id	sid	tid	token	lemma	pos
cana-1619	1	1	communications	communication	NOUN
cana-1619	1	2	on	on	ADP
cana-1619	1	3	applied	apply	VERB
cana-1619	1	4	nonlinear	nonlinear	ADJ
cana-1619	1	5	analysis	analysis	NOUN
cana-1619	1	6	issn	issn	NOUN
cana-1619	1	7	:	:	PUNCT
cana-1619	1	8	1074	1074	NUM
cana-1619	1	9	-	-	PUNCT
cana-1619	1	10	133x	133x	NUM
cana-1619	1	11	vol	vol	NOUN
cana-1619	1	12	32	32	NUM
cana-1619	1	13	no	no	NOUN
cana-1619	1	14	.	.	NOUN
cana-1619	1	15	1	1	NUM
cana-1619	1	16	(	(	PUNCT
cana-1619	1	17	2025	2025	NUM
cana-1619	1	18	)	)	PUNCT
cana-1619	1	19	35	35	NUM
cana-1619	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	1	21	existence	existence	NOUN
cana-1619	1	22	and	and	CCONJ
cana-1619	1	23	approximate	approximate	ADJ
cana-1619	1	24	controllability	controllability	NOUN
cana-1619	1	25	of	of	ADP
cana-1619	1	26	random	random	ADJ
cana-1619	1	27	impulsive	impulsive	ADJ
cana-1619	1	28	neutral	neutral	ADJ
cana-1619	1	29	functional	functional	ADJ
cana-1619	1	30	differential	differential	NOUN
cana-1619	1	31	equation	equation	NOUN
cana-1619	1	32	with	with	ADP
cana-1619	1	33	finite	finite	PROPN
cana-1619	1	34	delay	delay	NOUN
cana-1619	1	35	tharmalingam	tharmalingam	CCONJ
cana-1619	1	36	gunasekar1,2	gunasekar1,2	PROPN
cana-1619	1	37	,	,	PUNCT
cana-1619	1	38	srinivasan	srinivasan	PROPN
cana-1619	1	39	madhumitha1	madhumitha1	PROPN
cana-1619	1	40	,	,	PUNCT
cana-1619	1	41	prakaash	prakaash	NOUN
cana-1619	1	42	a.	a.	NOUN
cana-1619	1	43	s3	s3	PROPN
cana-1619	1	44	,	,	PUNCT
cana-1619	1	45	sakthi	sakthi	PROPN
cana-1619	1	46	r4	r4	PROPN
cana-1619	1	47	,	,	PUNCT
cana-1619	1	48	ganapathy	ganapathy	PROPN
cana-1619	1	49	g5	g5	NOUN
cana-1619	1	50	,	,	PUNCT
cana-1619	1	51	m.	m.	NOUN
cana-1619	1	52	suba6	suba6	PROPN
cana-1619	2	1	1department	1department	NUM
cana-1619	2	2	of	of	ADP
cana-1619	2	3	mathematics	mathematic	NOUN
cana-1619	2	4	,	,	PUNCT
cana-1619	2	5	vel	vel	PROPN
cana-1619	2	6	tech	tech	PROPN
cana-1619	2	7	rangarajan	rangarajan	PROPN
cana-1619	2	8	dr	dr	PROPN
cana-1619	2	9	.	.	PROPN
cana-1619	2	10	sagunthala	sagunthala	PROPN
cana-1619	2	11	r&d	r&d	PROPN
cana-1619	2	12	institute	institute	PROPN
cana-1619	2	13	of	of	ADP
cana-1619	2	14	science	science	NOUN
cana-1619	2	15	and	and	CCONJ
cana-1619	2	16	technology	technology	NOUN
cana-1619	2	17	,	,	PUNCT
cana-1619	2	18	chennai	chennai	NOUN
cana-1619	2	19	600062	600062	NUM
cana-1619	2	20	,	,	PUNCT
cana-1619	2	21	tamil	tamil	PROPN
cana-1619	2	22	nadu	nadu	PROPN
cana-1619	2	23	,	,	PUNCT
cana-1619	2	24	india	india	PROPN
cana-1619	2	25	.	.	PUNCT
cana-1619	3	1	tguna84@gmail.com1,2	tguna84@gmail.com1,2	PROPN
cana-1619	3	2	,	,	PUNCT
cana-1619	3	3	smadhumitha2410@gmail.com1	smadhumitha2410@gmail.com1	PROPN
cana-1619	3	4	2school	2school	PROPN
cana-1619	3	5	of	of	ADP
cana-1619	3	6	artificial	artificial	ADJ
cana-1619	3	7	intelligence	intelligence	NOUN
cana-1619	3	8	and	and	CCONJ
cana-1619	3	9	data	datum	NOUN
cana-1619	3	10	science	science	NOUN
cana-1619	3	11	,	,	PUNCT
cana-1619	3	12	indian	indian	PROPN
cana-1619	3	13	institute	institute	PROPN
cana-1619	3	14	of	of	ADP
cana-1619	3	15	technology	technology	PROPN
cana-1619	3	16	(	(	PUNCT
cana-1619	3	17	iit	iit	PROPN
cana-1619	3	18	)	)	PUNCT
cana-1619	3	19	,	,	PUNCT
cana-1619	3	20	jodhpur	jodhpur	PROPN
cana-1619	3	21	342030	342030	NUM
cana-1619	3	22	,	,	PUNCT
cana-1619	3	23	india	india	PROPN
cana-1619	3	24	.	.	PUNCT
cana-1619	4	1	3department	3department	NUM
cana-1619	4	2	of	of	ADP
cana-1619	4	3	mathematics	mathematic	NOUN
cana-1619	4	4	,	,	PUNCT
cana-1619	4	5	panimalar	panimalar	ADJ
cana-1619	4	6	engineering	engineering	NOUN
cana-1619	4	7	college	college	NOUN
cana-1619	4	8	chennai	chennai	PROPN
cana-1619	4	9	,	,	PUNCT
cana-1619	4	10	tamil	tamil	PROPN
cana-1619	4	11	nadu	nadu	PROPN
cana-1619	4	12	,	,	PUNCT
cana-1619	4	13	india	india	PROPN
cana-1619	4	14	,	,	PUNCT
cana-1619	4	15	prakaashphd333@gmail.com	prakaashphd333@gmail.com	X
cana-1619	5	1	4department	4department	NUM
cana-1619	5	2	of	of	ADP
cana-1619	5	3	science	science	NOUN
cana-1619	5	4	and	and	CCONJ
cana-1619	5	5	humanities	humanity	NOUN
cana-1619	5	6	,	,	PUNCT
cana-1619	5	7	r.m.k	r.m.k	NOUN
cana-1619	5	8	.	.	PUNCT
cana-1619	6	1	college	college	NOUN
cana-1619	6	2	of	of	ADP
cana-1619	6	3	engineering	engineering	NOUN
cana-1619	6	4	technology	technology	NOUN
cana-1619	6	5	,	,	PUNCT
cana-1619	6	6	puduvoyal	puduvoyal	VERB
cana-1619	6	7	601	601	NUM
cana-1619	6	8	206	206	NUM
cana-1619	6	9	,	,	PUNCT
cana-1619	6	10	tamil	tamil	PROPN
cana-1619	6	11	nadu	nadu	PROPN
cana-1619	6	12	,	,	PUNCT
cana-1619	6	13	india	india	PROPN
cana-1619	6	14	,	,	PUNCT
cana-1619	6	15	rsakth@gmail.com	rsakth@gmail.com	X
cana-1619	7	1	5department	5department	NUM
cana-1619	7	2	of	of	ADP
cana-1619	7	3	mathematics	mathematic	NOUN
cana-1619	7	4	,	,	PUNCT
cana-1619	7	5	r.m.d	r.m.d	PROPN
cana-1619	7	6	.	.	PUNCT
cana-1619	7	7	engineering	engineering	PROPN
cana-1619	7	8	college	college	PROPN
cana-1619	7	9	,	,	PUNCT
cana-1619	7	10	kavaraipettai	kavaraipettai	VERB
cana-1619	7	11	601	601	NUM
cana-1619	7	12	206	206	NUM
cana-1619	7	13	,	,	PUNCT
cana-1619	7	14	tamil	tamil	PROPN
cana-1619	7	15	nadu	nadu	PROPN
cana-1619	7	16	,	,	PUNCT
cana-1619	7	17	india	india	PROPN
cana-1619	7	18	.	.	PUNCT
cana-1619	8	1	barathganagandhi@gmail.com	barathganagandhi@gmail.com	X
cana-1619	9	1	6department	6department	NUM
cana-1619	9	2	of	of	ADP
cana-1619	9	3	mathematics	mathematics	PROPN
cana-1619	9	4	s.a	s.a	PROPN
cana-1619	9	5	.	.	PROPN
cana-1619	9	6	engineering	engineering	PROPN
cana-1619	9	7	college	college	PROPN
cana-1619	9	8	(	(	PUNCT
cana-1619	9	9	autonomous	autonomous	ADJ
cana-1619	9	10	)	)	PUNCT
cana-1619	9	11	chennai	chennai	PROPN
cana-1619	9	12	,	,	PUNCT
cana-1619	9	13	tamil	tamil	PROPN
cana-1619	9	14	nadu	nadu	PROPN
cana-1619	9	15	,	,	PUNCT
cana-1619	9	16	india	india	PROPN
cana-1619	9	17	.	.	PUNCT
cana-1619	10	1	suba.hari87@gmail.com	suba.hari87@gmail.com	X
cana-1619	10	2	article	article	NOUN
cana-1619	10	3	history	history	NOUN
cana-1619	10	4	:	:	PUNCT
cana-1619	10	5	received	receive	VERB
cana-1619	10	6	:	:	PUNCT
cana-1619	10	7	06	06	NUM
cana-1619	10	8	-	-	SYM
cana-1619	10	9	07	07	NUM
cana-1619	10	10	-	-	PUNCT
cana-1619	10	11	2024	2024	NUM
cana-1619	10	12	revised	revise	VERB
cana-1619	10	13	:	:	PUNCT
cana-1619	10	14	21	21	NUM
cana-1619	10	15	-	-	SYM
cana-1619	10	16	08	08	NUM
cana-1619	10	17	-	-	PUNCT
cana-1619	10	18	2024	2024	NUM
cana-1619	10	19	accepted	accept	VERB
cana-1619	10	20	:	:	PUNCT
cana-1619	10	21	03	03	NUM
cana-1619	10	22	-	-	PUNCT
cana-1619	10	23	09	09	NUM
cana-1619	10	24	-	-	PUNCT
cana-1619	10	25	2024	2024	NUM
cana-1619	10	26	abstract	abstract	NOUN
cana-1619	10	27	:	:	PUNCT
cana-1619	10	28	this	this	DET
cana-1619	10	29	study	study	NOUN
cana-1619	10	30	investigates	investigate	VERB
cana-1619	10	31	second	second	ADJ
cana-1619	10	32	-	-	PUNCT
cana-1619	10	33	order	order	NOUN
cana-1619	10	34	neutral	neutral	ADJ
cana-1619	10	35	functional	functional	ADJ
cana-1619	10	36	differential	differential	NOUN
cana-1619	10	37	equations	equation	NOUN
cana-1619	10	38	with	with	ADP
cana-1619	10	39	delays	delay	NOUN
cana-1619	10	40	,	,	PUNCT
cana-1619	10	41	prevalent	prevalent	ADJ
cana-1619	10	42	in	in	ADP
cana-1619	10	43	various	various	ADJ
cana-1619	10	44	scientific	scientific	ADJ
cana-1619	10	45	and	and	CCONJ
cana-1619	10	46	engineering	engineering	NOUN
cana-1619	10	47	fields	field	NOUN
cana-1619	10	48	.	.	PUNCT
cana-1619	11	1	these	these	DET
cana-1619	11	2	equations	equation	NOUN
cana-1619	11	3	,	,	PUNCT
cana-1619	11	4	characterized	characterize	VERB
cana-1619	11	5	by	by	ADP
cana-1619	11	6	their	their	PRON
cana-1619	11	7	neutral	neutral	ADJ
cana-1619	11	8	nature	nature	NOUN
cana-1619	11	9	and	and	CCONJ
cana-1619	11	10	delays	delay	NOUN
cana-1619	11	11	,	,	PUNCT
cana-1619	11	12	present	present	ADJ
cana-1619	11	13	unique	unique	ADJ
cana-1619	11	14	challenges	challenge	NOUN
cana-1619	11	15	within	within	ADP
cana-1619	11	16	banach	banach	NOUN
cana-1619	11	17	spaces	space	NOUN
cana-1619	11	18	.	.	PUNCT
cana-1619	12	1	the	the	DET
cana-1619	12	2	research	research	NOUN
cana-1619	12	3	focuses	focus	VERB
cana-1619	12	4	on	on	ADP
cana-1619	12	5	the	the	DET
cana-1619	12	6	existence	existence	NOUN
cana-1619	12	7	and	and	CCONJ
cana-1619	12	8	approximate	approximate	ADJ
cana-1619	12	9	controllability	controllability	NOUN
cana-1619	12	10	of	of	ADP
cana-1619	12	11	solutions	solution	NOUN
cana-1619	12	12	,	,	PUNCT
cana-1619	12	13	using	use	VERB
cana-1619	12	14	advanced	advanced	ADJ
cana-1619	12	15	mathematical	mathematical	ADJ
cana-1619	12	16	tools	tool	NOUN
cana-1619	12	17	like	like	ADP
cana-1619	12	18	cosine	cosine	NOUN
cana-1619	12	19	family	family	NOUN
cana-1619	12	20	theory	theory	NOUN
cana-1619	12	21	and	and	CCONJ
cana-1619	12	22	the	the	DET
cana-1619	12	23	leray	leray	ADJ
cana-1619	12	24	-	-	PUNCT
cana-1619	12	25	schauder	schauder	NOUN
cana-1619	12	26	theorem	theorem	VERB
cana-1619	12	27	to	to	PART
cana-1619	12	28	establish	establish	VERB
cana-1619	12	29	rigorous	rigorous	ADJ
cana-1619	12	30	solution	solution	NOUN
cana-1619	12	31	conditions	condition	NOUN
cana-1619	12	32	.	.	PUNCT
cana-1619	13	1	these	these	DET
cana-1619	13	2	theoretical	theoretical	ADJ
cana-1619	13	3	results	result	NOUN
cana-1619	13	4	are	be	AUX
cana-1619	13	5	empirically	empirically	ADV
cana-1619	13	6	validated	validate	VERB
cana-1619	13	7	through	through	ADP
cana-1619	13	8	practical	practical	ADJ
cana-1619	13	9	examples	example	NOUN
cana-1619	13	10	,	,	PUNCT
cana-1619	13	11	enhancing	enhance	VERB
cana-1619	13	12	understanding	understanding	NOUN
cana-1619	13	13	of	of	ADP
cana-1619	13	14	real	real	ADJ
cana-1619	13	15	-	-	PUNCT
cana-1619	13	16	life	life	NOUN
cana-1619	13	17	behavior	behavior	NOUN
cana-1619	13	18	and	and	CCONJ
cana-1619	13	19	bridging	bridging	NOUN
cana-1619	13	20	theory	theory	NOUN
cana-1619	13	21	with	with	ADP
cana-1619	13	22	practice	practice	NOUN
cana-1619	13	23	.	.	PUNCT
cana-1619	14	1	the	the	DET
cana-1619	14	2	study	study	NOUN
cana-1619	14	3	’s	’s	PART
cana-1619	14	4	findings	finding	NOUN
cana-1619	14	5	advance	advance	VERB
cana-1619	14	6	the	the	DET
cana-1619	14	7	understanding	understanding	NOUN
cana-1619	14	8	of	of	ADP
cana-1619	14	9	delayed	delay	VERB
cana-1619	14	10	feedback	feedback	NOUN
cana-1619	14	11	systems	system	NOUN
cana-1619	14	12	,	,	PUNCT
cana-1619	14	13	facilitating	facilitate	VERB
cana-1619	14	14	effective	effective	ADJ
cana-1619	14	15	control	control	NOUN
cana-1619	14	16	strategies	strategy	NOUN
cana-1619	14	17	and	and	CCONJ
cana-1619	14	18	practical	practical	ADJ
cana-1619	14	19	engineering	engineering	NOUN
cana-1619	14	20	solutions	solution	NOUN
cana-1619	14	21	,	,	PUNCT
cana-1619	14	22	thereby	thereby	ADV
cana-1619	14	23	contributing	contribute	VERB
cana-1619	14	24	significantly	significantly	ADV
cana-1619	14	25	to	to	ADP
cana-1619	14	26	dynamical	dynamical	ADJ
cana-1619	14	27	systems	system	NOUN
cana-1619	14	28	and	and	CCONJ
cana-1619	14	29	control	control	NOUN
cana-1619	14	30	theory	theory	NOUN
cana-1619	14	31	.	.	PUNCT
cana-1619	15	1	keywords	keyword	NOUN
cana-1619	15	2	:	:	PUNCT
cana-1619	15	3	differential	differential	ADJ
cana-1619	15	4	equation	equation	NOUN
cana-1619	15	5	;	;	PUNCT
cana-1619	15	6	lerray	lerray	ADJ
cana-1619	15	7	-	-	PUNCT
cana-1619	15	8	schauder	schauder	NOUN
cana-1619	15	9	fixed	fix	VERB
cana-1619	15	10	point	point	NOUN
cana-1619	15	11	;	;	PUNCT
cana-1619	15	12	mild	mild	ADJ
cana-1619	15	13	solution	solution	NOUN
cana-1619	15	14	;	;	PUNCT
cana-1619	15	15	finite	finite	PROPN
cana-1619	15	16	delay	delay	NOUN
cana-1619	15	17	;	;	PUNCT
cana-1619	15	18	semigroup	semigroup	PROPN
cana-1619	15	19	theory	theory	NOUN
cana-1619	15	20	;	;	PUNCT
cana-1619	15	21	approximate	approximate	ADJ
cana-1619	15	22	controllability	controllability	NOUN
cana-1619	15	23	.	.	PUNCT
cana-1619	16	1	msc	msc	PROPN
cana-1619	16	2	2010	2010	NUM
cana-1619	16	3	:	:	PUNCT
cana-1619	16	4	:	:	PUNCT
cana-1619	16	5	45j05	45j05	NUM
cana-1619	16	6	;	;	PUNCT
cana-1619	16	7	34k30	34k30	NUM
cana-1619	16	8	;	;	PUNCT
cana-1619	16	9	47g20	47g20	NUM
cana-1619	16	10	;	;	PUNCT
cana-1619	16	11	34k20	34k20	NUM
cana-1619	16	12	,	,	PUNCT
cana-1619	16	13	93b05	93b05	NUM
cana-1619	16	14	.	.	PUNCT
cana-1619	16	15	1	1	NUM
cana-1619	16	16	introduction	introduction	NOUN
cana-1619	16	17	in	in	ADP
cana-1619	16	18	the	the	DET
cana-1619	16	19	area	area	NOUN
cana-1619	16	20	of	of	ADP
cana-1619	16	21	mathematical	mathematical	ADJ
cana-1619	16	22	analysis	analysis	NOUN
cana-1619	16	23	and	and	CCONJ
cana-1619	16	24	its	its	PRON
cana-1619	16	25	interdisciplinary	interdisciplinary	ADJ
cana-1619	16	26	applications	application	NOUN
cana-1619	16	27	,	,	PUNCT
cana-1619	16	28	a	a	DET
cana-1619	16	29	diverse	diverse	ADJ
cana-1619	16	30	array	array	NOUN
cana-1619	16	31	of	of	ADP
cana-1619	16	32	theories	theory	NOUN
cana-1619	16	33	,	,	PUNCT
cana-1619	16	34	techniques	technique	NOUN
cana-1619	16	35	,	,	PUNCT
cana-1619	16	36	and	and	CCONJ
cana-1619	16	37	models	model	NOUN
cana-1619	16	38	has	have	AUX
cana-1619	16	39	emerged	emerge	VERB
cana-1619	16	40	to	to	PART
cana-1619	16	41	address	address	VERB
cana-1619	16	42	complex	complex	ADJ
cana-1619	16	43	phenomena	phenomenon	NOUN
cana-1619	16	44	across	across	ADP
cana-1619	16	45	various	various	ADJ
cana-1619	16	46	scientific	scientific	ADJ
cana-1619	16	47	domains	domain	NOUN
cana-1619	16	48	.	.	PUNCT
cana-1619	17	1	this	this	DET
cana-1619	17	2	introduction	introduction	NOUN
cana-1619	17	3	highlights	highlight	VERB
cana-1619	17	4	a	a	DET
cana-1619	17	5	selection	selection	NOUN
cana-1619	17	6	of	of	ADP
cana-1619	17	7	seminal	seminal	ADJ
cana-1619	17	8	works	work	NOUN
cana-1619	17	9	and	and	CCONJ
cana-1619	17	10	recent	recent	ADJ
cana-1619	17	11	research	research	NOUN
cana-1619	17	12	contributions	contribution	NOUN
cana-1619	17	13	that	that	PRON
cana-1619	17	14	delve	delve	VERB
cana-1619	17	15	into	into	ADP
cana-1619	17	16	the	the	DET
cana-1619	17	17	intricate	intricate	ADJ
cana-1619	17	18	landscapes	landscape	NOUN
cana-1619	17	19	of	of	ADP
cana-1619	17	20	neutral	neutral	ADJ
cana-1619	17	21	functional	functional	ADJ
cana-1619	17	22	differential	differential	NOUN
cana-1619	17	23	equations	equation	NOUN
cana-1619	17	24	,	,	PUNCT
cana-1619	17	25	impulsive	impulsive	ADJ
cana-1619	17	26	systems	system	NOUN
cana-1619	17	27	,	,	PUNCT
cana-1619	17	28	controllability	controllability	NOUN
cana-1619	17	29	theories	theory	NOUN
cana-1619	17	30	,	,	PUNCT
cana-1619	17	31	and	and	CCONJ
cana-1619	17	32	interdisciplinary	interdisciplinary	ADJ
cana-1619	17	33	interactions	interaction	NOUN
cana-1619	17	34	bridging	bridge	VERB
cana-1619	17	35	mathematics	mathematic	NOUN
cana-1619	17	36	with	with	ADP
cana-1619	17	37	physics	physics	PROPN
cana-1619	17	38	.	.	PUNCT
cana-1619	18	1	n.	n.	PROPN
cana-1619	18	2	u.	u.	PROPN
cana-1619	18	3	ahmed	ahmed	PROPN
cana-1619	18	4	’s	’s	PART
cana-1619	18	5	seminal	seminal	ADJ
cana-1619	18	6	work	work	NOUN
cana-1619	18	7	,	,	PUNCT
cana-1619	18	8	"	"	PUNCT
cana-1619	18	9	semigroup	semigroup	ADJ
cana-1619	18	10	theory	theory	NOUN
cana-1619	18	11	with	with	ADP
cana-1619	18	12	applications	application	NOUN
cana-1619	18	13	to	to	ADP
cana-1619	18	14	systems	system	NOUN
cana-1619	18	15	and	and	CCONJ
cana-1619	18	16	control	control	NOUN
cana-1619	18	17	"	"	PUNCT
cana-1619	19	1	[	[	X
cana-1619	19	2	1	1	NUM
cana-1619	19	3	]	]	PUNCT
cana-1619	19	4	,	,	PUNCT
cana-1619	19	5	serves	serve	VERB
cana-1619	19	6	as	as	ADP
cana-1619	19	7	a	a	DET
cana-1619	19	8	cornerstone	cornerstone	NOUN
cana-1619	19	9	in	in	ADP
cana-1619	19	10	understanding	understand	VERB
cana-1619	19	11	the	the	DET
cana-1619	19	12	fundamental	fundamental	ADJ
cana-1619	19	13	principles	principle	NOUN
cana-1619	19	14	of	of	ADP
cana-1619	19	15	semigroup	semigroup	PROPN
cana-1619	19	16	theory	theory	NOUN
cana-1619	19	17	and	and	CCONJ
cana-1619	19	18	its	its	PRON
cana-1619	19	19	versatile	versatile	ADJ
cana-1619	19	20	applications	application	NOUN
cana-1619	19	21	in	in	ADP
cana-1619	19	22	systems	system	NOUN
cana-1619	19	23	and	and	CCONJ
cana-1619	19	24	control	control	PROPN
cana-1619	19	25	theory	theory	NOUN
cana-1619	19	26	.	.	PUNCT
cana-1619	20	1	ahmed	ahmed	PROPN
cana-1619	20	2	’s	’s	PART
cana-1619	20	3	text	text	NOUN
cana-1619	20	4	provides	provide	VERB
cana-1619	20	5	a	a	DET
cana-1619	20	6	comprehensive	comprehensive	ADJ
cana-1619	20	7	exploration	exploration	NOUN
cana-1619	20	8	of	of	ADP
cana-1619	20	9	semigroups	semigroup	NOUN
cana-1619	20	10	,	,	PUNCT
cana-1619	20	11	offering	offer	VERB
cana-1619	20	12	insights	insight	NOUN
cana-1619	20	13	into	into	ADP
cana-1619	20	14	their	their	PRON
cana-1619	20	15	algebraic	algebraic	ADJ
cana-1619	20	16	structures	structure	NOUN
cana-1619	20	17	and	and	CCONJ
cana-1619	20	18	their	their	PRON
cana-1619	20	19	pivotal	pivotal	ADJ
cana-1619	20	20	role	role	NOUN
cana-1619	20	21	in	in	ADP
cana-1619	20	22	analyzing	analyze	VERB
cana-1619	20	23	dynamic	dynamic	ADJ
cana-1619	20	24	mailto:tguna84@gmail.coma	mailto:tguna84@gmail.coma	PROPN
cana-1619	20	25	communications	communication	NOUN
cana-1619	20	26	on	on	ADP
cana-1619	20	27	applied	apply	VERB
cana-1619	20	28	nonlinear	nonlinear	ADJ
cana-1619	20	29	analysis	analysis	NOUN
cana-1619	20	30	issn	issn	NOUN
cana-1619	20	31	:	:	PUNCT
cana-1619	20	32	1074	1074	NUM
cana-1619	20	33	-	-	PUNCT
cana-1619	20	34	133x	133x	NUM
cana-1619	20	35	vol	vol	NOUN
cana-1619	20	36	32	32	NUM
cana-1619	20	37	no	no	NOUN
cana-1619	20	38	.	.	NOUN
cana-1619	20	39	1	1	NUM
cana-1619	20	40	(	(	PUNCT
cana-1619	20	41	2025	2025	NUM
cana-1619	20	42	)	)	PUNCT
cana-1619	20	43	36	36	NUM
cana-1619	20	44	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	20	45	systems	system	NOUN
cana-1619	20	46	and	and	CCONJ
cana-1619	20	47	control	control	NOUN
cana-1619	20	48	processes	process	NOUN
cana-1619	20	49	.	.	PUNCT
cana-1619	21	1	the	the	DET
cana-1619	21	2	works	work	NOUN
cana-1619	21	3	by	by	ADP
cana-1619	21	4	baghli	baghli	NOUN
cana-1619	21	5	and	and	CCONJ
cana-1619	21	6	benchohra	benchohra	NOUN
cana-1619	21	7	[	[	X
cana-1619	21	8	2	2	NUM
cana-1619	21	9	]	]	PUNCT
cana-1619	21	10	delve	delve	VERB
cana-1619	21	11	into	into	ADP
cana-1619	21	12	the	the	DET
cana-1619	21	13	uniqueness	uniqueness	NOUN
cana-1619	21	14	and	and	CCONJ
cana-1619	21	15	existence	existence	NOUN
cana-1619	21	16	results	result	VERB
cana-1619	21	17	for	for	ADP
cana-1619	21	18	partial	partial	ADJ
cana-1619	21	19	and	and	CCONJ
cana-1619	21	20	neutral	neutral	ADJ
cana-1619	21	21	functional	functional	ADJ
cana-1619	21	22	differential	differential	NOUN
cana-1619	21	23	equations	equation	NOUN
cana-1619	21	24	in	in	ADP
cana-1619	21	25	frechet	frechet	PROPN
cana-1619	21	26	spaces	space	NOUN
cana-1619	21	27	,	,	PUNCT
cana-1619	21	28	shedding	shed	VERB
cana-1619	21	29	light	light	NOUN
cana-1619	21	30	on	on	ADP
cana-1619	21	31	the	the	DET
cana-1619	21	32	intricate	intricate	ADJ
cana-1619	21	33	dynamics	dynamic	NOUN
cana-1619	21	34	of	of	ADP
cana-1619	21	35	these	these	DET
cana-1619	21	36	equations	equation	NOUN
cana-1619	21	37	with	with	ADP
cana-1619	21	38	infinite	infinite	ADJ
cana-1619	21	39	delay	delay	NOUN
cana-1619	21	40	.	.	PUNCT
cana-1619	22	1	additionally	additionally	ADV
cana-1619	22	2	,	,	PUNCT
cana-1619	22	3	lupulescu	lupulescu	ADJ
cana-1619	22	4	and	and	CCONJ
cana-1619	22	5	lungan	lungan	VERB
cana-1619	23	1	[	[	X
cana-1619	23	2	5	5	X
cana-1619	23	3	]	]	PUNCT
cana-1619	23	4	contribute	contribute	VERB
cana-1619	23	5	to	to	ADP
cana-1619	23	6	the	the	DET
cana-1619	23	7	field	field	NOUN
cana-1619	23	8	by	by	ADP
cana-1619	23	9	studying	study	VERB
cana-1619	23	10	random	random	ADJ
cana-1619	23	11	integral	integral	ADJ
cana-1619	23	12	equations	equation	NOUN
cana-1619	23	13	on	on	ADP
cana-1619	23	14	time	time	NOUN
cana-1619	23	15	scales	scale	NOUN
cana-1619	23	16	,	,	PUNCT
cana-1619	23	17	offering	offer	VERB
cana-1619	23	18	novel	novel	ADJ
cana-1619	23	19	perspectives	perspective	NOUN
cana-1619	23	20	on	on	ADP
cana-1619	23	21	the	the	DET
cana-1619	23	22	interplay	interplay	NOUN
cana-1619	23	23	between	between	ADP
cana-1619	23	24	randomness	randomness	NOUN
cana-1619	23	25	and	and	CCONJ
cana-1619	23	26	differential	differential	ADJ
cana-1619	23	27	equations	equation	NOUN
cana-1619	23	28	.	.	PUNCT
cana-1619	24	1	gunasekar	gunasekar	PROPN
cana-1619	24	2	et	et	PROPN
cana-1619	24	3	all	all	PRON
cana-1619	25	1	[	[	X
cana-1619	25	2	12,23,24	12,23,24	X
cana-1619	25	3	]	]	PUNCT
cana-1619	25	4	explore	explore	VERB
cana-1619	25	5	the	the	DET
cana-1619	25	6	existence	existence	NOUN
cana-1619	25	7	results	result	VERB
cana-1619	25	8	for	for	ADP
cana-1619	25	9	nonlocal	nonlocal	ADJ
cana-1619	25	10	impulsive	impulsive	ADJ
cana-1619	25	11	neutral	neutral	ADJ
cana-1619	25	12	functional	functional	ADJ
cana-1619	25	13	integro	integro	ADJ
cana-1619	25	14	-	-	PUNCT
cana-1619	25	15	differential	differential	NOUN
cana-1619	25	16	equations	equation	NOUN
cana-1619	25	17	,	,	PUNCT
cana-1619	25	18	unraveling	unravel	VERB
cana-1619	25	19	the	the	DET
cana-1619	25	20	complexities	complexity	NOUN
cana-1619	25	21	of	of	ADP
cana-1619	25	22	impulsive	impulsive	ADJ
cana-1619	25	23	systems	system	NOUN
cana-1619	25	24	with	with	ADP
cana-1619	25	25	nonlocal	nonlocal	ADJ
cana-1619	25	26	interactions	interaction	NOUN
cana-1619	25	27	.	.	PUNCT
cana-1619	26	1	furthermore	furthermore	ADV
cana-1619	26	2	,	,	PUNCT
cana-1619	26	3	baleanu	baleanu	NOUN
cana-1619	26	4	et	et	PROPN
cana-1619	26	5	al	al	PROPN
cana-1619	26	6	.	.	PROPN
cana-1619	26	7	investigate	investigate	VERB
cana-1619	26	8	the	the	DET
cana-1619	26	9	approximate	approximate	ADJ
cana-1619	26	10	controllability	controllability	NOUN
cana-1619	26	11	of	of	ADP
cana-1619	26	12	second	second	ADJ
cana-1619	26	13	-	-	PUNCT
cana-1619	26	14	order	order	NOUN
cana-1619	26	15	nonlocal	nonlocal	ADJ
cana-1619	26	16	impulsive	impulsive	ADJ
cana-1619	26	17	functional	functional	ADJ
cana-1619	26	18	integro	integro	ADJ
cana-1619	26	19	-	-	PUNCT
cana-1619	26	20	differential	differential	NOUN
cana-1619	26	21	systems	system	NOUN
cana-1619	26	22	in	in	ADP
cana-1619	26	23	banach	banach	NOUN
cana-1619	26	24	spaces	space	NOUN
cana-1619	26	25	,	,	PUNCT
cana-1619	26	26	providing	provide	VERB
cana-1619	26	27	valuable	valuable	ADJ
cana-1619	26	28	insights	insight	NOUN
cana-1619	26	29	into	into	ADP
cana-1619	26	30	the	the	DET
cana-1619	26	31	controllability	controllability	NOUN
cana-1619	26	32	properties	property	NOUN
cana-1619	26	33	of	of	ADP
cana-1619	26	34	such	such	ADJ
cana-1619	26	35	systems	system	NOUN
cana-1619	26	36	.	.	PUNCT
cana-1619	27	1	recent	recent	ADJ
cana-1619	27	2	research	research	NOUN
cana-1619	27	3	has	have	AUX
cana-1619	27	4	also	also	ADV
cana-1619	27	5	focused	focus	VERB
cana-1619	27	6	on	on	ADP
cana-1619	27	7	exploring	explore	VERB
cana-1619	27	8	the	the	DET
cana-1619	27	9	synergies	synergy	NOUN
cana-1619	27	10	between	between	ADP
cana-1619	27	11	physics	physics	NOUN
cana-1619	27	12	,	,	PUNCT
cana-1619	27	13	mathematics	mathematic	NOUN
cana-1619	27	14	,	,	PUNCT
cana-1619	27	15	and	and	CCONJ
cana-1619	27	16	computer	computer	NOUN
cana-1619	27	17	science	science	NOUN
cana-1619	27	18	.	.	PUNCT
cana-1619	28	1	hazra	hazra	VERB
cana-1619	28	2	et	et	PROPN
cana-1619	28	3	al	al	PROPN
cana-1619	28	4	.	.	PUNCT
cana-1619	29	1	[	[	X
cana-1619	29	2	21	21	NUM
cana-1619	29	3	]	]	PUNCT
cana-1619	29	4	present	present	VERB
cana-1619	29	5	a	a	DET
cana-1619	29	6	modeling	modeling	NOUN
cana-1619	29	7	framework	framework	NOUN
cana-1619	29	8	that	that	PRON
cana-1619	29	9	elucidates	elucidate	VERB
cana-1619	29	10	the	the	DET
cana-1619	29	11	interdisciplinary	interdisciplinary	ADJ
cana-1619	29	12	interactions	interaction	NOUN
cana-1619	29	13	among	among	ADP
cana-1619	29	14	these	these	DET
cana-1619	29	15	fields	field	NOUN
cana-1619	29	16	,	,	PUNCT
cana-1619	29	17	fostering	foster	VERB
cana-1619	29	18	a	a	DET
cana-1619	29	19	deeper	deep	ADJ
cana-1619	29	20	understanding	understanding	NOUN
cana-1619	29	21	of	of	ADP
cana-1619	29	22	complex	complex	ADJ
cana-1619	29	23	phenomena	phenomenon	NOUN
cana-1619	29	24	.	.	PUNCT
cana-1619	30	1	similarly	similarly	ADV
cana-1619	30	2	,	,	PUNCT
cana-1619	30	3	han	han	PROPN
cana-1619	30	4	et	et	PROPN
cana-1619	30	5	al	al	PROPN
cana-1619	30	6	.	.	PUNCT
cana-1619	31	1	[	[	X
cana-1619	31	2	22	22	NUM
cana-1619	31	3	]	]	PUNCT
cana-1619	31	4	delve	delve	VERB
cana-1619	31	5	into	into	ADP
cana-1619	31	6	the	the	DET
cana-1619	31	7	formation	formation	NOUN
cana-1619	31	8	of	of	ADP
cana-1619	31	9	trade	trade	NOUN
cana-1619	31	10	networks	network	NOUN
cana-1619	31	11	,	,	PUNCT
cana-1619	31	12	highlighting	highlight	VERB
cana-1619	31	13	the	the	DET
cana-1619	31	14	role	role	NOUN
cana-1619	31	15	of	of	ADP
cana-1619	31	16	economies	economy	NOUN
cana-1619	31	17	of	of	ADP
cana-1619	31	18	scale	scale	NOUN
cana-1619	31	19	and	and	CCONJ
cana-1619	31	20	product	product	NOUN
cana-1619	31	21	differentiation	differentiation	NOUN
cana-1619	31	22	in	in	ADP
cana-1619	31	23	shaping	shape	VERB
cana-1619	31	24	global	global	ADJ
cana-1619	31	25	economic	economic	ADJ
cana-1619	31	26	dynamics	dynamic	NOUN
cana-1619	31	27	.	.	PUNCT
cana-1619	32	1	in	in	ADP
cana-1619	32	2	mathematical	mathematical	ADJ
cana-1619	32	3	and	and	CCONJ
cana-1619	32	4	control	control	NOUN
cana-1619	32	5	theory	theory	NOUN
cana-1619	32	6	research	research	NOUN
cana-1619	32	7	,	,	PUNCT
cana-1619	32	8	various	various	ADJ
cana-1619	32	9	studies	study	NOUN
cana-1619	32	10	delve	delve	VERB
cana-1619	32	11	into	into	ADP
cana-1619	32	12	the	the	DET
cana-1619	32	13	analysis	analysis	NOUN
cana-1619	32	14	and	and	CCONJ
cana-1619	32	15	controllability	controllability	NOUN
cana-1619	32	16	of	of	ADP
cana-1619	32	17	complex	complex	ADJ
cana-1619	32	18	dynamical	dynamical	ADJ
cana-1619	32	19	systems	system	NOUN
cana-1619	32	20	,	,	PUNCT
cana-1619	32	21	aiming	aim	VERB
cana-1619	32	22	to	to	PART
cana-1619	32	23	understand	understand	VERB
cana-1619	32	24	their	their	PRON
cana-1619	32	25	behavior	behavior	NOUN
cana-1619	32	26	and	and	CCONJ
cana-1619	32	27	design	design	VERB
cana-1619	32	28	effective	effective	ADJ
cana-1619	32	29	control	control	NOUN
cana-1619	32	30	strategies	strategy	NOUN
cana-1619	32	31	.	.	PUNCT
cana-1619	33	1	the	the	DET
cana-1619	33	2	research	research	NOUN
cana-1619	33	3	by	by	ADP
cana-1619	33	4	baleanu	baleanu	NOUN
cana-1619	33	5	et	et	PROPN
cana-1619	33	6	al	al	PROPN
cana-1619	33	7	.	.	PROPN
cana-1619	33	8	focuses	focus	VERB
cana-1619	33	9	on	on	ADP
cana-1619	33	10	the	the	DET
cana-1619	33	11	approximate	approximate	ADJ
cana-1619	33	12	controllability	controllability	NOUN
cana-1619	33	13	of	of	ADP
cana-1619	33	14	second	second	ADJ
cana-1619	33	15	-	-	PUNCT
cana-1619	33	16	order	order	NOUN
cana-1619	33	17	nonlocal	nonlocal	ADJ
cana-1619	33	18	impulsive	impulsive	ADJ
cana-1619	33	19	functional	functional	ADJ
cana-1619	33	20	integro	integro	ADJ
cana-1619	33	21	-	-	PUNCT
cana-1619	33	22	differential	differential	NOUN
cana-1619	33	23	systems	system	NOUN
cana-1619	33	24	in	in	ADP
cana-1619	33	25	banach	banach	NOUN
cana-1619	33	26	spaces	space	NOUN
cana-1619	33	27	.	.	PUNCT
cana-1619	34	1	their	their	PRON
cana-1619	34	2	study	study	NOUN
cana-1619	34	3	investigates	investigate	VERB
cana-1619	34	4	the	the	DET
cana-1619	34	5	ability	ability	NOUN
cana-1619	34	6	to	to	PART
cana-1619	34	7	steer	steer	VERB
cana-1619	34	8	such	such	ADJ
cana-1619	34	9	systems	system	NOUN
cana-1619	34	10	arbitrarily	arbitrarily	ADV
cana-1619	34	11	close	close	ADJ
cana-1619	34	12	to	to	ADP
cana-1619	34	13	desired	desire	VERB
cana-1619	34	14	states	state	NOUN
cana-1619	34	15	using	use	VERB
cana-1619	34	16	control	control	NOUN
cana-1619	34	17	inputs	input	NOUN
cana-1619	34	18	.	.	PUNCT
cana-1619	35	1	this	this	DET
cana-1619	35	2	research	research	NOUN
cana-1619	35	3	contributes	contribute	VERB
cana-1619	35	4	to	to	ADP
cana-1619	35	5	understanding	understand	VERB
cana-1619	35	6	the	the	DET
cana-1619	35	7	controllability	controllability	NOUN
cana-1619	35	8	properties	property	NOUN
cana-1619	35	9	of	of	ADP
cana-1619	35	10	systems	system	NOUN
cana-1619	35	11	with	with	ADP
cana-1619	35	12	impulsive	impulsive	ADJ
cana-1619	35	13	and	and	CCONJ
cana-1619	35	14	nonlocal	nonlocal	ADJ
cana-1619	35	15	behaviors	behavior	NOUN
cana-1619	35	16	.	.	PUNCT
cana-1619	36	1	anguraj	anguraj	PROPN
cana-1619	36	2	et	et	PROPN
cana-1619	36	3	al	al	PROPN
cana-1619	36	4	.	.	PROPN
cana-1619	37	1	explore	explore	VERB
cana-1619	37	2	the	the	DET
cana-1619	37	3	existence	existence	NOUN
cana-1619	37	4	results	result	VERB
cana-1619	37	5	for	for	ADP
cana-1619	37	6	an	an	DET
cana-1619	37	7	impulsive	impulsive	ADJ
cana-1619	37	8	neutral	neutral	ADJ
cana-1619	37	9	functional	functional	ADJ
cana-1619	37	10	differential	differential	NOUN
cana-1619	37	11	equation	equation	NOUN
cana-1619	37	12	with	with	ADP
cana-1619	37	13	state	state	NOUN
cana-1619	37	14	-	-	PUNCT
cana-1619	37	15	dependent	dependent	ADJ
cana-1619	37	16	delay	delay	NOUN
cana-1619	37	17	.	.	PUNCT
cana-1619	38	1	by	by	ADP
cana-1619	38	2	analyzing	analyze	VERB
cana-1619	38	3	the	the	DET
cana-1619	38	4	existence	existence	NOUN
cana-1619	38	5	of	of	ADP
cana-1619	38	6	solutions	solution	NOUN
cana-1619	38	7	to	to	ADP
cana-1619	38	8	this	this	DET
cana-1619	38	9	equation	equation	NOUN
cana-1619	38	10	,	,	PUNCT
cana-1619	38	11	the	the	DET
cana-1619	38	12	study	study	NOUN
cana-1619	38	13	provides	provide	VERB
cana-1619	38	14	theoretical	theoretical	ADJ
cana-1619	38	15	insights	insight	NOUN
cana-1619	38	16	into	into	ADP
cana-1619	38	17	the	the	DET
cana-1619	38	18	behavior	behavior	NOUN
cana-1619	38	19	of	of	ADP
cana-1619	38	20	impulsive	impulsive	ADJ
cana-1619	38	21	systems	system	NOUN
cana-1619	38	22	with	with	ADP
cana-1619	38	23	state	state	NOUN
cana-1619	38	24	-	-	PUNCT
cana-1619	38	25	dependent	dependent	ADJ
cana-1619	38	26	delays	delay	NOUN
cana-1619	38	27	.	.	PUNCT
cana-1619	39	1	these	these	DET
cana-1619	39	2	references	reference	NOUN
cana-1619	39	3	collectively	collectively	ADV
cana-1619	39	4	contribute	contribute	VERB
cana-1619	39	5	to	to	ADP
cana-1619	39	6	advancing	advance	VERB
cana-1619	39	7	our	our	PRON
cana-1619	39	8	understanding	understanding	NOUN
cana-1619	39	9	of	of	ADP
cana-1619	39	10	the	the	DET
cana-1619	39	11	controllability	controllability	NOUN
cana-1619	39	12	properties	property	NOUN
cana-1619	39	13	of	of	ADP
cana-1619	39	14	complex	complex	ADJ
cana-1619	39	15	dynamical	dynamical	ADJ
cana-1619	39	16	systems	system	NOUN
cana-1619	39	17	,	,	PUNCT
cana-1619	39	18	particularly	particularly	ADV
cana-1619	39	19	those	those	PRON
cana-1619	39	20	involving	involve	VERB
cana-1619	39	21	impulses	impulse	NOUN
cana-1619	39	22	,	,	PUNCT
cana-1619	39	23	delays	delay	NOUN
cana-1619	39	24	,	,	PUNCT
cana-1619	39	25	and	and	CCONJ
cana-1619	39	26	nonlocal	nonlocal	ADJ
cana-1619	39	27	interactions	interaction	NOUN
cana-1619	39	28	.	.	PUNCT
cana-1619	40	1	they	they	PRON
cana-1619	40	2	provide	provide	VERB
cana-1619	40	3	valuable	valuable	ADJ
cana-1619	40	4	theoretical	theoretical	ADJ
cana-1619	40	5	insights	insight	NOUN
cana-1619	40	6	and	and	CCONJ
cana-1619	40	7	mathematical	mathematical	ADJ
cana-1619	40	8	techniques	technique	NOUN
cana-1619	40	9	for	for	ADP
cana-1619	40	10	analyzing	analyze	VERB
cana-1619	40	11	and	and	CCONJ
cana-1619	40	12	designing	design	VERB
cana-1619	40	13	control	control	NOUN
cana-1619	40	14	strategies	strategy	NOUN
cana-1619	40	15	for	for	ADP
cana-1619	40	16	such	such	ADJ
cana-1619	40	17	systems	system	NOUN
cana-1619	40	18	,	,	PUNCT
cana-1619	40	19	with	with	ADP
cana-1619	40	20	implications	implication	NOUN
cana-1619	40	21	for	for	ADP
cana-1619	40	22	various	various	ADJ
cana-1619	40	23	scientific	scientific	ADJ
cana-1619	40	24	and	and	CCONJ
cana-1619	40	25	engineering	engineering	NOUN
cana-1619	40	26	applications	application	NOUN
cana-1619	40	27	.	.	PUNCT
cana-1619	41	1	the	the	DET
cana-1619	41	2	second	second	ADJ
cana-1619	41	3	order	order	NOUN
cana-1619	41	4	impulsive	impulsive	ADJ
cana-1619	41	5	neutral	neutral	ADJ
cana-1619	41	6	functional	functional	ADJ
cana-1619	41	7	differential	differential	NOUN
cana-1619	41	8	equation	equation	NOUN
cana-1619	41	9	with	with	ADP
cana-1619	41	10	delay	delay	NOUN
cana-1619	41	11	and	and	CCONJ
cana-1619	41	12	random	random	ADJ
cana-1619	41	13	effects	effect	NOUN
cana-1619	41	14	is	be	AUX
cana-1619	41	15	of	of	ADP
cana-1619	41	16	the	the	DET
cana-1619	41	17	form	form	NOUN
cana-1619	41	18	.	.	PUNCT
cana-1619	42	1	𝑑	𝑑	PRON
cana-1619	42	2	𝑑ℎ	𝑑ℎ	PROPN
cana-1619	43	1	[	[	X
cana-1619	43	2	𝜑′(ℎ	𝜑′(ℎ	ADP
cana-1619	43	3	,	,	PUNCT
cana-1619	43	4	ℵ	ℵ	NOUN
cana-1619	43	5	)	)	PUNCT
cana-1619	44	1	+	+	CCONJ
cana-1619	44	2	𝜌(ℎ	𝜌(ℎ	PROPN
cana-1619	44	3	,	,	PUNCT
cana-1619	44	4	𝜑ℎ	𝜑ℎ	PROPN
cana-1619	44	5	(	(	PUNCT
cana-1619	44	6	.	.	PUNCT
cana-1619	44	7	,	,	PUNCT
cana-1619	44	8	ℵ	ℵ	NOUN
cana-1619	44	9	)	)	PUNCT
cana-1619	44	10	,	,	PUNCT
cana-1619	44	11	ℵ	ℵ	NOUN
cana-1619	44	12	)	)	PUNCT
cana-1619	44	13	]	]	PUNCT
cana-1619	45	1	=	=	PUNCT
cana-1619	46	1	𝐴𝜑(ℎ	𝐴𝜑(ℎ	NOUN
cana-1619	46	2	,	,	PUNCT
cana-1619	46	3	ℵ	ℵ	NOUN
cana-1619	46	4	)	)	PUNCT
cana-1619	46	5	+	+	NUM
cana-1619	46	6	υ(ℎ,𝜛	υ(ℎ,𝜛	NOUN
cana-1619	46	7	,	,	PUNCT
cana-1619	46	8	𝜑ℎ	𝜑ℎ	NOUN
cana-1619	46	9	(	(	PUNCT
cana-1619	46	10	.	.	PUNCT
cana-1619	46	11	,	,	PUNCT
cana-1619	46	12	ℵ	ℵ	NOUN
cana-1619	46	13	)	)	PUNCT
cana-1619	46	14	,	,	PUNCT
cana-1619	46	15	ℵ	ℵ	NOUN
cana-1619	46	16	)	)	PUNCT
cana-1619	46	17	;	;	PUNCT
cana-1619	46	18	ℎ	ℎ	PROPN
cana-1619	46	19	∈	∈	PROPN
cana-1619	46	20	𝐽	𝐽	PROPN
cana-1619	46	21	=	=	SYM
cana-1619	46	22	(	(	PUNCT
cana-1619	46	23	0	0	NUM
cana-1619	46	24	,	,	PUNCT
cana-1619	46	25	𝜚	𝜚	NOUN
cana-1619	46	26	]	]	X
cana-1619	46	27	,	,	PUNCT
cana-1619	46	28	ℎ	ℎ	PROPN
cana-1619	46	29	≠	≠	PROPN
cana-1619	46	30	ℎ𝜉	ℎ𝜉	ADP
cana-1619	46	31	,	,	PUNCT
cana-1619	46	32	𝜑(0	𝜑(0	NOUN
cana-1619	46	33	,	,	PUNCT
cana-1619	46	34	ℵ	ℵ	NOUN
cana-1619	46	35	)	)	PUNCT
cana-1619	46	36	=	=	SYM
cana-1619	46	37	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	46	38	)	)	PUNCT
cana-1619	46	39	,	,	PUNCT
cana-1619	46	40	𝜉	𝜉	X
cana-1619	46	41	=	=	NOUN
cana-1619	46	42	1,2,3	1,2,3	NUM
cana-1619	46	43	,	,	PUNCT
cana-1619	46	44	.	.	PUNCT
cana-1619	46	45	.	.	PUNCT
cana-1619	46	46	.	.	PUNCT
cana-1619	46	47	,	,	PUNCT
cana-1619	46	48	𝑚	𝑚	PROPN
cana-1619	46	49	𝜑′(0	𝜑′(0	PROPN
cana-1619	46	50	,	,	PUNCT
cana-1619	46	51	ℵ	ℵ	NOUN
cana-1619	46	52	)	)	PUNCT
cana-1619	46	53	=	=	SYM
cana-1619	46	54	𝜙′	𝜙′	X
cana-1619	46	55	0	0	NUM
cana-1619	46	56	(	(	PUNCT
cana-1619	46	57	ℵ	ℵ	NOUN
cana-1619	46	58	)	)	PUNCT
cana-1619	46	59	,	,	PUNCT
cana-1619	46	60	δ𝜑(ℎ𝜉	δ𝜑(ℎ𝜉	NOUN
cana-1619	46	61	,	,	PUNCT
cana-1619	46	62	ℵ	ℵ	NOUN
cana-1619	46	63	)	)	PUNCT
cana-1619	46	64	=	=	SYM
cana-1619	47	1	𝐼𝜉	𝐼𝜉	PROPN
cana-1619	47	2	(	(	PUNCT
cana-1619	47	3	𝜑(ℎ𝜉	𝜑(ℎ𝜉	NOUN
cana-1619	47	4	,	,	PUNCT
cana-1619	47	5	ℵ	ℵ	NOUN
cana-1619	47	6	)	)	PUNCT
cana-1619	47	7	)	)	PUNCT
cana-1619	47	8	,	,	PUNCT
cana-1619	47	9	δ′𝜑(ℎ𝜉	δ′𝜑(ℎ𝜉	NOUN
cana-1619	47	10	,	,	PUNCT
cana-1619	47	11	ℵ	ℵ	NOUN
cana-1619	47	12	)	)	PUNCT
cana-1619	47	13	=	=	VERB
cana-1619	47	14	𝐼𝜉′	𝐼𝜉′	NOUN
cana-1619	47	15	(	(	PUNCT
cana-1619	47	16	𝜑(ℎ𝜉	𝜑(ℎ𝜉	NOUN
cana-1619	47	17	,	,	PUNCT
cana-1619	47	18	ℵ	ℵ	NOUN
cana-1619	47	19	)	)	PUNCT
cana-1619	47	20	)	)	PUNCT
cana-1619	47	21	.	.	PUNCT
cana-1619	48	1	(	(	PUNCT
cana-1619	48	2	1	1	X
cana-1619	48	3	)	)	PUNCT
cana-1619	48	4	communications	communication	NOUN
cana-1619	48	5	on	on	ADP
cana-1619	48	6	applied	apply	VERB
cana-1619	48	7	nonlinear	nonlinear	ADJ
cana-1619	48	8	analysis	analysis	NOUN
cana-1619	48	9	issn	issn	NOUN
cana-1619	48	10	:	:	PUNCT
cana-1619	48	11	1074	1074	NUM
cana-1619	48	12	-	-	PUNCT
cana-1619	48	13	133x	133x	NUM
cana-1619	48	14	vol	vol	NOUN
cana-1619	48	15	32	32	NUM
cana-1619	48	16	no	no	NOUN
cana-1619	48	17	.	.	NOUN
cana-1619	48	18	1	1	NUM
cana-1619	48	19	(	(	PUNCT
cana-1619	48	20	2025	2025	NUM
cana-1619	48	21	)	)	PUNCT
cana-1619	48	22	37	37	NUM
cana-1619	48	23	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	48	24	the	the	DET
cana-1619	48	25	approximate	approximate	ADJ
cana-1619	48	26	controllability	controllability	NOUN
cana-1619	48	27	of	of	ADP
cana-1619	48	28	random	random	ADJ
cana-1619	48	29	impulsive	impulsive	ADJ
cana-1619	48	30	neutral	neutral	ADJ
cana-1619	48	31	functional	functional	ADJ
cana-1619	48	32	differential	differential	NOUN
cana-1619	48	33	equation	equation	NOUN
cana-1619	48	34	with	with	ADP
cana-1619	48	35	finite	finite	ADJ
cana-1619	48	36	delay	delay	NOUN
cana-1619	48	37	.	.	PUNCT
cana-1619	49	1	𝑑	𝑑	PRON
cana-1619	49	2	𝑑ℎ	𝑑ℎ	PROPN
cana-1619	50	1	[	[	X
cana-1619	50	2	𝜑′(ℎ	𝜑′(ℎ	ADP
cana-1619	50	3	,	,	PUNCT
cana-1619	50	4	ℵ	ℵ	NOUN
cana-1619	50	5	)	)	PUNCT
cana-1619	51	1	+	+	CCONJ
cana-1619	51	2	𝜌(ℎ	𝜌(ℎ	PROPN
cana-1619	51	3	,	,	PUNCT
cana-1619	51	4	𝜑ℎ	𝜑ℎ	PROPN
cana-1619	51	5	(	(	PUNCT
cana-1619	51	6	.	.	PUNCT
cana-1619	51	7	,	,	PUNCT
cana-1619	51	8	ℵ	ℵ	NOUN
cana-1619	51	9	)	)	PUNCT
cana-1619	51	10	,	,	PUNCT
cana-1619	51	11	ℵ	ℵ	NOUN
cana-1619	51	12	)	)	PUNCT
cana-1619	51	13	]	]	PUNCT
cana-1619	52	1	=	=	PUNCT
cana-1619	52	2	𝐴𝜑(ℎ	𝐴𝜑(ℎ	NOUN
cana-1619	52	3	,	,	PUNCT
cana-1619	52	4	ℵ	ℵ	NOUN
cana-1619	52	5	)	)	PUNCT
cana-1619	52	6	+	+	CCONJ
cana-1619	52	7	υ(h	υ(h	NOUN
cana-1619	52	8	,	,	PUNCT
cana-1619	52	9	𝜑ℎ	𝜑ℎ	NOUN
cana-1619	52	10	(	(	PUNCT
cana-1619	52	11	.	.	PUNCT
cana-1619	52	12	,	,	PUNCT
cana-1619	52	13	ℵ	ℵ	NOUN
cana-1619	52	14	)	)	PUNCT
cana-1619	52	15	,	,	PUNCT
cana-1619	52	16	ℵ	ℵ	X
cana-1619	52	17	)	)	PUNCT
cana-1619	52	18	+	+	CCONJ
cana-1619	52	19	𝐵𝑦(ℎ	𝐵𝑦(ℎ	ADJ
cana-1619	52	20	,	,	PUNCT
cana-1619	52	21	ℵ	ℵ	NOUN
cana-1619	52	22	)	)	PUNCT
cana-1619	52	23	;	;	PUNCT
cana-1619	52	24	ℎ	ℎ	PROPN
cana-1619	52	25	∈	∈	PROPN
cana-1619	52	26	𝐽	𝐽	PROPN
cana-1619	52	27	𝜑(0	𝜑(0	NOUN
cana-1619	52	28	,	,	PUNCT
cana-1619	52	29	ℵ	ℵ	NOUN
cana-1619	52	30	)	)	PUNCT
cana-1619	52	31	=	=	SYM
cana-1619	52	32	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	52	33	)	)	PUNCT
cana-1619	52	34	,	,	PUNCT
cana-1619	52	35	𝜑′(0	𝜑′(0	PROPN
cana-1619	52	36	,	,	PUNCT
cana-1619	52	37	ℵ	ℵ	NOUN
cana-1619	52	38	)	)	PUNCT
cana-1619	52	39	=	=	SYM
cana-1619	52	40	𝜙′0(ℵ	𝜙′0(ℵ	NOUN
cana-1619	52	41	)	)	PUNCT
cana-1619	52	42	,	,	PUNCT
cana-1619	52	43	δ𝜑(ℎ𝜉	δ𝜑(ℎ𝜉	NOUN
cana-1619	52	44	,	,	PUNCT
cana-1619	52	45	ℵ	ℵ	NOUN
cana-1619	52	46	)	)	PUNCT
cana-1619	52	47	=	=	SYM
cana-1619	52	48	𝐼𝜉(𝜑(ℎ𝜉	𝐼𝜉(𝜑(ℎ𝜉	PUNCT
cana-1619	52	49	,	,	PUNCT
cana-1619	52	50	ℵ	ℵ	NOUN
cana-1619	52	51	)	)	PUNCT
cana-1619	52	52	)	)	PUNCT
cana-1619	52	53	,	,	PUNCT
cana-1619	52	54	δ′𝜑(ℎ𝜉	δ′𝜑(ℎ𝜉	NOUN
cana-1619	52	55	,	,	PUNCT
cana-1619	52	56	ℵ	ℵ	NOUN
cana-1619	52	57	)	)	PUNCT
cana-1619	52	58	=	=	SYM
cana-1619	52	59	𝐼𝜉′(𝜑(ℎ𝜉	𝐼𝜉′(𝜑(ℎ𝜉	NOUN
cana-1619	52	60	,	,	PUNCT
cana-1619	52	61	ℵ	ℵ	NOUN
cana-1619	52	62	)	)	PUNCT
cana-1619	52	63	)	)	PUNCT
cana-1619	52	64	.	.	PUNCT
cana-1619	53	1	(	(	PUNCT
cana-1619	53	2	2	2	X
cana-1619	53	3	)	)	PUNCT
cana-1619	53	4	𝐴	𝐴	PROPN
cana-1619	53	5	symbolizes	symbolize	VERB
cana-1619	53	6	the	the	DET
cana-1619	53	7	infinitesimal	infinitesimal	ADJ
cana-1619	53	8	source	source	NOUN
cana-1619	53	9	of	of	ADP
cana-1619	53	10	a	a	DET
cana-1619	53	11	constantly	constantly	ADV
cana-1619	53	12	evolving	evolve	VERB
cana-1619	53	13	set	set	NOUN
cana-1619	53	14	of	of	ADP
cana-1619	53	15	cosine	cosine	NOUN
cana-1619	53	16	transformations	transformation	NOUN
cana-1619	53	17	denoted	denote	VERB
cana-1619	53	18	by	by	ADP
cana-1619	53	19	{	{	PUNCT
cana-1619	53	20	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	53	21	):	):	PUNCT
cana-1619	53	22	ℎ	ℎ	PROPN
cana-1619	53	23	∈	∈	PROPN
cana-1619	53	24	ℝ	ℝ	PROPN
cana-1619	53	25	}	}	PUNCT
cana-1619	53	26	,	,	PUNCT
cana-1619	53	27	where	where	SCONJ
cana-1619	53	28	these	these	DET
cana-1619	53	29	transformations	transformation	NOUN
cana-1619	53	30	are	be	AUX
cana-1619	53	31	bounded	bound	VERB
cana-1619	53	32	linear	linear	ADJ
cana-1619	53	33	operations	operation	NOUN
cana-1619	53	34	occurring	occur	VERB
cana-1619	53	35	within	within	ADP
cana-1619	53	36	a	a	DET
cana-1619	53	37	banach	banach	NOUN
cana-1619	53	38	space	space	NOUN
cana-1619	53	39	𝒮	𝒮	PROPN
cana-1619	53	40	,	,	PUNCT
cana-1619	53	41	defined	define	VERB
cana-1619	53	42	with	with	ADP
cana-1619	53	43	the	the	DET
cana-1619	53	44	norm	norm	NOUN
cana-1619	53	45	||	||	PROPN
cana-1619	53	46	.	.	PUNCT
cana-1619	54	1	||	||	NOUN
cana-1619	55	1	and	and	CCONJ
cana-1619	55	2	υ	υ	NOUN
cana-1619	55	3	:	:	PUNCT
cana-1619	55	4	𝐽	𝐽	PROPN
cana-1619	56	1	×	×	NOUN
cana-1619	57	1	𝐽	𝐽	NOUN
cana-1619	58	1	×	×	NOUN
cana-1619	58	2	𝒟	𝒟	NOUN
cana-1619	58	3	×	×	PROPN
cana-1619	58	4	ω	ω	PROPN
cana-1619	58	5	→	→	SYM
cana-1619	58	6	𝒮	𝒮	PROPN
cana-1619	58	7	,	,	PUNCT
cana-1619	58	8	𝜌	𝜌	ADP
cana-1619	58	9	:	:	PUNCT
cana-1619	58	10	𝐽	𝐽	PROPN
cana-1619	58	11	∗	∗	NOUN
cana-1619	58	12	𝒟	𝒟	PROPN
cana-1619	58	13	×	×	PROPN
cana-1619	58	14	ω	ω	PROPN
cana-1619	58	15	→	→	SYM
cana-1619	58	16	𝒮	𝒮	NOUN
cana-1619	58	17	are	be	AUX
cana-1619	58	18	continuous	continuous	ADJ
cana-1619	58	19	functions	function	NOUN
cana-1619	58	20	and	and	CCONJ
cana-1619	58	21	𝐵	𝐵	NOUN
cana-1619	58	22	:	:	PUNCT
cana-1619	58	23	ℰ	ℰ	PROPN
cana-1619	58	24	→	→	PUNCT
cana-1619	58	25	ℝ+	ℝ+	PUNCT
cana-1619	58	26	where	where	SCONJ
cana-1619	58	27	ℰ	ℰ	PROPN
cana-1619	58	28	is	be	AUX
cana-1619	58	29	the	the	DET
cana-1619	58	30	banach	banach	NOUN
cana-1619	58	31	space	space	NOUN
cana-1619	58	32	and	and	CCONJ
cana-1619	58	33	ω	ω	PROPN
cana-1619	58	34	is	be	AUX
cana-1619	58	35	a	a	DET
cana-1619	58	36	random	random	ADJ
cana-1619	58	37	operator	operator	NOUN
cana-1619	58	38	in	in	ADP
cana-1619	58	39	a	a	DET
cana-1619	58	40	stochastic	stochastic	ADJ
cana-1619	58	41	domain	domain	NOUN
cana-1619	58	42	.	.	PUNCT
cana-1619	58	43	2	2	NUM
cana-1619	58	44	preliminaries	preliminary	NOUN
cana-1619	58	45	in	in	ADP
cana-1619	58	46	this	this	DET
cana-1619	58	47	section	section	NOUN
cana-1619	58	48	,	,	PUNCT
cana-1619	58	49	we	we	PRON
cana-1619	58	50	’ll	’ll	AUX
cana-1619	58	51	review	review	VERB
cana-1619	58	52	fundamental	fundamental	ADJ
cana-1619	58	53	concepts	concept	NOUN
cana-1619	58	54	and	and	CCONJ
cana-1619	58	55	terminology	terminology	NOUN
cana-1619	58	56	that	that	PRON
cana-1619	58	57	are	be	AUX
cana-1619	58	58	essential	essential	ADJ
cana-1619	58	59	for	for	ADP
cana-1619	58	60	understanding	understand	VERB
cana-1619	58	61	the	the	DET
cana-1619	58	62	key	key	ADJ
cana-1619	58	63	findings	finding	NOUN
cana-1619	58	64	of	of	ADP
cana-1619	58	65	our	our	PRON
cana-1619	58	66	study	study	NOUN
cana-1619	58	67	.	.	PUNCT
cana-1619	59	1	lately	lately	ADV
cana-1619	59	2	,	,	PUNCT
cana-1619	59	3	there	there	PRON
cana-1619	59	4	’s	’s	AUX
cana-1619	59	5	been	be	AUX
cana-1619	59	6	more	more	ADJ
cana-1619	59	7	interest	interest	NOUN
cana-1619	59	8	in	in	ADP
cana-1619	59	9	studying	study	VERB
cana-1619	59	10	a	a	DET
cana-1619	59	11	specific	specific	ADJ
cana-1619	59	12	type	type	NOUN
cana-1619	59	13	of	of	ADP
cana-1619	59	14	problem	problem	NOUN
cana-1619	59	15	involving	involve	VERB
cana-1619	59	16	how	how	SCONJ
cana-1619	59	17	things	thing	NOUN
cana-1619	59	18	change	change	VERB
cana-1619	59	19	over	over	ADP
cana-1619	59	20	time	time	NOUN
cana-1619	59	21	,	,	PUNCT
cana-1619	59	22	even	even	ADV
cana-1619	59	23	when	when	SCONJ
cana-1619	59	24	the	the	DET
cana-1619	59	25	speed	speed	NOUN
cana-1619	59	26	of	of	ADP
cana-1619	59	27	change	change	NOUN
cana-1619	59	28	is	be	AUX
cana-1619	59	29	n’t	not	PART
cana-1619	59	30	fixed	fix	VERB
cana-1619	59	31	.	.	PUNCT
cana-1619	60	1	𝜑′′(ℎ	𝜑′′(ℎ	NOUN
cana-1619	60	2	,	,	PUNCT
cana-1619	60	3	ℵ	ℵ	NOUN
cana-1619	60	4	)	)	PUNCT
cana-1619	60	5	=	=	PUNCT
cana-1619	61	1	𝐴𝜑(ℎ	𝐴𝜑(ℎ	NOUN
cana-1619	61	2	,	,	PUNCT
cana-1619	61	3	ℵ	ℵ	NOUN
cana-1619	61	4	)	)	PUNCT
cana-1619	61	5	+	+	CCONJ
cana-1619	61	6	υ(ℎ	υ(ℎ	PROPN
cana-1619	61	7	,	,	PUNCT
cana-1619	61	8	ℵ	ℵ	NOUN
cana-1619	61	9	)	)	PUNCT
cana-1619	61	10	,	,	PUNCT
cana-1619	61	11	0	0	NUM
cana-1619	61	12	≤	≤	NUM
cana-1619	61	13	ℎ	ℎ	NOUN
cana-1619	61	14	≤	≤	NOUN
cana-1619	61	15	𝜚	𝜚	PRON
cana-1619	61	16	𝜑(0	𝜑(0	NOUN
cana-1619	61	17	,	,	PUNCT
cana-1619	61	18	ℵ	ℵ	NOUN
cana-1619	61	19	)	)	PUNCT
cana-1619	61	20	=	=	SYM
cana-1619	61	21	𝑥0(ℵ	𝑥0(ℵ	NUM
cana-1619	61	22	)	)	PUNCT
cana-1619	61	23	,	,	PUNCT
cana-1619	61	24	𝜑′(0	𝜑′(0	PROPN
cana-1619	61	25	,	,	PUNCT
cana-1619	61	26	ℵ	ℵ	NOUN
cana-1619	61	27	)	)	PUNCT
cana-1619	61	28	=	=	SYM
cana-1619	61	29	𝑦0(ℵ	𝑦0(ℵ	PROPN
cana-1619	61	30	)	)	PUNCT
cana-1619	61	31	(	(	PUNCT
cana-1619	61	32	3	3	X
cana-1619	61	33	)	)	PUNCT
cana-1619	61	34	here	here	ADV
cana-1619	61	35	,	,	PUNCT
cana-1619	61	36	𝐴:𝐷(𝐴	𝐴:𝐷(𝐴	PROPN
cana-1619	61	37	)	)	PUNCT
cana-1619	61	38	⊆	⊆	NUM
cana-1619	61	39	𝒮	𝒮	PROPN
cana-1619	61	40	→	→	SYM
cana-1619	61	41	𝒮	𝒮	PROPN
cana-1619	61	42	,	,	PUNCT
cana-1619	61	43	where	where	SCONJ
cana-1619	61	44	ℎ	ℎ	PROPN
cana-1619	61	45	∈	∈	PROPN
cana-1619	61	46	𝐽	𝐽	NOUN
cana-1619	61	47	=	=	PUNCT
cana-1619	62	1	[	[	X
cana-1619	62	2	0	0	NUM
cana-1619	62	3	,	,	PUNCT
cana-1619	62	4	𝜚	𝜚	NOUN
cana-1619	62	5	]	]	X
cana-1619	62	6	,	,	PUNCT
cana-1619	62	7	denotes	denote	VERB
cana-1619	62	8	a	a	DET
cana-1619	62	9	closed	closed	ADJ
cana-1619	62	10	operator	operator	NOUN
cana-1619	62	11	that	that	PRON
cana-1619	62	12	is	be	AUX
cana-1619	62	13	densely	densely	ADV
cana-1619	62	14	defined	define	VERB
cana-1619	62	15	.	.	PUNCT
cana-1619	63	1	furthermore	furthermore	ADV
cana-1619	63	2	,	,	PUNCT
cana-1619	63	3	let	let	VERB
cana-1619	63	4	υ	υ	NOUN
cana-1619	63	5	:	:	PUNCT
cana-1619	63	6	𝐽	𝐽	PROPN
cana-1619	63	7	×	×	PROPN
cana-1619	63	8	ω	ω	PROPN
cana-1619	63	9	→	→	SYM
cana-1619	63	10	𝒮	𝒮	PROPN
cana-1619	63	11	denote	denote	VERB
cana-1619	63	12	an	an	DET
cana-1619	63	13	appropriate	appropriate	ADJ
cana-1619	63	14	function	function	NOUN
cana-1619	63	15	.	.	PUNCT
cana-1619	64	1	numerous	numerous	ADJ
cana-1619	64	2	studies	study	NOUN
cana-1619	64	3	have	have	AUX
cana-1619	64	4	examined	examine	VERB
cana-1619	64	5	equations	equation	NOUN
cana-1619	64	6	of	of	ADP
cana-1619	64	7	this	this	DET
cana-1619	64	8	nature	nature	NOUN
cana-1619	64	9	.	.	PUNCT
cana-1619	65	1	typically	typically	ADV
cana-1619	65	2	,	,	PUNCT
cana-1619	65	3	the	the	DET
cana-1619	65	4	solutions	solution	NOUN
cana-1619	65	5	of	of	ADP
cana-1619	65	6	the	the	DET
cana-1619	65	7	problem	problem	NOUN
cana-1619	65	8	is	be	AUX
cana-1619	65	9	linked	link	VERB
cana-1619	65	10	to	to	ADP
cana-1619	65	11	the	the	DET
cana-1619	65	12	presence	presence	NOUN
cana-1619	65	13	of	of	ADP
cana-1619	65	14	an	an	DET
cana-1619	65	15	evolution	evolution	NOUN
cana-1619	65	16	operator	operator	NOUN
cana-1619	65	17	𝑇2(ℎ,𝜛	𝑇2(ℎ,𝜛	NOUN
cana-1619	65	18	)	)	PUNCT
cana-1619	65	19	for	for	ADP
cana-1619	65	20	the	the	DET
cana-1619	65	21	corresponding	corresponding	ADJ
cana-1619	65	22	homogeneous	homogeneous	ADJ
cana-1619	65	23	equation	equation	NOUN
cana-1619	65	24	.	.	PUNCT
cana-1619	66	1	𝜑′′(ℎ	𝜑′′(ℎ	NOUN
cana-1619	66	2	,	,	PUNCT
cana-1619	66	3	ℵ	ℵ	NOUN
cana-1619	66	4	)	)	PUNCT
cana-1619	66	5	=	=	PUNCT
cana-1619	67	1	𝐴𝜑(ℎ	𝐴𝜑(ℎ	NOUN
cana-1619	67	2	,	,	PUNCT
cana-1619	67	3	ℵ	ℵ	NOUN
cana-1619	67	4	)	)	PUNCT
cana-1619	67	5	,	,	PUNCT
cana-1619	67	6	0	0	NUM
cana-1619	67	7	≤	≤	NUM
cana-1619	67	8	𝜛	𝜛	X
cana-1619	67	9	,	,	PUNCT
cana-1619	67	10	ℎ	ℎ	X
cana-1619	67	11	≤	≤	NOUN
cana-1619	67	12	𝜚	𝜚	NUM
cana-1619	67	13	,	,	PUNCT
cana-1619	67	14	(	(	PUNCT
cana-1619	67	15	4	4	X
cana-1619	67	16	)	)	PUNCT
cana-1619	67	17	definition	definition	NOUN
cana-1619	67	18	1	1	NUM
cana-1619	67	19	let	let	VERB
cana-1619	67	20	(	(	PUNCT
cana-1619	67	21	𝒟	𝒟	NOUN
cana-1619	67	22	,	,	PUNCT
cana-1619	67	23	∥⋅∥𝒟	∥⋅∥𝒟	NUM
cana-1619	67	24	)	)	PUNCT
cana-1619	67	25	be	be	VERB
cana-1619	67	26	a	a	DET
cana-1619	67	27	seminormed	seminormed	ADJ
cana-1619	67	28	linear	linear	ADJ
cana-1619	67	29	space	space	NOUN
cana-1619	67	30	of	of	ADP
cana-1619	67	31	functions	function	NOUN
cana-1619	67	32	defined	define	VERB
cana-1619	67	33	on	on	ADP
cana-1619	67	34	(	(	PUNCT
cana-1619	67	35	−δ	−δ	ADJ
cana-1619	67	36	,	,	PUNCT
cana-1619	67	37	0	0	NUM
cana-1619	67	38	]	]	PUNCT
cana-1619	67	39	and	and	CCONJ
cana-1619	67	40	taking	take	VERB
cana-1619	67	41	values	value	NOUN
cana-1619	67	42	in	in	ADP
cana-1619	67	43	a	a	DET
cana-1619	67	44	banach	banach	NOUN
cana-1619	67	45	space	space	NOUN
cana-1619	67	46	𝒮.	𝒮.	NOUN
cana-1619	67	47	the	the	DET
cana-1619	67	48	space	space	NOUN
cana-1619	67	49	𝒟	𝒟	PROPN
cana-1619	67	50	satisfies	satisfy	VERB
cana-1619	67	51	the	the	DET
cana-1619	67	52	following	follow	VERB
cana-1619	67	53	axioms	axiom	NOUN
cana-1619	67	54	:	:	PUNCT
cana-1619	67	55	(	(	PUNCT
cana-1619	67	56	a)for	a)for	ADP
cana-1619	67	57	any	any	DET
cana-1619	67	58	continuous	continuous	ADJ
cana-1619	67	59	function	function	NOUN
cana-1619	67	60	φ	φ	NOUN
cana-1619	67	61	:	:	PUNCT
cana-1619	67	62	(	(	PUNCT
cana-1619	67	63	−δ	−δ	ADJ
cana-1619	67	64	,	,	PUNCT
cana-1619	67	65	0	0	NUM
cana-1619	67	66	]	]	PUNCT
cana-1619	67	67	→	→	SYM
cana-1619	67	68	𝒮	𝒮	PROPN
cana-1619	67	69	and	and	CCONJ
cana-1619	67	70	ϕ0	ϕ0	NOUN
cana-1619	67	71	∈	∈	PROPN
cana-1619	67	72	𝒟	𝒟	PROPN
cana-1619	67	73	,	,	PUNCT
cana-1619	67	74	the	the	DET
cana-1619	67	75	following	follow	VERB
cana-1619	67	76	conditions	condition	NOUN
cana-1619	67	77	hold	hold	VERB
cana-1619	67	78	for	for	ADP
cana-1619	67	79	all	all	DET
cana-1619	67	80	h	h	NOUN
cana-1619	67	81	∈	∈	PROPN
cana-1619	67	82	j	j	PROPN
cana-1619	67	83	1	1	NUM
cana-1619	67	84	.	.	PUNCT
cana-1619	68	1	the	the	DET
cana-1619	68	2	function	function	NOUN
cana-1619	68	3	φh	φh	ADP
cana-1619	68	4	∈	∈	PROPN
cana-1619	68	5	𝒟.	𝒟.	PROPN
cana-1619	68	6	2	2	NUM
cana-1619	68	7	.	.	PUNCT
cana-1619	68	8	there	there	PRON
cana-1619	68	9	exists	exist	VERB
cana-1619	68	10	a	a	DET
cana-1619	68	11	positive	positive	ADJ
cana-1619	68	12	constant	constant	ADJ
cana-1619	68	13	k	k	NOUN
cana-1619	68	14	such	such	ADJ
cana-1619	68	15	that	that	SCONJ
cana-1619	68	16	|φ(h	|φ(h	PROPN
cana-1619	68	17	,	,	PUNCT
cana-1619	68	18	ℵ)|	ℵ)|	DET
cana-1619	68	19	≤	≤	PUNCT
cana-1619	69	1	k	k	X
cana-1619	69	2	∥	∥	PUNCT
cana-1619	69	3	φh(⋅	φh(⋅	NOUN
cana-1619	69	4	,	,	PUNCT
cana-1619	69	5	ℵ	ℵ	NOUN
cana-1619	69	6	)	)	PUNCT
cana-1619	69	7	∥𝒟.	∥𝒟.	VERB
cana-1619	69	8	furthermore	furthermore	ADV
cana-1619	69	9	,	,	PUNCT
cana-1619	69	10	there	there	PRON
cana-1619	69	11	exist	exist	VERB
cana-1619	69	12	functions	function	NOUN
cana-1619	69	13	u	u	NOUN
cana-1619	69	14	,	,	PUNCT
cana-1619	69	15	ϑ	ϑ	PROPN
cana-1619	69	16	,	,	PUNCT
cana-1619	69	17	ϑ′:ℝ+	ϑ′:ℝ+	NOUN
cana-1619	69	18	→	→	SYM
cana-1619	69	19	ℝ+	ℝ+	ADP
cana-1619	69	20	,	,	PUNCT
cana-1619	69	21	where	where	SCONJ
cana-1619	69	22	u	u	NOUN
cana-1619	69	23	is	be	AUX
cana-1619	69	24	continuous	continuous	ADJ
cana-1619	69	25	and	and	CCONJ
cana-1619	69	26	bounded	bound	VERB
cana-1619	69	27	,	,	PUNCT
cana-1619	69	28	and	and	CCONJ
cana-1619	69	29	ϑ	ϑ	X
cana-1619	69	30	,	,	PUNCT
cana-1619	69	31	ϑ′	ϑ′	VERB
cana-1619	69	32	are	be	AUX
cana-1619	69	33	locally	locally	ADV
cana-1619	69	34	bounded	bound	VERB
cana-1619	69	35	and	and	CCONJ
cana-1619	69	36	independent	independent	ADJ
cana-1619	69	37	of	of	ADP
cana-1619	69	38	φ	φ	PROPN
cana-1619	69	39	,	,	PUNCT
cana-1619	69	40	such	such	ADJ
cana-1619	69	41	that	that	SCONJ
cana-1619	69	42	∥	∥	PROPN
cana-1619	69	43	φh(⋅	φh(⋅	NOUN
cana-1619	69	44	,	,	PUNCT
cana-1619	69	45	ℵ	ℵ	NOUN
cana-1619	69	46	)	)	PUNCT
cana-1619	69	47	∥x≤	∥x≤	NOUN
cana-1619	69	48	u(h)sup{|φ(m	u(h)sup{|φ(m	PROPN
cana-1619	69	49	,	,	PUNCT
cana-1619	69	50	ℵ)|:−δ	ℵ)|:−δ	PROPN
cana-1619	69	51	≤	≤	PROPN
cana-1619	69	52	m	m	VERB
cana-1619	69	53	≤	≤	NOUN
cana-1619	69	54	0	0	NUM
cana-1619	69	55	}	}	PUNCT
cana-1619	70	1	+	+	CCONJ
cana-1619	70	2	ϑ	ϑ	X
cana-1619	70	3	∥	∥	X
cana-1619	70	4	ϕ0(ℵ	ϕ0(ℵ	PROPN
cana-1619	70	5	)	)	PUNCT
cana-1619	70	6	∥𝒟+	∥𝒟+	PROPN
cana-1619	70	7	ϑ′	ϑ′	VERB
cana-1619	70	8	∥	∥	PROPN
cana-1619	70	9	ϕ0′(ℵ	ϕ0′(ℵ	NOUN
cana-1619	70	10	)	)	PUNCT
cana-1619	70	11	∥𝒟.	∥𝒟.	PROPN
cana-1619	70	12	(	(	PUNCT
cana-1619	70	13	b)the	b)the	DET
cana-1619	70	14	function	function	NOUN
cana-1619	70	15	φh	φh	NOUN
cana-1619	70	16	is	be	AUX
cana-1619	70	17	𝒟-valued	𝒟-valued	ADJ
cana-1619	70	18	and	and	CCONJ
cana-1619	70	19	continuous	continuous	ADJ
cana-1619	70	20	on	on	ADP
cana-1619	70	21	j	j	PROPN
cana-1619	70	22	for	for	ADP
cana-1619	70	23	the	the	DET
cana-1619	70	24	functions	function	NOUN
cana-1619	70	25	φ	φ	PROPN
cana-1619	70	26	described	describe	VERB
cana-1619	70	27	in	in	ADP
cana-1619	70	28	(	(	PUNCT
cana-1619	70	29	a	a	NOUN
cana-1619	70	30	)	)	PUNCT
cana-1619	70	31	.	.	PUNCT
cana-1619	71	1	(	(	PUNCT
cana-1619	71	2	c)the	c)the	PROPN
cana-1619	71	3	space	space	NOUN
cana-1619	71	4	𝒟	𝒟	PROPN
cana-1619	71	5	is	be	AUX
cana-1619	71	6	complete	complete	ADJ
cana-1619	71	7	.	.	PUNCT
cana-1619	72	1	communications	communication	NOUN
cana-1619	72	2	on	on	ADP
cana-1619	72	3	applied	apply	VERB
cana-1619	72	4	nonlinear	nonlinear	ADJ
cana-1619	72	5	analysis	analysis	NOUN
cana-1619	72	6	issn	issn	NOUN
cana-1619	72	7	:	:	PUNCT
cana-1619	72	8	1074	1074	NUM
cana-1619	72	9	-	-	PUNCT
cana-1619	72	10	133x	133x	NUM
cana-1619	72	11	vol	vol	NOUN
cana-1619	72	12	32	32	NUM
cana-1619	72	13	no	no	NOUN
cana-1619	72	14	.	.	NOUN
cana-1619	72	15	1	1	NUM
cana-1619	72	16	(	(	PUNCT
cana-1619	72	17	2025	2025	NUM
cana-1619	72	18	)	)	PUNCT
cana-1619	72	19	38	38	NUM
cana-1619	72	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	72	21	definition	definition	NOUN
cana-1619	72	22	2	2	NUM
cana-1619	72	23	a	a	DET
cana-1619	72	24	collection	collection	NOUN
cana-1619	72	25	of	of	ADP
cana-1619	72	26	bounded	bounded	ADJ
cana-1619	72	27	linear	linear	PROPN
cana-1619	72	28	maps	maps	PROPN
cana-1619	72	29	{	{	PUNCT
cana-1619	72	30	t1(h	t1(h	ADJ
cana-1619	72	31	):	):	PUNCT
cana-1619	72	32	h	h	PROPN
cana-1619	72	33	∈	∈	PROPN
cana-1619	72	34	𝒥	𝒥	PROPN
cana-1619	72	35	}	}	PUNCT
cana-1619	72	36	in	in	ADP
cana-1619	72	37	the	the	DET
cana-1619	72	38	banach	banach	NOUN
cana-1619	72	39	space	space	NOUN
cana-1619	72	40	𝒮	𝒮	PROPN
cana-1619	72	41	is	be	AUX
cana-1619	72	42	considered	consider	VERB
cana-1619	72	43	a	a	DET
cana-1619	72	44	strongly	strongly	ADV
cana-1619	72	45	continuous	continuous	ADJ
cana-1619	72	46	cosine	cosine	NOUN
cana-1619	72	47	function	function	NOUN
cana-1619	72	48	when	when	SCONJ
cana-1619	72	49	it	it	PRON
cana-1619	72	50	meets	meet	VERB
cana-1619	72	51	these	these	DET
cana-1619	72	52	criteria	criterion	NOUN
cana-1619	72	53	1	1	NUM
cana-1619	72	54	.	.	PUNCT
cana-1619	73	1	addition	addition	NOUN
cana-1619	73	2	condition	condition	NOUN
cana-1619	73	3	:	:	PUNCT
cana-1619	74	1	t1(ϖ	t1(ϖ	NUM
cana-1619	74	2	+	+	NUM
cana-1619	74	3	h	h	NOUN
cana-1619	74	4	)	)	PUNCT
cana-1619	74	5	+	+	CCONJ
cana-1619	74	6	t1(ϖ	t1(ϖ	NUM
cana-1619	74	7	−	−	PROPN
cana-1619	74	8	h	h	NOUN
cana-1619	74	9	)	)	PUNCT
cana-1619	74	10	=	=	NUM
cana-1619	74	11	2t1(ϖ)t1(h	2t1(ϖ)t1(h	NOUN
cana-1619	74	12	)	)	PUNCT
cana-1619	74	13	for	for	ADP
cana-1619	74	14	all	all	DET
cana-1619	74	15	ϖ	ϖ	PROPN
cana-1619	74	16	,	,	PUNCT
cana-1619	74	17	h	h	NOUN
cana-1619	74	18	∈	∈	PROPN
cana-1619	74	19	𝒥.	𝒥.	PROPN
cana-1619	74	20	2	2	NUM
cana-1619	74	21	.	.	PUNCT
cana-1619	74	22	identity	identity	NOUN
cana-1619	74	23	property	property	NOUN
cana-1619	74	24	:	:	PUNCT
cana-1619	74	25	t1(0	t1(0	PROPN
cana-1619	74	26	)	)	PUNCT
cana-1619	75	1	=	=	PUNCT
cana-1619	75	2	i	i	PROPN
cana-1619	75	3	,	,	PUNCT
cana-1619	75	4	where	where	SCONJ
cana-1619	75	5	i	i	PRON
cana-1619	75	6	denotes	denote	VERB
cana-1619	75	7	the	the	DET
cana-1619	75	8	identity	identity	NOUN
cana-1619	75	9	operator	operator	NOUN
cana-1619	75	10	.	.	PUNCT
cana-1619	76	1	3	3	X
cana-1619	76	2	.	.	X
cana-1619	76	3	continuity	continuity	NOUN
cana-1619	76	4	requirement	requirement	NOUN
cana-1619	76	5	:	:	PUNCT
cana-1619	76	6	t1(h)φ	t1(h)φ	NOUN
cana-1619	76	7	remains	remain	VERB
cana-1619	76	8	continuously	continuously	ADV
cana-1619	76	9	dependent	dependent	ADJ
cana-1619	76	10	on	on	ADP
cana-1619	76	11	h	h	NOUN
cana-1619	76	12	over	over	ADP
cana-1619	76	13	𝒥	𝒥	PROPN
cana-1619	76	14	for	for	ADP
cana-1619	76	15	any	any	DET
cana-1619	76	16	fixed	fix	VERB
cana-1619	76	17	φ	φ	PROPN
cana-1619	76	18	∈	∈	PROPN
cana-1619	76	19	𝒮.	𝒮.	PROPN
cana-1619	76	20	in	in	ADP
cana-1619	76	21	this	this	DET
cana-1619	76	22	scenario	scenario	NOUN
cana-1619	76	23	,	,	PUNCT
cana-1619	76	24	a	a	DET
cana-1619	76	25	serves	serve	NOUN
cana-1619	76	26	as	as	ADP
cana-1619	76	27	the	the	DET
cana-1619	76	28	fundamental	fundamental	ADJ
cana-1619	76	29	element	element	NOUN
cana-1619	76	30	behind	behind	ADP
cana-1619	76	31	a	a	DET
cana-1619	76	32	continuously	continuously	ADV
cana-1619	76	33	evolving	evolve	VERB
cana-1619	76	34	set	set	NOUN
cana-1619	76	35	of	of	ADP
cana-1619	76	36	operations	operation	NOUN
cana-1619	76	37	known	know	VERB
cana-1619	76	38	as	as	ADP
cana-1619	76	39	the	the	DET
cana-1619	76	40	strongly	strongly	ADV
cana-1619	76	41	continuous	continuous	ADJ
cana-1619	76	42	cosine	cosine	NOUN
cana-1619	76	43	function	function	NOUN
cana-1619	76	44	,	,	PUNCT
cana-1619	76	45	denoted	denote	VERB
cana-1619	76	46	by	by	ADP
cana-1619	76	47	{	{	PUNCT
cana-1619	76	48	t1(h	t1(h	ADJ
cana-1619	76	49	):	):	PUNCT
cana-1619	76	50	h	h	PROPN
cana-1619	76	51	∈	∈	PROPN
cana-1619	76	52	𝒥	𝒥	PROPN
cana-1619	76	53	}	}	PUNCT
cana-1619	76	54	.	.	PUNCT
cana-1619	77	1	these	these	DET
cana-1619	77	2	operations	operation	NOUN
cana-1619	77	3	involve	involve	VERB
cana-1619	77	4	bounded	bound	VERB
cana-1619	77	5	linear	linear	PROPN
cana-1619	77	6	maps	map	NOUN
cana-1619	77	7	defined	define	VERB
cana-1619	77	8	within	within	ADP
cana-1619	77	9	the	the	DET
cana-1619	77	10	banach	banach	NOUN
cana-1619	77	11	space	space	NOUN
cana-1619	77	12	𝒮	𝒮	PROPN
cana-1619	77	13	,	,	PUNCT
cana-1619	77	14	where	where	SCONJ
cana-1619	77	15	distances	distance	NOUN
cana-1619	77	16	are	be	AUX
cana-1619	77	17	measured	measure	VERB
cana-1619	77	18	using	use	VERB
cana-1619	77	19	the	the	DET
cana-1619	77	20	norm	norm	NOUN
cana-1619	77	21	∥⋅∥	∥⋅∥	PROPN
cana-1619	77	22	.	.	PUNCT
cana-1619	78	1	the	the	DET
cana-1619	78	2	associated	associated	ADJ
cana-1619	78	3	sine	sine	ADJ
cana-1619	78	4	function	function	NOUN
cana-1619	78	5	with	with	ADP
cana-1619	78	6	{	{	PUNCT
cana-1619	78	7	t1(h	t1(h	ADJ
cana-1619	78	8	):	):	PUNCT
cana-1619	78	9	h	h	PROPN
cana-1619	78	10	∈	∈	PROPN
cana-1619	78	11	ℝ	ℝ	PROPN
cana-1619	78	12	}	}	PUNCT
cana-1619	78	13	,	,	PUNCT
cana-1619	78	14	denoted	denote	VERB
cana-1619	78	15	as	as	ADP
cana-1619	78	16	{	{	PUNCT
cana-1619	78	17	t2(h	t2(h	NUM
cana-1619	78	18	):	):	PUNCT
cana-1619	78	19	h	h	PROPN
cana-1619	78	20	∈	∈	PROPN
cana-1619	78	21	𝒥	𝒥	PROPN
cana-1619	78	22	}	}	PUNCT
cana-1619	78	23	,	,	PUNCT
cana-1619	78	24	is	be	AUX
cana-1619	78	25	expressed	express	VERB
cana-1619	78	26	as	as	ADP
cana-1619	78	27	t2(h)φ	t2(h)φ	PROPN
cana-1619	78	28	=	=	SYM
cana-1619	78	29	∫	∫	PROPN
cana-1619	78	30	h	h	PROPN
cana-1619	78	31	0	0	PROPN
cana-1619	78	32	t1(ϖ)φ	t1(ϖ)φ	PUNCT
cana-1619	78	33	dϖ	dϖ	PROPN
cana-1619	78	34	forφ	forφ	NOUN
cana-1619	78	35	∈	∈	PROPN
cana-1619	78	36	𝒟andh	𝒟andh	PROPN
cana-1619	78	37	∈	∈	PROPN
cana-1619	78	38	𝒥.	𝒥.	NOUN
cana-1619	78	39	additionally	additionally	ADV
cana-1619	78	40	,	,	PUNCT
cana-1619	78	41	ϑ	ϑ	X
cana-1619	78	42	and	and	CCONJ
cana-1619	78	43	ϑa	ϑa	PROPN
cana-1619	78	44	represent	represent	VERB
cana-1619	78	45	positive	positive	ADJ
cana-1619	78	46	constants	constant	NOUN
cana-1619	78	47	ensuring	ensure	VERB
cana-1619	78	48	∥	∥	PROPN
cana-1619	78	49	t1(h	t1(h	PROPN
cana-1619	78	50	)	)	PUNCT
cana-1619	78	51	∥≤	∥≤	PROPN
cana-1619	78	52	ϑ	ϑ	X
cana-1619	78	53	and	and	CCONJ
cana-1619	78	54	∥	∥	NUM
cana-1619	78	55	t2(h	t2(h	NUM
cana-1619	78	56	)	)	PUNCT
cana-1619	78	57	∥≤	∥≤	NOUN
cana-1619	78	58	ϑa	ϑa	ADV
cana-1619	78	59	for	for	ADP
cana-1619	78	60	every	every	DET
cana-1619	78	61	h	h	NOUN
cana-1619	78	62	∈	∈	PROPN
cana-1619	78	63	j.	j.	PROPN
cana-1619	78	64	definition	definition	NOUN
cana-1619	78	65	3	3	NUM
cana-1619	78	66	approximate	approximate	ADJ
cana-1619	78	67	controllability	controllability	NOUN
cana-1619	78	68	,	,	PUNCT
cana-1619	78	69	an	an	DET
cana-1619	78	70	essential	essential	ADJ
cana-1619	78	71	concept	concept	NOUN
cana-1619	78	72	in	in	ADP
cana-1619	78	73	control	control	NOUN
cana-1619	78	74	theory	theory	NOUN
cana-1619	78	75	,	,	PUNCT
cana-1619	78	76	addresses	address	VERB
cana-1619	78	77	the	the	DET
cana-1619	78	78	capability	capability	NOUN
cana-1619	78	79	to	to	PART
cana-1619	78	80	roughly	roughly	ADV
cana-1619	78	81	guide	guide	VERB
cana-1619	78	82	a	a	DET
cana-1619	78	83	system	system	NOUN
cana-1619	78	84	from	from	ADP
cana-1619	78	85	one	one	NUM
cana-1619	78	86	state	state	NOUN
cana-1619	78	87	to	to	ADP
cana-1619	78	88	another	another	PRON
cana-1619	78	89	utilizing	utilize	VERB
cana-1619	78	90	control	control	NOUN
cana-1619	78	91	inputs	input	NOUN
cana-1619	78	92	within	within	ADP
cana-1619	78	93	a	a	DET
cana-1619	78	94	designated	designate	VERB
cana-1619	78	95	timeframe	timeframe	NOUN
cana-1619	78	96	.	.	PUNCT
cana-1619	79	1	formally	formally	ADV
cana-1619	79	2	,	,	PUNCT
cana-1619	79	3	system	system	NOUN
cana-1619	79	4	represented	represent	VERB
cana-1619	79	5	by	by	ADP
cana-1619	79	6	a	a	DET
cana-1619	79	7	state	state	NOUN
cana-1619	79	8	space	space	NOUN
cana-1619	79	9	𝒟	𝒟	NOUN
cana-1619	79	10	,	,	PUNCT
cana-1619	79	11	where	where	SCONJ
cana-1619	79	12	we	we	PRON
cana-1619	79	13	can	can	AUX
cana-1619	79	14	influence	influence	VERB
cana-1619	79	15	its	its	PRON
cana-1619	79	16	behavior	behavior	NOUN
cana-1619	79	17	through	through	ADP
cana-1619	79	18	admissible	admissible	ADJ
cana-1619	79	19	control	control	NOUN
cana-1619	79	20	inputs	input	NOUN
cana-1619	79	21	from	from	ADP
cana-1619	79	22	the	the	DET
cana-1619	79	23	space	space	NOUN
cana-1619	79	24	u.	u.	VERB
cana-1619	79	25	the	the	DET
cana-1619	79	26	evolution	evolution	NOUN
cana-1619	79	27	of	of	ADP
cana-1619	79	28	this	this	DET
cana-1619	79	29	system	system	NOUN
cana-1619	79	30	is	be	AUX
cana-1619	79	31	described	describe	VERB
cana-1619	79	32	by	by	ADP
cana-1619	79	33	an	an	DET
cana-1619	79	34	equation	equation	NOUN
cana-1619	79	35	:	:	PUNCT
cana-1619	79	36	φ′(h	φ′(h	X
cana-1619	79	37	,	,	PUNCT
cana-1619	79	38	ℵ	ℵ	NOUN
cana-1619	79	39	)	)	PUNCT
cana-1619	79	40	=	=	SYM
cana-1619	79	41	aφ(h	aφ(h	NOUN
cana-1619	79	42	,	,	PUNCT
cana-1619	79	43	ℵ	ℵ	NOUN
cana-1619	79	44	)	)	PUNCT
cana-1619	79	45	+	+	NUM
cana-1619	79	46	by(h	by(h	VERB
cana-1619	79	47	,	,	PUNCT
cana-1619	79	48	ℵ	ℵ	NOUN
cana-1619	79	49	)	)	PUNCT
cana-1619	79	50	,	,	PUNCT
cana-1619	79	51	where	where	SCONJ
cana-1619	79	52	φ(h	φ(h	NOUN
cana-1619	79	53	,	,	PUNCT
cana-1619	79	54	ℵ	ℵ	NOUN
cana-1619	79	55	)	)	PUNCT
cana-1619	79	56	∈	∈	PROPN
cana-1619	79	57	𝒟	𝒟	NOUN
cana-1619	79	58	denotes	denote	VERB
cana-1619	79	59	the	the	DET
cana-1619	79	60	system	system	NOUN
cana-1619	79	61	’s	’s	PART
cana-1619	79	62	state	state	NOUN
cana-1619	79	63	at	at	ADP
cana-1619	79	64	time	time	NOUN
cana-1619	79	65	h	h	NOUN
cana-1619	79	66	,	,	PUNCT
cana-1619	79	67	y(h	y(h	NOUN
cana-1619	79	68	,	,	PUNCT
cana-1619	79	69	ℵ	ℵ	NOUN
cana-1619	79	70	)	)	PUNCT
cana-1619	79	71	∈	∈	NOUN
cana-1619	79	72	u	u	NOUN
cana-1619	79	73	denotes	denote	VERB
cana-1619	79	74	the	the	DET
cana-1619	79	75	control	control	NOUN
cana-1619	79	76	input	input	NOUN
cana-1619	79	77	,	,	PUNCT
cana-1619	79	78	a	a	PRON
cana-1619	79	79	is	be	AUX
cana-1619	79	80	the	the	DET
cana-1619	79	81	system	system	NOUN
cana-1619	79	82	’s	’s	PART
cana-1619	79	83	operator	operator	NOUN
cana-1619	79	84	or	or	CCONJ
cana-1619	79	85	matrix	matrix	NOUN
cana-1619	79	86	,	,	PUNCT
cana-1619	79	87	and	and	CCONJ
cana-1619	79	88	b	b	NOUN
cana-1619	79	89	is	be	AUX
cana-1619	79	90	the	the	DET
cana-1619	79	91	control	control	NOUN
cana-1619	79	92	operator	operator	NOUN
cana-1619	79	93	or	or	CCONJ
cana-1619	79	94	matrix	matrix	NOUN
cana-1619	79	95	.	.	PUNCT
cana-1619	80	1	approximate	approximate	ADJ
cana-1619	80	2	controllability	controllability	NOUN
cana-1619	80	3	is	be	AUX
cana-1619	80	4	achieved	achieve	VERB
cana-1619	80	5	if	if	SCONJ
cana-1619	80	6	,	,	PUNCT
cana-1619	80	7	given	give	VERB
cana-1619	80	8	any	any	DET
cana-1619	80	9	starting	start	VERB
cana-1619	80	10	state	state	NOUN
cana-1619	80	11	x0	x0	PROPN
cana-1619	80	12	and	and	CCONJ
cana-1619	80	13	any	any	DET
cana-1619	80	14	desired	desire	VERB
cana-1619	80	15	terminal	terminal	ADJ
cana-1619	80	16	state	state	NOUN
cana-1619	80	17	xf	xf	PROPN
cana-1619	80	18	,	,	PUNCT
cana-1619	80	19	there	there	PRON
cana-1619	80	20	is	be	VERB
cana-1619	80	21	a	a	DET
cana-1619	80	22	sequence	sequence	NOUN
cana-1619	80	23	of	of	ADP
cana-1619	80	24	control	control	NOUN
cana-1619	80	25	inputs	input	NOUN
cana-1619	80	26	{	{	PUNCT
cana-1619	80	27	φξ(h	φξ(h	NOUN
cana-1619	80	28	,	,	PUNCT
cana-1619	80	29	ℵ	ℵ	NOUN
cana-1619	80	30	)	)	PUNCT
cana-1619	80	31	}	}	PUNCT
cana-1619	80	32	such	such	ADJ
cana-1619	80	33	that	that	SCONJ
cana-1619	80	34	the	the	DET
cana-1619	80	35	system	system	NOUN
cana-1619	80	36	’s	’s	PART
cana-1619	80	37	solution	solution	NOUN
cana-1619	80	38	ζ(h	ζ(h	NOUN
cana-1619	80	39	,	,	PUNCT
cana-1619	80	40	ℵ	ℵ	NOUN
cana-1619	80	41	)	)	PUNCT
cana-1619	80	42	of	of	ADP
cana-1619	80	43	the	the	DET
cana-1619	80	44	dynamical	dynamical	ADJ
cana-1619	80	45	system	system	NOUN
cana-1619	80	46	satisfies	satisfy	VERB
cana-1619	80	47	x(0	x(0	PROPN
cana-1619	80	48	,	,	PUNCT
cana-1619	80	49	ℵ	ℵ	NOUN
cana-1619	80	50	)	)	PUNCT
cana-1619	80	51	=	=	SYM
cana-1619	80	52	ϕ0(ℵ	ϕ0(ℵ	PROPN
cana-1619	80	53	)	)	PUNCT
cana-1619	80	54	and	and	CCONJ
cana-1619	80	55	limξ→∞xξ(ϱ	limξ→∞xξ(ϱ	NOUN
cana-1619	80	56	,	,	PUNCT
cana-1619	80	57	ℵ	ℵ	NOUN
cana-1619	80	58	)	)	PUNCT
cana-1619	80	59	=	=	SYM
cana-1619	80	60	ϕ′0(ℵ	ϕ′0(ℵ	NOUN
cana-1619	80	61	)	)	PUNCT
cana-1619	80	62	for	for	ADP
cana-1619	80	63	some	some	DET
cana-1619	80	64	finite	finite	ADJ
cana-1619	80	65	time	time	NOUN
cana-1619	80	66	ϱ	ϱ	ADP
cana-1619	80	67	,	,	PUNCT
cana-1619	80	68	where	where	SCONJ
cana-1619	80	69	xξ(h	xξ(h	X
cana-1619	80	70	,	,	PUNCT
cana-1619	80	71	ℵ	ℵ	X
cana-1619	80	72	)	)	PUNCT
cana-1619	80	73	is	be	AUX
cana-1619	80	74	the	the	DET
cana-1619	80	75	system"s	system"s	ADJ
cana-1619	80	76	solution	solution	NOUN
cana-1619	80	77	resulting	result	VERB
cana-1619	80	78	from	from	ADP
cana-1619	80	79	the	the	DET
cana-1619	80	80	control	control	NOUN
cana-1619	80	81	input	input	NOUN
cana-1619	80	82	φξ(h	φξ(h	NOUN
cana-1619	80	83	,	,	PUNCT
cana-1619	80	84	ℵ	ℵ	NOUN
cana-1619	80	85	)	)	PUNCT
cana-1619	80	86	.	.	PUNCT
cana-1619	81	1	lemma	lemma	PROPN
cana-1619	81	2	1	1	NUM
cana-1619	81	3	(	(	PUNCT
cana-1619	81	4	leray	leray	ADJ
cana-1619	81	5	-	-	PUNCT
cana-1619	81	6	schauder	schauder	NOUN
cana-1619	81	7	nonlinear	nonlinear	ADJ
cana-1619	81	8	alternative	alternative	NOUN
cana-1619	81	9	)	)	PUNCT
cana-1619	81	10	let	let	VERB
cana-1619	81	11	us	we	PRON
cana-1619	81	12	denote	denote	VERB
cana-1619	81	13	a	a	DET
cana-1619	81	14	banach	banach	NOUN
cana-1619	81	15	space	space	NOUN
cana-1619	81	16	𝒮.	𝒮.	PROPN
cana-1619	81	17	inside	inside	ADP
cana-1619	81	18	𝒮	𝒮	PROPN
cana-1619	81	19	,	,	PUNCT
cana-1619	81	20	there	there	PRON
cana-1619	81	21	’s	’	VERB
cana-1619	81	22	a	a	DET
cana-1619	81	23	closed	closed	ADJ
cana-1619	81	24	and	and	CCONJ
cana-1619	81	25	convex	convex	PROPN
cana-1619	81	26	subset	subset	VERB
cana-1619	81	27	z.	z.	PROPN
cana-1619	81	28	within	within	ADP
cana-1619	81	29	z	z	PROPN
cana-1619	81	30	,	,	PUNCT
cana-1619	81	31	there	there	PRON
cana-1619	81	32	’s	’	VERB
cana-1619	81	33	a	a	DET
cana-1619	81	34	relatively	relatively	ADV
cana-1619	81	35	open	open	ADJ
cana-1619	81	36	subset	subset	ADJ
cana-1619	81	37	u	u	NOUN
cana-1619	81	38	containing	contain	VERB
cana-1619	81	39	the	the	DET
cana-1619	81	40	point	point	NOUN
cana-1619	81	41	0	0	NUM
cana-1619	81	42	.	.	PUNCT
cana-1619	82	1	then	then	ADV
cana-1619	82	2	,	,	PUNCT
cana-1619	82	3	there	there	PRON
cana-1619	82	4	’s	’	VERB
cana-1619	82	5	a	a	DET
cana-1619	82	6	mapping	mapping	NOUN
cana-1619	82	7	υ	υ	NOUN
cana-1619	82	8	:	:	PUNCT
cana-1619	82	9	u	u	NOUN
cana-1619	82	10	→	→	SYM
cana-1619	82	11	z	z	PROPN
cana-1619	82	12	that	that	PRON
cana-1619	82	13	’s	’	VERB
cana-1619	82	14	compact	compact	ADJ
cana-1619	82	15	,	,	PUNCT
cana-1619	82	16	meaning	mean	VERB
cana-1619	82	17	it	it	PRON
cana-1619	82	18	preserves	preserve	VERB
cana-1619	82	19	the	the	DET
cana-1619	82	20	"	"	PUNCT
cana-1619	82	21	closeness	closeness	NOUN
cana-1619	82	22	"	"	PUNCT
cana-1619	82	23	of	of	ADP
cana-1619	82	24	points	point	NOUN
cana-1619	82	25	when	when	SCONJ
cana-1619	82	26	mapping	mapping	NOUN
cana-1619	82	27	from	from	ADP
cana-1619	82	28	u	u	PRON
cana-1619	82	29	to	to	ADP
cana-1619	82	30	z.	z.	PROPN
cana-1619	82	31	in	in	ADP
cana-1619	82	32	that	that	DET
cana-1619	82	33	case	case	NOUN
cana-1619	82	34	,	,	PUNCT
cana-1619	82	35	either	either	CCONJ
cana-1619	82	36	1	1	X
cana-1619	82	37	.	.	PUNCT
cana-1619	83	1	υ	υ	PROPN
cana-1619	83	2	possesses	possess	VERB
cana-1619	83	3	a	a	DET
cana-1619	83	4	fixed	fix	VERB
cana-1619	83	5	point	point	NOUN
cana-1619	83	6	in	in	ADP
cana-1619	83	7	u	u	NOUN
cana-1619	83	8	,	,	PUNCT
cana-1619	83	9	or	or	CCONJ
cana-1619	83	10	2	2	NUM
cana-1619	83	11	.	.	PUNCT
cana-1619	83	12	a	a	DET
cana-1619	83	13	point	point	NOUN
cana-1619	83	14	ζ	ζ	NOUN
cana-1619	83	15	∈	∈	NOUN
cana-1619	83	16	∂u	∂u	PROPN
cana-1619	83	17	satisfies	satisfy	VERB
cana-1619	83	18	ζ	ζ	PROPN
cana-1619	83	19	∈	∈	PROPN
cana-1619	83	20	λυ(ζ	λυ(ζ	NOUN
cana-1619	83	21	)	)	PUNCT
cana-1619	83	22	for	for	ADP
cana-1619	83	23	some	some	DET
cana-1619	83	24	λ	λ	PROPN
cana-1619	83	25	∈	∈	PROPN
cana-1619	83	26	(	(	PUNCT
cana-1619	83	27	0,1	0,1	NUM
cana-1619	83	28	)	)	PUNCT
cana-1619	83	29	.	.	PUNCT
cana-1619	84	1	lemma	lemma	PROPN
cana-1619	84	2	2	2	NUM
cana-1619	84	3	a	a	DET
cana-1619	84	4	set	set	NOUN
cana-1619	84	5	𝒟	𝒟	PROPN
cana-1619	84	6	⊂	⊂	PROPN
cana-1619	84	7	𝒮	𝒮	PROPN
cana-1619	84	8	is	be	AUX
cana-1619	84	9	relatively	relatively	ADV
cana-1619	84	10	compact	compact	ADJ
cana-1619	84	11	in	in	ADP
cana-1619	84	12	𝒮	𝒮	PROPN
cana-1619	84	13	if	if	SCONJ
cana-1619	84	14	and	and	CCONJ
cana-1619	84	15	only	only	ADV
cana-1619	84	16	𝒟ξ	𝒟ξ	PROPN
cana-1619	84	17	is	be	AUX
cana-1619	84	18	relatively	relatively	ADV
cana-1619	84	19	compact	compact	ADJ
cana-1619	84	20	in	in	ADP
cana-1619	84	21	c[(hξ	c[(hξ	PROPN
cana-1619	84	22	,	,	PUNCT
cana-1619	84	23	hξ+1	hξ+1	X
cana-1619	84	24	]	]	X
cana-1619	84	25	;	;	PUNCT
cana-1619	84	26	𝒮	𝒮	NOUN
cana-1619	84	27	)	)	PUNCT
cana-1619	84	28	for	for	ADP
cana-1619	84	29	each	each	DET
cana-1619	84	30	ξ	ξ	PROPN
cana-1619	84	31	=	=	SYM
cana-1619	84	32	0,1	0,1	NUM
cana-1619	84	33	,	,	PUNCT
cana-1619	84	34	…	…	PUNCT
cana-1619	84	35	,	,	PUNCT
cana-1619	84	36	n.	n.	NOUN
cana-1619	84	37	communications	communication	NOUN
cana-1619	84	38	on	on	ADP
cana-1619	84	39	applied	apply	VERB
cana-1619	84	40	nonlinear	nonlinear	ADJ
cana-1619	84	41	analysis	analysis	NOUN
cana-1619	84	42	issn	issn	NOUN
cana-1619	84	43	:	:	PUNCT
cana-1619	84	44	1074	1074	NUM
cana-1619	84	45	-	-	PUNCT
cana-1619	84	46	133x	133x	NUM
cana-1619	84	47	vol	vol	NOUN
cana-1619	84	48	32	32	NUM
cana-1619	84	49	no	no	NOUN
cana-1619	84	50	.	.	NOUN
cana-1619	84	51	1	1	NUM
cana-1619	84	52	(	(	PUNCT
cana-1619	84	53	2025	2025	NUM
cana-1619	84	54	)	)	PUNCT
cana-1619	84	55	39	39	NUM
cana-1619	84	56	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	85	1	now	now	ADV
cana-1619	85	2	,	,	PUNCT
cana-1619	85	3	let	let	VERB
cana-1619	85	4	’s	’s	PRON
cana-1619	85	5	discuss	discuss	VERB
cana-1619	85	6	how	how	SCONJ
cana-1619	85	7	we	we	PRON
cana-1619	85	8	can	can	AUX
cana-1619	85	9	determine	determine	VERB
cana-1619	85	10	if	if	SCONJ
cana-1619	85	11	the	the	DET
cana-1619	85	12	equations	equation	NOUN
cana-1619	85	13	are	be	AUX
cana-1619	85	14	approximately	approximately	ADV
cana-1619	85	15	controllable	controllable	ADJ
cana-1619	85	16	within	within	ADP
cana-1619	85	17	their	their	PRON
cana-1619	85	18	interior	interior	NOUN
cana-1619	85	19	,	,	PUNCT
cana-1619	85	20	without	without	ADP
cana-1619	85	21	involving	involve	VERB
cana-1619	85	22	impulses	impulse	NOUN
cana-1619	85	23	,	,	PUNCT
cana-1619	85	24	delays	delay	NOUN
cana-1619	85	25	,	,	PUNCT
cana-1619	85	26	or	or	CCONJ
cana-1619	85	27	nonlocal	nonlocal	ADJ
cana-1619	85	28	conditions	condition	NOUN
cana-1619	85	29	.	.	PUNCT
cana-1619	86	1	to	to	PART
cana-1619	86	2	do	do	VERB
cana-1619	86	3	this	this	PRON
cana-1619	86	4	,	,	PUNCT
cana-1619	86	5	we	we	PRON
cana-1619	86	6	consider	consider	VERB
cana-1619	86	7	the	the	DET
cana-1619	86	8	following	follow	VERB
cana-1619	86	9	scenario	scenario	NOUN
cana-1619	86	10	:	:	PUNCT
cana-1619	86	11	for	for	ADP
cana-1619	86	12	any	any	DET
cana-1619	86	13	starting	starting	NOUN
cana-1619	86	14	point	point	NOUN
cana-1619	86	15	φ0	φ0	PROPN
cana-1619	86	16	within	within	ADP
cana-1619	86	17	our	our	PRON
cana-1619	86	18	space	space	NOUN
cana-1619	86	19	𝒮	𝒮	NOUN
cana-1619	86	20	and	and	CCONJ
cana-1619	86	21	any	any	DET
cana-1619	86	22	function	function	NOUN
cana-1619	86	23	y	y	PROPN
cana-1619	86	24	belonging	belong	VERB
cana-1619	86	25	to	to	ADP
cana-1619	86	26	the	the	DET
cana-1619	86	27	l2	l2	NOUN
cana-1619	86	28	space	space	NOUN
cana-1619	86	29	over	over	ADP
cana-1619	86	30	the	the	DET
cana-1619	86	31	interval	interval	NOUN
cana-1619	86	32	(	(	PUNCT
cana-1619	86	33	0	0	NUM
cana-1619	86	34	,	,	PUNCT
cana-1619	86	35	ϱ	ϱ	ADP
cana-1619	86	36	]	]	PUNCT
cana-1619	86	37	with	with	ADP
cana-1619	86	38	values	value	NOUN
cana-1619	86	39	in	in	ADP
cana-1619	86	40	u	u	NOUN
cana-1619	86	41	,	,	PUNCT
cana-1619	86	42	we	we	PRON
cana-1619	86	43	examine	examine	VERB
cana-1619	86	44	the	the	DET
cana-1619	86	45	initial	initial	ADJ
cana-1619	86	46	-	-	PUNCT
cana-1619	86	47	value	value	NOUN
cana-1619	86	48	problem	problem	NOUN
cana-1619	86	49	:	:	PUNCT
cana-1619	86	50	φ′(h	φ′(h	X
cana-1619	86	51	,	,	PUNCT
cana-1619	86	52	ℵ	ℵ	NOUN
cana-1619	86	53	)	)	PUNCT
cana-1619	86	54	=	=	SYM
cana-1619	86	55	aφ(h	aφ(h	NOUN
cana-1619	86	56	,	,	PUNCT
cana-1619	86	57	ℵ	ℵ	NOUN
cana-1619	86	58	)	)	PUNCT
cana-1619	86	59	+	+	NUM
cana-1619	86	60	by(h	by(h	VERB
cana-1619	86	61	,	,	PUNCT
cana-1619	86	62	ℵ	ℵ	NOUN
cana-1619	86	63	)	)	PUNCT
cana-1619	86	64	,	,	PUNCT
cana-1619	86	65	φ	φ	PROPN
cana-1619	86	66	∈	∈	PROPN
cana-1619	86	67	𝒮	𝒮	PROPN
cana-1619	86	68	,	,	PUNCT
cana-1619	86	69	φ(0	φ(0	ADJ
cana-1619	86	70	,	,	PUNCT
cana-1619	86	71	ℵ	ℵ	NOUN
cana-1619	86	72	)	)	PUNCT
cana-1619	86	73	)	)	PUNCT
cana-1619	86	74	=	=	PUNCT
cana-1619	87	1	φ0(ℵ	φ0(ℵ	NOUN
cana-1619	87	2	)	)	PUNCT
cana-1619	87	3	,	,	PUNCT
cana-1619	87	4	(	(	PUNCT
cana-1619	87	5	5	5	X
cana-1619	87	6	)	)	PUNCT
cana-1619	87	7	where	where	SCONJ
cana-1619	87	8	the	the	DET
cana-1619	87	9	control	control	NOUN
cana-1619	87	10	function	function	PROPN
cana-1619	87	11	φ	φ	PROPN
cana-1619	87	12	belongs	belong	VERB
cana-1619	87	13	to	to	ADP
cana-1619	87	14	l2(0	l2(0	PROPN
cana-1619	87	15	,	,	PUNCT
cana-1619	87	16	ϱ	ϱ	ADP
cana-1619	87	17	;	;	PUNCT
cana-1619	87	18	u	u	NOUN
cana-1619	87	19	)	)	PUNCT
cana-1619	87	20	,	,	PUNCT
cana-1619	87	21	has	have	VERB
cana-1619	87	22	precisely	precisely	ADV
cana-1619	87	23	one	one	NUM
cana-1619	87	24	mild	mild	ADJ
cana-1619	87	25	solution	solution	NOUN
cana-1619	87	26	represented	represent	VERB
cana-1619	87	27	by	by	ADP
cana-1619	87	28	φ(h	φ(h	NOUN
cana-1619	87	29	,	,	PUNCT
cana-1619	87	30	ℵ	ℵ	NOUN
cana-1619	87	31	)	)	PUNCT
cana-1619	87	32	=	=	SYM
cana-1619	87	33	t(h)φ0(ℵ	t(h)φ0(ℵ	PROPN
cana-1619	87	34	)	)	PUNCT
cana-1619	88	1	+	+	NUM
cana-1619	88	2	∫	∫	PROPN
cana-1619	88	3	h	h	NOUN
cana-1619	88	4	0	0	NUM
cana-1619	88	5	t(h	t(h	NOUN
cana-1619	88	6	−	−	PROPN
cana-1619	88	7	ϖ)by(ϖ	ϖ)by(ϖ	NOUN
cana-1619	88	8	,	,	PUNCT
cana-1619	88	9	ℵ	ℵ	NOUN
cana-1619	88	10	)	)	PUNCT
cana-1619	88	11	dϖ	dϖ	NOUN
cana-1619	88	12	,	,	PUNCT
cana-1619	88	13	h	h	NOUN
cana-1619	88	14	∈	∈	PROPN
cana-1619	88	15	(	(	PUNCT
cana-1619	88	16	0	0	NUM
cana-1619	88	17	,	,	PUNCT
cana-1619	88	18	ϱ	ϱ	ADP
cana-1619	88	19	]	]	PUNCT
cana-1619	88	20	.	.	PUNCT
cana-1619	89	1	definition	definition	NOUN
cana-1619	89	2	4	4	NUM
cana-1619	89	3	for	for	ADP
cana-1619	89	4	the	the	DET
cana-1619	89	5	above	above	ADJ
cana-1619	89	6	system	system	NOUN
cana-1619	89	7	,	,	PUNCT
cana-1619	89	8	the	the	DET
cana-1619	89	9	controllability	controllability	NOUN
cana-1619	89	10	mapping	mapping	NOUN
cana-1619	89	11	g	g	NOUN
cana-1619	89	12	:	:	PUNCT
cana-1619	89	13	l2((0	l2((0	PROPN
cana-1619	89	14	,	,	PUNCT
cana-1619	89	15	ϱ	ϱ	ADP
cana-1619	89	16	]	]	PUNCT
cana-1619	89	17	;	;	PUNCT
cana-1619	89	18	u	u	NOUN
cana-1619	89	19	)	)	PUNCT
cana-1619	89	20	→	→	SYM
cana-1619	89	21	𝒮	𝒮	NOUN
cana-1619	89	22	is	be	AUX
cana-1619	89	23	defined	define	VERB
cana-1619	89	24	for	for	ADP
cana-1619	89	25	h	h	NOUN
cana-1619	89	26	>	>	X
cana-1619	89	27	0	0	PUNCT
cana-1619	90	1	as	as	SCONJ
cana-1619	90	2	follows	follow	VERB
cana-1619	90	3	:	:	PUNCT
cana-1619	90	4	gu	gu	NOUN
cana-1619	90	5	=	=	SYM
cana-1619	90	6	∫	∫	PROPN
cana-1619	90	7	h	h	NOUN
cana-1619	90	8	0	0	NUM
cana-1619	90	9	t(h	t(h	NOUN
cana-1619	90	10	−	−	PROPN
cana-1619	90	11	ϖ)by(ϖ	ϖ)by(ϖ	NOUN
cana-1619	90	12	,	,	PUNCT
cana-1619	90	13	ℵ	ℵ	NOUN
cana-1619	90	14	)	)	PUNCT
cana-1619	90	15	dϖ.	dϖ.	ADP
cana-1619	91	1	the	the	DET
cana-1619	91	2	corresponding	corresponding	ADJ
cana-1619	91	3	adjoint	adjoint	NOUN
cana-1619	91	4	operator	operator	NOUN
cana-1619	91	5	g∗	g∗	PROPN
cana-1619	91	6	:	:	PUNCT
cana-1619	91	7	𝒮	𝒮	PROPN
cana-1619	91	8	→	→	SYM
cana-1619	91	9	l2((0	l2((0	PROPN
cana-1619	91	10	,	,	PUNCT
cana-1619	91	11	ϱ	ϱ	ADP
cana-1619	91	12	]	]	PUNCT
cana-1619	91	13	;	;	PUNCT
cana-1619	91	14	𝒮	𝒮	NOUN
cana-1619	91	15	)	)	PUNCT
cana-1619	91	16	is	be	AUX
cana-1619	91	17	determined	determine	VERB
cana-1619	91	18	by	by	ADP
cana-1619	91	19	the	the	DET
cana-1619	91	20	rule	rule	NOUN
cana-1619	91	21	(	(	PUNCT
cana-1619	91	22	g∗φ)(ϖ	g∗φ)(ϖ	PROPN
cana-1619	91	23	)	)	PUNCT
cana-1619	91	24	=	=	PUNCT
cana-1619	91	25	b∗t∗(ϱ	b∗t∗(ϱ	PUNCT
cana-1619	91	26	−	−	NOUN
cana-1619	91	27	ϖ)φ	ϖ)φ	PUNCT
cana-1619	91	28	∀ϖ	∀ϖ	ADJ
cana-1619	91	29	∈	∈	PROPN
cana-1619	92	1	[	[	X
cana-1619	92	2	0	0	NUM
cana-1619	92	3	,	,	PUNCT
cana-1619	92	4	ϱ	ϱ	ADP
cana-1619	92	5	]	]	PUNCT
cana-1619	92	6	,	,	PUNCT
cana-1619	92	7	∀z	∀z	PROPN
cana-1619	92	8	∈	∈	PROPN
cana-1619	92	9	𝒮.	𝒮.	PROPN
cana-1619	92	10	consequently	consequently	ADV
cana-1619	92	11	,	,	PUNCT
cana-1619	92	12	the	the	DET
cana-1619	92	13	grammian	grammian	ADJ
cana-1619	92	14	operator	operator	NOUN
cana-1619	92	15	w:𝒮	w:𝒮	PRON
cana-1619	92	16	→	→	SYM
cana-1619	92	17	𝒮	𝒮	PROPN
cana-1619	92	18	is	be	AUX
cana-1619	92	19	kφ	kφ	NOUN
cana-1619	92	20	=	=	PUNCT
cana-1619	93	1	gg∗φ	gg∗φ	PROPN
cana-1619	93	2	=	=	SYM
cana-1619	93	3	∫	∫	PROPN
cana-1619	93	4	τ	τ	PROPN
cana-1619	93	5	0	0	PROPN
cana-1619	93	6	t(ϱ	t(ϱ	PROPN
cana-1619	93	7	−	−	PROPN
cana-1619	93	8	ϖ)bb∗t∗(ϱ	ϖ)bb∗t∗(ϱ	NOUN
cana-1619	93	9	−	−	NOUN
cana-1619	93	10	ϖ	ϖ	NOUN
cana-1619	93	11	)	)	PUNCT
cana-1619	93	12	dϖ.	dϖ.	AUX
cana-1619	93	13	remark	remark	VERB
cana-1619	93	14	1	1	NUM
cana-1619	93	15	the	the	DET
cana-1619	93	16	series	series	NOUN
cana-1619	93	17	of	of	ADP
cana-1619	93	18	linear	linear	PROPN
cana-1619	93	19	operators	operator	NOUN
cana-1619	93	20	(	(	PUNCT
cana-1619	93	21	γ(ℵ))α	γ(ℵ))α	NOUN
cana-1619	93	22	:	:	PUNCT
cana-1619	93	23	𝒮	𝒮	PROPN
cana-1619	93	24	→	→	SYM
cana-1619	93	25	l2((0	l2((0	PROPN
cana-1619	93	26	,	,	PUNCT
cana-1619	93	27	ϱ	ϱ	ADP
cana-1619	93	28	]	]	PUNCT
cana-1619	93	29	;	;	PUNCT
cana-1619	93	30	u	u	NOUN
cana-1619	93	31	)	)	PUNCT
cana-1619	93	32	,	,	PUNCT
cana-1619	93	33	where	where	SCONJ
cana-1619	93	34	0	0	X
cana-1619	93	35	<	<	X
cana-1619	93	36	α	α	PROPN
cana-1619	93	37	≤	≤	NUM
cana-1619	93	38	1	1	NUM
cana-1619	93	39	,	,	PUNCT
cana-1619	93	40	can	can	AUX
cana-1619	93	41	be	be	AUX
cana-1619	93	42	defined	define	VERB
cana-1619	93	43	as	as	SCONJ
cana-1619	93	44	follows	follow	VERB
cana-1619	93	45	:	:	PUNCT
cana-1619	93	46	(	(	PUNCT
cana-1619	93	47	γ(ℵ))αφ	γ(ℵ))αφ	PROPN
cana-1619	93	48	=	=	SYM
cana-1619	93	49	b	b	X
cana-1619	93	50	∗t∗(⋅)(αi	∗t∗(⋅)(αi	NOUN
cana-1619	93	51	+	+	CCONJ
cana-1619	93	52	gg∗)−1φ	gg∗)−1φ	PROPN
cana-1619	93	53	=	=	SYM
cana-1619	93	54	g∗(αi	g∗(αi	NOUN
cana-1619	93	55	+	+	X
cana-1619	93	56	gg∗)−1φ	gg∗)−1φ	PROPN
cana-1619	93	57	,	,	PUNCT
cana-1619	93	58	(	(	PUNCT
cana-1619	93	59	3.6	3.6	NUM
cana-1619	93	60	)	)	PUNCT
cana-1619	93	61	this	this	DET
cana-1619	93	62	set	set	NOUN
cana-1619	93	63	of	of	ADP
cana-1619	93	64	operators	operator	NOUN
cana-1619	93	65	fulfills	fulfill	VERB
cana-1619	93	66	the	the	DET
cana-1619	93	67	condition	condition	NOUN
cana-1619	93	68	:	:	PUNCT
cana-1619	94	1	lim	lim	PROPN
cana-1619	94	2	α→0	α→0	NOUN
cana-1619	94	3	g(γ(ℵ))α	g(γ(ℵ))α	ADV
cana-1619	94	4	=	=	SYM
cana-1619	94	5	i	i	PROPN
cana-1619	94	6	,	,	PUNCT
cana-1619	94	7	in	in	ADP
cana-1619	94	8	the	the	DET
cana-1619	94	9	strong	strong	ADJ
cana-1619	94	10	topology	topology	NOUN
cana-1619	94	11	.	.	PUNCT
cana-1619	95	1	3	3	NUM
cana-1619	95	2	existence	existence	NOUN
cana-1619	95	3	results	result	VERB
cana-1619	95	4	in	in	ADP
cana-1619	95	5	this	this	DET
cana-1619	95	6	section	section	NOUN
cana-1619	95	7	,	,	PUNCT
cana-1619	95	8	we	we	PRON
cana-1619	95	9	show	show	VERB
cana-1619	95	10	that	that	SCONJ
cana-1619	95	11	there	there	PRON
cana-1619	95	12	are	be	VERB
cana-1619	95	13	solutions	solution	NOUN
cana-1619	95	14	to	to	ADP
cana-1619	95	15	the	the	DET
cana-1619	95	16	problem	problem	NOUN
cana-1619	95	17	described	describe	VERB
cana-1619	95	18	by	by	ADP
cana-1619	95	19	equations	equation	NOUN
cana-1619	95	20	(	(	PUNCT
cana-1619	95	21	1.1	1.1	NUM
cana-1619	95	22	)	)	PUNCT
cana-1619	95	23	.	.	PUNCT
cana-1619	96	1	to	to	PART
cana-1619	96	2	do	do	VERB
cana-1619	96	3	this	this	PRON
cana-1619	96	4	,	,	PUNCT
cana-1619	96	5	we	we	PRON
cana-1619	96	6	list	list	VERB
cana-1619	96	7	some	some	DET
cana-1619	96	8	conditions	condition	NOUN
cana-1619	96	9	we	we	PRON
cana-1619	96	10	’ll	’ll	AUX
cana-1619	96	11	need	need	VERB
cana-1619	96	12	to	to	PART
cana-1619	96	13	consider	consider	VERB
cana-1619	96	14	.	.	PUNCT
cana-1619	97	1	definition	definition	NOUN
cana-1619	97	2	5	5	NUM
cana-1619	97	3	if	if	SCONJ
cana-1619	97	4	φ0	φ0	ADJ
cana-1619	97	5	=	=	NOUN
cana-1619	97	6	∅	∅	NOUN
cana-1619	97	7	and	and	CCONJ
cana-1619	97	8	the	the	DET
cana-1619	97	9	continuous	continuous	ADJ
cana-1619	97	10	function	function	NOUN
cana-1619	97	11	x	x	NOUN
cana-1619	97	12	:	:	PUNCT
cana-1619	97	13	(	(	PUNCT
cana-1619	97	14	0	0	NUM
cana-1619	97	15	,	,	PUNCT
cana-1619	97	16	ϱ	ϱ	ADP
cana-1619	97	17	]	]	X
cana-1619	97	18	×	×	PROPN
cana-1619	97	19	ω	ω	PROPN
cana-1619	97	20	→	→	SYM
cana-1619	97	21	𝒮	𝒮	PROPN
cana-1619	97	22	,	,	PUNCT
cana-1619	97	23	t	t	PROPN
cana-1619	97	24	>	>	X
cana-1619	97	25	0	0	PUNCT
cana-1619	98	1	and	and	CCONJ
cana-1619	98	2	𝒟	𝒟	PROPN
cana-1619	98	3	=	=	PUNCT
cana-1619	98	4	c[(−δ	c[(−δ	PROPN
cana-1619	98	5	,	,	PUNCT
cana-1619	98	6	ϱ	ϱ	ADP
cana-1619	98	7	]	]	PUNCT
cana-1619	98	8	,	,	PUNCT
cana-1619	98	9	𝒮	𝒮	PROPN
cana-1619	98	10	]	]	PUNCT
cana-1619	98	11	solves	solve	VERB
cana-1619	98	12	the	the	DET
cana-1619	98	13	integral	integral	ADJ
cana-1619	98	14	equation	equation	NOUN
cana-1619	98	15	then	then	ADV
cana-1619	98	16	it	it	PRON
cana-1619	98	17	is	be	AUX
cana-1619	98	18	considered	consider	VERB
cana-1619	98	19	a	a	DET
cana-1619	98	20	mild	mild	ADJ
cana-1619	98	21	solution	solution	NOUN
cana-1619	98	22	to	to	ADP
cana-1619	98	23	equation	equation	NOUN
cana-1619	98	24	(	(	PUNCT
cana-1619	98	25	1.1	1.1	NUM
cana-1619	98	26	)	)	PUNCT
cana-1619	98	27	.	.	PUNCT
cana-1619	99	1	ζ(h	ζ(h	NOUN
cana-1619	99	2	,	,	PUNCT
cana-1619	99	3	ℵ	ℵ	NOUN
cana-1619	99	4	)	)	PUNCT
cana-1619	99	5	=	=	SYM
cana-1619	99	6	t1(h)ϕ0(ℵ	t1(h)ϕ0(ℵ	X
cana-1619	99	7	)	)	PUNCT
cana-1619	99	8	+	+	CCONJ
cana-1619	99	9	t2(h)[ϕ′0(ℵ	t2(h)[ϕ′0(ℵ	NUM
cana-1619	99	10	)	)	PUNCT
cana-1619	100	1	+	+	CCONJ
cana-1619	101	1	ρ(0	ρ(0	PROPN
cana-1619	101	2	,	,	PUNCT
cana-1619	101	3	ϕ0(ℵ	ϕ0(ℵ	PROPN
cana-1619	101	4	)	)	PUNCT
cana-1619	101	5	,	,	PUNCT
cana-1619	101	6	ℵ	ℵ	NOUN
cana-1619	101	7	)	)	PUNCT
cana-1619	101	8	]	]	PUNCT
cana-1619	102	1	−	−	PROPN
cana-1619	102	2	∫	∫	PROPN
cana-1619	102	3	h	h	NOUN
cana-1619	102	4	0	0	PUNCT
cana-1619	103	1	t1(h	t1(h	PRON
cana-1619	103	2	−	−	PROPN
cana-1619	103	3	ϖ)ρ(ϖ,φϖ	ϖ)ρ(ϖ,φϖ	PROPN
cana-1619	103	4	(	(	PUNCT
cana-1619	103	5	.	.	PUNCT
cana-1619	103	6	,	,	PUNCT
cana-1619	103	7	ℵ	ℵ	NOUN
cana-1619	103	8	)	)	PUNCT
cana-1619	103	9	,	,	PUNCT
cana-1619	103	10	ℵ)dϖ	ℵ)dϖ	PROPN
cana-1619	103	11	+	+	NUM
cana-1619	103	12	∫	∫	PROPN
cana-1619	103	13	h	h	NOUN
cana-1619	103	14	0	0	PUNCT
cana-1619	104	1	t2(h	t2(h	X
cana-1619	104	2	−	−	PROPN
cana-1619	104	3	ϖ)υ(ϖ,φϖ	ϖ)υ(ϖ,φϖ	NOUN
cana-1619	104	4	(	(	PUNCT
cana-1619	104	5	.	.	PUNCT
cana-1619	104	6	,	,	PUNCT
cana-1619	104	7	ℵ	ℵ	NOUN
cana-1619	104	8	)	)	PUNCT
cana-1619	104	9	,	,	PUNCT
cana-1619	104	10	ℵ)dϖ	ℵ)dϖ	PROPN
cana-1619	104	11	+	+	NUM
cana-1619	104	12	∑0	∑0	PROPN
cana-1619	104	13	<	<	X
cana-1619	104	14	hξ	hξ	X
cana-1619	104	15	<	<	X
cana-1619	104	16	h	h	PRON
cana-1619	104	17	t1(h	t1(h	X
cana-1619	104	18	−	−	NOUN
cana-1619	104	19	hξ)iξ(φ(hξ	hξ)iξ(φ(hξ	NOUN
cana-1619	104	20	,	,	PUNCT
cana-1619	104	21	ℵ	ℵ	NOUN
cana-1619	104	22	)	)	PUNCT
cana-1619	104	23	)	)	PUNCT
cana-1619	105	1	+	+	PUNCT
cana-1619	105	2	∑0	∑0	X
cana-1619	105	3	<	<	X
cana-1619	105	4	hξ	hξ	X
cana-1619	105	5	<	<	X
cana-1619	105	6	h	h	PRON
cana-1619	105	7	t2(h	t2(h	X
cana-1619	105	8	−	−	X
cana-1619	105	9	hξ)i′ξ(φ(hξ	hξ)i′ξ(φ(hξ	PROPN
cana-1619	105	10	,	,	PUNCT
cana-1619	105	11	ℵ	ℵ	NOUN
cana-1619	105	12	)	)	PUNCT
cana-1619	105	13	)	)	PUNCT
cana-1619	105	14	.	.	PUNCT
cana-1619	106	1	for	for	ADP
cana-1619	106	2	your	your	PRON
cana-1619	106	3	convenience	convenience	NOUN
cana-1619	106	4	,	,	PUNCT
cana-1619	106	5	we	we	PRON
cana-1619	106	6	have	have	AUX
cana-1619	106	7	listed	list	VERB
cana-1619	106	8	the	the	DET
cana-1619	106	9	hypotheses	hypothesis	NOUN
cana-1619	106	10	that	that	PRON
cana-1619	106	11	will	will	AUX
cana-1619	106	12	be	be	AUX
cana-1619	106	13	discussed	discuss	VERB
cana-1619	106	14	in	in	ADP
cana-1619	106	15	the	the	DET
cana-1619	106	16	following	follow	VERB
cana-1619	106	17	section	section	NOUN
cana-1619	106	18	.	.	PUNCT
cana-1619	107	1	(	(	PUNCT
cana-1619	107	2	g1)there	g1)there	ADV
cana-1619	107	3	exist	exist	VERB
cana-1619	107	4	a	a	DET
cana-1619	107	5	continuous	continuous	ADJ
cana-1619	107	6	function	function	NOUN
cana-1619	107	7	a0	a0	PROPN
cana-1619	107	8	,	,	PUNCT
cana-1619	107	9	b0	b0	NOUN
cana-1619	107	10	,	,	PUNCT
cana-1619	107	11	c0	c0	NOUN
cana-1619	107	12	,	,	PUNCT
cana-1619	107	13	d0	d0	NOUN
cana-1619	107	14	:	:	PUNCT
cana-1619	107	15	j	j	PROPN
cana-1619	107	16	×	×	PROPN
cana-1619	107	17	ω	ω	PROPN
cana-1619	107	18	→	→	SYM
cana-1619	107	19	ℝ	ℝ	PROPN
cana-1619	107	20	such	such	ADJ
cana-1619	107	21	that	that	DET
cana-1619	107	22	||υ(h	||υ(h	NOUN
cana-1619	107	23	,	,	PUNCT
cana-1619	107	24	x	x	PRON
cana-1619	107	25	,	,	PUNCT
cana-1619	107	26	ℵ)||	ℵ)||	NUM
cana-1619	107	27	≤	≤	NOUN
cana-1619	107	28	a0(ℵ)||x	a0(ℵ)||x	ADP
cana-1619	107	29	,	,	PUNCT
cana-1619	107	30	ℵ||𝒟	ℵ||𝒟	NOUN
cana-1619	107	31	α0	α0	ADJ
cana-1619	107	32	+	+	CCONJ
cana-1619	107	33	b0(ℵ	b0(ℵ	PROPN
cana-1619	107	34	)	)	PUNCT
cana-1619	107	35	communications	communication	NOUN
cana-1619	107	36	on	on	ADP
cana-1619	107	37	applied	apply	VERB
cana-1619	107	38	nonlinear	nonlinear	ADJ
cana-1619	107	39	analysis	analysis	NOUN
cana-1619	107	40	issn	issn	NOUN
cana-1619	107	41	:	:	PUNCT
cana-1619	107	42	1074	1074	NUM
cana-1619	107	43	-	-	PUNCT
cana-1619	107	44	133x	133x	NUM
cana-1619	107	45	vol	vol	NOUN
cana-1619	107	46	32	32	NUM
cana-1619	107	47	no	no	NOUN
cana-1619	107	48	.	.	NOUN
cana-1619	107	49	1	1	NUM
cana-1619	107	50	(	(	PUNCT
cana-1619	107	51	2025	2025	NUM
cana-1619	107	52	)	)	PUNCT
cana-1619	107	53	40	40	NUM
cana-1619	107	54	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	107	55	||ρ(h	||ρ(h	NOUN
cana-1619	107	56	,	,	PUNCT
cana-1619	107	57	x	x	PRON
cana-1619	107	58	,	,	PUNCT
cana-1619	107	59	ℵ)||	ℵ)||	NOUN
cana-1619	107	60	≤	≤	NOUN
cana-1619	107	61	c0(ℵ)||x	c0(ℵ)||x	NOUN
cana-1619	107	62	,	,	PUNCT
cana-1619	107	63	ℵ||𝒟	ℵ||𝒟	PRON
cana-1619	107	64	β0	β0	NOUN
cana-1619	107	65	+	+	CCONJ
cana-1619	107	66	d0(ℵ	d0(ℵ	NOUN
cana-1619	107	67	)	)	PUNCT
cana-1619	107	68	for	for	ADP
cana-1619	107	69	all	all	DET
cana-1619	107	70	x	x	SYM
cana-1619	107	71	∈	∈	PROPN
cana-1619	107	72	𝒮	𝒮	PROPN
cana-1619	107	73	,	,	PUNCT
cana-1619	107	74	ℵ	ℵ	PROPN
cana-1619	107	75	∈	∈	PROPN
cana-1619	107	76	ω	ω	NOUN
cana-1619	107	77	(	(	PUNCT
cana-1619	107	78	g2)(i)for	g2)(i)for	ADP
cana-1619	107	79	all	all	DET
cana-1619	107	80	h,ϖ	h,ϖ	PROPN
cana-1619	107	81	∈	∈	PROPN
cana-1619	107	82	j	j	PROPN
cana-1619	107	83	,	,	PUNCT
cana-1619	107	84	the	the	DET
cana-1619	107	85	function	function	NOUN
cana-1619	107	86	υ(h	υ(h	NOUN
cana-1619	107	87	,	,	PUNCT
cana-1619	107	88	.	.	PUNCT
cana-1619	108	1	,	,	PUNCT
cana-1619	108	2	.	.	PUNCT
cana-1619	109	1	):	):	PUNCT
cana-1619	109	2	𝒟	𝒟	NOUN
cana-1619	109	3	×	×	PROPN
cana-1619	109	4	ω	ω	PROPN
cana-1619	109	5	→	→	SYM
cana-1619	109	6	𝒮	𝒮	PROPN
cana-1619	109	7	is	be	AUX
cana-1619	109	8	continuous	continuous	ADJ
cana-1619	109	9	and	and	CCONJ
cana-1619	109	10	for	for	ADP
cana-1619	110	1	all	all	PRON
cana-1619	110	2	(	(	PUNCT
cana-1619	110	3	x	x	NOUN
cana-1619	110	4	,	,	PUNCT
cana-1619	110	5	ℵ	ℵ	NOUN
cana-1619	110	6	)	)	PUNCT
cana-1619	110	7	∈	∈	PROPN
cana-1619	110	8	𝒟	𝒟	NOUN
cana-1619	110	9	×	×	PROPN
cana-1619	110	10	ω	ω	NUM
cana-1619	110	11	the	the	DET
cana-1619	110	12	function	function	NOUN
cana-1619	110	13	υ	υ	PROPN
cana-1619	110	14	(	(	PUNCT
cana-1619	110	15	.	.	PUNCT
cana-1619	110	16	,	,	PUNCT
cana-1619	110	17	x	x	NOUN
cana-1619	110	18	,	,	PUNCT
cana-1619	110	19	ℵ	ℵ	NUM
cana-1619	110	20	):	):	PUNCT
cana-1619	110	21	j	j	PROPN
cana-1619	110	22	→	→	SYM
cana-1619	110	23	𝒮	𝒮	PROPN
cana-1619	110	24	is	be	AUX
cana-1619	110	25	strongly	strongly	ADV
cana-1619	110	26	measurable	measurable	ADJ
cana-1619	110	27	.	.	PUNCT
cana-1619	111	1	(	(	PUNCT
cana-1619	111	2	ii	ii	NOUN
cana-1619	111	3	)	)	PUNCT
cana-1619	111	4	for	for	ADP
cana-1619	111	5	all	all	DET
cana-1619	111	6	h	h	NOUN
cana-1619	111	7	∈	∈	PROPN
cana-1619	111	8	j	j	PROPN
cana-1619	111	9	,	,	PUNCT
cana-1619	111	10	the	the	DET
cana-1619	111	11	function	function	NOUN
cana-1619	111	12	υ(h	υ(h	NOUN
cana-1619	111	13	,	,	PUNCT
cana-1619	111	14	.	.	PUNCT
cana-1619	111	15	,	,	PUNCT
cana-1619	111	16	.	.	PUNCT
cana-1619	112	1	):	):	PUNCT
cana-1619	112	2	𝒟	𝒟	NOUN
cana-1619	112	3	×	×	PROPN
cana-1619	112	4	ω	ω	PROPN
cana-1619	112	5	→	→	SYM
cana-1619	112	6	𝒮	𝒮	PROPN
cana-1619	112	7	is	be	AUX
cana-1619	112	8	continuous	continuous	ADJ
cana-1619	112	9	and	and	CCONJ
cana-1619	112	10	for	for	ADP
cana-1619	113	1	all	all	PRON
cana-1619	113	2	(	(	PUNCT
cana-1619	113	3	x	x	NOUN
cana-1619	113	4	,	,	PUNCT
cana-1619	113	5	ℵ	ℵ	NOUN
cana-1619	113	6	)	)	PUNCT
cana-1619	113	7	∈	∈	PROPN
cana-1619	113	8	𝒟	𝒟	NOUN
cana-1619	113	9	×	×	PROPN
cana-1619	113	10	ω	ω	NUM
cana-1619	113	11	the	the	DET
cana-1619	113	12	function	function	NOUN
cana-1619	113	13	υ	υ	PROPN
cana-1619	113	14	(	(	PUNCT
cana-1619	113	15	.	.	PUNCT
cana-1619	113	16	,	,	PUNCT
cana-1619	113	17	x	x	NOUN
cana-1619	113	18	,	,	PUNCT
cana-1619	113	19	ℵ	ℵ	NUM
cana-1619	113	20	):	):	PUNCT
cana-1619	113	21	j	j	PROPN
cana-1619	113	22	→	→	SYM
cana-1619	113	23	𝒮	𝒮	PROPN
cana-1619	113	24	is	be	AUX
cana-1619	113	25	strongly	strongly	ADV
cana-1619	113	26	measurable	measurable	ADJ
cana-1619	113	27	.	.	PUNCT
cana-1619	114	1	(	(	PUNCT
cana-1619	114	2	g4)let	g4)let	NOUN
cana-1619	114	3	iξ	iξ	NOUN
cana-1619	114	4	,	,	PUNCT
cana-1619	114	5	i′ξ	i′ξ	PROPN
cana-1619	114	6	∈	∈	PROPN
cana-1619	114	7	c(𝒮	c(𝒮	PROPN
cana-1619	114	8	,	,	PUNCT
cana-1619	114	9	𝒮	𝒮	PROPN
cana-1619	114	10	)	)	PUNCT
cana-1619	114	11	,	,	PUNCT
cana-1619	114	12	ξ	ξ	X
cana-1619	114	13	=	=	SYM
cana-1619	114	14	1,2,3	1,2,3	NUM
cana-1619	114	15	,	,	PUNCT
cana-1619	114	16	.	.	PUNCT
cana-1619	114	17	.	.	PUNCT
cana-1619	114	18	.	.	PUNCT
cana-1619	115	1	,	,	PUNCT
cana-1619	115	2	m	m	NOUN
cana-1619	115	3	are	be	AUX
cana-1619	115	4	all	all	PRON
cana-1619	115	5	compact	compact	ADJ
cana-1619	115	6	operator	operator	NOUN
cana-1619	115	7	||iξ(h	||iξ(h	NOUN
cana-1619	115	8	,	,	PUNCT
cana-1619	115	9	x	x	PRON
cana-1619	115	10	,	,	PUNCT
cana-1619	115	11	ℵ)||	ℵ)||	PROPN
cana-1619	115	12	≤	≤	NOUN
cana-1619	115	13	aξ(ℵ)||x	aξ(ℵ)||x	ADP
cana-1619	115	14	,	,	PUNCT
cana-1619	115	15	ℵ||ℝ	ℵ||ℝ	VERB
cana-1619	115	16	αξ	αξ	PROPN
cana-1619	115	17	||i′ξ(h	||i′ξ(h	NOUN
cana-1619	115	18	,	,	PUNCT
cana-1619	115	19	x	x	PRON
cana-1619	115	20	,	,	PUNCT
cana-1619	115	21	ℵ)||	ℵ)||	NOUN
cana-1619	115	22	≤	≤	ADJ
cana-1619	115	23	a′ξ(ℵ)||x	a′ξ(ℵ)||x	NOUN
cana-1619	115	24	,	,	PUNCT
cana-1619	115	25	ℵ||ℝ	ℵ||ℝ	VERB
cana-1619	115	26	αξ	αξ	NOUN
cana-1619	115	27	(	(	PUNCT
cana-1619	115	28	g5)the	g5)the	PROPN
cana-1619	115	29	function	function	NOUN
cana-1619	115	30	υ	υ	PROPN
cana-1619	115	31	:	:	PUNCT
cana-1619	115	32	j	j	PROPN
cana-1619	115	33	×	×	PROPN
cana-1619	115	34	j	j	PROPN
cana-1619	115	35	×	×	NOUN
cana-1619	115	36	𝒟	𝒟	PROPN
cana-1619	115	37	×	×	PROPN
cana-1619	115	38	ω	ω	PROPN
cana-1619	115	39	→	→	SYM
cana-1619	115	40	𝒮	𝒮	PROPN
cana-1619	115	41	,	,	PUNCT
cana-1619	115	42	ρ	ρ	PROPN
cana-1619	115	43	:	:	PUNCT
cana-1619	115	44	j	j	PROPN
cana-1619	115	45	×	×	PROPN
cana-1619	115	46	𝒟	𝒟	PROPN
cana-1619	115	47	×	×	PROPN
cana-1619	115	48	ω	ω	PROPN
cana-1619	115	49	→	→	SYM
cana-1619	115	50	𝒮	𝒮	PROPN
cana-1619	115	51	is	be	AUX
cana-1619	115	52	continuous	continuous	ADJ
cana-1619	115	53	,	,	PUNCT
cana-1619	115	54	and	and	CCONJ
cana-1619	115	55	a	a	DET
cana-1619	115	56	constant	constant	ADJ
cana-1619	115	57	ℒ	ℒ	NOUN
cana-1619	115	58	exists	exist	VERB
cana-1619	115	59	for	for	ADP
cana-1619	115	60	which	which	PRON
cana-1619	115	61	||υ(h	||υ(h	PROPN
cana-1619	115	62	,	,	PUNCT
cana-1619	115	63	x1	x1	PROPN
cana-1619	115	64	,	,	PUNCT
cana-1619	115	65	ℵ	ℵ	NOUN
cana-1619	115	66	)	)	PUNCT
cana-1619	116	1	−	−	NOUN
cana-1619	116	2	υ(h	υ(h	NOUN
cana-1619	116	3	,	,	PUNCT
cana-1619	116	4	x2	x2	PROPN
cana-1619	116	5	,	,	PUNCT
cana-1619	116	6	ℵ)||	ℵ)||	NUM
cana-1619	116	7	≤	≤	NOUN
cana-1619	116	8	ℒ(ℵ)(||(x1	ℒ(ℵ)(||(x1	PROPN
cana-1619	116	9	,	,	PUNCT
cana-1619	116	10	ℵ	ℵ	NOUN
cana-1619	116	11	)	)	PUNCT
cana-1619	116	12	−	−	PROPN
cana-1619	116	13	(	(	PUNCT
cana-1619	116	14	x2	x2	PROPN
cana-1619	116	15	,	,	PUNCT
cana-1619	116	16	ℵ)||𝒟	ℵ)||𝒟	NUM
cana-1619	116	17	α0	α0	ADJ
cana-1619	116	18	)	)	PUNCT
cana-1619	116	19	||ρ(h	||ρ(h	NOUN
cana-1619	116	20	,	,	PUNCT
cana-1619	116	21	x1	x1	PROPN
cana-1619	116	22	,	,	PUNCT
cana-1619	116	23	ℵ	ℵ	NOUN
cana-1619	116	24	)	)	PUNCT
cana-1619	116	25	−	−	PROPN
cana-1619	116	26	ρ(h	ρ(h	PROPN
cana-1619	116	27	,	,	PUNCT
cana-1619	116	28	x2	x2	PROPN
cana-1619	116	29	,	,	PUNCT
cana-1619	116	30	ℵ)||	ℵ)||	NOUN
cana-1619	116	31	≤	≤	NOUN
cana-1619	116	32	ℒ1(ℵ)(||(x1	ℒ1(ℵ)(||(x1	NOUN
cana-1619	116	33	,	,	PUNCT
cana-1619	116	34	ℵ	ℵ	NOUN
cana-1619	116	35	)	)	PUNCT
cana-1619	116	36	−	−	PROPN
cana-1619	116	37	(	(	PUNCT
cana-1619	116	38	x2	x2	PROPN
cana-1619	116	39	,	,	PUNCT
cana-1619	116	40	ℵ)||𝒟	ℵ)||𝒟	NUM
cana-1619	116	41	β0	β0	NOUN
cana-1619	116	42	)	)	PUNCT
cana-1619	116	43	(	(	PUNCT
cana-1619	116	44	g6	g6	ADJ
cana-1619	116	45	)	)	PUNCT
cana-1619	116	46	there	there	PRON
cana-1619	116	47	is	be	VERB
cana-1619	116	48	a	a	DET
cana-1619	116	49	random	random	ADJ
cana-1619	116	50	funtion	funtion	NOUN
cana-1619	116	51	r	r	NOUN
cana-1619	116	52	:	:	PUNCT
cana-1619	116	53	ω	ω	PROPN
cana-1619	116	54	→	→	SYM
cana-1619	116	55	ℝ+	ℝ+	PUNCT
cana-1619	116	56	such	such	ADJ
cana-1619	116	57	that	that	DET
cana-1619	116	58	ϑ||ϕ0||	ϑ||ϕ0||	PROPN
cana-1619	116	59	+	+	CCONJ
cana-1619	116	60	ϑa||ϕ′0(ℵ	ϑa||ϕ′0(ℵ	NOUN
cana-1619	116	61	)	)	PUNCT
cana-1619	116	62	+	+	CCONJ
cana-1619	117	1	ρ(0	ρ(0	PROPN
cana-1619	117	2	,	,	PUNCT
cana-1619	117	3	ϕ0(ℵ	ϕ0(ℵ	PROPN
cana-1619	117	4	)	)	PUNCT
cana-1619	117	5	,	,	PUNCT
cana-1619	117	6	ℵ)||	ℵ)||	NUM
cana-1619	117	7	+	+	NOUN
cana-1619	117	8	ϑahb0(ℵ	ϑahb0(ℵ	NOUN
cana-1619	117	9	)	)	PUNCT
cana-1619	118	1	+	+	SYM
cana-1619	118	2	ϑhd0(ℵ	ϑhd0(ℵ	NOUN
cana-1619	118	3	)	)	PUNCT
cana-1619	118	4	+	+	NUM
cana-1619	118	5	ϑ∑0	ϑ∑0	NOUN
cana-1619	118	6	<	<	X
cana-1619	118	7	hξ	hξ	X
cana-1619	118	8	<	<	X
cana-1619	118	9	h	h	PROPN
cana-1619	118	10	aξ(ℵ)||ζ(hξ	aξ(ℵ)||ζ(hξ	PROPN
cana-1619	118	11	,	,	PUNCT
cana-1619	118	12	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	118	13	αξ	αξ	NOUN
cana-1619	118	14	+	+	CCONJ
cana-1619	118	15	ϑa∑0	ϑa∑0	PROPN
cana-1619	118	16	<	<	X
cana-1619	118	17	hξ	hξ	X
cana-1619	118	18	<	<	X
cana-1619	118	19	h	h	NOUN
cana-1619	118	20	a′ξ(ℵ)||ζ(hξ	a′ξ(ℵ)||ζ(hξ	PROPN
cana-1619	118	21	,	,	PUNCT
cana-1619	118	22	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	118	23	αξ	αξ	NOUN
cana-1619	118	24	+	+	CCONJ
cana-1619	118	25	ϑa	ϑa	INTJ
cana-1619	118	26	∫	∫	PROPN
cana-1619	118	27	h	h	NOUN
cana-1619	118	28	0	0	NUM
cana-1619	119	1	||	||	NUM
cana-1619	120	1	[	[	PUNCT
cana-1619	120	2	sup	sup	NOUN
cana-1619	120	3	ϖ∈(0.ϱ	ϖ∈(0.ϱ	PROPN
cana-1619	120	4	]	]	PUNCT
cana-1619	120	5	||ζϖ	||ζϖ	NUM
cana-1619	120	6	(	(	PUNCT
cana-1619	120	7	.	.	PUNCT
cana-1619	120	8	,	,	PUNCT
cana-1619	120	9	ℵ	ℵ	NOUN
cana-1619	120	10	)	)	PUNCT
cana-1619	120	11	,	,	PUNCT
cana-1619	120	12	ℵ||𝒟	ℵ||𝒟	PRON
cana-1619	120	13	α0dϖ	α0dϖ	PUNCT
cana-1619	121	1	+	+	PUNCT
cana-1619	121	2	ϑ∫	ϑ∫	NUM
cana-1619	121	3	h	h	NOUN
cana-1619	121	4	0	0	NUM
cana-1619	121	5	||	||	NUM
cana-1619	122	1	[	[	PUNCT
cana-1619	122	2	sup	sup	NOUN
cana-1619	122	3	ϖ∈(0.ϱ	ϖ∈(0.ϱ	PROPN
cana-1619	122	4	]	]	PUNCT
cana-1619	122	5	||ζϖ	||ζϖ	NUM
cana-1619	122	6	(	(	PUNCT
cana-1619	122	7	.	.	PUNCT
cana-1619	122	8	,	,	PUNCT
cana-1619	122	9	ℵ	ℵ	NOUN
cana-1619	122	10	)	)	PUNCT
cana-1619	122	11	,	,	PUNCT
cana-1619	122	12	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	122	13	β0dϖ	β0dϖ	PUNCT
cana-1619	122	14	≤	≤	X
cana-1619	122	15	r(ℵ	r(ℵ	PROPN
cana-1619	122	16	)	)	PUNCT
cana-1619	122	17	.	.	PUNCT
cana-1619	123	1	theorem	theorem	VERB
cana-1619	123	2	3.1	3.1	NUM
cana-1619	123	3	assuming	assume	VERB
cana-1619	123	4	that	that	SCONJ
cana-1619	123	5	conditions	condition	NOUN
cana-1619	123	6	(	(	PUNCT
cana-1619	123	7	g1)-(g6	g1)-(g6	PROPN
cana-1619	123	8	)	)	PUNCT
cana-1619	123	9	are	be	AUX
cana-1619	123	10	met	meet	VERB
cana-1619	123	11	,	,	PUNCT
cana-1619	123	12	the	the	DET
cana-1619	123	13	problem	problem	NOUN
cana-1619	123	14	described	describe	VERB
cana-1619	123	15	in	in	ADP
cana-1619	123	16	(	(	PUNCT
cana-1619	123	17	1.1	1.1	NUM
cana-1619	123	18	)	)	PUNCT
cana-1619	123	19	will	will	AUX
cana-1619	123	20	have	have	VERB
cana-1619	123	21	a	a	DET
cana-1619	123	22	mild	mild	ADJ
cana-1619	123	23	random	random	ADJ
cana-1619	123	24	solution	solution	NOUN
cana-1619	123	25	on	on	ADP
cana-1619	123	26	the	the	DET
cana-1619	123	27	interval	interval	NOUN
cana-1619	123	28	(	(	PUNCT
cana-1619	123	29	0	0	NUM
cana-1619	123	30	,	,	PUNCT
cana-1619	123	31	ϱ	ϱ	ADP
cana-1619	123	32	]	]	PUNCT
cana-1619	123	33	.	.	PUNCT
cana-1619	124	1	proof	proof	NOUN
cana-1619	124	2	:	:	PUNCT
cana-1619	124	3	let	let	VERB
cana-1619	124	4	us	we	PRON
cana-1619	124	5	consider	consider	VERB
cana-1619	124	6	a	a	DET
cana-1619	124	7	map	map	NOUN
cana-1619	124	8	(	(	PUNCT
cana-1619	124	9	γ(ℵ	γ(ℵ	PROPN
cana-1619	124	10	)	)	PUNCT
cana-1619	124	11	):	):	PUNCT
cana-1619	125	1	ω	ω	NUM
cana-1619	125	2	×	×	NOUN
cana-1619	125	3	pcδ	pcδ	NOUN
cana-1619	125	4	=	=	PUNCT
cana-1619	126	1	[	[	X
cana-1619	126	2	(	(	PUNCT
cana-1619	126	3	−δ	−δ	ADJ
cana-1619	126	4	,	,	PUNCT
cana-1619	126	5	ϱ	ϱ	ADP
cana-1619	126	6	]	]	PUNCT
cana-1619	126	7	,	,	PUNCT
cana-1619	126	8	𝒮	𝒮	PROPN
cana-1619	126	9	]	]	PUNCT
cana-1619	126	10	→	→	PUNCT
cana-1619	126	11	pcδ	pcδ	X
cana-1619	126	12	be	be	AUX
cana-1619	126	13	a	a	DET
cana-1619	126	14	random	random	ADJ
cana-1619	126	15	operator	operator	NOUN
cana-1619	126	16	is	be	AUX
cana-1619	126	17	defined	define	VERB
cana-1619	126	18	by	by	ADP
cana-1619	126	19	(	(	PUNCT
cana-1619	126	20	γ(ℵ))ζ(h	γ(ℵ))ζ(h	NOUN
cana-1619	126	21	)	)	PUNCT
cana-1619	127	1	where	where	SCONJ
cana-1619	127	2	h	h	NOUN
cana-1619	127	3	∈	∈	PROPN
cana-1619	127	4	(	(	PUNCT
cana-1619	127	5	−δ	−δ	ADJ
cana-1619	127	6	,	,	PUNCT
cana-1619	127	7	ϱ	ϱ	ADP
cana-1619	127	8	]	]	X
cana-1619	127	9	(	(	PUNCT
cana-1619	127	10	γ(ℵ))ζ(h	γ(ℵ))ζ(h	NOUN
cana-1619	127	11	,	,	PUNCT
cana-1619	127	12	ℵ	ℵ	NOUN
cana-1619	127	13	)	)	PUNCT
cana-1619	127	14	=	=	SYM
cana-1619	127	15	{	{	PUNCT
cana-1619	127	16	υ(h	υ(h	NOUN
cana-1619	127	17	,	,	PUNCT
cana-1619	127	18	ℵ	ℵ	NOUN
cana-1619	127	19	)	)	PUNCT
cana-1619	127	20	,	,	PUNCT
cana-1619	127	21	h	h	NOUN
cana-1619	127	22	∈	∈	PROPN
cana-1619	127	23	(	(	PUNCT
cana-1619	127	24	−δ	−δ	ADJ
cana-1619	127	25	,	,	PUNCT
cana-1619	127	26	ϱ	ϱ	ADP
cana-1619	127	27	]	]	X
cana-1619	127	28	t1(h)ϕ0(ℵ	t1(h)ϕ0(ℵ	X
cana-1619	127	29	)	)	PUNCT
cana-1619	127	30	+	+	CCONJ
cana-1619	127	31	t2(h)[ϕ′0(ℵ	t2(h)[ϕ′0(ℵ	NUM
cana-1619	127	32	)	)	PUNCT
cana-1619	127	33	+	+	CCONJ
cana-1619	128	1	ρ(0	ρ(0	PROPN
cana-1619	128	2	,	,	PUNCT
cana-1619	128	3	ϕ0(ℵ	ϕ0(ℵ	PROPN
cana-1619	128	4	)	)	PUNCT
cana-1619	128	5	,	,	PUNCT
cana-1619	128	6	ℵ	ℵ	NOUN
cana-1619	128	7	)	)	PUNCT
cana-1619	128	8	]	]	PUNCT
cana-1619	129	1	−	−	PROPN
cana-1619	129	2	∫	∫	PROPN
cana-1619	129	3	h	h	NOUN
cana-1619	129	4	0	0	PUNCT
cana-1619	130	1	t1(h	t1(h	ADP
cana-1619	130	2	−	−	NOUN
cana-1619	130	3	ϖ)ρ(ϖ	ϖ)ρ(ϖ	NOUN
cana-1619	130	4	,	,	PUNCT
cana-1619	130	5	ζϖ	ζϖ	NOUN
cana-1619	130	6	(	(	PUNCT
cana-1619	130	7	.	.	PUNCT
cana-1619	130	8	,	,	PUNCT
cana-1619	130	9	ℵ	ℵ	NOUN
cana-1619	130	10	)	)	PUNCT
cana-1619	130	11	,	,	PUNCT
cana-1619	130	12	ℵ)dϖ	ℵ)dϖ	PROPN
cana-1619	130	13	+	+	NUM
cana-1619	130	14	∫	∫	PROPN
cana-1619	130	15	h	h	NOUN
cana-1619	130	16	0	0	PUNCT
cana-1619	131	1	t2(h	t2(h	PRON
cana-1619	131	2	−	−	PROPN
cana-1619	131	3	ϖ)υ(ϖ	ϖ)υ(ϖ	NOUN
cana-1619	131	4	,	,	PUNCT
cana-1619	131	5	ζϖ	ζϖ	NOUN
cana-1619	131	6	(	(	PUNCT
cana-1619	131	7	.	.	PUNCT
cana-1619	131	8	,	,	PUNCT
cana-1619	131	9	ℵ	ℵ	NOUN
cana-1619	131	10	)	)	PUNCT
cana-1619	131	11	,	,	PUNCT
cana-1619	132	1	ℵ)dϖ	ℵ)dϖ	PROPN
cana-1619	132	2	+	+	PROPN
cana-1619	132	3	∑0	∑0	PROPN
cana-1619	132	4	<	<	X
cana-1619	132	5	hξ	hξ	X
cana-1619	132	6	<	<	X
cana-1619	132	7	h	h	PRON
cana-1619	132	8	t1(h	t1(h	X
cana-1619	132	9	−	−	NOUN
cana-1619	132	10	hξ)iξ(ζ(hξ	hξ)iξ(ζ(hξ	ADJ
cana-1619	132	11	,	,	PUNCT
cana-1619	132	12	ℵ	ℵ	NOUN
cana-1619	132	13	)	)	PUNCT
cana-1619	132	14	)	)	PUNCT
cana-1619	133	1	+	+	CCONJ
cana-1619	133	2	∑0	∑0	PROPN
cana-1619	133	3	<	<	X
cana-1619	133	4	hξ	hξ	X
cana-1619	133	5	<	<	X
cana-1619	133	6	h	h	NOUN
cana-1619	133	7	t2(h	t2(h	X
cana-1619	133	8	−	−	PROPN
cana-1619	133	9	hξ)i′ξ(ζ(hξ	hξ)i′ξ(ζ(hξ	PROPN
cana-1619	133	10	,	,	PUNCT
cana-1619	133	11	ℵ	ℵ	NOUN
cana-1619	133	12	)	)	PUNCT
cana-1619	133	13	)	)	PUNCT
cana-1619	133	14	,	,	PUNCT
cana-1619	133	15	h	h	NOUN
cana-1619	133	16	,	,	PUNCT
cana-1619	133	17	ϖ	ϖ	PROPN
cana-1619	133	18	∈	∈	PROPN
cana-1619	133	19	j	j	PROPN
cana-1619	133	20	(	(	PUNCT
cana-1619	133	21	6	6	NUM
cana-1619	133	22	)	)	PUNCT
cana-1619	133	23	we	we	PRON
cana-1619	133	24	aim	aim	VERB
cana-1619	133	25	to	to	PART
cana-1619	133	26	illustrate	illustrate	VERB
cana-1619	133	27	that	that	PRON
cana-1619	133	28	(	(	PUNCT
cana-1619	133	29	γ(ℵ	γ(ℵ	PROPN
cana-1619	133	30	)	)	PUNCT
cana-1619	133	31	)	)	PUNCT
cana-1619	133	32	satisfies	satisfy	VERB
cana-1619	133	33	all	all	DET
cana-1619	133	34	conditions	condition	NOUN
cana-1619	133	35	outlined	outline	VERB
cana-1619	133	36	in	in	ADP
cana-1619	133	37	lemma	lemma	PROPN
cana-1619	133	38	2.1	2.1	NUM
cana-1619	133	39	.	.	PUNCT
cana-1619	133	40	to	to	PART
cana-1619	133	41	enhance	enhance	VERB
cana-1619	133	42	clarity	clarity	NOUN
cana-1619	133	43	,	,	PUNCT
cana-1619	133	44	the	the	DET
cana-1619	133	45	proof	proof	NOUN
cana-1619	133	46	will	will	AUX
cana-1619	133	47	be	be	AUX
cana-1619	133	48	broken	break	VERB
cana-1619	133	49	down	down	ADP
cana-1619	133	50	into	into	ADP
cana-1619	133	51	many	many	ADJ
cana-1619	133	52	stages	stage	NOUN
cana-1619	133	53	.	.	PUNCT
cana-1619	134	1	step	step	NOUN
cana-1619	134	2	1	1	NUM
cana-1619	134	3	:	:	PUNCT
cana-1619	134	4	the	the	DET
cana-1619	134	5	mapping	mapping	NOUN
cana-1619	134	6	(	(	PUNCT
cana-1619	134	7	γ(ℵ	γ(ℵ	PROPN
cana-1619	134	8	)	)	PUNCT
cana-1619	134	9	)	)	PUNCT
cana-1619	134	10	takes	take	VERB
cana-1619	134	11	sets	set	NOUN
cana-1619	134	12	that	that	PRON
cana-1619	134	13	are	be	AUX
cana-1619	134	14	bounded	bound	VERB
cana-1619	134	15	and	and	CCONJ
cana-1619	134	16	maps	map	VERB
cana-1619	134	17	them	they	PRON
cana-1619	134	18	into	into	ADP
cana-1619	134	19	other	other	ADJ
cana-1619	134	20	bounded	bound	VERB
cana-1619	134	21	sets	set	NOUN
cana-1619	134	22	.	.	PUNCT
cana-1619	135	1	to	to	PART
cana-1619	135	2	demonstrate	demonstrate	VERB
cana-1619	135	3	this	this	PRON
cana-1619	135	4	,	,	PUNCT
cana-1619	135	5	it	it	PRON
cana-1619	135	6	’s	’	VERB
cana-1619	135	7	sufficient	sufficient	ADJ
cana-1619	135	8	to	to	PART
cana-1619	135	9	establish	establish	VERB
cana-1619	135	10	that	that	SCONJ
cana-1619	135	11	there	there	PRON
cana-1619	135	12	is	be	VERB
cana-1619	135	13	a	a	DET
cana-1619	135	14	+	+	PROPN
cana-1619	135	15	ve	ve	NOUN
cana-1619	135	16	constant	constant	ADJ
cana-1619	135	17	r(ℵ	r(ℵ	NOUN
cana-1619	135	18	)	)	PUNCT
cana-1619	135	19	so	so	SCONJ
cana-1619	135	20	that	that	SCONJ
cana-1619	135	21	for	for	ADP
cana-1619	135	22	every	every	DET
cana-1619	135	23	ζ	ζ	PROPN
cana-1619	135	24	∈	∈	PROPN
cana-1619	135	25	ℬr(δ	ℬr(δ	NOUN
cana-1619	135	26	)	)	PUNCT
cana-1619	135	27	,	,	PUNCT
cana-1619	135	28	where	where	SCONJ
cana-1619	135	29	δ	δ	PROPN
cana-1619	135	30	is	be	AUX
cana-1619	135	31	defined	define	VERB
cana-1619	135	32	as	as	SCONJ
cana-1619	135	33	follows	follow	VERB
cana-1619	135	34	:	:	PUNCT
cana-1619	135	35	communications	communication	NOUN
cana-1619	135	36	on	on	ADP
cana-1619	135	37	applied	apply	VERB
cana-1619	135	38	nonlinear	nonlinear	ADJ
cana-1619	135	39	analysis	analysis	NOUN
cana-1619	135	40	issn	issn	NOUN
cana-1619	135	41	:	:	PUNCT
cana-1619	135	42	1074	1074	NUM
cana-1619	135	43	-	-	PUNCT
cana-1619	135	44	133x	133x	NUM
cana-1619	135	45	vol	vol	NOUN
cana-1619	135	46	32	32	NUM
cana-1619	135	47	no	no	NOUN
cana-1619	135	48	.	.	NOUN
cana-1619	135	49	1	1	NUM
cana-1619	135	50	(	(	PUNCT
cana-1619	135	51	2025	2025	NUM
cana-1619	135	52	)	)	PUNCT
cana-1619	135	53	41	41	NUM
cana-1619	135	54	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-1619	135	55	ℬr(δ	ℬr(δ	NOUN
cana-1619	135	56	):	):	PUNCT
cana-1619	135	57	=	=	SYM
cana-1619	135	58	{	{	PUNCT
cana-1619	135	59	ζ	ζ	NOUN
cana-1619	135	60	∈	∈	PROPN
cana-1619	135	61	pcδ	pcδ	NOUN
cana-1619	135	62	:	:	PUNCT
cana-1619	135	63	sup	sup	NOUN
cana-1619	135	64	δ≤h≤ϱ	δ≤h≤ϱ	PUNCT
cana-1619	135	65	∥	∥	X
cana-1619	135	66	ζ(h	ζ(h	NOUN
cana-1619	135	67	,	,	PUNCT
cana-1619	135	68	ℵ	ℵ	NOUN
cana-1619	135	69	)	)	PUNCT
cana-1619	135	70	∥≤	∥≤	PROPN
cana-1619	135	71	r(ℵ	r(ℵ	PROPN
cana-1619	135	72	)	)	PUNCT
cana-1619	135	73	}	}	PUNCT
cana-1619	135	74	one	one	PRON
cana-1619	135	75	has	have	AUX
cana-1619	135	76	∥	∥	NUM
cana-1619	135	77	(	(	PUNCT
cana-1619	135	78	γ(ℵ))ζ	γ(ℵ))ζ	PROPN
cana-1619	135	79	∥pc≤	∥pc≤	NUM
cana-1619	135	80	r(ℵ	r(ℵ	PROPN
cana-1619	135	81	)	)	PUNCT
cana-1619	135	82	.	.	PUNCT
cana-1619	136	1	||(γ(ℵ))𝜁(ℎ)||	||(γ(ℵ))𝜁(ℎ)||	NOUN
cana-1619	136	2	≤	≤	PUNCT
cana-1619	136	3	||𝑇1(ℎ)𝜙0(ℵ)||	||𝑇1(ℎ)𝜙0(ℵ)||	NOUN
cana-1619	136	4	+	+	CCONJ
cana-1619	136	5	||𝑇2(ℎ)[𝜙′0(ℵ	||𝑇2(ℎ)[𝜙′0(ℵ	ADJ
cana-1619	136	6	)	)	PUNCT
cana-1619	137	1	+	+	CCONJ
cana-1619	137	2	𝜌(0	𝜌(0	PROPN
cana-1619	137	3	,	,	PUNCT
cana-1619	137	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	137	5	)	)	PUNCT
cana-1619	137	6	,	,	PUNCT
cana-1619	137	7	ℵ)]||	ℵ)]||	PUNCT
cana-1619	138	1	+	+	ADJ
cana-1619	138	2	∫	∫	PROPN
cana-1619	138	3	ℎ	ℎ	PART
cana-1619	138	4	0	0	NUM
cana-1619	138	5	||𝑇1(ℎ	||𝑇1(ℎ	NOUN
cana-1619	138	6	−	−	PROPN
cana-1619	138	7	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	NOUN
cana-1619	138	8	,	,	PUNCT
cana-1619	138	9	𝜁𝜛	𝜁𝜛	ADV
cana-1619	138	10	(	(	PUNCT
cana-1619	138	11	.	.	PUNCT
cana-1619	138	12	,	,	PUNCT
cana-1619	138	13	ℵ	ℵ	NOUN
cana-1619	138	14	)	)	PUNCT
cana-1619	138	15	,	,	PUNCT
cana-1619	138	16	ℵ)𝑑𝜛||	ℵ)𝑑𝜛||	NOUN
cana-1619	138	17	+	+	CCONJ
cana-1619	138	18	||∫	||∫	ADJ
cana-1619	138	19	ℎ	ℎ	NOUN
cana-1619	138	20	0	0	PUNCT
cana-1619	139	1	𝑇2(ℎ	𝑇2(ℎ	ADJ
cana-1619	139	2	−	−	NOUN
cana-1619	139	3	𝜛)υ(𝜛	𝜛)υ(𝜛	NOUN
cana-1619	139	4	,	,	PUNCT
cana-1619	139	5	𝜁𝜛	𝜁𝜛	ADV
cana-1619	139	6	(	(	PUNCT
cana-1619	139	7	.	.	PUNCT
cana-1619	139	8	,	,	PUNCT
cana-1619	139	9	ℵ	ℵ	NOUN
cana-1619	139	10	)	)	PUNCT
cana-1619	139	11	,	,	PUNCT
cana-1619	139	12	ℵ)||𝑑𝜛	ℵ)||𝑑𝜛	NOUN
cana-1619	140	1	+	+	PROPN
cana-1619	140	2	||	||	ADV
cana-1619	140	3	∑	∑	PUNCT
cana-1619	140	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	VERB
cana-1619	140	5	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	140	6	−	−	PROPN
cana-1619	141	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	141	2	,	,	PUNCT
cana-1619	141	3	ℵ))||	ℵ))||	NOUN
cana-1619	142	1	+	+	CCONJ
cana-1619	142	2	||	||	NUM
cana-1619	142	3	∑	∑	PUNCT
cana-1619	142	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	142	5	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	142	6	−	−	PROPN
cana-1619	142	7	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	142	8	,	,	PUNCT
cana-1619	142	9	ℵ))||𝑑𝜛	ℵ))||𝑑𝜛	VERB
cana-1619	142	10	≤	≤	ADJ
cana-1619	142	11	𝜗||𝜙0(ℵ)||	𝜗||𝜙0(ℵ)||	PROPN
cana-1619	142	12	+	+	NUM
cana-1619	142	13	𝜗𝑎||𝜙′0(ℵ	𝜗𝑎||𝜙′0(ℵ	PROPN
cana-1619	142	14	)	)	PUNCT
cana-1619	142	15	+	+	SYM
cana-1619	143	1	𝜌(0	𝜌(0	PROPN
cana-1619	143	2	,	,	PUNCT
cana-1619	143	3	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	143	4	)	)	PUNCT
cana-1619	143	5	,	,	PUNCT
cana-1619	143	6	ℵ)||	ℵ)||	PROPN
cana-1619	143	7	+	+	NOUN
cana-1619	143	8	𝜗∫	𝜗∫	VERB
cana-1619	143	9	ℎ	ℎ	PROPN
cana-1619	143	10	0	0	NUM
cana-1619	143	11	||𝜌(𝜛	||𝜌(𝜛	NOUN
cana-1619	143	12	,	,	PUNCT
cana-1619	143	13	𝜁𝜛	𝜁𝜛	ADV
cana-1619	143	14	(	(	PUNCT
cana-1619	143	15	.	.	PUNCT
cana-1619	143	16	,	,	PUNCT
cana-1619	143	17	ℵ	ℵ	NOUN
cana-1619	143	18	)	)	PUNCT
cana-1619	143	19	,	,	PUNCT
cana-1619	143	20	ℵ)𝑑𝜛||	ℵ)𝑑𝜛||	NOUN
cana-1619	144	1	+	+	NOUN
cana-1619	144	2	𝜗𝑎∫	𝜗𝑎∫	NOUN
cana-1619	144	3	ℎ	ℎ	NOUN
cana-1619	144	4	0	0	NUM
cana-1619	144	5	||υ(𝜛	||υ(𝜛	ADV
cana-1619	144	6	,	,	PUNCT
cana-1619	144	7	𝜁𝜛	𝜁𝜛	ADV
cana-1619	144	8	(	(	PUNCT
cana-1619	144	9	.	.	PUNCT
cana-1619	144	10	,	,	PUNCT
cana-1619	144	11	ℵ	ℵ	NOUN
cana-1619	144	12	)	)	PUNCT
cana-1619	144	13	,	,	PUNCT
cana-1619	144	14	ℵ)||𝑑𝜛	ℵ)||𝑑𝜛	NOUN
cana-1619	144	15	+	+	CCONJ
cana-1619	144	16	𝜗	𝜗	PROPN
cana-1619	144	17	∑	∑	ADP
cana-1619	144	18	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	144	19	||𝐼𝜉(𝜁(ℎ𝜉	||𝐼𝜉(𝜁(ℎ𝜉	X
cana-1619	144	20	,	,	PUNCT
cana-1619	144	21	ℵ))||	ℵ))||	NOUN
cana-1619	144	22	+	+	CCONJ
cana-1619	144	23	𝜗𝑎	𝜗𝑎	ADP
cana-1619	144	24	∑	∑	ADV
cana-1619	144	25	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	144	26	||𝐼′𝜉(𝜁(ℎ𝜉	||𝐼′𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	144	27	,	,	PUNCT
cana-1619	144	28	ℵ))||	ℵ))||	NOUN
cana-1619	144	29	≤	≤	PUNCT
cana-1619	145	1	𝜗||𝜙0||	𝜗||𝜙0||	PROPN
cana-1619	145	2	+	+	NUM
cana-1619	145	3	𝜗𝑎||𝜙′0(ℵ	𝜗𝑎||𝜙′0(ℵ	PROPN
cana-1619	145	4	)	)	PUNCT
cana-1619	145	5	+	+	SYM
cana-1619	145	6	𝜌(0	𝜌(0	PROPN
cana-1619	145	7	,	,	PUNCT
cana-1619	145	8	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	145	9	)	)	PUNCT
cana-1619	145	10	,	,	PUNCT
cana-1619	145	11	ℵ)||	ℵ)||	PROPN
cana-1619	145	12	+	+	NOUN
cana-1619	145	13	𝜗∫	𝜗∫	VERB
cana-1619	145	14	ℎ	ℎ	X
cana-1619	145	15	0	0	PUNCT
cana-1619	146	1	[	[	PUNCT
cana-1619	146	2	sup	sup	NOUN
cana-1619	146	3	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	146	4	]	]	PUNCT
cana-1619	146	5	||𝜁𝜛	||𝜁𝜛	NOUN
cana-1619	146	6	(	(	PUNCT
cana-1619	146	7	.	.	PUNCT
cana-1619	146	8	,	,	PUNCT
cana-1619	146	9	ℵ	ℵ	NOUN
cana-1619	146	10	)	)	PUNCT
cana-1619	146	11	,	,	PUNCT
cana-1619	146	12	ℵ||𝒟	ℵ||𝒟	NOUN
cana-1619	146	13	𝛽0	𝛽0	VERB
cana-1619	146	14	+	+	CCONJ
cana-1619	146	15	𝑑0(ℵ)]𝑑𝜛	𝑑0(ℵ)]𝑑𝜛	NOUN
cana-1619	147	1	+	+	VERB
cana-1619	147	2	𝜗𝑎∫	𝜗𝑎∫	NOUN
cana-1619	147	3	ℎ	ℎ	NOUN
cana-1619	147	4	0	0	PUNCT
cana-1619	148	1	[	[	PUNCT
cana-1619	148	2	sup	sup	NOUN
cana-1619	148	3	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	148	4	]	]	PUNCT
cana-1619	148	5	||𝜁𝜛	||𝜁𝜛	NOUN
cana-1619	148	6	(	(	PUNCT
cana-1619	148	7	.	.	PUNCT
cana-1619	148	8	,	,	PUNCT
cana-1619	148	9	ℵ	ℵ	NOUN
cana-1619	148	10	)	)	PUNCT
cana-1619	148	11	,	,	PUNCT
cana-1619	148	12	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	148	13	𝛼0	𝛼0	NOUN
cana-1619	149	1	+	+	CCONJ
cana-1619	149	2	𝑏0(ℵ)]𝑑𝜛	𝑏0(ℵ)]𝑑𝜛	PROPN
cana-1619	149	3	+	+	CCONJ
cana-1619	149	4	𝜗	𝜗	NOUN
cana-1619	149	5	∑	∑	ADP
cana-1619	149	6	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	VERB
cana-1619	149	7	𝑎𝜉(ℵ)||𝜁(ℎ𝜉	𝑎𝜉(ℵ)||𝜁(ℎ𝜉	NUM
cana-1619	149	8	,	,	PUNCT
cana-1619	149	9	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	149	10	𝛼𝜉	𝛼𝜉	NOUN
cana-1619	150	1	+	+	NOUN
cana-1619	150	2	𝜗𝑎	𝜗𝑎	ADV
cana-1619	150	3	∑	∑	ADV
cana-1619	150	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	150	5	𝑎′𝜉(ℵ)||𝜁(ℎ𝜉	𝑎′𝜉(ℵ)||𝜁(ℎ𝜉	PROPN
cana-1619	150	6	,	,	PUNCT
cana-1619	150	7	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	150	8	𝛼𝜉	𝛼𝜉	NUM
cana-1619	150	9	≤	≤	PROPN
cana-1619	150	10	𝜗||𝜙0||	𝜗||𝜙0||	PROPN
cana-1619	150	11	+	+	NUM
cana-1619	150	12	𝜗𝑎||𝜙′0(ℵ	𝜗𝑎||𝜙′0(ℵ	PROPN
cana-1619	150	13	)	)	PUNCT
cana-1619	150	14	+	+	SYM
cana-1619	150	15	𝜌(0	𝜌(0	PROPN
cana-1619	150	16	,	,	PUNCT
cana-1619	150	17	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	150	18	)	)	PUNCT
cana-1619	150	19	,	,	PUNCT
cana-1619	150	20	ℵ)||	ℵ)||	NOUN
cana-1619	150	21	+	+	NOUN
cana-1619	150	22	𝜗𝑎ℎ𝑏0(ℵ	𝜗𝑎ℎ𝑏0(ℵ	ADJ
cana-1619	150	23	)	)	PUNCT
cana-1619	150	24	+	+	NUM
cana-1619	150	25	𝜗ℎ𝑑0(ℵ	𝜗ℎ𝑑0(ℵ	X
cana-1619	150	26	)	)	PUNCT
cana-1619	151	1	+	+	X
cana-1619	151	2	𝜗	𝜗	SYM
cana-1619	151	3	∑	∑	ADP
cana-1619	151	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	VERB
cana-1619	151	5	𝑎𝜉(ℵ)||𝜁(ℎ𝜉	𝑎𝜉(ℵ)||𝜁(ℎ𝜉	NUM
cana-1619	151	6	,	,	PUNCT
cana-1619	151	7	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	151	8	𝛼𝜉	𝛼𝜉	NOUN
cana-1619	152	1	+	+	NOUN
cana-1619	152	2	𝜗𝑎	𝜗𝑎	ADV
cana-1619	152	3	∑	∑	ADV
cana-1619	152	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	152	5	𝑎′𝜉(ℵ)||𝜁(ℎ𝜉	𝑎′𝜉(ℵ)||𝜁(ℎ𝜉	PROPN
cana-1619	152	6	,	,	PUNCT
cana-1619	152	7	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	152	8	𝛼𝜉	𝛼𝜉	NOUN
cana-1619	152	9	+	+	NUM
cana-1619	152	10	𝜗𝑎∫	𝜗𝑎∫	NOUN
cana-1619	152	11	ℎ	ℎ	NOUN
cana-1619	152	12	0	0	NUM
cana-1619	152	13	||	||	NUM
cana-1619	152	14	[	[	PUNCT
cana-1619	152	15	sup	sup	NOUN
cana-1619	152	16	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	152	17	]	]	PUNCT
cana-1619	152	18	||𝜁𝜛	||𝜁𝜛	NOUN
cana-1619	152	19	(	(	PUNCT
cana-1619	152	20	.	.	PUNCT
cana-1619	152	21	,	,	PUNCT
cana-1619	152	22	ℵ	ℵ	NOUN
cana-1619	152	23	)	)	PUNCT
cana-1619	152	24	,	,	PUNCT
cana-1619	152	25	ℵ||𝒟	ℵ||𝒟	PRON
cana-1619	152	26	𝛼0𝑑𝜛	𝛼0𝑑𝜛	PUNCT
cana-1619	153	1	+	+	CCONJ
cana-1619	153	2	𝜗∫	𝜗∫	VERB
cana-1619	153	3	ℎ	ℎ	PROPN
cana-1619	153	4	0	0	NUM
cana-1619	153	5	||	||	NUM
cana-1619	153	6	[	[	PUNCT
cana-1619	153	7	sup	sup	NOUN
cana-1619	153	8	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	153	9	]	]	PUNCT
cana-1619	153	10	||𝜁𝜛	||𝜁𝜛	NOUN
cana-1619	153	11	(	(	PUNCT
cana-1619	153	12	.	.	PUNCT
cana-1619	153	13	,	,	PUNCT
cana-1619	153	14	ℵ	ℵ	NOUN
cana-1619	153	15	)	)	PUNCT
cana-1619	153	16	,	,	PUNCT
cana-1619	153	17	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	153	18	𝛽0𝑑𝜛	𝛽0𝑑𝜛	ADP
cana-1619	153	19	≤	≤	NOUN
cana-1619	153	20	𝑅(ℵ	𝑅(ℵ	NUM
cana-1619	153	21	)	)	PUNCT
cana-1619	153	22	hence	hence	ADV
cana-1619	153	23	(	(	PUNCT
cana-1619	153	24	γ(ℵ	γ(ℵ	PROPN
cana-1619	153	25	)	)	PUNCT
cana-1619	153	26	)	)	PUNCT
cana-1619	153	27	is	be	AUX
cana-1619	153	28	bounded	bound	VERB
cana-1619	153	29	set	set	VERB
cana-1619	153	30	in	in	ADP
cana-1619	153	31	𝑃𝐶𝛿.	𝑃𝐶𝛿.	VERB
cana-1619	153	32	step	step	NOUN
cana-1619	153	33	2	2	NUM
cana-1619	153	34	:	:	PUNCT
cana-1619	153	35	we	we	PRON
cana-1619	153	36	now	now	ADV
cana-1619	153	37	show	show	VERB
cana-1619	153	38	that	that	SCONJ
cana-1619	153	39	(	(	PUNCT
cana-1619	153	40	γ(ℵ	γ(ℵ	PROPN
cana-1619	153	41	)	)	PUNCT
cana-1619	153	42	)	)	PUNCT
cana-1619	153	43	is	be	AUX
cana-1619	153	44	continuous	continuous	ADJ
cana-1619	153	45	on	on	ADP
cana-1619	153	46	ℬ𝑟(𝛿	ℬ𝑟(𝛿	NUM
cana-1619	153	47	)	)	PUNCT
cana-1619	153	48	.	.	PUNCT
cana-1619	154	1	let	let	VERB
cana-1619	154	2	us	we	PRON
cana-1619	154	3	consider	consider	VERB
cana-1619	154	4	that	that	PRON
cana-1619	154	5	for	for	ADP
cana-1619	154	6	𝜁1	𝜁1	ADJ
cana-1619	154	7	,	,	PUNCT
cana-1619	154	8	𝜁2	𝜁2	NOUN
cana-1619	154	9	∈	∈	PROPN
cana-1619	154	10	ℬ𝑟(𝛿	ℬ𝑟(𝛿	NOUN
cana-1619	154	11	)	)	PUNCT
cana-1619	154	12	,	,	PUNCT
cana-1619	154	13	ℎ	ℎ	PROPN
cana-1619	154	14	∈	∈	PROPN
cana-1619	154	15	𝐽	𝐽	PROPN
cana-1619	154	16	,	,	PUNCT
cana-1619	154	17	communications	communication	NOUN
cana-1619	154	18	on	on	ADP
cana-1619	154	19	applied	apply	VERB
cana-1619	154	20	nonlinear	nonlinear	ADJ
cana-1619	154	21	analysis	analysis	NOUN
cana-1619	154	22	issn	issn	NOUN
cana-1619	154	23	:	:	PUNCT
cana-1619	154	24	1074	1074	NUM
cana-1619	154	25	-	-	PUNCT
cana-1619	154	26	133x	133x	NUM
cana-1619	154	27	vol	vol	NOUN
cana-1619	154	28	32	32	NUM
cana-1619	155	1	no	no	NOUN
cana-1619	155	2	.	.	NOUN
cana-1619	155	3	1	1	NUM
cana-1619	155	4	(	(	PUNCT
cana-1619	155	5	2025	2025	NUM
cana-1619	155	6	)	)	PUNCT
cana-1619	155	7	42	42	NUM
cana-1619	155	8	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	155	9	||(γ(ℵ))𝜁1(ℎ	||(γ(ℵ))𝜁1(ℎ	NOUN
cana-1619	155	10	)	)	PUNCT
cana-1619	155	11	−	−	PROPN
cana-1619	156	1	(	(	PUNCT
cana-1619	156	2	γ(ℵ))𝜁2(ℎ)||	γ(ℵ))𝜁2(ℎ)||	PROPN
cana-1619	156	3	≤	≤	PROPN
cana-1619	156	4	||∫	||∫	ADP
cana-1619	156	5	ℎ	ℎ	PROPN
cana-1619	156	6	0	0	PROPN
cana-1619	156	7	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	156	8	−	−	PROPN
cana-1619	156	9	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	PROPN
cana-1619	156	10	,	,	PUNCT
cana-1619	156	11	𝜁1,𝜛	𝜁1,𝜛	PROPN
cana-1619	156	12	(	(	PUNCT
cana-1619	156	13	.	.	PUNCT
cana-1619	156	14	,	,	PUNCT
cana-1619	156	15	ℵ	ℵ	NOUN
cana-1619	156	16	)	)	PUNCT
cana-1619	156	17	,	,	PUNCT
cana-1619	156	18	ℵ	ℵ	NOUN
cana-1619	156	19	)	)	PUNCT
cana-1619	156	20	−	−	PROPN
cana-1619	156	21	𝜌(𝜛	𝜌(𝜛	PROPN
cana-1619	156	22	,	,	PUNCT
cana-1619	156	23	𝜁2,𝜛	𝜁2,𝜛	PROPN
cana-1619	156	24	(	(	PUNCT
cana-1619	156	25	.	.	PUNCT
cana-1619	156	26	,	,	PUNCT
cana-1619	156	27	ℵ	ℵ	NOUN
cana-1619	156	28	)	)	PUNCT
cana-1619	156	29	,	,	PUNCT
cana-1619	156	30	ℵ)||𝑑𝜛	ℵ)||𝑑𝜛	NOUN
cana-1619	157	1	+	+	PROPN
cana-1619	157	2	||∫	||∫	ADJ
cana-1619	157	3	ℎ	ℎ	NOUN
cana-1619	157	4	0	0	PUNCT
cana-1619	157	5	𝑇2(ℎ	𝑇2(ℎ	ADJ
cana-1619	157	6	−	−	PROPN
cana-1619	157	7	𝜛)υ(𝜛	𝜛)υ(𝜛	NOUN
cana-1619	157	8	,	,	PUNCT
cana-1619	157	9	𝜁1,𝜛	𝜁1,𝜛	PROPN
cana-1619	157	10	(	(	PUNCT
cana-1619	157	11	.	.	PUNCT
cana-1619	157	12	,	,	PUNCT
cana-1619	157	13	ℵ	ℵ	NOUN
cana-1619	157	14	)	)	PUNCT
cana-1619	157	15	,	,	PUNCT
cana-1619	157	16	ℵ	ℵ	NOUN
cana-1619	157	17	)	)	PUNCT
cana-1619	157	18	−	−	ADP
cana-1619	157	19	υ(𝜛	υ(𝜛	PROPN
cana-1619	157	20	,	,	PUNCT
cana-1619	157	21	𝜁2,𝜛	𝜁2,𝜛	PROPN
cana-1619	157	22	(	(	PUNCT
cana-1619	157	23	.	.	PUNCT
cana-1619	157	24	,	,	PUNCT
cana-1619	157	25	ℵ	ℵ	NOUN
cana-1619	157	26	)	)	PUNCT
cana-1619	157	27	,	,	PUNCT
cana-1619	157	28	ℵ)||𝑑𝜛	ℵ)||𝑑𝜛	NOUN
cana-1619	158	1	+	+	PROPN
cana-1619	158	2	||	||	ADV
cana-1619	158	3	∑	∑	PUNCT
cana-1619	158	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	VERB
cana-1619	158	5	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	158	6	−	−	PROPN
cana-1619	159	1	ℎ𝜉)[𝐼𝜉(𝜁1(ℎ𝜉	ℎ𝜉)[𝐼𝜉(𝜁1(ℎ𝜉	PROPN
cana-1619	159	2	,	,	PUNCT
cana-1619	159	3	ℵ	ℵ	NOUN
cana-1619	159	4	)	)	PUNCT
cana-1619	159	5	)	)	PUNCT
cana-1619	160	1	−	−	PROPN
cana-1619	160	2	𝐼𝜉(𝜁2(ℎ𝜉	𝐼𝜉(𝜁2(ℎ𝜉	NOUN
cana-1619	160	3	,	,	PUNCT
cana-1619	160	4	ℵ))]||	ℵ))]||	ADJ
cana-1619	160	5	+	+	ADV
cana-1619	160	6	||	||	ADJ
cana-1619	160	7	∑	∑	PUNCT
cana-1619	160	8	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	160	9	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	160	10	−	−	PROPN
cana-1619	160	11	ℎ𝜉)[𝐼′𝜉(𝜁1(ℎ𝜉	ℎ𝜉)[𝐼′𝜉(𝜁1(ℎ𝜉	NOUN
cana-1619	160	12	,	,	PUNCT
cana-1619	160	13	ℵ	ℵ	NOUN
cana-1619	160	14	)	)	PUNCT
cana-1619	160	15	)	)	PUNCT
cana-1619	161	1	−	−	PROPN
cana-1619	161	2	𝐼′𝜉(𝜁2(ℎ𝜉	𝐼′𝜉(𝜁2(ℎ𝜉	NOUN
cana-1619	161	3	,	,	PUNCT
cana-1619	161	4	ℵ))]||𝑑𝜛	ℵ))]||𝑑𝜛	NOUN
cana-1619	161	5	≤	≤	NOUN
cana-1619	161	6	𝜗∫	𝜗∫	VERB
cana-1619	161	7	ℎ	ℎ	PROPN
cana-1619	161	8	0	0	NUM
cana-1619	161	9	||𝜌(𝜛	||𝜌(𝜛	NOUN
cana-1619	161	10	,	,	PUNCT
cana-1619	161	11	𝜁1,𝜛	𝜁1,𝜛	PROPN
cana-1619	161	12	(	(	PUNCT
cana-1619	161	13	.	.	PUNCT
cana-1619	161	14	,	,	PUNCT
cana-1619	161	15	ℵ	ℵ	NOUN
cana-1619	161	16	)	)	PUNCT
cana-1619	161	17	,	,	PUNCT
cana-1619	161	18	ℵ	ℵ	NOUN
cana-1619	161	19	)	)	PUNCT
cana-1619	161	20	−	−	PROPN
cana-1619	161	21	𝜌(𝜛	𝜌(𝜛	PROPN
cana-1619	161	22	,	,	PUNCT
cana-1619	161	23	𝜁2,𝜛	𝜁2,𝜛	PROPN
cana-1619	161	24	(	(	PUNCT
cana-1619	161	25	.	.	PUNCT
cana-1619	161	26	,	,	PUNCT
cana-1619	161	27	ℵ	ℵ	NOUN
cana-1619	161	28	)	)	PUNCT
cana-1619	161	29	,	,	PUNCT
cana-1619	161	30	ℵ)||𝑑𝜛	ℵ)||𝑑𝜛	NOUN
cana-1619	162	1	+	+	PROPN
cana-1619	162	2	𝜗𝑎∫	𝜗𝑎∫	NOUN
cana-1619	162	3	ℎ	ℎ	NOUN
cana-1619	162	4	0	0	NUM
cana-1619	162	5	||υ(𝜛	||υ(𝜛	NOUN
cana-1619	162	6	,	,	PUNCT
cana-1619	162	7	𝜁1,𝜛	𝜁1,𝜛	PROPN
cana-1619	162	8	(	(	PUNCT
cana-1619	162	9	.	.	PUNCT
cana-1619	162	10	,	,	PUNCT
cana-1619	162	11	ℵ	ℵ	NOUN
cana-1619	162	12	)	)	PUNCT
cana-1619	162	13	,	,	PUNCT
cana-1619	162	14	ℵ	ℵ	NOUN
cana-1619	162	15	)	)	PUNCT
cana-1619	162	16	−	−	ADP
cana-1619	162	17	υ(𝜛	υ(𝜛	PROPN
cana-1619	162	18	,	,	PUNCT
cana-1619	162	19	𝜁2,𝜛	𝜁2,𝜛	PROPN
cana-1619	162	20	(	(	PUNCT
cana-1619	162	21	.	.	PUNCT
cana-1619	162	22	,	,	PUNCT
cana-1619	162	23	ℵ	ℵ	NOUN
cana-1619	162	24	)	)	PUNCT
cana-1619	162	25	,	,	PUNCT
cana-1619	162	26	ℵ)||𝑑𝜛	ℵ)||𝑑𝜛	NOUN
cana-1619	163	1	+	+	PROPN
cana-1619	163	2	𝜗	𝜗	NOUN
cana-1619	163	3	∑	∑	ADP
cana-1619	163	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	PROPN
cana-1619	163	5	||𝐼𝜉(𝜁1(ℎ𝜉	||𝐼𝜉(𝜁1(ℎ𝜉	PROPN
cana-1619	163	6	,	,	PUNCT
cana-1619	163	7	ℵ	ℵ	NOUN
cana-1619	163	8	)	)	PUNCT
cana-1619	163	9	)	)	PUNCT
cana-1619	164	1	−	−	PROPN
cana-1619	164	2	𝐼𝜉(𝜁2(ℎ𝜉	𝐼𝜉(𝜁2(ℎ𝜉	NOUN
cana-1619	164	3	,	,	PUNCT
cana-1619	164	4	ℵ))||	ℵ))||	NOUN
cana-1619	164	5	+	+	CCONJ
cana-1619	164	6	𝜗𝑎	𝜗𝑎	ADV
cana-1619	164	7	∑	∑	ADV
cana-1619	164	8	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	X
cana-1619	164	9	||𝐼′𝜉(𝜁1(ℎ𝜉	||𝐼′𝜉(𝜁1(ℎ𝜉	X
cana-1619	164	10	,	,	PUNCT
cana-1619	164	11	ℵ	ℵ	NOUN
cana-1619	164	12	)	)	PUNCT
cana-1619	164	13	)	)	PUNCT
cana-1619	165	1	−	−	PROPN
cana-1619	166	1	𝐼′𝜉(𝜁2(ℎ𝜉	𝐼′𝜉(𝜁2(ℎ𝜉	NOUN
cana-1619	166	2	,	,	PUNCT
cana-1619	166	3	ℵ))||	ℵ))||	NOUN
cana-1619	166	4	≤	≤	NOUN
cana-1619	166	5	𝜗∫	𝜗∫	VERB
cana-1619	166	6	ℎ	ℎ	X
cana-1619	166	7	0	0	NUM
cana-1619	166	8	sup	sup	PROPN
cana-1619	166	9	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	166	10	]	]	X
cana-1619	166	11	||(𝜁1,𝜛	||(𝜁1,𝜛	NOUN
cana-1619	166	12	(	(	PUNCT
cana-1619	166	13	.	.	PUNCT
cana-1619	166	14	,	,	PUNCT
cana-1619	166	15	ℵ	ℵ	NOUN
cana-1619	166	16	)	)	PUNCT
cana-1619	166	17	,	,	PUNCT
cana-1619	166	18	ℵ	ℵ	NOUN
cana-1619	166	19	)	)	PUNCT
cana-1619	166	20	−	−	PROPN
cana-1619	166	21	(	(	PUNCT
cana-1619	166	22	𝜁2,𝜛	𝜁2,𝜛	PROPN
cana-1619	166	23	(	(	PUNCT
cana-1619	166	24	.	.	PUNCT
cana-1619	166	25	,	,	PUNCT
cana-1619	166	26	ℵ	ℵ	NOUN
cana-1619	166	27	)	)	PUNCT
cana-1619	166	28	,	,	PUNCT
cana-1619	166	29	ℵ)||𝒟	ℵ)||𝒟	NUM
cana-1619	166	30	𝛽0𝑑𝜛	𝛽0𝑑𝜛	PUNCT
cana-1619	167	1	+	+	NOUN
cana-1619	167	2	𝜗𝑎∫	𝜗𝑎∫	NOUN
cana-1619	167	3	ℎ	ℎ	NOUN
cana-1619	167	4	0	0	NUM
cana-1619	167	5	sup	sup	NOUN
cana-1619	167	6	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	167	7	]	]	X
cana-1619	167	8	||(𝜁1,𝜛	||(𝜁1,𝜛	NOUN
cana-1619	167	9	(	(	PUNCT
cana-1619	167	10	.	.	PUNCT
cana-1619	167	11	,	,	PUNCT
cana-1619	167	12	ℵ	ℵ	NOUN
cana-1619	167	13	)	)	PUNCT
cana-1619	167	14	,	,	PUNCT
cana-1619	167	15	ℵ	ℵ	NOUN
cana-1619	167	16	)	)	PUNCT
cana-1619	167	17	−	−	PROPN
cana-1619	167	18	(	(	PUNCT
cana-1619	167	19	𝜁2,𝜛	𝜁2,𝜛	PROPN
cana-1619	167	20	(	(	PUNCT
cana-1619	167	21	.	.	PUNCT
cana-1619	167	22	,	,	PUNCT
cana-1619	167	23	ℵ	ℵ	NOUN
cana-1619	167	24	)	)	PUNCT
cana-1619	167	25	,	,	PUNCT
cana-1619	167	26	ℵ)||𝒟	ℵ)||𝒟	NUM
cana-1619	167	27	𝛼0𝑑𝜛	𝛼0𝑑𝜛	NUM
cana-1619	168	1	+	+	NUM
cana-1619	168	2	𝜗	𝜗	NOUN
cana-1619	168	3	∑	∑	ADV
cana-1619	168	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	VERB
cana-1619	168	5	𝑎𝜉(ℵ)||𝜁1(ℎ𝜉	𝑎𝜉(ℵ)||𝜁1(ℎ𝜉	NOUN
cana-1619	168	6	,	,	PUNCT
cana-1619	168	7	ℵ	ℵ	NOUN
cana-1619	168	8	)	)	PUNCT
cana-1619	168	9	−	−	PROPN
cana-1619	168	10	𝜁2(ℎ𝜉	𝜁2(ℎ𝜉	PROPN
cana-1619	168	11	,	,	PUNCT
cana-1619	168	12	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	168	13	𝛼𝜉	𝛼𝜉	NOUN
cana-1619	168	14	+	+	ADP
cana-1619	168	15	𝜗𝑎	𝜗𝑎	ADV
cana-1619	168	16	∑	∑	ADV
cana-1619	168	17	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	168	18	𝑎′𝜉(ℵ)||𝜁1(ℎ𝜉	𝑎′𝜉(ℵ)||𝜁1(ℎ𝜉	NUM
cana-1619	168	19	,	,	PUNCT
cana-1619	168	20	ℵ	ℵ	NOUN
cana-1619	168	21	)	)	PUNCT
cana-1619	168	22	−	−	PROPN
cana-1619	168	23	𝜁2(ℎ𝜉	𝜁2(ℎ𝜉	PROPN
cana-1619	168	24	,	,	PUNCT
cana-1619	168	25	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	168	26	𝛼𝜉	𝛼𝜉	NUM
cana-1619	168	27	||(γ(ℵ))𝜁1(ℎ	||(γ(ℵ))𝜁1(ℎ	NOUN
cana-1619	168	28	)	)	PUNCT
cana-1619	168	29	−	−	PROPN
cana-1619	169	1	(	(	PUNCT
cana-1619	169	2	γ(ℵ))𝜁2(ℎ)||	γ(ℵ))𝜁2(ℎ)||	PROPN
cana-1619	169	3	≤	≤	NUM
cana-1619	169	4	𝜗	𝜗	ADP
cana-1619	169	5	∑0<ℎ𝜉<ℎ	∑0<ℎ𝜉<ℎ	PROPN
cana-1619	169	6	𝑎𝜉(ℵ)||𝜁1(ℎ𝜉	𝑎𝜉(ℵ)||𝜁1(ℎ𝜉	NOUN
cana-1619	169	7	,	,	PUNCT
cana-1619	169	8	ℵ	ℵ	NOUN
cana-1619	169	9	)	)	PUNCT
cana-1619	169	10	−	−	PROPN
cana-1619	169	11	𝜁2(ℎ𝜉	𝜁2(ℎ𝜉	PROPN
cana-1619	169	12	,	,	PUNCT
cana-1619	169	13	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	169	14	𝛽𝜉	𝛽𝜉	NOUN
cana-1619	169	15	+	+	PROPN
cana-1619	169	16	𝜗	𝜗	NOUN
cana-1619	170	1	∫	∫	NOUN
cana-1619	170	2	ℎ	ℎ	NOUN
cana-1619	170	3	0	0	NUM
cana-1619	170	4	sup	sup	PROPN
cana-1619	170	5	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	170	6	]	]	X
cana-1619	170	7	||(𝜁1,𝜛	||(𝜁1,𝜛	NOUN
cana-1619	170	8	(	(	PUNCT
cana-1619	170	9	.	.	PUNCT
cana-1619	170	10	,	,	PUNCT
cana-1619	170	11	ℵ	ℵ	NOUN
cana-1619	170	12	)	)	PUNCT
cana-1619	170	13	,	,	PUNCT
cana-1619	170	14	ℵ	ℵ	NOUN
cana-1619	170	15	)	)	PUNCT
cana-1619	170	16	−	−	PROPN
cana-1619	170	17	(	(	PUNCT
cana-1619	170	18	𝜁2,𝜛	𝜁2,𝜛	PROPN
cana-1619	170	19	(	(	PUNCT
cana-1619	170	20	.	.	PUNCT
cana-1619	170	21	,	,	PUNCT
cana-1619	170	22	ℵ	ℵ	NOUN
cana-1619	170	23	)	)	PUNCT
cana-1619	170	24	,	,	PUNCT
cana-1619	170	25	ℵ)||𝒟	ℵ)||𝒟	NUM
cana-1619	170	26	𝛽0𝑑𝜛	𝛽0𝑑𝜛	PUNCT
cana-1619	171	1	+	+	PUNCT
cana-1619	171	2	𝜗𝑎	𝜗𝑎	PRON
cana-1619	171	3	∑0<ℎ𝜉<ℎ	∑0<ℎ𝜉<ℎ	PROPN
cana-1619	171	4	𝑎′𝜉(ℵ)||𝜁1(ℎ𝜉	𝑎′𝜉(ℵ)||𝜁1(ℎ𝜉	NUM
cana-1619	171	5	,	,	PUNCT
cana-1619	171	6	ℵ	ℵ	NOUN
cana-1619	171	7	)	)	PUNCT
cana-1619	171	8	−	−	PROPN
cana-1619	171	9	𝜁2(ℎ𝜉	𝜁2(ℎ𝜉	PROPN
cana-1619	171	10	,	,	PUNCT
cana-1619	171	11	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	171	12	𝛼𝜉	𝛼𝜉	NOUN
cana-1619	172	1	+	+	NOUN
cana-1619	172	2	𝜗𝑎	𝜗𝑎	PRON
cana-1619	172	3	∫	∫	PROPN
cana-1619	172	4	ℎ	ℎ	PROPN
cana-1619	172	5	0	0	NUM
cana-1619	172	6	sup	sup	PROPN
cana-1619	172	7	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	172	8	]	]	X
cana-1619	172	9	||(𝜁1,𝜛	||(𝜁1,𝜛	NOUN
cana-1619	172	10	(	(	PUNCT
cana-1619	172	11	.	.	PUNCT
cana-1619	172	12	,	,	PUNCT
cana-1619	172	13	ℵ	ℵ	NOUN
cana-1619	172	14	)	)	PUNCT
cana-1619	172	15	,	,	PUNCT
cana-1619	172	16	ℵ	ℵ	NOUN
cana-1619	172	17	)	)	PUNCT
cana-1619	172	18	−	−	PROPN
cana-1619	172	19	(	(	PUNCT
cana-1619	172	20	𝜁2,𝜛	𝜁2,𝜛	PROPN
cana-1619	172	21	(	(	PUNCT
cana-1619	172	22	.	.	PUNCT
cana-1619	172	23	,	,	PUNCT
cana-1619	172	24	ℵ	ℵ	NOUN
cana-1619	172	25	)	)	PUNCT
cana-1619	172	26	,	,	PUNCT
cana-1619	172	27	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	172	28	𝛼0𝑑𝜛	𝛼0𝑑𝜛	NUM
cana-1619	172	29	for	for	ADP
cana-1619	172	30	all	all	PRON
cana-1619	172	31	ℎ	ℎ	PART
cana-1619	172	32	∈	∈	PROPN
cana-1619	172	33	(	(	PUNCT
cana-1619	172	34	−𝛿	−𝛿	NOUN
cana-1619	172	35	,	,	PUNCT
cana-1619	172	36	𝜚	𝜚	NOUN
cana-1619	172	37	]	]	PUNCT
cana-1619	172	38	,	,	PUNCT
cana-1619	172	39	and	and	CCONJ
cana-1619	172	40	their	their	PRON
cana-1619	172	41	compactness	compactness	NOUN
cana-1619	172	42	for	for	ADP
cana-1619	172	43	ℎ	ℎ	X
cana-1619	172	44	>	>	X
cana-1619	172	45	0	0	NUM
cana-1619	172	46	proves	prove	VERB
cana-1619	172	47	the	the	DET
cana-1619	172	48	uniform	uniform	ADJ
cana-1619	172	49	operator	operator	NOUN
cana-1619	172	50	topology	topology	NOUN
cana-1619	172	51	is	be	AUX
cana-1619	172	52	continuous	continuous	ADJ
cana-1619	172	53	.	.	PUNCT
cana-1619	173	1	since	since	SCONJ
cana-1619	173	2	𝜁1	𝜁1	PROPN
cana-1619	173	3	,	,	PUNCT
cana-1619	173	4	𝜁2	𝜁2	NOUN
cana-1619	173	5	∈	∈	PROPN
cana-1619	173	6	ℬ𝑟(𝛿	ℬ𝑟(𝛿	NOUN
cana-1619	173	7	)	)	PUNCT
cana-1619	173	8	,	,	PUNCT
cana-1619	173	9	the	the	DET
cana-1619	173	10	righthand	righthand	NOUN
cana-1619	173	11	side	side	NOUN
cana-1619	173	12	of	of	ADP
cana-1619	173	13	the	the	DET
cana-1619	173	14	above	above	ADJ
cana-1619	173	15	inequalities	inequality	NOUN
cana-1619	173	16	are	be	AUX
cana-1619	173	17	independent.therefore	independent.therefore	PRON
cana-1619	173	18	||((γ(ℵ))𝜁1)(ℎ	||((γ(ℵ))𝜁1)(ℎ	NOUN
cana-1619	173	19	)	)	PUNCT
cana-1619	173	20	−	−	PROPN
cana-1619	174	1	(	(	PUNCT
cana-1619	174	2	(	(	PUNCT
cana-1619	174	3	γ(ℵ))𝜁2)(ℎ)||	γ(ℵ))𝜁2)(ℎ)||	NOUN
cana-1619	174	4	→	→	SYM
cana-1619	174	5	0	0	NUM
cana-1619	174	6	as	as	ADP
cana-1619	174	7	(	(	PUNCT
cana-1619	174	8	𝜁1	𝜁1	ADJ
cana-1619	174	9	−	−	PROPN
cana-1619	174	10	𝜁2	𝜁2	NOUN
cana-1619	174	11	)	)	PUNCT
cana-1619	174	12	→	→	SYM
cana-1619	174	13	0	0	X
cana-1619	174	14	.	.	PUNCT
cana-1619	175	1	hence	hence	ADV
cana-1619	175	2	(	(	PUNCT
cana-1619	175	3	γ(ℵ	γ(ℵ	PROPN
cana-1619	175	4	)	)	PUNCT
cana-1619	175	5	)	)	PUNCT
cana-1619	175	6	is	be	AUX
cana-1619	175	7	continuous	continuous	ADJ
cana-1619	175	8	.	.	PUNCT
cana-1619	176	1	step	step	NOUN
cana-1619	176	2	3	3	NUM
cana-1619	176	3	:	:	PUNCT
cana-1619	176	4	the	the	DET
cana-1619	176	5	operator	operator	NOUN
cana-1619	176	6	(	(	PUNCT
cana-1619	176	7	γ(ℵ	γ(ℵ	PROPN
cana-1619	176	8	)	)	PUNCT
cana-1619	176	9	)	)	PUNCT
cana-1619	176	10	is	be	AUX
cana-1619	176	11	compact	compact	ADJ
cana-1619	176	12	.	.	PUNCT
cana-1619	177	1	to	to	PART
cana-1619	177	2	establish	establish	VERB
cana-1619	177	3	this	this	PRON
cana-1619	177	4	,	,	PUNCT
cana-1619	177	5	we	we	PRON
cana-1619	177	6	decompose	decompose	VERB
cana-1619	177	7	(	(	PUNCT
cana-1619	177	8	γ(ℵ	γ(ℵ	PROPN
cana-1619	177	9	)	)	PUNCT
cana-1619	177	10	)	)	PUNCT
cana-1619	177	11	into	into	ADP
cana-1619	177	12	(	(	PUNCT
cana-1619	177	13	γ1(ℵ	γ1(ℵ	NUM
cana-1619	177	14	)	)	PUNCT
cana-1619	177	15	)	)	PUNCT
cana-1619	178	1	+	+	CCONJ
cana-1619	178	2	(	(	PUNCT
cana-1619	178	3	γ(ℵ))2	γ(ℵ))2	NOUN
cana-1619	178	4	,	,	PUNCT
cana-1619	178	5	where	where	SCONJ
cana-1619	178	6	both	both	PRON
cana-1619	178	7	(	(	PUNCT
cana-1619	178	8	γ1(ℵ	γ1(ℵ	NUM
cana-1619	178	9	)	)	PUNCT
cana-1619	178	10	)	)	PUNCT
cana-1619	178	11	and	and	CCONJ
cana-1619	178	12	(	(	PUNCT
cana-1619	178	13	γ2(ℵ	γ2(ℵ	NOUN
cana-1619	178	14	)	)	PUNCT
cana-1619	178	15	)	)	PUNCT
cana-1619	178	16	communications	communication	NOUN
cana-1619	178	17	on	on	ADP
cana-1619	178	18	applied	apply	VERB
cana-1619	178	19	nonlinear	nonlinear	ADJ
cana-1619	178	20	analysis	analysis	NOUN
cana-1619	178	21	issn	issn	NOUN
cana-1619	178	22	:	:	PUNCT
cana-1619	178	23	1074	1074	NUM
cana-1619	178	24	-	-	PUNCT
cana-1619	178	25	133x	133x	NUM
cana-1619	178	26	vol	vol	NOUN
cana-1619	178	27	32	32	NUM
cana-1619	179	1	no	no	NOUN
cana-1619	179	2	.	.	NOUN
cana-1619	179	3	1	1	NUM
cana-1619	179	4	(	(	PUNCT
cana-1619	179	5	2025	2025	NUM
cana-1619	179	6	)	)	PUNCT
cana-1619	179	7	43	43	NUM
cana-1619	179	8	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	179	9	are	be	AUX
cana-1619	179	10	operators	operator	NOUN
cana-1619	179	11	acting	act	VERB
cana-1619	179	12	on	on	ADP
cana-1619	179	13	ℬ𝑟(𝛿	ℬ𝑟(𝛿	ADJ
cana-1619	179	14	)	)	PUNCT
cana-1619	179	15	.	.	PUNCT
cana-1619	180	1	specifically	specifically	ADV
cana-1619	180	2	,	,	PUNCT
cana-1619	180	3	they	they	PRON
cana-1619	180	4	are	be	AUX
cana-1619	180	5	characterized	characterize	VERB
cana-1619	180	6	as	as	ADP
cana-1619	180	7	follows	follow	VERB
cana-1619	180	8	(	(	PUNCT
cana-1619	180	9	γ1(ℵ))𝜁(ℎ	γ1(ℵ))𝜁(ℎ	X
cana-1619	180	10	)	)	PUNCT
cana-1619	180	11	=	=	SYM
cana-1619	180	12	𝑇1(ℎ)𝜙0(ℵ	𝑇1(ℎ)𝜙0(ℵ	NOUN
cana-1619	180	13	)	)	PUNCT
cana-1619	180	14	+	+	NUM
cana-1619	180	15	𝑇2(ℎ)[𝜙′0(ℵ	𝑇2(ℎ)[𝜙′0(ℵ	NOUN
cana-1619	180	16	)	)	PUNCT
cana-1619	181	1	+	+	CCONJ
cana-1619	181	2	𝜌(0	𝜌(0	PROPN
cana-1619	181	3	,	,	PUNCT
cana-1619	181	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	181	5	)	)	PUNCT
cana-1619	181	6	,	,	PUNCT
cana-1619	181	7	ℵ	ℵ	NOUN
cana-1619	181	8	)	)	PUNCT
cana-1619	181	9	]	]	PUNCT
cana-1619	182	1	−	−	PROPN
cana-1619	182	2	∫	∫	INTJ
cana-1619	182	3	ℎ	ℎ	PROPN
cana-1619	182	4	0	0	PROPN
cana-1619	183	1	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	184	1	−	−	PROPN
cana-1619	184	2	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	NOUN
cana-1619	184	3	,	,	PUNCT
cana-1619	184	4	𝜁𝜛	𝜁𝜛	ADV
cana-1619	184	5	(	(	PUNCT
cana-1619	184	6	.	.	PUNCT
cana-1619	184	7	,	,	PUNCT
cana-1619	184	8	ℵ	ℵ	NOUN
cana-1619	184	9	)	)	PUNCT
cana-1619	184	10	,	,	PUNCT
cana-1619	185	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	185	2	+	+	PROPN
cana-1619	185	3	∫	∫	PROPN
cana-1619	185	4	ℎ	ℎ	X
cana-1619	185	5	0	0	SYM
cana-1619	185	6	𝑇2(ℎ	𝑇2(ℎ	ADJ
cana-1619	185	7	−	−	NOUN
cana-1619	185	8	𝜛)υ(𝜛	𝜛)υ(𝜛	NOUN
cana-1619	185	9	,	,	PUNCT
cana-1619	185	10	𝜁𝜛	𝜁𝜛	ADV
cana-1619	185	11	(	(	PUNCT
cana-1619	185	12	.	.	PUNCT
cana-1619	185	13	,	,	PUNCT
cana-1619	185	14	ℵ	ℵ	NOUN
cana-1619	185	15	)	)	PUNCT
cana-1619	185	16	,	,	PUNCT
cana-1619	185	17	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	185	18	and	and	CCONJ
cana-1619	185	19	(	(	PUNCT
cana-1619	185	20	γ2(ℵ))𝜁(ℎ	γ2(ℵ))𝜁(ℎ	NOUN
cana-1619	185	21	)	)	PUNCT
cana-1619	185	22	=	=	PUNCT
cana-1619	185	23	∑	∑	PUNCT
cana-1619	185	24	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	VERB
cana-1619	185	25	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	185	26	−	−	PROPN
cana-1619	186	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	186	2	,	,	PUNCT
cana-1619	186	3	ℵ	ℵ	NOUN
cana-1619	186	4	)	)	PUNCT
cana-1619	186	5	)	)	PUNCT
cana-1619	187	1	+	+	CCONJ
cana-1619	187	2	∑	∑	PUNCT
cana-1619	187	3	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	187	4	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	187	5	−	−	PROPN
cana-1619	187	6	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	187	7	,	,	PUNCT
cana-1619	187	8	ℵ	ℵ	NOUN
cana-1619	187	9	)	)	PUNCT
cana-1619	187	10	)	)	PUNCT
cana-1619	187	11	,	,	PUNCT
cana-1619	187	12	forall	forall	VERB
cana-1619	187	13	ℎ	ℎ	PROPN
cana-1619	187	14	∈	∈	PROPN
cana-1619	187	15	(	(	PUNCT
cana-1619	187	16	−𝛿	−𝛿	NOUN
cana-1619	187	17	,	,	PUNCT
cana-1619	187	18	𝜚	𝜚	NOUN
cana-1619	187	19	]	]	PUNCT
cana-1619	187	20	.	.	PUNCT
cana-1619	188	1	we	we	PRON
cana-1619	188	2	will	will	AUX
cana-1619	188	3	begin	begin	VERB
cana-1619	188	4	by	by	ADP
cana-1619	188	5	demonstrating	demonstrate	VERB
cana-1619	188	6	that	that	SCONJ
cana-1619	188	7	(	(	PUNCT
cana-1619	188	8	γ1(ℵ	γ1(ℵ	NUM
cana-1619	188	9	)	)	PUNCT
cana-1619	188	10	)	)	PUNCT
cana-1619	188	11	is	be	AUX
cana-1619	188	12	a	a	DET
cana-1619	188	13	compact	compact	ADJ
cana-1619	188	14	operator	operator	NOUN
cana-1619	188	15	.	.	PUNCT
cana-1619	189	1	(	(	PUNCT
cana-1619	189	2	i)the	i)the	DET
cana-1619	189	3	set	set	NOUN
cana-1619	189	4	(	(	PUNCT
cana-1619	189	5	γ1(ℵ))(ℬ𝑟(𝛿	γ1(ℵ))(ℬ𝑟(𝛿	PROPN
cana-1619	189	6	)	)	PUNCT
cana-1619	189	7	)	)	PUNCT
cana-1619	189	8	exhibits	exhibit	VERB
cana-1619	189	9	equicontinuity	equicontinuity	NOUN
cana-1619	189	10	.	.	PUNCT
cana-1619	190	1	now	now	ADV
cana-1619	190	2	,	,	PUNCT
cana-1619	190	3	consider	consider	VERB
cana-1619	190	4	𝛿	𝛿	ADJ
cana-1619	190	5	≤	≤	ADJ
cana-1619	190	6	ℎ1	ℎ1	PROPN
cana-1619	190	7	<	<	X
cana-1619	190	8	ℎ2	ℎ2	ADJ
cana-1619	190	9	≤	≤	NUM
cana-1619	190	10	𝜚	𝜚	NOUN
cana-1619	190	11	and	and	CCONJ
cana-1619	190	12	let	let	VERB
cana-1619	190	13	𝜖	𝜖	PROPN
cana-1619	190	14	>	>	X
cana-1619	190	15	0	0	PUNCT
cana-1619	190	16	be	be	AUX
cana-1619	190	17	small	small	ADJ
cana-1619	190	18	.	.	PUNCT
cana-1619	191	1	then	then	ADV
cana-1619	191	2	communications	communication	NOUN
cana-1619	191	3	on	on	ADP
cana-1619	191	4	applied	apply	VERB
cana-1619	191	5	nonlinear	nonlinear	ADJ
cana-1619	191	6	analysis	analysis	NOUN
cana-1619	191	7	issn	issn	NOUN
cana-1619	191	8	:	:	PUNCT
cana-1619	191	9	1074	1074	NUM
cana-1619	191	10	-	-	PUNCT
cana-1619	191	11	133x	133x	NUM
cana-1619	191	12	vol	vol	NOUN
cana-1619	191	13	32	32	NUM
cana-1619	191	14	no	no	NOUN
cana-1619	191	15	.	.	NOUN
cana-1619	191	16	1	1	NUM
cana-1619	191	17	(	(	PUNCT
cana-1619	191	18	2025	2025	NUM
cana-1619	191	19	)	)	PUNCT
cana-1619	191	20	44	44	NUM
cana-1619	191	21	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	191	22	||(γ1(ℵ))𝜁(ℎ2	||(γ1(ℵ))𝜁(ℎ2	PROPN
cana-1619	191	23	)	)	PUNCT
cana-1619	191	24	−	−	PROPN
cana-1619	192	1	(	(	PUNCT
cana-1619	192	2	γ1(ℵ))𝜁(ℎ1)||	γ1(ℵ))𝜁(ℎ1)||	NOUN
cana-1619	192	3	≤	≤	NUM
cana-1619	192	4	||[𝑇1(ℎ2	||[𝑇1(ℎ2	PROPN
cana-1619	192	5	)	)	PUNCT
cana-1619	192	6	−	−	PROPN
cana-1619	192	7	𝑇1(ℎ2)]𝜙0(ℵ)||	𝑇1(ℎ2)]𝜙0(ℵ)||	NOUN
cana-1619	192	8	+	+	CCONJ
cana-1619	192	9	||[𝑇2(ℎ2	||[𝑇2(ℎ2	NOUN
cana-1619	192	10	)	)	PUNCT
cana-1619	192	11	−	−	PROPN
cana-1619	192	12	𝑇2(ℎ1	𝑇2(ℎ1	NUM
cana-1619	192	13	)	)	PUNCT
cana-1619	192	14	]	]	PUNCT
cana-1619	193	1	[	[	X
cana-1619	193	2	,	,	PUNCT
cana-1619	193	3	ℵ)]||	ℵ)]||	PUNCT
cana-1619	193	4	+	+	ADP
cana-1619	193	5	||∫	||∫	ADJ
cana-1619	193	6	ℎ1	ℎ1	PROPN
cana-1619	193	7	0	0	PUNCT
cana-1619	194	1	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	194	2	−	−	PROPN
cana-1619	194	3	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	NOUN
cana-1619	194	4	,	,	PUNCT
cana-1619	194	5	𝜁𝜛	𝜁𝜛	ADV
cana-1619	194	6	(	(	PUNCT
cana-1619	194	7	.	.	PUNCT
cana-1619	194	8	,	,	PUNCT
cana-1619	194	9	ℵ	ℵ	NOUN
cana-1619	194	10	)	)	PUNCT
cana-1619	194	11	,	,	PUNCT
cana-1619	194	12	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	194	13	−∫	−∫	NOUN
cana-1619	194	14	ℎ2	ℎ2	NOUN
cana-1619	194	15	0	0	NUM
cana-1619	194	16	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	194	17	−	−	PROPN
cana-1619	195	1	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	NOUN
cana-1619	195	2	,	,	PUNCT
cana-1619	195	3	𝜁𝜛	𝜁𝜛	ADV
cana-1619	195	4	(	(	PUNCT
cana-1619	195	5	.	.	PUNCT
cana-1619	195	6	,	,	PUNCT
cana-1619	195	7	ℵ	ℵ	NOUN
cana-1619	195	8	)	)	PUNCT
cana-1619	195	9	,	,	PUNCT
cana-1619	195	10	ℵ)𝑑𝜛||	ℵ)𝑑𝜛||	NOUN
cana-1619	195	11	+	+	CCONJ
cana-1619	195	12	||∫	||∫	ADJ
cana-1619	195	13	ℎ1	ℎ1	PROPN
cana-1619	195	14	0	0	PUNCT
cana-1619	195	15	𝑇2(ℎ2	𝑇2(ℎ2	NOUN
cana-1619	195	16	−𝜛)υ(𝜛	−𝜛)υ(𝜛	PROPN
cana-1619	195	17	,	,	PUNCT
cana-1619	195	18	𝜁𝜛	𝜁𝜛	ADV
cana-1619	195	19	(	(	PUNCT
cana-1619	195	20	.	.	PUNCT
cana-1619	195	21	,	,	PUNCT
cana-1619	195	22	ℵ	ℵ	NOUN
cana-1619	195	23	)	)	PUNCT
cana-1619	195	24	,	,	PUNCT
cana-1619	195	25	ℵ	ℵ	NOUN
cana-1619	195	26	)	)	PUNCT
cana-1619	195	27	−	−	NOUN
cana-1619	195	28	∫	∫	NOUN
cana-1619	195	29	ℎ2	ℎ2	NOUN
cana-1619	195	30	0	0	NUM
cana-1619	196	1	𝑇2(ℎ1	𝑇2(ℎ1	ADJ
cana-1619	196	2	−𝜛)υ(𝜛	−𝜛)υ(𝜛	NOUN
cana-1619	196	3	,	,	PUNCT
cana-1619	196	4	𝜁𝜛	𝜁𝜛	ADV
cana-1619	196	5	(	(	PUNCT
cana-1619	196	6	.	.	PUNCT
cana-1619	196	7	,	,	PUNCT
cana-1619	196	8	ℵ	ℵ	NOUN
cana-1619	196	9	)	)	PUNCT
cana-1619	196	10	,	,	PUNCT
cana-1619	196	11	ℵ)||𝑑𝜛	ℵ)||𝑑𝜛	NOUN
cana-1619	196	12	≤	≤	ADJ
cana-1619	196	13	||[𝑇1(ℎ2	||[𝑇1(ℎ2	NOUN
cana-1619	196	14	)	)	PUNCT
cana-1619	196	15	−	−	PROPN
cana-1619	196	16	𝑇1(ℎ2)]𝜙0(ℵ)||	𝑇1(ℎ2)]𝜙0(ℵ)||	NOUN
cana-1619	196	17	+	+	CCONJ
cana-1619	196	18	||[𝑇2(ℎ2	||[𝑇2(ℎ2	NOUN
cana-1619	196	19	)	)	PUNCT
cana-1619	196	20	−	−	PROPN
cana-1619	196	21	𝑇2(ℎ1)][𝜙′0(ℵ	𝑇2(ℎ1)][𝜙′0(ℵ	PROPN
cana-1619	196	22	)	)	PUNCT
cana-1619	196	23	+	+	SYM
cana-1619	197	1	𝜌(0	𝜌(0	PROPN
cana-1619	197	2	,	,	PUNCT
cana-1619	197	3	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	197	4	)	)	PUNCT
cana-1619	197	5	,	,	PUNCT
cana-1619	197	6	ℵ)]||	ℵ)]||	PUNCT
cana-1619	198	1	+	+	ADP
cana-1619	198	2	||∫	||∫	ADJ
cana-1619	198	3	ℎ1−𝜖	ℎ1−𝜖	PROPN
cana-1619	198	4	0	0	NUM
cana-1619	198	5	(	(	PUNCT
cana-1619	198	6	𝑇1(ℎ2	𝑇1(ℎ2	NOUN
cana-1619	198	7	−𝜛	−𝜛	ADV
cana-1619	198	8	)	)	PUNCT
cana-1619	198	9	−	−	PROPN
cana-1619	199	1	𝑇1(ℎ1	𝑇1(ℎ1	DET
cana-1619	199	2	−𝜛))𝜌(𝜛	−𝜛))𝜌(𝜛	NOUN
cana-1619	199	3	,	,	PUNCT
cana-1619	199	4	𝜁𝜛	𝜁𝜛	ADV
cana-1619	199	5	(	(	PUNCT
cana-1619	199	6	.	.	PUNCT
cana-1619	199	7	,	,	PUNCT
cana-1619	199	8	ℵ	ℵ	NOUN
cana-1619	199	9	)	)	PUNCT
cana-1619	199	10	,	,	PUNCT
cana-1619	199	11	ℵ)𝑑𝜛||	ℵ)𝑑𝜛||	NOUN
cana-1619	199	12	+	+	CCONJ
cana-1619	199	13	||∫	||∫	PROPN
cana-1619	199	14	ℎ1−𝜖	ℎ1−𝜖	PROPN
cana-1619	199	15	0	0	NUM
cana-1619	199	16	(	(	PUNCT
cana-1619	199	17	𝑇2(ℎ2	𝑇2(ℎ2	NOUN
cana-1619	199	18	−𝜛	−𝜛	ADJ
cana-1619	199	19	)	)	PUNCT
cana-1619	199	20	−	−	PROPN
cana-1619	200	1	𝑇2(ℎ1	𝑇2(ℎ1	PROPN
cana-1619	200	2	−𝜛))υ(𝜛	−𝜛))υ(𝜛	PROPN
cana-1619	200	3	,	,	PUNCT
cana-1619	200	4	𝜁𝜛	𝜁𝜛	ADV
cana-1619	200	5	(	(	PUNCT
cana-1619	200	6	.	.	PUNCT
cana-1619	200	7	,	,	PUNCT
cana-1619	200	8	ℵ	ℵ	NOUN
cana-1619	200	9	)	)	PUNCT
cana-1619	200	10	,	,	PUNCT
cana-1619	200	11	ℵ)𝑑𝜛||	ℵ)𝑑𝜛||	NOUN
cana-1619	201	1	+	+	CCONJ
cana-1619	201	2	||∫	||∫	ADJ
cana-1619	201	3	ℎ1	ℎ1	PROPN
cana-1619	201	4	ℎ1−𝜖	ℎ1−𝜖	PROPN
cana-1619	201	5	𝑇1(ℎ2	𝑇1(ℎ2	VERB
cana-1619	201	6	−𝜛	−𝜛	ADV
cana-1619	201	7	)	)	PUNCT
cana-1619	201	8	−	−	PROPN
cana-1619	202	1	𝑇1(ℎ1	𝑇1(ℎ1	DET
cana-1619	202	2	−𝜛))𝜌(𝜛	−𝜛))𝜌(𝜛	NOUN
cana-1619	202	3	,	,	PUNCT
cana-1619	202	4	𝜁𝜛	𝜁𝜛	ADV
cana-1619	202	5	(	(	PUNCT
cana-1619	202	6	.	.	PUNCT
cana-1619	202	7	,	,	PUNCT
cana-1619	202	8	ℵ	ℵ	NOUN
cana-1619	202	9	)	)	PUNCT
cana-1619	202	10	,	,	PUNCT
cana-1619	202	11	ℵ)𝑑𝜛||	ℵ)𝑑𝜛||	NOUN
cana-1619	203	1	+	+	CCONJ
cana-1619	203	2	||∫	||∫	ADJ
cana-1619	203	3	ℎ1	ℎ1	PROPN
cana-1619	203	4	ℎ1−𝜖	ℎ1−𝜖	PROPN
cana-1619	203	5	𝑇2(ℎ2	𝑇2(ℎ2	VERB
cana-1619	203	6	−𝜛	−𝜛	ADV
cana-1619	203	7	)	)	PUNCT
cana-1619	203	8	−	−	PROPN
cana-1619	204	1	𝑇2(ℎ1	𝑇2(ℎ1	PROPN
cana-1619	204	2	−𝜛))υ(𝜛	−𝜛))υ(𝜛	PROPN
cana-1619	204	3	,	,	PUNCT
cana-1619	204	4	𝜁𝜛	𝜁𝜛	ADV
cana-1619	204	5	(	(	PUNCT
cana-1619	204	6	.	.	PUNCT
cana-1619	204	7	,	,	PUNCT
cana-1619	204	8	ℵ	ℵ	NOUN
cana-1619	204	9	)	)	PUNCT
cana-1619	204	10	,	,	PUNCT
cana-1619	204	11	ℵ)𝑑𝜛||	ℵ)𝑑𝜛||	NOUN
cana-1619	205	1	+	+	CCONJ
cana-1619	205	2	||∫	||∫	ADJ
cana-1619	205	3	ℎ2	ℎ2	NOUN
cana-1619	205	4	ℎ1	ℎ1	PROPN
cana-1619	205	5	𝑇1(ℎ2	𝑇1(ℎ2	VERB
cana-1619	205	6	−𝜛	−𝜛	ADV
cana-1619	205	7	)	)	PUNCT
cana-1619	205	8	−	−	PROPN
cana-1619	206	1	𝑇1(ℎ1	𝑇1(ℎ1	DET
cana-1619	206	2	−𝜛))𝜌(𝜛	−𝜛))𝜌(𝜛	NOUN
cana-1619	206	3	,	,	PUNCT
cana-1619	206	4	𝜁𝜛	𝜁𝜛	ADV
cana-1619	206	5	(	(	PUNCT
cana-1619	206	6	.	.	PUNCT
cana-1619	206	7	,	,	PUNCT
cana-1619	206	8	ℵ	ℵ	NOUN
cana-1619	206	9	)	)	PUNCT
cana-1619	206	10	,	,	PUNCT
cana-1619	206	11	ℵ)||𝑑𝜛	ℵ)||𝑑𝜛	NOUN
cana-1619	207	1	+	+	SYM
cana-1619	207	2	||∫	||∫	ADJ
cana-1619	207	3	ℎ2	ℎ2	ADJ
cana-1619	207	4	ℎ1	ℎ1	PROPN
cana-1619	207	5	𝑇2(ℎ2	𝑇2(ℎ2	NOUN
cana-1619	207	6	−𝜛	−𝜛	ADJ
cana-1619	207	7	)	)	PUNCT
cana-1619	207	8	−	−	PROPN
cana-1619	208	1	𝑇2(ℎ1	𝑇2(ℎ1	PROPN
cana-1619	208	2	−𝜛))υ(𝜛	−𝜛))υ(𝜛	PROPN
cana-1619	208	3	,	,	PUNCT
cana-1619	208	4	𝜁𝜛	𝜁𝜛	ADV
cana-1619	208	5	(	(	PUNCT
cana-1619	208	6	.	.	PUNCT
cana-1619	208	7	,	,	PUNCT
cana-1619	208	8	ℵ	ℵ	NOUN
cana-1619	208	9	)	)	PUNCT
cana-1619	208	10	,	,	PUNCT
cana-1619	208	11	ℵ)||𝑑𝜛	ℵ)||𝑑𝜛	NOUN
cana-1619	208	12	≤	≤	ADJ
cana-1619	208	13	||[𝑇1(ℎ2	||[𝑇1(ℎ2	NOUN
cana-1619	208	14	)	)	PUNCT
cana-1619	208	15	−	−	PROPN
cana-1619	208	16	𝑇1(ℎ2)]𝜙0(ℵ)||	𝑇1(ℎ2)]𝜙0(ℵ)||	NOUN
cana-1619	208	17	+	+	CCONJ
cana-1619	208	18	||[𝑇2(ℎ2	||[𝑇2(ℎ2	NOUN
cana-1619	208	19	)	)	PUNCT
cana-1619	208	20	−	−	PROPN
cana-1619	208	21	𝑇2(ℎ1)][𝜙′0(ℵ	𝑇2(ℎ1)][𝜙′0(ℵ	PROPN
cana-1619	208	22	)	)	PUNCT
cana-1619	208	23	+	+	SYM
cana-1619	209	1	𝜌(0	𝜌(0	PROPN
cana-1619	209	2	,	,	PUNCT
cana-1619	209	3	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	209	4	)	)	PUNCT
cana-1619	209	5	,	,	PUNCT
cana-1619	209	6	ℵ)]||	ℵ)]||	PUNCT
cana-1619	210	1	+	+	ADJ
cana-1619	210	2	∫	∫	PROPN
cana-1619	210	3	ℎ1−𝜖	ℎ1−𝜖	PROPN
cana-1619	210	4	0	0	NUM
cana-1619	210	5	||𝑇1(ℎ2	||𝑇1(ℎ2	NOUN
cana-1619	210	6	−𝜛	−𝜛	NOUN
cana-1619	210	7	)	)	PUNCT
cana-1619	210	8	−	−	PROPN
cana-1619	211	1	𝑇1(ℎ1	𝑇1(ℎ1	DET
cana-1619	211	2	−𝜛)||	−𝜛)||	NOUN
cana-1619	211	3	[	[	PUNCT
cana-1619	211	4	sup	sup	NOUN
cana-1619	211	5	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	211	6	]	]	PUNCT
cana-1619	211	7	||𝜁𝜛	||𝜁𝜛	NOUN
cana-1619	211	8	(	(	PUNCT
cana-1619	211	9	.	.	PUNCT
cana-1619	211	10	,	,	PUNCT
cana-1619	211	11	ℵ	ℵ	NOUN
cana-1619	211	12	)	)	PUNCT
cana-1619	211	13	,	,	PUNCT
cana-1619	211	14	ℵ||𝒟	ℵ||𝒟	NOUN
cana-1619	211	15	𝛽0	𝛽0	VERB
cana-1619	211	16	+	+	CCONJ
cana-1619	211	17	𝑑0(ℵ)]𝑑𝜛	𝑑0(ℵ)]𝑑𝜛	ADJ
cana-1619	212	1	+	+	ADJ
cana-1619	212	2	∫	∫	PROPN
cana-1619	212	3	ℎ1−𝜖	ℎ1−𝜖	PROPN
cana-1619	212	4	0	0	NUM
cana-1619	212	5	||𝑇2(ℎ2	||𝑇2(ℎ2	NOUN
cana-1619	212	6	−𝜛	−𝜛	ADJ
cana-1619	212	7	)	)	PUNCT
cana-1619	212	8	−	−	PROPN
cana-1619	213	1	𝑇2(ℎ1	𝑇2(ℎ1	ADJ
cana-1619	213	2	−𝜛)||	−𝜛)||	NOUN
cana-1619	213	3	[	[	PUNCT
cana-1619	213	4	sup	sup	NOUN
cana-1619	213	5	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	213	6	]	]	PUNCT
cana-1619	213	7	||𝜁𝜛	||𝜁𝜛	NOUN
cana-1619	213	8	(	(	PUNCT
cana-1619	213	9	.	.	PUNCT
cana-1619	213	10	,	,	PUNCT
cana-1619	213	11	ℵ	ℵ	NOUN
cana-1619	213	12	)	)	PUNCT
cana-1619	213	13	,	,	PUNCT
cana-1619	213	14	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	213	15	𝛼0	𝛼0	NOUN
cana-1619	214	1	+	+	CCONJ
cana-1619	214	2	𝑏0(ℵ)]𝑑𝜛	𝑏0(ℵ)]𝑑𝜛	PROPN
cana-1619	214	3	+	+	ADJ
cana-1619	214	4	∫	∫	NOUN
cana-1619	214	5	ℎ1	ℎ1	PROPN
cana-1619	214	6	ℎ1−𝜖	ℎ1−𝜖	PROPN
cana-1619	214	7	||𝑇1(ℎ2	||𝑇1(ℎ2	VERB
cana-1619	214	8	−𝜛	−𝜛	NOUN
cana-1619	214	9	)	)	PUNCT
cana-1619	214	10	−	−	PROPN
cana-1619	215	1	𝑇1(ℎ1	𝑇1(ℎ1	DET
cana-1619	215	2	−𝜛)||	−𝜛)||	NOUN
cana-1619	215	3	[	[	PUNCT
cana-1619	215	4	sup	sup	NOUN
cana-1619	215	5	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	215	6	]	]	PUNCT
cana-1619	215	7	||𝜁𝜛	||𝜁𝜛	NOUN
cana-1619	215	8	(	(	PUNCT
cana-1619	215	9	.	.	PUNCT
cana-1619	215	10	,	,	PUNCT
cana-1619	215	11	ℵ	ℵ	NOUN
cana-1619	215	12	)	)	PUNCT
cana-1619	215	13	,	,	PUNCT
cana-1619	215	14	ℵ||𝒟	ℵ||𝒟	NOUN
cana-1619	215	15	𝛽0	𝛽0	VERB
cana-1619	215	16	+	+	CCONJ
cana-1619	215	17	𝑑0(ℵ)]𝑑𝜛	𝑑0(ℵ)]𝑑𝜛	NUM
cana-1619	216	1	+	+	NUM
cana-1619	216	2	∫	∫	ADJ
cana-1619	216	3	ℎ1	ℎ1	PROPN
cana-1619	216	4	ℎ1−𝜖	ℎ1−𝜖	PROPN
cana-1619	216	5	||𝑇2(ℎ2	||𝑇2(ℎ2	NOUN
cana-1619	216	6	−𝜛	−𝜛	NOUN
cana-1619	216	7	)	)	PUNCT
cana-1619	216	8	−	−	PROPN
cana-1619	217	1	𝑇2(ℎ1	𝑇2(ℎ1	ADJ
cana-1619	217	2	−𝜛)||	−𝜛)||	NOUN
cana-1619	217	3	[	[	PUNCT
cana-1619	217	4	sup	sup	NOUN
cana-1619	217	5	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	217	6	]	]	PUNCT
cana-1619	217	7	||𝜁𝜛	||𝜁𝜛	NOUN
cana-1619	217	8	(	(	PUNCT
cana-1619	217	9	.	.	PUNCT
cana-1619	217	10	,	,	PUNCT
cana-1619	217	11	ℵ	ℵ	NOUN
cana-1619	217	12	)	)	PUNCT
cana-1619	217	13	,	,	PUNCT
cana-1619	217	14	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	217	15	𝛼0	𝛼0	NOUN
cana-1619	218	1	+	+	CCONJ
cana-1619	218	2	𝑏0(ℵ)]𝑑𝜛	𝑏0(ℵ)]𝑑𝜛	PROPN
cana-1619	218	3	+	+	ADJ
cana-1619	218	4	∫	∫	NOUN
cana-1619	218	5	ℎ2	ℎ2	NOUN
cana-1619	218	6	ℎ1	ℎ1	PROPN
cana-1619	218	7	||𝑇1(ℎ2	||𝑇1(ℎ2	VERB
cana-1619	218	8	−𝜛	−𝜛	ADJ
cana-1619	218	9	)	)	PUNCT
cana-1619	218	10	−	−	PROPN
cana-1619	219	1	𝑇1(ℎ1	𝑇1(ℎ1	DET
cana-1619	219	2	−𝜛)||	−𝜛)||	NOUN
cana-1619	219	3	[	[	PUNCT
cana-1619	219	4	sup	sup	NOUN
cana-1619	219	5	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	219	6	]	]	PUNCT
cana-1619	219	7	||𝜁𝜛	||𝜁𝜛	NOUN
cana-1619	219	8	(	(	PUNCT
cana-1619	219	9	.	.	PUNCT
cana-1619	219	10	,	,	PUNCT
cana-1619	219	11	ℵ	ℵ	NOUN
cana-1619	219	12	)	)	PUNCT
cana-1619	219	13	,	,	PUNCT
cana-1619	219	14	ℵ||𝒟	ℵ||𝒟	NOUN
cana-1619	219	15	𝛽0	𝛽0	VERB
cana-1619	219	16	+	+	CCONJ
cana-1619	219	17	𝑑0(ℵ)]𝑑𝜛	𝑑0(ℵ)]𝑑𝜛	ADJ
cana-1619	220	1	+	+	NUM
cana-1619	220	2	∫	∫	NOUN
cana-1619	220	3	ℎ2	ℎ2	ADJ
cana-1619	220	4	ℎ1	ℎ1	PROPN
cana-1619	220	5	||𝑇2(ℎ2	||𝑇2(ℎ2	NOUN
cana-1619	220	6	−𝜛	−𝜛	ADV
cana-1619	220	7	)	)	PUNCT
cana-1619	220	8	−	−	PROPN
cana-1619	221	1	𝑇2(ℎ1	𝑇2(ℎ1	ADJ
cana-1619	221	2	−𝜛)||	−𝜛)||	NOUN
cana-1619	221	3	[	[	PUNCT
cana-1619	221	4	sup	sup	NOUN
cana-1619	221	5	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	221	6	]	]	PUNCT
cana-1619	221	7	||𝜁𝜛	||𝜁𝜛	NOUN
cana-1619	221	8	(	(	PUNCT
cana-1619	221	9	.	.	PUNCT
cana-1619	221	10	,	,	PUNCT
cana-1619	221	11	ℵ	ℵ	NOUN
cana-1619	221	12	)	)	PUNCT
cana-1619	221	13	,	,	PUNCT
cana-1619	221	14	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	221	15	𝛼0	𝛼0	NOUN
cana-1619	222	1	+	+	CCONJ
cana-1619	222	2	𝑏0(ℵ)]𝑑𝜛	𝑏0(ℵ)]𝑑𝜛	NOUN
cana-1619	222	3	we	we	PRON
cana-1619	222	4	observe	observe	VERB
cana-1619	222	5	that	that	SCONJ
cana-1619	222	6	as	as	SCONJ
cana-1619	222	7	ℎ2	ℎ2	NOUN
cana-1619	222	8	−	−	NUM
cana-1619	222	9	ℎ1	ℎ1	PROPN
cana-1619	222	10	approaches	approach	VERB
cana-1619	222	11	zero	zero	NUM
cana-1619	222	12	,	,	PUNCT
cana-1619	222	13	|	|	ADV
cana-1619	222	14	|(γ1(ℵ))𝜁(ℎ2	|(γ1(ℵ))𝜁(ℎ2	NOUN
cana-1619	222	15	)	)	PUNCT
cana-1619	222	16	−	−	PROPN
cana-1619	223	1	(	(	PUNCT
cana-1619	223	2	γ(ℵ))𝜁(ℎ1)|	γ(ℵ))𝜁(ℎ1)|	NOUN
cana-1619	223	3	|	|	ADV
cana-1619	223	4	tends	tend	VERB
cana-1619	223	5	to	to	ADP
cana-1619	223	6	zero	zero	NUM
cana-1619	223	7	regardless	regardless	ADV
cana-1619	223	8	of	of	ADP
cana-1619	223	9	𝜁	𝜁	PROPN
cana-1619	223	10	∈	∈	PROPN
cana-1619	223	11	ℬ𝑟(𝛿	ℬ𝑟(𝛿	NOUN
cana-1619	223	12	)	)	PUNCT
cana-1619	223	13	.	.	PUNCT
cana-1619	224	1	because	because	SCONJ
cana-1619	224	2	the	the	DET
cana-1619	224	3	operator	operator	NOUN
cana-1619	224	4	𝑇2(ℎ	𝑇2(ℎ	NOUN
cana-1619	224	5	)	)	PUNCT
cana-1619	224	6	is	be	AUX
cana-1619	224	7	compact	compact	ADJ
cana-1619	224	8	for	for	ADP
cana-1619	224	9	ℎ	ℎ	X
cana-1619	224	10	>	>	X
cana-1619	224	11	0	0	NUM
cana-1619	224	12	,	,	PUNCT
cana-1619	224	13	it	it	PRON
cana-1619	224	14	ensures	ensure	VERB
cana-1619	224	15	continuity	continuity	NOUN
cana-1619	224	16	in	in	ADP
cana-1619	224	17	the	the	DET
cana-1619	224	18	uniform	uniform	ADJ
cana-1619	224	19	operator	operator	NOUN
cana-1619	224	20	topology	topology	NOUN
cana-1619	224	21	.	.	PUNCT
cana-1619	225	1	as	as	ADP
cana-1619	225	2	a	a	DET
cana-1619	225	3	result	result	NOUN
cana-1619	225	4	,	,	PUNCT
cana-1619	225	5	(	(	PUNCT
cana-1619	225	6	γ1(ℵ	γ1(ℵ	NOUN
cana-1619	225	7	)	)	PUNCT
cana-1619	225	8	)	)	PUNCT
cana-1619	225	9	transforms	transform	VERB
cana-1619	225	10	ℬ𝑟(𝛿	ℬ𝑟(𝛿	ADJ
cana-1619	225	11	)	)	PUNCT
cana-1619	225	12	into	into	ADP
cana-1619	225	13	a	a	DET
cana-1619	225	14	family	family	NOUN
cana-1619	225	15	of	of	ADP
cana-1619	225	16	functions	function	NOUN
cana-1619	225	17	that	that	PRON
cana-1619	225	18	are	be	AUX
cana-1619	225	19	equicontinuous	equicontinuous	ADJ
cana-1619	225	20	.	.	PUNCT
cana-1619	226	1	next	next	ADV
cana-1619	226	2	,	,	PUNCT
cana-1619	226	3	we	we	PRON
cana-1619	226	4	need	need	VERB
cana-1619	226	5	to	to	PART
cana-1619	226	6	demonstrate	demonstrate	VERB
cana-1619	226	7	that	that	SCONJ
cana-1619	226	8	the	the	DET
cana-1619	226	9	set	set	NOUN
cana-1619	226	10	(	(	PUNCT
cana-1619	226	11	γ1(ℵ))(ℬ𝑟(𝛿))(ℎ	γ1(ℵ))(ℬ𝑟(𝛿))(ℎ	NOUN
cana-1619	226	12	)	)	PUNCT
cana-1619	226	13	is	be	AUX
cana-1619	226	14	precompact	precompact	ADJ
cana-1619	226	15	within	within	ADP
cana-1619	226	16	𝒮.	𝒮.	PROPN
cana-1619	226	17	consider	consider	VERB
cana-1619	226	18	fixed	fixed	ADJ
cana-1619	226	19	values	value	NOUN
cana-1619	226	20	𝛿	𝛿	X
cana-1619	226	21	<	<	X
cana-1619	226	22	ℎ	ℎ	X
cana-1619	226	23	≤	≤	NOUN
cana-1619	226	24	𝜛	𝜛	X
cana-1619	226	25	≤	≤	NUM
cana-1619	226	26	𝜚	𝜚	NOUN
cana-1619	226	27	,	,	PUNCT
cana-1619	226	28	and	and	CCONJ
cana-1619	226	29	let	let	VERB
cana-1619	226	30	𝜖	𝜖	PROPN
cana-1619	226	31	be	be	AUX
cana-1619	226	32	a	a	DET
cana-1619	226	33	real	real	ADJ
cana-1619	226	34	number	number	NOUN
cana-1619	226	35	such	such	ADJ
cana-1619	226	36	that	that	SCONJ
cana-1619	226	37	0	0	NUM
cana-1619	226	38	<	<	X
cana-1619	226	39	𝜖	𝜖	X
cana-1619	226	40	<	<	X
cana-1619	226	41	ℎ.	ℎ.	NOUN
cana-1619	226	42	for	for	ADP
cana-1619	226	43	𝜁	𝜁	PROPN
cana-1619	226	44	∈	∈	PROPN
cana-1619	226	45	communications	communication	NOUN
cana-1619	226	46	on	on	ADP
cana-1619	226	47	applied	apply	VERB
cana-1619	226	48	nonlinear	nonlinear	ADJ
cana-1619	226	49	analysis	analysis	NOUN
cana-1619	226	50	issn	issn	NOUN
cana-1619	226	51	:	:	PUNCT
cana-1619	226	52	1074	1074	NUM
cana-1619	226	53	-	-	PUNCT
cana-1619	226	54	133x	133x	NUM
cana-1619	226	55	vol	vol	NOUN
cana-1619	226	56	32	32	NUM
cana-1619	226	57	no	no	NOUN
cana-1619	226	58	.	.	NOUN
cana-1619	226	59	1	1	NUM
cana-1619	226	60	(	(	PUNCT
cana-1619	226	61	2025	2025	NUM
cana-1619	226	62	)	)	PUNCT
cana-1619	226	63	45	45	NUM
cana-1619	226	64	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	226	65	𝐵𝑟(𝛿	𝐵𝑟(𝛿	NOUN
cana-1619	226	66	)	)	PUNCT
cana-1619	226	67	,	,	PUNCT
cana-1619	226	68	(	(	PUNCT
cana-1619	226	69	(	(	PUNCT
cana-1619	226	70	γ1(ℵ	γ1(ℵ	NOUN
cana-1619	226	71	)	)	PUNCT
cana-1619	226	72	)	)	PUNCT
cana-1619	226	73	,	,	PUNCT
cana-1619	226	74	𝜖)(ℎ	𝜖)(ℎ	X
cana-1619	226	75	)	)	PUNCT
cana-1619	226	76	is	be	AUX
cana-1619	226	77	given	give	VERB
cana-1619	226	78	by	by	ADP
cana-1619	226	79	𝑇1(ℎ)𝜙0(ℵ	𝑇1(ℎ)𝜙0(ℵ	NOUN
cana-1619	226	80	)	)	PUNCT
cana-1619	226	81	+	+	NUM
cana-1619	226	82	𝑇2(ℎ)[𝜙′0(ℵ	𝑇2(ℎ)[𝜙′0(ℵ	NOUN
cana-1619	226	83	)	)	PUNCT
cana-1619	227	1	+	+	CCONJ
cana-1619	228	1	𝜌(0	𝜌(0	PROPN
cana-1619	228	2	,	,	PUNCT
cana-1619	228	3	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	228	4	)	)	PUNCT
cana-1619	228	5	,	,	PUNCT
cana-1619	228	6	ℵ	ℵ	NOUN
cana-1619	228	7	)	)	PUNCT
cana-1619	228	8	]	]	PUNCT
cana-1619	229	1	−	−	PROPN
cana-1619	229	2	∫	∫	PROPN
cana-1619	229	3	ℎ−𝜖	ℎ−𝜖	ADV
cana-1619	229	4	0	0	PUNCT
cana-1619	230	1	𝑇2(ℎ	𝑇2(ℎ	ADJ
cana-1619	230	2	−	−	PROPN
cana-1619	230	3	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	NOUN
cana-1619	230	4	,	,	PUNCT
cana-1619	230	5	𝜁𝜛	𝜁𝜛	ADV
cana-1619	230	6	(	(	PUNCT
cana-1619	230	7	.	.	PUNCT
cana-1619	230	8	,	,	PUNCT
cana-1619	230	9	ℵ	ℵ	NOUN
cana-1619	230	10	)	)	PUNCT
cana-1619	230	11	,	,	PUNCT
cana-1619	231	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	231	2	+	+	PROPN
cana-1619	231	3	∫	∫	PROPN
cana-1619	231	4	ℎ−𝜖	ℎ−𝜖	ADV
cana-1619	231	5	0	0	PUNCT
cana-1619	232	1	𝑇2(ℎ	𝑇2(ℎ	NOUN
cana-1619	232	2	−	−	ADP
cana-1619	232	3	𝜛)υ(𝜛	𝜛)υ(𝜛	NOUN
cana-1619	232	4	,	,	PUNCT
cana-1619	232	5	𝜁𝜛	𝜁𝜛	ADV
cana-1619	232	6	(	(	PUNCT
cana-1619	232	7	.	.	PUNCT
cana-1619	232	8	,	,	PUNCT
cana-1619	232	9	ℵ	ℵ	NOUN
cana-1619	232	10	)	)	PUNCT
cana-1619	232	11	,	,	PUNCT
cana-1619	233	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	233	2	utilizing	utilize	VERB
cana-1619	233	3	the	the	DET
cana-1619	233	4	compactness	compactness	NOUN
cana-1619	233	5	property	property	NOUN
cana-1619	233	6	of	of	ADP
cana-1619	233	7	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	233	8	)	)	PUNCT
cana-1619	233	9	for	for	ADP
cana-1619	233	10	ℎ	ℎ	X
cana-1619	233	11	>	>	X
cana-1619	233	12	0	0	NUM
cana-1619	233	13	,	,	PUNCT
cana-1619	233	14	we	we	PRON
cana-1619	233	15	establish	establish	VERB
cana-1619	233	16	that	that	SCONJ
cana-1619	233	17	the	the	DET
cana-1619	233	18	set	set	NOUN
cana-1619	233	19	{	{	PUNCT
cana-1619	233	20	(	(	PUNCT
cana-1619	233	21	(	(	PUNCT
cana-1619	233	22	γ(ℵ))1,𝜖𝜁)(ℎ	γ(ℵ))1,𝜖𝜁)(ℎ	NUM
cana-1619	233	23	):	):	PUNCT
cana-1619	233	24	𝜁	𝜁	PROPN
cana-1619	233	25	∈	∈	PROPN
cana-1619	233	26	𝐵𝑟(𝛿	𝐵𝑟(𝛿	NOUN
cana-1619	233	27	)	)	PUNCT
cana-1619	233	28	}	}	PUNCT
cana-1619	233	29	is	be	AUX
cana-1619	233	30	precompact	precompact	ADJ
cana-1619	233	31	for	for	ADP
cana-1619	233	32	𝜁	𝜁	PROPN
cana-1619	233	33	∈	∈	PROPN
cana-1619	233	34	𝐵𝑟(𝛿	𝐵𝑟(𝛿	NOUN
cana-1619	233	35	)	)	PUNCT
cana-1619	233	36	and	and	CCONJ
cana-1619	233	37	0	0	NUM
cana-1619	233	38	<	<	X
cana-1619	233	39	𝜖	𝜖	X
cana-1619	233	40	<	<	X
cana-1619	233	41	ℎ.	ℎ.	NOUN
cana-1619	233	42	additionally	additionally	ADV
cana-1619	233	43	,	,	PUNCT
cana-1619	233	44	for	for	ADP
cana-1619	233	45	each	each	DET
cana-1619	233	46	𝜁	𝜁	PROPN
cana-1619	233	47	∈	∈	PROPN
cana-1619	233	48	𝐵𝑟(𝛿	𝐵𝑟(𝛿	NOUN
cana-1619	233	49	)	)	PUNCT
cana-1619	233	50	,	,	PUNCT
cana-1619	233	51	we	we	PRON
cana-1619	233	52	ensure	ensure	VERB
cana-1619	233	53	that	that	SCONJ
cana-1619	233	54	||((γ1(ℵ))𝜁)(ℎ	||((γ1(ℵ))𝜁)(ℎ	NUM
cana-1619	233	55	)	)	PUNCT
cana-1619	233	56	−	−	PROPN
cana-1619	233	57	(	(	PUNCT
cana-1619	233	58	(	(	PUNCT
cana-1619	233	59	γ(ℵ))1,𝜖𝜁)(ℎ)||	γ(ℵ))1,𝜖𝜁)(ℎ)||	PROPN
cana-1619	233	60	≤	≤	NUM
cana-1619	233	61	∫	∫	PROPN
cana-1619	233	62	ℎ	ℎ	X
cana-1619	233	63	ℎ−𝜖	ℎ−𝜖	ADV
cana-1619	233	64	||𝑇1(ℎ	||𝑇1(ℎ	VERB
cana-1619	233	65	−	−	PROPN
cana-1619	233	66	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	PROPN
cana-1619	233	67	,	,	PUNCT
cana-1619	233	68	𝜂	𝜂	NOUN
cana-1619	233	69	,	,	PUNCT
cana-1619	233	70	𝜁𝜛	𝜁𝜛	ADV
cana-1619	233	71	(	(	PUNCT
cana-1619	233	72	.	.	PUNCT
cana-1619	233	73	,	,	PUNCT
cana-1619	233	74	ℵ	ℵ	NOUN
cana-1619	233	75	)	)	PUNCT
cana-1619	233	76	,	,	PUNCT
cana-1619	234	1	ℵ)||	ℵ)||	PROPN
cana-1619	235	1	+	+	NUM
cana-1619	235	2	∫	∫	PROPN
cana-1619	235	3	ℎ	ℎ	X
cana-1619	235	4	ℎ−𝜖	ℎ−𝜖	ADV
cana-1619	235	5	||𝑇2(ℎ	||𝑇2(ℎ	NOUN
cana-1619	235	6	−	−	PROPN
cana-1619	235	7	𝜛)υ(𝜛	𝜛)υ(𝜛	NOUN
cana-1619	235	8	,	,	PUNCT
cana-1619	235	9	𝜁𝜛	𝜁𝜛	ADV
cana-1619	235	10	(	(	PUNCT
cana-1619	235	11	.	.	PUNCT
cana-1619	235	12	,	,	PUNCT
cana-1619	235	13	ℵ	ℵ	NOUN
cana-1619	235	14	)	)	PUNCT
cana-1619	235	15	,	,	PUNCT
cana-1619	235	16	ℵ)||	ℵ)||	NUM
cana-1619	235	17	≤	≤	NOUN
cana-1619	235	18	𝜗	𝜗	X
cana-1619	235	19	∫	∫	PROPN
cana-1619	235	20	ℎ	ℎ	X
cana-1619	235	21	ℎ−𝜖	ℎ−𝜖	ADV
cana-1619	235	22	[	[	PUNCT
cana-1619	235	23	sup	sup	NOUN
cana-1619	235	24	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	235	25	]	]	PUNCT
cana-1619	235	26	||𝜁𝜛	||𝜁𝜛	NOUN
cana-1619	235	27	(	(	PUNCT
cana-1619	235	28	.	.	PUNCT
cana-1619	235	29	,	,	PUNCT
cana-1619	235	30	ℵ	ℵ	NOUN
cana-1619	235	31	)	)	PUNCT
cana-1619	235	32	,	,	PUNCT
cana-1619	235	33	ℵ||𝒟	ℵ||𝒟	NOUN
cana-1619	235	34	𝛽0	𝛽0	VERB
cana-1619	235	35	+	+	CCONJ
cana-1619	235	36	𝑑0(ℵ)]𝑑𝜛	𝑑0(ℵ)]𝑑𝜛	NOUN
cana-1619	236	1	+	+	ADP
cana-1619	236	2	𝜗𝑎	𝜗𝑎	NOUN
cana-1619	236	3	∫	∫	PROPN
cana-1619	236	4	ℎ	ℎ	X
cana-1619	236	5	ℎ−𝜖	ℎ−𝜖	ADV
cana-1619	236	6	[	[	PUNCT
cana-1619	236	7	sup	sup	NOUN
cana-1619	236	8	𝜛∈(0.𝜚	𝜛∈(0.𝜚	PROPN
cana-1619	236	9	]	]	PUNCT
cana-1619	236	10	||𝜁𝜛	||𝜁𝜛	NOUN
cana-1619	236	11	(	(	PUNCT
cana-1619	236	12	.	.	PUNCT
cana-1619	236	13	,	,	PUNCT
cana-1619	236	14	ℵ	ℵ	NOUN
cana-1619	236	15	)	)	PUNCT
cana-1619	236	16	,	,	PUNCT
cana-1619	236	17	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	236	18	𝛼0	𝛼0	NOUN
cana-1619	237	1	+	+	CCONJ
cana-1619	237	2	𝑏0(ℵ)]𝑑𝜛	𝑏0(ℵ)]𝑑𝜛	PROPN
cana-1619	237	3	thus	thus	ADV
cana-1619	237	4	,	,	PUNCT
cana-1619	237	5	there	there	PRON
cana-1619	237	6	is	be	VERB
cana-1619	237	7	a	a	DET
cana-1619	237	8	precompact	precompact	ADJ
cana-1619	237	9	sets	set	NOUN
cana-1619	237	10	that	that	PRON
cana-1619	237	11	can	can	AUX
cana-1619	237	12	be	be	AUX
cana-1619	237	13	made	make	VERB
cana-1619	237	14	arbitrarily	arbitrarily	ADV
cana-1619	237	15	close	close	ADJ
cana-1619	237	16	to	to	ADP
cana-1619	237	17	the	the	DET
cana-1619	237	18	set	set	NOUN
cana-1619	237	19	{	{	PUNCT
cana-1619	237	20	(	(	PUNCT
cana-1619	237	21	(	(	PUNCT
cana-1619	237	22	γ1(ℵ))𝜁	γ1(ℵ))𝜁	PROPN
cana-1619	237	23	):	):	PUNCT
cana-1619	237	24	𝜁	𝜁	PROPN
cana-1619	237	25	∈	∈	PROPN
cana-1619	237	26	𝐵𝑟(𝛿	𝐵𝑟(𝛿	NOUN
cana-1619	237	27	)	)	PUNCT
cana-1619	237	28	}	}	PUNCT
cana-1619	237	29	.	.	PUNCT
cana-1619	238	1	therefore	therefore	ADV
cana-1619	238	2	,	,	PUNCT
cana-1619	238	3	the	the	DET
cana-1619	238	4	set	set	NOUN
cana-1619	238	5	{	{	PUNCT
cana-1619	238	6	(	(	PUNCT
cana-1619	238	7	(	(	PUNCT
cana-1619	238	8	γ1(ℵ))𝜁	γ1(ℵ))𝜁	PROPN
cana-1619	238	9	):	):	PUNCT
cana-1619	238	10	𝜁	𝜁	PROPN
cana-1619	238	11	∈	∈	PROPN
cana-1619	238	12	𝐵𝑟(𝛿	𝐵𝑟(𝛿	NOUN
cana-1619	238	13	)	)	PUNCT
cana-1619	238	14	}	}	PUNCT
cana-1619	238	15	is	be	AUX
cana-1619	238	16	relatively	relatively	ADV
cana-1619	238	17	compact	compact	ADJ
cana-1619	238	18	in	in	ADP
cana-1619	238	19	𝒮	𝒮	PROPN
cana-1619	238	20	.	.	PUNCT
cana-1619	239	1	it	it	PRON
cana-1619	239	2	’s	’	VERB
cana-1619	239	3	evident	evident	ADJ
cana-1619	239	4	that	that	SCONJ
cana-1619	239	5	(	(	PUNCT
cana-1619	239	6	γ1(ℵ))(𝐵𝑟(𝛿	γ1(ℵ))(𝐵𝑟(𝛿	PROPN
cana-1619	239	7	)	)	PUNCT
cana-1619	239	8	)	)	PUNCT
cana-1619	239	9	is	be	AUX
cana-1619	239	10	bounded	bound	VERB
cana-1619	239	11	uniformly.since	uniformly.since	PROPN
cana-1619	239	12	we	we	PRON
cana-1619	239	13	have	have	AUX
cana-1619	239	14	established	establish	VERB
cana-1619	239	15	that	that	PRON
cana-1619	239	16	(	(	PUNCT
cana-1619	239	17	γ1(ℵ))(𝐵𝑟(𝛿	γ1(ℵ))(𝐵𝑟(𝛿	PROPN
cana-1619	239	18	)	)	PUNCT
cana-1619	239	19	)	)	PUNCT
cana-1619	239	20	forms	form	VERB
cana-1619	239	21	an	an	DET
cana-1619	239	22	equicontinuous	equicontinuous	ADJ
cana-1619	239	23	family	family	NOUN
cana-1619	239	24	,	,	PUNCT
cana-1619	239	25	the	the	DET
cana-1619	239	26	arzelà	arzelà	PROPN
cana-1619	239	27	-	-	PUNCT
cana-1619	239	28	ascoli	ascoli	PROPN
cana-1619	239	29	theorem	theorem	NOUN
cana-1619	239	30	indicates	indicate	VERB
cana-1619	239	31	that	that	SCONJ
cana-1619	239	32	it	it	PRON
cana-1619	239	33	is	be	AUX
cana-1619	239	34	sufficient	sufficient	ADJ
cana-1619	239	35	to	to	PART
cana-1619	239	36	show	show	VERB
cana-1619	239	37	that	that	SCONJ
cana-1619	239	38	(	(	PUNCT
cana-1619	239	39	γ1(ℵ	γ1(ℵ	NUM
cana-1619	239	40	)	)	PUNCT
cana-1619	239	41	)	)	PUNCT
cana-1619	239	42	maps	map	VERB
cana-1619	239	43	𝐵𝑟(𝛿	𝐵𝑟(𝛿	NOUN
cana-1619	239	44	)	)	PUNCT
cana-1619	239	45	into	into	ADP
cana-1619	239	46	a	a	DET
cana-1619	239	47	relatively	relatively	ADV
cana-1619	239	48	compact	compact	ADJ
cana-1619	239	49	set	set	NOUN
cana-1619	239	50	in	in	ADP
cana-1619	239	51	𝒮.	𝒮.	PROPN
cana-1619	239	52	now	now	ADV
cana-1619	239	53	,	,	PUNCT
cana-1619	239	54	we	we	PRON
cana-1619	239	55	need	need	VERB
cana-1619	239	56	to	to	PART
cana-1619	239	57	confirm	confirm	VERB
cana-1619	239	58	that	that	SCONJ
cana-1619	239	59	(	(	PUNCT
cana-1619	239	60	γ(ℵ))2	γ(ℵ))2	NOUN
cana-1619	239	61	is	be	AUX
cana-1619	239	62	a	a	DET
cana-1619	239	63	compact	compact	ADJ
cana-1619	239	64	operator	operator	NOUN
cana-1619	239	65	as	as	ADV
cana-1619	239	66	well	well	ADV
cana-1619	239	67	.	.	PUNCT
cana-1619	240	1	by	by	ADP
cana-1619	240	2	applying	apply	VERB
cana-1619	240	3	lemma	lemma	PROPN
cana-1619	240	4	2.1	2.1	NUM
cana-1619	240	5	,	,	PUNCT
cana-1619	240	6	we	we	PRON
cana-1619	240	7	establish	establish	VERB
cana-1619	240	8	its	its	PRON
cana-1619	240	9	complete	complete	ADJ
cana-1619	240	10	continuity	continuity	NOUN
cana-1619	240	11	.	.	PUNCT
cana-1619	241	1	the	the	DET
cana-1619	241	2	property	property	NOUN
cana-1619	241	3	of	of	ADP
cana-1619	241	4	(	(	PUNCT
cana-1619	241	5	γ(ℵ))2	γ(ℵ))2	NOUN
cana-1619	241	6	being	be	AUX
cana-1619	241	7	continuous	continuous	ADJ
cana-1619	241	8	can	can	AUX
cana-1619	241	9	be	be	AUX
cana-1619	241	10	demonstrated	demonstrate	VERB
cana-1619	241	11	by	by	ADP
cana-1619	241	12	considering	consider	VERB
cana-1619	241	13	the	the	DET
cana-1619	241	14	state	state	NOUN
cana-1619	241	15	space	space	NOUN
cana-1619	241	16	.	.	PUNCT
cana-1619	242	1	conversely	conversely	ADV
cana-1619	242	2	,	,	PUNCT
cana-1619	242	3	for	for	ADP
cana-1619	242	4	𝑟	𝑟	X
cana-1619	242	5	>	>	X
cana-1619	242	6	0	0	NUM
cana-1619	242	7	,	,	PUNCT
cana-1619	242	8	ℎ	ℎ	PROPN
cana-1619	242	9	∈	∈	PROPN
cana-1619	242	10	(	(	PUNCT
cana-1619	242	11	ℎ𝜉	ℎ𝜉	NOUN
cana-1619	242	12	,	,	PUNCT
cana-1619	242	13	ℎ𝜉+1	ℎ𝜉+1	PROPN
cana-1619	242	14	]	]	X
cana-1619	242	15	∩	∩	NOUN
cana-1619	242	16	(	(	PUNCT
cana-1619	242	17	0	0	NUM
cana-1619	242	18	,	,	PUNCT
cana-1619	242	19	𝜚	𝜚	NOUN
cana-1619	242	20	]	]	X
cana-1619	242	21	,	,	PUNCT
cana-1619	242	22	𝑖	𝑖	X
cana-1619	242	23	≥	≥	NOUN
cana-1619	242	24	1	1	NUM
cana-1619	242	25	,	,	PUNCT
cana-1619	242	26	and	and	CCONJ
cana-1619	242	27	𝜁	𝜁	DET
cana-1619	242	28	∈	∈	PROPN
cana-1619	242	29	ℬ𝑟	ℬ𝑟	PROPN
cana-1619	242	30	=	=	PUNCT
cana-1619	242	31	ℬ𝑟(0	ℬ𝑟(0	PROPN
cana-1619	242	32	,	,	PUNCT
cana-1619	242	33	ℬ𝑟(𝛿	ℬ𝑟(𝛿	ADJ
cana-1619	242	34	)	)	PUNCT
cana-1619	242	35	)	)	PUNCT
cana-1619	242	36	,	,	PUNCT
cana-1619	242	37	we	we	PRON
cana-1619	242	38	observe	observe	VERB
cana-1619	242	39	that	that	SCONJ
cana-1619	242	40	(	(	PUNCT
cana-1619	242	41	γ(ℵ))𝜁(ℎ	γ(ℵ))𝜁(ℎ	PROPN
cana-1619	242	42	)	)	PUNCT
cana-1619	242	43	∈	∈	PROPN
cana-1619	242	44	{	{	PUNCT
cana-1619	242	45	∑	∑	NOUN
cana-1619	242	46	𝜉	𝜉	PROPN
cana-1619	242	47	𝑗=1	𝑗=1	PROPN
cana-1619	242	48	𝑇(ℎ	𝑇(ℎ	NUM
cana-1619	242	49	−	−	PROPN
cana-1619	242	50	ℎ𝑗)𝐼𝑗(ℬ𝑟∗(0	ℎ𝑗)𝐼𝑗(ℬ𝑟∗(0	NOUN
cana-1619	242	51	,	,	PUNCT
cana-1619	242	52	𝒮	𝒮	PROPN
cana-1619	242	53	)	)	PUNCT
cana-1619	242	54	)	)	PUNCT
cana-1619	242	55	,	,	PUNCT
cana-1619	242	56	ℎ	ℎ	PROPN
cana-1619	242	57	∈	∈	PROPN
cana-1619	242	58	(	(	PUNCT
cana-1619	242	59	ℎ𝜉	ℎ𝜉	NOUN
cana-1619	242	60	,	,	PUNCT
cana-1619	242	61	ℎ𝜉+1	ℎ𝜉+1	PROPN
cana-1619	242	62	)	)	PUNCT
cana-1619	242	63	,	,	PUNCT
cana-1619	243	1	∑𝜉𝑗=0	∑𝜉𝑗=0	PROPN
cana-1619	243	2	𝑇(ℎ𝜉+1	𝑇(ℎ𝜉+1	PROPN
cana-1619	243	3	−	−	PROPN
cana-1619	243	4	ℎ𝑗)𝐼𝑗(ℬ𝑟∗(0	ℎ𝑗)𝐼𝑗(ℬ𝑟∗(0	NOUN
cana-1619	243	5	,	,	PUNCT
cana-1619	243	6	𝒮	𝒮	PROPN
cana-1619	243	7	)	)	PUNCT
cana-1619	243	8	)	)	PUNCT
cana-1619	243	9	,	,	PUNCT
cana-1619	243	10	ℎ	ℎ	X
cana-1619	243	11	=	=	SYM
cana-1619	243	12	ℎ𝜉+1	ℎ𝜉+1	PROPN
cana-1619	243	13	,	,	PUNCT
cana-1619	243	14	∑𝜉𝑗=0	∑𝜉𝑗=0	PROPN
cana-1619	243	15	𝑇(ℎ𝜉	𝑇(ℎ𝜉	NOUN
cana-1619	243	16	−	−	PROPN
cana-1619	243	17	ℎ𝑗)𝐼𝑗(ℬ𝑟∗(0	ℎ𝑗)𝐼𝑗(ℬ𝑟∗(0	NOUN
cana-1619	243	18	,	,	PUNCT
cana-1619	243	19	𝒮	𝒮	PROPN
cana-1619	243	20	)	)	PUNCT
cana-1619	243	21	)	)	PUNCT
cana-1619	244	1	+	+	CCONJ
cana-1619	244	2	𝐼𝜉(ℬ𝑟∗(0	𝐼𝜉(ℬ𝑟∗(0	NOUN
cana-1619	244	3	,	,	PUNCT
cana-1619	244	4	𝒮	𝒮	NOUN
cana-1619	244	5	)	)	PUNCT
cana-1619	244	6	)	)	PUNCT
cana-1619	244	7	,	,	PUNCT
cana-1619	244	8	ℎ	ℎ	PROPN
cana-1619	244	9	=	=	SYM
cana-1619	244	10	ℎ𝜉	ℎ𝜉	PROPN
cana-1619	244	11	(	(	PUNCT
cana-1619	244	12	7	7	X
cana-1619	244	13	)	)	PUNCT
cana-1619	244	14	this	this	PRON
cana-1619	244	15	demonstrates	demonstrate	VERB
cana-1619	244	16	that	that	SCONJ
cana-1619	244	17	[	[	X
cana-1619	244	18	(	(	PUNCT
cana-1619	244	19	γ(ℵ))2(𝐵𝑟)]𝜉(ℎ	γ(ℵ))2(𝐵𝑟)]𝜉(ℎ	X
cana-1619	244	20	)	)	PUNCT
cana-1619	244	21	is	be	AUX
cana-1619	244	22	relatively	relatively	ADV
cana-1619	244	23	compact	compact	ADJ
cana-1619	244	24	in	in	ADP
cana-1619	244	25	𝒮	𝒮	PROPN
cana-1619	244	26	for	for	ADP
cana-1619	244	27	each	each	DET
cana-1619	244	28	ℎ	ℎ	PART
cana-1619	244	29	∈	∈	PROPN
cana-1619	245	1	[	[	X
cana-1619	245	2	ℎ𝜉	ℎ𝜉	NOUN
cana-1619	245	3	,	,	PUNCT
cana-1619	245	4	ℎ𝜉+1	ℎ𝜉+1	PROPN
cana-1619	245	5	]	]	PUNCT
cana-1619	245	6	,	,	PUNCT
cana-1619	245	7	as	as	SCONJ
cana-1619	245	8	the	the	DET
cana-1619	245	9	maps	map	NOUN
cana-1619	245	10	𝐼𝑗	𝐼𝑗	PROPN
cana-1619	245	11	are	be	AUX
cana-1619	245	12	completely	completely	ADV
cana-1619	245	13	continuous	continuous	ADJ
cana-1619	245	14	.	.	PUNCT
cana-1619	245	15	additionally	additionally	ADV
cana-1619	245	16	,	,	PUNCT
cana-1619	245	17	by	by	ADP
cana-1619	245	18	leveraging	leverage	VERB
cana-1619	245	19	the	the	DET
cana-1619	245	20	compactness	compactness	NOUN
cana-1619	245	21	of	of	ADP
cana-1619	245	22	the	the	DET
cana-1619	245	23	operators	operator	NOUN
cana-1619	245	24	𝐼𝜉	𝐼𝜉	PROPN
cana-1619	245	25	along	along	ADP
cana-1619	245	26	with	with	ADP
cana-1619	245	27	the	the	DET
cana-1619	245	28	strong	strong	ADJ
cana-1619	245	29	continuity	continuity	NOUN
cana-1619	245	30	of	of	ADP
cana-1619	245	31	(	(	PUNCT
cana-1619	245	32	𝑇(ℎ))𝑡0	𝑇(ℎ))𝑡0	PROPN
cana-1619	245	33	,	,	PUNCT
cana-1619	245	34	we	we	PRON
cana-1619	245	35	can	can	AUX
cana-1619	245	36	show	show	VERB
cana-1619	245	37	that	that	SCONJ
cana-1619	245	38	[	[	X
cana-1619	245	39	(	(	PUNCT
cana-1619	245	40	γ(ℵ))2(𝐵𝑟)]𝜉	γ(ℵ))2(𝐵𝑟)]𝜉	NOUN
cana-1619	245	41	is	be	AUX
cana-1619	245	42	uniformly	uniformly	ADV
cana-1619	245	43	continuous	continuous	ADJ
cana-1619	245	44	at	at	ADP
cana-1619	245	45	ℎ	ℎ	PROPN
cana-1619	245	46	for	for	ADP
cana-1619	245	47	every	every	DET
cana-1619	245	48	ℎ	ℎ	PROPN
cana-1619	245	49	∈	∈	PROPN
cana-1619	245	50	[	[	X
cana-1619	245	51	ℎ𝜉	ℎ𝜉	NOUN
cana-1619	245	52	,	,	PUNCT
cana-1619	245	53	ℎ𝜉+1	ℎ𝜉+1	PROPN
cana-1619	245	54	]	]	PUNCT
cana-1619	245	55	and	and	CCONJ
cana-1619	245	56	for	for	ADP
cana-1619	245	57	each	each	DET
cana-1619	245	58	𝜉	𝜉	NOUN
cana-1619	245	59	=	=	SYM
cana-1619	245	60	1,2	1,2	NUM
cana-1619	245	61	,	,	PUNCT
cana-1619	245	62	…	…	PUNCT
cana-1619	245	63	,	,	PUNCT
cana-1619	245	64	𝑛.	𝑛.	NOUN
cana-1619	245	65	therefore	therefore	ADV
cana-1619	245	66	,	,	PUNCT
cana-1619	245	67	according	accord	VERB
cana-1619	245	68	to	to	ADP
cana-1619	245	69	lemma	lemma	PROPN
cana-1619	245	70	2.2	2.2	NUM
cana-1619	245	71	,	,	PUNCT
cana-1619	245	72	(	(	PUNCT
cana-1619	245	73	γ(ℵ))2	γ(ℵ))2	NOUN
cana-1619	245	74	is	be	AUX
cana-1619	245	75	completely	completely	ADV
cana-1619	245	76	continuous	continuous	ADJ
cana-1619	245	77	.	.	PUNCT
cana-1619	246	1	step	step	NOUN
cana-1619	246	2	4	4	NUM
cana-1619	246	3	:	:	PUNCT
cana-1619	246	4	certainly	certainly	ADV
cana-1619	246	5	,	,	PUNCT
cana-1619	246	6	our	our	PRON
cana-1619	246	7	goal	goal	NOUN
cana-1619	246	8	is	be	AUX
cana-1619	246	9	to	to	PART
cana-1619	246	10	identify	identify	VERB
cana-1619	246	11	an	an	DET
cana-1619	246	12	open	open	ADJ
cana-1619	246	13	set	set	NOUN
cana-1619	247	1	𝑈	𝑈	PROPN
cana-1619	247	2	⊆	⊆	NUM
cana-1619	247	3	𝑃𝐶𝛿	𝑃𝐶𝛿	NOUN
cana-1619	247	4	such	such	ADJ
cana-1619	247	5	that	that	PRON
cana-1619	247	6	for	for	ADP
cana-1619	247	7	any	any	DET
cana-1619	247	8	point	point	NOUN
cana-1619	247	9	𝜁	𝜁	ADP
cana-1619	247	10	lying	lie	VERB
cana-1619	247	11	on	on	ADP
cana-1619	247	12	the	the	DET
cana-1619	247	13	boundary	boundary	NOUN
cana-1619	247	14	of	of	ADP
cana-1619	247	15	𝑈	𝑈	PROPN
cana-1619	247	16	,	,	PUNCT
cana-1619	247	17	it	it	PRON
cana-1619	247	18	won’h	won’h	AUX
cana-1619	247	19	be	be	AUX
cana-1619	247	20	in	in	ADP
cana-1619	247	21	the	the	DET
cana-1619	247	22	set	set	NOUN
cana-1619	247	23	𝜆(γ(ℵ))(𝜁	𝜆(γ(ℵ))(𝜁	NUM
cana-1619	247	24	)	)	PUNCT
cana-1619	247	25	for	for	ADP
cana-1619	247	26	𝜆	𝜆	DET
cana-1619	247	27	∈	∈	PROPN
cana-1619	247	28	(	(	PUNCT
cana-1619	247	29	0,1	0,1	NUM
cana-1619	247	30	)	)	PUNCT
cana-1619	247	31	.	.	PUNCT
cana-1619	248	1	therefore	therefore	ADV
cana-1619	248	2	,	,	PUNCT
cana-1619	248	3	for	for	ADP
cana-1619	248	4	every	every	DET
cana-1619	248	5	ℎ	ℎ	PROPN
cana-1619	248	6	∈	∈	PROPN
cana-1619	248	7	(	(	PUNCT
cana-1619	248	8	0	0	NUM
cana-1619	248	9	,	,	PUNCT
cana-1619	248	10	𝜚	𝜚	NOUN
cana-1619	248	11	]	]	X
cana-1619	248	12	,	,	PUNCT
cana-1619	248	13	communications	communication	NOUN
cana-1619	248	14	on	on	ADP
cana-1619	248	15	applied	apply	VERB
cana-1619	248	16	nonlinear	nonlinear	ADJ
cana-1619	248	17	analysis	analysis	NOUN
cana-1619	248	18	issn	issn	NOUN
cana-1619	248	19	:	:	PUNCT
cana-1619	248	20	1074	1074	NUM
cana-1619	248	21	-	-	PUNCT
cana-1619	248	22	133x	133x	NUM
cana-1619	248	23	vol	vol	NOUN
cana-1619	248	24	32	32	NUM
cana-1619	248	25	no	no	NOUN
cana-1619	248	26	.	.	NOUN
cana-1619	248	27	1	1	NUM
cana-1619	248	28	(	(	PUNCT
cana-1619	248	29	2025	2025	NUM
cana-1619	248	30	)	)	PUNCT
cana-1619	248	31	46	46	NUM
cana-1619	248	32	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	248	33	(	(	PUNCT
cana-1619	248	34	γ(ℵ))𝜁(ℎ	γ(ℵ))𝜁(ℎ	PROPN
cana-1619	248	35	)	)	PUNCT
cana-1619	248	36	=	=	SYM
cana-1619	249	1	𝜆𝜁(ℎ	𝜆𝜁(ℎ	NOUN
cana-1619	249	2	,	,	PUNCT
cana-1619	249	3	ℵ	ℵ	NOUN
cana-1619	249	4	)	)	PUNCT
cana-1619	249	5	=	=	SYM
cana-1619	249	6	𝜆𝑇1(ℎ)𝜙0(ℵ	𝜆𝑇1(ℎ)𝜙0(ℵ	X
cana-1619	249	7	)	)	PUNCT
cana-1619	249	8	+	+	CCONJ
cana-1619	249	9	𝜆𝑇2(ℎ)[𝜙′0(ℵ	𝜆𝑇2(ℎ)[𝜙′0(ℵ	NOUN
cana-1619	249	10	)	)	PUNCT
cana-1619	249	11	+	+	CCONJ
cana-1619	250	1	𝜌(0	𝜌(0	PROPN
cana-1619	250	2	,	,	PUNCT
cana-1619	250	3	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	250	4	)	)	PUNCT
cana-1619	250	5	,	,	PUNCT
cana-1619	250	6	ℵ	ℵ	NOUN
cana-1619	250	7	)	)	PUNCT
cana-1619	250	8	]	]	PUNCT
cana-1619	251	1	−	−	PROPN
cana-1619	251	2	𝜆∫	𝜆∫	PROPN
cana-1619	251	3	ℎ−𝜖	ℎ−𝜖	ADV
cana-1619	251	4	0	0	NUM
cana-1619	251	5	𝑇2(ℎ)𝜌(𝜛	𝑇2(ℎ)𝜌(𝜛	NUM
cana-1619	251	6	,	,	PUNCT
cana-1619	251	7	𝜁𝜛	𝜁𝜛	ADV
cana-1619	251	8	(	(	PUNCT
cana-1619	251	9	.	.	PUNCT
cana-1619	251	10	,	,	PUNCT
cana-1619	251	11	ℵ	ℵ	NOUN
cana-1619	251	12	)	)	PUNCT
cana-1619	251	13	,	,	PUNCT
cana-1619	252	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	252	2	+	+	PROPN
cana-1619	252	3	𝜆∫	𝜆∫	ADJ
cana-1619	252	4	ℎ	ℎ	PART
cana-1619	252	5	0	0	PUNCT
cana-1619	252	6	𝑇2(ℎ	𝑇2(ℎ	ADJ
cana-1619	252	7	−	−	NOUN
cana-1619	252	8	𝜛)υ(𝜛	𝜛)υ(𝜛	NOUN
cana-1619	252	9	,	,	PUNCT
cana-1619	252	10	𝜁𝜛	𝜁𝜛	ADV
cana-1619	252	11	(	(	PUNCT
cana-1619	252	12	.	.	PUNCT
cana-1619	252	13	,	,	PUNCT
cana-1619	252	14	ℵ	ℵ	NOUN
cana-1619	252	15	)	)	PUNCT
cana-1619	252	16	,	,	PUNCT
cana-1619	253	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	253	2	+	+	CCONJ
cana-1619	253	3	𝜆	𝜆	PROPN
cana-1619	253	4	∑	∑	ADV
cana-1619	253	5	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	253	6	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	253	7	−	−	PROPN
cana-1619	254	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	254	2	,	,	PUNCT
cana-1619	254	3	ℵ	ℵ	NOUN
cana-1619	254	4	)	)	PUNCT
cana-1619	254	5	)	)	PUNCT
cana-1619	255	1	+	+	ADP
cana-1619	255	2	𝜆	𝜆	DET
cana-1619	255	3	∑	∑	ADV
cana-1619	255	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	255	5	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	255	6	−	−	PROPN
cana-1619	255	7	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	255	8	,	,	PUNCT
cana-1619	255	9	ℵ	ℵ	NOUN
cana-1619	255	10	)	)	PUNCT
cana-1619	255	11	)	)	PUNCT
cana-1619	255	12	for	for	ADP
cana-1619	255	13	each	each	DET
cana-1619	255	14	ℎ	ℎ	PROPN
cana-1619	255	15	∈	∈	PROPN
cana-1619	255	16	(	(	PUNCT
cana-1619	255	17	0	0	NUM
cana-1619	255	18	,	,	PUNCT
cana-1619	255	19	𝜚	𝜚	NOUN
cana-1619	255	20	]	]	X
cana-1619	255	21	,	,	PUNCT
cana-1619	255	22	we	we	PRON
cana-1619	255	23	have	have	VERB
cana-1619	255	24	||𝜁(ℎ	||𝜁(ℎ	ADJ
cana-1619	255	25	,	,	PUNCT
cana-1619	255	26	ℵ)||	ℵ)||	NUM
cana-1619	255	27	≤	≤	NOUN
cana-1619	255	28	||(γ(ℵ))𝜁(ℎ)||	||(γ(ℵ))𝜁(ℎ)||	NOUN
cana-1619	255	29	and	and	CCONJ
cana-1619	255	30	||(γ(ℵ))𝜁(ℎ)||	||(γ(ℵ))𝜁(ℎ)||	NOUN
cana-1619	255	31	≤	≤	NOUN
cana-1619	255	32	||𝑇1(ℎ)𝜙0(ℵ)||	||𝑇1(ℎ)𝜙0(ℵ)||	NOUN
cana-1619	255	33	+	+	CCONJ
cana-1619	255	34	||𝑇2(ℎ)[𝜙′0(ℵ	||𝑇2(ℎ)[𝜙′0(ℵ	ADJ
cana-1619	255	35	)	)	PUNCT
cana-1619	256	1	+	+	CCONJ
cana-1619	256	2	𝜌(0	𝜌(0	PROPN
cana-1619	256	3	,	,	PUNCT
cana-1619	256	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	256	5	)	)	PUNCT
cana-1619	256	6	,	,	PUNCT
cana-1619	256	7	ℵ)]||	ℵ)]||	PUNCT
cana-1619	257	1	+	+	ADJ
cana-1619	257	2	∫	∫	PROPN
cana-1619	257	3	ℎ	ℎ	SYM
cana-1619	257	4	0	0	PROPN
cana-1619	257	5	||𝑇2(ℎ	||𝑇2(ℎ	NOUN
cana-1619	257	6	−	−	PROPN
cana-1619	257	7	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	NOUN
cana-1619	257	8	,	,	PUNCT
cana-1619	257	9	𝜁𝜛	𝜁𝜛	ADV
cana-1619	257	10	(	(	PUNCT
cana-1619	257	11	.	.	PUNCT
cana-1619	257	12	,	,	PUNCT
cana-1619	257	13	ℵ	ℵ	NOUN
cana-1619	257	14	)	)	PUNCT
cana-1619	257	15	,	,	PUNCT
cana-1619	257	16	ℵ)||𝑑𝜛	ℵ)||𝑑𝜛	PROPN
cana-1619	257	17	+	+	PROPN
cana-1619	257	18	∫	∫	PROPN
cana-1619	257	19	ℎ	ℎ	SYM
cana-1619	257	20	0	0	PROPN
cana-1619	257	21	||𝑇2(ℎ	||𝑇2(ℎ	NOUN
cana-1619	257	22	−	−	PROPN
cana-1619	257	23	𝜛)υ(π	𝜛)υ(π	NOUN
cana-1619	257	24	,	,	PUNCT
cana-1619	257	25	𝜁𝜛	𝜁𝜛	ADV
cana-1619	257	26	(	(	PUNCT
cana-1619	257	27	.	.	PUNCT
cana-1619	257	28	,	,	PUNCT
cana-1619	257	29	ℵ	ℵ	NOUN
cana-1619	257	30	)	)	PUNCT
cana-1619	257	31	,	,	PUNCT
cana-1619	257	32	ℵ)||𝑑𝜛	ℵ)||𝑑𝜛	NOUN
cana-1619	258	1	+	+	PROPN
cana-1619	258	2	||	||	ADV
cana-1619	258	3	∑	∑	PUNCT
cana-1619	258	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	VERB
cana-1619	258	5	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	258	6	−	−	PROPN
cana-1619	259	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	259	2	,	,	PUNCT
cana-1619	259	3	ℵ))||	ℵ))||	NOUN
cana-1619	260	1	+	+	CCONJ
cana-1619	260	2	||	||	NUM
cana-1619	260	3	∑	∑	PUNCT
cana-1619	260	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	260	5	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	260	6	−	−	PROPN
cana-1619	260	7	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	260	8	,	,	PUNCT
cana-1619	260	9	ℵ))||	ℵ))||	NOUN
cana-1619	260	10	by	by	ADP
cana-1619	260	11	step	step	NOUN
cana-1619	260	12	1	1	NUM
cana-1619	260	13	,	,	PUNCT
cana-1619	260	14	||(γ(ℵ))𝜁(ℎ)||	||(γ(ℵ))𝜁(ℎ)||	PROPN
cana-1619	260	15	≤	≤	NOUN
cana-1619	260	16	𝑅(ℵ	𝑅(ℵ	NUM
cana-1619	260	17	)	)	PUNCT
cana-1619	260	18	we	we	PRON
cana-1619	260	19	can	can	AUX
cana-1619	260	20	find	find	VERB
cana-1619	260	21	a	a	DET
cana-1619	260	22	constant	constant	ADJ
cana-1619	260	23	𝑅(ℵ	𝑅(ℵ	NUM
cana-1619	260	24	)	)	PUNCT
cana-1619	260	25	such	such	ADJ
cana-1619	260	26	that	that	SCONJ
cana-1619	260	27	∥	∥	NUM
cana-1619	260	28	𝜁	𝜁	X
cana-1619	260	29	∥𝑃𝐶≠	∥𝑃𝐶≠	PROPN
cana-1619	260	30	𝑅(ℵ	𝑅(ℵ	NUM
cana-1619	260	31	)	)	PUNCT
cana-1619	260	32	.	.	PUNCT
cana-1619	261	1	set	set	VERB
cana-1619	261	2	𝑈	𝑈	PROPN
cana-1619	261	3	=	=	PUNCT
cana-1619	261	4	{	{	PUNCT
cana-1619	261	5	𝜁	𝜁	PROPN
cana-1619	261	6	∈	∈	PROPN
cana-1619	261	7	𝑃𝐶([𝛿	𝑃𝐶([𝛿	NOUN
cana-1619	261	8	,	,	PUNCT
cana-1619	261	9	𝜚	𝜚	NOUN
cana-1619	261	10	]	]	X
cana-1619	261	11	,	,	PUNCT
cana-1619	261	12	𝒮	𝒮	NOUN
cana-1619	261	13	)	)	PUNCT
cana-1619	262	1	|	|	ADV
cana-1619	262	2	sup	sup	NOUN
cana-1619	262	3	𝛿≤ℎ≤𝜚	𝛿≤ℎ≤𝜚	NOUN
cana-1619	262	4	∥	∥	X
cana-1619	262	5	𝜁(ℎ	𝜁(ℎ	NOUN
cana-1619	262	6	,	,	PUNCT
cana-1619	262	7	ℵ	ℵ	NOUN
cana-1619	262	8	)	)	PUNCT
cana-1619	262	9	∥	∥	X
cana-1619	262	10	<	<	X
cana-1619	262	11	𝑅(ℵ	𝑅(ℵ	NUM
cana-1619	262	12	)	)	PUNCT
cana-1619	262	13	}	}	PUNCT
cana-1619	262	14	the	the	DET
cana-1619	262	15	results	result	NOUN
cana-1619	262	16	obtained	obtain	VERB
cana-1619	262	17	from	from	ADP
cana-1619	262	18	steps	step	NOUN
cana-1619	262	19	1	1	NUM
cana-1619	262	20	-	-	SYM
cana-1619	262	21	3	3	NUM
cana-1619	262	22	in	in	ADP
cana-1619	262	23	theorem	theorem	ADJ
cana-1619	262	24	3.1	3.1	NUM
cana-1619	262	25	imply	imply	NOUN
cana-1619	262	26	that	that	SCONJ
cana-1619	262	27	it	it	PRON
cana-1619	262	28	’s	’	VERB
cana-1619	262	29	enough	enough	ADV
cana-1619	262	30	to	to	PART
cana-1619	262	31	show	show	VERB
cana-1619	262	32	that	that	SCONJ
cana-1619	262	33	(	(	PUNCT
cana-1619	262	34	γ(ℵ)):𝑈	γ(ℵ)):𝑈	PROPN
cana-1619	262	35	→	→	SYM
cana-1619	262	36	𝑃𝐶𝛿	𝑃𝐶𝛿	PROPN
cana-1619	262	37	is	be	AUX
cana-1619	262	38	a	a	DET
cana-1619	262	39	compact	compact	ADJ
cana-1619	262	40	mapping	mapping	NOUN
cana-1619	262	41	.	.	PUNCT
cana-1619	263	1	with	with	ADP
cana-1619	263	2	the	the	DET
cana-1619	263	3	selection	selection	NOUN
cana-1619	263	4	of	of	ADP
cana-1619	263	5	𝑈	𝑈	PROPN
cana-1619	263	6	,	,	PUNCT
cana-1619	263	7	no	no	DET
cana-1619	263	8	𝜑	𝜑	NOUN
cana-1619	263	9	∈	∈	PROPN
cana-1619	263	10	𝜕𝑈	𝜕𝑈	NOUN
cana-1619	263	11	exists	exist	VERB
cana-1619	263	12	for	for	ADP
cana-1619	263	13	which	which	PRON
cana-1619	263	14	𝜁	𝜁	PROPN
cana-1619	263	15	∈	∈	PROPN
cana-1619	263	16	𝜆(γ(ℵ))(𝜁	𝜆(γ(ℵ))(𝜁	PROPN
cana-1619	263	17	)	)	PUNCT
cana-1619	263	18	for	for	ADP
cana-1619	263	19	𝜆	𝜆	DET
cana-1619	263	20	∈	∈	PROPN
cana-1619	263	21	(	(	PUNCT
cana-1619	263	22	0,1	0,1	NOUN
cana-1619	263	23	)	)	PUNCT
cana-1619	263	24	.	.	PUNCT
cana-1619	264	1	based	base	VERB
cana-1619	264	2	on	on	ADP
cana-1619	264	3	lemma	lemma	PROPN
cana-1619	264	4	2.1	2.1	NUM
cana-1619	264	5	,	,	PUNCT
cana-1619	264	6	we	we	PRON
cana-1619	264	7	assume	assume	VERB
cana-1619	264	8	that	that	SCONJ
cana-1619	264	9	the	the	DET
cana-1619	264	10	operator	operator	NOUN
cana-1619	264	11	(	(	PUNCT
cana-1619	264	12	γ(ℵ	γ(ℵ	PROPN
cana-1619	264	13	)	)	PUNCT
cana-1619	264	14	)	)	PUNCT
cana-1619	264	15	has	have	AUX
cana-1619	264	16	a	a	DET
cana-1619	264	17	fixed	fix	VERB
cana-1619	264	18	point	point	NOUN
cana-1619	264	19	𝜁∗	𝜁∗	PROPN
cana-1619	264	20	∈	∈	PROPN
cana-1619	264	21	𝑈	𝑈	PROPN
cana-1619	264	22	..	..	PUNCT
cana-1619	264	23	thus	thus	ADV
cana-1619	264	24	,	,	PUNCT
cana-1619	264	25	we	we	PRON
cana-1619	264	26	obtain	obtain	VERB
cana-1619	264	27	𝜁∗(ℎ	𝜁∗(ℎ	PROPN
cana-1619	264	28	,	,	PUNCT
cana-1619	264	29	ℵ	ℵ	NOUN
cana-1619	264	30	)	)	PUNCT
cana-1619	264	31	=	=	SYM
cana-1619	264	32	𝑇1(ℎ)𝜙0(ℵ	𝑇1(ℎ)𝜙0(ℵ	NOUN
cana-1619	264	33	)	)	PUNCT
cana-1619	265	1	+	+	NUM
cana-1619	266	1	𝑇2(ℎ)[𝜙′0(ℵ	𝑇2(ℎ)[𝜙′0(ℵ	NOUN
cana-1619	266	2	)	)	PUNCT
cana-1619	267	1	+	+	CCONJ
cana-1619	267	2	𝜌(0	𝜌(0	PROPN
cana-1619	267	3	,	,	PUNCT
cana-1619	267	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	267	5	)	)	PUNCT
cana-1619	267	6	,	,	PUNCT
cana-1619	267	7	ℵ	ℵ	NOUN
cana-1619	267	8	)	)	PUNCT
cana-1619	267	9	]	]	PUNCT
cana-1619	268	1	+	+	CCONJ
cana-1619	268	2	∫	∫	X
cana-1619	268	3	ℎ	ℎ	X
cana-1619	268	4	0	0	SYM
cana-1619	268	5	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	268	6	−	−	PROPN
cana-1619	268	7	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	NOUN
cana-1619	268	8	,	,	PUNCT
cana-1619	268	9	𝜁𝜛	𝜁𝜛	ADV
cana-1619	268	10	∗	∗	NOUN
cana-1619	268	11	(	(	PUNCT
cana-1619	268	12	.	.	PUNCT
cana-1619	268	13	,	,	PUNCT
cana-1619	268	14	ℵ	ℵ	NOUN
cana-1619	268	15	)	)	PUNCT
cana-1619	268	16	,	,	PUNCT
cana-1619	269	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	269	2	+	+	PROPN
cana-1619	269	3	∫	∫	PROPN
cana-1619	269	4	ℎ	ℎ	X
cana-1619	269	5	0	0	SYM
cana-1619	269	6	𝑇2(ℎ	𝑇2(ℎ	ADJ
cana-1619	269	7	−	−	PROPN
cana-1619	269	8	𝜛)υ(π	𝜛)υ(π	NOUN
cana-1619	269	9	,	,	PUNCT
cana-1619	269	10	𝜁𝜛	𝜁𝜛	ADV
cana-1619	269	11	∗	∗	NOUN
cana-1619	269	12	(	(	PUNCT
cana-1619	269	13	.	.	PUNCT
cana-1619	269	14	,	,	PUNCT
cana-1619	269	15	ℵ	ℵ	NOUN
cana-1619	269	16	)	)	PUNCT
cana-1619	269	17	,	,	PUNCT
cana-1619	270	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	270	2	+	+	CCONJ
cana-1619	270	3	∑0<ℎ𝜉<ℎ	∑0<ℎ𝜉<ℎ	PROPN
cana-1619	271	1	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	272	1	−	−	PROPN
cana-1619	273	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	273	2	,	,	PUNCT
cana-1619	273	3	ℵ	ℵ	NOUN
cana-1619	273	4	)	)	PUNCT
cana-1619	273	5	)	)	PUNCT
cana-1619	274	1	+	+	VERB
cana-1619	274	2	∑0<ℎ𝜉<ℎ	∑0<ℎ𝜉<ℎ	PROPN
cana-1619	274	3	𝑇2(ℎ	𝑇2(ℎ	NOUN
cana-1619	274	4	−	−	ADP
cana-1619	274	5	ℎ𝜉)𝐼′𝜉(𝜁	ℎ𝜉)𝐼′𝜉(𝜁	PROPN
cana-1619	274	6	∗(ℎ𝜉	∗(ℎ𝜉	NOUN
cana-1619	274	7	,	,	PUNCT
cana-1619	274	8	ℵ	ℵ	NOUN
cana-1619	274	9	)	)	PUNCT
cana-1619	274	10	)	)	PUNCT
cana-1619	274	11	(	(	PUNCT
cana-1619	274	12	8)	8)	NUM
cana-1619	274	13	this	this	PRON
cana-1619	274	14	suggests	suggest	VERB
cana-1619	274	15	that	that	SCONJ
cana-1619	274	16	𝜁∗(ℎ	𝜁∗(ℎ	PROPN
cana-1619	274	17	,	,	PUNCT
cana-1619	274	18	ℵ	ℵ	NOUN
cana-1619	274	19	)	)	PUNCT
cana-1619	274	20	possesses	possess	VERB
cana-1619	274	21	a	a	DET
cana-1619	274	22	fixed	fix	VERB
cana-1619	274	23	point	point	NOUN
cana-1619	274	24	and	and	CCONJ
cana-1619	274	25	serves	serve	VERB
cana-1619	274	26	as	as	ADP
cana-1619	274	27	a	a	DET
cana-1619	274	28	mild	mild	ADJ
cana-1619	274	29	solution	solution	NOUN
cana-1619	274	30	to	to	ADP
cana-1619	274	31	problem	problem	NOUN
cana-1619	274	32	(	(	PUNCT
cana-1619	274	33	1.1	1.1	NUM
cana-1619	274	34	)	)	PUNCT
cana-1619	274	35	.	.	PUNCT
cana-1619	275	1	this	this	PRON
cana-1619	275	2	concludes	conclude	VERB
cana-1619	275	3	the	the	DET
cana-1619	275	4	proof	proof	NOUN
cana-1619	275	5	of	of	ADP
cana-1619	275	6	the	the	DET
cana-1619	275	7	theorem	theorem	NOUN
cana-1619	275	8	.	.	PROPN
cana-1619	275	9	4	4	NUM
cana-1619	275	10	approximate	approximate	ADJ
cana-1619	275	11	contollability	contollability	NOUN
cana-1619	275	12	of	of	ADP
cana-1619	275	13	random	random	ADJ
cana-1619	275	14	neutral	neutral	ADJ
cana-1619	275	15	functional	functional	ADJ
cana-1619	275	16	differential	differential	NOUN
cana-1619	275	17	equation	equation	NOUN
cana-1619	275	18	definition	definition	NOUN
cana-1619	275	19	6	6	NUM
cana-1619	275	20	the	the	DET
cana-1619	275	21	problem	problem	NOUN
cana-1619	275	22	(	(	PUNCT
cana-1619	275	23	1.2	1.2	NUM
cana-1619	275	24	)	)	PUNCT
cana-1619	275	25	is	be	AUX
cana-1619	275	26	controllable	controllable	ADJ
cana-1619	275	27	on	on	ADP
cana-1619	275	28	the	the	DET
cana-1619	275	29	interval	interval	NOUN
cana-1619	275	30	(	(	PUNCT
cana-1619	275	31	0	0	NUM
cana-1619	275	32	,	,	PUNCT
cana-1619	275	33	ϱ	ϱ	ADP
cana-1619	275	34	]	]	PUNCT
cana-1619	275	35	if	if	SCONJ
cana-1619	275	36	,	,	PUNCT
cana-1619	275	37	for	for	ADP
cana-1619	275	38	any	any	DET
cana-1619	275	39	given	give	VERB
cana-1619	275	40	final	final	ADJ
cana-1619	275	41	state	state	NOUN
cana-1619	275	42	ζ1(ℵ	ζ1(ℵ	NUM
cana-1619	275	43	)	)	PUNCT
cana-1619	275	44	,	,	PUNCT
cana-1619	275	45	there	there	PRON
cana-1619	275	46	is	be	VERB
cana-1619	275	47	a	a	DET
cana-1619	275	48	control	control	NOUN
cana-1619	275	49	y(h	y(h	NOUN
cana-1619	275	50	,	,	PUNCT
cana-1619	275	51	ℵ	ℵ	NOUN
cana-1619	275	52	)	)	PUNCT
cana-1619	275	53	in	in	ADP
cana-1619	275	54	l2(j	l2(j	PROPN
cana-1619	275	55	,	,	PUNCT
cana-1619	275	56	ω	ω	NOUN
cana-1619	275	57	)	)	PUNCT
cana-1619	275	58	such	such	ADJ
cana-1619	275	59	that	that	SCONJ
cana-1619	275	60	the	the	DET
cana-1619	275	61	solution	solution	NOUN
cana-1619	275	62	ζ(h	ζ(h	NOUN
cana-1619	275	63	,	,	PUNCT
cana-1619	275	64	ℵ	ℵ	NOUN
cana-1619	275	65	)	)	PUNCT
cana-1619	275	66	of	of	ADP
cana-1619	275	67	(	(	PUNCT
cana-1619	275	68	1.2	1.2	NUM
cana-1619	275	69	)	)	PUNCT
cana-1619	275	70	reaches	reach	VERB
cana-1619	275	71	ζ1(ℵ	ζ1(ℵ	NUM
cana-1619	275	72	)	)	PUNCT
cana-1619	275	73	at	at	ADP
cana-1619	275	74	time	time	NOUN
cana-1619	275	75	ϱ.	ϱ.	X
cana-1619	276	1	we	we	PRON
cana-1619	276	2	now	now	ADV
cana-1619	276	3	present	present	VERB
cana-1619	276	4	our	our	PRON
cana-1619	276	5	primary	primary	ADJ
cana-1619	276	6	existence	existence	NOUN
cana-1619	276	7	result	result	NOUN
cana-1619	276	8	regarding	regard	VERB
cana-1619	276	9	problem	problem	NOUN
cana-1619	276	10	(	(	PUNCT
cana-1619	276	11	1.2	1.2	NUM
cana-1619	276	12	)	)	PUNCT
cana-1619	276	13	.	.	PUNCT
cana-1619	277	1	the	the	DET
cana-1619	277	2	definition	definition	NOUN
cana-1619	277	3	of	of	ADP
cana-1619	277	4	a	a	DET
cana-1619	277	5	mild	mild	ADJ
cana-1619	277	6	random	random	ADJ
cana-1619	277	7	solution	solution	NOUN
cana-1619	277	8	comes	come	VERB
cana-1619	277	9	first	first	ADV
cana-1619	277	10	.	.	PUNCT
cana-1619	278	1	if	if	SCONJ
cana-1619	278	2	ζ0	ζ0	NOUN
cana-1619	278	3	=	=	SYM
cana-1619	278	4	∅	∅	NOUN
cana-1619	278	5	and	and	CCONJ
cana-1619	278	6	the	the	DET
cana-1619	278	7	continuous	continuous	ADJ
cana-1619	278	8	function	function	NOUN
cana-1619	278	9	ζ	ζ	NOUN
cana-1619	278	10	:	:	PUNCT
cana-1619	278	11	pc(j	pc(j	NOUN
cana-1619	278	12	,	,	PUNCT
cana-1619	278	13	𝒮	𝒮	NOUN
cana-1619	278	14	)	)	PUNCT
cana-1619	278	15	×	×	PROPN
cana-1619	278	16	ω	ω	PROPN
cana-1619	278	17	→	→	SYM
cana-1619	278	18	pc(j	pc(j	NOUN
cana-1619	278	19	,	,	PUNCT
cana-1619	278	20	𝒮	𝒮	NOUN
cana-1619	278	21	)	)	PUNCT
cana-1619	278	22	and	and	CCONJ
cana-1619	278	23	𝒟	𝒟	NOUN
cana-1619	278	24	=	=	SYM
cana-1619	278	25	[	[	X
cana-1619	278	26	(	(	PUNCT
cana-1619	278	27	−δ	−δ	ADJ
cana-1619	278	28	,	,	PUNCT
cana-1619	278	29	ϱ	ϱ	ADP
cana-1619	278	30	]	]	PUNCT
cana-1619	278	31	,	,	PUNCT
cana-1619	278	32	𝒮	𝒮	PROPN
cana-1619	278	33	]	]	PUNCT
cana-1619	278	34	solves	solve	VERB
cana-1619	278	35	the	the	DET
cana-1619	278	36	integral	integral	ADJ
cana-1619	278	37	equation	equation	NOUN
cana-1619	278	38	then	then	ADV
cana-1619	278	39	it	it	PRON
cana-1619	278	40	is	be	AUX
cana-1619	278	41	referred	refer	VERB
cana-1619	278	42	to	to	ADP
cana-1619	278	43	as	as	ADP
cana-1619	278	44	a	a	DET
cana-1619	278	45	mild	mild	ADJ
cana-1619	278	46	solution	solution	NOUN
cana-1619	278	47	to	to	ADP
cana-1619	278	48	equation	equation	NOUN
cana-1619	278	49	(	(	PUNCT
cana-1619	278	50	1.1	1.1	NUM
cana-1619	278	51	)	)	PUNCT
cana-1619	278	52	.	.	PUNCT
cana-1619	279	1	definition	definition	NOUN
cana-1619	279	2	7	7	NUM
cana-1619	279	3	a	a	DET
cana-1619	279	4	function	function	NOUN
cana-1619	279	5	ζ(⋅	ζ(⋅	NUM
cana-1619	279	6	,	,	PUNCT
cana-1619	279	7	ℵ	ℵ	NOUN
cana-1619	279	8	)	)	PUNCT
cana-1619	279	9	∈	∈	NOUN
cana-1619	279	10	pc(j	pc(j	NOUN
cana-1619	279	11	,	,	PUNCT
cana-1619	279	12	𝒮	𝒮	NOUN
cana-1619	279	13	)	)	PUNCT
cana-1619	279	14	is	be	AUX
cana-1619	279	15	considered	consider	VERB
cana-1619	279	16	a	a	DET
cana-1619	279	17	mild	mild	ADJ
cana-1619	279	18	solution	solution	NOUN
cana-1619	279	19	of	of	ADP
cana-1619	279	20	problem	problem	NOUN
cana-1619	279	21	(	(	PUNCT
cana-1619	279	22	1.2	1.2	NUM
cana-1619	279	23	)	)	PUNCT
cana-1619	279	24	with	with	ADP
cana-1619	279	25	initial	initial	ADJ
cana-1619	279	26	conditions	condition	NOUN
cana-1619	279	27	if	if	SCONJ
cana-1619	279	28	it	it	PRON
cana-1619	279	29	satisfies	satisfy	VERB
cana-1619	279	30	the	the	DET
cana-1619	279	31	following	follow	VERB
cana-1619	279	32	integral	integral	ADJ
cana-1619	279	33	equation	equation	NOUN
cana-1619	279	34	.	.	PUNCT
cana-1619	280	1	communications	communication	NOUN
cana-1619	280	2	on	on	ADP
cana-1619	280	3	applied	apply	VERB
cana-1619	280	4	nonlinear	nonlinear	ADJ
cana-1619	280	5	analysis	analysis	NOUN
cana-1619	280	6	issn	issn	NOUN
cana-1619	280	7	:	:	PUNCT
cana-1619	280	8	1074	1074	NUM
cana-1619	280	9	-	-	PUNCT
cana-1619	280	10	133x	133x	NUM
cana-1619	280	11	vol	vol	NOUN
cana-1619	280	12	32	32	NUM
cana-1619	280	13	no	no	NOUN
cana-1619	280	14	.	.	NOUN
cana-1619	280	15	1	1	NUM
cana-1619	280	16	(	(	PUNCT
cana-1619	280	17	2025	2025	NUM
cana-1619	280	18	)	)	PUNCT
cana-1619	280	19	47	47	NUM
cana-1619	280	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	280	21	ζ(h	ζ(h	NOUN
cana-1619	280	22	,	,	PUNCT
cana-1619	280	23	ℵ	ℵ	NOUN
cana-1619	280	24	)	)	PUNCT
cana-1619	280	25	=	=	SYM
cana-1619	281	1	t1(h)ϕ0(ℵ	t1(h)ϕ0(ℵ	X
cana-1619	281	2	)	)	PUNCT
cana-1619	281	3	+	+	CCONJ
cana-1619	281	4	t2(h)[ϕ′0(ℵ	t2(h)[ϕ′0(ℵ	NUM
cana-1619	281	5	)	)	PUNCT
cana-1619	281	6	+	+	CCONJ
cana-1619	282	1	ρ(0	ρ(0	PROPN
cana-1619	282	2	,	,	PUNCT
cana-1619	282	3	ϕ0(ℵ	ϕ0(ℵ	PROPN
cana-1619	282	4	)	)	PUNCT
cana-1619	282	5	,	,	PUNCT
cana-1619	282	6	ℵ	ℵ	NOUN
cana-1619	282	7	)	)	PUNCT
cana-1619	282	8	]	]	PUNCT
cana-1619	283	1	−	−	PROPN
cana-1619	283	2	∫	∫	PROPN
cana-1619	283	3	h	h	NOUN
cana-1619	283	4	0	0	PUNCT
cana-1619	284	1	t2(h	t2(h	ADP
cana-1619	284	2	−	−	NOUN
cana-1619	284	3	ϖ)ρ(ϖ	ϖ)ρ(ϖ	NOUN
cana-1619	284	4	,	,	PUNCT
cana-1619	284	5	ζϖ	ζϖ	NOUN
cana-1619	284	6	(	(	PUNCT
cana-1619	284	7	.	.	PUNCT
cana-1619	284	8	,	,	PUNCT
cana-1619	284	9	ℵ	ℵ	NOUN
cana-1619	284	10	)	)	PUNCT
cana-1619	284	11	,	,	PUNCT
cana-1619	284	12	ℵ)dϖ	ℵ)dϖ	PROPN
cana-1619	284	13	+	+	NUM
cana-1619	284	14	∫	∫	PROPN
cana-1619	284	15	h	h	NOUN
cana-1619	284	16	0	0	PUNCT
cana-1619	285	1	t2(h	t2(h	ADP
cana-1619	285	2	−	−	NOUN
cana-1619	285	3	ϖ)[υ(ϖ	ϖ)[υ(ϖ	NOUN
cana-1619	285	4	,	,	PUNCT
cana-1619	285	5	ζϖ	ζϖ	NOUN
cana-1619	285	6	(	(	PUNCT
cana-1619	285	7	.	.	PUNCT
cana-1619	285	8	,	,	PUNCT
cana-1619	285	9	ℵ	ℵ	NOUN
cana-1619	285	10	)	)	PUNCT
cana-1619	285	11	,	,	PUNCT
cana-1619	285	12	ℵ	ℵ	NOUN
cana-1619	285	13	)	)	PUNCT
cana-1619	285	14	+	+	CCONJ
cana-1619	285	15	by(h	by(h	NOUN
cana-1619	285	16	,	,	PUNCT
cana-1619	285	17	ℵ)]dϖ	ℵ)]dϖ	X
cana-1619	286	1	+	+	PUNCT
cana-1619	286	2	∑0	∑0	X
cana-1619	286	3	<	<	X
cana-1619	286	4	hξ	hξ	X
cana-1619	286	5	<	<	X
cana-1619	286	6	h	h	PRON
cana-1619	286	7	t1(h	t1(h	X
cana-1619	286	8	−	−	NOUN
cana-1619	286	9	hξ)iξ(ζ(hξ	hξ)iξ(ζ(hξ	ADJ
cana-1619	286	10	,	,	PUNCT
cana-1619	286	11	ℵ	ℵ	NOUN
cana-1619	286	12	)	)	PUNCT
cana-1619	286	13	)	)	PUNCT
cana-1619	287	1	+	+	CCONJ
cana-1619	287	2	∑0	∑0	PROPN
cana-1619	287	3	<	<	X
cana-1619	287	4	hξ	hξ	X
cana-1619	287	5	<	<	X
cana-1619	287	6	h	h	NOUN
cana-1619	287	7	t2(h	t2(h	X
cana-1619	287	8	−	−	PROPN
cana-1619	287	9	hξ)i′ξ(ζ(hξ	hξ)i′ξ(ζ(hξ	PROPN
cana-1619	287	10	,	,	PUNCT
cana-1619	287	11	ℵ	ℵ	NOUN
cana-1619	287	12	)	)	PUNCT
cana-1619	287	13	)	)	PUNCT
cana-1619	287	14	for	for	ADP
cana-1619	287	15	your	your	PRON
cana-1619	287	16	convenience	convenience	NOUN
cana-1619	287	17	,	,	PUNCT
cana-1619	287	18	we	we	PRON
cana-1619	287	19	have	have	AUX
cana-1619	287	20	listed	list	VERB
cana-1619	287	21	the	the	DET
cana-1619	287	22	additional	additional	ADJ
cana-1619	287	23	hypotheses	hypothesis	NOUN
cana-1619	287	24	that	that	PRON
cana-1619	287	25	will	will	AUX
cana-1619	287	26	be	be	AUX
cana-1619	287	27	discussed	discuss	VERB
cana-1619	287	28	in	in	ADP
cana-1619	287	29	the	the	DET
cana-1619	287	30	following	follow	VERB
cana-1619	287	31	section	section	NOUN
cana-1619	287	32	.	.	PUNCT
cana-1619	288	1	let	let	VERB
cana-1619	288	2	(	(	PUNCT
cana-1619	288	3	g7	g7	PROPN
cana-1619	288	4	)	)	PUNCT
cana-1619	288	5	the	the	DET
cana-1619	288	6	linear	linear	ADJ
cana-1619	288	7	operator	operator	NOUN
cana-1619	289	1	k	k	NOUN
cana-1619	289	2	:	:	PUNCT
cana-1619	289	3	l2(j	l2(j	NUM
cana-1619	289	4	,	,	PUNCT
cana-1619	289	5	𝒮	𝒮	PROPN
cana-1619	289	6	)	)	PUNCT
cana-1619	289	7	→	→	SYM
cana-1619	289	8	𝒮	𝒮	NOUN
cana-1619	289	9	given	give	VERB
cana-1619	289	10	by	by	ADP
cana-1619	289	11	ky	ky	PROPN
cana-1619	289	12	=	=	SYM
cana-1619	289	13	∫	∫	PROPN
cana-1619	289	14	ϱ	ϱ	ADP
cana-1619	289	15	0	0	NUM
cana-1619	289	16	t2(ϱ	t2(ϱ	ADP
cana-1619	289	17	−	−	PROPN
cana-1619	289	18	ϖ)by(ϖ	ϖ)by(ϖ	ADV
cana-1619	289	19	,	,	PUNCT
cana-1619	289	20	ℵ)dϖ	ℵ)dϖ	PROPN
cana-1619	289	21	has	have	VERB
cana-1619	289	22	a	a	DET
cana-1619	289	23	pseudo	pseudo	NOUN
cana-1619	289	24	-	-	ADJ
cana-1619	289	25	inverse	inverse	ADJ
cana-1619	289	26	operator	operator	NOUN
cana-1619	289	27	k−1	k−1	PROPN
cana-1619	289	28	in	in	ADP
cana-1619	289	29	l2(j	l2(j	PROPN
cana-1619	289	30	,	,	PUNCT
cana-1619	289	31	s)/kerk	s)/kerk	PROPN
cana-1619	289	32	(	(	PUNCT
cana-1619	289	33	g8	g8	PROPN
cana-1619	289	34	)	)	PUNCT
cana-1619	289	35	there	there	PRON
cana-1619	289	36	exist	exist	VERB
cana-1619	289	37	a	a	DET
cana-1619	289	38	random	random	ADJ
cana-1619	289	39	function	function	NOUN
cana-1619	289	40	q	q	NOUN
cana-1619	289	41	:	:	PUNCT
cana-1619	289	42	ω	ω	PROPN
cana-1619	289	43	→	→	PUNCT
cana-1619	289	44	ℝ+	ℝ+	PUNCT
cana-1619	289	45	where	where	SCONJ
cana-1619	289	46	ϑabk	ϑabk	ADP
cana-1619	289	47	−1	−1	PROPN
cana-1619	289	48	∫	∫	PROPN
cana-1619	289	49	h	h	NOUN
cana-1619	289	50	0	0	PUNCT
cana-1619	290	1	[	[	X
cana-1619	290	2	||ζ1(ℵ)||	||ζ1(ℵ)||	NOUN
cana-1619	290	3	+	+	CCONJ
cana-1619	290	4	ϑ||ϕ0(ℵ)||	ϑ||ϕ0(ℵ)||	PROPN
cana-1619	290	5	+	+	NUM
cana-1619	290	6	ϑa||ϕ′0(ℵ	ϑa||ϕ′0(ℵ	NOUN
cana-1619	290	7	)	)	PUNCT
cana-1619	290	8	+	+	CCONJ
cana-1619	291	1	ρ(0	ρ(0	PROPN
cana-1619	291	2	,	,	PUNCT
cana-1619	291	3	ϕ0(ℵ	ϕ0(ℵ	PROPN
cana-1619	291	4	)	)	PUNCT
cana-1619	291	5	,	,	PUNCT
cana-1619	291	6	ℵ)||	ℵ)||	PRON
cana-1619	292	1	+	+	NOUN
cana-1619	292	2	ϑ∫	ϑ∫	VERB
cana-1619	292	3	ϱ	ϱ	ADP
cana-1619	292	4	0	0	NUM
cana-1619	292	5	[	[	PUNCT
cana-1619	292	6	sup	sup	NOUN
cana-1619	292	7	η∈(0.ϱ	η∈(0.ϱ	PROPN
cana-1619	292	8	]	]	PUNCT
cana-1619	292	9	||ζη	||ζη	PROPN
cana-1619	292	10	(	(	PUNCT
cana-1619	292	11	.	.	PUNCT
cana-1619	292	12	,	,	PUNCT
cana-1619	292	13	ℵ	ℵ	NOUN
cana-1619	292	14	)	)	PUNCT
cana-1619	292	15	,	,	PUNCT
cana-1619	293	1	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	293	2	β0	β0	NOUN
cana-1619	293	3	+	+	CCONJ
cana-1619	293	4	d0(ℵ)]dη	d0(ℵ)]dη	PROPN
cana-1619	293	5	+	+	CCONJ
cana-1619	293	6	ϑa	ϑa	INTJ
cana-1619	293	7	∫	∫	PROPN
cana-1619	293	8	ϱ	ϱ	ADP
cana-1619	293	9	0	0	NUM
cana-1619	293	10	[	[	PUNCT
cana-1619	293	11	sup	sup	PROPN
cana-1619	293	12	η∈(0.ϱ	η∈(0.ϱ	PROPN
cana-1619	293	13	]	]	PUNCT
cana-1619	293	14	||ζη	||ζη	PROPN
cana-1619	293	15	(	(	PUNCT
cana-1619	293	16	.	.	PUNCT
cana-1619	293	17	,	,	PUNCT
cana-1619	293	18	ℵ	ℵ	NOUN
cana-1619	293	19	)	)	PUNCT
cana-1619	293	20	,	,	PUNCT
cana-1619	293	21	ℵ||𝒟	ℵ||𝒟	NOUN
cana-1619	293	22	α0	α0	ADJ
cana-1619	293	23	+	+	CCONJ
cana-1619	293	24	b0(ℵ)]dη	b0(ℵ)]dη	NOUN
cana-1619	293	25	+	+	NOUN
cana-1619	293	26	ϑ∑0	ϑ∑0	NOUN
cana-1619	293	27	<	<	X
cana-1619	293	28	hξ<ϱ	hξ<ϱ	PROPN
cana-1619	293	29	aξ(ℵ)||ζ(hξ	aξ(ℵ)||ζ(hξ	PROPN
cana-1619	293	30	,	,	PUNCT
cana-1619	293	31	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	293	32	αξ	αξ	NOUN
cana-1619	293	33	+	+	CCONJ
cana-1619	293	34	ϑa∑0	ϑa∑0	ADV
cana-1619	293	35	<	<	X
cana-1619	293	36	hξ<ϱ	hξ<ϱ	PROPN
cana-1619	293	37	a′ξ(ℵ)||ζ(hξ	a′ξ(ℵ)||ζ(hξ	PROPN
cana-1619	293	38	,	,	PUNCT
cana-1619	293	39	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	293	40	αξ]dϖ	αξ]dϖ	NOUN
cana-1619	293	41	≤	≤	NUM
cana-1619	293	42	q(ℵ	q(ℵ	NUM
cana-1619	293	43	)	)	PUNCT
cana-1619	293	44	theorem	theorem	VERB
cana-1619	293	45	4.1	4.1	NUM
cana-1619	293	46	if	if	SCONJ
cana-1619	293	47	(	(	PUNCT
cana-1619	293	48	𝐺1	𝐺1	NOUN
cana-1619	293	49	)	)	PUNCT
cana-1619	293	50	(	(	PUNCT
cana-1619	293	51	𝐺8	𝐺8	PROPN
cana-1619	293	52	)	)	PUNCT
cana-1619	293	53	are	be	AUX
cana-1619	293	54	fulfilled	fulfil	VERB
cana-1619	293	55	,	,	PUNCT
cana-1619	293	56	then	then	ADV
cana-1619	293	57	the	the	DET
cana-1619	293	58	problem	problem	NOUN
cana-1619	293	59	(	(	PUNCT
cana-1619	293	60	1.2	1.2	NUM
cana-1619	293	61	)	)	PUNCT
cana-1619	293	62	is	be	AUX
cana-1619	293	63	approximately	approximately	ADV
cana-1619	293	64	controllable	controllable	ADJ
cana-1619	293	65	on	on	ADP
cana-1619	293	66	𝐽.	𝐽.	ADJ
cana-1619	293	67	proof	proof	NOUN
cana-1619	293	68	:	:	PUNCT
cana-1619	293	69	let	let	VERB
cana-1619	293	70	us	we	PRON
cana-1619	293	71	specify	specify	VERB
cana-1619	293	72	the	the	DET
cana-1619	293	73	control	control	NOUN
cana-1619	293	74	:	:	PUNCT
cana-1619	293	75	𝑦(ℎ	𝑦(ℎ	ADJ
cana-1619	293	76	,	,	PUNCT
cana-1619	293	77	ℵ	ℵ	NOUN
cana-1619	293	78	)	)	PUNCT
cana-1619	293	79	=	=	SYM
cana-1619	293	80	𝑘−1(𝜁1(ℵ	𝑘−1(𝜁1(ℵ	NOUN
cana-1619	293	81	)	)	PUNCT
cana-1619	293	82	−	−	NOUN
cana-1619	293	83	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	293	84	)	)	PUNCT
cana-1619	293	85	−	−	ADP
cana-1619	293	86	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	293	87	)	)	PUNCT
cana-1619	294	1	+	+	SYM
cana-1619	294	2	𝜌(0	𝜌(0	PROPN
cana-1619	294	3	,	,	PUNCT
cana-1619	294	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	294	5	)	)	PUNCT
cana-1619	294	6	,	,	PUNCT
cana-1619	294	7	ℵ	ℵ	NOUN
cana-1619	294	8	)	)	PUNCT
cana-1619	294	9	]	]	PUNCT
cana-1619	295	1	+	+	CCONJ
cana-1619	295	2	∫	∫	PROPN
cana-1619	295	3	𝜚	𝜚	NOUN
cana-1619	295	4	0	0	NUM
cana-1619	295	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	295	6	−	−	PROPN
cana-1619	295	7	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	NOUN
cana-1619	295	8	,	,	PUNCT
cana-1619	295	9	𝜁𝜛	𝜁𝜛	ADV
cana-1619	295	10	(	(	PUNCT
cana-1619	295	11	.	.	PUNCT
cana-1619	295	12	,	,	PUNCT
cana-1619	295	13	ℵ	ℵ	NOUN
cana-1619	295	14	)	)	PUNCT
cana-1619	295	15	,	,	PUNCT
cana-1619	296	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	296	2	−∫	−∫	VERB
cana-1619	296	3	𝜚	𝜚	NOUN
cana-1619	296	4	0	0	NUM
cana-1619	296	5	𝑇2(𝜚	𝑇2(𝜚	NOUN
cana-1619	296	6	−	−	PROPN
cana-1619	296	7	𝜛)υ(π	𝜛)υ(π	NOUN
cana-1619	296	8	,	,	PUNCT
cana-1619	296	9	𝜁𝜛	𝜁𝜛	ADV
cana-1619	296	10	(	(	PUNCT
cana-1619	296	11	.	.	PUNCT
cana-1619	296	12	,	,	PUNCT
cana-1619	296	13	ℵ	ℵ	NOUN
cana-1619	296	14	)	)	PUNCT
cana-1619	296	15	,	,	PUNCT
cana-1619	297	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	297	2	−	−	PROPN
cana-1619	298	1	∑	∑	PROPN
cana-1619	298	2	0<ℎ𝜉<𝜚	0<ℎ𝜉<𝜚	PROPN
cana-1619	298	3	𝑇1(𝜚	𝑇1(𝜚	PROPN
cana-1619	298	4	−	−	PROPN
cana-1619	298	5	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	298	6	,	,	PUNCT
cana-1619	298	7	ℵ	ℵ	NOUN
cana-1619	298	8	)	)	PUNCT
cana-1619	298	9	)	)	PUNCT
cana-1619	299	1	−	−	PROPN
cana-1619	300	1	∑	∑	PROPN
cana-1619	300	2	0<ℎ𝜉<𝜚	0<ℎ𝜉<𝜚	PROPN
cana-1619	300	3	𝑇2(𝜚	𝑇2(𝜚	PROPN
cana-1619	301	1	−	−	PROPN
cana-1619	301	2	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	301	3	,	,	PUNCT
cana-1619	301	4	ℵ	ℵ	NOUN
cana-1619	301	5	)	)	PUNCT
cana-1619	301	6	)	)	PUNCT
cana-1619	302	1	we	we	PRON
cana-1619	302	2	define	define	VERB
cana-1619	302	3	the	the	DET
cana-1619	302	4	operator	operator	NOUN
cana-1619	302	5	(	(	PUNCT
cana-1619	302	6	γ(ℵ))′	γ(ℵ))′	NOUN
cana-1619	302	7	:	:	PUNCT
cana-1619	302	8	𝑃𝐶𝛿	𝑃𝐶𝛿	PROPN
cana-1619	302	9	=	=	SYM
cana-1619	302	10	ω	ω	NUM
cana-1619	302	11	×	×	PROPN
cana-1619	302	12	𝑃𝐶([𝛿	𝑃𝐶([𝛿	NOUN
cana-1619	302	13	,	,	PUNCT
cana-1619	302	14	𝜚	𝜚	NOUN
cana-1619	302	15	]	]	X
cana-1619	302	16	,	,	PUNCT
cana-1619	302	17	𝒮	𝒮	NOUN
cana-1619	302	18	)	)	PUNCT
cana-1619	302	19	→	→	SYM
cana-1619	302	20	𝑃𝐶𝛿	𝑃𝐶𝛿	NOUN
cana-1619	302	21	be	be	VERB
cana-1619	302	22	a	a	DET
cana-1619	302	23	random	random	ADJ
cana-1619	302	24	operator	operator	NOUN
cana-1619	302	25	and	and	CCONJ
cana-1619	302	26	is	be	AUX
cana-1619	302	27	defined	define	VERB
cana-1619	302	28	by	by	ADP
cana-1619	302	29	communications	communication	NOUN
cana-1619	302	30	on	on	ADP
cana-1619	302	31	applied	apply	VERB
cana-1619	302	32	nonlinear	nonlinear	ADJ
cana-1619	302	33	analysis	analysis	NOUN
cana-1619	302	34	issn	issn	NOUN
cana-1619	302	35	:	:	PUNCT
cana-1619	302	36	1074	1074	NUM
cana-1619	302	37	-	-	PUNCT
cana-1619	302	38	133x	133x	NUM
cana-1619	302	39	vol	vol	NOUN
cana-1619	302	40	32	32	NUM
cana-1619	302	41	no	no	NOUN
cana-1619	302	42	.	.	NOUN
cana-1619	302	43	1	1	NUM
cana-1619	302	44	(	(	PUNCT
cana-1619	302	45	2025	2025	NUM
cana-1619	302	46	)	)	PUNCT
cana-1619	302	47	48	48	NUM
cana-1619	302	48	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	302	49	(	(	PUNCT
cana-1619	302	50	(	(	PUNCT
cana-1619	302	51	γ(ℵ))′𝜁)(ℎ	γ(ℵ))′𝜁)(ℎ	X
cana-1619	302	52	)	)	PUNCT
cana-1619	302	53	=	=	SYM
cana-1619	302	54	𝑇1(ℎ)𝜙0(ℵ	𝑇1(ℎ)𝜙0(ℵ	NOUN
cana-1619	302	55	)	)	PUNCT
cana-1619	302	56	+	+	NUM
cana-1619	302	57	𝑇2(ℎ)[𝜙′0(ℵ	𝑇2(ℎ)[𝜙′0(ℵ	NOUN
cana-1619	302	58	)	)	PUNCT
cana-1619	303	1	+	+	CCONJ
cana-1619	303	2	𝜌(0	𝜌(0	PROPN
cana-1619	303	3	,	,	PUNCT
cana-1619	303	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	303	5	)	)	PUNCT
cana-1619	303	6	,	,	PUNCT
cana-1619	303	7	ℵ	ℵ	NOUN
cana-1619	303	8	)	)	PUNCT
cana-1619	303	9	]	]	PUNCT
cana-1619	304	1	−	−	PROPN
cana-1619	304	2	∫	∫	INTJ
cana-1619	304	3	ℎ	ℎ	PROPN
cana-1619	304	4	0	0	PROPN
cana-1619	305	1	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	306	1	−	−	PROPN
cana-1619	306	2	𝜛)[𝜌(𝜛	𝜛)[𝜌(𝜛	PROPN
cana-1619	306	3	,	,	PUNCT
cana-1619	306	4	𝜁𝜛	𝜁𝜛	ADV
cana-1619	306	5	(	(	PUNCT
cana-1619	306	6	.	.	PUNCT
cana-1619	306	7	,	,	PUNCT
cana-1619	306	8	ℵ	ℵ	NOUN
cana-1619	306	9	)	)	PUNCT
cana-1619	306	10	,	,	PUNCT
cana-1619	307	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	307	2	+	+	PROPN
cana-1619	307	3	∫	∫	PROPN
cana-1619	307	4	ℎ	ℎ	X
cana-1619	307	5	0	0	PUNCT
cana-1619	307	6	𝑇2(ℎ	𝑇2(ℎ	NOUN
cana-1619	307	7	−	−	NOUN
cana-1619	307	8	𝜛)[υ(𝜛	𝜛)[υ(𝜛	NOUN
cana-1619	307	9	,	,	PUNCT
cana-1619	307	10	𝜁𝜛	𝜁𝜛	ADV
cana-1619	307	11	(	(	PUNCT
cana-1619	307	12	.	.	PUNCT
cana-1619	307	13	,	,	PUNCT
cana-1619	307	14	ℵ	ℵ	NOUN
cana-1619	307	15	)	)	PUNCT
cana-1619	307	16	,	,	PUNCT
cana-1619	308	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	308	2	+	+	PROPN
cana-1619	308	3	∫	∫	PROPN
cana-1619	308	4	ℎ	ℎ	X
cana-1619	308	5	0	0	PUNCT
cana-1619	308	6	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	308	7	−	−	PROPN
cana-1619	308	8	𝜛)𝐵𝑘	𝜛)𝐵𝑘	NOUN
cana-1619	308	9	−1[(𝜁1(ℵ	−1[(𝜁1(ℵ	NOUN
cana-1619	308	10	)	)	PUNCT
cana-1619	308	11	−	−	NOUN
cana-1619	308	12	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	308	13	)	)	PUNCT
cana-1619	308	14	−	−	ADP
cana-1619	308	15	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	308	16	)	)	PUNCT
cana-1619	309	1	+	+	SYM
cana-1619	309	2	𝜌(0	𝜌(0	PROPN
cana-1619	309	3	,	,	PUNCT
cana-1619	309	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	309	5	)	)	PUNCT
cana-1619	309	6	,	,	PUNCT
cana-1619	309	7	ℵ	ℵ	NOUN
cana-1619	309	8	)	)	PUNCT
cana-1619	309	9	]	]	PUNCT
cana-1619	310	1	+	+	NUM
cana-1619	310	2	∫	∫	PROPN
cana-1619	310	3	𝜚	𝜚	NOUN
cana-1619	310	4	0	0	PUNCT
cana-1619	310	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	310	6	−	−	NOUN
cana-1619	310	7	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	310	8	,	,	PUNCT
cana-1619	310	9	𝜁𝜂	𝜁𝜂	X
cana-1619	310	10	(	(	PUNCT
cana-1619	310	11	.	.	PUNCT
cana-1619	310	12	,	,	PUNCT
cana-1619	310	13	ℵ	ℵ	NOUN
cana-1619	310	14	)	)	PUNCT
cana-1619	310	15	,	,	PUNCT
cana-1619	311	1	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	311	2	−	−	PROPN
cana-1619	311	3	∫	∫	PROPN
cana-1619	311	4	𝜚	𝜚	NOUN
cana-1619	311	5	0	0	NUM
cana-1619	311	6	𝑇2(𝜚	𝑇2(𝜚	PROPN
cana-1619	312	1	−	−	PROPN
cana-1619	312	2	𝜂)υ(η	𝜂)υ(η	NOUN
cana-1619	312	3	,	,	PUNCT
cana-1619	312	4	𝜁𝜂	𝜁𝜂	X
cana-1619	312	5	(	(	PUNCT
cana-1619	312	6	.	.	PUNCT
cana-1619	312	7	,	,	PUNCT
cana-1619	312	8	ℵ	ℵ	NOUN
cana-1619	312	9	)	)	PUNCT
cana-1619	312	10	,	,	PUNCT
cana-1619	313	1	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	313	2	−	−	PROPN
cana-1619	313	3	∑	∑	PROPN
cana-1619	313	4	0<ℎ𝜉<𝜚	0<ℎ𝜉<𝜚	PROPN
cana-1619	313	5	𝑇1(𝜚	𝑇1(𝜚	PROPN
cana-1619	313	6	−	−	PROPN
cana-1619	314	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	314	2	,	,	PUNCT
cana-1619	314	3	ℵ	ℵ	NOUN
cana-1619	314	4	)	)	PUNCT
cana-1619	314	5	)	)	PUNCT
cana-1619	314	6	)	)	PUNCT
cana-1619	314	7	]	]	PUNCT
cana-1619	315	1	−	−	PUNCT
cana-1619	315	2	∑	∑	PUNCT
cana-1619	315	3	0<ℎ𝜉<𝜚	0<ℎ𝜉<𝜚	PROPN
cana-1619	315	4	𝑇2(𝜚	𝑇2(𝜚	PROPN
cana-1619	315	5	−	−	PROPN
cana-1619	315	6	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	315	7	,	,	PUNCT
cana-1619	315	8	ℵ))]𝑑𝜛	ℵ))]𝑑𝜛	PROPN
cana-1619	315	9	+	+	CCONJ
cana-1619	315	10	∑	∑	PUNCT
cana-1619	315	11	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	VERB
cana-1619	315	12	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	315	13	−	−	PROPN
cana-1619	316	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	316	2	,	,	PUNCT
cana-1619	316	3	ℵ	ℵ	NOUN
cana-1619	316	4	)	)	PUNCT
cana-1619	316	5	)	)	PUNCT
cana-1619	317	1	+	+	CCONJ
cana-1619	317	2	∑	∑	PUNCT
cana-1619	317	3	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	317	4	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	317	5	−	−	PROPN
cana-1619	317	6	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	317	7	,	,	PUNCT
cana-1619	317	8	ℵ	ℵ	NOUN
cana-1619	317	9	)	)	PUNCT
cana-1619	317	10	)	)	PUNCT
cana-1619	317	11	]	]	PUNCT
cana-1619	318	1	ℎ	ℎ	PROPN
cana-1619	318	2	∈	∈	PROPN
cana-1619	318	3	(	(	PUNCT
cana-1619	318	4	−𝛿	−𝛿	NOUN
cana-1619	318	5	,	,	PUNCT
cana-1619	318	6	𝜚	𝜚	NOUN
cana-1619	318	7	]	]	X
cana-1619	318	8	.	.	PUNCT
cana-1619	319	1	(	(	PUNCT
cana-1619	319	2	γ(ℵ))′	γ(ℵ))′	X
cana-1619	319	3	=	=	PUNCT
cana-1619	319	4	(	(	PUNCT
cana-1619	319	5	γ(ℵ))′1	γ(ℵ))′1	PROPN
cana-1619	319	6	+	+	CCONJ
cana-1619	319	7	(	(	PUNCT
cana-1619	319	8	γ(ℵ))′2	γ(ℵ))′2	PROPN
cana-1619	319	9	(	(	PUNCT
cana-1619	319	10	γ(ℵ))′1𝜁(ℎ	γ(ℵ))′1𝜁(ℎ	PROPN
cana-1619	319	11	)	)	PUNCT
cana-1619	319	12	=	=	SYM
cana-1619	319	13	𝑇1(ℎ)𝜙0(ℵ	𝑇1(ℎ)𝜙0(ℵ	NOUN
cana-1619	319	14	)	)	PUNCT
cana-1619	319	15	+	+	NUM
cana-1619	319	16	𝑇2(ℎ)[𝜙′0(ℵ	𝑇2(ℎ)[𝜙′0(ℵ	NOUN
cana-1619	319	17	)	)	PUNCT
cana-1619	320	1	+	+	CCONJ
cana-1619	321	1	𝜌(0	𝜌(0	PROPN
cana-1619	321	2	,	,	PUNCT
cana-1619	321	3	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	321	4	)	)	PUNCT
cana-1619	321	5	,	,	PUNCT
cana-1619	321	6	ℵ	ℵ	NOUN
cana-1619	321	7	)	)	PUNCT
cana-1619	321	8	]	]	PUNCT
cana-1619	322	1	−	−	PROPN
cana-1619	322	2	∫	∫	INTJ
cana-1619	322	3	ℎ	ℎ	PROPN
cana-1619	322	4	0	0	SYM
cana-1619	322	5	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	322	6	−	−	PROPN
cana-1619	322	7	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	NOUN
cana-1619	322	8	,	,	PUNCT
cana-1619	322	9	𝜁𝜛	𝜁𝜛	ADV
cana-1619	322	10	(	(	PUNCT
cana-1619	322	11	.	.	PUNCT
cana-1619	322	12	,	,	PUNCT
cana-1619	322	13	ℵ	ℵ	NOUN
cana-1619	322	14	)	)	PUNCT
cana-1619	322	15	,	,	PUNCT
cana-1619	322	16	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	323	1	+	+	PROPN
cana-1619	323	2	∫	∫	PROPN
cana-1619	323	3	ℎ	ℎ	X
cana-1619	323	4	0	0	SYM
cana-1619	323	5	𝑇2(ℎ	𝑇2(ℎ	ADJ
cana-1619	323	6	−	−	NOUN
cana-1619	323	7	𝜛)υ(𝜛	𝜛)υ(𝜛	NOUN
cana-1619	323	8	,	,	PUNCT
cana-1619	323	9	𝜁𝜛	𝜁𝜛	ADV
cana-1619	323	10	(	(	PUNCT
cana-1619	323	11	.	.	PUNCT
cana-1619	323	12	,	,	PUNCT
cana-1619	323	13	ℵ	ℵ	NOUN
cana-1619	323	14	)	)	PUNCT
cana-1619	323	15	,	,	PUNCT
cana-1619	324	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	324	2	+	+	CCONJ
cana-1619	324	3	∑	∑	PUNCT
cana-1619	324	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	VERB
cana-1619	324	5	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	324	6	−	−	PROPN
cana-1619	325	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	325	2	,	,	PUNCT
cana-1619	325	3	ℵ	ℵ	NOUN
cana-1619	325	4	)	)	PUNCT
cana-1619	325	5	)	)	PUNCT
cana-1619	326	1	+	+	CCONJ
cana-1619	326	2	∑	∑	PUNCT
cana-1619	326	3	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	326	4	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	326	5	−	−	PROPN
cana-1619	326	6	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	326	7	,	,	PUNCT
cana-1619	326	8	ℵ	ℵ	NOUN
cana-1619	326	9	)	)	PUNCT
cana-1619	326	10	)	)	PUNCT
cana-1619	326	11	(	(	PUNCT
cana-1619	326	12	γ(ℵ))′2𝜁(ℎ	γ(ℵ))′2𝜁(ℎ	PROPN
cana-1619	326	13	)	)	PUNCT
cana-1619	326	14	=	=	SYM
cana-1619	327	1	∫	∫	PROPN
cana-1619	327	2	ℎ	ℎ	PROPN
cana-1619	327	3	0	0	PUNCT
cana-1619	327	4	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	327	5	−	−	PROPN
cana-1619	327	6	𝜛)𝐵𝑘	𝜛)𝐵𝑘	NOUN
cana-1619	327	7	−1[𝜁1(ℵ	−1[𝜁1(ℵ	NOUN
cana-1619	327	8	)	)	PUNCT
cana-1619	327	9	−	−	NOUN
cana-1619	327	10	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	327	11	)	)	PUNCT
cana-1619	327	12	−	−	ADP
cana-1619	327	13	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	327	14	)	)	PUNCT
cana-1619	327	15	+	+	SYM
cana-1619	327	16	𝜌(0	𝜌(0	PROPN
cana-1619	327	17	,	,	PUNCT
cana-1619	327	18	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	327	19	)	)	PUNCT
cana-1619	327	20	,	,	PUNCT
cana-1619	327	21	ℵ	ℵ	NOUN
cana-1619	327	22	)	)	PUNCT
cana-1619	327	23	]	]	PUNCT
cana-1619	328	1	+	+	CCONJ
cana-1619	328	2	∫	∫	PROPN
cana-1619	328	3	𝜚	𝜚	NOUN
cana-1619	328	4	0	0	NUM
cana-1619	328	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	328	6	−	−	NOUN
cana-1619	328	7	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	328	8	,	,	PUNCT
cana-1619	328	9	𝜁𝜂	𝜁𝜂	X
cana-1619	328	10	(	(	PUNCT
cana-1619	328	11	.	.	PUNCT
cana-1619	328	12	,	,	PUNCT
cana-1619	328	13	ℵ	ℵ	NOUN
cana-1619	328	14	)	)	PUNCT
cana-1619	328	15	,	,	PUNCT
cana-1619	329	1	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	329	2	−	−	PROPN
cana-1619	329	3	∫	∫	PROPN
cana-1619	329	4	𝜚	𝜚	NOUN
cana-1619	329	5	0	0	NUM
cana-1619	329	6	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	329	7	−	−	NOUN
cana-1619	329	8	𝜂)υ(𝜂	𝜂)υ(𝜂	NOUN
cana-1619	329	9	,	,	PUNCT
cana-1619	329	10	𝜁𝜂	𝜁𝜂	PRON
cana-1619	329	11	(	(	PUNCT
cana-1619	329	12	.	.	PUNCT
cana-1619	329	13	,	,	PUNCT
cana-1619	329	14	ℵ	ℵ	NOUN
cana-1619	329	15	)	)	PUNCT
cana-1619	329	16	,	,	PUNCT
cana-1619	329	17	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	329	18	−∑0<ℎ𝜉<𝜚	−∑0<ℎ𝜉<𝜚	PROPN
cana-1619	329	19	𝑇1(𝜚	𝑇1(𝜚	PROPN
cana-1619	329	20	−	−	NOUN
cana-1619	330	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	330	2	,	,	PUNCT
cana-1619	330	3	ℵ	ℵ	NOUN
cana-1619	330	4	)	)	PUNCT
cana-1619	330	5	)	)	PUNCT
cana-1619	331	1	−	−	PROPN
cana-1619	331	2	∑0<ℎ𝜉<𝜚	∑0<ℎ𝜉<𝜚	PROPN
cana-1619	331	3	𝑇2(𝜚	𝑇2(𝜚	PROPN
cana-1619	332	1	−	−	PROPN
cana-1619	332	2	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	332	3	,	,	PUNCT
cana-1619	332	4	ℵ))]𝑑𝜛	ℵ))]𝑑𝜛	CCONJ
cana-1619	332	5	we	we	PRON
cana-1619	332	6	have	have	AUX
cana-1619	332	7	already	already	ADV
cana-1619	332	8	outlined	outline	VERB
cana-1619	332	9	four	four	NUM
cana-1619	332	10	scenarios	scenario	NOUN
cana-1619	332	11	for	for	ADP
cana-1619	332	12	(	(	PUNCT
cana-1619	332	13	γ1(ℵ	γ1(ℵ	NOUN
cana-1619	332	14	)	)	PUNCT
cana-1619	332	15	)	)	PUNCT
cana-1619	332	16	in	in	ADP
cana-1619	332	17	theorem(3.1	theorem(3.1	NOUN
cana-1619	332	18	)	)	PUNCT
cana-1619	332	19	.	.	PUNCT
cana-1619	333	1	hence	hence	ADV
cana-1619	333	2	,	,	PUNCT
cana-1619	333	3	it	it	PRON
cana-1619	333	4	suffices	suffice	VERB
cana-1619	333	5	to	to	PART
cana-1619	333	6	validate	validate	VERB
cana-1619	333	7	the	the	DET
cana-1619	333	8	outcome	outcome	NOUN
cana-1619	333	9	for	for	ADP
cana-1619	333	10	(	(	PUNCT
cana-1619	333	11	γ(ℵ))2	γ(ℵ))2	NOUN
cana-1619	333	12	.	.	PUNCT
cana-1619	334	1	step	step	NOUN
cana-1619	334	2	1	1	NUM
cana-1619	334	3	:	:	PUNCT
cana-1619	334	4	(	(	PUNCT
cana-1619	334	5	γ(ℵ))2	γ(ℵ))2	PRON
cana-1619	334	6	takes	take	VERB
cana-1619	334	7	bounded	bounded	ADJ
cana-1619	334	8	sets	set	NOUN
cana-1619	334	9	and	and	CCONJ
cana-1619	334	10	maps	map	VERB
cana-1619	334	11	them	they	PRON
cana-1619	334	12	to	to	ADP
cana-1619	334	13	bounded	bound	VERB
cana-1619	334	14	sets	set	NOUN
cana-1619	334	15	.	.	PUNCT
cana-1619	335	1	specifically	specifically	ADV
cana-1619	335	2	,	,	PUNCT
cana-1619	335	3	it	it	PRON
cana-1619	335	4	is	be	AUX
cana-1619	335	5	sufficient	sufficient	ADJ
cana-1619	335	6	to	to	PART
cana-1619	335	7	establish	establish	VERB
cana-1619	335	8	that	that	SCONJ
cana-1619	335	9	we	we	PRON
cana-1619	335	10	can	can	AUX
cana-1619	335	11	find	find	VERB
cana-1619	335	12	a	a	DET
cana-1619	335	13	+	+	NOUN
cana-1619	335	14	ve	ve	NOUN
cana-1619	335	15	constant	constant	ADJ
cana-1619	335	16	𝑞(ℵ	𝑞(ℵ	NOUN
cana-1619	335	17	)	)	PUNCT
cana-1619	335	18	such	such	ADJ
cana-1619	335	19	that	that	PRON
cana-1619	335	20	for	for	ADP
cana-1619	335	21	every	every	DET
cana-1619	335	22	𝜁	𝜁	PROPN
cana-1619	335	23	∈	∈	PROPN
cana-1619	335	24	ℬ𝑞(𝛿	ℬ𝑞(𝛿	NOUN
cana-1619	335	25	)	)	PUNCT
cana-1619	335	26	,	,	PUNCT
cana-1619	335	27	defined	define	VERB
cana-1619	335	28	as	as	ADP
cana-1619	335	29	:	:	PUNCT
cana-1619	335	30	ℬ𝑟(𝛿):=	ℬ𝑟(𝛿):=	ADJ
cana-1619	335	31	{	{	PUNCT
cana-1619	335	32	𝜁	𝜁	PROPN
cana-1619	335	33	∈	∈	PROPN
cana-1619	335	34	𝑃𝐶𝛿	𝑃𝐶𝛿	VERB
cana-1619	335	35	:	:	PUNCT
cana-1619	335	36	sup	sup	NOUN
cana-1619	335	37	𝛿≤ℎ≤𝜚	𝛿≤ℎ≤𝜚	NOUN
cana-1619	335	38	∥	∥	X
cana-1619	335	39	𝜁(ℎ	𝜁(ℎ	NOUN
cana-1619	335	40	,	,	PUNCT
cana-1619	335	41	ℵ	ℵ	NOUN
cana-1619	335	42	)	)	PUNCT
cana-1619	335	43	∥≤	∥≤	PROPN
cana-1619	335	44	𝑞(ℵ	𝑞(ℵ	ADJ
cana-1619	335	45	)	)	PUNCT
cana-1619	335	46	}	}	PUNCT
cana-1619	335	47	one	one	NOUN
cana-1619	335	48	has	have	VERB
cana-1619	335	49	∥	∥	PROPN
cana-1619	335	50	(	(	PUNCT
cana-1619	335	51	γ(ℵ))2𝜁	γ(ℵ))2𝜁	PROPN
cana-1619	335	52	∥𝑃𝐶≤	∥𝑃𝐶≤	PROPN
cana-1619	335	53	𝑄(ℵ	𝑄(ℵ	NOUN
cana-1619	335	54	)	)	PUNCT
cana-1619	335	55	.	.	PUNCT
cana-1619	336	1	communications	communication	NOUN
cana-1619	336	2	on	on	ADP
cana-1619	336	3	applied	apply	VERB
cana-1619	336	4	nonlinear	nonlinear	ADJ
cana-1619	336	5	analysis	analysis	NOUN
cana-1619	336	6	issn	issn	NOUN
cana-1619	336	7	:	:	PUNCT
cana-1619	336	8	1074	1074	NUM
cana-1619	336	9	-	-	PUNCT
cana-1619	336	10	133x	133x	NUM
cana-1619	336	11	vol	vol	NOUN
cana-1619	336	12	32	32	NUM
cana-1619	336	13	no	no	NOUN
cana-1619	336	14	.	.	NOUN
cana-1619	336	15	1	1	NUM
cana-1619	336	16	(	(	PUNCT
cana-1619	336	17	2025	2025	NUM
cana-1619	336	18	)	)	PUNCT
cana-1619	336	19	49	49	NUM
cana-1619	336	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	336	21	||(γ(ℵ))′2𝜁(ℎ)||	||(γ(ℵ))′2𝜁(ℎ)||	NOUN
cana-1619	337	1	≤	≤	NUM
cana-1619	337	2	∫	∫	PROPN
cana-1619	337	3	ℎ	ℎ	PROPN
cana-1619	337	4	0	0	PROPN
cana-1619	337	5	||𝑇2(ℎ	||𝑇2(ℎ	NOUN
cana-1619	337	6	−	−	PROPN
cana-1619	337	7	𝜛)𝐵𝑘	𝜛)𝐵𝑘	NOUN
cana-1619	337	8	−1[𝜁1(ℵ	−1[𝜁1(ℵ	NOUN
cana-1619	337	9	)	)	PUNCT
cana-1619	337	10	−	−	NOUN
cana-1619	337	11	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	337	12	)	)	PUNCT
cana-1619	337	13	−	−	ADP
cana-1619	337	14	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	337	15	)	)	PUNCT
cana-1619	338	1	+	+	SYM
cana-1619	338	2	𝜌(0	𝜌(0	PROPN
cana-1619	338	3	,	,	PUNCT
cana-1619	338	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	338	5	)	)	PUNCT
cana-1619	338	6	,	,	PUNCT
cana-1619	338	7	ℵ	ℵ	NOUN
cana-1619	338	8	)	)	PUNCT
cana-1619	338	9	]	]	PUNCT
cana-1619	339	1	+	+	NUM
cana-1619	339	2	∫	∫	PROPN
cana-1619	339	3	𝜚	𝜚	NOUN
cana-1619	339	4	0	0	PUNCT
cana-1619	339	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	339	6	−	−	NOUN
cana-1619	339	7	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	339	8	,	,	PUNCT
cana-1619	339	9	𝜁𝜂	𝜁𝜂	X
cana-1619	339	10	(	(	PUNCT
cana-1619	339	11	.	.	PUNCT
cana-1619	339	12	,	,	PUNCT
cana-1619	339	13	ℵ	ℵ	NOUN
cana-1619	339	14	)	)	PUNCT
cana-1619	339	15	,	,	PUNCT
cana-1619	340	1	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	340	2	−	−	PROPN
cana-1619	340	3	∫	∫	PROPN
cana-1619	340	4	𝜚	𝜚	NOUN
cana-1619	340	5	0	0	NUM
cana-1619	340	6	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	340	7	−	−	NOUN
cana-1619	340	8	𝜂)υ(𝜂	𝜂)υ(𝜂	NOUN
cana-1619	340	9	,	,	PUNCT
cana-1619	340	10	𝜁𝜂	𝜁𝜂	PRON
cana-1619	340	11	(	(	PUNCT
cana-1619	340	12	.	.	PUNCT
cana-1619	340	13	,	,	PUNCT
cana-1619	340	14	ℵ	ℵ	NOUN
cana-1619	340	15	)	)	PUNCT
cana-1619	340	16	,	,	PUNCT
cana-1619	340	17	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	340	18	−∑0<ℎ𝜉<𝜚	−∑0<ℎ𝜉<𝜚	PROPN
cana-1619	340	19	𝑇1(𝜚	𝑇1(𝜚	PROPN
cana-1619	340	20	−	−	NOUN
cana-1619	341	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	341	2	,	,	PUNCT
cana-1619	341	3	ℵ	ℵ	NOUN
cana-1619	341	4	)	)	PUNCT
cana-1619	341	5	)	)	PUNCT
cana-1619	342	1	−	−	PROPN
cana-1619	342	2	∑0<ℎ𝜉<𝜚	∑0<ℎ𝜉<𝜚	PROPN
cana-1619	342	3	𝑇2(𝜚	𝑇2(𝜚	PROPN
cana-1619	343	1	−	−	PROPN
cana-1619	343	2	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	343	3	,	,	PUNCT
cana-1619	343	4	ℵ))]||𝑑𝜛	ℵ))]||𝑑𝜛	VERB
cana-1619	343	5	≤	≤	NUM
cana-1619	343	6	∫	∫	PROPN
cana-1619	343	7	ℎ	ℎ	PROPN
cana-1619	343	8	0	0	PROPN
cana-1619	343	9	||𝑇2(ℎ	||𝑇2(ℎ	NOUN
cana-1619	343	10	−	−	PROPN
cana-1619	343	11	𝜛)||𝐵𝑘	𝜛)||𝐵𝑘	NOUN
cana-1619	344	1	−1[||𝜁1(ℵ)||	−1[||𝜁1(ℵ)||	NOUN
cana-1619	345	1	+	+	CCONJ
cana-1619	345	2	||𝑇1(𝜚)𝜙0(ℵ)||	||𝑇1(𝜚)𝜙0(ℵ)||	NOUN
cana-1619	345	3	+	+	CCONJ
cana-1619	345	4	||𝑇2(𝜚)[𝜙	||𝑇2(𝜚)[𝜙	PRON
cana-1619	345	5	′	′	NOUN
cana-1619	345	6	0	0	NUM
cana-1619	346	1	(	(	PUNCT
cana-1619	346	2	ℵ]||	ℵ]||	NOUN
cana-1619	346	3	+	+	PROPN
cana-1619	346	4	||	||	NOUN
cana-1619	346	5	∫	∫	PROPN
cana-1619	347	1	𝜚	𝜚	NOUN
cana-1619	347	2	0	0	PUNCT
cana-1619	347	3	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	347	4	−	−	NOUN
cana-1619	347	5	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	347	6	,	,	PUNCT
cana-1619	347	7	𝜁𝜂	𝜁𝜂	X
cana-1619	347	8	(	(	PUNCT
cana-1619	347	9	.	.	PUNCT
cana-1619	347	10	,	,	PUNCT
cana-1619	347	11	ℵ	ℵ	NOUN
cana-1619	347	12	)	)	PUNCT
cana-1619	347	13	,	,	PUNCT
cana-1619	347	14	ℵ)𝑑𝜂||	ℵ)𝑑𝜂||	NOUN
cana-1619	348	1	+	+	CCONJ
cana-1619	348	2	||	||	NUM
cana-1619	348	3	∫	∫	PROPN
cana-1619	349	1	𝜚	𝜚	NOUN
cana-1619	349	2	0	0	NUM
cana-1619	349	3	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	349	4	−	−	NOUN
cana-1619	349	5	𝜂)υ(𝜂	𝜂)υ(𝜂	NOUN
cana-1619	349	6	,	,	PUNCT
cana-1619	349	7	𝜁𝜂	𝜁𝜂	PRON
cana-1619	349	8	(	(	PUNCT
cana-1619	349	9	.	.	PUNCT
cana-1619	349	10	,	,	PUNCT
cana-1619	349	11	ℵ	ℵ	NOUN
cana-1619	349	12	)	)	PUNCT
cana-1619	349	13	,	,	PUNCT
cana-1619	349	14	ℵ)𝑑𝜂||	ℵ)𝑑𝜂||	VERB
cana-1619	350	1	+	+	CCONJ
cana-1619	350	2	∑0<ℎ𝜉<𝜚	∑0<ℎ𝜉<𝜚	ADJ
cana-1619	350	3	||𝑇1(𝜚	||𝑇1(𝜚	NOUN
cana-1619	350	4	−	−	NOUN
cana-1619	351	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	351	2	,	,	PUNCT
cana-1619	351	3	ℵ))||	ℵ))||	NOUN
cana-1619	351	4	+	+	CCONJ
cana-1619	351	5	||	||	NOUN
cana-1619	351	6	∑0<ℎ𝜉<𝜚	∑0<ℎ𝜉<𝜚	PROPN
cana-1619	352	1	𝑇2(𝜚	𝑇2(𝜚	PROPN
cana-1619	353	1	−	−	PROPN
cana-1619	353	2	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	353	3	,	,	PUNCT
cana-1619	353	4	ℵ))||]𝑑𝜛	ℵ))||]𝑑𝜛	PROPN
cana-1619	353	5	≤	≤	NOUN
cana-1619	353	6	𝜗𝑎𝐵𝑘	𝜗𝑎𝐵𝑘	PROPN
cana-1619	353	7	−1	−1	NOUN
cana-1619	353	8	∫	∫	PROPN
cana-1619	353	9	ℎ	ℎ	X
cana-1619	353	10	0	0	PUNCT
cana-1619	354	1	[	[	X
cana-1619	354	2	||𝜁1(ℵ)||	||𝜁1(ℵ)||	NOUN
cana-1619	354	3	+	+	CCONJ
cana-1619	354	4	𝜗||𝜙0(ℵ)||	𝜗||𝜙0(ℵ)||	PROPN
cana-1619	354	5	+	+	CCONJ
cana-1619	354	6	𝜗𝑎||𝜙′0(ℵ	𝜗𝑎||𝜙′0(ℵ	PROPN
cana-1619	354	7	)	)	PUNCT
cana-1619	355	1	+	+	SYM
cana-1619	355	2	𝜌(0	𝜌(0	PROPN
cana-1619	355	3	,	,	PUNCT
cana-1619	355	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	355	5	)	)	PUNCT
cana-1619	355	6	,	,	PUNCT
cana-1619	355	7	ℵ)||	ℵ)||	PRON
cana-1619	356	1	+	+	NOUN
cana-1619	356	2	𝜗	𝜗	NOUN
cana-1619	356	3	∫	∫	NOUN
cana-1619	356	4	𝜚	𝜚	NOUN
cana-1619	356	5	0	0	NUM
cana-1619	356	6	[	[	PUNCT
cana-1619	356	7	sup	sup	NOUN
cana-1619	356	8	𝜂∈(0.𝜚	𝜂∈(0.𝜚	PROPN
cana-1619	356	9	]	]	X
cana-1619	356	10	||𝜁𝜂	||𝜁𝜂	NOUN
cana-1619	356	11	(	(	PUNCT
cana-1619	356	12	.	.	PUNCT
cana-1619	356	13	,	,	PUNCT
cana-1619	356	14	ℵ	ℵ	NOUN
cana-1619	356	15	)	)	PUNCT
cana-1619	356	16	,	,	PUNCT
cana-1619	356	17	ℵ||𝒟	ℵ||𝒟	NOUN
cana-1619	356	18	𝛽0	𝛽0	VERB
cana-1619	356	19	+	+	CCONJ
cana-1619	357	1	𝑑0(ℵ)]𝑑𝜂	𝑑0(ℵ)]𝑑𝜂	ADJ
cana-1619	358	1	+	+	NUM
cana-1619	358	2	𝜗𝑎	𝜗𝑎	ADP
cana-1619	358	3	∫	∫	PROPN
cana-1619	358	4	𝜚	𝜚	NOUN
cana-1619	358	5	0	0	NUM
cana-1619	358	6	[	[	PUNCT
cana-1619	358	7	sup	sup	NOUN
cana-1619	358	8	𝜂∈(0.𝜚	𝜂∈(0.𝜚	PROPN
cana-1619	358	9	]	]	X
cana-1619	358	10	||𝜁𝜂	||𝜁𝜂	NOUN
cana-1619	358	11	(	(	PUNCT
cana-1619	358	12	.	.	PUNCT
cana-1619	358	13	,	,	PUNCT
cana-1619	358	14	ℵ	ℵ	NOUN
cana-1619	358	15	)	)	PUNCT
cana-1619	358	16	,	,	PUNCT
cana-1619	358	17	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	358	18	𝛼0	𝛼0	PROPN
cana-1619	359	1	+	+	ADV
cana-1619	359	2	𝜗∑0<ℎ𝜉<𝜚	𝜗∑0<ℎ𝜉<𝜚	PROPN
cana-1619	359	3	𝑎𝜉(ℵ)||𝜁(ℎ𝜉	𝑎𝜉(ℵ)||𝜁(ℎ𝜉	NUM
cana-1619	359	4	,	,	PUNCT
cana-1619	359	5	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	359	6	𝛼𝜉	𝛼𝜉	NOUN
cana-1619	359	7	+	+	NUM
cana-1619	359	8	𝜗𝑎	𝜗𝑎	ADP
cana-1619	359	9	∑0<ℎ𝜉<𝜚	∑0<ℎ𝜉<𝜚	PROPN
cana-1619	359	10	𝑎′𝜉(ℵ)||𝜁(ℎ𝜉	𝑎′𝜉(ℵ)||𝜁(ℎ𝜉	PROPN
cana-1619	359	11	,	,	PUNCT
cana-1619	359	12	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	359	13	𝛼𝜉]𝑑𝜛	𝛼𝜉]𝑑𝜛	PROPN
cana-1619	359	14	≤	≤	PROPN
cana-1619	359	15	𝑄(ℵ	𝑄(ℵ	NOUN
cana-1619	359	16	)	)	PUNCT
cana-1619	359	17	(	(	PUNCT
cana-1619	359	18	9	9	NUM
cana-1619	359	19	)	)	PUNCT
cana-1619	359	20	hence	hence	ADV
cana-1619	359	21	(	(	PUNCT
cana-1619	359	22	γ(ℵ))′2	γ(ℵ))′2	PROPN
cana-1619	359	23	is	be	AUX
cana-1619	359	24	bounded	bound	VERB
cana-1619	359	25	in	in	ADP
cana-1619	359	26	𝑃𝐶𝛿	𝑃𝐶𝛿	NOUN
cana-1619	359	27	step	step	NOUN
cana-1619	359	28	2	2	NUM
cana-1619	359	29	:	:	PUNCT
cana-1619	359	30	we	we	PRON
cana-1619	359	31	now	now	ADV
cana-1619	359	32	demonstrate	demonstrate	VERB
cana-1619	359	33	that	that	SCONJ
cana-1619	359	34	(	(	PUNCT
cana-1619	359	35	γ(ℵ))′2	γ(ℵ))′2	PROPN
cana-1619	359	36	is	be	AUX
cana-1619	359	37	continuous	continuous	ADJ
cana-1619	359	38	on	on	ADP
cana-1619	359	39	ℬ𝑟(𝛿	ℬ𝑟(𝛿	NUM
cana-1619	359	40	)	)	PUNCT
cana-1619	359	41	.	.	PUNCT
cana-1619	360	1	let	let	VERB
cana-1619	360	2	us	we	PRON
cana-1619	360	3	consider	consider	VERB
cana-1619	360	4	𝜁1	𝜁1	ADJ
cana-1619	360	5	,	,	PUNCT
cana-1619	360	6	𝜁2	𝜁2	NOUN
cana-1619	360	7	∈	∈	PROPN
cana-1619	360	8	ℬ𝑟(𝛿	ℬ𝑟(𝛿	NOUN
cana-1619	360	9	)	)	PUNCT
cana-1619	360	10	and	and	CCONJ
cana-1619	360	11	ℎ	ℎ	ADP
cana-1619	360	12	∈	∈	PROPN
cana-1619	360	13	𝐽.	𝐽.	PROPN
cana-1619	360	14	||(γ(ℵ))′2𝜁1(ℎ	||(γ(ℵ))′2𝜁1(ℎ	PROPN
cana-1619	360	15	)	)	PUNCT
cana-1619	360	16	−	−	PROPN
cana-1619	361	1	(	(	PUNCT
cana-1619	361	2	γ(ℵ))′2𝜁2(ℎ)||	γ(ℵ))′2𝜁2(ℎ)||	PROPN
cana-1619	361	3	≤	≤	NUM
cana-1619	361	4	∫	∫	PROPN
cana-1619	361	5	ℎ	ℎ	PROPN
cana-1619	361	6	0	0	NUM
cana-1619	361	7	||𝑇1(ℎ	||𝑇1(ℎ	NOUN
cana-1619	361	8	−	−	PROPN
cana-1619	361	9	𝜛)𝐵𝑘	𝜛)𝐵𝑘	NOUN
cana-1619	362	1	−1[∫	−1[∫	NUM
cana-1619	362	2	𝜚	𝜚	NOUN
cana-1619	362	3	0	0	NUM
cana-1619	362	4	𝑇1(𝜚	𝑇1(𝜚	PROPN
cana-1619	362	5	−	−	PROPN
cana-1619	362	6	𝜂)[𝜌(𝜂	𝜂)[𝜌(𝜂	PROPN
cana-1619	362	7	,	,	PUNCT
cana-1619	362	8	(	(	PUNCT
cana-1619	362	9	𝜁1,𝜂	𝜁1,𝜂	PROPN
cana-1619	362	10	(	(	PUNCT
cana-1619	362	11	.	.	PUNCT
cana-1619	362	12	,	,	PUNCT
cana-1619	362	13	ℵ	ℵ	NOUN
cana-1619	362	14	)	)	PUNCT
cana-1619	362	15	,	,	PUNCT
cana-1619	362	16	ℵ	ℵ	NOUN
cana-1619	362	17	)	)	PUNCT
cana-1619	362	18	,	,	PUNCT
cana-1619	362	19	ℵ	ℵ	NOUN
cana-1619	362	20	)	)	PUNCT
cana-1619	362	21	−𝜌(𝜂	−𝜌(𝜂	PROPN
cana-1619	362	22	,	,	PUNCT
cana-1619	362	23	(	(	PUNCT
cana-1619	362	24	𝜁2,𝜂	𝜁2,𝜂	PROPN
cana-1619	362	25	(	(	PUNCT
cana-1619	362	26	.	.	PUNCT
cana-1619	362	27	,	,	PUNCT
cana-1619	362	28	ℵ	ℵ	NOUN
cana-1619	362	29	)	)	PUNCT
cana-1619	362	30	,	,	PUNCT
cana-1619	362	31	ℵ	ℵ	NOUN
cana-1619	362	32	)	)	PUNCT
cana-1619	362	33	,	,	PUNCT
cana-1619	362	34	ℵ)]𝑑𝜂	ℵ)]𝑑𝜂	CCONJ
cana-1619	362	35	−∫	−∫	VERB
cana-1619	362	36	𝜚	𝜚	NOUN
cana-1619	362	37	0	0	NUM
cana-1619	362	38	𝑇2(𝜚	𝑇2(𝜚	NOUN
cana-1619	362	39	−	−	PROPN
cana-1619	362	40	𝜂)[υ(𝜂	𝜂)[υ(𝜂	NOUN
cana-1619	362	41	,	,	PUNCT
cana-1619	362	42	(	(	PUNCT
cana-1619	362	43	𝜁1,𝜂	𝜁1,𝜂	PROPN
cana-1619	362	44	(	(	PUNCT
cana-1619	362	45	.	.	PUNCT
cana-1619	362	46	,	,	PUNCT
cana-1619	362	47	ℵ	ℵ	NOUN
cana-1619	362	48	)	)	PUNCT
cana-1619	362	49	,	,	PUNCT
cana-1619	362	50	ℵ	ℵ	NOUN
cana-1619	362	51	)	)	PUNCT
cana-1619	362	52	,	,	PUNCT
cana-1619	362	53	ℵ	ℵ	NOUN
cana-1619	362	54	)	)	PUNCT
cana-1619	362	55	−	−	NOUN
cana-1619	362	56	υ(𝜂	υ(𝜂	NOUN
cana-1619	362	57	,	,	PUNCT
cana-1619	362	58	(	(	PUNCT
cana-1619	362	59	𝜁2,𝜂	𝜁2,𝜂	PROPN
cana-1619	362	60	(	(	PUNCT
cana-1619	362	61	.	.	PUNCT
cana-1619	362	62	,	,	PUNCT
cana-1619	362	63	ℵ	ℵ	NOUN
cana-1619	362	64	)	)	PUNCT
cana-1619	362	65	,	,	PUNCT
cana-1619	362	66	ℵ	ℵ	NOUN
cana-1619	362	67	)	)	PUNCT
cana-1619	362	68	,	,	PUNCT
cana-1619	362	69	ℵ)]𝑑𝜂	ℵ)]𝑑𝜂	NUM
cana-1619	362	70	−	−	PROPN
cana-1619	362	71	∑	∑	PROPN
cana-1619	362	72	0<ℎ𝜉<𝜚	0<ℎ𝜉<𝜚	PROPN
cana-1619	362	73	𝑇1(𝜚	𝑇1(𝜚	PROPN
cana-1619	362	74	−	−	PROPN
cana-1619	363	1	ℎ𝜉)[𝐼𝜉(𝜁1(ℎ𝜉	ℎ𝜉)[𝐼𝜉(𝜁1(ℎ𝜉	PROPN
cana-1619	363	2	,	,	PUNCT
cana-1619	363	3	ℵ	ℵ	NOUN
cana-1619	363	4	)	)	PUNCT
cana-1619	363	5	)	)	PUNCT
cana-1619	364	1	−	−	PROPN
cana-1619	364	2	𝐼𝜉(𝜁2(ℎ𝜉	𝐼𝜉(𝜁2(ℎ𝜉	NOUN
cana-1619	364	3	,	,	PUNCT
cana-1619	364	4	ℵ	ℵ	NOUN
cana-1619	364	5	)	)	PUNCT
cana-1619	364	6	)	)	PUNCT
cana-1619	364	7	]	]	PUNCT
cana-1619	365	1	−	−	PUNCT
cana-1619	365	2	∑	∑	PUNCT
cana-1619	365	3	0<ℎ𝜉<𝜚	0<ℎ𝜉<𝜚	PROPN
cana-1619	365	4	𝑇2(𝜚	𝑇2(𝜚	PROPN
cana-1619	365	5	−	−	PROPN
cana-1619	365	6	ℎ𝜉)[𝐼′𝜉(𝜁1(ℎ𝜉	ℎ𝜉)[𝐼′𝜉(𝜁1(ℎ𝜉	NOUN
cana-1619	365	7	,	,	PUNCT
cana-1619	365	8	ℵ	ℵ	NOUN
cana-1619	365	9	)	)	PUNCT
cana-1619	365	10	)	)	PUNCT
cana-1619	366	1	−	−	PROPN
cana-1619	366	2	𝐼′𝜉(𝜁2(ℎ𝜉	𝐼′𝜉(𝜁2(ℎ𝜉	NOUN
cana-1619	366	3	,	,	PUNCT
cana-1619	366	4	ℵ))]||]𝑑𝜛	ℵ))]||]𝑑𝜛	PROPN
cana-1619	366	5	≤	≤	NUM
cana-1619	366	6	∫	∫	PROPN
cana-1619	366	7	ℎ	ℎ	PROPN
cana-1619	366	8	0	0	NUM
cana-1619	366	9	𝜗𝑎𝐵𝑘	𝜗𝑎𝐵𝑘	NOUN
cana-1619	366	10	−1[∫	−1[∫	NUM
cana-1619	366	11	𝜚	𝜚	NOUN
cana-1619	366	12	0	0	NUM
cana-1619	366	13	𝜗	𝜗	NOUN
cana-1619	366	14	sup	sup	NOUN
cana-1619	366	15	𝜂∈(0.𝜚	𝜂∈(0.𝜚	PROPN
cana-1619	366	16	]	]	X
cana-1619	366	17	||(𝜁1,𝜂	||(𝜁1,𝜂	NOUN
cana-1619	366	18	(	(	PUNCT
cana-1619	366	19	.	.	PUNCT
cana-1619	366	20	,	,	PUNCT
cana-1619	366	21	ℵ	ℵ	NOUN
cana-1619	366	22	)	)	PUNCT
cana-1619	366	23	,	,	PUNCT
cana-1619	366	24	ℵ	ℵ	NOUN
cana-1619	366	25	)	)	PUNCT
cana-1619	366	26	−	−	PROPN
cana-1619	366	27	(	(	PUNCT
cana-1619	366	28	𝜁2,𝜂	𝜁2,𝜂	PROPN
cana-1619	366	29	(	(	PUNCT
cana-1619	366	30	.	.	PUNCT
cana-1619	366	31	,	,	PUNCT
cana-1619	366	32	ℵ	ℵ	NOUN
cana-1619	366	33	)	)	PUNCT
cana-1619	366	34	,	,	PUNCT
cana-1619	366	35	ℵ)||𝒟	ℵ)||𝒟	NUM
cana-1619	366	36	𝛽0𝑑𝜂	𝛽0𝑑𝜂	PUNCT
cana-1619	366	37	+	+	NOUN
cana-1619	366	38	∫	∫	PROPN
cana-1619	366	39	𝜚	𝜚	NOUN
cana-1619	366	40	0	0	NUM
cana-1619	366	41	𝜗𝑎	𝜗𝑎	ADP
cana-1619	366	42	sup	sup	PROPN
cana-1619	366	43	𝜂∈(0.𝜚	𝜂∈(0.𝜚	PROPN
cana-1619	366	44	]	]	X
cana-1619	366	45	||(𝜁1,𝜂	||(𝜁1,𝜂	NOUN
cana-1619	366	46	(	(	PUNCT
cana-1619	366	47	.	.	PUNCT
cana-1619	366	48	,	,	PUNCT
cana-1619	366	49	ℵ	ℵ	NOUN
cana-1619	366	50	)	)	PUNCT
cana-1619	366	51	,	,	PUNCT
cana-1619	366	52	ℵ	ℵ	NOUN
cana-1619	366	53	)	)	PUNCT
cana-1619	366	54	−	−	PROPN
cana-1619	366	55	(	(	PUNCT
cana-1619	366	56	𝜁2,𝜂	𝜁2,𝜂	PROPN
cana-1619	366	57	(	(	PUNCT
cana-1619	366	58	.	.	PUNCT
cana-1619	366	59	,	,	PUNCT
cana-1619	366	60	ℵ	ℵ	NOUN
cana-1619	366	61	)	)	PUNCT
cana-1619	366	62	,	,	PUNCT
cana-1619	366	63	ℵ)||𝒟	ℵ)||𝒟	NUM
cana-1619	366	64	𝛼0𝑑𝜂	𝛼0𝑑𝜂	X
cana-1619	366	65	+	+	NOUN
cana-1619	366	66	𝜗	𝜗	NOUN
cana-1619	366	67	∑	∑	PROPN
cana-1619	366	68	0<ℎ𝜉<𝜚	0<ℎ𝜉<𝜚	PROPN
cana-1619	366	69	𝑎𝜉(ℵ)||𝜁1(ℎ𝜉	𝑎𝜉(ℵ)||𝜁1(ℎ𝜉	NOUN
cana-1619	366	70	,	,	PUNCT
cana-1619	366	71	ℵ	ℵ	NOUN
cana-1619	366	72	)	)	PUNCT
cana-1619	366	73	−	−	PROPN
cana-1619	366	74	𝜁2(ℎ𝜉	𝜁2(ℎ𝜉	PROPN
cana-1619	366	75	,	,	PUNCT
cana-1619	366	76	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	366	77	𝛼𝜉	𝛼𝜉	NOUN
cana-1619	367	1	+	+	ADP
cana-1619	367	2	𝜗𝑎	𝜗𝑎	PRON
cana-1619	367	3	∑	∑	PROPN
cana-1619	367	4	0<ℎ𝜉<𝜚	0<ℎ𝜉<𝜚	PROPN
cana-1619	367	5	𝑎′𝜉(ℵ)||𝜁1(ℎ𝜉	𝑎′𝜉(ℵ)||𝜁1(ℎ𝜉	NUM
cana-1619	367	6	,	,	PUNCT
cana-1619	367	7	ℵ	ℵ	NOUN
cana-1619	367	8	)	)	PUNCT
cana-1619	367	9	−	−	PROPN
cana-1619	367	10	𝜁2(ℎ𝜉	𝜁2(ℎ𝜉	PROPN
cana-1619	367	11	,	,	PUNCT
cana-1619	367	12	ℵ)||ℝ	ℵ)||ℝ	NUM
cana-1619	367	13	𝛼𝜉]𝑑𝜛	𝛼𝜉]𝑑𝜛	NOUN
cana-1619	367	14	for	for	ADP
cana-1619	367	15	all	all	PRON
cana-1619	367	16	ℎ	ℎ	PART
cana-1619	367	17	∈	∈	PROPN
cana-1619	367	18	(	(	PUNCT
cana-1619	367	19	−𝛿	−𝛿	NOUN
cana-1619	367	20	,	,	PUNCT
cana-1619	367	21	𝜚	𝜚	NOUN
cana-1619	367	22	]	]	X
cana-1619	367	23	,	,	PUNCT
cana-1619	367	24	and	and	CCONJ
cana-1619	367	25	due	due	ADP
cana-1619	367	26	to	to	ADP
cana-1619	367	27	their	their	PRON
cana-1619	367	28	compactness	compactness	NOUN
cana-1619	367	29	for	for	ADP
cana-1619	367	30	ℎ	ℎ	X
cana-1619	367	31	>	>	X
cana-1619	367	32	0	0	PROPN
cana-1619	367	33	,	,	PUNCT
cana-1619	367	34	the	the	DET
cana-1619	367	35	uniform	uniform	ADJ
cana-1619	367	36	operator	operator	NOUN
cana-1619	367	37	topology	topology	NOUN
cana-1619	367	38	is	be	AUX
cana-1619	367	39	continuous	continuous	ADJ
cana-1619	367	40	.	.	PUNCT
cana-1619	368	1	given	give	VERB
cana-1619	368	2	𝜁1	𝜁1	PROPN
cana-1619	368	3	,	,	PUNCT
cana-1619	368	4	𝜁2	𝜁2	NOUN
cana-1619	368	5	∈	∈	PROPN
cana-1619	368	6	ℬ𝑟(𝛿	ℬ𝑟(𝛿	NOUN
cana-1619	368	7	)	)	PUNCT
cana-1619	368	8	,	,	PUNCT
cana-1619	368	9	the	the	DET
cana-1619	368	10	independence	independence	NOUN
cana-1619	368	11	of	of	ADP
cana-1619	368	12	the	the	DET
cana-1619	368	13	right	right	ADJ
cana-1619	368	14	side	side	NOUN
cana-1619	368	15	of	of	ADP
cana-1619	368	16	the	the	DET
cana-1619	368	17	inequalities	inequality	NOUN
cana-1619	368	18	above	above	ADV
cana-1619	368	19	is	be	AUX
cana-1619	368	20	evident	evident	ADJ
cana-1619	368	21	.	.	PUNCT
cana-1619	369	1	consequently	consequently	ADV
cana-1619	369	2	,	,	PUNCT
cana-1619	369	3	as	as	ADP
cana-1619	369	4	(	(	PUNCT
cana-1619	369	5	𝜁1	𝜁1	ADJ
cana-1619	369	6	−	−	PROPN
cana-1619	369	7	𝜁2	𝜁2	NOUN
cana-1619	369	8	)	)	PUNCT
cana-1619	369	9	→	→	SYM
cana-1619	369	10	0	0	NUM
cana-1619	369	11	,	,	PUNCT
cana-1619	369	12	we	we	PRON
cana-1619	369	13	have	have	VERB
cana-1619	369	14	∥	∥	NUM
cana-1619	369	15	(	(	PUNCT
cana-1619	369	16	(	(	PUNCT
cana-1619	369	17	γ(ℵ))′2𝜁1)(ℎ	γ(ℵ))′2𝜁1)(ℎ	NUM
cana-1619	369	18	)	)	PUNCT
cana-1619	369	19	−	−	PROPN
cana-1619	370	1	(	(	PUNCT
cana-1619	370	2	(	(	PUNCT
cana-1619	370	3	γ(ℵ))′2𝜁2)(ℎ	γ(ℵ))′2𝜁2)(ℎ	NOUN
cana-1619	370	4	)	)	PUNCT
cana-1619	370	5	∥→	∥→	ADV
cana-1619	370	6	0	0	NUM
cana-1619	370	7	.	.	PUNCT
cana-1619	371	1	this	this	PRON
cana-1619	371	2	implies	imply	VERB
cana-1619	371	3	that	that	SCONJ
cana-1619	371	4	(	(	PUNCT
cana-1619	371	5	γ(ℵ	γ(ℵ	PROPN
cana-1619	371	6	)	)	PUNCT
cana-1619	371	7	)	)	PUNCT
cana-1619	371	8	is	be	AUX
cana-1619	371	9	continuous	continuous	ADJ
cana-1619	371	10	.	.	PUNCT
cana-1619	372	1	communications	communication	NOUN
cana-1619	372	2	on	on	ADP
cana-1619	372	3	applied	apply	VERB
cana-1619	372	4	nonlinear	nonlinear	ADJ
cana-1619	372	5	analysis	analysis	NOUN
cana-1619	372	6	issn	issn	NOUN
cana-1619	372	7	:	:	PUNCT
cana-1619	372	8	1074	1074	NUM
cana-1619	372	9	-	-	PUNCT
cana-1619	372	10	133x	133x	NUM
cana-1619	372	11	vol	vol	NOUN
cana-1619	372	12	32	32	NUM
cana-1619	372	13	no	no	NOUN
cana-1619	372	14	.	.	NOUN
cana-1619	372	15	1	1	NUM
cana-1619	372	16	(	(	PUNCT
cana-1619	372	17	2025	2025	NUM
cana-1619	372	18	)	)	PUNCT
cana-1619	372	19	50	50	NUM
cana-1619	372	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	372	21	step	step	NOUN
cana-1619	372	22	3	3	NUM
cana-1619	372	23	:	:	PUNCT
cana-1619	372	24	(	(	PUNCT
cana-1619	372	25	γ(ℵ))′2	γ(ℵ))′2	PROPN
cana-1619	372	26	is	be	AUX
cana-1619	372	27	a	a	DET
cana-1619	372	28	compact	compact	ADJ
cana-1619	372	29	operator	operator	NOUN
cana-1619	372	30	.	.	PUNCT
cana-1619	373	1	to	to	PART
cana-1619	373	2	establish	establish	VERB
cana-1619	373	3	this	this	PRON
cana-1619	373	4	,	,	PUNCT
cana-1619	373	5	we	we	PRON
cana-1619	373	6	analyze	analyze	VERB
cana-1619	373	7	the	the	DET
cana-1619	373	8	decomposition	decomposition	NOUN
cana-1619	373	9	(	(	PUNCT
cana-1619	373	10	γ(ℵ))′2	γ(ℵ))′2	PROPN
cana-1619	373	11	=	=	SYM
cana-1619	373	12	(	(	PUNCT
cana-1619	373	13	γ𝑎(ℵ))′2	γ𝑎(ℵ))′2	PROPN
cana-1619	373	14	+	+	CCONJ
cana-1619	373	15	(	(	PUNCT
cana-1619	373	16	γ𝑏(ℵ))′2	γ𝑏(ℵ))′2	PROPN
cana-1619	373	17	,	,	PUNCT
cana-1619	373	18	where	where	SCONJ
cana-1619	373	19	(	(	PUNCT
cana-1619	373	20	γ1(ℵ	γ1(ℵ	NUM
cana-1619	373	21	)	)	PUNCT
cana-1619	373	22	)	)	PUNCT
cana-1619	373	23	and	and	CCONJ
cana-1619	373	24	(	(	PUNCT
cana-1619	373	25	γ(ℵ))2	γ(ℵ))2	PROPN
cana-1619	373	26	denote	denote	VERB
cana-1619	373	27	operators	operator	NOUN
cana-1619	373	28	on	on	ADP
cana-1619	373	29	ℬ𝑟(𝛿	ℬ𝑟(𝛿	ADJ
cana-1619	373	30	)	)	PUNCT
cana-1619	373	31	.	.	PUNCT
cana-1619	374	1	they	they	PRON
cana-1619	374	2	are	be	AUX
cana-1619	374	3	defined	define	VERB
cana-1619	374	4	as	as	SCONJ
cana-1619	374	5	follows	follow	VERB
cana-1619	374	6	:	:	PUNCT
cana-1619	374	7	(	(	PUNCT
cana-1619	374	8	γ𝑎(ℵ))′2	γ𝑎(ℵ))′2	PROPN
cana-1619	374	9	=	=	SYM
cana-1619	374	10	∫	∫	PROPN
cana-1619	374	11	ℎ	ℎ	PROPN
cana-1619	374	12	0	0	PROPN
cana-1619	374	13	||𝑇2(ℎ	||𝑇2(ℎ	NOUN
cana-1619	374	14	−	−	PROPN
cana-1619	374	15	𝜛)𝐵𝑘	𝜛)𝐵𝑘	NOUN
cana-1619	374	16	−1[𝜁1(ℵ	−1[𝜁1(ℵ	NOUN
cana-1619	374	17	)	)	PUNCT
cana-1619	374	18	−	−	NOUN
cana-1619	374	19	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	374	20	)	)	PUNCT
cana-1619	374	21	−	−	ADP
cana-1619	374	22	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	374	23	)	)	PUNCT
cana-1619	375	1	+	+	SYM
cana-1619	375	2	𝜌(0	𝜌(0	PROPN
cana-1619	375	3	,	,	PUNCT
cana-1619	375	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	375	5	)	)	PUNCT
cana-1619	375	6	,	,	PUNCT
cana-1619	375	7	ℵ	ℵ	NOUN
cana-1619	375	8	)	)	PUNCT
cana-1619	375	9	]	]	PUNCT
cana-1619	376	1	+	+	NUM
cana-1619	376	2	∫	∫	PROPN
cana-1619	376	3	𝜚	𝜚	NOUN
cana-1619	376	4	0	0	NUM
cana-1619	376	5	𝑇1(𝜚	𝑇1(𝜚	PROPN
cana-1619	376	6	−	−	PROPN
cana-1619	376	7	𝜂)[𝜌(𝜂	𝜂)[𝜌(𝜂	PROPN
cana-1619	376	8	,	,	PUNCT
cana-1619	376	9	𝜁𝜂	𝜁𝜂	X
cana-1619	376	10	(	(	PUNCT
cana-1619	376	11	.	.	PUNCT
cana-1619	376	12	,	,	PUNCT
cana-1619	376	13	ℵ	ℵ	NOUN
cana-1619	376	14	)	)	PUNCT
cana-1619	376	15	,	,	PUNCT
cana-1619	376	16	ℵ)]𝑑𝜂	ℵ)]𝑑𝜂	NUM
cana-1619	376	17	−	−	NUM
cana-1619	376	18	∫	∫	NOUN
cana-1619	376	19	𝜚	𝜚	NOUN
cana-1619	376	20	0	0	NUM
cana-1619	376	21	𝑇2(𝜚	𝑇2(𝜚	PROPN
cana-1619	376	22	−	−	PROPN
cana-1619	376	23	𝜂)[υ(𝜂	𝜂)[υ(𝜂	NOUN
cana-1619	376	24	,	,	PUNCT
cana-1619	376	25	𝜁𝜂	𝜁𝜂	X
cana-1619	376	26	(	(	PUNCT
cana-1619	376	27	.	.	PUNCT
cana-1619	376	28	,	,	PUNCT
cana-1619	376	29	ℵ	ℵ	NOUN
cana-1619	376	30	)	)	PUNCT
cana-1619	376	31	,	,	PUNCT
cana-1619	376	32	ℵ)]𝑑𝜂]𝑑𝜛	ℵ)]𝑑𝜂]𝑑𝜛	NOUN
cana-1619	377	1	(	(	PUNCT
cana-1619	377	2	γ𝑏(ℵ))′2	γ𝑏(ℵ))′2	PROPN
cana-1619	377	3	=	=	PUNCT
cana-1619	377	4	∫	∫	PROPN
cana-1619	377	5	ℎ	ℎ	PROPN
cana-1619	377	6	0	0	PROPN
cana-1619	377	7	||𝑇2(ℎ	||𝑇2(ℎ	NOUN
cana-1619	377	8	−	−	PROPN
cana-1619	377	9	𝜛)𝐵𝑘	𝜛)𝐵𝑘	NOUN
cana-1619	377	10	−1	−1	NOUN
cana-1619	377	11	[	[	PUNCT
cana-1619	377	12	∑	∑	PUNCT
cana-1619	377	13	0<ℎ𝜉<𝜚	0<ℎ𝜉<𝜚	PROPN
cana-1619	377	14	𝑇1(𝜚	𝑇1(𝜚	PROPN
cana-1619	377	15	−	−	PROPN
cana-1619	378	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	378	2	,	,	PUNCT
cana-1619	378	3	ℵ	ℵ	NOUN
cana-1619	378	4	)	)	PUNCT
cana-1619	378	5	)	)	PUNCT
cana-1619	378	6	−	−	PROPN
cana-1619	379	1	∑	∑	PROPN
cana-1619	379	2	0<ℎ𝜉<𝜚	0<ℎ𝜉<𝜚	PROPN
cana-1619	379	3	𝑇2(𝜚	𝑇2(𝜚	PROPN
cana-1619	379	4	−	−	PROPN
cana-1619	379	5	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	379	6	,	,	PUNCT
cana-1619	379	7	ℵ))]𝑑𝜛	ℵ))]𝑑𝜛	CCONJ
cana-1619	379	8	we	we	PRON
cana-1619	379	9	first	first	ADV
cana-1619	379	10	prove	prove	VERB
cana-1619	379	11	that	that	SCONJ
cana-1619	379	12	(	(	PUNCT
cana-1619	379	13	γ(ℵ))2,𝑎(ℬ𝑟(𝛿	γ(ℵ))2,𝑎(ℬ𝑟(𝛿	NOUN
cana-1619	379	14	)	)	PUNCT
cana-1619	379	15	)	)	PUNCT
cana-1619	379	16	is	be	AUX
cana-1619	379	17	equicontinuous	equicontinuous	ADJ
cana-1619	379	18	.	.	PUNCT
cana-1619	380	1	let	let	VERB
cana-1619	380	2	𝛿	𝛿	PRON
cana-1619	380	3	≤	≤	ADJ
cana-1619	380	4	ℎ1	ℎ1	PROPN
cana-1619	380	5	<	<	X
cana-1619	380	6	ℎ2	ℎ2	ADJ
cana-1619	380	7	≤	≤	NUM
cana-1619	380	8	𝜚	𝜚	NOUN
cana-1619	380	9	and	and	CCONJ
cana-1619	380	10	𝜖	𝜖	X
cana-1619	380	11	>	>	X
cana-1619	380	12	0	0	NUM
cana-1619	380	13	be	be	AUX
cana-1619	380	14	small	small	ADJ
cana-1619	380	15	,	,	PUNCT
cana-1619	380	16	then	then	ADV
cana-1619	380	17	||(γ𝑎	||(γ𝑎	NOUN
cana-1619	380	18	(	(	PUNCT
cana-1619	380	19	ℵ))′2𝜁(ℎ2	ℵ))′2𝜁(ℎ2	NOUN
cana-1619	380	20	)	)	PUNCT
cana-1619	380	21	−	−	PROPN
cana-1619	381	1	(	(	PUNCT
cana-1619	381	2	γ𝑎(ℵ))′2𝜁(ℎ1)||	γ𝑎(ℵ))′2𝜁(ℎ1)||	NOUN
cana-1619	381	3	≤	≤	X
cana-1619	381	4	∫	∫	NOUN
cana-1619	382	1	ℎ1	ℎ1	PROPN
cana-1619	382	2	0	0	NUM
cana-1619	382	3	||𝑇2(ℎ2	||𝑇2(ℎ2	PROPN
cana-1619	382	4	−𝜛)𝐵𝑘	−𝜛)𝐵𝑘	NOUN
cana-1619	382	5	−1[𝜁1(ℵ	−1[𝜁1(ℵ	NOUN
cana-1619	382	6	)	)	PUNCT
cana-1619	382	7	−	−	NOUN
cana-1619	382	8	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	382	9	)	)	PUNCT
cana-1619	382	10	−	−	PROPN
cana-1619	383	1	𝑇2(𝜚	𝑇2(𝜚	NOUN
cana-1619	383	2	)	)	PUNCT
cana-1619	384	1	[	[	X
cana-1619	384	2	𝜙′0(ℵ	𝜙′0(ℵ	NOUN
cana-1619	384	3	)	)	PUNCT
cana-1619	384	4	+	+	SYM
cana-1619	385	1	𝜌(0	𝜌(0	PROPN
cana-1619	385	2	,	,	PUNCT
cana-1619	385	3	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	385	4	)	)	PUNCT
cana-1619	385	5	,	,	PUNCT
cana-1619	385	6	ℵ	ℵ	NOUN
cana-1619	385	7	)	)	PUNCT
cana-1619	385	8	]	]	PUNCT
cana-1619	386	1	+	+	CCONJ
cana-1619	386	2	∫	∫	PROPN
cana-1619	386	3	𝜚	𝜚	NOUN
cana-1619	386	4	0	0	NUM
cana-1619	386	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	386	6	−	−	NOUN
cana-1619	386	7	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	386	8	,	,	PUNCT
cana-1619	386	9	𝜁𝜂	𝜁𝜂	X
cana-1619	386	10	(	(	PUNCT
cana-1619	386	11	.	.	PUNCT
cana-1619	386	12	,	,	PUNCT
cana-1619	386	13	ℵ	ℵ	NOUN
cana-1619	386	14	)	)	PUNCT
cana-1619	386	15	,	,	PUNCT
cana-1619	387	1	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	387	2	−	−	PROPN
cana-1619	387	3	∫	∫	PROPN
cana-1619	387	4	𝜚	𝜚	NOUN
cana-1619	387	5	0	0	NUM
cana-1619	387	6	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	387	7	−	−	NOUN
cana-1619	387	8	𝜂)υ(𝜂	𝜂)υ(𝜂	NOUN
cana-1619	387	9	,	,	PUNCT
cana-1619	387	10	𝜁𝜂	𝜁𝜂	PRON
cana-1619	387	11	(	(	PUNCT
cana-1619	387	12	.	.	PUNCT
cana-1619	387	13	,	,	PUNCT
cana-1619	387	14	ℵ	ℵ	NOUN
cana-1619	387	15	)	)	PUNCT
cana-1619	387	16	,	,	PUNCT
cana-1619	387	17	ℵ)𝑑𝜂]𝑑𝜛	ℵ)𝑑𝜂]𝑑𝜛	NOUN
cana-1619	387	18	−∫	−∫	NOUN
cana-1619	387	19	ℎ2	ℎ2	NOUN
cana-1619	387	20	0	0	PUNCT
cana-1619	388	1	𝑇2(ℎ1	𝑇2(ℎ1	ADJ
cana-1619	388	2	−𝜛)𝐵𝑘	−𝜛)𝐵𝑘	NOUN
cana-1619	388	3	−1[𝜁1(ℵ	−1[𝜁1(ℵ	NOUN
cana-1619	388	4	)	)	PUNCT
cana-1619	388	5	−	−	NOUN
cana-1619	388	6	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	388	7	)	)	PUNCT
cana-1619	388	8	−	−	ADP
cana-1619	388	9	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	388	10	)	)	PUNCT
cana-1619	389	1	+	+	SYM
cana-1619	389	2	𝜌(0	𝜌(0	PROPN
cana-1619	389	3	,	,	PUNCT
cana-1619	389	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	389	5	)	)	PUNCT
cana-1619	389	6	,	,	PUNCT
cana-1619	389	7	ℵ	ℵ	NOUN
cana-1619	389	8	)	)	PUNCT
cana-1619	389	9	]	]	PUNCT
cana-1619	390	1	+	+	NUM
cana-1619	390	2	∫	∫	PROPN
cana-1619	390	3	𝜚	𝜚	NOUN
cana-1619	390	4	0	0	PUNCT
cana-1619	390	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	390	6	−	−	NOUN
cana-1619	390	7	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	390	8	,	,	PUNCT
cana-1619	390	9	𝜁𝜂	𝜁𝜂	X
cana-1619	390	10	(	(	PUNCT
cana-1619	390	11	.	.	PUNCT
cana-1619	390	12	,	,	PUNCT
cana-1619	390	13	ℵ	ℵ	NOUN
cana-1619	390	14	)	)	PUNCT
cana-1619	390	15	,	,	PUNCT
cana-1619	391	1	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	391	2	−	−	PROPN
cana-1619	391	3	∫	∫	PROPN
cana-1619	391	4	𝜚	𝜚	NOUN
cana-1619	391	5	0	0	NUM
cana-1619	391	6	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	391	7	−	−	NOUN
cana-1619	391	8	𝜂)υ(𝜂	𝜂)υ(𝜂	NOUN
cana-1619	391	9	,	,	PUNCT
cana-1619	391	10	𝜁𝜂	𝜁𝜂	PRON
cana-1619	391	11	(	(	PUNCT
cana-1619	391	12	.	.	PUNCT
cana-1619	391	13	,	,	PUNCT
cana-1619	391	14	ℵ	ℵ	NOUN
cana-1619	391	15	)	)	PUNCT
cana-1619	391	16	,	,	PUNCT
cana-1619	391	17	ℵ)𝑑𝜂]||𝑑𝜛	ℵ)𝑑𝜂]||𝑑𝜛	PROPN
cana-1619	391	18	≤	≤	NUM
cana-1619	391	19	∫	∫	PROPN
cana-1619	391	20	ℎ1−𝜃	ℎ1−𝜃	PROPN
cana-1619	391	21	0	0	NUM
cana-1619	391	22	||𝑇2(ℎ2	||𝑇2(ℎ2	NOUN
cana-1619	391	23	−𝜛	−𝜛	ADJ
cana-1619	391	24	)	)	PUNCT
cana-1619	391	25	−	−	PUNCT
cana-1619	392	1	𝑇2(ℎ1	𝑇2(ℎ1	ADJ
cana-1619	392	2	−𝜛)𝐵𝑘	−𝜛)𝐵𝑘	NOUN
cana-1619	392	3	−1[𝜁1(ℵ	−1[𝜁1(ℵ	NOUN
cana-1619	392	4	)	)	PUNCT
cana-1619	392	5	−	−	NOUN
cana-1619	392	6	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	392	7	)	)	PUNCT
cana-1619	392	8	−	−	ADP
cana-1619	392	9	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	392	10	)	)	PUNCT
cana-1619	392	11	+	+	SYM
cana-1619	392	12	𝜌(0	𝜌(0	PROPN
cana-1619	392	13	,	,	PUNCT
cana-1619	392	14	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	392	15	)	)	PUNCT
cana-1619	392	16	,	,	PUNCT
cana-1619	392	17	ℵ	ℵ	NOUN
cana-1619	392	18	)	)	PUNCT
cana-1619	392	19	]	]	PUNCT
cana-1619	393	1	+	+	NUM
cana-1619	393	2	∫	∫	PROPN
cana-1619	393	3	𝜚	𝜚	NOUN
cana-1619	393	4	0	0	PUNCT
cana-1619	393	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	393	6	−	−	NOUN
cana-1619	393	7	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	393	8	,	,	PUNCT
cana-1619	393	9	𝜁𝜂	𝜁𝜂	X
cana-1619	393	10	(	(	PUNCT
cana-1619	393	11	.	.	PUNCT
cana-1619	393	12	,	,	PUNCT
cana-1619	393	13	ℵ	ℵ	NOUN
cana-1619	393	14	)	)	PUNCT
cana-1619	393	15	,	,	PUNCT
cana-1619	394	1	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	394	2	−	−	PROPN
cana-1619	394	3	∫	∫	PROPN
cana-1619	394	4	𝜚	𝜚	NOUN
cana-1619	394	5	0	0	NUM
cana-1619	394	6	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	394	7	−	−	NOUN
cana-1619	394	8	𝜂)υ(𝜂	𝜂)υ(𝜂	NOUN
cana-1619	394	9	,	,	PUNCT
cana-1619	394	10	𝜁𝜂	𝜁𝜂	PRON
cana-1619	394	11	(	(	PUNCT
cana-1619	394	12	.	.	PUNCT
cana-1619	394	13	,	,	PUNCT
cana-1619	394	14	ℵ	ℵ	NOUN
cana-1619	394	15	)	)	PUNCT
cana-1619	394	16	,	,	PUNCT
cana-1619	394	17	ℵ)𝑑𝜂]||𝑑𝜛	ℵ)𝑑𝜂]||𝑑𝜛	PRON
cana-1619	395	1	+	+	NOUN
cana-1619	395	2	||	||	NOUN
cana-1619	395	3	∫	∫	NOUN
cana-1619	396	1	ℎ1	ℎ1	PROPN
cana-1619	396	2	ℎ1−𝜃	ℎ1−𝜃	PROPN
cana-1619	396	3	||𝑇2(ℎ2	||𝑇2(ℎ2	NOUN
cana-1619	396	4	−𝜛	−𝜛	ADV
cana-1619	396	5	)	)	PUNCT
cana-1619	396	6	−	−	PUNCT
cana-1619	397	1	𝑇2(ℎ1	𝑇2(ℎ1	ADJ
cana-1619	397	2	−𝜛)𝐵𝑘	−𝜛)𝐵𝑘	NOUN
cana-1619	397	3	−1[𝜁1(ℵ	−1[𝜁1(ℵ	NOUN
cana-1619	397	4	)	)	PUNCT
cana-1619	397	5	−	−	NOUN
cana-1619	397	6	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	397	7	)	)	PUNCT
cana-1619	397	8	−	−	ADP
cana-1619	397	9	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	397	10	)	)	PUNCT
cana-1619	397	11	+	+	SYM
cana-1619	397	12	𝜌(0	𝜌(0	PROPN
cana-1619	397	13	,	,	PUNCT
cana-1619	397	14	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	397	15	)	)	PUNCT
cana-1619	397	16	,	,	PUNCT
cana-1619	397	17	ℵ	ℵ	NOUN
cana-1619	397	18	)	)	PUNCT
cana-1619	397	19	]	]	PUNCT
cana-1619	398	1	+	+	NUM
cana-1619	398	2	∫	∫	PROPN
cana-1619	398	3	𝜚	𝜚	NOUN
cana-1619	398	4	0	0	PUNCT
cana-1619	398	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	398	6	−	−	NOUN
cana-1619	398	7	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	398	8	,	,	PUNCT
cana-1619	398	9	𝜁𝜂	𝜁𝜂	X
cana-1619	398	10	(	(	PUNCT
cana-1619	398	11	.	.	PUNCT
cana-1619	398	12	,	,	PUNCT
cana-1619	398	13	ℵ	ℵ	NOUN
cana-1619	398	14	)	)	PUNCT
cana-1619	398	15	,	,	PUNCT
cana-1619	399	1	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	399	2	−	−	PROPN
cana-1619	399	3	∫	∫	PROPN
cana-1619	399	4	𝜚	𝜚	NOUN
cana-1619	399	5	0	0	NUM
cana-1619	399	6	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	399	7	−	−	NOUN
cana-1619	399	8	𝜂)υ(𝜂	𝜂)υ(𝜂	NOUN
cana-1619	399	9	,	,	PUNCT
cana-1619	399	10	𝜁𝜂	𝜁𝜂	PRON
cana-1619	399	11	(	(	PUNCT
cana-1619	399	12	.	.	PUNCT
cana-1619	399	13	,	,	PUNCT
cana-1619	399	14	ℵ	ℵ	NOUN
cana-1619	399	15	)	)	PUNCT
cana-1619	399	16	,	,	PUNCT
cana-1619	399	17	ℵ)𝑑𝜂]||𝑑𝜛	ℵ)𝑑𝜂]||𝑑𝜛	PRON
cana-1619	400	1	+	+	ADJ
cana-1619	400	2	∫	∫	PROPN
cana-1619	400	3	ℎ1	ℎ1	PROPN
cana-1619	400	4	ℎ1−𝜃	ℎ1−𝜃	PROPN
cana-1619	400	5	||𝑇2(ℎ2	||𝑇2(ℎ2	NOUN
cana-1619	400	6	−𝜛	−𝜛	ADV
cana-1619	400	7	)	)	PUNCT
cana-1619	400	8	−	−	PUNCT
cana-1619	401	1	𝑇2(ℎ1	𝑇2(ℎ1	ADJ
cana-1619	401	2	−𝜛)𝐵𝑘	−𝜛)𝐵𝑘	NOUN
cana-1619	401	3	−1[𝜁1(ℵ	−1[𝜁1(ℵ	NOUN
cana-1619	401	4	)	)	PUNCT
cana-1619	401	5	−	−	NOUN
cana-1619	401	6	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	401	7	)	)	PUNCT
cana-1619	401	8	−	−	ADP
cana-1619	401	9	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	401	10	)	)	PUNCT
cana-1619	401	11	+	+	SYM
cana-1619	401	12	𝜌(0	𝜌(0	PROPN
cana-1619	401	13	,	,	PUNCT
cana-1619	401	14	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	401	15	)	)	PUNCT
cana-1619	401	16	,	,	PUNCT
cana-1619	401	17	ℵ	ℵ	NOUN
cana-1619	401	18	)	)	PUNCT
cana-1619	401	19	]	]	PUNCT
cana-1619	402	1	+	+	NUM
cana-1619	402	2	∫	∫	PROPN
cana-1619	402	3	𝜚	𝜚	NOUN
cana-1619	402	4	0	0	PUNCT
cana-1619	402	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	402	6	−	−	NOUN
cana-1619	402	7	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	402	8	,	,	PUNCT
cana-1619	402	9	𝜁𝜂	𝜁𝜂	X
cana-1619	402	10	(	(	PUNCT
cana-1619	402	11	.	.	PUNCT
cana-1619	402	12	,	,	PUNCT
cana-1619	402	13	ℵ	ℵ	NOUN
cana-1619	402	14	)	)	PUNCT
cana-1619	402	15	,	,	PUNCT
cana-1619	403	1	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	403	2	+	+	NUM
cana-1619	403	3	∫	∫	PROPN
cana-1619	403	4	𝜚	𝜚	NOUN
cana-1619	403	5	0	0	NUM
cana-1619	403	6	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	403	7	−	−	NOUN
cana-1619	403	8	𝜂)υ(𝜂	𝜂)υ(𝜂	NOUN
cana-1619	403	9	,	,	PUNCT
cana-1619	403	10	𝜁𝜂	𝜁𝜂	PRON
cana-1619	403	11	(	(	PUNCT
cana-1619	403	12	.	.	PUNCT
cana-1619	403	13	,	,	PUNCT
cana-1619	403	14	ℵ	ℵ	NOUN
cana-1619	403	15	)	)	PUNCT
cana-1619	403	16	,	,	PUNCT
cana-1619	403	17	ℵ)𝑑𝜂]||𝑑𝜛	ℵ)𝑑𝜂]||𝑑𝜛	PROPN
cana-1619	403	18	≤	≤	NUM
cana-1619	403	19	∫	∫	PROPN
cana-1619	403	20	ℎ1−𝜃	ℎ1−𝜃	PROPN
cana-1619	403	21	0	0	NUM
cana-1619	403	22	||𝑇2(ℎ2	||𝑇2(ℎ2	NOUN
cana-1619	403	23	−𝜛	−𝜛	ADJ
cana-1619	403	24	)	)	PUNCT
cana-1619	403	25	−	−	PUNCT
cana-1619	404	1	𝑇2(ℎ1	𝑇2(ℎ1	ADJ
cana-1619	404	2	−𝜛)𝐵𝑘	−𝜛)𝐵𝑘	NOUN
cana-1619	404	3	−1[𝜁1(ℵ	−1[𝜁1(ℵ	NOUN
cana-1619	404	4	)	)	PUNCT
cana-1619	404	5	−	−	NOUN
cana-1619	404	6	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	404	7	)	)	PUNCT
cana-1619	404	8	−	−	ADP
cana-1619	404	9	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	404	10	)	)	PUNCT
cana-1619	404	11	+	+	SYM
cana-1619	404	12	𝜌(0	𝜌(0	PROPN
cana-1619	404	13	,	,	PUNCT
cana-1619	404	14	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	404	15	)	)	PUNCT
cana-1619	404	16	,	,	PUNCT
cana-1619	404	17	ℵ	ℵ	NOUN
cana-1619	404	18	)	)	PUNCT
cana-1619	404	19	]	]	PUNCT
cana-1619	405	1	+	+	NUM
cana-1619	405	2	∫	∫	PROPN
cana-1619	405	3	𝜚	𝜚	NOUN
cana-1619	405	4	0	0	PUNCT
cana-1619	405	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	405	6	−	−	NOUN
cana-1619	405	7	𝜂	𝜂	NOUN
cana-1619	405	8	)	)	PUNCT
cana-1619	405	9	[	[	PUNCT
cana-1619	405	10	sup	sup	NOUN
cana-1619	405	11	𝜂∈(0.𝜚	𝜂∈(0.𝜚	PROPN
cana-1619	405	12	]	]	X
cana-1619	405	13	||𝜁𝜂	||𝜁𝜂	NOUN
cana-1619	405	14	(	(	PUNCT
cana-1619	405	15	.	.	PUNCT
cana-1619	405	16	,	,	PUNCT
cana-1619	405	17	ℵ	ℵ	NOUN
cana-1619	405	18	)	)	PUNCT
cana-1619	405	19	,	,	PUNCT
cana-1619	405	20	ℵ||𝒟	ℵ||𝒟	NOUN
cana-1619	405	21	𝛽0	𝛽0	VERB
cana-1619	405	22	+	+	CCONJ
cana-1619	406	1	𝑑0(ℵ)]𝑑𝜂	𝑑0(ℵ)]𝑑𝜂	ADJ
cana-1619	407	1	+	+	CCONJ
cana-1619	407	2	∫	∫	PROPN
cana-1619	407	3	𝜚	𝜚	NOUN
cana-1619	407	4	0	0	NUM
cana-1619	407	5	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	407	6	−	−	PROPN
cana-1619	408	1	𝜂	𝜂	NOUN
cana-1619	408	2	)	)	PUNCT
cana-1619	408	3	[	[	PUNCT
cana-1619	408	4	sup	sup	NOUN
cana-1619	408	5	𝜂∈(0.𝜚	𝜂∈(0.𝜚	PROPN
cana-1619	408	6	]	]	X
cana-1619	408	7	||𝜁𝜂	||𝜁𝜂	NOUN
cana-1619	408	8	(	(	PUNCT
cana-1619	408	9	.	.	PUNCT
cana-1619	408	10	,	,	PUNCT
cana-1619	408	11	ℵ	ℵ	NOUN
cana-1619	408	12	)	)	PUNCT
cana-1619	408	13	,	,	PUNCT
cana-1619	408	14	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	408	15	𝛼0	𝛼0	NOUN
cana-1619	408	16	+	+	CCONJ
cana-1619	409	1	𝑏0(ℵ)]𝑑𝜂]||𝑑𝜛	𝑏0(ℵ)]𝑑𝜂]||𝑑𝜛	PROPN
cana-1619	409	2	+	+	PROPN
cana-1619	409	3	||	||	NOUN
cana-1619	409	4	∫	∫	NOUN
cana-1619	410	1	ℎ1	ℎ1	PROPN
cana-1619	410	2	ℎ1−𝜃	ℎ1−𝜃	PROPN
cana-1619	410	3	||𝑇2(ℎ2	||𝑇2(ℎ2	NOUN
cana-1619	410	4	−𝜛	−𝜛	ADV
cana-1619	410	5	)	)	PUNCT
cana-1619	410	6	−	−	PUNCT
cana-1619	411	1	𝑇2(ℎ1	𝑇2(ℎ1	ADJ
cana-1619	411	2	−𝜛)𝐵𝑘	−𝜛)𝐵𝑘	NOUN
cana-1619	411	3	−1[𝜁1(ℵ	−1[𝜁1(ℵ	NOUN
cana-1619	411	4	)	)	PUNCT
cana-1619	411	5	−	−	NOUN
cana-1619	411	6	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	411	7	)	)	PUNCT
cana-1619	411	8	−	−	ADP
cana-1619	411	9	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	411	10	)	)	PUNCT
cana-1619	411	11	+	+	SYM
cana-1619	411	12	𝜌(0	𝜌(0	PROPN
cana-1619	411	13	,	,	PUNCT
cana-1619	411	14	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	411	15	)	)	PUNCT
cana-1619	411	16	,	,	PUNCT
cana-1619	411	17	ℵ	ℵ	NOUN
cana-1619	411	18	)	)	PUNCT
cana-1619	411	19	]	]	PUNCT
cana-1619	412	1	+	+	NUM
cana-1619	412	2	∫	∫	PROPN
cana-1619	412	3	𝜚	𝜚	NOUN
cana-1619	412	4	0	0	PUNCT
cana-1619	412	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	412	6	−	−	NOUN
cana-1619	412	7	𝜂	𝜂	NOUN
cana-1619	412	8	)	)	PUNCT
cana-1619	412	9	[	[	PUNCT
cana-1619	412	10	sup	sup	NOUN
cana-1619	412	11	𝜂∈(0.𝜚	𝜂∈(0.𝜚	PROPN
cana-1619	412	12	]	]	X
cana-1619	412	13	||𝜁𝜂	||𝜁𝜂	NOUN
cana-1619	412	14	(	(	PUNCT
cana-1619	412	15	.	.	PUNCT
cana-1619	412	16	,	,	PUNCT
cana-1619	412	17	ℵ	ℵ	NOUN
cana-1619	412	18	)	)	PUNCT
cana-1619	412	19	,	,	PUNCT
cana-1619	412	20	ℵ||𝒟	ℵ||𝒟	NOUN
cana-1619	412	21	𝛽0	𝛽0	VERB
cana-1619	412	22	+	+	CCONJ
cana-1619	413	1	𝑑0(ℵ)]𝑑𝜂	𝑑0(ℵ)]𝑑𝜂	ADJ
cana-1619	414	1	+	+	CCONJ
cana-1619	414	2	∫	∫	PROPN
cana-1619	414	3	𝜚	𝜚	NOUN
cana-1619	414	4	0	0	NUM
cana-1619	414	5	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	414	6	−	−	PROPN
cana-1619	415	1	𝜂	𝜂	NOUN
cana-1619	415	2	)	)	PUNCT
cana-1619	415	3	[	[	PUNCT
cana-1619	415	4	sup	sup	NOUN
cana-1619	415	5	𝜂∈(0.𝜚	𝜂∈(0.𝜚	PROPN
cana-1619	415	6	]	]	X
cana-1619	415	7	||𝜁𝜂	||𝜁𝜂	NOUN
cana-1619	415	8	(	(	PUNCT
cana-1619	415	9	.	.	PUNCT
cana-1619	415	10	,	,	PUNCT
cana-1619	415	11	ℵ	ℵ	NOUN
cana-1619	415	12	)	)	PUNCT
cana-1619	415	13	,	,	PUNCT
cana-1619	415	14	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	415	15	𝛼0	𝛼0	NOUN
cana-1619	415	16	+	+	CCONJ
cana-1619	416	1	𝑏0(ℵ)]𝑑𝜂]||𝑑𝜛	𝑏0(ℵ)]𝑑𝜂]||𝑑𝜛	PROPN
cana-1619	416	2	+	+	PROPN
cana-1619	416	3	∫	∫	PROPN
cana-1619	416	4	ℎ1	ℎ1	PROPN
cana-1619	416	5	ℎ1−𝜃	ℎ1−𝜃	PROPN
cana-1619	416	6	||𝑇2(ℎ2	||𝑇2(ℎ2	NOUN
cana-1619	416	7	−𝜛	−𝜛	ADV
cana-1619	416	8	)	)	PUNCT
cana-1619	416	9	−	−	PUNCT
cana-1619	417	1	𝑇2(ℎ1	𝑇2(ℎ1	ADJ
cana-1619	417	2	−𝜛)𝐵𝑘	−𝜛)𝐵𝑘	NOUN
cana-1619	417	3	−1[𝜁1(ℵ	−1[𝜁1(ℵ	NOUN
cana-1619	417	4	)	)	PUNCT
cana-1619	417	5	−	−	NOUN
cana-1619	417	6	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	417	7	)	)	PUNCT
cana-1619	417	8	−	−	ADP
cana-1619	417	9	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	417	10	)	)	PUNCT
cana-1619	417	11	+	+	SYM
cana-1619	417	12	𝜌(0	𝜌(0	PROPN
cana-1619	417	13	,	,	PUNCT
cana-1619	417	14	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	417	15	)	)	PUNCT
cana-1619	417	16	,	,	PUNCT
cana-1619	417	17	ℵ	ℵ	NOUN
cana-1619	417	18	)	)	PUNCT
cana-1619	417	19	]	]	PUNCT
cana-1619	418	1	+	+	NUM
cana-1619	418	2	∫	∫	PROPN
cana-1619	418	3	𝜚	𝜚	NOUN
cana-1619	418	4	0	0	PUNCT
cana-1619	418	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	418	6	−	−	NOUN
cana-1619	418	7	𝜂	𝜂	NOUN
cana-1619	418	8	)	)	PUNCT
cana-1619	418	9	[	[	PUNCT
cana-1619	418	10	sup	sup	NOUN
cana-1619	418	11	𝜂∈(0.𝜚	𝜂∈(0.𝜚	PROPN
cana-1619	418	12	]	]	X
cana-1619	418	13	||𝜁𝜂	||𝜁𝜂	NOUN
cana-1619	418	14	(	(	PUNCT
cana-1619	418	15	.	.	PUNCT
cana-1619	418	16	,	,	PUNCT
cana-1619	418	17	ℵ	ℵ	NOUN
cana-1619	418	18	)	)	PUNCT
cana-1619	418	19	,	,	PUNCT
cana-1619	418	20	ℵ||𝒟	ℵ||𝒟	NOUN
cana-1619	418	21	𝛽0	𝛽0	VERB
cana-1619	418	22	+	+	CCONJ
cana-1619	418	23	𝑑0(ℵ	𝑑0(ℵ	PROPN
cana-1619	418	24	)	)	PUNCT
cana-1619	419	1	+	+	NUM
cana-1619	419	2	∫	∫	PROPN
cana-1619	419	3	𝜚	𝜚	NOUN
cana-1619	419	4	0	0	NUM
cana-1619	419	5	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	419	6	−	−	PROPN
cana-1619	420	1	𝜂	𝜂	NOUN
cana-1619	420	2	)	)	PUNCT
cana-1619	420	3	[	[	PUNCT
cana-1619	420	4	sup	sup	NOUN
cana-1619	420	5	𝜂∈(0.𝜚	𝜂∈(0.𝜚	PROPN
cana-1619	420	6	]	]	X
cana-1619	420	7	||𝜁𝜂	||𝜁𝜂	NOUN
cana-1619	420	8	(	(	PUNCT
cana-1619	420	9	.	.	PUNCT
cana-1619	420	10	,	,	PUNCT
cana-1619	420	11	ℵ	ℵ	NOUN
cana-1619	420	12	)	)	PUNCT
cana-1619	420	13	,	,	PUNCT
cana-1619	420	14	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	420	15	𝛼0	𝛼0	NOUN
cana-1619	420	16	+	+	CCONJ
cana-1619	420	17	𝑏0(ℵ)]𝑑𝜂]||𝑑𝜛	𝑏0(ℵ)]𝑑𝜂]||𝑑𝜛	PROPN
cana-1619	420	18	as	as	ADP
cana-1619	420	19	ℎ2	ℎ2	NOUN
cana-1619	420	20	−	−	PROPN
cana-1619	420	21	ℎ1	ℎ1	PROPN
cana-1619	420	22	approaches	approach	VERB
cana-1619	420	23	zero	zero	NUM
cana-1619	420	24	,	,	PUNCT
cana-1619	420	25	|	|	ADV
cana-1619	420	26	|(γ𝑎(ℵ))′2𝜁(ℎ2	|(γ𝑎(ℵ))′2𝜁(ℎ2	NOUN
cana-1619	420	27	)	)	PUNCT
cana-1619	420	28	−	−	PROPN
cana-1619	421	1	(	(	PUNCT
cana-1619	421	2	γ𝑎(ℵ))′2𝜁(ℎ1)|	γ𝑎(ℵ))′2𝜁(ℎ1)|	PRON
cana-1619	421	3	|	|	ADV
cana-1619	421	4	tends	tend	VERB
cana-1619	421	5	to	to	ADP
cana-1619	421	6	zero	zero	NUM
cana-1619	421	7	for	for	ADP
cana-1619	421	8	any	any	DET
cana-1619	421	9	𝜁	𝜁	PROPN
cana-1619	421	10	∈	∈	PROPN
cana-1619	421	11	ℬ𝑟(𝛿	ℬ𝑟(𝛿	NOUN
cana-1619	421	12	)	)	PUNCT
cana-1619	421	13	.	.	PUNCT
cana-1619	422	1	this	this	DET
cana-1619	422	2	convergence	convergence	NOUN
cana-1619	422	3	is	be	AUX
cana-1619	422	4	due	due	ADJ
cana-1619	422	5	to	to	ADP
cana-1619	422	6	the	the	DET
cana-1619	422	7	operator	operator	NOUN
cana-1619	422	8	’s	’s	PART
cana-1619	422	9	compactness	compactness	NOUN
cana-1619	422	10	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	422	11	)	)	PUNCT
cana-1619	422	12	for	for	ADP
cana-1619	422	13	ℎ	ℎ	X
cana-1619	422	14	>	>	X
cana-1619	422	15	0	0	NUM
cana-1619	422	16	,	,	PUNCT
cana-1619	422	17	ensuring	ensure	VERB
cana-1619	422	18	continuity	continuity	NOUN
cana-1619	422	19	in	in	ADP
cana-1619	422	20	the	the	DET
cana-1619	422	21	uniform	uniform	ADJ
cana-1619	422	22	operator	operator	NOUN
cana-1619	422	23	norm	norm	NOUN
cana-1619	422	24	.	.	PUNCT
cana-1619	423	1	consequently	consequently	ADV
cana-1619	423	2	,	,	PUNCT
cana-1619	423	3	(	(	PUNCT
cana-1619	423	4	γ1(ℵ	γ1(ℵ	NOUN
cana-1619	423	5	)	)	PUNCT
cana-1619	423	6	)	)	PUNCT
cana-1619	423	7	maps	map	VERB
cana-1619	423	8	ℬ𝑟(𝛿	ℬ𝑟(𝛿	ADJ
cana-1619	423	9	)	)	PUNCT
cana-1619	423	10	into	into	ADP
cana-1619	423	11	an	an	DET
cana-1619	423	12	uniformly	uniformly	ADV
cana-1619	423	13	continuous	continuous	ADJ
cana-1619	423	14	communications	communication	NOUN
cana-1619	423	15	on	on	ADP
cana-1619	423	16	applied	apply	VERB
cana-1619	423	17	nonlinear	nonlinear	ADJ
cana-1619	423	18	analysis	analysis	NOUN
cana-1619	423	19	issn	issn	NOUN
cana-1619	423	20	:	:	PUNCT
cana-1619	423	21	1074	1074	NUM
cana-1619	423	22	-	-	PUNCT
cana-1619	423	23	133x	133x	NUM
cana-1619	423	24	vol	vol	NOUN
cana-1619	423	25	32	32	NUM
cana-1619	423	26	no	no	NOUN
cana-1619	423	27	.	.	NOUN
cana-1619	423	28	1	1	NUM
cana-1619	423	29	(	(	PUNCT
cana-1619	423	30	2025	2025	NUM
cana-1619	423	31	)	)	PUNCT
cana-1619	423	32	51	51	NUM
cana-1619	423	33	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	423	34	family	family	NOUN
cana-1619	423	35	of	of	ADP
cana-1619	423	36	functions	function	NOUN
cana-1619	423	37	.	.	PUNCT
cana-1619	424	1	we	we	PRON
cana-1619	424	2	now	now	ADV
cana-1619	424	3	aim	aim	VERB
cana-1619	424	4	to	to	PART
cana-1619	424	5	demonstrate	demonstrate	VERB
cana-1619	424	6	that	that	SCONJ
cana-1619	424	7	the	the	DET
cana-1619	424	8	set	set	NOUN
cana-1619	424	9	(	(	PUNCT
cana-1619	424	10	γ𝑎(ℵ))′2(ℬ𝑟(𝛿))(ℎ	γ𝑎(ℵ))′2(ℬ𝑟(𝛿))(ℎ	PROPN
cana-1619	424	11	)	)	PUNCT
cana-1619	424	12	is	be	AUX
cana-1619	424	13	precompact	precompact	ADJ
cana-1619	424	14	in	in	ADP
cana-1619	424	15	𝒮.	𝒮.	PROPN
cana-1619	424	16	given	give	VERB
cana-1619	424	17	𝛿	𝛿	PROPN
cana-1619	424	18	<	<	X
cana-1619	424	19	ℎ	ℎ	X
cana-1619	424	20	≤	≤	NOUN
cana-1619	424	21	𝜛	𝜛	X
cana-1619	424	22	≤	≤	NUM
cana-1619	424	23	𝜚	𝜚	NOUN
cana-1619	424	24	,	,	PUNCT
cana-1619	424	25	let	let	VERB
cana-1619	424	26	𝜖	𝜖	PRON
cana-1619	424	27	be	be	AUX
cana-1619	424	28	a	a	DET
cana-1619	424	29	real	real	ADJ
cana-1619	424	30	number	number	NOUN
cana-1619	424	31	where	where	SCONJ
cana-1619	424	32	0	0	NUM
cana-1619	424	33	<	<	X
cana-1619	424	34	𝜖	𝜖	X
cana-1619	424	35	<	<	X
cana-1619	424	36	ℎ	ℎ	PROPN
cana-1619	424	37	.	.	PUNCT
cana-1619	425	1	for	for	ADP
cana-1619	425	2	𝜁	𝜁	PROPN
cana-1619	425	3	∈	∈	PROPN
cana-1619	425	4	ℬ𝑟(𝛿	ℬ𝑟(𝛿	PROPN
cana-1619	425	5	)	)	PUNCT
cana-1619	425	6	,	,	PUNCT
cana-1619	425	7	we	we	PRON
cana-1619	425	8	specify	specify	VERB
cana-1619	425	9	(	(	PUNCT
cana-1619	425	10	(	(	PUNCT
cana-1619	425	11	γ(ℵ))′2,𝑎,𝜖𝜁)(ℎ	γ(ℵ))′2,𝑎,𝜖𝜁)(ℎ	NUM
cana-1619	425	12	)	)	PUNCT
cana-1619	425	13	as	as	ADP
cana-1619	425	14	∫	∫	PROPN
cana-1619	425	15	ℎ−𝜖	ℎ−𝜖	ADV
cana-1619	425	16	0	0	NUM
cana-1619	426	1	𝑇2(ℎ2	𝑇2(ℎ2	VERB
cana-1619	426	2	−𝜛)𝐵𝑘	−𝜛)𝐵𝑘	NOUN
cana-1619	426	3	−1[𝜁1(ℵ	−1[𝜁1(ℵ	NOUN
cana-1619	426	4	)	)	PUNCT
cana-1619	426	5	−	−	NOUN
cana-1619	426	6	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	426	7	)	)	PUNCT
cana-1619	427	1	−	−	ADP
cana-1619	427	2	𝑇2(𝜚)[𝜙′0(ℵ	𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	427	3	)	)	PUNCT
cana-1619	427	4	+	+	SYM
cana-1619	428	1	𝜌(0	𝜌(0	PROPN
cana-1619	428	2	,	,	PUNCT
cana-1619	428	3	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	428	4	)	)	PUNCT
cana-1619	428	5	,	,	PUNCT
cana-1619	428	6	ℵ	ℵ	NOUN
cana-1619	428	7	)	)	PUNCT
cana-1619	428	8	]	]	PUNCT
cana-1619	428	9	−∫	−∫	X
cana-1619	428	10	𝜚	𝜚	NOUN
cana-1619	428	11	0	0	NUM
cana-1619	428	12	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	428	13	−	−	NOUN
cana-1619	428	14	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	428	15	,	,	PUNCT
cana-1619	428	16	𝜁𝜂	𝜁𝜂	X
cana-1619	428	17	(	(	PUNCT
cana-1619	428	18	.	.	PUNCT
cana-1619	428	19	,	,	PUNCT
cana-1619	428	20	ℵ	ℵ	NOUN
cana-1619	428	21	)	)	PUNCT
cana-1619	428	22	,	,	PUNCT
cana-1619	428	23	ℵ	ℵ	X
cana-1619	428	24	)	)	PUNCT
cana-1619	428	25	+	+	NUM
cana-1619	428	26	∫	∫	PROPN
cana-1619	428	27	𝜚	𝜚	NOUN
cana-1619	428	28	0	0	NUM
cana-1619	428	29	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	428	30	−	−	NOUN
cana-1619	428	31	𝜂)υ(𝜂	𝜂)υ(𝜂	NOUN
cana-1619	428	32	,	,	PUNCT
cana-1619	428	33	𝜁𝜂	𝜁𝜂	PRON
cana-1619	428	34	(	(	PUNCT
cana-1619	428	35	.	.	PUNCT
cana-1619	428	36	,	,	PUNCT
cana-1619	428	37	ℵ	ℵ	NOUN
cana-1619	428	38	)	)	PUNCT
cana-1619	428	39	,	,	PUNCT
cana-1619	428	40	ℵ)]𝑑𝜂	ℵ)]𝑑𝜂	CCONJ
cana-1619	428	41	by	by	ADP
cana-1619	428	42	leveraging	leverage	VERB
cana-1619	428	43	the	the	DET
cana-1619	428	44	compactness	compactness	NOUN
cana-1619	428	45	of	of	ADP
cana-1619	428	46	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	428	47	)	)	PUNCT
cana-1619	428	48	for	for	ADP
cana-1619	428	49	ℎ	ℎ	X
cana-1619	428	50	>	>	X
cana-1619	428	51	0	0	NUM
cana-1619	428	52	,	,	PUNCT
cana-1619	428	53	we	we	PRON
cana-1619	428	54	conclude	conclude	VERB
cana-1619	428	55	that	that	SCONJ
cana-1619	428	56	the	the	DET
cana-1619	428	57	set	set	NOUN
cana-1619	428	58	{	{	PUNCT
cana-1619	428	59	(	(	PUNCT
cana-1619	428	60	(	(	PUNCT
cana-1619	428	61	γ(ℵ))′2,𝑎,𝜖𝜁)(ℎ	γ(ℵ))′2,𝑎,𝜖𝜁)(ℎ	NUM
cana-1619	428	62	):	):	PUNCT
cana-1619	428	63	𝜁	𝜁	PROPN
cana-1619	428	64	∈	∈	PROPN
cana-1619	428	65	ℬ𝑟(𝛿	ℬ𝑟(𝛿	NOUN
cana-1619	428	66	)	)	PUNCT
cana-1619	428	67	}	}	PUNCT
cana-1619	428	68	is	be	AUX
cana-1619	428	69	precompact	precompact	ADJ
cana-1619	428	70	for	for	ADP
cana-1619	428	71	𝜁	𝜁	PROPN
cana-1619	428	72	∈	∈	PROPN
cana-1619	428	73	ℬ𝑟(𝛿	ℬ𝑟(𝛿	PROPN
cana-1619	428	74	)	)	PUNCT
cana-1619	428	75	and	and	CCONJ
cana-1619	428	76	0	0	NUM
cana-1619	428	77	<	<	X
cana-1619	428	78	𝜖	𝜖	X
cana-1619	428	79	<	<	X
cana-1619	428	80	ℎ.	ℎ.	NOUN
cana-1619	428	81	moreover	moreover	ADV
cana-1619	428	82	,	,	PUNCT
cana-1619	428	83	for	for	ADP
cana-1619	428	84	every	every	DET
cana-1619	428	85	𝜁	𝜁	PROPN
cana-1619	428	86	∈	∈	PROPN
cana-1619	428	87	ℬ𝑟(𝛿	ℬ𝑟(𝛿	PROPN
cana-1619	428	88	)	)	PUNCT
cana-1619	428	89	,	,	PUNCT
cana-1619	428	90	we	we	PRON
cana-1619	428	91	assert	assert	VERB
cana-1619	428	92	||((γ𝑎(ℵ))2𝜁)(ℎ	||((γ𝑎(ℵ))2𝜁)(ℎ	NUM
cana-1619	428	93	)	)	PUNCT
cana-1619	428	94	−	−	PROPN
cana-1619	429	1	(	(	PUNCT
cana-1619	429	2	(	(	PUNCT
cana-1619	429	3	γ(ℵ))2,𝑎,𝜖𝜁)(ℎ)||	γ(ℵ))2,𝑎,𝜖𝜁)(ℎ)||	NOUN
cana-1619	429	4	≤	≤	NUM
cana-1619	429	5	∫	∫	PROPN
cana-1619	429	6	ℎ	ℎ	X
cana-1619	429	7	ℎ−𝜖	ℎ−𝜖	ADV
cana-1619	429	8	||𝑇2(ℎ2	||𝑇2(ℎ2	NOUN
cana-1619	429	9	−𝜛)𝐵𝑘	−𝜛)𝐵𝑘	NOUN
cana-1619	430	1	−1[∫	−1[∫	NUM
cana-1619	430	2	𝜚	𝜚	NOUN
cana-1619	430	3	0	0	NUM
cana-1619	430	4	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	430	5	−	−	NOUN
cana-1619	430	6	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	430	7	,	,	PUNCT
cana-1619	430	8	𝜁𝜂	𝜁𝜂	X
cana-1619	430	9	(	(	PUNCT
cana-1619	430	10	.	.	PUNCT
cana-1619	430	11	,	,	PUNCT
cana-1619	430	12	ℵ	ℵ	NOUN
cana-1619	430	13	)	)	PUNCT
cana-1619	430	14	,	,	PUNCT
cana-1619	430	15	ℵ)||𝑑𝜂	ℵ)||𝑑𝜂	NOUN
cana-1619	431	1	+	+	NOUN
cana-1619	431	2	∫	∫	PROPN
cana-1619	431	3	𝜚	𝜚	NOUN
cana-1619	431	4	0	0	NUM
cana-1619	431	5	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	431	6	−	−	NOUN
cana-1619	431	7	𝜂)υ(𝜂	𝜂)υ(𝜂	NOUN
cana-1619	431	8	,	,	PUNCT
cana-1619	431	9	𝜁𝜂	𝜁𝜂	PRON
cana-1619	431	10	(	(	PUNCT
cana-1619	431	11	.	.	PUNCT
cana-1619	431	12	,	,	PUNCT
cana-1619	431	13	ℵ	ℵ	NOUN
cana-1619	431	14	)	)	PUNCT
cana-1619	431	15	,	,	PUNCT
cana-1619	431	16	ℵ)||𝑑𝜂]𝑑𝜛	ℵ)||𝑑𝜂]𝑑𝜛	X
cana-1619	431	17	≤	≤	NUM
cana-1619	431	18	∫	∫	PROPN
cana-1619	431	19	ℎ	ℎ	X
cana-1619	431	20	ℎ−𝜖	ℎ−𝜖	ADV
cana-1619	431	21	𝜗𝑎𝐵𝑘	𝜗𝑎𝐵𝑘	NOUN
cana-1619	432	1	−1[∫	−1[∫	INTJ
cana-1619	432	2	𝜚	𝜚	NOUN
cana-1619	432	3	0	0	NUM
cana-1619	432	4	𝜗	𝜗	NOUN
cana-1619	432	5	[	[	PUNCT
cana-1619	432	6	sup	sup	NOUN
cana-1619	432	7	𝜂∈(0.𝜚	𝜂∈(0.𝜚	PROPN
cana-1619	432	8	]	]	X
cana-1619	432	9	||𝜁𝜂	||𝜁𝜂	NOUN
cana-1619	432	10	(	(	PUNCT
cana-1619	432	11	.	.	PUNCT
cana-1619	432	12	,	,	PUNCT
cana-1619	432	13	ℵ	ℵ	NOUN
cana-1619	432	14	)	)	PUNCT
cana-1619	432	15	,	,	PUNCT
cana-1619	432	16	ℵ||𝒟	ℵ||𝒟	NOUN
cana-1619	432	17	𝛽0	𝛽0	VERB
cana-1619	432	18	+	+	CCONJ
cana-1619	432	19	𝑑0(ℵ)]𝑑𝜂	𝑑0(ℵ)]𝑑𝜂	ADJ
cana-1619	433	1	+	+	PROPN
cana-1619	434	1	∫	∫	PROPN
cana-1619	434	2	𝜚	𝜚	NOUN
cana-1619	434	3	0	0	SYM
cana-1619	434	4	𝜗𝑎	𝜗𝑎	ADP
cana-1619	434	5	[	[	PUNCT
cana-1619	434	6	sup	sup	NOUN
cana-1619	434	7	𝜂∈(0.𝜚	𝜂∈(0.𝜚	PROPN
cana-1619	434	8	]	]	X
cana-1619	434	9	||𝜁𝜂	||𝜁𝜂	NOUN
cana-1619	434	10	(	(	PUNCT
cana-1619	434	11	.	.	PUNCT
cana-1619	434	12	,	,	PUNCT
cana-1619	434	13	ℵ	ℵ	NOUN
cana-1619	434	14	)	)	PUNCT
cana-1619	434	15	,	,	PUNCT
cana-1619	434	16	ℵ||𝒟	ℵ||𝒟	NUM
cana-1619	434	17	𝛼0	𝛼0	PROPN
cana-1619	435	1	+	+	CCONJ
cana-1619	435	2	𝑏0(ℵ)]𝑑𝜂]𝑑𝜛	𝑏0(ℵ)]𝑑𝜂]𝑑𝜛	PROPN
cana-1619	435	3	thus	thus	ADV
cana-1619	435	4	,	,	PUNCT
cana-1619	435	5	we	we	PRON
cana-1619	435	6	can	can	AUX
cana-1619	435	7	find	find	VERB
cana-1619	435	8	sets	set	NOUN
cana-1619	435	9	that	that	PRON
cana-1619	435	10	are	be	AUX
cana-1619	435	11	precompact	precompact	ADJ
cana-1619	435	12	and	and	CCONJ
cana-1619	435	13	close	close	ADJ
cana-1619	435	14	to	to	ADP
cana-1619	435	15	{	{	PUNCT
cana-1619	435	16	(	(	PUNCT
cana-1619	435	17	(	(	PUNCT
cana-1619	435	18	γ𝑎(ℵ))′2𝜁	γ𝑎(ℵ))′2𝜁	NOUN
cana-1619	435	19	):	):	PUNCT
cana-1619	435	20	𝜁	𝜁	PROPN
cana-1619	435	21	∈	∈	PROPN
cana-1619	435	22	𝐵𝑟(𝛿	𝐵𝑟(𝛿	NOUN
cana-1619	435	23	)	)	PUNCT
cana-1619	435	24	}	}	PUNCT
cana-1619	435	25	.	.	PUNCT
cana-1619	436	1	as	as	ADP
cana-1619	436	2	a	a	DET
cana-1619	436	3	result	result	NOUN
cana-1619	436	4	,	,	PUNCT
cana-1619	436	5	{	{	PUNCT
cana-1619	436	6	(	(	PUNCT
cana-1619	436	7	(	(	PUNCT
cana-1619	436	8	γ𝑎(ℵ))′2𝜁	γ𝑎(ℵ))′2𝜁	NOUN
cana-1619	436	9	):	):	PUNCT
cana-1619	436	10	𝜁	𝜁	PROPN
cana-1619	436	11	∈	∈	PROPN
cana-1619	436	12	𝐵𝑟(𝛿	𝐵𝑟(𝛿	NOUN
cana-1619	436	13	)	)	PUNCT
cana-1619	436	14	}	}	PUNCT
cana-1619	436	15	itself	itself	PRON
cana-1619	436	16	becomes	become	VERB
cana-1619	436	17	precompact	precompact	ADJ
cana-1619	436	18	within	within	ADP
cana-1619	436	19	𝒮.	𝒮.	PROPN
cana-1619	436	20	it	it	PRON
cana-1619	436	21	’s	’	VERB
cana-1619	436	22	clear	clear	ADJ
cana-1619	436	23	that	that	SCONJ
cana-1619	436	24	(	(	PUNCT
cana-1619	436	25	γ𝑎(ℵ))′2(𝐵𝑟(𝛿	γ𝑎(ℵ))′2(𝐵𝑟(𝛿	PROPN
cana-1619	436	26	)	)	PUNCT
cana-1619	436	27	)	)	PUNCT
cana-1619	436	28	is	be	AUX
cana-1619	436	29	uniformly	uniformly	ADV
cana-1619	436	30	bounded	bound	VERB
cana-1619	436	31	.	.	PUNCT
cana-1619	437	1	given	give	VERB
cana-1619	437	2	that	that	SCONJ
cana-1619	437	3	we	we	PRON
cana-1619	437	4	have	have	AUX
cana-1619	437	5	demonstrated	demonstrate	VERB
cana-1619	437	6	(	(	PUNCT
cana-1619	437	7	γ𝑎(ℵ))′2(𝐵𝑟(𝛿	γ𝑎(ℵ))′2(𝐵𝑟(𝛿	PROPN
cana-1619	437	8	)	)	PUNCT
cana-1619	437	9	)	)	PUNCT
cana-1619	437	10	constitutes	constitute	VERB
cana-1619	437	11	an	an	DET
cana-1619	437	12	equicontinuous	equicontinuous	ADJ
cana-1619	437	13	family	family	NOUN
cana-1619	437	14	,	,	PUNCT
cana-1619	437	15	the	the	DET
cana-1619	437	16	arzelà	arzelà	PROPN
cana-1619	437	17	-	-	PUNCT
cana-1619	437	18	ascoli	ascoli	PROPN
cana-1619	437	19	theorem	theorem	PROPN
cana-1619	437	20	implies	imply	VERB
cana-1619	437	21	that	that	SCONJ
cana-1619	437	22	it	it	PRON
cana-1619	437	23	is	be	AUX
cana-1619	437	24	sufficient	sufficient	ADJ
cana-1619	437	25	to	to	PART
cana-1619	437	26	show	show	VERB
cana-1619	437	27	that	that	SCONJ
cana-1619	437	28	(	(	PUNCT
cana-1619	437	29	γ𝑎(ℵ))′2	γ𝑎(ℵ))′2	PROPN
cana-1619	437	30	maps	map	VERB
cana-1619	437	31	𝐵𝑟(𝛿	𝐵𝑟(𝛿	NOUN
cana-1619	437	32	)	)	PUNCT
cana-1619	437	33	into	into	ADP
cana-1619	437	34	a	a	DET
cana-1619	437	35	precompact	precompact	NOUN
cana-1619	437	36	set	set	VERB
cana-1619	437	37	in	in	ADP
cana-1619	437	38	𝒮.	𝒮.	PROPN
cana-1619	437	39	next	next	ADV
cana-1619	437	40	,	,	PUNCT
cana-1619	437	41	it	it	PRON
cana-1619	437	42	is	be	AUX
cana-1619	437	43	necessary	necessary	ADJ
cana-1619	437	44	to	to	PART
cana-1619	437	45	confirm	confirm	VERB
cana-1619	437	46	that	that	SCONJ
cana-1619	437	47	(	(	PUNCT
cana-1619	437	48	γ𝑏(ℵ))′2	γ𝑏(ℵ))′2	NOUN
cana-1619	437	49	is	be	AUX
cana-1619	437	50	also	also	ADV
cana-1619	437	51	a	a	DET
cana-1619	437	52	compact	compact	ADJ
cana-1619	437	53	operator	operator	NOUN
cana-1619	437	54	.	.	PUNCT
cana-1619	438	1	by	by	ADP
cana-1619	438	2	step	step	NOUN
cana-1619	438	3	3	3	NUM
cana-1619	438	4	of	of	ADP
cana-1619	438	5	theorem	theorem	ADJ
cana-1619	438	6	3.1(above	3.1(above	NUM
cana-1619	438	7	theorem	theorem	NOUN
cana-1619	438	8	)	)	PUNCT
cana-1619	438	9	we	we	PRON
cana-1619	438	10	prove	prove	VERB
cana-1619	438	11	that	that	SCONJ
cana-1619	438	12	(	(	PUNCT
cana-1619	438	13	γ𝑏(ℵ))′2	γ𝑏(ℵ))′2	NOUN
cana-1619	438	14	is	be	AUX
cana-1619	438	15	compact	compact	ADJ
cana-1619	438	16	.	.	PUNCT
cana-1619	439	1	step	step	NOUN
cana-1619	439	2	4	4	NUM
cana-1619	439	3	:	:	PUNCT
cana-1619	439	4	next	next	ADV
cana-1619	439	5	,	,	PUNCT
cana-1619	439	6	we	we	PRON
cana-1619	439	7	establish	establish	VERB
cana-1619	439	8	the	the	DET
cana-1619	439	9	existence	existence	NOUN
cana-1619	439	10	of	of	ADP
cana-1619	439	11	an	an	DET
cana-1619	439	12	open	open	ADJ
cana-1619	439	13	set	set	NOUN
cana-1619	439	14	𝑈	𝑈	PROPN
cana-1619	439	15	⊆	⊆	NUM
cana-1619	439	16	𝑃𝐶𝛿	𝑃𝐶𝛿	NOUN
cana-1619	439	17	such	such	ADJ
cana-1619	439	18	that	that	SCONJ
cana-1619	439	19	𝜁	𝜁	PROPN
cana-1619	439	20	∉	∉	PROPN
cana-1619	439	21	𝜆(γ(ℵ))′(𝜁	𝜆(γ(ℵ))′(𝜁	NUM
cana-1619	439	22	)	)	PUNCT
cana-1619	439	23	for	for	ADP
cana-1619	439	24	𝜆	𝜆	DET
cana-1619	439	25	∈	∈	PROPN
cana-1619	439	26	(	(	PUNCT
cana-1619	439	27	0,1	0,1	NUM
cana-1619	439	28	)	)	PUNCT
cana-1619	439	29	and	and	CCONJ
cana-1619	439	30	𝜁	𝜁	PRON
cana-1619	439	31	∈	∈	PROPN
cana-1619	439	32	𝜕𝑈.	𝜕𝑈.	VERB
cana-1619	439	33	consider	consider	VERB
cana-1619	439	34	𝜆	𝜆	DET
cana-1619	439	35	∈	∈	PROPN
cana-1619	439	36	(	(	PUNCT
cana-1619	439	37	0,1	0,1	NUM
cana-1619	439	38	)	)	PUNCT
cana-1619	439	39	and	and	CCONJ
cana-1619	439	40	let	let	VERB
cana-1619	439	41	𝜁	𝜁	PROPN
cana-1619	439	42	∈	∈	PROPN
cana-1619	439	43	𝑃𝐶𝛿	𝑃𝐶𝛿	NOUN
cana-1619	439	44	be	be	VERB
cana-1619	439	45	a	a	DET
cana-1619	439	46	potential	potential	ADJ
cana-1619	439	47	solution	solution	NOUN
cana-1619	439	48	of	of	ADP
cana-1619	439	49	𝜁	𝜁	PROPN
cana-1619	439	50	=	=	SYM
cana-1619	439	51	𝜆(γ(ℵ))′(𝜁	𝜆(γ(ℵ))′(𝜁	PROPN
cana-1619	439	52	)	)	PUNCT
cana-1619	439	53	for	for	ADP
cana-1619	439	54	some	some	PRON
cana-1619	439	55	0	0	NUM
cana-1619	439	56	<	<	X
cana-1619	439	57	𝜆	𝜆	X
cana-1619	439	58	<	<	X
cana-1619	439	59	1	1	NUM
cana-1619	439	60	.	.	PUNCT
cana-1619	439	61	consequently	consequently	ADV
cana-1619	439	62	,	,	PUNCT
cana-1619	439	63	for	for	ADP
cana-1619	439	64	every	every	DET
cana-1619	439	65	ℎ	ℎ	PROPN
cana-1619	439	66	∈	∈	PROPN
cana-1619	439	67	(	(	PUNCT
cana-1619	439	68	0	0	NUM
cana-1619	439	69	,	,	PUNCT
cana-1619	439	70	𝜚	𝜚	NOUN
cana-1619	439	71	]	]	X
cana-1619	439	72	,	,	PUNCT
cana-1619	439	73	we	we	PRON
cana-1619	439	74	have	have	VERB
cana-1619	439	75	communications	communication	NOUN
cana-1619	439	76	on	on	ADP
cana-1619	439	77	applied	apply	VERB
cana-1619	439	78	nonlinear	nonlinear	ADJ
cana-1619	439	79	analysis	analysis	NOUN
cana-1619	439	80	issn	issn	NOUN
cana-1619	439	81	:	:	PUNCT
cana-1619	439	82	1074	1074	NUM
cana-1619	439	83	-	-	PUNCT
cana-1619	439	84	133x	133x	NUM
cana-1619	439	85	vol	vol	NOUN
cana-1619	439	86	32	32	NUM
cana-1619	439	87	no	no	NOUN
cana-1619	439	88	.	.	NOUN
cana-1619	439	89	1	1	NUM
cana-1619	439	90	(	(	PUNCT
cana-1619	439	91	2025	2025	NUM
cana-1619	439	92	)	)	PUNCT
cana-1619	440	1	52	52	NUM
cana-1619	440	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	440	3	𝜁(ℎ	𝜁(ℎ	PROPN
cana-1619	440	4	,	,	PUNCT
cana-1619	440	5	ℵ	ℵ	NOUN
cana-1619	440	6	)	)	PUNCT
cana-1619	440	7	=	=	SYM
cana-1619	440	8	𝜆𝑇1(ℎ)𝜙0(ℵ	𝜆𝑇1(ℎ)𝜙0(ℵ	X
cana-1619	440	9	)	)	PUNCT
cana-1619	440	10	+	+	CCONJ
cana-1619	440	11	𝜆𝑇2(ℎ)[𝜙′0(ℵ	𝜆𝑇2(ℎ)[𝜙′0(ℵ	NOUN
cana-1619	440	12	)	)	PUNCT
cana-1619	440	13	+	+	CCONJ
cana-1619	440	14	𝜌(0	𝜌(0	PROPN
cana-1619	440	15	,	,	PUNCT
cana-1619	440	16	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	440	17	)	)	PUNCT
cana-1619	440	18	,	,	PUNCT
cana-1619	440	19	ℵ	ℵ	NOUN
cana-1619	440	20	)	)	PUNCT
cana-1619	440	21	]	]	PUNCT
cana-1619	441	1	−	−	PROPN
cana-1619	441	2	𝜆∫	𝜆∫	ADJ
cana-1619	441	3	ℎ	ℎ	PROPN
cana-1619	441	4	0	0	PROPN
cana-1619	442	1	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	443	1	−	−	PROPN
cana-1619	443	2	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	NOUN
cana-1619	443	3	,	,	PUNCT
cana-1619	443	4	𝜁𝜛	𝜁𝜛	ADV
cana-1619	443	5	(	(	PUNCT
cana-1619	443	6	.	.	PUNCT
cana-1619	443	7	,	,	PUNCT
cana-1619	443	8	ℵ	ℵ	NOUN
cana-1619	443	9	)	)	PUNCT
cana-1619	443	10	,	,	PUNCT
cana-1619	444	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	444	2	+	+	PROPN
cana-1619	444	3	𝜆∫	𝜆∫	ADJ
cana-1619	444	4	ℎ	ℎ	PART
cana-1619	444	5	0	0	PUNCT
cana-1619	444	6	𝑇2(ℎ	𝑇2(ℎ	ADJ
cana-1619	444	7	−	−	NOUN
cana-1619	444	8	𝜛)υ(𝜛	𝜛)υ(𝜛	NOUN
cana-1619	444	9	,	,	PUNCT
cana-1619	444	10	𝜁𝜛	𝜁𝜛	ADV
cana-1619	444	11	(	(	PUNCT
cana-1619	444	12	.	.	PUNCT
cana-1619	444	13	,	,	PUNCT
cana-1619	444	14	ℵ	ℵ	NOUN
cana-1619	444	15	)	)	PUNCT
cana-1619	444	16	,	,	PUNCT
cana-1619	445	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	445	2	+	+	CCONJ
cana-1619	445	3	𝜆∫	𝜆∫	ADJ
cana-1619	445	4	ℎ	ℎ	PROPN
cana-1619	445	5	0	0	PUNCT
cana-1619	446	1	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	446	2	−	−	PROPN
cana-1619	446	3	𝜛)𝐵𝑘	𝜛)𝐵𝑘	NOUN
cana-1619	446	4	−1[(𝜁1(ℵ	−1[(𝜁1(ℵ	NOUN
cana-1619	446	5	)	)	PUNCT
cana-1619	446	6	−	−	NOUN
cana-1619	446	7	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	446	8	)	)	PUNCT
cana-1619	446	9	−𝑇2(𝜚)[𝜙′0(ℵ	−𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	446	10	)	)	PUNCT
cana-1619	447	1	+	+	CCONJ
cana-1619	447	2	𝜌(0	𝜌(0	PROPN
cana-1619	447	3	,	,	PUNCT
cana-1619	447	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	447	5	)	)	PUNCT
cana-1619	447	6	,	,	PUNCT
cana-1619	447	7	ℵ	ℵ	NOUN
cana-1619	447	8	)	)	PUNCT
cana-1619	447	9	]	]	PUNCT
cana-1619	448	1	+	+	CCONJ
cana-1619	448	2	∫	∫	PROPN
cana-1619	448	3	𝜚	𝜚	NOUN
cana-1619	448	4	0	0	NUM
cana-1619	448	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	448	6	−	−	NOUN
cana-1619	448	7	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	448	8	,	,	PUNCT
cana-1619	448	9	𝜁𝜂	𝜁𝜂	X
cana-1619	448	10	(	(	PUNCT
cana-1619	448	11	.	.	PUNCT
cana-1619	448	12	,	,	PUNCT
cana-1619	448	13	ℵ	ℵ	NOUN
cana-1619	448	14	)	)	PUNCT
cana-1619	448	15	,	,	PUNCT
cana-1619	448	16	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	448	17	−∫	−∫	X
cana-1619	448	18	𝜚	𝜚	NOUN
cana-1619	448	19	0	0	NUM
cana-1619	448	20	𝑇2(𝜚	𝑇2(𝜚	NOUN
cana-1619	448	21	−	−	NOUN
cana-1619	448	22	𝜂)υ(𝜂	𝜂)υ(𝜂	NOUN
cana-1619	448	23	,	,	PUNCT
cana-1619	448	24	𝜁𝜂	𝜁𝜂	PRON
cana-1619	448	25	(	(	PUNCT
cana-1619	448	26	.	.	PUNCT
cana-1619	448	27	,	,	PUNCT
cana-1619	448	28	ℵ	ℵ	NOUN
cana-1619	448	29	)	)	PUNCT
cana-1619	448	30	,	,	PUNCT
cana-1619	449	1	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	449	2	−	−	PROPN
cana-1619	450	1	∑	∑	PROPN
cana-1619	450	2	0<ℎ𝜉<𝜚	0<ℎ𝜉<𝜚	PROPN
cana-1619	450	3	𝑇1(𝜚	𝑇1(𝜚	PROPN
cana-1619	450	4	−	−	PROPN
cana-1619	450	5	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	450	6	,	,	PUNCT
cana-1619	450	7	ℵ	ℵ	NOUN
cana-1619	450	8	)	)	PUNCT
cana-1619	450	9	)	)	PUNCT
cana-1619	450	10	)	)	PUNCT
cana-1619	451	1	−	−	PUNCT
cana-1619	452	1	∑	∑	PUNCT
cana-1619	452	2	0<ℎ𝜉<𝜚	0<ℎ𝜉<𝜚	PROPN
cana-1619	452	3	𝑇2(𝜚	𝑇2(𝜚	PROPN
cana-1619	453	1	−	−	PROPN
cana-1619	453	2	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	453	3	,	,	PUNCT
cana-1619	453	4	ℵ))]𝑑𝜛	ℵ))]𝑑𝜛	PROPN
cana-1619	454	1	+	+	CCONJ
cana-1619	454	2	𝜆	𝜆	PROPN
cana-1619	454	3	∑	∑	ADV
cana-1619	454	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	454	5	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	454	6	−	−	PROPN
cana-1619	455	1	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼𝜉(𝜁(ℎ𝜉	PROPN
cana-1619	455	2	,	,	PUNCT
cana-1619	455	3	ℵ	ℵ	NOUN
cana-1619	455	4	)	)	PUNCT
cana-1619	455	5	)	)	PUNCT
cana-1619	456	1	+	+	ADP
cana-1619	456	2	𝜆	𝜆	DET
cana-1619	456	3	∑	∑	ADV
cana-1619	456	4	0<ℎ𝜉<ℎ	0<ℎ𝜉<ℎ	ADJ
cana-1619	456	5	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	456	6	−	−	PROPN
cana-1619	456	7	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	ℎ𝜉)𝐼′𝜉(𝜁(ℎ𝜉	NOUN
cana-1619	456	8	,	,	PUNCT
cana-1619	456	9	ℵ	ℵ	NOUN
cana-1619	456	10	)	)	PUNCT
cana-1619	456	11	)	)	PUNCT
cana-1619	456	12	by	by	ADP
cana-1619	456	13	step	step	NOUN
cana-1619	456	14	1	1	NUM
cana-1619	456	15	of	of	ADP
cana-1619	456	16	theorem	theorem	ADJ
cana-1619	456	17	3.1	3.1	NUM
cana-1619	456	18	and	and	CCONJ
cana-1619	456	19	3.2	3.2	NUM
cana-1619	456	20	,	,	PUNCT
cana-1619	456	21	||(γ(ℵ))′𝜁(ℎ)||	||(γ(ℵ))′𝜁(ℎ)||	NUM
cana-1619	456	22	≤	≤	NOUN
cana-1619	456	23	𝑅(ℵ	𝑅(ℵ	NUM
cana-1619	456	24	)	)	PUNCT
cana-1619	456	25	+	+	PUNCT
cana-1619	456	26	𝑄(ℵ	𝑄(ℵ	X
cana-1619	456	27	)	)	PUNCT
cana-1619	456	28	we	we	PRON
cana-1619	456	29	can	can	AUX
cana-1619	456	30	find	find	VERB
cana-1619	456	31	a	a	DET
cana-1619	456	32	constant	constant	ADJ
cana-1619	456	33	𝑅(ℵ	𝑅(ℵ	NUM
cana-1619	456	34	)	)	PUNCT
cana-1619	456	35	+	+	PUNCT
cana-1619	456	36	𝑄(ℵ	𝑄(ℵ	X
cana-1619	456	37	)	)	PUNCT
cana-1619	456	38	such	such	ADJ
cana-1619	456	39	that	that	SCONJ
cana-1619	456	40	∥	∥	NUM
cana-1619	456	41	𝜁	𝜁	X
cana-1619	456	42	∥𝑃𝐶≠	∥𝑃𝐶≠	PROPN
cana-1619	456	43	𝑅(ℵ	𝑅(ℵ	NUM
cana-1619	456	44	)	)	PUNCT
cana-1619	456	45	+	+	PUNCT
cana-1619	456	46	𝑄(ℵ	𝑄(ℵ	NUM
cana-1619	456	47	)	)	PUNCT
cana-1619	456	48	.	.	PUNCT
cana-1619	457	1	set	set	VERB
cana-1619	457	2	𝑈	𝑈	PROPN
cana-1619	457	3	=	=	PUNCT
cana-1619	457	4	{	{	PUNCT
cana-1619	457	5	𝜁	𝜁	PROPN
cana-1619	457	6	∈	∈	PROPN
cana-1619	457	7	𝑃𝐶([𝛿	𝑃𝐶([𝛿	NOUN
cana-1619	457	8	,	,	PUNCT
cana-1619	457	9	𝜚	𝜚	NOUN
cana-1619	457	10	]	]	X
cana-1619	457	11	,	,	PUNCT
cana-1619	457	12	𝒮	𝒮	NOUN
cana-1619	457	13	)	)	PUNCT
cana-1619	458	1	|	|	ADV
cana-1619	458	2	sup	sup	NOUN
cana-1619	458	3	𝛿≤ℎ≤𝜚	𝛿≤ℎ≤𝜚	NOUN
cana-1619	458	4	∥	∥	X
cana-1619	458	5	𝜁(ℎ	𝜁(ℎ	NOUN
cana-1619	458	6	)	)	PUNCT
cana-1619	459	1	∥	∥	X
cana-1619	459	2	<	<	X
cana-1619	459	3	𝑅(ℵ	𝑅(ℵ	PROPN
cana-1619	459	4	)	)	PUNCT
cana-1619	459	5	+	+	PUNCT
cana-1619	459	6	𝑄(ℵ	𝑄(ℵ	X
cana-1619	459	7	)	)	PUNCT
cana-1619	459	8	}	}	PUNCT
cana-1619	460	1	based	base	VERB
cana-1619	460	2	on	on	ADP
cana-1619	460	3	steps	step	NOUN
cana-1619	460	4	1	1	NUM
cana-1619	460	5	-	-	SYM
cana-1619	460	6	3	3	NUM
cana-1619	460	7	of	of	ADP
cana-1619	460	8	theorem	theorem	NOUN
cana-1619	460	9	3.2	3.2	NUM
cana-1619	460	10	,	,	PUNCT
cana-1619	460	11	it	it	PRON
cana-1619	460	12	is	be	AUX
cana-1619	460	13	sufficient	sufficient	ADJ
cana-1619	460	14	to	to	PART
cana-1619	460	15	show	show	VERB
cana-1619	460	16	that	that	SCONJ
cana-1619	460	17	(	(	PUNCT
cana-1619	460	18	γ(ℵ))′	γ(ℵ))′	PROPN
cana-1619	460	19	:	:	PUNCT
cana-1619	460	20	𝑈	𝑈	PROPN
cana-1619	460	21	→	→	SYM
cana-1619	460	22	𝑃𝐶𝛿	𝑃𝐶𝛿	NOUN
cana-1619	460	23	is	be	AUX
cana-1619	460	24	a	a	DET
cana-1619	460	25	compact	compact	ADJ
cana-1619	460	26	map	map	NOUN
cana-1619	460	27	.	.	PUNCT
cana-1619	461	1	given	give	VERB
cana-1619	461	2	the	the	DET
cana-1619	461	3	choice	choice	NOUN
cana-1619	461	4	of	of	ADP
cana-1619	461	5	𝑈	𝑈	PROPN
cana-1619	461	6	,	,	PUNCT
cana-1619	461	7	there	there	PRON
cana-1619	461	8	is	be	VERB
cana-1619	461	9	no	no	DET
cana-1619	461	10	𝜑	𝜑	NOUN
cana-1619	461	11	∈	∈	PROPN
cana-1619	461	12	𝜕𝑈	𝜕𝑈	PROPN
cana-1619	461	13	for	for	ADP
cana-1619	461	14	which	which	PRON
cana-1619	461	15	𝜁	𝜁	PROPN
cana-1619	461	16	∈	∈	PROPN
cana-1619	461	17	𝜆(γ(ℵ))(𝜁	𝜆(γ(ℵ))(𝜁	PROPN
cana-1619	461	18	)	)	PUNCT
cana-1619	461	19	with	with	ADP
cana-1619	461	20	𝜆	𝜆	DET
cana-1619	461	21	∈	∈	PROPN
cana-1619	461	22	(	(	PUNCT
cana-1619	461	23	0,1	0,1	NUM
cana-1619	461	24	)	)	PUNCT
cana-1619	461	25	.	.	PUNCT
cana-1619	462	1	according	accord	VERB
cana-1619	462	2	to	to	ADP
cana-1619	462	3	lemma	lemma	PROPN
cana-1619	462	4	2.1	2.1	NUM
cana-1619	462	5	,	,	PUNCT
cana-1619	462	6	we	we	PRON
cana-1619	462	7	assume	assume	VERB
cana-1619	462	8	that	that	SCONJ
cana-1619	462	9	the	the	DET
cana-1619	462	10	operator	operator	NOUN
cana-1619	462	11	(	(	PUNCT
cana-1619	462	12	γ(ℵ	γ(ℵ	PROPN
cana-1619	462	13	)	)	PUNCT
cana-1619	462	14	)	)	PUNCT
cana-1619	462	15	has	have	VERB
cana-1619	462	16	a	a	DET
cana-1619	462	17	fixed	fix	VERB
cana-1619	462	18	point	point	NOUN
cana-1619	462	19	𝜁∗	𝜁∗	PROPN
cana-1619	462	20	∈	∈	PROPN
cana-1619	462	21	𝑈.	𝑈.	PROPN
cana-1619	462	22	thus	thus	ADV
cana-1619	462	23	,	,	PUNCT
cana-1619	462	24	we	we	PRON
cana-1619	462	25	derive	derive	VERB
cana-1619	462	26	𝜁∗(ℎ	𝜁∗(ℎ	PROPN
cana-1619	462	27	,	,	PUNCT
cana-1619	462	28	ℵ	ℵ	NOUN
cana-1619	462	29	)	)	PUNCT
cana-1619	462	30	=	=	SYM
cana-1619	462	31	𝑇1(ℎ)𝜙0(ℵ	𝑇1(ℎ)𝜙0(ℵ	NOUN
cana-1619	462	32	)	)	PUNCT
cana-1619	462	33	+	+	NUM
cana-1619	462	34	𝑇2(ℎ)[𝜙′0(ℵ	𝑇2(ℎ)[𝜙′0(ℵ	NOUN
cana-1619	462	35	)	)	PUNCT
cana-1619	463	1	+	+	CCONJ
cana-1619	463	2	𝜌(0	𝜌(0	PROPN
cana-1619	463	3	,	,	PUNCT
cana-1619	463	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	463	5	)	)	PUNCT
cana-1619	463	6	,	,	PUNCT
cana-1619	463	7	ℵ	ℵ	NOUN
cana-1619	463	8	)	)	PUNCT
cana-1619	463	9	]	]	PUNCT
cana-1619	464	1	−	−	PROPN
cana-1619	464	2	𝜆	𝜆	DET
cana-1619	464	3	∫	∫	PROPN
cana-1619	464	4	ℎ	ℎ	PROPN
cana-1619	464	5	0	0	PROPN
cana-1619	465	1	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	466	1	−	−	PROPN
cana-1619	466	2	𝜛)𝜌(𝜛	𝜛)𝜌(𝜛	NOUN
cana-1619	466	3	,	,	PUNCT
cana-1619	466	4	𝜁𝜛	𝜁𝜛	ADV
cana-1619	466	5	∗	∗	NOUN
cana-1619	466	6	(	(	PUNCT
cana-1619	466	7	.	.	PUNCT
cana-1619	466	8	,	,	PUNCT
cana-1619	466	9	ℵ	ℵ	NOUN
cana-1619	466	10	)	)	PUNCT
cana-1619	466	11	,	,	PUNCT
cana-1619	467	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	467	2	+	+	PROPN
cana-1619	467	3	𝜆	𝜆	NOUN
cana-1619	467	4	∫	∫	PROPN
cana-1619	467	5	ℎ	ℎ	PROPN
cana-1619	467	6	0	0	SYM
cana-1619	467	7	𝑇2(ℎ	𝑇2(ℎ	ADJ
cana-1619	467	8	−	−	PROPN
cana-1619	467	9	𝜛)υ(𝜛	𝜛)υ(𝜛	NOUN
cana-1619	467	10	,	,	PUNCT
cana-1619	467	11	𝜁𝜛	𝜁𝜛	ADV
cana-1619	467	12	∗	∗	NOUN
cana-1619	467	13	(	(	PUNCT
cana-1619	467	14	.	.	PUNCT
cana-1619	467	15	,	,	PUNCT
cana-1619	467	16	ℵ	ℵ	NOUN
cana-1619	467	17	)	)	PUNCT
cana-1619	467	18	,	,	PUNCT
cana-1619	468	1	ℵ)𝑑𝜛	ℵ)𝑑𝜛	PROPN
cana-1619	468	2	+	+	CCONJ
cana-1619	468	3	∫	∫	PROPN
cana-1619	468	4	ℎ	ℎ	X
cana-1619	468	5	0	0	PUNCT
cana-1619	468	6	𝑇2(ℎ	𝑇2(ℎ	PROPN
cana-1619	468	7	−	−	PROPN
cana-1619	468	8	𝜛)𝐵𝑘	𝜛)𝐵𝑘	PROPN
cana-1619	468	9	−1[(𝜁∗,1(ℵ	−1[(𝜁∗,1(ℵ	PROPN
cana-1619	468	10	)	)	PUNCT
cana-1619	468	11	−	−	NOUN
cana-1619	468	12	𝑇1(𝜚)𝜙0(ℵ	𝑇1(𝜚)𝜙0(ℵ	NOUN
cana-1619	468	13	)	)	PUNCT
cana-1619	468	14	−𝑇2(𝜚)[𝜙′0(ℵ	−𝑇2(𝜚)[𝜙′0(ℵ	NOUN
cana-1619	468	15	)	)	PUNCT
cana-1619	469	1	+	+	CCONJ
cana-1619	469	2	𝜌(0	𝜌(0	PROPN
cana-1619	469	3	,	,	PUNCT
cana-1619	469	4	𝜙0(ℵ	𝜙0(ℵ	NOUN
cana-1619	469	5	)	)	PUNCT
cana-1619	469	6	,	,	PUNCT
cana-1619	469	7	ℵ	ℵ	NOUN
cana-1619	469	8	)	)	PUNCT
cana-1619	469	9	]	]	PUNCT
cana-1619	470	1	+	+	CCONJ
cana-1619	470	2	∫	∫	PROPN
cana-1619	470	3	𝜚	𝜚	NOUN
cana-1619	470	4	0	0	NUM
cana-1619	470	5	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	470	6	−	−	NOUN
cana-1619	470	7	𝜂)𝜌(𝜂	𝜂)𝜌(𝜂	ADJ
cana-1619	470	8	,	,	PUNCT
cana-1619	470	9	𝜁𝜂	𝜁𝜂	NOUN
cana-1619	470	10	∗	∗	NOUN
cana-1619	470	11	(	(	PUNCT
cana-1619	470	12	.	.	PUNCT
cana-1619	470	13	,	,	PUNCT
cana-1619	470	14	ℵ	ℵ	NOUN
cana-1619	470	15	)	)	PUNCT
cana-1619	470	16	,	,	PUNCT
cana-1619	471	1	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	471	2	−	−	PROPN
cana-1619	471	3	∫	∫	PROPN
cana-1619	471	4	𝜚	𝜚	NOUN
cana-1619	471	5	0	0	NUM
cana-1619	471	6	𝑇2(𝜚	𝑇2(𝜚	ADJ
cana-1619	471	7	−	−	NOUN
cana-1619	471	8	𝜂)υ(𝜂	𝜂)υ(𝜂	NOUN
cana-1619	471	9	,	,	PUNCT
cana-1619	471	10	𝜁𝜂	𝜁𝜂	NOUN
cana-1619	471	11	∗	∗	NOUN
cana-1619	471	12	(	(	PUNCT
cana-1619	471	13	.	.	PUNCT
cana-1619	471	14	,	,	PUNCT
cana-1619	471	15	ℵ	ℵ	NOUN
cana-1619	471	16	)	)	PUNCT
cana-1619	471	17	,	,	PUNCT
cana-1619	471	18	ℵ)𝑑𝜂	ℵ)𝑑𝜂	PROPN
cana-1619	471	19	−	−	PROPN
cana-1619	471	20	∑0<ℎ𝜉<𝜚	∑0<ℎ𝜉<𝜚	PROPN
cana-1619	471	21	𝑇1(𝜚	𝑇1(𝜚	VERB
cana-1619	471	22	−	−	PROPN
cana-1619	471	23	ℎ𝜉)𝐼𝜉(𝜁	ℎ𝜉)𝐼𝜉(𝜁	PROPN
cana-1619	471	24	∗(ℎ𝜉	∗(ℎ𝜉	NOUN
cana-1619	471	25	,	,	PUNCT
cana-1619	471	26	ℵ	ℵ	NOUN
cana-1619	471	27	)	)	PUNCT
cana-1619	471	28	)	)	PUNCT
cana-1619	471	29	)	)	PUNCT
cana-1619	472	1	−∑0<ℎ𝜉<𝜚	−∑0<ℎ𝜉<𝜚	PROPN
cana-1619	472	2	𝑇2(𝜚	𝑇2(𝜚	PROPN
cana-1619	473	1	−	−	NOUN
cana-1619	473	2	ℎ𝜉)𝐼′𝜉(𝜁	ℎ𝜉)𝐼′𝜉(𝜁	PROPN
cana-1619	473	3	∗(ℎ𝜉	∗(ℎ𝜉	NOUN
cana-1619	473	4	,	,	PUNCT
cana-1619	473	5	ℵ))]𝑑𝜛	ℵ))]𝑑𝜛	PROPN
cana-1619	474	1	+	+	CCONJ
cana-1619	474	2	𝜆∑0<ℎ𝜉<ℎ	𝜆∑0<ℎ𝜉<ℎ	PROPN
cana-1619	475	1	𝑇1(ℎ	𝑇1(ℎ	PROPN
cana-1619	475	2	−	−	PROPN
cana-1619	475	3	ℎ𝜉)𝐼𝜉(𝜁	ℎ𝜉)𝐼𝜉(𝜁	PROPN
cana-1619	475	4	∗(ℎ𝜉	∗(ℎ𝜉	NOUN
cana-1619	475	5	,	,	PUNCT
cana-1619	475	6	ℵ	ℵ	NOUN
cana-1619	475	7	)	)	PUNCT
cana-1619	475	8	)	)	PUNCT
cana-1619	476	1	+	+	ADP
cana-1619	476	2	𝜆∑0<ℎ𝜉<ℎ	𝜆∑0<ℎ𝜉<ℎ	PROPN
cana-1619	476	3	𝑇2(ℎ	𝑇2(ℎ	ADJ
cana-1619	476	4	−	−	NUM
cana-1619	476	5	ℎ𝜉)𝐼′𝜉(𝜁	ℎ𝜉)𝐼′𝜉(𝜁	PROPN
cana-1619	476	6	∗(ℎ𝜉	∗(ℎ𝜉	NOUN
cana-1619	476	7	,	,	PUNCT
cana-1619	476	8	ℵ	ℵ	NOUN
cana-1619	476	9	)	)	PUNCT
cana-1619	476	10	)	)	PUNCT
cana-1619	476	11	this	this	PRON
cana-1619	476	12	implies	imply	VERB
cana-1619	476	13	,	,	PUNCT
cana-1619	476	14	that	that	DET
cana-1619	476	15	𝜁∗(ℎ	𝜁∗(ℎ	PROPN
cana-1619	476	16	,	,	PUNCT
cana-1619	476	17	ℵ	ℵ	NOUN
cana-1619	476	18	)	)	PUNCT
cana-1619	476	19	has	have	VERB
cana-1619	476	20	a	a	DET
cana-1619	476	21	fixed	fix	VERB
cana-1619	476	22	point	point	NOUN
cana-1619	476	23	and	and	CCONJ
cana-1619	476	24	𝜁∗(ℎ	𝜁∗(ℎ	PROPN
cana-1619	476	25	,	,	PUNCT
cana-1619	476	26	ℵ	ℵ	NOUN
cana-1619	476	27	)	)	PUNCT
cana-1619	476	28	is	be	AUX
cana-1619	476	29	a	a	DET
cana-1619	476	30	mild	mild	ADJ
cana-1619	476	31	solution	solution	NOUN
cana-1619	476	32	of	of	ADP
cana-1619	476	33	problem	problem	NOUN
cana-1619	476	34	(	(	PUNCT
cana-1619	476	35	1.2	1.2	NUM
cana-1619	476	36	)	)	PUNCT
cana-1619	476	37	.	.	PUNCT
cana-1619	477	1	this	this	PRON
cana-1619	477	2	completes	complete	VERB
cana-1619	477	3	the	the	DET
cana-1619	477	4	proof	proof	NOUN
cana-1619	477	5	of	of	ADP
cana-1619	477	6	this	this	DET
cana-1619	477	7	theorem	theorem	NOUN
cana-1619	477	8	.	.	PROPN
cana-1619	477	9	5	5	NUM
cana-1619	477	10	example	example	NOUN
cana-1619	477	11	this	this	DET
cana-1619	477	12	section	section	NOUN
cana-1619	477	13	introduces	introduce	VERB
cana-1619	477	14	an	an	DET
cana-1619	477	15	example	example	NOUN
cana-1619	477	16	to	to	PART
cana-1619	477	17	illustrate	illustrate	VERB
cana-1619	477	18	our	our	PRON
cana-1619	477	19	findings	finding	NOUN
cana-1619	477	20	.	.	PUNCT
cana-1619	478	1	before	before	ADP
cana-1619	478	2	delving	delve	VERB
cana-1619	478	3	into	into	ADP
cana-1619	478	4	the	the	DET
cana-1619	478	5	application	application	NOUN
cana-1619	478	6	of	of	ADP
cana-1619	478	7	our	our	PRON
cana-1619	478	8	abstract	abstract	ADJ
cana-1619	478	9	results	result	NOUN
cana-1619	478	10	,	,	PUNCT
cana-1619	478	11	we	we	PRON
cana-1619	478	12	must	must	AUX
cana-1619	478	13	first	first	ADV
cana-1619	478	14	establish	establish	VERB
cana-1619	478	15	some	some	DET
cana-1619	478	16	technical	technical	ADJ
cana-1619	478	17	prerequisites	prerequisite	NOUN
cana-1619	478	18	.	.	PUNCT
cana-1619	479	1	in	in	ADP
cana-1619	479	2	what	what	PRON
cana-1619	479	3	follows	follow	VERB
cana-1619	479	4	,	,	PUNCT
cana-1619	479	5	let	let	VERB
cana-1619	479	6	𝒮	𝒮	PRON
cana-1619	479	7	=	=	SYM
cana-1619	479	8	𝐿2([0	𝐿2([0	PROPN
cana-1619	479	9	,	,	PUNCT
cana-1619	479	10	𝜋	𝜋	NOUN
cana-1619	479	11	]	]	X
cana-1619	479	12	)	)	PUNCT
cana-1619	479	13	,	,	PUNCT
cana-1619	479	14	𝐷(𝐴	𝐷(𝐴	NOUN
cana-1619	479	15	)	)	PUNCT
cana-1619	479	16	=	=	PRON
cana-1619	479	17	{	{	PUNCT
cana-1619	479	18	𝜑	𝜑	NOUN
cana-1619	479	19	∈	∈	PROPN
cana-1619	479	20	𝒮	𝒮	PROPN
cana-1619	479	21	:	:	PUNCT
cana-1619	479	22	𝑥′′	𝑥′′	PROPN
cana-1619	479	23	∈	∈	PROPN
cana-1619	479	24	𝒮	𝒮	PROPN
cana-1619	479	25	,	,	PUNCT
cana-1619	479	26	𝜑(0	𝜑(0	NOUN
cana-1619	479	27	)	)	PUNCT
cana-1619	479	28	=	=	SYM
cana-1619	479	29	𝜑(𝜋	𝜑(𝜋	X
cana-1619	479	30	)	)	PUNCT
cana-1619	479	31	=	=	SYM
cana-1619	479	32	0	0	NUM
cana-1619	479	33	}	}	PUNCT
cana-1619	479	34	,	,	PUNCT
cana-1619	479	35	and	and	CCONJ
cana-1619	479	36	𝐴:𝐷(𝐴	𝐴:𝐷(𝐴	PROPN
cana-1619	479	37	)	)	PUNCT
cana-1619	479	38	⊆	⊆	NUM
cana-1619	479	39	𝒮	𝒮	NOUN
cana-1619	479	40	→	→	SYM
cana-1619	479	41	𝒮	𝒮	PROPN
cana-1619	479	42	denote	denote	VERB
cana-1619	479	43	the	the	DET
cana-1619	479	44	linear	linear	ADJ
cana-1619	479	45	operator	operator	NOUN
cana-1619	479	46	defined	define	VERB
cana-1619	479	47	by	by	ADP
cana-1619	479	48	𝐴𝜑	𝐴𝜑	PROPN
cana-1619	479	49	=	=	PUNCT
cana-1619	479	50	𝜑′′.it	𝜑′′.it	PROPN
cana-1619	479	51	’s	’s	PART
cana-1619	479	52	widely	widely	ADV
cana-1619	479	53	recognized	recognize	VERB
cana-1619	479	54	that	that	SCONJ
cana-1619	479	55	𝐴	𝐴	PROPN
cana-1619	479	56	acts	act	VERB
cana-1619	479	57	as	as	ADP
cana-1619	479	58	the	the	DET
cana-1619	479	59	infinitesimal	infinitesimal	ADJ
cana-1619	479	60	generator	generator	NOUN
cana-1619	479	61	of	of	ADP
cana-1619	479	62	a	a	DET
cana-1619	479	63	strongly	strongly	ADV
cana-1619	479	64	continuous	continuous	ADJ
cana-1619	479	65	cosine	cosine	NOUN
cana-1619	479	66	family	family	NOUN
cana-1619	479	67	(	(	PUNCT
cana-1619	479	68	𝑇1(ℎ))ℎ∈ℝ	𝑇1(ℎ))ℎ∈ℝ	NOUN
cana-1619	479	69	on	on	ADP
cana-1619	479	70	𝒮	𝒮	PROPN
cana-1619	479	71	.	.	PUNCT
cana-1619	480	1	moreover	moreover	ADV
cana-1619	480	2	,	,	PUNCT
cana-1619	480	3	𝐴	𝐴	PROPN
cana-1619	480	4	has	have	VERB
cana-1619	480	5	a	a	DET
cana-1619	480	6	discrete	discrete	ADJ
cana-1619	480	7	spectrum	spectrum	NOUN
cana-1619	480	8	,	,	PUNCT
cana-1619	480	9	with	with	ADP
cana-1619	480	10	eigenvalues	eigenvalue	VERB
cana-1619	480	11	−𝑛2	−𝑛2	PROPN
cana-1619	480	12	for	for	ADP
cana-1619	480	13	𝑛	𝑛	DET
cana-1619	480	14	∈	∈	PROPN
cana-1619	480	15	𝜗	𝜗	NOUN
cana-1619	480	16	,	,	PUNCT
cana-1619	480	17	each	each	PRON
cana-1619	480	18	corresponding	correspond	VERB
cana-1619	480	19	to	to	ADP
cana-1619	480	20	the	the	DET
cana-1619	480	21	eigenvectors	eigenvector	NOUN
cana-1619	480	22	𝑧𝑛(𝜚	𝑧𝑛(𝜚	NOUN
cana-1619	480	23	)	)	PUNCT
cana-1619	480	24	=	=	PRON
cana-1619	480	25	(	(	PUNCT
cana-1619	480	26	2	2	NUM
cana-1619	480	27	𝜋	𝜋	NOUN
cana-1619	480	28	)	)	PUNCT
cana-1619	480	29	1/2	1/2	NUM
cana-1619	480	30	.	.	PUNCT
cana-1619	481	1	communications	communication	NOUN
cana-1619	481	2	on	on	ADP
cana-1619	481	3	applied	apply	VERB
cana-1619	481	4	nonlinear	nonlinear	ADJ
cana-1619	481	5	analysis	analysis	NOUN
cana-1619	481	6	issn	issn	NOUN
cana-1619	481	7	:	:	PUNCT
cana-1619	481	8	1074	1074	NUM
cana-1619	481	9	-	-	PUNCT
cana-1619	481	10	133x	133x	NUM
cana-1619	481	11	vol	vol	NOUN
cana-1619	481	12	32	32	NUM
cana-1619	481	13	no	no	NOUN
cana-1619	481	14	.	.	NOUN
cana-1619	481	15	1	1	NUM
cana-1619	481	16	(	(	PUNCT
cana-1619	481	17	2025	2025	NUM
cana-1619	481	18	)	)	PUNCT
cana-1619	482	1	53	53	NUM
cana-1619	482	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	482	3	consider	consider	VERB
cana-1619	482	4	the	the	DET
cana-1619	482	5	following	follow	VERB
cana-1619	482	6	impulsive	impulsive	ADJ
cana-1619	482	7	partial	partial	ADJ
cana-1619	482	8	neutral	neutral	ADJ
cana-1619	482	9	functional	functional	ADJ
cana-1619	482	10	integro	integro	ADJ
cana-1619	482	11	-	-	PUNCT
cana-1619	482	12	differential	differential	NOUN
cana-1619	482	13	equation	equation	NOUN
cana-1619	482	14	of	of	ADP
cana-1619	482	15	the	the	DET
cana-1619	482	16	form	form	NOUN
cana-1619	482	17	:	:	PUNCT
cana-1619	482	18	𝜕	𝜕	PROPN
cana-1619	482	19	𝜕	𝜕	PROPN
cana-1619	482	20	[	[	PUNCT
cana-1619	482	21	𝜕	𝜕	NOUN
cana-1619	482	22	𝜕ℎ	𝜕ℎ	PROPN
cana-1619	482	23	𝑧(ℎ	𝑧(ℎ	PROPN
cana-1619	482	24	,	,	PUNCT
cana-1619	482	25	𝑥	𝑥	NOUN
cana-1619	482	26	,	,	PUNCT
cana-1619	482	27	ℵ	ℵ	NOUN
cana-1619	482	28	)	)	PUNCT
cana-1619	482	29	−	−	NOUN
cana-1619	482	30	𝜌(ℎ	𝜌(ℎ	PROPN
cana-1619	482	31	,	,	PUNCT
cana-1619	482	32	𝑧(cosℎ	𝑧(cosℎ	PROPN
cana-1619	482	33	,	,	PUNCT
cana-1619	482	34	𝑥	𝑥	NOUN
cana-1619	482	35	,	,	PUNCT
cana-1619	482	36	ℵ	ℵ	NOUN
cana-1619	482	37	)	)	PUNCT
cana-1619	482	38	,	,	PUNCT
cana-1619	482	39	ℵ	ℵ	NOUN
cana-1619	482	40	)	)	PUNCT
cana-1619	482	41	=	=	PUNCT
cana-1619	483	1	𝜕2	𝜕2	NUM
cana-1619	483	2	𝜕𝑥2	𝜕𝑥2	PROPN
cana-1619	483	3	𝑧(ℎ	𝑧(ℎ	PROPN
cana-1619	483	4	,	,	PUNCT
cana-1619	483	5	𝑥	𝑥	NOUN
cana-1619	483	6	,	,	PUNCT
cana-1619	483	7	ℵ	ℵ	NOUN
cana-1619	483	8	)	)	PUNCT
cana-1619	484	1	+	+	CCONJ
cana-1619	484	2	υ(h	υ(h	NOUN
cana-1619	484	3	,	,	PUNCT
cana-1619	484	4	𝑧(sinℎ	𝑧(sinℎ	ADJ
cana-1619	484	5	,	,	PUNCT
cana-1619	484	6	𝑥	𝑥	NOUN
cana-1619	484	7	,	,	PUNCT
cana-1619	484	8	ℵ	ℵ	NOUN
cana-1619	484	9	)	)	PUNCT
cana-1619	484	10	,	,	PUNCT
cana-1619	484	11	ℵ	ℵ	NOUN
cana-1619	484	12	)	)	PUNCT
cana-1619	484	13	,	,	PUNCT
cana-1619	484	14	ℵ	ℵ	X
cana-1619	484	15	∈	∈	PROPN
cana-1619	484	16	(	(	PUNCT
cana-1619	484	17	−∞	−∞	NOUN
cana-1619	484	18	,	,	PUNCT
cana-1619	484	19	0	0	NUM
cana-1619	484	20	]	]	X
cana-1619	484	21	(	(	PUNCT
cana-1619	484	22	11	11	NUM
cana-1619	484	23	)	)	PUNCT
cana-1619	484	24	δ𝑧(ℎ𝜉	δ𝑧(ℎ𝜉	NOUN
cana-1619	484	25	,	,	PUNCT
cana-1619	484	26	𝑥	𝑥	NOUN
cana-1619	484	27	,	,	PUNCT
cana-1619	484	28	ℵ	ℵ	NOUN
cana-1619	484	29	)	)	PUNCT
cana-1619	484	30	=	=	SYM
cana-1619	484	31	∫	∫	PROPN
cana-1619	484	32	𝜋	𝜋	NOUN
cana-1619	484	33	0	0	NUM
cana-1619	484	34	𝑞𝜉(𝑥	𝑞𝜉(𝑥	NUM
cana-1619	484	35	,	,	PUNCT
cana-1619	484	36	𝑦)𝑧(ℎ𝜉	𝑦)𝑧(ℎ𝜉	NOUN
cana-1619	484	37	,	,	PUNCT
cana-1619	484	38	𝑦	𝑦	X
cana-1619	484	39	,	,	PUNCT
cana-1619	484	40	ℵ)𝑑𝑦	ℵ)𝑑𝑦	PROPN
cana-1619	484	41	and	and	CCONJ
cana-1619	484	42	δ′𝑧(ℎ𝜉	δ′𝑧(ℎ𝜉	NOUN
cana-1619	484	43	,	,	PUNCT
cana-1619	484	44	𝑥	𝑥	NOUN
cana-1619	484	45	,	,	PUNCT
cana-1619	484	46	ℵ	ℵ	NOUN
cana-1619	484	47	)	)	PUNCT
cana-1619	484	48	=	=	SYM
cana-1619	484	49	∫	∫	PROPN
cana-1619	484	50	𝜋	𝜋	NOUN
cana-1619	484	51	0	0	NUM
cana-1619	484	52	𝑞′𝜉(𝑥	𝑞′𝜉(𝑥	X
cana-1619	484	53	,	,	PUNCT
cana-1619	484	54	𝑦)𝑧(ℎ𝜉	𝑦)𝑧(ℎ𝜉	NOUN
cana-1619	484	55	,	,	PUNCT
cana-1619	484	56	𝑦	𝑦	X
cana-1619	484	57	,	,	PUNCT
cana-1619	484	58	ℵ)𝑑𝑦	ℵ)𝑑𝑦	NOUN
cana-1619	484	59	,	,	PUNCT
cana-1619	484	60	𝜉	𝜉	NOUN
cana-1619	484	61	=	=	SYM
cana-1619	484	62	1	1	NUM
cana-1619	484	63	,	,	PUNCT
cana-1619	484	64	…	…	PUNCT
cana-1619	484	65	,	,	PUNCT
cana-1619	484	66	𝑚	𝑚	NOUN
cana-1619	484	67	,	,	PUNCT
cana-1619	484	68	(	(	PUNCT
cana-1619	484	69	12	12	NUM
cana-1619	484	70	)	)	PUNCT
cana-1619	484	71	𝑧(ℎ	𝑧(ℎ	PROPN
cana-1619	484	72	,	,	PUNCT
cana-1619	484	73	0	0	NUM
cana-1619	484	74	,	,	PUNCT
cana-1619	484	75	ℵ	ℵ	NOUN
cana-1619	484	76	)	)	PUNCT
cana-1619	484	77	=	=	SYM
cana-1619	484	78	𝑧(ℎ	𝑧(ℎ	PROPN
cana-1619	484	79	,	,	PUNCT
cana-1619	484	80	𝜋	𝜋	NOUN
cana-1619	484	81	,	,	PUNCT
cana-1619	484	82	ℵ	ℵ	NOUN
cana-1619	484	83	)	)	PUNCT
cana-1619	484	84	=	=	SYM
cana-1619	484	85	0	0	NUM
cana-1619	484	86	;	;	PUNCT
cana-1619	484	87	𝑧(0	𝑧(0	PROPN
cana-1619	484	88	,	,	PUNCT
cana-1619	484	89	𝑥	𝑥	NOUN
cana-1619	484	90	,	,	PUNCT
cana-1619	484	91	ℵ	ℵ	NOUN
cana-1619	484	92	)	)	PUNCT
cana-1619	484	93	=	=	SYM
cana-1619	484	94	𝑧0(𝑥	𝑧0(𝑥	PROPN
cana-1619	484	95	,	,	PUNCT
cana-1619	484	96	ℵ	ℵ	NOUN
cana-1619	484	97	)	)	PUNCT
cana-1619	484	98	;	;	PUNCT
cana-1619	484	99	𝑧ℎ(0	𝑧ℎ(0	NOUN
cana-1619	484	100	,	,	PUNCT
cana-1619	484	101	𝑥	𝑥	NOUN
cana-1619	484	102	,	,	PUNCT
cana-1619	484	103	ℵ	ℵ	NOUN
cana-1619	484	104	)	)	PUNCT
cana-1619	484	105	=	=	SYM
cana-1619	484	106	𝑧1(𝑥	𝑧1(𝑥	NOUN
cana-1619	484	107	,	,	PUNCT
cana-1619	484	108	ℵ	ℵ	NOUN
cana-1619	484	109	)	)	PUNCT
cana-1619	484	110	,	,	PUNCT
cana-1619	484	111	ℎ	ℎ	PROPN
cana-1619	484	112	∈	∈	PROPN
cana-1619	484	113	𝐽	𝐽	NOUN
cana-1619	484	114	=	=	PUNCT
cana-1619	485	1	[	[	X
cana-1619	485	2	0,1	0,1	NUM
cana-1619	485	3	]	]	PUNCT
cana-1619	485	4	,	,	PUNCT
cana-1619	485	5	0	0	NUM
cana-1619	485	6	≤	≤	NUM
cana-1619	485	7	𝑥	𝑥	DET
cana-1619	485	8	≤	≤	NUM
cana-1619	485	9	𝜋	𝜋	NOUN
cana-1619	485	10	,	,	PUNCT
cana-1619	485	11	(	(	PUNCT
cana-1619	485	12	13	13	NUM
cana-1619	485	13	)	)	PUNCT
cana-1619	485	14	𝑧(0	𝑧(0	PROPN
cana-1619	485	15	,	,	PUNCT
cana-1619	485	16	𝑥	𝑥	NOUN
cana-1619	485	17	,	,	PUNCT
cana-1619	485	18	ℵ	ℵ	NOUN
cana-1619	485	19	)	)	PUNCT
cana-1619	485	20	=	=	SYM
cana-1619	485	21	𝑧0(𝑥	𝑧0(𝑥	PROPN
cana-1619	485	22	,	,	PUNCT
cana-1619	485	23	ℵ	ℵ	NOUN
cana-1619	485	24	)	)	PUNCT
cana-1619	485	25	,	,	PUNCT
cana-1619	485	26	and	and	CCONJ
cana-1619	485	27	𝑧ℎ(0	𝑧ℎ(0	NOUN
cana-1619	485	28	,	,	PUNCT
cana-1619	485	29	𝑥	𝑥	NOUN
cana-1619	485	30	,	,	PUNCT
cana-1619	485	31	ℵ	ℵ	NOUN
cana-1619	485	32	)	)	PUNCT
cana-1619	485	33	=	=	SYM
cana-1619	485	34	𝑧1(𝑥	𝑧1(𝑥	NOUN
cana-1619	485	35	,	,	PUNCT
cana-1619	485	36	ℵ	ℵ	NOUN
cana-1619	485	37	)	)	PUNCT
cana-1619	485	38	,	,	PUNCT
cana-1619	485	39	0	0	NUM
cana-1619	485	40	≤	≤	NUM
cana-1619	486	1	𝑥	𝑥	DET
cana-1619	486	2	≤	≤	NUM
cana-1619	486	3	𝜋.	𝜋.	NOUN
cana-1619	486	4	(	(	PUNCT
cana-1619	486	5	14	14	NUM
cana-1619	486	6	)	)	PUNCT
cana-1619	486	7	where	where	SCONJ
cana-1619	486	8	we	we	PRON
cana-1619	486	9	assume	assume	VERB
cana-1619	486	10	the	the	DET
cana-1619	486	11	following	follow	VERB
cana-1619	486	12	conditions	condition	NOUN
cana-1619	486	13	:	:	PUNCT
cana-1619	486	14	the	the	DET
cana-1619	486	15	functions	function	NOUN
cana-1619	486	16	υ(⋅	υ(⋅	NOUN
cana-1619	486	17	,	,	PUNCT
cana-1619	486	18	ℵ	ℵ	NOUN
cana-1619	486	19	)	)	PUNCT
cana-1619	486	20	and	and	CCONJ
cana-1619	486	21	are	be	AUX
cana-1619	486	22	continuous	continuous	ADJ
cana-1619	486	23	on	on	ADP
cana-1619	486	24	[	[	X
cana-1619	486	25	0,1	0,1	NUM
cana-1619	486	26	]	]	PUNCT
cana-1619	486	27	with	with	ADP
cana-1619	486	28	𝑛	𝑛	PROPN
cana-1619	486	29	=	=	SYM
cana-1619	486	30	sup0≤𝜛≤1|υ(𝜛	sup0≤𝜛≤1|υ(𝜛	NOUN
cana-1619	486	31	,	,	PUNCT
cana-1619	486	32	ℵ)|	ℵ)|	PRON
cana-1619	486	33	<	<	X
cana-1619	486	34	1	1	NUM
cana-1619	486	35	.	.	PUNCT
cana-1619	487	1	the	the	DET
cana-1619	487	2	functions	function	NOUN
cana-1619	487	3	𝑞𝜉	𝑞𝜉	ADV
cana-1619	487	4	,	,	PUNCT
cana-1619	487	5	𝑞′𝜉	𝑞′𝜉	PROPN
cana-1619	487	6	:	:	PUNCT
cana-1619	487	7	[	[	X
cana-1619	487	8	0	0	NUM
cana-1619	487	9	,	,	PUNCT
cana-1619	487	10	𝜋	𝜋	NOUN
cana-1619	487	11	]	]	X
cana-1619	487	12	×	×	NOUN
cana-1619	487	13	[	[	X
cana-1619	487	14	0	0	NUM
cana-1619	487	15	,	,	PUNCT
cana-1619	487	16	𝜋	𝜋	NOUN
cana-1619	487	17	]	]	X
cana-1619	487	18	→	→	SYM
cana-1619	487	19	ℝ	ℝ	PROPN
cana-1619	487	20	,	,	PUNCT
cana-1619	487	21	𝑘	𝑘	NOUN
cana-1619	487	22	=	=	SYM
cana-1619	487	23	1,1	1,1	NUM
cana-1619	487	24	,	,	PUNCT
cana-1619	487	25	…	…	PUNCT
cana-1619	487	26	,	,	PUNCT
cana-1619	487	27	𝑚	𝑚	NOUN
cana-1619	487	28	,	,	PUNCT
cana-1619	487	29	are	be	AUX
cana-1619	487	30	continuously	continuously	ADV
cana-1619	487	31	differentiable	differentiable	ADJ
cana-1619	487	32	,	,	PUNCT
cana-1619	487	33	and	and	CCONJ
cana-1619	487	34	𝜓𝜉	𝜓𝜉	X
cana-1619	487	35	=	=	SYM
cana-1619	487	36	(	(	PUNCT
cana-1619	487	37	∫	∫	PROPN
cana-1619	487	38	𝜋	𝜋	NOUN
cana-1619	487	39	0	0	NUM
cana-1619	487	40	∫	∫	PROPN
cana-1619	487	41	𝜋	𝜋	NOUN
cana-1619	487	42	0	0	NUM
cana-1619	488	1	(	(	PUNCT
cana-1619	488	2	𝜕	𝜕	NOUN
cana-1619	488	3	𝜕𝑥	𝜕𝑥	X
cana-1619	488	4	𝑞𝜉(𝑥	𝑞𝜉(𝑥	PROPN
cana-1619	488	5	,	,	PUNCT
cana-1619	488	6	𝑦	𝑦	NOUN
cana-1619	488	7	)	)	PUNCT
cana-1619	488	8	)	)	PUNCT
cana-1619	488	9	2	2	NUM
cana-1619	488	10	𝑑𝑥𝑑𝑦	𝑑𝑥𝑑𝑦	X
cana-1619	488	11	)	)	PUNCT
cana-1619	488	12	1	1	NUM
cana-1619	488	13	2	2	NUM
cana-1619	488	14	<	<	X
cana-1619	488	15	∞	∞	NUM
cana-1619	488	16	𝜓′𝜉	𝜓′𝜉	NOUN
cana-1619	488	17	=	=	PUNCT
cana-1619	488	18	(	(	PUNCT
cana-1619	488	19	∫	∫	PROPN
cana-1619	488	20	𝜋	𝜋	NOUN
cana-1619	488	21	0	0	NUM
cana-1619	488	22	∫	∫	PROPN
cana-1619	488	23	𝜋	𝜋	NOUN
cana-1619	488	24	0	0	NUM
cana-1619	488	25	(	(	PUNCT
cana-1619	488	26	𝜕	𝜕	NOUN
cana-1619	488	27	𝜕𝑥	𝜕𝑥	X
cana-1619	488	28	𝑞′𝜉(𝑥	𝑞′𝜉(𝑥	NOUN
cana-1619	488	29	,	,	PUNCT
cana-1619	488	30	𝑦	𝑦	NOUN
cana-1619	488	31	)	)	PUNCT
cana-1619	488	32	)	)	PUNCT
cana-1619	488	33	2	2	NUM
cana-1619	488	34	𝑑𝑥𝑑𝑦	𝑑𝑥𝑑𝑦	X
cana-1619	488	35	)	)	PUNCT
cana-1619	488	36	1	1	NUM
cana-1619	488	37	2	2	NUM
cana-1619	488	38	<	<	X
cana-1619	488	39	∞	∞	PROPN
cana-1619	488	40	,	,	PUNCT
cana-1619	488	41	for	for	ADP
cana-1619	488	42	every	every	DET
cana-1619	488	43	𝜉	𝜉	X
cana-1619	488	44	=	=	SYM
cana-1619	488	45	1,2	1,2	NUM
cana-1619	488	46	,	,	PUNCT
cana-1619	488	47	…	…	PUNCT
cana-1619	488	48	,	,	PUNCT
cana-1619	488	49	𝑚.	𝑚.	ADJ
cana-1619	488	50	to	to	PART
cana-1619	488	51	address	address	VERB
cana-1619	488	52	this	this	DET
cana-1619	488	53	system	system	NOUN
cana-1619	488	54	,	,	PUNCT
cana-1619	488	55	we	we	PRON
cana-1619	488	56	introduce	introduce	VERB
cana-1619	488	57	the	the	DET
cana-1619	488	58	operators	operator	NOUN
cana-1619	488	59	in	in	ADP
cana-1619	488	60	the	the	DET
cana-1619	488	61	following	follow	VERB
cana-1619	488	62	manner	manner	NOUN
cana-1619	488	63	υ	υ	NOUN
cana-1619	488	64	:	:	PUNCT
cana-1619	488	65	𝐽	𝐽	PROPN
cana-1619	488	66	×	×	NOUN
cana-1619	488	67	𝐽	𝐽	NOUN
cana-1619	488	68	×	×	NOUN
cana-1619	488	69	𝒟	𝒟	NOUN
cana-1619	488	70	×	×	PROPN
cana-1619	488	71	ω	ω	PROPN
cana-1619	488	72	→	→	SYM
cana-1619	488	73	𝒮	𝒮	PROPN
cana-1619	488	74	,	,	PUNCT
cana-1619	488	75	and	and	CCONJ
cana-1619	488	76	𝜌	𝜌	ADP
cana-1619	488	77	:	:	PUNCT
cana-1619	488	78	𝐽	𝐽	PROPN
cana-1619	488	79	×	×	NOUN
cana-1619	488	80	𝒟	𝒟	NOUN
cana-1619	488	81	×	×	PROPN
cana-1619	488	82	ω	ω	PROPN
cana-1619	488	83	→	→	SYM
cana-1619	488	84	𝒮	𝒮	PROPN
cana-1619	488	85	,	,	PUNCT
cana-1619	488	86	𝜌(ℎ	𝜌(ℎ	PROPN
cana-1619	488	87	,	,	PUNCT
cana-1619	488	88	𝑧ℎ	𝑧ℎ	PROPN
cana-1619	488	89	(	(	PUNCT
cana-1619	488	90	.	.	PUNCT
cana-1619	488	91	,	,	PUNCT
cana-1619	488	92	ℵ	ℵ	NOUN
cana-1619	488	93	)	)	PUNCT
cana-1619	488	94	,	,	PUNCT
cana-1619	488	95	ℵ)(𝑥	ℵ)(𝑥	NUM
cana-1619	488	96	)	)	PUNCT
cana-1619	488	97	=	=	SYM
cana-1619	489	1	𝜌(ℎ	𝜌(ℎ	PROPN
cana-1619	489	2	,	,	PUNCT
cana-1619	489	3	𝑧(cosℎ	𝑧(cosℎ	PROPN
cana-1619	489	4	,	,	PUNCT
cana-1619	489	5	𝑥	𝑥	NOUN
cana-1619	489	6	,	,	PUNCT
cana-1619	489	7	ℵ	ℵ	NOUN
cana-1619	489	8	)	)	PUNCT
cana-1619	489	9	,	,	PUNCT
cana-1619	489	10	ℵ	ℵ	NOUN
cana-1619	489	11	)	)	PUNCT
cana-1619	489	12	υ(h	υ(h	NOUN
cana-1619	489	13	,	,	PUNCT
cana-1619	489	14	𝑧ℎ	𝑧ℎ	X
cana-1619	489	15	(	(	PUNCT
cana-1619	489	16	.	.	PUNCT
cana-1619	489	17	,	,	PUNCT
cana-1619	489	18	ℵ	ℵ	NOUN
cana-1619	489	19	)	)	PUNCT
cana-1619	489	20	,	,	PUNCT
cana-1619	489	21	ℵ)(𝑥	ℵ)(𝑥	NUM
cana-1619	489	22	)	)	PUNCT
cana-1619	489	23	=	=	SYM
cana-1619	489	24	υ(h	υ(h	X
cana-1619	489	25	,	,	PUNCT
cana-1619	489	26	𝑧(sinℎ	𝑧(sinℎ	PROPN
cana-1619	489	27	,	,	PUNCT
cana-1619	489	28	𝑥	𝑥	NOUN
cana-1619	489	29	,	,	PUNCT
cana-1619	489	30	ℵ	ℵ	NOUN
cana-1619	489	31	)	)	PUNCT
cana-1619	489	32	,	,	PUNCT
cana-1619	489	33	ℵ	ℵ	NOUN
cana-1619	489	34	)	)	PUNCT
cana-1619	489	35	𝐼𝜉(𝑧	𝐼𝜉(𝑧	NOUN
cana-1619	489	36	,	,	PUNCT
cana-1619	489	37	ℵ)(𝑥	ℵ)(𝑥	NUM
cana-1619	489	38	)	)	PUNCT
cana-1619	489	39	=	=	SYM
cana-1619	489	40	∫	∫	PROPN
cana-1619	489	41	𝜋	𝜋	NOUN
cana-1619	489	42	0	0	NUM
cana-1619	489	43	𝑞𝜉(𝑥	𝑞𝜉(𝑥	NUM
cana-1619	489	44	,	,	PUNCT
cana-1619	489	45	𝑦)𝑧(ℎ𝜉	𝑦)𝑧(ℎ𝜉	NOUN
cana-1619	489	46	,	,	PUNCT
cana-1619	489	47	𝑦	𝑦	X
cana-1619	489	48	,	,	PUNCT
cana-1619	489	49	ℵ)𝑑𝑦	ℵ)𝑑𝑦	PROPN
cana-1619	489	50	𝜉	𝜉	NOUN
cana-1619	489	51	=	=	SYM
cana-1619	489	52	1,2	1,2	NUM
cana-1619	489	53	,	,	PUNCT
cana-1619	489	54	.	.	PUNCT
cana-1619	489	55	.	.	PUNCT
cana-1619	489	56	.	.	PUNCT
cana-1619	490	1	,	,	PUNCT
cana-1619	490	2	𝑚	𝑚	ADP
cana-1619	490	3	𝐼′𝜉(𝑧	𝐼′𝜉(𝑧	NOUN
cana-1619	490	4	,	,	PUNCT
cana-1619	490	5	ℵ)(𝑥	ℵ)(𝑥	NUM
cana-1619	490	6	)	)	PUNCT
cana-1619	490	7	=	=	SYM
cana-1619	491	1	∫	∫	PROPN
cana-1619	491	2	𝜋	𝜋	NOUN
cana-1619	491	3	0	0	NUM
cana-1619	491	4	𝑞′𝜉(𝑥	𝑞′𝜉(𝑥	X
cana-1619	491	5	,	,	PUNCT
cana-1619	491	6	𝑦)𝑧(ℎ𝜉	𝑦)𝑧(ℎ𝜉	NOUN
cana-1619	491	7	,	,	PUNCT
cana-1619	491	8	𝑦	𝑦	X
cana-1619	491	9	,	,	PUNCT
cana-1619	491	10	ℵ)𝑑𝑦	ℵ)𝑑𝑦	PROPN
cana-1619	491	11	𝜉	𝜉	NOUN
cana-1619	491	12	=	=	SYM
cana-1619	491	13	1,2	1,2	NUM
cana-1619	491	14	,	,	PUNCT
cana-1619	491	15	.	.	PUNCT
cana-1619	491	16	.	.	PUNCT
cana-1619	492	1	.	.	PUNCT
cana-1619	493	1	,	,	PUNCT
cana-1619	493	2	𝑚.	𝑚.	ADV
cana-1619	493	3	sure	sure	ADV
cana-1619	493	4	,	,	PUNCT
cana-1619	493	5	here	here	ADV
cana-1619	493	6	’s	’	VERB
cana-1619	493	7	a	a	DET
cana-1619	493	8	simplified	simplified	ADJ
cana-1619	493	9	version	version	NOUN
cana-1619	493	10	:	:	PUNCT
cana-1619	493	11	the	the	DET
cana-1619	493	12	equations	equation	NOUN
cana-1619	493	13	(	(	PUNCT
cana-1619	493	14	5.13	5.13	NUM
cana-1619	493	15	-	-	SYM
cana-1619	493	16	5.16	5.16	NUM
cana-1619	493	17	)	)	PUNCT
cana-1619	493	18	can	can	AUX
cana-1619	493	19	be	be	AUX
cana-1619	493	20	transformed	transform	VERB
cana-1619	493	21	into	into	ADP
cana-1619	493	22	a	a	DET
cana-1619	493	23	more	more	ADV
cana-1619	493	24	general	general	ADJ
cana-1619	493	25	form	form	NOUN
cana-1619	493	26	,	,	PUNCT
cana-1619	493	27	denoted	denote	VERB
cana-1619	493	28	as	as	ADP
cana-1619	493	29	(	(	PUNCT
cana-1619	493	30	1.1	1.1	NUM
cana-1619	493	31	)	)	PUNCT
cana-1619	493	32	.	.	PUNCT
cana-1619	494	1	by	by	ADP
cana-1619	494	2	using	use	VERB
cana-1619	494	3	the	the	DET
cana-1619	494	4	functions	function	NOUN
cana-1619	494	5	mentioned	mention	VERB
cana-1619	494	6	earlier	early	ADV
cana-1619	494	7	,	,	PUNCT
cana-1619	494	8	we	we	PRON
cana-1619	494	9	meet	meet	VERB
cana-1619	494	10	the	the	DET
cana-1619	494	11	requirements	requirement	NOUN
cana-1619	494	12	stated	state	VERB
cana-1619	494	13	in	in	ADP
cana-1619	494	14	theorem	theorem	NOUN
cana-1619	494	15	3.1	3.1	NUM
cana-1619	494	16	.	.	PUNCT
cana-1619	495	1	therefore	therefore	ADV
cana-1619	495	2	,	,	PUNCT
cana-1619	495	3	according	accord	VERB
cana-1619	495	4	to	to	ADP
cana-1619	495	5	theorem	theorem	NOUN
cana-1619	495	6	3.1	3.1	NUM
cana-1619	495	7	,	,	PUNCT
cana-1619	495	8	we	we	PRON
cana-1619	495	9	can	can	AUX
cana-1619	495	10	conclude	conclude	VERB
cana-1619	495	11	that	that	SCONJ
cana-1619	495	12	the	the	DET
cana-1619	495	13	given	give	VERB
cana-1619	495	14	nonlocal	nonlocal	ADJ
cana-1619	495	15	impulsive	impulsive	ADJ
cana-1619	495	16	cauchy	cauchy	ADJ
cana-1619	495	17	problem	problem	NOUN
cana-1619	495	18	(	(	PUNCT
cana-1619	495	19	5.13	5.13	NUM
cana-1619	495	20	-	-	SYM
cana-1619	495	21	5.16	5.16	NUM
cana-1619	495	22	)	)	PUNCT
cana-1619	495	23	has	have	VERB
cana-1619	495	24	a	a	DET
cana-1619	495	25	mild	mild	ADJ
cana-1619	495	26	solution	solution	NOUN
cana-1619	495	27	over	over	ADP
cana-1619	495	28	the	the	DET
cana-1619	495	29	interval	interval	NOUN
cana-1619	495	30	𝐽.	𝐽.	PROPN
cana-1619	495	31	6	6	NUM
cana-1619	495	32	conclusion	conclusion	NOUN
cana-1619	495	33	this	this	DET
cana-1619	495	34	study	study	NOUN
cana-1619	495	35	delves	delve	VERB
cana-1619	495	36	into	into	ADP
cana-1619	495	37	a	a	DET
cana-1619	495	38	specific	specific	ADJ
cana-1619	495	39	class	class	NOUN
cana-1619	495	40	of	of	ADP
cana-1619	495	41	mathematical	mathematical	ADJ
cana-1619	495	42	problems	problem	NOUN
cana-1619	495	43	concerning	concern	VERB
cana-1619	495	44	second	second	ADJ
cana-1619	495	45	-	-	PUNCT
cana-1619	495	46	order	order	NOUN
cana-1619	495	47	equations	equation	NOUN
cana-1619	495	48	with	with	ADP
cana-1619	495	49	delays	delay	NOUN
cana-1619	495	50	,	,	PUNCT
cana-1619	495	51	a	a	DET
cana-1619	495	52	topic	topic	NOUN
cana-1619	495	53	widespread	widespread	ADJ
cana-1619	495	54	in	in	ADP
cana-1619	495	55	scientific	scientific	ADJ
cana-1619	495	56	and	and	CCONJ
cana-1619	495	57	engineering	engineering	NOUN
cana-1619	495	58	disciplines	discipline	NOUN
cana-1619	495	59	.	.	PUNCT
cana-1619	496	1	by	by	ADP
cana-1619	496	2	situating	situate	VERB
cana-1619	496	3	these	these	DET
cana-1619	496	4	equations	equation	NOUN
cana-1619	496	5	within	within	ADP
cana-1619	496	6	the	the	DET
cana-1619	496	7	realm	realm	NOUN
cana-1619	496	8	of	of	ADP
cana-1619	496	9	banach	banach	NOUN
cana-1619	496	10	spaces	space	NOUN
cana-1619	496	11	,	,	PUNCT
cana-1619	496	12	distinct	distinct	ADJ
cana-1619	496	13	challenges	challenge	NOUN
cana-1619	496	14	and	and	CCONJ
cana-1619	496	15	pathways	pathway	NOUN
cana-1619	496	16	for	for	ADP
cana-1619	496	17	analysis	analysis	NOUN
cana-1619	496	18	and	and	CCONJ
cana-1619	496	19	control	control	NOUN
cana-1619	496	20	are	be	AUX
cana-1619	496	21	uncovered	uncover	VERB
cana-1619	496	22	.	.	PUNCT
cana-1619	497	1	through	through	ADP
cana-1619	497	2	rigorous	rigorous	ADJ
cana-1619	497	3	examination	examination	NOUN
cana-1619	497	4	of	of	ADP
cana-1619	497	5	the	the	DET
cana-1619	497	6	existence	existence	NOUN
cana-1619	497	7	and	and	CCONJ
cana-1619	497	8	approximate	approximate	ADJ
cana-1619	497	9	controllability	controllability	NOUN
cana-1619	497	10	of	of	ADP
cana-1619	497	11	solutions	solution	NOUN
cana-1619	497	12	,	,	PUNCT
cana-1619	497	13	this	this	DET
cana-1619	497	14	research	research	NOUN
cana-1619	497	15	significantly	significantly	ADV
cana-1619	497	16	contributes	contribute	VERB
cana-1619	497	17	to	to	ADP
cana-1619	497	18	understanding	understand	VERB
cana-1619	497	19	dynamical	dynamical	ADJ
cana-1619	497	20	systems	system	NOUN
cana-1619	497	21	with	with	ADP
cana-1619	497	22	delayed	delay	VERB
cana-1619	497	23	communications	communication	NOUN
cana-1619	497	24	on	on	ADP
cana-1619	497	25	applied	apply	VERB
cana-1619	497	26	nonlinear	nonlinear	ADJ
cana-1619	497	27	analysis	analysis	NOUN
cana-1619	497	28	issn	issn	NOUN
cana-1619	497	29	:	:	PUNCT
cana-1619	497	30	1074	1074	NUM
cana-1619	497	31	-	-	PUNCT
cana-1619	497	32	133x	133x	NUM
cana-1619	497	33	vol	vol	NOUN
cana-1619	497	34	32	32	NUM
cana-1619	497	35	no	no	NOUN
cana-1619	497	36	.	.	NOUN
cana-1619	497	37	1	1	NUM
cana-1619	497	38	(	(	PUNCT
cana-1619	497	39	2025	2025	NUM
cana-1619	497	40	)	)	PUNCT
cana-1619	497	41	54	54	NUM
cana-1619	497	42	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	497	43	feedback	feedback	NOUN
cana-1619	497	44	.	.	PUNCT
cana-1619	498	1	mathematical	mathematical	ADJ
cana-1619	498	2	tools	tool	NOUN
cana-1619	498	3	such	such	ADJ
cana-1619	498	4	as	as	ADP
cana-1619	498	5	cosine	cosine	NOUN
cana-1619	498	6	family	family	NOUN
cana-1619	498	7	theory	theory	NOUN
cana-1619	498	8	and	and	CCONJ
cana-1619	498	9	the	the	DET
cana-1619	498	10	leray	leray	ADJ
cana-1619	498	11	-	-	PUNCT
cana-1619	498	12	schauder	schauder	NOUN
cana-1619	498	13	theorem	theorem	NOUN
cana-1619	498	14	are	be	AUX
cana-1619	498	15	leveraged	leverage	VERB
cana-1619	498	16	to	to	PART
cana-1619	498	17	establish	establish	VERB
cana-1619	498	18	stringent	stringent	ADJ
cana-1619	498	19	conditions	condition	NOUN
cana-1619	498	20	for	for	ADP
cana-1619	498	21	solution	solution	NOUN
cana-1619	498	22	existence	existence	NOUN
cana-1619	498	23	,	,	PUNCT
cana-1619	498	24	with	with	ADP
cana-1619	498	25	implications	implication	NOUN
cana-1619	498	26	for	for	ADP
cana-1619	498	27	theoretical	theoretical	ADJ
cana-1619	498	28	advancements	advancement	NOUN
cana-1619	498	29	and	and	CCONJ
cana-1619	498	30	practical	practical	ADJ
cana-1619	498	31	applications	application	NOUN
cana-1619	498	32	.	.	PUNCT
cana-1619	499	1	moreover	moreover	ADV
cana-1619	499	2	,	,	PUNCT
cana-1619	499	3	empirical	empirical	ADJ
cana-1619	499	4	validation	validation	NOUN
cana-1619	499	5	through	through	ADP
cana-1619	499	6	a	a	DET
cana-1619	499	7	practical	practical	ADJ
cana-1619	499	8	example	example	NOUN
cana-1619	499	9	provides	provide	VERB
cana-1619	499	10	invaluable	invaluable	ADJ
cana-1619	499	11	insights	insight	NOUN
cana-1619	499	12	into	into	ADP
cana-1619	499	13	the	the	DET
cana-1619	499	14	behavior	behavior	NOUN
cana-1619	499	15	of	of	ADP
cana-1619	499	16	these	these	DET
cana-1619	499	17	equations	equation	NOUN
cana-1619	499	18	in	in	ADP
cana-1619	499	19	real	real	ADJ
cana-1619	499	20	-	-	PUNCT
cana-1619	499	21	world	world	NOUN
cana-1619	499	22	scenarios	scenario	NOUN
cana-1619	499	23	,	,	PUNCT
cana-1619	499	24	effectively	effectively	ADV
cana-1619	499	25	bridging	bridge	VERB
cana-1619	499	26	the	the	DET
cana-1619	499	27	gap	gap	NOUN
cana-1619	499	28	between	between	ADP
cana-1619	499	29	theory	theory	NOUN
cana-1619	499	30	and	and	CCONJ
cana-1619	499	31	application	application	NOUN
cana-1619	499	32	.	.	PUNCT
cana-1619	500	1	this	this	DET
cana-1619	500	2	comprehensive	comprehensive	ADJ
cana-1619	500	3	investigation	investigation	NOUN
cana-1619	500	4	advances	advance	VERB
cana-1619	500	5	understanding	understanding	NOUN
cana-1619	500	6	of	of	ADP
cana-1619	500	7	complex	complex	ADJ
cana-1619	500	8	dynamical	dynamical	ADJ
cana-1619	500	9	systems	system	NOUN
cana-1619	500	10	with	with	ADP
cana-1619	500	11	delayed	delay	VERB
cana-1619	500	12	feedback	feedback	NOUN
cana-1619	500	13	and	and	CCONJ
cana-1619	500	14	offers	offer	VERB
cana-1619	500	15	practical	practical	ADJ
cana-1619	500	16	insights	insight	NOUN
cana-1619	500	17	for	for	ADP
cana-1619	500	18	developing	develop	VERB
cana-1619	500	19	robust	robust	ADJ
cana-1619	500	20	control	control	NOUN
cana-1619	500	21	strategies	strategy	NOUN
cana-1619	500	22	and	and	CCONJ
cana-1619	500	23	engineering	engineering	NOUN
cana-1619	500	24	solutions	solution	NOUN
cana-1619	500	25	across	across	ADP
cana-1619	500	26	various	various	ADJ
cana-1619	500	27	domains	domain	NOUN
cana-1619	500	28	.	.	PUNCT
cana-1619	501	1	references	reference	NOUN
cana-1619	501	2	[	[	X
cana-1619	501	3	1	1	NUM
cana-1619	501	4	]	]	PUNCT
cana-1619	501	5	ahmed	ahmed	PROPN
cana-1619	501	6	,	,	PUNCT
cana-1619	501	7	n.	n.	PROPN
cana-1619	501	8	u.	u.	PROPN
cana-1619	501	9	(	(	PUNCT
cana-1619	501	10	1991	1991	NUM
cana-1619	501	11	)	)	PUNCT
cana-1619	501	12	.	.	PUNCT
cana-1619	502	1	semigroup	semigroup	PROPN
cana-1619	502	2	theory	theory	NOUN
cana-1619	502	3	with	with	ADP
cana-1619	502	4	applications	application	NOUN
cana-1619	502	5	to	to	ADP
cana-1619	502	6	systems	system	NOUN
cana-1619	502	7	and	and	CCONJ
cana-1619	502	8	control	control	NOUN
cana-1619	502	9	.	.	PUNCT
cana-1619	503	1	new	new	PROPN
cana-1619	503	2	york	york	PROPN
cana-1619	503	3	:	:	PUNCT
cana-1619	503	4	wiley	wiley	PROPN
cana-1619	503	5	.	.	PUNCT
cana-1619	504	1	[	[	X
cana-1619	504	2	2	2	NUM
cana-1619	504	3	]	]	SYM
cana-1619	504	4	baghli	baghli	NOUN
cana-1619	504	5	,	,	PUNCT
cana-1619	504	6	s.	s.	PROPN
cana-1619	504	7	,	,	PUNCT
cana-1619	504	8	&	&	CCONJ
cana-1619	504	9	benchohra	benchohra	NOUN
cana-1619	504	10	,	,	PUNCT
cana-1619	504	11	m.	m.	NOUN
cana-1619	504	12	(	(	PUNCT
cana-1619	504	13	2008	2008	NUM
cana-1619	504	14	)	)	PUNCT
cana-1619	504	15	.	.	PUNCT
cana-1619	505	1	uniqueness	uniqueness	NOUN
cana-1619	505	2	results	result	NOUN
cana-1619	505	3	for	for	ADP
cana-1619	505	4	partial	partial	ADJ
cana-1619	505	5	functional	functional	ADJ
cana-1619	505	6	differential	differential	ADJ
cana-1619	505	7	equations	equation	NOUN
cana-1619	505	8	in	in	ADP
cana-1619	505	9	frechet	frechet	PROPN
cana-1619	505	10	spaces	space	NOUN
cana-1619	505	11	.	.	PUNCT
cana-1619	506	1	fixed	fix	VERB
cana-1619	506	2	point	point	NOUN
cana-1619	506	3	theory	theory	NOUN
cana-1619	506	4	,	,	PUNCT
cana-1619	506	5	9	9	NUM
cana-1619	506	6	,	,	PUNCT
cana-1619	506	7	395406	395406	NUM
cana-1619	506	8	.	.	PUNCT
cana-1619	507	1	[	[	X
cana-1619	507	2	3	3	NUM
cana-1619	507	3	]	]	X
cana-1619	507	4	dhage	dhage	NOUN
cana-1619	507	5	,	,	PUNCT
cana-1619	507	6	b.	b.	PROPN
cana-1619	507	7	c.	c.	PROPN
cana-1619	507	8	,	,	PUNCT
cana-1619	507	9	&	&	CCONJ
cana-1619	507	10	ntouyas	ntouyas	PROPN
cana-1619	507	11	,	,	PUNCT
cana-1619	507	12	s.	s.	PROPN
cana-1619	507	13	k.	k.	PROPN
cana-1619	507	14	(	(	PUNCT
cana-1619	507	15	2010	2010	NUM
cana-1619	507	16	)	)	PUNCT
cana-1619	507	17	.	.	PUNCT
cana-1619	508	1	existence	existence	NOUN
cana-1619	508	2	and	and	CCONJ
cana-1619	508	3	attractivity	attractivity	NOUN
cana-1619	508	4	results	result	NOUN
cana-1619	508	5	for	for	ADP
cana-1619	508	6	nonlinear	nonlinear	ADJ
cana-1619	508	7	first	first	ADJ
cana-1619	508	8	order	order	NOUN
cana-1619	508	9	random	random	ADJ
cana-1619	508	10	differential	differential	NOUN
cana-1619	508	11	equations	equation	NOUN
cana-1619	508	12	.	.	PUNCT
cana-1619	509	1	opuscula	opuscula	PROPN
cana-1619	509	2	math	math	PROPN
cana-1619	509	3	.	.	PUNCT
cana-1619	509	4	,	,	PUNCT
cana-1619	509	5	30	30	NUM
cana-1619	509	6	,	,	PUNCT
cana-1619	509	7	411	411	NUM
cana-1619	509	8	-	-	SYM
cana-1619	509	9	429	429	NUM
cana-1619	509	10	.	.	PUNCT
cana-1619	510	1	[	[	X
cana-1619	510	2	4	4	NUM
cana-1619	510	3	]	]	PUNCT
cana-1619	510	4	dhage	dhage	NOUN
cana-1619	510	5	,	,	PUNCT
cana-1619	510	6	b.	b.	PROPN
cana-1619	510	7	c.	c.	PROPN
cana-1619	510	8	(	(	PUNCT
cana-1619	510	9	2009	2009	NUM
cana-1619	510	10	)	)	PUNCT
cana-1619	510	11	.	.	PUNCT
cana-1619	511	1	on	on	ADP
cana-1619	511	2	global	global	ADJ
cana-1619	511	3	existence	existence	NOUN
cana-1619	511	4	and	and	CCONJ
cana-1619	511	5	attractivity	attractivity	NOUN
cana-1619	511	6	results	result	NOUN
cana-1619	511	7	for	for	ADP
cana-1619	511	8	nonlinear	nonlinear	ADJ
cana-1619	511	9	random	random	ADJ
cana-1619	511	10	integral	integral	ADJ
cana-1619	511	11	equations	equation	NOUN
cana-1619	511	12	.	.	PUNCT
cana-1619	512	1	panamer	panamer	PROPN
cana-1619	512	2	.	.	PUNCT
cana-1619	512	3	math	math	PROPN
cana-1619	512	4	.	.	PUNCT
cana-1619	513	1	j.	j.	PROPN
cana-1619	513	2	,	,	PUNCT
cana-1619	513	3	19	19	NUM
cana-1619	513	4	,	,	PUNCT
cana-1619	513	5	97	97	NUM
cana-1619	513	6	-	-	SYM
cana-1619	513	7	111	111	NUM
cana-1619	513	8	.	.	PUNCT
cana-1619	514	1	[	[	X
cana-1619	514	2	5	5	NUM
cana-1619	514	3	]	]	X
cana-1619	514	4	lupulescu	lupulescu	NOUN
cana-1619	514	5	,	,	PUNCT
cana-1619	514	6	v.	v.	ADV
cana-1619	514	7	,	,	PUNCT
cana-1619	514	8	&	&	CCONJ
cana-1619	514	9	lungan	lungan	PROPN
cana-1619	514	10	,	,	PUNCT
cana-1619	514	11	c.	c.	PROPN
cana-1619	514	12	(	(	PUNCT
cana-1619	514	13	2013	2013	NUM
cana-1619	514	14	)	)	PUNCT
cana-1619	514	15	.	.	PUNCT
cana-1619	515	1	random	random	ADJ
cana-1619	515	2	integral	integral	ADJ
cana-1619	515	3	equations	equation	NOUN
cana-1619	515	4	on	on	ADP
cana-1619	515	5	time	time	NOUN
cana-1619	515	6	scales	scale	NOUN
cana-1619	515	7	.	.	PUNCT
cana-1619	516	1	opuscula	opuscula	PROPN
cana-1619	516	2	math	math	PROPN
cana-1619	516	3	.	.	PUNCT
cana-1619	516	4	,	,	PUNCT
cana-1619	516	5	33	33	NUM
cana-1619	516	6	,	,	PUNCT
cana-1619	516	7	323?335	323?335	NOUN
cana-1619	516	8	.	.	PUNCT
cana-1619	517	1	[	[	X
cana-1619	517	2	6	6	NUM
cana-1619	517	3	]	]	X
cana-1619	517	4	pazy	pazy	NOUN
cana-1619	517	5	,	,	PUNCT
cana-1619	517	6	a.	a.	NOUN
cana-1619	517	7	(	(	PUNCT
cana-1619	517	8	1983	1983	NUM
cana-1619	517	9	)	)	PUNCT
cana-1619	517	10	.	.	PUNCT
cana-1619	518	1	semigroups	semigroup	NOUN
cana-1619	518	2	of	of	ADP
cana-1619	518	3	linear	linear	PROPN
cana-1619	518	4	operators	operator	NOUN
cana-1619	518	5	and	and	CCONJ
cana-1619	518	6	applications	application	NOUN
cana-1619	518	7	to	to	ADP
cana-1619	518	8	partial	partial	ADJ
cana-1619	518	9	differential	differential	NOUN
cana-1619	518	10	equations	equation	NOUN
cana-1619	518	11	.	.	PUNCT
cana-1619	519	1	new	new	PROPN
cana-1619	519	2	york	york	PROPN
cana-1619	519	3	:	:	PUNCT
cana-1619	519	4	springer	springer	NOUN
cana-1619	519	5	-	-	PUNCT
cana-1619	519	6	verlag	verlag	PROPN
cana-1619	519	7	.	.	PUNCT
cana-1619	520	1	[	[	X
cana-1619	520	2	7	7	X
cana-1619	520	3	]	]	PUNCT
cana-1619	520	4	tsokos	tsokos	ADJ
cana-1619	520	5	,	,	PUNCT
cana-1619	520	6	c.	c.	PROPN
cana-1619	520	7	p.	p.	PROPN
cana-1619	520	8	,	,	PUNCT
cana-1619	520	9	&	&	CCONJ
cana-1619	520	10	padgett	padgett	PROPN
cana-1619	520	11	,	,	PUNCT
cana-1619	520	12	w.	w.	PROPN
cana-1619	520	13	j.	j.	PROPN
cana-1619	520	14	(	(	PUNCT
cana-1619	520	15	1974	1974	NUM
cana-1619	520	16	)	)	PUNCT
cana-1619	520	17	.	.	PUNCT
cana-1619	521	1	random	random	ADJ
cana-1619	521	2	integral	integral	ADJ
cana-1619	521	3	equations	equation	NOUN
cana-1619	521	4	with	with	ADP
cana-1619	521	5	applications	application	NOUN
cana-1619	521	6	in	in	ADP
cana-1619	521	7	life	life	NOUN
cana-1619	521	8	sciences	science	NOUN
cana-1619	521	9	and	and	CCONJ
cana-1619	521	10	engineering	engineering	NOUN
cana-1619	521	11	.	.	PUNCT
cana-1619	522	1	new	new	PROPN
cana-1619	522	2	york	york	PROPN
cana-1619	522	3	:	:	PUNCT
cana-1619	523	1	academic	academic	ADJ
cana-1619	523	2	.	.	PUNCT
cana-1619	524	1	[	[	X
cana-1619	524	2	8	8	NUM
cana-1619	524	3	]	]	X
cana-1619	524	4	reddy	reddy	PROPN
cana-1619	524	5	cs	cs	PROPN
cana-1619	524	6	,	,	PUNCT
cana-1619	524	7	yookesh	yookesh	PROPN
cana-1619	524	8	tl	tl	PROPN
cana-1619	524	9	,	,	PUNCT
cana-1619	524	10	kumar	kumar	PROPN
cana-1619	524	11	eb	eb	PROPN
cana-1619	524	12	.	.	PUNCT
cana-1619	525	1	a	a	DET
cana-1619	525	2	study	study	NOUN
cana-1619	525	3	on	on	ADP
cana-1619	525	4	convergence	convergence	NOUN
cana-1619	525	5	analysis	analysis	NOUN
cana-1619	525	6	of	of	ADP
cana-1619	525	7	runge	runge	NOUN
cana-1619	525	8	-	-	PUNCT
cana-1619	525	9	kutta	kutta	NOUN
cana-1619	525	10	fehlberg	fehlberg	NOUN
cana-1619	525	11	method	method	NOUN
cana-1619	525	12	to	to	PART
cana-1619	525	13	solve	solve	VERB
cana-1619	525	14	fuzzy	fuzzy	ADJ
cana-1619	525	15	delay	delay	NOUN
cana-1619	525	16	differential	differential	ADJ
cana-1619	525	17	equations	equation	NOUN
cana-1619	525	18	.	.	PUNCT
cana-1619	526	1	journal	journal	NOUN
cana-1619	526	2	of	of	ADP
cana-1619	526	3	algebraic	algebraic	PROPN
cana-1619	526	4	statistics	statistic	NOUN
cana-1619	526	5	.	.	PUNCT
cana-1619	527	1	2022	2022	NUM
cana-1619	527	2	jun	jun	PROPN
cana-1619	527	3	4;13(2):2832	4;13(2):2832	NUM
cana-1619	527	4	-	-	SYM
cana-1619	527	5	8	8	NUM
cana-1619	527	6	.	.	PUNCT
cana-1619	528	1	[	[	X
cana-1619	528	2	9	9	NUM
cana-1619	528	3	]	]	X
cana-1619	528	4	dhakne	dhakne	NOUN
cana-1619	528	5	,	,	PUNCT
cana-1619	528	6	m.	m.	PROPN
cana-1619	528	7	b.	b.	PROPN
cana-1619	528	8	,	,	PUNCT
cana-1619	528	9	&	&	CCONJ
cana-1619	528	10	kucche	kucche	PROPN
cana-1619	528	11	,	,	PUNCT
cana-1619	528	12	k.	k.	PROPN
cana-1619	528	13	d.	d.	PROPN
cana-1619	528	14	(	(	PUNCT
cana-1619	528	15	2012	2012	NUM
cana-1619	528	16	)	)	PUNCT
cana-1619	528	17	.	.	PUNCT
cana-1619	529	1	second	second	ADJ
cana-1619	529	2	order	order	NOUN
cana-1619	529	3	volterra	volterra	NOUN
cana-1619	529	4	-	-	PUNCT
cana-1619	529	5	fredholm	fredholm	NOUN
cana-1619	529	6	functional	functional	ADJ
cana-1619	529	7	integrodifferential	integrodifferential	ADJ
cana-1619	529	8	equations	equation	NOUN
cana-1619	529	9	.	.	PUNCT
cana-1619	530	1	malaya	malaya	PROPN
cana-1619	530	2	journal	journal	PROPN
cana-1619	530	3	of	of	ADP
cana-1619	530	4	mathematics	mathematic	NOUN
cana-1619	530	5	,	,	PUNCT
cana-1619	530	6	1(1	1(1	NUM
cana-1619	530	7	)	)	PUNCT
cana-1619	530	8	,	,	PUNCT
cana-1619	530	9	1?8	1?8	NOUN
cana-1619	530	10	.	.	PUNCT
cana-1619	531	1	[	[	X
cana-1619	531	2	10	10	NUM
cana-1619	531	3	]	]	X
cana-1619	531	4	tidke	tidke	ADJ
cana-1619	531	5	,	,	PUNCT
cana-1619	531	6	h.	h.	PROPN
cana-1619	531	7	l.	l.	PROPN
cana-1619	531	8	,	,	PUNCT
cana-1619	531	9	&	&	CCONJ
cana-1619	531	10	dhakne	dhakne	PROPN
cana-1619	531	11	,	,	PUNCT
cana-1619	531	12	m.	m.	PROPN
cana-1619	531	13	b.	b.	PROPN
cana-1619	531	14	(	(	PUNCT
cana-1619	531	15	2010	2010	NUM
cana-1619	531	16	)	)	PUNCT
cana-1619	531	17	.	.	PUNCT
cana-1619	531	18	existence	existence	NOUN
cana-1619	531	19	and	and	CCONJ
cana-1619	531	20	uniqueness	uniqueness	NOUN
cana-1619	531	21	of	of	ADP
cana-1619	531	22	solutions	solution	NOUN
cana-1619	531	23	of	of	ADP
cana-1619	531	24	certain	certain	ADJ
cana-1619	531	25	second	second	ADJ
cana-1619	531	26	order	order	NOUN
cana-1619	531	27	nonlinear	nonlinear	ADJ
cana-1619	531	28	equations	equation	NOUN
cana-1619	531	29	.	.	PUNCT
cana-1619	532	1	note	note	VERB
cana-1619	532	2	de	de	PROPN
cana-1619	532	3	mathematica	mathematica	PROPN
cana-1619	532	4	,	,	PUNCT
cana-1619	532	5	30(2	30(2	NUM
cana-1619	532	6	)	)	PUNCT
cana-1619	532	7	,	,	PUNCT
cana-1619	533	1	73?81	73?81	X
cana-1619	533	2	.	.	PUNCT
cana-1619	534	1	[	[	X
cana-1619	534	2	11	11	NUM
cana-1619	534	3	]	]	X
cana-1619	534	4	pavlackova	pavlackova	PROPN
cana-1619	534	5	,	,	PUNCT
cana-1619	534	6	m.	m.	NOUN
cana-1619	534	7	,	,	PUNCT
cana-1619	534	8	&	&	CCONJ
cana-1619	534	9	taddei	taddei	PROPN
cana-1619	534	10	,	,	PUNCT
cana-1619	534	11	v.	v.	PROPN
cana-1619	534	12	(	(	PUNCT
cana-1619	534	13	2022	2022	NUM
cana-1619	534	14	)	)	PUNCT
cana-1619	534	15	.	.	PUNCT
cana-1619	535	1	mild	mild	ADJ
cana-1619	535	2	solutions	solution	NOUN
cana-1619	535	3	of	of	ADP
cana-1619	535	4	second	second	ADJ
cana-1619	535	5	-	-	PUNCT
cana-1619	535	6	order	order	NOUN
cana-1619	535	7	semilinear	semilinear	ADJ
cana-1619	535	8	impulsive	impulsive	ADJ
cana-1619	535	9	differential	differential	ADJ
cana-1619	535	10	inclusions	inclusion	NOUN
cana-1619	535	11	in	in	ADP
cana-1619	535	12	banach	banach	NOUN
cana-1619	535	13	spaces	space	NOUN
cana-1619	535	14	,	,	PUNCT
cana-1619	535	15	10	10	NUM
cana-1619	535	16	,	,	PUNCT
cana-1619	535	17	672	672	NUM
cana-1619	535	18	.	.	PUNCT
cana-1619	536	1	[	[	X
cana-1619	536	2	12	12	NUM
cana-1619	536	3	]	]	X
cana-1619	536	4	suresh	suresh	PROPN
cana-1619	536	5	,	,	PUNCT
cana-1619	536	6	m.	m.	PROPN
cana-1619	536	7	l.	l.	PROPN
cana-1619	536	8	,	,	PUNCT
cana-1619	536	9	gunasekar	gunasekar	PROPN
cana-1619	536	10	,	,	PUNCT
cana-1619	536	11	t.	t.	PROPN
cana-1619	536	12	,	,	PUNCT
cana-1619	536	13	&	&	CCONJ
cana-1619	536	14	samuel	samuel	PROPN
cana-1619	536	15	,	,	PUNCT
cana-1619	536	16	f.	f.	PROPN
cana-1619	536	17	p.	p.	PROPN
cana-1619	536	18	(	(	PUNCT
cana-1619	536	19	2017	2017	NUM
cana-1619	536	20	)	)	PUNCT
cana-1619	536	21	.	.	PUNCT
cana-1619	537	1	existence	existence	NOUN
cana-1619	537	2	results	result	VERB
cana-1619	537	3	for	for	ADP
cana-1619	537	4	nonlocal	nonlocal	ADJ
cana-1619	537	5	impulsive	impulsive	ADJ
cana-1619	537	6	neutral	neutral	ADJ
cana-1619	537	7	functional	functional	ADJ
cana-1619	537	8	integro	integro	ADJ
cana-1619	537	9	-	-	PUNCT
cana-1619	537	10	differential	differential	NOUN
cana-1619	537	11	equations	equation	NOUN
cana-1619	537	12	.	.	PUNCT
cana-1619	538	1	international	international	ADJ
cana-1619	538	2	journal	journal	NOUN
cana-1619	538	3	of	of	ADP
cana-1619	538	4	pure	pure	ADJ
cana-1619	538	5	and	and	CCONJ
cana-1619	538	6	applied	applied	ADJ
cana-1619	538	7	mathematics	mathematic	NOUN
cana-1619	538	8	,	,	PUNCT
cana-1619	538	9	116(23	116(23	NOUN
cana-1619	538	10	)	)	PUNCT
cana-1619	538	11	,	,	PUNCT
cana-1619	538	12	337	337	NUM
cana-1619	538	13	-	-	SYM
cana-1619	538	14	345	345	NUM
cana-1619	538	15	.	.	PUNCT
cana-1619	539	1	[	[	X
cana-1619	539	2	13	13	NUM
cana-1619	539	3	]	]	X
cana-1619	539	4	dhakne	dhakne	NOUN
cana-1619	539	5	,	,	PUNCT
cana-1619	539	6	m.	m.	PROPN
cana-1619	539	7	b.	b.	PROPN
cana-1619	539	8	,	,	PUNCT
cana-1619	539	9	&	&	CCONJ
cana-1619	539	10	kucche	kucche	PROPN
cana-1619	539	11	,	,	PUNCT
cana-1619	539	12	k.	k.	PROPN
cana-1619	539	13	d.	d.	PROPN
cana-1619	539	14	(	(	PUNCT
cana-1619	539	15	2012	2012	NUM
cana-1619	539	16	)	)	PUNCT
cana-1619	539	17	.	.	PUNCT
cana-1619	540	1	global	global	ADJ
cana-1619	540	2	existence	existence	NOUN
cana-1619	540	3	for	for	ADP
cana-1619	540	4	abstract	abstract	ADJ
cana-1619	540	5	nonlinear	nonlinear	PROPN
cana-1619	540	6	volterra	volterra	PROPN
cana-1619	540	7	fredholm	fredholm	PROPN
cana-1619	540	8	functional	functional	ADJ
cana-1619	540	9	integrodifferential	integrodifferential	ADJ
cana-1619	540	10	equation	equation	NOUN
cana-1619	540	11	.	.	PUNCT
cana-1619	541	1	demonstratio	demonstratio	PROPN
cana-1619	541	2	mathematica	mathematica	PROPN
cana-1619	541	3	,	,	PUNCT
cana-1619	541	4	45(1	45(1	NOUN
cana-1619	541	5	)	)	PUNCT
cana-1619	541	6	,	,	PUNCT
cana-1619	541	7	117	117	NUM
cana-1619	541	8	-	-	SYM
cana-1619	541	9	127	127	NUM
cana-1619	541	10	.	.	PUNCT
cana-1619	542	1	[	[	X
cana-1619	542	2	14	14	NUM
cana-1619	542	3	]	]	X
cana-1619	542	4	yookesh	yookesh	ADJ
cana-1619	542	5	,	,	PUNCT
cana-1619	542	6	t.	t.	PROPN
cana-1619	542	7	l.	l.	PROPN
cana-1619	542	8	,	,	PUNCT
cana-1619	542	9	et	et	PROPN
cana-1619	542	10	al	al	PROPN
cana-1619	542	11	.	.	PUNCT
cana-1619	543	1	"	"	PUNCT
cana-1619	543	2	efficiency	efficiency	NOUN
cana-1619	543	3	of	of	ADP
cana-1619	543	4	iterative	iterative	ADJ
cana-1619	543	5	filtering	filtering	NOUN
cana-1619	543	6	method	method	NOUN
cana-1619	543	7	for	for	ADP
cana-1619	543	8	solving	solve	VERB
cana-1619	543	9	volterra	volterra	NOUN
cana-1619	543	10	fuzzy	fuzzy	ADJ
cana-1619	543	11	integral	integral	ADJ
cana-1619	543	12	equations	equation	NOUN
cana-1619	543	13	with	with	ADP
cana-1619	543	14	a	a	DET
cana-1619	543	15	delay	delay	NOUN
cana-1619	543	16	and	and	CCONJ
cana-1619	543	17	material	material	NOUN
cana-1619	543	18	investigation	investigation	NOUN
cana-1619	543	19	.	.	PUNCT
cana-1619	543	20	"	"	PUNCT
cana-1619	544	1	materials	material	NOUN
cana-1619	544	2	today	today	NOUN
cana-1619	544	3	:	:	PUNCT
cana-1619	544	4	proceedings	proceeding	NOUN
cana-1619	544	5	47	47	NUM
cana-1619	544	6	(	(	PUNCT
cana-1619	544	7	2021	2021	NUM
cana-1619	544	8	):	):	PUNCT
cana-1619	544	9	6101	6101	NUM
cana-1619	544	10	-	-	SYM
cana-1619	544	11	6104	6104	NUM
cana-1619	544	12	.	.	PUNCT
cana-1619	545	1	[	[	X
cana-1619	545	2	15	15	NUM
cana-1619	545	3	]	]	X
cana-1619	545	4	hino	hino	NOUN
cana-1619	545	5	,	,	PUNCT
cana-1619	545	6	y.	y.	NOUN
cana-1619	545	7	,	,	PUNCT
cana-1619	545	8	murakami	murakami	NOUN
cana-1619	545	9	,	,	PUNCT
cana-1619	545	10	s.	s.	PROPN
cana-1619	545	11	,	,	PUNCT
cana-1619	545	12	&	&	CCONJ
cana-1619	545	13	naito	naito	PROPN
cana-1619	545	14	,	,	PUNCT
cana-1619	545	15	t.	t.	PROPN
cana-1619	545	16	(	(	PUNCT
cana-1619	545	17	1991	1991	NUM
cana-1619	545	18	)	)	PUNCT
cana-1619	545	19	.	.	PUNCT
cana-1619	546	1	functional	functional	ADJ
cana-1619	546	2	differential	differential	ADJ
cana-1619	546	3	equations	equation	NOUN
cana-1619	546	4	with	with	ADP
cana-1619	546	5	unbounded	unbounded	ADJ
cana-1619	546	6	delay	delay	NOUN
cana-1619	546	7	.	.	PUNCT
cana-1619	547	1	berlin	berlin	ADJ
cana-1619	547	2	:	:	PUNCT
cana-1619	547	3	springer	springer	NOUN
cana-1619	547	4	-	-	PUNCT
cana-1619	547	5	verlag	verlag	PROPN
cana-1619	547	6	.	.	PUNCT
cana-1619	548	1	[	[	X
cana-1619	548	2	16	16	NUM
cana-1619	548	3	]	]	PUNCT
cana-1619	548	4	travis	travis	PROPN
cana-1619	548	5	,	,	PUNCT
cana-1619	548	6	c.	c.	PROPN
cana-1619	548	7	c.	c.	PROPN
cana-1619	548	8	,	,	PUNCT
cana-1619	548	9	&	&	CCONJ
cana-1619	548	10	webb	webb	PROPN
cana-1619	548	11	,	,	PUNCT
cana-1619	548	12	g.	g.	PROPN
cana-1619	548	13	f.	f.	PROPN
cana-1619	548	14	(	(	PUNCT
cana-1619	548	15	1978	1978	NUM
cana-1619	548	16	)	)	PUNCT
cana-1619	548	17	.	.	PUNCT
cana-1619	549	1	compactness	compactness	NOUN
cana-1619	549	2	,	,	PUNCT
cana-1619	549	3	regularity	regularity	NOUN
cana-1619	549	4	and	and	CCONJ
cana-1619	549	5	uniform	uniform	ADJ
cana-1619	549	6	continuity	continuity	NOUN
cana-1619	549	7	properties	property	NOUN
cana-1619	549	8	of	of	ADP
cana-1619	549	9	strongly	strongly	ADV
cana-1619	549	10	continuous	continuous	ADJ
cana-1619	549	11	cosine	cosine	NOUN
cana-1619	549	12	families	family	NOUN
cana-1619	549	13	.	.	PUNCT
cana-1619	550	1	houston	houston	PROPN
cana-1619	550	2	journal	journal	PROPN
cana-1619	550	3	of	of	ADP
cana-1619	550	4	mathematics	mathematic	NOUN
cana-1619	550	5	,	,	PUNCT
cana-1619	550	6	3	3	NUM
cana-1619	550	7	,	,	PUNCT
cana-1619	550	8	555	555	NUM
cana-1619	550	9	-	-	SYM
cana-1619	550	10	567	567	NUM
cana-1619	550	11	.	.	PUNCT
cana-1619	551	1	[	[	X
cana-1619	551	2	17	17	NUM
cana-1619	551	3	]	]	X
cana-1619	551	4	pachpatte	pachpatte	NOUN
cana-1619	551	5	,	,	PUNCT
cana-1619	551	6	b.	b.	PROPN
cana-1619	551	7	g.	g.	PROPN
cana-1619	551	8	(	(	PUNCT
cana-1619	551	9	2006	2006	NUM
cana-1619	551	10	)	)	PUNCT
cana-1619	551	11	.	.	PUNCT
cana-1619	552	1	integral	integral	ADJ
cana-1619	552	2	and	and	CCONJ
cana-1619	552	3	finite	finite	ADJ
cana-1619	552	4	difference	difference	NOUN
cana-1619	552	5	inequalities	inequality	NOUN
cana-1619	552	6	and	and	CCONJ
cana-1619	552	7	applications	application	NOUN
cana-1619	552	8	.	.	PUNCT
cana-1619	553	1	north	north	NOUN
cana-1619	553	2	-	-	PUNCT
cana-1619	553	3	holland	holland	PROPN
cana-1619	553	4	mathematics	mathematics	PROPN
cana-1619	553	5	studies	study	NOUN
cana-1619	553	6	,	,	PUNCT
cana-1619	553	7	vol.205	vol.205	VERB
cana-1619	553	8	.	.	PUNCT
cana-1619	554	1	elsevier	elsevier	PROPN
cana-1619	554	2	science	science	PROPN
cana-1619	554	3	b.v	b.v	PROPN
cana-1619	554	4	.	.	PROPN
cana-1619	554	5	,	,	PUNCT
cana-1619	554	6	amsterdam	amsterdam	PROPN
cana-1619	554	7	.	.	PUNCT
cana-1619	555	1	[	[	X
cana-1619	555	2	18	18	NUM
cana-1619	555	3	]	]	PUNCT
cana-1619	555	4	nakagiri	nakagiri	PROPN
cana-1619	555	5	,	,	PUNCT
cana-1619	555	6	s.	s.	PROPN
cana-1619	555	7	,	,	PUNCT
cana-1619	555	8	&	&	CCONJ
cana-1619	555	9	yamamoto	yamamoto	PROPN
cana-1619	555	10	,	,	PUNCT
cana-1619	555	11	r.	r.	PROPN
cana-1619	555	12	(	(	PUNCT
cana-1619	555	13	1989	1989	NUM
cana-1619	555	14	)	)	PUNCT
cana-1619	555	15	.	.	PUNCT
cana-1619	556	1	controllability	controllability	NOUN
cana-1619	556	2	and	and	CCONJ
cana-1619	556	3	observability	observability	NOUN
cana-1619	556	4	for	for	ADP
cana-1619	556	5	linear	linear	ADJ
cana-1619	556	6	retarded	retarded	ADJ
cana-1619	556	7	systems	system	NOUN
cana-1619	556	8	in	in	ADP
cana-1619	556	9	banach	banach	NOUN
cana-1619	556	10	space	space	NOUN
cana-1619	556	11	.	.	PUNCT
cana-1619	557	1	international	international	ADJ
cana-1619	557	2	journal	journal	PROPN
cana-1619	557	3	of	of	ADP
cana-1619	557	4	control	control	NOUN
cana-1619	557	5	,	,	PUNCT
cana-1619	557	6	49(5	49(5	NUM
cana-1619	557	7	)	)	PUNCT
cana-1619	557	8	,	,	PUNCT
cana-1619	557	9	1489?1504	1489?1504	NUM
cana-1619	557	10	.	.	PUNCT
cana-1619	558	1	[	[	X
cana-1619	558	2	19	19	NUM
cana-1619	558	3	]	]	X
cana-1619	558	4	balachandran	balachandran	NOUN
cana-1619	558	5	,	,	PUNCT
cana-1619	558	6	k.	k.	PROPN
cana-1619	558	7	,	,	PUNCT
cana-1619	558	8	and	and	CCONJ
cana-1619	558	9	s.	s.	PROPN
cana-1619	558	10	marshal	marshal	PROPN
cana-1619	558	11	anthoni	anthoni	VERB
cana-1619	558	12	.	.	PUNCT
cana-1619	559	1	"	"	PUNCT
cana-1619	559	2	controllability	controllability	NOUN
cana-1619	559	3	of	of	ADP
cana-1619	559	4	second	second	ADJ
cana-1619	559	5	-	-	PUNCT
cana-1619	559	6	order	order	NOUN
cana-1619	559	7	semilinear	semilinear	ADJ
cana-1619	559	8	neutral	neutral	ADJ
cana-1619	559	9	functional	functional	ADJ
cana-1619	559	10	differential	differential	NOUN
cana-1619	559	11	systems	system	NOUN
cana-1619	559	12	in	in	ADP
cana-1619	559	13	banach	banach	NOUN
cana-1619	559	14	spaces	space	NOUN
cana-1619	559	15	.	.	PUNCT
cana-1619	559	16	"	"	PUNCT
cana-1619	560	1	computers	computer	NOUN
cana-1619	560	2	&	&	CCONJ
cana-1619	560	3	mathematics	mathematic	NOUN
cana-1619	560	4	with	with	ADP
cana-1619	560	5	applications	application	NOUN
cana-1619	560	6	41.10	41.10	NUM
cana-1619	560	7	-	-	SYM
cana-1619	560	8	11	11	NUM
cana-1619	560	9	(	(	PUNCT
cana-1619	560	10	2001	2001	NUM
cana-1619	560	11	):	):	PUNCT
cana-1619	560	12	1223	1223	NUM
cana-1619	560	13	-	-	SYM
cana-1619	560	14	1235	1235	NUM
cana-1619	560	15	.	.	PUNCT
cana-1619	561	1	[	[	X
cana-1619	561	2	20	20	NUM
cana-1619	561	3	]	]	X
cana-1619	561	4	gong	gong	NOUN
cana-1619	561	5	,	,	PUNCT
cana-1619	561	6	xue	xue	PROPN
cana-1619	561	7	,	,	PUNCT
cana-1619	561	8	et	et	PROPN
cana-1619	561	9	al	al	PROPN
cana-1619	561	10	.	.	PUNCT
cana-1619	562	1	"	"	PUNCT
cana-1619	562	2	higher	high	ADJ
cana-1619	562	3	-	-	PUNCT
cana-1619	562	4	order	order	NOUN
cana-1619	562	5	connection	connection	NOUN
cana-1619	562	6	laplacians	laplacian	NOUN
cana-1619	562	7	for	for	ADP
cana-1619	562	8	directed	direct	VERB
cana-1619	562	9	simplicial	simplicial	ADJ
cana-1619	562	10	complexes	complex	NOUN
cana-1619	562	11	.	.	PUNCT
cana-1619	562	12	"	"	PUNCT
cana-1619	563	1	arxiv	arxiv	PROPN
cana-1619	563	2	preprint	preprint	NOUN
cana-1619	563	3	communications	communication	NOUN
cana-1619	563	4	on	on	ADP
cana-1619	563	5	applied	apply	VERB
cana-1619	563	6	nonlinear	nonlinear	ADJ
cana-1619	563	7	analysis	analysis	NOUN
cana-1619	563	8	issn	issn	NOUN
cana-1619	563	9	:	:	PUNCT
cana-1619	563	10	1074	1074	NUM
cana-1619	563	11	-	-	PUNCT
cana-1619	563	12	133x	133x	NUM
cana-1619	563	13	vol	vol	NOUN
cana-1619	563	14	32	32	NUM
cana-1619	563	15	no	no	NOUN
cana-1619	563	16	.	.	NOUN
cana-1619	563	17	1	1	NUM
cana-1619	563	18	(	(	PUNCT
cana-1619	563	19	2025	2025	NUM
cana-1619	563	20	)	)	PUNCT
cana-1619	563	21	55	55	NUM
cana-1619	563	22	https://internationalpubls.com	https://internationalpubls.com	X
cana-1619	563	23	arxiv:2402.07631	arxiv:2402.07631	NUM
cana-1619	563	24	(	(	PUNCT
cana-1619	563	25	2024	2024	NUM
cana-1619	563	26	)	)	PUNCT
cana-1619	563	27	.	.	PUNCT
cana-1619	564	1	[	[	X
cana-1619	564	2	21	21	NUM
cana-1619	564	3	]	]	X
cana-1619	564	4	hazra	hazra	X
cana-1619	564	5	,	,	PUNCT
cana-1619	564	6	r.	r.	PROPN
cana-1619	564	7	,	,	PUNCT
cana-1619	564	8	singh	singh	PROPN
cana-1619	564	9	,	,	PUNCT
cana-1619	564	10	m.	m.	NOUN
cana-1619	564	11	,	,	PUNCT
cana-1619	564	12	goyal	goyal	PROPN
cana-1619	564	13	,	,	PUNCT
cana-1619	564	14	p.	p.	NOUN
cana-1619	564	15	,	,	PUNCT
cana-1619	564	16	adhikari	adhikari	PROPN
cana-1619	564	17	,	,	PUNCT
cana-1619	564	18	b.	b.	PROPN
cana-1619	564	19	,	,	PUNCT
cana-1619	564	20	&	&	CCONJ
cana-1619	564	21	mukherjee	mukherjee	PROPN
cana-1619	564	22	,	,	PUNCT
cana-1619	564	23	a.	a.	NOUN
cana-1619	564	24	(	(	PUNCT
cana-1619	564	25	2023	2023	NUM
cana-1619	564	26	)	)	PUNCT
cana-1619	564	27	.	.	PUNCT
cana-1619	565	1	modeling	model	VERB
cana-1619	565	2	interdisciplinary	interdisciplinary	ADJ
cana-1619	565	3	interactions	interaction	NOUN
cana-1619	565	4	among	among	ADP
cana-1619	565	5	physics	physics	NOUN
cana-1619	565	6	,	,	PUNCT
cana-1619	565	7	mathematics	mathematic	NOUN
cana-1619	565	8	and	and	CCONJ
cana-1619	565	9	computer	computer	NOUN
cana-1619	565	10	science.journal	science.journal	PROPN
cana-1619	565	11	of	of	ADP
cana-1619	565	12	physics	physics	NOUN
cana-1619	565	13	:	:	PUNCT
cana-1619	565	14	complexity	complexity	NOUN
cana-1619	565	15	,	,	PUNCT
cana-1619	565	16	4(4	4(4	NUM
cana-1619	565	17	)	)	PUNCT
cana-1619	565	18	,	,	PUNCT
cana-1619	565	19	045001	045001	NUM
cana-1619	565	20	.	.	PUNCT
cana-1619	566	1	[	[	X
cana-1619	566	2	22	22	NUM
cana-1619	566	3	]	]	SYM
cana-1619	566	4	han	han	PROPN
cana-1619	566	5	,	,	PUNCT
cana-1619	566	6	chengyuan	chengyuan	PROPN
cana-1619	566	7	,	,	PUNCT
cana-1619	566	8	et	et	PROPN
cana-1619	566	9	al	al	PROPN
cana-1619	566	10	.	.	PUNCT
cana-1619	566	11	"	"	PUNCT
cana-1619	566	12	formation	formation	NOUN
cana-1619	566	13	of	of	ADP
cana-1619	566	14	trade	trade	NOUN
cana-1619	566	15	networks	network	NOUN
cana-1619	566	16	by	by	ADP
cana-1619	566	17	economies	economy	NOUN
cana-1619	566	18	of	of	ADP
cana-1619	566	19	scale	scale	NOUN
cana-1619	566	20	and	and	CCONJ
cana-1619	566	21	product	product	NOUN
cana-1619	566	22	differentiation	differentiation	NOUN
cana-1619	566	23	.	.	PUNCT
cana-1619	566	24	"	"	PUNCT
cana-1619	567	1	journal	journal	PROPN
cana-1619	567	2	of	of	ADP
cana-1619	567	3	physics	physics	NOUN
cana-1619	567	4	:	:	PUNCT
cana-1619	567	5	complexity	complexity	NOUN
cana-1619	567	6	4.2	4.2	NUM
cana-1619	567	7	(	(	PUNCT
cana-1619	567	8	2023	2023	NUM
cana-1619	567	9	):	):	PUNCT
cana-1619	567	10	025006	025006	NUM
cana-1619	567	11	.	.	PUNCT
cana-1619	568	1	[	[	X
cana-1619	568	2	23	23	NUM
cana-1619	568	3	]	]	PUNCT
cana-1619	568	4	subramaniyan	subramaniyan	ADJ
cana-1619	568	5	,	,	PUNCT
cana-1619	568	6	g.	g.	PROPN
cana-1619	568	7	v.	v.	PROPN
cana-1619	568	8	,	,	PUNCT
cana-1619	568	9	s.	s.	PROPN
cana-1619	568	10	manimaran	manimaran	PROPN
cana-1619	568	11	,	,	PUNCT
cana-1619	568	12	t.	t.	PROPN
cana-1619	568	13	gunasekar	gunasekar	PROPN
cana-1619	568	14	,	,	PUNCT
cana-1619	568	15	and	and	CCONJ
cana-1619	568	16	m.	m.	PROPN
cana-1619	568	17	suba	suba	PROPN
cana-1619	568	18	.	.	PUNCT
cana-1619	569	1	"	"	PUNCT
cana-1619	569	2	controllability	controllability	NOUN
cana-1619	569	3	of	of	ADP
cana-1619	569	4	second	second	ADJ
cana-1619	569	5	order	order	NOUN
cana-1619	569	6	impulsive	impulsive	ADJ
cana-1619	569	7	neutral	neutral	ADJ
cana-1619	569	8	functional	functional	ADJ
cana-1619	569	9	integrodifferential	integrodifferential	ADJ
cana-1619	569	10	inclusions	inclusion	NOUN
cana-1619	569	11	with	with	ADP
cana-1619	569	12	an	an	DET
cana-1619	569	13	infinite	infinite	ADJ
cana-1619	569	14	delay	delay	NOUN
cana-1619	569	15	.	.	PUNCT
cana-1619	569	16	"	"	PUNCT
cana-1619	570	1	advances	advance	NOUN
cana-1619	570	2	and	and	CCONJ
cana-1619	570	3	applications	application	NOUN
cana-1619	570	4	in	in	ADP
cana-1619	570	5	fluid	fluid	ADJ
cana-1619	570	6	mechanics	mechanic	NOUN
cana-1619	570	7	18	18	NUM
cana-1619	570	8	(	(	PUNCT
cana-1619	570	9	1	1	NUM
cana-1619	570	10	)	)	PUNCT
cana-1619	570	11	,	,	PUNCT
cana-1619	570	12	(	(	PUNCT
cana-1619	570	13	2015	2015	NUM
cana-1619	570	14	)	)	PUNCT
cana-1619	570	15	,	,	PUNCT
cana-1619	570	16	1	1	NUM
cana-1619	570	17	-	-	SYM
cana-1619	570	18	30	30	NUM
cana-1619	570	19	.	.	PUNCT
cana-1619	571	1	[	[	X
cana-1619	571	2	24	24	NUM
cana-1619	571	3	]	]	PUNCT
cana-1619	571	4	manimaran	manimaran	NOUN
cana-1619	571	5	,	,	PUNCT
cana-1619	571	6	s.	s.	PROPN
cana-1619	571	7	,	,	PUNCT
cana-1619	571	8	t.	t.	PROPN
cana-1619	571	9	gunasekar	gunasekar	PROPN
cana-1619	571	10	,	,	PUNCT
cana-1619	571	11	g.	g.	PROPN
cana-1619	571	12	v.	v.	ADP
cana-1619	571	13	subramaniyan	subramaniyan	PROPN
cana-1619	571	14	,	,	PUNCT
cana-1619	571	15	and	and	CCONJ
cana-1619	571	16	m.	m.	PROPN
cana-1619	571	17	suba	suba	PROPN
cana-1619	571	18	.	.	PUNCT
cana-1619	572	1	"	"	PUNCT
cana-1619	572	2	controllability	controllability	NOUN
cana-1619	572	3	of	of	ADP
cana-1619	572	4	impulsive	impulsive	ADJ
cana-1619	572	5	neutral	neutral	ADJ
cana-1619	572	6	functional	functional	ADJ
cana-1619	572	7	integrodifferential	integrodifferential	ADJ
cana-1619	572	8	inclusions	inclusion	NOUN
cana-1619	572	9	with	with	ADP
cana-1619	572	10	an	an	DET
cana-1619	572	11	infinite	infinite	ADJ
cana-1619	572	12	delay	delay	NOUN
cana-1619	572	13	.	.	PUNCT
cana-1619	572	14	"	"	PUNCT
cana-1619	573	1	global	global	ADJ
cana-1619	573	2	journal	journal	NOUN
cana-1619	573	3	of	of	ADP
cana-1619	573	4	pure	pure	ADJ
cana-1619	573	5	and	and	CCONJ
cana-1619	573	6	applied	applied	ADJ
cana-1619	573	7	mathematics	mathematic	NOUN
cana-1619	573	8	10	10	NUM
cana-1619	573	9	(	(	PUNCT
cana-1619	573	10	6	6	NUM
cana-1619	573	11	)	)	PUNCT
cana-1619	573	12	(	(	PUNCT
cana-1619	573	13	2014	2014	NUM
cana-1619	573	14	)	)	PUNCT
cana-1619	573	15	,	,	PUNCT
cana-1619	573	16	817	817	NUM
cana-1619	573	17	-	-	SYM
cana-1619	573	18	834	834	NUM
cana-1619	573	19	.	.	PUNCT