id	sid	tid	token	lemma	pos
ejpam-454	1	1	3_454_wu.dvi	3_454_wu.dvi	NUM
ejpam-454	1	2	european	european	ADJ
ejpam-454	1	3	journal	journal	NOUN
ejpam-454	1	4	of	of	ADP
ejpam-454	1	5	pure	pure	ADJ
ejpam-454	1	6	and	and	CCONJ
ejpam-454	1	7	applied	apply	VERB
ejpam-454	1	8	mathematics	mathematic	NOUN
ejpam-454	1	9	vol	vol	NOUN
ejpam-454	1	10	.	.	PUNCT
ejpam-454	2	1	3	3	NUM
ejpam-454	2	2	,	,	PUNCT
ejpam-454	2	3	no	no	INTJ
ejpam-454	2	4	.	.	NOUN
ejpam-454	2	5	5	5	NUM
ejpam-454	2	6	,	,	PUNCT
ejpam-454	2	7	2010	2010	NUM
ejpam-454	2	8	,	,	PUNCT
ejpam-454	2	9	806	806	NUM
ejpam-454	2	10	-	-	SYM
ejpam-454	2	11	818	818	NUM
ejpam-454	2	12	issn	issn	PROPN
ejpam-454	2	13	1307	1307	NUM
ejpam-454	2	14	-	-	SYM
ejpam-454	2	15	5543	5543	NUM
ejpam-454	2	16	–	–	PUNCT
ejpam-454	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-454	2	18	global	global	ADJ
ejpam-454	2	19	asymptotical	asymptotical	ADJ
ejpam-454	2	20	stability	stability	NOUN
ejpam-454	2	21	of	of	ADP
ejpam-454	2	22	delayed	delay	VERB
ejpam-454	2	23	impulsive	impulsive	ADJ
ejpam-454	2	24	neural	neural	ADJ
ejpam-454	2	25	networks	network	NOUN
ejpam-454	2	26	without	without	ADP
ejpam-454	2	27	lipschitz	lipschitz	NOUN
ejpam-454	2	28	neuron	neuron	NOUN
ejpam-454	2	29	activations	activation	NOUN
ejpam-454	2	30	ailong	ailong	ADP
ejpam-454	2	31	wu1	wu1	PROPN
ejpam-454	2	32	,	,	PUNCT
ejpam-454	2	33	jine	jine	PROPN
ejpam-454	2	34	zhang2	zhang2	PROPN
ejpam-454	2	35	,	,	PUNCT
ejpam-454	2	36	and	and	CCONJ
ejpam-454	2	37	chaojin	chaojin	VERB
ejpam-454	2	38	fu3,∗	fu3,∗	PROPN
ejpam-454	2	39	1	1	NUM
ejpam-454	2	40	department	department	NOUN
ejpam-454	2	41	of	of	ADP
ejpam-454	2	42	control	control	PROPN
ejpam-454	2	43	science	science	NOUN
ejpam-454	2	44	and	and	CCONJ
ejpam-454	2	45	engineering	engineering	NOUN
ejpam-454	2	46	,	,	PUNCT
ejpam-454	2	47	huazhong	huazhong	PROPN
ejpam-454	2	48	university	university	PROPN
ejpam-454	2	49	of	of	ADP
ejpam-454	2	50	science	science	NOUN
ejpam-454	2	51	and	and	CCONJ
ejpam-454	2	52	technology	technology	NOUN
ejpam-454	2	53	,	,	PUNCT
ejpam-454	2	54	wuhan	wuhan	PROPN
ejpam-454	2	55	430074	430074	PROPN
ejpam-454	2	56	,	,	PUNCT
ejpam-454	2	57	china	china	PROPN
ejpam-454	2	58	2	2	NUM
ejpam-454	2	59	school	school	NOUN
ejpam-454	2	60	of	of	ADP
ejpam-454	2	61	basic	basic	ADJ
ejpam-454	2	62	science	science	NOUN
ejpam-454	2	63	,	,	PUNCT
ejpam-454	2	64	east	east	PROPN
ejpam-454	2	65	china	china	PROPN
ejpam-454	2	66	jiaotong	jiaotong	PROPN
ejpam-454	2	67	university	university	PROPN
ejpam-454	2	68	,	,	PUNCT
ejpam-454	2	69	nanchang	nanchang	PROPN
ejpam-454	2	70	330013	330013	PROPN
ejpam-454	2	71	,	,	PUNCT
ejpam-454	2	72	china	china	PROPN
ejpam-454	2	73	3	3	NUM
ejpam-454	2	74	college	college	NOUN
ejpam-454	2	75	of	of	ADP
ejpam-454	2	76	mathematics	mathematic	NOUN
ejpam-454	2	77	and	and	CCONJ
ejpam-454	2	78	statistics	statistic	NOUN
ejpam-454	2	79	,	,	PUNCT
ejpam-454	2	80	hubei	hubei	PROPN
ejpam-454	2	81	normal	normal	ADJ
ejpam-454	2	82	university	university	NOUN
ejpam-454	2	83	,	,	PUNCT
ejpam-454	2	84	huangshi	huangshi	NOUN
ejpam-454	2	85	435002	435002	NUM
ejpam-454	2	86	,	,	PUNCT
ejpam-454	2	87	china	china	PROPN
ejpam-454	2	88	abstract	abstract	NOUN
ejpam-454	2	89	.	.	PUNCT
ejpam-454	3	1	in	in	ADP
ejpam-454	3	2	this	this	DET
ejpam-454	3	3	paper	paper	NOUN
ejpam-454	3	4	,	,	PUNCT
ejpam-454	3	5	based	base	VERB
ejpam-454	3	6	on	on	ADP
ejpam-454	3	7	the	the	DET
ejpam-454	3	8	homeomorphism	homeomorphism	PROPN
ejpam-454	3	9	theory	theory	NOUN
ejpam-454	3	10	and	and	CCONJ
ejpam-454	3	11	lyapunov	lyapunov	ADJ
ejpam-454	3	12	functional	functional	ADJ
ejpam-454	3	13	method	method	NOUN
ejpam-454	3	14	,	,	PUNCT
ejpam-454	3	15	we	we	PRON
ejpam-454	3	16	investigate	investigate	VERB
ejpam-454	3	17	global	global	ADJ
ejpam-454	3	18	asymptotical	asymptotical	ADJ
ejpam-454	3	19	stability	stability	NOUN
ejpam-454	3	20	for	for	ADP
ejpam-454	3	21	a	a	DET
ejpam-454	3	22	novel	novel	ADJ
ejpam-454	3	23	class	class	NOUN
ejpam-454	3	24	of	of	ADP
ejpam-454	3	25	delayed	delay	VERB
ejpam-454	3	26	impulsive	impulsive	ADJ
ejpam-454	3	27	neural	neural	ADJ
ejpam-454	3	28	networks	network	NOUN
ejpam-454	3	29	without	without	ADP
ejpam-454	3	30	lipschitz	lipschitz	NOUN
ejpam-454	3	31	neuron	neuron	NOUN
ejpam-454	3	32	activations	activation	NOUN
ejpam-454	3	33	.	.	PUNCT
ejpam-454	4	1	some	some	DET
ejpam-454	4	2	sufficient	sufficient	ADJ
ejpam-454	4	3	conditions	condition	NOUN
ejpam-454	4	4	are	be	AUX
ejpam-454	4	5	derived	derive	VERB
ejpam-454	4	6	which	which	PRON
ejpam-454	4	7	ensure	ensure	VERB
ejpam-454	4	8	the	the	DET
ejpam-454	4	9	existence	existence	NOUN
ejpam-454	4	10	,	,	PUNCT
ejpam-454	4	11	uniqueness	uniqueness	NOUN
ejpam-454	4	12	,	,	PUNCT
ejpam-454	4	13	and	and	CCONJ
ejpam-454	4	14	global	global	ADJ
ejpam-454	4	15	asymptotical	asymptotical	ADJ
ejpam-454	4	16	stability	stability	NOUN
ejpam-454	4	17	of	of	ADP
ejpam-454	4	18	the	the	DET
ejpam-454	4	19	equilibrium	equilibrium	NOUN
ejpam-454	4	20	point	point	NOUN
ejpam-454	4	21	of	of	ADP
ejpam-454	4	22	neural	neural	ADJ
ejpam-454	4	23	networks	network	NOUN
ejpam-454	4	24	.	.	PUNCT
ejpam-454	5	1	finally	finally	ADV
ejpam-454	5	2	,	,	PUNCT
ejpam-454	5	3	a	a	DET
ejpam-454	5	4	numerical	numerical	ADJ
ejpam-454	5	5	example	example	NOUN
ejpam-454	5	6	is	be	AUX
ejpam-454	5	7	given	give	VERB
ejpam-454	5	8	to	to	PART
ejpam-454	5	9	demonstrate	demonstrate	VERB
ejpam-454	5	10	the	the	DET
ejpam-454	5	11	improvements	improvement	NOUN
ejpam-454	5	12	of	of	ADP
ejpam-454	5	13	the	the	DET
ejpam-454	5	14	paper	paper	NOUN
ejpam-454	5	15	.	.	PUNCT
ejpam-454	6	1	2000	2000	NUM
ejpam-454	6	2	mathematics	mathematic	NOUN
ejpam-454	6	3	subject	subject	NOUN
ejpam-454	6	4	classifications	classification	NOUN
ejpam-454	6	5	:	:	PUNCT
ejpam-454	6	6	37b25	37b25	NUM
ejpam-454	6	7	;	;	PUNCT
ejpam-454	6	8	92b20	92b20	NUM
ejpam-454	6	9	;	;	PUNCT
ejpam-454	6	10	34d23	34d23	NUM
ejpam-454	6	11	key	key	ADJ
ejpam-454	6	12	words	word	NOUN
ejpam-454	6	13	and	and	CCONJ
ejpam-454	6	14	phrases	phrase	NOUN
ejpam-454	6	15	:	:	PUNCT
ejpam-454	6	16	neural	neural	ADJ
ejpam-454	6	17	networks	network	NOUN
ejpam-454	6	18	,	,	PUNCT
ejpam-454	6	19	global	global	ADJ
ejpam-454	6	20	asymptotical	asymptotical	ADJ
ejpam-454	6	21	stability	stability	NOUN
ejpam-454	6	22	,	,	PUNCT
ejpam-454	6	23	impulses	impulse	NOUN
ejpam-454	6	24	.	.	PUNCT
ejpam-454	7	1	1	1	X
ejpam-454	7	2	.	.	X
ejpam-454	7	3	introduction	introduction	NOUN
ejpam-454	7	4	in	in	ADP
ejpam-454	7	5	the	the	DET
ejpam-454	7	6	design	design	NOUN
ejpam-454	7	7	of	of	ADP
ejpam-454	7	8	neural	neural	ADJ
ejpam-454	7	9	networks	network	NOUN
ejpam-454	7	10	,	,	PUNCT
ejpam-454	7	11	the	the	DET
ejpam-454	7	12	model	model	NOUN
ejpam-454	7	13	of	of	ADP
ejpam-454	7	14	neural	neural	ADJ
ejpam-454	7	15	networks	network	NOUN
ejpam-454	7	16	is	be	AUX
ejpam-454	7	17	descried	descry	VERB
ejpam-454	7	18	by	by	ADP
ejpam-454	7	19	the	the	DET
ejpam-454	7	20	system	system	NOUN
ejpam-454	7	21	of	of	ADP
ejpam-454	7	22	nonlinear	nonlinear	ADJ
ejpam-454	7	23	ordinary	ordinary	ADJ
ejpam-454	7	24	differential	differential	ADJ
ejpam-454	7	25	equations	equation	NOUN
ejpam-454	7	26	or	or	CCONJ
ejpam-454	7	27	the	the	DET
ejpam-454	7	28	system	system	NOUN
ejpam-454	7	29	of	of	ADP
ejpam-454	7	30	nonlinear	nonlinear	ADJ
ejpam-454	7	31	functional	functional	ADJ
ejpam-454	7	32	differential	differential	ADJ
ejpam-454	7	33	equations	equation	NOUN
ejpam-454	7	34	.	.	PUNCT
ejpam-454	8	1	in	in	ADP
ejpam-454	8	2	generality	generality	NOUN
ejpam-454	8	3	,	,	PUNCT
ejpam-454	8	4	these	these	DET
ejpam-454	8	5	nonlinear	nonlinear	ADJ
ejpam-454	8	6	systems	system	NOUN
ejpam-454	8	7	possibly	possibly	ADV
ejpam-454	8	8	show	show	VERB
ejpam-454	8	9	complex	complex	ADJ
ejpam-454	8	10	dynamic	dynamic	ADJ
ejpam-454	8	11	behaviors	behavior	NOUN
ejpam-454	8	12	,	,	PUNCT
ejpam-454	8	13	such	such	ADJ
ejpam-454	8	14	as	as	ADP
ejpam-454	8	15	,	,	PUNCT
ejpam-454	8	16	periodic	periodic	ADJ
ejpam-454	8	17	oscillatory	oscillatory	ADJ
ejpam-454	8	18	,	,	PUNCT
ejpam-454	8	19	bifurcation	bifurcation	NOUN
ejpam-454	8	20	,	,	PUNCT
ejpam-454	8	21	chaos	chaos	NOUN
ejpam-454	8	22	,	,	PUNCT
ejpam-454	8	23	etc	etc	X
ejpam-454	8	24	.	.	X
ejpam-454	9	1	however	however	ADV
ejpam-454	9	2	,	,	PUNCT
ejpam-454	9	3	in	in	ADP
ejpam-454	9	4	practical	practical	ADJ
ejpam-454	9	5	applications	application	NOUN
ejpam-454	9	6	,	,	PUNCT
ejpam-454	9	7	especially	especially	ADV
ejpam-454	9	8	for	for	ADP
ejpam-454	9	9	solving	solve	VERB
ejpam-454	9	10	linear	linear	ADJ
ejpam-454	9	11	and	and	CCONJ
ejpam-454	9	12	quadratic	quadratic	ADJ
ejpam-454	9	13	programming	programming	NOUN
ejpam-454	9	14	problems	problem	NOUN
ejpam-454	9	15	in	in	ADP
ejpam-454	9	16	real	real	ADJ
ejpam-454	9	17	time	time	NOUN
ejpam-454	9	18	,	,	PUNCT
ejpam-454	9	19	it	it	PRON
ejpam-454	9	20	requires	require	VERB
ejpam-454	9	21	that	that	SCONJ
ejpam-454	9	22	networks	network	NOUN
ejpam-454	9	23	have	have	VERB
ejpam-454	9	24	good	good	ADJ
ejpam-454	9	25	convergent	convergent	NOUN
ejpam-454	9	26	property	property	NOUN
ejpam-454	9	27	.	.	PUNCT
ejpam-454	10	1	under	under	ADP
ejpam-454	10	2	these	these	DET
ejpam-454	10	3	good	good	ADJ
ejpam-454	10	4	convergent	convergent	NOUN
ejpam-454	10	5	property	property	NOUN
ejpam-454	10	6	,	,	PUNCT
ejpam-454	10	7	the	the	DET
ejpam-454	10	8	validity	validity	NOUN
ejpam-454	10	9	can	can	AUX
ejpam-454	10	10	be	be	AUX
ejpam-454	10	11	guaranteed	guarantee	VERB
ejpam-454	10	12	during	during	ADP
ejpam-454	10	13	numeral	numeral	ADJ
ejpam-454	10	14	solving	solving	NOUN
ejpam-454	10	15	.	.	PUNCT
ejpam-454	11	1	due	due	ADP
ejpam-454	11	2	to	to	ADP
ejpam-454	11	3	these	these	PRON
ejpam-454	11	4	,	,	PUNCT
ejpam-454	11	5	stability	stability	NOUN
ejpam-454	11	6	analysis	analysis	NOUN
ejpam-454	11	7	for	for	ADP
ejpam-454	11	8	neural	neural	ADJ
ejpam-454	11	9	networks	network	NOUN
ejpam-454	11	10	with	with	ADP
ejpam-454	11	11	or	or	CCONJ
ejpam-454	11	12	without	without	ADP
ejpam-454	11	13	time	time	NOUN
ejpam-454	11	14	delays	delay	NOUN
ejpam-454	11	15	has	have	AUX
ejpam-454	11	16	received	receive	VERB
ejpam-454	11	17	a	a	DET
ejpam-454	11	18	great	great	ADJ
ejpam-454	11	19	of	of	ADP
ejpam-454	11	20	attention	attention	NOUN
ejpam-454	11	21	(	(	PUNCT
ejpam-454	11	22	see	see	VERB
ejpam-454	11	23	[	[	X
ejpam-454	11	24	1−	1−	NUM
ejpam-454	11	25	10	10	NUM
ejpam-454	11	26	]	]	PUNCT
ejpam-454	11	27	)	)	PUNCT
ejpam-454	11	28	.	.	PUNCT
ejpam-454	12	1	recently	recently	ADV
ejpam-454	12	2	,	,	PUNCT
ejpam-454	12	3	impulsive	impulsive	ADJ
ejpam-454	12	4	neural	neural	ADJ
ejpam-454	12	5	networks	network	NOUN
ejpam-454	12	6	have	have	AUX
ejpam-454	12	7	been	be	AUX
ejpam-454	12	8	extensively	extensively	ADV
ejpam-454	12	9	studied	study	VERB
ejpam-454	12	10	in	in	ADP
ejpam-454	12	11	both	both	DET
ejpam-454	12	12	theory	theory	NOUN
ejpam-454	12	13	and	and	CCONJ
ejpam-454	12	14	applications	application	NOUN
ejpam-454	12	15	(	(	PUNCT
ejpam-454	12	16	see	see	VERB
ejpam-454	12	17	[	[	X
ejpam-454	12	18	5−10	5−10	NUM
ejpam-454	12	19	]	]	X
ejpam-454	12	20	)	)	PUNCT
ejpam-454	12	21	.	.	PUNCT
ejpam-454	13	1	however	however	ADV
ejpam-454	13	2	,	,	PUNCT
ejpam-454	13	3	in	in	ADP
ejpam-454	13	4	the	the	DET
ejpam-454	13	5	existing	exist	VERB
ejpam-454	13	6	literatures	literature	NOUN
ejpam-454	13	7	,	,	PUNCT
ejpam-454	13	8	almost	almost	ADV
ejpam-454	13	9	all	all	PRON
ejpam-454	13	10	results	result	NOUN
ejpam-454	13	11	on	on	ADP
ejpam-454	13	12	the	the	DET
ejpam-454	13	13	stability	stability	NOUN
ejpam-454	13	14	of	of	ADP
ejpam-454	13	15	neural	neural	ADJ
ejpam-454	13	16	networks	network	NOUN
ejpam-454	13	17	are	be	AUX
ejpam-454	13	18	obtained	obtain	VERB
ejpam-454	13	19	under	under	ADP
ejpam-454	13	20	lipschitz	lipschitz	NOUN
ejpam-454	13	21	neuron	neuron	NOUN
ejpam-454	13	22	activations	activation	NOUN
ejpam-454	13	23	[	[	X
ejpam-454	13	24	1−6,9,10	1−6,9,10	NUM
ejpam-454	13	25	]	]	PUNCT
ejpam-454	13	26	.	.	PUNCT
ejpam-454	14	1	when	when	SCONJ
ejpam-454	14	2	neuron	neuron	NOUN
ejpam-454	14	3	activation	activation	NOUN
ejpam-454	14	4	functions	function	NOUN
ejpam-454	14	5	do	do	AUX
ejpam-454	14	6	not	not	PART
ejpam-454	14	7	satisfy	satisfy	VERB
ejpam-454	14	8	lipschitz	lipschitz	NOUN
ejpam-454	14	9	conditions	condition	NOUN
ejpam-454	14	10	,	,	PUNCT
ejpam-454	14	11	people	people	NOUN
ejpam-454	14	12	want	want	VERB
ejpam-454	14	13	to	to	PART
ejpam-454	14	14	know	know	VERB
ejpam-454	14	15	whether	whether	SCONJ
ejpam-454	14	16	the	the	DET
ejpam-454	14	17	neural	neural	ADJ
ejpam-454	14	18	networks	network	NOUN
ejpam-454	14	19	is	be	AUX
ejpam-454	14	20	stable	stable	ADJ
ejpam-454	14	21	.	.	PUNCT
ejpam-454	15	1	in	in	ADP
ejpam-454	15	2	practical	practical	ADJ
ejpam-454	15	3	engineering	engineering	NOUN
ejpam-454	15	4	applications	application	NOUN
ejpam-454	15	5	,	,	PUNCT
ejpam-454	15	6	people	people	NOUN
ejpam-454	15	7	also	also	ADV
ejpam-454	15	8	need	need	VERB
ejpam-454	15	9	to	to	PART
ejpam-454	15	10	present	present	VERB
ejpam-454	15	11	new	new	ADJ
ejpam-454	15	12	neural	neural	ADJ
ejpam-454	15	13	∗corresponding	∗corresponde	VERB
ejpam-454	15	14	author	author	NOUN
ejpam-454	15	15	.	.	PUNCT
ejpam-454	16	1	email	email	NOUN
ejpam-454	16	2	addresses	address	NOUN
ejpam-454	16	3	:	:	PUNCT
ejpam-454	16	4	alwu83	alwu83	NOUN
ejpam-454	16	5	�	�	NOUN
ejpam-454	16	6	gmail	gmail	NOUN
ejpam-454	16	7	.	.	PUNCT
ejpam-454	17	1	om	om	PROPN
ejpam-454	17	2	(	(	PUNCT
ejpam-454	17	3	a.	a.	PROPN
ejpam-454	17	4	wu	wu	PROPN
ejpam-454	17	5	)	)	PUNCT
ejpam-454	17	6	,	,	PUNCT
ejpam-454	17	7	jezhang	jezhang	PROPN
ejpam-454	17	8	�	�	PROPN
ejpam-454	17	9	126	126	NUM
ejpam-454	17	10	.	.	PUNCT
ejpam-454	18	1	om	om	PROPN
ejpam-454	18	2	(	(	PUNCT
ejpam-454	18	3	j.	j.	PROPN
ejpam-454	18	4	zhang	zhang	PROPN
ejpam-454	18	5	)	)	PUNCT
ejpam-454	18	6	,	,	PUNCT
ejpam-454	18	7	haojinfu	haojinfu	PROPN
ejpam-454	18	8	�	�	PROPN
ejpam-454	18	9	126	126	NUM
ejpam-454	18	10	.	.	PUNCT
ejpam-454	19	1	om	om	PROPN
ejpam-454	19	2	(	(	PUNCT
ejpam-454	19	3	c.	c.	PROPN
ejpam-454	19	4	fu	fu	PROPN
ejpam-454	19	5	)	)	PUNCT
ejpam-454	19	6	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-454	20	1	806	806	NUM
ejpam-454	20	2	c	c	X
ejpam-454	20	3	©	©	PROPN
ejpam-454	20	4	2010	2010	NUM
ejpam-454	20	5	ejpam	ejpam	NOUN
ejpam-454	20	6	all	all	DET
ejpam-454	20	7	rights	right	NOUN
ejpam-454	20	8	reserved	reserve	VERB
ejpam-454	20	9	.	.	PUNCT
ejpam-454	21	1	a.	a.	PROPN
ejpam-454	21	2	wu	wu	PROPN
ejpam-454	21	3	,	,	PUNCT
ejpam-454	21	4	j.	j.	PROPN
ejpam-454	21	5	zhang	zhang	PROPN
ejpam-454	21	6	,	,	PUNCT
ejpam-454	21	7	c.	c.	PROPN
ejpam-454	21	8	fu	fu	PROPN
ejpam-454	21	9	/	/	SYM
ejpam-454	21	10	eur	eur	PROPN
ejpam-454	21	11	.	.	PUNCT
ejpam-454	22	1	j.	j.	PROPN
ejpam-454	22	2	pure	pure	PROPN
ejpam-454	22	3	appl	appl	PROPN
ejpam-454	22	4	.	.	PROPN
ejpam-454	22	5	math	math	PROPN
ejpam-454	22	6	,	,	PUNCT
ejpam-454	22	7	3	3	NUM
ejpam-454	22	8	(	(	PUNCT
ejpam-454	22	9	2010	2010	NUM
ejpam-454	22	10	)	)	PUNCT
ejpam-454	22	11	,	,	PUNCT
ejpam-454	22	12	806	806	NUM
ejpam-454	22	13	-	-	SYM
ejpam-454	22	14	818	818	NUM
ejpam-454	22	15	807	807	NUM
ejpam-454	22	16	networks	network	NOUN
ejpam-454	22	17	.	.	PUNCT
ejpam-454	23	1	therefore	therefore	ADV
ejpam-454	23	2	,	,	PUNCT
ejpam-454	23	3	developing	develop	VERB
ejpam-454	23	4	a	a	DET
ejpam-454	23	5	new	new	ADJ
ejpam-454	23	6	class	class	NOUN
ejpam-454	23	7	of	of	ADP
ejpam-454	23	8	neural	neural	ADJ
ejpam-454	23	9	networks	network	NOUN
ejpam-454	23	10	without	without	ADP
ejpam-454	23	11	lipschitz	lipschitz	NOUN
ejpam-454	23	12	neuron	neuron	NOUN
ejpam-454	23	13	activation	activation	NOUN
ejpam-454	23	14	functions	function	NOUN
ejpam-454	23	15	and	and	CCONJ
ejpam-454	23	16	giving	give	VERB
ejpam-454	23	17	the	the	DET
ejpam-454	23	18	conditions	condition	NOUN
ejpam-454	23	19	of	of	ADP
ejpam-454	23	20	the	the	DET
ejpam-454	23	21	stability	stability	NOUN
ejpam-454	23	22	of	of	ADP
ejpam-454	23	23	new	new	ADJ
ejpam-454	23	24	neural	neural	ADJ
ejpam-454	23	25	networks	network	NOUN
ejpam-454	23	26	are	be	AUX
ejpam-454	23	27	very	very	ADV
ejpam-454	23	28	interesting	interesting	ADJ
ejpam-454	23	29	and	and	CCONJ
ejpam-454	23	30	valuable	valuable	ADJ
ejpam-454	23	31	.	.	PUNCT
ejpam-454	24	1	in	in	ADP
ejpam-454	24	2	this	this	DET
ejpam-454	24	3	paper	paper	NOUN
ejpam-454	24	4	,	,	PUNCT
ejpam-454	24	5	we	we	PRON
ejpam-454	24	6	investigate	investigate	VERB
ejpam-454	24	7	a	a	DET
ejpam-454	24	8	general	general	ADJ
ejpam-454	24	9	class	class	NOUN
ejpam-454	24	10	of	of	ADP
ejpam-454	24	11	delayed	delay	VERB
ejpam-454	24	12	neural	neural	ADJ
ejpam-454	24	13	networks	network	NOUN
ejpam-454	24	14	with	with	ADP
ejpam-454	24	15	impulses	impulse	NOUN
ejpam-454	24	16	where	where	SCONJ
ejpam-454	24	17	the	the	DET
ejpam-454	24	18	neuron	neuron	NOUN
ejpam-454	24	19	activations	activation	NOUN
ejpam-454	24	20	do	do	AUX
ejpam-454	24	21	not	not	PART
ejpam-454	24	22	satisfy	satisfy	VERB
ejpam-454	24	23	lipschitz	lipschitz	NOUN
ejpam-454	24	24	conditions	condition	NOUN
ejpam-454	24	25	.	.	PUNCT
ejpam-454	25	1	to	to	ADP
ejpam-454	25	2	the	the	DET
ejpam-454	25	3	best	good	ADJ
ejpam-454	25	4	of	of	ADP
ejpam-454	25	5	authors	author	NOUN
ejpam-454	25	6	’	'	PUNCT
ejpam-454	25	7	knowledge	knowledge	NOUN
ejpam-454	25	8	,	,	PUNCT
ejpam-454	25	9	this	this	PRON
ejpam-454	25	10	is	be	AUX
ejpam-454	25	11	the	the	DET
ejpam-454	25	12	first	first	ADJ
ejpam-454	25	13	time	time	NOUN
ejpam-454	25	14	to	to	PART
ejpam-454	25	15	study	study	VERB
ejpam-454	25	16	the	the	DET
ejpam-454	25	17	existence	existence	NOUN
ejpam-454	25	18	,	,	PUNCT
ejpam-454	25	19	uniqueness	uniqueness	NOUN
ejpam-454	25	20	,	,	PUNCT
ejpam-454	25	21	and	and	CCONJ
ejpam-454	25	22	global	global	ADJ
ejpam-454	25	23	asymptotical	asymptotical	ADJ
ejpam-454	25	24	stability	stability	NOUN
ejpam-454	25	25	of	of	ADP
ejpam-454	25	26	equilibrium	equilibrium	NOUN
ejpam-454	25	27	point	point	NOUN
ejpam-454	25	28	for	for	ADP
ejpam-454	25	29	the	the	DET
ejpam-454	25	30	neural	neural	ADJ
ejpam-454	25	31	networks	network	NOUN
ejpam-454	25	32	developed	develop	VERB
ejpam-454	25	33	by	by	ADP
ejpam-454	25	34	us	we	PRON
ejpam-454	25	35	.	.	PUNCT
ejpam-454	26	1	consider	consider	VERB
ejpam-454	26	2	a	a	DET
ejpam-454	26	3	general	general	ADJ
ejpam-454	26	4	delayed	delay	VERB
ejpam-454	26	5	neural	neural	ADJ
ejpam-454	26	6	networks	network	NOUN
ejpam-454	26	7	with	with	ADP
ejpam-454	26	8	impulses	impulse	NOUN
ejpam-454	26	9	:	:	PUNCT
ejpam-454	26	10			PROPN
ejpam-454	26	11			PROPN
ejpam-454	26	12			NOUN
ejpam-454	26	13	ẋ	ẋ	PROPN
ejpam-454	26	14	i(t	i(t	PROPN
ejpam-454	26	15	)	)	PUNCT
ejpam-454	26	16	=	=	SYM
ejpam-454	27	1	−di	−di	NOUN
ejpam-454	27	2	x	x	SYM
ejpam-454	27	3	i(t	i(t	PROPN
ejpam-454	27	4	)	)	PUNCT
ejpam-454	27	5	+	+	CCONJ
ejpam-454	28	1	n	n	X
ejpam-454	28	2	∑	∑	PUNCT
ejpam-454	28	3	j=1	j=1	PROPN
ejpam-454	28	4	ai	ai	VERB
ejpam-454	28	5	j	j	PROPN
ejpam-454	28	6	g	g	PROPN
ejpam-454	28	7	j(x	j(x	PROPN
ejpam-454	28	8	j(t	j(t	PROPN
ejpam-454	28	9	)	)	PUNCT
ejpam-454	28	10	)	)	PUNCT
ejpam-454	29	1	+	+	CCONJ
ejpam-454	30	1	n	n	X
ejpam-454	30	2	∑	∑	ADP
ejpam-454	30	3	j=1	j=1	ADJ
ejpam-454	30	4	bi	bi	PROPN
ejpam-454	30	5	j	j	PROPN
ejpam-454	30	6	g	g	PROPN
ejpam-454	30	7	j(x	j(x	PROPN
ejpam-454	30	8	j(t	j(t	PROPN
ejpam-454	30	9	−τi	−τi	PROPN
ejpam-454	30	10	j	j	PROPN
ejpam-454	30	11	)	)	PUNCT
ejpam-454	30	12	)	)	PUNCT
ejpam-454	31	1	+	+	CCONJ
ejpam-454	31	2	ii	ii	PROPN
ejpam-454	31	3	,	,	PUNCT
ejpam-454	31	4	t	t	PROPN
ejpam-454	31	5	6=	6=	PROPN
ejpam-454	31	6	tk	tk	PROPN
ejpam-454	31	7	,	,	PUNCT
ejpam-454	31	8	△	△	X
ejpam-454	31	9	x	x	SYM
ejpam-454	31	10	i(tk	i(tk	NOUN
ejpam-454	31	11	)	)	PUNCT
ejpam-454	31	12	=	=	SYM
ejpam-454	31	13	x	x	PUNCT
ejpam-454	31	14	i(t	i(t	PROPN
ejpam-454	31	15	+	+	CCONJ
ejpam-454	31	16	k	k	NOUN
ejpam-454	31	17	)	)	PUNCT
ejpam-454	32	1	−	−	PROPN
ejpam-454	32	2	x	x	PUNCT
ejpam-454	32	3	i(t	i(t	PROPN
ejpam-454	32	4	−	−	PROPN
ejpam-454	32	5	k	k	NOUN
ejpam-454	32	6	)	)	PUNCT
ejpam-454	33	1	=	=	PUNCT
ejpam-454	33	2	jik(x	jik(x	PROPN
ejpam-454	33	3	i(tk	i(tk	NOUN
ejpam-454	33	4	)	)	PUNCT
ejpam-454	33	5	)	)	PUNCT
ejpam-454	33	6	,	,	PUNCT
ejpam-454	33	7	k	k	X
ejpam-454	33	8	=	=	SYM
ejpam-454	33	9	1,2	1,2	NUM
ejpam-454	33	10	,	,	PUNCT
ejpam-454	33	11	·	·	PUNCT
ejpam-454	33	12	·	·	PUNCT
ejpam-454	33	13	·	·	PUNCT
ejpam-454	33	14	,	,	PUNCT
ejpam-454	33	15	i	i	PRON
ejpam-454	33	16	=	=	NOUN
ejpam-454	33	17	1	1	NUM
ejpam-454	33	18	,	,	PUNCT
ejpam-454	33	19	·	·	PUNCT
ejpam-454	33	20	·	·	PUNCT
ejpam-454	33	21	·	·	PUNCT
ejpam-454	33	22	,	,	PUNCT
ejpam-454	33	23	n	n	CCONJ
ejpam-454	33	24	,	,	PUNCT
ejpam-454	33	25	(	(	PUNCT
ejpam-454	33	26	1	1	X
ejpam-454	33	27	)	)	PUNCT
ejpam-454	33	28	where	where	SCONJ
ejpam-454	33	29	n	n	PRON
ejpam-454	33	30	denotes	denote	VERB
ejpam-454	33	31	the	the	DET
ejpam-454	33	32	number	number	NOUN
ejpam-454	33	33	of	of	ADP
ejpam-454	33	34	the	the	DET
ejpam-454	33	35	neurons	neuron	NOUN
ejpam-454	33	36	;	;	PUNCT
ejpam-454	33	37	x	x	SYM
ejpam-454	33	38	i(t	i(t	NOUN
ejpam-454	33	39	)	)	PUNCT
ejpam-454	33	40	is	be	AUX
ejpam-454	33	41	the	the	DET
ejpam-454	33	42	state	state	NOUN
ejpam-454	33	43	of	of	ADP
ejpam-454	33	44	the	the	DET
ejpam-454	33	45	ith	ith	PROPN
ejpam-454	33	46	neuron	neuron	NOUN
ejpam-454	33	47	at	at	ADP
ejpam-454	33	48	time	time	NOUN
ejpam-454	33	49	t	t	PROPN
ejpam-454	33	50	;	;	PUNCT
ejpam-454	33	51	di	di	X
ejpam-454	33	52	>	>	X
ejpam-454	33	53	0	0	NUM
ejpam-454	33	54	is	be	AUX
ejpam-454	33	55	the	the	DET
ejpam-454	33	56	neural	neural	ADJ
ejpam-454	33	57	self	self	NOUN
ejpam-454	33	58	-	-	PUNCT
ejpam-454	33	59	inhibitions	inhibition	NOUN
ejpam-454	33	60	of	of	ADP
ejpam-454	33	61	the	the	DET
ejpam-454	33	62	ith	ith	PROPN
ejpam-454	33	63	neuron	neuron	NOUN
ejpam-454	33	64	;	;	PUNCT
ejpam-454	33	65	g	g	PROPN
ejpam-454	33	66	j	j	PROPN
ejpam-454	33	67	(	(	PUNCT
ejpam-454	33	68	·	·	PUNCT
ejpam-454	33	69	)	)	PUNCT
ejpam-454	33	70	represents	represent	VERB
ejpam-454	33	71	the	the	DET
ejpam-454	33	72	input	input	NOUN
ejpam-454	33	73	-	-	PUNCT
ejpam-454	33	74	output	output	NOUN
ejpam-454	33	75	activation	activation	NOUN
ejpam-454	33	76	of	of	ADP
ejpam-454	33	77	the	the	DET
ejpam-454	33	78	jth	jth	PROPN
ejpam-454	33	79	neuron	neuron	PROPN
ejpam-454	33	80	,	,	PUNCT
ejpam-454	33	81	g	g	PROPN
ejpam-454	33	82	j	j	PROPN
ejpam-454	33	83	(	(	PUNCT
ejpam-454	33	84	·	·	PUNCT
ejpam-454	33	85	)	)	PUNCT
ejpam-454	33	86	is	be	AUX
ejpam-454	33	87	continuous	continuous	ADJ
ejpam-454	33	88	and	and	CCONJ
ejpam-454	33	89	monotone	monotone	ADJ
ejpam-454	33	90	nondecreasing	nondecreasing	NOUN
ejpam-454	33	91	;	;	PUNCT
ejpam-454	33	92	ai	ai	AUX
ejpam-454	33	93	j	j	PROPN
ejpam-454	33	94	and	and	CCONJ
ejpam-454	33	95	bi	bi	PROPN
ejpam-454	33	96	j	j	PROPN
ejpam-454	33	97	denote	denote	VERB
ejpam-454	33	98	the	the	DET
ejpam-454	33	99	connection	connection	NOUN
ejpam-454	33	100	of	of	ADP
ejpam-454	33	101	the	the	DET
ejpam-454	33	102	jth	jth	PROPN
ejpam-454	33	103	neuron	neuron	PROPN
ejpam-454	33	104	to	to	ADP
ejpam-454	33	105	the	the	DET
ejpam-454	33	106	ith	ith	PROPN
ejpam-454	33	107	neuron	neuron	NOUN
ejpam-454	33	108	at	at	ADP
ejpam-454	33	109	time	time	NOUN
ejpam-454	33	110	t	t	PROPN
ejpam-454	33	111	and	and	CCONJ
ejpam-454	33	112	t	t	PROPN
ejpam-454	33	113	−τi	−τi	PROPN
ejpam-454	33	114	j	j	PROPN
ejpam-454	33	115	,	,	PUNCT
ejpam-454	33	116	respectively	respectively	ADV
ejpam-454	33	117	;	;	PUNCT
ejpam-454	33	118	ii	ii	X
ejpam-454	33	119	is	be	AUX
ejpam-454	33	120	the	the	DET
ejpam-454	33	121	external	external	ADJ
ejpam-454	33	122	bias	bias	NOUN
ejpam-454	33	123	on	on	ADP
ejpam-454	33	124	the	the	DET
ejpam-454	33	125	ith	ith	PROPN
ejpam-454	33	126	neuron	neuron	NOUN
ejpam-454	33	127	;	;	PUNCT
ejpam-454	33	128	0	0	NUM
ejpam-454	33	129	≤	≤	NUM
ejpam-454	33	130	τi	τi	VERB
ejpam-454	33	131	j	j	PROPN
ejpam-454	33	132	≤	≤	PROPN
ejpam-454	33	133	τ	τ	PROPN
ejpam-454	33	134	,	,	PUNCT
ejpam-454	33	135	τ	τ	PROPN
ejpam-454	33	136	is	be	AUX
ejpam-454	33	137	a	a	DET
ejpam-454	33	138	positive	positive	ADJ
ejpam-454	33	139	constant	constant	NOUN
ejpam-454	33	140	;	;	PUNCT
ejpam-454	33	141	jik	jik	PROPN
ejpam-454	33	142	shows	show	VERB
ejpam-454	33	143	impulsive	impulsive	ADJ
ejpam-454	33	144	perturbation	perturbation	NOUN
ejpam-454	33	145	of	of	ADP
ejpam-454	33	146	the	the	DET
ejpam-454	33	147	ith	ith	PROPN
ejpam-454	33	148	neuron	neuron	NOUN
ejpam-454	33	149	at	at	ADP
ejpam-454	33	150	time	time	NOUN
ejpam-454	33	151	tk	tk	PROPN
ejpam-454	33	152	;	;	PUNCT
ejpam-454	33	153	△	△	X
ejpam-454	33	154	x	x	SYM
ejpam-454	33	155	i(tk	i(tk	NOUN
ejpam-454	33	156	)	)	PUNCT
ejpam-454	33	157	=	=	SYM
ejpam-454	33	158	x	x	PUNCT
ejpam-454	33	159	i(t	i(t	PROPN
ejpam-454	33	160	+	+	CCONJ
ejpam-454	33	161	k	k	NOUN
ejpam-454	33	162	)	)	PUNCT
ejpam-454	33	163	−	−	PROPN
ejpam-454	33	164	x	x	PUNCT
ejpam-454	33	165	i(t	i(t	PROPN
ejpam-454	33	166	−	−	PROPN
ejpam-454	33	167	k	k	PROPN
ejpam-454	33	168	)	)	PUNCT
ejpam-454	33	169	,	,	PUNCT
ejpam-454	33	170	k	k	X
ejpam-454	33	171	=	=	SYM
ejpam-454	33	172	1,2	1,2	NUM
ejpam-454	33	173	,	,	PUNCT
ejpam-454	33	174	·	·	PUNCT
ejpam-454	33	175	·	·	PUNCT
ejpam-454	33	176	·	·	PUNCT
ejpam-454	33	177	,	,	PUNCT
ejpam-454	33	178	are	be	AUX
ejpam-454	33	179	the	the	DET
ejpam-454	33	180	impulses	impulse	NOUN
ejpam-454	33	181	at	at	ADP
ejpam-454	33	182	moments	moment	NOUN
ejpam-454	33	183	tk	tk	PROPN
ejpam-454	33	184	,	,	PUNCT
ejpam-454	33	185	and	and	CCONJ
ejpam-454	33	186	0	0	NUM
ejpam-454	33	187	<	<	X
ejpam-454	33	188	t1	t1	NOUN
ejpam-454	33	189	<	<	X
ejpam-454	33	190	t2	t2	PROPN
ejpam-454	33	191	<	<	X
ejpam-454	33	192	·	·	PUNCT
ejpam-454	33	193	·	·	PUNCT
ejpam-454	33	194	·	·	PUNCT
ejpam-454	33	195	is	be	AUX
ejpam-454	33	196	a	a	DET
ejpam-454	33	197	strictly	strictly	ADV
ejpam-454	33	198	increasing	increase	VERB
ejpam-454	33	199	sequence	sequence	NOUN
ejpam-454	33	200	such	such	ADJ
ejpam-454	33	201	that	that	SCONJ
ejpam-454	33	202	lim	lim	PROPN
ejpam-454	33	203	k→∞	k→∞	PROPN
ejpam-454	33	204	tk	tk	PROPN
ejpam-454	34	1	=	=	NOUN
ejpam-454	34	2	∞.	∞.	PROPN
ejpam-454	34	3	the	the	DET
ejpam-454	34	4	system	system	NOUN
ejpam-454	34	5	(	(	PUNCT
ejpam-454	34	6	1	1	X
ejpam-454	34	7	)	)	PUNCT
ejpam-454	34	8	is	be	AUX
ejpam-454	34	9	supplemented	supplement	VERB
ejpam-454	34	10	with	with	ADP
ejpam-454	34	11	the	the	DET
ejpam-454	34	12	initial	initial	ADJ
ejpam-454	34	13	conditions	condition	NOUN
ejpam-454	34	14	of	of	ADP
ejpam-454	34	15	the	the	DET
ejpam-454	34	16	type	type	NOUN
ejpam-454	34	17	x(t	x(t	PROPN
ejpam-454	34	18	)	)	PUNCT
ejpam-454	34	19	=	=	SYM
ejpam-454	34	20	φ(t	φ(t	PROPN
ejpam-454	34	21	)	)	PUNCT
ejpam-454	34	22	=	=	SYM
ejpam-454	34	23	(	(	PUNCT
ejpam-454	34	24	φ1	φ1	PROPN
ejpam-454	34	25	,	,	PUNCT
ejpam-454	34	26	·	·	PUNCT
ejpam-454	34	27	·	·	PUNCT
ejpam-454	34	28	·	·	PUNCT
ejpam-454	34	29	,	,	PUNCT
ejpam-454	34	30	φn	φn	NOUN
ejpam-454	34	31	)	)	PUNCT
ejpam-454	34	32	t	t	NOUN
ejpam-454	34	33	,	,	PUNCT
ejpam-454	34	34	−τ	−τ	ADJ
ejpam-454	34	35	≤	≤	X
ejpam-454	34	36	t	t	PROPN
ejpam-454	34	37	≤	≤	NOUN
ejpam-454	34	38	0	0	NUM
ejpam-454	34	39	in	in	ADP
ejpam-454	34	40	which	which	PRON
ejpam-454	34	41	φ(t	φ(t	PROPN
ejpam-454	34	42	)	)	PUNCT
ejpam-454	34	43	∈	∈	PROPN
ejpam-454	34	44	c([−τ	c([−τ	PROPN
ejpam-454	34	45	,	,	PUNCT
ejpam-454	34	46	0	0	NUM
ejpam-454	34	47	]	]	PUNCT
ejpam-454	34	48	;	;	PUNCT
ejpam-454	34	49	rn	rn	X
ejpam-454	34	50	)	)	PUNCT
ejpam-454	34	51	is	be	AUX
ejpam-454	34	52	a	a	DET
ejpam-454	34	53	continuous	continuous	ADJ
ejpam-454	34	54	function	function	NOUN
ejpam-454	34	55	.	.	PUNCT
ejpam-454	35	1	c([−τ	c([−τ	PROPN
ejpam-454	35	2	,	,	PUNCT
ejpam-454	35	3	0	0	NUM
ejpam-454	35	4	]	]	PUNCT
ejpam-454	35	5	;	;	PUNCT
ejpam-454	35	6	rn	rn	X
ejpam-454	35	7	)	)	PUNCT
ejpam-454	35	8	is	be	AUX
ejpam-454	35	9	a	a	DET
ejpam-454	35	10	banach	banach	NOUN
ejpam-454	35	11	space	space	NOUN
ejpam-454	35	12	of	of	ADP
ejpam-454	35	13	continuous	continuous	ADJ
ejpam-454	35	14	mapping	mapping	NOUN
ejpam-454	35	15	which	which	PRON
ejpam-454	35	16	maps	map	VERB
ejpam-454	35	17	[	[	X
ejpam-454	35	18	−τ	−τ	NOUN
ejpam-454	35	19	,	,	PUNCT
ejpam-454	35	20	0	0	NUM
ejpam-454	35	21	]	]	PUNCT
ejpam-454	35	22	into	into	ADP
ejpam-454	35	23	rn	rn	PROPN
ejpam-454	35	24	with	with	ADP
ejpam-454	35	25	a	a	DET
ejpam-454	35	26	topology	topology	NOUN
ejpam-454	35	27	of	of	ADP
ejpam-454	35	28	uniform	uniform	ADJ
ejpam-454	35	29	convergence	convergence	NOUN
ejpam-454	35	30	.	.	PUNCT
ejpam-454	36	1	for	for	ADP
ejpam-454	36	2	convenience	convenience	NOUN
ejpam-454	36	3	,	,	PUNCT
ejpam-454	36	4	we	we	PRON
ejpam-454	36	5	introduce	introduce	VERB
ejpam-454	36	6	the	the	DET
ejpam-454	36	7	following	following	ADJ
ejpam-454	36	8	notations	notation	NOUN
ejpam-454	36	9	:	:	PUNCT
ejpam-454	36	10	let	let	VERB
ejpam-454	36	11	matrix	matrix	NOUN
ejpam-454	36	12	q	q	NOUN
ejpam-454	37	1	=	=	PUNCT
ejpam-454	37	2	(	(	PUNCT
ejpam-454	37	3	qi	qi	PROPN
ejpam-454	37	4	j)n×n	j)n×n	PROPN
ejpam-454	37	5	,	,	PUNCT
ejpam-454	37	6	r	r	NOUN
ejpam-454	37	7	=	=	SYM
ejpam-454	37	8	(	(	PUNCT
ejpam-454	37	9	ri	ri	PROPN
ejpam-454	37	10	j)m×n	j)m×n	PROPN
ejpam-454	37	11	,	,	PUNCT
ejpam-454	37	12	q−1	q−1	PROPN
ejpam-454	37	13	denotes	denote	VERB
ejpam-454	37	14	the	the	DET
ejpam-454	37	15	inverse	inverse	NOUN
ejpam-454	37	16	of	of	ADP
ejpam-454	37	17	q	q	ADJ
ejpam-454	37	18	,	,	PUNCT
ejpam-454	37	19	‖r‖1	‖r‖1	NOUN
ejpam-454	37	20	and	and	CCONJ
ejpam-454	37	21	‖r‖∞	‖r‖∞	PROPN
ejpam-454	37	22	represent	represent	VERB
ejpam-454	37	23	the	the	DET
ejpam-454	37	24	first	first	ADJ
ejpam-454	37	25	norm	norm	NOUN
ejpam-454	37	26	and	and	CCONJ
ejpam-454	37	27	infinity	infinity	NOUN
ejpam-454	37	28	norm	norm	NOUN
ejpam-454	37	29	of	of	ADP
ejpam-454	37	30	matrix	matrix	NOUN
ejpam-454	37	31	r	r	NOUN
ejpam-454	37	32	,	,	PUNCT
ejpam-454	37	33	respectively	respectively	ADV
ejpam-454	37	34	.	.	PUNCT
ejpam-454	38	1	that	that	PRON
ejpam-454	38	2	is	be	AUX
ejpam-454	38	3	,	,	PUNCT
ejpam-454	38	4	‖r‖1	‖r‖1	ADJ
ejpam-454	38	5	=	=	SYM
ejpam-454	38	6	max	max	PROPN
ejpam-454	38	7	1≤	1≤	X
ejpam-454	38	8	j≤n	j≤n	PROPN
ejpam-454	38	9	m	m	VERB
ejpam-454	38	10	∑	∑	PROPN
ejpam-454	38	11	i=1	i=1	PROPN
ejpam-454	38	12	�	�	PROPN
ejpam-454	38	13	�	�	PROPN
ejpam-454	38	14	ri	ri	PROPN
ejpam-454	38	15	j	j	PROPN
ejpam-454	38	16	�	�	PROPN
ejpam-454	38	17	�	�	PROPN
ejpam-454	38	18	,	,	PUNCT
ejpam-454	38	19	‖r‖∞	‖r‖∞	PROPN
ejpam-454	38	20	=	=	SYM
ejpam-454	38	21	max	max	PROPN
ejpam-454	38	22	1≤i≤m	1≤i≤m	NUM
ejpam-454	38	23	n	n	NOUN
ejpam-454	38	24	∑	∑	ADP
ejpam-454	38	25	j=1	j=1	PROPN
ejpam-454	38	26	�	�	PROPN
ejpam-454	38	27	�	�	PROPN
ejpam-454	38	28	ri	ri	PROPN
ejpam-454	38	29	j	j	PROPN
ejpam-454	38	30	�	�	PROPN
ejpam-454	38	31	�	�	PROPN
ejpam-454	38	32	.	.	PUNCT
ejpam-454	39	1	symmetric	symmetric	ADJ
ejpam-454	39	2	matrix	matrix	NOUN
ejpam-454	39	3	s	s	PART
ejpam-454	39	4	=	=	PUNCT
ejpam-454	39	5	(	(	PUNCT
ejpam-454	39	6	si	si	X
ejpam-454	39	7	j)n×n	j)n×n	PROPN
ejpam-454	39	8	,	,	PUNCT
ejpam-454	39	9	s	s	PART
ejpam-454	39	10	>	>	X
ejpam-454	39	11	0	0	PUNCT
ejpam-454	40	1	(	(	PUNCT
ejpam-454	40	2	s	s	X
ejpam-454	40	3	≥	≥	NOUN
ejpam-454	40	4	0,s	0,s	NOUN
ejpam-454	40	5	<	<	X
ejpam-454	40	6	0,s	0,s	ADJ
ejpam-454	40	7	≤	≤	NUM
ejpam-454	40	8	0	0	NUM
ejpam-454	40	9	)	)	PUNCT
ejpam-454	40	10	means	mean	VERB
ejpam-454	40	11	that	that	SCONJ
ejpam-454	40	12	s	s	VERB
ejpam-454	40	13	is	be	AUX
ejpam-454	40	14	positive	positive	ADJ
ejpam-454	40	15	definite	definite	ADJ
ejpam-454	40	16	(	(	PUNCT
ejpam-454	40	17	positive	positive	ADJ
ejpam-454	40	18	semi	semi	ADJ
ejpam-454	40	19	-	-	ADJ
ejpam-454	40	20	definite	definite	ADJ
ejpam-454	40	21	,	,	PUNCT
ejpam-454	40	22	negative	negative	ADJ
ejpam-454	40	23	definite	definite	ADJ
ejpam-454	40	24	,	,	PUNCT
ejpam-454	40	25	negative	negative	ADJ
ejpam-454	40	26	semi	semi	ADJ
ejpam-454	40	27	-	-	ADJ
ejpam-454	40	28	definite	definite	ADJ
ejpam-454	40	29	)	)	PUNCT
ejpam-454	40	30	.	.	PUNCT
ejpam-454	41	1	given	give	VERB
ejpam-454	41	2	the	the	DET
ejpam-454	41	3	vector	vector	NOUN
ejpam-454	41	4	ψ	ψ	NOUN
ejpam-454	41	5	=	=	PUNCT
ejpam-454	41	6	(	(	PUNCT
ejpam-454	41	7	ψ1	ψ1	PROPN
ejpam-454	41	8	,	,	PUNCT
ejpam-454	41	9	·	·	PUNCT
ejpam-454	41	10	·	·	PUNCT
ejpam-454	41	11	·	·	PUNCT
ejpam-454	41	12	,	,	PUNCT
ejpam-454	41	13	ψn	ψn	NUM
ejpam-454	41	14	)	)	PUNCT
ejpam-454	41	15	t	t	PROPN
ejpam-454	41	16	∈	∈	PROPN
ejpam-454	41	17	rn	rn	PROPN
ejpam-454	41	18	,	,	PUNCT
ejpam-454	41	19	ψ	ψ	X
ejpam-454	41	20	=	=	SYM
ejpam-454	41	21	max	max	PROPN
ejpam-454	41	22	1≤i≤n	1≤i≤n	NUM
ejpam-454	41	23	�	�	PROPN
ejpam-454	41	24	�	�	PROPN
ejpam-454	41	25	ψi	ψi	PROPN
ejpam-454	41	26	�	�	PROPN
ejpam-454	41	27	�	�	PROPN
ejpam-454	41	28	.	.	PUNCT
ejpam-454	42	1	i	i	PRON
ejpam-454	42	2	denotes	denote	VERB
ejpam-454	42	3	identical	identical	ADJ
ejpam-454	42	4	matrix	matrix	NOUN
ejpam-454	42	5	.	.	PUNCT
ejpam-454	43	1	we	we	PRON
ejpam-454	43	2	will	will	AUX
ejpam-454	43	3	sometimes	sometimes	ADV
ejpam-454	43	4	write	write	VERB
ejpam-454	43	5	x(t	x(t	PROPN
ejpam-454	43	6	)	)	PUNCT
ejpam-454	43	7	as	as	ADP
ejpam-454	43	8	x	x	X
ejpam-454	43	9	,	,	PUNCT
ejpam-454	43	10	f	f	PROPN
ejpam-454	43	11	(	(	PUNCT
ejpam-454	43	12	x(t	x(t	PROPN
ejpam-454	43	13	)	)	PUNCT
ejpam-454	43	14	)	)	PUNCT
ejpam-454	43	15	as	as	ADP
ejpam-454	43	16	f	f	PROPN
ejpam-454	43	17	(	(	PUNCT
ejpam-454	43	18	x	x	NOUN
ejpam-454	43	19	)	)	PUNCT
ejpam-454	43	20	.	.	PUNCT
ejpam-454	44	1	definition	definition	NOUN
ejpam-454	44	2	1	1	NUM
ejpam-454	44	3	.	.	PUNCT
ejpam-454	45	1	a	a	DET
ejpam-454	45	2	function	function	NOUN
ejpam-454	45	3	x(t	x(t	PROPN
ejpam-454	45	4	)	)	PUNCT
ejpam-454	45	5	:	:	PUNCT
ejpam-454	46	1	[	[	X
ejpam-454	46	2	−τ,+∞]→	−τ,+∞]→	PROPN
ejpam-454	46	3	rn	rn	PROPN
ejpam-454	46	4	is	be	AUX
ejpam-454	46	5	said	say	VERB
ejpam-454	46	6	to	to	PART
ejpam-454	46	7	be	be	AUX
ejpam-454	46	8	a	a	DET
ejpam-454	46	9	solution	solution	NOUN
ejpam-454	46	10	of	of	ADP
ejpam-454	46	11	system	system	NOUN
ejpam-454	46	12	(	(	PUNCT
ejpam-454	46	13	1	1	NUM
ejpam-454	46	14	)	)	PUNCT
ejpam-454	46	15	with	with	ADP
ejpam-454	46	16	initial	initial	ADJ
ejpam-454	46	17	conditions	condition	NOUN
ejpam-454	46	18	x(t	x(t	PROPN
ejpam-454	46	19	)	)	PUNCT
ejpam-454	46	20	=	=	SYM
ejpam-454	46	21	φ(t	φ(t	PROPN
ejpam-454	46	22	)	)	PUNCT
ejpam-454	46	23	,	,	PUNCT
ejpam-454	46	24	t	t	PROPN
ejpam-454	46	25	∈	∈	PROPN
ejpam-454	47	1	[	[	X
ejpam-454	47	2	−τ	−τ	NOUN
ejpam-454	47	3	,	,	PUNCT
ejpam-454	47	4	0	0	NUM
ejpam-454	47	5	]	]	PUNCT
ejpam-454	47	6	,	,	PUNCT
ejpam-454	47	7	if	if	SCONJ
ejpam-454	47	8	the	the	DET
ejpam-454	47	9	following	follow	VERB
ejpam-454	47	10	conditions	condition	NOUN
ejpam-454	47	11	are	be	AUX
ejpam-454	47	12	satisfied	satisfied	ADJ
ejpam-454	47	13	:	:	PUNCT
ejpam-454	47	14	(	(	PUNCT
ejpam-454	47	15	1	1	X
ejpam-454	47	16	)	)	PUNCT
ejpam-454	47	17	x(t	x(t	PROPN
ejpam-454	47	18	)	)	PUNCT
ejpam-454	47	19	is	be	AUX
ejpam-454	47	20	piecewise	piecewise	NOUN
ejpam-454	47	21	continuous	continuous	ADJ
ejpam-454	47	22	with	with	ADP
ejpam-454	47	23	first	first	ADJ
ejpam-454	47	24	kind	kind	ADJ
ejpam-454	47	25	discontinuity	discontinuity	NOUN
ejpam-454	47	26	at	at	ADP
ejpam-454	47	27	points	point	NOUN
ejpam-454	47	28	tk	tk	PROPN
ejpam-454	47	29	,	,	PUNCT
ejpam-454	47	30	k	k	PROPN
ejpam-454	47	31	=	=	SYM
ejpam-454	47	32	1,2	1,2	NUM
ejpam-454	47	33	,	,	PUNCT
ejpam-454	47	34	·	·	PUNCT
ejpam-454	47	35	·	·	PUNCT
ejpam-454	47	36	·	·	PUNCT
ejpam-454	47	37	.	.	PUNCT
ejpam-454	48	1	moreover	moreover	ADV
ejpam-454	48	2	,	,	PUNCT
ejpam-454	48	3	x(t	x(t	PROPN
ejpam-454	48	4	)	)	PUNCT
ejpam-454	48	5	is	be	AUX
ejpam-454	48	6	right	right	ADV
ejpam-454	48	7	continuous	continuous	ADJ
ejpam-454	48	8	at	at	ADP
ejpam-454	48	9	each	each	DET
ejpam-454	48	10	discontinuity	discontinuity	NOUN
ejpam-454	48	11	points	point	NOUN
ejpam-454	48	12	;	;	PUNCT
ejpam-454	48	13	(	(	PUNCT
ejpam-454	48	14	2	2	X
ejpam-454	48	15	)	)	PUNCT
ejpam-454	48	16	x(t	x(t	PROPN
ejpam-454	48	17	)	)	PUNCT
ejpam-454	48	18	satisfies	satisfie	NOUN
ejpam-454	48	19	system	system	NOUN
ejpam-454	48	20	(	(	PUNCT
ejpam-454	48	21	1	1	NUM
ejpam-454	48	22	)	)	PUNCT
ejpam-454	48	23	for	for	ADP
ejpam-454	48	24	t	t	PROPN
ejpam-454	48	25	≥	≥	PROPN
ejpam-454	48	26	0	0	NUM
ejpam-454	48	27	,	,	PUNCT
ejpam-454	48	28	and	and	CCONJ
ejpam-454	48	29	x(s	x(s	PROPN
ejpam-454	48	30	)	)	PUNCT
ejpam-454	48	31	=	=	PUNCT
ejpam-454	48	32	φ(s	φ(s	NOUN
ejpam-454	48	33	)	)	PUNCT
ejpam-454	48	34	for	for	ADP
ejpam-454	48	35	s	s	PROPN
ejpam-454	48	36	∈	∈	PROPN
ejpam-454	48	37	[	[	X
ejpam-454	48	38	−τ	−τ	NOUN
ejpam-454	48	39	,	,	PUNCT
ejpam-454	48	40	0	0	NUM
ejpam-454	48	41	]	]	PUNCT
ejpam-454	48	42	.	.	PUNCT
ejpam-454	49	1	definition	definition	NOUN
ejpam-454	49	2	2	2	NUM
ejpam-454	49	3	.	.	PUNCT
ejpam-454	50	1	a	a	DET
ejpam-454	50	2	constant	constant	ADJ
ejpam-454	50	3	vector	vector	NOUN
ejpam-454	50	4	x∗	x∗	NOUN
ejpam-454	50	5	=	=	PUNCT
ejpam-454	50	6	(	(	PUNCT
ejpam-454	50	7	x∗1	x∗1	ADJ
ejpam-454	50	8	,	,	PUNCT
ejpam-454	50	9	·	·	PUNCT
ejpam-454	50	10	·	·	PUNCT
ejpam-454	50	11	·	·	PUNCT
ejpam-454	50	12	,	,	PUNCT
ejpam-454	50	13	x∗n	x∗n	NOUN
ejpam-454	50	14	)	)	PUNCT
ejpam-454	50	15	t	t	PROPN
ejpam-454	50	16	∈	∈	PROPN
ejpam-454	50	17	rn	rn	PROPN
ejpam-454	50	18	is	be	AUX
ejpam-454	50	19	an	an	DET
ejpam-454	50	20	equilibrium	equilibrium	NOUN
ejpam-454	50	21	point	point	NOUN
ejpam-454	50	22	of	of	ADP
ejpam-454	50	23	system	system	NOUN
ejpam-454	50	24	(	(	PUNCT
ejpam-454	50	25	1.1	1.1	NUM
ejpam-454	50	26	)	)	PUNCT
ejpam-454	50	27	a.	a.	NOUN
ejpam-454	50	28	wu	wu	PROPN
ejpam-454	50	29	,	,	PUNCT
ejpam-454	50	30	j.	j.	PROPN
ejpam-454	50	31	zhang	zhang	PROPN
ejpam-454	50	32	,	,	PUNCT
ejpam-454	50	33	c.	c.	PROPN
ejpam-454	50	34	fu	fu	PROPN
ejpam-454	50	35	/	/	SYM
ejpam-454	50	36	eur	eur	PROPN
ejpam-454	50	37	.	.	PUNCT
ejpam-454	51	1	j.	j.	PROPN
ejpam-454	51	2	pure	pure	PROPN
ejpam-454	51	3	appl	appl	PROPN
ejpam-454	51	4	.	.	PROPN
ejpam-454	51	5	math	math	PROPN
ejpam-454	51	6	,	,	PUNCT
ejpam-454	51	7	3	3	NUM
ejpam-454	51	8	(	(	PUNCT
ejpam-454	51	9	2010	2010	NUM
ejpam-454	51	10	)	)	PUNCT
ejpam-454	51	11	,	,	PUNCT
ejpam-454	51	12	806	806	NUM
ejpam-454	51	13	-	-	SYM
ejpam-454	51	14	818	818	NUM
ejpam-454	51	15	808	808	NUM
ejpam-454	51	16	if	if	SCONJ
ejpam-454	51	17	and	and	CCONJ
ejpam-454	51	18	only	only	ADV
ejpam-454	51	19	if	if	SCONJ
ejpam-454	51	20	x∗	x∗	PROPN
ejpam-454	51	21	is	be	AUX
ejpam-454	51	22	a	a	DET
ejpam-454	51	23	solution	solution	NOUN
ejpam-454	51	24	of	of	ADP
ejpam-454	51	25	the	the	DET
ejpam-454	51	26	following	follow	VERB
ejpam-454	51	27	equations	equation	NOUN
ejpam-454	51	28	:	:	PUNCT
ejpam-454	51	29	−di	−di	PROPN
ejpam-454	51	30	x	x	PUNCT
ejpam-454	52	1	i	i	PRON
ejpam-454	52	2	+	+	CCONJ
ejpam-454	52	3	n	n	CCONJ
ejpam-454	52	4	∑	∑	ADV
ejpam-454	52	5	j=1	j=1	PROPN
ejpam-454	52	6	(	(	PUNCT
ejpam-454	52	7	ai	ai	INTJ
ejpam-454	52	8	j	j	PROPN
ejpam-454	52	9	+	+	CCONJ
ejpam-454	52	10	bi	bi	ADJ
ejpam-454	52	11	j)g	j)g	PROPN
ejpam-454	52	12	j(x	j(x	PROPN
ejpam-454	52	13	j	j	PROPN
ejpam-454	52	14	)	)	PUNCT
ejpam-454	53	1	+	+	NUM
ejpam-454	53	2	ii	ii	X
ejpam-454	53	3	=	=	SYM
ejpam-454	53	4	0	0	PROPN
ejpam-454	53	5	,	,	PUNCT
ejpam-454	53	6	i	i	PRON
ejpam-454	53	7	=	=	NOUN
ejpam-454	53	8	1	1	NUM
ejpam-454	53	9	,	,	PUNCT
ejpam-454	53	10	·	·	PUNCT
ejpam-454	53	11	·	·	PUNCT
ejpam-454	53	12	·	·	PUNCT
ejpam-454	53	13	,	,	PUNCT
ejpam-454	53	14	n	n	CCONJ
ejpam-454	53	15	,	,	PUNCT
ejpam-454	53	16	(	(	PUNCT
ejpam-454	53	17	2	2	NUM
ejpam-454	53	18	)	)	PUNCT
ejpam-454	53	19	and	and	CCONJ
ejpam-454	53	20	the	the	DET
ejpam-454	53	21	impulsive	impulsive	ADJ
ejpam-454	53	22	jumps	jump	VERB
ejpam-454	53	23	jik	jik	PROPN
ejpam-454	53	24	(	(	PUNCT
ejpam-454	53	25	·	·	PUNCT
ejpam-454	53	26	)	)	PUNCT
ejpam-454	53	27	are	be	AUX
ejpam-454	53	28	assumed	assume	VERB
ejpam-454	53	29	to	to	PART
ejpam-454	53	30	satisfy	satisfy	VERB
ejpam-454	53	31	jik(x	jik(x	PROPN
ejpam-454	53	32	∗	∗	NOUN
ejpam-454	53	33	i	i	NOUN
ejpam-454	53	34	)	)	PUNCT
ejpam-454	54	1	=	=	PUNCT
ejpam-454	54	2	0	0	NUM
ejpam-454	54	3	,	,	PUNCT
ejpam-454	54	4	k	k	NOUN
ejpam-454	54	5	=	=	SYM
ejpam-454	54	6	1,2	1,2	NUM
ejpam-454	54	7	,	,	PUNCT
ejpam-454	54	8	·	·	PUNCT
ejpam-454	54	9	·	·	PUNCT
ejpam-454	54	10	·	·	PUNCT
ejpam-454	54	11	,	,	PUNCT
ejpam-454	54	12	i	i	PRON
ejpam-454	54	13	=	=	NOUN
ejpam-454	54	14	1	1	NUM
ejpam-454	54	15	,	,	PUNCT
ejpam-454	54	16	·	·	PUNCT
ejpam-454	54	17	·	·	PUNCT
ejpam-454	54	18	·	·	PUNCT
ejpam-454	54	19	,	,	PUNCT
ejpam-454	54	20	n.	n.	PROPN
ejpam-454	54	21	lemma	lemma	PROPN
ejpam-454	55	1	1	1	NUM
ejpam-454	55	2	.	.	PUNCT
ejpam-454	55	3	continuous	continuous	ADJ
ejpam-454	55	4	map	map	NOUN
ejpam-454	55	5	h(x	h(x	PROPN
ejpam-454	55	6	)	)	PUNCT
ejpam-454	55	7	:	:	PUNCT
ejpam-454	55	8	rn	rn	PROPN
ejpam-454	55	9	→	→	SYM
ejpam-454	55	10	rn	rn	PROPN
ejpam-454	55	11	is	be	AUX
ejpam-454	55	12	homeomorphic	homeomorphic	ADJ
ejpam-454	55	13	,	,	PUNCT
ejpam-454	55	14	if	if	SCONJ
ejpam-454	55	15	:	:	PUNCT
ejpam-454	55	16	(	(	PUNCT
ejpam-454	55	17	1	1	X
ejpam-454	55	18	)	)	PUNCT
ejpam-454	55	19	h(x	h(x	PROPN
ejpam-454	55	20	)	)	PUNCT
ejpam-454	55	21	is	be	AUX
ejpam-454	55	22	injective	injective	ADJ
ejpam-454	55	23	;	;	PUNCT
ejpam-454	55	24	(	(	PUNCT
ejpam-454	55	25	2	2	X
ejpam-454	55	26	)	)	PUNCT
ejpam-454	55	27	lim	lim	PROPN
ejpam-454	55	28	‖x‖p→∞	‖x‖p→∞	PROPN
ejpam-454	55	29	‖h(x)‖p	‖h(x)‖p	PROPN
ejpam-454	56	1	=	=	PRON
ejpam-454	56	2	∞.	∞.	PROPN
ejpam-454	56	3	2	2	NUM
ejpam-454	56	4	.	.	PUNCT
ejpam-454	56	5	existence	existence	NOUN
ejpam-454	56	6	and	and	CCONJ
ejpam-454	56	7	uniqueness	uniqueness	NOUN
ejpam-454	56	8	of	of	ADP
ejpam-454	56	9	the	the	DET
ejpam-454	56	10	equilibrium	equilibrium	NOUN
ejpam-454	56	11	point	point	NOUN
ejpam-454	56	12	first	first	ADV
ejpam-454	57	1	,	,	PUNCT
ejpam-454	57	2	we	we	PRON
ejpam-454	57	3	definite	definite	VERB
ejpam-454	57	4	the	the	DET
ejpam-454	57	5	map	map	NOUN
ejpam-454	57	6	h(x	h(x	PROPN
ejpam-454	57	7	)	)	PUNCT
ejpam-454	57	8	associated	associate	VERB
ejpam-454	57	9	with	with	ADP
ejpam-454	57	10	(	(	PUNCT
ejpam-454	57	11	2	2	NUM
ejpam-454	57	12	)	)	PUNCT
ejpam-454	57	13	as	as	SCONJ
ejpam-454	57	14	follows	follow	VERB
ejpam-454	57	15	:	:	PUNCT
ejpam-454	57	16	h(x	h(x	PROPN
ejpam-454	57	17	)	)	PUNCT
ejpam-454	58	1	=	=	PRON
ejpam-454	58	2	(	(	PUNCT
ejpam-454	58	3	h1(x	h1(x	NOUN
ejpam-454	58	4	)	)	PUNCT
ejpam-454	58	5	,	,	PUNCT
ejpam-454	58	6	·	·	PUNCT
ejpam-454	58	7	·	·	PUNCT
ejpam-454	58	8	·	·	PUNCT
ejpam-454	58	9	,	,	PUNCT
ejpam-454	58	10	hn(x	hn(x	X
ejpam-454	58	11	)	)	PUNCT
ejpam-454	58	12	)	)	PUNCT
ejpam-454	59	1	t	t	NOUN
ejpam-454	59	2	(	(	PUNCT
ejpam-454	59	3	3	3	NUM
ejpam-454	59	4	)	)	PUNCT
ejpam-454	59	5	where	where	SCONJ
ejpam-454	59	6	hi(x	hi(x	NOUN
ejpam-454	59	7	)	)	PUNCT
ejpam-454	59	8	=	=	SYM
ejpam-454	60	1	−di	−di	NOUN
ejpam-454	60	2	x	x	X
ejpam-454	61	1	i	i	PRON
ejpam-454	61	2	+	+	CCONJ
ejpam-454	61	3	n	n	CCONJ
ejpam-454	61	4	∑	∑	ADV
ejpam-454	61	5	j=1	j=1	PROPN
ejpam-454	61	6	(	(	PUNCT
ejpam-454	61	7	ai	ai	INTJ
ejpam-454	61	8	j	j	PROPN
ejpam-454	61	9	+	+	CCONJ
ejpam-454	61	10	bi	bi	ADJ
ejpam-454	61	11	j)g	j)g	PROPN
ejpam-454	61	12	j(x	j(x	PROPN
ejpam-454	61	13	j	j	PROPN
ejpam-454	61	14	)	)	PUNCT
ejpam-454	62	1	+	+	NUM
ejpam-454	62	2	ii	ii	NOUN
ejpam-454	62	3	,	,	PUNCT
ejpam-454	62	4	i	i	PRON
ejpam-454	62	5	=	=	NOUN
ejpam-454	62	6	1	1	NUM
ejpam-454	62	7	,	,	PUNCT
ejpam-454	62	8	·	·	PUNCT
ejpam-454	62	9	·	·	PUNCT
ejpam-454	62	10	·	·	PUNCT
ejpam-454	62	11	,	,	PUNCT
ejpam-454	62	12	n.	n.	PROPN
ejpam-454	62	13	theorem	theorem	VERB
ejpam-454	62	14	1	1	NUM
ejpam-454	62	15	.	.	PUNCT
ejpam-454	63	1	if	if	SCONJ
ejpam-454	63	2	there	there	PRON
ejpam-454	63	3	exist	exist	VERB
ejpam-454	63	4	positive	positive	ADJ
ejpam-454	63	5	constants	constant	NOUN
ejpam-454	63	6	pi	pi	ADV
ejpam-454	63	7	>	>	X
ejpam-454	63	8	0	0	NUM
ejpam-454	63	9	,	,	PUNCT
ejpam-454	63	10	i	i	PRON
ejpam-454	63	11	=	=	NOUN
ejpam-454	63	12	1	1	NUM
ejpam-454	63	13	,	,	PUNCT
ejpam-454	63	14	·	·	PUNCT
ejpam-454	63	15	·	·	PUNCT
ejpam-454	63	16	·	·	PUNCT
ejpam-454	63	17	,	,	PUNCT
ejpam-454	63	18	n	n	CCONJ
ejpam-454	63	19	,	,	PUNCT
ejpam-454	63	20	such	such	ADJ
ejpam-454	63	21	that	that	SCONJ
ejpam-454	63	22	pi(−aii	pi(−aii	PROPN
ejpam-454	63	23	−	−	PROPN
ejpam-454	63	24	�	�	PROPN
ejpam-454	63	25	�	�	PROPN
ejpam-454	63	26	bii	bii	PROPN
ejpam-454	63	27	�	�	PROPN
ejpam-454	63	28	�	�	PROPN
ejpam-454	63	29	)	)	PUNCT
ejpam-454	63	30	−	−	PROPN
ejpam-454	63	31	n	n	CCONJ
ejpam-454	63	32	∑	∑	PROPN
ejpam-454	63	33	j=1	j=1	PROPN
ejpam-454	63	34	,	,	PUNCT
ejpam-454	63	35	j	j	PROPN
ejpam-454	63	36	6	6	NUM
ejpam-454	64	1	=	=	NOUN
ejpam-454	64	2	i	i	PROPN
ejpam-454	64	3	p	p	PROPN
ejpam-454	64	4	j	j	PROPN
ejpam-454	64	5	(	(	PUNCT
ejpam-454	64	6	�	�	PROPN
ejpam-454	64	7	�	�	PROPN
ejpam-454	64	8	a	a	DET
ejpam-454	64	9	ji	ji	PROPN
ejpam-454	64	10	�	�	PROPN
ejpam-454	64	11	�	�	PROPN
ejpam-454	64	12	+	+	PROPN
ejpam-454	64	13	�	�	PROPN
ejpam-454	64	14	�	�	PROPN
ejpam-454	64	15	b	b	PROPN
ejpam-454	64	16	ji	ji	PROPN
ejpam-454	64	17	�	�	PROPN
ejpam-454	64	18	�	�	PROPN
ejpam-454	64	19	)	)	PUNCT
ejpam-454	64	20	≥	≥	NOUN
ejpam-454	64	21	0	0	NUM
ejpam-454	64	22	,	,	PUNCT
ejpam-454	64	23	i	i	PRON
ejpam-454	64	24	=	=	NOUN
ejpam-454	64	25	1	1	NUM
ejpam-454	64	26	,	,	PUNCT
ejpam-454	64	27	·	·	PUNCT
ejpam-454	64	28	·	·	PUNCT
ejpam-454	64	29	·	·	PUNCT
ejpam-454	64	30	,	,	PUNCT
ejpam-454	64	31	n	n	CCONJ
ejpam-454	64	32	,	,	PUNCT
ejpam-454	64	33	then	then	ADV
ejpam-454	64	34	eq.(2	eq.(2	ADJ
ejpam-454	64	35	)	)	PUNCT
ejpam-454	64	36	has	have	VERB
ejpam-454	64	37	a	a	DET
ejpam-454	64	38	unique	unique	ADJ
ejpam-454	64	39	solution	solution	NOUN
ejpam-454	64	40	.	.	PUNCT
ejpam-454	65	1	proof	proof	NOUN
ejpam-454	65	2	.	.	PUNCT
ejpam-454	66	1	in	in	ADP
ejpam-454	66	2	order	order	NOUN
ejpam-454	66	3	to	to	PART
ejpam-454	66	4	complete	complete	VERB
ejpam-454	66	5	the	the	DET
ejpam-454	66	6	proof	proof	NOUN
ejpam-454	66	7	,	,	PUNCT
ejpam-454	66	8	we	we	PRON
ejpam-454	66	9	divide	divide	VERB
ejpam-454	66	10	the	the	DET
ejpam-454	66	11	proof	proof	NOUN
ejpam-454	66	12	into	into	ADP
ejpam-454	66	13	two	two	NUM
ejpam-454	66	14	steps	step	NOUN
ejpam-454	66	15	.	.	PUNCT
ejpam-454	67	1	step	step	NOUN
ejpam-454	67	2	1	1	NUM
ejpam-454	67	3	.	.	PUNCT
ejpam-454	68	1	let	let	VERB
ejpam-454	68	2	x	x	PRON
ejpam-454	68	3	and	and	CCONJ
ejpam-454	68	4	y	y	PROPN
ejpam-454	68	5	be	be	AUX
ejpam-454	68	6	two	two	NUM
ejpam-454	68	7	different	different	ADJ
ejpam-454	68	8	vectors	vector	NOUN
ejpam-454	68	9	in	in	ADP
ejpam-454	68	10	rn	rn	PROPN
ejpam-454	68	11	,	,	PUNCT
ejpam-454	68	12	then	then	ADV
ejpam-454	68	13	we	we	PRON
ejpam-454	68	14	have	have	VERB
ejpam-454	68	15	n	n	NUM
ejpam-454	68	16	∑	∑	PROPN
ejpam-454	68	17	i=1	i=1	PROPN
ejpam-454	68	18	pisi	pisi	X
ejpam-454	68	19	gn(x	gn(x	INTJ
ejpam-454	68	20	i	i	PRON
ejpam-454	68	21	−	−	PROPN
ejpam-454	68	22	yi)(hi(x)−hi(y	yi)(hi(x)−hi(y	NOUN
ejpam-454	68	23	)	)	PUNCT
ejpam-454	68	24	)	)	PUNCT
ejpam-454	69	1	≤	≤	NUM
ejpam-454	69	2	−	−	ADP
ejpam-454	70	1	n	n	NOUN
ejpam-454	70	2	∑	∑	ADP
ejpam-454	70	3	i=1	i=1	PROPN
ejpam-454	70	4	pidi	pidi	PROPN
ejpam-454	70	5	�	�	PROPN
ejpam-454	70	6	�	�	PROPN
ejpam-454	70	7	x	x	PROPN
ejpam-454	70	8	i	i	PRON
ejpam-454	70	9	−	−	PROPN
ejpam-454	70	10	yi	yi	PROPN
ejpam-454	70	11	�	�	PROPN
ejpam-454	70	12	�	�	PROPN
ejpam-454	70	13	+	+	PROPN
ejpam-454	70	14	n	n	CCONJ
ejpam-454	70	15	∑	∑	PUNCT
ejpam-454	70	16	i=1	i=1	PROPN
ejpam-454	70	17	pi(aii	pi(aii	PROPN
ejpam-454	70	18	+	+	CCONJ
ejpam-454	70	19	bii	bii	NOUN
ejpam-454	70	20	)	)	PUNCT
ejpam-454	70	21	�	�	PROPN
ejpam-454	70	22	�	�	PROPN
ejpam-454	70	23	gi(x	gi(x	PROPN
ejpam-454	70	24	i)−	i)−	PROPN
ejpam-454	70	25	gi(yi	gi(yi	PROPN
ejpam-454	70	26	)	)	PUNCT
ejpam-454	70	27	�	�	PROPN
ejpam-454	70	28	�	�	PROPN
ejpam-454	70	29	+	+	CCONJ
ejpam-454	71	1	n	n	CCONJ
ejpam-454	71	2	∑	∑	ADP
ejpam-454	71	3	i=1	i=1	PROPN
ejpam-454	71	4	n	n	PROPN
ejpam-454	71	5	∑	∑	ADV
ejpam-454	71	6	j=1	j=1	PROPN
ejpam-454	71	7	,	,	PUNCT
ejpam-454	71	8	j	j	PROPN
ejpam-454	71	9	6	6	NUM
ejpam-454	71	10	=	=	NOUN
ejpam-454	71	11	i	i	PRON
ejpam-454	71	12	pi	pi	VERB
ejpam-454	71	13	(	(	PUNCT
ejpam-454	71	14	�	�	PROPN
ejpam-454	71	15	�	�	PROPN
ejpam-454	71	16	ai	ai	PROPN
ejpam-454	71	17	j	j	PROPN
ejpam-454	71	18	�	�	PROPN
ejpam-454	71	19	�	�	PROPN
ejpam-454	71	20	+	+	PROPN
ejpam-454	71	21	�	�	PROPN
ejpam-454	71	22	�	�	PROPN
ejpam-454	71	23	bi	bi	PROPN
ejpam-454	71	24	j	j	PROPN
ejpam-454	71	25	�	�	PROPN
ejpam-454	71	26	�	�	PROPN
ejpam-454	71	27	)	)	PUNCT
ejpam-454	71	28	·	·	PUNCT
ejpam-454	71	29	�	�	PROPN
ejpam-454	71	30	�	�	PROPN
ejpam-454	71	31	g	g	PROPN
ejpam-454	71	32	j(x	j(x	PROPN
ejpam-454	71	33	j)−	j)−	PROPN
ejpam-454	71	34	g	g	PROPN
ejpam-454	71	35	j(y	j(y	PROPN
ejpam-454	71	36	j	j	PROPN
ejpam-454	71	37	)	)	PUNCT
ejpam-454	71	38	�	�	PROPN
ejpam-454	71	39	�	�	PROPN
ejpam-454	71	40	≤	≤	PROPN
ejpam-454	71	41	−	−	PROPN
ejpam-454	71	42	n	n	NOUN
ejpam-454	71	43	∑	∑	ADP
ejpam-454	71	44	i=1	i=1	PROPN
ejpam-454	71	45	pidi	pidi	PROPN
ejpam-454	71	46	�	�	PROPN
ejpam-454	71	47	�	�	PROPN
ejpam-454	71	48	x	x	PROPN
ejpam-454	71	49	i	i	PRON
ejpam-454	71	50	−	−	PROPN
ejpam-454	71	51	yi	yi	PROPN
ejpam-454	71	52	�	�	PROPN
ejpam-454	71	53	�	�	PROPN
ejpam-454	71	54	+	+	PROPN
ejpam-454	71	55	n	n	CCONJ
ejpam-454	71	56	∑	∑	PUNCT
ejpam-454	71	57	i=1	i=1	PROPN
ejpam-454	71	58	pi(aii	pi(aii	PROPN
ejpam-454	71	59	+	+	NUM
ejpam-454	71	60	�	�	PROPN
ejpam-454	71	61	�	�	PROPN
ejpam-454	71	62	bii	bii	PROPN
ejpam-454	71	63	�	�	PROPN
ejpam-454	71	64	�	�	PROPN
ejpam-454	71	65	)	)	PUNCT
ejpam-454	71	66	�	�	PROPN
ejpam-454	71	67	�	�	PROPN
ejpam-454	71	68	gi(x	gi(x	PROPN
ejpam-454	71	69	i)−	i)−	PROPN
ejpam-454	71	70	gi(yi	gi(yi	PROPN
ejpam-454	71	71	)	)	PUNCT
ejpam-454	71	72	�	�	PROPN
ejpam-454	71	73	�	�	PROPN
ejpam-454	71	74	+	+	CCONJ
ejpam-454	71	75	n	n	CCONJ
ejpam-454	71	76	∑	∑	ADP
ejpam-454	71	77	i=1	i=1	PROPN
ejpam-454	71	78	n	n	PROPN
ejpam-454	71	79	∑	∑	ADV
ejpam-454	71	80	j=1	j=1	PROPN
ejpam-454	71	81	,	,	PUNCT
ejpam-454	71	82	j	j	PROPN
ejpam-454	71	83	6	6	NUM
ejpam-454	71	84	=	=	NOUN
ejpam-454	71	85	i	i	PROPN
ejpam-454	71	86	p	p	PROPN
ejpam-454	71	87	j	j	PROPN
ejpam-454	71	88	(	(	PUNCT
ejpam-454	71	89	�	�	PROPN
ejpam-454	71	90	�	�	PROPN
ejpam-454	71	91	a	a	DET
ejpam-454	71	92	ji	ji	PROPN
ejpam-454	71	93	�	�	PROPN
ejpam-454	71	94	�	�	PROPN
ejpam-454	71	95	+	+	PROPN
ejpam-454	71	96	�	�	PROPN
ejpam-454	71	97	�	�	PROPN
ejpam-454	71	98	b	b	PROPN
ejpam-454	71	99	ji	ji	PROPN
ejpam-454	71	100	�	�	PROPN
ejpam-454	71	101	�	�	PROPN
ejpam-454	71	102	)	)	PUNCT
ejpam-454	71	103	·	·	PUNCT
ejpam-454	71	104	�	�	PROPN
ejpam-454	71	105	�	�	PROPN
ejpam-454	71	106	gi(x	gi(x	PROPN
ejpam-454	71	107	i)−	i)−	PROPN
ejpam-454	71	108	gi(yi	gi(yi	PROPN
ejpam-454	71	109	)	)	PUNCT
ejpam-454	71	110	�	�	PROPN
ejpam-454	71	111	�	�	PROPN
ejpam-454	71	112	≤	≤	PROPN
ejpam-454	71	113	−	−	PROPN
ejpam-454	71	114	n	n	NOUN
ejpam-454	71	115	∑	∑	ADP
ejpam-454	71	116	i=1	i=1	PROPN
ejpam-454	71	117	pidi	pidi	PROPN
ejpam-454	71	118	�	�	PROPN
ejpam-454	71	119	�	�	PROPN
ejpam-454	71	120	x	x	PROPN
ejpam-454	71	121	i	i	PRON
ejpam-454	71	122	−	−	PROPN
ejpam-454	71	123	yi	yi	PROPN
ejpam-454	71	124	�	�	PROPN
ejpam-454	71	125	�	�	PROPN
ejpam-454	71	126	<	<	X
ejpam-454	71	127	0	0	NUM
ejpam-454	71	128	(	(	PUNCT
ejpam-454	71	129	4	4	NUM
ejpam-454	71	130	)	)	PUNCT
ejpam-454	71	131	a.	a.	NOUN
ejpam-454	71	132	wu	wu	PROPN
ejpam-454	71	133	,	,	PUNCT
ejpam-454	71	134	j.	j.	PROPN
ejpam-454	71	135	zhang	zhang	PROPN
ejpam-454	71	136	,	,	PUNCT
ejpam-454	71	137	c.	c.	PROPN
ejpam-454	71	138	fu	fu	PROPN
ejpam-454	71	139	/	/	SYM
ejpam-454	71	140	eur	eur	PROPN
ejpam-454	71	141	.	.	PUNCT
ejpam-454	72	1	j.	j.	PROPN
ejpam-454	72	2	pure	pure	PROPN
ejpam-454	72	3	appl	appl	PROPN
ejpam-454	72	4	.	.	PROPN
ejpam-454	72	5	math	math	PROPN
ejpam-454	72	6	,	,	PUNCT
ejpam-454	72	7	3	3	NUM
ejpam-454	72	8	(	(	PUNCT
ejpam-454	72	9	2010	2010	NUM
ejpam-454	72	10	)	)	PUNCT
ejpam-454	72	11	,	,	PUNCT
ejpam-454	72	12	806	806	NUM
ejpam-454	72	13	-	-	SYM
ejpam-454	72	14	818	818	NUM
ejpam-454	72	15	809	809	NUM
ejpam-454	72	16	moreover	moreover	ADV
ejpam-454	73	1	,	,	PUNCT
ejpam-454	73	2	there	there	PRON
ejpam-454	73	3	exists	exist	VERB
ejpam-454	73	4	k0	k0	PROPN
ejpam-454	73	5	∈	∈	PROPN
ejpam-454	73	6	{	{	PUNCT
ejpam-454	73	7	1	1	NUM
ejpam-454	73	8	,	,	PUNCT
ejpam-454	73	9	·	·	PUNCT
ejpam-454	73	10	·	·	PUNCT
ejpam-454	73	11	·	·	PUNCT
ejpam-454	73	12	,	,	PUNCT
ejpam-454	73	13	n	n	CCONJ
ejpam-454	73	14	}	}	PUNCT
ejpam-454	73	15	such	such	ADJ
ejpam-454	73	16	that	that	SCONJ
ejpam-454	73	17	hk0	hk0	PROPN
ejpam-454	73	18	(	(	PUNCT
ejpam-454	73	19	x	x	X
ejpam-454	73	20	)	)	PUNCT
ejpam-454	73	21	6=	6=	ADP
ejpam-454	73	22	hk0	hk0	PROPN
ejpam-454	73	23	(	(	PUNCT
ejpam-454	73	24	y	y	NOUN
ejpam-454	73	25	)	)	PUNCT
ejpam-454	73	26	.	.	PUNCT
ejpam-454	74	1	that	that	PRON
ejpam-454	74	2	is	be	AUX
ejpam-454	74	3	,	,	PUNCT
ejpam-454	74	4	h(x	h(x	PROPN
ejpam-454	74	5	)	)	PUNCT
ejpam-454	75	1	6=	6=	ADP
ejpam-454	75	2	h(y	h(y	ADV
ejpam-454	75	3	)	)	PUNCT
ejpam-454	75	4	for	for	ADP
ejpam-454	75	5	all	all	DET
ejpam-454	75	6	x	x	SYM
ejpam-454	75	7	6=	6=	ADP
ejpam-454	75	8	y.	y.	NOUN
ejpam-454	75	9	step	step	NOUN
ejpam-454	75	10	2	2	NUM
ejpam-454	75	11	.	.	PUNCT
ejpam-454	76	1	in	in	ADP
ejpam-454	76	2	(	(	PUNCT
ejpam-454	76	3	4	4	NUM
ejpam-454	76	4	)	)	PUNCT
ejpam-454	76	5	,	,	PUNCT
ejpam-454	76	6	let	let	VERB
ejpam-454	76	7	y	y	PROPN
ejpam-454	76	8	=	=	SYM
ejpam-454	76	9	0	0	PROPN
ejpam-454	76	10	,	,	PUNCT
ejpam-454	76	11	we	we	PRON
ejpam-454	76	12	get	get	VERB
ejpam-454	76	13	n	n	PRON
ejpam-454	76	14	∑	∑	ADV
ejpam-454	76	15	i=1	i=1	PROPN
ejpam-454	76	16	pi(hi(x)−hi(0))si	pi(hi(x)−hi(0))si	ADV
ejpam-454	76	17	gn(x	gn(x	NUM
ejpam-454	77	1	i	i	PRON
ejpam-454	77	2	−	−	VERB
ejpam-454	77	3	0)≤	0)≤	NOUN
ejpam-454	77	4	−	−	PROPN
ejpam-454	78	1	n	n	CCONJ
ejpam-454	78	2	∑	∑	ADP
ejpam-454	78	3	i=1	i=1	PROPN
ejpam-454	78	4	pidi	pidi	PROPN
ejpam-454	78	5	�	�	PROPN
ejpam-454	78	6	�	�	PROPN
ejpam-454	78	7	x	x	PROPN
ejpam-454	78	8	i	i	PROPN
ejpam-454	78	9	�	�	PROPN
ejpam-454	78	10	�	�	PROPN
ejpam-454	78	11	≤	≤	PROPN
ejpam-454	78	12	−pmin	−pmin	ADP
ejpam-454	78	13	n	n	CCONJ
ejpam-454	78	14	∑	∑	PROPN
ejpam-454	78	15	i=1	i=1	PROPN
ejpam-454	78	16	�	�	PROPN
ejpam-454	78	17	�	�	PROPN
ejpam-454	78	18	x	x	PROPN
ejpam-454	78	19	i	i	PROPN
ejpam-454	78	20	�	�	PROPN
ejpam-454	78	21	�	�	PROPN
ejpam-454	78	22	(	(	PUNCT
ejpam-454	78	23	5	5	NUM
ejpam-454	78	24	)	)	PUNCT
ejpam-454	78	25	where	where	SCONJ
ejpam-454	78	26	pmin	pmin	NOUN
ejpam-454	78	27	=	=	SYM
ejpam-454	78	28	min	min	PROPN
ejpam-454	78	29	1≤i≤n	1≤i≤n	NUM
ejpam-454	78	30	�	�	PROPN
ejpam-454	78	31	pidi	pidi	NOUN
ejpam-454	78	32	.	.	PUNCT
ejpam-454	79	1	from	from	ADP
ejpam-454	79	2	(	(	PUNCT
ejpam-454	79	3	5	5	NUM
ejpam-454	79	4	)	)	PUNCT
ejpam-454	79	5	,	,	PUNCT
ejpam-454	79	6	it	it	PRON
ejpam-454	79	7	follows	follow	VERB
ejpam-454	79	8	that	that	SCONJ
ejpam-454	79	9	pmin‖x‖1	pmin‖x‖1	NOUN
ejpam-454	79	10	≤	≤	PROPN
ejpam-454	79	11	�	�	PROPN
ejpam-454	79	12	�	�	PROPN
ejpam-454	79	13	�	�	PROPN
ejpam-454	79	14	�	�	PROPN
ejpam-454	79	15	�	�	PROPN
ejpam-454	79	16	n	n	CCONJ
ejpam-454	79	17	∑	∑	PROPN
ejpam-454	79	18	i=1	i=1	PROPN
ejpam-454	79	19	pi(hi(x)−hi(0	pi(hi(x)−hi(0	NOUN
ejpam-454	79	20	)	)	PUNCT
ejpam-454	79	21	)	)	PUNCT
ejpam-454	79	22	�	�	PROPN
ejpam-454	79	23	�	�	PROPN
ejpam-454	79	24	�	�	PROPN
ejpam-454	79	25	�	�	PROPN
ejpam-454	79	26	�	�	PROPN
ejpam-454	79	27	≤	≤	PROPN
ejpam-454	79	28	pmax	pmax	PROPN
ejpam-454	79	29	n	n	CCONJ
ejpam-454	79	30	∑	∑	PUNCT
ejpam-454	79	31	i=1	i=1	PROPN
ejpam-454	79	32	�	�	PROPN
ejpam-454	79	33	�	�	PROPN
ejpam-454	79	34	(	(	PUNCT
ejpam-454	79	35	hi(x)−hi(0	hi(x)−hi(0	PROPN
ejpam-454	79	36	)	)	PUNCT
ejpam-454	79	37	)	)	PUNCT
ejpam-454	79	38	�	�	PROPN
ejpam-454	79	39	�	�	PROPN
ejpam-454	79	40	≤	≤	PROPN
ejpam-454	79	41	pmax‖h(x)−h(0)‖1	pmax‖h(x)−h(0)‖1	NOUN
ejpam-454	79	42	≤	≤	NUM
ejpam-454	79	43	pmax(‖h(x)‖1	pmax(‖h(x)‖1	NOUN
ejpam-454	79	44	+	+	CCONJ
ejpam-454	79	45	‖h(0)‖1	‖h(0)‖1	NOUN
ejpam-454	79	46	)	)	PUNCT
ejpam-454	79	47	where	where	SCONJ
ejpam-454	79	48	pmax	pmax	ADJ
ejpam-454	79	49	=	=	SYM
ejpam-454	79	50	max	max	PROPN
ejpam-454	79	51	�	�	PROPN
ejpam-454	79	52	p1	p1	PROPN
ejpam-454	79	53	,	,	PUNCT
ejpam-454	79	54	·	·	PUNCT
ejpam-454	79	55	·	·	PUNCT
ejpam-454	80	1	·	·	PUNCT
ejpam-454	80	2	,	,	PUNCT
ejpam-454	80	3	pn	pn	PROPN
ejpam-454	80	4	.	.	PUNCT
ejpam-454	81	1	we	we	PRON
ejpam-454	81	2	obtain	obtain	VERB
ejpam-454	81	3	‖h(x)‖1	‖h(x)‖1	NOUN
ejpam-454	81	4	≥	≥	NOUN
ejpam-454	81	5	pmin‖x‖1	pmin‖x‖1	VERB
ejpam-454	81	6	−	−	NOUN
ejpam-454	81	7	pmax‖h(0)‖1	pmax‖h(0)‖1	NOUN
ejpam-454	81	8	pmax	pmax	ADJ
ejpam-454	81	9	from	from	ADP
ejpam-454	81	10	which	which	PRON
ejpam-454	81	11	it	it	PRON
ejpam-454	81	12	can	can	AUX
ejpam-454	81	13	be	be	AUX
ejpam-454	81	14	easily	easily	ADV
ejpam-454	81	15	concluded	conclude	VERB
ejpam-454	81	16	that	that	SCONJ
ejpam-454	81	17	‖h(x)‖1	‖h(x)‖1	NOUN
ejpam-454	81	18	→	→	SYM
ejpam-454	81	19	∞	∞	NUM
ejpam-454	81	20	as	as	ADP
ejpam-454	81	21	‖x‖1	‖x‖1	PROPN
ejpam-454	81	22	→	→	SYM
ejpam-454	81	23	∞.	∞.	PROPN
ejpam-454	81	24	hence	hence	ADV
ejpam-454	81	25	,	,	PUNCT
ejpam-454	81	26	we	we	PRON
ejpam-454	81	27	have	have	AUX
ejpam-454	81	28	proved	prove	VERB
ejpam-454	81	29	that	that	SCONJ
ejpam-454	81	30	h(x	h(x	PROPN
ejpam-454	81	31	)	)	PUNCT
ejpam-454	81	32	is	be	AUX
ejpam-454	81	33	a	a	DET
ejpam-454	81	34	homeomorphism	homeomorphism	NOUN
ejpam-454	81	35	on	on	ADP
ejpam-454	81	36	rn	rn	PROPN
ejpam-454	81	37	.	.	PROPN
ejpam-454	82	1	that	that	PRON
ejpam-454	82	2	is	is	ADV
ejpam-454	82	3	,	,	PUNCT
ejpam-454	82	4	eq.(2	eq.(2	ADJ
ejpam-454	82	5	)	)	PUNCT
ejpam-454	82	6	has	have	VERB
ejpam-454	82	7	a	a	DET
ejpam-454	82	8	unique	unique	ADJ
ejpam-454	82	9	solution	solution	NOUN
ejpam-454	82	10	.	.	PUNCT
ejpam-454	83	1	theorem	theorem	NOUN
ejpam-454	83	2	2	2	NUM
ejpam-454	83	3	.	.	PUNCT
ejpam-454	84	1	if	if	SCONJ
ejpam-454	84	2	�	�	PROPN
ejpam-454	84	3	�	�	PROPN
ejpam-454	84	4	gi(x	gi(x	PROPN
ejpam-454	84	5	i	i	PROPN
ejpam-454	84	6	)	)	PUNCT
ejpam-454	84	7	�	�	PROPN
ejpam-454	84	8	�	�	PROPN
ejpam-454	84	9	→	→	SYM
ejpam-454	84	10	∞	∞	PROPN
ejpam-454	84	11	as	as	ADP
ejpam-454	84	12	�	�	PROPN
ejpam-454	84	13	�	�	PROPN
ejpam-454	84	14	x	x	PROPN
ejpam-454	84	15	i	i	PROPN
ejpam-454	84	16	�	�	PROPN
ejpam-454	84	17	�	�	PROPN
ejpam-454	84	18	→	→	SYM
ejpam-454	84	19	∞	∞	PROPN
ejpam-454	84	20	,	,	PUNCT
ejpam-454	84	21	i	i	PRON
ejpam-454	84	22	=	=	NOUN
ejpam-454	84	23	1	1	NUM
ejpam-454	84	24	,	,	PUNCT
ejpam-454	84	25	·	·	PUNCT
ejpam-454	84	26	·	·	PUNCT
ejpam-454	84	27	·	·	PUNCT
ejpam-454	84	28	,	,	PUNCT
ejpam-454	84	29	n	n	CCONJ
ejpam-454	84	30	,	,	PUNCT
ejpam-454	84	31	and	and	CCONJ
ejpam-454	84	32	there	there	PRON
ejpam-454	84	33	exists	exist	VERB
ejpam-454	84	34	a	a	DET
ejpam-454	84	35	positive	positive	ADJ
ejpam-454	84	36	constant	constant	ADJ
ejpam-454	84	37	r	r	NOUN
ejpam-454	84	38	such	such	ADJ
ejpam-454	84	39	that	that	SCONJ
ejpam-454	84	40	a+at	a+at	PROPN
ejpam-454	84	41	+	+	CCONJ
ejpam-454	84	42	(	(	PUNCT
ejpam-454	84	43	1	1	NUM
ejpam-454	84	44	r	r	NOUN
ejpam-454	84	45	‖b‖∞	‖b‖∞	PROPN
ejpam-454	84	46	+	+	NUM
ejpam-454	84	47	r‖b‖1)i	r‖b‖1)i	PROPN
ejpam-454	84	48	≤	≤	NOUN
ejpam-454	84	49	0	0	NUM
ejpam-454	85	1	where	where	SCONJ
ejpam-454	85	2	a=	a=	PROPN
ejpam-454	85	3	(	(	PUNCT
ejpam-454	85	4	ai	ai	VERB
ejpam-454	85	5	j)n×n	j)n×n	PROPN
ejpam-454	85	6	and	and	CCONJ
ejpam-454	85	7	b	b	NOUN
ejpam-454	85	8	=	=	SYM
ejpam-454	85	9	(	(	PUNCT
ejpam-454	85	10	bi	bi	PROPN
ejpam-454	85	11	j)n×n	j)n×n	PROPN
ejpam-454	85	12	,	,	PUNCT
ejpam-454	85	13	then	then	ADV
ejpam-454	85	14	eq.(2	eq.(2	ADJ
ejpam-454	85	15	)	)	PUNCT
ejpam-454	85	16	has	have	VERB
ejpam-454	85	17	a	a	DET
ejpam-454	85	18	unique	unique	ADJ
ejpam-454	85	19	solution	solution	NOUN
ejpam-454	85	20	.	.	PUNCT
ejpam-454	86	1	proof	proof	NOUN
ejpam-454	86	2	.	.	PUNCT
ejpam-454	87	1	in	in	ADP
ejpam-454	87	2	order	order	NOUN
ejpam-454	87	3	to	to	PART
ejpam-454	87	4	complete	complete	VERB
ejpam-454	87	5	the	the	DET
ejpam-454	87	6	proof	proof	NOUN
ejpam-454	87	7	,	,	PUNCT
ejpam-454	87	8	we	we	PRON
ejpam-454	87	9	divide	divide	VERB
ejpam-454	87	10	the	the	DET
ejpam-454	87	11	proof	proof	NOUN
ejpam-454	87	12	into	into	ADP
ejpam-454	87	13	two	two	NUM
ejpam-454	87	14	steps	step	NOUN
ejpam-454	87	15	.	.	PUNCT
ejpam-454	88	1	step	step	NOUN
ejpam-454	88	2	1	1	NUM
ejpam-454	88	3	.	.	PUNCT
ejpam-454	89	1	let	let	VERB
ejpam-454	89	2	x	x	PRON
ejpam-454	89	3	and	and	CCONJ
ejpam-454	89	4	y	y	PROPN
ejpam-454	89	5	be	be	AUX
ejpam-454	89	6	two	two	NUM
ejpam-454	89	7	different	different	ADJ
ejpam-454	89	8	vectors	vector	NOUN
ejpam-454	89	9	in	in	ADP
ejpam-454	89	10	rn	rn	PROPN
ejpam-454	89	11	,	,	PUNCT
ejpam-454	89	12	by	by	ADP
ejpam-454	89	13	gi	gi	INTJ
ejpam-454	89	14	(	(	PUNCT
ejpam-454	89	15	·	·	PUNCT
ejpam-454	89	16	)	)	PUNCT
ejpam-454	89	17	is	be	AUX
ejpam-454	89	18	monotone	monotone	ADJ
ejpam-454	89	19	nondecreasing	nondecrease	VERB
ejpam-454	89	20	,	,	PUNCT
ejpam-454	89	21	x	x	SYM
ejpam-454	89	22	6=	6=	NUM
ejpam-454	89	23	y	y	PROPN
ejpam-454	89	24	will	will	AUX
ejpam-454	89	25	imply	imply	VERB
ejpam-454	89	26	two	two	NUM
ejpam-454	89	27	cases	case	NOUN
ejpam-454	89	28	:	:	PUNCT
ejpam-454	89	29	(	(	PUNCT
ejpam-454	89	30	i	i	NOUN
ejpam-454	89	31	)	)	PUNCT
ejpam-454	89	32	x	x	SYM
ejpam-454	90	1	6=	6=	NUM
ejpam-454	90	2	y	y	PROPN
ejpam-454	90	3	and	and	CCONJ
ejpam-454	90	4	g(x)−	g(x)−	PROPN
ejpam-454	90	5	g(y	g(y	PROPN
ejpam-454	90	6	)	)	PUNCT
ejpam-454	90	7	6=	6=	ADP
ejpam-454	90	8	0	0	NUM
ejpam-454	90	9	;	;	PUNCT
ejpam-454	90	10	(	(	PUNCT
ejpam-454	90	11	ii	ii	NOUN
ejpam-454	90	12	)	)	PUNCT
ejpam-454	90	13	x	x	SYM
ejpam-454	91	1	6=	6=	ADP
ejpam-454	91	2	y	y	PROPN
ejpam-454	91	3	and	and	CCONJ
ejpam-454	91	4	g(x)−	g(x)−	PROPN
ejpam-454	91	5	g(y	g(y	PROPN
ejpam-454	91	6	)	)	PUNCT
ejpam-454	91	7	=	=	PUNCT
ejpam-454	92	1	0	0	X
ejpam-454	92	2	.	.	PUNCT
ejpam-454	93	1	first	first	ADV
ejpam-454	93	2	,	,	PUNCT
ejpam-454	93	3	consider	consider	VERB
ejpam-454	93	4	the	the	DET
ejpam-454	93	5	case	case	NOUN
ejpam-454	93	6	(	(	PUNCT
ejpam-454	93	7	i	i	NOUN
ejpam-454	93	8	)	)	PUNCT
ejpam-454	94	1	where	where	SCONJ
ejpam-454	94	2	x	x	X
ejpam-454	94	3	6=	6=	ADP
ejpam-454	94	4	y	y	PROPN
ejpam-454	94	5	and	and	CCONJ
ejpam-454	94	6	g(x)−	g(x)−	PROPN
ejpam-454	94	7	g(y	g(y	PROPN
ejpam-454	94	8	)	)	PUNCT
ejpam-454	94	9	6=	6=	ADP
ejpam-454	94	10	0	0	X
ejpam-454	94	11	.	.	PUNCT
ejpam-454	95	1	in	in	ADP
ejpam-454	95	2	this	this	DET
ejpam-454	95	3	case	case	NOUN
ejpam-454	95	4	,	,	PUNCT
ejpam-454	95	5	there	there	PRON
ejpam-454	95	6	exists	exist	VERB
ejpam-454	95	7	h	h	PROPN
ejpam-454	95	8	∈	∈	PROPN
ejpam-454	95	9	{	{	PUNCT
ejpam-454	95	10	1	1	NUM
ejpam-454	95	11	,	,	PUNCT
ejpam-454	95	12	·	·	PUNCT
ejpam-454	95	13	·	·	PUNCT
ejpam-454	95	14	·	·	PUNCT
ejpam-454	95	15	,	,	PUNCT
ejpam-454	95	16	n	n	CCONJ
ejpam-454	95	17	}	}	PUNCT
ejpam-454	95	18	such	such	ADJ
ejpam-454	95	19	that	that	SCONJ
ejpam-454	95	20	(	(	PUNCT
ejpam-454	95	21	xh−	xh−	PROPN
ejpam-454	95	22	yh)(gh(xh)−	yh)(gh(xh)−	X
ejpam-454	95	23	gh(yh	gh(yh	PROPN
ejpam-454	95	24	)	)	PUNCT
ejpam-454	95	25	)	)	PUNCT
ejpam-454	95	26	>	>	X
ejpam-454	95	27	0	0	PUNCT
ejpam-454	96	1	and	and	CCONJ
ejpam-454	96	2	(	(	PUNCT
ejpam-454	96	3	x	x	X
ejpam-454	96	4	i	i	PRON
ejpam-454	96	5	−	−	PROPN
ejpam-454	96	6	yi)(gi(x	yi)(gi(x	PROPN
ejpam-454	96	7	i)−	i)−	PROPN
ejpam-454	96	8	gi(yi	gi(yi	PROPN
ejpam-454	96	9	)	)	PUNCT
ejpam-454	96	10	)	)	PUNCT
ejpam-454	96	11	≥	≥	NOUN
ejpam-454	96	12	0	0	NUM
ejpam-454	96	13	for	for	SCONJ
ejpam-454	96	14	i	i	PROPN
ejpam-454	96	15	6=	6=	PROPN
ejpam-454	96	16	h.	h.	PROPN
ejpam-454	96	17	moreover	moreover	ADV
ejpam-454	96	18	,	,	PUNCT
ejpam-454	96	19	we	we	PRON
ejpam-454	96	20	have	have	VERB
ejpam-454	96	21	2(g(x)−	2(g(x)−	NUM
ejpam-454	96	22	g(y))t	g(y))t	PROPN
ejpam-454	96	23	·	·	PUNCT
ejpam-454	96	24	(	(	PUNCT
ejpam-454	96	25	h(x)−h(y	h(x)−h(y	ADV
ejpam-454	96	26	)	)	PUNCT
ejpam-454	96	27	)	)	PUNCT
ejpam-454	97	1	≤	≤	NUM
ejpam-454	97	2	−2	−2	NOUN
ejpam-454	97	3	n	n	CCONJ
ejpam-454	97	4	∑	∑	PROPN
ejpam-454	97	5	i=1	i=1	PROPN
ejpam-454	97	6	di(x	di(x	NOUN
ejpam-454	97	7	i	i	PRON
ejpam-454	97	8	−	−	NOUN
ejpam-454	97	9	yi)(gi(x	yi)(gi(x	PROPN
ejpam-454	97	10	i)−	i)−	PROPN
ejpam-454	97	11	gi(yi))+	gi(yi))+	NOUN
ejpam-454	97	12	(	(	PUNCT
ejpam-454	97	13	g(x)−	g(x)−	NOUN
ejpam-454	97	14	g(y))t	g(y))t	PROPN
ejpam-454	97	15	(	(	PUNCT
ejpam-454	97	16	a+at	a+at	PROPN
ejpam-454	97	17	)	)	PUNCT
ejpam-454	97	18	(	(	PUNCT
ejpam-454	97	19	g(x)−	g(x)−	PROPN
ejpam-454	97	20	g(y	g(y	PROPN
ejpam-454	97	21	)	)	PUNCT
ejpam-454	97	22	)	)	PUNCT
ejpam-454	98	1	+	+	CCONJ
ejpam-454	98	2	n	n	CCONJ
ejpam-454	98	3	∑	∑	ADP
ejpam-454	98	4	i=1	i=1	PROPN
ejpam-454	98	5	n	n	ADV
ejpam-454	98	6	∑	∑	ADV
ejpam-454	98	7	j=1	j=1	NOUN
ejpam-454	98	8	1	1	NUM
ejpam-454	98	9	r	r	NOUN
ejpam-454	98	10	�	�	PROPN
ejpam-454	98	11	�	�	PROPN
ejpam-454	98	12	bi	bi	PROPN
ejpam-454	98	13	j	j	PROPN
ejpam-454	98	14	�	�	PROPN
ejpam-454	98	15	�	�	PROPN
ejpam-454	98	16	(	(	PUNCT
ejpam-454	98	17	gi(x	gi(x	PROPN
ejpam-454	98	18	i)−	i)−	PROPN
ejpam-454	98	19	gi(yi	gi(yi	PROPN
ejpam-454	98	20	)	)	PUNCT
ejpam-454	98	21	)	)	PUNCT
ejpam-454	99	1	2	2	NUM
ejpam-454	99	2	+	+	NUM
ejpam-454	99	3	n	n	CCONJ
ejpam-454	99	4	∑	∑	ADP
ejpam-454	99	5	i=1	i=1	PROPN
ejpam-454	99	6	n	n	ADV
ejpam-454	99	7	∑	∑	ADV
ejpam-454	99	8	j=1	j=1	PROPN
ejpam-454	99	9	r	r	PROPN
ejpam-454	99	10	�	�	PROPN
ejpam-454	99	11	�	�	PROPN
ejpam-454	99	12	bi	bi	PROPN
ejpam-454	99	13	j	j	PROPN
ejpam-454	99	14	�	�	PROPN
ejpam-454	99	15	�	�	PROPN
ejpam-454	99	16	(	(	PUNCT
ejpam-454	99	17	g	g	PROPN
ejpam-454	99	18	j(x	j(x	PROPN
ejpam-454	99	19	j)−	j)−	PROPN
ejpam-454	99	20	g	g	PROPN
ejpam-454	99	21	j(y	j(y	PROPN
ejpam-454	99	22	j	j	PROPN
ejpam-454	99	23	)	)	PUNCT
ejpam-454	99	24	)	)	PUNCT
ejpam-454	99	25	2	2	NUM
ejpam-454	99	26	a.	a.	NOUN
ejpam-454	99	27	wu	wu	PROPN
ejpam-454	99	28	,	,	PUNCT
ejpam-454	99	29	j.	j.	PROPN
ejpam-454	99	30	zhang	zhang	PROPN
ejpam-454	99	31	,	,	PUNCT
ejpam-454	99	32	c.	c.	PROPN
ejpam-454	99	33	fu	fu	PROPN
ejpam-454	99	34	/	/	SYM
ejpam-454	99	35	eur	eur	PROPN
ejpam-454	99	36	.	.	PUNCT
ejpam-454	100	1	j.	j.	PROPN
ejpam-454	100	2	pure	pure	PROPN
ejpam-454	100	3	appl	appl	PROPN
ejpam-454	100	4	.	.	PROPN
ejpam-454	100	5	math	math	PROPN
ejpam-454	100	6	,	,	PUNCT
ejpam-454	100	7	3	3	NUM
ejpam-454	100	8	(	(	PUNCT
ejpam-454	100	9	2010	2010	NUM
ejpam-454	100	10	)	)	PUNCT
ejpam-454	100	11	,	,	PUNCT
ejpam-454	100	12	806	806	NUM
ejpam-454	100	13	-	-	SYM
ejpam-454	100	14	818	818	NUM
ejpam-454	100	15	810	810	NUM
ejpam-454	100	16	≤	≤	NUM
ejpam-454	100	17	−2	−2	NOUN
ejpam-454	101	1	n	n	CCONJ
ejpam-454	101	2	∑	∑	PROPN
ejpam-454	101	3	i=1	i=1	PROPN
ejpam-454	101	4	di(x	di(x	NOUN
ejpam-454	102	1	i	i	PRON
ejpam-454	102	2	−	−	NOUN
ejpam-454	103	1	yi)(gi(x	yi)(gi(x	PROPN
ejpam-454	103	2	i)−	i)−	PROPN
ejpam-454	103	3	gi(yi	gi(yi	PROPN
ejpam-454	103	4	)	)	PUNCT
ejpam-454	103	5	)	)	PUNCT
ejpam-454	104	1	+	+	CCONJ
ejpam-454	104	2	(	(	PUNCT
ejpam-454	104	3	g(x)−	g(x)−	NOUN
ejpam-454	104	4	g(y))t	g(y))t	PROPN
ejpam-454	105	1	[	[	X
ejpam-454	105	2	a+	a+	PUNCT
ejpam-454	105	3	at	at	ADP
ejpam-454	105	4	+	+	CCONJ
ejpam-454	105	5	(	(	PUNCT
ejpam-454	105	6	1	1	NUM
ejpam-454	105	7	r	r	NOUN
ejpam-454	105	8	‖b‖∞	‖b‖∞	PROPN
ejpam-454	105	9	+	+	CCONJ
ejpam-454	105	10	r‖b‖1)i	r‖b‖1)i	X
ejpam-454	105	11	]	]	X
ejpam-454	105	12	·	·	PUNCT
ejpam-454	105	13	(	(	PUNCT
ejpam-454	105	14	g(x)−	g(x)−	PROPN
ejpam-454	105	15	g(y	g(y	PROPN
ejpam-454	105	16	)	)	PUNCT
ejpam-454	105	17	)	)	PUNCT
ejpam-454	105	18	≤	≤	NUM
ejpam-454	105	19	−2	−2	NOUN
ejpam-454	105	20	n	n	CCONJ
ejpam-454	105	21	∑	∑	PROPN
ejpam-454	105	22	i=1	i=1	PROPN
ejpam-454	105	23	di(x	di(x	NOUN
ejpam-454	106	1	i	i	PRON
ejpam-454	106	2	−	−	NOUN
ejpam-454	107	1	yi)(gi(x	yi)(gi(x	PROPN
ejpam-454	107	2	i)−	i)−	PROPN
ejpam-454	107	3	gi(yi	gi(yi	PROPN
ejpam-454	107	4	)	)	PUNCT
ejpam-454	107	5	)	)	PUNCT
ejpam-454	108	1	≤	≤	NUM
ejpam-454	108	2	−2dh(xh−	−2dh(xh−	PROPN
ejpam-454	108	3	yh)(gh(xh)−	yh)(gh(xh)−	PROPN
ejpam-454	108	4	gh(yh	gh(yh	PROPN
ejpam-454	108	5	)	)	PUNCT
ejpam-454	108	6	)	)	PUNCT
ejpam-454	108	7	<	<	X
ejpam-454	108	8	0	0	PUNCT
ejpam-454	108	9	(	(	PUNCT
ejpam-454	108	10	6	6	NUM
ejpam-454	108	11	)	)	PUNCT
ejpam-454	108	12	hence	hence	ADV
ejpam-454	108	13	,	,	PUNCT
ejpam-454	108	14	hh(x	hh(x	X
ejpam-454	108	15	)	)	PUNCT
ejpam-454	108	16	6=	6=	ADP
ejpam-454	108	17	hh(y	hh(y	NOUN
ejpam-454	108	18	)	)	PUNCT
ejpam-454	108	19	.	.	PUNCT
ejpam-454	109	1	that	that	PRON
ejpam-454	109	2	is	be	AUX
ejpam-454	109	3	,	,	PUNCT
ejpam-454	109	4	h(x	h(x	PROPN
ejpam-454	109	5	)	)	PUNCT
ejpam-454	110	1	6=	6=	ADP
ejpam-454	110	2	h(y	h(y	ADV
ejpam-454	110	3	)	)	PUNCT
ejpam-454	111	1	when	when	SCONJ
ejpam-454	111	2	x	x	PROPN
ejpam-454	111	3	6=	6=	ADP
ejpam-454	111	4	y	y	PROPN
ejpam-454	111	5	and	and	CCONJ
ejpam-454	111	6	g(x	g(x	NOUN
ejpam-454	111	7	)	)	PUNCT
ejpam-454	111	8	6=	6=	AUX
ejpam-454	111	9	g(y	g(y	NOUN
ejpam-454	111	10	)	)	PUNCT
ejpam-454	111	11	.	.	PUNCT
ejpam-454	112	1	now	now	ADV
ejpam-454	112	2	consider	consider	VERB
ejpam-454	112	3	the	the	DET
ejpam-454	112	4	case	case	NOUN
ejpam-454	112	5	(	(	PUNCT
ejpam-454	112	6	ii	ii	NOUN
ejpam-454	112	7	)	)	PUNCT
ejpam-454	112	8	where	where	SCONJ
ejpam-454	112	9	x	x	X
ejpam-454	112	10	6=	6=	ADP
ejpam-454	112	11	y	y	PROPN
ejpam-454	112	12	and	and	CCONJ
ejpam-454	112	13	g(x)−	g(x)−	PROPN
ejpam-454	112	14	g(y	g(y	PROPN
ejpam-454	112	15	)	)	PUNCT
ejpam-454	112	16	=	=	PUNCT
ejpam-454	113	1	0	0	X
ejpam-454	113	2	.	.	PUNCT
ejpam-454	114	1	in	in	ADP
ejpam-454	114	2	the	the	DET
ejpam-454	114	3	case	case	NOUN
ejpam-454	114	4	,	,	PUNCT
ejpam-454	114	5	we	we	PRON
ejpam-454	114	6	have	have	VERB
ejpam-454	114	7	h(x)−h(y	h(x)−h(y	X
ejpam-454	114	8	)	)	PUNCT
ejpam-454	114	9	=	=	SYM
ejpam-454	114	10	−d(x	−d(x	NOUN
ejpam-454	114	11	−	−	PROPN
ejpam-454	114	12	y	y	PROPN
ejpam-454	114	13	)	)	PUNCT
ejpam-454	114	14	6=	6=	ADP
ejpam-454	114	15	0	0	NUM
ejpam-454	114	16	where	where	SCONJ
ejpam-454	114	17	d	d	NOUN
ejpam-454	114	18	=	=	PUNCT
ejpam-454	114	19	diag(d1	diag(d1	NOUN
ejpam-454	114	20	,	,	PUNCT
ejpam-454	114	21	·	·	PUNCT
ejpam-454	114	22	·	·	PUNCT
ejpam-454	114	23	·	·	PUNCT
ejpam-454	114	24	,	,	PUNCT
ejpam-454	114	25	dn	dn	PROPN
ejpam-454	114	26	)	)	PUNCT
ejpam-454	114	27	.	.	PUNCT
ejpam-454	115	1	thus	thus	ADV
ejpam-454	115	2	,	,	PUNCT
ejpam-454	115	3	h(x	h(x	PROPN
ejpam-454	115	4	)	)	PUNCT
ejpam-454	116	1	6=	6=	ADP
ejpam-454	116	2	h(y	h(y	ADV
ejpam-454	116	3	)	)	PUNCT
ejpam-454	116	4	for	for	ADP
ejpam-454	116	5	all	all	DET
ejpam-454	116	6	x	x	SYM
ejpam-454	116	7	6=	6=	ADP
ejpam-454	116	8	y	y	PROPN
ejpam-454	116	9	and	and	CCONJ
ejpam-454	116	10	g(x	g(x	NOUN
ejpam-454	116	11	)	)	PUNCT
ejpam-454	117	1	=	=	SYM
ejpam-454	117	2	g(y	g(y	NOUN
ejpam-454	117	3	)	)	PUNCT
ejpam-454	117	4	.	.	PUNCT
ejpam-454	118	1	hence	hence	ADV
ejpam-454	118	2	,	,	PUNCT
ejpam-454	118	3	we	we	PRON
ejpam-454	118	4	have	have	AUX
ejpam-454	118	5	proved	prove	VERB
ejpam-454	118	6	that	that	SCONJ
ejpam-454	118	7	h(x	h(x	PROPN
ejpam-454	118	8	)	)	PUNCT
ejpam-454	118	9	6=	6=	ADP
ejpam-454	118	10	h(y	h(y	ADV
ejpam-454	118	11	)	)	PUNCT
ejpam-454	119	1	when	when	SCONJ
ejpam-454	119	2	x	x	PRON
ejpam-454	119	3	6=	6=	PROPN
ejpam-454	119	4	y.	y.	NOUN
ejpam-454	119	5	step	step	NOUN
ejpam-454	119	6	2	2	NUM
ejpam-454	119	7	.	.	PUNCT
ejpam-454	119	8	in	in	ADP
ejpam-454	119	9	(	(	PUNCT
ejpam-454	119	10	2.4	2.4	NUM
ejpam-454	119	11	)	)	PUNCT
ejpam-454	119	12	,	,	PUNCT
ejpam-454	119	13	let	let	VERB
ejpam-454	119	14	y	y	PROPN
ejpam-454	119	15	=	=	SYM
ejpam-454	119	16	0	0	PROPN
ejpam-454	119	17	,	,	PUNCT
ejpam-454	119	18	we	we	PRON
ejpam-454	119	19	get	get	VERB
ejpam-454	119	20	2(g(x)−	2(g(x)−	NUM
ejpam-454	119	21	g(0))t	g(0))t	NOUN
ejpam-454	119	22	·	·	PUNCT
ejpam-454	119	23	(	(	PUNCT
ejpam-454	119	24	h(x)−h(0))≤	h(x)−h(0))≤	NUM
ejpam-454	119	25	−2	−2	NOUN
ejpam-454	119	26	n	n	NOUN
ejpam-454	119	27	∑	∑	PROPN
ejpam-454	119	28	i=1	i=1	PROPN
ejpam-454	119	29	di(x	di(x	NOUN
ejpam-454	120	1	i	i	PRON
ejpam-454	120	2	−	−	PROPN
ejpam-454	120	3	0)(gi(x	0)(gi(x	NOUN
ejpam-454	121	1	i)−	i)−	PROPN
ejpam-454	121	2	gi(0	gi(0	PROPN
ejpam-454	121	3	)	)	PUNCT
ejpam-454	121	4	)	)	PUNCT
ejpam-454	122	1	≤	≤	NOUN
ejpam-454	123	1	−2d	−2d	PROPN
ejpam-454	123	2	x	x	SYM
ejpam-454	123	3	t(g(x)−	t(g(x)−	NOUN
ejpam-454	123	4	g(0	g(0	NOUN
ejpam-454	123	5	)	)	PUNCT
ejpam-454	123	6	)	)	PUNCT
ejpam-454	123	7	(	(	PUNCT
ejpam-454	123	8	7	7	X
ejpam-454	123	9	)	)	PUNCT
ejpam-454	123	10	where	where	SCONJ
ejpam-454	123	11	d	d	PROPN
ejpam-454	123	12	=	=	NOUN
ejpam-454	123	13	min	min	X
ejpam-454	123	14	�	�	PROPN
ejpam-454	123	15	d1	d1	PROPN
ejpam-454	123	16	,	,	PUNCT
ejpam-454	123	17	·	·	PUNCT
ejpam-454	123	18	·	·	PUNCT
ejpam-454	123	19	·	·	PUNCT
ejpam-454	123	20	,	,	PUNCT
ejpam-454	124	1	dn	dn	INTJ
ejpam-454	124	2	.	.	PUNCT
ejpam-454	125	1	from	from	ADP
ejpam-454	125	2	(	(	PUNCT
ejpam-454	125	3	7	7	NUM
ejpam-454	125	4	)	)	PUNCT
ejpam-454	125	5	and	and	CCONJ
ejpam-454	125	6	gi	gi	PROPN
ejpam-454	125	7	is	be	AUX
ejpam-454	125	8	monotone	monotone	ADJ
ejpam-454	125	9	nondecreasing	nondecrease	VERB
ejpam-454	125	10	,	,	PUNCT
ejpam-454	125	11	it	it	PRON
ejpam-454	125	12	follows	follow	VERB
ejpam-454	125	13	that	that	SCONJ
ejpam-454	125	14	0≤	0≤	NUM
ejpam-454	126	1	d	d	NOUN
ejpam-454	126	2	n	n	X
ejpam-454	126	3	∑	∑	ADV
ejpam-454	126	4	i=1	i=1	PROPN
ejpam-454	126	5	x	x	SYM
ejpam-454	126	6	i(gi(x	i(gi(x	PROPN
ejpam-454	126	7	i)−	i)−	PROPN
ejpam-454	126	8	gi(0))≤	gi(0))≤	PROPN
ejpam-454	126	9	n	n	ADP
ejpam-454	126	10	∑	∑	PROPN
ejpam-454	126	11	i=1	i=1	PROPN
ejpam-454	126	12	�	�	PROPN
ejpam-454	126	13	�	�	PROPN
ejpam-454	126	14	(	(	PUNCT
ejpam-454	126	15	gi(x	gi(x	PROPN
ejpam-454	126	16	i)−	i)−	PROPN
ejpam-454	126	17	gi(0	gi(0	PROPN
ejpam-454	126	18	)	)	PUNCT
ejpam-454	126	19	)	)	PUNCT
ejpam-454	126	20	·	·	PUNCT
ejpam-454	126	21	(	(	PUNCT
ejpam-454	126	22	hi(x)−hi(0	hi(x)−hi(0	PROPN
ejpam-454	126	23	)	)	PUNCT
ejpam-454	126	24	)	)	PUNCT
ejpam-454	126	25	�	�	PROPN
ejpam-454	126	26	�	�	PROPN
ejpam-454	126	27	.	.	PUNCT
ejpam-454	127	1	(	(	PUNCT
ejpam-454	127	2	8)	8)	NUM
ejpam-454	127	3	if	if	SCONJ
ejpam-454	127	4	lim	lim	PROPN
ejpam-454	127	5	‖x‖→∞	‖x‖→∞	PROPN
ejpam-454	127	6	‖h(x)‖	‖h(x)‖	PROPN
ejpam-454	128	1	6=∞	6=∞	NUM
ejpam-454	128	2	,	,	PUNCT
ejpam-454	128	3	then	then	ADV
ejpam-454	128	4	there	there	PRON
ejpam-454	128	5	exists	exist	VERB
ejpam-454	128	6	a	a	DET
ejpam-454	128	7	sequence	sequence	NOUN
ejpam-454	128	8	{	{	PUNCT
ejpam-454	128	9	x	x	NOUN
ejpam-454	128	10	p	p	X
ejpam-454	128	11	}	}	PUNCT
ejpam-454	128	12	such	such	ADJ
ejpam-454	128	13	that	that	SCONJ
ejpam-454	128	14	lim	lim	PROPN
ejpam-454	128	15	p→∞	p→∞	NUM
ejpam-454	128	16	‖x	‖x	PROPN
ejpam-454	128	17	p‖	p‖	PROPN
ejpam-454	129	1	=	=	NOUN
ejpam-454	129	2	∞	∞	PROPN
ejpam-454	129	3	and	and	CCONJ
ejpam-454	129	4	for	for	ADP
ejpam-454	129	5	all	all	DET
ejpam-454	129	6	p	p	NOUN
ejpam-454	129	7	,	,	PUNCT
ejpam-454	129	8	‖h(x	‖h(x	PART
ejpam-454	129	9	p)‖	p)‖	VERB
ejpam-454	129	10	≤	≤	NUM
ejpam-454	129	11	m1	m1	NOUN
ejpam-454	129	12	,	,	PUNCT
ejpam-454	129	13	where	where	SCONJ
ejpam-454	129	14	m1	m1	PROPN
ejpam-454	129	15	is	be	AUX
ejpam-454	129	16	a	a	DET
ejpam-454	129	17	positive	positive	ADJ
ejpam-454	129	18	constant	constant	NOUN
ejpam-454	129	19	.	.	PUNCT
ejpam-454	130	1	therefore	therefore	ADV
ejpam-454	130	2	,	,	PUNCT
ejpam-454	130	3	there	there	PRON
ejpam-454	130	4	exists	exist	VERB
ejpam-454	130	5	a	a	DET
ejpam-454	130	6	subsequence	subsequence	NOUN
ejpam-454	130	7	(	(	PUNCT
ejpam-454	130	8	for	for	ADP
ejpam-454	130	9	convenience	convenience	NOUN
ejpam-454	130	10	,	,	PUNCT
ejpam-454	130	11	we	we	PRON
ejpam-454	130	12	also	also	ADV
ejpam-454	130	13	denote	denote	VERB
ejpam-454	130	14	it	it	PRON
ejpam-454	130	15	as	as	ADP
ejpam-454	130	16	{	{	PUNCT
ejpam-454	130	17	x	x	X
ejpam-454	130	18	p	p	NOUN
ejpam-454	130	19	}	}	PUNCT
ejpam-454	130	20	)	)	PUNCT
ejpam-454	130	21	and	and	CCONJ
ejpam-454	130	22	a	a	DET
ejpam-454	130	23	nonempty	nonempty	ADV
ejpam-454	130	24	set	set	VERB
ejpam-454	130	25	w	w	ADP
ejpam-454	130	26	⊂	⊂	PROPN
ejpam-454	130	27	{	{	PUNCT
ejpam-454	130	28	1	1	NUM
ejpam-454	130	29	,	,	PUNCT
ejpam-454	130	30	·	·	PUNCT
ejpam-454	130	31	·	·	PUNCT
ejpam-454	130	32	·	·	PUNCT
ejpam-454	130	33	,	,	PUNCT
ejpam-454	130	34	n	n	CCONJ
ejpam-454	130	35	}	}	PUNCT
ejpam-454	130	36	,	,	PUNCT
ejpam-454	130	37	such	such	ADJ
ejpam-454	130	38	that	that	SCONJ
ejpam-454	130	39	the	the	DET
ejpam-454	130	40	follows	follow	VERB
ejpam-454	130	41	hold	hold	VERB
ejpam-454	130	42	:	:	PUNCT
ejpam-454	130	43	(	(	PUNCT
ejpam-454	130	44	1	1	X
ejpam-454	130	45	)	)	PUNCT
ejpam-454	130	46	lim	lim	PROPN
ejpam-454	130	47	p→∞	p→∞	PROPN
ejpam-454	130	48	�	�	PROPN
ejpam-454	130	49	�	�	PROPN
ejpam-454	130	50	x	x	PROPN
ejpam-454	130	51	p	p	X
ejpam-454	130	52	i	i	PROPN
ejpam-454	130	53	�	�	PROPN
ejpam-454	130	54	�	�	PROPN
ejpam-454	131	1	=	=	NUM
ejpam-454	131	2	∞	∞	PROPN
ejpam-454	131	3	for	for	ADP
ejpam-454	131	4	all	all	PRON
ejpam-454	131	5	i	i	PRON
ejpam-454	131	6	∈w	∈w	VERB
ejpam-454	131	7	;	;	PUNCT
ejpam-454	131	8	(	(	PUNCT
ejpam-454	131	9	2	2	X
ejpam-454	131	10	)	)	PUNCT
ejpam-454	131	11	there	there	PRON
ejpam-454	131	12	exists	exist	VERB
ejpam-454	131	13	a	a	DET
ejpam-454	131	14	positive	positive	ADJ
ejpam-454	131	15	constant	constant	ADJ
ejpam-454	131	16	m2	m2	NOUN
ejpam-454	131	17	such	such	ADJ
ejpam-454	131	18	that	that	SCONJ
ejpam-454	131	19	�	�	PROPN
ejpam-454	131	20	�	�	PROPN
ejpam-454	131	21	x	x	PROPN
ejpam-454	131	22	p	p	X
ejpam-454	131	23	i	i	PROPN
ejpam-454	131	24	�	�	PROPN
ejpam-454	131	25	�	�	PROPN
ejpam-454	131	26	≤	≤	NUM
ejpam-454	131	27	m2	m2	PROPN
ejpam-454	131	28	for	for	ADP
ejpam-454	131	29	all	all	DET
ejpam-454	131	30	p	p	NOUN
ejpam-454	131	31	and	and	CCONJ
ejpam-454	131	32	i	i	PRON
ejpam-454	131	33	∈	∈	PROPN
ejpam-454	131	34	{	{	PUNCT
ejpam-454	131	35	1	1	NUM
ejpam-454	131	36	,	,	PUNCT
ejpam-454	131	37	·	·	PUNCT
ejpam-454	131	38	·	·	PUNCT
ejpam-454	131	39	·	·	PUNCT
ejpam-454	131	40	,	,	PUNCT
ejpam-454	131	41	n	n	CCONJ
ejpam-454	131	42	}	}	PUNCT
ejpam-454	131	43	\w	\w	ADJ
ejpam-454	131	44	;	;	PUNCT
ejpam-454	131	45	(	(	PUNCT
ejpam-454	131	46	3	3	X
ejpam-454	131	47	)	)	PUNCT
ejpam-454	131	48	hi(x	hi(x	NOUN
ejpam-454	131	49	p	p	NOUN
ejpam-454	131	50	)	)	PUNCT
ejpam-454	131	51	≤	≤	NOUN
ejpam-454	131	52	m1	m1	NOUN
ejpam-454	131	53	for	for	ADP
ejpam-454	131	54	all	all	DET
ejpam-454	131	55	i	i	PRON
ejpam-454	131	56	and	and	CCONJ
ejpam-454	131	57	p.	p.	NOUN
ejpam-454	131	58	since	since	SCONJ
ejpam-454	131	59	gi(s	gi(s	NOUN
ejpam-454	131	60	)	)	PUNCT
ejpam-454	131	61	is	be	AUX
ejpam-454	131	62	continuous	continuous	ADJ
ejpam-454	131	63	on	on	ADP
ejpam-454	131	64	[	[	X
ejpam-454	131	65	−m2	−m2	NOUN
ejpam-454	131	66	,	,	PUNCT
ejpam-454	131	67	m2	m2	PROPN
ejpam-454	131	68	]	]	PUNCT
ejpam-454	131	69	,	,	PUNCT
ejpam-454	131	70	there	there	PRON
ejpam-454	131	71	exists	exist	VERB
ejpam-454	131	72	a	a	DET
ejpam-454	131	73	positive	positive	ADJ
ejpam-454	131	74	constant	constant	ADJ
ejpam-454	131	75	m3	m3	NOUN
ejpam-454	131	76	such	such	ADJ
ejpam-454	131	77	that	that	SCONJ
ejpam-454	131	78	�	�	PROPN
ejpam-454	131	79	�	�	PROPN
ejpam-454	131	80	gi(s	gi(s	NOUN
ejpam-454	131	81	)	)	PUNCT
ejpam-454	131	82	�	�	PROPN
ejpam-454	131	83	�	�	PROPN
ejpam-454	131	84	≤	≤	PROPN
ejpam-454	131	85	m3	m3	PROPN
ejpam-454	131	86	for	for	ADP
ejpam-454	131	87	all	all	DET
ejpam-454	131	88	s	s	PART
ejpam-454	131	89	∈	∈	NOUN
ejpam-454	131	90	[	[	X
ejpam-454	131	91	−m2	−m2	NOUN
ejpam-454	131	92	,	,	PUNCT
ejpam-454	131	93	m2	m2	PROPN
ejpam-454	131	94	]	]	PUNCT
ejpam-454	131	95	and	and	CCONJ
ejpam-454	131	96	i	i	PRON
ejpam-454	131	97	∈	∈	PROPN
ejpam-454	131	98	{	{	PUNCT
ejpam-454	131	99	1	1	NUM
ejpam-454	131	100	,	,	PUNCT
ejpam-454	131	101	·	·	PUNCT
ejpam-454	131	102	·	·	PUNCT
ejpam-454	131	103	·	·	PUNCT
ejpam-454	131	104	,	,	PUNCT
ejpam-454	131	105	n	n	CCONJ
ejpam-454	131	106	}	}	PUNCT
ejpam-454	131	107	\w	\w	ADJ
ejpam-454	131	108	.	.	PUNCT
ejpam-454	132	1	thus	thus	ADV
ejpam-454	132	2	,	,	PUNCT
ejpam-454	132	3	�	�	PROPN
ejpam-454	132	4	�	�	PROPN
ejpam-454	132	5	gi(x	gi(x	PROPN
ejpam-454	132	6	p	p	PROPN
ejpam-454	132	7	i	i	PROPN
ejpam-454	132	8	)	)	PUNCT
ejpam-454	132	9	�	�	PROPN
ejpam-454	132	10	�	�	PROPN
ejpam-454	132	11	≤	≤	PROPN
ejpam-454	132	12	m3	m3	PROPN
ejpam-454	132	13	for	for	ADP
ejpam-454	132	14	all	all	DET
ejpam-454	132	15	p	p	NOUN
ejpam-454	132	16	and	and	CCONJ
ejpam-454	132	17	i	i	PRON
ejpam-454	132	18	∈	∈	PROPN
ejpam-454	132	19	{	{	PUNCT
ejpam-454	132	20	1	1	NUM
ejpam-454	132	21	,	,	PUNCT
ejpam-454	132	22	·	·	PUNCT
ejpam-454	132	23	·	·	PUNCT
ejpam-454	132	24	·	·	PUNCT
ejpam-454	132	25	,	,	PUNCT
ejpam-454	132	26	n}\w	n}\w	NOUN
ejpam-454	132	27	.	.	PUNCT
ejpam-454	133	1	moreover	moreover	ADV
ejpam-454	133	2	,	,	PUNCT
ejpam-454	133	3	we	we	PRON
ejpam-454	133	4	have	have	VERB
ejpam-454	133	5	n	n	NUM
ejpam-454	133	6	∑	∑	PROPN
ejpam-454	133	7	i=1	i=1	PROPN
ejpam-454	133	8	�	�	PROPN
ejpam-454	133	9	�	�	PROPN
ejpam-454	133	10	(	(	PUNCT
ejpam-454	133	11	gi(x	gi(x	NOUN
ejpam-454	133	12	p	p	PROPN
ejpam-454	133	13	i	i	PROPN
ejpam-454	133	14	)	)	PUNCT
ejpam-454	133	15	−	−	PROPN
ejpam-454	134	1	gi(0	gi(0	PROPN
ejpam-454	134	2	)	)	PUNCT
ejpam-454	134	3	)	)	PUNCT
ejpam-454	134	4	·	·	PUNCT
ejpam-454	135	1	(	(	PUNCT
ejpam-454	135	2	hi(x	hi(x	PROPN
ejpam-454	135	3	p)−hi(0	p)−hi(0	PROPN
ejpam-454	135	4	)	)	PUNCT
ejpam-454	135	5	)	)	PUNCT
ejpam-454	135	6	�	�	PROPN
ejpam-454	135	7	�	�	PROPN
ejpam-454	135	8	=	=	SYM
ejpam-454	135	9	∑	∑	PROPN
ejpam-454	135	10	i∈w	i∈w	PROPN
ejpam-454	135	11	�	�	PROPN
ejpam-454	135	12	�	�	PROPN
ejpam-454	135	13	(	(	PUNCT
ejpam-454	135	14	gi(x	gi(x	PROPN
ejpam-454	135	15	p	p	PROPN
ejpam-454	135	16	i	i	PROPN
ejpam-454	135	17	)	)	PUNCT
ejpam-454	135	18	−	−	PROPN
ejpam-454	135	19	gi(0	gi(0	PROPN
ejpam-454	135	20	)	)	PUNCT
ejpam-454	135	21	)	)	PUNCT
ejpam-454	135	22	·	·	PUNCT
ejpam-454	136	1	(	(	PUNCT
ejpam-454	136	2	hi(x	hi(x	PROPN
ejpam-454	136	3	p)−hi(0	p)−hi(0	PROPN
ejpam-454	136	4	)	)	PUNCT
ejpam-454	136	5	)	)	PUNCT
ejpam-454	136	6	�	�	PROPN
ejpam-454	136	7	�	�	PROPN
ejpam-454	136	8	a.	a.	PROPN
ejpam-454	136	9	wu	wu	PROPN
ejpam-454	136	10	,	,	PUNCT
ejpam-454	136	11	j.	j.	PROPN
ejpam-454	136	12	zhang	zhang	PROPN
ejpam-454	136	13	,	,	PUNCT
ejpam-454	136	14	c.	c.	PROPN
ejpam-454	136	15	fu	fu	PROPN
ejpam-454	136	16	/	/	SYM
ejpam-454	136	17	eur	eur	PROPN
ejpam-454	136	18	.	.	PUNCT
ejpam-454	137	1	j.	j.	PROPN
ejpam-454	137	2	pure	pure	PROPN
ejpam-454	137	3	appl	appl	PROPN
ejpam-454	137	4	.	.	PROPN
ejpam-454	137	5	math	math	PROPN
ejpam-454	137	6	,	,	PUNCT
ejpam-454	137	7	3	3	NUM
ejpam-454	137	8	(	(	PUNCT
ejpam-454	137	9	2010	2010	NUM
ejpam-454	137	10	)	)	PUNCT
ejpam-454	137	11	,	,	PUNCT
ejpam-454	137	12	806	806	NUM
ejpam-454	137	13	-	-	SYM
ejpam-454	137	14	818	818	NUM
ejpam-454	137	15	811	811	NUM
ejpam-454	137	16	+	+	CCONJ
ejpam-454	137	17	∑	∑	PROPN
ejpam-454	137	18	i	i	PRON
ejpam-454	137	19	/∈w	/∈w	PUNCT
ejpam-454	137	20	�	�	PROPN
ejpam-454	137	21	�	�	PROPN
ejpam-454	137	22	(	(	PUNCT
ejpam-454	137	23	gi(x	gi(x	NOUN
ejpam-454	137	24	p	p	PROPN
ejpam-454	138	1	i	i	PROPN
ejpam-454	138	2	)	)	PUNCT
ejpam-454	138	3	−	−	PROPN
ejpam-454	138	4	gi(0	gi(0	PROPN
ejpam-454	138	5	)	)	PUNCT
ejpam-454	138	6	)	)	PUNCT
ejpam-454	138	7	·	·	PUNCT
ejpam-454	139	1	(	(	PUNCT
ejpam-454	139	2	hi(x	hi(x	PROPN
ejpam-454	139	3	p)−hi(0	p)−hi(0	PROPN
ejpam-454	139	4	)	)	PUNCT
ejpam-454	139	5	)	)	PUNCT
ejpam-454	139	6	�	�	PROPN
ejpam-454	139	7	�	�	PROPN
ejpam-454	139	8	≤	≤	PROPN
ejpam-454	139	9	∑	∑	PUNCT
ejpam-454	139	10	i∈w	i∈w	NUM
ejpam-454	139	11	�	�	PROPN
ejpam-454	139	12	�	�	PROPN
ejpam-454	139	13	gi(x	gi(x	PROPN
ejpam-454	139	14	p	p	PROPN
ejpam-454	139	15	i	i	PROPN
ejpam-454	139	16	)	)	PUNCT
ejpam-454	139	17	−	−	PROPN
ejpam-454	139	18	gi(0	gi(0	PROPN
ejpam-454	139	19	)	)	PUNCT
ejpam-454	139	20	�	�	PROPN
ejpam-454	139	21	�	�	PROPN
ejpam-454	139	22	·	·	PUNCT
ejpam-454	139	23	(	(	PUNCT
ejpam-454	139	24	m1	m1	PROPN
ejpam-454	139	25	+	+	CCONJ
ejpam-454	139	26	�	�	PROPN
ejpam-454	139	27	�	�	PROPN
ejpam-454	139	28	hi(0	hi(0	PROPN
ejpam-454	139	29	)	)	PUNCT
ejpam-454	139	30	�	�	PROPN
ejpam-454	139	31	�	�	PROPN
ejpam-454	139	32	)	)	PUNCT
ejpam-454	140	1	+	+	CCONJ
ejpam-454	140	2	∑	∑	PROPN
ejpam-454	140	3	i	i	PRON
ejpam-454	140	4	/∈w	/∈w	PUNCT
ejpam-454	140	5	(	(	PUNCT
ejpam-454	140	6	m3	m3	PROPN
ejpam-454	140	7	+	+	CCONJ
ejpam-454	140	8	�	�	PROPN
ejpam-454	140	9	�	�	PROPN
ejpam-454	140	10	gi(0	gi(0	PROPN
ejpam-454	140	11	)	)	PUNCT
ejpam-454	140	12	�	�	PROPN
ejpam-454	140	13	�	�	PROPN
ejpam-454	140	14	)	)	PUNCT
ejpam-454	140	15	·	·	PUNCT
ejpam-454	140	16	(	(	PUNCT
ejpam-454	140	17	m1	m1	PROPN
ejpam-454	140	18	+	+	CCONJ
ejpam-454	140	19	�	�	PROPN
ejpam-454	140	20	�	�	PROPN
ejpam-454	140	21	hi(0	hi(0	PROPN
ejpam-454	140	22	)	)	PUNCT
ejpam-454	140	23	�	�	PROPN
ejpam-454	140	24	�	�	PROPN
ejpam-454	140	25	)	)	PUNCT
ejpam-454	140	26	≤	≤	NUM
ejpam-454	140	27	m	m	VERB
ejpam-454	140	28	∑	∑	PROPN
ejpam-454	140	29	i∈w	i∈w	PROPN
ejpam-454	140	30	�	�	PROPN
ejpam-454	140	31	�	�	PROPN
ejpam-454	140	32	gi(x	gi(x	PROPN
ejpam-454	140	33	p	p	PROPN
ejpam-454	140	34	i	i	PROPN
ejpam-454	140	35	)	)	PUNCT
ejpam-454	140	36	−	−	PROPN
ejpam-454	141	1	gi(0	gi(0	PROPN
ejpam-454	141	2	)	)	PUNCT
ejpam-454	141	3	�	�	PROPN
ejpam-454	141	4	�	�	PROPN
ejpam-454	141	5	+	+	PROPN
ejpam-454	141	6	m	m	PROPN
ejpam-454	141	7	(	(	PUNCT
ejpam-454	141	8	9	9	NUM
ejpam-454	141	9	)	)	PUNCT
ejpam-454	142	1	where	where	SCONJ
ejpam-454	142	2	m	m	NOUN
ejpam-454	142	3	=	=	VERB
ejpam-454	142	4	max{max	max{max	NOUN
ejpam-454	142	5	1≤	1≤	NUM
ejpam-454	142	6	j≤n	j≤n	PROPN
ejpam-454	142	7	¦	¦	PROPN
ejpam-454	142	8	m1	m1	PROPN
ejpam-454	142	9	+	+	CCONJ
ejpam-454	142	10	�	�	PROPN
ejpam-454	142	11	�	�	PROPN
ejpam-454	142	12	h	h	PROPN
ejpam-454	142	13	j(0	j(0	PROPN
ejpam-454	142	14	)	)	PUNCT
ejpam-454	142	15	�	�	PROPN
ejpam-454	142	16	�	�	PROPN
ejpam-454	142	17	©	©	PROPN
ejpam-454	142	18	,	,	PUNCT
ejpam-454	142	19	∑	∑	PROPN
ejpam-454	142	20	i	i	PRON
ejpam-454	142	21	/∈w	/∈w	PUNCT
ejpam-454	142	22	(	(	PUNCT
ejpam-454	142	23	m3	m3	PROPN
ejpam-454	142	24	+	+	CCONJ
ejpam-454	142	25	�	�	PROPN
ejpam-454	142	26	�	�	PROPN
ejpam-454	142	27	gi(0	gi(0	PROPN
ejpam-454	142	28	)	)	PUNCT
ejpam-454	142	29	�	�	PROPN
ejpam-454	142	30	�	�	PROPN
ejpam-454	142	31	)	)	PUNCT
ejpam-454	142	32	·	·	PUNCT
ejpam-454	142	33	(	(	PUNCT
ejpam-454	142	34	m1	m1	PROPN
ejpam-454	142	35	+	+	CCONJ
ejpam-454	142	36	�	�	PROPN
ejpam-454	142	37	�	�	PROPN
ejpam-454	142	38	hi(0	hi(0	PROPN
ejpam-454	142	39	)	)	PUNCT
ejpam-454	142	40	�	�	PROPN
ejpam-454	142	41	�	�	PROPN
ejpam-454	142	42	)	)	PUNCT
ejpam-454	142	43	}	}	PUNCT
ejpam-454	142	44	.	.	PUNCT
ejpam-454	143	1	by	by	ADP
ejpam-454	143	2	gi	gi	INTJ
ejpam-454	143	3	(	(	PUNCT
ejpam-454	143	4	·	·	PUNCT
ejpam-454	143	5	)	)	PUNCT
ejpam-454	143	6	is	be	AUX
ejpam-454	143	7	monotone	monotone	ADJ
ejpam-454	143	8	nondecreasing	nondecrease	VERB
ejpam-454	143	9	,	,	PUNCT
ejpam-454	143	10	then	then	ADV
ejpam-454	143	11	we	we	PRON
ejpam-454	143	12	have	have	VERB
ejpam-454	143	13	n	n	NUM
ejpam-454	143	14	∑	∑	ADV
ejpam-454	143	15	i=1	i=1	PROPN
ejpam-454	143	16	x	x	X
ejpam-454	144	1	p	p	X
ejpam-454	144	2	i	i	PRON
ejpam-454	144	3	(	(	PUNCT
ejpam-454	144	4	gi(x	gi(x	PROPN
ejpam-454	144	5	p	p	X
ejpam-454	144	6	i	i	PROPN
ejpam-454	144	7	)	)	PUNCT
ejpam-454	144	8	−	−	PROPN
ejpam-454	144	9	gi(0	gi(0	PROPN
ejpam-454	144	10	)	)	PUNCT
ejpam-454	144	11	)	)	PUNCT
ejpam-454	145	1	=	=	PUNCT
ejpam-454	145	2	∑	∑	PUNCT
ejpam-454	145	3	i∈w	i∈w	NOUN
ejpam-454	145	4	x	x	PUNCT
ejpam-454	146	1	p	p	X
ejpam-454	146	2	i	i	PRON
ejpam-454	146	3	(	(	PUNCT
ejpam-454	146	4	gi(x	gi(x	PROPN
ejpam-454	146	5	p	p	X
ejpam-454	146	6	i	i	PROPN
ejpam-454	146	7	)	)	PUNCT
ejpam-454	146	8	−	−	PROPN
ejpam-454	146	9	gi(0))+	gi(0))+	VERB
ejpam-454	146	10	∑	∑	PROPN
ejpam-454	146	11	i	i	PRON
ejpam-454	146	12	/∈w	/∈w	PUNCT
ejpam-454	147	1	x	x	X
ejpam-454	147	2	p	p	X
ejpam-454	147	3	i	i	PRON
ejpam-454	147	4	(	(	PUNCT
ejpam-454	147	5	gi(x	gi(x	PROPN
ejpam-454	147	6	p	p	X
ejpam-454	147	7	i	i	PROPN
ejpam-454	147	8	)	)	PUNCT
ejpam-454	147	9	−	−	PROPN
ejpam-454	147	10	gi(0	gi(0	PROPN
ejpam-454	147	11	)	)	PUNCT
ejpam-454	147	12	)	)	PUNCT
ejpam-454	147	13	≥	≥	NOUN
ejpam-454	147	14	∑	∑	PUNCT
ejpam-454	147	15	i∈w	i∈w	PROPN
ejpam-454	147	16	�	�	PROPN
ejpam-454	147	17	�	�	PROPN
ejpam-454	147	18	x	x	PROPN
ejpam-454	147	19	p	p	X
ejpam-454	147	20	i	i	PROPN
ejpam-454	147	21	�	�	PROPN
ejpam-454	147	22	�	�	PROPN
ejpam-454	147	23	·	·	SYM
ejpam-454	147	24	�	�	PROPN
ejpam-454	147	25	�	�	PROPN
ejpam-454	147	26	(	(	PUNCT
ejpam-454	147	27	gi(x	gi(x	NOUN
ejpam-454	147	28	p	p	PROPN
ejpam-454	147	29	i	i	PROPN
ejpam-454	147	30	)	)	PUNCT
ejpam-454	147	31	−	−	PROPN
ejpam-454	147	32	gi(0	gi(0	PROPN
ejpam-454	147	33	)	)	PUNCT
ejpam-454	147	34	�	�	PROPN
ejpam-454	147	35	�	�	PROPN
ejpam-454	147	36	(	(	PUNCT
ejpam-454	147	37	10	10	NUM
ejpam-454	147	38	)	)	PUNCT
ejpam-454	147	39	substituting	substitute	VERB
ejpam-454	147	40	(	(	PUNCT
ejpam-454	147	41	9	9	NUM
ejpam-454	147	42	)	)	PUNCT
ejpam-454	147	43	and	and	CCONJ
ejpam-454	147	44	(	(	PUNCT
ejpam-454	147	45	10	10	NUM
ejpam-454	147	46	)	)	PUNCT
ejpam-454	147	47	into	into	ADP
ejpam-454	147	48	(	(	PUNCT
ejpam-454	147	49	8)	8)	NUM
ejpam-454	147	50	,	,	PUNCT
ejpam-454	147	51	we	we	PRON
ejpam-454	147	52	can	can	AUX
ejpam-454	147	53	obtain	obtain	VERB
ejpam-454	147	54	for	for	ADP
ejpam-454	147	55	all	all	DET
ejpam-454	147	56	p	p	NOUN
ejpam-454	147	57	d	d	X
ejpam-454	147	58	∑	∑	PROPN
ejpam-454	147	59	i∈w	i∈w	PROPN
ejpam-454	147	60	�	�	PROPN
ejpam-454	147	61	�	�	PROPN
ejpam-454	147	62	x	x	PROPN
ejpam-454	147	63	p	p	X
ejpam-454	147	64	i	i	PROPN
ejpam-454	147	65	�	�	PROPN
ejpam-454	147	66	�	�	PROPN
ejpam-454	147	67	·	·	SYM
ejpam-454	147	68	�	�	PROPN
ejpam-454	147	69	�	�	PROPN
ejpam-454	147	70	(	(	PUNCT
ejpam-454	147	71	gi(x	gi(x	NOUN
ejpam-454	147	72	p	p	PROPN
ejpam-454	147	73	i	i	PROPN
ejpam-454	147	74	)	)	PUNCT
ejpam-454	147	75	−	−	PROPN
ejpam-454	148	1	gi(0	gi(0	PROPN
ejpam-454	148	2	)	)	PUNCT
ejpam-454	148	3	�	�	PROPN
ejpam-454	148	4	�	�	PROPN
ejpam-454	148	5	≤	≤	PROPN
ejpam-454	148	6	d	d	PROPN
ejpam-454	148	7	n	n	PROPN
ejpam-454	148	8	∑	∑	ADV
ejpam-454	148	9	i=1	i=1	PROPN
ejpam-454	148	10	x	x	X
ejpam-454	149	1	p	p	X
ejpam-454	149	2	i	i	PRON
ejpam-454	149	3	(	(	PUNCT
ejpam-454	149	4	gi(x	gi(x	PROPN
ejpam-454	149	5	p	p	X
ejpam-454	149	6	i	i	PROPN
ejpam-454	149	7	)	)	PUNCT
ejpam-454	149	8	−	−	PROPN
ejpam-454	149	9	gi(0	gi(0	PROPN
ejpam-454	149	10	)	)	PUNCT
ejpam-454	149	11	)	)	PUNCT
ejpam-454	149	12	≤	≤	NOUN
ejpam-454	150	1	n	n	CCONJ
ejpam-454	150	2	∑	∑	PUNCT
ejpam-454	150	3	i=1	i=1	PROPN
ejpam-454	150	4	�	�	PROPN
ejpam-454	150	5	�	�	PROPN
ejpam-454	150	6	(	(	PUNCT
ejpam-454	150	7	gi(x	gi(x	NOUN
ejpam-454	150	8	p	p	PROPN
ejpam-454	150	9	i	i	PROPN
ejpam-454	150	10	)	)	PUNCT
ejpam-454	150	11	−	−	PROPN
ejpam-454	150	12	gi(0	gi(0	PROPN
ejpam-454	150	13	)	)	PUNCT
ejpam-454	150	14	)	)	PUNCT
ejpam-454	150	15	·	·	PUNCT
ejpam-454	151	1	(	(	PUNCT
ejpam-454	151	2	hi(x	hi(x	PROPN
ejpam-454	151	3	p	p	X
ejpam-454	151	4	i	i	PROPN
ejpam-454	151	5	)	)	PUNCT
ejpam-454	151	6	−hi(0	−hi(0	X
ejpam-454	151	7	)	)	PUNCT
ejpam-454	151	8	)	)	PUNCT
ejpam-454	151	9	�	�	PROPN
ejpam-454	151	10	�	�	PROPN
ejpam-454	151	11	≤	≤	NUM
ejpam-454	151	12	m	m	VERB
ejpam-454	151	13	∑	∑	PROPN
ejpam-454	151	14	i∈w	i∈w	PROPN
ejpam-454	151	15	�	�	PROPN
ejpam-454	151	16	�	�	PROPN
ejpam-454	151	17	gi(x	gi(x	PROPN
ejpam-454	151	18	p	p	PROPN
ejpam-454	151	19	i	i	PROPN
ejpam-454	151	20	)	)	PUNCT
ejpam-454	151	21	−	−	PROPN
ejpam-454	152	1	gi(0	gi(0	PROPN
ejpam-454	152	2	)	)	PUNCT
ejpam-454	152	3	�	�	PROPN
ejpam-454	152	4	�	�	PROPN
ejpam-454	152	5	+	+	PROPN
ejpam-454	152	6	m	m	VERB
ejpam-454	152	7	so	so	SCONJ
ejpam-454	152	8	we	we	PRON
ejpam-454	152	9	have	have	VERB
ejpam-454	153	1	∑	∑	PROPN
ejpam-454	153	2	i∈w	i∈w	PROPN
ejpam-454	153	3	(	(	PUNCT
ejpam-454	153	4	d	d	PROPN
ejpam-454	153	5	�	�	PROPN
ejpam-454	153	6	�	�	PROPN
ejpam-454	153	7	x	x	PROPN
ejpam-454	154	1	p	p	X
ejpam-454	154	2	i	i	PROPN
ejpam-454	154	3	�	�	PROPN
ejpam-454	154	4	�	�	NOUN
ejpam-454	154	5	−m	−m	NOUN
ejpam-454	154	6	)	)	PUNCT
ejpam-454	154	7	·	·	PUNCT
ejpam-454	154	8	�	�	PROPN
ejpam-454	154	9	�	�	PROPN
ejpam-454	154	10	gi(x	gi(x	PROPN
ejpam-454	154	11	p	p	NOUN
ejpam-454	154	12	i	i	PROPN
ejpam-454	154	13	)	)	PUNCT
ejpam-454	154	14	−	−	PROPN
ejpam-454	155	1	gi(0	gi(0	PROPN
ejpam-454	155	2	)	)	PUNCT
ejpam-454	155	3	�	�	PROPN
ejpam-454	155	4	�	�	PROPN
ejpam-454	155	5	≤	≤	PROPN
ejpam-454	155	6	m	m	PROPN
ejpam-454	155	7	(	(	PUNCT
ejpam-454	155	8	11	11	NUM
ejpam-454	155	9	)	)	PUNCT
ejpam-454	155	10	since	since	SCONJ
ejpam-454	155	11	lim	lim	PROPN
ejpam-454	155	12	p→∞	p→∞	PROPN
ejpam-454	155	13	�	�	PROPN
ejpam-454	155	14	�	�	PROPN
ejpam-454	155	15	x	x	PROPN
ejpam-454	156	1	p	p	X
ejpam-454	156	2	i	i	PROPN
ejpam-454	156	3	�	�	PROPN
ejpam-454	156	4	�	�	PROPN
ejpam-454	156	5	=	=	NUM
ejpam-454	156	6	∞	∞	PROPN
ejpam-454	156	7	for	for	ADP
ejpam-454	156	8	all	all	PRON
ejpam-454	156	9	i	i	PRON
ejpam-454	156	10	∈	∈	PROPN
ejpam-454	156	11	w	w	PROPN
ejpam-454	156	12	and	and	CCONJ
ejpam-454	156	13	lim	lim	PROPN
ejpam-454	156	14	|xi|→∞	|xi|→∞	NUM
ejpam-454	156	15	�	�	PROPN
ejpam-454	156	16	�	�	PROPN
ejpam-454	156	17	gi(x	gi(x	PROPN
ejpam-454	156	18	i	i	PROPN
ejpam-454	156	19	)	)	PUNCT
ejpam-454	156	20	�	�	PROPN
ejpam-454	156	21	�	�	PROPN
ejpam-454	156	22	=	=	SYM
ejpam-454	156	23	∞	∞	PROPN
ejpam-454	156	24	,	,	PUNCT
ejpam-454	156	25	there	there	PRON
ejpam-454	156	26	exists	exist	VERB
ejpam-454	156	27	a	a	DET
ejpam-454	156	28	positive	positive	ADJ
ejpam-454	156	29	constant	constant	ADJ
ejpam-454	156	30	p	p	NOUN
ejpam-454	156	31	such	such	ADJ
ejpam-454	156	32	that	that	PRON
ejpam-454	156	33	for	for	ADP
ejpam-454	156	34	all	all	PRON
ejpam-454	156	35	p	p	X
ejpam-454	156	36	>	>	X
ejpam-454	156	37	p	p	X
ejpam-454	156	38	,	,	PUNCT
ejpam-454	156	39	�	�	PROPN
ejpam-454	156	40	�	�	PROPN
ejpam-454	156	41	(	(	PUNCT
ejpam-454	156	42	gi(x	gi(x	NOUN
ejpam-454	156	43	p	p	PROPN
ejpam-454	156	44	i	i	PROPN
ejpam-454	156	45	)	)	PUNCT
ejpam-454	156	46	−	−	PROPN
ejpam-454	156	47	gi(0	gi(0	PROPN
ejpam-454	156	48	)	)	PUNCT
ejpam-454	156	49	�	�	PROPN
ejpam-454	156	50	�	�	PROPN
ejpam-454	156	51	≥	≥	NUM
ejpam-454	156	52	1	1	NUM
ejpam-454	156	53	and	and	CCONJ
ejpam-454	156	54	�	�	PROPN
ejpam-454	156	55	�	�	PROPN
ejpam-454	156	56	x	x	PROPN
ejpam-454	157	1	p	p	X
ejpam-454	157	2	i	i	PROPN
ejpam-454	157	3	�	�	PROPN
ejpam-454	157	4	�	�	PROPN
ejpam-454	157	5	>	>	PROPN
ejpam-454	157	6	2	2	NUM
ejpam-454	157	7	m	m	NOUN
ejpam-454	157	8	d	d	NOUN
ejpam-454	157	9	.	.	PUNCT
ejpam-454	158	1	hence	hence	ADV
ejpam-454	158	2	,	,	PUNCT
ejpam-454	158	3	∑	∑	PROPN
ejpam-454	158	4	i∈w	i∈w	NOUN
ejpam-454	158	5	(	(	PUNCT
ejpam-454	158	6	d	d	PROPN
ejpam-454	158	7	�	�	PROPN
ejpam-454	158	8	�	�	PROPN
ejpam-454	158	9	x	x	PROPN
ejpam-454	158	10	p	p	X
ejpam-454	158	11	i	i	PROPN
ejpam-454	158	12	�	�	PROPN
ejpam-454	158	13	�	�	NOUN
ejpam-454	158	14	−m	−m	NOUN
ejpam-454	158	15	)	)	PUNCT
ejpam-454	158	16	·	·	PUNCT
ejpam-454	158	17	�	�	PROPN
ejpam-454	158	18	�	�	PROPN
ejpam-454	158	19	gi(x	gi(x	PROPN
ejpam-454	158	20	p	p	NOUN
ejpam-454	158	21	i	i	PROPN
ejpam-454	158	22	)	)	PUNCT
ejpam-454	158	23	−	−	PROPN
ejpam-454	159	1	gi(0	gi(0	PROPN
ejpam-454	159	2	)	)	PUNCT
ejpam-454	159	3	�	�	PROPN
ejpam-454	159	4	�	�	PROPN
ejpam-454	159	5	>	>	X
ejpam-454	159	6	m	m	PROPN
ejpam-454	159	7	(	(	PUNCT
ejpam-454	159	8	12	12	NUM
ejpam-454	159	9	)	)	PUNCT
ejpam-454	159	10	which	which	PRON
ejpam-454	159	11	is	be	AUX
ejpam-454	159	12	contradict	contradict	ADJ
ejpam-454	159	13	to	to	ADP
ejpam-454	159	14	(	(	PUNCT
ejpam-454	159	15	11	11	NUM
ejpam-454	159	16	)	)	PUNCT
ejpam-454	159	17	.	.	PUNCT
ejpam-454	160	1	so	so	ADV
ejpam-454	160	2	h(x	h(x	PROPN
ejpam-454	160	3	)	)	PUNCT
ejpam-454	160	4	is	be	AUX
ejpam-454	160	5	a	a	DET
ejpam-454	160	6	homeomorphism	homeomorphism	NOUN
ejpam-454	160	7	on	on	ADP
ejpam-454	160	8	rn	rn	PROPN
ejpam-454	160	9	.	.	PROPN
ejpam-454	161	1	that	that	PRON
ejpam-454	161	2	is	is	ADV
ejpam-454	161	3	,	,	PUNCT
ejpam-454	161	4	eq.(2	eq.(2	ADJ
ejpam-454	161	5	)	)	PUNCT
ejpam-454	161	6	has	have	VERB
ejpam-454	161	7	a	a	DET
ejpam-454	161	8	unique	unique	ADJ
ejpam-454	161	9	solution	solution	NOUN
ejpam-454	161	10	.	.	PUNCT
ejpam-454	162	1	theorem	theorem	NOUN
ejpam-454	162	2	3	3	NUM
ejpam-454	162	3	.	.	PUNCT
ejpam-454	163	1	under	under	ADP
ejpam-454	163	2	assumptions	assumption	NOUN
ejpam-454	163	3	of	of	ADP
ejpam-454	163	4	theorem	theorem	ADJ
ejpam-454	163	5	1	1	NUM
ejpam-454	163	6	(	(	PUNCT
ejpam-454	163	7	or	or	CCONJ
ejpam-454	163	8	theorem	theorem	VERB
ejpam-454	163	9	2	2	NUM
ejpam-454	163	10	)	)	PUNCT
ejpam-454	163	11	,	,	PUNCT
ejpam-454	163	12	system	system	NOUN
ejpam-454	163	13	(	(	PUNCT
ejpam-454	163	14	1	1	X
ejpam-454	163	15	)	)	PUNCT
ejpam-454	163	16	has	have	VERB
ejpam-454	163	17	a	a	DET
ejpam-454	163	18	unique	unique	ADJ
ejpam-454	163	19	equilibrium	equilibrium	NOUN
ejpam-454	163	20	point	point	NOUN
ejpam-454	163	21	x∗	x∗	PROPN
ejpam-454	164	1	=	=	SYM
ejpam-454	164	2	(	(	PUNCT
ejpam-454	164	3	x∗1	x∗1	ADJ
ejpam-454	164	4	,	,	PUNCT
ejpam-454	164	5	·	·	PUNCT
ejpam-454	164	6	·	·	PUNCT
ejpam-454	164	7	·	·	PUNCT
ejpam-454	164	8	,	,	PUNCT
ejpam-454	164	9	x∗n	x∗n	NUM
ejpam-454	164	10	)	)	PUNCT
ejpam-454	164	11	t	t	NOUN
ejpam-454	164	12	.	.	PUNCT
ejpam-454	165	1	proof	proof	NOUN
ejpam-454	165	2	.	.	PUNCT
ejpam-454	166	1	by	by	ADP
ejpam-454	166	2	definition	definition	NOUN
ejpam-454	166	3	2	2	NUM
ejpam-454	166	4	and	and	CCONJ
ejpam-454	166	5	theorem	theorem	VERB
ejpam-454	166	6	1	1	NUM
ejpam-454	166	7	(	(	PUNCT
ejpam-454	166	8	or	or	CCONJ
ejpam-454	166	9	theorem	theorem	VERB
ejpam-454	166	10	2	2	NUM
ejpam-454	166	11	)	)	PUNCT
ejpam-454	166	12	,	,	PUNCT
ejpam-454	166	13	it	it	PRON
ejpam-454	166	14	is	be	AUX
ejpam-454	166	15	obvious	obvious	ADJ
ejpam-454	166	16	that	that	SCONJ
ejpam-454	166	17	the	the	DET
ejpam-454	166	18	constant	constant	ADJ
ejpam-454	166	19	vector	vector	NOUN
ejpam-454	166	20	x∗	x∗	PROPN
ejpam-454	166	21	is	be	AUX
ejpam-454	166	22	the	the	DET
ejpam-454	166	23	unique	unique	ADJ
ejpam-454	166	24	equilibrium	equilibrium	NOUN
ejpam-454	166	25	point	point	NOUN
ejpam-454	166	26	of	of	ADP
ejpam-454	166	27	system	system	NOUN
ejpam-454	166	28	(	(	PUNCT
ejpam-454	166	29	1	1	NUM
ejpam-454	166	30	)	)	PUNCT
ejpam-454	166	31	.	.	PUNCT
ejpam-454	167	1	a.	a.	PROPN
ejpam-454	167	2	wu	wu	PROPN
ejpam-454	167	3	,	,	PUNCT
ejpam-454	167	4	j.	j.	PROPN
ejpam-454	167	5	zhang	zhang	PROPN
ejpam-454	167	6	,	,	PUNCT
ejpam-454	167	7	c.	c.	PROPN
ejpam-454	167	8	fu	fu	PROPN
ejpam-454	167	9	/	/	SYM
ejpam-454	167	10	eur	eur	PROPN
ejpam-454	167	11	.	.	PUNCT
ejpam-454	168	1	j.	j.	PROPN
ejpam-454	168	2	pure	pure	PROPN
ejpam-454	168	3	appl	appl	PROPN
ejpam-454	168	4	.	.	PROPN
ejpam-454	168	5	math	math	PROPN
ejpam-454	168	6	,	,	PUNCT
ejpam-454	168	7	3	3	NUM
ejpam-454	168	8	(	(	PUNCT
ejpam-454	168	9	2010	2010	NUM
ejpam-454	168	10	)	)	PUNCT
ejpam-454	168	11	,	,	PUNCT
ejpam-454	168	12	806	806	NUM
ejpam-454	168	13	-	-	SYM
ejpam-454	168	14	818	818	NUM
ejpam-454	168	15	812	812	NUM
ejpam-454	168	16	3	3	NUM
ejpam-454	168	17	.	.	PUNCT
ejpam-454	168	18	global	global	ADJ
ejpam-454	168	19	asymptotic	asymptotic	ADJ
ejpam-454	168	20	stability	stability	NOUN
ejpam-454	168	21	of	of	ADP
ejpam-454	168	22	the	the	DET
ejpam-454	168	23	equilibrium	equilibrium	NOUN
ejpam-454	168	24	point	point	NOUN
ejpam-454	168	25	in	in	ADP
ejpam-454	168	26	this	this	DET
ejpam-454	168	27	section	section	NOUN
ejpam-454	169	1	,	,	PUNCT
ejpam-454	169	2	we	we	PRON
ejpam-454	169	3	aim	aim	VERB
ejpam-454	169	4	to	to	PART
ejpam-454	169	5	find	find	VERB
ejpam-454	169	6	some	some	DET
ejpam-454	169	7	sufficient	sufficient	ADJ
ejpam-454	169	8	conditions	condition	NOUN
ejpam-454	169	9	ensuring	ensure	VERB
ejpam-454	169	10	the	the	DET
ejpam-454	169	11	global	global	ADJ
ejpam-454	169	12	asymptotic	asymptotic	ADJ
ejpam-454	169	13	stability	stability	NOUN
ejpam-454	169	14	of	of	ADP
ejpam-454	169	15	the	the	DET
ejpam-454	169	16	equilibrium	equilibrium	NOUN
ejpam-454	169	17	point	point	NOUN
ejpam-454	169	18	of	of	ADP
ejpam-454	169	19	system	system	NOUN
ejpam-454	169	20	(	(	PUNCT
ejpam-454	169	21	1	1	NUM
ejpam-454	169	22	)	)	PUNCT
ejpam-454	169	23	.	.	PUNCT
ejpam-454	170	1	the	the	DET
ejpam-454	170	2	equilibrium	equilibrium	NOUN
ejpam-454	170	3	point	point	NOUN
ejpam-454	170	4	of	of	ADP
ejpam-454	170	5	system	system	NOUN
ejpam-454	170	6	(	(	PUNCT
ejpam-454	170	7	1	1	X
ejpam-454	170	8	)	)	PUNCT
ejpam-454	170	9	is	be	AUX
ejpam-454	170	10	said	say	VERB
ejpam-454	170	11	to	to	PART
ejpam-454	170	12	be	be	AUX
ejpam-454	170	13	globally	globally	ADV
ejpam-454	170	14	asymptotically	asymptotically	ADV
ejpam-454	170	15	stale	stale	ADJ
ejpam-454	170	16	if	if	SCONJ
ejpam-454	170	17	it	it	PRON
ejpam-454	170	18	is	be	AUX
ejpam-454	170	19	locally	locally	ADV
ejpam-454	170	20	stable	stable	ADJ
ejpam-454	170	21	in	in	ADP
ejpam-454	170	22	sense	sense	NOUN
ejpam-454	170	23	of	of	ADP
ejpam-454	170	24	lyapunov	lyapunov	NOUN
ejpam-454	170	25	and	and	CCONJ
ejpam-454	170	26	globally	globally	ADV
ejpam-454	170	27	attractive	attractive	ADJ
ejpam-454	170	28	,	,	PUNCT
ejpam-454	170	29	i.e.	i.e.	X
ejpam-454	170	30	,	,	PUNCT
ejpam-454	170	31	every	every	DET
ejpam-454	170	32	solution	solution	NOUN
ejpam-454	170	33	of	of	ADP
ejpam-454	170	34	system	system	NOUN
ejpam-454	170	35	(	(	PUNCT
ejpam-454	170	36	1	1	X
ejpam-454	170	37	)	)	PUNCT
ejpam-454	170	38	corresponding	correspond	VERB
ejpam-454	170	39	to	to	ADP
ejpam-454	170	40	an	an	DET
ejpam-454	170	41	arbitrary	arbitrary	ADJ
ejpam-454	170	42	given	give	VERB
ejpam-454	170	43	set	set	NOUN
ejpam-454	170	44	of	of	ADP
ejpam-454	170	45	initial	initial	ADJ
ejpam-454	170	46	conditions	condition	NOUN
ejpam-454	170	47	satisfy	satisfy	VERB
ejpam-454	170	48	lim	lim	PROPN
ejpam-454	170	49	t→∞	t→∞	X
ejpam-454	170	50	x	x	SYM
ejpam-454	170	51	i(t	i(t	PROPN
ejpam-454	170	52	)	)	PUNCT
ejpam-454	170	53	=	=	PUNCT
ejpam-454	171	1	x∗	x∗	PROPN
ejpam-454	172	1	i	i	PRON
ejpam-454	172	2	,	,	PUNCT
ejpam-454	172	3	i	i	PRON
ejpam-454	172	4	=	=	NOUN
ejpam-454	172	5	1	1	NUM
ejpam-454	172	6	,	,	PUNCT
ejpam-454	172	7	·	·	PUNCT
ejpam-454	172	8	·	·	PUNCT
ejpam-454	172	9	·	·	PUNCT
ejpam-454	172	10	,	,	PUNCT
ejpam-454	172	11	n.	n.	NOUN
ejpam-454	172	12	to	to	PART
ejpam-454	172	13	prove	prove	VERB
ejpam-454	172	14	the	the	DET
ejpam-454	172	15	global	global	ADJ
ejpam-454	172	16	asymptotic	asymptotic	ADJ
ejpam-454	172	17	stability	stability	NOUN
ejpam-454	172	18	of	of	ADP
ejpam-454	172	19	the	the	DET
ejpam-454	172	20	equilibrium	equilibrium	NOUN
ejpam-454	172	21	point	point	NOUN
ejpam-454	172	22	,	,	PUNCT
ejpam-454	172	23	we	we	PRON
ejpam-454	172	24	will	will	AUX
ejpam-454	172	25	employ	employ	VERB
ejpam-454	172	26	the	the	DET
ejpam-454	172	27	lyapunov	lyapunov	ADJ
ejpam-454	172	28	direct	direct	ADJ
ejpam-454	172	29	method	method	NOUN
ejpam-454	172	30	.	.	PUNCT
ejpam-454	173	1	namely	namely	ADV
ejpam-454	173	2	,	,	PUNCT
ejpam-454	173	3	the	the	DET
ejpam-454	173	4	equilibrium	equilibrium	NOUN
ejpam-454	173	5	point	point	NOUN
ejpam-454	173	6	x∗	x∗	PROPN
ejpam-454	173	7	is	be	AUX
ejpam-454	173	8	stable	stable	ADJ
ejpam-454	173	9	and	and	CCONJ
ejpam-454	173	10	every	every	DET
ejpam-454	173	11	solution	solution	NOUN
ejpam-454	173	12	is	be	AUX
ejpam-454	173	13	bounded	bound	VERB
ejpam-454	173	14	if	if	SCONJ
ejpam-454	173	15	there	there	PRON
ejpam-454	173	16	exists	exist	VERB
ejpam-454	173	17	a	a	DET
ejpam-454	173	18	continuously	continuously	ADV
ejpam-454	173	19	differentiable	differentiable	ADJ
ejpam-454	173	20	lyapunov	lyapunov	NOUN
ejpam-454	173	21	function	function	VERB
ejpam-454	173	22	v	v	ADP
ejpam-454	173	23	:	:	PUNCT
ejpam-454	173	24	rn→	rn→	PROPN
ejpam-454	173	25	r	r	X
ejpam-454	173	26	which	which	PRON
ejpam-454	173	27	is	be	AUX
ejpam-454	173	28	positive	positive	ADJ
ejpam-454	173	29	definite	definite	ADJ
ejpam-454	173	30	and	and	CCONJ
ejpam-454	173	31	radially	radially	ADV
ejpam-454	173	32	unbounded	unbounde	VERB
ejpam-454	173	33	,	,	PUNCT
ejpam-454	173	34	i.e.	i.e.	X
ejpam-454	173	35	,	,	PUNCT
ejpam-454	173	36	v	v	INTJ
ejpam-454	173	37	(	(	PUNCT
ejpam-454	173	38	x∗	x∗	PROPN
ejpam-454	173	39	)	)	PUNCT
ejpam-454	173	40	=	=	SYM
ejpam-454	174	1	0	0	NUM
ejpam-454	174	2	,	,	PUNCT
ejpam-454	174	3	v	v	NOUN
ejpam-454	174	4	(	(	PUNCT
ejpam-454	174	5	x	x	X
ejpam-454	174	6	)	)	PUNCT
ejpam-454	174	7	>	>	X
ejpam-454	174	8	0	0	PUNCT
ejpam-454	175	1	for	for	ADP
ejpam-454	175	2	x	x	SYM
ejpam-454	175	3	6=	6=	PROPN
ejpam-454	175	4	0	0	NUM
ejpam-454	175	5	,	,	PUNCT
ejpam-454	175	6	lim	lim	PROPN
ejpam-454	175	7	‖x−x∗‖→∞	‖x−x∗‖→∞	PUNCT
ejpam-454	175	8	v	v	PROPN
ejpam-454	175	9	(	(	PUNCT
ejpam-454	175	10	x	x	NOUN
ejpam-454	175	11	)	)	PUNCT
ejpam-454	175	12	=	=	SYM
ejpam-454	175	13	∞	∞	PROPN
ejpam-454	175	14	,	,	PUNCT
ejpam-454	175	15	such	such	ADJ
ejpam-454	175	16	that	that	SCONJ
ejpam-454	175	17	the	the	DET
ejpam-454	175	18	time	time	NOUN
ejpam-454	175	19	-	-	PUNCT
ejpam-454	175	20	derivative	derivative	NOUN
ejpam-454	175	21	of	of	ADP
ejpam-454	175	22	v	v	NOUN
ejpam-454	175	23	along	along	ADP
ejpam-454	175	24	the	the	DET
ejpam-454	175	25	solution	solution	NOUN
ejpam-454	175	26	of	of	ADP
ejpam-454	175	27	system	system	NOUN
ejpam-454	175	28	(	(	PUNCT
ejpam-454	175	29	1	1	X
ejpam-454	175	30	)	)	PUNCT
ejpam-454	175	31	is	be	AUX
ejpam-454	175	32	negative	negative	ADJ
ejpam-454	175	33	semi	semi	ADJ
ejpam-454	175	34	-	-	ADJ
ejpam-454	175	35	definite	definite	ADJ
ejpam-454	175	36	.	.	PUNCT
ejpam-454	176	1	if	if	SCONJ
ejpam-454	176	2	,	,	PUNCT
ejpam-454	176	3	in	in	ADP
ejpam-454	176	4	addition	addition	NOUN
ejpam-454	176	5	,	,	PUNCT
ejpam-454	176	6	v̇	v̇	PROPN
ejpam-454	176	7	(	(	PUNCT
ejpam-454	176	8	x	x	X
ejpam-454	176	9	)	)	PUNCT
ejpam-454	176	10	is	be	AUX
ejpam-454	176	11	negative	negative	ADJ
ejpam-454	176	12	definite	definite	ADJ
ejpam-454	176	13	,	,	PUNCT
ejpam-454	176	14	then	then	ADV
ejpam-454	176	15	the	the	DET
ejpam-454	176	16	equilibrium	equilibrium	NOUN
ejpam-454	176	17	point	point	NOUN
ejpam-454	176	18	of	of	ADP
ejpam-454	176	19	system	system	NOUN
ejpam-454	176	20	(	(	PUNCT
ejpam-454	176	21	1	1	X
ejpam-454	176	22	)	)	PUNCT
ejpam-454	176	23	is	be	AUX
ejpam-454	176	24	globally	globally	ADV
ejpam-454	176	25	asymptotically	asymptotically	ADV
ejpam-454	176	26	stable	stable	ADJ
ejpam-454	176	27	.	.	PUNCT
ejpam-454	177	1	theorem	theorem	ADJ
ejpam-454	177	2	4	4	NUM
ejpam-454	177	3	.	.	PUNCT
ejpam-454	178	1	under	under	ADP
ejpam-454	178	2	assumptions	assumption	NOUN
ejpam-454	178	3	of	of	ADP
ejpam-454	178	4	theorem	theorem	NOUN
ejpam-454	178	5	1	1	NUM
ejpam-454	178	6	,	,	PUNCT
ejpam-454	178	7	further	far	ADV
ejpam-454	178	8	if	if	SCONJ
ejpam-454	178	9	the	the	DET
ejpam-454	178	10	following	follow	VERB
ejpam-454	178	11	conditions	condition	NOUN
ejpam-454	178	12	are	be	AUX
ejpam-454	178	13	satisfied	satisfied	ADJ
ejpam-454	178	14	jik(x	jik(x	PROPN
ejpam-454	178	15	i(tk	i(tk	NOUN
ejpam-454	178	16	)	)	PUNCT
ejpam-454	178	17	)	)	PUNCT
ejpam-454	179	1	=	=	SYM
ejpam-454	179	2	−γik(x	−γik(x	PROPN
ejpam-454	179	3	i(tk)−	i(tk)−	NOUN
ejpam-454	179	4	x∗i	x∗i	NUM
ejpam-454	179	5	)	)	PUNCT
ejpam-454	179	6	,	,	PUNCT
ejpam-454	179	7	k	k	X
ejpam-454	179	8	=	=	SYM
ejpam-454	179	9	1,2	1,2	NUM
ejpam-454	179	10	,	,	PUNCT
ejpam-454	179	11	·	·	PUNCT
ejpam-454	179	12	·	·	PUNCT
ejpam-454	179	13	·	·	PUNCT
ejpam-454	179	14	,	,	PUNCT
ejpam-454	179	15	i	i	PRON
ejpam-454	179	16	=	=	NOUN
ejpam-454	179	17	1	1	NUM
ejpam-454	179	18	,	,	PUNCT
ejpam-454	179	19	·	·	PUNCT
ejpam-454	179	20	·	·	PUNCT
ejpam-454	179	21	·	·	PUNCT
ejpam-454	179	22	,	,	PUNCT
ejpam-454	179	23	n	n	CCONJ
ejpam-454	179	24	,	,	PUNCT
ejpam-454	179	25	where	where	SCONJ
ejpam-454	179	26	x∗	x∗	PROPN
ejpam-454	179	27	=	=	SYM
ejpam-454	179	28	(	(	PUNCT
ejpam-454	179	29	x∗1	x∗1	ADJ
ejpam-454	179	30	,	,	PUNCT
ejpam-454	179	31	·	·	PUNCT
ejpam-454	179	32	·	·	PUNCT
ejpam-454	179	33	·	·	PUNCT
ejpam-454	179	34	,	,	PUNCT
ejpam-454	179	35	x∗n	x∗n	X
ejpam-454	179	36	)	)	PUNCT
ejpam-454	179	37	t	t	PROPN
ejpam-454	179	38	is	be	AUX
ejpam-454	179	39	the	the	DET
ejpam-454	179	40	equilibrium	equilibrium	NOUN
ejpam-454	179	41	point	point	NOUN
ejpam-454	179	42	of	of	ADP
ejpam-454	179	43	system	system	NOUN
ejpam-454	179	44	(	(	PUNCT
ejpam-454	179	45	1	1	NUM
ejpam-454	179	46	)	)	PUNCT
ejpam-454	179	47	,	,	PUNCT
ejpam-454	179	48	0	0	PUNCT
ejpam-454	179	49	<	<	X
ejpam-454	179	50	γik	γik	X
ejpam-454	179	51	<	<	X
ejpam-454	179	52	2	2	NUM
ejpam-454	179	53	,	,	PUNCT
ejpam-454	179	54	then	then	ADV
ejpam-454	179	55	system	system	NOUN
ejpam-454	179	56	(	(	PUNCT
ejpam-454	179	57	1	1	X
ejpam-454	179	58	)	)	PUNCT
ejpam-454	179	59	has	have	VERB
ejpam-454	179	60	a	a	DET
ejpam-454	179	61	unique	unique	ADJ
ejpam-454	179	62	equilibrium	equilibrium	NOUN
ejpam-454	179	63	point	point	NOUN
ejpam-454	179	64	which	which	PRON
ejpam-454	179	65	is	be	AUX
ejpam-454	179	66	globally	globally	ADV
ejpam-454	179	67	asymptotically	asymptotically	ADV
ejpam-454	179	68	stable	stable	ADJ
ejpam-454	179	69	.	.	PUNCT
ejpam-454	180	1	proof	proof	NOUN
ejpam-454	180	2	.	.	PUNCT
ejpam-454	181	1	in	in	ADP
ejpam-454	181	2	order	order	NOUN
ejpam-454	181	3	to	to	PART
ejpam-454	181	4	complete	complete	VERB
ejpam-454	181	5	the	the	DET
ejpam-454	181	6	proof	proof	NOUN
ejpam-454	181	7	,	,	PUNCT
ejpam-454	181	8	we	we	PRON
ejpam-454	181	9	divide	divide	VERB
ejpam-454	181	10	the	the	DET
ejpam-454	181	11	proof	proof	NOUN
ejpam-454	181	12	into	into	ADP
ejpam-454	181	13	four	four	NUM
ejpam-454	181	14	steps	step	NOUN
ejpam-454	181	15	.	.	PUNCT
ejpam-454	182	1	step	step	NOUN
ejpam-454	182	2	1	1	NUM
ejpam-454	182	3	.	.	PUNCT
ejpam-454	183	1	consider	consider	VERB
ejpam-454	183	2	the	the	DET
ejpam-454	183	3	following	follow	VERB
ejpam-454	183	4	system	system	NOUN
ejpam-454	183	5	:	:	PUNCT
ejpam-454	183	6			PROPN
ejpam-454	183	7			PROPN
ejpam-454	183	8			NOUN
ejpam-454	183	9	ẋ	ẋ	PROPN
ejpam-454	183	10	i(t	i(t	PROPN
ejpam-454	183	11	)	)	PUNCT
ejpam-454	183	12	=	=	SYM
ejpam-454	184	1	−di	−di	NOUN
ejpam-454	184	2	x	x	SYM
ejpam-454	184	3	i(t	i(t	PROPN
ejpam-454	184	4	)	)	PUNCT
ejpam-454	184	5	+	+	CCONJ
ejpam-454	185	1	n	n	X
ejpam-454	185	2	∑	∑	PUNCT
ejpam-454	185	3	j=1	j=1	PROPN
ejpam-454	185	4	ai	ai	VERB
ejpam-454	185	5	j	j	PROPN
ejpam-454	185	6	g	g	PROPN
ejpam-454	185	7	j(x	j(x	PROPN
ejpam-454	185	8	j(t	j(t	PROPN
ejpam-454	185	9	)	)	PUNCT
ejpam-454	185	10	)	)	PUNCT
ejpam-454	186	1	+	+	CCONJ
ejpam-454	187	1	n	n	X
ejpam-454	187	2	∑	∑	ADP
ejpam-454	187	3	j=1	j=1	ADJ
ejpam-454	187	4	bi	bi	PROPN
ejpam-454	187	5	j	j	PROPN
ejpam-454	187	6	g	g	PROPN
ejpam-454	187	7	j(x	j(x	PROPN
ejpam-454	187	8	j(t	j(t	PROPN
ejpam-454	187	9	−τi	−τi	PROPN
ejpam-454	187	10	j	j	PROPN
ejpam-454	187	11	)	)	PUNCT
ejpam-454	187	12	)	)	PUNCT
ejpam-454	188	1	+	+	CCONJ
ejpam-454	188	2	ii	ii	PROPN
ejpam-454	188	3	,	,	PUNCT
ejpam-454	188	4	t	t	PROPN
ejpam-454	188	5	∈	∈	PROPN
ejpam-454	189	1	[	[	X
ejpam-454	189	2	0	0	NUM
ejpam-454	189	3	,	,	PUNCT
ejpam-454	189	4	t1	t1	NOUN
ejpam-454	189	5	]	]	X
ejpam-454	189	6	,	,	PUNCT
ejpam-454	189	7	x	x	SYM
ejpam-454	189	8	i(t	i(t	PROPN
ejpam-454	189	9	)	)	PUNCT
ejpam-454	189	10	=	=	SYM
ejpam-454	189	11	φi(t	φi(t	NOUN
ejpam-454	189	12	)	)	PUNCT
ejpam-454	189	13	,	,	PUNCT
ejpam-454	189	14	t	t	PROPN
ejpam-454	189	15	∈	∈	PROPN
ejpam-454	189	16	[	[	X
ejpam-454	189	17	−τ	−τ	NOUN
ejpam-454	189	18	,	,	PUNCT
ejpam-454	189	19	0	0	NUM
ejpam-454	189	20	]	]	PUNCT
ejpam-454	189	21	,	,	PUNCT
ejpam-454	189	22	i	i	PRON
ejpam-454	189	23	=	=	NOUN
ejpam-454	189	24	1	1	NUM
ejpam-454	189	25	,	,	PUNCT
ejpam-454	189	26	·	·	PUNCT
ejpam-454	189	27	·	·	PUNCT
ejpam-454	189	28	·	·	PUNCT
ejpam-454	189	29	,	,	PUNCT
ejpam-454	189	30	n.	n.	NOUN
ejpam-454	189	31	(	(	PUNCT
ejpam-454	189	32	13	13	NUM
ejpam-454	189	33	)	)	PUNCT
ejpam-454	189	34	by	by	ADP
ejpam-454	189	35	g	g	PROPN
ejpam-454	189	36	j	j	PROPN
ejpam-454	189	37	is	be	AUX
ejpam-454	189	38	a	a	DET
ejpam-454	189	39	continuous	continuous	ADJ
ejpam-454	189	40	function	function	NOUN
ejpam-454	189	41	,	,	PUNCT
ejpam-454	189	42	ui(t	ui(t	NOUN
ejpam-454	189	43	)	)	PUNCT
ejpam-454	190	1	=	=	SYM
ejpam-454	190	2	−di	−di	NOUN
ejpam-454	190	3	x	x	SYM
ejpam-454	190	4	i(t)+	i(t)+	ADJ
ejpam-454	190	5	n	n	NOUN
ejpam-454	190	6	∑	∑	PROPN
ejpam-454	190	7	j=1	j=1	PROPN
ejpam-454	190	8	ai	ai	VERB
ejpam-454	190	9	j	j	PROPN
ejpam-454	190	10	g	g	PROPN
ejpam-454	190	11	j(x	j(x	PROPN
ejpam-454	190	12	j(t))+	j(t))+	VERB
ejpam-454	190	13	n	n	SYM
ejpam-454	190	14	∑	∑	ADV
ejpam-454	191	1	j=1	j=1	ADJ
ejpam-454	191	2	bi	bi	PROPN
ejpam-454	191	3	j	j	PROPN
ejpam-454	191	4	g	g	PROPN
ejpam-454	191	5	j(x	j(x	PROPN
ejpam-454	191	6	j(t−τi	j(t−τi	PROPN
ejpam-454	191	7	j))+	j))+	PROPN
ejpam-454	191	8	ii	ii	PROPN
ejpam-454	191	9	is	be	AUX
ejpam-454	191	10	continuous	continuous	ADJ
ejpam-454	191	11	and	and	CCONJ
ejpam-454	191	12	local	local	ADJ
ejpam-454	191	13	bounded	bound	VERB
ejpam-454	191	14	.	.	PUNCT
ejpam-454	192	1	it	it	PRON
ejpam-454	192	2	is	be	AUX
ejpam-454	192	3	easy	easy	ADJ
ejpam-454	192	4	to	to	PART
ejpam-454	192	5	obtain	obtain	VERB
ejpam-454	192	6	the	the	DET
ejpam-454	192	7	existence	existence	NOUN
ejpam-454	192	8	of	of	ADP
ejpam-454	192	9	a	a	DET
ejpam-454	192	10	solution	solution	NOUN
ejpam-454	192	11	of	of	ADP
ejpam-454	192	12	system	system	NOUN
ejpam-454	192	13	(	(	PUNCT
ejpam-454	192	14	3.1	3.1	NUM
ejpam-454	192	15	)	)	PUNCT
ejpam-454	192	16	on	on	ADP
ejpam-454	192	17	[	[	X
ejpam-454	192	18	0	0	NUM
ejpam-454	192	19	,	,	PUNCT
ejpam-454	192	20	t∗(φ	t∗(φ	PROPN
ejpam-454	192	21	)	)	PUNCT
ejpam-454	192	22	)	)	PUNCT
ejpam-454	192	23	,	,	PUNCT
ejpam-454	192	24	where	where	SCONJ
ejpam-454	192	25	t∗(φ	t∗(φ	X
ejpam-454	192	26	)	)	PUNCT
ejpam-454	192	27	∈	∈	PROPN
ejpam-454	192	28	(	(	PUNCT
ejpam-454	192	29	0	0	NUM
ejpam-454	192	30	,	,	PUNCT
ejpam-454	192	31	t1	t1	NOUN
ejpam-454	192	32	)	)	PUNCT
ejpam-454	192	33	or	or	CCONJ
ejpam-454	192	34	t∗(φ	t∗(φ	NUM
ejpam-454	192	35	)	)	PUNCT
ejpam-454	193	1	=	=	SYM
ejpam-454	193	2	t1	t1	NOUN
ejpam-454	193	3	,	,	PUNCT
ejpam-454	193	4	and	and	CCONJ
ejpam-454	193	5	[	[	X
ejpam-454	193	6	0	0	NUM
ejpam-454	193	7	,	,	PUNCT
ejpam-454	193	8	t∗(φ	t∗(φ	PROPN
ejpam-454	193	9	)	)	PUNCT
ejpam-454	193	10	)	)	PUNCT
ejpam-454	193	11	is	be	AUX
ejpam-454	193	12	the	the	DET
ejpam-454	193	13	maximal	maximal	ADJ
ejpam-454	193	14	rightside	rightside	NOUN
ejpam-454	193	15	existence	existence	NOUN
ejpam-454	193	16	interval	interval	NOUN
ejpam-454	193	17	of	of	ADP
ejpam-454	193	18	the	the	DET
ejpam-454	193	19	solution	solution	NOUN
ejpam-454	193	20	of	of	ADP
ejpam-454	193	21	system	system	NOUN
ejpam-454	193	22	(	(	PUNCT
ejpam-454	193	23	13	13	NUM
ejpam-454	193	24	)	)	PUNCT
ejpam-454	193	25	.	.	PUNCT
ejpam-454	194	1	we	we	PRON
ejpam-454	194	2	denote	denote	VERB
ejpam-454	194	3	this	this	DET
ejpam-454	194	4	solution	solution	NOUN
ejpam-454	194	5	by	by	ADP
ejpam-454	194	6	x(t	x(t	PROPN
ejpam-454	194	7	,	,	PUNCT
ejpam-454	194	8	φ	φ	NOUN
ejpam-454	194	9	)	)	PUNCT
ejpam-454	194	10	,	,	PUNCT
ejpam-454	194	11	x(t	x(t	PROPN
ejpam-454	194	12	,	,	PUNCT
ejpam-454	194	13	φ	φ	NOUN
ejpam-454	194	14	)	)	PUNCT
ejpam-454	194	15	=	=	SYM
ejpam-454	194	16	(	(	PUNCT
ejpam-454	194	17	x1(t	x1(t	PROPN
ejpam-454	194	18	,	,	PUNCT
ejpam-454	194	19	φ1	φ1	PROPN
ejpam-454	194	20	)	)	PUNCT
ejpam-454	194	21	,	,	PUNCT
ejpam-454	194	22	·	·	PUNCT
ejpam-454	194	23	·	·	PUNCT
ejpam-454	194	24	·	·	PUNCT
ejpam-454	194	25	,	,	PUNCT
ejpam-454	194	26	xn(t	xn(t	NUM
ejpam-454	194	27	,	,	PUNCT
ejpam-454	194	28	φn	φn	NOUN
ejpam-454	194	29	)	)	PUNCT
ejpam-454	194	30	)	)	PUNCT
ejpam-454	195	1	t	t	PROPN
ejpam-454	195	2	.	.	PUNCT
ejpam-454	196	1	make	make	VERB
ejpam-454	196	2	a	a	DET
ejpam-454	196	3	transformation	transformation	NOUN
ejpam-454	196	4	z(t	z(t	NOUN
ejpam-454	196	5	)	)	PUNCT
ejpam-454	196	6	=	=	SYM
ejpam-454	196	7	x(t)−	x(t)−	PROPN
ejpam-454	196	8	x∗	x∗	PROPN
ejpam-454	196	9	,	,	PUNCT
ejpam-454	196	10	system	system	NOUN
ejpam-454	196	11	(	(	PUNCT
ejpam-454	196	12	13	13	NUM
ejpam-454	196	13	)	)	PUNCT
ejpam-454	196	14	is	be	AUX
ejpam-454	196	15	transformed	transform	VERB
ejpam-454	196	16	into	into	ADP
ejpam-454	196	17	żi(t	żi(t	NOUN
ejpam-454	196	18	)	)	PUNCT
ejpam-454	196	19	=	=	SYM
ejpam-454	197	1	−dizi(t	−dizi(t	NUM
ejpam-454	197	2	)	)	PUNCT
ejpam-454	197	3	+	+	CCONJ
ejpam-454	198	1	n	n	X
ejpam-454	198	2	∑	∑	PUNCT
ejpam-454	198	3	j=1	j=1	PROPN
ejpam-454	198	4	ai	ai	VERB
ejpam-454	198	5	j	j	PROPN
ejpam-454	198	6	f	f	PROPN
ejpam-454	198	7	j(z	j(z	PROPN
ejpam-454	198	8	j(t	j(t	PROPN
ejpam-454	198	9	)	)	PUNCT
ejpam-454	198	10	)	)	PUNCT
ejpam-454	199	1	+	+	CCONJ
ejpam-454	199	2	n	n	X
ejpam-454	199	3	∑	∑	ADP
ejpam-454	200	1	j=1	j=1	ADJ
ejpam-454	200	2	bi	bi	NOUN
ejpam-454	200	3	j	j	PROPN
ejpam-454	200	4	f	f	PROPN
ejpam-454	200	5	j(z	j(z	PROPN
ejpam-454	200	6	j(t	j(t	PROPN
ejpam-454	200	7	−τi	−τi	PROPN
ejpam-454	200	8	j	j	PROPN
ejpam-454	200	9	)	)	PUNCT
ejpam-454	200	10	)	)	PUNCT
ejpam-454	201	1	,	,	PUNCT
ejpam-454	201	2	t	t	PROPN
ejpam-454	201	3	∈	∈	PROPN
ejpam-454	202	1	[	[	X
ejpam-454	202	2	0	0	NUM
ejpam-454	202	3	,	,	PUNCT
ejpam-454	202	4	t1	t1	NOUN
ejpam-454	202	5	]	]	X
ejpam-454	202	6	,	,	PUNCT
ejpam-454	202	7	i	i	PRON
ejpam-454	202	8	=	=	NOUN
ejpam-454	202	9	1	1	NUM
ejpam-454	202	10	,	,	PUNCT
ejpam-454	202	11	·	·	PUNCT
ejpam-454	202	12	·	·	PUNCT
ejpam-454	202	13	·	·	PUNCT
ejpam-454	202	14	,	,	PUNCT
ejpam-454	202	15	n	n	CCONJ
ejpam-454	202	16	,	,	PUNCT
ejpam-454	202	17	(	(	PUNCT
ejpam-454	202	18	14	14	NUM
ejpam-454	202	19	)	)	PUNCT
ejpam-454	202	20	where	where	SCONJ
ejpam-454	202	21	fi(zi(t	fi(zi(t	NOUN
ejpam-454	202	22	)	)	PUNCT
ejpam-454	202	23	)	)	PUNCT
ejpam-454	203	1	=	=	SYM
ejpam-454	203	2	gi(zi(t)+	gi(zi(t)+	NOUN
ejpam-454	203	3	x∗i	x∗i	NUM
ejpam-454	203	4	)	)	PUNCT
ejpam-454	203	5	−	−	PROPN
ejpam-454	203	6	gi(x	gi(x	NUM
ejpam-454	203	7	∗	∗	NOUN
ejpam-454	203	8	i	i	PRON
ejpam-454	203	9	)	)	PUNCT
ejpam-454	203	10	.	.	PUNCT
ejpam-454	204	1	hence	hence	ADV
ejpam-454	204	2	,	,	PUNCT
ejpam-454	204	3	z(t	z(t	PROPN
ejpam-454	204	4	,	,	PUNCT
ejpam-454	204	5	φ̃	φ̃	PROPN
ejpam-454	204	6	)	)	PUNCT
ejpam-454	204	7	=	=	SYM
ejpam-454	204	8	x(t	x(t	PROPN
ejpam-454	204	9	,	,	PUNCT
ejpam-454	204	10	φ)−	φ)−	PROPN
ejpam-454	204	11	x∗	x∗	PROPN
ejpam-454	204	12	is	be	AUX
ejpam-454	204	13	a	a	DET
ejpam-454	204	14	solution	solution	NOUN
ejpam-454	204	15	of	of	ADP
ejpam-454	204	16	system	system	NOUN
ejpam-454	204	17	(	(	PUNCT
ejpam-454	204	18	14	14	NUM
ejpam-454	204	19	)	)	PUNCT
ejpam-454	204	20	with	with	ADP
ejpam-454	204	21	initial	initial	ADJ
ejpam-454	204	22	conditions	condition	NOUN
ejpam-454	204	23	z(t	z(t	NOUN
ejpam-454	204	24	)	)	PUNCT
ejpam-454	204	25	=	=	SYM
ejpam-454	204	26	φ(t)−	φ(t)−	PROPN
ejpam-454	204	27	x∗	x∗	PROPN
ejpam-454	204	28	,	,	PUNCT
ejpam-454	204	29	t	t	PROPN
ejpam-454	204	30	∈	∈	PROPN
ejpam-454	205	1	[	[	X
ejpam-454	205	2	−τ	−τ	NOUN
ejpam-454	205	3	,	,	PUNCT
ejpam-454	205	4	0	0	NUM
ejpam-454	205	5	]	]	PUNCT
ejpam-454	205	6	on	on	ADP
ejpam-454	205	7	[	[	X
ejpam-454	205	8	0	0	NUM
ejpam-454	205	9	,	,	PUNCT
ejpam-454	205	10	t∗(φ	t∗(φ	PROPN
ejpam-454	205	11	)	)	PUNCT
ejpam-454	205	12	)	)	PUNCT
ejpam-454	205	13	.	.	PUNCT
ejpam-454	206	1	step	step	NOUN
ejpam-454	206	2	2	2	NUM
ejpam-454	206	3	.	.	PUNCT
ejpam-454	206	4	consider	consider	VERB
ejpam-454	206	5	the	the	DET
ejpam-454	206	6	following	follow	VERB
ejpam-454	206	7	lyapunov	lyapunov	ADJ
ejpam-454	206	8	functional	functional	ADJ
ejpam-454	206	9	v	v	NOUN
ejpam-454	206	10	(	(	PUNCT
ejpam-454	206	11	z(t	z(t	NOUN
ejpam-454	206	12	)	)	PUNCT
ejpam-454	206	13	)	)	PUNCT
ejpam-454	207	1	=	=	PUNCT
ejpam-454	208	1	n	n	CCONJ
ejpam-454	208	2	∑	∑	NOUN
ejpam-454	208	3	i=1	i=1	PROPN
ejpam-454	208	4	pi	pi	PROPN
ejpam-454	208	5	{	{	PUNCT
ejpam-454	208	6	�	�	PROPN
ejpam-454	208	7	�	�	PROPN
ejpam-454	208	8	zi(t	zi(t	NOUN
ejpam-454	208	9	)	)	PUNCT
ejpam-454	208	10	�	�	PROPN
ejpam-454	208	11	�	�	PROPN
ejpam-454	208	12	+	+	PROPN
ejpam-454	208	13	n	n	CCONJ
ejpam-454	208	14	∑	∑	ADP
ejpam-454	208	15	j=1	j=1	PROPN
ejpam-454	208	16	∫	∫	PROPN
ejpam-454	208	17	t	t	PROPN
ejpam-454	208	18	t−τi	t−τi	NUM
ejpam-454	208	19	j	j	PROPN
ejpam-454	208	20	�	�	PROPN
ejpam-454	208	21	�	�	PROPN
ejpam-454	208	22	bi	bi	PROPN
ejpam-454	208	23	j	j	PROPN
ejpam-454	208	24	�	�	PROPN
ejpam-454	208	25	�	�	PROPN
ejpam-454	208	26	·	·	PUNCT
ejpam-454	208	27	�	�	PROPN
ejpam-454	208	28	�	�	PROPN
ejpam-454	208	29	f	f	PROPN
ejpam-454	208	30	j(z	j(z	PROPN
ejpam-454	208	31	j(θ	j(θ	PROPN
ejpam-454	208	32	)	)	PUNCT
ejpam-454	208	33	)	)	PUNCT
ejpam-454	208	34	�	�	PROPN
ejpam-454	208	35	�	�	PROPN
ejpam-454	208	36	dθ	dθ	PROPN
ejpam-454	208	37	}	}	PUNCT
ejpam-454	208	38	.	.	PUNCT
ejpam-454	209	1	(	(	PUNCT
ejpam-454	209	2	15	15	NUM
ejpam-454	209	3	)	)	PUNCT
ejpam-454	209	4	a.	a.	NOUN
ejpam-454	209	5	wu	wu	PROPN
ejpam-454	209	6	,	,	PUNCT
ejpam-454	209	7	j.	j.	PROPN
ejpam-454	209	8	zhang	zhang	PROPN
ejpam-454	209	9	,	,	PUNCT
ejpam-454	209	10	c.	c.	PROPN
ejpam-454	209	11	fu	fu	PROPN
ejpam-454	209	12	/	/	SYM
ejpam-454	209	13	eur	eur	PROPN
ejpam-454	209	14	.	.	PUNCT
ejpam-454	210	1	j.	j.	PROPN
ejpam-454	210	2	pure	pure	PROPN
ejpam-454	210	3	appl	appl	PROPN
ejpam-454	210	4	.	.	PROPN
ejpam-454	210	5	math	math	PROPN
ejpam-454	210	6	,	,	PUNCT
ejpam-454	210	7	3	3	NUM
ejpam-454	210	8	(	(	PUNCT
ejpam-454	210	9	2010	2010	NUM
ejpam-454	210	10	)	)	PUNCT
ejpam-454	210	11	,	,	PUNCT
ejpam-454	210	12	806	806	NUM
ejpam-454	210	13	-	-	SYM
ejpam-454	210	14	818	818	NUM
ejpam-454	210	15	813	813	NUM
ejpam-454	210	16	obviously	obviously	ADV
ejpam-454	210	17	,	,	PUNCT
ejpam-454	210	18	v	v	X
ejpam-454	210	19	(	(	PUNCT
ejpam-454	210	20	z	z	NOUN
ejpam-454	210	21	)	)	PUNCT
ejpam-454	210	22	is	be	AUX
ejpam-454	210	23	positive	positive	ADJ
ejpam-454	210	24	definite	definite	ADJ
ejpam-454	210	25	and	and	CCONJ
ejpam-454	210	26	lim	lim	PROPN
ejpam-454	210	27	‖z‖→∞	‖z‖→∞	PROPN
ejpam-454	210	28	v	v	PROPN
ejpam-454	210	29	(	(	PUNCT
ejpam-454	210	30	z	z	NOUN
ejpam-454	210	31	)	)	PUNCT
ejpam-454	211	1	=	=	SYM
ejpam-454	211	2	∞.	∞.	PROPN
ejpam-454	211	3	calculating	calculate	VERB
ejpam-454	211	4	the	the	DET
ejpam-454	211	5	derivative	derivative	NOUN
ejpam-454	211	6	of	of	ADP
ejpam-454	211	7	v	v	NOUN
ejpam-454	211	8	(	(	PUNCT
ejpam-454	211	9	z	z	NOUN
ejpam-454	211	10	)	)	PUNCT
ejpam-454	211	11	along	along	ADP
ejpam-454	211	12	the	the	DET
ejpam-454	211	13	solution	solution	NOUN
ejpam-454	211	14	z(t	z(t	PROPN
ejpam-454	211	15	,	,	PUNCT
ejpam-454	211	16	φ̃	φ̃	PROPN
ejpam-454	211	17	)	)	PUNCT
ejpam-454	211	18	of	of	ADP
ejpam-454	211	19	system	system	NOUN
ejpam-454	211	20	(	(	PUNCT
ejpam-454	211	21	14	14	NUM
ejpam-454	211	22	)	)	PUNCT
ejpam-454	211	23	on	on	ADP
ejpam-454	211	24	[	[	X
ejpam-454	211	25	0	0	NUM
ejpam-454	211	26	,	,	PUNCT
ejpam-454	211	27	t∗(φ	t∗(φ	PROPN
ejpam-454	211	28	)	)	PUNCT
ejpam-454	211	29	)	)	PUNCT
ejpam-454	211	30	,	,	PUNCT
ejpam-454	211	31	then	then	ADV
ejpam-454	211	32	we	we	PRON
ejpam-454	211	33	can	can	AUX
ejpam-454	211	34	get	get	VERB
ejpam-454	211	35	v̇	v̇	NOUN
ejpam-454	211	36	(	(	PUNCT
ejpam-454	211	37	z(t	z(t	PROPN
ejpam-454	211	38	,	,	PUNCT
ejpam-454	211	39	φ̃))≤	φ̃))≤	NOUN
ejpam-454	211	40	−	−	PROPN
ejpam-454	212	1	n	n	PROPN
ejpam-454	212	2	∑	∑	PROPN
ejpam-454	212	3	i=1	i=1	PROPN
ejpam-454	212	4	{	{	PUNCT
ejpam-454	212	5	pidi	pidi	PROPN
ejpam-454	212	6	�	�	PROPN
ejpam-454	212	7	�	�	PROPN
ejpam-454	212	8	zi(t	zi(t	NOUN
ejpam-454	212	9	,	,	PUNCT
ejpam-454	212	10	φ̃	φ̃	PROPN
ejpam-454	212	11	)	)	PUNCT
ejpam-454	212	12	�	�	PROPN
ejpam-454	212	13	�	�	PROPN
ejpam-454	212	14	−	−	PROPN
ejpam-454	213	1	pi(aii	pi(aii	PROPN
ejpam-454	213	2	+	+	NUM
ejpam-454	213	3	�	�	PROPN
ejpam-454	213	4	�	�	PROPN
ejpam-454	213	5	bii	bii	PROPN
ejpam-454	213	6	�	�	PROPN
ejpam-454	213	7	�	�	PROPN
ejpam-454	213	8	)	)	PUNCT
ejpam-454	213	9	�	�	PROPN
ejpam-454	213	10	�	�	PROPN
ejpam-454	213	11	fi(zi(t	fi(zi(t	PROPN
ejpam-454	213	12	,	,	PUNCT
ejpam-454	213	13	φ̃	φ̃	PROPN
ejpam-454	213	14	)	)	PUNCT
ejpam-454	213	15	)	)	PUNCT
ejpam-454	213	16	�	�	PROPN
ejpam-454	213	17	�	�	PROPN
ejpam-454	213	18	−	−	PROPN
ejpam-454	213	19	n	n	CCONJ
ejpam-454	213	20	∑	∑	PROPN
ejpam-454	213	21	j=1	j=1	PROPN
ejpam-454	213	22	,	,	PUNCT
ejpam-454	213	23	j	j	PROPN
ejpam-454	213	24	6	6	NUM
ejpam-454	213	25	=	=	NOUN
ejpam-454	213	26	i	i	PRON
ejpam-454	213	27	pi	pi	VERB
ejpam-454	213	28	(	(	PUNCT
ejpam-454	213	29	�	�	PROPN
ejpam-454	213	30	�	�	PROPN
ejpam-454	213	31	ai	ai	PROPN
ejpam-454	213	32	j	j	PROPN
ejpam-454	213	33	�	�	PROPN
ejpam-454	213	34	�	�	PROPN
ejpam-454	213	35	+	+	PROPN
ejpam-454	213	36	�	�	PROPN
ejpam-454	213	37	�	�	PROPN
ejpam-454	213	38	bi	bi	PROPN
ejpam-454	213	39	j	j	PROPN
ejpam-454	213	40	�	�	PROPN
ejpam-454	213	41	�	�	PROPN
ejpam-454	213	42	)	)	PUNCT
ejpam-454	213	43	·	·	PUNCT
ejpam-454	213	44	�	�	PROPN
ejpam-454	213	45	�	�	PROPN
ejpam-454	214	1	f	f	PROPN
ejpam-454	214	2	j(z	j(z	PROPN
ejpam-454	214	3	j(t	j(t	PROPN
ejpam-454	214	4	,	,	PUNCT
ejpam-454	214	5	φ̃	φ̃	PROPN
ejpam-454	214	6	)	)	PUNCT
ejpam-454	214	7	)	)	PUNCT
ejpam-454	214	8	�	�	PROPN
ejpam-454	214	9	�	�	PROPN
ejpam-454	214	10	}	}	PUNCT
ejpam-454	214	11	=	=	SYM
ejpam-454	214	12	−	−	PROPN
ejpam-454	215	1	n	n	CCONJ
ejpam-454	215	2	∑	∑	PROPN
ejpam-454	215	3	i=1	i=1	PROPN
ejpam-454	215	4	{	{	PUNCT
ejpam-454	215	5	pidi	pidi	PROPN
ejpam-454	215	6	�	�	PROPN
ejpam-454	215	7	�	�	PROPN
ejpam-454	215	8	zi(t	zi(t	NOUN
ejpam-454	215	9	,	,	PUNCT
ejpam-454	215	10	φ̃	φ̃	PROPN
ejpam-454	215	11	)	)	PUNCT
ejpam-454	215	12	�	�	PROPN
ejpam-454	215	13	�	�	PROPN
ejpam-454	215	14	−	−	PROPN
ejpam-454	216	1	pi(aii	pi(aii	PROPN
ejpam-454	216	2	+	+	NUM
ejpam-454	216	3	�	�	PROPN
ejpam-454	216	4	�	�	PROPN
ejpam-454	216	5	bii	bii	PROPN
ejpam-454	216	6	�	�	PROPN
ejpam-454	216	7	�	�	PROPN
ejpam-454	216	8	)	)	PUNCT
ejpam-454	216	9	�	�	PROPN
ejpam-454	216	10	�	�	PROPN
ejpam-454	216	11	fi(zi(t	fi(zi(t	PROPN
ejpam-454	216	12	,	,	PUNCT
ejpam-454	216	13	φ̃	φ̃	PROPN
ejpam-454	216	14	)	)	PUNCT
ejpam-454	216	15	)	)	PUNCT
ejpam-454	216	16	�	�	PROPN
ejpam-454	216	17	�	�	PROPN
ejpam-454	216	18	−	−	PROPN
ejpam-454	216	19	n	n	CCONJ
ejpam-454	216	20	∑	∑	PROPN
ejpam-454	216	21	j=1	j=1	PROPN
ejpam-454	216	22	,	,	PUNCT
ejpam-454	216	23	j	j	PROPN
ejpam-454	216	24	6	6	NUM
ejpam-454	216	25	=	=	NOUN
ejpam-454	216	26	i	i	PROPN
ejpam-454	216	27	p	p	PROPN
ejpam-454	216	28	j	j	PROPN
ejpam-454	216	29	(	(	PUNCT
ejpam-454	216	30	�	�	PROPN
ejpam-454	216	31	�	�	PROPN
ejpam-454	216	32	a	a	DET
ejpam-454	216	33	ji	ji	PROPN
ejpam-454	216	34	�	�	PROPN
ejpam-454	216	35	�	�	PROPN
ejpam-454	216	36	+	+	PROPN
ejpam-454	216	37	�	�	PROPN
ejpam-454	216	38	�	�	PROPN
ejpam-454	216	39	b	b	PROPN
ejpam-454	216	40	ji	ji	PROPN
ejpam-454	216	41	�	�	PROPN
ejpam-454	216	42	�	�	PROPN
ejpam-454	216	43	)	)	PUNCT
ejpam-454	216	44	·	·	PUNCT
ejpam-454	216	45	�	�	PROPN
ejpam-454	216	46	�	�	PROPN
ejpam-454	216	47	fi(zi(t	fi(zi(t	PROPN
ejpam-454	216	48	,	,	PUNCT
ejpam-454	216	49	φ̃	φ̃	PROPN
ejpam-454	216	50	)	)	PUNCT
ejpam-454	216	51	)	)	PUNCT
ejpam-454	216	52	�	�	PROPN
ejpam-454	216	53	�	�	PROPN
ejpam-454	216	54	}	}	PUNCT
ejpam-454	216	55	≤	≤	NOUN
ejpam-454	216	56	−pmin	−pmin	ADP
ejpam-454	216	57	n	n	CCONJ
ejpam-454	216	58	∑	∑	PROPN
ejpam-454	216	59	i=1	i=1	PROPN
ejpam-454	216	60	�	�	PROPN
ejpam-454	216	61	�	�	PROPN
ejpam-454	216	62	zi(t	zi(t	NOUN
ejpam-454	216	63	,	,	PUNCT
ejpam-454	216	64	φ̃	φ̃	PROPN
ejpam-454	216	65	)	)	PUNCT
ejpam-454	216	66	�	�	PROPN
ejpam-454	216	67	�	�	PROPN
ejpam-454	216	68	<	<	X
ejpam-454	216	69	0	0	NUM
ejpam-454	216	70	where	where	SCONJ
ejpam-454	216	71	pmin	pmin	NOUN
ejpam-454	216	72	=	=	SYM
ejpam-454	216	73	min	min	PROPN
ejpam-454	216	74	1≤i≤n	1≤i≤n	NUM
ejpam-454	216	75	�	�	PROPN
ejpam-454	216	76	pidi	pidi	NOUN
ejpam-454	216	77	.	.	PUNCT
ejpam-454	217	1	this	this	PRON
ejpam-454	217	2	implies	imply	VERB
ejpam-454	217	3	v	v	NUM
ejpam-454	217	4	(	(	PUNCT
ejpam-454	217	5	z(t	z(t	PROPN
ejpam-454	217	6	,	,	PUNCT
ejpam-454	217	7	φ̃	φ̃	PROPN
ejpam-454	217	8	)	)	PUNCT
ejpam-454	217	9	)	)	PUNCT
ejpam-454	217	10	<	<	X
ejpam-454	217	11	v	v	X
ejpam-454	217	12	(	(	PUNCT
ejpam-454	217	13	z(0	z(0	NOUN
ejpam-454	217	14	)	)	PUNCT
ejpam-454	217	15	)	)	PUNCT
ejpam-454	217	16	,	,	PUNCT
ejpam-454	217	17	t	t	PROPN
ejpam-454	217	18	∈	∈	PROPN
ejpam-454	218	1	[	[	X
ejpam-454	218	2	0	0	NUM
ejpam-454	218	3	,	,	PUNCT
ejpam-454	218	4	t∗(φ	t∗(φ	PROPN
ejpam-454	218	5	)	)	PUNCT
ejpam-454	218	6	)	)	PUNCT
ejpam-454	218	7	.	.	PUNCT
ejpam-454	219	1	by	by	ADP
ejpam-454	219	2	(	(	PUNCT
ejpam-454	219	3	15	15	NUM
ejpam-454	219	4	)	)	PUNCT
ejpam-454	219	5	,	,	PUNCT
ejpam-454	219	6	we	we	PRON
ejpam-454	219	7	can	can	AUX
ejpam-454	219	8	get	get	VERB
ejpam-454	219	9	n	n	PRON
ejpam-454	219	10	∑	∑	PROPN
ejpam-454	219	11	i=1	i=1	PROPN
ejpam-454	219	12	pi	pi	PROPN
ejpam-454	219	13	�	�	PROPN
ejpam-454	219	14	�	�	PROPN
ejpam-454	219	15	zi(t	zi(t	NOUN
ejpam-454	219	16	,	,	PUNCT
ejpam-454	219	17	φ̃	φ̃	PROPN
ejpam-454	219	18	)	)	PUNCT
ejpam-454	219	19	�	�	PROPN
ejpam-454	219	20	�	�	PROPN
ejpam-454	219	21	<	<	X
ejpam-454	219	22	v	v	PROPN
ejpam-454	219	23	(	(	PUNCT
ejpam-454	219	24	z(0	z(0	NOUN
ejpam-454	219	25	)	)	PUNCT
ejpam-454	219	26	)	)	PUNCT
ejpam-454	219	27	(	(	PUNCT
ejpam-454	219	28	16	16	NUM
ejpam-454	219	29	)	)	PUNCT
ejpam-454	219	30	according	accord	VERB
ejpam-454	219	31	to	to	ADP
ejpam-454	219	32	(	(	PUNCT
ejpam-454	219	33	16	16	NUM
ejpam-454	219	34	)	)	PUNCT
ejpam-454	219	35	,	,	PUNCT
ejpam-454	219	36	it	it	PRON
ejpam-454	219	37	is	be	AUX
ejpam-454	219	38	easy	easy	ADJ
ejpam-454	219	39	to	to	PART
ejpam-454	219	40	derive	derive	VERB
ejpam-454	219	41	that	that	SCONJ
ejpam-454	219	42	zi(t	zi(t	NOUN
ejpam-454	219	43	,	,	PUNCT
ejpam-454	219	44	φ̃	φ̃	PROPN
ejpam-454	219	45	)	)	PUNCT
ejpam-454	219	46	,	,	PUNCT
ejpam-454	220	1	i	i	NOUN
ejpam-454	220	2	=	=	NOUN
ejpam-454	220	3	1	1	NUM
ejpam-454	220	4	,	,	PUNCT
ejpam-454	220	5	·	·	PUNCT
ejpam-454	220	6	·	·	PUNCT
ejpam-454	220	7	·	·	PUNCT
ejpam-454	220	8	,	,	PUNCT
ejpam-454	220	9	n	n	CCONJ
ejpam-454	220	10	,	,	PUNCT
ejpam-454	220	11	are	be	AUX
ejpam-454	220	12	bounded	bound	VERB
ejpam-454	220	13	on	on	ADP
ejpam-454	220	14	[	[	X
ejpam-454	220	15	0	0	NUM
ejpam-454	220	16	,	,	PUNCT
ejpam-454	220	17	t∗(φ	t∗(φ	PROPN
ejpam-454	220	18	)	)	PUNCT
ejpam-454	220	19	)	)	PUNCT
ejpam-454	220	20	.	.	PUNCT
ejpam-454	221	1	by	by	ADP
ejpam-454	221	2	virtue	virtue	NOUN
ejpam-454	221	3	of	of	ADP
ejpam-454	221	4	the	the	DET
ejpam-454	221	5	continuous	continuous	ADJ
ejpam-454	221	6	theorem	theorem	NOUN
ejpam-454	221	7	of	of	ADP
ejpam-454	221	8	differential	differential	ADJ
ejpam-454	221	9	equations	equation	NOUN
ejpam-454	221	10	,	,	PUNCT
ejpam-454	221	11	we	we	PRON
ejpam-454	221	12	can	can	AUX
ejpam-454	221	13	conclude	conclude	VERB
ejpam-454	221	14	that	that	DET
ejpam-454	221	15	system	system	NOUN
ejpam-454	221	16	(	(	PUNCT
ejpam-454	221	17	14	14	NUM
ejpam-454	221	18	)	)	PUNCT
ejpam-454	221	19	has	have	VERB
ejpam-454	221	20	a	a	DET
ejpam-454	221	21	solution	solution	NOUN
ejpam-454	221	22	on	on	ADP
ejpam-454	221	23	[	[	X
ejpam-454	221	24	0	0	NUM
ejpam-454	221	25	,	,	PUNCT
ejpam-454	221	26	t1	t1	NOUN
ejpam-454	221	27	]	]	X
ejpam-454	221	28	,	,	PUNCT
ejpam-454	221	29	i.e.	i.e.	X
ejpam-454	221	30	,	,	PUNCT
ejpam-454	221	31	system	system	NOUN
ejpam-454	221	32	(	(	PUNCT
ejpam-454	221	33	13	13	NUM
ejpam-454	221	34	)	)	PUNCT
ejpam-454	221	35	has	have	VERB
ejpam-454	221	36	a	a	DET
ejpam-454	221	37	solution	solution	NOUN
ejpam-454	221	38	on	on	ADP
ejpam-454	221	39	[	[	X
ejpam-454	221	40	0	0	NUM
ejpam-454	221	41	,	,	PUNCT
ejpam-454	221	42	t1	t1	NOUN
ejpam-454	221	43	]	]	X
ejpam-454	221	44	.	.	PUNCT
ejpam-454	222	1	we	we	PRON
ejpam-454	222	2	denote	denote	VERB
ejpam-454	222	3	this	this	DET
ejpam-454	222	4	solution	solution	NOUN
ejpam-454	222	5	of	of	ADP
ejpam-454	222	6	system	system	NOUN
ejpam-454	222	7	(	(	PUNCT
ejpam-454	222	8	13	13	NUM
ejpam-454	222	9	)	)	PUNCT
ejpam-454	222	10	by	by	ADP
ejpam-454	222	11	x0(t	x0(t	PROPN
ejpam-454	222	12	)	)	PUNCT
ejpam-454	222	13	.	.	PUNCT
ejpam-454	223	1	step	step	NOUN
ejpam-454	223	2	3	3	NUM
ejpam-454	223	3	.	.	PUNCT
ejpam-454	224	1	consider	consider	VERB
ejpam-454	224	2	the	the	DET
ejpam-454	224	3	following	follow	VERB
ejpam-454	224	4	system	system	NOUN
ejpam-454	224	5	:	:	PUNCT
ejpam-454	224	6			PROPN
ejpam-454	224	7			PROPN
ejpam-454	224	8			NOUN
ejpam-454	224	9	ẋ	ẋ	PROPN
ejpam-454	224	10	i(t	i(t	PROPN
ejpam-454	224	11	)	)	PUNCT
ejpam-454	224	12	=	=	SYM
ejpam-454	225	1	−di	−di	NOUN
ejpam-454	225	2	x	x	SYM
ejpam-454	225	3	i(t	i(t	PROPN
ejpam-454	225	4	)	)	PUNCT
ejpam-454	225	5	+	+	CCONJ
ejpam-454	226	1	n	n	X
ejpam-454	226	2	∑	∑	PUNCT
ejpam-454	226	3	j=1	j=1	PROPN
ejpam-454	226	4	ai	ai	VERB
ejpam-454	226	5	j	j	PROPN
ejpam-454	226	6	g	g	PROPN
ejpam-454	226	7	j(x	j(x	PROPN
ejpam-454	226	8	j(t	j(t	PROPN
ejpam-454	226	9	)	)	PUNCT
ejpam-454	226	10	)	)	PUNCT
ejpam-454	227	1	+	+	CCONJ
ejpam-454	228	1	n	n	X
ejpam-454	228	2	∑	∑	ADP
ejpam-454	228	3	j=1	j=1	ADJ
ejpam-454	228	4	bi	bi	PROPN
ejpam-454	228	5	j	j	PROPN
ejpam-454	228	6	g	g	PROPN
ejpam-454	228	7	j(x	j(x	PROPN
ejpam-454	228	8	j(t	j(t	PROPN
ejpam-454	228	9	−τi	−τi	PROPN
ejpam-454	228	10	j))+	j))+	PROPN
ejpam-454	228	11	ii	ii	PROPN
ejpam-454	228	12	,	,	PUNCT
ejpam-454	228	13	t	t	PROPN
ejpam-454	228	14	∈	∈	PROPN
ejpam-454	229	1	[	[	X
ejpam-454	229	2	t1	t1	NOUN
ejpam-454	229	3	,	,	PUNCT
ejpam-454	229	4	t2	t2	NOUN
ejpam-454	229	5	]	]	PUNCT
ejpam-454	229	6	,	,	PUNCT
ejpam-454	229	7	x	x	SYM
ejpam-454	229	8	i(t1	i(t1	NOUN
ejpam-454	229	9	)	)	PUNCT
ejpam-454	229	10	=	=	SYM
ejpam-454	230	1	x0	x0	PROPN
ejpam-454	231	1	i	i	PRON
ejpam-454	231	2	(	(	PUNCT
ejpam-454	231	3	t1	t1	NOUN
ejpam-454	231	4	)	)	PUNCT
ejpam-454	232	1	+	+	CCONJ
ejpam-454	232	2	ji1(x	ji1(x	PROPN
ejpam-454	232	3	0	0	PUNCT
ejpam-454	233	1	i	i	PRON
ejpam-454	233	2	(	(	PUNCT
ejpam-454	233	3	t1	t1	NOUN
ejpam-454	233	4	)	)	PUNCT
ejpam-454	233	5	)	)	PUNCT
ejpam-454	233	6	,	,	PUNCT
ejpam-454	233	7	i	i	PRON
ejpam-454	233	8	=	=	NOUN
ejpam-454	233	9	1	1	NUM
ejpam-454	233	10	,	,	PUNCT
ejpam-454	233	11	·	·	PUNCT
ejpam-454	233	12	·	·	PUNCT
ejpam-454	233	13	·	·	PUNCT
ejpam-454	233	14	,	,	PUNCT
ejpam-454	233	15	n.	n.	PROPN
ejpam-454	233	16	(	(	PUNCT
ejpam-454	233	17	17	17	NUM
ejpam-454	233	18	)	)	PUNCT
ejpam-454	233	19	arguing	argue	VERB
ejpam-454	233	20	as	as	ADP
ejpam-454	233	21	in	in	ADP
ejpam-454	233	22	step	step	NOUN
ejpam-454	233	23	1	1	NUM
ejpam-454	233	24	and	and	CCONJ
ejpam-454	233	25	step	step	NOUN
ejpam-454	233	26	2	2	NUM
ejpam-454	233	27	,	,	PUNCT
ejpam-454	233	28	system	system	NOUN
ejpam-454	233	29	(	(	PUNCT
ejpam-454	233	30	17	17	NUM
ejpam-454	233	31	)	)	PUNCT
ejpam-454	233	32	has	have	VERB
ejpam-454	233	33	a	a	DET
ejpam-454	233	34	solution	solution	NOUN
ejpam-454	233	35	x1(t	x1(t	PUNCT
ejpam-454	233	36	)	)	PUNCT
ejpam-454	233	37	on	on	ADP
ejpam-454	233	38	[	[	X
ejpam-454	233	39	t1	t1	NOUN
ejpam-454	233	40	,	,	PUNCT
ejpam-454	233	41	t2	t2	NOUN
ejpam-454	233	42	]	]	PUNCT
ejpam-454	233	43	.	.	PUNCT
ejpam-454	234	1	as	as	ADP
ejpam-454	234	2	inductive	inductive	ADJ
ejpam-454	234	3	step	step	NOUN
ejpam-454	234	4	,	,	PUNCT
ejpam-454	234	5	we	we	PRON
ejpam-454	234	6	can	can	AUX
ejpam-454	234	7	derive	derive	VERB
ejpam-454	234	8	that	that	SCONJ
ejpam-454	234	9	the	the	DET
ejpam-454	234	10	following	follow	VERB
ejpam-454	234	11	system	system	NOUN
ejpam-454	234	12	:	:	PUNCT
ejpam-454	234	13			PROPN
ejpam-454	234	14			PROPN
ejpam-454	234	15			NOUN
ejpam-454	234	16	ẋ	ẋ	PROPN
ejpam-454	234	17	i(t	i(t	PROPN
ejpam-454	234	18	)	)	PUNCT
ejpam-454	234	19	=	=	SYM
ejpam-454	234	20	−di	−di	NOUN
ejpam-454	234	21	x	x	SYM
ejpam-454	234	22	i(t	i(t	PROPN
ejpam-454	234	23	)	)	PUNCT
ejpam-454	234	24	+	+	CCONJ
ejpam-454	235	1	n	n	X
ejpam-454	235	2	∑	∑	PUNCT
ejpam-454	235	3	j=1	j=1	PROPN
ejpam-454	235	4	ai	ai	VERB
ejpam-454	235	5	j	j	PROPN
ejpam-454	235	6	g	g	PROPN
ejpam-454	235	7	j(x	j(x	PROPN
ejpam-454	235	8	j(t	j(t	PROPN
ejpam-454	235	9	)	)	PUNCT
ejpam-454	235	10	)	)	PUNCT
ejpam-454	236	1	+	+	CCONJ
ejpam-454	237	1	n	n	X
ejpam-454	237	2	∑	∑	ADP
ejpam-454	237	3	j=1	j=1	ADJ
ejpam-454	237	4	bi	bi	PROPN
ejpam-454	237	5	j	j	PROPN
ejpam-454	237	6	g	g	PROPN
ejpam-454	237	7	j(x	j(x	PROPN
ejpam-454	237	8	j(t	j(t	PROPN
ejpam-454	237	9	−τi	−τi	PROPN
ejpam-454	237	10	j	j	PROPN
ejpam-454	237	11	)	)	PUNCT
ejpam-454	237	12	)	)	PUNCT
ejpam-454	238	1	+	+	CCONJ
ejpam-454	238	2	ii	ii	PROPN
ejpam-454	238	3	,	,	PUNCT
ejpam-454	238	4	t	t	PROPN
ejpam-454	238	5	∈	∈	PROPN
ejpam-454	239	1	[	[	X
ejpam-454	239	2	tm	tm	NOUN
ejpam-454	239	3	,	,	PUNCT
ejpam-454	239	4	tm+1	tm+1	X
ejpam-454	239	5	]	]	X
ejpam-454	239	6	,	,	PUNCT
ejpam-454	239	7	x	x	SYM
ejpam-454	239	8	i(tm	i(tm	NOUN
ejpam-454	239	9	)	)	PUNCT
ejpam-454	239	10	=	=	SYM
ejpam-454	240	1	xm−1	xm−1	PROPN
ejpam-454	240	2	i	i	PRON
ejpam-454	240	3	(	(	PUNCT
ejpam-454	240	4	tm	tm	NOUN
ejpam-454	240	5	)	)	PUNCT
ejpam-454	240	6	+	+	PUNCT
ejpam-454	241	1	jim(x	jim(x	PROPN
ejpam-454	241	2	m−1	m−1	PROPN
ejpam-454	241	3	i	i	PRON
ejpam-454	241	4	(	(	PUNCT
ejpam-454	241	5	tm	tm	NOUN
ejpam-454	241	6	)	)	PUNCT
ejpam-454	241	7	)	)	PUNCT
ejpam-454	241	8	,	,	PUNCT
ejpam-454	241	9	i	i	PRON
ejpam-454	241	10	=	=	NOUN
ejpam-454	241	11	1	1	NUM
ejpam-454	241	12	,	,	PUNCT
ejpam-454	241	13	·	·	PUNCT
ejpam-454	241	14	·	·	PUNCT
ejpam-454	241	15	·	·	PUNCT
ejpam-454	241	16	,	,	PUNCT
ejpam-454	241	17	n	n	CCONJ
ejpam-454	241	18	,	,	PUNCT
ejpam-454	241	19	also	also	ADV
ejpam-454	241	20	has	have	VERB
ejpam-454	241	21	a	a	DET
ejpam-454	241	22	solution	solution	NOUN
ejpam-454	241	23	xm(t	xm(t	PUNCT
ejpam-454	241	24	)	)	PUNCT
ejpam-454	241	25	on	on	ADP
ejpam-454	241	26	[	[	X
ejpam-454	241	27	tm	tm	NOUN
ejpam-454	241	28	,	,	PUNCT
ejpam-454	241	29	tm+1	tm+1	X
ejpam-454	241	30	]	]	X
ejpam-454	241	31	,	,	PUNCT
ejpam-454	241	32	m=	m=	X
ejpam-454	241	33	2,3	2,3	NUM
ejpam-454	241	34	,	,	PUNCT
ejpam-454	241	35	·	·	PUNCT
ejpam-454	241	36	·	·	PUNCT
ejpam-454	241	37	·	·	PUNCT
ejpam-454	241	38	.	.	PUNCT
ejpam-454	242	1	a.	a.	PROPN
ejpam-454	242	2	wu	wu	PROPN
ejpam-454	242	3	,	,	PUNCT
ejpam-454	242	4	j.	j.	PROPN
ejpam-454	242	5	zhang	zhang	PROPN
ejpam-454	242	6	,	,	PUNCT
ejpam-454	242	7	c.	c.	PROPN
ejpam-454	242	8	fu	fu	PROPN
ejpam-454	242	9	/	/	SYM
ejpam-454	242	10	eur	eur	PROPN
ejpam-454	242	11	.	.	PUNCT
ejpam-454	243	1	j.	j.	PROPN
ejpam-454	243	2	pure	pure	PROPN
ejpam-454	243	3	appl	appl	PROPN
ejpam-454	243	4	.	.	PROPN
ejpam-454	243	5	math	math	PROPN
ejpam-454	243	6	,	,	PUNCT
ejpam-454	243	7	3	3	NUM
ejpam-454	243	8	(	(	PUNCT
ejpam-454	243	9	2010	2010	NUM
ejpam-454	243	10	)	)	PUNCT
ejpam-454	243	11	,	,	PUNCT
ejpam-454	243	12	806	806	NUM
ejpam-454	243	13	-	-	SYM
ejpam-454	243	14	818	818	NUM
ejpam-454	243	15	814	814	NUM
ejpam-454	243	16	define	define	VERB
ejpam-454	243	17	x(t	x(t	PROPN
ejpam-454	243	18	,	,	PUNCT
ejpam-454	243	19	φ	φ	NOUN
ejpam-454	243	20	)	)	PUNCT
ejpam-454	243	21	=	=	SYM
ejpam-454	243	22			PROPN
ejpam-454	243	23			PROPN
ejpam-454	243	24			PROPN
ejpam-454	243	25			NOUN
ejpam-454	243	26			PROPN
ejpam-454	243	27			PROPN
ejpam-454	243	28			NOUN
ejpam-454	243	29	x0(t	x0(t	PROPN
ejpam-454	243	30	)	)	PUNCT
ejpam-454	243	31	,	,	PUNCT
ejpam-454	243	32	t	t	PROPN
ejpam-454	243	33	∈	∈	PROPN
ejpam-454	244	1	[	[	X
ejpam-454	244	2	0	0	NUM
ejpam-454	244	3	,	,	PUNCT
ejpam-454	244	4	t1	t1	NOUN
ejpam-454	244	5	]	]	X
ejpam-454	244	6	,	,	PUNCT
ejpam-454	244	7	x1(t	x1(t	PROPN
ejpam-454	244	8	)	)	PUNCT
ejpam-454	244	9	,	,	PUNCT
ejpam-454	244	10	t	t	PROPN
ejpam-454	244	11	∈	∈	PROPN
ejpam-454	244	12	(	(	PUNCT
ejpam-454	244	13	t1	t1	NOUN
ejpam-454	244	14	,	,	PUNCT
ejpam-454	244	15	t2	t2	NOUN
ejpam-454	244	16	]	]	PUNCT
ejpam-454	244	17	,	,	PUNCT
ejpam-454	244	18	·	·	PUNCT
ejpam-454	244	19	·	·	PUNCT
ejpam-454	244	20	·	·	PUNCT
ejpam-454	244	21	,	,	PUNCT
ejpam-454	244	22	xm(t	xm(t	PROPN
ejpam-454	244	23	)	)	PUNCT
ejpam-454	244	24	,	,	PUNCT
ejpam-454	244	25	t	t	PROPN
ejpam-454	244	26	∈	∈	PROPN
ejpam-454	244	27	(	(	PUNCT
ejpam-454	244	28	tm	tm	PROPN
ejpam-454	244	29	,	,	PUNCT
ejpam-454	244	30	tm+1	tm+1	X
ejpam-454	244	31	]	]	X
ejpam-454	244	32	,	,	PUNCT
ejpam-454	244	33	·	·	PUNCT
ejpam-454	244	34	·	·	PUNCT
ejpam-454	244	35	·	·	PUNCT
ejpam-454	244	36	,	,	PUNCT
ejpam-454	244	37	then	then	ADV
ejpam-454	244	38	x(t	x(t	PROPN
ejpam-454	244	39	,	,	PUNCT
ejpam-454	244	40	φ	φ	NUM
ejpam-454	244	41	)	)	PUNCT
ejpam-454	244	42	is	be	AUX
ejpam-454	244	43	the	the	DET
ejpam-454	244	44	solution	solution	NOUN
ejpam-454	244	45	of	of	ADP
ejpam-454	244	46	system	system	NOUN
ejpam-454	244	47	(	(	PUNCT
ejpam-454	244	48	1	1	NUM
ejpam-454	244	49	)	)	PUNCT
ejpam-454	244	50	with	with	ADP
ejpam-454	244	51	initial	initial	ADJ
ejpam-454	244	52	conditions	condition	NOUN
ejpam-454	244	53	x(s	x(s	PROPN
ejpam-454	244	54	)	)	PUNCT
ejpam-454	244	55	=	=	PUNCT
ejpam-454	244	56	φ(s	φ(s	NOUN
ejpam-454	244	57	)	)	PUNCT
ejpam-454	244	58	,	,	PUNCT
ejpam-454	244	59	s	s	VERB
ejpam-454	244	60	∈	∈	PROPN
ejpam-454	245	1	[	[	X
ejpam-454	245	2	−τ	−τ	NOUN
ejpam-454	245	3	,	,	PUNCT
ejpam-454	245	4	0	0	NUM
ejpam-454	245	5	]	]	PUNCT
ejpam-454	245	6	.	.	PUNCT
ejpam-454	246	1	this	this	PRON
ejpam-454	246	2	completes	complete	VERB
ejpam-454	246	3	the	the	DET
ejpam-454	246	4	proof	proof	NOUN
ejpam-454	246	5	of	of	ADP
ejpam-454	246	6	the	the	DET
ejpam-454	246	7	existence	existence	NOUN
ejpam-454	246	8	of	of	ADP
ejpam-454	246	9	solutions	solution	NOUN
ejpam-454	246	10	of	of	ADP
ejpam-454	246	11	system	system	NOUN
ejpam-454	246	12	(	(	PUNCT
ejpam-454	246	13	1	1	NUM
ejpam-454	246	14	)	)	PUNCT
ejpam-454	246	15	.	.	PUNCT
ejpam-454	247	1	step	step	NOUN
ejpam-454	247	2	4	4	NUM
ejpam-454	247	3	.	.	PUNCT
ejpam-454	247	4	assume	assume	VERB
ejpam-454	247	5	that	that	SCONJ
ejpam-454	247	6	x(t	x(t	PROPN
ejpam-454	247	7	)	)	PUNCT
ejpam-454	247	8	is	be	AUX
ejpam-454	247	9	a	a	DET
ejpam-454	247	10	solution	solution	NOUN
ejpam-454	247	11	of	of	ADP
ejpam-454	247	12	system	system	NOUN
ejpam-454	247	13	(	(	PUNCT
ejpam-454	247	14	1	1	NUM
ejpam-454	247	15	)	)	PUNCT
ejpam-454	247	16	,	,	PUNCT
ejpam-454	247	17	and	and	CCONJ
ejpam-454	247	18	x∗	x∗	PROPN
ejpam-454	247	19	is	be	AUX
ejpam-454	247	20	the	the	DET
ejpam-454	247	21	unique	unique	ADJ
ejpam-454	247	22	equilibrium	equilibrium	NOUN
ejpam-454	247	23	point	point	NOUN
ejpam-454	247	24	of	of	ADP
ejpam-454	247	25	system	system	NOUN
ejpam-454	247	26	(	(	PUNCT
ejpam-454	247	27	1	1	NUM
ejpam-454	247	28	)	)	PUNCT
ejpam-454	247	29	.	.	PUNCT
ejpam-454	248	1	make	make	VERB
ejpam-454	248	2	a	a	DET
ejpam-454	248	3	transformation	transformation	NOUN
ejpam-454	248	4	z(t	z(t	NOUN
ejpam-454	248	5	)	)	PUNCT
ejpam-454	248	6	=	=	SYM
ejpam-454	248	7	x(t)−	x(t)−	PROPN
ejpam-454	248	8	x∗	x∗	PROPN
ejpam-454	248	9	,	,	PUNCT
ejpam-454	248	10	then	then	ADV
ejpam-454	248	11	system	system	NOUN
ejpam-454	248	12	(	(	PUNCT
ejpam-454	248	13	1	1	X
ejpam-454	248	14	)	)	PUNCT
ejpam-454	248	15	is	be	AUX
ejpam-454	248	16	transformed	transform	VERB
ejpam-454	248	17	into	into	ADP
ejpam-454	248	18	the	the	DET
ejpam-454	248	19	following	follow	VERB
ejpam-454	248	20	system	system	NOUN
ejpam-454	248	21	:	:	PUNCT
ejpam-454	248	22			NOUN
ejpam-454	248	23			ADP
ejpam-454	248	24			NOUN
ejpam-454	248	25	żi(t	żi(t	NOUN
ejpam-454	248	26	)	)	PUNCT
ejpam-454	248	27	=	=	SYM
ejpam-454	249	1	−dizi(t	−dizi(t	NOUN
ejpam-454	249	2	)	)	PUNCT
ejpam-454	249	3	+	+	CCONJ
ejpam-454	250	1	n	n	X
ejpam-454	250	2	∑	∑	PUNCT
ejpam-454	250	3	j=1	j=1	PROPN
ejpam-454	250	4	ai	ai	VERB
ejpam-454	250	5	j	j	PROPN
ejpam-454	250	6	f	f	PROPN
ejpam-454	250	7	j(z	j(z	PROPN
ejpam-454	250	8	j(t	j(t	PROPN
ejpam-454	250	9	)	)	PUNCT
ejpam-454	250	10	)	)	PUNCT
ejpam-454	251	1	+	+	CCONJ
ejpam-454	251	2	n	n	X
ejpam-454	251	3	∑	∑	ADP
ejpam-454	252	1	j=1	j=1	ADJ
ejpam-454	252	2	bi	bi	NOUN
ejpam-454	252	3	j	j	PROPN
ejpam-454	252	4	f	f	PROPN
ejpam-454	252	5	j(z	j(z	PROPN
ejpam-454	252	6	j(t	j(t	PROPN
ejpam-454	252	7	−τi	−τi	PROPN
ejpam-454	252	8	j	j	PROPN
ejpam-454	252	9	)	)	PUNCT
ejpam-454	252	10	)	)	PUNCT
ejpam-454	252	11	,	,	PUNCT
ejpam-454	252	12	t	t	PROPN
ejpam-454	252	13	6=	6=	NUM
ejpam-454	252	14	tk	tk	PROPN
ejpam-454	252	15	,	,	PUNCT
ejpam-454	252	16	△	△	NOUN
ejpam-454	252	17	zi(tk	zi(tk	NOUN
ejpam-454	252	18	)	)	PUNCT
ejpam-454	252	19	=	=	SYM
ejpam-454	252	20	jik(zi(tk	jik(zi(tk	NOUN
ejpam-454	252	21	)	)	PUNCT
ejpam-454	252	22	)	)	PUNCT
ejpam-454	253	1	=	=	SYM
ejpam-454	253	2	−γikzi(tk	−γikzi(tk	NOUN
ejpam-454	253	3	)	)	PUNCT
ejpam-454	253	4	,	,	PUNCT
ejpam-454	253	5	k	k	X
ejpam-454	253	6	=	=	SYM
ejpam-454	253	7	1,2	1,2	NUM
ejpam-454	253	8	,	,	PUNCT
ejpam-454	253	9	·	·	PUNCT
ejpam-454	253	10	·	·	PUNCT
ejpam-454	253	11	·	·	PUNCT
ejpam-454	253	12	,	,	PUNCT
ejpam-454	253	13	i	i	PRON
ejpam-454	253	14	=	=	NOUN
ejpam-454	253	15	1	1	NUM
ejpam-454	253	16	,	,	PUNCT
ejpam-454	253	17	·	·	PUNCT
ejpam-454	253	18	·	·	PUNCT
ejpam-454	253	19	·	·	PUNCT
ejpam-454	253	20	,	,	PUNCT
ejpam-454	253	21	n	n	CCONJ
ejpam-454	253	22	,	,	PUNCT
ejpam-454	253	23	(	(	PUNCT
ejpam-454	253	24	18	18	NUM
ejpam-454	253	25	)	)	PUNCT
ejpam-454	253	26	where	where	SCONJ
ejpam-454	253	27	fi(zi(t	fi(zi(t	NOUN
ejpam-454	253	28	)	)	PUNCT
ejpam-454	253	29	)	)	PUNCT
ejpam-454	254	1	=	=	SYM
ejpam-454	254	2	gi(zi(t	gi(zi(t	NOUN
ejpam-454	254	3	)	)	PUNCT
ejpam-454	255	1	+	+	CCONJ
ejpam-454	255	2	x∗	x∗	PROPN
ejpam-454	255	3	i	i	PRON
ejpam-454	255	4	)	)	PUNCT
ejpam-454	255	5	−	−	PROPN
ejpam-454	256	1	gi(x	gi(x	NUM
ejpam-454	256	2	∗	∗	NOUN
ejpam-454	256	3	i	i	PRON
ejpam-454	256	4	)	)	PUNCT
ejpam-454	256	5	.	.	PUNCT
ejpam-454	257	1	consider	consider	VERB
ejpam-454	257	2	lyapunov	lyapunov	PROPN
ejpam-454	257	3	functional	functional	ADJ
ejpam-454	257	4	v	v	NOUN
ejpam-454	257	5	(	(	PUNCT
ejpam-454	257	6	z(t	z(t	NOUN
ejpam-454	257	7	)	)	PUNCT
ejpam-454	257	8	)	)	PUNCT
ejpam-454	257	9	,	,	PUNCT
ejpam-454	257	10	the	the	DET
ejpam-454	257	11	v	v	NOUN
ejpam-454	257	12	(	(	PUNCT
ejpam-454	257	13	z(t	z(t	PROPN
ejpam-454	257	14	)	)	PUNCT
ejpam-454	257	15	)	)	PUNCT
ejpam-454	257	16	is	be	AUX
ejpam-454	257	17	the	the	DET
ejpam-454	257	18	same	same	ADJ
ejpam-454	257	19	as	as	ADP
ejpam-454	257	20	(	(	PUNCT
ejpam-454	257	21	15	15	NUM
ejpam-454	257	22	)	)	PUNCT
ejpam-454	257	23	.	.	PUNCT
ejpam-454	258	1	calculating	calculate	VERB
ejpam-454	258	2	the	the	DET
ejpam-454	258	3	derivative	derivative	NOUN
ejpam-454	258	4	of	of	ADP
ejpam-454	258	5	v	v	NOUN
ejpam-454	258	6	(	(	PUNCT
ejpam-454	258	7	z(t	z(t	PROPN
ejpam-454	258	8	)	)	PUNCT
ejpam-454	258	9	)	)	PUNCT
ejpam-454	258	10	along	along	ADP
ejpam-454	258	11	the	the	DET
ejpam-454	258	12	solution	solution	NOUN
ejpam-454	258	13	z(t	z(t	NOUN
ejpam-454	258	14	)	)	PUNCT
ejpam-454	258	15	of	of	ADP
ejpam-454	258	16	system	system	NOUN
ejpam-454	258	17	(	(	PUNCT
ejpam-454	258	18	18	18	NUM
ejpam-454	258	19	)	)	PUNCT
ejpam-454	258	20	for	for	ADP
ejpam-454	258	21	any	any	DET
ejpam-454	258	22	t	t	PROPN
ejpam-454	258	23	,	,	PUNCT
ejpam-454	258	24	t	t	PROPN
ejpam-454	258	25	6=	6=	PROPN
ejpam-454	258	26	tk	tk	PROPN
ejpam-454	258	27	,	,	PUNCT
ejpam-454	258	28	k	k	PROPN
ejpam-454	258	29	=	=	SYM
ejpam-454	258	30	1,2	1,2	NUM
ejpam-454	258	31	,	,	PUNCT
ejpam-454	258	32	·	·	PUNCT
ejpam-454	258	33	·	·	PUNCT
ejpam-454	258	34	·	·	PUNCT
ejpam-454	258	35	.	.	PUNCT
ejpam-454	259	1	arguing	argue	VERB
ejpam-454	259	2	as	as	ADP
ejpam-454	259	3	in	in	ADP
ejpam-454	259	4	step	step	NOUN
ejpam-454	259	5	2	2	NUM
ejpam-454	259	6	,	,	PUNCT
ejpam-454	259	7	we	we	PRON
ejpam-454	259	8	have	have	VERB
ejpam-454	259	9	v̇	v̇	NOUN
ejpam-454	259	10	(	(	PUNCT
ejpam-454	259	11	z(t	z(t	PROPN
ejpam-454	259	12	)	)	PUNCT
ejpam-454	259	13	)	)	PUNCT
ejpam-454	260	1	<	<	X
ejpam-454	260	2	0	0	NUM
ejpam-454	260	3	,	,	PUNCT
ejpam-454	260	4	t	t	PROPN
ejpam-454	260	5	6=	6=	PROPN
ejpam-454	260	6	tk	tk	PROPN
ejpam-454	260	7	,	,	PUNCT
ejpam-454	260	8	k	k	PROPN
ejpam-454	260	9	=	=	SYM
ejpam-454	260	10	1,2	1,2	NUM
ejpam-454	260	11	,	,	PUNCT
ejpam-454	260	12	·	·	PUNCT
ejpam-454	260	13	·	·	PUNCT
ejpam-454	260	14	·	·	PUNCT
ejpam-454	260	15	.	.	PUNCT
ejpam-454	261	1	also	also	ADV
ejpam-454	261	2	,	,	PUNCT
ejpam-454	261	3	v	v	X
ejpam-454	261	4	(	(	PUNCT
ejpam-454	261	5	z(tk	z(tk	PROPN
ejpam-454	261	6	+	+	CCONJ
ejpam-454	261	7	0	0	NUM
ejpam-454	261	8	)	)	PUNCT
ejpam-454	261	9	)	)	PUNCT
ejpam-454	262	1	=	=	PUNCT
ejpam-454	263	1	n	n	CCONJ
ejpam-454	263	2	∑	∑	NOUN
ejpam-454	263	3	i=1	i=1	PROPN
ejpam-454	263	4	pi	pi	PROPN
ejpam-454	263	5	{	{	PUNCT
ejpam-454	263	6	�	�	PROPN
ejpam-454	263	7	�	�	PROPN
ejpam-454	263	8	zi(tk	zi(tk	PROPN
ejpam-454	263	9	+	+	CCONJ
ejpam-454	263	10	0	0	X
ejpam-454	263	11	)	)	PUNCT
ejpam-454	263	12	�	�	PROPN
ejpam-454	263	13	�	�	PROPN
ejpam-454	263	14	+	+	PROPN
ejpam-454	263	15	n	n	CCONJ
ejpam-454	263	16	∑	∑	ADP
ejpam-454	263	17	j=1	j=1	PROPN
ejpam-454	263	18	∫	∫	PROPN
ejpam-454	263	19	(	(	PUNCT
ejpam-454	263	20	tk+0	tk+0	PROPN
ejpam-454	263	21	)	)	PUNCT
ejpam-454	263	22	(	(	PUNCT
ejpam-454	263	23	tk+0)−τi	tk+0)−τi	VERB
ejpam-454	263	24	j	j	PROPN
ejpam-454	263	25	�	�	PROPN
ejpam-454	263	26	�	�	PROPN
ejpam-454	263	27	bi	bi	PROPN
ejpam-454	263	28	j	j	PROPN
ejpam-454	263	29	�	�	PROPN
ejpam-454	263	30	�	�	PROPN
ejpam-454	263	31	·	·	PUNCT
ejpam-454	263	32	�	�	PROPN
ejpam-454	263	33	�	�	PROPN
ejpam-454	263	34	f	f	PROPN
ejpam-454	263	35	j(z	j(z	PROPN
ejpam-454	263	36	j(θ	j(θ	PROPN
ejpam-454	263	37	)	)	PUNCT
ejpam-454	263	38	)	)	PUNCT
ejpam-454	263	39	�	�	PROPN
ejpam-454	263	40	�	�	PROPN
ejpam-454	263	41	dθ	dθ	PROPN
ejpam-454	263	42	}	}	PUNCT
ejpam-454	263	43	=	=	SYM
ejpam-454	263	44	n	n	CCONJ
ejpam-454	263	45	∑	∑	PROPN
ejpam-454	263	46	i=1	i=1	PROPN
ejpam-454	263	47	pi	pi	PROPN
ejpam-454	263	48	{	{	PUNCT
ejpam-454	263	49	�	�	PROPN
ejpam-454	263	50	�	�	PROPN
ejpam-454	263	51	(	(	PUNCT
ejpam-454	263	52	1−	1−	NUM
ejpam-454	263	53	γik)zi(tk	γik)zi(tk	NUM
ejpam-454	263	54	)	)	PUNCT
ejpam-454	263	55	�	�	PROPN
ejpam-454	263	56	�	�	PROPN
ejpam-454	263	57	+	+	PROPN
ejpam-454	263	58	n	n	CCONJ
ejpam-454	263	59	∑	∑	ADP
ejpam-454	263	60	j=1	j=1	PROPN
ejpam-454	263	61	∫	∫	PROPN
ejpam-454	263	62	tk	tk	PROPN
ejpam-454	263	63	tk−τi	tk−τi	PROPN
ejpam-454	263	64	j	j	PROPN
ejpam-454	263	65	�	�	PROPN
ejpam-454	263	66	�	�	PROPN
ejpam-454	263	67	bi	bi	PROPN
ejpam-454	263	68	j	j	PROPN
ejpam-454	263	69	�	�	PROPN
ejpam-454	263	70	�	�	PROPN
ejpam-454	263	71	·	·	PUNCT
ejpam-454	263	72	�	�	PROPN
ejpam-454	263	73	�	�	PROPN
ejpam-454	264	1	f	f	PROPN
ejpam-454	264	2	j(z	j(z	PROPN
ejpam-454	264	3	j(θ	j(θ	PROPN
ejpam-454	264	4	)	)	PUNCT
ejpam-454	264	5	)	)	PUNCT
ejpam-454	264	6	�	�	PROPN
ejpam-454	264	7	�	�	PROPN
ejpam-454	264	8	dθ	dθ	PROPN
ejpam-454	264	9	}	}	PUNCT
ejpam-454	264	10	<	<	X
ejpam-454	264	11	v	v	X
ejpam-454	264	12	(	(	PUNCT
ejpam-454	264	13	z(tk	z(tk	PROPN
ejpam-454	264	14	)	)	PUNCT
ejpam-454	264	15	)	)	PUNCT
ejpam-454	264	16	,	,	PUNCT
ejpam-454	265	1	k	k	X
ejpam-454	265	2	=	=	SYM
ejpam-454	265	3	1,2	1,2	NUM
ejpam-454	265	4	,	,	PUNCT
ejpam-454	265	5	·	·	PUNCT
ejpam-454	265	6	·	·	PUNCT
ejpam-454	265	7	·	·	PUNCT
ejpam-454	265	8	.	.	PUNCT
ejpam-454	266	1	then	then	ADV
ejpam-454	266	2	we	we	PRON
ejpam-454	266	3	can	can	AUX
ejpam-454	266	4	easily	easily	ADV
ejpam-454	266	5	follow	follow	VERB
ejpam-454	266	6	that	that	DET
ejpam-454	266	7	v̇	v̇	NOUN
ejpam-454	266	8	(	(	PUNCT
ejpam-454	266	9	z(t	z(t	PROPN
ejpam-454	266	10	)	)	PUNCT
ejpam-454	266	11	)	)	PUNCT
ejpam-454	266	12	<	<	X
ejpam-454	266	13	0	0	PUNCT
ejpam-454	267	1	for	for	ADP
ejpam-454	267	2	t	t	PROPN
ejpam-454	267	3	>	>	X
ejpam-454	267	4	0	0	PROPN
ejpam-454	267	5	.	.	PUNCT
ejpam-454	268	1	therefore	therefore	ADV
ejpam-454	268	2	,	,	PUNCT
ejpam-454	268	3	the	the	DET
ejpam-454	268	4	equilibrium	equilibrium	NOUN
ejpam-454	268	5	point	point	NOUN
ejpam-454	268	6	x∗	x∗	PROPN
ejpam-454	268	7	of	of	ADP
ejpam-454	268	8	system	system	NOUN
ejpam-454	268	9	(	(	PUNCT
ejpam-454	268	10	1	1	X
ejpam-454	268	11	)	)	PUNCT
ejpam-454	268	12	is	be	AUX
ejpam-454	268	13	globally	globally	ADV
ejpam-454	268	14	asymptotically	asymptotically	ADV
ejpam-454	268	15	stable	stable	ADJ
ejpam-454	268	16	.	.	PUNCT
ejpam-454	269	1	this	this	DET
ejpam-454	269	2	proof	proof	NOUN
ejpam-454	269	3	is	be	AUX
ejpam-454	269	4	completed	complete	VERB
ejpam-454	269	5	.	.	PUNCT
ejpam-454	270	1	theorem	theorem	NOUN
ejpam-454	270	2	5	5	NUM
ejpam-454	270	3	.	.	PUNCT
ejpam-454	271	1	under	under	ADP
ejpam-454	271	2	assumptions	assumption	NOUN
ejpam-454	271	3	of	of	ADP
ejpam-454	271	4	theorem	theorem	NOUN
ejpam-454	271	5	2	2	NUM
ejpam-454	271	6	,	,	PUNCT
ejpam-454	271	7	further	far	ADV
ejpam-454	271	8	if	if	SCONJ
ejpam-454	271	9	the	the	DET
ejpam-454	271	10	following	follow	VERB
ejpam-454	271	11	conditions	condition	NOUN
ejpam-454	271	12	are	be	AUX
ejpam-454	271	13	satisfied	satisfied	ADJ
ejpam-454	271	14	jik(x	jik(x	PROPN
ejpam-454	271	15	i(tk	i(tk	NOUN
ejpam-454	271	16	)	)	PUNCT
ejpam-454	271	17	)	)	PUNCT
ejpam-454	272	1	=	=	SYM
ejpam-454	272	2	−γik(x	−γik(x	PROPN
ejpam-454	272	3	i(tk)−	i(tk)−	NOUN
ejpam-454	272	4	x∗i	x∗i	NUM
ejpam-454	272	5	)	)	PUNCT
ejpam-454	272	6	,	,	PUNCT
ejpam-454	272	7	k	k	X
ejpam-454	272	8	=	=	SYM
ejpam-454	272	9	1,2	1,2	NUM
ejpam-454	272	10	,	,	PUNCT
ejpam-454	272	11	·	·	PUNCT
ejpam-454	272	12	·	·	PUNCT
ejpam-454	272	13	·	·	PUNCT
ejpam-454	272	14	,	,	PUNCT
ejpam-454	272	15	i	i	PRON
ejpam-454	272	16	=	=	NOUN
ejpam-454	272	17	1	1	NUM
ejpam-454	272	18	,	,	PUNCT
ejpam-454	272	19	·	·	PUNCT
ejpam-454	272	20	·	·	PUNCT
ejpam-454	272	21	·	·	PUNCT
ejpam-454	272	22	,	,	PUNCT
ejpam-454	272	23	n	n	CCONJ
ejpam-454	272	24	,	,	PUNCT
ejpam-454	272	25	where	where	SCONJ
ejpam-454	272	26	x∗	x∗	PROPN
ejpam-454	272	27	=	=	SYM
ejpam-454	272	28	(	(	PUNCT
ejpam-454	272	29	x∗1	x∗1	ADJ
ejpam-454	272	30	,	,	PUNCT
ejpam-454	272	31	·	·	PUNCT
ejpam-454	272	32	·	·	PUNCT
ejpam-454	272	33	·	·	PUNCT
ejpam-454	272	34	,	,	PUNCT
ejpam-454	272	35	x∗n	x∗n	X
ejpam-454	272	36	)	)	PUNCT
ejpam-454	272	37	t	t	PROPN
ejpam-454	272	38	is	be	AUX
ejpam-454	272	39	the	the	DET
ejpam-454	272	40	equilibrium	equilibrium	NOUN
ejpam-454	272	41	point	point	NOUN
ejpam-454	272	42	of	of	ADP
ejpam-454	272	43	system	system	NOUN
ejpam-454	272	44	(	(	PUNCT
ejpam-454	272	45	1	1	NUM
ejpam-454	272	46	)	)	PUNCT
ejpam-454	272	47	,	,	PUNCT
ejpam-454	272	48	0	0	PUNCT
ejpam-454	272	49	<	<	X
ejpam-454	272	50	γik	γik	X
ejpam-454	272	51	<	<	X
ejpam-454	272	52	1	1	NUM
ejpam-454	272	53	,	,	PUNCT
ejpam-454	272	54	then	then	ADV
ejpam-454	272	55	system	system	NOUN
ejpam-454	272	56	(	(	PUNCT
ejpam-454	272	57	1	1	X
ejpam-454	272	58	)	)	PUNCT
ejpam-454	272	59	has	have	VERB
ejpam-454	272	60	a	a	DET
ejpam-454	272	61	unique	unique	ADJ
ejpam-454	272	62	equilibrium	equilibrium	NOUN
ejpam-454	272	63	point	point	NOUN
ejpam-454	272	64	which	which	PRON
ejpam-454	272	65	is	be	AUX
ejpam-454	272	66	stable	stable	ADJ
ejpam-454	272	67	and	and	CCONJ
ejpam-454	272	68	every	every	DET
ejpam-454	272	69	solution	solution	NOUN
ejpam-454	272	70	is	be	AUX
ejpam-454	272	71	bounded	bound	VERB
ejpam-454	272	72	.	.	PUNCT
ejpam-454	273	1	if	if	SCONJ
ejpam-454	273	2	,	,	PUNCT
ejpam-454	273	3	in	in	ADP
ejpam-454	273	4	addition	addition	NOUN
ejpam-454	273	5	,	,	PUNCT
ejpam-454	273	6	gi(s	gi(s	NOUN
ejpam-454	273	7	)	)	PUNCT
ejpam-454	273	8	,	,	PUNCT
ejpam-454	273	9	i	i	PRON
ejpam-454	273	10	=	=	NOUN
ejpam-454	273	11	1	1	NUM
ejpam-454	273	12	,	,	PUNCT
ejpam-454	273	13	·	·	PUNCT
ejpam-454	273	14	·	·	PUNCT
ejpam-454	273	15	·	·	PUNCT
ejpam-454	273	16	,	,	PUNCT
ejpam-454	273	17	n	n	CCONJ
ejpam-454	273	18	,	,	PUNCT
ejpam-454	273	19	are	be	AUX
ejpam-454	273	20	strictly	strictly	ADV
ejpam-454	273	21	increasing	increase	VERB
ejpam-454	273	22	functions	function	NOUN
ejpam-454	273	23	,	,	PUNCT
ejpam-454	273	24	then	then	ADV
ejpam-454	273	25	the	the	DET
ejpam-454	273	26	unique	unique	ADJ
ejpam-454	273	27	equilibrium	equilibrium	NOUN
ejpam-454	273	28	point	point	NOUN
ejpam-454	273	29	of	of	ADP
ejpam-454	273	30	system	system	NOUN
ejpam-454	273	31	(	(	PUNCT
ejpam-454	273	32	1	1	X
ejpam-454	273	33	)	)	PUNCT
ejpam-454	273	34	is	be	AUX
ejpam-454	273	35	globally	globally	ADV
ejpam-454	273	36	asymptotically	asymptotically	ADV
ejpam-454	273	37	stable	stable	ADJ
ejpam-454	273	38	.	.	PUNCT
ejpam-454	274	1	proof	proof	NOUN
ejpam-454	274	2	.	.	PUNCT
ejpam-454	275	1	in	in	ADP
ejpam-454	275	2	order	order	NOUN
ejpam-454	275	3	to	to	PART
ejpam-454	275	4	complete	complete	VERB
ejpam-454	275	5	the	the	DET
ejpam-454	275	6	proof	proof	NOUN
ejpam-454	275	7	,	,	PUNCT
ejpam-454	275	8	we	we	PRON
ejpam-454	275	9	divide	divide	VERB
ejpam-454	275	10	the	the	DET
ejpam-454	275	11	proof	proof	NOUN
ejpam-454	275	12	into	into	ADP
ejpam-454	275	13	four	four	NUM
ejpam-454	275	14	steps	step	NOUN
ejpam-454	275	15	:	:	PUNCT
ejpam-454	275	16	step	step	VERB
ejpam-454	275	17	a	a	PRON
ejpam-454	275	18	,	,	PUNCT
ejpam-454	275	19	step	step	NOUN
ejpam-454	275	20	b	b	NOUN
ejpam-454	275	21	,	,	PUNCT
ejpam-454	275	22	step	step	NOUN
ejpam-454	275	23	c	c	NOUN
ejpam-454	275	24	,	,	PUNCT
ejpam-454	275	25	step	step	NOUN
ejpam-454	275	26	d.	d.	PROPN
ejpam-454	275	27	a.	a.	PROPN
ejpam-454	275	28	wu	wu	PROPN
ejpam-454	275	29	,	,	PUNCT
ejpam-454	275	30	j.	j.	PROPN
ejpam-454	275	31	zhang	zhang	PROPN
ejpam-454	275	32	,	,	PUNCT
ejpam-454	275	33	c.	c.	PROPN
ejpam-454	275	34	fu	fu	PROPN
ejpam-454	275	35	/	/	SYM
ejpam-454	275	36	eur	eur	PROPN
ejpam-454	275	37	.	.	PUNCT
ejpam-454	276	1	j.	j.	PROPN
ejpam-454	276	2	pure	pure	PROPN
ejpam-454	276	3	appl	appl	PROPN
ejpam-454	276	4	.	.	PROPN
ejpam-454	276	5	math	math	PROPN
ejpam-454	276	6	,	,	PUNCT
ejpam-454	276	7	3	3	NUM
ejpam-454	276	8	(	(	PUNCT
ejpam-454	276	9	2010	2010	NUM
ejpam-454	276	10	)	)	PUNCT
ejpam-454	276	11	,	,	PUNCT
ejpam-454	276	12	806	806	NUM
ejpam-454	276	13	-	-	SYM
ejpam-454	276	14	818	818	NUM
ejpam-454	276	15	815	815	NUM
ejpam-454	276	16	step	step	NOUN
ejpam-454	276	17	a.	a.	NOUN
ejpam-454	277	1	it	it	PRON
ejpam-454	277	2	is	be	AUX
ejpam-454	277	3	the	the	DET
ejpam-454	277	4	same	same	ADJ
ejpam-454	277	5	as	as	ADP
ejpam-454	277	6	step	step	NOUN
ejpam-454	277	7	1	1	NUM
ejpam-454	277	8	of	of	ADP
ejpam-454	277	9	theorem	theorem	ADJ
ejpam-454	277	10	4	4	NUM
ejpam-454	277	11	,	,	PUNCT
ejpam-454	277	12	so	so	SCONJ
ejpam-454	277	13	we	we	PRON
ejpam-454	277	14	do	do	AUX
ejpam-454	277	15	not	not	PART
ejpam-454	277	16	repeat	repeat	VERB
ejpam-454	277	17	it	it	PRON
ejpam-454	277	18	here	here	ADV
ejpam-454	277	19	.	.	PUNCT
ejpam-454	278	1	step	step	NOUN
ejpam-454	278	2	b.	b.	PROPN
ejpam-454	278	3	consider	consider	VERB
ejpam-454	278	4	the	the	DET
ejpam-454	278	5	following	follow	VERB
ejpam-454	278	6	lyapunov	lyapunov	ADJ
ejpam-454	278	7	functional	functional	ADJ
ejpam-454	278	8	v	v	NOUN
ejpam-454	278	9	(	(	PUNCT
ejpam-454	278	10	z(t	z(t	NOUN
ejpam-454	278	11	)	)	PUNCT
ejpam-454	278	12	)	)	PUNCT
ejpam-454	279	1	=	=	SYM
ejpam-454	279	2	2	2	NUM
ejpam-454	279	3	n	n	NUM
ejpam-454	279	4	∑	∑	PROPN
ejpam-454	279	5	i=1	i=1	PROPN
ejpam-454	279	6	∫	∫	PROPN
ejpam-454	279	7	zi(t	zi(t	NOUN
ejpam-454	279	8	)	)	PUNCT
ejpam-454	279	9	0	0	NUM
ejpam-454	280	1	fi(s)ds+	fi(s)ds+	NOUN
ejpam-454	280	2	r	r	NOUN
ejpam-454	280	3	n	n	NOUN
ejpam-454	280	4	∑	∑	PROPN
ejpam-454	280	5	i=1	i=1	PROPN
ejpam-454	280	6	n	n	ADV
ejpam-454	280	7	∑	∑	PUNCT
ejpam-454	280	8	j=1	j=1	PROPN
ejpam-454	280	9	∫	∫	PROPN
ejpam-454	281	1	t	t	PROPN
ejpam-454	281	2	t−τ	t−τ	PROPN
ejpam-454	281	3	j	j	PROPN
ejpam-454	282	1	i	i	PROPN
ejpam-454	282	2	�	�	PROPN
ejpam-454	282	3	�	�	PROPN
ejpam-454	282	4	b	b	PROPN
ejpam-454	282	5	ji	ji	PROPN
ejpam-454	282	6	�	�	PROPN
ejpam-454	282	7	�	�	PROPN
ejpam-454	282	8	·	·	PUNCT
ejpam-454	282	9	f	f	PROPN
ejpam-454	282	10	2	2	NUM
ejpam-454	282	11	i	i	NOUN
ejpam-454	282	12	(	(	PUNCT
ejpam-454	282	13	zi(θ))dθ	zi(θ))dθ	NOUN
ejpam-454	282	14	.	.	PUNCT
ejpam-454	283	1	(	(	PUNCT
ejpam-454	283	2	19	19	NUM
ejpam-454	283	3	)	)	PUNCT
ejpam-454	283	4	obviously	obviously	ADV
ejpam-454	283	5	,	,	PUNCT
ejpam-454	283	6	v	v	X
ejpam-454	283	7	(	(	PUNCT
ejpam-454	283	8	z	z	NOUN
ejpam-454	283	9	)	)	PUNCT
ejpam-454	283	10	is	be	AUX
ejpam-454	283	11	positive	positive	ADJ
ejpam-454	283	12	definite	definite	ADJ
ejpam-454	283	13	and	and	CCONJ
ejpam-454	283	14	lim	lim	PROPN
ejpam-454	283	15	‖z‖→∞	‖z‖→∞	PROPN
ejpam-454	283	16	v	v	PROPN
ejpam-454	283	17	(	(	PUNCT
ejpam-454	283	18	z	z	NOUN
ejpam-454	283	19	)	)	PUNCT
ejpam-454	284	1	=	=	SYM
ejpam-454	284	2	∞.	∞.	PROPN
ejpam-454	284	3	calculating	calculate	VERB
ejpam-454	284	4	the	the	DET
ejpam-454	284	5	derivative	derivative	NOUN
ejpam-454	284	6	of	of	ADP
ejpam-454	284	7	v	v	NOUN
ejpam-454	284	8	(	(	PUNCT
ejpam-454	284	9	z	z	NOUN
ejpam-454	284	10	)	)	PUNCT
ejpam-454	284	11	along	along	ADP
ejpam-454	284	12	the	the	DET
ejpam-454	284	13	solution	solution	NOUN
ejpam-454	284	14	z(t	z(t	PROPN
ejpam-454	284	15	,	,	PUNCT
ejpam-454	284	16	φ̃	φ̃	PROPN
ejpam-454	284	17	)	)	PUNCT
ejpam-454	284	18	of	of	ADP
ejpam-454	284	19	system	system	NOUN
ejpam-454	284	20	(	(	PUNCT
ejpam-454	284	21	14	14	NUM
ejpam-454	284	22	)	)	PUNCT
ejpam-454	284	23	on	on	ADP
ejpam-454	284	24	[	[	X
ejpam-454	284	25	0	0	NUM
ejpam-454	284	26	,	,	PUNCT
ejpam-454	284	27	t∗(φ	t∗(φ	PROPN
ejpam-454	284	28	)	)	PUNCT
ejpam-454	284	29	)	)	PUNCT
ejpam-454	284	30	,	,	PUNCT
ejpam-454	284	31	then	then	ADV
ejpam-454	284	32	we	we	PRON
ejpam-454	284	33	can	can	AUX
ejpam-454	284	34	get	get	VERB
ejpam-454	284	35	v̇	v̇	NOUN
ejpam-454	284	36	(	(	PUNCT
ejpam-454	284	37	z(t	z(t	PROPN
ejpam-454	284	38	,	,	PUNCT
ejpam-454	284	39	φ̃	φ̃	PROPN
ejpam-454	284	40	)	)	PUNCT
ejpam-454	284	41	)	)	PUNCT
ejpam-454	285	1	=	=	SYM
ejpam-454	285	2	−2	−2	NOUN
ejpam-454	286	1	n	n	CCONJ
ejpam-454	286	2	∑	∑	PROPN
ejpam-454	286	3	i=1	i=1	PROPN
ejpam-454	286	4	di	di	PROPN
ejpam-454	286	5	fi(zi(t	fi(zi(t	PROPN
ejpam-454	286	6	,	,	PUNCT
ejpam-454	286	7	φ̃))zi(t	φ̃))zi(t	NOUN
ejpam-454	286	8	,	,	PUNCT
ejpam-454	286	9	φ̃	φ̃	PROPN
ejpam-454	286	10	)	)	PUNCT
ejpam-454	286	11	+	+	CCONJ
ejpam-454	286	12	2	2	NUM
ejpam-454	286	13	n	n	NOUN
ejpam-454	286	14	∑	∑	NOUN
ejpam-454	286	15	i=1	i=1	PROPN
ejpam-454	286	16	n	n	ADV
ejpam-454	286	17	∑	∑	PROPN
ejpam-454	286	18	j=1	j=1	PROPN
ejpam-454	286	19	ai	ai	VERB
ejpam-454	286	20	j	j	PROPN
ejpam-454	286	21	fi(zi(t	fi(zi(t	NOUN
ejpam-454	286	22	,	,	PUNCT
ejpam-454	286	23	φ̃	φ̃	PROPN
ejpam-454	286	24	)	)	PUNCT
ejpam-454	286	25	)	)	PUNCT
ejpam-454	286	26	·	·	PUNCT
ejpam-454	287	1	f	f	X
ejpam-454	287	2	j(z	j(z	PROPN
ejpam-454	287	3	j(t	j(t	PROPN
ejpam-454	287	4	,	,	PUNCT
ejpam-454	287	5	φ̃	φ̃	PROPN
ejpam-454	287	6	)	)	PUNCT
ejpam-454	287	7	)	)	PUNCT
ejpam-454	288	1	+	+	CCONJ
ejpam-454	288	2	2	2	NUM
ejpam-454	288	3	n	n	NOUN
ejpam-454	288	4	∑	∑	NOUN
ejpam-454	288	5	i=1	i=1	PROPN
ejpam-454	288	6	n	n	ADV
ejpam-454	288	7	∑	∑	ADV
ejpam-454	288	8	j=1	j=1	ADJ
ejpam-454	288	9	bi	bi	NOUN
ejpam-454	288	10	j	j	PROPN
ejpam-454	288	11	fi(zi(t	fi(zi(t	PROPN
ejpam-454	288	12	,	,	PUNCT
ejpam-454	288	13	φ̃	φ̃	PROPN
ejpam-454	288	14	)	)	PUNCT
ejpam-454	288	15	)	)	PUNCT
ejpam-454	288	16	·	·	PUNCT
ejpam-454	289	1	f	f	X
ejpam-454	290	1	j(z	j(z	PROPN
ejpam-454	290	2	j(t	j(t	PROPN
ejpam-454	290	3	−τi	−τi	PROPN
ejpam-454	290	4	j	j	PROPN
ejpam-454	290	5	,	,	PUNCT
ejpam-454	290	6	φ̃	φ̃	PROPN
ejpam-454	290	7	)	)	PUNCT
ejpam-454	290	8	)	)	PUNCT
ejpam-454	291	1	+	+	CCONJ
ejpam-454	291	2	r	r	NOUN
ejpam-454	291	3	n	n	NUM
ejpam-454	291	4	∑	∑	PUNCT
ejpam-454	291	5	i=1	i=1	PROPN
ejpam-454	291	6	n	n	PROPN
ejpam-454	291	7	∑	∑	PROPN
ejpam-454	291	8	j=1	j=1	PROPN
ejpam-454	291	9	�	�	PROPN
ejpam-454	291	10	�	�	PROPN
ejpam-454	291	11	b	b	PROPN
ejpam-454	291	12	ji	ji	PROPN
ejpam-454	291	13	�	�	PROPN
ejpam-454	291	14	�	�	PROPN
ejpam-454	291	15	f	f	PROPN
ejpam-454	291	16	2	2	NUM
ejpam-454	291	17	i	i	NOUN
ejpam-454	291	18	(	(	PUNCT
ejpam-454	291	19	zi(t	zi(t	NOUN
ejpam-454	291	20	,	,	PUNCT
ejpam-454	291	21	φ̃	φ̃	PROPN
ejpam-454	291	22	)	)	PUNCT
ejpam-454	291	23	)	)	PUNCT
ejpam-454	292	1	−	−	NOUN
ejpam-454	292	2	r	r	NOUN
ejpam-454	292	3	n	n	NUM
ejpam-454	292	4	∑	∑	PROPN
ejpam-454	292	5	i=1	i=1	PROPN
ejpam-454	292	6	n	n	PROPN
ejpam-454	292	7	∑	∑	PROPN
ejpam-454	292	8	j=1	j=1	PROPN
ejpam-454	292	9	�	�	PROPN
ejpam-454	292	10	�	�	PROPN
ejpam-454	292	11	b	b	PROPN
ejpam-454	292	12	ji	ji	PROPN
ejpam-454	292	13	�	�	PROPN
ejpam-454	292	14	�	�	PROPN
ejpam-454	292	15	f	f	PROPN
ejpam-454	292	16	2	2	NUM
ejpam-454	292	17	i	i	NOUN
ejpam-454	292	18	(	(	PUNCT
ejpam-454	292	19	zi(t	zi(t	NUM
ejpam-454	292	20	−τ	−τ	PROPN
ejpam-454	292	21	ji	ji	PROPN
ejpam-454	292	22	,	,	PUNCT
ejpam-454	292	23	φ̃	φ̃	PROPN
ejpam-454	292	24	)	)	PUNCT
ejpam-454	292	25	)	)	PUNCT
ejpam-454	292	26	≤	≤	NUM
ejpam-454	292	27	−2	−2	NOUN
ejpam-454	292	28	n	n	CCONJ
ejpam-454	292	29	∑	∑	PROPN
ejpam-454	292	30	i=1	i=1	PROPN
ejpam-454	292	31	di	di	PROPN
ejpam-454	292	32	fi(zi(t	fi(zi(t	PROPN
ejpam-454	292	33	,	,	PUNCT
ejpam-454	292	34	φ̃))zi(t	φ̃))zi(t	NOUN
ejpam-454	292	35	,	,	PUNCT
ejpam-454	292	36	φ̃	φ̃	PROPN
ejpam-454	292	37	)	)	PUNCT
ejpam-454	292	38	+	+	CCONJ
ejpam-454	292	39	2	2	NUM
ejpam-454	292	40	n	n	NOUN
ejpam-454	292	41	∑	∑	NOUN
ejpam-454	292	42	i=1	i=1	PROPN
ejpam-454	292	43	n	n	ADV
ejpam-454	292	44	∑	∑	PROPN
ejpam-454	292	45	j=1	j=1	PROPN
ejpam-454	292	46	ai	ai	VERB
ejpam-454	292	47	j	j	PROPN
ejpam-454	292	48	fi(zi(t	fi(zi(t	NOUN
ejpam-454	292	49	,	,	PUNCT
ejpam-454	292	50	φ̃	φ̃	PROPN
ejpam-454	292	51	)	)	PUNCT
ejpam-454	292	52	)	)	PUNCT
ejpam-454	292	53	·	·	PUNCT
ejpam-454	293	1	f	f	X
ejpam-454	293	2	j(z	j(z	PROPN
ejpam-454	293	3	j(t	j(t	PROPN
ejpam-454	293	4	,	,	PUNCT
ejpam-454	293	5	φ̃	φ̃	PROPN
ejpam-454	293	6	)	)	PUNCT
ejpam-454	293	7	)	)	PUNCT
ejpam-454	294	1	+	+	CCONJ
ejpam-454	294	2	2	2	NUM
ejpam-454	294	3	n	n	NOUN
ejpam-454	294	4	∑	∑	NOUN
ejpam-454	294	5	i=1	i=1	PROPN
ejpam-454	294	6	n	n	ADV
ejpam-454	294	7	∑	∑	PROPN
ejpam-454	294	8	j=1	j=1	PROPN
ejpam-454	294	9	�	�	PROPN
ejpam-454	294	10	�	�	PROPN
ejpam-454	294	11	bi	bi	PROPN
ejpam-454	294	12	j	j	PROPN
ejpam-454	294	13	�	�	PROPN
ejpam-454	294	14	�	�	PROPN
ejpam-454	294	15	�	�	PROPN
ejpam-454	294	16	�	�	PROPN
ejpam-454	294	17	fi(zi(t	fi(zi(t	PROPN
ejpam-454	294	18	,	,	PUNCT
ejpam-454	294	19	φ̃	φ̃	PROPN
ejpam-454	294	20	)	)	PUNCT
ejpam-454	294	21	)	)	PUNCT
ejpam-454	294	22	�	�	PROPN
ejpam-454	294	23	�	�	PROPN
ejpam-454	294	24	·	·	PUNCT
ejpam-454	294	25	�	�	PROPN
ejpam-454	294	26	�	�	PROPN
ejpam-454	294	27	f	f	PROPN
ejpam-454	295	1	j(z	j(z	PROPN
ejpam-454	295	2	j(t	j(t	PROPN
ejpam-454	295	3	−τi	−τi	PROPN
ejpam-454	295	4	j	j	PROPN
ejpam-454	295	5	,	,	PUNCT
ejpam-454	295	6	φ̃	φ̃	PROPN
ejpam-454	295	7	)	)	PUNCT
ejpam-454	295	8	)	)	PUNCT
ejpam-454	295	9	�	�	PROPN
ejpam-454	295	10	�	�	PROPN
ejpam-454	295	11	+	+	NOUN
ejpam-454	295	12	r	r	PROPN
ejpam-454	295	13	n	n	NUM
ejpam-454	295	14	∑	∑	PROPN
ejpam-454	295	15	i=1	i=1	PROPN
ejpam-454	295	16	n	n	PROPN
ejpam-454	295	17	∑	∑	PROPN
ejpam-454	295	18	j=1	j=1	PROPN
ejpam-454	295	19	�	�	PROPN
ejpam-454	295	20	�	�	PROPN
ejpam-454	295	21	b	b	PROPN
ejpam-454	295	22	ji	ji	PROPN
ejpam-454	295	23	�	�	PROPN
ejpam-454	295	24	�	�	PROPN
ejpam-454	295	25	f	f	PROPN
ejpam-454	295	26	2	2	NUM
ejpam-454	295	27	i	i	NOUN
ejpam-454	295	28	(	(	PUNCT
ejpam-454	295	29	zi(t	zi(t	NOUN
ejpam-454	295	30	,	,	PUNCT
ejpam-454	295	31	φ̃	φ̃	PROPN
ejpam-454	295	32	)	)	PUNCT
ejpam-454	295	33	)	)	PUNCT
ejpam-454	296	1	−	−	NOUN
ejpam-454	296	2	r	r	NOUN
ejpam-454	296	3	n	n	NUM
ejpam-454	296	4	∑	∑	PROPN
ejpam-454	296	5	i=1	i=1	PROPN
ejpam-454	296	6	n	n	PROPN
ejpam-454	296	7	∑	∑	PROPN
ejpam-454	296	8	j=1	j=1	PROPN
ejpam-454	296	9	�	�	PROPN
ejpam-454	296	10	�	�	PROPN
ejpam-454	296	11	b	b	PROPN
ejpam-454	296	12	ji	ji	PROPN
ejpam-454	296	13	�	�	PROPN
ejpam-454	296	14	�	�	PROPN
ejpam-454	296	15	f	f	PROPN
ejpam-454	296	16	2	2	NUM
ejpam-454	296	17	i	i	NOUN
ejpam-454	296	18	(	(	PUNCT
ejpam-454	296	19	zi(t	zi(t	NUM
ejpam-454	296	20	−τ	−τ	PROPN
ejpam-454	296	21	ji	ji	PROPN
ejpam-454	296	22	,	,	PUNCT
ejpam-454	296	23	φ̃	φ̃	PROPN
ejpam-454	296	24	)	)	PUNCT
ejpam-454	296	25	)	)	PUNCT
ejpam-454	296	26	.	.	PUNCT
ejpam-454	297	1	(	(	PUNCT
ejpam-454	297	2	20	20	NUM
ejpam-454	297	3	)	)	PUNCT
ejpam-454	297	4	since	since	SCONJ
ejpam-454	297	5	2	2	NUM
ejpam-454	297	6	�	�	PROPN
ejpam-454	297	7	�	�	PROPN
ejpam-454	297	8	fi(zi(t	fi(zi(t	PROPN
ejpam-454	297	9	,	,	PUNCT
ejpam-454	297	10	φ̃	φ̃	PROPN
ejpam-454	297	11	)	)	PUNCT
ejpam-454	297	12	)	)	PUNCT
ejpam-454	297	13	�	�	PROPN
ejpam-454	297	14	�	�	PROPN
ejpam-454	297	15	·	·	PUNCT
ejpam-454	297	16	�	�	PROPN
ejpam-454	297	17	�	�	PROPN
ejpam-454	297	18	f	f	PROPN
ejpam-454	298	1	j(z	j(z	PROPN
ejpam-454	298	2	j(t	j(t	PROPN
ejpam-454	298	3	−τi	−τi	PROPN
ejpam-454	298	4	j	j	PROPN
ejpam-454	298	5	,	,	PUNCT
ejpam-454	298	6	φ̃	φ̃	PROPN
ejpam-454	298	7	)	)	PUNCT
ejpam-454	298	8	)	)	PUNCT
ejpam-454	298	9	�	�	PROPN
ejpam-454	298	10	�	�	PROPN
ejpam-454	298	11	≤	≤	NUM
ejpam-454	298	12	1	1	NUM
ejpam-454	298	13	r	r	NOUN
ejpam-454	298	14	f	f	NOUN
ejpam-454	298	15	2	2	NUM
ejpam-454	298	16	i	i	NOUN
ejpam-454	298	17	(	(	PUNCT
ejpam-454	298	18	zi(t	zi(t	NUM
ejpam-454	298	19	,	,	PUNCT
ejpam-454	298	20	φ̃))+	φ̃))+	NOUN
ejpam-454	298	21	r	r	NOUN
ejpam-454	298	22	f	f	PROPN
ejpam-454	298	23	2	2	NUM
ejpam-454	298	24	j	j	PROPN
ejpam-454	298	25	(	(	PUNCT
ejpam-454	298	26	z	z	PROPN
ejpam-454	298	27	j(t	j(t	PROPN
ejpam-454	298	28	−τi	−τi	PROPN
ejpam-454	298	29	j	j	PROPN
ejpam-454	298	30	,	,	PUNCT
ejpam-454	298	31	φ̃	φ̃	PROPN
ejpam-454	298	32	)	)	PUNCT
ejpam-454	298	33	)	)	PUNCT
ejpam-454	298	34	then	then	ADV
ejpam-454	298	35	we	we	PRON
ejpam-454	298	36	get	get	VERB
ejpam-454	298	37	v̇	v̇	NOUN
ejpam-454	298	38	(	(	PUNCT
ejpam-454	298	39	z(t	z(t	PROPN
ejpam-454	298	40	,	,	PUNCT
ejpam-454	298	41	φ̃))≤	φ̃))≤	NOUN
ejpam-454	298	42	−2	−2	NOUN
ejpam-454	299	1	n	n	CCONJ
ejpam-454	299	2	∑	∑	PROPN
ejpam-454	299	3	i=1	i=1	PROPN
ejpam-454	299	4	di	di	PROPN
ejpam-454	299	5	fi(zi(t	fi(zi(t	PROPN
ejpam-454	299	6	,	,	PUNCT
ejpam-454	299	7	φ̃))zi(t	φ̃))zi(t	NOUN
ejpam-454	299	8	,	,	PUNCT
ejpam-454	299	9	φ̃	φ̃	PROPN
ejpam-454	299	10	)	)	PUNCT
ejpam-454	299	11	+	+	CCONJ
ejpam-454	299	12	2	2	NUM
ejpam-454	299	13	n	n	NOUN
ejpam-454	299	14	∑	∑	NOUN
ejpam-454	299	15	i=1	i=1	PROPN
ejpam-454	299	16	n	n	ADV
ejpam-454	299	17	∑	∑	PROPN
ejpam-454	299	18	j=1	j=1	PROPN
ejpam-454	299	19	ai	ai	VERB
ejpam-454	299	20	j	j	PROPN
ejpam-454	299	21	fi(zi(t	fi(zi(t	NOUN
ejpam-454	299	22	,	,	PUNCT
ejpam-454	299	23	φ̃	φ̃	PROPN
ejpam-454	299	24	)	)	PUNCT
ejpam-454	299	25	)	)	PUNCT
ejpam-454	299	26	·	·	PUNCT
ejpam-454	300	1	f	f	X
ejpam-454	300	2	j(z	j(z	PROPN
ejpam-454	300	3	j(t	j(t	PROPN
ejpam-454	300	4	,	,	PUNCT
ejpam-454	300	5	φ̃	φ̃	PROPN
ejpam-454	300	6	)	)	PUNCT
ejpam-454	300	7	)	)	PUNCT
ejpam-454	301	1	+	+	CCONJ
ejpam-454	301	2	n	n	CCONJ
ejpam-454	301	3	∑	∑	ADP
ejpam-454	301	4	i=1	i=1	PROPN
ejpam-454	301	5	n	n	ADV
ejpam-454	301	6	∑	∑	ADV
ejpam-454	301	7	j=1	j=1	NOUN
ejpam-454	301	8	1	1	NUM
ejpam-454	301	9	r	r	NOUN
ejpam-454	301	10	�	�	PROPN
ejpam-454	301	11	�	�	PROPN
ejpam-454	301	12	bi	bi	PROPN
ejpam-454	301	13	j	j	PROPN
ejpam-454	301	14	�	�	PROPN
ejpam-454	301	15	�	�	PROPN
ejpam-454	301	16	f	f	PROPN
ejpam-454	301	17	2	2	NUM
ejpam-454	301	18	i	i	NOUN
ejpam-454	301	19	(	(	PUNCT
ejpam-454	301	20	zi(t	zi(t	NOUN
ejpam-454	301	21	,	,	PUNCT
ejpam-454	301	22	φ̃	φ̃	PROPN
ejpam-454	301	23	)	)	PUNCT
ejpam-454	301	24	)	)	PUNCT
ejpam-454	302	1	+	+	CCONJ
ejpam-454	302	2	n	n	CCONJ
ejpam-454	302	3	∑	∑	ADP
ejpam-454	302	4	i=1	i=1	PROPN
ejpam-454	302	5	n	n	ADV
ejpam-454	302	6	∑	∑	ADV
ejpam-454	302	7	j=1	j=1	PROPN
ejpam-454	302	8	r	r	PROPN
ejpam-454	302	9	�	�	PROPN
ejpam-454	302	10	�	�	PROPN
ejpam-454	302	11	bi	bi	PROPN
ejpam-454	302	12	j	j	PROPN
ejpam-454	302	13	�	�	PROPN
ejpam-454	302	14	�	�	PROPN
ejpam-454	302	15	f	f	PROPN
ejpam-454	302	16	2	2	NUM
ejpam-454	302	17	j	j	PROPN
ejpam-454	302	18	(	(	PUNCT
ejpam-454	302	19	z	z	PROPN
ejpam-454	302	20	j(t	j(t	PROPN
ejpam-454	302	21	−τi	−τi	PROPN
ejpam-454	302	22	j	j	PROPN
ejpam-454	302	23	,	,	PUNCT
ejpam-454	302	24	φ̃	φ̃	PROPN
ejpam-454	302	25	)	)	PUNCT
ejpam-454	302	26	)	)	PUNCT
ejpam-454	303	1	+	+	CCONJ
ejpam-454	303	2	r	r	NOUN
ejpam-454	303	3	n	n	NUM
ejpam-454	303	4	∑	∑	PUNCT
ejpam-454	303	5	i=1	i=1	PROPN
ejpam-454	303	6	n	n	PROPN
ejpam-454	303	7	∑	∑	PROPN
ejpam-454	303	8	j=1	j=1	PROPN
ejpam-454	303	9	�	�	PROPN
ejpam-454	303	10	�	�	PROPN
ejpam-454	303	11	b	b	PROPN
ejpam-454	303	12	ji	ji	PROPN
ejpam-454	303	13	�	�	PROPN
ejpam-454	303	14	�	�	PROPN
ejpam-454	303	15	f	f	PROPN
ejpam-454	303	16	2	2	NUM
ejpam-454	303	17	i	i	NOUN
ejpam-454	303	18	(	(	PUNCT
ejpam-454	303	19	zi(t	zi(t	NUM
ejpam-454	303	20	,	,	PUNCT
ejpam-454	303	21	φ̃))−	φ̃))−	NUM
ejpam-454	303	22	r	r	NOUN
ejpam-454	303	23	n	n	NUM
ejpam-454	303	24	∑	∑	PROPN
ejpam-454	303	25	i=1	i=1	PROPN
ejpam-454	303	26	n	n	PROPN
ejpam-454	303	27	∑	∑	PROPN
ejpam-454	303	28	j=1	j=1	PROPN
ejpam-454	303	29	�	�	PROPN
ejpam-454	303	30	�	�	PROPN
ejpam-454	303	31	b	b	PROPN
ejpam-454	303	32	ji	ji	PROPN
ejpam-454	303	33	�	�	PROPN
ejpam-454	303	34	�	�	PROPN
ejpam-454	303	35	f	f	PROPN
ejpam-454	303	36	2	2	NUM
ejpam-454	303	37	i	i	NOUN
ejpam-454	303	38	(	(	PUNCT
ejpam-454	303	39	zi(t	zi(t	NUM
ejpam-454	303	40	−τ	−τ	PROPN
ejpam-454	303	41	ji	ji	PROPN
ejpam-454	303	42	,	,	PUNCT
ejpam-454	303	43	φ̃	φ̃	PROPN
ejpam-454	303	44	)	)	PUNCT
ejpam-454	303	45	)	)	PUNCT
ejpam-454	304	1	=	=	SYM
ejpam-454	304	2	−2	−2	NOUN
ejpam-454	305	1	n	n	CCONJ
ejpam-454	305	2	∑	∑	PROPN
ejpam-454	305	3	i=1	i=1	PROPN
ejpam-454	305	4	di	di	PROPN
ejpam-454	305	5	fi(zi(t	fi(zi(t	PROPN
ejpam-454	305	6	,	,	PUNCT
ejpam-454	305	7	φ̃))zi(t	φ̃))zi(t	NOUN
ejpam-454	305	8	,	,	PUNCT
ejpam-454	305	9	φ̃	φ̃	PROPN
ejpam-454	305	10	)	)	PUNCT
ejpam-454	305	11	+	+	CCONJ
ejpam-454	305	12	2	2	NUM
ejpam-454	305	13	n	n	NOUN
ejpam-454	305	14	∑	∑	NOUN
ejpam-454	305	15	i=1	i=1	PROPN
ejpam-454	305	16	n	n	ADV
ejpam-454	305	17	∑	∑	PROPN
ejpam-454	305	18	j=1	j=1	PROPN
ejpam-454	305	19	ai	ai	VERB
ejpam-454	305	20	j	j	PROPN
ejpam-454	305	21	fi(zi(t	fi(zi(t	NOUN
ejpam-454	305	22	,	,	PUNCT
ejpam-454	305	23	φ̃	φ̃	PROPN
ejpam-454	305	24	)	)	PUNCT
ejpam-454	305	25	)	)	PUNCT
ejpam-454	305	26	·	·	PUNCT
ejpam-454	306	1	f	f	X
ejpam-454	306	2	j(z	j(z	PROPN
ejpam-454	306	3	j(t	j(t	PROPN
ejpam-454	306	4	,	,	PUNCT
ejpam-454	306	5	φ̃	φ̃	PROPN
ejpam-454	306	6	)	)	PUNCT
ejpam-454	306	7	)	)	PUNCT
ejpam-454	306	8	a.	a.	PROPN
ejpam-454	306	9	wu	wu	PROPN
ejpam-454	306	10	,	,	PUNCT
ejpam-454	306	11	j.	j.	PROPN
ejpam-454	306	12	zhang	zhang	PROPN
ejpam-454	306	13	,	,	PUNCT
ejpam-454	306	14	c.	c.	PROPN
ejpam-454	306	15	fu	fu	PROPN
ejpam-454	306	16	/	/	SYM
ejpam-454	306	17	eur	eur	PROPN
ejpam-454	306	18	.	.	PUNCT
ejpam-454	307	1	j.	j.	PROPN
ejpam-454	307	2	pure	pure	PROPN
ejpam-454	307	3	appl	appl	PROPN
ejpam-454	307	4	.	.	PROPN
ejpam-454	307	5	math	math	PROPN
ejpam-454	307	6	,	,	PUNCT
ejpam-454	307	7	3	3	NUM
ejpam-454	307	8	(	(	PUNCT
ejpam-454	307	9	2010	2010	NUM
ejpam-454	307	10	)	)	PUNCT
ejpam-454	307	11	,	,	PUNCT
ejpam-454	307	12	806	806	NUM
ejpam-454	307	13	-	-	SYM
ejpam-454	307	14	818	818	NUM
ejpam-454	307	15	816	816	NUM
ejpam-454	307	16	+	+	CCONJ
ejpam-454	307	17	n	n	CCONJ
ejpam-454	307	18	∑	∑	ADP
ejpam-454	307	19	i=1	i=1	PROPN
ejpam-454	307	20	n	n	ADV
ejpam-454	307	21	∑	∑	ADV
ejpam-454	307	22	j=1	j=1	NOUN
ejpam-454	307	23	1	1	NUM
ejpam-454	307	24	r	r	NOUN
ejpam-454	307	25	�	�	PROPN
ejpam-454	307	26	�	�	PROPN
ejpam-454	307	27	bi	bi	PROPN
ejpam-454	307	28	j	j	PROPN
ejpam-454	307	29	�	�	PROPN
ejpam-454	307	30	�	�	PROPN
ejpam-454	307	31	f	f	PROPN
ejpam-454	307	32	2	2	NUM
ejpam-454	307	33	i	i	NOUN
ejpam-454	307	34	(	(	PUNCT
ejpam-454	307	35	zi(t	zi(t	NOUN
ejpam-454	307	36	,	,	PUNCT
ejpam-454	307	37	φ̃	φ̃	PROPN
ejpam-454	307	38	)	)	PUNCT
ejpam-454	307	39	)	)	PUNCT
ejpam-454	308	1	+	+	CCONJ
ejpam-454	308	2	r	r	NOUN
ejpam-454	308	3	n	n	NUM
ejpam-454	308	4	∑	∑	PUNCT
ejpam-454	308	5	i=1	i=1	PROPN
ejpam-454	308	6	n	n	PROPN
ejpam-454	308	7	∑	∑	PROPN
ejpam-454	308	8	j=1	j=1	PROPN
ejpam-454	308	9	�	�	PROPN
ejpam-454	308	10	�	�	PROPN
ejpam-454	308	11	b	b	PROPN
ejpam-454	308	12	ji	ji	PROPN
ejpam-454	308	13	�	�	PROPN
ejpam-454	308	14	�	�	PROPN
ejpam-454	308	15	f	f	PROPN
ejpam-454	308	16	2	2	NUM
ejpam-454	308	17	i	i	NOUN
ejpam-454	308	18	(	(	PUNCT
ejpam-454	308	19	zi(t	zi(t	NOUN
ejpam-454	308	20	,	,	PUNCT
ejpam-454	308	21	φ̃	φ̃	PROPN
ejpam-454	308	22	)	)	PUNCT
ejpam-454	308	23	)	)	PUNCT
ejpam-454	308	24	≤	≤	NUM
ejpam-454	308	25	−2	−2	NOUN
ejpam-454	308	26	n	n	CCONJ
ejpam-454	308	27	∑	∑	PROPN
ejpam-454	308	28	i=1	i=1	PROPN
ejpam-454	308	29	di	di	PROPN
ejpam-454	308	30	fi(zi(t	fi(zi(t	PROPN
ejpam-454	308	31	,	,	PUNCT
ejpam-454	308	32	φ̃))zi(t	φ̃))zi(t	NOUN
ejpam-454	308	33	,	,	PUNCT
ejpam-454	308	34	φ̃	φ̃	PROPN
ejpam-454	308	35	)	)	PUNCT
ejpam-454	309	1	+	+	NUM
ejpam-454	309	2	f	f	PROPN
ejpam-454	309	3	t	t	PROPN
ejpam-454	309	4	(	(	PUNCT
ejpam-454	309	5	z(t	z(t	PROPN
ejpam-454	309	6	,	,	PUNCT
ejpam-454	309	7	φ̃	φ̃	PROPN
ejpam-454	309	8	)	)	PUNCT
ejpam-454	309	9	)	)	PUNCT
ejpam-454	309	10	·	·	PUNCT
ejpam-454	309	11	(	(	PUNCT
ejpam-454	309	12	a+at	a+at	NOUN
ejpam-454	309	13	)	)	PUNCT
ejpam-454	309	14	·	·	PUNCT
ejpam-454	310	1	f	f	X
ejpam-454	310	2	(	(	PUNCT
ejpam-454	310	3	z(t	z(t	PROPN
ejpam-454	310	4	,	,	PUNCT
ejpam-454	310	5	φ̃	φ̃	PROPN
ejpam-454	310	6	)	)	PUNCT
ejpam-454	310	7	)	)	PUNCT
ejpam-454	311	1	+	+	CCONJ
ejpam-454	311	2	1	1	NUM
ejpam-454	311	3	r	r	NOUN
ejpam-454	311	4	‖b‖∞	‖b‖∞	PROPN
ejpam-454	311	5	f	f	PROPN
ejpam-454	311	6	t	t	PROPN
ejpam-454	311	7	(	(	PUNCT
ejpam-454	311	8	z(t	z(t	PROPN
ejpam-454	311	9	,	,	PUNCT
ejpam-454	311	10	φ̃	φ̃	PROPN
ejpam-454	311	11	)	)	PUNCT
ejpam-454	311	12	)	)	PUNCT
ejpam-454	311	13	f	f	PROPN
ejpam-454	311	14	(	(	PUNCT
ejpam-454	311	15	z(t	z(t	PROPN
ejpam-454	311	16	,	,	PUNCT
ejpam-454	311	17	φ̃	φ̃	PROPN
ejpam-454	311	18	)	)	PUNCT
ejpam-454	311	19	)	)	PUNCT
ejpam-454	312	1	+	+	CCONJ
ejpam-454	312	2	r‖b‖1	r‖b‖1	PROPN
ejpam-454	312	3	f	f	PROPN
ejpam-454	312	4	t	t	PROPN
ejpam-454	312	5	(	(	PUNCT
ejpam-454	312	6	z(t	z(t	PROPN
ejpam-454	312	7	,	,	PUNCT
ejpam-454	312	8	φ̃	φ̃	PROPN
ejpam-454	312	9	)	)	PUNCT
ejpam-454	312	10	)	)	PUNCT
ejpam-454	312	11	f	f	PROPN
ejpam-454	312	12	(	(	PUNCT
ejpam-454	312	13	z(t	z(t	PROPN
ejpam-454	312	14	,	,	PUNCT
ejpam-454	312	15	φ̃	φ̃	PROPN
ejpam-454	312	16	)	)	PUNCT
ejpam-454	312	17	)	)	PUNCT
ejpam-454	313	1	=	=	SYM
ejpam-454	313	2	−2	−2	NOUN
ejpam-454	314	1	n	n	CCONJ
ejpam-454	314	2	∑	∑	PROPN
ejpam-454	314	3	i=1	i=1	PROPN
ejpam-454	314	4	di	di	PROPN
ejpam-454	314	5	fi(zi(t	fi(zi(t	PROPN
ejpam-454	314	6	,	,	PUNCT
ejpam-454	314	7	φ̃))zi(t	φ̃))zi(t	NOUN
ejpam-454	314	8	,	,	PUNCT
ejpam-454	314	9	φ̃	φ̃	PROPN
ejpam-454	314	10	)	)	PUNCT
ejpam-454	315	1	+	+	NUM
ejpam-454	315	2	f	f	PROPN
ejpam-454	315	3	t	t	PROPN
ejpam-454	315	4	(	(	PUNCT
ejpam-454	315	5	z(t	z(t	PROPN
ejpam-454	315	6	,	,	PUNCT
ejpam-454	315	7	φ̃	φ̃	PROPN
ejpam-454	315	8	)	)	PUNCT
ejpam-454	315	9	)	)	PUNCT
ejpam-454	315	10	·	·	PUNCT
ejpam-454	316	1	[	[	X
ejpam-454	316	2	a+	a+	PUNCT
ejpam-454	316	3	at	at	ADP
ejpam-454	316	4	+	+	CCONJ
ejpam-454	316	5	(	(	PUNCT
ejpam-454	316	6	1	1	NUM
ejpam-454	316	7	r	r	NOUN
ejpam-454	316	8	‖b‖∞	‖b‖∞	PROPN
ejpam-454	316	9	+	+	CCONJ
ejpam-454	316	10	r‖b‖1)i	r‖b‖1)i	X
ejpam-454	316	11	]	]	X
ejpam-454	316	12	·	·	PUNCT
ejpam-454	316	13	f	f	X
ejpam-454	316	14	(	(	PUNCT
ejpam-454	316	15	z(t	z(t	PROPN
ejpam-454	316	16	,	,	PUNCT
ejpam-454	316	17	φ̃	φ̃	PROPN
ejpam-454	316	18	)	)	PUNCT
ejpam-454	316	19	)	)	PUNCT
ejpam-454	316	20	≤	≤	NUM
ejpam-454	316	21	−2	−2	NOUN
ejpam-454	316	22	n	n	CCONJ
ejpam-454	316	23	∑	∑	PROPN
ejpam-454	316	24	i=1	i=1	PROPN
ejpam-454	316	25	di	di	PROPN
ejpam-454	316	26	fi(zi(t	fi(zi(t	PROPN
ejpam-454	316	27	,	,	PUNCT
ejpam-454	316	28	φ̃))zi(t	φ̃))zi(t	NOUN
ejpam-454	316	29	,	,	PUNCT
ejpam-454	316	30	φ̃)≤	φ̃)≤	VERB
ejpam-454	316	31	0	0	X
ejpam-454	316	32	.	.	PUNCT
ejpam-454	317	1	the	the	DET
ejpam-454	317	2	rest	rest	NOUN
ejpam-454	317	3	of	of	ADP
ejpam-454	317	4	step	step	NOUN
ejpam-454	317	5	b	b	NOUN
ejpam-454	317	6	and	and	CCONJ
ejpam-454	317	7	step	step	NOUN
ejpam-454	317	8	c	c	NOUN
ejpam-454	317	9	are	be	AUX
ejpam-454	317	10	similar	similar	ADJ
ejpam-454	317	11	as	as	ADP
ejpam-454	317	12	step	step	NOUN
ejpam-454	317	13	2	2	NUM
ejpam-454	317	14	and	and	CCONJ
ejpam-454	317	15	step	step	NOUN
ejpam-454	317	16	3	3	NUM
ejpam-454	317	17	of	of	ADP
ejpam-454	317	18	theorem	theorem	ADJ
ejpam-454	317	19	4	4	NUM
ejpam-454	317	20	,	,	PUNCT
ejpam-454	317	21	respectively	respectively	ADV
ejpam-454	317	22	,	,	PUNCT
ejpam-454	317	23	so	so	SCONJ
ejpam-454	317	24	we	we	PRON
ejpam-454	317	25	also	also	ADV
ejpam-454	317	26	do	do	AUX
ejpam-454	317	27	not	not	PART
ejpam-454	317	28	repeat	repeat	VERB
ejpam-454	317	29	them	they	PRON
ejpam-454	317	30	,	,	PUNCT
ejpam-454	317	31	then	then	ADV
ejpam-454	317	32	we	we	PRON
ejpam-454	317	33	can	can	AUX
ejpam-454	317	34	easily	easily	ADV
ejpam-454	317	35	obtain	obtain	VERB
ejpam-454	317	36	the	the	DET
ejpam-454	317	37	existence	existence	NOUN
ejpam-454	317	38	of	of	ADP
ejpam-454	317	39	solutions	solution	NOUN
ejpam-454	317	40	of	of	ADP
ejpam-454	317	41	system	system	NOUN
ejpam-454	317	42	(	(	PUNCT
ejpam-454	317	43	1	1	NUM
ejpam-454	317	44	)	)	PUNCT
ejpam-454	317	45	.	.	PUNCT
ejpam-454	318	1	step	step	NOUN
ejpam-454	318	2	d.	d.	PROPN
ejpam-454	318	3	consider	consider	VERB
ejpam-454	318	4	lyapunov	lyapunov	PROPN
ejpam-454	318	5	functional	functional	ADJ
ejpam-454	318	6	v	v	NOUN
ejpam-454	318	7	(	(	PUNCT
ejpam-454	318	8	z(t	z(t	NOUN
ejpam-454	318	9	)	)	PUNCT
ejpam-454	318	10	)	)	PUNCT
ejpam-454	318	11	,	,	PUNCT
ejpam-454	318	12	the	the	DET
ejpam-454	318	13	v	v	NOUN
ejpam-454	318	14	(	(	PUNCT
ejpam-454	318	15	z(t	z(t	PROPN
ejpam-454	318	16	)	)	PUNCT
ejpam-454	318	17	)	)	PUNCT
ejpam-454	318	18	is	be	AUX
ejpam-454	318	19	the	the	DET
ejpam-454	318	20	same	same	ADJ
ejpam-454	318	21	as	as	ADP
ejpam-454	318	22	(	(	PUNCT
ejpam-454	318	23	19	19	NUM
ejpam-454	318	24	)	)	PUNCT
ejpam-454	318	25	.	.	PUNCT
ejpam-454	319	1	calculating	calculate	VERB
ejpam-454	319	2	the	the	DET
ejpam-454	319	3	derivative	derivative	NOUN
ejpam-454	319	4	of	of	ADP
ejpam-454	319	5	v	v	NOUN
ejpam-454	319	6	(	(	PUNCT
ejpam-454	319	7	z(t	z(t	PROPN
ejpam-454	319	8	)	)	PUNCT
ejpam-454	319	9	)	)	PUNCT
ejpam-454	319	10	along	along	ADP
ejpam-454	319	11	the	the	DET
ejpam-454	319	12	solution	solution	NOUN
ejpam-454	319	13	z(t	z(t	NOUN
ejpam-454	319	14	)	)	PUNCT
ejpam-454	319	15	of	of	ADP
ejpam-454	319	16	system	system	NOUN
ejpam-454	319	17	(	(	PUNCT
ejpam-454	319	18	3.6	3.6	NUM
ejpam-454	319	19	)	)	PUNCT
ejpam-454	319	20	for	for	ADP
ejpam-454	319	21	any	any	DET
ejpam-454	319	22	t	t	PROPN
ejpam-454	319	23	,	,	PUNCT
ejpam-454	319	24	t	t	PROPN
ejpam-454	319	25	6=	6=	PROPN
ejpam-454	319	26	tk	tk	PROPN
ejpam-454	319	27	,	,	PUNCT
ejpam-454	319	28	k	k	PROPN
ejpam-454	319	29	=	=	SYM
ejpam-454	319	30	1,2	1,2	NUM
ejpam-454	319	31	,	,	PUNCT
ejpam-454	319	32	·	·	PUNCT
ejpam-454	319	33	·	·	PUNCT
ejpam-454	319	34	·	·	PUNCT
ejpam-454	319	35	.	.	PUNCT
ejpam-454	320	1	arguing	argue	VERB
ejpam-454	320	2	as	as	ADP
ejpam-454	320	3	in	in	ADP
ejpam-454	320	4	step	step	NOUN
ejpam-454	320	5	b	b	NOUN
ejpam-454	320	6	,	,	PUNCT
ejpam-454	320	7	we	we	PRON
ejpam-454	320	8	have	have	VERB
ejpam-454	320	9	v̇	v̇	NOUN
ejpam-454	320	10	(	(	PUNCT
ejpam-454	320	11	z(t	z(t	PROPN
ejpam-454	320	12	)	)	PUNCT
ejpam-454	320	13	)	)	PUNCT
ejpam-454	321	1	≤	≤	ADV
ejpam-454	321	2	0	0	NUM
ejpam-454	321	3	,	,	PUNCT
ejpam-454	321	4	t	t	PROPN
ejpam-454	321	5	6=	6=	PROPN
ejpam-454	321	6	tk	tk	PROPN
ejpam-454	321	7	,	,	PUNCT
ejpam-454	321	8	k	k	PROPN
ejpam-454	321	9	=	=	SYM
ejpam-454	321	10	1,2	1,2	NUM
ejpam-454	321	11	,	,	PUNCT
ejpam-454	321	12	·	·	PUNCT
ejpam-454	321	13	·	·	PUNCT
ejpam-454	321	14	·	·	PUNCT
ejpam-454	321	15	.	.	PUNCT
ejpam-454	322	1	also	also	ADV
ejpam-454	322	2	,	,	PUNCT
ejpam-454	322	3	v	v	X
ejpam-454	322	4	(	(	PUNCT
ejpam-454	322	5	z(tk	z(tk	PROPN
ejpam-454	322	6	+	+	CCONJ
ejpam-454	322	7	0	0	NUM
ejpam-454	322	8	)	)	PUNCT
ejpam-454	322	9	)	)	PUNCT
ejpam-454	323	1	=	=	SYM
ejpam-454	323	2	2	2	NUM
ejpam-454	323	3	n	n	NUM
ejpam-454	323	4	∑	∑	PROPN
ejpam-454	323	5	i=1	i=1	PROPN
ejpam-454	323	6	∫	∫	PROPN
ejpam-454	323	7	zi(tk+0	zi(tk+0	PROPN
ejpam-454	323	8	)	)	PUNCT
ejpam-454	323	9	0	0	NUM
ejpam-454	324	1	fi(s)ds+	fi(s)ds+	NOUN
ejpam-454	324	2	r	r	NOUN
ejpam-454	324	3	n	n	NOUN
ejpam-454	324	4	∑	∑	PROPN
ejpam-454	324	5	i=1	i=1	PROPN
ejpam-454	324	6	n	n	ADV
ejpam-454	324	7	∑	∑	ADV
ejpam-454	324	8	j=1	j=1	PROPN
ejpam-454	324	9	∫	∫	PROPN
ejpam-454	324	10	(	(	PUNCT
ejpam-454	324	11	tk+0	tk+0	PROPN
ejpam-454	324	12	)	)	PUNCT
ejpam-454	324	13	(	(	PUNCT
ejpam-454	324	14	tk+0)−τ	tk+0)−τ	NOUN
ejpam-454	324	15	j	j	X
ejpam-454	325	1	i	i	PROPN
ejpam-454	325	2	�	�	PROPN
ejpam-454	325	3	�	�	PROPN
ejpam-454	325	4	b	b	PROPN
ejpam-454	325	5	ji	ji	PROPN
ejpam-454	325	6	�	�	PROPN
ejpam-454	325	7	�	�	PROPN
ejpam-454	325	8	·	·	PUNCT
ejpam-454	325	9	f	f	PROPN
ejpam-454	325	10	2	2	NUM
ejpam-454	325	11	i	i	NOUN
ejpam-454	325	12	(	(	PUNCT
ejpam-454	325	13	zi(θ))dθ	zi(θ))dθ	NOUN
ejpam-454	325	14	=	=	SYM
ejpam-454	325	15	v	v	PROPN
ejpam-454	325	16	(	(	PUNCT
ejpam-454	325	17	z(tk))+	z(tk))+	NOUN
ejpam-454	325	18	2	2	NUM
ejpam-454	325	19	n	n	NOUN
ejpam-454	325	20	∑	∑	PROPN
ejpam-454	325	21	i=1	i=1	PROPN
ejpam-454	325	22	∫	∫	PROPN
ejpam-454	325	23	(	(	PUNCT
ejpam-454	325	24	1−γik)zi(tk	1−γik)zi(tk	NUM
ejpam-454	325	25	)	)	PUNCT
ejpam-454	325	26	zi(tk	zi(tk	PROPN
ejpam-454	325	27	)	)	PUNCT
ejpam-454	325	28	fi(s)ds	fi(s)d	VERB
ejpam-454	325	29	≤	≤	NUM
ejpam-454	325	30	v	v	NOUN
ejpam-454	325	31	(	(	PUNCT
ejpam-454	325	32	z(tk	z(tk	PROPN
ejpam-454	325	33	)	)	PUNCT
ejpam-454	325	34	)	)	PUNCT
ejpam-454	325	35	,	,	PUNCT
ejpam-454	325	36	k	k	X
ejpam-454	325	37	=	=	SYM
ejpam-454	325	38	1,2	1,2	NUM
ejpam-454	325	39	,	,	PUNCT
ejpam-454	325	40	·	·	PUNCT
ejpam-454	325	41	·	·	PUNCT
ejpam-454	325	42	·	·	PUNCT
ejpam-454	325	43	.	.	PUNCT
ejpam-454	326	1	then	then	ADV
ejpam-454	326	2	we	we	PRON
ejpam-454	326	3	can	can	AUX
ejpam-454	326	4	easily	easily	ADV
ejpam-454	326	5	follow	follow	VERB
ejpam-454	326	6	that	that	DET
ejpam-454	326	7	v̇	v̇	NOUN
ejpam-454	326	8	(	(	PUNCT
ejpam-454	326	9	z(t	z(t	PROPN
ejpam-454	326	10	)	)	PUNCT
ejpam-454	326	11	)	)	PUNCT
ejpam-454	326	12	≤	≤	NUM
ejpam-454	326	13	0	0	NUM
ejpam-454	326	14	for	for	ADP
ejpam-454	326	15	t	t	PROPN
ejpam-454	326	16	>	>	X
ejpam-454	326	17	0	0	PROPN
ejpam-454	326	18	.	.	PUNCT
ejpam-454	327	1	therefore	therefore	ADV
ejpam-454	327	2	,	,	PUNCT
ejpam-454	327	3	the	the	DET
ejpam-454	327	4	equilibrium	equilibrium	NOUN
ejpam-454	327	5	point	point	NOUN
ejpam-454	327	6	x∗	x∗	PROPN
ejpam-454	327	7	of	of	ADP
ejpam-454	327	8	system	system	NOUN
ejpam-454	327	9	(	(	PUNCT
ejpam-454	327	10	1	1	X
ejpam-454	327	11	)	)	PUNCT
ejpam-454	327	12	is	be	AUX
ejpam-454	327	13	stable	stable	ADJ
ejpam-454	327	14	and	and	CCONJ
ejpam-454	327	15	every	every	DET
ejpam-454	327	16	solution	solution	NOUN
ejpam-454	327	17	is	be	AUX
ejpam-454	327	18	bounded	bound	VERB
ejpam-454	327	19	.	.	PUNCT
ejpam-454	328	1	if	if	SCONJ
ejpam-454	328	2	,	,	PUNCT
ejpam-454	328	3	in	in	ADP
ejpam-454	328	4	addition	addition	NOUN
ejpam-454	328	5	,	,	PUNCT
ejpam-454	328	6	gi(s	gi(s	NOUN
ejpam-454	328	7	)	)	PUNCT
ejpam-454	328	8	,	,	PUNCT
ejpam-454	328	9	i	i	PRON
ejpam-454	328	10	=	=	NOUN
ejpam-454	328	11	1	1	NUM
ejpam-454	328	12	,	,	PUNCT
ejpam-454	328	13	·	·	PUNCT
ejpam-454	328	14	·	·	PUNCT
ejpam-454	328	15	·	·	PUNCT
ejpam-454	328	16	,	,	PUNCT
ejpam-454	328	17	n	n	CCONJ
ejpam-454	328	18	,	,	PUNCT
ejpam-454	328	19	are	be	AUX
ejpam-454	328	20	strictly	strictly	ADV
ejpam-454	328	21	increasing	increase	VERB
ejpam-454	328	22	functions	function	NOUN
ejpam-454	328	23	,	,	PUNCT
ejpam-454	328	24	then	then	ADV
ejpam-454	328	25	v̇	v̇	PROPN
ejpam-454	328	26	(	(	PUNCT
ejpam-454	328	27	z(t	z(t	PROPN
ejpam-454	328	28	)	)	PUNCT
ejpam-454	328	29	)	)	PUNCT
ejpam-454	329	1	<	<	X
ejpam-454	329	2	0	0	PUNCT
ejpam-454	329	3	is	be	AUX
ejpam-454	329	4	negative	negative	ADJ
ejpam-454	329	5	definite	definite	ADJ
ejpam-454	329	6	.	.	PUNCT
ejpam-454	330	1	thus	thus	ADV
ejpam-454	330	2	,	,	PUNCT
ejpam-454	330	3	the	the	DET
ejpam-454	330	4	unique	unique	ADJ
ejpam-454	330	5	equilibrium	equilibrium	NOUN
ejpam-454	330	6	point	point	NOUN
ejpam-454	330	7	of	of	ADP
ejpam-454	330	8	system	system	NOUN
ejpam-454	330	9	(	(	PUNCT
ejpam-454	330	10	1	1	X
ejpam-454	330	11	)	)	PUNCT
ejpam-454	330	12	is	be	AUX
ejpam-454	330	13	globally	globally	ADV
ejpam-454	330	14	asymptotically	asymptotically	ADV
ejpam-454	330	15	stable	stable	ADJ
ejpam-454	330	16	.	.	PUNCT
ejpam-454	331	1	remark	remark	PROPN
ejpam-454	331	2	1	1	NUM
ejpam-454	331	3	.	.	PUNCT
ejpam-454	332	1	compared	compare	VERB
ejpam-454	332	2	to	to	ADP
ejpam-454	332	3	the	the	DET
ejpam-454	332	4	existing	exist	VERB
ejpam-454	332	5	literatures	literature	NOUN
ejpam-454	332	6	,	,	PUNCT
ejpam-454	332	7	our	our	PRON
ejpam-454	332	8	results	result	NOUN
ejpam-454	332	9	have	have	AUX
ejpam-454	332	10	improved	improve	VERB
ejpam-454	332	11	those	those	DET
ejpam-454	332	12	results	result	NOUN
ejpam-454	332	13	.	.	PUNCT
ejpam-454	333	1	the	the	DET
ejpam-454	333	2	results	result	NOUN
ejpam-454	333	3	of	of	ADP
ejpam-454	333	4	[	[	X
ejpam-454	333	5	5	5	NUM
ejpam-454	333	6	,	,	PUNCT
ejpam-454	333	7	6	6	NUM
ejpam-454	333	8	,	,	PUNCT
ejpam-454	333	9	9	9	NUM
ejpam-454	333	10	,	,	PUNCT
ejpam-454	333	11	10	10	NUM
ejpam-454	333	12	]	]	PUNCT
ejpam-454	333	13	are	be	AUX
ejpam-454	333	14	obtained	obtain	VERB
ejpam-454	333	15	under	under	ADP
ejpam-454	333	16	lipschitz	lipschitz	NOUN
ejpam-454	333	17	neuron	neuron	NOUN
ejpam-454	333	18	activations	activation	NOUN
ejpam-454	333	19	.	.	PUNCT
ejpam-454	334	1	at	at	ADP
ejpam-454	334	2	the	the	DET
ejpam-454	334	3	same	same	ADJ
ejpam-454	334	4	time	time	NOUN
ejpam-454	334	5	,	,	PUNCT
ejpam-454	334	6	our	our	PRON
ejpam-454	334	7	results	result	NOUN
ejpam-454	334	8	are	be	AUX
ejpam-454	334	9	easy	easy	ADJ
ejpam-454	334	10	to	to	PART
ejpam-454	334	11	be	be	AUX
ejpam-454	334	12	checked	check	VERB
ejpam-454	334	13	.	.	PUNCT
ejpam-454	335	1	in	in	ADP
ejpam-454	335	2	order	order	NOUN
ejpam-454	335	3	to	to	PART
ejpam-454	335	4	show	show	VERB
ejpam-454	335	5	that	that	SCONJ
ejpam-454	335	6	the	the	DET
ejpam-454	335	7	conditions	condition	NOUN
ejpam-454	335	8	we	we	PRON
ejpam-454	335	9	have	have	AUX
ejpam-454	335	10	obtained	obtain	VERB
ejpam-454	335	11	in	in	ADP
ejpam-454	335	12	this	this	DET
ejpam-454	335	13	paper	paper	NOUN
ejpam-454	335	14	provide	provide	VERB
ejpam-454	335	15	new	new	ADJ
ejpam-454	335	16	sufficient	sufficient	ADJ
ejpam-454	335	17	criteria	criterion	NOUN
ejpam-454	335	18	for	for	ADP
ejpam-454	335	19	system	system	NOUN
ejpam-454	335	20	(	(	PUNCT
ejpam-454	335	21	1	1	NUM
ejpam-454	335	22	)	)	PUNCT
ejpam-454	335	23	,	,	PUNCT
ejpam-454	335	24	we	we	PRON
ejpam-454	335	25	consider	consider	VERB
ejpam-454	335	26	the	the	DET
ejpam-454	335	27	following	follow	VERB
ejpam-454	335	28	example	example	NOUN
ejpam-454	335	29	.	.	PUNCT
ejpam-454	336	1	example	example	NOUN
ejpam-454	337	1	1	1	NUM
ejpam-454	337	2	.	.	X
ejpam-454	337	3	consider	consider	VERB
ejpam-454	337	4	the	the	DET
ejpam-454	337	5	following	follow	VERB
ejpam-454	337	6	delayed	delay	VERB
ejpam-454	337	7	impulsive	impulsive	ADJ
ejpam-454	337	8	two	two	NUM
ejpam-454	337	9	-	-	PUNCT
ejpam-454	337	10	neuron	neuron	NOUN
ejpam-454	337	11	network	network	NOUN
ejpam-454	337	12	model	model	NOUN
ejpam-454	337	13	(	(	PUNCT
ejpam-454	337	14	1	1	X
ejpam-454	337	15	)	)	PUNCT
ejpam-454	337	16	descried	descry	VERB
ejpam-454	337	17	by	by	ADP
ejpam-454	337	18	:	:	PUNCT
ejpam-454	337	19	ẋ1(t	ẋ1(t	PROPN
ejpam-454	337	20	)	)	PUNCT
ejpam-454	338	1	=	=	PUNCT
ejpam-454	338	2	−	−	PROPN
ejpam-454	338	3	2	2	NUM
ejpam-454	338	4	21	21	NUM
ejpam-454	338	5	x1(t)−	x1(t)−	PROPN
ejpam-454	338	6	10	10	NUM
ejpam-454	338	7	21	21	NUM
ejpam-454	338	8	g1(x1(t	g1(x1(t	NOUN
ejpam-454	338	9	)	)	PUNCT
ejpam-454	338	10	)	)	PUNCT
ejpam-454	339	1	+	+	CCONJ
ejpam-454	339	2	2	2	NUM
ejpam-454	339	3	21	21	NUM
ejpam-454	339	4	g2(x2(t	g2(x2(t	PROPN
ejpam-454	339	5	−τ2))+	−τ2))+	PROPN
ejpam-454	339	6	i1	i1	PROPN
ejpam-454	339	7	,	,	PUNCT
ejpam-454	339	8	references	reference	VERB
ejpam-454	339	9	817	817	NUM
ejpam-454	339	10	ẋ2(t	ẋ2(t	PROPN
ejpam-454	339	11	)	)	PUNCT
ejpam-454	340	1	=	=	PUNCT
ejpam-454	341	1	−	−	PROPN
ejpam-454	341	2	5	5	NUM
ejpam-454	341	3	21	21	NUM
ejpam-454	341	4	x2(t	x2(t	PROPN
ejpam-454	341	5	)	)	PUNCT
ejpam-454	342	1	+	+	CCONJ
ejpam-454	342	2	2	2	NUM
ejpam-454	342	3	21	21	NUM
ejpam-454	342	4	g1(x1(t	g1(x1(t	NOUN
ejpam-454	342	5	−τ1))−	−τ1))−	NOUN
ejpam-454	342	6	6	6	NUM
ejpam-454	342	7	21	21	NUM
ejpam-454	342	8	g2(x2(t	g2(x2(t	NOUN
ejpam-454	342	9	)	)	PUNCT
ejpam-454	342	10	)	)	PUNCT
ejpam-454	343	1	+	+	NUM
ejpam-454	343	2	i2	i2	PROPN
ejpam-454	343	3	,	,	PUNCT
ejpam-454	343	4	△	△	NOUN
ejpam-454	343	5	x1(tk	x1(tk	X
ejpam-454	343	6	)	)	PUNCT
ejpam-454	343	7	=	=	SYM
ejpam-454	343	8	−0.2(x1(tk)−	−0.2(x1(tk)−	PROPN
ejpam-454	343	9	x∗1	x∗1	ADV
ejpam-454	343	10	)	)	PUNCT
ejpam-454	343	11	,	,	PUNCT
ejpam-454	343	12	△	△	NOUN
ejpam-454	343	13	x2(tk	x2(tk	NUM
ejpam-454	343	14	)	)	PUNCT
ejpam-454	343	15	=	=	SYM
ejpam-454	343	16	−0.3(x2(tk)−	−0.3(x2(tk)−	PROPN
ejpam-454	343	17	x∗2	x∗2	PROPN
ejpam-454	343	18	)	)	PUNCT
ejpam-454	343	19	,	,	PUNCT
ejpam-454	343	20	tk	tk	PROPN
ejpam-454	343	21	=	=	SYM
ejpam-454	343	22	kt	kt	PROPN
ejpam-454	343	23	,	,	PUNCT
ejpam-454	343	24	k	k	NOUN
ejpam-454	343	25	=	=	SYM
ejpam-454	343	26	1,2	1,2	NUM
ejpam-454	343	27	,	,	PUNCT
ejpam-454	343	28	·	·	PUNCT
ejpam-454	343	29	·	·	PUNCT
ejpam-454	343	30	·	·	PUNCT
ejpam-454	343	31	.	.	PUNCT
ejpam-454	344	1	(	(	PUNCT
ejpam-454	344	2	21	21	NUM
ejpam-454	344	3	)	)	PUNCT
ejpam-454	344	4	where	where	SCONJ
ejpam-454	344	5	t	t	PROPN
ejpam-454	344	6	>	>	X
ejpam-454	344	7	0	0	PUNCT
ejpam-454	344	8	is	be	AUX
ejpam-454	344	9	a	a	DET
ejpam-454	344	10	positive	positive	ADJ
ejpam-454	344	11	constant	constant	ADJ
ejpam-454	344	12	,	,	PUNCT
ejpam-454	344	13	g1(θ	g1(θ	PROPN
ejpam-454	344	14	)	)	PUNCT
ejpam-454	344	15	=	=	SYM
ejpam-454	344	16	arctan(θ	arctan(θ	NOUN
ejpam-454	344	17	)	)	PUNCT
ejpam-454	344	18	,	,	PUNCT
ejpam-454	344	19	g2(θ	g2(θ	NOUN
ejpam-454	344	20	)	)	PUNCT
ejpam-454	345	1	=	=	SYM
ejpam-454	345	2	θ	θ	PROPN
ejpam-454	345	3	3	3	NUM
ejpam-454	345	4	,	,	PUNCT
ejpam-454	345	5	x∗	x∗	X
ejpam-454	345	6	=	=	PUNCT
ejpam-454	345	7	(	(	PUNCT
ejpam-454	345	8	x∗1	x∗1	ADJ
ejpam-454	345	9	,	,	PUNCT
ejpam-454	345	10	x∗2	x∗2	PROPN
ejpam-454	345	11	)	)	PUNCT
ejpam-454	345	12	t	t	PROPN
ejpam-454	345	13	is	be	AUX
ejpam-454	345	14	the	the	DET
ejpam-454	345	15	equilibrium	equilibrium	NOUN
ejpam-454	345	16	point	point	NOUN
ejpam-454	345	17	of	of	ADP
ejpam-454	345	18	system	system	NOUN
ejpam-454	345	19	(	(	PUNCT
ejpam-454	345	20	21	21	NUM
ejpam-454	345	21	)	)	PUNCT
ejpam-454	345	22	.	.	PUNCT
ejpam-454	346	1	obviously	obviously	ADV
ejpam-454	346	2	,	,	PUNCT
ejpam-454	346	3	those	those	PRON
ejpam-454	346	4	results	result	NOUN
ejpam-454	346	5	in	in	ADP
ejpam-454	346	6	[	[	X
ejpam-454	346	7	5	5	NUM
ejpam-454	346	8	,	,	PUNCT
ejpam-454	346	9	6	6	NUM
ejpam-454	346	10	,	,	PUNCT
ejpam-454	346	11	8	8	NUM
ejpam-454	346	12	,	,	PUNCT
ejpam-454	346	13	9	9	NUM
ejpam-454	346	14	,	,	PUNCT
ejpam-454	346	15	10	10	NUM
ejpam-454	346	16	]	]	PUNCT
ejpam-454	346	17	would	would	AUX
ejpam-454	346	18	fail	fail	VERB
ejpam-454	346	19	when	when	SCONJ
ejpam-454	346	20	applying	apply	VERB
ejpam-454	346	21	to	to	ADP
ejpam-454	346	22	this	this	DET
ejpam-454	346	23	example	example	NOUN
ejpam-454	346	24	.	.	PUNCT
ejpam-454	347	1	however	however	ADV
ejpam-454	347	2	,	,	PUNCT
ejpam-454	347	3	we	we	PRON
ejpam-454	347	4	select	select	VERB
ejpam-454	347	5	p1	p1	NOUN
ejpam-454	347	6	=	=	NOUN
ejpam-454	347	7	p2	p2	PROPN
ejpam-454	347	8	=	=	SYM
ejpam-454	347	9	1	1	NUM
ejpam-454	347	10	(	(	PUNCT
ejpam-454	347	11	or	or	CCONJ
ejpam-454	347	12	by	by	ADP
ejpam-454	347	13	a+	a+	PUNCT
ejpam-454	347	14	at	at	ADP
ejpam-454	347	15	+	+	CCONJ
ejpam-454	347	16	(	(	PUNCT
ejpam-454	347	17	‖b‖∞	‖b‖∞	PROPN
ejpam-454	348	1	+	+	NUM
ejpam-454	349	1	‖b‖1)i	‖b‖1)i	X
ejpam-454	349	2	=	=	SYM
ejpam-454	349	3	−diag(16	−diag(16	NOUN
ejpam-454	349	4	21	21	NUM
ejpam-454	349	5	,	,	PUNCT
ejpam-454	349	6	8	8	NUM
ejpam-454	349	7	21	21	NUM
ejpam-454	349	8	)	)	PUNCT
ejpam-454	349	9	<	<	X
ejpam-454	349	10	0	0	NUM
ejpam-454	349	11	)	)	PUNCT
ejpam-454	349	12	,	,	PUNCT
ejpam-454	349	13	from	from	ADP
ejpam-454	349	14	theorem	theorem	ADJ
ejpam-454	349	15	4	4	NUM
ejpam-454	349	16	(	(	PUNCT
ejpam-454	349	17	or	or	CCONJ
ejpam-454	349	18	theorem	theorem	VERB
ejpam-454	349	19	5	5	NUM
ejpam-454	349	20	)	)	PUNCT
ejpam-454	349	21	,	,	PUNCT
ejpam-454	349	22	system	system	NOUN
ejpam-454	349	23	(	(	PUNCT
ejpam-454	349	24	21	21	NUM
ejpam-454	349	25	)	)	PUNCT
ejpam-454	349	26	has	have	VERB
ejpam-454	349	27	a	a	DET
ejpam-454	349	28	unique	unique	ADJ
ejpam-454	349	29	equilibrium	equilibrium	NOUN
ejpam-454	349	30	point	point	NOUN
ejpam-454	349	31	x∗	x∗	PROPN
ejpam-454	349	32	which	which	PRON
ejpam-454	349	33	is	be	AUX
ejpam-454	349	34	globally	globally	ADV
ejpam-454	349	35	asymptotically	asymptotically	ADV
ejpam-454	349	36	stable	stable	ADJ
ejpam-454	349	37	.	.	PUNCT
ejpam-454	350	1	therefore	therefore	ADV
ejpam-454	350	2	,	,	PUNCT
ejpam-454	350	3	our	our	PRON
ejpam-454	350	4	results	result	NOUN
ejpam-454	350	5	establish	establish	VERB
ejpam-454	350	6	new	new	ADJ
ejpam-454	350	7	criteria	criterion	NOUN
ejpam-454	350	8	for	for	ADP
ejpam-454	350	9	the	the	DET
ejpam-454	350	10	global	global	ADJ
ejpam-454	350	11	asymptotic	asymptotic	ADJ
ejpam-454	350	12	stability	stability	NOUN
ejpam-454	350	13	of	of	ADP
ejpam-454	350	14	delayed	delay	VERB
ejpam-454	350	15	neural	neural	ADJ
ejpam-454	350	16	networks	network	NOUN
ejpam-454	350	17	with	with	ADP
ejpam-454	350	18	impulses	impulse	NOUN
ejpam-454	350	19	and	and	CCONJ
ejpam-454	350	20	improve	improve	VERB
ejpam-454	350	21	those	those	DET
ejpam-454	350	22	results	result	NOUN
ejpam-454	350	23	in	in	ADP
ejpam-454	350	24	the	the	DET
ejpam-454	350	25	existing	exist	VERB
ejpam-454	350	26	literatures	literature	NOUN
ejpam-454	350	27	.	.	PUNCT
ejpam-454	351	1	4	4	X
ejpam-454	351	2	.	.	X
ejpam-454	351	3	conclusion	conclusion	NOUN
ejpam-454	351	4	this	this	DET
ejpam-454	351	5	paper	paper	NOUN
ejpam-454	351	6	has	have	AUX
ejpam-454	351	7	developed	develop	VERB
ejpam-454	351	8	a	a	DET
ejpam-454	351	9	class	class	NOUN
ejpam-454	351	10	of	of	ADP
ejpam-454	351	11	delayed	delay	VERB
ejpam-454	351	12	neural	neural	ADJ
ejpam-454	351	13	networks	network	NOUN
ejpam-454	351	14	with	with	ADP
ejpam-454	351	15	impulses	impulse	NOUN
ejpam-454	351	16	,	,	PUNCT
ejpam-454	351	17	where	where	SCONJ
ejpam-454	351	18	the	the	DET
ejpam-454	351	19	neuron	neuron	NOUN
ejpam-454	351	20	activations	activation	NOUN
ejpam-454	351	21	do	do	AUX
ejpam-454	351	22	not	not	PART
ejpam-454	351	23	satisfy	satisfy	VERB
ejpam-454	351	24	lipschitz	lipschitz	NOUN
ejpam-454	351	25	conditions	condition	NOUN
ejpam-454	351	26	.	.	PUNCT
ejpam-454	352	1	some	some	DET
ejpam-454	352	2	general	general	ADJ
ejpam-454	352	3	sufficient	sufficient	ADJ
ejpam-454	352	4	conditions	condition	NOUN
ejpam-454	352	5	are	be	AUX
ejpam-454	352	6	derived	derive	VERB
ejpam-454	352	7	for	for	ADP
ejpam-454	352	8	the	the	DET
ejpam-454	352	9	global	global	ADJ
ejpam-454	352	10	asymptotic	asymptotic	ADJ
ejpam-454	352	11	stability	stability	NOUN
ejpam-454	352	12	of	of	ADP
ejpam-454	352	13	delayed	delay	VERB
ejpam-454	352	14	neural	neural	ADJ
ejpam-454	352	15	networks	network	NOUN
ejpam-454	352	16	with	with	ADP
ejpam-454	352	17	impulses	impulse	NOUN
ejpam-454	352	18	.	.	PUNCT
ejpam-454	353	1	a	a	DET
ejpam-454	353	2	comparison	comparison	NOUN
ejpam-454	353	3	between	between	ADP
ejpam-454	353	4	our	our	PRON
ejpam-454	353	5	results	result	NOUN
ejpam-454	353	6	and	and	CCONJ
ejpam-454	353	7	the	the	DET
ejpam-454	353	8	previous	previous	ADJ
ejpam-454	353	9	results	result	NOUN
ejpam-454	353	10	is	be	AUX
ejpam-454	353	11	also	also	ADV
ejpam-454	353	12	given	give	VERB
ejpam-454	353	13	,	,	PUNCT
ejpam-454	353	14	which	which	PRON
ejpam-454	353	15	shows	show	VERB
ejpam-454	353	16	that	that	SCONJ
ejpam-454	353	17	our	our	PRON
ejpam-454	353	18	results	result	NOUN
ejpam-454	353	19	establish	establish	VERB
ejpam-454	353	20	a	a	DET
ejpam-454	353	21	new	new	ADJ
ejpam-454	353	22	criteria	criterion	NOUN
ejpam-454	353	23	for	for	ADP
ejpam-454	353	24	global	global	ADJ
ejpam-454	353	25	asymptotic	asymptotic	ADJ
ejpam-454	353	26	stability	stability	NOUN
ejpam-454	353	27	of	of	ADP
ejpam-454	353	28	delayed	delay	VERB
ejpam-454	353	29	neural	neural	ADJ
ejpam-454	353	30	networks	network	NOUN
ejpam-454	353	31	with	with	ADP
ejpam-454	353	32	impulses	impulse	NOUN
ejpam-454	353	33	.	.	PUNCT
ejpam-454	354	1	at	at	ADP
ejpam-454	354	2	the	the	DET
ejpam-454	354	3	same	same	ADJ
ejpam-454	354	4	time	time	NOUN
ejpam-454	354	5	,	,	PUNCT
ejpam-454	354	6	the	the	DET
ejpam-454	354	7	criteria	criterion	NOUN
ejpam-454	354	8	in	in	ADP
ejpam-454	354	9	this	this	DET
ejpam-454	354	10	paper	paper	NOUN
ejpam-454	354	11	is	be	AUX
ejpam-454	354	12	also	also	ADV
ejpam-454	354	13	valuable	valuable	ADJ
ejpam-454	354	14	in	in	ADP
ejpam-454	354	15	the	the	DET
ejpam-454	354	16	design	design	NOUN
ejpam-454	354	17	of	of	ADP
ejpam-454	354	18	neural	neural	ADJ
ejpam-454	354	19	networks	network	NOUN
ejpam-454	354	20	which	which	PRON
ejpam-454	354	21	is	be	AUX
ejpam-454	354	22	used	use	VERB
ejpam-454	354	23	to	to	PART
ejpam-454	354	24	solve	solve	VERB
ejpam-454	354	25	efficiently	efficiently	ADJ
ejpam-454	354	26	classes	class	NOUN
ejpam-454	354	27	of	of	ADP
ejpam-454	354	28	optimization	optimization	NOUN
ejpam-454	354	29	problems	problem	NOUN
ejpam-454	354	30	arising	arise	VERB
ejpam-454	354	31	in	in	ADP
ejpam-454	354	32	practical	practical	ADJ
ejpam-454	354	33	engineering	engineering	NOUN
ejpam-454	354	34	applications	application	NOUN
ejpam-454	354	35	.	.	PUNCT
ejpam-454	355	1	acknowledgements	acknowledgement	NOUN
ejpam-454	355	2	the	the	DET
ejpam-454	355	3	work	work	NOUN
ejpam-454	355	4	is	be	AUX
ejpam-454	355	5	supported	support	VERB
ejpam-454	355	6	by	by	ADP
ejpam-454	355	7	key	key	ADJ
ejpam-454	355	8	science	science	NOUN
ejpam-454	355	9	foundation	foundation	NOUN
ejpam-454	355	10	of	of	ADP
ejpam-454	355	11	educational	educational	ADJ
ejpam-454	355	12	department	department	PROPN
ejpam-454	355	13	of	of	ADP
ejpam-454	355	14	hubei	hubei	PROPN
ejpam-454	355	15	province	province	PROPN
ejpam-454	355	16	under	under	ADP
ejpam-454	355	17	grant	grant	NOUN
ejpam-454	355	18	d20082201	d20082201	NOUN
ejpam-454	355	19	and	and	CCONJ
ejpam-454	355	20	innovation	innovation	NOUN
ejpam-454	355	21	teams	team	NOUN
ejpam-454	355	22	of	of	ADP
ejpam-454	355	23	hubei	hubei	PROPN
ejpam-454	355	24	normal	normal	ADJ
ejpam-454	355	25	university	university	NOUN
ejpam-454	355	26	.	.	PUNCT
ejpam-454	356	1	references	reference	NOUN
ejpam-454	356	2	[	[	X
ejpam-454	356	3	1	1	NUM
ejpam-454	356	4	]	]	PUNCT
ejpam-454	356	5	l.	l.	PROPN
ejpam-454	356	6	zhou	zhou	PROPN
ejpam-454	356	7	and	and	CCONJ
ejpam-454	356	8	g.	g.	PROPN
ejpam-454	356	9	hu	hu	PROPN
ejpam-454	356	10	,	,	PUNCT
ejpam-454	356	11	global	global	ADJ
ejpam-454	356	12	exponential	exponential	ADJ
ejpam-454	356	13	periodicity	periodicity	NOUN
ejpam-454	356	14	and	and	CCONJ
ejpam-454	356	15	stability	stability	NOUN
ejpam-454	356	16	of	of	ADP
ejpam-454	356	17	cellular	cellular	ADJ
ejpam-454	356	18	neural	neural	ADJ
ejpam-454	356	19	networks	network	NOUN
ejpam-454	356	20	with	with	ADP
ejpam-454	356	21	variable	variable	ADJ
ejpam-454	356	22	and	and	CCONJ
ejpam-454	356	23	distributed	distribute	VERB
ejpam-454	356	24	delays	delay	NOUN
ejpam-454	356	25	,	,	PUNCT
ejpam-454	356	26	applied	apply	VERB
ejpam-454	356	27	mathematics	mathematic	NOUN
ejpam-454	356	28	and	and	CCONJ
ejpam-454	356	29	computation	computation	NOUN
ejpam-454	356	30	,	,	PUNCT
ejpam-454	356	31	195	195	NUM
ejpam-454	356	32	,	,	PUNCT
ejpam-454	356	33	402	402	NUM
ejpam-454	356	34	-	-	SYM
ejpam-454	356	35	411	411	NUM
ejpam-454	356	36	.	.	PUNCT
ejpam-454	356	37	2008	2008	NUM
ejpam-454	356	38	.	.	PUNCT
ejpam-454	357	1	[	[	X
ejpam-454	357	2	2	2	X
ejpam-454	357	3	]	]	PUNCT
ejpam-454	357	4	t.	t.	PROPN
ejpam-454	357	5	li	li	PROPN
ejpam-454	357	6	and	and	CCONJ
ejpam-454	357	7	s.	s.	PROPN
ejpam-454	357	8	fei	fei	PROPN
ejpam-454	357	9	,	,	PUNCT
ejpam-454	357	10	stability	stability	NOUN
ejpam-454	357	11	analysis	analysis	NOUN
ejpam-454	357	12	of	of	ADP
ejpam-454	357	13	cohen	cohen	PROPN
ejpam-454	357	14	-	-	PUNCT
ejpam-454	357	15	grossberg	grossberg	PROPN
ejpam-454	357	16	neural	neural	ADJ
ejpam-454	357	17	networks	network	NOUN
ejpam-454	357	18	with	with	ADP
ejpam-454	357	19	time	time	NOUN
ejpam-454	357	20	-	-	PUNCT
ejpam-454	357	21	varying	vary	VERB
ejpam-454	357	22	and	and	CCONJ
ejpam-454	357	23	distributed	distribute	VERB
ejpam-454	357	24	delays	delay	NOUN
ejpam-454	357	25	,	,	PUNCT
ejpam-454	357	26	neurocomputing	neurocomputing	NOUN
ejpam-454	357	27	,	,	PUNCT
ejpam-454	357	28	71	71	NUM
ejpam-454	357	29	,	,	PUNCT
ejpam-454	357	30	1069	1069	NUM
ejpam-454	357	31	-	-	SYM
ejpam-454	357	32	1081	1081	NUM
ejpam-454	357	33	.	.	PUNCT
ejpam-454	358	1	2008	2008	NUM
ejpam-454	358	2	.	.	PUNCT
ejpam-454	359	1	[	[	X
ejpam-454	359	2	3	3	X
ejpam-454	359	3	]	]	PUNCT
ejpam-454	359	4	q.	q.	PROPN
ejpam-454	359	5	zhang	zhang	PROPN
ejpam-454	359	6	,	,	PUNCT
ejpam-454	359	7	x.	x.	PROPN
ejpam-454	359	8	wei	wei	PROPN
ejpam-454	359	9	,	,	PUNCT
ejpam-454	359	10	and	and	CCONJ
ejpam-454	359	11	j.	j.	PROPN
ejpam-454	359	12	xu	xu	PROPN
ejpam-454	359	13	,	,	PUNCT
ejpam-454	359	14	delay	delay	NOUN
ejpam-454	359	15	-	-	PUNCT
ejpam-454	359	16	dependent	dependent	ADJ
ejpam-454	359	17	exponential	exponential	ADJ
ejpam-454	359	18	stability	stability	NOUN
ejpam-454	359	19	criteria	criterion	NOUN
ejpam-454	359	20	for	for	ADP
ejpam-454	359	21	nonautonomous	nonautonomous	ADJ
ejpam-454	359	22	cellular	cellular	ADJ
ejpam-454	359	23	neural	neural	ADJ
ejpam-454	359	24	networks	network	NOUN
ejpam-454	359	25	with	with	ADP
ejpam-454	359	26	time	time	NOUN
ejpam-454	359	27	-	-	PUNCT
ejpam-454	359	28	varying	vary	VERB
ejpam-454	359	29	delays	delay	NOUN
ejpam-454	359	30	,	,	PUNCT
ejpam-454	359	31	chaos	chaos	NOUN
ejpam-454	359	32	,	,	PUNCT
ejpam-454	359	33	solitons	soliton	NOUN
ejpam-454	359	34	and	and	CCONJ
ejpam-454	359	35	fractals	fractal	NOUN
ejpam-454	359	36	,	,	PUNCT
ejpam-454	359	37	36	36	NUM
ejpam-454	359	38	,	,	PUNCT
ejpam-454	359	39	985	985	NUM
ejpam-454	359	40	-	-	SYM
ejpam-454	359	41	990	990	NUM
ejpam-454	359	42	.	.	PUNCT
ejpam-454	359	43	2008	2008	NUM
ejpam-454	359	44	.	.	PUNCT
ejpam-454	360	1	references	reference	NOUN
ejpam-454	360	2	818	818	NUM
ejpam-454	360	3	[	[	X
ejpam-454	360	4	4	4	NUM
ejpam-454	360	5	]	]	PUNCT
ejpam-454	360	6	w.	w.	PROPN
ejpam-454	360	7	zhao	zhao	PROPN
ejpam-454	360	8	,	,	PUNCT
ejpam-454	360	9	dynamics	dynamic	NOUN
ejpam-454	360	10	of	of	ADP
ejpam-454	360	11	cohen	cohen	PROPN
ejpam-454	360	12	-	-	PUNCT
ejpam-454	360	13	grossberg	grossberg	PROPN
ejpam-454	360	14	neural	neural	ADJ
ejpam-454	360	15	network	network	NOUN
ejpam-454	360	16	with	with	ADP
ejpam-454	360	17	variable	variable	ADJ
ejpam-454	360	18	coefficients	coefficient	NOUN
ejpam-454	360	19	and	and	CCONJ
ejpam-454	360	20	time	time	NOUN
ejpam-454	360	21	-	-	PUNCT
ejpam-454	360	22	varying	vary	VERB
ejpam-454	360	23	delays	delay	NOUN
ejpam-454	360	24	,	,	PUNCT
ejpam-454	360	25	nonlinear	nonlinear	ADJ
ejpam-454	360	26	analysis	analysis	NOUN
ejpam-454	360	27	:	:	PUNCT
ejpam-454	360	28	real	real	ADJ
ejpam-454	360	29	world	world	NOUN
ejpam-454	360	30	applications	application	NOUN
ejpam-454	360	31	,	,	PUNCT
ejpam-454	360	32	9	9	NUM
ejpam-454	360	33	,	,	PUNCT
ejpam-454	360	34	1024	1024	NUM
ejpam-454	360	35	-	-	SYM
ejpam-454	360	36	1037	1037	NUM
ejpam-454	360	37	.	.	PUNCT
ejpam-454	361	1	2008	2008	NUM
ejpam-454	361	2	.	.	PUNCT
ejpam-454	362	1	[	[	X
ejpam-454	362	2	5	5	X
ejpam-454	362	3	]	]	PUNCT
ejpam-454	362	4	w.	w.	PROPN
ejpam-454	362	5	xiong	xiong	PROPN
ejpam-454	362	6	,	,	PUNCT
ejpam-454	362	7	q.	q.	PROPN
ejpam-454	362	8	zhou	zhou	PROPN
ejpam-454	362	9	,	,	PUNCT
ejpam-454	362	10	b.	b.	PROPN
ejpam-454	362	11	xiao	xiao	PROPN
ejpam-454	362	12	,	,	PUNCT
ejpam-454	362	13	and	and	CCONJ
ejpam-454	362	14	y.	y.	PROPN
ejpam-454	362	15	yu	yu	PROPN
ejpam-454	362	16	,	,	PUNCT
ejpam-454	362	17	global	global	ADJ
ejpam-454	362	18	exponential	exponential	ADJ
ejpam-454	362	19	stability	stability	NOUN
ejpam-454	362	20	of	of	ADP
ejpam-454	362	21	cellular	cellular	ADJ
ejpam-454	362	22	neural	neural	ADJ
ejpam-454	362	23	networks	network	NOUN
ejpam-454	362	24	with	with	ADP
ejpam-454	362	25	mixed	mixed	ADJ
ejpam-454	362	26	delays	delay	NOUN
ejpam-454	362	27	and	and	CCONJ
ejpam-454	362	28	impulses	impulse	NOUN
ejpam-454	362	29	,	,	PUNCT
ejpam-454	362	30	chaos	chaos	NOUN
ejpam-454	362	31	,	,	PUNCT
ejpam-454	362	32	solitons	soliton	NOUN
ejpam-454	362	33	and	and	CCONJ
ejpam-454	362	34	fractals	fractal	NOUN
ejpam-454	362	35	,	,	PUNCT
ejpam-454	362	36	34	34	NUM
ejpam-454	362	37	,	,	PUNCT
ejpam-454	362	38	896	896	NUM
ejpam-454	362	39	-	-	SYM
ejpam-454	362	40	902	902	NUM
ejpam-454	362	41	.	.	PUNCT
ejpam-454	362	42	2007	2007	NUM
ejpam-454	362	43	.	.	PUNCT
ejpam-454	363	1	[	[	X
ejpam-454	363	2	6	6	NUM
ejpam-454	363	3	]	]	PUNCT
ejpam-454	363	4	z.	z.	PROPN
ejpam-454	363	5	huang	huang	PROPN
ejpam-454	363	6	,	,	PUNCT
ejpam-454	363	7	q.	q.	PROPN
ejpam-454	363	8	yang	yang	PROPN
ejpam-454	363	9	,	,	PUNCT
ejpam-454	363	10	and	and	CCONJ
ejpam-454	363	11	x.	x.	PROPN
ejpam-454	363	12	luo	luo	PROPN
ejpam-454	363	13	,	,	PUNCT
ejpam-454	363	14	exponential	exponential	ADJ
ejpam-454	363	15	stability	stability	NOUN
ejpam-454	363	16	of	of	ADP
ejpam-454	363	17	impulsive	impulsive	ADJ
ejpam-454	363	18	neural	neural	ADJ
ejpam-454	363	19	networks	network	NOUN
ejpam-454	363	20	with	with	ADP
ejpam-454	363	21	time	time	NOUN
ejpam-454	363	22	-	-	PUNCT
ejpam-454	363	23	varying	vary	VERB
ejpam-454	363	24	delays	delay	NOUN
ejpam-454	363	25	,	,	PUNCT
ejpam-454	363	26	chaos	chaos	NOUN
ejpam-454	363	27	,	,	PUNCT
ejpam-454	363	28	solitons	soliton	NOUN
ejpam-454	363	29	and	and	CCONJ
ejpam-454	363	30	fractals	fractal	NOUN
ejpam-454	363	31	,	,	PUNCT
ejpam-454	363	32	35	35	NUM
ejpam-454	363	33	,	,	PUNCT
ejpam-454	363	34	770	770	NUM
ejpam-454	363	35	-	-	SYM
ejpam-454	363	36	780	780	NUM
ejpam-454	363	37	.	.	PUNCT
ejpam-454	363	38	2008	2008	NUM
ejpam-454	363	39	.	.	PUNCT
ejpam-454	364	1	[	[	X
ejpam-454	364	2	7	7	X
ejpam-454	364	3	]	]	X
ejpam-454	364	4	s.	s.	PROPN
ejpam-454	364	5	long	long	PROPN
ejpam-454	364	6	and	and	CCONJ
ejpam-454	364	7	d.	d.	PROPN
ejpam-454	364	8	xu	xu	PROPN
ejpam-454	364	9	,	,	PUNCT
ejpam-454	364	10	delay	delay	NOUN
ejpam-454	364	11	-	-	PUNCT
ejpam-454	364	12	dependent	dependent	ADJ
ejpam-454	364	13	stability	stability	NOUN
ejpam-454	364	14	analysis	analysis	NOUN
ejpam-454	364	15	for	for	ADP
ejpam-454	364	16	impulsive	impulsive	ADJ
ejpam-454	364	17	neural	neural	ADJ
ejpam-454	364	18	networks	network	NOUN
ejpam-454	364	19	with	with	ADP
ejpam-454	364	20	time	time	NOUN
ejpam-454	364	21	-	-	PUNCT
ejpam-454	364	22	varying	vary	VERB
ejpam-454	364	23	delays	delay	NOUN
ejpam-454	364	24	,	,	PUNCT
ejpam-454	364	25	neurocomputing	neurocomputing	NOUN
ejpam-454	364	26	,	,	PUNCT
ejpam-454	364	27	71	71	NUM
ejpam-454	364	28	,	,	PUNCT
ejpam-454	364	29	1705	1705	NUM
ejpam-454	364	30	-	-	SYM
ejpam-454	364	31	1713	1713	NUM
ejpam-454	364	32	.	.	PUNCT
ejpam-454	365	1	2008	2008	NUM
ejpam-454	365	2	.	.	PUNCT
ejpam-454	366	1	[	[	X
ejpam-454	366	2	8	8	X
ejpam-454	366	3	]	]	X
ejpam-454	366	4	h.	h.	PROPN
ejpam-454	366	5	wu	wu	PROPN
ejpam-454	366	6	and	and	CCONJ
ejpam-454	366	7	x.	x.	PROPN
ejpam-454	366	8	xue	xue	PROPN
ejpam-454	366	9	,	,	PUNCT
ejpam-454	366	10	stability	stability	NOUN
ejpam-454	366	11	analysis	analysis	NOUN
ejpam-454	366	12	for	for	ADP
ejpam-454	366	13	neural	neural	ADJ
ejpam-454	366	14	networks	network	NOUN
ejpam-454	366	15	with	with	ADP
ejpam-454	366	16	inverse	inverse	NOUN
ejpam-454	366	17	lipschitzian	lipschitzian	ADJ
ejpam-454	366	18	neuron	neuron	NOUN
ejpam-454	366	19	activations	activation	NOUN
ejpam-454	366	20	and	and	CCONJ
ejpam-454	366	21	impulses	impulse	NOUN
ejpam-454	366	22	,	,	PUNCT
ejpam-454	366	23	applied	apply	VERB
ejpam-454	366	24	mathematical	mathematical	ADJ
ejpam-454	366	25	modelling	modelling	NOUN
ejpam-454	366	26	,	,	PUNCT
ejpam-454	366	27	32	32	NUM
ejpam-454	366	28	,	,	PUNCT
ejpam-454	366	29	2347	2347	NUM
ejpam-454	366	30	-	-	SYM
ejpam-454	366	31	2359	2359	NUM
ejpam-454	366	32	.	.	PUNCT
ejpam-454	367	1	2008	2008	NUM
ejpam-454	367	2	.	.	PUNCT
ejpam-454	368	1	[	[	X
ejpam-454	368	2	9	9	NUM
ejpam-454	368	3	]	]	PUNCT
ejpam-454	368	4	q.	q.	NOUN
ejpam-454	368	5	song	song	NOUN
ejpam-454	368	6	and	and	CCONJ
ejpam-454	368	7	j.	j.	PROPN
ejpam-454	368	8	zhang	zhang	PROPN
ejpam-454	368	9	,	,	PUNCT
ejpam-454	368	10	global	global	ADJ
ejpam-454	368	11	exponential	exponential	ADJ
ejpam-454	368	12	stability	stability	NOUN
ejpam-454	368	13	of	of	ADP
ejpam-454	368	14	impulsive	impulsive	ADJ
ejpam-454	368	15	cohen	cohen	PROPN
ejpam-454	368	16	-	-	PUNCT
ejpam-454	368	17	grossberg	grossberg	PROPN
ejpam-454	368	18	neural	neural	ADJ
ejpam-454	368	19	network	network	NOUN
ejpam-454	368	20	with	with	ADP
ejpam-454	368	21	time	time	NOUN
ejpam-454	368	22	-	-	PUNCT
ejpam-454	368	23	varying	vary	VERB
ejpam-454	368	24	delays	delay	NOUN
ejpam-454	368	25	,	,	PUNCT
ejpam-454	368	26	nonlinear	nonlinear	ADJ
ejpam-454	368	27	analysis	analysis	NOUN
ejpam-454	368	28	:	:	PUNCT
ejpam-454	368	29	real	real	ADJ
ejpam-454	368	30	world	world	NOUN
ejpam-454	368	31	applications	application	NOUN
ejpam-454	368	32	,	,	PUNCT
ejpam-454	368	33	9	9	NUM
ejpam-454	368	34	,	,	PUNCT
ejpam-454	368	35	500510	500510	NUM
ejpam-454	368	36	.	.	PUNCT
ejpam-454	369	1	2008	2008	NUM
ejpam-454	369	2	.	.	PUNCT
ejpam-454	370	1	[	[	X
ejpam-454	370	2	10	10	NUM
ejpam-454	370	3	]	]	X
ejpam-454	370	4	s.	s.	PROPN
ejpam-454	370	5	ahmada	ahmada	PROPN
ejpam-454	370	6	and	and	CCONJ
ejpam-454	370	7	i.	i.	PROPN
ejpam-454	370	8	stamov	stamov	PROPN
ejpam-454	370	9	,	,	PUNCT
ejpam-454	370	10	global	global	ADJ
ejpam-454	370	11	exponential	exponential	ADJ
ejpam-454	370	12	stability	stability	NOUN
ejpam-454	370	13	for	for	ADP
ejpam-454	370	14	impulsive	impulsive	ADJ
ejpam-454	370	15	cellular	cellular	ADJ
ejpam-454	370	16	neural	neural	ADJ
ejpam-454	370	17	networks	network	NOUN
ejpam-454	370	18	with	with	ADP
ejpam-454	370	19	time	time	NOUN
ejpam-454	370	20	-	-	PUNCT
ejpam-454	370	21	varying	vary	VERB
ejpam-454	370	22	delays	delay	NOUN
ejpam-454	370	23	,	,	PUNCT
ejpam-454	370	24	nonlinear	nonlinear	ADJ
ejpam-454	370	25	analysis	analysis	NOUN
ejpam-454	370	26	,	,	PUNCT
ejpam-454	370	27	69	69	NUM
ejpam-454	370	28	,	,	PUNCT
ejpam-454	370	29	786	786	NUM
ejpam-454	370	30	-	-	SYM
ejpam-454	370	31	795	795	NUM
ejpam-454	370	32	.	.	PUNCT
ejpam-454	370	33	2008	2008	NUM
ejpam-454	370	34	.	.	PUNCT