id	sid	tid	token	lemma	pos
cana-602	1	1	communications	communication	NOUN
cana-602	1	2	on	on	ADP
cana-602	1	3	applied	apply	VERB
cana-602	1	4	nonlinear	nonlinear	ADJ
cana-602	1	5	analysis	analysis	NOUN
cana-602	1	6	issn	issn	NOUN
cana-602	1	7	:	:	PUNCT
cana-602	1	8	1074	1074	NUM
cana-602	1	9	-	-	PUNCT
cana-602	1	10	133x	133x	NUM
cana-602	1	11	vol	vol	NOUN
cana-602	1	12	31	31	NUM
cana-602	1	13	no	no	NOUN
cana-602	1	14	.	.	PUNCT
cana-602	2	1	2s	2s	NUM
cana-602	2	2	(	(	PUNCT
cana-602	2	3	2024	2024	NUM
cana-602	2	4	)	)	PUNCT
cana-602	2	5	113	113	NUM
cana-602	2	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-602	2	7	topological	topological	ADJ
cana-602	2	8	methods	method	NOUN
cana-602	2	9	for	for	ADP
cana-602	2	10	solving	solve	VERB
cana-602	2	11	nonlinear	nonlinear	ADJ
cana-602	2	12	equations	equation	NOUN
cana-602	2	13	in	in	ADP
cana-602	2	14	financial	financial	ADJ
cana-602	2	15	mathematics	mathematics	PROPN
cana-602	2	16	dr	dr	PROPN
cana-602	2	17	.	.	PROPN
cana-602	2	18	nidhi	nidhi	PROPN
cana-602	2	19	jain¹	jain¹	PROPN
cana-602	2	20	,	,	PUNCT
cana-602	2	21	dr	dr	PROPN
cana-602	2	22	.	.	PROPN
cana-602	2	23	shweta	shweta	PROPN
cana-602	2	24	kulshrestha²	kulshrestha²	PROPN
cana-602	2	25	,	,	PUNCT
cana-602	2	26	megha	megha	PROPN
cana-602	2	27	sharma³	sharma³	PROPN
cana-602	2	28	,	,	PUNCT
cana-602	2	29	neema	neema	PROPN
cana-602	2	30	gupta⁴	gupta⁴	PROPN
cana-602	2	31	,	,	PUNCT
cana-602	2	32	raj	raj	PROPN
cana-602	2	33	gaurang	gaurang	PROPN
cana-602	2	34	tiwari⁵	tiwari⁵	PROPN
cana-602	2	35	,	,	PUNCT
cana-602	2	36	ambuj	ambuj	PROPN
cana-602	2	37	kumar	kumar	PROPN
cana-602	2	38	agarwal⁶	agarwal⁶	PROPN
cana-602	2	39	,	,	PUNCT
cana-602	2	40	soumi	soumi	X
cana-602	2	41	datta⁷	datta⁷	X
cana-602	2	42	¹	¹	NUM
cana-602	2	43	assistant	assistant	NOUN
cana-602	2	44	professor	professor	NOUN
cana-602	2	45	,	,	PUNCT
cana-602	2	46	department	department	PROPN
cana-602	2	47	of	of	ADP
cana-602	2	48	commerce	commerce	PROPN
cana-602	2	49	,	,	PUNCT
cana-602	2	50	shyam	shyam	PROPN
cana-602	2	51	lal	lal	PROPN
cana-602	2	52	college	college	PROPN
cana-602	2	53	,	,	PUNCT
cana-602	2	54	university	university	PROPN
cana-602	2	55	of	of	ADP
cana-602	2	56	delhi	delhi	PROPN
cana-602	2	57	,	,	PUNCT
cana-602	2	58	nidhijain794@gmail.com	nidhijain794@gmail.com	PUNCT
cana-602	2	59	²assistant	²assistant	PROPN
cana-602	2	60	professor	professor	NOUN
cana-602	2	61	,	,	PUNCT
cana-602	2	62	galgotias	galgotias	PROPN
cana-602	2	63	university	university	NOUN
cana-602	2	64	,	,	PUNCT
cana-602	2	65	greater	great	ADJ
cana-602	2	66	noida	noida	PROPN
cana-602	2	67	,	,	PUNCT
cana-602	2	68	shwetakul15@gmail.com	shwetakul15@gmail.com	PROPN
cana-602	2	69	³associate	³associate	PROPN
cana-602	2	70	professor	professor	NOUN
cana-602	2	71	,	,	PUNCT
cana-602	2	72	iimt	iimt	ADJ
cana-602	2	73	,	,	PUNCT
cana-602	2	74	greater	great	ADJ
cana-602	2	75	noida	noida	PROPN
cana-602	2	76	,	,	PUNCT
cana-602	2	77	meghaofficial1@gmail.com	meghaofficial1@gmail.com	PROPN
cana-602	2	78	⁴	⁴	NUM
cana-602	2	79	associate	associate	NOUN
cana-602	2	80	professor	professor	NOUN
cana-602	2	81	,	,	PUNCT
cana-602	2	82	university	university	NOUN
cana-602	2	83	school	school	NOUN
cana-602	2	84	of	of	ADP
cana-602	2	85	business	business	NOUN
cana-602	2	86	,	,	PUNCT
cana-602	2	87	chandigarh	chandigarh	PROPN
cana-602	2	88	university	university	NOUN
cana-602	2	89	,	,	PUNCT
cana-602	2	90	neema.gupta.gupta@gmail.com	neema.gupta.gupta@gmail.com	PROPN
cana-602	2	91	⁵	⁵	NUM
cana-602	2	92	chitkara	chitkara	PROPN
cana-602	2	93	university	university	PROPN
cana-602	2	94	institute	institute	NOUN
cana-602	2	95	of	of	ADP
cana-602	2	96	engineering	engineering	NOUN
cana-602	2	97	and	and	CCONJ
cana-602	2	98	technology	technology	NOUN
cana-602	2	99	,	,	PUNCT
cana-602	2	100	chitkara	chitkara	ADJ
cana-602	2	101	university	university	NOUN
cana-602	2	102	,	,	PUNCT
cana-602	2	103	punjab	punjab	PROPN
cana-602	2	104	,	,	PUNCT
cana-602	2	105	india	india	PROPN
cana-602	2	106	,	,	PUNCT
cana-602	2	107	rajgaurang@chitkara.edu.in	rajgaurang@chitkara.edu.in	NOUN
cana-602	2	108	⁶	⁶	NUM
cana-602	2	109	professor	professor	NOUN
cana-602	2	110	,	,	PUNCT
cana-602	2	111	department	department	NOUN
cana-602	2	112	of	of	ADP
cana-602	2	113	computer	computer	NOUN
cana-602	2	114	science	science	NOUN
cana-602	2	115	and	and	CCONJ
cana-602	2	116	engineering	engineering	NOUN
cana-602	2	117	,	,	PUNCT
cana-602	2	118	sharda	sharda	PROPN
cana-602	2	119	school	school	NOUN
cana-602	2	120	of	of	ADP
cana-602	2	121	engineering	engineering	NOUN
cana-602	2	122	and	and	CCONJ
cana-602	2	123	technology	technology	NOUN
cana-602	2	124	,	,	PUNCT
cana-602	2	125	sharda	sharda	PROPN
cana-602	2	126	university	university	PROPN
cana-602	2	127	,	,	PUNCT
cana-602	2	128	greater	great	ADJ
cana-602	2	129	noida	noida	PROPN
cana-602	2	130	,	,	PUNCT
cana-602	2	131	ambuj4u@gmail.com	ambuj4u@gmail.com	PROPN
cana-602	2	132	⁷associate	⁷associate	PROPN
cana-602	2	133	professor	professor	NOUN
cana-602	2	134	,	,	PUNCT
cana-602	2	135	sister	sister	NOUN
cana-602	2	136	nivedita	nivedita	PROPN
cana-602	2	137	university	university	PROPN
cana-602	2	138	,	,	PUNCT
cana-602	2	139	india	india	PROPN
cana-602	2	140	,	,	PUNCT
cana-602	2	141	soumi.it@gmail.com	soumi.it@gmail.com	PROPN
cana-602	2	142	corresponding	correspond	VERB
cana-602	2	143	author	author	NOUN
cana-602	2	144	email	email	NOUN
cana-602	2	145	:	:	PUNCT
cana-602	2	146	ambuj4u@gmail.com	ambuj4u@gmail.com	PROPN
cana-602	2	147	article	article	PROPN
cana-602	2	148	history	history	NOUN
cana-602	2	149	:	:	PUNCT
cana-602	2	150	received	receive	VERB
cana-602	2	151	:	:	PUNCT
cana-602	2	152	10	10	NUM
cana-602	2	153	-	-	SYM
cana-602	2	154	03	03	NUM
cana-602	2	155	-	-	PUNCT
cana-602	2	156	2024	2024	NUM
cana-602	2	157	revised	revise	VERB
cana-602	2	158	:	:	PUNCT
cana-602	2	159	22	22	NUM
cana-602	2	160	-	-	PUNCT
cana-602	2	161	04	04	NUM
cana-602	2	162	-	-	PUNCT
cana-602	2	163	2024	2024	NUM
cana-602	2	164	accepted	accept	VERB
cana-602	2	165	:	:	PUNCT
cana-602	2	166	12	12	NUM
cana-602	2	167	-	-	PUNCT
cana-602	2	168	05	05	NUM
cana-602	2	169	-	-	PUNCT
cana-602	2	170	2024	2024	NUM
cana-602	2	171	abstract	abstract	NOUN
cana-602	2	172	:	:	PUNCT
cana-602	2	173	this	this	DET
cana-602	2	174	paper	paper	NOUN
cana-602	2	175	explores	explore	VERB
cana-602	2	176	the	the	DET
cana-602	2	177	integration	integration	NOUN
cana-602	2	178	of	of	ADP
cana-602	2	179	topological	topological	ADJ
cana-602	2	180	methods	method	NOUN
cana-602	2	181	in	in	ADP
cana-602	2	182	solving	solve	VERB
cana-602	2	183	nonlinear	nonlinear	ADJ
cana-602	2	184	equations	equation	NOUN
cana-602	2	185	within	within	ADP
cana-602	2	186	the	the	DET
cana-602	2	187	realm	realm	NOUN
cana-602	2	188	of	of	ADP
cana-602	2	189	financial	financial	ADJ
cana-602	2	190	mathematics	mathematic	NOUN
cana-602	2	191	.	.	PUNCT
cana-602	3	1	it	it	PRON
cana-602	3	2	highlights	highlight	VERB
cana-602	3	3	the	the	DET
cana-602	3	4	application	application	NOUN
cana-602	3	5	of	of	ADP
cana-602	3	6	the	the	DET
cana-602	3	7	homotopy	homotopy	NOUN
cana-602	3	8	analysis	analysis	NOUN
cana-602	3	9	method	method	NOUN
cana-602	3	10	(	(	PUNCT
cana-602	3	11	ham	ham	PROPN
cana-602	3	12	)	)	PUNCT
cana-602	3	13	,	,	PUNCT
cana-602	3	14	topological	topological	ADJ
cana-602	3	15	degree	degree	NOUN
cana-602	3	16	theory	theory	NOUN
cana-602	3	17	,	,	PUNCT
cana-602	3	18	and	and	CCONJ
cana-602	3	19	iterative	iterative	NOUN
cana-602	3	20	methods	method	NOUN
cana-602	3	21	derived	derive	VERB
cana-602	3	22	from	from	ADP
cana-602	3	23	topological	topological	ADJ
cana-602	3	24	concepts	concept	NOUN
cana-602	3	25	,	,	PUNCT
cana-602	3	26	underscoring	underscore	VERB
cana-602	3	27	their	their	PRON
cana-602	3	28	theoretical	theoretical	ADJ
cana-602	3	29	foundations	foundation	NOUN
cana-602	3	30	and	and	CCONJ
cana-602	3	31	practical	practical	ADJ
cana-602	3	32	implications	implication	NOUN
cana-602	3	33	.	.	PUNCT
cana-602	4	1	by	by	ADP
cana-602	4	2	applying	apply	VERB
cana-602	4	3	these	these	DET
cana-602	4	4	advanced	advanced	ADJ
cana-602	4	5	mathematical	mathematical	ADJ
cana-602	4	6	techniques	technique	NOUN
cana-602	4	7	,	,	PUNCT
cana-602	4	8	the	the	DET
cana-602	4	9	paper	paper	NOUN
cana-602	4	10	illustrates	illustrate	VERB
cana-602	4	11	how	how	SCONJ
cana-602	4	12	complex	complex	ADJ
cana-602	4	13	financial	financial	ADJ
cana-602	4	14	models	model	NOUN
cana-602	4	15	,	,	PUNCT
cana-602	4	16	especially	especially	ADV
cana-602	4	17	those	those	PRON
cana-602	4	18	involving	involve	VERB
cana-602	4	19	derivative	derivative	ADJ
cana-602	4	20	pricing	pricing	NOUN
cana-602	4	21	,	,	PUNCT
cana-602	4	22	risk	risk	NOUN
cana-602	4	23	management	management	NOUN
cana-602	4	24	,	,	PUNCT
cana-602	4	25	and	and	CCONJ
cana-602	4	26	macroeconomic	macroeconomic	ADJ
cana-602	4	27	forecasting	forecasting	NOUN
cana-602	4	28	,	,	PUNCT
cana-602	4	29	can	can	AUX
cana-602	4	30	be	be	AUX
cana-602	4	31	effectively	effectively	ADV
cana-602	4	32	addressed	address	VERB
cana-602	4	33	.	.	PUNCT
cana-602	5	1	theoretical	theoretical	ADJ
cana-602	5	2	formulations	formulation	NOUN
cana-602	5	3	are	be	AUX
cana-602	5	4	accompanied	accompany	VERB
cana-602	5	5	by	by	ADP
cana-602	5	6	practical	practical	ADJ
cana-602	5	7	examples	example	NOUN
cana-602	5	8	,	,	PUNCT
cana-602	5	9	demonstrating	demonstrate	VERB
cana-602	5	10	the	the	DET
cana-602	5	11	utility	utility	NOUN
cana-602	5	12	and	and	CCONJ
cana-602	5	13	flexibility	flexibility	NOUN
cana-602	5	14	of	of	ADP
cana-602	5	15	topological	topological	ADJ
cana-602	5	16	methods	method	NOUN
cana-602	5	17	in	in	ADP
cana-602	5	18	navigating	navigate	VERB
cana-602	5	19	the	the	DET
cana-602	5	20	complexities	complexity	NOUN
cana-602	5	21	of	of	ADP
cana-602	5	22	financial	financial	ADJ
cana-602	5	23	systems	system	NOUN
cana-602	5	24	.	.	PUNCT
cana-602	6	1	keywords	keyword	NOUN
cana-602	6	2	:	:	PUNCT
cana-602	7	1	topological	topological	ADJ
cana-602	7	2	,	,	PUNCT
cana-602	7	3	homotopy	homotopy	NOUN
cana-602	7	4	,	,	PUNCT
cana-602	7	5	risk	risk	NOUN
cana-602	7	6	,	,	PUNCT
cana-602	7	7	pricing	pricing	NOUN
cana-602	7	8	,	,	PUNCT
cana-602	7	9	mathematics	mathematics	PROPN
cana-602	7	10	1	1	NUM
cana-602	7	11	.	.	PUNCT
cana-602	7	12	introduction	introduction	NOUN
cana-602	7	13	in	in	ADP
cana-602	7	14	the	the	DET
cana-602	7	15	field	field	NOUN
cana-602	7	16	of	of	ADP
cana-602	7	17	financial	financial	ADJ
cana-602	7	18	mathematics	mathematic	NOUN
cana-602	7	19	,	,	PUNCT
cana-602	7	20	nonlinear	nonlinear	ADJ
cana-602	7	21	equations	equation	NOUN
cana-602	7	22	are	be	AUX
cana-602	7	23	indispensable	indispensable	ADJ
cana-602	7	24	for	for	ADP
cana-602	7	25	capturing	capture	VERB
cana-602	7	26	the	the	DET
cana-602	7	27	complexities	complexity	NOUN
cana-602	7	28	and	and	CCONJ
cana-602	7	29	dynamics	dynamic	NOUN
cana-602	7	30	inherent	inherent	ADJ
cana-602	7	31	in	in	ADP
cana-602	7	32	financial	financial	ADJ
cana-602	7	33	markets	market	NOUN
cana-602	7	34	.	.	PUNCT
cana-602	8	1	these	these	DET
cana-602	8	2	equations	equation	NOUN
cana-602	8	3	underpin	underpin	VERB
cana-602	8	4	numerous	numerous	ADJ
cana-602	8	5	financial	financial	ADJ
cana-602	8	6	models	model	NOUN
cana-602	8	7	across	across	ADP
cana-602	8	8	various	various	ADJ
cana-602	8	9	domains	domain	NOUN
cana-602	8	10	,	,	PUNCT
cana-602	8	11	including	include	VERB
cana-602	8	12	derivative	derivative	ADJ
cana-602	8	13	pricing	pricing	NOUN
cana-602	8	14	,	,	PUNCT
cana-602	8	15	risk	risk	NOUN
cana-602	8	16	management	management	NOUN
cana-602	8	17	,	,	PUNCT
cana-602	8	18	and	and	CCONJ
cana-602	8	19	macroeconomic	macroeconomic	ADJ
cana-602	8	20	forecasting	forecasting	NOUN
cana-602	8	21	[	[	X
cana-602	8	22	1	1	NUM
cana-602	8	23	]	]	PUNCT
cana-602	8	24	.	.	PUNCT
cana-602	9	1	traditional	traditional	ADJ
cana-602	9	2	financial	financial	ADJ
cana-602	9	3	models	model	NOUN
cana-602	9	4	like	like	ADP
cana-602	9	5	the	the	DET
cana-602	9	6	black	black	ADJ
cana-602	9	7	-	-	PUNCT
cana-602	9	8	scholes	schole	NOUN
cana-602	9	9	equation	equation	NOUN
cana-602	9	10	,	,	PUNCT
cana-602	9	11	which	which	PRON
cana-602	9	12	originally	originally	ADV
cana-602	9	13	assumed	assume	VERB
cana-602	9	14	linear	linear	ADJ
cana-602	9	15	behaviors	behavior	NOUN
cana-602	9	16	,	,	PUNCT
cana-602	9	17	must	must	AUX
cana-602	9	18	be	be	AUX
cana-602	9	19	adapted	adapt	VERB
cana-602	9	20	to	to	PART
cana-602	9	21	accommodate	accommodate	VERB
cana-602	9	22	more	more	ADV
cana-602	9	23	intricate	intricate	ADJ
cana-602	9	24	phenomena	phenomenon	NOUN
cana-602	9	25	such	such	ADJ
cana-602	9	26	as	as	ADP
cana-602	9	27	stochastic	stochastic	ADJ
cana-602	9	28	volatility	volatility	NOUN
cana-602	9	29	and	and	CCONJ
cana-602	9	30	jump	jump	NOUN
cana-602	9	31	diffusions	diffusion	NOUN
cana-602	9	32	.	.	PUNCT
cana-602	10	1	moreover	moreover	ADV
cana-602	10	2	,	,	PUNCT
cana-602	10	3	nonlinear	nonlinear	ADJ
cana-602	10	4	equations	equation	NOUN
cana-602	10	5	are	be	AUX
cana-602	10	6	pivotal	pivotal	ADJ
cana-602	10	7	in	in	ADP
cana-602	10	8	risk	risk	NOUN
cana-602	10	9	management	management	NOUN
cana-602	10	10	through	through	ADP
cana-602	10	11	models	model	NOUN
cana-602	10	12	that	that	PRON
cana-602	10	13	elucidate	elucidate	VERB
cana-602	10	14	nonlinear	nonlinear	ADJ
cana-602	10	15	dependencies	dependency	NOUN
cana-602	10	16	and	and	CCONJ
cana-602	10	17	tail	tail	NOUN
cana-602	10	18	risks	risk	NOUN
cana-602	10	19	.	.	PUNCT
cana-602	11	1	for	for	ADP
cana-602	11	2	instance	instance	NOUN
cana-602	11	3	,	,	PUNCT
cana-602	11	4	the	the	DET
cana-602	11	5	value	value	NOUN
cana-602	11	6	-	-	PUNCT
cana-602	11	7	at	at	ADP
cana-602	11	8	-	-	PUNCT
cana-602	11	9	risk	risk	NOUN
cana-602	11	10	(	(	PUNCT
cana-602	11	11	var	var	NOUN
cana-602	11	12	)	)	PUNCT
cana-602	11	13	for	for	ADP
cana-602	11	14	a	a	DET
cana-602	11	15	portfolio	portfolio	NOUN
cana-602	11	16	can	can	AUX
cana-602	11	17	be	be	AUX
cana-602	11	18	more	more	ADV
cana-602	11	19	accurately	accurately	ADV
cana-602	11	20	estimated	estimate	VERB
cana-602	11	21	through	through	ADP
cana-602	11	22	nonlinear	nonlinear	ADJ
cana-602	11	23	time	time	NOUN
cana-602	11	24	series	series	PROPN
cana-602	11	25	models	model	NOUN
cana-602	11	26	like	like	ADP
cana-602	11	27	garch	garch	NOUN
cana-602	11	28	,	,	PUNCT
cana-602	11	29	which	which	PRON
cana-602	11	30	enhance	enhance	VERB
cana-602	11	31	the	the	DET
cana-602	11	32	forecasting	forecasting	NOUN
cana-602	11	33	of	of	ADP
cana-602	11	34	volatility	volatility	NOUN
cana-602	11	35	and	and	CCONJ
cana-602	11	36	potential	potential	ADJ
cana-602	11	37	losses	loss	NOUN
cana-602	11	38	.	.	PUNCT
cana-602	12	1	these	these	DET
cana-602	12	2	applications	application	NOUN
cana-602	12	3	highlight	highlight	VERB
cana-602	12	4	the	the	DET
cana-602	12	5	critical	critical	ADJ
cana-602	12	6	role	role	NOUN
cana-602	12	7	of	of	ADP
cana-602	12	8	nonlinear	nonlinear	ADJ
cana-602	12	9	equations	equation	NOUN
cana-602	12	10	in	in	ADP
cana-602	12	11	providing	provide	VERB
cana-602	12	12	a	a	DET
cana-602	12	13	more	more	ADV
cana-602	12	14	nuanced	nuanced	ADJ
cana-602	12	15	and	and	CCONJ
cana-602	12	16	effective	effective	ADJ
cana-602	12	17	toolkit	toolkit	NOUN
cana-602	12	18	for	for	ADP
cana-602	12	19	navigating	navigate	VERB
cana-602	12	20	the	the	DET
cana-602	12	21	intricacies	intricacy	NOUN
cana-602	12	22	and	and	CCONJ
cana-602	12	23	volatilities	volatility	NOUN
cana-602	12	24	of	of	ADP
cana-602	12	25	financial	financial	ADJ
cana-602	12	26	systems	system	NOUN
cana-602	12	27	[	[	X
cana-602	12	28	2	2	NUM
cana-602	12	29	]	]	PUNCT
cana-602	12	30	.	.	PUNCT
cana-602	13	1	communications	communication	NOUN
cana-602	13	2	on	on	ADP
cana-602	13	3	applied	apply	VERB
cana-602	13	4	nonlinear	nonlinear	ADJ
cana-602	13	5	analysis	analysis	NOUN
cana-602	13	6	issn	issn	NOUN
cana-602	13	7	:	:	PUNCT
cana-602	13	8	1074	1074	NUM
cana-602	13	9	-	-	PUNCT
cana-602	13	10	133x	133x	NUM
cana-602	13	11	vol	vol	NOUN
cana-602	13	12	31	31	NUM
cana-602	13	13	no	no	NOUN
cana-602	13	14	.	.	PUNCT
cana-602	14	1	2s	2s	NUM
cana-602	14	2	(	(	PUNCT
cana-602	14	3	2024	2024	NUM
cana-602	14	4	)	)	PUNCT
cana-602	14	5	114	114	NUM
cana-602	14	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-602	14	7	a.	a.	NOUN
cana-602	14	8	option	option	NOUN
cana-602	14	9	pricing	pricing	NOUN
cana-602	14	10	models	model	NOUN
cana-602	14	11	nonlinear	nonlinear	ADJ
cana-602	14	12	equations	equation	NOUN
cana-602	14	13	form	form	VERB
cana-602	14	14	the	the	DET
cana-602	14	15	backbone	backbone	NOUN
cana-602	14	16	of	of	ADP
cana-602	14	17	many	many	ADJ
cana-602	14	18	advanced	advanced	ADJ
cana-602	14	19	models	model	NOUN
cana-602	14	20	in	in	ADP
cana-602	14	21	financial	financial	ADJ
cana-602	14	22	mathematics	mathematic	NOUN
cana-602	14	23	,	,	PUNCT
cana-602	14	24	capturing	capture	VERB
cana-602	14	25	the	the	DET
cana-602	14	26	complex	complex	ADJ
cana-602	14	27	interactions	interaction	NOUN
cana-602	14	28	and	and	CCONJ
cana-602	14	29	dynamics	dynamic	NOUN
cana-602	14	30	of	of	ADP
cana-602	14	31	financial	financial	ADJ
cana-602	14	32	systems	system	NOUN
cana-602	14	33	that	that	PRON
cana-602	14	34	linear	linear	ADJ
cana-602	14	35	equations	equation	NOUN
cana-602	14	36	can	can	AUX
cana-602	14	37	not	not	PART
cana-602	14	38	.	.	PUNCT
cana-602	15	1	in	in	ADP
cana-602	15	2	the	the	DET
cana-602	15	3	financial	financial	ADJ
cana-602	15	4	industry	industry	NOUN
cana-602	15	5	,	,	PUNCT
cana-602	15	6	nonlinear	nonlinear	ADJ
cana-602	15	7	equations	equation	NOUN
cana-602	15	8	are	be	AUX
cana-602	15	9	applied	apply	VERB
cana-602	15	10	across	across	ADP
cana-602	15	11	various	various	ADJ
cana-602	15	12	domains	domain	NOUN
cana-602	15	13	,	,	PUNCT
cana-602	15	14	from	from	ADP
cana-602	15	15	derivative	derivative	ADJ
cana-602	15	16	pricing	pricing	NOUN
cana-602	15	17	to	to	PART
cana-602	15	18	risk	risk	VERB
cana-602	15	19	management	management	NOUN
cana-602	15	20	and	and	CCONJ
cana-602	15	21	macroeconomic	macroeconomic	ADJ
cana-602	15	22	modeling	modeling	NOUN
cana-602	15	23	.	.	PUNCT
cana-602	16	1	traditional	traditional	ADJ
cana-602	16	2	models	model	NOUN
cana-602	16	3	like	like	ADP
cana-602	16	4	the	the	DET
cana-602	16	5	black	black	ADJ
cana-602	16	6	-	-	PUNCT
cana-602	16	7	scholes	schole	NOUN
cana-602	16	8	equation	equation	NOUN
cana-602	16	9	originally	originally	ADV
cana-602	16	10	assume	assume	VERB
cana-602	16	11	a	a	DET
cana-602	16	12	linear	linear	ADJ
cana-602	16	13	behavior	behavior	NOUN
cana-602	16	14	but	but	CCONJ
cana-602	16	15	must	must	AUX
cana-602	16	16	be	be	AUX
cana-602	16	17	adapted	adapt	VERB
cana-602	16	18	to	to	PART
cana-602	16	19	handle	handle	VERB
cana-602	16	20	more	more	ADJ
cana-602	16	21	complex	complex	ADJ
cana-602	16	22	phenomena	phenomenon	NOUN
cana-602	16	23	such	such	ADJ
cana-602	16	24	as	as	ADP
cana-602	16	25	stochastic	stochastic	ADJ
cana-602	16	26	volatility	volatility	NOUN
cana-602	16	27	and	and	CCONJ
cana-602	16	28	jump	jump	NOUN
cana-602	16	29	diffusions	diffusion	NOUN
cana-602	16	30	[	[	X
cana-602	16	31	3	3	NUM
cana-602	16	32	]	]	PUNCT
cana-602	16	33	.	.	PUNCT
cana-602	17	1	these	these	DET
cana-602	17	2	adaptations	adaptation	NOUN
cana-602	17	3	lead	lead	VERB
cana-602	17	4	to	to	ADP
cana-602	17	5	nonlinear	nonlinear	ADJ
cana-602	17	6	stochastic	stochastic	ADJ
cana-602	17	7	differential	differential	ADJ
cana-602	17	8	equations	equation	NOUN
cana-602	17	9	(	(	PUNCT
cana-602	17	10	sdes	sde	NOUN
cana-602	17	11	)	)	PUNCT
cana-602	17	12	,	,	PUNCT
cana-602	17	13	such	such	ADJ
cana-602	17	14	as	as	ADP
cana-602	17	15	the	the	DET
cana-602	17	16	extended	extended	ADJ
cana-602	17	17	black	black	ADJ
cana-602	17	18	-	-	PUNCT
cana-602	17	19	scholes	schole	NOUN
cana-602	17	20	equation	equation	NOUN
cana-602	17	21	for	for	ADP
cana-602	17	22	a	a	DET
cana-602	17	23	european	european	ADJ
cana-602	17	24	call	call	NOUN
cana-602	17	25	option	option	NOUN
cana-602	17	26	under	under	ADP
cana-602	17	27	stochastic	stochastic	ADJ
cana-602	17	28	volatility	volatility	NOUN
cana-602	17	29	:	:	PUNCT
cana-602	17	30	dv	dv	PROPN
cana-602	17	31	/	/	SYM
cana-602	17	32	dt	dt	PROPN
cana-602	18	1	+	+	NUM
cana-602	18	2	1/2	1/2	NUM
cana-602	18	3	σ^2	σ^2	NOUN
cana-602	18	4	s^2	s^2	NOUN
cana-602	18	5	d²v	d²v	NOUN
cana-602	18	6	/	/	SYM
cana-602	18	7	ds²	ds²	NOUN
cana-602	18	8	+	+	CCONJ
cana-602	18	9	rs	rs	PROPN
cana-602	18	10	dv	dv	PROPN
cana-602	18	11	/	/	SYM
cana-602	18	12	ds	ds	ADJ
cana-602	18	13	rv	rv	NOUN
cana-602	18	14	=	=	SYM
cana-602	18	15	0	0	NUM
cana-602	18	16	…	…	PUNCT
cana-602	18	17	…	…	PUNCT
cana-602	18	18	…	…	PUNCT
cana-602	18	19	.(1	.(1	NUM
cana-602	18	20	)	)	PUNCT
cana-602	18	21	b.	b.	PROPN
cana-602	18	22	risk	risk	PROPN
cana-602	18	23	management	management	PROPN
cana-602	18	24	nonlinear	nonlinear	ADJ
cana-602	18	25	equations	equation	NOUN
cana-602	18	26	are	be	AUX
cana-602	18	27	pivotal	pivotal	ADJ
cana-602	18	28	in	in	ADP
cana-602	18	29	quantifying	quantify	VERB
cana-602	18	30	risk	risk	NOUN
cana-602	18	31	through	through	ADP
cana-602	18	32	models	model	NOUN
cana-602	18	33	that	that	PRON
cana-602	18	34	capture	capture	VERB
cana-602	18	35	nonlinear	nonlinear	ADJ
cana-602	18	36	dependencies	dependency	NOUN
cana-602	18	37	and	and	CCONJ
cana-602	18	38	tail	tail	NOUN
cana-602	18	39	risks	risk	NOUN
cana-602	18	40	[	[	X
cana-602	18	41	4	4	NUM
cana-602	18	42	]	]	PUNCT
cana-602	18	43	.	.	PUNCT
cana-602	19	1	for	for	ADP
cana-602	19	2	instance	instance	NOUN
cana-602	19	3	,	,	PUNCT
cana-602	19	4	the	the	DET
cana-602	19	5	value	value	NOUN
cana-602	19	6	-	-	PUNCT
cana-602	19	7	at	at	ADP
cana-602	19	8	-	-	PUNCT
cana-602	19	9	risk	risk	NOUN
cana-602	19	10	(	(	PUNCT
cana-602	19	11	var	var	NOUN
cana-602	19	12	)	)	PUNCT
cana-602	19	13	for	for	ADP
cana-602	19	14	a	a	DET
cana-602	19	15	portfolio	portfolio	NOUN
cana-602	19	16	can	can	AUX
cana-602	19	17	be	be	AUX
cana-602	19	18	estimated	estimate	VERB
cana-602	19	19	through	through	ADP
cana-602	19	20	nonlinear	nonlinear	ADJ
cana-602	19	21	time	time	NOUN
cana-602	19	22	series	series	PROPN
cana-602	19	23	models	model	NOUN
cana-602	19	24	like	like	ADP
cana-602	19	25	garch	garch	NOUN
cana-602	19	26	to	to	PART
cana-602	19	27	forecast	forecast	VERB
cana-602	19	28	volatility	volatility	NOUN
cana-602	19	29	and	and	CCONJ
cana-602	19	30	potential	potential	ADJ
cana-602	19	31	losses	loss	NOUN
cana-602	19	32	better	well	ADV
cana-602	19	33	:	:	PUNCT
cana-602	19	34	σ²_t	σ²_t	NOUN
cana-602	19	35	=	=	SYM
cana-602	19	36	α₀	α₀	PROPN
cana-602	19	37	+	+	PRON
cana-602	19	38	α₁ε²_{t-1	α₁ε²_{t-1	NUM
cana-602	19	39	}	}	PUNCT
cana-602	19	40	+	+	CCONJ
cana-602	19	41	β₁σ²_{t-1	β₁σ²_{t-1	NUM
cana-602	19	42	}	}	PUNCT
cana-602	19	43	…	…	PUNCT
cana-602	19	44	…	…	PUNCT
cana-602	19	45	…	…	SYM
cana-602	19	46	.(2	.(2	NOUN
cana-602	19	47	)	)	PUNCT
cana-602	19	48	c.	c.	PROPN
cana-602	19	49	macroeconomic	macroeconomic	ADJ
cana-602	19	50	models	model	NOUN
cana-602	19	51	nonlinear	nonlinear	ADJ
cana-602	19	52	dynamics	dynamic	NOUN
cana-602	19	53	are	be	AUX
cana-602	19	54	integral	integral	ADJ
cana-602	19	55	in	in	ADP
cana-602	19	56	macroeconomic	macroeconomic	ADJ
cana-602	19	57	models	model	NOUN
cana-602	19	58	which	which	PRON
cana-602	19	59	describe	describe	VERB
cana-602	19	60	economic	economic	ADJ
cana-602	19	61	growth	growth	NOUN
cana-602	19	62	,	,	PUNCT
cana-602	19	63	business	business	NOUN
cana-602	19	64	cycles	cycle	NOUN
cana-602	19	65	,	,	PUNCT
cana-602	19	66	and	and	CCONJ
cana-602	19	67	market	market	NOUN
cana-602	19	68	equilibriums	equilibrium	NOUN
cana-602	19	69	[	[	X
cana-602	19	70	5	5	NUM
cana-602	19	71	]	]	PUNCT
cana-602	19	72	.	.	PUNCT
cana-602	20	1	for	for	ADP
cana-602	20	2	example	example	NOUN
cana-602	20	3	,	,	PUNCT
cana-602	20	4	the	the	DET
cana-602	20	5	solow	solow	PROPN
cana-602	20	6	growth	growth	NOUN
cana-602	20	7	model	model	NOUN
cana-602	20	8	can	can	AUX
cana-602	20	9	be	be	AUX
cana-602	20	10	extended	extend	VERB
cana-602	20	11	into	into	ADP
cana-602	20	12	a	a	DET
cana-602	20	13	nonlinear	nonlinear	ADJ
cana-602	20	14	format	format	NOUN
cana-602	20	15	to	to	PART
cana-602	20	16	incorporate	incorporate	VERB
cana-602	20	17	more	more	ADV
cana-602	20	18	realistic	realistic	ADJ
cana-602	20	19	mechanisms	mechanism	NOUN
cana-602	20	20	of	of	ADP
cana-602	20	21	technological	technological	ADJ
cana-602	20	22	growth	growth	NOUN
cana-602	20	23	and	and	CCONJ
cana-602	20	24	capital	capital	NOUN
cana-602	20	25	accumulation	accumulation	NOUN
cana-602	20	26	:	:	PUNCT
cana-602	20	27	dk	dk	X
cana-602	20	28	/	/	SYM
cana-602	20	29	dt	dt	PROPN
cana-602	21	1	=	=	SYM
cana-602	21	2	sy	sy	PROPN
cana-602	21	3	δk	δk	PROPN
cana-602	21	4	,	,	PUNCT
cana-602	21	5	y	y	PROPN
cana-602	21	6	=	=	PUNCT
cana-602	21	7	k^α	k^α	PROPN
cana-602	21	8	l^{1	l^{1	PROPN
cana-602	21	9	-	-	PUNCT
cana-602	21	10	α	α	NOUN
cana-602	21	11	}	}	PUNCT
cana-602	21	12	e^{gt	e^{gt	PROPN
cana-602	21	13	}	}	PUNCT
cana-602	21	14	…	…	PUNCT
cana-602	21	15	…	…	PUNCT
cana-602	21	16	…	…	PUNCT
cana-602	21	17	.(3	.(3	SYM
cana-602	21	18	)	)	PUNCT
cana-602	21	19	2	2	NUM
cana-602	21	20	.	.	X
cana-602	21	21	introduction	introduction	NOUN
cana-602	21	22	to	to	ADP
cana-602	21	23	topological	topological	ADJ
cana-602	21	24	methods	method	NOUN
cana-602	21	25	a.	a.	NOUN
cana-602	21	26	fixed	fix	VERB
cana-602	21	27	-	-	PUNCT
cana-602	21	28	point	point	NOUN
cana-602	21	29	theorems	theorem	NOUN
cana-602	21	30	fixed	fix	VERB
cana-602	21	31	-	-	PUNCT
cana-602	21	32	point	point	NOUN
cana-602	21	33	theorems	theorem	NOUN
cana-602	21	34	are	be	AUX
cana-602	21	35	crucial	crucial	ADJ
cana-602	21	36	in	in	ADP
cana-602	21	37	financial	financial	ADJ
cana-602	21	38	models	model	NOUN
cana-602	21	39	to	to	PART
cana-602	21	40	ensure	ensure	VERB
cana-602	21	41	the	the	DET
cana-602	21	42	existence	existence	NOUN
cana-602	21	43	of	of	ADP
cana-602	21	44	equilibrium	equilibrium	NOUN
cana-602	21	45	states	state	NOUN
cana-602	21	46	.	.	PUNCT
cana-602	22	1	the	the	DET
cana-602	22	2	brouwer	brouwer	NOUN
cana-602	22	3	fixed	fix	VERB
cana-602	22	4	-	-	PUNCT
cana-602	22	5	point	point	NOUN
cana-602	22	6	theorem	theorem	NOUN
cana-602	22	7	,	,	PUNCT
cana-602	22	8	for	for	ADP
cana-602	22	9	example	example	NOUN
cana-602	22	10	,	,	PUNCT
cana-602	22	11	guarantees	guarantee	VERB
cana-602	22	12	that	that	SCONJ
cana-602	22	13	any	any	DET
cana-602	22	14	continuous	continuous	ADJ
cana-602	22	15	function	function	NOUN
cana-602	22	16	from	from	ADP
cana-602	22	17	a	a	DET
cana-602	22	18	compact	compact	ADJ
cana-602	22	19	convex	convex	NOUN
cana-602	22	20	set	set	VERB
cana-602	22	21	to	to	ADP
cana-602	22	22	itself	itself	PRON
cana-602	22	23	has	have	VERB
cana-602	22	24	at	at	ADV
cana-602	22	25	least	least	ADV
cana-602	22	26	one	one	NUM
cana-602	22	27	fixed	fix	VERB
cana-602	22	28	point	point	NOUN
cana-602	22	29	.	.	PUNCT
cana-602	23	1	this	this	DET
cana-602	23	2	principle	principle	NOUN
cana-602	23	3	can	can	AUX
cana-602	23	4	be	be	AUX
cana-602	23	5	applied	apply	VERB
cana-602	23	6	to	to	PART
cana-602	23	7	prove	prove	VERB
cana-602	23	8	the	the	DET
cana-602	23	9	existence	existence	NOUN
cana-602	23	10	of	of	ADP
cana-602	23	11	an	an	DET
cana-602	23	12	equilibrium	equilibrium	NOUN
cana-602	23	13	in	in	ADP
cana-602	23	14	financial	financial	ADJ
cana-602	23	15	models	model	NOUN
cana-602	23	16	where	where	SCONJ
cana-602	23	17	direct	direct	ADJ
cana-602	23	18	solutions	solution	NOUN
cana-602	23	19	are	be	AUX
cana-602	23	20	intractable	intractable	ADJ
cana-602	23	21	.	.	PUNCT
cana-602	24	1	b.	b.	PROPN
cana-602	24	2	homotopy	homotopy	PROPN
cana-602	24	3	methods	method	NOUN
cana-602	24	4	homotopy	homotopy	VERB
cana-602	24	5	methods	method	NOUN
cana-602	24	6	continuously	continuously	ADV
cana-602	24	7	deform	deform	VERB
cana-602	24	8	a	a	DET
cana-602	24	9	complex	complex	ADJ
cana-602	24	10	,	,	PUNCT
cana-602	24	11	unsolvable	unsolvable	ADJ
cana-602	24	12	equation	equation	NOUN
cana-602	24	13	into	into	ADP
cana-602	24	14	a	a	DET
cana-602	24	15	simpler	simple	ADJ
cana-602	24	16	one	one	NUM
cana-602	24	17	whose	whose	DET
cana-602	24	18	solutions	solution	NOUN
cana-602	24	19	can	can	AUX
cana-602	24	20	be	be	AUX
cana-602	24	21	easily	easily	ADV
cana-602	24	22	computed	compute	VERB
cana-602	24	23	[	[	PUNCT
cana-602	24	24	6	6	NUM
cana-602	24	25	]	]	PUNCT
cana-602	24	26	.	.	PUNCT
cana-602	25	1	these	these	DET
cana-602	25	2	solutions	solution	NOUN
cana-602	25	3	then	then	ADV
cana-602	25	4	trace	trace	VERB
cana-602	25	5	back	back	ADP
cana-602	25	6	to	to	PART
cana-602	25	7	solve	solve	VERB
cana-602	25	8	the	the	DET
cana-602	25	9	original	original	ADJ
cana-602	25	10	equation	equation	NOUN
cana-602	25	11	.	.	PUNCT
cana-602	26	1	the	the	DET
cana-602	26	2	homotopy	homotopy	NOUN
cana-602	26	3	analysis	analysis	NOUN
cana-602	26	4	method	method	NOUN
cana-602	26	5	(	(	PUNCT
cana-602	26	6	ham	ham	NOUN
cana-602	26	7	)	)	PUNCT
cana-602	26	8	constructs	construct	VERB
cana-602	26	9	a	a	DET
cana-602	26	10	homotopy	homotopy	NOUN
cana-602	26	11	h(x	h(x	PROPN
cana-602	26	12	,	,	PUNCT
cana-602	26	13	t	t	PROPN
cana-602	26	14	)	)	PUNCT
cana-602	26	15	as	as	ADP
cana-602	26	16	:	:	PUNCT
cana-602	26	17	h(x	h(x	PROPN
cana-602	26	18	,	,	PUNCT
cana-602	26	19	t	t	PROPN
cana-602	26	20	)	)	PUNCT
cana-602	26	21	=	=	PUNCT
cana-602	26	22	(	(	PUNCT
cana-602	26	23	1	1	NUM
cana-602	26	24	t	t	NOUN
cana-602	26	25	)	)	PUNCT
cana-602	26	26	(	(	PUNCT
cana-602	26	27	x	x	SYM
cana-602	26	28	g(x	g(x	NOUN
cana-602	26	29	)	)	PUNCT
cana-602	26	30	)	)	PUNCT
cana-602	27	1	+	+	NUM
cana-602	27	2	t	t	PROPN
cana-602	27	3	f(x	f(x	PROPN
cana-602	27	4	)	)	PUNCT
cana-602	27	5	=	=	SYM
cana-602	27	6	0	0	NUM
cana-602	27	7	…	…	PUNCT
cana-602	27	8	…	…	PUNCT
cana-602	27	9	…	…	PUNCT
cana-602	27	10	.(4	.(4	NUM
cana-602	27	11	)	)	PUNCT
cana-602	27	12	c.	c.	PROPN
cana-602	27	13	topological	topological	PROPN
cana-602	27	14	degree	degree	NOUN
cana-602	27	15	theory	theory	PROPN
cana-602	27	16	topological	topological	PROPN
cana-602	27	17	degree	degree	NOUN
cana-602	27	18	theory	theory	NOUN
cana-602	27	19	provides	provide	VERB
cana-602	27	20	a	a	DET
cana-602	27	21	way	way	NOUN
cana-602	27	22	to	to	PART
cana-602	27	23	count	count	VERB
cana-602	27	24	the	the	DET
cana-602	27	25	number	number	NOUN
cana-602	27	26	of	of	ADP
cana-602	27	27	solutions	solution	NOUN
cana-602	27	28	to	to	ADP
cana-602	27	29	a	a	DET
cana-602	27	30	nonlinear	nonlinear	ADJ
cana-602	27	31	equation	equation	NOUN
cana-602	27	32	within	within	ADP
cana-602	27	33	a	a	DET
cana-602	27	34	given	give	VERB
cana-602	27	35	boundary	boundary	NOUN
cana-602	27	36	by	by	ADP
cana-602	27	37	considering	consider	VERB
cana-602	27	38	the	the	DET
cana-602	27	39	changes	change	NOUN
cana-602	27	40	in	in	ADP
cana-602	27	41	topological	topological	ADJ
cana-602	27	42	properties	property	NOUN
cana-602	27	43	.	.	PUNCT
cana-602	28	1	it	it	PRON
cana-602	28	2	is	be	AUX
cana-602	28	3	useful	useful	ADJ
cana-602	28	4	in	in	ADP
cana-602	28	5	financial	financial	ADJ
cana-602	28	6	models	model	NOUN
cana-602	28	7	for	for	ADP
cana-602	28	8	determining	determine	VERB
cana-602	28	9	the	the	DET
cana-602	28	10	stability	stability	NOUN
cana-602	28	11	and	and	CCONJ
cana-602	28	12	bifurcation	bifurcation	NOUN
cana-602	28	13	points	point	NOUN
cana-602	28	14	and	and	CCONJ
cana-602	28	15	can	can	AUX
cana-602	28	16	guide	guide	VERB
cana-602	28	17	numerical	numerical	ADJ
cana-602	28	18	algorithms	algorithm	NOUN
cana-602	28	19	for	for	ADP
cana-602	28	20	communications	communication	NOUN
cana-602	28	21	on	on	ADP
cana-602	28	22	applied	apply	VERB
cana-602	28	23	nonlinear	nonlinear	ADJ
cana-602	28	24	analysis	analysis	NOUN
cana-602	28	25	issn	issn	NOUN
cana-602	28	26	:	:	PUNCT
cana-602	28	27	1074	1074	NUM
cana-602	28	28	-	-	PUNCT
cana-602	28	29	133x	133x	NUM
cana-602	28	30	vol	vol	NOUN
cana-602	28	31	31	31	NUM
cana-602	28	32	no	no	NOUN
cana-602	28	33	.	.	PUNCT
cana-602	29	1	2s	2s	NUM
cana-602	29	2	(	(	PUNCT
cana-602	29	3	2024	2024	NUM
cana-602	29	4	)	)	PUNCT
cana-602	29	5	115	115	NUM
cana-602	29	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-602	29	7	finding	find	VERB
cana-602	29	8	solutions	solution	NOUN
cana-602	29	9	to	to	ADP
cana-602	29	10	complex	complex	ADJ
cana-602	29	11	equations	equation	NOUN
cana-602	29	12	[	[	X
cana-602	29	13	7	7	NUM
cana-602	29	14	]	]	PUNCT
cana-602	29	15	.	.	PUNCT
cana-602	30	1	advanced	advanced	ADJ
cana-602	30	2	topological	topological	ADJ
cana-602	30	3	methods	method	NOUN
cana-602	30	4	for	for	ADP
cana-602	30	5	solving	solve	VERB
cana-602	30	6	nonlinear	nonlinear	ADJ
cana-602	30	7	equations	equation	NOUN
cana-602	30	8	in	in	ADP
cana-602	30	9	financial	financial	ADJ
cana-602	30	10	mathematics	mathematic	NOUN
cana-602	30	11	.	.	PUNCT
cana-602	31	1	this	this	DET
cana-602	31	2	section	section	NOUN
cana-602	31	3	delves	delve	VERB
cana-602	31	4	deeply	deeply	ADV
cana-602	31	5	into	into	ADP
cana-602	31	6	the	the	DET
cana-602	31	7	mathematical	mathematical	ADJ
cana-602	31	8	framework	framework	NOUN
cana-602	31	9	of	of	ADP
cana-602	31	10	topological	topological	ADJ
cana-602	31	11	methods	method	NOUN
cana-602	31	12	applied	apply	VERB
cana-602	31	13	to	to	ADP
cana-602	31	14	nonlinear	nonlinear	ADJ
cana-602	31	15	equations	equation	NOUN
cana-602	31	16	in	in	ADP
cana-602	31	17	financial	financial	ADJ
cana-602	31	18	mathematics	mathematic	NOUN
cana-602	31	19	,	,	PUNCT
cana-602	31	20	focusing	focus	VERB
cana-602	31	21	on	on	ADP
cana-602	31	22	the	the	DET
cana-602	31	23	homotopy	homotopy	NOUN
cana-602	31	24	analysis	analysis	NOUN
cana-602	31	25	method	method	NOUN
cana-602	31	26	(	(	PUNCT
cana-602	31	27	ham	ham	PROPN
cana-602	31	28	)	)	PUNCT
cana-602	31	29	,	,	PUNCT
cana-602	31	30	topological	topological	ADJ
cana-602	31	31	degree	degree	NOUN
cana-602	31	32	theory	theory	NOUN
cana-602	31	33	,	,	PUNCT
cana-602	31	34	and	and	CCONJ
cana-602	31	35	iterative	iterative	NOUN
cana-602	31	36	methods	method	NOUN
cana-602	31	37	inspired	inspire	VERB
cana-602	31	38	by	by	ADP
cana-602	31	39	topological	topological	ADJ
cana-602	31	40	concepts	concept	NOUN
cana-602	31	41	[	[	X
cana-602	31	42	8	8	NUM
cana-602	31	43	]	]	PUNCT
cana-602	31	44	.	.	PUNCT
cana-602	32	1	the	the	DET
cana-602	32	2	content	content	NOUN
cana-602	32	3	is	be	AUX
cana-602	32	4	structured	structure	VERB
cana-602	32	5	to	to	PART
cana-602	32	6	emphasize	emphasize	VERB
cana-602	32	7	theorems	theorem	NOUN
cana-602	32	8	,	,	PUNCT
cana-602	32	9	corollaries	corollary	NOUN
cana-602	32	10	,	,	PUNCT
cana-602	32	11	and	and	CCONJ
cana-602	32	12	the	the	DET
cana-602	32	13	mathematical	mathematical	ADJ
cana-602	32	14	formulations	formulation	NOUN
cana-602	32	15	that	that	PRON
cana-602	32	16	underpin	underpin	VERB
cana-602	32	17	these	these	DET
cana-602	32	18	methods	method	NOUN
cana-602	32	19	.	.	PUNCT
cana-602	33	1	i.	i.	PROPN
cana-602	33	2	homotopy	homotopy	PROPN
cana-602	33	3	analysis	analysis	NOUN
cana-602	33	4	method	method	NOUN
cana-602	33	5	(	(	PUNCT
cana-602	33	6	ham	ham	NOUN
cana-602	33	7	)	)	PUNCT
cana-602	33	8	theorem	theorem	NOUN
cana-602	33	9	1	1	NUM
cana-602	33	10	:	:	PUNCT
cana-602	33	11	basic	basic	ADJ
cana-602	33	12	construction	construction	NOUN
cana-602	33	13	of	of	ADP
cana-602	33	14	ham	ham	NOUN
cana-602	33	15	given	give	VERB
cana-602	33	16	a	a	DET
cana-602	33	17	nonlinear	nonlinear	ADJ
cana-602	33	18	operator	operator	NOUN
cana-602	33	19	f	f	PROPN
cana-602	33	20	on	on	ADP
cana-602	33	21	a	a	DET
cana-602	33	22	banach	banach	NOUN
cana-602	33	23	space	space	NOUN
cana-602	33	24	,	,	PUNCT
cana-602	33	25	and	and	CCONJ
cana-602	33	26	an	an	DET
cana-602	33	27	auxiliary	auxiliary	ADJ
cana-602	33	28	linear	linear	ADJ
cana-602	33	29	operator	operator	NOUN
cana-602	33	30	l	l	NOUN
cana-602	33	31	,	,	PUNCT
cana-602	33	32	we	we	PRON
cana-602	33	33	define	define	VERB
cana-602	33	34	a	a	DET
cana-602	33	35	homotopy	homotopy	NOUN
cana-602	33	36	h	h	NOUN
cana-602	33	37	:	:	PUNCT
cana-602	33	38	v	v	NUM
cana-602	33	39	×	×	NOUN
cana-602	34	1	[	[	X
cana-602	34	2	0,1	0,1	NUM
cana-602	34	3	]	]	PUNCT
cana-602	34	4	→	→	SYM
cana-602	34	5	w	w	ADP
cana-602	34	6	as	as	ADP
cana-602	34	7	:	:	PUNCT
cana-602	34	8	h(v	h(v	PROPN
cana-602	34	9	,	,	PUNCT
cana-602	34	10	t	t	PROPN
cana-602	34	11	)	)	PUNCT
cana-602	34	12	=	=	PUNCT
cana-602	34	13	(	(	PUNCT
cana-602	34	14	1	1	NUM
cana-602	34	15	-	-	PUNCT
cana-602	34	16	t)[l(v	t)[l(v	NOUN
cana-602	34	17	)	)	PUNCT
cana-602	34	18	l(v_0	l(v_0	PROPN
cana-602	34	19	)	)	PUNCT
cana-602	34	20	]	]	PUNCT
cana-602	35	1	+	+	CCONJ
cana-602	35	2	tf(v	tf(v	NOUN
cana-602	35	3	)	)	PUNCT
cana-602	35	4	,	,	PUNCT
cana-602	35	5	where	where	SCONJ
cana-602	35	6	v_0	v_0	PROPN
cana-602	35	7	is	be	AUX
cana-602	35	8	an	an	DET
cana-602	35	9	initial	initial	ADJ
cana-602	35	10	approximation	approximation	NOUN
cana-602	35	11	and	and	CCONJ
cana-602	35	12	t	t	NOUN
cana-602	35	13	is	be	AUX
cana-602	35	14	the	the	DET
cana-602	35	15	homotopy	homotopy	PROPN
cana-602	35	16	parameter	parameter	NOUN
cana-602	35	17	.	.	PUNCT
cana-602	36	1	corollary	corollary	ADJ
cana-602	36	2	1.1	1.1	NUM
cana-602	36	3	:	:	PUNCT
cana-602	36	4	convergence	convergence	NOUN
cana-602	36	5	if	if	SCONJ
cana-602	36	6	l	l	NOUN
cana-602	36	7	is	be	AUX
cana-602	36	8	properly	properly	ADV
cana-602	36	9	chosen	choose	VERB
cana-602	36	10	such	such	ADJ
cana-602	36	11	that	that	SCONJ
cana-602	36	12	l	l	NOUN
cana-602	36	13	f	f	PROPN
cana-602	36	14	is	be	AUX
cana-602	36	15	compact	compact	ADJ
cana-602	36	16	,	,	PUNCT
cana-602	36	17	then	then	ADV
cana-602	36	18	the	the	DET
cana-602	36	19	zero	zero	NUM
cana-602	36	20	path	path	NOUN
cana-602	36	21	h(v	h(v	PROPN
cana-602	36	22	,	,	PUNCT
cana-602	36	23	t	t	PROPN
cana-602	36	24	)	)	PUNCT
cana-602	37	1	=	=	SYM
cana-602	37	2	0	0	NUM
cana-602	37	3	continuously	continuously	ADV
cana-602	37	4	deforms	deform	VERB
cana-602	37	5	v_0	v_0	PROPN
cana-602	37	6	into	into	ADP
cana-602	37	7	a	a	DET
cana-602	37	8	solution	solution	NOUN
cana-602	37	9	of	of	ADP
cana-602	37	10	f(v	f(v	NOUN
cana-602	37	11	)	)	PUNCT
cana-602	38	1	=	=	SYM
cana-602	38	2	0	0	PUNCT
cana-602	39	1	as	as	SCONJ
cana-602	39	2	t	t	PROPN
cana-602	39	3	moves	move	NOUN
cana-602	39	4	from	from	ADP
cana-602	39	5	0	0	NUM
cana-602	39	6	to	to	ADP
cana-602	39	7	1	1	NUM
cana-602	39	8	[	[	X
cana-602	39	9	9	9	NUM
cana-602	39	10	]	]	PUNCT
cana-602	39	11	.	.	PUNCT
cana-602	40	1	application	application	NOUN
cana-602	40	2	in	in	ADP
cana-602	40	3	financial	financial	ADJ
cana-602	40	4	models	model	NOUN
cana-602	40	5	:	:	PUNCT
cana-602	40	6	utilize	utilize	VERB
cana-602	40	7	ham	ham	NOUN
cana-602	40	8	to	to	PART
cana-602	40	9	solve	solve	VERB
cana-602	40	10	a	a	DET
cana-602	40	11	high	high	ADV
cana-602	40	12	-	-	PUNCT
cana-602	40	13	dimensional	dimensional	ADJ
cana-602	40	14	nonlinear	nonlinear	ADJ
cana-602	40	15	black	black	ADJ
cana-602	40	16	-	-	PUNCT
cana-602	40	17	scholes	schole	NOUN
cana-602	40	18	equation	equation	NOUN
cana-602	40	19	modified	modify	VERB
cana-602	40	20	for	for	ADP
cana-602	40	21	stochastic	stochastic	ADJ
cana-602	40	22	volatility	volatility	NOUN
cana-602	40	23	:	:	PUNCT
cana-602	40	24	∂v/∂t	∂v/∂t	PROPN
cana-602	40	25	+	+	CCONJ
cana-602	40	26	1/2	1/2	NUM
cana-602	40	27	σ²(t	σ²(t	NOUN
cana-602	40	28	,	,	PUNCT
cana-602	40	29	s	s	PART
cana-602	40	30	)	)	PUNCT
cana-602	40	31	s²	s²	ADJ
cana-602	40	32	∂²v/∂s²	∂²v/∂s²	NOUN
cana-602	41	1	+	+	CCONJ
cana-602	41	2	rs∂v/∂s	rs∂v/∂s	NOUN
cana-602	41	3	rv	rv	NOUN
cana-602	41	4	=	=	SYM
cana-602	41	5	0	0	PROPN
cana-602	41	6	,	,	PUNCT
cana-602	41	7	where	where	SCONJ
cana-602	41	8	σ(t	σ(t	PROPN
cana-602	41	9	,	,	PUNCT
cana-602	41	10	s	s	PART
cana-602	41	11	)	)	PUNCT
cana-602	41	12	may	may	AUX
cana-602	41	13	itself	itself	PRON
cana-602	41	14	be	be	AUX
cana-602	41	15	governed	govern	VERB
cana-602	41	16	by	by	ADP
cana-602	41	17	a	a	DET
cana-602	41	18	nonlinear	nonlinear	ADJ
cana-602	41	19	equation	equation	NOUN
cana-602	41	20	dependent	dependent	ADJ
cana-602	41	21	on	on	ADP
cana-602	41	22	v	v	NUM
cana-602	41	23	or	or	CCONJ
cana-602	41	24	s.	s.	PROPN
cana-602	41	25	ii	ii	PROPN
cana-602	41	26	.	.	PUNCT
cana-602	42	1	topological	topological	PROPN
cana-602	42	2	degree	degree	NOUN
cana-602	42	3	theory	theory	NOUN
cana-602	42	4	theorem	theorem	VERB
cana-602	42	5	2	2	NUM
cana-602	42	6	:	:	PUNCT
cana-602	42	7	existence	existence	NOUN
cana-602	42	8	of	of	ADP
cana-602	42	9	solutions	solution	NOUN
cana-602	42	10	using	use	VERB
cana-602	42	11	topological	topological	ADJ
cana-602	42	12	degree	degree	NOUN
cana-602	42	13	let	let	VERB
cana-602	43	1	d	d	NOUN
cana-602	43	2	⊂	⊂	PRON
cana-602	44	1	ℝⁿ	ℝⁿ	ADV
cana-602	44	2	be	be	AUX
cana-602	44	3	open	open	ADJ
cana-602	44	4	and	and	CCONJ
cana-602	44	5	bounded	bound	VERB
cana-602	44	6	,	,	PUNCT
cana-602	44	7	and	and	CCONJ
cana-602	44	8	f	f	X
cana-602	44	9	:	:	PUNCT
cana-602	44	10	d̅	d̅	PROPN
cana-602	45	1	→	→	PUNCT
cana-602	45	2	ℝⁿ	ℝⁿ	ADV
cana-602	45	3	be	be	AUX
cana-602	45	4	a	a	DET
cana-602	45	5	continuous	continuous	ADJ
cana-602	45	6	mapping	mapping	NOUN
cana-602	45	7	.	.	PUNCT
cana-602	46	1	if	if	SCONJ
cana-602	46	2	for	for	ADP
cana-602	46	3	every	every	DET
cana-602	46	4	x	x	SYM
cana-602	46	5	∈	∈	PROPN
cana-602	46	6	∂d	∂d	PROPN
cana-602	46	7	,	,	PUNCT
cana-602	46	8	f(x	f(x	PROPN
cana-602	46	9	)	)	PUNCT
cana-602	46	10	≠	≠	PROPN
cana-602	46	11	0	0	NUM
cana-602	46	12	,	,	PUNCT
cana-602	46	13	and	and	CCONJ
cana-602	46	14	the	the	DET
cana-602	46	15	degree	degree	NOUN
cana-602	46	16	deg(f	deg(f	PROPN
cana-602	46	17	,	,	PUNCT
cana-602	46	18	d	d	NOUN
cana-602	46	19	,	,	PUNCT
cana-602	46	20	0	0	NUM
cana-602	46	21	)	)	PUNCT
cana-602	46	22	≠	≠	PROPN
cana-602	46	23	0	0	NUM
cana-602	46	24	,	,	PUNCT
cana-602	46	25	then	then	ADV
cana-602	46	26	f	f	PROPN
cana-602	46	27	has	have	VERB
cana-602	46	28	at	at	ADV
cana-602	46	29	least	least	ADJ
cana-602	46	30	one	one	NUM
cana-602	46	31	zero	zero	NUM
cana-602	46	32	in	in	ADP
cana-602	46	33	d.	d.	PROPN
cana-602	46	34	corollary	corollary	PROPN
cana-602	46	35	2.1	2.1	NUM
cana-602	46	36	:	:	PUNCT
cana-602	46	37	uniqueness	uniqueness	NOUN
cana-602	46	38	if	if	SCONJ
cana-602	46	39	f	f	PROPN
cana-602	46	40	is	be	AUX
cana-602	46	41	also	also	ADV
cana-602	46	42	a	a	DET
cana-602	46	43	local	local	ADJ
cana-602	46	44	homeomorphism	homeomorphism	NOUN
cana-602	46	45	,	,	PUNCT
cana-602	46	46	then	then	ADV
cana-602	46	47	f	f	PROPN
cana-602	46	48	has	have	VERB
cana-602	46	49	a	a	DET
cana-602	46	50	unique	unique	ADJ
cana-602	46	51	zero	zero	NUM
cana-602	46	52	in	in	ADP
cana-602	46	53	d.	d.	PROPN
cana-602	46	54	apply	apply	VERB
cana-602	46	55	topological	topological	PROPN
cana-602	46	56	degree	degree	NOUN
cana-602	46	57	theory	theory	NOUN
cana-602	46	58	to	to	PART
cana-602	46	59	ensure	ensure	VERB
cana-602	46	60	the	the	DET
cana-602	46	61	global	global	ADJ
cana-602	46	62	convergence	convergence	NOUN
cana-602	46	63	of	of	ADP
cana-602	46	64	an	an	DET
cana-602	46	65	algorithm	algorithm	NOUN
cana-602	46	66	used	use	VERB
cana-602	46	67	for	for	ADP
cana-602	46	68	solving	solve	VERB
cana-602	46	69	the	the	DET
cana-602	46	70	equilibrium	equilibrium	NOUN
cana-602	46	71	state	state	NOUN
cana-602	46	72	in	in	ADP
cana-602	46	73	a	a	DET
cana-602	46	74	nonlinear	nonlinear	ADJ
cana-602	46	75	economic	economic	ADJ
cana-602	46	76	model	model	NOUN
cana-602	46	77	,	,	PUNCT
cana-602	46	78	possibly	possibly	ADV
cana-602	46	79	represented	represent	VERB
cana-602	46	80	by	by	ADP
cana-602	46	81	a	a	DET
cana-602	46	82	system	system	NOUN
cana-602	46	83	of	of	ADP
cana-602	46	84	equations	equation	NOUN
cana-602	46	85	involving	involve	VERB
cana-602	46	86	expectations	expectation	NOUN
cana-602	46	87	of	of	ADP
cana-602	46	88	future	future	ADJ
cana-602	46	89	states	state	NOUN
cana-602	46	90	[	[	X
cana-602	46	91	10	10	NUM
cana-602	46	92	]	]	PUNCT
cana-602	46	93	.	.	PUNCT
cana-602	47	1	iii	iii	X
cana-602	47	2	.	.	PROPN
cana-602	47	3	iterative	iterative	NOUN
cana-602	47	4	methods	method	NOUN
cana-602	47	5	derived	derive	VERB
cana-602	47	6	from	from	ADP
cana-602	47	7	topological	topological	ADJ
cana-602	47	8	concepts	concept	NOUN
cana-602	47	9	theorem	theorem	VERB
cana-602	47	10	3	3	NUM
cana-602	47	11	:	:	PUNCT
cana-602	47	12	convergence	convergence	NOUN
cana-602	47	13	of	of	ADP
cana-602	47	14	newton	newton	PROPN
cana-602	47	15	’s	’s	PART
cana-602	47	16	method	method	NOUN
cana-602	47	17	for	for	ADP
cana-602	47	18	f	f	NOUN
cana-602	47	19	:	:	PUNCT
cana-602	48	1	ℝⁿ	ℝⁿ	X
cana-602	48	2	→	→	SYM
cana-602	48	3	ℝⁿ	ℝⁿ	ADV
cana-602	48	4	,	,	PUNCT
cana-602	48	5	suppose	suppose	VERB
cana-602	48	6	f	f	PROPN
cana-602	48	7	is	be	AUX
cana-602	48	8	continuously	continuously	ADV
cana-602	48	9	differentiable	differentiable	ADJ
cana-602	48	10	and	and	CCONJ
cana-602	48	11	let	let	VERB
cana-602	48	12	j_f(x	j_f(x	NOUN
cana-602	48	13	)	)	PUNCT
cana-602	48	14	be	be	AUX
cana-602	48	15	the	the	DET
cana-602	48	16	jacobian	jacobian	ADJ
cana-602	48	17	matrix	matrix	NOUN
cana-602	48	18	of	of	ADP
cana-602	48	19	f	f	PROPN
cana-602	48	20	at	at	ADP
cana-602	48	21	x.	x.	PROPN
cana-602	48	22	if	if	SCONJ
cana-602	48	23	j_f(x	j_f(x	PROPN
cana-602	48	24	)	)	PUNCT
cana-602	48	25	is	be	AUX
cana-602	48	26	non	non	ADJ
cana-602	48	27	-	-	ADJ
cana-602	48	28	singular	singular	ADJ
cana-602	48	29	at	at	ADP
cana-602	48	30	the	the	DET
cana-602	48	31	root	root	NOUN
cana-602	48	32	x	x	X
cana-602	48	33	*	*	PUNCT
cana-602	48	34	and	and	CCONJ
cana-602	48	35	an	an	DET
cana-602	48	36	initial	initial	ADJ
cana-602	48	37	guess	guess	NOUN
cana-602	48	38	x₀	x₀	PROPN
cana-602	48	39	is	be	AUX
cana-602	48	40	sufficiently	sufficiently	ADV
cana-602	48	41	close	close	ADJ
cana-602	48	42	to	to	ADP
cana-602	48	43	x	x	X
cana-602	48	44	*	*	PUNCT
cana-602	48	45	,	,	PUNCT
cana-602	48	46	then	then	ADV
cana-602	48	47	the	the	DET
cana-602	48	48	newton	newton	PROPN
cana-602	48	49	iteration	iteration	NOUN
cana-602	48	50	:	:	PUNCT
cana-602	48	51	communications	communication	NOUN
cana-602	48	52	on	on	ADP
cana-602	48	53	applied	apply	VERB
cana-602	48	54	nonlinear	nonlinear	ADJ
cana-602	48	55	analysis	analysis	NOUN
cana-602	48	56	issn	issn	NOUN
cana-602	48	57	:	:	PUNCT
cana-602	48	58	1074	1074	NUM
cana-602	48	59	-	-	PUNCT
cana-602	48	60	133x	133x	NUM
cana-602	48	61	vol	vol	NOUN
cana-602	48	62	31	31	NUM
cana-602	48	63	no	no	NOUN
cana-602	48	64	.	.	PUNCT
cana-602	49	1	2s	2s	NUM
cana-602	49	2	(	(	PUNCT
cana-602	49	3	2024	2024	NUM
cana-602	49	4	)	)	PUNCT
cana-602	49	5	116	116	NUM
cana-602	49	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-602	49	7	xₙ₊₁	xₙ₊₁	NOUN
cana-602	49	8	=	=	PUNCT
cana-602	49	9	xₙ	xₙ	PROPN
cana-602	49	10	j_f(xₙ)⁻¹f(xₙ	j_f(xₙ)⁻¹f(xₙ	PROPN
cana-602	49	11	)	)	PUNCT
cana-602	49	12	,	,	PUNCT
cana-602	49	13	converges	converge	VERB
cana-602	49	14	quadratically	quadratically	ADV
cana-602	49	15	to	to	ADP
cana-602	49	16	x	x	X
cana-602	49	17	*	*	NOUN
cana-602	49	18	.	.	PUNCT
cana-602	50	1	corollary	corollary	ADJ
cana-602	50	2	3.1	3.1	NUM
cana-602	50	3	:	:	PUNCT
cana-602	50	4	modified	modified	PROPN
cana-602	50	5	newton	newton	PROPN
cana-602	50	6	’s	’s	PART
cana-602	50	7	method	method	NOUN
cana-602	50	8	for	for	ADP
cana-602	50	9	financial	financial	ADJ
cana-602	50	10	models	model	NOUN
cana-602	50	11	in	in	ADP
cana-602	50	12	financial	financial	ADJ
cana-602	50	13	models	model	NOUN
cana-602	50	14	where	where	SCONJ
cana-602	50	15	derivatives	derivative	NOUN
cana-602	50	16	might	might	AUX
cana-602	50	17	not	not	PART
cana-602	50	18	be	be	AUX
cana-602	50	19	readily	readily	ADV
cana-602	50	20	calculable	calculable	ADJ
cana-602	50	21	or	or	CCONJ
cana-602	50	22	are	be	AUX
cana-602	50	23	expensive	expensive	ADJ
cana-602	50	24	to	to	PART
cana-602	50	25	compute	compute	VERB
cana-602	50	26	,	,	PUNCT
cana-602	50	27	modified	modify	VERB
cana-602	50	28	newton	newton	PROPN
cana-602	50	29	methods	method	NOUN
cana-602	50	30	utilizing	utilize	VERB
cana-602	50	31	approximate	approximate	ADJ
cana-602	50	32	jacobians	jacobian	NOUN
cana-602	50	33	or	or	CCONJ
cana-602	50	34	difference	difference	NOUN
cana-602	50	35	approximations	approximation	NOUN
cana-602	50	36	can	can	AUX
cana-602	50	37	be	be	AUX
cana-602	50	38	employed	employ	VERB
cana-602	50	39	to	to	PART
cana-602	50	40	maintain	maintain	VERB
cana-602	50	41	the	the	DET
cana-602	50	42	convergence	convergence	NOUN
cana-602	50	43	properties	property	NOUN
cana-602	50	44	while	while	SCONJ
cana-602	50	45	reducing	reduce	VERB
cana-602	50	46	computational	computational	ADJ
cana-602	50	47	overhead	overhead	NOUN
cana-602	51	1	[	[	X
cana-602	51	2	11	11	NUM
cana-602	51	3	]	]	PUNCT
cana-602	51	4	.	.	PUNCT
cana-602	52	1	some	some	DET
cana-602	52	2	analyses	analysis	NOUN
cana-602	52	3	in	in	ADP
cana-602	52	4	financial	financial	ADJ
cana-602	52	5	applications	application	NOUN
cana-602	52	6	are	be	AUX
cana-602	52	7	like	like	ADP
cana-602	52	8	investigating	investigate	VERB
cana-602	52	9	the	the	DET
cana-602	52	10	efficiency	efficiency	NOUN
cana-602	52	11	of	of	ADP
cana-602	52	12	newton	newton	PROPN
cana-602	52	13	's	's	PART
cana-602	52	14	method	method	NOUN
cana-602	52	15	and	and	CCONJ
cana-602	52	16	its	its	PRON
cana-602	52	17	variants	variant	NOUN
cana-602	52	18	in	in	ADP
cana-602	52	19	dynamic	dynamic	ADJ
cana-602	52	20	portfolio	portfolio	NOUN
cana-602	52	21	optimization	optimization	NOUN
cana-602	52	22	where	where	SCONJ
cana-602	52	23	the	the	DET
cana-602	52	24	return	return	NOUN
cana-602	52	25	function	function	NOUN
cana-602	52	26	is	be	AUX
cana-602	52	27	highly	highly	ADV
cana-602	52	28	nonlinear	nonlinear	ADJ
cana-602	52	29	and	and	CCONJ
cana-602	52	30	subject	subject	ADJ
cana-602	52	31	to	to	ADP
cana-602	52	32	rapid	rapid	ADJ
cana-602	52	33	changes	change	NOUN
cana-602	52	34	in	in	ADP
cana-602	52	35	market	market	NOUN
cana-602	52	36	conditions	condition	NOUN
cana-602	52	37	.	.	PUNCT
cana-602	53	1	these	these	DET
cana-602	53	2	advanced	advanced	ADJ
cana-602	53	3	topological	topological	ADJ
cana-602	53	4	methods	method	NOUN
cana-602	53	5	provide	provide	VERB
cana-602	53	6	a	a	DET
cana-602	53	7	robust	robust	ADJ
cana-602	53	8	mathematical	mathematical	ADJ
cana-602	53	9	framework	framework	NOUN
cana-602	53	10	for	for	ADP
cana-602	53	11	addressing	address	VERB
cana-602	53	12	complex	complex	ADJ
cana-602	53	13	nonlinear	nonlinear	ADJ
cana-602	53	14	problems	problem	NOUN
cana-602	53	15	in	in	ADP
cana-602	53	16	financial	financial	ADJ
cana-602	53	17	mathematics	mathematic	NOUN
cana-602	53	18	.	.	PUNCT
cana-602	54	1	by	by	ADP
cana-602	54	2	integrating	integrate	VERB
cana-602	54	3	detailed	detailed	ADJ
cana-602	54	4	theorems	theorem	NOUN
cana-602	54	5	,	,	PUNCT
cana-602	54	6	practical	practical	ADJ
cana-602	54	7	applications	application	NOUN
cana-602	54	8	,	,	PUNCT
cana-602	54	9	and	and	CCONJ
cana-602	54	10	corollaries	corollary	NOUN
cana-602	54	11	,	,	PUNCT
cana-602	54	12	this	this	DET
cana-602	54	13	approach	approach	NOUN
cana-602	54	14	not	not	PART
cana-602	54	15	only	only	ADV
cana-602	54	16	enhances	enhance	VERB
cana-602	54	17	the	the	DET
cana-602	54	18	theoretical	theoretical	ADJ
cana-602	54	19	understanding	understanding	NOUN
cana-602	54	20	but	but	CCONJ
cana-602	54	21	also	also	ADV
cana-602	54	22	fosters	foster	VERB
cana-602	54	23	the	the	DET
cana-602	54	24	development	development	NOUN
cana-602	54	25	of	of	ADP
cana-602	54	26	computationally	computationally	ADV
cana-602	54	27	efficient	efficient	ADJ
cana-602	54	28	algorithms	algorithm	NOUN
cana-602	54	29	tailored	tailor	VERB
cana-602	54	30	to	to	ADP
cana-602	54	31	the	the	DET
cana-602	54	32	intricate	intricate	ADJ
cana-602	54	33	dynamics	dynamic	NOUN
cana-602	54	34	of	of	ADP
cana-602	54	35	financial	financial	ADJ
cana-602	54	36	markets	market	NOUN
cana-602	54	37	.	.	PUNCT
cana-602	55	1	3	3	X
cana-602	55	2	.	.	X
cana-602	55	3	conclusion	conclusion	NOUN
cana-602	55	4	the	the	DET
cana-602	55	5	exploration	exploration	NOUN
cana-602	55	6	of	of	ADP
cana-602	55	7	topological	topological	ADJ
cana-602	55	8	methods	method	NOUN
cana-602	55	9	in	in	ADP
cana-602	55	10	financial	financial	ADJ
cana-602	55	11	mathematics	mathematic	NOUN
cana-602	55	12	,	,	PUNCT
cana-602	55	13	as	as	SCONJ
cana-602	55	14	presented	present	VERB
cana-602	55	15	in	in	ADP
cana-602	55	16	this	this	DET
cana-602	55	17	paper	paper	NOUN
cana-602	55	18	,	,	PUNCT
cana-602	55	19	provides	provide	VERB
cana-602	55	20	compelling	compelling	ADJ
cana-602	55	21	evidence	evidence	NOUN
cana-602	55	22	of	of	ADP
cana-602	55	23	their	their	PRON
cana-602	55	24	capacity	capacity	NOUN
cana-602	55	25	to	to	PART
cana-602	55	26	solve	solve	VERB
cana-602	55	27	complex	complex	ADJ
cana-602	55	28	nonlinear	nonlinear	ADJ
cana-602	55	29	problems	problem	NOUN
cana-602	55	30	inherent	inherent	ADJ
cana-602	55	31	in	in	ADP
cana-602	55	32	financial	financial	ADJ
cana-602	55	33	models	model	NOUN
cana-602	55	34	.	.	PUNCT
cana-602	56	1	through	through	ADP
cana-602	56	2	detailed	detailed	ADJ
cana-602	56	3	theorems	theorem	NOUN
cana-602	56	4	,	,	PUNCT
cana-602	56	5	practical	practical	ADJ
cana-602	56	6	applications	application	NOUN
cana-602	56	7	,	,	PUNCT
cana-602	56	8	and	and	CCONJ
cana-602	56	9	robust	robust	ADJ
cana-602	56	10	mathematical	mathematical	ADJ
cana-602	56	11	formulations	formulation	NOUN
cana-602	56	12	,	,	PUNCT
cana-602	56	13	this	this	DET
cana-602	56	14	study	study	NOUN
cana-602	56	15	not	not	PART
cana-602	56	16	only	only	ADV
cana-602	56	17	enhances	enhance	VERB
cana-602	56	18	the	the	DET
cana-602	56	19	theoretical	theoretical	ADJ
cana-602	56	20	understanding	understanding	NOUN
cana-602	56	21	of	of	ADP
cana-602	56	22	these	these	DET
cana-602	56	23	methods	method	NOUN
cana-602	56	24	but	but	CCONJ
cana-602	56	25	also	also	ADV
cana-602	56	26	showcases	showcase	VERB
cana-602	56	27	their	their	PRON
cana-602	56	28	applicability	applicability	NOUN
cana-602	56	29	in	in	ADP
cana-602	56	30	dynamic	dynamic	ADJ
cana-602	56	31	financial	financial	ADJ
cana-602	56	32	markets	market	NOUN
cana-602	56	33	.	.	PUNCT
cana-602	57	1	the	the	DET
cana-602	57	2	integration	integration	NOUN
cana-602	57	3	of	of	ADP
cana-602	57	4	topological	topological	ADJ
cana-602	57	5	methods	method	NOUN
cana-602	57	6	offers	offer	VERB
cana-602	57	7	significant	significant	ADJ
cana-602	57	8	potential	potential	NOUN
cana-602	57	9	to	to	PART
cana-602	57	10	advance	advance	VERB
cana-602	57	11	financial	financial	ADJ
cana-602	57	12	modeling	modeling	NOUN
cana-602	57	13	and	and	CCONJ
cana-602	57	14	analysis	analysis	NOUN
cana-602	57	15	,	,	PUNCT
cana-602	57	16	suggesting	suggest	VERB
cana-602	57	17	a	a	DET
cana-602	57	18	promising	promising	ADJ
cana-602	57	19	direction	direction	NOUN
cana-602	57	20	for	for	ADP
cana-602	57	21	future	future	ADJ
cana-602	57	22	research	research	NOUN
cana-602	57	23	and	and	CCONJ
cana-602	57	24	application	application	NOUN
cana-602	57	25	in	in	ADP
cana-602	57	26	the	the	DET
cana-602	57	27	field	field	NOUN
cana-602	57	28	.	.	PUNCT
cana-602	58	1	this	this	DET
cana-602	58	2	research	research	NOUN
cana-602	58	3	underpins	underpin	VERB
cana-602	58	4	the	the	DET
cana-602	58	5	necessity	necessity	NOUN
cana-602	58	6	for	for	ADP
cana-602	58	7	continuous	continuous	ADJ
cana-602	58	8	advancement	advancement	NOUN
cana-602	58	9	in	in	ADP
cana-602	58	10	mathematical	mathematical	ADJ
cana-602	58	11	tools	tool	NOUN
cana-602	58	12	to	to	PART
cana-602	58	13	keep	keep	VERB
cana-602	58	14	pace	pace	NOUN
cana-602	58	15	with	with	ADP
cana-602	58	16	the	the	DET
cana-602	58	17	evolving	evolve	VERB
cana-602	58	18	complexities	complexity	NOUN
cana-602	58	19	of	of	ADP
cana-602	58	20	financial	financial	ADJ
cana-602	58	21	systems	system	NOUN
cana-602	58	22	.	.	PUNCT
cana-602	59	1	references	reference	NOUN
cana-602	59	2	[	[	X
cana-602	59	3	1	1	X
cana-602	59	4	]	]	PUNCT
cana-602	59	5	s.	s.	PROPN
cana-602	59	6	liao	liao	PROPN
cana-602	59	7	and	and	CCONJ
cana-602	59	8	y.	y.	PROPN
cana-602	59	9	tan	tan	PROPN
cana-602	59	10	,	,	PUNCT
cana-602	59	11	"	"	PUNCT
cana-602	59	12	a	a	DET
cana-602	59	13	general	general	ADJ
cana-602	59	14	approach	approach	NOUN
cana-602	59	15	to	to	PART
cana-602	59	16	obtain	obtain	VERB
cana-602	59	17	series	series	NOUN
cana-602	59	18	solutions	solution	NOUN
cana-602	59	19	of	of	ADP
cana-602	59	20	nonlinear	nonlinear	ADJ
cana-602	59	21	differential	differential	ADJ
cana-602	59	22	equations	equation	NOUN
cana-602	59	23	,	,	PUNCT
cana-602	59	24	"	"	PUNCT
cana-602	59	25	studies	study	NOUN
cana-602	59	26	in	in	ADP
cana-602	59	27	applied	applied	ADJ
cana-602	59	28	mathematics	mathematic	NOUN
cana-602	59	29	,	,	PUNCT
cana-602	59	30	vol	vol	NOUN
cana-602	59	31	.	.	PROPN
cana-602	59	32	119	119	NUM
cana-602	59	33	,	,	PUNCT
cana-602	59	34	pp	pp	ADJ
cana-602	59	35	.	.	PUNCT
cana-602	60	1	297–354	297–354	NUM
cana-602	60	2	,	,	PUNCT
cana-602	60	3	2007	2007	NUM
cana-602	60	4	.	.	PUNCT
cana-602	61	1	doi	doi	NOUN
cana-602	61	2	:	:	PUNCT
cana-602	61	3	10.1111	10.1111	NUM
cana-602	61	4	/	/	SYM
cana-602	61	5	j.1467	j.1467	PROPN
cana-602	61	6	-	-	PUNCT
cana-602	61	7	9590.2007.00387.x	9590.2007.00387.x	NOUN
cana-602	61	8	.	.	PUNCT
cana-602	62	1	[	[	X
cana-602	62	2	2	2	NUM
cana-602	62	3	]	]	PUNCT
cana-602	62	4	m.	m.	NOUN
cana-602	62	5	vrahatis	vrahatis	PROPN
cana-602	62	6	,	,	PUNCT
cana-602	62	7	"	"	PUNCT
cana-602	62	8	a	a	DET
cana-602	62	9	rapid	rapid	ADJ
cana-602	62	10	generalized	generalized	ADJ
cana-602	62	11	method	method	NOUN
cana-602	62	12	of	of	ADP
cana-602	62	13	bisection	bisection	NOUN
cana-602	62	14	for	for	ADP
cana-602	62	15	solving	solve	VERB
cana-602	62	16	systems	system	NOUN
cana-602	62	17	of	of	ADP
cana-602	62	18	non	non	ADJ
cana-602	62	19	-	-	ADJ
cana-602	62	20	linear	linear	ADJ
cana-602	62	21	equations	equation	NOUN
cana-602	62	22	,	,	PUNCT
cana-602	62	23	"	"	PUNCT
cana-602	62	24	numerische	numerische	PROPN
cana-602	62	25	mathematik	mathematik	PROPN
cana-602	62	26	,	,	PUNCT
cana-602	62	27	vol	vol	NOUN
cana-602	62	28	.	.	PROPN
cana-602	62	29	49	49	NUM
cana-602	62	30	,	,	PUNCT
cana-602	62	31	pp	pp	ADJ
cana-602	62	32	.	.	PUNCT
cana-602	63	1	123–138	123–138	NUM
cana-602	63	2	,	,	PUNCT
cana-602	63	3	1986	1986	NUM
cana-602	63	4	.	.	PUNCT
cana-602	64	1	doi	doi	NOUN
cana-602	64	2	:	:	PUNCT
cana-602	64	3	10.1007	10.1007	NUM
cana-602	64	4	/	/	SYM
cana-602	64	5	bf01389620	bf01389620	NOUN
cana-602	64	6	.	.	PUNCT
cana-602	65	1	[	[	X
cana-602	65	2	3	3	X
cana-602	65	3	]	]	X
cana-602	65	4	d.	d.	PROPN
cana-602	65	5	herceg	herceg	PROPN
cana-602	65	6	,	,	PUNCT
cana-602	65	7	"	"	PUNCT
cana-602	65	8	a	a	DET
cana-602	65	9	family	family	NOUN
cana-602	65	10	of	of	ADP
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cana-602	65	12	for	for	ADP
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cana-602	65	14	nonlinear	nonlinear	ADJ
cana-602	65	15	equations	equation	NOUN
cana-602	65	16	,	,	PUNCT
cana-602	65	17	"	"	PUNCT
cana-602	65	18	appl	appl	PROPN
cana-602	65	19	.	.	PROPN
cana-602	65	20	math	math	NOUN
cana-602	65	21	.	.	PUNCT
cana-602	66	1	comput	comput	NOUN
cana-602	66	2	.	.	PUNCT
cana-602	66	3	,	,	PUNCT
cana-602	66	4	vol	vol	NOUN
cana-602	66	5	.	.	PUNCT
cana-602	67	1	259	259	NUM
cana-602	67	2	,	,	PUNCT
cana-602	67	3	pp	pp	ADJ
cana-602	67	4	.	.	NOUN
cana-602	68	1	882	882	NUM
cana-602	68	2	–	–	PUNCT
cana-602	68	3	895	895	NUM
cana-602	68	4	,	,	PUNCT
cana-602	68	5	2015	2015	NUM
cana-602	68	6	.	.	PUNCT
cana-602	69	1	doi	doi	NOUN
cana-602	69	2	:	:	PUNCT
cana-602	69	3	10.1016	10.1016	NUM
cana-602	69	4	/	/	SYM
cana-602	69	5	j.amc.2015.03.028	j.amc.2015.03.028	NOUN
cana-602	69	6	.	.	PUNCT
cana-602	70	1	[	[	X
cana-602	70	2	4	4	X
cana-602	70	3	]	]	X
cana-602	70	4	j.	j.	PROPN
cana-602	70	5	cronin	cronin	PROPN
cana-602	70	6	,	,	PUNCT
cana-602	70	7	"	"	PUNCT
cana-602	70	8	fixed	fix	VERB
cana-602	70	9	points	point	NOUN
cana-602	70	10	and	and	CCONJ
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cana-602	70	12	degree	degree	NOUN
cana-602	70	13	in	in	ADP
cana-602	70	14	nonlinear	nonlinear	ADJ
cana-602	70	15	analysis	analysis	NOUN
cana-602	70	16	,	,	PUNCT
cana-602	70	17	"	"	PUNCT
cana-602	70	18	mathematical	mathematical	ADJ
cana-602	70	19	surveys	survey	NOUN
cana-602	70	20	and	and	CCONJ
cana-602	70	21	monographs	monograph	NOUN
cana-602	70	22	,	,	PUNCT
cana-602	70	23	no	no	INTJ
cana-602	70	24	.	.	NOUN
cana-602	70	25	11	11	NUM
cana-602	70	26	,	,	PUNCT
cana-602	70	27	american	american	PROPN
cana-602	70	28	mathematical	mathematical	ADJ
cana-602	70	29	society	society	NOUN
cana-602	70	30	,	,	PUNCT
cana-602	70	31	1995	1995	NUM
cana-602	70	32	.	.	PUNCT
cana-602	71	1	doi	doi	NOUN
cana-602	71	2	:	:	PUNCT
cana-602	71	3	10.1090	10.1090	NUM
cana-602	71	4	/	/	SYM
cana-602	71	5	surv/011	surv/011	NOUN
cana-602	71	6	.	.	PUNCT
cana-602	72	1	[	[	X
cana-602	72	2	5	5	NUM
cana-602	72	3	]	]	PUNCT
cana-602	72	4	p.	p.	PROPN
cana-602	72	5	watson	watson	PROPN
cana-602	72	6	,	,	PUNCT
cana-602	72	7	"	"	PUNCT
cana-602	72	8	topological	topological	ADJ
cana-602	72	9	methods	method	NOUN
cana-602	72	10	in	in	ADP
cana-602	72	11	nonlinear	nonlinear	ADJ
cana-602	72	12	analysis	analysis	NOUN
cana-602	72	13	,	,	PUNCT
cana-602	72	14	"	"	PUNCT
cana-602	72	15	bulletin	bulletin	NOUN
cana-602	72	16	of	of	ADP
cana-602	72	17	the	the	DET
cana-602	72	18	australian	australian	ADJ
cana-602	72	19	mathematical	mathematical	ADJ
cana-602	72	20	society	society	NOUN
cana-602	72	21	,	,	PUNCT
cana-602	72	22	vol	vol	NOUN
cana-602	72	23	.	.	PROPN
cana-602	72	24	58	58	NUM
cana-602	72	25	,	,	PUNCT
cana-602	72	26	pp	pp	ADJ
cana-602	72	27	.	.	PUNCT
cana-602	73	1	527	527	NUM
cana-602	73	2	-	-	SYM
cana-602	73	3	528	528	NUM
cana-602	73	4	,	,	PUNCT
cana-602	73	5	1998	1998	NUM
cana-602	73	6	.	.	PUNCT
cana-602	74	1	doi	doi	NOUN
cana-602	74	2	:	:	PUNCT
cana-602	74	3	10.1017	10.1017	NUM
cana-602	74	4	/	/	SYM
cana-602	74	5	s0004972700032524	s0004972700032524	NOUN
cana-602	74	6	.	.	PUNCT
cana-602	75	1	[	[	X
cana-602	75	2	6	6	NUM
cana-602	75	3	]	]	PUNCT
cana-602	75	4	b.	b.	PROPN
cana-602	75	5	kubica	kubica	PROPN
cana-602	75	6	and	and	CCONJ
cana-602	75	7	j.	j.	PROPN
cana-602	75	8	kurek	kurek	PROPN
cana-602	75	9	,	,	PUNCT
cana-602	75	10	"	"	PUNCT
cana-602	75	11	a	a	DET
cana-602	75	12	parallel	parallel	ADJ
cana-602	75	13	method	method	NOUN
cana-602	75	14	of	of	ADP
cana-602	75	15	verifying	verify	VERB
cana-602	75	16	solutions	solution	NOUN
cana-602	75	17	for	for	ADP
cana-602	75	18	systems	system	NOUN
cana-602	75	19	of	of	ADP
cana-602	75	20	two	two	NUM
cana-602	75	21	nonlinear	nonlinear	ADJ
cana-602	75	22	equations	equation	NOUN
cana-602	75	23	,	,	PUNCT
cana-602	75	24	"	"	PUNCT
cana-602	75	25	in	in	ADP
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cana-602	75	27	.	.	PUNCT
cana-602	75	28	of	of	ADP
cana-602	75	29	the	the	DET
cana-602	75	30	ieee	ieee	NOUN
cana-602	75	31	international	international	PROPN
cana-602	75	32	conference	conference	NOUN
cana-602	75	33	on	on	ADP
cana-602	75	34	computational	computational	ADJ
cana-602	75	35	science	science	NOUN
cana-602	75	36	and	and	CCONJ
cana-602	75	37	engineering	engineering	NOUN
cana-602	75	38	,	,	PUNCT
cana-602	75	39	vol	vol	NOUN
cana-602	75	40	.	.	PROPN
cana-602	75	41	4	4	NUM
cana-602	75	42	,	,	PUNCT
cana-602	75	43	pp	pp	ADJ
cana-602	75	44	.	.	PUNCT
cana-602	76	1	418	418	NUM
cana-602	76	2	-	-	SYM
cana-602	76	3	430	430	NUM
cana-602	76	4	,	,	PUNCT
cana-602	76	5	2019	2019	NUM
cana-602	76	6	.	.	PUNCT
cana-602	77	1	doi	doi	NOUN
cana-602	77	2	:	:	PUNCT
cana-602	77	3	10.1007/978	10.1007/978	NUM
cana-602	77	4	-	-	SYM
cana-602	77	5	3	3	NUM
cana-602	77	6	-	-	PUNCT
cana-602	77	7	030	030	NUM
cana-602	77	8	-	-	PUNCT
cana-602	77	9	43222	43222	NUM
cana-602	77	10	-	-	PUNCT
cana-602	77	11	5_37	5_37	NOUN
cana-602	77	12	.	.	PUNCT
cana-602	78	1	[	[	X
cana-602	78	2	7	7	X
cana-602	78	3	]	]	X
cana-602	78	4	c.	c.	PROPN
cana-602	78	5	l.	l.	PROPN
cana-602	78	6	karr	karr	PROPN
cana-602	78	7	,	,	PUNCT
cana-602	78	8	b.	b.	PROPN
cana-602	78	9	weck	weck	PROPN
cana-602	78	10	,	,	PUNCT
cana-602	78	11	and	and	CCONJ
cana-602	78	12	l.	l.	PROPN
cana-602	78	13	freeman	freeman	PROPN
cana-602	78	14	,	,	PUNCT
cana-602	78	15	"	"	PUNCT
cana-602	78	16	solutions	solution	NOUN
cana-602	78	17	to	to	ADP
cana-602	78	18	systems	system	NOUN
cana-602	78	19	of	of	ADP
cana-602	78	20	nonlinear	nonlinear	ADJ
cana-602	78	21	equations	equation	NOUN
cana-602	78	22	via	via	ADP
cana-602	78	23	a	a	DET
cana-602	78	24	genetic	genetic	ADJ
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cana-602	78	26	,	,	PUNCT
cana-602	78	27	"	"	PUNCT
cana-602	78	28	engineering	engineering	NOUN
cana-602	78	29	applications	application	NOUN
cana-602	78	30	of	of	ADP
cana-602	78	31	artificial	artificial	ADJ
cana-602	78	32	intelligence	intelligence	NOUN
cana-602	78	33	,	,	PUNCT
cana-602	78	34	vol	vol	NOUN
cana-602	78	35	.	.	PROPN
cana-602	78	36	11	11	NUM
cana-602	78	37	,	,	PUNCT
cana-602	78	38	no	no	INTJ
cana-602	78	39	.	.	NOUN
cana-602	78	40	3	3	NUM
cana-602	78	41	,	,	PUNCT
cana-602	78	42	pp	pp	ADJ
cana-602	78	43	.	.	PUNCT
cana-602	78	44	369	369	NUM
cana-602	78	45	-	-	SYM
cana-602	78	46	375	375	NUM
cana-602	78	47	,	,	PUNCT
cana-602	78	48	1998	1998	NUM
cana-602	78	49	.	.	PUNCT
cana-602	79	1	doi	doi	NOUN
cana-602	79	2	:	:	PUNCT
cana-602	79	3	10.1016	10.1016	NUM
cana-602	79	4	/	/	SYM
cana-602	79	5	s09521976(97)00067	s09521976(97)00067	PROPN
cana-602	79	6	-	-	PUNCT
cana-602	79	7	5	5	NUM
cana-602	79	8	.	.	PUNCT
cana-602	80	1	[	[	X
cana-602	80	2	8	8	NUM
cana-602	80	3	]	]	X
cana-602	80	4	l.	l.	PROPN
cana-602	80	5	górniewicz	górniewicz	PROPN
cana-602	80	6	,	,	PUNCT
cana-602	80	7	"	"	PUNCT
cana-602	80	8	solving	solve	VERB
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cana-602	80	10	by	by	ADP
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cana-602	80	12	methods	method	NOUN
cana-602	80	13	,	,	PUNCT
cana-602	80	14	"	"	PUNCT
cana-602	80	15	opuscula	opuscula	PROPN
cana-602	80	16	mathematica	mathematica	PROPN
cana-602	80	17	,	,	PUNCT
cana-602	80	18	vol	vol	NOUN
cana-602	80	19	.	.	PROPN
cana-602	80	20	25	25	NUM
cana-602	80	21	,	,	PUNCT
cana-602	80	22	pp	pp	ADJ
cana-602	80	23	.	.	PUNCT
cana-602	81	1	195	195	NUM
cana-602	81	2	-	-	SYM
cana-602	81	3	225	225	NUM
cana-602	81	4	,	,	PUNCT
cana-602	81	5	2005	2005	NUM
cana-602	81	6	.	.	PUNCT
cana-602	82	1	[	[	X
cana-602	82	2	9	9	NUM
cana-602	82	3	]	]	PUNCT
cana-602	82	4	m.	m.	NOUN
cana-602	82	5	shacham	shacham	PROPN
cana-602	82	6	,	,	PUNCT
cana-602	82	7	"	"	PUNCT
cana-602	82	8	an	an	DET
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cana-602	82	11	method	method	NOUN
cana-602	82	12	for	for	ADP
cana-602	82	13	the	the	DET
cana-602	82	14	solution	solution	NOUN
cana-602	82	15	of	of	ADP
cana-602	82	16	a	a	DET
cana-602	82	17	nonlinear	nonlinear	ADJ
cana-602	82	18	equation	equation	NOUN
cana-602	82	19	,	,	PUNCT
cana-602	82	20	"	"	PUNCT
cana-602	82	21	chemical	chemical	NOUN
cana-602	82	22	engineering	engineering	NOUN
cana-602	82	23	science	science	NOUN
cana-602	82	24	,	,	PUNCT
cana-602	82	25	vol	vol	NOUN
cana-602	82	26	.	.	PROPN
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cana-602	82	28	,	,	PUNCT
cana-602	82	29	pp	pp	ADJ
cana-602	82	30	.	.	PUNCT
cana-602	83	1	1495	1495	NUM
cana-602	83	2	-	-	SYM
cana-602	83	3	1501	1501	NUM
cana-602	83	4	,	,	PUNCT
cana-602	83	5	1989	1989	NUM
cana-602	83	6	.	.	PUNCT
cana-602	84	1	doi	doi	NOUN
cana-602	84	2	:	:	PUNCT
cana-602	84	3	10.1016/0009	10.1016/0009	NUM
cana-602	84	4	-	-	SYM
cana-602	84	5	2509(89)80026	2509(89)80026	NUM
cana-602	84	6	-	-	SYM
cana-602	84	7	0	0	NUM
cana-602	84	8	.	.	PUNCT
cana-602	85	1	[	[	X
cana-602	85	2	10	10	NUM
cana-602	85	3	]	]	X
cana-602	85	4	a.	a.	NOUN
cana-602	85	5	j.	j.	PROPN
cana-602	85	6	m.	m.	PROPN
cana-602	85	7	jawad	jawad	PROPN
cana-602	85	8	,	,	PUNCT
cana-602	85	9	m.	m.	NOUN
cana-602	85	10	petkovic	petkovic	PROPN
cana-602	85	11	,	,	PUNCT
cana-602	85	12	and	and	CCONJ
cana-602	85	13	a.	a.	PROPN
cana-602	85	14	biswas	biswas	PROPN
cana-602	85	15	,	,	PUNCT
cana-602	85	16	"	"	PUNCT
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cana-602	85	18	solutions	solution	NOUN
cana-602	85	19	of	of	ADP
cana-602	85	20	a	a	DET
cana-602	85	21	few	few	ADJ
cana-602	85	22	nonlinear	nonlinear	ADJ
cana-602	85	23	wave	wave	NOUN
cana-602	85	24	equations	equation	NOUN
cana-602	85	25	,	,	PUNCT
cana-602	85	26	"	"	PUNCT
cana-602	85	27	appl	appl	PROPN
cana-602	85	28	.	.	PROPN
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cana-602	85	30	.	.	PUNCT
cana-602	86	1	comput	comput	NOUN
cana-602	86	2	.	.	PUNCT
cana-602	86	3	,	,	PUNCT
cana-602	86	4	vol	vol	NOUN
cana-602	86	5	.	.	PROPN
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cana-602	87	2	,	,	PUNCT
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cana-602	87	4	.	.	PUNCT
cana-602	88	1	2649	2649	NUM
cana-602	88	2	-	-	SYM
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cana-602	88	4	,	,	PUNCT
cana-602	88	5	2010	2010	NUM
cana-602	88	6	.	.	PUNCT
cana-602	89	1	doi	doi	NOUN
cana-602	89	2	:	:	PUNCT
cana-602	89	3	10.1016	10.1016	NUM
cana-602	89	4	/	/	SYM
cana-602	89	5	j.amc.2010.03.110	j.amc.2010.03.110	PROPN
cana-602	89	6	.	.	PUNCT
cana-602	90	1	communications	communication	NOUN
cana-602	90	2	on	on	ADP
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cana-602	90	4	nonlinear	nonlinear	ADJ
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cana-602	90	7	:	:	PUNCT
cana-602	90	8	1074	1074	NUM
cana-602	90	9	-	-	PUNCT
cana-602	90	10	133x	133x	NUM
cana-602	90	11	vol	vol	NOUN
cana-602	90	12	31	31	NUM
cana-602	90	13	no	no	NOUN
cana-602	90	14	.	.	PUNCT
cana-602	91	1	2s	2s	NUM
cana-602	91	2	(	(	PUNCT
cana-602	91	3	2024	2024	NUM
cana-602	91	4	)	)	PUNCT
cana-602	91	5	117	117	NUM
cana-602	91	6	https://internationalpubls.com	https://internationalpubls.com	X
cana-602	92	1	[	[	X
cana-602	92	2	11	11	NUM
cana-602	92	3	]	]	PUNCT
cana-602	92	4	j.	j.	PROPN
cana-602	92	5	martínez	martínez	PROPN
cana-602	92	6	,	,	PUNCT
cana-602	92	7	"	"	PUNCT
cana-602	92	8	algorithms	algorithm	NOUN
cana-602	92	9	for	for	ADP
cana-602	92	10	solving	solve	VERB
cana-602	92	11	nonlinear	nonlinear	ADJ
cana-602	92	12	systems	system	NOUN
cana-602	92	13	of	of	ADP
cana-602	92	14	equations	equation	NOUN
cana-602	92	15	,	,	PUNCT
cana-602	92	16	"	"	PUNCT
cana-602	92	17	in	in	ADP
cana-602	92	18	proc	proc	NOUN
cana-602	92	19	.	.	PUNCT
cana-602	93	1	of	of	ADP
cana-602	93	2	the	the	DET
cana-602	93	3	2nd	2nd	ADJ
cana-602	93	4	workshop	workshop	NOUN
cana-602	93	5	on	on	ADP
cana-602	93	6	algorithm	algorithm	NOUN
cana-602	93	7	engineering	engineering	NOUN
cana-602	93	8	and	and	CCONJ
cana-602	93	9	experiments	experiment	NOUN
cana-602	93	10	,	,	PUNCT
cana-602	93	11	pp	pp	PROPN
cana-602	93	12	.	.	PUNCT
cana-602	93	13	81	81	NUM
cana-602	93	14	-	-	SYM
cana-602	93	15	108	108	NUM
cana-602	93	16	,	,	PUNCT
cana-602	93	17	1994	1994	NUM
cana-602	93	18	.	.	PUNCT
cana-602	94	1	doi	doi	NOUN
cana-602	94	2	:	:	PUNCT
cana-602	94	3	10.1007/978	10.1007/978	NUM
cana-602	94	4	-	-	SYM
cana-602	94	5	94	94	NUM
cana-602	94	6	-	-	PUNCT
cana-602	94	7	009	009	NUM
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cana-602	97	4	,	,	PUNCT
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cana-602	101	6	.	.	PUNCT
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cana-602	102	2	:	:	PUNCT
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cana-602	102	4	/	/	SYM
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cana-602	102	6	.	.	PUNCT