id	sid	tid	token	lemma	pos
cana-1996	1	1	communications	communication	NOUN
cana-1996	1	2	on	on	ADP
cana-1996	1	3	applied	apply	VERB
cana-1996	1	4	nonlinear	nonlinear	ADJ
cana-1996	1	5	analysis	analysis	NOUN
cana-1996	1	6	issn	issn	NOUN
cana-1996	1	7	:	:	PUNCT
cana-1996	1	8	1074	1074	NUM
cana-1996	1	9	-	-	PUNCT
cana-1996	1	10	133x	133x	NUM
cana-1996	1	11	vol	vol	NOUN
cana-1996	1	12	32	32	NUM
cana-1996	1	13	no	no	NOUN
cana-1996	1	14	.	.	NOUN
cana-1996	1	15	3	3	NUM
cana-1996	1	16	(	(	PUNCT
cana-1996	1	17	2025	2025	NUM
cana-1996	1	18	)	)	PUNCT
cana-1996	1	19	383	383	NUM
cana-1996	1	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	1	21	mathematical	mathematical	ADJ
cana-1996	1	22	analysis	analysis	NOUN
cana-1996	1	23	of	of	ADP
cana-1996	1	24	some	some	DET
cana-1996	1	25	(	(	PUNCT
cana-1996	1	26	3	3	NUM
cana-1996	1	27	+	+	NOUN
cana-1996	1	28	1)-d	1)-d	NUM
cana-1996	1	29	models	model	NOUN
cana-1996	1	30	via	via	ADP
cana-1996	1	31	rangaig	rangaig	ADJ
cana-1996	1	32	transform	transform	NOUN
cana-1996	1	33	1sandeep	1sandeep	NUM
cana-1996	1	34	sharma	sharma	NOUN
cana-1996	1	35	,	,	PUNCT
cana-1996	1	36	2inderdeep	2inderdeep	PROPN
cana-1996	1	37	singh	singh	NOUN
cana-1996	1	38	1,2sant	1,2sant	NUM
cana-1996	1	39	baba	baba	PROPN
cana-1996	1	40	bhag	bhag	PROPN
cana-1996	1	41	singh	singh	PROPN
cana-1996	1	42	university	university	PROPN
cana-1996	1	43	,	,	PUNCT
cana-1996	1	44	jalandhar-144030	jalandhar-144030	NOUN
cana-1996	1	45	,	,	PUNCT
cana-1996	1	46	punjab	punjab	ADJ
cana-1996	1	47	,	,	PUNCT
cana-1996	1	48	india	india	PROPN
cana-1996	1	49	email	email	NOUN
cana-1996	1	50	:	:	PUNCT
cana-1996	1	51	1	1	NUM
cana-1996	1	52	sandeepsharma200@gmail.com	sandeepsharma200@gmail.com	NUM
cana-1996	1	53	,	,	PUNCT
cana-1996	1	54	2inderdeeps.ma.12@gmail.com	2inderdeeps.ma.12@gmail.com	NUM
cana-1996	1	55	article	article	NOUN
cana-1996	1	56	history	history	NOUN
cana-1996	1	57	:	:	PUNCT
cana-1996	1	58	received	receive	VERB
cana-1996	1	59	:	:	PUNCT
cana-1996	1	60	05	05	NUM
cana-1996	1	61	-	-	SYM
cana-1996	1	62	08	08	NUM
cana-1996	1	63	-	-	PUNCT
cana-1996	1	64	2024	2024	NUM
cana-1996	1	65	revised	revise	VERB
cana-1996	1	66	:	:	PUNCT
cana-1996	1	67	24	24	NUM
cana-1996	1	68	-	-	PUNCT
cana-1996	1	69	09	09	NUM
cana-1996	1	70	-	-	PUNCT
cana-1996	1	71	2024	2024	NUM
cana-1996	1	72	accepted	accept	VERB
cana-1996	1	73	:	:	PUNCT
cana-1996	1	74	07	07	NUM
cana-1996	1	75	-	-	SYM
cana-1996	1	76	10	10	NUM
cana-1996	1	77	-	-	PUNCT
cana-1996	1	78	2024	2024	NUM
cana-1996	1	79	abstract	abstract	NOUN
cana-1996	1	80	:	:	PUNCT
cana-1996	1	81	in	in	ADP
cana-1996	1	82	this	this	DET
cana-1996	1	83	research	research	NOUN
cana-1996	1	84	,	,	PUNCT
cana-1996	1	85	we	we	PRON
cana-1996	1	86	suggest	suggest	VERB
cana-1996	1	87	a	a	DET
cana-1996	1	88	hybrid	hybrid	ADJ
cana-1996	1	89	method	method	NOUN
cana-1996	1	90	to	to	PART
cana-1996	1	91	solve	solve	VERB
cana-1996	1	92	(	(	PUNCT
cana-1996	1	93	3	3	NUM
cana-1996	1	94	+	+	NOUN
cana-1996	1	95	1)-d	1)-d	NUM
cana-1996	1	96	pdes	pde	NOUN
cana-1996	1	97	arising	arise	VERB
cana-1996	1	98	in	in	ADP
cana-1996	1	99	various	various	ADJ
cana-1996	1	100	applications	application	NOUN
cana-1996	1	101	of	of	ADP
cana-1996	1	102	sciences	science	NOUN
cana-1996	1	103	and	and	CCONJ
cana-1996	1	104	engineering	engineering	NOUN
cana-1996	1	105	.	.	PUNCT
cana-1996	2	1	the	the	DET
cana-1996	2	2	plausibility	plausibility	NOUN
cana-1996	2	3	of	of	ADP
cana-1996	2	4	the	the	DET
cana-1996	2	5	proposed	propose	VERB
cana-1996	2	6	method	method	NOUN
cana-1996	2	7	is	be	AUX
cana-1996	2	8	demonstrated	demonstrate	VERB
cana-1996	2	9	by	by	ADP
cana-1996	2	10	considering	consider	VERB
cana-1996	2	11	the	the	DET
cana-1996	2	12	“	"	PUNCT
cana-1996	2	13	rangaig	rangaig	ADJ
cana-1996	2	14	transform	transform	NOUN
cana-1996	2	15	”	"	PUNCT
cana-1996	2	16	and	and	CCONJ
cana-1996	2	17	the	the	DET
cana-1996	2	18	classical	classical	ADJ
cana-1996	2	19	“	"	PUNCT
cana-1996	2	20	homotopy	homotopy	VERB
cana-1996	2	21	analysis	analysis	NOUN
cana-1996	2	22	technique	technique	NOUN
cana-1996	2	23	”	"	PUNCT
cana-1996	2	24	.	.	PUNCT
cana-1996	3	1	some	some	DET
cana-1996	3	2	experimental	experimental	ADJ
cana-1996	3	3	work	work	NOUN
cana-1996	3	4	has	have	AUX
cana-1996	3	5	been	be	AUX
cana-1996	3	6	performed	perform	VERB
cana-1996	3	7	to	to	PART
cana-1996	3	8	demonstrate	demonstrate	VERB
cana-1996	3	9	the	the	DET
cana-1996	3	10	accuracy	accuracy	NOUN
cana-1996	3	11	and	and	CCONJ
cana-1996	3	12	simplicity	simplicity	NOUN
cana-1996	3	13	of	of	ADP
cana-1996	3	14	the	the	DET
cana-1996	3	15	proposed	propose	VERB
cana-1996	3	16	hybrid	hybrid	NOUN
cana-1996	3	17	scheme	scheme	NOUN
cana-1996	3	18	.	.	PUNCT
cana-1996	4	1	keywords	keyword	NOUN
cana-1996	4	2	:	:	PUNCT
cana-1996	4	3	the	the	DET
cana-1996	4	4	“	"	PUNCT
cana-1996	4	5	rangaig	rangaig	ADJ
cana-1996	4	6	transform	transform	NOUN
cana-1996	4	7	”	"	PUNCT
cana-1996	4	8	,	,	PUNCT
cana-1996	4	9	ham	ham	NOUN
cana-1996	4	10	,	,	PUNCT
cana-1996	4	11	“	"	PUNCT
cana-1996	4	12	(	(	PUNCT
cana-1996	4	13	3	3	NUM
cana-1996	4	14	+	+	SYM
cana-1996	4	15	1)-d	1)-d	NUM
cana-1996	4	16	telegraph	telegraph	NOUN
cana-1996	4	17	equation	equation	NOUN
cana-1996	4	18	”	"	PUNCT
cana-1996	4	19	,	,	PUNCT
cana-1996	4	20	“	"	PUNCT
cana-1996	4	21	(	(	PUNCT
cana-1996	4	22	3	3	NUM
cana-1996	4	23	+	+	SYM
cana-1996	4	24	1)-d	1)-d	NUM
cana-1996	4	25	diffusion	diffusion	NOUN
cana-1996	4	26	equation	equation	NOUN
cana-1996	4	27	”	"	PUNCT
cana-1996	4	28	,	,	PUNCT
cana-1996	4	29	“	"	PUNCT
cana-1996	4	30	(	(	PUNCT
cana-1996	4	31	3	3	NUM
cana-1996	4	32	+	+	SYM
cana-1996	4	33	1)-d	1)-d	NUM
cana-1996	4	34	schrodinger	schrodinger	NOUN
cana-1996	4	35	equations	equation	NOUN
cana-1996	4	36	”	"	PUNCT
cana-1996	4	37	,	,	PUNCT
cana-1996	4	38	test	test	NOUN
cana-1996	4	39	examples	example	NOUN
cana-1996	4	40	.	.	PUNCT
cana-1996	5	1	1	1	X
cana-1996	5	2	.	.	X
cana-1996	5	3	introduction	introduction	NOUN
cana-1996	5	4	:	:	PUNCT
cana-1996	5	5	the	the	DET
cana-1996	5	6	remaining	remain	VERB
cana-1996	5	7	higher	higher	ADV
cana-1996	5	8	-	-	PUNCT
cana-1996	5	9	dimensional	dimensional	ADJ
cana-1996	5	10	partial	partial	ADJ
cana-1996	5	11	differential	differential	NOUN
cana-1996	5	12	equations	equation	NOUN
cana-1996	5	13	(	(	PUNCT
cana-1996	5	14	pdes	pde	NOUN
cana-1996	5	15	)	)	PUNCT
cana-1996	5	16	are	be	AUX
cana-1996	5	17	in	in	ADP
cana-1996	5	18	great	great	ADJ
cana-1996	5	19	demand	demand	NOUN
cana-1996	5	20	in	in	ADP
cana-1996	5	21	the	the	DET
cana-1996	5	22	areas	area	NOUN
cana-1996	5	23	of	of	ADP
cana-1996	5	24	mathematical	mathematical	ADJ
cana-1996	5	25	physics	physics	NOUN
cana-1996	5	26	,	,	PUNCT
cana-1996	5	27	engineering	engineering	NOUN
cana-1996	5	28	,	,	PUNCT
cana-1996	5	29	and	and	CCONJ
cana-1996	5	30	many	many	ADJ
cana-1996	5	31	other	other	ADJ
cana-1996	5	32	applied	applied	ADJ
cana-1996	5	33	branches	branch	NOUN
cana-1996	5	34	.	.	PUNCT
cana-1996	6	1	in	in	ADP
cana-1996	6	2	general	general	ADJ
cana-1996	6	3	,	,	PUNCT
cana-1996	6	4	such	such	ADJ
cana-1996	6	5	equations	equation	NOUN
cana-1996	6	6	are	be	AUX
cana-1996	6	7	derived	derive	VERB
cana-1996	6	8	from	from	ADP
cana-1996	6	9	some	some	DET
cana-1996	6	10	problems	problem	NOUN
cana-1996	6	11	that	that	PRON
cana-1996	6	12	include	include	VERB
cana-1996	6	13	three	three	NUM
cana-1996	6	14	spatial	spatial	ADJ
cana-1996	6	15	and	and	CCONJ
cana-1996	6	16	one	one	NUM
cana-1996	6	17	temporal	temporal	ADJ
cana-1996	6	18	coordinate	coordinate	NOUN
cana-1996	6	19	,	,	PUNCT
cana-1996	6	20	such	such	ADJ
cana-1996	6	21	as	as	ADP
cana-1996	6	22	fluid	fluid	ADJ
cana-1996	6	23	dynamics	dynamic	NOUN
cana-1996	6	24	,	,	PUNCT
cana-1996	6	25	quantum	quantum	NOUN
cana-1996	6	26	,	,	PUNCT
cana-1996	6	27	electromagnetic	electromagnetic	NOUN
cana-1996	6	28	,	,	PUNCT
cana-1996	6	29	or	or	CCONJ
cana-1996	6	30	wave	wave	NOUN
cana-1996	6	31	theory	theory	NOUN
cana-1996	6	32	.	.	PUNCT
cana-1996	7	1	in	in	ADP
cana-1996	7	2	less	less	ADV
cana-1996	7	3	trivial	trivial	ADJ
cana-1996	7	4	(	(	PUNCT
cana-1996	7	5	significantly	significantly	ADV
cana-1996	7	6	non	non	ADJ
cana-1996	7	7	-	-	ADJ
cana-1996	7	8	linear	linear	ADJ
cana-1996	7	9	)	)	PUNCT
cana-1996	7	10	situations	situation	NOUN
cana-1996	7	11	,	,	PUNCT
cana-1996	7	12	what	what	PRON
cana-1996	7	13	these	these	DET
cana-1996	7	14	equations	equation	NOUN
cana-1996	7	15	look	look	VERB
cana-1996	7	16	like	like	ADP
cana-1996	7	17	can	can	AUX
cana-1996	7	18	be	be	AUX
cana-1996	7	19	quite	quite	ADV
cana-1996	7	20	complicated	complicated	ADJ
cana-1996	7	21	indeed	indeed	ADV
cana-1996	7	22	,	,	PUNCT
cana-1996	7	23	and	and	CCONJ
cana-1996	7	24	getting	get	VERB
cana-1996	7	25	hold	hold	NOUN
cana-1996	7	26	of	of	ADP
cana-1996	7	27	exact	exact	ADJ
cana-1996	7	28	or	or	CCONJ
cana-1996	7	29	approximate	approximate	ADJ
cana-1996	7	30	solutions	solution	NOUN
cana-1996	7	31	is	be	AUX
cana-1996	7	32	relatively	relatively	ADV
cana-1996	7	33	difficult	difficult	ADJ
cana-1996	7	34	.	.	PUNCT
cana-1996	8	1	this	this	PRON
cana-1996	8	2	is	be	AUX
cana-1996	8	3	achieved	achieve	VERB
cana-1996	8	4	using	use	VERB
cana-1996	8	5	advanced	advanced	ADJ
cana-1996	8	6	mathematics	mathematic	NOUN
cana-1996	8	7	,	,	PUNCT
cana-1996	8	8	which	which	PRON
cana-1996	8	9	writes	write	VERB
cana-1996	8	10	these	these	DET
cana-1996	8	11	equations	equation	NOUN
cana-1996	8	12	in	in	ADP
cana-1996	8	13	a	a	DET
cana-1996	8	14	form	form	NOUN
cana-1996	8	15	that	that	PRON
cana-1996	8	16	is	be	AUX
cana-1996	8	17	much	much	ADV
cana-1996	8	18	more	more	ADV
cana-1996	8	19	accessible	accessible	ADJ
cana-1996	8	20	for	for	SCONJ
cana-1996	8	21	some	some	DET
cana-1996	8	22	math	math	NOUN
cana-1996	8	23	to	to	PART
cana-1996	8	24	be	be	AUX
cana-1996	8	25	performed	perform	VERB
cana-1996	8	26	.	.	PUNCT
cana-1996	9	1	both	both	CCONJ
cana-1996	9	2	the	the	DET
cana-1996	9	3	rangaig	rangaig	ADJ
cana-1996	9	4	transform	transform	NOUN
cana-1996	9	5	and	and	CCONJ
cana-1996	9	6	homotopy	homotopy	VERB
cana-1996	9	7	analysis	analysis	NOUN
cana-1996	9	8	method	method	NOUN
cana-1996	9	9	(	(	PUNCT
cana-1996	9	10	ham	ham	NOUN
cana-1996	9	11	)	)	PUNCT
cana-1996	9	12	are	be	AUX
cana-1996	9	13	very	very	ADV
cana-1996	9	14	potent	potent	ADJ
cana-1996	9	15	in	in	ADP
cana-1996	9	16	manipulating	manipulate	VERB
cana-1996	9	17	the	the	DET
cana-1996	9	18	solution	solution	NOUN
cana-1996	9	19	of	of	ADP
cana-1996	9	20	(	(	PUNCT
cana-1996	9	21	3	3	NUM
cana-1996	9	22	+	+	NOUN
cana-1996	9	23	1)-dimensional	1)-dimensional	ADJ
cana-1996	9	24	pdes	pde	NOUN
cana-1996	9	25	.	.	PUNCT
cana-1996	10	1	the	the	DET
cana-1996	10	2	rangaig	rangaig	ADJ
cana-1996	10	3	transform	transform	NOUN
cana-1996	10	4	is	be	AUX
cana-1996	10	5	an	an	DET
cana-1996	10	6	integral	integral	ADJ
cana-1996	10	7	transform	transform	NOUN
cana-1996	10	8	that	that	PRON
cana-1996	10	9	goes	go	VERB
cana-1996	10	10	beyond	beyond	ADP
cana-1996	10	11	the	the	DET
cana-1996	10	12	conventional	conventional	ADJ
cana-1996	10	13	traditional	traditional	ADJ
cana-1996	10	14	employs	employ	NOUN
cana-1996	10	15	of	of	ADP
cana-1996	10	16	fourier	fourier	NOUN
cana-1996	10	17	and	and	CCONJ
cana-1996	10	18	laplace	laplace	NOUN
cana-1996	10	19	type	type	NOUN
cana-1996	10	20	transforms	transform	VERB
cana-1996	10	21	and	and	CCONJ
cana-1996	10	22	can	can	AUX
cana-1996	10	23	be	be	AUX
cana-1996	10	24	used	use	VERB
cana-1996	10	25	to	to	PART
cana-1996	10	26	offer	offer	VERB
cana-1996	10	27	a	a	DET
cana-1996	10	28	new	new	ADJ
cana-1996	10	29	perspective	perspective	NOUN
cana-1996	10	30	at	at	ADP
cana-1996	10	31	linear	linear	PROPN
cana-1996	10	32	,	,	PUNCT
cana-1996	10	33	nonlinear	nonlinear	ADJ
cana-1996	10	34	pdes	pde	NOUN
cana-1996	10	35	putting	put	VERB
cana-1996	10	36	them	they	PRON
cana-1996	10	37	in	in	ADP
cana-1996	10	38	simpler	simple	ADJ
cana-1996	10	39	algebraical	algebraical	ADJ
cana-1996	10	40	forms	form	NOUN
cana-1996	10	41	.	.	PUNCT
cana-1996	11	1	on	on	ADP
cana-1996	11	2	the	the	DET
cana-1996	11	3	other	other	ADJ
cana-1996	11	4	hand	hand	NOUN
cana-1996	11	5	,	,	PUNCT
cana-1996	11	6	ham	ham	X
cana-1996	12	1	[	[	X
cana-1996	12	2	15	15	NUM
cana-1996	12	3	-	-	SYM
cana-1996	12	4	17	17	NUM
cana-1996	12	5	]	]	PUNCT
cana-1996	12	6	is	be	AUX
cana-1996	12	7	an	an	DET
cana-1996	12	8	analytic	analytic	ADJ
cana-1996	12	9	method	method	NOUN
cana-1996	12	10	that	that	PRON
cana-1996	12	11	converges	converge	VERB
cana-1996	12	12	rapidly	rapidly	ADV
cana-1996	12	13	to	to	ADP
cana-1996	12	14	the	the	DET
cana-1996	12	15	approximate	approximate	ADJ
cana-1996	12	16	solutions	solution	NOUN
cana-1996	12	17	for	for	ADP
cana-1996	12	18	the	the	DET
cana-1996	12	19	nonlinear	nonlinear	ADJ
cana-1996	12	20	pdes	pde	NOUN
cana-1996	12	21	,	,	PUNCT
cana-1996	12	22	where	where	SCONJ
cana-1996	12	23	it	it	PRON
cana-1996	12	24	can	can	AUX
cana-1996	12	25	easily	easily	ADV
cana-1996	12	26	deform	deform	VERB
cana-1996	12	27	continuously	continuously	ADV
cana-1996	12	28	from	from	ADP
cana-1996	12	29	a	a	DET
cana-1996	12	30	simple	simple	ADJ
cana-1996	12	31	problem	problem	NOUN
cana-1996	12	32	to	to	ADP
cana-1996	12	33	another	another	DET
cana-1996	12	34	complex	complex	ADJ
cana-1996	12	35	problem	problem	NOUN
cana-1996	12	36	and	and	CCONJ
cana-1996	12	37	control	control	VERB
cana-1996	12	38	the	the	DET
cana-1996	12	39	convergence	convergence	NOUN
cana-1996	12	40	of	of	ADP
cana-1996	12	41	the	the	DET
cana-1996	12	42	solution	solution	NOUN
cana-1996	12	43	.	.	PUNCT
cana-1996	13	1	from	from	ADP
cana-1996	13	2	the	the	DET
cana-1996	13	3	papers	paper	NOUN
cana-1996	13	4	cited	cite	VERB
cana-1996	13	5	,	,	PUNCT
cana-1996	13	6	as	as	ADV
cana-1996	13	7	well	well	ADV
cana-1996	13	8	as	as	ADP
cana-1996	13	9	from	from	ADP
cana-1996	13	10	the	the	DET
cana-1996	13	11	applications	application	NOUN
cana-1996	13	12	seen	see	VERB
cana-1996	13	13	in	in	ADP
cana-1996	13	14	this	this	DET
cana-1996	13	15	section	section	NOUN
cana-1996	13	16	,	,	PUNCT
cana-1996	13	17	it	it	PRON
cana-1996	13	18	can	can	AUX
cana-1996	13	19	be	be	AUX
cana-1996	13	20	ascertained	ascertain	VERB
cana-1996	13	21	that	that	SCONJ
cana-1996	13	22	both	both	DET
cana-1996	13	23	methods	method	NOUN
cana-1996	13	24	are	be	AUX
cana-1996	13	25	efficacious	efficacious	ADJ
cana-1996	13	26	for	for	ADP
cana-1996	13	27	nonlinear	nonlinear	ADJ
cana-1996	13	28	(	(	PUNCT
cana-1996	13	29	3	3	NUM
cana-1996	13	30	+	+	NOUN
cana-1996	13	31	1)-d	1)-d	NUM
cana-1996	13	32	pdes	pde	NOUN
cana-1996	13	33	;	;	PUNCT
cana-1996	13	34	they	they	PRON
cana-1996	13	35	could	could	AUX
cana-1996	13	36	be	be	AUX
cana-1996	13	37	wave	wave	NOUN
cana-1996	13	38	equations	equation	NOUN
cana-1996	13	39	,	,	PUNCT
cana-1996	13	40	heat	heat	NOUN
cana-1996	13	41	equations	equation	NOUN
cana-1996	13	42	,	,	PUNCT
cana-1996	13	43	fluid	fluid	ADJ
cana-1996	13	44	dynamic	dynamic	ADJ
cana-1996	13	45	schemes	scheme	NOUN
cana-1996	13	46	,	,	PUNCT
cana-1996	13	47	and	and	CCONJ
cana-1996	13	48	others	other	NOUN
cana-1996	13	49	.	.	PUNCT
cana-1996	14	1	the	the	DET
cana-1996	14	2	use	use	NOUN
cana-1996	14	3	of	of	ADP
cana-1996	14	4	the	the	DET
cana-1996	14	5	concept	concept	NOUN
cana-1996	14	6	can	can	AUX
cana-1996	14	7	be	be	AUX
cana-1996	14	8	followed	follow	VERB
cana-1996	14	9	from	from	ADP
cana-1996	14	10	abstract	abstract	ADJ
cana-1996	14	11	theoretical	theoretical	ADJ
cana-1996	14	12	mathematical	mathematical	ADJ
cana-1996	14	13	physics	physics	NOUN
cana-1996	14	14	right	right	ADV
cana-1996	14	15	through	through	ADP
cana-1996	14	16	to	to	ADP
cana-1996	14	17	engineering	engineering	NOUN
cana-1996	14	18	divisions	division	NOUN
cana-1996	14	19	,	,	PUNCT
cana-1996	14	20	including	include	VERB
cana-1996	14	21	machine	machine	NOUN
cana-1996	14	22	learning	learning	NOUN
cana-1996	14	23	,	,	PUNCT
cana-1996	14	24	as	as	ADV
cana-1996	14	25	well	well	ADV
cana-1996	14	26	as	as	ADP
cana-1996	14	27	industrial	industrial	ADJ
cana-1996	14	28	divisions	division	NOUN
cana-1996	14	29	,	,	PUNCT
cana-1996	14	30	such	such	ADJ
cana-1996	14	31	as	as	ADP
cana-1996	14	32	financial	financial	ADJ
cana-1996	14	33	and	and	CCONJ
cana-1996	14	34	computational	computational	ADJ
cana-1996	14	35	sciences	science	NOUN
cana-1996	14	36	.	.	PUNCT
cana-1996	15	1	applying	apply	VERB
cana-1996	15	2	the	the	DET
cana-1996	15	3	“	"	PUNCT
cana-1996	15	4	rangaig	rangaig	ADJ
cana-1996	15	5	transform	transform	NOUN
cana-1996	15	6	”	"	PUNCT
cana-1996	15	7	with	with	ADP
cana-1996	15	8	the	the	DET
cana-1996	15	9	help	help	NOUN
cana-1996	15	10	of	of	ADP
cana-1996	15	11	ham	ham	NOUN
cana-1996	15	12	can	can	AUX
cana-1996	15	13	offer	offer	VERB
cana-1996	15	14	exact	exact	ADJ
cana-1996	15	15	&	&	CCONJ
cana-1996	15	16	approximate	approximate	ADJ
cana-1996	15	17	sophisticated	sophisticated	ADJ
cana-1996	15	18	multi	multi	ADJ
cana-1996	15	19	-	-	ADJ
cana-1996	15	20	dimensional	dimensional	ADJ
cana-1996	15	21	global	global	ADJ
cana-1996	15	22	problems	problem	NOUN
cana-1996	15	23	.	.	PUNCT
cana-1996	16	1	it	it	PRON
cana-1996	16	2	is	be	AUX
cana-1996	16	3	possible	possible	ADJ
cana-1996	16	4	,	,	PUNCT
cana-1996	16	5	and	and	CCONJ
cana-1996	16	6	such	such	ADJ
cana-1996	16	7	highly	highly	ADV
cana-1996	16	8	nontrivial	nontrivial	ADJ
cana-1996	16	9	,	,	PUNCT
cana-1996	16	10	(	(	PUNCT
cana-1996	16	11	3	3	NUM
cana-1996	16	12	+	+	NOUN
cana-1996	16	13	1)-dimensional	1)-dimensional	ADJ
cana-1996	16	14	systems	system	NOUN
cana-1996	16	15	,	,	PUNCT
cana-1996	16	16	sample	sample	NOUN
cana-1996	16	17	methods	method	NOUN
cana-1996	16	18	can	can	AUX
cana-1996	16	19	be	be	AUX
cana-1996	16	20	formulated	formulate	VERB
cana-1996	16	21	and	and	CCONJ
cana-1996	16	22	employed	employ	VERB
cana-1996	16	23	here	here	ADV
cana-1996	16	24	,	,	PUNCT
cana-1996	16	25	encouraging	encourage	VERB
cana-1996	16	26	their	their	PRON
cana-1996	16	27	possible	possible	ADJ
cana-1996	16	28	use	use	NOUN
cana-1996	16	29	in	in	ADP
cana-1996	16	30	the	the	DET
cana-1996	16	31	numerical	numerical	ADJ
cana-1996	16	32	solution	solution	NOUN
cana-1996	16	33	of	of	ADP
cana-1996	16	34	some	some	DET
cana-1996	16	35	actual	actual	ADJ
cana-1996	16	36	complex	complex	ADJ
cana-1996	16	37	physical	physical	ADJ
cana-1996	16	38	partial	partial	ADJ
cana-1996	16	39	differential	differential	NOUN
cana-1996	16	40	equation	equation	NOUN
cana-1996	16	41	.	.	PUNCT
cana-1996	17	1	communications	communication	NOUN
cana-1996	17	2	on	on	ADP
cana-1996	17	3	applied	apply	VERB
cana-1996	17	4	nonlinear	nonlinear	ADJ
cana-1996	17	5	analysis	analysis	NOUN
cana-1996	17	6	issn	issn	NOUN
cana-1996	17	7	:	:	PUNCT
cana-1996	17	8	1074	1074	NUM
cana-1996	17	9	-	-	PUNCT
cana-1996	17	10	133x	133x	NUM
cana-1996	17	11	vol	vol	NOUN
cana-1996	17	12	32	32	NUM
cana-1996	17	13	no	no	NOUN
cana-1996	17	14	.	.	NOUN
cana-1996	17	15	3	3	NUM
cana-1996	17	16	(	(	PUNCT
cana-1996	17	17	2025	2025	NUM
cana-1996	17	18	)	)	PUNCT
cana-1996	17	19	384	384	NUM
cana-1996	17	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	17	21	integral	integral	ADJ
cana-1996	17	22	transforms	transform	NOUN
cana-1996	17	23	have	have	AUX
cana-1996	17	24	significantly	significantly	ADV
cana-1996	17	25	evolved	evolve	VERB
cana-1996	17	26	over	over	ADP
cana-1996	17	27	the	the	DET
cana-1996	17	28	years	year	NOUN
cana-1996	17	29	,	,	PUNCT
cana-1996	17	30	providing	provide	VERB
cana-1996	17	31	powerful	powerful	ADJ
cana-1996	17	32	methods	method	NOUN
cana-1996	17	33	for	for	ADP
cana-1996	17	34	solving	solve	VERB
cana-1996	17	35	differential	differential	ADJ
cana-1996	17	36	equations	equation	NOUN
cana-1996	17	37	.	.	PUNCT
cana-1996	18	1	the	the	DET
cana-1996	18	2	rangaig	rangaig	PROPN
cana-1996	18	3	transform	transform	NOUN
cana-1996	18	4	,	,	PUNCT
cana-1996	18	5	introduced	introduce	VERB
cana-1996	18	6	by	by	ADP
cana-1996	18	7	rangaig	rangaig	PROPN
cana-1996	18	8	et	et	PROPN
cana-1996	18	9	al	al	PROPN
cana-1996	18	10	.	.	PROPN
cana-1996	18	11	(	(	PUNCT
cana-1996	18	12	2017	2017	NUM
cana-1996	18	13	)	)	PUNCT
cana-1996	18	14	,	,	PUNCT
cana-1996	18	15	is	be	AUX
cana-1996	18	16	one	one	NUM
cana-1996	18	17	such	such	ADJ
cana-1996	18	18	innovative	innovative	ADJ
cana-1996	18	19	tool	tool	NOUN
cana-1996	18	20	that	that	PRON
cana-1996	18	21	simplifies	simplify	VERB
cana-1996	18	22	the	the	DET
cana-1996	18	23	resolution	resolution	NOUN
cana-1996	18	24	of	of	ADP
cana-1996	18	25	partial	partial	ADJ
cana-1996	18	26	differential	differential	ADJ
cana-1996	18	27	equations	equation	NOUN
cana-1996	18	28	(	(	PUNCT
cana-1996	18	29	[	[	X
cana-1996	18	30	1	1	NUM
cana-1996	18	31	]	]	PUNCT
cana-1996	18	32	,	,	PUNCT
cana-1996	18	33	[	[	X
cana-1996	18	34	22	22	NUM
cana-1996	18	35	]	]	PUNCT
cana-1996	18	36	)	)	PUNCT
cana-1996	18	37	.	.	PUNCT
cana-1996	19	1	similarly	similarly	ADV
cana-1996	19	2	,	,	PUNCT
cana-1996	19	3	aboodh	aboodh	PROPN
cana-1996	19	4	's	's	PART
cana-1996	19	5	work	work	NOUN
cana-1996	19	6	on	on	ADP
cana-1996	19	7	the	the	DET
cana-1996	19	8	aboodh	aboodh	PROPN
cana-1996	19	9	transform	transform	NOUN
cana-1996	19	10	offers	offer	VERB
cana-1996	19	11	an	an	DET
cana-1996	19	12	effective	effective	ADJ
cana-1996	19	13	alternative	alternative	NOUN
cana-1996	19	14	for	for	ADP
cana-1996	19	15	integral	integral	ADJ
cana-1996	19	16	equations	equation	NOUN
cana-1996	19	17	,	,	PUNCT
cana-1996	19	18	advancing	advance	VERB
cana-1996	19	19	the	the	DET
cana-1996	19	20	computational	computational	ADJ
cana-1996	19	21	efficiency	efficiency	NOUN
cana-1996	19	22	of	of	ADP
cana-1996	19	23	these	these	DET
cana-1996	19	24	solutions	solution	NOUN
cana-1996	19	25	[	[	X
cana-1996	19	26	2	2	NUM
cana-1996	19	27	]	]	PUNCT
cana-1996	19	28	.	.	PUNCT
cana-1996	20	1	the	the	DET
cana-1996	20	2	homotopy	homotopy	NOUN
cana-1996	20	3	analysis	analysis	NOUN
cana-1996	20	4	method	method	NOUN
cana-1996	20	5	(	(	PUNCT
cana-1996	20	6	ham	ham	NOUN
cana-1996	20	7	)	)	PUNCT
cana-1996	20	8	has	have	AUX
cana-1996	20	9	also	also	ADV
cana-1996	20	10	been	be	AUX
cana-1996	20	11	utilized	utilize	VERB
cana-1996	20	12	to	to	PART
cana-1996	20	13	solve	solve	VERB
cana-1996	20	14	nonlinear	nonlinear	ADJ
cana-1996	20	15	schrödinger	schrödinger	ADJ
cana-1996	20	16	equations	equation	NOUN
cana-1996	20	17	,	,	PUNCT
cana-1996	20	18	with	with	ADP
cana-1996	20	19	significant	significant	ADJ
cana-1996	20	20	contributions	contribution	NOUN
cana-1996	20	21	from	from	ADP
cana-1996	20	22	alomari	alomari	NOUN
cana-1996	20	23	,	,	PUNCT
cana-1996	20	24	noorani	noorani	ADJ
cana-1996	20	25	,	,	PUNCT
cana-1996	20	26	and	and	CCONJ
cana-1996	20	27	nazar	nazar	NOUN
cana-1996	21	1	[	[	X
cana-1996	21	2	3	3	NUM
cana-1996	21	3	]	]	PUNCT
cana-1996	21	4	.	.	PUNCT
cana-1996	22	1	eltayeb	eltayeb	PROPN
cana-1996	22	2	and	and	CCONJ
cana-1996	22	3	kilicman	kilicman	PROPN
cana-1996	22	4	further	far	ADV
cana-1996	22	5	explored	explore	VERB
cana-1996	22	6	the	the	DET
cana-1996	22	7	utility	utility	NOUN
cana-1996	22	8	of	of	ADP
cana-1996	22	9	the	the	DET
cana-1996	22	10	sumudu	sumudu	NOUN
cana-1996	22	11	transform	transform	NOUN
cana-1996	22	12	in	in	ADP
cana-1996	22	13	differential	differential	ADJ
cana-1996	22	14	equations	equation	NOUN
cana-1996	22	15	,	,	PUNCT
cana-1996	22	16	expanding	expand	VERB
cana-1996	22	17	the	the	DET
cana-1996	22	18	scope	scope	NOUN
cana-1996	22	19	of	of	ADP
cana-1996	22	20	applicable	applicable	ADJ
cana-1996	22	21	mathematical	mathematical	ADJ
cana-1996	22	22	problems	problem	NOUN
cana-1996	22	23	[	[	X
cana-1996	22	24	4	4	NUM
cana-1996	22	25	]	]	PUNCT
cana-1996	22	26	.	.	PUNCT
cana-1996	23	1	on	on	ADP
cana-1996	23	2	a	a	DET
cana-1996	23	3	parallel	parallel	ADJ
cana-1996	23	4	track	track	NOUN
cana-1996	23	5	,	,	PUNCT
cana-1996	23	6	elzaki	elzaki	VERB
cana-1996	23	7	’s	’s	PART
cana-1996	23	8	contributions	contribution	NOUN
cana-1996	23	9	introduced	introduce	VERB
cana-1996	23	10	the	the	DET
cana-1996	23	11	elzaki	elzaki	NOUN
cana-1996	23	12	transform	transform	NOUN
cana-1996	23	13	,	,	PUNCT
cana-1996	23	14	applied	apply	VERB
cana-1996	23	15	to	to	ADP
cana-1996	23	16	both	both	CCONJ
cana-1996	23	17	linear	linear	ADJ
cana-1996	23	18	and	and	CCONJ
cana-1996	23	19	nonlinear	nonlinear	ADJ
cana-1996	23	20	equations	equation	NOUN
cana-1996	23	21	,	,	PUNCT
cana-1996	23	22	underscoring	underscore	VERB
cana-1996	23	23	the	the	DET
cana-1996	23	24	versatility	versatility	NOUN
cana-1996	23	25	of	of	ADP
cana-1996	23	26	integral	integral	ADJ
cana-1996	23	27	transforms	transform	NOUN
cana-1996	23	28	in	in	ADP
cana-1996	23	29	mathematical	mathematical	ADJ
cana-1996	23	30	modelling	modelling	NOUN
cana-1996	23	31	(	(	PUNCT
cana-1996	23	32	[	[	X
cana-1996	23	33	5	5	NUM
cana-1996	23	34	]	]	PUNCT
cana-1996	23	35	,	,	PUNCT
cana-1996	23	36	[	[	X
cana-1996	23	37	6	6	NUM
cana-1996	23	38	]	]	PUNCT
cana-1996	23	39	,	,	PUNCT
cana-1996	23	40	[	[	X
cana-1996	23	41	24	24	NUM
cana-1996	23	42	]	]	PUNCT
cana-1996	23	43	)	)	PUNCT
cana-1996	23	44	.	.	PUNCT
cana-1996	24	1	the	the	DET
cana-1996	24	2	homotopy	homotopy	NOUN
cana-1996	24	3	analysis	analysis	NOUN
cana-1996	24	4	method	method	NOUN
cana-1996	24	5	(	(	PUNCT
cana-1996	24	6	ham	ham	NOUN
cana-1996	24	7	)	)	PUNCT
cana-1996	24	8	continues	continue	VERB
cana-1996	24	9	to	to	PART
cana-1996	24	10	be	be	AUX
cana-1996	24	11	an	an	DET
cana-1996	24	12	effective	effective	ADJ
cana-1996	24	13	technique	technique	NOUN
cana-1996	24	14	in	in	ADP
cana-1996	24	15	solving	solve	VERB
cana-1996	24	16	nonlinear	nonlinear	ADJ
cana-1996	24	17	problems	problem	NOUN
cana-1996	24	18	,	,	PUNCT
cana-1996	24	19	as	as	SCONJ
cana-1996	24	20	evidenced	evidence	VERB
cana-1996	24	21	by	by	ADP
cana-1996	24	22	the	the	DET
cana-1996	24	23	research	research	NOUN
cana-1996	24	24	of	of	ADP
cana-1996	24	25	ganjiani	ganjiani	ADJ
cana-1996	24	26	[	[	X
cana-1996	24	27	7	7	NUM
cana-1996	24	28	]	]	PUNCT
cana-1996	24	29	,	,	PUNCT
cana-1996	24	30	gupta	gupta	PROPN
cana-1996	24	31	and	and	CCONJ
cana-1996	24	32	kumar	kumar	PROPN
cana-1996	25	1	[	[	X
cana-1996	25	2	8	8	NUM
cana-1996	25	3	]	]	PUNCT
cana-1996	25	4	,	,	PUNCT
cana-1996	25	5	and	and	CCONJ
cana-1996	25	6	jafari	jafari	ADJ
cana-1996	25	7	and	and	CCONJ
cana-1996	25	8	seifi	seifi	NOUN
cana-1996	26	1	[	[	X
cana-1996	26	2	9	9	NUM
cana-1996	26	3	]	]	PUNCT
cana-1996	26	4	.	.	PUNCT
cana-1996	27	1	furthermore	furthermore	ADV
cana-1996	27	2	,	,	PUNCT
cana-1996	27	3	new	new	ADJ
cana-1996	27	4	developments	development	NOUN
cana-1996	27	5	,	,	PUNCT
cana-1996	27	6	such	such	ADJ
cana-1996	27	7	as	as	ADP
cana-1996	27	8	the	the	DET
cana-1996	27	9	shehu	shehu	NOUN
cana-1996	27	10	transform	transform	NOUN
cana-1996	27	11	proposed	propose	VERB
cana-1996	27	12	by	by	ADP
cana-1996	27	13	maitama	maitama	PROPN
cana-1996	27	14	and	and	CCONJ
cana-1996	27	15	zhao	zhao	PROPN
cana-1996	28	1	[	[	X
cana-1996	28	2	18	18	NUM
cana-1996	28	3	]	]	PUNCT
cana-1996	28	4	and	and	CCONJ
cana-1996	28	5	generalizations	generalization	NOUN
cana-1996	28	6	of	of	ADP
cana-1996	28	7	the	the	DET
cana-1996	28	8	rangaig	rangaig	ADJ
cana-1996	28	9	transform	transform	NOUN
cana-1996	28	10	by	by	ADP
cana-1996	28	11	mansour	mansour	PROPN
cana-1996	28	12	and	and	CCONJ
cana-1996	28	13	kuffi	kuffi	PROPN
cana-1996	28	14	(	(	PUNCT
cana-1996	28	15	[	[	X
cana-1996	28	16	19	19	NUM
cana-1996	28	17	]	]	PUNCT
cana-1996	28	18	,	,	PUNCT
cana-1996	28	19	[	[	X
cana-1996	28	20	20	20	NUM
cana-1996	28	21	]	]	NUM
cana-1996	28	22	)	)	PUNCT
cana-1996	28	23	,	,	PUNCT
cana-1996	28	24	have	have	AUX
cana-1996	28	25	opened	open	VERB
cana-1996	28	26	new	new	ADJ
cana-1996	28	27	possibilities	possibility	NOUN
cana-1996	28	28	for	for	ADP
cana-1996	28	29	addressing	address	VERB
cana-1996	28	30	complex	complex	ADJ
cana-1996	28	31	mathematical	mathematical	ADJ
cana-1996	28	32	challenges	challenge	NOUN
cana-1996	28	33	.	.	PUNCT
cana-1996	29	1	in	in	ADP
cana-1996	29	2	this	this	DET
cana-1996	29	3	study	study	NOUN
cana-1996	29	4	,	,	PUNCT
cana-1996	29	5	the	the	DET
cana-1996	29	6	potential	potential	NOUN
cana-1996	29	7	of	of	ADP
cana-1996	29	8	the	the	DET
cana-1996	29	9	“	"	PUNCT
cana-1996	29	10	rangaig	rangaig	ADJ
cana-1996	29	11	transform”-based	transform”-base	VERB
cana-1996	29	12	“	"	PUNCT
cana-1996	29	13	homotopy	homotopy	VERB
cana-1996	29	14	analysis	analysis	NOUN
cana-1996	29	15	method	method	NOUN
cana-1996	29	16	”	"	PUNCT
cana-1996	29	17	(	(	PUNCT
cana-1996	29	18	rtham	rtham	NOUN
cana-1996	29	19	)	)	PUNCT
cana-1996	29	20	to	to	PART
cana-1996	29	21	solve	solve	VERB
cana-1996	29	22	some	some	DET
cana-1996	29	23	examples	example	NOUN
cana-1996	29	24	in	in	ADP
cana-1996	29	25	(	(	PUNCT
cana-1996	29	26	3	3	NUM
cana-1996	29	27	+	+	NOUN
cana-1996	29	28	1	1	NUM
cana-1996	29	29	)	)	PUNCT
cana-1996	29	30	dimensions	dimension	NOUN
cana-1996	29	31	pdes	pde	NOUN
cana-1996	29	32	is	be	AUX
cana-1996	29	33	investigated	investigate	VERB
cana-1996	29	34	.	.	PUNCT
cana-1996	30	1	in	in	ADP
cana-1996	30	2	the	the	DET
cana-1996	30	3	end	end	NOUN
cana-1996	30	4	,	,	PUNCT
cana-1996	30	5	we	we	PRON
cana-1996	30	6	will	will	AUX
cana-1996	30	7	scrutinize	scrutinize	VERB
cana-1996	30	8	its	its	PRON
cana-1996	30	9	possibility	possibility	NOUN
cana-1996	30	10	of	of	ADP
cana-1996	30	11	use	use	NOUN
cana-1996	30	12	in	in	ADP
cana-1996	30	13	various	various	ADJ
cana-1996	30	14	physical	physical	ADJ
cana-1996	30	15	problems	problem	NOUN
cana-1996	30	16	,	,	PUNCT
cana-1996	30	17	comparing	compare	VERB
cana-1996	30	18	it	it	PRON
cana-1996	30	19	with	with	ADP
cana-1996	30	20	previous	previous	ADJ
cana-1996	30	21	methods	method	NOUN
cana-1996	30	22	that	that	PRON
cana-1996	30	23	solve	solve	VERB
cana-1996	30	24	versatility	versatility	NOUN
cana-1996	30	25	and	and	CCONJ
cana-1996	30	26	convergence	convergence	NOUN
cana-1996	30	27	control	control	NOUN
cana-1996	30	28	over	over	ADP
cana-1996	30	29	various	various	ADJ
cana-1996	30	30	linear	linear	ADJ
cana-1996	30	31	and	and	CCONJ
cana-1996	30	32	nonlinear	nonlinear	ADJ
cana-1996	30	33	complex	complex	ADJ
cana-1996	30	34	scenario	scenario	NOUN
cana-1996	30	35	problems	problem	NOUN
cana-1996	30	36	.	.	PUNCT
cana-1996	31	1	the	the	DET
cana-1996	31	2	remainder	remainder	NOUN
cana-1996	31	3	of	of	ADP
cana-1996	31	4	this	this	DET
cana-1996	31	5	paper	paper	NOUN
cana-1996	31	6	is	be	AUX
cana-1996	31	7	organized	organize	VERB
cana-1996	31	8	as	as	SCONJ
cana-1996	31	9	follows	follow	VERB
cana-1996	31	10	:	:	PUNCT
cana-1996	31	11	section	section	NOUN
cana-1996	31	12	2	2	NUM
cana-1996	31	13	gives	give	VERB
cana-1996	31	14	the	the	DET
cana-1996	31	15	basic	basic	ADJ
cana-1996	31	16	definitions	definition	NOUN
cana-1996	31	17	and	and	CCONJ
cana-1996	31	18	concepts	concept	NOUN
cana-1996	31	19	utilized	utilize	VERB
cana-1996	31	20	in	in	ADP
cana-1996	31	21	the	the	DET
cana-1996	31	22	“	"	PUNCT
cana-1996	31	23	rangaig	rangaig	ADJ
cana-1996	31	24	transform	transform	NOUN
cana-1996	31	25	”	"	PUNCT
cana-1996	31	26	.	.	PUNCT
cana-1996	32	1	within	within	ADP
cana-1996	32	2	section	section	NOUN
cana-1996	32	3	3	3	NUM
cana-1996	32	4	,	,	PUNCT
cana-1996	32	5	the	the	DET
cana-1996	32	6	rebuilt	rebuild	VERB
cana-1996	32	7	resilient	resilient	ADJ
cana-1996	32	8	homotopy	homotopy	NOUN
cana-1996	32	9	examination	examination	NOUN
cana-1996	32	10	system	system	NOUN
cana-1996	32	11	has	have	AUX
cana-1996	32	12	been	be	AUX
cana-1996	32	13	mentioned	mention	VERB
cana-1996	32	14	.	.	PUNCT
cana-1996	33	1	the	the	DET
cana-1996	33	2	“	"	PUNCT
cana-1996	33	3	homotopy	homotopy	NOUN
cana-1996	33	4	analysis	analysis	NOUN
cana-1996	33	5	”	"	PUNCT
cana-1996	33	6	and	and	CCONJ
cana-1996	33	7	“	"	PUNCT
cana-1996	33	8	rangaig	rangaig	ADJ
cana-1996	33	9	transform	transform	NOUN
cana-1996	33	10	method	method	NOUN
cana-1996	33	11	”	"	PUNCT
cana-1996	33	12	for	for	ADP
cana-1996	33	13	solving	solve	VERB
cana-1996	33	14	(	(	PUNCT
cana-1996	33	15	3	3	NUM
cana-1996	33	16	+	+	NOUN
cana-1996	33	17	1)-d	1)-d	NUM
cana-1996	33	18	pdes	pde	NOUN
cana-1996	33	19	are	be	AUX
cana-1996	33	20	described	describe	VERB
cana-1996	33	21	in	in	ADP
cana-1996	33	22	section	section	NOUN
cana-1996	33	23	4	4	NUM
cana-1996	33	24	.	.	PUNCT
cana-1996	34	1	we	we	PRON
cana-1996	34	2	provide	provide	VERB
cana-1996	34	3	test	test	NOUN
cana-1996	34	4	problems	problem	NOUN
cana-1996	34	5	of	of	ADP
cana-1996	34	6	(	(	PUNCT
cana-1996	34	7	3	3	NUM
cana-1996	34	8	+	+	NOUN
cana-1996	34	9	1)-d	1)-d	NUM
cana-1996	34	10	“	"	PUNCT
cana-1996	34	11	telegraph	telegraph	NOUN
cana-1996	34	12	equation	equation	NOUN
cana-1996	34	13	”	"	PUNCT
cana-1996	34	14	,	,	PUNCT
cana-1996	34	15	“	"	PUNCT
cana-1996	34	16	diffusion	diffusion	NOUN
cana-1996	34	17	equation	equation	NOUN
cana-1996	34	18	”	"	PUNCT
cana-1996	34	19	,	,	PUNCT
cana-1996	34	20	and	and	CCONJ
cana-1996	34	21	“	"	PUNCT
cana-1996	34	22	klein	klein	PROPN
cana-1996	34	23	gordan	gordan	PROPN
cana-1996	34	24	equation	equation	PROPN
cana-1996	34	25	”	"	PUNCT
cana-1996	34	26	to	to	PART
cana-1996	34	27	be	be	AUX
cana-1996	34	28	solved	solve	VERB
cana-1996	34	29	in	in	ADP
cana-1996	34	30	section	section	NOUN
cana-1996	34	31	5	5	NUM
cana-1996	34	32	.	.	PUNCT
cana-1996	35	1	the	the	DET
cana-1996	35	2	discussion	discussion	NOUN
cana-1996	35	3	of	of	ADP
cana-1996	35	4	a	a	DET
cana-1996	35	5	conclusion	conclusion	NOUN
cana-1996	35	6	is	be	AUX
cana-1996	35	7	in	in	ADP
cana-1996	35	8	section	section	NOUN
cana-1996	35	9	6	6	NUM
cana-1996	35	10	.	.	NOUN
cana-1996	36	1	2	2	NUM
cana-1996	36	2	.	.	NOUN
cana-1996	36	3	basic	basic	ADJ
cana-1996	36	4	concept	concept	NOUN
cana-1996	36	5	of	of	ADP
cana-1996	36	6	“	"	PUNCT
cana-1996	36	7	rangaig	rangaig	ADJ
cana-1996	36	8	transform	transform	NOUN
cana-1996	36	9	”	"	PUNCT
cana-1996	36	10	[	[	X
cana-1996	36	11	19	19	NUM
cana-1996	36	12	-	-	SYM
cana-1996	36	13	22	22	NUM
cana-1996	36	14	]	]	PUNCT
cana-1996	36	15	the	the	DET
cana-1996	36	16	following	follow	VERB
cana-1996	36	17	part	part	NOUN
cana-1996	36	18	introduces	introduce	VERB
cana-1996	36	19	the	the	DET
cana-1996	36	20	fundamental	fundamental	ADJ
cana-1996	36	21	principles	principle	NOUN
cana-1996	36	22	and	and	CCONJ
cana-1996	36	23	features	feature	NOUN
cana-1996	36	24	of	of	ADP
cana-1996	36	25	another	another	DET
cana-1996	36	26	transform	transform	NOUN
cana-1996	36	27	,	,	PUNCT
cana-1996	36	28	the	the	DET
cana-1996	36	29	“	"	PUNCT
cana-1996	36	30	rangaig	rangaig	ADJ
cana-1996	36	31	transform	transform	NOUN
cana-1996	36	32	”	"	PUNCT
cana-1996	36	33	,	,	PUNCT
cana-1996	36	34	which	which	PRON
cana-1996	36	35	will	will	AUX
cana-1996	36	36	be	be	AUX
cana-1996	36	37	introduced	introduce	VERB
cana-1996	36	38	in	in	ADP
cana-1996	36	39	this	this	DET
cana-1996	36	40	work	work	NOUN
cana-1996	36	41	.	.	PUNCT
cana-1996	37	1	in	in	ADP
cana-1996	37	2	this	this	DET
cana-1996	37	3	study	study	NOUN
cana-1996	37	4	,	,	PUNCT
cana-1996	37	5	we	we	PRON
cana-1996	37	6	introduce	introduce	VERB
cana-1996	37	7	the	the	DET
cana-1996	37	8	“	"	PUNCT
cana-1996	37	9	rangaig	rangaig	ADJ
cana-1996	37	10	transform	transform	NOUN
cana-1996	37	11	”	"	PUNCT
cana-1996	37	12	as	as	ADP
cana-1996	37	13	a	a	DET
cana-1996	37	14	novel	novel	ADJ
cana-1996	37	15	transformation	transformation	NOUN
cana-1996	37	16	for	for	ADP
cana-1996	37	17	exponentially	exponentially	ADV
cana-1996	37	18	ordered	order	VERB
cana-1996	37	19	functions	function	NOUN
cana-1996	37	20	within	within	ADP
cana-1996	37	21	the	the	DET
cana-1996	37	22	set	set	NOUN
cana-1996	37	23	h.	h.	NOUN
cana-1996	37	24	𝐻	𝐻	PROPN
cana-1996	37	25	=	=	PUNCT
cana-1996	37	26	{	{	PUNCT
cana-1996	37	27	𝜂(𝑡	𝜂(𝑡	NOUN
cana-1996	37	28	)	)	PUNCT
cana-1996	37	29	∃𝑁	∃𝑁	NOUN
cana-1996	37	30	,	,	PUNCT
cana-1996	37	31	𝐴1	𝐴1	PROPN
cana-1996	37	32	,	,	PUNCT
cana-1996	37	33	𝐴2	𝐴2	PROPN
cana-1996	37	34	>	>	X
cana-1996	37	35	0	0	NUM
cana-1996	37	36	,	,	PUNCT
cana-1996	37	37	|𝜂(𝑡)|	|𝜂(𝑡)|	PROPN
cana-1996	37	38	>	>	X
cana-1996	37	39	𝑁𝑒𝐴𝑖|𝑡|	𝑁𝑒𝐴𝑖|𝑡|	NOUN
cana-1996	37	40	,	,	PUNCT
cana-1996	37	41	𝑡	𝑡	PROPN
cana-1996	37	42	∈	∈	PROPN
cana-1996	37	43	(	(	PUNCT
cana-1996	37	44	−1)𝑖−1	−1)𝑖−1	NOUN
cana-1996	37	45	×	×	NOUN
cana-1996	37	46	(	(	PUNCT
cana-1996	37	47	−∞	−∞	NOUN
cana-1996	37	48	,	,	PUNCT
cana-1996	37	49	0	0	NUM
cana-1996	37	50	)	)	PUNCT
cana-1996	37	51	}	}	PUNCT
cana-1996	37	52	(	(	PUNCT
cana-1996	37	53	1	1	X
cana-1996	37	54	)	)	PUNCT
cana-1996	37	55	𝑁	𝑁	PROPN
cana-1996	37	56	,	,	PUNCT
cana-1996	37	57	the	the	DET
cana-1996	37	58	arbitrary	arbitrary	ADJ
cana-1996	37	59	constant	constant	ADJ
cana-1996	37	60	one	one	PRON
cana-1996	37	61	can	can	AUX
cana-1996	37	62	have	have	VERB
cana-1996	37	63	an	an	DET
cana-1996	37	64	infinite	infinite	ADJ
cana-1996	37	65	or	or	CCONJ
cana-1996	37	66	endlessly	endlessly	ADV
cana-1996	37	67	finite	finite	VERB
cana-1996	37	68	value	value	NOUN
cana-1996	37	69	for	for	ADP
cana-1996	37	70	the	the	DET
cana-1996	37	71	arbitrary	arbitrary	ADJ
cana-1996	37	72	constant	constant	ADJ
cana-1996	37	73	𝐴1	𝐴1	PROPN
cana-1996	37	74	,	,	PUNCT
cana-1996	37	75	𝐴2	𝐴2	PROPN
cana-1996	37	76	.	.	PUNCT
cana-1996	38	1	we	we	PRON
cana-1996	38	2	now	now	ADV
cana-1996	38	3	introduce	introduce	VERB
cana-1996	38	4	a	a	DET
cana-1996	38	5	new	new	ADJ
cana-1996	38	6	transformation	transformation	NOUN
cana-1996	38	7	that	that	PRON
cana-1996	38	8	may	may	AUX
cana-1996	38	9	be	be	AUX
cana-1996	38	10	included	include	VERB
cana-1996	38	11	in	in	ADP
cana-1996	38	12	(	(	PUNCT
cana-1996	38	13	1	1	NUM
cana-1996	38	14	)	)	PUNCT
cana-1996	38	15	as	as	SCONJ
cana-1996	38	16	follows	follow	VERB
cana-1996	38	17	:	:	PUNCT
cana-1996	38	18	ℛ[𝜂(𝑡	ℛ[𝜂(𝑡	NOUN
cana-1996	38	19	)	)	PUNCT
cana-1996	38	20	]	]	PUNCT
cana-1996	39	1	=	=	PUNCT
cana-1996	39	2	𝑇(𝜛	𝑇(𝜛	X
cana-1996	39	3	)	)	PUNCT
cana-1996	39	4	=	=	SYM
cana-1996	40	1	1	1	NUM
cana-1996	40	2	𝜛	𝜛	SYM
cana-1996	40	3	∫	∫	PROPN
cana-1996	40	4	𝑐𝜛𝑡	𝑐𝜛𝑡	PROPN
cana-1996	40	5	0	0	PUNCT
cana-1996	41	1	−∞	−∞	ADP
cana-1996	41	2	ℎ(𝑡)𝑑𝑡	ℎ(𝑡)𝑑𝑡	PROPN
cana-1996	41	3	,	,	PUNCT
cana-1996	41	4	1	1	NUM
cana-1996	41	5	𝐴1	𝐴1	PROPN
cana-1996	41	6	≤	≤	X
cana-1996	41	7	𝜛	𝜛	X
cana-1996	41	8	≤	≤	NUM
cana-1996	41	9	1	1	NUM
cana-1996	41	10	𝐴2	𝐴2	NOUN
cana-1996	41	11	,	,	PUNCT
cana-1996	41	12	(	(	PUNCT
cana-1996	41	13	2	2	X
cana-1996	41	14	)	)	PUNCT
cana-1996	41	15	there	there	PRON
cana-1996	41	16	is	be	VERB
cana-1996	41	17	a	a	DET
cana-1996	41	18	transformation	transformation	NOUN
cana-1996	41	19	process	process	NOUN
cana-1996	41	20	known	know	VERB
cana-1996	41	21	as	as	ADP
cana-1996	41	22	the	the	DET
cana-1996	41	23	“	"	PUNCT
cana-1996	41	24	rangaig	rangaig	ADJ
cana-1996	41	25	transform	transform	NOUN
cana-1996	41	26	”	"	PUNCT
cana-1996	41	27	.	.	PUNCT
cana-1996	42	1	the	the	DET
cana-1996	42	2	definition	definition	NOUN
cana-1996	42	3	is	be	AUX
cana-1996	42	4	really	really	ADV
cana-1996	42	5	a	a	DET
cana-1996	42	6	statement	statement	NOUN
cana-1996	42	7	that	that	DET
cana-1996	42	8	factor	factor	NOUN
cana-1996	42	9	𝜛	𝜛	PROPN
cana-1996	42	10	takes	take	VERB
cana-1996	42	11	the	the	DET
cana-1996	42	12	place	place	NOUN
cana-1996	42	13	of	of	ADP
cana-1996	42	14	the	the	DET
cana-1996	42	15	variable	variable	ADJ
cana-1996	42	16	𝑡	𝑡	PROPN
cana-1996	42	17	in	in	ADP
cana-1996	42	18	the	the	DET
cana-1996	42	19	function	function	NOUN
cana-1996	42	20	ℎ.	ℎ.	NOUN
cana-1996	42	21	on	on	ADP
cana-1996	42	22	the	the	DET
cana-1996	42	23	other	other	ADJ
cana-1996	42	24	hand	hand	NOUN
cana-1996	42	25	,	,	PUNCT
cana-1996	42	26	it	it	PRON
cana-1996	42	27	is	be	AUX
cana-1996	42	28	possible	possible	ADJ
cana-1996	42	29	to	to	PART
cana-1996	42	30	claim	claim	VERB
cana-1996	42	31	that	that	SCONJ
cana-1996	42	32	there	there	PRON
cana-1996	42	33	is	be	VERB
cana-1996	42	34	a	a	DET
cana-1996	42	35	transition	transition	NOUN
cana-1996	42	36	to	to	ADP
cana-1996	42	37	a	a	DET
cana-1996	42	38	description	description	NOUN
cana-1996	42	39	of	of	ADP
cana-1996	42	40	the	the	DET
cana-1996	42	41	function	function	NOUN
cana-1996	42	42	𝜂(𝑡	𝜂(𝑡	NOUN
cana-1996	42	43	)	)	PUNCT
cana-1996	42	44	in	in	ADP
cana-1996	42	45	the	the	DET
cana-1996	42	46	pi	pi	ADJ
cana-1996	42	47	-	-	PUNCT
cana-1996	42	48	variant	variant	NOUN
cana-1996	42	49	communications	communication	NOUN
cana-1996	42	50	on	on	ADP
cana-1996	42	51	applied	apply	VERB
cana-1996	42	52	nonlinear	nonlinear	ADJ
cana-1996	42	53	analysis	analysis	NOUN
cana-1996	42	54	issn	issn	NOUN
cana-1996	42	55	:	:	PUNCT
cana-1996	42	56	1074	1074	NUM
cana-1996	42	57	-	-	PUNCT
cana-1996	42	58	133x	133x	NUM
cana-1996	42	59	vol	vol	NOUN
cana-1996	42	60	32	32	NUM
cana-1996	42	61	no	no	NOUN
cana-1996	42	62	.	.	NOUN
cana-1996	42	63	3	3	NUM
cana-1996	42	64	(	(	PUNCT
cana-1996	42	65	2025	2025	NUM
cana-1996	42	66	)	)	PUNCT
cana-1996	42	67	385	385	NUM
cana-1996	42	68	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	42	69	space	space	NOUN
cana-1996	42	70	𝑇(𝜛	𝑇(𝜛	NOUN
cana-1996	42	71	)	)	PUNCT
cana-1996	42	72	.	.	PUNCT
cana-1996	43	1	the	the	DET
cana-1996	43	2	following	following	NOUN
cana-1996	43	3	demonstrates	demonstrate	VERB
cana-1996	43	4	the	the	DET
cana-1996	43	5	application	application	NOUN
cana-1996	43	6	of	of	ADP
cana-1996	43	7	the	the	DET
cana-1996	43	8	“	"	PUNCT
cana-1996	43	9	rangaig	rangaig	ADJ
cana-1996	43	10	transform	transform	NOUN
cana-1996	43	11	”	"	PUNCT
cana-1996	43	12	in	in	ADP
cana-1996	43	13	obtaining	obtain	VERB
cana-1996	43	14	results	result	NOUN
cana-1996	43	15	for	for	ADP
cana-1996	43	16	a	a	DET
cana-1996	43	17	certain	certain	ADJ
cana-1996	43	18	type	type	NOUN
cana-1996	43	19	of	of	ADP
cana-1996	43	20	function	function	NOUN
cana-1996	43	21	[	[	X
cana-1996	43	22	19	19	NUM
cana-1996	43	23	-	-	SYM
cana-1996	43	24	22	22	NUM
cana-1996	43	25	]	]	PUNCT
cana-1996	43	26	.	.	PUNCT
cana-1996	44	1	the	the	DET
cana-1996	44	2	following	follow	VERB
cana-1996	44	3	“	"	PUNCT
cana-1996	44	4	rangaig	rangaig	ADJ
cana-1996	44	5	transform	transform	NOUN
cana-1996	44	6	”	"	PUNCT
cana-1996	44	7	is	be	AUX
cana-1996	44	8	accomplished	accomplish	VERB
cana-1996	44	9	in	in	ADP
cana-1996	44	10	some	some	DET
cana-1996	44	11	core	core	NOUN
cana-1996	44	12	forms	form	NOUN
cana-1996	44	13	.	.	PUNCT
cana-1996	45	1	the	the	DET
cana-1996	45	2	general	general	ADJ
cana-1996	45	3	function	function	NOUN
cana-1996	45	4	is	be	AUX
cana-1996	45	5	:	:	PUNCT
cana-1996	45	6	𝜂(𝑡	𝜂(𝑡	VERB
cana-1996	45	7	)	)	PUNCT
cana-1996	45	8	=	=	SYM
cana-1996	45	9	ℛ{𝜂(𝑡	ℛ{𝜂(𝑡	X
cana-1996	45	10	)	)	PUNCT
cana-1996	45	11	}	}	PUNCT
cana-1996	45	12	i.	i.	NOUN
cana-1996	45	13	ℛ{𝜂(𝑡	ℛ{𝜂(𝑡	PROPN
cana-1996	45	14	)	)	PUNCT
cana-1996	45	15	}	}	PUNCT
cana-1996	45	16	=	=	SYM
cana-1996	45	17	ℛ{1	ℛ{1	PROPN
cana-1996	45	18	}	}	PUNCT
cana-1996	45	19	=	=	SYM
cana-1996	45	20	1	1	NUM
cana-1996	45	21	𝜛2	𝜛2	PROPN
cana-1996	45	22	ii	ii	NOUN
cana-1996	45	23	.	.	PUNCT
cana-1996	46	1	ℛ{1	ℛ{1	PRON
cana-1996	46	2	}	}	PUNCT
cana-1996	46	3	=	=	SYM
cana-1996	46	4	−	−	PROPN
cana-1996	46	5	1	1	NUM
cana-1996	46	6	𝜛3	𝜛3	PROPN
cana-1996	46	7	iii	iii	NOUN
cana-1996	46	8	.	.	PUNCT
cana-1996	46	9	ℛ{𝑡	ℛ{𝑡	X
cana-1996	46	10	}	}	PUNCT
cana-1996	46	11	=	=	SYM
cana-1996	46	12	−	−	PROPN
cana-1996	46	13	1	1	NUM
cana-1996	46	14	𝜛3	𝜛3	PROPN
cana-1996	46	15	iv	iv	NOUN
cana-1996	46	16	.	.	PUNCT
cana-1996	47	1	ℛ{𝑡𝑛	ℛ{𝑡𝑛	PROPN
cana-1996	47	2	,	,	PUNCT
cana-1996	47	3	𝑛	𝑛	PRON
cana-1996	47	4	≥	≥	NOUN
cana-1996	47	5	0	0	NUM
cana-1996	47	6	}	}	PUNCT
cana-1996	47	7	=	=	SYM
cana-1996	47	8	(	(	PUNCT
cana-1996	47	9	−1)2𝑛	−1)2𝑛	NOUN
cana-1996	47	10	!	!	PUNCT
cana-1996	47	11	𝜛𝑛+2	𝜛𝑛+2	NUM
cana-1996	47	12	v.	v.	ADP
cana-1996	47	13	ℛ{𝑠𝑖𝑛(𝑡	ℛ{𝑠𝑖𝑛(𝑡	NOUN
cana-1996	47	14	)	)	PUNCT
cana-1996	47	15	}	}	PUNCT
cana-1996	47	16	=	=	PUNCT
cana-1996	48	1	−	−	PROPN
cana-1996	48	2	1	1	NUM
cana-1996	48	3	𝜛(𝜛2	𝜛(𝜛2	NOUN
cana-1996	48	4	+	+	PROPN
cana-1996	48	5	1	1	NUM
cana-1996	48	6	)	)	PUNCT
cana-1996	48	7	vi	vi	NOUN
cana-1996	48	8	.	.	PUNCT
cana-1996	49	1	ℛ{𝑐𝑜𝑠(𝑡	ℛ{𝑐𝑜𝑠(𝑡	NUM
cana-1996	50	1	)	)	PUNCT
cana-1996	50	2	}	}	PUNCT
cana-1996	50	3	=	=	SYM
cana-1996	50	4	1	1	X
cana-1996	50	5	(	(	PUNCT
cana-1996	50	6	𝜛2	𝜛2	VERB
cana-1996	50	7	+	+	NOUN
cana-1996	50	8	1	1	NUM
cana-1996	50	9	)	)	PUNCT
cana-1996	50	10	vii	vii	PROPN
cana-1996	50	11	.	.	PUNCT
cana-1996	50	12	ℛ{𝑡𝑛	ℛ{𝑡𝑛	PROPN
cana-1996	50	13	,	,	PUNCT
cana-1996	50	14	𝑛	𝑛	DET
cana-1996	50	15	≤	≤	NOUN
cana-1996	50	16	0	0	NUM
cana-1996	50	17	}	}	PUNCT
cana-1996	50	18	=	=	SYM
cana-1996	50	19	(	(	PUNCT
cana-1996	50	20	−1)𝑛+1γ(−𝑛	−1)𝑛+1γ(−𝑛	INTJ
cana-1996	50	21	)	)	PUNCT
cana-1996	50	22	𝜛𝑛	𝜛𝑛	NOUN
cana-1996	50	23	viii	viii	NOUN
cana-1996	50	24	.	.	PUNCT
cana-1996	51	1	ℛ{𝑒𝑎𝑡	ℛ{𝑒𝑎𝑡	NOUN
cana-1996	51	2	}	}	PUNCT
cana-1996	51	3	=	=	SYM
cana-1996	51	4	1	1	NUM
cana-1996	51	5	𝜛(𝜛+𝑎	𝜛(𝜛+𝑎	NUM
cana-1996	51	6	)	)	PUNCT
cana-1996	51	7	ix	ix	PROPN
cana-1996	51	8	.	.	PUNCT
cana-1996	52	1	ℛ{𝑀(𝑡	ℛ{𝑀(𝑡	PRON
cana-1996	52	2	−	−	NUM
cana-1996	52	3	𝑎	𝑎	NOUN
cana-1996	52	4	)	)	PUNCT
cana-1996	52	5	}	}	PUNCT
cana-1996	52	6	=	=	SYM
cana-1996	52	7	1	1	NUM
cana-1996	52	8	𝜛2	𝜛2	NOUN
cana-1996	52	9	𝑒𝑎𝑡	𝑒𝑎𝑡	NOUN
cana-1996	52	10	theorem	theorem	VERB
cana-1996	52	11	1	1	NUM
cana-1996	52	12	:	:	PUNCT
cana-1996	53	1	[	[	X
cana-1996	53	2	22	22	NUM
cana-1996	53	3	]	]	PUNCT
cana-1996	53	4	(	(	PUNCT
cana-1996	53	5	transformation	transformation	NOUN
cana-1996	53	6	of	of	ADP
cana-1996	53	7	rangaig	rangaig	ADJ
cana-1996	53	8	derivatives	derivative	NOUN
cana-1996	53	9	)	)	PUNCT
cana-1996	53	10	if	if	SCONJ
cana-1996	53	11	𝜂(𝑡	𝜂(𝑡	NOUN
cana-1996	53	12	)	)	PUNCT
cana-1996	53	13	,	,	PUNCT
cana-1996	53	14	𝜂1(𝑡	𝜂1(𝑡	NUM
cana-1996	53	15	)	)	PUNCT
cana-1996	53	16	,	,	PUNCT
cana-1996	53	17	𝜂𝑛(𝑡	𝜂𝑛(𝑡	X
cana-1996	53	18	)	)	PUNCT
cana-1996	53	19	∈	∈	PROPN
cana-1996	53	20	𝐻	𝐻	PROPN
cana-1996	53	21	,	,	PUNCT
cana-1996	53	22	then	then	ADV
cana-1996	53	23	ℛ[𝜂𝑛(𝑡	ℛ[𝜂𝑛(𝑡	NUM
cana-1996	53	24	)	)	PUNCT
cana-1996	53	25	]	]	PUNCT
cana-1996	54	1	=	=	PUNCT
cana-1996	54	2	𝑇(𝜛	𝑇(𝜛	X
cana-1996	54	3	)	)	PUNCT
cana-1996	54	4	=	=	SYM
cana-1996	54	5	(	(	PUNCT
cana-1996	54	6	−1)𝑛𝜛𝑛𝑇(𝜛	−1)𝑛𝜛𝑛𝑇(𝜛	NOUN
cana-1996	54	7	)	)	PUNCT
cana-1996	54	8	+	+	CCONJ
cana-1996	54	9	(	(	PUNCT
cana-1996	54	10	−1)𝑛+1	−1)𝑛+1	ADJ
cana-1996	54	11	∑	∑	PROPN
cana-1996	54	12	(	(	PUNCT
cana-1996	54	13	𝑛−1	𝑛−1	PROPN
cana-1996	54	14	𝓀=0	𝓀=0	NOUN
cana-1996	54	15	−	−	PROPN
cana-1996	54	16	1)𝓀𝜛𝑛−2−𝓀𝜂(𝓀)(0	1)𝓀𝜛𝑛−2−𝓀𝜂(𝓀)(0	NUM
cana-1996	54	17	)	)	PUNCT
cana-1996	54	18	(	(	PUNCT
cana-1996	54	19	3	3	X
cana-1996	54	20	)	)	PUNCT
cana-1996	54	21	theorem	theorem	NOUN
cana-1996	54	22	2	2	NUM
cana-1996	54	23	:	:	PUNCT
cana-1996	54	24	[	[	X
cana-1996	54	25	22	22	NUM
cana-1996	54	26	]	]	PUNCT
cana-1996	54	27	(	(	PUNCT
cana-1996	54	28	transformation	transformation	NOUN
cana-1996	54	29	of	of	ADP
cana-1996	54	30	rangaig	rangaig	ADJ
cana-1996	54	31	integrals	integral	NOUN
cana-1996	54	32	)	)	PUNCT
cana-1996	54	33	,	,	PUNCT
cana-1996	54	34	if	if	SCONJ
cana-1996	54	35	𝑚𝑛(𝑡	𝑚𝑛(𝑡	NOUN
cana-1996	54	36	)	)	PUNCT
cana-1996	54	37	=	=	SYM
cana-1996	55	1	∫	∫	PROPN
cana-1996	55	2	∫	∫	PROPN
cana-1996	55	3	∫	∫	PROPN
cana-1996	56	1	⋯	⋯	PROPN
cana-1996	56	2	𝑡3	𝑡3	PROPN
cana-1996	56	3	0	0	NUM
cana-1996	56	4	∫	∫	NOUN
cana-1996	56	5	𝜂(𝜏)(𝑑𝜏)𝑛	𝜂(𝜏)(𝑑𝜏)𝑛	NOUN
cana-1996	56	6	𝑡𝑛+1	𝑡𝑛+1	X
cana-1996	56	7	0	0	NUM
cana-1996	56	8	𝑡2	𝑡2	NOUN
cana-1996	56	9	0	0	NUM
cana-1996	56	10	,	,	PUNCT
cana-1996	56	11	𝑡1	𝑡1	NOUN
cana-1996	56	12	0	0	PUNCT
cana-1996	57	1	so	so	SCONJ
cana-1996	57	2	that	that	SCONJ
cana-1996	57	3	𝑚(t	𝑚(t	NOUN
cana-1996	57	4	)	)	PUNCT
cana-1996	57	5	∈	∈	PROPN
cana-1996	57	6	h.	h.	PROPN
cana-1996	57	7	next	next	ADV
cana-1996	57	8	,	,	PUNCT
cana-1996	57	9	we	we	PRON
cana-1996	57	10	define	define	VERB
cana-1996	57	11	the	the	DET
cana-1996	57	12	rangaig	rangaig	ADJ
cana-1996	57	13	transform	transform	NOUN
cana-1996	57	14	of	of	ADP
cana-1996	57	15	𝑚n(t	𝑚n(t	NOUN
cana-1996	57	16	)	)	PUNCT
cana-1996	57	17	as	as	SCONJ
cana-1996	57	18	follows	follow	VERB
cana-1996	57	19	:	:	PUNCT
cana-1996	57	20	ℛ[𝑚𝑛(𝑡	ℛ[𝑚𝑛(𝑡	NOUN
cana-1996	57	21	)	)	PUNCT
cana-1996	57	22	]	]	PUNCT
cana-1996	58	1	=	=	SYM
cana-1996	58	2	𝑇𝑛(𝜛	𝑇𝑛(𝜛	PROPN
cana-1996	58	3	)	)	PUNCT
cana-1996	58	4	=	=	PRON
cana-1996	58	5	(	(	PUNCT
cana-1996	58	6	−1	−1	NOUN
cana-1996	58	7	𝜛	𝜛	X
cana-1996	58	8	)	)	PUNCT
cana-1996	58	9	𝑛	𝑛	PRON
cana-1996	58	10	𝑇(𝜛	𝑇(𝜛	VERB
cana-1996	58	11	)	)	PUNCT
cana-1996	58	12	theorem	theorem	NOUN
cana-1996	58	13	3	3	NUM
cana-1996	58	14	:	:	PUNCT
cana-1996	58	15	[	[	X
cana-1996	58	16	22	22	NUM
cana-1996	58	17	]	]	PUNCT
cana-1996	58	18	the	the	DET
cana-1996	58	19	convolution	convolution	NOUN
cana-1996	58	20	identity	identity	NOUN
cana-1996	58	21	's	's	PART
cana-1996	58	22	rangaig	rangaig	ADJ
cana-1996	58	23	transform	transform	NOUN
cana-1996	58	24	is	be	AUX
cana-1996	58	25	provided	provide	VERB
cana-1996	58	26	by	by	ADP
cana-1996	58	27	:	:	PUNCT
cana-1996	58	28	ℛ[(𝜂	ℛ[(𝜂	NOUN
cana-1996	58	29	∗	∗	NOUN
cana-1996	58	30	𝜅)(𝑡	𝜅)(𝑡	PUNCT
cana-1996	58	31	)	)	PUNCT
cana-1996	58	32	]	]	PUNCT
cana-1996	59	1	=	=	SYM
cana-1996	59	2	−𝜛𝑇1(𝜛)𝑇2(𝜛	−𝜛𝑇1(𝜛)𝑇2(𝜛	PROPN
cana-1996	59	3	)	)	PUNCT
cana-1996	59	4	,	,	PUNCT
cana-1996	59	5	where	where	SCONJ
cana-1996	59	6	(	(	PUNCT
cana-1996	59	7	𝜂	𝜂	NOUN
cana-1996	59	8	∗	∗	NOUN
cana-1996	59	9	𝜅)(𝑡	𝜅)(𝑡	NUM
cana-1996	59	10	)	)	PUNCT
cana-1996	59	11	=	=	SYM
cana-1996	60	1	∫	∫	PROPN
cana-1996	60	2	𝜂	𝜂	X
cana-1996	60	3	𝑡	𝑡	PROPN
cana-1996	60	4	0	0	NUM
cana-1996	60	5	(	(	PUNCT
cana-1996	60	6	𝑡	𝑡	NOUN
cana-1996	60	7	−	−	PROPN
cana-1996	60	8	𝜏)𝜅(𝜏)𝑑𝜏	𝜏)𝜅(𝜏)𝑑𝜏	NOUN
cana-1996	60	9	,	,	PUNCT
cana-1996	60	10	𝑇1(𝜛	𝑇1(𝜛	PROPN
cana-1996	60	11	)	)	PUNCT
cana-1996	60	12	and	and	CCONJ
cana-1996	60	13	𝑇2(𝜛	𝑇2(𝜛	NUM
cana-1996	60	14	)	)	PUNCT
cana-1996	60	15	is	be	AUX
cana-1996	60	16	,	,	PUNCT
cana-1996	60	17	respectively	respectively	ADV
cana-1996	60	18	,	,	PUNCT
cana-1996	60	19	the	the	DET
cana-1996	60	20	rangaig	rangaig	ADJ
cana-1996	60	21	transform	transform	NOUN
cana-1996	60	22	of	of	ADP
cana-1996	60	23	𝜂(𝑡	𝜂(𝑡	NOUN
cana-1996	60	24	)	)	PUNCT
cana-1996	60	25	and	and	CCONJ
cana-1996	60	26	𝜅(𝑡	𝜅(𝑡	ADJ
cana-1996	60	27	)	)	PUNCT
cana-1996	60	28	.	.	PUNCT
cana-1996	61	1	communications	communication	NOUN
cana-1996	61	2	on	on	ADP
cana-1996	61	3	applied	apply	VERB
cana-1996	61	4	nonlinear	nonlinear	ADJ
cana-1996	61	5	analysis	analysis	NOUN
cana-1996	61	6	issn	issn	NOUN
cana-1996	61	7	:	:	PUNCT
cana-1996	61	8	1074	1074	NUM
cana-1996	61	9	-	-	PUNCT
cana-1996	61	10	133x	133x	NUM
cana-1996	61	11	vol	vol	NOUN
cana-1996	61	12	32	32	NUM
cana-1996	61	13	no	no	NOUN
cana-1996	61	14	.	.	NOUN
cana-1996	61	15	3	3	NUM
cana-1996	61	16	(	(	PUNCT
cana-1996	61	17	2025	2025	NUM
cana-1996	61	18	)	)	PUNCT
cana-1996	61	19	386	386	NUM
cana-1996	61	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	61	21	theorem	theorem	VERB
cana-1996	61	22	4	4	NUM
cana-1996	61	23	:	:	PUNCT
cana-1996	62	1	[	[	X
cana-1996	62	2	22	22	NUM
cana-1996	62	3	]	]	X
cana-1996	62	4	(	(	PUNCT
cana-1996	62	5	duality	duality	NOUN
cana-1996	62	6	relation	relation	NOUN
cana-1996	62	7	of	of	ADP
cana-1996	62	8	r	r	NOUN
cana-1996	62	9	-	-	PUNCT
cana-1996	62	10	transform	transform	NOUN
cana-1996	62	11	and	and	CCONJ
cana-1996	62	12	l	l	NOUN
cana-1996	62	13	-	-	NOUN
cana-1996	62	14	transform	transform	VERB
cana-1996	62	15	)	)	PUNCT
cana-1996	62	16	the	the	DET
cana-1996	62	17	transformation	transformation	NOUN
cana-1996	62	18	relation	relation	NOUN
cana-1996	62	19	between	between	ADP
cana-1996	62	20	“	"	PUNCT
cana-1996	62	21	rangaig	rangaig	ADJ
cana-1996	62	22	transform	transform	NOUN
cana-1996	62	23	”	"	PUNCT
cana-1996	62	24	𝑇(𝜛	𝑇(𝜛	NOUN
cana-1996	62	25	)	)	PUNCT
cana-1996	62	26	and	and	CCONJ
cana-1996	62	27	“	"	PUNCT
cana-1996	62	28	laplace	laplace	NOUN
cana-1996	62	29	transform	transform	NOUN
cana-1996	62	30	”	"	PUNCT
cana-1996	62	31	𝐹(𝜛	𝐹(𝜛	NOUN
cana-1996	62	32	)	)	PUNCT
cana-1996	62	33	of	of	ADP
cana-1996	62	34	𝜂(𝑡	𝜂(𝑡	NOUN
cana-1996	62	35	)	)	PUNCT
cana-1996	62	36	if	if	SCONJ
cana-1996	62	37	𝜂(𝑡	𝜂(𝑡	NOUN
cana-1996	62	38	)	)	PUNCT
cana-1996	62	39	and	and	CCONJ
cana-1996	62	40	𝜂(−𝑡	𝜂(−𝑡	ADV
cana-1996	62	41	)	)	PUNCT
cana-1996	62	42	exist	exist	VERB
cana-1996	62	43	over	over	ADP
cana-1996	62	44	𝐻.	𝐻.	PROPN
cana-1996	62	45	𝑇(𝜛	𝑇(𝜛	NOUN
cana-1996	62	46	)	)	PUNCT
cana-1996	62	47	=	=	PUNCT
cana-1996	62	48	1	1	NUM
cana-1996	62	49	𝜛	𝜛	NOUN
cana-1996	62	50	𝐹(−𝜛	𝐹(−𝜛	NOUN
cana-1996	62	51	)	)	PUNCT
cana-1996	62	52	proposition	proposition	NOUN
cana-1996	62	53	1	1	NUM
cana-1996	62	54	.	.	PUNCT
cana-1996	63	1	if	if	SCONJ
cana-1996	63	2	𝜕𝑤(𝑥,𝑡	𝜕𝑤(𝑥,𝑡	NOUN
cana-1996	63	3	)	)	PUNCT
cana-1996	64	1	𝜕𝑡	𝜕𝑡	NOUN
cana-1996	64	2	exist	exist	VERB
cana-1996	64	3	,	,	PUNCT
cana-1996	64	4	and	and	CCONJ
cana-1996	64	5	we	we	PRON
cana-1996	64	6	can	can	AUX
cana-1996	64	7	apply	apply	VERB
cana-1996	64	8	integration	integration	NOUN
cana-1996	64	9	by	by	ADP
cana-1996	64	10	parts	part	NOUN
cana-1996	64	11	,	,	PUNCT
cana-1996	64	12	we	we	PRON
cana-1996	64	13	get	get	VERB
cana-1996	64	14	the	the	DET
cana-1996	64	15	following	following	NOUN
cana-1996	64	16	:	:	PUNCT
cana-1996	64	17	ℛ	ℛ	PROPN
cana-1996	64	18	[	[	PUNCT
cana-1996	64	19	𝜕𝑤(𝑥	𝜕𝑤(𝑥	PROPN
cana-1996	64	20	,	,	PUNCT
cana-1996	64	21	𝑡	𝑡	NOUN
cana-1996	64	22	)	)	PUNCT
cana-1996	64	23	𝜕𝑡	𝜕𝑡	NOUN
cana-1996	64	24	]	]	X
cana-1996	64	25	=	=	SYM
cana-1996	64	26	−𝜛𝑇(𝑥,𝜛	−𝜛𝑇(𝑥,𝜛	NOUN
cana-1996	64	27	)	)	PUNCT
cana-1996	64	28	+	+	CCONJ
cana-1996	64	29	1	1	NUM
cana-1996	64	30	𝜛	𝜛	PRON
cana-1996	64	31	𝑤(𝑥	𝑤(𝑥	NOUN
cana-1996	64	32	,	,	PUNCT
cana-1996	64	33	0	0	NUM
cana-1996	64	34	)	)	PUNCT
cana-1996	64	35	(	(	PUNCT
cana-1996	64	36	4	4	X
cana-1996	64	37	)	)	PUNCT
cana-1996	64	38	proof	proof	NOUN
cana-1996	64	39	.	.	PUNCT
cana-1996	65	1	to	to	PART
cana-1996	65	2	illustrate	illustrate	VERB
cana-1996	65	3	it	it	PRON
cana-1996	65	4	,	,	PUNCT
cana-1996	65	5	we	we	PRON
cana-1996	65	6	use	use	VERB
cana-1996	65	7	the	the	DET
cana-1996	65	8	integration	integration	NOUN
cana-1996	65	9	by	by	ADP
cana-1996	65	10	parts	part	NOUN
cana-1996	65	11	and	and	CCONJ
cana-1996	65	12	formula	formula	NOUN
cana-1996	65	13	(	(	PUNCT
cana-1996	65	14	2	2	NUM
cana-1996	65	15	)	)	PUNCT
cana-1996	65	16	.	.	PUNCT
cana-1996	66	1	proposition	proposition	NOUN
cana-1996	66	2	2	2	NUM
cana-1996	66	3	.	.	PUNCT
cana-1996	67	1	if	if	SCONJ
cana-1996	67	2	we	we	PRON
cana-1996	67	3	assume	assume	VERB
cana-1996	67	4	that	that	SCONJ
cana-1996	67	5	𝑇(𝑥	𝑇(𝑥	PROPN
cana-1996	67	6	,	,	PUNCT
cana-1996	67	7	𝜛	𝜛	PROPN
cana-1996	67	8	)	)	PUNCT
cana-1996	67	9	is	be	AUX
cana-1996	67	10	the	the	DET
cana-1996	67	11	“	"	PUNCT
cana-1996	67	12	rangaig	rangaig	ADJ
cana-1996	67	13	transform	transform	NOUN
cana-1996	67	14	”	"	PUNCT
cana-1996	67	15	of	of	ADP
cana-1996	67	16	𝜇(𝑥	𝜇(𝑥	PROPN
cana-1996	67	17	,	,	PUNCT
cana-1996	67	18	𝑡	𝑡	PROPN
cana-1996	67	19	)	)	PUNCT
cana-1996	67	20	,	,	PUNCT
cana-1996	67	21	we	we	PRON
cana-1996	67	22	obtain	obtain	VERB
cana-1996	67	23	:	:	PUNCT
cana-1996	67	24	ℛ	ℛ	PROPN
cana-1996	67	25	[	[	PUNCT
cana-1996	67	26	𝜕𝑤(𝑥	𝜕𝑤(𝑥	PROPN
cana-1996	67	27	,	,	PUNCT
cana-1996	67	28	𝑡	𝑡	NOUN
cana-1996	67	29	)	)	PUNCT
cana-1996	67	30	𝜕𝑡	𝜕𝑡	NOUN
cana-1996	67	31	]	]	X
cana-1996	68	1	=	=	SYM
cana-1996	68	2	(	(	PUNCT
cana-1996	68	3	−1)𝑛𝜛𝑛𝑇(𝑥,𝜛	−1)𝑛𝜛𝑛𝑇(𝑥,𝜛	PROPN
cana-1996	68	4	)	)	PUNCT
cana-1996	68	5	+	+	CCONJ
cana-1996	68	6	(	(	PUNCT
cana-1996	68	7	−1)𝑛+1	−1)𝑛+1	ADJ
cana-1996	68	8	∑	∑	PROPN
cana-1996	68	9	(	(	PUNCT
cana-1996	68	10	𝑛−1	𝑛−1	PROPN
cana-1996	68	11	𝓀=0	𝓀=0	PROPN
cana-1996	68	12	−	−	PROPN
cana-1996	68	13	1)𝓀𝜛𝑛−2−𝓀	1)𝓀𝜛𝑛−2−𝓀	NUM
cana-1996	68	14	𝜕𝓀𝑤(𝑥	𝜕𝓀𝑤(𝑥	NOUN
cana-1996	68	15	,	,	PUNCT
cana-1996	68	16	0	0	NUM
cana-1996	68	17	)	)	PUNCT
cana-1996	68	18	𝜕𝑡𝓀	𝜕𝑡𝓀	PUNCT
cana-1996	69	1	(	(	PUNCT
cana-1996	69	2	5	5	X
cana-1996	69	3	)	)	PUNCT
cana-1996	69	4	proof	proof	NOUN
cana-1996	69	5	:	:	PUNCT
cana-1996	69	6	we	we	PRON
cana-1996	69	7	demonstrate	demonstrate	VERB
cana-1996	69	8	mathematical	mathematical	ADJ
cana-1996	69	9	induction	induction	NOUN
cana-1996	69	10	to	to	PART
cana-1996	69	11	show	show	VERB
cana-1996	69	12	that	that	SCONJ
cana-1996	69	13	(	(	PUNCT
cana-1996	69	14	5	5	NUM
cana-1996	69	15	)	)	PUNCT
cana-1996	69	16	is	be	AUX
cana-1996	69	17	valid	valid	ADJ
cana-1996	69	18	.	.	PUNCT
cana-1996	70	1	using	use	VERB
cana-1996	70	2	the	the	DET
cana-1996	70	3	formula	formula	NOUN
cana-1996	70	4	(	(	PUNCT
cana-1996	70	5	5	5	NUM
cana-1996	70	6	)	)	PUNCT
cana-1996	70	7	and	and	CCONJ
cana-1996	70	8	assuming	assume	VERB
cana-1996	70	9	𝑛	𝑛	PROPN
cana-1996	70	10	=	=	SYM
cana-1996	70	11	1	1	NUM
cana-1996	70	12	,	,	PUNCT
cana-1996	70	13	we	we	PRON
cana-1996	70	14	get	get	VERB
cana-1996	70	15	:	:	PUNCT
cana-1996	70	16	[	[	PUNCT
cana-1996	70	17	𝜕𝑤(𝑥	𝜕𝑤(𝑥	PROPN
cana-1996	70	18	,	,	PUNCT
cana-1996	70	19	𝑡	𝑡	NOUN
cana-1996	70	20	)	)	PUNCT
cana-1996	70	21	𝜕𝑡	𝜕𝑡	NOUN
cana-1996	70	22	]	]	X
cana-1996	70	23	=	=	SYM
cana-1996	71	1	−𝜛𝑇(𝑥,𝜛	−𝜛𝑇(𝑥,𝜛	NOUN
cana-1996	71	2	)	)	PUNCT
cana-1996	71	3	+	+	CCONJ
cana-1996	71	4	1	1	NUM
cana-1996	71	5	𝜛	𝜛	PRON
cana-1996	71	6	𝑤(𝑥	𝑤(𝑥	NOUN
cana-1996	71	7	,	,	PUNCT
cana-1996	71	8	0	0	NUM
cana-1996	71	9	)	)	PUNCT
cana-1996	71	10	(	(	PUNCT
cana-1996	71	11	6	6	NUM
cana-1996	71	12	)	)	PUNCT
cana-1996	71	13	thus	thus	ADV
cana-1996	71	14	,	,	PUNCT
cana-1996	71	15	we	we	PRON
cana-1996	71	16	observe	observe	VERB
cana-1996	71	17	that	that	SCONJ
cana-1996	71	18	the	the	DET
cana-1996	71	19	formula	formula	NOUN
cana-1996	71	20	holds	hold	VERB
cana-1996	71	21	when	when	SCONJ
cana-1996	71	22	𝑛	𝑛	PROPN
cana-1996	71	23	=	=	SYM
cana-1996	71	24	1	1	NUM
cana-1996	71	25	based	base	VERB
cana-1996	71	26	on	on	ADP
cana-1996	71	27	(	(	PUNCT
cana-1996	71	28	4	4	NUM
cana-1996	71	29	)	)	PUNCT
cana-1996	71	30	.	.	PUNCT
cana-1996	72	1	make	make	VERB
cana-1996	72	2	the	the	DET
cana-1996	72	3	inductive	inductive	ADJ
cana-1996	72	4	assumption	assumption	NOUN
cana-1996	72	5	that	that	SCONJ
cana-1996	72	6	the	the	DET
cana-1996	72	7	formula	formula	NOUN
cana-1996	72	8	is	be	AUX
cana-1996	72	9	valid	valid	ADJ
cana-1996	72	10	for	for	ADP
cana-1996	72	11	𝑛	𝑛	PRON
cana-1996	72	12	so	so	SCONJ
cana-1996	72	13	that	that	SCONJ
cana-1996	72	14	ℛ	ℛ	PROPN
cana-1996	72	15	[	[	PUNCT
cana-1996	72	16	𝜕𝑤(𝑥	𝜕𝑤(𝑥	PROPN
cana-1996	72	17	,	,	PUNCT
cana-1996	72	18	𝑡	𝑡	NOUN
cana-1996	72	19	)	)	PUNCT
cana-1996	72	20	𝜕𝑡	𝜕𝑡	NOUN
cana-1996	72	21	]	]	X
cana-1996	73	1	=	=	SYM
cana-1996	73	2	(	(	PUNCT
cana-1996	73	3	−1)𝑛𝜛𝑛𝑇(𝑥,𝜛	−1)𝑛𝜛𝑛𝑇(𝑥,𝜛	PROPN
cana-1996	73	4	)	)	PUNCT
cana-1996	73	5	+	+	CCONJ
cana-1996	73	6	(	(	PUNCT
cana-1996	73	7	−1)𝑛+1	−1)𝑛+1	ADJ
cana-1996	73	8	∑	∑	PROPN
cana-1996	73	9	(	(	PUNCT
cana-1996	73	10	𝑛−1	𝑛−1	PROPN
cana-1996	73	11	𝓀=0	𝓀=0	PROPN
cana-1996	73	12	−	−	PROPN
cana-1996	73	13	1)𝓀𝜛𝑛−2−𝓀	1)𝓀𝜛𝑛−2−𝓀	NUM
cana-1996	73	14	𝜕𝓀𝑤(𝑥	𝜕𝓀𝑤(𝑥	NOUN
cana-1996	73	15	,	,	PUNCT
cana-1996	73	16	0	0	NUM
cana-1996	73	17	)	)	PUNCT
cana-1996	73	18	𝜕𝑡𝓀	𝜕𝑡𝓀	PUNCT
cana-1996	74	1	(	(	PUNCT
cana-1996	74	2	7	7	X
cana-1996	74	3	)	)	PUNCT
cana-1996	74	4	demonstrate	demonstrate	VERB
cana-1996	74	5	that	that	SCONJ
cana-1996	74	6	it	it	PRON
cana-1996	74	7	remains	remain	VERB
cana-1996	74	8	valid	valid	ADJ
cana-1996	74	9	at	at	ADP
cana-1996	74	10	rank	rank	NOUN
cana-1996	74	11	𝑛	𝑛	PROPN
cana-1996	75	1	+	+	NOUN
cana-1996	75	2	1	1	X
cana-1996	75	3	.	.	X
cana-1996	75	4	assume	assume	VERB
cana-1996	75	5	𝜕𝑛𝑤(𝑥,𝑡	𝜕𝑛𝑤(𝑥,𝑡	ADJ
cana-1996	75	6	)	)	PUNCT
cana-1996	75	7	𝜕𝑡𝑛	𝜕𝑡𝑛	PUNCT
cana-1996	76	1	=	=	SYM
cana-1996	76	2	𝑣(𝑥	𝑣(𝑥	PROPN
cana-1996	76	3	,	,	PUNCT
cana-1996	76	4	𝑡	𝑡	X
cana-1996	76	5	)	)	PUNCT
cana-1996	76	6	and	and	CCONJ
cana-1996	76	7	according	accord	VERB
cana-1996	76	8	to	to	ADP
cana-1996	76	9	(	(	PUNCT
cana-1996	76	10	4	4	NUM
cana-1996	76	11	)	)	PUNCT
cana-1996	76	12	and	and	CCONJ
cana-1996	76	13	(	(	PUNCT
cana-1996	76	14	7	7	NUM
cana-1996	76	15	)	)	PUNCT
cana-1996	76	16	,	,	PUNCT
cana-1996	76	17	we	we	PRON
cana-1996	76	18	have	have	VERB
cana-1996	76	19	:	:	PUNCT
cana-1996	76	20	=	=	SYM
cana-1996	76	21	ℛ	ℛ	PROPN
cana-1996	76	22	[	[	PUNCT
cana-1996	76	23	𝜕𝑛+1𝑤(𝑥	𝜕𝑛+1𝑤(𝑥	NOUN
cana-1996	76	24	,	,	PUNCT
cana-1996	76	25	𝑡	𝑡	NOUN
cana-1996	76	26	)	)	PUNCT
cana-1996	76	27	𝜕𝑡𝑛+1	𝜕𝑡𝑛+1	NOUN
cana-1996	76	28	]	]	PUNCT
cana-1996	76	29	=	=	SYM
cana-1996	76	30	ℛ	ℛ	PROPN
cana-1996	76	31	[	[	PUNCT
cana-1996	76	32	𝜕𝑣(𝑥	𝜕𝑣(𝑥	NOUN
cana-1996	76	33	,	,	PUNCT
cana-1996	76	34	𝑡	𝑡	NOUN
cana-1996	76	35	)	)	PUNCT
cana-1996	76	36	𝜕𝑡	𝜕𝑡	NOUN
cana-1996	76	37	]	]	X
cana-1996	77	1	=	=	SYM
cana-1996	77	2	−𝜛ℛ[𝑣(𝑥	−𝜛ℛ[𝑣(𝑥	PROPN
cana-1996	77	3	,	,	PUNCT
cana-1996	77	4	𝑡	𝑡	PROPN
cana-1996	77	5	)	)	PUNCT
cana-1996	77	6	]	]	PUNCT
cana-1996	78	1	+	+	CCONJ
cana-1996	78	2	1	1	NUM
cana-1996	78	3	𝜛	𝜛	PRON
cana-1996	78	4	𝑣(𝑥	𝑣(𝑥	PROPN
cana-1996	78	5	,	,	PUNCT
cana-1996	78	6	0	0	NUM
cana-1996	78	7	)	)	PUNCT
cana-1996	78	8	=	=	SYM
cana-1996	79	1	−𝜛	−𝜛	ADP
cana-1996	79	2	[	[	X
cana-1996	79	3	(	(	PUNCT
cana-1996	79	4	−1)𝑛𝜛𝑛𝑇(𝑥	−1)𝑛𝜛𝑛𝑇(𝑥	NOUN
cana-1996	79	5	,	,	PUNCT
cana-1996	79	6	𝜛	𝜛	PROPN
cana-1996	79	7	)	)	PUNCT
cana-1996	80	1	+	+	CCONJ
cana-1996	80	2	(	(	PUNCT
cana-1996	80	3	−1)𝑛+1	−1)𝑛+1	ADJ
cana-1996	80	4	∑	∑	PROPN
cana-1996	80	5	(	(	PUNCT
cana-1996	80	6	𝑛−1	𝑛−1	PROPN
cana-1996	80	7	𝓀=0	𝓀=0	PROPN
cana-1996	80	8	−	−	PROPN
cana-1996	80	9	1)𝓀𝜛𝑛−2−𝓀	1)𝓀𝜛𝑛−2−𝓀	NUM
cana-1996	80	10	𝜕𝓀𝑤(𝑥	𝜕𝓀𝑤(𝑥	NOUN
cana-1996	80	11	,	,	PUNCT
cana-1996	80	12	0	0	NUM
cana-1996	80	13	)	)	PUNCT
cana-1996	80	14	𝜕𝑡𝓀	𝜕𝑡𝓀	PUNCT
cana-1996	81	1	]	]	PUNCT
cana-1996	82	1	+	+	CCONJ
cana-1996	82	2	1	1	NUM
cana-1996	82	3	𝜛	𝜛	NOUN
cana-1996	82	4	𝜕𝑛𝑤(𝑥	𝜕𝑛𝑤(𝑥	NUM
cana-1996	82	5	,	,	PUNCT
cana-1996	82	6	𝑡	𝑡	NOUN
cana-1996	82	7	)	)	PUNCT
cana-1996	82	8	𝜕𝑡𝑛	𝜕𝑡𝑛	PUNCT
cana-1996	83	1	=	=	SYM
cana-1996	83	2	(	(	PUNCT
cana-1996	83	3	−1)𝑛+1𝜛𝑛+1𝑇(𝑥,𝜛	−1)𝑛+1𝜛𝑛+1𝑇(𝑥,𝜛	PROPN
cana-1996	83	4	)	)	PUNCT
cana-1996	83	5	+	+	CCONJ
cana-1996	83	6	(	(	PUNCT
cana-1996	83	7	−1)𝑛+2	−1)𝑛+2	ADV
cana-1996	83	8	∑	∑	PROPN
cana-1996	83	9	(	(	PUNCT
cana-1996	83	10	𝑛−1	𝑛−1	PROPN
cana-1996	83	11	𝓀=0	𝓀=0	PROPN
cana-1996	83	12	−	−	PROPN
cana-1996	83	13	1)𝓀𝜛𝑛−1−𝓀	1)𝓀𝜛𝑛−1−𝓀	NUM
cana-1996	83	14	𝜕𝓀𝑤(𝑥	𝜕𝓀𝑤(𝑥	NOUN
cana-1996	83	15	,	,	PUNCT
cana-1996	83	16	0	0	NUM
cana-1996	83	17	)	)	PUNCT
cana-1996	83	18	𝜕𝑡𝓀	𝜕𝑡𝓀	PUNCT
cana-1996	84	1	+	+	CCONJ
cana-1996	84	2	1	1	NUM
cana-1996	84	3	𝜛	𝜛	NOUN
cana-1996	84	4	𝜕𝑛𝑤(𝑥	𝜕𝑛𝑤(𝑥	NUM
cana-1996	84	5	,	,	PUNCT
cana-1996	84	6	𝑡	𝑡	NOUN
cana-1996	84	7	)	)	PUNCT
cana-1996	84	8	𝜕𝑡𝑛	𝜕𝑡𝑛	PUNCT
cana-1996	85	1	=	=	SYM
cana-1996	85	2	(	(	PUNCT
cana-1996	85	3	−1)𝑛+1𝜛𝑛+1𝑇(𝑥	−1)𝑛+1𝜛𝑛+1𝑇(𝑥	PROPN
cana-1996	85	4	,	,	PUNCT
cana-1996	85	5	𝜛	𝜛	PROPN
cana-1996	85	6	)	)	PUNCT
cana-1996	85	7	+	+	CCONJ
cana-1996	85	8	(	(	PUNCT
cana-1996	85	9	−1)𝑛+2	−1)𝑛+2	ADV
cana-1996	85	10	∑	∑	PROPN
cana-1996	85	11	(	(	PUNCT
cana-1996	85	12	𝑛	𝑛	PROPN
cana-1996	85	13	𝓀=0	𝓀=0	PROPN
cana-1996	85	14	−	−	PROPN
cana-1996	85	15	1)𝓀𝜛𝑛−1−𝓀	1)𝓀𝜛𝑛−1−𝓀	NUM
cana-1996	85	16	𝜕𝓀𝑤(𝑥	𝜕𝓀𝑤(𝑥	NOUN
cana-1996	85	17	,	,	PUNCT
cana-1996	85	18	0	0	NUM
cana-1996	85	19	)	)	PUNCT
cana-1996	85	20	𝜕𝑡𝓀	𝜕𝑡𝓀	PUNCT
cana-1996	86	1	communications	communication	NOUN
cana-1996	86	2	on	on	ADP
cana-1996	86	3	applied	apply	VERB
cana-1996	86	4	nonlinear	nonlinear	ADJ
cana-1996	86	5	analysis	analysis	NOUN
cana-1996	86	6	issn	issn	NOUN
cana-1996	86	7	:	:	PUNCT
cana-1996	86	8	1074	1074	NUM
cana-1996	86	9	-	-	PUNCT
cana-1996	86	10	133x	133x	NUM
cana-1996	86	11	vol	vol	NOUN
cana-1996	86	12	32	32	NUM
cana-1996	86	13	no	no	NOUN
cana-1996	86	14	.	.	NOUN
cana-1996	86	15	3	3	NUM
cana-1996	86	16	(	(	PUNCT
cana-1996	86	17	2025	2025	NUM
cana-1996	86	18	)	)	PUNCT
cana-1996	86	19	387	387	NUM
cana-1996	86	20	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	86	21	therefore	therefore	ADV
cana-1996	86	22	,	,	PUNCT
cana-1996	86	23	the	the	DET
cana-1996	86	24	formula	formula	NOUN
cana-1996	86	25	(	(	PUNCT
cana-1996	86	26	5	5	X
cana-1996	86	27	)	)	PUNCT
cana-1996	86	28	holds	hold	VERB
cana-1996	86	29	for	for	ADP
cana-1996	86	30	every	every	DET
cana-1996	86	31	𝑛	𝑛	PRON
cana-1996	86	32	≥	≥	NOUN
cana-1996	86	33	1	1	NUM
cana-1996	86	34	according	accord	VERB
cana-1996	86	35	to	to	ADP
cana-1996	86	36	the	the	DET
cana-1996	86	37	principle	principle	NOUN
cana-1996	86	38	of	of	ADP
cana-1996	86	39	mathematical	mathematical	ADJ
cana-1996	86	40	induction	induction	NOUN
cana-1996	86	41	.	.	PUNCT
cana-1996	87	1	3	3	X
cana-1996	87	2	.	.	X
cana-1996	87	3	homotopy	homotopy	VERB
cana-1996	87	4	analysis	analysis	NOUN
cana-1996	87	5	method	method	NOUN
cana-1996	87	6	[	[	X
cana-1996	87	7	13	13	NUM
cana-1996	87	8	-	-	SYM
cana-1996	87	9	17	17	NUM
cana-1996	87	10	]	]	PUNCT
cana-1996	87	11	as	as	ADP
cana-1996	87	12	a	a	DET
cana-1996	87	13	subsequent	subsequent	ADJ
cana-1996	87	14	step	step	NOUN
cana-1996	87	15	,	,	PUNCT
cana-1996	87	16	the	the	DET
cana-1996	87	17	next	next	ADJ
cana-1996	87	18	nonlinear	nonlinear	ADJ
cana-1996	87	19	differential	differential	ADJ
cana-1996	87	20	equation	equation	NOUN
cana-1996	87	21	was	be	AUX
cana-1996	87	22	considered	consider	VERB
cana-1996	87	23	.	.	PUNCT
cana-1996	88	1	when	when	SCONJ
cana-1996	88	2	𝒩	𝒩	PROPN
cana-1996	88	3	is	be	AUX
cana-1996	88	4	a	a	DET
cana-1996	88	5	nonlinear	nonlinear	ADJ
cana-1996	88	6	operator	operator	NOUN
cana-1996	88	7	,	,	PUNCT
cana-1996	88	8	𝑤(υ	𝑤(υ	PROPN
cana-1996	88	9	,	,	PUNCT
cana-1996	88	10	𝑡	𝑡	X
cana-1996	88	11	)	)	PUNCT
cana-1996	88	12	is	be	AUX
cana-1996	88	13	an	an	DET
cana-1996	88	14	unknown	unknown	ADJ
cana-1996	88	15	function	function	NOUN
cana-1996	88	16	,	,	PUNCT
cana-1996	88	17	and	and	CCONJ
cana-1996	88	18	υ	υ	NOUN
cana-1996	88	19	might	might	AUX
cana-1996	88	20	be	be	AUX
cana-1996	88	21	{	{	PUNCT
cana-1996	88	22	𝑥	𝑥	NOUN
cana-1996	88	23	,	,	PUNCT
cana-1996	88	24	𝑦	𝑦	NOUN
cana-1996	88	25	,	,	PUNCT
cana-1996	88	26	𝑧	𝑧	NOUN
cana-1996	88	27	}	}	PUNCT
cana-1996	88	28	.	.	PUNCT
cana-1996	89	1	the	the	DET
cana-1996	89	2	observed	observe	VERB
cana-1996	89	3	independent	independent	ADJ
cana-1996	89	4	variables	variable	NOUN
cana-1996	89	5	for	for	ADP
cana-1996	89	6	time	time	NOUN
cana-1996	89	7	and	and	CCONJ
cana-1996	89	8	space	space	NOUN
cana-1996	89	9	are	be	AUX
cana-1996	89	10	,	,	PUNCT
cana-1996	89	11	in	in	ADP
cana-1996	89	12	that	that	DET
cana-1996	89	13	order	order	NOUN
cana-1996	89	14	,	,	PUNCT
cana-1996	89	15	the	the	DET
cana-1996	89	16	variables	variable	NOUN
cana-1996	89	17	𝑥	𝑥	PROPN
cana-1996	89	18	,	,	PUNCT
cana-1996	89	19	𝑦	𝑦	NOUN
cana-1996	89	20	,	,	PUNCT
cana-1996	89	21	𝑧	𝑧	PUNCT
cana-1996	89	22	and	and	CCONJ
cana-1996	89	23	𝑡	𝑡	PROPN
cana-1996	89	24	with	with	ADP
cana-1996	89	25	liao	liao	PROPN
cana-1996	89	26	's	's	PART
cana-1996	89	27	invention	invention	NOUN
cana-1996	89	28	,	,	PUNCT
cana-1996	89	29	the	the	DET
cana-1996	89	30	conventional	conventional	ADJ
cana-1996	89	31	homotopy	homotopy	NOUN
cana-1996	89	32	technique	technique	NOUN
cana-1996	89	33	.	.	PUNCT
cana-1996	90	1	first	first	ADV
cana-1996	90	2	,	,	PUNCT
cana-1996	90	3	we	we	PRON
cana-1996	90	4	use	use	VERB
cana-1996	90	5	𝑤0(υ	𝑤0(υ	PROPN
cana-1996	90	6	,	,	PUNCT
cana-1996	90	7	𝑡	𝑡	PROPN
cana-1996	90	8	)	)	PUNCT
cana-1996	90	9	as	as	ADP
cana-1996	90	10	the	the	DET
cana-1996	90	11	initial	initial	ADJ
cana-1996	90	12	estimate	estimate	NOUN
cana-1996	90	13	for	for	ADP
cana-1996	90	14	the	the	DET
cana-1996	90	15	equilibrium	equilibrium	NOUN
cana-1996	90	16	concentrations	concentration	NOUN
cana-1996	90	17	of	of	ADP
cana-1996	90	18	𝑤(υ	𝑤(υ	PROPN
cana-1996	90	19	,	,	PUNCT
cana-1996	90	20	𝑡	𝑡	NOUN
cana-1996	90	21	)	)	PUNCT
cana-1996	90	22	.	.	PUNCT
cana-1996	91	1	lastly	lastly	ADV
cana-1996	91	2	,	,	PUNCT
cana-1996	91	3	ℎ	ℎ	PROPN
cana-1996	91	4	is	be	AUX
cana-1996	91	5	an	an	DET
cana-1996	91	6	added	add	VERB
cana-1996	91	7	parameter	parameter	NOUN
cana-1996	91	8	which	which	PRON
cana-1996	91	9	is	be	AUX
cana-1996	91	10	not	not	PART
cana-1996	91	11	the	the	DET
cana-1996	91	12	zero	zero	NUM
cana-1996	91	13	while	while	SCONJ
cana-1996	91	14	𝓅	𝓅	NOUN
cana-1996	91	15	is	be	AUX
cana-1996	91	16	the	the	DET
cana-1996	91	17	embedding	embed	VERB
cana-1996	91	18	parameter	parameter	NOUN
cana-1996	91	19	ranging	range	VERB
cana-1996	91	20	from	from	ADP
cana-1996	91	21	0	0	NUM
cana-1996	91	22	𝑡𝑜	𝑡𝑜	PROPN
cana-1996	91	23	1	1	NUM
cana-1996	91	24	;	;	PUNCT
cana-1996	91	25	ℒ	ℒ	PROPN
cana-1996	91	26	is	be	AUX
cana-1996	91	27	an	an	DET
cana-1996	91	28	added	add	VERB
cana-1996	91	29	linear	linear	NOUN
cana-1996	91	30	operator	operator	NOUN
cana-1996	91	31	;	;	PUNCT
cana-1996	91	32	𝐻(υ	𝐻(υ	NOUN
cana-1996	91	33	,	,	PUNCT
cana-1996	91	34	𝑡	𝑡	NOUN
cana-1996	91	35	)	)	PUNCT
cana-1996	91	36	=	=	SYM
cana-1996	91	37	1	1	NUM
cana-1996	91	38	is	be	AUX
cana-1996	91	39	an	an	DET
cana-1996	91	40	auxiliary	auxiliary	ADJ
cana-1996	91	41	function	function	NOUN
cana-1996	91	42	;	;	PUNCT
cana-1996	91	43	ℎ	ℎ	PROPN
cana-1996	91	44	≠	≠	PROPN
cana-1996	91	45	0	0	NUM
cana-1996	91	46	is	be	AUX
cana-1996	91	47	an	an	DET
cana-1996	91	48	auxiliary	auxiliary	ADJ
cana-1996	91	49	parameter	parameter	NOUN
cana-1996	91	50	;	;	PUNCT
cana-1996	91	51	while	while	SCONJ
cana-1996	91	52	the	the	DET
cana-1996	91	53	𝛿	𝛿	ADJ
cana-1996	91	54	(	(	PUNCT
cana-1996	91	55	υ	υ	PROPN
cana-1996	91	56	,	,	PUNCT
cana-1996	91	57	𝑡	𝑡	PROPN
cana-1996	91	58	;	;	PUNCT
cana-1996	91	59	𝓅	𝓅	NOUN
cana-1996	91	60	)	)	PUNCT
cana-1996	91	61	is	be	AUX
cana-1996	91	62	an	an	DET
cana-1996	91	63	unknown	unknown	ADJ
cana-1996	91	64	function	function	NOUN
cana-1996	91	65	.	.	PUNCT
cana-1996	92	1	if	if	SCONJ
cana-1996	92	2	𝓅	𝓅	PROPN
cana-1996	92	3	=	=	SYM
cana-1996	92	4	0	0	PROPN
cana-1996	92	5	&	&	CCONJ
cana-1996	92	6	𝓅	𝓅	NOUN
cana-1996	92	7	=	=	SYM
cana-1996	92	8	1	1	NUM
cana-1996	92	9	,	,	PUNCT
cana-1996	92	10	we	we	PRON
cana-1996	92	11	obtain	obtain	VERB
cana-1996	92	12	𝛿	𝛿	ADJ
cana-1996	92	13	(	(	PUNCT
cana-1996	92	14	υ	υ	PROPN
cana-1996	92	15	,	,	PUNCT
cana-1996	92	16	𝑡	𝑡	X
cana-1996	92	17	;	;	PUNCT
cana-1996	92	18	0	0	X
cana-1996	92	19	)	)	PUNCT
cana-1996	92	20	=	=	SYM
cana-1996	92	21	𝑤0(υ	𝑤0(υ	PROPN
cana-1996	92	22	,	,	PUNCT
cana-1996	92	23	𝑡	𝑡	X
cana-1996	92	24	)	)	PUNCT
cana-1996	92	25	,	,	PUNCT
cana-1996	92	26	and	and	CCONJ
cana-1996	92	27	𝛿	𝛿	ADJ
cana-1996	92	28	(	(	PUNCT
cana-1996	92	29	υ	υ	PROPN
cana-1996	92	30	,	,	PUNCT
cana-1996	92	31	𝑡	𝑡	X
cana-1996	92	32	;	;	PUNCT
cana-1996	92	33	1	1	X
cana-1996	92	34	)	)	PUNCT
cana-1996	92	35	=	=	PUNCT
cana-1996	92	36	𝑤(υ	𝑤(υ	PROPN
cana-1996	92	37	,	,	PUNCT
cana-1996	92	38	𝑡	𝑡	NOUN
cana-1996	92	39	)	)	PUNCT
cana-1996	92	40	,	,	PUNCT
cana-1996	92	41	as	as	ADP
cana-1996	92	42	a	a	DET
cana-1996	92	43	consequence	consequence	NOUN
cana-1996	92	44	,	,	PUNCT
cana-1996	92	45	solution	solution	NOUN
cana-1996	92	46	𝛿	𝛿	PROPN
cana-1996	92	47	(	(	PUNCT
cana-1996	92	48	υ	υ	PROPN
cana-1996	92	49	,	,	PUNCT
cana-1996	92	50	𝑡	𝑡	PROPN
cana-1996	92	51	;	;	PUNCT
cana-1996	92	52	𝓅	𝓅	NOUN
cana-1996	92	53	)	)	PUNCT
cana-1996	92	54	shifts	shift	NOUN
cana-1996	92	55	from	from	ADP
cana-1996	92	56	starting	start	VERB
cana-1996	92	57	guess	guess	NOUN
cana-1996	92	58	𝑤0(υ	𝑤0(υ	PROPN
cana-1996	92	59	,	,	PUNCT
cana-1996	92	60	𝑡	𝑡	X
cana-1996	92	61	)	)	PUNCT
cana-1996	92	62	to	to	PART
cana-1996	92	63	exact	exact	ADJ
cana-1996	92	64	result	result	NOUN
cana-1996	92	65	𝑤(υ	𝑤(υ	PROPN
cana-1996	92	66	,	,	PUNCT
cana-1996	92	67	𝑡	𝑡	NOUN
cana-1996	92	68	)	)	PUNCT
cana-1996	92	69	as	as	SCONJ
cana-1996	92	70	𝓅	𝓅	PROPN
cana-1996	92	71	traverses	traverse	NOUN
cana-1996	92	72	range	range	VERB
cana-1996	92	73	[	[	X
cana-1996	92	74	0	0	NUM
cana-1996	92	75	,	,	PUNCT
cana-1996	92	76	1	1	NUM
cana-1996	92	77	]	]	PUNCT
cana-1996	92	78	.	.	PUNCT
cana-1996	93	1	when	when	SCONJ
cana-1996	93	2	we	we	PRON
cana-1996	93	3	expand	expand	VERB
cana-1996	93	4	𝛿	𝛿	ADJ
cana-1996	93	5	(	(	PUNCT
cana-1996	93	6	υ	υ	PROPN
cana-1996	93	7	,	,	PUNCT
cana-1996	93	8	𝑡	𝑡	PROPN
cana-1996	93	9	;	;	PUNCT
cana-1996	93	10	𝓅	𝓅	NOUN
cana-1996	93	11	)	)	PUNCT
cana-1996	93	12	in	in	ADP
cana-1996	93	13	the	the	DET
cana-1996	93	14	taylor	taylor	PROPN
cana-1996	93	15	series	series	PROPN
cana-1996	93	16	with	with	ADP
cana-1996	93	17	respect	respect	NOUN
cana-1996	93	18	to	to	ADP
cana-1996	93	19	𝓅	𝓅	NOUN
cana-1996	93	20	,	,	PUNCT
cana-1996	93	21	we	we	PRON
cana-1996	93	22	obtain	obtain	VERB
cana-1996	93	23	where	where	SCONJ
cana-1996	93	24	,	,	PUNCT
cana-1996	93	25	𝑤𝑚(υ	𝑤𝑚(υ	NUM
cana-1996	93	26	,	,	PUNCT
cana-1996	93	27	𝑡	𝑡	NOUN
cana-1996	93	28	)	)	PUNCT
cana-1996	93	29	=	=	SYM
cana-1996	93	30	1	1	NUM
cana-1996	93	31	𝑚	𝑚	NOUN
cana-1996	93	32	!	!	PROPN
cana-1996	93	33	𝜕𝑚𝛿(υ	𝜕𝑚𝛿(υ	NOUN
cana-1996	93	34	,	,	PUNCT
cana-1996	93	35	𝑡	𝑡	NOUN
cana-1996	93	36	;	;	PUNCT
cana-1996	93	37	𝓅	𝓅	NOUN
cana-1996	93	38	)	)	PUNCT
cana-1996	93	39	𝜕𝓅𝑚	𝜕𝓅𝑚	ADV
cana-1996	93	40	|	|	ADV
cana-1996	93	41	𝓅=0	𝓅=0	PUNCT
cana-1996	93	42	if	if	SCONJ
cana-1996	93	43	the	the	DET
cana-1996	93	44	auxiliary	auxiliary	ADJ
cana-1996	93	45	function	function	NOUN
cana-1996	93	46	,	,	PUNCT
cana-1996	93	47	auxiliary	auxiliary	ADJ
cana-1996	93	48	linear	linear	NOUN
cana-1996	93	49	operator	operator	NOUN
cana-1996	93	50	,	,	PUNCT
cana-1996	93	51	auxiliary	auxiliary	ADJ
cana-1996	93	52	parameter	parameter	NOUN
cana-1996	93	53	ℎ	ℎ	PROPN
cana-1996	93	54	,	,	PUNCT
cana-1996	93	55	and	and	CCONJ
cana-1996	93	56	initial	initial	ADJ
cana-1996	93	57	estimate	estimate	NOUN
cana-1996	93	58	are	be	AUX
cana-1996	93	59	all	all	ADV
cana-1996	93	60	correctly	correctly	ADV
cana-1996	93	61	chosen	choose	VERB
cana-1996	93	62	,	,	PUNCT
cana-1996	93	63	then	then	ADV
cana-1996	93	64	the	the	DET
cana-1996	93	65	series	series	NOUN
cana-1996	93	66	(	(	PUNCT
cana-1996	93	67	10	10	NUM
cana-1996	93	68	)	)	PUNCT
cana-1996	93	69	converges	converge	NOUN
cana-1996	93	70	at	at	ADP
cana-1996	93	71	𝓅	𝓅	NOUN
cana-1996	93	72	=	=	SYM
cana-1996	93	73	1	1	NUM
cana-1996	93	74	,	,	PUNCT
cana-1996	93	75	and	and	CCONJ
cana-1996	93	76	we	we	PRON
cana-1996	93	77	obtain	obtain	VERB
cana-1996	93	78	this	this	PRON
cana-1996	93	79	ought	ought	AUX
cana-1996	93	80	to	to	PART
cana-1996	93	81	be	be	AUX
cana-1996	93	82	an	an	DET
cana-1996	93	83	acceptable	acceptable	ADJ
cana-1996	93	84	solution	solution	NOUN
cana-1996	93	85	for	for	ADP
cana-1996	93	86	the	the	DET
cana-1996	93	87	initial	initial	ADJ
cana-1996	93	88	nonlinear	nonlinear	ADJ
cana-1996	93	89	equation	equation	NOUN
cana-1996	93	90	.	.	PUNCT
cana-1996	94	1	by	by	ADP
cana-1996	94	2	definition	definition	NOUN
cana-1996	94	3	(	(	PUNCT
cana-1996	94	4	11	11	NUM
cana-1996	94	5	)	)	PUNCT
cana-1996	94	6	the	the	DET
cana-1996	94	7	governing	govern	VERB
cana-1996	94	8	equation	equation	NOUN
cana-1996	94	9	might	might	AUX
cana-1996	94	10	be	be	AUX
cana-1996	94	11	obtained	obtain	VERB
cana-1996	94	12	from	from	ADP
cana-1996	94	13	the	the	DET
cana-1996	94	14	0	0	NUM
cana-1996	94	15	-	-	PUNCT
cana-1996	94	16	order	order	NOUN
cana-1996	94	17	deformation	deformation	NOUN
cana-1996	94	18	equation	equation	NOUN
cana-1996	94	19	(	(	PUNCT
cana-1996	94	20	9	9	NUM
cana-1996	94	21	)	)	PUNCT
cana-1996	94	22	.	.	PUNCT
cana-1996	95	1	explain	explain	VERB
cana-1996	95	2	the	the	DET
cana-1996	95	3	vector	vector	NOUN
cana-1996	95	4	.	.	PUNCT
cana-1996	96	1	𝑤𝑛⃗⃗⃗⃗	𝑤𝑛⃗⃗⃗⃗	PUNCT
cana-1996	96	2	⃗	⃗	PROPN
cana-1996	96	3	=	=	SYM
cana-1996	96	4	𝑤0(υ	𝑤0(υ	PROPN
cana-1996	96	5	,	,	PUNCT
cana-1996	96	6	𝑡	𝑡	NOUN
cana-1996	96	7	)	)	PUNCT
cana-1996	96	8	,	,	PUNCT
cana-1996	96	9	𝑤1(υ	𝑤1(υ	PROPN
cana-1996	96	10	,	,	PUNCT
cana-1996	96	11	𝑡	𝑡	NOUN
cana-1996	96	12	)	)	PUNCT
cana-1996	96	13	,	,	PUNCT
cana-1996	96	14	𝑤2(υ	𝑤2(υ	PROPN
cana-1996	96	15	,	,	PUNCT
cana-1996	96	16	𝑡	𝑡	PROPN
cana-1996	96	17	)	)	PUNCT
cana-1996	96	18	…	…	PUNCT
cana-1996	96	19	…	…	PUNCT
cana-1996	96	20	……	……	X
cana-1996	96	21	.𝑤𝑛(υ	.𝑤𝑛(υ	NUM
cana-1996	96	22	,	,	PUNCT
cana-1996	96	23	𝑡	𝑡	NOUN
cana-1996	96	24	)	)	PUNCT
cana-1996	96	25	𝒩[𝑤(υ	𝒩[𝑤(υ	NOUN
cana-1996	96	26	,	,	PUNCT
cana-1996	96	27	𝑡	𝑡	X
cana-1996	96	28	)	)	PUNCT
cana-1996	96	29	]	]	PUNCT
cana-1996	97	1	=	=	SYM
cana-1996	97	2	0	0	PUNCT
cana-1996	97	3	(	(	PUNCT
cana-1996	97	4	8)	8)	NUM
cana-1996	97	5	(	(	PUNCT
cana-1996	97	6	1	1	NUM
cana-1996	97	7	−	−	NOUN
cana-1996	97	8	𝓅)ℒ[𝛿(υ	𝓅)ℒ[𝛿(υ	NOUN
cana-1996	97	9	,	,	PUNCT
cana-1996	97	10	𝑡	𝑡	PROPN
cana-1996	97	11	;	;	PUNCT
cana-1996	97	12	𝓅	𝓅	NOUN
cana-1996	97	13	)	)	PUNCT
cana-1996	97	14	−	−	PROPN
cana-1996	97	15	𝑤0(υ	𝑤0(υ	PROPN
cana-1996	97	16	,	,	PUNCT
cana-1996	97	17	𝑡	𝑡	X
cana-1996	97	18	)	)	PUNCT
cana-1996	97	19	]	]	PUNCT
cana-1996	98	1	=	=	SYM
cana-1996	98	2	𝓅ℎ𝐻(υ	𝓅ℎ𝐻(υ	NOUN
cana-1996	98	3	,	,	PUNCT
cana-1996	98	4	𝑡)𝒩[𝛿(υ	𝑡)𝒩[𝛿(υ	NOUN
cana-1996	98	5	,	,	PUNCT
cana-1996	98	6	𝑡	𝑡	NOUN
cana-1996	98	7	;	;	PUNCT
cana-1996	98	8	𝓅	𝓅	PROPN
cana-1996	98	9	)	)	PUNCT
cana-1996	98	10	]	]	PUNCT
cana-1996	98	11	(	(	PUNCT
cana-1996	98	12	9	9	X
cana-1996	98	13	)	)	PUNCT
cana-1996	98	14	𝛿	𝛿	ADJ
cana-1996	98	15	(	(	PUNCT
cana-1996	98	16	υ	υ	PROPN
cana-1996	98	17	,	,	PUNCT
cana-1996	98	18	𝑡	𝑡	PROPN
cana-1996	98	19	;	;	PUNCT
cana-1996	98	20	𝓅	𝓅	NOUN
cana-1996	98	21	)	)	PUNCT
cana-1996	98	22	=	=	SYM
cana-1996	98	23	𝑤0(υ	𝑤0(υ	PROPN
cana-1996	98	24	,	,	PUNCT
cana-1996	98	25	𝑡	𝑡	X
cana-1996	98	26	)	)	PUNCT
cana-1996	98	27	+	+	CCONJ
cana-1996	98	28	∑	∑	PROPN
cana-1996	98	29	𝑤𝑚	𝑤𝑚	NOUN
cana-1996	98	30	(	(	PUNCT
cana-1996	98	31	υ	υ	PROPN
cana-1996	98	32	,	,	PUNCT
cana-1996	98	33	𝑡)𝓅𝑚	𝑡)𝓅𝑚	PROPN
cana-1996	98	34	∞	∞	PROPN
cana-1996	98	35	𝑚=1	𝑚=1	X
cana-1996	98	36	(	(	PUNCT
cana-1996	98	37	10	10	NUM
cana-1996	98	38	)	)	PUNCT
cana-1996	98	39	𝑤(υ	𝑤(υ	NOUN
cana-1996	98	40	,	,	PUNCT
cana-1996	98	41	𝑡	𝑡	X
cana-1996	98	42	)	)	PUNCT
cana-1996	98	43	=	=	SYM
cana-1996	98	44	𝑤0(υ	𝑤0(υ	PROPN
cana-1996	98	45	,	,	PUNCT
cana-1996	98	46	𝑡	𝑡	X
cana-1996	98	47	)	)	PUNCT
cana-1996	98	48	+	+	CCONJ
cana-1996	98	49	∑	∑	PROPN
cana-1996	98	50	𝑤𝑚	𝑤𝑚	NOUN
cana-1996	98	51	∞	∞	NUM
cana-1996	98	52	𝑚=1	𝑚=1	X
cana-1996	98	53	(	(	PUNCT
cana-1996	98	54	υ	υ	NOUN
cana-1996	98	55	,	,	PUNCT
cana-1996	98	56	𝑡	𝑡	NOUN
cana-1996	98	57	)	)	PUNCT
cana-1996	98	58	,	,	PUNCT
cana-1996	98	59	(	(	PUNCT
cana-1996	98	60	11	11	X
cana-1996	98	61	)	)	PUNCT
cana-1996	98	62	communications	communication	NOUN
cana-1996	98	63	on	on	ADP
cana-1996	98	64	applied	apply	VERB
cana-1996	98	65	nonlinear	nonlinear	ADJ
cana-1996	98	66	analysis	analysis	NOUN
cana-1996	98	67	issn	issn	NOUN
cana-1996	98	68	:	:	PUNCT
cana-1996	98	69	1074	1074	NUM
cana-1996	98	70	-	-	PUNCT
cana-1996	98	71	133x	133x	NUM
cana-1996	98	72	vol	vol	NOUN
cana-1996	98	73	32	32	NUM
cana-1996	98	74	no	no	NOUN
cana-1996	98	75	.	.	NOUN
cana-1996	98	76	3	3	NUM
cana-1996	98	77	(	(	PUNCT
cana-1996	98	78	2025	2025	NUM
cana-1996	98	79	)	)	PUNCT
cana-1996	98	80	388	388	NUM
cana-1996	98	81	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	98	82	considering	consider	VERB
cana-1996	98	83	the	the	DET
cana-1996	98	84	embedding	embed	VERB
cana-1996	98	85	parameter	parameter	NOUN
cana-1996	98	86	𝓅	𝓅	PROPN
cana-1996	98	87	,	,	PUNCT
cana-1996	98	88	differentiating	differentiate	VERB
cana-1996	98	89	the	the	DET
cana-1996	98	90	0	0	NUM
cana-1996	98	91	-	-	PUNCT
cana-1996	98	92	order	order	NOUN
cana-1996	98	93	deformation	deformation	NOUN
cana-1996	98	94	equation	equation	NOUN
cana-1996	98	95	(	(	PUNCT
cana-1996	98	96	9	9	X
cana-1996	98	97	)	)	PUNCT
cana-1996	98	98	𝑚times	𝑚time	NOUN
cana-1996	98	99	.	.	PUNCT
cana-1996	99	1	after	after	ADP
cana-1996	99	2	splitting	split	VERB
cana-1996	99	3	𝑚	𝑚	PRON
cana-1996	99	4	!	!	PUNCT
cana-1996	99	5	by	by	ADP
cana-1996	99	6	𝓅	𝓅	NOUN
cana-1996	99	7	=	=	SYM
cana-1996	99	8	0	0	PROPN
cana-1996	99	9	,	,	PUNCT
cana-1996	99	10	the	the	DET
cana-1996	99	11	equation	equation	NOUN
cana-1996	99	12	for	for	ADP
cana-1996	99	13	the	the	DET
cana-1996	99	14	𝑚th	𝑚th	NOUN
cana-1996	99	15	-	-	PUNCT
cana-1996	99	16	order	order	NOUN
cana-1996	99	17	deformation	deformation	NOUN
cana-1996	99	18	looks	look	VERB
cana-1996	99	19	like	like	ADP
cana-1996	99	20	this	this	PRON
cana-1996	99	21	:	:	PUNCT
cana-1996	99	22	ℒ[𝑤𝑚(υ	ℒ[𝑤𝑚(υ	NOUN
cana-1996	99	23	,	,	PUNCT
cana-1996	99	24	𝑡	𝑡	NOUN
cana-1996	99	25	)	)	PUNCT
cana-1996	99	26	−	−	PROPN
cana-1996	99	27	𝜒𝑚	𝜒𝑚	PROPN
cana-1996	99	28	𝑤𝑚−1	𝑤𝑚−1	PROPN
cana-1996	99	29	(	(	PUNCT
cana-1996	99	30	υ	υ	PROPN
cana-1996	99	31	,	,	PUNCT
cana-1996	99	32	𝑡	𝑡	NOUN
cana-1996	99	33	)	)	PUNCT
cana-1996	99	34	]	]	PUNCT
cana-1996	100	1	=	=	SYM
cana-1996	100	2	ℎℛ𝑚[𝑤𝑚−1	ℎℛ𝑚[𝑤𝑚−1	X
cana-1996	100	3	(	(	PUNCT
cana-1996	100	4	υ	υ	NOUN
cana-1996	100	5	,	,	PUNCT
cana-1996	100	6	𝑡	𝑡	NOUN
cana-1996	100	7	)	)	PUNCT
cana-1996	100	8	]	]	PUNCT
cana-1996	101	1	whereas	whereas	SCONJ
cana-1996	101	2	ℛ𝑚	ℛ𝑚	PROPN
cana-1996	101	3	(	(	PUNCT
cana-1996	101	4	𝑤𝑚−1)⃗⃗	𝑤𝑚−1)⃗⃗	NUM
cana-1996	101	5	⃗⃗	⃗⃗	PROPN
cana-1996	101	6	⃗⃗	⃗⃗	PROPN
cana-1996	101	7	⃗⃗	⃗⃗	PROPN
cana-1996	101	8	⃗⃗	⃗⃗	PROPN
cana-1996	101	9	⃗⃗	⃗⃗	PROPN
cana-1996	101	10	⃗	⃗	PROPN
cana-1996	101	11	=	=	SYM
cana-1996	101	12	1	1	NUM
cana-1996	101	13	𝑚	𝑚	NOUN
cana-1996	101	14	−	−	PROPN
cana-1996	101	15	1	1	NUM
cana-1996	101	16	!	!	PUNCT
cana-1996	102	1	𝜕𝑚−1	𝜕𝑚−1	PROPN
cana-1996	102	2	𝒩	𝒩	PROPN
cana-1996	103	1	[	[	X
cana-1996	103	2	𝛿(υ	𝛿(υ	NOUN
cana-1996	103	3	,	,	PUNCT
cana-1996	103	4	𝑡	𝑡	X
cana-1996	103	5	;	;	PUNCT
cana-1996	103	6	𝓅	𝓅	X
cana-1996	103	7	)	)	PUNCT
cana-1996	103	8	𝜕𝓅𝑚−1	𝜕𝓅𝑚−1	VERB
cana-1996	103	9	|	|	CCONJ
cana-1996	103	10	𝓅	𝓅	NOUN
cana-1996	103	11	=	=	SYM
cana-1996	103	12	0	0	NUM
cana-1996	104	1	and	and	CCONJ
cana-1996	104	2	𝜒𝑚	𝜒𝑚	NOUN
cana-1996	104	3	=	=	SYM
cana-1996	104	4	{	{	PUNCT
cana-1996	104	5	0	0	NUM
cana-1996	104	6	,	,	PUNCT
cana-1996	104	7	𝑚	𝑚	PROPN
cana-1996	104	8	≤	≤	NUM
cana-1996	104	9	1	1	NUM
cana-1996	104	10	1	1	NUM
cana-1996	104	11	,	,	PUNCT
cana-1996	104	12	𝑚	𝑚	X
cana-1996	104	13	>	>	X
cana-1996	104	14	1	1	NUM
cana-1996	104	15	.	.	PUNCT
cana-1996	105	1	4	4	X
cana-1996	105	2	.	.	X
cana-1996	105	3	rangaig	rangaig	ADJ
cana-1996	105	4	transform	transform	VERB
cana-1996	105	5	based	base	VERB
cana-1996	105	6	homotopy	homotopy	NOUN
cana-1996	105	7	analysis	analysis	NOUN
cana-1996	105	8	method	method	NOUN
cana-1996	105	9	(	(	PUNCT
cana-1996	105	10	rt	rt	NOUN
cana-1996	105	11	-	-	PUNCT
cana-1996	105	12	ham	ham	NOUN
cana-1996	105	13	)	)	PUNCT
cana-1996	105	14	take	take	VERB
cana-1996	105	15	the	the	DET
cana-1996	105	16	following	follow	VERB
cana-1996	105	17	partial	partial	ADJ
cana-1996	105	18	differential	differential	ADJ
cana-1996	105	19	equation	equation	NOUN
cana-1996	105	20	of	of	ADP
cana-1996	105	21	3	3	PROPN
cana-1996	105	22	-	-	PUNCT
cana-1996	105	23	d.	d.	NOUN
cana-1996	105	24	𝜇𝑡𝑡(υ	𝜇𝑡𝑡(υ	PROPN
cana-1996	105	25	)	)	PUNCT
cana-1996	106	1	=	=	PRON
cana-1996	106	2	{	{	PUNCT
cana-1996	106	3	ℒ(𝜇	ℒ(𝜇	NUM
cana-1996	106	4	)	)	PUNCT
cana-1996	106	5	+	+	CCONJ
cana-1996	106	6	𝒩(𝜇	𝒩(𝜇	NUM
cana-1996	106	7	)	)	PUNCT
cana-1996	106	8	+	+	CCONJ
cana-1996	106	9	𝑓(υ	𝑓(υ	NOUN
cana-1996	106	10	)	)	PUNCT
cana-1996	106	11	}	}	PUNCT
cana-1996	106	12	.	.	PUNCT
cana-1996	107	1	(	(	PUNCT
cana-1996	107	2	12	12	NUM
cana-1996	107	3	)	)	PUNCT
cana-1996	107	4	where	where	SCONJ
cana-1996	107	5	𝑓(υ	𝑓(υ	NOUN
cana-1996	107	6	)	)	PUNCT
cana-1996	107	7	refers	refer	VERB
cana-1996	107	8	to	to	ADP
cana-1996	107	9	the	the	DET
cana-1996	107	10	functions	function	NOUN
cana-1996	107	11	of	of	ADP
cana-1996	107	12	𝑥	𝑥	PROPN
cana-1996	107	13	,	,	PUNCT
cana-1996	107	14	𝑦	𝑦	NOUN
cana-1996	107	15	,	,	PUNCT
cana-1996	107	16	𝑧	𝑧	VERB
cana-1996	107	17	,	,	PUNCT
cana-1996	107	18	while	while	SCONJ
cana-1996	107	19	ℒ	ℒ	PROPN
cana-1996	107	20	indicates	indicate	VERB
cana-1996	107	21	the	the	DET
cana-1996	107	22	linear	linear	NOUN
cana-1996	107	23	and	and	CCONJ
cana-1996	107	24	𝒩	𝒩	PROPN
cana-1996	107	25	nonlinear	nonlinear	ADJ
cana-1996	107	26	parts	part	NOUN
cana-1996	107	27	.	.	PUNCT
cana-1996	107	28	respectively	respectively	ADV
cana-1996	107	29	.	.	PUNCT
cana-1996	108	1	considering	consider	VERB
cana-1996	108	2	both	both	DET
cana-1996	108	3	sides	side	NOUN
cana-1996	108	4	of	of	ADP
cana-1996	108	5	the	the	DET
cana-1996	108	6	“	"	PUNCT
cana-1996	108	7	rangaig	rangaig	ADJ
cana-1996	108	8	transform	transform	NOUN
cana-1996	108	9	”	"	PUNCT
cana-1996	108	10	,	,	PUNCT
cana-1996	108	11	we	we	PRON
cana-1996	108	12	obtain	obtain	VERB
cana-1996	108	13	ℛ{𝜇𝑡𝑡(υ	ℛ{𝜇𝑡𝑡(υ	PROPN
cana-1996	108	14	)	)	PUNCT
cana-1996	108	15	}	}	PUNCT
cana-1996	109	1	=	=	SYM
cana-1996	109	2	ℛ{ℒ(𝜇	ℛ{ℒ(𝜇	NOUN
cana-1996	109	3	)	)	PUNCT
cana-1996	109	4	+	+	ADJ
cana-1996	109	5	𝒩(𝜇	𝒩(𝜇	NUM
cana-1996	109	6	)	)	PUNCT
cana-1996	109	7	+	+	CCONJ
cana-1996	109	8	𝑓(υ	𝑓(υ	NOUN
cana-1996	109	9	)	)	PUNCT
cana-1996	109	10	}	}	PUNCT
cana-1996	109	11	.	.	PUNCT
cana-1996	110	1	(	(	PUNCT
cana-1996	110	2	13	13	NUM
cana-1996	110	3	)	)	PUNCT
cana-1996	110	4	with	with	ADP
cana-1996	110	5	the	the	DET
cana-1996	110	6	help	help	NOUN
cana-1996	110	7	of	of	ADP
cana-1996	110	8	“	"	PUNCT
cana-1996	110	9	rangaig	rangaig	ADJ
cana-1996	110	10	transform	transform	NOUN
cana-1996	110	11	”	"	PUNCT
cana-1996	110	12	and	and	CCONJ
cana-1996	110	13	an	an	DET
cana-1996	110	14	initial	initial	ADJ
cana-1996	110	15	condition	condition	NOUN
cana-1996	110	16	,	,	PUNCT
cana-1996	110	17	we	we	PRON
cana-1996	110	18	get	get	VERB
cana-1996	110	19	ℛ{𝜇(υ	ℛ{𝜇(υ	NOUN
cana-1996	110	20	,	,	PUNCT
cana-1996	110	21	𝑡	𝑡	NOUN
cana-1996	110	22	)	)	PUNCT
cana-1996	110	23	}	}	PUNCT
cana-1996	110	24	=	=	SYM
cana-1996	110	25	1	1	NUM
cana-1996	110	26	𝑤2	𝑤2	NOUN
cana-1996	110	27	𝜇0(υ	𝜇0(υ	NOUN
cana-1996	110	28	)	)	PUNCT
cana-1996	110	29	−	−	PROPN
cana-1996	110	30	1	1	NUM
cana-1996	110	31	𝑤3	𝑤3	PROPN
cana-1996	110	32	𝜕𝜇0	𝜕𝜇0	ADV
cana-1996	110	33	𝜕𝑡	𝜕𝑡	PROPN
cana-1996	110	34	+	+	CCONJ
cana-1996	110	35	1	1	NUM
cana-1996	110	36	𝑤2	𝑤2	NOUN
cana-1996	110	37	ℛ{ℒ(𝜇	ℛ{ℒ(𝜇	NOUN
cana-1996	110	38	)	)	PUNCT
cana-1996	110	39	+	+	ADJ
cana-1996	110	40	𝒩(𝜇	𝒩(𝜇	NUM
cana-1996	110	41	)	)	PUNCT
cana-1996	110	42	+	+	CCONJ
cana-1996	110	43	𝑓(υ	𝑓(υ	NOUN
cana-1996	110	44	)	)	PUNCT
cana-1996	110	45	}	}	PUNCT
cana-1996	110	46	.	.	PUNCT
cana-1996	111	1	(	(	PUNCT
cana-1996	111	2	14	14	X
cana-1996	111	3	)	)	PUNCT
cana-1996	111	4	taking	take	VERB
cana-1996	111	5	the	the	DET
cana-1996	111	6	nonlinear	nonlinear	ADJ
cana-1996	111	7	part	part	NOUN
cana-1996	111	8	as	as	ADP
cana-1996	111	9	:	:	PUNCT
cana-1996	111	10	𝒩[𝛿(υ	𝒩[𝛿(υ	NOUN
cana-1996	111	11	,	,	PUNCT
cana-1996	111	12	𝑡	𝑡	X
cana-1996	111	13	;	;	PUNCT
cana-1996	111	14	𝓅	𝓅	NOUN
cana-1996	111	15	)	)	PUNCT
cana-1996	111	16	]	]	PUNCT
cana-1996	112	1	=	=	SYM
cana-1996	112	2	ℛ{𝜇(υ	ℛ{𝜇(υ	NOUN
cana-1996	112	3	,	,	PUNCT
cana-1996	112	4	𝑡	𝑡	NOUN
cana-1996	112	5	)	)	PUNCT
cana-1996	112	6	}	}	PUNCT
cana-1996	112	7	−	−	PROPN
cana-1996	113	1	[	[	PUNCT
cana-1996	113	2	1	1	NUM
cana-1996	113	3	𝑤2	𝑤2	NOUN
cana-1996	113	4	𝜇0(υ	𝜇0(υ	NOUN
cana-1996	113	5	)	)	PUNCT
cana-1996	113	6	−	−	PROPN
cana-1996	113	7	1	1	NUM
cana-1996	113	8	𝑤3	𝑤3	PROPN
cana-1996	113	9	𝜕𝜇0	𝜕𝜇0	ADV
cana-1996	113	10	𝜕𝑡	𝜕𝑡	PROPN
cana-1996	113	11	+	+	CCONJ
cana-1996	113	12	1	1	NUM
cana-1996	113	13	𝑤2	𝑤2	NOUN
cana-1996	113	14	ℛ{ℒ(𝜇	ℛ{ℒ(𝜇	NOUN
cana-1996	113	15	)	)	PUNCT
cana-1996	113	16	+	+	ADJ
cana-1996	113	17	𝒩(𝜇	𝒩(𝜇	NUM
cana-1996	113	18	)	)	PUNCT
cana-1996	113	19	+	+	CCONJ
cana-1996	113	20	𝑓(υ	𝑓(υ	NOUN
cana-1996	113	21	)	)	PUNCT
cana-1996	113	22	}	}	PUNCT
cana-1996	113	23	]	]	PUNCT
cana-1996	113	24	.	.	PUNCT
cana-1996	114	1	we	we	PRON
cana-1996	114	2	begin	begin	VERB
cana-1996	114	3	by	by	ADP
cana-1996	114	4	setting	set	VERB
cana-1996	114	5	up	up	ADP
cana-1996	114	6	the	the	DET
cana-1996	114	7	zero	zero	NUM
cana-1996	114	8	-	-	PUNCT
cana-1996	114	9	order	order	NOUN
cana-1996	114	10	deformation	deformation	NOUN
cana-1996	114	11	equation	equation	NOUN
cana-1996	114	12	;	;	PUNCT
cana-1996	114	13	we	we	PRON
cana-1996	114	14	have	have	VERB
cana-1996	114	15	(	(	PUNCT
cana-1996	114	16	1	1	NUM
cana-1996	114	17	−	−	NOUN
cana-1996	114	18	𝓅)ℛ{𝛿(υ	𝓅)ℛ{𝛿(υ	NOUN
cana-1996	114	19	,	,	PUNCT
cana-1996	114	20	𝑡	𝑡	NOUN
cana-1996	114	21	)	)	PUNCT
cana-1996	114	22	−	−	PRON
cana-1996	114	23	𝜇0(υ	𝜇0(υ	PROPN
cana-1996	114	24	,	,	PUNCT
cana-1996	114	25	𝑡	𝑡	NOUN
cana-1996	114	26	)	)	PUNCT
cana-1996	114	27	}	}	PUNCT
cana-1996	114	28	=	=	SYM
cana-1996	114	29	𝓅ℎ𝐻(υ	𝓅ℎ𝐻(υ	NOUN
cana-1996	114	30	,	,	PUNCT
cana-1996	114	31	𝑡)𝒩[𝛿(υ	𝑡)𝒩[𝛿(υ	NOUN
cana-1996	114	32	,	,	PUNCT
cana-1996	114	33	𝑡	𝑡	NOUN
cana-1996	114	34	;	;	PUNCT
cana-1996	114	35	𝓅	𝓅	NOUN
cana-1996	114	36	)	)	PUNCT
cana-1996	114	37	]	]	PUNCT
cana-1996	114	38	.	.	PUNCT
cana-1996	115	1	(	(	PUNCT
cana-1996	115	2	15	15	NUM
cana-1996	115	3	)	)	PUNCT
cana-1996	115	4	𝐻(υ	𝐻(υ	NOUN
cana-1996	115	5	,	,	PUNCT
cana-1996	115	6	𝑡	𝑡	NOUN
cana-1996	115	7	)	)	PUNCT
cana-1996	115	8	=	=	SYM
cana-1996	115	9	1	1	NUM
cana-1996	115	10	is	be	AUX
cana-1996	115	11	an	an	DET
cana-1996	115	12	auxiliary	auxiliary	ADJ
cana-1996	115	13	function	function	NOUN
cana-1996	115	14	,	,	PUNCT
cana-1996	115	15	ℎ	ℎ	PROPN
cana-1996	115	16	≠	≠	PROPN
cana-1996	115	17	0	0	NUM
cana-1996	115	18	is	be	AUX
cana-1996	115	19	an	an	DET
cana-1996	115	20	auxiliary	auxiliary	ADJ
cana-1996	115	21	parameter	parameter	NOUN
cana-1996	115	22	,	,	PUNCT
cana-1996	115	23	ℛ	ℛ	PROPN
cana-1996	115	24	is	be	AUX
cana-1996	115	25	an	an	DET
cana-1996	115	26	auxiliary	auxiliary	ADJ
cana-1996	115	27	linear	linear	ADJ
cana-1996	115	28	rangaig	rangaig	ADJ
cana-1996	115	29	operator	operator	NOUN
cana-1996	115	30	.	.	PUNCT
cana-1996	116	1	when	when	SCONJ
cana-1996	116	2	𝓅	𝓅	PROPN
cana-1996	116	3	=	=	SYM
cana-1996	116	4	0	0	PROPN
cana-1996	116	5	&	&	CCONJ
cana-1996	116	6	𝓅	𝓅	NOUN
cana-1996	116	7	=	=	SYM
cana-1996	116	8	1	1	NUM
cana-1996	116	9	,	,	PUNCT
cana-1996	116	10	we	we	PRON
cana-1996	116	11	get	get	VERB
cana-1996	116	12	,	,	PUNCT
cana-1996	116	13	{	{	PUNCT
cana-1996	116	14	𝛿(υ	𝛿(υ	NOUN
cana-1996	116	15	,	,	PUNCT
cana-1996	116	16	𝑡	𝑡	X
cana-1996	116	17	;	;	PUNCT
cana-1996	116	18	0	0	NUM
cana-1996	116	19	)	)	PUNCT
cana-1996	116	20	=	=	SYM
cana-1996	117	1	𝜇0(υ	𝜇0(υ	PROPN
cana-1996	117	2	,	,	PUNCT
cana-1996	117	3	0	0	NUM
cana-1996	117	4	)	)	PUNCT
cana-1996	117	5	𝛿(υ	𝛿(υ	NOUN
cana-1996	117	6	,	,	PUNCT
cana-1996	117	7	𝑡	𝑡	NOUN
cana-1996	117	8	;	;	PUNCT
cana-1996	117	9	1	1	X
cana-1996	117	10	)	)	PUNCT
cana-1996	117	11	=	=	SYM
cana-1996	118	1	𝜇(υ	𝜇(υ	PROPN
cana-1996	118	2	,	,	PUNCT
cana-1996	118	3	𝑡	𝑡	NOUN
cana-1996	118	4	)	)	PUNCT
cana-1996	118	5	.	.	PUNCT
cana-1996	119	1	as	as	ADP
cana-1996	119	2	a	a	DET
cana-1996	119	3	result	result	NOUN
cana-1996	119	4	,	,	PUNCT
cana-1996	119	5	we	we	PRON
cana-1996	119	6	have	have	VERB
cana-1996	119	7	an	an	DET
cana-1996	119	8	equation	equation	NOUN
cana-1996	119	9	of	of	ADP
cana-1996	119	10	deformation	deformation	NOUN
cana-1996	119	11	of	of	ADP
cana-1996	119	12	order	order	NOUN
cana-1996	119	13	𝑚.	𝑚.	PROPN
cana-1996	119	14	ℛ{𝜇𝑚(υ	ℛ{𝜇𝑚(υ	PROPN
cana-1996	119	15	,	,	PUNCT
cana-1996	119	16	𝑡	𝑡	PROPN
cana-1996	119	17	)	)	PUNCT
cana-1996	119	18	−	−	PROPN
cana-1996	120	1	𝜒𝑚𝜇𝑚−1	𝜒𝑚𝜇𝑚−1	PROPN
cana-1996	120	2	(	(	PUNCT
cana-1996	120	3	υ	υ	PROPN
cana-1996	120	4	,	,	PUNCT
cana-1996	120	5	𝑡	𝑡	NOUN
cana-1996	120	6	)	)	PUNCT
cana-1996	120	7	}	}	PUNCT
cana-1996	120	8	=	=	SYM
cana-1996	120	9	ℎ	ℎ	PROPN
cana-1996	120	10	ℛ𝑚(𝜇𝑚−1	ℛ𝑚(𝜇𝑚−1	PROPN
cana-1996	120	11	⃗⃗	⃗⃗	PROPN
cana-1996	120	12	⃗⃗	⃗⃗	PROPN
cana-1996	120	13	⃗⃗	⃗⃗	PROPN
cana-1996	120	14	⃗⃗	⃗⃗	PROPN
cana-1996	120	15	⃗⃗	⃗⃗	PROPN
cana-1996	120	16	⃗(υ	⃗(υ	PROPN
cana-1996	120	17	,	,	PUNCT
cana-1996	120	18	𝑡	𝑡	X
cana-1996	120	19	)	)	PUNCT
cana-1996	120	20	)	)	PUNCT
cana-1996	120	21	.	.	PUNCT
cana-1996	121	1	(	(	PUNCT
cana-1996	121	2	16	16	X
cana-1996	121	3	)	)	PUNCT
cana-1996	121	4	applying	apply	VERB
cana-1996	121	5	the	the	DET
cana-1996	121	6	“	"	PUNCT
cana-1996	121	7	inverse	inverse	ADJ
cana-1996	121	8	rangaig	rangaig	ADJ
cana-1996	121	9	transform	transform	NOUN
cana-1996	121	10	”	"	PUNCT
cana-1996	121	11	to	to	ADP
cana-1996	121	12	both	both	DET
cana-1996	121	13	sides	side	NOUN
cana-1996	121	14	of	of	ADP
cana-1996	121	15	equation	equation	NOUN
cana-1996	121	16	(	(	PUNCT
cana-1996	121	17	16	16	NUM
cana-1996	121	18	)	)	PUNCT
cana-1996	121	19	,	,	PUNCT
cana-1996	121	20	we	we	PRON
cana-1996	121	21	obtain	obtain	VERB
cana-1996	121	22	𝜇𝑚(υ	𝜇𝑚(υ	NOUN
cana-1996	121	23	,	,	PUNCT
cana-1996	121	24	𝑡	𝑡	NOUN
cana-1996	121	25	)	)	PUNCT
cana-1996	121	26	−	−	PROPN
cana-1996	122	1	𝜒𝑚𝜇𝑚−1	𝜒𝑚𝜇𝑚−1	PROPN
cana-1996	122	2	(	(	PUNCT
cana-1996	122	3	υ	υ	PROPN
cana-1996	122	4	,	,	PUNCT
cana-1996	122	5	𝑡	𝑡	NOUN
cana-1996	122	6	)	)	PUNCT
cana-1996	122	7	=	=	PUNCT
cana-1996	122	8	ℛ−1{ℎ	ℛ−1{ℎ	NOUN
cana-1996	123	1	ℛ𝑚	ℛ𝑚	PROPN
cana-1996	123	2	(	(	PUNCT
cana-1996	123	3	𝜇𝑚−1⃗⃗	𝜇𝑚−1⃗⃗	PROPN
cana-1996	123	4	⃗⃗	⃗⃗	PROPN
cana-1996	123	5	⃗⃗	⃗⃗	PROPN
cana-1996	123	6	⃗⃗	⃗⃗	PROPN
cana-1996	123	7	⃗⃗	⃗⃗	PROPN
cana-1996	123	8	(	(	PUNCT
cana-1996	123	9	υ	υ	PROPN
cana-1996	123	10	,	,	PUNCT
cana-1996	123	11	𝑡	𝑡	NOUN
cana-1996	123	12	)	)	PUNCT
cana-1996	123	13	)	)	PUNCT
cana-1996	123	14	}	}	PUNCT
cana-1996	123	15	.	.	PUNCT
cana-1996	124	1	(	(	PUNCT
cana-1996	124	2	17	17	NUM
cana-1996	124	3	)	)	PUNCT
cana-1996	124	4	from	from	ADP
cana-1996	124	5	the	the	DET
cana-1996	124	6	above	above	ADJ
cana-1996	124	7	equation	equation	NOUN
cana-1996	124	8	we	we	PRON
cana-1996	124	9	get	get	VERB
cana-1996	124	10	𝜇1(υ	𝜇1(υ	ADJ
cana-1996	124	11	,	,	PUNCT
cana-1996	124	12	𝑡	𝑡	NOUN
cana-1996	124	13	)	)	PUNCT
cana-1996	124	14	=	=	SYM
cana-1996	125	1	−ℛ−1{ℛ1(𝜇0⃗⃗⃗⃗	−ℛ−1{ℛ1(𝜇0⃗⃗⃗⃗	PROPN
cana-1996	125	2	(	(	PUNCT
cana-1996	125	3	υ	υ	NOUN
cana-1996	125	4	,	,	PUNCT
cana-1996	125	5	𝑡	𝑡	NOUN
cana-1996	125	6	)	)	PUNCT
cana-1996	125	7	)	)	PUNCT
cana-1996	125	8	}	}	PUNCT
cana-1996	125	9	,	,	PUNCT
cana-1996	125	10	communications	communication	NOUN
cana-1996	125	11	on	on	ADP
cana-1996	125	12	applied	apply	VERB
cana-1996	125	13	nonlinear	nonlinear	ADJ
cana-1996	125	14	analysis	analysis	NOUN
cana-1996	125	15	issn	issn	NOUN
cana-1996	125	16	:	:	PUNCT
cana-1996	125	17	1074	1074	NUM
cana-1996	125	18	-	-	PUNCT
cana-1996	125	19	133x	133x	NUM
cana-1996	125	20	vol	vol	NOUN
cana-1996	125	21	32	32	NUM
cana-1996	125	22	no	no	NOUN
cana-1996	125	23	.	.	NOUN
cana-1996	125	24	3	3	NUM
cana-1996	125	25	(	(	PUNCT
cana-1996	125	26	2025	2025	NUM
cana-1996	125	27	)	)	PUNCT
cana-1996	125	28	389	389	NUM
cana-1996	125	29	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	125	30	𝜇2(υ	𝜇2(υ	PROPN
cana-1996	125	31	,	,	PUNCT
cana-1996	125	32	𝑡	𝑡	X
cana-1996	125	33	)	)	PUNCT
cana-1996	125	34	=	=	SYM
cana-1996	125	35	𝜇1(υ	𝜇1(υ	PROPN
cana-1996	125	36	,	,	PUNCT
cana-1996	125	37	𝑡	𝑡	NOUN
cana-1996	125	38	)	)	PUNCT
cana-1996	125	39	−	−	NOUN
cana-1996	125	40	ℛ−1{ℛ2(𝜇1⃗⃗⃗⃗	ℛ−1{ℛ2(𝜇1⃗⃗⃗⃗	NOUN
cana-1996	125	41	(	(	PUNCT
cana-1996	125	42	υ	υ	NOUN
cana-1996	125	43	,	,	PUNCT
cana-1996	125	44	𝑡	𝑡	NOUN
cana-1996	125	45	)	)	PUNCT
cana-1996	125	46	)	)	PUNCT
cana-1996	125	47	}	}	PUNCT
cana-1996	125	48	,	,	PUNCT
cana-1996	125	49	𝜇3(υ	𝜇3(υ	PROPN
cana-1996	125	50	,	,	PUNCT
cana-1996	125	51	𝑡	𝑡	NOUN
cana-1996	125	52	)	)	PUNCT
cana-1996	125	53	=	=	SYM
cana-1996	126	1	𝜇2(υ	𝜇2(υ	PROPN
cana-1996	126	2	,	,	PUNCT
cana-1996	126	3	𝑡	𝑡	NOUN
cana-1996	126	4	)	)	PUNCT
cana-1996	126	5	−	−	NOUN
cana-1996	126	6	ℛ−1{ℛ3(𝜇2⃗⃗⃗⃗	ℛ−1{ℛ3(𝜇2⃗⃗⃗⃗	ADV
cana-1996	126	7	(	(	PUNCT
cana-1996	126	8	υ	υ	NOUN
cana-1996	126	9	,	,	PUNCT
cana-1996	126	10	𝑡	𝑡	NOUN
cana-1996	126	11	)	)	PUNCT
cana-1996	126	12	)	)	PUNCT
cana-1996	126	13	}	}	PUNCT
cana-1996	126	14	,	,	PUNCT
cana-1996	126	15	⋮	⋮	NOUN
cana-1996	126	16	therefore	therefore	ADV
cana-1996	126	17	,	,	PUNCT
cana-1996	126	18	the	the	DET
cana-1996	126	19	solution	solution	NOUN
cana-1996	126	20	is	be	AUX
cana-1996	126	21	:	:	PUNCT
cana-1996	126	22	𝜇(υ	𝜇(υ	NOUN
cana-1996	126	23	,	,	PUNCT
cana-1996	126	24	𝑡	𝑡	NOUN
cana-1996	126	25	)	)	PUNCT
cana-1996	126	26	=	=	SYM
cana-1996	126	27	𝜇0	𝜇0	PROPN
cana-1996	126	28	+	+	CCONJ
cana-1996	126	29	𝜇1	𝜇1	PROPN
cana-1996	126	30	+	+	CCONJ
cana-1996	126	31	𝜇2	𝜇2	PROPN
cana-1996	126	32	+	+	SYM
cana-1996	126	33	⋯	⋯	PROPN
cana-1996	126	34	(	(	PUNCT
cana-1996	126	35	18	18	NUM
cana-1996	126	36	)	)	PUNCT
cana-1996	126	37	3	3	NUM
cana-1996	126	38	.	.	PUNCT
cana-1996	126	39	test	test	NOUN
cana-1996	126	40	examples	example	NOUN
cana-1996	126	41	:	:	PUNCT
cana-1996	126	42	within	within	ADP
cana-1996	126	43	this	this	DET
cana-1996	126	44	segment	segment	NOUN
cana-1996	126	45	,	,	PUNCT
cana-1996	126	46	we	we	PRON
cana-1996	126	47	will	will	AUX
cana-1996	126	48	adopt	adopt	VERB
cana-1996	126	49	both	both	CCONJ
cana-1996	126	50	the	the	DET
cana-1996	126	51	“	"	PUNCT
cana-1996	126	52	rangaig	rangaig	ADJ
cana-1996	126	53	transform	transform	NOUN
cana-1996	126	54	”	"	PUNCT
cana-1996	126	55	and	and	CCONJ
cana-1996	126	56	the	the	DET
cana-1996	126	57	traditional	traditional	ADJ
cana-1996	126	58	“	"	PUNCT
cana-1996	126	59	homotopy	homotopy	VERB
cana-1996	126	60	analysis	analysis	NOUN
cana-1996	126	61	technique	technique	NOUN
cana-1996	126	62	(	(	PUNCT
cana-1996	126	63	ham	ham	NOUN
cana-1996	126	64	)	)	PUNCT
cana-1996	126	65	”	"	PUNCT
cana-1996	126	66	to	to	PART
cana-1996	126	67	solve	solve	VERB
cana-1996	126	68	a	a	DET
cana-1996	126	69	couple	couple	NOUN
cana-1996	126	70	of	of	ADP
cana-1996	126	71	examples	example	NOUN
cana-1996	126	72	of	of	ADP
cana-1996	126	73	semi	semi	ADJ
cana-1996	126	74	-	-	ADJ
cana-1996	126	75	analytical	analytical	ADJ
cana-1996	126	76	solutions	solution	NOUN
cana-1996	126	77	for	for	ADP
cana-1996	126	78	(	(	PUNCT
cana-1996	126	79	3	3	NUM
cana-1996	126	80	+	+	NOUN
cana-1996	126	81	1)-d	1)-d	NUM
cana-1996	126	82	pdes	pde	NOUN
cana-1996	126	83	including	include	VERB
cana-1996	126	84	the	the	DET
cana-1996	126	85	“	"	PUNCT
cana-1996	126	86	(	(	PUNCT
cana-1996	126	87	3	3	NUM
cana-1996	126	88	+	+	SYM
cana-1996	126	89	1)-d	1)-d	NUM
cana-1996	126	90	telegraph	telegraph	NOUN
cana-1996	126	91	equation	equation	NOUN
cana-1996	126	92	”	"	PUNCT
cana-1996	126	93	,	,	PUNCT
cana-1996	126	94	“	"	PUNCT
cana-1996	126	95	(	(	PUNCT
cana-1996	126	96	3	3	NUM
cana-1996	126	97	+	+	SYM
cana-1996	126	98	1)-d	1)-d	NUM
cana-1996	126	99	diffusion	diffusion	NOUN
cana-1996	126	100	equation	equation	NOUN
cana-1996	126	101	”	"	PUNCT
cana-1996	126	102	,	,	PUNCT
cana-1996	126	103	and	and	CCONJ
cana-1996	126	104	“	"	PUNCT
cana-1996	126	105	(	(	PUNCT
cana-1996	126	106	3	3	NUM
cana-1996	126	107	+	+	SYM
cana-1996	126	108	1)-d	1)-d	NUM
cana-1996	126	109	klein	klein	PROPN
cana-1996	126	110	gordan	gordan	PROPN
cana-1996	126	111	equation	equation	PROPN
cana-1996	126	112	”	"	PUNCT
cana-1996	126	113	.	.	PUNCT
cana-1996	127	1	example	example	NOUN
cana-1996	127	2	1	1	NUM
cana-1996	127	3	:	:	PUNCT
cana-1996	127	4	consider	consider	VERB
cana-1996	127	5	the	the	DET
cana-1996	127	6	(	(	PUNCT
cana-1996	127	7	3	3	NUM
cana-1996	127	8	+	+	SYM
cana-1996	127	9	1)-d	1)-d	NUM
cana-1996	127	10	telegraph	telegraph	NOUN
cana-1996	127	11	equation	equation	NOUN
cana-1996	127	12	of	of	ADP
cana-1996	127	13	the	the	DET
cana-1996	127	14	form	form	NOUN
cana-1996	127	15	:	:	PUNCT
cana-1996	127	16	𝜇𝑡𝑡	𝜇𝑡𝑡	ADV
cana-1996	127	17	−	−	NOUN
cana-1996	127	18	2𝜋2𝜇	2𝜋2𝜇	NOUN
cana-1996	128	1	=	=	SYM
cana-1996	128	2	1	1	NUM
cana-1996	128	3	3	3	NUM
cana-1996	128	4	(	(	PUNCT
cana-1996	128	5	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	128	6	+	+	CCONJ
cana-1996	128	7	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	128	8	+	+	CCONJ
cana-1996	128	9	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	128	10	)	)	PUNCT
cana-1996	128	11	(	(	PUNCT
cana-1996	128	12	19	19	NUM
cana-1996	128	13	)	)	PUNCT
cana-1996	128	14	with	with	ADP
cana-1996	128	15	initial	initial	ADJ
cana-1996	128	16	condition	condition	NOUN
cana-1996	128	17	𝜇(υ	𝜇(υ	NOUN
cana-1996	128	18	,	,	PUNCT
cana-1996	128	19	0	0	NUM
cana-1996	128	20	)	)	PUNCT
cana-1996	128	21	=	=	SYM
cana-1996	128	22	𝑠𝑖𝑛	𝑠𝑖𝑛	NOUN
cana-1996	128	23	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	128	24	𝑠𝑖𝑛	𝑠𝑖𝑛	PROPN
cana-1996	128	25	𝜋𝑦	𝜋𝑦	PROPN
cana-1996	128	26	𝑠𝑖𝑛	𝑠𝑖𝑛	PROPN
cana-1996	128	27	𝜋𝑧	𝜋𝑧	PROPN
cana-1996	128	28	,	,	PUNCT
cana-1996	128	29	we	we	PRON
cana-1996	128	30	use	use	VERB
cana-1996	128	31	υ	υ	NOUN
cana-1996	128	32	=	=	PUNCT
cana-1996	128	33	(	(	PUNCT
cana-1996	128	34	𝑥	𝑥	PROPN
cana-1996	128	35	,	,	PUNCT
cana-1996	128	36	𝑦	𝑦	NOUN
cana-1996	128	37	,	,	PUNCT
cana-1996	128	38	𝑧	𝑧	PART
cana-1996	128	39	)	)	PUNCT
cana-1996	128	40	,	,	PUNCT
cana-1996	128	41	the	the	DET
cana-1996	128	42	exact	exact	ADJ
cana-1996	128	43	solution	solution	NOUN
cana-1996	128	44	is	be	AUX
cana-1996	128	45	:	:	PUNCT
cana-1996	128	46	𝜇(υ	𝜇(υ	NOUN
cana-1996	128	47	,	,	PUNCT
cana-1996	128	48	𝑡	𝑡	NOUN
cana-1996	128	49	)	)	PUNCT
cana-1996	128	50	=	=	SYM
cana-1996	128	51	𝑒𝜋𝑡	𝑒𝜋𝑡	NOUN
cana-1996	128	52	sin	sin	NOUN
cana-1996	128	53	(	(	PUNCT
cana-1996	128	54	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	128	55	)	)	PUNCT
cana-1996	128	56	sin	sin	NOUN
cana-1996	128	57	(	(	PUNCT
cana-1996	128	58	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	128	59	)	)	PUNCT
cana-1996	128	60	sin	sin	NOUN
cana-1996	128	61	(	(	PUNCT
cana-1996	128	62	𝜋𝑧	𝜋𝑧	NOUN
cana-1996	128	63	)	)	PUNCT
cana-1996	128	64	rephrase	rephrase	VERB
cana-1996	128	65	the	the	DET
cana-1996	128	66	stated	state	VERB
cana-1996	128	67	issue	issue	NOUN
cana-1996	128	68	as	as	SCONJ
cana-1996	128	69	follows	follow	VERB
cana-1996	128	70	:	:	PUNCT
cana-1996	128	71	𝜇𝑡𝑡	𝜇𝑡𝑡	PROPN
cana-1996	128	72	=	=	NOUN
cana-1996	128	73	1	1	NUM
cana-1996	128	74	3	3	NUM
cana-1996	128	75	(	(	PUNCT
cana-1996	128	76	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	128	77	+	+	CCONJ
cana-1996	128	78	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	128	79	+	+	CCONJ
cana-1996	128	80	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	128	81	)	)	PUNCT
cana-1996	129	1	+	+	CCONJ
cana-1996	129	2	2𝜋2𝜇	2𝜋2𝜇	NUM
cana-1996	129	3	(	(	PUNCT
cana-1996	129	4	20	20	NUM
cana-1996	129	5	)	)	PUNCT
cana-1996	129	6	when	when	SCONJ
cana-1996	129	7	the	the	DET
cana-1996	129	8	“	"	PUNCT
cana-1996	129	9	rangaig	rangaig	ADJ
cana-1996	129	10	transform	transform	NOUN
cana-1996	129	11	”	"	PUNCT
cana-1996	129	12	is	be	AUX
cana-1996	129	13	carried	carry	VERB
cana-1996	129	14	out	out	ADP
cana-1996	129	15	to	to	ADP
cana-1996	129	16	both	both	DET
cana-1996	129	17	sides	side	NOUN
cana-1996	129	18	of	of	ADP
cana-1996	129	19	equation	equation	NOUN
cana-1996	129	20	(	(	PUNCT
cana-1996	129	21	20	20	NUM
cana-1996	129	22	)	)	PUNCT
cana-1996	129	23	,	,	PUNCT
cana-1996	129	24	we	we	PRON
cana-1996	129	25	get	get	VERB
cana-1996	129	26	,	,	PUNCT
cana-1996	129	27	ℛ	ℛ	PROPN
cana-1996	130	1	[	[	X
cana-1996	130	2	𝜇𝑡𝑡	𝜇𝑡𝑡	X
cana-1996	130	3	]	]	X
cana-1996	130	4	=	=	SYM
cana-1996	130	5	ℛ	ℛ	PROPN
cana-1996	130	6	[	[	PUNCT
cana-1996	130	7	1	1	NUM
cana-1996	130	8	3	3	NUM
cana-1996	130	9	(	(	PUNCT
cana-1996	130	10	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	130	11	+	+	CCONJ
cana-1996	130	12	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	130	13	+	+	CCONJ
cana-1996	130	14	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	130	15	)	)	PUNCT
cana-1996	131	1	+	+	CCONJ
cana-1996	131	2	2𝜋2𝜇	2𝜋2𝜇	X
cana-1996	131	3	]	]	X
cana-1996	131	4	this	this	PRON
cana-1996	131	5	implies	imply	VERB
cana-1996	131	6	(	(	PUNCT
cana-1996	131	7	−1)2𝜛2ℛ[𝜇	−1)2𝜛2ℛ[𝜇	NOUN
cana-1996	131	8	]	]	X
cana-1996	131	9	+	+	CCONJ
cana-1996	131	10	(	(	PUNCT
cana-1996	131	11	−1)3	−1)3	NOUN
cana-1996	131	12	∑	∑	INTJ
cana-1996	131	13	(	(	PUNCT
cana-1996	131	14	−1)𝓀	−1)𝓀	X
cana-1996	131	15	𝜛𝓀	𝜛𝓀	PROPN
cana-1996	131	16	1	1	NUM
cana-1996	131	17	𝓀=0	𝓀=0	NOUN
cana-1996	131	18	𝜕𝓀𝜇	𝜕𝓀𝜇	PUNCT
cana-1996	131	19	𝜕𝑡𝓀	𝜕𝑡𝓀	PUNCT
cana-1996	132	1	=	=	SYM
cana-1996	132	2	ℛ	ℛ	PROPN
cana-1996	132	3	[	[	PUNCT
cana-1996	132	4	1	1	NUM
cana-1996	132	5	3	3	NUM
cana-1996	132	6	(	(	PUNCT
cana-1996	132	7	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	132	8	+	+	CCONJ
cana-1996	132	9	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	132	10	+	+	CCONJ
cana-1996	132	11	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	132	12	)	)	PUNCT
cana-1996	133	1	+	+	CCONJ
cana-1996	133	2	2𝜋2𝜇	2𝜋2𝜇	X
cana-1996	133	3	]	]	X
cana-1996	133	4	this	this	DET
cana-1996	133	5	expression	expression	NOUN
cana-1996	133	6	can	can	AUX
cana-1996	133	7	be	be	AUX
cana-1996	133	8	expressed	express	VERB
cana-1996	133	9	as	as	ADP
cana-1996	133	10	:	:	PUNCT
cana-1996	133	11	𝜛2ℛ[𝜇	𝜛2ℛ[𝜇	PROPN
cana-1996	133	12	]	]	PUNCT
cana-1996	134	1	−	−	PROPN
cana-1996	134	2	[	[	PUNCT
cana-1996	134	3	1	1	NUM
cana-1996	134	4	𝜛0	𝜛0	PROPN
cana-1996	134	5	𝜇(υ	𝜇(υ	NOUN
cana-1996	134	6	,	,	PUNCT
cana-1996	134	7	0	0	NUM
cana-1996	134	8	)	)	PUNCT
cana-1996	134	9	+	+	CCONJ
cana-1996	134	10	(	(	PUNCT
cana-1996	134	11	−1)1	−1)1	NUM
cana-1996	134	12	𝜛1	𝜛1	PROPN
cana-1996	134	13	𝜕	𝜕	PROPN
cana-1996	134	14	𝜕𝑡	𝜕𝑡	PROPN
cana-1996	134	15	𝜇(υ	𝜇(υ	PROPN
cana-1996	134	16	,	,	PUNCT
cana-1996	134	17	0	0	NUM
cana-1996	134	18	)	)	PUNCT
cana-1996	134	19	]	]	PUNCT
cana-1996	135	1	=	=	SYM
cana-1996	135	2	ℛ	ℛ	PROPN
cana-1996	135	3	[	[	PUNCT
cana-1996	135	4	1	1	NUM
cana-1996	135	5	3	3	NUM
cana-1996	135	6	(	(	PUNCT
cana-1996	135	7	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	135	8	+	+	CCONJ
cana-1996	135	9	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	135	10	+	+	CCONJ
cana-1996	135	11	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	135	12	)	)	PUNCT
cana-1996	136	1	+	+	CCONJ
cana-1996	136	2	2𝜋2𝜇	2𝜋2𝜇	X
cana-1996	136	3	]	]	X
cana-1996	136	4	when	when	SCONJ
cana-1996	136	5	starting	start	VERB
cana-1996	136	6	conditions	condition	NOUN
cana-1996	136	7	are	be	AUX
cana-1996	136	8	applied	apply	VERB
cana-1996	136	9	,	,	PUNCT
cana-1996	136	10	we	we	PRON
cana-1996	136	11	get	get	VERB
cana-1996	136	12	𝜛2ℛ[𝜇	𝜛2ℛ[𝜇	PROPN
cana-1996	136	13	]	]	X
cana-1996	137	1	−	−	PROPN
cana-1996	137	2	(	(	PUNCT
cana-1996	137	3	1	1	NUM
cana-1996	137	4	−	−	PROPN
cana-1996	137	5	𝜋	𝜋	NOUN
cana-1996	137	6	𝜛1	𝜛1	NOUN
cana-1996	137	7	)	)	PUNCT
cana-1996	137	8	sin	sin	NOUN
cana-1996	137	9	(	(	PUNCT
cana-1996	137	10	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	137	11	)	)	PUNCT
cana-1996	137	12	sin	sin	NOUN
cana-1996	137	13	(	(	PUNCT
cana-1996	137	14	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	137	15	)	)	PUNCT
cana-1996	137	16	sin	sin	NOUN
cana-1996	137	17	(	(	PUNCT
cana-1996	137	18	𝜋𝑧	𝜋𝑧	NOUN
cana-1996	137	19	)	)	PUNCT
cana-1996	137	20	=	=	SYM
cana-1996	137	21	ℛ	ℛ	PROPN
cana-1996	137	22	[	[	PUNCT
cana-1996	137	23	1	1	NUM
cana-1996	137	24	3	3	NUM
cana-1996	137	25	(	(	PUNCT
cana-1996	137	26	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	137	27	+	+	CCONJ
cana-1996	137	28	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	137	29	+	+	CCONJ
cana-1996	137	30	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	137	31	)	)	PUNCT
cana-1996	137	32	+	+	CCONJ
cana-1996	137	33	2𝜋2𝜇	2𝜋2𝜇	X
cana-1996	137	34	]	]	X
cana-1996	137	35	that	that	PRON
cana-1996	137	36	suggests	suggest	VERB
cana-1996	137	37	ℛ[𝜇	ℛ[𝜇	X
cana-1996	137	38	]	]	X
cana-1996	137	39	−	−	PROPN
cana-1996	137	40	(	(	PUNCT
cana-1996	137	41	1	1	NUM
cana-1996	137	42	𝜛2	𝜛2	NOUN
cana-1996	137	43	−	−	PROPN
cana-1996	137	44	𝜋	𝜋	NOUN
cana-1996	137	45	𝜛3	𝜛3	PROPN
cana-1996	137	46	)	)	PUNCT
cana-1996	137	47	sin	sin	NOUN
cana-1996	137	48	(	(	PUNCT
cana-1996	137	49	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	137	50	)	)	PUNCT
cana-1996	137	51	sin	sin	NOUN
cana-1996	137	52	(	(	PUNCT
cana-1996	137	53	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	137	54	)	)	PUNCT
cana-1996	137	55	sin	sin	NOUN
cana-1996	137	56	(	(	PUNCT
cana-1996	137	57	𝜋𝑧	𝜋𝑧	NOUN
cana-1996	137	58	)	)	PUNCT
cana-1996	137	59	=	=	SYM
cana-1996	137	60	1	1	NUM
cana-1996	137	61	𝜛2	𝜛2	NOUN
cana-1996	137	62	ℛ	ℛ	PROPN
cana-1996	137	63	[	[	PUNCT
cana-1996	137	64	1	1	NUM
cana-1996	137	65	3	3	NUM
cana-1996	137	66	(	(	PUNCT
cana-1996	137	67	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	137	68	+	+	CCONJ
cana-1996	137	69	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	137	70	+	+	CCONJ
cana-1996	137	71	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	137	72	)	)	PUNCT
cana-1996	138	1	+	+	NUM
cana-1996	138	2	2𝜋2𝜇	2𝜋2𝜇	X
cana-1996	138	3	]	]	X
cana-1996	138	4	communications	communication	NOUN
cana-1996	138	5	on	on	ADP
cana-1996	138	6	applied	apply	VERB
cana-1996	138	7	nonlinear	nonlinear	ADJ
cana-1996	138	8	analysis	analysis	NOUN
cana-1996	138	9	issn	issn	NOUN
cana-1996	138	10	:	:	PUNCT
cana-1996	138	11	1074	1074	NUM
cana-1996	138	12	-	-	PUNCT
cana-1996	138	13	133x	133x	NUM
cana-1996	138	14	vol	vol	NOUN
cana-1996	138	15	32	32	NUM
cana-1996	138	16	no	no	NOUN
cana-1996	138	17	.	.	NOUN
cana-1996	138	18	3	3	NUM
cana-1996	138	19	(	(	PUNCT
cana-1996	138	20	2025	2025	NUM
cana-1996	138	21	)	)	PUNCT
cana-1996	138	22	390	390	NUM
cana-1996	138	23	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	138	24	or	or	CCONJ
cana-1996	138	25	ℛ[𝜇	ℛ[𝜇	PROPN
cana-1996	138	26	]	]	X
cana-1996	139	1	=	=	PUNCT
cana-1996	139	2	(	(	PUNCT
cana-1996	139	3	1	1	NUM
cana-1996	139	4	𝜛2	𝜛2	NOUN
cana-1996	139	5	−	−	PROPN
cana-1996	139	6	𝜋	𝜋	NOUN
cana-1996	139	7	𝜛3	𝜛3	PROPN
cana-1996	139	8	)	)	PUNCT
cana-1996	139	9	sin	sin	NOUN
cana-1996	139	10	(	(	PUNCT
cana-1996	139	11	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	139	12	)	)	PUNCT
cana-1996	139	13	sin	sin	NOUN
cana-1996	139	14	(	(	PUNCT
cana-1996	139	15	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	139	16	)	)	PUNCT
cana-1996	139	17	sin	sin	NOUN
cana-1996	139	18	(	(	PUNCT
cana-1996	139	19	𝜋𝑧	𝜋𝑧	NOUN
cana-1996	139	20	)	)	PUNCT
cana-1996	139	21	+	+	CCONJ
cana-1996	139	22	1	1	NUM
cana-1996	139	23	𝜛2	𝜛2	NOUN
cana-1996	139	24	ℛ	ℛ	NOUN
cana-1996	139	25	[	[	PUNCT
cana-1996	139	26	1	1	NUM
cana-1996	139	27	3	3	NUM
cana-1996	139	28	(	(	PUNCT
cana-1996	139	29	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	139	30	+	+	CCONJ
cana-1996	139	31	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	139	32	+	+	CCONJ
cana-1996	139	33	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	139	34	)	)	PUNCT
cana-1996	139	35	+	+	CCONJ
cana-1996	139	36	2𝜋2𝜇	2𝜋2𝜇	X
cana-1996	139	37	]	]	X
cana-1996	139	38	here	here	ADV
cana-1996	139	39	is	be	AUX
cana-1996	139	40	how	how	SCONJ
cana-1996	139	41	we	we	PRON
cana-1996	139	42	define	define	VERB
cana-1996	139	43	the	the	DET
cana-1996	139	44	nonlinear	nonlinear	ADJ
cana-1996	139	45	component	component	NOUN
cana-1996	139	46	:	:	PUNCT
cana-1996	139	47	𝒩[𝛿(υ	𝒩[𝛿(υ	NOUN
cana-1996	139	48	,	,	PUNCT
cana-1996	139	49	𝑡	𝑡	X
cana-1996	139	50	;	;	PUNCT
cana-1996	139	51	𝓅	𝓅	NOUN
cana-1996	139	52	)	)	PUNCT
cana-1996	139	53	]	]	PUNCT
cana-1996	140	1	=	=	PUNCT
cana-1996	141	1	ℛ[𝜇	ℛ[𝜇	X
cana-1996	141	2	]	]	X
cana-1996	142	1	−	−	PROPN
cana-1996	142	2	(	(	PUNCT
cana-1996	142	3	1	1	NUM
cana-1996	142	4	𝜛2	𝜛2	NOUN
cana-1996	142	5	−	−	PROPN
cana-1996	142	6	𝜋	𝜋	NOUN
cana-1996	142	7	𝜛3	𝜛3	PROPN
cana-1996	142	8	)	)	PUNCT
cana-1996	142	9	sin	sin	NOUN
cana-1996	142	10	(	(	PUNCT
cana-1996	142	11	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	142	12	)	)	PUNCT
cana-1996	142	13	sin	sin	NOUN
cana-1996	142	14	(	(	PUNCT
cana-1996	142	15	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	142	16	)	)	PUNCT
cana-1996	142	17	sin	sin	NOUN
cana-1996	142	18	(	(	PUNCT
cana-1996	142	19	𝜋𝑧	𝜋𝑧	NOUN
cana-1996	142	20	)	)	PUNCT
cana-1996	143	1	−	−	PROPN
cana-1996	143	2	1	1	NUM
cana-1996	143	3	𝜛2	𝜛2	NOUN
cana-1996	143	4	ℛ	ℛ	PROPN
cana-1996	143	5	[	[	PUNCT
cana-1996	143	6	1	1	NUM
cana-1996	143	7	3	3	NUM
cana-1996	143	8	(	(	PUNCT
cana-1996	143	9	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	143	10	+	+	CCONJ
cana-1996	143	11	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	143	12	+	+	CCONJ
cana-1996	143	13	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	143	14	)	)	PUNCT
cana-1996	144	1	+	+	CCONJ
cana-1996	144	2	2𝜋2𝜇	2𝜋2𝜇	X
cana-1996	144	3	]	]	X
cana-1996	144	4	(	(	PUNCT
cana-1996	144	5	21	21	NUM
cana-1996	144	6	)	)	PUNCT
cana-1996	144	7	we	we	PRON
cana-1996	144	8	begin	begin	VERB
cana-1996	144	9	by	by	ADP
cana-1996	144	10	setting	set	VERB
cana-1996	144	11	up	up	ADP
cana-1996	144	12	the	the	DET
cana-1996	144	13	0	0	NUM
cana-1996	144	14	-	-	PUNCT
cana-1996	144	15	order	order	NOUN
cana-1996	144	16	deformation	deformation	NOUN
cana-1996	144	17	according	accord	VERB
cana-1996	144	18	to	to	ADP
cana-1996	144	19	the	the	DET
cana-1996	144	20	assumption	assumption	NOUN
cana-1996	144	21	adopted	adopt	VERB
cana-1996	144	22	herein	herein	NOUN
cana-1996	144	23	,	,	PUNCT
cana-1996	144	24	namely	namely	ADV
cana-1996	144	25	,	,	PUNCT
cana-1996	144	26	𝐻(υ	𝐻(υ	NOUN
cana-1996	144	27	,	,	PUNCT
cana-1996	144	28	𝑡	𝑡	NOUN
cana-1996	144	29	)	)	PUNCT
cana-1996	144	30	=	=	SYM
cana-1996	145	1	1	1	NUM
cana-1996	145	2	;	;	PUNCT
cana-1996	145	3	we	we	PRON
cana-1996	145	4	have	have	VERB
cana-1996	145	5	(	(	PUNCT
cana-1996	145	6	1	1	NUM
cana-1996	145	7	−	−	NOUN
cana-1996	145	8	𝓅)ℛ{𝛿(υ	𝓅)ℛ{𝛿(υ	NOUN
cana-1996	145	9	,	,	PUNCT
cana-1996	145	10	𝑡	𝑡	NOUN
cana-1996	145	11	)	)	PUNCT
cana-1996	145	12	−	−	PRON
cana-1996	145	13	𝜇0(υ	𝜇0(υ	PROPN
cana-1996	145	14	,	,	PUNCT
cana-1996	145	15	𝑡	𝑡	NOUN
cana-1996	145	16	)	)	PUNCT
cana-1996	145	17	}	}	PUNCT
cana-1996	145	18	=	=	SYM
cana-1996	145	19	𝓅ℎ𝒩[𝛿(υ	𝓅ℎ𝒩[𝛿(υ	X
cana-1996	145	20	,	,	PUNCT
cana-1996	145	21	𝑡	𝑡	NOUN
cana-1996	145	22	;	;	PUNCT
cana-1996	145	23	𝓅	𝓅	NOUN
cana-1996	145	24	)	)	PUNCT
cana-1996	145	25	]	]	PUNCT
cana-1996	145	26	when	when	SCONJ
cana-1996	145	27	𝓅	𝓅	PROPN
cana-1996	145	28	=	=	SYM
cana-1996	145	29	0	0	PROPN
cana-1996	145	30	&	&	CCONJ
cana-1996	145	31	𝓅	𝓅	NOUN
cana-1996	145	32	=	=	SYM
cana-1996	145	33	1	1	NUM
cana-1996	145	34	,	,	PUNCT
cana-1996	145	35	we	we	PRON
cana-1996	145	36	have	have	VERB
cana-1996	145	37	{	{	PUNCT
cana-1996	145	38	𝛿(υ	𝛿(υ	NOUN
cana-1996	145	39	,	,	PUNCT
cana-1996	145	40	𝑡	𝑡	X
cana-1996	145	41	;	;	PUNCT
cana-1996	145	42	0	0	NUM
cana-1996	145	43	)	)	PUNCT
cana-1996	145	44	=	=	SYM
cana-1996	145	45	𝜇0(υ	𝜇0(υ	PROPN
cana-1996	145	46	,	,	PUNCT
cana-1996	145	47	0	0	NUM
cana-1996	145	48	)	)	PUNCT
cana-1996	145	49	𝛿(υ	𝛿(υ	NOUN
cana-1996	145	50	,	,	PUNCT
cana-1996	145	51	𝑡	𝑡	NOUN
cana-1996	145	52	;	;	PUNCT
cana-1996	145	53	1	1	X
cana-1996	145	54	)	)	PUNCT
cana-1996	145	55	=	=	SYM
cana-1996	145	56	𝜇(υ	𝜇(υ	PROPN
cana-1996	145	57	,	,	PUNCT
cana-1996	145	58	𝑡	𝑡	NOUN
cana-1996	145	59	)	)	PUNCT
cana-1996	145	60	so	so	ADV
cana-1996	145	61	,	,	PUNCT
cana-1996	145	62	the	the	DET
cana-1996	145	63	mth	mth	NOUN
cana-1996	145	64	-	-	PUNCT
cana-1996	145	65	order	order	NOUN
cana-1996	145	66	deformation	deformation	NOUN
cana-1996	145	67	eqn	eqn	NOUN
cana-1996	145	68	.	.	PUNCT
cana-1996	146	1	ℛ{𝜇𝑚(υ	ℛ{𝜇𝑚(υ	PROPN
cana-1996	146	2	,	,	PUNCT
cana-1996	146	3	𝑡	𝑡	NOUN
cana-1996	146	4	)	)	PUNCT
cana-1996	146	5	−	−	NOUN
cana-1996	146	6	𝜒𝑚𝜇𝑚−1(υ	𝜒𝑚𝜇𝑚−1(υ	NUM
cana-1996	146	7	,	,	PUNCT
cana-1996	146	8	𝑡	𝑡	NOUN
cana-1996	146	9	)	)	PUNCT
cana-1996	146	10	}	}	PUNCT
cana-1996	146	11	=	=	SYM
cana-1996	146	12	ℎℛ𝑚(𝜇𝑚−1⃗⃗	ℎℛ𝑚(𝜇𝑚−1⃗⃗	NUM
cana-1996	146	13	⃗⃗	⃗⃗	PROPN
cana-1996	146	14	⃗⃗	⃗⃗	PROPN
cana-1996	146	15	⃗⃗	⃗⃗	PROPN
cana-1996	146	16	⃗⃗	⃗⃗	PROPN
cana-1996	146	17	(	(	PUNCT
cana-1996	146	18	υ	υ	PROPN
cana-1996	146	19	,	,	PUNCT
cana-1996	146	20	𝑡	𝑡	NOUN
cana-1996	146	21	)	)	PUNCT
cana-1996	146	22	)	)	PUNCT
cana-1996	146	23	(	(	PUNCT
cana-1996	146	24	22	22	NUM
cana-1996	146	25	)	)	PUNCT
cana-1996	146	26	when	when	SCONJ
cana-1996	146	27	the	the	DET
cana-1996	146	28	“	"	PUNCT
cana-1996	146	29	inverse	inverse	ADJ
cana-1996	146	30	rangaig	rangaig	ADJ
cana-1996	146	31	transform	transform	NOUN
cana-1996	146	32	”	"	PUNCT
cana-1996	146	33	is	be	AUX
cana-1996	146	34	carried	carry	VERB
cana-1996	146	35	out	out	ADP
cana-1996	146	36	to	to	ADP
cana-1996	146	37	both	both	DET
cana-1996	146	38	sides	side	NOUN
cana-1996	146	39	of	of	ADP
cana-1996	146	40	equation	equation	NOUN
cana-1996	146	41	(	(	PUNCT
cana-1996	146	42	22	22	NUM
cana-1996	146	43	)	)	PUNCT
cana-1996	146	44	,	,	PUNCT
cana-1996	146	45	we	we	PRON
cana-1996	146	46	get	get	VERB
cana-1996	146	47	,	,	PUNCT
cana-1996	146	48	𝜇𝑚(υ	𝜇𝑚(υ	NOUN
cana-1996	146	49	,	,	PUNCT
cana-1996	146	50	𝑡	𝑡	NOUN
cana-1996	146	51	)	)	PUNCT
cana-1996	146	52	−	−	NOUN
cana-1996	146	53	𝜒𝑚𝜇𝑚−1	𝜒𝑚𝜇𝑚−1	PROPN
cana-1996	146	54	(	(	PUNCT
cana-1996	146	55	υ	υ	PROPN
cana-1996	146	56	,	,	PUNCT
cana-1996	146	57	𝑡	𝑡	NOUN
cana-1996	146	58	)	)	PUNCT
cana-1996	146	59	=	=	SYM
cana-1996	147	1	ℛ−1	ℛ−1	PROPN
cana-1996	147	2	{	{	PUNCT
cana-1996	147	3	ℎℛ𝑚(𝜇𝑚−1⃗⃗	ℎℛ𝑚(𝜇𝑚−1⃗⃗	PROPN
cana-1996	147	4	⃗⃗	⃗⃗	PROPN
cana-1996	147	5	⃗⃗	⃗⃗	PROPN
cana-1996	147	6	⃗⃗	⃗⃗	PROPN
cana-1996	147	7	⃗⃗	⃗⃗	PROPN
cana-1996	147	8	(	(	PUNCT
cana-1996	147	9	υ	υ	PROPN
cana-1996	147	10	,	,	PUNCT
cana-1996	147	11	𝑡	𝑡	NOUN
cana-1996	147	12	)	)	PUNCT
cana-1996	147	13	)	)	PUNCT
cana-1996	147	14	}	}	PUNCT
cana-1996	147	15	(	(	PUNCT
cana-1996	147	16	23	23	NUM
cana-1996	147	17	)	)	PUNCT
cana-1996	147	18	with	with	ADP
cana-1996	147	19	ℎ	ℎ	PROPN
cana-1996	147	20	=	=	SYM
cana-1996	147	21	−1	−1	NOUN
cana-1996	147	22	,	,	PUNCT
cana-1996	147	23	we	we	PRON
cana-1996	147	24	can	can	AUX
cana-1996	147	25	get	get	VERB
cana-1996	147	26	from	from	ADP
cana-1996	147	27	equation	equation	NOUN
cana-1996	147	28	(	(	PUNCT
cana-1996	147	29	23	23	NUM
cana-1996	147	30	)	)	PUNCT
cana-1996	147	31	𝜇1(υ	𝜇1(υ	NUM
cana-1996	147	32	,	,	PUNCT
cana-1996	147	33	𝑡	𝑡	NOUN
cana-1996	147	34	)	)	PUNCT
cana-1996	147	35	=	=	SYM
cana-1996	147	36	−ℛ−1{ℛ1	−ℛ−1{ℛ1	X
cana-1996	147	37	(	(	PUNCT
cana-1996	147	38	𝜇0⃗⃗⃗⃗	𝜇0⃗⃗⃗⃗	PROPN
cana-1996	147	39	(	(	PUNCT
cana-1996	147	40	υ	υ	PROPN
cana-1996	147	41	,	,	PUNCT
cana-1996	147	42	𝑡	𝑡	NOUN
cana-1996	147	43	)	)	PUNCT
cana-1996	147	44	)	)	PUNCT
cana-1996	147	45	}	}	PUNCT
cana-1996	147	46	,	,	PUNCT
cana-1996	147	47	𝜇2(υ	𝜇2(υ	NOUN
cana-1996	147	48	,	,	PUNCT
cana-1996	147	49	𝑡	𝑡	X
cana-1996	147	50	)	)	PUNCT
cana-1996	147	51	=	=	SYM
cana-1996	147	52	𝜇1(υ	𝜇1(υ	PROPN
cana-1996	147	53	,	,	PUNCT
cana-1996	147	54	𝑡	𝑡	NOUN
cana-1996	147	55	)	)	PUNCT
cana-1996	147	56	−	−	PROPN
cana-1996	147	57	ℛ−1	ℛ−1	PROPN
cana-1996	147	58	{	{	PUNCT
cana-1996	147	59	ℛ2(𝜇1⃗⃗⃗⃗	ℛ2(𝜇1⃗⃗⃗⃗	X
cana-1996	147	60	(	(	PUNCT
cana-1996	147	61	υ	υ	NOUN
cana-1996	147	62	,	,	PUNCT
cana-1996	147	63	𝑡	𝑡	NOUN
cana-1996	147	64	)	)	PUNCT
cana-1996	147	65	)	)	PUNCT
cana-1996	147	66	}	}	PUNCT
cana-1996	147	67	,	,	PUNCT
cana-1996	147	68	𝜇3(υ	𝜇3(υ	PROPN
cana-1996	147	69	,	,	PUNCT
cana-1996	147	70	𝑡	𝑡	NOUN
cana-1996	147	71	)	)	PUNCT
cana-1996	147	72	=	=	SYM
cana-1996	148	1	𝜇2(υ	𝜇2(υ	PROPN
cana-1996	148	2	,	,	PUNCT
cana-1996	148	3	𝑡	𝑡	NOUN
cana-1996	148	4	)	)	PUNCT
cana-1996	148	5	−	−	PROPN
cana-1996	149	1	ℛ−1	ℛ−1	PROPN
cana-1996	149	2	{	{	PUNCT
cana-1996	149	3	ℛ3(𝜇2⃗⃗⃗⃗	ℛ3(𝜇2⃗⃗⃗⃗	X
cana-1996	149	4	(	(	PUNCT
cana-1996	149	5	υ	υ	NOUN
cana-1996	149	6	,	,	PUNCT
cana-1996	149	7	𝑡	𝑡	NOUN
cana-1996	149	8	)	)	PUNCT
cana-1996	149	9	)	)	PUNCT
cana-1996	149	10	}	}	PUNCT
cana-1996	149	11	,	,	PUNCT
cana-1996	149	12	⋮	⋮	NOUN
cana-1996	149	13	where	where	SCONJ
cana-1996	149	14	”	"	PUNCT
cana-1996	149	15	ℛ1(𝜇0⃗⃗⃗⃗	ℛ1(𝜇0⃗⃗⃗⃗	X
cana-1996	149	16	(	(	PUNCT
cana-1996	149	17	υ	υ	NOUN
cana-1996	149	18	,	,	PUNCT
cana-1996	149	19	𝑡	𝑡	NOUN
cana-1996	149	20	)	)	PUNCT
cana-1996	149	21	)	)	PUNCT
cana-1996	150	1	=	=	PRON
cana-1996	150	2	(	(	PUNCT
cana-1996	150	3	𝜋	𝜋	NOUN
cana-1996	150	4	𝜛3	𝜛3	PROPN
cana-1996	150	5	−	−	PROPN
cana-1996	150	6	𝜋2	𝜋2	PROPN
cana-1996	150	7	𝜛4	𝜛4	NOUN
cana-1996	150	8	)	)	PUNCT
cana-1996	150	9	sin	sin	NOUN
cana-1996	150	10	(	(	PUNCT
cana-1996	150	11	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	150	12	)	)	PUNCT
cana-1996	150	13	sin	sin	NOUN
cana-1996	150	14	(	(	PUNCT
cana-1996	150	15	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	150	16	)	)	PUNCT
cana-1996	150	17	sin	sin	NOUN
cana-1996	150	18	(	(	PUNCT
cana-1996	150	19	𝜋𝑧	𝜋𝑧	NOUN
cana-1996	150	20	)	)	PUNCT
cana-1996	150	21	,	,	PUNCT
cana-1996	150	22	ℛ2(𝜇1⃗⃗⃗⃗	ℛ2(𝜇1⃗⃗⃗⃗	X
cana-1996	150	23	(	(	PUNCT
cana-1996	150	24	υ	υ	NOUN
cana-1996	150	25	,	,	PUNCT
cana-1996	150	26	𝑡	𝑡	NOUN
cana-1996	150	27	)	)	PUNCT
cana-1996	150	28	)	)	PUNCT
cana-1996	151	1	=	=	PRON
cana-1996	151	2	(	(	PUNCT
cana-1996	151	3	−	−	PROPN
cana-1996	151	4	𝜋	𝜋	NUM
cana-1996	151	5	𝜛3	𝜛3	PROPN
cana-1996	151	6	+	+	CCONJ
cana-1996	151	7	𝜋2	𝜋2	PROPN
cana-1996	151	8	𝜛4	𝜛4	NOUN
cana-1996	151	9	+	+	CCONJ
cana-1996	151	10	𝜋3	𝜋3	NOUN
cana-1996	151	11	𝜛5	𝜛5	VERB
cana-1996	151	12	−	−	PROPN
cana-1996	151	13	𝜋4	𝜋4	PROPN
cana-1996	151	14	𝜛6	𝜛6	PROPN
cana-1996	151	15	)	)	PUNCT
cana-1996	151	16	sin	sin	NOUN
cana-1996	151	17	(	(	PUNCT
cana-1996	151	18	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	151	19	)	)	PUNCT
cana-1996	151	20	sin	sin	NOUN
cana-1996	151	21	(	(	PUNCT
cana-1996	151	22	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	151	23	)	)	PUNCT
cana-1996	151	24	sin	sin	NOUN
cana-1996	151	25	(	(	PUNCT
cana-1996	151	26	𝜋𝑧	𝜋𝑧	PROPN
cana-1996	151	27	)	)	PUNCT
cana-1996	151	28	,	,	PUNCT
cana-1996	151	29	ℛ3(𝜇2⃗⃗⃗⃗	ℛ3(𝜇2⃗⃗⃗⃗	X
cana-1996	151	30	(	(	PUNCT
cana-1996	151	31	υ	υ	NOUN
cana-1996	151	32	,	,	PUNCT
cana-1996	151	33	𝑡	𝑡	NOUN
cana-1996	151	34	)	)	PUNCT
cana-1996	151	35	)	)	PUNCT
cana-1996	152	1	=	=	PRON
cana-1996	152	2	(	(	PUNCT
cana-1996	152	3	−	−	NOUN
cana-1996	152	4	𝜋3	𝜋3	NOUN
cana-1996	152	5	𝜛5	𝜛5	VERB
cana-1996	153	1	+	+	CCONJ
cana-1996	153	2	𝜋4	𝜋4	PROPN
cana-1996	153	3	𝜛6	𝜛6	PROPN
cana-1996	153	4	+	+	CCONJ
cana-1996	153	5	𝜋5	𝜋5	NOUN
cana-1996	153	6	𝜛7	𝜛7	NOUN
cana-1996	153	7	−	−	PROPN
cana-1996	153	8	𝜋6	𝜋6	PROPN
cana-1996	153	9	𝜛8	𝜛8	PROPN
cana-1996	153	10	)	)	PUNCT
cana-1996	153	11	sin	sin	NOUN
cana-1996	153	12	(	(	PUNCT
cana-1996	153	13	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	153	14	)	)	PUNCT
cana-1996	153	15	sin	sin	NOUN
cana-1996	153	16	(	(	PUNCT
cana-1996	153	17	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	153	18	)	)	PUNCT
cana-1996	153	19	sin	sin	NOUN
cana-1996	153	20	(	(	PUNCT
cana-1996	153	21	𝜋𝑧	𝜋𝑧	NOUN
cana-1996	153	22	)	)	PUNCT
cana-1996	153	23	,	,	PUNCT
cana-1996	153	24	⋮	⋮	NOUN
cana-1996	153	25	consequently	consequently	ADV
cana-1996	153	26	,	,	PUNCT
cana-1996	153	27	communications	communication	NOUN
cana-1996	153	28	on	on	ADP
cana-1996	153	29	applied	apply	VERB
cana-1996	153	30	nonlinear	nonlinear	ADJ
cana-1996	153	31	analysis	analysis	NOUN
cana-1996	153	32	issn	issn	NOUN
cana-1996	153	33	:	:	PUNCT
cana-1996	153	34	1074	1074	NUM
cana-1996	153	35	-	-	PUNCT
cana-1996	153	36	133x	133x	NUM
cana-1996	153	37	vol	vol	NOUN
cana-1996	153	38	32	32	NUM
cana-1996	153	39	no	no	NOUN
cana-1996	153	40	.	.	NOUN
cana-1996	153	41	3	3	NUM
cana-1996	153	42	(	(	PUNCT
cana-1996	153	43	2025	2025	NUM
cana-1996	153	44	)	)	PUNCT
cana-1996	153	45	391	391	NUM
cana-1996	153	46	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	153	47	𝜇1(υ	𝜇1(υ	PROPN
cana-1996	153	48	,	,	PUNCT
cana-1996	153	49	𝑡	𝑡	NOUN
cana-1996	153	50	)	)	PUNCT
cana-1996	153	51	=	=	PUNCT
cana-1996	153	52	(	(	PUNCT
cana-1996	153	53	𝜋𝑡	𝜋𝑡	VERB
cana-1996	153	54	+	+	X
cana-1996	153	55	(	(	PUNCT
cana-1996	153	56	𝜋𝑡)2	𝜋𝑡)2	PROPN
cana-1996	153	57	2	2	NUM
cana-1996	153	58	!	!	PUNCT
cana-1996	153	59	)	)	PUNCT
cana-1996	153	60	sin	sin	NOUN
cana-1996	153	61	(	(	PUNCT
cana-1996	153	62	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	153	63	)	)	PUNCT
cana-1996	153	64	sin	sin	NOUN
cana-1996	153	65	(	(	PUNCT
cana-1996	153	66	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	153	67	)	)	PUNCT
cana-1996	153	68	sin	sin	NOUN
cana-1996	153	69	(	(	PUNCT
cana-1996	153	70	𝜋𝑧	𝜋𝑧	NOUN
cana-1996	153	71	)	)	PUNCT
cana-1996	153	72	,	,	PUNCT
cana-1996	153	73	𝜇2(υ	𝜇2(υ	PROPN
cana-1996	153	74	,	,	PUNCT
cana-1996	153	75	𝑡	𝑡	PROPN
cana-1996	153	76	)	)	PUNCT
cana-1996	153	77	=	=	SYM
cana-1996	153	78	(	(	PUNCT
cana-1996	153	79	(	(	PUNCT
cana-1996	153	80	𝜋𝑡)3	𝜋𝑡)3	NOUN
cana-1996	153	81	3	3	NUM
cana-1996	153	82	!	!	PUNCT
cana-1996	154	1	+	+	CCONJ
cana-1996	154	2	(	(	PUNCT
cana-1996	154	3	𝜋𝑡)4	𝜋𝑡)4	NOUN
cana-1996	154	4	4	4	NUM
cana-1996	154	5	!	!	PUNCT
cana-1996	154	6	)	)	PUNCT
cana-1996	154	7	sin	sin	NOUN
cana-1996	154	8	(	(	PUNCT
cana-1996	154	9	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	154	10	)	)	PUNCT
cana-1996	154	11	sin	sin	NOUN
cana-1996	154	12	(	(	PUNCT
cana-1996	154	13	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	154	14	)	)	PUNCT
cana-1996	154	15	sin	sin	NOUN
cana-1996	154	16	(	(	PUNCT
cana-1996	154	17	𝜋𝑧	𝜋𝑧	NOUN
cana-1996	154	18	)	)	PUNCT
cana-1996	154	19	𝜇3(υ	𝜇3(υ	PROPN
cana-1996	154	20	,	,	PUNCT
cana-1996	154	21	𝑡	𝑡	PROPN
cana-1996	154	22	)	)	PUNCT
cana-1996	154	23	=	=	SYM
cana-1996	154	24	(	(	PUNCT
cana-1996	154	25	(	(	PUNCT
cana-1996	154	26	𝜋𝑡)5	𝜋𝑡)5	PROPN
cana-1996	154	27	5	5	NUM
cana-1996	154	28	!	!	PUNCT
cana-1996	155	1	+	+	CCONJ
cana-1996	155	2	(	(	PUNCT
cana-1996	155	3	𝜋𝑡)6	𝜋𝑡)6	X
cana-1996	155	4	6	6	NUM
cana-1996	155	5	!	!	PUNCT
cana-1996	155	6	)	)	PUNCT
cana-1996	155	7	sin	sin	NOUN
cana-1996	155	8	(	(	PUNCT
cana-1996	155	9	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	155	10	)	)	PUNCT
cana-1996	155	11	sin	sin	NOUN
cana-1996	155	12	(	(	PUNCT
cana-1996	155	13	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	155	14	)	)	PUNCT
cana-1996	155	15	sin	sin	NOUN
cana-1996	155	16	(	(	PUNCT
cana-1996	155	17	𝜋𝑧	𝜋𝑧	NOUN
cana-1996	155	18	)	)	PUNCT
cana-1996	155	19	⋮	⋮	NOUN
cana-1996	155	20	consequently	consequently	ADV
cana-1996	155	21	,	,	PUNCT
cana-1996	155	22	the	the	DET
cana-1996	155	23	solution	solution	NOUN
cana-1996	155	24	is	be	AUX
cana-1996	155	25	:	:	PUNCT
cana-1996	155	26	𝜇(υ	𝜇(υ	NOUN
cana-1996	155	27	,	,	PUNCT
cana-1996	155	28	𝑡	𝑡	NOUN
cana-1996	155	29	)	)	PUNCT
cana-1996	155	30	=	=	SYM
cana-1996	155	31	𝜇0	𝜇0	PROPN
cana-1996	155	32	+	+	CCONJ
cana-1996	155	33	𝜇1	𝜇1	PROPN
cana-1996	155	34	+	+	CCONJ
cana-1996	155	35	𝜇2	𝜇2	PROPN
cana-1996	155	36	+	+	SYM
cana-1996	155	37	⋯	⋯	PROPN
cana-1996	155	38	or	or	CCONJ
cana-1996	155	39	𝜇(υ	𝜇(υ	PROPN
cana-1996	155	40	,	,	PUNCT
cana-1996	155	41	𝑡	𝑡	NOUN
cana-1996	155	42	)	)	PUNCT
cana-1996	155	43	=	=	SYM
cana-1996	155	44	{	{	PUNCT
cana-1996	155	45	1	1	NUM
cana-1996	155	46	+	+	NUM
cana-1996	155	47	𝜋𝑡	𝜋𝑡	NOUN
cana-1996	155	48	+	+	CCONJ
cana-1996	155	49	(	(	PUNCT
cana-1996	155	50	𝜋𝑡)2	𝜋𝑡)2	PROPN
cana-1996	155	51	2	2	NUM
cana-1996	155	52	!	!	PUNCT
cana-1996	156	1	+	+	CCONJ
cana-1996	156	2	(	(	PUNCT
cana-1996	156	3	𝜋𝑡)3	𝜋𝑡)3	NOUN
cana-1996	156	4	3	3	NUM
cana-1996	156	5	!	!	PUNCT
cana-1996	157	1	+	+	CCONJ
cana-1996	157	2	(	(	PUNCT
cana-1996	157	3	𝜋𝑡)4	𝜋𝑡)4	NOUN
cana-1996	157	4	4	4	NUM
cana-1996	157	5	!	!	PUNCT
cana-1996	157	6	}	}	PUNCT
cana-1996	157	7	sin	sin	NOUN
cana-1996	157	8	(	(	PUNCT
cana-1996	157	9	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	157	10	)	)	PUNCT
cana-1996	157	11	sin	sin	NOUN
cana-1996	157	12	(	(	PUNCT
cana-1996	157	13	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	157	14	)	)	PUNCT
cana-1996	157	15	sin	sin	NOUN
cana-1996	157	16	(	(	PUNCT
cana-1996	157	17	𝜋𝑧	𝜋𝑧	NOUN
cana-1996	157	18	)	)	PUNCT
cana-1996	157	19	or	or	CCONJ
cana-1996	157	20	𝜇(υ	𝜇(υ	PROPN
cana-1996	157	21	,	,	PUNCT
cana-1996	157	22	𝑡	𝑡	NOUN
cana-1996	157	23	)	)	PUNCT
cana-1996	157	24	=	=	SYM
cana-1996	157	25	𝑒𝜋𝑡	𝑒𝜋𝑡	NOUN
cana-1996	157	26	sin	sin	NOUN
cana-1996	157	27	(	(	PUNCT
cana-1996	157	28	𝜋𝑥	𝜋𝑥	NOUN
cana-1996	157	29	)	)	PUNCT
cana-1996	157	30	sin	sin	NOUN
cana-1996	157	31	(	(	PUNCT
cana-1996	157	32	𝜋𝑦	𝜋𝑦	INTJ
cana-1996	157	33	)	)	PUNCT
cana-1996	157	34	sin	sin	NOUN
cana-1996	157	35	(	(	PUNCT
cana-1996	157	36	𝜋𝑧	𝜋𝑧	NOUN
cana-1996	157	37	)	)	PUNCT
cana-1996	157	38	figure	figure	NOUN
cana-1996	157	39	1	1	NUM
cana-1996	157	40	:	:	PUNCT
cana-1996	157	41	example	example	NOUN
cana-1996	157	42	1	1	NUM
cana-1996	157	43	's	's	PART
cana-1996	157	44	solutions	solution	NOUN
cana-1996	157	45	'	'	PART
cana-1996	157	46	physical	physical	ADJ
cana-1996	157	47	behavior	behavior	NOUN
cana-1996	157	48	at	at	ADP
cana-1996	157	49	𝒕	𝒕	NOUN
cana-1996	157	50	=	=	SYM
cana-1996	157	51	𝟏	𝟏	NUM
cana-1996	157	52	,	,	PUNCT
cana-1996	157	53	𝒛	𝒛	NOUN
cana-1996	157	54	=	=	SYM
cana-1996	157	55	𝟏	𝟏	PROPN
cana-1996	157	56	𝟐	𝟐	NUM
cana-1996	157	57	-1	-1	SYM
cana-1996	157	58	-0.5	-0.5	X
cana-1996	157	59	0	0	NUM
cana-1996	157	60	0.5	0.5	NUM
cana-1996	157	61	1	1	NUM
cana-1996	157	62	-1	-1	SYM
cana-1996	157	63	0	0	NUM
cana-1996	157	64	1	1	NUM
cana-1996	157	65	-40	-40	NUM
cana-1996	157	66	-20	-20	NUM
cana-1996	157	67	0	0	NUM
cana-1996	157	68	20	20	NUM
cana-1996	157	69	40	40	NUM
cana-1996	157	70	x	x	NOUN
cana-1996	157	71	example	example	NOUN
cana-1996	157	72	1	1	NUM
cana-1996	157	73	:	:	PUNCT
cana-1996	157	74	for	for	ADP
cana-1996	157	75	t	t	NOUN
cana-1996	157	76	=	=	SYM
cana-1996	157	77	1	1	NUM
cana-1996	157	78	y	y	PROPN
cana-1996	157	79	s	s	PART
cana-1996	157	80	o	o	X
cana-1996	157	81	lu	lu	NOUN
cana-1996	157	82	ti	ti	NOUN
cana-1996	157	83	o	o	NOUN
cana-1996	157	84	n	n	NOUN
cana-1996	157	85	s	s	PROPN
cana-1996	157	86	communications	communication	NOUN
cana-1996	157	87	on	on	ADP
cana-1996	157	88	applied	apply	VERB
cana-1996	157	89	nonlinear	nonlinear	ADJ
cana-1996	157	90	analysis	analysis	NOUN
cana-1996	157	91	issn	issn	NOUN
cana-1996	157	92	:	:	PUNCT
cana-1996	157	93	1074	1074	NUM
cana-1996	157	94	-	-	PUNCT
cana-1996	157	95	133x	133x	NUM
cana-1996	157	96	vol	vol	NOUN
cana-1996	157	97	32	32	NUM
cana-1996	157	98	no	no	NOUN
cana-1996	157	99	.	.	NOUN
cana-1996	157	100	3	3	NUM
cana-1996	157	101	(	(	PUNCT
cana-1996	157	102	2025	2025	NUM
cana-1996	157	103	)	)	PUNCT
cana-1996	157	104	392	392	NUM
cana-1996	157	105	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	157	106	figure	figure	NOUN
cana-1996	157	107	2	2	NUM
cana-1996	157	108	:	:	PUNCT
cana-1996	157	109	the	the	DET
cana-1996	157	110	contour	contour	NOUN
cana-1996	157	111	diagram	diagram	NOUN
cana-1996	157	112	obtained	obtain	VERB
cana-1996	157	113	from	from	ADP
cana-1996	157	114	solving	solve	VERB
cana-1996	157	115	example	example	NOUN
cana-1996	157	116	1	1	NUM
cana-1996	157	117	at	at	ADP
cana-1996	157	118	𝒕	𝒕	NOUN
cana-1996	157	119	=	=	SYM
cana-1996	157	120	𝟏	𝟏	NUM
cana-1996	157	121	,	,	PUNCT
cana-1996	157	122	𝒛	𝒛	NOUN
cana-1996	157	123	=	=	SYM
cana-1996	157	124	𝟏	𝟏	NUM
cana-1996	157	125	𝟐	𝟐	NUM
cana-1996	157	126	figures	figure	NOUN
cana-1996	157	127	1	1	NUM
cana-1996	157	128	and	and	CCONJ
cana-1996	157	129	2	2	NUM
cana-1996	157	130	depict	depict	NOUN
cana-1996	157	131	the	the	DET
cana-1996	157	132	physical	physical	ADJ
cana-1996	157	133	and	and	CCONJ
cana-1996	157	134	dynamic	dynamic	ADJ
cana-1996	157	135	behaviour	behaviour	NOUN
cana-1996	157	136	of	of	ADP
cana-1996	157	137	the	the	DET
cana-1996	157	138	solutions	solution	NOUN
cana-1996	157	139	found	find	VERB
cana-1996	157	140	at	at	ADP
cana-1996	157	141	𝑧	𝑧	NOUN
cana-1996	157	142	=	=	SYM
cana-1996	157	143	1	1	NUM
cana-1996	157	144	2	2	NUM
cana-1996	157	145	and	and	CCONJ
cana-1996	157	146	𝑡	𝑡	NOUN
cana-1996	157	147	=	=	NOUN
cana-1996	157	148	1	1	NUM
cana-1996	157	149	using	use	VERB
cana-1996	157	150	the	the	DET
cana-1996	157	151	"	"	PUNCT
cana-1996	157	152	homotopy	homotopy	VERB
cana-1996	157	153	analysis	analysis	NOUN
cana-1996	157	154	method	method	NOUN
cana-1996	157	155	"	"	PUNCT
cana-1996	157	156	based	base	VERB
cana-1996	157	157	on	on	ADP
cana-1996	157	158	the	the	DET
cana-1996	157	159	"	"	PUNCT
cana-1996	157	160	rangaig	rangaig	ADJ
cana-1996	157	161	transform	transform	NOUN
cana-1996	157	162	.	.	PUNCT
cana-1996	157	163	"	"	PUNCT
cana-1996	157	164	example	example	NOUN
cana-1996	158	1	2	2	NUM
cana-1996	158	2	:	:	PUNCT
cana-1996	158	3	consider	consider	VERB
cana-1996	158	4	the	the	DET
cana-1996	158	5	(	(	PUNCT
cana-1996	158	6	3	3	NUM
cana-1996	158	7	+	+	SYM
cana-1996	158	8	1)-d	1)-d	NUM
cana-1996	158	9	diffusion	diffusion	NOUN
cana-1996	158	10	equation	equation	NOUN
cana-1996	158	11	of	of	ADP
cana-1996	158	12	the	the	DET
cana-1996	158	13	form	form	NOUN
cana-1996	158	14	:	:	PUNCT
cana-1996	158	15	𝜇𝑡	𝜇𝑡	NOUN
cana-1996	158	16	=	=	SYM
cana-1996	158	17	1	1	NUM
cana-1996	158	18	3𝜋2	3𝜋2	NUM
cana-1996	158	19	(	(	PUNCT
cana-1996	158	20	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	158	21	+	+	CCONJ
cana-1996	158	22	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	158	23	+	+	CCONJ
cana-1996	158	24	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	158	25	)	)	PUNCT
cana-1996	158	26	(	(	PUNCT
cana-1996	158	27	24	24	NUM
cana-1996	158	28	)	)	PUNCT
cana-1996	158	29	with	with	ADP
cana-1996	158	30	initial	initial	ADJ
cana-1996	158	31	condition	condition	NOUN
cana-1996	158	32	𝜇(υ	𝜇(υ	NOUN
cana-1996	158	33	,	,	PUNCT
cana-1996	158	34	0	0	NUM
cana-1996	158	35	)	)	PUNCT
cana-1996	158	36	=	=	SYM
cana-1996	158	37	𝑒−𝑡	𝑒−𝑡	PROPN
cana-1996	158	38	sin	sin	VERB
cana-1996	158	39	𝜋𝑥	𝜋𝑥	PROPN
cana-1996	158	40	sin𝜋𝑦	sin𝜋𝑦	PROPN
cana-1996	158	41	sin	sin	PROPN
cana-1996	158	42	𝜋𝑧	𝜋𝑧	PROPN
cana-1996	158	43	,	,	PUNCT
cana-1996	158	44	we	we	PRON
cana-1996	158	45	use	use	VERB
cana-1996	158	46	υ	υ	NOUN
cana-1996	158	47	=	=	PUNCT
cana-1996	158	48	(	(	PUNCT
cana-1996	158	49	𝑥	𝑥	PROPN
cana-1996	158	50	,	,	PUNCT
cana-1996	158	51	𝑦	𝑦	NOUN
cana-1996	158	52	,	,	PUNCT
cana-1996	158	53	𝑧	𝑧	PART
cana-1996	158	54	)	)	PUNCT
cana-1996	158	55	,	,	PUNCT
cana-1996	158	56	the	the	DET
cana-1996	158	57	exact	exact	ADJ
cana-1996	158	58	solution	solution	NOUN
cana-1996	158	59	is	be	AUX
cana-1996	158	60	:	:	PUNCT
cana-1996	158	61	𝜇(υ	𝜇(υ	NOUN
cana-1996	158	62	,	,	PUNCT
cana-1996	158	63	𝑡	𝑡	NOUN
cana-1996	158	64	)	)	PUNCT
cana-1996	158	65	=	=	SYM
cana-1996	158	66	𝑒−𝑡	𝑒−𝑡	PROPN
cana-1996	158	67	sin	sin	VERB
cana-1996	158	68	𝜋𝑥	𝜋𝑥	PROPN
cana-1996	158	69	sin𝜋𝑦	sin𝜋𝑦	PROPN
cana-1996	158	70	sin	sin	NOUN
cana-1996	158	71	𝜋𝑧	𝜋𝑧	ADP
cana-1996	158	72	applying	apply	VERB
cana-1996	158	73	the	the	DET
cana-1996	158	74	“	"	PUNCT
cana-1996	158	75	rangaig	rangaig	ADJ
cana-1996	158	76	transform	transform	NOUN
cana-1996	158	77	”	"	PUNCT
cana-1996	158	78	to	to	ADP
cana-1996	158	79	both	both	DET
cana-1996	158	80	sides	side	NOUN
cana-1996	158	81	of	of	ADP
cana-1996	158	82	equation	equation	NOUN
cana-1996	158	83	(	(	PUNCT
cana-1996	158	84	24	24	NUM
cana-1996	158	85	)	)	PUNCT
cana-1996	158	86	,	,	PUNCT
cana-1996	158	87	we	we	PRON
cana-1996	158	88	obtain	obtain	VERB
cana-1996	158	89	,	,	PUNCT
cana-1996	158	90	ℛ[𝜇𝑡	ℛ[𝜇𝑡	PROPN
cana-1996	158	91	]	]	X
cana-1996	158	92	=	=	SYM
cana-1996	158	93	ℛ	ℛ	PROPN
cana-1996	158	94	[	[	PUNCT
cana-1996	158	95	1	1	NUM
cana-1996	158	96	3𝜋2	3𝜋2	NUM
cana-1996	158	97	(	(	PUNCT
cana-1996	158	98	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	158	99	+	+	CCONJ
cana-1996	158	100	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	158	101	+	+	CCONJ
cana-1996	158	102	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	158	103	)	)	PUNCT
cana-1996	158	104	]	]	PUNCT
cana-1996	159	1	this	this	PRON
cana-1996	159	2	implies	imply	VERB
cana-1996	159	3	(	(	PUNCT
cana-1996	159	4	−1)𝜛	−1)𝜛	X
cana-1996	159	5	ℛ[𝜇	ℛ[𝜇	X
cana-1996	159	6	]	]	X
cana-1996	160	1	+	+	CCONJ
cana-1996	160	2	1	1	NUM
cana-1996	160	3	𝜛	𝜛	X
cana-1996	160	4	𝜇	𝜇	X
cana-1996	160	5	(	(	PUNCT
cana-1996	160	6	υ	υ	NOUN
cana-1996	160	7	,	,	PUNCT
cana-1996	160	8	0	0	NUM
cana-1996	160	9	)	)	PUNCT
cana-1996	160	10	=	=	SYM
cana-1996	160	11	ℛ	ℛ	PROPN
cana-1996	160	12	[	[	PUNCT
cana-1996	160	13	1	1	NUM
cana-1996	160	14	3𝜋2	3𝜋2	NUM
cana-1996	160	15	(	(	PUNCT
cana-1996	160	16	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	160	17	+	+	CCONJ
cana-1996	160	18	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	160	19	+	+	CCONJ
cana-1996	160	20	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	160	21	)	)	PUNCT
cana-1996	160	22	]	]	PUNCT
cana-1996	160	23	.	.	PUNCT
cana-1996	161	1	this	this	PRON
cana-1996	161	2	implies	imply	VERB
cana-1996	161	3	ℛ[𝜇	ℛ[𝜇	X
cana-1996	161	4	]	]	X
cana-1996	161	5	−	−	PROPN
cana-1996	161	6	1	1	NUM
cana-1996	161	7	𝜛2	𝜛2	NOUN
cana-1996	161	8	𝜇	𝜇	X
cana-1996	161	9	(	(	PUNCT
cana-1996	161	10	υ	υ	NOUN
cana-1996	161	11	,	,	PUNCT
cana-1996	161	12	0	0	NUM
cana-1996	161	13	)	)	PUNCT
cana-1996	161	14	=	=	SYM
cana-1996	162	1	−	−	PROPN
cana-1996	162	2	1	1	NUM
cana-1996	162	3	𝜛	𝜛	PROPN
cana-1996	162	4	ℛ	ℛ	PROPN
cana-1996	162	5	[	[	PUNCT
cana-1996	162	6	1	1	NUM
cana-1996	162	7	3𝜋2	3𝜋2	NUM
cana-1996	162	8	(	(	PUNCT
cana-1996	162	9	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	162	10	+	+	CCONJ
cana-1996	162	11	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	162	12	+	+	CCONJ
cana-1996	162	13	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	162	14	)	)	PUNCT
cana-1996	162	15	]	]	PUNCT
cana-1996	163	1	when	when	SCONJ
cana-1996	163	2	starting	start	VERB
cana-1996	163	3	conditions	condition	NOUN
cana-1996	163	4	are	be	AUX
cana-1996	163	5	applied	apply	VERB
cana-1996	163	6	,	,	PUNCT
cana-1996	163	7	we	we	PRON
cana-1996	163	8	get	get	VERB
cana-1996	163	9	ℛ[𝜇	ℛ[𝜇	PRON
cana-1996	163	10	]	]	X
cana-1996	163	11	=	=	SYM
cana-1996	163	12	1	1	NUM
cana-1996	163	13	𝜛2	𝜛2	NOUN
cana-1996	163	14	sin	sin	NOUN
cana-1996	163	15	𝜋𝑥	𝜋𝑥	PROPN
cana-1996	163	16	sin𝜋𝑦	sin𝜋𝑦	PROPN
cana-1996	163	17	sin	sin	NOUN
cana-1996	163	18	𝜋𝑧	𝜋𝑧	ADP
cana-1996	163	19	−	−	NUM
cana-1996	163	20	1	1	NUM
cana-1996	163	21	𝜛	𝜛	PROPN
cana-1996	163	22	ℛ	ℛ	PROPN
cana-1996	163	23	[	[	PUNCT
cana-1996	163	24	1	1	NUM
cana-1996	163	25	3𝜋2	3𝜋2	NUM
cana-1996	163	26	(	(	PUNCT
cana-1996	163	27	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	163	28	+	+	CCONJ
cana-1996	163	29	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	163	30	+	+	CCONJ
cana-1996	163	31	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	163	32	)	)	PUNCT
cana-1996	163	33	]	]	PUNCT
cana-1996	164	1	x	x	PUNCT
cana-1996	164	2	y	y	PROPN
cana-1996	164	3	example	example	NOUN
cana-1996	164	4	1	1	NUM
cana-1996	164	5	:	:	PUNCT
cana-1996	164	6	for	for	ADP
cana-1996	164	7	t	t	NOUN
cana-1996	164	8	=	=	SYM
cana-1996	164	9	1	1	NUM
cana-1996	164	10	-1	-1	SYM
cana-1996	164	11	-0.5	-0.5	X
cana-1996	164	12	0	0	NUM
cana-1996	164	13	0.5	0.5	NUM
cana-1996	164	14	1	1	NUM
cana-1996	164	15	-1	-1	SYM
cana-1996	164	16	-0.5	-0.5	X
cana-1996	164	17	0	0	NUM
cana-1996	164	18	0.5	0.5	NUM
cana-1996	164	19	1	1	NUM
cana-1996	164	20	communications	communication	NOUN
cana-1996	164	21	on	on	ADP
cana-1996	164	22	applied	apply	VERB
cana-1996	164	23	nonlinear	nonlinear	ADJ
cana-1996	164	24	analysis	analysis	NOUN
cana-1996	164	25	issn	issn	NOUN
cana-1996	164	26	:	:	PUNCT
cana-1996	164	27	1074	1074	NUM
cana-1996	164	28	-	-	PUNCT
cana-1996	164	29	133x	133x	NUM
cana-1996	164	30	vol	vol	NOUN
cana-1996	164	31	32	32	NUM
cana-1996	164	32	no	no	NOUN
cana-1996	164	33	.	.	NOUN
cana-1996	164	34	3	3	NUM
cana-1996	164	35	(	(	PUNCT
cana-1996	164	36	2025	2025	NUM
cana-1996	164	37	)	)	PUNCT
cana-1996	164	38	393	393	NUM
cana-1996	164	39	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	164	40	here	here	ADV
cana-1996	164	41	is	be	AUX
cana-1996	164	42	how	how	SCONJ
cana-1996	164	43	we	we	PRON
cana-1996	164	44	define	define	VERB
cana-1996	164	45	the	the	DET
cana-1996	164	46	nonlinear	nonlinear	ADJ
cana-1996	164	47	component	component	NOUN
cana-1996	164	48	:	:	PUNCT
cana-1996	164	49	𝒩[𝛿(υ	𝒩[𝛿(υ	NOUN
cana-1996	164	50	,	,	PUNCT
cana-1996	164	51	𝑡	𝑡	X
cana-1996	164	52	;	;	PUNCT
cana-1996	164	53	𝓅	𝓅	NOUN
cana-1996	164	54	)	)	PUNCT
cana-1996	164	55	]	]	PUNCT
cana-1996	165	1	=	=	PUNCT
cana-1996	165	2	ℛ[𝜇	ℛ[𝜇	PROPN
cana-1996	165	3	]	]	X
cana-1996	165	4	−	−	PROPN
cana-1996	165	5	1	1	NUM
cana-1996	165	6	𝜛2	𝜛2	PROPN
cana-1996	165	7	sin	sin	NOUN
cana-1996	165	8	𝜋𝑥	𝜋𝑥	PROPN
cana-1996	165	9	sin𝜋𝑦	sin𝜋𝑦	PROPN
cana-1996	165	10	sin	sin	VERB
cana-1996	165	11	𝜋𝑧	𝜋𝑧	ADP
cana-1996	165	12	+	+	NUM
cana-1996	165	13	1	1	NUM
cana-1996	165	14	𝜛	𝜛	NOUN
cana-1996	165	15	ℛ	ℛ	PROPN
cana-1996	165	16	[	[	PUNCT
cana-1996	165	17	1	1	NUM
cana-1996	165	18	3𝜋2	3𝜋2	NUM
cana-1996	165	19	(	(	PUNCT
cana-1996	165	20	𝜇𝑥𝑥	𝜇𝑥𝑥	NOUN
cana-1996	165	21	+	+	CCONJ
cana-1996	165	22	𝜇𝑦𝑦	𝜇𝑦𝑦	PROPN
cana-1996	165	23	+	+	CCONJ
cana-1996	165	24	𝜇𝑧𝑧	𝜇𝑧𝑧	NOUN
cana-1996	165	25	)	)	PUNCT
cana-1996	165	26	]	]	PUNCT
cana-1996	166	1	(	(	PUNCT
cana-1996	166	2	25	25	NUM
cana-1996	166	3	)	)	PUNCT
cana-1996	166	4	we	we	PRON
cana-1996	166	5	begin	begin	VERB
cana-1996	166	6	by	by	ADP
cana-1996	166	7	setting	set	VERB
cana-1996	166	8	up	up	ADP
cana-1996	166	9	the	the	DET
cana-1996	166	10	0	0	NUM
cana-1996	166	11	-	-	PUNCT
cana-1996	166	12	order	order	NOUN
cana-1996	166	13	deformation	deformation	NOUN
cana-1996	166	14	according	accord	VERB
cana-1996	166	15	to	to	ADP
cana-1996	166	16	the	the	DET
cana-1996	166	17	assumption	assumption	NOUN
cana-1996	166	18	adopted	adopt	VERB
cana-1996	166	19	herein	herein	NOUN
cana-1996	166	20	,	,	PUNCT
cana-1996	166	21	namely	namely	ADV
cana-1996	166	22	,	,	PUNCT
cana-1996	166	23	𝐻(υ	𝐻(υ	NOUN
cana-1996	166	24	,	,	PUNCT
cana-1996	166	25	𝑡	𝑡	NOUN
cana-1996	166	26	)	)	PUNCT
cana-1996	166	27	=	=	SYM
cana-1996	166	28	1	1	NUM
cana-1996	166	29	;	;	PUNCT
cana-1996	166	30	we	we	PRON
cana-1996	166	31	have	have	VERB
cana-1996	166	32	(	(	PUNCT
cana-1996	166	33	1	1	NUM
cana-1996	166	34	−	−	NOUN
cana-1996	166	35	𝓅)ℛ{𝛿(υ	𝓅)ℛ{𝛿(υ	NOUN
cana-1996	166	36	,	,	PUNCT
cana-1996	166	37	𝑡	𝑡	NOUN
cana-1996	166	38	)	)	PUNCT
cana-1996	166	39	−	−	PRON
cana-1996	166	40	𝜇0(υ	𝜇0(υ	PROPN
cana-1996	166	41	,	,	PUNCT
cana-1996	166	42	𝑡	𝑡	NOUN
cana-1996	166	43	)	)	PUNCT
cana-1996	166	44	}	}	PUNCT
cana-1996	166	45	=	=	SYM
cana-1996	166	46	𝓅ℎ𝒩[𝛿(υ	𝓅ℎ𝒩[𝛿(υ	X
cana-1996	166	47	,	,	PUNCT
cana-1996	166	48	𝑡	𝑡	NOUN
cana-1996	166	49	;	;	PUNCT
cana-1996	166	50	𝓅	𝓅	NOUN
cana-1996	166	51	)	)	PUNCT
cana-1996	166	52	]	]	PUNCT
cana-1996	166	53	when	when	SCONJ
cana-1996	166	54	𝓅	𝓅	PROPN
cana-1996	166	55	=	=	SYM
cana-1996	166	56	0	0	PROPN
cana-1996	166	57	&	&	CCONJ
cana-1996	166	58	𝓅	𝓅	NOUN
cana-1996	166	59	=	=	SYM
cana-1996	166	60	1	1	NUM
cana-1996	166	61	,	,	PUNCT
cana-1996	166	62	we	we	PRON
cana-1996	166	63	have	have	VERB
cana-1996	166	64	{	{	PUNCT
cana-1996	166	65	𝛿(υ	𝛿(υ	NOUN
cana-1996	166	66	,	,	PUNCT
cana-1996	166	67	𝑡	𝑡	X
cana-1996	166	68	;	;	PUNCT
cana-1996	166	69	0	0	NUM
cana-1996	166	70	)	)	PUNCT
cana-1996	166	71	=	=	SYM
cana-1996	166	72	𝜇0(υ	𝜇0(υ	PROPN
cana-1996	166	73	,	,	PUNCT
cana-1996	166	74	0	0	NUM
cana-1996	166	75	)	)	PUNCT
cana-1996	166	76	𝛿(υ	𝛿(υ	NOUN
cana-1996	166	77	,	,	PUNCT
cana-1996	166	78	𝑡	𝑡	NOUN
cana-1996	166	79	;	;	PUNCT
cana-1996	166	80	1	1	X
cana-1996	166	81	)	)	PUNCT
cana-1996	166	82	=	=	SYM
cana-1996	166	83	𝜇(υ	𝜇(υ	PROPN
cana-1996	166	84	,	,	PUNCT
cana-1996	166	85	𝑡	𝑡	NOUN
cana-1996	166	86	)	)	PUNCT
cana-1996	166	87	so	so	ADV
cana-1996	166	88	,	,	PUNCT
cana-1996	166	89	the	the	DET
cana-1996	166	90	mth	mth	NOUN
cana-1996	166	91	-	-	PUNCT
cana-1996	166	92	order	order	NOUN
cana-1996	166	93	deformation	deformation	NOUN
cana-1996	166	94	eqn	eqn	NOUN
cana-1996	166	95	.	.	PUNCT
cana-1996	167	1	ℛ{𝜇𝑚(υ	ℛ{𝜇𝑚(υ	PROPN
cana-1996	167	2	,	,	PUNCT
cana-1996	167	3	𝑡	𝑡	NOUN
cana-1996	167	4	)	)	PUNCT
cana-1996	167	5	−	−	NOUN
cana-1996	167	6	𝜒𝑚𝜇𝑚−1(υ	𝜒𝑚𝜇𝑚−1(υ	NUM
cana-1996	167	7	,	,	PUNCT
cana-1996	167	8	𝑡	𝑡	NOUN
cana-1996	167	9	)	)	PUNCT
cana-1996	167	10	}	}	PUNCT
cana-1996	167	11	=	=	SYM
cana-1996	167	12	ℎℛ𝑚(𝜇𝑚−1⃗⃗	ℎℛ𝑚(𝜇𝑚−1⃗⃗	NUM
cana-1996	167	13	⃗⃗	⃗⃗	PROPN
cana-1996	167	14	⃗⃗	⃗⃗	PROPN
cana-1996	167	15	⃗⃗	⃗⃗	PROPN
cana-1996	167	16	⃗⃗	⃗⃗	PROPN
cana-1996	167	17	(	(	PUNCT
cana-1996	167	18	υ	υ	PROPN
cana-1996	167	19	,	,	PUNCT
cana-1996	167	20	𝑡	𝑡	NOUN
cana-1996	167	21	)	)	PUNCT
cana-1996	167	22	)	)	PUNCT
cana-1996	167	23	(	(	PUNCT
cana-1996	167	24	26	26	NUM
cana-1996	167	25	)	)	PUNCT
cana-1996	167	26	when	when	SCONJ
cana-1996	167	27	the	the	DET
cana-1996	167	28	“	"	PUNCT
cana-1996	167	29	inverse	inverse	ADJ
cana-1996	167	30	rangaig	rangaig	ADJ
cana-1996	167	31	transform	transform	NOUN
cana-1996	167	32	”	"	PUNCT
cana-1996	167	33	is	be	AUX
cana-1996	167	34	carried	carry	VERB
cana-1996	167	35	out	out	ADP
cana-1996	167	36	to	to	ADP
cana-1996	167	37	both	both	DET
cana-1996	167	38	sides	side	NOUN
cana-1996	167	39	of	of	ADP
cana-1996	167	40	equation	equation	NOUN
cana-1996	167	41	(	(	PUNCT
cana-1996	167	42	26	26	NUM
cana-1996	167	43	)	)	PUNCT
cana-1996	167	44	,	,	PUNCT
cana-1996	167	45	we	we	PRON
cana-1996	167	46	get	get	VERB
cana-1996	167	47	,	,	PUNCT
cana-1996	167	48	𝜇𝑚(υ	𝜇𝑚(υ	NOUN
cana-1996	167	49	,	,	PUNCT
cana-1996	167	50	𝑡	𝑡	NOUN
cana-1996	167	51	)	)	PUNCT
cana-1996	167	52	−	−	NOUN
cana-1996	167	53	𝜒𝑚𝜇𝑚−1(υ	𝜒𝑚𝜇𝑚−1(υ	NUM
cana-1996	167	54	,	,	PUNCT
cana-1996	167	55	𝑡	𝑡	NOUN
cana-1996	167	56	)	)	PUNCT
cana-1996	167	57	=	=	SYM
cana-1996	168	1	ℛ−1{ℎℛ𝑚(𝜇𝑚−1⃗⃗	ℛ−1{ℎℛ𝑚(𝜇𝑚−1⃗⃗	NUM
cana-1996	168	2	⃗⃗	⃗⃗	PROPN
cana-1996	168	3	⃗⃗	⃗⃗	PROPN
cana-1996	168	4	⃗⃗	⃗⃗	PROPN
cana-1996	168	5	⃗⃗	⃗⃗	PROPN
cana-1996	168	6	(	(	PUNCT
cana-1996	168	7	υ	υ	PROPN
cana-1996	168	8	,	,	PUNCT
cana-1996	168	9	𝑡	𝑡	NOUN
cana-1996	168	10	)	)	PUNCT
cana-1996	168	11	)	)	PUNCT
cana-1996	168	12	}	}	PUNCT
cana-1996	168	13	(	(	PUNCT
cana-1996	168	14	27	27	NUM
cana-1996	168	15	)	)	PUNCT
cana-1996	168	16	with	with	ADP
cana-1996	168	17	ℎ	ℎ	PROPN
cana-1996	168	18	=	=	SYM
cana-1996	168	19	−1	−1	NOUN
cana-1996	168	20	,	,	PUNCT
cana-1996	168	21	we	we	PRON
cana-1996	168	22	can	can	AUX
cana-1996	168	23	get	get	VERB
cana-1996	168	24	from	from	ADP
cana-1996	168	25	equation	equation	NOUN
cana-1996	168	26	(	(	PUNCT
cana-1996	168	27	27	27	NUM
cana-1996	168	28	)	)	PUNCT
cana-1996	168	29	𝜇1(υ	𝜇1(υ	NUM
cana-1996	168	30	,	,	PUNCT
cana-1996	168	31	𝑡	𝑡	NOUN
cana-1996	168	32	)	)	PUNCT
cana-1996	168	33	=	=	SYM
cana-1996	168	34	−ℛ−1	−ℛ−1	NOUN
cana-1996	168	35	{	{	PUNCT
cana-1996	168	36	ℛ1(𝜇0⃗⃗⃗⃗	ℛ1(𝜇0⃗⃗⃗⃗	X
cana-1996	168	37	(	(	PUNCT
cana-1996	168	38	υ	υ	NOUN
cana-1996	168	39	,	,	PUNCT
cana-1996	168	40	𝑡	𝑡	NOUN
cana-1996	168	41	)	)	PUNCT
cana-1996	168	42	)	)	PUNCT
cana-1996	168	43	}	}	PUNCT
cana-1996	168	44	,	,	PUNCT
cana-1996	168	45	𝜇2(υ	𝜇2(υ	NOUN
cana-1996	168	46	,	,	PUNCT
cana-1996	168	47	𝑡	𝑡	X
cana-1996	168	48	)	)	PUNCT
cana-1996	168	49	=	=	SYM
cana-1996	168	50	𝜇1(υ	𝜇1(υ	PROPN
cana-1996	168	51	,	,	PUNCT
cana-1996	168	52	𝑡	𝑡	NOUN
cana-1996	168	53	)	)	PUNCT
cana-1996	168	54	−	−	NOUN
cana-1996	168	55	ℛ−1{ℛ2(𝜇1⃗⃗⃗⃗	ℛ−1{ℛ2(𝜇1⃗⃗⃗⃗	NOUN
cana-1996	168	56	(	(	PUNCT
cana-1996	168	57	υ	υ	NOUN
cana-1996	168	58	,	,	PUNCT
cana-1996	168	59	𝑡	𝑡	NOUN
cana-1996	168	60	)	)	PUNCT
cana-1996	168	61	)	)	PUNCT
cana-1996	168	62	}	}	PUNCT
cana-1996	168	63	,	,	PUNCT
cana-1996	168	64	𝜇3(υ	𝜇3(υ	PROPN
cana-1996	168	65	,	,	PUNCT
cana-1996	168	66	𝑡	𝑡	NOUN
cana-1996	168	67	)	)	PUNCT
cana-1996	168	68	=	=	SYM
cana-1996	169	1	𝜇2(υ	𝜇2(υ	PROPN
cana-1996	169	2	,	,	PUNCT
cana-1996	169	3	𝑡	𝑡	NOUN
cana-1996	169	4	)	)	PUNCT
cana-1996	169	5	−	−	PROPN
cana-1996	170	1	ℛ−1	ℛ−1	PROPN
cana-1996	170	2	{	{	PUNCT
cana-1996	170	3	ℛ3	ℛ3	NOUN
cana-1996	170	4	(	(	PUNCT
cana-1996	170	5	𝜇2⃗⃗⃗⃗	𝜇2⃗⃗⃗⃗	X
cana-1996	170	6	(	(	PUNCT
cana-1996	170	7	υ	υ	NOUN
cana-1996	170	8	,	,	PUNCT
cana-1996	170	9	𝑡	𝑡	NOUN
cana-1996	170	10	)	)	PUNCT
cana-1996	170	11	)	)	PUNCT
cana-1996	170	12	}	}	PUNCT
cana-1996	170	13	,	,	PUNCT
cana-1996	170	14	⋮	⋮	NOUN
cana-1996	170	15	where	where	SCONJ
cana-1996	170	16	”	"	PUNCT
cana-1996	170	17	ℛ1(𝜇0⃗⃗⃗⃗	ℛ1(𝜇0⃗⃗⃗⃗	X
cana-1996	170	18	(	(	PUNCT
cana-1996	170	19	υ	υ	NOUN
cana-1996	170	20	,	,	PUNCT
cana-1996	170	21	𝑡	𝑡	NOUN
cana-1996	170	22	)	)	PUNCT
cana-1996	170	23	)	)	PUNCT
cana-1996	171	1	=	=	SYM
cana-1996	172	1	−	−	PROPN
cana-1996	172	2	1	1	NUM
cana-1996	172	3	𝑤3	𝑤3	PROPN
cana-1996	172	4	sin	sin	NOUN
cana-1996	172	5	𝜋𝑥	𝜋𝑥	PROPN
cana-1996	172	6	sin𝜋𝑦	sin𝜋𝑦	PROPN
cana-1996	172	7	sin	sin	PROPN
cana-1996	172	8	𝜋𝑧	𝜋𝑧	PROPN
cana-1996	172	9	,	,	PUNCT
cana-1996	172	10	ℛ2(𝜇1⃗⃗⃗⃗	ℛ2(𝜇1⃗⃗⃗⃗	X
cana-1996	172	11	(	(	PUNCT
cana-1996	172	12	υ	υ	NOUN
cana-1996	172	13	,	,	PUNCT
cana-1996	172	14	𝑡	𝑡	NOUN
cana-1996	172	15	)	)	PUNCT
cana-1996	172	16	)	)	PUNCT
cana-1996	173	1	=	=	PUNCT
cana-1996	173	2	(	(	PUNCT
cana-1996	173	3	1	1	NUM
cana-1996	173	4	𝜛3	𝜛3	PROPN
cana-1996	173	5	−	−	NOUN
cana-1996	173	6	1	1	NUM
cana-1996	173	7	𝜛4	𝜛4	NOUN
cana-1996	173	8	)	)	PUNCT
cana-1996	173	9	sin	sin	NOUN
cana-1996	173	10	𝜋𝑥	𝜋𝑥	PROPN
cana-1996	173	11	sin𝜋𝑦	sin𝜋𝑦	PROPN
cana-1996	173	12	sin	sin	PROPN
cana-1996	173	13	𝜋𝑧	𝜋𝑧	PROPN
cana-1996	173	14	,	,	PUNCT
cana-1996	173	15	ℛ3(𝜇2⃗⃗⃗⃗	ℛ3(𝜇2⃗⃗⃗⃗	X
cana-1996	173	16	(	(	PUNCT
cana-1996	173	17	υ	υ	NOUN
cana-1996	173	18	,	,	PUNCT
cana-1996	173	19	𝑡	𝑡	NOUN
cana-1996	173	20	)	)	PUNCT
cana-1996	173	21	)	)	PUNCT
cana-1996	174	1	=	=	PUNCT
cana-1996	174	2	(	(	PUNCT
cana-1996	174	3	1	1	NUM
cana-1996	174	4	𝜛4	𝜛4	NOUN
cana-1996	174	5	−	−	PROPN
cana-1996	174	6	1	1	NUM
cana-1996	174	7	𝜛5	𝜛5	NOUN
cana-1996	174	8	)	)	PUNCT
cana-1996	174	9	sin	sin	NOUN
cana-1996	174	10	𝜋𝑥	𝜋𝑥	PROPN
cana-1996	174	11	sin𝜋𝑦	sin𝜋𝑦	PROPN
cana-1996	174	12	sin	sin	PROPN
cana-1996	174	13	𝜋𝑧	𝜋𝑧	PROPN
cana-1996	174	14	,	,	PUNCT
cana-1996	174	15	⋮	⋮	NOUN
cana-1996	174	16	therefore	therefore	ADV
cana-1996	174	17	,	,	PUNCT
cana-1996	174	18	𝜇1(υ	𝜇1(υ	NUM
cana-1996	174	19	,	,	PUNCT
cana-1996	174	20	𝑡	𝑡	NOUN
cana-1996	174	21	)	)	PUNCT
cana-1996	174	22	=	=	SYM
cana-1996	175	1	−	−	PROPN
cana-1996	175	2	sin	sin	NOUN
cana-1996	175	3	𝜋𝑥	𝜋𝑥	PROPN
cana-1996	175	4	sin𝜋𝑦	sin𝜋𝑦	PROPN
cana-1996	175	5	sin	sin	PROPN
cana-1996	175	6	𝜋𝑧	𝜋𝑧	PROPN
cana-1996	175	7	,	,	PUNCT
cana-1996	175	8	𝜇2(υ	𝜇2(υ	PROPN
cana-1996	175	9	,	,	PUNCT
cana-1996	175	10	𝑡	𝑡	NOUN
cana-1996	175	11	)	)	PUNCT
cana-1996	175	12	=	=	SYM
cana-1996	175	13	𝑡2	𝑡2	NOUN
cana-1996	175	14	2	2	NUM
cana-1996	175	15	!	!	PUNCT
cana-1996	175	16	sin	sin	PROPN
cana-1996	175	17	𝜋𝑥	𝜋𝑥	PROPN
cana-1996	175	18	sin𝜋𝑦	sin𝜋𝑦	PROPN
cana-1996	175	19	sin	sin	PROPN
cana-1996	175	20	𝜋𝑧	𝜋𝑧	PROPN
cana-1996	175	21	,	,	PUNCT
cana-1996	175	22	𝜇3(υ	𝜇3(υ	PROPN
cana-1996	175	23	,	,	PUNCT
cana-1996	175	24	𝑡	𝑡	NOUN
cana-1996	175	25	)	)	PUNCT
cana-1996	175	26	=	=	SYM
cana-1996	175	27	−	−	PROPN
cana-1996	175	28	𝑡3	𝑡3	PROPN
cana-1996	175	29	3	3	NUM
cana-1996	175	30	!	!	PUNCT
cana-1996	175	31	sin	sin	PROPN
cana-1996	175	32	𝜋𝑥	𝜋𝑥	PROPN
cana-1996	175	33	sin𝜋𝑦	sin𝜋𝑦	PROPN
cana-1996	175	34	sin	sin	PROPN
cana-1996	175	35	𝜋𝑧	𝜋𝑧	PROPN
cana-1996	175	36	,	,	PUNCT
cana-1996	175	37	⋮	⋮	ADJ
cana-1996	175	38	communications	communication	NOUN
cana-1996	175	39	on	on	ADP
cana-1996	175	40	applied	apply	VERB
cana-1996	175	41	nonlinear	nonlinear	ADJ
cana-1996	175	42	analysis	analysis	NOUN
cana-1996	175	43	issn	issn	NOUN
cana-1996	175	44	:	:	PUNCT
cana-1996	175	45	1074	1074	NUM
cana-1996	175	46	-	-	PUNCT
cana-1996	175	47	133x	133x	NUM
cana-1996	175	48	vol	vol	NOUN
cana-1996	175	49	32	32	NUM
cana-1996	175	50	no	no	NOUN
cana-1996	175	51	.	.	NOUN
cana-1996	175	52	3	3	NUM
cana-1996	175	53	(	(	PUNCT
cana-1996	175	54	2025	2025	NUM
cana-1996	175	55	)	)	PUNCT
cana-1996	175	56	394	394	NUM
cana-1996	175	57	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	176	1	the	the	DET
cana-1996	176	2	solution	solution	NOUN
cana-1996	176	3	is	be	AUX
cana-1996	176	4	:	:	PUNCT
cana-1996	176	5	𝜇(υ	𝜇(υ	NOUN
cana-1996	176	6	,	,	PUNCT
cana-1996	176	7	𝑡	𝑡	NOUN
cana-1996	176	8	)	)	PUNCT
cana-1996	176	9	=	=	SYM
cana-1996	176	10	𝜇0	𝜇0	PROPN
cana-1996	176	11	+	+	CCONJ
cana-1996	176	12	𝜇1	𝜇1	PROPN
cana-1996	176	13	+	+	CCONJ
cana-1996	176	14	𝜇2	𝜇2	PROPN
cana-1996	176	15	+	+	SYM
cana-1996	176	16	⋯	⋯	PROPN
cana-1996	176	17	or	or	CCONJ
cana-1996	176	18	𝜇(υ	𝜇(υ	PROPN
cana-1996	176	19	,	,	PUNCT
cana-1996	176	20	𝑡	𝑡	NOUN
cana-1996	176	21	)	)	PUNCT
cana-1996	176	22	=	=	SYM
cana-1996	176	23	{	{	PUNCT
cana-1996	176	24	1	1	NUM
cana-1996	176	25	−	−	PROPN
cana-1996	176	26	𝑡	𝑡	PROPN
cana-1996	176	27	+	+	NOUN
cana-1996	176	28	𝑡2	𝑡2	PROPN
cana-1996	176	29	2	2	NUM
cana-1996	176	30	!	!	PUNCT
cana-1996	176	31	−	−	PROPN
cana-1996	176	32	𝑡3	𝑡3	PROPN
cana-1996	176	33	3	3	NUM
cana-1996	176	34	!	!	PUNCT
cana-1996	177	1	+	+	CCONJ
cana-1996	177	2	⋯	⋯	NOUN
cana-1996	177	3	}	}	PUNCT
cana-1996	177	4	sin	sin	NOUN
cana-1996	177	5	𝜋𝑥	𝜋𝑥	PROPN
cana-1996	177	6	sin𝜋𝑦	sin𝜋𝑦	PROPN
cana-1996	177	7	sin	sin	VERB
cana-1996	177	8	𝜋𝑧	𝜋𝑧	ADP
cana-1996	177	9	=	=	SYM
cana-1996	177	10	𝑒−𝑡	𝑒−𝑡	PROPN
cana-1996	177	11	sin	sin	NOUN
cana-1996	177	12	𝜋𝑥	𝜋𝑥	PROPN
cana-1996	177	13	sin𝜋𝑦	sin𝜋𝑦	PROPN
cana-1996	177	14	sin	sin	VERB
cana-1996	177	15	𝜋𝑧	𝜋𝑧	PART
cana-1996	177	16	figure	figure	NOUN
cana-1996	177	17	3	3	NUM
cana-1996	177	18	:	:	PUNCT
cana-1996	177	19	example	example	NOUN
cana-1996	177	20	2	2	NUM
cana-1996	177	21	's	's	PART
cana-1996	177	22	solutions	solution	NOUN
cana-1996	177	23	'	'	PART
cana-1996	177	24	physical	physical	ADJ
cana-1996	177	25	behavior	behavior	NOUN
cana-1996	177	26	at	at	ADP
cana-1996	177	27	𝒕	𝒕	NOUN
cana-1996	177	28	=	=	SYM
cana-1996	177	29	𝟐	𝟐	PROPN
cana-1996	177	30	,	,	PUNCT
cana-1996	177	31	𝒛	𝒛	NOUN
cana-1996	177	32	=	=	SYM
cana-1996	177	33	𝝅	𝝅	PRON
cana-1996	177	34	𝟐	𝟐	NUM
cana-1996	177	35	figure	figure	NOUN
cana-1996	177	36	4	4	NUM
cana-1996	177	37	:	:	PUNCT
cana-1996	178	1	the	the	DET
cana-1996	178	2	contour	contour	NOUN
cana-1996	178	3	diagram	diagram	NOUN
cana-1996	178	4	obtained	obtain	VERB
cana-1996	178	5	from	from	ADP
cana-1996	178	6	solving	solve	VERB
cana-1996	178	7	example	example	NOUN
cana-1996	178	8	2	2	NUM
cana-1996	178	9	at	at	ADP
cana-1996	178	10	𝒕	𝒕	NOUN
cana-1996	178	11	=	=	SYM
cana-1996	178	12	𝟐	𝟐	PROPN
cana-1996	178	13	,	,	PUNCT
cana-1996	178	14	𝒛	𝒛	NOUN
cana-1996	178	15	=	=	SYM
cana-1996	178	16	𝝅	𝝅	ADP
cana-1996	178	17	𝟐	𝟐	NUM
cana-1996	178	18	-2	-2	NOUN
cana-1996	178	19	-1	-1	NOUN
cana-1996	178	20	0	0	NUM
cana-1996	178	21	1	1	NUM
cana-1996	178	22	2	2	NUM
cana-1996	178	23	-2	-2	NOUN
cana-1996	178	24	0	0	NUM
cana-1996	178	25	2	2	NUM
cana-1996	178	26	-0.2	-0.2	PROPN
cana-1996	178	27	-0.1	-0.1	PROPN
cana-1996	178	28	0	0	NUM
cana-1996	178	29	0.1	0.1	NUM
cana-1996	178	30	0.2	0.2	NUM
cana-1996	178	31	x	x	NOUN
cana-1996	178	32	example	example	NOUN
cana-1996	178	33	2	2	NUM
cana-1996	178	34	:	:	PUNCT
cana-1996	178	35	for	for	ADP
cana-1996	178	36	t	t	NOUN
cana-1996	178	37	=	=	SYM
cana-1996	178	38	2	2	NUM
cana-1996	178	39	,	,	PUNCT
cana-1996	179	1	z	z	NOUN
cana-1996	179	2	=	=	SYM
cana-1996	179	3	pi/2	pi/2	PROPN
cana-1996	179	4	y	y	PROPN
cana-1996	179	5	s	s	PART
cana-1996	179	6	o	o	X
cana-1996	179	7	lu	lu	NOUN
cana-1996	179	8	ti	ti	NOUN
cana-1996	179	9	o	o	NOUN
cana-1996	179	10	n	n	X
cana-1996	179	11	s	s	NOUN
cana-1996	179	12	x	x	PART
cana-1996	179	13	y	y	PROPN
cana-1996	179	14	example	example	NOUN
cana-1996	179	15	2	2	NUM
cana-1996	179	16	:	:	PUNCT
cana-1996	179	17	for	for	ADP
cana-1996	179	18	t	t	NOUN
cana-1996	179	19	=	=	SYM
cana-1996	179	20	2	2	NUM
cana-1996	179	21	-2	-2	NOUN
cana-1996	179	22	-1.5	-1.5	NUM
cana-1996	179	23	-1	-1	PROPN
cana-1996	180	1	-0.5	-0.5	X
cana-1996	180	2	0	0	NUM
cana-1996	180	3	0.5	0.5	NUM
cana-1996	180	4	1	1	NUM
cana-1996	180	5	1.5	1.5	NUM
cana-1996	180	6	2	2	NUM
cana-1996	180	7	-2	-2	NOUN
cana-1996	180	8	-1.5	-1.5	NUM
cana-1996	180	9	-1	-1	PROPN
cana-1996	180	10	-0.5	-0.5	X
cana-1996	180	11	0	0	NUM
cana-1996	180	12	0.5	0.5	NUM
cana-1996	180	13	1	1	NUM
cana-1996	180	14	1.5	1.5	NUM
cana-1996	180	15	2	2	NUM
cana-1996	180	16	communications	communication	NOUN
cana-1996	180	17	on	on	ADP
cana-1996	180	18	applied	apply	VERB
cana-1996	180	19	nonlinear	nonlinear	ADJ
cana-1996	180	20	analysis	analysis	NOUN
cana-1996	180	21	issn	issn	NOUN
cana-1996	180	22	:	:	PUNCT
cana-1996	180	23	1074	1074	NUM
cana-1996	180	24	-	-	PUNCT
cana-1996	180	25	133x	133x	NUM
cana-1996	180	26	vol	vol	NOUN
cana-1996	180	27	32	32	NUM
cana-1996	180	28	no	no	NOUN
cana-1996	180	29	.	.	NOUN
cana-1996	180	30	3	3	NUM
cana-1996	180	31	(	(	PUNCT
cana-1996	180	32	2025	2025	NUM
cana-1996	180	33	)	)	PUNCT
cana-1996	180	34	395	395	NUM
cana-1996	180	35	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	180	36	figures	figure	NOUN
cana-1996	180	37	3	3	NUM
cana-1996	180	38	and	and	CCONJ
cana-1996	180	39	4	4	NUM
cana-1996	180	40	depict	depict	VERB
cana-1996	180	41	the	the	DET
cana-1996	180	42	physical	physical	ADJ
cana-1996	180	43	and	and	CCONJ
cana-1996	180	44	dynamic	dynamic	ADJ
cana-1996	180	45	behaviour	behaviour	NOUN
cana-1996	180	46	of	of	ADP
cana-1996	180	47	the	the	DET
cana-1996	180	48	solutions	solution	NOUN
cana-1996	180	49	found	find	VERB
cana-1996	180	50	at	at	ADP
cana-1996	180	51	𝑧	𝑧	PROPN
cana-1996	180	52	=	=	SYM
cana-1996	180	53	1	1	NUM
cana-1996	180	54	and	and	CCONJ
cana-1996	180	55	𝑡	𝑡	PROPN
cana-1996	180	56	=	=	VERB
cana-1996	180	57	𝜋	𝜋	NOUN
cana-1996	180	58	2	2	NUM
cana-1996	180	59	using	use	VERB
cana-1996	180	60	the	the	DET
cana-1996	180	61	"	"	PUNCT
cana-1996	180	62	homotopy	homotopy	VERB
cana-1996	180	63	analysis	analysis	NOUN
cana-1996	180	64	method	method	NOUN
cana-1996	180	65	"	"	PUNCT
cana-1996	180	66	based	base	VERB
cana-1996	180	67	on	on	ADP
cana-1996	180	68	the	the	DET
cana-1996	180	69	"	"	PUNCT
cana-1996	180	70	rangaig	rangaig	ADJ
cana-1996	180	71	transform	transform	NOUN
cana-1996	180	72	.	.	PUNCT
cana-1996	180	73	"	"	PUNCT
cana-1996	181	1	example	example	NOUN
cana-1996	181	2	3	3	NUM
cana-1996	181	3	:	:	PUNCT
cana-1996	181	4	consider	consider	VERB
cana-1996	181	5	the	the	DET
cana-1996	181	6	(	(	PUNCT
cana-1996	181	7	3	3	NUM
cana-1996	181	8	+	+	NOUN
cana-1996	181	9	1)-d	1)-d	NUM
cana-1996	181	10	“	"	PUNCT
cana-1996	181	11	klein	klein	PROPN
cana-1996	181	12	gordan	gordan	PROPN
cana-1996	181	13	equation	equation	PROPN
cana-1996	181	14	”	"	PUNCT
cana-1996	181	15	of	of	ADP
cana-1996	181	16	the	the	DET
cana-1996	181	17	form	form	NOUN
cana-1996	181	18	:	:	PUNCT
cana-1996	181	19	𝜇𝓉𝓉	𝜇𝓉𝓉	PROPN
cana-1996	181	20	−	−	PROPN
cana-1996	181	21	(	(	PUNCT
cana-1996	181	22	𝜇𝓍𝓍	𝜇𝓍𝓍	NOUN
cana-1996	181	23	+	+	CCONJ
cana-1996	181	24	𝜇𝓎𝓎	𝜇𝓎𝓎	NOUN
cana-1996	181	25	+	+	CCONJ
cana-1996	181	26	𝜇𝓏𝓏	𝜇𝓏𝓏	NOUN
cana-1996	181	27	)	)	PUNCT
cana-1996	182	1	+	+	X
cana-1996	182	2	𝜇	𝜇	X
cana-1996	182	3	=	=	X
cana-1996	182	4	2(sin	2(sin	NOUN
cana-1996	182	5	𝓍	𝓍	X
cana-1996	182	6	+	+	CCONJ
cana-1996	182	7	sin𝓎	sin𝓎	NOUN
cana-1996	182	8	+	+	CCONJ
cana-1996	182	9	sin	sin	NOUN
cana-1996	182	10	𝓏	𝓏	NOUN
cana-1996	182	11	)	)	PUNCT
cana-1996	182	12	(	(	PUNCT
cana-1996	182	13	28	28	NUM
cana-1996	182	14	)	)	PUNCT
cana-1996	182	15	with	with	ADP
cana-1996	182	16	initial	initial	ADJ
cana-1996	182	17	condition	condition	NOUN
cana-1996	182	18	(	(	PUNCT
cana-1996	182	19	𝜇(υ	𝜇(υ	NOUN
cana-1996	182	20	,	,	PUNCT
cana-1996	182	21	0	0	NUM
cana-1996	182	22	)	)	PUNCT
cana-1996	182	23	=	=	VERB
cana-1996	182	24	sin	sin	VERB
cana-1996	182	25	𝓍	𝓍	X
cana-1996	182	26	+	+	CCONJ
cana-1996	182	27	sin𝓎	sin𝓎	NOUN
cana-1996	182	28	+	+	CCONJ
cana-1996	182	29	sin	sin	NOUN
cana-1996	182	30	𝓏	𝓏	NOUN
cana-1996	182	31	,	,	PUNCT
cana-1996	182	32	we	we	PRON
cana-1996	182	33	use	use	VERB
cana-1996	182	34	υ	υ	NOUN
cana-1996	182	35	=	=	PUNCT
cana-1996	182	36	(	(	PUNCT
cana-1996	182	37	𝓍,𝓎	𝓍,𝓎	PROPN
cana-1996	182	38	,	,	PUNCT
cana-1996	182	39	𝓏	𝓏	NOUN
cana-1996	182	40	)	)	PUNCT
cana-1996	182	41	,	,	PUNCT
cana-1996	182	42	the	the	DET
cana-1996	182	43	exact	exact	ADJ
cana-1996	182	44	solution	solution	NOUN
cana-1996	182	45	is	be	AUX
cana-1996	182	46	:	:	PUNCT
cana-1996	182	47	𝜇(υ	𝜇(υ	PROPN
cana-1996	182	48	,	,	PUNCT
cana-1996	182	49	𝓉	𝓉	PRON
cana-1996	182	50	)	)	PUNCT
cana-1996	182	51	=	=	VERB
cana-1996	183	1	sin	sin	VERB
cana-1996	183	2	𝓍	𝓍	X
cana-1996	183	3	+	+	CCONJ
cana-1996	183	4	sin𝓎	sin𝓎	NOUN
cana-1996	183	5	+	+	CCONJ
cana-1996	183	6	sin	sin	NOUN
cana-1996	183	7	𝓏	𝓏	PROPN
cana-1996	183	8	+	+	CCONJ
cana-1996	183	9	sin	sin	NOUN
cana-1996	183	10	𝓉	𝓉	PROPN
cana-1996	183	11	rewrite	rewrite	VERB
cana-1996	183	12	the	the	DET
cana-1996	183	13	given	give	VERB
cana-1996	183	14	problem	problem	NOUN
cana-1996	183	15	as	as	ADP
cana-1996	183	16	:	:	PUNCT
cana-1996	183	17	𝜇𝓉𝓉	𝜇𝓉𝓉	PROPN
cana-1996	183	18	=	=	SYM
cana-1996	183	19	(	(	PUNCT
cana-1996	183	20	𝜇𝓍𝓍	𝜇𝓍𝓍	NOUN
cana-1996	183	21	+	+	CCONJ
cana-1996	183	22	𝜇𝓎𝓎	𝜇𝓎𝓎	NOUN
cana-1996	183	23	+	+	CCONJ
cana-1996	183	24	𝜇𝓏𝓏	𝜇𝓏𝓏	NOUN
cana-1996	183	25	)	)	PUNCT
cana-1996	183	26	−	−	NOUN
cana-1996	184	1	𝜇	𝜇	ADP
cana-1996	184	2	+	+	X
cana-1996	184	3	2(sin𝓍	2(sin𝓍	NUM
cana-1996	184	4	+	+	CCONJ
cana-1996	184	5	sin𝓎	sin𝓎	NOUN
cana-1996	184	6	+	+	CCONJ
cana-1996	184	7	sin	sin	NOUN
cana-1996	184	8	𝓏	𝓏	NOUN
cana-1996	184	9	)	)	PUNCT
cana-1996	184	10	(	(	PUNCT
cana-1996	184	11	29	29	NUM
cana-1996	184	12	)	)	PUNCT
cana-1996	184	13	applying	apply	VERB
cana-1996	184	14	the	the	DET
cana-1996	184	15	“	"	PUNCT
cana-1996	184	16	rangaig	rangaig	ADJ
cana-1996	184	17	transform	transform	NOUN
cana-1996	184	18	”	"	PUNCT
cana-1996	184	19	to	to	ADP
cana-1996	184	20	both	both	DET
cana-1996	184	21	sides	side	NOUN
cana-1996	184	22	of	of	ADP
cana-1996	184	23	equation	equation	NOUN
cana-1996	184	24	(	(	PUNCT
cana-1996	184	25	29	29	NUM
cana-1996	184	26	)	)	PUNCT
cana-1996	184	27	,	,	PUNCT
cana-1996	184	28	we	we	PRON
cana-1996	184	29	obtain	obtain	VERB
cana-1996	184	30	,	,	PUNCT
cana-1996	184	31	ℛ[𝜇𝓉𝓉	ℛ[𝜇𝓉𝓉	X
cana-1996	184	32	]	]	X
cana-1996	184	33	=	=	SYM
cana-1996	184	34	ℛ[(𝜇𝓍𝓍	ℛ[(𝜇𝓍𝓍	NUM
cana-1996	184	35	+	+	NUM
cana-1996	184	36	𝜇𝓎𝓎	𝜇𝓎𝓎	NOUN
cana-1996	184	37	+	+	CCONJ
cana-1996	184	38	𝜇𝓏𝓏	𝜇𝓏𝓏	NOUN
cana-1996	184	39	)	)	PUNCT
cana-1996	184	40	−	−	NOUN
cana-1996	185	1	𝜇	𝜇	SCONJ
cana-1996	185	2	+	+	X
cana-1996	185	3	2(sin	2(sin	NOUN
cana-1996	185	4	𝓍	𝓍	X
cana-1996	185	5	+	+	CCONJ
cana-1996	185	6	sin𝓎	sin𝓎	NOUN
cana-1996	185	7	+	+	CCONJ
cana-1996	185	8	sin	sin	NOUN
cana-1996	185	9	𝓏	𝓏	NOUN
cana-1996	185	10	)	)	PUNCT
cana-1996	185	11	]	]	PUNCT
cana-1996	185	12	this	this	PRON
cana-1996	185	13	implies	imply	VERB
cana-1996	185	14	(	(	PUNCT
cana-1996	185	15	−1)2𝜛2ℛ[𝜇	−1)2𝜛2ℛ[𝜇	NOUN
cana-1996	185	16	]	]	X
cana-1996	185	17	+	+	CCONJ
cana-1996	185	18	(	(	PUNCT
cana-1996	185	19	−1)3	−1)3	NOUN
cana-1996	185	20	∑	∑	INTJ
cana-1996	185	21	(	(	PUNCT
cana-1996	185	22	−1)𝓀	−1)𝓀	X
cana-1996	185	23	𝜛𝓀	𝜛𝓀	PROPN
cana-1996	185	24	1	1	NUM
cana-1996	185	25	𝓀=0	𝓀=0	NOUN
cana-1996	185	26	𝜕𝓀𝜇	𝜕𝓀𝜇	PRON
cana-1996	185	27	𝜕𝓉𝓀	𝜕𝓉𝓀	PUNCT
cana-1996	186	1	=	=	SYM
cana-1996	186	2	ℛ[(𝜇𝓍𝓍	ℛ[(𝜇𝓍𝓍	NUM
cana-1996	186	3	+	+	NUM
cana-1996	186	4	𝜇𝓎𝓎	𝜇𝓎𝓎	NOUN
cana-1996	186	5	+	+	CCONJ
cana-1996	186	6	𝜇𝓏𝓏	𝜇𝓏𝓏	NOUN
cana-1996	186	7	)	)	PUNCT
cana-1996	186	8	−	−	NOUN
cana-1996	186	9	𝜇	𝜇	ADP
cana-1996	186	10	+	+	X
cana-1996	186	11	2	2	NUM
cana-1996	186	12	(	(	PUNCT
cana-1996	186	13	sin	sin	NOUN
cana-1996	186	14	𝓍	𝓍	X
cana-1996	186	15	+	+	CCONJ
cana-1996	186	16	sin𝓎	sin𝓎	NOUN
cana-1996	186	17	+	+	CCONJ
cana-1996	186	18	sin	sin	NOUN
cana-1996	186	19	𝓏	𝓏	NOUN
cana-1996	186	20	)	)	PUNCT
cana-1996	186	21	]	]	PUNCT
cana-1996	186	22	.	.	PUNCT
cana-1996	187	1	this	this	PRON
cana-1996	187	2	implies	imply	VERB
cana-1996	187	3	𝜛2ℛ[𝜇	𝜛2ℛ[𝜇	PROPN
cana-1996	187	4	]	]	PUNCT
cana-1996	188	1	−	−	PROPN
cana-1996	188	2	[	[	PUNCT
cana-1996	188	3	1	1	NUM
cana-1996	188	4	𝜛0	𝜛0	PROPN
cana-1996	188	5	𝜇(υ	𝜇(υ	NOUN
cana-1996	188	6	,	,	PUNCT
cana-1996	188	7	0	0	NUM
cana-1996	188	8	)	)	PUNCT
cana-1996	188	9	+	+	CCONJ
cana-1996	188	10	(	(	PUNCT
cana-1996	188	11	−1)1	−1)1	NUM
cana-1996	188	12	𝜛1	𝜛1	PROPN
cana-1996	188	13	𝜕	𝜕	PROPN
cana-1996	188	14	𝜕𝓉	𝜕𝓉	PROPN
cana-1996	188	15	𝜇(υ	𝜇(υ	PROPN
cana-1996	188	16	,	,	PUNCT
cana-1996	188	17	0	0	NUM
cana-1996	188	18	)	)	PUNCT
cana-1996	188	19	]	]	PUNCT
cana-1996	189	1	=	=	SYM
cana-1996	189	2	1	1	NUM
cana-1996	189	3	𝜛2	𝜛2	VERB
cana-1996	189	4	ℛ[(𝜇𝓍𝓍	ℛ[(𝜇𝓍𝓍	NUM
cana-1996	189	5	+	+	NUM
cana-1996	189	6	𝜇𝓎𝓎	𝜇𝓎𝓎	NOUN
cana-1996	189	7	+	+	CCONJ
cana-1996	189	8	𝜇𝓏𝓏	𝜇𝓏𝓏	NOUN
cana-1996	189	9	)	)	PUNCT
cana-1996	189	10	−	−	NOUN
cana-1996	189	11	𝜇	𝜇	ADP
cana-1996	189	12	+	+	X
cana-1996	189	13	2	2	NUM
cana-1996	189	14	(	(	PUNCT
cana-1996	189	15	sin	sin	NOUN
cana-1996	189	16	𝓍	𝓍	X
cana-1996	189	17	+	+	CCONJ
cana-1996	189	18	sin𝓎	sin𝓎	NOUN
cana-1996	189	19	+	+	CCONJ
cana-1996	189	20	sin	sin	NOUN
cana-1996	189	21	𝓏	𝓏	NOUN
cana-1996	189	22	)	)	PUNCT
cana-1996	189	23	]	]	PUNCT
cana-1996	189	24	or	or	CCONJ
cana-1996	189	25	ℛ[𝜇	ℛ[𝜇	ADP
cana-1996	189	26	]	]	X
cana-1996	190	1	−	−	X
cana-1996	190	2	[	[	PUNCT
cana-1996	190	3	1	1	NUM
cana-1996	190	4	𝜛2	𝜛2	PROPN
cana-1996	190	5	𝜇(υ	𝜇(υ	NOUN
cana-1996	190	6	,	,	PUNCT
cana-1996	190	7	0	0	NUM
cana-1996	190	8	)	)	PUNCT
cana-1996	190	9	+	+	CCONJ
cana-1996	190	10	(	(	PUNCT
cana-1996	190	11	−1)1	−1)1	NUM
cana-1996	190	12	𝜛3	𝜛3	PROPN
cana-1996	190	13	𝜕	𝜕	PROPN
cana-1996	190	14	𝜕𝓉	𝜕𝓉	PROPN
cana-1996	190	15	𝜇(υ	𝜇(υ	PROPN
cana-1996	190	16	,	,	PUNCT
cana-1996	190	17	0	0	NUM
cana-1996	190	18	)	)	PUNCT
cana-1996	190	19	]	]	PUNCT
cana-1996	191	1	=	=	SYM
cana-1996	191	2	1	1	NUM
cana-1996	191	3	𝜛2	𝜛2	VERB
cana-1996	191	4	ℛ[(𝜇𝓍𝓍	ℛ[(𝜇𝓍𝓍	NUM
cana-1996	191	5	+	+	NUM
cana-1996	191	6	𝜇𝓎𝓎	𝜇𝓎𝓎	NOUN
cana-1996	191	7	+	+	CCONJ
cana-1996	191	8	𝜇𝓏𝓏	𝜇𝓏𝓏	NOUN
cana-1996	191	9	)	)	PUNCT
cana-1996	191	10	−	−	NOUN
cana-1996	191	11	𝜇	𝜇	ADP
cana-1996	191	12	+	+	X
cana-1996	191	13	2	2	NUM
cana-1996	191	14	(	(	PUNCT
cana-1996	191	15	sin	sin	NOUN
cana-1996	191	16	𝓍	𝓍	X
cana-1996	191	17	+	+	CCONJ
cana-1996	191	18	sin𝓎	sin𝓎	NOUN
cana-1996	191	19	+	+	CCONJ
cana-1996	191	20	sin	sin	NOUN
cana-1996	191	21	𝓏	𝓏	NOUN
cana-1996	191	22	)	)	PUNCT
cana-1996	191	23	]	]	PUNCT
cana-1996	191	24	when	when	SCONJ
cana-1996	191	25	the	the	DET
cana-1996	191	26	initial	initial	ADJ
cana-1996	191	27	conditions	condition	NOUN
cana-1996	191	28	are	be	AUX
cana-1996	191	29	applied	apply	VERB
cana-1996	191	30	,	,	PUNCT
cana-1996	191	31	we	we	PRON
cana-1996	191	32	get	get	VERB
cana-1996	191	33	ℛ[𝜇	ℛ[𝜇	PRON
cana-1996	191	34	]	]	X
cana-1996	192	1	=	=	SYM
cana-1996	192	2	(	(	PUNCT
cana-1996	192	3	1	1	NUM
cana-1996	192	4	𝜛2	𝜛2	NOUN
cana-1996	192	5	)	)	PUNCT
cana-1996	192	6	(	(	PUNCT
cana-1996	192	7	sin	sin	VERB
cana-1996	192	8	𝓍	𝓍	X
cana-1996	192	9	+	+	CCONJ
cana-1996	192	10	sin𝓎	sin𝓎	NOUN
cana-1996	192	11	+	+	CCONJ
cana-1996	192	12	sin	sin	NOUN
cana-1996	192	13	𝓏	𝓏	NOUN
cana-1996	192	14	)	)	PUNCT
cana-1996	192	15	−	−	PROPN
cana-1996	192	16	1	1	NUM
cana-1996	192	17	𝜛3	𝜛3	NOUN
cana-1996	192	18	+	+	CCONJ
cana-1996	192	19	1	1	NUM
cana-1996	192	20	𝜛2	𝜛2	NOUN
cana-1996	192	21	ℛ[(𝜇𝑥𝑥	ℛ[(𝜇𝑥𝑥	PROPN
cana-1996	192	22	+	+	CCONJ
cana-1996	192	23	𝜇𝑦𝑦	𝜇𝑦𝑦	NOUN
cana-1996	192	24	+	+	X
cana-1996	192	25	𝜇𝓏𝓏	𝜇𝓏𝓏	NOUN
cana-1996	192	26	)	)	PUNCT
cana-1996	192	27	−	−	NOUN
cana-1996	193	1	𝜇	𝜇	ADP
cana-1996	193	2	+	+	X
cana-1996	193	3	2(sin	2(sin	NOUN
cana-1996	193	4	𝓍	𝓍	X
cana-1996	193	5	+	+	CCONJ
cana-1996	193	6	sin𝓎	sin𝓎	NOUN
cana-1996	193	7	+	+	CCONJ
cana-1996	193	8	sin	sin	NOUN
cana-1996	193	9	𝓏	𝓏	NOUN
cana-1996	193	10	)	)	PUNCT
cana-1996	193	11	]	]	PUNCT
cana-1996	193	12	we	we	PRON
cana-1996	193	13	define	define	VERB
cana-1996	193	14	the	the	DET
cana-1996	193	15	nonlinear	nonlinear	ADJ
cana-1996	193	16	component	component	NOUN
cana-1996	193	17	as	as	SCONJ
cana-1996	193	18	follows	follow	VERB
cana-1996	193	19	:	:	PUNCT
cana-1996	193	20	𝒩[𝛿(υ	𝒩[𝛿(υ	NOUN
cana-1996	193	21	,	,	PUNCT
cana-1996	193	22	𝓉	𝓉	PRON
cana-1996	193	23	;	;	PUNCT
cana-1996	193	24	𝓅	𝓅	NOUN
cana-1996	193	25	)	)	PUNCT
cana-1996	193	26	]	]	PUNCT
cana-1996	194	1	=	=	PUNCT
cana-1996	195	1	ℛ[𝜇	ℛ[𝜇	X
cana-1996	195	2	]	]	X
cana-1996	195	3	−	−	PROPN
cana-1996	195	4	(	(	PUNCT
cana-1996	195	5	1	1	NUM
cana-1996	195	6	𝜛2	𝜛2	NOUN
cana-1996	195	7	)	)	PUNCT
cana-1996	195	8	(	(	PUNCT
cana-1996	195	9	sin	sin	VERB
cana-1996	195	10	𝓍	𝓍	X
cana-1996	195	11	+	+	CCONJ
cana-1996	195	12	sin𝓎	sin𝓎	NOUN
cana-1996	195	13	+	+	CCONJ
cana-1996	195	14	sin	sin	NOUN
cana-1996	195	15	𝓏	𝓏	NOUN
cana-1996	195	16	)	)	PUNCT
cana-1996	195	17	+	+	CCONJ
cana-1996	195	18	1	1	NUM
cana-1996	195	19	𝜛3	𝜛3	NOUN
cana-1996	195	20	(	(	PUNCT
cana-1996	195	21	30	30	NUM
cana-1996	195	22	)	)	PUNCT
cana-1996	195	23	communications	communication	NOUN
cana-1996	195	24	on	on	ADP
cana-1996	195	25	applied	apply	VERB
cana-1996	195	26	nonlinear	nonlinear	ADJ
cana-1996	195	27	analysis	analysis	NOUN
cana-1996	195	28	issn	issn	NOUN
cana-1996	195	29	:	:	PUNCT
cana-1996	195	30	1074	1074	NUM
cana-1996	195	31	-	-	PUNCT
cana-1996	195	32	133x	133x	NUM
cana-1996	195	33	vol	vol	NOUN
cana-1996	195	34	32	32	NUM
cana-1996	195	35	no	no	NOUN
cana-1996	195	36	.	.	NOUN
cana-1996	195	37	3	3	NUM
cana-1996	195	38	(	(	PUNCT
cana-1996	195	39	2025	2025	NUM
cana-1996	195	40	)	)	PUNCT
cana-1996	195	41	396	396	NUM
cana-1996	196	1	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	196	2	−	−	NOUN
cana-1996	196	3	1	1	NUM
cana-1996	196	4	𝜛2	𝜛2	NOUN
cana-1996	196	5	ℛ[(𝜇𝓍𝓍	ℛ[(𝜇𝓍𝓍	NUM
cana-1996	196	6	+	+	NUM
cana-1996	196	7	𝜇𝓎𝓎	𝜇𝓎𝓎	NOUN
cana-1996	196	8	+	+	CCONJ
cana-1996	196	9	𝜇𝓏𝓏	𝜇𝓏𝓏	NOUN
cana-1996	196	10	)	)	PUNCT
cana-1996	196	11	−	−	NOUN
cana-1996	196	12	𝜇	𝜇	ADP
cana-1996	196	13	+	+	X
cana-1996	196	14	2(sin	2(sin	NOUN
cana-1996	196	15	𝓍	𝓍	X
cana-1996	196	16	+	+	CCONJ
cana-1996	196	17	sin𝓎	sin𝓎	NOUN
cana-1996	196	18	+	+	CCONJ
cana-1996	196	19	sin	sin	NOUN
cana-1996	196	20	𝓏	𝓏	NOUN
cana-1996	196	21	)	)	PUNCT
cana-1996	196	22	]	]	PUNCT
cana-1996	197	1	we	we	PRON
cana-1996	197	2	begin	begin	VERB
cana-1996	197	3	by	by	ADP
cana-1996	197	4	setting	set	VERB
cana-1996	197	5	up	up	ADP
cana-1996	197	6	the	the	DET
cana-1996	197	7	0	0	NUM
cana-1996	197	8	-	-	PUNCT
cana-1996	197	9	order	order	NOUN
cana-1996	197	10	deformation	deformation	NOUN
cana-1996	197	11	according	accord	VERB
cana-1996	197	12	to	to	ADP
cana-1996	197	13	the	the	DET
cana-1996	197	14	assumption	assumption	NOUN
cana-1996	197	15	adopted	adopt	VERB
cana-1996	197	16	herein	herein	NOUN
cana-1996	197	17	,	,	PUNCT
cana-1996	197	18	namely	namely	ADV
cana-1996	197	19	,	,	PUNCT
cana-1996	197	20	𝐻(υ	𝐻(υ	NOUN
cana-1996	197	21	,	,	PUNCT
cana-1996	197	22	𝓉	𝓉	PRON
cana-1996	197	23	)	)	PUNCT
cana-1996	197	24	=	=	SYM
cana-1996	197	25	1	1	NUM
cana-1996	197	26	;	;	PUNCT
cana-1996	197	27	we	we	PRON
cana-1996	197	28	have	have	VERB
cana-1996	197	29	(	(	PUNCT
cana-1996	197	30	1	1	NUM
cana-1996	197	31	−	−	NOUN
cana-1996	197	32	𝓅)ℛ{𝛿(υ	𝓅)ℛ{𝛿(υ	NOUN
cana-1996	197	33	,	,	PUNCT
cana-1996	197	34	𝓉	𝓉	PROPN
cana-1996	197	35	)	)	PUNCT
cana-1996	197	36	−	−	PROPN
cana-1996	198	1	𝜇0(υ	𝜇0(υ	PROPN
cana-1996	198	2	,	,	PUNCT
cana-1996	198	3	𝓉	𝓉	PROPN
cana-1996	198	4	)	)	PUNCT
cana-1996	198	5	}	}	PUNCT
cana-1996	198	6	=	=	SYM
cana-1996	199	1	𝓅ℎ𝒩[𝛿(υ	𝓅ℎ𝒩[𝛿(υ	X
cana-1996	199	2	,	,	PUNCT
cana-1996	199	3	𝓉	𝓉	PRON
cana-1996	199	4	;	;	PUNCT
cana-1996	199	5	𝓅	𝓅	PROPN
cana-1996	199	6	)	)	PUNCT
cana-1996	199	7	]	]	PUNCT
cana-1996	199	8	when	when	SCONJ
cana-1996	199	9	𝓅	𝓅	PROPN
cana-1996	199	10	=	=	SYM
cana-1996	199	11	0	0	PROPN
cana-1996	199	12	&	&	CCONJ
cana-1996	199	13	𝓅	𝓅	NOUN
cana-1996	199	14	=	=	SYM
cana-1996	199	15	1	1	NUM
cana-1996	199	16	,	,	PUNCT
cana-1996	199	17	we	we	PRON
cana-1996	199	18	have	have	VERB
cana-1996	199	19	{	{	PUNCT
cana-1996	199	20	𝛿(υ	𝛿(υ	NOUN
cana-1996	199	21	,	,	PUNCT
cana-1996	199	22	𝓉	𝓉	PRON
cana-1996	199	23	;	;	PUNCT
cana-1996	199	24	0	0	X
cana-1996	199	25	)	)	PUNCT
cana-1996	199	26	=	=	SYM
cana-1996	199	27	𝜇0(υ	𝜇0(υ	PROPN
cana-1996	199	28	,	,	PUNCT
cana-1996	199	29	0	0	NUM
cana-1996	199	30	)	)	PUNCT
cana-1996	199	31	𝛿(υ	𝛿(υ	NOUN
cana-1996	199	32	,	,	PUNCT
cana-1996	199	33	𝓉	𝓉	PRON
cana-1996	199	34	;	;	PUNCT
cana-1996	199	35	1	1	X
cana-1996	199	36	)	)	PUNCT
cana-1996	199	37	=	=	SYM
cana-1996	200	1	𝜇(υ	𝜇(υ	PROPN
cana-1996	200	2	,	,	PUNCT
cana-1996	200	3	𝓉	𝓉	PRON
cana-1996	200	4	)	)	PUNCT
cana-1996	200	5	thus	thus	ADV
cana-1996	200	6	,	,	PUNCT
cana-1996	200	7	the	the	DET
cana-1996	200	8	equation	equation	NOUN
cana-1996	200	9	for	for	ADP
cana-1996	200	10	mth	mth	NOUN
cana-1996	200	11	-	-	PUNCT
cana-1996	200	12	order	order	NOUN
cana-1996	200	13	deformation	deformation	NOUN
cana-1996	200	14	.	.	PUNCT
cana-1996	201	1	ℛ{𝜇𝑚(υ	ℛ{𝜇𝑚(υ	PROPN
cana-1996	201	2	,	,	PUNCT
cana-1996	201	3	𝓉	𝓉	PROPN
cana-1996	201	4	)	)	PUNCT
cana-1996	201	5	−	−	NOUN
cana-1996	201	6	𝜒𝑚𝜇𝑚−1(υ	𝜒𝑚𝜇𝑚−1(υ	PROPN
cana-1996	201	7	,	,	PUNCT
cana-1996	201	8	𝓉	𝓉	PROPN
cana-1996	201	9	)	)	PUNCT
cana-1996	201	10	}	}	PUNCT
cana-1996	202	1	=	=	SYM
cana-1996	202	2	ℎℛ𝑚(𝜇𝑚−1⃗⃗	ℎℛ𝑚(𝜇𝑚−1⃗⃗	NUM
cana-1996	202	3	⃗⃗	⃗⃗	PROPN
cana-1996	202	4	⃗⃗	⃗⃗	PROPN
cana-1996	202	5	⃗⃗	⃗⃗	PROPN
cana-1996	202	6	⃗⃗	⃗⃗	PROPN
cana-1996	202	7	(	(	PUNCT
cana-1996	202	8	υ	υ	PROPN
cana-1996	202	9	,	,	PUNCT
cana-1996	202	10	𝓉	𝓉	PROPN
cana-1996	202	11	)	)	PUNCT
cana-1996	202	12	)	)	PUNCT
cana-1996	202	13	(	(	PUNCT
cana-1996	202	14	31	31	NUM
cana-1996	202	15	)	)	PUNCT
cana-1996	202	16	when	when	SCONJ
cana-1996	202	17	the	the	DET
cana-1996	202	18	“	"	PUNCT
cana-1996	202	19	inverse	inverse	ADJ
cana-1996	202	20	rangaig	rangaig	ADJ
cana-1996	202	21	transform	transform	NOUN
cana-1996	202	22	”	"	PUNCT
cana-1996	202	23	is	be	AUX
cana-1996	202	24	carried	carry	VERB
cana-1996	202	25	out	out	ADP
cana-1996	202	26	to	to	ADP
cana-1996	202	27	both	both	DET
cana-1996	202	28	sides	side	NOUN
cana-1996	202	29	of	of	ADP
cana-1996	202	30	equation	equation	NOUN
cana-1996	202	31	(	(	PUNCT
cana-1996	202	32	31	31	NUM
cana-1996	202	33	)	)	PUNCT
cana-1996	202	34	,	,	PUNCT
cana-1996	202	35	we	we	PRON
cana-1996	202	36	get	get	VERB
cana-1996	202	37	,	,	PUNCT
cana-1996	202	38	𝜇𝑚(υ	𝜇𝑚(υ	NOUN
cana-1996	202	39	,	,	PUNCT
cana-1996	202	40	𝓉	𝓉	PROPN
cana-1996	202	41	)	)	PUNCT
cana-1996	202	42	−	−	NOUN
cana-1996	202	43	𝜒𝑚𝜇𝑚−1(υ	𝜒𝑚𝜇𝑚−1(υ	PROPN
cana-1996	202	44	,	,	PUNCT
cana-1996	202	45	𝓉	𝓉	PRON
cana-1996	202	46	)	)	PUNCT
cana-1996	202	47	=	=	SYM
cana-1996	203	1	ℛ−1	ℛ−1	PROPN
cana-1996	203	2	{	{	PUNCT
cana-1996	203	3	ℎℛ𝑚(𝜇𝑚−1⃗⃗	ℎℛ𝑚(𝜇𝑚−1⃗⃗	PROPN
cana-1996	203	4	⃗⃗	⃗⃗	PROPN
cana-1996	203	5	⃗⃗	⃗⃗	PROPN
cana-1996	203	6	⃗⃗	⃗⃗	PROPN
cana-1996	203	7	⃗⃗	⃗⃗	PROPN
cana-1996	203	8	(	(	PUNCT
cana-1996	203	9	υ	υ	PROPN
cana-1996	203	10	,	,	PUNCT
cana-1996	203	11	𝓉	𝓉	PROPN
cana-1996	203	12	)	)	PUNCT
cana-1996	203	13	)	)	PUNCT
cana-1996	203	14	}	}	PUNCT
cana-1996	203	15	(	(	PUNCT
cana-1996	203	16	32	32	NUM
cana-1996	203	17	)	)	PUNCT
cana-1996	203	18	with	with	ADP
cana-1996	203	19	ℎ	ℎ	PROPN
cana-1996	203	20	=	=	SYM
cana-1996	203	21	−1	−1	NOUN
cana-1996	203	22	,	,	PUNCT
cana-1996	203	23	we	we	PRON
cana-1996	203	24	can	can	AUX
cana-1996	203	25	get	get	VERB
cana-1996	203	26	from	from	ADP
cana-1996	203	27	equation	equation	NOUN
cana-1996	203	28	(	(	PUNCT
cana-1996	203	29	32	32	NUM
cana-1996	203	30	)	)	PUNCT
cana-1996	203	31	𝜇1(υ	𝜇1(υ	NUM
cana-1996	203	32	,	,	PUNCT
cana-1996	203	33	𝓉	𝓉	PRON
cana-1996	203	34	)	)	PUNCT
cana-1996	203	35	=	=	SYM
cana-1996	203	36	−ℛ−1	−ℛ−1	NOUN
cana-1996	203	37	{	{	PUNCT
cana-1996	203	38	ℛ1(𝜇0⃗⃗⃗⃗	ℛ1(𝜇0⃗⃗⃗⃗	X
cana-1996	203	39	(	(	PUNCT
cana-1996	203	40	υ	υ	NOUN
cana-1996	203	41	,	,	PUNCT
cana-1996	203	42	𝓉	𝓉	PROPN
cana-1996	203	43	)	)	PUNCT
cana-1996	203	44	)	)	PUNCT
cana-1996	203	45	}	}	PUNCT
cana-1996	203	46	,	,	PUNCT
cana-1996	203	47	𝜇2(υ	𝜇2(υ	PROPN
cana-1996	203	48	,	,	PUNCT
cana-1996	203	49	𝓉	𝓉	PROPN
cana-1996	203	50	)	)	PUNCT
cana-1996	203	51	=	=	SYM
cana-1996	204	1	𝜇1(υ	𝜇1(υ	PROPN
cana-1996	204	2	,	,	PUNCT
cana-1996	204	3	𝓉	𝓉	PROPN
cana-1996	204	4	)	)	PUNCT
cana-1996	205	1	−	−	PROPN
cana-1996	205	2	ℛ−1	ℛ−1	PROPN
cana-1996	205	3	{	{	PUNCT
cana-1996	205	4	ℛ2(𝜇1⃗⃗⃗⃗	ℛ2(𝜇1⃗⃗⃗⃗	X
cana-1996	205	5	(	(	PUNCT
cana-1996	205	6	υ	υ	NOUN
cana-1996	205	7	,	,	PUNCT
cana-1996	205	8	𝓉	𝓉	PROPN
cana-1996	205	9	)	)	PUNCT
cana-1996	205	10	)	)	PUNCT
cana-1996	205	11	}	}	PUNCT
cana-1996	205	12	,	,	PUNCT
cana-1996	205	13	𝜇3(υ	𝜇3(υ	PROPN
cana-1996	205	14	,	,	PUNCT
cana-1996	205	15	𝓉	𝓉	PROPN
cana-1996	205	16	)	)	PUNCT
cana-1996	205	17	=	=	SYM
cana-1996	206	1	𝜇2(υ	𝜇2(υ	PROPN
cana-1996	206	2	,	,	PUNCT
cana-1996	206	3	𝓉	𝓉	PROPN
cana-1996	206	4	)	)	PUNCT
cana-1996	207	1	−	−	PROPN
cana-1996	208	1	ℛ−1	ℛ−1	INTJ
cana-1996	208	2	{	{	PUNCT
cana-1996	208	3	ℛ3(𝜇2⃗⃗⃗⃗	ℛ3(𝜇2⃗⃗⃗⃗	X
cana-1996	208	4	(	(	PUNCT
cana-1996	208	5	υ	υ	NOUN
cana-1996	208	6	,	,	PUNCT
cana-1996	208	7	𝓉	𝓉	PROPN
cana-1996	208	8	)	)	PUNCT
cana-1996	208	9	)	)	PUNCT
cana-1996	208	10	}	}	PUNCT
cana-1996	208	11	,	,	PUNCT
cana-1996	208	12	⋮	⋮	NOUN
cana-1996	208	13	where	where	SCONJ
cana-1996	208	14	”	"	PUNCT
cana-1996	208	15	ℛ1(𝜇0⃗⃗⃗⃗	ℛ1(𝜇0⃗⃗⃗⃗	X
cana-1996	208	16	(	(	PUNCT
cana-1996	208	17	υ	υ	INTJ
cana-1996	208	18	,	,	PUNCT
cana-1996	208	19	𝓉	𝓉	PROPN
cana-1996	208	20	)	)	PUNCT
cana-1996	208	21	)	)	PUNCT
cana-1996	209	1	=	=	SYM
cana-1996	209	2	1	1	NUM
cana-1996	209	3	𝑤3	𝑤3	PROPN
cana-1996	209	4	,	,	PUNCT
cana-1996	209	5	ℛ2(𝜇1⃗⃗⃗⃗	ℛ2(𝜇1⃗⃗⃗⃗	X
cana-1996	209	6	(	(	PUNCT
cana-1996	209	7	υ	υ	NOUN
cana-1996	209	8	,	,	PUNCT
cana-1996	209	9	𝓉	𝓉	PROPN
cana-1996	209	10	)	)	PUNCT
cana-1996	209	11	)	)	PUNCT
cana-1996	210	1	=	=	PRON
cana-1996	210	2	(	(	PUNCT
cana-1996	210	3	−	−	PROPN
cana-1996	210	4	1	1	NUM
cana-1996	210	5	𝜛3	𝜛3	PROPN
cana-1996	210	6	−	−	PROPN
cana-1996	210	7	1	1	NUM
cana-1996	210	8	𝜛5	𝜛5	NOUN
cana-1996	210	9	)	)	PUNCT
cana-1996	210	10	,	,	PUNCT
cana-1996	210	11	ℛ3(𝜇2⃗⃗⃗⃗	ℛ3(𝜇2⃗⃗⃗⃗	X
cana-1996	210	12	(	(	PUNCT
cana-1996	210	13	υ	υ	NOUN
cana-1996	210	14	,	,	PUNCT
cana-1996	210	15	𝓉	𝓉	PROPN
cana-1996	210	16	)	)	PUNCT
cana-1996	210	17	)	)	PUNCT
cana-1996	211	1	=	=	PUNCT
cana-1996	211	2	(	(	PUNCT
cana-1996	211	3	1	1	NUM
cana-1996	211	4	𝜛5	𝜛5	NOUN
cana-1996	211	5	+	+	CCONJ
cana-1996	211	6	1	1	NUM
cana-1996	211	7	𝜛7	𝜛7	NOUN
cana-1996	211	8	)	)	PUNCT
cana-1996	211	9	,	,	PUNCT
cana-1996	211	10	⋮	⋮	NOUN
cana-1996	211	11	therefore	therefore	ADV
cana-1996	211	12	,	,	PUNCT
cana-1996	211	13	𝜇1(υ	𝜇1(υ	PROPN
cana-1996	211	14	,	,	PUNCT
cana-1996	211	15	𝓉	𝓉	PROPN
cana-1996	211	16	)	)	PUNCT
cana-1996	211	17	=	=	SYM
cana-1996	211	18	𝓉	𝓉	PROPN
cana-1996	211	19	,	,	PUNCT
cana-1996	211	20	𝜇2(υ	𝜇2(υ	PROPN
cana-1996	211	21	,	,	PUNCT
cana-1996	211	22	𝓉	𝓉	PROPN
cana-1996	211	23	)	)	PUNCT
cana-1996	211	24	=	=	PUNCT
cana-1996	212	1	−	−	PROPN
cana-1996	212	2	𝓉3	𝓉3	PROPN
cana-1996	212	3	3	3	NUM
cana-1996	212	4	!	!	NUM
cana-1996	212	5	,	,	PUNCT
cana-1996	212	6	𝜇3(υ	𝜇3(υ	PROPN
cana-1996	212	7	,	,	PUNCT
cana-1996	212	8	𝓉	𝓉	PROPN
cana-1996	212	9	)	)	PUNCT
cana-1996	212	10	=	=	SYM
cana-1996	213	1	𝓉5	𝓉5	NOUN
cana-1996	213	2	5	5	NUM
cana-1996	213	3	!	!	NOUN
cana-1996	213	4	,	,	PUNCT
cana-1996	213	5	⋮	⋮	NOUN
cana-1996	213	6	communications	communication	NOUN
cana-1996	213	7	on	on	ADP
cana-1996	213	8	applied	apply	VERB
cana-1996	213	9	nonlinear	nonlinear	ADJ
cana-1996	213	10	analysis	analysis	NOUN
cana-1996	213	11	issn	issn	NOUN
cana-1996	213	12	:	:	PUNCT
cana-1996	213	13	1074	1074	NUM
cana-1996	213	14	-	-	PUNCT
cana-1996	213	15	133x	133x	NUM
cana-1996	213	16	vol	vol	NOUN
cana-1996	213	17	32	32	NUM
cana-1996	214	1	no	no	NOUN
cana-1996	214	2	.	.	NOUN
cana-1996	214	3	3	3	NUM
cana-1996	214	4	(	(	PUNCT
cana-1996	214	5	2025	2025	NUM
cana-1996	214	6	)	)	PUNCT
cana-1996	214	7	397	397	NUM
cana-1996	214	8	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	214	9	the	the	DET
cana-1996	214	10	solution	solution	NOUN
cana-1996	214	11	is	be	AUX
cana-1996	214	12	:	:	PUNCT
cana-1996	214	13	𝜇(υ	𝜇(υ	PROPN
cana-1996	214	14	,	,	PUNCT
cana-1996	214	15	𝓉	𝓉	PRON
cana-1996	214	16	)	)	PUNCT
cana-1996	214	17	=	=	SYM
cana-1996	214	18	𝜇0	𝜇0	PROPN
cana-1996	214	19	+	+	CCONJ
cana-1996	214	20	𝜇1	𝜇1	PROPN
cana-1996	214	21	+	+	CCONJ
cana-1996	214	22	𝜇2	𝜇2	PROPN
cana-1996	214	23	+	+	SYM
cana-1996	214	24	⋯	⋯	PROPN
cana-1996	214	25	or	or	CCONJ
cana-1996	214	26	𝜇(υ	𝜇(υ	PROPN
cana-1996	214	27	,	,	PUNCT
cana-1996	214	28	𝓉	𝓉	PRON
cana-1996	214	29	)	)	PUNCT
cana-1996	214	30	=	=	VERB
cana-1996	214	31	sin	sin	VERB
cana-1996	214	32	𝓍	𝓍	X
cana-1996	214	33	+	+	CCONJ
cana-1996	214	34	sin𝓎	sin𝓎	NOUN
cana-1996	214	35	+	+	CCONJ
cana-1996	214	36	sin	sin	NOUN
cana-1996	214	37	𝓏	𝓏	PROPN
cana-1996	214	38	+	+	X
cana-1996	214	39	(	(	PUNCT
cana-1996	214	40	𝓉	𝓉	PROPN
cana-1996	214	41	−	−	PROPN
cana-1996	214	42	𝓉3	𝓉3	PROPN
cana-1996	214	43	3	3	NUM
cana-1996	214	44	!	!	PUNCT
cana-1996	215	1	+	+	CCONJ
cana-1996	215	2	𝓉5	𝓉5	NOUN
cana-1996	215	3	5	5	NUM
cana-1996	215	4	!	!	PUNCT
cana-1996	216	1	−	−	PROPN
cana-1996	216	2	⋯	⋯	NOUN
cana-1996	216	3	)	)	PUNCT
cana-1996	216	4	or	or	CCONJ
cana-1996	216	5	𝜇(υ	𝜇(υ	PROPN
cana-1996	216	6	,	,	PUNCT
cana-1996	216	7	𝓉	𝓉	PRON
cana-1996	216	8	)	)	PUNCT
cana-1996	216	9	=	=	VERB
cana-1996	216	10	sin	sin	VERB
cana-1996	216	11	𝓍	𝓍	X
cana-1996	216	12	+	+	CCONJ
cana-1996	216	13	sin𝓎	sin𝓎	NOUN
cana-1996	216	14	+	+	CCONJ
cana-1996	216	15	sin	sin	NOUN
cana-1996	216	16	𝓏	𝓏	PROPN
cana-1996	216	17	+	+	CCONJ
cana-1996	216	18	sin	sin	NOUN
cana-1996	216	19	𝓉	𝓉	PROPN
cana-1996	216	20	figure	figure	VERB
cana-1996	216	21	5	5	NUM
cana-1996	216	22	:	:	PUNCT
cana-1996	216	23	example	example	NOUN
cana-1996	216	24	3	3	NUM
cana-1996	216	25	's	's	PART
cana-1996	216	26	solutions	solution	NOUN
cana-1996	216	27	'	'	PART
cana-1996	216	28	physical	physical	ADJ
cana-1996	216	29	behavior	behavior	NOUN
cana-1996	216	30	at	at	ADP
cana-1996	216	31	𝒛	𝒛	NOUN
cana-1996	216	32	=	=	SYM
cana-1996	216	33	𝟏	𝟏	PROPN
cana-1996	216	34	,	,	PUNCT
cana-1996	216	35	𝓽	𝓽	X
cana-1996	216	36	=	=	X
cana-1996	216	37	𝝅	𝝅	PRON
cana-1996	216	38	𝟐	𝟐	NUM
cana-1996	216	39	figure	figure	NOUN
cana-1996	216	40	6	6	NUM
cana-1996	216	41	:	:	PUNCT
cana-1996	216	42	the	the	DET
cana-1996	216	43	contour	contour	NOUN
cana-1996	216	44	diagram	diagram	NOUN
cana-1996	216	45	obtained	obtain	VERB
cana-1996	216	46	from	from	ADP
cana-1996	216	47	solving	solve	VERB
cana-1996	216	48	example	example	NOUN
cana-1996	216	49	3	3	NUM
cana-1996	216	50	at	at	ADP
cana-1996	216	51	𝒛	𝒛	PROPN
cana-1996	216	52	=	=	SYM
cana-1996	216	53	𝟏	𝟏	PROPN
cana-1996	216	54	,	,	PUNCT
cana-1996	216	55	𝓉	𝓉	PROPN
cana-1996	216	56	=	=	SYM
cana-1996	216	57	𝝅	𝝅	ADP
cana-1996	216	58	𝟐	𝟐	NUM
cana-1996	216	59	-2	-2	NOUN
cana-1996	216	60	-1	-1	NOUN
cana-1996	216	61	0	0	NUM
cana-1996	216	62	1	1	NUM
cana-1996	216	63	2	2	NUM
cana-1996	216	64	-2	-2	NOUN
cana-1996	216	65	0	0	NUM
cana-1996	216	66	2	2	NUM
cana-1996	216	67	-2	-2	NOUN
cana-1996	216	68	0	0	NUM
cana-1996	216	69	2	2	NUM
cana-1996	216	70	4	4	NUM
cana-1996	216	71	x	x	NOUN
cana-1996	216	72	example	example	NOUN
cana-1996	216	73	3	3	NUM
cana-1996	216	74	:	:	PUNCT
cana-1996	216	75	for	for	ADP
cana-1996	216	76	t	t	NOUN
cana-1996	216	77	=	=	SYM
cana-1996	216	78	pi/2	pi/2	PROPN
cana-1996	216	79	y	y	PROPN
cana-1996	216	80	s	s	PART
cana-1996	216	81	o	o	X
cana-1996	216	82	lu	lu	NOUN
cana-1996	216	83	ti	ti	NOUN
cana-1996	216	84	o	o	NOUN
cana-1996	216	85	n	n	X
cana-1996	216	86	s	s	NOUN
cana-1996	216	87	x	x	X
cana-1996	216	88	y	y	NOUN
cana-1996	216	89	-2	-2	INTJ
cana-1996	216	90	-1.5	-1.5	NUM
cana-1996	216	91	-1	-1	PROPN
cana-1996	217	1	-0.5	-0.5	X
cana-1996	217	2	0	0	NUM
cana-1996	217	3	0.5	0.5	NUM
cana-1996	217	4	1	1	NUM
cana-1996	217	5	1.5	1.5	NUM
cana-1996	217	6	2	2	NUM
cana-1996	217	7	-2	-2	NOUN
cana-1996	217	8	-1.5	-1.5	NUM
cana-1996	217	9	-1	-1	PROPN
cana-1996	217	10	-0.5	-0.5	X
cana-1996	217	11	0	0	NUM
cana-1996	217	12	0.5	0.5	NUM
cana-1996	217	13	1	1	NUM
cana-1996	217	14	1.5	1.5	NUM
cana-1996	217	15	2	2	NUM
cana-1996	217	16	communications	communication	NOUN
cana-1996	217	17	on	on	ADP
cana-1996	217	18	applied	apply	VERB
cana-1996	217	19	nonlinear	nonlinear	ADJ
cana-1996	217	20	analysis	analysis	NOUN
cana-1996	217	21	issn	issn	NOUN
cana-1996	217	22	:	:	PUNCT
cana-1996	217	23	1074	1074	NUM
cana-1996	217	24	-	-	PUNCT
cana-1996	217	25	133x	133x	NUM
cana-1996	217	26	vol	vol	NOUN
cana-1996	217	27	32	32	NUM
cana-1996	217	28	no	no	NOUN
cana-1996	217	29	.	.	NOUN
cana-1996	217	30	3	3	NUM
cana-1996	217	31	(	(	PUNCT
cana-1996	217	32	2025	2025	NUM
cana-1996	217	33	)	)	PUNCT
cana-1996	217	34	398	398	NUM
cana-1996	217	35	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	217	36	figures	figure	NOUN
cana-1996	217	37	5	5	NUM
cana-1996	217	38	and	and	CCONJ
cana-1996	217	39	6	6	NUM
cana-1996	217	40	depict	depict	NOUN
cana-1996	217	41	the	the	DET
cana-1996	217	42	physical	physical	ADJ
cana-1996	217	43	and	and	CCONJ
cana-1996	217	44	dynamic	dynamic	ADJ
cana-1996	217	45	behaviour	behaviour	NOUN
cana-1996	217	46	of	of	ADP
cana-1996	217	47	the	the	DET
cana-1996	217	48	solutions	solution	NOUN
cana-1996	217	49	found	find	VERB
cana-1996	217	50	at	at	ADP
cana-1996	217	51	𝑧	𝑧	PROPN
cana-1996	217	52	=	=	SYM
cana-1996	217	53	1	1	NUM
cana-1996	217	54	and	and	CCONJ
cana-1996	217	55	𝓉	𝓉	PROPN
cana-1996	217	56	=	=	PUNCT
cana-1996	217	57	𝜋	𝜋	NOUN
cana-1996	217	58	2	2	NUM
cana-1996	217	59	using	use	VERB
cana-1996	217	60	the	the	DET
cana-1996	217	61	"	"	PUNCT
cana-1996	217	62	homotopy	homotopy	VERB
cana-1996	217	63	analysis	analysis	NOUN
cana-1996	217	64	method	method	NOUN
cana-1996	217	65	"	"	PUNCT
cana-1996	217	66	based	base	VERB
cana-1996	217	67	on	on	ADP
cana-1996	217	68	the	the	DET
cana-1996	217	69	"	"	PUNCT
cana-1996	217	70	rangaig	rangaig	ADJ
cana-1996	217	71	transform	transform	NOUN
cana-1996	217	72	.	.	PUNCT
cana-1996	217	73	"	"	PUNCT
cana-1996	218	1	6	6	NUM
cana-1996	218	2	.	.	X
cana-1996	218	3	conclusion	conclusion	NOUN
cana-1996	218	4	the	the	DET
cana-1996	218	5	computational	computational	ADJ
cana-1996	218	6	results	result	NOUN
cana-1996	218	7	established	establish	VERB
cana-1996	218	8	from	from	ADP
cana-1996	218	9	the	the	DET
cana-1996	218	10	above	above	ADJ
cana-1996	218	11	data	datum	NOUN
cana-1996	218	12	indicate	indicate	VERB
cana-1996	218	13	that	that	SCONJ
cana-1996	218	14	the	the	DET
cana-1996	218	15	“	"	PUNCT
cana-1996	218	16	rangaig	rangaig	ADJ
cana-1996	218	17	transforms	transform	VERB
cana-1996	218	18	”	"	PUNCT
cana-1996	218	19	with	with	ADP
cana-1996	218	20	the	the	DET
cana-1996	218	21	“	"	PUNCT
cana-1996	218	22	homotopy	homotopy	VERB
cana-1996	218	23	analysis	analysis	NOUN
cana-1996	218	24	method	method	NOUN
cana-1996	218	25	”	"	PUNCT
cana-1996	218	26	is	be	AUX
cana-1996	218	27	a	a	DET
cana-1996	218	28	powerful	powerful	ADJ
cana-1996	218	29	and	and	CCONJ
cana-1996	218	30	simple	simple	ADJ
cana-1996	218	31	way	way	NOUN
cana-1996	218	32	to	to	PART
cana-1996	218	33	find	find	VERB
cana-1996	218	34	exact	exact	ADJ
cana-1996	218	35	solutions	solution	NOUN
cana-1996	218	36	of	of	ADP
cana-1996	218	37	a	a	DET
cana-1996	218	38	few	few	ADJ
cana-1996	218	39	“	"	PUNCT
cana-1996	218	40	(	(	PUNCT
cana-1996	218	41	3	3	NUM
cana-1996	218	42	+	+	NUM
cana-1996	218	43	1)d	1)d	NUM
cana-1996	218	44	telegraph	telegraph	NOUN
cana-1996	218	45	equations	equation	NOUN
cana-1996	218	46	”	"	PUNCT
cana-1996	218	47	,	,	PUNCT
cana-1996	218	48	“	"	PUNCT
cana-1996	218	49	(	(	PUNCT
cana-1996	218	50	3	3	NUM
cana-1996	218	51	+	+	SYM
cana-1996	218	52	1)-d	1)-d	NUM
cana-1996	218	53	diffusion	diffusion	NOUN
cana-1996	218	54	equations	equation	NOUN
cana-1996	218	55	”	"	PUNCT
cana-1996	218	56	,	,	PUNCT
cana-1996	218	57	and	and	CCONJ
cana-1996	218	58	“	"	PUNCT
cana-1996	218	59	(	(	PUNCT
cana-1996	218	60	3	3	NUM
cana-1996	218	61	+	+	NUM
cana-1996	218	62	1)d	1)d	PROPN
cana-1996	218	63	klein	klein	PROPN
cana-1996	218	64	gordan	gordan	PROPN
cana-1996	218	65	equations	equations	PROPN
cana-1996	218	66	”	"	PUNCT
cana-1996	218	67	.	.	PUNCT
cana-1996	219	1	these	these	DET
cana-1996	219	2	equations	equation	NOUN
cana-1996	219	3	are	be	AUX
cana-1996	219	4	used	use	VERB
cana-1996	219	5	in	in	ADP
cana-1996	219	6	various	various	ADJ
cana-1996	219	7	disciplines	discipline	NOUN
cana-1996	219	8	of	of	ADP
cana-1996	219	9	science	science	NOUN
cana-1996	219	10	and	and	CCONJ
cana-1996	219	11	engineering	engineering	NOUN
cana-1996	219	12	.	.	PUNCT
cana-1996	220	1	this	this	DET
cana-1996	220	2	approach	approach	NOUN
cana-1996	220	3	will	will	AUX
cana-1996	220	4	be	be	AUX
cana-1996	220	5	valid	valid	ADJ
cana-1996	220	6	in	in	ADP
cana-1996	220	7	the	the	DET
cana-1996	220	8	future	future	NOUN
cana-1996	220	9	for	for	ADP
cana-1996	220	10	fractional	fractional	ADJ
cana-1996	220	11	pdes	pde	NOUN
cana-1996	220	12	and	and	CCONJ
cana-1996	220	13	other	other	ADJ
cana-1996	220	14	problems	problem	NOUN
cana-1996	220	15	.	.	PUNCT
cana-1996	221	1	references	reference	NOUN
cana-1996	221	2	[	[	X
cana-1996	221	3	1	1	NUM
cana-1996	221	4	]	]	PUNCT
cana-1996	221	5	a.	a.	NOUN
cana-1996	221	6	rangaig	rangaig	PROPN
cana-1996	221	7	,	,	PUNCT
cana-1996	221	8	n.	n.	PROPN
cana-1996	221	9	,	,	PUNCT
cana-1996	221	10	d.	d.	PROPN
cana-1996	221	11	minor	minor	PROPN
cana-1996	221	12	,	,	PUNCT
cana-1996	221	13	n.	n.	PROPN
cana-1996	221	14	,	,	PUNCT
cana-1996	221	15	fe	fe	PROPN
cana-1996	221	16	i.	i.	PROPN
cana-1996	221	17	pe	pe	PROPN
cana-1996	221	18	~	~	PROPN
cana-1996	221	19	nonal	nonal	ADJ
cana-1996	221	20	,	,	PUNCT
cana-1996	221	21	g.	g.	PROPN
cana-1996	221	22	,	,	PUNCT
cana-1996	221	23	lord	lord	PROPN
cana-1996	221	24	dexter	dexter	PROPN
cana-1996	221	25	c.	c.	PROPN
cana-1996	221	26	filipinas	filipinas	PROPN
cana-1996	221	27	,	,	PUNCT
cana-1996	221	28	j.	j.	PROPN
cana-1996	221	29	,	,	PUNCT
cana-1996	221	30	&	&	CCONJ
cana-1996	221	31	c.	c.	PROPN
cana-1996	221	32	convicto	convicto	PROPN
cana-1996	221	33	,	,	PUNCT
cana-1996	221	34	v.	v.	PROPN
cana-1996	221	35	(	(	PUNCT
cana-1996	221	36	2017	2017	NUM
cana-1996	221	37	)	)	PUNCT
cana-1996	221	38	.	.	PUNCT
cana-1996	222	1	on	on	ADP
cana-1996	222	2	another	another	DET
cana-1996	222	3	type	type	NOUN
cana-1996	222	4	of	of	ADP
cana-1996	222	5	transform	transform	NOUN
cana-1996	222	6	called	call	VERB
cana-1996	222	7	rangaig	rangaig	ADJ
cana-1996	222	8	transform	transform	NOUN
cana-1996	222	9	.	.	PUNCT
cana-1996	223	1	international	international	ADJ
cana-1996	223	2	journal	journal	NOUN
cana-1996	223	3	of	of	ADP
cana-1996	223	4	partial	partial	ADJ
cana-1996	223	5	differential	differential	ADJ
cana-1996	223	6	equations	equation	NOUN
cana-1996	223	7	and	and	CCONJ
cana-1996	223	8	applications	application	NOUN
cana-1996	223	9	,	,	PUNCT
cana-1996	223	10	5(1	5(1	NUM
cana-1996	223	11	)	)	PUNCT
cana-1996	223	12	,	,	PUNCT
cana-1996	223	13	42–48	42–48	PROPN
cana-1996	223	14	.	.	PUNCT
cana-1996	223	15	https://doi.org/10.12691/ijpdea-5-1-6	https://doi.org/10.12691/ijpdea-5-1-6	PUNCT
cana-1996	224	1	[	[	X
cana-1996	224	2	2	2	NUM
cana-1996	224	3	]	]	PUNCT
cana-1996	224	4	aboodh	aboodh	PROPN
cana-1996	224	5	,	,	PUNCT
cana-1996	224	6	k.s	k.s	PROPN
cana-1996	224	7	.	.	PROPN
cana-1996	224	8	(	(	PUNCT
cana-1996	224	9	2013	2013	NUM
cana-1996	224	10	)	)	PUNCT
cana-1996	224	11	.	.	PUNCT
cana-1996	225	1	the	the	DET
cana-1996	225	2	new	new	ADJ
cana-1996	225	3	integrale	integrale	NOUN
cana-1996	225	4	transform	transform	VERB
cana-1996	225	5	aboodh	aboodh	ADJ
cana-1996	225	6	transform	transform	NOUN
cana-1996	225	7	.	.	PUNCT
cana-1996	226	1	global	global	ADJ
cana-1996	226	2	journal	journal	PROPN
cana-1996	226	3	of	of	ADP
cana-1996	226	4	pure	pure	ADJ
cana-1996	226	5	and	and	CCONJ
cana-1996	226	6	applied	applied	ADJ
cana-1996	226	7	mathematics	mathematic	NOUN
cana-1996	226	8	,	,	PUNCT
cana-1996	226	9	9(1	9(1	NUM
cana-1996	226	10	)	)	PUNCT
cana-1996	226	11	,	,	PUNCT
cana-1996	226	12	35	35	NUM
cana-1996	226	13	-	-	SYM
cana-1996	226	14	43	43	NUM
cana-1996	226	15	.	.	PUNCT
cana-1996	227	1	[	[	X
cana-1996	227	2	3	3	NUM
cana-1996	227	3	]	]	X
cana-1996	227	4	alomari	alomari	X
cana-1996	227	5	,	,	PUNCT
cana-1996	227	6	a.k	a.k	PROPN
cana-1996	227	7	.	.	PROPN
cana-1996	227	8	,	,	PUNCT
cana-1996	227	9	noorani	noorani	PROPN
cana-1996	227	10	,	,	PUNCT
cana-1996	227	11	m.s.m	m.s.m	PROPN
cana-1996	227	12	.	.	PROPN
cana-1996	227	13	and	and	CCONJ
cana-1996	227	14	nazar	nazar	PROPN
cana-1996	227	15	,	,	PUNCT
cana-1996	227	16	r.	r.	PROPN
cana-1996	227	17	explicit	explicit	ADJ
cana-1996	227	18	series	series	NOUN
cana-1996	227	19	solutions	solution	NOUN
cana-1996	227	20	of	of	ADP
cana-1996	227	21	some	some	DET
cana-1996	227	22	linear	linear	ADJ
cana-1996	227	23	and	and	CCONJ
cana-1996	227	24	nonlinear	nonlinear	ADJ
cana-1996	227	25	schrodinger	schrodinger	PROPN
cana-1996	227	26	equations	equation	NOUN
cana-1996	227	27	via	via	ADP
cana-1996	227	28	the	the	DET
cana-1996	227	29	homotopy	homotopy	NOUN
cana-1996	227	30	analysis	analysis	NOUN
cana-1996	227	31	method	method	NOUN
cana-1996	227	32	,	,	PUNCT
cana-1996	227	33	communications	communication	NOUN
cana-1996	227	34	in	in	ADP
cana-1996	227	35	nonlinear	nonlinear	ADJ
cana-1996	227	36	science	science	NOUN
cana-1996	227	37	and	and	CCONJ
cana-1996	227	38	numerical	numerical	PROPN
cana-1996	227	39	simulation	simulation	PROPN
cana-1996	227	40	.	.	PUNCT
cana-1996	228	1	2009	2009	NUM
cana-1996	228	2	,	,	PUNCT
cana-1996	228	3	14(4	14(4	NUM
cana-1996	228	4	):	):	PUNCT
cana-1996	228	5	1196–1207	1196–1207	NUM
cana-1996	228	6	.	.	PUNCT
cana-1996	229	1	[	[	X
cana-1996	229	2	4	4	NUM
cana-1996	229	3	]	]	X
cana-1996	229	4	eltayeb	eltayeb	PROPN
cana-1996	229	5	,	,	PUNCT
cana-1996	229	6	h.	h.	PROPN
cana-1996	229	7	and	and	CCONJ
cana-1996	229	8	kilicman	kilicman	PROPN
cana-1996	229	9	,	,	PUNCT
cana-1996	229	10	a.	a.	NOUN
cana-1996	229	11	a	a	DET
cana-1996	229	12	note	note	NOUN
cana-1996	229	13	on	on	ADP
cana-1996	229	14	the	the	DET
cana-1996	229	15	sumudu	sumudu	NOUN
cana-1996	229	16	transforms	transform	VERB
cana-1996	229	17	and	and	CCONJ
cana-1996	229	18	differential	differential	ADJ
cana-1996	229	19	equations	equation	NOUN
cana-1996	229	20	,	,	PUNCT
cana-1996	229	21	applied	apply	VERB
cana-1996	229	22	mathematical	mathematical	ADJ
cana-1996	229	23	sciences	science	NOUN
cana-1996	229	24	.	.	PUNCT
cana-1996	230	1	2010	2010	NUM
cana-1996	230	2	,	,	PUNCT
cana-1996	230	3	4(22	4(22	NUM
cana-1996	230	4	):	):	PUNCT
cana-1996	230	5	1089	1089	NUM
cana-1996	230	6	-	-	SYM
cana-1996	230	7	1098	1098	NUM
cana-1996	230	8	[	[	X
cana-1996	230	9	5	5	NUM
cana-1996	230	10	]	]	X
cana-1996	230	11	elzaki	elzaki	NOUN
cana-1996	230	12	,	,	PUNCT
cana-1996	230	13	t.m	t.m	PROPN
cana-1996	230	14	.	.	PROPN
cana-1996	230	15	and	and	CCONJ
cana-1996	230	16	elzaki	elzaki	PROPN
cana-1996	230	17	,	,	PUNCT
cana-1996	230	18	s.	s.	PROPN
cana-1996	230	19	m.	m.	PROPN
cana-1996	230	20	application	application	NOUN
cana-1996	230	21	of	of	ADP
cana-1996	230	22	new	new	ADJ
cana-1996	230	23	transform	transform	NOUN
cana-1996	230	24	“	"	PUNCT
cana-1996	230	25	elzaki	elzaki	NOUN
cana-1996	230	26	transform	transform	NOUN
cana-1996	230	27	”	"	PUNCT
cana-1996	230	28	to	to	ADP
cana-1996	230	29	partial	partial	ADJ
cana-1996	230	30	differential	differential	NOUN
cana-1996	230	31	equations	equation	NOUN
cana-1996	230	32	,	,	PUNCT
cana-1996	230	33	global	global	ADJ
cana-1996	230	34	journal	journal	NOUN
cana-1996	230	35	of	of	ADP
cana-1996	230	36	pure	pure	ADJ
cana-1996	230	37	and	and	CCONJ
cana-1996	230	38	applied	applied	ADJ
cana-1996	230	39	mathematics	mathematic	NOUN
cana-1996	230	40	.	.	PUNCT
cana-1996	231	1	2011	2011	NUM
cana-1996	231	2	,	,	PUNCT
cana-1996	231	3	1	1	NUM
cana-1996	231	4	:	:	SYM
cana-1996	231	5	65	65	NUM
cana-1996	231	6	-	-	SYM
cana-1996	231	7	70	70	NUM
cana-1996	231	8	.	.	PUNCT
cana-1996	232	1	[	[	X
cana-1996	232	2	6	6	NUM
cana-1996	232	3	]	]	PUNCT
cana-1996	232	4	elzaki	elzaki	NOUN
cana-1996	232	5	,	,	PUNCT
cana-1996	232	6	t.m	t.m	PROPN
cana-1996	232	7	.	.	PUNCT
cana-1996	233	1	the	the	DET
cana-1996	233	2	new	new	ADJ
cana-1996	233	3	integral	integral	ADJ
cana-1996	233	4	transform	transform	NOUN
cana-1996	233	5	“	"	PUNCT
cana-1996	233	6	elzaki	elzaki	NOUN
cana-1996	233	7	transform	transform	NOUN
cana-1996	233	8	”	"	PUNCT
cana-1996	233	9	global	global	ADJ
cana-1996	233	10	journal	journal	NOUN
cana-1996	233	11	of	of	ADP
cana-1996	233	12	pure	pure	ADJ
cana-1996	233	13	and	and	CCONJ
cana-1996	233	14	applied	applied	ADJ
cana-1996	233	15	mathematics	mathematic	NOUN
cana-1996	233	16	.	.	PUNCT
cana-1996	234	1	2011	2011	NUM
cana-1996	234	2	,	,	PUNCT
cana-1996	234	3	1	1	NUM
cana-1996	234	4	:	:	SYM
cana-1996	234	5	57	57	NUM
cana-1996	234	6	-	-	SYM
cana-1996	234	7	64	64	NUM
cana-1996	234	8	.	.	PUNCT
cana-1996	235	1	[	[	X
cana-1996	235	2	7	7	NUM
cana-1996	235	3	]	]	X
cana-1996	235	4	ganjiani	ganjiani	ADJ
cana-1996	235	5	,	,	PUNCT
cana-1996	235	6	m.	m.	NOUN
cana-1996	235	7	solution	solution	NOUN
cana-1996	235	8	of	of	ADP
cana-1996	235	9	nonlinear	nonlinear	ADJ
cana-1996	235	10	fractional	fractional	ADJ
cana-1996	235	11	differential	differential	NOUN
cana-1996	235	12	equation	equation	NOUN
cana-1996	235	13	using	use	VERB
cana-1996	235	14	homotopy	homotopy	NOUN
cana-1996	235	15	analysis	analysis	NOUN
cana-1996	235	16	method	method	NOUN
cana-1996	235	17	,	,	PUNCT
cana-1996	235	18	applied	apply	VERB
cana-1996	235	19	mathematical	mathematical	ADJ
cana-1996	235	20	modeling	modeling	NOUN
cana-1996	235	21	.	.	PUNCT
cana-1996	236	1	2010	2010	NUM
cana-1996	236	2	,	,	PUNCT
cana-1996	236	3	34	34	NUM
cana-1996	236	4	:	:	SYM
cana-1996	236	5	1634	1634	NUM
cana-1996	236	6	-	-	SYM
cana-1996	236	7	1641	1641	NUM
cana-1996	236	8	.	.	PUNCT
cana-1996	237	1	[	[	X
cana-1996	237	2	8	8	NUM
cana-1996	237	3	]	]	X
cana-1996	237	4	gupta	gupta	PROPN
cana-1996	237	5	,	,	PUNCT
cana-1996	237	6	v.g	v.g	PROPN
cana-1996	237	7	.	.	PROPN
cana-1996	237	8	,	,	PUNCT
cana-1996	237	9	&	&	CCONJ
cana-1996	237	10	kumar	kumar	PROPN
cana-1996	237	11	,	,	PUNCT
cana-1996	237	12	p.	p.	NOUN
cana-1996	237	13	(	(	PUNCT
cana-1996	237	14	2015	2015	NUM
cana-1996	237	15	)	)	PUNCT
cana-1996	237	16	.	.	PUNCT
cana-1996	238	1	approximate	approximate	ADJ
cana-1996	238	2	solutions	solution	NOUN
cana-1996	238	3	of	of	ADP
cana-1996	238	4	fractional	fractional	ADJ
cana-1996	238	5	linear	linear	ADJ
cana-1996	238	6	and	and	CCONJ
cana-1996	238	7	nonlinear	nonlinear	ADJ
cana-1996	238	8	differential	differential	ADJ
cana-1996	238	9	equations	equation	NOUN
cana-1996	238	10	using	use	VERB
cana-1996	238	11	laplace	laplace	NOUN
cana-1996	238	12	homotopy	homotopy	NOUN
cana-1996	238	13	analysis	analysis	NOUN
cana-1996	238	14	method	method	NOUN
cana-1996	238	15	.	.	PUNCT
cana-1996	239	1	international	international	ADJ
cana-1996	239	2	journal	journal	PROPN
cana-1996	239	3	of	of	ADP
cana-1996	239	4	nonlinear	nonlinear	PROPN
cana-1996	239	5	sciences	sciences	PROPN
cana-1996	239	6	,	,	PUNCT
cana-1996	239	7	19(2	19(2	NUM
cana-1996	239	8	)	)	PUNCT
cana-1996	239	9	,	,	PUNCT
cana-1996	239	10	113	113	NUM
cana-1996	239	11	-	-	SYM
cana-1996	239	12	120	120	NUM
cana-1996	239	13	.	.	PUNCT
cana-1996	240	1	[	[	X
cana-1996	240	2	9	9	NUM
cana-1996	240	3	]	]	X
cana-1996	240	4	jafari	jafari	X
cana-1996	240	5	,	,	PUNCT
cana-1996	240	6	h.	h.	PROPN
cana-1996	240	7	and	and	CCONJ
cana-1996	240	8	seifi	seifi	NOUN
cana-1996	240	9	,	,	PUNCT
cana-1996	240	10	s.	s.	PROPN
cana-1996	240	11	homotopy	homotopy	VERB
cana-1996	240	12	analysis	analysis	NOUN
cana-1996	240	13	method	method	NOUN
cana-1996	240	14	for	for	ADP
cana-1996	240	15	solving	solve	VERB
cana-1996	240	16	linear	linear	NOUN
cana-1996	240	17	and	and	CCONJ
cana-1996	240	18	nonlinear	nonlinear	ADJ
cana-1996	240	19	fractional	fractional	ADJ
cana-1996	240	20	diffusion	diffusion	NOUN
cana-1996	240	21	-	-	PUNCT
cana-1996	240	22	wave	wave	NOUN
cana-1996	240	23	equation	equation	NOUN
cana-1996	240	24	.	.	PUNCT
cana-1996	241	1	comun	comun	PROPN
cana-1996	241	2	.	.	PROPN
cana-1996	242	1	nonlin	nonlin	PROPN
cana-1996	242	2	.	.	PUNCT
cana-1996	243	1	sci	sci	PROPN
cana-1996	243	2	.	.	PUNCT
cana-1996	244	1	num	num	PROPN
cana-1996	244	2	.	.	PUNCT
cana-1996	245	1	sim	sim	PROPN
cana-1996	245	2	.	.	PUNCT
cana-1996	246	1	2009	2009	NUM
cana-1996	246	2	,	,	PUNCT
cana-1996	246	3	14(5	14(5	NUM
cana-1996	246	4	):	):	PUNCT
cana-1996	246	5	2006	2006	NUM
cana-1996	246	6	-	-	SYM
cana-1996	246	7	2012	2012	NUM
cana-1996	246	8	.	.	PUNCT
cana-1996	247	1	[	[	X
cana-1996	247	2	10	10	NUM
cana-1996	247	3	]	]	X
cana-1996	247	4	khan	khan	PROPN
cana-1996	247	5	,	,	PUNCT
cana-1996	247	6	z.h	z.h	PROPN
cana-1996	247	7	.	.	PROPN
cana-1996	247	8	,	,	PUNCT
cana-1996	247	9	&	&	CCONJ
cana-1996	247	10	khan	khan	PROPN
cana-1996	247	11	,	,	PUNCT
cana-1996	247	12	w.a	w.a	PROPN
cana-1996	247	13	.	.	PROPN
cana-1996	247	14	(	(	PUNCT
cana-1996	247	15	2008	2008	NUM
cana-1996	247	16	)	)	PUNCT
cana-1996	247	17	.	.	PUNCT
cana-1996	248	1	n	n	CCONJ
cana-1996	248	2	-	-	PUNCT
cana-1996	248	3	transform	transform	NOUN
cana-1996	248	4	properties	property	NOUN
cana-1996	248	5	and	and	CCONJ
cana-1996	248	6	applications	application	NOUN
cana-1996	248	7	.	.	PUNCT
cana-1996	249	1	nust	nust	PROPN
cana-1996	249	2	journal	journal	PROPN
cana-1996	249	3	of	of	ADP
cana-1996	249	4	engineering	engineering	NOUN
cana-1996	249	5	science	science	NOUN
cana-1996	249	6	,	,	PUNCT
cana-1996	249	7	1	1	NUM
cana-1996	249	8	,	,	PUNCT
cana-1996	249	9	127	127	NUM
cana-1996	249	10	-	-	SYM
cana-1996	249	11	133	133	NUM
cana-1996	249	12	[	[	X
cana-1996	249	13	11	11	NUM
cana-1996	249	14	]	]	SYM
cana-1996	249	15	khuri	khuri	PROPN
cana-1996	249	16	,	,	PUNCT
cana-1996	249	17	s.a	s.a	PROPN
cana-1996	249	18	.	.	PROPN
cana-1996	250	1	a	a	DET
cana-1996	250	2	new	new	ADJ
cana-1996	250	3	approach	approach	NOUN
cana-1996	250	4	to	to	ADP
cana-1996	250	5	the	the	DET
cana-1996	250	6	cubic	cubic	ADJ
cana-1996	250	7	schrodinger	schrodinger	PROPN
cana-1996	250	8	equation	equation	NOUN
cana-1996	250	9	:	:	PUNCT
cana-1996	250	10	an	an	DET
cana-1996	250	11	application	application	NOUN
cana-1996	250	12	of	of	ADP
cana-1996	250	13	the	the	DET
cana-1996	250	14	decomposition	decomposition	NOUN
cana-1996	250	15	technique	technique	NOUN
cana-1996	250	16	,	,	PUNCT
cana-1996	250	17	applied	apply	VERB
cana-1996	250	18	mathematics	mathematic	NOUN
cana-1996	250	19	and	and	CCONJ
cana-1996	250	20	computation	computation	NOUN
cana-1996	250	21	.	.	PUNCT
cana-1996	251	1	1998	1998	NUM
cana-1996	251	2	,	,	PUNCT
cana-1996	251	3	97	97	NUM
cana-1996	251	4	:	:	PUNCT
cana-1996	251	5	251–254	251–254	NUM
cana-1996	251	6	.	.	PUNCT
cana-1996	252	1	[	[	X
cana-1996	252	2	12	12	NUM
cana-1996	252	3	]	]	X
cana-1996	252	4	kilicman	kilicman	NOUN
cana-1996	252	5	a.	a.	PROPN
cana-1996	252	6	and	and	CCONJ
cana-1996	252	7	eltayeb	eltayeb	PROPN
cana-1996	252	8	,	,	PUNCT
cana-1996	252	9	h.	h.	PROPN
cana-1996	252	10	a	a	DET
cana-1996	252	11	note	note	NOUN
cana-1996	252	12	on	on	ADP
cana-1996	252	13	integral	integral	ADJ
cana-1996	252	14	transform	transform	NOUN
cana-1996	252	15	and	and	CCONJ
cana-1996	252	16	partial	partial	ADJ
cana-1996	252	17	differential	differential	NOUN
cana-1996	252	18	equation	equation	NOUN
cana-1996	252	19	,	,	PUNCT
cana-1996	252	20	applied	apply	VERB
cana-1996	252	21	mathematical	mathematical	ADJ
cana-1996	252	22	sciences	science	NOUN
cana-1996	252	23	.	.	PUNCT
cana-1996	253	1	2010	2010	NUM
cana-1996	253	2	,	,	PUNCT
cana-1996	253	3	4(3):109	4(3):109	NUM
cana-1996	253	4	-	-	SYM
cana-1996	253	5	118	118	NUM
cana-1996	253	6	.	.	PUNCT
cana-1996	254	1	[	[	X
cana-1996	254	2	13	13	NUM
cana-1996	254	3	]	]	X
cana-1996	254	4	liao	liao	PROPN
cana-1996	254	5	,	,	PUNCT
cana-1996	254	6	s.j	s.j	PROPN
cana-1996	254	7	.	.	PROPN
cana-1996	254	8	beyond	beyond	ADP
cana-1996	254	9	perturbation	perturbation	NOUN
cana-1996	254	10	:	:	PUNCT
cana-1996	254	11	introduction	introduction	NOUN
cana-1996	254	12	to	to	ADP
cana-1996	254	13	the	the	DET
cana-1996	254	14	homotopy	homotopy	NOUN
cana-1996	254	15	analysis	analysis	NOUN
cana-1996	254	16	method	method	NOUN
cana-1996	254	17	,	,	PUNCT
cana-1996	254	18	chapman	chapman	PROPN
cana-1996	254	19	&	&	CCONJ
cana-1996	254	20	hall	hall	PROPN
cana-1996	254	21	,	,	PUNCT
cana-1996	254	22	crc	crc	PROPN
cana-1996	254	23	press	press	PROPN
cana-1996	254	24	,	,	PUNCT
cana-1996	254	25	boca	boca	PROPN
cana-1996	254	26	raton	raton	PROPN
cana-1996	254	27	,	,	PUNCT
cana-1996	254	28	fla	fla	PROPN
cana-1996	254	29	,	,	PUNCT
cana-1996	254	30	usa	usa	PROPN
cana-1996	254	31	,	,	PUNCT
cana-1996	254	32	2003	2003	NUM
cana-1996	254	33	.	.	PUNCT
cana-1996	255	1	[	[	X
cana-1996	255	2	14	14	NUM
cana-1996	255	3	]	]	X
cana-1996	255	4	liao	liao	PROPN
cana-1996	255	5	,	,	PUNCT
cana-1996	255	6	s.j	s.j	PROPN
cana-1996	255	7	.	.	PROPN
cana-1996	255	8	a	a	DET
cana-1996	255	9	new	new	ADJ
cana-1996	255	10	branch	branch	NOUN
cana-1996	255	11	of	of	ADP
cana-1996	255	12	solutions	solution	NOUN
cana-1996	255	13	of	of	ADP
cana-1996	255	14	boundary	boundary	ADJ
cana-1996	255	15	-	-	PUNCT
cana-1996	255	16	layer	layer	NOUN
cana-1996	255	17	flows	flow	NOUN
cana-1996	255	18	over	over	ADP
cana-1996	255	19	an	an	DET
cana-1996	255	20	impermeable	impermeable	ADJ
cana-1996	255	21	stretched	stretch	VERB
cana-1996	255	22	plate	plate	NOUN
cana-1996	255	23	,	,	PUNCT
cana-1996	255	24	international	international	ADJ
cana-1996	255	25	journal	journal	NOUN
cana-1996	255	26	of	of	ADP
cana-1996	255	27	heat	heat	NOUN
cana-1996	255	28	and	and	CCONJ
cana-1996	255	29	mass	mass	NOUN
cana-1996	255	30	transfer	transfer	NOUN
cana-1996	255	31	.	.	PUNCT
cana-1996	256	1	2005	2005	NUM
cana-1996	256	2	,	,	PUNCT
cana-1996	256	3	48(12	48(12	NUM
cana-1996	256	4	):	):	PUNCT
cana-1996	256	5	2529–2539	2529–2539	NUM
cana-1996	256	6	.	.	PUNCT
cana-1996	257	1	[	[	X
cana-1996	257	2	15	15	NUM
cana-1996	257	3	]	]	X
cana-1996	257	4	liao	liao	PROPN
cana-1996	257	5	,	,	PUNCT
cana-1996	257	6	s.j	s.j	PROPN
cana-1996	257	7	.	.	PROPN
cana-1996	257	8	comparison	comparison	NOUN
cana-1996	257	9	between	between	ADP
cana-1996	257	10	the	the	DET
cana-1996	257	11	homotopy	homotopy	NOUN
cana-1996	257	12	analysis	analysis	NOUN
cana-1996	257	13	method	method	NOUN
cana-1996	257	14	and	and	CCONJ
cana-1996	257	15	homotopy	homotopy	VERB
cana-1996	257	16	perturbation	perturbation	NOUN
cana-1996	257	17	method	method	NOUN
cana-1996	257	18	,	,	PUNCT
cana-1996	257	19	appl	appl	PROPN
cana-1996	257	20	.	.	PROPN
cana-1996	257	21	math	math	NOUN
cana-1996	257	22	.	.	PUNCT
cana-1996	258	1	comput	comput	NOUN
cana-1996	258	2	.	.	PUNCT
cana-1996	259	1	2005	2005	NUM
cana-1996	259	2	,	,	PUNCT
cana-1996	259	3	169	169	NUM
cana-1996	259	4	:	:	SYM
cana-1996	259	5	1186–1194	1186–1194	NUM
cana-1996	259	6	.	.	PUNCT
cana-1996	260	1	[	[	X
cana-1996	260	2	16	16	NUM
cana-1996	260	3	]	]	X
cana-1996	260	4	liao	liao	PROPN
cana-1996	260	5	,	,	PUNCT
cana-1996	260	6	s.j	s.j	PROPN
cana-1996	260	7	.	.	PROPN
cana-1996	260	8	notes	note	NOUN
cana-1996	260	9	on	on	ADP
cana-1996	260	10	the	the	DET
cana-1996	260	11	homotopy	homotopy	NOUN
cana-1996	260	12	analysis	analysis	NOUN
cana-1996	260	13	method	method	NOUN
cana-1996	260	14	:	:	PUNCT
cana-1996	260	15	some	some	DET
cana-1996	260	16	definitions	definition	NOUN
cana-1996	260	17	and	and	CCONJ
cana-1996	260	18	theorems	theorem	NOUN
cana-1996	260	19	,	,	PUNCT
cana-1996	260	20	communications	communication	NOUN
cana-1996	260	21	in	in	ADP
cana-1996	260	22	nonlinear	nonlinear	ADJ
cana-1996	260	23	science	science	NOUN
cana-1996	260	24	and	and	CCONJ
cana-1996	260	25	numerical	numerical	PROPN
cana-1996	260	26	simulation	simulation	PROPN
cana-1996	260	27	.	.	PUNCT
cana-1996	260	28	2009	2009	NUM
cana-1996	260	29	,	,	PUNCT
cana-1996	260	30	14(4	14(4	NUM
cana-1996	260	31	):	):	PUNCT
cana-1996	260	32	983–997	983–997	NUM
cana-1996	260	33	.	.	PUNCT
cana-1996	261	1	[	[	X
cana-1996	261	2	17	17	NUM
cana-1996	261	3	]	]	X
cana-1996	261	4	liao	liao	PROPN
cana-1996	261	5	,	,	PUNCT
cana-1996	261	6	s.j	s.j	PROPN
cana-1996	261	7	.	.	PROPN
cana-1996	261	8	on	on	ADP
cana-1996	261	9	the	the	DET
cana-1996	261	10	homotopy	homotopy	NOUN
cana-1996	261	11	analysis	analysis	NOUN
cana-1996	261	12	method	method	NOUN
cana-1996	261	13	for	for	ADP
cana-1996	261	14	nonlinear	nonlinear	ADJ
cana-1996	261	15	problems	problem	NOUN
cana-1996	261	16	,	,	PUNCT
cana-1996	261	17	appl	appl	PROPN
cana-1996	261	18	.	.	PROPN
cana-1996	261	19	math	math	PROPN
cana-1996	261	20	.	.	PUNCT
cana-1996	262	1	comput	comput	NOUN
cana-1996	262	2	.	.	PUNCT
cana-1996	263	1	2004	2004	NUM
cana-1996	263	2	,	,	PUNCT
cana-1996	263	3	147	147	NUM
cana-1996	263	4	:	:	PUNCT
cana-1996	264	1	499–513	499–513	NUM
cana-1996	264	2	.	.	PUNCT
cana-1996	265	1	[	[	X
cana-1996	265	2	18	18	NUM
cana-1996	265	3	]	]	X
cana-1996	265	4	maitama	maitama	PROPN
cana-1996	265	5	,	,	PUNCT
cana-1996	265	6	s.	s.	PROPN
cana-1996	265	7	,	,	PUNCT
cana-1996	265	8	&	&	CCONJ
cana-1996	265	9	zhao	zhao	PROPN
cana-1996	265	10	,	,	PUNCT
cana-1996	265	11	w.	w.	PROPN
cana-1996	265	12	(	(	PUNCT
cana-1996	265	13	2019	2019	NUM
cana-1996	265	14	)	)	PUNCT
cana-1996	265	15	.	.	PUNCT
cana-1996	266	1	new	new	ADJ
cana-1996	266	2	integral	integral	ADJ
cana-1996	266	3	transform	transform	NOUN
cana-1996	266	4	:	:	PUNCT
cana-1996	266	5	shehu	shehu	PROPN
cana-1996	266	6	transform	transform	VERB
cana-1996	266	7	a	a	DET
cana-1996	266	8	generalization	generalization	NOUN
cana-1996	266	9	of	of	ADP
cana-1996	266	10	sumudu	sumudu	NOUN
cana-1996	266	11	and	and	CCONJ
cana-1996	266	12	laplace	laplace	NOUN
cana-1996	266	13	transform	transform	NOUN
cana-1996	266	14	for	for	ADP
cana-1996	266	15	solving	solve	VERB
cana-1996	266	16	differential	differential	ADJ
cana-1996	266	17	equations	equation	NOUN
cana-1996	266	18	.	.	PUNCT
cana-1996	267	1	international	international	ADJ
cana-1996	267	2	journal	journal	NOUN
cana-1996	267	3	of	of	ADP
cana-1996	267	4	analysis	analysis	NOUN
cana-1996	267	5	and	and	CCONJ
cana-1996	267	6	applications	application	NOUN
cana-1996	267	7	,	,	PUNCT
cana-1996	267	8	17(2	17(2	NUM
cana-1996	267	9	)	)	PUNCT
cana-1996	267	10	,	,	PUNCT
cana-1996	267	11	167	167	NUM
cana-1996	267	12	-	-	SYM
cana-1996	267	13	190	190	NUM
cana-1996	267	14	https://doi.org/10.12691/ijpdea-5-1-6	https://doi.org/10.12691/ijpdea-5-1-6	NOUN
cana-1996	267	15	communications	communication	NOUN
cana-1996	267	16	on	on	ADP
cana-1996	267	17	applied	apply	VERB
cana-1996	267	18	nonlinear	nonlinear	ADJ
cana-1996	267	19	analysis	analysis	NOUN
cana-1996	267	20	issn	issn	NOUN
cana-1996	267	21	:	:	PUNCT
cana-1996	267	22	1074	1074	NUM
cana-1996	267	23	-	-	PUNCT
cana-1996	267	24	133x	133x	NUM
cana-1996	267	25	vol	vol	NOUN
cana-1996	267	26	32	32	NUM
cana-1996	267	27	no	no	NOUN
cana-1996	267	28	.	.	NOUN
cana-1996	267	29	3	3	NUM
cana-1996	267	30	(	(	PUNCT
cana-1996	267	31	2025	2025	NUM
cana-1996	267	32	)	)	PUNCT
cana-1996	268	1	399	399	NUM
cana-1996	268	2	https://internationalpubls.com	https://internationalpubls.com	X
cana-1996	268	3	[	[	X
cana-1996	268	4	19	19	NUM
cana-1996	268	5	]	]	X
cana-1996	268	6	mansour	mansour	PROPN
cana-1996	268	7	,	,	PUNCT
cana-1996	268	8	e.	e.	PROPN
cana-1996	268	9	a.	a.	PROPN
cana-1996	268	10	,	,	PUNCT
cana-1996	268	11	&	&	CCONJ
cana-1996	268	12	kuffi	kuffi	PROPN
cana-1996	268	13	,	,	PUNCT
cana-1996	268	14	e.	e.	PROPN
cana-1996	268	15	a.	a.	PROPN
cana-1996	268	16	(	(	PUNCT
cana-1996	268	17	2022	2022	NUM
cana-1996	268	18	)	)	PUNCT
cana-1996	268	19	.	.	PUNCT
cana-1996	269	1	generalization	generalization	NOUN
cana-1996	269	2	of	of	ADP
cana-1996	269	3	rangaig	rangaig	ADJ
cana-1996	269	4	transform	transform	NOUN
cana-1996	269	5	.	.	PUNCT
cana-1996	270	1	international	international	ADJ
cana-1996	270	2	journal	journal	PROPN
cana-1996	270	3	of	of	ADP
cana-1996	270	4	nonlinear	nonlinear	ADJ
cana-1996	270	5	analysis	analysis	NOUN
cana-1996	270	6	and	and	CCONJ
cana-1996	270	7	applications	application	NOUN
cana-1996	270	8	,	,	PUNCT
cana-1996	270	9	13(1	13(1	NUM
cana-1996	270	10	)	)	PUNCT
cana-1996	270	11	,	,	PUNCT
cana-1996	270	12	2227–2231	2227–2231	NUM
cana-1996	270	13	.	.	PUNCT
cana-1996	271	1	[	[	X
cana-1996	271	2	20	20	NUM
cana-1996	271	3	]	]	X
cana-1996	271	4	mansour	mansour	PROPN
cana-1996	271	5	,	,	PUNCT
cana-1996	271	6	e.a	e.a	PROPN
cana-1996	271	7	.	.	PROPN
cana-1996	271	8	,	,	PUNCT
cana-1996	271	9	&	&	CCONJ
cana-1996	271	10	kuffi	kuffi	PROPN
cana-1996	271	11	,	,	PUNCT
cana-1996	271	12	e.a	e.a	PROPN
cana-1996	271	13	.	.	PROPN
cana-1996	271	14	(	(	PUNCT
cana-1996	271	15	2022	2022	NUM
cana-1996	271	16	)	)	PUNCT
cana-1996	271	17	.	.	PUNCT
cana-1996	271	18	generalization	generalization	NOUN
cana-1996	271	19	of	of	ADP
cana-1996	271	20	rangaig	rangaig	ADJ
cana-1996	271	21	transform	transform	NOUN
cana-1996	271	22	.	.	PUNCT
cana-1996	272	1	international	international	ADJ
cana-1996	272	2	journal	journal	PROPN
cana-1996	272	3	of	of	ADP
cana-1996	272	4	nonlinear	nonlinear	ADJ
cana-1996	272	5	analysis	analysis	NOUN
cana-1996	272	6	and	and	CCONJ
cana-1996	272	7	applications	application	NOUN
cana-1996	272	8	,	,	PUNCT
cana-1996	272	9	11(1	11(1	NUM
cana-1996	272	10	)	)	PUNCT
cana-1996	272	11	,	,	PUNCT
cana-1996	272	12	2227	2227	NUM
cana-1996	272	13	-	-	SYM
cana-1996	272	14	2231	2231	NUM
cana-1996	272	15	.	.	PUNCT
cana-1996	273	1	[	[	X
cana-1996	273	2	21	21	NUM
cana-1996	273	3	]	]	X
cana-1996	273	4	mohebbi	mohebbi	PROPN
cana-1996	273	5	,	,	PUNCT
cana-1996	273	6	a.	a.	NOUN
cana-1996	273	7	and	and	CCONJ
cana-1996	273	8	dehghan	dehghan	PROPN
cana-1996	273	9	,	,	PUNCT
cana-1996	273	10	m.	m.	NOUN
cana-1996	273	11	the	the	DET
cana-1996	273	12	use	use	NOUN
cana-1996	273	13	of	of	ADP
cana-1996	273	14	compact	compact	ADJ
cana-1996	273	15	boundary	boundary	ADJ
cana-1996	273	16	value	value	NOUN
cana-1996	273	17	method	method	NOUN
cana-1996	273	18	for	for	ADP
cana-1996	273	19	the	the	DET
cana-1996	273	20	solution	solution	NOUN
cana-1996	273	21	of	of	ADP
cana-1996	273	22	two	two	NUM
cana-1996	273	23	-	-	PUNCT
cana-1996	273	24	dimensional	dimensional	ADJ
cana-1996	273	25	schrodinger	schrodinger	NOUN
cana-1996	273	26	equation	equation	NOUN
cana-1996	273	27	,	,	PUNCT
cana-1996	273	28	journal	journal	NOUN
cana-1996	273	29	of	of	ADP
cana-1996	273	30	computational	computational	ADJ
cana-1996	273	31	and	and	CCONJ
cana-1996	273	32	applied	applied	ADJ
cana-1996	273	33	mathematics	mathematic	NOUN
cana-1996	273	34	,	,	PUNCT
cana-1996	273	35	2009	2009	NUM
cana-1996	273	36	,	,	PUNCT
cana-1996	273	37	225(1	225(1	NUM
cana-1996	273	38	):	):	PUNCT
cana-1996	273	39	124–134	124–134	NUM
cana-1996	273	40	.	.	PUNCT
cana-1996	274	1	[	[	X
cana-1996	274	2	22	22	NUM
cana-1996	274	3	]	]	PUNCT
cana-1996	274	4	rangaig	rangaig	PROPN
cana-1996	274	5	,	,	PUNCT
cana-1996	274	6	n.a	n.a	PROPN
cana-1996	274	7	.	.	PROPN
cana-1996	274	8	,	,	PUNCT
cana-1996	274	9	minor	minor	PROPN
cana-1996	274	10	,	,	PUNCT
cana-1996	274	11	n.d	n.d	PROPN
cana-1996	274	12	.	.	PROPN
cana-1996	274	13	,	,	PUNCT
cana-1996	274	14	penonal	penonal	PROPN
cana-1996	274	15	,	,	PUNCT
cana-1996	274	16	g.f.i	g.f.i	INTJ
cana-1996	274	17	.	.	PROPN
cana-1996	274	18	,	,	PUNCT
cana-1996	274	19	filipinas	filipinas	PROPN
cana-1996	274	20	,	,	PUNCT
cana-1996	274	21	j.l.d.c	j.l.d.c	PROPN
cana-1996	274	22	.	.	PROPN
cana-1996	274	23	,	,	PUNCT
cana-1996	274	24	&	&	CCONJ
cana-1996	274	25	convicto	convicto	PROPN
cana-1996	274	26	,	,	PUNCT
cana-1996	274	27	v.c	v.c	PROPN
cana-1996	274	28	.	.	PROPN
cana-1996	275	1	(	(	PUNCT
cana-1996	275	2	2017).on	2017).on	NUM
cana-1996	275	3	another	another	DET
cana-1996	275	4	type	type	NOUN
cana-1996	275	5	of	of	ADP
cana-1996	275	6	transform	transform	NOUN
cana-1996	275	7	called	call	VERB
cana-1996	275	8	rangaig	rangaig	ADJ
cana-1996	275	9	transform	transform	NOUN
cana-1996	275	10	.	.	PUNCT
cana-1996	276	1	international	international	ADJ
cana-1996	276	2	journal	journal	NOUN
cana-1996	276	3	of	of	ADP
cana-1996	276	4	partial	partial	ADJ
cana-1996	276	5	differential	differential	ADJ
cana-1996	276	6	equations	equation	NOUN
cana-1996	276	7	and	and	CCONJ
cana-1996	276	8	applications	application	NOUN
cana-1996	276	9	,	,	PUNCT
cana-1996	276	10	5(1	5(1	NUM
cana-1996	276	11	)	)	PUNCT
cana-1996	276	12	,	,	PUNCT
cana-1996	276	13	42	42	NUM
cana-1996	276	14	-	-	SYM
cana-1996	276	15	48	48	NUM
cana-1996	276	16	.	.	PUNCT
cana-1996	277	1	[	[	X
cana-1996	277	2	23	23	NUM
cana-1996	277	3	]	]	X
cana-1996	277	4	rathore	rathore	PROPN
cana-1996	277	5	,	,	PUNCT
cana-1996	277	6	s.	s.	PROPN
cana-1996	277	7	,	,	PUNCT
cana-1996	277	8	kumarb	kumarb	NOUN
cana-1996	277	9	,	,	PUNCT
cana-1996	277	10	d.	d.	PROPN
cana-1996	277	11	,	,	PUNCT
cana-1996	277	12	singh	singh	PROPN
cana-1996	277	13	,	,	PUNCT
cana-1996	277	14	j.	j.	PROPN
cana-1996	277	15	,	,	PUNCT
cana-1996	277	16	&	&	CCONJ
cana-1996	277	17	gupta	gupta	PROPN
cana-1996	277	18	,	,	PUNCT
cana-1996	277	19	s.	s.	PROPN
cana-1996	277	20	(	(	PUNCT
cana-1996	277	21	2012	2012	NUM
cana-1996	277	22	)	)	PUNCT
cana-1996	277	23	.	.	PUNCT
cana-1996	278	1	homotopy	homotopy	VERB
cana-1996	278	2	analysis	analysis	NOUN
cana-1996	278	3	sumudu	sumudu	NOUN
cana-1996	278	4	transform	transform	VERB
cana-1996	278	5	method	method	NOUN
cana-1996	278	6	for	for	ADP
cana-1996	278	7	nonlinear	nonlinear	ADJ
cana-1996	278	8	equations	equation	NOUN
cana-1996	278	9	.	.	PUNCT
cana-1996	279	1	international	international	ADJ
cana-1996	279	2	journal	journal	PROPN
cana-1996	279	3	of	of	ADP
cana-1996	279	4	industrial	industrial	ADJ
cana-1996	279	5	mathematics	mathematic	NOUN
cana-1996	279	6	,	,	PUNCT
cana-1996	279	7	4(4	4(4	NUM
cana-1996	279	8	)	)	PUNCT
cana-1996	279	9	,	,	PUNCT
cana-1996	279	10	301	301	NUM
cana-1996	279	11	-	-	SYM
cana-1996	279	12	314	314	NUM
cana-1996	279	13	[	[	SYM
cana-1996	279	14	24	24	NUM
cana-1996	279	15	]	]	PUNCT
cana-1996	279	16	sharma	sharma	PROPN
cana-1996	279	17	,	,	PUNCT
cana-1996	279	18	s.	s.	PROPN
cana-1996	279	19	,	,	PUNCT
cana-1996	279	20	&	&	CCONJ
cana-1996	279	21	singh	singh	PROPN
cana-1996	279	22	,	,	PUNCT
cana-1996	279	23	i.	i.	PROPN
cana-1996	279	24	(	(	PUNCT
cana-1996	279	25	2024	2024	NUM
cana-1996	279	26	)	)	PUNCT
cana-1996	279	27	.	.	PUNCT
cana-1996	280	1	elzaki	elzaki	PROPN
cana-1996	280	2	transform	transform	VERB
cana-1996	280	3	homotopy	homotopy	NOUN
cana-1996	280	4	analysis	analysis	NOUN
cana-1996	280	5	techniques	technique	NOUN
cana-1996	280	6	for	for	ADP
cana-1996	280	7	solving	solve	VERB
cana-1996	280	8	.	.	PUNCT
cana-1996	281	1	communications	communication	NOUN
cana-1996	281	2	on	on	ADP
cana-1996	281	3	applied	apply	VERB
cana-1996	281	4	nonlinear	nonlinear	ADJ
cana-1996	281	5	analysis	analysis	NOUN
cana-1996	281	6	,	,	PUNCT
cana-1996	281	7	31(6	31(6	NUM
cana-1996	281	8	)	)	PUNCT
cana-1996	281	9	,	,	PUNCT
cana-1996	281	10	305–317	305–317	NUM
cana-1996	281	11	.	.	PUNCT
cana-1996	282	1	https://doi.org/https://doi.org/10.52783/cana.v31.1224	https://doi.org/https://doi.org/10.52783/cana.v31.1224	PROPN
cana-1996	282	2	[	[	X
cana-1996	282	3	25	25	NUM
cana-1996	282	4	]	]	X
cana-1996	282	5	spiegel	spiegel	PROPN
cana-1996	282	6	,	,	PUNCT
cana-1996	282	7	m.r	m.r	PROPN
cana-1996	282	8	.	.	PROPN
cana-1996	282	9	(	(	PUNCT
cana-1996	282	10	1965	1965	NUM
cana-1996	282	11	)	)	PUNCT
cana-1996	282	12	.	.	PUNCT
cana-1996	283	1	theory	theory	NOUN
cana-1996	283	2	and	and	CCONJ
cana-1996	283	3	problems	problem	NOUN
cana-1996	283	4	of	of	ADP
cana-1996	283	5	laplace	laplace	NOUN
cana-1996	283	6	transform	transform	NOUN
cana-1996	283	7	.	.	PUNCT
cana-1996	284	1	schaum	schaum	PROPN
cana-1996	284	2	’s	’s	PART
cana-1996	284	3	outline	outline	PROPN
cana-1996	284	4	series	series	PROPN
cana-1996	284	5	,	,	PUNCT
cana-1996	284	6	new	new	PROPN
cana-1996	284	7	york	york	PROPN
cana-1996	284	8	:	:	PUNCT
cana-1996	284	9	mcgrawhill	mcgrawhill	NOUN
cana-1996	284	10	[	[	X
cana-1996	284	11	26	26	NUM
cana-1996	284	12	]	]	X
cana-1996	284	13	ziane	ziane	NOUN
cana-1996	284	14	,	,	PUNCT
cana-1996	284	15	d.	d.	PROPN
cana-1996	284	16	,	,	PUNCT
cana-1996	284	17	&	&	CCONJ
cana-1996	284	18	cherif	cherif	PROPN
cana-1996	284	19	,	,	PUNCT
cana-1996	284	20	m.	m.	PROPN
cana-1996	284	21	h.	h.	PROPN
cana-1996	284	22	(	(	PUNCT
cana-1996	284	23	2022	2022	NUM
cana-1996	284	24	)	)	PUNCT
cana-1996	284	25	.	.	PUNCT
cana-1996	285	1	the	the	DET
cana-1996	285	2	homotopy	homotopy	NOUN
cana-1996	285	3	analysis	analysis	NOUN
cana-1996	285	4	rangaig	rangaig	ADJ
cana-1996	285	5	transform	transform	VERB
cana-1996	285	6	method	method	NOUN
cana-1996	285	7	for	for	ADP
cana-1996	285	8	nonlinear	nonlinear	ADJ
cana-1996	285	9	partial	partial	ADJ
cana-1996	285	10	differential	differential	NOUN
cana-1996	285	11	equations	equation	NOUN
cana-1996	285	12	.	.	PUNCT
cana-1996	286	1	journal	journal	NOUN
cana-1996	286	2	of	of	ADP
cana-1996	286	3	applied	apply	VERB
cana-1996	286	4	mathematics	mathematic	NOUN
cana-1996	286	5	and	and	CCONJ
cana-1996	286	6	computational	computational	ADJ
cana-1996	286	7	mechanics	mechanic	NOUN
cana-1996	286	8	,	,	PUNCT
cana-1996	286	9	21(2	21(2	NUM
cana-1996	286	10	)	)	PUNCT
cana-1996	286	11	,	,	PUNCT
cana-1996	286	12	111–122	111–122	NUM
cana-1996	286	13	.	.	PUNCT
cana-1996	287	1	https://doi.org/10.17512/jamcm.2022.2.10	https://doi.org/10.17512/jamcm.2022.2.10	X
cana-1996	287	2	https://doi.org/10.17512/jamcm.2022.2.10	https://doi.org/10.17512/jamcm.2022.2.10	X