functions	function	NOUN
ejpam-1478	184	55	η1,η2	η1,η2	PROPN
ejpam-1478	184	56	∈	∈	PROPN
ejpam-1478	184	57	c(r+,r+	c(r+,r+	PROPN
ejpam-1478	184	58	)	)	PUNCT
ejpam-1478	184	59	.	.	PUNCT
ejpam-1478	185	1	then	then	ADV
ejpam-1478	185	2	for	for	ADP
ejpam-1478	185	3	the	the	DET
ejpam-1478	185	4	given	give	VERB
ejpam-1478	185	5	constants	constant	NOUN
ejpam-1478	185	6	0	0	NUM
ejpam-1478	185	7	<	<	X
ejpam-1478	185	8	λ	λ	X
ejpam-1478	185	9	<	<	X
ejpam-1478	185	10	λ	λ	X
ejpam-1478	185	11	such	such	ADJ
ejpam-1478	185	12	that	that	SCONJ
ejpam-1478	185	13	λ	λ	PROPN
ejpam-1478	185	14	∈	∈	PROPN
ejpam-1478	185	15	(	(	PUNCT
ejpam-1478	185	16	0,1	0,1	NUM
ejpam-1478	185	17	)	)	PUNCT
ejpam-1478	185	18	and	and	CCONJ
ejpam-1478	185	19	(	(	PUNCT
ejpam-1478	185	20	i	i	NOUN
ejpam-1478	185	21	)	)	PUNCT
ejpam-1478	185	22	there	there	PRON
ejpam-1478	185	23	exists	exist	VERB
ejpam-1478	185	24	a	a	DET
ejpam-1478	185	25	point	point	NOUN
ejpam-1478	185	26	t0	t0	PROPN
ejpam-1478	185	27	∈	∈	PROPN
ejpam-1478	185	28	r+	r+	NOUN
ejpam-1478	185	29	such	such	ADJ
ejpam-1478	185	30	that	that	SCONJ
ejpam-1478	185	31	η1(t0	η1(t0	NOUN
ejpam-1478	185	32	)	)	PUNCT
ejpam-1478	185	33	h	h	NOUN
ejpam-1478	186	1	λ1−p	λ1−p	PROPN
ejpam-1478	187	1	+	+	PUNCT
ejpam-1478	187	2	(	(	PUNCT
ejpam-1478	187	3	1−	1−	NUM
ejpam-1478	187	4	p)η2(t0	p)η2(t0	NOUN
ejpam-1478	187	5	)	)	PUNCT
ejpam-1478	187	6	i	i	PROPN
ejpam-1478	187	7	1	1	NUM
ejpam-1478	187	8	1−p	1−p	NUM
ejpam-1478	187	9	<	<	X
ejpam-1478	187	10	λ	λ	NOUN
ejpam-1478	187	11	,	,	PUNCT
ejpam-1478	187	12	then	then	ADV
ejpam-1478	187	13	the	the	DET
ejpam-1478	187	14	impulsive	impulsive	ADJ
ejpam-1478	187	15	differential	differential	ADJ
ejpam-1478	187	16	equation	equation	NOUN
ejpam-1478	187	17	with	with	ADP
ejpam-1478	187	18	“	"	PUNCT
ejpam-1478	187	19	supremum	supremum	ADJ
ejpam-1478	187	20	”	"	PUNCT
ejpam-1478	187	21	(	(	PUNCT
ejpam-1478	187	22	1	1	NUM
ejpam-1478	187	23	)	)	PUNCT
ejpam-1478	187	24	,	,	PUNCT
ejpam-1478	187	25	(	(	PUNCT
ejpam-1478	187	26	2	2	X
ejpam-1478	187	27	)	)	PUNCT
ejpam-1478	187	28	is	be	AUX
ejpam-1478	187	29	practically	practically	ADV
ejpam-1478	187	30	stable	stable	ADJ
ejpam-1478	187	31	with	with	ADP
ejpam-1478	187	32	respect	respect	NOUN
ejpam-1478	187	33	to	to	ADP
ejpam-1478	187	34	(	(	PUNCT
ejpam-1478	187	35	λ	λ	X
ejpam-1478	187	36	,	,	PUNCT
ejpam-1478	187	37	λ	λ	PROPN
ejpam-1478	187	38	)	)	PUNCT
ejpam-1478	187	39	;	;	PUNCT
ejpam-1478	187	40	s.	s.	PROPN
ejpam-1478	187	41	hristova	hristova	PROPN
ejpam-1478	187	42	,	,	PUNCT
ejpam-1478	187	43	k.	k.	PROPN
ejpam-1478	187	44	stefanova	stefanova	PROPN
ejpam-1478	187	45	/	/	SYM
ejpam-1478	187	46	eur	eur	PROPN
ejpam-1478	187	47	.	.	PUNCT
ejpam-1478	188	1	j.	j.	PROPN
ejpam-1478	188	2	pure	pure	PROPN
ejpam-1478	188	3	appl	appl	PROPN
ejpam-1478	188	4	.	.	PROPN
ejpam-1478	188	5	math	math	PROPN
ejpam-1478	188	6	,	,	PUNCT
ejpam-1478	188	7	5	5	NUM
ejpam-1478	188	8	(	(	PUNCT
ejpam-1478	188	9	2012	2012	NUM
ejpam-1478	188	10	)	)	PUNCT
ejpam-1478	188	11	,	,	PUNCT
ejpam-1478	188	12	30	30	NUM
ejpam-1478	188	13	-	-	SYM
ejpam-1478	188	14	44	44	NUM
ejpam-1478	188	15	39	39	NUM
ejpam-1478	188	16	(	(	PUNCT
ejpam-1478	188	17	ii	ii	NOUN
ejpam-1478	188	18	)	)	PUNCT
ejpam-1478	188	19	if	if	SCONJ
ejpam-1478	188	20	the	the	DET
ejpam-1478	188	21	functions	function	NOUN
ejpam-1478	188	22	η1(t	η1(t	PRON
ejpam-1478	188	23	)	)	PUNCT
ejpam-1478	188	24	and	and	CCONJ
ejpam-1478	188	25	η2(t	η2(t	PROPN
ejpam-1478	188	26	)	)	PUNCT
ejpam-1478	188	27	are	be	AUX
ejpam-1478	188	28	bounded	bound	VERB
ejpam-1478	188	29	,	,	PUNCT
ejpam-1478	188	30	i.e.	i.e.	X
ejpam-1478	188	31	there	there	PRON
ejpam-1478	188	32	exist	exist	VERB
ejpam-1478	188	33	constants	constant	NOUN
ejpam-1478	189	1	µ1,µ2	µ1,µ2	PROPN
ejpam-1478	189	2	>	>	X
ejpam-1478	189	3	0	0	PUNCT
ejpam-1478	189	4	such	such	ADJ
ejpam-1478	189	5	that	that	SCONJ
ejpam-1478	189	6	ηk(t	ηk(t	NOUN
ejpam-1478	189	7	)	)	PUNCT
ejpam-1478	189	8	≤	≤	NUM
ejpam-1478	189	9	µk	µk	ADP
ejpam-1478	189	10	,	,	PUNCT
ejpam-1478	189	11	(	(	PUNCT
ejpam-1478	189	12	k	k	NOUN
ejpam-1478	189	13	=	=	SYM
ejpam-1478	189	14	1,2	1,2	NUM
ejpam-1478	189	15	)	)	PUNCT
ejpam-1478	189	16	for	for	ADP
ejpam-1478	189	17	t	t	PROPN
ejpam-1478	189	18	∈	∈	PROPN
ejpam-1478	189	19	r+	r+	NOUN
ejpam-1478	189	20	,	,	PUNCT
ejpam-1478	189	21	and	and	CCONJ
ejpam-1478	189	22	µ1	µ1	NOUN
ejpam-1478	189	23	h	h	NOUN
ejpam-1478	189	24	λ1−p	λ1−p	PROPN
ejpam-1478	189	25	+	+	PUNCT
ejpam-1478	189	26	(	(	PUNCT
ejpam-1478	189	27	1−	1−	NUM
ejpam-1478	189	28	p)µ2	p)µ2	PROPN
ejpam-1478	189	29	�	�	PROPN
ejpam-1478	189	30	1	1	NUM
ejpam-1478	189	31	1−p	1−p	NUM
ejpam-1478	189	32	<	<	X
ejpam-1478	189	33	λ	λ	NOUN
ejpam-1478	189	34	,	,	PUNCT
ejpam-1478	189	35	then	then	ADV
ejpam-1478	189	36	the	the	DET
ejpam-1478	189	37	impulsive	impulsive	ADJ
ejpam-1478	189	38	differential	differential	ADJ
ejpam-1478	189	39	equation	equation	NOUN
ejpam-1478	189	40	with	with	ADP
ejpam-1478	189	41	“	"	PUNCT
ejpam-1478	189	42	supremum	supremum	ADJ
ejpam-1478	189	43	”	"	PUNCT
ejpam-1478	189	44	(	(	PUNCT
ejpam-1478	189	45	1	1	NUM
ejpam-1478	189	46	)	)	PUNCT
ejpam-1478	189	47	,	,	PUNCT
ejpam-1478	189	48	(	(	PUNCT
ejpam-1478	189	49	2	2	X
ejpam-1478	189	50	)	)	PUNCT
ejpam-1478	189	51	is	be	AUX
ejpam-1478	189	52	uniformly	uniformly	ADV
ejpam-1478	189	53	practically	practically	ADV
ejpam-1478	189	54	stable	stable	ADJ
ejpam-1478	189	55	with	with	ADP
ejpam-1478	189	56	respect	respect	NOUN
ejpam-1478	189	57	to	to	ADP
ejpam-1478	189	58	(	(	PUNCT
ejpam-1478	189	59	λ	λ	X
ejpam-1478	189	60	,	,	PUNCT
ejpam-1478	189	61	λ	λ	NOUN
ejpam-1478	189	62	)	)	PUNCT
ejpam-1478	189	63	.	.	PUNCT
ejpam-1478	190	1	proof	proof	NOUN
ejpam-1478	190	2	.	.	PUNCT
ejpam-1478	191	1	from	from	ADP
ejpam-1478	191	2	inequalities	inequality	NOUN
ejpam-1478	191	3	(	(	PUNCT
ejpam-1478	191	4	34	34	NUM
ejpam-1478	191	5	)	)	PUNCT
ejpam-1478	191	6	,	,	PUNCT
ejpam-1478	191	7	(	(	PUNCT
ejpam-1478	191	8	35	35	NUM
ejpam-1478	191	9	)	)	PUNCT
ejpam-1478	191	10	according	accord	VERB
ejpam-1478	191	11	to	to	ADP
ejpam-1478	191	12	theorem	theorem	NOUN
ejpam-1478	191	13	2	2	NUM
ejpam-1478	191	14	for	for	ADP
ejpam-1478	191	15	m	m	PROPN
ejpam-1478	191	16	=	=	SYM
ejpam-1478	191	17	2	2	NUM
ejpam-1478	191	18	,	,	PUNCT
ejpam-1478	191	19	α1(t	α1(t	NUM
ejpam-1478	191	20	)	)	PUNCT
ejpam-1478	191	21	≡	≡	PROPN
ejpam-1478	191	22	t	t	PROPN
ejpam-1478	191	23	,	,	PUNCT
ejpam-1478	191	24	α2(t	α2(t	NUM
ejpam-1478	191	25	)	)	PUNCT
ejpam-1478	191	26	≡	≡	PROPN
ejpam-1478	191	27	τ(t	τ(t	NOUN
ejpam-1478	191	28	)	)	PUNCT
ejpam-1478	191	29	,	,	PUNCT
ejpam-1478	191	30	u(t	u(t	NOUN
ejpam-1478	191	31	)	)	PUNCT
ejpam-1478	191	32	=	=	PUNCT
ejpam-1478	191	33	|x(t)|	|x(t)|	ADJ
ejpam-1478	191	34	,	,	PUNCT
ejpam-1478	191	35	m̃	m̃	PROPN
ejpam-1478	191	36	=	=	SYM
ejpam-1478	191	37	|φ|0	|φ|0	PROPN
ejpam-1478	191	38	,	,	PUNCT
ejpam-1478	191	39	a1(t	a1(t	ADJ
ejpam-1478	191	40	)	)	PUNCT
ejpam-1478	191	41	≡	≡	PROPN
ejpam-1478	191	42	a(t	a(t	PROPN
ejpam-1478	191	43	)	)	PUNCT
ejpam-1478	191	44	,	,	PUNCT
ejpam-1478	191	45	a2(t)≡	a2(t)≡	PUNCT
ejpam-1478	191	46	0	0	NUM
ejpam-1478	191	47	,	,	PUNCT
ejpam-1478	191	48	b1(t	b1(t	NUM
ejpam-1478	191	49	)	)	PUNCT
ejpam-1478	191	50	≡	≡	PROPN
ejpam-1478	191	51	0	0	NUM
ejpam-1478	191	52	,	,	PUNCT
ejpam-1478	191	53	b2(t	b2(t	PROPN
ejpam-1478	191	54	)	)	PUNCT
ejpam-1478	191	55	≡	≡	PROPN
ejpam-1478	191	56	b(τ−1(t))(τ−1(t	b(τ−1(t))(τ−1(t	VERB
ejpam-1478	191	57	)	)	PUNCT
ejpam-1478	191	58	)	)	PUNCT
ejpam-1478	191	59	′	′	NUM
ejpam-1478	192	1	for	for	ADP
ejpam-1478	192	2	t	t	PROPN
ejpam-1478	192	3	∈	∈	PROPN
ejpam-1478	193	1	[	[	X
ejpam-1478	193	2	τ(t0	τ(t0	NOUN
ejpam-1478	193	3	)	)	PUNCT
ejpam-1478	193	4	,	,	PUNCT
ejpam-1478	193	5	t	t	PROPN
ejpam-1478	193	6	)	)	PUNCT
ejpam-1478	193	7	,	,	PUNCT
ejpam-1478	193	8	p	p	PROPN
ejpam-1478	193	9	∈	∈	PROPN
ejpam-1478	193	10	(	(	PUNCT
ejpam-1478	193	11	0,1	0,1	NUM
ejpam-1478	193	12	)	)	PUNCT
ejpam-1478	193	13	and	and	CCONJ
ejpam-1478	193	14	t	t	PROPN
ejpam-1478	193	15	∈	∈	PROPN
ejpam-1478	194	1	[	[	X
ejpam-1478	194	2	t0	t0	PROPN
ejpam-1478	194	3	,	,	PUNCT
ejpam-1478	194	4	t	t	PROPN
ejpam-1478	194	5	)	)	PUNCT
ejpam-1478	194	6	we	we	PRON
ejpam-1478	194	7	obtain	obtain	VERB
ejpam-1478	194	8	|x(t)|	|x(t)|	PROPN
ejpam-1478	194	9	≤	≤	PROPN
ejpam-1478	194	10	�	�	PROPN
ejpam-1478	194	11	∏	∏	PROPN
ejpam-1478	194	12	t0	t0	PROPN
ejpam-1478	194	13	<	<	X
ejpam-1478	194	14	ti	ti	X
ejpam-1478	194	15	<	<	X
ejpam-1478	194	16	t	t	X
ejpam-1478	194	17	�	�	PROPN
ejpam-1478	194	18	1	1	NUM
ejpam-1478	194	19	+	+	CCONJ
ejpam-1478	194	20	βi|φ|p−1	βi|φ|p−1	NUM
ejpam-1478	194	21	0	0	NUM
ejpam-1478	194	22	�	�	PROPN
ejpam-1478	194	23	�	�	PROPN
ejpam-1478	194	24	×	×	PROPN
ejpam-1478	194	25	�	�	PROPN
ejpam-1478	194	26	|φ|1−p	|φ|1−p	NUM
ejpam-1478	194	27	0	0	NUM
ejpam-1478	195	1	+	+	CCONJ
ejpam-1478	195	2	(	(	PUNCT
ejpam-1478	195	3	1−	1−	NUM
ejpam-1478	195	4	p	p	NOUN
ejpam-1478	195	5	)	)	PUNCT
ejpam-1478	195	6	∫	∫	PROPN
ejpam-1478	195	7	t	t	PROPN
ejpam-1478	195	8	t0	t0	PROPN
ejpam-1478	195	9	h	h	NOUN
ejpam-1478	195	10	a(s)+	a(s)+	PROPN
ejpam-1478	195	11	b(s	b(s	PROPN
ejpam-1478	195	12	)	)	PUNCT
ejpam-1478	196	1	i	i	PRON
ejpam-1478	196	2	ds	ds	VERB
ejpam-1478	196	3	�	�	PROPN
ejpam-1478	196	4	1	1	NUM
ejpam-1478	196	5	1−p	1−p	NUM
ejpam-1478	196	6	.	.	PUNCT
ejpam-1478	197	1	(	(	PUNCT
ejpam-1478	197	2	38	38	NUM
ejpam-1478	197	3	)	)	PUNCT
ejpam-1478	197	4	let	let	VERB
ejpam-1478	197	5	|φ|0	|φ|0	VERB
ejpam-1478	197	6	<	<	X
ejpam-1478	197	7	λ	λ	PROPN
ejpam-1478	197	8	.	.	PROPN
ejpam-1478	198	1	then	then	ADV
ejpam-1478	198	2	from	from	ADP
ejpam-1478	198	3	1	1	NUM
ejpam-1478	198	4	+	+	CCONJ
ejpam-1478	198	5	βi|φ|p−1	βi|φ|p−1	NUM
ejpam-1478	198	6	0	0	NUM
ejpam-1478	198	7	≤	≤	NUM
ejpam-1478	198	8	1	1	NUM
ejpam-1478	198	9	+	+	NUM
ejpam-1478	198	10	βiλ	βiλ	VERB
ejpam-1478	198	11	p−1	p−1	PROPN
ejpam-1478	198	12	≤	≤	NUM
ejpam-1478	198	13	1	1	NUM
ejpam-1478	198	14	+	+	NUM
ejpam-1478	198	15	βi	βi	PROPN
ejpam-1478	198	16	,	,	PUNCT
ejpam-1478	198	17	the	the	DET
ejpam-1478	198	18	monotonic	monotonic	ADJ
ejpam-1478	198	19	property	property	NOUN
ejpam-1478	198	20	of	of	ADP
ejpam-1478	198	21	functions	function	NOUN
ejpam-1478	198	22	ψ(t0	ψ(t0	PROPN
ejpam-1478	198	23	,	,	PUNCT
ejpam-1478	198	24	t	t	PROPN
ejpam-1478	198	25	)	)	PUNCT
ejpam-1478	198	26	and	and	CCONJ
ejpam-1478	198	27	φ(t0	φ(t0	NOUN
ejpam-1478	198	28	,	,	PUNCT
ejpam-1478	198	29	t	t	PROPN
ejpam-1478	198	30	)	)	PUNCT
ejpam-1478	198	31	,	,	PUNCT
ejpam-1478	198	32	condition	condition	NOUN
ejpam-1478	198	33	2	2	NUM
ejpam-1478	198	34	of	of	ADP
ejpam-1478	198	35	theorem	theorem	ADJ
ejpam-1478	198	36	4	4	NUM
ejpam-1478	198	37	and	and	CCONJ
ejpam-1478	198	38	inequality	inequality	NOUN
ejpam-1478	198	39	(	(	PUNCT
ejpam-1478	198	40	38	38	NUM
ejpam-1478	198	41	)	)	PUNCT
ejpam-1478	198	42	we	we	PRON
ejpam-1478	198	43	get	get	VERB
ejpam-1478	198	44	|x(t)|	|x(t)|	PROPN
ejpam-1478	198	45	≤	≤	PROPN
ejpam-1478	198	46	ψ(t0	ψ(t0	PROPN
ejpam-1478	198	47	,	,	PUNCT
ejpam-1478	198	48	t	t	PROPN
ejpam-1478	198	49	)	)	PUNCT
ejpam-1478	198	50	h	h	NOUN
ejpam-1478	199	1	λ1−p	λ1−p	PROPN
ejpam-1478	200	1	+	+	PUNCT
ejpam-1478	200	2	(	(	PUNCT
ejpam-1478	200	3	1−	1−	NUM
ejpam-1478	200	4	p)φ(t0	p)φ(t0	NOUN
ejpam-1478	200	5	,	,	PUNCT
ejpam-1478	200	6	t	t	PROPN
ejpam-1478	200	7	)	)	PUNCT
ejpam-1478	200	8	i	i	PROPN
ejpam-1478	200	9	1	1	NUM
ejpam-1478	200	10	1−p	1−p	NUM
ejpam-1478	200	11	.	.	PUNCT
ejpam-1478	201	1	(	(	PUNCT
ejpam-1478	201	2	39	39	NUM
ejpam-1478	201	3	)	)	PUNCT
ejpam-1478	201	4	from	from	ADP
ejpam-1478	201	5	inequality	inequality	NOUN
ejpam-1478	201	6	(	(	PUNCT
ejpam-1478	201	7	39	39	NUM
ejpam-1478	201	8	)	)	PUNCT
ejpam-1478	201	9	according	accord	VERB
ejpam-1478	201	10	to	to	ADP
ejpam-1478	201	11	condition	condition	NOUN
ejpam-1478	201	12	2	2	NUM
ejpam-1478	201	13	of	of	ADP
ejpam-1478	201	14	the	the	DET
ejpam-1478	201	15	theorem	theorem	NOUN
ejpam-1478	201	16	it	it	PRON
ejpam-1478	201	17	follows	follow	VERB
ejpam-1478	201	18	|x(t)|	|x(t)|	PROPN
ejpam-1478	201	19	≤	≤	NUM
ejpam-1478	201	20	η1(t0	η1(t0	PROPN
ejpam-1478	201	21	)	)	PUNCT
ejpam-1478	201	22	h	h	NOUN
ejpam-1478	202	1	λ1−p	λ1−p	PROPN
ejpam-1478	203	1	+	+	PUNCT
ejpam-1478	203	2	(	(	PUNCT
ejpam-1478	203	3	1−	1−	NUM
ejpam-1478	203	4	p)η2(t0	p)η2(t0	NOUN
ejpam-1478	203	5	)	)	PUNCT
ejpam-1478	203	6	i	i	PROPN
ejpam-1478	203	7	1	1	NUM
ejpam-1478	203	8	1−p	1−p	NUM
ejpam-1478	203	9	.	.	PUNCT
ejpam-1478	204	1	(	(	PUNCT
ejpam-1478	204	2	40	40	NUM
ejpam-1478	204	3	)	)	PUNCT
ejpam-1478	204	4	the	the	DET
ejpam-1478	204	5	inequality	inequality	NOUN
ejpam-1478	204	6	(	(	PUNCT
ejpam-1478	204	7	40	40	NUM
ejpam-1478	204	8	)	)	PUNCT
ejpam-1478	204	9	proves	prove	VERB
ejpam-1478	204	10	the	the	DET
ejpam-1478	204	11	claim	claim	NOUN
ejpam-1478	204	12	of	of	ADP
ejpam-1478	204	13	theorem	theorem	ADJ
ejpam-1478	204	14	4	4	NUM
ejpam-1478	204	15	.	.	NOUN
ejpam-1478	204	16	5	5	NUM
ejpam-1478	204	17	.	.	PUNCT
ejpam-1478	204	18	applications	application	NOUN
ejpam-1478	204	19	now	now	ADV
ejpam-1478	204	20	we	we	PRON
ejpam-1478	204	21	will	will	AUX
ejpam-1478	204	22	apply	apply	VERB
ejpam-1478	204	23	some	some	PRON
ejpam-1478	204	24	of	of	ADP
ejpam-1478	204	25	the	the	DET
ejpam-1478	204	26	obtained	obtain	VERB
ejpam-1478	204	27	sufficient	sufficient	ADJ
ejpam-1478	204	28	conditions	condition	NOUN
ejpam-1478	204	29	for	for	ADP
ejpam-1478	204	30	special	special	ADJ
ejpam-1478	204	31	types	type	NOUN
ejpam-1478	204	32	of	of	ADP
ejpam-1478	204	33	impulsive	impulsive	ADJ
ejpam-1478	204	34	differential	differential	ADJ
ejpam-1478	204	35	equations	equation	NOUN
ejpam-1478	204	36	with	with	ADP
ejpam-1478	204	37	“	"	PUNCT
ejpam-1478	204	38	supremum	supremum	ADJ
ejpam-1478	204	39	”	"	PUNCT
ejpam-1478	204	40	(	(	PUNCT
ejpam-1478	204	41	1	1	NUM
ejpam-1478	204	42	)	)	PUNCT
ejpam-1478	204	43	,	,	PUNCT
ejpam-1478	204	44	(	(	PUNCT
ejpam-1478	204	45	2	2	NUM
ejpam-1478	204	46	)	)	PUNCT
ejpam-1478	204	47	.	.	PUNCT
ejpam-1478	205	1	theorem	theorem	NOUN
ejpam-1478	205	2	5	5	NUM
ejpam-1478	205	3	.	.	PUNCT
ejpam-1478	206	1	let	let	VERB
ejpam-1478	206	2	the	the	DET
ejpam-1478	206	3	following	follow	VERB
ejpam-1478	206	4	conditions	condition	NOUN
ejpam-1478	206	5	be	be	AUX
ejpam-1478	206	6	fulfilled	fulfil	VERB
ejpam-1478	206	7	:	:	PUNCT
ejpam-1478	207	1	1	1	X
ejpam-1478	207	2	.	.	PUNCT
ejpam-1478	208	1	the	the	DET
ejpam-1478	208	2	conditions	condition	NOUN
ejpam-1478	208	3	h1	h1	VERB
ejpam-1478	208	4	and	and	CCONJ
ejpam-1478	208	5	h4	h4	NOUN
ejpam-1478	208	6	are	be	AUX
ejpam-1478	208	7	satisfied	satisfied	ADJ
ejpam-1478	208	8	.	.	PUNCT
ejpam-1478	209	1	2	2	X
ejpam-1478	209	2	.	.	X
ejpam-1478	209	3	the	the	DET
ejpam-1478	209	4	function	function	NOUN
ejpam-1478	209	5	f	f	PROPN
ejpam-1478	209	6	∈	∈	PROPN
ejpam-1478	209	7	c(r+×r×r	c(r+×r×r	PROPN
ejpam-1478	209	8	,	,	PUNCT
ejpam-1478	209	9	r	r	NOUN
ejpam-1478	209	10	)	)	PUNCT
ejpam-1478	209	11	,	,	PUNCT
ejpam-1478	209	12	f	f	PROPN
ejpam-1478	209	13	(	(	PUNCT
ejpam-1478	209	14	t	t	PROPN
ejpam-1478	209	15	,	,	PUNCT
ejpam-1478	209	16	0,0	0,0	NUM
ejpam-1478	209	17	)	)	PUNCT
ejpam-1478	209	18	=	=	SYM
ejpam-1478	209	19	0	0	PUNCT
ejpam-1478	210	1	and	and	CCONJ
ejpam-1478	210	2	|	|	ADV
ejpam-1478	210	3	f	f	X
ejpam-1478	210	4	(	(	PUNCT
ejpam-1478	210	5	t	t	PROPN
ejpam-1478	210	6	,	,	PUNCT
ejpam-1478	210	7	x	x	X
ejpam-1478	210	8	,	,	PUNCT
ejpam-1478	210	9	y)|	y)|	ADJ
ejpam-1478	210	10	≤	≤	PUNCT
ejpam-1478	210	11	e−t	e−t	NOUN
ejpam-1478	210	12	h	h	NOUN
ejpam-1478	210	13	|x	|x	NOUN
ejpam-1478	210	14	|+	|+	PUNCT
ejpam-1478	211	1	|y|	|y|	VERB
ejpam-1478	211	2	i	i	PRON
ejpam-1478	211	3	for	for	ADP
ejpam-1478	211	4	x	x	X
ejpam-1478	211	5	,	,	PUNCT
ejpam-1478	211	6	y	y	PROPN
ejpam-1478	211	7	∈	∈	PROPN
ejpam-1478	211	8	r.	r.	PROPN
ejpam-1478	211	9	3	3	NUM
ejpam-1478	211	10	.	.	PUNCT
ejpam-1478	212	1	the	the	DET
ejpam-1478	212	2	functions	function	NOUN
ejpam-1478	212	3	ii	ii	NOUN
ejpam-1478	212	4	:	:	PUNCT
ejpam-1478	212	5	r→	r→	PROPN
ejpam-1478	212	6	r	r	PROPN
ejpam-1478	212	7	,	,	PUNCT
ejpam-1478	212	8	ii(0	ii(0	NOUN
ejpam-1478	212	9	)	)	PUNCT
ejpam-1478	212	10	=	=	SYM
ejpam-1478	212	11	0	0	NUM
ejpam-1478	212	12	and	and	CCONJ
ejpam-1478	212	13	|ii(x)|	|ii(x)|	NOUN
ejpam-1478	212	14	≤	≤	NUM
ejpam-1478	212	15	1	1	NUM
ejpam-1478	212	16	4i2	4i2	NUM
ejpam-1478	212	17	−	−	NUM
ejpam-1478	212	18	1	1	NUM
ejpam-1478	212	19	|x	|x	NOUN
ejpam-1478	212	20	|	|	ADV
ejpam-1478	212	21	for	for	ADP
ejpam-1478	212	22	x	x	PROPN
ejpam-1478	212	23	∈	∈	PROPN
ejpam-1478	212	24	r	r	NOUN
ejpam-1478	212	25	,	,	PUNCT
ejpam-1478	212	26	i	i	PRON
ejpam-1478	212	27	∈	∈	PROPN
ejpam-1478	212	28	z(t0	z(t0	NOUN
ejpam-1478	212	29	,	,	PUNCT
ejpam-1478	212	30	t	t	PROPN
ejpam-1478	212	31	)	)	PUNCT
ejpam-1478	212	32	.	.	PUNCT
ejpam-1478	213	1	s.	s.	PROPN
ejpam-1478	213	2	hristova	hristova	PROPN
ejpam-1478	213	3	,	,	PUNCT
ejpam-1478	213	4	k.	k.	PROPN
ejpam-1478	213	5	stefanova	stefanova	PROPN
ejpam-1478	213	6	/	/	SYM
ejpam-1478	213	7	eur	eur	PROPN
ejpam-1478	213	8	.	.	PUNCT
ejpam-1478	214	1	j.	j.	PROPN
ejpam-1478	214	2	pure	pure	PROPN
ejpam-1478	214	3	appl	appl	PROPN
ejpam-1478	214	4	.	.	PROPN
ejpam-1478	214	5	math	math	PROPN
ejpam-1478	214	6	,	,	PUNCT
ejpam-1478	214	7	5	5	NUM
ejpam-1478	214	8	(	(	PUNCT
ejpam-1478	214	9	2012	2012	NUM
ejpam-1478	214	10	)	)	PUNCT
ejpam-1478	214	11	,	,	PUNCT
ejpam-1478	214	12	30	30	NUM
ejpam-1478	214	13	-	-	SYM
ejpam-1478	214	14	44	44	NUM
ejpam-1478	214	15	40	40	NUM
ejpam-1478	214	16	then	then	ADV
ejpam-1478	214	17	:	:	PUNCT
ejpam-1478	214	18	(	(	PUNCT
ejpam-1478	214	19	i	i	NOUN
ejpam-1478	214	20	)	)	PUNCT
ejpam-1478	214	21	all	all	DET
ejpam-1478	214	22	solutions	solution	NOUN
ejpam-1478	214	23	of	of	ADP
ejpam-1478	214	24	the	the	DET
ejpam-1478	214	25	system	system	NOUN
ejpam-1478	214	26	of	of	ADP
ejpam-1478	214	27	impulsive	impulsive	ADJ
ejpam-1478	214	28	differential	differential	ADJ
ejpam-1478	214	29	equation	equation	NOUN
ejpam-1478	214	30	(	(	PUNCT
ejpam-1478	214	31	1	1	NUM
ejpam-1478	214	32	)	)	PUNCT
ejpam-1478	214	33	,	,	PUNCT
ejpam-1478	214	34	(	(	PUNCT
ejpam-1478	214	35	2	2	X
ejpam-1478	214	36	)	)	PUNCT
ejpam-1478	214	37	are	be	AUX
ejpam-1478	214	38	uniformly	uniformly	ADV
ejpam-1478	214	39	bounded	bound	VERB
ejpam-1478	214	40	;	;	PUNCT
ejpam-1478	214	41	(	(	PUNCT
ejpam-1478	214	42	ii	ii	NOUN
ejpam-1478	214	43	)	)	PUNCT
ejpam-1478	214	44	if	if	SCONJ
ejpam-1478	214	45	,	,	PUNCT
ejpam-1478	214	46	additionally	additionally	ADV
ejpam-1478	214	47	,	,	PUNCT
ejpam-1478	214	48	the	the	DET
ejpam-1478	214	49	given	give	VERB
ejpam-1478	214	50	positive	positive	ADJ
ejpam-1478	214	51	constants	constant	NOUN
ejpam-1478	214	52	λ	λ	PROPN
ejpam-1478	214	53	and	and	CCONJ
ejpam-1478	214	54	λ	λ	NOUN
ejpam-1478	214	55	are	be	AUX
ejpam-1478	214	56	such	such	ADJ
ejpam-1478	214	57	that	that	SCONJ
ejpam-1478	214	58	λπe2	λπe2	NOUN
ejpam-1478	214	59	<	<	X
ejpam-1478	214	60	2λ	2λ	PROPN
ejpam-1478	214	61	,	,	PUNCT
ejpam-1478	214	62	then	then	ADV
ejpam-1478	214	63	the	the	DET
ejpam-1478	214	64	impulsive	impulsive	ADJ
ejpam-1478	214	65	differential	differential	ADJ
ejpam-1478	214	66	equation	equation	NOUN
ejpam-1478	214	67	with	with	ADP
ejpam-1478	214	68	“	"	PUNCT
ejpam-1478	214	69	supremum	supremum	ADJ
ejpam-1478	214	70	”	"	PUNCT
ejpam-1478	214	71	(	(	PUNCT
ejpam-1478	214	72	1	1	NUM
ejpam-1478	214	73	)	)	PUNCT
ejpam-1478	214	74	,	,	PUNCT
ejpam-1478	214	75	(	(	PUNCT
ejpam-1478	214	76	2	2	X
ejpam-1478	214	77	)	)	PUNCT
ejpam-1478	214	78	is	be	AUX
ejpam-1478	214	79	uniformly	uniformly	ADV
ejpam-1478	214	80	practically	practically	ADV
ejpam-1478	214	81	stable	stable	ADJ
ejpam-1478	214	82	with	with	ADP
ejpam-1478	214	83	respect	respect	NOUN
ejpam-1478	214	84	to	to	ADP
ejpam-1478	214	85	(	(	PUNCT
ejpam-1478	214	86	λ	λ	X
ejpam-1478	214	87	,	,	PUNCT
ejpam-1478	214	88	λ	λ	NOUN
ejpam-1478	214	89	)	)	PUNCT
ejpam-1478	214	90	.	.	PUNCT
ejpam-1478	215	1	proof	proof	NOUN
ejpam-1478	215	2	.	.	PUNCT
ejpam-1478	216	1	according	accord	VERB
ejpam-1478	216	2	to	to	ADP
ejpam-1478	216	3	the	the	DET
ejpam-1478	216	4	notations	notation	NOUN
ejpam-1478	216	5	in	in	ADP
ejpam-1478	216	6	theorem	theorem	NOUN
ejpam-1478	216	7	3	3	NUM
ejpam-1478	216	8	we	we	PRON
ejpam-1478	216	9	have	have	VERB
ejpam-1478	216	10	φ(t0	φ(t0	NOUN
ejpam-1478	216	11	,	,	PUNCT
ejpam-1478	216	12	t	t	PROPN
ejpam-1478	216	13	)	)	PUNCT
ejpam-1478	216	14	=	=	SYM
ejpam-1478	217	1	∫	∫	PROPN
ejpam-1478	217	2	t	t	PROPN
ejpam-1478	217	3	t0	t0	PROPN
ejpam-1478	217	4	h	h	PROPN
ejpam-1478	217	5	e−s	e−s	PROPN
ejpam-1478	217	6	+	+	CCONJ
ejpam-1478	217	7	e−s	e−s	X
ejpam-1478	217	8	i	i	PRON
ejpam-1478	217	9	ds	ds	VERB
ejpam-1478	217	10	=	=	SYM
ejpam-1478	217	11	2(e−t0	2(e−t0	NUM
ejpam-1478	217	12	−	−	NOUN
ejpam-1478	217	13	e−t	e−t	NOUN
ejpam-1478	217	14	)	)	PUNCT
ejpam-1478	217	15	and	and	CCONJ
ejpam-1478	217	16	ψ(t0	ψ(t0	PROPN
ejpam-1478	217	17	,	,	PUNCT
ejpam-1478	217	18	t	t	PROPN
ejpam-1478	217	19	)	)	PUNCT
ejpam-1478	217	20	=	=	SYM
ejpam-1478	217	21	∏	∏	PROPN
ejpam-1478	217	22	t0	t0	PROPN
ejpam-1478	217	23	<	<	X
ejpam-1478	217	24	ti	ti	X
ejpam-1478	217	25	<	<	X
ejpam-1478	217	26	t	t	X
ejpam-1478	217	27	�	�	PROPN
ejpam-1478	217	28	1	1	NUM
ejpam-1478	217	29	+	+	NUM
ejpam-1478	217	30	1	1	NUM
ejpam-1478	217	31	4i2	4i2	NUM
ejpam-1478	217	32	−	−	NUM
ejpam-1478	217	33	1	1	NUM
ejpam-1478	217	34	�	�	PROPN
ejpam-1478	217	35	≤	≤	NUM
ejpam-1478	217	36	∞	∞	PROPN
ejpam-1478	217	37	∏	∏	PROPN
ejpam-1478	217	38	i=1	i=1	PROPN
ejpam-1478	217	39	�	�	PROPN
ejpam-1478	217	40	1	1	NUM
ejpam-1478	217	41	+	+	NUM
ejpam-1478	217	42	1	1	NUM
ejpam-1478	217	43	4i2	4i2	NUM
ejpam-1478	217	44	−	−	NUM
ejpam-1478	217	45	1	1	NUM
ejpam-1478	217	46	�	�	PROPN
ejpam-1478	217	47	.	.	PUNCT
ejpam-1478	218	1	using	use	VERB
ejpam-1478	218	2	the	the	DET
ejpam-1478	218	3	convergence	convergence	NOUN
ejpam-1478	218	4	of	of	ADP
ejpam-1478	218	5	wallis	wallis	PROPN
ejpam-1478	218	6	product	product	PROPN
ejpam-1478	218	7	∞	∞	PROPN
ejpam-1478	218	8	∏	∏	PROPN
ejpam-1478	218	9	n=1	n=1	PROPN
ejpam-1478	218	10	�	�	PROPN
ejpam-1478	218	11	1	1	NUM
ejpam-1478	218	12	+	+	NUM
ejpam-1478	218	13	1	1	NUM
ejpam-1478	218	14	4n2−1	4n2−1	PROPN
ejpam-1478	218	15	�	�	PROPN
ejpam-1478	219	1	=	=	PUNCT
ejpam-1478	219	2	π	π	PROPN
ejpam-1478	219	3	2	2	NUM
ejpam-1478	219	4	,	,	PUNCT
ejpam-1478	219	5	it	it	PRON
ejpam-1478	219	6	follows	follow	VERB
ejpam-1478	219	7	ψ(t0	ψ(t0	PROPN
ejpam-1478	219	8	,	,	PUNCT
ejpam-1478	219	9	t	t	PROPN
ejpam-1478	219	10	)	)	PUNCT
ejpam-1478	219	11	≤	≤	NUM
ejpam-1478	220	1	π	π	PROPN
ejpam-1478	220	2	2	2	NUM
ejpam-1478	220	3	for	for	ADP
ejpam-1478	220	4	any	any	DET
ejpam-1478	220	5	t	t	PROPN
ejpam-1478	220	6	,	,	PUNCT
ejpam-1478	220	7	t0	t0	PROPN
ejpam-1478	220	8	∈	∈	PROPN
ejpam-1478	220	9	r+	r+	X
ejpam-1478	220	10	.	.	PUNCT
ejpam-1478	221	1	also	also	ADV
ejpam-1478	221	2	lim	lim	PROPN
ejpam-1478	221	3	t→∞φ(t0	t→∞φ(t0	PROPN
ejpam-1478	221	4	,	,	PUNCT
ejpam-1478	221	5	t	t	PROPN
ejpam-1478	221	6	)	)	PUNCT
ejpam-1478	221	7	=	=	PUNCT
ejpam-1478	222	1	2e−t0	2e−t0	ADJ
ejpam-1478	222	2	≤	≤	NUM
ejpam-1478	222	3	2	2	NUM
ejpam-1478	222	4	.	.	PUNCT
ejpam-1478	223	1	therefore	therefore	ADV
ejpam-1478	223	2	the	the	DET
ejpam-1478	223	3	conditions	condition	NOUN
ejpam-1478	223	4	of	of	ADP
ejpam-1478	223	5	theorem	theorem	NOUN
ejpam-1478	223	6	3	3	NUM
ejpam-1478	223	7	are	be	AUX
ejpam-1478	223	8	satisfied	satisfied	ADJ
ejpam-1478	223	9	for	for	ADP
ejpam-1478	223	10	µ1	µ1	NOUN
ejpam-1478	223	11	=	=	SYM
ejpam-1478	223	12	π	π	PROPN
ejpam-1478	223	13	2	2	NUM
ejpam-1478	223	14	and	and	CCONJ
ejpam-1478	223	15	µ2	µ2	PROPN
ejpam-1478	223	16	=	=	PROPN
ejpam-1478	223	17	2	2	X
ejpam-1478	223	18	.	.	PUNCT
ejpam-1478	223	19	according	accord	VERB
ejpam-1478	223	20	to	to	ADP
ejpam-1478	223	21	claim	claim	NOUN
ejpam-1478	223	22	(	(	PUNCT
ejpam-1478	223	23	ii	ii	NOUN
ejpam-1478	223	24	)	)	PUNCT
ejpam-1478	223	25	of	of	ADP
ejpam-1478	223	26	theorem	theorem	ADJ
ejpam-1478	223	27	3	3	NUM
ejpam-1478	223	28	all	all	DET
ejpam-1478	223	29	solutions	solution	NOUN
ejpam-1478	223	30	of	of	ADP
ejpam-1478	223	31	the	the	DET
ejpam-1478	223	32	system	system	NOUN
ejpam-1478	223	33	(	(	PUNCT
ejpam-1478	223	34	1	1	NUM
ejpam-1478	223	35	)	)	PUNCT
ejpam-1478	223	36	,	,	PUNCT
ejpam-1478	223	37	(	(	PUNCT
ejpam-1478	223	38	2	2	X
ejpam-1478	223	39	)	)	PUNCT
ejpam-1478	223	40	are	be	AUX
ejpam-1478	223	41	uniformly	uniformly	ADV
ejpam-1478	223	42	bounded	bound	VERB
ejpam-1478	223	43	,	,	PUNCT
ejpam-1478	223	44	i.e.	i.e.	X
ejpam-1478	223	45	for	for	ADP
ejpam-1478	223	46	any	any	DET
ejpam-1478	223	47	number	number	NOUN
ejpam-1478	223	48	α	α	NOUN
ejpam-1478	223	49	>	>	X
ejpam-1478	223	50	0	0	PUNCT
ejpam-1478	224	1	the	the	DET
ejpam-1478	224	2	inequality	inequality	NOUN
ejpam-1478	224	3	|φ|0	|φ|0	VERB
ejpam-1478	224	4	<	<	X
ejpam-1478	224	5	α	α	PROPN
ejpam-1478	224	6	implies	imply	VERB
ejpam-1478	224	7	|x(t	|x(t	PROPN
ejpam-1478	224	8	;	;	PUNCT
ejpam-1478	224	9	t0,φ)|	t0,φ)|	X
ejpam-1478	224	10	<	<	X
ejpam-1478	224	11	e2απ	e2απ	X
ejpam-1478	224	12	2	2	NUM
ejpam-1478	224	13	for	for	ADP
ejpam-1478	224	14	all	all	DET
ejpam-1478	224	15	t0	t0	PROPN
ejpam-1478	224	16	∈	∈	PROPN
ejpam-1478	224	17	r+	r+	NOUN
ejpam-1478	224	18	.	.	PUNCT
ejpam-1478	225	1	if	if	SCONJ
ejpam-1478	225	2	,	,	PUNCT
ejpam-1478	225	3	additionally	additionally	ADV
ejpam-1478	225	4	,	,	PUNCT
ejpam-1478	225	5	the	the	DET
ejpam-1478	225	6	inequality	inequality	NOUN
ejpam-1478	225	7	λπe2	λπe2	NOUN
ejpam-1478	225	8	<	<	X
ejpam-1478	225	9	2λ	2λ	PROPN
ejpam-1478	225	10	holds	hold	VERB
ejpam-1478	225	11	,	,	PUNCT
ejpam-1478	225	12	then	then	ADV
ejpam-1478	225	13	according	accord	VERB
ejpam-1478	225	14	to	to	ADP
ejpam-1478	225	15	claim	claim	NOUN
ejpam-1478	225	16	(	(	PUNCT
ejpam-1478	225	17	iv	iv	X
ejpam-1478	225	18	)	)	PUNCT
ejpam-1478	225	19	of	of	ADP
ejpam-1478	225	20	theorem	theorem	NOUN
ejpam-1478	225	21	3	3	NUM
ejpam-1478	225	22	the	the	DET
ejpam-1478	225	23	impulsive	impulsive	ADJ
ejpam-1478	225	24	differential	differential	ADJ
ejpam-1478	225	25	equation	equation	NOUN
ejpam-1478	225	26	with	with	ADP
ejpam-1478	225	27	“	"	PUNCT
ejpam-1478	225	28	supremum	supremum	ADJ
ejpam-1478	225	29	”	"	PUNCT
ejpam-1478	225	30	(	(	PUNCT
ejpam-1478	225	31	1	1	NUM
ejpam-1478	225	32	)	)	PUNCT
ejpam-1478	225	33	,	,	PUNCT
ejpam-1478	225	34	(	(	PUNCT
ejpam-1478	225	35	2	2	X
ejpam-1478	225	36	)	)	PUNCT
ejpam-1478	225	37	is	be	AUX
ejpam-1478	225	38	uniformly	uniformly	ADV
ejpam-1478	225	39	practically	practically	ADV
ejpam-1478	225	40	stable	stable	ADJ
ejpam-1478	225	41	with	with	ADP
ejpam-1478	225	42	respect	respect	NOUN
ejpam-1478	225	43	to	to	ADP
ejpam-1478	225	44	(	(	PUNCT
ejpam-1478	225	45	λ	λ	X
ejpam-1478	225	46	,	,	PUNCT
ejpam-1478	225	47	λ	λ	NOUN
ejpam-1478	225	48	)	)	PUNCT
ejpam-1478	225	49	.	.	PUNCT
ejpam-1478	226	1	example	example	NOUN
ejpam-1478	227	1	1	1	X
ejpam-1478	227	2	.	.	X
ejpam-1478	227	3	consider	consider	VERB
ejpam-1478	227	4	the	the	DET
ejpam-1478	227	5	initial	initial	ADJ
ejpam-1478	227	6	value	value	NOUN
ejpam-1478	227	7	problem	problem	NOUN
ejpam-1478	227	8	for	for	ADP
ejpam-1478	227	9	the	the	DET
ejpam-1478	227	10	scalar	scalar	ADJ
ejpam-1478	227	11	impulsive	impulsive	ADJ
ejpam-1478	227	12	differential	differential	ADJ
ejpam-1478	227	13	equation	equation	NOUN
ejpam-1478	227	14			NOUN
ejpam-1478	227	15			ADP
ejpam-1478	227	16			NOUN
ejpam-1478	227	17	x	x	PUNCT
ejpam-1478	227	18	′	′	NUM
ejpam-1478	227	19	=	=	SYM
ejpam-1478	227	20	e−t	e−t	NOUN
ejpam-1478	227	21	x	x	PUNCT
ejpam-1478	227	22	for	for	ADP
ejpam-1478	227	23	t	t	PROPN
ejpam-1478	227	24	6=	6=	PROPN
ejpam-1478	227	25	n	n	CCONJ
ejpam-1478	227	26	,	,	PUNCT
ejpam-1478	227	27	x(n+	x(n+	PUNCT
ejpam-1478	228	1	0)−	0)−	PROPN
ejpam-1478	228	2	x(n−	x(n−	PROPN
ejpam-1478	228	3	0	0	NUM
ejpam-1478	228	4	)	)	PUNCT
ejpam-1478	228	5	=	=	NOUN
ejpam-1478	229	1	1	1	NUM
ejpam-1478	229	2	4n2−1	4n2−1	NUM
ejpam-1478	229	3	x(n−	x(n−	PROPN
ejpam-1478	229	4	0	0	NUM
ejpam-1478	229	5	)	)	PUNCT
ejpam-1478	229	6	for	for	ADP
ejpam-1478	229	7	n	n	PRON
ejpam-1478	229	8	∈	∈	PROPN
ejpam-1478	229	9	z(t0,∞	z(t0,∞	NUM
ejpam-1478	229	10	)	)	PUNCT
ejpam-1478	229	11	,	,	PUNCT
ejpam-1478	229	12	x(t0	x(t0	PROPN
ejpam-1478	229	13	)	)	PUNCT
ejpam-1478	230	1	=	=	PUNCT
ejpam-1478	230	2	x0	x0	PROPN
ejpam-1478	230	3	(	(	PUNCT
ejpam-1478	230	4	41	41	NUM
ejpam-1478	230	5	)	)	PUNCT
ejpam-1478	230	6	where	where	SCONJ
ejpam-1478	230	7	x	x	SYM
ejpam-1478	230	8	∈	∈	PROPN
ejpam-1478	230	9	r	r	NOUN
ejpam-1478	230	10	and	and	CCONJ
ejpam-1478	230	11	t0	t0	PROPN
ejpam-1478	230	12	∈	∈	PROPN
ejpam-1478	230	13	r+	r+	X
ejpam-1478	230	14	.	.	PUNCT
ejpam-1478	231	1	the	the	DET
ejpam-1478	231	2	solution	solution	NOUN
ejpam-1478	231	3	of	of	ADP
ejpam-1478	231	4	the	the	DET
ejpam-1478	231	5	initial	initial	ADJ
ejpam-1478	231	6	value	value	NOUN
ejpam-1478	231	7	problem	problem	NOUN
ejpam-1478	231	8	(	(	PUNCT
ejpam-1478	231	9	41	41	NUM
ejpam-1478	231	10	)	)	PUNCT
ejpam-1478	231	11	is	be	AUX
ejpam-1478	231	12	x(t	x(t	PROPN
ejpam-1478	231	13	;	;	PUNCT
ejpam-1478	231	14	t0	t0	PROPN
ejpam-1478	231	15	,	,	PUNCT
ejpam-1478	231	16	x0	x0	PROPN
ejpam-1478	231	17	)	)	PUNCT
ejpam-1478	232	1	=	=	SYM
ejpam-1478	232	2	�	�	PROPN
ejpam-1478	232	3	k	k	PROPN
ejpam-1478	232	4	∏	∏	PROPN
ejpam-1478	232	5	i=	i=	PROPN
ejpam-1478	232	6	j	j	PROPN
ejpam-1478	232	7	4i2	4i2	NUM
ejpam-1478	232	8	4i2	4i2	NUM
ejpam-1478	232	9	−	−	PROPN
ejpam-1478	232	10	1	1	NUM
ejpam-1478	232	11	�	�	PROPN
ejpam-1478	232	12	x0ee−t0−e−t	x0ee−t0−e−t	PROPN
ejpam-1478	232	13	for	for	ADP
ejpam-1478	232	14	t	t	PROPN
ejpam-1478	232	15	∈	∈	PROPN
ejpam-1478	232	16	(	(	PUNCT
ejpam-1478	232	17	k	k	NOUN
ejpam-1478	232	18	,	,	PUNCT
ejpam-1478	232	19	k+	k+	NOUN
ejpam-1478	232	20	1	1	NUM
ejpam-1478	232	21	]	]	PUNCT
ejpam-1478	232	22	,	,	PUNCT
ejpam-1478	232	23	where	where	SCONJ
ejpam-1478	232	24	j	j	PROPN
ejpam-1478	232	25	is	be	AUX
ejpam-1478	232	26	a	a	DET
ejpam-1478	232	27	natural	natural	ADJ
ejpam-1478	232	28	number	number	NOUN
ejpam-1478	232	29	such	such	ADJ
ejpam-1478	232	30	that	that	SCONJ
ejpam-1478	232	31	j−	j−	PROPN
ejpam-1478	232	32	1≤	1≤	NUM
ejpam-1478	233	1	t0	t0	X
ejpam-1478	233	2	<	<	X
ejpam-1478	233	3	j	j	PROPN
ejpam-1478	233	4	and	and	CCONJ
ejpam-1478	233	5	k	k	PROPN
ejpam-1478	233	6	=	=	SYM
ejpam-1478	233	7	j	j	PROPN
ejpam-1478	233	8	,	,	PUNCT
ejpam-1478	233	9	j	j	PROPN
ejpam-1478	233	10	=	=	SYM
ejpam-1478	233	11	1	1	NUM
ejpam-1478	233	12	,	,	PUNCT
ejpam-1478	233	13	j+	j+	NUM
ejpam-1478	233	14	2	2	NUM
ejpam-1478	233	15	,	,	PUNCT
ejpam-1478	233	16	.	.	PUNCT
ejpam-1478	233	17	.	.	PUNCT
ejpam-1478	233	18	.	.	PUNCT
ejpam-1478	234	1	.	.	PUNCT
ejpam-1478	235	1	it	it	PRON
ejpam-1478	235	2	is	be	AUX
ejpam-1478	235	3	easy	easy	ADJ
ejpam-1478	235	4	to	to	PART
ejpam-1478	235	5	see	see	VERB
ejpam-1478	235	6	the	the	DET
ejpam-1478	235	7	solution	solution	NOUN
ejpam-1478	235	8	is	be	AUX
ejpam-1478	235	9	uniformly	uniformly	ADV
ejpam-1478	235	10	bounded	bound	VERB
ejpam-1478	235	11	and	and	CCONJ
ejpam-1478	235	12	stable	stable	ADJ
ejpam-1478	235	13	.	.	PUNCT
ejpam-1478	236	1	s.	s.	PROPN
ejpam-1478	236	2	hristova	hristova	PROPN
ejpam-1478	236	3	,	,	PUNCT
ejpam-1478	236	4	k.	k.	PROPN
ejpam-1478	236	5	stefanova	stefanova	PROPN
ejpam-1478	236	6	/	/	SYM
ejpam-1478	236	7	eur	eur	PROPN
ejpam-1478	236	8	.	.	PUNCT
ejpam-1478	237	1	j.	j.	PROPN
ejpam-1478	237	2	pure	pure	PROPN
ejpam-1478	237	3	appl	appl	PROPN
ejpam-1478	237	4	.	.	PROPN
ejpam-1478	237	5	math	math	PROPN
ejpam-1478	237	6	,	,	PUNCT
ejpam-1478	237	7	5	5	NUM
ejpam-1478	237	8	(	(	PUNCT
ejpam-1478	237	9	2012	2012	NUM
ejpam-1478	237	10	)	)	PUNCT
ejpam-1478	237	11	,	,	PUNCT
ejpam-1478	237	12	30	30	NUM
ejpam-1478	237	13	-	-	SYM
ejpam-1478	237	14	44	44	NUM
ejpam-1478	237	15	41	41	NUM
ejpam-1478	237	16	now	now	ADV
ejpam-1478	237	17	we	we	PRON
ejpam-1478	237	18	will	will	AUX
ejpam-1478	237	19	perturb	perturb	VERB
ejpam-1478	237	20	the	the	DET
ejpam-1478	237	21	equation	equation	NOUN
ejpam-1478	237	22	(	(	PUNCT
ejpam-1478	237	23	41	41	NUM
ejpam-1478	237	24	)	)	PUNCT
ejpam-1478	237	25	by	by	ADP
ejpam-1478	237	26	the	the	DET
ejpam-1478	237	27	maximum	maximum	ADJ
ejpam-1478	237	28	function	function	NOUN
ejpam-1478	237	29	of	of	ADP
ejpam-1478	237	30	the	the	DET
ejpam-1478	237	31	unknown	unknown	ADJ
ejpam-1478	237	32	function	function	NOUN
ejpam-1478	237	33	,	,	PUNCT
ejpam-1478	237	34	i.e.	i.e.	X
ejpam-1478	237	35	consider	consider	VERB
ejpam-1478	237	36	the	the	DET
ejpam-1478	237	37	following	follow	VERB
ejpam-1478	237	38	impulsive	impulsive	ADJ
ejpam-1478	237	39	differential	differential	ADJ
ejpam-1478	237	40	equation	equation	NOUN
ejpam-1478	237	41	with	with	ADP
ejpam-1478	237	42	“	"	PUNCT
ejpam-1478	237	43	supremum	supremum	ADJ
ejpam-1478	237	44	”	"	PUNCT
ejpam-1478	237	45			NOUN
ejpam-1478	237	46			ADV
ejpam-1478	237	47			PRON
ejpam-1478	237	48			ADJ
ejpam-1478	237	49			NOUN
ejpam-1478	237	50	x	x	NOUN
ejpam-1478	237	51	′	′	NUM
ejpam-1478	237	52	=	=	SYM
ejpam-1478	237	53	e−t	e−t	NOUN
ejpam-1478	237	54	�	�	NOUN
ejpam-1478	237	55	x	x	SYM
ejpam-1478	237	56	+	+	NUM
ejpam-1478	237	57	sups∈[t−h	sups∈[t−h	NOUN
ejpam-1478	237	58	,	,	PUNCT
ejpam-1478	237	59	t	t	X
ejpam-1478	237	60	]	]	PUNCT
ejpam-1478	237	61	x(s	x(s	PROPN
ejpam-1478	237	62	)	)	PUNCT
ejpam-1478	237	63	�	�	PROPN
ejpam-1478	237	64	for	for	ADP
ejpam-1478	237	65	t	t	PROPN
ejpam-1478	237	66	≥	≥	PROPN
ejpam-1478	237	67	t0	t0	PROPN
ejpam-1478	237	68	,	,	PUNCT
ejpam-1478	237	69	t	t	PROPN
ejpam-1478	237	70	6=	6=	PROPN
ejpam-1478	237	71	n	n	CCONJ
ejpam-1478	237	72	,	,	PUNCT
ejpam-1478	237	73	x(n+	x(n+	PUNCT
ejpam-1478	238	1	0)−	0)−	PROPN
ejpam-1478	238	2	x(n−	x(n−	PROPN
ejpam-1478	238	3	0	0	NUM
ejpam-1478	238	4	)	)	PUNCT
ejpam-1478	238	5	=	=	NOUN
ejpam-1478	239	1	1	1	NUM
ejpam-1478	239	2	4n2−1	4n2−1	NUM
ejpam-1478	239	3	x(n−	x(n−	PROPN
ejpam-1478	239	4	0	0	NUM
ejpam-1478	239	5	)	)	PUNCT
ejpam-1478	239	6	for	for	ADP
ejpam-1478	239	7	n	n	PRON
ejpam-1478	239	8	∈	∈	PROPN
ejpam-1478	239	9	z(t0,∞	z(t0,∞	NUM
ejpam-1478	239	10	)	)	PUNCT
ejpam-1478	239	11	,	,	PUNCT
ejpam-1478	239	12	x(t	x(t	PROPN
ejpam-1478	239	13	)	)	PUNCT
ejpam-1478	239	14	=	=	PUNCT
ejpam-1478	239	15	ϕ(t	ϕ(t	PROPN
ejpam-1478	239	16	)	)	PUNCT
ejpam-1478	239	17	for	for	ADP
ejpam-1478	239	18	t	t	PROPN
ejpam-1478	239	19	∈	∈	PROPN
ejpam-1478	240	1	[	[	X
ejpam-1478	240	2	t0	t0	X
ejpam-1478	240	3	−	−	PROPN
ejpam-1478	240	4	h	h	PROPN
ejpam-1478	240	5	,	,	PUNCT
ejpam-1478	240	6	t0	t0	PROPN
ejpam-1478	240	7	]	]	PUNCT
ejpam-1478	240	8	,	,	PUNCT
ejpam-1478	240	9	(	(	PUNCT
ejpam-1478	240	10	42	42	NUM
ejpam-1478	240	11	)	)	PUNCT
ejpam-1478	240	12	where	where	SCONJ
ejpam-1478	240	13	x	x	SYM
ejpam-1478	240	14	∈	∈	PROPN
ejpam-1478	240	15	r	r	NOUN
ejpam-1478	240	16	and	and	CCONJ
ejpam-1478	240	17	h	h	NOUN
ejpam-1478	240	18	>	>	X
ejpam-1478	240	19	0	0	NUM
ejpam-1478	240	20	is	be	AUX
ejpam-1478	240	21	a	a	DET
ejpam-1478	240	22	given	give	VERB
ejpam-1478	240	23	constant	constant	NOUN
ejpam-1478	240	24	.	.	PUNCT
ejpam-1478	241	1	the	the	DET
ejpam-1478	241	2	initial	initial	ADJ
ejpam-1478	241	3	value	value	NOUN
ejpam-1478	241	4	problem	problem	NOUN
ejpam-1478	241	5	(	(	PUNCT
ejpam-1478	241	6	42	42	NUM
ejpam-1478	241	7	)	)	PUNCT
ejpam-1478	241	8	is	be	AUX
ejpam-1478	241	9	not	not	PART
ejpam-1478	241	10	possible	possible	ADJ
ejpam-1478	241	11	to	to	PART
ejpam-1478	241	12	be	be	AUX
ejpam-1478	241	13	solved	solve	VERB
ejpam-1478	241	14	in	in	ADP
ejpam-1478	241	15	analytical	analytical	ADJ
ejpam-1478	241	16	form	form	NOUN
ejpam-1478	241	17	,	,	PUNCT
ejpam-1478	241	18	but	but	CCONJ
ejpam-1478	241	19	according	accord	VERB
ejpam-1478	241	20	to	to	ADP
ejpam-1478	241	21	theorem	theorem	NOUN
ejpam-1478	241	22	5	5	NUM
ejpam-1478	241	23	its	its	PRON
ejpam-1478	241	24	solutions	solution	NOUN
ejpam-1478	241	25	are	be	AUX
ejpam-1478	241	26	uniformly	uniformly	ADV
ejpam-1478	241	27	bounded	bound	VERB
ejpam-1478	241	28	.	.	PUNCT
ejpam-1478	242	1	i.e.	i.e.	X
ejpam-1478	242	2	the	the	DET
ejpam-1478	242	3	perturbation	perturbation	NOUN
ejpam-1478	242	4	as	as	ADV
ejpam-1478	242	5	well	well	ADV
ejpam-1478	242	6	as	as	ADP
ejpam-1478	242	7	impulsive	impulsive	ADJ
ejpam-1478	242	8	conditions	condition	NOUN
ejpam-1478	242	9	could	could	AUX
ejpam-1478	242	10	save	save	VERB
ejpam-1478	242	11	the	the	DET
ejpam-1478	242	12	property	property	NOUN
ejpam-1478	242	13	boundedness	boundedness	NOUN
ejpam-1478	242	14	.	.	PUNCT
ejpam-1478	243	1	also	also	ADV
ejpam-1478	243	2	,	,	PUNCT
ejpam-1478	243	3	if	if	SCONJ
ejpam-1478	243	4	the	the	DET
ejpam-1478	243	5	positive	positive	ADJ
ejpam-1478	243	6	constants	constant	NOUN
ejpam-1478	243	7	λ	λ	VERB
ejpam-1478	243	8	and	and	CCONJ
ejpam-1478	243	9	λ	λ	PROPN
ejpam-1478	243	10	satisfy	satisfy	VERB
ejpam-1478	243	11	λπe2	λπe2	ADJ
ejpam-1478	243	12	<	<	X
ejpam-1478	243	13	2λ	2λ	PROPN
ejpam-1478	243	14	,	,	PUNCT
ejpam-1478	243	15	then	then	ADV
ejpam-1478	243	16	the	the	DET
ejpam-1478	243	17	solution	solution	NOUN
ejpam-1478	243	18	of	of	ADP
ejpam-1478	243	19	the	the	DET
ejpam-1478	243	20	impulsive	impulsive	ADJ
ejpam-1478	243	21	differential	differential	ADJ
ejpam-1478	243	22	equation	equation	NOUN
ejpam-1478	243	23	with	with	ADP
ejpam-1478	243	24	“	"	PUNCT
ejpam-1478	243	25	supremum	supremum	ADJ
ejpam-1478	243	26	”	"	PUNCT
ejpam-1478	243	27	(	(	PUNCT
ejpam-1478	243	28	42	42	NUM
ejpam-1478	243	29	)	)	PUNCT
ejpam-1478	243	30	is	be	AUX
ejpam-1478	243	31	uniformly	uniformly	ADV
ejpam-1478	243	32	practically	practically	ADV
ejpam-1478	243	33	stable	stable	ADJ
ejpam-1478	243	34	with	with	ADP
ejpam-1478	243	35	respect	respect	NOUN
ejpam-1478	243	36	to	to	ADP
ejpam-1478	243	37	(	(	PUNCT
ejpam-1478	243	38	λ	λ	X
ejpam-1478	243	39	,	,	PUNCT
ejpam-1478	243	40	λ	λ	NOUN
ejpam-1478	243	41	)	)	PUNCT
ejpam-1478	243	42	.	.	PUNCT
ejpam-1478	244	1	theorem	theorem	NOUN
ejpam-1478	244	2	6	6	NUM
ejpam-1478	244	3	.	.	PUNCT
ejpam-1478	245	1	let	let	VERB
ejpam-1478	245	2	the	the	DET
ejpam-1478	245	3	following	follow	VERB
ejpam-1478	245	4	conditions	condition	NOUN
ejpam-1478	245	5	be	be	AUX
ejpam-1478	245	6	fulfilled	fulfil	VERB
ejpam-1478	245	7	:	:	PUNCT
ejpam-1478	246	1	1	1	X
ejpam-1478	246	2	.	.	PUNCT
ejpam-1478	247	1	the	the	DET
ejpam-1478	247	2	conditions	condition	NOUN
ejpam-1478	247	3	1	1	NUM
ejpam-1478	247	4	and	and	CCONJ
ejpam-1478	247	5	2	2	NUM
ejpam-1478	247	6	of	of	ADP
ejpam-1478	247	7	theorem	theorem	ADJ
ejpam-1478	247	8	5	5	NUM
ejpam-1478	247	9	are	be	AUX
ejpam-1478	247	10	satisfied	satisfied	ADJ
ejpam-1478	247	11	.	.	PUNCT
ejpam-1478	248	1	2	2	X
ejpam-1478	248	2	.	.	X
ejpam-1478	248	3	the	the	DET
ejpam-1478	248	4	functions	function	NOUN
ejpam-1478	248	5	ii	ii	NOUN
ejpam-1478	248	6	:	:	PUNCT
ejpam-1478	248	7	r→	r→	PROPN
ejpam-1478	248	8	r	r	PROPN
ejpam-1478	248	9	,	,	PUNCT
ejpam-1478	248	10	ii(0	ii(0	NOUN
ejpam-1478	248	11	)	)	PUNCT
ejpam-1478	248	12	=	=	SYM
ejpam-1478	248	13	0	0	NUM
ejpam-1478	248	14	and	and	CCONJ
ejpam-1478	248	15	|ii(x)|	|ii(x)|	ADJ
ejpam-1478	248	16	≤	≤	NUM
ejpam-1478	248	17	1	1	NUM
ejpam-1478	248	18	2i	2i	NUM
ejpam-1478	248	19	|x	|x	NOUN
ejpam-1478	248	20	|	|	ADV
ejpam-1478	248	21	for	for	ADP
ejpam-1478	248	22	x	x	PROPN
ejpam-1478	248	23	∈	∈	PROPN
ejpam-1478	248	24	r	r	NOUN
ejpam-1478	248	25	,	,	PUNCT
ejpam-1478	248	26	i	i	PRON
ejpam-1478	248	27	∈	∈	PROPN
ejpam-1478	248	28	z(t0	z(t0	NOUN
ejpam-1478	248	29	,	,	PUNCT
ejpam-1478	248	30	t	t	PROPN
ejpam-1478	248	31	)	)	PUNCT
ejpam-1478	248	32	.	.	PUNCT
ejpam-1478	249	1	then	then	ADV
ejpam-1478	249	2	:	:	PUNCT
ejpam-1478	249	3	(	(	PUNCT
ejpam-1478	249	4	i	i	NOUN
ejpam-1478	249	5	)	)	PUNCT
ejpam-1478	249	6	all	all	DET
ejpam-1478	249	7	solutions	solution	NOUN
ejpam-1478	249	8	of	of	ADP
ejpam-1478	249	9	the	the	DET
ejpam-1478	249	10	system	system	NOUN
ejpam-1478	249	11	of	of	ADP
ejpam-1478	249	12	impulsive	impulsive	ADJ
ejpam-1478	249	13	differential	differential	ADJ
ejpam-1478	249	14	equation	equation	NOUN
ejpam-1478	249	15	(	(	PUNCT
ejpam-1478	249	16	1	1	NUM
ejpam-1478	249	17	)	)	PUNCT
ejpam-1478	249	18	,	,	PUNCT
ejpam-1478	249	19	(	(	PUNCT
ejpam-1478	249	20	2	2	X
ejpam-1478	249	21	)	)	PUNCT
ejpam-1478	249	22	are	be	AUX
ejpam-1478	249	23	uniformly	uniformly	ADV
ejpam-1478	249	24	bounded	bound	VERB
ejpam-1478	249	25	;	;	PUNCT
ejpam-1478	249	26	(	(	PUNCT
ejpam-1478	249	27	ii	ii	NOUN
ejpam-1478	249	28	)	)	PUNCT
ejpam-1478	249	29	if	if	SCONJ
ejpam-1478	249	30	,	,	PUNCT
ejpam-1478	249	31	additionally	additionally	ADV
ejpam-1478	249	32	,	,	PUNCT
ejpam-1478	249	33	the	the	DET
ejpam-1478	249	34	given	give	VERB
ejpam-1478	249	35	positive	positive	ADJ
ejpam-1478	249	36	constants	constant	NOUN
ejpam-1478	249	37	λ	λ	PROPN
ejpam-1478	249	38	and	and	CCONJ
ejpam-1478	249	39	λ	λ	NOUN
ejpam-1478	249	40	are	be	AUX
ejpam-1478	249	41	such	such	ADJ
ejpam-1478	249	42	that	that	SCONJ
ejpam-1478	249	43	λe3	λe3	ADV
ejpam-1478	249	44	<	<	X
ejpam-1478	249	45	λ	λ	PROPN
ejpam-1478	249	46	,	,	PUNCT
ejpam-1478	249	47	then	then	ADV
ejpam-1478	249	48	the	the	DET
ejpam-1478	249	49	impulsive	impulsive	ADJ
ejpam-1478	249	50	differential	differential	ADJ
ejpam-1478	249	51	equation	equation	NOUN
ejpam-1478	249	52	with	with	ADP
ejpam-1478	249	53	“	"	PUNCT
ejpam-1478	249	54	supremum	supremum	ADJ
ejpam-1478	249	55	”	"	PUNCT
ejpam-1478	249	56	(	(	PUNCT
ejpam-1478	249	57	1	1	NUM
ejpam-1478	249	58	)	)	PUNCT
ejpam-1478	249	59	,	,	PUNCT
ejpam-1478	249	60	(	(	PUNCT
ejpam-1478	249	61	2	2	X
ejpam-1478	249	62	)	)	PUNCT
ejpam-1478	249	63	is	be	AUX
ejpam-1478	249	64	uniformly	uniformly	ADV
ejpam-1478	249	65	practically	practically	ADV
ejpam-1478	249	66	stable	stable	ADJ
ejpam-1478	249	67	with	with	ADP
ejpam-1478	249	68	respect	respect	NOUN
ejpam-1478	249	69	to	to	ADP
ejpam-1478	249	70	(	(	PUNCT
ejpam-1478	249	71	λ	λ	X
ejpam-1478	249	72	,	,	PUNCT
ejpam-1478	249	73	λ	λ	NOUN
ejpam-1478	249	74	)	)	PUNCT
ejpam-1478	249	75	.	.	PUNCT
ejpam-1478	250	1	proof	proof	NOUN
ejpam-1478	250	2	.	.	PUNCT
ejpam-1478	251	1	the	the	DET
ejpam-1478	251	2	proof	proof	NOUN
ejpam-1478	251	3	of	of	ADP
ejpam-1478	251	4	the	the	DET
ejpam-1478	251	5	claim	claim	NOUN
ejpam-1478	251	6	follows	follow	VERB
ejpam-1478	251	7	by	by	ADP
ejpam-1478	251	8	the	the	DET
ejpam-1478	251	9	fact	fact	NOUN
ejpam-1478	251	10	that	that	SCONJ
ejpam-1478	251	11	∞	∞	PROPN
ejpam-1478	251	12	∏	∏	PROPN
ejpam-1478	251	13	i=1	i=1	PROPN
ejpam-1478	251	14	�	�	PROPN
ejpam-1478	251	15	1	1	NUM
ejpam-1478	251	16	+	+	NUM
ejpam-1478	251	17	1	1	NUM
ejpam-1478	251	18	2i	2i	NUM
ejpam-1478	251	19	�	�	PROPN
ejpam-1478	251	20	≤	≤	X
ejpam-1478	251	21	e	e	NOUN
ejpam-1478	251	22	∑∞	∑∞	NOUN
ejpam-1478	251	23	i=1	i=1	X
ejpam-1478	251	24	1	1	NUM
ejpam-1478	251	25	2i	2i	NUM
ejpam-1478	251	26	=	=	SYM
ejpam-1478	251	27	e	e	NOUN
ejpam-1478	251	28	and	and	CCONJ
ejpam-1478	251	29	theorem	theorem	VERB
ejpam-1478	251	30	3	3	NUM
ejpam-1478	251	31	.	.	PUNCT
ejpam-1478	251	32	theorem	theorem	NOUN
ejpam-1478	251	33	7	7	NUM
ejpam-1478	251	34	.	.	PUNCT
ejpam-1478	252	1	let	let	VERB
ejpam-1478	252	2	the	the	DET
ejpam-1478	252	3	following	follow	VERB
ejpam-1478	252	4	conditions	condition	NOUN
ejpam-1478	252	5	be	be	AUX
ejpam-1478	252	6	fulfilled	fulfil	VERB
ejpam-1478	252	7	:	:	PUNCT
ejpam-1478	253	1	1	1	X
ejpam-1478	253	2	.	.	PUNCT
ejpam-1478	254	1	the	the	DET
ejpam-1478	254	2	conditions	condition	NOUN
ejpam-1478	254	3	h1	h1	VERB
ejpam-1478	254	4	and	and	CCONJ
ejpam-1478	254	5	h4	h4	NOUN
ejpam-1478	254	6	are	be	AUX
ejpam-1478	254	7	satisfied	satisfied	ADJ
ejpam-1478	254	8	.	.	PUNCT
ejpam-1478	255	1	2	2	X
ejpam-1478	255	2	.	.	X
ejpam-1478	255	3	the	the	DET
ejpam-1478	255	4	function	function	NOUN
ejpam-1478	255	5	f	f	PROPN
ejpam-1478	255	6	∈	∈	PROPN
ejpam-1478	255	7	c(r+×r×r	c(r+×r×r	PROPN
ejpam-1478	255	8	,	,	PUNCT
ejpam-1478	255	9	r	r	NOUN
ejpam-1478	255	10	)	)	PUNCT
ejpam-1478	255	11	,	,	PUNCT
ejpam-1478	255	12	f	f	PROPN
ejpam-1478	255	13	(	(	PUNCT
ejpam-1478	255	14	t	t	PROPN
ejpam-1478	255	15	,	,	PUNCT
ejpam-1478	255	16	0,0	0,0	NUM
ejpam-1478	255	17	)	)	PUNCT
ejpam-1478	255	18	=	=	SYM
ejpam-1478	255	19	0	0	PUNCT
ejpam-1478	256	1	and	and	CCONJ
ejpam-1478	256	2	|	|	ADV
ejpam-1478	256	3	f	f	X
ejpam-1478	256	4	(	(	PUNCT
ejpam-1478	256	5	t	t	PROPN
ejpam-1478	256	6	,	,	PUNCT
ejpam-1478	256	7	x	x	X
ejpam-1478	256	8	,	,	PUNCT
ejpam-1478	256	9	y)|	y)|	ADJ
ejpam-1478	256	10	≤	≤	NUM
ejpam-1478	256	11	e−t	e−t	NOUN
ejpam-1478	256	12	h	h	NOUN
ejpam-1478	256	13	|x	|x	NOUN
ejpam-1478	256	14	|p+	|p+	PROPN
ejpam-1478	256	15	|y|p	|y|p	VERB
ejpam-1478	256	16	i	i	PRON
ejpam-1478	256	17	for	for	ADP
ejpam-1478	256	18	x	x	X
ejpam-1478	256	19	,	,	PUNCT
ejpam-1478	256	20	y	y	PROPN
ejpam-1478	256	21	∈	∈	PROPN
ejpam-1478	256	22	r	r	NOUN
ejpam-1478	256	23	,	,	PUNCT
ejpam-1478	256	24	where	where	SCONJ
ejpam-1478	256	25	the	the	DET
ejpam-1478	256	26	constant	constant	ADJ
ejpam-1478	256	27	p	p	X
ejpam-1478	256	28	∈	∈	PROPN
ejpam-1478	256	29	(	(	PUNCT
ejpam-1478	256	30	0,1	0,1	NUM
ejpam-1478	256	31	)	)	PUNCT
ejpam-1478	256	32	.	.	PUNCT
ejpam-1478	257	1	references	reference	NOUN
ejpam-1478	257	2	42	42	NUM
ejpam-1478	257	3	3	3	NUM
ejpam-1478	257	4	.	.	PUNCT
ejpam-1478	258	1	the	the	DET
ejpam-1478	258	2	functions	function	NOUN
ejpam-1478	258	3	ii	ii	NOUN
ejpam-1478	258	4	:	:	PUNCT
ejpam-1478	258	5	r→	r→	PROPN
ejpam-1478	258	6	r	r	PROPN
ejpam-1478	258	7	,	,	PUNCT
ejpam-1478	258	8	ii(0	ii(0	NOUN
ejpam-1478	258	9	)	)	PUNCT
ejpam-1478	258	10	=	=	SYM
ejpam-1478	258	11	0	0	NUM
ejpam-1478	258	12	and	and	CCONJ
ejpam-1478	258	13	|ii(x)|	|ii(x)|	NOUN
ejpam-1478	258	14	≤	≤	NUM
ejpam-1478	258	15	1	1	NUM
ejpam-1478	258	16	4i2	4i2	NUM
ejpam-1478	258	17	−	−	NUM
ejpam-1478	258	18	1	1	NUM
ejpam-1478	258	19	|x	|x	NOUN
ejpam-1478	258	20	|p	|p	PROPN
ejpam-1478	258	21	for	for	ADP
ejpam-1478	258	22	x	x	PROPN
ejpam-1478	258	23	∈	∈	PROPN
ejpam-1478	258	24	r	r	NOUN
ejpam-1478	258	25	,	,	PUNCT
ejpam-1478	258	26	i	i	PRON
ejpam-1478	258	27	∈	∈	PROPN
ejpam-1478	258	28	z(t0	z(t0	NOUN
ejpam-1478	258	29	,	,	PUNCT
ejpam-1478	258	30	t	t	PROPN
ejpam-1478	258	31	)	)	PUNCT
ejpam-1478	258	32	.	.	PUNCT
ejpam-1478	259	1	then	then	ADV
ejpam-1478	259	2	if	if	SCONJ
ejpam-1478	259	3	the	the	DET
ejpam-1478	259	4	given	give	VERB
ejpam-1478	259	5	constants	constant	NOUN
ejpam-1478	259	6	λ	λ	PROPN
ejpam-1478	259	7	∈	∈	PROPN
ejpam-1478	259	8	(	(	PUNCT
ejpam-1478	259	9	0,1	0,1	NUM
ejpam-1478	259	10	)	)	PUNCT
ejpam-1478	259	11	and	and	CCONJ
ejpam-1478	259	12	λ	λ	X
ejpam-1478	259	13	>	>	X
ejpam-1478	259	14	0	0	NUM
ejpam-1478	259	15	are	be	AUX
ejpam-1478	259	16	such	such	ADJ
ejpam-1478	259	17	that	that	SCONJ
ejpam-1478	259	18	π	π	PROPN
ejpam-1478	259	19	2	2	NUM
ejpam-1478	259	20	�	�	NOUN
ejpam-1478	259	21	λ1−p	λ1−p	PROPN
ejpam-1478	259	22	+	+	NUM
ejpam-1478	259	23	2(1−	2(1−	NUM
ejpam-1478	259	24	p	p	X
ejpam-1478	259	25	)	)	PUNCT
ejpam-1478	259	26	�	�	PROPN
ejpam-1478	259	27	1	1	NUM
ejpam-1478	259	28	1−p	1−p	NUM
ejpam-1478	259	29	<	<	X
ejpam-1478	259	30	λ	λ	NOUN
ejpam-1478	259	31	,	,	PUNCT
ejpam-1478	259	32	then	then	ADV
ejpam-1478	259	33	the	the	DET
ejpam-1478	259	34	impulsive	impulsive	ADJ
ejpam-1478	259	35	differential	differential	ADJ
ejpam-1478	259	36	equation	equation	NOUN
ejpam-1478	259	37	with	with	ADP
ejpam-1478	259	38	“	"	PUNCT
ejpam-1478	259	39	supremum	supremum	ADJ
ejpam-1478	259	40	”	"	PUNCT
ejpam-1478	259	41	(	(	PUNCT
ejpam-1478	259	42	1	1	NUM
ejpam-1478	259	43	)	)	PUNCT
ejpam-1478	259	44	,	,	PUNCT
ejpam-1478	259	45	(	(	PUNCT
ejpam-1478	259	46	2	2	X
ejpam-1478	259	47	)	)	PUNCT
ejpam-1478	259	48	is	be	AUX
ejpam-1478	259	49	uniformly	uniformly	ADV
ejpam-1478	259	50	practically	practically	ADV
ejpam-1478	259	51	stable	stable	ADJ
ejpam-1478	259	52	with	with	ADP
ejpam-1478	259	53	respect	respect	NOUN
ejpam-1478	259	54	to	to	ADP
ejpam-1478	259	55	(	(	PUNCT
ejpam-1478	259	56	λ	λ	X
ejpam-1478	259	57	,	,	PUNCT
ejpam-1478	259	58	λ	λ	NOUN
ejpam-1478	259	59	)	)	PUNCT
ejpam-1478	259	60	.	.	PUNCT
ejpam-1478	260	1	proof	proof	NOUN
ejpam-1478	260	2	.	.	PUNCT
ejpam-1478	261	1	as	as	ADP
ejpam-1478	261	2	in	in	ADP
ejpam-1478	261	3	the	the	DET
ejpam-1478	261	4	proof	proof	NOUN
ejpam-1478	261	5	of	of	ADP
ejpam-1478	261	6	theorem	theorem	NOUN
ejpam-1478	261	7	5	5	NUM
ejpam-1478	261	8	we	we	PRON
ejpam-1478	261	9	prove	prove	VERB
ejpam-1478	261	10	the	the	DET
ejpam-1478	261	11	conditions	condition	NOUN
ejpam-1478	261	12	of	of	ADP
ejpam-1478	261	13	theorem	theorem	ADJ
ejpam-1478	261	14	4	4	NUM
ejpam-1478	261	15	are	be	AUX
ejpam-1478	261	16	satisfied	satisfied	ADJ
ejpam-1478	261	17	and	and	CCONJ
ejpam-1478	261	18	therefore	therefore	ADV
ejpam-1478	261	19	if	if	SCONJ
ejpam-1478	261	20	λ	λ	PROPN
ejpam-1478	261	21	∈	∈	PROPN
ejpam-1478	261	22	(	(	PUNCT
ejpam-1478	261	23	0,1	0,1	NUM
ejpam-1478	261	24	)	)	PUNCT
ejpam-1478	261	25	and	and	CCONJ
ejpam-1478	261	26	π	π	PROPN
ejpam-1478	261	27	2	2	NUM
ejpam-1478	261	28	�	�	PROPN
ejpam-1478	261	29	λ1−p+2(1−p	λ1−p+2(1−p	PUNCT
ejpam-1478	261	30	)	)	PUNCT
ejpam-1478	261	31	�	�	PROPN
ejpam-1478	261	32	1	1	NUM
ejpam-1478	261	33	1−p	1−p	NUM
ejpam-1478	261	34	<	<	X
ejpam-1478	261	35	λ	λ	X
ejpam-1478	261	36	,	,	PUNCT
ejpam-1478	261	37	then	then	ADV
ejpam-1478	261	38	according	accord	VERB
ejpam-1478	261	39	to	to	ADP
ejpam-1478	261	40	claim	claim	NOUN
ejpam-1478	261	41	(	(	PUNCT
ejpam-1478	261	42	ii	ii	NOUN
ejpam-1478	261	43	)	)	PUNCT
ejpam-1478	261	44	of	of	ADP
ejpam-1478	261	45	theorem	theorem	NOUN
ejpam-1478	261	46	4	4	NUM
ejpam-1478	261	47	the	the	DET
ejpam-1478	261	48	impulsive	impulsive	ADJ
ejpam-1478	261	49	differential	differential	ADJ
ejpam-1478	261	50	equation	equation	NOUN
ejpam-1478	261	51	with	with	ADP
ejpam-1478	261	52	“	"	PUNCT
ejpam-1478	261	53	supremum	supremum	ADJ
ejpam-1478	261	54	”	"	PUNCT
ejpam-1478	261	55	(	(	PUNCT
ejpam-1478	261	56	1	1	NUM
ejpam-1478	261	57	)	)	PUNCT
ejpam-1478	261	58	,	,	PUNCT
ejpam-1478	261	59	(	(	PUNCT
ejpam-1478	261	60	2	2	X
ejpam-1478	261	61	)	)	PUNCT
ejpam-1478	261	62	is	be	AUX
ejpam-1478	261	63	uniformly	uniformly	ADV
ejpam-1478	261	64	practically	practically	ADV
ejpam-1478	261	65	stable	stable	ADJ
ejpam-1478	261	66	with	with	ADP
ejpam-1478	261	67	respect	respect	NOUN
ejpam-1478	261	68	to	to	ADP
ejpam-1478	261	69	(	(	PUNCT
ejpam-1478	261	70	λ	λ	X
ejpam-1478	261	71	,	,	PUNCT
ejpam-1478	261	72	λ	λ	NOUN
ejpam-1478	261	73	)	)	PUNCT
ejpam-1478	261	74	.	.	PUNCT
ejpam-1478	261	75	example	example	NOUN
ejpam-1478	262	1	2	2	NUM
ejpam-1478	262	2	.	.	X
ejpam-1478	262	3	consider	consider	VERB
ejpam-1478	262	4	the	the	DET
ejpam-1478	262	5	initial	initial	ADJ
ejpam-1478	262	6	value	value	NOUN
ejpam-1478	262	7	problem	problem	NOUN
ejpam-1478	262	8	for	for	ADP
ejpam-1478	262	9	the	the	DET
ejpam-1478	262	10	scalar	scalar	ADJ
ejpam-1478	262	11	impulsive	impulsive	ADJ
ejpam-1478	262	12	differential	differential	ADJ
ejpam-1478	262	13	equation	equation	NOUN
ejpam-1478	262	14	with	with	ADP
ejpam-1478	262	15	“	"	PUNCT
ejpam-1478	262	16	supremum	supremum	ADJ
ejpam-1478	262	17	”	"	PUNCT
ejpam-1478	262	18			NOUN
ejpam-1478	262	19			ADV
ejpam-1478	262	20			PRON
ejpam-1478	262	21			ADJ
ejpam-1478	262	22			NOUN
ejpam-1478	262	23	x	x	NOUN
ejpam-1478	262	24	′	′	NUM
ejpam-1478	262	25	=	=	SYM
ejpam-1478	262	26	e−t	e−t	NOUN
ejpam-1478	262	27	�	�	PROPN
ejpam-1478	262	28	p	p	NOUN
ejpam-1478	262	29	x	x	X
ejpam-1478	262	30	+	+	CCONJ
ejpam-1478	262	31	p	p	NOUN
ejpam-1478	262	32	sups∈[t−h	sups∈[t−h	NOUN
ejpam-1478	262	33	,	,	PUNCT
ejpam-1478	262	34	t	t	X
ejpam-1478	262	35	]	]	PUNCT
ejpam-1478	262	36	x(s	x(s	PROPN
ejpam-1478	262	37	)	)	PUNCT
ejpam-1478	262	38	�	�	PROPN
ejpam-1478	262	39	for	for	ADP
ejpam-1478	262	40	t	t	PROPN
ejpam-1478	262	41	≥	≥	PROPN
ejpam-1478	262	42	t0	t0	PROPN
ejpam-1478	262	43	,	,	PUNCT
ejpam-1478	262	44	t	t	PROPN
ejpam-1478	262	45	6=	6=	PROPN
ejpam-1478	262	46	n	n	CCONJ
ejpam-1478	262	47	,	,	PUNCT
ejpam-1478	262	48	x(n+	x(n+	PUNCT
ejpam-1478	263	1	0)−	0)−	PROPN
ejpam-1478	263	2	x(n−	x(n−	PROPN
ejpam-1478	263	3	0	0	NUM
ejpam-1478	263	4	)	)	PUNCT
ejpam-1478	263	5	=	=	NOUN
ejpam-1478	264	1	1	1	NUM
ejpam-1478	264	2	4n2−1	4n2−1	NUM
ejpam-1478	264	3	p	p	PRON
ejpam-1478	264	4	x(n−	x(n−	PROPN
ejpam-1478	264	5	0	0	NUM
ejpam-1478	264	6	)	)	PUNCT
ejpam-1478	264	7	for	for	ADP
ejpam-1478	264	8	n	n	PRON
ejpam-1478	264	9	∈	∈	PROPN
ejpam-1478	264	10	z(t0,∞	z(t0,∞	NUM
ejpam-1478	264	11	)	)	PUNCT
ejpam-1478	264	12	,	,	PUNCT
ejpam-1478	264	13	x(t	x(t	PROPN
ejpam-1478	264	14	)	)	PUNCT
ejpam-1478	264	15	=	=	PUNCT
ejpam-1478	265	1	ϕ(t	ϕ(t	PROPN
ejpam-1478	265	2	)	)	PUNCT
ejpam-1478	266	1	for	for	ADP
ejpam-1478	266	2	t	t	PROPN
ejpam-1478	266	3	∈	∈	PROPN
ejpam-1478	267	1	[	[	X
ejpam-1478	267	2	t0	t0	X
ejpam-1478	267	3	−	−	PROPN
ejpam-1478	267	4	h	h	PROPN
ejpam-1478	267	5	,	,	PUNCT
ejpam-1478	267	6	t0	t0	PROPN
ejpam-1478	267	7	]	]	PUNCT
ejpam-1478	267	8	,	,	PUNCT
ejpam-1478	267	9	(	(	PUNCT
ejpam-1478	267	10	43	43	NUM
ejpam-1478	267	11	)	)	PUNCT
ejpam-1478	267	12	where	where	SCONJ
ejpam-1478	267	13	x	x	SYM
ejpam-1478	267	14	∈	∈	PROPN
ejpam-1478	267	15	r	r	NOUN
ejpam-1478	267	16	,	,	PUNCT
ejpam-1478	267	17	h	h	NOUN
ejpam-1478	267	18	>	>	X
ejpam-1478	267	19	0	0	NUM
ejpam-1478	267	20	is	be	AUX
ejpam-1478	267	21	a	a	DET
ejpam-1478	267	22	given	give	VERB
ejpam-1478	267	23	constant	constant	ADJ
ejpam-1478	267	24	and	and	CCONJ
ejpam-1478	267	25	ϕ	ϕ	NOUN
ejpam-1478	267	26	∈	∈	PROPN
ejpam-1478	267	27	c([t0	c([t0	PROPN
ejpam-1478	267	28	−	−	PROPN
ejpam-1478	267	29	h	h	NOUN
ejpam-1478	267	30	,	,	PUNCT
ejpam-1478	267	31	t0],r+	t0],r+	NOUN
ejpam-1478	267	32	)	)	PUNCT
ejpam-1478	267	33	.	.	PUNCT
ejpam-1478	268	1	the	the	DET
ejpam-1478	268	2	conditions	condition	NOUN
ejpam-1478	268	3	of	of	ADP
ejpam-1478	268	4	theorem	theorem	NOUN
ejpam-1478	268	5	5	5	NUM
ejpam-1478	268	6	are	be	AUX
ejpam-1478	268	7	satisfied	satisfied	ADJ
ejpam-1478	268	8	for	for	ADP
ejpam-1478	268	9	p	p	NOUN
ejpam-1478	268	10	=	=	NOUN
ejpam-1478	268	11	1	1	NUM
ejpam-1478	268	12	2	2	NUM
ejpam-1478	268	13	.	.	PUNCT
ejpam-1478	269	1	then	then	ADV
ejpam-1478	269	2	if	if	SCONJ
ejpam-1478	269	3	the	the	DET
ejpam-1478	269	4	positive	positive	ADJ
ejpam-1478	269	5	constants	constant	NOUN
ejpam-1478	269	6	λ	λ	X
ejpam-1478	269	7	∈	∈	PROPN
ejpam-1478	269	8	(	(	PUNCT
ejpam-1478	269	9	0,1	0,1	NUM
ejpam-1478	269	10	)	)	PUNCT
ejpam-1478	269	11	and	and	CCONJ
ejpam-1478	269	12	λ	λ	NOUN
ejpam-1478	269	13	satisfy	satisfy	NOUN
ejpam-1478	269	14	π	π	PROPN
ejpam-1478	269	15	2	2	NUM
ejpam-1478	269	16	�	�	PROPN
ejpam-1478	269	17	p	p	NOUN
ejpam-1478	269	18	λ	λ	PROPN
ejpam-1478	269	19	+	+	CCONJ
ejpam-1478	269	20	1	1	NUM
ejpam-1478	269	21	�	�	NOUN
ejpam-1478	269	22	2	2	NUM
ejpam-1478	269	23	<	<	X
ejpam-1478	269	24	λ	λ	PROPN
ejpam-1478	269	25	,	,	PUNCT
ejpam-1478	269	26	then	then	ADV
ejpam-1478	269	27	the	the	DET
ejpam-1478	269	28	solution	solution	NOUN
ejpam-1478	269	29	of	of	ADP
ejpam-1478	269	30	the	the	DET
ejpam-1478	269	31	impulsive	impulsive	ADJ
ejpam-1478	269	32	differential	differential	ADJ
ejpam-1478	269	33	equation	equation	NOUN
ejpam-1478	269	34	with	with	ADP
ejpam-1478	269	35	“	"	PUNCT
ejpam-1478	269	36	supremum	supremum	ADJ
ejpam-1478	269	37	”	"	PUNCT
ejpam-1478	269	38	(	(	PUNCT
ejpam-1478	269	39	43	43	NUM
ejpam-1478	269	40	)	)	PUNCT
ejpam-1478	269	41	is	be	AUX
ejpam-1478	269	42	uniformly	uniformly	ADV
ejpam-1478	269	43	practically	practically	ADV
ejpam-1478	269	44	stable	stable	ADJ
ejpam-1478	269	45	with	with	ADP
ejpam-1478	269	46	respect	respect	NOUN
ejpam-1478	269	47	to	to	ADP
ejpam-1478	269	48	(	(	PUNCT
ejpam-1478	269	49	λ	λ	X
ejpam-1478	269	50	,	,	PUNCT
ejpam-1478	269	51	λ	λ	NOUN
ejpam-1478	269	52	)	)	PUNCT
ejpam-1478	269	53	.	.	PUNCT
ejpam-1478	270	1	acknowledgements	acknowledgement	NOUN
ejpam-1478	270	2	:	:	PUNCT
ejpam-1478	270	3	research	research	NOUN
ejpam-1478	270	4	was	be	AUX
ejpam-1478	270	5	partially	partially	ADV
ejpam-1478	270	6	supported	support	VERB
ejpam-1478	270	7	by	by	ADP
ejpam-1478	270	8	fund	fund	NOUN
ejpam-1478	270	9	“	"	PUNCT
ejpam-1478	270	10	scientific	scientific	ADJ
ejpam-1478	270	11	research	research	NOUN
ejpam-1478	270	12	”	"	PUNCT
ejpam-1478	270	13	mu11fmi005/29.05.2011	mu11fmi005/29.05.2011	NOUN
ejpam-1478	270	14	,	,	PUNCT
ejpam-1478	270	15	plovdiv	plovdiv	PROPN
ejpam-1478	270	16	university	university	PROPN
ejpam-1478	270	17	.	.	PUNCT
ejpam-1478	271	1	references	reference	NOUN
ejpam-1478	271	2	[	[	X
ejpam-1478	271	3	1	1	NUM
ejpam-1478	271	4	]	]	X
ejpam-1478	271	5	r	r	NOUN
ejpam-1478	271	6	agarwal	agarwal	PROPN
ejpam-1478	271	7	,	,	PUNCT
ejpam-1478	271	8	s	s	PROPN
ejpam-1478	271	9	deng	deng	PROPN
ejpam-1478	271	10	and	and	CCONJ
ejpam-1478	271	11	w	w	PROPN
ejpam-1478	271	12	zhang	zhang	PROPN
ejpam-1478	271	13	.	.	PUNCT
ejpam-1478	272	1	generalization	generalization	NOUN
ejpam-1478	272	2	of	of	ADP
ejpam-1478	272	3	a	a	DET
ejpam-1478	272	4	retarded	retarded	ADJ
ejpam-1478	272	5	gronwall	gronwall	ADJ
ejpam-1478	272	6	-	-	PUNCT
ejpam-1478	272	7	like	like	ADJ
ejpam-1478	272	8	inequality	inequality	NOUN
ejpam-1478	272	9	and	and	CCONJ
ejpam-1478	272	10	its	its	PRON
ejpam-1478	272	11	applications	application	NOUN
ejpam-1478	272	12	.	.	PUNCT
ejpam-1478	273	1	appl	appl	PROPN
ejpam-1478	273	2	.	.	PROPN
ejpam-1478	273	3	math	math	PROPN
ejpam-1478	273	4	.	.	PUNCT
ejpam-1478	274	1	comput	comput	NOUN
ejpam-1478	274	2	.	.	PUNCT
ejpam-1478	275	1	165(3):599–612	165(3):599–612	NUM
ejpam-1478	275	2	,	,	PUNCT
ejpam-1478	275	3	2005	2005	NUM
ejpam-1478	275	4	.	.	PUNCT
ejpam-1478	276	1	[	[	X
ejpam-1478	276	2	2	2	NUM
ejpam-1478	276	3	]	]	SYM
ejpam-1478	276	4	v	v	NOUN
ejpam-1478	276	5	angelov	angelov	NOUN
ejpam-1478	276	6	and	and	CCONJ
ejpam-1478	276	7	d	d	ADP
ejpam-1478	276	8	bainov	bainov	NOUN
ejpam-1478	276	9	.	.	PUNCT
ejpam-1478	277	1	on	on	ADP
ejpam-1478	277	2	the	the	DET
ejpam-1478	277	3	functional	functional	ADJ
ejpam-1478	277	4	differential	differential	ADJ
ejpam-1478	277	5	equations	equation	NOUN
ejpam-1478	277	6	with	with	ADP
ejpam-1478	277	7	“	"	PUNCT
ejpam-1478	277	8	maximums	maximum	NOUN
ejpam-1478	277	9	”	"	PUNCT
ejpam-1478	277	10	.	.	PUNCT
ejpam-1478	278	1	appl	appl	PROPN
ejpam-1478	278	2	.	.	PUNCT
ejpam-1478	279	1	anal	anal	PROPN
ejpam-1478	279	2	.	.	PUNCT
ejpam-1478	280	1	16:187–194	16:187–194	NUM
ejpam-1478	280	2	,	,	PUNCT
ejpam-1478	280	3	1983	1983	NUM
ejpam-1478	280	4	.	.	PUNCT
ejpam-1478	281	1	[	[	X
ejpam-1478	281	2	3	3	X
ejpam-1478	281	3	]	]	X
ejpam-1478	281	4	d	d	NOUN
ejpam-1478	281	5	bainov	bainov	NOUN
ejpam-1478	281	6	and	and	CCONJ
ejpam-1478	281	7	s	s	PROPN
ejpam-1478	281	8	hristova	hristova	X
ejpam-1478	281	9	.	.	PUNCT
ejpam-1478	282	1	differential	differential	ADJ
ejpam-1478	282	2	equations	equation	NOUN
ejpam-1478	282	3	with	with	ADP
ejpam-1478	282	4	maxima	maxima	PROPN
ejpam-1478	282	5	.	.	PUNCT
ejpam-1478	283	1	chapman	chapman	PROPN
ejpam-1478	283	2	and	and	CCONJ
ejpam-1478	283	3	hall	hall	PROPN
ejpam-1478	283	4	/	/	SYM
ejpam-1478	283	5	crc	crc	PROPN
ejpam-1478	283	6	,	,	PUNCT
ejpam-1478	283	7	usa	usa	PROPN
ejpam-1478	283	8	,	,	PUNCT
ejpam-1478	283	9	isbn-10	isbn-10	PROPN
ejpam-1478	283	10	:	:	PUNCT
ejpam-1478	283	11	1439867577	1439867577	NUM
ejpam-1478	283	12	,	,	PUNCT
ejpam-1478	283	13	2011	2011	NUM
ejpam-1478	283	14	.	.	PUNCT
ejpam-1478	284	1	[	[	X
ejpam-1478	284	2	4	4	NUM
ejpam-1478	284	3	]	]	X
ejpam-1478	284	4	d	d	NOUN
ejpam-1478	284	5	bainov	bainov	NOUN
ejpam-1478	284	6	and	and	CCONJ
ejpam-1478	284	7	s	s	PROPN
ejpam-1478	284	8	hristova	hristova	X
ejpam-1478	284	9	.	.	PUNCT
ejpam-1478	285	1	monotone	monotone	ADJ
ejpam-1478	285	2	-	-	PUNCT
ejpam-1478	285	3	iterative	iterative	NOUN
ejpam-1478	285	4	techniques	technique	NOUN
ejpam-1478	285	5	of	of	ADP
ejpam-1478	285	6	lakshmikantham	lakshmikantham	NOUN
ejpam-1478	285	7	for	for	ADP
ejpam-1478	285	8	a	a	DET
ejpam-1478	285	9	boundary	boundary	ADJ
ejpam-1478	285	10	value	value	NOUN
ejpam-1478	285	11	problem	problem	NOUN
ejpam-1478	285	12	for	for	ADP
ejpam-1478	285	13	systems	system	NOUN
ejpam-1478	285	14	of	of	ADP
ejpam-1478	285	15	differential	differential	ADJ
ejpam-1478	285	16	equations	equation	NOUN
ejpam-1478	285	17	with	with	ADP
ejpam-1478	285	18	“	"	PUNCT
ejpam-1478	285	19	maxima	maxima	PROPN
ejpam-1478	285	20	”	"	PUNCT
ejpam-1478	285	21	.	.	PUNCT
ejpam-1478	286	1	j.	j.	PROPN
ejpam-1478	286	2	math	math	PROPN
ejpam-1478	286	3	.	.	PUNCT
ejpam-1478	287	1	anal	anal	PROPN
ejpam-1478	287	2	.	.	PUNCT
ejpam-1478	287	3	appl	appl	PROPN
ejpam-1478	287	4	.	.	PUNCT
ejpam-1478	288	1	190(2):391–401	190(2):391–401	NUM
ejpam-1478	288	2	,	,	PUNCT
ejpam-1478	288	3	1995	1995	NUM
ejpam-1478	288	4	.	.	PUNCT
ejpam-1478	289	1	references	reference	NOUN
ejpam-1478	289	2	43	43	NUM
ejpam-1478	290	1	[	[	X
ejpam-1478	290	2	5	5	NUM
ejpam-1478	290	3	]	]	X
ejpam-1478	290	4	d	d	NOUN
ejpam-1478	290	5	bainov	bainov	NOUN
ejpam-1478	290	6	,	,	PUNCT
ejpam-1478	290	7	v	v	ADP
ejpam-1478	290	8	petrov	petrov	PROPN
ejpam-1478	290	9	and	and	CCONJ
ejpam-1478	290	10	v	v	NOUN
ejpam-1478	290	11	proytcheva	proytcheva	NOUN
ejpam-1478	290	12	.	.	PUNCT
ejpam-1478	291	1	existence	existence	NOUN
ejpam-1478	291	2	and	and	CCONJ
ejpam-1478	291	3	asymptotic	asymptotic	ADJ
ejpam-1478	291	4	behavior	behavior	NOUN
ejpam-1478	291	5	of	of	ADP
ejpam-1478	291	6	nonoscillatory	nonoscillatory	ADJ
ejpam-1478	291	7	solutions	solution	NOUN
ejpam-1478	291	8	of	of	ADP
ejpam-1478	291	9	second	second	ADJ
ejpam-1478	291	10	-	-	PUNCT
ejpam-1478	291	11	order	order	NOUN
ejpam-1478	291	12	neutral	neutral	ADJ
ejpam-1478	291	13	differential	differential	NOUN
ejpam-1478	291	14	equations	equation	NOUN
ejpam-1478	291	15	with	with	ADP
ejpam-1478	291	16	“	"	PUNCT
ejpam-1478	291	17	maxima	maxima	PROPN
ejpam-1478	291	18	”	"	PUNCT
ejpam-1478	291	19	.	.	PUNCT
ejpam-1478	292	1	j.	j.	PROPN
ejpam-1478	292	2	comput	comput	PROPN
ejpam-1478	292	3	.	.	PUNCT
ejpam-1478	293	1	appl	appl	PROPN
ejpam-1478	293	2	.	.	PROPN
ejpam-1478	293	3	math	math	PROPN
ejpam-1478	293	4	.	.	PUNCT
ejpam-1478	293	5	,	,	PUNCT
ejpam-1478	293	6	83(2):237–249	83(2):237–249	PROPN
ejpam-1478	293	7	,	,	PUNCT
ejpam-1478	293	8	1997	1997	NUM
ejpam-1478	293	9	.	.	PUNCT
ejpam-1478	294	1	[	[	X
ejpam-1478	294	2	6	6	NUM
ejpam-1478	294	3	]	]	X
ejpam-1478	294	4	d	d	NOUN
ejpam-1478	294	5	bainov	bainov	NOUN
ejpam-1478	294	6	,	,	PUNCT
ejpam-1478	294	7	v	v	ADP
ejpam-1478	294	8	petrov	petrov	PROPN
ejpam-1478	294	9	and	and	CCONJ
ejpam-1478	294	10	v	v	NOUN
ejpam-1478	294	11	proytcheva	proytcheva	NOUN
ejpam-1478	294	12	.	.	PUNCT
ejpam-1478	295	1	asymptotic	asymptotic	ADJ
ejpam-1478	295	2	behavior	behavior	NOUN
ejpam-1478	295	3	of	of	ADP
ejpam-1478	295	4	second	second	ADJ
ejpam-1478	295	5	order	order	NOUN
ejpam-1478	295	6	neutral	neutral	ADJ
ejpam-1478	295	7	differential	differential	ADJ
ejpam-1478	295	8	equations	equation	NOUN
ejpam-1478	295	9	with	with	ADP
ejpam-1478	295	10	“	"	PUNCT
ejpam-1478	295	11	maxima	maxima	NOUN
ejpam-1478	295	12	”	"	PUNCT
ejpam-1478	295	13	.	.	PUNCT
ejpam-1478	296	1	tamkang	tamkang	PROPN
ejpam-1478	296	2	j.	j.	PROPN
ejpam-1478	296	3	math	math	PROPN
ejpam-1478	296	4	.	.	PUNCT
ejpam-1478	296	5	,	,	PUNCT
ejpam-1478	296	6	26(3):267–275	26(3):267–275	NUM
ejpam-1478	296	7	,	,	PUNCT
ejpam-1478	296	8	1995	1995	NUM
ejpam-1478	296	9	.	.	PUNCT
ejpam-1478	297	1	[	[	X
ejpam-1478	297	2	7	7	X
ejpam-1478	297	3	]	]	X
ejpam-1478	297	4	w	w	PROPN
ejpam-1478	297	5	cheung	cheung	PROPN
ejpam-1478	297	6	.	.	PUNCT
ejpam-1478	298	1	some	some	DET
ejpam-1478	298	2	new	new	ADJ
ejpam-1478	298	3	nonlinear	nonlinear	ADJ
ejpam-1478	298	4	inequalities	inequality	NOUN
ejpam-1478	298	5	and	and	CCONJ
ejpam-1478	298	6	applications	application	NOUN
ejpam-1478	298	7	to	to	ADP
ejpam-1478	298	8	boundary	boundary	ADJ
ejpam-1478	298	9	value	value	NOUN
ejpam-1478	298	10	problems	problem	NOUN
ejpam-1478	298	11	.	.	PUNCT
ejpam-1478	299	1	nonlinear	nonlinear	ADJ
ejpam-1478	299	2	analysis	analysis	NOUN
ejpam-1478	299	3	,	,	PUNCT
ejpam-1478	299	4	64:2112–2128	64:2112–2128	NUM
ejpam-1478	299	5	,	,	PUNCT
ejpam-1478	299	6	2006	2006	NUM
ejpam-1478	299	7	.	.	PUNCT
ejpam-1478	300	1	[	[	X
ejpam-1478	300	2	8	8	NUM
ejpam-1478	300	3	]	]	PUNCT
ejpam-1478	300	4	a	a	DET
ejpam-1478	300	5	gallo	gallo	NOUN
ejpam-1478	300	6	and	and	CCONJ
ejpam-1478	300	7	a	a	DET
ejpam-1478	300	8	piccirillo	piccirillo	NOUN
ejpam-1478	300	9	.	.	PUNCT
ejpam-1478	301	1	about	about	ADP
ejpam-1478	301	2	new	new	ADJ
ejpam-1478	301	3	analogies	analogy	NOUN
ejpam-1478	301	4	of	of	ADP
ejpam-1478	301	5	gronwall	gronwall	ADJ
ejpam-1478	301	6	–	–	PUNCT
ejpam-1478	301	7	bellman	bellman	NOUN
ejpam-1478	301	8	–	–	PUNCT
ejpam-1478	301	9	bihari	bihari	PROPN
ejpam-1478	301	10	type	type	NOUN
ejpam-1478	301	11	inequalities	inequality	NOUN
ejpam-1478	301	12	for	for	ADP
ejpam-1478	301	13	discontinuous	discontinuous	ADJ
ejpam-1478	301	14	functions	function	NOUN
ejpam-1478	301	15	and	and	CCONJ
ejpam-1478	301	16	estimated	estimate	VERB
ejpam-1478	301	17	solutions	solution	NOUN
ejpam-1478	301	18	for	for	ADP
ejpam-1478	301	19	impulsive	impulsive	ADJ
ejpam-1478	301	20	differential	differential	ADJ
ejpam-1478	301	21	systems	system	NOUN
ejpam-1478	301	22	.	.	PUNCT
ejpam-1478	302	1	nonlinear	nonlinear	ADJ
ejpam-1478	302	2	analysis	analysis	NOUN
ejpam-1478	302	3	,	,	PUNCT
ejpam-1478	302	4	67:1550–1559	67:1550–1559	NUM
ejpam-1478	302	5	,	,	PUNCT
ejpam-1478	302	6	2007	2007	NUM
ejpam-1478	302	7	.	.	PUNCT
ejpam-1478	303	1	[	[	X
ejpam-1478	303	2	9	9	NUM
ejpam-1478	303	3	]	]	SYM
ejpam-1478	303	4	s	s	PART
ejpam-1478	303	5	hristova	hristova	X
ejpam-1478	303	6	.	.	PUNCT
ejpam-1478	304	1	qualitative	qualitative	ADJ
ejpam-1478	304	2	investigations	investigation	NOUN
ejpam-1478	304	3	and	and	CCONJ
ejpam-1478	304	4	approximate	approximate	ADJ
ejpam-1478	304	5	methods	method	NOUN
ejpam-1478	304	6	for	for	ADP
ejpam-1478	304	7	impulsive	impulsive	ADJ
ejpam-1478	304	8	equations	equation	NOUN
ejpam-1478	304	9	.	.	PUNCT
ejpam-1478	305	1	nova	nova	PROPN
ejpam-1478	305	2	science	science	PROPN
ejpam-1478	305	3	publ	publ	PROPN
ejpam-1478	305	4	.	.	PUNCT
ejpam-1478	306	1	,	,	PUNCT
ejpam-1478	306	2	new	new	PROPN
ejpam-1478	306	3	york	york	PROPN
ejpam-1478	306	4	,	,	PUNCT
ejpam-1478	306	5	2009	2009	NUM
ejpam-1478	306	6	.	.	PUNCT
ejpam-1478	307	1	[	[	X
ejpam-1478	307	2	10	10	NUM
ejpam-1478	307	3	]	]	SYM
ejpam-1478	307	4	s	s	PART
ejpam-1478	307	5	hristova	hristova	PROPN
ejpam-1478	307	6	and	and	CCONJ
ejpam-1478	307	7	d	d	ADP
ejpam-1478	307	8	bainov	bainov	NOUN
ejpam-1478	307	9	.	.	PUNCT
ejpam-1478	308	1	application	application	NOUN
ejpam-1478	308	2	of	of	ADP
ejpam-1478	308	3	the	the	DET
ejpam-1478	308	4	monotone	monotone	ADJ
ejpam-1478	308	5	-	-	PUNCT
ejpam-1478	308	6	iterative	iterative	NOUN
ejpam-1478	308	7	techniques	technique	NOUN
ejpam-1478	308	8	of	of	ADP
ejpam-1478	308	9	v.	v.	ADP
ejpam-1478	308	10	lakshmikantham	lakshmikantham	VERB
ejpam-1478	308	11	to	to	ADP
ejpam-1478	308	12	the	the	DET
ejpam-1478	308	13	solution	solution	NOUN
ejpam-1478	308	14	of	of	ADP
ejpam-1478	308	15	the	the	DET
ejpam-1478	308	16	initial	initial	ADJ
ejpam-1478	308	17	value	value	NOUN
ejpam-1478	308	18	problem	problem	NOUN
ejpam-1478	308	19	for	for	ADP
ejpam-1478	308	20	impulsive	impulsive	ADJ
ejpam-1478	308	21	differential	differential	ADJ
ejpam-1478	308	22	equations	equation	NOUN
ejpam-1478	308	23	with	with	ADP
ejpam-1478	308	24	“	"	PUNCT
ejpam-1478	308	25	supremum	supremum	ADJ
ejpam-1478	308	26	”	"	PUNCT
ejpam-1478	308	27	.	.	PUNCT
ejpam-1478	309	1	j.	j.	PROPN
ejpam-1478	309	2	math	math	PROPN
ejpam-1478	309	3	.	.	PUNCT
ejpam-1478	310	1	phys	phy	NOUN
ejpam-1478	310	2	.	.	PUNCT
ejpam-1478	311	1	sci	sci	PROPN
ejpam-1478	311	2	.	.	PROPN
ejpam-1478	311	3	,	,	PUNCT
ejpam-1478	311	4	25(1):69–80	25(1):69–80	NUM
ejpam-1478	311	5	,	,	PUNCT
ejpam-1478	311	6	1991	1991	NUM
ejpam-1478	311	7	.	.	PUNCT
ejpam-1478	312	1	[	[	X
ejpam-1478	312	2	11	11	NUM
ejpam-1478	312	3	]	]	SYM
ejpam-1478	312	4	s	s	PART
ejpam-1478	312	5	hristova	hristova	NOUN
ejpam-1478	312	6	and	and	CCONJ
ejpam-1478	312	7	l	l	PROPN
ejpam-1478	312	8	roberts	roberts	PROPN
ejpam-1478	312	9	.	.	PUNCT
ejpam-1478	313	1	boundedness	boundedness	NOUN
ejpam-1478	313	2	of	of	ADP
ejpam-1478	313	3	the	the	DET
ejpam-1478	313	4	solutions	solution	NOUN
ejpam-1478	313	5	of	of	ADP
ejpam-1478	313	6	differential	differential	ADJ
ejpam-1478	313	7	equations	equation	NOUN
ejpam-1478	313	8	with	with	ADP
ejpam-1478	313	9	“	"	PUNCT
ejpam-1478	313	10	maxima	maxima	NOUN
ejpam-1478	313	11	”	"	PUNCT
ejpam-1478	313	12	.	.	PUNCT
ejpam-1478	314	1	int	int	NOUN
ejpam-1478	314	2	.	.	PUNCT
ejpam-1478	315	1	j.	j.	PROPN
ejpam-1478	315	2	appl	appl	PROPN
ejpam-1478	315	3	.	.	PROPN
ejpam-1478	315	4	math	math	PROPN
ejpam-1478	315	5	.	.	PUNCT
ejpam-1478	316	1	4(2):231–240	4(2):231–240	NOUN
ejpam-1478	316	2	,	,	PUNCT
ejpam-1478	316	3	2000	2000	NUM
ejpam-1478	316	4	.	.	PUNCT
ejpam-1478	317	1	[	[	X
ejpam-1478	317	2	12	12	NUM
ejpam-1478	317	3	]	]	X
ejpam-1478	317	4	s	s	X
ejpam-1478	317	5	hristova	hristova	PROPN
ejpam-1478	317	6	and	and	CCONJ
ejpam-1478	317	7	k	k	PROPN
ejpam-1478	317	8	stefanova	stefanova	PROPN
ejpam-1478	317	9	.	.	PUNCT
ejpam-1478	318	1	some	some	DET
ejpam-1478	318	2	integral	integral	ADJ
ejpam-1478	318	3	inequalities	inequality	NOUN
ejpam-1478	318	4	with	with	ADP
ejpam-1478	318	5	maximum	maximum	NOUN
ejpam-1478	318	6	of	of	ADP
ejpam-1478	318	7	the	the	DET
ejpam-1478	318	8	unknown	unknown	ADJ
ejpam-1478	318	9	functions	function	NOUN
ejpam-1478	318	10	.	.	PUNCT
ejpam-1478	319	1	adv	adv	PROPN
ejpam-1478	319	2	.	.	PUNCT
ejpam-1478	320	1	dyn	dyn	PROPN
ejpam-1478	320	2	.	.	PUNCT
ejpam-1478	321	1	sys	sys	PROPN
ejpam-1478	321	2	.	.	PUNCT
ejpam-1478	321	3	appl	appl	PROPN
ejpam-1478	321	4	.	.	PROPN
ejpam-1478	321	5	,	,	PUNCT
ejpam-1478	321	6	6(1):57–69	6(1):57–69	NUM
ejpam-1478	321	7	,	,	PUNCT
ejpam-1478	321	8	2011	2011	NUM
ejpam-1478	321	9	.	.	PUNCT
ejpam-1478	322	1	[	[	X
ejpam-1478	322	2	13	13	NUM
ejpam-1478	322	3	]	]	X
ejpam-1478	322	4	y	y	PROPN
ejpam-1478	322	5	kim	kim	PROPN
ejpam-1478	322	6	.	.	PUNCT
ejpam-1478	323	1	on	on	ADP
ejpam-1478	323	2	some	some	DET
ejpam-1478	323	3	new	new	ADJ
ejpam-1478	323	4	integral	integral	ADJ
ejpam-1478	323	5	inequalities	inequality	NOUN
ejpam-1478	323	6	for	for	ADP
ejpam-1478	323	7	functions	function	NOUN
ejpam-1478	323	8	in	in	ADP
ejpam-1478	323	9	one	one	NUM
ejpam-1478	323	10	and	and	CCONJ
ejpam-1478	323	11	two	two	NUM
ejpam-1478	323	12	variables	variable	NOUN
ejpam-1478	323	13	.	.	PUNCT
ejpam-1478	324	1	acta	acta	PROPN
ejpam-1478	324	2	math	math	PROPN
ejpam-1478	324	3	.	.	PUNCT
ejpam-1478	325	1	sin	sin	NOUN
ejpam-1478	325	2	.	.	PUNCT
ejpam-1478	325	3	,	,	PUNCT
ejpam-1478	325	4	english	english	ADJ
ejpam-1478	325	5	series	series	NOUN
ejpam-1478	325	6	,	,	PUNCT
ejpam-1478	325	7	21(2):423–434	21(2):423–434	PROPN
ejpam-1478	325	8	,	,	PUNCT
ejpam-1478	325	9	2005	2005	NUM
ejpam-1478	325	10	.	.	PUNCT
ejpam-1478	326	1	[	[	X
ejpam-1478	326	2	14	14	NUM
ejpam-1478	326	3	]	]	SYM
ejpam-1478	326	4	v	v	ADP
ejpam-1478	326	5	lakshmikantham	lakshmikantham	NOUN
ejpam-1478	326	6	,	,	PUNCT
ejpam-1478	326	7	s.	s.	PROPN
ejpam-1478	326	8	leela	leela	PROPN
ejpam-1478	326	9	and	and	CCONJ
ejpam-1478	326	10	a.	a.	NOUN
ejpam-1478	326	11	martynyuk	martynyuk	PROPN
ejpam-1478	326	12	.	.	PUNCT
ejpam-1478	327	1	practical	practical	ADJ
ejpam-1478	327	2	stability	stability	NOUN
ejpam-1478	327	3	of	of	ADP
ejpam-1478	327	4	nonlinear	nonlinear	ADJ
ejpam-1478	327	5	systems	system	NOUN
ejpam-1478	327	6	.	.	PUNCT
ejpam-1478	328	1	world	world	NOUN
ejpam-1478	328	2	scientific	scientific	ADJ
ejpam-1478	328	3	,	,	PUNCT
ejpam-1478	328	4	1990	1990	NUM
ejpam-1478	328	5	.	.	PUNCT
ejpam-1478	329	1	[	[	X
ejpam-1478	329	2	15	15	NUM
ejpam-1478	329	3	]	]	X
ejpam-1478	329	4	q	q	X
ejpam-1478	329	5	ma	ma	PROPN
ejpam-1478	329	6	and	and	CCONJ
ejpam-1478	329	7	j	j	PROPN
ejpam-1478	329	8	pecaric	pecaric	NOUN
ejpam-1478	329	9	.	.	PUNCT
ejpam-1478	330	1	on	on	ADP
ejpam-1478	330	2	certain	certain	ADJ
ejpam-1478	330	3	new	new	ADJ
ejpam-1478	330	4	nonlinear	nonlinear	ADJ
ejpam-1478	330	5	retarded	retarded	ADJ
ejpam-1478	330	6	integral	integral	ADJ
ejpam-1478	330	7	inequalities	inequality	NOUN
ejpam-1478	330	8	for	for	ADP
ejpam-1478	330	9	functions	function	NOUN
ejpam-1478	330	10	in	in	ADP
ejpam-1478	330	11	two	two	NUM
ejpam-1478	330	12	variables	variable	NOUN
ejpam-1478	330	13	and	and	CCONJ
ejpam-1478	330	14	their	their	PRON
ejpam-1478	330	15	applications	application	NOUN
ejpam-1478	330	16	.	.	PUNCT
ejpam-1478	331	1	j.	j.	PROPN
ejpam-1478	331	2	korean	korean	PROPN
ejpam-1478	331	3	math	math	PROPN
ejpam-1478	331	4	.	.	PUNCT
ejpam-1478	332	1	soc	soc	PROPN
ejpam-1478	332	2	.	.	PUNCT
ejpam-1478	332	3	,	,	PUNCT
ejpam-1478	332	4	45(1):121–136	45(1):121–136	NUM
ejpam-1478	332	5	,	,	PUNCT
ejpam-1478	332	6	2008	2008	NUM
ejpam-1478	332	7	.	.	PUNCT
ejpam-1478	333	1	[	[	X
ejpam-1478	333	2	16	16	NUM
ejpam-1478	333	3	]	]	X
ejpam-1478	333	4	e	e	X
ejpam-1478	333	5	popov	popov	PROPN
ejpam-1478	333	6	.	.	PUNCT
ejpam-1478	333	7	automatic	automatic	ADJ
ejpam-1478	333	8	regulation	regulation	NOUN
ejpam-1478	333	9	and	and	CCONJ
ejpam-1478	333	10	control	control	NOUN
ejpam-1478	333	11	.	.	PUNCT
ejpam-1478	334	1	moscow	moscow	PROPN
ejpam-1478	334	2	1966	1966	NUM
ejpam-1478	334	3	(	(	PUNCT
ejpam-1478	334	4	in	in	ADP
ejpam-1478	334	5	russian	russian	NOUN
ejpam-1478	334	6	)	)	PUNCT
ejpam-1478	334	7	.	.	PUNCT
ejpam-1478	335	1	[	[	X
ejpam-1478	335	2	17	17	NUM
ejpam-1478	335	3	]	]	X
ejpam-1478	335	4	d	d	NOUN
ejpam-1478	335	5	snow	snow	NOUN
ejpam-1478	335	6	.	.	PUNCT
ejpam-1478	336	1	gronwall	gronwall	PROPN
ejpam-1478	336	2	’s	’s	PART
ejpam-1478	336	3	inequality	inequality	NOUN
ejpam-1478	336	4	for	for	ADP
ejpam-1478	336	5	systems	system	NOUN
ejpam-1478	336	6	of	of	ADP
ejpam-1478	336	7	partial	partial	ADJ
ejpam-1478	336	8	differential	differential	ADJ
ejpam-1478	336	9	equations	equation	NOUN
ejpam-1478	336	10	in	in	ADP
ejpam-1478	336	11	two	two	NUM
ejpam-1478	336	12	independent	independent	ADJ
ejpam-1478	336	13	variables	variable	NOUN
ejpam-1478	336	14	.	.	PUNCT
ejpam-1478	337	1	proc	proc	NOUN
ejpam-1478	337	2	.	.	PUNCT
ejpam-1478	338	1	amer	amer	PROPN
ejpam-1478	338	2	.	.	PUNCT
ejpam-1478	338	3	math	math	PROPN
ejpam-1478	338	4	.	.	PUNCT
ejpam-1478	339	1	soc	soc	PROPN
ejpam-1478	339	2	.	.	PUNCT
ejpam-1478	339	3	,	,	PUNCT
ejpam-1478	339	4	33(1):46–54	33(1):46–54	NUM
ejpam-1478	339	5	,	,	PUNCT
ejpam-1478	339	6	1972	1972	NUM
ejpam-1478	339	7	.	.	PUNCT
ejpam-1478	340	1	[	[	X
ejpam-1478	340	2	18	18	NUM
ejpam-1478	340	3	]	]	X
ejpam-1478	340	4	c	c	NOUN
ejpam-1478	340	5	tunc	tunc	NOUN
ejpam-1478	340	6	.	.	PUNCT
ejpam-1478	341	1	on	on	ADP
ejpam-1478	341	2	the	the	DET
ejpam-1478	341	3	instability	instability	NOUN
ejpam-1478	341	4	of	of	ADP
ejpam-1478	341	5	solutions	solution	NOUN
ejpam-1478	341	6	of	of	ADP
ejpam-1478	341	7	some	some	DET
ejpam-1478	341	8	fifth	fifth	ADJ
ejpam-1478	341	9	order	order	NOUN
ejpam-1478	341	10	nonlinear	nonlinear	ADJ
ejpam-1478	341	11	delay	delay	NOUN
ejpam-1478	341	12	differential	differential	PROPN
ejpam-1478	341	13	equations	equation	NOUN
ejpam-1478	341	14	.	.	PUNCT
ejpam-1478	342	1	appl	appl	PROPN
ejpam-1478	342	2	.	.	PROPN
ejpam-1478	343	1	math	math	PROPN
ejpam-1478	343	2	.	.	PUNCT
ejpam-1478	344	1	inf	inf	PROPN
ejpam-1478	344	2	.	.	PUNCT
ejpam-1478	345	1	sci	sci	PROPN
ejpam-1478	345	2	.	.	PROPN
ejpam-1478	345	3	,	,	PUNCT
ejpam-1478	345	4	5(1):112	5(1):112	NUM
ejpam-1478	345	5	-	-	SYM
ejpam-1478	345	6	121	121	NUM
ejpam-1478	345	7	,	,	PUNCT
ejpam-1478	345	8	2011	2011	NUM
ejpam-1478	345	9	.	.	PUNCT
ejpam-1478	346	1	[	[	X
ejpam-1478	346	2	19	19	NUM
ejpam-1478	346	3	]	]	X
ejpam-1478	346	4	c	c	NOUN
ejpam-1478	346	5	tunc	tunc	NOUN
ejpam-1478	346	6	.	.	PUNCT
ejpam-1478	347	1	further	further	ADJ
ejpam-1478	347	2	results	result	NOUN
ejpam-1478	347	3	on	on	ADP
ejpam-1478	347	4	the	the	DET
ejpam-1478	347	5	instability	instability	NOUN
ejpam-1478	347	6	of	of	ADP
ejpam-1478	347	7	solutions	solution	NOUN
ejpam-1478	347	8	of	of	ADP
ejpam-1478	347	9	certain	certain	ADJ
ejpam-1478	347	10	nonlinear	nonlinear	ADJ
ejpam-1478	347	11	vector	vector	NOUN
ejpam-1478	347	12	differential	differential	NOUN
ejpam-1478	347	13	equations	equation	NOUN
ejpam-1478	347	14	of	of	ADP
ejpam-1478	347	15	fifth	fifth	ADJ
ejpam-1478	347	16	order	order	NOUN
ejpam-1478	347	17	.	.	PUNCT
ejpam-1478	348	1	appl	appl	PROPN
ejpam-1478	348	2	.	.	PROPN
ejpam-1478	349	1	math	math	PROPN
ejpam-1478	349	2	.	.	PUNCT
ejpam-1478	350	1	inf	inf	PROPN
ejpam-1478	350	2	.	.	PUNCT
ejpam-1478	351	1	sci	sci	PROPN
ejpam-1478	351	2	.	.	PROPN
ejpam-1478	351	3	,	,	PUNCT
ejpam-1478	351	4	2(3):51–60	2(3):51–60	NUM
ejpam-1478	351	5	,	,	PUNCT
ejpam-1478	351	6	2008	2008	NUM
ejpam-1478	351	7	.	.	PUNCT
ejpam-1478	352	1	references	reference	NOUN
ejpam-1478	352	2	44	44	NUM
ejpam-1478	352	3	[	[	SYM
ejpam-1478	352	4	20	20	NUM
ejpam-1478	352	5	]	]	X
ejpam-1478	352	6	w	w	PROPN
ejpam-1478	352	7	wang	wang	PROPN
ejpam-1478	352	8	.	.	PUNCT
ejpam-1478	353	1	a	a	DET
ejpam-1478	353	2	generalized	generalize	VERB
ejpam-1478	353	3	retarded	retarded	ADJ
ejpam-1478	353	4	gronwall	gronwall	ADJ
ejpam-1478	353	5	-	-	PUNCT
ejpam-1478	353	6	like	like	ADJ
ejpam-1478	353	7	inequality	inequality	NOUN
ejpam-1478	353	8	in	in	ADP
ejpam-1478	353	9	two	two	NUM
ejpam-1478	353	10	variables	variable	NOUN
ejpam-1478	353	11	and	and	CCONJ
ejpam-1478	353	12	applications	application	NOUN
ejpam-1478	353	13	to	to	ADP
ejpam-1478	353	14	bvp	bvp	PROPN
ejpam-1478	353	15	.	.	PUNCT
ejpam-1478	354	1	appl	appl	PROPN
ejpam-1478	354	2	.	.	PROPN
ejpam-1478	354	3	math	math	PROPN
ejpam-1478	354	4	.	.	PUNCT
ejpam-1478	355	1	comput	comput	NOUN
ejpam-1478	355	2	.	.	PUNCT
ejpam-1478	355	3	,	,	PUNCT
ejpam-1478	355	4	191:144	191:144	PROPN
ejpam-1478	355	5	-	-	SYM
ejpam-1478	355	6	154	154	NUM
ejpam-1478	355	7	,	,	PUNCT
ejpam-1478	355	8	2007	2007	NUM
ejpam-1478	355	9	.	.	PUNCT
ejpam-1478	356	1	[	[	X
ejpam-1478	356	2	21	21	NUM
ejpam-1478	356	3	]	]	X
ejpam-1478	356	4	w	w	PROPN
ejpam-1478	356	5	wang	wang	PROPN
ejpam-1478	356	6	and	and	CCONJ
ejpam-1478	356	7	c	c	PROPN
ejpam-1478	356	8	shen	shen	PROPN
ejpam-1478	356	9	.	.	PUNCT
ejpam-1478	357	1	on	on	ADP
ejpam-1478	357	2	a	a	DET
ejpam-1478	357	3	generalized	generalized	ADJ
ejpam-1478	357	4	retarded	retarded	ADJ
ejpam-1478	357	5	integral	integral	ADJ
ejpam-1478	357	6	inequality	inequality	NOUN
ejpam-1478	357	7	with	with	ADP
ejpam-1478	357	8	two	two	NUM
ejpam-1478	357	9	variables	variable	NOUN
ejpam-1478	357	10	.	.	PUNCT
ejpam-1478	358	1	j.	j.	PROPN
ejpam-1478	358	2	ineq	ineq	PROPN
ejpam-1478	358	3	.	.	PUNCT
ejpam-1478	359	1	appl	appl	PROPN
ejpam-1478	359	2	.	.	PROPN
ejpam-1478	359	3	,	,	PUNCT
ejpam-1478	359	4	article	article	NOUN
ejpam-1478	359	5	i	i	PROPN
ejpam-1478	359	6	d	d	PROPN
ejpam-1478	359	7	518646	518646	NUM
ejpam-1478	359	8	,	,	PUNCT
ejpam-1478	359	9	9	9	NUM
ejpam-1478	359	10	p	p	NOUN
ejpam-1478	359	11	,	,	PUNCT
ejpam-1478	359	12	2008	2008	NUM
ejpam-1478	359	13	.	.	PUNCT
ejpam-1478	360	1	[	[	X
ejpam-1478	360	2	22	22	NUM
ejpam-1478	360	3	]	]	X
ejpam-1478	360	4	k	k	PROPN
ejpam-1478	360	5	zheng	zheng	PROPN
ejpam-1478	360	6	.	.	PUNCT
ejpam-1478	361	1	some	some	DET
ejpam-1478	361	2	retarded	retarded	ADJ
ejpam-1478	361	3	nonlinear	nonlinear	ADJ
ejpam-1478	361	4	integral	integral	ADJ
ejpam-1478	361	5	inequalities	inequality	NOUN
ejpam-1478	361	6	in	in	ADP
ejpam-1478	361	7	two	two	NUM
ejpam-1478	361	8	variables	variable	NOUN
ejpam-1478	361	9	and	and	CCONJ
ejpam-1478	361	10	applications	application	NOUN
ejpam-1478	361	11	.	.	PUNCT
ejpam-1478	362	1	j.	j.	PROPN
ejpam-1478	362	2	ineq	ineq	PROPN
ejpam-1478	362	3	.	.	PUNCT
ejpam-1478	363	1	pure	pure	ADJ
ejpam-1478	363	2	appl	appl	PROPN
ejpam-1478	363	3	.	.	PUNCT
ejpam-1478	363	4	math	math	PROPN
ejpam-1478	363	5	.	.	PUNCT
ejpam-1478	364	1	,	,	PUNCT
ejpam-1478	364	2	9	9	NUM
ejpam-1478	364	3	,	,	PUNCT
ejpam-1478	364	4	iss	iss	PROPN
ejpam-1478	364	5	.	.	PROPN
ejpam-1478	364	6	2	2	NUM
ejpam-1478	364	7	,	,	PUNCT
ejpam-1478	364	8	article	article	NOUN
ejpam-1478	364	9	57	57	NUM
ejpam-1478	364	10	,	,	PUNCT
ejpam-1478	364	11	11	11	NUM
ejpam-1478	364	12	pp	pp	ADJ
ejpam-1478	364	13	,	,	PUNCT
ejpam-1478	364	14	2008	2008	NUM
ejpam-1478	364	15	.	.	PUNCT