id	sid	tid	token	lemma	pos
american_scientific_journal-7274	1	1	118	118	NUM
american_scientific_journal-7274	1	2	american	american	ADJ
american_scientific_journal-7274	1	3	academic	academic	ADJ
american_scientific_journal-7274	1	4	scientific	scientific	ADJ
american_scientific_journal-7274	1	5	research	research	NOUN
american_scientific_journal-7274	1	6	journal	journal	NOUN
american_scientific_journal-7274	1	7	for	for	ADP
american_scientific_journal-7274	1	8	engineering	engineering	NOUN
american_scientific_journal-7274	1	9	,	,	PUNCT
american_scientific_journal-7274	1	10	technology	technology	NOUN
american_scientific_journal-7274	1	11	,	,	PUNCT
american_scientific_journal-7274	1	12	and	and	CCONJ
american_scientific_journal-7274	1	13	sciences	sciences	PROPN
american_scientific_journal-7274	1	14	issn	issn	PROPN
american_scientific_journal-7274	1	15	(	(	PUNCT
american_scientific_journal-7274	1	16	print	print	NOUN
american_scientific_journal-7274	1	17	)	)	PUNCT
american_scientific_journal-7274	1	18	2313	2313	NUM
american_scientific_journal-7274	1	19	-	-	SYM
american_scientific_journal-7274	1	20	4410	4410	NUM
american_scientific_journal-7274	1	21	,	,	PUNCT
american_scientific_journal-7274	1	22	issn	issn	PROPN
american_scientific_journal-7274	1	23	(	(	PUNCT
american_scientific_journal-7274	1	24	online	online	ADJ
american_scientific_journal-7274	1	25	)	)	PUNCT
american_scientific_journal-7274	1	26	2313	2313	NUM
american_scientific_journal-7274	1	27	-	-	SYM
american_scientific_journal-7274	1	28	4402	4402	NUM
american_scientific_journal-7274	1	29	http://asrjetsjournal.org/	http://asrjetsjournal.org/	NOUN
american_scientific_journal-7274	1	30	a	a	DET
american_scientific_journal-7274	1	31	pde	pde	NOUN
american_scientific_journal-7274	1	32	-	-	PUNCT
american_scientific_journal-7274	1	33	based	base	VERB
american_scientific_journal-7274	1	34	mathematical	mathematical	ADJ
american_scientific_journal-7274	1	35	method	method	NOUN
american_scientific_journal-7274	1	36	in	in	ADP
american_scientific_journal-7274	1	37	image	image	NOUN
american_scientific_journal-7274	1	38	processing	processing	NOUN
american_scientific_journal-7274	1	39	:	:	PUNCT
american_scientific_journal-7274	1	40	digital	digital	ADJ
american_scientific_journal-7274	1	41	-	-	PUNCT
american_scientific_journal-7274	1	42	discrete	discrete	ADJ
american_scientific_journal-7274	1	43	method	method	NOUN
american_scientific_journal-7274	1	44	for	for	ADP
american_scientific_journal-7274	1	45	perona	perona	NOUN
american_scientific_journal-7274	1	46	-	-	PUNCT
american_scientific_journal-7274	1	47	malik	malik	PROPN
american_scientific_journal-7274	1	48	equation	equation	NOUN
american_scientific_journal-7274	1	49	ahmet	ahmet	PROPN
american_scientific_journal-7274	1	50	yıldırıma	yıldırıma	PROPN
american_scientific_journal-7274	1	51	*	*	PROPN
american_scientific_journal-7274	1	52	,	,	PUNCT
american_scientific_journal-7274	1	53	i̇smet	i̇smet	PROPN
american_scientific_journal-7274	1	54	karacab	karacab	PROPN
american_scientific_journal-7274	1	55	a	a	PRON
american_scientific_journal-7274	1	56	,	,	PUNCT
american_scientific_journal-7274	1	57	bege	bege	PROPN
american_scientific_journal-7274	1	58	university	university	PROPN
american_scientific_journal-7274	1	59	,	,	PUNCT
american_scientific_journal-7274	1	60	faculty	faculty	NOUN
american_scientific_journal-7274	1	61	of	of	ADP
american_scientific_journal-7274	1	62	science	science	NOUN
american_scientific_journal-7274	1	63	,	,	PUNCT
american_scientific_journal-7274	1	64	department	department	NOUN
american_scientific_journal-7274	1	65	of	of	ADP
american_scientific_journal-7274	1	66	mathematics	mathematic	NOUN
american_scientific_journal-7274	1	67	,	,	PUNCT
american_scientific_journal-7274	1	68	35100	35100	NUM
american_scientific_journal-7274	1	69	,	,	PUNCT
american_scientific_journal-7274	1	70	bornova	bornova	PROPN
american_scientific_journal-7274	1	71	,	,	PUNCT
american_scientific_journal-7274	1	72	i̇zmir	i̇zmir	NOUN
american_scientific_journal-7274	1	73	,	,	PUNCT
american_scientific_journal-7274	1	74	turkey	turkey	NOUN
american_scientific_journal-7274	1	75	aemail	aemail	NOUN
american_scientific_journal-7274	1	76	:	:	PUNCT
american_scientific_journal-7274	1	77	yahmet49ege@gmail.com	yahmet49ege@gmail.com	X
american_scientific_journal-7274	1	78	bemail	bemail	PROPN
american_scientific_journal-7274	1	79	:	:	PUNCT
american_scientific_journal-7274	1	80	ismet.karaca@ege.edu.tr	ismet.karaca@ege.edu.tr	NOUN
american_scientific_journal-7274	1	81	abstract	abstract	ADJ
american_scientific_journal-7274	1	82	in	in	ADP
american_scientific_journal-7274	1	83	this	this	DET
american_scientific_journal-7274	1	84	study	study	NOUN
american_scientific_journal-7274	1	85	,	,	PUNCT
american_scientific_journal-7274	1	86	we	we	PRON
american_scientific_journal-7274	1	87	propose	propose	VERB
american_scientific_journal-7274	1	88	a	a	DET
american_scientific_journal-7274	1	89	new	new	ADJ
american_scientific_journal-7274	1	90	and	and	CCONJ
american_scientific_journal-7274	1	91	effective	effective	ADJ
american_scientific_journal-7274	1	92	algorithm	algorithm	NOUN
american_scientific_journal-7274	1	93	for	for	ADP
american_scientific_journal-7274	1	94	image	image	NOUN
american_scientific_journal-7274	1	95	processing	processing	NOUN
american_scientific_journal-7274	1	96	.	.	PUNCT
american_scientific_journal-7274	2	1	the	the	DET
american_scientific_journal-7274	2	2	method	method	NOUN
american_scientific_journal-7274	2	3	based	base	VERB
american_scientific_journal-7274	2	4	on	on	ADP
american_scientific_journal-7274	2	5	the	the	DET
american_scientific_journal-7274	2	6	combination	combination	NOUN
american_scientific_journal-7274	2	7	of	of	ADP
american_scientific_journal-7274	2	8	digital	digital	ADJ
american_scientific_journal-7274	2	9	topology	topology	NOUN
american_scientific_journal-7274	2	10	,	,	PUNCT
american_scientific_journal-7274	2	11	partial	partial	ADJ
american_scientific_journal-7274	2	12	differential	differential	ADJ
american_scientific_journal-7274	2	13	equations	equation	NOUN
american_scientific_journal-7274	2	14	and	and	CCONJ
american_scientific_journal-7274	2	15	finite	finite	ADJ
american_scientific_journal-7274	2	16	difference	difference	NOUN
american_scientific_journal-7274	2	17	scheme	scheme	NOUN
american_scientific_journal-7274	2	18	is	be	AUX
american_scientific_journal-7274	2	19	called	call	VERB
american_scientific_journal-7274	2	20	the	the	DET
american_scientific_journal-7274	2	21	digitaldiscrete	digitaldiscrete	ADJ
american_scientific_journal-7274	2	22	method	method	NOUN
american_scientific_journal-7274	2	23	.	.	PUNCT
american_scientific_journal-7274	3	1	we	we	PRON
american_scientific_journal-7274	3	2	try	try	VERB
american_scientific_journal-7274	3	3	to	to	PART
american_scientific_journal-7274	3	4	solve	solve	VERB
american_scientific_journal-7274	3	5	the	the	DET
american_scientific_journal-7274	3	6	perona	perona	NOUN
american_scientific_journal-7274	3	7	-	-	PUNCT
american_scientific_journal-7274	3	8	malik	malik	PROPN
american_scientific_journal-7274	3	9	equation	equation	NOUN
american_scientific_journal-7274	3	10	using	use	VERB
american_scientific_journal-7274	3	11	the	the	DET
american_scientific_journal-7274	3	12	digital	digital	ADJ
american_scientific_journal-7274	3	13	-	-	PUNCT
american_scientific_journal-7274	3	14	discrete	discrete	NOUN
american_scientific_journal-7274	3	15	method	method	NOUN
american_scientific_journal-7274	3	16	.	.	PUNCT
american_scientific_journal-7274	4	1	we	we	PRON
american_scientific_journal-7274	4	2	use	use	VERB
american_scientific_journal-7274	4	3	the	the	DET
american_scientific_journal-7274	4	4	matlab	matlab	PROPN
american_scientific_journal-7274	4	5	package	package	NOUN
american_scientific_journal-7274	4	6	program	program	NOUN
american_scientific_journal-7274	4	7	when	when	SCONJ
american_scientific_journal-7274	4	8	analyzing	analyzing	NOUN
american_scientific_journal-7274	4	9	images	image	NOUN
american_scientific_journal-7274	4	10	.	.	PUNCT
american_scientific_journal-7274	5	1	the	the	DET
american_scientific_journal-7274	5	2	analyzes	analyze	NOUN
american_scientific_journal-7274	5	3	we	we	PRON
american_scientific_journal-7274	5	4	make	make	VERB
american_scientific_journal-7274	5	5	on	on	ADP
american_scientific_journal-7274	5	6	the	the	DET
american_scientific_journal-7274	5	7	images	image	NOUN
american_scientific_journal-7274	5	8	show	show	VERB
american_scientific_journal-7274	5	9	how	how	SCONJ
american_scientific_journal-7274	5	10	the	the	DET
american_scientific_journal-7274	5	11	algorithm	algorithm	NOUN
american_scientific_journal-7274	5	12	is	be	AUX
american_scientific_journal-7274	5	13	useful	useful	ADJ
american_scientific_journal-7274	5	14	,	,	PUNCT
american_scientific_journal-7274	5	15	effective	effective	ADJ
american_scientific_journal-7274	5	16	and	and	CCONJ
american_scientific_journal-7274	5	17	open	open	ADJ
american_scientific_journal-7274	5	18	to	to	ADP
american_scientific_journal-7274	5	19	development	development	NOUN
american_scientific_journal-7274	5	20	.	.	PUNCT
american_scientific_journal-7274	6	1	keywords	keyword	NOUN
american_scientific_journal-7274	6	2	:	:	PUNCT
american_scientific_journal-7274	6	3	perona	perona	NOUN
american_scientific_journal-7274	6	4	-	-	PUNCT
american_scientific_journal-7274	6	5	malik	malik	PROPN
american_scientific_journal-7274	6	6	equation	equation	NOUN
american_scientific_journal-7274	6	7	;	;	PUNCT
american_scientific_journal-7274	6	8	digital	digital	ADJ
american_scientific_journal-7274	6	9	-	-	PUNCT
american_scientific_journal-7274	6	10	discrete	discrete	NOUN
american_scientific_journal-7274	6	11	method	method	NOUN
american_scientific_journal-7274	6	12	;	;	PUNCT
american_scientific_journal-7274	6	13	digital	digital	ADJ
american_scientific_journal-7274	6	14	topology	topology	NOUN
american_scientific_journal-7274	6	15	;	;	PUNCT
american_scientific_journal-7274	6	16	finite	finite	ADJ
american_scientific_journal-7274	6	17	difference	difference	NOUN
american_scientific_journal-7274	6	18	method	method	NOUN
american_scientific_journal-7274	6	19	;	;	PUNCT
american_scientific_journal-7274	6	20	image	image	NOUN
american_scientific_journal-7274	6	21	processing	processing	NOUN
american_scientific_journal-7274	6	22	.	.	PUNCT
american_scientific_journal-7274	7	1	1	1	X
american_scientific_journal-7274	7	2	.	.	X
american_scientific_journal-7274	7	3	introduction	introduction	NOUN
american_scientific_journal-7274	7	4	image	image	NOUN
american_scientific_journal-7274	7	5	processing	processing	NOUN
american_scientific_journal-7274	7	6	problem	problem	NOUN
american_scientific_journal-7274	7	7	is	be	AUX
american_scientific_journal-7274	7	8	one	one	NUM
american_scientific_journal-7274	7	9	of	of	ADP
american_scientific_journal-7274	7	10	the	the	DET
american_scientific_journal-7274	7	11	most	most	ADV
american_scientific_journal-7274	7	12	interested	interested	ADJ
american_scientific_journal-7274	7	13	subjects	subject	NOUN
american_scientific_journal-7274	7	14	in	in	ADP
american_scientific_journal-7274	7	15	the	the	DET
american_scientific_journal-7274	7	16	modern	modern	ADJ
american_scientific_journal-7274	7	17	world	world	NOUN
american_scientific_journal-7274	7	18	.	.	PUNCT
american_scientific_journal-7274	8	1	there	there	PRON
american_scientific_journal-7274	8	2	have	have	AUX
american_scientific_journal-7274	8	3	been	be	AUX
american_scientific_journal-7274	8	4	great	great	ADJ
american_scientific_journal-7274	8	5	advances	advance	NOUN
american_scientific_journal-7274	8	6	in	in	ADP
american_scientific_journal-7274	8	7	imaging	imaging	NOUN
american_scientific_journal-7274	8	8	processes	process	NOUN
american_scientific_journal-7274	8	9	,	,	PUNCT
american_scientific_journal-7274	8	10	especially	especially	ADV
american_scientific_journal-7274	8	11	in	in	ADP
american_scientific_journal-7274	8	12	the	the	DET
american_scientific_journal-7274	8	13	last	last	ADJ
american_scientific_journal-7274	8	14	20	20	NUM
american_scientific_journal-7274	8	15	years	year	NOUN
american_scientific_journal-7274	8	16	.	.	PUNCT
american_scientific_journal-7274	9	1	the	the	DET
american_scientific_journal-7274	9	2	widespread	widespread	ADJ
american_scientific_journal-7274	9	3	use	use	NOUN
american_scientific_journal-7274	9	4	of	of	ADP
american_scientific_journal-7274	9	5	mobile	mobile	ADJ
american_scientific_journal-7274	9	6	phones	phone	NOUN
american_scientific_journal-7274	9	7	and	and	CCONJ
american_scientific_journal-7274	9	8	computers	computer	NOUN
american_scientific_journal-7274	9	9	,	,	PUNCT
american_scientific_journal-7274	9	10	the	the	DET
american_scientific_journal-7274	9	11	continuous	continuous	ADJ
american_scientific_journal-7274	9	12	development	development	NOUN
american_scientific_journal-7274	9	13	of	of	ADP
american_scientific_journal-7274	9	14	tv	tv	NOUN
american_scientific_journal-7274	9	15	screens	screen	NOUN
american_scientific_journal-7274	9	16	,	,	PUNCT
american_scientific_journal-7274	9	17	and	and	CCONJ
american_scientific_journal-7274	9	18	advances	advance	NOUN
american_scientific_journal-7274	9	19	in	in	ADP
american_scientific_journal-7274	9	20	biomedical	biomedical	ADJ
american_scientific_journal-7274	9	21	imaging	imaging	NOUN
american_scientific_journal-7274	9	22	have	have	AUX
american_scientific_journal-7274	9	23	increased	increase	VERB
american_scientific_journal-7274	9	24	the	the	DET
american_scientific_journal-7274	9	25	interest	interest	NOUN
american_scientific_journal-7274	9	26	in	in	ADP
american_scientific_journal-7274	9	27	imaging	imaging	NOUN
american_scientific_journal-7274	9	28	processes	process	NOUN
american_scientific_journal-7274	9	29	.	.	PUNCT
american_scientific_journal-7274	10	1	the	the	DET
american_scientific_journal-7274	10	2	main	main	ADJ
american_scientific_journal-7274	10	3	aim	aim	NOUN
american_scientific_journal-7274	10	4	of	of	ADP
american_scientific_journal-7274	10	5	our	our	PRON
american_scientific_journal-7274	10	6	study	study	NOUN
american_scientific_journal-7274	10	7	is	be	AUX
american_scientific_journal-7274	10	8	to	to	PART
american_scientific_journal-7274	10	9	contribute	contribute	VERB
american_scientific_journal-7274	10	10	to	to	ADP
american_scientific_journal-7274	10	11	this	this	DET
american_scientific_journal-7274	10	12	development	development	NOUN
american_scientific_journal-7274	10	13	by	by	ADP
american_scientific_journal-7274	10	14	using	use	VERB
american_scientific_journal-7274	10	15	mathematical	mathematical	ADJ
american_scientific_journal-7274	10	16	tools	tool	NOUN
american_scientific_journal-7274	10	17	.	.	PUNCT
american_scientific_journal-7274	11	1	our	our	PRON
american_scientific_journal-7274	11	2	work	work	NOUN
american_scientific_journal-7274	11	3	is	be	AUX
american_scientific_journal-7274	11	4	an	an	DET
american_scientific_journal-7274	11	5	interdisciplinary	interdisciplinary	ADJ
american_scientific_journal-7274	11	6	study	study	NOUN
american_scientific_journal-7274	11	7	.	.	PUNCT
american_scientific_journal-7274	12	1	in	in	ADP
american_scientific_journal-7274	12	2	addition	addition	NOUN
american_scientific_journal-7274	12	3	to	to	ADP
american_scientific_journal-7274	12	4	mathematical	mathematical	ADJ
american_scientific_journal-7274	12	5	structures	structure	NOUN
american_scientific_journal-7274	12	6	such	such	ADJ
american_scientific_journal-7274	12	7	as	as	ADP
american_scientific_journal-7274	12	8	digital	digital	ADJ
american_scientific_journal-7274	12	9	topology	topology	NOUN
american_scientific_journal-7274	12	10	,	,	PUNCT
american_scientific_journal-7274	12	11	partial	partial	ADJ
american_scientific_journal-7274	12	12	differential	differential	NOUN
american_scientific_journal-7274	12	13	equations	equation	NOUN
american_scientific_journal-7274	12	14	,	,	PUNCT
american_scientific_journal-7274	12	15	and	and	CCONJ
american_scientific_journal-7274	12	16	finite	finite	VERB
american_scientific_journal-7274	12	17	differences	difference	NOUN
american_scientific_journal-7274	12	18	,	,	PUNCT
american_scientific_journal-7274	12	19	image	image	NOUN
american_scientific_journal-7274	12	20	processing	processing	NOUN
american_scientific_journal-7274	12	21	systems	system	NOUN
american_scientific_journal-7274	12	22	and	and	CCONJ
american_scientific_journal-7274	12	23	matlab	matlab	PROPN
american_scientific_journal-7274	12	24	package	package	NOUN
american_scientific_journal-7274	12	25	program	program	NOUN
american_scientific_journal-7274	12	26	formed	form	VERB
american_scientific_journal-7274	12	27	the	the	DET
american_scientific_journal-7274	12	28	basis	basis	NOUN
american_scientific_journal-7274	12	29	of	of	ADP
american_scientific_journal-7274	12	30	our	our	PRON
american_scientific_journal-7274	12	31	work	work	NOUN
american_scientific_journal-7274	12	32	.	.	PUNCT
american_scientific_journal-7274	13	1	-----------------------------------------------------------------------	-----------------------------------------------------------------------	PUNCT
american_scientific_journal-7274	14	1	*	*	PUNCT
american_scientific_journal-7274	14	2	corresponding	correspond	VERB
american_scientific_journal-7274	14	3	author	author	NOUN
american_scientific_journal-7274	14	4	.	.	PUNCT
american_scientific_journal-7274	15	1	http://asrjetsjournal.org/	http://asrjetsjournal.org/	PROPN
american_scientific_journal-7274	15	2	american	american	PROPN
american_scientific_journal-7274	15	3	academic	academic	PROPN
american_scientific_journal-7274	15	4	scientific	scientific	ADJ
american_scientific_journal-7274	15	5	research	research	NOUN
american_scientific_journal-7274	15	6	journal	journal	NOUN
american_scientific_journal-7274	15	7	for	for	ADP
american_scientific_journal-7274	15	8	engineering	engineering	NOUN
american_scientific_journal-7274	15	9	,	,	PUNCT
american_scientific_journal-7274	15	10	technology	technology	NOUN
american_scientific_journal-7274	15	11	,	,	PUNCT
american_scientific_journal-7274	15	12	and	and	CCONJ
american_scientific_journal-7274	15	13	sciences	science	NOUN
american_scientific_journal-7274	15	14	(	(	PUNCT
american_scientific_journal-7274	15	15	asrjets	asrjet	NOUN
american_scientific_journal-7274	15	16	)	)	PUNCT
american_scientific_journal-7274	15	17	(	(	PUNCT
american_scientific_journal-7274	15	18	2021	2021	NUM
american_scientific_journal-7274	15	19	)	)	PUNCT
american_scientific_journal-7274	15	20	volume	volume	NOUN
american_scientific_journal-7274	15	21	84	84	NUM
american_scientific_journal-7274	15	22	,	,	PUNCT
american_scientific_journal-7274	15	23	no1	no1	PROPN
american_scientific_journal-7274	15	24	,	,	PUNCT
american_scientific_journal-7274	15	25	pp	pp	ADP
american_scientific_journal-7274	15	26	118	118	NUM
american_scientific_journal-7274	15	27	-	-	SYM
american_scientific_journal-7274	15	28	129	129	NUM
american_scientific_journal-7274	15	29	119	119	NUM
american_scientific_journal-7274	15	30	especially	especially	ADV
american_scientific_journal-7274	15	31	in	in	ADP
american_scientific_journal-7274	15	32	the	the	DET
american_scientific_journal-7274	15	33	last	last	ADJ
american_scientific_journal-7274	15	34	20	20	NUM
american_scientific_journal-7274	15	35	years	year	NOUN
american_scientific_journal-7274	15	36	,	,	PUNCT
american_scientific_journal-7274	15	37	the	the	DET
american_scientific_journal-7274	15	38	use	use	NOUN
american_scientific_journal-7274	15	39	of	of	ADP
american_scientific_journal-7274	15	40	pdes	pde	NOUN
american_scientific_journal-7274	15	41	in	in	ADP
american_scientific_journal-7274	15	42	image	image	NOUN
american_scientific_journal-7274	15	43	processing	processing	NOUN
american_scientific_journal-7274	15	44	has	have	AUX
american_scientific_journal-7274	15	45	started	start	VERB
american_scientific_journal-7274	15	46	to	to	PART
american_scientific_journal-7274	15	47	increase	increase	VERB
american_scientific_journal-7274	15	48	.	.	PUNCT
american_scientific_journal-7274	16	1	mikula	mikula	PROPN
american_scientific_journal-7274	16	2	and	and	CCONJ
american_scientific_journal-7274	16	3	ramarosy	ramarosy	NOUN
american_scientific_journal-7274	16	4	implemented	implement	VERB
american_scientific_journal-7274	16	5	semi	semi	ADJ
american_scientific_journal-7274	16	6	-	-	ADJ
american_scientific_journal-7274	16	7	implicit	implicit	ADJ
american_scientific_journal-7274	16	8	finite	finite	ADJ
american_scientific_journal-7274	16	9	volume	volume	NOUN
american_scientific_journal-7274	16	10	scheme	scheme	NOUN
american_scientific_journal-7274	16	11	in	in	ADP
american_scientific_journal-7274	16	12	image	image	NOUN
american_scientific_journal-7274	16	13	processing	processing	NOUN
american_scientific_journal-7274	16	14	[	[	X
american_scientific_journal-7274	16	15	1	1	NUM
american_scientific_journal-7274	16	16	]	]	PUNCT
american_scientific_journal-7274	16	17	.	.	PUNCT
american_scientific_journal-7274	17	1	sarti	sarti	PROPN
american_scientific_journal-7274	17	2	and	and	CCONJ
american_scientific_journal-7274	17	3	his	his	PRON
american_scientific_journal-7274	17	4	colleagues	colleague	NOUN
american_scientific_journal-7274	17	5	used	use	VERB
american_scientific_journal-7274	17	6	evolutionary	evolutionary	ADJ
american_scientific_journal-7274	17	7	pdes	pde	NOUN
american_scientific_journal-7274	17	8	in	in	ADP
american_scientific_journal-7274	17	9	medical	medical	ADJ
american_scientific_journal-7274	17	10	imaging	imaging	NOUN
american_scientific_journal-7274	17	11	[	[	X
american_scientific_journal-7274	17	12	2	2	NUM
american_scientific_journal-7274	17	13	]	]	PUNCT
american_scientific_journal-7274	17	14	.	.	PUNCT
american_scientific_journal-7274	18	1	weickert	weickert	PROPN
american_scientific_journal-7274	18	2	applied	apply	VERB
american_scientific_journal-7274	18	3	additive	additive	NOUN
american_scientific_journal-7274	18	4	operator	operator	NOUN
american_scientific_journal-7274	18	5	splitting	splitting	NOUN
american_scientific_journal-7274	18	6	method	method	NOUN
american_scientific_journal-7274	18	7	to	to	ADP
american_scientific_journal-7274	18	8	nonlinear	nonlinear	ADJ
american_scientific_journal-7274	18	9	diffusion	diffusion	NOUN
american_scientific_journal-7274	18	10	equations	equation	NOUN
american_scientific_journal-7274	19	1	[	[	X
american_scientific_journal-7274	19	2	3	3	NUM
american_scientific_journal-7274	19	3	]	]	PUNCT
american_scientific_journal-7274	19	4	.	.	PUNCT
american_scientific_journal-7274	20	1	mikula	mikula	PROPN
american_scientific_journal-7274	20	2	performed	perform	VERB
american_scientific_journal-7274	20	3	image	image	NOUN
american_scientific_journal-7274	20	4	analysis	analysis	NOUN
american_scientific_journal-7274	20	5	using	use	VERB
american_scientific_journal-7274	20	6	different	different	ADJ
american_scientific_journal-7274	20	7	partial	partial	ADJ
american_scientific_journal-7274	20	8	differential	differential	NOUN
american_scientific_journal-7274	20	9	equations	equation	NOUN
american_scientific_journal-7274	20	10	[	[	X
american_scientific_journal-7274	20	11	4	4	NUM
american_scientific_journal-7274	20	12	]	]	PUNCT
american_scientific_journal-7274	20	13	.	.	PUNCT
american_scientific_journal-7274	21	1	gibou	gibou	PROPN
american_scientific_journal-7274	21	2	and	and	CCONJ
american_scientific_journal-7274	21	3	his	his	PRON
american_scientific_journal-7274	21	4	colleagues	colleague	NOUN
american_scientific_journal-7274	21	5	suggested	suggest	VERB
american_scientific_journal-7274	21	6	automatic	automatic	ADJ
american_scientific_journal-7274	21	7	algorithms	algorithm	NOUN
american_scientific_journal-7274	21	8	for	for	ADP
american_scientific_journal-7274	21	9	the	the	DET
american_scientific_journal-7274	21	10	segmentation	segmentation	NOUN
american_scientific_journal-7274	21	11	phase	phase	NOUN
american_scientific_journal-7274	21	12	of	of	ADP
american_scientific_journal-7274	21	13	radiotherapy	radiotherapy	NOUN
american_scientific_journal-7274	21	14	treatment	treatment	NOUN
american_scientific_journal-7274	21	15	planning	planning	NOUN
american_scientific_journal-7274	21	16	[	[	X
american_scientific_journal-7274	21	17	5	5	NUM
american_scientific_journal-7274	21	18	]	]	PUNCT
american_scientific_journal-7274	21	19	.	.	PUNCT
american_scientific_journal-7274	22	1	angenent	angenent	PROPN
american_scientific_journal-7274	22	2	and	and	CCONJ
american_scientific_journal-7274	22	3	his	his	PRON
american_scientific_journal-7274	22	4	colleagues	colleague	NOUN
american_scientific_journal-7274	22	5	used	use	VERB
american_scientific_journal-7274	22	6	pdes	pde	NOUN
american_scientific_journal-7274	22	7	in	in	ADP
american_scientific_journal-7274	22	8	medical	medical	ADJ
american_scientific_journal-7274	22	9	imaging	imaging	NOUN
american_scientific_journal-7274	22	10	[	[	X
american_scientific_journal-7274	22	11	6	6	NUM
american_scientific_journal-7274	22	12	]	]	PUNCT
american_scientific_journal-7274	22	13	.	.	PUNCT
american_scientific_journal-7274	23	1	kuijper	kuijper	PROPN
american_scientific_journal-7274	23	2	used	use	VERB
american_scientific_journal-7274	23	3	geometric	geometric	ADJ
american_scientific_journal-7274	23	4	and	and	CCONJ
american_scientific_journal-7274	23	5	variational	variational	ADJ
american_scientific_journal-7274	23	6	pdes	pde	NOUN
american_scientific_journal-7274	23	7	for	for	ADP
american_scientific_journal-7274	23	8	image	image	NOUN
american_scientific_journal-7274	23	9	processing	processing	NOUN
american_scientific_journal-7274	23	10	[	[	X
american_scientific_journal-7274	23	11	7	7	NUM
american_scientific_journal-7274	23	12	]	]	PUNCT
american_scientific_journal-7274	23	13	.	.	PUNCT
american_scientific_journal-7274	24	1	nadernejad	nadernejad	NOUN
american_scientific_journal-7274	24	2	and	and	CCONJ
american_scientific_journal-7274	24	3	his	his	PRON
american_scientific_journal-7274	24	4	colleagues	colleague	NOUN
american_scientific_journal-7274	24	5	implemented	implement	VERB
american_scientific_journal-7274	24	6	pdes	pde	NOUN
american_scientific_journal-7274	24	7	-	-	PUNCT
american_scientific_journal-7274	24	8	based	base	VERB
american_scientific_journal-7274	24	9	model	model	NOUN
american_scientific_journal-7274	24	10	in	in	ADP
american_scientific_journal-7274	24	11	image	image	NOUN
american_scientific_journal-7274	24	12	enhancement	enhancement	NOUN
american_scientific_journal-7274	24	13	[	[	X
american_scientific_journal-7274	24	14	8	8	NUM
american_scientific_journal-7274	24	15	]	]	PUNCT
american_scientific_journal-7274	24	16	.	.	PUNCT
american_scientific_journal-7274	25	1	kim	kim	PROPN
american_scientific_journal-7274	25	2	and	and	CCONJ
american_scientific_journal-7274	25	3	lim	lim	PROPN
american_scientific_journal-7274	25	4	applied	apply	VERB
american_scientific_journal-7274	25	5	fourth	fourth	ADJ
american_scientific_journal-7274	25	6	order	order	NOUN
american_scientific_journal-7274	25	7	pdes	pde	NOUN
american_scientific_journal-7274	25	8	-	-	PUNCT
american_scientific_journal-7274	25	9	based	base	VERB
american_scientific_journal-7274	25	10	methods	method	NOUN
american_scientific_journal-7274	25	11	in	in	ADP
american_scientific_journal-7274	25	12	image	image	NOUN
american_scientific_journal-7274	25	13	denoising	denoise	VERB
american_scientific_journal-7274	25	14	[	[	X
american_scientific_journal-7274	25	15	9	9	NUM
american_scientific_journal-7274	25	16	]	]	PUNCT
american_scientific_journal-7274	25	17	.	.	PUNCT
american_scientific_journal-7274	26	1	lin	lin	PROPN
american_scientific_journal-7274	26	2	and	and	CCONJ
american_scientific_journal-7274	26	3	his	his	PRON
american_scientific_journal-7274	26	4	colleagues	colleague	NOUN
american_scientific_journal-7274	26	5	designed	design	VERB
american_scientific_journal-7274	26	6	pdes	pde	NOUN
american_scientific_journal-7274	26	7	and	and	CCONJ
american_scientific_journal-7274	26	8	differential	differential	ADJ
american_scientific_journal-7274	26	9	invariants	invariant	NOUN
american_scientific_journal-7274	26	10	for	for	ADP
american_scientific_journal-7274	26	11	image	image	NOUN
american_scientific_journal-7274	26	12	problems	problem	NOUN
american_scientific_journal-7274	26	13	[	[	X
american_scientific_journal-7274	26	14	10	10	NUM
american_scientific_journal-7274	26	15	]	]	PUNCT
american_scientific_journal-7274	26	16	.	.	PUNCT
american_scientific_journal-7274	27	1	belaid	belaid	VERB
american_scientific_journal-7274	27	2	used	use	VERB
american_scientific_journal-7274	27	3	topological	topological	PROPN
american_scientific_journal-7274	27	4	gradient	gradient	NOUN
american_scientific_journal-7274	27	5	approach	approach	NOUN
american_scientific_journal-7274	27	6	in	in	ADP
american_scientific_journal-7274	27	7	image	image	NOUN
american_scientific_journal-7274	27	8	processing	processing	NOUN
american_scientific_journal-7274	28	1	[	[	X
american_scientific_journal-7274	28	2	11	11	NUM
american_scientific_journal-7274	28	3	]	]	PUNCT
american_scientific_journal-7274	28	4	.	.	PUNCT
american_scientific_journal-7274	29	1	niang	niang	PROPN
american_scientific_journal-7274	29	2	and	and	CCONJ
american_scientific_journal-7274	29	3	his	his	PRON
american_scientific_journal-7274	29	4	colleagues	colleague	NOUN
american_scientific_journal-7274	29	5	used	use	VERB
american_scientific_journal-7274	29	6	pdes	pde	NOUN
american_scientific_journal-7274	29	7	-	-	PUNCT
american_scientific_journal-7274	29	8	based	base	VERB
american_scientific_journal-7274	29	9	method	method	NOUN
american_scientific_journal-7274	29	10	for	for	ADP
american_scientific_journal-7274	29	11	image	image	NOUN
american_scientific_journal-7274	29	12	problems	problem	NOUN
american_scientific_journal-7274	29	13	[	[	X
american_scientific_journal-7274	29	14	12	12	NUM
american_scientific_journal-7274	29	15	]	]	PUNCT
american_scientific_journal-7274	29	16	.	.	PUNCT
american_scientific_journal-7274	30	1	shen	shen	PROPN
american_scientific_journal-7274	30	2	and	and	CCONJ
american_scientific_journal-7274	30	3	his	his	PRON
american_scientific_journal-7274	30	4	colleagues	colleague	NOUN
american_scientific_journal-7274	30	5	implemented	implement	VERB
american_scientific_journal-7274	30	6	an	an	DET
american_scientific_journal-7274	30	7	adaptive	adaptive	ADJ
american_scientific_journal-7274	30	8	partial	partial	ADJ
american_scientific_journal-7274	30	9	differential	differential	NOUN
american_scientific_journal-7274	30	10	equation	equation	NOUN
american_scientific_journal-7274	30	11	in	in	ADP
american_scientific_journal-7274	30	12	image	image	NOUN
american_scientific_journal-7274	30	13	processing	processing	NOUN
american_scientific_journal-7274	30	14	[	[	X
american_scientific_journal-7274	30	15	13	13	NUM
american_scientific_journal-7274	30	16	]	]	PUNCT
american_scientific_journal-7274	30	17	.	.	PUNCT
american_scientific_journal-7274	31	1	ghanbari	ghanbari	PROPN
american_scientific_journal-7274	31	2	and	and	CCONJ
american_scientific_journal-7274	31	3	his	his	PRON
american_scientific_journal-7274	31	4	colleagues	colleague	NOUN
american_scientific_journal-7274	31	5	used	use	VERB
american_scientific_journal-7274	31	6	a	a	DET
american_scientific_journal-7274	31	7	restarted	restart	VERB
american_scientific_journal-7274	31	8	iterative	iterative	NOUN
american_scientific_journal-7274	31	9	ham	ham	NOUN
american_scientific_journal-7274	31	10	for	for	ADP
american_scientific_journal-7274	31	11	tv	tv	NOUN
american_scientific_journal-7274	31	12	models	model	NOUN
american_scientific_journal-7274	31	13	[	[	X
american_scientific_journal-7274	31	14	14	14	NUM
american_scientific_journal-7274	31	15	]	]	PUNCT
american_scientific_journal-7274	31	16	.	.	PUNCT
american_scientific_journal-7274	32	1	liu	liu	PROPN
american_scientific_journal-7274	32	2	and	and	CCONJ
american_scientific_journal-7274	32	3	his	his	PRON
american_scientific_journal-7274	32	4	colleagues	colleague	NOUN
american_scientific_journal-7274	32	5	applied	apply	VERB
american_scientific_journal-7274	32	6	an	an	DET
american_scientific_journal-7274	32	7	adaptive	adaptive	ADJ
american_scientific_journal-7274	32	8	relaxation	relaxation	NOUN
american_scientific_journal-7274	32	9	method	method	NOUN
american_scientific_journal-7274	32	10	for	for	ADP
american_scientific_journal-7274	32	11	a	a	DET
american_scientific_journal-7274	32	12	fourth	fourth	ADJ
american_scientific_journal-7274	32	13	order	order	NOUN
american_scientific_journal-7274	32	14	pde	pde	NOUN
american_scientific_journal-7274	32	15	for	for	ADP
american_scientific_journal-7274	32	16	image	image	NOUN
american_scientific_journal-7274	32	17	problems	problem	NOUN
american_scientific_journal-7274	32	18	[	[	X
american_scientific_journal-7274	32	19	15	15	NUM
american_scientific_journal-7274	32	20	]	]	PUNCT
american_scientific_journal-7274	32	21	.	.	PUNCT
american_scientific_journal-7274	33	1	nnolim	nnolim	PROPN
american_scientific_journal-7274	33	2	proposed	propose	VERB
american_scientific_journal-7274	33	3	partial	partial	ADJ
american_scientific_journal-7274	33	4	differential	differential	NOUN
american_scientific_journal-7274	33	5	equation	equation	NOUN
american_scientific_journal-7274	33	6	-	-	PUNCT
american_scientific_journal-7274	33	7	based	base	VERB
american_scientific_journal-7274	33	8	method	method	NOUN
american_scientific_journal-7274	33	9	for	for	ADP
american_scientific_journal-7274	33	10	underwater	underwater	ADJ
american_scientific_journal-7274	33	11	image	image	NOUN
american_scientific_journal-7274	33	12	processing	processing	NOUN
american_scientific_journal-7274	33	13	[	[	X
american_scientific_journal-7274	33	14	16	16	NUM
american_scientific_journal-7274	33	15	]	]	PUNCT
american_scientific_journal-7274	33	16	.	.	PUNCT
american_scientific_journal-7274	34	1	yu	yu	PROPN
american_scientific_journal-7274	34	2	and	and	CCONJ
american_scientific_journal-7274	34	3	his	his	PRON
american_scientific_journal-7274	34	4	colleagues	colleague	NOUN
american_scientific_journal-7274	34	5	implemented	implement	VERB
american_scientific_journal-7274	34	6	quasi	quasi	ADJ
american_scientific_journal-7274	34	7	-	-	NOUN
american_scientific_journal-7274	34	8	interpolation	interpolation	ADJ
american_scientific_journal-7274	34	9	operators	operator	NOUN
american_scientific_journal-7274	34	10	for	for	ADP
american_scientific_journal-7274	34	11	bivariate	bivariate	ADJ
american_scientific_journal-7274	34	12	quintic	quintic	ADJ
american_scientific_journal-7274	34	13	spline	spline	NOUN
american_scientific_journal-7274	34	14	spaces	space	NOUN
american_scientific_journal-7274	34	15	in	in	ADP
american_scientific_journal-7274	34	16	image	image	NOUN
american_scientific_journal-7274	34	17	processing	processing	NOUN
american_scientific_journal-7274	34	18	[	[	X
american_scientific_journal-7274	34	19	17	17	NUM
american_scientific_journal-7274	34	20	]	]	PUNCT
american_scientific_journal-7274	34	21	.	.	PUNCT
american_scientific_journal-7274	35	1	huang	huang	PROPN
american_scientific_journal-7274	35	2	and	and	CCONJ
american_scientific_journal-7274	35	3	his	his	PRON
american_scientific_journal-7274	35	4	colleagues	colleague	NOUN
american_scientific_journal-7274	35	5	implemented	implement	VERB
american_scientific_journal-7274	35	6	hybrid	hybrid	ADJ
american_scientific_journal-7274	35	7	analog	analog	NOUN
american_scientific_journal-7274	35	8	-	-	PUNCT
american_scientific_journal-7274	35	9	digital	digital	ADJ
american_scientific_journal-7274	35	10	approach	approach	NOUN
american_scientific_journal-7274	35	11	for	for	ADP
american_scientific_journal-7274	35	12	image	image	NOUN
american_scientific_journal-7274	35	13	problems	problem	NOUN
american_scientific_journal-7274	35	14	[	[	X
american_scientific_journal-7274	35	15	18	18	NUM
american_scientific_journal-7274	35	16	]	]	PUNCT
american_scientific_journal-7274	35	17	.	.	PUNCT
american_scientific_journal-7274	36	1	benseghir	benseghir	NOUN
american_scientific_journal-7274	36	2	and	and	CCONJ
american_scientific_journal-7274	36	3	his	his	PRON
american_scientific_journal-7274	36	4	colleagues	colleague	NOUN
american_scientific_journal-7274	36	5	used	use	VERB
american_scientific_journal-7274	36	6	a	a	DET
american_scientific_journal-7274	36	7	partial	partial	ADJ
american_scientific_journal-7274	36	8	differential	differential	NOUN
american_scientific_journal-7274	36	9	equation	equation	NOUN
american_scientific_journal-7274	36	10	that	that	PRON
american_scientific_journal-7274	36	11	is	be	AUX
american_scientific_journal-7274	36	12	based	base	VERB
american_scientific_journal-7274	36	13	on	on	ADP
american_scientific_journal-7274	36	14	a	a	DET
american_scientific_journal-7274	36	15	nonlinear	nonlinear	ADJ
american_scientific_journal-7274	36	16	structure	structure	NOUN
american_scientific_journal-7274	36	17	tensor	tensor	NOUN
american_scientific_journal-7274	36	18	in	in	ADP
american_scientific_journal-7274	36	19	image	image	NOUN
american_scientific_journal-7274	36	20	processing	processing	NOUN
american_scientific_journal-7274	36	21	[	[	X
american_scientific_journal-7274	36	22	19	19	NUM
american_scientific_journal-7274	36	23	]	]	PUNCT
american_scientific_journal-7274	36	24	.	.	PUNCT
american_scientific_journal-7274	37	1	in	in	ADP
american_scientific_journal-7274	37	2	this	this	DET
american_scientific_journal-7274	37	3	paper	paper	NOUN
american_scientific_journal-7274	37	4	,	,	PUNCT
american_scientific_journal-7274	37	5	we	we	PRON
american_scientific_journal-7274	37	6	will	will	AUX
american_scientific_journal-7274	37	7	use	use	VERB
american_scientific_journal-7274	37	8	digital	digital	ADJ
american_scientific_journal-7274	37	9	-	-	PUNCT
american_scientific_journal-7274	37	10	discrete	discrete	ADJ
american_scientific_journal-7274	37	11	approach	approach	NOUN
american_scientific_journal-7274	37	12	for	for	ADP
american_scientific_journal-7274	37	13	perona	perona	NOUN
american_scientific_journal-7274	37	14	-	-	PUNCT
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american_scientific_journal-7274	37	16	equation	equation	NOUN
american_scientific_journal-7274	37	17	in	in	ADP
american_scientific_journal-7274	37	18	image	image	NOUN
american_scientific_journal-7274	37	19	processing	processing	NOUN
american_scientific_journal-7274	37	20	.	.	PUNCT
american_scientific_journal-7274	38	1	2	2	X
american_scientific_journal-7274	38	2	.	.	X
american_scientific_journal-7274	38	3	digital	digital	ADJ
american_scientific_journal-7274	38	4	continuous	continuous	ADJ
american_scientific_journal-7274	38	5	function	function	NOUN
american_scientific_journal-7274	38	6	(	(	PUNCT
american_scientific_journal-7274	38	7	dcf	dcf	PROPN
american_scientific_journal-7274	38	8	)	)	PUNCT
american_scientific_journal-7274	38	9	and	and	CCONJ
american_scientific_journal-7274	38	10	gradually	gradually	ADV
american_scientific_journal-7274	38	11	varied	varied	ADJ
american_scientific_journal-7274	38	12	function	function	NOUN
american_scientific_journal-7274	38	13	(	(	PUNCT
american_scientific_journal-7274	38	14	gvf	gvf	NOUN
american_scientific_journal-7274	38	15	)	)	PUNCT
american_scientific_journal-7274	38	16	2.1	2.1	NUM
american_scientific_journal-7274	38	17	.	.	PUNCT
american_scientific_journal-7274	39	1	digital	digital	ADJ
american_scientific_journal-7274	39	2	function	function	NOUN
american_scientific_journal-7274	39	3	(	(	PUNCT
american_scientific_journal-7274	39	4	df	df	NOUN
american_scientific_journal-7274	39	5	)	)	PUNCT
american_scientific_journal-7274	40	1	[	[	X
american_scientific_journal-7274	40	2	20	20	NUM
american_scientific_journal-7274	40	3	]	]	X
american_scientific_journal-7274	40	4	dcfs	dcfs	PROPN
american_scientific_journal-7274	40	5	and	and	CCONJ
american_scientific_journal-7274	40	6	gvfs	gvfs	PROPN
american_scientific_journal-7274	40	7	were	be	AUX
american_scientific_journal-7274	40	8	developed	develop	VERB
american_scientific_journal-7274	40	9	in	in	ADP
american_scientific_journal-7274	40	10	1980s	1980s	NUM
american_scientific_journal-7274	40	11	.	.	PUNCT
american_scientific_journal-7274	41	1	rosenfeld	rosenfeld	PROPN
american_scientific_journal-7274	41	2	suggested	suggest	VERB
american_scientific_journal-7274	41	3	digital	digital	PROPN
american_scientific_journal-7274	41	4	dcfs	dcfs	PROPN
american_scientific_journal-7274	41	5	in	in	ADP
american_scientific_journal-7274	41	6	digital	digital	ADJ
american_scientific_journal-7274	41	7	imaging	imaging	NOUN
american_scientific_journal-7274	42	1	[	[	X
american_scientific_journal-7274	42	2	21	21	NUM
american_scientific_journal-7274	42	3	]	]	PUNCT
american_scientific_journal-7274	42	4	.	.	PUNCT
american_scientific_journal-7274	43	1	chen	chen	PROPN
american_scientific_journal-7274	43	2	proposed	propose	VERB
american_scientific_journal-7274	43	3	gvfs	gvfs	NOUN
american_scientific_journal-7274	43	4	for	for	ADP
american_scientific_journal-7274	43	5	interpolating	interpolate	VERB
american_scientific_journal-7274	43	6	a	a	DET
american_scientific_journal-7274	43	7	digital	digital	ADJ
american_scientific_journal-7274	43	8	surface	surface	NOUN
american_scientific_journal-7274	44	1	[	[	X
american_scientific_journal-7274	44	2	22	22	NUM
american_scientific_journal-7274	44	3	]	]	PUNCT
american_scientific_journal-7274	44	4	.	.	PUNCT
american_scientific_journal-7274	45	1	khalimsky	khalimsky	PROPN
american_scientific_journal-7274	46	1	[	[	X
american_scientific_journal-7274	46	2	23	23	NUM
american_scientific_journal-7274	46	3	]	]	PUNCT
american_scientific_journal-7274	46	4	,	,	PUNCT
american_scientific_journal-7274	46	5	kong	kong	PROPN
american_scientific_journal-7274	47	1	[	[	X
american_scientific_journal-7274	47	2	24	24	NUM
american_scientific_journal-7274	47	3	]	]	PUNCT
american_scientific_journal-7274	47	4	,	,	PUNCT
american_scientific_journal-7274	47	5	boxer	boxer	NOUN
american_scientific_journal-7274	47	6	[	[	X
american_scientific_journal-7274	47	7	25	25	NUM
american_scientific_journal-7274	47	8	]	]	PUNCT
american_scientific_journal-7274	47	9	,	,	PUNCT
american_scientific_journal-7274	47	10	rosenfeld	rosenfeld	PROPN
american_scientific_journal-7274	48	1	[	[	X
american_scientific_journal-7274	48	2	26	26	NUM
american_scientific_journal-7274	48	3	]	]	PUNCT
american_scientific_journal-7274	48	4	developed	develop	VERB
american_scientific_journal-7274	48	5	methods	method	NOUN
american_scientific_journal-7274	48	6	for	for	ADP
american_scientific_journal-7274	48	7	digital	digital	ADJ
american_scientific_journal-7274	48	8	deformations	deformation	NOUN
american_scientific_journal-7274	48	9	.	.	PUNCT
american_scientific_journal-7274	49	1	agnarsson	agnarsson	NOUN
american_scientific_journal-7274	49	2	and	and	CCONJ
american_scientific_journal-7274	49	3	chen	chen	PROPN
american_scientific_journal-7274	49	4	established	establish	VERB
american_scientific_journal-7274	49	5	association	association	NOUN
american_scientific_journal-7274	49	6	between	between	ADP
american_scientific_journal-7274	49	7	graph	graph	NOUN
american_scientific_journal-7274	49	8	homomorphism	homomorphism	NOUN
american_scientific_journal-7274	49	9	and	and	CCONJ
american_scientific_journal-7274	49	10	gvfs	gvfs	VERB
american_scientific_journal-7274	49	11	and	and	CCONJ
american_scientific_journal-7274	49	12	[	[	X
american_scientific_journal-7274	49	13	27	27	NUM
american_scientific_journal-7274	49	14	]	]	PUNCT
american_scientific_journal-7274	49	15	.	.	PUNCT
american_scientific_journal-7274	50	1	chen	chen	PROPN
american_scientific_journal-7274	50	2	found	find	VERB
american_scientific_journal-7274	50	3	systematic	systematic	ADJ
american_scientific_journal-7274	50	4	digital	digital	ADJ
american_scientific_journal-7274	50	5	-	-	PUNCT
american_scientific_journal-7274	50	6	discrete	discrete	NOUN
american_scientific_journal-7274	50	7	method	method	NOUN
american_scientific_journal-7274	50	8	[	[	X
american_scientific_journal-7274	50	9	28	28	NUM
american_scientific_journal-7274	50	10	]	]	PUNCT
american_scientific_journal-7274	50	11	and	and	CCONJ
american_scientific_journal-7274	50	12	chen	chen	PROPN
american_scientific_journal-7274	50	13	and	and	CCONJ
american_scientific_journal-7274	50	14	luo	luo	PROPN
american_scientific_journal-7274	50	15	suggested	suggest	VERB
american_scientific_journal-7274	50	16	harmonic	harmonic	ADJ
american_scientific_journal-7274	50	17	functions	function	NOUN
american_scientific_journal-7274	50	18	in	in	ADP
american_scientific_journal-7274	50	19	image	image	NOUN
american_scientific_journal-7274	50	20	analysis	analysis	NOUN
american_scientific_journal-7274	50	21	[	[	X
american_scientific_journal-7274	50	22	29	29	NUM
american_scientific_journal-7274	50	23	]	]	PUNCT
american_scientific_journal-7274	50	24	.	.	PUNCT
american_scientific_journal-7274	51	1	the	the	DET
american_scientific_journal-7274	51	2	df	df	PROPN
american_scientific_journal-7274	51	3	is	be	AUX
american_scientific_journal-7274	51	4	essentially	essentially	ADV
american_scientific_journal-7274	51	5	a	a	DET
american_scientific_journal-7274	51	6	function	function	NOUN
american_scientific_journal-7274	51	7	defined	define	VERB
american_scientific_journal-7274	51	8	in	in	ADP
american_scientific_journal-7274	51	9	digital	digital	ADJ
american_scientific_journal-7274	51	10	spaces	space	NOUN
american_scientific_journal-7274	51	11	.	.	PUNCT
american_scientific_journal-7274	52	1	we	we	PRON
american_scientific_journal-7274	52	2	can	can	AUX
american_scientific_journal-7274	52	3	see	see	VERB
american_scientific_journal-7274	52	4	that	that	SCONJ
american_scientific_journal-7274	52	5	digital	digital	ADJ
american_scientific_journal-7274	52	6	space	space	NOUN
american_scientific_journal-7274	52	7	is	be	AUX
american_scientific_journal-7274	52	8	a	a	DET
american_scientific_journal-7274	52	9	subspace	subspace	NOUN
american_scientific_journal-7274	52	10	of	of	ADP
american_scientific_journal-7274	52	11	euclidean	euclidean	ADJ
american_scientific_journal-7274	52	12	space	space	NOUN
american_scientific_journal-7274	52	13	.	.	PUNCT
american_scientific_journal-7274	53	1	digital	digital	ADJ
american_scientific_journal-7274	53	2	space	space	NOUN
american_scientific_journal-7274	53	3	contains	contain	VERB
american_scientific_journal-7274	53	4	all	all	DET
american_scientific_journal-7274	53	5	grid	grid	ADJ
american_scientific_journal-7274	53	6	integer	integer	NOUN
american_scientific_journal-7274	53	7	points	point	NOUN
american_scientific_journal-7274	53	8	.	.	PUNCT
american_scientific_journal-7274	54	1	we	we	PRON
american_scientific_journal-7274	54	2	generally	generally	ADV
american_scientific_journal-7274	54	3	represent	represent	VERB
american_scientific_journal-7274	54	4	m	m	ADJ
american_scientific_journal-7274	54	5	-	-	ADJ
american_scientific_journal-7274	54	6	dimensional	dimensional	ADJ
american_scientific_journal-7274	54	7	digital	digital	ADJ
american_scientific_journal-7274	54	8	space	space	NOUN
american_scientific_journal-7274	54	9	with	with	ADP
american_scientific_journal-7274	54	10	∑𝑚.	∑𝑚.	PROPN
american_scientific_journal-7274	54	11	definition	definition	NOUN
american_scientific_journal-7274	54	12	2.1.1	2.1.1	NUM
american_scientific_journal-7274	54	13	.	.	PUNCT
american_scientific_journal-7274	55	1	[	[	X
american_scientific_journal-7274	55	2	20,21	20,21	NUM
american_scientific_journal-7274	55	3	]	]	X
american_scientific_journal-7274	55	4	:	:	PUNCT
american_scientific_journal-7274	55	5	a	a	DET
american_scientific_journal-7274	55	6	df	df	NOUN
american_scientific_journal-7274	55	7	is	be	AUX
american_scientific_journal-7274	55	8	a	a	DET
american_scientific_journal-7274	55	9	function	function	NOUN
american_scientific_journal-7274	55	10	from	from	ADP
american_scientific_journal-7274	55	11	digital	digital	ADJ
american_scientific_journal-7274	55	12	space	space	NOUN
american_scientific_journal-7274	55	13	i	i	PRON
american_scientific_journal-7274	55	14	defined	define	VERB
american_scientific_journal-7274	55	15	to	to	ADP
american_scientific_journal-7274	55	16	integers	integer	NOUN
american_scientific_journal-7274	55	17	.	.	PUNCT
american_scientific_journal-7274	56	1	usually	usually	ADV
american_scientific_journal-7274	56	2	we	we	PRON
american_scientific_journal-7274	56	3	use	use	VERB
american_scientific_journal-7274	56	4	{	{	PUNCT
american_scientific_journal-7274	56	5	1,2,	1,2,	NUM
american_scientific_journal-7274	56	6	...	...	PUNCT
american_scientific_journal-7274	56	7	,n	,n	NOUN
american_scientific_journal-7274	56	8	}	}	PUNCT
american_scientific_journal-7274	56	9	as	as	ADP
american_scientific_journal-7274	56	10	the	the	DET
american_scientific_journal-7274	56	11	display	display	NOUN
american_scientific_journal-7274	56	12	set	set	NOUN
american_scientific_journal-7274	56	13	of	of	ADP
american_scientific_journal-7274	56	14	the	the	DET
american_scientific_journal-7274	56	15	function	function	NOUN
american_scientific_journal-7274	56	16	.	.	PUNCT
american_scientific_journal-7274	57	1	for	for	ADP
american_scientific_journal-7274	57	2	example	example	NOUN
american_scientific_journal-7274	57	3	,	,	PUNCT
american_scientific_journal-7274	57	4	𝑓	𝑓	X
american_scientific_journal-7274	57	5	:	:	PUNCT
american_scientific_journal-7274	57	6	∑2	∑2	X
american_scientific_journal-7274	57	7	→	→	SYM
american_scientific_journal-7274	57	8	{	{	PUNCT
american_scientific_journal-7274	57	9	1,2	1,2	NUM
american_scientific_journal-7274	57	10	,	,	PUNCT
american_scientific_journal-7274	57	11	.	.	PUNCT
american_scientific_journal-7274	57	12	.	.	PUNCT
american_scientific_journal-7274	57	13	.	.	PUNCT
american_scientific_journal-7274	58	1	,	,	PUNCT
american_scientific_journal-7274	58	2	𝑛	𝑛	X
american_scientific_journal-7274	58	3	}	}	PUNCT
american_scientific_journal-7274	58	4	is	be	AUX
american_scientific_journal-7274	58	5	a	a	DET
american_scientific_journal-7274	58	6	digital	digital	ADJ
american_scientific_journal-7274	58	7	function	function	NOUN
american_scientific_journal-7274	58	8	.	.	PUNCT
american_scientific_journal-7274	59	1	also	also	ADV
american_scientific_journal-7274	59	2	we	we	PRON
american_scientific_journal-7274	59	3	can	can	AUX
american_scientific_journal-7274	59	4	see	see	VERB
american_scientific_journal-7274	59	5	the	the	DET
american_scientific_journal-7274	59	6	df	df	PROPN
american_scientific_journal-7274	59	7	as	as	ADP
american_scientific_journal-7274	59	8	a	a	DET
american_scientific_journal-7274	59	9	function	function	NOUN
american_scientific_journal-7274	59	10	in	in	ADP
american_scientific_journal-7274	59	11	general	general	ADJ
american_scientific_journal-7274	59	12	discrete	discrete	ADJ
american_scientific_journal-7274	59	13	space	space	NOUN
american_scientific_journal-7274	59	14	.	.	PUNCT
american_scientific_journal-7274	60	1	definition	definition	NOUN
american_scientific_journal-7274	60	2	2.1.2	2.1.2	NUM
american_scientific_journal-7274	60	3	.	.	PUNCT
american_scientific_journal-7274	61	1	[	[	X
american_scientific_journal-7274	61	2	20,21	20,21	NUM
american_scientific_journal-7274	61	3	]	]	X
american_scientific_journal-7274	61	4	:	:	PUNCT
american_scientific_journal-7274	61	5	a	a	DET
american_scientific_journal-7274	61	6	dcf	dcf	NOUN
american_scientific_journal-7274	61	7	can	can	AUX
american_scientific_journal-7274	61	8	be	be	AUX
american_scientific_journal-7274	61	9	defined	define	VERB
american_scientific_journal-7274	61	10	as	as	ADP
american_scientific_journal-7274	61	11	a	a	DET
american_scientific_journal-7274	61	12	function	function	NOUN
american_scientific_journal-7274	61	13	with	with	ADP
american_scientific_journal-7274	61	14	integer	integer	NOUN
american_scientific_journal-7274	61	15	values	value	NOUN
american_scientific_journal-7274	61	16	of	of	ADP
american_scientific_journal-7274	61	17	digital	digital	ADJ
american_scientific_journal-7274	61	18	points	point	NOUN
american_scientific_journal-7274	61	19	are	be	AUX
american_scientific_journal-7274	61	20	the	the	DET
american_scientific_journal-7274	61	21	same	same	ADJ
american_scientific_journal-7274	61	22	as	as	ADP
american_scientific_journal-7274	61	23	its	its	PRON
american_scientific_journal-7274	61	24	neighbor	neighbor	NOUN
american_scientific_journal-7274	61	25	or	or	CCONJ
american_scientific_journal-7274	61	26	differ	differ	VERB
american_scientific_journal-7274	61	27	by	by	ADP
american_scientific_journal-7274	61	28	at	at	ADV
american_scientific_journal-7274	61	29	most	most	ADV
american_scientific_journal-7274	61	30	1	1	NUM
american_scientific_journal-7274	61	31	.	.	PUNCT
american_scientific_journal-7274	61	32	american	american	ADJ
american_scientific_journal-7274	61	33	academic	academic	ADJ
american_scientific_journal-7274	61	34	scientific	scientific	ADJ
american_scientific_journal-7274	61	35	research	research	NOUN
american_scientific_journal-7274	61	36	journal	journal	NOUN
american_scientific_journal-7274	61	37	for	for	ADP
american_scientific_journal-7274	61	38	engineering	engineering	NOUN
american_scientific_journal-7274	61	39	,	,	PUNCT
american_scientific_journal-7274	61	40	technology	technology	NOUN
american_scientific_journal-7274	61	41	,	,	PUNCT
american_scientific_journal-7274	61	42	and	and	CCONJ
american_scientific_journal-7274	61	43	sciences	science	NOUN
american_scientific_journal-7274	61	44	(	(	PUNCT
american_scientific_journal-7274	61	45	asrjets	asrjet	NOUN
american_scientific_journal-7274	61	46	)	)	PUNCT
american_scientific_journal-7274	61	47	(	(	PUNCT
american_scientific_journal-7274	61	48	2021	2021	NUM
american_scientific_journal-7274	61	49	)	)	PUNCT
american_scientific_journal-7274	61	50	volume	volume	NOUN
american_scientific_journal-7274	61	51	84	84	NUM
american_scientific_journal-7274	61	52	,	,	PUNCT
american_scientific_journal-7274	61	53	no1	no1	PROPN
american_scientific_journal-7274	61	54	,	,	PUNCT
american_scientific_journal-7274	61	55	pp	pp	ADP
american_scientific_journal-7274	61	56	118	118	NUM
american_scientific_journal-7274	61	57	-	-	SYM
american_scientific_journal-7274	61	58	129	129	NUM
american_scientific_journal-7274	61	59	120	120	NUM
american_scientific_journal-7274	61	60	let	let	VERB
american_scientific_journal-7274	61	61	𝑓	𝑓	PRON
american_scientific_journal-7274	61	62	:	:	PUNCT
american_scientific_journal-7274	61	63	∑𝑘	∑𝑘	PROPN
american_scientific_journal-7274	61	64	→	→	SYM
american_scientific_journal-7274	61	65	{	{	PUNCT
american_scientific_journal-7274	61	66	…	…	PUNCT
american_scientific_journal-7274	61	67	,	,	PUNCT
american_scientific_journal-7274	61	68	1,2,3	1,2,3	NUM
american_scientific_journal-7274	61	69	,	,	PUNCT
american_scientific_journal-7274	61	70	…	…	PUNCT
american_scientific_journal-7274	61	71	}	}	PUNCT
american_scientific_journal-7274	61	72	be	be	AUX
american_scientific_journal-7274	61	73	a	a	DET
american_scientific_journal-7274	61	74	digital	digital	ADJ
american_scientific_journal-7274	61	75	function	function	NOUN
american_scientific_journal-7274	61	76	and	and	CCONJ
american_scientific_journal-7274	61	77	x	x	NOUN
american_scientific_journal-7274	61	78	,	,	PUNCT
american_scientific_journal-7274	61	79	y	y	PROPN
american_scientific_journal-7274	61	80	be	be	VERB
american_scientific_journal-7274	61	81	two	two	NUM
american_scientific_journal-7274	61	82	close	close	ADJ
american_scientific_journal-7274	61	83	points	point	NOUN
american_scientific_journal-7274	61	84	in	in	ADP
american_scientific_journal-7274	61	85	∑2	∑2	PROPN
american_scientific_journal-7274	61	86	.	.	PUNCT
american_scientific_journal-7274	62	1	if	if	SCONJ
american_scientific_journal-7274	62	2	|	|	ADV
american_scientific_journal-7274	62	3	𝑓(𝑥	𝑓(𝑥	VERB
american_scientific_journal-7274	62	4	)	)	PUNCT
american_scientific_journal-7274	62	5	−	−	NOUN
american_scientific_journal-7274	62	6	𝑓(𝑦)|	𝑓(𝑦)|	ADP
american_scientific_journal-7274	62	7	≤	≤	ADV
american_scientific_journal-7274	62	8	1	1	NUM
american_scientific_journal-7274	62	9	,	,	PUNCT
american_scientific_journal-7274	62	10	then	then	ADV
american_scientific_journal-7274	62	11	we	we	PRON
american_scientific_journal-7274	62	12	say	say	VERB
american_scientific_journal-7274	62	13	that	that	SCONJ
american_scientific_journal-7274	62	14	f	f	PROPN
american_scientific_journal-7274	62	15	is	be	AUX
american_scientific_journal-7274	62	16	a	a	DET
american_scientific_journal-7274	62	17	dcf	dcf	PROPN
american_scientific_journal-7274	62	18	.	.	PUNCT
american_scientific_journal-7274	63	1	proposition	proposition	NOUN
american_scientific_journal-7274	63	2	2.1.1	2.1.1	NUM
american_scientific_journal-7274	63	3	.	.	PUNCT
american_scientific_journal-7274	64	1	[	[	X
american_scientific_journal-7274	64	2	20,21	20,21	NUM
american_scientific_journal-7274	64	3	]	]	X
american_scientific_journal-7274	64	4	:	:	PUNCT
american_scientific_journal-7274	64	5	any	any	DET
american_scientific_journal-7274	64	6	dcf	dcf	NOUN
american_scientific_journal-7274	64	7	is	be	AUX
american_scientific_journal-7274	64	8	a	a	DET
american_scientific_journal-7274	64	9	lipschitz	lipschitz	NOUN
american_scientific_journal-7274	64	10	function	function	NOUN
american_scientific_journal-7274	64	11	.	.	PUNCT
american_scientific_journal-7274	65	1	because	because	SCONJ
american_scientific_journal-7274	65	2	|	|	ADV
american_scientific_journal-7274	65	3	𝑓(𝑥	𝑓(𝑥	NOUN
american_scientific_journal-7274	65	4	)	)	PUNCT
american_scientific_journal-7274	65	5	−	−	NOUN
american_scientific_journal-7274	65	6	𝑓(𝑦)|	𝑓(𝑦)|	ADP
american_scientific_journal-7274	65	7	≤	≤	X
american_scientific_journal-7274	65	8	𝑑(𝑥	𝑑(𝑥	PROPN
american_scientific_journal-7274	65	9	,	,	PUNCT
american_scientific_journal-7274	65	10	𝑦	𝑦	NOUN
american_scientific_journal-7274	65	11	)	)	PUNCT
american_scientific_journal-7274	65	12	is	be	AUX
american_scientific_journal-7274	65	13	satisfied	satisfied	ADJ
american_scientific_journal-7274	65	14	.	.	PUNCT
american_scientific_journal-7274	66	1	2.2	2.2	NUM
american_scientific_journal-7274	66	2	.	.	PUNCT
american_scientific_journal-7274	66	3	gradually	gradually	ADV
american_scientific_journal-7274	66	4	varied	varied	ADJ
american_scientific_journal-7274	66	5	function	function	NOUN
american_scientific_journal-7274	66	6	(	(	PUNCT
american_scientific_journal-7274	66	7	gvf	gvf	NOUN
american_scientific_journal-7274	66	8	)	)	PUNCT
american_scientific_journal-7274	66	9	[	[	X
american_scientific_journal-7274	66	10	20	20	NUM
american_scientific_journal-7274	66	11	]	]	X
american_scientific_journal-7274	66	12	gvf	gvf	NOUN
american_scientific_journal-7274	66	13	was	be	AUX
american_scientific_journal-7274	66	14	proposed	propose	VERB
american_scientific_journal-7274	66	15	by	by	ADP
american_scientific_journal-7274	66	16	chen	chen	PROPN
american_scientific_journal-7274	66	17	in	in	ADP
american_scientific_journal-7274	66	18	discrete	discrete	ADJ
american_scientific_journal-7274	66	19	and	and	CCONJ
american_scientific_journal-7274	66	20	digital	digital	ADJ
american_scientific_journal-7274	66	21	spaces	space	NOUN
american_scientific_journal-7274	66	22	[	[	X
american_scientific_journal-7274	66	23	20,22,30	20,22,30	NUM
american_scientific_journal-7274	66	24	]	]	PUNCT
american_scientific_journal-7274	66	25	.	.	PUNCT
american_scientific_journal-7274	67	1	𝐴1	𝐴1	PROPN
american_scientific_journal-7274	67	2	,	,	PUNCT
american_scientific_journal-7274	67	3	𝐴2,	𝐴2,	NOUN
american_scientific_journal-7274	67	4	…	…	X
american_scientific_journal-7274	67	5	.,𝐴𝑚	.,𝐴𝑚	PUNCT
american_scientific_journal-7274	67	6	∈	∈	PROPN
american_scientific_journal-7274	67	7	ℝ	ℝ	PROPN
american_scientific_journal-7274	67	8	,	,	PUNCT
american_scientific_journal-7274	67	9	𝐴1	𝐴1	PROPN
american_scientific_journal-7274	67	10	<	<	X
american_scientific_journal-7274	67	11	𝐴2	𝐴2	PROPN
american_scientific_journal-7274	67	12	<	<	X
american_scientific_journal-7274	67	13	⋯	⋯	X
american_scientific_journal-7274	67	14	<	<	X
american_scientific_journal-7274	67	15	𝐴𝑚	𝐴𝑚	PROPN
american_scientific_journal-7274	67	16	and	and	CCONJ
american_scientific_journal-7274	67	17	𝑝	𝑝	PROPN
american_scientific_journal-7274	67	18	,	,	PUNCT
american_scientific_journal-7274	67	19	𝑞	𝑞	PROPN
american_scientific_journal-7274	67	20	∈	∈	PROPN
american_scientific_journal-7274	67	21	∑2	∑2	PROPN
american_scientific_journal-7274	67	22	are	be	AUX
american_scientific_journal-7274	67	23	given	give	VERB
american_scientific_journal-7274	67	24	.	.	PUNCT
american_scientific_journal-7274	68	1	let	let	VERB
american_scientific_journal-7274	68	2	𝑓	𝑓	PRON
american_scientific_journal-7274	68	3	:	:	PUNCT
american_scientific_journal-7274	68	4	∑2(𝑜𝑟	∑2(𝑜𝑟	INTJ
american_scientific_journal-7274	68	5	𝑎𝑛𝑜𝑡ℎ𝑒𝑟	𝑎𝑛𝑜𝑡ℎ𝑒𝑟	PROPN
american_scientific_journal-7274	68	6	𝑑𝑖𝑠𝑐𝑟𝑒𝑡𝑒	𝑑𝑖𝑠𝑐𝑟𝑒𝑡𝑒	PROPN
american_scientific_journal-7274	68	7	𝑠𝑝𝑎𝑐𝑒	𝑠𝑝𝑎𝑐𝑒	ADV
american_scientific_journal-7274	68	8	)	)	PUNCT
american_scientific_journal-7274	68	9	→	→	SYM
american_scientific_journal-7274	68	10	{	{	PUNCT
american_scientific_journal-7274	68	11	𝐴1	𝐴1	PROPN
american_scientific_journal-7274	68	12	,	,	PUNCT
american_scientific_journal-7274	68	13	𝐴2,	𝐴2,	NOUN
american_scientific_journal-7274	68	14	…	…	X
american_scientific_journal-7274	68	15	.,𝐴𝑚	.,𝐴𝑚	ADJ
american_scientific_journal-7274	68	16	}	}	PUNCT
american_scientific_journal-7274	68	17	be	be	VERB
american_scientific_journal-7274	68	18	a	a	DET
american_scientific_journal-7274	68	19	function	function	NOUN
american_scientific_journal-7274	68	20	.	.	PUNCT
american_scientific_journal-7274	69	1	if	if	SCONJ
american_scientific_journal-7274	69	2	𝑓(𝑝	𝑓(𝑝	PROPN
american_scientific_journal-7274	69	3	)	)	PUNCT
american_scientific_journal-7274	69	4	=	=	SYM
american_scientific_journal-7274	69	5	𝐴𝑖	𝐴𝑖	PROPN
american_scientific_journal-7274	69	6	and	and	CCONJ
american_scientific_journal-7274	69	7	𝑓(𝑞	𝑓(𝑞	NOUN
american_scientific_journal-7274	69	8	)	)	PUNCT
american_scientific_journal-7274	70	1	=	=	PUNCT
american_scientific_journal-7274	71	1	𝐴𝑗	𝐴𝑗	PROPN
american_scientific_journal-7274	71	2	,	,	PUNCT
american_scientific_journal-7274	71	3	then	then	ADV
american_scientific_journal-7274	71	4	level	level	NOUN
american_scientific_journal-7274	71	5	difference	difference	NOUN
american_scientific_journal-7274	71	6	is	be	AUX
american_scientific_journal-7274	71	7	|	|	ADV
american_scientific_journal-7274	71	8	i	i	PROPN
american_scientific_journal-7274	71	9	-	-	PUNCT
american_scientific_journal-7274	71	10	j	j	PROPN
american_scientific_journal-7274	71	11	|	|	ADV
american_scientific_journal-7274	71	12	between	between	ADP
american_scientific_journal-7274	71	13	f(p	f(p	PROPN
american_scientific_journal-7274	71	14	)	)	PUNCT
american_scientific_journal-7274	71	15	and	and	CCONJ
american_scientific_journal-7274	71	16	f(q	f(q	NOUN
american_scientific_journal-7274	71	17	)	)	PUNCT
american_scientific_journal-7274	71	18	.	.	PUNCT
american_scientific_journal-7274	72	1	the	the	DET
american_scientific_journal-7274	72	2	gvf	gvf	PROPN
american_scientific_journal-7274	72	3	can	can	AUX
american_scientific_journal-7274	72	4	be	be	AUX
american_scientific_journal-7274	72	5	defined	define	VERB
american_scientific_journal-7274	72	6	as	as	ADP
american_scientific_journal-7274	72	7	follows	follow	VERB
american_scientific_journal-7274	72	8	.	.	PUNCT
american_scientific_journal-7274	73	1	definition	definition	NOUN
american_scientific_journal-7274	73	2	2.2.1	2.2.1	NUM
american_scientific_journal-7274	73	3	.	.	PUNCT
american_scientific_journal-7274	74	1	[	[	X
american_scientific_journal-7274	74	2	20,22,30	20,22,30	NUM
american_scientific_journal-7274	74	3	]	]	X
american_scientific_journal-7274	74	4	:	:	PUNCT
american_scientific_journal-7274	74	5	for	for	ADP
american_scientific_journal-7274	74	6	any	any	DET
american_scientific_journal-7274	74	7	p	p	NOUN
american_scientific_journal-7274	74	8	,	,	PUNCT
american_scientific_journal-7274	74	9	q	q	ADJ
american_scientific_journal-7274	74	10	close	close	ADJ
american_scientific_journal-7274	74	11	pair	pair	NOUN
american_scientific_journal-7274	74	12	in	in	ADP
american_scientific_journal-7274	74	13	∑2	∑2	PROPN
american_scientific_journal-7274	74	14	,	,	PUNCT
american_scientific_journal-7274	74	15	if	if	SCONJ
american_scientific_journal-7274	74	16	𝑓(𝑝	𝑓(𝑝	PROPN
american_scientific_journal-7274	74	17	)	)	PUNCT
american_scientific_journal-7274	74	18	=	=	SYM
american_scientific_journal-7274	74	19	𝐴𝑖	𝐴𝑖	PROPN
american_scientific_journal-7274	74	20	and	and	CCONJ
american_scientific_journal-7274	74	21	𝑓(𝑞	𝑓(𝑞	NOUN
american_scientific_journal-7274	74	22	)	)	PUNCT
american_scientific_journal-7274	75	1	=	=	SYM
american_scientific_journal-7274	75	2	𝐴𝑖−1	𝐴𝑖−1	PROPN
american_scientific_journal-7274	75	3	,	,	PUNCT
american_scientific_journal-7274	75	4	𝐴𝑖	𝐴𝑖	PROPN
american_scientific_journal-7274	75	5	𝑜𝑟	𝑜𝑟	NOUN
american_scientific_journal-7274	75	6	𝐴𝑖+1	𝐴𝑖+1	NOUN
american_scientific_journal-7274	75	7	,	,	PUNCT
american_scientific_journal-7274	75	8	then	then	ADV
american_scientific_journal-7274	75	9	f	f	PROPN
american_scientific_journal-7274	75	10	is	be	AUX
american_scientific_journal-7274	75	11	gvf	gvf	ADJ
american_scientific_journal-7274	75	12	on	on	ADP
american_scientific_journal-7274	75	13	p	p	PROPN
american_scientific_journal-7274	75	14	and	and	CCONJ
american_scientific_journal-7274	75	15	q.	q.	PROPN
american_scientific_journal-7274	75	16	definition	definition	NOUN
american_scientific_journal-7274	75	17	2.2.2	2.2.2	NUM
american_scientific_journal-7274	75	18	.	.	PUNCT
american_scientific_journal-7274	76	1	[	[	X
american_scientific_journal-7274	76	2	20,22,30	20,22,30	NUM
american_scientific_journal-7274	76	3	]	]	X
american_scientific_journal-7274	76	4	:	:	PUNCT
american_scientific_journal-7274	76	5	if	if	SCONJ
american_scientific_journal-7274	76	6	f	f	PROPN
american_scientific_journal-7274	76	7	is	be	AUX
american_scientific_journal-7274	76	8	gvf	gvf	ADJ
american_scientific_journal-7274	76	9	on	on	ADP
american_scientific_journal-7274	76	10	any	any	DET
american_scientific_journal-7274	76	11	p	p	NOUN
american_scientific_journal-7274	76	12	,	,	PUNCT
american_scientific_journal-7274	76	13	q	q	ADJ
american_scientific_journal-7274	76	14	close	close	ADJ
american_scientific_journal-7274	76	15	pair	pair	NOUN
american_scientific_journal-7274	76	16	in	in	ADP
american_scientific_journal-7274	76	17	∑2	∑2	PROPN
american_scientific_journal-7274	76	18	,	,	PUNCT
american_scientific_journal-7274	76	19	then	then	ADV
american_scientific_journal-7274	76	20	f	f	PROPN
american_scientific_journal-7274	76	21	is	be	AUX
american_scientific_journal-7274	76	22	gvf	gvf	PROPN
american_scientific_journal-7274	76	23	.	.	PUNCT
american_scientific_journal-7274	76	24	theorem	theorem	VERB
american_scientific_journal-7274	76	25	2.2.1	2.2.1	NUM
american_scientific_journal-7274	76	26	.	.	PUNCT
american_scientific_journal-7274	77	1	[	[	X
american_scientific_journal-7274	77	2	20,22,30	20,22,30	NUM
american_scientific_journal-7274	77	3	]	]	PUNCT
american_scientific_journal-7274	77	4	:	:	PUNCT
american_scientific_journal-7274	77	5	let	let	VERB
american_scientific_journal-7274	77	6	p	p	PRON
american_scientific_journal-7274	77	7	,	,	PUNCT
american_scientific_journal-7274	77	8	q	q	ADJ
american_scientific_journal-7274	77	9	be	be	AUX
american_scientific_journal-7274	77	10	points	point	NOUN
american_scientific_journal-7274	77	11	in	in	ADP
american_scientific_journal-7274	77	12	j	j	PROPN
american_scientific_journal-7274	77	13	,	,	PUNCT
american_scientific_journal-7274	77	14	if	if	SCONJ
american_scientific_journal-7274	77	15	a	a	DET
american_scientific_journal-7274	77	16	gradually	gradually	ADV
american_scientific_journal-7274	77	17	varied	varied	ADJ
american_scientific_journal-7274	77	18	interpolation	interpolation	NOUN
american_scientific_journal-7274	77	19	exists	exist	VERB
american_scientific_journal-7274	77	20	,	,	PUNCT
american_scientific_journal-7274	77	21	then	then	ADV
american_scientific_journal-7274	77	22	length	length	NOUN
american_scientific_journal-7274	77	23	of	of	ADP
american_scientific_journal-7274	77	24	the	the	DET
american_scientific_journal-7274	77	25	shortest	short	ADJ
american_scientific_journal-7274	77	26	path	path	NOUN
american_scientific_journal-7274	77	27	in	in	ADP
american_scientific_journal-7274	77	28	d	d	NOUN
american_scientific_journal-7274	77	29	between	between	ADP
american_scientific_journal-7274	77	30	p	p	NOUN
american_scientific_journal-7274	77	31	and	and	CCONJ
american_scientific_journal-7274	77	32	q	q	NOUN
american_scientific_journal-7274	77	33	is	be	AUX
american_scientific_journal-7274	77	34	not	not	PART
american_scientific_journal-7274	77	35	less	less	ADJ
american_scientific_journal-7274	77	36	than	than	ADP
american_scientific_journal-7274	77	37	level	level	NOUN
american_scientific_journal-7274	77	38	difference	difference	NOUN
american_scientific_journal-7274	77	39	between	between	ADP
american_scientific_journal-7274	77	40	f(p	f(p	PROPN
american_scientific_journal-7274	77	41	)	)	PUNCT
american_scientific_journal-7274	77	42	and	and	CCONJ
american_scientific_journal-7274	77	43	f(q	f(q	NOUN
american_scientific_journal-7274	77	44	)	)	PUNCT
american_scientific_journal-7274	77	45	.	.	PUNCT
american_scientific_journal-7274	78	1	gradually	gradually	ADV
american_scientific_journal-7274	78	2	varied	varied	ADJ
american_scientific_journal-7274	78	3	function	function	NOUN
american_scientific_journal-7274	78	4	(	(	PUNCT
american_scientific_journal-7274	78	5	gvf	gvf	NOUN
american_scientific_journal-7274	78	6	)	)	PUNCT
american_scientific_journal-7274	78	7	algorithm	algorithm	NOUN
american_scientific_journal-7274	79	1	[	[	X
american_scientific_journal-7274	79	2	20,31	20,31	NUM
american_scientific_journal-7274	79	3	]	]	X
american_scientific_journal-7274	79	4	:	:	PUNCT
american_scientific_journal-7274	79	5	j	j	PROPN
american_scientific_journal-7274	79	6	is	be	AUX
american_scientific_journal-7274	79	7	a	a	DET
american_scientific_journal-7274	79	8	non	non	ADJ
american_scientific_journal-7274	79	9	-	-	ADJ
american_scientific_journal-7274	79	10	empty	empty	ADJ
american_scientific_journal-7274	79	11	subset	subset	NOUN
american_scientific_journal-7274	79	12	of	of	ADP
american_scientific_journal-7274	79	13	d.	d.	PROPN
american_scientific_journal-7274	79	14	fj	fj	PROPN
american_scientific_journal-7274	79	15	is	be	AUX
american_scientific_journal-7274	79	16	a	a	DET
american_scientific_journal-7274	79	17	function	function	NOUN
american_scientific_journal-7274	79	18	defined	define	VERB
american_scientific_journal-7274	79	19	on	on	ADP
american_scientific_journal-7274	79	20	j.	j.	PROPN
american_scientific_journal-7274	79	21	step	step	PROPN
american_scientific_journal-7274	79	22	1	1	NUM
american_scientific_journal-7274	79	23	:	:	PUNCT
american_scientific_journal-7274	79	24	we	we	PRON
american_scientific_journal-7274	79	25	test	test	VERB
american_scientific_journal-7274	79	26	all	all	PRON
american_scientific_journal-7274	79	27	p	p	NOUN
american_scientific_journal-7274	79	28	and	and	CCONJ
american_scientific_journal-7274	79	29	p/	p/	NOUN
american_scientific_journal-7274	79	30	points	point	NOUN
american_scientific_journal-7274	79	31	in	in	ADP
american_scientific_journal-7274	79	32	j.	j.	PROPN
american_scientific_journal-7274	79	33	if	if	SCONJ
american_scientific_journal-7274	79	34	d(p	d(p	PROPN
american_scientific_journal-7274	79	35	,	,	PUNCT
american_scientific_journal-7274	79	36	p/	p/	NOUN
american_scientific_journal-7274	79	37	)	)	PUNCT
american_scientific_journal-7274	79	38	≥	≥	NOUN
american_scientific_journal-7274	79	39	ld(p	ld(p	NUM
american_scientific_journal-7274	79	40	,	,	PUNCT
american_scientific_journal-7274	79	41	p/	p/	NUM
american_scientific_journal-7274	79	42	)	)	PUNCT
american_scientific_journal-7274	79	43	is	be	AUX
american_scientific_journal-7274	79	44	not	not	PART
american_scientific_journal-7274	79	45	satisfied	satisfied	ADJ
american_scientific_journal-7274	79	46	,	,	PUNCT
american_scientific_journal-7274	79	47	then	then	ADV
american_scientific_journal-7274	79	48	there	there	PRON
american_scientific_journal-7274	79	49	is	be	VERB
american_scientific_journal-7274	79	50	no	no	DET
american_scientific_journal-7274	79	51	gvf	gvf	NOUN
american_scientific_journal-7274	79	52	.	.	PUNCT
american_scientific_journal-7274	80	1	take	take	VERB
american_scientific_journal-7274	80	2	d0	d0	PROPN
american_scientific_journal-7274	80	3	←	←	PROPN
american_scientific_journal-7274	80	4	j.	j.	PROPN
american_scientific_journal-7274	80	5	step	step	PROPN
american_scientific_journal-7274	80	6	2	2	NUM
american_scientific_journal-7274	80	7	:	:	PUNCT
american_scientific_journal-7274	80	8	we	we	PRON
american_scientific_journal-7274	80	9	take	take	VERB
american_scientific_journal-7274	80	10	x	x	PUNCT
american_scientific_journal-7274	80	11	from	from	ADP
american_scientific_journal-7274	80	12	d	d	X
american_scientific_journal-7274	80	13	−	−	NOUN
american_scientific_journal-7274	80	14	d0	d0	NOUN
american_scientific_journal-7274	80	15	where	where	SCONJ
american_scientific_journal-7274	80	16	x	x	PRON
american_scientific_journal-7274	80	17	has	have	VERB
american_scientific_journal-7274	80	18	an	an	DET
american_scientific_journal-7274	80	19	adjacent	adjacent	ADJ
american_scientific_journal-7274	80	20	vertex	vertex	NOUN
american_scientific_journal-7274	80	21	r	r	NOUN
american_scientific_journal-7274	80	22	in	in	ADP
american_scientific_journal-7274	80	23	d0	d0	NOUN
american_scientific_journal-7274	80	24	.	.	PUNCT
american_scientific_journal-7274	81	1	suppose	suppose	VERB
american_scientific_journal-7274	81	2	fd	fd	X
american_scientific_journal-7274	81	3	(	(	PUNCT
american_scientific_journal-7274	81	4	r	r	NOUN
american_scientific_journal-7274	81	5	)	)	PUNCT
american_scientific_journal-7274	81	6	=	=	PRON
american_scientific_journal-7274	81	7	ai	ai	VERB
american_scientific_journal-7274	81	8	.	.	NOUN
american_scientific_journal-7274	81	9	step	step	NOUN
american_scientific_journal-7274	81	10	3	3	NUM
american_scientific_journal-7274	81	11	:	:	PUNCT
american_scientific_journal-7274	81	12	we	we	PRON
american_scientific_journal-7274	81	13	take	take	VERB
american_scientific_journal-7274	81	14	fd(x	fd(x	PUNCT
american_scientific_journal-7274	81	15	)	)	PUNCT
american_scientific_journal-7274	81	16	=	=	SYM
american_scientific_journal-7274	81	17	fd(r	fd(r	NOUN
american_scientific_journal-7274	81	18	)	)	PUNCT
american_scientific_journal-7274	81	19	=	=	PRON
american_scientific_journal-7274	82	1	ai	ai	VERB
american_scientific_journal-7274	82	2	.	.	PUNCT
american_scientific_journal-7274	83	1	we	we	PRON
american_scientific_journal-7274	83	2	test	test	VERB
american_scientific_journal-7274	83	3	x	x	PUNCT
american_scientific_journal-7274	83	4	against	against	ADP
american_scientific_journal-7274	83	5	every	every	DET
american_scientific_journal-7274	83	6	vertex	vertex	NOUN
american_scientific_journal-7274	83	7	p	p	NOUN
american_scientific_journal-7274	83	8	in	in	ADP
american_scientific_journal-7274	83	9	d0	d0	NOUN
american_scientific_journal-7274	83	10	:	:	PUNCT
american_scientific_journal-7274	83	11	if	if	SCONJ
american_scientific_journal-7274	83	12	there	there	PRON
american_scientific_journal-7274	83	13	is	be	VERB
american_scientific_journal-7274	83	14	a	a	DET
american_scientific_journal-7274	83	15	p∈	p∈	PROPN
american_scientific_journal-7274	83	16	d0	d0	NOUN
american_scientific_journal-7274	83	17	when	when	SCONJ
american_scientific_journal-7274	83	18	d(x	d(x	PROPN
american_scientific_journal-7274	83	19	,	,	PUNCT
american_scientific_journal-7274	83	20	p	p	NOUN
american_scientific_journal-7274	83	21	)	)	PUNCT
american_scientific_journal-7274	83	22	<	<	X
american_scientific_journal-7274	83	23	ld(x	ld(x	X
american_scientific_journal-7274	83	24	,	,	PUNCT
american_scientific_journal-7274	83	25	p	p	NOUN
american_scientific_journal-7274	83	26	)	)	PUNCT
american_scientific_journal-7274	83	27	,	,	PUNCT
american_scientific_journal-7274	83	28	change	change	NOUN
american_scientific_journal-7274	83	29	fd(x	fd(x	PUNCT
american_scientific_journal-7274	83	30	)	)	PUNCT
american_scientific_journal-7274	83	31	to	to	ADP
american_scientific_journal-7274	83	32	ai−1	ai−1	PROPN
american_scientific_journal-7274	83	33	when	when	SCONJ
american_scientific_journal-7274	83	34	fd(p	fd(p	PUNCT
american_scientific_journal-7274	83	35	)	)	PUNCT
american_scientific_journal-7274	83	36	<	<	X
american_scientific_journal-7274	83	37	ai	ai	VERB
american_scientific_journal-7274	83	38	or	or	CCONJ
american_scientific_journal-7274	83	39	change	change	VERB
american_scientific_journal-7274	83	40	fd(x	fd(x	PUNCT
american_scientific_journal-7274	83	41	)	)	PUNCT
american_scientific_journal-7274	83	42	to	to	ADP
american_scientific_journal-7274	83	43	ai+1	ai+1	NUM
american_scientific_journal-7274	83	44	when	when	SCONJ
american_scientific_journal-7274	83	45	fd(p	fd(p	PUNCT
american_scientific_journal-7274	83	46	)	)	PUNCT
american_scientific_journal-7274	83	47	>	>	X
american_scientific_journal-7274	83	48	ai	ai	VERB
american_scientific_journal-7274	83	49	.	.	PROPN
american_scientific_journal-7274	84	1	step	step	NOUN
american_scientific_journal-7274	84	2	4	4	NUM
american_scientific_journal-7274	84	3	:	:	PUNCT
american_scientific_journal-7274	84	4	let	let	VERB
american_scientific_journal-7274	84	5	d0	d0	PROPN
american_scientific_journal-7274	84	6	←	←	PROPN
american_scientific_journal-7274	84	7	d0	d0	PROPN
american_scientific_journal-7274	84	8	∪	∪	VERB
american_scientific_journal-7274	84	9	{	{	PUNCT
american_scientific_journal-7274	84	10	x	x	NOUN
american_scientific_journal-7274	84	11	}	}	PUNCT
american_scientific_journal-7274	84	12	.	.	PUNCT
american_scientific_journal-7274	85	1	step	step	NOUN
american_scientific_journal-7274	85	2	5	5	NUM
american_scientific_journal-7274	85	3	:	:	PUNCT
american_scientific_journal-7274	85	4	we	we	PRON
american_scientific_journal-7274	85	5	repeat	repeat	VERB
american_scientific_journal-7274	85	6	2–4	2–4	NUM
american_scientific_journal-7274	85	7	until	until	ADP
american_scientific_journal-7274	85	8	d0	d0	NOUN
american_scientific_journal-7274	85	9	=	=	SYM
american_scientific_journal-7274	85	10	d.	d.	PROPN
american_scientific_journal-7274	85	11	american	american	PROPN
american_scientific_journal-7274	85	12	academic	academic	PROPN
american_scientific_journal-7274	85	13	scientific	scientific	ADJ
american_scientific_journal-7274	85	14	research	research	NOUN
american_scientific_journal-7274	85	15	journal	journal	NOUN
american_scientific_journal-7274	85	16	for	for	ADP
american_scientific_journal-7274	85	17	engineering	engineering	NOUN
american_scientific_journal-7274	85	18	,	,	PUNCT
american_scientific_journal-7274	85	19	technology	technology	NOUN
american_scientific_journal-7274	85	20	,	,	PUNCT
american_scientific_journal-7274	85	21	and	and	CCONJ
american_scientific_journal-7274	85	22	sciences	science	NOUN
american_scientific_journal-7274	85	23	(	(	PUNCT
american_scientific_journal-7274	85	24	asrjets	asrjet	NOUN
american_scientific_journal-7274	85	25	)	)	PUNCT
american_scientific_journal-7274	85	26	(	(	PUNCT
american_scientific_journal-7274	85	27	2021	2021	NUM
american_scientific_journal-7274	85	28	)	)	PUNCT
american_scientific_journal-7274	85	29	volume	volume	NOUN
american_scientific_journal-7274	85	30	84	84	NUM
american_scientific_journal-7274	85	31	,	,	PUNCT
american_scientific_journal-7274	85	32	no1	no1	PROPN
american_scientific_journal-7274	85	33	,	,	PUNCT
american_scientific_journal-7274	85	34	pp	pp	ADP
american_scientific_journal-7274	85	35	118	118	NUM
american_scientific_journal-7274	85	36	-	-	SYM
american_scientific_journal-7274	85	37	129	129	NUM
american_scientific_journal-7274	85	38	121	121	NUM
american_scientific_journal-7274	85	39	3	3	NUM
american_scientific_journal-7274	85	40	.	.	PUNCT
american_scientific_journal-7274	85	41	digital	digital	ADJ
american_scientific_journal-7274	85	42	-	-	PUNCT
american_scientific_journal-7274	85	43	discrete	discrete	ADJ
american_scientific_journal-7274	85	44	method	method	NOUN
american_scientific_journal-7274	85	45	for	for	ADP
american_scientific_journal-7274	85	46	perona	perona	NOUN
american_scientific_journal-7274	85	47	-	-	PUNCT
american_scientific_journal-7274	85	48	malik	malik	PROPN
american_scientific_journal-7274	85	49	equation	equation	NOUN
american_scientific_journal-7274	85	50	3.1	3.1	NUM
american_scientific_journal-7274	85	51	.	.	PUNCT
american_scientific_journal-7274	85	52	perona	perona	PROPN
american_scientific_journal-7274	85	53	-	-	PUNCT
american_scientific_journal-7274	85	54	malik	malik	PROPN
american_scientific_journal-7274	85	55	equation	equation	NOUN
american_scientific_journal-7274	86	1	[	[	X
american_scientific_journal-7274	86	2	32,33	32,33	X
american_scientific_journal-7274	86	3	]	]	X
american_scientific_journal-7274	86	4	the	the	DET
american_scientific_journal-7274	86	5	main	main	ADJ
american_scientific_journal-7274	86	6	purpose	purpose	NOUN
american_scientific_journal-7274	86	7	of	of	ADP
american_scientific_journal-7274	86	8	nonlinear	nonlinear	ADJ
american_scientific_journal-7274	86	9	diffusion	diffusion	NOUN
american_scientific_journal-7274	86	10	models	model	NOUN
american_scientific_journal-7274	86	11	is	be	AUX
american_scientific_journal-7274	86	12	to	to	PART
american_scientific_journal-7274	86	13	create	create	VERB
american_scientific_journal-7274	86	14	a	a	DET
american_scientific_journal-7274	86	15	measure	measure	NOUN
american_scientific_journal-7274	86	16	for	for	ADP
american_scientific_journal-7274	86	17	the	the	DET
american_scientific_journal-7274	86	18	preservation	preservation	NOUN
american_scientific_journal-7274	86	19	and	and	CCONJ
american_scientific_journal-7274	86	20	enhancement	enhancement	NOUN
american_scientific_journal-7274	86	21	of	of	ADP
american_scientific_journal-7274	86	22	edges	edge	NOUN
american_scientific_journal-7274	86	23	with	with	ADP
american_scientific_journal-7274	86	24	images	image	NOUN
american_scientific_journal-7274	86	25	.	.	PUNCT
american_scientific_journal-7274	87	1	the	the	DET
american_scientific_journal-7274	87	2	most	most	ADV
american_scientific_journal-7274	87	3	important	important	ADJ
american_scientific_journal-7274	87	4	tools	tool	NOUN
american_scientific_journal-7274	87	5	for	for	ADP
american_scientific_journal-7274	87	6	this	this	PRON
american_scientific_journal-7274	87	7	are	be	AUX
american_scientific_journal-7274	87	8	nonlinear	nonlinear	ADJ
american_scientific_journal-7274	87	9	partial	partial	ADJ
american_scientific_journal-7274	87	10	differential	differential	NOUN
american_scientific_journal-7274	87	11	equations	equation	NOUN
american_scientific_journal-7274	87	12	.	.	PUNCT
american_scientific_journal-7274	88	1	the	the	DET
american_scientific_journal-7274	88	2	first	first	ADJ
american_scientific_journal-7274	88	3	nonlinear	nonlinear	ADJ
american_scientific_journal-7274	88	4	diffusion	diffusion	NOUN
american_scientific_journal-7274	88	5	model	model	NOUN
american_scientific_journal-7274	88	6	used	use	VERB
american_scientific_journal-7274	88	7	in	in	ADP
american_scientific_journal-7274	88	8	image	image	NOUN
american_scientific_journal-7274	88	9	processing	processing	NOUN
american_scientific_journal-7274	88	10	is	be	AUX
american_scientific_journal-7274	88	11	called	call	VERB
american_scientific_journal-7274	88	12	anisotropic	anisotropic	NOUN
american_scientific_journal-7274	88	13	diffusion	diffusion	NOUN
american_scientific_journal-7274	88	14	.	.	PUNCT
american_scientific_journal-7274	89	1	the	the	DET
american_scientific_journal-7274	89	2	anisotropic	anisotropic	NOUN
american_scientific_journal-7274	89	3	diffusion	diffusion	NOUN
american_scientific_journal-7274	89	4	model	model	NOUN
american_scientific_journal-7274	89	5	was	be	AUX
american_scientific_journal-7274	89	6	first	first	ADV
american_scientific_journal-7274	89	7	proposed	propose	VERB
american_scientific_journal-7274	89	8	by	by	ADP
american_scientific_journal-7274	89	9	perona	perona	NOUN
american_scientific_journal-7274	89	10	and	and	CCONJ
american_scientific_journal-7274	89	11	malik	malik	PROPN
american_scientific_journal-7274	90	1	[	[	X
american_scientific_journal-7274	90	2	34	34	NUM
american_scientific_journal-7274	90	3	]	]	PUNCT
american_scientific_journal-7274	90	4	.	.	PUNCT
american_scientific_journal-7274	91	1	the	the	DET
american_scientific_journal-7274	91	2	perona	perona	PROPN
american_scientific_journal-7274	91	3	-	-	PUNCT
american_scientific_journal-7274	91	4	malik	malik	PROPN
american_scientific_journal-7274	91	5	equation	equation	NOUN
american_scientific_journal-7274	91	6	is	be	AUX
american_scientific_journal-7274	91	7	as	as	SCONJ
american_scientific_journal-7274	91	8	follows	follow	VERB
american_scientific_journal-7274	91	9	[	[	X
american_scientific_journal-7274	91	10	32,33,34	32,33,34	NUM
american_scientific_journal-7274	91	11	]	]	X
american_scientific_journal-7274	91	12	:	:	PUNCT
american_scientific_journal-7274	91	13	𝜕𝑢	𝜕𝑢	NOUN
american_scientific_journal-7274	91	14	𝜕𝑡	𝜕𝑡	NOUN
american_scientific_journal-7274	91	15	=	=	NOUN
american_scientific_journal-7274	91	16	𝑑𝑖𝑣(𝑔‖∇𝑢‖∇𝑢	𝑑𝑖𝑣(𝑔‖∇𝑢‖∇𝑢	NOUN
american_scientific_journal-7274	91	17	)	)	PUNCT
american_scientific_journal-7274	91	18	,	,	PUNCT
american_scientific_journal-7274	91	19	𝑡	𝑡	PROPN
american_scientific_journal-7274	91	20	≥	≥	NOUN
american_scientific_journal-7274	91	21	0	0	NUM
american_scientific_journal-7274	91	22	,	,	PUNCT
american_scientific_journal-7274	91	23	𝑥	𝑥	PRON
american_scientific_journal-7274	91	24	∈	∈	PROPN
american_scientific_journal-7274	91	25	ω	ω	NUM
american_scientific_journal-7274	91	26	𝑢0(𝑥	𝑢0(𝑥	NUM
american_scientific_journal-7274	91	27	)	)	PUNCT
american_scientific_journal-7274	91	28	=	=	SYM
american_scientific_journal-7274	91	29	𝑓(𝑥	𝑓(𝑥	NOUN
american_scientific_journal-7274	91	30	)	)	PUNCT
american_scientific_journal-7274	91	31	(	(	PUNCT
american_scientific_journal-7274	91	32	3.1.1	3.1.1	X
american_scientific_journal-7274	91	33	)	)	PUNCT
american_scientific_journal-7274	91	34	the	the	DET
american_scientific_journal-7274	91	35	perona	perona	NOUN
american_scientific_journal-7274	91	36	-	-	PUNCT
american_scientific_journal-7274	91	37	malik	malik	PROPN
american_scientific_journal-7274	91	38	equation	equation	NOUN
american_scientific_journal-7274	91	39	has	have	AUX
american_scientific_journal-7274	91	40	been	be	AUX
american_scientific_journal-7274	91	41	used	use	VERB
american_scientific_journal-7274	91	42	for	for	ADP
american_scientific_journal-7274	91	43	multiple	multiple	ADJ
american_scientific_journal-7274	91	44	scaling	scaling	NOUN
american_scientific_journal-7274	91	45	,	,	PUNCT
american_scientific_journal-7274	91	46	enhancement	enhancement	NOUN
american_scientific_journal-7274	91	47	and	and	CCONJ
american_scientific_journal-7274	91	48	splitting	splitting	NOUN
american_scientific_journal-7274	91	49	of	of	ADP
american_scientific_journal-7274	91	50	images	image	NOUN
american_scientific_journal-7274	91	51	.	.	PUNCT
american_scientific_journal-7274	92	1	in	in	ADP
american_scientific_journal-7274	92	2	equation	equation	NOUN
american_scientific_journal-7274	92	3	(	(	PUNCT
american_scientific_journal-7274	92	4	3.1.1	3.1.1	NUM
american_scientific_journal-7274	92	5	)	)	PUNCT
american_scientific_journal-7274	92	6	,	,	PUNCT
american_scientific_journal-7274	92	7	div	div	X
american_scientific_journal-7274	92	8	is	be	AUX
american_scientific_journal-7274	92	9	the	the	DET
american_scientific_journal-7274	92	10	divergence	divergence	NOUN
american_scientific_journal-7274	92	11	operator	operator	NOUN
american_scientific_journal-7274	92	12	and	and	CCONJ
american_scientific_journal-7274	92	13	u	u	NOUN
american_scientific_journal-7274	92	14	is	be	AUX
american_scientific_journal-7274	92	15	the	the	DET
american_scientific_journal-7274	92	16	smooth	smooth	ADJ
american_scientific_journal-7274	92	17	image	image	NOUN
american_scientific_journal-7274	92	18	at	at	ADP
american_scientific_journal-7274	92	19	time	time	NOUN
american_scientific_journal-7274	92	20	t.	t.	NOUN
american_scientific_journal-7274	92	21	‖∇𝑢‖	‖∇𝑢‖	PROPN
american_scientific_journal-7274	92	22	is	be	AUX
american_scientific_journal-7274	92	23	the	the	DET
american_scientific_journal-7274	92	24	gradient	gradient	ADJ
american_scientific_journal-7274	92	25	length	length	NOUN
american_scientific_journal-7274	92	26	of	of	ADP
american_scientific_journal-7274	92	27	u	u	NOUN
american_scientific_journal-7274	92	28	and	and	CCONJ
american_scientific_journal-7274	92	29	𝑔‖∇𝑢‖	𝑔‖∇𝑢‖	NOUN
american_scientific_journal-7274	92	30	is	be	AUX
american_scientific_journal-7274	92	31	the	the	DET
american_scientific_journal-7274	92	32	diffusivity	diffusivity	NOUN
american_scientific_journal-7274	92	33	function	function	NOUN
american_scientific_journal-7274	92	34	.	.	PUNCT
american_scientific_journal-7274	93	1	f(x	f(x	PROPN
american_scientific_journal-7274	93	2	)	)	PUNCT
american_scientific_journal-7274	93	3	is	be	AUX
american_scientific_journal-7274	93	4	initial	initial	ADJ
american_scientific_journal-7274	93	5	image	image	NOUN
american_scientific_journal-7274	93	6	.	.	PUNCT
american_scientific_journal-7274	94	1	the	the	DET
american_scientific_journal-7274	94	2	diffusivity	diffusivity	NOUN
american_scientific_journal-7274	94	3	function	function	NOUN
american_scientific_journal-7274	94	4	g	g	PROPN
american_scientific_journal-7274	94	5	is	be	AUX
american_scientific_journal-7274	94	6	non	non	ADJ
american_scientific_journal-7274	94	7	-	-	ADJ
american_scientific_journal-7274	94	8	negative	negative	ADJ
american_scientific_journal-7274	94	9	and	and	CCONJ
american_scientific_journal-7274	94	10	monotonically	monotonically	ADV
american_scientific_journal-7274	94	11	decreasing	decrease	VERB
american_scientific_journal-7274	94	12	.	.	PUNCT
american_scientific_journal-7274	95	1	it	it	PRON
american_scientific_journal-7274	95	2	has	have	AUX
american_scientific_journal-7274	95	3	following	follow	VERB
american_scientific_journal-7274	95	4	properties	property	NOUN
american_scientific_journal-7274	95	5	:	:	PUNCT
american_scientific_journal-7274	95	6	𝑔(0	𝑔(0	ADJ
american_scientific_journal-7274	95	7	)	)	PUNCT
american_scientific_journal-7274	95	8	=	=	SYM
american_scientific_journal-7274	95	9	1	1	NUM
american_scientific_journal-7274	95	10	,	,	PUNCT
american_scientific_journal-7274	95	11	𝑔(𝑠	𝑔(𝑠	NOUN
american_scientific_journal-7274	95	12	)	)	PUNCT
american_scientific_journal-7274	95	13	≥	≥	X
american_scientific_journal-7274	95	14	0	0	NUM
american_scientific_journal-7274	95	15	𝑎𝑛𝑑	𝑎𝑛𝑑	PROPN
american_scientific_journal-7274	95	16	lim	lim	PROPN
american_scientific_journal-7274	95	17	𝑠→∞	𝑠→∞	NUM
american_scientific_journal-7274	95	18	𝑔(𝑠	𝑔(𝑠	NOUN
american_scientific_journal-7274	95	19	)	)	PUNCT
american_scientific_journal-7274	95	20	=	=	SYM
american_scientific_journal-7274	95	21	0	0	X
american_scientific_journal-7274	95	22	.	.	PUNCT
american_scientific_journal-7274	95	23	perona	perona	PROPN
american_scientific_journal-7274	95	24	and	and	CCONJ
american_scientific_journal-7274	95	25	malik	malik	PROPN
american_scientific_journal-7274	95	26	proposed	propose	VERB
american_scientific_journal-7274	95	27	two	two	NUM
american_scientific_journal-7274	95	28	different	different	ADJ
american_scientific_journal-7274	95	29	choices	choice	NOUN
american_scientific_journal-7274	95	30	for	for	ADP
american_scientific_journal-7274	95	31	the	the	DET
american_scientific_journal-7274	95	32	diffusivity	diffusivity	NOUN
american_scientific_journal-7274	95	33	function	function	NOUN
american_scientific_journal-7274	96	1	[	[	X
american_scientific_journal-7274	96	2	32,33,34	32,33,34	NUM
american_scientific_journal-7274	96	3	]	]	NOUN
american_scientific_journal-7274	96	4	:	:	PUNCT
american_scientific_journal-7274	96	5	𝑔(𝑠	𝑔(𝑠	NOUN
american_scientific_journal-7274	96	6	)	)	PUNCT
american_scientific_journal-7274	96	7	=	=	SYM
american_scientific_journal-7274	96	8	1	1	NUM
american_scientific_journal-7274	96	9	1	1	NUM
american_scientific_journal-7274	96	10	+	+	NUM
american_scientific_journal-7274	96	11	𝑠2	𝑠2	NOUN
american_scientific_journal-7274	96	12	𝜆2	𝜆2	PROPN
american_scientific_journal-7274	96	13	(	(	PUNCT
american_scientific_journal-7274	96	14	3.1.2	3.1.2	NOUN
american_scientific_journal-7274	96	15	)	)	PUNCT
american_scientific_journal-7274	96	16	𝑔(𝑠	𝑔(𝑠	NOUN
american_scientific_journal-7274	96	17	)	)	PUNCT
american_scientific_journal-7274	96	18	=	=	PUNCT
american_scientific_journal-7274	96	19	𝑒	𝑒	PROPN
american_scientific_journal-7274	96	20	−	−	PROPN
american_scientific_journal-7274	96	21	𝑠2	𝑠2	PROPN
american_scientific_journal-7274	96	22	𝜆2	𝜆2	PROPN
american_scientific_journal-7274	96	23	(	(	PUNCT
american_scientific_journal-7274	96	24	3.1.3	3.1.3	NUM
american_scientific_journal-7274	96	25	)	)	PUNCT
american_scientific_journal-7274	96	26	3.2	3.2	NUM
american_scientific_journal-7274	96	27	.	.	PUNCT
american_scientific_journal-7274	97	1	a	a	DET
american_scientific_journal-7274	97	2	numerical	numerical	ADJ
american_scientific_journal-7274	97	3	approach	approach	NOUN
american_scientific_journal-7274	97	4	for	for	ADP
american_scientific_journal-7274	97	5	the	the	DET
american_scientific_journal-7274	97	6	perona	perona	PROPN
american_scientific_journal-7274	97	7	-	-	PUNCT
american_scientific_journal-7274	97	8	malik	malik	PROPN
american_scientific_journal-7274	97	9	equation	equation	NOUN
american_scientific_journal-7274	97	10	with	with	ADP
american_scientific_journal-7274	97	11	the	the	DET
american_scientific_journal-7274	97	12	finite	finite	ADJ
american_scientific_journal-7274	97	13	difference	difference	NOUN
american_scientific_journal-7274	97	14	method	method	NOUN
american_scientific_journal-7274	97	15	[	[	X
american_scientific_journal-7274	97	16	32,33,35	32,33,35	NOUN
american_scientific_journal-7274	97	17	]	]	PUNCT
american_scientific_journal-7274	97	18	let	let	VERB
american_scientific_journal-7274	97	19	's	us	PRON
american_scientific_journal-7274	97	20	make	make	VERB
american_scientific_journal-7274	97	21	the	the	DET
american_scientific_journal-7274	97	22	perona	perona	NOUN
american_scientific_journal-7274	97	23	-	-	PUNCT
american_scientific_journal-7274	97	24	malik	malik	PROPN
american_scientific_journal-7274	97	25	equation	equation	NOUN
american_scientific_journal-7274	97	26	given	give	VERB
american_scientific_journal-7274	97	27	in	in	ADP
american_scientific_journal-7274	97	28	(	(	PUNCT
american_scientific_journal-7274	97	29	3.1.1	3.1.1	NUM
american_scientific_journal-7274	97	30	)	)	PUNCT
american_scientific_journal-7274	97	31	discrete	discrete	NOUN
american_scientific_journal-7274	97	32	.	.	PUNCT
american_scientific_journal-7274	98	1	we	we	PRON
american_scientific_journal-7274	98	2	can	can	AUX
american_scientific_journal-7274	98	3	divide	divide	VERB
american_scientific_journal-7274	98	4	the	the	DET
american_scientific_journal-7274	98	5	ranges	range	NOUN
american_scientific_journal-7274	98	6	in	in	ADP
american_scientific_journal-7274	98	7	the	the	DET
american_scientific_journal-7274	98	8	form	form	NOUN
american_scientific_journal-7274	98	9	𝑥𝑖	𝑥𝑖	X
american_scientific_journal-7274	98	10	=	=	SYM
american_scientific_journal-7274	98	11	𝑖ℎ1	𝑖ℎ1	PROPN
american_scientific_journal-7274	98	12	,	,	PUNCT
american_scientific_journal-7274	98	13	𝑖	𝑖	NOUN
american_scientific_journal-7274	98	14	=	=	NOUN
american_scientific_journal-7274	98	15	1,2,3	1,2,3	NUM
american_scientific_journal-7274	98	16	,	,	PUNCT
american_scientific_journal-7274	98	17	…	…	PUNCT
american_scientific_journal-7274	98	18	,	,	PUNCT
american_scientific_journal-7274	98	19	𝑁	𝑁	PROPN
american_scientific_journal-7274	98	20	𝑦𝑗	𝑦𝑗	NOUN
american_scientific_journal-7274	98	21	=	=	PUNCT
american_scientific_journal-7274	98	22	𝑗ℎ2	𝑗ℎ2	NOUN
american_scientific_journal-7274	98	23	,	,	PUNCT
american_scientific_journal-7274	98	24	𝑗	𝑗	NOUN
american_scientific_journal-7274	98	25	=	=	NOUN
american_scientific_journal-7274	98	26	1,2,3	1,2,3	NUM
american_scientific_journal-7274	98	27	,	,	PUNCT
american_scientific_journal-7274	98	28	…	…	PUNCT
american_scientific_journal-7274	98	29	,	,	PUNCT
american_scientific_journal-7274	98	30	𝑀	𝑀	PROPN
american_scientific_journal-7274	98	31	(	(	PUNCT
american_scientific_journal-7274	98	32	3.2.1	3.2.1	NUM
american_scientific_journal-7274	98	33	)	)	PUNCT
american_scientific_journal-7274	98	34	𝑡𝑘	𝑡𝑘	ADV
american_scientific_journal-7274	98	35	=	=	PUNCT
american_scientific_journal-7274	99	1	𝑘.	𝑘.	PROPN
american_scientific_journal-7274	99	2	∆𝑡	∆𝑡	PROPN
american_scientific_journal-7274	99	3	,	,	PUNCT
american_scientific_journal-7274	99	4	𝑘	𝑘	X
american_scientific_journal-7274	99	5	=	=	NOUN
american_scientific_journal-7274	99	6	1,2,3	1,2,3	NUM
american_scientific_journal-7274	99	7	,	,	PUNCT
american_scientific_journal-7274	99	8	…	…	PUNCT
american_scientific_journal-7274	99	9	,	,	PUNCT
american_scientific_journal-7274	99	10	𝑛	𝑛	PRON
american_scientific_journal-7274	99	11	where	where	SCONJ
american_scientific_journal-7274	99	12	,	,	PUNCT
american_scientific_journal-7274	99	13	h1	h1	PROPN
american_scientific_journal-7274	99	14	and	and	CCONJ
american_scientific_journal-7274	99	15	h2	h2	PROPN
american_scientific_journal-7274	99	16	indicate	indicate	VERB
american_scientific_journal-7274	99	17	pixel	pixel	NOUN
american_scientific_journal-7274	99	18	placements	placement	NOUN
american_scientific_journal-7274	99	19	in	in	ADP
american_scientific_journal-7274	99	20	the	the	DET
american_scientific_journal-7274	99	21	x	x	NOUN
american_scientific_journal-7274	99	22	and	and	CCONJ
american_scientific_journal-7274	99	23	y	y	PROPN
american_scientific_journal-7274	99	24	directions	direction	NOUN
american_scientific_journal-7274	99	25	,	,	PUNCT
american_scientific_journal-7274	99	26	respectively	respectively	ADV
american_scientific_journal-7274	99	27	.	.	PUNCT
american_scientific_journal-7274	100	1	pixels	pixel	NOUN
american_scientific_journal-7274	100	2	are	be	AUX
american_scientific_journal-7274	100	3	generally	generally	ADV
american_scientific_journal-7274	100	4	american	american	ADJ
american_scientific_journal-7274	100	5	academic	academic	ADJ
american_scientific_journal-7274	100	6	scientific	scientific	ADJ
american_scientific_journal-7274	100	7	research	research	NOUN
american_scientific_journal-7274	100	8	journal	journal	NOUN
american_scientific_journal-7274	100	9	for	for	ADP
american_scientific_journal-7274	100	10	engineering	engineering	NOUN
american_scientific_journal-7274	100	11	,	,	PUNCT
american_scientific_journal-7274	100	12	technology	technology	NOUN
american_scientific_journal-7274	100	13	,	,	PUNCT
american_scientific_journal-7274	100	14	and	and	CCONJ
american_scientific_journal-7274	100	15	sciences	science	NOUN
american_scientific_journal-7274	100	16	(	(	PUNCT
american_scientific_journal-7274	100	17	asrjets	asrjet	NOUN
american_scientific_journal-7274	100	18	)	)	PUNCT
american_scientific_journal-7274	100	19	(	(	PUNCT
american_scientific_journal-7274	100	20	2021	2021	NUM
american_scientific_journal-7274	100	21	)	)	PUNCT
american_scientific_journal-7274	100	22	volume	volume	NOUN
american_scientific_journal-7274	100	23	84	84	NUM
american_scientific_journal-7274	100	24	,	,	PUNCT
american_scientific_journal-7274	100	25	no1	no1	PROPN
american_scientific_journal-7274	100	26	,	,	PUNCT
american_scientific_journal-7274	100	27	pp	pp	ADP
american_scientific_journal-7274	100	28	118	118	NUM
american_scientific_journal-7274	100	29	-	-	SYM
american_scientific_journal-7274	100	30	129	129	NUM
american_scientific_journal-7274	100	31	122	122	NUM
american_scientific_journal-7274	100	32	considered	consider	VERB
american_scientific_journal-7274	100	33	to	to	PART
american_scientific_journal-7274	100	34	have	have	VERB
american_scientific_journal-7274	100	35	a	a	DET
american_scientific_journal-7274	100	36	unit	unit	NOUN
american_scientific_journal-7274	100	37	length	length	NOUN
american_scientific_journal-7274	100	38	,	,	PUNCT
american_scientific_journal-7274	100	39	h1	h1	PROPN
american_scientific_journal-7274	100	40	=	=	PUNCT
american_scientific_journal-7274	100	41	h2	h2	NOUN
american_scientific_journal-7274	100	42	=	=	NOUN
american_scientific_journal-7274	100	43	1	1	NUM
american_scientific_journal-7274	100	44	.	.	PUNCT
american_scientific_journal-7274	101	1	we	we	PRON
american_scientific_journal-7274	101	2	obtain	obtain	VERB
american_scientific_journal-7274	101	3	a	a	DET
american_scientific_journal-7274	101	4	numerical	numerical	ADJ
american_scientific_journal-7274	101	5	approximation	approximation	NOUN
american_scientific_journal-7274	101	6	for	for	ADP
american_scientific_journal-7274	101	7	the	the	DET
american_scientific_journal-7274	101	8	gradient	gradient	NOUN
american_scientific_journal-7274	101	9	length	length	NOUN
american_scientific_journal-7274	101	10	‖∇𝑢𝑖,𝑗‖	‖∇𝑢𝑖,𝑗‖	PROPN
american_scientific_journal-7274	101	11	by	by	ADP
american_scientific_journal-7274	101	12	using	use	VERB
american_scientific_journal-7274	101	13	the	the	DET
american_scientific_journal-7274	101	14	central	central	ADJ
american_scientific_journal-7274	101	15	finite	finite	ADJ
american_scientific_journal-7274	101	16	difference	difference	NOUN
american_scientific_journal-7274	101	17	method	method	NOUN
american_scientific_journal-7274	101	18	and	and	CCONJ
american_scientific_journal-7274	101	19	we	we	PRON
american_scientific_journal-7274	101	20	use	use	VERB
american_scientific_journal-7274	101	21	this	this	DET
american_scientific_journal-7274	101	22	approximation	approximation	NOUN
american_scientific_journal-7274	101	23	to	to	PART
american_scientific_journal-7274	101	24	calculate	calculate	VERB
american_scientific_journal-7274	101	25	the	the	DET
american_scientific_journal-7274	101	26	diffusivity	diffusivity	NOUN
american_scientific_journal-7274	101	27	function	function	NOUN
american_scientific_journal-7274	101	28	𝑔‖∇𝑢𝑖,𝑗‖	𝑔‖∇𝑢𝑖,𝑗‖	PUNCT
american_scientific_journal-7274	102	1	[	[	X
american_scientific_journal-7274	102	2	32,33	32,33	NUM
american_scientific_journal-7274	102	3	]	]	PUNCT
american_scientific_journal-7274	102	4	:	:	PUNCT
american_scientific_journal-7274	102	5	‖∇𝑢𝑖,𝑗‖	‖∇𝑢𝑖,𝑗‖	PROPN
american_scientific_journal-7274	102	6	=	=	SYM
american_scientific_journal-7274	102	7	√	√	NUM
american_scientific_journal-7274	102	8	(	(	PUNCT
american_scientific_journal-7274	102	9	𝑑𝑢𝑖,𝑗	𝑑𝑢𝑖,𝑗	NOUN
american_scientific_journal-7274	102	10	𝑑𝑥	𝑑𝑥	VERB
american_scientific_journal-7274	102	11	)	)	PUNCT
american_scientific_journal-7274	102	12	2	2	NUM
american_scientific_journal-7274	102	13	+	+	CCONJ
american_scientific_journal-7274	102	14	(	(	PUNCT
american_scientific_journal-7274	102	15	𝑑𝑢𝑖,𝑗	𝑑𝑢𝑖,𝑗	NOUN
american_scientific_journal-7274	102	16	𝑑𝑦	𝑑𝑦	ADJ
american_scientific_journal-7274	102	17	)	)	PUNCT
american_scientific_journal-7274	102	18	2	2	NUM
american_scientific_journal-7274	102	19	≈	≈	NUM
american_scientific_journal-7274	102	20	√	√	PROPN
american_scientific_journal-7274	102	21	(	(	PUNCT
american_scientific_journal-7274	102	22	𝑢𝑖+1,𝑗	𝑢𝑖+1,𝑗	PROPN
american_scientific_journal-7274	102	23	−	−	PROPN
american_scientific_journal-7274	102	24	𝑢𝑖−1,𝑗	𝑢𝑖−1,𝑗	NOUN
american_scientific_journal-7274	102	25	2ℎ1	2ℎ1	NUM
american_scientific_journal-7274	102	26	)	)	PUNCT
american_scientific_journal-7274	102	27	2	2	NUM
american_scientific_journal-7274	103	1	+	+	CCONJ
american_scientific_journal-7274	103	2	(	(	PUNCT
american_scientific_journal-7274	103	3	𝑢𝑖,𝑗+1	𝑢𝑖,𝑗+1	X
american_scientific_journal-7274	103	4	−	−	PROPN
american_scientific_journal-7274	103	5	𝑢𝑖,𝑗−1	𝑢𝑖,𝑗−1	PROPN
american_scientific_journal-7274	103	6	2ℎ2	2ℎ2	NUM
american_scientific_journal-7274	103	7	)	)	PUNCT
american_scientific_journal-7274	103	8	2	2	NUM
american_scientific_journal-7274	103	9	(	(	PUNCT
american_scientific_journal-7274	103	10	3.2.2	3.2.2	NUM
american_scientific_journal-7274	103	11	)	)	PUNCT
american_scientific_journal-7274	103	12	the	the	DET
american_scientific_journal-7274	103	13	left	left	ADJ
american_scientific_journal-7274	103	14	side	side	NOUN
american_scientific_journal-7274	103	15	of	of	ADP
american_scientific_journal-7274	103	16	equation	equation	NOUN
american_scientific_journal-7274	103	17	(	(	PUNCT
american_scientific_journal-7274	103	18	3.1.1	3.1.1	NUM
american_scientific_journal-7274	103	19	)	)	PUNCT
american_scientific_journal-7274	103	20	can	can	AUX
american_scientific_journal-7274	103	21	be	be	AUX
american_scientific_journal-7274	103	22	discretized	discretize	VERB
american_scientific_journal-7274	103	23	as	as	ADP
american_scientific_journal-7274	103	24	[	[	X
american_scientific_journal-7274	103	25	32,33	32,33	NUM
american_scientific_journal-7274	103	26	]	]	X
american_scientific_journal-7274	103	27	:	:	PUNCT
american_scientific_journal-7274	103	28	𝜕𝑢	𝜕𝑢	NOUN
american_scientific_journal-7274	103	29	𝜕𝑡	𝜕𝑡	NOUN
american_scientific_journal-7274	103	30	=	=	NOUN
american_scientific_journal-7274	103	31	𝑢𝑖,𝑗	𝑢𝑖,𝑗	AUX
american_scientific_journal-7274	103	32	𝑘+1−𝑢𝑖,𝑗	𝑘+1−𝑢𝑖,𝑗	VERB
american_scientific_journal-7274	103	33	𝑘	𝑘	PRON
american_scientific_journal-7274	103	34	∆𝑡	∆𝑡	PROPN
american_scientific_journal-7274	103	35	(	(	PUNCT
american_scientific_journal-7274	103	36	3.2.3	3.2.3	NUM
american_scientific_journal-7274	103	37	)	)	PUNCT
american_scientific_journal-7274	103	38	the	the	DET
american_scientific_journal-7274	103	39	right	right	ADJ
american_scientific_journal-7274	103	40	side	side	NOUN
american_scientific_journal-7274	103	41	of	of	ADP
american_scientific_journal-7274	103	42	equation	equation	NOUN
american_scientific_journal-7274	103	43	(	(	PUNCT
american_scientific_journal-7274	103	44	3.1.1	3.1.1	NUM
american_scientific_journal-7274	103	45	)	)	PUNCT
american_scientific_journal-7274	103	46	can	can	AUX
american_scientific_journal-7274	103	47	be	be	AUX
american_scientific_journal-7274	103	48	discretized	discretize	VERB
american_scientific_journal-7274	103	49	as	as	ADP
american_scientific_journal-7274	103	50	[	[	X
american_scientific_journal-7274	103	51	32,33	32,33	NUM
american_scientific_journal-7274	103	52	]	]	X
american_scientific_journal-7274	103	53	:	:	PUNCT
american_scientific_journal-7274	103	54	𝜕	𝜕	NOUN
american_scientific_journal-7274	103	55	𝜕𝑥	𝜕𝑥	X
american_scientific_journal-7274	103	56	(	(	PUNCT
american_scientific_journal-7274	103	57	𝑔‖∇𝑢‖	𝑔‖∇𝑢‖	NOUN
american_scientific_journal-7274	103	58	)	)	PUNCT
american_scientific_journal-7274	103	59	𝑢𝑥	𝑢𝑥	ADP
american_scientific_journal-7274	103	60	+	+	NOUN
american_scientific_journal-7274	103	61	𝜕	𝜕	PROPN
american_scientific_journal-7274	103	62	𝜕𝑦	𝜕𝑦	NOUN
american_scientific_journal-7274	103	63	(	(	PUNCT
american_scientific_journal-7274	103	64	𝑔‖∇𝑢‖	𝑔‖∇𝑢‖	NOUN
american_scientific_journal-7274	103	65	)	)	PUNCT
american_scientific_journal-7274	103	66	𝑢𝑦	𝑢𝑦	PROPN
american_scientific_journal-7274	104	1	=	=	SYM
american_scientific_journal-7274	104	2	𝑔	𝑔	PROPN
american_scientific_journal-7274	104	3	𝑖+	𝑖+	ADP
american_scientific_journal-7274	104	4	1	1	NUM
american_scientific_journal-7274	104	5	2,𝑗	2,𝑗	NOUN
american_scientific_journal-7274	104	6	(	(	PUNCT
american_scientific_journal-7274	104	7	𝑢𝑖+1	𝑢𝑖+1	PROPN
american_scientific_journal-7274	104	8	,	,	PUNCT
american_scientific_journal-7274	104	9	𝑗	𝑗	PROPN
american_scientific_journal-7274	104	10	𝑘	𝑘	PRON
american_scientific_journal-7274	104	11	−	−	NOUN
american_scientific_journal-7274	104	12	𝑢𝑖	𝑢𝑖	NOUN
american_scientific_journal-7274	104	13	,	,	PUNCT
american_scientific_journal-7274	104	14	𝑗	𝑗	INTJ
american_scientific_journal-7274	104	15	𝑘	𝑘	NOUN
american_scientific_journal-7274	104	16	)	)	PUNCT
american_scientific_journal-7274	104	17	−𝑔	−𝑔	NOUN
american_scientific_journal-7274	104	18	𝑖−	𝑖−	VERB
american_scientific_journal-7274	104	19	1	1	NUM
american_scientific_journal-7274	104	20	2,𝑗	2,𝑗	NOUN
american_scientific_journal-7274	104	21	(	(	PUNCT
american_scientific_journal-7274	104	22	𝑢𝑖,𝑗	𝑢𝑖,𝑗	X
american_scientific_journal-7274	104	23	𝑘	𝑘	PRON
american_scientific_journal-7274	104	24	−	−	NOUN
american_scientific_journal-7274	104	25	𝑢𝑖−1,𝑗	𝑢𝑖−1,𝑗	NOUN
american_scientific_journal-7274	104	26	𝑘	𝑘	NOUN
american_scientific_journal-7274	104	27	)	)	PUNCT
american_scientific_journal-7274	104	28	ℎ1	ℎ1	PROPN
american_scientific_journal-7274	104	29	2	2	NUM
american_scientific_journal-7274	105	1	+	+	CCONJ
american_scientific_journal-7274	105	2	𝑔	𝑔	X
american_scientific_journal-7274	105	3	𝑖,𝑗+	𝑖,𝑗+	NUM
american_scientific_journal-7274	105	4	1	1	NUM
american_scientific_journal-7274	105	5	2	2	NUM
american_scientific_journal-7274	105	6	(	(	PUNCT
american_scientific_journal-7274	105	7	𝑢𝑖,𝑗+1	𝑢𝑖,𝑗+1	X
american_scientific_journal-7274	106	1	𝑘	𝑘	DET
american_scientific_journal-7274	106	2	−	−	NOUN
american_scientific_journal-7274	106	3	𝑢𝑖,𝑗	𝑢𝑖,𝑗	NOUN
american_scientific_journal-7274	106	4	𝑘	𝑘	NOUN
american_scientific_journal-7274	106	5	)	)	PUNCT
american_scientific_journal-7274	106	6	−𝑔	−𝑔	NOUN
american_scientific_journal-7274	106	7	𝑖,𝑗−	𝑖,𝑗−	PROPN
american_scientific_journal-7274	106	8	1	1	NUM
american_scientific_journal-7274	106	9	2	2	NUM
american_scientific_journal-7274	106	10	(	(	PUNCT
american_scientific_journal-7274	106	11	𝑢𝑖,𝑗	𝑢𝑖,𝑗	X
american_scientific_journal-7274	106	12	𝑘	𝑘	PRON
american_scientific_journal-7274	106	13	−	−	PROPN
american_scientific_journal-7274	106	14	𝑢𝑖,𝑗−1	𝑢𝑖,𝑗−1	PROPN
american_scientific_journal-7274	106	15	𝑘	𝑘	NOUN
american_scientific_journal-7274	106	16	)	)	PUNCT
american_scientific_journal-7274	106	17	ℎ2	ℎ2	ADJ
american_scientific_journal-7274	106	18	2	2	NUM
american_scientific_journal-7274	106	19	(	(	PUNCT
american_scientific_journal-7274	106	20	3.2.4	3.2.4	NUM
american_scientific_journal-7274	106	21	)	)	PUNCT
american_scientific_journal-7274	106	22	the	the	DET
american_scientific_journal-7274	106	23	lattice	lattice	NOUN
american_scientific_journal-7274	106	24	we	we	PRON
american_scientific_journal-7274	106	25	use	use	VERB
american_scientific_journal-7274	106	26	for	for	ADP
american_scientific_journal-7274	106	27	discretization	discretization	NOUN
american_scientific_journal-7274	106	28	in	in	ADP
american_scientific_journal-7274	106	29	equations	equation	NOUN
american_scientific_journal-7274	106	30	(	(	PUNCT
american_scientific_journal-7274	106	31	3.2.2	3.2.2	NUM
american_scientific_journal-7274	106	32	)	)	PUNCT
american_scientific_journal-7274	106	33	,	,	PUNCT
american_scientific_journal-7274	106	34	(	(	PUNCT
american_scientific_journal-7274	106	35	3.2.3),(3.2.4	3.2.3),(3.2.4	X
american_scientific_journal-7274	106	36	)	)	PUNCT
american_scientific_journal-7274	106	37	is	be	AUX
american_scientific_journal-7274	106	38	as	as	SCONJ
american_scientific_journal-7274	106	39	follows	follow	VERB
american_scientific_journal-7274	106	40	[	[	X
american_scientific_journal-7274	106	41	32,33	32,33	NUM
american_scientific_journal-7274	106	42	]	]	PUNCT
american_scientific_journal-7274	106	43	:	:	PUNCT
american_scientific_journal-7274	106	44	𝑢𝑖−1,𝑗−1	𝑢𝑖−1,𝑗−1	PROPN
american_scientific_journal-7274	106	45	𝑢𝑖,𝑗−1	𝑢𝑖,𝑗−1	PROPN
american_scientific_journal-7274	106	46	𝑢𝑖+1,𝑗−1	𝑢𝑖+1,𝑗−1	PROPN
american_scientific_journal-7274	106	47	𝑔	𝑔	PROPN
american_scientific_journal-7274	106	48	𝑖,𝑗−	𝑖,𝑗−	PROPN
american_scientific_journal-7274	106	49	1	1	NUM
american_scientific_journal-7274	106	50	2	2	NUM
american_scientific_journal-7274	106	51	𝑢𝑖−1,𝑗	𝑢𝑖−1,𝑗	NOUN
american_scientific_journal-7274	106	52	𝑔	𝑔	PROPN
american_scientific_journal-7274	106	53	𝑖−	𝑖−	PROPN
american_scientific_journal-7274	106	54	1	1	NUM
american_scientific_journal-7274	106	55	2	2	NUM
american_scientific_journal-7274	106	56	,	,	PUNCT
american_scientific_journal-7274	106	57	𝑗	𝑗	INTJ
american_scientific_journal-7274	106	58	𝑢𝑖,𝑗	𝑢𝑖,𝑗	X
american_scientific_journal-7274	106	59	𝑔	𝑔	X
american_scientific_journal-7274	106	60	𝑖+	𝑖+	ADP
american_scientific_journal-7274	106	61	1	1	NUM
american_scientific_journal-7274	106	62	2	2	NUM
american_scientific_journal-7274	106	63	,	,	PUNCT
american_scientific_journal-7274	106	64	𝑗	𝑗	PROPN
american_scientific_journal-7274	106	65	𝑢𝑖+1,𝑗	𝑢𝑖+1,𝑗	PROPN
american_scientific_journal-7274	106	66	𝑔	𝑔	PROPN
american_scientific_journal-7274	106	67	𝑖,𝑗+	𝑖,𝑗+	NUM
american_scientific_journal-7274	106	68	1	1	NUM
american_scientific_journal-7274	106	69	2	2	NUM
american_scientific_journal-7274	106	70	𝑢𝑖−1,𝑗+1	𝑢𝑖−1,𝑗+1	NOUN
american_scientific_journal-7274	106	71	𝑢𝑖,𝑗+1	𝑢𝑖,𝑗+1	VERB
american_scientific_journal-7274	106	72	𝑢𝑖+1,𝑗+1	𝑢𝑖+1,𝑗+1	NOUN
american_scientific_journal-7274	106	73	figure	figure	NOUN
american_scientific_journal-7274	106	74	3.2.1	3.2.1	NUM
american_scientific_journal-7274	106	75	in	in	ADP
american_scientific_journal-7274	106	76	the	the	DET
american_scientific_journal-7274	106	77	discretized	discretized	ADJ
american_scientific_journal-7274	106	78	state	state	NOUN
american_scientific_journal-7274	106	79	,	,	PUNCT
american_scientific_journal-7274	106	80	mid	mid	ADJ
american_scientific_journal-7274	106	81	-	-	ADJ
american_scientific_journal-7274	106	82	pixel	pixel	ADJ
american_scientific_journal-7274	106	83	points	point	NOUN
american_scientific_journal-7274	106	84	need	need	VERB
american_scientific_journal-7274	106	85	calculated	calculate	VERB
american_scientific_journal-7274	106	86	diffusivities	diffusivitie	NOUN
american_scientific_journal-7274	106	87	.	.	PUNCT
american_scientific_journal-7274	107	1	therefore	therefore	ADV
american_scientific_journal-7274	107	2	,	,	PUNCT
american_scientific_journal-7274	107	3	we	we	PRON
american_scientific_journal-7274	107	4	can	can	AUX
american_scientific_journal-7274	107	5	simply	simply	ADV
american_scientific_journal-7274	107	6	calculate	calculate	VERB
american_scientific_journal-7274	107	7	these	these	DET
american_scientific_journal-7274	107	8	values	value	NOUN
american_scientific_journal-7274	107	9	by	by	ADP
american_scientific_journal-7274	107	10	taking	take	VERB
american_scientific_journal-7274	107	11	advantage	advantage	NOUN
american_scientific_journal-7274	107	12	of	of	ADP
american_scientific_journal-7274	107	13	the	the	DET
american_scientific_journal-7274	107	14	diffusivity	diffusivity	NOUN
american_scientific_journal-7274	107	15	in	in	ADP
american_scientific_journal-7274	107	16	neighboring	neighboring	NOUN
american_scientific_journal-7274	107	17	pixels	pixel	NOUN
american_scientific_journal-7274	107	18	.	.	PUNCT
american_scientific_journal-7274	108	1	we	we	PRON
american_scientific_journal-7274	108	2	can	can	AUX
american_scientific_journal-7274	108	3	do	do	VERB
american_scientific_journal-7274	108	4	this	this	PRON
american_scientific_journal-7274	108	5	as	as	SCONJ
american_scientific_journal-7274	108	6	follows	follow	VERB
american_scientific_journal-7274	108	7	[	[	X
american_scientific_journal-7274	108	8	32,33	32,33	NUM
american_scientific_journal-7274	108	9	]	]	X
american_scientific_journal-7274	108	10	:	:	PUNCT
american_scientific_journal-7274	108	11	american	american	PROPN
american_scientific_journal-7274	108	12	academic	academic	ADJ
american_scientific_journal-7274	108	13	scientific	scientific	ADJ
american_scientific_journal-7274	108	14	research	research	NOUN
american_scientific_journal-7274	108	15	journal	journal	NOUN
american_scientific_journal-7274	108	16	for	for	ADP
american_scientific_journal-7274	108	17	engineering	engineering	NOUN
american_scientific_journal-7274	108	18	,	,	PUNCT
american_scientific_journal-7274	108	19	technology	technology	NOUN
american_scientific_journal-7274	108	20	,	,	PUNCT
american_scientific_journal-7274	108	21	and	and	CCONJ
american_scientific_journal-7274	108	22	sciences	science	NOUN
american_scientific_journal-7274	108	23	(	(	PUNCT
american_scientific_journal-7274	108	24	asrjets	asrjet	NOUN
american_scientific_journal-7274	108	25	)	)	PUNCT
american_scientific_journal-7274	108	26	(	(	PUNCT
american_scientific_journal-7274	108	27	2021	2021	NUM
american_scientific_journal-7274	108	28	)	)	PUNCT
american_scientific_journal-7274	108	29	volume	volume	NOUN
american_scientific_journal-7274	108	30	84	84	NUM
american_scientific_journal-7274	108	31	,	,	PUNCT
american_scientific_journal-7274	108	32	no1	no1	PROPN
american_scientific_journal-7274	108	33	,	,	PUNCT
american_scientific_journal-7274	108	34	pp	pp	ADP
american_scientific_journal-7274	108	35	118	118	NUM
american_scientific_journal-7274	108	36	-	-	SYM
american_scientific_journal-7274	108	37	129	129	NUM
american_scientific_journal-7274	108	38	123	123	NUM
american_scientific_journal-7274	108	39	𝑔	𝑔	NOUN
american_scientific_journal-7274	108	40	𝑖+	𝑖+	ADP
american_scientific_journal-7274	108	41	1	1	NUM
american_scientific_journal-7274	108	42	2	2	NUM
american_scientific_journal-7274	108	43	,	,	PUNCT
american_scientific_journal-7274	108	44	𝑗	𝑗	NOUN
american_scientific_journal-7274	108	45	=	=	NOUN
american_scientific_journal-7274	108	46	𝑔𝑖+1,𝑗	𝑔𝑖+1,𝑗	PROPN
american_scientific_journal-7274	108	47	+	+	CCONJ
american_scientific_journal-7274	108	48	𝑔𝑖,𝑗	𝑔𝑖,𝑗	NUM
american_scientific_journal-7274	108	49	2	2	NUM
american_scientific_journal-7274	108	50	𝑔	𝑔	PROPN
american_scientific_journal-7274	108	51	𝑖−	𝑖−	PROPN
american_scientific_journal-7274	108	52	1	1	NUM
american_scientific_journal-7274	108	53	2	2	NUM
american_scientific_journal-7274	108	54	,	,	PUNCT
american_scientific_journal-7274	108	55	𝑗	𝑗	NOUN
american_scientific_journal-7274	108	56	=	=	X
american_scientific_journal-7274	108	57	𝑔𝑖−1,𝑗	𝑔𝑖−1,𝑗	X
american_scientific_journal-7274	109	1	+	+	X
american_scientific_journal-7274	109	2	𝑔𝑖,𝑗	𝑔𝑖,𝑗	ADP
american_scientific_journal-7274	109	3	2	2	NUM
american_scientific_journal-7274	109	4	𝑔	𝑔	NOUN
american_scientific_journal-7274	109	5	𝑖,𝑗+	𝑖,𝑗+	NUM
american_scientific_journal-7274	109	6	1	1	NUM
american_scientific_journal-7274	109	7	2	2	NUM
american_scientific_journal-7274	109	8	=	=	NOUN
american_scientific_journal-7274	109	9	𝑔𝑖,𝑗+1	𝑔𝑖,𝑗+1	X
american_scientific_journal-7274	109	10	+	+	CCONJ
american_scientific_journal-7274	109	11	𝑔𝑖,𝑗	𝑔𝑖,𝑗	ADP
american_scientific_journal-7274	109	12	2	2	NUM
american_scientific_journal-7274	109	13	𝑔	𝑔	PROPN
american_scientific_journal-7274	109	14	𝑖,𝑗−	𝑖,𝑗−	NUM
american_scientific_journal-7274	109	15	1	1	NUM
american_scientific_journal-7274	109	16	2	2	NUM
american_scientific_journal-7274	109	17	=	=	NOUN
american_scientific_journal-7274	109	18	𝑔𝑖,𝑗−1	𝑔𝑖,𝑗−1	NOUN
american_scientific_journal-7274	109	19	+	+	CCONJ
american_scientific_journal-7274	109	20	𝑔𝑖,𝑗	𝑔𝑖,𝑗	X
american_scientific_journal-7274	109	21	2	2	NUM
american_scientific_journal-7274	109	22	(	(	PUNCT
american_scientific_journal-7274	109	23	3.2.5	3.2.5	NUM
american_scientific_journal-7274	109	24	)	)	PUNCT
american_scientific_journal-7274	109	25	as	as	ADP
american_scientific_journal-7274	109	26	a	a	DET
american_scientific_journal-7274	109	27	result	result	NOUN
american_scientific_journal-7274	109	28	of	of	ADP
american_scientific_journal-7274	109	29	the	the	DET
american_scientific_journal-7274	109	30	operations	operation	NOUN
american_scientific_journal-7274	109	31	,	,	PUNCT
american_scientific_journal-7274	109	32	the	the	DET
american_scientific_journal-7274	109	33	discretized	discretized	ADJ
american_scientific_journal-7274	109	34	version	version	NOUN
american_scientific_journal-7274	109	35	of	of	ADP
american_scientific_journal-7274	109	36	the	the	DET
american_scientific_journal-7274	109	37	perona	perona	NOUN
american_scientific_journal-7274	109	38	-	-	PUNCT
american_scientific_journal-7274	109	39	malik	malik	PROPN
american_scientific_journal-7274	109	40	equation	equation	NOUN
american_scientific_journal-7274	109	41	is	be	AUX
american_scientific_journal-7274	109	42	as	as	SCONJ
american_scientific_journal-7274	109	43	follows	follow	VERB
american_scientific_journal-7274	109	44	[	[	X
american_scientific_journal-7274	109	45	32,33	32,33	NUM
american_scientific_journal-7274	109	46	]	]	PUNCT
american_scientific_journal-7274	109	47	:	:	PUNCT
american_scientific_journal-7274	109	48	𝑢𝑖,𝑗	𝑢𝑖,𝑗	PUNCT
american_scientific_journal-7274	109	49	𝑘+1	𝑘+1	NUM
american_scientific_journal-7274	109	50	−	−	NOUN
american_scientific_journal-7274	109	51	𝑢𝑖,𝑗	𝑢𝑖,𝑗	VERB
american_scientific_journal-7274	109	52	𝑘	𝑘	NOUN
american_scientific_journal-7274	109	53	∆𝑡	∆𝑡	NOUN
american_scientific_journal-7274	109	54	=	=	PUNCT
american_scientific_journal-7274	109	55	(	(	PUNCT
american_scientific_journal-7274	109	56	𝑔𝑖+1,𝑗	𝑔𝑖+1,𝑗	PROPN
american_scientific_journal-7274	109	57	𝑘	𝑘	PROPN
american_scientific_journal-7274	109	58	+	+	PROPN
american_scientific_journal-7274	109	59	𝑔𝑖,𝑗	𝑔𝑖,𝑗	NOUN
american_scientific_journal-7274	109	60	𝑘	𝑘	X
american_scientific_journal-7274	109	61	)	)	PUNCT
american_scientific_journal-7274	110	1	[	[	X
american_scientific_journal-7274	110	2	𝑢𝑖+1,𝑗	𝑢𝑖+1,𝑗	NOUN
american_scientific_journal-7274	110	3	𝑘	𝑘	PROPN
american_scientific_journal-7274	110	4	−	−	NOUN
american_scientific_journal-7274	110	5	𝑢𝑖,𝑗	𝑢𝑖,𝑗	X
american_scientific_journal-7274	110	6	𝑘	𝑘	X
american_scientific_journal-7274	110	7	]	]	X
american_scientific_journal-7274	110	8	−	−	PROPN
american_scientific_journal-7274	110	9	(	(	PUNCT
american_scientific_journal-7274	110	10	𝑔𝑖,𝑗	𝑔𝑖,𝑗	VERB
american_scientific_journal-7274	110	11	𝑘	𝑘	X
american_scientific_journal-7274	110	12	+	+	X
american_scientific_journal-7274	110	13	𝑔𝑖−1,𝑗	𝑔𝑖−1,𝑗	ADJ
american_scientific_journal-7274	110	14	𝑘	𝑘	NOUN
american_scientific_journal-7274	110	15	)	)	PUNCT
american_scientific_journal-7274	111	1	[	[	X
american_scientific_journal-7274	111	2	𝑢𝑖,𝑗	𝑢𝑖,𝑗	X
american_scientific_journal-7274	111	3	𝑘	𝑘	PRON
american_scientific_journal-7274	111	4	−	−	NOUN
american_scientific_journal-7274	111	5	𝑢𝑖−1,𝑗	𝑢𝑖−1,𝑗	NOUN
american_scientific_journal-7274	111	6	𝑘	𝑘	X
american_scientific_journal-7274	111	7	]	]	X
american_scientific_journal-7274	111	8	+	+	ADJ
american_scientific_journal-7274	111	9	(	(	PUNCT
american_scientific_journal-7274	111	10	𝑔𝑖,𝑗+1	𝑔𝑖,𝑗+1	X
american_scientific_journal-7274	111	11	𝑘	𝑘	X
american_scientific_journal-7274	111	12	+	+	NOUN
american_scientific_journal-7274	111	13	𝑔𝑖,𝑗	𝑔𝑖,𝑗	NOUN
american_scientific_journal-7274	111	14	𝑘	𝑘	X
american_scientific_journal-7274	111	15	)	)	PUNCT
american_scientific_journal-7274	111	16	[	[	X
american_scientific_journal-7274	111	17	𝑢𝑖,𝑗+1	𝑢𝑖,𝑗+1	NOUN
american_scientific_journal-7274	111	18	𝑘	𝑘	DET
american_scientific_journal-7274	111	19	−	−	NOUN
american_scientific_journal-7274	111	20	𝑢𝑖,𝑗	𝑢𝑖,𝑗	X
american_scientific_journal-7274	111	21	𝑘	𝑘	X
american_scientific_journal-7274	111	22	]	]	X
american_scientific_journal-7274	111	23	−	−	PROPN
american_scientific_journal-7274	111	24	(	(	PUNCT
american_scientific_journal-7274	111	25	𝑔𝑖,𝑗	𝑔𝑖,𝑗	VERB
american_scientific_journal-7274	111	26	𝑘	𝑘	ADP
american_scientific_journal-7274	111	27	+	+	PUNCT
american_scientific_journal-7274	111	28	𝑔𝑖,𝑗−1	𝑔𝑖,𝑗−1	X
american_scientific_journal-7274	111	29	𝑘	𝑘	X
american_scientific_journal-7274	111	30	)	)	PUNCT
american_scientific_journal-7274	112	1	[	[	X
american_scientific_journal-7274	112	2	𝑢𝑖,𝑗	𝑢𝑖,𝑗	X
american_scientific_journal-7274	112	3	𝑘	𝑘	DET
american_scientific_journal-7274	112	4	−	−	PROPN
american_scientific_journal-7274	112	5	𝑢𝑖,𝑗−1	𝑢𝑖,𝑗−1	NOUN
american_scientific_journal-7274	112	6	𝑘	𝑘	X
american_scientific_journal-7274	112	7	]	]	X
american_scientific_journal-7274	112	8	(	(	PUNCT
american_scientific_journal-7274	112	9	3.2.6	3.2.6	NUM
american_scientific_journal-7274	112	10	)	)	PUNCT
american_scientific_journal-7274	112	11	‖∇𝑢𝑖,𝑗‖	‖∇𝑢𝑖,𝑗‖	NOUN
american_scientific_journal-7274	112	12	=	=	SYM
american_scientific_journal-7274	112	13	√	√	PROPN
american_scientific_journal-7274	112	14	(	(	PUNCT
american_scientific_journal-7274	112	15	𝑢𝑖+1,𝑗	𝑢𝑖+1,𝑗	PROPN
american_scientific_journal-7274	112	16	−	−	PROPN
american_scientific_journal-7274	112	17	𝑢𝑖−1,𝑗	𝑢𝑖−1,𝑗	NOUN
american_scientific_journal-7274	112	18	2	2	NUM
american_scientific_journal-7274	112	19	)	)	PUNCT
american_scientific_journal-7274	112	20	2	2	NUM
american_scientific_journal-7274	112	21	+	+	CCONJ
american_scientific_journal-7274	112	22	(	(	PUNCT
american_scientific_journal-7274	112	23	𝑢𝑖,𝑗+1	𝑢𝑖,𝑗+1	X
american_scientific_journal-7274	112	24	−	−	PROPN
american_scientific_journal-7274	112	25	𝑢𝑖,𝑗−1	𝑢𝑖,𝑗−1	PROPN
american_scientific_journal-7274	112	26	2	2	NUM
american_scientific_journal-7274	112	27	)	)	SYM
american_scientific_journal-7274	112	28	2	2	NUM
american_scientific_journal-7274	112	29	(	(	PUNCT
american_scientific_journal-7274	112	30	3.2.7	3.2.7	NUM
american_scientific_journal-7274	112	31	)	)	PUNCT
american_scientific_journal-7274	112	32	3.3	3.3	NUM
american_scientific_journal-7274	112	33	.	.	PUNCT
american_scientific_journal-7274	113	1	image	image	NOUN
american_scientific_journal-7274	113	2	processing	processing	NOUN
american_scientific_journal-7274	113	3	analysis	analysis	NOUN
american_scientific_journal-7274	113	4	by	by	ADP
american_scientific_journal-7274	113	5	using	use	VERB
american_scientific_journal-7274	113	6	digital	digital	ADJ
american_scientific_journal-7274	113	7	-	-	PUNCT
american_scientific_journal-7274	113	8	discrete	discrete	NOUN
american_scientific_journal-7274	113	9	method	method	NOUN
american_scientific_journal-7274	113	10	and	and	CCONJ
american_scientific_journal-7274	113	11	perona	perona	NOUN
american_scientific_journal-7274	113	12	-	-	PUNCT
american_scientific_journal-7274	113	13	malik	malik	PROPN
american_scientific_journal-7274	113	14	equation	equation	NOUN
american_scientific_journal-7274	113	15	we	we	PRON
american_scientific_journal-7274	113	16	discretized	discretize	VERB
american_scientific_journal-7274	113	17	the	the	DET
american_scientific_journal-7274	113	18	perona	perona	PROPN
american_scientific_journal-7274	113	19	-	-	PUNCT
american_scientific_journal-7274	113	20	malik	malik	PROPN
american_scientific_journal-7274	113	21	equation	equation	NOUN
american_scientific_journal-7274	113	22	using	use	VERB
american_scientific_journal-7274	113	23	the	the	DET
american_scientific_journal-7274	113	24	finite	finite	ADJ
american_scientific_journal-7274	113	25	difference	difference	NOUN
american_scientific_journal-7274	113	26	method	method	NOUN
american_scientific_journal-7274	113	27	in	in	ADP
american_scientific_journal-7274	113	28	section	section	NOUN
american_scientific_journal-7274	113	29	3.2	3.2	NUM
american_scientific_journal-7274	113	30	.	.	PUNCT
american_scientific_journal-7274	114	1	we	we	PRON
american_scientific_journal-7274	114	2	do	do	VERB
american_scientific_journal-7274	114	3	digitaldiscrete	digitaldiscrete	ADJ
american_scientific_journal-7274	114	4	adaptation	adaptation	NOUN
american_scientific_journal-7274	114	5	in	in	ADP
american_scientific_journal-7274	114	6	(	(	PUNCT
american_scientific_journal-7274	114	7	k+1	k+1	NOUN
american_scientific_journal-7274	114	8	)	)	PUNCT
american_scientific_journal-7274	114	9	so	so	SCONJ
american_scientific_journal-7274	114	10	that	that	PRON
american_scientific_journal-7274	114	11	𝑢𝑖,𝑗	𝑢𝑖,𝑗	VERB
american_scientific_journal-7274	114	12	𝑘+1	𝑘+1	PRON
american_scientific_journal-7274	114	13	←	←	PROPN
american_scientific_journal-7274	114	14	(	(	PUNCT
american_scientific_journal-7274	114	15	𝑢𝑖,𝑗	𝑢𝑖,𝑗	ADP
american_scientific_journal-7274	114	16	𝑘+1	𝑘+1	X
american_scientific_journal-7274	114	17	+	+	X
american_scientific_journal-7274	114	18	𝑔𝑣𝑓(𝑖	𝑔𝑣𝑓(𝑖	PROPN
american_scientific_journal-7274	114	19	,	,	PUNCT
american_scientific_journal-7274	114	20	𝑗)/2	𝑗)/2	PROPN
american_scientific_journal-7274	114	21	)	)	PUNCT
american_scientific_journal-7274	114	22	in	in	ADP
american_scientific_journal-7274	114	23	this	this	DET
american_scientific_journal-7274	114	24	chapter	chapter	NOUN
american_scientific_journal-7274	114	25	.	.	PUNCT
american_scientific_journal-7274	115	1	we	we	PRON
american_scientific_journal-7274	115	2	continue	continue	VERB
american_scientific_journal-7274	115	3	to	to	PART
american_scientific_journal-7274	115	4	adapt	adapt	VERB
american_scientific_journal-7274	115	5	in	in	ADP
american_scientific_journal-7274	115	6	this	this	DET
american_scientific_journal-7274	115	7	way	way	NOUN
american_scientific_journal-7274	115	8	.	.	PUNCT
american_scientific_journal-7274	116	1	while	while	SCONJ
american_scientific_journal-7274	116	2	creating	create	VERB
american_scientific_journal-7274	116	3	our	our	PRON
american_scientific_journal-7274	116	4	algorithm	algorithm	NOUN
american_scientific_journal-7274	116	5	,	,	PUNCT
american_scientific_journal-7274	116	6	we	we	PRON
american_scientific_journal-7274	116	7	take	take	VERB
american_scientific_journal-7274	116	8	advantage	advantage	NOUN
american_scientific_journal-7274	116	9	of	of	ADP
american_scientific_journal-7274	116	10	the	the	DET
american_scientific_journal-7274	116	11	gradually	gradually	ADV
american_scientific_journal-7274	116	12	varied	varied	ADJ
american_scientific_journal-7274	116	13	function	function	NOUN
american_scientific_journal-7274	116	14	structure	structure	NOUN
american_scientific_journal-7274	116	15	[	[	X
american_scientific_journal-7274	116	16	20	20	NUM
american_scientific_journal-7274	116	17	]	]	PUNCT
american_scientific_journal-7274	116	18	.	.	PUNCT
american_scientific_journal-7274	117	1	we	we	PRON
american_scientific_journal-7274	117	2	apply	apply	VERB
american_scientific_journal-7274	117	3	the	the	DET
american_scientific_journal-7274	117	4	finite	finite	ADJ
american_scientific_journal-7274	117	5	difference	difference	NOUN
american_scientific_journal-7274	117	6	scheme	scheme	NOUN
american_scientific_journal-7274	117	7	while	while	SCONJ
american_scientific_journal-7274	117	8	constructing	construct	VERB
american_scientific_journal-7274	117	9	the	the	DET
american_scientific_journal-7274	117	10	numerical	numerical	ADJ
american_scientific_journal-7274	117	11	structure	structure	NOUN
american_scientific_journal-7274	117	12	of	of	ADP
american_scientific_journal-7274	117	13	the	the	DET
american_scientific_journal-7274	117	14	perona	perona	NOUN
american_scientific_journal-7274	117	15	-	-	PUNCT
american_scientific_journal-7274	117	16	malik	malik	PROPN
american_scientific_journal-7274	117	17	equation	equation	NOUN
american_scientific_journal-7274	117	18	[	[	X
american_scientific_journal-7274	117	19	32,33,35	32,33,35	NOUN
american_scientific_journal-7274	117	20	]	]	PUNCT
american_scientific_journal-7274	117	21	.	.	PUNCT
american_scientific_journal-7274	118	1	our	our	PRON
american_scientific_journal-7274	118	2	algorithm	algorithm	NOUN
american_scientific_journal-7274	118	3	,	,	PUNCT
american_scientific_journal-7274	118	4	which	which	PRON
american_scientific_journal-7274	118	5	we	we	PRON
american_scientific_journal-7274	118	6	have	have	AUX
american_scientific_journal-7274	118	7	established	establish	VERB
american_scientific_journal-7274	118	8	with	with	ADP
american_scientific_journal-7274	118	9	the	the	DET
american_scientific_journal-7274	118	10	help	help	NOUN
american_scientific_journal-7274	118	11	of	of	ADP
american_scientific_journal-7274	118	12	the	the	DET
american_scientific_journal-7274	118	13	perona	perona	NOUN
american_scientific_journal-7274	118	14	-	-	PUNCT
american_scientific_journal-7274	118	15	malik	malik	PROPN
american_scientific_journal-7274	118	16	equation	equation	NOUN
american_scientific_journal-7274	118	17	and	and	CCONJ
american_scientific_journal-7274	118	18	the	the	DET
american_scientific_journal-7274	118	19	digital	digital	ADJ
american_scientific_journal-7274	118	20	-	-	PUNCT
american_scientific_journal-7274	118	21	discrete	discrete	NOUN
american_scientific_journal-7274	118	22	method	method	NOUN
american_scientific_journal-7274	118	23	,	,	PUNCT
american_scientific_journal-7274	118	24	is	be	AUX
american_scientific_journal-7274	118	25	given	give	VERB
american_scientific_journal-7274	118	26	below	below	ADP
american_scientific_journal-7274	118	27	[	[	X
american_scientific_journal-7274	118	28	20,32,33,35	20,32,33,35	NUM
american_scientific_journal-7274	118	29	]	]	SYM
american_scientific_journal-7274	118	30	:	:	PUNCT
american_scientific_journal-7274	118	31	algorithm	algorithm	NOUN
american_scientific_journal-7274	118	32	(	(	PUNCT
american_scientific_journal-7274	118	33	digital	digital	ADJ
american_scientific_journal-7274	118	34	-	-	PUNCT
american_scientific_journal-7274	118	35	discrete	discrete	ADJ
american_scientific_journal-7274	118	36	method	method	NOUN
american_scientific_journal-7274	118	37	for	for	ADP
american_scientific_journal-7274	118	38	perona	perona	NOUN
american_scientific_journal-7274	118	39	-	-	PUNCT
american_scientific_journal-7274	118	40	malik	malik	PROPN
american_scientific_journal-7274	118	41	equation	equation	NOUN
american_scientific_journal-7274	118	42	in	in	ADP
american_scientific_journal-7274	118	43	image	image	NOUN
american_scientific_journal-7274	118	44	processing	processing	NOUN
american_scientific_journal-7274	118	45	)	)	PUNCT
american_scientific_journal-7274	118	46	step	step	NOUN
american_scientific_journal-7274	118	47	1	1	NUM
american_scientific_journal-7274	118	48	:	:	PUNCT
american_scientific_journal-7274	118	49	upload	upload	VERB
american_scientific_journal-7274	118	50	the	the	DET
american_scientific_journal-7274	118	51	main	main	ADJ
american_scientific_journal-7274	118	52	points	point	NOUN
american_scientific_journal-7274	118	53	.	.	PUNCT
american_scientific_journal-7274	119	1	data	datum	NOUN
american_scientific_journal-7274	119	2	points	point	NOUN
american_scientific_journal-7274	119	3	with	with	ADP
american_scientific_journal-7274	119	4	observation	observation	NOUN
american_scientific_journal-7274	119	5	values	value	NOUN
american_scientific_journal-7274	119	6	are	be	AUX
american_scientific_journal-7274	119	7	loaded	load	VERB
american_scientific_journal-7274	119	8	.	.	PUNCT
american_scientific_journal-7274	120	1	step	step	NOUN
american_scientific_journal-7274	120	2	2	2	NUM
american_scientific_journal-7274	120	3	:	:	PUNCT
american_scientific_journal-7274	120	4	identify	identify	VERB
american_scientific_journal-7274	120	5	the	the	DET
american_scientific_journal-7274	120	6	solution	solution	NOUN
american_scientific_journal-7274	120	7	.	.	PUNCT
american_scientific_journal-7274	121	1	arrange	arrange	VERB
american_scientific_journal-7274	121	2	the	the	DET
american_scientific_journal-7274	121	3	points	point	NOUN
american_scientific_journal-7274	121	4	in	in	ADP
american_scientific_journal-7274	121	5	the	the	DET
american_scientific_journal-7274	121	6	lattice	lattice	NOUN
american_scientific_journal-7274	121	7	space	space	NOUN
american_scientific_journal-7274	121	8	.	.	PUNCT
american_scientific_journal-7274	122	1	step	step	NOUN
american_scientific_journal-7274	122	2	3	3	NUM
american_scientific_journal-7274	122	3	:	:	PUNCT
american_scientific_journal-7274	122	4	expand	expand	VERB
american_scientific_journal-7274	122	5	the	the	DET
american_scientific_journal-7274	122	6	function	function	NOUN
american_scientific_journal-7274	122	7	according	accord	VERB
american_scientific_journal-7274	122	8	to	to	ADP
american_scientific_journal-7274	122	9	theorem	theorem	ADJ
american_scientific_journal-7274	122	10	2.2.1	2.2.1	NUM
american_scientific_journal-7274	122	11	using	use	VERB
american_scientific_journal-7274	122	12	the	the	DET
american_scientific_journal-7274	122	13	local	local	ADJ
american_scientific_journal-7274	122	14	lipschitz	lipschitz	NOUN
american_scientific_journal-7274	122	15	condition	condition	NOUN
american_scientific_journal-7274	122	16	.	.	PUNCT
american_scientific_journal-7274	123	1	gvfs	gvfs	PROPN
american_scientific_journal-7274	123	2	are	be	AUX
american_scientific_journal-7274	123	3	obtained	obtain	VERB
american_scientific_journal-7274	123	4	.	.	PUNCT
american_scientific_journal-7274	124	1	(	(	PUNCT
american_scientific_journal-7274	124	2	we	we	PRON
american_scientific_journal-7274	124	3	use	use	VERB
american_scientific_journal-7274	124	4	gradually	gradually	ADV
american_scientific_journal-7274	124	5	varied	varied	ADJ
american_scientific_journal-7274	124	6	function	function	NOUN
american_scientific_journal-7274	124	7	(	(	PUNCT
american_scientific_journal-7274	124	8	gvf	gvf	NOUN
american_scientific_journal-7274	124	9	)	)	PUNCT
american_scientific_journal-7274	124	10	algorithm	algorithm	NOUN
american_scientific_journal-7274	124	11	)	)	PUNCT
american_scientific_journal-7274	124	12	step	step	NOUN
american_scientific_journal-7274	124	13	4	4	NUM
american_scientific_journal-7274	124	14	:	:	PUNCT
american_scientific_journal-7274	124	15	start	start	VERB
american_scientific_journal-7274	124	16	getting	get	VERB
american_scientific_journal-7274	124	17	the	the	DET
american_scientific_journal-7274	124	18	lattice	lattice	NOUN
american_scientific_journal-7274	124	19	points	point	NOUN
american_scientific_journal-7274	124	20	with	with	ADP
american_scientific_journal-7274	124	21	the	the	DET
american_scientific_journal-7274	124	22	iteration	iteration	NOUN
american_scientific_journal-7274	124	23	of	of	ADP
american_scientific_journal-7274	124	24	the	the	DET
american_scientific_journal-7274	124	25	perona	perona	NOUN
american_scientific_journal-7274	124	26	-	-	PUNCT
american_scientific_journal-7274	124	27	malik	malik	PROPN
american_scientific_journal-7274	124	28	equation	equation	NOUN
american_scientific_journal-7274	124	29	that	that	PRON
american_scientific_journal-7274	124	30	we	we	PRON
american_scientific_journal-7274	124	31	obtained	obtain	VERB
american_scientific_journal-7274	124	32	by	by	ADP
american_scientific_journal-7274	124	33	the	the	DET
american_scientific_journal-7274	124	34	finite	finite	ADJ
american_scientific_journal-7274	124	35	difference	difference	NOUN
american_scientific_journal-7274	124	36	method	method	NOUN
american_scientific_journal-7274	124	37	:	:	PUNCT
american_scientific_journal-7274	124	38	𝑢𝑖,𝑗	𝑢𝑖,𝑗	VERB
american_scientific_journal-7274	124	39	𝑘+1	𝑘+1	NUM
american_scientific_journal-7274	124	40	−	−	NOUN
american_scientific_journal-7274	124	41	𝑢𝑖,𝑗	𝑢𝑖,𝑗	VERB
american_scientific_journal-7274	124	42	𝑘	𝑘	NOUN
american_scientific_journal-7274	124	43	∆𝑡	∆𝑡	NOUN
american_scientific_journal-7274	124	44	=	=	PUNCT
american_scientific_journal-7274	124	45	(	(	PUNCT
american_scientific_journal-7274	124	46	𝑔𝑖+1,𝑗	𝑔𝑖+1,𝑗	PROPN
american_scientific_journal-7274	124	47	𝑘	𝑘	PROPN
american_scientific_journal-7274	124	48	+	+	PROPN
american_scientific_journal-7274	124	49	𝑔𝑖,𝑗	𝑔𝑖,𝑗	NOUN
american_scientific_journal-7274	124	50	𝑘	𝑘	X
american_scientific_journal-7274	124	51	)	)	PUNCT
american_scientific_journal-7274	125	1	[	[	X
american_scientific_journal-7274	125	2	𝑢𝑖+1,𝑗	𝑢𝑖+1,𝑗	NOUN
american_scientific_journal-7274	125	3	𝑘	𝑘	PROPN
american_scientific_journal-7274	125	4	−	−	NOUN
american_scientific_journal-7274	125	5	𝑢𝑖,𝑗	𝑢𝑖,𝑗	X
american_scientific_journal-7274	125	6	𝑘	𝑘	X
american_scientific_journal-7274	125	7	]	]	X
american_scientific_journal-7274	125	8	−	−	PROPN
american_scientific_journal-7274	125	9	(	(	PUNCT
american_scientific_journal-7274	125	10	𝑔𝑖,𝑗	𝑔𝑖,𝑗	VERB
american_scientific_journal-7274	125	11	𝑘	𝑘	X
american_scientific_journal-7274	125	12	+	+	X
american_scientific_journal-7274	125	13	𝑔𝑖−1,𝑗	𝑔𝑖−1,𝑗	ADJ
american_scientific_journal-7274	125	14	𝑘	𝑘	NOUN
american_scientific_journal-7274	125	15	)	)	PUNCT
american_scientific_journal-7274	126	1	[	[	X
american_scientific_journal-7274	126	2	𝑢𝑖,𝑗	𝑢𝑖,𝑗	X
american_scientific_journal-7274	126	3	𝑘	𝑘	PRON
american_scientific_journal-7274	126	4	−	−	NOUN
american_scientific_journal-7274	126	5	𝑢𝑖−1,𝑗	𝑢𝑖−1,𝑗	NOUN
american_scientific_journal-7274	126	6	𝑘	𝑘	X
american_scientific_journal-7274	126	7	]	]	PUNCT
american_scientific_journal-7274	126	8	american	american	PROPN
american_scientific_journal-7274	126	9	academic	academic	ADJ
american_scientific_journal-7274	126	10	scientific	scientific	ADJ
american_scientific_journal-7274	126	11	research	research	NOUN
american_scientific_journal-7274	126	12	journal	journal	NOUN
american_scientific_journal-7274	126	13	for	for	ADP
american_scientific_journal-7274	126	14	engineering	engineering	NOUN
american_scientific_journal-7274	126	15	,	,	PUNCT
american_scientific_journal-7274	126	16	technology	technology	NOUN
american_scientific_journal-7274	126	17	,	,	PUNCT
american_scientific_journal-7274	126	18	and	and	CCONJ
american_scientific_journal-7274	126	19	sciences	science	NOUN
american_scientific_journal-7274	126	20	(	(	PUNCT
american_scientific_journal-7274	126	21	asrjets	asrjet	NOUN
american_scientific_journal-7274	126	22	)	)	PUNCT
american_scientific_journal-7274	126	23	(	(	PUNCT
american_scientific_journal-7274	126	24	2021	2021	NUM
american_scientific_journal-7274	126	25	)	)	PUNCT
american_scientific_journal-7274	126	26	volume	volume	NOUN
american_scientific_journal-7274	126	27	84	84	NUM
american_scientific_journal-7274	126	28	,	,	PUNCT
american_scientific_journal-7274	126	29	no1	no1	PROPN
american_scientific_journal-7274	126	30	,	,	PUNCT
american_scientific_journal-7274	126	31	pp	pp	ADP
american_scientific_journal-7274	126	32	118	118	NUM
american_scientific_journal-7274	126	33	-	-	SYM
american_scientific_journal-7274	126	34	129	129	NUM
american_scientific_journal-7274	126	35	124	124	NUM
american_scientific_journal-7274	126	36	+	+	ADJ
american_scientific_journal-7274	126	37	(	(	PUNCT
american_scientific_journal-7274	126	38	𝑔𝑖,𝑗+1	𝑔𝑖,𝑗+1	X
american_scientific_journal-7274	126	39	𝑘	𝑘	X
american_scientific_journal-7274	126	40	+	+	NOUN
american_scientific_journal-7274	126	41	𝑔𝑖,𝑗	𝑔𝑖,𝑗	NOUN
american_scientific_journal-7274	126	42	𝑘	𝑘	X
american_scientific_journal-7274	126	43	)	)	PUNCT
american_scientific_journal-7274	126	44	[	[	X
american_scientific_journal-7274	126	45	𝑢𝑖,𝑗+1	𝑢𝑖,𝑗+1	NOUN
american_scientific_journal-7274	126	46	𝑘	𝑘	DET
american_scientific_journal-7274	126	47	−	−	NOUN
american_scientific_journal-7274	126	48	𝑢𝑖,𝑗	𝑢𝑖,𝑗	X
american_scientific_journal-7274	126	49	𝑘	𝑘	X
american_scientific_journal-7274	126	50	]	]	X
american_scientific_journal-7274	126	51	−	−	PROPN
american_scientific_journal-7274	126	52	(	(	PUNCT
american_scientific_journal-7274	126	53	𝑔𝑖,𝑗	𝑔𝑖,𝑗	VERB
american_scientific_journal-7274	126	54	𝑘	𝑘	ADP
american_scientific_journal-7274	126	55	+	+	PUNCT
american_scientific_journal-7274	126	56	𝑔𝑖,𝑗−1	𝑔𝑖,𝑗−1	X
american_scientific_journal-7274	126	57	𝑘	𝑘	X
american_scientific_journal-7274	126	58	)	)	PUNCT
american_scientific_journal-7274	126	59	[	[	X
american_scientific_journal-7274	126	60	𝑢𝑖,𝑗	𝑢𝑖,𝑗	X
american_scientific_journal-7274	126	61	𝑘	𝑘	DET
american_scientific_journal-7274	126	62	−	−	PROPN
american_scientific_journal-7274	126	63	𝑢𝑖,𝑗−1	𝑢𝑖,𝑗−1	PROPN
american_scientific_journal-7274	126	64	𝑘	𝑘	X
american_scientific_journal-7274	126	65	]	]	PUNCT
american_scientific_journal-7274	126	66	‖∇𝑢𝑖,𝑗‖	‖∇𝑢𝑖,𝑗‖	PROPN
american_scientific_journal-7274	126	67	=	=	SYM
american_scientific_journal-7274	126	68	√	√	PROPN
american_scientific_journal-7274	126	69	(	(	PUNCT
american_scientific_journal-7274	126	70	𝑢𝑖+1,𝑗	𝑢𝑖+1,𝑗	PROPN
american_scientific_journal-7274	126	71	−	−	PROPN
american_scientific_journal-7274	126	72	𝑢𝑖−1,𝑗	𝑢𝑖−1,𝑗	NOUN
american_scientific_journal-7274	126	73	2	2	NUM
american_scientific_journal-7274	126	74	)	)	PUNCT
american_scientific_journal-7274	126	75	2	2	NUM
american_scientific_journal-7274	126	76	+	+	CCONJ
american_scientific_journal-7274	126	77	(	(	PUNCT
american_scientific_journal-7274	126	78	𝑢𝑖,𝑗+1	𝑢𝑖,𝑗+1	X
american_scientific_journal-7274	126	79	−	−	PROPN
american_scientific_journal-7274	126	80	𝑢𝑖,𝑗−1	𝑢𝑖,𝑗−1	PROPN
american_scientific_journal-7274	126	81	2	2	NUM
american_scientific_journal-7274	126	82	)	)	PUNCT
american_scientific_journal-7274	126	83	2	2	NUM
american_scientific_journal-7274	126	84	step	step	NOUN
american_scientific_journal-7274	126	85	5	5	NUM
american_scientific_journal-7274	126	86	:	:	PUNCT
american_scientific_journal-7274	126	87	restore	restore	VERB
american_scientific_journal-7274	126	88	the	the	DET
american_scientific_journal-7274	126	89	current	current	ADJ
american_scientific_journal-7274	126	90	values	value	NOUN
american_scientific_journal-7274	126	91	obtained	obtain	VERB
american_scientific_journal-7274	126	92	in	in	ADP
american_scientific_journal-7274	126	93	step	step	NOUN
american_scientific_journal-7274	126	94	4	4	NUM
american_scientific_journal-7274	126	95	using	use	VERB
american_scientific_journal-7274	126	96	a	a	DET
american_scientific_journal-7274	126	97	gradually	gradually	ADV
american_scientific_journal-7274	126	98	varied	varied	ADJ
american_scientific_journal-7274	126	99	function	function	NOUN
american_scientific_journal-7274	126	100	:	:	PUNCT
american_scientific_journal-7274	126	101	we	we	PRON
american_scientific_journal-7274	126	102	continue	continue	VERB
american_scientific_journal-7274	126	103	to	to	PART
american_scientific_journal-7274	126	104	use	use	VERB
american_scientific_journal-7274	126	105	digital	digital	ADJ
american_scientific_journal-7274	126	106	-	-	PUNCT
american_scientific_journal-7274	126	107	discrete	discrete	NOUN
american_scientific_journal-7274	126	108	adaptation	adaptation	NOUN
american_scientific_journal-7274	126	109	in	in	ADP
american_scientific_journal-7274	126	110	(	(	PUNCT
american_scientific_journal-7274	126	111	k+1	k+1	NOUN
american_scientific_journal-7274	126	112	)	)	PUNCT
american_scientific_journal-7274	126	113	so	so	SCONJ
american_scientific_journal-7274	126	114	that	that	PRON
american_scientific_journal-7274	126	115	𝑢𝑖,𝑗	𝑢𝑖,𝑗	VERB
american_scientific_journal-7274	126	116	𝑘+1	𝑘+1	PRON
american_scientific_journal-7274	126	117	←	←	PROPN
american_scientific_journal-7274	126	118	(	(	PUNCT
american_scientific_journal-7274	126	119	𝑢𝑖,𝑗	𝑢𝑖,𝑗	ADP
american_scientific_journal-7274	126	120	𝑘+1	𝑘+1	X
american_scientific_journal-7274	126	121	+	+	X
american_scientific_journal-7274	126	122	𝑔𝑣𝑓(𝑖	𝑔𝑣𝑓(𝑖	PROPN
american_scientific_journal-7274	126	123	,	,	PUNCT
american_scientific_journal-7274	126	124	𝑗)/2	𝑗)/2	PROPN
american_scientific_journal-7274	126	125	)	)	PUNCT
american_scientific_journal-7274	126	126	step	step	NOUN
american_scientific_journal-7274	126	127	6	6	NUM
american_scientific_journal-7274	126	128	:	:	PUNCT
american_scientific_journal-7274	126	129	perform	perform	VERB
american_scientific_journal-7274	126	130	image	image	NOUN
american_scientific_journal-7274	126	131	processing	processing	NOUN
american_scientific_journal-7274	126	132	analysis	analysis	NOUN
american_scientific_journal-7274	126	133	with	with	ADP
american_scientific_journal-7274	126	134	the	the	DET
american_scientific_journal-7274	126	135	help	help	NOUN
american_scientific_journal-7274	126	136	of	of	ADP
american_scientific_journal-7274	126	137	the	the	DET
american_scientific_journal-7274	126	138	matlab	matlab	PROPN
american_scientific_journal-7274	126	139	-	-	PUNCT
american_scientific_journal-7274	126	140	r2020b	r2020b	PROPN
american_scientific_journal-7274	126	141	package	package	NOUN
american_scientific_journal-7274	126	142	program	program	NOUN
american_scientific_journal-7274	126	143	using	use	VERB
american_scientific_journal-7274	126	144	our	our	PRON
american_scientific_journal-7274	126	145	algorithm	algorithm	NOUN
american_scientific_journal-7274	126	146	.	.	PUNCT
american_scientific_journal-7274	127	1	we	we	PRON
american_scientific_journal-7274	127	2	obtained	obtain	VERB
american_scientific_journal-7274	127	3	images	image	NOUN
american_scientific_journal-7274	127	4	for	for	ADP
american_scientific_journal-7274	127	5	different	different	ADJ
american_scientific_journal-7274	127	6	t	t	NOUN
american_scientific_journal-7274	127	7	values	value	NOUN
american_scientific_journal-7274	127	8	in	in	ADP
american_scientific_journal-7274	127	9	figure	figure	NOUN
american_scientific_journal-7274	127	10	3.3.1	3.3.1	NUM
american_scientific_journal-7274	127	11	and	and	CCONJ
american_scientific_journal-7274	127	12	figure	figure	VERB
american_scientific_journal-7274	127	13	3.3.2	3.3.2	NUM
american_scientific_journal-7274	127	14	by	by	ADP
american_scientific_journal-7274	127	15	using	use	VERB
american_scientific_journal-7274	127	16	our	our	PRON
american_scientific_journal-7274	127	17	algorithm	algorithm	NOUN
american_scientific_journal-7274	127	18	.	.	PUNCT
american_scientific_journal-7274	128	1	original	original	ADJ
american_scientific_journal-7274	128	2	image	image	NOUN
american_scientific_journal-7274	128	3	american	american	ADJ
american_scientific_journal-7274	128	4	academic	academic	ADJ
american_scientific_journal-7274	128	5	scientific	scientific	ADJ
american_scientific_journal-7274	128	6	research	research	NOUN
american_scientific_journal-7274	128	7	journal	journal	NOUN
american_scientific_journal-7274	128	8	for	for	ADP
american_scientific_journal-7274	128	9	engineering	engineering	NOUN
american_scientific_journal-7274	128	10	,	,	PUNCT
american_scientific_journal-7274	128	11	technology	technology	NOUN
american_scientific_journal-7274	128	12	,	,	PUNCT
american_scientific_journal-7274	128	13	and	and	CCONJ
american_scientific_journal-7274	128	14	sciences	science	NOUN
american_scientific_journal-7274	128	15	(	(	PUNCT
american_scientific_journal-7274	128	16	asrjets	asrjet	NOUN
american_scientific_journal-7274	128	17	)	)	PUNCT
american_scientific_journal-7274	128	18	(	(	PUNCT
american_scientific_journal-7274	128	19	2021	2021	NUM
american_scientific_journal-7274	128	20	)	)	PUNCT
american_scientific_journal-7274	128	21	volume	volume	NOUN
american_scientific_journal-7274	128	22	84	84	NUM
american_scientific_journal-7274	128	23	,	,	PUNCT
american_scientific_journal-7274	128	24	no1	no1	PROPN
american_scientific_journal-7274	128	25	,	,	PUNCT
american_scientific_journal-7274	128	26	pp	pp	ADP
american_scientific_journal-7274	128	27	118	118	NUM
american_scientific_journal-7274	128	28	-	-	SYM
american_scientific_journal-7274	128	29	129	129	NUM
american_scientific_journal-7274	128	30	125	125	NUM
american_scientific_journal-7274	128	31	figure	figure	NOUN
american_scientific_journal-7274	128	32	3.3.1	3.3.1	NUM
american_scientific_journal-7274	128	33	original	original	ADJ
american_scientific_journal-7274	128	34	image	image	NOUN
american_scientific_journal-7274	128	35	american	american	ADJ
american_scientific_journal-7274	128	36	academic	academic	ADJ
american_scientific_journal-7274	128	37	scientific	scientific	ADJ
american_scientific_journal-7274	128	38	research	research	NOUN
american_scientific_journal-7274	128	39	journal	journal	NOUN
american_scientific_journal-7274	128	40	for	for	ADP
american_scientific_journal-7274	128	41	engineering	engineering	NOUN
american_scientific_journal-7274	128	42	,	,	PUNCT
american_scientific_journal-7274	128	43	technology	technology	NOUN
american_scientific_journal-7274	128	44	,	,	PUNCT
american_scientific_journal-7274	128	45	and	and	CCONJ
american_scientific_journal-7274	128	46	sciences	science	NOUN
american_scientific_journal-7274	128	47	(	(	PUNCT
american_scientific_journal-7274	128	48	asrjets	asrjet	NOUN
american_scientific_journal-7274	128	49	)	)	PUNCT
american_scientific_journal-7274	128	50	(	(	PUNCT
american_scientific_journal-7274	128	51	2021	2021	NUM
american_scientific_journal-7274	128	52	)	)	PUNCT
american_scientific_journal-7274	128	53	volume	volume	NOUN
american_scientific_journal-7274	128	54	84	84	NUM
american_scientific_journal-7274	128	55	,	,	PUNCT
american_scientific_journal-7274	128	56	no1	no1	PROPN
american_scientific_journal-7274	128	57	,	,	PUNCT
american_scientific_journal-7274	128	58	pp	pp	ADP
american_scientific_journal-7274	128	59	118	118	NUM
american_scientific_journal-7274	128	60	-	-	SYM
american_scientific_journal-7274	128	61	129	129	NUM
american_scientific_journal-7274	128	62	126	126	NUM
american_scientific_journal-7274	128	63	figure	figure	NOUN
american_scientific_journal-7274	128	64	3.3.2	3.3.2	NUM
american_scientific_journal-7274	128	65	american	american	ADJ
american_scientific_journal-7274	128	66	academic	academic	ADJ
american_scientific_journal-7274	128	67	scientific	scientific	ADJ
american_scientific_journal-7274	128	68	research	research	NOUN
american_scientific_journal-7274	128	69	journal	journal	NOUN
american_scientific_journal-7274	128	70	for	for	ADP
american_scientific_journal-7274	128	71	engineering	engineering	NOUN
american_scientific_journal-7274	128	72	,	,	PUNCT
american_scientific_journal-7274	128	73	technology	technology	NOUN
american_scientific_journal-7274	128	74	,	,	PUNCT
american_scientific_journal-7274	128	75	and	and	CCONJ
american_scientific_journal-7274	128	76	sciences	science	NOUN
american_scientific_journal-7274	128	77	(	(	PUNCT
american_scientific_journal-7274	128	78	asrjets	asrjet	NOUN
american_scientific_journal-7274	128	79	)	)	PUNCT
american_scientific_journal-7274	128	80	(	(	PUNCT
american_scientific_journal-7274	128	81	2021	2021	NUM
american_scientific_journal-7274	128	82	)	)	PUNCT
american_scientific_journal-7274	128	83	volume	volume	NOUN
american_scientific_journal-7274	128	84	84	84	NUM
american_scientific_journal-7274	128	85	,	,	PUNCT
american_scientific_journal-7274	128	86	no1	no1	PROPN
american_scientific_journal-7274	128	87	,	,	PUNCT
american_scientific_journal-7274	128	88	pp	pp	ADP
american_scientific_journal-7274	128	89	118	118	NUM
american_scientific_journal-7274	128	90	-	-	SYM
american_scientific_journal-7274	128	91	129	129	NUM
american_scientific_journal-7274	128	92	127	127	NUM
american_scientific_journal-7274	128	93	4	4	NUM
american_scientific_journal-7274	128	94	.	.	PUNCT
american_scientific_journal-7274	128	95	conclusion	conclusion	NOUN
american_scientific_journal-7274	128	96	in	in	ADP
american_scientific_journal-7274	128	97	this	this	DET
american_scientific_journal-7274	128	98	study	study	NOUN
american_scientific_journal-7274	129	1	,	,	PUNCT
american_scientific_journal-7274	129	2	we	we	PRON
american_scientific_journal-7274	129	3	applied	apply	VERB
american_scientific_journal-7274	129	4	a	a	DET
american_scientific_journal-7274	129	5	new	new	ADJ
american_scientific_journal-7274	129	6	and	and	CCONJ
american_scientific_journal-7274	129	7	effective	effective	ADJ
american_scientific_journal-7274	129	8	algorithm	algorithm	NOUN
american_scientific_journal-7274	129	9	for	for	ADP
american_scientific_journal-7274	129	10	image	image	NOUN
american_scientific_journal-7274	129	11	processing	processing	NOUN
american_scientific_journal-7274	129	12	.	.	PUNCT
american_scientific_journal-7274	130	1	we	we	PRON
american_scientific_journal-7274	130	2	used	use	VERB
american_scientific_journal-7274	130	3	the	the	DET
american_scientific_journal-7274	130	4	matlab	matlab	PROPN
american_scientific_journal-7274	130	5	-	-	PUNCT
american_scientific_journal-7274	130	6	r2020b	r2020b	PROPN
american_scientific_journal-7274	130	7	package	package	NOUN
american_scientific_journal-7274	130	8	program	program	NOUN
american_scientific_journal-7274	130	9	when	when	SCONJ
american_scientific_journal-7274	130	10	analyzing	analyzing	NOUN
american_scientific_journal-7274	130	11	images	image	NOUN
american_scientific_journal-7274	130	12	.	.	PUNCT
american_scientific_journal-7274	131	1	the	the	DET
american_scientific_journal-7274	131	2	greatest	great	ADJ
american_scientific_journal-7274	131	3	progress	progress	NOUN
american_scientific_journal-7274	131	4	we	we	PRON
american_scientific_journal-7274	131	5	have	have	AUX
american_scientific_journal-7274	131	6	achieved	achieve	VERB
american_scientific_journal-7274	131	7	in	in	ADP
american_scientific_journal-7274	131	8	image	image	NOUN
american_scientific_journal-7274	131	9	analysis	analysis	NOUN
american_scientific_journal-7274	131	10	is	be	AUX
american_scientific_journal-7274	131	11	the	the	DET
american_scientific_journal-7274	131	12	preservation	preservation	NOUN
american_scientific_journal-7274	131	13	of	of	ADP
american_scientific_journal-7274	131	14	image	image	NOUN
american_scientific_journal-7274	131	15	quality	quality	NOUN
american_scientific_journal-7274	131	16	and	and	CCONJ
american_scientific_journal-7274	131	17	the	the	DET
american_scientific_journal-7274	131	18	preservation	preservation	NOUN
american_scientific_journal-7274	131	19	of	of	ADP
american_scientific_journal-7274	131	20	images	image	NOUN
american_scientific_journal-7274	131	21	as	as	SCONJ
american_scientific_journal-7274	131	22	the	the	DET
american_scientific_journal-7274	131	23	t	t	PROPN
american_scientific_journal-7274	131	24	values	value	NOUN
american_scientific_journal-7274	131	25	increase	increase	VERB
american_scientific_journal-7274	131	26	.	.	PUNCT
american_scientific_journal-7274	132	1	the	the	DET
american_scientific_journal-7274	132	2	solution	solution	NOUN
american_scientific_journal-7274	132	3	algorithm	algorithm	NOUN
american_scientific_journal-7274	132	4	we	we	PRON
american_scientific_journal-7274	132	5	use	use	VERB
american_scientific_journal-7274	132	6	is	be	AUX
american_scientific_journal-7274	132	7	simpler	simple	ADJ
american_scientific_journal-7274	132	8	than	than	ADP
american_scientific_journal-7274	132	9	other	other	ADJ
american_scientific_journal-7274	132	10	algorithms	algorithm	NOUN
american_scientific_journal-7274	132	11	and	and	CCONJ
american_scientific_journal-7274	132	12	it	it	PRON
american_scientific_journal-7274	132	13	is	be	AUX
american_scientific_journal-7274	132	14	easier	easy	ADJ
american_scientific_journal-7274	132	15	to	to	PART
american_scientific_journal-7274	132	16	apply	apply	VERB
american_scientific_journal-7274	132	17	to	to	ADP
american_scientific_journal-7274	132	18	package	package	NOUN
american_scientific_journal-7274	132	19	programs	program	NOUN
american_scientific_journal-7274	132	20	such	such	ADJ
american_scientific_journal-7274	132	21	as	as	ADP
american_scientific_journal-7274	132	22	matlab	matlab	PROPN
american_scientific_journal-7274	132	23	.	.	PUNCT
american_scientific_journal-7274	133	1	since	since	SCONJ
american_scientific_journal-7274	133	2	the	the	DET
american_scientific_journal-7274	133	3	algorithm	algorithm	NOUN
american_scientific_journal-7274	133	4	is	be	AUX
american_scientific_journal-7274	133	5	based	base	VERB
american_scientific_journal-7274	133	6	on	on	ADP
american_scientific_journal-7274	133	7	topology	topology	NOUN
american_scientific_journal-7274	133	8	,	,	PUNCT
american_scientific_journal-7274	133	9	graph	graph	NOUN
american_scientific_journal-7274	133	10	theory	theory	NOUN
american_scientific_journal-7274	133	11	and	and	CCONJ
american_scientific_journal-7274	133	12	continuity	continuity	NOUN
american_scientific_journal-7274	133	13	,	,	PUNCT
american_scientific_journal-7274	133	14	the	the	DET
american_scientific_journal-7274	133	15	values	value	NOUN
american_scientific_journal-7274	133	16	we	we	PRON
american_scientific_journal-7274	133	17	obtained	obtain	VERB
american_scientific_journal-7274	133	18	in	in	ADP
american_scientific_journal-7274	133	19	the	the	DET
american_scientific_journal-7274	133	20	revised	revise	VERB
american_scientific_journal-7274	133	21	finite	finite	ADJ
american_scientific_journal-7274	133	22	difference	difference	NOUN
american_scientific_journal-7274	133	23	approach	approach	NOUN
american_scientific_journal-7274	133	24	with	with	ADP
american_scientific_journal-7274	133	25	digital	digital	ADJ
american_scientific_journal-7274	133	26	topology	topology	NOUN
american_scientific_journal-7274	133	27	are	be	AUX
american_scientific_journal-7274	133	28	efficient	efficient	ADJ
american_scientific_journal-7274	133	29	and	and	CCONJ
american_scientific_journal-7274	133	30	stable	stable	ADJ
american_scientific_journal-7274	133	31	.	.	PUNCT
american_scientific_journal-7274	134	1	we	we	PRON
american_scientific_journal-7274	134	2	are	be	AUX
american_scientific_journal-7274	134	3	considering	consider	VERB
american_scientific_journal-7274	134	4	using	use	VERB
american_scientific_journal-7274	134	5	the	the	DET
american_scientific_journal-7274	134	6	digital	digital	ADJ
american_scientific_journal-7274	134	7	-	-	PUNCT
american_scientific_journal-7274	134	8	discrete	discrete	NOUN
american_scientific_journal-7274	134	9	method	method	NOUN
american_scientific_journal-7274	134	10	and	and	CCONJ
american_scientific_journal-7274	134	11	the	the	DET
american_scientific_journal-7274	134	12	methods	method	NOUN
american_scientific_journal-7274	134	13	produced	produce	VERB
american_scientific_journal-7274	134	14	from	from	ADP
american_scientific_journal-7274	134	15	this	this	DET
american_scientific_journal-7274	134	16	method	method	NOUN
american_scientific_journal-7274	134	17	in	in	ADP
american_scientific_journal-7274	134	18	imaging	imaging	NOUN
american_scientific_journal-7274	134	19	systems	system	NOUN
american_scientific_journal-7274	134	20	in	in	ADP
american_scientific_journal-7274	134	21	other	other	ADJ
american_scientific_journal-7274	134	22	fields	field	NOUN
american_scientific_journal-7274	134	23	such	such	ADJ
american_scientific_journal-7274	134	24	as	as	ADP
american_scientific_journal-7274	134	25	underwater	underwater	ADJ
american_scientific_journal-7274	134	26	imaging	imaging	NOUN
american_scientific_journal-7274	134	27	systems	system	NOUN
american_scientific_journal-7274	134	28	and	and	CCONJ
american_scientific_journal-7274	134	29	biomedical	biomedical	ADJ
american_scientific_journal-7274	134	30	imaging	imaging	NOUN
american_scientific_journal-7274	134	31	systems	system	NOUN
american_scientific_journal-7274	134	32	.	.	PUNCT
american_scientific_journal-7274	135	1	acknowledgement	acknowledgement	NOUN
american_scientific_journal-7274	135	2	this	this	DET
american_scientific_journal-7274	135	3	study	study	NOUN
american_scientific_journal-7274	135	4	was	be	AUX
american_scientific_journal-7274	135	5	produced	produce	VERB
american_scientific_journal-7274	135	6	from	from	ADP
american_scientific_journal-7274	135	7	the	the	DET
american_scientific_journal-7274	135	8	first	first	ADJ
american_scientific_journal-7274	135	9	author	author	NOUN
american_scientific_journal-7274	135	10	's	's	PART
american_scientific_journal-7274	135	11	doctoral	doctoral	ADJ
american_scientific_journal-7274	135	12	thesis	thesis	NOUN
american_scientific_journal-7274	135	13	.	.	PUNCT
american_scientific_journal-7274	136	1	references	reference	NOUN
american_scientific_journal-7274	136	2	[	[	X
american_scientific_journal-7274	136	3	1	1	NUM
american_scientific_journal-7274	136	4	]	]	PUNCT
american_scientific_journal-7274	136	5	.	.	PUNCT
american_scientific_journal-7274	137	1	k.mikula	k.mikula	NOUN
american_scientific_journal-7274	137	2	,	,	PUNCT
american_scientific_journal-7274	137	3	n.ramarosy	n.ramarosy	ADJ
american_scientific_journal-7274	137	4	,	,	PUNCT
american_scientific_journal-7274	137	5	semi	semi	ADJ
american_scientific_journal-7274	137	6	-	-	ADJ
american_scientific_journal-7274	137	7	implicit	implicit	ADJ
american_scientific_journal-7274	137	8	finite	finite	ADJ
american_scientific_journal-7274	137	9	volume	volume	NOUN
american_scientific_journal-7274	137	10	scheme	scheme	NOUN
american_scientific_journal-7274	137	11	for	for	ADP
american_scientific_journal-7274	137	12	solving	solve	VERB
american_scientific_journal-7274	137	13	nonlinear	nonlinear	ADJ
american_scientific_journal-7274	137	14	diffusion	diffusion	NOUN
american_scientific_journal-7274	137	15	equations	equation	NOUN
american_scientific_journal-7274	137	16	in	in	ADP
american_scientific_journal-7274	137	17	image	image	NOUN
american_scientific_journal-7274	137	18	processing	processing	NOUN
american_scientific_journal-7274	137	19	,	,	PUNCT
american_scientific_journal-7274	137	20	numerische	numerische	PROPN
american_scientific_journal-7274	137	21	mathematik	mathematik	PROPN
american_scientific_journal-7274	137	22	89	89	NUM
american_scientific_journal-7274	137	23	(	(	PUNCT
american_scientific_journal-7274	137	24	2001	2001	NUM
american_scientific_journal-7274	137	25	)	)	PUNCT
american_scientific_journal-7274	138	1	561–590	561–590	NUM
american_scientific_journal-7274	138	2	[	[	X
american_scientific_journal-7274	138	3	2	2	NUM
american_scientific_journal-7274	138	4	]	]	PUNCT
american_scientific_journal-7274	138	5	.	.	PUNCT
american_scientific_journal-7274	139	1	a.sarti	a.sarti	PROPN
american_scientific_journal-7274	139	2	,	,	PUNCT
american_scientific_journal-7274	139	3	k.mikula	k.mikula	NOUN
american_scientific_journal-7274	139	4	,	,	PUNCT
american_scientific_journal-7274	139	5	f.sgallari	f.sgallari	ADJ
american_scientific_journal-7274	139	6	,	,	PUNCT
american_scientific_journal-7274	139	7	c.	c.	PROPN
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american_scientific_journal-7274	139	9	,	,	PUNCT
american_scientific_journal-7274	139	10	evolutionary	evolutionary	ADJ
american_scientific_journal-7274	139	11	partial	partial	ADJ
american_scientific_journal-7274	139	12	differential	differential	ADJ
american_scientific_journal-7274	139	13	equations	equation	NOUN
american_scientific_journal-7274	139	14	for	for	ADP
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american_scientific_journal-7274	139	16	image	image	NOUN
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american_scientific_journal-7274	139	18	,	,	PUNCT
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american_scientific_journal-7274	139	20	of	of	ADP
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american_scientific_journal-7274	139	22	informatics	informatic	NOUN
american_scientific_journal-7274	139	23	35	35	NUM
american_scientific_journal-7274	139	24	(	(	PUNCT
american_scientific_journal-7274	139	25	2002	2002	NUM
american_scientific_journal-7274	139	26	)	)	PUNCT
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american_scientific_journal-7274	141	2	3	3	NUM
american_scientific_journal-7274	141	3	]	]	PUNCT
american_scientific_journal-7274	141	4	.	.	PUNCT
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american_scientific_journal-7274	142	2	,	,	PUNCT
american_scientific_journal-7274	142	3	efficient	efficient	ADJ
american_scientific_journal-7274	142	4	image	image	NOUN
american_scientific_journal-7274	142	5	segmentation	segmentation	NOUN
american_scientific_journal-7274	142	6	using	use	VERB
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american_scientific_journal-7274	142	8	differential	differential	ADJ
american_scientific_journal-7274	142	9	equations	equation	NOUN
american_scientific_journal-7274	142	10	and	and	CCONJ
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american_scientific_journal-7274	142	15	34	34	NUM
american_scientific_journal-7274	142	16	(	(	PUNCT
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american_scientific_journal-7274	142	20	-	-	SYM
american_scientific_journal-7274	142	21	1824	1824	NUM
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american_scientific_journal-7274	143	2	4	4	NUM
american_scientific_journal-7274	143	3	]	]	PUNCT
american_scientific_journal-7274	143	4	.	.	PUNCT
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american_scientific_journal-7274	144	2	,	,	PUNCT
american_scientific_journal-7274	144	3	image	image	NOUN
american_scientific_journal-7274	144	4	processing	processing	NOUN
american_scientific_journal-7274	144	5	with	with	ADP
american_scientific_journal-7274	144	6	partial	partial	ADJ
american_scientific_journal-7274	144	7	differential	differential	NOUN
american_scientific_journal-7274	144	8	equations	equation	NOUN
american_scientific_journal-7274	144	9	,	,	PUNCT
american_scientific_journal-7274	144	10	modern	modern	ADJ
american_scientific_journal-7274	144	11	methods	method	NOUN
american_scientific_journal-7274	144	12	in	in	ADP
american_scientific_journal-7274	144	13	scientific	scientific	ADJ
american_scientific_journal-7274	144	14	computing	computing	NOUN
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american_scientific_journal-7274	144	17	75	75	NUM
american_scientific_journal-7274	144	18	(	(	PUNCT
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american_scientific_journal-7274	144	21	283	283	NUM
american_scientific_journal-7274	144	22	-	-	SYM
american_scientific_journal-7274	144	23	321	321	NUM
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american_scientific_journal-7274	145	4	.	.	PUNCT
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american_scientific_journal-7274	146	2	,	,	PUNCT
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american_scientific_journal-7274	146	4	differential	differential	NOUN
american_scientific_journal-7274	146	5	equations	equation	NOUN
american_scientific_journal-7274	146	6	-	-	PUNCT
american_scientific_journal-7274	146	7	based	base	VERB
american_scientific_journal-7274	146	8	segmentation	segmentation	NOUN
american_scientific_journal-7274	146	9	for	for	ADP
american_scientific_journal-7274	146	10	radiotherapy	radiotherapy	NOUN
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american_scientific_journal-7274	146	13	,	,	PUNCT
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american_scientific_journal-7274	146	15	biosciences	bioscience	NOUN
american_scientific_journal-7274	146	16	and	and	CCONJ
american_scientific_journal-7274	146	17	engineering	engineering	NOUN
american_scientific_journal-7274	146	18	2(2	2(2	NUM
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american_scientific_journal-7274	146	20	(	(	PUNCT
american_scientific_journal-7274	146	21	2005	2005	NUM
american_scientific_journal-7274	146	22	)	)	PUNCT
american_scientific_journal-7274	146	23	209	209	NUM
american_scientific_journal-7274	146	24	-	-	SYM
american_scientific_journal-7274	146	25	226	226	NUM
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american_scientific_journal-7274	147	2	6	6	NUM
american_scientific_journal-7274	147	3	]	]	PUNCT
american_scientific_journal-7274	147	4	.	.	PUNCT
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american_scientific_journal-7274	148	2	,	,	PUNCT
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american_scientific_journal-7274	148	4	,	,	PUNCT
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american_scientific_journal-7274	148	6	,	,	PUNCT
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american_scientific_journal-7274	148	9	in	in	ADP
american_scientific_journal-7274	148	10	medical	medical	ADJ
american_scientific_journal-7274	148	11	image	image	NOUN
american_scientific_journal-7274	148	12	processing	processing	NOUN
american_scientific_journal-7274	148	13	,	,	PUNCT
american_scientific_journal-7274	148	14	bulletin	bulletin	NOUN
american_scientific_journal-7274	148	15	(	(	PUNCT
american_scientific_journal-7274	148	16	new	new	ADJ
american_scientific_journal-7274	148	17	series	series	NOUN
american_scientific_journal-7274	148	18	)	)	PUNCT
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american_scientific_journal-7274	148	20	the	the	DET
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american_scientific_journal-7274	148	22	mathematical	mathematical	PROPN
american_scientific_journal-7274	148	23	society	society	PROPN
american_scientific_journal-7274	148	24	43(3	43(3	NUM
american_scientific_journal-7274	148	25	)	)	PUNCT
american_scientific_journal-7274	148	26	(	(	PUNCT
american_scientific_journal-7274	148	27	2006	2006	NUM
american_scientific_journal-7274	148	28	)	)	PUNCT
american_scientific_journal-7274	149	1	365–396	365–396	NUM
american_scientific_journal-7274	150	1	[	[	X
american_scientific_journal-7274	150	2	7	7	NUM
american_scientific_journal-7274	150	3	]	]	X
american_scientific_journal-7274	150	4	.	.	PUNCT
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american_scientific_journal-7274	151	2	,	,	PUNCT
american_scientific_journal-7274	151	3	image	image	NOUN
american_scientific_journal-7274	151	4	processing	processing	NOUN
american_scientific_journal-7274	151	5	with	with	ADP
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american_scientific_journal-7274	151	10	,	,	PUNCT
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american_scientific_journal-7274	151	12	annual	annual	ADJ
american_scientific_journal-7274	151	13	workshop	workshop	NOUN
american_scientific_journal-7274	151	14	of	of	ADP
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american_scientific_journal-7274	151	18	for	for	ADP
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american_scientific_journal-7274	151	21	(	(	PUNCT
american_scientific_journal-7274	151	22	oagm	oagm	ADJ
american_scientific_journal-7274	151	23	/	/	SYM
american_scientific_journal-7274	151	24	aapr	aapr	NOUN
american_scientific_journal-7274	151	25	)	)	PUNCT
american_scientific_journal-7274	151	26	,	,	PUNCT
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american_scientific_journal-7274	151	28	(	(	PUNCT
american_scientific_journal-7274	151	29	schloss	schloss	PROPN
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american_scientific_journal-7274	151	31	,	,	PUNCT
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american_scientific_journal-7274	151	33	,	,	PUNCT
american_scientific_journal-7274	151	34	may	may	AUX
american_scientific_journal-7274	151	35	3	3	NUM
american_scientific_journal-7274	151	36	-	-	SYM
american_scientific_journal-7274	151	37	4	4	NUM
american_scientific_journal-7274	151	38	,	,	PUNCT
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american_scientific_journal-7274	151	40	2007	2007	NUM
american_scientific_journal-7274	151	41	)	)	PUNCT
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american_scientific_journal-7274	151	43	-	-	SYM
american_scientific_journal-7274	151	44	96	96	NUM
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american_scientific_journal-7274	152	2	8	8	NUM
american_scientific_journal-7274	152	3	]	]	PUNCT
american_scientific_journal-7274	152	4	.	.	PUNCT
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american_scientific_journal-7274	153	2	,	,	PUNCT
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american_scientific_journal-7274	153	4	,	,	PUNCT
american_scientific_journal-7274	153	5	h.hassanpour	h.hassanpour	ADJ
american_scientific_journal-7274	153	6	,	,	PUNCT
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american_scientific_journal-7274	153	8	-	-	PUNCT
american_scientific_journal-7274	153	9	based	base	VERB
american_scientific_journal-7274	153	10	method	method	NOUN
american_scientific_journal-7274	153	11	for	for	ADP
american_scientific_journal-7274	153	12	image	image	NOUN
american_scientific_journal-7274	153	13	enhancement	enhancement	NOUN
american_scientific_journal-7274	153	14	,	,	PUNCT
american_scientific_journal-7274	153	15	applied	apply	VERB
american_scientific_journal-7274	153	16	mathematical	mathematical	ADJ
american_scientific_journal-7274	153	17	sciences	science	NOUN
american_scientific_journal-7274	153	18	,	,	PUNCT
american_scientific_journal-7274	153	19	2(20	2(20	NUM
american_scientific_journal-7274	153	20	)	)	PUNCT
american_scientific_journal-7274	153	21	(	(	PUNCT
american_scientific_journal-7274	153	22	2008	2008	NUM
american_scientific_journal-7274	153	23	)	)	PUNCT
american_scientific_journal-7274	154	1	981	981	NUM
american_scientific_journal-7274	154	2	-	-	SYM
american_scientific_journal-7274	154	3	993	993	NUM
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american_scientific_journal-7274	155	2	9	9	NUM
american_scientific_journal-7274	155	3	]	]	PUNCT
american_scientific_journal-7274	155	4	.	.	PUNCT
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american_scientific_journal-7274	156	2	.	.	PUNCT
american_scientific_journal-7274	157	1	h.lim	h.lim	PROPN
american_scientific_journal-7274	157	2	,	,	PUNCT
american_scientific_journal-7274	157	3	fourth	fourth	ADJ
american_scientific_journal-7274	157	4	-	-	PUNCT
american_scientific_journal-7274	157	5	order	order	NOUN
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american_scientific_journal-7274	157	11	image	image	NOUN
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american_scientific_journal-7274	157	13	,	,	PUNCT
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american_scientific_journal-7274	157	17	scientific	scientific	ADJ
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american_scientific_journal-7274	157	20	for	for	ADP
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american_scientific_journal-7274	157	22	,	,	PUNCT
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american_scientific_journal-7274	157	24	,	,	PUNCT
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american_scientific_journal-7274	157	27	(	(	PUNCT
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american_scientific_journal-7274	157	32	)	)	PUNCT
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american_scientific_journal-7274	157	35	,	,	PUNCT
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american_scientific_journal-7274	157	40	-	-	SYM
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american_scientific_journal-7274	157	42	128	128	NUM
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american_scientific_journal-7274	157	50	and	and	CCONJ
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american_scientific_journal-7274	157	53	,	,	PUNCT
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american_scientific_journal-7274	157	59	,	,	PUNCT
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american_scientific_journal-7274	157	61	.	.	PUNCT
american_scientific_journal-7274	158	1	17	17	NUM
american_scientific_journal-7274	158	2	(	(	PUNCT
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american_scientific_journal-7274	158	4	)	)	PUNCT
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american_scientific_journal-7274	158	8	]	]	PUNCT
american_scientific_journal-7274	158	9	.	.	PUNCT
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american_scientific_journal-7274	159	2	,	,	PUNCT
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american_scientific_journal-7274	159	4	,	,	PUNCT
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american_scientific_journal-7274	159	18	,	,	PUNCT
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american_scientific_journal-7274	159	22	,	,	PUNCT
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american_scientific_journal-7274	159	24	-	-	PUNCT
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american_scientific_journal-7274	159	26	-	-	PUNCT
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american_scientific_journal-7274	160	4	.	.	PUNCT
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american_scientific_journal-7274	161	2	,	,	PUNCT
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american_scientific_journal-7274	161	13	:	:	PUNCT
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american_scientific_journal-7274	162	8	,	,	PUNCT
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american_scientific_journal-7274	162	10	,	,	PUNCT
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american_scientific_journal-7274	162	13	equation	equation	NOUN
american_scientific_journal-7274	162	14	-	-	PUNCT
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american_scientific_journal-7274	162	17	for	for	ADP
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american_scientific_journal-7274	162	21	:	:	PUNCT
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american_scientific_journal-7274	162	23	on	on	ADP
american_scientific_journal-7274	162	24	image	image	NOUN
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american_scientific_journal-7274	162	26	,	,	PUNCT
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american_scientific_journal-7274	162	35	2012	2012	NUM
american_scientific_journal-7274	162	36	)	)	PUNCT
american_scientific_journal-7274	162	37	3991	3991	NUM
american_scientific_journal-7274	162	38	-	-	SYM
american_scientific_journal-7274	162	39	4001	4001	NUM
american_scientific_journal-7274	163	1	[	[	X
american_scientific_journal-7274	163	2	13	13	NUM
american_scientific_journal-7274	163	3	]	]	PUNCT
american_scientific_journal-7274	163	4	.	.	PUNCT
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american_scientific_journal-7274	164	2	,	,	PUNCT
american_scientific_journal-7274	164	3	c.	c.	PROPN
american_scientific_journal-7274	164	4	li	li	PROPN
american_scientific_journal-7274	164	5	,	,	PUNCT
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american_scientific_journal-7274	164	7	,	,	PUNCT
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american_scientific_journal-7274	164	10	partial	partial	ADJ
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american_scientific_journal-7274	164	12	equation	equation	NOUN
american_scientific_journal-7274	164	13	for	for	ADP
american_scientific_journal-7274	164	14	noise	noise	NOUN
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american_scientific_journal-7274	164	16	,	,	PUNCT
american_scientific_journal-7274	164	17	proceedings	proceeding	NOUN
american_scientific_journal-7274	164	18	of	of	ADP
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american_scientific_journal-7274	164	20	2nd	2nd	ADJ
american_scientific_journal-7274	164	21	international	international	ADJ
american_scientific_journal-7274	164	22	symposium	symposium	NOUN
american_scientific_journal-7274	164	23	on	on	ADP
american_scientific_journal-7274	164	24	computer	computer	NOUN
american_scientific_journal-7274	164	25	,	,	PUNCT
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american_scientific_journal-7274	164	27	,	,	PUNCT
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american_scientific_journal-7274	164	29	and	and	CCONJ
american_scientific_journal-7274	164	30	automation	automation	NOUN
american_scientific_journal-7274	164	31	4	4	NUM
american_scientific_journal-7274	164	32	(	(	PUNCT
american_scientific_journal-7274	164	33	2013	2013	NUM
american_scientific_journal-7274	164	34	)	)	PUNCT
american_scientific_journal-7274	164	35	5558	5558	NUM
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american_scientific_journal-7274	165	2	14	14	NUM
american_scientific_journal-7274	165	3	]	]	PUNCT
american_scientific_journal-7274	165	4	.	.	PUNCT
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american_scientific_journal-7274	166	2	,	,	PUNCT
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american_scientific_journal-7274	166	4	,	,	PUNCT
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american_scientific_journal-7274	166	6	,	,	PUNCT
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american_scientific_journal-7274	166	8	restarted	restart	VERB
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american_scientific_journal-7274	166	13	for	for	ADP
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american_scientific_journal-7274	166	16	models	model	NOUN
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american_scientific_journal-7274	166	19	processing	processing	NOUN
american_scientific_journal-7274	166	20	,	,	PUNCT
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american_scientific_journal-7274	166	22	journal	journal	NOUN
american_scientific_journal-7274	166	23	of	of	ADP
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american_scientific_journal-7274	166	27	)	)	PUNCT
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american_scientific_journal-7274	166	30	)	)	PUNCT
american_scientific_journal-7274	167	1	661–687	661–687	NUM
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american_scientific_journal-7274	167	3	15	15	NUM
american_scientific_journal-7274	167	4	]	]	PUNCT
american_scientific_journal-7274	167	5	.	.	PUNCT
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american_scientific_journal-7274	168	2	.	.	PROPN
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american_scientific_journal-7274	168	4	,	,	PUNCT
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american_scientific_journal-7274	168	15	-	-	PUNCT
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american_scientific_journal-7274	168	27	,	,	PUNCT
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american_scientific_journal-7274	168	40	-	-	SYM
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american_scientific_journal-7274	169	3	]	]	PUNCT
american_scientific_journal-7274	169	4	.	.	PUNCT
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american_scientific_journal-7274	170	2	,	,	PUNCT
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american_scientific_journal-7274	170	7	-	-	PUNCT
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american_scientific_journal-7274	170	13	,	,	PUNCT
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american_scientific_journal-7274	172	4	.	.	PUNCT
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american_scientific_journal-7274	173	2	,	,	PUNCT
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american_scientific_journal-7274	173	4	,	,	PUNCT
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american_scientific_journal-7274	173	6	,	,	PUNCT
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american_scientific_journal-7274	173	10	-	-	NOUN
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american_scientific_journal-7274	174	4	,	,	PUNCT
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american_scientific_journal-7274	174	15	-	-	PUNCT
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american_scientific_journal-7274	175	28	-	-	SYM
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american_scientific_journal-7274	181	7	sufficient	sufficient	ADJ
american_scientific_journal-7274	181	8	condition	condition	NOUN
american_scientific_journal-7274	181	9	and	and	CCONJ
american_scientific_journal-7274	181	10	the	the	DET
american_scientific_journal-7274	181	11	efficient	efficient	ADJ
american_scientific_journal-7274	181	12	algorithms	algorithm	NOUN
american_scientific_journal-7274	181	13	for	for	ADP
american_scientific_journal-7274	181	14	gradually	gradually	ADV
american_scientific_journal-7274	181	15	varied	varied	ADJ
american_scientific_journal-7274	181	16	fill	fill	NOUN
american_scientific_journal-7274	181	17	,	,	PUNCT
american_scientific_journal-7274	181	18	american	american	ADJ
american_scientific_journal-7274	181	19	academic	academic	ADJ
american_scientific_journal-7274	181	20	scientific	scientific	ADJ
american_scientific_journal-7274	181	21	research	research	NOUN
american_scientific_journal-7274	181	22	journal	journal	NOUN
american_scientific_journal-7274	181	23	for	for	ADP
american_scientific_journal-7274	181	24	engineering	engineering	NOUN
american_scientific_journal-7274	181	25	,	,	PUNCT
american_scientific_journal-7274	181	26	technology	technology	NOUN
american_scientific_journal-7274	181	27	,	,	PUNCT
american_scientific_journal-7274	181	28	and	and	CCONJ
american_scientific_journal-7274	181	29	sciences	science	NOUN
american_scientific_journal-7274	181	30	(	(	PUNCT
american_scientific_journal-7274	181	31	asrjets	asrjet	NOUN
american_scientific_journal-7274	181	32	)	)	PUNCT
american_scientific_journal-7274	181	33	(	(	PUNCT
american_scientific_journal-7274	181	34	2021	2021	NUM
american_scientific_journal-7274	181	35	)	)	PUNCT
american_scientific_journal-7274	181	36	volume	volume	NOUN
american_scientific_journal-7274	181	37	84	84	NUM
american_scientific_journal-7274	181	38	,	,	PUNCT
american_scientific_journal-7274	181	39	no1	no1	PROPN
american_scientific_journal-7274	181	40	,	,	PUNCT
american_scientific_journal-7274	181	41	pp	pp	ADP
american_scientific_journal-7274	181	42	118	118	NUM
american_scientific_journal-7274	181	43	-	-	SYM
american_scientific_journal-7274	181	44	129	129	NUM
american_scientific_journal-7274	181	45	129	129	NUM
american_scientific_journal-7274	181	46	chinese	chinese	ADJ
american_scientific_journal-7274	181	47	science	science	NOUN
american_scientific_journal-7274	181	48	bulletin	bulletin	NOUN
american_scientific_journal-7274	181	49	35	35	NUM
american_scientific_journal-7274	181	50	(	(	PUNCT
american_scientific_journal-7274	181	51	10	10	NUM
american_scientific_journal-7274	181	52	)	)	PUNCT
american_scientific_journal-7274	181	53	(	(	PUNCT
american_scientific_journal-7274	181	54	1990	1990	NUM
american_scientific_journal-7274	181	55	)	)	PUNCT
american_scientific_journal-7274	182	1	870–873	870–873	NUM
american_scientific_journal-7274	183	1	[	[	X
american_scientific_journal-7274	183	2	23	23	NUM
american_scientific_journal-7274	183	3	]	]	PUNCT
american_scientific_journal-7274	183	4	.	.	PUNCT
american_scientific_journal-7274	184	1	e.khalimsky	e.khalimsky	ADJ
american_scientific_journal-7274	184	2	,	,	PUNCT
american_scientific_journal-7274	184	3	motion	motion	NOUN
american_scientific_journal-7274	184	4	,	,	PUNCT
american_scientific_journal-7274	184	5	deformation	deformation	NOUN
american_scientific_journal-7274	184	6	,	,	PUNCT
american_scientific_journal-7274	184	7	and	and	CCONJ
american_scientific_journal-7274	184	8	homotopy	homotopy	NOUN
american_scientific_journal-7274	184	9	in	in	ADP
american_scientific_journal-7274	184	10	finite	finite	ADJ
american_scientific_journal-7274	184	11	spaces	space	NOUN
american_scientific_journal-7274	184	12	,	,	PUNCT
american_scientific_journal-7274	184	13	in	in	ADP
american_scientific_journal-7274	184	14	proceedings	proceeding	NOUN
american_scientific_journal-7274	184	15	ieee	ieee	VERB
american_scientific_journal-7274	184	16	international	international	ADJ
american_scientific_journal-7274	184	17	conference	conference	NOUN
american_scientific_journal-7274	184	18	on	on	ADP
american_scientific_journal-7274	184	19	systems	system	NOUN
american_scientific_journal-7274	184	20	,	,	PUNCT
american_scientific_journal-7274	184	21	man	man	NOUN
american_scientific_journal-7274	184	22	,	,	PUNCT
american_scientific_journal-7274	184	23	and	and	CCONJ
american_scientific_journal-7274	184	24	cybernetics	cybernetic	NOUN
american_scientific_journal-7274	184	25	,	,	PUNCT
american_scientific_journal-7274	184	26	chicago	chicago	PROPN
american_scientific_journal-7274	184	27	(	(	PUNCT
american_scientific_journal-7274	184	28	1987	1987	NUM
american_scientific_journal-7274	184	29	)	)	PUNCT
american_scientific_journal-7274	185	1	227–234	227–234	NUM
american_scientific_journal-7274	185	2	[	[	X
american_scientific_journal-7274	185	3	24	24	NUM
american_scientific_journal-7274	185	4	]	]	PUNCT
american_scientific_journal-7274	185	5	.	.	PUNCT
american_scientific_journal-7274	186	1	t.y.kong	t.y.kong	PROPN
american_scientific_journal-7274	186	2	,	,	PUNCT
american_scientific_journal-7274	186	3	a	a	DET
american_scientific_journal-7274	186	4	digital	digital	ADJ
american_scientific_journal-7274	186	5	fundamental	fundamental	ADJ
american_scientific_journal-7274	186	6	group	group	NOUN
american_scientific_journal-7274	186	7	,	,	PUNCT
american_scientific_journal-7274	186	8	computers	computer	NOUN
american_scientific_journal-7274	186	9	and	and	CCONJ
american_scientific_journal-7274	186	10	graphics	graphic	NOUN
american_scientific_journal-7274	186	11	13	13	NUM
american_scientific_journal-7274	186	12	(	(	PUNCT
american_scientific_journal-7274	186	13	1989	1989	NUM
american_scientific_journal-7274	186	14	)	)	PUNCT
american_scientific_journal-7274	186	15	159–166	159–166	NUM
american_scientific_journal-7274	187	1	[	[	X
american_scientific_journal-7274	187	2	25	25	NUM
american_scientific_journal-7274	187	3	]	]	PUNCT
american_scientific_journal-7274	187	4	.	.	PUNCT
american_scientific_journal-7274	188	1	l.boxer	l.boxer	PROPN
american_scientific_journal-7274	188	2	,	,	PUNCT
american_scientific_journal-7274	188	3	digitally	digitally	ADV
american_scientific_journal-7274	188	4	continuous	continuous	ADJ
american_scientific_journal-7274	188	5	functions	function	NOUN
american_scientific_journal-7274	188	6	,	,	PUNCT
american_scientific_journal-7274	188	7	pattern	pattern	NOUN
american_scientific_journal-7274	188	8	recognition	recognition	NOUN
american_scientific_journal-7274	188	9	letters	letter	NOUN
american_scientific_journal-7274	188	10	15(8	15(8	NUM
american_scientific_journal-7274	188	11	)	)	PUNCT
american_scientific_journal-7274	188	12	(	(	PUNCT
american_scientific_journal-7274	188	13	1994	1994	NUM
american_scientific_journal-7274	188	14	)	)	PUNCT
american_scientific_journal-7274	188	15	833–839	833–839	NUM
american_scientific_journal-7274	189	1	[	[	X
american_scientific_journal-7274	189	2	26	26	NUM
american_scientific_journal-7274	189	3	]	]	PUNCT
american_scientific_journal-7274	189	4	.	.	PUNCT
american_scientific_journal-7274	190	1	a.rosenfeld	a.rosenfeld	ADJ
american_scientific_journal-7274	190	2	,	,	PUNCT
american_scientific_journal-7274	190	3	,	,	PUNCT
american_scientific_journal-7274	190	4	contraction	contraction	NOUN
american_scientific_journal-7274	190	5	of	of	ADP
american_scientific_journal-7274	190	6	digital	digital	ADJ
american_scientific_journal-7274	190	7	curves	curve	NOUN
american_scientific_journal-7274	190	8	,	,	PUNCT
american_scientific_journal-7274	190	9	university	university	NOUN
american_scientific_journal-7274	190	10	of	of	ADP
american_scientific_journal-7274	190	11	maryland	maryland	PROPN
american_scientific_journal-7274	190	12	’s	’s	PART
american_scientific_journal-7274	190	13	technical	technical	ADJ
american_scientific_journal-7274	190	14	report	report	NOUN
american_scientific_journal-7274	190	15	(	(	PUNCT
american_scientific_journal-7274	190	16	1996	1996	NUM
american_scientific_journal-7274	190	17	)	)	PUNCT
american_scientific_journal-7274	191	1	[	[	X
american_scientific_journal-7274	191	2	27	27	NUM
american_scientific_journal-7274	191	3	]	]	PUNCT
american_scientific_journal-7274	191	4	.	.	PUNCT
american_scientific_journal-7274	192	1	g.agnarsson	g.agnarsson	NOUN
american_scientific_journal-7274	192	2	,	,	PUNCT
american_scientific_journal-7274	192	3	l.chen	l.chen	ADV
american_scientific_journal-7274	192	4	,	,	PUNCT
american_scientific_journal-7274	192	5	on	on	ADP
american_scientific_journal-7274	192	6	the	the	DET
american_scientific_journal-7274	192	7	extension	extension	NOUN
american_scientific_journal-7274	192	8	of	of	ADP
american_scientific_journal-7274	192	9	vertex	vertex	NOUN
american_scientific_journal-7274	192	10	maps	map	NOUN
american_scientific_journal-7274	192	11	to	to	PART
american_scientific_journal-7274	192	12	graph	graph	VERB
american_scientific_journal-7274	192	13	homomorphisms	homomorphism	NOUN
american_scientific_journal-7274	192	14	,	,	PUNCT
american_scientific_journal-7274	192	15	discrete	discrete	ADJ
american_scientific_journal-7274	192	16	mathematics	mathematic	NOUN
american_scientific_journal-7274	192	17	306(17	306(17	NUM
american_scientific_journal-7274	192	18	)	)	PUNCT
american_scientific_journal-7274	192	19	(	(	PUNCT
american_scientific_journal-7274	192	20	2006	2006	NUM
american_scientific_journal-7274	192	21	)	)	PUNCT
american_scientific_journal-7274	192	22	2021–2030	2021–2030	NUM
american_scientific_journal-7274	193	1	[	[	X
american_scientific_journal-7274	193	2	28	28	NUM
american_scientific_journal-7274	193	3	]	]	PUNCT
american_scientific_journal-7274	193	4	.	.	PUNCT
american_scientific_journal-7274	194	1	l.chen	l.chen	ADV
american_scientific_journal-7274	194	2	,	,	PUNCT
american_scientific_journal-7274	194	3	a	a	DET
american_scientific_journal-7274	194	4	digital	digital	ADJ
american_scientific_journal-7274	194	5	-	-	PUNCT
american_scientific_journal-7274	194	6	discrete	discrete	NOUN
american_scientific_journal-7274	194	7	method	method	NOUN
american_scientific_journal-7274	194	8	for	for	ADP
american_scientific_journal-7274	194	9	smooth	smooth	ADJ
american_scientific_journal-7274	194	10	-	-	PUNCT
american_scientific_journal-7274	194	11	continuous	continuous	ADJ
american_scientific_journal-7274	194	12	data	datum	NOUN
american_scientific_journal-7274	194	13	reconstruction	reconstruction	NOUN
american_scientific_journal-7274	194	14	,	,	PUNCT
american_scientific_journal-7274	194	15	journal	journal	NOUN
american_scientific_journal-7274	194	16	of	of	ADP
american_scientific_journal-7274	194	17	the	the	DET
american_scientific_journal-7274	194	18	washington	washington	PROPN
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american_scientific_journal-7274	194	20	of	of	ADP
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american_scientific_journal-7274	194	24	(	(	PUNCT
american_scientific_journal-7274	194	25	2010	2010	NUM
american_scientific_journal-7274	194	26	)	)	PUNCT
american_scientific_journal-7274	194	27	47–65	47–65	NUM
american_scientific_journal-7274	195	1	[	[	X
american_scientific_journal-7274	195	2	29	29	NUM
american_scientific_journal-7274	195	3	]	]	PUNCT
american_scientific_journal-7274	195	4	.	.	PUNCT
american_scientific_journal-7274	196	1	l.chen	l.chen	X
american_scientific_journal-7274	196	2	,	,	PUNCT
american_scientific_journal-7274	196	3	f.luo	f.luo	PROPN
american_scientific_journal-7274	196	4	,	,	PUNCT
american_scientific_journal-7274	196	5	harmonic	harmonic	ADJ
american_scientific_journal-7274	196	6	functions	function	NOUN
american_scientific_journal-7274	196	7	for	for	ADP
american_scientific_journal-7274	196	8	data	datum	NOUN
american_scientific_journal-7274	196	9	reconstruction	reconstruction	NOUN
american_scientific_journal-7274	196	10	on	on	ADP
american_scientific_journal-7274	196	11	3d	3d	PROPN
american_scientific_journal-7274	196	12	manifolds	manifold	NOUN
american_scientific_journal-7274	196	13	,	,	PUNCT
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american_scientific_journal-7274	197	1	[	[	X
american_scientific_journal-7274	197	2	math.na	math.na	X
american_scientific_journal-7274	197	3	]	]	PUNCT
american_scientific_journal-7274	198	1	[	[	X
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american_scientific_journal-7274	198	3	]	]	PUNCT
american_scientific_journal-7274	198	4	.	.	PUNCT
american_scientific_journal-7274	199	1	l.chen	l.chen	ADV
american_scientific_journal-7274	199	2	,	,	PUNCT
american_scientific_journal-7274	199	3	the	the	DET
american_scientific_journal-7274	199	4	properties	property	NOUN
american_scientific_journal-7274	199	5	and	and	CCONJ
american_scientific_journal-7274	199	6	the	the	DET
american_scientific_journal-7274	199	7	algorithms	algorithm	NOUN
american_scientific_journal-7274	199	8	for	for	ADP
american_scientific_journal-7274	199	9	gradually	gradually	ADV
american_scientific_journal-7274	199	10	varied	varied	ADJ
american_scientific_journal-7274	199	11	fill	fill	NOUN
american_scientific_journal-7274	199	12	,	,	PUNCT
american_scientific_journal-7274	199	13	chinese	chinese	ADJ
american_scientific_journal-7274	199	14	journal	journal	NOUN
american_scientific_journal-7274	199	15	of	of	ADP
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american_scientific_journal-7274	199	17	14(3	14(3	NUM
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american_scientific_journal-7274	199	19	(	(	PUNCT
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american_scientific_journal-7274	199	21	)	)	PUNCT
american_scientific_journal-7274	200	1	[	[	X
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american_scientific_journal-7274	200	3	]	]	PUNCT
american_scientific_journal-7274	200	4	.	.	PUNCT
american_scientific_journal-7274	201	1	t.h.cormen	t.h.corman	NOUN
american_scientific_journal-7274	201	2	,	,	PUNCT
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american_scientific_journal-7274	201	4	,	,	PUNCT
american_scientific_journal-7274	201	5	r.l.rivest	r.l.riv	ADJ
american_scientific_journal-7274	201	6	,	,	PUNCT
american_scientific_journal-7274	201	7	introduction	introduction	NOUN
american_scientific_journal-7274	201	8	to	to	ADP
american_scientific_journal-7274	201	9	algorithms	algorithm	NOUN
american_scientific_journal-7274	201	10	,	,	PUNCT
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american_scientific_journal-7274	201	12	,	,	PUNCT
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american_scientific_journal-7274	201	17	)	)	PUNCT
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american_scientific_journal-7274	202	3	]	]	PUNCT
american_scientific_journal-7274	202	4	.	.	PUNCT
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american_scientific_journal-7274	203	2	,	,	PUNCT
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american_scientific_journal-7274	203	5	,	,	PUNCT
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american_scientific_journal-7274	203	8	,	,	PUNCT
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american_scientific_journal-7274	203	10	of	of	ADP
american_scientific_journal-7274	203	11	computer	computer	NOUN
american_scientific_journal-7274	203	12	engineering	engineering	NOUN
american_scientific_journal-7274	203	13	lecture	lecture	NOUN
american_scientific_journal-7274	203	14	notes	note	NOUN
american_scientific_journal-7274	203	15	(	(	PUNCT
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american_scientific_journal-7274	203	17	)	)	PUNCT
american_scientific_journal-7274	203	18	1	1	NUM
american_scientific_journal-7274	203	19	-	-	SYM
american_scientific_journal-7274	203	20	15	15	NUM
american_scientific_journal-7274	204	1	[	[	X
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american_scientific_journal-7274	204	4	.	.	PUNCT
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american_scientific_journal-7274	205	2	,	,	PUNCT
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american_scientific_journal-7274	205	6	,	,	PUNCT
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american_scientific_journal-7274	205	10	,	,	PUNCT
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american_scientific_journal-7274	205	12	processing	processing	NOUN
american_scientific_journal-7274	205	13	with	with	ADP
american_scientific_journal-7274	205	14	matlab	matlab	PROPN
american_scientific_journal-7274	205	15	:	:	PUNCT
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american_scientific_journal-7274	205	17	in	in	ADP
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american_scientific_journal-7274	205	19	and	and	CCONJ
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american_scientific_journal-7274	205	21	,	,	PUNCT
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american_scientific_journal-7274	205	23	press	press	PROPN
american_scientific_journal-7274	205	24	:	:	PUNCT
american_scientific_journal-7274	205	25	taylor	taylor	PROPN
american_scientific_journal-7274	205	26	&	&	CCONJ
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american_scientific_journal-7274	205	29	,	,	PUNCT
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american_scientific_journal-7274	205	32	,	,	PUNCT
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american_scientific_journal-7274	206	4	.	.	PUNCT
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american_scientific_journal-7274	207	4	,	,	PUNCT
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american_scientific_journal-7274	207	6	-	-	PUNCT
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american_scientific_journal-7274	207	18	pattern	pattern	NOUN
american_scientific_journal-7274	207	19	analysis	analysis	NOUN
american_scientific_journal-7274	207	20	and	and	CCONJ
american_scientific_journal-7274	207	21	machine	machine	NOUN
american_scientific_journal-7274	207	22	intelligence	intelligence	NOUN
american_scientific_journal-7274	207	23	12(7	12(7	NUM
american_scientific_journal-7274	207	24	)	)	PUNCT
american_scientific_journal-7274	207	25	(	(	PUNCT
american_scientific_journal-7274	207	26	1990	1990	NUM
american_scientific_journal-7274	207	27	)	)	PUNCT
american_scientific_journal-7274	207	28	629	629	NUM
american_scientific_journal-7274	207	29	-	-	SYM
american_scientific_journal-7274	207	30	639	639	NUM
american_scientific_journal-7274	207	31	[	[	X
american_scientific_journal-7274	207	32	35	35	NUM
american_scientific_journal-7274	207	33	]	]	PUNCT
american_scientific_journal-7274	207	34	.	.	PUNCT
american_scientific_journal-7274	208	1	g.	g.	PROPN
american_scientific_journal-7274	208	2	d.	d.	PROPN
american_scientific_journal-7274	208	3	smith	smith	PROPN
american_scientific_journal-7274	208	4	,	,	PUNCT
american_scientific_journal-7274	208	5	numerical	numerical	ADJ
american_scientific_journal-7274	208	6	solution	solution	NOUN
american_scientific_journal-7274	208	7	of	of	ADP
american_scientific_journal-7274	208	8	partial	partial	ADJ
american_scientific_journal-7274	208	9	differential	differential	NOUN
american_scientific_journal-7274	208	10	equations	equation	NOUN
american_scientific_journal-7274	208	11	:	:	PUNCT
american_scientific_journal-7274	208	12	finite	finite	ADJ
american_scientific_journal-7274	208	13	difference	difference	NOUN
american_scientific_journal-7274	208	14	methods	method	NOUN
american_scientific_journal-7274	208	15	,	,	PUNCT
american_scientific_journal-7274	208	16	oxford	oxford	PROPN
american_scientific_journal-7274	208	17	applied	apply	VERB
american_scientific_journal-7274	208	18	mathematics	mathematic	NOUN
american_scientific_journal-7274	208	19	and	and	CCONJ
american_scientific_journal-7274	208	20	computing	compute	VERB
american_scientific_journal-7274	208	21	science	science	NOUN
american_scientific_journal-7274	208	22	series	series	NOUN
american_scientific_journal-7274	208	23	(	(	PUNCT
american_scientific_journal-7274	208	24	1985	1985	NUM
american_scientific_journal-7274	208	25	)	)	PUNCT