id	sid	tid	token	lemma	pos
cana-2100	1	1	communications	communication	NOUN
cana-2100	1	2	on	on	ADP
cana-2100	1	3	applied	apply	VERB
cana-2100	1	4	nonlinear	nonlinear	ADJ
cana-2100	1	5	analysis	analysis	NOUN
cana-2100	1	6	issn	issn	NOUN
cana-2100	1	7	:	:	PUNCT
cana-2100	1	8	1074	1074	NUM
cana-2100	1	9	-	-	PUNCT
cana-2100	1	10	133x	133x	NUM
cana-2100	1	11	vol	vol	NOUN
cana-2100	1	12	32	32	NUM
cana-2100	1	13	no	no	NOUN
cana-2100	1	14	.	.	PUNCT
cana-2100	2	1	1s	1s	NUM
cana-2100	2	2	(	(	PUNCT
cana-2100	2	3	2025	2025	NUM
cana-2100	2	4	)	)	PUNCT
cana-2100	2	5	45	45	NUM
cana-2100	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2100	2	7	formulation	formulation	NOUN
cana-2100	2	8	of	of	ADP
cana-2100	2	9	impulsive	impulsive	ADJ
cana-2100	2	10	differential	differential	ADJ
cana-2100	2	11	equations	equation	NOUN
cana-2100	2	12	with	with	ADP
cana-2100	2	13	time	time	NOUN
cana-2100	2	14	-	-	PUNCT
cana-2100	2	15	dependent	dependent	ADJ
cana-2100	2	16	continuous	continuous	ADJ
cana-2100	2	17	delay	delay	NOUN
cana-2100	2	18	venkatachalapathi	venkatachalapathi	PROPN
cana-2100	2	19	uday1	uday1	PROPN
cana-2100	2	20	,	,	PUNCT
cana-2100	2	21	dr	dr	PROPN
cana-2100	2	22	.	.	PROPN
cana-2100	2	23	gautam	gautam	PROPN
cana-2100	2	24	kumar	kumar	PROPN
cana-2100	2	25	rajput2	rajput2	PROPN
cana-2100	3	1	1research	1research	NUM
cana-2100	3	2	scholar	scholar	NOUN
cana-2100	3	3	,	,	PUNCT
cana-2100	3	4	department	department	NOUN
cana-2100	3	5	of	of	ADP
cana-2100	3	6	mathematics	mathematics	PROPN
cana-2100	3	7	,	,	PUNCT
cana-2100	3	8	sunrise	sunrise	VERB
cana-2100	3	9	university	university	NOUN
cana-2100	3	10	,	,	PUNCT
cana-2100	3	11	alwar	alwar	PROPN
cana-2100	3	12	,	,	PUNCT
cana-2100	3	13	rajasthan	rajasthan	PROPN
cana-2100	3	14	2associate	2associate	NUM
cana-2100	3	15	professor	professor	NOUN
cana-2100	3	16	,	,	PUNCT
cana-2100	3	17	department	department	NOUN
cana-2100	3	18	of	of	ADP
cana-2100	3	19	mathematics	mathematics	PROPN
cana-2100	3	20	,	,	PUNCT
cana-2100	3	21	sunrise	sunrise	VERB
cana-2100	3	22	university	university	NOUN
cana-2100	3	23	,	,	PUNCT
cana-2100	3	24	alwar	alwar	PROPN
cana-2100	3	25	,	,	PUNCT
cana-2100	3	26	rajasthan	rajasthan	NOUN
cana-2100	3	27	article	article	NOUN
cana-2100	3	28	history	history	NOUN
cana-2100	3	29	:	:	PUNCT
cana-2100	3	30	received	receive	VERB
cana-2100	3	31	:	:	PUNCT
cana-2100	3	32	06	06	NUM
cana-2100	3	33	-	-	SYM
cana-2100	3	34	08	08	NUM
cana-2100	3	35	-	-	PUNCT
cana-2100	3	36	2024	2024	NUM
cana-2100	3	37	revised	revise	VERB
cana-2100	3	38	:	:	PUNCT
cana-2100	3	39	25	25	NUM
cana-2100	3	40	-	-	PUNCT
cana-2100	3	41	09	09	NUM
cana-2100	3	42	-	-	PUNCT
cana-2100	3	43	2024	2024	NUM
cana-2100	3	44	accepted	accept	VERB
cana-2100	3	45	:	:	PUNCT
cana-2100	3	46	08	08	NUM
cana-2100	3	47	-	-	SYM
cana-2100	3	48	10	10	NUM
cana-2100	3	49	-	-	PUNCT
cana-2100	3	50	2024	2024	NUM
cana-2100	3	51	abstract	abstract	NOUN
cana-2100	3	52	:	:	PUNCT
cana-2100	3	53	research	research	NOUN
cana-2100	3	54	in	in	ADP
cana-2100	3	55	impulsive	impulsive	ADJ
cana-2100	3	56	delay	delay	NOUN
cana-2100	3	57	differential	differential	NOUN
cana-2100	3	58	equations	equation	NOUN
cana-2100	3	59	has	have	AUX
cana-2100	3	60	been	be	AUX
cana-2100	3	61	undergoing	undergo	VERB
cana-2100	3	62	some	some	DET
cana-2100	3	63	exciting	exciting	ADJ
cana-2100	3	64	growth	growth	NOUN
cana-2100	3	65	in	in	ADP
cana-2100	3	66	recent	recent	ADJ
cana-2100	3	67	times	time	NOUN
cana-2100	3	68	.	.	PUNCT
cana-2100	4	1	this	this	PRON
cana-2100	4	2	to	to	ADP
cana-2100	4	3	a	a	DET
cana-2100	4	4	large	large	ADJ
cana-2100	4	5	extent	extent	NOUN
cana-2100	4	6	can	can	AUX
cana-2100	4	7	be	be	AUX
cana-2100	4	8	attributed	attribute	VERB
cana-2100	4	9	to	to	ADP
cana-2100	4	10	the	the	DET
cana-2100	4	11	quest	quest	NOUN
cana-2100	4	12	by	by	ADP
cana-2100	4	13	mathematicians	mathematician	NOUN
cana-2100	4	14	in	in	ADP
cana-2100	4	15	particular	particular	ADJ
cana-2100	4	16	and	and	CCONJ
cana-2100	4	17	the	the	DET
cana-2100	4	18	science	science	NOUN
cana-2100	4	19	community	community	NOUN
cana-2100	4	20	as	as	ADP
cana-2100	4	21	a	a	DET
cana-2100	4	22	whole	whole	NOUN
cana-2100	4	23	to	to	PART
cana-2100	4	24	unveil	unveil	VERB
cana-2100	4	25	nature	nature	NOUN
cana-2100	4	26	the	the	DET
cana-2100	4	27	way	way	NOUN
cana-2100	4	28	it	it	PRON
cana-2100	4	29	truly	truly	ADV
cana-2100	4	30	is	be	AUX
cana-2100	4	31	.	.	PUNCT
cana-2100	5	1	the	the	DET
cana-2100	5	2	realization	realization	NOUN
cana-2100	5	3	that	that	SCONJ
cana-2100	5	4	differential	differential	ADJ
cana-2100	5	5	equations	equation	NOUN
cana-2100	5	6	,	,	PUNCT
cana-2100	5	7	in	in	ADP
cana-2100	5	8	general	general	ADJ
cana-2100	5	9	,	,	PUNCT
cana-2100	5	10	and	and	CCONJ
cana-2100	5	11	indeed	indeed	ADV
cana-2100	5	12	impulsive	impulsive	ADJ
cana-2100	5	13	delay	delay	NOUN
cana-2100	5	14	differential	differential	ADJ
cana-2100	5	15	equations	equation	NOUN
cana-2100	5	16	are	be	AUX
cana-2100	5	17	very	very	ADV
cana-2100	5	18	important	important	ADJ
cana-2100	5	19	models	model	NOUN
cana-2100	5	20	for	for	ADP
cana-2100	5	21	describing	describe	VERB
cana-2100	5	22	the	the	DET
cana-2100	5	23	true	true	ADJ
cana-2100	5	24	state	state	NOUN
cana-2100	5	25	of	of	ADP
cana-2100	5	26	several	several	ADJ
cana-2100	5	27	real	real	ADJ
cana-2100	5	28	-	-	PUNCT
cana-2100	5	29	life	life	NOUN
cana-2100	5	30	processes	process	NOUN
cana-2100	5	31	/	/	SYM
cana-2100	5	32	phenomena	phenomenon	NOUN
cana-2100	5	33	may	may	AUX
cana-2100	5	34	have	have	AUX
cana-2100	5	35	been	be	AUX
cana-2100	5	36	the	the	DET
cana-2100	5	37	tunic	tunic	NOUN
cana-2100	5	38	.	.	PUNCT
cana-2100	6	1	one	one	PRON
cana-2100	6	2	can	can	AUX
cana-2100	6	3	attest	attest	VERB
cana-2100	6	4	that	that	SCONJ
cana-2100	6	5	in	in	ADP
cana-2100	6	6	most	most	ADJ
cana-2100	6	7	human	human	ADJ
cana-2100	6	8	processes	process	NOUN
cana-2100	6	9	or	or	CCONJ
cana-2100	6	10	natural	natural	ADJ
cana-2100	6	11	phenomena	phenomenon	NOUN
cana-2100	6	12	,	,	PUNCT
cana-2100	6	13	the	the	DET
cana-2100	6	14	present	present	ADJ
cana-2100	6	15	state	state	NOUN
cana-2100	6	16	is	be	AUX
cana-2100	6	17	most	most	ADV
cana-2100	6	18	often	often	ADV
cana-2100	6	19	affected	affect	VERB
cana-2100	6	20	significantly	significantly	ADV
cana-2100	6	21	by	by	ADP
cana-2100	6	22	their	their	PRON
cana-2100	6	23	past	past	ADJ
cana-2100	6	24	state	state	NOUN
cana-2100	6	25	and	and	CCONJ
cana-2100	6	26	those	those	PRON
cana-2100	6	27	that	that	PRON
cana-2100	6	28	were	be	AUX
cana-2100	6	29	thought	think	VERB
cana-2100	6	30	of	of	ADP
cana-2100	6	31	as	as	ADP
cana-2100	6	32	continuous	continuous	ADJ
cana-2100	6	33	may	may	AUX
cana-2100	6	34	indeed	indeed	ADV
cana-2100	6	35	undergo	undergo	VERB
cana-2100	6	36	abrupt	abrupt	ADJ
cana-2100	6	37	change	change	NOUN
cana-2100	6	38	at	at	ADP
cana-2100	6	39	several	several	ADJ
cana-2100	6	40	points	point	NOUN
cana-2100	6	41	or	or	CCONJ
cana-2100	6	42	even	even	ADV
cana-2100	6	43	be	be	AUX
cana-2100	6	44	stochastic	stochastic	ADJ
cana-2100	6	45	.	.	PUNCT
cana-2100	7	1	in	in	ADP
cana-2100	7	2	this	this	DET
cana-2100	7	3	study	study	NOUN
cana-2100	7	4	,	,	PUNCT
cana-2100	7	5	a	a	DET
cana-2100	7	6	special	special	NOUN
cana-2100	7	7	strictly	strictly	ADV
cana-2100	7	8	ascending	ascend	VERB
cana-2100	7	9	continuous	continuous	ADJ
cana-2100	7	10	delay	delay	NOUN
cana-2100	7	11	is	be	AUX
cana-2100	7	12	constructed	construct	VERB
cana-2100	7	13	for	for	ADP
cana-2100	7	14	a	a	DET
cana-2100	7	15	class	class	NOUN
cana-2100	7	16	of	of	ADP
cana-2100	7	17	system	system	NOUN
cana-2100	7	18	of	of	ADP
cana-2100	7	19	impulsive	impulsive	ADJ
cana-2100	7	20	differential	differential	ADJ
cana-2100	7	21	equations	equation	NOUN
cana-2100	7	22	.	.	PUNCT
cana-2100	8	1	it	it	PRON
cana-2100	8	2	is	be	AUX
cana-2100	8	3	demonstrated	demonstrate	VERB
cana-2100	8	4	that	that	SCONJ
cana-2100	8	5	even	even	ADV
cana-2100	8	6	though	though	SCONJ
cana-2100	8	7	the	the	DET
cana-2100	8	8	dynamics	dynamic	NOUN
cana-2100	8	9	of	of	ADP
cana-2100	8	10	the	the	DET
cana-2100	8	11	system	system	NOUN
cana-2100	8	12	and	and	CCONJ
cana-2100	8	13	the	the	DET
cana-2100	8	14	delay	delay	NOUN
cana-2100	8	15	have	have	VERB
cana-2100	8	16	ideal	ideal	ADJ
cana-2100	8	17	continuity	continuity	NOUN
cana-2100	8	18	properties	property	NOUN
cana-2100	8	19	,	,	PUNCT
cana-2100	8	20	the	the	DET
cana-2100	8	21	right	right	ADJ
cana-2100	8	22	side	side	NOUN
cana-2100	8	23	may	may	AUX
cana-2100	8	24	not	not	PART
cana-2100	8	25	even	even	ADV
cana-2100	8	26	have	have	VERB
cana-2100	8	27	limits	limit	NOUN
cana-2100	8	28	at	at	ADP
cana-2100	8	29	some	some	DET
cana-2100	8	30	points	point	NOUN
cana-2100	8	31	due	due	ADP
cana-2100	8	32	to	to	ADP
cana-2100	8	33	the	the	DET
cana-2100	8	34	impact	impact	NOUN
cana-2100	8	35	of	of	ADP
cana-2100	8	36	past	past	ADJ
cana-2100	8	37	impulses	impulse	NOUN
cana-2100	8	38	in	in	ADP
cana-2100	8	39	the	the	DET
cana-2100	8	40	present	present	NOUN
cana-2100	8	41	.	.	PUNCT
cana-2100	9	1	the	the	DET
cana-2100	9	2	integral	integral	ADJ
cana-2100	9	3	equivalence	equivalence	NOUN
cana-2100	9	4	of	of	ADP
cana-2100	9	5	the	the	DET
cana-2100	9	6	formulated	formulated	ADJ
cana-2100	9	7	system	system	NOUN
cana-2100	9	8	of	of	ADP
cana-2100	9	9	equations	equation	NOUN
cana-2100	9	10	is	be	AUX
cana-2100	9	11	also	also	ADV
cana-2100	9	12	obtained	obtain	VERB
cana-2100	9	13	via	via	ADP
cana-2100	9	14	a	a	DET
cana-2100	9	15	scheme	scheme	NOUN
cana-2100	9	16	similar	similar	ADJ
cana-2100	9	17	to	to	ADP
cana-2100	9	18	that	that	PRON
cana-2100	9	19	of	of	ADP
cana-2100	9	20	perron	perron	PROPN
cana-2100	9	21	by	by	ADP
cana-2100	9	22	making	make	VERB
cana-2100	9	23	use	use	NOUN
cana-2100	9	24	of	of	ADP
cana-2100	9	25	certain	certain	ADJ
cana-2100	9	26	assumptions	assumption	NOUN
cana-2100	9	27	.	.	PUNCT
cana-2100	10	1	keywords	keyword	NOUN
cana-2100	10	2	:	:	PUNCT
cana-2100	10	3	impulsive	impulsive	ADJ
cana-2100	10	4	,	,	PUNCT
cana-2100	10	5	differential	differential	ADJ
cana-2100	10	6	equation	equation	NOUN
cana-2100	10	7	,	,	PUNCT
cana-2100	10	8	continuous	continuous	ADJ
cana-2100	10	9	delay	delay	NOUN
cana-2100	10	10	,	,	PUNCT
cana-2100	10	11	integral	integral	ADJ
cana-2100	10	12	equivalence	equivalence	NOUN
cana-2100	10	13	1	1	NUM
cana-2100	10	14	.	.	PUNCT
cana-2100	10	15	introduction	introduction	NOUN
cana-2100	10	16	and	and	CCONJ
cana-2100	10	17	statement	statement	NOUN
cana-2100	10	18	of	of	ADP
cana-2100	10	19	problem	problem	NOUN
cana-2100	10	20	the	the	DET
cana-2100	10	21	theory	theory	NOUN
cana-2100	10	22	of	of	ADP
cana-2100	10	23	impulsive	impulsive	ADJ
cana-2100	10	24	delay	delay	NOUN
cana-2100	10	25	differential	differential	ADJ
cana-2100	10	26	equations	equation	NOUN
cana-2100	10	27	(	(	PUNCT
cana-2100	10	28	ide	ide	NOUN
cana-2100	10	29	)	)	PUNCT
cana-2100	10	30	is	be	AUX
cana-2100	10	31	based	base	VERB
cana-2100	10	32	on	on	ADP
cana-2100	10	33	the	the	DET
cana-2100	10	34	behaviour	behaviour	NOUN
cana-2100	10	35	of	of	ADP
cana-2100	10	36	processes	process	NOUN
cana-2100	10	37	or	or	CCONJ
cana-2100	10	38	phenomena	phenomenon	NOUN
cana-2100	10	39	which	which	PRON
cana-2100	10	40	undergo	undergo	VERB
cana-2100	10	41	abrupt	abrupt	ADJ
cana-2100	10	42	changes	change	NOUN
cana-2100	10	43	in	in	ADP
cana-2100	10	44	their	their	PRON
cana-2100	10	45	state	state	NOUN
cana-2100	10	46	and	and	CCONJ
cana-2100	10	47	past	past	ADJ
cana-2100	10	48	events	event	NOUN
cana-2100	10	49	affect	affect	VERB
cana-2100	10	50	the	the	DET
cana-2100	10	51	current	current	ADJ
cana-2100	10	52	behaviour	behaviour	NOUN
cana-2100	10	53	(	(	PUNCT
cana-2100	10	54	delay	delay	PROPN
cana-2100	10	55	)	)	PUNCT
cana-2100	10	56	.	.	PUNCT
cana-2100	11	1	these	these	DET
cana-2100	11	2	kinds	kind	NOUN
cana-2100	11	3	of	of	ADP
cana-2100	11	4	processes	process	NOUN
cana-2100	11	5	are	be	AUX
cana-2100	11	6	best	well	ADV
cana-2100	11	7	described	describe	VERB
cana-2100	11	8	by	by	ADP
cana-2100	11	9	coupled	couple	VERB
cana-2100	11	10	systems	system	NOUN
cana-2100	11	11	of	of	ADP
cana-2100	11	12	differential	differential	ADJ
cana-2100	11	13	equations	equation	NOUN
cana-2100	11	14	,	,	PUNCT
cana-2100	11	15	either	either	CCONJ
cana-2100	11	16	starting	start	VERB
cana-2100	11	17	with	with	ADP
cana-2100	11	18	delay	delay	NOUN
cana-2100	11	19	differential	differential	ADJ
cana-2100	11	20	equations	equation	NOUN
cana-2100	11	21	and	and	CCONJ
cana-2100	11	22	adding	add	VERB
cana-2100	11	23	impulses	impulse	NOUN
cana-2100	11	24	or	or	CCONJ
cana-2100	11	25	starting	start	VERB
cana-2100	11	26	with	with	ADP
cana-2100	11	27	impulsive	impulsive	ADJ
cana-2100	11	28	differential	differential	ADJ
cana-2100	11	29	equations	equation	NOUN
cana-2100	11	30	and	and	CCONJ
cana-2100	11	31	adding	add	VERB
cana-2100	11	32	delay	delay	NOUN
cana-2100	11	33	arguments	argument	NOUN
cana-2100	11	34	.	.	PUNCT
cana-2100	12	1	whichever	whichever	PRON
cana-2100	12	2	is	be	AUX
cana-2100	12	3	the	the	DET
cana-2100	12	4	case	case	NOUN
cana-2100	12	5	,	,	PUNCT
cana-2100	12	6	a	a	DET
cana-2100	12	7	coupled	couple	VERB
cana-2100	12	8	problem	problem	NOUN
cana-2100	12	9	is	be	AUX
cana-2100	12	10	obtained	obtain	VERB
cana-2100	12	11	and	and	CCONJ
cana-2100	12	12	the	the	DET
cana-2100	12	13	structure	structure	NOUN
cana-2100	12	14	is	be	AUX
cana-2100	12	15	radically	radically	ADV
cana-2100	12	16	changed	change	VERB
cana-2100	12	17	.	.	PUNCT
cana-2100	13	1	several	several	ADJ
cana-2100	13	2	of	of	ADP
cana-2100	13	3	the	the	DET
cana-2100	13	4	properties	property	NOUN
cana-2100	13	5	of	of	ADP
cana-2100	13	6	solutions	solution	NOUN
cana-2100	13	7	in	in	ADP
cana-2100	13	8	ordinary	ordinary	ADJ
cana-2100	13	9	,	,	PUNCT
cana-2100	13	10	delay	delay	NOUN
cana-2100	13	11	,	,	PUNCT
cana-2100	13	12	or	or	CCONJ
cana-2100	13	13	impulsive	impulsive	ADJ
cana-2100	13	14	differential	differential	ADJ
cana-2100	13	15	equations	equation	NOUN
cana-2100	13	16	are	be	AUX
cana-2100	13	17	no	no	ADV
cana-2100	13	18	longer	long	ADV
cana-2100	13	19	sustained	sustain	VERB
cana-2100	13	20	.	.	PUNCT
cana-2100	14	1	the	the	DET
cana-2100	14	2	theory	theory	NOUN
cana-2100	14	3	of	of	ADP
cana-2100	14	4	impulsive	impulsive	ADJ
cana-2100	14	5	delay	delay	NOUN
cana-2100	14	6	differential	differential	NOUN
cana-2100	14	7	equations	equation	NOUN
cana-2100	14	8	has	have	AUX
cana-2100	14	9	been	be	AUX
cana-2100	14	10	relatively	relatively	ADV
cana-2100	14	11	less	less	ADV
cana-2100	14	12	developed	developed	ADJ
cana-2100	14	13	because	because	SCONJ
cana-2100	14	14	of	of	ADP
cana-2100	14	15	significant	significant	ADJ
cana-2100	14	16	technical	technical	ADJ
cana-2100	14	17	and	and	CCONJ
cana-2100	14	18	theoretical	theoretical	ADJ
cana-2100	14	19	difficulties	difficulty	NOUN
cana-2100	14	20	,	,	PUNCT
cana-2100	14	21	and	and	CCONJ
cana-2100	14	22	as	as	SCONJ
cana-2100	14	23	such	such	ADJ
cana-2100	14	24	only	only	ADV
cana-2100	14	25	a	a	DET
cana-2100	14	26	few	few	ADJ
cana-2100	14	27	pieces	piece	NOUN
cana-2100	14	28	of	of	ADP
cana-2100	14	29	literature	literature	NOUN
cana-2100	14	30	are	be	AUX
cana-2100	14	31	available	available	ADJ
cana-2100	14	32	.	.	PUNCT
cana-2100	15	1	however	however	ADV
cana-2100	15	2	,	,	PUNCT
cana-2100	15	3	interest	interest	NOUN
cana-2100	15	4	is	be	AUX
cana-2100	15	5	on	on	ADP
cana-2100	15	6	the	the	DET
cana-2100	15	7	increase	increase	NOUN
cana-2100	15	8	largely	largely	ADV
cana-2100	15	9	due	due	ADJ
cana-2100	15	10	to	to	ADP
cana-2100	15	11	the	the	DET
cana-2100	15	12	fact	fact	NOUN
cana-2100	15	13	that	that	SCONJ
cana-2100	15	14	a	a	DET
cana-2100	15	15	lot	lot	NOUN
cana-2100	15	16	of	of	ADP
cana-2100	15	17	everyday	everyday	ADJ
cana-2100	15	18	phenomena	phenomenon	NOUN
cana-2100	15	19	in	in	ADP
cana-2100	15	20	sciences	science	NOUN
cana-2100	15	21	,	,	PUNCT
cana-2100	15	22	economics	economic	NOUN
cana-2100	15	23	,	,	PUNCT
cana-2100	15	24	engineering	engineering	NOUN
cana-2100	15	25	,	,	PUNCT
cana-2100	15	26	space	space	NOUN
cana-2100	15	27	sciences	science	NOUN
cana-2100	15	28	,	,	PUNCT
cana-2100	15	29	and	and	CCONJ
cana-2100	15	30	control	control	NOUN
cana-2100	15	31	systems	system	NOUN
cana-2100	15	32	are	be	AUX
cana-2100	15	33	modeled	model	VERB
cana-2100	15	34	by	by	ADP
cana-2100	15	35	impulsive	impulsive	ADJ
cana-2100	15	36	delay	delay	NOUN
cana-2100	15	37	differential	differential	NOUN
cana-2100	15	38	equations	equation	NOUN
cana-2100	15	39	.	.	PUNCT
cana-2100	16	1	in	in	ADP
cana-2100	16	2	particular	particular	ADJ
cana-2100	16	3	,	,	PUNCT
cana-2100	16	4	ballinger	ballinger	PROPN
cana-2100	16	5	's	's	PART
cana-2100	16	6	ph.d	ph.d	PROPN
cana-2100	16	7	thesis	thesis	NOUN
cana-2100	16	8	and	and	CCONJ
cana-2100	16	9	his	his	PRON
cana-2100	16	10	subsequent	subsequent	ADJ
cana-2100	16	11	work	work	NOUN
cana-2100	16	12	provide	provide	VERB
cana-2100	16	13	a	a	DET
cana-2100	16	14	good	good	ADJ
cana-2100	16	15	working	working	NOUN
cana-2100	16	16	tool	tool	NOUN
cana-2100	16	17	for	for	ADP
cana-2100	16	18	further	further	ADJ
cana-2100	16	19	research	research	NOUN
cana-2100	16	20	work	work	NOUN
cana-2100	16	21	in	in	ADP
cana-2100	16	22	this	this	DET
cana-2100	16	23	area	area	NOUN
cana-2100	16	24	,	,	PUNCT
cana-2100	16	25	especially	especially	ADV
cana-2100	16	26	,	,	PUNCT
cana-2100	16	27	as	as	SCONJ
cana-2100	16	28	it	it	PRON
cana-2100	16	29	relates	relate	VERB
cana-2100	16	30	to	to	ADP
cana-2100	16	31	existence	existence	NOUN
cana-2100	16	32	,	,	PUNCT
cana-2100	16	33	uniqueness	uniqueness	NOUN
cana-2100	16	34	,	,	PUNCT
cana-2100	16	35	boundedness	boundedness	NOUN
cana-2100	16	36	,	,	PUNCT
cana-2100	16	37	continuation	continuation	NOUN
cana-2100	16	38	,	,	PUNCT
cana-2100	16	39	and	and	CCONJ
cana-2100	16	40	stability	stability	NOUN
cana-2100	16	41	of	of	ADP
cana-2100	16	42	solutions	solution	NOUN
cana-2100	16	43	of	of	ADP
cana-2100	16	44	impulsive	impulsive	ADJ
cana-2100	16	45	delay	delay	NOUN
cana-2100	16	46	differential	differential	ADJ
cana-2100	16	47	equations	equation	NOUN
cana-2100	16	48	(	(	PUNCT
cana-2100	16	49	idde	idde	VERB
cana-2100	16	50	)	)	PUNCT
cana-2100	16	51	.	.	PUNCT
cana-2100	17	1	this	this	PRON
cana-2100	17	2	happens	happen	VERB
cana-2100	17	3	to	to	PART
cana-2100	17	4	be	be	AUX
cana-2100	17	5	a	a	DET
cana-2100	17	6	fusion	fusion	NOUN
cana-2100	17	7	of	of	ADP
cana-2100	17	8	two	two	NUM
cana-2100	17	9	areas	area	NOUN
cana-2100	17	10	delay	delay	VERB
cana-2100	17	11	differential	differential	ADJ
cana-2100	17	12	equations	equation	NOUN
cana-2100	17	13	,	,	PUNCT
cana-2100	17	14	and	and	CCONJ
cana-2100	17	15	impulsive	impulsive	ADJ
cana-2100	17	16	differential	differential	ADJ
cana-2100	17	17	equations	equation	NOUN
cana-2100	17	18	.	.	PUNCT
cana-2100	18	1	several	several	ADJ
cana-2100	18	2	evolution	evolution	NOUN
cana-2100	18	3	processes	process	NOUN
cana-2100	18	4	in	in	ADP
cana-2100	18	5	sciences	science	NOUN
cana-2100	18	6	,	,	PUNCT
cana-2100	18	7	communications	communication	NOUN
cana-2100	18	8	on	on	ADP
cana-2100	18	9	applied	apply	VERB
cana-2100	18	10	nonlinear	nonlinear	ADJ
cana-2100	18	11	analysis	analysis	NOUN
cana-2100	18	12	issn	issn	NOUN
cana-2100	18	13	:	:	PUNCT
cana-2100	18	14	1074	1074	NUM
cana-2100	18	15	-	-	PUNCT
cana-2100	18	16	133x	133x	NUM
cana-2100	18	17	vol	vol	NOUN
cana-2100	18	18	32	32	NUM
cana-2100	18	19	no	no	NOUN
cana-2100	18	20	.	.	PUNCT
cana-2100	19	1	1s	1s	NUM
cana-2100	19	2	(	(	PUNCT
cana-2100	19	3	2025	2025	NUM
cana-2100	19	4	)	)	PUNCT
cana-2100	19	5	46	46	NUM
cana-2100	20	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-2100	20	2	engineering	engineering	NOUN
cana-2100	20	3	,	,	PUNCT
cana-2100	20	4	technology	technology	NOUN
cana-2100	20	5	,	,	PUNCT
cana-2100	20	6	economics	economic	NOUN
cana-2100	20	7	,	,	PUNCT
cana-2100	20	8	etc	etc	X
cana-2100	20	9	.	.	X
cana-2100	20	10	,	,	PUNCT
cana-2100	20	11	are	be	AUX
cana-2100	20	12	modeled	model	VERB
cana-2100	20	13	by	by	ADP
cana-2100	20	14	impulsive	impulsive	ADJ
cana-2100	20	15	differential	differential	ADJ
cana-2100	20	16	equations	equation	NOUN
cana-2100	20	17	with	with	ADP
cana-2100	20	18	delays	delay	NOUN
cana-2100	20	19	.	.	PUNCT
cana-2100	21	1	in	in	ADP
cana-2100	21	2	ordinary	ordinary	ADJ
cana-2100	21	3	or	or	CCONJ
cana-2100	21	4	delay	delay	VERB
cana-2100	21	5	differential	differential	ADJ
cana-2100	21	6	equations	equation	NOUN
cana-2100	21	7	,	,	PUNCT
cana-2100	21	8	the	the	DET
cana-2100	21	9	solutions	solution	NOUN
cana-2100	21	10	are	be	AUX
cana-2100	21	11	continuously	continuously	ADV
cana-2100	21	12	differentiable	differentiable	ADJ
cana-2100	21	13	,	,	PUNCT
cana-2100	21	14	at	at	ADP
cana-2100	21	15	least	least	ADJ
cana-2100	21	16	once	once	ADV
cana-2100	21	17	or	or	CCONJ
cana-2100	21	18	more	more	ADJ
cana-2100	21	19	,	,	PUNCT
cana-2100	21	20	whereas	whereas	SCONJ
cana-2100	21	21	impulsive	impulsive	ADJ
cana-2100	21	22	differential	differential	ADJ
cana-2100	21	23	equations	equation	NOUN
cana-2100	21	24	possess	possess	VERB
cana-2100	21	25	non	non	ADJ
cana-2100	21	26	-	-	ADJ
cana-2100	21	27	continuous	continuous	ADJ
cana-2100	21	28	(	(	PUNCT
cana-2100	21	29	piecewise	piecewise	NOUN
cana-2100	21	30	continuous	continuous	ADJ
cana-2100	21	31	)	)	PUNCT
cana-2100	21	32	solutions	solution	NOUN
cana-2100	21	33	.	.	PUNCT
cana-2100	22	1	intuitively	intuitively	ADV
cana-2100	22	2	,	,	PUNCT
cana-2100	22	3	it	it	PRON
cana-2100	22	4	is	be	AUX
cana-2100	22	5	expected	expect	VERB
cana-2100	22	6	that	that	SCONJ
cana-2100	22	7	the	the	DET
cana-2100	22	8	coupled	couple	VERB
cana-2100	22	9	problems	problem	NOUN
cana-2100	22	10	of	of	ADP
cana-2100	22	11	impulsive	impulsive	ADJ
cana-2100	22	12	delay	delay	NOUN
cana-2100	22	13	differential	differential	NOUN
cana-2100	22	14	equations	equation	NOUN
cana-2100	22	15	should	should	AUX
cana-2100	22	16	possess	possess	VERB
cana-2100	22	17	piecewise	piecewise	NOUN
cana-2100	22	18	continuously	continuously	ADV
cana-2100	22	19	differentiable	differentiable	ADJ
cana-2100	22	20	solutions	solution	NOUN
cana-2100	22	21	.	.	PUNCT
cana-2100	23	1	to	to	ADP
cana-2100	23	2	some	some	DET
cana-2100	23	3	extent	extent	NOUN
cana-2100	23	4	,	,	PUNCT
cana-2100	23	5	our	our	PRON
cana-2100	23	6	intuition	intuition	NOUN
cana-2100	23	7	may	may	AUX
cana-2100	23	8	be	be	AUX
cana-2100	23	9	true	true	ADJ
cana-2100	23	10	if	if	SCONJ
cana-2100	23	11	the	the	DET
cana-2100	23	12	delays	delay	NOUN
cana-2100	23	13	are	be	AUX
cana-2100	23	14	discrete	discrete	ADJ
cana-2100	23	15	.	.	PUNCT
cana-2100	24	1	when	when	SCONJ
cana-2100	24	2	continuous	continuous	ADJ
cana-2100	24	3	delays	delay	NOUN
cana-2100	24	4	interplay	interplay	NOUN
cana-2100	24	5	with	with	ADP
cana-2100	24	6	impulses	impulse	NOUN
cana-2100	24	7	,	,	PUNCT
cana-2100	24	8	the	the	DET
cana-2100	24	9	story	story	NOUN
cana-2100	24	10	may	may	AUX
cana-2100	24	11	become	become	VERB
cana-2100	24	12	significantly	significantly	ADV
cana-2100	24	13	different	different	ADJ
cana-2100	24	14	.	.	PUNCT
cana-2100	25	1	this	this	DET
cana-2100	25	2	surge	surge	NOUN
cana-2100	25	3	in	in	ADP
cana-2100	25	4	the	the	DET
cana-2100	25	5	number	number	NOUN
cana-2100	25	6	of	of	ADP
cana-2100	25	7	discontinuous	discontinuous	ADJ
cana-2100	25	8	points	point	NOUN
cana-2100	25	9	creates	create	VERB
cana-2100	25	10	several	several	ADJ
cana-2100	25	11	problems	problem	NOUN
cana-2100	25	12	as	as	SCONJ
cana-2100	25	13	it	it	PRON
cana-2100	25	14	pertains	pertain	VERB
cana-2100	25	15	to	to	PART
cana-2100	25	16	existence	existence	VERB
cana-2100	25	17	,	,	PUNCT
cana-2100	25	18	stability	stability	NOUN
cana-2100	25	19	/	/	SYM
cana-2100	25	20	instability	instability	NOUN
cana-2100	25	21	of	of	ADP
cana-2100	25	22	solutions	solution	NOUN
cana-2100	25	23	,	,	PUNCT
cana-2100	25	24	just	just	ADV
cana-2100	25	25	to	to	PART
cana-2100	25	26	mention	mention	VERB
cana-2100	25	27	a	a	DET
cana-2100	25	28	few	few	ADJ
cana-2100	25	29	.	.	PUNCT
cana-2100	26	1	since	since	SCONJ
cana-2100	26	2	the	the	DET
cana-2100	26	3	continuity	continuity	NOUN
cana-2100	26	4	properties	property	NOUN
cana-2100	26	5	of	of	ADP
cana-2100	26	6	the	the	DET
cana-2100	26	7	solutions	solution	NOUN
cana-2100	26	8	play	play	VERB
cana-2100	26	9	fundamental	fundamental	ADJ
cana-2100	26	10	roles	role	NOUN
cana-2100	26	11	in	in	ADP
cana-2100	26	12	the	the	DET
cana-2100	26	13	analysis	analysis	NOUN
cana-2100	26	14	of	of	ADP
cana-2100	26	15	their	their	PRON
cana-2100	26	16	behaviors	behavior	NOUN
cana-2100	26	17	,	,	PUNCT
cana-2100	26	18	the	the	DET
cana-2100	26	19	techniques	technique	NOUN
cana-2100	26	20	used	use	VERB
cana-2100	26	21	to	to	PART
cana-2100	26	22	handle	handle	VERB
cana-2100	26	23	the	the	DET
cana-2100	26	24	solutions	solution	NOUN
cana-2100	26	25	of	of	ADP
cana-2100	26	26	impulsive	impulsive	ADJ
cana-2100	26	27	delay	delay	NOUN
cana-2100	26	28	differential	differential	ADJ
cana-2100	26	29	equations	equation	NOUN
cana-2100	26	30	are	be	AUX
cana-2100	26	31	basically	basically	ADV
cana-2100	26	32	different	different	ADJ
cana-2100	26	33	from	from	ADP
cana-2100	26	34	those	those	PRON
cana-2100	26	35	of	of	ADP
cana-2100	26	36	ordinary	ordinary	ADJ
cana-2100	26	37	differential	differential	ADJ
cana-2100	26	38	equations	equation	NOUN
cana-2100	26	39	,	,	PUNCT
cana-2100	26	40	impulsive	impulsive	ADJ
cana-2100	26	41	differential	differential	ADJ
cana-2100	26	42	equations	equation	NOUN
cana-2100	26	43	and	and	CCONJ
cana-2100	26	44	delay	delay	VERB
cana-2100	26	45	differential	differential	ADJ
cana-2100	26	46	equations	equation	NOUN
cana-2100	26	47	.	.	PUNCT
cana-2100	27	1	however	however	ADV
cana-2100	27	2	,	,	PUNCT
cana-2100	27	3	some	some	DET
cana-2100	27	4	basic	basic	ADJ
cana-2100	27	5	concepts	concept	NOUN
cana-2100	27	6	are	be	AUX
cana-2100	27	7	still	still	ADV
cana-2100	27	8	valid	valid	ADJ
cana-2100	27	9	.	.	PUNCT
cana-2100	28	1	in	in	ADP
cana-2100	28	2	this	this	DET
cana-2100	28	3	study	study	NOUN
cana-2100	28	4	,	,	PUNCT
cana-2100	28	5	a	a	DET
cana-2100	28	6	system	system	NOUN
cana-2100	28	7	of	of	ADP
cana-2100	28	8	first	first	ADJ
cana-2100	28	9	-	-	PUNCT
cana-2100	28	10	order	order	NOUN
cana-2100	28	11	impulsive	impulsive	ADJ
cana-2100	28	12	differential	differential	ADJ
cana-2100	28	13	equations	equation	NOUN
cana-2100	28	14	with	with	ADP
cana-2100	28	15	continuous	continuous	ADJ
cana-2100	28	16	time	time	NOUN
cana-2100	28	17	-	-	PUNCT
cana-2100	28	18	dependent	dependent	ADJ
cana-2100	28	19	delays	delay	NOUN
cana-2100	28	20	and	and	CCONJ
cana-2100	28	21	fixed	fix	VERB
cana-2100	28	22	moments	moment	NOUN
cana-2100	28	23	of	of	ADP
cana-2100	28	24	impulse	impulse	ADJ
cana-2100	28	25	is	be	AUX
cana-2100	28	26	formulated	formulate	VERB
cana-2100	28	27	.	.	PUNCT
cana-2100	29	1	some	some	DET
cana-2100	29	2	recent	recent	ADJ
cana-2100	29	3	results	result	NOUN
cana-2100	29	4	in	in	ADP
cana-2100	29	5	impulsive	impulsive	ADJ
cana-2100	29	6	delay	delay	NOUN
cana-2100	29	7	differential	differential	NOUN
cana-2100	29	8	equations	equation	NOUN
cana-2100	29	9	with	with	ADP
cana-2100	29	10	constant	constant	ADJ
cana-2100	29	11	impulsive	impulsive	ADJ
cana-2100	29	12	jumps	jump	NOUN
cana-2100	29	13	.	.	PUNCT
cana-2100	30	1	preliminaries	preliminary	NOUN
cana-2100	30	2	the	the	DET
cana-2100	30	3	theory	theory	NOUN
cana-2100	30	4	of	of	ADP
cana-2100	30	5	impulsive	impulsive	ADJ
cana-2100	30	6	systems	system	NOUN
cana-2100	30	7	was	be	AUX
cana-2100	30	8	developed	develop	VERB
cana-2100	30	9	not	not	PART
cana-2100	30	10	long	long	ADV
cana-2100	30	11	ago	ago	ADV
cana-2100	30	12	as	as	ADP
cana-2100	30	13	an	an	DET
cana-2100	30	14	independent	independent	ADJ
cana-2100	30	15	area	area	NOUN
cana-2100	30	16	of	of	ADP
cana-2100	30	17	mathematical	mathematical	ADJ
cana-2100	30	18	analysis	analysis	NOUN
cana-2100	30	19	.	.	PUNCT
cana-2100	31	1	the	the	DET
cana-2100	31	2	development	development	NOUN
cana-2100	31	3	arose	arise	VERB
cana-2100	31	4	out	out	ADP
cana-2100	31	5	of	of	ADP
cana-2100	31	6	curiosity	curiosity	NOUN
cana-2100	31	7	to	to	PART
cana-2100	31	8	develop	develop	VERB
cana-2100	31	9	a	a	DET
cana-2100	31	10	mathematical	mathematical	ADJ
cana-2100	31	11	framework	framework	NOUN
cana-2100	31	12	that	that	PRON
cana-2100	31	13	truly	truly	ADV
cana-2100	31	14	describes	describe	VERB
cana-2100	31	15	physical	physical	ADJ
cana-2100	31	16	and	and	CCONJ
cana-2100	31	17	biological	biological	ADJ
cana-2100	31	18	processes	process	NOUN
cana-2100	31	19	as	as	SCONJ
cana-2100	31	20	they	they	PRON
cana-2100	31	21	occur	occur	VERB
cana-2100	31	22	in	in	ADP
cana-2100	31	23	nature	nature	NOUN
cana-2100	31	24	.	.	PUNCT
cana-2100	32	1	prior	prior	ADV
cana-2100	32	2	to	to	ADP
cana-2100	32	3	this	this	DET
cana-2100	32	4	noble	noble	ADJ
cana-2100	32	5	development	development	NOUN
cana-2100	32	6	,	,	PUNCT
cana-2100	32	7	scientists	scientist	NOUN
cana-2100	32	8	had	have	AUX
cana-2100	32	9	often	often	ADV
cana-2100	32	10	made	make	VERB
cana-2100	32	11	an	an	DET
cana-2100	32	12	underlying	underlying	ADJ
cana-2100	32	13	assumption	assumption	NOUN
cana-2100	32	14	that	that	SCONJ
cana-2100	32	15	the	the	DET
cana-2100	32	16	behaviors	behavior	NOUN
cana-2100	32	17	of	of	ADP
cana-2100	32	18	physical	physical	ADJ
cana-2100	32	19	and	and	CCONJ
cana-2100	32	20	biological	biological	ADJ
cana-2100	32	21	systems	system	NOUN
cana-2100	32	22	described	describe	VERB
cana-2100	32	23	by	by	ADP
cana-2100	32	24	ordinary	ordinary	ADJ
cana-2100	32	25	differential	differential	ADJ
cana-2100	32	26	equations	equation	NOUN
cana-2100	32	27	is	be	AUX
cana-2100	32	28	continuous	continuous	ADJ
cana-2100	32	29	and	and	CCONJ
cana-2100	32	30	integrable	integrable	ADJ
cana-2100	32	31	in	in	ADP
cana-2100	32	32	some	some	DET
cana-2100	32	33	sense	sense	NOUN
cana-2100	32	34	.	.	PUNCT
cana-2100	33	1	it	it	PRON
cana-2100	33	2	was	be	AUX
cana-2100	33	3	observed	observe	VERB
cana-2100	33	4	that	that	SCONJ
cana-2100	33	5	the	the	DET
cana-2100	33	6	state	state	NOUN
cana-2100	33	7	of	of	ADP
cana-2100	33	8	a	a	DET
cana-2100	33	9	system	system	NOUN
cana-2100	33	10	is	be	AUX
cana-2100	33	11	susceptible	susceptible	ADJ
cana-2100	33	12	to	to	ADP
cana-2100	33	13	changes	change	NOUN
cana-2100	33	14	,	,	PUNCT
cana-2100	33	15	and	and	CCONJ
cana-2100	33	16	in	in	ADP
cana-2100	33	17	some	some	DET
cana-2100	33	18	processes	process	NOUN
cana-2100	33	19	,	,	PUNCT
cana-2100	33	20	these	these	DET
cana-2100	33	21	changes	change	NOUN
cana-2100	33	22	are	be	AUX
cana-2100	33	23	often	often	ADV
cana-2100	33	24	characterized	characterize	VERB
cana-2100	33	25	by	by	ADP
cana-2100	33	26	short	short	ADJ
cana-2100	33	27	time	time	NOUN
cana-2100	33	28	perturbations	perturbation	NOUN
cana-2100	33	29	(	(	PUNCT
cana-2100	33	30	impulses	impulse	NOUN
cana-2100	33	31	)	)	PUNCT
cana-2100	33	32	whose	whose	DET
cana-2100	33	33	durations	duration	NOUN
cana-2100	33	34	are	be	AUX
cana-2100	33	35	negligible	negligible	ADJ
cana-2100	33	36	when	when	SCONJ
cana-2100	33	37	compared	compare	VERB
cana-2100	33	38	with	with	ADP
cana-2100	33	39	the	the	DET
cana-2100	33	40	total	total	ADJ
cana-2100	33	41	duration	duration	NOUN
cana-2100	33	42	of	of	ADP
cana-2100	33	43	their	their	PRON
cana-2100	33	44	entry	entry	NOUN
cana-2100	33	45	time	time	NOUN
cana-2100	33	46	evolution	evolution	NOUN
cana-2100	33	47	.	.	PUNCT
cana-2100	34	1	ides	ide	NOUN
cana-2100	34	2	are	be	AUX
cana-2100	34	3	adequate	adequate	ADJ
cana-2100	34	4	mathematical	mathematical	ADJ
cana-2100	34	5	models	model	NOUN
cana-2100	34	6	for	for	ADP
cana-2100	34	7	the	the	DET
cana-2100	34	8	description	description	NOUN
cana-2100	34	9	of	of	ADP
cana-2100	34	10	evolution	evolution	NOUN
cana-2100	34	11	processes	process	NOUN
cana-2100	34	12	characterized	characterize	VERB
cana-2100	34	13	by	by	ADP
cana-2100	34	14	the	the	DET
cana-2100	34	15	combination	combination	NOUN
cana-2100	34	16	of	of	ADP
cana-2100	34	17	continuous	continuous	ADJ
cana-2100	34	18	and	and	CCONJ
cana-2100	34	19	jump	jump	VERB
cana-2100	34	20	changes	change	NOUN
cana-2100	34	21	of	of	ADP
cana-2100	34	22	their	their	PRON
cana-2100	34	23	state	state	NOUN
cana-2100	34	24	.	.	PUNCT
cana-2100	35	1	for	for	ADP
cana-2100	35	2	the	the	DET
cana-2100	35	3	continuous	continuous	ADJ
cana-2100	35	4	change	change	NOUN
cana-2100	35	5	of	of	ADP
cana-2100	35	6	such	such	ADJ
cana-2100	35	7	processes	process	NOUN
cana-2100	35	8	,	,	PUNCT
cana-2100	35	9	ordinary	ordinary	ADJ
cana-2100	35	10	differential	differential	ADJ
cana-2100	35	11	equations	equation	NOUN
cana-2100	35	12	are	be	AUX
cana-2100	35	13	used	use	VERB
cana-2100	35	14	,	,	PUNCT
cana-2100	35	15	while	while	SCONJ
cana-2100	35	16	the	the	DET
cana-2100	35	17	moments	moment	NOUN
cana-2100	35	18	and	and	CCONJ
cana-2100	35	19	the	the	DET
cana-2100	35	20	magnitude	magnitude	NOUN
cana-2100	35	21	of	of	ADP
cana-2100	35	22	the	the	DET
cana-2100	35	23	jumps	jump	NOUN
cana-2100	35	24	are	be	AUX
cana-2100	35	25	given	give	VERB
cana-2100	35	26	by	by	ADP
cana-2100	35	27	the	the	DET
cana-2100	35	28	jump	jump	NOUN
cana-2100	35	29	conditions	condition	NOUN
cana-2100	35	30	.	.	PUNCT
cana-2100	36	1	impulsive	impulsive	ADJ
cana-2100	36	2	systems	system	NOUN
cana-2100	36	3	are	be	AUX
cana-2100	36	4	systems	system	NOUN
cana-2100	36	5	whose	whose	DET
cana-2100	36	6	states	state	NOUN
cana-2100	36	7	are	be	AUX
cana-2100	36	8	characterized	characterize	VERB
cana-2100	36	9	by	by	ADP
cana-2100	36	10	small	small	ADJ
cana-2100	36	11	perturbations	perturbation	NOUN
cana-2100	36	12	(	(	PUNCT
cana-2100	36	13	impulses	impulse	NOUN
cana-2100	36	14	)	)	PUNCT
cana-2100	36	15	in	in	ADP
cana-2100	36	16	the	the	DET
cana-2100	36	17	form	form	NOUN
cana-2100	36	18	of	of	ADP
cana-2100	36	19	jumps	jump	NOUN
cana-2100	36	20	.	.	PUNCT
cana-2100	37	1	ides	ide	NOUN
cana-2100	37	2	are	be	AUX
cana-2100	37	3	usually	usually	ADV
cana-2100	37	4	defined	define	VERB
cana-2100	37	5	by	by	ADP
cana-2100	37	6	a	a	DET
cana-2100	37	7	pair	pair	NOUN
cana-2100	37	8	of	of	ADP
cana-2100	37	9	equations	equation	NOUN
cana-2100	37	10	an	an	DET
cana-2100	37	11	ordinary	ordinary	ADJ
cana-2100	37	12	differential	differential	ADJ
cana-2100	37	13	equation	equation	NOUN
cana-2100	37	14	to	to	PART
cana-2100	37	15	be	be	AUX
cana-2100	37	16	satisfied	satisfied	ADJ
cana-2100	37	17	during	during	ADP
cana-2100	37	18	the	the	DET
cana-2100	37	19	continuous	continuous	ADJ
cana-2100	37	20	portion	portion	NOUN
cana-2100	37	21	of	of	ADP
cana-2100	37	22	the	the	DET
cana-2100	37	23	evolution	evolution	NOUN
cana-2100	37	24	,	,	PUNCT
cana-2100	37	25	and	and	CCONJ
cana-2100	37	26	difference	difference	NOUN
cana-2100	37	27	equations	equation	NOUN
cana-2100	37	28	defining	define	VERB
cana-2100	37	29	the	the	DET
cana-2100	37	30	change	change	NOUN
cana-2100	37	31	of	of	ADP
cana-2100	37	32	state	state	NOUN
cana-2100	37	33	at	at	ADP
cana-2100	37	34	the	the	DET
cana-2100	37	35	discrete	discrete	ADJ
cana-2100	37	36	impulsive	impulsive	ADJ
cana-2100	37	37	points	point	NOUN
cana-2100	37	38	.	.	PUNCT
cana-2100	38	1	this	this	PRON
cana-2100	38	2	is	be	AUX
cana-2100	38	3	the	the	DET
cana-2100	38	4	main	main	ADJ
cana-2100	38	5	formulation	formulation	NOUN
cana-2100	38	6	of	of	ADP
cana-2100	38	7	early	early	ADJ
cana-2100	38	8	scholars	scholar	NOUN
cana-2100	38	9	such	such	ADJ
cana-2100	38	10	as	as	ADP
cana-2100	38	11	bainov	bainov	NOUN
cana-2100	38	12	,	,	PUNCT
cana-2100	38	13	simeonov	simeonov	PROPN
cana-2100	38	14	,	,	PUNCT
cana-2100	38	15	lakshminkatham	lakshminkatham	PROPN
cana-2100	38	16	,	,	PUNCT
cana-2100	38	17	gopalsamy	gopalsamy	PROPN
cana-2100	38	18	,	,	PUNCT
cana-2100	38	19	zhang	zhang	PROPN
cana-2100	38	20	,	,	PUNCT
cana-2100	38	21	among	among	ADP
cana-2100	38	22	others	other	NOUN
cana-2100	38	23	.	.	PUNCT
cana-2100	39	1	solutions	solution	NOUN
cana-2100	39	2	are	be	AUX
cana-2100	39	3	usually	usually	ADV
cana-2100	39	4	considered	consider	VERB
cana-2100	39	5	to	to	PART
cana-2100	39	6	be	be	AUX
cana-2100	39	7	piecewise	piecewise	NOUN
cana-2100	39	8	continuously	continuously	ADV
cana-2100	39	9	differentiable	differentiable	ADJ
cana-2100	39	10	functions	function	NOUN
cana-2100	39	11	with	with	ADP
cana-2100	39	12	discontinuities	discontinuity	NOUN
cana-2100	39	13	occurring	occur	VERB
cana-2100	39	14	at	at	ADP
cana-2100	39	15	the	the	DET
cana-2100	39	16	impulsive	impulsive	ADJ
cana-2100	39	17	times	time	NOUN
cana-2100	39	18	.	.	PUNCT
cana-2100	40	1	impulsive	impulsive	ADJ
cana-2100	40	2	differential	differential	ADJ
cana-2100	40	3	equations	equation	NOUN
cana-2100	40	4	with	with	ADP
cana-2100	40	5	fixed	fix	VERB
cana-2100	40	6	moments	moment	NOUN
cana-2100	40	7	of	of	ADP
cana-2100	40	8	impulsive	impulsive	ADJ
cana-2100	40	9	effects	effect	NOUN
cana-2100	40	10	have	have	VERB
cana-2100	40	11	the	the	DET
cana-2100	40	12	form	form	NOUN
cana-2100	40	13	:	:	PUNCT
cana-2100	40	14	{	{	PUNCT
cana-2100	40	15	𝑥	𝑥	PRON
cana-2100	40	16	′(𝑡)=	′(𝑡)=	NOUN
cana-2100	40	17	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	40	18	,	,	PUNCT
cana-2100	40	19	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	40	20	)	)	PUNCT
cana-2100	40	21	)	)	PUNCT
cana-2100	40	22	,	,	PUNCT
cana-2100	40	23	⬚	⬚	PROPN
cana-2100	41	1	∀𝑡	∀𝑡	NOUN
cana-2100	41	2	∈	∈	PROPN
cana-2100	41	3	𝑇	𝑇	PROPN
cana-2100	41	4	∖	∖	NOUN
cana-2100	41	5	𝑆	𝑆	PROPN
cana-2100	41	6	δ𝑥(𝑡𝑘)=	δ𝑥(𝑡𝑘)=	VERB
cana-2100	41	7	𝑓(𝑡𝑘	𝑓(𝑡𝑘	PROPN
cana-2100	41	8	,	,	PUNCT
cana-2100	41	9	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NOUN
cana-2100	41	10	)	)	PUNCT
cana-2100	41	11	)	)	PUNCT
cana-2100	41	12	,	,	PUNCT
cana-2100	41	13	⬚	⬚	NUM
cana-2100	41	14	∀𝑡𝑘	∀𝑡𝑘	NOUN
cana-2100	41	15	∈	∈	PROPN
cana-2100	41	16	𝑆	𝑆	PROPN
cana-2100	41	17	where	where	SCONJ
cana-2100	41	18	𝑇	𝑇	PROPN
cana-2100	41	19	⊂	⊂	PROPN
cana-2100	41	20	𝑅	𝑅	PROPN
cana-2100	41	21	,	,	PUNCT
cana-2100	41	22	(	(	PUNCT
cana-2100	41	23	𝑡	𝑡	NOUN
cana-2100	41	24	,	,	PUNCT
cana-2100	41	25	𝑥	𝑥	NOUN
cana-2100	41	26	)	)	PUNCT
cana-2100	41	27	∈	∈	PROPN
cana-2100	41	28	ω	ω	NUM
cana-2100	41	29	⊂	⊂	PROPN
cana-2100	41	30	𝑅	𝑅	PROPN
cana-2100	41	31	×	×	NOUN
cana-2100	41	32	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	41	33	and	and	CCONJ
cana-2100	41	34	the	the	DET
cana-2100	41	35	real	real	ADJ
cana-2100	41	36	numerical	numerical	ADJ
cana-2100	41	37	sequence	sequence	NOUN
cana-2100	41	38	𝑆	𝑆	PROPN
cana-2100	41	39	=	=	SYM
cana-2100	41	40	{	{	PUNCT
cana-2100	41	41	𝑡𝑘}𝑘=1	𝑡𝑘}𝑘=1	VERB
cana-2100	41	42	∞	∞	NUM
cana-2100	41	43	increases	increase	NOUN
cana-2100	41	44	and	and	CCONJ
cana-2100	41	45	has	have	VERB
cana-2100	41	46	no	no	DET
cana-2100	41	47	finite	finite	ADJ
cana-2100	41	48	accumulation	accumulation	NOUN
cana-2100	41	49	point	point	NOUN
cana-2100	41	50	.	.	PUNCT
cana-2100	42	1	in	in	ADP
cana-2100	42	2	the	the	DET
cana-2100	42	3	case	case	NOUN
cana-2100	42	4	of	of	ADP
cana-2100	42	5	unfixed	unfixed	ADJ
cana-2100	42	6	moments	moment	NOUN
cana-2100	42	7	of	of	ADP
cana-2100	42	8	impulsive	impulsive	ADJ
cana-2100	42	9	effects	effect	NOUN
cana-2100	42	10	,	,	PUNCT
cana-2100	42	11	the	the	DET
cana-2100	42	12	impulse	impulse	ADJ
cana-2100	42	13	points	point	NOUN
cana-2100	42	14	may	may	AUX
cana-2100	42	15	be	be	AUX
cana-2100	42	16	time	time	NOUN
cana-2100	42	17	and	and	CCONJ
cana-2100	42	18	state	state	NOUN
cana-2100	42	19	dependent	dependent	ADJ
cana-2100	42	20	.	.	PUNCT
cana-2100	43	1	that	that	PRON
cana-2100	43	2	is	be	AUX
cana-2100	43	3	,	,	PUNCT
cana-2100	43	4	𝑡𝑘	𝑡𝑘	ADV
cana-2100	43	5	:	:	PUNCT
cana-2100	43	6	=	=	NUM
cana-2100	43	7	𝑡𝑘(𝑡	𝑡𝑘(𝑡	NOUN
cana-2100	43	8	,	,	PUNCT
cana-2100	43	9	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	43	10	)	)	PUNCT
cana-2100	43	11	)	)	PUNCT
cana-2100	43	12	.	.	PUNCT
cana-2100	44	1	when	when	SCONJ
cana-2100	44	2	the	the	DET
cana-2100	44	3	function	function	NOUN
cana-2100	44	4	𝑡𝑘	𝑡𝑘	ADV
cana-2100	44	5	depends	depend	VERB
cana-2100	44	6	on	on	ADP
cana-2100	44	7	the	the	DET
cana-2100	44	8	state	state	NOUN
cana-2100	44	9	of	of	ADP
cana-2100	44	10	the	the	DET
cana-2100	44	11	given	give	VERB
cana-2100	44	12	system	system	NOUN
cana-2100	44	13	,	,	PUNCT
cana-2100	44	14	it	it	PRON
cana-2100	44	15	is	be	AUX
cana-2100	44	16	said	say	VERB
cana-2100	44	17	to	to	PART
cana-2100	44	18	have	have	VERB
cana-2100	44	19	impulses	impulse	NOUN
cana-2100	44	20	at	at	ADP
cana-2100	44	21	variable	variable	ADJ
cana-2100	44	22	times	time	NOUN
cana-2100	44	23	.	.	PUNCT
cana-2100	45	1	this	this	PRON
cana-2100	45	2	is	be	AUX
cana-2100	45	3	reflected	reflect	VERB
cana-2100	45	4	in	in	ADP
cana-2100	45	5	the	the	DET
cana-2100	45	6	fact	fact	NOUN
cana-2100	45	7	that	that	SCONJ
cana-2100	45	8	different	different	ADJ
cana-2100	45	9	solutions	solution	NOUN
cana-2100	45	10	will	will	AUX
cana-2100	45	11	tend	tend	VERB
cana-2100	45	12	to	to	PART
cana-2100	45	13	undergo	undergo	VERB
cana-2100	45	14	impulses	impulse	NOUN
cana-2100	45	15	at	at	ADP
cana-2100	45	16	different	different	ADJ
cana-2100	45	17	times	time	NOUN
cana-2100	45	18	.	.	PUNCT
cana-2100	46	1	however	however	ADV
cana-2100	46	2	,	,	PUNCT
cana-2100	46	3	if	if	SCONJ
cana-2100	46	4	the	the	DET
cana-2100	46	5	functions	function	NOUN
cana-2100	46	6	𝑡𝑘	𝑡𝑘	ADV
cana-2100	46	7	are	be	AUX
cana-2100	46	8	communications	communication	NOUN
cana-2100	46	9	on	on	ADP
cana-2100	46	10	applied	apply	VERB
cana-2100	46	11	nonlinear	nonlinear	ADJ
cana-2100	46	12	analysis	analysis	NOUN
cana-2100	46	13	issn	issn	NOUN
cana-2100	46	14	:	:	PUNCT
cana-2100	46	15	1074	1074	NUM
cana-2100	46	16	-	-	PUNCT
cana-2100	46	17	133x	133x	NUM
cana-2100	46	18	vol	vol	NOUN
cana-2100	46	19	32	32	NUM
cana-2100	46	20	no	no	NOUN
cana-2100	46	21	.	.	PUNCT
cana-2100	47	1	1s	1s	NUM
cana-2100	47	2	(	(	PUNCT
cana-2100	47	3	2025	2025	NUM
cana-2100	47	4	)	)	PUNCT
cana-2100	47	5	47	47	NUM
cana-2100	47	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2100	47	7	all	all	DET
cana-2100	47	8	constants	constant	NOUN
cana-2100	47	9	,	,	PUNCT
cana-2100	47	10	the	the	DET
cana-2100	47	11	system	system	NOUN
cana-2100	47	12	is	be	AUX
cana-2100	47	13	said	say	VERB
cana-2100	47	14	to	to	PART
cana-2100	47	15	have	have	VERB
cana-2100	47	16	impulses	impulse	NOUN
cana-2100	47	17	at	at	ADP
cana-2100	47	18	fixed	fix	VERB
cana-2100	47	19	times	time	NOUN
cana-2100	47	20	which	which	PRON
cana-2100	47	21	implies	imply	VERB
cana-2100	47	22	that	that	SCONJ
cana-2100	47	23	all	all	DET
cana-2100	47	24	solutions	solution	NOUN
cana-2100	47	25	undergo	undergo	VERB
cana-2100	47	26	impulse	impulse	ADJ
cana-2100	47	27	actions	action	NOUN
cana-2100	47	28	at	at	ADP
cana-2100	47	29	the	the	DET
cana-2100	47	30	same	same	ADJ
cana-2100	47	31	time	time	NOUN
cana-2100	47	32	.	.	PUNCT
cana-2100	48	1	it	it	PRON
cana-2100	48	2	is	be	AUX
cana-2100	48	3	observed	observe	VERB
cana-2100	48	4	that	that	SCONJ
cana-2100	48	5	the	the	DET
cana-2100	48	6	question	question	NOUN
cana-2100	48	7	of	of	ADP
cana-2100	48	8	the	the	DET
cana-2100	48	9	existence	existence	NOUN
cana-2100	48	10	of	of	ADP
cana-2100	48	11	solutions	solution	NOUN
cana-2100	48	12	of	of	ADP
cana-2100	48	13	the	the	DET
cana-2100	48	14	system	system	NOUN
cana-2100	48	15	is	be	AUX
cana-2100	48	16	non	non	ADJ
cana-2100	48	17	-	-	ADJ
cana-2100	48	18	trivial	trivial	ADJ
cana-2100	48	19	when	when	SCONJ
cana-2100	48	20	impulses	impulse	NOUN
cana-2100	48	21	occur	occur	VERB
cana-2100	48	22	at	at	ADP
cana-2100	48	23	variable	variable	ADJ
cana-2100	48	24	times	time	NOUN
cana-2100	48	25	.	.	PUNCT
cana-2100	49	1	the	the	DET
cana-2100	49	2	precise	precise	ADJ
cana-2100	49	3	notion	notion	NOUN
cana-2100	49	4	of	of	ADP
cana-2100	49	5	what	what	PRON
cana-2100	49	6	a	a	DET
cana-2100	49	7	solution	solution	NOUN
cana-2100	49	8	is	be	AUX
cana-2100	49	9	must	must	AUX
cana-2100	49	10	be	be	AUX
cana-2100	49	11	carefully	carefully	ADV
cana-2100	49	12	stated	state	VERB
cana-2100	49	13	.	.	PUNCT
cana-2100	50	1	it	it	PRON
cana-2100	50	2	is	be	AUX
cana-2100	50	3	fairly	fairly	ADV
cana-2100	50	4	clear	clear	ADJ
cana-2100	50	5	that	that	SCONJ
cana-2100	50	6	solutions	solution	NOUN
cana-2100	50	7	should	should	AUX
cana-2100	50	8	be	be	AUX
cana-2100	50	9	piecewise	piecewise	NOUN
cana-2100	50	10	continuous	continuous	ADJ
cana-2100	50	11	and	and	CCONJ
cana-2100	50	12	in	in	ADP
cana-2100	50	13	fact	fact	NOUN
cana-2100	50	14	piecewise	piecewise	NOUN
cana-2100	50	15	continuously	continuously	ADV
cana-2100	50	16	differentiable	differentiable	VERB
cana-2100	50	17	(	(	PUNCT
cana-2100	50	18	or	or	CCONJ
cana-2100	50	19	piecewise	piecewise	VERB
cana-2100	50	20	absolutely	absolutely	ADV
cana-2100	50	21	differentiable	differentiable	ADJ
cana-2100	50	22	when	when	SCONJ
cana-2100	50	23	considering	consider	VERB
cana-2100	50	24	generalized	generalized	ADJ
cana-2100	50	25	types	type	NOUN
cana-2100	50	26	of	of	ADP
cana-2100	50	27	solutions	solution	NOUN
cana-2100	50	28	)	)	PUNCT
cana-2100	50	29	.	.	PUNCT
cana-2100	51	1	a	a	DET
cana-2100	51	2	solution	solution	NOUN
cana-2100	51	3	will	will	AUX
cana-2100	51	4	undergo	undergo	VERB
cana-2100	51	5	simple	simple	ADJ
cana-2100	51	6	jump	jump	NOUN
cana-2100	51	7	discontinuity	discontinuity	NOUN
cana-2100	51	8	when	when	SCONJ
cana-2100	51	9	it	it	PRON
cana-2100	51	10	intersects	intersect	VERB
cana-2100	51	11	impulse	impulse	ADJ
cana-2100	51	12	hypersurfaces	hypersurface	NOUN
cana-2100	51	13	.	.	PUNCT
cana-2100	52	1	even	even	ADV
cana-2100	52	2	after	after	ADP
cana-2100	52	3	focusing	focus	VERB
cana-2100	52	4	on	on	ADP
cana-2100	52	5	a	a	DET
cana-2100	52	6	particular	particular	ADJ
cana-2100	52	7	class	class	NOUN
cana-2100	52	8	of	of	ADP
cana-2100	52	9	relations	relation	NOUN
cana-2100	52	10	𝑡(𝑠	𝑡(𝑠	NOUN
cana-2100	52	11	,	,	PUNCT
cana-2100	52	12	𝑥(𝑠	𝑥(𝑠	NOUN
cana-2100	52	13	)	)	PUNCT
cana-2100	52	14	)	)	PUNCT
cana-2100	53	1	=	=	SYM
cana-2100	53	2	0	0	NUM
cana-2100	53	3	given	give	VERB
cana-2100	53	4	by	by	ADP
cana-2100	53	5	impulse	impulse	ADJ
cana-2100	53	6	hypersurfaces	hypersurface	NOUN
cana-2100	53	7	,	,	PUNCT
cana-2100	53	8	impulsive	impulsive	ADJ
cana-2100	53	9	differential	differential	ADJ
cana-2100	53	10	equations	equation	NOUN
cana-2100	53	11	still	still	ADV
cana-2100	53	12	exhibit	exhibit	VERB
cana-2100	53	13	some	some	DET
cana-2100	53	14	unusual	unusual	ADJ
cana-2100	53	15	behaviour	behaviour	NOUN
cana-2100	53	16	[	[	X
cana-2100	53	17	3	3	NUM
cana-2100	53	18	]	]	PUNCT
cana-2100	53	19	.	.	PUNCT
cana-2100	54	1	in	in	ADP
cana-2100	54	2	this	this	DET
cana-2100	54	3	study	study	NOUN
cana-2100	54	4	,	,	PUNCT
cana-2100	54	5	focus	focus	NOUN
cana-2100	54	6	will	will	AUX
cana-2100	54	7	be	be	AUX
cana-2100	54	8	placed	place	VERB
cana-2100	54	9	only	only	ADV
cana-2100	54	10	on	on	ADP
cana-2100	54	11	those	those	DET
cana-2100	54	12	equations	equation	NOUN
cana-2100	54	13	with	with	ADP
cana-2100	54	14	fixed	fix	VERB
cana-2100	54	15	moments	moment	NOUN
cana-2100	54	16	of	of	ADP
cana-2100	54	17	impulse	impulse	ADJ
cana-2100	54	18	effects	effect	NOUN
cana-2100	54	19	.	.	PUNCT
cana-2100	55	1	be	be	AUX
cana-2100	55	2	as	as	SCONJ
cana-2100	55	3	it	it	PRON
cana-2100	55	4	may	may	AUX
cana-2100	55	5	,	,	PUNCT
cana-2100	55	6	to	to	PART
cana-2100	55	7	obtain	obtain	VERB
cana-2100	55	8	or	or	CCONJ
cana-2100	55	9	discuss	discuss	VERB
cana-2100	55	10	the	the	DET
cana-2100	55	11	solution	solution	NOUN
cana-2100	55	12	of	of	ADP
cana-2100	55	13	an	an	DET
cana-2100	55	14	impulsive	impulsive	ADJ
cana-2100	55	15	differential	differential	ADJ
cana-2100	55	16	equation	equation	NOUN
cana-2100	55	17	,	,	PUNCT
cana-2100	55	18	certain	certain	ADJ
cana-2100	55	19	peculiarities	peculiarity	NOUN
cana-2100	55	20	of	of	ADP
cana-2100	55	21	the	the	DET
cana-2100	55	22	model	model	NOUN
cana-2100	55	23	must	must	AUX
cana-2100	55	24	be	be	AUX
cana-2100	55	25	taken	take	VERB
cana-2100	55	26	into	into	ADP
cana-2100	55	27	cognizance	cognizance	NOUN
cana-2100	55	28	.	.	PUNCT
cana-2100	56	1	it	it	PRON
cana-2100	56	2	assume	assume	VERB
cana-2100	56	3	that	that	SCONJ
cana-2100	56	4	for	for	SCONJ
cana-2100	56	5	𝑡	𝑡	PROPN
cana-2100	56	6	∈	∈	PROPN
cana-2100	56	7	𝑇	𝑇	PROPN
cana-2100	56	8	∖	∖	PROPN
cana-2100	56	9	𝑆	𝑆	PROPN
cana-2100	56	10	,	,	PUNCT
cana-2100	56	11	the	the	DET
cana-2100	56	12	solution	solution	NOUN
cana-2100	56	13	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	56	14	)	)	PUNCT
cana-2100	56	15	of	of	ADP
cana-2100	56	16	the	the	DET
cana-2100	56	17	earlier	early	ADV
cana-2100	56	18	stated	state	VERB
cana-2100	56	19	equation	equation	NOUN
cana-2100	56	20	is	be	AUX
cana-2100	56	21	determined	determine	VERB
cana-2100	56	22	by	by	ADP
cana-2100	56	23	the	the	DET
cana-2100	56	24	ordinary	ordinary	ADJ
cana-2100	56	25	differential	differential	ADJ
cana-2100	56	26	equation	equation	NOUN
cana-2100	56	27	𝑥	𝑥	PRON
cana-2100	56	28	′(𝑡	′(𝑡	NOUN
cana-2100	56	29	)	)	PUNCT
cana-2100	56	30	=	=	PUNCT
cana-2100	56	31	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	56	32	,	,	PUNCT
cana-2100	56	33	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	56	34	)	)	PUNCT
cana-2100	56	35	)	)	PUNCT
cana-2100	56	36	.	.	PUNCT
cana-2100	57	1	for	for	ADP
cana-2100	57	2	𝑡	𝑡	PROPN
cana-2100	57	3	∈	∈	PROPN
cana-2100	57	4	𝑆	𝑆	PROPN
cana-2100	57	5	,	,	PUNCT
cana-2100	57	6	a	a	DET
cana-2100	57	7	change	change	NOUN
cana-2100	57	8	by	by	ADP
cana-2100	57	9	jump	jump	NOUN
cana-2100	57	10	of	of	ADP
cana-2100	57	11	the	the	DET
cana-2100	57	12	solution	solution	NOUN
cana-2100	57	13	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	57	14	)	)	PUNCT
cana-2100	57	15	occurs	occur	VERB
cana-2100	57	16	so	so	SCONJ
cana-2100	57	17	that	that	SCONJ
cana-2100	57	18	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NUM
cana-2100	57	19	−	−	NOUN
cana-2100	57	20	)	)	PUNCT
cana-2100	57	21	=	=	PUNCT
cana-2100	58	1	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NOUN
cana-2100	58	2	)	)	PUNCT
cana-2100	58	3	and	and	CCONJ
cana-2100	58	4	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NUM
cana-2100	58	5	+	+	NOUN
cana-2100	58	6	)	)	PUNCT
cana-2100	58	7	=	=	SYM
cana-2100	58	8	𝑥(𝑡𝑘	𝑥(𝑡𝑘	X
cana-2100	58	9	)	)	PUNCT
cana-2100	58	10	+	+	NUM
cana-2100	58	11	δ𝑥(𝑡𝑘	δ𝑥(𝑡𝑘	NOUN
cana-2100	58	12	)	)	PUNCT
cana-2100	58	13	=	=	PUNCT
cana-2100	58	14	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NOUN
cana-2100	58	15	)	)	PUNCT
cana-2100	58	16	+	+	CCONJ
cana-2100	58	17	𝑓(𝑡𝑘	𝑓(𝑡𝑘	NOUN
cana-2100	58	18	,	,	PUNCT
cana-2100	58	19	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NOUN
cana-2100	58	20	)	)	PUNCT
cana-2100	58	21	)	)	PUNCT
cana-2100	58	22	.	.	PUNCT
cana-2100	59	1	after	after	ADP
cana-2100	59	2	the	the	DET
cana-2100	59	3	jump	jump	NOUN
cana-2100	59	4	,	,	PUNCT
cana-2100	59	5	at	at	ADP
cana-2100	59	6	the	the	DET
cana-2100	59	7	moment	moment	NOUN
cana-2100	59	8	𝑡	𝑡	X
cana-2100	59	9	=	=	VERB
cana-2100	59	10	𝑡𝑘	𝑡𝑘	ADV
cana-2100	59	11	,	,	PUNCT
cana-2100	59	12	the	the	DET
cana-2100	59	13	solution	solution	NOUN
cana-2100	59	14	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	59	15	)	)	PUNCT
cana-2100	59	16	of	of	ADP
cana-2100	59	17	the	the	DET
cana-2100	59	18	system	system	NOUN
cana-2100	59	19	coincides	coincide	VERB
cana-2100	59	20	with	with	ADP
cana-2100	59	21	the	the	DET
cana-2100	59	22	solution	solution	NOUN
cana-2100	59	23	𝑦(𝑡	𝑦(𝑡	NUM
cana-2100	59	24	)	)	PUNCT
cana-2100	59	25	of	of	ADP
cana-2100	59	26	the	the	DET
cana-2100	59	27	initial	initial	ADJ
cana-2100	59	28	value	value	NOUN
cana-2100	59	29	problem	problem	NOUN
cana-2100	59	30	[	[	X
cana-2100	59	31	15	15	NUM
cana-2100	59	32	]	]	X
cana-2100	59	33	:	:	PUNCT
cana-2100	59	34	{	{	PUNCT
cana-2100	59	35	𝑦	𝑦	NOUN
cana-2100	59	36	′(𝑡	′(𝑡	NOUN
cana-2100	59	37	)	)	PUNCT
cana-2100	59	38	=	=	PUNCT
cana-2100	60	1	𝑓(𝑡	𝑓(𝑡	PROPN
cana-2100	60	2	,	,	PUNCT
cana-2100	60	3	𝑦(𝑡)),𝑡𝑘	𝑦(𝑡)),𝑡𝑘	PROPN
cana-2100	60	4	<	<	X
cana-2100	60	5	𝑡	𝑡	X
cana-2100	60	6	≤𝑘+1	≤𝑘+1	PROPN
cana-2100	60	7	δ𝑦(𝑡𝑘	δ𝑦(𝑡𝑘	NOUN
cana-2100	60	8	)	)	PUNCT
cana-2100	60	9	=	=	PUNCT
cana-2100	60	10	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NUM
cana-2100	60	11	+	+	NOUN
cana-2100	60	12	)	)	PUNCT
cana-2100	60	13	,	,	PUNCT
cana-2100	60	14	𝑡	𝑡	PROPN
cana-2100	60	15	=	=	VERB
cana-2100	60	16	𝑡𝑘	𝑡𝑘	PROPN
cana-2100	60	17	∈	∈	PROPN
cana-2100	60	18	𝑆	𝑆	PROPN
cana-2100	60	19	this	this	PRON
cana-2100	60	20	simply	simply	ADV
cana-2100	60	21	means	mean	VERB
cana-2100	60	22	that	that	SCONJ
cana-2100	60	23	after	after	ADP
cana-2100	60	24	the	the	DET
cana-2100	60	25	jump	jump	NOUN
cana-2100	60	26	at	at	ADP
cana-2100	60	27	𝑡	𝑡	PROPN
cana-2100	60	28	=	=	VERB
cana-2100	60	29	𝑡𝑘	𝑡𝑘	ADV
cana-2100	60	30	,	,	PUNCT
cana-2100	60	31	a	a	DET
cana-2100	60	32	new	new	ADJ
cana-2100	60	33	function	function	NOUN
cana-2100	60	34	𝑦(𝑡	𝑦(𝑡	NOUN
cana-2100	60	35	)	)	PUNCT
cana-2100	60	36	takes	take	VERB
cana-2100	60	37	over	over	ADP
cana-2100	60	38	control	control	NOUN
cana-2100	60	39	from	from	ADP
cana-2100	60	40	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	60	41	)	)	PUNCT
cana-2100	60	42	.	.	PUNCT
cana-2100	61	1	let	let	VERB
cana-2100	61	2	𝑇	𝑇	PROPN
cana-2100	61	3	⊂	⊂	PROPN
cana-2100	61	4	𝑅	𝑅	PROPN
cana-2100	61	5	be	be	AUX
cana-2100	61	6	a	a	DET
cana-2100	61	7	set	set	NOUN
cana-2100	61	8	of	of	ADP
cana-2100	61	9	time	time	NOUN
cana-2100	61	10	points	point	NOUN
cana-2100	61	11	and	and	CCONJ
cana-2100	61	12	let	let	VERB
cana-2100	61	13	our	our	PRON
cana-2100	61	14	processes	process	NOUN
cana-2100	61	15	take	take	VERB
cana-2100	61	16	place	place	NOUN
cana-2100	61	17	in	in	ADP
cana-2100	61	18	𝑅𝑛.	𝑅𝑛.	PROPN
cana-2100	61	19	also	also	ADV
cana-2100	61	20	,	,	PUNCT
cana-2100	61	21	let	let	VERB
cana-2100	61	22	these	these	DET
cana-2100	61	23	processes	process	NOUN
cana-2100	61	24	be	be	AUX
cana-2100	61	25	described	describe	VERB
cana-2100	61	26	by	by	ADP
cana-2100	61	27	𝑥	𝑥	NOUN
cana-2100	61	28	:	:	PUNCT
cana-2100	61	29	𝑇	𝑇	PROPN
cana-2100	61	30	→	→	SYM
cana-2100	61	31	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	61	32	state	state	NOUN
cana-2100	61	33	functions	function	NOUN
cana-2100	61	34	,	,	PUNCT
cana-2100	61	35	assuming	assume	VERB
cana-2100	61	36	that	that	SCONJ
cana-2100	61	37	they	they	PRON
cana-2100	61	38	may	may	AUX
cana-2100	61	39	be	be	AUX
cana-2100	61	40	influenced	influence	VERB
cana-2100	61	41	by	by	ADP
cana-2100	61	42	past	past	ADJ
cana-2100	61	43	events	event	NOUN
cana-2100	61	44	defined	define	VERB
cana-2100	61	45	by	by	ADP
cana-2100	61	46	delay	delay	NOUN
cana-2100	61	47	functions	function	NOUN
cana-2100	61	48	ℎ𝑗	ℎ𝑗	PRON
cana-2100	61	49	:	:	PUNCT
cana-2100	61	50	𝑇	𝑇	PROPN
cana-2100	61	51	→	→	SYM
cana-2100	61	52	𝑅+	𝑅+	PROPN
cana-2100	61	53	.	.	PUNCT
cana-2100	62	1	the	the	DET
cana-2100	62	2	properties	property	NOUN
cana-2100	62	3	of	of	ADP
cana-2100	62	4	these	these	DET
cana-2100	62	5	functions	function	NOUN
cana-2100	62	6	will	will	AUX
cana-2100	62	7	be	be	AUX
cana-2100	62	8	specified	specify	VERB
cana-2100	62	9	later	later	ADV
cana-2100	62	10	as	as	SCONJ
cana-2100	62	11	progress	progress	NOUN
cana-2100	62	12	is	be	AUX
cana-2100	62	13	made	make	VERB
cana-2100	62	14	.	.	PUNCT
cana-2100	63	1	now	now	ADV
cana-2100	63	2	,	,	PUNCT
cana-2100	63	3	let	let	VERB
cana-2100	63	4	𝑔‾	𝑔‾	VERB
cana-2100	63	5	:	:	PUNCT
cana-2100	63	6	=	=	SYM
cana-2100	63	7	(	(	PUNCT
cana-2100	63	8	𝑔1	𝑔1	PROPN
cana-2100	63	9	,	,	PUNCT
cana-2100	63	10	𝑔2	𝑔2	VERB
cana-2100	63	11	,	,	PUNCT
cana-2100	63	12	…	…	PUNCT
cana-2100	63	13	,	,	PUNCT
cana-2100	63	14	𝑔𝑚	𝑔𝑚	NOUN
cana-2100	63	15	)	)	PUNCT
cana-2100	63	16	,	,	PUNCT
cana-2100	63	17	�	�	PROPN
cana-2100	63	18	̂	̂	NOUN
cana-2100	63	19	�	�	PROPN
cana-2100	63	20	:	:	PUNCT
cana-2100	63	21	=	=	SYM
cana-2100	63	22	(	(	PUNCT
cana-2100	63	23	𝑔	𝑔	NOUN
cana-2100	63	24	,	,	PUNCT
cana-2100	63	25	𝑔	𝑔	NOUN
cana-2100	63	26	,	,	PUNCT
cana-2100	63	27	…	…	PUNCT
cana-2100	63	28	,	,	PUNCT
cana-2100	63	29	𝑔	𝑔	X
cana-2100	63	30	)	)	PUNCT
cana-2100	63	31	∈	∈	NOUN
cana-2100	64	1	𝑅𝑚	𝑅𝑚	PROPN
cana-2100	64	2	and	and	CCONJ
cana-2100	64	3	𝑓	𝑓	DET
cana-2100	64	4	∘	∘	NOUN
cana-2100	64	5	𝑥‾	𝑥‾	NOUN
cana-2100	64	6	:	:	PUNCT
cana-2100	64	7	=	=	SYM
cana-2100	64	8	(	(	PUNCT
cana-2100	64	9	𝑓(𝑥1	𝑓(𝑥1	ADV
cana-2100	64	10	)	)	PUNCT
cana-2100	64	11	,	,	PUNCT
cana-2100	64	12	𝑓(𝑥2	𝑓(𝑥2	NOUN
cana-2100	64	13	)	)	PUNCT
cana-2100	64	14	,	,	PUNCT
cana-2100	64	15	…	…	PUNCT
cana-2100	64	16	,	,	PUNCT
cana-2100	64	17	𝑓(𝑥𝑚	𝑓(𝑥𝑚	NOUN
cana-2100	64	18	)	)	PUNCT
cana-2100	64	19	)	)	PUNCT
cana-2100	65	1	it	it	PRON
cana-2100	65	2	then	then	ADV
cana-2100	65	3	follows	follow	VERB
cana-2100	65	4	that	that	SCONJ
cana-2100	65	5	:	:	PUNCT
cana-2100	65	6	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	65	7	,	,	PUNCT
cana-2100	65	8	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	65	9	)	)	PUNCT
cana-2100	65	10	,	,	PUNCT
cana-2100	65	11	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	65	12	−	−	PROPN
cana-2100	65	13	ℎ𝑙(𝑡	ℎ𝑙(𝑡	NUM
cana-2100	65	14	)	)	PUNCT
cana-2100	65	15	)	)	PUNCT
cana-2100	65	16	,	,	PUNCT
cana-2100	65	17	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	65	18	−	−	PROPN
cana-2100	65	19	ℎ2(𝑡	ℎ2(𝑡	PROPN
cana-2100	65	20	)	)	PUNCT
cana-2100	65	21	)	)	PUNCT
cana-2100	65	22	,	,	PUNCT
cana-2100	65	23	…	…	PUNCT
cana-2100	65	24	…	…	PUNCT
cana-2100	65	25	,	,	PUNCT
cana-2100	65	26	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	65	27	−	−	NOUN
cana-2100	65	28	ℎ𝑚(𝑡	ℎ𝑚(𝑡	NUM
cana-2100	65	29	)	)	PUNCT
cana-2100	65	30	)	)	PUNCT
cana-2100	65	31	)	)	PUNCT
cana-2100	66	1	=	=	SYM
cana-2100	66	2	𝑓	𝑓	PROPN
cana-2100	66	3	(	(	PUNCT
cana-2100	66	4	𝑡	𝑡	NOUN
cana-2100	66	5	,	,	PUNCT
cana-2100	66	6	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	66	7	)	)	PUNCT
cana-2100	66	8	,	,	PUNCT
cana-2100	66	9	�	�	PROPN
cana-2100	66	10	̂	̂	SYM
cana-2100	66	11	�	�	PROPN
cana-2100	66	12	∘	∘	X
cana-2100	66	13	(	(	PUNCT
cana-2100	66	14	�	�	PROPN
cana-2100	66	15	̂	̂	PROPN
cana-2100	66	16	�	�	NOUN
cana-2100	66	17	−	−	PROPN
cana-2100	66	18	ℎ‾	ℎ‾	PROPN
cana-2100	66	19	∘	∘	PROPN
cana-2100	66	20	�	�	PROPN
cana-2100	66	21	̂	̂	NUM
cana-2100	66	22	�	�	NOUN
cana-2100	66	23	)	)	PUNCT
cana-2100	66	24	)	)	PUNCT
cana-2100	66	25	(	(	PUNCT
cana-2100	66	26	1	1	X
cana-2100	66	27	)	)	PUNCT
cana-2100	66	28	in	in	ADP
cana-2100	66	29	the	the	DET
cana-2100	66	30	course	course	NOUN
cana-2100	66	31	of	of	ADP
cana-2100	66	32	this	this	DET
cana-2100	66	33	work	work	NOUN
cana-2100	66	34	,	,	PUNCT
cana-2100	66	35	it	it	PRON
cana-2100	66	36	shall	shall	AUX
cana-2100	66	37	be	be	AUX
cana-2100	66	38	assumed	assume	VERB
cana-2100	66	39	that	that	SCONJ
cana-2100	66	40	(	(	PUNCT
cana-2100	66	41	𝑎	𝑎	X
cana-2100	66	42	,	,	PUNCT
cana-2100	66	43	𝑏	𝑏	NOUN
cana-2100	66	44	):	):	PUNCT
cana-2100	66	45	=	=	PUNCT
cana-2100	66	46	𝑇	𝑇	PROPN
cana-2100	66	47	⊂	⊂	PROPN
cana-2100	66	48	𝑅	𝑅	PROPN
cana-2100	66	49	is	be	AUX
cana-2100	66	50	a	a	DET
cana-2100	66	51	non	non	ADJ
cana-2100	66	52	-	-	ADJ
cana-2100	66	53	empty	empty	ADJ
cana-2100	66	54	open	open	ADJ
cana-2100	66	55	subset	subset	NOUN
cana-2100	66	56	of	of	ADP
cana-2100	66	57	𝑅.	𝑅.	NOUN
cana-2100	66	58	for	for	ADP
cana-2100	66	59	asymptotic	asymptotic	ADJ
cana-2100	66	60	investigation	investigation	NOUN
cana-2100	66	61	,	,	PUNCT
cana-2100	66	62	at	at	ADP
cana-2100	66	63	least	least	ADJ
cana-2100	66	64	𝑏	𝑏	NOUN
cana-2100	66	65	=	=	PUNCT
cana-2100	66	66	∞	∞	PROPN
cana-2100	66	67	is	be	AUX
cana-2100	66	68	assumed	assume	VERB
cana-2100	66	69	.	.	PUNCT
cana-2100	67	1	let	let	VERB
cana-2100	67	2	𝑆	𝑆	PROPN
cana-2100	67	3	:	:	PUNCT
cana-2100	67	4	=	=	SYM
cana-2100	67	5	{	{	PUNCT
cana-2100	67	6	𝑡𝑘}𝑘=1	𝑡𝑘}𝑘=1	VERB
cana-2100	67	7	∞	∞	NUM
cana-2100	67	8	or	or	CCONJ
cana-2100	67	9	𝑆	𝑆	PROPN
cana-2100	67	10	:	:	PUNCT
cana-2100	67	11	=	=	SYM
cana-2100	67	12	{	{	PUNCT
cana-2100	67	13	𝑡𝑘}𝑘=−∞	𝑡𝑘}𝑘=−∞	PROPN
cana-2100	67	14	∞	∞	PROPN
cana-2100	67	15	be	be	VERB
cana-2100	67	16	an	an	DET
cana-2100	67	17	increasing	increase	VERB
cana-2100	67	18	sequence	sequence	NOUN
cana-2100	67	19	of	of	ADP
cana-2100	67	20	numbers	number	NOUN
cana-2100	67	21	(	(	PUNCT
cana-2100	67	22	to	to	PART
cana-2100	67	23	be	be	AUX
cana-2100	67	24	referred	refer	VERB
cana-2100	67	25	to	to	ADP
cana-2100	67	26	as	as	ADP
cana-2100	67	27	impulse	impulse	ADJ
cana-2100	67	28	times	time	NOUN
cana-2100	67	29	or	or	CCONJ
cana-2100	67	30	points	point	NOUN
cana-2100	67	31	)	)	PUNCT
cana-2100	67	32	with	with	ADP
cana-2100	67	33	at	at	ADP
cana-2100	67	34	most	most	ADV
cana-2100	67	35	two	two	NUM
cana-2100	67	36	condensation	condensation	NOUN
cana-2100	67	37	points	point	NOUN
cana-2100	67	38	.	.	PUNCT
cana-2100	68	1	let	let	VERB
cana-2100	68	2	𝐷∗	𝐷∗	NOUN
cana-2100	68	3	:	:	PUNCT
cana-2100	68	4	=	=	SYM
cana-2100	68	5	𝑆	𝑆	PROPN
cana-2100	68	6	×	×	NOUN
cana-2100	68	7	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	68	8	and	and	CCONJ
cana-2100	68	9	𝐷	𝐷	PROPN
cana-2100	68	10	:	:	PUNCT
cana-2100	68	11	=	=	SYM
cana-2100	68	12	𝑇	𝑇	PROPN
cana-2100	68	13	×	×	NOUN
cana-2100	68	14	𝑅(𝑚+𝑙)×𝑛.	𝑅(𝑚+𝑙)×𝑛.	PROPN
cana-2100	68	15	also	also	ADV
cana-2100	68	16	,	,	PUNCT
cana-2100	68	17	let	let	VERB
cana-2100	68	18	𝑓	𝑓	DET
cana-2100	68	19	:	:	PUNCT
cana-2100	68	20	𝐷	𝐷	PROPN
cana-2100	68	21	→	→	SYM
cana-2100	68	22	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	68	23	and	and	CCONJ
cana-2100	68	24	𝑓∗	𝑓∗	PROPN
cana-2100	68	25	:	:	PUNCT
cana-2100	68	26	𝐷∗	𝐷∗	PROPN
cana-2100	68	27	→	→	PUNCT
cana-2100	68	28	𝑅𝑛	𝑅𝑛	NOUN
cana-2100	68	29	be	be	AUX
cana-2100	68	30	continuous	continuous	ADJ
cana-2100	68	31	functions	function	NOUN
cana-2100	68	32	fulfilling	fulfil	VERB
cana-2100	68	33	lipschitz	lipschitz	NOUN
cana-2100	68	34	condition	condition	NOUN
cana-2100	68	35	in	in	ADP
cana-2100	68	36	𝑥	𝑥	DET
cana-2100	68	37	∈	∈	PROPN
cana-2100	68	38	𝐷	𝐷	NOUN
cana-2100	68	39	and	and	CCONJ
cana-2100	68	40	𝑥	𝑥	PRON
cana-2100	68	41	∈	∈	PROPN
cana-2100	68	42	𝐷∗	𝐷∗	PROPN
cana-2100	68	43	,	,	PUNCT
cana-2100	68	44	respectively	respectively	ADV
cana-2100	68	45	,	,	PUNCT
cana-2100	68	46	at	at	ADP
cana-2100	68	47	each	each	DET
cana-2100	68	48	fixed	fix	VERB
cana-2100	68	49	𝑡	𝑡	PROPN
cana-2100	68	50	∈	∈	PROPN
cana-2100	68	51	𝑇.	𝑇.	PROPN
cana-2100	68	52	let	let	VERB
cana-2100	68	53	ℎ𝑖	ℎ𝑖	NOUN
cana-2100	68	54	:	:	PUNCT
cana-2100	68	55	𝑇	𝑇	PROPN
cana-2100	68	56	→	→	SYM
cana-2100	68	57	𝑅+	𝑅+	PROPN
cana-2100	68	58	be	be	VERB
cana-2100	68	59	continuous	continuous	ADJ
cana-2100	68	60	ascending	ascend	VERB
cana-2100	68	61	delay	delay	NOUN
cana-2100	68	62	function	function	VERB
cana-2100	68	63	such	such	ADJ
cana-2100	68	64	that	that	SCONJ
cana-2100	68	65	ℎ𝑖(𝑡	ℎ𝑖(𝑡	X
cana-2100	68	66	)	)	PUNCT
cana-2100	68	67	≤	≤	NUM
cana-2100	69	1	𝑡	𝑡	ADP
cana-2100	69	2	−	−	NOUN
cana-2100	69	3	𝑎	𝑎	NOUN
cana-2100	69	4	,	,	PUNCT
cana-2100	69	5	∀𝑡	∀𝑡	PROPN
cana-2100	69	6	∈	∈	PROPN
cana-2100	69	7	𝑇	𝑇	PROPN
cana-2100	69	8	,	,	PUNCT
cana-2100	69	9	⬚	⬚	PROPN
cana-2100	69	10	∀𝑙	∀𝑙	NOUN
cana-2100	69	11	≤	≤	NOUN
cana-2100	69	12	𝑖	𝑖	SYM
cana-2100	69	13	≤	≤	NOUN
cana-2100	69	14	𝑚.	𝑚.	ADV
cana-2100	69	15	then	then	ADV
cana-2100	69	16	from	from	ADP
cana-2100	69	17	the	the	DET
cana-2100	69	18	notation	notation	NOUN
cana-2100	69	19	in	in	ADP
cana-2100	69	20	equation	equation	NOUN
cana-2100	69	21	(	(	PUNCT
cana-2100	69	22	1	1	NUM
cana-2100	69	23	)	)	PUNCT
cana-2100	69	24	,	,	PUNCT
cana-2100	69	25	a	a	DET
cana-2100	69	26	system	system	NOUN
cana-2100	69	27	of	of	ADP
cana-2100	69	28	first	first	ADJ
cana-2100	69	29	-	-	PUNCT
cana-2100	69	30	order	order	NOUN
cana-2100	69	31	impulsive	impulsive	ADJ
cana-2100	69	32	differential	differential	ADJ
cana-2100	69	33	equations	equation	NOUN
cana-2100	69	34	with	with	ADP
cana-2100	69	35	continuous	continuous	ADJ
cana-2100	69	36	delay	delay	NOUN
cana-2100	69	37	is	be	AUX
cana-2100	69	38	of	of	ADP
cana-2100	69	39	the	the	DET
cana-2100	69	40	form	form	NOUN
cana-2100	69	41	:	:	PUNCT
cana-2100	69	42	{	{	PUNCT
cana-2100	69	43	𝑥	𝑥	NOUN
cana-2100	69	44	′(𝑡	′(𝑡	NOUN
cana-2100	69	45	)	)	PUNCT
cana-2100	69	46	=	=	PUNCT
cana-2100	70	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	70	2	,	,	PUNCT
cana-2100	70	3	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	70	4	)	)	PUNCT
cana-2100	70	5	,	,	PUNCT
cana-2100	70	6	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	70	7	−	−	PROPN
cana-2100	70	8	ℎ𝑙(𝑡	ℎ𝑙(𝑡	NUM
cana-2100	70	9	)	)	PUNCT
cana-2100	70	10	)	)	PUNCT
cana-2100	70	11	,	,	PUNCT
cana-2100	70	12	…	…	PUNCT
cana-2100	70	13	,	,	PUNCT
cana-2100	70	14	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	70	15	−	−	NOUN
cana-2100	70	16	ℎ𝑚(𝑡	ℎ𝑚(𝑡	NUM
cana-2100	70	17	)	)	PUNCT
cana-2100	70	18	)	)	PUNCT
cana-2100	70	19	)	)	PUNCT
cana-2100	70	20	,	,	PUNCT
cana-2100	70	21	∀𝑡	∀𝑡	PROPN
cana-2100	70	22	∈	∈	PROPN
cana-2100	70	23	𝑇	𝑇	PROPN
cana-2100	70	24	∖	∖	PROPN
cana-2100	70	25	𝑆	𝑆	PROPN
cana-2100	70	26	δ𝑥(𝑡𝑘	δ𝑥(𝑡𝑘	PROPN
cana-2100	70	27	)	)	PUNCT
cana-2100	70	28	=	=	PUNCT
cana-2100	70	29	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NUM
cana-2100	70	30	+	+	CCONJ
cana-2100	70	31	0	0	NUM
cana-2100	70	32	)	)	PUNCT
cana-2100	70	33	−	−	PROPN
cana-2100	70	34	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NUM
cana-2100	70	35	−	−	PROPN
cana-2100	70	36	0	0	NUM
cana-2100	70	37	)	)	PUNCT
cana-2100	70	38	=	=	SYM
cana-2100	70	39	𝑓∗(𝑡𝑘	𝑓∗(𝑡𝑘	NUM
cana-2100	70	40	,	,	PUNCT
cana-2100	70	41	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NOUN
cana-2100	70	42	)	)	PUNCT
cana-2100	70	43	)	)	PUNCT
cana-2100	70	44	,	,	PUNCT
cana-2100	70	45	∀𝑡𝑘	∀𝑡𝑘	NOUN
cana-2100	70	46	∈	∈	PROPN
cana-2100	70	47	𝑆	𝑆	PROPN
cana-2100	70	48	(	(	PUNCT
cana-2100	70	49	2	2	NUM
cana-2100	70	50	)	)	PUNCT
cana-2100	70	51	from	from	ADP
cana-2100	70	52	the	the	DET
cana-2100	70	53	notation	notation	NOUN
cana-2100	70	54	in	in	ADP
cana-2100	70	55	(	(	PUNCT
cana-2100	70	56	1	1	NUM
cana-2100	70	57	)	)	PUNCT
cana-2100	70	58	,	,	PUNCT
cana-2100	70	59	it	it	PRON
cana-2100	70	60	can	can	AUX
cana-2100	70	61	be	be	AUX
cana-2100	70	62	written	write	VERB
cana-2100	70	63	in	in	ADP
cana-2100	70	64	a	a	DET
cana-2100	70	65	more	more	ADV
cana-2100	70	66	compact	compact	ADJ
cana-2100	70	67	form	form	NOUN
cana-2100	70	68	as	as	ADP
cana-2100	70	69	:	:	PUNCT
cana-2100	70	70	{	{	PUNCT
cana-2100	70	71	𝑥	𝑥	NOUN
cana-2100	70	72	′(𝑡	′(𝑡	NOUN
cana-2100	70	73	)	)	PUNCT
cana-2100	70	74	=	=	PUNCT
cana-2100	70	75	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	70	76	,	,	PUNCT
cana-2100	70	77	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	70	78	)	)	PUNCT
cana-2100	70	79	,	,	PUNCT
cana-2100	70	80	𝑥	𝑥	PRON
cana-2100	70	81	∘	∘	X
cana-2100	70	82	(	(	PUNCT
cana-2100	70	83	�	�	PROPN
cana-2100	70	84	̂	̂	PROPN
cana-2100	70	85	�	�	NOUN
cana-2100	70	86	−	−	PROPN
cana-2100	70	87	ℎ‾	ℎ‾	PROPN
cana-2100	70	88	∘	∘	PROPN
cana-2100	70	89	�	�	PROPN
cana-2100	70	90	̂	̂	NUM
cana-2100	70	91	�	�	NOUN
cana-2100	70	92	)	)	PUNCT
cana-2100	70	93	)	)	PUNCT
cana-2100	70	94	,	,	PUNCT
cana-2100	70	95	⬚	⬚	PROPN
cana-2100	70	96	∀𝑡	∀𝑡	NOUN
cana-2100	70	97	∈	∈	PROPN
cana-2100	70	98	𝑇	𝑇	PROPN
cana-2100	70	99	∖	∖	PROPN
cana-2100	70	100	𝑆	𝑆	PROPN
cana-2100	70	101	δ𝑥(𝑡𝑘	δ𝑥(𝑡𝑘	PROPN
cana-2100	70	102	)	)	PUNCT
cana-2100	70	103	=	=	SYM
cana-2100	70	104	𝑓∗(𝑡𝑘	𝑓∗(𝑡𝑘	NUM
cana-2100	70	105	,	,	PUNCT
cana-2100	70	106	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NOUN
cana-2100	70	107	)	)	PUNCT
cana-2100	70	108	)	)	PUNCT
cana-2100	70	109	,	,	PUNCT
cana-2100	71	1	⬚	⬚	NUM
cana-2100	71	2	∀𝑡𝑘	∀𝑡𝑘	NOUN
cana-2100	71	3	∈	∈	PROPN
cana-2100	71	4	𝑆	𝑆	PROPN
cana-2100	71	5	(	(	PUNCT
cana-2100	71	6	3	3	NUM
cana-2100	71	7	)	)	PUNCT
cana-2100	71	8	communications	communication	NOUN
cana-2100	71	9	on	on	ADP
cana-2100	71	10	applied	apply	VERB
cana-2100	71	11	nonlinear	nonlinear	ADJ
cana-2100	71	12	analysis	analysis	NOUN
cana-2100	71	13	issn	issn	NOUN
cana-2100	71	14	:	:	PUNCT
cana-2100	71	15	1074	1074	NUM
cana-2100	71	16	-	-	PUNCT
cana-2100	71	17	133x	133x	NUM
cana-2100	71	18	vol	vol	NOUN
cana-2100	71	19	32	32	NUM
cana-2100	72	1	no	no	NOUN
cana-2100	72	2	.	.	PUNCT
cana-2100	73	1	1s	1s	NUM
cana-2100	73	2	(	(	PUNCT
cana-2100	73	3	2025	2025	NUM
cana-2100	73	4	)	)	PUNCT
cana-2100	73	5	48	48	NUM
cana-2100	73	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2100	73	7	let	let	VERB
cana-2100	73	8	𝑓:ω	𝑓:ω	NOUN
cana-2100	73	9	→	→	SYM
cana-2100	73	10	𝑅𝑛,ω	𝑅𝑛,ω	PROPN
cana-2100	73	11	⊂	⊂	SYM
cana-2100	73	12	𝑇	𝑇	PROPN
cana-2100	73	13	×	×	NOUN
cana-2100	73	14	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	73	15	be	be	AUX
cana-2100	73	16	continuous	continuous	ADJ
cana-2100	73	17	and	and	CCONJ
cana-2100	73	18	𝑥	𝑥	X
cana-2100	73	19	at	at	ADV
cana-2100	73	20	least	least	ADJ
cana-2100	73	21	once	once	ADV
cana-2100	73	22	differentiable	differentiable	ADJ
cana-2100	73	23	.	.	PUNCT
cana-2100	74	1	let	let	VERB
cana-2100	74	2	ℎ𝑗	ℎ𝑗	PRON
cana-2100	74	3	∈	∈	PROPN
cana-2100	74	4	𝐶(𝑡	𝐶(𝑡	X
cana-2100	74	5	)	)	PUNCT
cana-2100	74	6	be	be	AUX
cana-2100	74	7	continuous	continuous	ADJ
cana-2100	74	8	delay	delay	NOUN
cana-2100	74	9	functions	function	NOUN
cana-2100	74	10	,	,	PUNCT
cana-2100	74	11	𝑙	𝑙	PROPN
cana-2100	74	12	≤	≤	NUM
cana-2100	74	13	𝑗	𝑗	PRON
cana-2100	74	14	≤	≤	NOUN
cana-2100	74	15	𝑚	𝑚	X
cana-2100	74	16	and	and	CCONJ
cana-2100	74	17	ℎ‾	ℎ‾	ADP
cana-2100	74	18	∘	∘	PROPN
cana-2100	74	19	�	�	PROPN
cana-2100	74	20	̂	̂	SYM
cana-2100	74	21	�	�	NOUN
cana-2100	74	22	=	=	SYM
cana-2100	74	23	(	(	PUNCT
cana-2100	74	24	ℎ𝑙(𝑡	ℎ𝑙(𝑡	NUM
cana-2100	74	25	)	)	PUNCT
cana-2100	74	26	,	,	PUNCT
cana-2100	74	27	ℎ2(𝑡	ℎ2(𝑡	PROPN
cana-2100	74	28	)	)	PUNCT
cana-2100	74	29	,	,	PUNCT
cana-2100	74	30	…	…	PUNCT
cana-2100	74	31	,	,	PUNCT
cana-2100	74	32	ℎ𝑚(𝑡	ℎ𝑚(𝑡	NUM
cana-2100	74	33	)	)	PUNCT
cana-2100	74	34	)	)	PUNCT
cana-2100	74	35	be	be	AUX
cana-2100	74	36	a	a	DET
cana-2100	74	37	continuous	continuous	ADJ
cana-2100	74	38	delay	delay	NOUN
cana-2100	74	39	vector	vector	NOUN
cana-2100	74	40	,	,	PUNCT
cana-2100	74	41	then	then	ADV
cana-2100	74	42	𝑟	𝑟	X
cana-2100	74	43	=	=	SYM
cana-2100	74	44	sup	sup	NOUN
cana-2100	74	45	𝑡∈(𝑎,𝑏	𝑡∈(𝑎,𝑏	NOUN
cana-2100	74	46	)	)	PUNCT
cana-2100	74	47	 	 	SPACE
cana-2100	74	48	max1≤𝑗≤𝑛	max1≤𝑗≤𝑛	NOUN
cana-2100	74	49	 	 	SPACE
cana-2100	74	50	{	{	PUNCT
cana-2100	74	51	ℎ𝑗(𝑡	ℎ𝑗(𝑡	NOUN
cana-2100	74	52	)	)	PUNCT
cana-2100	74	53	}	}	PUNCT
cana-2100	74	54	is	be	AUX
cana-2100	74	55	called	call	VERB
cana-2100	74	56	the	the	DET
cana-2100	74	57	delay	delay	NOUN
cana-2100	74	58	constant	constant	ADJ
cana-2100	74	59	(	(	PUNCT
cana-2100	74	60	where	where	SCONJ
cana-2100	74	61	the	the	DET
cana-2100	74	62	delays	delay	NOUN
cana-2100	74	63	are	be	AUX
cana-2100	74	64	discrete	discrete	ADJ
cana-2100	74	65	,	,	PUNCT
cana-2100	74	66	that	that	ADV
cana-2100	74	67	is	be	AUX
cana-2100	74	68	,	,	PUNCT
cana-2100	74	69	=	=	SYM
cana-2100	74	70	max1≤𝑗≤𝑛	max1≤𝑗≤𝑛	NOUN
cana-2100	74	71	 	 	SPACE
cana-2100	74	72	{	{	PUNCT
cana-2100	74	73	ℎ𝑗	ℎ𝑗	PROPN
cana-2100	74	74	}	}	PUNCT
cana-2100	74	75	)	)	PUNCT
cana-2100	74	76	.	.	PUNCT
cana-2100	75	1	let	let	VERB
cana-2100	75	2	equation	equation	NOUN
cana-2100	75	3	(	(	PUNCT
cana-2100	75	4	2	2	NUM
cana-2100	75	5	)	)	PUNCT
cana-2100	75	6	or	or	CCONJ
cana-2100	75	7	equation	equation	NOUN
cana-2100	75	8	(	(	PUNCT
cana-2100	75	9	3	3	X
cana-2100	75	10	)	)	PUNCT
cana-2100	75	11	be	be	AUX
cana-2100	75	12	given	give	VERB
cana-2100	75	13	subject	subject	NOUN
cana-2100	75	14	to	to	ADP
cana-2100	75	15	the	the	DET
cana-2100	75	16	initial	initial	ADJ
cana-2100	75	17	or	or	CCONJ
cana-2100	75	18	history	history	NOUN
cana-2100	75	19	function	function	NOUN
cana-2100	75	20	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	75	21	)	)	PUNCT
cana-2100	75	22	=	=	SYM
cana-2100	76	1	𝜙(𝑡	𝜙(𝑡	PROPN
cana-2100	76	2	)	)	PUNCT
cana-2100	76	3	,	,	PUNCT
cana-2100	76	4	𝑡0	𝑡0	PROPN
cana-2100	77	1	−	−	PROPN
cana-2100	77	2	𝑟	𝑟	NOUN
cana-2100	77	3	≤	≤	NUM
cana-2100	77	4	𝑡	𝑡	PROPN
cana-2100	77	5	≤	≤	PROPN
cana-2100	77	6	𝑡0	𝑡0	NOUN
cana-2100	77	7	(	(	PUNCT
cana-2100	77	8	4	4	NUM
cana-2100	77	9	)	)	PUNCT
cana-2100	77	10	where	where	SCONJ
cana-2100	77	11	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NOUN
cana-2100	77	12	)	)	PUNCT
cana-2100	77	13	=	=	NUM
cana-2100	77	14	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NUM
cana-2100	77	15	−	−	PROPN
cana-2100	77	16	0	0	NUM
cana-2100	77	17	)	)	PUNCT
cana-2100	77	18	and	and	CCONJ
cana-2100	77	19	𝑓∗(𝑡𝑘	𝑓∗(𝑡𝑘	PROPN
cana-2100	77	20	,	,	PUNCT
cana-2100	77	21	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NOUN
cana-2100	77	22	)	)	PUNCT
cana-2100	77	23	)	)	PUNCT
cana-2100	77	24	prescribes	prescribe	VERB
cana-2100	77	25	the	the	DET
cana-2100	77	26	jump	jump	NOUN
cana-2100	77	27	at	at	ADP
cana-2100	77	28	each	each	DET
cana-2100	77	29	impulse	impulse	ADJ
cana-2100	77	30	point	point	NOUN
cana-2100	77	31	𝑡𝑘	𝑡𝑘	ADP
cana-2100	77	32	∈	∈	PROPN
cana-2100	77	33	𝑆	𝑆	PROPN
cana-2100	77	34	,	,	PUNCT
cana-2100	77	35	then	then	ADV
cana-2100	77	36	equation	equation	NOUN
cana-2100	77	37	(	(	PUNCT
cana-2100	77	38	2	2	NUM
cana-2100	77	39	)	)	PUNCT
cana-2100	77	40	or	or	CCONJ
cana-2100	77	41	(	(	PUNCT
cana-2100	77	42	3	3	X
cana-2100	77	43	)	)	PUNCT
cana-2100	77	44	is	be	AUX
cana-2100	77	45	called	call	VERB
cana-2100	77	46	a	a	DET
cana-2100	77	47	first	first	ADJ
cana-2100	77	48	-	-	PUNCT
cana-2100	77	49	order	order	NOUN
cana-2100	77	50	impulsive	impulsive	ADJ
cana-2100	77	51	delayed	delay	VERB
cana-2100	77	52	differential	differential	ADJ
cana-2100	77	53	equation	equation	NOUN
cana-2100	77	54	with	with	ADP
cana-2100	77	55	continuous	continuous	ADJ
cana-2100	77	56	delays	delay	NOUN
cana-2100	77	57	.	.	PUNCT
cana-2100	78	1	subject	subject	ADJ
cana-2100	78	2	to	to	ADP
cana-2100	78	3	equation	equation	NOUN
cana-2100	78	4	(	(	PUNCT
cana-2100	78	5	4	4	X
cana-2100	78	6	)	)	PUNCT
cana-2100	78	7	it	it	PRON
cana-2100	78	8	is	be	AUX
cana-2100	78	9	called	call	VERB
cana-2100	78	10	an	an	DET
cana-2100	78	11	initial	initial	ADJ
cana-2100	78	12	value	value	NOUN
cana-2100	78	13	or	or	CCONJ
cana-2100	78	14	function	function	NOUN
cana-2100	78	15	problem	problem	NOUN
cana-2100	78	16	.	.	PUNCT
cana-2100	79	1	let	let	VERB
cana-2100	79	2	𝐴	𝐴	PROPN
cana-2100	79	3	and	and	CCONJ
cana-2100	79	4	𝐵	𝐵	NOUN
cana-2100	79	5	be	be	AUX
cana-2100	79	6	real	real	ADJ
cana-2100	79	7	𝑛	𝑛	ADP
cana-2100	79	8	by	by	ADP
cana-2100	79	9	𝑛	𝑛	DET
cana-2100	79	10	matrix	matrix	NOUN
cana-2100	79	11	functions	function	NOUN
cana-2100	79	12	with	with	ADP
cana-2100	79	13	components	component	NOUN
cana-2100	79	14	in	in	ADP
cana-2100	79	15	𝐶(𝑎	𝐶(𝑎	PROPN
cana-2100	79	16	,	,	PUNCT
cana-2100	79	17	𝑏	𝑏	NOUN
cana-2100	79	18	)	)	PUNCT
cana-2100	79	19	;	;	PUNCT
cana-2100	79	20	let	let	VERB
cana-2100	79	21	�	�	PROPN
cana-2100	79	22	⃗	⃗	NOUN
cana-2100	79	23	�	�	PROPN
cana-2100	79	24	be	be	VERB
cana-2100	79	25	a	a	DET
cana-2100	79	26	vector	vector	NOUN
cana-2100	79	27	with	with	ADP
cana-2100	79	28	𝑛	𝑛	DET
cana-2100	79	29	components	component	NOUN
cana-2100	79	30	in	in	ADP
cana-2100	79	31	𝐶(𝑎	𝐶(𝑎	PROPN
cana-2100	79	32	,	,	PUNCT
cana-2100	79	33	𝑏	𝑏	NOUN
cana-2100	79	34	)	)	PUNCT
cana-2100	79	35	and	and	CCONJ
cana-2100	79	36	�	�	PROPN
cana-2100	79	37	̃	̃	PROPN
cana-2100	79	38	�	�	PROPN
cana-2100	79	39	𝑘	𝑘	PART
cana-2100	79	40	be	be	VERB
cana-2100	79	41	an	an	DET
cana-2100	79	42	𝑛	𝑛	NOUN
cana-2100	79	43	by	by	ADP
cana-2100	79	44	𝑛	𝑛	DET
cana-2100	79	45	matrix	matrix	NOUN
cana-2100	79	46	function	function	NOUN
cana-2100	79	47	on	on	ADP
cana-2100	79	48	𝑆	𝑆	PROPN
cana-2100	79	49	,	,	PUNCT
cana-2100	79	50	then	then	ADV
cana-2100	79	51	a	a	DET
cana-2100	79	52	system	system	NOUN
cana-2100	79	53	of	of	ADP
cana-2100	79	54	linear	linear	ADJ
cana-2100	79	55	impulsive	impulsive	ADJ
cana-2100	79	56	differential	differential	ADJ
cana-2100	79	57	equation	equation	NOUN
cana-2100	79	58	with	with	ADP
cana-2100	79	59	continuous	continuous	ADJ
cana-2100	79	60	delays	delay	NOUN
cana-2100	79	61	is	be	AUX
cana-2100	79	62	defined	define	VERB
cana-2100	79	63	as	as	ADP
cana-2100	79	64	:	:	PUNCT
cana-2100	79	65	{	{	PUNCT
cana-2100	79	66	𝑥	𝑥	NOUN
cana-2100	79	67	′(𝑡	′(𝑡	NOUN
cana-2100	79	68	)	)	PUNCT
cana-2100	79	69	=	=	SYM
cana-2100	80	1	𝐴(𝑡	𝐴(𝑡	PUNCT
cana-2100	80	2	)	)	PUNCT
cana-2100	80	3	+	+	CCONJ
cana-2100	80	4	𝐵(𝑡)	𝐵(𝑡)	ADJ
cana-2100	80	5	�	�	PROPN
cana-2100	80	6	̂	̂	SYM
cana-2100	80	7	�	�	PROPN
cana-2100	80	8	∘	∘	X
cana-2100	80	9	(	(	PUNCT
cana-2100	80	10	�	�	PROPN
cana-2100	80	11	̂	̂	SYM
cana-2100	80	12	�	�	NOUN
cana-2100	80	13	−	−	ADP
cana-2100	80	14	ℎ‾	ℎ‾	NOUN
cana-2100	80	15	�	�	PROPN
cana-2100	80	16	̂	̂	SYM
cana-2100	80	17	�	�	NOUN
cana-2100	80	18	)	)	PUNCT
cana-2100	80	19	+	+	NUM
cana-2100	80	20	�	�	PROPN
cana-2100	80	21	⃗	⃗	NOUN
cana-2100	80	22	�	�	PROPN
cana-2100	80	23	,	,	PUNCT
cana-2100	80	24	∀𝑡	∀𝑡	PROPN
cana-2100	80	25	∈	∈	PROPN
cana-2100	80	26	𝑇	𝑇	PROPN
cana-2100	80	27	∖	∖	PROPN
cana-2100	80	28	𝑆	𝑆	PROPN
cana-2100	80	29	δ𝑥(𝑡𝑘	δ𝑥(𝑡𝑘	PROPN
cana-2100	80	30	)	)	PUNCT
cana-2100	80	31	=	=	SYM
cana-2100	80	32	�	�	PROPN
cana-2100	80	33	̃	̃	PROPN
cana-2100	80	34	�	�	NOUN
cana-2100	80	35	𝑘𝑥(𝑡𝑘	𝑘𝑥(𝑡𝑘	NOUN
cana-2100	80	36	)	)	PUNCT
cana-2100	80	37	,	,	PUNCT
cana-2100	80	38	∀𝑡𝑘	∀𝑡𝑘	NOUN
cana-2100	80	39	∈	∈	PROPN
cana-2100	80	40	𝑆	𝑆	PROPN
cana-2100	80	41	(	(	PUNCT
cana-2100	80	42	5	5	NUM
cana-2100	80	43	)	)	PUNCT
cana-2100	80	44	if	if	SCONJ
cana-2100	80	45	�	�	NOUN
cana-2100	80	46	⃗	⃗	X
cana-2100	80	47	�	�	PROPN
cana-2100	80	48	is	be	AUX
cana-2100	80	49	identically	identically	ADV
cana-2100	80	50	zero	zero	NUM
cana-2100	80	51	,	,	PUNCT
cana-2100	80	52	equation	equation	NOUN
cana-2100	80	53	(	(	PUNCT
cana-2100	80	54	5	5	NUM
cana-2100	80	55	)	)	PUNCT
cana-2100	80	56	is	be	AUX
cana-2100	80	57	called	call	VERB
cana-2100	80	58	a	a	DET
cana-2100	80	59	homogeneous	homogeneous	ADJ
cana-2100	80	60	equation	equation	NOUN
cana-2100	80	61	and	and	CCONJ
cana-2100	80	62	is	be	AUX
cana-2100	80	63	given	give	VERB
cana-2100	80	64	by	by	ADP
cana-2100	80	65	:	:	PUNCT
cana-2100	80	66	{	{	PUNCT
cana-2100	80	67	𝑥	𝑥	NOUN
cana-2100	80	68	′(𝑡	′(𝑡	NOUN
cana-2100	80	69	)	)	PUNCT
cana-2100	80	70	=	=	SYM
cana-2100	80	71	𝐴(𝑡)𝑥(𝑡	𝐴(𝑡)𝑥(𝑡	NOUN
cana-2100	80	72	)	)	PUNCT
cana-2100	81	1	+	+	CCONJ
cana-2100	81	2	𝐵(𝑡)	𝐵(𝑡)	VERB
cana-2100	81	3	�	�	PROPN
cana-2100	81	4	̂	̂	SYM
cana-2100	81	5	�	�	PROPN
cana-2100	81	6	∘	∘	X
cana-2100	81	7	(	(	PUNCT
cana-2100	81	8	�	�	PROPN
cana-2100	81	9	̂	̂	SYM
cana-2100	81	10	�	�	NOUN
cana-2100	81	11	−	−	ADP
cana-2100	81	12	ℎ‾	ℎ‾	NOUN
cana-2100	81	13	�	�	PROPN
cana-2100	81	14	̂	̂	NUM
cana-2100	81	15	�	�	NOUN
cana-2100	81	16	)	)	PUNCT
cana-2100	81	17	,	,	PUNCT
cana-2100	81	18	∀𝑡	∀𝑡	PROPN
cana-2100	81	19	∈	∈	PROPN
cana-2100	81	20	𝑇	𝑇	PROPN
cana-2100	81	21	∖	∖	PROPN
cana-2100	81	22	𝑆	𝑆	PROPN
cana-2100	81	23	δ𝑥(𝑡𝑘	δ𝑥(𝑡𝑘	PROPN
cana-2100	81	24	)	)	PUNCT
cana-2100	81	25	=	=	SYM
cana-2100	81	26	�	�	PROPN
cana-2100	81	27	̃	̃	PROPN
cana-2100	81	28	�	�	NOUN
cana-2100	81	29	𝑘𝑥(𝑡𝑘	𝑘𝑥(𝑡𝑘	NOUN
cana-2100	81	30	)	)	PUNCT
cana-2100	81	31	,	,	PUNCT
cana-2100	81	32	∀𝑡𝑘	∀𝑡𝑘	NOUN
cana-2100	81	33	∈	∈	PROPN
cana-2100	81	34	𝑆	𝑆	PROPN
cana-2100	81	35	(	(	PUNCT
cana-2100	81	36	6	6	NUM
cana-2100	81	37	)	)	PUNCT
cana-2100	81	38	main	main	ADJ
cana-2100	81	39	results	result	NOUN
cana-2100	81	40	consider	consider	VERB
cana-2100	81	41	the	the	DET
cana-2100	81	42	system	system	NOUN
cana-2100	81	43	of	of	ADP
cana-2100	81	44	equations	equation	NOUN
cana-2100	81	45	given	give	VERB
cana-2100	81	46	by	by	ADP
cana-2100	81	47	{	{	PUNCT
cana-2100	81	48	𝑥	𝑥	NOUN
cana-2100	81	49	′(𝑡	′(𝑡	NOUN
cana-2100	81	50	)	)	PUNCT
cana-2100	81	51	=	=	PUNCT
cana-2100	82	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	82	2	,	,	PUNCT
cana-2100	82	3	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	82	4	)	)	PUNCT
cana-2100	82	5	,	,	PUNCT
cana-2100	82	6	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	82	7	−	−	PROPN
cana-2100	82	8	ℎ(𝑡	ℎ(𝑡	PROPN
cana-2100	82	9	)	)	PUNCT
cana-2100	82	10	)	)	PUNCT
cana-2100	82	11	)	)	PUNCT
cana-2100	82	12	,	,	PUNCT
cana-2100	82	13	∀𝑡	∀𝑡	PROPN
cana-2100	82	14	∈	∈	PROPN
cana-2100	82	15	𝑇	𝑇	PROPN
cana-2100	82	16	∖	∖	PROPN
cana-2100	82	17	𝑆	𝑆	PROPN
cana-2100	82	18	δ𝑥(𝑡𝑘	δ𝑥(𝑡𝑘	PROPN
cana-2100	82	19	)	)	PUNCT
cana-2100	82	20	=	=	SYM
cana-2100	82	21	𝑓∗(𝑡𝑘	𝑓∗(𝑡𝑘	NUM
cana-2100	82	22	,	,	PUNCT
cana-2100	82	23	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NOUN
cana-2100	82	24	)	)	PUNCT
cana-2100	82	25	)	)	PUNCT
cana-2100	82	26	,	,	PUNCT
cana-2100	82	27	∀𝑡𝑘	∀𝑡𝑘	NOUN
cana-2100	82	28	∈	∈	PROPN
cana-2100	82	29	𝑆	𝑆	PROPN
cana-2100	82	30	(	(	PUNCT
cana-2100	82	31	7	7	NUM
cana-2100	82	32	)	)	PUNCT
cana-2100	82	33	which	which	PRON
cana-2100	82	34	is	be	AUX
cana-2100	82	35	similar	similar	ADJ
cana-2100	82	36	to	to	ADP
cana-2100	82	37	the	the	DET
cana-2100	82	38	system	system	NOUN
cana-2100	82	39	(	(	PUNCT
cana-2100	82	40	6	6	NUM
cana-2100	82	41	)	)	PUNCT
cana-2100	82	42	.	.	PUNCT
cana-2100	83	1	this	this	DET
cana-2100	83	2	system	system	NOUN
cana-2100	83	3	assumes	assume	VERB
cana-2100	83	4	that	that	SCONJ
cana-2100	83	5	for	for	ADP
cana-2100	83	6	𝑡	𝑡	PROPN
cana-2100	83	7	∈	∈	PROPN
cana-2100	83	8	𝑇	𝑇	PROPN
cana-2100	83	9	∖	∖	PROPN
cana-2100	83	10	𝑆	𝑆	PROPN
cana-2100	83	11	,	,	PUNCT
cana-2100	83	12	the	the	DET
cana-2100	83	13	solution	solution	NOUN
cana-2100	83	14	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	83	15	)	)	PUNCT
cana-2100	83	16	is	be	AUX
cana-2100	83	17	determined	determine	VERB
cana-2100	83	18	by	by	ADP
cana-2100	83	19	the	the	DET
cana-2100	83	20	delay	delay	NOUN
cana-2100	83	21	differential	differential	NOUN
cana-2100	83	22	equation	equation	NOUN
cana-2100	83	23	𝑥	𝑥	PRON
cana-2100	83	24	′(𝑡	′(𝑡	NOUN
cana-2100	83	25	)	)	PUNCT
cana-2100	83	26	=	=	PUNCT
cana-2100	83	27	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	83	28	,	,	PUNCT
cana-2100	83	29	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	83	30	)	)	PUNCT
cana-2100	83	31	,	,	PUNCT
cana-2100	83	32	𝑥(	𝑥(	PROPN
cana-2100	83	33	�	�	PROPN
cana-2100	83	34	̂	̂	SYM
cana-2100	83	35	�	�	PROPN
cana-2100	83	36	−	−	PROPN
cana-2100	83	37	ℎ‾	ℎ‾	PROPN
cana-2100	83	38	∘	∘	PROPN
cana-2100	83	39	(	(	PUNCT
cana-2100	83	40	�	�	PROPN
cana-2100	83	41	̂	̂	NOUN
cana-2100	83	42	�	�	NOUN
cana-2100	83	43	)	)	PUNCT
cana-2100	83	44	)	)	PUNCT
cana-2100	83	45	)	)	PUNCT
cana-2100	83	46	and	and	CCONJ
cana-2100	83	47	for	for	ADP
cana-2100	83	48	𝑡	𝑡	PROPN
cana-2100	83	49	∈	∈	PROPN
cana-2100	83	50	𝑆	𝑆	PROPN
cana-2100	83	51	,	,	PUNCT
cana-2100	83	52	a	a	DET
cana-2100	83	53	change	change	NOUN
cana-2100	83	54	by	by	ADP
cana-2100	83	55	jump	jump	NOUN
cana-2100	83	56	of	of	ADP
cana-2100	83	57	the	the	DET
cana-2100	83	58	solution	solution	NOUN
cana-2100	83	59	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	83	60	)	)	PUNCT
cana-2100	83	61	occurs	occur	VERB
cana-2100	83	62	so	so	SCONJ
cana-2100	83	63	that	that	SCONJ
cana-2100	83	64	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NUM
cana-2100	83	65	−	−	NOUN
cana-2100	83	66	)	)	PUNCT
cana-2100	84	1	=	=	PUNCT
cana-2100	84	2	𝑥(𝑡𝑘	𝑥(𝑡𝑘	X
cana-2100	84	3	)	)	PUNCT
cana-2100	84	4	and𝑥(𝑡𝑘	and𝑥(𝑡𝑘	ADP
cana-2100	84	5	+	+	NOUN
cana-2100	84	6	)	)	PUNCT
cana-2100	84	7	=	=	SYM
cana-2100	84	8	𝑥(𝑡𝑘	𝑥(𝑡𝑘	X
cana-2100	84	9	)	)	PUNCT
cana-2100	84	10	+	+	X
cana-2100	84	11	𝑓∗(𝑡𝑘	𝑓∗(𝑡𝑘	NUM
cana-2100	84	12	,	,	PUNCT
cana-2100	84	13	𝑥(𝑡𝑘))[1	𝑥(𝑡𝑘))[1	NOUN
cana-2100	84	14	−	−	PROPN
cana-2100	84	15	5	5	NUM
cana-2100	84	16	]	]	PUNCT
cana-2100	84	17	.	.	PUNCT
cana-2100	85	1	here	here	ADV
cana-2100	85	2	,	,	PUNCT
cana-2100	85	3	a	a	DET
cana-2100	85	4	special	special	NOUN
cana-2100	85	5	strictly	strictly	ADV
cana-2100	85	6	ascending	ascend	VERB
cana-2100	85	7	continuous	continuous	ADJ
cana-2100	85	8	delay	delay	NOUN
cana-2100	85	9	for	for	ADP
cana-2100	85	10	the	the	DET
cana-2100	85	11	system	system	NOUN
cana-2100	85	12	of	of	ADP
cana-2100	85	13	equations	equation	NOUN
cana-2100	85	14	in	in	ADP
cana-2100	85	15	(	(	PUNCT
cana-2100	85	16	6	6	NUM
cana-2100	85	17	)	)	PUNCT
cana-2100	85	18	is	be	AUX
cana-2100	85	19	constructed	construct	VERB
cana-2100	85	20	.	.	PUNCT
cana-2100	86	1	the	the	DET
cana-2100	86	2	construction	construction	NOUN
cana-2100	86	3	will	will	AUX
cana-2100	86	4	take	take	VERB
cana-2100	86	5	several	several	ADJ
cana-2100	86	6	steps	step	NOUN
cana-2100	86	7	as	as	SCONJ
cana-2100	86	8	shown	show	VERB
cana-2100	86	9	below	below	ADV
cana-2100	86	10	:	:	PUNCT
cana-2100	86	11	step	step	NOUN
cana-2100	86	12	0	0	NUM
cana-2100	86	13	:	:	PUNCT
cana-2100	86	14	let	let	VERB
cana-2100	86	15	𝜌	𝜌	X
cana-2100	86	16	∈	∈	PROPN
cana-2100	86	17	(	(	PUNCT
cana-2100	86	18	𝑡𝑘	𝑡𝑘	ADV
cana-2100	86	19	,	,	PUNCT
cana-2100	86	20	𝑡𝑘	𝑡𝑘	ADV
cana-2100	86	21	+	+	ADJ
cana-2100	86	22	1	1	X
cana-2100	86	23	)	)	PUNCT
cana-2100	86	24	for	for	ADP
cana-2100	86	25	a	a	DET
cana-2100	86	26	fixed	fix	VERB
cana-2100	86	27	𝑘	𝑘	PROPN
cana-2100	86	28	∈	∈	PROPN
cana-2100	87	1	𝑍.	𝑍.	PROPN
cana-2100	88	1	it	it	PRON
cana-2100	88	2	is	be	AUX
cana-2100	88	3	assumed	assume	VERB
cana-2100	88	4	here	here	ADV
cana-2100	88	5	that	that	SCONJ
cana-2100	88	6	(	(	PUNCT
cana-2100	88	7	𝑡𝑘	𝑡𝑘	ADV
cana-2100	88	8	,	,	PUNCT
cana-2100	88	9	𝑡𝑘+1	𝑡𝑘+1	X
cana-2100	88	10	)	)	PUNCT
cana-2100	88	11	⊂	⊂	PROPN
cana-2100	88	12	(	(	PUNCT
cana-2100	88	13	𝜌	𝜌	X
cana-2100	88	14	−	−	PROPN
cana-2100	88	15	𝜋	𝜋	NOUN
cana-2100	88	16	,	,	PUNCT
cana-2100	88	17	𝜌	𝜌	X
cana-2100	88	18	+	+	X
cana-2100	88	19	𝜋	𝜋	NOUN
cana-2100	88	20	)	)	PUNCT
cana-2100	88	21	,	,	PUNCT
cana-2100	88	22	otherwise	otherwise	ADV
cana-2100	88	23	,	,	PUNCT
cana-2100	88	24	(	(	PUNCT
cana-2100	88	25	𝑡𝑘	𝑡𝑘	ADV
cana-2100	88	26	,	,	PUNCT
cana-2100	88	27	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	88	28	)	)	PUNCT
cana-2100	88	29	will	will	AUX
cana-2100	88	30	be	be	AUX
cana-2100	88	31	replaced	replace	VERB
cana-2100	88	32	by	by	ADP
cana-2100	88	33	(	(	PUNCT
cana-2100	88	34	𝛼𝑘	𝛼𝑘	NOUN
cana-2100	88	35	,	,	PUNCT
cana-2100	88	36	𝛼𝑘+1	𝛼𝑘+1	NUM
cana-2100	88	37	)	)	PUNCT
cana-2100	89	1	=	=	SYM
cana-2100	89	2	(	(	PUNCT
cana-2100	89	3	𝑡𝑘	𝑡𝑘	ADV
cana-2100	89	4	,	,	PUNCT
cana-2100	89	5	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	89	6	)	)	PUNCT
cana-2100	89	7	∩	∩	NOUN
cana-2100	89	8	(	(	PUNCT
cana-2100	89	9	𝜌	𝜌	X
cana-2100	89	10	−	−	PROPN
cana-2100	89	11	𝜋	𝜋	NOUN
cana-2100	89	12	,	,	PUNCT
cana-2100	89	13	𝜌	𝜌	X
cana-2100	89	14	+	+	X
cana-2100	89	15	𝜋	𝜋	NOUN
cana-2100	89	16	)	)	PUNCT
cana-2100	89	17	.	.	PUNCT
cana-2100	90	1	moreover	moreover	ADV
cana-2100	90	2	,	,	PUNCT
cana-2100	90	3	let	let	VERB
cana-2100	90	4	𝑡𝑠	𝑡𝑠	ADP
cana-2100	90	5	∈	∈	PROPN
cana-2100	90	6	𝑆	𝑆	PROPN
cana-2100	90	7	,	,	PUNCT
cana-2100	90	8	𝑡𝑠	𝑡𝑠	VERB
cana-2100	90	9	<	<	X
cana-2100	90	10	𝑡𝑘	𝑡𝑘	ADV
cana-2100	90	11	be	be	AUX
cana-2100	90	12	an	an	DET
cana-2100	90	13	impulse	impulse	ADJ
cana-2100	90	14	point	point	NOUN
cana-2100	90	15	in	in	ADP
cana-2100	90	16	the	the	DET
cana-2100	90	17	past	past	NOUN
cana-2100	90	18	.	.	PUNCT
cana-2100	91	1	step	step	NOUN
cana-2100	91	2	1	1	NUM
cana-2100	91	3	:	:	PUNCT
cana-2100	91	4	let	let	VERB
cana-2100	91	5	𝜙0	𝜙0	NOUN
cana-2100	91	6	:	:	PUNCT
cana-2100	91	7	(	(	PUNCT
cana-2100	91	8	𝑡𝑘	𝑡𝑘	ADV
cana-2100	91	9	,	,	PUNCT
cana-2100	91	10	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	91	11	)	)	PUNCT
cana-2100	91	12	→	→	PUNCT
cana-2100	91	13	𝑅+be	𝑅+be	PRON
cana-2100	91	14	defined	define	VERB
cana-2100	91	15	by	by	ADP
cana-2100	91	16	∅0(𝑡	∅0(𝑡	NUM
cana-2100	91	17	):	):	PUNCT
cana-2100	91	18	=	=	PRON
cana-2100	91	19	{	{	PUNCT
cana-2100	91	20	𝜌𝜖(𝑡𝑘	𝜌𝜖(𝑡𝑘	PROPN
cana-2100	91	21	,	,	PUNCT
cana-2100	91	22	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	91	23	)	)	PUNCT
cana-2100	91	24	,	,	PUNCT
cana-2100	91	25	∅0(𝜌𝜌	∅0(𝜌𝜌	PROPN
cana-2100	91	26	)	)	PUNCT
cana-2100	91	27	≔	≔	VERB
cana-2100	91	28	𝑠𝑖𝑛	𝑠𝑖𝑛	ADJ
cana-2100	91	29	1	1	NUM
cana-2100	91	30	|𝑡−𝜌|	|𝑡−𝜌|	NOUN
cana-2100	91	31	∀𝑡	∀𝑡	NOUN
cana-2100	91	32	≠	≠	X
cana-2100	91	33	𝜌	𝜌	ADP
cana-2100	91	34	0	0	NUM
cana-2100	91	35	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒	NOUN
cana-2100	91	36	remark	remark	NOUN
cana-2100	91	37	3.1	3.1	NUM
cana-2100	91	38	.	.	PUNCT
cana-2100	92	1	𝜙0	𝜙0	NOUN
cana-2100	92	2	has	have	VERB
cana-2100	92	3	roots	root	NOUN
cana-2100	92	4	at	at	ADP
cana-2100	92	5	𝑡	𝑡	X
cana-2100	92	6	=	=	SYM
cana-2100	92	7	𝜌	𝜌	PART
cana-2100	92	8	±	±	NUM
cana-2100	92	9	1	1	NUM
cana-2100	92	10	𝑘𝜋	𝑘𝜋	NOUN
cana-2100	92	11	,	,	PUNCT
cana-2100	92	12	𝑘	𝑘	PRON
cana-2100	92	13	∈	∈	NOUN
cana-2100	92	14	𝑁.	𝑁.	ADJ
cana-2100	92	15	step	step	NOUN
cana-2100	92	16	2	2	NUM
cana-2100	92	17	:	:	PUNCT
cana-2100	92	18	let	let	VERB
cana-2100	92	19	𝜙𝑙(𝑡	𝜙𝑙(𝑡	NUM
cana-2100	92	20	):	):	PUNCT
cana-2100	93	1	=	=	NOUN
cana-2100	93	2	∣	∣	PROPN
cana-2100	93	3	𝑡	𝑡	PROPN
cana-2100	93	4	−	−	NOUN
cana-2100	93	5	𝜌3𝜙0(𝑡	𝜌3𝜙0(𝑡	ADJ
cana-2100	93	6	)	)	PUNCT
cana-2100	93	7	,	,	PUNCT
cana-2100	93	8	∀𝑡	∀𝑡	PROPN
cana-2100	93	9	,	,	PUNCT
cana-2100	93	10	𝜌	𝜌	X
cana-2100	93	11	∈	∈	X
cana-2100	93	12	(	(	PUNCT
cana-2100	93	13	𝑡𝑘	𝑡𝑘	ADV
cana-2100	93	14	,	,	PUNCT
cana-2100	93	15	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	93	16	)	)	PUNCT
cana-2100	93	17	.	.	PUNCT
cana-2100	94	1	then	then	ADV
cana-2100	94	2	its	its	PRON
cana-2100	94	3	derivative	derivative	NOUN
cana-2100	94	4	is	be	AUX
cana-2100	94	5	:	:	PUNCT
cana-2100	94	6	communications	communication	NOUN
cana-2100	94	7	on	on	ADP
cana-2100	94	8	applied	apply	VERB
cana-2100	94	9	nonlinear	nonlinear	ADJ
cana-2100	94	10	analysis	analysis	NOUN
cana-2100	94	11	issn	issn	NOUN
cana-2100	94	12	:	:	PUNCT
cana-2100	94	13	1074	1074	NUM
cana-2100	94	14	-	-	PUNCT
cana-2100	94	15	133x	133x	NUM
cana-2100	94	16	vol	vol	NOUN
cana-2100	94	17	32	32	NUM
cana-2100	95	1	no	no	NOUN
cana-2100	95	2	.	.	PUNCT
cana-2100	96	1	1s	1s	NUM
cana-2100	96	2	(	(	PUNCT
cana-2100	96	3	2025	2025	NUM
cana-2100	96	4	)	)	PUNCT
cana-2100	96	5	49	49	NUM
cana-2100	96	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2100	96	7	𝑑𝜙𝑙(𝑡	𝑑𝜙𝑙(𝑡	NOUN
cana-2100	96	8	)	)	PUNCT
cana-2100	96	9	𝑑𝑡	𝑑𝑡	ADP
cana-2100	96	10	=	=	PUNCT
cana-2100	96	11	{	{	PUNCT
cana-2100	96	12	3|𝑡	3|𝑡	NUM
cana-2100	96	13	−	−	NOUN
cana-2100	96	14	𝜌|2𝜙0(𝑡	𝜌|2𝜙0(𝑡	ADJ
cana-2100	96	15	)	)	PUNCT
cana-2100	96	16	−	−	PROPN
cana-2100	96	17	|𝑡	|𝑡	NOUN
cana-2100	96	18	−	−	PROPN
cana-2100	96	19	𝜌|cos	𝜌|co	NOUN
cana-2100	96	20	1	1	NUM
cana-2100	96	21	|𝑡	|𝑡	NOUN
cana-2100	96	22	−	−	PROPN
cana-2100	96	23	𝜌|	𝜌|	PROPN
cana-2100	96	24	,	,	PUNCT
cana-2100	96	25	𝑡	𝑡	X
cana-2100	96	26	≠	≠	PROPN
cana-2100	96	27	𝜌	𝜌	ADP
cana-2100	96	28	0	0	NUM
cana-2100	96	29	otherwise	otherwise	ADV
cana-2100	96	30	∀𝑡	∀𝑡	PROPN
cana-2100	96	31	,	,	PUNCT
cana-2100	96	32	𝜌	𝜌	X
cana-2100	96	33	∈	∈	X
cana-2100	96	34	(	(	PUNCT
cana-2100	96	35	𝑡𝑘	𝑡𝑘	ADV
cana-2100	96	36	,	,	PUNCT
cana-2100	96	37	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	96	38	)	)	PUNCT
cana-2100	96	39	,	,	PUNCT
cana-2100	96	40	which	which	PRON
cana-2100	96	41	is	be	AUX
cana-2100	96	42	bounded	bound	VERB
cana-2100	96	43	by	by	ADP
cana-2100	96	44	3(𝑡𝑘+1	3(𝑡𝑘+1	NUM
cana-2100	96	45	−	−	PROPN
cana-2100	96	46	𝑡𝑘)2	𝑡𝑘)2	PROPN
cana-2100	96	47	.	.	PROPN
cana-2100	96	48	remark	remark	PROPN
cana-2100	96	49	3.2	3.2	NUM
cana-2100	96	50	in	in	ADP
cana-2100	96	51	addition	addition	NOUN
cana-2100	96	52	to	to	PART
cana-2100	96	53	remark	remark	VERB
cana-2100	96	54	3.1	3.1	NUM
cana-2100	96	55	,	,	PUNCT
cana-2100	96	56	1	1	NUM
cana-2100	96	57	is	be	AUX
cana-2100	96	58	continuously	continuously	ADV
cana-2100	96	59	differentiable	differentiable	ADJ
cana-2100	96	60	in	in	ADP
cana-2100	96	61	(	(	PUNCT
cana-2100	96	62	𝑡𝑘	𝑡𝑘	ADV
cana-2100	96	63	,	,	PUNCT
cana-2100	96	64	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	96	65	)	)	PUNCT
cana-2100	96	66	.	.	PUNCT
cana-2100	97	1	step	step	NOUN
cana-2100	97	2	3	3	NUM
cana-2100	97	3	:	:	PUNCT
cana-2100	97	4	let	let	VERB
cana-2100	97	5	us	we	PRON
cana-2100	97	6	consider	consider	VERB
cana-2100	97	7	another	another	DET
cana-2100	97	8	function	function	NOUN
cana-2100	97	9	:	:	PUNCT
cana-2100	97	10	𝝓2(𝑡	𝝓2(𝑡	ADJ
cana-2100	97	11	)	)	PUNCT
cana-2100	97	12	=	=	SYM
cana-2100	97	13	(	(	PUNCT
cana-2100	97	14	𝑡	𝑡	NOUN
cana-2100	97	15	−	−	NOUN
cana-2100	97	16	𝑡𝑘)2(𝑡	𝑡𝑘)2(𝑡	NOUN
cana-2100	97	17	−	−	PROPN
cana-2100	97	18	𝑡𝑘+1)2𝝓𝑙(𝑡	𝑡𝑘+1)2𝝓𝑙(𝑡	NUM
cana-2100	97	19	)	)	PUNCT
cana-2100	97	20	,	,	PUNCT
cana-2100	97	21	∀𝑡	∀𝑡	PROPN
cana-2100	97	22	∈	∈	PROPN
cana-2100	97	23	(	(	PUNCT
cana-2100	97	24	𝑡𝑘	𝑡𝑘	ADV
cana-2100	97	25	,	,	PUNCT
cana-2100	97	26	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	97	27	)	)	PUNCT
cana-2100	97	28	this	this	PRON
cana-2100	97	29	is	be	AUX
cana-2100	97	30	continuously	continuously	ADV
cana-2100	97	31	differentiable	differentiable	ADJ
cana-2100	97	32	in	in	ADP
cana-2100	97	33	(	(	PUNCT
cana-2100	97	34	𝑡𝑘	𝑡𝑘	ADV
cana-2100	97	35	,	,	PUNCT
cana-2100	97	36	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	97	37	)	)	PUNCT
cana-2100	97	38	,	,	PUNCT
cana-2100	97	39	its	its	PRON
cana-2100	97	40	derivative	derivative	NOUN
cana-2100	97	41	is	be	AUX
cana-2100	97	42	0	0	NUM
cana-2100	97	43	at	at	ADP
cana-2100	97	44	𝑡𝑘	𝑡𝑘	ADV
cana-2100	97	45	and	and	CCONJ
cana-2100	97	46	𝑡𝑘+𝑙	𝑡𝑘+𝑙	PROPN
cana-2100	97	47	,	,	PUNCT
cana-2100	97	48	and	and	CCONJ
cana-2100	97	49	hence	hence	ADV
cana-2100	97	50	,	,	PUNCT
cana-2100	97	51	it	it	PRON
cana-2100	97	52	has	have	VERB
cana-2100	97	53	a	a	DET
cana-2100	97	54	continuously	continuously	ADV
cana-2100	97	55	differentiable	differentiable	ADJ
cana-2100	97	56	extension	extension	NOUN
cana-2100	97	57	to	to	ADP
cana-2100	97	58	𝑇.	𝑇.	PROPN
cana-2100	97	59	remark	remark	NOUN
cana-2100	97	60	3.3	3.3	NUM
cana-2100	97	61	in	in	ADP
cana-2100	97	62	addition	addition	NOUN
cana-2100	97	63	to	to	PART
cana-2100	97	64	remark	remark	VERB
cana-2100	97	65	3.2	3.2	NUM
cana-2100	97	66	,	,	PUNCT
cana-2100	97	67	𝜙2(𝑡	𝜙2(𝑡	PROPN
cana-2100	97	68	)	)	PUNCT
cana-2100	97	69	fulfils	fulfil	VERB
cana-2100	97	70	𝜙2(𝑡𝑘	𝜙2(𝑡𝑘	NOUN
cana-2100	97	71	)	)	PUNCT
cana-2100	97	72	=	=	SYM
cana-2100	97	73	𝜙	𝜙	X
cana-2100	97	74	2′	2′	NUM
cana-2100	97	75	(	(	PUNCT
cana-2100	97	76	𝑡𝑘	𝑡𝑘	NOUN
cana-2100	97	77	)	)	PUNCT
cana-2100	97	78	=	=	SYM
cana-2100	97	79	𝜙2(𝑡𝑘+1	𝜙2(𝑡𝑘+1	NOUN
cana-2100	97	80	)	)	PUNCT
cana-2100	97	81	=	=	PUNCT
cana-2100	97	82	𝜙	𝜙	X
cana-2100	97	83	2′	2′	NUM
cana-2100	97	84	(	(	PUNCT
cana-2100	97	85	𝑡𝑘+1	𝑡𝑘+1	X
cana-2100	97	86	)	)	PUNCT
cana-2100	97	87	=	=	SYM
cana-2100	98	1	0	0	X
cana-2100	98	2	.	.	PUNCT
cana-2100	98	3	hence	hence	ADV
cana-2100	98	4	𝜙(𝑡	𝜙(𝑡	PROPN
cana-2100	98	5	)	)	PUNCT
cana-2100	99	1	=	=	PRON
cana-2100	99	2	{	{	PUNCT
cana-2100	99	3	𝜙2(𝑡	𝜙2(𝑡	NOUN
cana-2100	99	4	)	)	PUNCT
cana-2100	99	5	,	,	PUNCT
cana-2100	99	6	𝑡	𝑡	PROPN
cana-2100	99	7	∈	∈	PROPN
cana-2100	99	8	(	(	PUNCT
cana-2100	99	9	𝑡𝑘	𝑡𝑘	ADV
cana-2100	99	10	,	,	PUNCT
cana-2100	99	11	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	99	12	)	)	PUNCT
cana-2100	99	13	0	0	NUM
cana-2100	99	14	,	,	PUNCT
cana-2100	99	15	otherwise	otherwise	ADV
cana-2100	99	16	ℎ𝜀(𝑡	ℎ𝜀(𝑡	PUNCT
cana-2100	99	17	)	)	PUNCT
cana-2100	99	18	=	=	SYM
cana-2100	99	19	1	1	NUM
cana-2100	99	20	−	−	NUM
cana-2100	99	21	𝜙𝜀(𝑡	𝜙𝜀(𝑡	NOUN
cana-2100	99	22	)	)	PUNCT
cana-2100	99	23	=	=	SYM
cana-2100	100	1	𝑡	𝑡	PROPN
cana-2100	100	2	−	−	NOUN
cana-2100	100	3	(	(	PUNCT
cana-2100	100	4	𝑡𝑠	𝑡𝑠	X
cana-2100	100	5	+	+	ADP
cana-2100	100	6	𝜀	𝜀	X
cana-2100	100	7	𝑀	𝑀	NOUN
cana-2100	101	1	+	+	CCONJ
cana-2100	101	2	1	1	NUM
cana-2100	101	3	(	(	PUNCT
cana-2100	101	4	𝑡	𝑡	NOUN
cana-2100	101	5	−	−	PROPN
cana-2100	101	6	𝑡𝑘)2(𝑡	𝑡𝑘)2(𝑡	NOUN
cana-2100	101	7	−	−	PROPN
cana-2100	101	8	𝑡𝑘+1)2|𝑡	𝑡𝑘+1)2|𝑡	NOUN
cana-2100	101	9	−	−	NUM
cana-2100	101	10	𝜌|3𝜙0(𝑡	𝜌|3𝜙0(𝑡	NUM
cana-2100	101	11	)	)	PUNCT
cana-2100	101	12	)	)	PUNCT
cana-2100	101	13	,	,	PUNCT
cana-2100	101	14	∀𝑡	∀𝑡	PROPN
cana-2100	101	15	∈	∈	PROPN
cana-2100	101	16	(	(	PUNCT
cana-2100	101	17	𝑡𝑘	𝑡𝑘	ADV
cana-2100	101	18	,	,	PUNCT
cana-2100	101	19	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	101	20	)	)	PUNCT
cana-2100	101	21	and	and	CCONJ
cana-2100	101	22	𝑡𝑠	𝑡𝑠	PROPN
cana-2100	101	23	∈	∈	PROPN
cana-2100	101	24	𝑆	𝑆	PROPN
cana-2100	101	25	;	;	PUNCT
cana-2100	101	26	then	then	ADV
cana-2100	101	27	the	the	DET
cana-2100	101	28	following	following	NOUN
cana-2100	101	29	can	can	AUX
cana-2100	101	30	be	be	AUX
cana-2100	101	31	asserted	assert	VERB
cana-2100	101	32	:	:	PUNCT
cana-2100	101	33	remark	remark	NOUN
cana-2100	101	34	3.5	3.5	NUM
cana-2100	101	35	based	base	VERB
cana-2100	101	36	on	on	ADP
cana-2100	101	37	remark	remark	NOUN
cana-2100	101	38	3.4	3.4	NUM
cana-2100	101	39	,	,	PUNCT
cana-2100	101	40	ℎ𝜀(𝑡	ℎ𝜀(𝑡	NUM
cana-2100	101	41	)	)	PUNCT
cana-2100	101	42	is	be	AUX
cana-2100	101	43	continuously	continuously	ADV
cana-2100	101	44	differentiable	differentiable	ADJ
cana-2100	101	45	in	in	ADP
cana-2100	101	46	[	[	X
cana-2100	101	47	𝑡𝑘	𝑡𝑘	ADV
cana-2100	101	48	,	,	PUNCT
cana-2100	101	49	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	101	50	]	]	PUNCT
cana-2100	101	51	and	and	CCONJ
cana-2100	101	52	its	its	PRON
cana-2100	101	53	derivative	derivative	NOUN
cana-2100	101	54	is	be	AUX
cana-2100	101	55	greater	great	ADJ
cana-2100	101	56	than	than	ADP
cana-2100	101	57	1	1	NUM
cana-2100	101	58	−	−	NOUN
cana-2100	101	59	𝜀	𝜀	PROPN
cana-2100	101	60	>	>	X
cana-2100	101	61	0	0	NUM
cana-2100	101	62	,	,	PUNCT
cana-2100	101	63	hence	hence	ADV
cana-2100	101	64	it	it	PRON
cana-2100	101	65	is	be	AUX
cana-2100	101	66	strictly	strictly	ADV
cana-2100	101	67	ascending	ascend	VERB
cana-2100	101	68	.	.	PUNCT
cana-2100	102	1	theorem	theorem	VERB
cana-2100	102	2	3.1	3.1	NUM
cana-2100	102	3	the	the	DET
cana-2100	102	4	delay	delay	NOUN
cana-2100	102	5	ℎ𝜀(𝑡	ℎ𝜀(𝑡	PUNCT
cana-2100	102	6	)	)	PUNCT
cana-2100	102	7	≤	≤	NUM
cana-2100	103	1	𝑡	𝑡	PROPN
cana-2100	103	2	is	be	AUX
cana-2100	103	3	a	a	DET
cana-2100	103	4	continuous	continuous	ADJ
cana-2100	103	5	strictly	strictly	ADV
cana-2100	103	6	ascending	ascend	VERB
cana-2100	103	7	function	function	NOUN
cana-2100	103	8	such	such	ADJ
cana-2100	103	9	that	that	SCONJ
cana-2100	103	10	the	the	DET
cana-2100	103	11	composite	composite	ADJ
cana-2100	103	12	function	function	NOUN
cana-2100	103	13	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	103	14	,	,	PUNCT
cana-2100	103	15	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	103	16	)	)	PUNCT
cana-2100	103	17	,	,	PUNCT
cana-2100	103	18	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	103	19	−	−	PROPN
cana-2100	103	20	ℎ𝜀(𝑡	ℎ𝜀(𝑡	NUM
cana-2100	103	21	)	)	PUNCT
cana-2100	103	22	)	)	PUNCT
cana-2100	103	23	)	)	PUNCT
cana-2100	103	24	has	have	VERB
cana-2100	103	25	no	no	DET
cana-2100	103	26	limit	limit	NOUN
cana-2100	103	27	at	at	ADP
cana-2100	103	28	𝜌	𝜌	X
cana-2100	103	29	for	for	ADP
cana-2100	103	30	𝑡𝑠	𝑡𝑠	NOUN
cana-2100	103	31	<	<	X
cana-2100	103	32	𝑡𝑘	𝑡𝑘	ADV
cana-2100	103	33	<	<	X
cana-2100	103	34	𝑡	𝑡	X
cana-2100	103	35	<	<	X
cana-2100	103	36	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	103	37	.	.	PUNCT
cana-2100	104	1	proof	proof	NOUN
cana-2100	104	2	:	:	PUNCT
cana-2100	104	3	note	note	VERB
cana-2100	104	4	that	that	SCONJ
cana-2100	104	5	𝑡	𝑡	ADP
cana-2100	104	6	−	−	NOUN
cana-2100	104	7	ℎ𝜀(𝑡	ℎ𝜀(𝑡	PUNCT
cana-2100	104	8	)	)	PUNCT
cana-2100	104	9	=	=	PUNCT
cana-2100	104	10	𝜙𝜀(𝑡	𝜙𝜀(𝑡	NOUN
cana-2100	104	11	)	)	PUNCT
cana-2100	104	12	and	and	CCONJ
cana-2100	104	13	𝜙𝜀(𝑡	𝜙𝜀(𝑡	NOUN
cana-2100	104	14	)	)	PUNCT
cana-2100	104	15	passes	pass	VERB
cana-2100	104	16	𝑡𝑠	𝑡𝑠	VERB
cana-2100	104	17	at	at	ADP
cana-2100	104	18	𝑡	𝑡	NOUN
cana-2100	104	19	=	=	SYM
cana-2100	104	20	𝜌	𝜌	X
cana-2100	104	21	±	±	NUM
cana-2100	104	22	1	1	NUM
cana-2100	104	23	𝑘𝜋	𝑘𝜋	NOUN
cana-2100	104	24	,	,	PUNCT
cana-2100	104	25	0	0	PUNCT
cana-2100	104	26	<	<	X
cana-2100	104	27	𝑘	𝑘	X
cana-2100	104	28	<	<	X
cana-2100	104	29	∞.	∞.	PROPN
cana-2100	104	30	hence	hence	ADV
cana-2100	104	31	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	104	32	−	−	PROPN
cana-2100	104	33	ℎ𝜀(𝑡	ℎ𝜀(𝑡	NUM
cana-2100	104	34	)	)	PUNCT
cana-2100	104	35	)	)	PUNCT
cana-2100	104	36	has	have	VERB
cana-2100	104	37	a	a	DET
cana-2100	104	38	jump	jump	NOUN
cana-2100	104	39	of	of	ADP
cana-2100	104	40	the	the	DET
cana-2100	104	41	size	size	NOUN
cana-2100	104	42	of	of	ADP
cana-2100	104	43	𝑓∗(𝑡𝑠	𝑓∗(𝑡𝑠	NOUN
cana-2100	104	44	,	,	PUNCT
cana-2100	104	45	𝑥(𝑡𝑠	𝑥(𝑡𝑠	NUM
cana-2100	104	46	)	)	PUNCT
cana-2100	104	47	)	)	PUNCT
cana-2100	104	48	at	at	ADP
cana-2100	104	49	each	each	DET
cana-2100	104	50	𝑡	𝑡	PROPN
cana-2100	104	51	=	=	SYM
cana-2100	104	52	𝜌	𝜌	PART
cana-2100	104	53	±	±	NUM
cana-2100	104	54	1	1	NUM
cana-2100	104	55	𝑘𝜋	𝑘𝜋	NOUN
cana-2100	104	56	,	,	PUNCT
cana-2100	104	57	0	0	PUNCT
cana-2100	104	58	<	<	X
cana-2100	104	59	𝑘	𝑘	X
cana-2100	104	60	<	<	X
cana-2100	104	61	∞.	∞.	PROPN
cana-2100	104	62	thus	thus	ADV
cana-2100	104	63	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	104	64	,	,	PUNCT
cana-2100	104	65	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	104	66	)	)	PUNCT
cana-2100	104	67	,	,	PUNCT
cana-2100	104	68	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	104	69	−	−	PROPN
cana-2100	104	70	ℎ𝜀(𝑡	ℎ𝜀(𝑡	NUM
cana-2100	104	71	)	)	PUNCT
cana-2100	104	72	)	)	PUNCT
cana-2100	104	73	)	)	PUNCT
cana-2100	104	74	has	have	VERB
cana-2100	104	75	no	no	DET
cana-2100	104	76	limit	limit	NOUN
cana-2100	104	77	at	at	ADP
cana-2100	104	78	𝜌	𝜌	ADP
cana-2100	104	79	∈	∈	PROPN
cana-2100	104	80	(	(	PUNCT
cana-2100	104	81	𝑡𝑘	𝑡𝑘	ADV
cana-2100	104	82	,	,	PUNCT
cana-2100	104	83	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	104	84	)	)	PUNCT
cana-2100	104	85	.	.	PUNCT
cana-2100	105	1	discussion	discussion	NOUN
cana-2100	105	2	3.1	3.1	NUM
cana-2100	105	3	by	by	ADP
cana-2100	105	4	using	use	VERB
cana-2100	105	5	continuous	continuous	ADJ
cana-2100	105	6	delays	delay	NOUN
cana-2100	105	7	,	,	PUNCT
cana-2100	105	8	the	the	DET
cana-2100	105	9	continuity	continuity	NOUN
cana-2100	105	10	of	of	ADP
cana-2100	105	11	𝑓(𝑡	𝑓(𝑡	PROPN
cana-2100	105	12	,	,	PUNCT
cana-2100	105	13	𝑥(𝑡)𝑥(𝑡	𝑥(𝑡)𝑥(𝑡	NOUN
cana-2100	105	14	−	−	PROPN
cana-2100	105	15	ℎ(𝑡	ℎ(𝑡	PROPN
cana-2100	105	16	)	)	PUNCT
cana-2100	105	17	)	)	PUNCT
cana-2100	105	18	)	)	PUNCT
cana-2100	105	19	can	can	AUX
cana-2100	105	20	no	no	ADV
cana-2100	105	21	longer	long	ADV
cana-2100	105	22	be	be	AUX
cana-2100	105	23	relied	rely	VERB
cana-2100	105	24	on	on	ADP
cana-2100	105	25	as	as	SCONJ
cana-2100	105	26	it	it	PRON
cana-2100	105	27	is	be	AUX
cana-2100	105	28	currently	currently	ADV
cana-2100	105	29	assumed	assume	VERB
cana-2100	105	30	in	in	ADP
cana-2100	105	31	the	the	DET
cana-2100	105	32	literature	literature	NOUN
cana-2100	105	33	since	since	SCONJ
cana-2100	105	34	the	the	DET
cana-2100	105	35	delay	delay	NOUN
cana-2100	105	36	maps	map	VERB
cana-2100	105	37	the	the	DET
cana-2100	105	38	discontinuity	discontinuity	NOUN
cana-2100	105	39	of	of	ADP
cana-2100	105	40	x	x	PUNCT
cana-2100	105	41	at	at	ADP
cana-2100	105	42	𝑡𝑠	𝑡𝑠	NOUN
cana-2100	105	43	into	into	ADP
cana-2100	105	44	the	the	DET
cana-2100	105	45	interval	interval	NOUN
cana-2100	105	46	(	(	PUNCT
cana-2100	105	47	𝑡𝑘	𝑡𝑘	ADV
cana-2100	105	48	,	,	PUNCT
cana-2100	105	49	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	105	50	)	)	PUNCT
cana-2100	105	51	as	as	ADP
cana-2100	105	52	an	an	DET
cana-2100	105	53	impact	impact	NOUN
cana-2100	105	54	of	of	ADP
cana-2100	105	55	the	the	DET
cana-2100	105	56	event	event	NOUN
cana-2100	105	57	at	at	ADP
cana-2100	105	58	𝑡𝑠	𝑡𝑠	ADJ
cana-2100	105	59	on	on	ADP
cana-2100	105	60	the	the	DET
cana-2100	105	61	dynamics	dynamic	NOUN
cana-2100	105	62	of	of	ADP
cana-2100	105	63	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	105	64	,	,	PUNCT
cana-2100	105	65	𝑥(𝑡)𝑥(𝑡	𝑥(𝑡)𝑥(𝑡	NOUN
cana-2100	106	1	−	−	PROPN
cana-2100	106	2	ℎ(𝑡	ℎ(𝑡	PROPN
cana-2100	106	3	)	)	PUNCT
cana-2100	106	4	)	)	PUNCT
cana-2100	106	5	)	)	PUNCT
cana-2100	107	1	at	at	ADP
cana-2100	107	2	present	present	ADJ
cana-2100	107	3	.	.	PUNCT
cana-2100	108	1	in	in	ADP
cana-2100	108	2	other	other	ADJ
cana-2100	108	3	words	word	NOUN
cana-2100	108	4	,	,	PUNCT
cana-2100	108	5	positive	positive	ADJ
cana-2100	108	6	increasing	increase	VERB
cana-2100	108	7	continuous	continuous	ADJ
cana-2100	108	8	functions	function	NOUN
cana-2100	108	9	as	as	ADP
cana-2100	108	10	delays	delay	NOUN
cana-2100	108	11	can	can	AUX
cana-2100	108	12	be	be	AUX
cana-2100	108	13	found	find	VERB
cana-2100	108	14	such	such	ADJ
cana-2100	108	15	that	that	SCONJ
cana-2100	108	16	𝑓(𝑡	𝑓(𝑡	PROPN
cana-2100	108	17	,	,	PUNCT
cana-2100	108	18	𝑥(𝑡)𝑥(𝑡	𝑥(𝑡)𝑥(𝑡	NOUN
cana-2100	108	19	−	−	PROPN
cana-2100	108	20	ℎ(𝑡	ℎ(𝑡	PROPN
cana-2100	108	21	)	)	PUNCT
cana-2100	108	22	)	)	PUNCT
cana-2100	108	23	)	)	PUNCT
cana-2100	108	24	is	be	AUX
cana-2100	108	25	discontinuous	discontinuous	ADJ
cana-2100	108	26	/	/	PUNCT
cana-2100	108	27	has	have	VERB
cana-2100	108	28	no	no	DET
cana-2100	108	29	limit	limit	NOUN
cana-2100	108	30	at	at	ADP
cana-2100	108	31	some	some	DET
cana-2100	108	32	point(s	point(s	NOUN
cana-2100	108	33	)	)	PUNCT
cana-2100	108	34	in	in	ADP
cana-2100	108	35	(	(	PUNCT
cana-2100	108	36	𝑡𝑘	𝑡𝑘	ADV
cana-2100	108	37	,	,	PUNCT
cana-2100	108	38	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	108	39	)	)	PUNCT
cana-2100	108	40	.	.	PUNCT
cana-2100	109	1	furthermore	furthermore	ADV
cana-2100	109	2	,	,	PUNCT
cana-2100	109	3	in	in	ADP
cana-2100	109	4	this	this	DET
cana-2100	109	5	study	study	NOUN
cana-2100	109	6	,	,	PUNCT
cana-2100	109	7	the	the	DET
cana-2100	109	8	integral	integral	ADJ
cana-2100	109	9	equivalence	equivalence	NOUN
cana-2100	109	10	of	of	ADP
cana-2100	109	11	the	the	DET
cana-2100	109	12	formulated	formulated	ADJ
cana-2100	109	13	system	system	NOUN
cana-2100	109	14	of	of	ADP
cana-2100	109	15	impulsive	impulsive	ADJ
cana-2100	109	16	delay	delay	NOUN
cana-2100	109	17	differential	differential	NOUN
cana-2100	109	18	equations	equation	NOUN
cana-2100	109	19	is	be	AUX
cana-2100	109	20	to	to	PART
cana-2100	109	21	be	be	AUX
cana-2100	109	22	obtained	obtain	VERB
cana-2100	109	23	for	for	ADP
cana-2100	109	24	the	the	DET
cana-2100	109	25	purpose	purpose	NOUN
cana-2100	109	26	of	of	ADP
cana-2100	109	27	analysis	analysis	NOUN
cana-2100	109	28	of	of	ADP
cana-2100	109	29	its	its	PRON
cana-2100	109	30	qualitative	qualitative	ADJ
cana-2100	109	31	properties	property	NOUN
cana-2100	109	32	.	.	PUNCT
cana-2100	110	1	in	in	ADP
cana-2100	110	2	order	order	NOUN
cana-2100	110	3	to	to	PART
cana-2100	110	4	achieve	achieve	VERB
cana-2100	110	5	this	this	PRON
cana-2100	110	6	,	,	PUNCT
cana-2100	110	7	the	the	DET
cana-2100	110	8	following	follow	VERB
cana-2100	110	9	underlying	underlying	ADJ
cana-2100	110	10	assumptions	assumption	NOUN
cana-2100	110	11	are	be	AUX
cana-2100	110	12	employed	employ	VERB
cana-2100	110	13	:	:	PUNCT
cana-2100	110	14	assumtion	assumtion	NOUN
cana-2100	110	15	3.1	3.1	NUM
cana-2100	110	16	•	•	NOUN
cana-2100	110	17	when	when	SCONJ
cana-2100	110	18	𝑡	𝑡	PROPN
cana-2100	110	19	∉	∉	PROPN
cana-2100	110	20	𝑆	𝑆	PROPN
cana-2100	110	21	,	,	PUNCT
cana-2100	110	22	equation	equation	NOUN
cana-2100	110	23	(	(	PUNCT
cana-2100	110	24	2	2	X
cana-2100	110	25	)	)	PUNCT
cana-2100	110	26	reduces	reduce	VERB
cana-2100	110	27	to	to	ADP
cana-2100	110	28	a	a	DET
cana-2100	110	29	delay	delay	NOUN
cana-2100	110	30	differential	differential	ADJ
cana-2100	110	31	equation	equation	NOUN
cana-2100	110	32	and	and	CCONJ
cana-2100	110	33	solution	solution	NOUN
cana-2100	110	34	is	be	AUX
cana-2100	110	35	obtained	obtain	VERB
cana-2100	110	36	from	from	ADP
cana-2100	110	37	𝑥	𝑥	DET
cana-2100	110	38	′(𝑡	′(𝑡	NOUN
cana-2100	110	39	)	)	PUNCT
cana-2100	110	40	=	=	PUNCT
cana-2100	111	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	111	2	,	,	PUNCT
cana-2100	111	3	𝑥(𝑡	𝑥(𝑡	PROPN
cana-2100	111	4	)	)	PUNCT
cana-2100	111	5	,	,	PUNCT
cana-2100	111	6	�	�	PROPN
cana-2100	111	7	̂	̂	SYM
cana-2100	111	8	�	�	PROPN
cana-2100	111	9	∘	∘	X
cana-2100	111	10	(	(	PUNCT
cana-2100	111	11	𝑡	𝑡	X
cana-2100	111	12	−	−	PROPN
cana-2100	111	13	ℎ‾	ℎ‾	ADP
cana-2100	111	14	∘	∘	PROPN
cana-2100	111	15	�	�	PROPN
cana-2100	111	16	̂	̂	NUM
cana-2100	111	17	�	�	NOUN
cana-2100	111	18	)	)	PUNCT
cana-2100	111	19	)	)	PUNCT
cana-2100	111	20	,	,	PUNCT
cana-2100	111	21	𝑡	𝑡	PROPN
cana-2100	111	22	∈	∈	PROPN
cana-2100	111	23	𝑇	𝑇	PROPN
cana-2100	111	24	∖	∖	PROPN
cana-2100	111	25	𝑆	𝑆	PROPN
cana-2100	111	26	;	;	PUNCT
cana-2100	111	27	•	•	ADP
cana-2100	111	28	𝑓	𝑓	NOUN
cana-2100	111	29	is	be	AUX
cana-2100	111	30	continuous	continuous	ADJ
cana-2100	111	31	in	in	ADP
cana-2100	111	32	ω	ω	PROPN
cana-2100	111	33	an	an	DET
cana-2100	111	34	open	open	ADJ
cana-2100	111	35	subset	subset	NOUN
cana-2100	111	36	of	of	ADP
cana-2100	111	37	𝑇	𝑇	PROPN
cana-2100	111	38	×	×	PROPN
cana-2100	111	39	𝑅(𝑚+𝑙)×𝑛	𝑅(𝑚+𝑙)×𝑛	ADJ
cana-2100	111	40	;	;	PUNCT
cana-2100	111	41	•	•	NOUN
cana-2100	111	42	for	for	ADP
cana-2100	111	43	each	each	DET
cana-2100	111	44	𝑡𝑘	𝑡𝑘	PROPN
cana-2100	111	45	∈	∈	PROPN
cana-2100	111	46	𝑆	𝑆	PROPN
cana-2100	111	47	,	,	PUNCT
cana-2100	111	48	𝑥	𝑥	PROPN
cana-2100	111	49	is	be	AUX
cana-2100	111	50	left	leave	VERB
cana-2100	111	51	continuous	continuous	ADJ
cana-2100	111	52	at	at	ADP
cana-2100	111	53	𝑡𝑘	𝑡𝑘	ADP
cana-2100	111	54	,	,	PUNCT
cana-2100	111	55	i.e.	i.e.	X
cana-2100	111	56	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NUM
cana-2100	111	57	−	−	NUM
cana-2100	111	58	)	)	PUNCT
cana-2100	111	59	=	=	PUNCT
cana-2100	111	60	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NOUN
cana-2100	111	61	)	)	PUNCT
cana-2100	111	62	,	,	PUNCT
cana-2100	111	63	and	and	CCONJ
cana-2100	111	64	there	there	PRON
cana-2100	111	65	is	be	VERB
cana-2100	111	66	a	a	DET
cana-2100	111	67	jump	jump	NOUN
cana-2100	111	68	change	change	NOUN
cana-2100	111	69	at	at	ADP
cana-2100	111	70	each	each	PRON
cana-2100	111	71	of	of	ADP
cana-2100	111	72	these	these	DET
cana-2100	111	73	impulse	impulse	ADJ
cana-2100	111	74	points	point	NOUN
cana-2100	111	75	given	give	VERB
cana-2100	111	76	by	by	ADP
cana-2100	111	77	is	be	AUX
cana-2100	111	78	a	a	DET
cana-2100	111	79	continuously	continuously	ADV
cana-2100	111	80	differentiable	differentiable	ADJ
cana-2100	111	81	extension	extension	NOUN
cana-2100	111	82	of	of	ADP
cana-2100	111	83	𝜙2(𝑡	𝜙2(𝑡	NOUN
cana-2100	111	84	)	)	PUNCT
cana-2100	111	85	from	from	ADP
cana-2100	111	86	(	(	PUNCT
cana-2100	111	87	𝑡𝑘	𝑡𝑘	ADV
cana-2100	111	88	,	,	PUNCT
cana-2100	111	89	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	111	90	)	)	PUNCT
cana-2100	111	91	to	to	AUX
cana-2100	111	92	𝑅.	𝑅.	ADJ
cana-2100	111	93	communications	communication	NOUN
cana-2100	111	94	on	on	ADP
cana-2100	111	95	applied	apply	VERB
cana-2100	111	96	nonlinear	nonlinear	ADJ
cana-2100	111	97	analysis	analysis	NOUN
cana-2100	111	98	issn	issn	NOUN
cana-2100	111	99	:	:	PUNCT
cana-2100	111	100	1074	1074	NUM
cana-2100	111	101	-	-	PUNCT
cana-2100	111	102	133x	133x	NUM
cana-2100	111	103	vol	vol	NOUN
cana-2100	111	104	32	32	NUM
cana-2100	112	1	no	no	NOUN
cana-2100	112	2	.	.	PUNCT
cana-2100	113	1	1s	1s	NUM
cana-2100	113	2	(	(	PUNCT
cana-2100	113	3	2025	2025	NUM
cana-2100	113	4	)	)	PUNCT
cana-2100	113	5	50	50	NUM
cana-2100	113	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2100	113	7	step	step	NOUN
cana-2100	113	8	4	4	NUM
cana-2100	113	9	:	:	PUNCT
cana-2100	113	10	let	let	VERB
cana-2100	113	11	us	we	PRON
cana-2100	113	12	define	define	VERB
cana-2100	113	13	yet	yet	ADV
cana-2100	113	14	another	another	PRON
cana-2100	113	15	function	function	NOUN
cana-2100	113	16	by	by	ADP
cana-2100	113	17	𝜙𝜀(𝑡	𝜙𝜀(𝑡	NOUN
cana-2100	113	18	)	)	PUNCT
cana-2100	113	19	=	=	PRON
cana-2100	114	1	𝑡𝑠	𝑡𝑠	ADP
cana-2100	114	2	+	+	NUM
cana-2100	114	3	𝜀	𝜀	X
cana-2100	114	4	𝑀+1	𝑀+1	ADJ
cana-2100	114	5	𝜙2(𝑡)∀𝑡	𝜙2(𝑡)∀𝑡	PROPN
cana-2100	114	6	∈	∈	PROPN
cana-2100	114	7	(	(	PUNCT
cana-2100	114	8	𝑡𝑘	𝑡𝑘	ADV
cana-2100	114	9	,	,	PUNCT
cana-2100	114	10	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	114	11	)	)	PUNCT
cana-2100	114	12	⬚	⬚	PROPN
cana-2100	114	13	and	and	CCONJ
cana-2100	114	14	⬚	⬚	NUM
cana-2100	114	15	𝑡𝑠	𝑡𝑠	ADJ
cana-2100	114	16	∈	∈	PROPN
cana-2100	114	17	𝑆	𝑆	PROPN
cana-2100	114	18	,	,	PUNCT
cana-2100	114	19	where	where	SCONJ
cana-2100	114	20	𝑀	𝑀	PROPN
cana-2100	114	21	=	=	PROPN
cana-2100	114	22	max𝑡∈𝑡𝑘,𝑡𝑘+1𝐽	max𝑡∈𝑡𝑘,𝑡𝑘+1𝐽	PROPN
cana-2100	114	23	 	 	SPACE
cana-2100	114	24	max{|𝜙2(𝑡)|	max{|𝜙2(𝑡)|	NOUN
cana-2100	114	25	,	,	PUNCT
cana-2100	114	26	|𝜙2	|𝜙2	X
cana-2100	114	27	′(𝑡)|	′(𝑡)|	X
cana-2100	114	28	}	}	PUNCT
cana-2100	114	29	.	.	PUNCT
cana-2100	115	1	remark	remark	VERB
cana-2100	115	2	3.4	3.4	NUM
cana-2100	115	3	in	in	ADP
cana-2100	115	4	addition	addition	NOUN
cana-2100	115	5	to	to	PART
cana-2100	115	6	remark	remark	VERB
cana-2100	115	7	3.3	3.3	NUM
cana-2100	115	8	,	,	PUNCT
cana-2100	115	9	𝝓𝜀	𝝓𝜀	ADP
cana-2100	115	10	fulfils	fulfil	VERB
cana-2100	115	11	thecondition	thecondition	NOUN
cana-2100	115	12	that	that	SCONJ
cana-2100	115	13	max	max	PROPN
cana-2100	115	14	𝑡∈[𝑡𝑘,𝑡𝑘+1	𝑡∈[𝑡𝑘,𝑡𝑘+1	PROPN
cana-2100	115	15	]	]	PUNCT
cana-2100	115	16	 	 	SPACE
cana-2100	115	17	max	max	PROPN
cana-2100	115	18	 	 	SPACE
cana-2100	115	19	{	{	PUNCT
cana-2100	115	20	𝜙𝜀(𝑡)|	𝜙𝜀(𝑡)|	X
cana-2100	115	21	,	,	PUNCT
cana-2100	115	22	|𝜙𝜀	|𝜙𝜀	X
cana-2100	115	23	⬚	⬚	ADJ
cana-2100	115	24	′(𝑡	′(𝑡	NOUN
cana-2100	115	25	)	)	PUNCT
cana-2100	115	26	∣	∣	NOUN
cana-2100	115	27	}	}	PUNCT
cana-2100	115	28	<	<	X
cana-2100	115	29	𝜀	𝜀	X
cana-2100	115	30	step	step	NOUN
cana-2100	115	31	5	5	NUM
cana-2100	115	32	:	:	PUNCT
cana-2100	115	33	let	let	VERB
cana-2100	115	34	0.5	0.5	NUM
cana-2100	115	35	>	>	SYM
cana-2100	115	36	ε>0	ε>0	NUM
cana-2100	115	37	.	.	PUNCT
cana-2100	116	1	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NUM
cana-2100	116	2	+	+	NOUN
cana-2100	116	3	)	)	PUNCT
cana-2100	116	4	=	=	SYM
cana-2100	116	5	𝑥(𝑡𝑘	𝑥(𝑡𝑘	X
cana-2100	116	6	)	)	PUNCT
cana-2100	116	7	+	+	NUM
cana-2100	116	8	δ𝑥(𝑡𝑘	δ𝑥(𝑡𝑘	NOUN
cana-2100	116	9	)	)	PUNCT
cana-2100	116	10	=	=	PUNCT
cana-2100	116	11	𝑥(𝑡𝑘	𝑥(𝑡𝑘	X
cana-2100	116	12	)	)	PUNCT
cana-2100	116	13	+	+	X
cana-2100	116	14	𝑓∗(𝑡𝑘	𝑓∗(𝑡𝑘	NUM
cana-2100	116	15	,	,	PUNCT
cana-2100	116	16	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NOUN
cana-2100	116	17	)	)	PUNCT
cana-2100	116	18	)	)	PUNCT
cana-2100	117	1	(	(	PUNCT
cana-2100	117	2	8)	8)	NUM
cana-2100	117	3	iv	iv	NUM
cana-2100	117	4	)	)	PUNCT
cana-2100	117	5	after	after	ADP
cana-2100	117	6	the	the	DET
cana-2100	117	7	jump	jump	NOUN
cana-2100	117	8	at	at	ADP
cana-2100	117	9	the	the	DET
cana-2100	117	10	moments	moment	NOUN
cana-2100	117	11	𝑡	𝑡	PROPN
cana-2100	117	12	=	=	PUNCT
cana-2100	117	13	𝑡𝑘	𝑡𝑘	ADV
cana-2100	117	14	,	,	PUNCT
cana-2100	117	15	𝑘	𝑘	X
cana-2100	117	16	=	=	NOUN
cana-2100	117	17	0,1,2	0,1,2	NUM
cana-2100	117	18	,	,	PUNCT
cana-2100	117	19	…	…	PUNCT
cana-2100	117	20	,	,	PUNCT
cana-2100	117	21	the	the	DET
cana-2100	117	22	solution	solution	NOUN
cana-2100	117	23	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	117	24	)	)	PUNCT
cana-2100	117	25	of	of	ADP
cana-2100	117	26	equation	equation	NOUN
cana-2100	117	27	(	(	PUNCT
cana-2100	117	28	2	2	X
cana-2100	117	29	)	)	PUNCT
cana-2100	117	30	coincides	coincide	VERB
cana-2100	117	31	with	with	ADP
cana-2100	117	32	the	the	DET
cana-2100	117	33	solution	solution	NOUN
cana-2100	117	34	𝑦(𝑡	𝑦(𝑡	NUM
cana-2100	117	35	)	)	PUNCT
cana-2100	117	36	of	of	ADP
cana-2100	117	37	the	the	DET
cana-2100	117	38	initial	initial	ADJ
cana-2100	117	39	function	function	NOUN
cana-2100	117	40	problem	problem	NOUN
cana-2100	117	41	𝑦	𝑦	NOUN
cana-2100	117	42	′(𝑡	′(𝑡	NOUN
cana-2100	117	43	)	)	PUNCT
cana-2100	117	44	=	=	SYM
cana-2100	118	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	118	2	,	,	PUNCT
cana-2100	118	3	𝑦(𝑡	𝑦(𝑡	NUM
cana-2100	118	4	)	)	PUNCT
cana-2100	118	5	,	,	PUNCT
cana-2100	118	6	�	�	PROPN
cana-2100	118	7	̂	̂	SYM
cana-2100	118	8	�	�	PROPN
cana-2100	118	9	∘	∘	X
cana-2100	118	10	(	(	PUNCT
cana-2100	118	11	𝑡	𝑡	X
cana-2100	118	12	−	−	PROPN
cana-2100	118	13	ℎ‾	ℎ‾	ADP
cana-2100	118	14	∘	∘	PROPN
cana-2100	118	15	�	�	PROPN
cana-2100	118	16	̂	̂	NUM
cana-2100	118	17	�	�	NOUN
cana-2100	118	18	)	)	PUNCT
cana-2100	118	19	)	)	PUNCT
cana-2100	118	20	,	,	PUNCT
cana-2100	118	21	𝑡𝑘	𝑡𝑘	ADV
cana-2100	118	22	<	<	X
cana-2100	118	23	𝑡	𝑡	PROPN
cana-2100	118	24	≤	≤	X
cana-2100	118	25	𝑡𝑘+1	𝑡𝑘+1	NUM
cana-2100	118	26	𝑦(𝑡	𝑦(𝑡	NUM
cana-2100	118	27	)	)	PUNCT
cana-2100	118	28	=	=	SYM
cana-2100	118	29	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	118	30	)	)	PUNCT
cana-2100	118	31	,	,	PUNCT
cana-2100	118	32	𝑡	𝑡	X
cana-2100	118	33	<	<	X
cana-2100	118	34	𝑡𝑘	𝑡𝑘	PRON
cana-2100	118	35	and	and	CCONJ
cana-2100	118	36	𝑦(𝑡𝑘	𝑦(𝑡𝑘	NOUN
cana-2100	118	37	)	)	PUNCT
cana-2100	118	38	=	=	PUNCT
cana-2100	118	39	𝑥(𝑡𝑘	𝑥(𝑡𝑘	X
cana-2100	118	40	)	)	PUNCT
cana-2100	118	41	+	+	X
cana-2100	118	42	𝑓∗(𝑡𝑘	𝑓∗(𝑡𝑘	NUM
cana-2100	118	43	,	,	PUNCT
cana-2100	118	44	𝑥(𝑡𝑘	𝑥(𝑡𝑘	NOUN
cana-2100	118	45	)	)	PUNCT
cana-2100	118	46	)	)	PUNCT
cana-2100	118	47	(	(	PUNCT
cana-2100	118	48	9	9	X
cana-2100	118	49	)	)	PUNCT
cana-2100	118	50	v	v	NOUN
cana-2100	118	51	)	)	PUNCT
cana-2100	118	52	the	the	DET
cana-2100	118	53	function	function	NOUN
cana-2100	118	54	𝑓(𝑡	𝑓(𝑡	PROPN
cana-2100	118	55	,	,	PUNCT
cana-2100	118	56	𝑥(𝑡)𝑥(𝑡	𝑥(𝑡)𝑥(𝑡	NOUN
cana-2100	118	57	−	−	PROPN
cana-2100	118	58	ℎ(𝑡	ℎ(𝑡	PROPN
cana-2100	118	59	)	)	PUNCT
cana-2100	118	60	)	)	PUNCT
cana-2100	118	61	)	)	PUNCT
cana-2100	119	1	is	be	AUX
cana-2100	119	2	continuous	continuous	ADJ
cana-2100	119	3	in	in	ADP
cana-2100	119	4	𝑥	𝑥	PROPN
cana-2100	119	5	for	for	ADP
cana-2100	119	6	each	each	DET
cana-2100	119	7	fixed	fix	VERB
cana-2100	119	8	𝑡	𝑡	PROPN
cana-2100	119	9	in	in	ADP
cana-2100	119	10	(	(	PUNCT
cana-2100	119	11	𝑡𝑘	𝑡𝑘	ADV
cana-2100	119	12	,	,	PUNCT
cana-2100	119	13	𝑡𝑘+1	𝑡𝑘+1	NOUN
cana-2100	119	14	)	)	PUNCT
cana-2100	119	15	and	and	CCONJ
cana-2100	119	16	measurable	measurable	ADJ
cana-2100	119	17	in	in	ADP
cana-2100	119	18	𝑡	𝑡	PROPN
cana-2100	119	19	for	for	ADP
cana-2100	119	20	each	each	DET
cana-2100	119	21	fixed	fix	VERB
cana-2100	119	22	𝑥.	𝑥.	ADJ
cana-2100	119	23	to	to	PART
cana-2100	119	24	enable	enable	VERB
cana-2100	119	25	us	we	PRON
cana-2100	119	26	follow	follow	VERB
cana-2100	119	27	the	the	DET
cana-2100	119	28	content	content	NOUN
cana-2100	119	29	of	of	ADP
cana-2100	119	30	this	this	DET
cana-2100	119	31	work	work	NOUN
cana-2100	119	32	smoothly	smoothly	ADV
cana-2100	119	33	,	,	PUNCT
cana-2100	119	34	it	it	PRON
cana-2100	119	35	is	be	AUX
cana-2100	119	36	necessary	necessary	ADJ
cana-2100	119	37	to	to	PART
cana-2100	119	38	define	define	VERB
cana-2100	119	39	some	some	DET
cana-2100	119	40	basic	basic	ADJ
cana-2100	119	41	terms	term	NOUN
cana-2100	119	42	,	,	PUNCT
cana-2100	119	43	concepts	concept	NOUN
cana-2100	119	44	,	,	PUNCT
cana-2100	119	45	notations	notation	NOUN
cana-2100	119	46	and	and	CCONJ
cana-2100	119	47	lemmas	lemma	NOUN
cana-2100	119	48	that	that	PRON
cana-2100	119	49	may	may	AUX
cana-2100	119	50	be	be	AUX
cana-2100	119	51	used	use	VERB
cana-2100	119	52	in	in	ADP
cana-2100	119	53	the	the	DET
cana-2100	119	54	sequel	sequel	NOUN
cana-2100	119	55	.	.	PUNCT
cana-2100	120	1	definition	definition	NOUN
cana-2100	120	2	3.1	3.1	NUM
cana-2100	120	3	let	let	VERB
cana-2100	120	4	𝐴	𝐴	PROPN
cana-2100	120	5	⊂	⊂	PROPN
cana-2100	120	6	𝐵	𝐵	PROPN
cana-2100	120	7	be	be	VERB
cana-2100	120	8	non	non	ADJ
cana-2100	120	9	-	-	ADJ
cana-2100	120	10	empty	empty	ADJ
cana-2100	120	11	and	and	CCONJ
cana-2100	120	12	𝑓	𝑓	PRON
cana-2100	120	13	:	:	PUNCT
cana-2100	120	14	𝐵	𝐵	PROPN
cana-2100	120	15	→	→	SYM
cana-2100	120	16	𝑅	𝑅	PROPN
cana-2100	120	17	,	,	PUNCT
cana-2100	120	18	then	then	ADV
cana-2100	120	19	𝑓|𝐴(𝑥	𝑓|𝐴(𝑥	NUM
cana-2100	120	20	)	)	PUNCT
cana-2100	120	21	=	=	SYM
cana-2100	120	22	𝑓(𝑥	𝑓(𝑥	NOUN
cana-2100	120	23	)	)	PUNCT
cana-2100	120	24	,	,	PUNCT
cana-2100	120	25	∀𝑥	∀𝑥	PROPN
cana-2100	120	26	∈	∈	PROPN
cana-2100	120	27	𝐴	𝐴	PROPN
cana-2100	120	28	is	be	AUX
cana-2100	120	29	called	call	VERB
cana-2100	120	30	the	the	DET
cana-2100	120	31	restriction	restriction	NOUN
cana-2100	120	32	of	of	ADP
cana-2100	120	33	𝑓	𝑓	DET
cana-2100	120	34	to	to	PART
cana-2100	120	35	𝐴.	𝐴.	PROPN
cana-2100	120	36	definition	definition	NOUN
cana-2100	120	37	3.2	3.2	NUM
cana-2100	120	38	pc	pc	NOUN
cana-2100	120	39	[	[	X
cana-2100	120	40	t	t	PROPN
cana-2100	120	41	,	,	PUNCT
cana-2100	120	42	rn	rn	PROPN
cana-2100	120	43	]	]	PUNCT
cana-2100	120	44	=	=	PUNCT
cana-2100	121	1	𝑓	𝑓	PRON
cana-2100	121	2	|	|	ADV
cana-2100	121	3	𝑓	𝑓	DET
cana-2100	121	4	∶	∶	NOUN
cana-2100	121	5	𝑇	𝑇	PROPN
cana-2100	121	6	→	→	SYM
cana-2100	121	7	rn	rn	PROPN
cana-2100	121	8	,	,	PUNCT
cana-2100	121	9	𝑓	𝑓	PRON
cana-2100	121	10	|	|	ADV
cana-2100	121	11	[	[	X
cana-2100	121	12	𝑡𝑗,𝑡𝑗+1	𝑡𝑗,𝑡𝑗+1	X
cana-2100	121	13	]	]	X
cana-2100	121	14	⊂𝐶[(𝑡𝑗	⊂𝐶[(𝑡𝑗	X
cana-2100	121	15	,	,	PUNCT
cana-2100	121	16	𝑡𝑗+1	𝑡𝑗+1	PROPN
cana-2100	121	17	]	]	PUNCT
cana-2100	121	18	,	,	PUNCT
cana-2100	121	19	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	121	20	]	]	PUNCT
cana-2100	121	21	⇒	⇒	NOUN
cana-2100	121	22	∃𝑓(𝑡𝑗	∃𝑓(𝑡𝑗	X
cana-2100	122	1	+	+	CCONJ
cana-2100	122	2	0	0	X
cana-2100	122	3	)	)	PUNCT
cana-2100	122	4	∈	∈	NOUN
cana-2100	123	1	𝑅∀	𝑅∀	ADP
cana-2100	123	2	−	−	NOUN
cana-2100	124	1	∞	∞	PROPN
cana-2100	124	2	<	<	X
cana-2100	124	3	𝑗	𝑗	X
cana-2100	124	4	<	<	X
cana-2100	124	5	∞.	∞.	PROPN
cana-2100	124	6	that	that	PRON
cana-2100	124	7	is	be	AUX
cana-2100	124	8	,	,	PUNCT
cana-2100	124	9	𝑓	𝑓	PRON
cana-2100	124	10	restricted	restrict	VERB
cana-2100	124	11	to	to	ADP
cana-2100	124	12	(	(	PUNCT
cana-2100	124	13	𝑡𝑗	𝑡𝑗	PROPN
cana-2100	124	14	,	,	PUNCT
cana-2100	124	15	𝑡𝑗+1	𝑡𝑗+1	X
cana-2100	124	16	)	)	PUNCT
cana-2100	124	17	is	be	AUX
cana-2100	124	18	continuous	continuous	ADJ
cana-2100	124	19	.	.	PUNCT
cana-2100	125	1	definition	definition	NOUN
cana-2100	125	2	3.3𝑃𝐶[[𝑎	3.3𝑃𝐶[[𝑎	NUM
cana-2100	125	3	,	,	PUNCT
cana-2100	125	4	𝑏	𝑏	NOUN
cana-2100	125	5	]	]	X
cana-2100	125	6	,	,	PUNCT
cana-2100	125	7	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	125	8	]	]	PUNCT
cana-2100	125	9	=	=	PUNCT
cana-2100	126	1	𝑓⌊	𝑓⌊	VERB
cana-2100	126	2	⬚	⬚	NOUN
cana-2100	126	3	𝑎,𝑏	𝑎,𝑏	NOUN
cana-2100	126	4	]	]	PUNCT
cana-2100	126	5	:	:	PUNCT
cana-2100	126	6	𝑓	𝑓	PROPN
cana-2100	126	7	∈	∈	PROPN
cana-2100	126	8	𝑃𝐶[𝑇	𝑃𝐶[𝑇	PROPN
cana-2100	126	9	,	,	PUNCT
cana-2100	126	10	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	126	11	]	]	PUNCT
cana-2100	126	12	,	,	PUNCT
cana-2100	126	13	where	where	SCONJ
cana-2100	126	14	[	[	X
cana-2100	126	15	𝑎	𝑎	X
cana-2100	126	16	,	,	PUNCT
cana-2100	126	17	𝑏	𝑏	NOUN
cana-2100	126	18	]	]	X
cana-2100	126	19	⊂	⊂	PROPN
cana-2100	126	20	𝑇.	𝑇.	PROPN
cana-2100	126	21	notation	notation	NOUN
cana-2100	126	22	3.1	3.1	NUM
cana-2100	126	23	let	let	VERB
cana-2100	126	24	i	i	PRON
cana-2100	126	25	)	)	PUNCT
cana-2100	127	1	[	[	X
cana-2100	127	2	𝑎	𝑎	X
cana-2100	127	3	,	,	PUNCT
cana-2100	127	4	𝑏	𝑏	NOUN
cana-2100	127	5	]	]	X
cana-2100	127	6	=	=	PUNCT
cana-2100	128	1	[	[	X
cana-2100	128	2	𝑎	𝑎	X
cana-2100	128	3	,	,	PUNCT
cana-2100	128	4	𝑡𝑗𝑎	𝑡𝑗𝑎	PRON
cana-2100	128	5	]	]	PUNCT
cana-2100	128	6	∪	∪	ADP
cana-2100	128	7	[	[	X
cana-2100	128	8	𝑡𝑗𝑎	𝑡𝑗𝑎	PRON
cana-2100	128	9	,	,	PUNCT
cana-2100	128	10	𝑡𝑗	𝑡𝑗	PROPN
cana-2100	128	11	]	]	PUNCT
cana-2100	128	12	∪	∪	X
cana-2100	128	13	[	[	PUNCT
cana-2100	128	14	𝑡𝑗	𝑡𝑗	X
cana-2100	128	15	,	,	PUNCT
cana-2100	128	16	𝑡𝑗+1	𝑡𝑗+1	PROPN
cana-2100	128	17	]	]	PUNCT
cana-2100	128	18	∪	∪	X
cana-2100	128	19	[	[	PUNCT
cana-2100	128	20	𝑡𝑗+1	𝑡𝑗+1	NOUN
cana-2100	128	21	,	,	PUNCT
cana-2100	128	22	𝑡𝑗+2	𝑡𝑗+2	NOUN
cana-2100	128	23	]	]	PUNCT
cana-2100	128	24	⋯	⋯	NOUN
cana-2100	128	25	…	…	PUNCT
cana-2100	128	26	∪	∪	X
cana-2100	128	27	[	[	X
cana-2100	128	28	𝑡𝑗𝑏−1	𝑡𝑗𝑏−1	NOUN
cana-2100	128	29	,	,	PUNCT
cana-2100	128	30	𝑡𝑗𝑏	𝑡𝑗𝑏	NOUN
cana-2100	128	31	]	]	PUNCT
cana-2100	128	32	∪	∪	ADP
cana-2100	128	33	[	[	X
cana-2100	128	34	𝑡𝑗𝑏	𝑡𝑗𝑏	NOUN
cana-2100	128	35	,	,	PUNCT
cana-2100	128	36	𝑏	𝑏	PROPN
cana-2100	128	37	]	]	X
cana-2100	128	38	;	;	PUNCT
cana-2100	128	39	ii	ii	X
cana-2100	128	40	)	)	PUNCT
cana-2100	128	41	𝐴𝑗𝑎−1	𝐴𝑗𝑎−1	NOUN
cana-2100	128	42	=	=	PUNCT
cana-2100	129	1	[	[	X
cana-2100	129	2	𝑎	𝑎	X
cana-2100	129	3	,	,	PUNCT
cana-2100	129	4	𝑡𝑗𝑎	𝑡𝑗𝑎	PRON
cana-2100	129	5	]	]	PUNCT
cana-2100	129	6	,	,	PUNCT
cana-2100	130	1	𝐴𝑗	𝐴𝑗	PROPN
cana-2100	130	2	=	=	PUNCT
cana-2100	131	1	[	[	X
cana-2100	131	2	𝑡𝑗	𝑡𝑗	X
cana-2100	131	3	,	,	PUNCT
cana-2100	131	4	𝑡𝑗+1	𝑡𝑗+1	PROPN
cana-2100	131	5	]	]	PUNCT
cana-2100	131	6	,	,	PUNCT
cana-2100	131	7	∀𝑗𝑎	∀𝑗𝑎	VERB
cana-2100	131	8	≤	≤	NUM
cana-2100	131	9	𝑗	𝑗	INTJ
cana-2100	131	10	<	<	X
cana-2100	131	11	𝑗𝑏	𝑗𝑏	ADP
cana-2100	131	12	⬚	⬚	PROPN
cana-2100	131	13	and	and	CCONJ
cana-2100	131	14	𝐴𝑗𝑏	𝐴𝑗𝑏	PROPN
cana-2100	131	15	=	=	PUNCT
cana-2100	132	1	[	[	X
cana-2100	132	2	𝑡𝑗𝑏	𝑡𝑗𝑏	X
cana-2100	132	3	,	,	PUNCT
cana-2100	132	4	𝑏	𝑏	NOUN
cana-2100	132	5	]	]	PUNCT
cana-2100	132	6	.	.	PUNCT
cana-2100	132	7	iii	iii	X
cana-2100	132	8	)	)	PUNCT
cana-2100	132	9	𝐶[𝐴𝑗	𝐶[𝐴𝑗	NOUN
cana-2100	132	10	,	,	PUNCT
cana-2100	132	11	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	132	12	]	]	PUNCT
cana-2100	132	13	denote	denote	VERB
cana-2100	132	14	the	the	DET
cana-2100	132	15	set	set	NOUN
cana-2100	132	16	of	of	ADP
cana-2100	132	17	continuous	continuous	ADJ
cana-2100	132	18	𝑅𝑛-valued	𝑅𝑛-valued	ADJ
cana-2100	132	19	functions	function	NOUN
cana-2100	132	20	on	on	ADP
cana-2100	132	21	the	the	DET
cana-2100	132	22	closed	closed	ADJ
cana-2100	132	23	and	and	CCONJ
cana-2100	132	24	bounded	bound	VERB
cana-2100	132	25	interval	interval	NOUN
cana-2100	132	26	𝐴𝑗	𝐴𝑗	PROPN
cana-2100	132	27	,	,	PUNCT
cana-2100	132	28	where	where	SCONJ
cana-2100	132	29	𝑗𝑎	𝑗𝑎	ADP
cana-2100	132	30	−	−	PROPN
cana-2100	132	31	𝑙	𝑙	PROPN
cana-2100	132	32	≤	≤	NUM
cana-2100	132	33	𝑗	𝑗	PRON
cana-2100	132	34	≤	≤	PROPN
cana-2100	132	35	𝑗𝑏.	𝑗𝑏.	NOUN
cana-2100	132	36	lemma	lemma	PROPN
cana-2100	132	37	3.1	3.1	NUM
cana-2100	132	38	if	if	SCONJ
cana-2100	132	39	𝑓	𝑓	PRON
cana-2100	132	40	∈	∈	PROPN
cana-2100	132	41	𝑃𝐶[𝑇	𝑃𝐶[𝑇	NOUN
cana-2100	132	42	,	,	PUNCT
cana-2100	132	43	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	132	44	]	]	PUNCT
cana-2100	132	45	and	and	CCONJ
cana-2100	132	46	[	[	X
cana-2100	132	47	𝑎	𝑎	X
cana-2100	132	48	,	,	PUNCT
cana-2100	132	49	𝑏	𝑏	NOUN
cana-2100	132	50	]	]	X
cana-2100	132	51	⊂	⊂	PROPN
cana-2100	132	52	𝑇	𝑇	PROPN
cana-2100	132	53	,	,	PUNCT
cana-2100	132	54	then‖𝑓‖[𝑎,𝑏	then‖𝑓‖[𝑎,𝑏	PROPN
cana-2100	132	55	]	]	X
cana-2100	132	56	=	=	PUNCT
cana-2100	132	57	sup	sup	NOUN
cana-2100	132	58	𝑥∈[𝑎,𝑏	𝑥∈[𝑎,𝑏	PROPN
cana-2100	132	59	]	]	PUNCT
cana-2100	132	60	 	 	SPACE
cana-2100	132	61	‖𝑓(𝑥)‖	‖𝑓(𝑥)‖	PUNCT
cana-2100	132	62	is	be	AUX
cana-2100	132	63	a	a	DET
cana-2100	132	64	norm	norm	NOUN
cana-2100	132	65	and	and	CCONJ
cana-2100	132	66	the	the	DET
cana-2100	132	67	ordered	order	VERB
cana-2100	132	68	pair	pair	NOUN
cana-2100	132	69	,	,	PUNCT
cana-2100	132	70	{	{	PUNCT
cana-2100	132	71	𝑃𝐶([𝑎	𝑃𝐶([𝑎	NOUN
cana-2100	132	72	,	,	PUNCT
cana-2100	132	73	𝑏	𝑏	NOUN
cana-2100	132	74	]	]	PUNCT
cana-2100	132	75	,	,	PUNCT
cana-2100	132	76	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	132	77	)	)	PUNCT
cana-2100	132	78	,	,	PUNCT
cana-2100	133	1	‖	‖	PROPN
cana-2100	133	2	∗	∗	NOUN
cana-2100	133	3	‖[𝑎,𝑏	‖[𝑎,𝑏	NOUN
cana-2100	133	4	]	]	PUNCT
cana-2100	133	5	}	}	PUNCT
cana-2100	133	6	is	be	AUX
cana-2100	133	7	a	a	DET
cana-2100	133	8	banach	banach	NOUN
cana-2100	133	9	space	space	NOUN
cana-2100	133	10	.	.	PUNCT
cana-2100	134	1	proof	proof	NOUN
cana-2100	134	2	:	:	PUNCT
cana-2100	134	3	i	i	NOUN
cana-2100	134	4	)	)	PUNCT
cana-2100	134	5	since	since	SCONJ
cana-2100	134	6	[	[	X
cana-2100	134	7	𝑎	𝑎	X
cana-2100	134	8	,	,	PUNCT
cana-2100	134	9	𝑏	𝑏	NOUN
cana-2100	134	10	]	]	X
cana-2100	134	11	⊂	⊂	PROPN
cana-2100	134	12	𝑇	𝑇	PROPN
cana-2100	134	13	is	be	AUX
cana-2100	134	14	a	a	DET
cana-2100	134	15	closed	closed	ADJ
cana-2100	134	16	and	and	CCONJ
cana-2100	134	17	bounded	bound	VERB
cana-2100	134	18	interval	interval	NOUN
cana-2100	134	19	such	such	ADJ
cana-2100	134	20	that	that	SCONJ
cana-2100	134	21	𝑠0	𝑠0	NOUN
cana-2100	134	22	<	<	X
cana-2100	134	23	𝑎	𝑎	X
cana-2100	134	24	<	<	X
cana-2100	134	25	𝑏	𝑏	X
cana-2100	134	26	<	<	X
cana-2100	134	27	𝑠1	𝑠1	PROPN
cana-2100	134	28	,	,	PUNCT
cana-2100	134	29	𝑆[𝑎,𝑏	𝑆[𝑎,𝑏	VERB
cana-2100	134	30	]	]	PUNCT
cana-2100	134	31	=	=	PUNCT
cana-2100	135	1	[	[	X
cana-2100	135	2	𝑎	𝑎	X
cana-2100	135	3	,	,	PUNCT
cana-2100	135	4	𝑏	𝑏	NOUN
cana-2100	135	5	]	]	PUNCT
cana-2100	135	6	∩	∩	X
cana-2100	135	7	𝑆	𝑆	PROPN
cana-2100	135	8	is	be	AUX
cana-2100	135	9	a	a	DET
cana-2100	135	10	finite	finite	NOUN
cana-2100	135	11	set	set	NOUN
cana-2100	135	12	since	since	SCONJ
cana-2100	135	13	s	s	PROPN
cana-2100	135	14	has	have	VERB
cana-2100	135	15	no	no	DET
cana-2100	135	16	condensation	condensation	NOUN
cana-2100	135	17	point	point	NOUN
cana-2100	135	18	in	in	ADP
cana-2100	135	19	[	[	X
cana-2100	135	20	a	a	PRON
cana-2100	135	21	,	,	PUNCT
cana-2100	135	22	b	b	NOUN
cana-2100	135	23	]	]	PUNCT
cana-2100	135	24	.	.	PUNCT
cana-2100	136	1	let	let	VERB
cana-2100	136	2	𝑆[𝑎,𝑏	𝑆[𝑎,𝑏	VERB
cana-2100	136	3	]	]	X
cana-2100	137	1	=	=	PUNCT
cana-2100	138	1	[	[	X
cana-2100	138	2	𝑎	𝑎	X
cana-2100	138	3	,	,	PUNCT
cana-2100	138	4	𝑏	𝑏	NOUN
cana-2100	138	5	]	]	PUNCT
cana-2100	138	6	∩	∩	ADJ
cana-2100	138	7	𝑆	𝑆	PROPN
cana-2100	138	8	=	=	SYM
cana-2100	138	9	{	{	PUNCT
cana-2100	138	10	𝑡𝑗	𝑡𝑗	PROPN
cana-2100	138	11	}	}	PUNCT
cana-2100	138	12	𝑗=𝑗𝑎−1	𝑗=𝑗𝑎−1	NOUN
cana-2100	138	13	𝑗𝑏	𝑗𝑏	ADP
cana-2100	138	14	⊂	⊂	PROPN
cana-2100	139	1	[	[	X
cana-2100	139	2	𝑎	𝑎	X
cana-2100	139	3	,	,	PUNCT
cana-2100	139	4	𝑏	𝑏	NOUN
cana-2100	139	5	]	]	X
cana-2100	139	6	⊂	⊂	PROPN
cana-2100	139	7	𝑇	𝑇	PROPN
cana-2100	139	8	⬚	⬚	PROPN
cana-2100	139	9	,	,	PUNCT
cana-2100	139	10	then	then	ADV
cana-2100	139	11	ii	ii	NOUN
cana-2100	139	12	)	)	PUNCT
cana-2100	139	13	if	if	SCONJ
cana-2100	139	14	𝑎	𝑎	X
cana-2100	139	15	,	,	PUNCT
cana-2100	139	16	𝑏	𝑏	PROPN
cana-2100	139	17	∈	∈	PROPN
cana-2100	139	18	𝑆	𝑆	PROPN
cana-2100	139	19	,	,	PUNCT
cana-2100	139	20	then	then	ADV
cana-2100	139	21	𝑎	𝑎	NOUN
cana-2100	139	22	=	=	PUNCT
cana-2100	139	23	𝑡𝑗𝑎	𝑡𝑗𝑎	NOUN
cana-2100	139	24	and	and	CCONJ
cana-2100	139	25	𝑏	𝑏	NOUN
cana-2100	139	26	=	=	NOUN
cana-2100	139	27	𝑡𝑗𝑏	𝑡𝑗𝑏	PROPN
cana-2100	139	28	.	.	PUNCT
cana-2100	140	1	hence	hence	ADV
cana-2100	140	2	,	,	PUNCT
cana-2100	140	3	[	[	X
cana-2100	140	4	𝑎	𝑎	X
cana-2100	140	5	,	,	PUNCT
cana-2100	140	6	𝑡𝑗𝑎	𝑡𝑗𝑎	PRON
cana-2100	140	7	]	]	PUNCT
cana-2100	140	8	=	=	PUNCT
cana-2100	140	9	{	{	PUNCT
cana-2100	140	10	𝑡𝑗𝑎	𝑡𝑗𝑎	ADV
cana-2100	140	11	}	}	PUNCT
cana-2100	140	12	⊂	⊂	PUNCT
cana-2100	140	13	[	[	X
cana-2100	140	14	𝑡𝑗𝑎	𝑡𝑗𝑎	ADV
cana-2100	140	15	,	,	PUNCT
cana-2100	140	16	𝑡𝑗𝑎+1	𝑡𝑗𝑎+1	X
cana-2100	140	17	]	]	X
cana-2100	140	18	⬚	⬚	NOUN
cana-2100	140	19	and	and	CCONJ
cana-2100	140	20	⬚	⬚	PROPN
cana-2100	140	21	[	[	X
cana-2100	140	22	𝑡𝑗𝑏	𝑡𝑗𝑏	X
cana-2100	140	23	,	,	PUNCT
cana-2100	140	24	𝑏	𝑏	NOUN
cana-2100	140	25	]	]	X
cana-2100	140	26	=	=	SYM
cana-2100	140	27	{	{	PUNCT
cana-2100	140	28	𝑡𝑗𝑏	𝑡𝑗𝑏	PROPN
cana-2100	140	29	}	}	PUNCT
cana-2100	140	30	⊂	⊂	PROPN
cana-2100	141	1	[	[	X
cana-2100	141	2	𝑡𝑗𝑏−1	𝑡𝑗𝑏−1	NOUN
cana-2100	141	3	,	,	PUNCT
cana-2100	141	4	𝑡𝑗𝑏	𝑡𝑗𝑏	X
cana-2100	141	5	]	]	X
cana-2100	141	6	.	.	PUNCT
cana-2100	142	1	otherwise	otherwise	ADV
cana-2100	142	2	,	,	PUNCT
cana-2100	142	3	if	if	SCONJ
cana-2100	142	4	𝑎	𝑎	PRON
cana-2100	142	5	∉	∉	PROPN
cana-2100	142	6	𝑆	𝑆	PROPN
cana-2100	142	7	,	,	PUNCT
cana-2100	142	8	then	then	ADV
cana-2100	142	9	[	[	X
cana-2100	142	10	𝑎	𝑎	X
cana-2100	142	11	,	,	PUNCT
cana-2100	142	12	𝑡𝑗𝑎	𝑡𝑗𝑎	PRON
cana-2100	142	13	]	]	PUNCT
cana-2100	142	14	is	be	AUX
cana-2100	142	15	a	a	DET
cana-2100	142	16	closed	closed	ADJ
cana-2100	142	17	bounded	bounded	ADJ
cana-2100	142	18	interval	interval	NOUN
cana-2100	142	19	and	and	CCONJ
cana-2100	142	20	‖𝑓().‖isacontinuousfunctiononit	‖𝑓().‖isacontinuousfunctiononit	NOUN
cana-2100	142	21	.	.	PUNCT
cana-2100	143	1	communications	communication	NOUN
cana-2100	143	2	on	on	ADP
cana-2100	143	3	applied	apply	VERB
cana-2100	143	4	nonlinear	nonlinear	ADJ
cana-2100	143	5	analysis	analysis	NOUN
cana-2100	143	6	issn	issn	NOUN
cana-2100	143	7	:	:	PUNCT
cana-2100	143	8	1074	1074	NUM
cana-2100	143	9	-	-	PUNCT
cana-2100	143	10	133x	133x	NUM
cana-2100	143	11	vol	vol	NOUN
cana-2100	143	12	32	32	NUM
cana-2100	143	13	no	no	NOUN
cana-2100	143	14	.	.	PUNCT
cana-2100	144	1	1s	1s	NUM
cana-2100	144	2	(	(	PUNCT
cana-2100	144	3	2025	2025	NUM
cana-2100	144	4	)	)	PUNCT
cana-2100	144	5	51	51	NUM
cana-2100	144	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2100	145	1	if	if	SCONJ
cana-2100	145	2	𝑏	𝑏	PROPN
cana-2100	145	3	∉	∉	PROPN
cana-2100	145	4	𝑆	𝑆	PROPN
cana-2100	145	5	,	,	PUNCT
cana-2100	145	6	then	then	ADV
cana-2100	145	7	[	[	X
cana-2100	145	8	𝑡𝑗𝑏	𝑡𝑗𝑏	X
cana-2100	145	9	,	,	PUNCT
cana-2100	145	10	𝑏	𝑏	NOUN
cana-2100	145	11	]	]	PUNCT
cana-2100	145	12	is	be	AUX
cana-2100	145	13	a	a	DET
cana-2100	145	14	closed	closed	ADJ
cana-2100	145	15	and	and	CCONJ
cana-2100	145	16	bounded	bounded	ADJ
cana-2100	145	17	interval	interval	NOUN
cana-2100	145	18	and	and	CCONJ
cana-2100	145	19	‖𝑓().‖hasacontinuousextensiononitbytheexistingright	‖𝑓().‖hasacontinuousextensiononitbytheexistingright	ADV
cana-2100	145	20	limit	limit	VERB
cana-2100	145	21	𝑓(𝑡𝑗𝑏	𝑓(𝑡𝑗𝑏	PROPN
cana-2100	145	22	+	+	NOUN
cana-2100	145	23	0	0	NUM
cana-2100	145	24	)	)	PUNCT
cana-2100	145	25	.	.	PUNCT
cana-2100	146	1	finally	finally	ADV
cana-2100	146	2	,	,	PUNCT
cana-2100	146	3	‖𝑓().‖hasacontinuousextension	‖𝑓().‖hasacontinuousextension	ADP
cana-2100	146	4	from	from	ADP
cana-2100	146	5	(	(	PUNCT
cana-2100	146	6	𝑡𝑗	𝑡𝑗	PROPN
cana-2100	146	7	,	,	PUNCT
cana-2100	146	8	𝑡𝑗+1	𝑡𝑗+1	PROPN
cana-2100	146	9	]	]	PUNCT
cana-2100	146	10	to	to	ADP
cana-2100	146	11	[	[	X
cana-2100	146	12	𝑡𝑗	𝑡𝑗	X
cana-2100	146	13	,	,	PUNCT
cana-2100	146	14	𝑡𝑗+1	𝑡𝑗+1	PROPN
cana-2100	146	15	]	]	PUNCT
cana-2100	146	16	by	by	ADP
cana-2100	146	17	the	the	DET
cana-2100	146	18	existence	existence	NOUN
cana-2100	146	19	of	of	ADP
cana-2100	146	20	the	the	DET
cana-2100	146	21	right	right	ADJ
cana-2100	146	22	limit	limit	NOUN
cana-2100	146	23	𝑓(𝑡𝑗	𝑓(𝑡𝑗	PROPN
cana-2100	146	24	+	+	NOUN
cana-2100	146	25	0	0	NUM
cana-2100	146	26	)	)	PUNCT
cana-2100	146	27	,	,	PUNCT
cana-2100	146	28	∀𝑗𝑎	∀𝑗𝑎	VERB
cana-2100	146	29	≤	≤	NUM
cana-2100	146	30	𝑗	𝑗	INTJ
cana-2100	146	31	<	<	X
cana-2100	146	32	𝑗𝑏.	𝑗𝑏.	X
cana-2100	146	33	thus	thus	ADV
cana-2100	146	34	iii	iii	X
cana-2100	146	35	)	)	PUNCT
cana-2100	146	36	‖𝑓‖𝑗𝑎−1	‖𝑓‖𝑗𝑎−1	PUNCT
cana-2100	147	1	=	=	NOUN
cana-2100	147	2	sup	sup	NOUN
cana-2100	147	3	𝑥∈[𝑎,𝑡𝑗𝑎	𝑥∈[𝑎,𝑡𝑗𝑎	PUNCT
cana-2100	147	4	]	]	PUNCT
cana-2100	147	5	 	 	SPACE
cana-2100	147	6	‖𝑓(𝑥)‖	‖𝑓(𝑥)‖	X
cana-2100	147	7	(	(	PUNCT
cana-2100	147	8	10	10	NUM
cana-2100	147	9	)	)	PUNCT
cana-2100	147	10	and	and	CCONJ
cana-2100	147	11	‖𝑓‖𝑗𝑏	‖𝑓‖𝑗𝑏	INTJ
cana-2100	147	12	=	=	NOUN
cana-2100	147	13	sup	sup	NOUN
cana-2100	147	14	𝑥∈[𝑡𝑗𝑏	𝑥∈[𝑡𝑗𝑏	NOUN
cana-2100	147	15	,	,	PUNCT
cana-2100	147	16	𝑏	𝑏	NOUN
cana-2100	147	17	]	]	PUNCT
cana-2100	147	18	 	 	SPACE
cana-2100	147	19	‖𝑓(𝑥)‖	‖𝑓(𝑥)‖	X
cana-2100	147	20	(	(	PUNCT
cana-2100	147	21	11	11	NUM
cana-2100	147	22	)	)	PUNCT
cana-2100	147	23	are	be	AUX
cana-2100	147	24	finite	finite	VERB
cana-2100	147	25	by	by	ADP
cana-2100	147	26	condition	condition	NOUN
cana-2100	147	27	(	(	PUNCT
cana-2100	147	28	ii	ii	NOUN
cana-2100	147	29	)	)	PUNCT
cana-2100	147	30	.	.	PUNCT
cana-2100	148	1	again	again	ADV
cana-2100	148	2	,	,	PUNCT
cana-2100	148	3	‖𝑓‖[𝑎,𝑏	‖𝑓‖[𝑎,𝑏	INTJ
cana-2100	148	4	]	]	X
cana-2100	148	5	=	=	PUNCT
cana-2100	148	6	sup	sup	NOUN
cana-2100	148	7	𝑥∈[𝑎,𝑏	𝑥∈[𝑎,𝑏	PROPN
cana-2100	148	8	]	]	PUNCT
cana-2100	148	9	 	 	SPACE
cana-2100	148	10	‖𝑓(𝑥)‖	‖𝑓(𝑥)‖	PUNCT
cana-2100	149	1	=	=	SYM
cana-2100	149	2	max	max	PROPN
cana-2100	149	3	𝑗𝑎−<𝑗<𝑗𝑏	𝑗𝑎−<𝑗<𝑗𝑏	PROPN
cana-2100	149	4	 	 	SPACE
cana-2100	149	5	‖𝑓‖𝑗	‖𝑓‖𝑗	PROPN
cana-2100	149	6	(	(	PUNCT
cana-2100	149	7	12	12	NUM
cana-2100	149	8	)	)	PUNCT
cana-2100	149	9	iv	iv	NOUN
cana-2100	149	10	)	)	PUNCT
cana-2100	149	11	since	since	SCONJ
cana-2100	149	12	𝑃𝐶[[𝑎	𝑃𝐶[[𝑎	PROPN
cana-2100	149	13	,	,	PUNCT
cana-2100	149	14	𝑏	𝑏	NOUN
cana-2100	149	15	]	]	X
cana-2100	149	16	,	,	PUNCT
cana-2100	149	17	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	149	18	]	]	X
cana-2100	149	19	⊂	⊂	PROPN
cana-2100	149	20	𝐿∞[[𝑎	𝐿∞[[𝑎	PROPN
cana-2100	149	21	,	,	PUNCT
cana-2100	149	22	𝑏	𝑏	NOUN
cana-2100	149	23	]	]	X
cana-2100	149	24	,	,	PUNCT
cana-2100	149	25	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	149	26	]	]	X
cana-2100	149	27	⬚	⬚	PROPN
cana-2100	149	28	and	and	CCONJ
cana-2100	149	29	𝐿∞[[𝑎	𝐿∞[[𝑎	ADJ
cana-2100	149	30	,	,	PUNCT
cana-2100	149	31	𝑏	𝑏	NOUN
cana-2100	149	32	]	]	X
cana-2100	149	33	,	,	PUNCT
cana-2100	149	34	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	149	35	]	]	PUNCT
cana-2100	149	36	is	be	AUX
cana-2100	149	37	a	a	DET
cana-2100	149	38	banach	banach	NOUN
cana-2100	149	39	space	space	NOUN
cana-2100	149	40	with	with	ADP
cana-2100	149	41	essential	essential	ADJ
cana-2100	149	42	sup	sup	NOUN
cana-2100	149	43	norm	norm	NOUN
cana-2100	149	44	,	,	PUNCT
cana-2100	149	45	it	it	PRON
cana-2100	149	46	follows	follow	VERB
cana-2100	149	47	that	that	SCONJ
cana-2100	149	48	‖	‖	ADJ
cana-2100	149	49	⋅	⋅	PROPN
cana-2100	149	50	‖[𝑎,𝑏	‖[𝑎,𝑏	X
cana-2100	149	51	]	]	PUNCT
cana-2100	149	52	is	be	AUX
cana-2100	149	53	a	a	DET
cana-2100	149	54	norm	norm	NOUN
cana-2100	149	55	,	,	PUNCT
cana-2100	149	56	where	where	SCONJ
cana-2100	149	57	𝐿∞[[𝑎	𝐿∞[[𝑎	ADJ
cana-2100	149	58	,	,	PUNCT
cana-2100	149	59	𝑏	𝑏	NOUN
cana-2100	149	60	]	]	X
cana-2100	149	61	,	,	PUNCT
cana-2100	149	62	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	149	63	]	]	PUNCT
cana-2100	149	64	is	be	AUX
cana-2100	149	65	called	call	VERB
cana-2100	149	66	a	a	DET
cana-2100	149	67	banach	banach	NOUN
cana-2100	149	68	space	space	NOUN
cana-2100	149	69	.	.	PUNCT
cana-2100	150	1	𝑓	𝑓	DET
cana-2100	150	2	∈	∈	PROPN
cana-2100	150	3	𝐿∞[[𝑎	𝐿∞[[𝑎	PROPN
cana-2100	150	4	,	,	PUNCT
cana-2100	150	5	𝑏	𝑏	NOUN
cana-2100	150	6	]	]	X
cana-2100	150	7	,	,	PUNCT
cana-2100	150	8	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	150	9	]	]	PUNCT
cana-2100	150	10	with	with	ADP
cana-2100	150	11	‖𝑓‖∞	‖𝑓‖∞	PROPN
cana-2100	150	12	=	=	SYM
cana-2100	150	13	0	0	PROPN
cana-2100	150	14	⇒	⇒	NOUN
cana-2100	150	15	𝑓	𝑓	PROPN
cana-2100	150	16	=	=	NOUN
cana-2100	150	17	0	0	NUM
cana-2100	150	18	almost	almost	ADV
cana-2100	150	19	everywhere	everywhere	ADV
cana-2100	150	20	and	and	CCONJ
cana-2100	150	21	not	not	PART
cana-2100	150	22	everywhere	everywhere	ADV
cana-2100	150	23	.	.	PUNCT
cana-2100	151	1	hence	hence	ADV
cana-2100	151	2	the	the	DET
cana-2100	151	3	real	real	ADJ
cana-2100	151	4	banach	banach	NOUN
cana-2100	151	5	space	space	NOUN
cana-2100	151	6	is	be	AUX
cana-2100	151	7	the	the	DET
cana-2100	151	8	factor	factor	NOUN
cana-2100	151	9	space	space	NOUN
cana-2100	151	10	𝐿∞[[𝑎	𝐿∞[[𝑎	PROPN
cana-2100	151	11	,	,	PUNCT
cana-2100	151	12	𝑏	𝑏	NOUN
cana-2100	151	13	]	]	X
cana-2100	151	14	,	,	PUNCT
cana-2100	151	15	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	151	16	]	]	PUNCT
cana-2100	151	17	with	with	ADP
cana-2100	151	18	{	{	PUNCT
cana-2100	151	19	𝑓	𝑓	DET
cana-2100	151	20	∣	∣	ADJ
cana-2100	151	21	𝑓	𝑓	DET
cana-2100	151	22	∈	∈	PROPN
cana-2100	151	23	𝐿∞[[𝑎	𝐿∞[[𝑎	PROPN
cana-2100	151	24	,	,	PUNCT
cana-2100	151	25	𝑏	𝑏	NOUN
cana-2100	151	26	]	]	X
cana-2100	151	27	,	,	PUNCT
cana-2100	151	28	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	151	29	]	]	PUNCT
cana-2100	151	30	,	,	PUNCT
cana-2100	151	31	‖𝑓‖∞	‖𝑓‖∞	PROPN
cana-2100	151	32	=	=	SYM
cana-2100	151	33	0	0	NUM
cana-2100	151	34	}	}	PUNCT
cana-2100	151	35	(	(	PUNCT
cana-2100	151	36	13	13	NUM
cana-2100	151	37	)	)	PUNCT
cana-2100	151	38	however	however	ADV
cana-2100	151	39	,	,	PUNCT
cana-2100	151	40	𝑃𝐶[[𝑎	𝑃𝐶[[𝑎	PROPN
cana-2100	151	41	,	,	PUNCT
cana-2100	151	42	𝑏	𝑏	NOUN
cana-2100	151	43	]	]	X
cana-2100	151	44	,	,	PUNCT
cana-2100	151	45	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	151	46	]	]	X
cana-2100	151	47	∩	∩	NOUN
cana-2100	151	48	{	{	PUNCT
cana-2100	151	49	𝑓	𝑓	PROPN
cana-2100	151	50	∣	∣	ADJ
cana-2100	151	51	𝑓	𝑓	DET
cana-2100	151	52	∈	∈	PROPN
cana-2100	151	53	𝐿∞[[𝑎	𝐿∞[[𝑎	PROPN
cana-2100	151	54	,	,	PUNCT
cana-2100	151	55	𝑏	𝑏	NOUN
cana-2100	151	56	]	]	X
cana-2100	151	57	,	,	PUNCT
cana-2100	151	58	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	151	59	]	]	PUNCT
cana-2100	151	60	,	,	PUNCT
cana-2100	151	61	‖𝑓‖∞	‖𝑓‖∞	PROPN
cana-2100	151	62	=	=	PUNCT
cana-2100	151	63	0	0	NUM
cana-2100	151	64	}	}	PUNCT
cana-2100	151	65	=	=	PRON
cana-2100	151	66	{	{	PUNCT
cana-2100	151	67	0}hence	0}hence	NOUN
cana-2100	151	68	,	,	PUNCT
cana-2100	151	69	the	the	DET
cana-2100	151	70	supremum	supremum	ADJ
cana-2100	151	71	so	so	ADV
cana-2100	151	72	defined	define	VERB
cana-2100	151	73	gives	give	VERB
cana-2100	151	74	a	a	DET
cana-2100	151	75	norm	norm	NOUN
cana-2100	151	76	on	on	ADP
cana-2100	151	77	𝑃𝐶[[𝑎	𝑃𝐶[[𝑎	PROPN
cana-2100	151	78	,	,	PUNCT
cana-2100	151	79	𝑏	𝑏	NOUN
cana-2100	151	80	]	]	X
cana-2100	151	81	,	,	PUNCT
cana-2100	151	82	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	151	83	]	]	PUNCT
cana-2100	151	84	which	which	PRON
cana-2100	151	85	is	be	AUX
cana-2100	151	86	a	a	DET
cana-2100	151	87	closed	closed	ADJ
cana-2100	151	88	linear	linear	ADJ
cana-2100	151	89	subspace	subspace	NOUN
cana-2100	151	90	of	of	ADP
cana-2100	151	91	𝐿∞[[𝑎	𝐿∞[[𝑎	PROPN
cana-2100	151	92	,	,	PUNCT
cana-2100	151	93	𝑏	𝑏	NOUN
cana-2100	151	94	]	]	X
cana-2100	151	95	,	,	PUNCT
cana-2100	151	96	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	151	97	]	]	PUNCT
cana-2100	151	98	.	.	PUNCT
cana-2100	152	1	now	now	ADV
cana-2100	152	2	,	,	PUNCT
cana-2100	152	3	let	let	VERB
cana-2100	152	4	the	the	DET
cana-2100	152	5	sequence	sequence	NOUN
cana-2100	152	6	{	{	PUNCT
cana-2100	152	7	𝑓𝑗	𝑓𝑗	ADJ
cana-2100	152	8	}	}	PUNCT
cana-2100	152	9	𝑗=1	𝑗=1	PROPN
cana-2100	152	10	∞	∞	NUM
cana-2100	152	11	⊂	⊂	PROPN
cana-2100	152	12	𝑃𝐶[[𝑎	𝑃𝐶[[𝑎	PROPN
cana-2100	152	13	,	,	PUNCT
cana-2100	152	14	𝑏	𝑏	NOUN
cana-2100	152	15	]	]	X
cana-2100	152	16	,	,	PUNCT
cana-2100	152	17	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	152	18	]	]	X
cana-2100	152	19	⊂	⊂	PROPN
cana-2100	152	20	𝐿∞[[𝑎	𝐿∞[[𝑎	PROPN
cana-2100	152	21	,	,	PUNCT
cana-2100	152	22	𝑏	𝑏	NOUN
cana-2100	152	23	]	]	X
cana-2100	152	24	,	,	PUNCT
cana-2100	152	25	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	152	26	]	]	PUNCT
cana-2100	152	27	be	be	AUX
cana-2100	152	28	convergent	convergent	ADJ
cana-2100	152	29	to	to	ADP
cana-2100	152	30	𝑓	𝑓	DET
cana-2100	152	31	∈	∈	PROPN
cana-2100	152	32	𝐿∞[[𝑎	𝐿∞[[𝑎	PROPN
cana-2100	152	33	,	,	PUNCT
cana-2100	152	34	𝑏	𝑏	NOUN
cana-2100	152	35	]	]	X
cana-2100	152	36	,	,	PUNCT
cana-2100	152	37	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	152	38	]	]	PUNCT
cana-2100	152	39	.	.	PUNCT
cana-2100	153	1	then	then	ADV
cana-2100	153	2	⬚	⬚	PROPN
cana-2100	153	3	from	from	ADP
cana-2100	153	4	⬚	⬚	NOUN
cana-2100	153	5	‖ℎ‖[𝑎,𝑏	‖ℎ‖[𝑎,𝑏	NOUN
cana-2100	153	6	]	]	X
cana-2100	153	7	=	=	SYM
cana-2100	153	8	sup	sup	NUM
cana-2100	153	9	𝑥∈𝑎,𝑏	𝑥∈𝑎,𝑏	NOUN
cana-2100	153	10	]	]	PUNCT
cana-2100	153	11	 	 	SPACE
cana-2100	153	12	‖ℎ(𝑥)‖	‖ℎ(𝑥)‖	PUNCT
cana-2100	154	1	=	=	NOUN
cana-2100	154	2	max𝑗𝑎≤𝑗≤𝑗𝑏	max𝑗𝑎≤𝑗≤𝑗𝑏	NOUN
cana-2100	154	3	 	 	SPACE
cana-2100	154	4	‖ℎ‖𝑗	‖ℎ‖𝑗	PROPN
cana-2100	154	5	≥	≥	NUM
cana-2100	154	6	‖ℎ‖𝑘	‖ℎ‖𝑘	NOUN
cana-2100	154	7	,	,	PUNCT
cana-2100	154	8	∀𝑗𝑎	∀𝑗𝑎	VERB
cana-2100	154	9	−	−	NOUN
cana-2100	154	10	𝑙	𝑙	SYM
cana-2100	154	11	≤	≤	NOUN
cana-2100	154	12	𝑘	𝑘	DET
cana-2100	154	13	≤	≤	NOUN
cana-2100	154	14	𝑗𝑏	𝑗𝑏	ADP
cana-2100	154	15	⬚	⬚	PROPN
cana-2100	154	16	,	,	PUNCT
cana-2100	154	17	⬚	⬚	PROPN
cana-2100	154	18	it	it	PRON
cana-2100	154	19	follows	follow	VERB
cana-2100	154	20	that	that	SCONJ
cana-2100	154	21	𝑓𝑗	𝑓𝑗	ADJ
cana-2100	154	22	→	→	PUNCT
cana-2100	154	23	𝑓	𝑓	PROPN
cana-2100	154	24	∈	∈	PROPN
cana-2100	154	25	𝐿∞[[𝑎	𝐿∞[[𝑎	PROPN
cana-2100	154	26	,	,	PUNCT
cana-2100	154	27	𝑏	𝑏	NOUN
cana-2100	154	28	]	]	X
cana-2100	154	29	,	,	PUNCT
cana-2100	154	30	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	154	31	]	]	PUNCT
cana-2100	154	32	for	for	ADP
cana-2100	154	33	𝑗	𝑗	PROPN
cana-2100	154	34	→	→	SYM
cana-2100	154	35	∞	∞	PROPN
cana-2100	154	36	in	in	ADP
cana-2100	154	37	‖	‖	PROPN
cana-2100	154	38	⋅	⋅	PROPN
cana-2100	154	39	‖[𝑎,𝑏	‖[𝑎,𝑏	PROPN
cana-2100	154	40	]	]	PUNCT
cana-2100	154	41	⇒	⇒	VERB
cana-2100	154	42	𝑓𝑗	𝑓𝑗	NOUN
cana-2100	154	43	→	→	PUNCT
cana-2100	154	44	𝑓	𝑓	PROPN
cana-2100	154	45	∈	∈	PROPN
cana-2100	154	46	𝐶𝑘[[𝑎	𝐶𝑘[[𝑎	PROPN
cana-2100	154	47	,	,	PUNCT
cana-2100	154	48	𝑏	𝑏	NOUN
cana-2100	154	49	]	]	X
cana-2100	154	50	,	,	PUNCT
cana-2100	154	51	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	154	52	]	]	PUNCT
cana-2100	154	53	in	in	ADP
cana-2100	154	54	‖	‖	PROPN
cana-2100	154	55	⋅	⋅	PROPN
cana-2100	154	56	‖𝑘∀𝑗𝑎	‖𝑘∀𝑗𝑎	X
cana-2100	155	1	−	−	PROPN
cana-2100	155	2	𝑙	𝑙	PROPN
cana-2100	155	3	≤	≤	NOUN
cana-2100	155	4	𝑘	𝑘	DET
cana-2100	155	5	≤	≤	NOUN
cana-2100	155	6	𝑗𝑏	𝑗𝑏	ADP
cana-2100	155	7	hence	hence	ADV
cana-2100	155	8	the	the	DET
cana-2100	155	9	sequence	sequence	NOUN
cana-2100	155	10	of	of	ADP
cana-2100	155	11	functions	function	NOUN
cana-2100	155	12	in	in	ADP
cana-2100	155	13	𝑃𝐶[[𝑎	𝑃𝐶[[𝑎	PROPN
cana-2100	155	14	,	,	PUNCT
cana-2100	155	15	𝑏	𝑏	NOUN
cana-2100	155	16	]	]	X
cana-2100	155	17	,	,	PUNCT
cana-2100	155	18	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	155	19	]	]	PUNCT
cana-2100	155	20	is	be	AUX
cana-2100	155	21	continuous	continuous	ADJ
cana-2100	155	22	and	and	CCONJ
cana-2100	155	23	convergent	convergent	NOUN
cana-2100	155	24	to	to	ADP
cana-2100	155	25	f	f	PROPN
cana-2100	155	26	uniformly	uniformly	ADV
cana-2100	155	27	in	in	ADP
cana-2100	155	28	each	each	DET
cana-2100	155	29	interval	interval	NOUN
cana-2100	155	30	𝐴𝑘	𝐴𝑘	PROPN
cana-2100	155	31	,	,	PUNCT
cana-2100	155	32	and	and	CCONJ
cana-2100	155	33	this	this	PRON
cana-2100	155	34	proves	prove	VERB
cana-2100	155	35	that	that	SCONJ
cana-2100	155	36	f	f	PROPN
cana-2100	155	37	is	be	AUX
cana-2100	155	38	continuous	continuous	ADJ
cana-2100	155	39	on	on	ADP
cana-2100	155	40	these	these	DET
cana-2100	155	41	intervals	interval	NOUN
cana-2100	155	42	∀𝑗𝑎	∀𝑗𝑎	VERB
cana-2100	156	1	−	−	PROPN
cana-2100	157	1	𝑙	𝑙	SYM
cana-2100	157	2	≤	≤	NOUN
cana-2100	157	3	𝑘	𝑘	DET
cana-2100	157	4	≤	≤	PROPN
cana-2100	157	5	𝑗𝑏.	𝑗𝑏.	NOUN
cana-2100	157	6	thus	thus	ADV
cana-2100	157	7	𝑓	𝑓	PRON
cana-2100	157	8	∈	∈	PROPN
cana-2100	157	9	𝑃𝐶[[𝑎	𝑃𝐶[[𝑎	PROPN
cana-2100	157	10	,	,	PUNCT
cana-2100	157	11	𝑏	𝑏	NOUN
cana-2100	157	12	]	]	PUNCT
cana-2100	157	13	,	,	PUNCT
cana-2100	157	14	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	157	15	]	]	PUNCT
cana-2100	157	16	.	.	PUNCT
cana-2100	158	1	lemma	lemma	PROPN
cana-2100	158	2	3.2	3.2	NUM
cana-2100	158	3	let	let	VERB
cana-2100	158	4	f	f	PROPN
cana-2100	158	5	∈	∈	PROPN
cana-2100	158	6	𝑃𝐶𝑙[𝑇	𝑃𝐶𝑙[𝑇	PROPN
cana-2100	158	7	,	,	PUNCT
cana-2100	158	8	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	158	9	]	]	PUNCT
cana-2100	158	10	.	.	PUNCT
cana-2100	159	1	then	then	ADV
cana-2100	159	2	𝑓|[𝑡𝑗,𝑡𝑗+1	𝑓|[𝑡𝑗,𝑡𝑗+1	X
cana-2100	159	3	]	]	X
cana-2100	159	4	⊂	⊂	PROPN
cana-2100	159	5	𝐶𝑙	𝐶𝑙	PROPN
cana-2100	159	6	(	(	PUNCT
cana-2100	159	7	(	(	PUNCT
cana-2100	159	8	𝑡𝑗	𝑡𝑗	PROPN
cana-2100	159	9	,	,	PUNCT
cana-2100	159	10	𝑡𝑗+1	𝑡𝑗+1	PROPN
cana-2100	159	11	]	]	PUNCT
cana-2100	159	12	,	,	PUNCT
cana-2100	159	13	𝑅𝑛	𝑅𝑛	PROPN
cana-2100	159	14	)	)	PUNCT
cana-2100	159	15	and	and	CCONJ
cana-2100	159	16	𝑓|[𝑡𝑗,𝑡𝑗+1](𝑡	𝑓|[𝑡𝑗,𝑡𝑗+1](𝑡	NUM
cana-2100	159	17	)	)	PUNCT
cana-2100	159	18	=	=	SYM
cana-2100	159	19	𝑓(𝑡𝑗	𝑓(𝑡𝑗	PROPN
cana-2100	159	20	+	+	NOUN
cana-2100	159	21	0	0	NUM
cana-2100	159	22	)	)	PUNCT
cana-2100	160	1	+	+	NUM
cana-2100	160	2	∫	∫	PROPN
cana-2100	160	3	  	  	SPACE
cana-2100	160	4	𝑡	𝑡	X
cana-2100	160	5	𝑡𝑗	𝑡𝑗	PROPN
cana-2100	160	6	 	 	SPACE
cana-2100	160	7	𝑓	𝑓	DET
cana-2100	160	8	′(𝑠)𝑑𝑠∀𝑡	′(𝑠)𝑑𝑠∀𝑡	PROPN
cana-2100	160	9	∈	∈	PROPN
cana-2100	160	10	(	(	PUNCT
cana-2100	160	11	𝑡𝑗	𝑡𝑗	NOUN
cana-2100	160	12	,	,	PUNCT
cana-2100	160	13	𝑡𝑗+1	𝑡𝑗+1	PROPN
cana-2100	160	14	]	]	PUNCT
cana-2100	160	15	,	,	PUNCT
cana-2100	160	16	−∞	−∞	X
cana-2100	160	17	<	<	X
cana-2100	160	18	𝑗	𝑗	X
cana-2100	160	19	<	<	X
cana-2100	160	20	∞(14)proof	∞(14)proof	NUM
cana-2100	160	21	:	:	PUNCT
cana-2100	160	22	this	this	PRON
cana-2100	160	23	follows	follow	VERB
cana-2100	160	24	from	from	ADP
cana-2100	160	25	properties	property	NOUN
cana-2100	160	26	of	of	ADP
cana-2100	160	27	indefinite	indefinite	ADJ
cana-2100	160	28	integrals	integral	NOUN
cana-2100	160	29	.	.	PUNCT
cana-2100	161	1	now	now	ADV
cana-2100	161	2	,	,	PUNCT
cana-2100	161	3	to	to	PART
cana-2100	161	4	establish	establish	VERB
cana-2100	161	5	the	the	DET
cana-2100	161	6	qualitative	qualitative	ADJ
cana-2100	161	7	properties	property	NOUN
cana-2100	161	8	of	of	ADP
cana-2100	161	9	equations	equation	NOUN
cana-2100	161	10	(	(	PUNCT
cana-2100	161	11	2	2	NUM
cana-2100	161	12	)	)	PUNCT
cana-2100	161	13	and	and	CCONJ
cana-2100	161	14	(	(	PUNCT
cana-2100	161	15	4	4	X
cana-2100	161	16	)	)	PUNCT
cana-2100	161	17	such	such	ADJ
cana-2100	161	18	as	as	ADP
cana-2100	161	19	the	the	DET
cana-2100	161	20	existence	existence	NOUN
cana-2100	161	21	of	of	ADP
cana-2100	161	22	solution	solution	NOUN
cana-2100	161	23	of	of	ADP
cana-2100	161	24	the	the	DET
cana-2100	161	25	initial	initial	ADJ
cana-2100	161	26	function	function	NOUN
cana-2100	161	27	problem	problem	NOUN
cana-2100	161	28	,	,	PUNCT
cana-2100	161	29	the	the	DET
cana-2100	161	30	continuous	continuous	ADJ
cana-2100	161	31	dependence	dependence	NOUN
cana-2100	161	32	of	of	ADP
cana-2100	161	33	the	the	DET
cana-2100	161	34	solutions	solution	NOUN
cana-2100	161	35	on	on	ADP
cana-2100	161	36	the	the	DET
cana-2100	161	37	initial	initial	ADJ
cana-2100	161	38	function	function	NOUN
cana-2100	161	39	(	(	PUNCT
cana-2100	161	40	4	4	NUM
cana-2100	161	41	)	)	PUNCT
cana-2100	161	42	and	and	CCONJ
cana-2100	161	43	stability	stability	NOUN
cana-2100	161	44	of	of	ADP
cana-2100	161	45	the	the	DET
cana-2100	161	46	solutions	solution	NOUN
cana-2100	161	47	,	,	PUNCT
cana-2100	161	48	the	the	DET
cana-2100	161	49	integral	integral	ADJ
cana-2100	161	50	equivalence	equivalence	NOUN
cana-2100	161	51	of	of	ADP
cana-2100	161	52	the	the	DET
cana-2100	161	53	problem	problem	NOUN
cana-2100	161	54	is	be	AUX
cana-2100	161	55	adopted	adopt	VERB
cana-2100	161	56	.	.	PUNCT
cana-2100	162	1	using	use	VERB
cana-2100	162	2	lemma	lemma	PROPN
cana-2100	162	3	3.2	3.2	NUM
cana-2100	162	4	and	and	CCONJ
cana-2100	162	5	notation	notation	NOUN
cana-2100	162	6	(	(	PUNCT
cana-2100	162	7	1.1	1.1	NUM
cana-2100	162	8	)	)	PUNCT
cana-2100	162	9	equation	equation	NOUN
cana-2100	162	10	(	(	PUNCT
cana-2100	162	11	2	2	X
cana-2100	162	12	)	)	PUNCT
cana-2100	162	13	is	be	AUX
cana-2100	162	14	re	re	VERB
cana-2100	162	15	-	-	VERB
cana-2100	162	16	written	write	VERB
cana-2100	162	17	as	as	ADP
cana-2100	162	18	:	:	PUNCT
cana-2100	162	19	𝑥‾	𝑥‾	PROPN
cana-2100	162	20	∘	∘	PROPN
cana-2100	162	21	�	�	PROPN
cana-2100	162	22	̂	̂	NUM
cana-2100	162	23	�	�	NOUN
cana-2100	162	24	=	=	PUNCT
cana-2100	162	25	𝑥(𝑡𝑘	𝑥(𝑡𝑘	X
cana-2100	162	26	)	)	PUNCT
cana-2100	163	1	+	+	NUM
cana-2100	163	2	∫	∫	PROPN
cana-2100	163	3	  	  	SPACE
cana-2100	163	4	𝑡	𝑡	PROPN
cana-2100	163	5	𝑡𝑘	𝑡𝑘	ADV
cana-2100	163	6	 	 	SPACE
cana-2100	163	7	𝑓(𝑠	𝑓(𝑠	NOUN
cana-2100	163	8	,	,	PUNCT
cana-2100	163	9	𝑥(𝑠	𝑥(𝑠	PROPN
cana-2100	163	10	)	)	PUNCT
cana-2100	163	11	,	,	PUNCT
cana-2100	163	12	�	�	PROPN
cana-2100	163	13	̂	̂	SYM
cana-2100	163	14	�	�	PROPN
cana-2100	163	15	∘	∘	X
cana-2100	163	16	(	(	PUNCT
cana-2100	163	17	�	�	PROPN
cana-2100	163	18	̂	̂	PROPN
cana-2100	163	19	�	�	NOUN
cana-2100	163	20	−	−	PROPN
cana-2100	163	21	ℎ‾	ℎ‾	PROPN
cana-2100	163	22	∘	∘	PROPN
cana-2100	163	23	�	�	PROPN
cana-2100	163	24	̂	̂	NUM
cana-2100	163	25	�	�	NOUN
cana-2100	163	26	))𝑑𝑠	))𝑑𝑠	NOUN
cana-2100	163	27	+	+	CCONJ
cana-2100	163	28	∑	∑	PUNCT
cana-2100	163	29	  	  	SPACE
cana-2100	163	30	𝑡𝑚≤𝑡𝑘<𝑡	𝑡𝑚≤𝑡𝑘<𝑡	PROPN
cana-2100	163	31	 	 	SPACE
cana-2100	163	32	𝑓∗(𝑡𝑚	𝑓∗(𝑡𝑚	PROPN
cana-2100	163	33	,	,	PUNCT
cana-2100	163	34	𝑥(𝑡𝑚	𝑥(𝑡𝑚	PROPN
cana-2100	163	35	)	)	PUNCT
cana-2100	163	36	)	)	PUNCT
cana-2100	163	37	(	(	PUNCT
cana-2100	163	38	15	15	X
cana-2100	163	39	)	)	PUNCT
cana-2100	163	40	communications	communication	NOUN
cana-2100	163	41	on	on	ADP
cana-2100	163	42	applied	apply	VERB
cana-2100	163	43	nonlinear	nonlinear	ADJ
cana-2100	163	44	analysis	analysis	NOUN
cana-2100	163	45	issn	issn	NOUN
cana-2100	163	46	:	:	PUNCT
cana-2100	163	47	1074	1074	NUM
cana-2100	163	48	-	-	PUNCT
cana-2100	163	49	133x	133x	NUM
cana-2100	163	50	vol	vol	NOUN
cana-2100	163	51	32	32	NUM
cana-2100	163	52	no	no	NOUN
cana-2100	163	53	.	.	PUNCT
cana-2100	164	1	1s	1s	NUM
cana-2100	164	2	(	(	PUNCT
cana-2100	164	3	2025	2025	NUM
cana-2100	164	4	)	)	PUNCT
cana-2100	164	5	52	52	NUM
cana-2100	164	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2100	164	7	where	where	SCONJ
cana-2100	164	8	𝑓∗(𝑡𝑚	𝑓∗(𝑡𝑚	PROPN
cana-2100	164	9	,	,	PUNCT
cana-2100	164	10	𝑥(𝑡𝑚	𝑥(𝑡𝑚	PROPN
cana-2100	164	11	)	)	PUNCT
cana-2100	164	12	)	)	PUNCT
cana-2100	165	1	=	=	PUNCT
cana-2100	165	2	𝑥(𝑡𝑚	𝑥(𝑡𝑚	NOUN
cana-2100	165	3	+	+	CCONJ
cana-2100	165	4	)	)	PUNCT
cana-2100	166	1	−	−	PRON
cana-2100	166	2	𝑥(𝑡𝑚	𝑥(𝑡𝑚	NOUN
cana-2100	166	3	)	)	PUNCT
cana-2100	166	4	is	be	AUX
cana-2100	166	5	the	the	DET
cana-2100	166	6	prescribed	prescribed	ADJ
cana-2100	166	7	jump	jump	NOUN
cana-2100	166	8	at	at	ADP
cana-2100	166	9	the	the	DET
cana-2100	166	10	impulse	impulse	ADJ
cana-2100	166	11	point	point	NOUN
cana-2100	166	12	𝑡𝑚	𝑡𝑚	ADP
cana-2100	166	13	∈	∈	PROPN
cana-2100	166	14	𝑆	𝑆	PROPN
cana-2100	166	15	,	,	PUNCT
cana-2100	166	16	∀𝑘	∀𝑘	X
cana-2100	166	17	=	=	SYM
cana-2100	166	18	1,2,3	1,2,3	NUM
cana-2100	166	19	,	,	PUNCT
cana-2100	166	20	…	…	PUNCT
cana-2100	166	21	and	and	CCONJ
cana-2100	166	22	𝑡	𝑡	X
cana-2100	166	23	>	>	X
cana-2100	166	24	𝑡𝑘.	𝑡𝑘.	NOUN
cana-2100	166	25	with	with	ADP
cana-2100	166	26	the	the	DET
cana-2100	166	27	formulation	formulation	NOUN
cana-2100	166	28	(	(	PUNCT
cana-2100	166	29	15	15	NUM
cana-2100	166	30	)	)	PUNCT
cana-2100	166	31	above	above	ADV
cana-2100	166	32	,	,	PUNCT
cana-2100	166	33	some	some	DET
cana-2100	166	34	conditions	condition	NOUN
cana-2100	166	35	are	be	AUX
cana-2100	166	36	imposed	impose	VERB
cana-2100	166	37	on	on	ADP
cana-2100	166	38	𝑓	𝑓	PRON
cana-2100	166	39	and	and	CCONJ
cana-2100	166	40	𝑥	𝑥	NOUN
cana-2100	166	41	to	to	PART
cana-2100	166	42	ensure	ensure	VERB
cana-2100	166	43	the	the	DET
cana-2100	166	44	existence	existence	NOUN
cana-2100	166	45	and	and	CCONJ
cana-2100	166	46	uniqueness	uniqueness	NOUN
cana-2100	166	47	of	of	ADP
cana-2100	166	48	solutions	solution	NOUN
cana-2100	166	49	and	and	CCONJ
cana-2100	166	50	the	the	DET
cana-2100	166	51	continuous	continuous	ADJ
cana-2100	166	52	dependence	dependence	NOUN
cana-2100	166	53	of	of	ADP
cana-2100	166	54	solutions	solution	NOUN
cana-2100	166	55	on	on	ADP
cana-2100	166	56	the	the	DET
cana-2100	166	57	initial	initial	ADJ
cana-2100	166	58	function	function	NOUN
cana-2100	166	59	.	.	PUNCT
cana-2100	167	1	to	to	PART
cana-2100	167	2	obtain	obtain	VERB
cana-2100	167	3	the	the	DET
cana-2100	167	4	stability	stability	NOUN
cana-2100	167	5	of	of	ADP
cana-2100	167	6	solutions	solution	NOUN
cana-2100	167	7	,	,	PUNCT
cana-2100	167	8	the	the	DET
cana-2100	167	9	problem	problem	NOUN
cana-2100	167	10	is	be	AUX
cana-2100	167	11	re	re	VERB
cana-2100	167	12	-	-	VERB
cana-2100	167	13	formulated	formulate	VERB
cana-2100	167	14	slightly	slightly	ADV
cana-2100	167	15	by	by	ADP
cana-2100	167	16	separating	separate	VERB
cana-2100	167	17	the	the	DET
cana-2100	167	18	linear	linear	ADJ
cana-2100	167	19	components	component	NOUN
cana-2100	167	20	of	of	ADP
cana-2100	167	21	𝑓	𝑓	PRON
cana-2100	167	22	from	from	ADP
cana-2100	167	23	the	the	DET
cana-2100	167	24	non	non	ADJ
cana-2100	167	25	-	-	ADJ
cana-2100	167	26	linear	linear	ADJ
cana-2100	167	27	component	component	NOUN
cana-2100	167	28	as	as	SCONJ
cana-2100	167	29	follows	follow	VERB
cana-2100	167	30	:	:	PUNCT
cana-2100	167	31	(	(	PUNCT
cana-2100	167	32	16	16	NUM
cana-2100	167	33	)	)	PUNCT
cana-2100	167	34	where	where	SCONJ
cana-2100	167	35	𝑓	𝑓	PRON
cana-2100	167	36	and	and	CCONJ
cana-2100	167	37	𝑓∗	𝑓∗	NOUN
cana-2100	167	38	are	be	AUX
cana-2100	167	39	respectively	respectively	ADV
cana-2100	167	40	the	the	DET
cana-2100	167	41	linear	linear	ADJ
cana-2100	167	42	and	and	CCONJ
cana-2100	167	43	non	non	ADJ
cana-2100	167	44	-	-	ADJ
cana-2100	167	45	linear	linear	ADJ
cana-2100	167	46	components	component	NOUN
cana-2100	167	47	of	of	ADP
cana-2100	167	48	𝑓.	𝑓.	NOUN
cana-2100	167	49	this	this	DET
cana-2100	167	50	formulation	formulation	NOUN
cana-2100	167	51	enables	enable	VERB
cana-2100	167	52	us	we	PRON
cana-2100	167	53	to	to	PART
cana-2100	167	54	develop	develop	VERB
cana-2100	167	55	a	a	DET
cana-2100	167	56	scheme	scheme	NOUN
cana-2100	167	57	for	for	ADP
cana-2100	167	58	stability	stability	NOUN
cana-2100	167	59	of	of	ADP
cana-2100	167	60	solutions	solution	NOUN
cana-2100	167	61	similar	similar	ADJ
cana-2100	167	62	to	to	ADP
cana-2100	167	63	that	that	PRON
cana-2100	167	64	of	of	ADP
cana-2100	167	65	perron	perron	PROPN
cana-2100	167	66	.	.	PUNCT
cana-2100	168	1	in	in	ADP
cana-2100	168	2	his	his	PRON
cana-2100	168	3	work	work	NOUN
cana-2100	168	4	[	[	X
cana-2100	168	5	27	27	NUM
cana-2100	168	6	]	]	PUNCT
cana-2100	168	7	,	,	PUNCT
cana-2100	168	8	perron	perron	PROPN
cana-2100	168	9	discussed	discuss	VERB
cana-2100	168	10	the	the	DET
cana-2100	168	11	stability	stability	NOUN
cana-2100	168	12	and	and	CCONJ
cana-2100	168	13	asymptotic	asymptotic	ADJ
cana-2100	168	14	stability	stability	NOUN
cana-2100	168	15	of	of	ADP
cana-2100	168	16	solutions	solution	NOUN
cana-2100	168	17	of	of	ADP
cana-2100	168	18	𝑥	𝑥	NOUN
cana-2100	168	19	′(𝑡	′(𝑡	NOUN
cana-2100	168	20	)	)	PUNCT
cana-2100	168	21	=	=	PUNCT
cana-2100	169	1	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	169	2	,	,	PUNCT
cana-2100	169	3	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	169	4	)	)	PUNCT
cana-2100	169	5	)	)	PUNCT
cana-2100	170	1	+	+	CCONJ
cana-2100	170	2	𝑓∗(𝑡	𝑓∗(𝑡	PROPN
cana-2100	170	3	,	,	PUNCT
cana-2100	170	4	𝑥(𝑡	𝑥(𝑡	NOUN
cana-2100	170	5	)	)	PUNCT
cana-2100	170	6	)	)	PUNCT
cana-2100	170	7	(	(	PUNCT
cana-2100	170	8	17	17	NUM
cana-2100	170	9	)	)	PUNCT
cana-2100	170	10	with	with	ADP
cana-2100	170	11	respect	respect	NOUN
cana-2100	170	12	to	to	ADP
cana-2100	170	13	the	the	DET
cana-2100	170	14	stability	stability	NOUN
cana-2100	170	15	and	and	CCONJ
cana-2100	170	16	asymptotic	asymptotic	ADJ
cana-2100	170	17	stability	stability	NOUN
cana-2100	170	18	of	of	ADP
cana-2100	170	19	the	the	DET
cana-2100	170	20	solution	solution	NOUN
cana-2100	170	21	of	of	ADP
cana-2100	170	22	the	the	DET
cana-2100	170	23	homogeneous	homogeneous	ADJ
cana-2100	170	24	linear	linear	PROPN
cana-2100	170	25	system	system	NOUN
cana-2100	170	26	𝑦	𝑦	NOUN
cana-2100	170	27	′(𝑡	′(𝑡	NOUN
cana-2100	170	28	)	)	PUNCT
cana-2100	170	29	=	=	SYM
cana-2100	170	30	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	170	31	,	,	PUNCT
cana-2100	170	32	𝑦(𝑡	𝑦(𝑡	NUM
cana-2100	170	33	)	)	PUNCT
cana-2100	170	34	)	)	PUNCT
cana-2100	170	35	(	(	PUNCT
cana-2100	170	36	18	18	NUM
cana-2100	170	37	)	)	PUNCT
cana-2100	170	38	in	in	ADP
cana-2100	170	39	line	line	NOUN
cana-2100	170	40	with	with	ADP
cana-2100	170	41	perron	perron	PROPN
cana-2100	170	42	's	's	PART
cana-2100	170	43	formulation	formulation	NOUN
cana-2100	170	44	,	,	PUNCT
cana-2100	170	45	in	in	ADP
cana-2100	170	46	place	place	NOUN
cana-2100	170	47	of	of	ADP
cana-2100	170	48	relation	relation	NOUN
cana-2100	170	49	(	(	PUNCT
cana-2100	170	50	16	16	NUM
cana-2100	170	51	)	)	PUNCT
cana-2100	170	52	,	,	PUNCT
cana-2100	170	53	the	the	DET
cana-2100	170	54	system	system	NOUN
cana-2100	170	55	{	{	PUNCT
cana-2100	170	56	𝑦	𝑦	NOUN
cana-2100	170	57	′(𝑡	′(𝑡	NOUN
cana-2100	170	58	)	)	PUNCT
cana-2100	170	59	=	=	PUNCT
cana-2100	170	60	𝑓(𝑡	𝑓(𝑡	NOUN
cana-2100	170	61	,	,	PUNCT
cana-2100	170	62	𝑦(𝑡	𝑦(𝑡	NUM
cana-2100	170	63	)	)	PUNCT
cana-2100	170	64	,	,	PUNCT
cana-2100	170	65	�	�	PROPN
cana-2100	170	66	̂	̂	SYM
cana-2100	170	67	�	�	PROPN
cana-2100	170	68	∘	∘	X
cana-2100	170	69	(	(	PUNCT
cana-2100	170	70	�	�	PROPN
cana-2100	170	71	̂	̂	PROPN
cana-2100	170	72	�	�	NOUN
cana-2100	170	73	−	−	PROPN
cana-2100	170	74	ℎ‾	ℎ‾	PROPN
cana-2100	170	75	∘	∘	PROPN
cana-2100	170	76	�	�	PROPN
cana-2100	170	77	̂	̂	NUM
cana-2100	170	78	�	�	NOUN
cana-2100	170	79	))∀𝑡	))∀𝑡	PRON
cana-2100	170	80	∈	∈	PROPN
cana-2100	170	81	𝑇	𝑇	PROPN
cana-2100	170	82	∖	∖	PROPN
cana-2100	170	83	𝑆	𝑆	PROPN
cana-2100	170	84	δ𝑦(𝑡𝑘	δ𝑦(𝑡𝑘	PROPN
cana-2100	170	85	)	)	PUNCT
cana-2100	170	86	=	=	SYM
cana-2100	170	87	𝑓∗(𝑡𝑘	𝑓∗(𝑡𝑘	NUM
cana-2100	170	88	,	,	PUNCT
cana-2100	170	89	𝑦(𝑡𝑘))∀𝑡	𝑦(𝑡𝑘))∀𝑡	PROPN
cana-2100	170	90	∈	∈	PROPN
cana-2100	170	91	𝑆	𝑆	PROPN
cana-2100	170	92	(	(	PUNCT
cana-2100	170	93	19	19	NUM
cana-2100	170	94	)	)	PUNCT
cana-2100	170	95	will	will	AUX
cana-2100	170	96	be	be	AUX
cana-2100	170	97	examined	examine	VERB
cana-2100	170	98	subject	subject	ADJ
cana-2100	170	99	to	to	ADP
cana-2100	170	100	the	the	DET
cana-2100	170	101	initial	initial	ADJ
cana-2100	170	102	condition	condition	NOUN
cana-2100	170	103	in	in	ADP
cana-2100	170	104	equation	equation	NOUN
cana-2100	170	105	(	(	PUNCT
cana-2100	170	106	4	4	NUM
cana-2100	170	107	)	)	PUNCT
cana-2100	170	108	,	,	PUNCT
cana-2100	170	109	where	where	SCONJ
cana-2100	170	110	𝑓∗(𝑡𝑘	𝑓∗(𝑡𝑘	NOUN
cana-2100	170	111	,	,	PUNCT
cana-2100	170	112	𝑦(𝑡𝑘	𝑦(𝑡𝑘	NOUN
cana-2100	170	113	)	)	PUNCT
cana-2100	170	114	)	)	PUNCT
cana-2100	170	115	prescribes	prescribe	VERB
cana-2100	170	116	the	the	DET
cana-2100	170	117	jump	jump	NOUN
cana-2100	170	118	at	at	ADP
cana-2100	170	119	𝑡𝑘.	𝑡𝑘.	NOUN
cana-2100	170	120	therefore	therefore	ADV
cana-2100	170	121	,	,	PUNCT
cana-2100	170	122	the	the	DET
cana-2100	170	123	integral	integral	ADJ
cana-2100	170	124	equivalence	equivalence	NOUN
cana-2100	170	125	of	of	ADP
cana-2100	170	126	this	this	PRON
cana-2100	170	127	is	be	AUX
cana-2100	170	128	:	:	PUNCT
cana-2100	170	129	𝑦‾	𝑦‾	ADP
cana-2100	170	130	∘	∘	ADJ
cana-2100	170	131	�	�	PROPN
cana-2100	170	132	̂	̂	VERB
cana-2100	170	133	�	�	PROPN
cana-2100	170	134	=	=	PUNCT
cana-2100	170	135	𝑦(𝑡𝑘	𝑦(𝑡𝑘	PROPN
cana-2100	170	136	)	)	PUNCT
cana-2100	170	137	+	+	NUM
cana-2100	170	138	∫	∫	PROPN
cana-2100	170	139	  	  	SPACE
cana-2100	170	140	𝑡	𝑡	PROPN
cana-2100	170	141	𝑡𝑘	𝑡𝑘	ADV
cana-2100	170	142	 	 	SPACE
cana-2100	170	143	𝑓(𝑠	𝑓(𝑠	PROPN
cana-2100	170	144	,	,	PUNCT
cana-2100	170	145	𝑦(𝑠	𝑦(𝑠	PROPN
cana-2100	170	146	)	)	PUNCT
cana-2100	170	147	,	,	PUNCT
cana-2100	170	148	�	�	PROPN
cana-2100	170	149	̂	̂	SYM
cana-2100	170	150	�	�	PROPN
cana-2100	170	151	∘	∘	X
cana-2100	170	152	(	(	PUNCT
cana-2100	170	153	�	�	PROPN
cana-2100	170	154	̂	̂	PROPN
cana-2100	170	155	�	�	NOUN
cana-2100	170	156	−	−	PROPN
cana-2100	170	157	ℎ‾	ℎ‾	PROPN
cana-2100	170	158	∘	∘	PROPN
cana-2100	170	159	�	�	PROPN
cana-2100	170	160	̂	̂	NUM
cana-2100	170	161	�	�	NOUN
cana-2100	170	162	))𝑑𝑠	))𝑑𝑠	NOUN
cana-2100	170	163	+	+	CCONJ
cana-2100	170	164	∑	∑	ADJ
cana-2100	170	165	  	  	SPACE
cana-2100	170	166	𝑡𝑚⊴𝑘	𝑡𝑚⊴𝑘	NOUN
cana-2100	170	167	<	<	X
cana-2100	170	168	 	 	SPACE
cana-2100	170	169	𝑓∗(𝑡𝑚	𝑓∗(𝑡𝑚	PROPN
cana-2100	170	170	,	,	PUNCT
cana-2100	170	171	𝑦(𝑡𝑚	𝑦(𝑡𝑚	PROPN
cana-2100	170	172	)	)	PUNCT
cana-2100	170	173	)	)	PUNCT
cana-2100	170	174	(	(	PUNCT
cana-2100	170	175	20	20	X
cana-2100	170	176	)	)	PUNCT
cana-2100	170	177	conclusion	conclusion	NOUN
cana-2100	170	178	the	the	DET
cana-2100	170	179	solutions	solution	NOUN
cana-2100	170	180	of	of	ADP
cana-2100	170	181	impulsive	impulsive	ADJ
cana-2100	170	182	differential	differential	ADJ
cana-2100	170	183	equations	equation	NOUN
cana-2100	170	184	with	with	ADP
cana-2100	170	185	the	the	DET
cana-2100	170	186	general	general	ADJ
cana-2100	170	187	concept	concept	NOUN
cana-2100	170	188	of	of	ADP
cana-2100	170	189	delays	delay	NOUN
cana-2100	170	190	are	be	AUX
cana-2100	170	191	,	,	PUNCT
cana-2100	170	192	however	however	ADV
cana-2100	170	193	,	,	PUNCT
cana-2100	170	194	fundamentally	fundamentally	ADV
cana-2100	170	195	different	different	ADJ
cana-2100	170	196	from	from	ADP
cana-2100	170	197	those	those	PRON
cana-2100	170	198	of	of	ADP
cana-2100	170	199	ordinary	ordinary	ADJ
cana-2100	170	200	differential	differential	ADJ
cana-2100	170	201	equations	equation	NOUN
cana-2100	170	202	.	.	PUNCT
cana-2100	171	1	it	it	PRON
cana-2100	171	2	is	be	AUX
cana-2100	171	3	observed	observe	VERB
cana-2100	171	4	that	that	SCONJ
cana-2100	171	5	the	the	DET
cana-2100	171	6	derivative	derivative	NOUN
cana-2100	171	7	of	of	ADP
cana-2100	171	8	the	the	DET
cana-2100	171	9	solutions	solution	NOUN
cana-2100	171	10	become	become	VERB
cana-2100	171	11	discontinuous	discontinuous	ADJ
cana-2100	171	12	even	even	ADV
cana-2100	171	13	at	at	ADP
cana-2100	171	14	non	non	ADJ
cana-2100	171	15	-	-	ADJ
cana-2100	171	16	impulse	impulse	ADJ
cana-2100	171	17	points	point	NOUN
cana-2100	171	18	and	and	CCONJ
cana-2100	171	19	so	so	ADV
cana-2100	171	20	ceases	cease	VERB
cana-2100	171	21	to	to	PART
cana-2100	171	22	be	be	AUX
cana-2100	171	23	differentiable	differentiable	ADJ
cana-2100	171	24	.	.	PUNCT
cana-2100	172	1	also	also	ADV
cana-2100	172	2	,	,	PUNCT
cana-2100	172	3	the	the	DET
cana-2100	172	4	forcing	force	VERB
cana-2100	172	5	function	function	NOUN
cana-2100	172	6	has	have	VERB
cana-2100	172	7	no	no	DET
cana-2100	172	8	limit	limit	NOUN
cana-2100	172	9	even	even	ADV
cana-2100	172	10	when	when	SCONJ
cana-2100	172	11	the	the	DET
cana-2100	172	12	delays	delay	NOUN
cana-2100	172	13	are	be	AUX
cana-2100	172	14	strictly	strictly	ADV
cana-2100	172	15	ascending	ascend	VERB
cana-2100	172	16	and	and	CCONJ
cana-2100	172	17	continuously	continuously	ADV
cana-2100	172	18	differentiable	differentiable	ADJ
cana-2100	172	19	functions	function	NOUN
cana-2100	172	20	.	.	PUNCT
cana-2100	173	1	here	here	ADV
cana-2100	173	2	,	,	PUNCT
cana-2100	173	3	it	it	PRON
cana-2100	173	4	has	have	AUX
cana-2100	173	5	been	be	AUX
cana-2100	173	6	shown	show	VERB
cana-2100	173	7	that	that	SCONJ
cana-2100	173	8	it	it	PRON
cana-2100	173	9	is	be	AUX
cana-2100	173	10	possible	possible	ADJ
cana-2100	173	11	to	to	PART
cana-2100	173	12	define	define	VERB
cana-2100	173	13	a	a	DET
cana-2100	173	14	continuous	continuous	ADJ
cana-2100	173	15	ascending	ascend	VERB
cana-2100	173	16	delay	delay	NOUN
cana-2100	173	17	function	function	NOUN
cana-2100	173	18	whose	whose	DET
cana-2100	173	19	derivative	derivative	ADJ
cana-2100	173	20	exists	exist	VERB
cana-2100	173	21	everywhere	everywhere	ADV
cana-2100	173	22	on	on	ADP
cana-2100	173	23	an	an	DET
cana-2100	173	24	interval	interval	NOUN
cana-2100	173	25	𝐼𝑘	𝐼𝑘	PRON
cana-2100	173	26	extendible	extendible	ADJ
cana-2100	173	27	to	to	ADP
cana-2100	173	28	𝑇	𝑇	PROPN
cana-2100	173	29	,	,	PUNCT
cana-2100	173	30	whereas	whereas	SCONJ
cana-2100	173	31	the	the	DET
cana-2100	173	32	right	right	ADJ
cana-2100	173	33	-	-	PUNCT
cana-2100	173	34	hand	hand	NOUN
cana-2100	173	35	side	side	NOUN
cana-2100	173	36	of	of	ADP
cana-2100	173	37	equation	equation	NOUN
cana-2100	173	38	(	(	PUNCT
cana-2100	173	39	2	2	X
cana-2100	173	40	)	)	PUNCT
cana-2100	173	41	does	do	AUX
cana-2100	173	42	not	not	PART
cana-2100	173	43	have	have	VERB
cana-2100	173	44	limits	limit	NOUN
cana-2100	173	45	at	at	ADP
cana-2100	173	46	certain	certain	ADJ
cana-2100	173	47	other	other	ADJ
cana-2100	173	48	points	point	NOUN
cana-2100	173	49	which	which	PRON
cana-2100	173	50	are	be	AUX
cana-2100	173	51	not	not	PART
cana-2100	173	52	even	even	ADV
cana-2100	173	53	impulse	impulse	ADJ
cana-2100	173	54	points	point	NOUN
cana-2100	173	55	.	.	PUNCT
cana-2100	174	1	the	the	DET
cana-2100	174	2	integral	integral	ADJ
cana-2100	174	3	equivalence	equivalence	NOUN
cana-2100	174	4	of	of	ADP
cana-2100	174	5	the	the	DET
cana-2100	174	6	formulated	formulated	ADJ
cana-2100	174	7	system	system	NOUN
cana-2100	174	8	of	of	ADP
cana-2100	174	9	impulsive	impulsive	ADJ
cana-2100	174	10	delay	delay	NOUN
cana-2100	174	11	differential	differential	NOUN
cana-2100	174	12	equations	equation	NOUN
cana-2100	174	13	has	have	AUX
cana-2100	174	14	also	also	ADV
cana-2100	174	15	been	be	AUX
cana-2100	174	16	obtained	obtain	VERB
cana-2100	174	17	.	.	PUNCT
cana-2100	175	1	references	reference	NOUN
cana-2100	175	2	[	[	X
cana-2100	175	3	1	1	NUM
cana-2100	175	4	]	]	X
cana-2100	175	5	abasiekwere	abasiekwere	PROPN
cana-2100	175	6	,	,	PUNCT
cana-2100	175	7	u.	u.	PROPN
cana-2100	175	8	a.	a.	PROPN
cana-2100	175	9	,	,	PUNCT
cana-2100	175	10	esuabana	esuabana	PROPN
cana-2100	175	11	,	,	PUNCT
cana-2100	175	12	i.	i.	NOUN
cana-2100	175	13	m.	m.	PROPN
cana-2100	175	14	,	,	PUNCT
cana-2100	175	15	isaac	isaac	PROPN
cana-2100	175	16	,	,	PUNCT
cana-2100	175	17	i.	i.	PROPN
cana-2100	175	18	o.	o.	PROPN
cana-2100	175	19	,	,	PUNCT
cana-2100	175	20	lipcsey	lipcsey	ADJ
cana-2100	175	21	,	,	PUNCT
cana-2100	175	22	z	z	NOUN
cana-2100	175	23	,	,	PUNCT
cana-2100	175	24	classification	classification	NOUN
cana-2100	175	25	of	of	ADP
cana-2100	175	26	non	non	ADJ
cana-2100	175	27	-	-	ADJ
cana-2100	175	28	oscillatory	oscillatory	ADJ
cana-2100	175	29	solutions	solution	NOUN
cana-2100	175	30	of	of	ADP
cana-2100	175	31	nonlinear	nonlinear	ADJ
cana-2100	175	32	neutral	neutral	ADJ
cana-2100	175	33	delay	delay	NOUN
cana-2100	175	34	impulsive	impulsive	ADJ
cana-2100	175	35	differential	differential	ADJ
cana-2100	175	36	equations	equation	NOUN
cana-2100	175	37	,	,	PUNCT
cana-2100	175	38	global	global	ADJ
cana-2100	175	39	journal	journal	NOUN
cana-2100	175	40	of	of	ADP
cana-2100	175	41	science	science	PROPN
cana-2100	175	42	frontier	frontier	NOUN
cana-2100	175	43	research	research	NOUN
cana-2100	175	44	:	:	PUNCT
cana-2100	175	45	mathematics	mathematic	NOUN
cana-2100	175	46	and	and	CCONJ
cana-2100	175	47	decision	decision	NOUN
cana-2100	175	48	sciences	sciences	PROPN
cana-2100	175	49	(	(	PUNCT
cana-2100	175	50	usa	usa	PROPN
cana-2100	175	51	)	)	PUNCT
cana-2100	175	52	,	,	PUNCT
cana-2100	175	53	volume	volume	NOUN
cana-2100	175	54	18	18	NUM
cana-2100	175	55	,	,	PUNCT
cana-2100	175	56	issue	issue	NOUN
cana-2100	175	57	1	1	NUM
cana-2100	175	58	,	,	PUNCT
cana-2100	175	59	49	49	NUM
cana-2100	175	60	-	-	SYM
cana-2100	175	61	63	63	NUM
cana-2100	175	62	,	,	PUNCT
cana-2100	175	63	2018	2018	NUM
cana-2100	175	64	,	,	PUNCT
cana-2100	175	65	doi:10.17406	doi:10.17406	ADJ
cana-2100	175	66	/	/	SYM
cana-2100	175	67	gjsfr	gjsfr	NOUN
cana-2100	175	68	.	.	PUNCT
cana-2100	176	1	[	[	X
cana-2100	176	2	2	2	NUM
cana-2100	176	3	]	]	X
cana-2100	176	4	abasiekwere	abasiekwere	NOUN
cana-2100	176	5	,	,	PUNCT
cana-2100	176	6	u.	u.	PROPN
cana-2100	176	7	a.	a.	PROPN
cana-2100	176	8	,	,	PUNCT
cana-2100	176	9	esuabana	esuabana	PROPN
cana-2100	176	10	,	,	PUNCT
cana-2100	176	11	i.	i.	NOUN
cana-2100	176	12	m.	m.	NOUN
cana-2100	176	13	,	,	PUNCT
cana-2100	176	14	asymptotic	asymptotic	ADJ
cana-2100	176	15	behaviour	behaviour	NOUN
cana-2100	176	16	of	of	ADP
cana-2100	176	17	nonoscillating	nonoscillate	VERB
cana-2100	176	18	solutions	solution	NOUN
cana-2100	176	19	of	of	ADP
cana-2100	176	20	neutral	neutral	ADJ
cana-2100	176	21	delay	delay	NOUN
cana-2100	176	22	differential	differential	ADJ
cana-2100	176	23	equations	equation	NOUN
cana-2100	176	24	of	of	ADP
cana-2100	176	25	the	the	DET
cana-2100	176	26	second	second	ADJ
cana-2100	176	27	order	order	NOUN
cana-2100	176	28	with	with	ADP
cana-2100	176	29	impulses	impulse	NOUN
cana-2100	176	30	,	,	PUNCT
cana-2100	176	31	journal	journal	NOUN
cana-2100	176	32	of	of	ADP
cana-2100	176	33	mathematical	mathematical	ADJ
cana-2100	176	34	and	and	CCONJ
cana-2100	176	35	computational	computational	ADJ
cana-2100	176	36	science	science	NOUN
cana-2100	176	37	,	,	PUNCT
cana-2100	176	38	vol	vol	NOUN
cana-2100	176	39	8	8	NUM
cana-2100	176	40	,	,	PUNCT
cana-2100	176	41	no	no	DET
cana-2100	176	42	5	5	NUM
cana-2100	176	43	(	(	PUNCT
cana-2100	176	44	2018	2018	NUM
cana-2100	176	45	)	)	PUNCT
cana-2100	176	46	,	,	PUNCT
cana-2100	176	47	620	620	NUM
cana-2100	176	48	-	-	SYM
cana-2100	176	49	629	629	NUM
cana-2100	176	50	,	,	PUNCT
cana-2100	176	51	doi	doi	NOUN
cana-2100	176	52	:	:	PUNCT
cana-2100	176	53	10.28919	10.28919	NUM
cana-2100	176	54	/	/	SYM
cana-2100	176	55	jmcs/3765	jmcs/3765	PROPN
cana-2100	176	56	.	.	PUNCT
cana-2100	177	1	[	[	X
cana-2100	177	2	3	3	NUM
cana-2100	177	3	]	]	X
cana-2100	177	4	arino	arino	NOUN
cana-2100	177	5	,	,	PUNCT
cana-2100	177	6	o.	o.	NOUN
cana-2100	177	7	and	and	CCONJ
cana-2100	177	8	pituk	pituk	NOUN
cana-2100	177	9	,	,	PUNCT
cana-2100	177	10	m.	m.	NOUN
cana-2100	177	11	(	(	PUNCT
cana-2100	177	12	2001	2001	NUM
cana-2100	177	13	)	)	PUNCT
cana-2100	177	14	,	,	PUNCT
cana-2100	177	15	more	more	ADJ
cana-2100	177	16	on	on	ADP
cana-2100	177	17	linear	linear	PROPN
cana-2100	177	18	differential	differential	NOUN
cana-2100	177	19	systems	system	NOUN
cana-2100	177	20	with	with	ADP
cana-2100	177	21	small	small	ADJ
cana-2100	177	22	delays	delay	NOUN
cana-2100	177	23	,	,	PUNCT
cana-2100	177	24	journal	journal	NOUN
cana-2100	177	25	of	of	ADP
cana-2100	177	26	differential	differential	ADJ
cana-2100	177	27	equations	equation	NOUN
cana-2100	177	28	,	,	PUNCT
cana-2100	177	29	vol	vol	NOUN
cana-2100	177	30	17	17	NUM
cana-2100	177	31	,	,	PUNCT
cana-2100	177	32	pp	pp	ADJ
cana-2100	177	33	.	.	PUNCT
cana-2100	178	1	381	381	NUM
cana-2100	178	2	-	-	SYM
cana-2100	178	3	407	407	NUM
cana-2100	178	4	.	.	PUNCT
cana-2100	179	1	communications	communication	NOUN
cana-2100	179	2	on	on	ADP
cana-2100	179	3	applied	apply	VERB
cana-2100	179	4	nonlinear	nonlinear	ADJ
cana-2100	179	5	analysis	analysis	NOUN
cana-2100	179	6	issn	issn	NOUN
cana-2100	179	7	:	:	PUNCT
cana-2100	179	8	1074	1074	NUM
cana-2100	179	9	-	-	PUNCT
cana-2100	179	10	133x	133x	NUM
cana-2100	179	11	vol	vol	NOUN
cana-2100	179	12	32	32	NUM
cana-2100	179	13	no	no	NOUN
cana-2100	179	14	.	.	PUNCT
cana-2100	180	1	1s	1s	NUM
cana-2100	180	2	(	(	PUNCT
cana-2100	180	3	2025	2025	NUM
cana-2100	180	4	)	)	PUNCT
cana-2100	180	5	53	53	NUM
cana-2100	180	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-2100	181	1	[	[	X
cana-2100	181	2	4	4	NUM
cana-2100	181	3	]	]	X
cana-2100	181	4	bastinec	bastinec	PROPN
cana-2100	181	5	,	,	PUNCT
cana-2100	181	6	j.	j.	PROPN
cana-2100	181	7	,	,	PUNCT
cana-2100	181	8	diblik	diblik	PROPN
cana-2100	181	9	,	,	PUNCT
cana-2100	181	10	j.	j.	PROPN
cana-2100	181	11	and	and	CCONJ
cana-2100	181	12	smarda	smarda	PROPN
cana-2100	181	13	,	,	PUNCT
cana-2100	181	14	z.	z.	PROPN
cana-2100	181	15	(	(	PUNCT
cana-2100	181	16	2000	2000	NUM
cana-2100	181	17	)	)	PUNCT
cana-2100	181	18	,	,	PUNCT
cana-2100	181	19	convergence	convergence	NOUN
cana-2100	181	20	tests	test	VERB
cana-2100	181	21	for	for	ADP
cana-2100	181	22	one	one	NUM
cana-2100	181	23	scalar	scalar	ADJ
cana-2100	181	24	differential	differential	NOUN
cana-2100	181	25	equation	equation	NOUN
cana-2100	181	26	with	with	ADP
cana-2100	181	27	vanishing	vanish	VERB
cana-2100	181	28	delay	delay	NOUN
cana-2100	181	29	,	,	PUNCT
cana-2100	181	30	arch	arch	NOUN
cana-2100	181	31	.	.	PUNCT
cana-2100	182	1	math	math	NOUN
cana-2100	182	2	.	.	PUNCT
cana-2100	183	1	(	(	PUNCT
cana-2100	183	2	brno	brno	NOUN
cana-2100	183	3	)	)	PUNCT
cana-2100	183	4	,	,	PUNCT
cana-2100	183	5	36	36	NUM
cana-2100	183	6	,	,	PUNCT
cana-2100	183	7	pp	pp	ADJ
cana-2100	183	8	.	.	PUNCT
cana-2100	184	1	405	405	NUM
cana-2100	184	2	-	-	SYM
cana-2100	184	3	414	414	NUM
cana-2100	184	4	.	.	PUNCT
cana-2100	184	5	cdde	cdde	NOUN
cana-2100	184	6	issue	issue	NOUN
cana-2100	184	7	.	.	PUNCT
cana-2100	185	1	[	[	X
cana-2100	185	2	5	5	NUM
cana-2100	185	3	]	]	PUNCT
cana-2100	185	4	bainov	bainov	NOUN
cana-2100	185	5	,	,	PUNCT
cana-2100	185	6	d.	d.	PROPN
cana-2100	185	7	d.	d.	PROPN
cana-2100	185	8	and	and	CCONJ
cana-2100	185	9	simeonov	simeonov	PROPN
cana-2100	185	10	,	,	PUNCT
cana-2100	185	11	p.	p.	PROPN
cana-2100	185	12	s.	s.	PROPN
cana-2100	185	13	(	(	PUNCT
cana-2100	185	14	1995	1995	NUM
cana-2100	185	15	)	)	PUNCT
cana-2100	185	16	,	,	PUNCT
cana-2100	185	17	impulsive	impulsive	ADJ
cana-2100	185	18	differential	differential	ADJ
cana-2100	185	19	equations	equation	NOUN
cana-2100	185	20	asymptotic	asymptotic	ADJ
cana-2100	185	21	properties	property	NOUN
cana-2100	185	22	of	of	ADP
cana-2100	185	23	the	the	DET
cana-2100	185	24	solutions	solution	NOUN
cana-2100	185	25	,	,	PUNCT
cana-2100	185	26	world	world	NOUN
cana-2100	185	27	scientific	scientific	ADJ
cana-2100	185	28	pub	pub	NOUN
cana-2100	185	29	.	.	PUNCT
cana-2100	185	30	coy	coy	PROPN
cana-2100	185	31	.	.	PUNCT
cana-2100	185	32	pte	pte	PROPN
cana-2100	185	33	.	.	PROPN
cana-2100	185	34	ltd	ltd	PROPN
cana-2100	185	35	,	,	PUNCT
cana-2100	185	36	singapore	singapore	PROPN
cana-2100	185	37	.	.	PUNCT
cana-2100	186	1	[	[	X
cana-2100	186	2	6	6	NUM
cana-2100	186	3	]	]	X
cana-2100	186	4	bereketoglu	bereketoglu	PROPN
cana-2100	186	5	,	,	PUNCT
cana-2100	186	6	h.	h.	PROPN
cana-2100	186	7	and	and	CCONJ
cana-2100	186	8	karakoc	karakoc	PROPN
cana-2100	186	9	,	,	PUNCT
cana-2100	186	10	f.	f.	PROPN
cana-2100	186	11	(	(	PUNCT
cana-2100	186	12	2008	2008	NUM
cana-2100	186	13	)	)	PUNCT
cana-2100	186	14	.	.	PUNCT
cana-2100	187	1	asymptotic	asymptotic	ADJ
cana-2100	187	2	,	,	PUNCT
cana-2100	187	3	constancy	constancy	NOUN
cana-2100	187	4	for	for	ADP
cana-2100	187	5	impulsive	impulsive	ADJ
cana-2100	187	6	delay	delay	NOUN
cana-2100	187	7	differential	differential	NOUN
cana-2100	187	8	equations	equation	NOUN
cana-2100	187	9	.	.	PUNCT
cana-2100	188	1	dynamic	dynamic	ADJ
cana-2100	188	2	systems	system	NOUN
cana-2100	188	3	and	and	CCONJ
cana-2100	188	4	applications	application	NOUN
cana-2100	188	5	,	,	PUNCT
cana-2100	188	6	17	17	NUM
cana-2100	188	7	,	,	PUNCT
cana-2100	188	8	pp	pp	ADJ
cana-2100	188	9	.	.	PUNCT
cana-2100	189	1	71	71	NUM
cana-2100	189	2	-	-	SYM
cana-2100	189	3	84	84	NUM
cana-2100	189	4	.	.	PUNCT
cana-2100	190	1	[	[	X
cana-2100	190	2	7	7	NUM
cana-2100	190	3	]	]	X
cana-2100	190	4	bainov	bainov	NOUN
cana-2100	190	5	,	,	PUNCT
cana-2100	190	6	d.	d.	PROPN
cana-2100	190	7	d.	d.	PROPN
cana-2100	190	8	and	and	CCONJ
cana-2100	190	9	simeonov	simeonov	PROPN
cana-2100	190	10	,	,	PUNCT
cana-2100	190	11	p.	p.	PROPN
cana-2100	190	12	s.	s.	PROPN
cana-2100	190	13	(	(	PUNCT
cana-2100	190	14	1989	1989	NUM
cana-2100	190	15	)	)	PUNCT
cana-2100	190	16	,	,	PUNCT
cana-2100	190	17	systems	system	NOUN
cana-2100	190	18	with	with	ADP
cana-2100	190	19	impulse	impulse	ADJ
cana-2100	190	20	effects	effect	NOUN
cana-2100	190	21	,	,	PUNCT
cana-2100	190	22	stability	stability	NOUN
cana-2100	190	23	,	,	PUNCT
cana-2100	190	24	theory	theory	NOUN
cana-2100	190	25	and	and	CCONJ
cana-2100	190	26	applications	application	NOUN
cana-2100	190	27	,	,	PUNCT
cana-2100	190	28	ellis	ellis	PROPN
cana-2100	190	29	horwood	horwood	PROPN
cana-2100	190	30	series	series	PROPN
cana-2100	190	31	in	in	ADP
cana-2100	190	32	mathematics	mathematics	PROPN
cana-2100	190	33	and	and	CCONJ
cana-2100	190	34	its	its	PRON
cana-2100	190	35	applications	application	NOUN
cana-2100	190	36	.	.	PUNCT
cana-2100	191	1	[	[	X
cana-2100	191	2	8	8	NUM
cana-2100	191	3	]	]	SYM
cana-2100	191	4	coddington	coddington	PROPN
cana-2100	191	5	,	,	PUNCT
cana-2100	191	6	a.	a.	PROPN
cana-2100	191	7	e.	e.	PROPN
cana-2100	191	8	and	and	CCONJ
cana-2100	191	9	levinson	levinson	PROPN
cana-2100	191	10	,	,	PUNCT
cana-2100	191	11	n.	n.	PROPN
cana-2100	191	12	(	(	PUNCT
cana-2100	191	13	1955	1955	NUM
cana-2100	191	14	)	)	PUNCT
cana-2100	191	15	,	,	PUNCT
cana-2100	191	16	theory	theory	NOUN
cana-2100	191	17	of	of	ADP
cana-2100	191	18	ordinary	ordinary	ADJ
cana-2100	191	19	differential	differential	ADJ
cana-2100	191	20	equations	equation	NOUN
cana-2100	191	21	,	,	PUNCT
cana-2100	191	22	mcgraw	mcgraw	PROPN
cana-2100	191	23	-	-	PUNCT
cana-2100	191	24	hill	hill	NOUN
cana-2100	191	25	book	book	NOUN
cana-2100	191	26	company	company	NOUN
cana-2100	191	27	,	,	PUNCT
cana-2100	191	28	new	new	PROPN
cana-2100	191	29	york	york	PROPN
cana-2100	191	30	.	.	PUNCT
cana-2100	192	1	[	[	X
cana-2100	192	2	9	9	NUM
cana-2100	192	3	]	]	PUNCT
cana-2100	192	4	dubeau	dubeau	NOUN
cana-2100	192	5	,	,	PUNCT
cana-2100	192	6	f.	f.	PROPN
cana-2100	192	7	and	and	CCONJ
cana-2100	192	8	karrakchou	karrakchou	PROPN
cana-2100	192	9	,	,	PUNCT
cana-2100	192	10	j.	j.	PROPN
cana-2100	192	11	(	(	PUNCT
cana-2100	192	12	2002	2002	NUM
cana-2100	192	13	)	)	PUNCT
cana-2100	192	14	.	.	PUNCT
cana-2100	193	1	state	state	NOUN
cana-2100	193	2	-	-	PUNCT
cana-2100	193	3	dependent	dependent	ADJ
cana-2100	193	4	impulsive	impulsive	ADJ
cana-2100	193	5	delay	delay	NOUN
cana-2100	193	6	differential	differential	NOUN
cana-2100	193	7	equations	equation	NOUN
cana-2100	193	8	,	,	PUNCT
cana-2100	193	9	applied	apply	VERB
cana-2100	193	10	mathematics	mathematics	NOUN
cana-2100	193	11	letters	letter	NOUN
cana-2100	193	12	,	,	PUNCT
cana-2100	193	13	15	15	NUM
cana-2100	193	14	,	,	PUNCT
cana-2100	193	15	pp	pp	ADJ
cana-2100	193	16	.	.	PUNCT
cana-2100	194	1	333	333	NUM
cana-2100	194	2	-	-	SYM
cana-2100	194	3	338	338	NUM
cana-2100	194	4	.	.	PUNCT
cana-2100	195	1	[	[	X
cana-2100	195	2	10	10	NUM
cana-2100	195	3	]	]	X
cana-2100	195	4	esuabana	esuabana	PROPN
cana-2100	195	5	,	,	PUNCT
cana-2100	195	6	i.	i.	NOUN
cana-2100	195	7	m.	m.	PROPN
cana-2100	195	8	and	and	CCONJ
cana-2100	195	9	abasiekwere	abasiekwere	PROPN
cana-2100	195	10	,	,	PUNCT
cana-2100	195	11	u.	u.	PROPN
cana-2100	195	12	a.	a.	PROPN
cana-2100	195	13	,	,	PUNCT
cana-2100	195	14	on	on	ADP
cana-2100	195	15	stability	stability	NOUN
cana-2100	195	16	of	of	ADP
cana-2100	195	17	first	first	ADJ
cana-2100	195	18	order	order	NOUN
cana-2100	195	19	linear	linear	ADJ
cana-2100	195	20	impulsive	impulsive	ADJ
cana-2100	195	21	differential	differential	ADJ
cana-2100	195	22	equations	equation	NOUN
cana-2100	195	23	,	,	PUNCT
cana-2100	195	24	international	international	ADJ
cana-2100	195	25	journal	journal	NOUN
cana-2100	195	26	of	of	ADP
cana-2100	195	27	statistics	statistic	NOUN
cana-2100	195	28	and	and	CCONJ
cana-2100	195	29	applied	apply	VERB
cana-2100	195	30	,	,	PUNCT
cana-2100	195	31	mathematics	mathematic	NOUN
cana-2100	195	32	,	,	PUNCT
cana-2100	195	33	volume	volume	NOUN
cana-2100	195	34	3	3	NUM
cana-2100	195	35	,	,	PUNCT
cana-2100	195	36	issue	issue	NOUN
cana-2100	195	37	3c	3c	NUM
cana-2100	195	38	,	,	PUNCT
cana-2100	195	39	231	231	NUM
cana-2100	195	40	-	-	SYM
cana-2100	195	41	236	236	NUM
cana-2100	195	42	,	,	PUNCT
cana-2100	195	43	2018	2018	NUM
cana-2100	195	44	.	.	PUNCT
cana-2100	196	1	[	[	X
cana-2100	196	2	11	11	NUM
cana-2100	196	3	]	]	X
cana-2100	196	4	gopalsamy	gopalsamy	PROPN
cana-2100	196	5	,	,	PUNCT
cana-2100	196	6	k.	k.	PROPN
cana-2100	196	7	(	(	PUNCT
cana-2100	196	8	1992	1992	NUM
cana-2100	196	9	)	)	PUNCT
cana-2100	196	10	,	,	PUNCT
cana-2100	196	11	stability	stability	NOUN
cana-2100	196	12	and	and	CCONJ
cana-2100	196	13	oscillation	oscillation	NOUN
cana-2100	196	14	in	in	ADP
cana-2100	196	15	delay	delay	NOUN
cana-2100	196	16	differential	differential	ADJ
cana-2100	196	17	equations	equation	NOUN
cana-2100	196	18	of	of	ADP
cana-2100	196	19	population	population	NOUN
cana-2100	196	20	dynamics	dynamic	NOUN
cana-2100	196	21	,	,	PUNCT
cana-2100	196	22	kluwer	kluwer	PROPN
cana-2100	196	23	academics	academics	PROPN
cana-2100	196	24	,	,	PUNCT
cana-2100	196	25	dordrecht	dordrecht	PROPN
cana-2100	196	26	.	.	PUNCT
cana-2100	197	1	[	[	X
cana-2100	197	2	12	12	NUM
cana-2100	197	3	]	]	X
cana-2100	197	4	liu	liu	PROPN
cana-2100	197	5	,	,	PUNCT
cana-2100	197	6	x.	x.	NOUN
cana-2100	197	7	and	and	CCONJ
cana-2100	197	8	ballinger	ballinger	PROPN
cana-2100	197	9	,	,	PUNCT
cana-2100	197	10	g.	g.	PROPN
cana-2100	197	11	(	(	PUNCT
cana-2100	197	12	2002	2002	NUM
cana-2100	197	13	)	)	PUNCT
cana-2100	197	14	.	.	PUNCT
cana-2100	198	1	existence	existence	NOUN
cana-2100	198	2	and	and	CCONJ
cana-2100	198	3	continuability	continuability	NOUN
cana-2100	198	4	of	of	ADP
cana-2100	198	5	solutions	solution	NOUN
cana-2100	198	6	for	for	ADP
cana-2100	198	7	differential	differential	ADJ
cana-2100	198	8	equations	equation	NOUN
cana-2100	198	9	with	with	ADP
cana-2100	198	10	delays	delay	NOUN
cana-2100	198	11	and	and	CCONJ
cana-2100	198	12	statedependent	statedependent	ADJ
cana-2100	198	13	impulses	impulse	NOUN
cana-2100	198	14	,	,	PUNCT
cana-2100	198	15	nonlinear	nonlinear	ADJ
cana-2100	198	16	analysis	analysis	NOUN
cana-2100	198	17	tma	tma	PROPN
cana-2100	198	18	,	,	PUNCT
cana-2100	198	19	51	51	NUM
cana-2100	198	20	,	,	PUNCT
cana-2100	198	21	pp	pp	ADJ
cana-2100	198	22	.	.	PUNCT
cana-2100	199	1	633	633	NUM
cana-2100	199	2	-	-	SYM
cana-2100	199	3	647	647	NUM
cana-2100	199	4	.	.	PUNCT
cana-2100	200	1	[	[	X
cana-2100	200	2	13	13	NUM
cana-2100	200	3	]	]	SYM
cana-2100	200	4	lakshmikantham	lakshmikantham	ADV
cana-2100	200	5	,	,	PUNCT
cana-2100	200	6	v.	v.	ADV
cana-2100	200	7	,	,	PUNCT
cana-2100	200	8	bainov	bainov	PROPN
cana-2100	200	9	,	,	PUNCT
cana-2100	200	10	d.	d.	PROPN
cana-2100	200	11	d.	d.	PROPN
cana-2100	200	12	and	and	CCONJ
cana-2100	200	13	simeonov	simeonov	PROPN
cana-2100	200	14	,	,	PUNCT
cana-2100	200	15	p.	p.	PROPN
cana-2100	200	16	s.	s.	PROPN
cana-2100	200	17	(	(	PUNCT
cana-2100	200	18	1989	1989	NUM
cana-2100	200	19	)	)	PUNCT
cana-2100	200	20	,	,	PUNCT
cana-2100	200	21	theory	theory	NOUN
cana-2100	200	22	of	of	ADP
cana-2100	200	23	impulsive	impulsive	ADJ
cana-2100	200	24	differential	differential	ADJ
cana-2100	200	25	equations	equation	NOUN
cana-2100	200	26	,	,	PUNCT
cana-2100	200	27	world	world	NOUN
cana-2100	200	28	scientific	scientific	ADJ
cana-2100	200	29	publishing	publishing	NOUN
cana-2100	200	30	company	company	NOUN
cana-2100	200	31	limited	limit	VERB
cana-2100	200	32	,	,	PUNCT
cana-2100	200	33	singapore	singapore	PROPN
cana-2100	200	34	.	.	PUNCT
cana-2100	201	1	[	[	X
cana-2100	201	2	14	14	NUM
cana-2100	201	3	]	]	X
cana-2100	201	4	oyelami	oyelami	NOUN
cana-2100	201	5	,	,	PUNCT
cana-2100	201	6	b.	b.	PROPN
cana-2100	201	7	o.	o.	PROPN
cana-2100	201	8	(	(	PUNCT
cana-2100	201	9	1999	1999	NUM
cana-2100	201	10	)	)	PUNCT
cana-2100	201	11	,	,	PUNCT
cana-2100	201	12	on	on	ADP
cana-2100	201	13	military	military	ADJ
cana-2100	201	14	model	model	NOUN
cana-2100	201	15	for	for	ADP
cana-2100	201	16	impulsive	impulsive	ADJ
cana-2100	201	17	reinforcement	reinforcement	NOUN
cana-2100	201	18	functions	function	NOUN
cana-2100	201	19	using	use	VERB
cana-2100	201	20	exclusion	exclusion	NOUN
cana-2100	201	21	and	and	CCONJ
cana-2100	201	22	marginalization	marginalization	NOUN
cana-2100	201	23	techniques	technique	NOUN
cana-2100	201	24	,	,	PUNCT
cana-2100	201	25	nonlinear	nonlinear	ADJ
cana-2100	201	26	analysis	analysis	NOUN
cana-2100	201	27	,	,	PUNCT
cana-2100	201	28	vol	vol	NOUN
cana-2100	201	29	35	35	NUM
cana-2100	201	30	,	,	PUNCT
cana-2100	201	31	pp	pp	ADJ
cana-2100	201	32	.	.	PUNCT
cana-2100	202	1	947	947	NUM
cana-2100	202	2	-	-	SYM
cana-2100	202	3	958	958	NUM
cana-2100	202	4	.	.	PUNCT
cana-2100	203	1	[	[	X
cana-2100	203	2	15	15	NUM
cana-2100	203	3	]	]	X
cana-2100	203	4	oyelami	oyelami	NOUN
cana-2100	203	5	,	,	PUNCT
cana-2100	203	6	b.	b.	PROPN
cana-2100	203	7	,	,	PUNCT
cana-2100	203	8	ale	ale	PROPN
cana-2100	203	9	,	,	PUNCT
cana-2100	203	10	s.	s.	PROPN
cana-2100	203	11	o.	o.	PROPN
cana-2100	203	12	,	,	PUNCT
cana-2100	203	13	ogidi	ogidi	PROPN
cana-2100	203	14	,	,	PUNCT
cana-2100	203	15	j.	j.	PROPN
cana-2100	203	16	a.	a.	PROPN
cana-2100	203	17	,	,	PUNCT
cana-2100	203	18	and	and	CCONJ
cana-2100	203	19	onumanyi	onumanyi	PROPN
cana-2100	203	20	,	,	PUNCT
cana-2100	203	21	p.	p.	NOUN
cana-2100	203	22	(	(	PUNCT
cana-2100	203	23	2003	2003	NUM
cana-2100	203	24	)	)	PUNCT
cana-2100	203	25	,	,	PUNCT
cana-2100	203	26	impulsive	impulsive	ADJ
cana-2100	203	27	hiv	hiv	PROPN
cana-2100	203	28	1	1	NUM
cana-2100	203	29	model	model	NOUN
cana-2100	203	30	in	in	ADP
cana-2100	203	31	the	the	DET
cana-2100	203	32	presence	presence	NOUN
cana-2100	203	33	of	of	ADP
cana-2100	203	34	antiretroval	antiretroval	NOUN
cana-2100	203	35	drugs	drug	NOUN
cana-2100	203	36	using	use	VERB
cana-2100	203	37	b	b	NUM
cana-2100	203	38	transform	transform	NOUN
cana-2100	203	39	method	method	NOUN
cana-2100	203	40	,	,	PUNCT
cana-2100	203	41	proceedings	proceeding	NOUN
cana-2100	203	42	of	of	ADP
cana-2100	203	43	african	african	PROPN
cana-2100	203	44	mathematical	mathematical	PROPN
cana-2100	203	45	union	union	NOUN
cana-2100	203	46	,	,	PUNCT
cana-2100	203	47	1	1	NUM
cana-2100	203	48	,	,	PUNCT
cana-2100	203	49	pp	pp	ADJ
cana-2100	203	50	.	.	PUNCT
cana-2100	204	1	62	62	NUM
cana-2100	204	2	-	-	SYM
cana-2100	204	3	76	76	NUM
cana-2100	204	4	.	.	PUNCT
cana-2100	205	1	[	[	X
cana-2100	205	2	16	16	NUM
cana-2100	205	3	]	]	X
cana-2100	205	4	simeonov	simeonov	PROPN
cana-2100	205	5	,	,	PUNCT
cana-2100	205	6	p.	p.	PROPN
cana-2100	205	7	s.	s.	PROPN
cana-2100	205	8	and	and	CCONJ
cana-2100	205	9	bainov	bainov	PROPN
cana-2100	205	10	,	,	PUNCT
cana-2100	205	11	d.	d.	PROPN
cana-2100	205	12	d.	d.	PROPN
cana-2100	205	13	(	(	PUNCT
cana-2100	205	14	1988	1988	NUM
cana-2100	205	15	)	)	PUNCT
cana-2100	205	16	.	.	PUNCT
cana-2100	206	1	differentiability	differentiability	NOUN
cana-2100	206	2	of	of	ADP
cana-2100	206	3	solutions	solution	NOUN
cana-2100	206	4	of	of	ADP
cana-2100	206	5	systems	system	NOUN
cana-2100	206	6	with	with	ADP
cana-2100	206	7	impulse	impulse	ADJ
cana-2100	206	8	effects	effect	NOUN
cana-2100	206	9	with	with	ADP
cana-2100	206	10	respect	respect	NOUN
cana-2100	206	11	to	to	ADP
cana-2100	206	12	initial	initial	ADJ
cana-2100	206	13	data	datum	NOUN
cana-2100	206	14	and	and	CCONJ
cana-2100	206	15	parameters	parameter	NOUN
cana-2100	206	16	,	,	PUNCT
cana-2100	206	17	proceedings	proceeding	NOUN
cana-2100	206	18	of	of	ADP
cana-2100	206	19	edinburgh	edinburgh	PROPN
cana-2100	206	20	maths	maths	PROPN
cana-2100	206	21	society	society	NOUN
cana-2100	206	22	,	,	PUNCT
cana-2100	206	23	31	31	NUM
cana-2100	206	24	,	,	PUNCT
cana-2100	206	25	pp	pp	ADJ
cana-2100	206	26	.	.	PUNCT
cana-2100	207	1	353	353	NUM
cana-2100	207	2	-	-	SYM
cana-2100	207	3	368	368	NUM
cana-2100	207	4	.	.	PUNCT
cana-2100	208	1	[	[	X
cana-2100	208	2	17	17	NUM
cana-2100	208	3	]	]	X
cana-2100	208	4	samaoilenko	samaoilenko	NOUN
cana-2100	208	5	,	,	PUNCT
cana-2100	208	6	a.	a.	NOUN
cana-2100	208	7	m.	m.	NOUN
cana-2100	208	8	and	and	CCONJ
cana-2100	208	9	perestyuk	perestyuk	PROPN
cana-2100	208	10	,	,	PUNCT
cana-2100	208	11	j.	j.	PROPN
cana-2100	208	12	j.	j.	PROPN
cana-2100	208	13	j.	j.	PROPN
cana-2100	208	14	(	(	PUNCT
cana-2100	208	15	1995	1995	NUM
cana-2100	208	16	)	)	PUNCT
cana-2100	208	17	,	,	PUNCT
cana-2100	208	18	impulsive	impulsive	ADJ
cana-2100	208	19	differential	differential	ADJ
cana-2100	208	20	equations	equation	NOUN
cana-2100	208	21	,	,	PUNCT
cana-2100	208	22	world	world	NOUN
cana-2100	208	23	scientific	scientific	ADJ
cana-2100	208	24	,	,	PUNCT
cana-2100	208	25	new	new	PROPN
cana-2100	208	26	york	york	PROPN
cana-2100	208	27	.	.	PUNCT
cana-2100	209	1	[	[	X
cana-2100	209	2	18	18	NUM
cana-2100	209	3	]	]	PUNCT
cana-2100	209	4	ugbohj	ugbohj	PROPN
cana-2100	209	5	.	.	PUNCT
cana-2100	209	6	a.	a.	PROPN
cana-2100	209	7	,	,	PUNCT
cana-2100	209	8	esuabanai	esuabanai	PROPN
cana-2100	209	9	.	.	PUNCT
cana-2100	210	1	m.	m.	NOUN
cana-2100	210	2	,	,	PUNCT
cana-2100	210	3	existence	existence	NOUN
cana-2100	210	4	and	and	CCONJ
cana-2100	210	5	uniqueness	uniqueness	NOUN
cana-2100	210	6	result	result	NOUN
cana-2100	210	7	for	for	ADP
cana-2100	210	8	a	a	DET
cana-2100	210	9	class	class	NOUN
cana-2100	210	10	of	of	ADP
cana-2100	210	11	impulsive	impulsive	ADJ
cana-2100	210	12	delay	delay	NOUN
cana-2100	210	13	differential	differential	NOUN
cana-2100	210	14	equations	equation	NOUN
cana-2100	210	15	,	,	PUNCT
cana-2100	210	16	international	international	ADJ
cana-2100	210	17	journal	journal	NOUN
cana-2100	210	18	of	of	ADP
cana-2100	210	19	chemistry	chemistry	NOUN
cana-2100	210	20	,	,	PUNCT
cana-2100	210	21	mathematics	mathematic	NOUN
cana-2100	210	22	and	and	CCONJ
cana-2100	210	23	physics	physics	NOUN
cana-2100	210	24	,	,	PUNCT
cana-2100	210	25	vol	vol	NOUN
cana-2100	210	26	.	.	PROPN
cana-2100	210	27	2	2	NUM
cana-2100	210	28	(	(	PUNCT
cana-2100	210	29	4	4	NUM
cana-2100	210	30	)	)	PUNCT
cana-2100	210	31	,	,	PUNCT
cana-2100	210	32	27	27	NUM
cana-2100	210	33	-	-	SYM
cana-2100	210	34	32	32	NUM
cana-2100	210	35	,	,	PUNCT
cana-2100	210	36	2018	2018	NUM
cana-2100	210	37	,	,	PUNCT
cana-2100	210	38	doi:10.22161	doi:10.22161	ADJ
cana-2100	210	39	/	/	SYM
cana-2100	210	40	ijcmp.2.4.1	ijcmp.2.4.1	ADJ
cana-2100	210	41	.	.	PUNCT
cana-2100	211	1	[	[	X
cana-2100	211	2	19	19	NUM
cana-2100	211	3	]	]	X
cana-2100	211	4	yan	yan	PROPN
cana-2100	211	5	,	,	PUNCT
cana-2100	211	6	j.	j.	PROPN
cana-2100	211	7	(	(	PUNCT
cana-2100	211	8	2004	2004	NUM
cana-2100	211	9	)	)	PUNCT
cana-2100	211	10	,	,	PUNCT
cana-2100	211	11	oscillation	oscillation	NOUN
cana-2100	211	12	properties	property	NOUN
cana-2100	211	13	of	of	ADP
cana-2100	211	14	a	a	DET
cana-2100	211	15	second	second	ADJ
cana-2100	211	16	order	order	NOUN
cana-2100	211	17	impulsive	impulsive	ADJ
cana-2100	211	18	delay	delay	NOUN
cana-2100	211	19	differential	differential	ADJ
cana-2100	211	20	equation	equation	NOUN
cana-2100	211	21	,	,	PUNCT
cana-2100	211	22	comp	comp	NOUN
cana-2100	211	23	.	.	PUNCT
cana-2100	212	1	and	and	CCONJ
cana-2100	212	2	math	math	NOUN
cana-2100	212	3	.	.	PUNCT
cana-2100	213	1	with	with	ADP
cana-2100	213	2	applications	application	NOUN
cana-2100	213	3	,	,	PUNCT
cana-2100	213	4	47	47	NUM
cana-2100	213	5	,	,	PUNCT
cana-2100	213	6	pp	pp	ADJ
cana-2100	213	7	.	.	PUNCT
cana-2100	213	8	253	253	NUM
cana-2100	213	9	-	-	SYM
cana-2100	213	10	258	258	NUM
cana-2100	213	11	.	.	PUNCT