id	sid	tid	token	lemma	pos
cana-5531	1	1	communications	communication	NOUN
cana-5531	1	2	on	on	ADP
cana-5531	1	3	applied	apply	VERB
cana-5531	1	4	nonlinear	nonlinear	ADJ
cana-5531	1	5	analysis	analysis	NOUN
cana-5531	1	6	issn	issn	NOUN
cana-5531	1	7	:	:	PUNCT
cana-5531	1	8	1074	1074	NUM
cana-5531	1	9	-	-	PUNCT
cana-5531	1	10	133x	133x	NUM
cana-5531	1	11	vol	vol	NOUN
cana-5531	1	12	32	32	NUM
cana-5531	1	13	no	no	NOUN
cana-5531	1	14	.	.	NOUN
cana-5531	1	15	3	3	NUM
cana-5531	1	16	(	(	PUNCT
cana-5531	1	17	2025	2025	NUM
cana-5531	1	18	)	)	PUNCT
cana-5531	1	19	964	964	NUM
cana-5531	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	1	21	variational	variational	ADJ
cana-5531	1	22	analysis	analysis	NOUN
cana-5531	1	23	of	of	ADP
cana-5531	1	24	a	a	DET
cana-5531	1	25	dynamic	dynamic	ADJ
cana-5531	1	26	frictional	frictional	ADJ
cana-5531	1	27	contact	contact	NOUN
cana-5531	1	28	problem	problem	NOUN
cana-5531	1	29	with	with	ADP
cana-5531	1	30	adhesion	adhesion	NOUN
cana-5531	1	31	and	and	CCONJ
cana-5531	1	32	long	long	ADJ
cana-5531	1	33	memory	memory	NOUN
cana-5531	1	34	in	in	ADP
cana-5531	1	35	viscoelastic	viscoelastic	ADJ
cana-5531	1	36	materials	material	NOUN
cana-5531	1	37	h.	h.	PROPN
cana-5531	1	38	hammar	hammar	PROPN
cana-5531	1	39	1	1	PROPN
cana-5531	1	40	,	,	PUNCT
cana-5531	1	41	s.	s.	PROPN
cana-5531	1	42	boutechebak	boutechebak	NOUN
cana-5531	1	43	2	2	NUM
cana-5531	1	44	1	1	NUM
cana-5531	1	45	applied	apply	VERB
cana-5531	1	46	mathematics	mathematic	NOUN
cana-5531	1	47	laboratory	laboratory	NOUN
cana-5531	1	48	,	,	PUNCT
cana-5531	1	49	department	department	NOUN
cana-5531	1	50	of	of	ADP
cana-5531	1	51	mathematics	mathematic	NOUN
cana-5531	1	52	,	,	PUNCT
cana-5531	1	53	faculty	faculty	NOUN
cana-5531	1	54	of	of	ADP
cana-5531	1	55	sciences	science	NOUN
cana-5531	1	56	,	,	PUNCT
cana-5531	1	57	university	university	NOUN
cana-5531	1	58	of	of	ADP
cana-5531	1	59	setif	setif	PROPN
cana-5531	1	60	1	1	NUM
cana-5531	1	61	,	,	PUNCT
cana-5531	1	62	19000	19000	NUM
cana-5531	1	63	,	,	PUNCT
cana-5531	1	64	algeria	algeria	PROPN
cana-5531	1	65	.	.	PUNCT
cana-5531	2	1	e-mail:hena.hammar@univ-setif.dz	e-mail:hena.hammar@univ-setif.dz	NOUN
cana-5531	2	2	2	2	NUM
cana-5531	2	3	applied	apply	VERB
cana-5531	2	4	mathematics	mathematic	NOUN
cana-5531	2	5	laboratory	laboratory	NOUN
cana-5531	2	6	,	,	PUNCT
cana-5531	2	7	department	department	NOUN
cana-5531	2	8	of	of	ADP
cana-5531	2	9	mathematics	mathematic	NOUN
cana-5531	2	10	,	,	PUNCT
cana-5531	2	11	faculty	faculty	NOUN
cana-5531	2	12	of	of	ADP
cana-5531	2	13	sciences	science	NOUN
cana-5531	2	14	,	,	PUNCT
cana-5531	2	15	university	university	NOUN
cana-5531	2	16	of	of	ADP
cana-5531	2	17	setif	setif	PROPN
cana-5531	2	18	1	1	NUM
cana-5531	2	19	,	,	PUNCT
cana-5531	2	20	19000	19000	NUM
cana-5531	2	21	,	,	PUNCT
cana-5531	2	22	algeria	algeria	PROPN
cana-5531	2	23	.	.	PUNCT
cana-5531	3	1	e	e	X
cana-5531	3	2	-	-	NOUN
cana-5531	3	3	mail	mail	NOUN
cana-5531	3	4	:	:	PUNCT
cana-5531	3	5	souraya.boutechbak@univ-setif.dz	souraya.boutechbak@univ-setif.dz	PROPN
cana-5531	3	6	article	article	NOUN
cana-5531	3	7	history	history	NOUN
cana-5531	3	8	:	:	PUNCT
cana-5531	3	9	received	receive	VERB
cana-5531	3	10	:	:	PUNCT
cana-5531	3	11	26	26	NUM
cana-5531	3	12	-	-	SYM
cana-5531	3	13	01	01	NUM
cana-5531	3	14	-	-	PUNCT
cana-5531	3	15	2025	2025	NUM
cana-5531	3	16	revised	revise	VERB
cana-5531	3	17	:	:	PUNCT
cana-5531	3	18	15	15	NUM
cana-5531	3	19	-	-	SYM
cana-5531	3	20	03	03	NUM
cana-5531	3	21	-	-	PUNCT
cana-5531	3	22	2025	2025	NUM
cana-5531	3	23	accepted	accept	VERB
cana-5531	3	24	:	:	PUNCT
cana-5531	3	25	28	28	NUM
cana-5531	3	26	-	-	SYM
cana-5531	3	27	05	05	NUM
cana-5531	3	28	-	-	PUNCT
cana-5531	3	29	2025	2025	NUM
cana-5531	3	30	abstract	abstract	NOUN
cana-5531	3	31	:	:	PUNCT
cana-5531	3	32	we	we	PRON
cana-5531	3	33	consider	consider	VERB
cana-5531	3	34	a	a	DET
cana-5531	3	35	mathematical	mathematical	ADJ
cana-5531	3	36	model	model	NOUN
cana-5531	3	37	that	that	PRON
cana-5531	3	38	describes	describe	VERB
cana-5531	3	39	a	a	DET
cana-5531	3	40	dynamic	dynamic	ADJ
cana-5531	3	41	frictional	frictional	ADJ
cana-5531	3	42	contact	contact	NOUN
cana-5531	3	43	between	between	ADP
cana-5531	3	44	a	a	DET
cana-5531	3	45	foundation	foundation	NOUN
cana-5531	3	46	and	and	CCONJ
cana-5531	3	47	a	a	DET
cana-5531	3	48	viscoelastic	viscoelastic	ADJ
cana-5531	3	49	body	body	NOUN
cana-5531	3	50	with	with	ADP
cana-5531	3	51	long	long	ADJ
cana-5531	3	52	memory	memory	NOUN
cana-5531	3	53	.	.	PUNCT
cana-5531	4	1	the	the	DET
cana-5531	4	2	contact	contact	NOUN
cana-5531	4	3	is	be	AUX
cana-5531	4	4	modelled	model	VERB
cana-5531	4	5	with	with	ADP
cana-5531	4	6	a	a	DET
cana-5531	4	7	normal	normal	ADJ
cana-5531	4	8	compliance	compliance	NOUN
cana-5531	4	9	condition	condition	NOUN
cana-5531	4	10	in	in	ADP
cana-5531	4	11	that	that	SCONJ
cana-5531	4	12	the	the	DET
cana-5531	4	13	penetration	penetration	NOUN
cana-5531	4	14	is	be	AUX
cana-5531	4	15	limited	limit	VERB
cana-5531	4	16	and	and	CCONJ
cana-5531	4	17	restricted	restrict	VERB
cana-5531	4	18	to	to	ADP
cana-5531	4	19	a	a	DET
cana-5531	4	20	unilateral	unilateral	ADJ
cana-5531	4	21	constraint	constraint	NOUN
cana-5531	4	22	and	and	CCONJ
cana-5531	4	23	associated	associate	VERB
cana-5531	4	24	to	to	ADP
cana-5531	4	25	the	the	DET
cana-5531	4	26	nonlocal	nonlocal	ADJ
cana-5531	4	27	friction	friction	NOUN
cana-5531	4	28	law	law	NOUN
cana-5531	4	29	with	with	ADP
cana-5531	4	30	adhesion	adhesion	NOUN
cana-5531	4	31	,	,	PUNCT
cana-5531	4	32	where	where	SCONJ
cana-5531	4	33	the	the	DET
cana-5531	4	34	coefficient	coefficient	NOUN
cana-5531	4	35	of	of	ADP
cana-5531	4	36	friction	friction	NOUN
cana-5531	4	37	is	be	AUX
cana-5531	4	38	an	an	DET
cana-5531	4	39	independent	independent	ADJ
cana-5531	4	40	solution	solution	NOUN
cana-5531	4	41	.	.	PUNCT
cana-5531	5	1	the	the	DET
cana-5531	5	2	adhesion	adhesion	NOUN
cana-5531	5	3	of	of	ADP
cana-5531	5	4	the	the	DET
cana-5531	5	5	contact	contact	NOUN
cana-5531	5	6	surfaces	surface	NOUN
cana-5531	5	7	is	be	AUX
cana-5531	5	8	considered	consider	VERB
cana-5531	5	9	and	and	CCONJ
cana-5531	5	10	modelled	model	VERB
cana-5531	5	11	with	with	ADP
cana-5531	5	12	a	a	DET
cana-5531	5	13	surface	surface	NOUN
cana-5531	5	14	variable	variable	NOUN
cana-5531	5	15	.	.	PUNCT
cana-5531	6	1	we	we	PRON
cana-5531	6	2	derive	derive	VERB
cana-5531	6	3	a	a	DET
cana-5531	6	4	variational	variational	ADJ
cana-5531	6	5	formulation	formulation	NOUN
cana-5531	6	6	written	write	VERB
cana-5531	6	7	as	as	ADP
cana-5531	6	8	the	the	DET
cana-5531	6	9	coupling	coupling	NOUN
cana-5531	6	10	between	between	ADP
cana-5531	6	11	a	a	DET
cana-5531	6	12	variational	variational	ADJ
cana-5531	6	13	inequality	inequality	NOUN
cana-5531	6	14	and	and	CCONJ
cana-5531	6	15	a	a	DET
cana-5531	6	16	differential	differential	ADJ
cana-5531	6	17	equation	equation	NOUN
cana-5531	6	18	.	.	PUNCT
cana-5531	7	1	the	the	DET
cana-5531	7	2	existence	existence	NOUN
cana-5531	7	3	and	and	CCONJ
cana-5531	7	4	uniqueness	uniqueness	ADJ
cana-5531	7	5	result	result	NOUN
cana-5531	7	6	of	of	ADP
cana-5531	7	7	the	the	DET
cana-5531	7	8	weak	weak	ADJ
cana-5531	7	9	solution	solution	NOUN
cana-5531	7	10	under	under	ADP
cana-5531	7	11	a	a	DET
cana-5531	7	12	smallness	smallness	NOUN
cana-5531	7	13	assumption	assumption	NOUN
cana-5531	7	14	on	on	ADP
cana-5531	7	15	the	the	DET
cana-5531	7	16	coefficient	coefficient	NOUN
cana-5531	7	17	of	of	ADP
cana-5531	7	18	friction	friction	NOUN
cana-5531	7	19	is	be	AUX
cana-5531	7	20	established	establish	VERB
cana-5531	7	21	.	.	PUNCT
cana-5531	8	1	the	the	DET
cana-5531	8	2	proof	proof	NOUN
cana-5531	8	3	is	be	AUX
cana-5531	8	4	based	base	VERB
cana-5531	8	5	on	on	ADP
cana-5531	8	6	arguments	argument	NOUN
cana-5531	8	7	of	of	ADP
cana-5531	8	8	nonlinear	nonlinear	ADJ
cana-5531	8	9	evolution	evolution	NOUN
cana-5531	8	10	equation	equation	NOUN
cana-5531	8	11	with	with	ADP
cana-5531	8	12	monotone	monotone	ADJ
cana-5531	8	13	operators	operator	NOUN
cana-5531	8	14	,	,	PUNCT
cana-5531	8	15	a	a	DET
cana-5531	8	16	classical	classical	ADJ
cana-5531	8	17	existence	existence	NOUN
cana-5531	8	18	,	,	PUNCT
cana-5531	8	19	differential	differential	ADJ
cana-5531	8	20	equations	equation	NOUN
cana-5531	8	21	,	,	PUNCT
cana-5531	8	22	and	and	CCONJ
cana-5531	8	23	the	the	DET
cana-5531	8	24	banach	banach	ADV
cana-5531	8	25	fixed	fix	VERB
cana-5531	8	26	point	point	NOUN
cana-5531	8	27	theorem	theorem	ADJ
cana-5531	8	28	.	.	PUNCT
cana-5531	9	1	keywords	keyword	NOUN
cana-5531	9	2	:	:	PUNCT
cana-5531	9	3	viscoelastic	viscoelastic	ADJ
cana-5531	9	4	;	;	PUNCT
cana-5531	9	5	normal	normal	ADJ
cana-5531	9	6	compliance	compliance	NOUN
cana-5531	9	7	;	;	PUNCT
cana-5531	9	8	dynamic	dynamic	ADJ
cana-5531	9	9	process	process	NOUN
cana-5531	9	10	;	;	PUNCT
cana-5531	9	11	adhesion	adhesion	NOUN
cana-5531	9	12	;	;	PUNCT
cana-5531	9	13	differential	differential	ADJ
cana-5531	9	14	equations	equation	NOUN
cana-5531	9	15	;	;	PUNCT
cana-5531	9	16	friction	friction	NOUN
cana-5531	9	17	;	;	PUNCT
cana-5531	9	18	weak	weak	ADJ
cana-5531	9	19	solution	solution	NOUN
cana-5531	9	20	..	..	PUNCT
cana-5531	10	1	mathematics	mathematic	NOUN
cana-5531	10	2	subject	subject	ADJ
cana-5531	10	3	classification	classification	NOUN
cana-5531	10	4	2010	2010	NUM
cana-5531	10	5	:	:	PUNCT
cana-5531	10	6	74m15	74m15	NUM
cana-5531	10	7	,	,	PUNCT
cana-5531	10	8	74m10	74m10	NUM
cana-5531	10	9	,	,	PUNCT
cana-5531	10	10	74f15	74f15	NUM
cana-5531	10	11	,	,	PUNCT
cana-5531	10	12	49j40	49j40	NUM
cana-5531	10	13	.	.	PUNCT
cana-5531	11	1	1	1	X
cana-5531	11	2	.	.	X
cana-5531	11	3	introduction	introduction	NOUN
cana-5531	11	4	contact	contact	NOUN
cana-5531	11	5	issues	issue	NOUN
cana-5531	11	6	with	with	ADP
cana-5531	11	7	deformable	deformable	ADJ
cana-5531	11	8	bodies	body	NOUN
cana-5531	11	9	are	be	AUX
cana-5531	11	10	prevalent	prevalent	ADJ
cana-5531	11	11	in	in	ADP
cana-5531	11	12	industrial	industrial	ADJ
cana-5531	11	13	applications	application	NOUN
cana-5531	11	14	and	and	CCONJ
cana-5531	11	15	daily	daily	ADJ
cana-5531	11	16	life	life	NOUN
cana-5531	11	17	,	,	PUNCT
cana-5531	11	18	significantly	significantly	ADV
cana-5531	11	19	impacting	impact	VERB
cana-5531	11	20	structural	structural	ADJ
cana-5531	11	21	and	and	CCONJ
cana-5531	11	22	mechanical	mechanical	ADJ
cana-5531	11	23	systems	system	NOUN
cana-5531	11	24	.	.	PUNCT
cana-5531	12	1	the	the	DET
cana-5531	12	2	last	last	ADJ
cana-5531	12	3	fifty	fifty	NUM
cana-5531	12	4	years	year	NOUN
cana-5531	12	5	,	,	PUNCT
cana-5531	12	6	variational	variational	ADJ
cana-5531	12	7	inequalities	inequality	NOUN
cana-5531	12	8	have	have	AUX
cana-5531	12	9	become	become	VERB
cana-5531	12	10	a	a	DET
cana-5531	12	11	formidable	formidable	ADJ
cana-5531	12	12	tool	tool	NOUN
cana-5531	12	13	in	in	ADP
cana-5531	12	14	the	the	DET
cana-5531	12	15	mathematical	mathematical	ADJ
cana-5531	12	16	study	study	NOUN
cana-5531	12	17	of	of	ADP
cana-5531	12	18	many	many	ADJ
cana-5531	12	19	non	non	ADJ
cana-5531	12	20	-	-	ADJ
cana-5531	12	21	linear	linear	ADJ
cana-5531	12	22	problems	problem	NOUN
cana-5531	12	23	in	in	ADP
cana-5531	12	24	physics	physics	NOUN
cana-5531	12	25	and	and	CCONJ
cana-5531	12	26	mechanics	mechanic	NOUN
cana-5531	12	27	and	and	CCONJ
cana-5531	12	28	the	the	DET
cana-5531	12	29	analysis	analysis	NOUN
cana-5531	12	30	of	of	ADP
cana-5531	12	31	mathematical	mathematical	ADJ
cana-5531	12	32	models	model	NOUN
cana-5531	12	33	in	in	ADP
cana-5531	12	34	contact	contact	NOUN
cana-5531	12	35	mechanics	mechanic	NOUN
cana-5531	12	36	has	have	AUX
cana-5531	12	37	expanded	expand	VERB
cana-5531	12	38	quickly	quickly	ADV
cana-5531	12	39	over	over	ADP
cana-5531	12	40	the	the	DET
cana-5531	12	41	past	past	ADJ
cana-5531	12	42	few	few	ADJ
cana-5531	12	43	decades	decade	NOUN
cana-5531	12	44	,	,	PUNCT
cana-5531	12	45	the	the	DET
cana-5531	12	46	complexity	complexity	NOUN
cana-5531	12	47	of	of	ADP
cana-5531	12	48	the	the	DET
cana-5531	12	49	boundary	boundary	ADJ
cana-5531	12	50	conditions	condition	NOUN
cana-5531	12	51	and	and	CCONJ
cana-5531	12	52	the	the	DET
cana-5531	12	53	diversity	diversity	NOUN
cana-5531	12	54	of	of	ADP
cana-5531	12	55	the	the	DET
cana-5531	12	56	constituent	constituent	ADJ
cana-5531	12	57	equations	equation	NOUN
cana-5531	12	58	leading	lead	VERB
cana-5531	12	59	to	to	ADP
cana-5531	12	60	variational	variational	ADJ
cana-5531	12	61	formulations	formulation	NOUN
cana-5531	12	62	of	of	ADP
cana-5531	12	63	the	the	DET
cana-5531	12	64	inequation	inequation	NOUN
cana-5531	12	65	type	type	NOUN
cana-5531	12	66	.	.	PUNCT
cana-5531	13	1	the	the	DET
cana-5531	13	2	state	state	NOUN
cana-5531	13	3	of	of	ADP
cana-5531	13	4	the	the	DET
cana-5531	13	5	art	art	NOUN
cana-5531	13	6	in	in	ADP
cana-5531	13	7	mathematics	mathematic	NOUN
cana-5531	13	8	,	,	PUNCT
cana-5531	13	9	mechanics	mechanic	NOUN
cana-5531	13	10	and	and	CCONJ
cana-5531	13	11	numerical	numerical	ADJ
cana-5531	13	12	analysis	analysis	NOUN
cana-5531	13	13	is	be	AUX
cana-5531	13	14	contained	contain	VERB
cana-5531	13	15	in	in	ADP
cana-5531	13	16	[	[	X
cana-5531	13	17	18	18	NUM
cana-5531	13	18	]	]	PUNCT
cana-5531	13	19	.	.	PUNCT
cana-5531	14	1	this	this	DET
cana-5531	14	2	reference	reference	NOUN
cana-5531	14	3	finds	find	VERB
cana-5531	14	4	numerical	numerical	ADJ
cana-5531	14	5	investigations	investigation	NOUN
cana-5531	14	6	and	and	CCONJ
cana-5531	14	7	a	a	DET
cana-5531	14	8	thorough	thorough	ADJ
cana-5531	14	9	analysis	analysis	NOUN
cana-5531	14	10	of	of	ADP
cana-5531	14	11	the	the	DET
cana-5531	14	12	adhesive	adhesive	ADJ
cana-5531	14	13	contact	contact	NOUN
cana-5531	14	14	problem	problem	NOUN
cana-5531	14	15	.	.	PUNCT
cana-5531	15	1	general	general	ADJ
cana-5531	15	2	models	model	NOUN
cana-5531	15	3	for	for	ADP
cana-5531	15	4	unilateral	unilateral	ADJ
cana-5531	15	5	and	and	CCONJ
cana-5531	15	6	frictional	frictional	ADJ
cana-5531	15	7	contact	contact	NOUN
cana-5531	15	8	problems	problem	NOUN
cana-5531	15	9	with	with	ADP
cana-5531	15	10	adhesion	adhesion	NOUN
cana-5531	15	11	can	can	AUX
cana-5531	15	12	be	be	AUX
cana-5531	15	13	found	find	VERB
cana-5531	15	14	in	in	ADP
cana-5531	15	15	[	[	X
cana-5531	15	16	5	5	NUM
cana-5531	15	17	,	,	PUNCT
cana-5531	15	18	7	7	NUM
cana-5531	15	19	,	,	PUNCT
cana-5531	15	20	9	9	NUM
cana-5531	15	21	,	,	PUNCT
cana-5531	15	22	13	13	NUM
cana-5531	15	23	,	,	PUNCT
cana-5531	15	24	19	19	NUM
cana-5531	15	25	,	,	PUNCT
cana-5531	15	26	20	20	NUM
cana-5531	15	27	]	]	PUNCT
cana-5531	15	28	.	.	PUNCT
cana-5531	16	1	in	in	ADP
cana-5531	16	2	[	[	X
cana-5531	16	3	21	21	NUM
cana-5531	16	4	]	]	X
cana-5531	16	5	,	,	PUNCT
cana-5531	16	6	a	a	DET
cana-5531	16	7	quasistatic	quasistatic	ADJ
cana-5531	16	8	viscoelastic	viscoelastic	ADJ
cana-5531	16	9	unilateral	unilateral	ADJ
cana-5531	16	10	and	and	CCONJ
cana-5531	16	11	frictional	frictional	ADJ
cana-5531	16	12	contact	contact	NOUN
cana-5531	16	13	problem	problem	NOUN
cana-5531	16	14	with	with	ADP
cana-5531	16	15	adhesion	adhesion	NOUN
cana-5531	16	16	and	and	CCONJ
cana-5531	16	17	long	long	ADJ
cana-5531	16	18	memory	memory	NOUN
cana-5531	16	19	was	be	AUX
cana-5531	16	20	studied	study	VERB
cana-5531	16	21	.	.	PUNCT
cana-5531	17	1	this	this	DET
cana-5531	17	2	paper	paper	NOUN
cana-5531	17	3	aims	aim	VERB
cana-5531	17	4	to	to	PART
cana-5531	17	5	model	model	VERB
cana-5531	17	6	and	and	CCONJ
cana-5531	17	7	establish	establish	VERB
cana-5531	17	8	the	the	DET
cana-5531	17	9	mailto:hena.hammar@univ-setif.dz	mailto:hena.hammar@univ-setif.dz	PROPN
cana-5531	17	10	mailto:souraya.boutechbak@univ-setif.dz	mailto:souraya.boutechbak@univ-setif.dz	PROPN
cana-5531	17	11	communications	communication	NOUN
cana-5531	17	12	on	on	ADP
cana-5531	17	13	applied	apply	VERB
cana-5531	17	14	nonlinear	nonlinear	ADJ
cana-5531	17	15	analysis	analysis	NOUN
cana-5531	17	16	issn	issn	NOUN
cana-5531	17	17	:	:	PUNCT
cana-5531	17	18	1074	1074	NUM
cana-5531	17	19	-	-	PUNCT
cana-5531	17	20	133x	133x	NUM
cana-5531	17	21	vol	vol	NOUN
cana-5531	17	22	32	32	NUM
cana-5531	17	23	no	no	NOUN
cana-5531	17	24	.	.	NOUN
cana-5531	17	25	3	3	NUM
cana-5531	17	26	(	(	PUNCT
cana-5531	17	27	2025	2025	NUM
cana-5531	17	28	)	)	PUNCT
cana-5531	17	29	965	965	NUM
cana-5531	17	30	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	17	31	variational	variational	ADJ
cana-5531	17	32	analysis	analysis	NOUN
cana-5531	17	33	for	for	ADP
cana-5531	17	34	a	a	DET
cana-5531	17	35	dynamic	dynamic	ADJ
cana-5531	17	36	process	process	NOUN
cana-5531	17	37	of	of	ADP
cana-5531	17	38	unilateral	unilateral	ADJ
cana-5531	17	39	and	and	CCONJ
cana-5531	17	40	frictional	frictional	ADJ
cana-5531	17	41	contact	contact	NOUN
cana-5531	17	42	with	with	ADP
cana-5531	17	43	adhesion	adhesion	NOUN
cana-5531	17	44	and	and	CCONJ
cana-5531	17	45	long	long	ADJ
cana-5531	17	46	memory	memory	NOUN
cana-5531	17	47	.	.	PUNCT
cana-5531	18	1	remember	remember	VERB
cana-5531	18	2	that	that	SCONJ
cana-5531	18	3	[	[	X
cana-5531	18	4	2	2	NUM
cana-5531	18	5	,	,	PUNCT
cana-5531	18	6	3	3	NUM
cana-5531	18	7	,	,	PUNCT
cana-5531	18	8	4	4	NUM
cana-5531	18	9	,	,	PUNCT
cana-5531	18	10	6	6	NUM
cana-5531	18	11	,	,	PUNCT
cana-5531	18	12	12	12	NUM
cana-5531	18	13	,	,	PUNCT
cana-5531	18	14	14	14	NUM
cana-5531	18	15	,	,	PUNCT
cana-5531	18	16	15	15	NUM
cana-5531	18	17	,	,	PUNCT
cana-5531	18	18	16	16	NUM
cana-5531	18	19	]	]	PUNCT
cana-5531	18	20	has	have	AUX
cana-5531	18	21	studied	study	VERB
cana-5531	18	22	models	model	NOUN
cana-5531	18	23	for	for	ADP
cana-5531	18	24	dynamic	dynamic	ADJ
cana-5531	18	25	or	or	CCONJ
cana-5531	18	26	quasistatic	quasistatic	ADJ
cana-5531	18	27	processes	process	NOUN
cana-5531	18	28	of	of	ADP
cana-5531	18	29	frictionless	frictionless	ADJ
cana-5531	18	30	adhesive	adhesive	ADJ
cana-5531	18	31	contact	contact	NOUN
cana-5531	18	32	between	between	ADP
cana-5531	18	33	a	a	DET
cana-5531	18	34	deformable	deformable	ADJ
cana-5531	18	35	body	body	NOUN
cana-5531	18	36	and	and	CCONJ
cana-5531	18	37	foundation	foundation	NOUN
cana-5531	18	38	.	.	PUNCT
cana-5531	19	1	following	follow	VERB
cana-5531	19	2	[	[	X
cana-5531	19	3	10,11	10,11	NOUN
cana-5531	19	4	]	]	PUNCT
cana-5531	19	5	,	,	PUNCT
cana-5531	19	6	the	the	DET
cana-5531	19	7	bondind	bondind	NOUN
cana-5531	19	8	field	field	NOUN
cana-5531	19	9	is	be	AUX
cana-5531	19	10	used	use	VERB
cana-5531	19	11	as	as	ADP
cana-5531	19	12	an	an	DET
cana-5531	19	13	extra	extra	ADJ
cana-5531	19	14	variable	variable	NOUN
cana-5531	19	15	β	β	X
cana-5531	19	16	wich	wich	PRON
cana-5531	19	17	satisfies	satisfy	VERB
cana-5531	19	18	the	the	DET
cana-5531	19	19	restriction	restriction	NOUN
cana-5531	19	20	0	0	NUM
cana-5531	19	21	≤	≤	NUM
cana-5531	19	22	𝛽	𝛽	NOUN
cana-5531	19	23	≤	≤	NOUN
cana-5531	19	24	1	1	NUM
cana-5531	19	25	,	,	PUNCT
cana-5531	19	26	at	at	ADP
cana-5531	19	27	a	a	DET
cana-5531	19	28	point	point	NOUN
cana-5531	19	29	of	of	ADP
cana-5531	19	30	the	the	DET
cana-5531	19	31	contact	contact	NOUN
cana-5531	19	32	surface	surface	NOUN
cana-5531	19	33	of	of	ADP
cana-5531	19	34	the	the	DET
cana-5531	19	35	boundary	boundary	NOUN
cana-5531	19	36	,	,	PUNCT
cana-5531	19	37	when	when	SCONJ
cana-5531	19	38	𝛽	𝛽	NOUN
cana-5531	19	39	=	=	SYM
cana-5531	19	40	1	1	NUM
cana-5531	19	41	all	all	PRON
cana-5531	19	42	of	of	ADP
cana-5531	19	43	the	the	DET
cana-5531	19	44	bonds	bond	NOUN
cana-5531	19	45	are	be	AUX
cana-5531	19	46	active	active	ADJ
cana-5531	19	47	and	and	CCONJ
cana-5531	19	48	the	the	DET
cana-5531	19	49	adhesion	adhesion	NOUN
cana-5531	19	50	is	be	AUX
cana-5531	19	51	complete	complete	ADJ
cana-5531	19	52	and	and	CCONJ
cana-5531	19	53	for	for	ADP
cana-5531	19	54	𝛽	𝛽	NOUN
cana-5531	19	55	=	=	SYM
cana-5531	19	56	0	0	PUNCT
cana-5531	20	1	the	the	DET
cana-5531	20	2	bonds	bond	NOUN
cana-5531	20	3	are	be	AUX
cana-5531	20	4	inactive	inactive	ADJ
cana-5531	20	5	,	,	PUNCT
cana-5531	20	6	severed	sever	VERB
cana-5531	20	7	and	and	CCONJ
cana-5531	20	8	there	there	PRON
cana-5531	20	9	is	be	VERB
cana-5531	20	10	no	no	DET
cana-5531	20	11	adhesion	adhesion	NOUN
cana-5531	20	12	;	;	PUNCT
cana-5531	20	13	when	when	SCONJ
cana-5531	20	14	0	0	NUM
cana-5531	20	15	<	<	X
cana-5531	20	16	𝛽	𝛽	X
cana-5531	20	17	<	<	X
cana-5531	20	18	1	1	NUM
cana-5531	20	19	the	the	DET
cana-5531	20	20	adhesion	adhesion	NOUN
cana-5531	20	21	is	be	AUX
cana-5531	20	22	partial	partial	ADJ
cana-5531	20	23	and	and	CCONJ
cana-5531	20	24	only	only	ADV
cana-5531	20	25	a	a	DET
cana-5531	20	26	fraction	fraction	NOUN
cana-5531	20	27	𝛽	𝛽	NOUN
cana-5531	20	28	of	of	ADP
cana-5531	20	29	the	the	DET
cana-5531	20	30	bonds	bond	NOUN
cana-5531	20	31	is	be	AUX
cana-5531	20	32	active	active	ADJ
cana-5531	20	33	.	.	PUNCT
cana-5531	21	1	we	we	PRON
cana-5531	21	2	direct	direct	VERB
cana-5531	21	3	the	the	DET
cana-5531	21	4	reader	reader	NOUN
cana-5531	21	5	’s	’s	PART
cana-5531	21	6	attention	attention	NOUN
cana-5531	21	7	to	to	ADP
cana-5531	21	8	the	the	DET
cana-5531	21	9	comprehensive	comprehensive	ADJ
cana-5531	21	10	bibgraphy	bibgraphy	NOUN
cana-5531	21	11	on	on	ADP
cana-5531	21	12	the	the	DET
cana-5531	21	13	topic	topic	NOUN
cana-5531	21	14	in	in	ADP
cana-5531	21	15	[	[	X
cana-5531	21	16	1	1	NUM
cana-5531	21	17	,	,	PUNCT
cana-5531	21	18	10	10	NUM
cana-5531	21	19	,	,	PUNCT
cana-5531	21	20	17	17	NUM
cana-5531	21	21	,	,	PUNCT
cana-5531	21	22	18	18	NUM
cana-5531	21	23	,	,	PUNCT
cana-5531	21	24	19	19	NUM
cana-5531	21	25	]	]	PUNCT
cana-5531	21	26	.	.	PUNCT
cana-5531	22	1	in	in	ADP
cana-5531	22	2	this	this	DET
cana-5531	22	3	paper	paper	NOUN
cana-5531	22	4	,	,	PUNCT
cana-5531	22	5	we	we	PRON
cana-5531	22	6	deal	deal	VERB
cana-5531	22	7	with	with	ADP
cana-5531	22	8	the	the	DET
cana-5531	22	9	study	study	NOUN
cana-5531	22	10	of	of	ADP
cana-5531	22	11	a	a	DET
cana-5531	22	12	dynamic	dynamic	ADJ
cana-5531	22	13	problem	problem	NOUN
cana-5531	22	14	,	,	PUNCT
cana-5531	22	15	we	we	PRON
cana-5531	22	16	derive	derive	VERB
cana-5531	22	17	a	a	DET
cana-5531	22	18	variational	variational	ADJ
cana-5531	22	19	formulation	formulation	NOUN
cana-5531	22	20	of	of	ADP
cana-5531	22	21	the	the	DET
cana-5531	22	22	problem	problem	NOUN
cana-5531	22	23	which	which	PRON
cana-5531	22	24	is	be	AUX
cana-5531	22	25	set	set	VERB
cana-5531	22	26	a	a	DET
cana-5531	22	27	system	system	NOUN
cana-5531	22	28	coupling	couple	VERB
cana-5531	22	29	a	a	DET
cana-5531	22	30	variational	variational	ADJ
cana-5531	22	31	second	second	ADJ
cana-5531	22	32	order	order	NOUN
cana-5531	22	33	evolution	evolution	NOUN
cana-5531	22	34	inequality	inequality	NOUN
cana-5531	22	35	.	.	PUNCT
cana-5531	23	1	we	we	PRON
cana-5531	23	2	establish	establish	VERB
cana-5531	23	3	the	the	DET
cana-5531	23	4	existence	existence	NOUN
cana-5531	23	5	and	and	CCONJ
cana-5531	23	6	the	the	DET
cana-5531	23	7	uniqueness	uniqueness	NOUN
cana-5531	23	8	of	of	ADP
cana-5531	23	9	a	a	DET
cana-5531	23	10	weak	weak	ADJ
cana-5531	23	11	solution	solution	NOUN
cana-5531	23	12	of	of	ADP
cana-5531	23	13	the	the	DET
cana-5531	23	14	model	model	NOUN
cana-5531	23	15	.	.	PUNCT
cana-5531	24	1	the	the	DET
cana-5531	24	2	idea	idea	NOUN
cana-5531	24	3	is	be	AUX
cana-5531	24	4	to	to	PART
cana-5531	24	5	reduce	reduce	VERB
cana-5531	24	6	the	the	DET
cana-5531	24	7	second	second	ADJ
cana-5531	24	8	order	order	NOUN
cana-5531	24	9	evolution	evolution	NOUN
cana-5531	24	10	inequality	inequality	NOUN
cana-5531	24	11	of	of	ADP
cana-5531	24	12	the	the	DET
cana-5531	24	13	system	system	NOUN
cana-5531	24	14	to	to	PART
cana-5531	24	15	first	first	ADJ
cana-5531	24	16	order	order	NOUN
cana-5531	24	17	evolution	evolution	NOUN
cana-5531	24	18	inequality	inequality	NOUN
cana-5531	24	19	.	.	PUNCT
cana-5531	25	1	after	after	ADP
cana-5531	25	2	this	this	PRON
cana-5531	25	3	,	,	PUNCT
cana-5531	25	4	we	we	PRON
cana-5531	25	5	use	use	VERB
cana-5531	25	6	classical	classical	ADJ
cana-5531	25	7	results	result	NOUN
cana-5531	25	8	on	on	ADP
cana-5531	25	9	first	first	ADJ
cana-5531	25	10	order	order	NOUN
cana-5531	25	11	evolution	evolution	NOUN
cana-5531	25	12	inequalities	inequality	NOUN
cana-5531	25	13	and	and	CCONJ
cana-5531	25	14	differential	differential	ADJ
cana-5531	25	15	equations	equation	NOUN
cana-5531	25	16	and	and	CCONJ
cana-5531	25	17	the	the	DET
cana-5531	25	18	fixed	fix	VERB
cana-5531	25	19	point	point	NOUN
cana-5531	25	20	arguments	argument	NOUN
cana-5531	25	21	.	.	PUNCT
cana-5531	26	1	the	the	DET
cana-5531	26	2	rest	rest	NOUN
cana-5531	26	3	of	of	ADP
cana-5531	26	4	the	the	DET
cana-5531	26	5	paper	paper	NOUN
cana-5531	26	6	is	be	AUX
cana-5531	26	7	structured	structure	VERB
cana-5531	26	8	as	as	SCONJ
cana-5531	26	9	follows	follow	VERB
cana-5531	26	10	.	.	PUNCT
cana-5531	27	1	in	in	ADP
cana-5531	27	2	section	section	NOUN
cana-5531	27	3	2	2	NUM
cana-5531	27	4	and	and	CCONJ
cana-5531	27	5	3	3	NUM
cana-5531	27	6	we	we	PRON
cana-5531	27	7	present	present	VERB
cana-5531	27	8	some	some	DET
cana-5531	27	9	notations	notation	NOUN
cana-5531	27	10	and	and	CCONJ
cana-5531	27	11	preliminaires	preliminaire	NOUN
cana-5531	27	12	,	,	PUNCT
cana-5531	27	13	and	and	CCONJ
cana-5531	27	14	the	the	DET
cana-5531	27	15	viscoelastic	viscoelastic	ADJ
cana-5531	27	16	unilateral	unilateral	ADJ
cana-5531	27	17	and	and	CCONJ
cana-5531	27	18	frictional	frictional	ADJ
cana-5531	27	19	contact	contact	NOUN
cana-5531	27	20	model	model	NOUN
cana-5531	27	21	with	with	ADP
cana-5531	27	22	adhesion	adhesion	NOUN
cana-5531	27	23	and	and	CCONJ
cana-5531	27	24	long	long	ADJ
cana-5531	27	25	memory	memory	NOUN
cana-5531	27	26	,	,	PUNCT
cana-5531	27	27	and	and	CCONJ
cana-5531	27	28	provide	provide	VERB
cana-5531	27	29	comments	comment	NOUN
cana-5531	27	30	on	on	ADP
cana-5531	27	31	the	the	DET
cana-5531	27	32	contact	contact	NOUN
cana-5531	27	33	boundary	boundary	ADJ
cana-5531	27	34	conditions	condition	NOUN
cana-5531	27	35	.	.	PUNCT
cana-5531	28	1	in	in	ADP
cana-5531	28	2	section	section	NOUN
cana-5531	28	3	4	4	NUM
cana-5531	28	4	,	,	PUNCT
cana-5531	28	5	we	we	PRON
cana-5531	28	6	list	list	VERB
cana-5531	28	7	the	the	DET
cana-5531	28	8	assumptions	assumption	NOUN
cana-5531	28	9	on	on	ADP
cana-5531	28	10	the	the	DET
cana-5531	28	11	data	datum	NOUN
cana-5531	28	12	and	and	CCONJ
cana-5531	28	13	derive	derive	VERB
cana-5531	28	14	the	the	DET
cana-5531	28	15	variational	variational	ADJ
cana-5531	28	16	formulation	formulation	NOUN
cana-5531	28	17	.	.	PUNCT
cana-5531	29	1	in	in	ADP
cana-5531	29	2	section	section	NOUN
cana-5531	29	3	5	5	NUM
cana-5531	29	4	,	,	PUNCT
cana-5531	29	5	we	we	PRON
cana-5531	29	6	present	present	VERB
cana-5531	29	7	our	our	PRON
cana-5531	29	8	main	main	ADJ
cana-5531	29	9	results	result	NOUN
cana-5531	29	10	on	on	ADP
cana-5531	29	11	existence	existence	NOUN
cana-5531	29	12	and	and	CCONJ
cana-5531	29	13	uniqueness	uniqueness	NOUN
cana-5531	29	14	which	which	PRON
cana-5531	29	15	state	state	VERB
cana-5531	29	16	the	the	DET
cana-5531	29	17	unique	unique	ADJ
cana-5531	29	18	weak	weak	ADJ
cana-5531	29	19	solvability	solvability	NOUN
cana-5531	29	20	.	.	PUNCT
cana-5531	30	1	2	2	X
cana-5531	30	2	.	.	NUM
cana-5531	30	3	notations	notation	NOUN
cana-5531	30	4	and	and	CCONJ
cana-5531	30	5	preliminaries	preliminary	NOUN
cana-5531	30	6	throughout	throughout	ADP
cana-5531	30	7	this	this	DET
cana-5531	30	8	paper	paper	NOUN
cana-5531	30	9	,	,	PUNCT
cana-5531	30	10	𝕊𝑑	𝕊𝑑	PROPN
cana-5531	30	11	represents	represent	VERB
cana-5531	30	12	the	the	DET
cana-5531	30	13	space	space	NOUN
cana-5531	30	14	of	of	ADP
cana-5531	30	15	second	second	ADJ
cana-5531	30	16	order	order	NOUN
cana-5531	30	17	symmetric	symmetric	ADJ
cana-5531	30	18	tensors	tensor	NOUN
cana-5531	30	19	on	on	ADP
cana-5531	30	20	ℝ𝑑(d	ℝ𝑑(d	NOUN
cana-5531	30	21	=	=	NOUN
cana-5531	30	22	2,3	2,3	NUM
cana-5531	30	23	)	)	PUNCT
cana-5531	30	24	while	while	SCONJ
cana-5531	30	25	|	|	ADV
cana-5531	30	26	.	.	PUNCT
cana-5531	31	1	|	|	ADV
cana-5531	31	2	represents	represent	VERB
cana-5531	31	3	the	the	DET
cana-5531	31	4	euclidean	euclidean	ADJ
cana-5531	31	5	norm	norm	NOUN
cana-5531	31	6	on	on	ADP
cana-5531	31	7	ℝ𝑑and	ℝ𝑑and	PROPN
cana-5531	31	8	𝕊𝑑	𝕊𝑑	PROPN
cana-5531	31	9	.	.	PUNCT
cana-5531	32	1	thus	thus	ADV
cana-5531	32	2	,	,	PUNCT
cana-5531	32	3	for	for	ADP
cana-5531	32	4	every	every	DET
cana-5531	32	5	𝑢	𝑢	PROPN
cana-5531	32	6	,	,	PUNCT
cana-5531	32	7	𝑣	𝑣	PRON
cana-5531	32	8	∈	∈	PROPN
cana-5531	33	1	ℝ𝑑	ℝ𝑑	PROPN
cana-5531	33	2	,	,	PUNCT
cana-5531	33	3	𝑢.	𝑢.	NOUN
cana-5531	33	4	𝜐	𝜐	PROPN
cana-5531	33	5	=	=	NOUN
cana-5531	33	6	𝑢𝑖𝜐𝑖	𝑢𝑖𝜐𝑖	NOUN
cana-5531	33	7	and	and	CCONJ
cana-5531	33	8	|𝜐|	|𝜐|	PROPN
cana-5531	33	9	=	=	PUNCT
cana-5531	33	10	(	(	PUNCT
cana-5531	33	11	𝜐	𝜐	X
cana-5531	33	12	,	,	PUNCT
cana-5531	33	13	𝜐	𝜐	NOUN
cana-5531	33	14	)	)	PUNCT
cana-5531	33	15	1	1	NUM
cana-5531	33	16	2	2	NUM
cana-5531	33	17	,	,	PUNCT
cana-5531	33	18	and	and	CCONJ
cana-5531	33	19	for	for	ADP
cana-5531	33	20	every	every	DET
cana-5531	33	21	𝜎	𝜎	PROPN
cana-5531	33	22	,	,	PUNCT
cana-5531	33	23	𝜏	𝜏	X
cana-5531	33	24	∈	∈	PROPN
cana-5531	33	25	𝕊𝑑	𝕊𝑑	PROPN
cana-5531	33	26	,	,	PUNCT
cana-5531	33	27	𝜎.	𝜎.	ADJ
cana-5531	33	28	𝜏	𝜏	X
cana-5531	33	29	=	=	SYM
cana-5531	33	30	𝜎𝑖𝑗𝜏𝑖𝑗	𝜎𝑖𝑗𝜏𝑖𝑗	VERB
cana-5531	33	31	,	,	PUNCT
cana-5531	33	32	|𝜏|	|𝜏|	PROPN
cana-5531	33	33	=	=	PUNCT
cana-5531	33	34	(	(	PUNCT
cana-5531	33	35	𝜏.	𝜏.	NOUN
cana-5531	33	36	𝜏	𝜏	NUM
cana-5531	33	37	)	)	PUNCT
cana-5531	33	38	1	1	NUM
cana-5531	33	39	2	2	NUM
cana-5531	33	40	.	.	PUNCT
cana-5531	34	1	the	the	DET
cana-5531	34	2	summing	sum	VERB
cana-5531	34	3	convention	convention	NOUN
cana-5531	34	4	over	over	ADP
cana-5531	34	5	represented	represent	VERB
cana-5531	34	6	indices	index	NOUN
cana-5531	34	7	is	be	AUX
cana-5531	34	8	used	use	VERB
cana-5531	34	9	here	here	ADV
cana-5531	34	10	and	and	CCONJ
cana-5531	34	11	below	below	ADV
cana-5531	34	12	,	,	PUNCT
cana-5531	34	13	where	where	SCONJ
cana-5531	34	14	the	the	DET
cana-5531	34	15	indices	index	NOUN
cana-5531	34	16	𝑖	𝑖	X
cana-5531	34	17	and	and	CCONJ
cana-5531	34	18	𝑗	𝑗	PRON
cana-5531	34	19	range	range	NOUN
cana-5531	34	20	from	from	ADP
cana-5531	34	21	1	1	NUM
cana-5531	34	22	to	to	ADP
cana-5531	34	23	d.	d.	PROPN
cana-5531	34	24	let	let	VERB
cana-5531	35	1	ω	ω	PROPN
cana-5531	35	2	⊂	⊂	PROPN
cana-5531	36	1	ℝ𝑑	ℝ𝑑	PROPN
cana-5531	36	2	be	be	AUX
cana-5531	36	3	a	a	DET
cana-5531	36	4	bounded	bounded	ADJ
cana-5531	36	5	domain	domain	NOUN
cana-5531	36	6	with	with	ADP
cana-5531	36	7	a	a	DET
cana-5531	36	8	lipschitz	lipschitz	ADJ
cana-5531	36	9	boundary	boundary	ADJ
cana-5531	36	10	γand	γand	NOUN
cana-5531	36	11	let	let	VERB
cana-5531	36	12	𝜈	𝜈	PRON
cana-5531	36	13	denote	denote	VERB
cana-5531	36	14	the	the	DET
cana-5531	36	15	unit	unit	NOUN
cana-5531	36	16	outer	outer	NOUN
cana-5531	36	17	normal	normal	ADJ
cana-5531	36	18	on	on	ADP
cana-5531	36	19	γ	γ	PROPN
cana-5531	36	20	.	.	PROPN
cana-5531	36	21	for	for	ADP
cana-5531	36	22	lebesgue	lebesgue	NOUN
cana-5531	36	23	and	and	CCONJ
cana-5531	36	24	sololev	sololev	NOUN
cana-5531	36	25	spaces	space	NOUN
cana-5531	36	26	associated	associate	VERB
cana-5531	36	27	to	to	ADP
cana-5531	36	28	ω	ω	NUM
cana-5531	36	29	and	and	CCONJ
cana-5531	36	30	γand	γand	NOUN
cana-5531	36	31	introduce	introduce	VERB
cana-5531	36	32	the	the	DET
cana-5531	36	33	spaces	space	NOUN
cana-5531	36	34	,	,	PUNCT
cana-5531	37	1	𝐻	𝐻	PROPN
cana-5531	37	2	=	=	SYM
cana-5531	37	3	𝕃2(ω)𝑑	𝕃2(ω)𝑑	PROPN
cana-5531	37	4	=	=	SYM
cana-5531	37	5	{	{	PUNCT
cana-5531	37	6	𝑢	𝑢	X
cana-5531	37	7	=	=	SYM
cana-5531	37	8	(	(	PUNCT
cana-5531	37	9	𝑢𝑖)/𝑢𝑖	𝑢𝑖)/𝑢𝑖	X
cana-5531	37	10	∈	∈	PROPN
cana-5531	37	11	𝕃	𝕃	NOUN
cana-5531	37	12	2(ω	2(ω	NUM
cana-5531	37	13	)	)	PUNCT
cana-5531	37	14	}	}	PUNCT
cana-5531	37	15	,	,	PUNCT
cana-5531	37	16	ℋ=	ℋ=	PROPN
cana-5531	37	17	{	{	PUNCT
cana-5531	37	18	𝜎	𝜎	NOUN
cana-5531	37	19	=	=	X
cana-5531	37	20	(	(	PUNCT
cana-5531	37	21	𝜎𝑖𝑗	𝜎𝑖𝑗	PROPN
cana-5531	37	22	)	)	PUNCT
cana-5531	37	23	/𝜎𝑖𝑗	/𝜎𝑖𝑗	PUNCT
cana-5531	38	1	=	=	PUNCT
cana-5531	38	2	𝜎𝑗𝑖	𝜎𝑗𝑖	NOUN
cana-5531	38	3	∈	∈	PROPN
cana-5531	38	4	𝕃	𝕃	NOUN
cana-5531	38	5	2(ω	2(ω	NUM
cana-5531	38	6	)	)	PUNCT
cana-5531	38	7	}	}	PUNCT
cana-5531	38	8	,	,	PUNCT
cana-5531	38	9	h1	h1	PROPN
cana-5531	38	10	=	=	SYM
cana-5531	38	11	{	{	PUNCT
cana-5531	38	12	u	u	NOUN
cana-5531	38	13	=	=	SYM
cana-5531	38	14	(	(	PUNCT
cana-5531	38	15	ui)/ε(u	ui)/ε(u	PROPN
cana-5531	38	16	)	)	PUNCT
cana-5531	38	17	∈	∈	PROPN
cana-5531	38	18	ℋ	ℋ	PROPN
cana-5531	38	19	}	}	PUNCT
cana-5531	38	20	,	,	PUNCT
cana-5531	38	21	ℋ1	ℋ1	PROPN
cana-5531	38	22	=	=	PUNCT
cana-5531	38	23	{	{	PUNCT
cana-5531	38	24	σ	σ	PROPN
cana-5531	38	25	∈	∈	PROPN
cana-5531	38	26	ℋ/di𝜐σ	ℋ/di𝜐σ	NUM
cana-5531	38	27	∈	∈	PROPN
cana-5531	38	28	h	h	NOUN
cana-5531	38	29	}	}	PUNCT
cana-5531	38	30	.	.	PUNCT
cana-5531	39	1	here	here	ADV
cana-5531	39	2	the	the	DET
cana-5531	39	3	deformation	deformation	NOUN
cana-5531	39	4	ε	ε	PROPN
cana-5531	39	5	and	and	CCONJ
cana-5531	39	6	divergence	divergence	NOUN
cana-5531	39	7	di𝜐	di𝜐	NOUN
cana-5531	39	8	are	be	AUX
cana-5531	39	9	operators	operator	NOUN
cana-5531	39	10	defined	define	VERB
cana-5531	39	11	by	by	ADP
cana-5531	39	12	𝜀(𝑢	𝜀(𝑢	ADJ
cana-5531	39	13	)	)	PUNCT
cana-5531	39	14	=	=	SYM
cana-5531	39	15	(	(	PUNCT
cana-5531	39	16	𝜀𝑖𝑗(𝑢	𝜀𝑖𝑗(𝑢	PROPN
cana-5531	39	17	)	)	PUNCT
cana-5531	39	18	)	)	PUNCT
cana-5531	39	19	,	,	PUNCT
cana-5531	39	20	𝜀𝑖𝑗(𝑢	𝜀𝑖𝑗(𝑢	PROPN
cana-5531	39	21	)	)	PUNCT
cana-5531	39	22	=	=	SYM
cana-5531	39	23	1	1	NUM
cana-5531	39	24	2	2	NUM
cana-5531	39	25	(	(	PUNCT
cana-5531	39	26	𝑢𝑖,𝑗	𝑢𝑖,𝑗	X
cana-5531	39	27	+	+	CCONJ
cana-5531	39	28	𝑢𝑗,𝑖	𝑢𝑗,𝑖	NUM
cana-5531	39	29	)	)	PUNCT
cana-5531	39	30	,	,	PUNCT
cana-5531	39	31	𝐷𝑖𝜐𝜎	𝐷𝑖𝜐𝜎	PROPN
cana-5531	39	32	=	=	PUNCT
cana-5531	39	33	(	(	PUNCT
cana-5531	39	34	𝜎𝑖𝑗,𝑗	𝜎𝑖𝑗,𝑗	NOUN
cana-5531	39	35	)	)	PUNCT
cana-5531	39	36	.	.	PUNCT
cana-5531	40	1	the	the	DET
cana-5531	40	2	spaces	space	NOUN
cana-5531	40	3	h	h	NOUN
cana-5531	40	4	,	,	PUNCT
cana-5531	40	5	ℋ	ℋ	PROPN
cana-5531	40	6	,	,	PUNCT
cana-5531	40	7	h1	h1	NOUN
cana-5531	40	8	and	and	CCONJ
cana-5531	40	9	ℋ1	ℋ1	PROPN
cana-5531	40	10	are	be	AUX
cana-5531	40	11	real	real	ADJ
cana-5531	40	12	hilbert	hilbert	NOUN
cana-5531	40	13	spaces	space	NOUN
cana-5531	40	14	endowed	endow	VERB
cana-5531	40	15	with	with	ADP
cana-5531	40	16	the	the	DET
cana-5531	40	17	canonical	canonical	ADJ
cana-5531	40	18	inner	inner	ADJ
cana-5531	40	19	products	product	NOUN
cana-5531	40	20	given	give	VERB
cana-5531	40	21	by	by	ADP
cana-5531	40	22	communications	communication	NOUN
cana-5531	40	23	on	on	ADP
cana-5531	40	24	applied	apply	VERB
cana-5531	40	25	nonlinear	nonlinear	ADJ
cana-5531	40	26	analysis	analysis	NOUN
cana-5531	40	27	issn	issn	NOUN
cana-5531	40	28	:	:	PUNCT
cana-5531	40	29	1074	1074	NUM
cana-5531	40	30	-	-	PUNCT
cana-5531	40	31	133x	133x	NUM
cana-5531	40	32	vol	vol	NOUN
cana-5531	40	33	32	32	NUM
cana-5531	40	34	no	no	NOUN
cana-5531	40	35	.	.	NOUN
cana-5531	40	36	3	3	NUM
cana-5531	40	37	(	(	PUNCT
cana-5531	40	38	2025	2025	NUM
cana-5531	40	39	)	)	PUNCT
cana-5531	40	40	966	966	NUM
cana-5531	40	41	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	40	42	(	(	PUNCT
cana-5531	40	43	𝑢	𝑢	X
cana-5531	40	44	,	,	PUNCT
cana-5531	40	45	𝜐)𝐻	𝜐)𝐻	NOUN
cana-5531	40	46	=	=	SYM
cana-5531	40	47	∫	∫	NOUN
cana-5531	40	48	𝑢𝑖𝜐𝑖	𝑢𝑖𝜐𝑖	NOUN
cana-5531	40	49	𝑑𝑥	𝑑𝑥	VERB
cana-5531	40	50	ω	ω	X
cana-5531	40	51	∀	∀	X
cana-5531	40	52	𝑢	𝑢	NOUN
cana-5531	40	53	,	,	PUNCT
cana-5531	40	54	𝜐	𝜐	PROPN
cana-5531	40	55	∈	∈	PROPN
cana-5531	40	56	𝐻	𝐻	PROPN
cana-5531	40	57	,	,	PUNCT
cana-5531	40	58	(	(	PUNCT
cana-5531	40	59	𝜎	𝜎	INTJ
cana-5531	40	60	,	,	PUNCT
cana-5531	40	61	𝜏)ℋ	𝜏)ℋ	VERB
cana-5531	40	62	=	=	SYM
cana-5531	40	63	∫	∫	PROPN
cana-5531	40	64	𝜎𝑖𝑗𝜏𝑖𝑗	𝜎𝑖𝑗𝜏𝑖𝑗	VERB
cana-5531	40	65	𝑑𝑥	𝑑𝑥	VERB
cana-5531	40	66	ω	ω	NUM
cana-5531	40	67	∀𝜎	∀𝜎	NOUN
cana-5531	40	68	,	,	PUNCT
cana-5531	40	69	𝜏	𝜏	PROPN
cana-5531	40	70	∈	∈	PROPN
cana-5531	40	71	ℋ	ℋ	PROPN
cana-5531	40	72	,	,	PUNCT
cana-5531	40	73	(	(	PUNCT
cana-5531	40	74	u	u	NOUN
cana-5531	40	75	,	,	PUNCT
cana-5531	40	76	𝜐)h1	𝜐)h1	NOUN
cana-5531	40	77	=	=	SYM
cana-5531	40	78	(	(	PUNCT
cana-5531	40	79	u	u	NOUN
cana-5531	40	80	,	,	PUNCT
cana-5531	40	81	𝜐)h	𝜐)h	X
cana-5531	40	82	+	+	CCONJ
cana-5531	40	83	(	(	PUNCT
cana-5531	40	84	𝜀(𝑢	𝜀(𝑢	ADJ
cana-5531	40	85	)	)	PUNCT
cana-5531	40	86	,	,	PUNCT
cana-5531	40	87	𝜀(𝜐))ℋ	𝜀(𝜐))ℋ	NOUN
cana-5531	40	88	∀u	∀u	PROPN
cana-5531	40	89	,	,	PUNCT
cana-5531	40	90	𝜐	𝜐	PROPN
cana-5531	40	91	∈	∈	PROPN
cana-5531	40	92	h1	h1	PROPN
cana-5531	40	93	,	,	PUNCT
cana-5531	40	94	(	(	PUNCT
cana-5531	40	95	𝜎	𝜎	INTJ
cana-5531	40	96	,	,	PUNCT
cana-5531	40	97	𝜏	𝜏	NOUN
cana-5531	40	98	)	)	PUNCT
cana-5531	40	99	ℋ1	ℋ1	NOUN
cana-5531	40	100	=	=	SYM
cana-5531	40	101	(	(	PUNCT
cana-5531	40	102	𝜎	𝜎	PROPN
cana-5531	40	103	,	,	PUNCT
cana-5531	40	104	𝜏	𝜏	NOUN
cana-5531	40	105	)	)	PUNCT
cana-5531	40	106	ℋ	ℋ	NOUN
cana-5531	40	107	+	+	CCONJ
cana-5531	40	108	(	(	PUNCT
cana-5531	40	109	di𝜐σ	di𝜐σ	NOUN
cana-5531	40	110	,	,	PUNCT
cana-5531	40	111	di𝜐τ	di𝜐τ	NOUN
cana-5531	40	112	)	)	PUNCT
cana-5531	40	113	h	h	NOUN
cana-5531	40	114	∀σ	∀σ	PROPN
cana-5531	40	115	,	,	PUNCT
cana-5531	40	116	τ	τ	PROPN
cana-5531	40	117	∈	∈	PROPN
cana-5531	40	118	ℋ1	ℋ1	PROPN
cana-5531	40	119	.	.	PUNCT
cana-5531	41	1	the	the	DET
cana-5531	41	2	associated	associated	ADJ
cana-5531	41	3	norms	norm	NOUN
cana-5531	41	4	on	on	ADP
cana-5531	41	5	the	the	DET
cana-5531	41	6	spaces	space	NOUN
cana-5531	41	7	h	h	NOUN
cana-5531	41	8	,	,	PUNCT
cana-5531	41	9	ℋ	ℋ	PROPN
cana-5531	41	10	,	,	PUNCT
cana-5531	41	11	h1	h1	NOUN
cana-5531	41	12	and	and	CCONJ
cana-5531	41	13	ℋ1	ℋ1	PROPN
cana-5531	41	14	are	be	AUX
cana-5531	41	15	denoted	denote	VERB
cana-5531	41	16	by	by	ADP
cana-5531	41	17	|.|h,|	|.|h,|	NOUN
cana-5531	41	18	.	.	PUNCT
cana-5531	42	1	|ℋ	|ℋ	NOUN
cana-5531	42	2	,	,	PUNCT
cana-5531	42	3	|.|h1	|.|h1	NOUN
cana-5531	42	4	and	and	CCONJ
cana-5531	42	5	|	|	ADV
cana-5531	42	6	.	.	PUNCT
cana-5531	43	1	|ℋ1	|ℋ1	NOUN
cana-5531	43	2	,	,	PUNCT
cana-5531	43	3	respectively	respectively	ADV
cana-5531	43	4	.	.	PUNCT
cana-5531	44	1	for	for	ADP
cana-5531	44	2	every	every	DET
cana-5531	44	3	element	element	NOUN
cana-5531	44	4	𝜐	𝜐	PROPN
cana-5531	44	5	∈	∈	PROPN
cana-5531	44	6	h1	h1	NOUN
cana-5531	44	7	we	we	PRON
cana-5531	44	8	also	also	ADV
cana-5531	44	9	use	use	VERB
cana-5531	44	10	the	the	DET
cana-5531	44	11	notation	notation	NOUN
cana-5531	44	12	𝜈	𝜈	X
cana-5531	44	13	for	for	ADP
cana-5531	44	14	the	the	DET
cana-5531	44	15	trace	trace	NOUN
cana-5531	44	16	of	of	ADP
cana-5531	44	17	𝜈	𝜈	PRON
cana-5531	44	18	on	on	ADP
cana-5531	44	19	γ	γ	NOUN
cana-5531	44	20	and	and	CCONJ
cana-5531	44	21	we	we	PRON
cana-5531	44	22	denote	denote	VERB
cana-5531	44	23	by	by	ADP
cana-5531	44	24	𝜐𝜈	𝜐𝜈	INTJ
cana-5531	44	25	and	and	CCONJ
cana-5531	44	26	𝜐𝜏	𝜐𝜏	ADP
cana-5531	44	27	the	the	DET
cana-5531	44	28	normal	normal	ADJ
cana-5531	44	29	and	and	CCONJ
cana-5531	44	30	the	the	DET
cana-5531	44	31	tangential	tangential	ADJ
cana-5531	44	32	components	component	NOUN
cana-5531	44	33	of	of	ADP
cana-5531	44	34	𝜐	𝜐	PROPN
cana-5531	44	35	on	on	ADP
cana-5531	44	36	γ	γ	NOUN
cana-5531	44	37	given	give	VERB
cana-5531	44	38	by	by	ADP
cana-5531	44	39	𝜐𝜈	𝜐𝜈	NOUN
cana-5531	44	40	=	=	NOUN
cana-5531	44	41	𝜐.	𝜐.	NOUN
cana-5531	44	42	𝜈	𝜈	NOUN
cana-5531	44	43	,	,	PUNCT
cana-5531	44	44	𝜐𝜏	𝜐𝜏	ADP
cana-5531	44	45	=	=	SYM
cana-5531	45	1	𝜐	𝜐	PROPN
cana-5531	45	2	−	−	NOUN
cana-5531	45	3	𝜐𝜈𝜈.	𝜐𝜈𝜈.	NOUN
cana-5531	45	4	(	(	PUNCT
cana-5531	45	5	2.1	2.1	NUM
cana-5531	45	6	)	)	PUNCT
cana-5531	45	7	we	we	PRON
cana-5531	45	8	also	also	ADV
cana-5531	45	9	denote	denote	VERB
cana-5531	45	10	by	by	ADP
cana-5531	45	11	𝜐𝜈	𝜐𝜈	INTJ
cana-5531	45	12	and	and	CCONJ
cana-5531	45	13	𝜐𝜏	𝜐𝜏	ADP
cana-5531	45	14	the	the	DET
cana-5531	45	15	normal	normal	ADJ
cana-5531	45	16	and	and	CCONJ
cana-5531	45	17	tangential	tangential	ADJ
cana-5531	45	18	traces	trace	NOUN
cana-5531	45	19	of	of	ADP
cana-5531	45	20	a	a	DET
cana-5531	45	21	function	function	NOUN
cana-5531	45	22	𝜎	𝜎	PROPN
cana-5531	45	23	∈	∈	PROPN
cana-5531	45	24	ℋ1	ℋ1	NOUN
cana-5531	46	1	and	and	CCONJ
cana-5531	46	2	we	we	PRON
cana-5531	46	3	recall	recall	VERB
cana-5531	46	4	that	that	SCONJ
cana-5531	46	5	when	when	SCONJ
cana-5531	46	6	σ	σ	PROPN
cana-5531	46	7	is	be	AUX
cana-5531	46	8	a	a	DET
cana-5531	46	9	regular	regular	ADJ
cana-5531	46	10	function	function	NOUN
cana-5531	46	11	then	then	ADV
cana-5531	46	12	𝜎𝜈	𝜎𝜈	ADV
cana-5531	46	13	=	=	SYM
cana-5531	46	14	(	(	PUNCT
cana-5531	46	15	𝜎𝜈	𝜎𝜈	NOUN
cana-5531	46	16	)	)	PUNCT
cana-5531	46	17	.	.	PUNCT
cana-5531	47	1	𝜈	𝜈	X
cana-5531	47	2	,	,	PUNCT
cana-5531	47	3	𝜎𝜏	𝜎𝜏	X
cana-5531	47	4	=	=	PUNCT
cana-5531	47	5	𝜎𝜈	𝜎𝜈	ADP
cana-5531	47	6	−	−	NOUN
cana-5531	47	7	𝜎𝜈𝜈.	𝜎𝜈𝜈.	X
cana-5531	47	8	(	(	PUNCT
cana-5531	47	9	2.2	2.2	NUM
cana-5531	47	10	)	)	PUNCT
cana-5531	47	11	and	and	CCONJ
cana-5531	47	12	the	the	DET
cana-5531	47	13	following	follow	VERB
cana-5531	47	14	green	green	PROPN
cana-5531	47	15	’s	’s	PART
cana-5531	47	16	formula	formula	NOUN
cana-5531	47	17	holds	hold	VERB
cana-5531	47	18	:	:	PUNCT
cana-5531	47	19	(	(	PUNCT
cana-5531	47	20	𝜎	𝜎	INTJ
cana-5531	47	21	,	,	PUNCT
cana-5531	47	22	𝜀(𝜐	𝜀(𝜐	ADJ
cana-5531	47	23	)	)	PUNCT
cana-5531	47	24	)	)	PUNCT
cana-5531	48	1	ℋ	ℋ	PROPN
cana-5531	48	2	+	+	CCONJ
cana-5531	48	3	(	(	PUNCT
cana-5531	48	4	𝐷𝑖𝜐𝜎	𝐷𝑖𝜐𝜎	PROPN
cana-5531	48	5	,	,	PUNCT
cana-5531	48	6	𝜐)𝐻	𝜐)𝐻	NOUN
cana-5531	48	7	=	=	SYM
cana-5531	48	8	∫	∫	PROPN
cana-5531	48	9	𝜎𝜈.	𝜎𝜈.	NOUN
cana-5531	48	10	𝜐	𝜐	PROPN
cana-5531	48	11	𝑑𝑎	𝑑𝑎	PROPN
cana-5531	48	12	∀𝜐	∀𝜐	PROPN
cana-5531	48	13	∈	∈	PROPN
cana-5531	48	14	𝐻1,γ	𝐻1,γ	PROPN
cana-5531	48	15	(	(	PUNCT
cana-5531	48	16	2.3	2.3	NUM
cana-5531	48	17	)	)	PUNCT
cana-5531	48	18	where	where	SCONJ
cana-5531	48	19	the	the	DET
cana-5531	48	20	surface	surface	NOUN
cana-5531	48	21	measure	measure	NOUN
cana-5531	48	22	element	element	NOUN
cana-5531	48	23	is	be	AUX
cana-5531	48	24	da	da	ADJ
cana-5531	48	25	.	.	PUNCT
cana-5531	49	1	let	let	VERB
cana-5531	49	2	𝑇	𝑇	PROPN
cana-5531	49	3	>	>	X
cana-5531	49	4	0	0	NUM
cana-5531	49	5	,	,	PUNCT
cana-5531	49	6	for	for	ADP
cana-5531	49	7	every	every	DET
cana-5531	49	8	real	real	ADJ
cana-5531	49	9	hilbert	hilbert	NOUN
cana-5531	49	10	space	space	NOUN
cana-5531	49	11	𝑋	𝑋	PROPN
cana-5531	49	12	we	we	PRON
cana-5531	49	13	employ	employ	VERB
cana-5531	49	14	the	the	DET
cana-5531	49	15	usual	usual	ADJ
cana-5531	49	16	notation	notation	NOUN
cana-5531	49	17	for	for	ADP
cana-5531	49	18	the	the	DET
cana-5531	49	19	spaces	space	NOUN
cana-5531	49	20	𝕃𝑝(0,𝑇;𝑋	𝕃𝑝(0,𝑇;𝑋	PROPN
cana-5531	49	21	)	)	PUNCT
cana-5531	49	22	,	,	PUNCT
cana-5531	49	23	1	1	NUM
cana-5531	49	24	≤	≤	PROPN
cana-5531	49	25	𝑝	𝑝	ADP
cana-5531	49	26	≤∞	≤∞	PROPN
cana-5531	49	27	and	and	CCONJ
cana-5531	49	28	𝑊1,∞	𝑊1,∞	PROPN
cana-5531	49	29	(	(	PUNCT
cana-5531	49	30	0	0	NUM
cana-5531	49	31	,	,	PUNCT
cana-5531	49	32	𝑇;𝑋	𝑇;𝑋	NOUN
cana-5531	49	33	)	)	PUNCT
cana-5531	49	34	.	.	PUNCT
cana-5531	50	1	recall	recall	VERB
cana-5531	50	2	that	that	SCONJ
cana-5531	50	3	the	the	DET
cana-5531	50	4	norm	norm	NOUN
cana-5531	50	5	on	on	ADP
cana-5531	50	6	the	the	DET
cana-5531	50	7	space	space	NOUN
cana-5531	50	8	𝑊1,∞	𝑊1,∞	NOUN
cana-5531	50	9	(	(	PUNCT
cana-5531	50	10	0,𝑇	0,𝑇	NUM
cana-5531	50	11	;	;	PUNCT
cana-5531	50	12	𝑋	𝑋	PROPN
cana-5531	50	13	)	)	PUNCT
cana-5531	50	14	is	be	AUX
cana-5531	50	15	given	give	VERB
cana-5531	50	16	by	by	ADP
cana-5531	50	17	‖𝑢‖𝑊1,∞(0.𝑇;𝑋	‖𝑢‖𝑊1,∞(0.𝑇;𝑋	NOUN
cana-5531	50	18	)	)	PUNCT
cana-5531	50	19	=	=	SYM
cana-5531	50	20	‖𝑢‖𝕃∞(0.𝑇;𝑋	‖𝑢‖𝕃∞(0.𝑇;𝑋	NOUN
cana-5531	50	21	)	)	PUNCT
cana-5531	50	22	+	+	CCONJ
cana-5531	50	23	‖	‖	PROPN
cana-5531	50	24	�	�	PROPN
cana-5531	50	25	̇	̇	NOUN
cana-5531	50	26	�	�	NOUN
cana-5531	50	27	‖𝕃∞(0.𝑇,𝑋	‖𝕃∞(0.𝑇,𝑋	NUM
cana-5531	50	28	)	)	PUNCT
cana-5531	50	29	,	,	PUNCT
cana-5531	50	30	where	where	SCONJ
cana-5531	50	31	�	�	PROPN
cana-5531	50	32	̇	̇	PROPN
cana-5531	50	33	�	�	PROPN
cana-5531	50	34	denote	denote	VERB
cana-5531	50	35	the	the	DET
cana-5531	50	36	first	first	ADJ
cana-5531	50	37	derivative	derivative	NOUN
cana-5531	50	38	of	of	ADP
cana-5531	50	39	u	u	NOUN
cana-5531	50	40	with	with	ADP
cana-5531	50	41	respect	respect	NOUN
cana-5531	50	42	to	to	ADP
cana-5531	50	43	time	time	NOUN
cana-5531	50	44	.	.	PUNCT
cana-5531	51	1	fanilly	fanilly	ADV
cana-5531	51	2	,	,	PUNCT
cana-5531	51	3	the	the	DET
cana-5531	51	4	space	space	NOUN
cana-5531	51	5	of	of	ADP
cana-5531	51	6	continuous	continuous	ADJ
cana-5531	51	7	functions	function	NOUN
cana-5531	51	8	from	from	ADP
cana-5531	51	9	[	[	X
cana-5531	51	10	0	0	NUM
cana-5531	51	11	,	,	PUNCT
cana-5531	51	12	t	t	NOUN
cana-5531	51	13	]	]	PUNCT
cana-5531	51	14	to	to	PART
cana-5531	51	15	x	x	PROPN
cana-5531	51	16	is	be	AUX
cana-5531	51	17	denoted	denote	VERB
cana-5531	51	18	by	by	ADP
cana-5531	51	19	c	c	PROPN
cana-5531	51	20	(	(	PUNCT
cana-5531	51	21	[	[	X
cana-5531	51	22	0,t	0,t	X
cana-5531	51	23	]	]	PUNCT
cana-5531	51	24	;	;	PUNCT
cana-5531	51	25	x	x	X
cana-5531	51	26	)	)	PUNCT
cana-5531	51	27	with	with	ADP
cana-5531	51	28	the	the	DET
cana-5531	51	29	norm	norm	NOUN
cana-5531	51	30	‖𝑥‖𝐶([0,𝑇];𝑋	‖𝑥‖𝐶([0,𝑇];𝑋	PROPN
cana-5531	51	31	)	)	PUNCT
cana-5531	51	32	=	=	SYM
cana-5531	51	33	max	max	PROPN
cana-5531	51	34	𝑡∈[0,𝑇	𝑡∈[0,𝑇	PROPN
cana-5531	51	35	]	]	PUNCT
cana-5531	51	36	‖𝑥(𝑡)‖𝑋.	‖𝑥(𝑡)‖𝑋.	VERB
cana-5531	51	37	moreover	moreover	ADV
cana-5531	51	38	,	,	PUNCT
cana-5531	51	39	for	for	ADP
cana-5531	51	40	a	a	DET
cana-5531	51	41	real	real	ADJ
cana-5531	51	42	number	number	NOUN
cana-5531	51	43	r	r	NOUN
cana-5531	51	44	,	,	PUNCT
cana-5531	51	45	r+	r+	NUM
cana-5531	51	46	is	be	AUX
cana-5531	51	47	used	use	VERB
cana-5531	51	48	to	to	PART
cana-5531	51	49	represent	represent	VERB
cana-5531	51	50	its	its	PRON
cana-5531	51	51	positive	positive	ADJ
cana-5531	51	52	part	part	NOUN
cana-5531	51	53	,	,	PUNCT
cana-5531	51	54	that	that	PRON
cana-5531	51	55	is	is	ADV
cana-5531	51	56	r+	r+	PUNCT
cana-5531	51	57	=	=	SYM
cana-5531	51	58	max	max	X
cana-5531	51	59	{	{	PUNCT
cana-5531	51	60	r,0	r,0	PROPN
cana-5531	51	61	}	}	PUNCT
cana-5531	51	62	.	.	PUNCT
cana-5531	52	1	3	3	X
cana-5531	52	2	.	.	X
cana-5531	52	3	problem	problem	NOUN
cana-5531	52	4	statement	statement	NOUN
cana-5531	52	5	the	the	DET
cana-5531	52	6	physical	physical	ADJ
cana-5531	52	7	setting	setting	NOUN
cana-5531	52	8	is	be	AUX
cana-5531	52	9	the	the	DET
cana-5531	52	10	following	following	NOUN
cana-5531	52	11	.	.	PUNCT
cana-5531	53	1	a	a	DET
cana-5531	53	2	viscoelastic	viscoelastic	ADJ
cana-5531	53	3	body	body	NOUN
cana-5531	53	4	with	with	ADP
cana-5531	53	5	long	long	ADJ
cana-5531	53	6	memory	memory	NOUN
cana-5531	53	7	occupies	occupy	VERB
cana-5531	53	8	a	a	DET
cana-5531	53	9	bounded	bounded	ADJ
cana-5531	53	10	domain	domain	NOUN
cana-5531	53	11	ω	ω	X
cana-5531	53	12	⊂	⊂	PROPN
cana-5531	53	13	ℝ𝑑(d	ℝ𝑑(d	NOUN
cana-5531	53	14	=	=	PUNCT
cana-5531	53	15	2	2	NUM
cana-5531	53	16	,	,	PUNCT
cana-5531	53	17	3	3	NUM
cana-5531	53	18	)	)	PUNCT
cana-5531	53	19	with	with	ADP
cana-5531	53	20	a	a	DET
cana-5531	53	21	regular	regular	ADJ
cana-5531	53	22	boundary	boundary	ADJ
cana-5531	53	23	γ	γ	NOUN
cana-5531	53	24	that	that	PRON
cana-5531	53	25	is	be	AUX
cana-5531	53	26	partitioned	partition	VERB
cana-5531	53	27	into	into	ADP
cana-5531	53	28	three	three	NUM
cana-5531	53	29	disjoint	disjoint	ADJ
cana-5531	53	30	measurable	measurable	ADJ
cana-5531	53	31	parts	part	NOUN
cana-5531	53	32	γ1	γ1	NOUN
cana-5531	53	33	,	,	PUNCT
cana-5531	53	34	γ2	γ2	NOUN
cana-5531	53	35	and	and	CCONJ
cana-5531	53	36	γ3such	γ3such	ADJ
cana-5531	53	37	that	that	DET
cana-5531	53	38	meas	meas	PROPN
cana-5531	53	39	γ1	γ1	PROPN
cana-5531	53	40	>	>	X
cana-5531	53	41	0	0	PROPN
cana-5531	53	42	.	.	PUNCT
cana-5531	54	1	the	the	DET
cana-5531	54	2	body	body	NOUN
cana-5531	54	3	is	be	AUX
cana-5531	54	4	acted	act	VERB
cana-5531	54	5	upon	upon	SCONJ
cana-5531	54	6	by	by	ADP
cana-5531	54	7	a	a	DET
cana-5531	54	8	volume	volume	NOUN
cana-5531	54	9	force	force	NOUN
cana-5531	54	10	of	of	ADP
cana-5531	54	11	density	density	NOUN
cana-5531	54	12	𝜑1on	𝜑1on	PUNCT
cana-5531	54	13	ω	ω	PROPN
cana-5531	54	14	and	and	CCONJ
cana-5531	54	15	a	a	DET
cana-5531	54	16	surface	surface	NOUN
cana-5531	54	17	traction	traction	NOUN
cana-5531	54	18	of	of	ADP
cana-5531	54	19	density	density	NOUN
cana-5531	54	20	𝜑2on	𝜑2on	PUNCT
cana-5531	54	21	γ2	γ2	PROPN
cana-5531	55	1	and	and	CCONJ
cana-5531	55	2	it	it	PRON
cana-5531	55	3	is	be	AUX
cana-5531	55	4	in	in	ADP
cana-5531	55	5	unilate	unilate	ADJ
cana-5531	55	6	contact	contact	NOUN
cana-5531	55	7	with	with	ADP
cana-5531	55	8	adhesion	adhesion	NOUN
cana-5531	55	9	following	follow	VERB
cana-5531	55	10	the	the	DET
cana-5531	55	11	nonlocal	nonlocal	ADJ
cana-5531	55	12	friction	friction	NOUN
cana-5531	55	13	law	law	NOUN
cana-5531	55	14	with	with	ADP
cana-5531	55	15	a	a	DET
cana-5531	55	16	foundation	foundation	NOUN
cana-5531	55	17	,	,	PUNCT
cana-5531	55	18	over	over	ADP
cana-5531	55	19	the	the	DET
cana-5531	55	20	potential	potential	ADJ
cana-5531	55	21	contact	contact	NOUN
cana-5531	55	22	surfaceγ3	surfaceγ3	PROPN
cana-5531	55	23	.	.	PUNCT
cana-5531	56	1	therefore	therefore	ADV
cana-5531	56	2	,	,	PUNCT
cana-5531	56	3	the	the	DET
cana-5531	56	4	mechanical	mechanical	ADJ
cana-5531	56	5	problem	problem	NOUN
cana-5531	56	6	’s	’s	PART
cana-5531	56	7	classical	classical	ADJ
cana-5531	56	8	formulation	formulation	NOUN
cana-5531	56	9	is	be	AUX
cana-5531	56	10	written	write	VERB
cana-5531	56	11	as	as	SCONJ
cana-5531	56	12	follows	follow	VERB
cana-5531	56	13	.	.	PUNCT
cana-5531	57	1	problem	problem	PROPN
cana-5531	57	2	p1	p1	PROPN
cana-5531	57	3	.	.	PUNCT
cana-5531	57	4	find	find	VERB
cana-5531	57	5	a	a	DET
cana-5531	57	6	displacement	displacement	ADJ
cana-5531	57	7	field	field	NOUN
cana-5531	57	8	u	u	NOUN
cana-5531	57	9	:	:	PUNCT
cana-5531	57	10	ω	ω	NUM
cana-5531	57	11	×	×	NOUN
cana-5531	58	1	[	[	X
cana-5531	58	2	0,t	0,t	X
cana-5531	58	3	]	]	X
cana-5531	58	4	→ℝ𝑑	→ℝ𝑑	PUNCT
cana-5531	58	5	,	,	PUNCT
cana-5531	58	6	a	a	DET
cana-5531	58	7	stress	stress	NOUN
cana-5531	58	8	field	field	NOUN
cana-5531	58	9	𝜎	𝜎	NOUN
cana-5531	58	10	:	:	PUNCT
cana-5531	58	11	ω	ω	NUM
cana-5531	58	12	×	×	NOUN
cana-5531	59	1	[	[	X
cana-5531	59	2	0,t	0,t	X
cana-5531	59	3	]	]	PUNCT
cana-5531	59	4	→	→	PUNCT
cana-5531	59	5	𝕊𝑑and	𝕊𝑑and	NOUN
cana-5531	59	6	a	a	DET
cana-5531	59	7	bonding	bonding	NOUN
cana-5531	59	8	field	field	NOUN
cana-5531	59	9	β	β	NOUN
cana-5531	59	10	:	:	PUNCT
cana-5531	59	11	γ3×	γ3×	PROPN
cana-5531	60	1	[	[	X
cana-5531	60	2	0,t	0,t	X
cana-5531	60	3	]	]	X
cana-5531	60	4	→	→	PUNCT
cana-5531	60	5	[	[	X
cana-5531	60	6	0,1	0,1	NUM
cana-5531	60	7	]	]	PUNCT
cana-5531	60	8	such	such	ADJ
cana-5531	60	9	that	that	SCONJ
cana-5531	60	10	for	for	ADP
cana-5531	60	11	all	all	DET
cana-5531	60	12	𝑡	𝑡	ADP
cana-5531	60	13	∈	∈	PROPN
cana-5531	60	14	[	[	X
cana-5531	60	15	0,t	0,t	X
cana-5531	60	16	]	]	X
cana-5531	60	17	:	:	PUNCT
cana-5531	60	18	communications	communication	NOUN
cana-5531	60	19	on	on	ADP
cana-5531	60	20	applied	apply	VERB
cana-5531	60	21	nonlinear	nonlinear	ADJ
cana-5531	60	22	analysis	analysis	NOUN
cana-5531	60	23	issn	issn	NOUN
cana-5531	60	24	:	:	PUNCT
cana-5531	60	25	1074	1074	NUM
cana-5531	60	26	-	-	PUNCT
cana-5531	60	27	133x	133x	NUM
cana-5531	60	28	vol	vol	NOUN
cana-5531	60	29	32	32	NUM
cana-5531	60	30	no	no	NOUN
cana-5531	60	31	.	.	NOUN
cana-5531	60	32	3	3	NUM
cana-5531	60	33	(	(	PUNCT
cana-5531	60	34	2025	2025	NUM
cana-5531	60	35	)	)	PUNCT
cana-5531	60	36	967	967	NUM
cana-5531	60	37	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	60	38	𝜎(𝑡	𝜎(𝑡	NUM
cana-5531	60	39	)	)	PUNCT
cana-5531	60	40	=	=	SYM
cana-5531	60	41	𝒜𝜀(𝑢(𝑡	𝒜𝜀(𝑢(𝑡	NOUN
cana-5531	60	42	)	)	PUNCT
cana-5531	60	43	)	)	PUNCT
cana-5531	61	1	+	+	CCONJ
cana-5531	61	2	𝒢𝜀(	𝒢𝜀(	PRON
cana-5531	61	3	�	�	PROPN
cana-5531	61	4	̇	̇	NOUN
cana-5531	61	5	�	�	PROPN
cana-5531	61	6	(𝑡	(𝑡	NOUN
cana-5531	61	7	)	)	PUNCT
cana-5531	61	8	)	)	PUNCT
cana-5531	62	1	+	+	CCONJ
cana-5531	62	2	∫	∫	PROPN
cana-5531	62	3	ℱ(𝑡	ℱ(𝑡	PRON
cana-5531	62	4	−	−	ADP
cana-5531	62	5	𝑠)𝜀(𝑢(𝑠))𝑑𝑠	𝑠)𝜀(𝑢(𝑠))𝑑𝑠	PROPN
cana-5531	62	6	𝑡	𝑡	X
cana-5531	62	7	0	0	NUM
cana-5531	62	8	in	in	ADP
cana-5531	62	9	ω	ω	NUM
cana-5531	62	10	,	,	PUNCT
cana-5531	62	11	(	(	PUNCT
cana-5531	62	12	3.1	3.1	NUM
cana-5531	62	13	)	)	PUNCT
cana-5531	62	14	𝐷𝑖𝜐𝜎(𝑡	𝐷𝑖𝜐𝜎(𝑡	PROPN
cana-5531	62	15	)	)	PUNCT
cana-5531	62	16	+	+	PUNCT
cana-5531	62	17	𝜑1(𝑡	𝜑1(𝑡	X
cana-5531	62	18	)	)	PUNCT
cana-5531	62	19	=	=	PUNCT
cana-5531	62	20	𝜌	𝜌	X
cana-5531	62	21	�	�	PROPN
cana-5531	62	22	̈	̈	X
cana-5531	62	23	�	�	PROPN
cana-5531	62	24	in	in	ADP
cana-5531	62	25	ω	ω	PROPN
cana-5531	62	26	,	,	PUNCT
cana-5531	62	27	(	(	PUNCT
cana-5531	62	28	3.2	3.2	NUM
cana-5531	62	29	)	)	PUNCT
cana-5531	62	30	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5531	62	31	)	)	PUNCT
cana-5531	62	32	=	=	SYM
cana-5531	62	33	0	0	NUM
cana-5531	62	34	on	on	ADP
cana-5531	62	35	γ1	γ1	PROPN
cana-5531	62	36	,	,	PUNCT
cana-5531	62	37	(	(	PUNCT
cana-5531	62	38	3.3	3.3	NUM
cana-5531	62	39	)	)	PUNCT
cana-5531	62	40	𝜎(𝑡)𝜈	𝜎(𝑡)𝜈	NOUN
cana-5531	62	41	=	=	PRON
cana-5531	62	42	𝜑2	𝜑2	PROPN
cana-5531	62	43	on	on	ADP
cana-5531	62	44	γ2	γ2	PROPN
cana-5531	62	45	,	,	PUNCT
cana-5531	62	46	(	(	PUNCT
cana-5531	62	47	3.4	3.4	NUM
cana-5531	62	48	)	)	PUNCT
cana-5531	62	49	𝑢𝜈	𝑢𝜈	PROPN
cana-5531	62	50	≤	≤	PROPN
cana-5531	62	51	𝑔	𝑔	NOUN
cana-5531	62	52	;	;	PUNCT
cana-5531	62	53	𝜎𝜈(𝑡	𝜎𝜈(𝑡	X
cana-5531	62	54	)	)	PUNCT
cana-5531	62	55	+	+	CCONJ
cana-5531	62	56	𝑝(𝑢𝜈(𝑡	𝑝(𝑢𝜈(𝑡	NUM
cana-5531	62	57	)	)	PUNCT
cana-5531	62	58	)	)	PUNCT
cana-5531	63	1	−	−	PROPN
cana-5531	63	2	𝑐𝜈𝛽	𝑐𝜈𝛽	VERB
cana-5531	63	3	2(𝑡)𝑅𝜈(𝑢𝜈(𝑡	2(𝑡)𝑅𝜈(𝑢𝜈(𝑡	NUM
cana-5531	63	4	)	)	PUNCT
cana-5531	63	5	)	)	PUNCT
cana-5531	63	6	≤	≤	NUM
cana-5531	63	7	0	0	NUM
cana-5531	63	8	(	(	PUNCT
cana-5531	63	9	𝜎𝜈(𝑡	𝜎𝜈(𝑡	X
cana-5531	63	10	)	)	PUNCT
cana-5531	63	11	+	+	CCONJ
cana-5531	63	12	𝑝(𝑢𝜈(𝑡	𝑝(𝑢𝜈(𝑡	NUM
cana-5531	63	13	)	)	PUNCT
cana-5531	63	14	)	)	PUNCT
cana-5531	64	1	−	−	PROPN
cana-5531	64	2	𝑐𝜈𝛽	𝑐𝜈𝛽	VERB
cana-5531	64	3	2(𝑡)𝑅𝜈(𝑢𝜈(𝑡	2(𝑡)𝑅𝜈(𝑢𝜈(𝑡	NUM
cana-5531	64	4	)	)	PUNCT
cana-5531	64	5	)	)	PUNCT
cana-5531	64	6	)	)	PUNCT
cana-5531	64	7	(	(	PUNCT
cana-5531	64	8	𝑢𝜈(𝑡	𝑢𝜈(𝑡	X
cana-5531	64	9	)	)	PUNCT
cana-5531	64	10	−	−	PROPN
cana-5531	65	1	𝑔	𝑔	X
cana-5531	65	2	)	)	PUNCT
cana-5531	65	3	=	=	SYM
cana-5531	65	4	0	0	X
cana-5531	65	5	}	}	PUNCT
cana-5531	65	6	on	on	ADP
cana-5531	65	7	γ3	γ3	NOUN
cana-5531	65	8	,	,	PUNCT
cana-5531	65	9	(	(	PUNCT
cana-5531	65	10	3.5	3.5	NUM
cana-5531	65	11	)	)	PUNCT
cana-5531	65	12	|𝜎𝜏(𝑡	|𝜎𝜏(𝑡	NOUN
cana-5531	65	13	)	)	PUNCT
cana-5531	65	14	+	+	CCONJ
cana-5531	65	15	𝑐𝜏𝛽	𝑐𝜏𝛽	PROPN
cana-5531	65	16	2(𝑡)𝑅𝜏(𝑢𝜏(𝑡))|	2(𝑡)𝑅𝜏(𝑢𝜏(𝑡))|	NUM
cana-5531	65	17	≤	≤	NOUN
cana-5531	65	18	𝜇|𝑅𝜎𝜏(𝑢(𝑡))|	𝜇|𝑅𝜎𝜏(𝑢(𝑡))|	PROPN
cana-5531	65	19	|𝜎𝜏(𝑡	|𝜎𝜏(𝑡	NUM
cana-5531	65	20	)	)	PUNCT
cana-5531	66	1	+	+	CCONJ
cana-5531	66	2	𝑐𝜏𝛽	𝑐𝜏𝛽	NOUN
cana-5531	66	3	2(𝑡)𝑅𝜏(𝑢𝜏(𝑡))|	2(𝑡)𝑅𝜏(𝑢𝜏(𝑡))|	NUM
cana-5531	66	4	<	<	X
cana-5531	66	5	𝜇|𝑅𝜎𝜏(𝑢(𝑡))|	𝜇|𝑅𝜎𝜏(𝑢(𝑡))|	PROPN
cana-5531	66	6	⇒	⇒	NOUN
cana-5531	66	7	𝑢𝜏(𝑡	𝑢𝜏(𝑡	NOUN
cana-5531	66	8	)	)	PUNCT
cana-5531	66	9	=	=	SYM
cana-5531	66	10	0	0	NUM
cana-5531	66	11	|𝜎𝜏(𝑡	|𝜎𝜏(𝑡	NOUN
cana-5531	66	12	)	)	PUNCT
cana-5531	67	1	+	+	CCONJ
cana-5531	67	2	𝑐𝜏𝛽	𝑐𝜏𝛽	NOUN
cana-5531	67	3	2(𝑡)𝑅𝜏(𝑢𝜏(𝑡))|	2(𝑡)𝑅𝜏(𝑢𝜏(𝑡))|	NUM
cana-5531	67	4	=	=	PUNCT
cana-5531	67	5	𝜇|𝑅𝜎𝜏(𝑢(𝑡))|	𝜇|𝑅𝜎𝜏(𝑢(𝑡))|	PROPN
cana-5531	67	6	⟹	⟹	VERB
cana-5531	67	7	∃𝜆	∃𝜆	PROPN
cana-5531	67	8	≥	≥	NOUN
cana-5531	67	9	0	0	NUM
cana-5531	67	10	𝑠𝑢𝑐ℎ	𝑠𝑢𝑐ℎ	PROPN
cana-5531	67	11	𝑡ℎ𝑎𝑡	𝑡ℎ𝑎𝑡	ADJ
cana-5531	67	12	𝑢𝜏(𝑡	𝑢𝜏(𝑡	NOUN
cana-5531	67	13	)	)	PUNCT
cana-5531	67	14	=	=	SYM
cana-5531	67	15	−𝜆	−𝜆	NOUN
cana-5531	67	16	(	(	PUNCT
cana-5531	67	17	𝜎𝜏(𝑡	𝜎𝜏(𝑡	PROPN
cana-5531	67	18	)	)	PUNCT
cana-5531	67	19	+	+	CCONJ
cana-5531	67	20	𝑐𝜏𝛽	𝑐𝜏𝛽	PROPN
cana-5531	67	21	2(𝑡)𝑅𝜏(𝑢𝜏(𝑡	2(𝑡)𝑅𝜏(𝑢𝜏(𝑡	NUM
cana-5531	67	22	)	)	PUNCT
cana-5531	67	23	)	)	PUNCT
cana-5531	67	24	)	)	PUNCT
cana-5531	67	25	}	}	PUNCT
cana-5531	67	26	on	on	ADP
cana-5531	67	27	γ3	γ3	NOUN
cana-5531	67	28	,	,	PUNCT
cana-5531	67	29	(	(	PUNCT
cana-5531	67	30	3.6	3.6	NUM
cana-5531	67	31	)	)	PUNCT
cana-5531	67	32	�	�	PROPN
cana-5531	67	33	̇	̇	PROPN
cana-5531	67	34	�	�	PROPN
cana-5531	67	35	(𝑡	(𝑡	NOUN
cana-5531	67	36	)	)	PUNCT
cana-5531	67	37	=	=	SYM
cana-5531	67	38	−	−	PROPN
cana-5531	68	1	[	[	X
cana-5531	68	2	𝛽(𝑡	𝛽(𝑡	PROPN
cana-5531	68	3	)	)	PUNCT
cana-5531	68	4	(	(	PUNCT
cana-5531	68	5	𝑐𝜈	𝑐𝜈	NOUN
cana-5531	68	6	(	(	PUNCT
cana-5531	68	7	𝑅𝜈(𝑢𝜈(𝑡	𝑅𝜈(𝑢𝜈(𝑡	ADJ
cana-5531	68	8	)	)	PUNCT
cana-5531	68	9	)	)	PUNCT
cana-5531	68	10	)	)	PUNCT
cana-5531	68	11	2	2	NUM
cana-5531	69	1	+	+	NUM
cana-5531	69	2	𝑐𝜏|𝑅𝜈𝑢𝜏(𝑡)|	𝑐𝜏|𝑅𝜈𝑢𝜏(𝑡)|	ADJ
cana-5531	69	3	2	2	NUM
cana-5531	69	4	−	−	NOUN
cana-5531	69	5	𝜀𝑎	𝜀𝑎	NOUN
cana-5531	69	6	)	)	PUNCT
cana-5531	69	7	]	]	PUNCT
cana-5531	70	1	+	+	CCONJ
cana-5531	70	2	on	on	ADP
cana-5531	70	3	γ3	γ3	NOUN
cana-5531	70	4	,	,	PUNCT
cana-5531	70	5	(	(	PUNCT
cana-5531	70	6	3.7	3.7	NUM
cana-5531	70	7	)	)	PUNCT
cana-5531	70	8	β	β	X
cana-5531	70	9	(	(	PUNCT
cana-5531	70	10	0	0	NUM
cana-5531	70	11	)	)	PUNCT
cana-5531	70	12	=	=	SYM
cana-5531	70	13	β0	β0	ADJ
cana-5531	70	14	on	on	ADP
cana-5531	70	15	γ3	γ3	NOUN
cana-5531	70	16	,	,	PUNCT
cana-5531	70	17	(	(	PUNCT
cana-5531	70	18	3.8	3.8	NUM
cana-5531	70	19	)	)	PUNCT
cana-5531	70	20	𝑢(0	𝑢(0	PROPN
cana-5531	70	21	)	)	PUNCT
cana-5531	70	22	=	=	SYM
cana-5531	70	23	𝑢0	𝑢0	PROPN
cana-5531	70	24	,	,	PUNCT
cana-5531	70	25	𝑢(𝑡	𝑢(𝑡	NOUN
cana-5531	70	26	)	)	PUNCT
cana-5531	71	1	=	=	NOUN
cana-5531	71	2	𝑢1̇	𝑢1̇	NOUN
cana-5531	71	3	in	in	ADP
cana-5531	71	4	ω	ω	PROPN
cana-5531	71	5	.	.	PUNCT
cana-5531	72	1	(	(	PUNCT
cana-5531	72	2	3.9	3.9	NUM
cana-5531	72	3	)	)	PUNCT
cana-5531	72	4	the	the	DET
cana-5531	72	5	viscoelastic	viscoelastic	ADJ
cana-5531	72	6	constitutive	constitutive	ADJ
cana-5531	72	7	law	law	NOUN
cana-5531	72	8	with	with	ADP
cana-5531	72	9	long	long	ADJ
cana-5531	72	10	memory	memory	NOUN
cana-5531	72	11	of	of	ADP
cana-5531	72	12	the	the	DET
cana-5531	72	13	material	material	NOUN
cana-5531	72	14	is	be	AUX
cana-5531	72	15	represented	represent	VERB
cana-5531	72	16	by	by	ADP
cana-5531	72	17	the	the	DET
cana-5531	72	18	equation	equation	NOUN
cana-5531	72	19	(	(	PUNCT
cana-5531	72	20	3.1	3.1	NUM
cana-5531	72	21	)	)	PUNCT
cana-5531	72	22	.	.	PUNCT
cana-5531	73	1	here	here	ADV
cana-5531	73	2	𝒢	𝒢	PROPN
cana-5531	73	3	and	and	CCONJ
cana-5531	73	4	𝒜	𝒜	NOUN
cana-5531	73	5	are	be	AUX
cana-5531	73	6	nonlinear	nonlinear	ADJ
cana-5531	73	7	operators	operator	NOUN
cana-5531	73	8	describing	describe	VERB
cana-5531	73	9	the	the	DET
cana-5531	73	10	purely	purely	ADV
cana-5531	73	11	viscous	viscous	ADJ
cana-5531	73	12	and	and	CCONJ
cana-5531	73	13	the	the	DET
cana-5531	73	14	elastic	elastic	ADJ
cana-5531	73	15	properties	property	NOUN
cana-5531	73	16	of	of	ADP
cana-5531	73	17	the	the	DET
cana-5531	73	18	material	material	NOUN
cana-5531	73	19	,	,	PUNCT
cana-5531	73	20	respectively	respectively	ADV
cana-5531	73	21	and	and	CCONJ
cana-5531	73	22	∫	∫	PROPN
cana-5531	73	23	ℱ(𝑡	ℱ(𝑡	PRON
cana-5531	73	24	−	−	X
cana-5531	73	25	𝑠)𝜀(𝑢(𝑠))𝑑𝑠	𝑠)𝜀(𝑢(𝑠))𝑑𝑠	PROPN
cana-5531	73	26	𝑡	𝑡	NOUN
cana-5531	73	27	0	0	NUM
cana-5531	73	28	is	be	AUX
cana-5531	73	29	the	the	DET
cana-5531	73	30	memory	memory	NOUN
cana-5531	73	31	term	term	NOUN
cana-5531	73	32	in	in	ADP
cana-5531	73	33	which	which	PRON
cana-5531	73	34	ℱ	ℱ	PROPN
cana-5531	73	35	denotes	denote	VERB
cana-5531	73	36	the	the	DET
cana-5531	73	37	tensor	tensor	NOUN
cana-5531	73	38	of	of	ADP
cana-5531	73	39	relaxation	relaxation	NOUN
cana-5531	73	40	,	,	PUNCT
cana-5531	73	41	the	the	DET
cana-5531	73	42	stress	stress	NOUN
cana-5531	73	43	σ	σ	PROPN
cana-5531	73	44	(	(	PUNCT
cana-5531	73	45	t	t	PROPN
cana-5531	73	46	)	)	PUNCT
cana-5531	73	47	at	at	ADP
cana-5531	73	48	current	current	ADJ
cana-5531	73	49	instant	instant	ADJ
cana-5531	73	50	t	t	PROPN
cana-5531	73	51	depends	depend	VERB
cana-5531	73	52	on	on	ADP
cana-5531	73	53	the	the	DET
cana-5531	73	54	whole	whole	ADJ
cana-5531	73	55	history	history	NOUN
cana-5531	73	56	of	of	ADP
cana-5531	73	57	strains	strain	NOUN
cana-5531	73	58	up	up	ADP
cana-5531	73	59	to	to	ADP
cana-5531	73	60	this	this	DET
cana-5531	73	61	moment	moment	NOUN
cana-5531	73	62	of	of	ADP
cana-5531	73	63	time	time	NOUN
cana-5531	73	64	.	.	PUNCT
cana-5531	74	1	equation	equation	NOUN
cana-5531	74	2	(	(	PUNCT
cana-5531	74	3	3.2	3.2	NUM
cana-5531	74	4	)	)	PUNCT
cana-5531	74	5	represents	represent	VERB
cana-5531	74	6	the	the	DET
cana-5531	74	7	equation	equation	NOUN
cana-5531	74	8	of	of	ADP
cana-5531	74	9	motion	motion	NOUN
cana-5531	74	10	where	where	SCONJ
cana-5531	74	11	ρ	ρ	PROPN
cana-5531	74	12	denotes	denote	VERB
cana-5531	74	13	the	the	DET
cana-5531	74	14	material	material	NOUN
cana-5531	74	15	mass	mass	NOUN
cana-5531	74	16	density	density	NOUN
cana-5531	74	17	,	,	PUNCT
cana-5531	74	18	while	while	SCONJ
cana-5531	74	19	(	(	PUNCT
cana-5531	74	20	3.3	3.3	NUM
cana-5531	74	21	)	)	PUNCT
cana-5531	74	22	and	and	CCONJ
cana-5531	74	23	(	(	PUNCT
cana-5531	74	24	3.4	3.4	NUM
cana-5531	74	25	)	)	PUNCT
cana-5531	74	26	are	be	AUX
cana-5531	74	27	the	the	DET
cana-5531	74	28	displacement	displacement	NOUN
cana-5531	74	29	and	and	CCONJ
cana-5531	74	30	traction	traction	NOUN
cana-5531	74	31	boundary	boundary	ADJ
cana-5531	74	32	conditions	condition	NOUN
cana-5531	74	33	,	,	PUNCT
cana-5531	74	34	respectively	respectively	ADV
cana-5531	74	35	,	,	PUNCT
cana-5531	74	36	in	in	ADP
cana-5531	74	37	which	which	PRON
cana-5531	74	38	𝜎𝜈	𝜎𝜈	ADP
cana-5531	74	39	represents	represent	VERB
cana-5531	74	40	the	the	DET
cana-5531	74	41	cauchy	cauchy	ADJ
cana-5531	74	42	stress	stress	NOUN
cana-5531	74	43	vector	vector	NOUN
cana-5531	74	44	.	.	PUNCT
cana-5531	75	1	the	the	DET
cana-5531	75	2	conditions	condition	NOUN
cana-5531	75	3	(	(	PUNCT
cana-5531	75	4	3.5	3.5	NUM
cana-5531	75	5	)	)	PUNCT
cana-5531	75	6	represents	represent	VERB
cana-5531	75	7	the	the	DET
cana-5531	75	8	unilateral	unilateral	ADJ
cana-5531	75	9	contact	contact	NOUN
cana-5531	75	10	with	with	ADP
cana-5531	75	11	adhesion	adhesion	NOUN
cana-5531	75	12	in	in	ADP
cana-5531	75	13	which	which	PRON
cana-5531	75	14	𝑐𝜈	𝑐𝜈	NOUN
cana-5531	75	15	is	be	AUX
cana-5531	75	16	a	a	DET
cana-5531	75	17	given	give	VERB
cana-5531	75	18	a	a	DET
cana-5531	75	19	adhesion	adhesion	NOUN
cana-5531	75	20	coefficient	coefficient	NOUN
cana-5531	75	21	which	which	PRON
cana-5531	75	22	may	may	AUX
cana-5531	75	23	dependent	dependent	VERB
cana-5531	75	24	on	on	ADP
cana-5531	75	25	𝑥	𝑥	DET
cana-5531	75	26	∈	∈	PROPN
cana-5531	75	27	γ3	γ3	NOUN
cana-5531	75	28	and	and	CCONJ
cana-5531	75	29	𝑅𝜈	𝑅𝜈	ADP
cana-5531	75	30	𝑎𝑛𝑑	𝑎𝑛𝑑	ADJ
cana-5531	75	31	𝑅𝜏	𝑅𝜏	PROPN
cana-5531	75	32	are	be	AUX
cana-5531	75	33	truncation	truncation	NOUN
cana-5531	75	34	operators	operator	NOUN
cana-5531	75	35	defined	define	VERB
cana-5531	75	36	by	by	ADP
cana-5531	75	37	𝑅𝜈(𝑠	𝑅𝜈(𝑠	NOUN
cana-5531	75	38	)	)	PUNCT
cana-5531	75	39	=	=	SYM
cana-5531	75	40	{	{	PUNCT
cana-5531	75	41	𝐿	𝐿	PROPN
cana-5531	76	1	𝑖𝑓	𝑖𝑓	NOUN
cana-5531	76	2	𝑠	𝑠	PROPN
cana-5531	76	3	<	<	X
cana-5531	77	1	−𝐿	−𝐿	PROPN
cana-5531	78	1	−𝑠	−𝑠	ADV
cana-5531	78	2	𝑖𝑓	𝑖𝑓	ADP
cana-5531	78	3	−	−	PROPN
cana-5531	78	4	𝐿	𝐿	PROPN
cana-5531	78	5	≤	≤	PROPN
cana-5531	78	6	𝑠	𝑠	DET
cana-5531	78	7	≤	≤	NUM
cana-5531	78	8	0	0	NUM
cana-5531	78	9	0	0	NUM
cana-5531	79	1	𝑖𝑓	𝑖𝑓	NUM
cana-5531	79	2	𝑠	𝑠	INTJ
cana-5531	79	3	>	>	X
cana-5531	79	4	0	0	NUM
cana-5531	79	5	,	,	PUNCT
cana-5531	79	6	𝑅𝜏(𝑠	𝑅𝜏(𝑠	PROPN
cana-5531	79	7	)	)	PUNCT
cana-5531	79	8	=	=	PRON
cana-5531	80	1	{	{	PUNCT
cana-5531	80	2	𝜐	𝜐	NOUN
cana-5531	80	3	𝑖𝑓	𝑖𝑓	NOUN
cana-5531	80	4	|𝜐|	|𝜐|	PROPN
cana-5531	80	5	≤	≤	PROPN
cana-5531	80	6	𝐿	𝐿	PROPN
cana-5531	80	7	,	,	PUNCT
cana-5531	80	8	𝐿	𝐿	PROPN
cana-5531	80	9	𝜐	𝜐	PROPN
cana-5531	81	1	|𝜐|	|𝜐|	PROPN
cana-5531	81	2	𝑖𝑓	𝑖𝑓	ADP
cana-5531	81	3	|𝜐|	|𝜐|	PROPN
cana-5531	81	4	>	>	X
cana-5531	81	5	𝐿.	𝐿.	PROPN
cana-5531	81	6	here	here	ADV
cana-5531	81	7	𝐿	𝐿	PROPN
cana-5531	81	8	>	>	X
cana-5531	81	9	0	0	NUM
cana-5531	81	10	is	be	AUX
cana-5531	81	11	the	the	DET
cana-5531	81	12	characteristic	characteristic	ADJ
cana-5531	81	13	length	length	NOUN
cana-5531	81	14	of	of	ADP
cana-5531	81	15	the	the	DET
cana-5531	81	16	bond	bond	NOUN
cana-5531	81	17	,	,	PUNCT
cana-5531	81	18	beyond	beyond	ADP
cana-5531	81	19	which	which	PRON
cana-5531	81	20	the	the	DET
cana-5531	81	21	latter	latter	NOUN
cana-5531	81	22	has	have	VERB
cana-5531	81	23	no	no	DET
cana-5531	81	24	additional	additional	ADJ
cana-5531	81	25	traction	traction	NOUN
cana-5531	81	26	(	(	PUNCT
cana-5531	81	27	see	see	VERB
cana-5531	81	28	[	[	X
cana-5531	81	29	18	18	NUM
cana-5531	81	30	]	]	PUNCT
cana-5531	81	31	)	)	PUNCT
cana-5531	81	32	and	and	CCONJ
cana-5531	81	33	p	p	NOUN
cana-5531	81	34	is	be	AUX
cana-5531	81	35	a	a	DET
cana-5531	81	36	normal	normal	ADJ
cana-5531	81	37	compliance	compliance	NOUN
cana-5531	81	38	function	function	NOUN
cana-5531	81	39	which	which	PRON
cana-5531	81	40	satisfies	satisfy	VERB
cana-5531	81	41	the	the	DET
cana-5531	81	42	assumption	assumption	NOUN
cana-5531	81	43	(	(	PUNCT
cana-5531	81	44	4.14	4.14	NUM
cana-5531	81	45	)	)	PUNCT
cana-5531	81	46	,	,	PUNCT
cana-5531	81	47	𝑔	𝑔	PROPN
cana-5531	81	48	denotes	denote	VERB
cana-5531	81	49	the	the	DET
cana-5531	81	50	maximum	maximum	ADJ
cana-5531	81	51	value	value	NOUN
cana-5531	81	52	of	of	ADP
cana-5531	81	53	the	the	DET
cana-5531	81	54	penetration	penetration	NOUN
cana-5531	81	55	which	which	PRON
cana-5531	81	56	satisfies	satisfy	VERB
cana-5531	81	57	𝑔	𝑔	PROPN
cana-5531	81	58	≥	≥	NOUN
cana-5531	81	59	0	0	NUM
cana-5531	81	60	.	.	PUNCT
cana-5531	82	1	when	when	SCONJ
cana-5531	82	2	𝑢𝜈	𝑢𝜈	ADP
cana-5531	82	3	<	<	X
cana-5531	82	4	0	0	PUNCT
cana-5531	82	5	i.e.	i.e.	X
cana-5531	82	6	when	when	SCONJ
cana-5531	82	7	there	there	PRON
cana-5531	82	8	is	be	VERB
cana-5531	82	9	separation	separation	NOUN
cana-5531	82	10	between	between	ADP
cana-5531	82	11	the	the	DET
cana-5531	82	12	body	body	NOUN
cana-5531	82	13	and	and	CCONJ
cana-5531	82	14	the	the	DET
cana-5531	82	15	foundation	foundation	NOUN
cana-5531	82	16	then	then	ADV
cana-5531	82	17	the	the	DET
cana-5531	82	18	condition	condition	NOUN
cana-5531	82	19	(	(	PUNCT
cana-5531	82	20	3.5	3.5	NUM
cana-5531	82	21	)	)	PUNCT
cana-5531	82	22	combined	combine	VERB
cana-5531	82	23	with	with	ADP
cana-5531	82	24	hypothese	hypothese	PROPN
cana-5531	82	25	(	(	PUNCT
cana-5531	82	26	3.23	3.23	NUM
cana-5531	82	27	)	)	PUNCT
cana-5531	82	28	and	and	CCONJ
cana-5531	82	29	definition	definition	NOUN
cana-5531	82	30	of	of	ADP
cana-5531	82	31	𝑅𝜈	𝑅𝜈	ADP
cana-5531	82	32	shows	show	VERB
cana-5531	82	33	that	that	SCONJ
cana-5531	82	34	𝜎𝜈	𝜎𝜈	ADP
cana-5531	82	35	=	=	PUNCT
cana-5531	82	36	𝑐𝜈𝛽	𝑐𝜈𝛽	NOUN
cana-5531	82	37	2𝑅𝜈(𝑢𝜈	2𝑅𝜈(𝑢𝜈	NUM
cana-5531	82	38	)	)	PUNCT
cana-5531	82	39	and	and	CCONJ
cana-5531	82	40	does	do	AUX
cana-5531	82	41	not	not	PART
cana-5531	82	42	exeed	exeed	VERB
cana-5531	82	43	the	the	DET
cana-5531	82	44	value	value	NOUN
cana-5531	82	45	𝐿	𝐿	PROPN
cana-5531	82	46	cν	cν	NOUN
cana-5531	82	47	l∞(γ3	l∞(γ3	NOUN
cana-5531	82	48	)	)	PUNCT
cana-5531	82	49	.	.	PUNCT
cana-5531	83	1	when	when	SCONJ
cana-5531	83	2	g	g	PROPN
cana-5531	83	3	>	>	X
cana-5531	83	4	0	0	PROPN
cana-5531	83	5	,	,	PUNCT
cana-5531	83	6	the	the	DET
cana-5531	83	7	body	body	NOUN
cana-5531	83	8	may	may	AUX
cana-5531	83	9	interpenetrate	interpenetrate	VERB
cana-5531	83	10	into	into	ADP
cana-5531	83	11	the	the	DET
cana-5531	83	12	fondation	fondation	NOUN
cana-5531	83	13	,	,	PUNCT
cana-5531	83	14	but	but	CCONJ
cana-5531	83	15	the	the	DET
cana-5531	83	16	communications	communication	NOUN
cana-5531	83	17	on	on	ADP
cana-5531	83	18	applied	apply	VERB
cana-5531	83	19	nonlinear	nonlinear	ADJ
cana-5531	83	20	analysis	analysis	NOUN
cana-5531	83	21	issn	issn	NOUN
cana-5531	83	22	:	:	PUNCT
cana-5531	83	23	1074	1074	NUM
cana-5531	83	24	-	-	PUNCT
cana-5531	83	25	133x	133x	NUM
cana-5531	83	26	vol	vol	NOUN
cana-5531	83	27	32	32	NUM
cana-5531	83	28	no	no	NOUN
cana-5531	83	29	.	.	NOUN
cana-5531	83	30	3	3	NUM
cana-5531	83	31	(	(	PUNCT
cana-5531	83	32	2025	2025	NUM
cana-5531	83	33	)	)	PUNCT
cana-5531	83	34	968	968	NUM
cana-5531	83	35	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	83	36	penetration	penetration	NOUN
cana-5531	83	37	is	be	AUX
cana-5531	83	38	limited	limit	VERB
cana-5531	83	39	that	that	PRON
cana-5531	83	40	is	be	AUX
cana-5531	83	41	uν	uν	ADP
cana-5531	83	42	≤	≤	NUM
cana-5531	83	43	𝑔.	𝑔.	NOUN
cana-5531	83	44	in	in	ADP
cana-5531	83	45	this	this	DET
cana-5531	83	46	case	case	NOUN
cana-5531	83	47	of	of	ADP
cana-5531	83	48	penetration	penetration	NOUN
cana-5531	83	49	(	(	PUNCT
cana-5531	83	50	i.e.	i.e.	X
cana-5531	83	51	uν	uν	ADP
cana-5531	83	52	≥	≥	NOUN
cana-5531	83	53	0	0	NUM
cana-5531	83	54	)	)	PUNCT
cana-5531	83	55	,	,	PUNCT
cana-5531	83	56	when	when	SCONJ
cana-5531	83	57	0	0	NUM
cana-5531	83	58	≤	≤	PUNCT
cana-5531	83	59	uν	uν	ADP
cana-5531	83	60	<	<	X
cana-5531	83	61	𝑔	𝑔	PROPN
cana-5531	83	62	then	then	ADV
cana-5531	83	63	−σν	−σν	VERB
cana-5531	83	64	=	=	SYM
cana-5531	83	65	p(uν	p(uν	X
cana-5531	83	66	)	)	PUNCT
cana-5531	83	67	which	which	PRON
cana-5531	83	68	means	mean	VERB
cana-5531	83	69	that	that	SCONJ
cana-5531	83	70	the	the	DET
cana-5531	83	71	reaction	reaction	NOUN
cana-5531	83	72	of	of	ADP
cana-5531	83	73	the	the	DET
cana-5531	83	74	foundation	foundation	NOUN
cana-5531	83	75	is	be	AUX
cana-5531	83	76	uniquely	uniquely	ADV
cana-5531	83	77	determined	determine	VERB
cana-5531	83	78	by	by	ADP
cana-5531	83	79	the	the	DET
cana-5531	83	80	normal	normal	ADJ
cana-5531	83	81	displacement	displacement	NOUN
cana-5531	83	82	and	and	CCONJ
cana-5531	83	83	σν	σν	DET
cana-5531	83	84	≤	≤	NUM
cana-5531	83	85	0	0	NUM
cana-5531	83	86	.	.	PUNCT
cana-5531	84	1	since	since	SCONJ
cana-5531	84	2	p	p	NOUN
cana-5531	84	3	is	be	AUX
cana-5531	84	4	an	an	DET
cana-5531	84	5	increasing	increase	VERB
cana-5531	84	6	function	function	NOUN
cana-5531	84	7	then	then	ADV
cana-5531	84	8	the	the	DET
cana-5531	84	9	reaction	reaction	NOUN
cana-5531	84	10	is	be	AUX
cana-5531	84	11	increasing	increase	VERB
cana-5531	84	12	with	with	ADP
cana-5531	84	13	the	the	DET
cana-5531	84	14	penetration	penetration	NOUN
cana-5531	84	15	.	.	PUNCT
cana-5531	85	1	when	when	SCONJ
cana-5531	85	2	uν	uν	PROPN
cana-5531	85	3	=	=	PROPN
cana-5531	85	4	𝑔	𝑔	PROPN
cana-5531	85	5	then	then	ADV
cana-5531	85	6	−σν	−σν	VERB
cana-5531	85	7	≥	≥	NOUN
cana-5531	85	8	p	p	X
cana-5531	85	9	(	(	PUNCT
cana-5531	85	10	𝑔	𝑔	NOUN
cana-5531	85	11	)	)	PUNCT
cana-5531	85	12	and	and	CCONJ
cana-5531	85	13	σν	σν	PRON
cana-5531	85	14	is	be	AUX
cana-5531	85	15	not	not	PART
cana-5531	85	16	uniquely	uniquely	ADV
cana-5531	85	17	determined	determine	VERB
cana-5531	85	18	.	.	PUNCT
cana-5531	86	1	when	when	SCONJ
cana-5531	86	2	𝑔	𝑔	X
cana-5531	86	3	>	>	X
cana-5531	86	4	0	0	PROPN
cana-5531	86	5	and	and	CCONJ
cana-5531	86	6	p	p	X
cana-5531	86	7	=	=	NOUN
cana-5531	86	8	0	0	NUM
cana-5531	86	9	,	,	PUNCT
cana-5531	86	10	condition	condition	NOUN
cana-5531	86	11	(	(	PUNCT
cana-5531	86	12	3.5	3.5	NUM
cana-5531	86	13	)	)	PUNCT
cana-5531	86	14	become	become	VERB
cana-5531	86	15	the	the	DET
cana-5531	86	16	signorini	signorini	NOUN
cana-5531	86	17	’s	’s	PART
cana-5531	86	18	contact	contact	NOUN
cana-5531	86	19	conditions	condition	NOUN
cana-5531	86	20	with	with	ADP
cana-5531	86	21	a	a	DET
cana-5531	86	22	gap	gap	NOUN
cana-5531	86	23	and	and	CCONJ
cana-5531	86	24	adhesion	adhesion	NOUN
cana-5531	86	25	uν	uν	ADP
cana-5531	86	26	≤	≤	PROPN
cana-5531	86	27	𝑔	𝑔	NOUN
cana-5531	86	28	,	,	PUNCT
cana-5531	86	29	σν	σν	PRON
cana-5531	86	30	−	−	PROPN
cana-5531	86	31	cνβ	cνβ	NOUN
cana-5531	86	32	2𝑅ν(uν	2𝑅ν(uν	NUM
cana-5531	86	33	)	)	PUNCT
cana-5531	86	34	≤	≤	NOUN
cana-5531	86	35	0	0	NUM
cana-5531	86	36	,	,	PUNCT
cana-5531	86	37	(	(	PUNCT
cana-5531	86	38	σν	σν	INTJ
cana-5531	86	39	−	−	PROPN
cana-5531	86	40	cνβ	cνβ	NOUN
cana-5531	86	41	2𝑅ν(uν))(uν	2𝑅ν(uν))(uν	NUM
cana-5531	86	42	−	−	PROPN
cana-5531	86	43	𝑔	𝑔	NOUN
cana-5531	86	44	)	)	PUNCT
cana-5531	86	45	=	=	SYM
cana-5531	87	1	0	0	X
cana-5531	87	2	.	.	PUNCT
cana-5531	88	1	when	when	SCONJ
cana-5531	88	2	𝑔	𝑔	PROPN
cana-5531	88	3	=	=	SYM
cana-5531	88	4	0	0	PROPN
cana-5531	88	5	,	,	PUNCT
cana-5531	88	6	the	the	DET
cana-5531	88	7	conditions	condition	NOUN
cana-5531	88	8	(	(	PUNCT
cana-5531	88	9	3.5	3.5	NUM
cana-5531	88	10	)	)	PUNCT
cana-5531	88	11	combined	combine	VERB
cana-5531	88	12	with	with	ADP
cana-5531	88	13	hypothese	hypothese	PROPN
cana-5531	88	14	(	(	PUNCT
cana-5531	88	15	3.23	3.23	NUM
cana-5531	88	16	)	)	PUNCT
cana-5531	88	17	lead	lead	NOUN
cana-5531	88	18	to	to	ADP
cana-5531	88	19	the	the	DET
cana-5531	88	20	signorini	signorini	ADJ
cana-5531	88	21	contact	contact	NOUN
cana-5531	88	22	conditions	condition	NOUN
cana-5531	88	23	with	with	ADP
cana-5531	88	24	adhesion	adhesion	NOUN
cana-5531	88	25	,	,	PUNCT
cana-5531	88	26	with	with	ADP
cana-5531	88	27	zero	zero	NUM
cana-5531	88	28	gap	gap	NOUN
cana-5531	88	29	,	,	PUNCT
cana-5531	88	30	given	give	VERB
cana-5531	88	31	by	by	ADP
cana-5531	88	32	uν	uν	ADP
cana-5531	88	33	≤	≤	NUM
cana-5531	88	34	0	0	NUM
cana-5531	88	35	,	,	PUNCT
cana-5531	88	36	σν	σν	DET
cana-5531	88	37	−	−	PROPN
cana-5531	88	38	cνβ	cνβ	NOUN
cana-5531	88	39	2𝑅ν(uν	2𝑅ν(uν	NUM
cana-5531	88	40	)	)	PUNCT
cana-5531	88	41	≤	≤	NOUN
cana-5531	88	42	0	0	NUM
cana-5531	88	43	,	,	PUNCT
cana-5531	88	44	(	(	PUNCT
cana-5531	88	45	σν	σν	INTJ
cana-5531	88	46	−	−	NOUN
cana-5531	88	47	cνβ	cνβ	NOUN
cana-5531	88	48	2𝑅ν(uν))uν	2𝑅ν(uν))uν	NUM
cana-5531	88	49	=	=	SYM
cana-5531	89	1	0	0	X
cana-5531	89	2	.	.	PUNCT
cana-5531	90	1	these	these	DET
cana-5531	90	2	contact	contact	NOUN
cana-5531	90	3	conditions	condition	NOUN
cana-5531	90	4	were	be	AUX
cana-5531	90	5	used	use	VERB
cana-5531	90	6	in	in	ADP
cana-5531	90	7	[	[	X
cana-5531	90	8	20	20	NUM
cana-5531	90	9	]	]	PUNCT
cana-5531	90	10	.	.	PUNCT
cana-5531	91	1	it	it	PRON
cana-5531	91	2	follows	follow	VERB
cana-5531	91	3	from	from	ADP
cana-5531	91	4	(	(	PUNCT
cana-5531	91	5	3.5	3.5	NUM
cana-5531	91	6	)	)	PUNCT
cana-5531	91	7	that	that	SCONJ
cana-5531	91	8	there	there	PRON
cana-5531	91	9	is	be	VERB
cana-5531	91	10	no	no	DET
cana-5531	91	11	penetration	penetration	NOUN
cana-5531	91	12	between	between	ADP
cana-5531	91	13	the	the	DET
cana-5531	91	14	body	body	NOUN
cana-5531	91	15	and	and	CCONJ
cana-5531	91	16	the	the	DET
cana-5531	91	17	foundation	foundation	NOUN
cana-5531	91	18	,	,	PUNCT
cana-5531	91	19	since	since	SCONJ
cana-5531	91	20	uν	uν	ADP
cana-5531	91	21	≤	≤	NOUN
cana-5531	91	22	0	0	NUM
cana-5531	91	23	during	during	ADP
cana-5531	91	24	the	the	DET
cana-5531	91	25	process	process	NOUN
cana-5531	91	26	.	.	PUNCT
cana-5531	92	1	also	also	ADV
cana-5531	92	2	,	,	PUNCT
cana-5531	92	3	note	note	VERB
cana-5531	92	4	that	that	SCONJ
cana-5531	92	5	when	when	SCONJ
cana-5531	92	6	the	the	DET
cana-5531	92	7	bonding	bonding	NOUN
cana-5531	92	8	field	field	NOUN
cana-5531	92	9	vanishes	vanish	VERB
cana-5531	92	10	,	,	PUNCT
cana-5531	92	11	then	then	ADV
cana-5531	92	12	the	the	DET
cana-5531	92	13	contact	contact	NOUN
cana-5531	92	14	conditions	condition	NOUN
cana-5531	92	15	(	(	PUNCT
cana-5531	92	16	3.5	3.5	NUM
cana-5531	92	17	)	)	PUNCT
cana-5531	92	18	become	become	VERB
cana-5531	92	19	the	the	DET
cana-5531	92	20	classical	classical	ADJ
cana-5531	92	21	signorini	signorini	NOUN
cana-5531	92	22	contact	contact	NOUN
cana-5531	92	23	conditions	condition	NOUN
cana-5531	92	24	with	with	ADP
cana-5531	92	25	zero	zero	NUM
cana-5531	92	26	gap	gap	NOUN
cana-5531	92	27	,	,	PUNCT
cana-5531	92	28	that	that	ADV
cana-5531	92	29	is	is	ADV
cana-5531	92	30	,	,	PUNCT
cana-5531	92	31	uν	uν	ADP
cana-5531	92	32	≤	≤	NOUN
cana-5531	92	33	0	0	NUM
cana-5531	92	34	,	,	PUNCT
cana-5531	92	35	σν	σν	DET
cana-5531	92	36	≤	≤	NUM
cana-5531	92	37	0	0	NUM
cana-5531	92	38	,	,	PUNCT
cana-5531	92	39	σνuν	σνuν	NOUN
cana-5531	92	40	=	=	SYM
cana-5531	92	41	0	0	X
cana-5531	92	42	.	.	PUNCT
cana-5531	93	1	condition	condition	NOUN
cana-5531	93	2	(	(	PUNCT
cana-5531	93	3	3.6	3.6	NUM
cana-5531	93	4	)	)	PUNCT
cana-5531	93	5	represent	represent	VERB
cana-5531	93	6	couloub	couloub	PROPN
cana-5531	93	7	’s	’s	PART
cana-5531	93	8	law	law	NOUN
cana-5531	93	9	of	of	ADP
cana-5531	93	10	dry	dry	ADJ
cana-5531	93	11	friction	friction	NOUN
cana-5531	93	12	with	with	ADP
cana-5531	93	13	adhesion	adhesion	NOUN
cana-5531	93	14	where	where	SCONJ
cana-5531	93	15	𝜇	𝜇	ADP
cana-5531	93	16	denotes	denote	NOUN
cana-5531	93	17	the	the	DET
cana-5531	93	18	coefficient	coefficient	NOUN
cana-5531	93	19	of	of	ADP
cana-5531	93	20	friction	friction	NOUN
cana-5531	93	21	.	.	PUNCT
cana-5531	94	1	equation	equation	NOUN
cana-5531	94	2	(	(	PUNCT
cana-5531	94	3	3.7	3.7	NUM
cana-5531	94	4	)	)	PUNCT
cana-5531	94	5	represents	represent	VERB
cana-5531	94	6	the	the	DET
cana-5531	94	7	ordinary	ordinary	ADJ
cana-5531	94	8	differentail	differentail	NOUN
cana-5531	94	9	equation	equation	NOUN
cana-5531	94	10	which	which	PRON
cana-5531	94	11	describes	describe	VERB
cana-5531	94	12	the	the	DET
cana-5531	94	13	evolution	evolution	NOUN
cana-5531	94	14	of	of	ADP
cana-5531	94	15	the	the	DET
cana-5531	94	16	bonding	bonding	NOUN
cana-5531	94	17	field	field	NOUN
cana-5531	94	18	and	and	CCONJ
cana-5531	94	19	it	it	PRON
cana-5531	94	20	was	be	AUX
cana-5531	94	21	already	already	ADV
cana-5531	94	22	used	use	VERB
cana-5531	94	23	in	in	ADP
cana-5531	94	24	[	[	X
cana-5531	94	25	20	20	NUM
cana-5531	94	26	,	,	PUNCT
cana-5531	94	27	21	21	NUM
cana-5531	94	28	]	]	PUNCT
cana-5531	94	29	.	.	PUNCT
cana-5531	95	1	since	since	SCONJ
cana-5531	95	2	β	β	PROPN
cana-5531	95	3	≤	≤	X
cana-5531	95	4	0	0	NUM
cana-5531	95	5	on	on	ADP
cana-5531	95	6	𝛤3×[0	𝛤3×[0	PROPN
cana-5531	95	7	,	,	PUNCT
cana-5531	95	8	t	t	X
cana-5531	95	9	]	]	PUNCT
cana-5531	95	10	,	,	PUNCT
cana-5531	95	11	once	once	SCONJ
cana-5531	95	12	debonding	debonde	VERB
cana-5531	95	13	occurs	occur	VERB
cana-5531	95	14	bonding	bonding	NOUN
cana-5531	95	15	can	can	AUX
cana-5531	95	16	not	not	PART
cana-5531	95	17	be	be	AUX
cana-5531	95	18	reestablished	reestablish	VERB
cana-5531	95	19	,	,	PUNCT
cana-5531	95	20	indeed	indeed	ADV
cana-5531	95	21	,	,	PUNCT
cana-5531	95	22	the	the	DET
cana-5531	95	23	adhesion	adhesion	NOUN
cana-5531	95	24	process	process	NOUN
cana-5531	95	25	is	be	AUX
cana-5531	95	26	irreversible	irreversible	ADJ
cana-5531	95	27	.	.	PUNCT
cana-5531	96	1	also	also	ADV
cana-5531	96	2	from	from	ADP
cana-5531	96	3	[	[	X
cana-5531	96	4	19	19	NUM
cana-5531	96	5	]	]	X
cana-5531	96	6	it	it	PRON
cana-5531	96	7	must	must	AUX
cana-5531	96	8	be	be	AUX
cana-5531	96	9	pointed	point	VERB
cana-5531	96	10	out	out	ADP
cana-5531	96	11	clearly	clearly	ADV
cana-5531	96	12	that	that	SCONJ
cana-5531	96	13	condition	condition	NOUN
cana-5531	96	14	(	(	PUNCT
cana-5531	96	15	3.7	3.7	NUM
cana-5531	96	16	)	)	PUNCT
cana-5531	96	17	does	do	AUX
cana-5531	96	18	not	not	PART
cana-5531	96	19	allow	allow	VERB
cana-5531	96	20	for	for	ADP
cana-5531	96	21	complete	complete	ADJ
cana-5531	96	22	debonding	debonding	NOUN
cana-5531	96	23	in	in	ADP
cana-5531	96	24	finite	finite	ADJ
cana-5531	96	25	time	time	NOUN
cana-5531	96	26	.	.	PUNCT
cana-5531	97	1	in	in	ADP
cana-5531	97	2	equation	equation	NOUN
cana-5531	97	3	(	(	PUNCT
cana-5531	97	4	3.8	3.8	NUM
cana-5531	97	5	)	)	PUNCT
cana-5531	97	6	β0	β0	NOUN
cana-5531	97	7	denotes	denote	VERB
cana-5531	97	8	the	the	DET
cana-5531	97	9	initial	initial	ADJ
cana-5531	97	10	bonding	bonding	NOUN
cana-5531	97	11	.	.	PUNCT
cana-5531	98	1	finally	finally	ADV
cana-5531	98	2	,	,	PUNCT
cana-5531	98	3	in	in	ADP
cana-5531	98	4	equation	equation	NOUN
cana-5531	98	5	(	(	PUNCT
cana-5531	98	6	3.9	3.9	NUM
cana-5531	98	7	)	)	PUNCT
cana-5531	98	8	u0	u0	PROPN
cana-5531	98	9	is	be	AUX
cana-5531	98	10	the	the	DET
cana-5531	98	11	initial	initial	ADJ
cana-5531	98	12	displacement	displacement	NOUN
cana-5531	98	13	and	and	CCONJ
cana-5531	98	14	u1	u1	VERB
cana-5531	98	15	the	the	DET
cana-5531	98	16	initial	initial	ADJ
cana-5531	98	17	velocity	velocity	NOUN
cana-5531	98	18	.	.	PUNCT
cana-5531	99	1	4	4	X
cana-5531	99	2	.	.	X
cana-5531	99	3	variational	variational	ADJ
cana-5531	99	4	formulation	formulation	NOUN
cana-5531	99	5	for	for	ADP
cana-5531	99	6	a	a	DET
cana-5531	99	7	weak	weak	ADJ
cana-5531	99	8	formulation	formulation	NOUN
cana-5531	99	9	of	of	ADP
cana-5531	99	10	problem	problem	NOUN
cana-5531	99	11	p1	p1	PROPN
cana-5531	99	12	,	,	PUNCT
cana-5531	99	13	let	let	VERB
cana-5531	99	14	v	v	PART
cana-5531	99	15	be	be	AUX
cana-5531	99	16	the	the	DET
cana-5531	99	17	closed	closed	ADJ
cana-5531	99	18	subspace	subspace	NOUN
cana-5531	99	19	of	of	ADP
cana-5531	99	20	h1	h1	PROPN
cana-5531	99	21	defined	define	VERB
cana-5531	99	22	by	by	ADP
cana-5531	99	23	v	v	NOUN
cana-5531	99	24	=	=	SYM
cana-5531	99	25	{	{	PUNCT
cana-5531	99	26	𝜐	𝜐	PROPN
cana-5531	99	27	∈	∈	PROPN
cana-5531	99	28	h1	h1	NOUN
cana-5531	99	29	:	:	PUNCT
cana-5531	100	1	𝜐	𝜐	X
cana-5531	100	2	=	=	SYM
cana-5531	100	3	0	0	NUM
cana-5531	100	4	on	on	ADP
cana-5531	100	5	γ1	γ1	PROPN
cana-5531	100	6	}	}	PUNCT
cana-5531	100	7	.	.	PUNCT
cana-5531	101	1	and	and	CCONJ
cana-5531	101	2	the	the	DET
cana-5531	101	3	convex	convex	NOUN
cana-5531	101	4	subset	subset	NOUN
cana-5531	101	5	of	of	ADP
cana-5531	101	6	admissible	admissible	ADJ
cana-5531	101	7	displacement	displacement	NOUN
cana-5531	101	8	given	give	VERB
cana-5531	101	9	by	by	ADP
cana-5531	101	10	k	k	PROPN
cana-5531	101	11	=	=	PRON
cana-5531	101	12	{	{	PUNCT
cana-5531	101	13	𝜐	𝜐	PROPN
cana-5531	101	14	∈	∈	PROPN
cana-5531	102	1	v	v	NOUN
cana-5531	102	2	:	:	PUNCT
cana-5531	102	3	𝜐ν	𝜐ν	NOUN
cana-5531	102	4	≤	≤	NUM
cana-5531	102	5	𝑔	𝑔	PROPN
cana-5531	102	6	a.e	a.e	PROPN
cana-5531	102	7	on	on	ADP
cana-5531	102	8	γ3	γ3	NOUN
cana-5531	102	9	}	}	PUNCT
cana-5531	102	10	.	.	PUNCT
cana-5531	103	1	since	since	SCONJ
cana-5531	103	2	meas	meas	PROPN
cana-5531	103	3	γ1	γ1	PROPN
cana-5531	103	4	>	>	X
cana-5531	103	5	0	0	PROPN
cana-5531	103	6	,	,	PUNCT
cana-5531	103	7	the	the	DET
cana-5531	103	8	following	follow	VERB
cana-5531	103	9	korn	korn	PROPN
cana-5531	103	10	’s	’s	PART
cana-5531	103	11	inequality	inequality	NOUN
cana-5531	103	12	holds	hold	VERB
cana-5531	103	13	[	[	X
cana-5531	103	14	8	8	NUM
cana-5531	103	15	]	]	X
cana-5531	103	16	ε	ε	PROPN
cana-5531	103	17	(	(	PUNCT
cana-5531	103	18	𝜐	𝜐	NOUN
cana-5531	103	19	)	)	PUNCT
cana-5531	103	20	ℋ	ℋ	NOUN
cana-5531	103	21	≥	≥	NUM
cana-5531	103	22	𝑐ω	𝑐ω	INTJ
cana-5531	103	23	𝜐	𝜐	PROPN
cana-5531	103	24	h1	h1	PROPN
cana-5531	103	25	∀𝜐	∀𝜐	PROPN
cana-5531	103	26	∈	∈	PROPN
cana-5531	103	27	v.	v.	ADP
cana-5531	103	28	(	(	PUNCT
cana-5531	103	29	4.1	4.1	NUM
cana-5531	103	30	)	)	PUNCT
cana-5531	103	31	where	where	SCONJ
cana-5531	103	32	𝑐ω	𝑐ω	INTJ
cana-5531	103	33	>	>	X
cana-5531	103	34	0	0	NUM
cana-5531	103	35	is	be	AUX
cana-5531	103	36	a	a	DET
cana-5531	103	37	constant	constant	ADJ
cana-5531	103	38	which	which	PRON
cana-5531	103	39	depends	depend	VERB
cana-5531	103	40	only	only	ADV
cana-5531	103	41	on	on	ADP
cana-5531	103	42	ω	ω	NUM
cana-5531	103	43	and	and	CCONJ
cana-5531	103	44	γ1	γ1	PROPN
cana-5531	103	45	.	.	PUNCT
cana-5531	104	1	we	we	PRON
cana-5531	104	2	equip	equip	VERB
cana-5531	104	3	𝑉	𝑉	PROPN
cana-5531	104	4	with	with	ADP
cana-5531	104	5	the	the	DET
cana-5531	104	6	inner	inner	ADJ
cana-5531	104	7	product	product	NOUN
cana-5531	104	8	(	(	PUNCT
cana-5531	104	9	𝑢	𝑢	X
cana-5531	104	10	,	,	PUNCT
cana-5531	104	11	𝜐)𝑉	𝜐)𝑉	NOUN
cana-5531	104	12	=	=	PUNCT
cana-5531	104	13	〈	〈	NOUN
cana-5531	104	14	𝜀(𝑢	𝜀(𝑢	ADJ
cana-5531	104	15	)	)	PUNCT
cana-5531	104	16	,	,	PUNCT
cana-5531	104	17	𝜀(𝜐)〉ℋ	𝜀(𝜐)〉ℋ	PROPN
cana-5531	104	18	.	.	PUNCT
cana-5531	105	1	and	and	CCONJ
cana-5531	105	2	.	.	PUNCT
cana-5531	106	1	v	v	NOUN
cana-5531	106	2	is	be	AUX
cana-5531	106	3	the	the	DET
cana-5531	106	4	associated	associated	ADJ
cana-5531	106	5	norm	norm	NOUN
cana-5531	106	6	.	.	PUNCT
cana-5531	107	1	it	it	PRON
cana-5531	107	2	follows	follow	VERB
cana-5531	107	3	from	from	ADP
cana-5531	107	4	korn	korn	PROPN
cana-5531	107	5	’s	’s	PART
cana-5531	107	6	inequality	inequality	NOUN
cana-5531	107	7	(	(	PUNCT
cana-5531	107	8	4.1	4.1	NUM
cana-5531	107	9	)	)	PUNCT
cana-5531	107	10	that	that	SCONJ
cana-5531	107	11	the	the	DET
cana-5531	107	12	norms	norm	NOUN
cana-5531	107	13	.	.	PUNCT
cana-5531	108	1	h1	h1	PROPN
cana-5531	108	2	and	and	CCONJ
cana-5531	108	3	.	.	PUNCT
cana-5531	109	1	v	v	NOUN
cana-5531	109	2	are	be	AUX
cana-5531	109	3	equivalent	equivalent	ADJ
cana-5531	109	4	on	on	ADP
cana-5531	110	1	v.	v.	ADP
cana-5531	110	2	then	then	ADV
cana-5531	110	3	(	(	PUNCT
cana-5531	110	4	v	v	NOUN
cana-5531	110	5	,	,	PUNCT
cana-5531	110	6	.	.	PUNCT
cana-5531	111	1	v	v	X
cana-5531	111	2	)	)	PUNCT
cana-5531	111	3	is	be	AUX
cana-5531	111	4	a	a	DET
cana-5531	111	5	real	real	ADJ
cana-5531	111	6	hilbert	hilbert	NOUN
cana-5531	111	7	space	space	NOUN
cana-5531	111	8	.	.	PUNCT
cana-5531	112	1	moreover	moreover	ADV
cana-5531	112	2	by	by	SCONJ
cana-5531	112	3	sobolev	sobolev	NOUN
cana-5531	112	4	’s	’s	PART
cana-5531	112	5	trace	trace	NOUN
cana-5531	112	6	theorem	theorem	VERB
cana-5531	112	7	,	,	PUNCT
cana-5531	112	8	there	there	PRON
cana-5531	112	9	exists	exist	VERB
cana-5531	112	10	𝑑ω	𝑑ω	NOUN
cana-5531	112	11	>	>	X
cana-5531	112	12	0	0	NUM
cana-5531	112	13	which	which	PRON
cana-5531	112	14	only	only	ADV
cana-5531	112	15	depends	depend	VERB
cana-5531	112	16	on	on	ADP
cana-5531	112	17	the	the	DET
cana-5531	112	18	domain	domain	NOUN
cana-5531	112	19	ω	ω	PROPN
cana-5531	112	20	,	,	PUNCT
cana-5531	112	21	γ1	γ1	NOUN
cana-5531	112	22	and	and	CCONJ
cana-5531	112	23	γ3	γ3	NOUN
cana-5531	112	24	such	such	ADJ
cana-5531	112	25	that	that	SCONJ
cana-5531	112	26	communications	communication	NOUN
cana-5531	112	27	on	on	ADP
cana-5531	112	28	applied	apply	VERB
cana-5531	112	29	nonlinear	nonlinear	ADJ
cana-5531	112	30	analysis	analysis	NOUN
cana-5531	112	31	issn	issn	NOUN
cana-5531	112	32	:	:	PUNCT
cana-5531	112	33	1074	1074	NUM
cana-5531	112	34	-	-	PUNCT
cana-5531	112	35	133x	133x	NUM
cana-5531	112	36	vol	vol	NOUN
cana-5531	112	37	32	32	NUM
cana-5531	112	38	no	no	NOUN
cana-5531	112	39	.	.	NOUN
cana-5531	112	40	3	3	NUM
cana-5531	112	41	(	(	PUNCT
cana-5531	112	42	2025	2025	NUM
cana-5531	112	43	)	)	PUNCT
cana-5531	112	44	969	969	NUM
cana-5531	112	45	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	112	46	𝜐	𝜐	PROPN
cana-5531	112	47	(	(	PUNCT
cana-5531	112	48	𝕃2(γ3))d	𝕃2(γ3))d	PROPN
cana-5531	112	49	≤	≤	PUNCT
cana-5531	112	50	𝑑ω	𝑑ω	NOUN
cana-5531	112	51	𝜐	𝜐	PROPN
cana-5531	112	52	v	v	X
cana-5531	112	53	∀𝜐	∀𝜐	X
cana-5531	112	54	∈	∈	PROPN
cana-5531	112	55	v.	v.	CCONJ
cana-5531	112	56	(	(	PUNCT
cana-5531	112	57	4.2	4.2	NUM
cana-5531	112	58	)	)	PUNCT
cana-5531	112	59	the	the	DET
cana-5531	112	60	body	body	NOUN
cana-5531	112	61	forces	force	NOUN
cana-5531	112	62	and	and	CCONJ
cana-5531	112	63	surface	surface	NOUN
cana-5531	112	64	tractions	traction	NOUN
cana-5531	112	65	have	have	VERB
cana-5531	112	66	the	the	DET
cana-5531	112	67	regularity	regularity	NOUN
cana-5531	112	68	𝜑1	𝜑1	VERB
cana-5531	112	69	∈	∈	NOUN
cana-5531	112	70	𝐶([0	𝐶([0	PROPN
cana-5531	112	71	,	,	PUNCT
cana-5531	112	72	𝑇	𝑇	PROPN
cana-5531	112	73	]	]	PUNCT
cana-5531	112	74	;	;	PUNCT
cana-5531	112	75	𝐻	𝐻	PROPN
cana-5531	112	76	)	)	PUNCT
cana-5531	112	77	,	,	PUNCT
cana-5531	112	78	𝜑2	𝜑2	PROPN
cana-5531	112	79	∈	∈	PROPN
cana-5531	112	80	𝐶	𝐶	PROPN
cana-5531	112	81	(	(	PUNCT
cana-5531	112	82	[	[	X
cana-5531	112	83	0	0	NUM
cana-5531	112	84	,	,	PUNCT
cana-5531	112	85	𝑇	𝑇	PROPN
cana-5531	112	86	]	]	PUNCT
cana-5531	112	87	;	;	PUNCT
cana-5531	112	88	(	(	PUNCT
cana-5531	112	89	𝕃	𝕃	PROPN
cana-5531	112	90	2(γ3	2(γ3	NUM
cana-5531	112	91	)	)	PUNCT
cana-5531	112	92	)	)	PUNCT
cana-5531	113	1	𝑑	𝑑	NOUN
cana-5531	113	2	)	)	PUNCT
cana-5531	113	3	(	(	PUNCT
cana-5531	113	4	4.3	4.3	NUM
cana-5531	113	5	)	)	PUNCT
cana-5531	113	6	the	the	DET
cana-5531	113	7	function	function	NOUN
cana-5531	113	8	𝑓	𝑓	X
cana-5531	113	9	:	:	PUNCT
cana-5531	113	10	[	[	X
cana-5531	113	11	0.t	0.t	X
cana-5531	113	12	]	]	PUNCT
cana-5531	113	13	→	→	SYM
cana-5531	113	14	v	v	NOUN
cana-5531	113	15	defined	define	VERB
cana-5531	113	16	by	by	ADP
cana-5531	113	17	(	(	PUNCT
cana-5531	113	18	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5531	113	19	)	)	PUNCT
cana-5531	113	20	,	,	PUNCT
cana-5531	113	21	𝜐)𝑉	𝜐)𝑉	NOUN
cana-5531	113	22	=	=	SYM
cana-5531	113	23	∫	∫	X
cana-5531	113	24	𝜑1(𝑡)𝜐𝑑𝑥ω	𝜑1(𝑡)𝜐𝑑𝑥ω	X
cana-5531	113	25	+	+	CCONJ
cana-5531	113	26	∫	∫	PROPN
cana-5531	113	27	𝜑2(𝑡)𝑑𝑎	𝜑2(𝑡)𝑑𝑎	NOUN
cana-5531	113	28	∀𝜐	∀𝜐	NOUN
cana-5531	113	29	∈	∈	PROPN
cana-5531	113	30	𝑉,γ2	𝑉,γ2	PROPN
cana-5531	113	31	𝑡	𝑡	X
cana-5531	113	32	∈	∈	PROPN
cana-5531	114	1	[	[	X
cana-5531	114	2	0	0	NUM
cana-5531	114	3	,	,	PUNCT
cana-5531	114	4	𝑇	𝑇	PROPN
cana-5531	114	5	]	]	PUNCT
cana-5531	114	6	,	,	PUNCT
cana-5531	114	7	(	(	PUNCT
cana-5531	114	8	4.4	4.4	NUM
cana-5531	114	9	)	)	PUNCT
cana-5531	114	10	and	and	CCONJ
cana-5531	114	11	that	that	SCONJ
cana-5531	114	12	(	(	PUNCT
cana-5531	114	13	4.3	4.3	NUM
cana-5531	114	14	)	)	PUNCT
cana-5531	114	15	and	and	CCONJ
cana-5531	114	16	(	(	PUNCT
cana-5531	114	17	4.4	4.4	NUM
cana-5531	114	18	)	)	PUNCT
cana-5531	114	19	imply	imply	VERB
cana-5531	114	20	𝑓	𝑓	DET
cana-5531	114	21	∈	∈	PROPN
cana-5531	114	22	c	c	X
cana-5531	114	23	(	(	PUNCT
cana-5531	114	24	[	[	X
cana-5531	114	25	0.t	0.t	X
cana-5531	114	26	]	]	PUNCT
cana-5531	114	27	;	;	PUNCT
cana-5531	114	28	v	v	X
cana-5531	114	29	)	)	PUNCT
cana-5531	114	30	in	in	ADP
cana-5531	114	31	the	the	DET
cana-5531	114	32	study	study	NOUN
cana-5531	114	33	of	of	ADP
cana-5531	114	34	the	the	DET
cana-5531	114	35	mechanical	mechanical	ADJ
cana-5531	114	36	problem	problem	NOUN
cana-5531	114	37	p1	p1	PROPN
cana-5531	114	38	(	(	PUNCT
cana-5531	114	39	3.1)-(3.9	3.1)-(3.9	NUM
cana-5531	114	40	)	)	PUNCT
cana-5531	114	41	let	let	VERB
cana-5531	114	42	the	the	DET
cana-5531	114	43	following	follow	VERB
cana-5531	114	44	assumptions	assumption	NOUN
cana-5531	114	45	:	:	PUNCT
cana-5531	115	1	the	the	DET
cana-5531	115	2	elasticity	elasticity	NOUN
cana-5531	115	3	operator	operator	NOUN
cana-5531	115	4	𝒜	𝒜	NOUN
cana-5531	115	5	satisfies	satisfie	NOUN
cana-5531	115	6	{	{	PUNCT
cana-5531	115	7	(	(	PUNCT
cana-5531	115	8	𝑎	𝑎	NOUN
cana-5531	115	9	)	)	PUNCT
cana-5531	115	10	𝒜	𝒜	NOUN
cana-5531	115	11	:	:	PUNCT
cana-5531	115	12	ω	ω	NUM
cana-5531	115	13	×	×	NOUN
cana-5531	115	14	𝕊𝑑	𝕊𝑑	PROPN
cana-5531	115	15	⟶	⟶	NOUN
cana-5531	115	16	𝕊𝑑	𝕊𝑑	PROPN
cana-5531	115	17	,	,	PUNCT
cana-5531	115	18	(	(	PUNCT
cana-5531	115	19	𝑏	𝑏	NOUN
cana-5531	115	20	)	)	PUNCT
cana-5531	115	21	𝑡ℎ𝑒𝑟𝑒	𝑡ℎ𝑒𝑟𝑒	NOUN
cana-5531	115	22	𝑒𝑥𝑖𝑠𝑡𝑠	𝑒𝑥𝑖𝑠𝑡𝑠	NOUN
cana-5531	115	23	𝑀	𝑀	PROPN
cana-5531	115	24	>	>	SYM
cana-5531	115	25	0	0	NUM
cana-5531	115	26	𝑠𝑢𝑐ℎ	𝑠𝑢𝑐ℎ	NOUN
cana-5531	115	27	𝑡ℎ𝑎𝑡	𝑡ℎ𝑎𝑡	PROPN
cana-5531	115	28	∶	∶	NOUN
cana-5531	115	29	|𝒜(𝑥	|𝒜(𝑥	ADJ
cana-5531	115	30	,	,	PUNCT
cana-5531	115	31	𝜀1	𝜀1	PROPN
cana-5531	115	32	)	)	PUNCT
cana-5531	115	33	−	−	PROPN
cana-5531	115	34	𝒜(𝑥	𝒜(𝑥	PROPN
cana-5531	115	35	,	,	PUNCT
cana-5531	115	36	𝜀2)|	𝜀2)|	VERB
cana-5531	115	37	≤	≤	NUM
cana-5531	115	38	𝑀|𝜀1	𝑀|𝜀1	NOUN
cana-5531	115	39	−	−	PROPN
cana-5531	115	40	𝜀2|	𝜀2|	PROPN
cana-5531	115	41	∀𝜀1	∀𝜀1	PROPN
cana-5531	115	42	,	,	PUNCT
cana-5531	115	43	𝜀2	𝜀2	PROPN
cana-5531	115	44	∈	∈	PROPN
cana-5531	115	45	𝕊	𝕊	PROPN
cana-5531	115	46	𝑑	𝑑	PROPN
cana-5531	115	47	,	,	PUNCT
cana-5531	115	48	𝑎.	𝑎.	PROPN
cana-5531	115	49	𝑒.	𝑒.	VERB
cana-5531	116	1	𝑥	𝑥	X
cana-5531	116	2	∈	∈	PROPN
cana-5531	116	3	ω	ω	X
cana-5531	116	4	(	(	PUNCT
cana-5531	116	5	𝑐	𝑐	NOUN
cana-5531	116	6	)	)	PUNCT
cana-5531	116	7	𝑡ℎ𝑒𝑟𝑒	𝑡ℎ𝑒𝑟𝑒	NOUN
cana-5531	116	8	𝑒𝑥𝑖𝑠𝑡𝑠	𝑒𝑥𝑖𝑠𝑡𝑠	NOUN
cana-5531	116	9	𝑚	𝑚	ADP
cana-5531	116	10	>	>	SYM
cana-5531	116	11	0	0	NUM
cana-5531	116	12	𝑠𝑢𝑐ℎ	𝑠𝑢𝑐ℎ	NOUN
cana-5531	116	13	𝑡ℎ𝑎𝑡	𝑡ℎ𝑎𝑡	PROPN
cana-5531	116	14	∶	∶	PROPN
cana-5531	116	15	(	(	PUNCT
cana-5531	116	16	𝒜(𝑥	𝒜(𝑥	NOUN
cana-5531	116	17	,	,	PUNCT
cana-5531	116	18	𝜀1	𝜀1	PROPN
cana-5531	116	19	)	)	PUNCT
cana-5531	116	20	−	−	PROPN
cana-5531	116	21	𝒜(𝑥	𝒜(𝑥	SYM
cana-5531	116	22	,	,	PUNCT
cana-5531	116	23	𝜀2	𝜀2	PROPN
cana-5531	116	24	)	)	PUNCT
cana-5531	116	25	)	)	PUNCT
cana-5531	116	26	.	.	PUNCT
cana-5531	117	1	(	(	PUNCT
cana-5531	117	2	𝜀1	𝜀1	X
cana-5531	117	3	−	−	PROPN
cana-5531	117	4	𝜀2	𝜀2	PROPN
cana-5531	117	5	)	)	PUNCT
cana-5531	117	6	≥	≥	NOUN
cana-5531	118	1	𝑚|𝜀1	𝑚|𝜀1	NUM
cana-5531	118	2	−	−	NOUN
cana-5531	118	3	𝜀2|	𝜀2|	NOUN
cana-5531	118	4	2	2	NUM
cana-5531	118	5	∀	∀	NOUN
cana-5531	118	6	𝜀1	𝜀1	PROPN
cana-5531	118	7	,	,	PUNCT
cana-5531	118	8	𝜀2	𝜀2	PROPN
cana-5531	118	9	∈	∈	PROPN
cana-5531	118	10	𝕊	𝕊	PROPN
cana-5531	118	11	𝑑	𝑑	PROPN
cana-5531	118	12	,	,	PUNCT
cana-5531	118	13	𝑎.	𝑎.	PROPN
cana-5531	118	14	𝑒.	𝑒.	VERB
cana-5531	119	1	𝑥	𝑥	X
cana-5531	119	2	∈	∈	PROPN
cana-5531	119	3	ω	ω	PROPN
cana-5531	119	4	,	,	PUNCT
cana-5531	119	5	(	(	PUNCT
cana-5531	119	6	𝑑	𝑑	NOUN
cana-5531	119	7	)	)	PUNCT
cana-5531	119	8	𝑡ℎ𝑒	𝑡ℎ𝑒	ADJ
cana-5531	119	9	𝑚𝑎𝑝𝑝𝑖𝑛𝑔	𝑚𝑎𝑝𝑝𝑖𝑛𝑔	NOUN
cana-5531	119	10	𝑥	𝑥	X
cana-5531	119	11	⟶	⟶	NOUN
cana-5531	119	12	𝒜(𝑥	𝒜(𝑥	X
cana-5531	119	13	,	,	PUNCT
cana-5531	119	14	𝜀	𝜀	PROPN
cana-5531	119	15	)	)	PUNCT
cana-5531	119	16	𝑖𝑠	𝑖𝑠	PROPN
cana-5531	119	17	𝑙𝑒𝑏𝑒𝑠𝑔𝑢𝑒	𝑙𝑒𝑏𝑒𝑠𝑔𝑢𝑒	PROPN
cana-5531	119	18	𝑚𝑒𝑎𝑠𝑢𝑟𝑎𝑏𝑙𝑒	𝑚𝑒𝑎𝑠𝑢𝑟𝑎𝑏𝑙𝑒	VERB
cana-5531	119	19	𝑖𝑛	𝑖𝑛	PROPN
cana-5531	119	20	ω	ω	X
cana-5531	119	21	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
cana-5531	119	22	𝑎𝑙𝑙	𝑎𝑙𝑙	NOUN
cana-5531	119	23	𝜀	𝜀	X
cana-5531	119	24	∈	∈	PROPN
cana-5531	119	25	𝕊𝑑	𝕊𝑑	PROPN
cana-5531	119	26	(	(	PUNCT
cana-5531	119	27	𝑒	𝑒	NOUN
cana-5531	119	28	)	)	PUNCT
cana-5531	119	29	𝑡ℎ𝑒	𝑡ℎ𝑒	ADJ
cana-5531	119	30	𝑚𝑎𝑝𝑝𝑖𝑛𝑔	𝑚𝑎𝑝𝑝𝑖𝑛𝑔	NOUN
cana-5531	119	31	𝑥	𝑥	X
cana-5531	119	32	⟶	⟶	NOUN
cana-5531	119	33	𝒜(𝑥	𝒜(𝑥	SYM
cana-5531	119	34	,	,	PUNCT
cana-5531	119	35	0	0	NUM
cana-5531	119	36	)	)	PUNCT
cana-5531	119	37	∈	∈	PROPN
cana-5531	119	38	ℋ.	ℋ.	PROPN
cana-5531	119	39	(	(	PUNCT
cana-5531	119	40	4.5	4.5	NUM
cana-5531	119	41	)	)	PUNCT
cana-5531	119	42	the	the	DET
cana-5531	119	43	viscosity	viscosity	NOUN
cana-5531	119	44	operator	operator	NOUN
cana-5531	119	45	𝒢	𝒢	NOUN
cana-5531	119	46	satisfies	satisfie	NOUN
cana-5531	119	47	{	{	PUNCT
cana-5531	119	48	(	(	PUNCT
cana-5531	119	49	𝑎	𝑎	NOUN
cana-5531	119	50	)	)	PUNCT
cana-5531	119	51	𝒢	𝒢	NOUN
cana-5531	119	52	:	:	PUNCT
cana-5531	119	53	ω	ω	NUM
cana-5531	119	54	×	×	NOUN
cana-5531	119	55	𝕊𝑑	𝕊𝑑	PROPN
cana-5531	119	56	⟶	⟶	NOUN
cana-5531	119	57	𝕊𝑑	𝕊𝑑	PROPN
cana-5531	119	58	,	,	PUNCT
cana-5531	119	59	(	(	PUNCT
cana-5531	119	60	𝑏	𝑏	NOUN
cana-5531	119	61	)	)	PUNCT
cana-5531	119	62	𝑡ℎ𝑒𝑟𝑒	𝑡ℎ𝑒𝑟𝑒	NOUN
cana-5531	119	63	𝑒𝑥𝑖𝑠𝑡𝑠	𝑒𝑥𝑖𝑠𝑡𝑠	NOUN
cana-5531	119	64	𝐿𝒢	𝐿𝒢	PROPN
cana-5531	119	65	>	>	SYM
cana-5531	119	66	0	0	NUM
cana-5531	119	67	𝑠𝑢𝑐ℎ	𝑠𝑢𝑐ℎ	PROPN
cana-5531	119	68	𝑡ℎ𝑎𝑡	𝑡ℎ𝑎𝑡	ADJ
cana-5531	119	69	:	:	PUNCT
cana-5531	119	70	|𝒢(𝑥	|𝒢(𝑥	PROPN
cana-5531	119	71	,	,	PUNCT
cana-5531	119	72	𝜉1	𝜉1	PROPN
cana-5531	119	73	)	)	PUNCT
cana-5531	119	74	−	−	PROPN
cana-5531	120	1	𝒢(𝑥	𝒢(𝑥	NOUN
cana-5531	120	2	,	,	PUNCT
cana-5531	120	3	𝜉2)|	𝜉2)|	PROPN
cana-5531	120	4	≤	≤	NOUN
cana-5531	120	5	𝐿𝒢|𝜉1	𝐿𝒢|𝜉1	NOUN
cana-5531	120	6	−	−	PROPN
cana-5531	120	7	𝜉2|	𝜉2|	PROPN
cana-5531	120	8	∀𝜉1	∀𝜉1	PROPN
cana-5531	120	9	,	,	PUNCT
cana-5531	120	10	𝜉2	𝜉2	PROPN
cana-5531	120	11	∈	∈	PROPN
cana-5531	120	12	𝕊	𝕊	PROPN
cana-5531	120	13	𝑑	𝑑	PROPN
cana-5531	120	14	,	,	PUNCT
cana-5531	120	15	(	(	PUNCT
cana-5531	120	16	𝑐	𝑐	NOUN
cana-5531	120	17	)	)	PUNCT
cana-5531	120	18	𝑡ℎ𝑒	𝑡ℎ𝑒	ADJ
cana-5531	120	19	𝑚𝑎𝑝𝑝𝑖𝑛𝑔	𝑚𝑎𝑝𝑝𝑖𝑛𝑔	ADJ
cana-5531	120	20	𝑥	𝑥	X
cana-5531	120	21	⟶	⟶	PROPN
cana-5531	120	22	𝒢(𝑥	𝒢(𝑥	NOUN
cana-5531	120	23	,	,	PUNCT
cana-5531	120	24	𝜉	𝜉	NOUN
cana-5531	120	25	)	)	PUNCT
cana-5531	120	26	𝑖𝑠	𝑖𝑠	NOUN
cana-5531	120	27	𝑙𝑒𝑏𝑒𝑠𝑔𝑢𝑒	𝑙𝑒𝑏𝑒𝑠𝑔𝑢𝑒	PROPN
cana-5531	120	28	𝑚𝑒𝑎𝑠𝑢𝑟𝑎𝑏𝑙𝑒	𝑚𝑒𝑎𝑠𝑢𝑟𝑎𝑏𝑙𝑒	VERB
cana-5531	120	29	𝑖𝑛	𝑖𝑛	PROPN
cana-5531	120	30	ω	ω	X
cana-5531	120	31	𝑓𝑜𝑟	𝑓𝑜𝑟	NOUN
cana-5531	120	32	𝑎𝑙𝑙	𝑎𝑙𝑙	NOUN
cana-5531	120	33	𝜉	𝜉	X
cana-5531	120	34	∈	∈	PROPN
cana-5531	121	1	𝕊𝑑	𝕊𝑑	PROPN
cana-5531	121	2	,	,	PUNCT
cana-5531	121	3	(	(	PUNCT
cana-5531	121	4	𝑑	𝑑	NOUN
cana-5531	121	5	)	)	PUNCT
cana-5531	121	6	𝑡ℎ𝑒	𝑡ℎ𝑒	ADJ
cana-5531	121	7	𝑚𝑎𝑝𝑝𝑖𝑛𝑔	𝑚𝑎𝑝𝑝𝑖𝑛𝑔	ADJ
cana-5531	121	8	𝑥	𝑥	X
cana-5531	121	9	⟶	⟶	NOUN
cana-5531	121	10	𝒢(𝑥	𝒢(𝑥	NOUN
cana-5531	121	11	,	,	PUNCT
cana-5531	121	12	0	0	NUM
cana-5531	121	13	)	)	PUNCT
cana-5531	121	14	∈	∈	PROPN
cana-5531	121	15	ℋ.	ℋ.	PROPN
cana-5531	121	16	(	(	PUNCT
cana-5531	121	17	4.6	4.6	NUM
cana-5531	121	18	)	)	PUNCT
cana-5531	121	19	the	the	DET
cana-5531	121	20	mass	mass	ADJ
cana-5531	121	21	density	density	NOUN
cana-5531	121	22	satisfies	satisfy	VERB
cana-5531	121	23	ρ	ρ	PROPN
cana-5531	121	24	∈	∈	PROPN
cana-5531	121	25	𝕃∞	𝕃∞	NOUN
cana-5531	121	26	(	(	PUNCT
cana-5531	121	27	ω	ω	NOUN
cana-5531	121	28	)	)	PUNCT
cana-5531	121	29	,	,	PUNCT
cana-5531	121	30	there	there	PRON
cana-5531	121	31	exists	exist	VERB
cana-5531	121	32	ρ∗	ρ∗	PROPN
cana-5531	121	33	>	>	X
cana-5531	121	34	0	0	NUM
cana-5531	122	1	such	such	ADJ
cana-5531	122	2	that	that	DET
cana-5531	122	3	ρ(x	ρ(x	NOUN
cana-5531	122	4	)	)	PUNCT
cana-5531	122	5	≥	≥	NOUN
cana-5531	123	1	ρ∗	ρ∗	PROPN
cana-5531	123	2	,	,	PUNCT
cana-5531	123	3	a.e	a.e	PROPN
cana-5531	123	4	.	.	PROPN
cana-5531	123	5	x	x	SYM
cana-5531	123	6	∈	∈	PROPN
cana-5531	123	7	ω	ω	PROPN
cana-5531	123	8	.	.	PUNCT
cana-5531	124	1	(	(	PUNCT
cana-5531	124	2	4.7	4.7	NUM
cana-5531	124	3	)	)	PUNCT
cana-5531	124	4	the	the	DET
cana-5531	124	5	space	space	NOUN
cana-5531	124	6	of	of	ADP
cana-5531	124	7	the	the	DET
cana-5531	124	8	tensors	tensor	NOUN
cana-5531	124	9	of	of	ADP
cana-5531	124	10	fourth	fourth	ADJ
cana-5531	124	11	order	order	NOUN
cana-5531	124	12	defined	define	VERB
cana-5531	124	13	by	by	ADP
cana-5531	124	14	ℋ∞	ℋ∞	PROPN
cana-5531	124	15	=	=	SYM
cana-5531	124	16	{	{	PUNCT
cana-5531	124	17	𝜀	𝜀	X
cana-5531	124	18	=	=	SYM
cana-5531	124	19	(	(	PUNCT
cana-5531	124	20	𝜀𝑖𝑗𝑘𝑙	𝜀𝑖𝑗𝑘𝑙	PROPN
cana-5531	124	21	):	):	PUNCT
cana-5531	125	1	𝜀𝑖𝑗𝑘𝑙	𝜀𝑖𝑗𝑘𝑙	PROPN
cana-5531	125	2	=	=	NUM
cana-5531	125	3	𝜀𝑗𝑖𝑘𝑙	𝜀𝑗𝑖𝑘𝑙	NOUN
cana-5531	125	4	=	=	PUNCT
cana-5531	125	5	𝜀𝑘𝑙𝑖𝑗	𝜀𝑘𝑙𝑖𝑗	NOUN
cana-5531	125	6	∈	∈	PROPN
cana-5531	125	7	𝕃∞	𝕃∞	NOUN
cana-5531	125	8	(	(	PUNCT
cana-5531	125	9	ω	ω	NOUN
cana-5531	125	10	)	)	PUNCT
cana-5531	125	11	,	,	PUNCT
cana-5531	125	12	1	1	NUM
cana-5531	125	13	≤	≤	X
cana-5531	125	14	i	i	PROPN
cana-5531	125	15	,	,	PUNCT
cana-5531	125	16	j	j	PROPN
cana-5531	125	17	,	,	PUNCT
cana-5531	125	18	k	k	PROPN
cana-5531	125	19	,	,	PUNCT
cana-5531	125	20	l	l	PROPN
cana-5531	125	21	≤	≤	NUM
cana-5531	125	22	d	d	NOUN
cana-5531	125	23	}	}	PUNCT
cana-5531	125	24	.	.	PUNCT
cana-5531	126	1	which	which	PRON
cana-5531	126	2	is	be	AUX
cana-5531	126	3	the	the	DET
cana-5531	126	4	real	real	ADJ
cana-5531	126	5	banach	banach	NOUN
cana-5531	126	6	space	space	NOUN
cana-5531	126	7	with	with	ADP
cana-5531	126	8	the	the	DET
cana-5531	126	9	norm	norm	NOUN
cana-5531	126	10	‖𝜀‖ℋ∞	‖𝜀‖ℋ∞	ADV
cana-5531	126	11	=	=	SYM
cana-5531	126	12	max	max	PROPN
cana-5531	126	13	1≤𝑖,𝑗,𝑘,𝑙≤𝑑	1≤𝑖,𝑗,𝑘,𝑙≤𝑑	NUM
cana-5531	126	14	‖𝜀𝑖𝑗𝑘𝑙‖𝕃∞(ω	‖𝜀𝑖𝑗𝑘𝑙‖𝕃∞(ω	NOUN
cana-5531	126	15	)	)	PUNCT
cana-5531	126	16	.	.	PUNCT
cana-5531	127	1	the	the	DET
cana-5531	127	2	tensor	tensor	NOUN
cana-5531	127	3	of	of	ADP
cana-5531	127	4	relaxation	relaxation	NOUN
cana-5531	127	5	ℱ	ℱ	PROPN
cana-5531	127	6	satisfies	satisfy	VERB
cana-5531	127	7	ℱ	ℱ	PROPN
cana-5531	127	8	∈𝐶	∈𝐶	PROPN
cana-5531	127	9	(	(	PUNCT
cana-5531	127	10	[	[	X
cana-5531	127	11	0.t	0.t	X
cana-5531	127	12	]	]	PUNCT
cana-5531	127	13	;	;	PUNCT
cana-5531	127	14	ℋ∞	ℋ∞	PROPN
cana-5531	127	15	)	)	PUNCT
cana-5531	127	16	(	(	PUNCT
cana-5531	127	17	4.8	4.8	NUM
cana-5531	127	18	)	)	PUNCT
cana-5531	127	19	communications	communication	NOUN
cana-5531	127	20	on	on	ADP
cana-5531	127	21	applied	apply	VERB
cana-5531	127	22	nonlinear	nonlinear	ADJ
cana-5531	127	23	analysis	analysis	NOUN
cana-5531	127	24	issn	issn	NOUN
cana-5531	127	25	:	:	PUNCT
cana-5531	127	26	1074	1074	NUM
cana-5531	127	27	-	-	PUNCT
cana-5531	127	28	133x	133x	NUM
cana-5531	127	29	vol	vol	NOUN
cana-5531	127	30	32	32	NUM
cana-5531	127	31	no	no	NOUN
cana-5531	127	32	.	.	NOUN
cana-5531	127	33	3	3	NUM
cana-5531	127	34	(	(	PUNCT
cana-5531	127	35	2025	2025	NUM
cana-5531	127	36	)	)	PUNCT
cana-5531	127	37	970	970	NUM
cana-5531	127	38	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	127	39	the	the	DET
cana-5531	127	40	adhesion	adhesion	NOUN
cana-5531	127	41	coefficients	coefficient	VERB
cana-5531	127	42	cν	cν	NOUN
cana-5531	127	43	,	,	PUNCT
cana-5531	127	44	cτ	cτ	VERB
cana-5531	127	45	and	and	CCONJ
cana-5531	127	46	εa	εa	PROPN
cana-5531	127	47	satisfy	satisfy	PROPN
cana-5531	127	48	cν	cν	PROPN
cana-5531	127	49	,	,	PUNCT
cana-5531	127	50	cτ	cτ	ADP
cana-5531	127	51	∈	∈	NOUN
cana-5531	127	52	𝕃∞	𝕃∞	X
cana-5531	127	53	(	(	PUNCT
cana-5531	127	54	γ3	γ3	NOUN
cana-5531	127	55	)	)	PUNCT
cana-5531	127	56	,	,	PUNCT
cana-5531	127	57	εa	εa	PROPN
cana-5531	127	58	∈	∈	PROPN
cana-5531	127	59	𝕃2	𝕃2	NOUN
cana-5531	127	60	(	(	PUNCT
cana-5531	127	61	γ3	γ3	NOUN
cana-5531	127	62	)	)	PUNCT
cana-5531	127	63	and	and	CCONJ
cana-5531	127	64	cν	cν	VERB
cana-5531	127	65	,	,	PUNCT
cana-5531	127	66	cτ	cτ	INTJ
cana-5531	127	67	,	,	PUNCT
cana-5531	127	68	εa	εa	VERB
cana-5531	127	69	>	>	X
cana-5531	127	70	0	0	PUNCT
cana-5531	128	1	a.e	a.e	PROPN
cana-5531	128	2	.	.	PROPN
cana-5531	128	3	on	on	ADP
cana-5531	128	4	γ3	γ3	NOUN
cana-5531	128	5	.	.	PUNCT
cana-5531	129	1	(	(	PUNCT
cana-5531	129	2	4.9	4.9	NUM
cana-5531	129	3	)	)	PUNCT
cana-5531	129	4	that	that	SCONJ
cana-5531	129	5	the	the	DET
cana-5531	129	6	initial	initial	ADJ
cana-5531	129	7	bonding	bonding	NOUN
cana-5531	129	8	field	field	NOUN
cana-5531	129	9	satisfies	satisfy	VERB
cana-5531	129	10	β0	β0	PROPN
cana-5531	129	11	∈	∈	PROPN
cana-5531	129	12	𝕃2	𝕃2	NOUN
cana-5531	129	13	(	(	PUNCT
cana-5531	129	14	γ3	γ3	NOUN
cana-5531	129	15	)	)	PUNCT
cana-5531	129	16	,	,	PUNCT
cana-5531	129	17	0	0	NUM
cana-5531	129	18	≤	≤	NUM
cana-5531	129	19	β0	β0	ADJ
cana-5531	129	20	≤	≤	NUM
cana-5531	129	21	1	1	NUM
cana-5531	129	22	a.e	a.e	NOUN
cana-5531	129	23	on	on	ADP
cana-5531	129	24	γ3	γ3	NOUN
cana-5531	129	25	.	.	PUNCT
cana-5531	130	1	(	(	PUNCT
cana-5531	130	2	4.10	4.10	NUM
cana-5531	130	3	)	)	PUNCT
cana-5531	130	4	finally	finally	ADV
cana-5531	130	5	,	,	PUNCT
cana-5531	130	6	the	the	DET
cana-5531	130	7	initial	initial	ADJ
cana-5531	130	8	data	datum	NOUN
cana-5531	130	9	satisfy	satisfy	VERB
cana-5531	130	10	u0	u0	PROPN
cana-5531	130	11	∈	∈	PROPN
cana-5531	130	12	v	v	NOUN
cana-5531	130	13	and	and	CCONJ
cana-5531	130	14	u1	u1	PROPN
cana-5531	130	15	∈	∈	PROPN
cana-5531	130	16	h.	h.	PROPN
cana-5531	130	17	(	(	PUNCT
cana-5531	130	18	4.11	4.11	NUM
cana-5531	130	19	)	)	PUNCT
cana-5531	130	20	a	a	DET
cana-5531	130	21	modified	modify	VERB
cana-5531	130	22	inner	inner	ADJ
cana-5531	130	23	product	product	NOUN
cana-5531	130	24	on	on	ADP
cana-5531	130	25	the	the	DET
cana-5531	130	26	hilbert	hilbert	NOUN
cana-5531	130	27	space	space	NOUN
cana-5531	130	28	h	h	NOUN
cana-5531	130	29	=	=	NOUN
cana-5531	130	30	𝕃2	𝕃2	NOUN
cana-5531	130	31	(	(	PUNCT
cana-5531	130	32	ω)d	ω)d	VERB
cana-5531	130	33	given	give	VERB
cana-5531	130	34	by	by	ADP
cana-5531	130	35	(	(	PUNCT
cana-5531	130	36	(	(	PUNCT
cana-5531	130	37	u	u	NOUN
cana-5531	130	38	,	,	PUNCT
cana-5531	130	39	𝜐))h	𝜐))h	NOUN
cana-5531	130	40	=	=	SYM
cana-5531	130	41	(	(	PUNCT
cana-5531	130	42	ρu	ρu	NOUN
cana-5531	130	43	,	,	PUNCT
cana-5531	130	44	𝜐)h	𝜐)h	ADJ
cana-5531	130	45	∀u	∀u	NOUN
cana-5531	130	46	,	,	PUNCT
cana-5531	130	47	𝜐	𝜐	PROPN
cana-5531	130	48	∈	∈	PROPN
cana-5531	130	49	h	h	NOUN
cana-5531	130	50	,	,	PUNCT
cana-5531	130	51	that	that	SCONJ
cana-5531	130	52	,	,	PUNCT
cana-5531	130	53	it	it	PRON
cana-5531	130	54	is	be	AUX
cana-5531	130	55	weighted	weight	VERB
cana-5531	130	56	with	with	ADP
cana-5531	130	57	ρ	ρ	NOUN
cana-5531	130	58	and	and	CCONJ
cana-5531	130	59	let	let	VERB
cana-5531	130	60	.	.	PUNCT
cana-5531	131	1	h	h	PROPN
cana-5531	131	2	be	be	AUX
cana-5531	131	3	the	the	DET
cana-5531	131	4	associated	associated	ADJ
cana-5531	131	5	norm	norm	NOUN
cana-5531	131	6	i.e.	i.e.	X
cana-5531	131	7	‖𝜐‖𝐻	‖𝜐‖𝐻	NOUN
cana-5531	131	8	=	=	SYM
cana-5531	131	9	(	(	PUNCT
cana-5531	131	10	𝜌𝜐	𝜌𝜐	X
cana-5531	131	11	,	,	PUNCT
cana-5531	131	12	𝜐)𝐻	𝜐)𝐻	NOUN
cana-5531	131	13	1	1	NUM
cana-5531	131	14	2	2	NUM
cana-5531	131	15	∀𝜐	∀𝜐	NOUN
cana-5531	131	16	∈	∈	PROPN
cana-5531	131	17	𝐻.	𝐻.	PROPN
cana-5531	131	18	it	it	PRON
cana-5531	131	19	follows	follow	VERB
cana-5531	131	20	from	from	ADP
cana-5531	131	21	assumptions	assumption	NOUN
cana-5531	131	22	(	(	PUNCT
cana-5531	131	23	4.7	4.7	NUM
cana-5531	131	24	)	)	PUNCT
cana-5531	131	25	that	that	PRON
cana-5531	131	26	.	.	PUNCT
cana-5531	132	1	h	h	PROPN
cana-5531	132	2	and	and	CCONJ
cana-5531	132	3	|.|h	|.|h	PROPN
cana-5531	132	4	are	be	AUX
cana-5531	132	5	equivalent	equivalent	ADJ
cana-5531	132	6	norms	norm	NOUN
cana-5531	132	7	on	on	ADP
cana-5531	132	8	h	h	NOUN
cana-5531	132	9	and	and	CCONJ
cana-5531	132	10	also	also	ADV
cana-5531	132	11	the	the	DET
cana-5531	132	12	inclusion	inclusion	NOUN
cana-5531	132	13	mapping	mapping	NOUN
cana-5531	132	14	of	of	ADP
cana-5531	132	15	(	(	PUNCT
cana-5531	132	16	v	v	NOUN
cana-5531	132	17	,	,	PUNCT
cana-5531	132	18	|.|v	|.|v	NOUN
cana-5531	132	19	)	)	PUNCT
cana-5531	132	20	into	into	ADP
cana-5531	132	21	(	(	PUNCT
cana-5531	132	22	h	h	NOUN
cana-5531	132	23	,	,	PUNCT
cana-5531	132	24	|.|h	|.|h	NOUN
cana-5531	132	25	)	)	PUNCT
cana-5531	132	26	is	be	AUX
cana-5531	132	27	continuons	continuon	NOUN
cana-5531	132	28	and	and	CCONJ
cana-5531	132	29	dense	dense	ADJ
cana-5531	132	30	.	.	PUNCT
cana-5531	133	1	let	let	VERB
cana-5531	133	2	𝑉	𝑉	PROPN
cana-5531	133	3	́	́	AUX
cana-5531	133	4	be	be	AUX
cana-5531	133	5	the	the	DET
cana-5531	133	6	dual	dual	ADJ
cana-5531	133	7	space	space	NOUN
cana-5531	133	8	of	of	ADP
cana-5531	133	9	𝑉.	𝑉.	NOUN
cana-5531	133	10	identifying	identify	VERB
cana-5531	133	11	h	h	NOUN
cana-5531	133	12	with	with	ADP
cana-5531	133	13	its	its	PRON
cana-5531	133	14	own	own	ADJ
cana-5531	133	15	dual	dual	NOUN
cana-5531	133	16	,	,	PUNCT
cana-5531	133	17	it	it	PRON
cana-5531	133	18	can	can	AUX
cana-5531	133	19	write	write	VERB
cana-5531	133	20	the	the	DET
cana-5531	133	21	gelfand	gelfand	ADJ
cana-5531	133	22	triple	triple	ADJ
cana-5531	133	23	𝑉	𝑉	PROPN
cana-5531	133	24	⊂	⊂	PROPN
cana-5531	133	25	h	h	NOUN
cana-5531	133	26	⊂	⊂	PROPN
cana-5531	133	27	𝑉	𝑉	PROPN
cana-5531	133	28	́	́	PROPN
cana-5531	133	29	;	;	PUNCT
cana-5531	133	30	the	the	DET
cana-5531	133	31	notation	notation	NOUN
cana-5531	133	32	(	(	PUNCT
cana-5531	133	33	.	.	PUNCT
cana-5531	133	34	,	,	PUNCT
cana-5531	133	35	.	.	PUNCT
cana-5531	133	36	)	)	PUNCT
cana-5531	134	1	𝑉′×𝑉	𝑉′×𝑉	NOUN
cana-5531	134	2	represents	represent	VERB
cana-5531	134	3	the	the	DET
cana-5531	134	4	duality	duality	NOUN
cana-5531	134	5	pairing	pair	VERB
cana-5531	134	6	between	between	ADP
cana-5531	134	7	𝑉′and	𝑉′and	PROPN
cana-5531	134	8	v	v	NOUN
cana-5531	134	9	recall	recall	NOUN
cana-5531	134	10	that	that	SCONJ
cana-5531	134	11	(	(	PUNCT
cana-5531	134	12	𝑢	𝑢	X
cana-5531	134	13	,	,	PUNCT
cana-5531	134	14	𝜐)𝑉′×𝑉	𝜐)𝑉′×𝑉	NOUN
cana-5531	134	15	=	=	PUNCT
cana-5531	134	16	(	(	PUNCT
cana-5531	134	17	(	(	PUNCT
cana-5531	134	18	𝑢	𝑢	X
cana-5531	134	19	,	,	PUNCT
cana-5531	134	20	𝜐))𝐻	𝜐))𝐻	NOUN
cana-5531	134	21	∀𝑢	∀𝑢	DET
cana-5531	134	22	∈	∈	PROPN
cana-5531	134	23	𝐻	𝐻	PROPN
cana-5531	134	24	,	,	PUNCT
cana-5531	134	25	∀𝜐	∀𝜐	NOUN
cana-5531	134	26	∈	∈	PROPN
cana-5531	134	27	𝑉.	𝑉.	PROPN
cana-5531	134	28	next	next	ADV
cana-5531	134	29	,	,	PUNCT
cana-5531	134	30	the	the	DET
cana-5531	134	31	subset	subset	NOUN
cana-5531	134	32	𝑊	𝑊	PROPN
cana-5531	134	33	of	of	ADP
cana-5531	134	34	h1	h1	PROPN
cana-5531	134	35	are	be	AUX
cana-5531	134	36	defined	define	VERB
cana-5531	134	37	as	as	ADP
cana-5531	134	38	𝑊	𝑊	PROPN
cana-5531	134	39	=	=	SYM
cana-5531	134	40	{	{	PUNCT
cana-5531	134	41	𝜐	𝜐	PROPN
cana-5531	134	42	∈	∈	PROPN
cana-5531	134	43	h1	h1	NOUN
cana-5531	134	44	:	:	PUNCT
cana-5531	134	45	div	div	X
cana-5531	134	46	(	(	PUNCT
cana-5531	134	47	𝜐	𝜐	NOUN
cana-5531	134	48	)	)	PUNCT
cana-5531	134	49	∈	∈	PROPN
cana-5531	134	50	h	h	NOUN
cana-5531	134	51	}	}	PUNCT
cana-5531	134	52	,	,	PUNCT
cana-5531	134	53	and	and	CCONJ
cana-5531	134	54	let	let	VERB
cana-5531	134	55	𝑗c	𝑗c	PRON
cana-5531	134	56	:	:	PUNCT
cana-5531	134	57	v×v	v×v	PROPN
cana-5531	134	58	→	→	SYM
cana-5531	134	59	r	r	NOUN
cana-5531	134	60	,	,	PUNCT
cana-5531	134	61	𝑗f	𝑗f	INTJ
cana-5531	134	62	:	:	PUNCT
cana-5531	134	63	(	(	PUNCT
cana-5531	134	64	v	v	NOUN
cana-5531	134	65	∩	∩	X
cana-5531	134	66	w	w	NOUN
cana-5531	134	67	)	)	PUNCT
cana-5531	134	68	×	×	NOUN
cana-5531	134	69	v	v	NOUN
cana-5531	134	70	→	→	PUNCT
cana-5531	134	71	ℝ	ℝ	PROPN
cana-5531	134	72	be	be	AUX
cana-5531	134	73	the	the	DET
cana-5531	134	74	functionals	functional	NOUN
cana-5531	134	75	given	give	VERB
cana-5531	134	76	by	by	ADP
cana-5531	134	77	𝑗𝑐(𝑢	𝑗𝑐(𝑢	PROPN
cana-5531	134	78	,	,	PUNCT
cana-5531	134	79	𝜐	𝜐	X
cana-5531	134	80	)	)	PUNCT
cana-5531	135	1	=	=	SYM
cana-5531	135	2	∫	∫	NOUN
cana-5531	135	3	𝑝(𝑢𝜈)𝜐𝜈𝑑𝑎	𝑝(𝑢𝜈)𝜐𝜈𝑑𝑎	X
cana-5531	136	1	∀(𝑢	∀(𝑢	NUM
cana-5531	136	2	,	,	PUNCT
cana-5531	136	3	𝜐	𝜐	X
cana-5531	136	4	)	)	PUNCT
cana-5531	136	5	∈	∈	PROPN
cana-5531	136	6	𝑉	𝑉	PROPN
cana-5531	136	7	×	×	NOUN
cana-5531	136	8	𝑉,γ3	𝑉,γ3	NUM
cana-5531	136	9	𝑗𝑓(𝑢	𝑗𝑓(𝑢	ADV
cana-5531	136	10	,	,	PUNCT
cana-5531	136	11	𝜐	𝜐	NOUN
cana-5531	136	12	)	)	PUNCT
cana-5531	137	1	=	=	SYM
cana-5531	137	2	∫	∫	PROPN
cana-5531	137	3	𝜇|𝑅𝜎𝜈(𝑢)||𝜐𝜏|𝑑𝑎	𝜇|𝑅𝜎𝜈(𝑢)||𝜐𝜏|𝑑𝑎	VERB
cana-5531	137	4	∀(𝑢	∀(𝑢	NUM
cana-5531	137	5	,	,	PUNCT
cana-5531	137	6	𝜐	𝜐	NOUN
cana-5531	137	7	)	)	PUNCT
cana-5531	137	8	∈	∈	PROPN
cana-5531	137	9	(	(	PUNCT
cana-5531	137	10	𝑉	𝑉	PROPN
cana-5531	137	11	∩𝑊	∩𝑊	NOUN
cana-5531	137	12	)	)	PUNCT
cana-5531	137	13	×	×	NOUN
cana-5531	137	14	𝑉,γ3	𝑉,γ3	NUM
cana-5531	137	15	where	where	SCONJ
cana-5531	137	16	𝑅	𝑅	NOUN
cana-5531	137	17	:	:	PUNCT
cana-5531	137	18	𝐻	𝐻	PROPN
cana-5531	137	19	1	1	NUM
cana-5531	137	20	2(γ	2(γ	NUM
cana-5531	137	21	)	)	PUNCT
cana-5531	137	22	⟶	⟶	NOUN
cana-5531	137	23	𝕃2(γ3	𝕃2(γ3	NOUN
cana-5531	137	24	)	)	PUNCT
cana-5531	137	25	is	be	AUX
cana-5531	137	26	a	a	DET
cana-5531	137	27	linear	linear	ADJ
cana-5531	137	28	and	and	CCONJ
cana-5531	137	29	continuous	continuous	ADJ
cana-5531	137	30	mapping	mapping	NOUN
cana-5531	137	31	(	(	PUNCT
cana-5531	137	32	𝑠𝑒𝑒	𝑠𝑒𝑒	ADJ
cana-5531	137	33	[	[	X
cana-5531	137	34	7	7	NUM
cana-5531	137	35	]	]	NUM
cana-5531	137	36	)	)	PUNCT
cana-5531	137	37	.	.	PUNCT
cana-5531	138	1	(	(	PUNCT
cana-5531	138	2	4.12	4.12	NUM
cana-5531	138	3	)	)	PUNCT
cana-5531	138	4	the	the	DET
cana-5531	138	5	coefficient	coefficient	NOUN
cana-5531	138	6	of	of	ADP
cana-5531	138	7	friction	friction	NOUN
cana-5531	138	8	𝜇	𝜇	ADP
cana-5531	138	9	is	be	AUX
cana-5531	138	10	assumed	assume	VERB
cana-5531	138	11	to	to	PART
cana-5531	138	12	satisfy	satisfy	VERB
cana-5531	138	13	𝜇	𝜇	ADP
cana-5531	138	14	∈	∈	NOUN
cana-5531	138	15	𝕃∞	𝕃∞	X
cana-5531	138	16	(	(	PUNCT
cana-5531	138	17	γ3	γ3	NOUN
cana-5531	138	18	)	)	PUNCT
cana-5531	138	19	and	and	CCONJ
cana-5531	138	20	𝜇	𝜇	X
cana-5531	138	21	≥	≥	NOUN
cana-5531	138	22	0	0	NUM
cana-5531	138	23	a.e	a.e	NOUN
cana-5531	138	24	on	on	ADP
cana-5531	138	25	γ3	γ3	NOUN
cana-5531	138	26	(	(	PUNCT
cana-5531	138	27	4.13	4.13	NUM
cana-5531	138	28	)	)	PUNCT
cana-5531	138	29	next	next	ADV
cana-5531	138	30	,	,	PUNCT
cana-5531	138	31	let	let	VERB
cana-5531	138	32	𝑗=	𝑗=	NOUN
cana-5531	138	33	𝑗c	𝑗c	NOUN
cana-5531	139	1	+	+	CCONJ
cana-5531	139	2	𝑗f	𝑗f	NOUN
cana-5531	139	3	communications	communication	NOUN
cana-5531	139	4	on	on	ADP
cana-5531	139	5	applied	apply	VERB
cana-5531	139	6	nonlinear	nonlinear	ADJ
cana-5531	139	7	analysis	analysis	NOUN
cana-5531	139	8	issn	issn	NOUN
cana-5531	139	9	:	:	PUNCT
cana-5531	139	10	1074	1074	NUM
cana-5531	139	11	-	-	PUNCT
cana-5531	139	12	133x	133x	NUM
cana-5531	139	13	vol	vol	NOUN
cana-5531	139	14	32	32	NUM
cana-5531	139	15	no	no	NOUN
cana-5531	139	16	.	.	NOUN
cana-5531	139	17	3	3	NUM
cana-5531	139	18	(	(	PUNCT
cana-5531	139	19	2025	2025	NUM
cana-5531	139	20	)	)	PUNCT
cana-5531	139	21	971	971	NUM
cana-5531	139	22	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	139	23	the	the	DET
cana-5531	139	24	functional	functional	ADJ
cana-5531	139	25	ℎ	ℎ	NOUN
cana-5531	139	26	is	be	AUX
cana-5531	139	27	defined	define	VERB
cana-5531	139	28	by	by	ADP
cana-5531	139	29	h	h	NOUN
cana-5531	139	30	:	:	PUNCT
cana-5531	139	31	𝕃2	𝕃2	PROPN
cana-5531	139	32	(	(	PUNCT
cana-5531	139	33	γ3	γ3	NOUN
cana-5531	139	34	)	)	PUNCT
cana-5531	139	35	×	×	NOUN
cana-5531	139	36	v	v	NUM
cana-5531	139	37	×	×	PROPN
cana-5531	139	38	v→	v→	PRON
cana-5531	139	39	ℝ	ℝ	PROPN
cana-5531	139	40	,	,	PUNCT
cana-5531	139	41	ℎ(𝛽	ℎ(𝛽	PROPN
cana-5531	139	42	,	,	PUNCT
cana-5531	139	43	𝑢	𝑢	X
cana-5531	139	44	,	,	PUNCT
cana-5531	139	45	𝜐	𝜐	NOUN
cana-5531	139	46	)	)	PUNCT
cana-5531	139	47	=	=	SYM
cana-5531	140	1	∫	∫	PROPN
cana-5531	140	2	(	(	PUNCT
cana-5531	140	3	−𝑐𝜈𝛽	−𝑐𝜈𝛽	NOUN
cana-5531	140	4	2𝑅𝜈(𝑢𝜈)𝜐𝜈	2𝑅𝜈(𝑢𝜈)𝜐𝜈	NUM
cana-5531	141	1	+	+	CCONJ
cana-5531	141	2	𝑐𝜏𝛽	𝑐𝜏𝛽	PROPN
cana-5531	141	3	2𝑅𝜏(𝑢𝜏)𝜐𝜏)𝑑𝑎	2𝑅𝜏(𝑢𝜏)𝜐𝜏)𝑑𝑎	NUM
cana-5531	141	4	,	,	PUNCT
cana-5531	141	5	∀(𝛽	∀(𝛽	NUM
cana-5531	141	6	,	,	PUNCT
cana-5531	141	7	𝑢	𝑢	PROPN
cana-5531	141	8	,	,	PUNCT
cana-5531	141	9	𝜐	𝜐	NOUN
cana-5531	141	10	)	)	PUNCT
cana-5531	141	11	∈	∈	PROPN
cana-5531	141	12	𝕃	𝕃	PROPN
cana-5531	141	13	2(γ3	2(γ3	NUM
cana-5531	141	14	)	)	PUNCT
cana-5531	141	15	×	×	NOUN
cana-5531	141	16	𝑉	𝑉	PROPN
cana-5531	141	17	×	×	NOUN
cana-5531	141	18	𝑉	𝑉	PROPN
cana-5531	141	19	γ3	γ3	NOUN
cana-5531	141	20	where	where	SCONJ
cana-5531	141	21	the	the	DET
cana-5531	141	22	normal	normal	ADJ
cana-5531	141	23	compliance	compliance	NOUN
cana-5531	141	24	function	function	VERB
cana-5531	141	25	𝑝	𝑝	NOUN
cana-5531	141	26	satisfies	satisfie	NOUN
cana-5531	141	27	:	:	PUNCT
cana-5531	141	28	{	{	PUNCT
cana-5531	141	29	(	(	PUNCT
cana-5531	141	30	𝑎	𝑎	NOUN
cana-5531	141	31	)	)	PUNCT
cana-5531	141	32	𝑝	𝑝	NOUN
cana-5531	141	33	:	:	PUNCT
cana-5531	141	34	γ3	γ3	NOUN
cana-5531	141	35	×	×	NOUN
cana-5531	141	36	ℝ⟶	ℝ⟶	PROPN
cana-5531	141	37	ℝ+	ℝ+	NOUN
cana-5531	141	38	,	,	PUNCT
cana-5531	141	39	(	(	PUNCT
cana-5531	141	40	𝑏	𝑏	NOUN
cana-5531	141	41	)	)	PUNCT
cana-5531	141	42	∃𝐿𝑝	∃𝐿𝑝	NUM
cana-5531	141	43	𝑠𝑢𝑐ℎ	𝑠𝑢𝑐ℎ	NOUN
cana-5531	141	44	𝑡ℎ𝑎𝑡	𝑡ℎ𝑎𝑡	PROPN
cana-5531	141	45	∶	∶	PROPN
cana-5531	141	46	|𝑝(𝑥	|𝑝(𝑥	PROPN
cana-5531	141	47	−	−	PROPN
cana-5531	141	48	𝑟1	𝑟1	NOUN
cana-5531	141	49	)	)	PUNCT
cana-5531	141	50	−	−	PROPN
cana-5531	142	1	𝑝(𝑥	𝑝(𝑥	NUM
cana-5531	142	2	−	−	PROPN
cana-5531	142	3	𝑟2)|	𝑟2)|	PROPN
cana-5531	142	4	≤	≤	PROPN
cana-5531	142	5	𝐿𝑝|𝑟1	𝐿𝑝|𝑟1	PROPN
cana-5531	142	6	−	−	NUM
cana-5531	142	7	𝑟2|	𝑟2|	NUM
cana-5531	142	8	∀	∀	X
cana-5531	142	9	𝑟1	𝑟1	NOUN
cana-5531	142	10	,	,	PUNCT
cana-5531	142	11	𝑟2	𝑟2	NOUN
cana-5531	142	12	∈	∈	PROPN
cana-5531	142	13	ℝ	ℝ	PROPN
cana-5531	142	14	,	,	PUNCT
cana-5531	142	15	𝑎.	𝑎.	PROPN
cana-5531	142	16	𝑒.	𝑒.	VERB
cana-5531	143	1	𝑥	𝑥	DET
cana-5531	143	2	∈	∈	PROPN
cana-5531	143	3	γ3	γ3	NOUN
cana-5531	143	4	,	,	PUNCT
cana-5531	143	5	(	(	PUNCT
cana-5531	143	6	𝑐	𝑐	NOUN
cana-5531	143	7	)	)	PUNCT
cana-5531	143	8	(	(	PUNCT
cana-5531	143	9	𝑝(𝑥	𝑝(𝑥	NOUN
cana-5531	143	10	,	,	PUNCT
cana-5531	143	11	𝑟1	𝑟1	NOUN
cana-5531	143	12	)	)	PUNCT
cana-5531	143	13	−	−	PROPN
cana-5531	143	14	𝑝(𝑥	𝑝(𝑥	PROPN
cana-5531	143	15	,	,	PUNCT
cana-5531	143	16	𝑟2))(𝑟1	𝑟2))(𝑟1	NUM
cana-5531	143	17	−	−	NOUN
cana-5531	143	18	𝑟2	𝑟2	NOUN
cana-5531	143	19	)	)	PUNCT
cana-5531	143	20	≥	≥	NOUN
cana-5531	143	21	0	0	NUM
cana-5531	143	22	,	,	PUNCT
cana-5531	143	23	∀	∀	X
cana-5531	143	24	𝑟1	𝑟1	NOUN
cana-5531	143	25	,	,	PUNCT
cana-5531	143	26	𝑟2	𝑟2	NOUN
cana-5531	143	27	∈	∈	PROPN
cana-5531	143	28	ℝ	ℝ	PROPN
cana-5531	143	29	,	,	PUNCT
cana-5531	143	30	𝑎.	𝑎.	PROPN
cana-5531	143	31	𝑒.	𝑒.	VERB
cana-5531	144	1	𝑥	𝑥	DET
cana-5531	144	2	∈	∈	PROPN
cana-5531	144	3	γ3	γ3	NOUN
cana-5531	144	4	,	,	PUNCT
cana-5531	144	5	(	(	PUNCT
cana-5531	144	6	𝑑	𝑑	NOUN
cana-5531	144	7	)	)	PUNCT
cana-5531	144	8	𝑡ℎ𝑒	𝑡ℎ𝑒	ADJ
cana-5531	144	9	𝑚𝑎𝑝𝑝𝑖𝑛𝑔	𝑚𝑎𝑝𝑝𝑖𝑛𝑔	ADJ
cana-5531	144	10	𝑥	𝑥	X
cana-5531	144	11	⟶	⟶	NOUN
cana-5531	144	12	𝑝(𝑥	𝑝(𝑥	PROPN
cana-5531	144	13	,	,	PUNCT
cana-5531	144	14	𝑟	𝑟	NOUN
cana-5531	144	15	)	)	PUNCT
cana-5531	144	16	𝑖𝑠	𝑖𝑠	PUNCT
cana-5531	145	1	𝐿𝑒𝑏𝑒𝑠𝑔𝑢𝑒	𝐿𝑒𝑏𝑒𝑠𝑔𝑢𝑒	PROPN
cana-5531	145	2	𝑚𝑒𝑎𝑠𝑢𝑟𝑎𝑏𝑙𝑒	𝑚𝑒𝑎𝑠𝑢𝑟𝑎𝑏𝑙𝑒	VERB
cana-5531	145	3	𝑜𝑛	𝑜𝑛	PROPN
cana-5531	145	4	γ3	γ3	NOUN
cana-5531	145	5	,	,	PUNCT
cana-5531	145	6	𝑓𝑜𝑟	𝑓𝑜𝑟	ADV
cana-5531	145	7	𝑒𝑣𝑒𝑟𝑦	𝑒𝑣𝑒𝑟𝑦	VERB
cana-5531	145	8	𝑟	𝑟	X
cana-5531	145	9	∈	∈	PROPN
cana-5531	145	10	ℝ	ℝ	PROPN
cana-5531	145	11	,	,	PUNCT
cana-5531	145	12	(	(	PUNCT
cana-5531	145	13	𝑒	𝑒	NOUN
cana-5531	145	14	)	)	PUNCT
cana-5531	145	15	𝑝(𝑥	𝑝(𝑥	NOUN
cana-5531	145	16	,	,	PUNCT
cana-5531	145	17	0	0	NUM
cana-5531	145	18	)	)	PUNCT
cana-5531	145	19	=	=	SYM
cana-5531	145	20	0	0	NUM
cana-5531	145	21	,	,	PUNCT
cana-5531	145	22	𝑎.	𝑎.	PROPN
cana-5531	145	23	𝑒.	𝑒.	VERB
cana-5531	146	1	𝑥	𝑥	DET
cana-5531	146	2	∈	∈	PROPN
cana-5531	146	3	γ3	γ3	NOUN
cana-5531	146	4	.	.	PUNCT
cana-5531	147	1	(	(	PUNCT
cana-5531	147	2	4.14	4.14	NUM
cana-5531	147	3	)	)	PUNCT
cana-5531	147	4	finaly	finaly	VERB
cana-5531	147	5	,	,	PUNCT
cana-5531	147	6	the	the	DET
cana-5531	147	7	following	follow	VERB
cana-5531	147	8	set	set	NOUN
cana-5531	147	9	of	of	ADP
cana-5531	147	10	the	the	DET
cana-5531	147	11	bonding	bonding	NOUN
cana-5531	147	12	field	field	NOUN
cana-5531	147	13	:	:	PUNCT
cana-5531	147	14	𝐵	𝐵	NOUN
cana-5531	147	15	=	=	PUNCT
cana-5531	147	16	{	{	PUNCT
cana-5531	147	17	𝜃	𝜃	NOUN
cana-5531	147	18	:	:	PUNCT
cana-5531	148	1	[	[	X
cana-5531	148	2	0	0	NUM
cana-5531	148	3	,	,	PUNCT
cana-5531	148	4	𝑇	𝑇	PROPN
cana-5531	148	5	]	]	PUNCT
cana-5531	148	6	⟶	⟶	NOUN
cana-5531	148	7	𝕃2(γ3	𝕃2(γ3	NOUN
cana-5531	148	8	):	):	PUNCT
cana-5531	148	9	0	0	NUM
cana-5531	148	10	≤	≤	NUM
cana-5531	148	11	𝜃(𝑡	𝜃(𝑡	PROPN
cana-5531	148	12	)	)	PUNCT
cana-5531	148	13	≤	≤	NUM
cana-5531	148	14	1	1	NUM
cana-5531	148	15	,	,	PUNCT
cana-5531	148	16	∀∈	∀∈	ADP
cana-5531	148	17	[	[	X
cana-5531	148	18	0	0	NUM
cana-5531	148	19	,	,	PUNCT
cana-5531	148	20	𝑇	𝑇	PROPN
cana-5531	148	21	]	]	PUNCT
cana-5531	148	22	,	,	PUNCT
cana-5531	148	23	𝑎.	𝑎.	PROPN
cana-5531	148	24	𝑒.	𝑒.	PROPN
cana-5531	148	25	𝑜𝑛	𝑜𝑛	PROPN
cana-5531	148	26	γ3	γ3	NOUN
cana-5531	148	27	}	}	PUNCT
cana-5531	148	28	.	.	PUNCT
cana-5531	149	1	by	by	ADP
cana-5531	149	2	a	a	DET
cana-5531	149	3	standard	standard	ADJ
cana-5531	149	4	procedure	procedure	NOUN
cana-5531	149	5	based	base	VERB
cana-5531	149	6	on	on	ADP
cana-5531	149	7	green	green	PROPN
cana-5531	149	8	’s	’s	PART
cana-5531	149	9	formula	formula	NOUN
cana-5531	149	10	the	the	DET
cana-5531	149	11	following	follow	VERB
cana-5531	149	12	variational	variational	ADJ
cana-5531	149	13	formulation	formulation	NOUN
cana-5531	149	14	of	of	ADP
cana-5531	149	15	problem	problem	NOUN
cana-5531	149	16	p1	p1	PROPN
cana-5531	149	17	is	be	AUX
cana-5531	149	18	derived	derive	VERB
cana-5531	149	19	in	in	ADP
cana-5531	149	20	terms	term	NOUN
cana-5531	149	21	of	of	ADP
cana-5531	149	22	displacement	displacement	NOUN
cana-5531	149	23	and	and	CCONJ
cana-5531	149	24	bonding	bonding	NOUN
cana-5531	149	25	field	field	NOUN
cana-5531	149	26	.	.	PUNCT
cana-5531	150	1	problem	problem	NOUN
cana-5531	150	2	pv	pv	INTJ
cana-5531	150	3	.	.	PUNCT
cana-5531	151	1	find	find	VERB
cana-5531	151	2	a	a	DET
cana-5531	151	3	displacement	displacement	ADJ
cana-5531	151	4	field	field	NOUN
cana-5531	151	5	u	u	NOUN
cana-5531	151	6	:	:	PUNCT
cana-5531	151	7	ω	ω	X
cana-5531	151	8	×[0.t	×[0.t	X
cana-5531	151	9	]	]	PUNCT
cana-5531	152	1	→	→	PUNCT
cana-5531	152	2	ℝ𝑑	ℝ𝑑	PROPN
cana-5531	152	3	,	,	PUNCT
cana-5531	152	4	a	a	DET
cana-5531	152	5	stress	stress	NOUN
cana-5531	152	6	field	field	NOUN
cana-5531	152	7	σ	σ	NOUN
cana-5531	152	8	:	:	PUNCT
cana-5531	152	9	ω	ω	NUM
cana-5531	152	10	×	×	NOUN
cana-5531	152	11	[	[	X
cana-5531	152	12	0.t	0.t	NUM
cana-5531	152	13	]	]	X
cana-5531	152	14	→	→	PUNCT
cana-5531	152	15	𝕊𝑑	𝕊𝑑	PROPN
cana-5531	152	16	and	and	CCONJ
cana-5531	152	17	a	a	DET
cana-5531	152	18	bonding	bonding	NOUN
cana-5531	152	19	field	field	NOUN
cana-5531	152	20	β	β	NOUN
cana-5531	152	21	:	:	PUNCT
cana-5531	152	22	γ3	γ3	NOUN
cana-5531	152	23	×	×	NOUN
cana-5531	153	1	[	[	X
cana-5531	153	2	0.t	0.t	X
cana-5531	153	3	]	]	PUNCT
cana-5531	153	4	→[0.1	→[0.1	X
cana-5531	153	5	]	]	X
cana-5531	153	6	such	such	ADJ
cana-5531	153	7	that	that	SCONJ
cana-5531	153	8	u	u	PROPN
cana-5531	153	9	(	(	PUNCT
cana-5531	153	10	t	t	NOUN
cana-5531	153	11	)	)	PUNCT
cana-5531	153	12	∈	∈	PROPN
cana-5531	153	13	𝐾	𝐾	PROPN
cana-5531	153	14	∩	∩	ADJ
cana-5531	153	15	𝑊	𝑊	PROPN
cana-5531	153	16	,	,	PUNCT
cana-5531	153	17	𝜎(𝑡	𝜎(𝑡	NUM
cana-5531	153	18	)	)	PUNCT
cana-5531	153	19	=	=	NOUN
cana-5531	153	20	𝒜𝜀(𝑢(𝑡	𝒜𝜀(𝑢(𝑡	NOUN
cana-5531	153	21	)	)	PUNCT
cana-5531	153	22	)	)	PUNCT
cana-5531	154	1	+	+	CCONJ
cana-5531	154	2	𝒢𝜀(	𝒢𝜀(	PRON
cana-5531	154	3	�	�	PROPN
cana-5531	154	4	̇	̇	NOUN
cana-5531	154	5	�	�	PROPN
cana-5531	154	6	(𝑡	(𝑡	NOUN
cana-5531	154	7	)	)	PUNCT
cana-5531	154	8	)	)	PUNCT
cana-5531	155	1	+	+	CCONJ
cana-5531	155	2	∫	∫	PROPN
cana-5531	155	3	ℱ(𝑡	ℱ(𝑡	X
cana-5531	156	1	−	−	PROPN
cana-5531	156	2	𝑠)𝜀(𝑢(𝑠))𝑑𝑠	𝑠)𝜀(𝑢(𝑠))𝑑𝑠	PROPN
cana-5531	156	3	𝑎.	𝑎.	NOUN
cana-5531	156	4	𝑒.	𝑒.	NOUN
cana-5531	157	1	𝑡	𝑡	PROPN
cana-5531	157	2	∈	∈	PROPN
cana-5531	158	1	[	[	X
cana-5531	158	2	0	0	NUM
cana-5531	158	3	,	,	PUNCT
cana-5531	158	4	𝑇	𝑇	PROPN
cana-5531	158	5	]	]	X
cana-5531	158	6	1	1	NUM
cana-5531	158	7	0	0	NUM
cana-5531	158	8	(	(	PUNCT
cana-5531	158	9	(	(	PUNCT
cana-5531	158	10	𝑢,̈	𝑢,̈	ADP
cana-5531	158	11	𝜔	𝜔	PART
cana-5531	158	12	−	−	PROPN
cana-5531	158	13	�	�	PROPN
cana-5531	158	14	̇	̇	PROPN
cana-5531	158	15	�	�	PROPN
cana-5531	158	16	)	)	PUNCT
cana-5531	158	17	)	)	PUNCT
cana-5531	159	1	𝐻	𝐻	PROPN
cana-5531	159	2	+	+	CCONJ
cana-5531	159	3	(	(	PUNCT
cana-5531	159	4	𝒜𝜀(𝑢	𝒜𝜀(𝑢	ADJ
cana-5531	159	5	)	)	PUNCT
cana-5531	159	6	,	,	PUNCT
cana-5531	159	7	𝜀(𝜔	𝜀(𝜔	NOUN
cana-5531	159	8	)	)	PUNCT
cana-5531	159	9	−	−	ADP
cana-5531	159	10	𝜀(	𝜀(	NOUN
cana-5531	159	11	�	�	PROPN
cana-5531	159	12	̇	̇	PROPN
cana-5531	159	13	�	�	PROPN
cana-5531	159	14	)	)	PUNCT
cana-5531	159	15	)	)	PUNCT
cana-5531	160	1	ℋ	ℋ	PROPN
cana-5531	160	2	+	+	CCONJ
cana-5531	160	3	(	(	PUNCT
cana-5531	160	4	𝒢𝜀(	𝒢𝜀(	ADJ
cana-5531	160	5	�	�	PROPN
cana-5531	160	6	̇	̇	NOUN
cana-5531	160	7	�	�	PROPN
cana-5531	160	8	)	)	PUNCT
cana-5531	160	9	,	,	PUNCT
cana-5531	160	10	𝜀(𝜔	𝜀(𝜔	NOUN
cana-5531	160	11	)	)	PUNCT
cana-5531	160	12	−	−	ADP
cana-5531	160	13	𝜀(	𝜀(	NOUN
cana-5531	160	14	�	�	PROPN
cana-5531	160	15	̇	̇	PROPN
cana-5531	160	16	�	�	PROPN
cana-5531	160	17	)	)	PUNCT
cana-5531	160	18	)	)	PUNCT
cana-5531	161	1	ℋ	ℋ	PROPN
cana-5531	161	2	+	+	PROPN
cana-5531	161	3	(	(	PUNCT
cana-5531	161	4	∫	∫	PROPN
cana-5531	161	5	ℱ(𝑡	ℱ(𝑡	X
cana-5531	161	6	−	−	PROPN
cana-5531	161	7	𝑠)𝜀(𝑢(𝑠))𝑑𝑠	𝑠)𝜀(𝑢(𝑠))𝑑𝑠	PROPN
cana-5531	161	8	,	,	PUNCT
cana-5531	161	9	𝜀(𝜔	𝜀(𝜔	NOUN
cana-5531	161	10	)	)	PUNCT
cana-5531	161	11	−	−	ADP
cana-5531	161	12	𝜀(	𝜀(	NOUN
cana-5531	161	13	�	�	PROPN
cana-5531	161	14	̇	̇	PROPN
cana-5531	161	15	�	�	PROPN
cana-5531	161	16	)	)	PUNCT
cana-5531	161	17	𝑡	𝑡	PROPN
cana-5531	161	18	0	0	NUM
cana-5531	161	19	)	)	PUNCT
cana-5531	161	20	ℋ	ℋ	PROPN
cana-5531	161	21	+	+	NUM
cana-5531	161	22	ℎ(𝛽(𝑡	ℎ(𝛽(𝑡	PROPN
cana-5531	161	23	)	)	PUNCT
cana-5531	161	24	,	,	PUNCT
cana-5531	161	25	𝑢(𝑡	𝑢(𝑡	PROPN
cana-5531	161	26	)	)	PUNCT
cana-5531	161	27	,	,	PUNCT
cana-5531	161	28	𝜔	𝜔	ADP
cana-5531	161	29	−	−	PROPN
cana-5531	161	30	�	�	PROPN
cana-5531	161	31	̇	̇	NOUN
cana-5531	161	32	�	�	PROPN
cana-5531	161	33	)	)	PUNCT
cana-5531	161	34	+	+	NUM
cana-5531	161	35	𝑗𝑐(𝑢(𝑡	𝑗𝑐(𝑢(𝑡	X
cana-5531	161	36	)	)	PUNCT
cana-5531	161	37	,	,	PUNCT
cana-5531	161	38	𝜔	𝜔	NOUN
cana-5531	161	39	)	)	PUNCT
cana-5531	161	40	−𝑗𝑐(𝑢(𝑡	−𝑗𝑐(𝑢(𝑡	NUM
cana-5531	161	41	)	)	PUNCT
cana-5531	161	42	,	,	PUNCT
cana-5531	161	43	�	�	PROPN
cana-5531	161	44	̇	̇	PROPN
cana-5531	161	45	�	�	PROPN
cana-5531	161	46	)	)	PUNCT
cana-5531	161	47	+	+	NUM
cana-5531	161	48	𝑗𝑓(𝑢(𝑡	𝑗𝑓(𝑢(𝑡	NOUN
cana-5531	161	49	)	)	PUNCT
cana-5531	161	50	,	,	PUNCT
cana-5531	161	51	𝜔	𝜔	NOUN
cana-5531	161	52	)	)	PUNCT
cana-5531	161	53	−	−	PRON
cana-5531	161	54	𝑗𝑓(𝑢(𝑡	𝑗𝑓(𝑢(𝑡	NOUN
cana-5531	161	55	)	)	PUNCT
cana-5531	161	56	,	,	PUNCT
cana-5531	161	57	�	�	PROPN
cana-5531	161	58	̇	̇	PROPN
cana-5531	161	59	�	�	PROPN
cana-5531	161	60	)	)	PUNCT
cana-5531	161	61	≥	≥	NOUN
cana-5531	161	62	(	(	PUNCT
cana-5531	161	63	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5531	161	64	)	)	PUNCT
cana-5531	161	65	,	,	PUNCT
cana-5531	161	66	𝜔(𝑡	𝜔(𝑡	PROPN
cana-5531	161	67	)	)	PUNCT
cana-5531	161	68	−	−	PROPN
cana-5531	161	69	�	�	PROPN
cana-5531	161	70	̇	̇	PROPN
cana-5531	161	71	�	�	PROPN
cana-5531	161	72	(𝑡	(𝑡	NOUN
cana-5531	161	73	)	)	PUNCT
cana-5531	161	74	)	)	PUNCT
cana-5531	162	1	𝑉	𝑉	PROPN
cana-5531	162	2	(	(	PUNCT
cana-5531	162	3	4.15	4.15	NUM
cana-5531	162	4	)	)	PUNCT
cana-5531	162	5	�	�	PROPN
cana-5531	162	6	̇	̇	PROPN
cana-5531	162	7	�	�	PROPN
cana-5531	162	8	(𝑡	(𝑡	NOUN
cana-5531	162	9	)	)	PUNCT
cana-5531	162	10	=	=	SYM
cana-5531	162	11	−	−	PROPN
cana-5531	163	1	[	[	X
cana-5531	163	2	𝛽(𝑡	𝛽(𝑡	PROPN
cana-5531	163	3	)	)	PUNCT
cana-5531	163	4	(	(	PUNCT
cana-5531	163	5	𝑐𝜈	𝑐𝜈	NOUN
cana-5531	163	6	(	(	PUNCT
cana-5531	163	7	𝑅𝜈(𝑢𝜈(𝑡	𝑅𝜈(𝑢𝜈(𝑡	ADJ
cana-5531	163	8	)	)	PUNCT
cana-5531	163	9	)	)	PUNCT
cana-5531	163	10	)	)	PUNCT
cana-5531	163	11	2	2	NUM
cana-5531	164	1	+	+	NUM
cana-5531	164	2	𝑐𝜏|𝑅𝜏(𝑢𝜏(𝑡))|	𝑐𝜏|𝑅𝜏(𝑢𝜏(𝑡))|	NOUN
cana-5531	164	3	2	2	NUM
cana-5531	164	4	−	−	NOUN
cana-5531	164	5	𝜀𝑎	𝜀𝑎	NOUN
cana-5531	164	6	)	)	PUNCT
cana-5531	164	7	]	]	PUNCT
cana-5531	165	1	+	+	CCONJ
cana-5531	166	1	𝑎.	𝑎.	PROPN
cana-5531	166	2	𝑒.	𝑒.	PROPN
cana-5531	167	1	𝑡	𝑡	PROPN
cana-5531	167	2	∈	∈	PROPN
cana-5531	168	1	[	[	X
cana-5531	168	2	0	0	NUM
cana-5531	168	3	,	,	PUNCT
cana-5531	168	4	𝑇	𝑇	PROPN
cana-5531	168	5	]	]	X
cana-5531	168	6	(	(	PUNCT
cana-5531	168	7	4.16	4.16	NUM
cana-5531	168	8	)	)	PUNCT
cana-5531	168	9	𝑢(0	𝑢(0	PROPN
cana-5531	168	10	)	)	PUNCT
cana-5531	168	11	=	=	SYM
cana-5531	168	12	𝑢0	𝑢0	PROPN
cana-5531	168	13	,	,	PUNCT
cana-5531	168	14	�	�	PROPN
cana-5531	168	15	̇	̇	PROPN
cana-5531	168	16	�	�	PROPN
cana-5531	168	17	(0	(0	X
cana-5531	168	18	)	)	PUNCT
cana-5531	168	19	=	=	SYM
cana-5531	168	20	𝑢1	𝑢1	NOUN
cana-5531	168	21	=	=	NOUN
cana-5531	168	22	𝜐0	𝜐0	NOUN
cana-5531	168	23	,	,	PUNCT
cana-5531	168	24	𝛽(0	𝛽(0	PROPN
cana-5531	168	25	)	)	PUNCT
cana-5531	168	26	=	=	SYM
cana-5531	168	27	𝛽0	𝛽0	PROPN
cana-5531	168	28	.	.	PUNCT
cana-5531	169	1	(	(	PUNCT
cana-5531	169	2	4.17	4.17	NUM
cana-5531	169	3	)	)	PUNCT
cana-5531	169	4	5	5	NUM
cana-5531	169	5	.	.	PUNCT
cana-5531	170	1	existence	existence	NOUN
cana-5531	170	2	and	and	CCONJ
cana-5531	170	3	uniqueness	uniqueness	NOUN
cana-5531	170	4	result	result	VERB
cana-5531	170	5	the	the	DET
cana-5531	170	6	main	main	ADJ
cana-5531	170	7	result	result	NOUN
cana-5531	170	8	in	in	ADP
cana-5531	170	9	this	this	DET
cana-5531	170	10	section	section	NOUN
cana-5531	170	11	is	be	AUX
cana-5531	170	12	the	the	DET
cana-5531	170	13	following	follow	VERB
cana-5531	170	14	existence	existence	NOUN
cana-5531	170	15	and	and	CCONJ
cana-5531	170	16	uniqueness	uniqueness	NOUN
cana-5531	170	17	result	result	NOUN
cana-5531	170	18	.	.	PUNCT
cana-5531	171	1	theorem	theorem	VERB
cana-5531	171	2	5.1	5.1	NUM
cana-5531	171	3	:	:	PUNCT
cana-5531	171	4	let	let	VERB
cana-5531	171	5	the	the	DET
cana-5531	171	6	assumptions	assumption	NOUN
cana-5531	171	7	(	(	PUNCT
cana-5531	171	8	4.3)-(4.13	4.3)-(4.13	NUM
cana-5531	171	9	)	)	PUNCT
cana-5531	171	10	hold	hold	VERB
cana-5531	171	11	.	.	PUNCT
cana-5531	172	1	then	then	ADV
cana-5531	172	2	,	,	PUNCT
cana-5531	172	3	there	there	PRON
cana-5531	172	4	exists	exist	VERB
cana-5531	172	5	a	a	DET
cana-5531	172	6	constant	constant	ADJ
cana-5531	172	7	𝜇0	𝜇0	NOUN
cana-5531	172	8	>	>	X
cana-5531	172	9	0	0	NUM
cana-5531	173	1	such	such	ADJ
cana-5531	173	2	that	that	DET
cana-5531	173	3	problem	problem	NOUN
cana-5531	173	4	pv	pv	INTJ
cana-5531	173	5	has	have	VERB
cana-5531	173	6	a	a	DET
cana-5531	173	7	unique	unique	ADJ
cana-5531	173	8	solution	solution	NOUN
cana-5531	173	9	(	(	PUNCT
cana-5531	173	10	u	u	NOUN
cana-5531	173	11	,	,	PUNCT
cana-5531	173	12	σ	σ	PROPN
cana-5531	173	13	,	,	PUNCT
cana-5531	173	14	β	β	NOUN
cana-5531	173	15	)	)	PUNCT
cana-5531	173	16	which	which	PRON
cana-5531	173	17	satisfies	satisfy	VERB
cana-5531	173	18	if	if	SCONJ
cana-5531	173	19	‖𝜇‖𝕃∞(γ3	‖𝜇‖𝕃∞(γ3	PROPN
cana-5531	173	20	)	)	PUNCT
cana-5531	173	21	<	<	X
cana-5531	173	22	𝜇0	𝜇0	PROPN
cana-5531	173	23	.	.	PUNCT
cana-5531	174	1	communications	communication	NOUN
cana-5531	174	2	on	on	ADP
cana-5531	174	3	applied	apply	VERB
cana-5531	174	4	nonlinear	nonlinear	ADJ
cana-5531	174	5	analysis	analysis	NOUN
cana-5531	174	6	issn	issn	NOUN
cana-5531	174	7	:	:	PUNCT
cana-5531	174	8	1074	1074	NUM
cana-5531	174	9	-	-	PUNCT
cana-5531	174	10	133x	133x	NUM
cana-5531	174	11	vol	vol	NOUN
cana-5531	174	12	32	32	NUM
cana-5531	174	13	no	no	NOUN
cana-5531	174	14	.	.	NOUN
cana-5531	174	15	3	3	NUM
cana-5531	174	16	(	(	PUNCT
cana-5531	174	17	2025	2025	NUM
cana-5531	174	18	)	)	PUNCT
cana-5531	174	19	972	972	NUM
cana-5531	174	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	175	1	the	the	DET
cana-5531	175	2	proof	proof	NOUN
cana-5531	175	3	of	of	ADP
cana-5531	175	4	theorem	theorem	ADJ
cana-5531	175	5	5.1	5.1	NUM
cana-5531	175	6	is	be	AUX
cana-5531	175	7	carried	carry	VERB
cana-5531	175	8	out	out	ADP
cana-5531	175	9	several	several	ADJ
cana-5531	175	10	steps	step	NOUN
cana-5531	175	11	.	.	PUNCT
cana-5531	176	1	in	in	ADP
cana-5531	176	2	the	the	DET
cana-5531	176	3	first	first	ADJ
cana-5531	176	4	step	step	NOUN
cana-5531	176	5	,	,	PUNCT
cana-5531	176	6	the	the	DET
cana-5531	176	7	closed	closed	ADJ
cana-5531	176	8	subset	subset	NOUN
cana-5531	176	9	z	z	NOUN
cana-5531	176	10	of	of	ADP
cana-5531	176	11	the	the	DET
cana-5531	176	12	space	space	NOUN
cana-5531	176	13	𝐶([0.t	𝐶([0.t	PROPN
cana-5531	176	14	]	]	PUNCT
cana-5531	176	15	;	;	PUNCT
cana-5531	176	16	𝕃2(γ3	𝕃2(γ3	PROPN
cana-5531	176	17	)	)	PUNCT
cana-5531	176	18	)	)	PUNCT
cana-5531	176	19	is	be	AUX
cana-5531	176	20	defined	define	VERB
cana-5531	176	21	as	as	ADP
cana-5531	176	22	𝑍	𝑍	NOUN
cana-5531	176	23	=	=	SYM
cana-5531	176	24	{	{	PUNCT
cana-5531	176	25	𝜃	𝜃	NOUN
cana-5531	176	26	∈	∈	NOUN
cana-5531	176	27	𝐶([0	𝐶([0	PROPN
cana-5531	176	28	,	,	PUNCT
cana-5531	176	29	𝑇	𝑇	PROPN
cana-5531	176	30	]	]	X
cana-5531	176	31	;	;	PUNCT
cana-5531	176	32	𝕃2(γ3	𝕃2(γ3	PROPN
cana-5531	176	33	)	)	PUNCT
cana-5531	176	34	)	)	PUNCT
cana-5531	176	35	∩	∩	ADJ
cana-5531	176	36	𝐵	𝐵	NOUN
cana-5531	176	37	:	:	PUNCT
cana-5531	176	38	𝜃(0	𝜃(0	PROPN
cana-5531	176	39	)	)	PUNCT
cana-5531	176	40	=	=	SYM
cana-5531	176	41	𝛽0	𝛽0	PROPN
cana-5531	176	42	}	}	PUNCT
cana-5531	176	43	,	,	PUNCT
cana-5531	176	44	where	where	SCONJ
cana-5531	176	45	the	the	DET
cana-5531	176	46	banach	banach	NOUN
cana-5531	176	47	space	space	NOUN
cana-5531	176	48	𝐶([0.t	𝐶([0.t	PROPN
cana-5531	176	49	]	]	PUNCT
cana-5531	176	50	;	;	PUNCT
cana-5531	176	51	𝕃2(γ3	𝕃2(γ3	PROPN
cana-5531	176	52	)	)	PUNCT
cana-5531	176	53	)	)	PUNCT
cana-5531	176	54	is	be	AUX
cana-5531	176	55	endowed	endow	VERB
cana-5531	176	56	with	with	ADP
cana-5531	176	57	the	the	DET
cana-5531	176	58	norm	norm	NOUN
cana-5531	176	59	‖𝐵‖𝑘	‖𝐵‖𝑘	VERB
cana-5531	176	60	=	=	SYM
cana-5531	176	61	max	max	PROPN
cana-5531	176	62	𝑡∈[0,𝑇	𝑡∈[0,𝑇	NOUN
cana-5531	176	63	]	]	PUNCT
cana-5531	177	1	[	[	X
cana-5531	177	2	𝑒𝑥𝑝(−𝑘𝑡)‖𝛽(𝑡)‖𝕃2(γ3	𝑒𝑥𝑝(−𝑘𝑡)‖𝛽(𝑡)‖𝕃2(γ3	NOUN
cana-5531	177	3	)	)	PUNCT
cana-5531	177	4	]	]	PUNCT
cana-5531	177	5	,	,	PUNCT
cana-5531	177	6	𝑘	𝑘	X
cana-5531	177	7	>	>	X
cana-5531	177	8	0	0	NUM
cana-5531	177	9	.	.	PUNCT
cana-5531	178	1	next	next	ADJ
cana-5531	178	2	for	for	ADP
cana-5531	178	3	a	a	DET
cana-5531	178	4	given	give	VERB
cana-5531	178	5	ξ	ξ	PROPN
cana-5531	178	6	∈	∈	PROPN
cana-5531	178	7	z	z	NOUN
cana-5531	178	8	,	,	PUNCT
cana-5531	178	9	let	let	VERB
cana-5531	178	10	the	the	DET
cana-5531	178	11	following	follow	VERB
cana-5531	178	12	variational	variational	ADJ
cana-5531	178	13	problem	problem	NOUN
cana-5531	178	14	.	.	PUNCT
cana-5531	179	1	problem	problem	NOUN
cana-5531	179	2	p1ξ	p1ξ	NOUN
cana-5531	179	3	.	.	PUNCT
cana-5531	180	1	find	find	VERB
cana-5531	180	2	𝑢𝜉	𝑢𝜉	VERB
cana-5531	180	3	∈	∈	PROPN
cana-5531	180	4	𝐶	𝐶	PROPN
cana-5531	180	5	(	(	PUNCT
cana-5531	180	6	[	[	X
cana-5531	180	7	0.t	0.t	X
cana-5531	180	8	]	]	PUNCT
cana-5531	180	9	;	;	PUNCT
cana-5531	180	10	𝑉	𝑉	PROPN
cana-5531	180	11	)	)	PUNCT
cana-5531	180	12	such	such	ADJ
cana-5531	180	13	that	that	SCONJ
cana-5531	180	14	𝑢𝜉	𝑢𝜉	VERB
cana-5531	180	15	∈	∈	PROPN
cana-5531	180	16	k	k	PROPN
cana-5531	180	17	∩	∩	PROPN
cana-5531	180	18	w	w	PROPN
cana-5531	180	19	(	(	PUNCT
cana-5531	180	20	(	(	PUNCT
cana-5531	180	21	�	�	NOUN
cana-5531	180	22	̈	̈	X
cana-5531	180	23	�	�	NOUN
cana-5531	180	24	𝜉	𝜉	NOUN
cana-5531	180	25	,	,	PUNCT
cana-5531	180	26	𝜔	𝜔	PART
cana-5531	180	27	−	−	PROPN
cana-5531	180	28	�	�	PROPN
cana-5531	180	29	̇	̇	NOUN
cana-5531	180	30	�	�	PROPN
cana-5531	180	31	𝜉	𝜉	NOUN
cana-5531	180	32	)	)	PUNCT
cana-5531	180	33	)	)	PUNCT
cana-5531	181	1	+	+	CCONJ
cana-5531	181	2	(	(	PUNCT
cana-5531	181	3	𝒜𝜀(𝑢𝜉	𝒜𝜀(𝑢𝜉	ADJ
cana-5531	181	4	)	)	PUNCT
cana-5531	181	5	,	,	PUNCT
cana-5531	181	6	𝜀(𝜔	𝜀(𝜔	NOUN
cana-5531	181	7	)	)	PUNCT
cana-5531	181	8	−	−	ADP
cana-5531	181	9	𝜀(	𝜀(	NOUN
cana-5531	181	10	�	�	PROPN
cana-5531	181	11	̇	̇	PROPN
cana-5531	181	12	�	�	PROPN
cana-5531	181	13	𝜉	𝜉	NOUN
cana-5531	181	14	)	)	PUNCT
cana-5531	181	15	)	)	PUNCT
cana-5531	182	1	ℋ	ℋ	PROPN
cana-5531	182	2	+	+	CCONJ
cana-5531	182	3	(	(	PUNCT
cana-5531	182	4	𝒢𝜀(	𝒢𝜀(	ADJ
cana-5531	182	5	�	�	PROPN
cana-5531	182	6	̇	̇	NOUN
cana-5531	182	7	�	�	PROPN
cana-5531	182	8	𝜉	𝜉	NOUN
cana-5531	182	9	)	)	PUNCT
cana-5531	182	10	,	,	PUNCT
cana-5531	182	11	𝜀(𝜔	𝜀(𝜔	NOUN
cana-5531	182	12	)	)	PUNCT
cana-5531	182	13	−	−	ADP
cana-5531	182	14	𝜀(	𝜀(	NOUN
cana-5531	182	15	�	�	PROPN
cana-5531	182	16	̇	̇	PROPN
cana-5531	182	17	�	�	PROPN
cana-5531	182	18	𝜉	𝜉	NOUN
cana-5531	182	19	)	)	PUNCT
cana-5531	182	20	)	)	PUNCT
cana-5531	183	1	ℋ	ℋ	PROPN
cana-5531	183	2	+	+	PROPN
cana-5531	183	3	(	(	PUNCT
cana-5531	183	4	∫	∫	PROPN
cana-5531	183	5	ℱ(𝑡	ℱ(𝑡	PRON
cana-5531	183	6	−	−	PROPN
cana-5531	183	7	𝑠	𝑠	NOUN
cana-5531	183	8	)	)	PUNCT
cana-5531	183	9	𝑡	𝑡	PROPN
cana-5531	183	10	0	0	NUM
cana-5531	183	11	𝜀	𝜀	PROPN
cana-5531	183	12	(	(	PUNCT
cana-5531	183	13	𝑢𝜉(𝑠	𝑢𝜉(𝑠	NUM
cana-5531	183	14	)	)	PUNCT
cana-5531	183	15	)	)	PUNCT
cana-5531	183	16	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	183	17	,	,	PUNCT
cana-5531	183	18	𝜀(𝜔	𝜀(𝜔	NOUN
cana-5531	183	19	)	)	PUNCT
cana-5531	183	20	−	−	ADP
cana-5531	183	21	𝜀(	𝜀(	NOUN
cana-5531	183	22	�	�	PROPN
cana-5531	183	23	̇	̇	PROPN
cana-5531	183	24	�	�	PROPN
cana-5531	183	25	𝜉	𝜉	NOUN
cana-5531	183	26	)	)	PUNCT
cana-5531	183	27	)	)	PUNCT
cana-5531	184	1	ℋ	ℋ	PROPN
cana-5531	184	2	+	+	NUM
cana-5531	184	3	ℎ(𝛽(𝑡	ℎ(𝛽(𝑡	PROPN
cana-5531	184	4	)	)	PUNCT
cana-5531	184	5	,	,	PUNCT
cana-5531	184	6	𝑢𝜉(𝑡	𝑢𝜉(𝑡	NUM
cana-5531	184	7	)	)	PUNCT
cana-5531	184	8	,	,	PUNCT
cana-5531	184	9	𝜔	𝜔	ADP
cana-5531	184	10	−	−	PROPN
cana-5531	184	11	�	�	PROPN
cana-5531	184	12	̇	̇	NOUN
cana-5531	184	13	�	�	NOUN
cana-5531	184	14	𝜉	𝜉	NOUN
cana-5531	184	15	)	)	PUNCT
cana-5531	184	16	+	+	CCONJ
cana-5531	184	17	𝑗𝑐(𝑢𝜉(𝑡	𝑗𝑐(𝑢𝜉(𝑡	NUM
cana-5531	184	18	)	)	PUNCT
cana-5531	184	19	,	,	PUNCT
cana-5531	184	20	𝜔	𝜔	NOUN
cana-5531	184	21	)	)	PUNCT
cana-5531	184	22	−	−	PROPN
cana-5531	184	23	𝑗𝑐(𝑢𝜉(𝑡	𝑗𝑐(𝑢𝜉(𝑡	NUM
cana-5531	184	24	)	)	PUNCT
cana-5531	184	25	,	,	PUNCT
cana-5531	184	26	�	�	PROPN
cana-5531	184	27	̇	̇	PROPN
cana-5531	184	28	�	�	NOUN
cana-5531	184	29	𝜉	𝜉	NOUN
cana-5531	184	30	)	)	PUNCT
cana-5531	184	31	+	+	NUM
cana-5531	184	32	𝑗𝑓(𝑢𝜉(𝑡	𝑗𝑓(𝑢𝜉(𝑡	NUM
cana-5531	184	33	)	)	PUNCT
cana-5531	184	34	,	,	PUNCT
cana-5531	184	35	𝜔	𝜔	NOUN
cana-5531	184	36	)	)	PUNCT
cana-5531	184	37	−	−	NOUN
cana-5531	184	38	𝑗𝑓(𝑢𝜉(𝑡	𝑗𝑓(𝑢𝜉(𝑡	NOUN
cana-5531	184	39	)	)	PUNCT
cana-5531	184	40	,	,	PUNCT
cana-5531	184	41	�	�	PROPN
cana-5531	184	42	̇	̇	PROPN
cana-5531	184	43	�	�	PROPN
cana-5531	184	44	𝜉	𝜉	NOUN
cana-5531	184	45	)	)	PUNCT
cana-5531	184	46	≥	≥	NOUN
cana-5531	184	47	(	(	PUNCT
cana-5531	184	48	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5531	184	49	)	)	PUNCT
cana-5531	184	50	,	,	PUNCT
cana-5531	184	51	𝜔(𝑡	𝜔(𝑡	PROPN
cana-5531	184	52	)	)	PUNCT
cana-5531	184	53	−	−	PROPN
cana-5531	184	54	�	�	PROPN
cana-5531	184	55	̇	̇	PROPN
cana-5531	184	56	�	�	PROPN
cana-5531	184	57	𝜉(𝑡	𝜉(𝑡	NOUN
cana-5531	184	58	)	)	PUNCT
cana-5531	184	59	)	)	PUNCT
cana-5531	185	1	𝑉	𝑉	NOUN
cana-5531	185	2	∀	∀	NOUN
cana-5531	185	3	𝜔	𝜔	PART
cana-5531	185	4	∈	∈	PROPN
cana-5531	185	5	𝐾	𝐾	PROPN
cana-5531	185	6	,	,	PUNCT
cana-5531	185	7	𝑡	𝑡	PROPN
cana-5531	185	8	∈	∈	PROPN
cana-5531	185	9	[	[	X
cana-5531	185	10	0	0	NUM
cana-5531	185	11	,	,	PUNCT
cana-5531	185	12	𝑇	𝑇	PROPN
cana-5531	185	13	]	]	X
cana-5531	185	14	(	(	PUNCT
cana-5531	185	15	5.1	5.1	NUM
cana-5531	185	16	)	)	PUNCT
cana-5531	185	17	we	we	PRON
cana-5531	185	18	have	have	VERB
cana-5531	185	19	the	the	DET
cana-5531	185	20	following	follow	VERB
cana-5531	185	21	results	result	NOUN
cana-5531	185	22	theorem	theorem	VERB
cana-5531	185	23	5.2	5.2	NUM
cana-5531	185	24	.	.	PUNCT
cana-5531	186	1	there	there	PRON
cana-5531	186	2	exists	exist	VERB
cana-5531	186	3	a	a	DET
cana-5531	186	4	constant	constant	ADJ
cana-5531	186	5	µ1	µ1	NOUN
cana-5531	186	6	>	>	X
cana-5531	186	7	0	0	NUM
cana-5531	187	1	such	such	ADJ
cana-5531	187	2	that	that	DET
cana-5531	187	3	problem	problem	NOUN
cana-5531	187	4	pξ	pξ	ADV
cana-5531	187	5	has	have	VERB
cana-5531	187	6	a	a	DET
cana-5531	187	7	unique	unique	ADJ
cana-5531	187	8	solution	solution	NOUN
cana-5531	187	9	if	if	SCONJ
cana-5531	187	10	µ	µ	X
cana-5531	187	11	𝕃∞(γ3	𝕃∞(γ3	NOUN
cana-5531	187	12	)	)	PUNCT
cana-5531	187	13	<	<	X
cana-5531	187	14	µ1	µ1	PROPN
cana-5531	187	15	let	let	VERB
cana-5531	187	16	𝜂	𝜂	X
cana-5531	187	17	∈𝐶	∈𝐶	PROPN
cana-5531	187	18	(	(	PUNCT
cana-5531	187	19	[	[	X
cana-5531	187	20	0.t	0.t	X
cana-5531	187	21	]	]	PUNCT
cana-5531	187	22	;	;	PUNCT
cana-5531	187	23	v	v	X
cana-5531	187	24	)	)	PUNCT
cana-5531	187	25	be	be	AUX
cana-5531	187	26	given	give	VERB
cana-5531	187	27	the	the	DET
cana-5531	187	28	following	following	ADJ
cana-5531	187	29	intermediate	intermediate	ADJ
cana-5531	187	30	problem	problem	NOUN
cana-5531	187	31	is	be	AUX
cana-5531	187	32	introduced	introduce	VERB
cana-5531	187	33	by	by	ADP
cana-5531	187	34	:	:	PUNCT
cana-5531	187	35	problem	problem	NOUN
cana-5531	187	36	𝑃𝜉𝜂.	𝑃𝜉𝜂.	PROPN
cana-5531	187	37	find	find	VERB
cana-5531	187	38	𝑢𝜉𝜂	𝑢𝜉𝜂	PROPN
cana-5531	187	39	∈	∈	PROPN
cana-5531	187	40	𝐶([0	𝐶([0	PROPN
cana-5531	187	41	,	,	PUNCT
cana-5531	187	42	𝑇	𝑇	PROPN
cana-5531	187	43	]	]	PUNCT
cana-5531	187	44	;	;	PUNCT
cana-5531	187	45	𝑉	𝑉	PROPN
cana-5531	187	46	)	)	PUNCT
cana-5531	187	47	such	such	ADJ
cana-5531	187	48	that	that	DET
cana-5531	187	49	𝑢𝜉𝜂	𝑢𝜉𝜂	PROPN
cana-5531	187	50	∈	∈	PROPN
cana-5531	187	51	𝐾	𝐾	PROPN
cana-5531	187	52	∩𝑊	∩𝑊	NOUN
cana-5531	187	53	(	(	PUNCT
cana-5531	187	54	(	(	PUNCT
cana-5531	187	55	�	�	PROPN
cana-5531	187	56	̈	̈	X
cana-5531	187	57	�	�	NOUN
cana-5531	187	58	𝜉𝜂	𝜉𝜂	NOUN
cana-5531	187	59	,	,	PUNCT
cana-5531	187	60	𝜔	𝜔	PART
cana-5531	187	61	−	−	PROPN
cana-5531	187	62	�	�	PROPN
cana-5531	187	63	̇	̇	PROPN
cana-5531	187	64	�	�	PROPN
cana-5531	187	65	𝜉𝜂	𝜉𝜂	NOUN
cana-5531	187	66	)	)	PUNCT
cana-5531	187	67	)	)	PUNCT
cana-5531	188	1	+	+	CCONJ
cana-5531	188	2	(	(	PUNCT
cana-5531	188	3	𝒢𝜀(	𝒢𝜀(	ADJ
cana-5531	188	4	�	�	PROPN
cana-5531	188	5	̇	̇	NOUN
cana-5531	188	6	�	�	PROPN
cana-5531	188	7	𝜉𝜂	𝜉𝜂	NOUN
cana-5531	188	8	)	)	PUNCT
cana-5531	188	9	,	,	PUNCT
cana-5531	188	10	𝜀(𝜔	𝜀(𝜔	NOUN
cana-5531	188	11	)	)	PUNCT
cana-5531	188	12	−	−	ADP
cana-5531	188	13	𝜀(	𝜀(	NOUN
cana-5531	188	14	�	�	PROPN
cana-5531	188	15	̇	̇	PROPN
cana-5531	188	16	�	�	PROPN
cana-5531	188	17	𝜉𝜂	𝜉𝜂	NOUN
cana-5531	188	18	)	)	PUNCT
cana-5531	188	19	)	)	PUNCT
cana-5531	189	1	ℋ	ℋ	NOUN
cana-5531	189	2	+	+	CCONJ
cana-5531	189	3	(	(	PUNCT
cana-5531	189	4	𝜂(𝑡	𝜂(𝑡	NOUN
cana-5531	189	5	)	)	PUNCT
cana-5531	189	6	,	,	PUNCT
cana-5531	189	7	𝜀(𝜔	𝜀(𝜔	NOUN
cana-5531	189	8	)	)	PUNCT
cana-5531	189	9	−	−	ADP
cana-5531	189	10	𝜀(	𝜀(	NOUN
cana-5531	189	11	�	�	PROPN
cana-5531	189	12	̇	̇	PROPN
cana-5531	189	13	�	�	PROPN
cana-5531	189	14	𝜉𝜂	𝜉𝜂	NOUN
cana-5531	189	15	)	)	PUNCT
cana-5531	189	16	)	)	PUNCT
cana-5531	190	1	ℋ	ℋ	PROPN
cana-5531	190	2	+	+	PROPN
cana-5531	190	3	𝑗𝑓(𝑢𝜉𝜂(𝑡	𝑗𝑓(𝑢𝜉𝜂(𝑡	NOUN
cana-5531	190	4	)	)	PUNCT
cana-5531	190	5	,	,	PUNCT
cana-5531	190	6	𝜔	𝜔	NOUN
cana-5531	190	7	)	)	PUNCT
cana-5531	190	8	−	−	PROPN
cana-5531	190	9	𝑗𝑓(𝑢𝜉𝜂(𝑡	𝑗𝑓(𝑢𝜉𝜂(𝑡	NOUN
cana-5531	190	10	)	)	PUNCT
cana-5531	190	11	,	,	PUNCT
cana-5531	190	12	�	�	PROPN
cana-5531	190	13	̇	̇	PROPN
cana-5531	190	14	�	�	PROPN
cana-5531	190	15	𝜉𝜂	𝜉𝜂	NOUN
cana-5531	190	16	)	)	PUNCT
cana-5531	190	17	≥	≥	NOUN
cana-5531	190	18	(	(	PUNCT
cana-5531	190	19	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5531	190	20	)	)	PUNCT
cana-5531	190	21	,	,	PUNCT
cana-5531	190	22	𝜔(𝑡	𝜔(𝑡	PROPN
cana-5531	190	23	)	)	PUNCT
cana-5531	190	24	−	−	PROPN
cana-5531	190	25	�	�	PROPN
cana-5531	190	26	̇	̇	PROPN
cana-5531	190	27	�	�	PROPN
cana-5531	190	28	𝜉𝜂(𝑡	𝜉𝜂(𝑡	NUM
cana-5531	190	29	)	)	PUNCT
cana-5531	190	30	)	)	PUNCT
cana-5531	191	1	𝑉	𝑉	PROPN
cana-5531	191	2	𝑢𝜉𝜂(0	𝑢𝜉𝜂(0	NOUN
cana-5531	191	3	)	)	PUNCT
cana-5531	191	4	=	=	SYM
cana-5531	191	5	𝑢0	𝑢0	PROPN
cana-5531	191	6	,	,	PUNCT
cana-5531	191	7	�	�	PROPN
cana-5531	191	8	̇	̇	PROPN
cana-5531	191	9	�	�	NOUN
cana-5531	191	10	𝜉𝜂(0	𝜉𝜂(0	NOUN
cana-5531	191	11	)	)	PUNCT
cana-5531	191	12	=	=	SYM
cana-5531	191	13	𝑢1	𝑢1	PROPN
cana-5531	191	14	∀	∀	X
cana-5531	191	15	𝜔∈	𝜔∈	CCONJ
cana-5531	191	16	𝐾	𝐾	PROPN
cana-5531	191	17	,	,	PUNCT
cana-5531	191	18	𝑡	𝑡	PROPN
cana-5531	191	19	∈	∈	PROPN
cana-5531	192	1	[	[	X
cana-5531	192	2	0	0	NUM
cana-5531	192	3	,	,	PUNCT
cana-5531	192	4	𝑇	𝑇	PROPN
cana-5531	192	5	]	]	X
cana-5531	192	6	(	(	PUNCT
cana-5531	192	7	5.2	5.2	NUM
cana-5531	192	8	)	)	PUNCT
cana-5531	192	9	since	since	SCONJ
cana-5531	192	10	riesz	riesz	PROPN
cana-5531	192	11	’s	’s	PART
cana-5531	192	12	representation	representation	NOUN
cana-5531	192	13	theorem	theorem	NOUN
cana-5531	192	14	representation	representation	NOUN
cana-5531	192	15	theorem	theorem	NOUN
cana-5531	192	16	implies	imply	VERB
cana-5531	192	17	that	that	SCONJ
cana-5531	192	18	there	there	PRON
cana-5531	192	19	exists	exist	VERB
cana-5531	192	20	an	an	DET
cana-5531	192	21	element	element	NOUN
cana-5531	192	22	𝑓𝜂∈	𝑓𝜂∈	PROPN
cana-5531	192	23	𝐶	𝐶	PROPN
cana-5531	192	24	(	(	PUNCT
cana-5531	192	25	[	[	X
cana-5531	192	26	0.t	0.t	X
cana-5531	192	27	]	]	PUNCT
cana-5531	192	28	;	;	PUNCT
cana-5531	192	29	v	v	X
cana-5531	192	30	)	)	PUNCT
cana-5531	192	31	such	such	ADJ
cana-5531	192	32	that	that	SCONJ
cana-5531	192	33	(	(	PUNCT
cana-5531	192	34	𝑓𝜂(𝑡	𝑓𝜂(𝑡	NOUN
cana-5531	192	35	)	)	PUNCT
cana-5531	192	36	,	,	PUNCT
cana-5531	192	37	𝜔)𝑉	𝜔)𝑉	X
cana-5531	192	38	=	=	X
cana-5531	192	39	(	(	PUNCT
cana-5531	192	40	𝑓(𝑡	𝑓(𝑡	PROPN
cana-5531	192	41	)	)	PUNCT
cana-5531	192	42	,	,	PUNCT
cana-5531	192	43	𝜔)𝑉	𝜔)𝑉	NOUN
cana-5531	192	44	−	−	PROPN
cana-5531	192	45	(	(	PUNCT
cana-5531	192	46	𝜂(𝑡	𝜂(𝑡	NOUN
cana-5531	192	47	)	)	PUNCT
cana-5531	192	48	,	,	PUNCT
cana-5531	192	49	𝜀(𝜔))ℋ	𝜀(𝜔))ℋ	PROPN
cana-5531	192	50	,	,	PUNCT
cana-5531	192	51	the	the	DET
cana-5531	192	52	problem	problem	NOUN
cana-5531	192	53	𝑃𝜉𝜂	𝑃𝜉𝜂	PROPN
cana-5531	192	54	is	be	AUX
cana-5531	192	55	equivalent	equivalent	ADJ
cana-5531	192	56	to	to	ADP
cana-5531	192	57	the	the	DET
cana-5531	192	58	following	follow	VERB
cana-5531	192	59	problem	problem	NOUN
cana-5531	192	60	.	.	PUNCT
cana-5531	193	1	problem	problem	NOUN
cana-5531	193	2	𝑃2𝜉𝜂	𝑃2𝜉𝜂	PROPN
cana-5531	193	3	.	.	PUNCT
cana-5531	194	1	find	find	VERB
cana-5531	194	2	𝑢𝜉𝜂	𝑢𝜉𝜂	PROPN
cana-5531	194	3	∈	∈	PROPN
cana-5531	194	4	𝐶	𝐶	PROPN
cana-5531	194	5	(	(	PUNCT
cana-5531	194	6	[	[	X
cana-5531	194	7	0.t	0.t	X
cana-5531	194	8	]	]	PUNCT
cana-5531	194	9	;	;	PUNCT
cana-5531	194	10	𝑉	𝑉	PROPN
cana-5531	194	11	)	)	PUNCT
cana-5531	194	12	such	such	ADJ
cana-5531	194	13	that	that	DET
cana-5531	194	14	𝑢𝜉𝜂	𝑢𝜉𝜂	PROPN
cana-5531	194	15	∈	∈	PROPN
cana-5531	194	16	𝐾	𝐾	PROPN
cana-5531	194	17	∩𝑊	∩𝑊	NOUN
cana-5531	194	18	,	,	PUNCT
cana-5531	194	19	(	(	PUNCT
cana-5531	194	20	(	(	PUNCT
cana-5531	194	21	�	�	PROPN
cana-5531	194	22	̈	̈	X
cana-5531	194	23	�	�	NOUN
cana-5531	194	24	𝜉𝜂	𝜉𝜂	NOUN
cana-5531	194	25	,	,	PUNCT
cana-5531	194	26	𝜔	𝜔	PART
cana-5531	194	27	−	−	PROPN
cana-5531	194	28	�	�	PROPN
cana-5531	194	29	̇	̇	PROPN
cana-5531	194	30	�	�	PROPN
cana-5531	194	31	𝜉𝜂	𝜉𝜂	NOUN
cana-5531	194	32	)	)	PUNCT
cana-5531	194	33	)	)	PUNCT
cana-5531	195	1	+	+	CCONJ
cana-5531	195	2	(	(	PUNCT
cana-5531	195	3	𝒢𝜀(	𝒢𝜀(	ADJ
cana-5531	195	4	�	�	PROPN
cana-5531	195	5	̇	̇	NOUN
cana-5531	195	6	�	�	PROPN
cana-5531	195	7	𝜉𝜂	𝜉𝜂	NOUN
cana-5531	195	8	)	)	PUNCT
cana-5531	195	9	,	,	PUNCT
cana-5531	195	10	𝜀(𝜔	𝜀(𝜔	NOUN
cana-5531	195	11	)	)	PUNCT
cana-5531	195	12	−	−	ADP
cana-5531	195	13	𝜀(	𝜀(	NOUN
cana-5531	195	14	�	�	PROPN
cana-5531	195	15	̇	̇	PROPN
cana-5531	195	16	�	�	PROPN
cana-5531	195	17	𝜉𝜂	𝜉𝜂	NOUN
cana-5531	195	18	)	)	PUNCT
cana-5531	195	19	)	)	PUNCT
cana-5531	196	1	ℋ	ℋ	PROPN
cana-5531	196	2	+	+	PROPN
cana-5531	196	3	𝑗𝑓(𝑢𝜉𝜂(𝑡	𝑗𝑓(𝑢𝜉𝜂(𝑡	NOUN
cana-5531	196	4	)	)	PUNCT
cana-5531	196	5	,	,	PUNCT
cana-5531	196	6	𝜔	𝜔	NOUN
cana-5531	196	7	)	)	PUNCT
cana-5531	196	8	−	−	PROPN
cana-5531	196	9	𝑗𝑓(𝑢𝜉𝜂(𝑡	𝑗𝑓(𝑢𝜉𝜂(𝑡	NOUN
cana-5531	196	10	)	)	PUNCT
cana-5531	196	11	,	,	PUNCT
cana-5531	196	12	�	�	PROPN
cana-5531	196	13	̇	̇	PROPN
cana-5531	196	14	�	�	PROPN
cana-5531	196	15	𝜉𝜂	𝜉𝜂	NOUN
cana-5531	196	16	)	)	PUNCT
cana-5531	196	17	≥	≥	NUM
cana-5531	196	18	(	(	PUNCT
cana-5531	196	19	𝑓𝜂(𝑡),𝜔	𝑓𝜂(𝑡),𝜔	ADJ
cana-5531	197	1	−	−	ADP
cana-5531	197	2	𝑢𝜉𝜂)𝑉	𝑢𝜉𝜂)𝑉	NOUN
cana-5531	197	3	∀𝜔	∀𝜔	PROPN
cana-5531	197	4	∈	∈	PROPN
cana-5531	197	5	𝐾	𝐾	PROPN
cana-5531	197	6	,	,	PUNCT
cana-5531	197	7	𝑡	𝑡	PROPN
cana-5531	197	8	∈	∈	PROPN
cana-5531	198	1	[	[	X
cana-5531	198	2	0	0	NUM
cana-5531	198	3	,	,	PUNCT
cana-5531	198	4	𝑇	𝑇	PROPN
cana-5531	198	5	]	]	X
cana-5531	198	6	(	(	PUNCT
cana-5531	198	7	5.3	5.3	NUM
cana-5531	198	8	)	)	PUNCT
cana-5531	198	9	communications	communication	NOUN
cana-5531	198	10	on	on	ADP
cana-5531	198	11	applied	apply	VERB
cana-5531	198	12	nonlinear	nonlinear	ADJ
cana-5531	198	13	analysis	analysis	NOUN
cana-5531	198	14	issn	issn	NOUN
cana-5531	198	15	:	:	PUNCT
cana-5531	198	16	1074	1074	NUM
cana-5531	198	17	-	-	PUNCT
cana-5531	198	18	133x	133x	NUM
cana-5531	198	19	vol	vol	NOUN
cana-5531	198	20	32	32	NUM
cana-5531	198	21	no	no	NOUN
cana-5531	198	22	.	.	NOUN
cana-5531	198	23	3	3	NUM
cana-5531	198	24	(	(	PUNCT
cana-5531	198	25	2025	2025	NUM
cana-5531	198	26	)	)	PUNCT
cana-5531	198	27	973	973	NUM
cana-5531	198	28	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	198	29	lemma	lemma	PROPN
cana-5531	198	30	5.3	5.3	NUM
cana-5531	198	31	there	there	ADV
cana-5531	198	32	exists	exist	VERB
cana-5531	198	33	a	a	DET
cana-5531	198	34	constant	constant	ADJ
cana-5531	198	35	𝜇1	𝜇1	NOUN
cana-5531	198	36	>	>	X
cana-5531	198	37	0	0	NUM
cana-5531	199	1	such	such	ADJ
cana-5531	199	2	that	that	DET
cana-5531	199	3	problem	problem	NOUN
cana-5531	199	4	p2ξη	p2ξη	PUNCT
cana-5531	199	5	has	have	VERB
cana-5531	199	6	a	a	DET
cana-5531	199	7	unique	unique	ADJ
cana-5531	199	8	solution	solution	NOUN
cana-5531	199	9	if	if	SCONJ
cana-5531	199	10	µ	µ	X
cana-5531	199	11	𝕃	𝕃	NOUN
cana-5531	199	12	∞(γ	∞(γ	PROPN
cana-5531	199	13	)	)	PUNCT
cana-5531	200	1	<	<	X
cana-5531	200	2	µ1	µ1	PROPN
cana-5531	200	3	.	.	PUNCT
cana-5531	201	1	the	the	DET
cana-5531	201	2	proof	proof	NOUN
cana-5531	201	3	is	be	AUX
cana-5531	201	4	based	base	VERB
cana-5531	201	5	on	on	ADP
cana-5531	201	6	several	several	ADJ
cana-5531	201	7	step	step	NOUN
cana-5531	201	8	by	by	ADP
cana-5531	201	9	using	use	VERB
cana-5531	201	10	arguments	argument	NOUN
cana-5531	201	11	on	on	ADP
cana-5531	201	12	banach	banach	ADV
cana-5531	201	13	fixed	fix	VERB
cana-5531	201	14	point	point	NOUN
cana-5531	201	15	theorem	theorem	VERB
cana-5531	201	16	.	.	PUNCT
cana-5531	202	1	indeed	indeed	ADV
cana-5531	202	2	,	,	PUNCT
cana-5531	202	3	let	let	VERB
cana-5531	202	4	q	q	PROPN
cana-5531	202	5	∈	∈	PROPN
cana-5531	202	6	c+	c+	VERB
cana-5531	202	7	where	where	SCONJ
cana-5531	202	8	c+	c+	NOUN
cana-5531	202	9	is	be	AUX
cana-5531	202	10	a	a	DET
cana-5531	202	11	non	non	ADJ
cana-5531	202	12	-	-	ADJ
cana-5531	202	13	empty	empty	ADJ
cana-5531	202	14	closed	closed	ADJ
cana-5531	202	15	subset	subset	NOUN
cana-5531	202	16	of	of	ADP
cana-5531	202	17	𝕃2(γ3	𝕃2(γ3	NOUN
cana-5531	202	18	)	)	PUNCT
cana-5531	202	19	defined	define	VERB
cana-5531	202	20	as	as	ADP
cana-5531	202	21	𝐶+	𝐶+	PROPN
cana-5531	202	22	=	=	PROPN
cana-5531	202	23	{	{	PUNCT
cana-5531	202	24	𝑠	𝑠	PROPN
cana-5531	202	25	∈	∈	PROPN
cana-5531	202	26	𝕃	𝕃	PROPN
cana-5531	202	27	2(γ3	2(γ3	NUM
cana-5531	202	28	)	)	PUNCT
cana-5531	202	29	;	;	PUNCT
cana-5531	202	30	𝑠	𝑠	PROPN
cana-5531	202	31	≥	≥	X
cana-5531	202	32	0	0	PUNCT
cana-5531	202	33	𝑎.	𝑎.	PROPN
cana-5531	202	34	𝑒.	𝑒.	PROPN
cana-5531	202	35	𝑜𝑛γ3	𝑜𝑛γ3	PROPN
cana-5531	202	36	}	}	PUNCT
cana-5531	202	37	and	and	CCONJ
cana-5531	202	38	let	let	VERB
cana-5531	202	39	the	the	DET
cana-5531	202	40	functional	functional	ADJ
cana-5531	202	41	𝑗𝑞	𝑗𝑞	NOUN
cana-5531	202	42	:	:	PUNCT
cana-5531	202	43	𝑉	𝑉	PROPN
cana-5531	202	44	⟶	⟶	NOUN
cana-5531	202	45	ℝ	ℝ	NOUN
cana-5531	202	46	given	give	VERB
cana-5531	202	47	by	by	ADP
cana-5531	202	48	𝑗𝑞(𝜐	𝑗𝑞(𝜐	PUNCT
cana-5531	202	49	)	)	PUNCT
cana-5531	203	1	=	=	SYM
cana-5531	203	2	∫	∫	PROPN
cana-5531	203	3	𝜇𝑞|𝜐𝜏|𝑑𝑎	𝜇𝑞|𝜐𝜏|𝑑𝑎	PROPN
cana-5531	203	4	∀𝜐	∀𝜐	PROPN
cana-5531	203	5	∈	∈	PROPN
cana-5531	203	6	𝑉.γ3	𝑉.γ3	NOUN
cana-5531	203	7	we	we	PRON
cana-5531	203	8	consider	consider	VERB
cana-5531	203	9	the	the	DET
cana-5531	203	10	following	follow	VERB
cana-5531	203	11	auxiliary	auxiliary	ADJ
cana-5531	203	12	problem	problem	NOUN
cana-5531	203	13	.	.	PUNCT
cana-5531	204	1	problem	problem	PROPN
cana-5531	204	2	𝑷𝝃𝜼𝒒.	𝑷𝝃𝜼𝒒.	PROPN
cana-5531	204	3	find	find	VERB
cana-5531	204	4	𝑢𝜉𝜂𝑞	𝑢𝜉𝜂𝑞	NOUN
cana-5531	204	5	∈	∈	PROPN
cana-5531	204	6	c	c	X
cana-5531	204	7	(	(	PUNCT
cana-5531	204	8	[	[	X
cana-5531	204	9	0.t	0.t	X
cana-5531	204	10	]	]	PUNCT
cana-5531	204	11	;	;	PUNCT
cana-5531	204	12	v	v	X
cana-5531	204	13	)	)	PUNCT
cana-5531	204	14	such	such	ADJ
cana-5531	204	15	that	that	SCONJ
cana-5531	204	16	𝑢𝜉𝜂𝑞	𝑢𝜉𝜂𝑞	VERB
cana-5531	204	17	∈	∈	PROPN
cana-5531	204	18	𝐾	𝐾	PROPN
cana-5531	204	19	,	,	PUNCT
cana-5531	204	20	(	(	PUNCT
cana-5531	204	21	(	(	PUNCT
cana-5531	204	22	�	�	NOUN
cana-5531	204	23	̈	̈	SYM
cana-5531	204	24	�	�	NOUN
cana-5531	204	25	𝜉𝜂𝑞	𝜉𝜂𝑞	NOUN
cana-5531	204	26	,	,	PUNCT
cana-5531	204	27	𝜔	𝜔	ADP
cana-5531	204	28	−	−	PROPN
cana-5531	204	29	�	�	PROPN
cana-5531	204	30	̇	̇	NOUN
cana-5531	204	31	�	�	NOUN
cana-5531	204	32	𝜉𝜂𝑞	𝜉𝜂𝑞	NOUN
cana-5531	204	33	)	)	PUNCT
cana-5531	204	34	)	)	PUNCT
cana-5531	205	1	+	+	CCONJ
cana-5531	205	2	(	(	PUNCT
cana-5531	205	3	𝒢𝜀(	𝒢𝜀(	ADJ
cana-5531	205	4	�	�	PROPN
cana-5531	205	5	̇	̇	NOUN
cana-5531	205	6	�	�	NOUN
cana-5531	205	7	𝜉𝜂𝑞	𝜉𝜂𝑞	NOUN
cana-5531	205	8	)	)	PUNCT
cana-5531	205	9	,	,	PUNCT
cana-5531	205	10	𝜀(𝜔	𝜀(𝜔	NOUN
cana-5531	205	11	)	)	PUNCT
cana-5531	205	12	−	−	ADP
cana-5531	205	13	𝜀(	𝜀(	NOUN
cana-5531	205	14	�	�	PROPN
cana-5531	205	15	̇	̇	NOUN
cana-5531	205	16	�	�	NOUN
cana-5531	205	17	𝜉𝜂𝑞	𝜉𝜂𝑞	NOUN
cana-5531	205	18	)	)	PUNCT
cana-5531	205	19	)	)	PUNCT
cana-5531	206	1	ℋ	ℋ	PROPN
cana-5531	206	2	+	+	NOUN
cana-5531	206	3	𝑗𝑞(𝜔	𝑗𝑞(𝜔	ADJ
cana-5531	206	4	)	)	PUNCT
cana-5531	206	5	−𝑗𝑞(𝑢𝜉𝜂𝑞(𝑡	−𝑗𝑞(𝑢𝜉𝜂𝑞(𝑡	NOUN
cana-5531	206	6	)	)	PUNCT
cana-5531	206	7	,	,	PUNCT
cana-5531	206	8	�	�	PROPN
cana-5531	206	9	̇	̇	PROPN
cana-5531	206	10	�	�	PROPN
cana-5531	206	11	𝜉𝜂𝑞	𝜉𝜂𝑞	NOUN
cana-5531	206	12	)	)	PUNCT
cana-5531	206	13	≥	≥	NOUN
cana-5531	206	14	(	(	PUNCT
cana-5531	206	15	𝑓𝜂(𝑡),𝜔	𝑓𝜂(𝑡),𝜔	X
cana-5531	206	16	−	−	PROPN
cana-5531	206	17	𝑢𝜉𝜂𝑞)𝑉	𝑢𝜉𝜂𝑞)𝑉	PROPN
cana-5531	206	18	;	;	PUNCT
cana-5531	206	19	∀𝜔	∀𝜔	NUM
cana-5531	206	20	∈	∈	PROPN
cana-5531	206	21	𝐾	𝐾	PROPN
cana-5531	206	22	,	,	PUNCT
cana-5531	206	23	𝑡	𝑡	PROPN
cana-5531	206	24	∈	∈	PROPN
cana-5531	207	1	[	[	X
cana-5531	207	2	0	0	NUM
cana-5531	207	3	,	,	PUNCT
cana-5531	207	4	𝑇	𝑇	PROPN
cana-5531	207	5	]	]	X
cana-5531	207	6	(	(	PUNCT
cana-5531	207	7	5.4	5.4	NUM
cana-5531	207	8	)	)	PUNCT
cana-5531	207	9	lemma	lemma	PROPN
cana-5531	207	10	5.4	5.4	NUM
cana-5531	207	11	.	.	PUNCT
cana-5531	208	1	problem	problem	NOUN
cana-5531	208	2	𝑷𝝃𝜼𝒒	𝑷𝝃𝜼𝒒	PROPN
cana-5531	208	3	has	have	VERB
cana-5531	208	4	a	a	DET
cana-5531	208	5	unique	unique	ADJ
cana-5531	208	6	solution	solution	NOUN
cana-5531	208	7	with	with	ADP
cana-5531	208	8	the	the	DET
cana-5531	208	9	regularity	regularity	NOUN
cana-5531	208	10	𝜐𝜉𝜂𝑞	𝜐𝜉𝜂𝑞	VERB
cana-5531	208	11	∈	∈	PROPN
cana-5531	208	12	c(0	c(0	PROPN
cana-5531	208	13	,	,	PUNCT
cana-5531	208	14	t	t	NOUN
cana-5531	208	15	;	;	PUNCT
cana-5531	208	16	h	h	X
cana-5531	208	17	)	)	PUNCT
cana-5531	208	18	∩	∩	ADJ
cana-5531	208	19	𝕃2(0	𝕃2(0	NOUN
cana-5531	208	20	,	,	PUNCT
cana-5531	208	21	t	t	NOUN
cana-5531	208	22	;	;	PUNCT
cana-5531	208	23	v	v	X
cana-5531	208	24	)	)	PUNCT
cana-5531	208	25	∩	∩	PROPN
cana-5531	208	26	w	w	PROPN
cana-5531	208	27	1,2(0	1,2(0	PROPN
cana-5531	208	28	,	,	PUNCT
cana-5531	208	29	t	t	PROPN
cana-5531	208	30	;	;	PUNCT
cana-5531	208	31	𝑉′	𝑉′	ADV
cana-5531	208	32	)	)	PUNCT
cana-5531	208	33	.	.	PUNCT
cana-5531	209	1	proof	proof	NOUN
cana-5531	209	2	:	:	PUNCT
cana-5531	209	3	the	the	DET
cana-5531	209	4	continuous	continuous	ADJ
cana-5531	209	5	injection	injection	NOUN
cana-5531	209	6	of	of	ADP
cana-5531	209	7	v	v	NOUN
cana-5531	209	8	into	into	ADP
cana-5531	209	9	𝕃2(γ3)d	𝕃2(γ3)d	PROPN
cana-5531	209	10	implies	imply	VERB
cana-5531	209	11	that	that	SCONJ
cana-5531	209	12	j	j	PROPN
cana-5531	209	13	is	be	AUX
cana-5531	209	14	continuous	continuous	ADJ
cana-5531	209	15	and	and	CCONJ
cana-5531	209	16	convex	convex	ADJ
cana-5531	209	17	.	.	PUNCT
cana-5531	210	1	we	we	PRON
cana-5531	210	2	define	define	VERB
cana-5531	210	3	the	the	DET
cana-5531	210	4	sequence	sequence	NOUN
cana-5531	210	5	:	:	PUNCT
cana-5531	210	6	𝑗𝜀(𝜐	𝑗𝜀(𝜐	PUNCT
cana-5531	210	7	)	)	PUNCT
cana-5531	210	8	=	=	PUNCT
cana-5531	211	1	∫	∫	PROPN
cana-5531	212	1	𝑢𝑞√|𝜐𝜏|2	𝑢𝑞√|𝜐𝜏|2	PROPN
cana-5531	212	2	+	+	CCONJ
cana-5531	212	3	𝜀2	𝜀2	PROPN
cana-5531	212	4	𝑑𝑠	𝑑𝑠	PRON
cana-5531	212	5	γ3	γ3	NOUN
cana-5531	212	6	∀	∀	NOUN
cana-5531	212	7	𝜐	𝜐	PROPN
cana-5531	212	8	∈	∈	PROPN
cana-5531	212	9	𝑉	𝑉	PROPN
cana-5531	212	10	,	,	PUNCT
cana-5531	212	11	∀𝜀	∀𝜀	X
cana-5531	212	12	>	>	X
cana-5531	212	13	0	0	PUNCT
cana-5531	213	1	its	its	PRON
cana-5531	213	2	derivative	derivative	NOUN
cana-5531	213	3	of	of	ADP
cana-5531	213	4	f	f	PROPN
cana-5531	213	5	ré	ré	PROPN
cana-5531	213	6	chet	chet	PROPN
cana-5531	213	7	is	be	AUX
cana-5531	213	8	given	give	VERB
cana-5531	213	9	by	by	ADP
cana-5531	213	10	:	:	PUNCT
cana-5531	213	11	𝑗𝜀	𝑗𝜀	PROPN
cana-5531	213	12	′(𝜐	′(𝜐	NOUN
cana-5531	213	13	)	)	PUNCT
cana-5531	213	14	.	.	PUNCT
cana-5531	214	1	𝜔	𝜔	X
cana-5531	214	2	=	=	SYM
cana-5531	214	3	∫	∫	PROPN
cana-5531	214	4	𝑢𝑞	𝑢𝑞	INTJ
cana-5531	214	5	(	(	PUNCT
cana-5531	214	6	𝜐𝜏,𝜔𝜏	𝜐𝜏,𝜔𝜏	NOUN
cana-5531	214	7	)	)	PUNCT
cana-5531	215	1	√|𝜐𝜏|	√|𝜐𝜏|	PROPN
cana-5531	215	2	2+𝜀2	2+𝜀2	NUM
cana-5531	215	3	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	215	4	,	,	PUNCT
cana-5531	215	5	∀𝜐	∀𝜐	NOUN
cana-5531	215	6	∈	∈	PROPN
cana-5531	215	7	𝑉	𝑉	PROPN
cana-5531	215	8	,	,	PUNCT
cana-5531	215	9	∀𝜀	∀𝜀	NOUN
cana-5531	215	10	>	>	X
cana-5531	215	11	0	0	X
cana-5531	215	12	.	.	PUNCT
cana-5531	216	1	γ3	γ3	NOUN
cana-5531	216	2	then	then	ADV
cana-5531	216	3	𝑗𝜀	𝑗𝜀	PROPN
cana-5531	216	4	is	be	AUX
cana-5531	216	5	of	of	ADP
cana-5531	216	6	class	class	NOUN
cana-5531	216	7	c1	c1	NOUN
cana-5531	216	8	.	.	PUNCT
cana-5531	217	1	direct	direct	ADJ
cana-5531	217	2	algebraic	algebraic	PROPN
cana-5531	217	3	calculations	calculation	NOUN
cana-5531	217	4	show	show	VERB
cana-5531	217	5	that	that	SCONJ
cana-5531	217	6	∀	∀	NOUN
cana-5531	217	7	α	α	PRON
cana-5531	217	8	≥	≥	NOUN
cana-5531	217	9	0	0	NUM
cana-5531	217	10	,	,	PUNCT
cana-5531	217	11	β	β	X
cana-5531	217	12	≥	≥	NUM
cana-5531	217	13	0	0	NUM
cana-5531	217	14	such	such	ADJ
cana-5531	217	15	that	that	SCONJ
cana-5531	217	16	α	α	PROPN
cana-5531	217	17	+	+	X
cana-5531	217	18	β	β	X
cana-5531	217	19	=	=	SYM
cana-5531	217	20	1	1	NUM
cana-5531	217	21	and	and	CCONJ
cana-5531	217	22	for	for	ADP
cana-5531	217	23	any	any	DET
cana-5531	217	24	real	real	ADJ
cana-5531	217	25	x	x	NOUN
cana-5531	217	26	and	and	CCONJ
cana-5531	217	27	y	y	PROPN
cana-5531	217	28	,	,	PUNCT
cana-5531	217	29	n	n	PRON
cana-5531	217	30	≥	≥	NOUN
cana-5531	217	31	1	1	NUM
cana-5531	217	32	:	:	PUNCT
cana-5531	217	33	√(𝛼𝑥	√(𝛼𝑥	ADJ
cana-5531	217	34	+	+	CCONJ
cana-5531	217	35	𝛽𝑦)2	𝛽𝑦)2	ADJ
cana-5531	217	36	+	+	CCONJ
cana-5531	217	37	1	1	NUM
cana-5531	217	38	𝑛	𝑛	PRON
cana-5531	217	39	≤	≤	PUNCT
cana-5531	217	40	𝛼√𝑥2	𝛼√𝑥2	NUM
cana-5531	218	1	+	+	CCONJ
cana-5531	219	1	1	1	NUM
cana-5531	219	2	𝑛	𝑛	VERB
cana-5531	219	3	+	+	CCONJ
cana-5531	219	4	𝛽√𝑦2	𝛽√𝑦2	PROPN
cana-5531	219	5	+	+	SYM
cana-5531	219	6	1	1	NUM
cana-5531	219	7	𝑛	𝑛	VERB
cana-5531	219	8	so	so	ADV
cana-5531	219	9	jε	jε	PROPN
cana-5531	219	10	is	be	AUX
cana-5531	219	11	convex	convex	ADJ
cana-5531	219	12	∀ε	∀ε	X
cana-5531	219	13	>	>	X
cana-5531	219	14	0	0	X
cana-5531	219	15	.	.	PUNCT
cana-5531	220	1	also	also	ADV
cana-5531	220	2	:	:	PUNCT
cana-5531	220	3	∃c	∃c	PROPN
cana-5531	220	4	>	>	X
cana-5531	220	5	0	0	PROPN
cana-5531	220	6	,	,	PUNCT
cana-5531	220	7	∀𝜔	∀𝜔	PROPN
cana-5531	220	8	∈	∈	PROPN
cana-5531	220	9	v	v	NOUN
cana-5531	220	10	,	,	PUNCT
cana-5531	220	11	|𝑗𝜀	|𝑗𝜀	DET
cana-5531	220	12	′(𝜔)|v	′(𝜔)|v	PROPN
cana-5531	220	13	′	′	NUM
cana-5531	220	14	≤	≤	NUM
cana-5531	220	15	c|𝑔|𝕃2(γ3	c|𝑔|𝕃2(γ3	NOUN
cana-5531	220	16	)	)	PUNCT
cana-5531	220	17	(	(	PUNCT
cana-5531	220	18	5.5	5.5	NUM
cana-5531	220	19	)	)	PUNCT
cana-5531	220	20	the	the	DET
cana-5531	220	21	hypothesis	hypothesis	NOUN
cana-5531	220	22	(	(	PUNCT
cana-5531	220	23	4.5	4.5	NUM
cana-5531	220	24	)	)	PUNCT
cana-5531	220	25	(	(	PUNCT
cana-5531	220	26	a	a	PRON
cana-5531	220	27	)	)	PUNCT
cana-5531	220	28	implies	imply	VERB
cana-5531	220	29	that	that	SCONJ
cana-5531	220	30	g	g	NOUN
cana-5531	220	31	:	:	PUNCT
cana-5531	220	32	v	v	X
cana-5531	220	33	→	→	PUNCT
cana-5531	220	34	𝑉′is	𝑉′is	ADP
cana-5531	220	35	a	a	DET
cana-5531	220	36	continuous	continuous	ADJ
cana-5531	220	37	lipschitz	lipschitz	NOUN
cana-5531	220	38	operator	operator	NOUN
cana-5531	220	39	.	.	PUNCT
cana-5531	221	1	since	since	SCONJ
cana-5531	221	2	𝑗𝜀	𝑗𝜀	NOUN
cana-5531	221	3	′	′	NUM
cana-5531	221	4	is	be	AUX
cana-5531	221	5	continuous	continuous	ADJ
cana-5531	221	6	then	then	ADV
cana-5531	221	7	g	g	PROPN
cana-5531	221	8	+	+	PROPN
cana-5531	221	9	𝑗𝜀	𝑗𝜀	PROPN
cana-5531	221	10	′	′	NOUN
cana-5531	221	11	is	be	AUX
cana-5531	221	12	a	a	DET
cana-5531	221	13	continuous	continuous	ADJ
cana-5531	221	14	and	and	CCONJ
cana-5531	221	15	therefore	therefore	ADV
cana-5531	221	16	hemicontinuous	hemicontinuous	ADJ
cana-5531	221	17	operator	operator	NOUN
cana-5531	221	18	.	.	PUNCT
cana-5531	222	1	now	now	ADV
cana-5531	222	2	,	,	PUNCT
cana-5531	222	3	according	accord	VERB
cana-5531	222	4	to	to	ADP
cana-5531	222	5	(	(	PUNCT
cana-5531	222	6	4.5)(b	4.5)(b	NUM
cana-5531	222	7	)	)	PUNCT
cana-5531	222	8	and	and	CCONJ
cana-5531	222	9	the	the	DET
cana-5531	222	10	monotony	monotony	NOUN
cana-5531	222	11	of	of	ADP
cana-5531	222	12	𝑗𝜀	𝑗𝜀	NOUN
cana-5531	222	13	′	′	INTJ
cana-5531	222	14	we	we	PRON
cana-5531	222	15	find	find	VERB
cana-5531	222	16	:	:	PUNCT
cana-5531	222	17	〈	〈	PROPN
cana-5531	222	18	(	(	PUNCT
cana-5531	222	19	𝐺	𝐺	PROPN
cana-5531	222	20	+	+	PROPN
cana-5531	222	21	𝑗𝜀	𝑗𝜀	PROPN
cana-5531	222	22	′)𝑢	′)𝑢	NUM
cana-5531	223	1	−	−	PROPN
cana-5531	224	1	(	(	PUNCT
cana-5531	224	2	𝐺	𝐺	NOUN
cana-5531	224	3	+	+	PROPN
cana-5531	224	4	𝑗𝜀	𝑗𝜀	ADP
cana-5531	224	5	′)𝜐	′)𝜐	PROPN
cana-5531	224	6	,	,	PUNCT
cana-5531	224	7	𝑢	𝑢	PRON
cana-5531	224	8	−	−	NOUN
cana-5531	224	9	𝜐〉𝑉′×𝑉	𝜐〉𝑉′×𝑉	ADJ
cana-5531	224	10	≥	≥	NOUN
cana-5531	224	11	𝑚𝒢|𝑢	𝑚𝒢|𝑢	PUNCT
cana-5531	225	1	−	−	NOUN
cana-5531	225	2	𝜐|𝑉	𝜐|𝑉	NOUN
cana-5531	225	3	2	2	NUM
cana-5531	225	4	∀𝑢	∀𝑢	NOUN
cana-5531	225	5	,	,	PUNCT
cana-5531	225	6	𝜐	𝜐	PROPN
cana-5531	225	7	∈	∈	PROPN
cana-5531	225	8	𝑉	𝑉	PROPN
cana-5531	225	9	(	(	PUNCT
cana-5531	225	10	5.6	5.6	NUM
cana-5531	225	11	)	)	PUNCT
cana-5531	225	12	communications	communication	NOUN
cana-5531	225	13	on	on	ADP
cana-5531	225	14	applied	apply	VERB
cana-5531	225	15	nonlinear	nonlinear	ADJ
cana-5531	225	16	analysis	analysis	NOUN
cana-5531	225	17	issn	issn	NOUN
cana-5531	225	18	:	:	PUNCT
cana-5531	225	19	1074	1074	NUM
cana-5531	225	20	-	-	PUNCT
cana-5531	225	21	133x	133x	NUM
cana-5531	225	22	vol	vol	NOUN
cana-5531	225	23	32	32	NUM
cana-5531	225	24	no	no	NOUN
cana-5531	225	25	.	.	NOUN
cana-5531	225	26	3	3	NUM
cana-5531	225	27	(	(	PUNCT
cana-5531	225	28	2025	2025	NUM
cana-5531	225	29	)	)	PUNCT
cana-5531	225	30	974	974	NUM
cana-5531	225	31	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	226	1	then	then	ADV
cana-5531	226	2	g	g	PROPN
cana-5531	226	3	+	+	PROPN
cana-5531	226	4	𝑗𝜀	𝑗𝜀	PROPN
cana-5531	226	5	′	′	NOUN
cana-5531	226	6	is	be	AUX
cana-5531	226	7	a	a	DET
cana-5531	226	8	monotone	monotone	ADJ
cana-5531	226	9	operator	operator	NOUN
cana-5531	226	10	.	.	PUNCT
cana-5531	227	1	by	by	ADP
cana-5531	227	2	taking	take	VERB
cana-5531	227	3	𝜐	𝜐	PROPN
cana-5531	227	4	=	=	NOUN
cana-5531	227	5	0𝑉	0𝑉	PROPN
cana-5531	227	6	on	on	ADP
cana-5531	227	7	(	(	PUNCT
cana-5531	227	8	5.6	5.6	NUM
cana-5531	227	9	)	)	PUNCT
cana-5531	227	10	and	and	CCONJ
cana-5531	227	11	using	use	VERB
cana-5531	227	12	the	the	DET
cana-5531	227	13	inequality	inequality	NOUN
cana-5531	227	14	𝑎𝑏	𝑎𝑏	ADP
cana-5531	227	15	≤	≤	ADJ
cana-5531	227	16	𝑚𝒢	𝑚𝒢	PROPN
cana-5531	227	17	2	2	NUM
cana-5531	227	18	𝑎2	𝑎2	NOUN
cana-5531	227	19	+	+	CCONJ
cana-5531	227	20	1	1	NUM
cana-5531	227	21	2𝑚𝒢	2𝑚𝒢	NUM
cana-5531	227	22	𝑏2	𝑏2	NOUN
cana-5531	227	23	,	,	PUNCT
cana-5531	227	24	it	it	PRON
cana-5531	227	25	results	result	VERB
cana-5531	227	26	∀u	∀u	NOUN
cana-5531	227	27	,	,	PUNCT
cana-5531	227	28	𝜐	𝜐	PROPN
cana-5531	227	29	∈	∈	PROPN
cana-5531	227	30	v	v	X
cana-5531	227	31	:	:	PUNCT
cana-5531	227	32	〈	〈	PROPN
cana-5531	227	33	(	(	PUNCT
cana-5531	227	34	𝐺	𝐺	NOUN
cana-5531	227	35	+	+	PROPN
cana-5531	227	36	𝑗𝜀	𝑗𝜀	NOUN
cana-5531	227	37	′)𝑢	′)𝑢	PROPN
cana-5531	227	38	,	,	PUNCT
cana-5531	227	39	𝑢〉𝑉′×𝑉	𝑢〉𝑉′×𝑉	NOUN
cana-5531	227	40	≥	≥	NOUN
cana-5531	227	41	𝑚𝒢|𝑢|𝑉	𝑚𝒢|𝑢|𝑉	NOUN
cana-5531	227	42	2	2	NUM
cana-5531	227	43	−	−	PROPN
cana-5531	227	44	|𝐺0𝑉|𝑉′	|𝐺0𝑉|𝑉′	PROPN
cana-5531	227	45	.	.	PUNCT
cana-5531	228	1	and	and	CCONJ
cana-5531	228	2	|𝑢|𝑉	|𝑢|𝑉	PROPN
cana-5531	228	3	≥	≥	NOUN
cana-5531	228	4	1	1	NUM
cana-5531	228	5	2	2	NUM
cana-5531	228	6	𝑚𝒢|𝑢|𝑉	𝑚𝒢|𝑢|𝑉	NOUN
cana-5531	228	7	2	2	NUM
cana-5531	228	8	−	−	NOUN
cana-5531	228	9	1	1	NUM
cana-5531	228	10	2𝑚𝒢	2𝑚𝒢	NUM
cana-5531	228	11	|𝐺0𝑉|𝑉′	|𝐺0𝑉|𝑉′	PROPN
cana-5531	228	12	2	2	NUM
cana-5531	228	13	,	,	PUNCT
cana-5531	228	14	for	for	ADP
cana-5531	228	15	𝜔	𝜔	PRON
cana-5531	228	16	=	=	SYM
cana-5531	228	17	1	1	NUM
cana-5531	228	18	2	2	NUM
cana-5531	228	19	𝑚𝒢	𝑚𝒢	NOUN
cana-5531	228	20	,	,	PUNCT
cana-5531	228	21	𝐶	𝐶	PROPN
cana-5531	228	22	=	=	NOUN
cana-5531	228	23	1	1	NUM
cana-5531	228	24	2𝑚𝒢	2𝑚𝒢	NUM
cana-5531	228	25	|𝐺0𝑉|𝑉′	|𝐺0𝑉|𝑉′	PROPN
cana-5531	228	26	2	2	NUM
cana-5531	228	27	∈	∈	NOUN
cana-5531	228	28	ℝ.	ℝ.	PROPN
cana-5531	228	29	next	next	ADV
cana-5531	228	30	,	,	PUNCT
cana-5531	228	31	by	by	ADP
cana-5531	228	32	using	use	VERB
cana-5531	228	33	(	(	PUNCT
cana-5531	228	34	4.5)(a	4.5)(a	NUM
cana-5531	228	35	)	)	PUNCT
cana-5531	228	36	and	and	CCONJ
cana-5531	228	37	(	(	PUNCT
cana-5531	228	38	5.5	5.5	NUM
cana-5531	228	39	)	)	PUNCT
cana-5531	228	40	then	then	ADV
cana-5531	228	41	:	:	PUNCT
cana-5531	228	42	|(𝐺	|(𝐺	ADJ
cana-5531	228	43	+	+	NUM
cana-5531	228	44	𝑗𝜀	𝑗𝜀	ADP
cana-5531	228	45	′)𝑢	′)𝑢	NUM
cana-5531	228	46	−	−	PROPN
cana-5531	228	47	(	(	PUNCT
cana-5531	228	48	𝐺	𝐺	NOUN
cana-5531	228	49	+	+	CCONJ
cana-5531	228	50	𝑗𝜀	𝑗𝜀	NOUN
cana-5531	228	51	′)𝜐|𝑉′	′)𝜐|𝑉′	NOUN
cana-5531	228	52	≤	≤	ADJ
cana-5531	228	53	𝐿𝒢|𝑢	𝐿𝒢|𝑢	NOUN
cana-5531	228	54	−	−	NOUN
cana-5531	228	55	𝜐|𝑉	𝜐|𝑉	NOUN
cana-5531	228	56	+	+	CCONJ
cana-5531	228	57	𝐶.	𝐶.	ADJ
cana-5531	228	58	choosing	choose	VERB
cana-5531	228	59	𝜐	𝜐	PROPN
cana-5531	228	60	=	=	NOUN
cana-5531	228	61	0𝑉	0𝑉	NOUN
cana-5531	228	62	it	it	PRON
cana-5531	228	63	result	result	VERB
cana-5531	228	64	:	:	PUNCT
cana-5531	228	65	|(𝐺	|(𝐺	ADJ
cana-5531	228	66	+	+	NUM
cana-5531	228	67	𝑗𝜀	𝑗𝜀	ADP
cana-5531	228	68	′)𝑢|𝑉′	′)𝑢|𝑉′	NOUN
cana-5531	228	69	≤	≤	ADV
cana-5531	228	70	𝐶(|𝑢	𝐶(|𝑢	PROPN
cana-5531	228	71	−	−	PROPN
cana-5531	228	72	𝜐|𝑉	𝜐|𝑉	NOUN
cana-5531	228	73	+	+	CCONJ
cana-5531	228	74	1	1	NUM
cana-5531	228	75	)	)	PUNCT
cana-5531	228	76	,	,	PUNCT
cana-5531	228	77	∀𝑢	∀𝑢	DET
cana-5531	228	78	∈	∈	PROPN
cana-5531	228	79	𝑉	𝑉	PROPN
cana-5531	228	80	finally	finally	ADV
cana-5531	228	81	,	,	PUNCT
cana-5531	228	82	by	by	ADP
cana-5531	228	83	using	use	VERB
cana-5531	228	84	(	(	PUNCT
cana-5531	228	85	4.11	4.11	NUM
cana-5531	228	86	)	)	PUNCT
cana-5531	228	87	that	that	SCONJ
cana-5531	228	88	there	there	PRON
cana-5531	228	89	exists	exist	VERB
cana-5531	228	90	𝜐𝜂	𝜐𝜂	ADP
cana-5531	228	91	𝜀∈	𝜀∈	PROPN
cana-5531	228	92	𝕃2(0	𝕃2(0	NOUN
cana-5531	228	93	,	,	PUNCT
cana-5531	228	94	t	t	NOUN
cana-5531	228	95	;	;	PUNCT
cana-5531	228	96	v	v	X
cana-5531	228	97	)	)	PUNCT
cana-5531	228	98	∩	∩	NOUN
cana-5531	228	99	c([0	c([0	NOUN
cana-5531	228	100	,	,	PUNCT
cana-5531	228	101	t	t	X
cana-5531	228	102	]	]	PUNCT
cana-5531	228	103	;	;	PUNCT
cana-5531	228	104	h	h	X
cana-5531	228	105	)	)	PUNCT
cana-5531	228	106	and	and	CCONJ
cana-5531	228	107	�	�	PROPN
cana-5531	228	108	̇	̇	PROPN
cana-5531	228	109	�	�	PROPN
cana-5531	228	110	𝜂	𝜂	PRON
cana-5531	228	111	𝜀	𝜀	PROPN
cana-5531	228	112	∈	∈	PROPN
cana-5531	228	113	𝕃2([0	𝕃2([0	NOUN
cana-5531	228	114	,	,	PUNCT
cana-5531	228	115	𝑇	𝑇	PROPN
cana-5531	228	116	]	]	X
cana-5531	228	117	;	;	PUNCT
cana-5531	228	118	𝑉′	𝑉′	NOUN
cana-5531	228	119	)	)	PUNCT
cana-5531	228	120	,	,	PUNCT
cana-5531	228	121	such	such	ADJ
cana-5531	228	122	that	that	PRON
cana-5531	228	123	:	:	PUNCT
cana-5531	228	124	{	{	PUNCT
cana-5531	228	125	�	�	NOUN
cana-5531	228	126	̇	̇	PROPN
cana-5531	228	127	�	�	PROPN
cana-5531	228	128	𝜂	𝜂	NOUN
cana-5531	228	129	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	228	130	)	)	PUNCT
cana-5531	228	131	+	+	PROPN
cana-5531	229	1	𝐺𝜐𝜂	𝐺𝜐𝜂	PROPN
cana-5531	229	2	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	229	3	)	)	PUNCT
cana-5531	230	1	+	+	CCONJ
cana-5531	230	2	𝑗𝜂	𝑗𝜂	VERB
cana-5531	230	3	𝜀(𝜐𝜂	𝜀(𝜐𝜂	PROPN
cana-5531	230	4	𝜀	𝜀	PROPN
cana-5531	230	5	)	)	PUNCT
cana-5531	230	6	=	=	PUNCT
cana-5531	231	1	𝑓𝜂(𝑡	𝑓𝜂(𝑡	X
cana-5531	231	2	)	)	PUNCT
cana-5531	231	3	𝑖𝑛	𝑖𝑛	NOUN
cana-5531	232	1	𝑉	𝑉	PROPN
cana-5531	232	2	′𝑎.	′𝑎.	PROPN
cana-5531	232	3	𝑒.	𝑒.	NOUN
cana-5531	232	4	𝑡	𝑡	X
cana-5531	232	5	∈	∈	PROPN
cana-5531	233	1	[	[	X
cana-5531	233	2	0	0	NUM
cana-5531	233	3	,	,	PUNCT
cana-5531	233	4	𝑇	𝑇	PROPN
cana-5531	233	5	]	]	PUNCT
cana-5531	233	6	,	,	PUNCT
cana-5531	233	7	𝜐𝜂	𝜐𝜂	X
cana-5531	233	8	𝜀(0	𝜀(0	PROPN
cana-5531	233	9	)	)	PUNCT
cana-5531	233	10	=	=	SYM
cana-5531	233	11	𝑢1	𝑢1	PROPN
cana-5531	233	12	.	.	PUNCT
cana-5531	234	1	(	(	PUNCT
cana-5531	234	2	5.7	5.7	NUM
cana-5531	234	3	)	)	PUNCT
cana-5531	234	4	(	(	PUNCT
cana-5531	234	5	)	)	PUNCT
cana-5531	234	6	then	then	ADV
cana-5531	234	7	𝜐𝜂	𝜐𝜂	ADP
cana-5531	234	8	𝜀	𝜀	PROPN
cana-5531	234	9	∈	∈	PROPN
cana-5531	234	10	𝕃2([0	𝕃2([0	PROPN
cana-5531	234	11	,	,	PUNCT
cana-5531	234	12	𝑇	𝑇	PROPN
cana-5531	234	13	]	]	PUNCT
cana-5531	234	14	;	;	PUNCT
cana-5531	234	15	𝑉	𝑉	PROPN
cana-5531	234	16	)	)	PUNCT
cana-5531	234	17	∩	∩	ADJ
cana-5531	234	18	𝑊1,2(0	𝑊1,2(0	NOUN
cana-5531	234	19	,	,	PUNCT
cana-5531	234	20	𝑇	𝑇	PROPN
cana-5531	234	21	;	;	PUNCT
cana-5531	234	22	𝑉′)whic	𝑉′)whic	ADJ
cana-5531	234	23	h	h	PROPN
cana-5531	234	24	sa	sa	PROPN
cana-5531	234	25	t	t	PROPN
cana-5531	235	1	i	i	PRON
cana-5531	235	2	s	s	VERB
cana-5531	235	3	f	f	X
cana-5531	236	1	i	i	NOUN
cana-5531	236	2	e	e	X
cana-5531	236	3	s	s	X
cana-5531	236	4	:	:	PUNCT
cana-5531	236	5	(	(	PUNCT
cana-5531	236	6	�	�	NOUN
cana-5531	236	7	̇	̇	PROPN
cana-5531	236	8	�	�	PROPN
cana-5531	236	9	𝜂	𝜂	NOUN
cana-5531	236	10	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	236	11	)	)	PUNCT
cana-5531	236	12	,	,	PUNCT
cana-5531	236	13	𝜔	𝜔	ADP
cana-5531	236	14	−	−	PROPN
cana-5531	236	15	𝜐𝜂	𝜐𝜂	ADP
cana-5531	236	16	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	236	17	)	)	PUNCT
cana-5531	236	18	)	)	PUNCT
cana-5531	237	1	𝑉′×𝑉	𝑉′×𝑉	PROPN
cana-5531	237	2	+	+	SYM
cana-5531	237	3	(	(	PUNCT
cana-5531	237	4	𝒢𝜐𝜂	𝒢𝜐𝜂	PROPN
cana-5531	237	5	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	237	6	)	)	PUNCT
cana-5531	237	7	,	,	PUNCT
cana-5531	237	8	𝜔	𝜔	ADP
cana-5531	237	9	−	−	PROPN
cana-5531	237	10	𝜐𝜂	𝜐𝜂	ADP
cana-5531	237	11	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	237	12	)	)	PUNCT
cana-5531	237	13	)	)	PUNCT
cana-5531	238	1	𝑉′×𝑉	𝑉′×𝑉	ADJ
cana-5531	238	2	+	+	NUM
cana-5531	238	3	𝑗𝜀(𝜔	𝑗𝜀(𝜔	NOUN
cana-5531	238	4	)	)	PUNCT
cana-5531	238	5	−	−	PROPN
cana-5531	238	6	𝑗𝜀(𝜐𝜂	𝑗𝜀(𝜐𝜂	PROPN
cana-5531	238	7	𝜀	𝜀	PROPN
cana-5531	238	8	)	)	PUNCT
cana-5531	238	9	≥	≥	NOUN
cana-5531	238	10	(	(	PUNCT
cana-5531	238	11	𝑓𝜂(𝑡	𝑓𝜂(𝑡	NOUN
cana-5531	238	12	)	)	PUNCT
cana-5531	238	13	,	,	PUNCT
cana-5531	238	14	𝜔	𝜔	PROPN
cana-5531	238	15	−	−	PROPN
cana-5531	238	16	𝜐𝜂	𝜐𝜂	ADP
cana-5531	238	17	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	238	18	)	)	PUNCT
cana-5531	238	19	)	)	PUNCT
cana-5531	239	1	𝑉′×𝑉	𝑉′×𝑉	VERB
cana-5531	239	2	𝜐𝜂(0	𝜐𝜂(0	NOUN
cana-5531	239	3	)	)	PUNCT
cana-5531	239	4	=	=	SYM
cana-5531	239	5	𝑢1	𝑢1	NOUN
cana-5531	239	6	(	(	PUNCT
cana-5531	239	7	5.8	5.8	NUM
cana-5531	239	8	)	)	PUNCT
cana-5531	239	9	using	use	VERB
cana-5531	239	10	(	(	PUNCT
cana-5531	239	11	5.7	5.7	NUM
cana-5531	239	12	)	)	PUNCT
cana-5531	239	13	to	to	PART
cana-5531	239	14	obtain	obtain	VERB
cana-5531	239	15	:	:	PUNCT
cana-5531	239	16	(	(	PUNCT
cana-5531	239	17	�	�	NOUN
cana-5531	239	18	̇	̇	PROPN
cana-5531	239	19	�	�	PROPN
cana-5531	239	20	𝜂	𝜂	NOUN
cana-5531	239	21	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	239	22	)	)	PUNCT
cana-5531	239	23	,	,	PUNCT
cana-5531	239	24	𝜐𝜂	𝜐𝜂	ADP
cana-5531	239	25	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	239	26	)	)	PUNCT
cana-5531	239	27	)	)	PUNCT
cana-5531	240	1	𝑉′×𝑉	𝑉′×𝑉	ADJ
cana-5531	240	2	+	+	SYM
cana-5531	240	3	(	(	PUNCT
cana-5531	240	4	𝒢𝜐𝜂	𝒢𝜐𝜂	PROPN
cana-5531	240	5	𝜀	𝜀	PROPN
cana-5531	240	6	(	(	PUNCT
cana-5531	240	7	𝑡	𝑡	NOUN
cana-5531	240	8	)	)	PUNCT
cana-5531	240	9	,	,	PUNCT
cana-5531	240	10	𝜐𝜂	𝜐𝜂	ADP
cana-5531	240	11	𝜀	𝜀	PROPN
cana-5531	240	12	(	(	PUNCT
cana-5531	240	13	𝑡))𝑉′×𝑉	𝑡))𝑉′×𝑉	X
cana-5531	240	14	+	+	CCONJ
cana-5531	240	15	(	(	PUNCT
cana-5531	240	16	𝑗𝜀	𝑗𝜀	ADP
cana-5531	240	17	′(𝜐𝜂	′(𝜐𝜂	PROPN
cana-5531	240	18	𝜀	𝜀	NOUN
cana-5531	240	19	)	)	PUNCT
cana-5531	240	20	,	,	PUNCT
cana-5531	240	21	𝜐𝜂	𝜐𝜂	ADP
cana-5531	240	22	𝜀	𝜀	PROPN
cana-5531	240	23	)	)	PUNCT
cana-5531	240	24	𝑉′×𝑉	𝑉′×𝑉	PROPN
cana-5531	240	25	=	=	SYM
cana-5531	240	26	(	(	PUNCT
cana-5531	240	27	𝑓𝜂(𝑡	𝑓𝜂(𝑡	NOUN
cana-5531	240	28	)	)	PUNCT
cana-5531	240	29	,	,	PUNCT
cana-5531	240	30	𝜐𝜂	𝜐𝜂	ADP
cana-5531	240	31	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	240	32	)	)	PUNCT
cana-5531	240	33	)	)	PUNCT
cana-5531	241	1	𝑉′×𝑉	𝑉′×𝑉	VERB
cana-5531	241	2	𝜐𝜂(0	𝜐𝜂(0	NOUN
cana-5531	241	3	)	)	PUNCT
cana-5531	241	4	=	=	SYM
cana-5531	241	5	𝑢1	𝑢1	NOUN
cana-5531	241	6	(	(	PUNCT
cana-5531	241	7	5.9	5.9	NUM
cana-5531	241	8	)	)	PUNCT
cana-5531	241	9	by	by	ADP
cana-5531	241	10	using	use	VERB
cana-5531	241	11	(	(	PUNCT
cana-5531	241	12	4.8	4.8	NUM
cana-5531	241	13	)	)	PUNCT
cana-5531	241	14	,	,	PUNCT
cana-5531	241	15	the	the	DET
cana-5531	241	16	monotony	monotony	NOUN
cana-5531	241	17	of	of	ADP
cana-5531	241	18	𝑗𝜀	𝑗𝜀	NOUN
cana-5531	241	19	′	′	PROPN
cana-5531	242	1	and	and	CCONJ
cana-5531	242	2	(	(	PUNCT
cana-5531	242	3	5.3	5.3	NUM
cana-5531	242	4	)	)	PUNCT
cana-5531	242	5	it	it	PRON
cana-5531	242	6	comes	come	VERB
cana-5531	242	7	that	that	SCONJ
cana-5531	242	8	:	:	PUNCT
cana-5531	242	9	∃	∃	PROPN
cana-5531	242	10	𝐶	𝐶	PROPN
cana-5531	242	11	>	>	X
cana-5531	242	12	0	0	PROPN
cana-5531	242	13	,	,	PUNCT
cana-5531	242	14	∀𝑡	∀𝑡	PROPN
cana-5531	242	15	∈	∈	PROPN
cana-5531	243	1	[	[	X
cana-5531	243	2	0	0	NUM
cana-5531	243	3	,	,	PUNCT
cana-5531	243	4	𝑇	𝑇	PROPN
cana-5531	243	5	]	]	PUNCT
cana-5531	243	6	,	,	PUNCT
cana-5531	243	7	|𝜐𝜂	|𝜐𝜂	PROPN
cana-5531	243	8	𝜀(𝑡)|	𝜀(𝑡)|	NOUN
cana-5531	243	9	𝐻	𝐻	PROPN
cana-5531	243	10	≤	≤	PROPN
cana-5531	243	11	𝐶	𝐶	PROPN
cana-5531	243	12	,	,	PUNCT
cana-5531	243	13	∫	∫	PROPN
cana-5531	244	1	|𝜐𝜂	|𝜐𝜂	PROPN
cana-5531	244	2	𝜀(𝑡)|	𝜀(𝑡)|	X
cana-5531	244	3	𝐻	𝐻	PROPN
cana-5531	244	4	2	2	NUM
cana-5531	244	5	𝑑𝑡	𝑑𝑡	ADP
cana-5531	244	6	≤	≤	PROPN
cana-5531	244	7	𝐶	𝐶	PROPN
cana-5531	244	8	,	,	PUNCT
cana-5531	244	9	∫	∫	PROPN
cana-5531	244	10	|	|	PROPN
cana-5531	244	11	�	�	PROPN
cana-5531	244	12	̇	̇	NOUN
cana-5531	244	13	�	�	PROPN
cana-5531	244	14	𝜂	𝜂	NOUN
cana-5531	244	15	𝜀(𝑡)|	𝜀(𝑡)|	NOUN
cana-5531	244	16	𝐻	𝐻	PROPN
cana-5531	244	17	2	2	NUM
cana-5531	244	18	𝑑𝑡	𝑑𝑡	ADP
cana-5531	244	19	≤	≤	ADV
cana-5531	244	20	𝐶.	𝐶.	PROPN
cana-5531	244	21	𝑇	𝑇	PROPN
cana-5531	244	22	0	0	NUM
cana-5531	244	23	𝑇	𝑇	PROPN
cana-5531	244	24	0	0	NUM
cana-5531	244	25	(	(	PUNCT
cana-5531	244	26	5.10	5.10	NUM
cana-5531	244	27	)	)	PUNCT
cana-5531	244	28	so	so	CCONJ
cana-5531	244	29	there	there	PRON
cana-5531	244	30	is	be	VERB
cana-5531	244	31	a	a	DET
cana-5531	244	32	sub	sub	NOUN
cana-5531	244	33	-	-	NOUN
cana-5531	244	34	sequence	sequence	NOUN
cana-5531	244	35	(	(	PUNCT
cana-5531	244	36	vη	vη	NOUN
cana-5531	244	37	)	)	PUNCT
cana-5531	244	38	such	such	ADJ
cana-5531	244	39	that	that	SCONJ
cana-5531	244	40	:	:	PUNCT
cana-5531	244	41	𝜐𝜂	𝜐𝜂	NOUN
cana-5531	244	42	𝜀	𝜀	PROPN
cana-5531	244	43	⟶	⟶	NOUN
cana-5531	244	44	𝜐𝜂weakly	𝜐𝜂weakly	ADV
cana-5531	244	45	in	in	ADP
cana-5531	244	46	𝕃2(0	𝕃2(0	NOUN
cana-5531	244	47	,	,	PUNCT
cana-5531	244	48	t	t	NOUN
cana-5531	244	49	;	;	PUNCT
cana-5531	244	50	v	v	NUM
cana-5531	244	51	)	)	PUNCT
cana-5531	244	52	and	and	CCONJ
cana-5531	244	53	weakly	weakly	ADJ
cana-5531	244	54	star	star	NOUN
cana-5531	244	55	in	in	ADP
cana-5531	244	56	𝕃∞(0	𝕃∞(0	PROPN
cana-5531	244	57	,	,	PUNCT
cana-5531	244	58	t	t	PROPN
cana-5531	244	59	;	;	PUNCT
cana-5531	244	60	h	h	X
cana-5531	244	61	)	)	PUNCT
cana-5531	244	62	.	.	PUNCT
cana-5531	245	1	�	�	PROPN
cana-5531	245	2	̇	̇	PROPN
cana-5531	245	3	�	�	PROPN
cana-5531	245	4	𝜂	𝜂	PRON
cana-5531	245	5	𝜀	𝜀	PROPN
cana-5531	245	6	⟶	⟶	PROPN
cana-5531	245	7	�	�	PROPN
cana-5531	245	8	̇	̇	PROPN
cana-5531	245	9	�	�	PROPN
cana-5531	245	10	η	η	PROPN
cana-5531	245	11	and	and	CCONJ
cana-5531	245	12	weakly	weakly	ADJ
cana-5531	245	13	star	star	NOUN
cana-5531	245	14	in	in	ADP
cana-5531	245	15	𝕃2(0	𝕃2(0	NOUN
cana-5531	245	16	,	,	PUNCT
cana-5531	245	17	t	t	NOUN
cana-5531	245	18	;	;	PUNCT
cana-5531	245	19	v	v	X
cana-5531	245	20	)	)	PUNCT
cana-5531	245	21	(	(	PUNCT
cana-5531	245	22	5.11	5.11	NUM
cana-5531	245	23	)	)	PUNCT
cana-5531	245	24	it	it	PRON
cana-5531	245	25	comes	come	VERB
cana-5531	245	26	that	that	PRON
cana-5531	245	27	:	:	PUNCT
cana-5531	245	28	𝜐𝜂	𝜐𝜂	X
cana-5531	245	29	∈	∈	PROPN
cana-5531	245	30	𝐶(0	𝐶(0	ADP
cana-5531	245	31	,	,	PUNCT
cana-5531	245	32	𝑇	𝑇	PROPN
cana-5531	245	33	;	;	PUNCT
cana-5531	245	34	𝐻	𝐻	PROPN
cana-5531	245	35	)	)	PUNCT
cana-5531	245	36	and	and	CCONJ
cana-5531	245	37	𝜐𝜂	𝜐𝜂	ADP
cana-5531	245	38	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	245	39	)	)	PUNCT
cana-5531	245	40	⟶	⟶	NOUN
cana-5531	245	41	𝜐𝜂(𝑡	𝜐𝜂(𝑡	NOUN
cana-5531	245	42	)	)	PUNCT
cana-5531	245	43	weakly	weakly	ADJ
cana-5531	245	44	in	in	ADP
cana-5531	245	45	𝐻	𝐻	PROPN
cana-5531	245	46	,	,	PUNCT
cana-5531	245	47	∀𝑡	∀𝑡	PROPN
cana-5531	245	48	∈	∈	PROPN
cana-5531	246	1	[	[	X
cana-5531	246	2	0	0	NUM
cana-5531	246	3	,	,	PUNCT
cana-5531	246	4	𝑇	𝑇	PROPN
cana-5531	246	5	]	]	PUNCT
cana-5531	246	6	.	.	PUNCT
cana-5531	247	1	(	(	PUNCT
cana-5531	247	2	5.12	5.12	NUM
cana-5531	247	3	)	)	PUNCT
cana-5531	247	4	communications	communication	NOUN
cana-5531	247	5	on	on	ADP
cana-5531	247	6	applied	apply	VERB
cana-5531	247	7	nonlinear	nonlinear	ADJ
cana-5531	247	8	analysis	analysis	NOUN
cana-5531	247	9	issn	issn	NOUN
cana-5531	247	10	:	:	PUNCT
cana-5531	247	11	1074	1074	NUM
cana-5531	247	12	-	-	PUNCT
cana-5531	247	13	133x	133x	NUM
cana-5531	247	14	vol	vol	NOUN
cana-5531	247	15	32	32	NUM
cana-5531	247	16	no	no	NOUN
cana-5531	247	17	.	.	NOUN
cana-5531	247	18	3	3	NUM
cana-5531	247	19	(	(	PUNCT
cana-5531	247	20	2025	2025	NUM
cana-5531	247	21	)	)	PUNCT
cana-5531	247	22	975	975	NUM
cana-5531	247	23	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	247	24	by	by	ADP
cana-5531	247	25	integration	integration	NOUN
cana-5531	247	26	of	of	ADP
cana-5531	247	27	(	(	PUNCT
cana-5531	247	28	5.8),then	5.8),then	PROPN
cana-5531	247	29	∀𝜔	∀𝜔	PROPN
cana-5531	247	30	∈	∈	NOUN
cana-5531	247	31	𝕃2(0	𝕃2(0	NOUN
cana-5531	247	32	,	,	PUNCT
cana-5531	247	33	t	t	NOUN
cana-5531	247	34	;	;	PUNCT
cana-5531	247	35	v	v	NOUN
cana-5531	247	36	)	)	PUNCT
cana-5531	247	37	:	:	PUNCT
cana-5531	248	1	∫	∫	PROPN
cana-5531	248	2	(	(	PUNCT
cana-5531	248	3	�	�	PROPN
cana-5531	248	4	̇	̇	PROPN
cana-5531	248	5	�	�	PROPN
cana-5531	248	6	𝜂	𝜂	NOUN
cana-5531	248	7	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	248	8	)	)	PUNCT
cana-5531	248	9	,	,	PUNCT
cana-5531	248	10	𝜔	𝜔	NOUN
cana-5531	248	11	)	)	PUNCT
cana-5531	248	12	𝑉′×𝑉	𝑉′×𝑉	ADJ
cana-5531	248	13	𝑑𝑡	𝑑𝑡	ADP
cana-5531	248	14	+	+	ADJ
cana-5531	248	15	∫	∫	PROPN
cana-5531	248	16	(	(	PUNCT
cana-5531	248	17	𝒢𝜐𝜂	𝒢𝜐𝜂	PROPN
cana-5531	248	18	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	248	19	)	)	PUNCT
cana-5531	248	20	,	,	PUNCT
cana-5531	248	21	𝜔	𝜔	NOUN
cana-5531	248	22	)	)	PUNCT
cana-5531	248	23	𝑉′×𝑉	𝑉′×𝑉	ADJ
cana-5531	248	24	𝑑𝑡	𝑑𝑡	ADP
cana-5531	248	25	+	+	ADJ
cana-5531	248	26	∫	∫	PROPN
cana-5531	248	27	𝑗𝜀(𝜔)𝑑𝑡	𝑗𝜀(𝜔)𝑑𝑡	PROPN
cana-5531	248	28	𝑇	𝑇	PROPN
cana-5531	248	29	0	0	NUM
cana-5531	248	30	𝑇	𝑇	PROPN
cana-5531	248	31	0	0	NUM
cana-5531	248	32	𝑇	𝑇	PROPN
cana-5531	248	33	0	0	NUM
cana-5531	248	34	≥	≥	NOUN
cana-5531	248	35	∫	∫	PROPN
cana-5531	248	36	(	(	PUNCT
cana-5531	248	37	�	�	PROPN
cana-5531	248	38	̇	̇	PROPN
cana-5531	248	39	�	�	PROPN
cana-5531	248	40	𝜂	𝜂	NOUN
cana-5531	248	41	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	248	42	)	)	PUNCT
cana-5531	248	43	,	,	PUNCT
cana-5531	248	44	𝜐𝜂	𝜐𝜂	ADP
cana-5531	248	45	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	248	46	)	)	PUNCT
cana-5531	248	47	)	)	PUNCT
cana-5531	249	1	𝑉′×𝑉	𝑉′×𝑉	ADJ
cana-5531	249	2	𝑑𝑡	𝑑𝑡	ADP
cana-5531	249	3	+	+	ADJ
cana-5531	249	4	∫	∫	PROPN
cana-5531	249	5	(	(	PUNCT
cana-5531	249	6	𝒢𝜐𝜂	𝒢𝜐𝜂	PROPN
cana-5531	249	7	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	249	8	)	)	PUNCT
cana-5531	249	9	,	,	PUNCT
cana-5531	249	10	𝜐𝜂	𝜐𝜂	ADP
cana-5531	249	11	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	249	12	)	)	PUNCT
cana-5531	249	13	)	)	PUNCT
cana-5531	250	1	𝑉′×𝑉	𝑉′×𝑉	VERB
cana-5531	250	2	𝑑𝑡	𝑑𝑡	ADP
cana-5531	250	3	𝑇	𝑇	PROPN
cana-5531	250	4	0	0	NUM
cana-5531	250	5	𝑇	𝑇	PROPN
cana-5531	250	6	0	0	NUM
cana-5531	251	1	+	+	NUM
cana-5531	251	2	∫	∫	PROPN
cana-5531	251	3	𝑗𝜀(𝜐𝜂	𝑗𝜀(𝜐𝜂	PROPN
cana-5531	251	4	𝜀)𝑑𝑡	𝜀)𝑑𝑡	PROPN
cana-5531	251	5	+	+	CCONJ
cana-5531	251	6	∫	∫	PROPN
cana-5531	251	7	(	(	PUNCT
cana-5531	251	8	𝑓𝜂(𝑡	𝑓𝜂(𝑡	NOUN
cana-5531	251	9	)	)	PUNCT
cana-5531	251	10	,	,	PUNCT
cana-5531	251	11	𝜔	𝜔	PROPN
cana-5531	251	12	−	−	PROPN
cana-5531	251	13	𝜐𝜂	𝜐𝜂	ADP
cana-5531	251	14	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	251	15	)	)	PUNCT
cana-5531	251	16	)	)	PUNCT
cana-5531	252	1	𝑉′×𝑉	𝑉′×𝑉	VERB
cana-5531	252	2	𝑑𝑡	𝑑𝑡	ADP
cana-5531	252	3	𝑇	𝑇	PROPN
cana-5531	252	4	0	0	NUM
cana-5531	252	5	𝑇	𝑇	PROPN
cana-5531	252	6	0	0	NUM
cana-5531	252	7	≥	≥	NOUN
cana-5531	252	8	1	1	NUM
cana-5531	252	9	2	2	NUM
cana-5531	252	10	|𝜐𝜂	|𝜐𝜂	NUM
cana-5531	252	11	𝜀(𝑇)|	𝜀(𝑇)|	NOUN
cana-5531	252	12	𝐻	𝐻	NOUN
cana-5531	252	13	2	2	NUM
cana-5531	252	14	−	−	NOUN
cana-5531	252	15	1	1	NUM
cana-5531	252	16	2	2	NUM
cana-5531	252	17	|𝜐𝜂	|𝜐𝜂	NUM
cana-5531	252	18	𝜀(0)|	𝜀(0)|	NOUN
cana-5531	252	19	𝐻	𝐻	PROPN
cana-5531	252	20	2	2	NUM
cana-5531	252	21	+	+	NUM
cana-5531	252	22	∫	∫	PROPN
cana-5531	252	23	(	(	PUNCT
cana-5531	252	24	𝒢𝜐𝜂	𝒢𝜐𝜂	PROPN
cana-5531	252	25	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	252	26	)	)	PUNCT
cana-5531	252	27	,	,	PUNCT
cana-5531	252	28	𝜐𝜂	𝜐𝜂	ADP
cana-5531	252	29	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	252	30	)	)	PUNCT
cana-5531	252	31	)	)	PUNCT
cana-5531	253	1	𝑉′×𝑉	𝑉′×𝑉	SYM
cana-5531	253	2	𝑇	𝑇	PROPN
cana-5531	253	3	0	0	PUNCT
cana-5531	254	1	+	+	NUM
cana-5531	254	2	∫	∫	PROPN
cana-5531	254	3	𝑗𝜀(𝜐𝜂	𝑗𝜀(𝜐𝜂	PROPN
cana-5531	254	4	𝜀)𝑑𝑡	𝜀)𝑑𝑡	PROPN
cana-5531	254	5	+	+	CCONJ
cana-5531	254	6	∫	∫	PROPN
cana-5531	254	7	(	(	PUNCT
cana-5531	254	8	𝑓𝜂(𝑡	𝑓𝜂(𝑡	NOUN
cana-5531	254	9	)	)	PUNCT
cana-5531	254	10	,	,	PUNCT
cana-5531	254	11	𝜔	𝜔	PROPN
cana-5531	254	12	−	−	PROPN
cana-5531	254	13	𝜐𝜂	𝜐𝜂	ADP
cana-5531	254	14	𝜀(𝑡	𝜀(𝑡	NOUN
cana-5531	254	15	)	)	PUNCT
cana-5531	254	16	)	)	PUNCT
cana-5531	255	1	𝑉′×𝑉	𝑉′×𝑉	NOUN
cana-5531	255	2	𝑑𝑡.	𝑑𝑡.	VERB
cana-5531	255	3	𝑇	𝑇	PROPN
cana-5531	255	4	0	0	NUM
cana-5531	255	5	𝑇	𝑇	PROPN
cana-5531	255	6	0	0	NUM
cana-5531	255	7	(	(	PUNCT
cana-5531	255	8	5.13	5.13	NUM
cana-5531	255	9	)	)	PUNCT
cana-5531	255	10	by	by	ADP
cana-5531	255	11	(	(	PUNCT
cana-5531	255	12	5.11	5.11	NUM
cana-5531	255	13	)	)	PUNCT
cana-5531	255	14	,	,	PUNCT
cana-5531	255	15	(	(	PUNCT
cana-5531	255	16	5.12	5.12	NUM
cana-5531	255	17	)	)	PUNCT
cana-5531	255	18	and	and	CCONJ
cana-5531	255	19	the	the	DET
cana-5531	255	20	weak	weak	ADJ
cana-5531	255	21	semi	semi	ADJ
cana-5531	255	22	-	-	NOUN
cana-5531	255	23	continuity	continuity	NOUN
cana-5531	255	24	below	below	ADP
cana-5531	255	25	it	it	PRON
cana-5531	255	26	result	result	VERB
cana-5531	255	27	that	that	SCONJ
cana-5531	255	28	:	:	PUNCT
cana-5531	255	29	∀𝜔	∀𝜔	NUM
cana-5531	255	30	∈	∈	NOUN
cana-5531	255	31	𝕃2(0	𝕃2(0	NOUN
cana-5531	255	32	,	,	PUNCT
cana-5531	255	33	𝑇	𝑇	PROPN
cana-5531	255	34	;	;	PUNCT
cana-5531	255	35	𝑉	𝑉	PROPN
cana-5531	255	36	)	)	PUNCT
cana-5531	255	37	,	,	PUNCT
cana-5531	255	38	∫	∫	PROPN
cana-5531	255	39	(	(	PUNCT
cana-5531	255	40	�	�	PROPN
cana-5531	255	41	̇	̇	PROPN
cana-5531	255	42	�	�	PROPN
cana-5531	255	43	𝜂(𝑡	𝜂(𝑡	NOUN
cana-5531	255	44	)	)	PUNCT
cana-5531	255	45	,	,	PUNCT
cana-5531	255	46	𝜔	𝜔	ADP
cana-5531	255	47	−	−	NOUN
cana-5531	255	48	𝜐𝜂(𝑡	𝜐𝜂(𝑡	NOUN
cana-5531	255	49	)	)	PUNCT
cana-5531	255	50	)	)	PUNCT
cana-5531	256	1	𝑉′×𝑉	𝑉′×𝑉	ADJ
cana-5531	256	2	𝑑𝑡	𝑑𝑡	ADP
cana-5531	256	3	+	+	ADJ
cana-5531	256	4	∫	∫	PROPN
cana-5531	256	5	(	(	PUNCT
cana-5531	256	6	𝒢𝜐𝜂(𝑡	𝒢𝜐𝜂(𝑡	NOUN
cana-5531	256	7	)	)	PUNCT
cana-5531	256	8	,	,	PUNCT
cana-5531	256	9	𝜔	𝜔	ADP
cana-5531	256	10	−	−	NOUN
cana-5531	256	11	𝜐𝜂(𝑡	𝜐𝜂(𝑡	NOUN
cana-5531	256	12	)	)	PUNCT
cana-5531	256	13	)	)	PUNCT
cana-5531	257	1	𝑉′×𝑉	𝑉′×𝑉	VERB
cana-5531	257	2	𝑑𝑡	𝑑𝑡	ADP
cana-5531	257	3	𝑇	𝑇	PROPN
cana-5531	257	4	0	0	NUM
cana-5531	257	5	𝑇	𝑇	PROPN
cana-5531	257	6	0	0	NUM
cana-5531	258	1	+	+	NUM
cana-5531	258	2	∫	∫	PROPN
cana-5531	258	3	(	(	PUNCT
cana-5531	258	4	𝑗𝑞(𝜔	𝑗𝑞(𝜔	PROPN
cana-5531	258	5	)	)	PUNCT
cana-5531	258	6	−	−	PROPN
cana-5531	259	1	𝑗𝑞(𝜐𝜂	𝑗𝑞(𝜐𝜂	ADJ
cana-5531	259	2	)	)	PUNCT
cana-5531	259	3	)	)	PUNCT
cana-5531	260	1	≥	≥	X
cana-5531	260	2	𝑇	𝑇	PROPN
cana-5531	260	3	0	0	NUM
cana-5531	260	4	∫	∫	PROPN
cana-5531	260	5	(	(	PUNCT
cana-5531	260	6	𝑓𝜂(𝑡	𝑓𝜂(𝑡	NOUN
cana-5531	260	7	)	)	PUNCT
cana-5531	260	8	,	,	PUNCT
cana-5531	260	9	𝜔	𝜔	ADP
cana-5531	260	10	−	−	NOUN
cana-5531	260	11	𝜐𝜂(𝑡	𝜐𝜂(𝑡	NOUN
cana-5531	260	12	)	)	PUNCT
cana-5531	260	13	)	)	PUNCT
cana-5531	261	1	𝑉′×𝑉	𝑉′×𝑉	VERB
cana-5531	261	2	𝑑𝑡	𝑑𝑡	ADP
cana-5531	261	3	𝑇	𝑇	PROPN
cana-5531	261	4	0	0	NUM
cana-5531	261	5	which	which	PRON
cana-5531	261	6	implies	imply	VERB
cana-5531	261	7	that	that	PRON
cana-5531	261	8	:	:	PUNCT
cana-5531	261	9	(	(	PUNCT
cana-5531	261	10	�	�	NOUN
cana-5531	261	11	̇	̇	PROPN
cana-5531	261	12	�	�	PROPN
cana-5531	261	13	𝜂(𝑡	𝜂(𝑡	NOUN
cana-5531	261	14	)	)	PUNCT
cana-5531	261	15	,	,	PUNCT
cana-5531	261	16	𝜔	𝜔	ADP
cana-5531	261	17	−	−	NOUN
cana-5531	261	18	𝜐𝜂(𝑡	𝜐𝜂(𝑡	NOUN
cana-5531	261	19	)	)	PUNCT
cana-5531	261	20	)	)	PUNCT
cana-5531	262	1	𝑉′×𝑉	𝑉′×𝑉	ADJ
cana-5531	262	2	+	+	CCONJ
cana-5531	262	3	(	(	PUNCT
cana-5531	262	4	𝒢𝜐𝜂(𝑡),𝜔	𝒢𝜐𝜂(𝑡),𝜔	PROPN
cana-5531	262	5	−	−	NUM
cana-5531	262	6	𝜐𝜂(𝑡	𝜐𝜂(𝑡	NOUN
cana-5531	262	7	)	)	PUNCT
cana-5531	262	8	)	)	PUNCT
cana-5531	263	1	𝑉′×𝑉	𝑉′×𝑉	ADJ
cana-5531	263	2	+	+	NOUN
cana-5531	263	3	𝑗𝑞(𝜔	𝑗𝑞(𝜔	X
cana-5531	263	4	)	)	PUNCT
cana-5531	263	5	−	−	PROPN
cana-5531	263	6	𝑗𝑞(𝜐𝜂	𝑗𝑞(𝜐𝜂	ADJ
cana-5531	263	7	)	)	PUNCT
cana-5531	263	8	≥	≥	PROPN
cana-5531	263	9	(	(	PUNCT
cana-5531	263	10	𝑓𝜂(𝑡),𝜔	𝑓𝜂(𝑡),𝜔	X
cana-5531	263	11	−	−	NOUN
cana-5531	263	12	𝜐𝜂(𝑡	𝜐𝜂(𝑡	NOUN
cana-5531	263	13	)	)	PUNCT
cana-5531	263	14	)	)	PUNCT
cana-5531	264	1	𝑉′×𝑉	𝑉′×𝑉	PROPN
cana-5531	264	2	,	,	PUNCT
cana-5531	264	3	∀𝜔	∀𝜔	PROPN
cana-5531	264	4	∈	∈	PROPN
cana-5531	264	5	𝑉	𝑉	PROPN
cana-5531	264	6	,	,	PUNCT
cana-5531	264	7	∀𝑡	∀𝑡	PROPN
cana-5531	264	8	∈	∈	PROPN
cana-5531	265	1	[	[	X
cana-5531	265	2	0	0	NUM
cana-5531	265	3	,	,	PUNCT
cana-5531	265	4	𝑇	𝑇	PROPN
cana-5531	265	5	]	]	PUNCT
cana-5531	265	6	.	.	PUNCT
cana-5531	266	1	so	so	ADV
cana-5531	266	2	the	the	DET
cana-5531	266	3	problem	problem	NOUN
cana-5531	266	4	𝑃𝜂𝑞	𝑃𝜂𝑞	PROPN
cana-5531	266	5	has	have	VERB
cana-5531	266	6	a	a	DET
cana-5531	266	7	solution	solution	NOUN
cana-5531	266	8	𝜐𝜂	𝜐𝜂	ADP
cana-5531	266	9	∈	∈	PROPN
cana-5531	266	10	𝐶(0	𝐶(0	ADP
cana-5531	266	11	,	,	PUNCT
cana-5531	266	12	𝑇;𝐻	𝑇;𝐻	ADJ
cana-5531	266	13	)	)	PUNCT
cana-5531	266	14	∩	∩	NOUN
cana-5531	266	15	𝕃	𝕃	PROPN
cana-5531	266	16	2(0	2(0	NUM
cana-5531	266	17	,	,	PUNCT
cana-5531	266	18	𝑇	𝑇	PROPN
cana-5531	266	19	;	;	PUNCT
cana-5531	266	20	𝑉	𝑉	PROPN
cana-5531	266	21	)	)	PUNCT
cana-5531	266	22	∩	∩	ADJ
cana-5531	266	23	𝑊1,2(0	𝑊1,2(0	NOUN
cana-5531	266	24	,	,	PUNCT
cana-5531	266	25	𝑇	𝑇	PROPN
cana-5531	266	26	;	;	PUNCT
cana-5531	266	27	𝑉′	𝑉′	NOUN
cana-5531	266	28	)	)	PUNCT
cana-5531	266	29	.	.	PUNCT
cana-5531	267	1	for	for	ADP
cana-5531	267	2	uniqueness	uniqueness	NOUN
cana-5531	267	3	,	,	PUNCT
cana-5531	267	4	let	let	VERB
cana-5531	267	5	𝜐𝜂	𝜐𝜂	ADP
cana-5531	267	6	1	1	NUM
cana-5531	267	7	,	,	PUNCT
cana-5531	267	8	𝜐𝜂	𝜐𝜂	ADP
cana-5531	267	9	2	2	NUM
cana-5531	267	10	be	be	AUX
cana-5531	267	11	two	two	NUM
cana-5531	267	12	solutions	solution	NOUN
cana-5531	267	13	of	of	ADP
cana-5531	267	14	𝑃𝜂𝑞	𝑃𝜂𝑞	PROPN
cana-5531	267	15	.	.	PUNCT
cana-5531	268	1	then	then	ADV
cana-5531	268	2	for	for	ADP
cana-5531	268	3	all	all	DET
cana-5531	268	4	𝑡	𝑡	ADP
cana-5531	268	5	∈	∈	PROPN
cana-5531	268	6	[	[	X
cana-5531	268	7	0	0	NUM
cana-5531	268	8	,	,	PUNCT
cana-5531	268	9	𝑇	𝑇	PROPN
cana-5531	268	10	]	]	PUNCT
cana-5531	268	11	,	,	PUNCT
cana-5531	268	12	(	(	PUNCT
cana-5531	268	13	�	�	NOUN
cana-5531	268	14	̇	̇	NOUN
cana-5531	268	15	�	�	PROPN
cana-5531	268	16	𝜂	𝜂	NOUN
cana-5531	268	17	2(𝑡	2(𝑡	NUM
cana-5531	268	18	)	)	PUNCT
cana-5531	268	19	−	−	PROPN
cana-5531	268	20	�	�	PROPN
cana-5531	268	21	̇	̇	NOUN
cana-5531	268	22	�	�	PROPN
cana-5531	268	23	𝜂	𝜂	NOUN
cana-5531	268	24	1(𝑡	1(𝑡	NUM
cana-5531	268	25	)	)	PUNCT
cana-5531	268	26	,	,	PUNCT
cana-5531	268	27	𝜐𝜂	𝜐𝜂	ADP
cana-5531	268	28	2(𝑡	2(𝑡	NUM
cana-5531	268	29	)	)	PUNCT
cana-5531	268	30	−	−	PROPN
cana-5531	268	31	𝜐𝜂	𝜐𝜂	NOUN
cana-5531	268	32	1(𝑡	1(𝑡	NUM
cana-5531	268	33	)	)	PUNCT
cana-5531	268	34	)	)	PUNCT
cana-5531	269	1	𝑉′×𝑉	𝑉′×𝑉	PROPN
cana-5531	269	2	+	+	SYM
cana-5531	269	3	(	(	PUNCT
cana-5531	269	4	𝒢𝜐𝜂	𝒢𝜐𝜂	PROPN
cana-5531	269	5	2(𝑡	2(𝑡	NUM
cana-5531	269	6	)	)	PUNCT
cana-5531	269	7	−	−	PROPN
cana-5531	269	8	𝒢𝜐𝜂	𝒢𝜐𝜂	PROPN
cana-5531	269	9	1(𝑡	1(𝑡	NUM
cana-5531	269	10	)	)	PUNCT
cana-5531	269	11	,	,	PUNCT
cana-5531	269	12	𝜐𝜂	𝜐𝜂	ADP
cana-5531	269	13	2(𝑡	2(𝑡	NUM
cana-5531	269	14	)	)	PUNCT
cana-5531	269	15	−	−	PROPN
cana-5531	269	16	𝜐𝜂	𝜐𝜂	NOUN
cana-5531	269	17	1(𝑡	1(𝑡	NUM
cana-5531	269	18	)	)	PUNCT
cana-5531	269	19	)	)	PUNCT
cana-5531	270	1	𝑉′×𝑉	𝑉′×𝑉	VERB
cana-5531	270	2	≤	≤	NUM
cana-5531	270	3	0	0	NUM
cana-5531	270	4	.	.	PUNCT
cana-5531	271	1	by	by	ADP
cana-5531	271	2	integrating	integrate	VERB
cana-5531	271	3	the	the	DET
cana-5531	271	4	previous	previous	ADJ
cana-5531	271	5	inequation	inequation	NOUN
cana-5531	271	6	and	and	CCONJ
cana-5531	271	7	using	use	VERB
cana-5531	271	8	(	(	PUNCT
cana-5531	271	9	4.5	4.5	NUM
cana-5531	271	10	)	)	PUNCT
cana-5531	271	11	then	then	ADV
cana-5531	271	12	:	:	PUNCT
cana-5531	271	13	1	1	NUM
cana-5531	271	14	2	2	NUM
cana-5531	271	15	|𝜐𝜂	|𝜐𝜂	NUM
cana-5531	271	16	2(𝑡	2(𝑡	NUM
cana-5531	271	17	)	)	PUNCT
cana-5531	271	18	−	−	PROPN
cana-5531	271	19	𝜐𝜂	𝜐𝜂	ADP
cana-5531	271	20	1(𝑡)|	1(𝑡)|	NUM
cana-5531	271	21	𝑉	𝑉	PROPN
cana-5531	271	22	2	2	NUM
cana-5531	271	23	+	+	ADJ
cana-5531	271	24	𝑚𝒢	𝑚𝒢	ADJ
cana-5531	271	25	∫	∫	PROPN
cana-5531	271	26	|𝜐𝜂	|𝜐𝜂	NUM
cana-5531	271	27	2(𝑠	2(𝑠	NUM
cana-5531	271	28	)	)	PUNCT
cana-5531	271	29	−	−	PROPN
cana-5531	271	30	𝜐𝜂	𝜐𝜂	ADP
cana-5531	271	31	1(𝑠)|	1(𝑠)|	NUM
cana-5531	271	32	𝑉	𝑉	NOUN
cana-5531	271	33	2𝑇	2𝑇	NOUN
cana-5531	271	34	0	0	NUM
cana-5531	271	35	𝑑𝑠	𝑑𝑠	VERB
cana-5531	271	36	≤	≤	NUM
cana-5531	271	37	0	0	NUM
cana-5531	271	38	,	,	PUNCT
cana-5531	271	39	∀𝑡	∀𝑡	PROPN
cana-5531	271	40	∈	∈	PROPN
cana-5531	272	1	[	[	X
cana-5531	272	2	0	0	NUM
cana-5531	272	3	,	,	PUNCT
cana-5531	272	4	𝑇	𝑇	PROPN
cana-5531	272	5	]	]	PUNCT
cana-5531	272	6	.	.	PUNCT
cana-5531	273	1	it	it	PRON
cana-5531	273	2	implies	imply	VERB
cana-5531	273	3	𝜐𝜂	𝜐𝜂	ADP
cana-5531	273	4	2=𝜐𝜂	2=𝜐𝜂	NUM
cana-5531	273	5	1	1	NUM
cana-5531	273	6	.	.	PUNCT
cana-5531	274	1	in	in	ADP
cana-5531	274	2	the	the	DET
cana-5531	274	3	study	study	NOUN
cana-5531	274	4	of	of	ADP
cana-5531	274	5	the	the	DET
cana-5531	274	6	problem	problem	NOUN
cana-5531	274	7	𝑃𝜂𝑞	𝑃𝜂𝑞	PROPN
cana-5531	274	8	we	we	PRON
cana-5531	274	9	have	have	VERB
cana-5531	274	10	the	the	DET
cana-5531	274	11	following	following	ADJ
cana-5531	274	12	result	result	NOUN
cana-5531	274	13	:	:	PUNCT
cana-5531	274	14	lemma	lemma	PROPN
cana-5531	274	15	5.5	5.5	NUM
cana-5531	274	16	:	:	PUNCT
cana-5531	274	17	the	the	DET
cana-5531	274	18	problem	problem	NOUN
cana-5531	274	19	𝑃𝜐𝜂𝑞	𝑃𝜐𝜂𝑞	PROPN
cana-5531	274	20	has	have	VERB
cana-5531	274	21	a	a	DET
cana-5531	274	22	unique	unique	ADJ
cana-5531	274	23	solution	solution	NOUN
cana-5531	274	24	𝑢𝜂𝑞	𝑢𝜂𝑞	VERB
cana-5531	274	25	∈	∈	PROPN
cana-5531	274	26	𝑊	𝑊	PROPN
cana-5531	274	27	1,2(0,t	1,2(0,t	NOUN
cana-5531	274	28	;	;	PUNCT
cana-5531	274	29	v	v	X
cana-5531	274	30	)	)	PUNCT
cana-5531	274	31	∩	∩	ADJ
cana-5531	274	32	c1(0	c1(0	PROPN
cana-5531	274	33	,	,	PUNCT
cana-5531	274	34	t	t	PROPN
cana-5531	274	35	;	;	PUNCT
cana-5531	274	36	𝐻	𝐻	PROPN
cana-5531	274	37	)	)	PUNCT
cana-5531	274	38	∩	∩	NOUN
cana-5531	274	39	𝑊2,2(0	𝑊2,2(0	NOUN
cana-5531	274	40	,	,	PUNCT
cana-5531	274	41	t	t	NOUN
cana-5531	274	42	;	;	PUNCT
cana-5531	274	43	𝑉′	𝑉′	ADV
cana-5531	274	44	)	)	PUNCT
cana-5531	274	45	.	.	PUNCT
cana-5531	275	1	moreover	moreover	ADV
cana-5531	275	2	,	,	PUNCT
cana-5531	275	3	if	if	SCONJ
cana-5531	275	4	𝑢1	𝑢1	PROPN
cana-5531	275	5	,	,	PUNCT
cana-5531	275	6	𝑢2	𝑢2	PROPN
cana-5531	275	7	two	two	NUM
cana-5531	275	8	solutions	solution	NOUN
cana-5531	275	9	of	of	ADP
cana-5531	275	10	the	the	DET
cana-5531	275	11	problem	problem	NOUN
cana-5531	275	12	𝑃𝜐𝜂𝑞	𝑃𝜐𝜂𝑞	PROPN
cana-5531	275	13	corresponding	correspond	VERB
cana-5531	275	14	to	to	ADP
cana-5531	275	15	the	the	DET
cana-5531	275	16	data	datum	NOUN
cana-5531	275	17	𝜂1	𝜂1	NOUN
cana-5531	275	18	,	,	PUNCT
cana-5531	275	19	𝜂2	𝜂2	NOUN
cana-5531	275	20	∈	∈	NOUN
cana-5531	275	21	𝕃2(0	𝕃2(0	NOUN
cana-5531	275	22	,	,	PUNCT
cana-5531	275	23	t	t	NOUN
cana-5531	275	24	;	;	PUNCT
cana-5531	275	25	𝑉′	𝑉′	ADV
cana-5531	275	26	)	)	PUNCT
cana-5531	275	27	and	and	CCONJ
cana-5531	275	28	𝑞1	𝑞1	PROPN
cana-5531	275	29	,	,	PUNCT
cana-5531	275	30	𝑞2∈	𝑞2∈	PROPN
cana-5531	275	31	c+	c+	VERB
cana-5531	275	32	then	then	ADV
cana-5531	275	33	there	there	PRON
cana-5531	275	34	exists	exist	VERB
cana-5531	275	35	c	c	NOUN
cana-5531	275	36	>	>	X
cana-5531	275	37	0	0	NUM
cana-5531	276	1	such	such	ADJ
cana-5531	276	2	that	that	PRON
cana-5531	276	3	:	:	PUNCT
cana-5531	276	4	|	|	X
cana-5531	276	5	�	�	NOUN
cana-5531	276	6	̇	̇	NOUN
cana-5531	276	7	�	�	PROPN
cana-5531	276	8	𝜂1𝑞1(𝑡	𝜂1𝑞1(𝑡	NOUN
cana-5531	276	9	)	)	PUNCT
cana-5531	276	10	−	−	PROPN
cana-5531	276	11	�	�	PROPN
cana-5531	276	12	̇	̇	NOUN
cana-5531	276	13	�	�	NOUN
cana-5531	276	14	𝜂2𝑞2(𝑡)|𝑉	𝜂2𝑞2(𝑡)|𝑉	NOUN
cana-5531	276	15	2	2	NUM
cana-5531	276	16	≤	≤	NUM
cana-5531	276	17	𝑐	𝑐	PROPN
cana-5531	276	18	∫	∫	PROPN
cana-5531	276	19	|𝜂1(𝑠	|𝜂1(𝑠	PROPN
cana-5531	276	20	)	)	PUNCT
cana-5531	276	21	−	−	NOUN
cana-5531	276	22	𝜂2(𝑠)|𝑉′	𝜂2(𝑠)|𝑉′	PROPN
cana-5531	276	23	2	2	NUM
cana-5531	276	24	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	276	25	+	+	X
cana-5531	276	26	∫	∫	PROPN
cana-5531	276	27	|𝑞1(𝑠	|𝑞1(𝑠	NUM
cana-5531	276	28	)	)	PUNCT
cana-5531	276	29	−	−	PROPN
cana-5531	276	30	𝑞2(𝑠)|𝑉′	𝑞2(𝑠)|𝑉′	NOUN
cana-5531	276	31	2	2	NUM
cana-5531	276	32	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	276	33	𝑡	𝑡	PROPN
cana-5531	276	34	0	0	PUNCT
cana-5531	276	35	𝑡	𝑡	PROPN
cana-5531	276	36	0	0	NUM
cana-5531	276	37	|𝑢𝜂1𝑞1(𝑡	|𝑢𝜂1𝑞1(𝑡	NOUN
cana-5531	276	38	)	)	PUNCT
cana-5531	276	39	−	−	PROPN
cana-5531	276	40	𝑢𝜂2𝑞2(𝑡)|𝑉	𝑢𝜂2𝑞2(𝑡)|𝑉	SYM
cana-5531	276	41	2	2	NUM
cana-5531	276	42	≤	≤	NOUN
cana-5531	276	43	𝑐	𝑐	PROPN
cana-5531	276	44	∫	∫	PROPN
cana-5531	276	45	|𝜂1(𝑠	|𝜂1(𝑠	PROPN
cana-5531	276	46	)	)	PUNCT
cana-5531	276	47	−	−	NOUN
cana-5531	277	1	𝜂2(𝑠)|𝑉′	𝜂2(𝑠)|𝑉′	PROPN
cana-5531	277	2	2	2	NUM
cana-5531	277	3	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	277	4	+	+	X
cana-5531	277	5	∫	∫	PROPN
cana-5531	277	6	|𝑞1(𝑠	|𝑞1(𝑠	NUM
cana-5531	277	7	)	)	PUNCT
cana-5531	277	8	−	−	PROPN
cana-5531	277	9	𝑞2(𝑠)|𝑉′	𝑞2(𝑠)|𝑉′	NOUN
cana-5531	277	10	2	2	NUM
cana-5531	277	11	𝑑𝑠.	𝑑𝑠.	NOUN
cana-5531	277	12	𝑡	𝑡	X
cana-5531	277	13	0	0	NUM
cana-5531	277	14	𝑡	𝑡	NOUN
cana-5531	277	15	0	0	NUM
cana-5531	277	16	(	(	PUNCT
cana-5531	277	17	5.14	5.14	NUM
cana-5531	277	18	)	)	PUNCT
cana-5531	277	19	communications	communication	NOUN
cana-5531	277	20	on	on	ADP
cana-5531	277	21	applied	apply	VERB
cana-5531	277	22	nonlinear	nonlinear	ADJ
cana-5531	277	23	analysis	analysis	NOUN
cana-5531	277	24	issn	issn	NOUN
cana-5531	277	25	:	:	PUNCT
cana-5531	277	26	1074	1074	NUM
cana-5531	277	27	-	-	PUNCT
cana-5531	277	28	133x	133x	NUM
cana-5531	277	29	vol	vol	NOUN
cana-5531	277	30	32	32	NUM
cana-5531	277	31	no	no	NOUN
cana-5531	277	32	.	.	NOUN
cana-5531	277	33	3	3	NUM
cana-5531	277	34	(	(	PUNCT
cana-5531	277	35	2025	2025	NUM
cana-5531	277	36	)	)	PUNCT
cana-5531	278	1	976	976	NUM
cana-5531	278	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	278	3	proof	proof	NOUN
cana-5531	278	4	:	:	PUNCT
cana-5531	278	5	the	the	DET
cana-5531	278	6	proof	proof	NOUN
cana-5531	278	7	is	be	AUX
cana-5531	278	8	a	a	DET
cana-5531	278	9	consequence	consequence	NOUN
cana-5531	278	10	of	of	ADP
cana-5531	278	11	the	the	DET
cana-5531	278	12	lemma	lemma	PROPN
cana-5531	278	13	(	(	PUNCT
cana-5531	278	14	5.4	5.4	NUM
cana-5531	278	15	)	)	PUNCT
cana-5531	278	16	and	and	CCONJ
cana-5531	278	17	the	the	DET
cana-5531	278	18	relation	relation	NOUN
cana-5531	278	19	(	(	PUNCT
cana-5531	278	20	4.5	4.5	NUM
cana-5531	278	21	)	)	PUNCT
cana-5531	278	22	.	.	PUNCT
cana-5531	279	1	for	for	ADP
cana-5531	279	2	proving	prove	VERB
cana-5531	279	3	the	the	DET
cana-5531	279	4	inequality	inequality	NOUN
cana-5531	279	5	(	(	PUNCT
cana-5531	279	6	5.14	5.14	NUM
cana-5531	279	7	)	)	PUNCT
cana-5531	279	8	,	,	PUNCT
cana-5531	279	9	let	let	VERB
cana-5531	279	10	𝑢𝜂1,𝑢𝜂2	𝑢𝜂1,𝑢𝜂2	PROPN
cana-5531	279	11	be	be	AUX
cana-5531	279	12	two	two	NUM
cana-5531	279	13	solutions	solution	NOUN
cana-5531	279	14	of	of	ADP
cana-5531	279	15	problems	problem	NOUN
cana-5531	279	16	𝑃𝜐𝜂1	𝑃𝜐𝜂1	NOUN
cana-5531	279	17	and	and	CCONJ
cana-5531	279	18	𝑃𝜐𝜂2	𝑃𝜐𝜂2	VERB
cana-5531	279	19	respectively	respectively	ADV
cana-5531	279	20	,	,	PUNCT
cana-5531	279	21	then	then	ADV
cana-5531	279	22	:	:	PUNCT
cana-5531	279	23	(	(	PUNCT
cana-5531	279	24	�	�	PROPN
cana-5531	279	25	̈	̈	X
cana-5531	279	26	�	�	NOUN
cana-5531	279	27	𝜂𝑖𝑞𝑖	𝜂𝑖𝑞𝑖	VERB
cana-5531	279	28	,	,	PUNCT
cana-5531	279	29	�	�	PROPN
cana-5531	279	30	̇	̇	PROPN
cana-5531	279	31	�	�	PROPN
cana-5531	279	32	𝜂𝑗𝑞𝑗	𝜂𝑗𝑞𝑗	NOUN
cana-5531	279	33	−	−	PROPN
cana-5531	279	34	�	�	PROPN
cana-5531	279	35	̇	̇	PROPN
cana-5531	279	36	�	�	NOUN
cana-5531	279	37	𝜂𝑖𝑞𝑖	𝜂𝑖𝑞𝑖	NOUN
cana-5531	279	38	)	)	PUNCT
cana-5531	280	1	+	+	CCONJ
cana-5531	280	2	(	(	PUNCT
cana-5531	280	3	𝒢	𝒢	PROPN
cana-5531	280	4	�	�	PROPN
cana-5531	280	5	̇	̇	NOUN
cana-5531	280	6	�	�	NOUN
cana-5531	280	7	𝜂𝑖𝑞𝑖	𝜂𝑖𝑞𝑖	NOUN
cana-5531	280	8	,	,	PUNCT
cana-5531	280	9	�	�	PROPN
cana-5531	280	10	̇	̇	NOUN
cana-5531	280	11	�	�	PROPN
cana-5531	280	12	𝜂𝑗𝑞𝑗	𝜂𝑗𝑞𝑗	NOUN
cana-5531	280	13	−	−	PROPN
cana-5531	280	14	�	�	PROPN
cana-5531	280	15	̇	̇	PROPN
cana-5531	280	16	�	�	NOUN
cana-5531	280	17	𝜂𝑖𝑞𝑖	𝜂𝑖𝑞𝑖	NOUN
cana-5531	280	18	)	)	PUNCT
cana-5531	281	1	+	+	CCONJ
cana-5531	281	2	𝑗𝑞	𝑗𝑞	PROPN
cana-5531	281	3	(	(	PUNCT
cana-5531	281	4	�	�	PROPN
cana-5531	281	5	̇	̇	NOUN
cana-5531	281	6	�	�	NOUN
cana-5531	281	7	𝜂𝑗𝑞𝑗	𝜂𝑗𝑞𝑗	NOUN
cana-5531	281	8	)	)	PUNCT
cana-5531	281	9	−𝑗𝑞(	−𝑗𝑞(	NUM
cana-5531	281	10	�	�	SYM
cana-5531	281	11	̇	̇	NOUN
cana-5531	281	12	�	�	NOUN
cana-5531	281	13	𝜂𝑖𝑞𝑖	𝜂𝑖𝑞𝑖	NOUN
cana-5531	281	14	)	)	PUNCT
cana-5531	281	15	≥	≥	NOUN
cana-5531	281	16	(	(	PUNCT
cana-5531	281	17	𝑓	𝑓	DET
cana-5531	281	18	−	−	PROPN
cana-5531	281	19	𝜂𝑖	𝜂𝑖	PROPN
cana-5531	281	20	,	,	PUNCT
cana-5531	281	21	�	�	PROPN
cana-5531	281	22	̇	̇	PROPN
cana-5531	281	23	�	�	PROPN
cana-5531	282	1	𝜂𝑗𝑞𝑗	𝜂𝑗𝑞𝑗	NOUN
cana-5531	282	2	−	−	PROPN
cana-5531	282	3	�	�	PROPN
cana-5531	282	4	̇	̇	PROPN
cana-5531	282	5	�	�	NOUN
cana-5531	282	6	𝜂𝑖𝑞𝑖	𝜂𝑖𝑞𝑖	NOUN
cana-5531	282	7	)	)	PUNCT
cana-5531	282	8	.	.	PUNCT
cana-5531	283	1	where	where	SCONJ
cana-5531	283	2	𝑖	𝑖	SYM
cana-5531	283	3	=	=	NOUN
cana-5531	283	4	1	1	NUM
cana-5531	283	5	if	if	SCONJ
cana-5531	283	6	𝑗	𝑗	ADJ
cana-5531	283	7	=	=	SYM
cana-5531	283	8	2	2	NUM
cana-5531	283	9	and	and	CCONJ
cana-5531	283	10	𝑖	𝑖	SYM
cana-5531	283	11	=	=	SYM
cana-5531	283	12	2	2	NUM
cana-5531	283	13	if	if	SCONJ
cana-5531	283	14	𝑗	𝑗	ADJ
cana-5531	283	15	=	=	NOUN
cana-5531	283	16	1	1	X
cana-5531	283	17	.	.	PUNCT
cana-5531	283	18	doing	do	VERB
cana-5531	283	19	the	the	DET
cana-5531	283	20	addition	addition	NOUN
cana-5531	283	21	so	so	SCONJ
cana-5531	283	22	we	we	PRON
cana-5531	283	23	have	have	VERB
cana-5531	283	24	(	(	PUNCT
cana-5531	283	25	�	�	NOUN
cana-5531	283	26	̈	̈	SYM
cana-5531	283	27	�	�	NOUN
cana-5531	283	28	𝜂1𝑞1	𝜂1𝑞1	PUNCT
cana-5531	283	29	−	−	PROPN
cana-5531	283	30	�	�	PROPN
cana-5531	283	31	̈	̈	X
cana-5531	283	32	�	�	PROPN
cana-5531	283	33	𝜂2𝑞2	𝜂2𝑞2	SYM
cana-5531	283	34	,	,	PUNCT
cana-5531	283	35	�	�	PROPN
cana-5531	283	36	̇	̇	PROPN
cana-5531	283	37	�	�	PROPN
cana-5531	283	38	𝜂2𝑞2	𝜂2𝑞2	SYM
cana-5531	283	39	−	−	PROPN
cana-5531	283	40	�	�	PROPN
cana-5531	283	41	̇	̇	PROPN
cana-5531	283	42	�	�	PROPN
cana-5531	283	43	𝜂1𝑞1	𝜂1𝑞1	X
cana-5531	283	44	)	)	PUNCT
cana-5531	283	45	+	+	CCONJ
cana-5531	283	46	(	(	PUNCT
cana-5531	283	47	𝒢	𝒢	PROPN
cana-5531	283	48	�	�	PROPN
cana-5531	283	49	̇	̇	NOUN
cana-5531	283	50	�	�	PROPN
cana-5531	283	51	𝜂1𝑞1	𝜂1𝑞1	PUNCT
cana-5531	283	52	−	−	PROPN
cana-5531	283	53	𝒢	𝒢	PROPN
cana-5531	283	54	�	�	PROPN
cana-5531	283	55	̇	̇	PROPN
cana-5531	283	56	�	�	PROPN
cana-5531	283	57	𝜂2𝑞2	𝜂2𝑞2	NUM
cana-5531	283	58	,	,	PUNCT
cana-5531	283	59	�	�	PROPN
cana-5531	283	60	̇	̇	PROPN
cana-5531	283	61	�	�	PROPN
cana-5531	283	62	𝜂2𝑞2	𝜂2𝑞2	SYM
cana-5531	283	63	−	−	PROPN
cana-5531	283	64	�	�	PROPN
cana-5531	283	65	̇	̇	PROPN
cana-5531	283	66	�	�	PROPN
cana-5531	283	67	𝜂1𝑞1	𝜂1𝑞1	PART
cana-5531	283	68	)	)	PUNCT
cana-5531	283	69	+	+	VERB
cana-5531	283	70	𝑗𝑞1(	𝑗𝑞1(	ADJ
cana-5531	283	71	�	�	PROPN
cana-5531	283	72	̇	̇	PROPN
cana-5531	283	73	�	�	PROPN
cana-5531	283	74	𝜂2𝑞2	𝜂2𝑞2	NOUN
cana-5531	283	75	)	)	PUNCT
cana-5531	283	76	−	−	PROPN
cana-5531	283	77	𝑗𝑞1(	𝑗𝑞1(	PROPN
cana-5531	283	78	�	�	PROPN
cana-5531	283	79	̇	̇	PROPN
cana-5531	283	80	�	�	PROPN
cana-5531	283	81	𝜂1𝑞1	𝜂1𝑞1	PART
cana-5531	283	82	)	)	PUNCT
cana-5531	283	83	+	+	NUM
cana-5531	283	84	𝑗𝑞2(	𝑗𝑞2(	NOUN
cana-5531	283	85	�	�	PROPN
cana-5531	283	86	̇	̇	PROPN
cana-5531	283	87	�	�	PROPN
cana-5531	283	88	𝜂1𝑞1	𝜂1𝑞1	PART
cana-5531	283	89	)	)	PUNCT
cana-5531	283	90	−	−	PROPN
cana-5531	283	91	𝑗𝑞2(	𝑗𝑞2(	PROPN
cana-5531	283	92	�	�	PROPN
cana-5531	283	93	̇	̇	PROPN
cana-5531	283	94	�	�	PROPN
cana-5531	283	95	𝜂2𝑞2	𝜂2𝑞2	NOUN
cana-5531	283	96	)	)	PUNCT
cana-5531	283	97	≥	≥	NOUN
cana-5531	283	98	(	(	PUNCT
cana-5531	283	99	𝜂1	𝜂1	PROPN
cana-5531	283	100	−	−	PROPN
cana-5531	283	101	𝜂2	𝜂2	PROPN
cana-5531	283	102	,	,	PUNCT
cana-5531	283	103	�	�	PROPN
cana-5531	283	104	̇	̇	PROPN
cana-5531	283	105	�	�	PROPN
cana-5531	283	106	𝜂1𝑞1	𝜂1𝑞1	PUNCT
cana-5531	283	107	−	−	PROPN
cana-5531	283	108	�	�	PROPN
cana-5531	283	109	̇	̇	PROPN
cana-5531	283	110	�	�	PROPN
cana-5531	283	111	𝜂2𝑞2	𝜂2𝑞2	NOUN
cana-5531	283	112	)	)	PUNCT
cana-5531	283	113	(	(	PUNCT
cana-5531	283	114	5.15	5.15	NUM
cana-5531	283	115	)	)	PUNCT
cana-5531	283	116	using	use	VERB
cana-5531	283	117	(	(	PUNCT
cana-5531	283	118	4.6	4.6	NUM
cana-5531	283	119	)	)	PUNCT
cana-5531	283	120	and	and	CCONJ
cana-5531	283	121	integring	integre	VERB
cana-5531	283	122	,	,	PUNCT
cana-5531	283	123	the	the	DET
cana-5531	283	124	inequation	inequation	NOUN
cana-5531	283	125	(	(	PUNCT
cana-5531	283	126	5.15	5.15	NUM
cana-5531	283	127	)	)	PUNCT
cana-5531	283	128	becomes	become	VERB
cana-5531	283	129	:	:	PUNCT
cana-5531	283	130	∫	∫	PROPN
cana-5531	283	131	(	(	PUNCT
cana-5531	283	132	�	�	PROPN
cana-5531	283	133	̈	̈	X
cana-5531	283	134	�	�	NOUN
cana-5531	283	135	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	283	136	)	)	PUNCT
cana-5531	283	137	−	−	PROPN
cana-5531	283	138	�	�	PROPN
cana-5531	283	139	̈	̈	X
cana-5531	283	140	�	�	NOUN
cana-5531	283	141	𝜂2𝑞2(𝑠	𝜂2𝑞2(𝑠	NUM
cana-5531	283	142	)	)	PUNCT
cana-5531	283	143	,	,	PUNCT
cana-5531	283	144	�	�	PROPN
cana-5531	283	145	̇	̇	PROPN
cana-5531	283	146	�	�	PROPN
cana-5531	283	147	𝜂2𝑞2(𝑠	𝜂2𝑞2(𝑠	NOUN
cana-5531	283	148	)	)	PUNCT
cana-5531	283	149	−	−	PROPN
cana-5531	283	150	�	�	PROPN
cana-5531	283	151	̇	̇	PROPN
cana-5531	283	152	�	�	PROPN
cana-5531	283	153	𝜂1𝑞1(𝑠))𝑑𝑠	𝜂1𝑞1(𝑠))𝑑𝑠	PROPN
cana-5531	283	154	𝑡	𝑡	PROPN
cana-5531	283	155	0	0	PUNCT
cana-5531	284	1	+	+	NUM
cana-5531	284	2	∫	∫	PROPN
cana-5531	284	3	(	(	PUNCT
cana-5531	284	4	𝒢	𝒢	PROPN
cana-5531	284	5	�	�	PROPN
cana-5531	284	6	̇	̇	PROPN
cana-5531	284	7	�	�	PROPN
cana-5531	284	8	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	284	9	)	)	PUNCT
cana-5531	284	10	−	−	PROPN
cana-5531	285	1	𝒢	𝒢	PROPN
cana-5531	285	2	�	�	PROPN
cana-5531	285	3	̇	̇	PROPN
cana-5531	285	4	�	�	NOUN
cana-5531	285	5	𝜂2𝑞2(𝑠	𝜂2𝑞2(𝑠	NUM
cana-5531	285	6	)	)	PUNCT
cana-5531	285	7	,	,	PUNCT
cana-5531	285	8	�	�	PROPN
cana-5531	285	9	̇	̇	PROPN
cana-5531	285	10	�	�	PROPN
cana-5531	285	11	𝜂2𝑞2(𝑠	𝜂2𝑞2(𝑠	NOUN
cana-5531	285	12	)	)	PUNCT
cana-5531	285	13	−	−	PROPN
cana-5531	285	14	�	�	PROPN
cana-5531	285	15	̇	̇	PROPN
cana-5531	285	16	�	�	PROPN
cana-5531	285	17	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NUM
cana-5531	285	18	)	)	PUNCT
cana-5531	285	19	)	)	PUNCT
cana-5531	286	1	𝑑𝑠	𝑑𝑠	ADP
cana-5531	286	2	+	+	NUM
cana-5531	286	3	∫	∫	PROPN
cana-5531	286	4	𝑞1|	𝑞1|	PROPN
cana-5531	286	5	�	�	PROPN
cana-5531	286	6	̇	̇	PROPN
cana-5531	286	7	�	�	PROPN
cana-5531	286	8	𝜂2𝑞2(𝑠)|𝑑𝑠	𝜂2𝑞2(𝑠)|𝑑𝑠	PROPN
cana-5531	286	9	𝑡	𝑡	X
cana-5531	286	10	0	0	NUM
cana-5531	286	11	𝑡	𝑡	NOUN
cana-5531	286	12	0	0	PUNCT
cana-5531	287	1	+	+	NUM
cana-5531	287	2	∫	∫	PROPN
cana-5531	287	3	𝑞1|	𝑞1|	PROPN
cana-5531	287	4	�	�	PROPN
cana-5531	287	5	̇	̇	NOUN
cana-5531	287	6	�	�	PROPN
cana-5531	287	7	𝜂1𝑞1(𝑠)|𝑑𝑠	𝜂1𝑞1(𝑠)|𝑑𝑠	VERB
cana-5531	287	8	+	+	NUM
cana-5531	287	9	∫	∫	PROPN
cana-5531	287	10	𝑞2|	𝑞2|	PROPN
cana-5531	287	11	�	�	PROPN
cana-5531	287	12	̇	̇	PROPN
cana-5531	287	13	�	�	PROPN
cana-5531	287	14	𝜂1𝑞1(𝑠)|𝑑𝑠	𝜂1𝑞1(𝑠)|𝑑𝑠	VERB
cana-5531	287	15	−	−	NUM
cana-5531	287	16	∫	∫	PROPN
cana-5531	287	17	𝑞2|	𝑞2|	PROPN
cana-5531	287	18	�	�	PROPN
cana-5531	287	19	̇	̇	PROPN
cana-5531	287	20	�	�	PROPN
cana-5531	287	21	𝜂2𝑞2(𝑠)|𝑑𝑠	𝜂2𝑞2(𝑠)|𝑑𝑠	PROPN
cana-5531	287	22	𝑡	𝑡	X
cana-5531	287	23	0	0	NUM
cana-5531	287	24	𝑡	𝑡	NOUN
cana-5531	287	25	0	0	NUM
cana-5531	287	26	𝑡	𝑡	SYM
cana-5531	287	27	0	0	NUM
cana-5531	287	28	−≥	−≥	PROPN
cana-5531	287	29	∫	∫	PROPN
cana-5531	287	30	|𝜂1(𝑠	|𝜂1(𝑠	PROPN
cana-5531	287	31	)	)	PUNCT
cana-5531	287	32	−	−	PROPN
cana-5531	287	33	𝑡	𝑡	PROPN
cana-5531	287	34	0	0	NUM
cana-5531	287	35	𝜂2(𝑠)|𝑉′|	𝜂2(𝑠)|𝑉′|	PROPN
cana-5531	287	36	�	�	PROPN
cana-5531	287	37	̇	̇	PROPN
cana-5531	287	38	�	�	PROPN
cana-5531	287	39	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	287	40	)	)	PUNCT
cana-5531	287	41	−	−	PROPN
cana-5531	287	42	�	�	PROPN
cana-5531	287	43	̇	̇	PROPN
cana-5531	287	44	�	�	PROPN
cana-5531	287	45	𝜂2𝑞2(𝑠)|𝑉𝑑𝑠.	𝜂2𝑞2(𝑠)|𝑉𝑑𝑠.	PROPN
cana-5531	287	46	and	and	CCONJ
cana-5531	287	47	we	we	PRON
cana-5531	287	48	have	have	VERB
cana-5531	287	49	〈	〈	PROPN
cana-5531	287	50	�	�	PROPN
cana-5531	287	51	̈	̈	SYM
cana-5531	287	52	�	�	PROPN
cana-5531	287	53	,	,	PUNCT
cana-5531	287	54	�	�	PROPN
cana-5531	287	55	̇	̇	NOUN
cana-5531	287	56	�	�	NOUN
cana-5531	287	57	〉	〉	NOUN
cana-5531	287	58	=	=	SYM
cana-5531	287	59	1	1	NUM
cana-5531	287	60	2	2	NUM
cana-5531	287	61	〈	〈	PROPN
cana-5531	287	62	�	�	PROPN
cana-5531	287	63	̇	̇	PROPN
cana-5531	287	64	�	�	PROPN
cana-5531	287	65	,	,	PUNCT
cana-5531	287	66	�	�	PROPN
cana-5531	287	67	̇	̇	PROPN
cana-5531	287	68	�	�	PROPN
cana-5531	287	69	〉′	〉′	NOUN
cana-5531	287	70	=	=	NOUN
cana-5531	287	71	1	1	NUM
cana-5531	287	72	2	2	NUM
cana-5531	287	73	𝑑	𝑑	NOUN
cana-5531	287	74	𝑑𝑡	𝑑𝑡	ADP
cana-5531	287	75	|	|	NOUN
cana-5531	287	76	�	�	NOUN
cana-5531	287	77	̇	̇	NOUN
cana-5531	287	78	�	�	NOUN
cana-5531	287	79	|′	|′	PART
cana-5531	287	80	according	accord	VERB
cana-5531	287	81	to	to	ADP
cana-5531	287	82	this	this	DET
cana-5531	287	83	equation	equation	NOUN
cana-5531	287	84	we	we	PRON
cana-5531	287	85	find	find	VERB
cana-5531	287	86	1	1	NUM
cana-5531	287	87	2	2	NUM
cana-5531	287	88	𝑑	𝑑	NOUN
cana-5531	287	89	𝑑𝑡	𝑑𝑡	ADP
cana-5531	287	90	|	|	NOUN
cana-5531	287	91	�	�	NOUN
cana-5531	287	92	̇	̇	PROPN
cana-5531	287	93	�	�	PROPN
cana-5531	287	94	𝜂1𝑞1	𝜂1𝑞1	PUNCT
cana-5531	287	95	−	−	PROPN
cana-5531	287	96	�	�	PROPN
cana-5531	287	97	̇	̇	NOUN
cana-5531	287	98	�	�	PROPN
cana-5531	287	99	𝜂2𝑞2|𝑉	𝜂2𝑞2|𝑉	NOUN
cana-5531	287	100	2	2	NUM
cana-5531	288	1	+	+	ADP
cana-5531	288	2	𝑚𝒢|	𝑚𝒢|	PROPN
cana-5531	288	3	�	�	PROPN
cana-5531	288	4	̇	̇	PROPN
cana-5531	288	5	�	�	PROPN
cana-5531	288	6	𝜂1𝑞1	𝜂1𝑞1	PUNCT
cana-5531	288	7	−	−	PROPN
cana-5531	288	8	�	�	PROPN
cana-5531	288	9	̇	̇	NOUN
cana-5531	288	10	�	�	PROPN
cana-5531	288	11	𝜂2𝑞2|𝑉	𝜂2𝑞2|𝑉	PROPN
cana-5531	288	12	2	2	NUM
cana-5531	288	13	≤	≤	NUM
cana-5531	288	14	|𝜂1	|𝜂1	NOUN
cana-5531	288	15	−	−	PROPN
cana-5531	288	16	𝜂2||	𝜂2||	PROPN
cana-5531	288	17	�	�	PROPN
cana-5531	288	18	̇	̇	NOUN
cana-5531	288	19	�	�	PROPN
cana-5531	288	20	𝜂1𝑞1	𝜂1𝑞1	PUNCT
cana-5531	288	21	−	−	PROPN
cana-5531	288	22	�	�	PROPN
cana-5531	288	23	̇	̇	PROPN
cana-5531	288	24	�	�	PROPN
cana-5531	288	25	𝜂2𝑞2|	𝜂2𝑞2|	PROPN
cana-5531	288	26	+	+	CCONJ
cana-5531	288	27	𝐴.	𝐴.	PROPN
cana-5531	288	28	with	with	ADP
cana-5531	288	29	𝐴	𝐴	PROPN
cana-5531	288	30	=	=	SYM
cana-5531	288	31	𝑗𝑞1(	𝑗𝑞1(	PROPN
cana-5531	288	32	�	�	PROPN
cana-5531	288	33	̇	̇	PROPN
cana-5531	288	34	�	�	PROPN
cana-5531	288	35	𝜂2𝑞2	𝜂2𝑞2	NOUN
cana-5531	288	36	)	)	PUNCT
cana-5531	288	37	−	−	PROPN
cana-5531	288	38	𝑗𝑞1(	𝑗𝑞1(	PROPN
cana-5531	288	39	�	�	PROPN
cana-5531	288	40	̇	̇	PROPN
cana-5531	288	41	�	�	PROPN
cana-5531	288	42	𝜂1𝑞1	𝜂1𝑞1	PART
cana-5531	288	43	)	)	PUNCT
cana-5531	288	44	+	+	NUM
cana-5531	288	45	𝑗𝑞2(	𝑗𝑞2(	NOUN
cana-5531	288	46	�	�	PROPN
cana-5531	288	47	̇	̇	PROPN
cana-5531	288	48	�	�	PROPN
cana-5531	288	49	𝜂1𝑞1	𝜂1𝑞1	PART
cana-5531	288	50	)	)	PUNCT
cana-5531	288	51	−	−	PROPN
cana-5531	288	52	𝑗𝑞2(	𝑗𝑞2(	PROPN
cana-5531	288	53	�	�	PROPN
cana-5531	288	54	̇	̇	PROPN
cana-5531	288	55	�	�	PROPN
cana-5531	288	56	𝜂2𝑞2	𝜂2𝑞2	NOUN
cana-5531	288	57	)	)	PUNCT
cana-5531	288	58	.	.	PUNCT
cana-5531	289	1	𝐴	𝐴	PROPN
cana-5531	289	2	=	=	SYM
cana-5531	289	3	∫	∫	PROPN
cana-5531	289	4	𝜇[(𝑞2	𝜇[(𝑞2	X
cana-5531	289	5	−	−	PROPN
cana-5531	289	6	𝑞1)|	𝑞1)|	PROPN
cana-5531	289	7	�	�	PROPN
cana-5531	289	8	̇	̇	NOUN
cana-5531	289	9	�	�	PROPN
cana-5531	289	10	𝜂1𝑞1(𝑠)|	𝜂1𝑞1(𝑠)|	NOUN
cana-5531	289	11	+	+	CCONJ
cana-5531	289	12	(	(	PUNCT
cana-5531	289	13	𝑞1	𝑞1	PROPN
cana-5531	289	14	−	−	PROPN
cana-5531	289	15	𝑞2)|	𝑞2)|	PROPN
cana-5531	289	16	�	�	PROPN
cana-5531	289	17	̇	̇	PROPN
cana-5531	289	18	�	�	PROPN
cana-5531	289	19	𝜂2𝑞2(𝑠)|]𝑑𝑠.	𝜂2𝑞2(𝑠)|]𝑑𝑠.	PROPN
cana-5531	289	20	γ3	γ3	NOUN
cana-5531	289	21	𝐴	𝐴	PROPN
cana-5531	289	22	≤	≤	VERB
cana-5531	289	23	𝜇1|𝑞2	𝜇1|𝑞2	PRON
cana-5531	289	24	−	−	PROPN
cana-5531	289	25	𝑞1|𝕃2(γ3)|	𝑞1|𝕃2(γ3)|	PROPN
cana-5531	289	26	�	�	PROPN
cana-5531	289	27	̇	̇	NOUN
cana-5531	289	28	�	�	PROPN
cana-5531	289	29	𝜂1𝑞1	𝜂1𝑞1	PUNCT
cana-5531	289	30	−	−	PROPN
cana-5531	289	31	�	�	PROPN
cana-5531	289	32	̇	̇	PROPN
cana-5531	289	33	�	�	PROPN
cana-5531	289	34	𝜂2𝑞2|𝕃2(ω	𝜂2𝑞2|𝕃2(ω	PROPN
cana-5531	289	35	)	)	PUNCT
cana-5531	289	36	.	.	PUNCT
cana-5531	290	1	then	then	ADV
cana-5531	290	2	:	:	PUNCT
cana-5531	290	3	1	1	NUM
cana-5531	290	4	2	2	NUM
cana-5531	290	5	|	|	NOUN
cana-5531	290	6	�	�	NOUN
cana-5531	290	7	̇	̇	NOUN
cana-5531	290	8	�	�	PROPN
cana-5531	290	9	𝜂1𝑞1	𝜂1𝑞1	PUNCT
cana-5531	290	10	−	−	PROPN
cana-5531	290	11	�	�	PROPN
cana-5531	290	12	̇	̇	NOUN
cana-5531	290	13	�	�	PROPN
cana-5531	290	14	𝜂2𝑞2|𝑉	𝜂2𝑞2|𝑉	NOUN
cana-5531	290	15	2	2	NUM
cana-5531	290	16	+	+	NUM
cana-5531	290	17	𝑚𝒢	𝑚𝒢	NOUN
cana-5531	290	18	2	2	NUM
cana-5531	290	19	∫	∫	NOUN
cana-5531	290	20	|	|	PRON
cana-5531	290	21	�	�	PROPN
cana-5531	290	22	̇	̇	PROPN
cana-5531	290	23	�	�	PROPN
cana-5531	290	24	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	290	25	)	)	PUNCT
cana-5531	290	26	−	−	PROPN
cana-5531	290	27	�	�	PROPN
cana-5531	290	28	̇	̇	PROPN
cana-5531	290	29	�	�	PROPN
cana-5531	290	30	𝜂2𝑞2(𝑠)|𝑉	𝜂2𝑞2(𝑠)|𝑉	PROPN
cana-5531	290	31	2	2	NUM
cana-5531	290	32	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	290	33	𝑡	𝑡	PROPN
cana-5531	290	34	0	0	SYM
cana-5531	290	35	≤	≤	NUM
cana-5531	290	36	∫	∫	NOUN
cana-5531	290	37	|𝜂1	|𝜂1	NOUN
cana-5531	290	38	−	−	PROPN
cana-5531	290	39	𝜂2||	𝜂2||	PROPN
cana-5531	290	40	�	�	PROPN
cana-5531	290	41	̇	̇	PROPN
cana-5531	290	42	�	�	PROPN
cana-5531	290	43	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	290	44	)	)	PUNCT
cana-5531	290	45	−	−	PROPN
cana-5531	290	46	�	�	PROPN
cana-5531	290	47	̇	̇	NOUN
cana-5531	290	48	�	�	PROPN
cana-5531	290	49	𝜂2𝑞2(𝑠)|𝑑𝑠	𝜂2𝑞2(𝑠)|𝑑𝑠	PROPN
cana-5531	290	50	+	+	CCONJ
cana-5531	290	51	∫	∫	PROPN
cana-5531	290	52	𝐴𝑑𝑠.	𝐴𝑑𝑠.	PROPN
cana-5531	290	53	𝑡	𝑡	PROPN
cana-5531	290	54	0	0	NUM
cana-5531	290	55	𝑡	𝑡	PROPN
cana-5531	290	56	0	0	PUNCT
cana-5531	291	1	so	so	ADV
cana-5531	291	2	communications	communication	NOUN
cana-5531	291	3	on	on	ADP
cana-5531	291	4	applied	apply	VERB
cana-5531	291	5	nonlinear	nonlinear	ADJ
cana-5531	291	6	analysis	analysis	NOUN
cana-5531	291	7	issn	issn	NOUN
cana-5531	291	8	:	:	PUNCT
cana-5531	291	9	1074	1074	NUM
cana-5531	291	10	-	-	PUNCT
cana-5531	291	11	133x	133x	NUM
cana-5531	291	12	vol	vol	NOUN
cana-5531	291	13	32	32	NUM
cana-5531	291	14	no	no	NOUN
cana-5531	291	15	.	.	NOUN
cana-5531	291	16	3	3	NUM
cana-5531	291	17	(	(	PUNCT
cana-5531	291	18	2025	2025	NUM
cana-5531	291	19	)	)	PUNCT
cana-5531	291	20	977	977	NUM
cana-5531	291	21	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	291	22	1	1	NUM
cana-5531	291	23	2	2	NUM
cana-5531	291	24	|	|	NOUN
cana-5531	291	25	�	�	NOUN
cana-5531	291	26	̇	̇	NOUN
cana-5531	291	27	�	�	PROPN
cana-5531	291	28	𝜂1𝑞1	𝜂1𝑞1	PUNCT
cana-5531	291	29	−	−	PROPN
cana-5531	291	30	�	�	PROPN
cana-5531	291	31	̇	̇	NOUN
cana-5531	291	32	�	�	PROPN
cana-5531	291	33	𝜂2𝑞2|𝑉	𝜂2𝑞2|𝑉	NOUN
cana-5531	291	34	2	2	NUM
cana-5531	291	35	+	+	ADV
cana-5531	291	36	𝑚𝒢∫	𝑚𝒢∫	VERB
cana-5531	291	37	|	|	PRON
cana-5531	291	38	�	�	NOUN
cana-5531	291	39	̇	̇	PROPN
cana-5531	291	40	�	�	PROPN
cana-5531	291	41	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	291	42	)	)	PUNCT
cana-5531	291	43	−	−	PROPN
cana-5531	291	44	�	�	PROPN
cana-5531	291	45	̇	̇	PROPN
cana-5531	291	46	�	�	PROPN
cana-5531	291	47	𝜂2𝑞2(𝑠)|𝑉	𝜂2𝑞2(𝑠)|𝑉	PROPN
cana-5531	291	48	2	2	NUM
cana-5531	291	49	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	291	50	𝑡	𝑡	PROPN
cana-5531	291	51	0	0	PROPN
cana-5531	291	52	≤	≤	NUM
cana-5531	291	53	∫	∫	NOUN
cana-5531	291	54	(	(	PUNCT
cana-5531	291	55	𝑚𝒢	𝑚𝒢	PROPN
cana-5531	291	56	2	2	NUM
cana-5531	291	57	|𝜂1(𝑠	|𝜂1(𝑠	NUM
cana-5531	291	58	)	)	PUNCT
cana-5531	292	1	−	−	PROPN
cana-5531	293	1	𝜂2(𝑠)|	𝜂2(𝑠)|	NOUN
cana-5531	293	2	2	2	NUM
cana-5531	293	3	+	+	CCONJ
cana-5531	293	4	1	1	NUM
cana-5531	293	5	2𝑚𝒢	2𝑚𝒢	NUM
cana-5531	293	6	|	|	NOUN
cana-5531	293	7	�	�	NOUN
cana-5531	293	8	̇	̇	PROPN
cana-5531	293	9	�	�	PROPN
cana-5531	293	10	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	293	11	)	)	PUNCT
cana-5531	293	12	−	−	PROPN
cana-5531	293	13	�	�	PROPN
cana-5531	293	14	̇	̇	NOUN
cana-5531	293	15	�	�	PROPN
cana-5531	293	16	𝜂2𝑞2(𝑠)|	𝜂2𝑞2(𝑠)|	NOUN
cana-5531	293	17	2	2	NUM
cana-5531	293	18	)	)	PUNCT
cana-5531	293	19	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	293	20	𝑡	𝑡	PROPN
cana-5531	293	21	0	0	PUNCT
cana-5531	294	1	+	+	NUM
cana-5531	294	2	∫	∫	PROPN
cana-5531	294	3	𝜇1|𝑞2	𝜇1|𝑞2	PROPN
cana-5531	294	4	−	−	PROPN
cana-5531	294	5	𝑞1|𝕃2(γ3)|	𝑞1|𝕃2(γ3)|	PROPN
cana-5531	294	6	�	�	PROPN
cana-5531	294	7	̇	̇	PROPN
cana-5531	294	8	�	�	PROPN
cana-5531	294	9	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	294	10	)	)	PUNCT
cana-5531	294	11	−	−	PROPN
cana-5531	294	12	�	�	PROPN
cana-5531	294	13	̇	̇	PROPN
cana-5531	294	14	�	�	PROPN
cana-5531	294	15	𝜂2𝑞2(𝑠)|𝕃2(ω)𝑑𝑠.	𝜂2𝑞2(𝑠)|𝕃2(ω)𝑑𝑠.	NOUN
cana-5531	294	16	𝑡	𝑡	PROPN
cana-5531	294	17	0	0	NUM
cana-5531	294	18	(	(	PUNCT
cana-5531	294	19	5.16	5.16	NUM
cana-5531	294	20	)	)	PUNCT
cana-5531	294	21	but	but	CCONJ
cana-5531	294	22	(	(	PUNCT
cana-5531	294	23	𝑎𝑏	𝑎𝑏	NOUN
cana-5531	294	24	≤	≤	ADJ
cana-5531	294	25	𝑚𝒢	𝑚𝒢	PROPN
cana-5531	294	26	2	2	NUM
cana-5531	294	27	𝑎2	𝑎2	NOUN
cana-5531	294	28	+	+	CCONJ
cana-5531	294	29	1	1	NUM
cana-5531	294	30	2𝑚𝒢	2𝑚𝒢	NUM
cana-5531	294	31	𝑏2	𝑏2	NOUN
cana-5531	294	32	)	)	PUNCT
cana-5531	294	33	then	then	ADV
cana-5531	294	34	:	:	PUNCT
cana-5531	294	35	1	1	NUM
cana-5531	294	36	2	2	NUM
cana-5531	294	37	|	|	NOUN
cana-5531	294	38	�	�	NOUN
cana-5531	294	39	̇	̇	NOUN
cana-5531	294	40	�	�	PROPN
cana-5531	294	41	𝜂1𝑞1	𝜂1𝑞1	PUNCT
cana-5531	294	42	−	−	PROPN
cana-5531	294	43	�	�	PROPN
cana-5531	294	44	̇	̇	NOUN
cana-5531	294	45	�	�	PROPN
cana-5531	294	46	𝜂2𝑞2|𝑉	𝜂2𝑞2|𝑉	NOUN
cana-5531	294	47	2	2	NUM
cana-5531	294	48	+	+	ADV
cana-5531	294	49	𝑚𝒢∫	𝑚𝒢∫	VERB
cana-5531	294	50	|	|	PRON
cana-5531	294	51	�	�	NOUN
cana-5531	294	52	̇	̇	PROPN
cana-5531	294	53	�	�	PROPN
cana-5531	294	54	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	294	55	)	)	PUNCT
cana-5531	294	56	−	−	PROPN
cana-5531	294	57	�	�	PROPN
cana-5531	294	58	̇	̇	PROPN
cana-5531	294	59	�	�	PROPN
cana-5531	294	60	𝜂2𝑞2(𝑠)|𝑉	𝜂2𝑞2(𝑠)|𝑉	PROPN
cana-5531	294	61	2	2	NUM
cana-5531	294	62	𝑑𝑠	𝑑𝑠	ADP
cana-5531	294	63	1	1	NUM
cana-5531	294	64	0	0	NUM
cana-5531	294	65	≤	≤	NUM
cana-5531	294	66	∫	∫	NOUN
cana-5531	294	67	(	(	PUNCT
cana-5531	294	68	𝑚𝒢	𝑚𝒢	ADJ
cana-5531	294	69	2	2	NUM
cana-5531	294	70	|	|	NOUN
cana-5531	294	71	�	�	NOUN
cana-5531	294	72	̇	̇	NOUN
cana-5531	294	73	�	�	NOUN
cana-5531	294	74	𝜂1𝑞2(𝑠	𝜂1𝑞2(𝑠	PART
cana-5531	294	75	)	)	PUNCT
cana-5531	294	76	−	−	PROPN
cana-5531	294	77	�	�	PROPN
cana-5531	294	78	̇	̇	NOUN
cana-5531	294	79	�	�	PROPN
cana-5531	294	80	𝜂2𝑞2|𝑉	𝜂2𝑞2|𝑉	NOUN
cana-5531	294	81	2	2	NUM
cana-5531	294	82	+	+	SYM
cana-5531	294	83	1	1	NUM
cana-5531	294	84	2𝑚𝒢	2𝑚𝒢	NUM
cana-5531	294	85	|𝜂1(𝑠	|𝜂1(𝑠	PROPN
cana-5531	294	86	)	)	PUNCT
cana-5531	294	87	−	−	NOUN
cana-5531	294	88	𝜂2(𝑠)|𝑉′	𝜂2(𝑠)|𝑉′	PROPN
cana-5531	294	89	2	2	NUM
cana-5531	294	90	)	)	PUNCT
cana-5531	294	91	𝑑𝑠.	𝑑𝑠.	NOUN
cana-5531	294	92	𝑡	𝑡	X
cana-5531	294	93	0	0	NUM
cana-5531	294	94	(	(	PUNCT
cana-5531	294	95	5.17	5.17	NUM
cana-5531	294	96	)	)	PUNCT
cana-5531	294	97	from	from	ADP
cana-5531	294	98	which	which	PRON
cana-5531	294	99	:	:	PUNCT
cana-5531	294	100	1	1	NUM
cana-5531	294	101	2	2	NUM
cana-5531	294	102	|	|	NOUN
cana-5531	294	103	�	�	NOUN
cana-5531	294	104	̇	̇	NOUN
cana-5531	294	105	�	�	PROPN
cana-5531	294	106	𝜂1𝑞1	𝜂1𝑞1	PUNCT
cana-5531	294	107	−	−	PROPN
cana-5531	294	108	�	�	PROPN
cana-5531	294	109	̇	̇	NOUN
cana-5531	294	110	�	�	PROPN
cana-5531	294	111	𝜂2𝑞2|𝑉	𝜂2𝑞2|𝑉	NOUN
cana-5531	294	112	2	2	NUM
cana-5531	294	113	+	+	NUM
cana-5531	294	114	𝑚𝒢	𝑚𝒢	NOUN
cana-5531	294	115	2	2	NUM
cana-5531	294	116	∫	∫	NOUN
cana-5531	294	117	|	|	PRON
cana-5531	294	118	�	�	PROPN
cana-5531	294	119	̇	̇	PROPN
cana-5531	294	120	�	�	PROPN
cana-5531	294	121	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	294	122	)	)	PUNCT
cana-5531	294	123	−	−	PROPN
cana-5531	294	124	�	�	PROPN
cana-5531	294	125	̇	̇	PROPN
cana-5531	294	126	�	�	PROPN
cana-5531	294	127	𝜂2𝑞2(𝑠)|𝑉	𝜂2𝑞2(𝑠)|𝑉	PROPN
cana-5531	294	128	2	2	NUM
cana-5531	294	129	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	294	130	𝑡	𝑡	PROPN
cana-5531	294	131	0	0	SYM
cana-5531	294	132	≤	≤	NUM
cana-5531	294	133	1	1	NUM
cana-5531	294	134	2𝑚𝒢	2𝑚𝒢	NUM
cana-5531	294	135	∫	∫	NOUN
cana-5531	294	136	|𝜂1(𝑠	|𝜂1(𝑠	PROPN
cana-5531	294	137	)	)	PUNCT
cana-5531	294	138	−	−	ADP
cana-5531	294	139	𝜂2(𝑠)|𝑉′	𝜂2(𝑠)|𝑉′	PROPN
cana-5531	294	140	2	2	NUM
cana-5531	294	141	𝑑𝑠	𝑑𝑠	ADP
cana-5531	294	142	𝑡	𝑡	X
cana-5531	294	143	0	0	PUNCT
cana-5531	294	144	(	(	PUNCT
cana-5531	294	145	5.18	5.18	NUM
cana-5531	294	146	)	)	PUNCT
cana-5531	294	147	it	it	PRON
cana-5531	294	148	comes	come	VERB
cana-5531	294	149	{	{	PUNCT
cana-5531	294	150	|	|	NOUN
cana-5531	294	151	�	�	NOUN
cana-5531	294	152	̇	̇	NOUN
cana-5531	294	153	�	�	PROPN
cana-5531	294	154	𝜂1𝑞1	𝜂1𝑞1	PUNCT
cana-5531	294	155	−	−	PROPN
cana-5531	294	156	�	�	PROPN
cana-5531	294	157	̇	̇	NOUN
cana-5531	294	158	�	�	PROPN
cana-5531	294	159	𝜂2𝑞2|𝑉	𝜂2𝑞2|𝑉	PROPN
cana-5531	294	160	2	2	NUM
cana-5531	294	161	≤	≤	NOUN
cana-5531	294	162	𝑐	𝑐	PROPN
cana-5531	294	163	∫	∫	PROPN
cana-5531	294	164	|𝜂1(𝑠	|𝜂1(𝑠	PROPN
cana-5531	294	165	)	)	PUNCT
cana-5531	294	166	−	−	ADP
cana-5531	295	1	𝜂2(𝑠)|𝑉′	𝜂2(𝑠)|𝑉′	PROPN
cana-5531	295	2	2	2	NUM
cana-5531	295	3	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	295	4	1	1	NUM
cana-5531	295	5	0	0	NUM
cana-5531	295	6	∫	∫	PROPN
cana-5531	295	7	|	|	PROPN
cana-5531	295	8	�	�	PROPN
cana-5531	295	9	̇	̇	PROPN
cana-5531	295	10	�	�	PROPN
cana-5531	295	11	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	295	12	)	)	PUNCT
cana-5531	295	13	−	−	PROPN
cana-5531	295	14	�	�	PROPN
cana-5531	295	15	̇	̇	PROPN
cana-5531	295	16	�	�	PROPN
cana-5531	295	17	𝜂2𝑞2(𝑠)|𝑉	𝜂2𝑞2(𝑠)|𝑉	PROPN
cana-5531	295	18	2𝑡	2𝑡	NOUN
cana-5531	295	19	0	0	NUM
cana-5531	295	20	𝑑𝑠	𝑑𝑠	X
cana-5531	295	21	≤	≤	PROPN
cana-5531	295	22	𝑐	𝑐	PROPN
cana-5531	295	23	∫	∫	PROPN
cana-5531	295	24	|𝜂1(𝑠	|𝜂1(𝑠	PROPN
cana-5531	295	25	)	)	PUNCT
cana-5531	295	26	−	−	ADP
cana-5531	295	27	𝜂2(𝑠)|𝑉′	𝜂2(𝑠)|𝑉′	PROPN
cana-5531	295	28	2	2	NUM
cana-5531	295	29	𝑑𝑠	𝑑𝑠	ADP
cana-5531	295	30	𝑡	𝑡	X
cana-5531	295	31	0	0	PUNCT
cana-5531	295	32	(	(	PUNCT
cana-5531	295	33	5.19	5.19	NUM
cana-5531	295	34	)	)	PUNCT
cana-5531	295	35	on	on	ADP
cana-5531	295	36	the	the	DET
cana-5531	295	37	other	other	ADJ
cana-5531	295	38	part	part	NOUN
cana-5531	295	39	of	of	ADP
cana-5531	295	40	𝑢1(0	𝑢1(0	NOUN
cana-5531	295	41	)	)	PUNCT
cana-5531	295	42	=	=	SYM
cana-5531	295	43	𝑢2(0	𝑢2(0	ADJ
cana-5531	295	44	)	)	PUNCT
cana-5531	295	45	=	=	SYM
cana-5531	295	46	𝑢0	𝑢0	PROPN
cana-5531	295	47	then	then	ADV
cana-5531	295	48	:	:	PUNCT
cana-5531	295	49	|𝑢𝜂1𝑞1(𝑠	|𝑢𝜂1𝑞1(𝑠	PROPN
cana-5531	295	50	)	)	PUNCT
cana-5531	295	51	−	−	PROPN
cana-5531	296	1	𝑢𝜂2𝑞2(𝑠)|𝑉	𝑢𝜂2𝑞2(𝑠)|𝑉	PROPN
cana-5531	296	2	2	2	NUM
cana-5531	296	3	≤	≤	NUM
cana-5531	296	4	∫	∫	PROPN
cana-5531	296	5	|	|	PROPN
cana-5531	296	6	�	�	PROPN
cana-5531	296	7	̇	̇	PROPN
cana-5531	296	8	�	�	PROPN
cana-5531	296	9	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	296	10	)	)	PUNCT
cana-5531	296	11	−	−	PROPN
cana-5531	296	12	�	�	PROPN
cana-5531	296	13	̇	̇	PROPN
cana-5531	296	14	�	�	PROPN
cana-5531	296	15	𝜂2𝑞2(𝑠)|𝑉𝑑𝑠	𝜂2𝑞2(𝑠)|𝑉𝑑𝑠	NOUN
cana-5531	296	16	𝑡	𝑡	X
cana-5531	296	17	0	0	NUM
cana-5531	296	18	(	(	PUNCT
cana-5531	296	19	5.20	5.20	NUM
cana-5531	296	20	)	)	PUNCT
cana-5531	296	21	and	and	CCONJ
cana-5531	296	22	:	:	PUNCT
cana-5531	296	23	|𝑢𝜂1𝑞1(𝑠	|𝑢𝜂1𝑞1(𝑠	PROPN
cana-5531	296	24	)	)	PUNCT
cana-5531	296	25	−	−	PROPN
cana-5531	297	1	𝑢𝜂2𝑞2(𝑠)|𝑉	𝑢𝜂2𝑞2(𝑠)|𝑉	PROPN
cana-5531	297	2	2	2	NUM
cana-5531	297	3	≤	≤	NUM
cana-5531	297	4	∫	∫	PROPN
cana-5531	297	5	|	|	PROPN
cana-5531	297	6	�	�	PROPN
cana-5531	297	7	̇	̇	PROPN
cana-5531	297	8	�	�	PROPN
cana-5531	297	9	𝜂1𝑞1(𝑠	𝜂1𝑞1(𝑠	NOUN
cana-5531	297	10	)	)	PUNCT
cana-5531	297	11	−	−	PROPN
cana-5531	297	12	�	�	PROPN
cana-5531	297	13	̇	̇	PROPN
cana-5531	297	14	�	�	PROPN
cana-5531	297	15	𝜂2𝑞2(𝑠)|𝑉	𝜂2𝑞2(𝑠)|𝑉	PROPN
cana-5531	297	16	2	2	NUM
cana-5531	297	17	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	297	18	𝑡	𝑡	X
cana-5531	297	19	0	0	PUNCT
cana-5531	297	20	(	(	PUNCT
cana-5531	297	21	5.21	5.21	NUM
cana-5531	297	22	)	)	PUNCT
cana-5531	297	23	and	and	CCONJ
cana-5531	297	24	so	so	ADV
cana-5531	297	25	:	:	PUNCT
cana-5531	297	26	|𝑢𝜂1𝑞1(𝑠	|𝑢𝜂1𝑞1(𝑠	PROPN
cana-5531	297	27	)	)	PUNCT
cana-5531	297	28	−	−	PROPN
cana-5531	298	1	𝑢𝜂2𝑞2(𝑠)|𝑉	𝑢𝜂2𝑞2(𝑠)|𝑉	PROPN
cana-5531	298	2	2	2	NUM
cana-5531	298	3	≤	≤	NOUN
cana-5531	298	4	𝑐	𝑐	PROPN
cana-5531	298	5	∫	∫	PROPN
cana-5531	298	6	|𝜂1(𝑠	|𝜂1(𝑠	PROPN
cana-5531	298	7	)	)	PUNCT
cana-5531	298	8	−	−	ADP
cana-5531	298	9	𝜂2(𝑠)|𝑉′	𝜂2(𝑠)|𝑉′	PROPN
cana-5531	298	10	2	2	NUM
cana-5531	298	11	𝑑𝑠	𝑑𝑠	ADP
cana-5531	298	12	𝑡	𝑡	X
cana-5531	298	13	0	0	PUNCT
cana-5531	298	14	(	(	PUNCT
cana-5531	298	15	5.22	5.22	NUM
cana-5531	298	16	)	)	PUNCT
cana-5531	298	17	hence	hence	ADV
cana-5531	298	18	it	it	PRON
cana-5531	298	19	result	result	VERB
cana-5531	298	20	(	(	PUNCT
cana-5531	298	21	5.14	5.14	NUM
cana-5531	298	22	)	)	PUNCT
cana-5531	298	23	.	.	PUNCT
cana-5531	299	1	now	now	ADV
cana-5531	299	2	,	,	PUNCT
cana-5531	299	3	let	let	VERB
cana-5531	299	4	the	the	DET
cana-5531	299	5	map	map	NOUN
cana-5531	299	6	ψt	ψt	VERB
cana-5531	299	7	:	:	PUNCT
cana-5531	299	8	c+	c+	NOUN
cana-5531	299	9	→c+	→c+	VERB
cana-5531	299	10	be	be	AUX
cana-5531	299	11	defined	define	VERB
cana-5531	299	12	by	by	ADP
cana-5531	299	13	𝜓𝑡(𝑞	𝜓𝑡(𝑞	NOUN
cana-5531	299	14	)	)	PUNCT
cana-5531	299	15	=	=	SYM
cana-5531	300	1	|𝑅𝜎𝜈	|𝑅𝜎𝜈	PROPN
cana-5531	300	2	(	(	PUNCT
cana-5531	300	3	𝑢𝜉𝜂𝑞(𝑡))|	𝑢𝜉𝜂𝑞(𝑡))|	PROPN
cana-5531	300	4	.	.	PUNCT
cana-5531	301	1	lemma	lemma	PROPN
cana-5531	301	2	5.6	5.6	NUM
cana-5531	301	3	there	there	PRON
cana-5531	301	4	exists	exist	VERB
cana-5531	301	5	a	a	DET
cana-5531	301	6	constant	constant	ADJ
cana-5531	301	7	µ1	µ1	NOUN
cana-5531	301	8	>	>	X
cana-5531	301	9	0	0	NUM
cana-5531	302	1	such	such	ADJ
cana-5531	302	2	that	that	SCONJ
cana-5531	302	3	the	the	DET
cana-5531	302	4	mapping	mapping	NOUN
cana-5531	302	5	ψt	ψt	NOUN
cana-5531	302	6	has	have	VERB
cana-5531	302	7	a	a	DET
cana-5531	302	8	unique	unique	ADJ
cana-5531	302	9	fixed	fix	VERB
cana-5531	302	10	point	point	NOUN
cana-5531	302	11	q∗	q∗	NOUN
cana-5531	302	12	and	and	CCONJ
cana-5531	302	13	𝑢𝜉𝜂𝑞∗	𝑢𝜉𝜂𝑞∗	NOUN
cana-5531	302	14	(	(	PUNCT
cana-5531	302	15	t	t	NOUN
cana-5531	302	16	)	)	PUNCT
cana-5531	302	17	is	be	AUX
cana-5531	302	18	a	a	DET
cana-5531	302	19	unique	unique	ADJ
cana-5531	302	20	solution	solution	NOUN
cana-5531	302	21	of	of	ADP
cana-5531	302	22	the	the	DET
cana-5531	302	23	inequality	inequality	NOUN
cana-5531	302	24	(	(	PUNCT
cana-5531	302	25	5.3	5.3	NUM
cana-5531	302	26	)	)	PUNCT
cana-5531	302	27	if	if	SCONJ
cana-5531	302	28	‖𝜇‖𝕃∞(γ3	‖𝜇‖𝕃∞(γ3	NOUN
cana-5531	302	29	)	)	PUNCT
cana-5531	302	30	<	<	X
cana-5531	302	31	𝜇1	𝜇1	ADJ
cana-5531	302	32	proof	proof	NOUN
cana-5531	302	33	.	.	PUNCT
cana-5531	303	1	let	let	VERB
cana-5531	303	2	q1	q1	PROPN
cana-5531	303	3	,	,	PUNCT
cana-5531	303	4	q2	q2	PROPN
cana-5531	303	5	∈	∈	PROPN
cana-5531	303	6	c+	c+	NOUN
cana-5531	303	7	.	.	PUNCT
cana-5531	304	1	using	use	VERB
cana-5531	304	2	(	(	PUNCT
cana-5531	304	3	4.16	4.16	NUM
cana-5531	304	4	)	)	PUNCT
cana-5531	304	5	,	,	PUNCT
cana-5531	304	6	it	it	PRON
cana-5531	304	7	follows	follow	VERB
cana-5531	304	8	that	that	SCONJ
cana-5531	304	9	there	there	PRON
cana-5531	304	10	exists	exist	VERB
cana-5531	304	11	a	a	DET
cana-5531	304	12	constant	constant	ADJ
cana-5531	304	13	c0	c0	NOUN
cana-5531	304	14	>	>	X
cana-5531	304	15	0	0	NUM
cana-5531	304	16	such	such	ADJ
cana-5531	304	17	that	that	SCONJ
cana-5531	304	18	communications	communication	NOUN
cana-5531	304	19	on	on	ADP
cana-5531	304	20	applied	apply	VERB
cana-5531	304	21	nonlinear	nonlinear	ADJ
cana-5531	304	22	analysis	analysis	NOUN
cana-5531	304	23	issn	issn	NOUN
cana-5531	304	24	:	:	PUNCT
cana-5531	304	25	1074	1074	NUM
cana-5531	304	26	-	-	PUNCT
cana-5531	304	27	133x	133x	NUM
cana-5531	304	28	vol	vol	NOUN
cana-5531	304	29	32	32	NUM
cana-5531	304	30	no	no	NOUN
cana-5531	304	31	.	.	NOUN
cana-5531	304	32	3	3	NUM
cana-5531	304	33	(	(	PUNCT
cana-5531	304	34	2025	2025	NUM
cana-5531	304	35	)	)	PUNCT
cana-5531	304	36	978	978	NUM
cana-5531	304	37	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	304	38	‖𝜓𝑡(𝑞1	‖𝜓𝑡(𝑞1	PROPN
cana-5531	304	39	)	)	PUNCT
cana-5531	305	1	−	−	PROPN
cana-5531	305	2	𝜓𝑡(𝑞2)‖𝕃2(γ3	𝜓𝑡(𝑞2)‖𝕃2(γ3	NOUN
cana-5531	305	3	)	)	PUNCT
cana-5531	305	4	≤	≤	NUM
cana-5531	305	5	𝑐0‖𝜎𝜈	𝑐0‖𝜎𝜈	NOUN
cana-5531	305	6	(	(	PUNCT
cana-5531	305	7	𝑢𝜉𝜂𝑞1(𝑡	𝑢𝜉𝜂𝑞1(𝑡	NOUN
cana-5531	305	8	)	)	PUNCT
cana-5531	305	9	)	)	PUNCT
cana-5531	306	1	−	−	ADP
cana-5531	306	2	𝜎𝜈	𝜎𝜈	X
cana-5531	306	3	(	(	PUNCT
cana-5531	306	4	𝑢𝜉𝜂𝑞2(𝑡))‖𝐻−	𝑢𝜉𝜂𝑞2(𝑡))‖𝐻−	PROPN
cana-5531	306	5	1	1	NUM
cana-5531	306	6	2(γ	2(γ	NUM
cana-5531	306	7	)	)	PUNCT
cana-5531	306	8	.	.	PUNCT
cana-5531	307	1	(	(	PUNCT
cana-5531	307	2	5.23	5.23	NUM
cana-5531	307	3	)	)	PUNCT
cana-5531	307	4	moreover	moreover	ADV
cana-5531	307	5	using	use	VERB
cana-5531	307	6	(	(	PUNCT
cana-5531	307	7	4.5	4.5	NUM
cana-5531	307	8	)	)	PUNCT
cana-5531	307	9	(	(	PUNCT
cana-5531	307	10	b	b	X
cana-5531	307	11	)	)	PUNCT
cana-5531	307	12	yields	yield	NOUN
cana-5531	307	13	‖𝜎𝜈	‖𝜎𝜈	NUM
cana-5531	307	14	(	(	PUNCT
cana-5531	307	15	𝑢𝜉𝜂𝑞1(𝑡	𝑢𝜉𝜂𝑞1(𝑡	NOUN
cana-5531	307	16	)	)	PUNCT
cana-5531	307	17	)	)	PUNCT
cana-5531	308	1	−	−	ADP
cana-5531	308	2	𝜎𝜈	𝜎𝜈	X
cana-5531	308	3	(	(	PUNCT
cana-5531	308	4	𝑢𝜉𝜂𝑞2(𝑡))‖𝐻−	𝑢𝜉𝜂𝑞2(𝑡))‖𝐻−	PROPN
cana-5531	308	5	1	1	NUM
cana-5531	308	6	2(γ	2(γ	NUM
cana-5531	308	7	)	)	PUNCT
cana-5531	308	8	≤	≤	NUM
cana-5531	308	9	𝑀‖𝑢𝜉𝜂𝑞1(𝑡	𝑀‖𝑢𝜉𝜂𝑞1(𝑡	NOUN
cana-5531	308	10	)	)	PUNCT
cana-5531	308	11	−	−	NOUN
cana-5531	308	12	𝑢𝜉𝜂𝑞2(𝑡)‖𝑉	𝑢𝜉𝜂𝑞2(𝑡)‖𝑉	NOUN
cana-5531	308	13	.	.	PUNCT
cana-5531	309	1	(	(	PUNCT
cana-5531	309	2	5.24	5.24	NUM
cana-5531	309	3	)	)	PUNCT
cana-5531	309	4	using	use	VERB
cana-5531	309	5	(	(	PUNCT
cana-5531	309	6	4.2	4.2	NUM
cana-5531	309	7	)	)	PUNCT
cana-5531	309	8	,	,	PUNCT
cana-5531	309	9	(	(	PUNCT
cana-5531	309	10	4.5	4.5	NUM
cana-5531	309	11	)	)	PUNCT
cana-5531	309	12	(	(	PUNCT
cana-5531	309	13	c	c	NOUN
cana-5531	309	14	)	)	PUNCT
cana-5531	309	15	,	,	PUNCT
cana-5531	309	16	(	(	PUNCT
cana-5531	309	17	4.13	4.13	NUM
cana-5531	309	18	)	)	PUNCT
cana-5531	309	19	(	(	PUNCT
cana-5531	309	20	c	c	X
cana-5531	309	21	)	)	PUNCT
cana-5531	309	22	and	and	CCONJ
cana-5531	309	23	the	the	DET
cana-5531	309	24	properties	property	NOUN
cana-5531	309	25	of	of	ADP
cana-5531	309	26	rν	rν	PROPN
cana-5531	309	27	and	and	CCONJ
cana-5531	309	28	rτ	rτ	NOUN
cana-5531	309	29	to	to	PART
cana-5531	309	30	find	find	VERB
cana-5531	309	31	after	after	ADP
cana-5531	309	32	some	some	DET
cana-5531	309	33	calculus	calculus	NOUN
cana-5531	309	34	algebra	algebra	NOUN
cana-5531	309	35	that	that	PRON
cana-5531	309	36	‖𝑢𝜉𝜂𝑞1(𝑡	‖𝑢𝜉𝜂𝑞1(𝑡	VERB
cana-5531	309	37	)	)	PUNCT
cana-5531	309	38	−	−	NOUN
cana-5531	309	39	𝑢𝜉𝜂𝑞2(𝑡)‖𝑉	𝑢𝜉𝜂𝑞2(𝑡)‖𝑉	VERB
cana-5531	309	40	≤	≤	PUNCT
cana-5531	309	41	‖𝜇‖𝕃∞(γ3	‖𝜇‖𝕃∞(γ3	PROPN
cana-5531	309	42	)	)	PUNCT
cana-5531	309	43	𝑑ω	𝑑ω	NOUN
cana-5531	309	44	𝑚	𝑚	ADP
cana-5531	309	45	‖𝑞1	‖𝑞1	PUNCT
cana-5531	309	46	−	−	NUM
cana-5531	309	47	𝑞2‖𝕃2(γ3	𝑞2‖𝕃2(γ3	NOUN
cana-5531	309	48	)	)	PUNCT
cana-5531	309	49	.	.	PUNCT
cana-5531	310	1	(	(	PUNCT
cana-5531	310	2	5.25	5.25	NUM
cana-5531	310	3	)	)	PUNCT
cana-5531	310	4	hence	hence	ADV
cana-5531	310	5	,	,	PUNCT
cana-5531	310	6	taking	take	VERB
cana-5531	310	7	into	into	ADP
cana-5531	310	8	account	account	NOUN
cana-5531	310	9	(	(	PUNCT
cana-5531	310	10	4.12	4.12	NUM
cana-5531	310	11	)	)	PUNCT
cana-5531	310	12	,	,	PUNCT
cana-5531	310	13	combining	combine	VERB
cana-5531	310	14	(	(	PUNCT
cana-5531	310	15	5.23	5.23	NUM
cana-5531	310	16	)	)	PUNCT
cana-5531	310	17	,	,	PUNCT
cana-5531	310	18	(	(	PUNCT
cana-5531	310	19	5.24	5.24	NUM
cana-5531	310	20	)	)	PUNCT
cana-5531	310	21	and	and	CCONJ
cana-5531	310	22	(	(	PUNCT
cana-5531	310	23	5.25	5.25	NUM
cana-5531	310	24	)	)	PUNCT
cana-5531	310	25	to	to	PART
cana-5531	310	26	deduce	deduce	VERB
cana-5531	310	27	that	that	DET
cana-5531	310	28	‖𝜓𝑡(𝑞1	‖𝜓𝑡(𝑞1	NOUN
cana-5531	310	29	)	)	PUNCT
cana-5531	311	1	−	−	PROPN
cana-5531	311	2	𝜓𝑡(𝑞2)‖𝕃2(γ3	𝜓𝑡(𝑞2)‖𝕃2(γ3	NOUN
cana-5531	311	3	)	)	PUNCT
cana-5531	311	4	≤	≤	NUM
cana-5531	311	5	‖𝜇‖𝕃∞(γ3	‖𝜇‖𝕃∞(γ3	PROPN
cana-5531	311	6	)	)	PUNCT
cana-5531	311	7	𝑐0𝑀𝑑ω	𝑐0𝑀𝑑ω	NOUN
cana-5531	311	8	𝑚	𝑚	ADP
cana-5531	311	9	‖𝑞1	‖𝑞1	PUNCT
cana-5531	311	10	−	−	NUM
cana-5531	311	11	𝑞2‖𝕃2(γ3	𝑞2‖𝕃2(γ3	NOUN
cana-5531	311	12	)	)	PUNCT
cana-5531	311	13	.	.	PUNCT
cana-5531	312	1	take	take	VERB
cana-5531	312	2	𝜇1	𝜇1	NOUN
cana-5531	312	3	=	=	PUNCT
cana-5531	312	4	𝑚	𝑚	PROPN
cana-5531	312	5	𝑐0𝑀𝑑ω⁄	𝑐0𝑀𝑑ω⁄	PROPN
cana-5531	312	6	,	,	PUNCT
cana-5531	312	7	then	then	ADV
cana-5531	312	8	this	this	DET
cana-5531	312	9	inequality	inequality	NOUN
cana-5531	312	10	shows	show	VERB
cana-5531	312	11	that	that	SCONJ
cana-5531	312	12	if	if	SCONJ
cana-5531	312	13	‖𝜇‖𝕃∞(γ3	‖𝜇‖𝕃∞(γ3	NOUN
cana-5531	312	14	)	)	PUNCT
cana-5531	312	15	<	<	X
cana-5531	312	16	𝜇1	𝜇1	PROPN
cana-5531	312	17	,	,	PUNCT
cana-5531	312	18	ψ	ψ	NOUN
cana-5531	312	19	is	be	AUX
cana-5531	312	20	a	a	DET
cana-5531	312	21	contraction	contraction	NOUN
cana-5531	312	22	;	;	PUNCT
cana-5531	312	23	thus	thus	ADV
cana-5531	312	24	it	it	PRON
cana-5531	312	25	has	have	AUX
cana-5531	312	26	unique	unique	ADJ
cana-5531	312	27	fixed	fix	VERB
cana-5531	312	28	point	point	NOUN
cana-5531	312	29	q∗	q∗	NOUN
cana-5531	312	30	and	and	CCONJ
cana-5531	312	31	uηq∗	uηq∗	NOUN
cana-5531	312	32	(	(	PUNCT
cana-5531	312	33	t	t	NOUN
cana-5531	312	34	)	)	PUNCT
cana-5531	312	35	is	be	AUX
cana-5531	312	36	a	a	DET
cana-5531	312	37	unique	unique	ADJ
cana-5531	312	38	solution	solution	NOUN
cana-5531	312	39	of	of	ADP
cana-5531	312	40	(	(	PUNCT
cana-5531	312	41	5.3	5.3	NUM
cana-5531	312	42	)	)	PUNCT
cana-5531	312	43	.	.	PUNCT
cana-5531	313	1	denote	denote	VERB
cana-5531	313	2	uξηq∗	uξηq∗	ADJ
cana-5531	313	3	=	=	PRON
cana-5531	313	4	uη.now	uη.now	PROPN
cana-5531	313	5	shall	shall	AUX
cana-5531	313	6	see	see	VERB
cana-5531	313	7	that	that	DET
cana-5531	313	8	uξη	uξη	PROPN
cana-5531	313	9	∈	∈	PROPN
cana-5531	313	10	c	c	X
cana-5531	313	11	(	(	PUNCT
cana-5531	313	12	[	[	X
cana-5531	313	13	0.t	0.t	X
cana-5531	313	14	]	]	X
cana-5531	313	15	;	;	PUNCT
cana-5531	313	16	v	v	NOUN
cana-5531	313	17	)	)	PUNCT
cana-5531	313	18	.	.	PUNCT
cana-5531	314	1	indeed	indeed	ADV
cana-5531	314	2	,	,	PUNCT
cana-5531	314	3	let	let	VERB
cana-5531	314	4	t1	t1	NOUN
cana-5531	314	5	,	,	PUNCT
cana-5531	314	6	t2	t2	PROPN
cana-5531	314	7	∈	∈	PROPN
cana-5531	315	1	[	[	X
cana-5531	315	2	0	0	NUM
cana-5531	315	3	,	,	PUNCT
cana-5531	315	4	t	t	PROPN
cana-5531	315	5	]	]	PUNCT
cana-5531	315	6	.	.	PUNCT
cana-5531	316	1	taking	take	VERB
cana-5531	316	2	𝜐	𝜐	PROPN
cana-5531	316	3	=	=	SYM
cana-5531	316	4	𝑢𝜉𝜂(𝑡2	𝑢𝜉𝜂(𝑡2	X
cana-5531	316	5	)	)	PUNCT
cana-5531	316	6	in	in	ADP
cana-5531	316	7	(	(	PUNCT
cana-5531	316	8	5.3	5.3	NUM
cana-5531	316	9	)	)	PUNCT
cana-5531	316	10	written	write	VERB
cana-5531	316	11	for	for	ADP
cana-5531	316	12	𝑡	𝑡	PROPN
cana-5531	316	13	=	=	SYM
cana-5531	316	14	𝑡1	𝑡1	NOUN
cana-5531	316	15	and	and	CCONJ
cana-5531	316	16	then	then	ADV
cana-5531	316	17	𝜐	𝜐	PROPN
cana-5531	316	18	=	=	PUNCT
cana-5531	316	19	𝑢𝜉𝜂(𝑡1	𝑢𝜉𝜂(𝑡1	PROPN
cana-5531	316	20	)	)	PUNCT
cana-5531	316	21	in	in	ADP
cana-5531	316	22	the	the	DET
cana-5531	316	23	same	same	ADJ
cana-5531	316	24	inequality	inequality	NOUN
cana-5531	316	25	written	write	VERB
cana-5531	316	26	for	for	ADP
cana-5531	316	27	𝑡	𝑡	PROPN
cana-5531	316	28	=	=	PROPN
cana-5531	316	29	𝑡2	𝑡2	PROPN
cana-5531	316	30	using	use	VERB
cana-5531	316	31	(	(	PUNCT
cana-5531	316	32	4.5	4.5	NUM
cana-5531	316	33	)	)	PUNCT
cana-5531	316	34	(	(	PUNCT
cana-5531	316	35	c	c	NOUN
cana-5531	316	36	)	)	PUNCT
cana-5531	316	37	,	,	PUNCT
cana-5531	316	38	(	(	PUNCT
cana-5531	316	39	4.11	4.11	NUM
cana-5531	316	40	)	)	PUNCT
cana-5531	316	41	,	,	PUNCT
cana-5531	316	42	(	(	PUNCT
cana-5531	316	43	4.13	4.13	NUM
cana-5531	316	44	)	)	PUNCT
cana-5531	316	45	(	(	PUNCT
cana-5531	316	46	c	c	X
cana-5531	316	47	)	)	PUNCT
cana-5531	316	48	and	and	CCONJ
cana-5531	316	49	the	the	DET
cana-5531	316	50	properties	property	NOUN
cana-5531	316	51	of	of	ADP
cana-5531	316	52	𝑅𝜈	𝑅𝜈	PROPN
cana-5531	316	53	and	and	CCONJ
cana-5531	316	54	𝑅𝜏	𝑅𝜏	PROPN
cana-5531	316	55	,	,	PUNCT
cana-5531	316	56	and	and	CCONJ
cana-5531	316	57	adding	add	VERB
cana-5531	316	58	the	the	DET
cana-5531	316	59	resulting	result	VERB
cana-5531	316	60	inequalities	inequality	NOUN
cana-5531	316	61	,	,	PUNCT
cana-5531	316	62	it	it	PRON
cana-5531	316	63	follows	follow	VERB
cana-5531	316	64	that	that	SCONJ
cana-5531	316	65	there	there	PRON
cana-5531	316	66	exists	exist	VERB
cana-5531	316	67	a	a	DET
cana-5531	316	68	constant	constant	ADJ
cana-5531	316	69	c1	c1	NOUN
cana-5531	316	70	>	>	X
cana-5531	316	71	0	0	PUNCT
cana-5531	317	1	such	such	ADJ
cana-5531	317	2	that	that	PRON
cana-5531	317	3	‖𝑢𝜉𝜂(𝑡2	‖𝑢𝜉𝜂(𝑡2	PROPN
cana-5531	317	4	)	)	PUNCT
cana-5531	317	5	−	−	PROPN
cana-5531	317	6	𝑢𝜉𝜂(𝑡1)‖𝑉	𝑢𝜉𝜂(𝑡1)‖𝑉	PROPN
cana-5531	317	7	≤	≤	PUNCT
cana-5531	317	8	𝑐1	𝑐1	NOUN
cana-5531	317	9	𝑚−‖𝜇‖𝕃∞(γ3	𝑚−‖𝜇‖𝕃∞(γ3	NOUN
cana-5531	317	10	)	)	PUNCT
cana-5531	317	11	(	(	PUNCT
cana-5531	317	12	‖𝜉(𝑡2	‖𝜉(𝑡2	PROPN
cana-5531	317	13	)	)	PUNCT
cana-5531	317	14	−	−	PROPN
cana-5531	317	15	𝜉(𝑡1)‖𝕃2(γ3	𝜉(𝑡1)‖𝕃2(γ3	NOUN
cana-5531	317	16	)	)	PUNCT
cana-5531	318	1	+	+	NOUN
cana-5531	318	2	‖𝜂(𝑡2	‖𝜂(𝑡2	NUM
cana-5531	318	3	)	)	PUNCT
cana-5531	318	4	−	−	PROPN
cana-5531	319	1	𝜂(𝑡1)‖ℋ	𝜂(𝑡1)‖ℋ	SYM
cana-5531	319	2	+	+	NOUN
cana-5531	319	3	‖𝑓(𝑡2	‖𝑓(𝑡2	PROPN
cana-5531	319	4	)	)	PUNCT
cana-5531	319	5	−	−	PROPN
cana-5531	319	6	𝑓(𝑡1)‖𝑉	𝑓(𝑡1)‖𝑉	NUM
cana-5531	319	7	)	)	PUNCT
cana-5531	319	8	.	.	PUNCT
cana-5531	320	1	then	then	ADV
cana-5531	320	2	,	,	PUNCT
cana-5531	320	3	as	as	ADP
cana-5531	320	4	𝜉	𝜉	PRON
cana-5531	320	5	∈	∈	PROPN
cana-5531	320	6	𝐶([0	𝐶([0	PROPN
cana-5531	320	7	,	,	PUNCT
cana-5531	320	8	𝑇	𝑇	PROPN
cana-5531	320	9	]	]	X
cana-5531	320	10	;	;	PUNCT
cana-5531	320	11	𝕃2(γ3	𝕃2(γ3	PROPN
cana-5531	320	12	)	)	PUNCT
cana-5531	320	13	)	)	PUNCT
cana-5531	320	14	,	,	PUNCT
cana-5531	320	15	𝜂	𝜂	X
cana-5531	320	16	∈	∈	PROPN
cana-5531	320	17	𝐶([0	𝐶([0	PROPN
cana-5531	320	18	,	,	PUNCT
cana-5531	320	19	𝑇];ℋ	𝑇];ℋ	NOUN
cana-5531	320	20	)	)	PUNCT
cana-5531	320	21	and𝑓	and𝑓	NOUN
cana-5531	320	22	∈	∈	PROPN
cana-5531	320	23	(	(	PUNCT
cana-5531	320	24	[	[	X
cana-5531	320	25	0	0	NUM
cana-5531	320	26	,	,	PUNCT
cana-5531	320	27	𝑇	𝑇	PROPN
cana-5531	320	28	]	]	PUNCT
cana-5531	320	29	;	;	PUNCT
cana-5531	320	30	𝑉),it	𝑉),it	PROPN
cana-5531	320	31	immediately	immediately	ADV
cana-5531	320	32	concludes	conclude	VERB
cana-5531	320	33	that	that	SCONJ
cana-5531	320	34	𝑢𝜉𝜂(𝑡	𝑢𝜉𝜂(𝑡	PROPN
cana-5531	320	35	)	)	PUNCT
cana-5531	320	36	∈	∈	PROPN
cana-5531	320	37	𝑊	𝑊	PROPN
cana-5531	320	38	,	,	PUNCT
cana-5531	320	39	∀𝑡	∀𝑡	PROPN
cana-5531	320	40	∈	∈	PROPN
cana-5531	321	1	[	[	X
cana-5531	321	2	0	0	NUM
cana-5531	321	3	,	,	PUNCT
cana-5531	321	4	𝑇	𝑇	PROPN
cana-5531	321	5	]	]	PUNCT
cana-5531	321	6	.	.	PUNCT
cana-5531	322	1	indeed	indeed	ADV
cana-5531	322	2	,	,	PUNCT
cana-5531	322	3	for	for	ADP
cana-5531	322	4	each	each	DET
cana-5531	322	5	t	t	NOUN
cana-5531	322	6	∈	∈	PROPN
cana-5531	323	1	[	[	X
cana-5531	323	2	0	0	NUM
cana-5531	323	3	,	,	PUNCT
cana-5531	323	4	t	t	X
cana-5531	323	5	]	]	PUNCT
cana-5531	323	6	,	,	PUNCT
cana-5531	323	7	denote	denote	VERB
cana-5531	323	8	𝜎	𝜎	PROPN
cana-5531	323	9	(	(	PUNCT
cana-5531	323	10	𝑢𝜉𝜂(𝑡	𝑢𝜉𝜂(𝑡	PROPN
cana-5531	323	11	)	)	PUNCT
cana-5531	323	12	)	)	PUNCT
cana-5531	324	1	=	=	PUNCT
cana-5531	324	2	𝒜𝜀	𝒜𝜀	PROPN
cana-5531	324	3	(	(	PUNCT
cana-5531	324	4	𝑢𝜉𝜂(𝑡	𝑢𝜉𝜂(𝑡	PROPN
cana-5531	324	5	)	)	PUNCT
cana-5531	324	6	)	)	PUNCT
cana-5531	325	1	+	+	CCONJ
cana-5531	325	2	𝜂(𝑡	𝜂(𝑡	NOUN
cana-5531	325	3	)	)	PUNCT
cana-5531	325	4	,	,	PUNCT
cana-5531	325	5	take	take	VERB
cana-5531	325	6	𝜐	𝜐	NOUN
cana-5531	325	7	=	=	SYM
cana-5531	325	8	𝑢𝜉𝜂(𝑡	𝑢𝜉𝜂(𝑡	PROPN
cana-5531	325	9	)	)	PUNCT
cana-5531	325	10	±	±	NUM
cana-5531	325	11	𝜑	𝜑	NOUN
cana-5531	325	12	in	in	ADP
cana-5531	325	13	inequality	inequality	NOUN
cana-5531	325	14	(	(	PUNCT
cana-5531	325	15	5.3	5.3	NUM
cana-5531	325	16	)	)	PUNCT
cana-5531	325	17	where	where	SCONJ
cana-5531	325	18	𝜑	𝜑	PROPN
cana-5531	325	19	∈	∈	PROPN
cana-5531	325	20	(	(	PUNCT
cana-5531	325	21	𝐶0	𝐶0	PROPN
cana-5531	325	22	∞(ω	∞(ω	PROPN
cana-5531	325	23	)	)	PUNCT
cana-5531	325	24	)	)	PUNCT
cana-5531	326	1	𝑑	𝑑	PRON
cana-5531	326	2	and	and	CCONJ
cana-5531	326	3	use	use	VERB
cana-5531	326	4	green	green	PROPN
cana-5531	326	5	’s	’s	PART
cana-5531	326	6	formula	formula	NOUN
cana-5531	326	7	with	with	ADP
cana-5531	326	8	regularity	regularity	NOUN
cana-5531	326	9	𝜑1(𝑡	𝜑1(𝑡	NOUN
cana-5531	326	10	)	)	PUNCT
cana-5531	326	11	∈	∈	NOUN
cana-5531	327	1	𝐻	𝐻	PROPN
cana-5531	327	2	leads	lead	VERB
cana-5531	327	3	to	to	ADP
cana-5531	327	4	div𝜎	div𝜎	VERB
cana-5531	327	5	(	(	PUNCT
cana-5531	327	6	𝑢𝜉𝜂(𝑡	𝑢𝜉𝜂(𝑡	PROPN
cana-5531	327	7	)	)	PUNCT
cana-5531	327	8	)	)	PUNCT
cana-5531	328	1	∈	∈	PROPN
cana-5531	328	2	𝐻	𝐻	PROPN
cana-5531	328	3	and	and	CCONJ
cana-5531	328	4	then	then	ADV
cana-5531	328	5	𝑢𝜉𝜂(𝑡	𝑢𝜉𝜂(𝑡	PROPN
cana-5531	328	6	)	)	PUNCT
cana-5531	328	7	∈	∈	PROPN
cana-5531	328	8	𝑊.	𝑊.	PROPN
cana-5531	328	9	now	now	ADV
cana-5531	328	10	introducing	introduce	VERB
cana-5531	328	11	the	the	DET
cana-5531	328	12	operator	operator	NOUN
cana-5531	328	13	λ𝜉	λ𝜉	X
cana-5531	328	14	:	:	PUNCT
cana-5531	328	15	𝐶([0,t];ℋ)⟶	𝐶([0,t];ℋ)⟶	NUM
cana-5531	328	16	𝐶([0	𝐶([0	ADJ
cana-5531	328	17	,	,	PUNCT
cana-5531	328	18	𝑇];ℋ	𝑇];ℋ	NOUN
cana-5531	328	19	)	)	PUNCT
cana-5531	328	20	with	with	ADP
cana-5531	328	21	𝜂	𝜂	NOUN
cana-5531	328	22	⟶	⟶	NOUN
cana-5531	328	23	λ𝜉	λ𝜉	ADV
cana-5531	328	24	defined	define	VERB
cana-5531	328	25	by	by	ADP
cana-5531	328	26	(	(	PUNCT
cana-5531	328	27	5.26	5.26	NUM
cana-5531	328	28	)	)	PUNCT
cana-5531	328	29	〈	〈	NOUN
cana-5531	328	30	λ𝜉𝜂	λ𝜉𝜂	NOUN
cana-5531	328	31	,	,	PUNCT
cana-5531	328	32	𝜔	𝜔	NOUN
cana-5531	328	33	〉	〉	NOUN
cana-5531	328	34	=	=	SYM
cana-5531	328	35	〈	〈	NOUN
cana-5531	328	36	𝒜𝜀(𝑢𝜉𝜂	𝒜𝜀(𝑢𝜉𝜂	NOUN
cana-5531	328	37	)	)	PUNCT
cana-5531	328	38	,	,	PUNCT
cana-5531	328	39	𝜀(𝜔)〉ℋ	𝜀(𝜔)〉ℋ	X
cana-5531	328	40	+	+	CCONJ
cana-5531	328	41	ℎ(𝑢𝛽𝜂	ℎ(𝑢𝛽𝜂	PROPN
cana-5531	328	42	,	,	PUNCT
cana-5531	328	43	𝜔	𝜔	PRON
cana-5531	328	44	)	)	PUNCT
cana-5531	328	45	+	+	CCONJ
cana-5531	328	46	𝑗𝑐(𝑢𝜉𝜂	𝑗𝑐(𝑢𝜉𝜂	PROPN
cana-5531	328	47	)	)	PUNCT
cana-5531	329	1	+	+	NOUN
cana-5531	329	2	∫	∫	PROPN
cana-5531	329	3	ℱ(𝑡	ℱ(𝑡	X
cana-5531	329	4	−	−	PROPN
cana-5531	329	5	𝑠)𝜀(𝑢𝜉𝜂)𝑑𝑠	𝑠)𝜀(𝑢𝜉𝜂)𝑑𝑠	PROPN
cana-5531	329	6	𝑡	𝑡	PROPN
cana-5531	329	7	0	0	PROPN
cana-5531	329	8	lemma	lemma	PROPN
cana-5531	329	9	5.7	5.7	NUM
cana-5531	329	10	.	.	PUNCT
cana-5531	330	1	the	the	DET
cana-5531	330	2	operator	operator	NOUN
cana-5531	330	3	λ𝜉	λ𝜉	VERB
cana-5531	330	4	has	have	VERB
cana-5531	330	5	a	a	DET
cana-5531	330	6	unique	unique	ADJ
cana-5531	330	7	fixed	fix	VERB
cana-5531	330	8	point	point	NOUN
cana-5531	330	9	𝜂𝜉.	𝜂𝜉.	NOUN
cana-5531	330	10	proof	proof	NOUN
cana-5531	330	11	.	.	PUNCT
cana-5531	331	1	let	let	VERB
cana-5531	331	2	𝜂1	𝜂1	NOUN
cana-5531	331	3	,	,	PUNCT
cana-5531	331	4	𝜂2	𝜂2	NOUN
cana-5531	331	5	∈	∈	NOUN
cana-5531	331	6	𝐶([0	𝐶([0	ADJ
cana-5531	331	7	,	,	PUNCT
cana-5531	331	8	𝑇];ℋ	𝑇];ℋ	NOUN
cana-5531	331	9	)	)	PUNCT
cana-5531	331	10	.	.	PUNCT
cana-5531	332	1	using	use	VERB
cana-5531	332	2	(	(	PUNCT
cana-5531	332	3	5.4	5.4	NUM
cana-5531	332	4	)	)	PUNCT
cana-5531	332	5	,	,	PUNCT
cana-5531	332	6	(	(	PUNCT
cana-5531	332	7	5.26	5.26	NUM
cana-5531	332	8	)	)	PUNCT
cana-5531	332	9	and	and	CCONJ
cana-5531	332	10	(	(	PUNCT
cana-5531	332	11	4.8	4.8	NUM
cana-5531	332	12	)	)	PUNCT
cana-5531	332	13	we	we	PRON
cana-5531	332	14	obtain	obtain	VERB
cana-5531	332	15	for	for	SCONJ
cana-5531	332	16	communications	communication	NOUN
cana-5531	332	17	on	on	ADP
cana-5531	332	18	applied	apply	VERB
cana-5531	332	19	nonlinear	nonlinear	ADJ
cana-5531	332	20	analysis	analysis	NOUN
cana-5531	332	21	issn	issn	NOUN
cana-5531	332	22	:	:	PUNCT
cana-5531	332	23	1074	1074	NUM
cana-5531	332	24	-	-	PUNCT
cana-5531	332	25	133x	133x	NUM
cana-5531	332	26	vol	vol	NOUN
cana-5531	332	27	32	32	NUM
cana-5531	332	28	no	no	NOUN
cana-5531	332	29	.	.	NOUN
cana-5531	332	30	3	3	NUM
cana-5531	332	31	(	(	PUNCT
cana-5531	332	32	2025	2025	NUM
cana-5531	332	33	)	)	PUNCT
cana-5531	332	34	979	979	NUM
cana-5531	332	35	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	332	36	‖𝜇‖𝕃∞(γ3	‖𝜇‖𝕃∞(γ3	PROPN
cana-5531	332	37	)	)	PUNCT
cana-5531	332	38	<	<	X
cana-5531	332	39	𝜇1at	𝜇1at	PUNCT
cana-5531	332	40	follow	follow	VERB
cana-5531	332	41	that	that	SCONJ
cana-5531	332	42	‖λ𝜉𝜂1(𝑡	‖λ𝜉𝜂1(𝑡	VERB
cana-5531	332	43	)	)	PUNCT
cana-5531	332	44	−	−	PROPN
cana-5531	333	1	λ𝜉𝜂2(𝑡)‖ℋ	λ𝜉𝜂2(𝑡)‖ℋ	NOUN
cana-5531	333	2	≤	≤	NUM
cana-5531	333	3	𝑐2	𝑐2	NOUN
cana-5531	333	4	∫	∫	PROPN
cana-5531	333	5	‖𝜂1(𝑡	‖𝜂1(𝑡	PROPN
cana-5531	333	6	)	)	PUNCT
cana-5531	333	7	−	−	PROPN
cana-5531	333	8	𝜂2(𝑡)‖ℋ𝑑𝑠.	𝜂2(𝑡)‖ℋ𝑑𝑠.	PROPN
cana-5531	333	9	𝑡	𝑡	PROPN
cana-5531	333	10	∈	∈	PROPN
cana-5531	333	11	[	[	X
cana-5531	333	12	0	0	NUM
cana-5531	333	13	,	,	PUNCT
cana-5531	333	14	𝑇	𝑇	PROPN
cana-5531	333	15	]	]	PUNCT
cana-5531	333	16	𝑡	𝑡	X
cana-5531	333	17	0	0	NUM
cana-5531	333	18	where	where	SCONJ
cana-5531	333	19	c2	c2	PROPN
cana-5531	333	20	>	>	X
cana-5531	333	21	0	0	PROPN
cana-5531	333	22	.	.	PUNCT
cana-5531	334	1	reiterating	reiterate	VERB
cana-5531	334	2	this	this	DET
cana-5531	334	3	inequality	inequality	NOUN
cana-5531	334	4	𝑛	𝑛	DET
cana-5531	334	5	times	time	NOUN
cana-5531	334	6	,	,	PUNCT
cana-5531	334	7	yields	yield	VERB
cana-5531	334	8	‖λ𝜉	‖λ𝜉	NUM
cana-5531	334	9	𝑛𝜂1(𝑡	𝑛𝜂1(𝑡	PROPN
cana-5531	334	10	)	)	PUNCT
cana-5531	334	11	−	−	NOUN
cana-5531	334	12	λ𝜉	λ𝜉	X
cana-5531	334	13	𝑛𝜂2(𝑡)‖𝐶([𝑂,𝑇];ℋ	𝑛𝜂2(𝑡)‖𝐶([𝑂,𝑇];ℋ	NOUN
cana-5531	334	14	)	)	PUNCT
cana-5531	334	15	≤	≤	NOUN
cana-5531	334	16	(	(	PUNCT
cana-5531	334	17	𝑐2𝑇	𝑐2𝑇	NOUN
cana-5531	334	18	)	)	PUNCT
cana-5531	335	1	𝑛	𝑛	PRON
cana-5531	335	2	𝑛	𝑛	PROPN
cana-5531	335	3	!	!	PUNCT
cana-5531	335	4	‖𝜂1	‖𝜂1	NOUN
cana-5531	335	5	−	−	PROPN
cana-5531	335	6	𝜂2‖𝐶([0,𝑇];ℋ	𝜂2‖𝐶([0,𝑇];ℋ	PROPN
cana-5531	335	7	)	)	PUNCT
cana-5531	335	8	as	as	ADP
cana-5531	335	9	lim	lim	PROPN
cana-5531	335	10	𝑛→+∞	𝑛→+∞	PROPN
cana-5531	335	11	(	(	PUNCT
cana-5531	335	12	𝑐2𝑇	𝑐2𝑇	NOUN
cana-5531	335	13	)	)	PUNCT
cana-5531	335	14	𝑛	𝑛	PRON
cana-5531	335	15	𝑛	𝑛	NOUN
cana-5531	335	16	!	!	PUNCT
cana-5531	336	1	=	=	SYM
cana-5531	336	2	0	0	NUM
cana-5531	336	3	,	,	PUNCT
cana-5531	336	4	it	it	PRON
cana-5531	336	5	follows	follow	VERB
cana-5531	336	6	that	that	SCONJ
cana-5531	336	7	for	for	ADP
cana-5531	336	8	a	a	DET
cana-5531	336	9	positive	positive	ADJ
cana-5531	336	10	integer	integer	NOUN
cana-5531	336	11	n	n	PRON
cana-5531	336	12	sufficiently	sufficiently	ADV
cana-5531	336	13	large	large	ADJ
cana-5531	336	14	,	,	PUNCT
cana-5531	336	15	λ𝜉	λ𝜉	ADP
cana-5531	336	16	𝑛	𝑛	PRON
cana-5531	336	17	is	be	AUX
cana-5531	336	18	a	a	DET
cana-5531	336	19	contraction	contraction	NOUN
cana-5531	336	20	;	;	PUNCT
cana-5531	336	21	then	then	ADV
cana-5531	336	22	,	,	PUNCT
cana-5531	336	23	by	by	ADP
cana-5531	336	24	using	use	VERB
cana-5531	336	25	the	the	DET
cana-5531	336	26	banach	banach	ADV
cana-5531	336	27	fixed	fix	VERB
cana-5531	336	28	point	point	NOUN
cana-5531	336	29	theorem	theorem	VERB
cana-5531	336	30	,	,	PUNCT
cana-5531	336	31	it	it	PRON
cana-5531	336	32	has	have	VERB
cana-5531	336	33	a	a	DET
cana-5531	336	34	unique	unique	ADJ
cana-5531	336	35	fixed	fix	VERB
cana-5531	336	36	point	point	NOUN
cana-5531	336	37	𝜂𝜉	𝜂𝜉	X
cana-5531	336	38	which	which	PRON
cana-5531	336	39	is	be	AUX
cana-5531	336	40	also	also	ADV
cana-5531	336	41	a	a	DET
cana-5531	336	42	unique	unique	ADJ
cana-5531	336	43	fixed	fixed	NOUN
cana-5531	336	44	of	of	ADP
cana-5531	336	45	λ𝜉	λ𝜉	X
cana-5531	336	46	i.e.	i.e.	X
cana-5531	336	47	,	,	PUNCT
cana-5531	336	48	λ𝜉𝜂𝜉	λ𝜉𝜂𝜉	ADJ
cana-5531	336	49	=	=	PRON
cana-5531	336	50	𝜂𝜉(𝑡	𝜂𝜉(𝑡	NUM
cana-5531	336	51	)	)	PUNCT
cana-5531	336	52	,	,	PUNCT
cana-5531	336	53	∀𝑡	∀𝑡	PROPN
cana-5531	336	54	∈	∈	PROPN
cana-5531	337	1	[	[	X
cana-5531	337	2	0	0	NUM
cana-5531	337	3	,	,	PUNCT
cana-5531	337	4	𝑇	𝑇	PROPN
cana-5531	337	5	]	]	X
cana-5531	337	6	(	(	PUNCT
cana-5531	337	7	5.27	5.27	NUM
cana-5531	337	8	)	)	PUNCT
cana-5531	337	9	then	then	ADV
cana-5531	337	10	by	by	ADP
cana-5531	337	11	(	(	PUNCT
cana-5531	337	12	4.3	4.3	NUM
cana-5531	337	13	)	)	PUNCT
cana-5531	337	14	and	and	CCONJ
cana-5531	337	15	(	(	PUNCT
cana-5531	337	16	4.27	4.27	NUM
cana-5531	337	17	)	)	PUNCT
cana-5531	337	18	we	we	PRON
cana-5531	337	19	conclude	conclude	VERB
cana-5531	337	20	that	that	SCONJ
cana-5531	337	21	𝑢𝜉𝜂𝜉	𝑢𝜉𝜂𝜉	NOUN
cana-5531	337	22	is	be	AUX
cana-5531	337	23	the	the	DET
cana-5531	337	24	unique	unique	ADJ
cana-5531	337	25	solution	solution	NOUN
cana-5531	337	26	of	of	ADP
cana-5531	337	27	problem	problem	NOUN
cana-5531	337	28	𝑃1𝜉	𝑃1𝜉	PROPN
cana-5531	337	29	.	.	PUNCT
cana-5531	338	1	in	in	ADP
cana-5531	338	2	the	the	DET
cana-5531	338	3	second	second	ADJ
cana-5531	338	4	step	step	NOUN
cana-5531	338	5	stating	state	VERB
cana-5531	338	6	the	the	DET
cana-5531	338	7	following	following	ADJ
cana-5531	338	8	problem	problem	NOUN
cana-5531	338	9	.	.	PUNCT
cana-5531	339	1	problem	problem	NOUN
cana-5531	339	2	𝑃𝑎𝑑.	𝑃𝑎𝑑.	PROPN
cana-5531	339	3	find	find	VERB
cana-5531	339	4	𝛽∗	𝛽∗	NOUN
cana-5531	339	5	:	:	PUNCT
cana-5531	340	1	[	[	X
cana-5531	340	2	0	0	NUM
cana-5531	340	3	,	,	PUNCT
cana-5531	340	4	t	t	X
cana-5531	340	5	]	]	PUNCT
cana-5531	340	6	→	→	PUNCT
cana-5531	340	7	𝕃2(γ3)such	𝕃2(γ3)such	ADJ
cana-5531	340	8	that	that	SCONJ
cana-5531	340	9	�	�	PROPN
cana-5531	340	10	̇	̇	PROPN
cana-5531	340	11	�	�	NOUN
cana-5531	340	12	∗(𝑡	∗(𝑡	PROPN
cana-5531	340	13	)	)	PUNCT
cana-5531	340	14	=	=	SYM
cana-5531	341	1	−	−	PROPN
cana-5531	342	1	[	[	X
cana-5531	342	2	𝛽∗(𝑡	𝛽∗(𝑡	NUM
cana-5531	342	3	)	)	PUNCT
cana-5531	342	4	(	(	PUNCT
cana-5531	342	5	𝑐𝜈	𝑐𝜈	NOUN
cana-5531	342	6	(	(	PUNCT
cana-5531	342	7	𝑅𝜈	𝑅𝜈	PROPN
cana-5531	342	8	(	(	PUNCT
cana-5531	342	9	𝑢𝛽∗𝜈(𝑡	𝑢𝛽∗𝜈(𝑡	NUM
cana-5531	342	10	)	)	PUNCT
cana-5531	342	11	)	)	PUNCT
cana-5531	342	12	)	)	PUNCT
cana-5531	342	13	2	2	NUM
cana-5531	343	1	+	+	CCONJ
cana-5531	343	2	𝑐𝜏	𝑐𝜏	PROPN
cana-5531	343	3	|𝑅𝜏	|𝑅𝜏	PROPN
cana-5531	343	4	(	(	PUNCT
cana-5531	343	5	𝑢𝛽∗𝜏(𝑡))|	𝑢𝛽∗𝜏(𝑡))|	PROPN
cana-5531	343	6	2	2	NUM
cana-5531	343	7	−	−	NOUN
cana-5531	343	8	𝜀𝑎	𝜀𝑎	NOUN
cana-5531	343	9	)	)	PUNCT
cana-5531	343	10	]	]	PUNCT
cana-5531	344	1	+	+	CCONJ
cana-5531	344	2	(	(	PUNCT
cana-5531	344	3	5.28	5.28	NUM
cana-5531	344	4	)	)	PUNCT
cana-5531	344	5	𝛽∗(0	𝛽∗(0	NOUN
cana-5531	344	6	)	)	PUNCT
cana-5531	344	7	=	=	SYM
cana-5531	344	8	𝛽0	𝛽0	NOUN
cana-5531	344	9	(	(	PUNCT
cana-5531	344	10	5.29	5.29	NUM
cana-5531	344	11	)	)	PUNCT
cana-5531	344	12	let	let	AUX
cana-5531	344	13	obtain	obtain	VERB
cana-5531	344	14	the	the	DET
cana-5531	344	15	following	follow	VERB
cana-5531	344	16	result	result	NOUN
cana-5531	344	17	be	be	AUX
cana-5531	344	18	given	give	VERB
cana-5531	344	19	proposition	proposition	NOUN
cana-5531	344	20	5.8	5.8	NUM
cana-5531	344	21	.	.	PUNCT
cana-5531	345	1	problem	problem	NOUN
cana-5531	345	2	pad	pad	NOUN
cana-5531	345	3	has	have	VERB
cana-5531	345	4	a	a	DET
cana-5531	345	5	unique	unique	ADJ
cana-5531	345	6	solution	solution	NOUN
cana-5531	345	7	𝛽∗which	𝛽∗which	NOUN
cana-5531	345	8	satisfies	satisfy	VERB
cana-5531	345	9	𝛽∗	𝛽∗	PROPN
cana-5531	345	10	∈	∈	PROPN
cana-5531	345	11	𝑊1,∞(0	𝑊1,∞(0	NOUN
cana-5531	345	12	,	,	PUNCT
cana-5531	345	13	𝑇	𝑇	PROPN
cana-5531	345	14	;	;	PUNCT
cana-5531	345	15	𝕃2(γ3	𝕃2(γ3	PROPN
cana-5531	345	16	)	)	PUNCT
cana-5531	345	17	)	)	PUNCT
cana-5531	345	18	∩	∩	NOUN
cana-5531	345	19	𝐵.	𝐵.	NOUN
cana-5531	345	20	proof	proof	NOUN
cana-5531	345	21	.	.	PUNCT
cana-5531	346	1	let	let	VERB
cana-5531	346	2	t	t	PROPN
cana-5531	346	3	∈	∈	PROPN
cana-5531	347	1	[	[	X
cana-5531	347	2	0	0	NUM
cana-5531	347	3	,	,	PUNCT
cana-5531	347	4	t	t	NOUN
cana-5531	347	5	]	]	PUNCT
cana-5531	347	6	and	and	CCONJ
cana-5531	347	7	consider	consider	VERB
cana-5531	347	8	the	the	DET
cana-5531	347	9	mapping	mapping	NOUN
cana-5531	347	10	ϕ:z	ϕ:z	NOUN
cana-5531	348	1	→	→	PUNCT
cana-5531	348	2	z	z	NOUN
cana-5531	348	3	defined	define	VERB
cana-5531	348	4	by	by	ADP
cana-5531	348	5	𝜙𝛽(𝑡	𝜙𝛽(𝑡	NOUN
cana-5531	348	6	)	)	PUNCT
cana-5531	348	7	=	=	SYM
cana-5531	348	8	𝛽0	𝛽0	NOUN
cana-5531	348	9	−∫	−∫	NOUN
cana-5531	348	10	[	[	X
cana-5531	348	11	𝛽(𝑠	𝛽(𝑠	X
cana-5531	348	12	)	)	PUNCT
cana-5531	348	13	(	(	PUNCT
cana-5531	348	14	𝑐𝜈	𝑐𝜈	NOUN
cana-5531	348	15	(	(	PUNCT
cana-5531	348	16	𝑅𝜈	𝑅𝜈	ADP
cana-5531	348	17	(	(	PUNCT
cana-5531	348	18	𝑢𝛽(𝑠	𝑢𝛽(𝑠	NOUN
cana-5531	348	19	)	)	PUNCT
cana-5531	348	20	)	)	PUNCT
cana-5531	348	21	)	)	PUNCT
cana-5531	348	22	)	)	PUNCT
cana-5531	348	23	2	2	NUM
cana-5531	349	1	+	+	CCONJ
cana-5531	349	2	𝑐𝜏	𝑐𝜏	PROPN
cana-5531	349	3	|𝑅𝜏	|𝑅𝜏	PROPN
cana-5531	349	4	(	(	PUNCT
cana-5531	349	5	𝑢𝛽𝜏(𝑠))|	𝑢𝛽𝜏(𝑠))|	NOUN
cana-5531	349	6	2	2	NUM
cana-5531	349	7	−	−	NOUN
cana-5531	349	8	𝜀𝑎	𝜀𝑎	X
cana-5531	349	9	]	]	X
cana-5531	349	10	+	+	CCONJ
cana-5531	349	11	𝑑𝑠	𝑑𝑠	PART
cana-5531	349	12	𝑡	𝑡	PROPN
cana-5531	349	13	0	0	NUM
cana-5531	349	14	,	,	PUNCT
cana-5531	349	15	where	where	SCONJ
cana-5531	349	16	𝑢𝛽	𝑢𝛽	NOUN
cana-5531	349	17	is	be	AUX
cana-5531	349	18	the	the	DET
cana-5531	349	19	solution	solution	NOUN
cana-5531	349	20	of	of	ADP
cana-5531	349	21	problem	problem	NOUN
cana-5531	349	22	𝑃1𝛽.	𝑃1𝛽.	ADP
cana-5531	349	23	for𝛽1	for𝛽1	PROPN
cana-5531	349	24	,	,	PUNCT
cana-5531	349	25	𝛽2	𝛽2	PROPN
cana-5531	349	26	∈	∈	PROPN
cana-5531	349	27	𝐵	𝐵	PROPN
cana-5531	349	28	,	,	PUNCT
cana-5531	349	29	there	there	PRON
cana-5531	349	30	exists	exist	VERB
cana-5531	349	31	a	a	DET
cana-5531	349	32	constant	constant	ADJ
cana-5531	349	33	c3	c3	NOUN
cana-5531	349	34	>	>	X
cana-5531	349	35	0	0	NUM
cana-5531	349	36	such	such	ADJ
cana-5531	349	37	that	that	DET
cana-5531	349	38	‖𝜙𝛽1(𝑡	‖𝜙𝛽1(𝑡	NOUN
cana-5531	349	39	)	)	PUNCT
cana-5531	349	40	−	−	PRON
cana-5531	350	1	𝜙𝛽2(𝑡)‖𝕃2(γ3	𝜙𝛽2(𝑡)‖𝕃2(γ3	PROPN
cana-5531	350	2	)	)	PUNCT
cana-5531	350	3	≤	≤	NUM
cana-5531	350	4	𝑐3	𝑐3	NOUN
cana-5531	350	5	∫	∫	PROPN
cana-5531	350	6	‖𝛽1(𝑠	‖𝛽1(𝑠	PROPN
cana-5531	350	7	)	)	PUNCT
cana-5531	350	8	(	(	PUNCT
cana-5531	350	9	𝑅𝜈	𝑅𝜈	ADP
cana-5531	350	10	(	(	PUNCT
cana-5531	350	11	𝑢𝛽1𝜈(𝑠	𝑢𝛽1𝜈(𝑠	NOUN
cana-5531	350	12	)	)	PUNCT
cana-5531	350	13	)	)	PUNCT
cana-5531	350	14	)	)	PUNCT
cana-5531	351	1	2	2	NUM
cana-5531	351	2	−	−	NOUN
cana-5531	351	3	𝛽2(𝑠	𝛽2(𝑠	NUM
cana-5531	351	4	)	)	PUNCT
cana-5531	351	5	(	(	PUNCT
cana-5531	351	6	𝑅𝜈	𝑅𝜈	ADP
cana-5531	351	7	(	(	PUNCT
cana-5531	351	8	𝑢𝛽2𝜈(𝑠	𝑢𝛽2𝜈(𝑠	NOUN
cana-5531	351	9	)	)	PUNCT
cana-5531	351	10	)	)	PUNCT
cana-5531	351	11	)	)	PUNCT
cana-5531	351	12	2	2	NUM
cana-5531	351	13	‖	‖	PROPN
cana-5531	351	14	𝕃2(γ3	𝕃2(γ3	PROPN
cana-5531	351	15	)	)	PUNCT
cana-5531	351	16	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	351	17	𝑡	𝑡	PROPN
cana-5531	351	18	0	0	PUNCT
cana-5531	352	1	+	+	NOUN
cana-5531	352	2	𝑐3	𝑐3	NOUN
cana-5531	352	3	∫	∫	X
cana-5531	352	4	‖𝛽1(𝑠	‖𝛽1(𝑠	PROPN
cana-5531	352	5	)	)	PUNCT
cana-5531	352	6	(	(	PUNCT
cana-5531	352	7	𝑅𝜏	𝑅𝜏	PROPN
cana-5531	352	8	(	(	PUNCT
cana-5531	352	9	𝑢𝛽1𝜏(𝑠	𝑢𝛽1𝜏(𝑠	NUM
cana-5531	352	10	)	)	PUNCT
cana-5531	352	11	)	)	PUNCT
cana-5531	352	12	)	)	PUNCT
cana-5531	352	13	2	2	NUM
cana-5531	353	1	−	−	NOUN
cana-5531	353	2	𝛽2(𝑠	𝛽2(𝑠	NUM
cana-5531	353	3	)	)	PUNCT
cana-5531	353	4	(	(	PUNCT
cana-5531	353	5	𝑅𝜏	𝑅𝜏	PROPN
cana-5531	353	6	(	(	PUNCT
cana-5531	353	7	𝑢𝛽2(𝑠	𝑢𝛽2(𝑠	PROPN
cana-5531	353	8	)	)	PUNCT
cana-5531	353	9	)	)	PUNCT
cana-5531	353	10	)	)	PUNCT
cana-5531	353	11	2	2	NUM
cana-5531	353	12	‖	‖	PROPN
cana-5531	353	13	𝕃2(γ3	𝕃2(γ3	PROPN
cana-5531	353	14	)	)	PUNCT
cana-5531	353	15	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	353	16	𝑡	𝑡	PROPN
cana-5531	353	17	0	0	PUNCT
cana-5531	353	18	as	as	ADP
cana-5531	353	19	in	in	ADP
cana-5531	353	20	[	[	X
cana-5531	353	21	20	20	NUM
cana-5531	353	22	,	,	PUNCT
cana-5531	353	23	21	21	NUM
cana-5531	353	24	]	]	PUNCT
cana-5531	353	25	it	it	PRON
cana-5531	353	26	deduces	deduce	VERB
cana-5531	353	27	‖𝜙𝛽1(𝑡	‖𝜙𝛽1(𝑡	NOUN
cana-5531	353	28	)	)	PUNCT
cana-5531	353	29	−	−	PRON
cana-5531	353	30	𝜙𝛽2(𝑡)‖𝕃2(γ3	𝜙𝛽2(𝑡)‖𝕃2(γ3	PROPN
cana-5531	353	31	)	)	PUNCT
cana-5531	353	32	≤	≤	NUM
cana-5531	353	33	𝑐4	𝑐4	NOUN
cana-5531	353	34	(	(	PUNCT
cana-5531	353	35	∫	∫	PROPN
cana-5531	353	36	‖𝛽1(𝑠	‖𝛽1(𝑠	PROPN
cana-5531	353	37	)	)	PUNCT
cana-5531	353	38	−	−	PROPN
cana-5531	353	39	𝛽2(𝑠)‖𝕃2(γ3	𝛽2(𝑠)‖𝕃2(γ3	PROPN
cana-5531	353	40	)	)	PUNCT
cana-5531	353	41	𝑡	𝑡	PROPN
cana-5531	353	42	0	0	NUM
cana-5531	353	43	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	353	44	+	+	NUM
cana-5531	353	45	∫	∫	PROPN
cana-5531	353	46	‖𝑢𝛽1(𝑠	‖𝑢𝛽1(𝑠	NUM
cana-5531	353	47	)	)	PUNCT
cana-5531	353	48	−	−	PROPN
cana-5531	354	1	𝑢𝛽2(𝑠)‖𝑉	𝑢𝛽2(𝑠)‖𝑉	PROPN
cana-5531	354	2	𝑡	𝑡	PROPN
cana-5531	354	3	0	0	NUM
cana-5531	354	4	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	354	5	)	)	PUNCT
cana-5531	354	6	.	.	PUNCT
cana-5531	355	1	communications	communication	NOUN
cana-5531	355	2	on	on	ADP
cana-5531	355	3	applied	apply	VERB
cana-5531	355	4	nonlinear	nonlinear	ADJ
cana-5531	355	5	analysis	analysis	NOUN
cana-5531	355	6	issn	issn	NOUN
cana-5531	355	7	:	:	PUNCT
cana-5531	355	8	1074	1074	NUM
cana-5531	355	9	-	-	PUNCT
cana-5531	355	10	133x	133x	NUM
cana-5531	355	11	vol	vol	NOUN
cana-5531	355	12	32	32	NUM
cana-5531	355	13	no	no	NOUN
cana-5531	355	14	.	.	NOUN
cana-5531	355	15	3	3	NUM
cana-5531	355	16	(	(	PUNCT
cana-5531	355	17	2025	2025	NUM
cana-5531	355	18	)	)	PUNCT
cana-5531	355	19	980	980	NUM
cana-5531	355	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	355	21	(	(	PUNCT
cana-5531	355	22	5.30	5.30	NUM
cana-5531	355	23	)	)	PUNCT
cana-5531	355	24	for	for	ADP
cana-5531	355	25	some	some	DET
cana-5531	355	26	constant	constant	ADJ
cana-5531	355	27	𝑐4	𝑐4	NOUN
cana-5531	355	28	>	>	X
cana-5531	355	29	0	0	X
cana-5531	355	30	.	.	PUNCT
cana-5531	356	1	now	now	ADV
cana-5531	356	2	to	to	PART
cana-5531	356	3	continue	continue	VERB
cana-5531	356	4	the	the	DET
cana-5531	356	5	proof	proof	NOUN
cana-5531	356	6	it	it	PRON
cana-5531	356	7	has	have	AUX
cana-5531	356	8	needed	need	VERB
cana-5531	356	9	to	to	PART
cana-5531	356	10	prove	prove	VERB
cana-5531	356	11	the	the	DET
cana-5531	356	12	following	follow	VERB
cana-5531	356	13	lemma	lemma	PROPN
cana-5531	356	14	.	.	PUNCT
cana-5531	357	1	lemma	lemma	PROPN
cana-5531	357	2	5.9	5.9	NUM
cana-5531	357	3	.	.	PUNCT
cana-5531	358	1	there	there	PRON
cana-5531	358	2	exists	exist	VERB
cana-5531	358	3	a	a	DET
cana-5531	358	4	constant	constant	ADJ
cana-5531	358	5	𝜇0	𝜇0	NOUN
cana-5531	358	6	>	>	X
cana-5531	358	7	0	0	NUM
cana-5531	358	8	such	such	ADJ
cana-5531	358	9	that	that	SCONJ
cana-5531	358	10	:	:	PUNCT
cana-5531	358	11	‖𝑢𝛽1(𝑡	‖𝑢𝛽1(𝑡	X
cana-5531	358	12	)	)	PUNCT
cana-5531	358	13	−	−	PROPN
cana-5531	358	14	𝑢𝛽2(𝑡)‖𝑉	𝑢𝛽2(𝑡)‖𝑉	ADJ
cana-5531	358	15	≤	≤	NUM
cana-5531	358	16	𝑐‖𝛽1(𝑡	𝑐‖𝛽1(𝑡	NOUN
cana-5531	358	17	)	)	PUNCT
cana-5531	358	18	−	−	NOUN
cana-5531	358	19	𝛽2(𝑡)‖𝕃2(γ3	𝛽2(𝑡)‖𝕃2(γ3	NOUN
cana-5531	358	20	)	)	PUNCT
cana-5531	358	21	∀t	∀t	PROPN
cana-5531	358	22	∈	∈	PROPN
cana-5531	359	1	[	[	X
cana-5531	359	2	0	0	NUM
cana-5531	359	3	,	,	PUNCT
cana-5531	359	4	t	t	X
cana-5531	359	5	]	]	PUNCT
cana-5531	359	6	,	,	PUNCT
cana-5531	359	7	proof	proof	NOUN
cana-5531	359	8	.	.	PUNCT
cana-5531	360	1	let	let	VERB
cana-5531	360	2	t	t	PROPN
cana-5531	360	3	∈	∈	PROPN
cana-5531	361	1	[	[	X
cana-5531	361	2	0	0	NUM
cana-5531	361	3	,	,	PUNCT
cana-5531	361	4	t	t	NOUN
cana-5531	361	5	]	]	PUNCT
cana-5531	361	6	.	.	PUNCT
cana-5531	362	1	take	take	VERB
cana-5531	362	2	𝑢𝛽2	𝑢𝛽2	PROPN
cana-5531	362	3	(	(	PUNCT
cana-5531	362	4	t	t	NOUN
cana-5531	362	5	)	)	PUNCT
cana-5531	362	6	in	in	ADP
cana-5531	362	7	(	(	PUNCT
cana-5531	362	8	4.1	4.1	NUM
cana-5531	362	9	)	)	PUNCT
cana-5531	362	10	satisfied	satisfy	VERB
cana-5531	362	11	by	by	ADP
cana-5531	362	12	𝑢𝛽1	𝑢𝛽1	NOUN
cana-5531	362	13	(	(	PUNCT
cana-5531	362	14	t	t	PROPN
cana-5531	362	15	)	)	PUNCT
cana-5531	362	16	,	,	PUNCT
cana-5531	362	17	then	then	ADV
cana-5531	362	18	take	take	VERB
cana-5531	362	19	𝑢𝛽1	𝑢𝛽1	NOUN
cana-5531	362	20	(	(	PUNCT
cana-5531	362	21	t	t	NOUN
cana-5531	362	22	)	)	PUNCT
cana-5531	362	23	in	in	ADP
cana-5531	362	24	the	the	DET
cana-5531	362	25	same	same	ADJ
cana-5531	362	26	inequality	inequality	NOUN
cana-5531	362	27	satisfied	satisfy	VERB
cana-5531	362	28	by	by	ADP
cana-5531	362	29	𝑢𝛽2	𝑢𝛽2	PROPN
cana-5531	362	30	(	(	PUNCT
cana-5531	362	31	t	t	PROPN
cana-5531	362	32	)	)	PUNCT
cana-5531	362	33	;	;	PUNCT
cana-5531	362	34	by	by	ADP
cana-5531	362	35	addding	addde	VERB
cana-5531	362	36	the	the	DET
cana-5531	362	37	resulting	result	VERB
cana-5531	362	38	inequalities	inequality	NOUN
cana-5531	362	39	〈	〈	PROPN
cana-5531	362	40	�	�	PROPN
cana-5531	362	41	̈	̈	SYM
cana-5531	362	42	�	�	NOUN
cana-5531	362	43	1	1	NUM
cana-5531	362	44	−	−	PROPN
cana-5531	362	45	�	�	PROPN
cana-5531	362	46	̈	̈	X
cana-5531	362	47	�	�	NOUN
cana-5531	362	48	2	2	NUM
cana-5531	362	49	,	,	PUNCT
cana-5531	362	50	�	�	PROPN
cana-5531	362	51	̇	̇	NOUN
cana-5531	362	52	�	�	PROPN
cana-5531	362	53	1	1	NUM
cana-5531	362	54	−	−	PROPN
cana-5531	362	55	�	�	PROPN
cana-5531	362	56	̇	̇	VERB
cana-5531	362	57	�	�	NOUN
cana-5531	362	58	2	2	NUM
cana-5531	362	59	〉	〉	NOUN
cana-5531	362	60	+	+	CCONJ
cana-5531	362	61	〈	〈	ADJ
cana-5531	362	62	𝒜𝜀	𝒜𝜀	PROPN
cana-5531	362	63	(	(	PUNCT
cana-5531	362	64	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	362	65	)	)	PUNCT
cana-5531	362	66	)	)	PUNCT
cana-5531	363	1	−	−	PROPN
cana-5531	364	1	𝒜𝜀	𝒜𝜀	PROPN
cana-5531	364	2	(	(	PUNCT
cana-5531	364	3	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	364	4	)	)	PUNCT
cana-5531	364	5	)	)	PUNCT
cana-5531	364	6	,	,	PUNCT
cana-5531	364	7	𝜀	𝜀	PROPN
cana-5531	364	8	(	(	PUNCT
cana-5531	364	9	�	�	PROPN
cana-5531	364	10	̇	̇	PROPN
cana-5531	364	11	�	�	PROPN
cana-5531	364	12	𝛽1(𝑡	𝛽1(𝑡	NOUN
cana-5531	364	13	)	)	PUNCT
cana-5531	364	14	)	)	PUNCT
cana-5531	364	15	−	−	PROPN
cana-5531	365	1	𝜀	𝜀	PROPN
cana-5531	365	2	(	(	PUNCT
cana-5531	365	3	�	�	PROPN
cana-5531	365	4	̇	̇	NOUN
cana-5531	365	5	�	�	PROPN
cana-5531	365	6	𝛽2(𝑡))〉ℋ	𝛽2(𝑡))〉ℋ	NOUN
cana-5531	365	7	≤	≤	PUNCT
cana-5531	365	8	〈	〈	PROPN
cana-5531	365	9	∫	∫	PROPN
cana-5531	365	10	ℱ(𝑡	ℱ(𝑡	X
cana-5531	365	11	−	−	PROPN
cana-5531	365	12	𝑠	𝑠	NOUN
cana-5531	365	13	)	)	PUNCT
cana-5531	365	14	(	(	PUNCT
cana-5531	365	15	𝜀	𝜀	PROPN
cana-5531	365	16	(	(	PUNCT
cana-5531	365	17	𝑢𝛽1(𝑠	𝑢𝛽1(𝑠	PROPN
cana-5531	365	18	)	)	PUNCT
cana-5531	365	19	)	)	PUNCT
cana-5531	366	1	−	−	PROPN
cana-5531	366	2	𝜀	𝜀	PROPN
cana-5531	366	3	(	(	PUNCT
cana-5531	366	4	𝑢𝛽2(𝑠	𝑢𝛽2(𝑠	PROPN
cana-5531	366	5	)	)	PUNCT
cana-5531	366	6	)	)	PUNCT
cana-5531	366	7	)	)	PUNCT
cana-5531	367	1	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	367	2	,	,	PUNCT
cana-5531	367	3	𝜀	𝜀	PROPN
cana-5531	367	4	(	(	PUNCT
cana-5531	367	5	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	367	6	)	)	PUNCT
cana-5531	367	7	)	)	PUNCT
cana-5531	368	1	−	−	PROPN
cana-5531	368	2	𝜀	𝜀	PROPN
cana-5531	368	3	(	(	PUNCT
cana-5531	368	4	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	368	5	)	)	PUNCT
cana-5531	368	6	)	)	PUNCT
cana-5531	369	1	𝑡	𝑡	PROPN
cana-5531	369	2	0	0	NUM
cana-5531	369	3	〉	〉	NOUN
cana-5531	369	4	ℋ	ℋ	NOUN
cana-5531	369	5	+	+	NUM
cana-5531	369	6	〈	〈	PROPN
cana-5531	369	7	𝒢𝜀	𝒢𝜀	PROPN
cana-5531	369	8	(	(	PUNCT
cana-5531	369	9	�	�	PROPN
cana-5531	369	10	̇	̇	PROPN
cana-5531	369	11	�	�	PROPN
cana-5531	369	12	𝛽1(𝑡	𝛽1(𝑡	NOUN
cana-5531	369	13	)	)	PUNCT
cana-5531	369	14	)	)	PUNCT
cana-5531	370	1	−	−	PROPN
cana-5531	371	1	𝒢𝜀	𝒢𝜀	PROPN
cana-5531	371	2	(	(	PUNCT
cana-5531	371	3	�	�	PROPN
cana-5531	371	4	̇	̇	PROPN
cana-5531	371	5	�	�	PROPN
cana-5531	371	6	𝛽2(𝑡	𝛽2(𝑡	PROPN
cana-5531	371	7	)	)	PUNCT
cana-5531	371	8	)	)	PUNCT
cana-5531	371	9	,	,	PUNCT
cana-5531	371	10	𝜀	𝜀	PROPN
cana-5531	371	11	(	(	PUNCT
cana-5531	371	12	�	�	PROPN
cana-5531	371	13	̇	̇	PROPN
cana-5531	371	14	�	�	PROPN
cana-5531	371	15	𝛽2(𝑡	𝛽2(𝑡	PROPN
cana-5531	371	16	)	)	PUNCT
cana-5531	371	17	)	)	PUNCT
cana-5531	371	18	−	−	PROPN
cana-5531	372	1	𝜀	𝜀	PROPN
cana-5531	372	2	(	(	PUNCT
cana-5531	372	3	�	�	PROPN
cana-5531	372	4	̇	̇	PROPN
cana-5531	372	5	�	�	PROPN
cana-5531	372	6	𝛽1(𝑡))〉ℋ	𝛽1(𝑡))〉ℋ	VERB
cana-5531	372	7	+	+	ADJ
cana-5531	372	8	ℎ	ℎ	NOUN
cana-5531	372	9	(	(	PUNCT
cana-5531	372	10	𝛽1(𝑡	𝛽1(𝑡	NOUN
cana-5531	372	11	)	)	PUNCT
cana-5531	372	12	,	,	PUNCT
cana-5531	372	13	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	372	14	)	)	PUNCT
cana-5531	372	15	,	,	PUNCT
cana-5531	372	16	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	PROPN
cana-5531	372	17	)	)	PUNCT
cana-5531	372	18	−	−	PROPN
cana-5531	372	19	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	372	20	)	)	PUNCT
cana-5531	372	21	)	)	PUNCT
cana-5531	373	1	+	+	CCONJ
cana-5531	373	2	𝑗𝑐	𝑗𝑐	INTJ
cana-5531	373	3	(	(	PUNCT
cana-5531	373	4	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	373	5	)	)	PUNCT
cana-5531	373	6	,	,	PUNCT
cana-5531	373	7	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	373	8	)	)	PUNCT
cana-5531	373	9	)	)	PUNCT
cana-5531	374	1	+	+	VERB
cana-5531	374	2	ℎ	ℎ	X
cana-5531	374	3	(	(	PUNCT
cana-5531	374	4	𝛽2(𝑡	𝛽2(𝑡	PROPN
cana-5531	374	5	)	)	PUNCT
cana-5531	374	6	,	,	PUNCT
cana-5531	374	7	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	PROPN
cana-5531	374	8	)	)	PUNCT
cana-5531	374	9	,	,	PUNCT
cana-5531	374	10	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	374	11	)	)	PUNCT
cana-5531	374	12	−	−	PROPN
cana-5531	374	13	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	374	14	)	)	PUNCT
cana-5531	374	15	)	)	PUNCT
cana-5531	374	16	−	−	PROPN
cana-5531	375	1	𝑗𝑐	𝑗𝑐	INTJ
cana-5531	375	2	(	(	PUNCT
cana-5531	375	3	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	PROPN
cana-5531	375	4	)	)	PUNCT
cana-5531	375	5	,	,	PUNCT
cana-5531	375	6	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	375	7	)	)	PUNCT
cana-5531	375	8	)	)	PUNCT
cana-5531	376	1	+	+	X
cana-5531	376	2	𝑗𝑐	𝑗𝑐	INTJ
cana-5531	376	3	(	(	PUNCT
cana-5531	376	4	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	376	5	)	)	PUNCT
cana-5531	376	6	,	,	PUNCT
cana-5531	376	7	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	376	8	)	)	PUNCT
cana-5531	376	9	)	)	PUNCT
cana-5531	376	10	−	−	PROPN
cana-5531	377	1	𝑗𝑐	𝑗𝑐	INTJ
cana-5531	377	2	(	(	PUNCT
cana-5531	377	3	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	PROPN
cana-5531	377	4	)	)	PUNCT
cana-5531	377	5	,	,	PUNCT
cana-5531	377	6	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	377	7	)	)	PUNCT
cana-5531	377	8	)	)	PUNCT
cana-5531	378	1	+	+	CCONJ
cana-5531	378	2	𝑗𝑓	𝑗𝑓	X
cana-5531	378	3	(	(	PUNCT
cana-5531	378	4	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	378	5	)	)	PUNCT
cana-5531	378	6	,	,	PUNCT
cana-5531	378	7	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	378	8	)	)	PUNCT
cana-5531	378	9	)	)	PUNCT
cana-5531	379	1	−𝑗𝑓	−𝑗𝑓	NOUN
cana-5531	379	2	(	(	PUNCT
cana-5531	379	3	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	379	4	)	)	PUNCT
cana-5531	379	5	,	,	PUNCT
cana-5531	379	6	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	379	7	)	)	PUNCT
cana-5531	379	8	)	)	PUNCT
cana-5531	380	1	+	+	CCONJ
cana-5531	380	2	𝑗𝑓	𝑗𝑓	PRON
cana-5531	380	3	(	(	PUNCT
cana-5531	380	4	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	380	5	)	)	PUNCT
cana-5531	380	6	,	,	PUNCT
cana-5531	380	7	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	380	8	)	)	PUNCT
cana-5531	380	9	)	)	PUNCT
cana-5531	381	1	−	−	ADP
cana-5531	381	2	𝑗𝑓	𝑗𝑓	INTJ
cana-5531	381	3	(	(	PUNCT
cana-5531	381	4	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	381	5	)	)	PUNCT
cana-5531	381	6	,	,	PUNCT
cana-5531	381	7	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	381	8	)	)	PUNCT
cana-5531	381	9	)	)	PUNCT
cana-5531	381	10	.	.	PUNCT
cana-5531	382	1	and	and	CCONJ
cana-5531	382	2	using	use	VERB
cana-5531	382	3	(	(	PUNCT
cana-5531	382	4	4.4	4.4	NUM
cana-5531	382	5	)	)	PUNCT
cana-5531	382	6	(	(	PUNCT
cana-5531	382	7	b	b	X
cana-5531	382	8	)	)	PUNCT
cana-5531	382	9	then	then	ADV
cana-5531	382	10	we	we	PRON
cana-5531	382	11	obtain	obtain	VERB
cana-5531	382	12	1	1	NUM
cana-5531	382	13	2	2	NUM
cana-5531	382	14	𝑑	𝑑	NOUN
cana-5531	382	15	𝑑𝑡	𝑑𝑡	ADP
cana-5531	382	16	|	|	NOUN
cana-5531	382	17	�	�	NOUN
cana-5531	382	18	̇	̇	NOUN
cana-5531	382	19	�	�	PROPN
cana-5531	382	20	1	1	NUM
cana-5531	382	21	−	−	PROPN
cana-5531	382	22	�	�	PROPN
cana-5531	382	23	̇	̇	PROPN
cana-5531	382	24	�	�	PROPN
cana-5531	382	25	2|	2|	NUM
cana-5531	382	26	2	2	NUM
cana-5531	382	27	+	+	NOUN
cana-5531	382	28	𝑚‖𝑢𝛽1(𝑡	𝑚‖𝑢𝛽1(𝑡	NOUN
cana-5531	382	29	)	)	PUNCT
cana-5531	382	30	−	−	PROPN
cana-5531	382	31	𝑢𝛽2(𝑡)‖𝑉	𝑢𝛽2(𝑡)‖𝑉	PROPN
cana-5531	382	32	2	2	NUM
cana-5531	382	33	≤	≤	NUM
cana-5531	382	34	〈	〈	PROPN
cana-5531	382	35	∫	∫	PROPN
cana-5531	382	36	ℱ(𝑡	ℱ(𝑡	PRON
cana-5531	382	37	−	−	PROPN
cana-5531	382	38	𝑠	𝑠	NOUN
cana-5531	382	39	)	)	PUNCT
cana-5531	382	40	(	(	PUNCT
cana-5531	382	41	𝜀	𝜀	PROPN
cana-5531	382	42	(	(	PUNCT
cana-5531	382	43	𝑢𝛽1(𝑠	𝑢𝛽1(𝑠	PROPN
cana-5531	382	44	)	)	PUNCT
cana-5531	382	45	)	)	PUNCT
cana-5531	383	1	−	−	PROPN
cana-5531	383	2	𝜀	𝜀	PROPN
cana-5531	383	3	(	(	PUNCT
cana-5531	383	4	𝑢𝛽2(𝑠	𝑢𝛽2(𝑠	PROPN
cana-5531	383	5	)	)	PUNCT
cana-5531	383	6	)	)	PUNCT
cana-5531	383	7	)	)	PUNCT
cana-5531	384	1	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	384	2	,	,	PUNCT
cana-5531	384	3	𝜀	𝜀	PROPN
cana-5531	384	4	(	(	PUNCT
cana-5531	384	5	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	384	6	)	)	PUNCT
cana-5531	384	7	−	−	PROPN
cana-5531	384	8	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	384	9	)	)	PUNCT
cana-5531	384	10	)	)	PUNCT
cana-5531	384	11	𝑡	𝑡	PROPN
cana-5531	384	12	0	0	NUM
cana-5531	384	13	〉	〉	NOUN
cana-5531	384	14	ℋ	ℋ	PROPN
cana-5531	384	15	+	+	NOUN
cana-5531	384	16	〈	〈	PROPN
cana-5531	384	17	𝒢𝜀(	𝒢𝜀(	ADJ
cana-5531	384	18	�	�	PROPN
cana-5531	384	19	̇	̇	NOUN
cana-5531	384	20	�	�	PROPN
cana-5531	384	21	𝛽1	𝛽1	NOUN
cana-5531	384	22	)	)	PUNCT
cana-5531	384	23	−	−	ADP
cana-5531	384	24	𝒢𝜀(	𝒢𝜀(	PROPN
cana-5531	384	25	�	�	PROPN
cana-5531	384	26	̇	̇	NOUN
cana-5531	384	27	�	�	NOUN
cana-5531	384	28	𝛽2	𝛽2	NOUN
cana-5531	384	29	)	)	PUNCT
cana-5531	384	30	,	,	PUNCT
cana-5531	384	31	𝜀	𝜀	PROPN
cana-5531	384	32	(	(	PUNCT
cana-5531	384	33	�	�	PROPN
cana-5531	384	34	̇	̇	PROPN
cana-5531	384	35	�	�	PROPN
cana-5531	384	36	𝛽2(𝑡	𝛽2(𝑡	PROPN
cana-5531	384	37	)	)	PUNCT
cana-5531	384	38	)	)	PUNCT
cana-5531	384	39	−	−	PROPN
cana-5531	385	1	𝜀	𝜀	PROPN
cana-5531	385	2	(	(	PUNCT
cana-5531	385	3	�	�	PROPN
cana-5531	385	4	̇	̇	PROPN
cana-5531	385	5	�	�	PROPN
cana-5531	385	6	𝛽1(𝑡))〉ℋ	𝛽1(𝑡))〉ℋ	VERB
cana-5531	385	7	+	+	ADJ
cana-5531	385	8	ℎ	ℎ	NOUN
cana-5531	385	9	(	(	PUNCT
cana-5531	385	10	𝛽1(𝑡	𝛽1(𝑡	NOUN
cana-5531	385	11	)	)	PUNCT
cana-5531	385	12	,	,	PUNCT
cana-5531	385	13	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	385	14	)	)	PUNCT
cana-5531	385	15	,	,	PUNCT
cana-5531	385	16	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	PROPN
cana-5531	385	17	)	)	PUNCT
cana-5531	385	18	−	−	PROPN
cana-5531	385	19	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	385	20	)	)	PUNCT
cana-5531	385	21	)	)	PUNCT
cana-5531	386	1	+	+	CCONJ
cana-5531	386	2	ℎ	ℎ	X
cana-5531	386	3	(	(	PUNCT
cana-5531	386	4	𝛽2(𝑡	𝛽2(𝑡	PROPN
cana-5531	386	5	)	)	PUNCT
cana-5531	386	6	,	,	PUNCT
cana-5531	386	7	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	PROPN
cana-5531	386	8	)	)	PUNCT
cana-5531	386	9	,	,	PUNCT
cana-5531	386	10	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	386	11	)	)	PUNCT
cana-5531	386	12	−	−	PROPN
cana-5531	386	13	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	386	14	)	)	PUNCT
cana-5531	386	15	)	)	PUNCT
cana-5531	387	1	+	+	X
cana-5531	387	2	𝑗𝑐	𝑗𝑐	INTJ
cana-5531	387	3	(	(	PUNCT
cana-5531	387	4	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	387	5	)	)	PUNCT
cana-5531	387	6	,	,	PUNCT
cana-5531	387	7	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	387	8	)	)	PUNCT
cana-5531	387	9	)	)	PUNCT
cana-5531	387	10	−	−	PROPN
cana-5531	388	1	𝑗𝑐	𝑗𝑐	INTJ
cana-5531	388	2	(	(	PUNCT
cana-5531	388	3	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	388	4	)	)	PUNCT
cana-5531	388	5	,	,	PUNCT
cana-5531	388	6	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	388	7	)	)	PUNCT
cana-5531	388	8	)	)	PUNCT
cana-5531	389	1	+	+	CCONJ
cana-5531	389	2	𝑗𝑐	𝑗𝑐	INTJ
cana-5531	389	3	(	(	PUNCT
cana-5531	389	4	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	389	5	)	)	PUNCT
cana-5531	389	6	,	,	PUNCT
cana-5531	389	7	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	389	8	)	)	PUNCT
cana-5531	389	9	)	)	PUNCT
cana-5531	389	10	−𝑗𝑐	−𝑗𝑐	NOUN
cana-5531	389	11	(	(	PUNCT
cana-5531	389	12	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	PROPN
cana-5531	389	13	)	)	PUNCT
cana-5531	389	14	,	,	PUNCT
cana-5531	389	15	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	389	16	)	)	PUNCT
cana-5531	389	17	)	)	PUNCT
cana-5531	390	1	+	+	CCONJ
cana-5531	390	2	𝑗𝑓	𝑗𝑓	X
cana-5531	390	3	(	(	PUNCT
cana-5531	390	4	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	390	5	)	)	PUNCT
cana-5531	390	6	,	,	PUNCT
cana-5531	390	7	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	390	8	)	)	PUNCT
cana-5531	390	9	)	)	PUNCT
cana-5531	391	1	−	−	PROPN
cana-5531	391	2	𝑗𝑓	𝑗𝑓	INTJ
cana-5531	391	3	(	(	PUNCT
cana-5531	391	4	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	391	5	)	)	PUNCT
cana-5531	391	6	,	,	PUNCT
cana-5531	391	7	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	391	8	)	)	PUNCT
cana-5531	391	9	)	)	PUNCT
cana-5531	392	1	+	+	VERB
cana-5531	392	2	𝑗𝑓	𝑗𝑓	INTJ
cana-5531	392	3	(	(	PUNCT
cana-5531	392	4	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	392	5	)	)	PUNCT
cana-5531	392	6	,	,	PUNCT
cana-5531	392	7	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	392	8	)	)	PUNCT
cana-5531	392	9	)	)	PUNCT
cana-5531	392	10	−	−	ADP
cana-5531	392	11	𝑗𝑓	𝑗𝑓	INTJ
cana-5531	392	12	(	(	PUNCT
cana-5531	392	13	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	392	14	)	)	PUNCT
cana-5531	392	15	,	,	PUNCT
cana-5531	392	16	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	392	17	)	)	PUNCT
cana-5531	392	18	)	)	PUNCT
cana-5531	392	19	(	(	PUNCT
cana-5531	392	20	5.31	5.31	NUM
cana-5531	392	21	)	)	PUNCT
cana-5531	392	22	we	we	PRON
cana-5531	392	23	have	have	VERB
cana-5531	392	24	〈	〈	PROPN
cana-5531	392	25	∫	∫	PROPN
cana-5531	392	26	ℱ(𝑡	ℱ(𝑡	PRON
cana-5531	392	27	−	−	PROPN
cana-5531	392	28	𝑠	𝑠	NOUN
cana-5531	392	29	)	)	PUNCT
cana-5531	392	30	(	(	PUNCT
cana-5531	392	31	𝜀	𝜀	PROPN
cana-5531	392	32	(	(	PUNCT
cana-5531	392	33	𝑢𝛽1(𝑠	𝑢𝛽1(𝑠	PROPN
cana-5531	392	34	)	)	PUNCT
cana-5531	393	1	−	−	PROPN
cana-5531	393	2	𝜀(𝑢𝛽2(𝑠	𝜀(𝑢𝛽2(𝑠	PROPN
cana-5531	393	3	)	)	PUNCT
cana-5531	393	4	)	)	PUNCT
cana-5531	394	1	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	394	2	,	,	PUNCT
cana-5531	394	3	𝜀	𝜀	PROPN
cana-5531	394	4	(	(	PUNCT
cana-5531	394	5	�	�	PROPN
cana-5531	394	6	̇	̇	PROPN
cana-5531	394	7	�	�	PROPN
cana-5531	394	8	𝛽2(𝑡	𝛽2(𝑡	PROPN
cana-5531	394	9	)	)	PUNCT
cana-5531	394	10	)	)	PUNCT
cana-5531	395	1	−	−	PROPN
cana-5531	395	2	𝜀	𝜀	PROPN
cana-5531	395	3	(	(	PUNCT
cana-5531	395	4	�	�	PROPN
cana-5531	395	5	̇	̇	PROPN
cana-5531	395	6	�	�	PROPN
cana-5531	395	7	𝛽1(𝑡	𝛽1(𝑡	NOUN
cana-5531	395	8	)	)	PUNCT
cana-5531	395	9	)	)	PUNCT
cana-5531	395	10	)	)	PUNCT
cana-5531	396	1	𝑡	𝑡	PROPN
cana-5531	396	2	0	0	NUM
cana-5531	396	3	〉	〉	NOUN
cana-5531	396	4	ℋ	ℋ	NOUN
cana-5531	396	5	communications	communication	NOUN
cana-5531	396	6	on	on	ADP
cana-5531	396	7	applied	apply	VERB
cana-5531	396	8	nonlinear	nonlinear	ADJ
cana-5531	396	9	analysis	analysis	NOUN
cana-5531	396	10	issn	issn	NOUN
cana-5531	396	11	:	:	PUNCT
cana-5531	396	12	1074	1074	NUM
cana-5531	396	13	-	-	PUNCT
cana-5531	396	14	133x	133x	NUM
cana-5531	396	15	vol	vol	NOUN
cana-5531	396	16	32	32	NUM
cana-5531	396	17	no	no	NOUN
cana-5531	396	18	.	.	NOUN
cana-5531	396	19	3	3	NUM
cana-5531	396	20	(	(	PUNCT
cana-5531	396	21	2025	2025	NUM
cana-5531	396	22	)	)	PUNCT
cana-5531	396	23	981	981	NUM
cana-5531	396	24	https://internationalpubls.com	https://internationalpubls.com	NUM
cana-5531	396	25	≤	≤	NUM
cana-5531	396	26	𝑐5	𝑐5	PROPN
cana-5531	396	27	(	(	PUNCT
cana-5531	396	28	∫	∫	PROPN
cana-5531	396	29	‖𝑢𝛽1(𝑠	‖𝑢𝛽1(𝑠	PROPN
cana-5531	396	30	)	)	PUNCT
cana-5531	396	31	−	−	PROPN
cana-5531	397	1	𝑢𝛽2(𝑠)‖𝑉	𝑢𝛽2(𝑠)‖𝑉	PROPN
cana-5531	397	2	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	397	3	𝑡	𝑡	PROPN
cana-5531	397	4	0	0	NUM
cana-5531	397	5	)	)	PUNCT
cana-5531	397	6	‖𝑢𝛽1(𝑡	‖𝑢𝛽1(𝑡	NOUN
cana-5531	397	7	)	)	PUNCT
cana-5531	397	8	−	−	PUNCT
cana-5531	397	9	𝑢𝛽2(𝑡)‖𝑉	𝑢𝛽2(𝑡)‖𝑉	VERB
cana-5531	397	10	for	for	ADP
cana-5531	397	11	some	some	DET
cana-5531	397	12	positive	positive	ADJ
cana-5531	397	13	constant	constant	ADJ
cana-5531	397	14	c5.using	c5.use	VERB
cana-5531	397	15	young	young	PROPN
cana-5531	397	16	’s	’s	PART
cana-5531	397	17	inequality	inequality	NOUN
cana-5531	397	18	,	,	PUNCT
cana-5531	397	19	it	it	PRON
cana-5531	397	20	finds	find	VERB
cana-5531	397	21	〈	〈	PROPN
cana-5531	397	22	∫	∫	PROPN
cana-5531	397	23	ℱ(𝑡	ℱ(𝑡	X
cana-5531	397	24	−	−	PROPN
cana-5531	397	25	𝑠	𝑠	NOUN
cana-5531	397	26	)	)	PUNCT
cana-5531	397	27	(	(	PUNCT
cana-5531	397	28	𝜀	𝜀	PROPN
cana-5531	397	29	(	(	PUNCT
cana-5531	397	30	𝑢𝛽1(𝑠	𝑢𝛽1(𝑠	PROPN
cana-5531	397	31	)	)	PUNCT
cana-5531	397	32	)	)	PUNCT
cana-5531	398	1	−	−	PROPN
cana-5531	398	2	𝜀(𝑢𝛽2(𝑠	𝜀(𝑢𝛽2(𝑠	PROPN
cana-5531	398	3	)	)	PUNCT
cana-5531	398	4	)	)	PUNCT
cana-5531	398	5	)	)	PUNCT
cana-5531	399	1	𝑡	𝑡	PROPN
cana-5531	399	2	0	0	NUM
cana-5531	399	3	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	399	4	,	,	PUNCT
cana-5531	399	5	𝜀	𝜀	PROPN
cana-5531	399	6	(	(	PUNCT
cana-5531	399	7	�	�	PROPN
cana-5531	399	8	̇	̇	PROPN
cana-5531	399	9	�	�	PROPN
cana-5531	399	10	𝛽1(𝑡	𝛽1(𝑡	NOUN
cana-5531	399	11	)	)	PUNCT
cana-5531	399	12	)	)	PUNCT
cana-5531	400	1	−	−	ADP
cana-5531	400	2	𝜀(	𝜀(	PROPN
cana-5531	400	3	�	�	PROPN
cana-5531	400	4	̇	̇	NOUN
cana-5531	400	5	�	�	PROPN
cana-5531	400	6	𝛽2(𝑡))〉ℋ	𝛽2(𝑡))〉ℋ	NOUN
cana-5531	400	7	≤	≤	NUM
cana-5531	400	8	𝑐5	𝑐5	ADJ
cana-5531	400	9	2	2	NUM
cana-5531	400	10	2𝑚	2𝑚	NOUN
cana-5531	400	11	(	(	PUNCT
cana-5531	400	12	∫	∫	PROPN
cana-5531	400	13	‖𝑢𝛽1(𝑠	‖𝑢𝛽1(𝑠	PROPN
cana-5531	400	14	)	)	PUNCT
cana-5531	401	1	−	−	NOUN
cana-5531	401	2	𝑢𝛽2(𝑠)‖𝑉𝑑𝑠	𝑢𝛽2(𝑠)‖𝑉𝑑𝑠	PUNCT
cana-5531	401	3	𝑡	𝑡	X
cana-5531	401	4	0	0	NUM
cana-5531	401	5	)	)	PUNCT
cana-5531	401	6	2	2	NUM
cana-5531	402	1	+	+	CCONJ
cana-5531	402	2	𝑚	𝑚	SYM
cana-5531	402	3	2	2	NUM
cana-5531	402	4	‖𝑢𝛽1(𝑡	‖𝑢𝛽1(𝑡	NUM
cana-5531	402	5	)	)	PUNCT
cana-5531	402	6	−	−	PROPN
cana-5531	402	7	𝑢𝛽2(𝑡)‖𝑉	𝑢𝛽2(𝑡)‖𝑉	PROPN
cana-5531	402	8	2	2	NUM
cana-5531	402	9	(	(	PUNCT
cana-5531	402	10	5.32	5.32	NUM
cana-5531	402	11	)	)	PUNCT
cana-5531	402	12	using	use	VERB
cana-5531	402	13	the	the	DET
cana-5531	402	14	properties	property	NOUN
cana-5531	402	15	of	of	ADP
cana-5531	402	16	rν	rν	PROPN
cana-5531	402	17	and	and	CCONJ
cana-5531	402	18	rτ	rτ	NOUN
cana-5531	402	19	(	(	PUNCT
cana-5531	402	20	see	see	VERB
cana-5531	402	21	[	[	X
cana-5531	402	22	1	1	NUM
cana-5531	402	23	,	,	PUNCT
cana-5531	402	24	20,21	20,21	NUM
cana-5531	402	25	]	]	PUNCT
cana-5531	402	26	)	)	PUNCT
cana-5531	402	27	,	,	PUNCT
cana-5531	402	28	we	we	PRON
cana-5531	402	29	have	have	VERB
cana-5531	402	30	ℎ	ℎ	X
cana-5531	402	31	(	(	PUNCT
cana-5531	402	32	𝛽1(𝑡	𝛽1(𝑡	NOUN
cana-5531	402	33	)	)	PUNCT
cana-5531	402	34	,	,	PUNCT
cana-5531	402	35	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	402	36	)	)	PUNCT
cana-5531	402	37	,	,	PUNCT
cana-5531	402	38	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	PROPN
cana-5531	402	39	)	)	PUNCT
cana-5531	402	40	−	−	PROPN
cana-5531	402	41	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	NOUN
cana-5531	402	42	)	)	PUNCT
cana-5531	402	43	)	)	PUNCT
cana-5531	403	1	+	+	CCONJ
cana-5531	403	2	ℎ	ℎ	X
cana-5531	403	3	(	(	PUNCT
cana-5531	403	4	𝛽2(𝑡	𝛽2(𝑡	PROPN
cana-5531	403	5	)	)	PUNCT
cana-5531	403	6	,	,	PUNCT
cana-5531	403	7	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	PROPN
cana-5531	403	8	)	)	PUNCT
cana-5531	403	9	,	,	PUNCT
cana-5531	403	10	𝑢𝛽1(𝑡	𝑢𝛽1(𝑡	PROPN
cana-5531	403	11	)	)	PUNCT
cana-5531	403	12	−	−	PROPN
cana-5531	403	13	𝑢𝛽2(𝑡	𝑢𝛽2(𝑡	NOUN
cana-5531	403	14	)	)	PUNCT
cana-5531	403	15	)	)	PUNCT
cana-5531	403	16	≤	≤	NUM
cana-5531	403	17	𝑐6‖𝛽1(𝑡	𝑐6‖𝛽1(𝑡	NOUN
cana-5531	403	18	)	)	PUNCT
cana-5531	403	19	−	−	ADP
cana-5531	403	20	𝛽2(𝑡)‖𝕃2(γ3)‖𝑢𝛽1(𝑡	𝛽2(𝑡)‖𝕃2(γ3)‖𝑢𝛽1(𝑡	NOUN
cana-5531	403	21	)	)	PUNCT
cana-5531	403	22	−	−	PROPN
cana-5531	403	23	𝑢𝛽2(𝑡)‖𝑉	𝑢𝛽2(𝑡)‖𝑉	PROPN
cana-5531	403	24	where	where	SCONJ
cana-5531	403	25	c6	c6	PROPN
cana-5531	403	26	>	>	X
cana-5531	403	27	0	0	X
cana-5531	403	28	.	.	PUNCT
cana-5531	404	1	using	use	VERB
cana-5531	404	2	also	also	ADV
cana-5531	404	3	(	(	PUNCT
cana-5531	404	4	4.2	4.2	NUM
cana-5531	404	5	)	)	PUNCT
cana-5531	404	6	,	,	PUNCT
cana-5531	404	7	(	(	PUNCT
cana-5531	404	8	4.13	4.13	NUM
cana-5531	404	9	)	)	PUNCT
cana-5531	404	10	and	and	CCONJ
cana-5531	404	11	(	(	PUNCT
cana-5531	404	12	4.14	4.14	NUM
cana-5531	404	13	)	)	PUNCT
cana-5531	404	14	(	(	PUNCT
cana-5531	404	15	c	c	X
cana-5531	404	16	)	)	PUNCT
cana-5531	404	17	yields	yield	NOUN
cana-5531	404	18	and	and	CCONJ
cana-5531	404	19	using	use	VERB
cana-5531	404	20	young	young	PROPN
cana-5531	404	21	’s	’s	PART
cana-5531	404	22	inequality	inequality	NOUN
cana-5531	404	23	it	it	PRON
cana-5531	404	24	results	result	VERB
cana-5531	404	25	:	:	PUNCT
cana-5531	404	26	𝑐6‖𝛽1(𝑡	𝑐6‖𝛽1(𝑡	NOUN
cana-5531	404	27	)	)	PUNCT
cana-5531	404	28	−	−	ADP
cana-5531	404	29	𝛽2(𝑡)‖𝕃2(γ3)‖𝑢𝛽1(𝑡	𝛽2(𝑡)‖𝕃2(γ3)‖𝑢𝛽1(𝑡	NOUN
cana-5531	404	30	)	)	PUNCT
cana-5531	404	31	−	−	ADP
cana-5531	404	32	𝑢𝛽2(𝑡)‖𝑉	𝑢𝛽2(𝑡)‖𝑉	ADJ
cana-5531	404	33	≤	≤	NUM
cana-5531	404	34	𝑐7‖𝛽1(𝑡	𝑐7‖𝛽1(𝑡	NOUN
cana-5531	404	35	)	)	PUNCT
cana-5531	404	36	−	−	NOUN
cana-5531	404	37	𝛽2(𝑡)‖𝕃2(γ3	𝛽2(𝑡)‖𝕃2(γ3	NOUN
cana-5531	404	38	)	)	PUNCT
cana-5531	404	39	2	2	NUM
cana-5531	405	1	+	+	CCONJ
cana-5531	405	2	𝑚	𝑚	SYM
cana-5531	405	3	4	4	NUM
cana-5531	405	4	‖𝑢𝛽1(𝑡	‖𝑢𝛽1(𝑡	NUM
cana-5531	405	5	)	)	PUNCT
cana-5531	405	6	−	−	PROPN
cana-5531	405	7	𝑢𝛽2(𝑡)‖𝑉	𝑢𝛽2(𝑡)‖𝑉	PROPN
cana-5531	405	8	2	2	NUM
cana-5531	405	9	(	(	PUNCT
cana-5531	405	10	5.33	5.33	NUM
cana-5531	405	11	)	)	PUNCT
cana-5531	405	12	for	for	ADP
cana-5531	405	13	some	some	DET
cana-5531	405	14	contant	contant	PROPN
cana-5531	405	15	c7	c7	PROPN
cana-5531	405	16	>	>	X
cana-5531	405	17	0	0	PROPN
cana-5531	405	18	.	.	PUNCT
cana-5531	406	1	then	then	ADV
cana-5531	406	2	(	(	PUNCT
cana-5531	406	3	5.33	5.33	NUM
cana-5531	406	4	)	)	PUNCT
cana-5531	406	5	implies	imply	VERB
cana-5531	406	6	that	that	SCONJ
cana-5531	406	7	1	1	NUM
cana-5531	406	8	2	2	NUM
cana-5531	406	9	𝑑	𝑑	NOUN
cana-5531	406	10	𝑑𝑡	𝑑𝑡	ADP
cana-5531	406	11	|	|	NOUN
cana-5531	406	12	�	�	NOUN
cana-5531	406	13	̇	̇	NOUN
cana-5531	406	14	�	�	PROPN
cana-5531	406	15	1	1	NUM
cana-5531	406	16	−	−	PROPN
cana-5531	406	17	�	�	PROPN
cana-5531	406	18	̇	̇	PROPN
cana-5531	406	19	�	�	PROPN
cana-5531	406	20	2|	2|	NUM
cana-5531	406	21	2	2	NUM
cana-5531	406	22	+	+	CCONJ
cana-5531	406	23	𝑚	𝑚	SYM
cana-5531	406	24	4	4	NUM
cana-5531	406	25	‖𝑢𝛽1(𝑡	‖𝑢𝛽1(𝑡	NUM
cana-5531	406	26	)	)	PUNCT
cana-5531	406	27	−	−	PROPN
cana-5531	406	28	𝑢𝛽2(𝑡)‖𝑉	𝑢𝛽2(𝑡)‖𝑉	PROPN
cana-5531	406	29	2	2	NUM
cana-5531	406	30	≤	≤	NOUN
cana-5531	406	31	𝑐0𝑀𝑑ω‖𝜇‖𝕃∞(γ3)‖𝑢𝛽1(𝑡	𝑐0𝑀𝑑ω‖𝜇‖𝕃∞(γ3)‖𝑢𝛽1(𝑡	NOUN
cana-5531	406	32	)	)	PUNCT
cana-5531	406	33	−	−	PROPN
cana-5531	406	34	𝑢𝛽2(𝑡)‖𝑉	𝑢𝛽2(𝑡)‖𝑉	PROPN
cana-5531	406	35	2	2	NUM
cana-5531	406	36	+	+	CCONJ
cana-5531	406	37	𝑐5	𝑐5	ADJ
cana-5531	406	38	2	2	NUM
cana-5531	406	39	2𝑚	2𝑚	NOUN
cana-5531	406	40	(	(	PUNCT
cana-5531	406	41	∫	∫	PROPN
cana-5531	406	42	‖𝑢𝛽1(𝑠	‖𝑢𝛽1(𝑠	PROPN
cana-5531	406	43	)	)	PUNCT
cana-5531	406	44	−	−	NOUN
cana-5531	406	45	𝑢𝛽2(𝑠)‖𝑉𝑑𝑠	𝑢𝛽2(𝑠)‖𝑉𝑑𝑠	PUNCT
cana-5531	406	46	𝑡	𝑡	X
cana-5531	406	47	0	0	NUM
cana-5531	406	48	)	)	PUNCT
cana-5531	406	49	2	2	NUM
cana-5531	406	50	+	+	NOUN
cana-5531	406	51	𝑐7‖𝛽1(𝑡	𝑐7‖𝛽1(𝑡	NOUN
cana-5531	406	52	)	)	PUNCT
cana-5531	406	53	−	−	NOUN
cana-5531	406	54	𝛽2(𝑡)‖𝕃2(γ3	𝛽2(𝑡)‖𝕃2(γ3	NOUN
cana-5531	406	55	)	)	PUNCT
cana-5531	406	56	2	2	NUM
cana-5531	407	1	+	+	CCONJ
cana-5531	407	2	𝑚𝒢	𝑚𝒢	ADJ
cana-5531	407	3	2	2	NUM
cana-5531	407	4	|	|	NOUN
cana-5531	407	5	�	�	NOUN
cana-5531	407	6	̇	̇	NOUN
cana-5531	407	7	�	�	PROPN
cana-5531	407	8	1	1	NUM
cana-5531	407	9	−	−	PROPN
cana-5531	407	10	�	�	PROPN
cana-5531	407	11	̇	̇	PROPN
cana-5531	407	12	�	�	PROPN
cana-5531	407	13	2|	2|	NUM
cana-5531	407	14	2	2	NUM
cana-5531	407	15	let	let	VERB
cana-5531	407	16	now	now	ADV
cana-5531	407	17	𝜇0	𝜇0	PROPN
cana-5531	407	18	=	=	SYM
cana-5531	407	19	𝜇1	𝜇1	PROPN
cana-5531	407	20	4	4	NUM
cana-5531	407	21	,	,	PUNCT
cana-5531	407	22	then	then	ADV
cana-5531	407	23	if	if	SCONJ
cana-5531	407	24	‖𝜇‖𝕃2(γ3	‖𝜇‖𝕃2(γ3	NOUN
cana-5531	407	25	)	)	PUNCT
cana-5531	407	26	<	<	X
cana-5531	407	27	𝜇0	𝜇0	PROPN
cana-5531	407	28	,	,	PUNCT
cana-5531	407	29	it	it	PRON
cana-5531	407	30	deduces	deduce	VERB
cana-5531	407	31	that	that	SCONJ
cana-5531	407	32	there	there	PRON
cana-5531	407	33	exists	exist	VERB
cana-5531	407	34	a	a	DET
cana-5531	407	35	constant	constant	ADJ
cana-5531	407	36	𝑐8	𝑐8	NOUN
cana-5531	407	37	>	>	X
cana-5531	407	38	0	0	PUNCT
cana-5531	408	1	such	such	ADJ
cana-5531	408	2	that	that	DET
cana-5531	408	3	∫	∫	PROPN
cana-5531	408	4	1	1	NUM
cana-5531	408	5	2	2	NUM
cana-5531	408	6	𝑑	𝑑	NOUN
cana-5531	408	7	𝑑𝑡	𝑑𝑡	ADP
cana-5531	408	8	|	|	NOUN
cana-5531	408	9	�	�	NOUN
cana-5531	408	10	̇	̇	NOUN
cana-5531	408	11	�	�	PROPN
cana-5531	408	12	1	1	NUM
cana-5531	408	13	−	−	PROPN
cana-5531	408	14	�	�	PROPN
cana-5531	408	15	̇	̇	PROPN
cana-5531	408	16	�	�	PROPN
cana-5531	408	17	2|	2|	NUM
cana-5531	408	18	2𝑑𝑡	2𝑑𝑡	NOUN
cana-5531	408	19	𝑠	𝑠	ADP
cana-5531	408	20	0	0	NUM
cana-5531	409	1	+	+	NUM
cana-5531	409	2	∫	∫	PROPN
cana-5531	409	3	‖𝑢𝛽1(𝑡	‖𝑢𝛽1(𝑡	SYM
cana-5531	409	4	)	)	PUNCT
cana-5531	409	5	−	−	PROPN
cana-5531	409	6	𝑢𝛽2(𝑡)‖𝑉	𝑢𝛽2(𝑡)‖𝑉	PROPN
cana-5531	409	7	2	2	NUM
cana-5531	409	8	𝑑𝑡	𝑑𝑡	ADP
cana-5531	409	9	𝑠	𝑠	PROPN
cana-5531	409	10	0	0	NUM
cana-5531	409	11	≤	≤	NOUN
cana-5531	409	12	𝑐8	𝑐8	NOUN
cana-5531	409	13	∫	∫	PROPN
cana-5531	409	14	(	(	PUNCT
cana-5531	409	15	∫	∫	PROPN
cana-5531	409	16	‖𝑢𝛽1(𝑠	‖𝑢𝛽1(𝑠	PROPN
cana-5531	409	17	)	)	PUNCT
cana-5531	410	1	−	−	NOUN
cana-5531	411	1	𝑢𝛽2(𝑠)‖𝑉	𝑢𝛽2(𝑠)‖𝑉	PROPN
cana-5531	411	2	2	2	NUM
cana-5531	411	3	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	411	4	+	+	NOUN
cana-5531	411	5	‖𝛽1(𝑡	‖𝛽1(𝑡	NOUN
cana-5531	411	6	)	)	PUNCT
cana-5531	411	7	−	−	NOUN
cana-5531	411	8	𝛽2(𝑡)‖𝕃2(γ3	𝛽2(𝑡)‖𝕃2(γ3	NOUN
cana-5531	411	9	)	)	PUNCT
cana-5531	411	10	2𝑡	2𝑡	NOUN
cana-5531	411	11	0	0	NUM
cana-5531	411	12	)	)	PUNCT
cana-5531	411	13	𝑠	𝑠	ADP
cana-5531	411	14	0	0	NUM
cana-5531	411	15	𝑑𝑡	𝑑𝑡	ADP
cana-5531	411	16	+	+	CCONJ
cana-5531	411	17	𝑀𝒢	𝑀𝒢	PROPN
cana-5531	411	18	2	2	NUM
cana-5531	411	19	|	|	NOUN
cana-5531	411	20	�	�	NOUN
cana-5531	411	21	̇	̇	NOUN
cana-5531	411	22	�	�	PROPN
cana-5531	411	23	1	1	NUM
cana-5531	411	24	−	−	PROPN
cana-5531	411	25	�	�	PROPN
cana-5531	411	26	̇	̇	PROPN
cana-5531	411	27	�	�	PROPN
cana-5531	411	28	2|	2|	PROPN
cana-5531	411	29	2	2	NUM
cana-5531	411	30	.	.	PUNCT
cana-5531	411	31	then	then	ADV
cana-5531	411	32	using	use	VERB
cana-5531	411	33	gronwall	gronwall	PROPN
cana-5531	411	34	’s	’s	PART
cana-5531	411	35	argument	argument	NOUN
cana-5531	411	36	,	,	PUNCT
cana-5531	411	37	it	it	PRON
cana-5531	411	38	follows	follow	VERB
cana-5531	411	39	that	that	SCONJ
cana-5531	411	40	there	there	PRON
cana-5531	411	41	exists	exist	VERB
cana-5531	411	42	a	a	DET
cana-5531	411	43	constant	constant	ADJ
cana-5531	411	44	𝑐	𝑐	NOUN
cana-5531	411	45	>	>	X
cana-5531	411	46	0	0	NUM
cana-5531	411	47	such	such	ADJ
cana-5531	411	48	that	that	SCONJ
cana-5531	411	49	1	1	NUM
cana-5531	411	50	2	2	NUM
cana-5531	411	51	|	|	NOUN
cana-5531	411	52	�	�	NOUN
cana-5531	411	53	̇	̇	NOUN
cana-5531	411	54	�	�	PROPN
cana-5531	411	55	1	1	NUM
cana-5531	411	56	−	−	PROPN
cana-5531	411	57	�	�	PROPN
cana-5531	411	58	̇	̇	PROPN
cana-5531	411	59	�	�	PROPN
cana-5531	411	60	2|	2|	NUM
cana-5531	411	61	2	2	NUM
cana-5531	412	1	+	+	NOUN
cana-5531	412	2	∫	∫	NOUN
cana-5531	412	3	‖𝑢𝛽1(𝑡	‖𝑢𝛽1(𝑡	INTJ
cana-5531	412	4	)	)	PUNCT
cana-5531	412	5	−	−	PROPN
cana-5531	413	1	𝑢𝛽2(𝑡)‖𝑉	𝑢𝛽2(𝑡)‖𝑉	PROPN
cana-5531	413	2	2	2	NUM
cana-5531	413	3	𝑑𝑡	𝑑𝑡	ADP
cana-5531	413	4	𝑠	𝑠	PROPN
cana-5531	413	5	0	0	NUM
cana-5531	413	6	∫	∫	PROPN
cana-5531	413	7	(	(	PUNCT
cana-5531	413	8	∫	∫	PROPN
cana-5531	413	9	‖𝑢𝛽1(𝑠	‖𝑢𝛽1(𝑠	PROPN
cana-5531	413	10	)	)	PUNCT
cana-5531	414	1	−	−	NOUN
cana-5531	415	1	𝑢𝛽2(𝑠)‖𝑉	𝑢𝛽2(𝑠)‖𝑉	PROPN
cana-5531	415	2	2	2	NUM
cana-5531	415	3	𝑑𝑠	𝑑𝑠	NOUN
cana-5531	415	4	+	+	NOUN
cana-5531	415	5	‖𝛽1(𝑠	‖𝛽1(𝑠	PROPN
cana-5531	415	6	)	)	PUNCT
cana-5531	415	7	−	−	PROPN
cana-5531	415	8	𝛽2(𝑠)‖𝕃2(γ3	𝛽2(𝑠)‖𝕃2(γ3	PROPN
cana-5531	415	9	)	)	PUNCT
cana-5531	415	10	2	2	NUM
cana-5531	415	11	𝑡	𝑡	NOUN
cana-5531	415	12	0	0	NUM
cana-5531	415	13	)	)	PUNCT
cana-5531	415	14	𝑑𝑡	𝑑𝑡	ADP
cana-5531	415	15	𝑠	𝑠	PROPN
cana-5531	415	16	0	0	PUNCT
cana-5531	416	1	+	+	CCONJ
cana-5531	416	2	𝑀𝒢	𝑀𝒢	PROPN
cana-5531	416	3	2	2	NUM
cana-5531	416	4	|	|	NOUN
cana-5531	416	5	�	�	NOUN
cana-5531	416	6	̇	̇	NOUN
cana-5531	416	7	�	�	PROPN
cana-5531	416	8	1	1	NUM
cana-5531	416	9	−	−	PROPN
cana-5531	416	10	�	�	PROPN
cana-5531	416	11	̇	̇	PROPN
cana-5531	416	12	�	�	PROPN
cana-5531	416	13	2|	2|	PROPN
cana-5531	416	14	2	2	NUM
cana-5531	416	15	.	.	PUNCT
cana-5531	417	1	(	(	PUNCT
cana-5531	417	2	5.34	5.34	NUM
cana-5531	417	3	)	)	PUNCT
cana-5531	417	4	communications	communication	NOUN
cana-5531	417	5	on	on	ADP
cana-5531	417	6	applied	apply	VERB
cana-5531	417	7	nonlinear	nonlinear	ADJ
cana-5531	417	8	analysis	analysis	NOUN
cana-5531	417	9	issn	issn	NOUN
cana-5531	417	10	:	:	PUNCT
cana-5531	417	11	1074	1074	NUM
cana-5531	417	12	-	-	PUNCT
cana-5531	417	13	133x	133x	NUM
cana-5531	417	14	vol	vol	NOUN
cana-5531	417	15	32	32	NUM
cana-5531	417	16	no	no	NOUN
cana-5531	417	17	.	.	NOUN
cana-5531	417	18	3	3	NUM
cana-5531	417	19	(	(	PUNCT
cana-5531	417	20	2025	2025	NUM
cana-5531	417	21	)	)	PUNCT
cana-5531	417	22	982	982	NUM
cana-5531	417	23	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	417	24	now	now	ADV
cana-5531	417	25	to	to	PART
cana-5531	417	26	end	end	VERB
cana-5531	417	27	the	the	DET
cana-5531	417	28	proof	proof	NOUN
cana-5531	417	29	of	of	ADP
cana-5531	417	30	proposition	proposition	NOUN
cana-5531	417	31	5.8	5.8	NUM
cana-5531	417	32	using	use	VERB
cana-5531	417	33	(	(	PUNCT
cana-5531	417	34	5.30	5.30	NUM
cana-5531	417	35	)	)	PUNCT
cana-5531	417	36	and	and	CCONJ
cana-5531	417	37	(	(	PUNCT
cana-5531	417	38	5.34	5.34	NUM
cana-5531	417	39	)	)	PUNCT
cana-5531	417	40	to	to	PART
cana-5531	417	41	deduce	deduce	VERB
cana-5531	417	42	‖𝜙𝛽1(𝑡	‖𝜙𝛽1(𝑡	NOUN
cana-5531	417	43	)	)	PUNCT
cana-5531	418	1	−	−	PRON
cana-5531	418	2	𝜙𝛽2(𝑡)‖𝕃2(γ3	𝜙𝛽2(𝑡)‖𝕃2(γ3	PROPN
cana-5531	418	3	)	)	PUNCT
cana-5531	418	4	≤	≤	NUM
cana-5531	418	5	𝑐9	𝑐9	NOUN
cana-5531	418	6	∫	∫	PROPN
cana-5531	418	7	‖𝛽1(𝑠	‖𝛽1(𝑠	PROPN
cana-5531	418	8	)	)	PUNCT
cana-5531	418	9	−	−	ADP
cana-5531	418	10	𝛽2(𝑠)‖𝕃2(γ3)𝑑𝑠	𝛽2(𝑠)‖𝕃2(γ3)𝑑𝑠	VERB
cana-5531	418	11	∀𝑡	∀𝑡	PROPN
cana-5531	418	12	∈	∈	PROPN
cana-5531	419	1	[	[	X
cana-5531	419	2	0	0	NUM
cana-5531	419	3	,	,	PUNCT
cana-5531	419	4	𝑇	𝑇	PROPN
cana-5531	419	5	]	]	PUNCT
cana-5531	419	6	𝑡	𝑡	X
cana-5531	419	7	0	0	NUM
cana-5531	419	8	,	,	PUNCT
cana-5531	419	9	where	where	SCONJ
cana-5531	419	10	c9	c9	NOUN
cana-5531	419	11	>	>	X
cana-5531	419	12	0	0	PUNCT
cana-5531	420	1	and	and	CCONJ
cana-5531	420	2	then	then	ADV
cana-5531	420	3	we	we	PRON
cana-5531	420	4	obtain	obtain	VERB
cana-5531	420	5	and	and	CCONJ
cana-5531	420	6	reiterating	reiterate	VERB
cana-5531	420	7	this	this	DET
cana-5531	420	8	inequality	inequality	NOUN
cana-5531	420	9	n	n	PRON
cana-5531	420	10	times	time	NOUN
cana-5531	420	11	,	,	PUNCT
cana-5531	420	12	yield	yield	VERB
cana-5531	420	13	‖𝜙𝛽1	‖𝜙𝛽1	NOUN
cana-5531	420	14	−	−	NOUN
cana-5531	420	15	𝜙𝛽2‖𝕃2(γ3	𝜙𝛽2‖𝕃2(γ3	NOUN
cana-5531	420	16	)	)	PUNCT
cana-5531	420	17	≤	≤	NUM
cana-5531	420	18	𝑐9	𝑐9	NOUN
cana-5531	420	19	𝑘	𝑘	PROPN
cana-5531	420	20	‖𝛽1	‖𝛽1	NOUN
cana-5531	420	21	−	−	PUNCT
cana-5531	420	22	𝛽2‖𝕃2(γ3	𝛽2‖𝕃2(γ3	NOUN
cana-5531	420	23	)	)	PUNCT
cana-5531	420	24	.	.	PUNCT
cana-5531	421	1	‖𝜙𝑛𝛽1(𝑡	‖𝜙𝑛𝛽1(𝑡	NOUN
cana-5531	421	2	)	)	PUNCT
cana-5531	421	3	−	−	NOUN
cana-5531	421	4	𝜙	𝜙	PRON
cana-5531	421	5	𝑛𝛽2(𝑡)‖𝕃2(γ3	𝑛𝛽2(𝑡)‖𝕃2(γ3	NOUN
cana-5531	421	6	)	)	PUNCT
cana-5531	421	7	≤	≤	NOUN
cana-5531	421	8	(	(	PUNCT
cana-5531	421	9	𝑐9𝑇	𝑐9𝑇	NOUN
cana-5531	421	10	𝑘	𝑘	X
cana-5531	421	11	)	)	PUNCT
cana-5531	421	12	𝑛	𝑛	PROPN
cana-5531	421	13	1	1	NUM
cana-5531	421	14	𝑛	𝑛	NOUN
cana-5531	421	15	!	!	PUNCT
cana-5531	422	1	‖𝛽1	‖𝛽1	NOUN
cana-5531	422	2	−	−	PUNCT
cana-5531	422	3	𝛽2‖𝕃2(γ3	𝛽2‖𝕃2(γ3	NOUN
cana-5531	422	4	)	)	PUNCT
cana-5531	422	5	.	.	PUNCT
cana-5531	423	1	as	as	ADP
cana-5531	423	2	lim	lim	PROPN
cana-5531	423	3	𝑛→+∞	𝑛→+∞	PROPN
cana-5531	423	4	(	(	PUNCT
cana-5531	423	5	𝑐9𝑇	𝑐9𝑇	NOUN
cana-5531	423	6	𝑘	𝑘	X
cana-5531	423	7	)	)	PUNCT
cana-5531	423	8	𝑛	𝑛	PROPN
cana-5531	423	9	1	1	NUM
cana-5531	423	10	𝑛	𝑛	NOUN
cana-5531	423	11	!	!	PUNCT
cana-5531	423	12	=	=	SYM
cana-5531	423	13	0	0	NUM
cana-5531	423	14	,	,	PUNCT
cana-5531	423	15	it	it	PRON
cana-5531	423	16	follows	follow	VERB
cana-5531	423	17	that	that	SCONJ
cana-5531	423	18	for	for	SCONJ
cana-5531	423	19	a	a	DET
cana-5531	423	20	position	position	NOUN
cana-5531	423	21	integer	integer	NOUN
cana-5531	423	22	𝑛	𝑛	ADP
cana-5531	423	23	sufficiently	sufficiently	ADV
cana-5531	423	24	large	large	ADJ
cana-5531	423	25	,	,	PUNCT
cana-5531	423	26	𝜙𝑛	𝜙𝑛	PRON
cana-5531	423	27	is	be	AUX
cana-5531	423	28	a	a	DET
cana-5531	423	29	contraction	contraction	NOUN
cana-5531	423	30	;	;	PUNCT
cana-5531	423	31	then	then	ADV
cana-5531	423	32	,	,	PUNCT
cana-5531	423	33	by	by	ADP
cana-5531	423	34	using	use	VERB
cana-5531	423	35	the	the	DET
cana-5531	423	36	banach	banach	ADV
cana-5531	423	37	fixed	fix	VERB
cana-5531	423	38	point	point	NOUN
cana-5531	423	39	theorem	theorem	VERB
cana-5531	423	40	,	,	PUNCT
cana-5531	423	41	it	it	PRON
cana-5531	423	42	has	have	VERB
cana-5531	423	43	a	a	DET
cana-5531	423	44	unique	unique	ADJ
cana-5531	423	45	fixed	fix	VERB
cana-5531	423	46	point	point	NOUN
cana-5531	423	47	𝛽∗	𝛽∗	NOUN
cana-5531	423	48	which	which	PRON
cana-5531	423	49	satisfies	satisfy	VERB
cana-5531	423	50	(	(	PUNCT
cana-5531	423	51	5.28	5.28	NUM
cana-5531	423	52	)	)	PUNCT
cana-5531	423	53	and	and	CCONJ
cana-5531	423	54	(	(	PUNCT
cana-5531	423	55	5.29	5.29	NUM
cana-5531	423	56	)	)	PUNCT
cana-5531	423	57	.	.	PUNCT
cana-5531	424	1	now	now	ADV
cana-5531	424	2	we	we	PRON
cana-5531	424	3	have	have	VERB
cana-5531	424	4	all	all	DET
cana-5531	424	5	ingredients	ingredient	NOUN
cana-5531	424	6	to	to	PART
cana-5531	424	7	prove	prove	VERB
cana-5531	424	8	theorem	theorem	VERB
cana-5531	424	9	5.1	5.1	NUM
cana-5531	424	10	.	.	PUNCT
cana-5531	425	1	proof	proof	NOUN
cana-5531	425	2	of	of	ADP
cana-5531	425	3	theorem	theorem	ADJ
cana-5531	425	4	5.1	5.1	NUM
cana-5531	425	5	.	.	PUNCT
cana-5531	426	1	existence	existence	NOUN
cana-5531	426	2	.	.	PUNCT
cana-5531	427	1	let	let	VERB
cana-5531	427	2	𝛽	𝛽	NOUN
cana-5531	427	3	=	=	SYM
cana-5531	427	4	𝜉∗	𝜉∗	VERB
cana-5531	427	5	and	and	CCONJ
cana-5531	427	6	let	let	VERB
cana-5531	427	7	𝑢𝜉∗	𝑢𝜉∗	VERB
cana-5531	427	8	the	the	DET
cana-5531	427	9	solution	solution	NOUN
cana-5531	427	10	of	of	ADP
cana-5531	427	11	problem	problem	NOUN
cana-5531	427	12	p1	p1	PROPN
cana-5531	427	13	.	.	PUNCT
cana-5531	428	1	we	we	PRON
cana-5531	428	2	conclude	conclude	VERB
cana-5531	428	3	by	by	ADP
cana-5531	428	4	(	(	PUNCT
cana-5531	428	5	5.1	5.1	NUM
cana-5531	428	6	)	)	PUNCT
cana-5531	428	7	,	,	PUNCT
cana-5531	428	8	(	(	PUNCT
cana-5531	428	9	5.28	5.28	NUM
cana-5531	428	10	)	)	PUNCT
cana-5531	428	11	and	and	CCONJ
cana-5531	428	12	(	(	PUNCT
cana-5531	428	13	5.29	5.29	NUM
cana-5531	428	14	)	)	PUNCT
cana-5531	428	15	that	that	SCONJ
cana-5531	428	16	(	(	PUNCT
cana-5531	428	17	𝑢𝜉∗	𝑢𝜉∗	PROPN
cana-5531	428	18	,	,	PUNCT
cana-5531	428	19	𝜉	𝜉	NOUN
cana-5531	428	20	∗	∗	NOUN
cana-5531	428	21	)	)	PUNCT
cana-5531	428	22	is	be	AUX
cana-5531	428	23	a	a	DET
cana-5531	428	24	solution	solution	NOUN
cana-5531	428	25	of	of	ADP
cana-5531	428	26	problem	problem	NOUN
cana-5531	428	27	pv	pv	INTJ
cana-5531	428	28	.	.	PUNCT
cana-5531	429	1	uniqueness	uniqueness	PROPN
cana-5531	429	2	.	.	PUNCT
cana-5531	430	1	suppose	suppose	VERB
cana-5531	430	2	that	that	SCONJ
cana-5531	430	3	(	(	PUNCT
cana-5531	430	4	𝑢	𝑢	X
cana-5531	430	5	,	,	PUNCT
cana-5531	430	6	𝛽	𝛽	NOUN
cana-5531	430	7	)	)	PUNCT
cana-5531	430	8	is	be	AUX
cana-5531	430	9	a	a	DET
cana-5531	430	10	solution	solution	NOUN
cana-5531	430	11	of	of	ADP
cana-5531	430	12	problem	problem	NOUN
cana-5531	430	13	pv	pv	INTJ
cana-5531	430	14	which	which	PRON
cana-5531	430	15	satisfies	satisfy	VERB
cana-5531	430	16	(	(	PUNCT
cana-5531	430	17	4.15	4.15	NUM
cana-5531	430	18	)	)	PUNCT
cana-5531	430	19	,	,	PUNCT
cana-5531	430	20	(	(	PUNCT
cana-5531	430	21	4.16	4.16	NUM
cana-5531	430	22	)	)	PUNCT
cana-5531	430	23	and	and	CCONJ
cana-5531	430	24	(	(	PUNCT
cana-5531	430	25	4.17	4.17	NUM
cana-5531	430	26	)	)	PUNCT
cana-5531	430	27	.	.	PUNCT
cana-5531	431	1	it	it	PRON
cana-5531	431	2	follows	follow	VERB
cana-5531	431	3	from	from	ADP
cana-5531	431	4	(	(	PUNCT
cana-5531	431	5	4.15	4.15	NUM
cana-5531	431	6	)	)	PUNCT
cana-5531	431	7	that	that	SCONJ
cana-5531	431	8	𝑢	𝑢	PROPN
cana-5531	431	9	is	be	AUX
cana-5531	431	10	a	a	DET
cana-5531	431	11	solution	solution	NOUN
cana-5531	431	12	to	to	PART
cana-5531	431	13	problem	problem	VERB
cana-5531	431	14	𝑃1𝜉	𝑃1𝜉	PROPN
cana-5531	431	15	and	and	CCONJ
cana-5531	431	16	from	from	ADP
cana-5531	431	17	theorem	theorem	ADJ
cana-5531	431	18	5.2	5.2	NUM
cana-5531	431	19	that	that	PRON
cana-5531	431	20	𝑢	𝑢	ADJ
cana-5531	431	21	=	=	NOUN
cana-5531	431	22	𝑢𝛽.take	𝑢𝛽.take	X
cana-5531	431	23	𝑢	𝑢	X
cana-5531	431	24	=	=	X
cana-5531	431	25	𝑢𝛽in	𝑢𝛽in	X
cana-5531	431	26	(	(	PUNCT
cana-5531	431	27	4.15	4.15	NUM
cana-5531	431	28	)	)	PUNCT
cana-5531	431	29	and	and	CCONJ
cana-5531	431	30	use	use	VERB
cana-5531	431	31	the	the	DET
cana-5531	431	32	initial	initial	ADJ
cana-5531	431	33	condition	condition	NOUN
cana-5531	431	34	(	(	PUNCT
cana-5531	431	35	4.17	4.17	NUM
cana-5531	431	36	)	)	PUNCT
cana-5531	431	37	,	,	PUNCT
cana-5531	431	38	we	we	PRON
cana-5531	431	39	deduce	deduce	VERB
cana-5531	431	40	that	that	SCONJ
cana-5531	431	41	𝛽	𝛽	NOUN
cana-5531	431	42	is	be	AUX
cana-5531	431	43	a	a	DET
cana-5531	431	44	solution	solution	NOUN
cana-5531	431	45	to	to	ADP
cana-5531	431	46	problem𝑃𝑎𝑑	problem𝑃𝑎𝑑	VERB
cana-5531	431	47	..	..	PUNCT
cana-5531	431	48	therefor	therefor	ADV
cana-5531	431	49	,	,	PUNCT
cana-5531	431	50	we	we	PRON
cana-5531	431	51	obtain	obtain	VERB
cana-5531	431	52	from	from	ADP
cana-5531	431	53	proposition	proposition	NOUN
cana-5531	431	54	5.8	5.8	NUM
cana-5531	431	55	that	that	PRON
cana-5531	431	56	𝛽	𝛽	NOUN
cana-5531	431	57	=	=	SYM
cana-5531	431	58	𝛽∗	𝛽∗	NOUN
cana-5531	432	1	and	and	CCONJ
cana-5531	432	2	then	then	ADV
cana-5531	432	3	we	we	PRON
cana-5531	432	4	conclude	conclude	VERB
cana-5531	432	5	that	that	PRON
cana-5531	432	6	(	(	PUNCT
cana-5531	432	7	𝑢𝛽∗	𝑢𝛽∗	NOUN
cana-5531	432	8	,	,	PUNCT
cana-5531	432	9	𝛽	𝛽	NOUN
cana-5531	432	10	∗	∗	NOUN
cana-5531	432	11	)	)	PUNCT
cana-5531	432	12	is	be	AUX
cana-5531	432	13	a	a	DET
cana-5531	432	14	unique	unique	ADJ
cana-5531	432	15	solution	solution	NOUN
cana-5531	432	16	to	to	ADP
cana-5531	432	17	problem	problem	NOUN
cana-5531	433	1	pv	pv	INTJ
cana-5531	433	2	.	.	PUNCT
cana-5531	434	1	let	let	VERB
cana-5531	434	2	now	now	ADV
cana-5531	434	3	𝜎∗	𝜎∗	PROPN
cana-5531	434	4	be	be	AUX
cana-5531	434	5	the	the	DET
cana-5531	434	6	function	function	NOUN
cana-5531	434	7	defined	define	VERB
cana-5531	434	8	by	by	ADP
cana-5531	434	9	(	(	PUNCT
cana-5531	434	10	3.1	3.1	NUM
cana-5531	434	11	)	)	PUNCT
cana-5531	434	12	which	which	PRON
cana-5531	434	13	corresponds	correspond	VERB
cana-5531	434	14	to	to	ADP
cana-5531	434	15	the	the	DET
cana-5531	434	16	function	function	NOUN
cana-5531	434	17	uβ∗	uβ∗	NOUN
cana-5531	434	18	.	.	PUNCT
cana-5531	435	1	then	then	ADV
cana-5531	435	2	,	,	PUNCT
cana-5531	435	3	it	it	PRON
cana-5531	435	4	results	result	VERB
cana-5531	435	5	from	from	ADP
cana-5531	435	6	(	(	PUNCT
cana-5531	435	7	4.5	4.5	NUM
cana-5531	435	8	)	)	PUNCT
cana-5531	435	9	,	,	PUNCT
cana-5531	435	10	(	(	PUNCT
cana-5531	435	11	4.6	4.6	NUM
cana-5531	435	12	)	)	PUNCT
cana-5531	435	13	and	and	CCONJ
cana-5531	435	14	(	(	PUNCT
cana-5531	435	15	4.8	4.8	NUM
cana-5531	435	16	)	)	PUNCT
cana-5531	435	17	that𝜎∗	that𝜎∗	PROPN
cana-5531	435	18	∈	∈	PROPN
cana-5531	435	19	𝐶([0	𝐶([0	PROPN
cana-5531	435	20	,	,	PUNCT
cana-5531	435	21	𝑇];ℋ).using	𝑇];ℋ).use	VERB
cana-5531	435	22	also	also	ADV
cana-5531	435	23	a	a	DET
cana-5531	435	24	standard	standard	ADJ
cana-5531	435	25	argument	argument	NOUN
cana-5531	435	26	,	,	PUNCT
cana-5531	435	27	it	it	PRON
cana-5531	435	28	follows	follow	VERB
cana-5531	435	29	from	from	ADP
cana-5531	435	30	the	the	DET
cana-5531	435	31	inequality	inequality	NOUN
cana-5531	435	32	(	(	PUNCT
cana-5531	435	33	4.15	4.15	NUM
cana-5531	435	34	)	)	PUNCT
cana-5531	435	35	that	that	DET
cana-5531	435	36	𝐷𝑖𝜐𝜎∗(𝑡	𝐷𝑖𝜐𝜎∗(𝑡	NOUN
cana-5531	435	37	)	)	PUNCT
cana-5531	435	38	+	+	PUNCT
cana-5531	435	39	𝜑1(𝑡	𝜑1(𝑡	X
cana-5531	435	40	)	)	PUNCT
cana-5531	435	41	=	=	NOUN
cana-5531	436	1	𝜌𝑢	𝜌𝑢	NOUN
cana-5531	436	2	̈	̈	X
cana-5531	436	3	𝑖𝑛	𝑖𝑛	NOUN
cana-5531	436	4	ω	ω	PROPN
cana-5531	436	5	,	,	PUNCT
cana-5531	436	6	for	for	ADP
cana-5531	436	7	all	all	DET
cana-5531	436	8	t	t	NOUN
cana-5531	436	9	∈	∈	PROPN
cana-5531	437	1	[	[	X
cana-5531	437	2	0	0	NUM
cana-5531	437	3	,	,	PUNCT
cana-5531	437	4	𝑇	𝑇	PROPN
cana-5531	437	5	]	]	PUNCT
cana-5531	437	6	.	.	PUNCT
cana-5531	438	1	therefor	therefor	PROPN
cana-5531	438	2	,	,	PUNCT
cana-5531	438	3	using	use	VERB
cana-5531	438	4	the	the	DET
cana-5531	438	5	regularity	regularity	NOUN
cana-5531	438	6	𝜑1	𝜑1	NOUN
cana-5531	438	7	∈	∈	NOUN
cana-5531	438	8	c	c	NOUN
cana-5531	438	9	(	(	PUNCT
cana-5531	438	10	[	[	X
cana-5531	438	11	0	0	NUM
cana-5531	438	12	,	,	PUNCT
cana-5531	438	13	t	t	X
cana-5531	438	14	]	]	PUNCT
cana-5531	438	15	;	;	PUNCT
cana-5531	438	16	h	h	X
cana-5531	438	17	)	)	PUNCT
cana-5531	438	18	,	,	PUNCT
cana-5531	438	19	we	we	PRON
cana-5531	438	20	deduce	deduce	VERB
cana-5531	438	21	that	that	SCONJ
cana-5531	438	22	div	div	PROPN
cana-5531	438	23	σ∗	σ∗	VERB
cana-5531	438	24	∈	∈	PROPN
cana-5531	438	25	c	c	X
cana-5531	438	26	(	(	PUNCT
cana-5531	438	27	[	[	X
cana-5531	438	28	0	0	NUM
cana-5531	438	29	,	,	PUNCT
cana-5531	438	30	t	t	X
cana-5531	438	31	]	]	PUNCT
cana-5531	438	32	;	;	PUNCT
cana-5531	438	33	h	h	X
cana-5531	438	34	)	)	PUNCT
cana-5531	438	35	which	which	PRON
cana-5531	438	36	implies	imply	VERB
cana-5531	438	37	that	that	SCONJ
cana-5531	438	38	σ∗	σ∗	PROPN
cana-5531	438	39	∈	∈	PROPN
cana-5531	438	40	c	c	X
cana-5531	438	41	(	(	PUNCT
cana-5531	438	42	[	[	X
cana-5531	438	43	0	0	NUM
cana-5531	438	44	,	,	PUNCT
cana-5531	438	45	t	t	X
cana-5531	438	46	]	]	PUNCT
cana-5531	438	47	;	;	PUNCT
cana-5531	438	48	ℋ1	ℋ1	NOUN
cana-5531	438	49	)	)	PUNCT
cana-5531	438	50	.	.	PUNCT
cana-5531	439	1	the	the	DET
cana-5531	439	2	triple	triple	ADJ
cana-5531	439	3	(	(	PUNCT
cana-5531	439	4	uβ∗	uβ∗	NOUN
cana-5531	439	5	,	,	PUNCT
cana-5531	439	6	σ∗	σ∗	PROPN
cana-5531	439	7	,	,	PUNCT
cana-5531	439	8	β∗	β∗	PROPN
cana-5531	439	9	)	)	PUNCT
cana-5531	439	10	which	which	PRON
cana-5531	439	11	satisfies	satisfy	VERB
cana-5531	439	12	(	(	PUNCT
cana-5531	439	13	3.1	3.1	NUM
cana-5531	439	14	)	)	PUNCT
cana-5531	439	15	and	and	CCONJ
cana-5531	439	16	(	(	PUNCT
cana-5531	439	17	4.15)−(4.17	4.15)−(4.17	NOUN
cana-5531	439	18	)	)	PUNCT
cana-5531	439	19	is	be	AUX
cana-5531	439	20	called	call	VERB
cana-5531	439	21	a	a	DET
cana-5531	439	22	weak	weak	ADJ
cana-5531	439	23	solution	solution	NOUN
cana-5531	439	24	of	of	ADP
cana-5531	439	25	problem	problem	NOUN
cana-5531	439	26	p1.moreover	p1.moreover	PROPN
cana-5531	439	27	,	,	PUNCT
cana-5531	439	28	the	the	DET
cana-5531	439	29	regularity	regularity	NOUN
cana-5531	439	30	of	of	ADP
cana-5531	439	31	the	the	DET
cana-5531	439	32	weak	weak	ADJ
cana-5531	439	33	solution	solution	NOUN
cana-5531	439	34	is	be	AUX
cana-5531	439	35	uβ∗	uβ∗	PROPN
cana-5531	439	36	∈	∈	PROPN
cana-5531	439	37	c	c	X
cana-5531	439	38	(	(	PUNCT
cana-5531	439	39	[	[	X
cana-5531	439	40	0	0	NUM
cana-5531	439	41	,	,	PUNCT
cana-5531	439	42	t	t	X
cana-5531	439	43	]	]	PUNCT
cana-5531	439	44	;	;	PUNCT
cana-5531	439	45	v	v	X
cana-5531	439	46	)	)	PUNCT
cana-5531	439	47	,	,	PUNCT
cana-5531	440	1	σ∗	σ∗	PROPN
cana-5531	440	2	∈	∈	PROPN
cana-5531	440	3	c	c	X
cana-5531	440	4	(	(	PUNCT
cana-5531	440	5	[	[	X
cana-5531	440	6	0	0	NUM
cana-5531	440	7	,	,	PUNCT
cana-5531	440	8	t	t	X
cana-5531	440	9	]	]	PUNCT
cana-5531	440	10	;	;	PUNCT
cana-5531	440	11	ℋ1	ℋ1	NOUN
cana-5531	440	12	)	)	PUNCT
cana-5531	440	13	and	and	CCONJ
cana-5531	440	14	β∗	β∗	NOUN
cana-5531	440	15	∈	∈	PROPN
cana-5531	440	16	w	w	ADP
cana-5531	440	17	1,∞([0	1,∞([0	NUM
cana-5531	440	18	,	,	PUNCT
cana-5531	440	19	t	t	X
cana-5531	440	20	]	]	PUNCT
cana-5531	440	21	;	;	PUNCT
cana-5531	440	22	𝕃2(γ3	𝕃2(γ3	PROPN
cana-5531	440	23	)	)	PUNCT
cana-5531	440	24	)	)	PUNCT
cana-5531	440	25	∩	∩	PROPN
cana-5531	440	26	b.	b.	PROPN
cana-5531	440	27	6	6	X
cana-5531	440	28	.	.	PUNCT
cana-5531	440	29	concluding	conclude	VERB
cana-5531	440	30	remark	remark	NOUN
cana-5531	440	31	scientific	scientific	ADJ
cana-5531	440	32	study	study	NOUN
cana-5531	440	33	and	and	CCONJ
cana-5531	440	34	contemporary	contemporary	ADJ
cana-5531	440	35	publication	publication	NOUN
cana-5531	440	36	in	in	ADP
cana-5531	440	37	mechanics	mechanic	NOUN
cana-5531	440	38	focus	focus	VERB
cana-5531	440	39	on	on	ADP
cana-5531	440	40	two	two	NUM
cana-5531	440	41	primary	primary	ADJ
cana-5531	440	42	components	component	NOUN
cana-5531	440	43	:	:	PUNCT
cana-5531	440	44	one	one	NUM
cana-5531	440	45	pertaining	pertain	VERB
cana-5531	440	46	to	to	ADP
cana-5531	440	47	the	the	DET
cana-5531	440	48	laws	law	NOUN
cana-5531	440	49	of	of	ADP
cana-5531	440	50	behaviour	behaviour	NOUN
cana-5531	440	51	and	and	CCONJ
cana-5531	440	52	other	other	ADJ
cana-5531	440	53	concerning	concern	VERB
cana-5531	440	54	the	the	DET
cana-5531	440	55	boundary	boundary	ADJ
cana-5531	440	56	conditions	condition	NOUN
cana-5531	440	57	imposed	impose	VERB
cana-5531	440	58	in	in	ADP
cana-5531	440	59	the	the	DET
cana-5531	440	60	body	body	NOUN
cana-5531	440	61	.	.	PUNCT
cana-5531	441	1	numerous	numerous	ADJ
cana-5531	441	2	publications	publication	NOUN
cana-5531	441	3	have	have	AUX
cana-5531	441	4	employed	employ	VERB
cana-5531	441	5	constitutive	constitutive	ADJ
cana-5531	441	6	laws	law	NOUN
cana-5531	441	7	incorporating	incorporate	VERB
cana-5531	441	8	internal	internal	ADJ
cana-5531	441	9	variables	variable	NOUN
cana-5531	441	10	to	to	PART
cana-5531	441	11	represent	represent	VERB
cana-5531	441	12	the	the	DET
cana-5531	441	13	influence	influence	NOUN
cana-5531	441	14	of	of	ADP
cana-5531	441	15	internal	internal	ADJ
cana-5531	441	16	variable	variable	NOUN
cana-5531	441	17	on	on	ADP
cana-5531	441	18	the	the	DET
cana-5531	441	19	behaviour	behaviour	NOUN
cana-5531	441	20	of	of	ADP
cana-5531	441	21	materials	material	NOUN
cana-5531	441	22	such	such	ADJ
cana-5531	441	23	as	as	ADP
cana-5531	441	24	metals	metal	NOUN
cana-5531	441	25	,	,	PUNCT
cana-5531	441	26	rocks	rock	NOUN
cana-5531	441	27	and	and	CCONJ
cana-5531	441	28	communications	communication	NOUN
cana-5531	441	29	on	on	ADP
cana-5531	441	30	applied	apply	VERB
cana-5531	441	31	nonlinear	nonlinear	ADJ
cana-5531	441	32	analysis	analysis	NOUN
cana-5531	441	33	issn	issn	NOUN
cana-5531	441	34	:	:	PUNCT
cana-5531	441	35	1074	1074	NUM
cana-5531	441	36	-	-	PUNCT
cana-5531	441	37	133x	133x	NUM
cana-5531	441	38	vol	vol	NOUN
cana-5531	441	39	32	32	NUM
cana-5531	441	40	no	no	NOUN
cana-5531	441	41	.	.	NOUN
cana-5531	441	42	3	3	NUM
cana-5531	441	43	(	(	PUNCT
cana-5531	441	44	2025	2025	NUM
cana-5531	441	45	)	)	PUNCT
cana-5531	441	46	983	983	NUM
cana-5531	441	47	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	441	48	polymers	polymer	NOUN
cana-5531	441	49	,	,	PUNCT
cana-5531	441	50	wherein	wherein	SCONJ
cana-5531	441	51	the	the	DET
cana-5531	441	52	rate	rate	NOUN
cana-5531	441	53	of	of	ADP
cana-5531	441	54	deformation	deformation	NOUN
cana-5531	441	55	is	be	AUX
cana-5531	441	56	contingent	contingent	ADJ
cana-5531	441	57	upon	upon	SCONJ
cana-5531	441	58	these	these	DET
cana-5531	441	59	internal	internal	ADJ
cana-5531	441	60	variables	variable	NOUN
cana-5531	441	61	.	.	PUNCT
cana-5531	442	1	our	our	PRON
cana-5531	442	2	model	model	NOUN
cana-5531	442	3	is	be	AUX
cana-5531	442	4	obtained	obtain	VERB
cana-5531	442	5	by	by	ADP
cana-5531	442	6	comnining	comnine	VERB
cana-5531	442	7	the	the	DET
cana-5531	442	8	viscoelastic	viscoelastic	ADJ
cana-5531	442	9	constitutive	constitutive	ADJ
cana-5531	442	10	law	law	NOUN
cana-5531	442	11	with	with	ADP
cana-5531	442	12	friction	friction	NOUN
cana-5531	442	13	,	,	PUNCT
cana-5531	442	14	long	long	ADJ
cana-5531	442	15	memory	memory	NOUN
cana-5531	442	16	and	and	CCONJ
cana-5531	442	17	internal	internal	ADJ
cana-5531	442	18	state	state	NOUN
cana-5531	442	19	variable	variable	NOUN
cana-5531	442	20	β	β	NOUN
cana-5531	442	21	,	,	PUNCT
cana-5531	442	22	which	which	PRON
cana-5531	442	23	describes	describe	VERB
cana-5531	442	24	the	the	DET
cana-5531	442	25	pointwise	pointwise	ADJ
cana-5531	442	26	fractional	fractional	ADJ
cana-5531	442	27	density	density	NOUN
cana-5531	442	28	of	of	ADP
cana-5531	442	29	active	active	ADJ
cana-5531	442	30	bonds	bond	NOUN
cana-5531	442	31	on	on	ADP
cana-5531	442	32	the	the	DET
cana-5531	442	33	contact	contact	NOUN
cana-5531	442	34	surface	surface	NOUN
cana-5531	442	35	and	and	CCONJ
cana-5531	442	36	is	be	AUX
cana-5531	442	37	sometimes	sometimes	ADV
cana-5531	442	38	referred	refer	VERB
cana-5531	442	39	to	to	ADP
cana-5531	442	40	as	as	ADP
cana-5531	442	41	the	the	DET
cana-5531	442	42	intensity	intensity	NOUN
cana-5531	442	43	of	of	ADP
cana-5531	442	44	adhesion	adhesion	NOUN
cana-5531	442	45	.	.	PUNCT
cana-5531	443	1	mathematically	mathematically	ADV
cana-5531	443	2	,	,	PUNCT
cana-5531	443	3	the	the	DET
cana-5531	443	4	idea	idea	NOUN
cana-5531	443	5	is	be	AUX
cana-5531	443	6	to	to	PART
cana-5531	443	7	reduce	reduce	VERB
cana-5531	443	8	the	the	DET
cana-5531	443	9	second	second	ADJ
cana-5531	443	10	order	order	NOUN
cana-5531	443	11	nonlinear	nonlinear	ADJ
cana-5531	443	12	evolution	evolution	NOUN
cana-5531	443	13	inequality	inequality	NOUN
cana-5531	443	14	of	of	ADP
cana-5531	443	15	the	the	DET
cana-5531	443	16	system	system	NOUN
cana-5531	443	17	to	to	ADP
cana-5531	443	18	the	the	DET
cana-5531	443	19	first	first	ADJ
cana-5531	443	20	order	order	NOUN
cana-5531	443	21	evolution	evolution	NOUN
cana-5531	443	22	inequality	inequality	NOUN
cana-5531	443	23	.	.	PUNCT
cana-5531	444	1	after	after	ADP
cana-5531	444	2	this	this	PRON
cana-5531	444	3	,	,	PUNCT
cana-5531	444	4	we	we	PRON
cana-5531	444	5	use	use	VERB
cana-5531	444	6	classical	classical	ADJ
cana-5531	444	7	results	result	NOUN
cana-5531	444	8	on	on	ADP
cana-5531	444	9	first	first	ADJ
cana-5531	444	10	order	order	NOUN
cana-5531	444	11	evolution	evolution	PROPN
cana-5531	444	12	nonlinear	nonlinear	PROPN
cana-5531	444	13	inequalities	inequality	NOUN
cana-5531	444	14	,	,	PUNCT
cana-5531	444	15	differential	differential	ADJ
cana-5531	444	16	equations	equation	NOUN
cana-5531	444	17	and	and	CCONJ
cana-5531	444	18	the	the	DET
cana-5531	444	19	fixed	fix	VERB
cana-5531	444	20	point	point	NOUN
cana-5531	444	21	arguments	argument	NOUN
cana-5531	444	22	.	.	PUNCT
cana-5531	445	1	references	reference	NOUN
cana-5531	445	2	[	[	X
cana-5531	445	3	1	1	NUM
cana-5531	445	4	]	]	PUNCT
cana-5531	445	5	l.	l.	PROPN
cana-5531	445	6	cangemi	cangemi	PROPN
cana-5531	445	7	.	.	PUNCT
cana-5531	446	1	frottement	frottement	PROPN
cana-5531	446	2	et	et	PROPN
cana-5531	446	3	adh´erence	adh´erence	PROPN
cana-5531	446	4	:	:	PUNCT
cana-5531	446	5	mod`ele	mod`ele	PROPN
cana-5531	446	6	,	,	PUNCT
cana-5531	446	7	traitement	traitement	NOUN
cana-5531	446	8	num´erique	num´erique	PROPN
cana-5531	446	9	application	application	NOUN
cana-5531	446	10	a	a	DET
cana-5531	446	11	`	`	PUNCT
cana-5531	446	12	l’interface	l’interface	PROPN
cana-5531	446	13	fibre/	fibre/	NUM
cana-5531	446	14	matrice	matrice	NOUN
cana-5531	446	15	,	,	PUNCT
cana-5531	446	16	ph	ph	PROPN
cana-5531	446	17	.	.	PROPN
cana-5531	446	18	d.	d.	PROPN
cana-5531	446	19	thesis	thesis	PROPN
cana-5531	446	20	,	,	PUNCT
cana-5531	446	21	univ	univ	PROPN
cana-5531	446	22	.	.	PUNCT
cana-5531	446	23	m´editerran´ee	m´editerran´ee	PROPN
cana-5531	446	24	,	,	PUNCT
cana-5531	446	25	aix	aix	NOUN
cana-5531	446	26	marseille	marseille	NOUN
cana-5531	446	27	i	i	PRON
cana-5531	446	28	,	,	PUNCT
cana-5531	446	29	1997	1997	NUM
cana-5531	446	30	.	.	PUNCT
cana-5531	447	1	[	[	X
cana-5531	447	2	2	2	NUM
cana-5531	447	3	]	]	PUNCT
cana-5531	447	4	o.	o.	NOUN
cana-5531	447	5	chau	chau	PROPN
cana-5531	447	6	,	,	PUNCT
cana-5531	447	7	j.	j.	PROPN
cana-5531	447	8	fernandez	fernandez	PROPN
cana-5531	447	9	,	,	PUNCT
cana-5531	447	10	w.	w.	PROPN
cana-5531	447	11	han	han	PROPN
cana-5531	447	12	and	and	CCONJ
cana-5531	447	13	m.	m.	PROPN
cana-5531	447	14	sofonea	sofonea	PROPN
cana-5531	447	15	,	,	PUNCT
cana-5531	447	16	variational	variational	ADJ
cana-5531	447	17	and	and	CCONJ
cana-5531	447	18	numerical	numerical	ADJ
cana-5531	447	19	analysis	analysis	NOUN
cana-5531	447	20	of	of	ADP
cana-5531	447	21	a	a	DET
cana-5531	447	22	dynamic	dynamic	ADJ
cana-5531	447	23	frictionless	frictionless	NOUN
cana-5531	447	24	contact	contact	NOUN
cana-5531	447	25	problem	problem	NOUN
cana-5531	447	26	with	with	ADP
cana-5531	447	27	adhesion	adhesion	NOUN
cana-5531	447	28	,	,	PUNCT
cana-5531	447	29	journal	journal	NOUN
cana-5531	447	30	of	of	ADP
cana-5531	447	31	computational	computational	ADJ
cana-5531	447	32	and	and	CCONJ
cana-5531	447	33	applied	applied	ADJ
cana-5531	447	34	mathematics	mathematic	NOUN
cana-5531	447	35	,	,	PUNCT
cana-5531	447	36	156	156	NUM
cana-5531	447	37	(	(	PUNCT
cana-5531	447	38	2003	2003	NUM
cana-5531	447	39	)	)	PUNCT
cana-5531	447	40	,	,	PUNCT
cana-5531	447	41	127	127	NUM
cana-5531	447	42	-	-	SYM
cana-5531	447	43	157	157	NUM
cana-5531	447	44	.	.	PUNCT
cana-5531	448	1	[	[	X
cana-5531	448	2	3	3	X
cana-5531	448	3	]	]	X
cana-5531	448	4	o.	o.	NOUN
cana-5531	448	5	chau	chau	PROPN
cana-5531	448	6	,	,	PUNCT
cana-5531	448	7	j.r	j.r	PROPN
cana-5531	448	8	.	.	PROPN
cana-5531	448	9	fernandes	fernandes	PROPN
cana-5531	448	10	,	,	PUNCT
cana-5531	448	11	m.	m.	NOUN
cana-5531	448	12	shillor	shillor	PROPN
cana-5531	448	13	and	and	CCONJ
cana-5531	448	14	m.	m.	NOUN
cana-5531	448	15	sofonea	sofonea	PROPN
cana-5531	448	16	.	.	PUNCT
cana-5531	449	1	variational	variational	ADJ
cana-5531	449	2	and	and	CCONJ
cana-5531	449	3	numerical	numerical	ADJ
cana-5531	449	4	analysis	analysis	NOUN
cana-5531	449	5	of	of	ADP
cana-5531	449	6	a	a	DET
cana-5531	449	7	quasistatic	quasistatic	ADJ
cana-5531	449	8	viscoelastic	viscoelastic	ADJ
cana-5531	449	9	contact	contact	NOUN
cana-5531	449	10	problem	problem	NOUN
cana-5531	449	11	with	with	ADP
cana-5531	449	12	adhesion	adhesion	NOUN
cana-5531	449	13	,	,	PUNCT
cana-5531	449	14	journal	journal	NOUN
cana-5531	449	15	of	of	ADP
cana-5531	449	16	computational	computational	ADJ
cana-5531	449	17	and	and	CCONJ
cana-5531	449	18	applied	applied	ADJ
cana-5531	449	19	mathematics	mathematic	NOUN
cana-5531	449	20	,	,	PUNCT
cana-5531	449	21	159(2003	159(2003	NOUN
cana-5531	449	22	)	)	PUNCT
cana-5531	449	23	,	,	PUNCT
cana-5531	449	24	431	431	NUM
cana-5531	449	25	-	-	SYM
cana-5531	449	26	465	465	NUM
cana-5531	449	27	.	.	PUNCT
cana-5531	450	1	[	[	X
cana-5531	450	2	4	4	X
cana-5531	450	3	]	]	X
cana-5531	450	4	o.	o.	NOUN
cana-5531	450	5	chau	chau	PROPN
cana-5531	450	6	,	,	PUNCT
cana-5531	450	7	m.	m.	NOUN
cana-5531	450	8	shillor	shillor	PROPN
cana-5531	450	9	and	and	CCONJ
cana-5531	450	10	m.	m.	NOUN
cana-5531	450	11	sofonea	sofonea	PROPN
cana-5531	450	12	.	.	PUNCT
cana-5531	451	1	dynamic	dynamic	ADJ
cana-5531	451	2	frictionless	frictionless	ADJ
cana-5531	451	3	contact	contact	NOUN
cana-5531	451	4	with	with	ADP
cana-5531	451	5	adhesion	adhesion	NOUN
cana-5531	451	6	,	,	PUNCT
cana-5531	451	7	j.	j.	PROPN
cana-5531	451	8	appl	appl	PROPN
cana-5531	451	9	.	.	PROPN
cana-5531	451	10	math	math	PROPN
cana-5531	451	11	.	.	PUNCT
cana-5531	452	1	phys	phy	NOUN
cana-5531	452	2	.	.	PUNCT
cana-5531	453	1	(	(	PUNCT
cana-5531	453	2	zamp	zamp	NOUN
cana-5531	453	3	)	)	PUNCT
cana-5531	453	4	,	,	PUNCT
cana-5531	453	5	55	55	NUM
cana-5531	453	6	(	(	PUNCT
cana-5531	453	7	2004	2004	NUM
cana-5531	453	8	)	)	PUNCT
cana-5531	453	9	,	,	PUNCT
cana-5531	453	10	32	32	NUM
cana-5531	453	11	-	-	SYM
cana-5531	453	12	47	47	NUM
cana-5531	453	13	.	.	PUNCT
cana-5531	454	1	[	[	X
cana-5531	454	2	5	5	NUM
cana-5531	454	3	]	]	PUNCT
cana-5531	454	4	m.	m.	NOUN
cana-5531	454	5	cocou	cocou	NOUN
cana-5531	454	6	and	and	CCONJ
cana-5531	454	7	r.	r.	PROPN
cana-5531	454	8	rocca	rocca	PROPN
cana-5531	454	9	.	.	PROPN
cana-5531	454	10	existence	existence	NOUN
cana-5531	454	11	results	result	VERB
cana-5531	454	12	for	for	ADP
cana-5531	454	13	unilateral	unilateral	ADJ
cana-5531	454	14	quasistatic	quasistatic	ADJ
cana-5531	454	15	contact	contact	NOUN
cana-5531	454	16	problems	problem	NOUN
cana-5531	454	17	with	with	ADP
cana-5531	454	18	friction	friction	NOUN
cana-5531	454	19	and	and	CCONJ
cana-5531	454	20	adhesion	adhesion	NOUN
cana-5531	454	21	.	.	PUNCT
cana-5531	455	1	math	math	NOUN
cana-5531	455	2	.	.	PUNCT
cana-5531	456	1	model	model	PROPN
cana-5531	456	2	.	.	PUNCT
cana-5531	457	1	num	num	ADJ
cana-5531	457	2	.	.	PROPN
cana-5531	457	3	anal	anal	PROPN
cana-5531	457	4	.	.	PUNCT
cana-5531	458	1	34	34	NUM
cana-5531	458	2	(	(	PUNCT
cana-5531	458	3	2000	2000	NUM
cana-5531	458	4	)	)	PUNCT
cana-5531	458	5	,	,	PUNCT
cana-5531	458	6	981	981	NUM
cana-5531	458	7	-	-	SYM
cana-5531	458	8	1001	1001	NUM
cana-5531	458	9	.	.	PUNCT
cana-5531	459	1	[	[	X
cana-5531	459	2	6	6	NUM
cana-5531	459	3	]	]	PUNCT
cana-5531	459	4	m.	m.	NOUN
cana-5531	459	5	cocou	cocou	NOUN
cana-5531	459	6	,	,	PUNCT
cana-5531	459	7	m.	m.	NOUN
cana-5531	459	8	schyvre	schyvre	NOUN
cana-5531	459	9	and	and	CCONJ
cana-5531	459	10	m.	m.	NOUN
cana-5531	459	11	raous	raous	ADJ
cana-5531	459	12	,	,	PUNCT
cana-5531	459	13	a	a	DET
cana-5531	459	14	dynamic	dynamic	ADJ
cana-5531	459	15	unilateral	unilateral	ADJ
cana-5531	459	16	contact	contact	NOUN
cana-5531	459	17	problem	problem	NOUN
cana-5531	459	18	with	with	ADP
cana-5531	459	19	adhesion	adhesion	NOUN
cana-5531	459	20	and	and	CCONJ
cana-5531	459	21	friction	friction	NOUN
cana-5531	459	22	in	in	ADP
cana-5531	459	23	viscoelasticity	viscoelasticity	NOUN
cana-5531	459	24	,	,	PUNCT
cana-5531	459	25	z.	z.	PROPN
cana-5531	459	26	angew	angew	PROPN
cana-5531	459	27	.	.	PUNCT
cana-5531	459	28	math	math	NOUN
cana-5531	459	29	.	.	PUNCT
cana-5531	460	1	phys	phy	NOUN
cana-5531	460	2	.	.	PUNCT
cana-5531	461	1	61	61	NUM
cana-5531	461	2	(	(	PUNCT
cana-5531	461	3	2010	2010	NUM
cana-5531	461	4	)	)	PUNCT
cana-5531	461	5	,	,	PUNCT
cana-5531	461	6	721	721	NUM
cana-5531	461	7	-	-	SYM
cana-5531	461	8	743	743	NUM
cana-5531	462	1	[	[	X
cana-5531	462	2	7	7	NUM
cana-5531	462	3	]	]	X
cana-5531	462	4	g.	g.	PROPN
cana-5531	462	5	duvaut	duvaut	PROPN
cana-5531	462	6	,	,	PUNCT
cana-5531	462	7	equilibre	equilibre	PROPN
cana-5531	462	8	d’un	d’un	PROPN
cana-5531	462	9	solide	solide	PROPN
cana-5531	462	10	´	´	PROPN
cana-5531	462	11	elastique	elastique	ADJ
cana-5531	462	12	avec	avec	PROPN
cana-5531	462	13	contact	contact	PROPN
cana-5531	462	14	unit´eral	unit´eral	PROPN
cana-5531	462	15	et	et	PROPN
cana-5531	462	16	frottement	frottement	PROPN
cana-5531	462	17	de	de	PROPN
cana-5531	462	18	coulomb	coulomb	PROPN
cana-5531	462	19	,	,	PUNCT
cana-5531	462	20	c.	c.	PROPN
cana-5531	462	21	r.	r.	PROPN
cana-5531	462	22	acad	acad	PROPN
cana-5531	462	23	.	.	PUNCT
cana-5531	463	1	sci	sci	PROPN
cana-5531	463	2	.	.	PROPN
cana-5531	463	3	paris	paris	PROPN
cana-5531	463	4	,	,	PUNCT
cana-5531	463	5	s´erie	s´erie	VERB
cana-5531	463	6	a	a	PRON
cana-5531	463	7	,	,	PUNCT
cana-5531	463	8	290	290	NUM
cana-5531	463	9	(	(	PUNCT
cana-5531	463	10	1980	1980	NUM
cana-5531	463	11	)	)	PUNCT
cana-5531	463	12	,	,	PUNCT
cana-5531	463	13	263	263	NUM
cana-5531	463	14	.	.	PUNCT
cana-5531	464	1	[	[	X
cana-5531	464	2	8	8	NUM
cana-5531	464	3	]	]	X
cana-5531	464	4	g.	g.	NOUN
cana-5531	464	5	duvant	duvant	PROPN
cana-5531	464	6	and	and	CCONJ
cana-5531	464	7	j.	j.	PROPN
cana-5531	464	8	l.	l.	PROPN
cana-5531	464	9	lions	lions	PROPN
cana-5531	464	10	,	,	PUNCT
cana-5531	464	11	les	les	X
cana-5531	464	12	in´equations	in´equation	NOUN
cana-5531	464	13	en	en	ADP
cana-5531	464	14	m´ecanique	m´ecanique	NOUN
cana-5531	464	15	et	et	PROPN
cana-5531	464	16	en	en	X
cana-5531	464	17	physique	physique	PROPN
cana-5531	464	18	,	,	PUNCT
cana-5531	464	19	dunod	dunod	PROPN
cana-5531	464	20	,	,	PUNCT
cana-5531	464	21	paris	paris	PROPN
cana-5531	464	22	,	,	PUNCT
cana-5531	464	23	1972	1972	NUM
cana-5531	464	24	.	.	PUNCT
cana-5531	465	1	[	[	X
cana-5531	465	2	9	9	NUM
cana-5531	465	3	]	]	X
cana-5531	465	4	c.	c.	PROPN
cana-5531	465	5	eck	eck	PROPN
cana-5531	465	6	,	,	PUNCT
cana-5531	465	7	j.	j.	PROPN
cana-5531	465	8	jarusek	jarusek	PROPN
cana-5531	465	9	and	and	CCONJ
cana-5531	465	10	m.	m.	PROPN
cana-5531	465	11	krbec	krbec	PROPN
cana-5531	465	12	.	.	PUNCT
cana-5531	465	13	unilateral	unilateral	ADJ
cana-5531	465	14	contact	contact	NOUN
cana-5531	465	15	problems	problem	NOUN
cana-5531	465	16	.	.	PUNCT
cana-5531	466	1	variational	variational	ADJ
cana-5531	466	2	methods	method	NOUN
cana-5531	466	3	and	and	CCONJ
cana-5531	466	4	existence	existence	NOUN
cana-5531	466	5	theorems	theorem	VERB
cana-5531	466	6	.	.	PUNCT
cana-5531	467	1	pure	pure	ADJ
cana-5531	467	2	appl	appl	PROPN
cana-5531	467	3	.	.	PUNCT
cana-5531	467	4	math	math	NOUN
cana-5531	467	5	.	.	PUNCT
cana-5531	468	1	270	270	NUM
cana-5531	468	2	,	,	PUNCT
cana-5531	468	3	chapman	chapman	PROPN
cana-5531	468	4	&	&	CCONJ
cana-5531	468	5	hall	hall	PROPN
cana-5531	468	6	crc	crc	PROPN
cana-5531	468	7	press	press	PROPN
cana-5531	468	8	,	,	PUNCT
cana-5531	468	9	boca	boca	PROPN
cana-5531	468	10	raton	raton	PROPN
cana-5531	468	11	,	,	PUNCT
cana-5531	468	12	florida	florida	PROPN
cana-5531	468	13	,	,	PUNCT
cana-5531	468	14	2005	2005	NUM
cana-5531	468	15	.	.	PUNCT
cana-5531	469	1	[	[	X
cana-5531	469	2	10	10	NUM
cana-5531	469	3	]	]	PUNCT
cana-5531	469	4	m.	m.	NOUN
cana-5531	469	5	frémond	frémond	PROPN
cana-5531	469	6	.	.	PUNCT
cana-5531	470	1	equilibre	equilibre	PROPN
cana-5531	470	2	des	des	PROPN
cana-5531	470	3	structures	structures	PROPN
cana-5531	470	4	qui	qui	X
cana-5531	470	5	adh´erent	adh´erent	NUM
cana-5531	470	6	a	a	DET
cana-5531	470	7	`	`	PUNCT
cana-5531	470	8	leur	leur	ADJ
cana-5531	470	9	support	support	NOUN
cana-5531	470	10	,	,	PUNCT
cana-5531	470	11	c.	c.	PROPN
cana-5531	470	12	r.	r.	PROPN
cana-5531	470	13	acad	acad	PROPN
cana-5531	470	14	.	.	PUNCT
cana-5531	471	1	sci	sci	PROPN
cana-5531	471	2	.	.	PROPN
cana-5531	471	3	paris	paris	PROPN
cana-5531	471	4	,	,	PUNCT
cana-5531	471	5	sér	sér	PROPN
cana-5531	471	6	ii	ii	PROPN
cana-5531	471	7	295	295	NUM
cana-5531	471	8	(	(	PUNCT
cana-5531	471	9	1982	1982	NUM
cana-5531	471	10	)	)	PUNCT
cana-5531	471	11	,	,	PUNCT
cana-5531	471	12	913	913	NUM
cana-5531	471	13	-	-	SYM
cana-5531	471	14	916	916	NUM
cana-5531	471	15	.	.	PUNCT
cana-5531	472	1	[	[	X
cana-5531	472	2	11	11	NUM
cana-5531	472	3	]	]	PUNCT
cana-5531	472	4	m.	m.	NOUN
cana-5531	472	5	frémond	frémond	PROPN
cana-5531	472	6	.	.	PUNCT
cana-5531	473	1	adh´erence	adh´erence	PUNCT
cana-5531	473	2	des	des	X
cana-5531	473	3	solides	solide	NOUN
cana-5531	473	4	,	,	PUNCT
cana-5531	473	5	j.	j.	PROPN
cana-5531	473	6	m´ec	m´ec	PROPN
cana-5531	473	7	.	.	PUNCT
cana-5531	473	8	théor	théor	PROPN
cana-5531	473	9	.	.	PUNCT
cana-5531	473	10	appl	appl	PROPN
cana-5531	473	11	.	.	PROPN
cana-5531	473	12	6	6	NUM
cana-5531	473	13	(	(	PUNCT
cana-5531	473	14	1987	1987	NUM
cana-5531	473	15	)	)	PUNCT
cana-5531	473	16	,	,	PUNCT
cana-5531	473	17	383	383	NUM
cana-5531	473	18	-	-	SYM
cana-5531	473	19	407	407	NUM
cana-5531	473	20	.	.	PUNCT
cana-5531	474	1	[	[	X
cana-5531	474	2	12	12	NUM
cana-5531	474	3	]	]	PUNCT
cana-5531	474	4	a.	a.	NOUN
cana-5531	474	5	kasri	kasri	PROPN
cana-5531	474	6	,	,	PUNCT
cana-5531	474	7	a	a	DET
cana-5531	474	8	frictional	frictional	ADJ
cana-5531	474	9	contact	contact	NOUN
cana-5531	474	10	problem	problem	NOUN
cana-5531	474	11	with	with	ADP
cana-5531	474	12	adhesion	adhesion	NOUN
cana-5531	474	13	for	for	ADP
cana-5531	474	14	viscoelastic	viscoelastic	NOUN
cana-5531	474	15	matherials	matherial	NOUN
cana-5531	474	16	with	with	ADP
cana-5531	474	17	long	long	ADJ
cana-5531	474	18	memory	memory	NOUN
cana-5531	474	19	,	,	PUNCT
cana-5531	474	20	applications	application	NOUN
cana-5531	474	21	of	of	ADP
cana-5531	474	22	mathematics	mathematic	NOUN
cana-5531	474	23	,	,	PUNCT
cana-5531	474	24	vol	vol	NOUN
cana-5531	474	25	.	.	PROPN
cana-5531	474	26	66	66	NUM
cana-5531	474	27	(	(	PUNCT
cana-5531	474	28	2021	2021	NUM
cana-5531	474	29	)	)	PUNCT
cana-5531	474	30	,	,	PUNCT
cana-5531	474	31	no	no	INTJ
cana-5531	474	32	.	.	NOUN
cana-5531	474	33	4	4	NUM
cana-5531	474	34	,	,	PUNCT
cana-5531	474	35	479	479	NUM
cana-5531	474	36	-	-	SYM
cana-5531	474	37	508	508	NUM
cana-5531	474	38	.	.	PUNCT
cana-5531	475	1	[	[	X
cana-5531	475	2	13	13	NUM
cana-5531	475	3	]	]	PUNCT
cana-5531	475	4	n.	n.	NOUN
cana-5531	475	5	point	point	NOUN
cana-5531	475	6	.	.	PUNCT
cana-5531	476	1	unilateral	unilateral	ADJ
cana-5531	476	2	contact	contact	NOUN
cana-5531	476	3	with	with	ADP
cana-5531	476	4	adherence	adherence	NOUN
cana-5531	476	5	.	.	PUNCT
cana-5531	477	1	math	math	NOUN
cana-5531	477	2	.	.	PUNCT
cana-5531	478	1	methods	method	NOUN
cana-5531	478	2	appl	appl	PROPN
cana-5531	478	3	.	.	PUNCT
cana-5531	479	1	sci	sci	PROPN
cana-5531	479	2	.	.	PROPN
cana-5531	480	1	10	10	NUM
cana-5531	480	2	(	(	PUNCT
cana-5531	480	3	1988	1988	NUM
cana-5531	480	4	)	)	PUNCT
cana-5531	480	5	,	,	PUNCT
cana-5531	480	6	67399	67399	NUM
cana-5531	480	7	.	.	PUNCT
cana-5531	481	1	[	[	X
cana-5531	481	2	14	14	NUM
cana-5531	481	3	]	]	PUNCT
cana-5531	481	4	j.	j.	PROPN
cana-5531	481	5	r.	r.	PROPN
cana-5531	481	6	fernandez	fernandez	PROPN
cana-5531	481	7	,	,	PUNCT
cana-5531	481	8	m.	m.	NOUN
cana-5531	481	9	shillor	shillor	PROPN
cana-5531	481	10	and	and	CCONJ
cana-5531	481	11	m.	m.	NOUN
cana-5531	481	12	sofonea	sofonea	PROPN
cana-5531	481	13	.	.	PUNCT
cana-5531	482	1	analysis	analysis	NOUN
cana-5531	482	2	and	and	CCONJ
cana-5531	482	3	numerical	numerical	ADJ
cana-5531	482	4	simulations	simulation	NOUN
cana-5531	482	5	of	of	ADP
cana-5531	482	6	a	a	DET
cana-5531	482	7	communications	communication	NOUN
cana-5531	482	8	on	on	ADP
cana-5531	482	9	applied	apply	VERB
cana-5531	482	10	nonlinear	nonlinear	ADJ
cana-5531	482	11	analysis	analysis	NOUN
cana-5531	482	12	issn	issn	NOUN
cana-5531	482	13	:	:	PUNCT
cana-5531	482	14	1074	1074	NUM
cana-5531	482	15	-	-	PUNCT
cana-5531	482	16	133x	133x	NUM
cana-5531	482	17	vol	vol	NOUN
cana-5531	482	18	32	32	NUM
cana-5531	482	19	no	no	NOUN
cana-5531	482	20	.	.	NOUN
cana-5531	482	21	3	3	NUM
cana-5531	482	22	(	(	PUNCT
cana-5531	482	23	2025	2025	NUM
cana-5531	482	24	)	)	PUNCT
cana-5531	482	25	984	984	NUM
cana-5531	482	26	https://internationalpubls.com	https://internationalpubls.com	X
cana-5531	482	27	dynamic	dynamic	ADJ
cana-5531	482	28	contact	contact	NOUN
cana-5531	482	29	problem	problem	NOUN
cana-5531	482	30	with	with	ADP
cana-5531	482	31	adhesion	adhesion	NOUN
cana-5531	482	32	.	.	PUNCT
cana-5531	483	1	math	math	NOUN
cana-5531	483	2	.	.	PUNCT
cana-5531	484	1	comput	comput	NOUN
cana-5531	484	2	.	.	PUNCT
cana-5531	485	1	modelling	model	VERB
cana-5531	485	2	37	37	NUM
cana-5531	485	3	(	(	PUNCT
cana-5531	485	4	2003	2003	NUM
cana-5531	485	5	)	)	PUNCT
cana-5531	485	6	,	,	PUNCT
cana-5531	485	7	1317	1317	NUM
cana-5531	485	8	−	−	NOUN
cana-5531	485	9	1333	1333	NUM
cana-5531	485	10	.	.	PUNCT
cana-5531	486	1	[	[	X
cana-5531	486	2	15	15	NUM
cana-5531	486	3	]	]	PUNCT
cana-5531	486	4	m.	m.	NOUN
cana-5531	486	5	raous	raous	ADJ
cana-5531	486	6	,	,	PUNCT
cana-5531	486	7	l.	l.	PROPN
cana-5531	486	8	cang´emi	cang´emi	PROPN
cana-5531	486	9	and	and	CCONJ
cana-5531	486	10	m.	m.	NOUN
cana-5531	486	11	cocu	cocu	PROPN
cana-5531	486	12	.	.	PUNCT
cana-5531	487	1	a	a	DET
cana-5531	487	2	consistent	consistent	ADJ
cana-5531	487	3	model	model	NOUN
cana-5531	487	4	coupling	coupling	NOUN
cana-5531	487	5	adhesion	adhesion	NOUN
cana-5531	487	6	,	,	PUNCT
cana-5531	487	7	friction	friction	NOUN
cana-5531	487	8	,	,	PUNCT
cana-5531	487	9	and	and	CCONJ
cana-5531	487	10	unilateral	unilateral	ADJ
cana-5531	487	11	contact	contact	NOUN
cana-5531	487	12	.	.	PUNCT
cana-5531	488	1	comput	comput	NOUN
cana-5531	488	2	.	.	PUNCT
cana-5531	489	1	methods	method	NOUN
cana-5531	489	2	appl	appl	PROPN
cana-5531	489	3	.	.	PROPN
cana-5531	489	4	mech	mech	PROPN
cana-5531	489	5	.	.	PUNCT
cana-5531	490	1	engrg	engrg	PROPN
cana-5531	490	2	.	.	PROPN
cana-5531	491	1	177	177	NUM
cana-5531	491	2	(	(	PUNCT
cana-5531	491	3	1999	1999	NUM
cana-5531	491	4	)	)	PUNCT
cana-5531	491	5	,	,	PUNCT
cana-5531	491	6	383	383	NUM
cana-5531	491	7	-	-	SYM
cana-5531	491	8	399	399	NUM
cana-5531	491	9	.	.	PUNCT
cana-5531	492	1	[	[	X
cana-5531	492	2	16	16	NUM
cana-5531	492	3	]	]	X
cana-5531	492	4	j.	j.	PROPN
cana-5531	492	5	rojek	rojek	PROPN
cana-5531	492	6	and	and	CCONJ
cana-5531	492	7	j.	j.	PROPN
cana-5531	492	8	j.	j.	PROPN
cana-5531	492	9	telega	telega	PROPN
cana-5531	492	10	.	.	PUNCT
cana-5531	493	1	contact	contact	NOUN
cana-5531	493	2	problems	problem	NOUN
cana-5531	493	3	with	with	ADP
cana-5531	493	4	friction	friction	NOUN
cana-5531	493	5	,	,	PUNCT
cana-5531	493	6	adhesion	adhesion	NOUN
cana-5531	493	7	and	and	CCONJ
cana-5531	493	8	wear	wear	VERB
cana-5531	493	9	in	in	ADP
cana-5531	493	10	or	or	CCONJ
cana-5531	494	1	thopeadic	thopeadic	ADJ
cana-5531	494	2	biomechanics	biomechanic	NOUN
cana-5531	494	3	i	i	PRON
cana-5531	494	4	:	:	PUNCT
cana-5531	494	5	general	general	ADJ
cana-5531	494	6	developements	developements	PROPN
cana-5531	494	7	,	,	PUNCT
cana-5531	494	8	j.	j.	PROPN
cana-5531	494	9	theory	theory	PROPN
cana-5531	494	10	.	.	PUNCT
cana-5531	495	1	appl	appl	PROPN
cana-5531	495	2	.	.	PROPN
cana-5531	495	3	mech	mech	PROPN
cana-5531	495	4	.	.	PUNCT
cana-5531	496	1	39	39	NUM
cana-5531	496	2	(	(	PUNCT
cana-5531	496	3	2001	2001	NUM
cana-5531	496	4	)	)	PUNCT
cana-5531	496	5	,	,	PUNCT
cana-5531	496	6	655	655	NUM
cana-5531	496	7	-	-	SYM
cana-5531	496	8	677	677	NUM
cana-5531	496	9	.	.	PUNCT
cana-5531	497	1	[	[	X
cana-5531	497	2	17	17	NUM
cana-5531	497	3	]	]	PUNCT
cana-5531	497	4	m.	m.	NOUN
cana-5531	497	5	selmani	selmani	NOUN
cana-5531	497	6	and	and	CCONJ
cana-5531	497	7	l.	l.	PROPN
cana-5531	497	8	selmani	selmani	PROPN
cana-5531	497	9	.	.	PUNCT
cana-5531	498	1	analysis	analysis	NOUN
cana-5531	498	2	of	of	ADP
cana-5531	498	3	a	a	DET
cana-5531	498	4	frictionaless	frictionaless	NOUN
cana-5531	498	5	contact	contact	NOUN
cana-5531	498	6	problem	problem	NOUN
cana-5531	498	7	for	for	ADP
cana-5531	498	8	elastic	elastic	ADJ
cana-5531	498	9	viscoplastic	viscoplastic	ADJ
cana-5531	498	10	materials	material	NOUN
cana-5531	498	11	.	.	PUNCT
cana-5531	499	1	nonlinear	nonlinear	ADJ
cana-5531	499	2	analysis	analysis	NOUN
cana-5531	499	3	:	:	PUNCT
cana-5531	499	4	modelling	modelling	NOUN
cana-5531	499	5	and	and	CCONJ
cana-5531	499	6	control	control	NOUN
cana-5531	499	7	,	,	PUNCT
cana-5531	499	8	2012	2012	NUM
cana-5531	499	9	,	,	PUNCT
cana-5531	499	10	vol	vol	NOUN
cana-5531	499	11	.	.	PROPN
cana-5531	499	12	17	17	NUM
cana-5531	499	13	,	,	PUNCT
cana-5531	499	14	no	no	INTJ
cana-5531	499	15	.	.	NOUN
cana-5531	499	16	1	1	NUM
cana-5531	499	17	,	,	PUNCT
cana-5531	499	18	99	99	NUM
cana-5531	499	19	-	-	SYM
cana-5531	499	20	117	117	NUM
cana-5531	499	21	.	.	PUNCT
cana-5531	500	1	[	[	X
cana-5531	500	2	18	18	NUM
cana-5531	500	3	]	]	PUNCT
cana-5531	500	4	m.	m.	NOUN
cana-5531	500	5	sofonea	sofonea	PROPN
cana-5531	500	6	,	,	PUNCT
cana-5531	500	7	w.	w.	PROPN
cana-5531	500	8	han	han	PROPN
cana-5531	500	9	and	and	CCONJ
cana-5531	500	10	m.	m.	PROPN
cana-5531	500	11	shillor	shillor	PROPN
cana-5531	500	12	.	.	PUNCT
cana-5531	501	1	analysis	analysis	NOUN
cana-5531	501	2	and	and	CCONJ
cana-5531	501	3	approximations	approximation	NOUN
cana-5531	501	4	of	of	ADP
cana-5531	501	5	contact	contact	NOUN
cana-5531	501	6	problems	problem	NOUN
cana-5531	501	7	with	with	ADP
cana-5531	501	8	adhesion	adhesion	NOUN
cana-5531	501	9	or	or	CCONJ
cana-5531	501	10	damage	damage	NOUN
cana-5531	501	11	,	,	PUNCT
cana-5531	501	12	pure	pure	ADJ
cana-5531	501	13	and	and	CCONJ
cana-5531	501	14	applied	applied	ADJ
cana-5531	501	15	mathematics	mathematic	NOUN
cana-5531	501	16	,	,	PUNCT
cana-5531	501	17	276	276	NUM
cana-5531	501	18	,	,	PUNCT
cana-5531	501	19	chapman	chapman	PROPN
cana-5531	501	20	&	&	CCONJ
cana-5531	501	21	hall/	hall/	PROPN
cana-5531	501	22	crc	crc	PROPN
cana-5531	501	23	press	press	PROPN
cana-5531	501	24	,	,	PUNCT
cana-5531	501	25	boca	boca	PROPN
cana-5531	501	26	raton	raton	PROPN
cana-5531	501	27	,	,	PUNCT
cana-5531	501	28	florida	florida	PROPN
cana-5531	501	29	,	,	PUNCT
cana-5531	501	30	2006	2006	NUM
cana-5531	501	31	.	.	PUNCT
cana-5531	502	1	[	[	X
cana-5531	502	2	19	19	NUM
cana-5531	502	3	]	]	PUNCT
cana-5531	502	4	a.	a.	NOUN
cana-5531	502	5	touzaline	touzaline	NOUN
cana-5531	502	6	.	.	PUNCT
cana-5531	503	1	aquasistatic	aquasistatic	ADJ
cana-5531	503	2	unilateral	unilateral	ADJ
cana-5531	503	3	and	and	CCONJ
cana-5531	503	4	frictional	frictional	ADJ
cana-5531	503	5	contact	contact	NOUN
cana-5531	503	6	problem	problem	NOUN
cana-5531	503	7	with	with	ADP
cana-5531	503	8	adhesion	adhesion	NOUN
cana-5531	503	9	for	for	ADP
cana-5531	503	10	elastic	elastic	ADJ
cana-5531	503	11	materials	material	NOUN
cana-5531	503	12	.	.	PUNCT
cana-5531	504	1	applications	application	NOUN
cana-5531	504	2	mathematicae	mathematicae	PROPN
cana-5531	504	3	,	,	PUNCT
cana-5531	504	4	36	36	NUM
cana-5531	504	5	(	(	PUNCT
cana-5531	504	6	2009	2009	NUM
cana-5531	504	7	)	)	PUNCT
cana-5531	504	8	,	,	PUNCT
cana-5531	504	9	no	no	INTJ
cana-5531	504	10	.	.	NOUN
cana-5531	504	11	1	1	NUM
cana-5531	504	12	,	,	PUNCT
cana-5531	504	13	107	107	NUM
cana-5531	504	14	-	-	SYM
cana-5531	504	15	127	127	NUM
cana-5531	504	16	.	.	PUNCT
cana-5531	505	1	[	[	X
cana-5531	505	2	20	20	NUM
cana-5531	505	3	]	]	PUNCT
cana-5531	505	4	a.	a.	NOUN
cana-5531	505	5	touzaline	touzaline	NOUN
cana-5531	505	6	,	,	PUNCT
cana-5531	505	7	study	study	NOUN
cana-5531	505	8	of	of	ADP
cana-5531	505	9	a	a	DET
cana-5531	505	10	viscoelastic	viscoelastic	ADJ
cana-5531	505	11	frictional	frictional	ADJ
cana-5531	505	12	contact	contact	NOUN
cana-5531	505	13	problem	problem	NOUN
cana-5531	505	14	with	with	ADP
cana-5531	505	15	adhesion	adhesion	NOUN
cana-5531	505	16	,	,	PUNCT
cana-5531	505	17	com	com	NOUN
cana-5531	505	18	ment	ment	PROPN
cana-5531	505	19	.	.	PUNCT
cana-5531	505	20	math	math	PROPN
cana-5531	505	21	.	.	PUNCT
cana-5531	506	1	univ	univ	PROPN
cana-5531	506	2	.	.	PUNCT
cana-5531	507	1	carolin	carolin	PROPN
cana-5531	507	2	.	.	PROPN
cana-5531	507	3	,	,	PUNCT
cana-5531	507	4	52	52	NUM
cana-5531	507	5	(	(	PUNCT
cana-5531	507	6	2011	2011	NUM
cana-5531	507	7	)	)	PUNCT
cana-5531	507	8	,	,	PUNCT
cana-5531	507	9	no	no	INTJ
cana-5531	507	10	.	.	NOUN
cana-5531	507	11	2	2	NUM
cana-5531	507	12	,	,	PUNCT
cana-5531	507	13	257	257	NUM
cana-5531	507	14	-	-	SYM
cana-5531	507	15	272	272	NUM
cana-5531	507	16	.	.	PUNCT
cana-5531	508	1	[	[	X
cana-5531	508	2	21	21	NUM
cana-5531	508	3	]	]	PUNCT
cana-5531	508	4	a.	a.	NOUN
cana-5531	508	5	touzaline	touzaline	NOUN
cana-5531	508	6	,	,	PUNCT
cana-5531	508	7	analysis	analysis	NOUN
cana-5531	508	8	of	of	ADP
cana-5531	508	9	a	a	DET
cana-5531	508	10	viscoelastic	viscoelastic	ADJ
cana-5531	508	11	unilateral	unilateral	ADJ
cana-5531	508	12	and	and	CCONJ
cana-5531	508	13	frictional	frictional	ADJ
cana-5531	508	14	contact	contact	NOUN
cana-5531	508	15	problem	problem	NOUN
cana-5531	508	16	contact	contact	NOUN
cana-5531	508	17	problem	problem	NOUN
cana-5531	508	18	with	with	ADP
cana-5531	508	19	adhesion	adhesion	NOUN
cana-5531	508	20	,	,	PUNCT
cana-5531	508	21	stud	stud	NOUN
cana-5531	508	22	.	.	PUNCT
cana-5531	509	1	univ	univ	PROPN
cana-5531	509	2	.	.	PUNCT
cana-5531	510	1	babes	babe	NOUN
cana-5531	510	2	-	-	PUNCT
cana-5531	510	3	bolyai	bolyai	NOUN
cana-5531	510	4	math	math	NOUN
cana-5531	510	5	.	.	PUNCT
cana-5531	511	1	58	58	NUM
cana-5531	511	2	(	(	PUNCT
cana-5531	511	3	2013	2013	NUM
cana-5531	511	4	)	)	PUNCT
cana-5531	511	5	,	,	PUNCT
cana-5531	511	6	no	no	INTJ
cana-5531	511	7	.	.	NOUN
cana-5531	511	8	2	2	NUM
cana-5531	511	9	,	,	PUNCT
cana-5531	511	10	263	263	NUM
cana-5531	511	11	-	-	SYM
cana-5531	511	12	278	278	NUM
cana-5531	511	13	.	.	PUNCT