id	sid	tid	token	lemma	pos
iajs-3671	1	1	465	465	NUM
iajs-3671	1	2	©	©	ADP
iajs-3671	1	3	2025	2025	NUM
iajs-3671	1	4	the	the	DET
iajs-3671	1	5	author(s	author(s	NOUN
iajs-3671	1	6	)	)	PUNCT
iajs-3671	1	7	.	.	PUNCT
iajs-3671	2	1	published	publish	VERB
iajs-3671	2	2	by	by	ADP
iajs-3671	2	3	college	college	NOUN
iajs-3671	2	4	of	of	ADP
iajs-3671	2	5	education	education	NOUN
iajs-3671	2	6	for	for	ADP
iajs-3671	2	7	pure	pure	ADJ
iajs-3671	2	8	science	science	NOUN
iajs-3671	2	9	(	(	PUNCT
iajs-3671	2	10	ibn	ibn	PROPN
iajs-3671	2	11	al	al	PROPN
iajs-3671	2	12	-	-	PUNCT
iajs-3671	2	13	haitham	haitham	PROPN
iajs-3671	2	14	)	)	PUNCT
iajs-3671	2	15	,	,	PUNCT
iajs-3671	2	16	university	university	NOUN
iajs-3671	2	17	of	of	ADP
iajs-3671	2	18	baghdad	baghdad	PROPN
iajs-3671	2	19	.	.	PUNCT
iajs-3671	3	1	this	this	PRON
iajs-3671	3	2	is	be	AUX
iajs-3671	3	3	an	an	DET
iajs-3671	3	4	open	open	ADJ
iajs-3671	3	5	-	-	PUNCT
iajs-3671	3	6	access	access	NOUN
iajs-3671	3	7	article	article	NOUN
iajs-3671	3	8	distributed	distribute	VERB
iajs-3671	3	9	under	under	ADP
iajs-3671	3	10	the	the	DET
iajs-3671	3	11	terms	term	NOUN
iajs-3671	3	12	of	of	ADP
iajs-3671	3	13	the	the	DET
iajs-3671	3	14	creative	creative	ADJ
iajs-3671	3	15	commons	common	NOUN
iajs-3671	3	16	attribution	attribution	NOUN
iajs-3671	3	17	4.0	4.0	NUM
iajs-3671	3	18	international	international	ADJ
iajs-3671	3	19	license	license	NOUN
iajs-3671	3	20	timewise	timewise	ADV
iajs-3671	3	21	–	–	PUNCT
iajs-3671	3	22	dependent	dependent	ADJ
iajs-3671	3	23	coefficients	coefficient	NOUN
iajs-3671	3	24	identification	identification	NOUN
iajs-3671	3	25	problems	problem	NOUN
iajs-3671	3	26	for	for	ADP
iajs-3671	3	27	third	third	ADJ
iajs-3671	3	28	-	-	PUNCT
iajs-3671	3	29	order	order	NOUN
iajs-3671	3	30	pseudo	pseudo	NOUN
iajs-3671	3	31	-	-	ADJ
iajs-3671	3	32	parabolic	parabolic	ADJ
iajs-3671	3	33	equations	equation	NOUN
iajs-3671	3	34	from	from	ADP
iajs-3671	3	35	nonlocal	nonlocal	ADJ
iajs-3671	3	36	extra	extra	ADJ
iajs-3671	3	37	conditions	condition	NOUN
iajs-3671	3	38	sayl	sayl	VERB
iajs-3671	3	39	gani1	gani1	NOUN
iajs-3671	3	40	,	,	PUNCT
iajs-3671	4	1	mohammed	mohammed	PROPN
iajs-3671	4	2	s.	s.	PROPN
iajs-3671	4	3	hussein2	hussein2	PROPN
iajs-3671	5	1	*	*	PUNCT
iajs-3671	5	2	,	,	PUNCT
iajs-3671	5	3	and	and	CCONJ
iajs-3671	5	4	taysir	taysir	PROPN
iajs-3671	5	5	e.	e.	PROPN
iajs-3671	5	6	dyhoum3	dyhoum3	PROPN
iajs-3671	6	1	1department	1department	NUM
iajs-3671	6	2	of	of	ADP
iajs-3671	6	3	computer	computer	NOUN
iajs-3671	6	4	techniques	technique	NOUN
iajs-3671	6	5	engineering	engineering	NOUN
iajs-3671	6	6	,	,	PUNCT
iajs-3671	6	7	imam	imam	PROPN
iajs-3671	6	8	al	al	PROPN
iajs-3671	6	9	-	-	PUNCT
iajs-3671	6	10	kadhum	kadhum	PROPN
iajs-3671	6	11	college	college	PROPN
iajs-3671	6	12	,	,	PUNCT
iajs-3671	6	13	baghdad	baghdad	PROPN
iajs-3671	6	14	,	,	PUNCT
iajs-3671	6	15	iraq	iraq	PROPN
iajs-3671	6	16	.	.	PUNCT
iajs-3671	7	1	2department	2department	NUM
iajs-3671	7	2	of	of	ADP
iajs-3671	7	3	mathematics	mathematic	NOUN
iajs-3671	7	4	,	,	PUNCT
iajs-3671	7	5	college	college	NOUN
iajs-3671	7	6	of	of	ADP
iajs-3671	7	7	science	science	NOUN
iajs-3671	7	8	,	,	PUNCT
iajs-3671	7	9	university	university	NOUN
iajs-3671	7	10	of	of	ADP
iajs-3671	7	11	baghdad	baghdad	PROPN
iajs-3671	7	12	,	,	PUNCT
iajs-3671	7	13	baghdad	baghdad	PROPN
iajs-3671	7	14	,	,	PUNCT
iajs-3671	7	15	iraq	iraq	PROPN
iajs-3671	7	16	.	.	PUNCT
iajs-3671	8	1	3department	3department	NUM
iajs-3671	8	2	of	of	ADP
iajs-3671	8	3	computing	computing	NOUN
iajs-3671	8	4	and	and	CCONJ
iajs-3671	8	5	mathematics	mathematic	NOUN
iajs-3671	8	6	,	,	PUNCT
iajs-3671	8	7	faculty	faculty	NOUN
iajs-3671	8	8	of	of	ADP
iajs-3671	8	9	science	science	NOUN
iajs-3671	8	10	and	and	CCONJ
iajs-3671	8	11	engineering	engineering	NOUN
iajs-3671	8	12	,	,	PUNCT
iajs-3671	8	13	manchester	manchester	PROPN
iajs-3671	8	14	metropolitan	metropolitan	PROPN
iajs-3671	8	15	university	university	PROPN
iajs-3671	8	16	,	,	PUNCT
iajs-3671	8	17	manchester	manchester	PROPN
iajs-3671	8	18	,	,	PUNCT
iajs-3671	8	19	uk	uk	PROPN
iajs-3671	8	20	.	.	PROPN
iajs-3671	8	21	*	*	PUNCT
iajs-3671	8	22	corresponding	correspond	VERB
iajs-3671	8	23	author	author	NOUN
iajs-3671	8	24	.	.	PUNCT
iajs-3671	9	1	received:10	received:10	PROPN
iajs-3671	10	1	september	september	PROPN
iajs-3671	10	2	2023	2023	NUM
iajs-3671	10	3	accepted:13	accepted:13	X
iajs-3671	10	4	november	november	PROPN
iajs-3671	10	5	2023	2023	NUM
iajs-3671	10	6	published:20	published:20	NOUN
iajs-3671	10	7	january	january	PROPN
iajs-3671	10	8	2025	2025	NUM
iajs-3671	10	9	doi.org/10.30526/38.1.3671	doi.org/10.30526/38.1.3671	NOUN
iajs-3671	10	10	abstract	abstract	ADV
iajs-3671	10	11	this	this	DET
iajs-3671	10	12	study	study	NOUN
iajs-3671	10	13	aims	aim	VERB
iajs-3671	10	14	to	to	PART
iajs-3671	10	15	find	find	VERB
iajs-3671	10	16	the	the	DET
iajs-3671	10	17	time	time	NOUN
iajs-3671	10	18	-	-	PUNCT
iajs-3671	10	19	dependent	dependent	ADJ
iajs-3671	10	20	potential	potential	ADJ
iajs-3671	10	21	terms	term	NOUN
iajs-3671	10	22	in	in	ADP
iajs-3671	10	23	the	the	DET
iajs-3671	10	24	two	two	NUM
iajs-3671	10	25	inverse	inverse	NOUN
iajs-3671	10	26	problems	problem	NOUN
iajs-3671	10	27	of	of	ADP
iajs-3671	10	28	the	the	DET
iajs-3671	10	29	third	third	ADJ
iajs-3671	10	30	-	-	PUNCT
iajs-3671	10	31	order	order	NOUN
iajs-3671	10	32	pseudo	pseudo	NOUN
iajs-3671	10	33	-	-	NOUN
iajs-3671	10	34	parabolic	parabolic	NOUN
iajs-3671	10	35	with	with	ADP
iajs-3671	10	36	initial	initial	ADJ
iajs-3671	10	37	and	and	CCONJ
iajs-3671	10	38	various	various	ADJ
iajs-3671	10	39	boundary	boundary	ADJ
iajs-3671	10	40	conditions	condition	NOUN
iajs-3671	10	41	supplemented	supplement	VERB
iajs-3671	10	42	by	by	ADP
iajs-3671	10	43	the	the	DET
iajs-3671	10	44	overdetermination	overdetermination	NOUN
iajs-3671	10	45	data	datum	NOUN
iajs-3671	10	46	.	.	PUNCT
iajs-3671	11	1	the	the	DET
iajs-3671	11	2	nonlinear	nonlinear	ADJ
iajs-3671	11	3	inverse	inverse	NOUN
iajs-3671	11	4	problems	problem	NOUN
iajs-3671	11	5	have	have	VERB
iajs-3671	11	6	significant	significant	ADJ
iajs-3671	11	7	applications	application	NOUN
iajs-3671	11	8	in	in	ADP
iajs-3671	11	9	physics	physics	NOUN
iajs-3671	11	10	and	and	CCONJ
iajs-3671	11	11	engineering	engineering	NOUN
iajs-3671	11	12	fields	field	NOUN
iajs-3671	11	13	.	.	PUNCT
iajs-3671	12	1	we	we	PRON
iajs-3671	12	2	proved	prove	VERB
iajs-3671	12	3	the	the	DET
iajs-3671	12	4	existence	existence	NOUN
iajs-3671	12	5	and	and	CCONJ
iajs-3671	12	6	uniqueness	uniqueness	NOUN
iajs-3671	12	7	of	of	ADP
iajs-3671	12	8	the	the	DET
iajs-3671	12	9	solution	solution	NOUN
iajs-3671	12	10	of	of	ADP
iajs-3671	12	11	the	the	DET
iajs-3671	12	12	two	two	NUM
iajs-3671	12	13	problems	problem	NOUN
iajs-3671	12	14	are	be	AUX
iajs-3671	12	15	being	be	AUX
iajs-3671	12	16	proved	prove	VERB
iajs-3671	12	17	,	,	PUNCT
iajs-3671	12	18	but	but	CCONJ
iajs-3671	12	19	they	they	PRON
iajs-3671	12	20	still	still	ADV
iajs-3671	12	21	need	need	VERB
iajs-3671	12	22	to	to	PART
iajs-3671	12	23	be	be	AUX
iajs-3671	12	24	proposed	propose	VERB
iajs-3671	12	25	(	(	PUNCT
iajs-3671	12	26	since	since	SCONJ
iajs-3671	12	27	tiny	tiny	ADJ
iajs-3671	12	28	perturbations	perturbation	NOUN
iajs-3671	12	29	in	in	ADP
iajs-3671	12	30	input	input	NOUN
iajs-3671	12	31	data	datum	NOUN
iajs-3671	12	32	cause	cause	VERB
iajs-3671	12	33	considerable	considerable	ADJ
iajs-3671	12	34	errors	error	NOUN
iajs-3671	12	35	in	in	ADP
iajs-3671	12	36	the	the	DET
iajs-3671	12	37	output	output	NOUN
iajs-3671	12	38	potential	potential	ADJ
iajs-3671	12	39	term	term	NOUN
iajs-3671	12	40	)	)	PUNCT
iajs-3671	12	41	.	.	PUNCT
iajs-3671	13	1	consequently	consequently	ADV
iajs-3671	13	2	,	,	PUNCT
iajs-3671	13	3	the	the	DET
iajs-3671	13	4	regularized	regularize	VERB
iajs-3671	13	5	methods	method	NOUN
iajs-3671	13	6	should	should	AUX
iajs-3671	13	7	be	be	AUX
iajs-3671	13	8	employed	employ	VERB
iajs-3671	13	9	.	.	PUNCT
iajs-3671	14	1	a	a	DET
iajs-3671	14	2	finite	finite	ADJ
iajs-3671	14	3	difference	difference	NOUN
iajs-3671	14	4	schema	schema	NOUN
iajs-3671	14	5	is	be	AUX
iajs-3671	14	6	used	use	VERB
iajs-3671	14	7	for	for	ADP
iajs-3671	14	8	solving	solve	VERB
iajs-3671	14	9	direct	direct	ADJ
iajs-3671	14	10	problems	problem	NOUN
iajs-3671	14	11	.	.	PUNCT
iajs-3671	15	1	in	in	ADP
iajs-3671	15	2	contrast	contrast	NOUN
iajs-3671	15	3	,	,	PUNCT
iajs-3671	15	4	the	the	DET
iajs-3671	15	5	inverse	inverse	NOUN
iajs-3671	15	6	problems	problem	NOUN
iajs-3671	15	7	were	be	AUX
iajs-3671	15	8	reformulated	reformulate	VERB
iajs-3671	15	9	as	as	ADP
iajs-3671	15	10	nonlinear	nonlinear	ADJ
iajs-3671	15	11	least	least	ADJ
iajs-3671	15	12	-	-	PUNCT
iajs-3671	15	13	square	square	NOUN
iajs-3671	15	14	minimization	minimization	NOUN
iajs-3671	15	15	and	and	CCONJ
iajs-3671	15	16	solved	solve	VERB
iajs-3671	15	17	efficiently	efficiently	ADV
iajs-3671	15	18	by	by	ADP
iajs-3671	15	19	optimizing	optimize	VERB
iajs-3671	15	20	matlab	matlab	PROPN
iajs-3671	15	21	routine	routine	PROPN
iajs-3671	15	22	lsqnonlin	lsqnonlin	PROPN
iajs-3671	15	23	.	.	PUNCT
iajs-3671	16	1	tikhonov	tikhonov	PROPN
iajs-3671	16	2	's	's	PART
iajs-3671	16	3	regularization	regularization	NOUN
iajs-3671	16	4	method	method	NOUN
iajs-3671	16	5	was	be	AUX
iajs-3671	16	6	applied	apply	VERB
iajs-3671	16	7	to	to	PART
iajs-3671	16	8	get	get	VERB
iajs-3671	16	9	stable	stable	ADJ
iajs-3671	16	10	results	result	NOUN
iajs-3671	16	11	.	.	PUNCT
iajs-3671	17	1	the	the	DET
iajs-3671	17	2	numerical	numerical	ADJ
iajs-3671	17	3	results	result	NOUN
iajs-3671	17	4	were	be	AUX
iajs-3671	17	5	explained	explain	VERB
iajs-3671	17	6	by	by	ADP
iajs-3671	17	7	presenting	present	VERB
iajs-3671	17	8	a	a	DET
iajs-3671	17	9	test	test	NOUN
iajs-3671	17	10	example	example	NOUN
iajs-3671	17	11	for	for	ADP
iajs-3671	17	12	each	each	DET
iajs-3671	17	13	problem	problem	NOUN
iajs-3671	17	14	.	.	PUNCT
iajs-3671	18	1	in	in	ADP
iajs-3671	18	2	addition	addition	NOUN
iajs-3671	18	3	,	,	PUNCT
iajs-3671	18	4	the	the	DET
iajs-3671	18	5	stability	stability	NOUN
iajs-3671	18	6	was	be	AUX
iajs-3671	18	7	discussed	discuss	VERB
iajs-3671	18	8	by	by	ADP
iajs-3671	18	9	utilizing	utilize	VERB
iajs-3671	18	10	the	the	DET
iajs-3671	18	11	von	von	PROPN
iajs-3671	18	12	neumann	neumann	PROPN
iajs-3671	18	13	stability	stability	PROPN
iajs-3671	18	14	analysis	analysis	NOUN
iajs-3671	18	15	.	.	PUNCT
iajs-3671	19	1	the	the	DET
iajs-3671	19	2	results	result	NOUN
iajs-3671	19	3	showed	show	VERB
iajs-3671	19	4	that	that	SCONJ
iajs-3671	19	5	the	the	DET
iajs-3671	19	6	time	time	NOUN
iajs-3671	19	7	-	-	PUNCT
iajs-3671	19	8	dependent	dependent	ADJ
iajs-3671	19	9	potential	potential	ADJ
iajs-3671	19	10	terms	term	NOUN
iajs-3671	19	11	were	be	AUX
iajs-3671	19	12	reconstructed	reconstruct	VERB
iajs-3671	19	13	successfully	successfully	ADV
iajs-3671	19	14	and	and	CCONJ
iajs-3671	19	15	were	be	AUX
iajs-3671	19	16	stable	stable	ADJ
iajs-3671	19	17	and	and	CCONJ
iajs-3671	19	18	accurate	accurate	ADJ
iajs-3671	19	19	.	.	PUNCT
iajs-3671	20	1	keywords	keyword	NOUN
iajs-3671	20	2	:	:	PUNCT
iajs-3671	20	3	von	von	PROPN
iajs-3671	20	4	neumann	neumann	PROPN
iajs-3671	20	5	stability	stability	PROPN
iajs-3671	20	6	analysis	analysis	NOUN
iajs-3671	20	7	,	,	PUNCT
iajs-3671	20	8	finite	finite	ADJ
iajs-3671	20	9	difference	difference	NOUN
iajs-3671	20	10	method	method	NOUN
iajs-3671	20	11	,	,	PUNCT
iajs-3671	20	12	tikhonov	tikhonov	VERB
iajs-3671	20	13	regularization	regularization	NOUN
iajs-3671	20	14	method	method	NOUN
iajs-3671	20	15	,	,	PUNCT
iajs-3671	20	16	pseudoparabolic	pseudoparabolic	ADJ
iajs-3671	20	17	inverse	inverse	NOUN
iajs-3671	20	18	problem	problem	NOUN
iajs-3671	20	19	,	,	PUNCT
iajs-3671	20	20	inverse	inverse	NOUN
iajs-3671	20	21	problem	problem	NOUN
iajs-3671	20	22	.	.	PUNCT
iajs-3671	21	1	1	1	X
iajs-3671	21	2	.	.	X
iajs-3671	21	3	introduction	introduction	NOUN
iajs-3671	21	4	for	for	ADP
iajs-3671	21	5	the	the	DET
iajs-3671	21	6	inverse	inverse	NOUN
iajs-3671	21	7	problems	problem	NOUN
iajs-3671	21	8	,	,	PUNCT
iajs-3671	21	9	identifying	identify	VERB
iajs-3671	21	10	the	the	DET
iajs-3671	21	11	unknown	unknown	ADJ
iajs-3671	21	12	coefficients	coefficient	NOUN
iajs-3671	21	13	of	of	ADP
iajs-3671	21	14	the	the	DET
iajs-3671	21	15	parabolic	parabolic	ADJ
iajs-3671	21	16	problem	problem	NOUN
iajs-3671	21	17	has	have	VERB
iajs-3671	21	18	many	many	ADJ
iajs-3671	21	19	applications	application	NOUN
iajs-3671	21	20	in	in	ADP
iajs-3671	21	21	engineering	engineering	NOUN
iajs-3671	21	22	and	and	CCONJ
iajs-3671	21	23	science	science	NOUN
iajs-3671	21	24	.	.	PUNCT
iajs-3671	22	1	many	many	ADJ
iajs-3671	22	2	researchers	researcher	NOUN
iajs-3671	22	3	have	have	AUX
iajs-3671	22	4	identified	identify	VERB
iajs-3671	22	5	the	the	DET
iajs-3671	22	6	unknown	unknown	ADJ
iajs-3671	22	7	coefficients	coefficient	NOUN
iajs-3671	22	8	of	of	ADP
iajs-3671	22	9	the	the	DET
iajs-3671	22	10	parabolic	parabolic	ADJ
iajs-3671	22	11	inverse	inverse	NOUN
iajs-3671	22	12	problem	problem	NOUN
iajs-3671	22	13	recently	recently	ADV
iajs-3671	22	14	.	.	PUNCT
iajs-3671	23	1	for	for	ADP
iajs-3671	23	2	example	example	NOUN
iajs-3671	23	3	,	,	PUNCT
iajs-3671	23	4	hussian	hussian	PROPN
iajs-3671	23	5	et	et	PROPN
iajs-3671	23	6	al	al	PROPN
iajs-3671	23	7	.	.	PROPN
iajs-3671	23	8	investigated	investigate	VERB
iajs-3671	23	9	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3671	23	10	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3671	23	11	https://doi.org/10.30526/38.1.3501	https://doi.org/10.30526/38.1.3501	PROPN
iajs-3671	23	12	https://orcid.org/0000-0003-4595-2251	https://orcid.org/0000-0003-4595-2251	PROPN
iajs-3671	23	13	mailto:saylgani@alkadhum-col.edu.iq	mailto:saylgani@alkadhum-col.edu.iq	PROPN
iajs-3671	23	14	https://orcid.org/0000-0002-9456-4303	https://orcid.org/0000-0002-9456-4303	PROPN
iajs-3671	23	15	mailto:mmmsh@sc.uobaghdad.edu.iq	mailto:mmmsh@sc.uobaghdad.edu.iq	PROPN
iajs-3671	23	16	https://orcid.org/0000-0002-1761-5904	https://orcid.org/0000-0002-1761-5904	PROPN
iajs-3671	23	17	mailto:t.dyhoum@mmu.ac.uk	mailto:t.dyhoum@mmu.ac.uk	PROPN
iajs-3671	23	18	ihjpas	ihjpas	PROPN
iajs-3671	23	19	.	.	PUNCT
iajs-3671	24	1	2025	2025	NUM
iajs-3671	24	2	,	,	PUNCT
iajs-3671	24	3	38	38	NUM
iajs-3671	24	4	(	(	PUNCT
iajs-3671	24	5	1	1	NUM
iajs-3671	24	6	)	)	PUNCT
iajs-3671	24	7	466	466	NUM
iajs-3671	24	8	the	the	DET
iajs-3671	24	9	parabolic	parabolic	ADJ
iajs-3671	24	10	inverse	inverse	NOUN
iajs-3671	24	11	problem	problem	NOUN
iajs-3671	24	12	to	to	PART
iajs-3671	24	13	identify	identify	VERB
iajs-3671	24	14	the	the	DET
iajs-3671	24	15	multiple	multiple	ADJ
iajs-3671	24	16	time	time	NOUN
iajs-3671	24	17	-	-	PUNCT
iajs-3671	24	18	dependent	dependent	ADJ
iajs-3671	24	19	coefficients	coefficient	NOUN
iajs-3671	24	20	of	of	ADP
iajs-3671	24	21	thermal	thermal	ADJ
iajs-3671	24	22	problems	problem	NOUN
iajs-3671	24	23	with	with	ADP
iajs-3671	24	24	unknown	unknown	ADJ
iajs-3671	24	25	free	free	ADJ
iajs-3671	24	26	boundary	boundary	ADJ
iajs-3671	24	27	conditions	condition	NOUN
iajs-3671	24	28	in	in	ADP
iajs-3671	24	29	(	(	PUNCT
iajs-3671	24	30	1	1	NUM
iajs-3671	24	31	)	)	PUNCT
iajs-3671	24	32	.	.	PUNCT
iajs-3671	25	1	hussein	hussein	PROPN
iajs-3671	25	2	and	and	CCONJ
iajs-3671	25	3	lesnic	lesnic	PROPN
iajs-3671	25	4	investigated	investigate	VERB
iajs-3671	25	5	the	the	DET
iajs-3671	25	6	one	one	NUM
iajs-3671	25	7	-	-	PUNCT
iajs-3671	25	8	dimensional	dimensional	ADJ
iajs-3671	25	9	parabolic	parabolic	ADJ
iajs-3671	25	10	inverse	inverse	NOUN
iajs-3671	25	11	problem	problem	NOUN
iajs-3671	25	12	for	for	ADP
iajs-3671	25	13	determining	determine	VERB
iajs-3671	25	14	the	the	DET
iajs-3671	25	15	two	two	NUM
iajs-3671	25	16	time	time	NOUN
iajs-3671	25	17	-	-	PUNCT
iajs-3671	25	18	dependent	dependent	ADJ
iajs-3671	25	19	conductivity	conductivity	NOUN
iajs-3671	25	20	with	with	ADP
iajs-3671	25	21	cauchy	cauchy	PROPN
iajs-3671	25	22	data	datum	NOUN
iajs-3671	25	23	and	and	CCONJ
iajs-3671	25	24	heat	heat	NOUN
iajs-3671	25	25	capacity	capacity	NOUN
iajs-3671	25	26	storage	storage	NOUN
iajs-3671	25	27	in	in	ADP
iajs-3671	25	28	(	(	PUNCT
iajs-3671	25	29	2	2	NUM
iajs-3671	25	30	)	)	PUNCT
iajs-3671	25	31	.	.	PUNCT
iajs-3671	26	1	while	while	SCONJ
iajs-3671	26	2	in	in	ADP
iajs-3671	26	3	(	(	PUNCT
iajs-3671	26	4	3	3	NUM
iajs-3671	26	5	)	)	PUNCT
iajs-3671	26	6	,	,	PUNCT
iajs-3671	26	7	the	the	DET
iajs-3671	26	8	authors	author	NOUN
iajs-3671	26	9	presented	present	VERB
iajs-3671	26	10	two	two	NUM
iajs-3671	26	11	parabolic	parabolic	ADJ
iajs-3671	26	12	inverse	inverse	NOUN
iajs-3671	26	13	problems	problem	NOUN
iajs-3671	26	14	for	for	ADP
iajs-3671	26	15	identifying	identify	VERB
iajs-3671	26	16	the	the	DET
iajs-3671	26	17	space	space	NOUN
iajs-3671	26	18	and	and	CCONJ
iajs-3671	26	19	time	time	NOUN
iajs-3671	26	20	-	-	PUNCT
iajs-3671	26	21	dependent	dependent	ADJ
iajs-3671	26	22	coefficients	coefficient	NOUN
iajs-3671	26	23	from	from	ADP
iajs-3671	26	24	the	the	DET
iajs-3671	26	25	overdetermination	overdetermination	NOUN
iajs-3671	26	26	conditions	condition	NOUN
iajs-3671	26	27	.	.	PUNCT
iajs-3671	27	1	in	in	ADP
iajs-3671	27	2	(	(	PUNCT
iajs-3671	27	3	4	4	NUM
iajs-3671	27	4	)	)	PUNCT
iajs-3671	27	5	,	,	PUNCT
iajs-3671	27	6	the	the	DET
iajs-3671	27	7	authors	author	NOUN
iajs-3671	27	8	presented	present	VERB
iajs-3671	27	9	the	the	DET
iajs-3671	27	10	one	one	NUM
iajs-3671	27	11	-	-	PUNCT
iajs-3671	27	12	dimensional	dimensional	ADJ
iajs-3671	27	13	parabolic	parabolic	ADJ
iajs-3671	27	14	inverse	inverse	NOUN
iajs-3671	27	15	problem	problem	NOUN
iajs-3671	27	16	for	for	ADP
iajs-3671	27	17	recovering	recover	VERB
iajs-3671	27	18	the	the	DET
iajs-3671	27	19	heat	heat	NOUN
iajs-3671	27	20	source	source	NOUN
iajs-3671	27	21	and	and	CCONJ
iajs-3671	27	22	time	time	NOUN
iajs-3671	27	23	-	-	PUNCT
iajs-3671	27	24	dependent	dependent	ADJ
iajs-3671	27	25	thermal	thermal	ADJ
iajs-3671	27	26	conductivity	conductivity	NOUN
iajs-3671	27	27	with	with	ADP
iajs-3671	27	28	the	the	DET
iajs-3671	27	29	heat	heat	NOUN
iajs-3671	27	30	flux	flux	NOUN
iajs-3671	27	31	overdetermination	overdetermination	NOUN
iajs-3671	27	32	condition	condition	NOUN
iajs-3671	27	33	for	for	ADP
iajs-3671	27	34	the	the	DET
iajs-3671	27	35	other	other	ADJ
iajs-3671	27	36	related	related	ADJ
iajs-3671	27	37	work	work	NOUN
iajs-3671	27	38	see	see	NOUN
iajs-3671	27	39	(	(	PUNCT
iajs-3671	27	40	5	5	NUM
iajs-3671	27	41	-	-	SYM
iajs-3671	27	42	8)	8)	NUM
iajs-3671	27	43	.	.	PUNCT
iajs-3671	28	1	the	the	DET
iajs-3671	28	2	pseudo	pseudo	NOUN
iajs-3671	28	3	-	-	ADJ
iajs-3671	28	4	parabolic	parabolic	ADJ
iajs-3671	28	5	equations	equation	NOUN
iajs-3671	28	6	of	of	ADP
iajs-3671	28	7	a	a	DET
iajs-3671	28	8	higher	high	ADJ
iajs-3671	28	9	order	order	NOUN
iajs-3671	28	10	play	play	VERB
iajs-3671	28	11	an	an	DET
iajs-3671	28	12	essential	essential	ADJ
iajs-3671	28	13	role	role	NOUN
iajs-3671	28	14	in	in	ADP
iajs-3671	28	15	the	the	DET
iajs-3671	28	16	mathematical	mathematical	ADJ
iajs-3671	28	17	modelling	modelling	NOUN
iajs-3671	28	18	of	of	ADP
iajs-3671	28	19	moisture	moisture	NOUN
iajs-3671	28	20	transfer	transfer	NOUN
iajs-3671	28	21	,	,	PUNCT
iajs-3671	28	22	fluid	fluid	ADJ
iajs-3671	28	23	filtration	filtration	NOUN
iajs-3671	28	24	and	and	CCONJ
iajs-3671	28	25	heat	heat	NOUN
iajs-3671	28	26	propagation	propagation	NOUN
iajs-3671	28	27	(	(	PUNCT
iajs-3671	28	28	9	9	NUM
iajs-3671	28	29	)	)	PUNCT
iajs-3671	28	30	and	and	CCONJ
iajs-3671	28	31	(	(	PUNCT
iajs-3671	28	32	10	10	NUM
iajs-3671	28	33	)	)	PUNCT
iajs-3671	28	34	.	.	PUNCT
iajs-3671	29	1	the	the	DET
iajs-3671	29	2	pseudoparabolic	pseudoparabolic	ADJ
iajs-3671	29	3	inverse	inverse	NOUN
iajs-3671	29	4	problems	problem	NOUN
iajs-3671	29	5	have	have	AUX
iajs-3671	29	6	been	be	AUX
iajs-3671	29	7	utilized	utilize	VERB
iajs-3671	29	8	in	in	ADP
iajs-3671	29	9	modelling	model	VERB
iajs-3671	29	10	various	various	ADJ
iajs-3671	29	11	phenomena	phenomenon	NOUN
iajs-3671	29	12	such	such	ADJ
iajs-3671	29	13	as	as	ADP
iajs-3671	29	14	the	the	DET
iajs-3671	29	15	wave	wave	NOUN
iajs-3671	29	16	processes	process	NOUN
iajs-3671	29	17	,	,	PUNCT
iajs-3671	29	18	chemical	chemical	NOUN
iajs-3671	29	19	,	,	PUNCT
iajs-3671	29	20	engineering	engineering	NOUN
iajs-3671	29	21	,	,	PUNCT
iajs-3671	29	22	diffusion	diffusion	NOUN
iajs-3671	29	23	,	,	PUNCT
iajs-3671	29	24	plasma	plasma	NOUN
iajs-3671	29	25	physics	physics	NOUN
iajs-3671	29	26	and	and	CCONJ
iajs-3671	29	27	heat	heat	NOUN
iajs-3671	29	28	conduction	conduction	NOUN
iajs-3671	29	29	(	(	PUNCT
iajs-3671	29	30	11	11	NUM
iajs-3671	29	31	)	)	PUNCT
iajs-3671	29	32	.	.	PUNCT
iajs-3671	30	1	in	in	ADP
iajs-3671	30	2	addition	addition	NOUN
iajs-3671	30	3	,	,	PUNCT
iajs-3671	30	4	they	they	PRON
iajs-3671	30	5	have	have	VERB
iajs-3671	30	6	many	many	ADJ
iajs-3671	30	7	applications	application	NOUN
iajs-3671	30	8	in	in	ADP
iajs-3671	30	9	real	real	ADJ
iajs-3671	30	10	-	-	PUNCT
iajs-3671	30	11	life	life	NOUN
iajs-3671	30	12	phenomena	phenomenon	NOUN
iajs-3671	30	13	,	,	PUNCT
iajs-3671	30	14	such	such	ADJ
iajs-3671	30	15	as	as	ADP
iajs-3671	30	16	the	the	DET
iajs-3671	30	17	theory	theory	NOUN
iajs-3671	30	18	of	of	ADP
iajs-3671	30	19	small	small	ADJ
iajs-3671	30	20	oscillation	oscillation	NOUN
iajs-3671	30	21	of	of	ADP
iajs-3671	30	22	a	a	DET
iajs-3671	30	23	rotating	rotate	VERB
iajs-3671	30	24	fluid	fluid	NOUN
iajs-3671	30	25	(	(	PUNCT
iajs-3671	30	26	12	12	NUM
iajs-3671	30	27	)	)	PUNCT
iajs-3671	30	28	and	and	CCONJ
iajs-3671	30	29	the	the	DET
iajs-3671	30	30	infiltration	infiltration	NOUN
iajs-3671	30	31	of	of	ADP
iajs-3671	30	32	homogeneous	homogeneous	ADJ
iajs-3671	30	33	fluids	fluid	NOUN
iajs-3671	30	34	in	in	ADP
iajs-3671	30	35	strata	strata	NOUN
iajs-3671	30	36	(	(	PUNCT
iajs-3671	30	37	13	13	NUM
iajs-3671	30	38	)	)	PUNCT
iajs-3671	30	39	.	.	PUNCT
iajs-3671	31	1	moreover	moreover	ADV
iajs-3671	31	2	,	,	PUNCT
iajs-3671	31	3	lyubonova	lyubonova	PROPN
iajs-3671	31	4	and	and	CCONJ
iajs-3671	31	5	tani	tani	PROPN
iajs-3671	31	6	(	(	PUNCT
iajs-3671	31	7	14	14	NUM
iajs-3671	31	8	)	)	PUNCT
iajs-3671	31	9	discussed	discuss	VERB
iajs-3671	31	10	the	the	DET
iajs-3671	31	11	stabilization	stabilization	NOUN
iajs-3671	31	12	of	of	ADP
iajs-3671	31	13	a	a	DET
iajs-3671	31	14	multi	multi	ADJ
iajs-3671	31	15	-	-	ADJ
iajs-3671	31	16	dimensional	dimensional	ADJ
iajs-3671	31	17	pseudoparabolic	pseudoparabolic	ADJ
iajs-3671	31	18	inverse	inverse	NOUN
iajs-3671	31	19	problem	problem	NOUN
iajs-3671	31	20	with	with	ADP
iajs-3671	31	21	a	a	DET
iajs-3671	31	22	coefficient	coefficient	NOUN
iajs-3671	31	23	of	of	ADP
iajs-3671	31	24	piezo	piezo	NOUN
iajs-3671	31	25	conductivity	conductivity	NOUN
iajs-3671	31	26	and	and	CCONJ
iajs-3671	31	27	the	the	DET
iajs-3671	31	28	regularity	regularity	NOUN
iajs-3671	31	29	of	of	ADP
iajs-3671	31	30	the	the	DET
iajs-3671	31	31	solution	solution	NOUN
iajs-3671	31	32	.	.	PUNCT
iajs-3671	32	1	in	in	ADP
iajs-3671	32	2	(	(	PUNCT
iajs-3671	32	3	15	15	NUM
iajs-3671	32	4	)	)	PUNCT
iajs-3671	32	5	,	,	PUNCT
iajs-3671	32	6	the	the	DET
iajs-3671	32	7	authors	author	NOUN
iajs-3671	32	8	analyzed	analyze	VERB
iajs-3671	32	9	the	the	DET
iajs-3671	32	10	uniqueness	uniqueness	NOUN
iajs-3671	32	11	and	and	CCONJ
iajs-3671	32	12	existence	existence	NOUN
iajs-3671	32	13	of	of	ADP
iajs-3671	32	14	the	the	DET
iajs-3671	32	15	solution	solution	NOUN
iajs-3671	32	16	of	of	ADP
iajs-3671	32	17	the	the	DET
iajs-3671	32	18	thirdorder	thirdorder	NOUN
iajs-3671	32	19	pseudo	pseudo	NOUN
iajs-3671	32	20	-	-	ADJ
iajs-3671	32	21	parabolic	parabolic	ADJ
iajs-3671	32	22	inverse	inverse	NOUN
iajs-3671	32	23	problem	problem	NOUN
iajs-3671	32	24	with	with	ADP
iajs-3671	32	25	periodic	periodic	ADJ
iajs-3671	32	26	and	and	CCONJ
iajs-3671	32	27	integral	integral	ADJ
iajs-3671	32	28	conditions	condition	NOUN
iajs-3671	32	29	.	.	PUNCT
iajs-3671	33	1	abylkairov	abylkairov	PROPN
iajs-3671	33	2	and	and	CCONJ
iajs-3671	33	3	khompysh	khompysh	NOUN
iajs-3671	33	4	(	(	PUNCT
iajs-3671	33	5	16	16	NUM
iajs-3671	33	6	)	)	PUNCT
iajs-3671	33	7	studied	study	VERB
iajs-3671	33	8	the	the	DET
iajs-3671	33	9	existence	existence	NOUN
iajs-3671	33	10	and	and	CCONJ
iajs-3671	33	11	uniqueness	uniqueness	NOUN
iajs-3671	33	12	of	of	ADP
iajs-3671	33	13	a	a	DET
iajs-3671	33	14	solution	solution	NOUN
iajs-3671	33	15	for	for	ADP
iajs-3671	33	16	the	the	DET
iajs-3671	33	17	right	right	ADJ
iajs-3671	33	18	side	side	NOUN
iajs-3671	33	19	of	of	ADP
iajs-3671	33	20	the	the	DET
iajs-3671	33	21	pseudoparabolic	pseudoparabolic	ADJ
iajs-3671	33	22	inverse	inverse	NOUN
iajs-3671	33	23	problem	problem	NOUN
iajs-3671	33	24	,	,	PUNCT
iajs-3671	33	25	which	which	PRON
iajs-3671	33	26	was	be	AUX
iajs-3671	33	27	described	describe	VERB
iajs-3671	33	28	as	as	ADP
iajs-3671	33	29	the	the	DET
iajs-3671	33	30	motion	motion	NOUN
iajs-3671	33	31	of	of	ADP
iajs-3671	33	32	kelvin	kelvin	PROPN
iajs-3671	33	33	voight	voight	PROPN
iajs-3671	33	34	fluids	fluids	PROPN
iajs-3671	33	35	.	.	PUNCT
iajs-3671	34	1	antotsev	antotsev	PROPN
iajs-3671	34	2	et	et	PROPN
iajs-3671	34	3	al	al	PROPN
iajs-3671	34	4	.	.	PROPN
iajs-3671	35	1	(	(	PUNCT
iajs-3671	35	2	17	17	NUM
iajs-3671	35	3	)	)	PUNCT
iajs-3671	35	4	proved	prove	VERB
iajs-3671	35	5	the	the	DET
iajs-3671	35	6	unique	unique	ADJ
iajs-3671	35	7	solvability	solvability	NOUN
iajs-3671	35	8	for	for	ADP
iajs-3671	35	9	the	the	DET
iajs-3671	35	10	pseudo	pseudo	NOUN
iajs-3671	35	11	-	-	ADJ
iajs-3671	35	12	parabolic	parabolic	ADJ
iajs-3671	35	13	inverse	inverse	NOUN
iajs-3671	35	14	problem	problem	NOUN
iajs-3671	35	15	with	with	ADP
iajs-3671	35	16	a	a	DET
iajs-3671	35	17	plaplacian	plaplacian	NOUN
iajs-3671	35	18	and	and	CCONJ
iajs-3671	35	19	under	under	ADP
iajs-3671	35	20	a	a	DET
iajs-3671	35	21	nonlocal	nonlocal	ADJ
iajs-3671	35	22	integral	integral	ADJ
iajs-3671	35	23	overdetermination	overdetermination	NOUN
iajs-3671	35	24	condition	condition	NOUN
iajs-3671	35	25	by	by	ADP
iajs-3671	35	26	using	use	VERB
iajs-3671	35	27	the	the	DET
iajs-3671	35	28	galerkin	galerkin	ADJ
iajs-3671	35	29	method	method	NOUN
iajs-3671	35	30	.	.	PUNCT
iajs-3671	36	1	many	many	ADJ
iajs-3671	36	2	other	other	ADJ
iajs-3671	36	3	researchers	researcher	NOUN
iajs-3671	36	4	have	have	AUX
iajs-3671	36	5	examined	examine	VERB
iajs-3671	36	6	the	the	DET
iajs-3671	36	7	pseudo	pseudo	NOUN
iajs-3671	36	8	-	-	ADJ
iajs-3671	36	9	parabolic	parabolic	ADJ
iajs-3671	36	10	inverse	inverse	NOUN
iajs-3671	36	11	problem	problem	NOUN
iajs-3671	36	12	to	to	PART
iajs-3671	36	13	identify	identify	VERB
iajs-3671	36	14	the	the	DET
iajs-3671	36	15	unknown	unknown	ADJ
iajs-3671	36	16	time	time	NOUN
iajs-3671	36	17	-	-	PUNCT
iajs-3671	36	18	dependent	dependent	ADJ
iajs-3671	36	19	coefficients	coefficient	NOUN
iajs-3671	36	20	.	.	PUNCT
iajs-3671	37	1	in	in	ADP
iajs-3671	37	2	studies	study	NOUN
iajs-3671	37	3	(	(	PUNCT
iajs-3671	37	4	18	18	NUM
iajs-3671	37	5	,	,	PUNCT
iajs-3671	37	6	19	19	NUM
iajs-3671	37	7	)	)	PUNCT
iajs-3671	37	8	,	,	PUNCT
iajs-3671	37	9	the	the	DET
iajs-3671	37	10	pseudo	pseudo	NOUN
iajs-3671	37	11	-	-	ADJ
iajs-3671	37	12	parabolic	parabolic	ADJ
iajs-3671	37	13	inverse	inverse	NOUN
iajs-3671	37	14	problem	problem	NOUN
iajs-3671	37	15	was	be	AUX
iajs-3671	37	16	presented	present	VERB
iajs-3671	37	17	to	to	PART
iajs-3671	37	18	determine	determine	VERB
iajs-3671	37	19	the	the	DET
iajs-3671	37	20	unknown	unknown	ADJ
iajs-3671	37	21	coefficient	coefficient	NOUN
iajs-3671	37	22	of	of	ADP
iajs-3671	37	23	filtration	filtration	NOUN
iajs-3671	37	24	and	and	CCONJ
iajs-3671	37	25	diffusion	diffusion	NOUN
iajs-3671	37	26	.	.	PUNCT
iajs-3671	38	1	in	in	ADP
iajs-3671	38	2	addition	addition	NOUN
iajs-3671	38	3	,	,	PUNCT
iajs-3671	38	4	the	the	DET
iajs-3671	38	5	asymptotic	asymptotic	ADJ
iajs-3671	38	6	behaviour	behaviour	NOUN
iajs-3671	38	7	of	of	ADP
iajs-3671	38	8	the	the	DET
iajs-3671	38	9	pseudo	pseudo	NOUN
iajs-3671	38	10	-	-	ADJ
iajs-3671	38	11	parabolic	parabolic	ADJ
iajs-3671	38	12	inverse	inverse	NOUN
iajs-3671	38	13	problem	problem	NOUN
iajs-3671	38	14	to	to	PART
iajs-3671	38	15	determine	determine	VERB
iajs-3671	38	16	unknown	unknown	ADJ
iajs-3671	38	17	source	source	NOUN
iajs-3671	38	18	terms	term	NOUN
iajs-3671	38	19	with	with	ADP
iajs-3671	38	20	integral	integral	ADJ
iajs-3671	38	21	conditions	condition	NOUN
iajs-3671	38	22	has	have	AUX
iajs-3671	38	23	been	be	AUX
iajs-3671	38	24	considered	consider	VERB
iajs-3671	38	25	by	by	ADP
iajs-3671	38	26	yaman	yaman	PROPN
iajs-3671	38	27	and	and	CCONJ
iajs-3671	38	28	g¨ozükizil	g¨ozükizil	PROPN
iajs-3671	38	29	(	(	PUNCT
iajs-3671	38	30	20	20	NUM
iajs-3671	38	31	)	)	PUNCT
iajs-3671	38	32	.	.	PUNCT
iajs-3671	39	1	a	a	DET
iajs-3671	39	2	few	few	ADJ
iajs-3671	39	3	years	year	NOUN
iajs-3671	39	4	ago	ago	ADV
iajs-3671	39	5	,	,	PUNCT
iajs-3671	39	6	the	the	DET
iajs-3671	39	7	numerical	numerical	ADJ
iajs-3671	39	8	solution	solution	NOUN
iajs-3671	39	9	containing	contain	VERB
iajs-3671	39	10	unknown	unknown	ADJ
iajs-3671	39	11	coefficients	coefficient	NOUN
iajs-3671	39	12	was	be	AUX
iajs-3671	39	13	investigated	investigate	VERB
iajs-3671	39	14	by	by	ADP
iajs-3671	39	15	beshtokv	beshtokv	NOUN
iajs-3671	39	16	for	for	ADP
iajs-3671	39	17	the	the	DET
iajs-3671	39	18	pseudo	pseudo	NOUN
iajs-3671	39	19	-	-	ADJ
iajs-3671	39	20	parabolic	parabolic	ADJ
iajs-3671	39	21	equations	equation	NOUN
iajs-3671	39	22	from	from	ADP
iajs-3671	39	23	a	a	DET
iajs-3671	39	24	class	class	NOUN
iajs-3671	39	25	of	of	ADP
iajs-3671	39	26	the	the	DET
iajs-3671	39	27	third	third	ADJ
iajs-3671	39	28	-	-	PUNCT
iajs-3671	39	29	order	order	NOUN
iajs-3671	39	30	(	(	PUNCT
iajs-3671	39	31	21	21	NUM
iajs-3671	39	32	)	)	PUNCT
iajs-3671	39	33	.	.	PUNCT
iajs-3671	40	1	the	the	DET
iajs-3671	40	2	third	third	ADJ
iajs-3671	40	3	-	-	PUNCT
iajs-3671	40	4	order	order	NOUN
iajs-3671	40	5	pseudo	pseudo	NOUN
iajs-3671	40	6	-	-	ADJ
iajs-3671	40	7	parabolic	parabolic	ADJ
iajs-3671	40	8	equations	equation	NOUN
iajs-3671	40	9	result	result	VERB
iajs-3671	40	10	from	from	ADP
iajs-3671	40	11	the	the	DET
iajs-3671	40	12	problem	problem	NOUN
iajs-3671	40	13	with	with	ADP
iajs-3671	40	14	heat	heat	NOUN
iajs-3671	40	15	and	and	CCONJ
iajs-3671	40	16	moisture	moisture	NOUN
iajs-3671	40	17	transmission	transmission	NOUN
iajs-3671	40	18	and	and	CCONJ
iajs-3671	40	19	fluid	fluid	ADJ
iajs-3671	40	20	filtration	filtration	NOUN
iajs-3671	40	21	(	(	PUNCT
iajs-3671	40	22	22,23	22,23	NOUN
iajs-3671	40	23	)	)	PUNCT
iajs-3671	40	24	.	.	PUNCT
iajs-3671	41	1	an	an	DET
iajs-3671	41	2	inverse	inverse	ADJ
iajs-3671	41	3	problem	problem	NOUN
iajs-3671	41	4	of	of	ADP
iajs-3671	41	5	reformulating	reformulate	VERB
iajs-3671	41	6	an	an	DET
iajs-3671	41	7	unknown	unknown	ADJ
iajs-3671	41	8	potential	potential	ADJ
iajs-3671	41	9	element	element	NOUN
iajs-3671	41	10	has	have	AUX
iajs-3671	41	11	been	be	AUX
iajs-3671	41	12	studied	study	VERB
iajs-3671	41	13	(	(	PUNCT
iajs-3671	41	14	24	24	NUM
iajs-3671	41	15	)	)	PUNCT
iajs-3671	41	16	.	.	PUNCT
iajs-3671	42	1	moreover	moreover	ADV
iajs-3671	42	2	,	,	PUNCT
iajs-3671	42	3	both	both	PRON
iajs-3671	42	4	huntual	huntual	ADJ
iajs-3671	42	5	et	et	PROPN
iajs-3671	42	6	al	al	PROPN
iajs-3671	42	7	.	.	PROPN
iajs-3671	43	1	(	(	PUNCT
iajs-3671	43	2	25,26	25,26	NUM
iajs-3671	43	3	)	)	PUNCT
iajs-3671	43	4	and	and	CCONJ
iajs-3671	43	5	ramazanova	ramazanova	VERB
iajs-3671	43	6	et	et	PROPN
iajs-3671	43	7	al	al	PROPN
iajs-3671	43	8	.	.	PROPN
iajs-3671	44	1	(	(	PUNCT
iajs-3671	44	2	27	27	NUM
iajs-3671	44	3	)	)	PUNCT
iajs-3671	44	4	examined	examine	VERB
iajs-3671	44	5	the	the	DET
iajs-3671	44	6	fourth	fourth	ADJ
iajs-3671	44	7	-	-	PUNCT
iajs-3671	44	8	order	order	NOUN
iajs-3671	44	9	inverse	inverse	NOUN
iajs-3671	44	10	problem	problem	NOUN
iajs-3671	44	11	for	for	ADP
iajs-3671	44	12	identifying	identify	VERB
iajs-3671	44	13	the	the	DET
iajs-3671	44	14	time	time	NOUN
iajs-3671	44	15	-	-	PUNCT
iajs-3671	44	16	dependent	dependent	ADJ
iajs-3671	44	17	potential	potential	ADJ
iajs-3671	44	18	coefficient	coefficient	NOUN
iajs-3671	44	19	from	from	ADP
iajs-3671	44	20	additional	additional	ADJ
iajs-3671	44	21	conditions	condition	NOUN
iajs-3671	44	22	and	and	CCONJ
iajs-3671	44	23	the	the	DET
iajs-3671	44	24	cubic	cubic	ADJ
iajs-3671	44	25	-	-	PUNCT
iajs-3671	44	26	spline	spline	NOUN
iajs-3671	44	27	method	method	NOUN
iajs-3671	44	28	as	as	ADP
iajs-3671	44	29	a	a	DET
iajs-3671	44	30	direct	direct	ADJ
iajs-3671	44	31	method	method	NOUN
iajs-3671	44	32	.	.	PUNCT
iajs-3671	45	1	in	in	ADP
iajs-3671	45	2	this	this	DET
iajs-3671	45	3	work	work	NOUN
iajs-3671	45	4	,	,	PUNCT
iajs-3671	45	5	two	two	NUM
iajs-3671	45	6	pseudo	pseudo	NOUN
iajs-3671	45	7	-	-	ADJ
iajs-3671	45	8	parabolic	parabolic	ADJ
iajs-3671	45	9	inverse	inverse	NOUN
iajs-3671	45	10	problems	problem	NOUN
iajs-3671	45	11	were	be	AUX
iajs-3671	45	12	presented	present	VERB
iajs-3671	45	13	from	from	ADP
iajs-3671	45	14	the	the	DET
iajs-3671	45	15	third	third	ADJ
iajs-3671	45	16	-	-	PUNCT
iajs-3671	45	17	order	order	NOUN
iajs-3671	45	18	equation	equation	NOUN
iajs-3671	45	19	to	to	PART
iajs-3671	45	20	recover	recover	VERB
iajs-3671	45	21	the	the	DET
iajs-3671	45	22	potential	potential	ADJ
iajs-3671	45	23	time	time	NOUN
iajs-3671	45	24	-	-	PUNCT
iajs-3671	45	25	dependent	dependent	ADJ
iajs-3671	45	26	coefficient	coefficient	NOUN
iajs-3671	45	27	numerically	numerically	ADV
iajs-3671	45	28	with	with	ADP
iajs-3671	45	29	different	different	ADJ
iajs-3671	45	30	boundary	boundary	ADJ
iajs-3671	45	31	conditions	condition	NOUN
iajs-3671	45	32	.	.	PUNCT
iajs-3671	46	1	since	since	SCONJ
iajs-3671	46	2	the	the	DET
iajs-3671	46	3	periodic	periodic	ADJ
iajs-3671	46	4	conditions	condition	NOUN
iajs-3671	46	5	were	be	AUX
iajs-3671	46	6	used	use	VERB
iajs-3671	46	7	for	for	ADP
iajs-3671	46	8	both	both	DET
iajs-3671	46	9	problems	problem	NOUN
iajs-3671	46	10	,	,	PUNCT
iajs-3671	46	11	the	the	DET
iajs-3671	46	12	neuman	neuman	NOUN
iajs-3671	46	13	and	and	CCONJ
iajs-3671	46	14	nonlocal	nonlocal	ADJ
iajs-3671	46	15	integral	integral	ADJ
iajs-3671	46	16	conditions	condition	NOUN
iajs-3671	46	17	were	be	AUX
iajs-3671	46	18	used	use	VERB
iajs-3671	46	19	with	with	ADP
iajs-3671	46	20	the	the	DET
iajs-3671	46	21	first	first	ADJ
iajs-3671	46	22	and	and	CCONJ
iajs-3671	46	23	second	second	ADJ
iajs-3671	46	24	problems	problem	NOUN
iajs-3671	46	25	,	,	PUNCT
iajs-3671	46	26	respectively	respectively	ADV
iajs-3671	46	27	.	.	PUNCT
iajs-3671	47	1	for	for	ADP
iajs-3671	47	2	both	both	DET
iajs-3671	47	3	problems	problem	NOUN
iajs-3671	47	4	,	,	PUNCT
iajs-3671	47	5	the	the	DET
iajs-3671	47	6	over	over	ADP
iajs-3671	47	7	-	-	PUNCT
iajs-3671	47	8	specification	specification	NOUN
iajs-3671	47	9	data	datum	NOUN
iajs-3671	47	10	was	be	AUX
iajs-3671	47	11	utilized	utilize	VERB
iajs-3671	47	12	for	for	ADP
iajs-3671	47	13	recovering	recover	VERB
iajs-3671	47	14	the	the	DET
iajs-3671	47	15	unique	unique	ADJ
iajs-3671	47	16	potential	potential	ADJ
iajs-3671	47	17	terms	term	NOUN
iajs-3671	47	18	.	.	PUNCT
iajs-3671	48	1	the	the	DET
iajs-3671	48	2	uniqueness	uniqueness	NOUN
iajs-3671	48	3	and	and	CCONJ
iajs-3671	48	4	existence	existence	NOUN
iajs-3671	48	5	were	be	AUX
iajs-3671	48	6	proved	prove	VERB
iajs-3671	48	7	in	in	ADP
iajs-3671	48	8	(	(	PUNCT
iajs-3671	48	9	28	28	NUM
iajs-3671	48	10	)	)	PUNCT
iajs-3671	48	11	for	for	ADP
iajs-3671	48	12	the	the	DET
iajs-3671	48	13	first	first	ADJ
iajs-3671	48	14	problem	problem	NOUN
iajs-3671	48	15	and	and	CCONJ
iajs-3671	48	16	in	in	ADP
iajs-3671	48	17	(	(	PUNCT
iajs-3671	48	18	29	29	NUM
iajs-3671	48	19	)	)	PUNCT
iajs-3671	48	20	for	for	ADP
iajs-3671	48	21	the	the	DET
iajs-3671	48	22	second	second	ADJ
iajs-3671	48	23	ihjpas	ihjpa	NOUN
iajs-3671	48	24	.	.	PUNCT
iajs-3671	49	1	2025	2025	NUM
iajs-3671	49	2	,	,	PUNCT
iajs-3671	49	3	38	38	NUM
iajs-3671	49	4	(	(	PUNCT
iajs-3671	49	5	1	1	NUM
iajs-3671	49	6	)	)	PUNCT
iajs-3671	49	7	467	467	NUM
iajs-3671	49	8	one	one	NUM
iajs-3671	49	9	.	.	PUNCT
iajs-3671	50	1	the	the	DET
iajs-3671	50	2	formation	formation	NOUN
iajs-3671	50	3	of	of	ADP
iajs-3671	50	4	this	this	DET
iajs-3671	50	5	study	study	NOUN
iajs-3671	50	6	is	be	AUX
iajs-3671	50	7	as	as	SCONJ
iajs-3671	50	8	follows	follow	VERB
iajs-3671	50	9	:	:	PUNCT
iajs-3671	50	10	section	section	NOUN
iajs-3671	50	11	2	2	NUM
iajs-3671	50	12	presents	present	VERB
iajs-3671	50	13	the	the	DET
iajs-3671	50	14	mathematical	mathematical	ADJ
iajs-3671	50	15	form	form	NOUN
iajs-3671	50	16	of	of	ADP
iajs-3671	50	17	the	the	DET
iajs-3671	50	18	inverse	inverse	NOUN
iajs-3671	50	19	problem	problem	NOUN
iajs-3671	50	20	i	i	PRON
iajs-3671	50	21	and	and	CCONJ
iajs-3671	50	22	ii	ii	PROPN
iajs-3671	50	23	,	,	PUNCT
iajs-3671	50	24	which	which	PRON
iajs-3671	50	25	are	be	AUX
iajs-3671	50	26	contained	contain	VERB
iajs-3671	50	27	in	in	ADP
iajs-3671	50	28	subsection	subsection	NOUN
iajs-3671	50	29	1	1	NUM
iajs-3671	50	30	.	.	PUNCT
iajs-3671	51	1	the	the	DET
iajs-3671	51	2	fdm	fdm	NOUN
iajs-3671	51	3	is	be	AUX
iajs-3671	51	4	used	use	VERB
iajs-3671	51	5	to	to	PART
iajs-3671	51	6	discretize	discretize	VERB
iajs-3671	51	7	the	the	DET
iajs-3671	51	8	direct	direct	ADJ
iajs-3671	51	9	problems	problem	NOUN
iajs-3671	51	10	i	i	PRON
iajs-3671	51	11	and	and	CCONJ
iajs-3671	51	12	ii	ii	PROPN
iajs-3671	51	13	,	,	PUNCT
iajs-3671	51	14	subsection	subsection	NOUN
iajs-3671	51	15	2	2	NUM
iajs-3671	51	16	,	,	PUNCT
iajs-3671	51	17	and	and	CCONJ
iajs-3671	51	18	the	the	DET
iajs-3671	51	19	stability	stability	NOUN
iajs-3671	51	20	analysis	analysis	NOUN
iajs-3671	51	21	is	be	AUX
iajs-3671	51	22	provided	provide	VERB
iajs-3671	51	23	in	in	ADP
iajs-3671	51	24	subsection	subsection	NOUN
iajs-3671	51	25	3	3	NUM
iajs-3671	51	26	,	,	PUNCT
iajs-3671	51	27	examples	example	NOUN
iajs-3671	51	28	of	of	ADP
iajs-3671	51	29	tests	test	NOUN
iajs-3671	51	30	for	for	ADP
iajs-3671	51	31	direct	direct	ADJ
iajs-3671	51	32	problems	problem	NOUN
iajs-3671	51	33	i	i	PRON
iajs-3671	51	34	and	and	CCONJ
iajs-3671	51	35	ii	ii	PROPN
iajs-3671	51	36	.	.	PROPN
iajs-3671	51	37	section	section	PROPN
iajs-3671	51	38	3	3	NUM
iajs-3671	51	39	presents	present	VERB
iajs-3671	51	40	the	the	DET
iajs-3671	51	41	numerical	numerical	ADJ
iajs-3671	51	42	technique	technique	NOUN
iajs-3671	51	43	of	of	ADP
iajs-3671	51	44	functional	functional	ADJ
iajs-3671	51	45	minimization	minimization	NOUN
iajs-3671	51	46	and	and	CCONJ
iajs-3671	51	47	numerical	numerical	ADJ
iajs-3671	51	48	results	result	NOUN
iajs-3671	51	49	of	of	ADP
iajs-3671	51	50	the	the	DET
iajs-3671	51	51	inverse	inverse	NOUN
iajs-3671	51	52	problems	problem	NOUN
iajs-3671	51	53	i	i	PRON
iajs-3671	51	54	and	and	CCONJ
iajs-3671	51	55	ii	ii	PROPN
iajs-3671	51	56	.	.	PUNCT
iajs-3671	52	1	finally	finally	ADV
iajs-3671	52	2	,	,	PUNCT
iajs-3671	52	3	in	in	ADP
iajs-3671	52	4	section	section	NOUN
iajs-3671	52	5	4	4	NUM
iajs-3671	52	6	,	,	PUNCT
iajs-3671	52	7	the	the	DET
iajs-3671	52	8	conclusions	conclusion	NOUN
iajs-3671	52	9	are	be	AUX
iajs-3671	52	10	highlighted	highlight	VERB
iajs-3671	52	11	.	.	PUNCT
iajs-3671	53	1	2	2	X
iajs-3671	53	2	.	.	X
iajs-3671	53	3	mathematical	mathematical	ADJ
iajs-3671	53	4	formulation	formulation	NOUN
iajs-3671	53	5	of	of	ADP
iajs-3671	53	6	the	the	DET
iajs-3671	53	7	inverse	inverse	NOUN
iajs-3671	53	8	problem	problem	NOUN
iajs-3671	53	9	i	i	PRON
iajs-3671	53	10	and	and	CCONJ
iajs-3671	53	11	ii	ii	PROPN
iajs-3671	53	12	in	in	ADP
iajs-3671	53	13	rectangle	rectangle	ADJ
iajs-3671	53	14	domain	domain	NOUN
iajs-3671	53	15	𝑄𝑇	𝑄𝑇	PROPN
iajs-3671	53	16	≔	≔	NOUN
iajs-3671	53	17	{	{	PUNCT
iajs-3671	53	18	0	0	NUM
iajs-3671	53	19	≤	≤	NUM
iajs-3671	53	20	𝑥	𝑥	PUNCT
iajs-3671	53	21	≤	≤	NUM
iajs-3671	53	22	1	1	NUM
iajs-3671	53	23	,	,	PUNCT
iajs-3671	53	24	0	0	NUM
iajs-3671	53	25	≤	≤	NUM
iajs-3671	53	26	𝑡	𝑡	PROPN
iajs-3671	53	27	≤	≤	PROPN
iajs-3671	53	28	𝑇	𝑇	PROPN
iajs-3671	53	29	}	}	PUNCT
iajs-3671	53	30	,	,	PUNCT
iajs-3671	53	31	consider	consider	VERB
iajs-3671	53	32	the	the	DET
iajs-3671	53	33	inverse	inverse	NOUN
iajs-3671	53	34	problems	problem	NOUN
iajs-3671	53	35	of	of	ADP
iajs-3671	53	36	identifying	identify	VERB
iajs-3671	53	37	a	a	DET
iajs-3671	53	38	pair	pair	NOUN
iajs-3671	53	39	of	of	ADP
iajs-3671	53	40	functions	function	NOUN
iajs-3671	53	41	(	(	PUNCT
iajs-3671	53	42	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	53	43	,	,	PUNCT
iajs-3671	53	44	𝑡	𝑡	PROPN
iajs-3671	53	45	)	)	PUNCT
iajs-3671	53	46	,	,	PUNCT
iajs-3671	53	47	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	53	48	)	)	PUNCT
iajs-3671	53	49	)	)	PUNCT
iajs-3671	53	50	,	,	PUNCT
iajs-3671	53	51	which	which	PRON
iajs-3671	53	52	satisfy	satisfy	VERB
iajs-3671	53	53	the	the	DET
iajs-3671	53	54	1d	1d	NUM
iajs-3671	53	55	pseudo	pseudo	NOUN
iajs-3671	53	56	-	-	ADJ
iajs-3671	53	57	parabolic	parabolic	ADJ
iajs-3671	53	58	equation	equation	NOUN
iajs-3671	53	59	𝜕𝑢(𝑥	𝜕𝑢(𝑥	PROPN
iajs-3671	53	60	,	,	PUNCT
iajs-3671	53	61	𝑡	𝑡	NOUN
iajs-3671	53	62	)	)	PUNCT
iajs-3671	53	63	𝜕𝑡	𝜕𝑡	NOUN
iajs-3671	53	64	=	=	NOUN
iajs-3671	53	65	𝑏	𝑏	PROPN
iajs-3671	53	66	𝜕3𝑢(𝑥	𝜕3𝑢(𝑥	PROPN
iajs-3671	53	67	,	,	PUNCT
iajs-3671	53	68	𝑡	𝑡	NOUN
iajs-3671	53	69	)	)	PUNCT
iajs-3671	53	70	𝜕𝑥2𝜕𝑡	𝜕𝑥2𝜕𝑡	PART
iajs-3671	53	71	+	+	NUM
iajs-3671	53	72	𝑎(𝑡	𝑎(𝑡	NOUN
iajs-3671	53	73	)	)	PUNCT
iajs-3671	53	74	𝜕2𝑢(𝑥	𝜕2𝑢(𝑥	NOUN
iajs-3671	53	75	,	,	PUNCT
iajs-3671	53	76	𝑡	𝑡	NOUN
iajs-3671	53	77	)	)	PUNCT
iajs-3671	53	78	𝜕𝑥2	𝜕𝑥2	NOUN
iajs-3671	53	79	+	+	CCONJ
iajs-3671	53	80	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	53	81	)	)	PUNCT
iajs-3671	53	82	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	53	83	,	,	PUNCT
iajs-3671	53	84	𝑡	𝑡	NOUN
iajs-3671	53	85	)	)	PUNCT
iajs-3671	53	86	+	+	NUM
iajs-3671	53	87	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3671	53	88	,	,	PUNCT
iajs-3671	53	89	𝑡	𝑡	NOUN
iajs-3671	53	90	)	)	PUNCT
iajs-3671	53	91	(	(	PUNCT
iajs-3671	53	92	𝑥	𝑥	NOUN
iajs-3671	53	93	,	,	PUNCT
iajs-3671	53	94	𝑡	𝑡	PROPN
iajs-3671	53	95	)	)	PUNCT
iajs-3671	53	96	𝜖	𝜖	PROPN
iajs-3671	53	97	𝑄𝑇	𝑄𝑇	PROPN
iajs-3671	53	98	(	(	PUNCT
iajs-3671	53	99	1	1	NUM
iajs-3671	53	100	)	)	PUNCT
iajs-3671	53	101	the	the	DET
iajs-3671	53	102	initial	initial	ADJ
iajs-3671	53	103	condition	condition	NOUN
iajs-3671	53	104	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	53	105	,	,	PUNCT
iajs-3671	53	106	0	0	NUM
iajs-3671	53	107	)	)	PUNCT
iajs-3671	53	108	=	=	SYM
iajs-3671	53	109	𝜑(𝑥	𝜑(𝑥	NOUN
iajs-3671	53	110	)	)	PUNCT
iajs-3671	53	111	,	,	PUNCT
iajs-3671	54	1	0	0	NUM
iajs-3671	54	2	≤	≤	NUM
iajs-3671	54	3	𝑥	𝑥	PUNCT
iajs-3671	54	4	≤	≤	NUM
iajs-3671	54	5	1	1	NUM
iajs-3671	54	6	,	,	PUNCT
iajs-3671	54	7	(	(	PUNCT
iajs-3671	54	8	2	2	X
iajs-3671	54	9	)	)	PUNCT
iajs-3671	54	10	the	the	DET
iajs-3671	54	11	periodic	periodic	ADJ
iajs-3671	54	12	condition	condition	NOUN
iajs-3671	54	13	𝑢(0	𝑢(0	PROPN
iajs-3671	54	14	,	,	PUNCT
iajs-3671	54	15	𝑡	𝑡	PROPN
iajs-3671	54	16	)	)	PUNCT
iajs-3671	54	17	=	=	SYM
iajs-3671	54	18	𝑢(1	𝑢(1	NOUN
iajs-3671	54	19	,	,	PUNCT
iajs-3671	54	20	𝑡	𝑡	NOUN
iajs-3671	54	21	)	)	PUNCT
iajs-3671	54	22	,	,	PUNCT
iajs-3671	54	23	0	0	NUM
iajs-3671	54	24	≤	≤	NUM
iajs-3671	54	25	𝑡	𝑡	PROPN
iajs-3671	54	26	≤	≤	PROPN
iajs-3671	54	27	𝑇	𝑇	PROPN
iajs-3671	54	28	,	,	PUNCT
iajs-3671	54	29	(	(	PUNCT
iajs-3671	54	30	3	3	X
iajs-3671	54	31	)	)	PUNCT
iajs-3671	54	32	the	the	DET
iajs-3671	54	33	neumann	neumann	PROPN
iajs-3671	54	34	condition	condition	PROPN
iajs-3671	54	35	𝑢𝑥(1	𝑢𝑥(1	PROPN
iajs-3671	54	36	,	,	PUNCT
iajs-3671	54	37	𝑡	𝑡	X
iajs-3671	54	38	)	)	PUNCT
iajs-3671	54	39	=	=	SYM
iajs-3671	54	40	0	0	NUM
iajs-3671	54	41	,	,	PUNCT
iajs-3671	54	42	0	0	NUM
iajs-3671	54	43	≤	≤	NUM
iajs-3671	54	44	𝑡	𝑡	PROPN
iajs-3671	54	45	≤	≤	ADJ
iajs-3671	54	46	𝑇	𝑇	PROPN
iajs-3671	54	47	(	(	PUNCT
iajs-3671	54	48	4	4	NUM
iajs-3671	54	49	)	)	PUNCT
iajs-3671	54	50	the	the	DET
iajs-3671	54	51	nonlocal	nonlocal	ADJ
iajs-3671	54	52	integral	integral	ADJ
iajs-3671	54	53	condition	condition	NOUN
iajs-3671	54	54	∫𝑢(𝑥	∫𝑢(𝑥	NOUN
iajs-3671	54	55	,	,	PUNCT
iajs-3671	54	56	𝑡	𝑡	X
iajs-3671	54	57	)	)	PUNCT
iajs-3671	54	58	=	=	SYM
iajs-3671	54	59	0	0	NUM
iajs-3671	54	60	,	,	PUNCT
iajs-3671	54	61	1	1	NUM
iajs-3671	54	62	0	0	NUM
iajs-3671	54	63	0	0	NUM
iajs-3671	54	64	≤	≤	NUM
iajs-3671	54	65	𝑡	𝑡	PROPN
iajs-3671	54	66	≤	≤	ADJ
iajs-3671	54	67	𝑇	𝑇	PROPN
iajs-3671	54	68	(	(	PUNCT
iajs-3671	54	69	5	5	NUM
iajs-3671	54	70	)	)	PUNCT
iajs-3671	54	71	and	and	CCONJ
iajs-3671	54	72	the	the	DET
iajs-3671	54	73	additional	additional	ADJ
iajs-3671	54	74	conditions	condition	NOUN
iajs-3671	54	75	are	be	AUX
iajs-3671	54	76	𝑢	𝑢	PRON
iajs-3671	54	77	(	(	PUNCT
iajs-3671	54	78	1	1	NUM
iajs-3671	54	79	2	2	NUM
iajs-3671	54	80	,	,	PUNCT
iajs-3671	54	81	𝑡	𝑡	NOUN
iajs-3671	54	82	)	)	PUNCT
iajs-3671	54	83	+	+	CCONJ
iajs-3671	55	1	∫𝑢(𝑥	∫𝑢(𝑥	NOUN
iajs-3671	55	2	,	,	PUNCT
iajs-3671	55	3	𝑡)𝑑𝑥	𝑡)𝑑𝑥	PROPN
iajs-3671	55	4	1	1	NUM
iajs-3671	55	5	0	0	NUM
iajs-3671	55	6	=	=	SYM
iajs-3671	55	7	ℎ1(𝑡	ℎ1(𝑡	NOUN
iajs-3671	55	8	)	)	PUNCT
iajs-3671	55	9	,	,	PUNCT
iajs-3671	55	10	0	0	NUM
iajs-3671	55	11	≤	≤	NUM
iajs-3671	55	12	𝑡	𝑡	PROPN
iajs-3671	55	13	≤	≤	ADJ
iajs-3671	55	14	𝑇	𝑇	PROPN
iajs-3671	55	15	(	(	PUNCT
iajs-3671	55	16	6	6	NUM
iajs-3671	55	17	)	)	PUNCT
iajs-3671	55	18	𝑢(𝑥0	𝑢(𝑥0	ADJ
iajs-3671	55	19	,	,	PUNCT
iajs-3671	55	20	𝑡	𝑡	NOUN
iajs-3671	55	21	)	)	PUNCT
iajs-3671	55	22	=	=	SYM
iajs-3671	55	23	ℎ2(𝑡	ℎ2(𝑡	PROPN
iajs-3671	55	24	)	)	PUNCT
iajs-3671	55	25	,	,	PUNCT
iajs-3671	55	26	0	0	NUM
iajs-3671	55	27	≤	≤	NUM
iajs-3671	55	28	𝑡	𝑡	PROPN
iajs-3671	55	29	≤	≤	PROPN
iajs-3671	55	30	𝑇	𝑇	PROPN
iajs-3671	55	31	,	,	PUNCT
iajs-3671	55	32	(	(	PUNCT
iajs-3671	55	33	7	7	X
iajs-3671	55	34	)	)	PUNCT
iajs-3671	55	35	where	where	SCONJ
iajs-3671	55	36	𝑥0	𝑥0	PROPN
iajs-3671	55	37	∈	∈	PROPN
iajs-3671	55	38	(	(	PUNCT
iajs-3671	55	39	0,1	0,1	NOUN
iajs-3671	55	40	)	)	PUNCT
iajs-3671	55	41	,	,	PUNCT
iajs-3671	55	42	and	and	CCONJ
iajs-3671	55	43	𝑏	𝑏	DET
iajs-3671	55	44	>	>	SYM
iajs-3671	55	45	0	0	NUM
iajs-3671	55	46	is	be	AUX
iajs-3671	55	47	a	a	DET
iajs-3671	55	48	given	give	VERB
iajs-3671	55	49	number	number	NOUN
iajs-3671	55	50	.	.	PUNCT
iajs-3671	56	1	we	we	PRON
iajs-3671	56	2	call	call	VERB
iajs-3671	56	3	equations	equation	NOUN
iajs-3671	56	4	(	(	PUNCT
iajs-3671	56	5	1	1	NUM
iajs-3671	56	6	)	)	PUNCT
iajs-3671	56	7	(	(	PUNCT
iajs-3671	56	8	4	4	NUM
iajs-3671	56	9	)	)	PUNCT
iajs-3671	56	10	,	,	PUNCT
iajs-3671	56	11	(	(	PUNCT
iajs-3671	56	12	6	6	NUM
iajs-3671	56	13	)	)	PUNCT
iajs-3671	56	14	as	as	ADP
iajs-3671	56	15	the	the	DET
iajs-3671	56	16	inverse	inverse	NOUN
iajs-3671	56	17	problem	problem	NOUN
iajs-3671	56	18	i	i	PRON
iajs-3671	56	19	(	(	PUNCT
iajs-3671	56	20	ip	ip	NOUN
iajs-3671	56	21	-	-	ADJ
iajs-3671	56	22	i	i	NOUN
iajs-3671	56	23	)	)	PUNCT
iajs-3671	56	24	where	where	SCONJ
iajs-3671	56	25	𝑎	𝑎	NOUN
iajs-3671	56	26	is	be	AUX
iajs-3671	56	27	constant	constant	ADJ
iajs-3671	56	28	and	and	CCONJ
iajs-3671	56	29	the	the	DET
iajs-3671	56	30	equations	equation	NOUN
iajs-3671	56	31	(	(	PUNCT
iajs-3671	56	32	1)-(3	1)-(3	NUM
iajs-3671	56	33	)	)	PUNCT
iajs-3671	56	34	,	,	PUNCT
iajs-3671	56	35	(	(	PUNCT
iajs-3671	56	36	5	5	NUM
iajs-3671	56	37	)	)	PUNCT
iajs-3671	56	38	,	,	PUNCT
iajs-3671	56	39	(	(	PUNCT
iajs-3671	56	40	7	7	X
iajs-3671	56	41	)	)	PUNCT
iajs-3671	56	42	as	as	ADP
iajs-3671	56	43	the	the	DET
iajs-3671	56	44	inverse	inverse	NOUN
iajs-3671	56	45	problem	problem	NOUN
iajs-3671	56	46	ii	ii	PROPN
iajs-3671	56	47	(	(	PUNCT
iajs-3671	56	48	ip	ip	PROPN
iajs-3671	56	49	-	-	PUNCT
iajs-3671	56	50	ii	ii	NOUN
iajs-3671	56	51	)	)	PUNCT
iajs-3671	56	52	,	,	PUNCT
iajs-3671	56	53	where	where	SCONJ
iajs-3671	56	54	𝑎	𝑎	NOUN
iajs-3671	56	55	is	be	AUX
iajs-3671	56	56	time	time	NOUN
iajs-3671	56	57	-	-	PUNCT
iajs-3671	56	58	dependent	dependent	ADJ
iajs-3671	56	59	function	function	NOUN
iajs-3671	56	60	.	.	PUNCT
iajs-3671	57	1	in	in	ADP
iajs-3671	57	2	particular	particular	ADJ
iajs-3671	57	3	,	,	PUNCT
iajs-3671	57	4	if	if	SCONJ
iajs-3671	57	5	we	we	PRON
iajs-3671	57	6	put	put	VERB
iajs-3671	57	7	𝑏	𝑏	NOUN
iajs-3671	57	8	=	=	NOUN
iajs-3671	57	9	0	0	NUM
iajs-3671	57	10	in	in	ADP
iajs-3671	57	11	equation	equation	NOUN
iajs-3671	57	12	(	(	PUNCT
iajs-3671	57	13	1	1	NUM
iajs-3671	57	14	)	)	PUNCT
iajs-3671	57	15	,	,	PUNCT
iajs-3671	57	16	then	then	ADV
iajs-3671	57	17	the	the	DET
iajs-3671	57	18	resulting	result	VERB
iajs-3671	57	19	is	be	AUX
iajs-3671	57	20	a	a	DET
iajs-3671	57	21	heat	heat	NOUN
iajs-3671	57	22	equation	equation	NOUN
iajs-3671	57	23	which	which	PRON
iajs-3671	57	24	has	have	AUX
iajs-3671	57	25	been	be	AUX
iajs-3671	57	26	investigated	investigate	VERB
iajs-3671	57	27	previously	previously	ADV
iajs-3671	57	28	by	by	ADP
iajs-3671	57	29	many	many	ADJ
iajs-3671	57	30	authors	author	NOUN
iajs-3671	57	31	such	such	ADJ
iajs-3671	57	32	as(7	as(7	NOUN
iajs-3671	57	33	,	,	PUNCT
iajs-3671	57	34	8	8	NUM
iajs-3671	57	35	,	,	PUNCT
iajs-3671	57	36	30	30	NUM
iajs-3671	57	37	)	)	PUNCT
iajs-3671	57	38	.	.	PUNCT
iajs-3671	58	1	the	the	DET
iajs-3671	58	2	functions	function	NOUN
iajs-3671	58	3	𝑓	𝑓	PRON
iajs-3671	58	4	,	,	PUNCT
iajs-3671	58	5	𝜑	𝜑	PROPN
iajs-3671	58	6	and	and	CCONJ
iajs-3671	58	7	ℎ1	ℎ1	PROPN
iajs-3671	58	8	and	and	CCONJ
iajs-3671	58	9	ℎ2	ℎ2	NOUN
iajs-3671	58	10	are	be	AUX
iajs-3671	58	11	ihjpas	ihjpa	NOUN
iajs-3671	58	12	.	.	PUNCT
iajs-3671	59	1	2025	2025	NUM
iajs-3671	59	2	,	,	PUNCT
iajs-3671	59	3	38	38	NUM
iajs-3671	59	4	(	(	PUNCT
iajs-3671	59	5	1	1	NUM
iajs-3671	59	6	)	)	PUNCT
iajs-3671	59	7	468	468	NUM
iajs-3671	59	8	given	give	VERB
iajs-3671	59	9	functions	function	NOUN
iajs-3671	59	10	.	.	PUNCT
iajs-3671	60	1	in	in	ADP
iajs-3671	60	2	these	these	DET
iajs-3671	60	3	problems	problem	NOUN
iajs-3671	60	4	,	,	PUNCT
iajs-3671	60	5	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	60	6	)	)	PUNCT
iajs-3671	60	7	is	be	AUX
iajs-3671	60	8	a	a	DET
iajs-3671	60	9	potential	potential	ADJ
iajs-3671	60	10	term	term	NOUN
iajs-3671	60	11	and	and	CCONJ
iajs-3671	60	12	(	(	PUNCT
iajs-3671	60	13	𝑈𝑋	𝑈𝑋	PROPN
iajs-3671	60	14	,	,	PUNCT
iajs-3671	60	15	𝑡	𝑡	NOUN
iajs-3671	60	16	)	)	PUNCT
iajs-3671	60	17	is	be	AUX
iajs-3671	60	18	the	the	DET
iajs-3671	60	19	temperature	temperature	NOUN
iajs-3671	60	20	distribution	distribution	NOUN
iajs-3671	60	21	,	,	PUNCT
iajs-3671	60	22	and	and	CCONJ
iajs-3671	60	23	these	these	DET
iajs-3671	60	24	functions	function	NOUN
iajs-3671	60	25	are	be	AUX
iajs-3671	60	26	unknown	unknown	ADJ
iajs-3671	60	27	.	.	PUNCT
iajs-3671	61	1	these	these	DET
iajs-3671	61	2	problems	problem	NOUN
iajs-3671	61	3	have	have	AUX
iajs-3671	61	4	been	be	AUX
iajs-3671	61	5	utilized	utilize	VERB
iajs-3671	61	6	in	in	ADP
iajs-3671	61	7	the	the	DET
iajs-3671	61	8	modelling	modelling	NOUN
iajs-3671	61	9	of	of	ADP
iajs-3671	61	10	various	various	ADJ
iajs-3671	61	11	phenomena	phenomenon	NOUN
iajs-3671	61	12	such	such	ADJ
iajs-3671	61	13	as	as	ADP
iajs-3671	61	14	wave	wave	NOUN
iajs-3671	61	15	processes	process	NOUN
iajs-3671	61	16	,	,	PUNCT
iajs-3671	61	17	chemical	chemical	NOUN
iajs-3671	61	18	,	,	PUNCT
iajs-3671	61	19	engineering	engineering	NOUN
iajs-3671	61	20	,	,	PUNCT
iajs-3671	61	21	diffusion	diffusion	NOUN
iajs-3671	61	22	,	,	PUNCT
iajs-3671	61	23	plasma	plasma	NOUN
iajs-3671	61	24	physics	physics	NOUN
iajs-3671	61	25	and	and	CCONJ
iajs-3671	61	26	heat	heat	NOUN
iajs-3671	61	27	conduction	conduction	NOUN
iajs-3671	61	28	(	(	PUNCT
iajs-3671	61	29	11	11	NUM
iajs-3671	61	30	)	)	PUNCT
iajs-3671	61	31	.	.	PUNCT
iajs-3671	62	1	the	the	DET
iajs-3671	62	2	unique	unique	ADJ
iajs-3671	62	3	solvability	solvability	NOUN
iajs-3671	62	4	of	of	ADP
iajs-3671	62	5	ip	ip	NOUN
iajs-3671	62	6	-	-	PUNCT
iajs-3671	62	7	i	i	PRON
iajs-3671	62	8	has	have	AUX
iajs-3671	62	9	been	be	AUX
iajs-3671	62	10	established	establish	VERB
iajs-3671	62	11	in	in	ADP
iajs-3671	62	12	(	(	PUNCT
iajs-3671	62	13	28	28	NUM
iajs-3671	62	14	)	)	PUNCT
iajs-3671	62	15	,	,	PUNCT
iajs-3671	62	16	whilst	whilst	SCONJ
iajs-3671	62	17	for	for	ADP
iajs-3671	62	18	ip	ip	NOUN
iajs-3671	62	19	-	-	PUNCT
iajs-3671	62	20	ii	ii	NOUN
iajs-3671	62	21	in	in	ADP
iajs-3671	62	22	(	(	PUNCT
iajs-3671	62	23	29	29	NUM
iajs-3671	62	24	)	)	PUNCT
iajs-3671	62	25	and	and	CCONJ
iajs-3671	62	26	the	the	DET
iajs-3671	62	27	following	follow	VERB
iajs-3671	62	28	their	their	PRON
iajs-3671	62	29	unique	unique	ADJ
iajs-3671	62	30	solvability	solvability	NOUN
iajs-3671	62	31	theorems	theorem	NOUN
iajs-3671	62	32	:	:	PUNCT
iajs-3671	62	33	definition	definition	NOUN
iajs-3671	62	34	:	:	PUNCT
iajs-3671	62	35	the	the	DET
iajs-3671	62	36	classical	classical	ADJ
iajs-3671	62	37	solution	solution	NOUN
iajs-3671	62	38	of	of	ADP
iajs-3671	62	39	the	the	DET
iajs-3671	62	40	ip	ip	NOUN
iajs-3671	62	41	-	-	PUNCT
iajs-3671	62	42	i	i	PRON
iajs-3671	62	43	and	and	CCONJ
iajs-3671	62	44	ip	ip	PROPN
iajs-3671	62	45	-	-	PUNCT
iajs-3671	62	46	ii	ii	NOUN
iajs-3671	62	47	is	be	AUX
iajs-3671	62	48	the	the	DET
iajs-3671	62	49	pair	pair	NOUN
iajs-3671	62	50	{	{	PUNCT
iajs-3671	62	51	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	62	52	,	,	PUNCT
iajs-3671	62	53	𝑡	𝑡	PROPN
iajs-3671	62	54	)	)	PUNCT
iajs-3671	62	55	,	,	PUNCT
iajs-3671	62	56	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	62	57	)	)	PUNCT
iajs-3671	62	58	}	}	PUNCT
iajs-3671	62	59	satisfies	satisfy	VERB
iajs-3671	62	60	the	the	DET
iajs-3671	62	61	following	follow	VERB
iajs-3671	62	62	properties	property	NOUN
iajs-3671	62	63	:	:	PUNCT
iajs-3671	62	64	i𝑢(𝑥	i𝑢(𝑥	NOUN
iajs-3671	62	65	,	,	PUNCT
iajs-3671	62	66	𝑡	𝑡	NOUN
iajs-3671	62	67	)	)	PUNCT
iajs-3671	62	68	is	be	AUX
iajs-3671	62	69	continuous	continuous	ADJ
iajs-3671	62	70	in	in	ADP
iajs-3671	62	71	𝑄𝑇	𝑄𝑇	PROPN
iajs-3671	62	72	with	with	ADP
iajs-3671	62	73	all	all	DET
iajs-3671	62	74	its	its	PRON
iajs-3671	62	75	derivatives	derivative	NOUN
iajs-3671	62	76	.	.	PUNCT
iajs-3671	63	1	ii𝑝(𝑡	ii𝑝(𝑡	X
iajs-3671	63	2	)	)	PUNCT
iajs-3671	63	3	is	be	AUX
iajs-3671	63	4	continuous	continuous	ADJ
iajs-3671	63	5	on	on	ADP
iajs-3671	63	6	[	[	X
iajs-3671	63	7	0	0	NUM
iajs-3671	63	8	,	,	PUNCT
iajs-3671	63	9	𝑇	𝑇	PROPN
iajs-3671	63	10	]	]	PUNCT
iajs-3671	63	11	.	.	PUNCT
iajs-3671	64	1	iiiall	iiiall	ADJ
iajs-3671	64	2	equation	equation	NOUN
iajs-3671	64	3	(	(	PUNCT
iajs-3671	64	4	1	1	NUM
iajs-3671	64	5	)	)	PUNCT
iajs-3671	64	6	–	–	PUNCT
iajs-3671	64	7	(	(	PUNCT
iajs-3671	64	8	5	5	X
iajs-3671	64	9	)	)	PUNCT
iajs-3671	64	10	conditions	condition	NOUN
iajs-3671	64	11	are	be	AUX
iajs-3671	64	12	satisfied	satisfied	ADJ
iajs-3671	64	13	in	in	ADP
iajs-3671	64	14	the	the	DET
iajs-3671	64	15	ordinary	ordinary	ADJ
iajs-3671	64	16	sense	sense	NOUN
iajs-3671	64	17	.	.	PUNCT
iajs-3671	65	1	lemma	lemma	PROPN
iajs-3671	65	2	1	1	NUM
iajs-3671	65	3	for	for	ADP
iajs-3671	65	4	ip	ip	NOUN
iajs-3671	65	5	-	-	VERB
iajs-3671	65	6	i	i	PRON
iajs-3671	65	7	:	:	PUNCT
iajs-3671	65	8	suppose	suppose	VERB
iajs-3671	65	9	that	that	SCONJ
iajs-3671	65	10	𝑎	𝑎	X
iajs-3671	65	11	>	>	X
iajs-3671	65	12	0	0	NUM
iajs-3671	65	13	,	,	PUNCT
iajs-3671	65	14	𝑏	𝑏	PROPN
iajs-3671	65	15	>	>	X
iajs-3671	65	16	0	0	NUM
iajs-3671	65	17	,	,	PUNCT
iajs-3671	65	18	𝜑(𝑥	𝜑(𝑥	PROPN
iajs-3671	65	19	)	)	PUNCT
iajs-3671	65	20	∈	∈	PROPN
iajs-3671	65	21	𝐶[0,1	𝐶[0,1	ADP
iajs-3671	65	22	]	]	PUNCT
iajs-3671	65	23	,	,	PUNCT
iajs-3671	65	24	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3671	65	25	,	,	PUNCT
iajs-3671	65	26	𝑡	𝑡	NOUN
iajs-3671	65	27	)	)	PUNCT
iajs-3671	65	28	∈	∈	PROPN
iajs-3671	65	29	𝐶(𝑄𝑇	𝐶(𝑄𝑇	NOUN
iajs-3671	65	30	)	)	PUNCT
iajs-3671	65	31	,	,	PUNCT
iajs-3671	65	32	ℎ1(𝑡	ℎ1(𝑡	NOUN
iajs-3671	65	33	)	)	PUNCT
iajs-3671	65	34	∈	∈	PROPN
iajs-3671	65	35	𝐶1[0	𝐶1[0	PROPN
iajs-3671	65	36	,	,	PUNCT
iajs-3671	65	37	𝑇	𝑇	PROPN
iajs-3671	65	38	]	]	PUNCT
iajs-3671	65	39	,	,	PUNCT
iajs-3671	65	40	ℎ1(𝑡	ℎ1(𝑡	NOUN
iajs-3671	65	41	)	)	PUNCT
iajs-3671	65	42	≠	≠	PROPN
iajs-3671	65	43	0	0	NUM
iajs-3671	65	44	for	for	ADP
iajs-3671	65	45	(	(	PUNCT
iajs-3671	65	46	0	0	NUM
iajs-3671	65	47	≤	≤	NUM
iajs-3671	65	48	𝑡	𝑡	PROPN
iajs-3671	65	49	≤	≤	PROPN
iajs-3671	65	50	𝑇	𝑇	PROPN
iajs-3671	65	51	)	)	PUNCT
iajs-3671	65	52	and	and	CCONJ
iajs-3671	65	53	𝜑	𝜑	PROPN
iajs-3671	65	54	(	(	PUNCT
iajs-3671	65	55	1	1	NUM
iajs-3671	65	56	2	2	NUM
iajs-3671	65	57	)	)	PUNCT
iajs-3671	65	58	+	+	CCONJ
iajs-3671	65	59	∫	∫	X
iajs-3671	65	60	𝜑(𝑥	𝜑(𝑥	PRON
iajs-3671	65	61	)	)	PUNCT
iajs-3671	65	62	1	1	NUM
iajs-3671	65	63	0	0	NUM
iajs-3671	65	64	𝑑𝑥	𝑑𝑥	NOUN
iajs-3671	65	65	=	=	SYM
iajs-3671	65	66	ℎ1(0	ℎ1(0	PROPN
iajs-3671	65	67	)	)	PUNCT
iajs-3671	65	68	.	.	PUNCT
iajs-3671	66	1	then	then	ADV
iajs-3671	66	2	the	the	DET
iajs-3671	66	3	problem	problem	NOUN
iajs-3671	66	4	of	of	ADP
iajs-3671	66	5	defining	define	VERB
iajs-3671	66	6	the	the	DET
iajs-3671	66	7	functions	function	NOUN
iajs-3671	66	8	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	66	9	,	,	PUNCT
iajs-3671	66	10	𝑡	𝑡	PROPN
iajs-3671	66	11	)	)	PUNCT
iajs-3671	66	12	and	and	CCONJ
iajs-3671	66	13	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	66	14	)	)	PUNCT
iajs-3671	66	15	is	be	AUX
iajs-3671	66	16	equivalent	equivalent	ADJ
iajs-3671	66	17	to	to	ADP
iajs-3671	66	18	the	the	DET
iajs-3671	66	19	problem	problem	NOUN
iajs-3671	66	20	of	of	ADP
iajs-3671	66	21	finding	find	VERB
iajs-3671	66	22	the	the	DET
iajs-3671	66	23	solution	solution	NOUN
iajs-3671	66	24	of	of	ADP
iajs-3671	66	25	problem	problem	NOUN
iajs-3671	66	26	equations	equation	NOUN
iajs-3671	66	27	(	(	PUNCT
iajs-3671	66	28	1	1	NUM
iajs-3671	66	29	)	)	PUNCT
iajs-3671	66	30	–	–	PUNCT
iajs-3671	66	31	(	(	PUNCT
iajs-3671	66	32	4	4	NUM
iajs-3671	66	33	)	)	PUNCT
iajs-3671	66	34	,	,	PUNCT
iajs-3671	66	35	(	(	PUNCT
iajs-3671	66	36	6	6	X
iajs-3671	66	37	)	)	PUNCT
iajs-3671	66	38	possessing	possess	VERB
iajs-3671	66	39	the	the	DET
iajs-3671	66	40	properties	property	NOUN
iajs-3671	66	41	(	(	PUNCT
iajs-3671	66	42	i	i	NOUN
iajs-3671	66	43	)	)	PUNCT
iajs-3671	66	44	and	and	CCONJ
iajs-3671	66	45	(	(	PUNCT
iajs-3671	66	46	ii	ii	NOUN
iajs-3671	66	47	)	)	PUNCT
iajs-3671	66	48	of	of	ADP
iajs-3671	66	49	the	the	DET
iajs-3671	66	50	solution	solution	NOUN
iajs-3671	66	51	of	of	ADP
iajs-3671	66	52	problem	problem	NOUN
iajs-3671	66	53	equations	equation	NOUN
iajs-3671	66	54	(	(	PUNCT
iajs-3671	66	55	1)–(4	1)–(4	NUM
iajs-3671	66	56	)	)	PUNCT
iajs-3671	66	57	,	,	PUNCT
iajs-3671	66	58	(	(	PUNCT
iajs-3671	66	59	6	6	NUM
iajs-3671	66	60	)	)	PUNCT
iajs-3671	66	61	from	from	ADP
iajs-3671	66	62	relations	relation	NOUN
iajs-3671	66	63	equations	equation	NOUN
iajs-3671	66	64	(	(	PUNCT
iajs-3671	66	65	1)–(4	1)–(4	NUM
iajs-3671	66	66	)	)	PUNCT
iajs-3671	66	67	,	,	PUNCT
iajs-3671	66	68	and	and	CCONJ
iajs-3671	66	69	ℎ1	ℎ1	PROPN
iajs-3671	66	70	′(𝑡	′(𝑡	NOUN
iajs-3671	66	71	)	)	PUNCT
iajs-3671	67	1	+	+	CCONJ
iajs-3671	67	2	𝑏	𝑏	PROPN
iajs-3671	67	3	(	(	PUNCT
iajs-3671	67	4	𝑢𝑡𝑥(0	𝑢𝑡𝑥(0	NOUN
iajs-3671	67	5	,	,	PUNCT
iajs-3671	67	6	𝑡	𝑡	PROPN
iajs-3671	67	7	)	)	PUNCT
iajs-3671	67	8	+	+	CCONJ
iajs-3671	67	9	𝑢𝑡𝑥𝑥	𝑢𝑡𝑥𝑥	ADJ
iajs-3671	67	10	(	(	PUNCT
iajs-3671	67	11	1	1	NUM
iajs-3671	67	12	2	2	NUM
iajs-3671	67	13	,	,	PUNCT
iajs-3671	67	14	𝑡	𝑡	NOUN
iajs-3671	67	15	)	)	PUNCT
iajs-3671	67	16	)	)	PUNCT
iajs-3671	68	1	+	+	CCONJ
iajs-3671	69	1	𝑎	𝑎	X
iajs-3671	69	2	(	(	PUNCT
iajs-3671	69	3	𝑢𝑥(0	𝑢𝑥(0	PROPN
iajs-3671	69	4	,	,	PUNCT
iajs-3671	69	5	𝑡	𝑡	X
iajs-3671	69	6	)	)	PUNCT
iajs-3671	69	7	+	+	CCONJ
iajs-3671	69	8	𝑢𝑥𝑥	𝑢𝑥𝑥	NOUN
iajs-3671	69	9	(	(	PUNCT
iajs-3671	69	10	1	1	NUM
iajs-3671	69	11	2	2	NUM
iajs-3671	69	12	,	,	PUNCT
iajs-3671	69	13	𝑡	𝑡	NOUN
iajs-3671	69	14	)	)	PUNCT
iajs-3671	69	15	)	)	PUNCT
iajs-3671	69	16	=	=	SYM
iajs-3671	69	17	𝑝(𝑡)ℎ1(𝑡	𝑝(𝑡)ℎ1(𝑡	NOUN
iajs-3671	69	18	)	)	PUNCT
iajs-3671	69	19	+	+	CCONJ
iajs-3671	69	20	𝑓	𝑓	PRON
iajs-3671	69	21	(	(	PUNCT
iajs-3671	69	22	1	1	NUM
iajs-3671	69	23	2	2	NUM
iajs-3671	69	24	,	,	PUNCT
iajs-3671	69	25	𝑡	𝑡	NOUN
iajs-3671	69	26	)	)	PUNCT
iajs-3671	69	27	+	+	NUM
iajs-3671	69	28	∫𝑓(𝑥	∫𝑓(𝑥	NOUN
iajs-3671	69	29	,	,	PUNCT
iajs-3671	69	30	𝑡	𝑡	NOUN
iajs-3671	69	31	)	)	PUNCT
iajs-3671	69	32	1	1	NUM
iajs-3671	69	33	0	0	NUM
iajs-3671	69	34	𝑑𝑥	𝑑𝑥	NOUN
iajs-3671	69	35	,	,	PUNCT
iajs-3671	69	36	(	(	PUNCT
iajs-3671	69	37	0	0	NUM
iajs-3671	69	38	≤	≤	NUM
iajs-3671	69	39	𝑡	𝑡	PROPN
iajs-3671	69	40	≤	≤	PROPN
iajs-3671	69	41	𝑇	𝑇	PROPN
iajs-3671	69	42	)	)	PUNCT
iajs-3671	69	43	(	(	PUNCT
iajs-3671	69	44	8)	8)	NUM
iajs-3671	69	45	theorem	theorem	NOUN
iajs-3671	69	46	1	1	NUM
iajs-3671	69	47	for	for	ADP
iajs-3671	69	48	ip	ip	PROPN
iajs-3671	69	49	-	-	PUNCT
iajs-3671	69	50	i.	i.	NOUN
iajs-3671	69	51	let	let	VERB
iajs-3671	69	52	the	the	DET
iajs-3671	69	53	problem	problem	NOUN
iajs-3671	69	54	equations	equation	NOUN
iajs-3671	69	55	(	(	PUNCT
iajs-3671	69	56	1	1	NUM
iajs-3671	69	57	)	)	PUNCT
iajs-3671	69	58	–	–	PUNCT
iajs-3671	69	59	(	(	PUNCT
iajs-3671	69	60	4	4	NUM
iajs-3671	69	61	)	)	PUNCT
iajs-3671	69	62	,	,	PUNCT
iajs-3671	69	63	(	(	PUNCT
iajs-3671	69	64	8)	8)	NUM
iajs-3671	69	65	satisfy	satisfy	VERB
iajs-3671	69	66	the	the	DET
iajs-3671	69	67	following	follow	VERB
iajs-3671	69	68	conditions	condition	NOUN
iajs-3671	69	69	:	:	PUNCT
iajs-3671	69	70	1	1	X
iajs-3671	69	71	.	.	X
iajs-3671	69	72	𝜑(𝑥	𝜑(𝑥	NOUN
iajs-3671	69	73	)	)	PUNCT
iajs-3671	69	74	∈	∈	PROPN
iajs-3671	69	75	𝐶2[0,1	𝐶2[0,1	NOUN
iajs-3671	69	76	]	]	X
iajs-3671	69	77	,	,	PUNCT
iajs-3671	69	78	𝜑′′′(𝑥	𝜑′′′(𝑥	PROPN
iajs-3671	69	79	)	)	PUNCT
iajs-3671	69	80	∈	∈	PROPN
iajs-3671	69	81	𝐿2(0,1	𝐿2(0,1	NOUN
iajs-3671	69	82	)	)	PUNCT
iajs-3671	69	83	,	,	PUNCT
iajs-3671	69	84	𝜑(0	𝜑(0	NOUN
iajs-3671	69	85	)	)	PUNCT
iajs-3671	69	86	=	=	SYM
iajs-3671	69	87	𝜑(1	𝜑(1	PROPN
iajs-3671	69	88	)	)	PUNCT
iajs-3671	69	89	,	,	PUNCT
iajs-3671	69	90	𝜑′(1	𝜑′(1	PROPN
iajs-3671	69	91	)	)	PUNCT
iajs-3671	69	92	=	=	SYM
iajs-3671	69	93	0	0	NUM
iajs-3671	69	94	,	,	PUNCT
iajs-3671	69	95	𝜑′′(0	𝜑′′(0	NOUN
iajs-3671	69	96	)	)	PUNCT
iajs-3671	69	97	=	=	SYM
iajs-3671	69	98	𝜑′′(1	𝜑′′(1	PROPN
iajs-3671	69	99	)	)	PUNCT
iajs-3671	69	100	;	;	PUNCT
iajs-3671	69	101	(	(	PUNCT
iajs-3671	69	102	9	9	X
iajs-3671	69	103	)	)	SYM
iajs-3671	69	104	2	2	NUM
iajs-3671	69	105	.	.	PUNCT
iajs-3671	70	1	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3671	70	2	,	,	PUNCT
iajs-3671	70	3	𝑡	𝑡	NOUN
iajs-3671	70	4	)	)	PUNCT
iajs-3671	70	5	∈	∈	PROPN
iajs-3671	70	6	𝐶(𝑄𝑇	𝐶(𝑄𝑇	NOUN
iajs-3671	70	7	)	)	PUNCT
iajs-3671	70	8	,	,	PUNCT
iajs-3671	70	9	𝑓𝑥(𝑥	𝑓𝑥(𝑥	NUM
iajs-3671	70	10	,	,	PUNCT
iajs-3671	70	11	𝑡	𝑡	NOUN
iajs-3671	70	12	)	)	PUNCT
iajs-3671	70	13	∈	∈	PROPN
iajs-3671	70	14	𝐿2(𝑄𝑇	𝐿2(𝑄𝑇	NOUN
iajs-3671	70	15	)	)	PUNCT
iajs-3671	70	16	,	,	PUNCT
iajs-3671	70	17	𝑓(0	𝑓(0	PROPN
iajs-3671	70	18	,	,	PUNCT
iajs-3671	70	19	𝑡	𝑡	NOUN
iajs-3671	70	20	)	)	PUNCT
iajs-3671	70	21	=	=	SYM
iajs-3671	71	1	𝑓(1	𝑓(1	NOUN
iajs-3671	71	2	,	,	PUNCT
iajs-3671	71	3	𝑡	𝑡	NOUN
iajs-3671	71	4	)	)	PUNCT
iajs-3671	71	5	,	,	PUNCT
iajs-3671	71	6	(	(	PUNCT
iajs-3671	71	7	0	0	NUM
iajs-3671	71	8	≤	≤	NUM
iajs-3671	71	9	𝑡	𝑡	PROPN
iajs-3671	71	10	≤	≤	PROPN
iajs-3671	71	11	𝑇	𝑇	PROPN
iajs-3671	71	12	)	)	PUNCT
iajs-3671	71	13	.	.	PUNCT
iajs-3671	72	1	(	(	PUNCT
iajs-3671	72	2	10	10	NUM
iajs-3671	72	3	)	)	PUNCT
iajs-3671	72	4	3	3	NUM
iajs-3671	72	5	.	.	X
iajs-3671	73	1	𝑎	𝑎	X
iajs-3671	73	2	>	>	X
iajs-3671	73	3	0	0	NUM
iajs-3671	73	4	,	,	PUNCT
iajs-3671	73	5	𝑏	𝑏	PROPN
iajs-3671	73	6	>	>	X
iajs-3671	73	7	0	0	NUM
iajs-3671	73	8	,	,	PUNCT
iajs-3671	73	9	ℎ1(𝑡	ℎ1(𝑡	NOUN
iajs-3671	73	10	)	)	PUNCT
iajs-3671	73	11	∈	∈	PROPN
iajs-3671	73	12	𝐶	𝐶	PROPN
iajs-3671	73	13	1[0	1[0	PROPN
iajs-3671	73	14	,	,	PUNCT
iajs-3671	73	15	𝑇	𝑇	PROPN
iajs-3671	73	16	]	]	PUNCT
iajs-3671	73	17	,	,	PUNCT
iajs-3671	73	18	ℎ1(𝑡	ℎ1(𝑡	NOUN
iajs-3671	73	19	)	)	PUNCT
iajs-3671	73	20	≠	≠	PROPN
iajs-3671	73	21	0	0	NUM
iajs-3671	73	22	(	(	PUNCT
iajs-3671	73	23	0	0	NUM
iajs-3671	73	24	≤	≤	NUM
iajs-3671	73	25	𝑡	𝑡	PROPN
iajs-3671	73	26	≤	≤	PROPN
iajs-3671	73	27	𝑇	𝑇	PROPN
iajs-3671	73	28	)	)	PUNCT
iajs-3671	73	29	.	.	PUNCT
iajs-3671	74	1	(	(	PUNCT
iajs-3671	74	2	11	11	NUM
iajs-3671	74	3	)	)	PUNCT
iajs-3671	74	4	4	4	NUM
iajs-3671	74	5	.	.	X
iajs-3671	74	6	𝜑	𝜑	PROPN
iajs-3671	74	7	(	(	PUNCT
iajs-3671	74	8	1	1	NUM
iajs-3671	74	9	2	2	NUM
iajs-3671	74	10	)	)	PUNCT
iajs-3671	74	11	+	+	CCONJ
iajs-3671	74	12	∫	∫	PROPN
iajs-3671	74	13	𝜑(𝑥)𝑑𝑥	𝜑(𝑥)𝑑𝑥	PART
iajs-3671	74	14	1	1	NUM
iajs-3671	74	15	0	0	NUM
iajs-3671	74	16	=	=	SYM
iajs-3671	74	17	ℎ1(0	ℎ1(0	PROPN
iajs-3671	74	18	)	)	PUNCT
iajs-3671	74	19	.	.	PUNCT
iajs-3671	75	1	(	(	PUNCT
iajs-3671	75	2	12	12	NUM
iajs-3671	75	3	)	)	PUNCT
iajs-3671	75	4	ihjpas	ihjpa	NOUN
iajs-3671	75	5	.	.	PUNCT
iajs-3671	76	1	2025	2025	NUM
iajs-3671	76	2	,	,	PUNCT
iajs-3671	76	3	38	38	NUM
iajs-3671	76	4	(	(	PUNCT
iajs-3671	76	5	1	1	NUM
iajs-3671	76	6	)	)	PUNCT
iajs-3671	76	7	469	469	NUM
iajs-3671	76	8	then	then	ADV
iajs-3671	76	9	ip	ip	NOUN
iajs-3671	76	10	-	-	PUNCT
iajs-3671	76	11	i	i	PRON
iajs-3671	76	12	has	have	VERB
iajs-3671	76	13	a	a	DET
iajs-3671	76	14	unique	unique	ADJ
iajs-3671	76	15	solution	solution	NOUN
iajs-3671	76	16	in	in	ADP
iajs-3671	76	17	the	the	DET
iajs-3671	76	18	ball	ball	NOUN
iajs-3671	76	19	k	k	PROPN
iajs-3671	77	1	=	=	PUNCT
iajs-3671	77	2	𝐾𝑅‖𝑧‖𝐸𝑇3	𝐾𝑅‖𝑧‖𝐸𝑇3	PROPN
iajs-3671	77	3	≤	≤	ADJ
iajs-3671	77	4	r	r	NOUN
iajs-3671	77	5	=	=	PUNCT
iajs-3671	77	6	(	(	PUNCT
iajs-3671	77	7	a(t	a(t	PROPN
iajs-3671	77	8	)	)	PUNCT
iajs-3671	77	9	+	+	CCONJ
iajs-3671	77	10	2	2	X
iajs-3671	77	11	)	)	PUNCT
iajs-3671	77	12	of	of	ADP
iajs-3671	77	13	the	the	DET
iajs-3671	77	14	space	space	NOUN
iajs-3671	77	15	𝐸𝑇	𝐸𝑇	NOUN
iajs-3671	77	16	3	3	NUM
iajs-3671	77	17	in	in	ADP
iajs-3671	77	18	banach	banach	NOUN
iajs-3671	77	19	space	space	NOUN
iajs-3671	77	20	.	.	PUNCT
iajs-3671	78	1	where	where	SCONJ
iajs-3671	78	2	,	,	PUNCT
iajs-3671	78	3	𝐴(𝑇	𝐴(𝑇	PROPN
iajs-3671	78	4	)	)	PUNCT
iajs-3671	78	5	=	=	SYM
iajs-3671	78	6	1	1	NUM
iajs-3671	78	7	3	3	NUM
iajs-3671	78	8	‖𝜑(𝑥)‖𝐿2(0,1	‖𝜑(𝑥)‖𝐿2(0,1	NOUN
iajs-3671	78	9	)	)	PUNCT
iajs-3671	79	1	+	+	CCONJ
iajs-3671	79	2	1	1	NUM
iajs-3671	79	3	3	3	NUM
iajs-3671	79	4	√𝑇‖𝑓(𝑥	√𝑇‖𝑓(𝑥	NOUN
iajs-3671	79	5	,	,	PUNCT
iajs-3671	79	6	𝑡)‖𝐿2(𝑄𝑇	𝑡)‖𝐿2(𝑄𝑇	NOUN
iajs-3671	79	7	)	)	PUNCT
iajs-3671	80	1	+	+	CCONJ
iajs-3671	80	2	‖ℎ1	‖ℎ1	ADJ
iajs-3671	80	3	−1(𝑡)‖	−1(𝑡)‖	NUM
iajs-3671	80	4	𝐶[0,𝑇	𝐶[0,𝑇	NOUN
iajs-3671	80	5	]	]	X
iajs-3671	80	6	‖ℎ1	‖ℎ1	NUM
iajs-3671	80	7	′(𝑡	′(𝑡	NOUN
iajs-3671	80	8	)	)	PUNCT
iajs-3671	81	1	−	−	PROPN
iajs-3671	82	1	𝑓	𝑓	PROPN
iajs-3671	82	2	(	(	PUNCT
iajs-3671	82	3	1	1	NUM
iajs-3671	82	4	2	2	NUM
iajs-3671	82	5	,	,	PUNCT
iajs-3671	82	6	𝑡	𝑡	NOUN
iajs-3671	82	7	)	)	PUNCT
iajs-3671	82	8	−	−	NUM
iajs-3671	82	9	∫	∫	PROPN
iajs-3671	82	10	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3671	82	11	,	,	PUNCT
iajs-3671	82	12	𝑡)𝑑𝑥	𝑡)𝑑𝑥	PROPN
iajs-3671	82	13	1	1	NUM
iajs-3671	82	14	0	0	NUM
iajs-3671	82	15	‖	‖	ADJ
iajs-3671	82	16	𝐶[0,𝑇	𝐶[0,𝑇	NOUN
iajs-3671	82	17	]	]	X
iajs-3671	83	1	+	+	CCONJ
iajs-3671	83	2	(	(	PUNCT
iajs-3671	83	3	√6	√6	PROPN
iajs-3671	83	4	2	2	NUM
iajs-3671	83	5	+	+	NUM
iajs-3671	83	6	4𝑎	4𝑎	PROPN
iajs-3671	83	7	𝑏2	𝑏2	PROPN
iajs-3671	83	8	𝑇	𝑇	PROPN
iajs-3671	83	9	+	+	CCONJ
iajs-3671	83	10	√3𝑎	√3𝑎	X
iajs-3671	83	11	3𝑏	3𝑏	NUM
iajs-3671	83	12	‖ℎ1	‖ℎ1	ADJ
iajs-3671	83	13	−1(𝑡)‖	−1(𝑡)‖	NUM
iajs-3671	83	14	𝐶[0,𝑇	𝐶[0,𝑇	NUM
iajs-3671	83	15	)	)	PUNCT
iajs-3671	83	16	)	)	PUNCT
iajs-3671	84	1	‖𝜑′′′(𝑥)‖𝐿2[0,1	‖𝜑′′′(𝑥)‖𝐿2[0,1	X
iajs-3671	84	2	]	]	PUNCT
iajs-3671	85	1	+	+	ADJ
iajs-3671	85	2	(	(	PUNCT
iajs-3671	85	3	√6𝑇	√6𝑇	NOUN
iajs-3671	85	4	2𝑏	2𝑏	NUM
iajs-3671	85	5	+	+	CCONJ
iajs-3671	85	6	4	4	NUM
iajs-3671	85	7	(	(	PUNCT
iajs-3671	85	8	1	1	NUM
iajs-3671	85	9	𝑏	𝑏	NOUN
iajs-3671	85	10	+	+	NUM
iajs-3671	85	11	𝑎	𝑎	PROPN
iajs-3671	85	12	𝑏3	𝑏3	NOUN
iajs-3671	85	13	𝑇)√𝑇	𝑇)√𝑇	NOUN
iajs-3671	85	14	+	+	CCONJ
iajs-3671	85	15	√3𝑇𝑎	√3𝑇𝑎	NOUN
iajs-3671	85	16	3𝑏2	3𝑏2	NUM
iajs-3671	85	17	‖ℎ1	‖ℎ1	ADJ
iajs-3671	85	18	−1(𝑡)‖	−1(𝑡)‖	NUM
iajs-3671	85	19	𝐶[0,𝑇	𝐶[0,𝑇	NOUN
iajs-3671	85	20	]	]	PUNCT
iajs-3671	85	21	)	)	PUNCT
iajs-3671	85	22	×	×	NOUN
iajs-3671	85	23	‖𝑓𝑥(𝑥	‖𝑓𝑥(𝑥	PROPN
iajs-3671	85	24	,	,	PUNCT
iajs-3671	85	25	𝑡)‖𝐿2(𝑄𝑇	𝑡)‖𝐿2(𝑄𝑇	NOUN
iajs-3671	85	26	)	)	PUNCT
iajs-3671	85	27	+	+	NUM
iajs-3671	85	28	2‖𝑥𝜑′′′(𝑥	2‖𝑥𝜑′′′(𝑥	NUM
iajs-3671	85	29	)	)	PUNCT
iajs-3671	86	1	+	+	NUM
iajs-3671	86	2	3𝜑′′(𝑥)‖𝐿2(0,1	3𝜑′′(𝑥)‖𝐿2(0,1	NOUN
iajs-3671	86	3	)	)	PUNCT
iajs-3671	87	1	+	+	CCONJ
iajs-3671	87	2	√3	√3	PROPN
iajs-3671	87	3	3	3	NUM
iajs-3671	87	4	‖ℎ1	‖ℎ1	ADJ
iajs-3671	87	5	−1(𝑡)‖	−1(𝑡)‖	NUM
iajs-3671	87	6	𝐶[0,𝑇	𝐶[0,𝑇	NOUN
iajs-3671	87	7	]	]	PUNCT
iajs-3671	87	8	×	×	NOUN
iajs-3671	87	9	‖‖𝑓𝑥(𝑥	‖‖𝑓𝑥(𝑥	PROPN
iajs-3671	87	10	,	,	PUNCT
iajs-3671	87	11	𝑡)‖𝐶[0,𝑇]‖𝐿2(0,1	𝑡)‖𝐶[0,𝑇]‖𝐿2(0,1	NOUN
iajs-3671	87	12	)	)	PUNCT
iajs-3671	87	13	,	,	PUNCT
iajs-3671	87	14	(	(	PUNCT
iajs-3671	87	15	13	13	X
iajs-3671	87	16	)	)	PUNCT
iajs-3671	87	17	𝐵(𝑇	𝐵(𝑇	PROPN
iajs-3671	87	18	)	)	PUNCT
iajs-3671	88	1	=	=	PUNCT
iajs-3671	88	2	(	(	PUNCT
iajs-3671	88	3	1	1	NUM
iajs-3671	88	4	+	+	SYM
iajs-3671	88	5	1	1	NUM
iajs-3671	88	6	𝑏	𝑏	NOUN
iajs-3671	88	7	(	(	PUNCT
iajs-3671	88	8	2√2	2√2	NUM
iajs-3671	88	9	+	+	NUM
iajs-3671	88	10	√3	√3	PROPN
iajs-3671	88	11	)	)	PUNCT
iajs-3671	88	12	+	+	CCONJ
iajs-3671	89	1	4√2	4√2	PROPN
iajs-3671	89	2	𝑏	𝑏	NOUN
iajs-3671	89	3	(	(	PUNCT
iajs-3671	89	4	1	1	NUM
iajs-3671	89	5	+	+	CCONJ
iajs-3671	89	6	𝑎	𝑎	PRON
iajs-3671	89	7	𝑏2	𝑏2	NOUN
iajs-3671	89	8	𝑇))𝑇	𝑇))𝑇	NOUN
iajs-3671	89	9	+	+	CCONJ
iajs-3671	89	10	(	(	PUNCT
iajs-3671	89	11	𝑎	𝑎	X
iajs-3671	89	12	𝑏	𝑏	NOUN
iajs-3671	89	13	𝑇	𝑇	PROPN
iajs-3671	89	14	+	+	CCONJ
iajs-3671	89	15	𝑏	𝑏	NOUN
iajs-3671	89	16	)	)	PUNCT
iajs-3671	89	17	‖ℎ1	‖ℎ1	ADJ
iajs-3671	89	18	−1(𝑡)‖	−1(𝑡)‖	NUM
iajs-3671	89	19	𝐶[0,𝑇	𝐶[0,𝑇	NOUN
iajs-3671	89	20	]	]	PUNCT
iajs-3671	89	21	,	,	PUNCT
iajs-3671	89	22	(	(	PUNCT
iajs-3671	89	23	14	14	X
iajs-3671	89	24	)	)	PUNCT
iajs-3671	89	25	lemma	lemma	PROPN
iajs-3671	89	26	2	2	NUM
iajs-3671	89	27	for	for	ADP
iajs-3671	89	28	ip	ip	NOUN
iajs-3671	89	29	-	-	PUNCT
iajs-3671	89	30	ii	ii	NOUN
iajs-3671	89	31	:	:	PUNCT
iajs-3671	89	32	suppose	suppose	VERB
iajs-3671	89	33	that	that	SCONJ
iajs-3671	89	34	𝑎(𝑡	𝑎(𝑡	NOUN
iajs-3671	89	35	)	)	PUNCT
iajs-3671	89	36	>	>	X
iajs-3671	89	37	0	0	NUM
iajs-3671	89	38	,	,	PUNCT
iajs-3671	89	39	𝑏	𝑏	PROPN
iajs-3671	89	40	>	>	X
iajs-3671	89	41	0	0	NUM
iajs-3671	89	42	,	,	PUNCT
iajs-3671	89	43	𝑎(𝑡	𝑎(𝑡	PROPN
iajs-3671	89	44	)	)	PUNCT
iajs-3671	89	45	∈	∈	PROPN
iajs-3671	89	46	𝐶[0	𝐶[0	PROPN
iajs-3671	89	47	,	,	PUNCT
iajs-3671	89	48	𝑇	𝑇	PROPN
iajs-3671	89	49	]	]	PUNCT
iajs-3671	89	50	,	,	PUNCT
iajs-3671	89	51	𝜑(𝑥	𝜑(𝑥	PROPN
iajs-3671	89	52	)	)	PUNCT
iajs-3671	89	53	∈	∈	NOUN
iajs-3671	90	1	[	[	X
iajs-3671	90	2	0,1	0,1	NUM
iajs-3671	90	3	]	]	PUNCT
iajs-3671	90	4	,	,	PUNCT
iajs-3671	90	5	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3671	90	6	,	,	PUNCT
iajs-3671	90	7	𝑡	𝑡	NOUN
iajs-3671	90	8	)	)	PUNCT
iajs-3671	90	9	∈	∈	PROPN
iajs-3671	90	10	𝐶(𝑄𝑇	𝐶(𝑄𝑇	NOUN
iajs-3671	90	11	)	)	PUNCT
iajs-3671	90	12	,	,	PUNCT
iajs-3671	90	13	ℎ2(𝑡	ℎ2(𝑡	PROPN
iajs-3671	90	14	)	)	PUNCT
iajs-3671	90	15	∈	∈	PROPN
iajs-3671	90	16	𝐶	𝐶	PROPN
iajs-3671	90	17	1[0	1[0	PROPN
iajs-3671	90	18	,	,	PUNCT
iajs-3671	90	19	𝑇	𝑇	PROPN
iajs-3671	90	20	]	]	X
iajs-3671	90	21	,	,	PUNCT
iajs-3671	90	22	ℎ2(𝑡	ℎ2(𝑡	PROPN
iajs-3671	90	23	)	)	PUNCT
iajs-3671	90	24	≠	≠	PROPN
iajs-3671	90	25	0	0	NUM
iajs-3671	90	26	,	,	PUNCT
iajs-3671	90	27	∫	∫	PROPN
iajs-3671	90	28	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3671	90	29	,	,	PUNCT
iajs-3671	91	1	𝑡)𝑑𝑥	𝑡)𝑑𝑥	PROPN
iajs-3671	91	2	=	=	NOUN
iajs-3671	91	3	0	0	NUM
iajs-3671	91	4	1	1	NUM
iajs-3671	91	5	0	0	NUM
iajs-3671	91	6	for	for	ADP
iajs-3671	91	7	(	(	PUNCT
iajs-3671	91	8	0	0	NUM
iajs-3671	91	9	≤	≤	NUM
iajs-3671	91	10	𝑡	𝑡	PROPN
iajs-3671	91	11	≤	≤	PROPN
iajs-3671	91	12	𝑇	𝑇	PROPN
iajs-3671	91	13	)	)	PUNCT
iajs-3671	91	14	,	,	PUNCT
iajs-3671	91	15	∫	∫	PROPN
iajs-3671	91	16	𝜑(𝑥	𝜑(𝑥	X
iajs-3671	91	17	)	)	PUNCT
iajs-3671	91	18	1	1	NUM
iajs-3671	91	19	0	0	NUM
iajs-3671	91	20	𝑑𝑥	𝑑𝑥	NOUN
iajs-3671	91	21	=	=	SYM
iajs-3671	91	22	0	0	NUM
iajs-3671	91	23	,	,	PUNCT
iajs-3671	91	24	𝜑′(0	𝜑′(0	PROPN
iajs-3671	91	25	)	)	PUNCT
iajs-3671	91	26	=	=	SYM
iajs-3671	91	27	𝜑′(1	𝜑′(1	NOUN
iajs-3671	91	28	)	)	PUNCT
iajs-3671	91	29	,	,	PUNCT
iajs-3671	91	30	𝜑(𝑥0	𝜑(𝑥0	NUM
iajs-3671	91	31	)	)	PUNCT
iajs-3671	91	32	=	=	SYM
iajs-3671	91	33	ℎ2(0	ℎ2(0	PROPN
iajs-3671	91	34	)	)	PUNCT
iajs-3671	91	35	.	.	PUNCT
iajs-3671	92	1	then	then	ADV
iajs-3671	92	2	,	,	PUNCT
iajs-3671	92	3	the	the	DET
iajs-3671	92	4	problem	problem	NOUN
iajs-3671	92	5	of	of	ADP
iajs-3671	92	6	defining	define	VERB
iajs-3671	92	7	the	the	DET
iajs-3671	92	8	functions	function	NOUN
iajs-3671	92	9	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	92	10	,	,	PUNCT
iajs-3671	92	11	𝑡	𝑡	PROPN
iajs-3671	92	12	)	)	PUNCT
iajs-3671	92	13	and	and	CCONJ
iajs-3671	92	14	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	92	15	)	)	PUNCT
iajs-3671	92	16	is	be	AUX
iajs-3671	92	17	equivalent	equivalent	ADJ
iajs-3671	92	18	to	to	ADP
iajs-3671	92	19	the	the	DET
iajs-3671	92	20	problem	problem	NOUN
iajs-3671	92	21	of	of	ADP
iajs-3671	92	22	finding	find	VERB
iajs-3671	92	23	the	the	DET
iajs-3671	92	24	solution	solution	NOUN
iajs-3671	92	25	of	of	ADP
iajs-3671	92	26	ip	ip	NOUN
iajs-3671	92	27	-	-	PUNCT
iajs-3671	92	28	ii	ii	NOUN
iajs-3671	92	29	,	,	PUNCT
iajs-3671	92	30	possessing	possess	VERB
iajs-3671	92	31	the	the	DET
iajs-3671	92	32	properties	property	NOUN
iajs-3671	92	33	(	(	PUNCT
iajs-3671	92	34	i	i	NOUN
iajs-3671	92	35	)	)	PUNCT
iajs-3671	92	36	and	and	CCONJ
iajs-3671	92	37	(	(	PUNCT
iajs-3671	92	38	ii	ii	NOUN
iajs-3671	92	39	)	)	PUNCT
iajs-3671	92	40	of	of	ADP
iajs-3671	92	41	the	the	DET
iajs-3671	92	42	solution	solution	NOUN
iajs-3671	92	43	of	of	ADP
iajs-3671	92	44	ip	ip	NOUN
iajs-3671	92	45	-	-	PUNCT
iajs-3671	92	46	ii	ii	NOUN
iajs-3671	92	47	,	,	PUNCT
iajs-3671	92	48	from	from	ADP
iajs-3671	92	49	relations	relation	NOUN
iajs-3671	92	50	(	(	PUNCT
iajs-3671	92	51	i)–(iii	i)–(iii	NOUN
iajs-3671	92	52	)	)	PUNCT
iajs-3671	92	53	,	,	PUNCT
iajs-3671	92	54	and	and	CCONJ
iajs-3671	92	55	𝑢𝑥(0	𝑢𝑥(0	PROPN
iajs-3671	92	56	,	,	PUNCT
iajs-3671	92	57	𝑡	𝑡	X
iajs-3671	92	58	)	)	PUNCT
iajs-3671	92	59	=	=	SYM
iajs-3671	92	60	𝑢𝑥(1	𝑢𝑥(1	PROPN
iajs-3671	92	61	,	,	PUNCT
iajs-3671	92	62	𝑡	𝑡	NOUN
iajs-3671	92	63	)	)	PUNCT
iajs-3671	92	64	,	,	PUNCT
iajs-3671	92	65	0	0	NUM
iajs-3671	92	66	≤	≤	NUM
iajs-3671	92	67	𝑡	𝑡	PROPN
iajs-3671	92	68	≤	≤	PROPN
iajs-3671	92	69	𝑇	𝑇	PROPN
iajs-3671	92	70	,	,	PUNCT
iajs-3671	92	71	(	(	PUNCT
iajs-3671	92	72	15	15	NUM
iajs-3671	92	73	)	)	PUNCT
iajs-3671	92	74	ℎ2	ℎ2	NOUN
iajs-3671	92	75	′(𝑡	′(𝑡	NOUN
iajs-3671	92	76	)	)	PUNCT
iajs-3671	92	77	−	−	PROPN
iajs-3671	92	78	𝑏𝑢𝑡𝑥𝑥(𝑥0	𝑏𝑢𝑡𝑥𝑥(𝑥0	PROPN
iajs-3671	92	79	,	,	PUNCT
iajs-3671	92	80	𝑡	𝑡	PROPN
iajs-3671	92	81	)	)	PUNCT
iajs-3671	92	82	−	−	PROPN
iajs-3671	92	83	𝑎(𝑡)𝑢𝑥𝑥(𝑥0	𝑎(𝑡)𝑢𝑥𝑥(𝑥0	PROPN
iajs-3671	92	84	,	,	PUNCT
iajs-3671	92	85	𝑡	𝑡	PROPN
iajs-3671	92	86	)	)	PUNCT
iajs-3671	92	87	=	=	SYM
iajs-3671	92	88	𝑝(𝑡)ℎ2(𝑡	𝑝(𝑡)ℎ2(𝑡	NOUN
iajs-3671	92	89	)	)	PUNCT
iajs-3671	92	90	+	+	SYM
iajs-3671	92	91	𝑓(𝑥0	𝑓(𝑥0	ADJ
iajs-3671	92	92	,	,	PUNCT
iajs-3671	92	93	𝑡	𝑡	PROPN
iajs-3671	92	94	)	)	PUNCT
iajs-3671	92	95	(	(	PUNCT
iajs-3671	92	96	0	0	NUM
iajs-3671	92	97	≤	≤	NUM
iajs-3671	92	98	𝑡	𝑡	PROPN
iajs-3671	92	99	≤	≤	PROPN
iajs-3671	92	100	𝑇	𝑇	PROPN
iajs-3671	92	101	)	)	PUNCT
iajs-3671	92	102	(	(	PUNCT
iajs-3671	92	103	16	16	NUM
iajs-3671	92	104	)	)	PUNCT
iajs-3671	92	105	theorem	theorem	NOUN
iajs-3671	92	106	2	2	NUM
iajs-3671	92	107	for	for	ADP
iajs-3671	92	108	ip	ip	NOUN
iajs-3671	92	109	-	-	PUNCT
iajs-3671	92	110	ii	ii	NOUN
iajs-3671	92	111	.	.	PUNCT
iajs-3671	93	1	let	let	VERB
iajs-3671	93	2	the	the	DET
iajs-3671	93	3	problem	problem	NOUN
iajs-3671	93	4	equations	equation	NOUN
iajs-3671	93	5	(	(	PUNCT
iajs-3671	93	6	1	1	NUM
iajs-3671	93	7	)	)	PUNCT
iajs-3671	93	8	–	–	PUNCT
iajs-3671	93	9	(	(	PUNCT
iajs-3671	93	10	3	3	NUM
iajs-3671	93	11	)	)	PUNCT
iajs-3671	93	12	,	,	PUNCT
iajs-3671	93	13	(	(	PUNCT
iajs-3671	93	14	5	5	NUM
iajs-3671	93	15	)	)	PUNCT
iajs-3671	93	16	,	,	PUNCT
iajs-3671	93	17	(	(	PUNCT
iajs-3671	93	18	16	16	X
iajs-3671	93	19	)	)	PUNCT
iajs-3671	93	20	satisfy	satisfy	VERB
iajs-3671	93	21	the	the	DET
iajs-3671	93	22	following	following	NOUN
iajs-3671	93	23	:	:	PUNCT
iajs-3671	93	24	1	1	X
iajs-3671	93	25	.	.	X
iajs-3671	93	26	𝜑(𝑥	𝜑(𝑥	NOUN
iajs-3671	93	27	)	)	PUNCT
iajs-3671	93	28	∈	∈	PROPN
iajs-3671	93	29	𝐶2[0,1	𝐶2[0,1	NOUN
iajs-3671	93	30	]	]	X
iajs-3671	93	31	,	,	PUNCT
iajs-3671	93	32	𝜑′′′(𝑥	𝜑′′′(𝑥	PROPN
iajs-3671	93	33	)	)	PUNCT
iajs-3671	93	34	∈	∈	PROPN
iajs-3671	93	35	𝐿2(0,1	𝐿2(0,1	NOUN
iajs-3671	93	36	)	)	PUNCT
iajs-3671	93	37	,	,	PUNCT
iajs-3671	93	38	𝜑(0	𝜑(0	NOUN
iajs-3671	93	39	)	)	PUNCT
iajs-3671	93	40	=	=	SYM
iajs-3671	93	41	𝜑(1	𝜑(1	PROPN
iajs-3671	93	42	)	)	PUNCT
iajs-3671	93	43	,	,	PUNCT
iajs-3671	93	44	𝜑	𝜑	PROPN
iajs-3671	93	45	′(0	′(0	PROPN
iajs-3671	93	46	)	)	PUNCT
iajs-3671	93	47	=	=	SYM
iajs-3671	93	48	𝜑′(1	𝜑′(1	NOUN
iajs-3671	93	49	)	)	PUNCT
iajs-3671	93	50	,	,	PUNCT
iajs-3671	93	51	𝜑′′(0	𝜑′′(0	NOUN
iajs-3671	93	52	)	)	PUNCT
iajs-3671	93	53	=	=	SYM
iajs-3671	93	54	𝜑′′(1	𝜑′′(1	PROPN
iajs-3671	93	55	)	)	PUNCT
iajs-3671	93	56	.	.	PUNCT
iajs-3671	94	1	(	(	PUNCT
iajs-3671	94	2	17	17	NUM
iajs-3671	94	3	)	)	SYM
iajs-3671	94	4	2	2	NUM
iajs-3671	94	5	.	.	PUNCT
iajs-3671	95	1	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3671	95	2	,	,	PUNCT
iajs-3671	95	3	𝑡	𝑡	NOUN
iajs-3671	95	4	)	)	PUNCT
iajs-3671	95	5	∈	∈	PROPN
iajs-3671	95	6	𝐶(𝑄𝑇	𝐶(𝑄𝑇	NOUN
iajs-3671	95	7	)	)	PUNCT
iajs-3671	95	8	,	,	PUNCT
iajs-3671	95	9	𝑓𝑥(𝑥	𝑓𝑥(𝑥	NUM
iajs-3671	95	10	,	,	PUNCT
iajs-3671	95	11	𝑡	𝑡	NOUN
iajs-3671	95	12	)	)	PUNCT
iajs-3671	95	13	∈	∈	PROPN
iajs-3671	95	14	𝐿2(𝑄𝑇	𝐿2(𝑄𝑇	NOUN
iajs-3671	95	15	)	)	PUNCT
iajs-3671	95	16	,	,	PUNCT
iajs-3671	95	17	𝑓(0	𝑓(0	PROPN
iajs-3671	95	18	,	,	PUNCT
iajs-3671	95	19	𝑡	𝑡	NOUN
iajs-3671	95	20	)	)	PUNCT
iajs-3671	95	21	=	=	SYM
iajs-3671	96	1	𝑓(1	𝑓(1	NOUN
iajs-3671	96	2	,	,	PUNCT
iajs-3671	96	3	𝑡	𝑡	NOUN
iajs-3671	96	4	)	)	PUNCT
iajs-3671	96	5	,	,	PUNCT
iajs-3671	96	6	(	(	PUNCT
iajs-3671	96	7	0	0	NUM
iajs-3671	96	8	≤	≤	NUM
iajs-3671	96	9	𝑡	𝑡	PROPN
iajs-3671	96	10	≤	≤	PROPN
iajs-3671	96	11	𝑇	𝑇	PROPN
iajs-3671	96	12	)	)	PUNCT
iajs-3671	96	13	.	.	PUNCT
iajs-3671	97	1	(	(	PUNCT
iajs-3671	97	2	18	18	NUM
iajs-3671	97	3	)	)	PUNCT
iajs-3671	97	4	ihjpas	ihjpa	NOUN
iajs-3671	97	5	.	.	PUNCT
iajs-3671	98	1	2025	2025	NUM
iajs-3671	98	2	,	,	PUNCT
iajs-3671	98	3	38	38	NUM
iajs-3671	98	4	(	(	PUNCT
iajs-3671	98	5	1	1	NUM
iajs-3671	98	6	)	)	PUNCT
iajs-3671	98	7	470	470	NUM
iajs-3671	98	8	3.𝑎(𝑡	3.𝑎(𝑡	NUM
iajs-3671	98	9	)	)	PUNCT
iajs-3671	98	10	>	>	X
iajs-3671	98	11	0	0	NUM
iajs-3671	98	12	,	,	PUNCT
iajs-3671	98	13	𝑏	𝑏	PROPN
iajs-3671	98	14	>	>	X
iajs-3671	98	15	0	0	PROPN
iajs-3671	98	16	,	,	PUNCT
iajs-3671	98	17	𝐶	𝐶	PROPN
iajs-3671	99	1	[	[	X
iajs-3671	99	2	0	0	NUM
iajs-3671	99	3	,	,	PUNCT
iajs-3671	99	4	𝑇	𝑇	PROPN
iajs-3671	99	5	]	]	PUNCT
iajs-3671	99	6	,	,	PUNCT
iajs-3671	99	7	ℎ2(𝑡	ℎ2(𝑡	PROPN
iajs-3671	99	8	)	)	PUNCT
iajs-3671	99	9	∈	∈	PROPN
iajs-3671	99	10	𝐶	𝐶	PROPN
iajs-3671	99	11	1[0	1[0	PROPN
iajs-3671	99	12	,	,	PUNCT
iajs-3671	99	13	𝑇	𝑇	PROPN
iajs-3671	99	14	]	]	X
iajs-3671	99	15	,	,	PUNCT
iajs-3671	99	16	ℎ2(𝑡	ℎ2(𝑡	PROPN
iajs-3671	99	17	)	)	PUNCT
iajs-3671	99	18	≠	≠	PROPN
iajs-3671	99	19	0	0	NUM
iajs-3671	99	20	(	(	PUNCT
iajs-3671	99	21	0	0	NUM
iajs-3671	99	22	≤	≤	NUM
iajs-3671	99	23	𝑡	𝑡	PROPN
iajs-3671	99	24	≤	≤	PROPN
iajs-3671	99	25	𝑇	𝑇	PROPN
iajs-3671	99	26	)	)	PUNCT
iajs-3671	99	27	.	.	PUNCT
iajs-3671	100	1	(	(	PUNCT
iajs-3671	100	2	19	19	NUM
iajs-3671	100	3	)	)	SYM
iajs-3671	100	4	4	4	NUM
iajs-3671	100	5	.	.	NUM
iajs-3671	100	6	𝜑(𝑥0	𝜑(𝑥0	NOUN
iajs-3671	100	7	)	)	PUNCT
iajs-3671	100	8	=	=	SYM
iajs-3671	100	9	ℎ2(0	ℎ2(0	PROPN
iajs-3671	100	10	)	)	PUNCT
iajs-3671	100	11	.	.	PUNCT
iajs-3671	101	1	(	(	PUNCT
iajs-3671	101	2	20	20	NUM
iajs-3671	101	3	)	)	PUNCT
iajs-3671	101	4	then	then	ADV
iajs-3671	101	5	ipii	ipii	PROPN
iajs-3671	101	6	has	have	VERB
iajs-3671	101	7	a	a	DET
iajs-3671	101	8	unique	unique	ADJ
iajs-3671	101	9	solution	solution	NOUN
iajs-3671	101	10	in	in	ADP
iajs-3671	101	11	the	the	DET
iajs-3671	101	12	ball	ball	NOUN
iajs-3671	101	13	k	k	PROPN
iajs-3671	101	14	=	=	PUNCT
iajs-3671	101	15	𝐾𝑅	𝐾𝑅	PROPN
iajs-3671	101	16	(	(	PUNCT
iajs-3671	101	17	‖𝑧‖𝐸𝑇3	‖𝑧‖𝐸𝑇3	NOUN
iajs-3671	101	18	≤	≤	NUM
iajs-3671	101	19	r	r	NOUN
iajs-3671	101	20	=	=	SYM
iajs-3671	101	21	a	a	PRON
iajs-3671	101	22	(	(	PUNCT
iajs-3671	101	23	t	t	NOUN
iajs-3671	101	24	)	)	PUNCT
iajs-3671	102	1	+	+	CCONJ
iajs-3671	102	2	2	2	X
iajs-3671	102	3	)	)	PUNCT
iajs-3671	102	4	of	of	ADP
iajs-3671	102	5	the	the	DET
iajs-3671	102	6	space	space	NOUN
iajs-3671	102	7	𝐸𝑇	𝐸𝑇	NOUN
iajs-3671	102	8	3	3	NUM
iajs-3671	102	9	in	in	ADP
iajs-3671	102	10	banach	banach	NOUN
iajs-3671	102	11	space	space	NOUN
iajs-3671	102	12	.	.	PUNCT
iajs-3671	103	1	where	where	SCONJ
iajs-3671	103	2	𝐴1(𝑇	𝐴1(𝑇	X
iajs-3671	103	3	)	)	PUNCT
iajs-3671	103	4	=	=	SYM
iajs-3671	103	5	‖𝜑(𝑥)‖𝐿2(0,1	‖𝜑(𝑥)‖𝐿2(0,1	NOUN
iajs-3671	103	6	)	)	PUNCT
iajs-3671	104	1	+	+	NUM
iajs-3671	104	2	√𝑇‖𝑓(𝑥	√𝑇‖𝑓(𝑥	NOUN
iajs-3671	104	3	,	,	PUNCT
iajs-3671	104	4	𝑡)‖𝐿2(𝑄𝑇	𝑡)‖𝐿2(𝑄𝑇	NOUN
iajs-3671	104	5	)	)	PUNCT
iajs-3671	105	1	+	+	CCONJ
iajs-3671	105	2	2√3‖𝜑	2√3‖𝜑	NUM
iajs-3671	105	3	′′′(𝑥)‖𝐿2(0,1	′′′(𝑥)‖𝐿2(0,1	NUM
iajs-3671	105	4	)	)	PUNCT
iajs-3671	106	1	+	+	NUM
iajs-3671	106	2	2√3	2√3	NUM
iajs-3671	106	3	𝑏	𝑏	NOUN
iajs-3671	106	4	√𝑇‖𝑓𝑥(𝑥	√𝑇‖𝑓𝑥(𝑥	ADJ
iajs-3671	106	5	,	,	PUNCT
iajs-3671	106	6	𝑡)‖𝐿2(𝑄𝑇	𝑡)‖𝐿2(𝑄𝑇	NOUN
iajs-3671	106	7	)	)	PUNCT
iajs-3671	106	8	,	,	PUNCT
iajs-3671	106	9	(	(	PUNCT
iajs-3671	106	10	21	21	NUM
iajs-3671	106	11	)	)	PUNCT
iajs-3671	106	12	𝐴2(𝑇	𝐴2(𝑇	PROPN
iajs-3671	106	13	)	)	PUNCT
iajs-3671	106	14	=	=	PUNCT
iajs-3671	106	15	‖[ℎ2(𝑡	‖[ℎ2(𝑡	PROPN
iajs-3671	106	16	)	)	PUNCT
iajs-3671	106	17	]	]	PUNCT
iajs-3671	107	1	−1‖𝐶[0,𝑇	−1‖𝐶[0,𝑇	NOUN
iajs-3671	107	2	]	]	X
iajs-3671	107	3	{	{	PUNCT
iajs-3671	107	4	‖ℎ2	‖ℎ2	ADJ
iajs-3671	107	5	′(𝑡	′(𝑡	NOUN
iajs-3671	107	6	)	)	PUNCT
iajs-3671	107	7	−	−	PROPN
iajs-3671	107	8	𝑓(𝑥0	𝑓(𝑥0	PROPN
iajs-3671	107	9	,	,	PUNCT
iajs-3671	107	10	𝑡)‖𝐶[0,𝑇	𝑡)‖𝐶[0,𝑇	PROPN
iajs-3671	107	11	]	]	PUNCT
iajs-3671	107	12	+	+	CCONJ
iajs-3671	107	13	2	2	NUM
iajs-3671	107	14	√6	√6	PROPN
iajs-3671	107	15	‖‖𝑓𝑥(𝑥	‖‖𝑓𝑥(𝑥	PROPN
iajs-3671	107	16	,	,	PUNCT
iajs-3671	107	17	𝑡)‖𝐶[0,𝑇]‖𝐿2(0,1	𝑡)‖𝐶[0,𝑇]‖𝐿2(0,1	NOUN
iajs-3671	107	18	)	)	PUNCT
iajs-3671	107	19	+	+	CCONJ
iajs-3671	107	20	2	2	NUM
iajs-3671	107	21	√6	√6	NOUN
iajs-3671	107	22	‖𝜑′(𝑥)‖𝐿2(0,1	‖𝜑′(𝑥)‖𝐿2(0,1	ADV
iajs-3671	107	23	)	)	PUNCT
iajs-3671	108	1	+	+	CCONJ
iajs-3671	108	2	2	2	NUM
iajs-3671	108	3	𝑏√6	𝑏√6	ADP
iajs-3671	108	4	‖𝑎(𝑡)‖𝐶[0,𝑇](‖𝜑	‖𝑎(𝑡)‖𝐶[0,𝑇](‖𝜑	NOUN
iajs-3671	108	5	′(𝑥)‖𝐿2(0,1	′(𝑥)‖𝐿2(0,1	NOUN
iajs-3671	108	6	)	)	PUNCT
iajs-3671	108	7	+	+	CCONJ
iajs-3671	108	8	‖𝑓(𝑥	‖𝑓(𝑥	NOUN
iajs-3671	108	9	,	,	PUNCT
iajs-3671	108	10	𝑡)‖𝐿2(𝑄𝑇	𝑡)‖𝐿2(𝑄𝑇	NOUN
iajs-3671	108	11	)	)	PUNCT
iajs-3671	108	12	)	)	PUNCT
iajs-3671	108	13	}	}	PUNCT
iajs-3671	108	14	(	(	PUNCT
iajs-3671	108	15	22	22	X
iajs-3671	108	16	)	)	PUNCT
iajs-3671	108	17	𝐵1(𝑇	𝐵1(𝑇	PROPN
iajs-3671	108	18	)	)	PUNCT
iajs-3671	108	19	=	=	PUNCT
iajs-3671	108	20	(	(	PUNCT
iajs-3671	108	21	1	1	NUM
iajs-3671	108	22	+	+	NUM
iajs-3671	108	23	2√3	2√3	NUM
iajs-3671	108	24	𝑏	𝑏	NOUN
iajs-3671	108	25	)	)	PUNCT
iajs-3671	108	26	𝑇	𝑇	PROPN
iajs-3671	108	27	,	,	PUNCT
iajs-3671	108	28	(	(	PUNCT
iajs-3671	108	29	23	23	NUM
iajs-3671	108	30	)	)	PUNCT
iajs-3671	108	31	𝐵2(𝑇	𝐵2(𝑇	PROPN
iajs-3671	108	32	)	)	PUNCT
iajs-3671	108	33	=	=	SYM
iajs-3671	108	34	2	2	NUM
iajs-3671	108	35	√6	√6	NOUN
iajs-3671	108	36	(	(	PUNCT
iajs-3671	108	37	1	1	NUM
iajs-3671	108	38	+	+	SYM
iajs-3671	108	39	1	1	NUM
iajs-3671	108	40	𝑏2	𝑏2	PROPN
iajs-3671	108	41	𝑇‖𝑎(𝑡)‖𝐶[0,𝑇	𝑇‖𝑎(𝑡)‖𝐶[0,𝑇	PROPN
iajs-3671	108	42	]	]	PUNCT
iajs-3671	108	43	)	)	PUNCT
iajs-3671	108	44	‖[ℎ2(𝑡	‖[ℎ2(𝑡	PROPN
iajs-3671	108	45	)	)	PUNCT
iajs-3671	108	46	]	]	PUNCT
iajs-3671	109	1	−1‖𝐶[0,𝑇	−1‖𝐶[0,𝑇	NOUN
iajs-3671	109	2	]	]	X
iajs-3671	109	3	,	,	PUNCT
iajs-3671	109	4	(	(	PUNCT
iajs-3671	109	5	24	24	NUM
iajs-3671	109	6	)	)	PUNCT
iajs-3671	109	7	where	where	SCONJ
iajs-3671	109	8	𝐴(𝑇	𝐴(𝑇	NOUN
iajs-3671	109	9	)	)	PUNCT
iajs-3671	109	10	=	=	SYM
iajs-3671	109	11	𝐴1(𝑇	𝐴1(𝑇	PROPN
iajs-3671	109	12	)	)	PUNCT
iajs-3671	109	13	+	+	PUNCT
iajs-3671	109	14	𝐴2(𝑇	𝐴2(𝑇	PROPN
iajs-3671	109	15	)	)	PUNCT
iajs-3671	109	16	,	,	PUNCT
iajs-3671	109	17	𝐵(𝑇	𝐵(𝑇	PROPN
iajs-3671	109	18	)	)	PUNCT
iajs-3671	109	19	=	=	SYM
iajs-3671	109	20	𝐵1(𝑇	𝐵1(𝑇	PROPN
iajs-3671	109	21	)	)	PUNCT
iajs-3671	109	22	+	+	X
iajs-3671	109	23	𝐵2(𝑇	𝐵2(𝑇	PROPN
iajs-3671	109	24	)	)	PUNCT
iajs-3671	109	25	.	.	PUNCT
iajs-3671	110	1	(	(	PUNCT
iajs-3671	110	2	25	25	NUM
iajs-3671	110	3	)	)	PUNCT
iajs-3671	110	4	2.1	2.1	NUM
iajs-3671	110	5	discretization	discretization	NOUN
iajs-3671	110	6	of	of	ADP
iajs-3671	110	7	the	the	DET
iajs-3671	110	8	direct	direct	ADJ
iajs-3671	110	9	solver	solver	NOUN
iajs-3671	110	10	consider	consider	VERB
iajs-3671	110	11	the	the	DET
iajs-3671	110	12	direct	direct	ADJ
iajs-3671	110	13	solver	solver	NOUN
iajs-3671	110	14	for	for	ADP
iajs-3671	110	15	ip	ip	ADJ
iajs-3671	110	16	-	-	PUNCT
iajs-3671	110	17	i	i	PRON
iajs-3671	110	18	contains	contain	VERB
iajs-3671	110	19	the	the	DET
iajs-3671	110	20	equations	equation	NOUN
iajs-3671	110	21	(	(	PUNCT
iajs-3671	110	22	1)(4	1)(4	NUM
iajs-3671	110	23	)	)	PUNCT
iajs-3671	110	24	and	and	CCONJ
iajs-3671	110	25	required	require	VERB
iajs-3671	110	26	data	data	NOUN
iajs-3671	110	27	equation	equation	NOUN
iajs-3671	110	28	(	(	PUNCT
iajs-3671	110	29	6	6	NUM
iajs-3671	110	30	)	)	PUNCT
iajs-3671	110	31	.	.	PUNCT
iajs-3671	111	1	also	also	ADV
iajs-3671	111	2	,	,	PUNCT
iajs-3671	111	3	the	the	DET
iajs-3671	111	4	direct	direct	ADJ
iajs-3671	111	5	solver	solver	NOUN
iajs-3671	111	6	for	for	ADP
iajs-3671	111	7	ip	ip	PROPN
iajs-3671	111	8	-	-	PUNCT
iajs-3671	111	9	ii	ii	NOUN
iajs-3671	111	10	contains	contain	VERB
iajs-3671	111	11	the	the	DET
iajs-3671	111	12	equations	equation	NOUN
iajs-3671	111	13	(	(	PUNCT
iajs-3671	111	14	1)-(3	1)-(3	NUM
iajs-3671	111	15	)	)	PUNCT
iajs-3671	111	16	,	,	PUNCT
iajs-3671	111	17	(	(	PUNCT
iajs-3671	111	18	5	5	NUM
iajs-3671	111	19	)	)	PUNCT
iajs-3671	111	20	and	and	CCONJ
iajs-3671	111	21	the	the	DET
iajs-3671	111	22	required	require	VERB
iajs-3671	111	23	data	data	NOUN
iajs-3671	111	24	equation	equation	NOUN
iajs-3671	111	25	(	(	PUNCT
iajs-3671	111	26	7	7	NUM
iajs-3671	111	27	)	)	PUNCT
iajs-3671	111	28	.	.	PUNCT
iajs-3671	112	1	in	in	ADP
iajs-3671	112	2	these	these	DET
iajs-3671	112	3	direct	direct	ADJ
iajs-3671	112	4	problems	problem	NOUN
iajs-3671	112	5	,	,	PUNCT
iajs-3671	112	6	the	the	DET
iajs-3671	112	7	only	only	ADJ
iajs-3671	112	8	unknown	unknown	ADJ
iajs-3671	112	9	quantity	quantity	NOUN
iajs-3671	112	10	that	that	PRON
iajs-3671	112	11	should	should	AUX
iajs-3671	112	12	be	be	AUX
iajs-3671	112	13	determined	determine	VERB
iajs-3671	112	14	is	be	AUX
iajs-3671	112	15	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	112	16	,	,	PUNCT
iajs-3671	112	17	𝑡	𝑡	NOUN
iajs-3671	112	18	)	)	PUNCT
iajs-3671	112	19	,	,	PUNCT
iajs-3671	112	20	that	that	ADV
iajs-3671	112	21	is	is	ADV
iajs-3671	112	22	,	,	PUNCT
iajs-3671	112	23	all	all	DET
iajs-3671	112	24	other	other	ADJ
iajs-3671	112	25	components	component	NOUN
iajs-3671	112	26	are	be	AUX
iajs-3671	112	27	known	know	VERB
iajs-3671	112	28	.	.	PUNCT
iajs-3671	113	1	discretising	discretise	VERB
iajs-3671	113	2	equation	equation	NOUN
iajs-3671	113	3	(	(	PUNCT
iajs-3671	113	4	1	1	NUM
iajs-3671	113	5	)	)	PUNCT
iajs-3671	113	6	by	by	ADP
iajs-3671	113	7	a	a	DET
iajs-3671	113	8	form	form	NOUN
iajs-3671	113	9	of	of	ADP
iajs-3671	113	10	(	(	PUNCT
iajs-3671	113	11	fdm	fdm	NOUN
iajs-3671	113	12	)	)	PUNCT
iajs-3671	113	13	as	as	SCONJ
iajs-3671	113	14	follows	follow	VERB
iajs-3671	113	15	:	:	PUNCT
iajs-3671	113	16	ihjpas	ihjpas	PROPN
iajs-3671	113	17	.	.	PUNCT
iajs-3671	114	1	2025	2025	NUM
iajs-3671	114	2	,	,	PUNCT
iajs-3671	114	3	38	38	NUM
iajs-3671	114	4	(	(	PUNCT
iajs-3671	114	5	1	1	NUM
iajs-3671	114	6	)	)	PUNCT
iajs-3671	114	7	471	471	NUM
iajs-3671	114	8	denote	denote	NOUN
iajs-3671	114	9	for	for	ADP
iajs-3671	114	10	𝑢(𝑥𝑖	𝑢(𝑥𝑖	PROPN
iajs-3671	114	11	,	,	PUNCT
iajs-3671	114	12	𝑡𝑗	𝑡𝑗	NOUN
iajs-3671	114	13	)	)	PUNCT
iajs-3671	114	14	=	=	SYM
iajs-3671	114	15	𝑢𝑖,𝑗	𝑢𝑖,𝑗	NOUN
iajs-3671	114	16	,	,	PUNCT
iajs-3671	114	17	and	and	CCONJ
iajs-3671	114	18	𝑓(𝑥𝑖	𝑓(𝑥𝑖	PROPN
iajs-3671	114	19	,	,	PUNCT
iajs-3671	114	20	𝑡𝑗	𝑡𝑗	PROPN
iajs-3671	114	21	)	)	PUNCT
iajs-3671	114	22	=	=	NOUN
iajs-3671	114	23	𝑓𝑖,𝑗	𝑓𝑖,𝑗	NOUN
iajs-3671	114	24	where	where	SCONJ
iajs-3671	114	25	space	space	NOUN
iajs-3671	114	26	node	node	NOUN
iajs-3671	114	27	𝑥𝑖	𝑥𝑖	PROPN
iajs-3671	115	1	=	=	PUNCT
iajs-3671	115	2	𝑖∆𝑥	𝑖∆𝑥	PROPN
iajs-3671	115	3	,	,	PUNCT
iajs-3671	115	4	time	time	NOUN
iajs-3671	115	5	node	node	VERB
iajs-3671	115	6	𝑡𝑗	𝑡𝑗	ADP
iajs-3671	115	7	=	=	SYM
iajs-3671	115	8	𝑗∆𝑡	𝑗∆𝑡	PROPN
iajs-3671	115	9	,	,	PUNCT
iajs-3671	115	10	the	the	DET
iajs-3671	115	11	space	space	NOUN
iajs-3671	115	12	step	step	NOUN
iajs-3671	115	13	length	length	NOUN
iajs-3671	115	14	∆𝑥	∆𝑥	PROPN
iajs-3671	115	15	=	=	SYM
iajs-3671	115	16	1	1	NUM
iajs-3671	115	17	𝑀	𝑀	NOUN
iajs-3671	115	18	and	and	CCONJ
iajs-3671	115	19	time	time	NOUN
iajs-3671	115	20	step	step	NOUN
iajs-3671	115	21	length	length	NOUN
iajs-3671	116	1	∆𝑡	∆𝑡	PROPN
iajs-3671	116	2	=	=	SYM
iajs-3671	116	3	𝑇	𝑇	PROPN
iajs-3671	116	4	𝑁	𝑁	PROPN
iajs-3671	116	5	for	for	ADP
iajs-3671	116	6	𝑖	𝑖	NOUN
iajs-3671	116	7	=	=	SYM
iajs-3671	116	8	0,1	0,1	NUM
iajs-3671	116	9	,	,	PUNCT
iajs-3671	116	10	…	…	PUNCT
iajs-3671	116	11	,	,	PUNCT
iajs-3671	116	12	𝑀	𝑀	PROPN
iajs-3671	116	13	,	,	PUNCT
iajs-3671	116	14	𝑗	𝑗	NOUN
iajs-3671	116	15	=	=	NOUN
iajs-3671	116	16	0,1,2	0,1,2	NUM
iajs-3671	116	17	,	,	PUNCT
iajs-3671	116	18	…	…	PUNCT
iajs-3671	116	19	,	,	PUNCT
iajs-3671	116	20	𝑁	𝑁	PROPN
iajs-3671	116	21	where	where	SCONJ
iajs-3671	116	22	𝑀,𝑁	𝑀,𝑁	NOUN
iajs-3671	116	23	are	be	AUX
iajs-3671	116	24	positive	positive	ADJ
iajs-3671	116	25	integers	integer	NOUN
iajs-3671	116	26	.	.	PUNCT
iajs-3671	117	1	based	base	VERB
iajs-3671	117	2	on	on	ADP
iajs-3671	117	3	the	the	DET
iajs-3671	117	4	finite	finite	ADJ
iajs-3671	117	5	difference	difference	NOUN
iajs-3671	117	6	method	method	NOUN
iajs-3671	117	7	,	,	PUNCT
iajs-3671	117	8	equation	equation	NOUN
iajs-3671	117	9	(	(	PUNCT
iajs-3671	117	10	1	1	X
iajs-3671	117	11	)	)	PUNCT
iajs-3671	117	12	can	can	AUX
iajs-3671	117	13	be	be	AUX
iajs-3671	117	14	expressed	express	VERB
iajs-3671	117	15	as	as	ADP
iajs-3671	117	16	:	:	PUNCT
iajs-3671	117	17	𝑢𝑖,𝑗+1	𝑢𝑖,𝑗+1	NOUN
iajs-3671	117	18	−	−	NOUN
iajs-3671	117	19	𝑢𝑖,𝑗	𝑢𝑖,𝑗	VERB
iajs-3671	117	20	∆𝑡	∆𝑡	NOUN
iajs-3671	118	1	=	=	SYM
iajs-3671	118	2	𝑎𝑗	𝑎𝑗	PROPN
iajs-3671	118	3	(	(	PUNCT
iajs-3671	118	4	𝑢𝑖+1,𝑗	𝑢𝑖+1,𝑗	PROPN
iajs-3671	118	5	−	−	PROPN
iajs-3671	118	6	2𝑢𝑖,𝑗	2𝑢𝑖,𝑗	NUM
iajs-3671	118	7	+	+	CCONJ
iajs-3671	118	8	𝑢𝑖−1,𝑗	𝑢𝑖−1,𝑗	NOUN
iajs-3671	118	9	(	(	PUNCT
iajs-3671	118	10	∆𝑥)2	∆𝑥)2	PROPN
iajs-3671	118	11	)	)	PUNCT
iajs-3671	118	12	+	+	CCONJ
iajs-3671	119	1	𝑏	𝑏	PROPN
iajs-3671	119	2	∆𝑡	∆𝑡	PROPN
iajs-3671	119	3	(	(	PUNCT
iajs-3671	119	4	𝑢𝑖+1,𝑗+1	𝑢𝑖+1,𝑗+1	NOUN
iajs-3671	119	5	−	−	PROPN
iajs-3671	119	6	2𝑢𝑖,𝑗+1	2𝑢𝑖,𝑗+1	NUM
iajs-3671	119	7	+	+	CCONJ
iajs-3671	119	8	𝑢𝑖−1,𝑗+1	𝑢𝑖−1,𝑗+1	PROPN
iajs-3671	119	9	(	(	PUNCT
iajs-3671	119	10	∆𝑥)2	∆𝑥)2	PROPN
iajs-3671	119	11	)	)	PUNCT
iajs-3671	119	12	−	−	PROPN
iajs-3671	119	13	𝑏	𝑏	NOUN
iajs-3671	119	14	∆𝑡	∆𝑡	PROPN
iajs-3671	119	15	(	(	PUNCT
iajs-3671	119	16	𝑢𝑖+1,𝑗−2𝑢𝑖,𝑗+𝑢𝑖−1,𝑗	𝑢𝑖+1,𝑗−2𝑢𝑖,𝑗+𝑢𝑖−1,𝑗	PROPN
iajs-3671	119	17	(	(	PUNCT
iajs-3671	119	18	∆𝑥)2	∆𝑥)2	INTJ
iajs-3671	119	19	)	)	PUNCT
iajs-3671	119	20	+	+	CCONJ
iajs-3671	119	21	𝑝𝑗𝑢𝑖𝑗	𝑝𝑗𝑢𝑖𝑗	NOUN
iajs-3671	119	22	+	+	CCONJ
iajs-3671	119	23	𝑓𝑖,𝑗	𝑓𝑖,𝑗	NOUN
iajs-3671	119	24	(	(	PUNCT
iajs-3671	119	25	26	26	NUM
iajs-3671	119	26	)	)	PUNCT
iajs-3671	119	27	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	119	28	,	,	PUNCT
iajs-3671	119	29	0	0	NUM
iajs-3671	119	30	)	)	PUNCT
iajs-3671	119	31	=	=	SYM
iajs-3671	119	32	𝜑(𝑥𝑖	𝜑(𝑥𝑖	PROPN
iajs-3671	119	33	)	)	PUNCT
iajs-3671	119	34	,	,	PUNCT
iajs-3671	119	35	𝑖	𝑖	NOUN
iajs-3671	119	36	=	=	SYM
iajs-3671	119	37	0	0	NUM
iajs-3671	119	38	,	,	PUNCT
iajs-3671	119	39	1	1	NUM
iajs-3671	119	40	,	,	PUNCT
iajs-3671	119	41	…	…	PUNCT
iajs-3671	119	42	,	,	PUNCT
iajs-3671	119	43	𝑀	𝑀	PROPN
iajs-3671	119	44	,	,	PUNCT
iajs-3671	119	45	(	(	PUNCT
iajs-3671	119	46	27	27	NUM
iajs-3671	119	47	)	)	PUNCT
iajs-3671	119	48	𝑢(0	𝑢(0	PROPN
iajs-3671	119	49	,	,	PUNCT
iajs-3671	119	50	𝑡𝑗	𝑡𝑗	PROPN
iajs-3671	119	51	)	)	PUNCT
iajs-3671	119	52	=	=	SYM
iajs-3671	119	53	𝑢(1	𝑢(1	PROPN
iajs-3671	119	54	,	,	PUNCT
iajs-3671	119	55	𝑡𝑗	𝑡𝑗	NOUN
iajs-3671	119	56	)	)	PUNCT
iajs-3671	119	57	,	,	PUNCT
iajs-3671	119	58	𝑗	𝑗	NOUN
iajs-3671	119	59	=	=	SYM
iajs-3671	119	60	0,1	0,1	NUM
iajs-3671	119	61	,	,	PUNCT
iajs-3671	119	62	…	…	PUNCT
iajs-3671	119	63	,	,	PUNCT
iajs-3671	119	64	𝑁	𝑁	PROPN
iajs-3671	119	65	,	,	PUNCT
iajs-3671	119	66	(	(	PUNCT
iajs-3671	119	67	28	28	NUM
iajs-3671	119	68	)	)	PUNCT
iajs-3671	119	69	the	the	DET
iajs-3671	119	70	neumann	neumann	PROPN
iajs-3671	119	71	condition	condition	PROPN
iajs-3671	119	72	𝑢𝑥(1	𝑢𝑥(1	PROPN
iajs-3671	119	73	,	,	PUNCT
iajs-3671	119	74	𝑡	𝑡	X
iajs-3671	119	75	)	)	PUNCT
iajs-3671	119	76	=	=	SYM
iajs-3671	119	77	0	0	PROPN
iajs-3671	119	78	gives	give	VERB
iajs-3671	119	79	𝑢𝑀+1,𝑗	𝑢𝑀+1,𝑗	NOUN
iajs-3671	120	1	=	=	SYM
iajs-3671	121	1	𝑢𝑀−1,𝑗	𝑢𝑀−1,𝑗	PROPN
iajs-3671	121	2	,	,	PUNCT
iajs-3671	121	3	𝑗	𝑗	NOUN
iajs-3671	121	4	=	=	SYM
iajs-3671	121	5	0,1	0,1	NUM
iajs-3671	121	6	,	,	PUNCT
iajs-3671	121	7	…	…	PUNCT
iajs-3671	121	8	,	,	PUNCT
iajs-3671	121	9	𝑁	𝑁	PROPN
iajs-3671	121	10	(	(	PUNCT
iajs-3671	121	11	29	29	NUM
iajs-3671	121	12	)	)	PUNCT
iajs-3671	121	13	via	via	ADP
iajs-3671	121	14	central	central	ADJ
iajs-3671	121	15	difference	difference	NOUN
iajs-3671	121	16	formula	formula	NOUN
iajs-3671	121	17	.	.	PUNCT
iajs-3671	122	1	using	use	VERB
iajs-3671	122	2	the	the	DET
iajs-3671	122	3	trapezoidal	trapezoidal	ADJ
iajs-3671	122	4	rule	rule	NOUN
iajs-3671	122	5	approximation	approximation	NOUN
iajs-3671	122	6	to	to	ADP
iajs-3671	122	7	the	the	DET
iajs-3671	122	8	integral	integral	ADJ
iajs-3671	122	9	in	in	ADP
iajs-3671	122	10	equation	equation	NOUN
iajs-3671	122	11	(	(	PUNCT
iajs-3671	122	12	5	5	NUM
iajs-3671	122	13	)	)	PUNCT
iajs-3671	122	14	,	,	PUNCT
iajs-3671	122	15	we	we	PRON
iajs-3671	122	16	get	get	VERB
iajs-3671	122	17	the	the	DET
iajs-3671	122	18	following	follow	VERB
iajs-3671	122	19	formula	formula	NOUN
iajs-3671	122	20	∑𝑢𝑖𝑗	∑𝑢𝑖𝑗	ADJ
iajs-3671	122	21	𝑀	𝑀	PROPN
iajs-3671	122	22	𝑖=1	𝑖=1	PUNCT
iajs-3671	123	1	=	=	SYM
iajs-3671	123	2	0	0	PROPN
iajs-3671	123	3	,	,	PUNCT
iajs-3671	123	4	𝑗	𝑗	NOUN
iajs-3671	123	5	=	=	SYM
iajs-3671	123	6	0,1	0,1	NUM
iajs-3671	123	7	,	,	PUNCT
iajs-3671	123	8	…	…	PUNCT
iajs-3671	123	9	,	,	PUNCT
iajs-3671	123	10	𝑁.	𝑁.	PROPN
iajs-3671	123	11	(	(	PUNCT
iajs-3671	123	12	30	30	NUM
iajs-3671	123	13	)	)	PUNCT
iajs-3671	123	14	also	also	ADV
iajs-3671	123	15	,	,	PUNCT
iajs-3671	123	16	the	the	DET
iajs-3671	123	17	approximate	approximate	ADJ
iajs-3671	123	18	formula	formula	NOUN
iajs-3671	123	19	for	for	ADP
iajs-3671	123	20	overdetermination	overdetermination	NOUN
iajs-3671	123	21	condition	condition	NOUN
iajs-3671	123	22	equation	equation	NOUN
iajs-3671	123	23	(	(	PUNCT
iajs-3671	123	24	6	6	NUM
iajs-3671	123	25	)	)	PUNCT
iajs-3671	123	26	via	via	ADP
iajs-3671	123	27	trapezoidal	trapezoidal	ADJ
iajs-3671	123	28	rule	rule	NOUN
iajs-3671	123	29	is	be	AUX
iajs-3671	123	30	given	give	VERB
iajs-3671	123	31	as	as	ADP
iajs-3671	123	32	:	:	PUNCT
iajs-3671	123	33	ℎ1(𝑡𝑗	ℎ1(𝑡𝑗	NUM
iajs-3671	123	34	)	)	PUNCT
iajs-3671	123	35	=	=	SYM
iajs-3671	123	36	𝑢	𝑢	X
iajs-3671	123	37	(	(	PUNCT
iajs-3671	123	38	𝑀	𝑀	PROPN
iajs-3671	123	39	2	2	NUM
iajs-3671	123	40	,	,	PUNCT
iajs-3671	123	41	𝑡𝑗	𝑡𝑗	PROPN
iajs-3671	123	42	)	)	PUNCT
iajs-3671	123	43	+	+	CCONJ
iajs-3671	123	44	1	1	NUM
iajs-3671	123	45	𝑀	𝑀	PROPN
iajs-3671	123	46	∑𝑢𝑖𝑗	∑𝑢𝑖𝑗	ADJ
iajs-3671	123	47	𝑀	𝑀	PROPN
iajs-3671	123	48	𝑖=1	𝑖=1	PROPN
iajs-3671	123	49	,	,	PUNCT
iajs-3671	123	50	(	(	PUNCT
iajs-3671	123	51	31	31	NUM
iajs-3671	123	52	)	)	PUNCT
iajs-3671	123	53	and	and	CCONJ
iajs-3671	123	54	the	the	DET
iajs-3671	123	55	overdetermination	overdetermination	NOUN
iajs-3671	123	56	condition	condition	NOUN
iajs-3671	123	57	equation	equation	NOUN
iajs-3671	123	58	(	(	PUNCT
iajs-3671	123	59	7	7	X
iajs-3671	123	60	)	)	PUNCT
iajs-3671	123	61	is	be	AUX
iajs-3671	123	62	given	give	VERB
iajs-3671	123	63	as	as	ADP
iajs-3671	123	64	:	:	PUNCT
iajs-3671	123	65	ℎ2(𝑡𝑗	ℎ2(𝑡𝑗	PROPN
iajs-3671	123	66	)	)	PUNCT
iajs-3671	123	67	=	=	SYM
iajs-3671	123	68	𝑢(𝑥0	𝑢(𝑥0	ADJ
iajs-3671	123	69	,	,	PUNCT
iajs-3671	123	70	𝑗	𝑗	NOUN
iajs-3671	123	71	)	)	PUNCT
iajs-3671	123	72	,	,	PUNCT
iajs-3671	123	73	𝑗	𝑗	NOUN
iajs-3671	123	74	=	=	SYM
iajs-3671	123	75	0,1	0,1	NUM
iajs-3671	123	76	,	,	PUNCT
iajs-3671	123	77	…	…	PUNCT
iajs-3671	123	78	,	,	PUNCT
iajs-3671	123	79	𝑁.	𝑁.	PROPN
iajs-3671	123	80	(	(	PUNCT
iajs-3671	123	81	32	32	NUM
iajs-3671	123	82	)	)	PUNCT
iajs-3671	123	83	then	then	ADV
iajs-3671	123	84	,	,	PUNCT
iajs-3671	123	85	the	the	DET
iajs-3671	123	86	discrete	discrete	ADJ
iajs-3671	123	87	difference	difference	NOUN
iajs-3671	123	88	equation	equation	NOUN
iajs-3671	123	89	governing	govern	VERB
iajs-3671	123	90	equation	equation	NOUN
iajs-3671	123	91	(	(	PUNCT
iajs-3671	123	92	26	26	NUM
iajs-3671	123	93	)	)	PUNCT
iajs-3671	123	94	using	use	VERB
iajs-3671	123	95	the	the	DET
iajs-3671	123	96	fdm	fdm	NOUN
iajs-3671	123	97	scheme	scheme	NOUN
iajs-3671	123	98	,	,	PUNCT
iajs-3671	123	99	we	we	PRON
iajs-3671	123	100	obtain	obtain	VERB
iajs-3671	123	101	the	the	DET
iajs-3671	123	102	following	follow	VERB
iajs-3671	123	103	difference	difference	NOUN
iajs-3671	123	104	equation	equation	NOUN
iajs-3671	123	105	.	.	PUNCT
iajs-3671	124	1	−𝛼𝑢𝑖−1,𝑗+1	−𝛼𝑢𝑖−1,𝑗+1	PROPN
iajs-3671	124	2	+	+	CCONJ
iajs-3671	124	3	(	(	PUNCT
iajs-3671	124	4	1	1	NUM
iajs-3671	124	5	+	+	NUM
iajs-3671	124	6	2𝛼)𝑢𝑖,𝑗+1	2𝛼)𝑢𝑖,𝑗+1	NUM
iajs-3671	124	7	−	−	NOUN
iajs-3671	124	8	𝛼𝑢𝑖+1,𝑗+1	𝛼𝑢𝑖+1,𝑗+1	NOUN
iajs-3671	124	9	=	=	SYM
iajs-3671	124	10	𝛾𝑗𝑢𝑖−1,𝑗	𝛾𝑗𝑢𝑖−1,𝑗	X
iajs-3671	124	11	+	+	CCONJ
iajs-3671	124	12	(	(	PUNCT
iajs-3671	124	13	1	1	NUM
iajs-3671	124	14	−	−	NOUN
iajs-3671	124	15	2𝛾𝑗	2𝛾𝑗	ADJ
iajs-3671	124	16	+	+	NUM
iajs-3671	124	17	𝑐𝑗)𝑢𝑖,𝑗	𝑐𝑗)𝑢𝑖,𝑗	NOUN
iajs-3671	124	18	+	+	ADJ
iajs-3671	124	19	𝛾𝑗𝑢𝑖+1,𝑗	𝛾𝑗𝑢𝑖+1,𝑗	NOUN
iajs-3671	124	20	+	+	CCONJ
iajs-3671	124	21	∆𝑡𝑓𝑖,𝑗	∆𝑡𝑓𝑖,𝑗	NOUN
iajs-3671	124	22	,	,	PUNCT
iajs-3671	124	23	𝑖	𝑖	NOUN
iajs-3671	124	24	=	=	SYM
iajs-3671	124	25	1,2	1,2	NUM
iajs-3671	124	26	,	,	PUNCT
iajs-3671	124	27	…	…	PUNCT
iajs-3671	124	28	,	,	PUNCT
iajs-3671	124	29	𝑀	𝑀	PROPN
iajs-3671	124	30	,	,	PUNCT
iajs-3671	124	31	𝑗	𝑗	NOUN
iajs-3671	124	32	=	=	NOUN
iajs-3671	124	33	0,1,2	0,1,2	NUM
iajs-3671	124	34	,	,	PUNCT
iajs-3671	124	35	…	…	PUNCT
iajs-3671	124	36	𝑁	𝑁	PROPN
iajs-3671	124	37	,	,	PUNCT
iajs-3671	124	38	(	(	PUNCT
iajs-3671	124	39	33	33	NUM
iajs-3671	124	40	)	)	PUNCT
iajs-3671	124	41	where	where	SCONJ
iajs-3671	124	42	ihjpas	ihjpa	NOUN
iajs-3671	124	43	.	.	PUNCT
iajs-3671	125	1	2025	2025	NUM
iajs-3671	125	2	,	,	PUNCT
iajs-3671	125	3	38	38	NUM
iajs-3671	125	4	(	(	PUNCT
iajs-3671	125	5	1	1	NUM
iajs-3671	125	6	)	)	PUNCT
iajs-3671	125	7	472	472	NUM
iajs-3671	125	8	𝛼	𝛼	NOUN
iajs-3671	125	9	=	=	SYM
iajs-3671	125	10	𝑏	𝑏	PROPN
iajs-3671	125	11	(	(	PUNCT
iajs-3671	125	12	∆𝑥)2	∆𝑥)2	INTJ
iajs-3671	125	13	,	,	PUNCT
iajs-3671	125	14	𝛾𝑗	𝛾𝑗	ADV
iajs-3671	125	15	=	=	PUNCT
iajs-3671	125	16	𝑎𝑗∆𝑡	𝑎𝑗∆𝑡	PROPN
iajs-3671	125	17	(	(	PUNCT
iajs-3671	125	18	∆𝑥)2	∆𝑥)2	PROPN
iajs-3671	125	19	−	−	PROPN
iajs-3671	125	20	𝑏	𝑏	PROPN
iajs-3671	125	21	(	(	PUNCT
iajs-3671	125	22	∆𝑥)2	∆𝑥)2	INTJ
iajs-3671	125	23	,	,	PUNCT
iajs-3671	125	24	𝑐𝑗	𝑐𝑗	NOUN
iajs-3671	125	25	=	=	SYM
iajs-3671	125	26	∆𝑡	∆𝑡	PROPN
iajs-3671	125	27	𝑝𝑗	𝑝𝑗	PROPN
iajs-3671	125	28	(	(	PUNCT
iajs-3671	125	29	34	34	NUM
iajs-3671	125	30	)	)	PUNCT
iajs-3671	125	31	the	the	DET
iajs-3671	125	32	last	last	ADJ
iajs-3671	125	33	difference	difference	NOUN
iajs-3671	125	34	equation	equation	NOUN
iajs-3671	125	35	(	(	PUNCT
iajs-3671	125	36	33	33	NUM
iajs-3671	125	37	)	)	PUNCT
iajs-3671	125	38	can	can	AUX
iajs-3671	125	39	be	be	AUX
iajs-3671	125	40	encoded	encode	VERB
iajs-3671	125	41	by	by	ADP
iajs-3671	125	42	the	the	DET
iajs-3671	125	43	following	follow	VERB
iajs-3671	125	44	linear	linear	ADJ
iajs-3671	125	45	system	system	NOUN
iajs-3671	125	46	for	for	ADP
iajs-3671	125	47	equations	equation	NOUN
iajs-3671	125	48	(	(	PUNCT
iajs-3671	125	49	1)-(4	1)-(4	NUM
iajs-3671	125	50	)	)	PUNCT
iajs-3671	125	51	𝑫1𝑣	𝑫1𝑣	NOUN
iajs-3671	126	1	𝑗+1	𝑗+1	X
iajs-3671	127	1	=	=	PUNCT
iajs-3671	127	2	𝑬1𝑣	𝑬1𝑣	PROPN
iajs-3671	127	3	𝑗	𝑗	X
iajs-3671	127	4	+	+	X
iajs-3671	127	5	𝑍1	𝑍1	NOUN
iajs-3671	127	6	,	,	PUNCT
iajs-3671	127	7	𝑗	𝑗	NOUN
iajs-3671	127	8	=	=	NOUN
iajs-3671	127	9	0,1,2	0,1,2	NUM
iajs-3671	127	10	,	,	PUNCT
iajs-3671	127	11	…	…	PUNCT
iajs-3671	127	12	,	,	PUNCT
iajs-3671	127	13	𝑁	𝑁	PROPN
iajs-3671	127	14	,	,	PUNCT
iajs-3671	127	15	(	(	PUNCT
iajs-3671	127	16	35	35	NUM
iajs-3671	127	17	)	)	PUNCT
iajs-3671	127	18	and	and	CCONJ
iajs-3671	127	19	for	for	ADP
iajs-3671	127	20	equations	equation	NOUN
iajs-3671	127	21	(	(	PUNCT
iajs-3671	127	22	1)-(3	1)-(3	NUM
iajs-3671	127	23	)	)	PUNCT
iajs-3671	127	24	and	and	CCONJ
iajs-3671	127	25	(	(	PUNCT
iajs-3671	127	26	5	5	X
iajs-3671	127	27	)	)	PUNCT
iajs-3671	127	28	𝑫2𝑣	𝑫2𝑣	PROPN
iajs-3671	127	29	𝑗+1	𝑗+1	X
iajs-3671	128	1	=	=	PUNCT
iajs-3671	128	2	𝑬2𝑣	𝑬2𝑣	PROPN
iajs-3671	128	3	𝑗	𝑗	INTJ
iajs-3671	129	1	+	+	CCONJ
iajs-3671	129	2	𝑍2	𝑍2	ADJ
iajs-3671	129	3	,	,	PUNCT
iajs-3671	129	4	𝑗	𝑗	NOUN
iajs-3671	129	5	=	=	NOUN
iajs-3671	129	6	0,1,2	0,1,2	NUM
iajs-3671	129	7	,	,	PUNCT
iajs-3671	129	8	…	…	PUNCT
iajs-3671	129	9	,	,	PUNCT
iajs-3671	129	10	𝑁	𝑁	PROPN
iajs-3671	129	11	,	,	PUNCT
iajs-3671	129	12	(	(	PUNCT
iajs-3671	129	13	36	36	NUM
iajs-3671	129	14	)	)	PUNCT
iajs-3671	129	15	where	where	SCONJ
iajs-3671	129	16	the	the	DET
iajs-3671	129	17	matrices	matrix	NOUN
iajs-3671	129	18	have	have	VERB
iajs-3671	129	19	the	the	DET
iajs-3671	129	20	form	form	NOUN
iajs-3671	129	21	𝐷1	𝐷1	NOUN
iajs-3671	129	22	=	=	PUNCT
iajs-3671	129	23	(	(	PUNCT
iajs-3671	129	24	1	1	NUM
iajs-3671	129	25	+	+	NUM
iajs-3671	129	26	2𝛼	2𝛼	PROPN
iajs-3671	129	27	−𝛼	−𝛼	PROPN
iajs-3671	129	28	0	0	PUNCT
iajs-3671	130	1	⋯	⋯	ADP
iajs-3671	130	2	0	0	NUM
iajs-3671	130	3	0	0	NUM
iajs-3671	130	4	−𝛼	−𝛼	PROPN
iajs-3671	130	5	−𝛼	−𝛼	PROPN
iajs-3671	130	6	1	1	NUM
iajs-3671	130	7	+	+	NUM
iajs-3671	130	8	2𝛼	2𝛼	PROPN
iajs-3671	130	9	−𝛼	−𝛼	PROPN
iajs-3671	130	10	⋯	⋯	ADP
iajs-3671	130	11	0	0	NUM
iajs-3671	130	12	0	0	NUM
iajs-3671	130	13	0	0	NUM
iajs-3671	130	14	⋮	⋮	NOUN
iajs-3671	130	15	⋮	⋮	ADJ
iajs-3671	130	16	⋮	⋮	NOUN
iajs-3671	130	17	⋱	⋱	PUNCT
iajs-3671	130	18	⋮	⋮	NOUN
iajs-3671	130	19	⋮	⋮	ADJ
iajs-3671	130	20	⋮	⋮	NOUN
iajs-3671	130	21	0	0	NUM
iajs-3671	130	22	0	0	NUM
iajs-3671	130	23	0	0	NUM
iajs-3671	130	24	⋯	⋯	VERB
iajs-3671	130	25	−𝛼	−𝛼	PROPN
iajs-3671	130	26	1	1	NUM
iajs-3671	130	27	+	+	NUM
iajs-3671	130	28	2𝛼	2𝛼	PROPN
iajs-3671	130	29	−𝛼	−𝛼	PROPN
iajs-3671	130	30	0	0	NUM
iajs-3671	130	31	0	0	NUM
iajs-3671	130	32	0	0	NUM
iajs-3671	131	1	⋯	⋯	NOUN
iajs-3671	131	2	0	0	SYM
iajs-3671	131	3	−2𝛼	−2𝛼	PROPN
iajs-3671	131	4	1	1	NUM
iajs-3671	131	5	+	+	NUM
iajs-3671	131	6	2𝛼	2𝛼	NUM
iajs-3671	131	7	)	)	PUNCT
iajs-3671	131	8	𝑀×𝑀	𝑀×𝑀	VERB
iajs-3671	131	9	𝐷2	𝐷2	NOUN
iajs-3671	131	10	=	=	SYM
iajs-3671	131	11	(	(	PUNCT
iajs-3671	131	12	2	2	NUM
iajs-3671	131	13	2	2	NUM
iajs-3671	131	14	2	2	NUM
iajs-3671	131	15	2	2	NUM
iajs-3671	131	16	2	2	NUM
iajs-3671	131	17	2	2	NUM
iajs-3671	131	18	0	0	NUM
iajs-3671	131	19	−𝛼	−𝛼	ADJ
iajs-3671	131	20	1	1	NUM
iajs-3671	131	21	+	+	NUM
iajs-3671	131	22	2𝛼	2𝛼	NUM
iajs-3671	131	23	−𝛼	−𝛼	PROPN
iajs-3671	131	24	0	0	NUM
iajs-3671	131	25	0	0	NUM
iajs-3671	131	26	0	0	NUM
iajs-3671	131	27	0	0	NUM
iajs-3671	131	28	0	0	NUM
iajs-3671	132	1	−𝛼	−𝛼	ADJ
iajs-3671	132	2	1	1	NUM
iajs-3671	132	3	+	+	NUM
iajs-3671	132	4	2𝛼	2𝛼	NUM
iajs-3671	132	5	−𝛼	−𝛼	PROPN
iajs-3671	132	6	0	0	NUM
iajs-3671	132	7	0	0	NUM
iajs-3671	132	8	0	0	NUM
iajs-3671	132	9	⋮	⋮	NOUN
iajs-3671	132	10	⋮	⋮	ADJ
iajs-3671	132	11	⋮	⋮	NOUN
iajs-3671	132	12	⋱	⋱	PUNCT
iajs-3671	132	13	⋮	⋮	NOUN
iajs-3671	132	14	⋮	⋮	ADJ
iajs-3671	132	15	⋮	⋮	NOUN
iajs-3671	132	16	0	0	NUM
iajs-3671	132	17	0	0	NUM
iajs-3671	132	18	0	0	NUM
iajs-3671	132	19	⋯	⋯	VERB
iajs-3671	132	20	−𝛼	−𝛼	PROPN
iajs-3671	132	21	1	1	NUM
iajs-3671	132	22	+	+	NUM
iajs-3671	132	23	2𝛼	2𝛼	PROPN
iajs-3671	132	24	−𝛼	−𝛼	PROPN
iajs-3671	132	25	0	0	NUM
iajs-3671	132	26	2	2	NUM
iajs-3671	132	27	2	2	NUM
iajs-3671	132	28	⋯	⋯	SYM
iajs-3671	132	29	2	2	NUM
iajs-3671	132	30	2	2	NUM
iajs-3671	132	31	2	2	NUM
iajs-3671	132	32	)	)	PUNCT
iajs-3671	132	33	𝑀+1×𝑀+1	𝑀+1×𝑀+1	NOUN
iajs-3671	132	34	𝐸1	𝐸1	NOUN
iajs-3671	132	35	=	=	PUNCT
iajs-3671	132	36	(	(	PUNCT
iajs-3671	132	37	𝛾𝑗	𝛾𝑗	INTJ
iajs-3671	132	38	1	1	NUM
iajs-3671	132	39	+	+	CCONJ
iajs-3671	132	40	2𝛾𝑗	2𝛾𝑗	ADJ
iajs-3671	133	1	+	+	CCONJ
iajs-3671	133	2	𝑐𝑗	𝑐𝑗	ADV
iajs-3671	133	3	𝛾𝑗	𝛾𝑗	INTJ
iajs-3671	133	4	0	0	NUM
iajs-3671	133	5	⋯	⋯	VERB
iajs-3671	133	6	0	0	NUM
iajs-3671	133	7	0	0	NUM
iajs-3671	133	8	0	0	NUM
iajs-3671	133	9	0	0	NUM
iajs-3671	133	10	𝛾𝑗	𝛾𝑗	INTJ
iajs-3671	133	11	1	1	NUM
iajs-3671	133	12	+	+	CCONJ
iajs-3671	133	13	2𝛾𝑗	2𝛾𝑗	ADJ
iajs-3671	134	1	+	+	CCONJ
iajs-3671	134	2	𝑐𝑗	𝑐𝑗	INTJ
iajs-3671	134	3	𝛾𝑗	𝛾𝑗	INTJ
iajs-3671	134	4	⋯	⋯	ADP
iajs-3671	134	5	0	0	NUM
iajs-3671	134	6	0	0	NUM
iajs-3671	134	7	0	0	NUM
iajs-3671	134	8	⋮	⋮	NOUN
iajs-3671	134	9	⋮	⋮	ADJ
iajs-3671	134	10	⋮	⋮	ADJ
iajs-3671	134	11	⋮	⋮	PROPN
iajs-3671	134	12	⋱	⋱	PUNCT
iajs-3671	134	13	⋮	⋮	NOUN
iajs-3671	134	14	⋮	⋮	ADJ
iajs-3671	134	15	⋮	⋮	NOUN
iajs-3671	134	16	0	0	NUM
iajs-3671	134	17	0	0	NUM
iajs-3671	134	18	0	0	NUM
iajs-3671	134	19	0	0	NUM
iajs-3671	134	20	⋯	⋯	VERB
iajs-3671	134	21	𝛾𝑗	𝛾𝑗	INTJ
iajs-3671	134	22	1	1	NUM
iajs-3671	134	23	+	+	CCONJ
iajs-3671	134	24	2𝛾𝑗	2𝛾𝑗	ADJ
iajs-3671	135	1	+	+	CCONJ
iajs-3671	135	2	𝑐𝑗	𝑐𝑗	ADV
iajs-3671	135	3	𝛾𝑗	𝛾𝑗	INTJ
iajs-3671	135	4	0	0	NUM
iajs-3671	135	5	0	0	NUM
iajs-3671	135	6	0	0	NUM
iajs-3671	135	7	0	0	NUM
iajs-3671	136	1	⋯	⋯	NOUN
iajs-3671	136	2	0	0	NUM
iajs-3671	136	3	2𝛾𝑗	2𝛾𝑗	NOUN
iajs-3671	136	4	1	1	NUM
iajs-3671	136	5	+	+	NUM
iajs-3671	136	6	2𝛾𝑗	2𝛾𝑗	ADJ
iajs-3671	136	7	+	+	CCONJ
iajs-3671	136	8	𝑐𝑗	𝑐𝑗	X
iajs-3671	136	9	)	)	PUNCT
iajs-3671	136	10	𝑀×𝑀	𝑀×𝑀	VERB
iajs-3671	136	11	𝐸2	𝐸2	NOUN
iajs-3671	136	12	=	=	PUNCT
iajs-3671	136	13	(	(	PUNCT
iajs-3671	136	14	0	0	NUM
iajs-3671	136	15	0	0	NUM
iajs-3671	136	16	0	0	NUM
iajs-3671	136	17	0	0	NUM
iajs-3671	136	18	0	0	NUM
iajs-3671	136	19	0	0	NUM
iajs-3671	136	20	0	0	NUM
iajs-3671	136	21	𝛾𝑗	𝛾𝑗	INTJ
iajs-3671	136	22	1	1	NUM
iajs-3671	136	23	+	+	CCONJ
iajs-3671	136	24	2𝛾𝑗	2𝛾𝑗	ADJ
iajs-3671	137	1	+	+	CCONJ
iajs-3671	137	2	𝑐𝑗	𝑐𝑗	ADV
iajs-3671	137	3	𝛾𝑗	𝛾𝑗	INTJ
iajs-3671	137	4	0	0	NUM
iajs-3671	137	5	0	0	NUM
iajs-3671	137	6	0	0	NUM
iajs-3671	137	7	0	0	NUM
iajs-3671	137	8	0	0	NUM
iajs-3671	137	9	𝛾𝑗	𝛾𝑗	INTJ
iajs-3671	137	10	1	1	NUM
iajs-3671	138	1	+	+	CCONJ
iajs-3671	138	2	2𝛾𝑗	2𝛾𝑗	ADJ
iajs-3671	139	1	+	+	CCONJ
iajs-3671	139	2	𝑐𝑗	𝑐𝑗	ADV
iajs-3671	139	3	𝛾𝑗	𝛾𝑗	INTJ
iajs-3671	139	4	0	0	NUM
iajs-3671	139	5	0	0	NUM
iajs-3671	139	6	0	0	NUM
iajs-3671	139	7	⋮	⋮	NOUN
iajs-3671	139	8	⋮	⋮	ADJ
iajs-3671	139	9	⋮	⋮	NOUN
iajs-3671	139	10	⋱	⋱	PUNCT
iajs-3671	139	11	⋮	⋮	NOUN
iajs-3671	139	12	⋮	⋮	ADJ
iajs-3671	139	13	⋮	⋮	NOUN
iajs-3671	139	14	0	0	NUM
iajs-3671	139	15	0	0	NUM
iajs-3671	139	16	0	0	NUM
iajs-3671	140	1	⋯	⋯	VERB
iajs-3671	140	2	𝛾𝑗	𝛾𝑗	INTJ
iajs-3671	140	3	1	1	NUM
iajs-3671	140	4	+	+	CCONJ
iajs-3671	140	5	2𝛾𝑗	2𝛾𝑗	ADJ
iajs-3671	141	1	+	+	CCONJ
iajs-3671	141	2	𝑐𝑗	𝑐𝑗	ADV
iajs-3671	141	3	𝛾𝑗	𝛾𝑗	INTJ
iajs-3671	141	4	0	0	NUM
iajs-3671	141	5	0	0	NUM
iajs-3671	141	6	0	0	NUM
iajs-3671	142	1	⋯	⋯	ADP
iajs-3671	142	2	0	0	NUM
iajs-3671	142	3	0	0	NUM
iajs-3671	142	4	0	0	NUM
iajs-3671	142	5	)	)	PUNCT
iajs-3671	142	6	𝑀+1×𝑀+1	𝑀+1×𝑀+1	NOUN
iajs-3671	142	7	ihjpas	ihjpas	PROPN
iajs-3671	142	8	.	.	PUNCT
iajs-3671	143	1	2025	2025	NUM
iajs-3671	143	2	,	,	PUNCT
iajs-3671	143	3	38	38	NUM
iajs-3671	143	4	(	(	PUNCT
iajs-3671	143	5	1	1	NUM
iajs-3671	143	6	)	)	PUNCT
iajs-3671	143	7	473	473	NUM
iajs-3671	143	8	𝑍1	𝑍1	NOUN
iajs-3671	143	9	=	=	SYM
iajs-3671	143	10	(	(	PUNCT
iajs-3671	143	11	∆𝑡𝑓1,𝑗	∆𝑡𝑓1,𝑗	PROPN
iajs-3671	143	12	∆𝑡𝑓2,𝑗	∆𝑡𝑓2,𝑗	PROPN
iajs-3671	143	13	⋮	⋮	NOUN
iajs-3671	143	14	∆𝑡𝑓𝑀−1,𝑗	∆𝑡𝑓𝑀−1,𝑗	NOUN
iajs-3671	143	15	∆𝑡𝑓𝑀,𝑗	∆𝑡𝑓𝑀,𝑗	PROPN
iajs-3671	143	16	)	)	PUNCT
iajs-3671	143	17	,	,	PUNCT
iajs-3671	143	18	𝑍2	𝑍2	VERB
iajs-3671	143	19	=	=	SYM
iajs-3671	143	20	(	(	PUNCT
iajs-3671	143	21	0	0	NUM
iajs-3671	143	22	∆𝑡𝑓1,𝑗	∆𝑡𝑓1,𝑗	PROPN
iajs-3671	143	23	∆𝑡𝑓2,𝑗	∆𝑡𝑓2,𝑗	PROPN
iajs-3671	143	24	⋮	⋮	NOUN
iajs-3671	143	25	∆𝑡𝑓𝑀−1,𝑗	∆𝑡𝑓𝑀−1,𝑗	NOUN
iajs-3671	143	26	0	0	NUM
iajs-3671	143	27	)	)	PUNCT
iajs-3671	143	28	,	,	PUNCT
iajs-3671	143	29	where	where	SCONJ
iajs-3671	143	30	,	,	PUNCT
iajs-3671	143	31	𝑣𝑗+1	𝑣𝑗+1	PROPN
iajs-3671	143	32	=	=	SYM
iajs-3671	143	33	(	(	PUNCT
iajs-3671	143	34	𝑢1,𝑗+1	𝑢1,𝑗+1	PROPN
iajs-3671	143	35	,	,	PUNCT
iajs-3671	143	36	𝑢2,𝑗+1	𝑢2,𝑗+1	PROPN
iajs-3671	143	37	,	,	PUNCT
iajs-3671	143	38	…	…	PUNCT
iajs-3671	143	39	,	,	PUNCT
iajs-3671	143	40	𝑢𝑀,𝑗+1	𝑢𝑀,𝑗+1	PROPN
iajs-3671	143	41	)	)	PUNCT
iajs-3671	143	42	and	and	CCONJ
iajs-3671	143	43	𝑣𝑗	𝑣𝑗	ADP
iajs-3671	143	44	=	=	SYM
iajs-3671	143	45	(	(	PUNCT
iajs-3671	143	46	𝑢1,𝑗	𝑢1,𝑗	PROPN
iajs-3671	143	47	,	,	PUNCT
iajs-3671	143	48	𝑢2,𝑗	𝑢2,𝑗	PROPN
iajs-3671	143	49	,	,	PUNCT
iajs-3671	143	50	…	…	PUNCT
iajs-3671	143	51	,	,	PUNCT
iajs-3671	143	52	𝑢𝑀,𝑗	𝑢𝑀,𝑗	NOUN
iajs-3671	143	53	)	)	PUNCT
iajs-3671	143	54	.	.	PUNCT
iajs-3671	144	1	2.2	2.2	NUM
iajs-3671	144	2	stability	stability	NOUN
iajs-3671	144	3	analysis	analysis	NOUN
iajs-3671	144	4	in	in	ADP
iajs-3671	144	5	this	this	DET
iajs-3671	144	6	section	section	NOUN
iajs-3671	144	7	,	,	PUNCT
iajs-3671	144	8	we	we	PRON
iajs-3671	144	9	apply	apply	VERB
iajs-3671	144	10	the	the	DET
iajs-3671	144	11	von	von	PROPN
iajs-3671	144	12	neumann	neumann	PROPN
iajs-3671	144	13	stability	stability	PROPN
iajs-3671	144	14	analysis	analysis	NOUN
iajs-3671	144	15	(	(	PUNCT
iajs-3671	144	16	24	24	NUM
iajs-3671	144	17	,	,	PUNCT
iajs-3671	144	18	31	31	NUM
iajs-3671	144	19	)	)	PUNCT
iajs-3671	144	20	for	for	ADP
iajs-3671	144	21	direct	direct	ADJ
iajs-3671	144	22	problems	problem	NOUN
iajs-3671	144	23	i	i	PRON
iajs-3671	144	24	and	and	CCONJ
iajs-3671	144	25	ii	ii	PROPN
iajs-3671	144	26	.	.	PROPN
iajs-3671	144	27	assume	assume	VERB
iajs-3671	144	28	that	that	SCONJ
iajs-3671	144	29	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3671	144	30	,	,	PUNCT
iajs-3671	144	31	𝑡	𝑡	NOUN
iajs-3671	144	32	)	)	PUNCT
iajs-3671	144	33	=	=	SYM
iajs-3671	145	1	0	0	NUM
iajs-3671	145	2	,	,	PUNCT
iajs-3671	145	3	for	for	ADP
iajs-3671	145	4	simplicity	simplicity	NOUN
iajs-3671	145	5	,	,	PUNCT
iajs-3671	145	6	and	and	CCONJ
iajs-3671	145	7	local	local	ADJ
iajs-3671	145	8	constant	constant	ADJ
iajs-3671	145	9	𝑝𝑗	𝑝𝑗	PROPN
iajs-3671	145	10	=	=	SYM
iajs-3671	145	11	�	�	PROPN
iajs-3671	145	12	̂	̂	PROPN
iajs-3671	145	13	�	�	PROPN
iajs-3671	145	14	for	for	ADP
iajs-3671	145	15	known	know	VERB
iajs-3671	145	16	time	time	NOUN
iajs-3671	145	17	level	level	NOUN
iajs-3671	145	18	in	in	ADP
iajs-3671	145	19	equation	equation	NOUN
iajs-3671	145	20	(	(	PUNCT
iajs-3671	145	21	33	33	NUM
iajs-3671	145	22	)	)	PUNCT
iajs-3671	146	1	where	where	SCONJ
iajs-3671	146	2	�	�	PROPN
iajs-3671	146	3	̂	̂	VERB
iajs-3671	146	4	�	�	NOUN
iajs-3671	146	5	=	=	SYM
iajs-3671	146	6	max	max	PROPN
iajs-3671	146	7	𝑡=[0,𝑇	𝑡=[0,𝑇	PROPN
iajs-3671	146	8	]	]	PUNCT
iajs-3671	146	9	|𝑝(𝑡)|	|𝑝(𝑡)|	NOUN
iajs-3671	146	10	,	,	PUNCT
iajs-3671	146	11	and	and	CCONJ
iajs-3671	146	12	�	�	PROPN
iajs-3671	146	13	̂	̂	VERB
iajs-3671	146	14	�	�	NOUN
iajs-3671	146	15	=	=	SYM
iajs-3671	146	16	max	max	PROPN
iajs-3671	146	17	𝑡=[0,𝑇	𝑡=[0,𝑇	PROPN
iajs-3671	146	18	]	]	PUNCT
iajs-3671	146	19	|𝑎(𝑡)|	|𝑎(𝑡)|	NOUN
iajs-3671	146	20	,	,	PUNCT
iajs-3671	146	21	then	then	ADV
iajs-3671	146	22	we	we	PRON
iajs-3671	146	23	obtain	obtain	VERB
iajs-3671	146	24	:	:	PUNCT
iajs-3671	146	25	−𝛼𝑢𝑖−1,𝑗+1	−𝛼𝑢𝑖−1,𝑗+1	PROPN
iajs-3671	146	26	+	+	CCONJ
iajs-3671	146	27	(	(	PUNCT
iajs-3671	146	28	1	1	NUM
iajs-3671	146	29	+	+	NUM
iajs-3671	146	30	2𝛼)𝑢𝑖,𝑗+1	2𝛼)𝑢𝑖,𝑗+1	NUM
iajs-3671	146	31	−	−	NOUN
iajs-3671	146	32	𝛼𝑢𝑖+1,𝑗+1	𝛼𝑢𝑖+1,𝑗+1	NOUN
iajs-3671	146	33	=	=	SYM
iajs-3671	146	34	𝛾𝑢𝑖−1,𝑗	𝛾𝑢𝑖−1,𝑗	X
iajs-3671	146	35	+	+	CCONJ
iajs-3671	146	36	(	(	PUNCT
iajs-3671	146	37	1	1	NUM
iajs-3671	146	38	−	−	NOUN
iajs-3671	146	39	2𝛾	2𝛾	NOUN
iajs-3671	146	40	+	+	CCONJ
iajs-3671	146	41	∆𝑡	∆𝑡	PROPN
iajs-3671	146	42	∗	∗	NOUN
iajs-3671	146	43	�	�	PROPN
iajs-3671	146	44	̂	̂	NOUN
iajs-3671	146	45	�	�	NOUN
iajs-3671	146	46	)𝑢𝑖,𝑗	)𝑢𝑖,𝑗	PUNCT
iajs-3671	146	47	+	+	ADJ
iajs-3671	146	48	𝛾𝑢𝑖+1,𝑗	𝛾𝑢𝑖+1,𝑗	NOUN
iajs-3671	146	49	(	(	PUNCT
iajs-3671	146	50	37	37	NUM
iajs-3671	146	51	)	)	PUNCT
iajs-3671	146	52	where	where	SCONJ
iajs-3671	146	53	,	,	PUNCT
iajs-3671	146	54	𝛼	𝛼	NOUN
iajs-3671	146	55	=	=	SYM
iajs-3671	146	56	𝑏	𝑏	PROPN
iajs-3671	146	57	(	(	PUNCT
iajs-3671	146	58	∆𝑥)2	∆𝑥)2	INTJ
iajs-3671	146	59	,	,	PUNCT
iajs-3671	146	60	𝛾	𝛾	PROPN
iajs-3671	146	61	=	=	SYM
iajs-3671	146	62	�	�	PROPN
iajs-3671	146	63	̂	̂	NOUN
iajs-3671	146	64	�	�	NOUN
iajs-3671	146	65	∆𝑡	∆𝑡	PROPN
iajs-3671	146	66	(	(	PUNCT
iajs-3671	146	67	∆𝑥)2	∆𝑥)2	INTJ
iajs-3671	146	68	−	−	PROPN
iajs-3671	146	69	𝑏	𝑏	PROPN
iajs-3671	146	70	(	(	PUNCT
iajs-3671	146	71	∆𝑥)2	∆𝑥)2	INTJ
iajs-3671	146	72	,	,	PUNCT
iajs-3671	146	73	(	(	PUNCT
iajs-3671	146	74	38	38	NUM
iajs-3671	146	75	)	)	PUNCT
iajs-3671	146	76	apply	apply	VERB
iajs-3671	146	77	decomposition	decomposition	NOUN
iajs-3671	146	78	of	of	ADP
iajs-3671	146	79	the	the	DET
iajs-3671	146	80	numerical	numerical	ADJ
iajs-3671	146	81	solution	solution	NOUN
iajs-3671	146	82	into	into	ADP
iajs-3671	146	83	a	a	DET
iajs-3671	146	84	fourier	fourier	ADJ
iajs-3671	146	85	sum	sum	NOUN
iajs-3671	146	86	as	as	ADP
iajs-3671	146	87	𝑢𝑖,𝑗	𝑢𝑖,𝑗	NOUN
iajs-3671	147	1	=	=	SYM
iajs-3671	147	2	𝑆𝑗𝑒𝑤𝑖𝜃	𝑆𝑗𝑒𝑤𝑖𝜃	PROPN
iajs-3671	147	3	,	,	PUNCT
iajs-3671	147	4	(	(	PUNCT
iajs-3671	147	5	39	39	NUM
iajs-3671	147	6	)	)	PUNCT
iajs-3671	147	7	where	where	SCONJ
iajs-3671	147	8	s	s	NOUN
iajs-3671	147	9	is	be	AUX
iajs-3671	147	10	the	the	DET
iajs-3671	147	11	amplification	amplification	NOUN
iajs-3671	147	12	factor	factor	NOUN
iajs-3671	147	13	,	,	PUNCT
iajs-3671	147	14	the	the	DET
iajs-3671	147	15	phase	phase	NOUN
iajs-3671	147	16	angle	angle	NOUN
iajs-3671	147	17	𝜃	𝜃	X
iajs-3671	147	18	=	=	NOUN
iajs-3671	147	19	∅ℎ	∅ℎ	ADJ
iajs-3671	147	20	where	where	SCONJ
iajs-3671	147	21	∅	∅	NOUN
iajs-3671	147	22	=	=	SYM
iajs-3671	147	23	2𝜋	2𝜋	NOUN
iajs-3671	147	24	𝑁	𝑁	PROPN
iajs-3671	147	25	and	and	CCONJ
iajs-3671	147	26	𝑤	𝑤	NOUN
iajs-3671	147	27	=	=	SYM
iajs-3671	147	28	√−1	√−1	PROPN
iajs-3671	147	29	.	.	PUNCT
iajs-3671	148	1	the	the	DET
iajs-3671	148	2	amplification	amplification	NOUN
iajs-3671	148	3	factor	factor	NOUN
iajs-3671	148	4	s	s	PART
iajs-3671	148	5	is	be	AUX
iajs-3671	148	6	said	say	VERB
iajs-3671	148	7	to	to	PART
iajs-3671	148	8	satisfy	satisfy	VERB
iajs-3671	148	9	the	the	DET
iajs-3671	148	10	von	von	PROPN
iajs-3671	148	11	neumann	neumann	PROPN
iajs-3671	148	12	condition	condition	NOUN
iajs-3671	148	13	if	if	SCONJ
iajs-3671	148	14	|s|	|s|	NOUN
iajs-3671	148	15	<	<	X
iajs-3671	148	16	1	1	NUM
iajs-3671	148	17	.	.	PUNCT
iajs-3671	148	18	to	to	PART
iajs-3671	148	19	find	find	VERB
iajs-3671	148	20	s	s	NOUN
iajs-3671	148	21	,	,	PUNCT
iajs-3671	148	22	plug	plug	VERB
iajs-3671	148	23	equation	equation	NOUN
iajs-3671	148	24	(	(	PUNCT
iajs-3671	148	25	39	39	NUM
iajs-3671	148	26	)	)	PUNCT
iajs-3671	148	27	into	into	ADP
iajs-3671	148	28	equation	equation	NOUN
iajs-3671	148	29	(	(	PUNCT
iajs-3671	148	30	37	37	NUM
iajs-3671	148	31	)	)	PUNCT
iajs-3671	148	32	as	as	SCONJ
iajs-3671	148	33	follows	follow	VERB
iajs-3671	148	34	:	:	PUNCT
iajs-3671	148	35	−𝛼𝑆𝑗+1𝑒𝑤𝜃(𝑖−1	−𝛼𝑆𝑗+1𝑒𝑤𝜃(𝑖−1	NUM
iajs-3671	148	36	)	)	PUNCT
iajs-3671	149	1	+	+	CCONJ
iajs-3671	149	2	(	(	PUNCT
iajs-3671	149	3	1	1	NUM
iajs-3671	149	4	+	+	NUM
iajs-3671	149	5	2𝛼)𝑆𝑗+1𝑒𝑤𝑖𝜃	2𝛼)𝑆𝑗+1𝑒𝑤𝑖𝜃	NUM
iajs-3671	149	6	−	−	NUM
iajs-3671	149	7	𝛼𝑆𝑗+1𝑒𝑤𝜃(𝑖+1	𝛼𝑆𝑗+1𝑒𝑤𝜃(𝑖+1	NOUN
iajs-3671	149	8	)	)	PUNCT
iajs-3671	149	9	=	=	SYM
iajs-3671	149	10	𝛾𝑆𝑗𝑒𝑤𝜃(𝑖−1	𝛾𝑆𝑗𝑒𝑤𝜃(𝑖−1	X
iajs-3671	149	11	)	)	PUNCT
iajs-3671	149	12	+	+	CCONJ
iajs-3671	149	13	(	(	PUNCT
iajs-3671	149	14	1	1	NUM
iajs-3671	149	15	−	−	NUM
iajs-3671	149	16	2𝛾)𝑆𝑗𝑒𝑤𝜃(𝑖	2𝛾)𝑆𝑗𝑒𝑤𝜃(𝑖	NUM
iajs-3671	149	17	)	)	PUNCT
iajs-3671	149	18	+	+	CCONJ
iajs-3671	149	19	𝛾𝑆𝑗𝑒𝑤𝜃(𝑖+1	𝛾𝑆𝑗𝑒𝑤𝜃(𝑖+1	NOUN
iajs-3671	149	20	)	)	PUNCT
iajs-3671	149	21	,	,	PUNCT
iajs-3671	149	22	(	(	PUNCT
iajs-3671	149	23	40	40	NUM
iajs-3671	149	24	)	)	PUNCT
iajs-3671	149	25	after	after	ADP
iajs-3671	149	26	simplifying	simplify	VERB
iajs-3671	149	27	above	above	ADP
iajs-3671	149	28	equation	equation	NOUN
iajs-3671	149	29	,	,	PUNCT
iajs-3671	149	30	we	we	PRON
iajs-3671	149	31	get	get	VERB
iajs-3671	149	32	:	:	PUNCT
iajs-3671	149	33	−2𝛼	−2𝛼	PROPN
iajs-3671	149	34	𝑆	𝑆	PROPN
iajs-3671	149	35	(	(	PUNCT
iajs-3671	149	36	𝑒−𝑤𝜃	𝑒−𝑤𝜃	NOUN
iajs-3671	149	37	+	+	CCONJ
iajs-3671	149	38	𝑒𝑤𝜃	𝑒𝑤𝜃	ADJ
iajs-3671	149	39	2	2	NUM
iajs-3671	149	40	)	)	PUNCT
iajs-3671	149	41	+	+	CCONJ
iajs-3671	149	42	(	(	PUNCT
iajs-3671	149	43	1	1	NUM
iajs-3671	149	44	+	+	NUM
iajs-3671	149	45	2𝛼)𝑆	2𝛼)𝑆	PROPN
iajs-3671	149	46	=	=	SYM
iajs-3671	149	47	2𝛾	2𝛾	NUM
iajs-3671	149	48	(	(	PUNCT
iajs-3671	149	49	𝑒−𝑤𝜃	𝑒−𝑤𝜃	NOUN
iajs-3671	149	50	+	+	CCONJ
iajs-3671	149	51	𝑒𝑤𝜃	𝑒𝑤𝜃	ADJ
iajs-3671	149	52	2	2	NUM
iajs-3671	149	53	)	)	PUNCT
iajs-3671	149	54	+	+	CCONJ
iajs-3671	149	55	(	(	PUNCT
iajs-3671	149	56	1	1	NUM
iajs-3671	149	57	−	−	NOUN
iajs-3671	149	58	2𝛾	2𝛾	NOUN
iajs-3671	149	59	)	)	PUNCT
iajs-3671	149	60	,	,	PUNCT
iajs-3671	149	61	(	(	PUNCT
iajs-3671	149	62	41	41	NUM
iajs-3671	149	63	)	)	PUNCT
iajs-3671	149	64	ihjpas	ihjpa	NOUN
iajs-3671	149	65	.	.	PUNCT
iajs-3671	150	1	2025	2025	NUM
iajs-3671	150	2	,	,	PUNCT
iajs-3671	150	3	38	38	NUM
iajs-3671	150	4	(	(	PUNCT
iajs-3671	150	5	1	1	NUM
iajs-3671	150	6	)	)	PUNCT
iajs-3671	150	7	474	474	NUM
iajs-3671	150	8	this	this	DET
iajs-3671	150	9	equation	equation	NOUN
iajs-3671	150	10	gives	give	VERB
iajs-3671	150	11	the	the	DET
iajs-3671	150	12	following	following	NOUN
iajs-3671	150	13	:	:	PUNCT
iajs-3671	150	14	(	(	PUNCT
iajs-3671	150	15	(	(	PUNCT
iajs-3671	150	16	1	1	NUM
iajs-3671	150	17	+	+	NUM
iajs-3671	150	18	2𝛼	2𝛼	NUM
iajs-3671	150	19	)	)	PUNCT
iajs-3671	151	1	−	−	PROPN
iajs-3671	151	2	2𝛼	2𝛼	PROPN
iajs-3671	151	3	cos	cos	PROPN
iajs-3671	151	4	𝜃)𝑆	𝜃)𝑆	NOUN
iajs-3671	151	5	=	=	SYM
iajs-3671	151	6	(	(	PUNCT
iajs-3671	151	7	1	1	NUM
iajs-3671	151	8	−	−	NOUN
iajs-3671	151	9	2𝛾	2𝛾	NOUN
iajs-3671	151	10	)	)	PUNCT
iajs-3671	152	1	+	+	NUM
iajs-3671	152	2	2𝛾	2𝛾	NUM
iajs-3671	152	3	cos	cos	PROPN
iajs-3671	152	4	𝜃	𝜃	X
iajs-3671	152	5	(	(	PUNCT
iajs-3671	152	6	42	42	NUM
iajs-3671	152	7	)	)	PUNCT
iajs-3671	152	8	equation	equation	NOUN
iajs-3671	152	9	(	(	PUNCT
iajs-3671	152	10	42	42	NUM
iajs-3671	152	11	)	)	PUNCT
iajs-3671	152	12	which	which	PRON
iajs-3671	152	13	can	can	AUX
iajs-3671	152	14	be	be	AUX
iajs-3671	152	15	written	write	VERB
iajs-3671	152	16	as	as	ADP
iajs-3671	152	17	,	,	PUNCT
iajs-3671	152	18	𝑆	𝑆	PROPN
iajs-3671	152	19	=	=	SYM
iajs-3671	152	20	(	(	PUNCT
iajs-3671	152	21	1	1	NUM
iajs-3671	152	22	−	−	NOUN
iajs-3671	152	23	2𝛾	2𝛾	NOUN
iajs-3671	152	24	)	)	PUNCT
iajs-3671	153	1	+	+	NUM
iajs-3671	153	2	2𝛾	2𝛾	NUM
iajs-3671	153	3	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3671	153	4	𝜃	𝜃	X
iajs-3671	153	5	(	(	PUNCT
iajs-3671	153	6	1	1	NUM
iajs-3671	153	7	+	+	NUM
iajs-3671	153	8	2𝛼	2𝛼	NUM
iajs-3671	153	9	)	)	PUNCT
iajs-3671	154	1	−	−	PROPN
iajs-3671	154	2	2𝛼	2𝛼	NUM
iajs-3671	154	3	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3671	154	4	𝜃	𝜃	X
iajs-3671	154	5	.	.	PUNCT
iajs-3671	155	1	(	(	PUNCT
iajs-3671	155	2	43	43	NUM
iajs-3671	155	3	)	)	PUNCT
iajs-3671	155	4	in	in	ADP
iajs-3671	155	5	order	order	NOUN
iajs-3671	155	6	to	to	PART
iajs-3671	155	7	ensure	ensure	VERB
iajs-3671	155	8	the	the	DET
iajs-3671	155	9	stability	stability	NOUN
iajs-3671	155	10	,	,	PUNCT
iajs-3671	155	11	the	the	DET
iajs-3671	155	12	last	last	ADJ
iajs-3671	155	13	quantity	quantity	NOUN
iajs-3671	155	14	should	should	AUX
iajs-3671	155	15	be	be	AUX
iajs-3671	155	16	less	less	ADJ
iajs-3671	155	17	than	than	ADP
iajs-3671	155	18	one	one	NUM
iajs-3671	155	19	in	in	ADP
iajs-3671	155	20	the	the	DET
iajs-3671	155	21	sense	sense	NOUN
iajs-3671	155	22	of	of	ADP
iajs-3671	155	23	absolute	absolute	ADJ
iajs-3671	155	24	value	value	NOUN
iajs-3671	155	25	,	,	PUNCT
iajs-3671	155	26	that	that	PRON
iajs-3671	155	27	is	be	AUX
iajs-3671	155	28	|s|	|s|	NOUN
iajs-3671	155	29	=	=	SYM
iajs-3671	155	30	|	|	NOUN
iajs-3671	155	31	(	(	PUNCT
iajs-3671	155	32	1	1	NUM
iajs-3671	155	33	−	−	NOUN
iajs-3671	155	34	2𝛾	2𝛾	NOUN
iajs-3671	155	35	)	)	PUNCT
iajs-3671	156	1	+	+	NUM
iajs-3671	156	2	2𝛾	2𝛾	NUM
iajs-3671	156	3	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3671	156	4	𝜃	𝜃	X
iajs-3671	156	5	(	(	PUNCT
iajs-3671	156	6	1	1	NUM
iajs-3671	156	7	+	+	NUM
iajs-3671	156	8	2𝛼	2𝛼	NUM
iajs-3671	156	9	)	)	PUNCT
iajs-3671	157	1	−	−	PROPN
iajs-3671	158	1	2𝛼	2𝛼	NUM
iajs-3671	158	2	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3671	159	1	𝜃	𝜃	X
iajs-3671	159	2	|	|	ADV
iajs-3671	159	3	<	<	X
iajs-3671	159	4	1	1	NUM
iajs-3671	159	5	(	(	PUNCT
iajs-3671	159	6	44	44	NUM
iajs-3671	159	7	)	)	PUNCT
iajs-3671	159	8	this	this	PRON
iajs-3671	159	9	gives	give	VERB
iajs-3671	159	10	|(1	|(1	PROPN
iajs-3671	159	11	+	+	CCONJ
iajs-3671	159	12	2𝛼	2𝛼	NUM
iajs-3671	159	13	)	)	PUNCT
iajs-3671	160	1	−	−	PROPN
iajs-3671	161	1	2𝛼	2𝛼	PROPN
iajs-3671	161	2	𝑐𝑜𝑠	𝑐𝑜𝑠	NOUN
iajs-3671	161	3	𝜃|	𝜃|	PROPN
iajs-3671	161	4	≤	≤	NUM
iajs-3671	161	5	|1	|1	NUM
iajs-3671	162	1	+	+	NUM
iajs-3671	162	2	2𝛼|	2𝛼|	NUM
iajs-3671	162	3	+	+	SYM
iajs-3671	162	4	2𝛼|cos	2𝛼|cos	NUM
iajs-3671	162	5	𝜃|	𝜃|	NOUN
iajs-3671	162	6	≤	≤	NUM
iajs-3671	162	7	|1	|1	NUM
iajs-3671	163	1	+	+	NUM
iajs-3671	163	2	2𝛼|	2𝛼|	NUM
iajs-3671	163	3	+	+	CCONJ
iajs-3671	163	4	2𝛼	2𝛼	NUM
iajs-3671	163	5	,	,	PUNCT
iajs-3671	163	6	(	(	PUNCT
iajs-3671	163	7	45	45	NUM
iajs-3671	163	8	)	)	PUNCT
iajs-3671	163	9	since	since	SCONJ
iajs-3671	163	10	𝑀	𝑀	PROPN
iajs-3671	163	11	>	>	X
iajs-3671	163	12	0	0	PROPN
iajs-3671	163	13	,	,	PUNCT
iajs-3671	163	14	𝛼	𝛼	NOUN
iajs-3671	163	15	=	=	SYM
iajs-3671	163	16	𝑏	𝑏	PROPN
iajs-3671	163	17	(	(	PUNCT
iajs-3671	163	18	∆𝑥)2	∆𝑥)2	PROPN
iajs-3671	163	19	=	=	SYM
iajs-3671	163	20	𝑏𝑀2	𝑏𝑀2	PROPN
iajs-3671	163	21	,	,	PUNCT
iajs-3671	163	22	applying	apply	VERB
iajs-3671	163	23	in	in	ADP
iajs-3671	163	24	equation	equation	NOUN
iajs-3671	163	25	(	(	PUNCT
iajs-3671	163	26	45	45	NUM
iajs-3671	163	27	)	)	PUNCT
iajs-3671	163	28	this	this	PRON
iajs-3671	163	29	gives	give	VERB
iajs-3671	163	30	≤	≤	NOUN
iajs-3671	163	31	|1	|1	PRON
iajs-3671	164	1	+	+	NUM
iajs-3671	164	2	2𝑏𝑀2|	2𝑏𝑀2|	NUM
iajs-3671	164	3	+	+	CCONJ
iajs-3671	164	4	2𝑏𝑀2	2𝑏𝑀2	NUM
iajs-3671	164	5	=	=	SYM
iajs-3671	164	6	1	1	NUM
iajs-3671	164	7	+	+	SYM
iajs-3671	164	8	2𝑏𝑀2	2𝑏𝑀2	NUM
iajs-3671	164	9	+	+	CCONJ
iajs-3671	164	10	𝑏𝑀2	𝑏𝑀2	PROPN
iajs-3671	164	11	=	=	SYM
iajs-3671	164	12	1	1	NUM
iajs-3671	165	1	+	+	CCONJ
iajs-3671	165	2	4𝑏𝑀2	4𝑏𝑀2	NUM
iajs-3671	165	3	>	>	SYM
iajs-3671	165	4	1	1	NUM
iajs-3671	165	5	(	(	PUNCT
iajs-3671	165	6	46	46	NUM
iajs-3671	165	7	)	)	PUNCT
iajs-3671	165	8	since	since	SCONJ
iajs-3671	165	9	b	b	PROPN
iajs-3671	165	10	>	>	X
iajs-3671	165	11	0	0	NUM
iajs-3671	166	1	we	we	PRON
iajs-3671	166	2	guarantee	guarantee	VERB
iajs-3671	166	3	that	that	SCONJ
iajs-3671	166	4	|s|	|s|	VERB
iajs-3671	166	5	<	<	X
iajs-3671	166	6	1	1	NUM
iajs-3671	166	7	,	,	PUNCT
iajs-3671	166	8	therefor	therefor	ADP
iajs-3671	166	9	method	method	NOUN
iajs-3671	166	10	is	be	AUX
iajs-3671	166	11	unconditionally	unconditionally	ADV
iajs-3671	166	12	stable	stable	ADJ
iajs-3671	166	13	.	.	PUNCT
iajs-3671	167	1	the	the	DET
iajs-3671	167	2	convergence	convergence	NOUN
iajs-3671	167	3	of	of	ADP
iajs-3671	167	4	the	the	DET
iajs-3671	167	5	proposed	propose	VERB
iajs-3671	167	6	scheme	scheme	NOUN
iajs-3671	167	7	is	be	AUX
iajs-3671	167	8	obtained	obtain	VERB
iajs-3671	167	9	from	from	ADP
iajs-3671	167	10	the	the	DET
iajs-3671	167	11	lax	lax	ADJ
iajs-3671	167	12	-	-	PUNCT
iajs-3671	167	13	richtmyer	richtmyer	NOUN
iajs-3671	167	14	equivalence	equivalence	NOUN
iajs-3671	167	15	theorem	theorem	VERB
iajs-3671	167	16	,	,	PUNCT
iajs-3671	167	17	which	which	PRON
iajs-3671	167	18	states	state	VERB
iajs-3671	167	19	that	that	SCONJ
iajs-3671	167	20	"	"	PUNCT
iajs-3671	167	21	a	a	DET
iajs-3671	167	22	consistent	consistent	ADJ
iajs-3671	167	23	finite	finite	ADJ
iajs-3671	167	24	-	-	PUNCT
iajs-3671	167	25	difference	difference	NOUN
iajs-3671	167	26	scheme	scheme	NOUN
iajs-3671	167	27	for	for	ADP
iajs-3671	167	28	a	a	DET
iajs-3671	167	29	linear	linear	ADJ
iajs-3671	167	30	non	non	ADJ
iajs-3671	167	31	-	-	ADJ
iajs-3671	167	32	fractional	fractional	ADJ
iajs-3671	167	33	partial	partial	ADJ
iajs-3671	167	34	differential	differential	NOUN
iajs-3671	167	35	equation	equation	NOUN
iajs-3671	167	36	for	for	ADP
iajs-3671	167	37	which	which	PRON
iajs-3671	167	38	the	the	DET
iajs-3671	167	39	initial	initial	ADJ
iajs-3671	167	40	-	-	PUNCT
iajs-3671	167	41	value	value	NOUN
iajs-3671	167	42	problem	problem	NOUN
iajs-3671	167	43	is	be	AUX
iajs-3671	167	44	well	well	ADV
iajs-3671	167	45	posed	pose	VERB
iajs-3671	167	46	is	be	AUX
iajs-3671	167	47	convergent	convergent	ADJ
iajs-3671	167	48	if	if	SCONJ
iajs-3671	167	49	and	and	CCONJ
iajs-3671	167	50	only	only	ADV
iajs-3671	167	51	if	if	SCONJ
iajs-3671	167	52	it	it	PRON
iajs-3671	167	53	is	be	AUX
iajs-3671	167	54	stable	stable	ADJ
iajs-3671	167	55	”	"	PUNCT
iajs-3671	167	56	.	.	PUNCT
iajs-3671	168	1	for	for	ADP
iajs-3671	168	2	a	a	DET
iajs-3671	168	3	proof	proof	NOUN
iajs-3671	168	4	,	,	PUNCT
iajs-3671	168	5	see	see	VERB
iajs-3671	168	6	(	(	PUNCT
iajs-3671	168	7	32	32	NUM
iajs-3671	168	8	)	)	PUNCT
iajs-3671	168	9	.	.	PUNCT
iajs-3671	169	1	2.3	2.3	NUM
iajs-3671	169	2	examples	example	NOUN
iajs-3671	169	3	of	of	ADP
iajs-3671	169	4	direct	direct	ADJ
iajs-3671	169	5	problems	problem	NOUN
iajs-3671	169	6	2.3.1	2.3.1	NUM
iajs-3671	169	7	example	example	NOUN
iajs-3671	169	8	for	for	ADP
iajs-3671	169	9	problem	problem	NOUN
iajs-3671	169	10	i	i	PRON
iajs-3671	169	11	we	we	PRON
iajs-3671	169	12	consider	consider	VERB
iajs-3671	169	13	the	the	DET
iajs-3671	169	14	direct	direct	ADJ
iajs-3671	169	15	problem	problem	NOUN
iajs-3671	169	16	i	i	PRON
iajs-3671	169	17	equations	equation	VERB
iajs-3671	169	18	(	(	PUNCT
iajs-3671	169	19	1)-(4	1)-(4	NUM
iajs-3671	169	20	)	)	PUNCT
iajs-3671	169	21	with	with	ADP
iajs-3671	169	22	t=1	t=1	ADV
iajs-3671	169	23	with	with	ADP
iajs-3671	169	24	𝑎	𝑎	PROPN
iajs-3671	169	25	=	=	SYM
iajs-3671	169	26	𝑏	𝑏	NOUN
iajs-3671	169	27	=	=	NOUN
iajs-3671	169	28	0.01	0.01	NUM
iajs-3671	169	29	and	and	CCONJ
iajs-3671	169	30	the	the	DET
iajs-3671	169	31	following	follow	VERB
iajs-3671	169	32	input	input	NOUN
iajs-3671	169	33	data	datum	NOUN
iajs-3671	169	34	:	:	PUNCT
iajs-3671	169	35	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	169	36	,	,	PUNCT
iajs-3671	169	37	0	0	NUM
iajs-3671	169	38	)	)	PUNCT
iajs-3671	169	39	=	=	SYM
iajs-3671	169	40	cos(2𝜋𝑥	cos(2𝜋𝑥	NUM
iajs-3671	169	41	)	)	PUNCT
iajs-3671	169	42	𝑒1	𝑒1	NOUN
iajs-3671	169	43	,	,	PUNCT
iajs-3671	169	44	𝑥	𝑥	PRON
iajs-3671	169	45	∈	∈	PROPN
iajs-3671	170	1	[	[	X
iajs-3671	170	2	0,1	0,1	NUM
iajs-3671	170	3	]	]	PUNCT
iajs-3671	170	4	(	(	PUNCT
iajs-3671	170	5	47	47	NUM
iajs-3671	170	6	)	)	PUNCT
iajs-3671	170	7	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	170	8	)	)	PUNCT
iajs-3671	170	9	=	=	SYM
iajs-3671	170	10	cos(2	cos(2	VERB
iajs-3671	170	11	𝜋	𝜋	NOUN
iajs-3671	170	12	𝑡	𝑡	PROPN
iajs-3671	170	13	)	)	PUNCT
iajs-3671	170	14	,	,	PUNCT
iajs-3671	170	15	𝑡	𝑡	PROPN
iajs-3671	170	16	∈	∈	PROPN
iajs-3671	171	1	[	[	X
iajs-3671	171	2	0	0	NUM
iajs-3671	171	3	,	,	PUNCT
iajs-3671	171	4	𝑇	𝑇	PROPN
iajs-3671	171	5	]	]	X
iajs-3671	171	6	(	(	PUNCT
iajs-3671	171	7	48	48	NUM
iajs-3671	171	8	)	)	PUNCT
iajs-3671	171	9	ihjpas	ihjpa	NOUN
iajs-3671	171	10	.	.	PUNCT
iajs-3671	172	1	2025	2025	NUM
iajs-3671	172	2	,	,	PUNCT
iajs-3671	172	3	38	38	NUM
iajs-3671	172	4	(	(	PUNCT
iajs-3671	172	5	1	1	NUM
iajs-3671	172	6	)	)	PUNCT
iajs-3671	172	7	475	475	NUM
iajs-3671	172	8	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3671	172	9	,	,	PUNCT
iajs-3671	172	10	𝑡	𝑡	NOUN
iajs-3671	172	11	)	)	PUNCT
iajs-3671	172	12	=	=	SYM
iajs-3671	172	13	𝑒−𝑡(−0.367879	𝑒−𝑡(−0.367879	NOUN
iajs-3671	172	14	−	−	NOUN
iajs-3671	172	15	0.367879	0.367879	NUM
iajs-3671	172	16	cos(2𝜋	cos(2𝜋	PROPN
iajs-3671	172	17	𝑡	𝑡	X
iajs-3671	172	18	)	)	PUNCT
iajs-3671	172	19	)	)	PUNCT
iajs-3671	173	1	cos(2𝜋𝑥	cos(2𝜋𝑥	NUM
iajs-3671	173	2	)	)	PUNCT
iajs-3671	174	1	,	,	PUNCT
iajs-3671	174	2	(	(	PUNCT
iajs-3671	174	3	𝑥	𝑥	NOUN
iajs-3671	174	4	,	,	PUNCT
iajs-3671	174	5	𝑡	𝑡	NOUN
iajs-3671	174	6	)	)	PUNCT
iajs-3671	174	7	∈	∈	PROPN
iajs-3671	174	8	𝑄𝑇	𝑄𝑇	PROPN
iajs-3671	174	9	(	(	PUNCT
iajs-3671	174	10	49	49	NUM
iajs-3671	174	11	)	)	PUNCT
iajs-3671	174	12	the	the	DET
iajs-3671	174	13	analytic	analytic	ADJ
iajs-3671	174	14	solution	solution	NOUN
iajs-3671	174	15	is	be	AUX
iajs-3671	174	16	given	give	VERB
iajs-3671	174	17	by	by	ADP
iajs-3671	174	18	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	174	19	,	,	PUNCT
iajs-3671	174	20	𝑡	𝑡	X
iajs-3671	174	21	)	)	PUNCT
iajs-3671	174	22	=	=	SYM
iajs-3671	174	23	𝑒−1−𝑡	𝑒−1−𝑡	NUM
iajs-3671	174	24	cos(2𝜋𝑥	cos(2𝜋𝑥	NUM
iajs-3671	174	25	)	)	PUNCT
iajs-3671	174	26	,	,	PUNCT
iajs-3671	174	27	(	(	PUNCT
iajs-3671	174	28	𝑥	𝑥	NOUN
iajs-3671	174	29	,	,	PUNCT
iajs-3671	174	30	𝑡	𝑡	NOUN
iajs-3671	174	31	)	)	PUNCT
iajs-3671	174	32	∈	∈	PROPN
iajs-3671	174	33	𝑄𝑇	𝑄𝑇	PROPN
iajs-3671	174	34	,	,	PUNCT
iajs-3671	174	35	(	(	PUNCT
iajs-3671	174	36	50	50	NUM
iajs-3671	174	37	)	)	PUNCT
iajs-3671	174	38	and	and	CCONJ
iajs-3671	174	39	overdetermination	overdetermination	NOUN
iajs-3671	174	40	condition	condition	NOUN
iajs-3671	174	41	ℎ1(𝑡	ℎ1(𝑡	NOUN
iajs-3671	174	42	)	)	PUNCT
iajs-3671	174	43	=	=	SYM
iajs-3671	174	44	−𝑒	−𝑒	NOUN
iajs-3671	174	45	−1−𝑡	−1−𝑡	NOUN
iajs-3671	174	46	,	,	PUNCT
iajs-3671	174	47	𝑡	𝑡	PROPN
iajs-3671	174	48	∈	∈	PROPN
iajs-3671	175	1	[	[	X
iajs-3671	175	2	0	0	NUM
iajs-3671	175	3	,	,	PUNCT
iajs-3671	175	4	𝑇	𝑇	PROPN
iajs-3671	175	5	]	]	PUNCT
iajs-3671	175	6	.	.	PUNCT
iajs-3671	176	1	(	(	PUNCT
iajs-3671	176	2	51	51	NUM
iajs-3671	176	3	)	)	PUNCT
iajs-3671	176	4	the	the	DET
iajs-3671	176	5	numerical	numerical	ADJ
iajs-3671	176	6	and	and	CCONJ
iajs-3671	176	7	exact	exact	ADJ
iajs-3671	176	8	solution	solution	NOUN
iajs-3671	176	9	of	of	ADP
iajs-3671	176	10	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	176	11	,	,	PUNCT
iajs-3671	176	12	𝑡	𝑡	PROPN
iajs-3671	176	13	)	)	PUNCT
iajs-3671	176	14	and	and	CCONJ
iajs-3671	176	15	the	the	DET
iajs-3671	176	16	absolute	absolute	ADJ
iajs-3671	176	17	error	error	NOUN
iajs-3671	176	18	is	be	AUX
iajs-3671	176	19	plotted	plot	VERB
iajs-3671	176	20	in	in	ADP
iajs-3671	176	21	figure	figure	NOUN
iajs-3671	176	22	1	1	NUM
iajs-3671	176	23	.	.	PUNCT
iajs-3671	177	1	when	when	SCONJ
iajs-3671	177	2	𝑀	𝑀	PROPN
iajs-3671	177	3	=	=	SYM
iajs-3671	177	4	𝑁	𝑁	PROPN
iajs-3671	177	5	=	=	NOUN
iajs-3671	177	6	40	40	NUM
iajs-3671	177	7	.	.	PUNCT
iajs-3671	178	1	this	this	DET
iajs-3671	178	2	figure	figure	NOUN
iajs-3671	178	3	shows	show	VERB
iajs-3671	178	4	the	the	DET
iajs-3671	178	5	excellent	excellent	ADJ
iajs-3671	178	6	matching	matching	NOUN
iajs-3671	178	7	with	with	ADP
iajs-3671	178	8	the	the	DET
iajs-3671	178	9	error	error	NOUN
iajs-3671	178	10	magnitude	magnitude	NOUN
iajs-3671	178	11	of	of	ADP
iajs-3671	178	12	order	order	NOUN
iajs-3671	178	13	o(10−3	o(10−3	NOUN
iajs-3671	178	14	)	)	PUNCT
iajs-3671	178	15	.	.	PUNCT
iajs-3671	179	1	figure	figure	NOUN
iajs-3671	179	2	2	2	NUM
iajs-3671	179	3	.	.	PUNCT
iajs-3671	179	4	presents	present	VERB
iajs-3671	179	5	the	the	DET
iajs-3671	179	6	comparison	comparison	NOUN
iajs-3671	179	7	between	between	ADP
iajs-3671	179	8	the	the	DET
iajs-3671	179	9	exact	exact	ADJ
iajs-3671	179	10	solution	solution	NOUN
iajs-3671	179	11	and	and	CCONJ
iajs-3671	179	12	numerical	numerical	ADJ
iajs-3671	179	13	for	for	ADP
iajs-3671	179	14	desired	desire	VERB
iajs-3671	179	15	outputs	output	NOUN
iajs-3671	179	16	ℎ1(𝑡	ℎ1(𝑡	NOUN
iajs-3671	179	17	)	)	PUNCT
iajs-3671	179	18	.	.	PUNCT
iajs-3671	180	1	also	also	ADV
iajs-3671	180	2	,	,	PUNCT
iajs-3671	180	3	excellent	excellent	ADJ
iajs-3671	180	4	agreements	agreement	NOUN
iajs-3671	180	5	were	be	AUX
iajs-3671	180	6	obtained	obtain	VERB
iajs-3671	180	7	.	.	PUNCT
iajs-3671	181	1	figure	figure	NOUN
iajs-3671	181	2	1	1	NUM
iajs-3671	181	3	.	.	PUNCT
iajs-3671	182	1	the	the	DET
iajs-3671	182	2	exact	exact	ADJ
iajs-3671	182	3	and	and	CCONJ
iajs-3671	182	4	numerical	numerical	ADJ
iajs-3671	182	5	solutions	solution	NOUN
iajs-3671	182	6	with	with	ADP
iajs-3671	182	7	an	an	DET
iajs-3671	182	8	absolute	absolute	ADJ
iajs-3671	182	9	error	error	NOUN
iajs-3671	182	10	when	when	SCONJ
iajs-3671	182	11	m	m	VERB
iajs-3671	182	12	=	=	SYM
iajs-3671	182	13	n	n	PROPN
iajs-3671	182	14	=	=	SYM
iajs-3671	182	15	40	40	NUM
iajs-3671	182	16	,	,	PUNCT
iajs-3671	182	17	for	for	ADP
iajs-3671	182	18	example	example	NOUN
iajs-3671	182	19	,	,	PUNCT
iajs-3671	182	20	of	of	ADP
iajs-3671	182	21	the	the	DET
iajs-3671	182	22	inverse	inverse	NOUN
iajs-3671	182	23	problem	problem	NOUN
iajs-3671	182	24	i.	i.	PROPN
iajs-3671	182	25	ihjpas	ihjpas	PROPN
iajs-3671	182	26	.	.	PUNCT
iajs-3671	183	1	2025	2025	NUM
iajs-3671	183	2	,	,	PUNCT
iajs-3671	183	3	38	38	NUM
iajs-3671	183	4	(	(	PUNCT
iajs-3671	183	5	1	1	NUM
iajs-3671	183	6	)	)	PUNCT
iajs-3671	183	7	476	476	NUM
iajs-3671	183	8	figure	figure	NOUN
iajs-3671	183	9	2	2	NUM
iajs-3671	183	10	.	.	PUNCT
iajs-3671	184	1	the	the	DET
iajs-3671	184	2	required	require	VERB
iajs-3671	184	3	output	output	NOUN
iajs-3671	184	4	ℎ1(𝑡	ℎ1(𝑡	NOUN
iajs-3671	184	5	)	)	PUNCT
iajs-3671	184	6	,	,	PUNCT
iajs-3671	184	7	with	with	ADP
iajs-3671	184	8	𝑁	𝑁	PROPN
iajs-3671	184	9	=	=	PUNCT
iajs-3671	184	10	𝑀	𝑀	PROPN
iajs-3671	184	11	=	=	NUM
iajs-3671	184	12	40	40	NUM
iajs-3671	184	13	,	,	PUNCT
iajs-3671	184	14	for	for	ADP
iajs-3671	184	15	example	example	NOUN
iajs-3671	184	16	of	of	ADP
iajs-3671	184	17	inverse	inverse	NOUN
iajs-3671	184	18	problem	problem	NOUN
iajs-3671	184	19	i.	i.	PROPN
iajs-3671	184	20	2.3.2	2.3.2	NUM
iajs-3671	184	21	example	example	NOUN
iajs-3671	184	22	of	of	ADP
iajs-3671	184	23	direct	direct	ADJ
iajs-3671	184	24	problem	problem	NOUN
iajs-3671	184	25	ii	ii	PROPN
iajs-3671	184	26	consider	consider	VERB
iajs-3671	184	27	the	the	DET
iajs-3671	184	28	direct	direct	ADJ
iajs-3671	184	29	problem	problem	NOUN
iajs-3671	184	30	ii	ii	PROPN
iajs-3671	184	31	equations	equation	NOUN
iajs-3671	184	32	(	(	PUNCT
iajs-3671	184	33	1)-(3	1)-(3	NUM
iajs-3671	184	34	)	)	PUNCT
iajs-3671	184	35	and	and	CCONJ
iajs-3671	184	36	(	(	PUNCT
iajs-3671	184	37	5	5	NUM
iajs-3671	184	38	)	)	PUNCT
iajs-3671	184	39	with	with	ADP
iajs-3671	184	40	t=1	t=1	PROPN
iajs-3671	184	41	,	,	PUNCT
iajs-3671	184	42	𝑥0	𝑥0	NOUN
iajs-3671	184	43	=	=	SYM
iajs-3671	184	44	1	1	NUM
iajs-3671	184	45	2	2	NUM
iajs-3671	184	46	,	,	PUNCT
iajs-3671	184	47	𝑎	𝑎	NOUN
iajs-3671	184	48	=	=	SYM
iajs-3671	184	49	𝑏	𝑏	NOUN
iajs-3671	184	50	=	=	NOUN
iajs-3671	184	51	0.01	0.01	NUM
iajs-3671	184	52	and	and	CCONJ
iajs-3671	184	53	the	the	DET
iajs-3671	184	54	following	follow	VERB
iajs-3671	184	55	input	input	NOUN
iajs-3671	184	56	data	datum	NOUN
iajs-3671	184	57	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	184	58	,	,	PUNCT
iajs-3671	184	59	0	0	NUM
iajs-3671	184	60	)	)	PUNCT
iajs-3671	184	61	=	=	SYM
iajs-3671	184	62	−	−	PROPN
iajs-3671	184	63	cos(2𝜋𝑥	cos(2𝜋𝑥	NUM
iajs-3671	184	64	)	)	PUNCT
iajs-3671	184	65	𝑒1	𝑒1	NOUN
iajs-3671	184	66	,	,	PUNCT
iajs-3671	184	67	𝑥	𝑥	PRON
iajs-3671	184	68	∈	∈	PROPN
iajs-3671	185	1	[	[	X
iajs-3671	185	2	0,1	0,1	NUM
iajs-3671	185	3	]	]	PUNCT
iajs-3671	185	4	,	,	PUNCT
iajs-3671	185	5	(	(	PUNCT
iajs-3671	185	6	52	52	NUM
iajs-3671	185	7	)	)	PUNCT
iajs-3671	185	8	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	185	9	)	)	PUNCT
iajs-3671	185	10	=	=	NOUN
iajs-3671	185	11	sin(2	sin(2	ADJ
iajs-3671	185	12	𝜋	𝜋	NOUN
iajs-3671	185	13	𝑡	𝑡	PROPN
iajs-3671	185	14	)	)	PUNCT
iajs-3671	185	15	,	,	PUNCT
iajs-3671	185	16	𝑡	𝑡	PROPN
iajs-3671	185	17	∈	∈	PROPN
iajs-3671	186	1	[	[	X
iajs-3671	186	2	0	0	NUM
iajs-3671	186	3	,	,	PUNCT
iajs-3671	186	4	𝑇	𝑇	PROPN
iajs-3671	186	5	]	]	X
iajs-3671	186	6	(	(	PUNCT
iajs-3671	186	7	53	53	NUM
iajs-3671	186	8	)	)	PUNCT
iajs-3671	186	9	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3671	186	10	,	,	PUNCT
iajs-3671	186	11	𝑡	𝑡	NOUN
iajs-3671	186	12	)	)	PUNCT
iajs-3671	186	13	=	=	SYM
iajs-3671	187	1	1	1	NUM
iajs-3671	187	2	√1	√1	PROPN
iajs-3671	187	3	+	+	CCONJ
iajs-3671	187	4	𝑡	𝑡	PROPN
iajs-3671	187	5	𝑒−√1+𝑡(0.697392	𝑒−√1+𝑡(0.697392	NUM
iajs-3671	187	6	−	−	NOUN
iajs-3671	187	7	0.394784√1	0.394784√1	NOUN
iajs-3671	187	8	+	+	PUNCT
iajs-3671	187	9	𝑡	𝑡	X
iajs-3671	187	10	)	)	PUNCT
iajs-3671	187	11	+	+	PUNCT
iajs-3671	187	12	√1	√1	PROPN
iajs-3671	187	13	+	+	CCONJ
iajs-3671	187	14	𝑡	𝑡	PROPN
iajs-3671	187	15	sin(2𝜋𝑡	sin(2𝜋𝑡	PROPN
iajs-3671	187	16	)	)	PUNCT
iajs-3671	187	17	cos(2𝜋𝑥	cos(2𝜋𝑥	NUM
iajs-3671	187	18	)	)	PUNCT
iajs-3671	187	19	,	,	PUNCT
iajs-3671	187	20	(	(	PUNCT
iajs-3671	187	21	𝑥	𝑥	NOUN
iajs-3671	187	22	,	,	PUNCT
iajs-3671	187	23	𝑡	𝑡	NOUN
iajs-3671	187	24	)	)	PUNCT
iajs-3671	187	25	∈	∈	PROPN
iajs-3671	187	26	𝑄𝑇	𝑄𝑇	PROPN
iajs-3671	187	27	(	(	PUNCT
iajs-3671	187	28	54	54	NUM
iajs-3671	187	29	)	)	PUNCT
iajs-3671	187	30	the	the	DET
iajs-3671	187	31	analytic	analytic	ADJ
iajs-3671	187	32	solution	solution	NOUN
iajs-3671	187	33	is	be	AUX
iajs-3671	187	34	given	give	VERB
iajs-3671	187	35	as	as	ADP
iajs-3671	187	36	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	187	37	,	,	PUNCT
iajs-3671	187	38	𝑡	𝑡	X
iajs-3671	187	39	)	)	PUNCT
iajs-3671	187	40	=	=	VERB
iajs-3671	187	41	−𝑒−√1+𝑡	−𝑒−√1+𝑡	PROPN
iajs-3671	187	42	cos(2𝜋𝑥	cos(2𝜋𝑥	NUM
iajs-3671	187	43	)	)	PUNCT
iajs-3671	187	44	,	,	PUNCT
iajs-3671	187	45	(	(	PUNCT
iajs-3671	187	46	𝑥	𝑥	NOUN
iajs-3671	187	47	,	,	PUNCT
iajs-3671	187	48	𝑡	𝑡	NOUN
iajs-3671	187	49	)	)	PUNCT
iajs-3671	187	50	∈	∈	PROPN
iajs-3671	187	51	𝑄𝑇	𝑄𝑇	PROPN
iajs-3671	187	52	(	(	PUNCT
iajs-3671	187	53	55	55	NUM
iajs-3671	187	54	)	)	PUNCT
iajs-3671	187	55	and	and	CCONJ
iajs-3671	187	56	overdetermination	overdetermination	NOUN
iajs-3671	187	57	condition	condition	NOUN
iajs-3671	187	58	ℎ2(𝑡	ℎ2(𝑡	PROPN
iajs-3671	187	59	)	)	PUNCT
iajs-3671	187	60	=	=	SYM
iajs-3671	187	61	𝑒	𝑒	X
iajs-3671	187	62	−√1+𝑡	−√1+𝑡	PROPN
iajs-3671	187	63	,	,	PUNCT
iajs-3671	187	64	𝑡	𝑡	PROPN
iajs-3671	187	65	∈	∈	PROPN
iajs-3671	188	1	[	[	X
iajs-3671	188	2	0	0	NUM
iajs-3671	188	3	,	,	PUNCT
iajs-3671	188	4	𝑇	𝑇	PROPN
iajs-3671	188	5	]	]	X
iajs-3671	188	6	(	(	PUNCT
iajs-3671	188	7	56	56	NUM
iajs-3671	188	8	)	)	PUNCT
iajs-3671	188	9	that	that	PRON
iajs-3671	188	10	can	can	AUX
iajs-3671	188	11	be	be	AUX
iajs-3671	188	12	checked	check	VERB
iajs-3671	188	13	by	by	ADP
iajs-3671	188	14	direct	direct	ADJ
iajs-3671	188	15	substitution	substitution	NOUN
iajs-3671	188	16	.	.	PUNCT
iajs-3671	189	1	figure	figure	NOUN
iajs-3671	189	2	3	3	NUM
iajs-3671	189	3	.	.	PUNCT
iajs-3671	189	4	presents	present	VERB
iajs-3671	189	5	the	the	DET
iajs-3671	189	6	numerical	numerical	ADJ
iajs-3671	189	7	solution	solution	NOUN
iajs-3671	189	8	,	,	PUNCT
iajs-3671	189	9	exact	exact	ADJ
iajs-3671	189	10	solution	solution	NOUN
iajs-3671	189	11	and	and	CCONJ
iajs-3671	189	12	the	the	DET
iajs-3671	189	13	absolute	absolute	ADJ
iajs-3671	189	14	error	error	NOUN
iajs-3671	189	15	between	between	ADP
iajs-3671	189	16	them	they	PRON
iajs-3671	189	17	for	for	ADP
iajs-3671	189	18	the	the	DET
iajs-3671	189	19	temperature	temperature	NOUN
iajs-3671	189	20	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	189	21	,	,	PUNCT
iajs-3671	189	22	𝑡	𝑡	PROPN
iajs-3671	189	23	)	)	PUNCT
iajs-3671	190	1	when	when	SCONJ
iajs-3671	190	2	𝑀	𝑀	PROPN
iajs-3671	190	3	=	=	SYM
iajs-3671	190	4	𝑁	𝑁	PROPN
iajs-3671	190	5	=	=	SYM
iajs-3671	190	6	40	40	NUM
iajs-3671	191	1	.	.	PUNCT
iajs-3671	192	1	the	the	DET
iajs-3671	192	2	figure	figure	NOUN
iajs-3671	192	3	shows	show	VERB
iajs-3671	192	4	an	an	DET
iajs-3671	192	5	excellent	excellent	ADJ
iajs-3671	192	6	agreement	agreement	NOUN
iajs-3671	192	7	between	between	ADP
iajs-3671	192	8	0	0	NUM
iajs-3671	192	9	0.1	0.1	NUM
iajs-3671	192	10	0.2	0.2	NUM
iajs-3671	192	11	0.3	0.3	NUM
iajs-3671	192	12	0.4	0.4	NUM
iajs-3671	192	13	0.5	0.5	NUM
iajs-3671	192	14	0.6	0.6	NUM
iajs-3671	192	15	0.7	0.7	NUM
iajs-3671	192	16	0.8	0.8	NUM
iajs-3671	192	17	0.9	0.9	NUM
iajs-3671	192	18	1	1	NUM
iajs-3671	192	19	t	t	NOUN
iajs-3671	192	20	-0.4	-0.4	NUM
iajs-3671	192	21	-0.35	-0.35	PROPN
iajs-3671	192	22	-0.3	-0.3	PROPN
iajs-3671	192	23	-0.25	-0.25	NUM
iajs-3671	192	24	-0.2	-0.2	NOUN
iajs-3671	192	25	-0.15	-0.15	NUM
iajs-3671	192	26	-0.1	-0.1	PROPN
iajs-3671	192	27	h	h	PROPN
iajs-3671	192	28	(	(	PUNCT
iajs-3671	192	29	t	t	NOUN
iajs-3671	192	30	)	)	PUNCT
iajs-3671	192	31	exact	exact	ADJ
iajs-3671	192	32	and	and	CCONJ
iajs-3671	192	33	numerical	numerical	ADJ
iajs-3671	192	34	values	value	NOUN
iajs-3671	192	35	of	of	ADP
iajs-3671	192	36	h(t	h(t	PROPN
iajs-3671	192	37	)	)	PUNCT
iajs-3671	192	38	exact	exact	ADJ
iajs-3671	192	39	numerical	numerical	ADJ
iajs-3671	192	40	ihjpas	ihjpas	PROPN
iajs-3671	192	41	.	.	PUNCT
iajs-3671	193	1	2025	2025	NUM
iajs-3671	193	2	,	,	PUNCT
iajs-3671	193	3	38	38	NUM
iajs-3671	193	4	(	(	PUNCT
iajs-3671	193	5	1	1	NUM
iajs-3671	193	6	)	)	PUNCT
iajs-3671	193	7	477	477	NUM
iajs-3671	193	8	the	the	DET
iajs-3671	193	9	exact	exact	ADJ
iajs-3671	193	10	and	and	CCONJ
iajs-3671	193	11	numerical	numerical	ADJ
iajs-3671	193	12	solutions	solution	NOUN
iajs-3671	193	13	with	with	ADP
iajs-3671	193	14	the	the	DET
iajs-3671	193	15	error	error	NOUN
iajs-3671	193	16	magnitude	magnitude	NOUN
iajs-3671	193	17	of	of	ADP
iajs-3671	193	18	order	order	NOUN
iajs-3671	193	19	𝑂(10−4	𝑂(10−4	ADJ
iajs-3671	193	20	)	)	PUNCT
iajs-3671	193	21	.	.	PUNCT
iajs-3671	194	1	figure	figure	NOUN
iajs-3671	194	2	4	4	NUM
iajs-3671	194	3	.	.	PUNCT
iajs-3671	194	4	shows	show	VERB
iajs-3671	194	5	the	the	DET
iajs-3671	194	6	comparison	comparison	NOUN
iajs-3671	194	7	between	between	ADP
iajs-3671	194	8	the	the	DET
iajs-3671	194	9	exact	exact	ADJ
iajs-3671	194	10	and	and	CCONJ
iajs-3671	194	11	numerical	numerical	ADJ
iajs-3671	194	12	solutions	solution	NOUN
iajs-3671	194	13	of	of	ADP
iajs-3671	194	14	ℎ2(𝑡	ℎ2(𝑡	PROPN
iajs-3671	194	15	)	)	PUNCT
iajs-3671	194	16	.	.	PUNCT
iajs-3671	195	1	figure	figure	VERB
iajs-3671	195	2	3	3	NUM
iajs-3671	195	3	.	.	PUNCT
iajs-3671	196	1	the	the	DET
iajs-3671	196	2	exact	exact	ADJ
iajs-3671	196	3	and	and	CCONJ
iajs-3671	196	4	numerical	numerical	ADJ
iajs-3671	196	5	solutions	solution	NOUN
iajs-3671	196	6	with	with	ADP
iajs-3671	196	7	the	the	DET
iajs-3671	196	8	corresponding	corresponding	ADJ
iajs-3671	196	9	absolute	absolute	ADJ
iajs-3671	196	10	error	error	NOUN
iajs-3671	196	11	when	when	SCONJ
iajs-3671	196	12	m	m	VERB
iajs-3671	196	13	=	=	SYM
iajs-3671	196	14	n	n	PROPN
iajs-3671	196	15	=	=	SYM
iajs-3671	196	16	40	40	NUM
iajs-3671	196	17	,	,	PUNCT
iajs-3671	196	18	for	for	ADP
iajs-3671	196	19	example	example	NOUN
iajs-3671	196	20	,	,	PUNCT
iajs-3671	196	21	direct	direct	PROPN
iajs-3671	196	22	problem	problem	PROPN
iajs-3671	196	23	ii	ii	PROPN
iajs-3671	196	24	.	.	PROPN
iajs-3671	196	25	figure	figure	VERB
iajs-3671	196	26	4	4	NUM
iajs-3671	196	27	.	.	PUNCT
iajs-3671	197	1	the	the	DET
iajs-3671	197	2	required	require	VERB
iajs-3671	197	3	output	output	NOUN
iajs-3671	197	4	ℎ2(𝑡	ℎ2(𝑡	PROPN
iajs-3671	197	5	)	)	PUNCT
iajs-3671	197	6	,	,	PUNCT
iajs-3671	197	7	with	with	ADP
iajs-3671	197	8	𝑁	𝑁	PROPN
iajs-3671	197	9	=	=	PUNCT
iajs-3671	197	10	𝑀	𝑀	PROPN
iajs-3671	197	11	=	=	NUM
iajs-3671	197	12	40	40	NUM
iajs-3671	197	13	,	,	PUNCT
iajs-3671	197	14	for	for	ADP
iajs-3671	197	15	example	example	NOUN
iajs-3671	197	16	of	of	ADP
iajs-3671	197	17	direct	direct	PROPN
iajs-3671	197	18	problem	problem	PROPN
iajs-3671	197	19	ii	ii	PROPN
iajs-3671	197	20	.	.	PROPN
iajs-3671	198	1	3	3	X
iajs-3671	198	2	.	.	X
iajs-3671	198	3	computational	computational	ADJ
iajs-3671	198	4	approach	approach	NOUN
iajs-3671	198	5	for	for	ADP
iajs-3671	198	6	inverse	inverse	NOUN
iajs-3671	198	7	problems	problem	NOUN
iajs-3671	198	8	our	our	PRON
iajs-3671	198	9	goal	goal	NOUN
iajs-3671	198	10	in	in	ADP
iajs-3671	198	11	this	this	DET
iajs-3671	198	12	section	section	NOUN
iajs-3671	198	13	is	be	AUX
iajs-3671	198	14	devoted	devote	VERB
iajs-3671	198	15	to	to	ADP
iajs-3671	198	16	solving	solve	VERB
iajs-3671	198	17	ipi	ipi	PROPN
iajs-3671	198	18	and	and	CCONJ
iajs-3671	198	19	ip	ip	PROPN
iajs-3671	198	20	-	-	PUNCT
iajs-3671	198	21	ii	ii	NOUN
iajs-3671	198	22	.	.	PUNCT
iajs-3671	199	1	to	to	PART
iajs-3671	199	2	find	find	VERB
iajs-3671	199	3	stable	stable	ADJ
iajs-3671	199	4	reconstructions	reconstruction	NOUN
iajs-3671	199	5	for	for	ADP
iajs-3671	199	6	unknown	unknown	ADJ
iajs-3671	199	7	coefficient	coefficient	NOUN
iajs-3671	199	8	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	199	9	)	)	PUNCT
iajs-3671	199	10	,	,	PUNCT
iajs-3671	199	11	in	in	ADP
iajs-3671	199	12	addition	addition	NOUN
iajs-3671	199	13	to	to	PART
iajs-3671	199	14	heat	heat	VERB
iajs-3671	199	15	distribution	distribution	NOUN
iajs-3671	199	16	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	199	17	,	,	PUNCT
iajs-3671	199	18	𝑡	𝑡	PROPN
iajs-3671	199	19	)	)	PUNCT
iajs-3671	199	20	which	which	PRON
iajs-3671	199	21	satisfy	satisfy	VERB
iajs-3671	199	22	equation	equation	NOUN
iajs-3671	199	23	(	(	PUNCT
iajs-3671	199	24	1	1	NUM
iajs-3671	199	25	)	)	PUNCT
iajs-3671	199	26	(	(	PUNCT
iajs-3671	199	27	4	4	NUM
iajs-3671	199	28	)	)	PUNCT
iajs-3671	199	29	,	,	PUNCT
iajs-3671	199	30	(	(	PUNCT
iajs-3671	199	31	6	6	NUM
iajs-3671	199	32	)	)	PUNCT
iajs-3671	199	33	for	for	ADP
iajs-3671	199	34	ip	ip	NOUN
iajs-3671	199	35	-	-	PUNCT
iajs-3671	199	36	i	i	PRON
iajs-3671	199	37	and	and	CCONJ
iajs-3671	199	38	equations	equation	NOUN
iajs-3671	199	39	(	(	PUNCT
iajs-3671	199	40	1)-(3),(5	1)-(3),(5	NUM
iajs-3671	199	41	)	)	PUNCT
iajs-3671	199	42	,	,	PUNCT
iajs-3671	199	43	(	(	PUNCT
iajs-3671	199	44	7	7	X
iajs-3671	199	45	)	)	PUNCT
iajs-3671	199	46	for	for	ADP
iajs-3671	199	47	ip	ip	PROPN
iajs-3671	199	48	-	-	PUNCT
iajs-3671	199	49	ii	ii	NOUN
iajs-3671	199	50	.	.	PUNCT
iajs-3671	200	1	these	these	DET
iajs-3671	200	2	problems	problem	NOUN
iajs-3671	200	3	are	be	AUX
iajs-3671	200	4	reformulated	reformulate	VERB
iajs-3671	200	5	as	as	ADP
iajs-3671	200	6	0	0	NUM
iajs-3671	200	7	0.1	0.1	NUM
iajs-3671	200	8	0.2	0.2	NUM
iajs-3671	200	9	0.3	0.3	NUM
iajs-3671	200	10	0.4	0.4	NUM
iajs-3671	200	11	0.5	0.5	NUM
iajs-3671	200	12	0.6	0.6	NUM
iajs-3671	200	13	0.7	0.7	NUM
iajs-3671	200	14	0.8	0.8	NUM
iajs-3671	200	15	0.9	0.9	NUM
iajs-3671	200	16	1	1	NUM
iajs-3671	200	17	t	t	NOUN
iajs-3671	200	18	0.24	0.24	NUM
iajs-3671	200	19	0.26	0.26	NUM
iajs-3671	200	20	0.28	0.28	NUM
iajs-3671	200	21	0.3	0.3	NUM
iajs-3671	200	22	0.32	0.32	NUM
iajs-3671	200	23	0.34	0.34	NUM
iajs-3671	200	24	0.36	0.36	NUM
iajs-3671	200	25	0.38	0.38	NUM
iajs-3671	200	26	h	h	NOUN
iajs-3671	200	27	(	(	PUNCT
iajs-3671	200	28	t	t	NOUN
iajs-3671	200	29	)	)	PUNCT
iajs-3671	200	30	exact	exact	ADJ
iajs-3671	200	31	and	and	CCONJ
iajs-3671	200	32	numerical	numerical	ADJ
iajs-3671	200	33	values	value	NOUN
iajs-3671	200	34	of	of	ADP
iajs-3671	200	35	h(t	h(t	PROPN
iajs-3671	200	36	)	)	PUNCT
iajs-3671	200	37	exact	exact	ADJ
iajs-3671	200	38	numerical	numerical	ADJ
iajs-3671	200	39	ihjpas	ihjpas	PROPN
iajs-3671	200	40	.	.	PUNCT
iajs-3671	201	1	2025	2025	NUM
iajs-3671	201	2	,	,	PUNCT
iajs-3671	201	3	38	38	NUM
iajs-3671	201	4	(	(	PUNCT
iajs-3671	201	5	1	1	NUM
iajs-3671	201	6	)	)	PUNCT
iajs-3671	201	7	478	478	NUM
iajs-3671	201	8	nonlinear	nonlinear	ADJ
iajs-3671	201	9	optimization	optimization	NOUN
iajs-3671	201	10	problems	problem	NOUN
iajs-3671	201	11	and	and	CCONJ
iajs-3671	201	12	solved	solve	VERB
iajs-3671	201	13	numerically	numerically	ADV
iajs-3671	201	14	by	by	ADP
iajs-3671	201	15	minimizing	minimize	VERB
iajs-3671	201	16	the	the	DET
iajs-3671	201	17	gap	gap	NOUN
iajs-3671	201	18	between	between	ADP
iajs-3671	201	19	extra	extra	ADJ
iajs-3671	201	20	measurement	measurement	NOUN
iajs-3671	201	21	data	data	NOUN
iajs-3671	201	22	equations	equation	NOUN
iajs-3671	201	23	(	(	PUNCT
iajs-3671	201	24	6	6	NUM
iajs-3671	201	25	)	)	PUNCT
iajs-3671	201	26	or	or	CCONJ
iajs-3671	201	27	(	(	PUNCT
iajs-3671	201	28	7	7	NUM
iajs-3671	201	29	)	)	PUNCT
iajs-3671	201	30	and	and	CCONJ
iajs-3671	201	31	the	the	DET
iajs-3671	201	32	associated	associate	VERB
iajs-3671	201	33	computed	compute	VERB
iajs-3671	201	34	solution	solution	NOUN
iajs-3671	201	35	.	.	PUNCT
iajs-3671	202	1	to	to	PART
iajs-3671	202	2	gain	gain	VERB
iajs-3671	202	3	reliable	reliable	ADJ
iajs-3671	202	4	results	result	NOUN
iajs-3671	202	5	we	we	PRON
iajs-3671	202	6	apply	apply	VERB
iajs-3671	202	7	the	the	DET
iajs-3671	202	8	tikhonov	tikhonov	NOUN
iajs-3671	202	9	’s	’s	PART
iajs-3671	202	10	regularization	regularization	NOUN
iajs-3671	202	11	method	method	NOUN
iajs-3671	202	12	due	due	ADP
iajs-3671	202	13	to	to	ADP
iajs-3671	202	14	the	the	DET
iajs-3671	202	15	ill	ill	ADJ
iajs-3671	202	16	-	-	PUNCT
iajs-3671	202	17	possedness	possedness	NOUN
iajs-3671	202	18	of	of	ADP
iajs-3671	202	19	the	the	DET
iajs-3671	202	20	under	under	ADP
iajs-3671	202	21	investigation	investigation	NOUN
iajs-3671	202	22	problems	problem	NOUN
iajs-3671	202	23	.	.	PUNCT
iajs-3671	203	1	the	the	DET
iajs-3671	203	2	cost	cost	NOUN
iajs-3671	203	3	functional	functional	NOUN
iajs-3671	203	4	can	can	AUX
iajs-3671	203	5	be	be	AUX
iajs-3671	203	6	constructed	construct	VERB
iajs-3671	203	7	as	as	ADP
iajs-3671	203	8	(	(	PUNCT
iajs-3671	203	9	33	33	NUM
iajs-3671	203	10	-	-	SYM
iajs-3671	203	11	40	40	NUM
iajs-3671	203	12	)	)	PUNCT
iajs-3671	203	13	.	.	PUNCT
iajs-3671	204	1	𝐾𝐼(𝑝	𝐾𝐼(𝑝	PROPN
iajs-3671	204	2	)	)	PUNCT
iajs-3671	205	1	=	=	PUNCT
iajs-3671	205	2	‖𝑢	‖𝑢	NOUN
iajs-3671	205	3	(	(	PUNCT
iajs-3671	205	4	1	1	NUM
iajs-3671	205	5	2	2	NUM
iajs-3671	205	6	,	,	PUNCT
iajs-3671	205	7	𝑡	𝑡	NOUN
iajs-3671	205	8	)	)	PUNCT
iajs-3671	205	9	+	+	CCONJ
iajs-3671	205	10	∫𝑢(𝑥	∫𝑢(𝑥	NOUN
iajs-3671	205	11	,	,	PUNCT
iajs-3671	205	12	𝑡)𝑑𝑥	𝑡)𝑑𝑥	PROPN
iajs-3671	205	13	−	−	PROPN
iajs-3671	205	14	ℎ1(𝑡	ℎ1(𝑡	NOUN
iajs-3671	205	15	)	)	PUNCT
iajs-3671	205	16	1	1	NUM
iajs-3671	205	17	0	0	NUM
iajs-3671	205	18	‖	‖	PROPN
iajs-3671	205	19	2	2	NUM
iajs-3671	205	20	+	+	CCONJ
iajs-3671	205	21	𝛽‖𝑝(𝑡)‖2	𝛽‖𝑝(𝑡)‖2	NOUN
iajs-3671	205	22	,	,	PUNCT
iajs-3671	205	23	(	(	PUNCT
iajs-3671	205	24	57	57	NUM
iajs-3671	205	25	)	)	PUNCT
iajs-3671	205	26	for	for	ADP
iajs-3671	205	27	ip	ip	NOUN
iajs-3671	205	28	-	-	PUNCT
iajs-3671	205	29	i	i	PRON
iajs-3671	205	30	and	and	CCONJ
iajs-3671	205	31	the	the	DET
iajs-3671	205	32	functional	functional	ADJ
iajs-3671	205	33	𝐾𝐼𝐼(𝑝	𝐾𝐼𝐼(𝑝	NOUN
iajs-3671	205	34	)	)	PUNCT
iajs-3671	205	35	=	=	SYM
iajs-3671	205	36	‖𝑢(𝑥0	‖𝑢(𝑥0	NUM
iajs-3671	205	37	,	,	PUNCT
iajs-3671	205	38	𝑡	𝑡	PROPN
iajs-3671	205	39	)	)	PUNCT
iajs-3671	205	40	−	−	ADP
iajs-3671	205	41	ℎ2(𝑡)‖	ℎ2(𝑡)‖	CCONJ
iajs-3671	205	42	2	2	NUM
iajs-3671	205	43	+	+	CCONJ
iajs-3671	205	44	𝛽‖𝑝(𝑡)‖2	𝛽‖𝑝(𝑡)‖2	NOUN
iajs-3671	205	45	,	,	PUNCT
iajs-3671	205	46	(	(	PUNCT
iajs-3671	205	47	58	58	NUM
iajs-3671	205	48	)	)	PUNCT
iajs-3671	205	49	for	for	ADP
iajs-3671	205	50	ip	ip	PROPN
iajs-3671	205	51	-	-	PUNCT
iajs-3671	205	52	ii	ii	NOUN
iajs-3671	205	53	,	,	PUNCT
iajs-3671	205	54	where	where	SCONJ
iajs-3671	205	55	β	β	X
iajs-3671	205	56	≥	≥	VERB
iajs-3671	205	57	0	0	NUM
iajs-3671	205	58	the	the	DET
iajs-3671	205	59	regularization	regularization	NOUN
iajs-3671	205	60	parameter	parameter	NOUN
iajs-3671	205	61	,	,	PUNCT
iajs-3671	205	62	should	should	AUX
iajs-3671	205	63	be	be	AUX
iajs-3671	205	64	selected	select	VERB
iajs-3671	205	65	according	accord	VERB
iajs-3671	205	66	to	to	ADP
iajs-3671	205	67	some	some	DET
iajs-3671	205	68	selection	selection	NOUN
iajs-3671	205	69	strategy	strategy	NOUN
iajs-3671	205	70	such	such	ADJ
iajs-3671	205	71	as	as	ADP
iajs-3671	205	72	l	l	NOUN
iajs-3671	205	73	-	-	NOUN
iajs-3671	205	74	curve	curve	NOUN
iajs-3671	205	75	(	(	PUNCT
iajs-3671	205	76	41	41	NUM
iajs-3671	205	77	)	)	PUNCT
iajs-3671	205	78	,	,	PUNCT
iajs-3671	205	79	mozorov	mozorov	VERB
iajs-3671	205	80	discriperey	discriperey	PROPN
iajs-3671	205	81	principle	principle	NOUN
iajs-3671	205	82	(	(	PUNCT
iajs-3671	205	83	42	42	NUM
iajs-3671	205	84	)	)	PUNCT
iajs-3671	205	85	,	,	PUNCT
iajs-3671	205	86	or	or	CCONJ
iajs-3671	205	87	trial	trial	NOUN
iajs-3671	205	88	and	and	CCONJ
iajs-3671	205	89	error	error	NOUN
iajs-3671	205	90	as	as	ADP
iajs-3671	205	91	in	in	ADP
iajs-3671	205	92	(	(	PUNCT
iajs-3671	205	93	43	43	NUM
iajs-3671	205	94	,	,	PUNCT
iajs-3671	205	95	44	44	NUM
iajs-3671	205	96	)	)	PUNCT
iajs-3671	205	97	.	.	PUNCT
iajs-3671	206	1	the	the	DET
iajs-3671	206	2	approximate	approximate	ADJ
iajs-3671	206	3	form	form	NOUN
iajs-3671	206	4	of	of	ADP
iajs-3671	206	5	the	the	DET
iajs-3671	206	6	above	above	ADJ
iajs-3671	206	7	functionals	functional	NOUN
iajs-3671	206	8	are	be	AUX
iajs-3671	206	9	:	:	PUNCT
iajs-3671	206	10	𝐾𝐼	𝐾𝐼	PROPN
iajs-3671	206	11	(	(	PUNCT
iajs-3671	206	12	𝑝	𝑝	NOUN
iajs-3671	206	13	)	)	PUNCT
iajs-3671	206	14	=	=	SYM
iajs-3671	206	15	∑(𝑢	∑(𝑢	PROPN
iajs-3671	206	16	(	(	PUNCT
iajs-3671	206	17	1	1	NUM
iajs-3671	206	18	2	2	NUM
iajs-3671	206	19	,	,	PUNCT
iajs-3671	206	20	𝑡𝑗	𝑡𝑗	PROPN
iajs-3671	206	21	)	)	PUNCT
iajs-3671	206	22	+	+	NUM
iajs-3671	206	23	∫𝑢(𝑥	∫𝑢(𝑥	PROPN
iajs-3671	206	24	,	,	PUNCT
iajs-3671	206	25	𝑡𝑗)𝑑𝑥	𝑡𝑗)𝑑𝑥	PUNCT
iajs-3671	206	26	−	−	PUNCT
iajs-3671	206	27	ℎ1(𝑡𝑗	ℎ1(𝑡𝑗	NOUN
iajs-3671	206	28	)	)	PUNCT
iajs-3671	206	29	1	1	NUM
iajs-3671	206	30	0	0	NUM
iajs-3671	206	31	)	)	PUNCT
iajs-3671	206	32	2	2	NUM
iajs-3671	206	33	𝑁	𝑁	PROPN
iajs-3671	206	34	𝑗=1	𝑗=1	PROPN
iajs-3671	206	35	+	+	NUM
iajs-3671	206	36	𝛽∑𝑝𝑗	𝛽∑𝑝𝑗	NOUN
iajs-3671	206	37	2	2	NUM
iajs-3671	206	38	𝑁	𝑁	PROPN
iajs-3671	206	39	𝑗=1	𝑗=1	PROPN
iajs-3671	206	40	,	,	PUNCT
iajs-3671	206	41	(	(	PUNCT
iajs-3671	206	42	59	59	NUM
iajs-3671	206	43	)	)	PUNCT
iajs-3671	206	44	𝐾𝐼𝐼	𝐾𝐼𝐼	PROPN
iajs-3671	206	45	(	(	PUNCT
iajs-3671	206	46	𝑝	𝑝	NOUN
iajs-3671	206	47	)	)	PUNCT
iajs-3671	206	48	=	=	SYM
iajs-3671	206	49	∑(𝑢(𝑥0	∑(𝑢(𝑥0	ADJ
iajs-3671	206	50	,	,	PUNCT
iajs-3671	206	51	𝑡𝑗	𝑡𝑗	PROPN
iajs-3671	206	52	)	)	PUNCT
iajs-3671	206	53	−	−	PROPN
iajs-3671	206	54	ℎ2(𝑡𝑗	ℎ2(𝑡𝑗	PROPN
iajs-3671	206	55	)	)	PUNCT
iajs-3671	206	56	)	)	PUNCT
iajs-3671	206	57	2	2	NUM
iajs-3671	206	58	𝑁	𝑁	PROPN
iajs-3671	206	59	𝑗=1	𝑗=1	PROPN
iajs-3671	206	60	+	+	NUM
iajs-3671	206	61	𝛽∑𝑝𝑗	𝛽∑𝑝𝑗	NOUN
iajs-3671	206	62	2	2	NUM
iajs-3671	206	63	𝑁	𝑁	PROPN
iajs-3671	206	64	𝑗=1	𝑗=1	PROPN
iajs-3671	206	65	,	,	PUNCT
iajs-3671	206	66	(	(	PUNCT
iajs-3671	206	67	60	60	NUM
iajs-3671	206	68	)	)	PUNCT
iajs-3671	206	69	for	for	ADP
iajs-3671	206	70	ip	ip	NOUN
iajs-3671	206	71	-	-	PUNCT
iajs-3671	206	72	i	i	PRON
iajs-3671	206	73	and	and	CCONJ
iajs-3671	206	74	ip	ip	PROPN
iajs-3671	206	75	-	-	PUNCT
iajs-3671	206	76	ii	ii	NOUN
iajs-3671	206	77	,	,	PUNCT
iajs-3671	206	78	respectively	respectively	ADV
iajs-3671	206	79	.	.	PUNCT
iajs-3671	207	1	the	the	DET
iajs-3671	207	2	objective	objective	ADJ
iajs-3671	207	3	functions	function	NOUN
iajs-3671	207	4	equations	equation	NOUN
iajs-3671	207	5	(	(	PUNCT
iajs-3671	207	6	25	25	NUM
iajs-3671	207	7	)	)	PUNCT
iajs-3671	207	8	and	and	CCONJ
iajs-3671	207	9	(	(	PUNCT
iajs-3671	207	10	26	26	NUM
iajs-3671	207	11	)	)	PUNCT
iajs-3671	207	12	,	,	PUNCT
iajs-3671	207	13	it	it	PRON
iajs-3671	207	14	is	be	AUX
iajs-3671	207	15	minimized	minimize	VERB
iajs-3671	207	16	via	via	ADP
iajs-3671	207	17	the	the	DET
iajs-3671	207	18	subroutine	subroutine	ADJ
iajs-3671	207	19	lsqnonlin	lsqnonlin	NOUN
iajs-3671	207	20	from	from	ADP
iajs-3671	207	21	the	the	DET
iajs-3671	207	22	matlab	matlab	PROPN
iajs-3671	207	23	optimization	optimization	NOUN
iajs-3671	207	24	toolbox	toolbox	NOUN
iajs-3671	207	25	.	.	PUNCT
iajs-3671	208	1	this	this	DET
iajs-3671	208	2	routine	routine	NOUN
iajs-3671	208	3	tries	try	VERB
iajs-3671	208	4	to	to	PART
iajs-3671	208	5	solve	solve	VERB
iajs-3671	208	6	nonlinear	nonlinear	ADJ
iajs-3671	208	7	least	least	ADJ
iajs-3671	208	8	-	-	PUNCT
iajs-3671	208	9	squares	square	NOUN
iajs-3671	208	10	curve	curve	NOUN
iajs-3671	208	11	fitting	fitting	ADJ
iajs-3671	208	12	problems	problem	NOUN
iajs-3671	208	13	starting	start	VERB
iajs-3671	208	14	from	from	ADP
iajs-3671	208	15	the	the	DET
iajs-3671	208	16	initial	initial	ADJ
iajs-3671	208	17	guess	guess	NOUN
iajs-3671	208	18	for	for	ADP
iajs-3671	208	19	unknown	unknown	ADJ
iajs-3671	208	20	coefficient	coefficient	NOUN
iajs-3671	208	21	𝑝.	𝑝.	VERB
iajs-3671	208	22	the	the	DET
iajs-3671	208	23	upper	upper	ADJ
iajs-3671	208	24	and	and	CCONJ
iajs-3671	208	25	lower	low	ADJ
iajs-3671	208	26	bounds	bound	NOUN
iajs-3671	208	27	on	on	ADP
iajs-3671	208	28	the	the	DET
iajs-3671	208	29	variable	variable	ADJ
iajs-3671	208	30	𝑝	𝑝	PROPN
iajs-3671	208	31	are	be	AUX
iajs-3671	208	32	specified	specify	VERB
iajs-3671	208	33	as	as	ADP
iajs-3671	208	34	10−2	10−2	NUM
iajs-3671	208	35	≤	≤	NOUN
iajs-3671	208	36	𝑝	𝑝	NOUN
iajs-3671	208	37	≤	≤	NUM
iajs-3671	208	38	102	102	NUM
iajs-3671	208	39	.	.	PUNCT
iajs-3671	209	1	also	also	ADV
iajs-3671	209	2	,	,	PUNCT
iajs-3671	209	3	in	in	ADP
iajs-3671	209	4	this	this	DET
iajs-3671	209	5	routine	routine	NOUN
iajs-3671	209	6	,	,	PUNCT
iajs-3671	209	7	there	there	PRON
iajs-3671	209	8	is	be	VERB
iajs-3671	209	9	no	no	DET
iajs-3671	209	10	need	need	NOUN
iajs-3671	209	11	to	to	PART
iajs-3671	209	12	calculate	calculate	VERB
iajs-3671	209	13	the	the	DET
iajs-3671	209	14	gradient	gradient	NOUN
iajs-3671	209	15	separately	separately	ADV
iajs-3671	209	16	;	;	PUNCT
iajs-3671	209	17	this	this	PRON
iajs-3671	209	18	is	be	AUX
iajs-3671	209	19	something	something	PRON
iajs-3671	209	20	impeded	impede	VERB
iajs-3671	209	21	inside	inside	ADP
iajs-3671	209	22	the	the	DET
iajs-3671	209	23	routine	routine	ADJ
iajs-3671	209	24	package	package	NOUN
iajs-3671	209	25	.	.	PUNCT
iajs-3671	210	1	the	the	DET
iajs-3671	210	2	following	follow	VERB
iajs-3671	210	3	parameters	parameter	NOUN
iajs-3671	210	4	are	be	AUX
iajs-3671	210	5	essential	essential	ADJ
iajs-3671	210	6	to	to	PART
iajs-3671	210	7	initiate	initiate	VERB
iajs-3671	210	8	the	the	DET
iajs-3671	210	9	optimization	optimization	NOUN
iajs-3671	210	10	process	process	NOUN
iajs-3671	210	11	of	of	ADP
iajs-3671	210	12	equations	equation	NOUN
iajs-3671	210	13	(	(	PUNCT
iajs-3671	210	14	57	57	NUM
iajs-3671	210	15	)	)	PUNCT
iajs-3671	210	16	or	or	CCONJ
iajs-3671	210	17	(	(	PUNCT
iajs-3671	210	18	58	58	NUM
iajs-3671	210	19	)	)	PUNCT
iajs-3671	210	20	;	;	PUNCT
iajs-3671	210	21	the	the	DET
iajs-3671	210	22	minimization	minimization	NOUN
iajs-3671	210	23	process	process	NOUN
iajs-3671	210	24	will	will	AUX
iajs-3671	210	25	terminate	terminate	VERB
iajs-3671	210	26	when	when	SCONJ
iajs-3671	210	27	the	the	DET
iajs-3671	210	28	following	follow	VERB
iajs-3671	210	29	prescribed	prescribed	ADJ
iajs-3671	210	30	parameters	parameter	NOUN
iajs-3671	210	31	are	be	AUX
iajs-3671	210	32	reached	reach	VERB
iajs-3671	210	33	:	:	PUNCT
iajs-3671	210	34	ihjpas	ihjpas	PROPN
iajs-3671	210	35	.	.	PUNCT
iajs-3671	211	1	2025	2025	NUM
iajs-3671	211	2	,	,	PUNCT
iajs-3671	211	3	38	38	NUM
iajs-3671	211	4	(	(	PUNCT
iajs-3671	211	5	1	1	NUM
iajs-3671	211	6	)	)	PUNCT
iajs-3671	211	7	479	479	NUM
iajs-3671	211	8	•	•	ADV
iajs-3671	211	9	allowed	allow	VERB
iajs-3671	211	10	number	number	NOUN
iajs-3671	211	11	of	of	ADP
iajs-3671	211	12	iterations	iteration	NOUN
iajs-3671	211	13	=	=	SYM
iajs-3671	211	14	6000	6000	NUM
iajs-3671	211	15	.	.	PUNCT
iajs-3671	212	1	•	•	NUM
iajs-3671	212	2	specified	specify	VERB
iajs-3671	212	3	solution	solution	NOUN
iajs-3671	212	4	and	and	CCONJ
iajs-3671	212	5	objective	objective	ADJ
iajs-3671	212	6	function	function	NOUN
iajs-3671	212	7	tolerance	tolerance	NOUN
iajs-3671	212	8	=	=	SYM
iajs-3671	212	9	10−20	10−20	PROPN
iajs-3671	212	10	.	.	PUNCT
iajs-3671	213	1	the	the	DET
iajs-3671	213	2	inverse	inverse	NOUN
iajs-3671	213	3	problems	problem	NOUN
iajs-3671	213	4	i	i	PRON
iajs-3671	213	5	or	or	CCONJ
iajs-3671	213	6	ii	ii	PROPN
iajs-3671	213	7	are	be	AUX
iajs-3671	213	8	solved	solve	VERB
iajs-3671	213	9	concerning	concern	VERB
iajs-3671	213	10	noisy/	noisy/	NUM
iajs-3671	213	11	exact	exact	ADJ
iajs-3671	213	12	measurement	measurement	NOUN
iajs-3671	213	13	data	datum	NOUN
iajs-3671	213	14	in	in	ADP
iajs-3671	213	15	equations	equation	NOUN
iajs-3671	213	16	(	(	PUNCT
iajs-3671	213	17	6	6	NUM
iajs-3671	213	18	)	)	PUNCT
iajs-3671	213	19	or	or	CCONJ
iajs-3671	213	20	(	(	PUNCT
iajs-3671	213	21	7	7	NUM
iajs-3671	213	22	)	)	PUNCT
iajs-3671	213	23	.	.	PUNCT
iajs-3671	214	1	the	the	DET
iajs-3671	214	2	additive	additive	ADJ
iajs-3671	214	3	noise	noise	NOUN
iajs-3671	214	4	type	type	NOUN
iajs-3671	214	5	as	as	SCONJ
iajs-3671	214	6	presented	present	VERB
iajs-3671	214	7	in	in	ADP
iajs-3671	214	8	(	(	PUNCT
iajs-3671	214	9	4550	4550	NUM
iajs-3671	214	10	):	):	PUNCT
iajs-3671	214	11	ℎ𝑙	ℎ𝑙	PROPN
iajs-3671	214	12	𝜖(𝑡𝑗	𝜖(𝑡𝑗	PROPN
iajs-3671	214	13	)	)	PUNCT
iajs-3671	214	14	=	=	SYM
iajs-3671	214	15	ℎ𝑙(𝑡𝑗	ℎ𝑙(𝑡𝑗	PROPN
iajs-3671	214	16	)	)	PUNCT
iajs-3671	215	1	+	+	CCONJ
iajs-3671	215	2	𝜖𝑗	𝜖𝑗	INTJ
iajs-3671	215	3	,	,	PUNCT
iajs-3671	215	4	𝑗	𝑗	NOUN
iajs-3671	215	5	=	=	SYM
iajs-3671	215	6	1,2	1,2	NUM
iajs-3671	215	7	,	,	PUNCT
iajs-3671	215	8	…	…	PUNCT
iajs-3671	215	9	,	,	PUNCT
iajs-3671	215	10	𝑁	𝑁	PROPN
iajs-3671	215	11	,	,	PUNCT
iajs-3671	215	12	𝑙	𝑙	X
iajs-3671	215	13	=	=	SYM
iajs-3671	215	14	1,2	1,2	NUM
iajs-3671	215	15	,	,	PUNCT
iajs-3671	215	16	(	(	PUNCT
iajs-3671	215	17	61	61	NUM
iajs-3671	215	18	)	)	PUNCT
iajs-3671	215	19	where	where	SCONJ
iajs-3671	215	20	𝜖	𝜖	PROPN
iajs-3671	215	21	is	be	AUX
iajs-3671	215	22	a	a	DET
iajs-3671	215	23	gaussian	gaussian	ADJ
iajs-3671	215	24	random	random	ADJ
iajs-3671	215	25	vector	vector	NOUN
iajs-3671	215	26	,	,	PUNCT
iajs-3671	215	27	and	and	CCONJ
iajs-3671	215	28	standard	standard	ADJ
iajs-3671	215	29	deviation	deviation	NOUN
iajs-3671	215	30	𝜇	𝜇	ADP
iajs-3671	215	31	is	be	AUX
iajs-3671	215	32	:	:	PUNCT
iajs-3671	215	33	𝜇𝑙	𝜇𝑙	PROPN
iajs-3671	215	34	=	=	PUNCT
iajs-3671	215	35	𝑞	𝑞	PROPN
iajs-3671	215	36	×	×	PROPN
iajs-3671	215	37	max	max	PROPN
iajs-3671	215	38	𝑡∈[0,𝑇	𝑡∈[0,𝑇	X
iajs-3671	215	39	]	]	PUNCT
iajs-3671	215	40	|ℎ𝑙(𝑡)|	|ℎ𝑙(𝑡)|	X
iajs-3671	215	41	,	,	PUNCT
iajs-3671	215	42	𝑙	𝑙	X
iajs-3671	215	43	=	=	SYM
iajs-3671	215	44	1,2	1,2	NUM
iajs-3671	215	45	,	,	PUNCT
iajs-3671	215	46	(	(	PUNCT
iajs-3671	215	47	62	62	NUM
iajs-3671	215	48	)	)	PUNCT
iajs-3671	215	49	where	where	SCONJ
iajs-3671	215	50	𝑞	𝑞	PRON
iajs-3671	215	51	represents	represent	VERB
iajs-3671	215	52	the	the	DET
iajs-3671	215	53	percentage	percentage	NOUN
iajs-3671	215	54	of	of	ADP
iajs-3671	215	55	noise	noise	NOUN
iajs-3671	215	56	.	.	PUNCT
iajs-3671	216	1	here	here	ADV
iajs-3671	216	2	,	,	PUNCT
iajs-3671	216	3	we	we	PRON
iajs-3671	216	4	use	use	VERB
iajs-3671	216	5	the	the	DET
iajs-3671	216	6	normrnd	normrnd	NOUN
iajs-3671	216	7	built	build	VERB
iajs-3671	216	8	-	-	PUNCT
iajs-3671	216	9	in	in	ADP
iajs-3671	216	10	function	function	NOUN
iajs-3671	216	11	to	to	PART
iajs-3671	216	12	generate	generate	VERB
iajs-3671	216	13	the	the	DET
iajs-3671	216	14	random	random	ADJ
iajs-3671	216	15	variables	variable	NOUN
iajs-3671	216	16	𝜖	𝜖	X
iajs-3671	216	17	=	=	X
iajs-3671	216	18	(	(	PUNCT
iajs-3671	216	19	𝜖𝑗	𝜖𝑗	NOUN
iajs-3671	216	20	)	)	PUNCT
iajs-3671	216	21	𝑗	𝑗	NOUN
iajs-3671	216	22	=	=	SYM
iajs-3671	216	23	1,2	1,2	NUM
iajs-3671	216	24	,	,	PUNCT
iajs-3671	216	25	…	…	PUNCT
iajs-3671	216	26	,	,	PUNCT
iajs-3671	216	27	𝑁	𝑁	PROPN
iajs-3671	216	28	as	as	SCONJ
iajs-3671	216	29	follows	follow	VERB
iajs-3671	216	30	:	:	PUNCT
iajs-3671	216	31	𝜖	𝜖	X
iajs-3671	216	32	=	=	PUNCT
iajs-3671	216	33	𝑛𝑜𝑟𝑚𝑟𝑛𝑑(0	𝑛𝑜𝑟𝑚𝑟𝑛𝑑(0	PROPN
iajs-3671	216	34	,	,	PUNCT
iajs-3671	216	35	𝜇𝑙	𝜇𝑙	INTJ
iajs-3671	216	36	,	,	PUNCT
iajs-3671	216	37	𝑁	𝑁	PROPN
iajs-3671	216	38	)	)	PUNCT
iajs-3671	216	39	𝑙	𝑙	NOUN
iajs-3671	216	40	=	=	SYM
iajs-3671	216	41	1,2	1,2	NUM
iajs-3671	216	42	(	(	PUNCT
iajs-3671	216	43	63	63	NUM
iajs-3671	216	44	)	)	SYM
iajs-3671	216	45	3.1	3.1	NUM
iajs-3671	216	46	results	result	NOUN
iajs-3671	216	47	and	and	CCONJ
iajs-3671	216	48	discussion	discussion	NOUN
iajs-3671	216	49	we	we	PRON
iajs-3671	216	50	introduce	introduce	VERB
iajs-3671	216	51	a	a	DET
iajs-3671	216	52	test	test	NOUN
iajs-3671	216	53	example	example	NOUN
iajs-3671	216	54	for	for	ADP
iajs-3671	216	55	each	each	DET
iajs-3671	216	56	inverse	inverse	NOUN
iajs-3671	216	57	problem	problem	NOUN
iajs-3671	216	58	.	.	PUNCT
iajs-3671	217	1	to	to	PART
iajs-3671	217	2	explain	explain	VERB
iajs-3671	217	3	the	the	DET
iajs-3671	217	4	stability	stability	NOUN
iajs-3671	217	5	and	and	CCONJ
iajs-3671	217	6	accuracy	accuracy	NOUN
iajs-3671	217	7	of	of	ADP
iajs-3671	217	8	the	the	DET
iajs-3671	217	9	computational	computational	ADJ
iajs-3671	217	10	procedure	procedure	NOUN
iajs-3671	217	11	that	that	PRON
iajs-3671	217	12	is	be	AUX
iajs-3671	217	13	based	base	VERB
iajs-3671	217	14	on	on	ADP
iajs-3671	217	15	the	the	DET
iajs-3671	217	16	finite	finite	ADJ
iajs-3671	217	17	difference	difference	NOUN
iajs-3671	217	18	method	method	NOUN
iajs-3671	217	19	combined	combine	VERB
iajs-3671	217	20	with	with	ADP
iajs-3671	217	21	the	the	DET
iajs-3671	217	22	depreciation	depreciation	NOUN
iajs-3671	217	23	of	of	ADP
iajs-3671	217	24	tikhonov	tikhonov	NOUN
iajs-3671	217	25	's	's	PART
iajs-3671	217	26	functional	functional	ADJ
iajs-3671	217	27	equations	equation	NOUN
iajs-3671	217	28	(	(	PUNCT
iajs-3671	217	29	59	59	NUM
iajs-3671	217	30	)	)	PUNCT
iajs-3671	217	31	and	and	CCONJ
iajs-3671	217	32	(	(	PUNCT
iajs-3671	217	33	60	60	NUM
iajs-3671	217	34	)	)	PUNCT
iajs-3671	217	35	.	.	PUNCT
iajs-3671	218	1	to	to	PART
iajs-3671	218	2	assess	assess	VERB
iajs-3671	218	3	the	the	DET
iajs-3671	218	4	reconstruction	reconstruction	NOUN
iajs-3671	218	5	accuracy	accuracy	NOUN
iajs-3671	218	6	of	of	ADP
iajs-3671	218	7	the	the	DET
iajs-3671	218	8	potential	potential	ADJ
iajs-3671	218	9	term	term	NOUN
iajs-3671	218	10	,	,	PUNCT
iajs-3671	218	11	we	we	PRON
iajs-3671	218	12	use	use	VERB
iajs-3671	218	13	root	root	NOUN
iajs-3671	218	14	mean	mean	NOUN
iajs-3671	218	15	squares	square	NOUN
iajs-3671	218	16	error	error	NOUN
iajs-3671	218	17	rmse	rmse	NOUN
iajs-3671	218	18	,	,	PUNCT
iajs-3671	218	19	which	which	PRON
iajs-3671	218	20	is	be	AUX
iajs-3671	218	21	given	give	VERB
iajs-3671	218	22	by	by	ADP
iajs-3671	218	23	the	the	DET
iajs-3671	218	24	following	follow	VERB
iajs-3671	218	25	expression	expression	NOUN
iajs-3671	218	26	(	(	PUNCT
iajs-3671	218	27	51	51	NUM
iajs-3671	218	28	):	):	PUNCT
iajs-3671	218	29	𝑟𝑚𝑠𝑒(𝑝	𝑟𝑚𝑠𝑒(𝑝	NUM
iajs-3671	218	30	)	)	PUNCT
iajs-3671	218	31	=	=	PUNCT
iajs-3671	219	1	√	√	ADP
iajs-3671	219	2	1	1	NUM
iajs-3671	219	3	𝑁	𝑁	PROPN
iajs-3671	219	4	∑(𝑝𝑗	∑(𝑝𝑗	NOUN
iajs-3671	219	5	−	−	NOUN
iajs-3671	219	6	𝑝𝑒𝑥𝑎𝑐𝑡(𝑡𝑗	𝑝𝑒𝑥𝑎𝑐𝑡(𝑡𝑗	PROPN
iajs-3671	219	7	)	)	PUNCT
iajs-3671	219	8	)	)	PUNCT
iajs-3671	220	1	2	2	NUM
iajs-3671	220	2	𝑁	𝑁	PROPN
iajs-3671	220	3	𝑗=1	𝑗=1	PROPN
iajs-3671	220	4	,	,	PUNCT
iajs-3671	220	5	(	(	PUNCT
iajs-3671	220	6	64	64	NUM
iajs-3671	220	7	)	)	PUNCT
iajs-3671	220	8	3.2	3.2	NUM
iajs-3671	220	9	numerical	numerical	ADJ
iajs-3671	220	10	results	result	NOUN
iajs-3671	220	11	for	for	ADP
iajs-3671	220	12	ipi	ipi	PROPN
iajs-3671	220	13	assume	assume	VERB
iajs-3671	220	14	the	the	DET
iajs-3671	220	15	inverse	inverse	NOUN
iajs-3671	220	16	problem	problem	NOUN
iajs-3671	220	17	i	i	PRON
iajs-3671	220	18	with	with	ADP
iajs-3671	220	19	t	t	NOUN
iajs-3671	220	20	=	=	SYM
iajs-3671	220	21	1	1	NUM
iajs-3671	220	22	and	and	CCONJ
iajs-3671	220	23	input	input	NOUN
iajs-3671	220	24	data	datum	NOUN
iajs-3671	220	25	𝑎	𝑎	NOUN
iajs-3671	220	26	=	=	SYM
iajs-3671	220	27	𝑏	𝑏	NOUN
iajs-3671	220	28	=	=	NOUN
iajs-3671	220	29	0.01	0.01	NUM
iajs-3671	220	30	:	:	PUNCT
iajs-3671	220	31	𝑢(𝑥	𝑢(𝑥	NUM
iajs-3671	220	32	,	,	PUNCT
iajs-3671	220	33	0	0	NUM
iajs-3671	220	34	)	)	PUNCT
iajs-3671	220	35	=	=	SYM
iajs-3671	220	36	cos(2𝜋𝑥	cos(2𝜋𝑥	NUM
iajs-3671	220	37	)	)	PUNCT
iajs-3671	220	38	𝑒1	𝑒1	NOUN
iajs-3671	220	39	,	,	PUNCT
iajs-3671	220	40	𝑥	𝑥	PRON
iajs-3671	220	41	∈	∈	PROPN
iajs-3671	221	1	[	[	X
iajs-3671	221	2	0,1	0,1	NUM
iajs-3671	221	3	]	]	PUNCT
iajs-3671	221	4	,	,	PUNCT
iajs-3671	221	5	(	(	PUNCT
iajs-3671	221	6	65	65	NUM
iajs-3671	221	7	)	)	PUNCT
iajs-3671	221	8	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	221	9	)	)	PUNCT
iajs-3671	221	10	=	=	SYM
iajs-3671	221	11	cos(2	cos(2	VERB
iajs-3671	221	12	𝜋	𝜋	NOUN
iajs-3671	221	13	𝑡	𝑡	PROPN
iajs-3671	221	14	)	)	PUNCT
iajs-3671	221	15	,	,	PUNCT
iajs-3671	221	16	𝑡	𝑡	PROPN
iajs-3671	221	17	∈	∈	PROPN
iajs-3671	222	1	[	[	X
iajs-3671	222	2	0	0	NUM
iajs-3671	222	3	,	,	PUNCT
iajs-3671	222	4	𝑇	𝑇	PROPN
iajs-3671	222	5	]	]	PUNCT
iajs-3671	222	6	,	,	PUNCT
iajs-3671	222	7	(	(	PUNCT
iajs-3671	222	8	66	66	NUM
iajs-3671	222	9	)	)	PUNCT
iajs-3671	222	10	ihjpas	ihjpa	NOUN
iajs-3671	222	11	.	.	PUNCT
iajs-3671	223	1	2025	2025	NUM
iajs-3671	223	2	,	,	PUNCT
iajs-3671	223	3	38	38	NUM
iajs-3671	223	4	(	(	PUNCT
iajs-3671	223	5	1	1	NUM
iajs-3671	223	6	)	)	PUNCT
iajs-3671	223	7	480	480	NUM
iajs-3671	223	8	𝑓(𝑥	𝑓(𝑥	NOUN
iajs-3671	223	9	,	,	PUNCT
iajs-3671	223	10	𝑡	𝑡	NOUN
iajs-3671	223	11	)	)	PUNCT
iajs-3671	224	1	=	=	SYM
iajs-3671	224	2	𝑒−𝑡(−0.367879	𝑒−𝑡(−0.367879	NOUN
iajs-3671	224	3	−	−	NOUN
iajs-3671	224	4	0.367879	0.367879	NUM
iajs-3671	224	5	cos(2𝜋	cos(2𝜋	PROPN
iajs-3671	224	6	𝑡	𝑡	X
iajs-3671	224	7	)	)	PUNCT
iajs-3671	224	8	)	)	PUNCT
iajs-3671	224	9	cos(2𝜋𝑥	cos(2𝜋𝑥	NUM
iajs-3671	224	10	)	)	PUNCT
iajs-3671	224	11	,	,	PUNCT
iajs-3671	224	12	(	(	PUNCT
iajs-3671	224	13	𝑥	𝑥	NOUN
iajs-3671	224	14	,	,	PUNCT
iajs-3671	224	15	𝑡	𝑡	NOUN
iajs-3671	224	16	)	)	PUNCT
iajs-3671	224	17	∈	∈	PROPN
iajs-3671	224	18	𝑄𝑇	𝑄𝑇	PROPN
iajs-3671	224	19	(	(	PUNCT
iajs-3671	224	20	67	67	NUM
iajs-3671	224	21	)	)	PUNCT
iajs-3671	224	22	with	with	ADP
iajs-3671	224	23	the	the	DET
iajs-3671	224	24	analytic	analytic	ADJ
iajs-3671	224	25	solution	solution	NOUN
iajs-3671	224	26	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	224	27	,	,	PUNCT
iajs-3671	224	28	𝑡	𝑡	X
iajs-3671	224	29	)	)	PUNCT
iajs-3671	224	30	=	=	SYM
iajs-3671	224	31	𝑒−1−𝑡	𝑒−1−𝑡	NUM
iajs-3671	224	32	cos(2𝜋𝑥	cos(2𝜋𝑥	NUM
iajs-3671	224	33	)	)	PUNCT
iajs-3671	224	34	,	,	PUNCT
iajs-3671	224	35	(	(	PUNCT
iajs-3671	224	36	𝑥	𝑥	NOUN
iajs-3671	224	37	,	,	PUNCT
iajs-3671	224	38	𝑡	𝑡	NOUN
iajs-3671	224	39	)	)	PUNCT
iajs-3671	224	40	∈	∈	PROPN
iajs-3671	224	41	𝑄𝑇	𝑄𝑇	PROPN
iajs-3671	224	42	,	,	PUNCT
iajs-3671	224	43	(	(	PUNCT
iajs-3671	224	44	68	68	NUM
iajs-3671	224	45	)	)	PUNCT
iajs-3671	224	46	and	and	CCONJ
iajs-3671	224	47	overdetermination	overdetermination	NOUN
iajs-3671	224	48	condition	condition	NOUN
iajs-3671	224	49	ℎ1(𝑡	ℎ1(𝑡	NOUN
iajs-3671	224	50	)	)	PUNCT
iajs-3671	224	51	=	=	SYM
iajs-3671	224	52	−𝑒	−𝑒	NOUN
iajs-3671	224	53	−1−𝑡	−1−𝑡	NOUN
iajs-3671	224	54	,	,	PUNCT
iajs-3671	224	55	𝑡	𝑡	PROPN
iajs-3671	224	56	∈	∈	PROPN
iajs-3671	225	1	[	[	X
iajs-3671	225	2	0	0	NUM
iajs-3671	225	3	,	,	PUNCT
iajs-3671	225	4	𝑇	𝑇	PROPN
iajs-3671	225	5	]	]	X
iajs-3671	225	6	(	(	PUNCT
iajs-3671	225	7	69	69	NUM
iajs-3671	225	8	)	)	PUNCT
iajs-3671	225	9	that	that	PRON
iajs-3671	225	10	can	can	AUX
iajs-3671	225	11	be	be	AUX
iajs-3671	225	12	checked	check	VERB
iajs-3671	225	13	by	by	ADP
iajs-3671	225	14	direct	direct	ADJ
iajs-3671	225	15	substitution	substitution	NOUN
iajs-3671	225	16	.	.	PUNCT
iajs-3671	226	1	figure	figure	NOUN
iajs-3671	226	2	5	5	NUM
iajs-3671	226	3	.	.	PUNCT
iajs-3671	226	4	shows	show	VERB
iajs-3671	226	5	the	the	DET
iajs-3671	226	6	numerical	numerical	ADJ
iajs-3671	226	7	solution	solution	NOUN
iajs-3671	226	8	of	of	ADP
iajs-3671	226	9	the	the	DET
iajs-3671	226	10	time	time	NOUN
iajs-3671	226	11	-	-	PUNCT
iajs-3671	226	12	dependent	dependent	ADJ
iajs-3671	226	13	potential	potential	ADJ
iajs-3671	226	14	term	term	NOUN
iajs-3671	226	15	from	from	ADP
iajs-3671	226	16	overdetermination	overdetermination	NOUN
iajs-3671	226	17	equation	equation	NOUN
iajs-3671	226	18	(	(	PUNCT
iajs-3671	226	19	6	6	NUM
iajs-3671	226	20	)	)	PUNCT
iajs-3671	226	21	in	in	ADP
iajs-3671	226	22	comparison	comparison	NOUN
iajs-3671	226	23	with	with	ADP
iajs-3671	226	24	the	the	DET
iajs-3671	226	25	exact	exact	ADJ
iajs-3671	226	26	solution	solution	NOUN
iajs-3671	226	27	(	(	PUNCT
iajs-3671	226	28	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	226	29	)	)	PUNCT
iajs-3671	226	30	=	=	PRON
iajs-3671	226	31	cos(2	cos(2	VERB
iajs-3671	226	32	𝜋𝑥	𝜋𝑥	NOUN
iajs-3671	226	33	)	)	PUNCT
iajs-3671	226	34	)	)	PUNCT
iajs-3671	226	35	,	,	PUNCT
iajs-3671	226	36	obtained	obtain	VERB
iajs-3671	226	37	by	by	ADP
iajs-3671	226	38	solving	solve	VERB
iajs-3671	226	39	the	the	DET
iajs-3671	226	40	ip	ip	NOUN
iajs-3671	226	41	-	-	NOUN
iajs-3671	226	42	i	i	PRON
iajs-3671	226	43	with	with	ADP
iajs-3671	226	44	the	the	DET
iajs-3671	226	45	above	above	ADJ
iajs-3671	226	46	input	input	NOUN
iajs-3671	226	47	data	datum	NOUN
iajs-3671	226	48	using	use	VERB
iajs-3671	226	49	the	the	DET
iajs-3671	226	50	fdm	fdm	NOUN
iajs-3671	226	51	,	,	PUNCT
iajs-3671	226	52	described	describe	VERB
iajs-3671	226	53	in	in	ADP
iajs-3671	226	54	section	section	NOUN
iajs-3671	226	55	2	2	NUM
iajs-3671	226	56	,	,	PUNCT
iajs-3671	226	57	with	with	ADP
iajs-3671	226	58	𝑀	𝑀	PROPN
iajs-3671	226	59	=	=	PUNCT
iajs-3671	226	60	𝑁	𝑁	PROPN
iajs-3671	226	61	∈	∈	PROPN
iajs-3671	226	62	{	{	PUNCT
iajs-3671	226	63	10	10	NUM
iajs-3671	226	64	,	,	PUNCT
iajs-3671	226	65	20,30	20,30	NUM
iajs-3671	226	66	,	,	PUNCT
iajs-3671	226	67	40	40	NUM
iajs-3671	226	68	}	}	PUNCT
iajs-3671	226	69	.	.	PUNCT
iajs-3671	227	1	this	this	DET
iajs-3671	227	2	figure	figure	NOUN
iajs-3671	227	3	shows	show	VERB
iajs-3671	227	4	that	that	SCONJ
iajs-3671	227	5	as	as	ADP
iajs-3671	227	6	mesh	mesh	NOUN
iajs-3671	227	7	size	size	NOUN
iajs-3671	227	8	increases	increase	NOUN
iajs-3671	227	9	,	,	PUNCT
iajs-3671	227	10	the	the	DET
iajs-3671	227	11	retrieved	retrieve	VERB
iajs-3671	227	12	coefficients	coefficient	NOUN
iajs-3671	227	13	converge	converge	VERB
iajs-3671	227	14	to	to	ADP
iajs-3671	227	15	the	the	DET
iajs-3671	227	16	exact	exact	ADJ
iajs-3671	227	17	solution	solution	NOUN
iajs-3671	227	18	,	,	PUNCT
iajs-3671	227	19	revealing	reveal	VERB
iajs-3671	227	20	that	that	DET
iajs-3671	227	21	mesh	mesh	NOUN
iajs-3671	227	22	independence	independence	NOUN
iajs-3671	227	23	occurs	occur	VERB
iajs-3671	227	24	.	.	PUNCT
iajs-3671	228	1	figure	figure	VERB
iajs-3671	228	2	6	6	NUM
iajs-3671	228	3	.	.	PUNCT
iajs-3671	229	1	shows	show	VERB
iajs-3671	229	2	that	that	SCONJ
iajs-3671	229	3	the	the	DET
iajs-3671	229	4	convergent	convergent	ADJ
iajs-3671	229	5	objective	objective	ADJ
iajs-3671	229	6	function	function	NOUN
iajs-3671	229	7	equation	equation	NOUN
iajs-3671	229	8	(	(	PUNCT
iajs-3671	229	9	59	59	NUM
iajs-3671	229	10	)	)	PUNCT
iajs-3671	229	11	reaches	reach	VERB
iajs-3671	229	12	a	a	DET
iajs-3671	229	13	very	very	ADV
iajs-3671	229	14	low	low	ADJ
iajs-3671	229	15	threshold	threshold	NOUN
iajs-3671	229	16	stationary	stationary	ADJ
iajs-3671	229	17	value	value	NOUN
iajs-3671	229	18	of	of	ADP
iajs-3671	229	19	𝑂(10−8	𝑂(10−8	NOUN
iajs-3671	229	20	)	)	PUNCT
iajs-3671	229	21	and	and	CCONJ
iajs-3671	229	22	is	be	AUX
iajs-3671	229	23	plotted	plot	VERB
iajs-3671	229	24	with	with	ADP
iajs-3671	229	25	𝑀	𝑀	PROPN
iajs-3671	229	26	=	=	PUNCT
iajs-3671	229	27	𝑁	𝑁	PROPN
iajs-3671	229	28	∈	∈	PROPN
iajs-3671	229	29	{	{	PUNCT
iajs-3671	229	30	10	10	NUM
iajs-3671	229	31	,	,	PUNCT
iajs-3671	229	32	20,30	20,30	NUM
iajs-3671	229	33	,	,	PUNCT
iajs-3671	229	34	40	40	NUM
iajs-3671	229	35	}	}	PUNCT
iajs-3671	229	36	.	.	PUNCT
iajs-3671	230	1	from	from	ADP
iajs-3671	230	2	these	these	DET
iajs-3671	230	3	figures	figure	NOUN
iajs-3671	230	4	,	,	PUNCT
iajs-3671	230	5	it	it	PRON
iajs-3671	230	6	can	can	AUX
iajs-3671	230	7	be	be	AUX
iajs-3671	230	8	observed	observe	VERB
iajs-3671	230	9	a	a	DET
iajs-3671	230	10	speed	speed	NOUN
iajs-3671	230	11	convergence	convergence	NOUN
iajs-3671	230	12	is	be	AUX
iajs-3671	230	13	achieved	achieve	VERB
iajs-3671	230	14	in	in	ADP
iajs-3671	230	15	no	no	DET
iajs-3671	230	16	more	more	ADJ
iajs-3671	230	17	than	than	ADP
iajs-3671	230	18	15	15	NUM
iajs-3671	230	19	iterations	iteration	NOUN
iajs-3671	230	20	only	only	ADV
iajs-3671	230	21	to	to	PART
iajs-3671	230	22	reach	reach	VERB
iajs-3671	230	23	a	a	DET
iajs-3671	230	24	meagre	meagre	ADJ
iajs-3671	230	25	value	value	NOUN
iajs-3671	230	26	when	when	SCONJ
iajs-3671	230	27	𝑀	𝑀	PROPN
iajs-3671	230	28	=	=	SYM
iajs-3671	230	29	𝑁	𝑁	PROPN
iajs-3671	230	30	=	=	SYM
iajs-3671	230	31	40	40	NUM
iajs-3671	230	32	,	,	PUNCT
iajs-3671	230	33	for	for	ADP
iajs-3671	230	34	example	example	NOUN
iajs-3671	230	35	.	.	PUNCT
iajs-3671	231	1	next	next	ADV
iajs-3671	231	2	,	,	PUNCT
iajs-3671	231	3	we	we	PRON
iajs-3671	231	4	choose	choose	VERB
iajs-3671	231	5	𝑁	𝑁	PROPN
iajs-3671	231	6	=	=	SYM
iajs-3671	231	7	𝑀	𝑀	PROPN
iajs-3671	231	8	=	=	NUM
iajs-3671	231	9	40	40	NUM
iajs-3671	231	10	for	for	ADP
iajs-3671	231	11	the	the	DET
iajs-3671	231	12	rest	rest	NOUN
iajs-3671	231	13	of	of	ADP
iajs-3671	231	14	the	the	DET
iajs-3671	231	15	numerical	numerical	ADJ
iajs-3671	231	16	investigation	investigation	NOUN
iajs-3671	231	17	,	,	PUNCT
iajs-3671	231	18	with	with	ADP
iajs-3671	231	19	cases	case	NOUN
iajs-3671	231	20	(	(	PUNCT
iajs-3671	231	21	𝑞	𝑞	X
iajs-3671	231	22	=	=	SYM
iajs-3671	231	23	0	0	NUM
iajs-3671	231	24	%	%	NOUN
iajs-3671	231	25	,	,	PUNCT
iajs-3671	231	26	0.5	0.5	NUM
iajs-3671	231	27	%	%	NOUN
iajs-3671	231	28	,	,	PUNCT
iajs-3671	231	29	1	1	NUM
iajs-3671	231	30	%	%	NOUN
iajs-3671	231	31	)	)	PUNCT
iajs-3671	231	32	included	include	VERB
iajs-3671	231	33	in	in	ADP
iajs-3671	231	34	the	the	DET
iajs-3671	231	35	measurement	measurement	NOUN
iajs-3671	231	36	data	data	NOUN
iajs-3671	231	37	equation	equation	NOUN
iajs-3671	231	38	(	(	PUNCT
iajs-3671	231	39	6	6	NUM
iajs-3671	231	40	)	)	PUNCT
iajs-3671	231	41	.	.	PUNCT
iajs-3671	232	1	figure	figure	NOUN
iajs-3671	232	2	7	7	NUM
iajs-3671	232	3	.	.	PUNCT
iajs-3671	233	1	explains	explain	VERB
iajs-3671	233	2	the	the	DET
iajs-3671	233	3	plotting	plotting	NOUN
iajs-3671	233	4	of	of	ADP
iajs-3671	233	5	the	the	DET
iajs-3671	233	6	exact	exact	ADJ
iajs-3671	233	7	solution	solution	NOUN
iajs-3671	233	8	and	and	CCONJ
iajs-3671	233	9	numerical	numerical	ADJ
iajs-3671	233	10	results	result	NOUN
iajs-3671	233	11	for	for	ADP
iajs-3671	233	12	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	233	13	)	)	PUNCT
iajs-3671	233	14	with	with	ADP
iajs-3671	233	15	no	no	DET
iajs-3671	233	16	regularization	regularization	NOUN
iajs-3671	233	17	(	(	PUNCT
iajs-3671	233	18	𝛽	𝛽	NOUN
iajs-3671	233	19	=	=	NOUN
iajs-3671	233	20	0	0	NUM
iajs-3671	233	21	)	)	PUNCT
iajs-3671	233	22	and	and	CCONJ
iajs-3671	233	23	no	no	DET
iajs-3671	233	24	noise	noise	NOUN
iajs-3671	233	25	(	(	PUNCT
iajs-3671	233	26	𝑞	𝑞	X
iajs-3671	233	27	=	=	SYM
iajs-3671	233	28	0	0	NUM
iajs-3671	233	29	%	%	NOUN
iajs-3671	233	30	)	)	PUNCT
iajs-3671	233	31	and	and	CCONJ
iajs-3671	233	32	noise	noise	VERB
iajs-3671	233	33	𝑞	𝑞	X
iajs-3671	233	34	∈	∈	PROPN
iajs-3671	233	35	{	{	PUNCT
iajs-3671	233	36	0	0	NUM
iajs-3671	233	37	.	.	NOUN
iajs-3671	233	38	5	5	NUM
iajs-3671	233	39	%	%	NOUN
iajs-3671	233	40	,	,	PUNCT
iajs-3671	233	41	1	1	NUM
iajs-3671	233	42	%	%	NOUN
iajs-3671	233	43	}	}	PUNCT
iajs-3671	233	44	.	.	PUNCT
iajs-3671	234	1	it	it	PRON
iajs-3671	234	2	is	be	AUX
iajs-3671	234	3	clear	clear	ADJ
iajs-3671	234	4	that	that	SCONJ
iajs-3671	234	5	as	as	SCONJ
iajs-3671	234	6	the	the	DET
iajs-3671	234	7	noise	noise	NOUN
iajs-3671	234	8	percentage	percentage	NOUN
iajs-3671	234	9	increases	increase	VERB
iajs-3671	234	10	from	from	ADP
iajs-3671	234	11	0	0	NUM
iajs-3671	234	12	%	%	NOUN
iajs-3671	234	13	to	to	PART
iajs-3671	234	14	1	1	NUM
iajs-3671	234	15	%	%	NOUN
iajs-3671	234	16	,	,	PUNCT
iajs-3671	234	17	the	the	DET
iajs-3671	234	18	identified	identify	VERB
iajs-3671	234	19	coefficient	coefficient	NOUN
iajs-3671	234	20	has	have	VERB
iajs-3671	234	21	oscillatory	oscillatory	ADJ
iajs-3671	234	22	behaviour	behaviour	NOUN
iajs-3671	234	23	,	,	PUNCT
iajs-3671	234	24	which	which	PRON
iajs-3671	234	25	is	be	AUX
iajs-3671	234	26	expected	expect	VERB
iajs-3671	234	27	since	since	SCONJ
iajs-3671	234	28	the	the	DET
iajs-3671	234	29	problem	problem	NOUN
iajs-3671	234	30	under	under	ADP
iajs-3671	234	31	investigation	investigation	NOUN
iajs-3671	234	32	is	be	AUX
iajs-3671	234	33	ill	ill	ADV
iajs-3671	234	34	-	-	PUNCT
iajs-3671	234	35	posed	pose	VERB
iajs-3671	234	36	.	.	PUNCT
iajs-3671	235	1	therefore	therefore	ADV
iajs-3671	235	2	,	,	PUNCT
iajs-3671	235	3	a	a	DET
iajs-3671	235	4	sort	sort	NOUN
iajs-3671	235	5	of	of	ADP
iajs-3671	235	6	stabilization	stabilization	NOUN
iajs-3671	235	7	should	should	AUX
iajs-3671	235	8	be	be	AUX
iajs-3671	235	9	applied	apply	VERB
iajs-3671	235	10	in	in	ADP
iajs-3671	235	11	order	order	NOUN
iajs-3671	235	12	to	to	PART
iajs-3671	235	13	restore	restore	VERB
iajs-3671	235	14	stability	stability	NOUN
iajs-3671	235	15	and	and	CCONJ
iajs-3671	235	16	reduce	reduce	VERB
iajs-3671	235	17	the	the	DET
iajs-3671	235	18	oscillatory	oscillatory	ADJ
iajs-3671	235	19	behaviour	behaviour	NOUN
iajs-3671	235	20	.	.	PUNCT
iajs-3671	236	1	figure	figure	VERB
iajs-3671	236	2	5	5	NUM
iajs-3671	236	3	.	.	NOUN
iajs-3671	236	4	numerical	numerical	ADJ
iajs-3671	236	5	and	and	CCONJ
iajs-3671	236	6	exact	exact	ADJ
iajs-3671	236	7	solution	solution	NOUN
iajs-3671	236	8	for	for	ADP
iajs-3671	236	9	potential	potential	ADJ
iajs-3671	236	10	term	term	NOUN
iajs-3671	236	11	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	236	12	)	)	PUNCT
iajs-3671	237	1	when	when	SCONJ
iajs-3671	237	2	𝑀	𝑀	PROPN
iajs-3671	237	3	=	=	SYM
iajs-3671	237	4	𝑁	𝑁	PROPN
iajs-3671	237	5	∈	∈	PROPN
iajs-3671	237	6	{	{	PUNCT
iajs-3671	237	7	10	10	NUM
iajs-3671	237	8	,	,	PUNCT
iajs-3671	237	9	20	20	NUM
iajs-3671	237	10	,	,	PUNCT
iajs-3671	237	11	30,40	30,40	NUM
iajs-3671	237	12	}	}	PUNCT
iajs-3671	237	13	.	.	PUNCT
iajs-3671	237	14	0	0	NUM
iajs-3671	237	15	0.1	0.1	NUM
iajs-3671	237	16	0.2	0.2	NUM
iajs-3671	237	17	0.3	0.3	NUM
iajs-3671	237	18	0.4	0.4	NUM
iajs-3671	237	19	0.5	0.5	NUM
iajs-3671	237	20	0.6	0.6	NUM
iajs-3671	237	21	0.7	0.7	NUM
iajs-3671	237	22	0.8	0.8	NUM
iajs-3671	237	23	0.9	0.9	NUM
iajs-3671	237	24	1	1	NUM
iajs-3671	237	25	t	t	NOUN
iajs-3671	237	26	-1	-1	PUNCT
iajs-3671	237	27	-0.5	-0.5	X
iajs-3671	237	28	0	0	NUM
iajs-3671	237	29	0.5	0.5	NUM
iajs-3671	237	30	1	1	NUM
iajs-3671	237	31	1.5	1.5	NUM
iajs-3671	237	32	p	p	NOUN
iajs-3671	237	33	(	(	PUNCT
iajs-3671	237	34	t	t	PROPN
iajs-3671	237	35	)	)	PUNCT
iajs-3671	237	36	exact	exact	NOUN
iajs-3671	237	37	m	m	NOUN
iajs-3671	237	38	=	=	NOUN
iajs-3671	237	39	n=10	n=10	NOUN
iajs-3671	237	40	m	m	NOUN
iajs-3671	237	41	=	=	NOUN
iajs-3671	237	42	n=20	n=20	NOUN
iajs-3671	237	43	m	m	NOUN
iajs-3671	237	44	=	=	PROPN
iajs-3671	237	45	n=30	n=30	PROPN
iajs-3671	237	46	m	m	PART
iajs-3671	237	47	=	=	ADJ
iajs-3671	237	48	n=40	n=40	ADJ
iajs-3671	237	49	ihjpas	ihjpa	NOUN
iajs-3671	237	50	.	.	PUNCT
iajs-3671	238	1	2025	2025	NUM
iajs-3671	238	2	,	,	PUNCT
iajs-3671	238	3	38	38	NUM
iajs-3671	238	4	(	(	PUNCT
iajs-3671	238	5	1	1	NUM
iajs-3671	238	6	)	)	PUNCT
iajs-3671	238	7	481	481	NUM
iajs-3671	238	8	figure	figure	NOUN
iajs-3671	238	9	6	6	NUM
iajs-3671	238	10	.	.	PUNCT
iajs-3671	239	1	the	the	DET
iajs-3671	239	2	unregularized	unregularized	ADJ
iajs-3671	239	3	objective	objective	ADJ
iajs-3671	239	4	function	function	NOUN
iajs-3671	239	5	equation	equation	NOUN
iajs-3671	239	6	(	(	PUNCT
iajs-3671	239	7	59	59	NUM
iajs-3671	239	8	)	)	PUNCT
iajs-3671	239	9	,	,	PUNCT
iajs-3671	239	10	with	with	ADP
iajs-3671	239	11	(	(	PUNCT
iajs-3671	239	12	𝑞	𝑞	X
iajs-3671	239	13	=	=	NOUN
iajs-3671	239	14	0	0	NUM
iajs-3671	239	15	)	)	PUNCT
iajs-3671	239	16	and	and	CCONJ
iajs-3671	239	17	𝑀	𝑀	PROPN
iajs-3671	239	18	=	=	PUNCT
iajs-3671	239	19	𝑁	𝑁	PROPN
iajs-3671	239	20	∈	∈	PROPN
iajs-3671	239	21	{	{	PUNCT
iajs-3671	239	22	10	10	NUM
iajs-3671	239	23	,	,	PUNCT
iajs-3671	239	24	20	20	NUM
iajs-3671	239	25	,	,	PUNCT
iajs-3671	239	26	30,40	30,40	NUM
iajs-3671	239	27	}	}	PUNCT
iajs-3671	239	28	.	.	PUNCT
iajs-3671	240	1	the	the	DET
iajs-3671	240	2	associated	associated	PROPN
iajs-3671	240	3	numerical	numerical	ADJ
iajs-3671	240	4	results	result	NOUN
iajs-3671	240	5	for	for	ADP
iajs-3671	240	6	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	240	7	)	)	PUNCT
iajs-3671	240	8	after	after	ADP
iajs-3671	240	9	applying	apply	VERB
iajs-3671	240	10	tikhonov	tikhonov	NOUN
iajs-3671	240	11	’s	’s	PART
iajs-3671	240	12	regularization	regularization	NOUN
iajs-3671	240	13	method	method	NOUN
iajs-3671	240	14	with	with	ADP
iajs-3671	240	15	𝛽	𝛽	PROPN
iajs-3671	240	16	∈	∈	PROPN
iajs-3671	240	17	{	{	PUNCT
iajs-3671	240	18	10−4	10−4	NUM
iajs-3671	240	19	,	,	PUNCT
iajs-3671	240	20	10−5	10−5	NUM
iajs-3671	240	21	,	,	PUNCT
iajs-3671	240	22	10−6	10−6	NUM
iajs-3671	240	23	}	}	PUNCT
iajs-3671	240	24	for	for	ADP
iajs-3671	240	25	case	case	NOUN
iajs-3671	240	26	𝑞	𝑞	X
iajs-3671	240	27	=	=	PUNCT
iajs-3671	240	28	{	{	PUNCT
iajs-3671	240	29	0	0	NUM
iajs-3671	240	30	.	.	NOUN
iajs-3671	240	31	5	5	NUM
iajs-3671	240	32	%	%	NOUN
iajs-3671	240	33	}	}	PUNCT
iajs-3671	240	34	and	and	CCONJ
iajs-3671	240	35	𝛽	𝛽	PROPN
iajs-3671	240	36	∈	∈	PROPN
iajs-3671	240	37	{	{	PUNCT
iajs-3671	240	38	10−4	10−4	NUM
iajs-3671	240	39	,	,	PUNCT
iajs-3671	240	40	10−5	10−5	NUM
iajs-3671	240	41	}	}	PUNCT
iajs-3671	240	42	for	for	ADP
iajs-3671	240	43	case	case	NOUN
iajs-3671	240	44	𝑞	𝑞	X
iajs-3671	240	45	=	=	PUNCT
iajs-3671	240	46	{	{	PUNCT
iajs-3671	240	47	1	1	NUM
iajs-3671	240	48	%	%	NOUN
iajs-3671	240	49	}	}	PUNCT
iajs-3671	240	50	are	be	AUX
iajs-3671	240	51	presented	present	VERB
iajs-3671	240	52	in	in	ADP
iajs-3671	240	53	figures	figure	NOUN
iajs-3671	240	54	8	8	NUM
iajs-3671	240	55	.	.	PUNCT
iajs-3671	241	1	and	and	CCONJ
iajs-3671	241	2	9	9	NUM
iajs-3671	241	3	.	.	NUM
iajs-3671	241	4	,	,	PUNCT
iajs-3671	241	5	respectively	respectively	ADV
iajs-3671	241	6	.	.	PUNCT
iajs-3671	242	1	from	from	ADP
iajs-3671	242	2	this	this	DET
iajs-3671	242	3	figure	figure	NOUN
iajs-3671	242	4	,	,	PUNCT
iajs-3671	242	5	one	one	PRON
iajs-3671	242	6	can	can	AUX
iajs-3671	242	7	deduce	deduce	VERB
iajs-3671	242	8	that	that	PRON
iajs-3671	242	9	as	as	SCONJ
iajs-3671	242	10	𝛽	𝛽	PROPN
iajs-3671	242	11	=	=	SYM
iajs-3671	242	12	10−4	10−4	NUM
iajs-3671	242	13	recover	recover	VERB
iajs-3671	242	14	adequate	adequate	ADJ
iajs-3671	242	15	identification	identification	NOUN
iajs-3671	242	16	with	with	ADP
iajs-3671	242	17	reasonable	reasonable	ADJ
iajs-3671	242	18	accuracy	accuracy	NOUN
iajs-3671	242	19	with	with	ADP
iajs-3671	242	20	𝑟𝑚𝑠𝑒(𝑝	𝑟𝑚𝑠𝑒(𝑝	NOUN
iajs-3671	242	21	)	)	PUNCT
iajs-3671	242	22	=	=	PUNCT
iajs-3671	242	23	{	{	PUNCT
iajs-3671	242	24	0.2987	0.2987	NUM
iajs-3671	242	25	,	,	PUNCT
iajs-3671	242	26	0.3328	0.3328	NUM
iajs-3671	242	27	}	}	PUNCT
iajs-3671	242	28	for	for	ADP
iajs-3671	242	29	𝑞	𝑞	PROPN
iajs-3671	242	30	∈	∈	PROPN
iajs-3671	242	31	{	{	PUNCT
iajs-3671	242	32	0.5	0.5	NUM
iajs-3671	242	33	,	,	PUNCT
iajs-3671	242	34	1}%	1}%	NUM
iajs-3671	242	35	noise	noise	NOUN
iajs-3671	242	36	,	,	PUNCT
iajs-3671	242	37	respectively	respectively	ADV
iajs-3671	242	38	.	.	PUNCT
iajs-3671	243	1	the	the	DET
iajs-3671	243	2	3d	3d	NOUN
iajs-3671	243	3	graph	graph	NOUN
iajs-3671	243	4	for	for	ADP
iajs-3671	243	5	exact	exact	ADJ
iajs-3671	243	6	,	,	PUNCT
iajs-3671	243	7	numerical	numerical	ADJ
iajs-3671	243	8	and	and	CCONJ
iajs-3671	243	9	absolute	absolute	ADJ
iajs-3671	243	10	error	error	NOUN
iajs-3671	243	11	between	between	ADP
iajs-3671	243	12	the	the	DET
iajs-3671	243	13	exact	exact	ADJ
iajs-3671	243	14	solution	solution	NOUN
iajs-3671	243	15	and	and	CCONJ
iajs-3671	243	16	numerical	numerical	ADJ
iajs-3671	243	17	solution	solution	NOUN
iajs-3671	243	18	for	for	ADP
iajs-3671	243	19	temperatures	temperature	NOUN
iajs-3671	243	20	(	(	PUNCT
iajs-3671	243	21	𝑈𝑋	𝑈𝑋	PROPN
iajs-3671	243	22	,	,	PUNCT
iajs-3671	243	23	𝑡	𝑡	NOUN
iajs-3671	243	24	)	)	PUNCT
iajs-3671	243	25	plotted	plot	VERB
iajs-3671	243	26	in	in	ADP
iajs-3671	243	27	figure	figure	NOUN
iajs-3671	243	28	10	10	NUM
iajs-3671	243	29	.	.	PUNCT
iajs-3671	244	1	with	with	ADP
iajs-3671	244	2	(	(	PUNCT
iajs-3671	244	3	a	a	NOUN
iajs-3671	244	4	)	)	PUNCT
iajs-3671	244	5	𝑞	𝑞	NOUN
iajs-3671	244	6	=	=	SYM
iajs-3671	244	7	0.5	0.5	NUM
iajs-3671	244	8	%	%	NOUN
iajs-3671	244	9	and	and	CCONJ
iajs-3671	244	10	(	(	PUNCT
iajs-3671	244	11	b	b	NOUN
iajs-3671	244	12	)	)	PUNCT
iajs-3671	244	13	𝑞	𝑞	NOUN
iajs-3671	244	14	=	=	SYM
iajs-3671	244	15	1	1	NUM
iajs-3671	244	16	%	%	NOUN
iajs-3671	244	17	with	with	ADP
iajs-3671	244	18	𝛽	𝛽	NOUN
iajs-3671	244	19	=	=	SYM
iajs-3671	244	20	10−4	10−4	NUM
iajs-3671	244	21	and	and	CCONJ
iajs-3671	244	22	also	also	ADV
iajs-3671	244	23	accurate	accurate	ADJ
iajs-3671	244	24	identification	identification	NOUN
iajs-3671	244	25	is	be	AUX
iajs-3671	244	26	obtained	obtain	VERB
iajs-3671	244	27	in	in	ADP
iajs-3671	244	28	terms	term	NOUN
iajs-3671	244	29	of	of	ADP
iajs-3671	244	30	free	free	ADJ
iajs-3671	244	31	oscillation	oscillation	NOUN
iajs-3671	244	32	.	.	PUNCT
iajs-3671	245	1	next	next	ADV
iajs-3671	245	2	,	,	PUNCT
iajs-3671	245	3	in	in	ADP
iajs-3671	245	4	table	table	NOUN
iajs-3671	245	5	1	1	NUM
iajs-3671	245	6	.	.	PUNCT
iajs-3671	246	1	we	we	PRON
iajs-3671	246	2	compute	compute	VERB
iajs-3671	246	3	the	the	DET
iajs-3671	246	4	𝑟𝑚𝑠𝑒	𝑟𝑚𝑠𝑒	NOUN
iajs-3671	246	5	values	value	VERB
iajs-3671	246	6	equation	equation	NOUN
iajs-3671	246	7	(	(	PUNCT
iajs-3671	246	8	64	64	NUM
iajs-3671	246	9	)	)	PUNCT
iajs-3671	246	10	for	for	ADP
iajs-3671	246	11	𝛽	𝛽	NOUN
iajs-3671	246	12	∈	∈	PROPN
iajs-3671	246	13	{	{	PUNCT
iajs-3671	246	14	10−𝑖	10−𝑖	NUM
iajs-3671	246	15	,	,	PUNCT
iajs-3671	246	16	𝑖	𝑖	X
iajs-3671	246	17	=	=	SYM
iajs-3671	246	18	4	4	NUM
iajs-3671	246	19	,	,	PUNCT
iajs-3671	246	20	5	5	NUM
iajs-3671	246	21	,	,	PUNCT
iajs-3671	246	22	6	6	NUM
iajs-3671	246	23	}	}	PUNCT
iajs-3671	246	24	and	and	CCONJ
iajs-3671	246	25	𝑞	𝑞	X
iajs-3671	246	26	∈	∈	PROPN
iajs-3671	246	27	{	{	PUNCT
iajs-3671	246	28	0.5	0.5	NUM
iajs-3671	246	29	,	,	PUNCT
iajs-3671	246	30	1}%	1}%	NUM
iajs-3671	246	31	.	.	PUNCT
iajs-3671	247	1	figures	figure	NOUN
iajs-3671	247	2	8	8	NUM
iajs-3671	247	3	,	,	PUNCT
iajs-3671	247	4	9	9	NUM
iajs-3671	247	5	,	,	PUNCT
iajs-3671	247	6	10	10	NUM
iajs-3671	247	7	.	.	PUNCT
iajs-3671	248	1	and	and	CCONJ
iajs-3671	248	2	table	table	NOUN
iajs-3671	248	3	1	1	NUM
iajs-3671	248	4	.	.	PUNCT
iajs-3671	249	1	show	show	VERB
iajs-3671	249	2	good	good	ADJ
iajs-3671	249	3	correspondence	correspondence	NOUN
iajs-3671	249	4	and	and	CCONJ
iajs-3671	249	5	convergence	convergence	NOUN
iajs-3671	249	6	between	between	ADP
iajs-3671	249	7	the	the	DET
iajs-3671	249	8	numerical	numerical	ADJ
iajs-3671	249	9	solutions	solution	NOUN
iajs-3671	249	10	of	of	ADP
iajs-3671	249	11	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	249	12	)	)	PUNCT
iajs-3671	249	13	and	and	CCONJ
iajs-3671	249	14	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	249	15	,	,	PUNCT
iajs-3671	249	16	𝑡	𝑡	PROPN
iajs-3671	249	17	)	)	PUNCT
iajs-3671	249	18	with	with	ADP
iajs-3671	249	19	their	their	PRON
iajs-3671	249	20	corresponding	corresponding	ADJ
iajs-3671	249	21	exact	exact	ADJ
iajs-3671	249	22	solutions	solution	NOUN
iajs-3671	249	23	when	when	SCONJ
iajs-3671	249	24	𝑞	𝑞	PROPN
iajs-3671	249	25	decreases	decrease	VERB
iajs-3671	249	26	from	from	ADP
iajs-3671	249	27	1	1	NUM
iajs-3671	249	28	%	%	NOUN
iajs-3671	249	29	𝑡𝑜	𝑡𝑜	NOUN
iajs-3671	249	30	0.5	0.5	NUM
iajs-3671	249	31	%	%	NOUN
iajs-3671	249	32	and	and	CCONJ
iajs-3671	249	33	then	then	ADV
iajs-3671	249	34	to	to	ADP
iajs-3671	249	35	0	0	NUM
iajs-3671	249	36	%	%	NOUN
iajs-3671	249	37	.	.	PUNCT
iajs-3671	250	1	figure	figure	NOUN
iajs-3671	250	2	7	7	NUM
iajs-3671	250	3	.	.	PUNCT
iajs-3671	250	4	numerical	numerical	ADJ
iajs-3671	250	5	reconstructions	reconstruction	NOUN
iajs-3671	250	6	and	and	CCONJ
iajs-3671	250	7	exact	exact	ADJ
iajs-3671	250	8	solution	solution	NOUN
iajs-3671	250	9	for	for	ADP
iajs-3671	250	10	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	250	11	)	)	PUNCT
iajs-3671	250	12	,	,	PUNCT
iajs-3671	250	13	with	with	ADP
iajs-3671	250	14	noise	noise	NOUN
iajs-3671	250	15	level	level	NOUN
iajs-3671	250	16	𝑞	𝑞	X
iajs-3671	250	17	=	=	X
iajs-3671	250	18	{	{	PUNCT
iajs-3671	250	19	0	0	NUM
iajs-3671	250	20	,	,	PUNCT
iajs-3671	250	21	0.5	0.5	NUM
iajs-3671	250	22	%	%	NOUN
iajs-3671	250	23	,	,	PUNCT
iajs-3671	250	24	1	1	NUM
iajs-3671	250	25	%	%	NOUN
iajs-3671	250	26	}	}	PUNCT
iajs-3671	250	27	,	,	PUNCT
iajs-3671	250	28	without	without	SCONJ
iajs-3671	250	29	regularization	regularization	NOUN
iajs-3671	250	30	applied	apply	VERB
iajs-3671	250	31	for	for	ADP
iajs-3671	250	32	ipi	ipi	PROPN
iajs-3671	250	33	.	.	PUNCT
iajs-3671	250	34	0	0	NUM
iajs-3671	251	1	5	5	NUM
iajs-3671	251	2	10	10	NUM
iajs-3671	251	3	15	15	NUM
iajs-3671	251	4	number	number	NOUN
iajs-3671	251	5	of	of	ADP
iajs-3671	251	6	iterations	iteration	NOUN
iajs-3671	251	7	10	10	NUM
iajs-3671	251	8	-8	-8	NUM
iajs-3671	251	9	10	10	NUM
iajs-3671	251	10	-7	-7	NUM
iajs-3671	251	11	10	10	NUM
iajs-3671	251	12	-6	-6	NOUN
iajs-3671	251	13	10	10	NUM
iajs-3671	251	14	-5	-5	NUM
iajs-3671	251	15	10	10	NUM
iajs-3671	251	16	-4	-4	SYM
iajs-3671	251	17	10	10	NUM
iajs-3671	251	18	-3	-3	SYM
iajs-3671	251	19	10	10	NUM
iajs-3671	251	20	-2	-2	NOUN
iajs-3671	251	21	10	10	NUM
iajs-3671	251	22	-1	-1	SYM
iajs-3671	251	23	10	10	NUM
iajs-3671	251	24	0	0	NUM
iajs-3671	251	25	o	o	PROPN
iajs-3671	251	26	b	b	X
iajs-3671	251	27	je	je	X
iajs-3671	251	28	c	c	X
iajs-3671	251	29	ti	ti	X
iajs-3671	251	30	v	v	ADP
iajs-3671	251	31	e	e	X
iajs-3671	251	32	f	f	PROPN
iajs-3671	251	33	u	u	PROPN
iajs-3671	251	34	n	n	ADV
iajs-3671	251	35	c	c	NOUN
iajs-3671	251	36	ti	ti	NOUN
iajs-3671	251	37	o	o	PROPN
iajs-3671	251	38	n	n	PROPN
iajs-3671	251	39	m	m	NOUN
iajs-3671	251	40	=	=	NOUN
iajs-3671	251	41	n=10	n=10	NOUN
iajs-3671	251	42	m	m	NOUN
iajs-3671	251	43	=	=	NOUN
iajs-3671	251	44	n=20	n=20	NOUN
iajs-3671	251	45	m	m	NOUN
iajs-3671	251	46	=	=	PROPN
iajs-3671	251	47	n=30	n=30	NOUN
iajs-3671	251	48	m	m	NOUN
iajs-3671	251	49	=	=	NOUN
iajs-3671	251	50	n=40	n=40	ADJ
iajs-3671	251	51	0	0	NUM
iajs-3671	251	52	0.1	0.1	NUM
iajs-3671	251	53	0.2	0.2	NUM
iajs-3671	251	54	0.3	0.3	NUM
iajs-3671	251	55	0.4	0.4	NUM
iajs-3671	251	56	0.5	0.5	NUM
iajs-3671	251	57	0.6	0.6	NUM
iajs-3671	251	58	0.7	0.7	NUM
iajs-3671	251	59	0.8	0.8	NUM
iajs-3671	251	60	0.9	0.9	NUM
iajs-3671	251	61	1	1	NUM
iajs-3671	251	62	t	t	NOUN
iajs-3671	252	1	-6	-6	INTJ
iajs-3671	252	2	-4	-4	INTJ
iajs-3671	253	1	-2	-2	NOUN
iajs-3671	253	2	0	0	NUM
iajs-3671	254	1	2	2	NUM
iajs-3671	254	2	4	4	NUM
iajs-3671	254	3	6	6	NUM
iajs-3671	254	4	p	p	NOUN
iajs-3671	254	5	(	(	PUNCT
iajs-3671	254	6	t	t	NOUN
iajs-3671	254	7	)	)	PUNCT
iajs-3671	254	8	exact	exact	ADJ
iajs-3671	254	9	q=0	q=0	NOUN
iajs-3671	254	10	%	%	NOUN
iajs-3671	254	11	q=0.5	q=0.5	NOUN
iajs-3671	254	12	%	%	NOUN
iajs-3671	254	13	q=1	q=1	NUM
iajs-3671	254	14	%	%	NOUN
iajs-3671	254	15	ihjpas	ihjpa	NOUN
iajs-3671	254	16	.	.	PUNCT
iajs-3671	255	1	2025	2025	NUM
iajs-3671	255	2	,	,	PUNCT
iajs-3671	255	3	38	38	NUM
iajs-3671	255	4	(	(	PUNCT
iajs-3671	255	5	1	1	NUM
iajs-3671	255	6	)	)	PUNCT
iajs-3671	255	7	482	482	NUM
iajs-3671	255	8	figure	figure	NOUN
iajs-3671	255	9	8	8	NUM
iajs-3671	255	10	.	.	PUNCT
iajs-3671	255	11	numerical	numerical	ADJ
iajs-3671	255	12	reconstructions	reconstruction	NOUN
iajs-3671	255	13	and	and	CCONJ
iajs-3671	255	14	exact	exact	ADJ
iajs-3671	255	15	solution	solution	NOUN
iajs-3671	255	16	for	for	ADP
iajs-3671	255	17	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	255	18	)	)	PUNCT
iajs-3671	255	19	,	,	PUNCT
iajs-3671	255	20	with	with	ADP
iajs-3671	255	21	regularization	regularization	NOUN
iajs-3671	255	22	parameter	parameter	NOUN
iajs-3671	255	23	𝛽	𝛽	PROPN
iajs-3671	255	24	=	=	PUNCT
iajs-3671	255	25	{	{	PUNCT
iajs-3671	255	26	10−4	10−4	NUM
iajs-3671	255	27	,	,	PUNCT
iajs-3671	255	28	10−5	10−5	NUM
iajs-3671	255	29	,	,	PUNCT
iajs-3671	255	30	10−6	10−6	NUM
iajs-3671	255	31	}	}	PUNCT
iajs-3671	255	32	and	and	CCONJ
iajs-3671	255	33	𝑞	𝑞	X
iajs-3671	255	34	=	=	SYM
iajs-3671	255	35	0.5	0.5	NUM
iajs-3671	255	36	%	%	NOUN
iajs-3671	255	37	noise	noise	NOUN
iajs-3671	255	38	.	.	PUNCT
iajs-3671	256	1	figure	figure	NOUN
iajs-3671	256	2	9	9	NUM
iajs-3671	256	3	.	.	PUNCT
iajs-3671	256	4	numerical	numerical	ADJ
iajs-3671	256	5	reconstructions	reconstruction	NOUN
iajs-3671	256	6	and	and	CCONJ
iajs-3671	256	7	exact	exact	ADJ
iajs-3671	256	8	solution	solution	NOUN
iajs-3671	256	9	for	for	ADP
iajs-3671	256	10	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	256	11	)	)	PUNCT
iajs-3671	256	12	,	,	PUNCT
iajs-3671	256	13	with	with	ADP
iajs-3671	256	14	regularization	regularization	NOUN
iajs-3671	256	15	parameter	parameter	NOUN
iajs-3671	256	16	𝛽	𝛽	PROPN
iajs-3671	256	17	=	=	PUNCT
iajs-3671	256	18	{	{	PUNCT
iajs-3671	256	19	10−4	10−4	NUM
iajs-3671	256	20	,	,	PUNCT
iajs-3671	256	21	10−5	10−5	NUM
iajs-3671	256	22	}	}	PUNCT
iajs-3671	256	23	and	and	CCONJ
iajs-3671	256	24	𝑞	𝑞	X
iajs-3671	256	25	=	=	SYM
iajs-3671	256	26	1	1	NUM
iajs-3671	256	27	%	%	NOUN
iajs-3671	256	28	noise	noise	NOUN
iajs-3671	256	29	,	,	PUNCT
iajs-3671	256	30	for	for	ADP
iajs-3671	256	31	ipi	ipi	PROPN
iajs-3671	256	32	.	.	PUNCT
iajs-3671	256	33	0	0	NUM
iajs-3671	256	34	0.1	0.1	NUM
iajs-3671	256	35	0.2	0.2	NUM
iajs-3671	256	36	0.3	0.3	NUM
iajs-3671	256	37	0.4	0.4	NUM
iajs-3671	256	38	0.5	0.5	NUM
iajs-3671	256	39	0.6	0.6	NUM
iajs-3671	256	40	0.7	0.7	NUM
iajs-3671	256	41	0.8	0.8	NUM
iajs-3671	256	42	0.9	0.9	NUM
iajs-3671	256	43	1	1	NUM
iajs-3671	256	44	t	t	NOUN
iajs-3671	256	45	-2	-2	NOUN
iajs-3671	256	46	-1.5	-1.5	NUM
iajs-3671	256	47	-1	-1	PROPN
iajs-3671	257	1	-0.5	-0.5	X
iajs-3671	257	2	0	0	NUM
iajs-3671	257	3	0.5	0.5	NUM
iajs-3671	257	4	1	1	NUM
iajs-3671	257	5	1.5	1.5	NUM
iajs-3671	257	6	2	2	NUM
iajs-3671	257	7	2.5	2.5	NUM
iajs-3671	257	8	p	p	NOUN
iajs-3671	257	9	(	(	PUNCT
iajs-3671	257	10	t	t	NOUN
iajs-3671	257	11	)	)	PUNCT
iajs-3671	257	12	exact	exact	ADJ
iajs-3671	257	13	1	1	NUM
iajs-3671	257	14	=	=	SYM
iajs-3671	257	15	10	10	NUM
iajs-3671	257	16	-4	-4	SYM
iajs-3671	257	17	2	2	NUM
iajs-3671	257	18	=	=	SYM
iajs-3671	257	19	10	10	NUM
iajs-3671	257	20	-5	-5	NOUN
iajs-3671	257	21	2	2	NUM
iajs-3671	257	22	=	=	SYM
iajs-3671	257	23	10	10	NUM
iajs-3671	258	1	-6	-6	NOUN
iajs-3671	258	2	0	0	NUM
iajs-3671	259	1	0.1	0.1	NUM
iajs-3671	259	2	0.2	0.2	NUM
iajs-3671	259	3	0.3	0.3	NUM
iajs-3671	259	4	0.4	0.4	NUM
iajs-3671	259	5	0.5	0.5	NUM
iajs-3671	259	6	0.6	0.6	NUM
iajs-3671	259	7	0.7	0.7	NUM
iajs-3671	259	8	0.8	0.8	NUM
iajs-3671	259	9	0.9	0.9	NUM
iajs-3671	259	10	1	1	NUM
iajs-3671	259	11	t	t	NOUN
iajs-3671	259	12	-2	-2	NOUN
iajs-3671	259	13	-1.5	-1.5	NUM
iajs-3671	259	14	-1	-1	PROPN
iajs-3671	259	15	-0.5	-0.5	X
iajs-3671	259	16	0	0	NUM
iajs-3671	259	17	0.5	0.5	NUM
iajs-3671	259	18	1	1	NUM
iajs-3671	259	19	1.5	1.5	NUM
iajs-3671	259	20	2	2	NUM
iajs-3671	259	21	p	p	PROPN
iajs-3671	259	22	(	(	PUNCT
iajs-3671	259	23	t	t	PROPN
iajs-3671	259	24	)	)	PUNCT
iajs-3671	259	25	exact	exact	ADJ
iajs-3671	259	26	1	1	NUM
iajs-3671	259	27	=	=	SYM
iajs-3671	259	28	10	10	NUM
iajs-3671	259	29	-4	-4	SYM
iajs-3671	259	30	2	2	NUM
iajs-3671	259	31	=	=	SYM
iajs-3671	259	32	10	10	NUM
iajs-3671	259	33	-5	-5	NUM
iajs-3671	259	34	ihjpas	ihjpas	PROPN
iajs-3671	259	35	.	.	PUNCT
iajs-3671	260	1	2025	2025	NUM
iajs-3671	260	2	,	,	PUNCT
iajs-3671	260	3	38	38	NUM
iajs-3671	260	4	(	(	PUNCT
iajs-3671	260	5	1	1	NUM
iajs-3671	260	6	)	)	PUNCT
iajs-3671	260	7	483	483	NUM
iajs-3671	260	8	(	(	PUNCT
iajs-3671	260	9	a	a	NOUN
iajs-3671	260	10	)	)	PUNCT
iajs-3671	260	11	(	(	PUNCT
iajs-3671	260	12	b	b	X
iajs-3671	260	13	)	)	PUNCT
iajs-3671	260	14	figure	figure	NOUN
iajs-3671	260	15	10	10	NUM
iajs-3671	260	16	.	.	PUNCT
iajs-3671	261	1	numerical	numerical	ADJ
iajs-3671	261	2	and	and	CCONJ
iajs-3671	261	3	exact	exact	ADJ
iajs-3671	261	4	temperature	temperature	NOUN
iajs-3671	261	5	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	261	6	,	,	PUNCT
iajs-3671	261	7	𝑡	𝑡	PROPN
iajs-3671	261	8	)	)	PUNCT
iajs-3671	261	9	with	with	ADP
iajs-3671	261	10	(	(	PUNCT
iajs-3671	261	11	a	a	X
iajs-3671	261	12	)	)	PUNCT
iajs-3671	261	13	𝑞	𝑞	NOUN
iajs-3671	261	14	=	=	SYM
iajs-3671	261	15	0.5	0.5	NUM
iajs-3671	261	16	%	%	NOUN
iajs-3671	261	17	and	and	CCONJ
iajs-3671	261	18	𝛽	𝛽	NOUN
iajs-3671	261	19	=	=	SYM
iajs-3671	261	20	10−4	10−4	PROPN
iajs-3671	261	21	,	,	PUNCT
iajs-3671	261	22	(	(	PUNCT
iajs-3671	261	23	b	b	X
iajs-3671	261	24	)	)	PUNCT
iajs-3671	261	25	𝑞	𝑞	NOUN
iajs-3671	261	26	=	=	SYM
iajs-3671	261	27	1	1	NUM
iajs-3671	261	28	%	%	NOUN
iajs-3671	261	29	noise	noise	NOUN
iajs-3671	261	30	and	and	CCONJ
iajs-3671	261	31	𝛽	𝛽	NOUN
iajs-3671	261	32	=	=	SYM
iajs-3671	261	33	10−4	10−4	PROPN
iajs-3671	261	34	,	,	PUNCT
iajs-3671	261	35	for	for	ADP
iajs-3671	261	36	ipi	ipi	PROPN
iajs-3671	261	37	.	.	PUNCT
iajs-3671	261	38	ihjpas	ihjpas	PROPN
iajs-3671	261	39	.	.	PUNCT
iajs-3671	262	1	2025	2025	NUM
iajs-3671	262	2	,	,	PUNCT
iajs-3671	262	3	38	38	NUM
iajs-3671	262	4	(	(	PUNCT
iajs-3671	262	5	1	1	NUM
iajs-3671	262	6	)	)	PUNCT
iajs-3671	262	7	484	484	NUM
iajs-3671	262	8	table	table	NOUN
iajs-3671	262	9	1	1	NUM
iajs-3671	262	10	.	.	PUNCT
iajs-3671	262	11	numerical	numerical	ADJ
iajs-3671	262	12	information	information	NOUN
iajs-3671	262	13	for	for	ADP
iajs-3671	262	14	ipi	ipi	PROPN
iajs-3671	262	15	with	with	ADP
iajs-3671	262	16	various	various	ADJ
iajs-3671	262	17	noise	noise	NOUN
iajs-3671	262	18	levels	level	NOUN
iajs-3671	262	19	.	.	PUNCT
iajs-3671	263	1	𝒒	𝒒	X
iajs-3671	264	1	=	=	PUNCT
iajs-3671	264	2	𝟎.	𝟎.	NOUN
iajs-3671	264	3	𝟓%	𝟓%	VERB
iajs-3671	264	4	𝛽	𝛽	NOUN
iajs-3671	264	5	=	=	SYM
iajs-3671	264	6	10−4	10−4	NUM
iajs-3671	264	7	𝛽	𝛽	NOUN
iajs-3671	264	8	=	=	SYM
iajs-3671	264	9	10−5	10−5	NUM
iajs-3671	264	10	𝛽	𝛽	NOUN
iajs-3671	264	11	=	=	SYM
iajs-3671	264	12	10−6	10−6	NUM
iajs-3671	264	13	no	no	NOUN
iajs-3671	264	14	.	.	PUNCT
iajs-3671	264	15	of	of	ADP
iajs-3671	264	16	iterations	iteration	NOUN
iajs-3671	265	1	48	48	NUM
iajs-3671	265	2	40	40	NUM
iajs-3671	265	3	37	37	NUM
iajs-3671	265	4	objective	objective	ADJ
iajs-3671	265	5	function	function	NOUN
iajs-3671	265	6	equation	equation	NOUN
iajs-3671	265	7	(	(	PUNCT
iajs-3671	265	8	59	59	NUM
iajs-3671	265	9	)	)	PUNCT
iajs-3671	265	10	at	at	ADP
iajs-3671	265	11	the	the	DET
iajs-3671	265	12	final	final	ADJ
iajs-3671	265	13	iteration	iteration	NOUN
iajs-3671	265	14	0.0015	0.0015	NUM
iajs-3671	265	15	2.8078e-04	2.8078e-04	NUM
iajs-3671	265	16	5.4229e-05	5.4229e-05	NUM
iajs-3671	265	17	𝒓𝒎𝒔𝒆(𝒑	𝒓𝒎𝒔𝒆(𝒑	NOUN
iajs-3671	265	18	)	)	PUNCT
iajs-3671	265	19	0.2987	0.2987	NUM
iajs-3671	265	20	0.3678	0.3678	NUM
iajs-3671	265	21	0.7326	0.7326	NUM
iajs-3671	265	22	𝐪	𝐪	X
iajs-3671	265	23	=	=	SYM
iajs-3671	265	24	𝟏%	𝟏%	PROPN
iajs-3671	265	25	𝛽	𝛽	PROPN
iajs-3671	265	26	=	=	SYM
iajs-3671	265	27	10−4	10−4	PROPN
iajs-3671	265	28	𝛽	𝛽	NOUN
iajs-3671	265	29	=	=	SYM
iajs-3671	265	30	10−5	10−5	NUM
iajs-3671	265	31	𝛽	𝛽	NOUN
iajs-3671	265	32	=	=	SYM
iajs-3671	265	33	10−6	10−6	NUM
iajs-3671	265	34	no	no	NOUN
iajs-3671	265	35	.	.	PUNCT
iajs-3671	265	36	of	of	ADP
iajs-3671	265	37	iterations	iteration	NOUN
iajs-3671	265	38	42	42	NUM
iajs-3671	265	39	45	45	NUM
iajs-3671	265	40	48	48	NUM
iajs-3671	265	41	objective	objective	ADJ
iajs-3671	265	42	function	function	NOUN
iajs-3671	265	43	equation	equation	NOUN
iajs-3671	265	44	(	(	PUNCT
iajs-3671	265	45	59	59	NUM
iajs-3671	265	46	)	)	PUNCT
iajs-3671	265	47	at	at	ADP
iajs-3671	265	48	the	the	DET
iajs-3671	265	49	final	final	ADJ
iajs-3671	265	50	iteration	iteration	NOUN
iajs-3671	265	51	0.0020	0.0020	NUM
iajs-3671	265	52	6.1036e-04	6.1036e-04	NUM
iajs-3671	265	53	1.6380e-04	1.6380e-04	NUM
iajs-3671	265	54	𝒓𝒎𝒔𝒆(𝒑	𝒓𝒎𝒔𝒆(𝒑	NOUN
iajs-3671	265	55	)	)	PUNCT
iajs-3671	265	56	0.3328	0.3328	NUM
iajs-3671	266	1	0.6661	0.6661	NUM
iajs-3671	266	2	1.4340	1.4340	NUM
iajs-3671	266	3	3.3	3.3	NUM
iajs-3671	266	4	.numerical	.numerical	NUM
iajs-3671	266	5	results	result	NOUN
iajs-3671	266	6	for	for	ADP
iajs-3671	266	7	ipii	ipii	ADJ
iajs-3671	266	8	consider	consider	VERB
iajs-3671	266	9	the	the	DET
iajs-3671	266	10	ipii	ipii	ADJ
iajs-3671	266	11	equations	equation	NOUN
iajs-3671	266	12	(	(	PUNCT
iajs-3671	266	13	1)-(3),(5	1)-(3),(5	NUM
iajs-3671	266	14	)	)	PUNCT
iajs-3671	266	15	and	and	CCONJ
iajs-3671	266	16	(	(	PUNCT
iajs-3671	266	17	7	7	X
iajs-3671	266	18	)	)	PUNCT
iajs-3671	266	19	with	with	ADP
iajs-3671	266	20	input	input	NOUN
iajs-3671	266	21	data	datum	NOUN
iajs-3671	266	22	in	in	ADP
iajs-3671	266	23	example	example	NOUN
iajs-3671	266	24	2.3.2	2.3.2	NUM
iajs-3671	266	25	.	.	PUNCT
iajs-3671	266	26	to	to	PART
iajs-3671	266	27	solve	solve	VERB
iajs-3671	266	28	this	this	DET
iajs-3671	266	29	problem	problem	NOUN
iajs-3671	266	30	,	,	PUNCT
iajs-3671	266	31	we	we	PRON
iajs-3671	266	32	employ	employ	VERB
iajs-3671	266	33	the	the	DET
iajs-3671	266	34	same	same	ADJ
iajs-3671	266	35	process	process	NOUN
iajs-3671	266	36	presented	present	VERB
iajs-3671	266	37	in	in	ADP
iajs-3671	266	38	section	section	NOUN
iajs-3671	266	39	3	3	NUM
iajs-3671	266	40	.	.	PUNCT
iajs-3671	267	1	here	here	ADV
iajs-3671	267	2	,	,	PUNCT
iajs-3671	267	3	all	all	DET
iajs-3671	267	4	the	the	DET
iajs-3671	267	5	conditions	condition	NOUN
iajs-3671	267	6	of	of	ADP
iajs-3671	267	7	inverse	inverse	NOUN
iajs-3671	267	8	problem	problem	NOUN
iajs-3671	267	9	ii	ii	PROPN
iajs-3671	267	10	are	be	AUX
iajs-3671	267	11	satisfied	satisfied	ADJ
iajs-3671	267	12	,	,	PUNCT
iajs-3671	267	13	and	and	CCONJ
iajs-3671	267	14	hence	hence	ADV
iajs-3671	267	15	,	,	PUNCT
iajs-3671	267	16	the	the	DET
iajs-3671	267	17	unique	unique	ADJ
iajs-3671	267	18	solvability	solvability	NOUN
iajs-3671	267	19	of	of	ADP
iajs-3671	267	20	the	the	DET
iajs-3671	267	21	solution	solution	NOUN
iajs-3671	267	22	is	be	AUX
iajs-3671	267	23	guaranteed	guarantee	VERB
iajs-3671	267	24	.	.	PUNCT
iajs-3671	268	1	initially	initially	ADV
iajs-3671	268	2	,	,	PUNCT
iajs-3671	268	3	we	we	PRON
iajs-3671	268	4	start	start	VERB
iajs-3671	268	5	with	with	ADP
iajs-3671	268	6	an	an	DET
iajs-3671	268	7	initial	initial	ADJ
iajs-3671	268	8	guess	guess	NOUN
iajs-3671	268	9	when	when	SCONJ
iajs-3671	268	10	t	t	PROPN
iajs-3671	268	11	=	=	SYM
iajs-3671	268	12	0	0	PUNCT
iajs-3671	268	13	(	(	PUNCT
iajs-3671	268	14	i.	i.	NOUN
iajs-3671	268	15	e	e	PROPN
iajs-3671	268	16	𝑝(0	𝑝(0	PROPN
iajs-3671	268	17	)	)	PUNCT
iajs-3671	268	18	=	=	SYM
iajs-3671	268	19	0	0	X
iajs-3671	268	20	)	)	PUNCT
iajs-3671	268	21	and	and	CCONJ
iajs-3671	268	22	retrieve	retrieve	VERB
iajs-3671	268	23	the	the	DET
iajs-3671	268	24	function	function	NOUN
iajs-3671	268	25	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	268	26	)	)	PUNCT
iajs-3671	268	27	and	and	CCONJ
iajs-3671	268	28	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	268	29	,	,	PUNCT
iajs-3671	268	30	𝑡	𝑡	PROPN
iajs-3671	268	31	)	)	PUNCT
iajs-3671	268	32	for	for	ADP
iajs-3671	268	33	noise	noise	NOUN
iajs-3671	268	34	-	-	PUNCT
iajs-3671	268	35	free	free	ADJ
iajs-3671	268	36	case	case	NOUN
iajs-3671	268	37	(	(	PUNCT
iajs-3671	268	38	q	q	NOUN
iajs-3671	268	39	=	=	NOUN
iajs-3671	268	40	0	0	NUM
iajs-3671	268	41	)	)	PUNCT
iajs-3671	268	42	(	(	PUNCT
iajs-3671	268	43	see	see	VERB
iajs-3671	268	44	figure	figure	NOUN
iajs-3671	268	45	11	11	NUM
iajs-3671	268	46	.	.	PUNCT
iajs-3671	268	47	)	)	PUNCT
iajs-3671	268	48	,	,	PUNCT
iajs-3671	268	49	then	then	ADV
iajs-3671	268	50	for	for	ADP
iajs-3671	268	51	q	q	PROPN
iajs-3671	268	52	∈	∈	PROPN
iajs-3671	268	53	{	{	PUNCT
iajs-3671	268	54	1	1	NUM
iajs-3671	268	55	%	%	NOUN
iajs-3671	268	56	,	,	PUNCT
iajs-3671	268	57	3	3	NUM
iajs-3671	268	58	%	%	NOUN
iajs-3671	268	59	}	}	PUNCT
iajs-3671	268	60	noisy	noisy	ADJ
iajs-3671	268	61	data	datum	NOUN
iajs-3671	268	62	.	.	PUNCT
iajs-3671	269	1	from	from	ADP
iajs-3671	269	2	this	this	DET
iajs-3671	269	3	figure	figure	NOUN
iajs-3671	269	4	,	,	PUNCT
iajs-3671	269	5	it	it	PRON
iajs-3671	269	6	is	be	AUX
iajs-3671	269	7	clear	clear	ADJ
iajs-3671	269	8	to	to	PART
iajs-3671	269	9	observe	observe	VERB
iajs-3671	269	10	the	the	DET
iajs-3671	269	11	excellent	excellent	ADJ
iajs-3671	269	12	matching	matching	NOUN
iajs-3671	269	13	when	when	SCONJ
iajs-3671	269	14	the	the	DET
iajs-3671	269	15	mesh	mesh	NOUN
iajs-3671	269	16	size	size	NOUN
iajs-3671	269	17	is	be	AUX
iajs-3671	269	18	chosen	choose	VERB
iajs-3671	269	19	as	as	ADP
iajs-3671	269	20	𝑀	𝑀	PROPN
iajs-3671	269	21	=	=	PROPN
iajs-3671	269	22	𝑁	𝑁	PROPN
iajs-3671	269	23	=	=	SYM
iajs-3671	269	24	40	40	NUM
iajs-3671	269	25	.	.	PUNCT
iajs-3671	270	1	the	the	DET
iajs-3671	270	2	objective	objective	ADJ
iajs-3671	270	3	function	function	NOUN
iajs-3671	270	4	equation	equation	NOUN
iajs-3671	270	5	(	(	PUNCT
iajs-3671	270	6	60	60	NUM
iajs-3671	270	7	)	)	PUNCT
iajs-3671	270	8	is	be	AUX
iajs-3671	270	9	plotted	plot	VERB
iajs-3671	270	10	as	as	ADP
iajs-3671	270	11	a	a	DET
iajs-3671	270	12	function	function	NOUN
iajs-3671	270	13	of	of	ADP
iajs-3671	270	14	the	the	DET
iajs-3671	270	15	number	number	NOUN
iajs-3671	270	16	of	of	ADP
iajs-3671	270	17	iterations	iteration	NOUN
iajs-3671	270	18	in	in	ADP
iajs-3671	270	19	figure	figure	NOUN
iajs-3671	270	20	12	12	NUM
iajs-3671	270	21	.	.	PUNCT
iajs-3671	271	1	for	for	ADP
iajs-3671	271	2	noise	noise	NOUN
iajs-3671	271	3	-	-	PUNCT
iajs-3671	271	4	free	free	ADJ
iajs-3671	271	5	cases	case	NOUN
iajs-3671	271	6	and	and	CCONJ
iajs-3671	271	7	for	for	ADP
iajs-3671	271	8	noise	noise	NOUN
iajs-3671	271	9	included	include	VERB
iajs-3671	271	10	.	.	PUNCT
iajs-3671	272	1	the	the	DET
iajs-3671	272	2	fast	fast	ADJ
iajs-3671	272	3	convergence	convergence	NOUN
iajs-3671	272	4	can	can	AUX
iajs-3671	272	5	be	be	AUX
iajs-3671	272	6	seen	see	VERB
iajs-3671	272	7	to	to	PART
iajs-3671	272	8	reach	reach	VERB
iajs-3671	272	9	a	a	DET
iajs-3671	272	10	very	very	ADV
iajs-3671	272	11	low	low	ADJ
iajs-3671	272	12	value	value	NOUN
iajs-3671	272	13	of	of	ADP
iajs-3671	272	14	o	o	PROPN
iajs-3671	272	15	(	(	PUNCT
iajs-3671	272	16	10−9	10−9	NUM
iajs-3671	272	17	)	)	PUNCT
iajs-3671	272	18	in	in	ADP
iajs-3671	272	19	just	just	ADV
iajs-3671	272	20	11	11	NUM
iajs-3671	272	21	iterations	iteration	NOUN
iajs-3671	272	22	.	.	PUNCT
iajs-3671	273	1	figure	figure	VERB
iajs-3671	273	2	11	11	NUM
iajs-3671	273	3	.	.	PUNCT
iajs-3671	274	1	numerical	numerical	ADJ
iajs-3671	274	2	and	and	CCONJ
iajs-3671	274	3	exact	exact	ADJ
iajs-3671	274	4	solution	solution	NOUN
iajs-3671	274	5	for	for	ADP
iajs-3671	274	6	potential	potential	ADJ
iajs-3671	274	7	term	term	NOUN
iajs-3671	274	8	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	274	9	)	)	PUNCT
iajs-3671	275	1	when	when	SCONJ
iajs-3671	275	2	𝑀	𝑀	PROPN
iajs-3671	275	3	=	=	SYM
iajs-3671	275	4	𝑁	𝑁	PROPN
iajs-3671	275	5	=	=	SYM
iajs-3671	275	6	40	40	NUM
iajs-3671	275	7	,	,	PUNCT
iajs-3671	275	8	for	for	ADP
iajs-3671	275	9	example	example	NOUN
iajs-3671	275	10	,	,	PUNCT
iajs-3671	275	11	in	in	ADP
iajs-3671	275	12	ip	ip	NOUN
iajs-3671	275	13	-	-	PUNCT
iajs-3671	275	14	ii	ii	NOUN
iajs-3671	275	15	.	.	PUNCT
iajs-3671	275	16	0	0	NUM
iajs-3671	275	17	0.1	0.1	NUM
iajs-3671	275	18	0.2	0.2	NUM
iajs-3671	275	19	0.3	0.3	NUM
iajs-3671	275	20	0.4	0.4	NUM
iajs-3671	275	21	0.5	0.5	NUM
iajs-3671	275	22	0.6	0.6	NUM
iajs-3671	275	23	0.7	0.7	NUM
iajs-3671	275	24	0.8	0.8	NUM
iajs-3671	275	25	0.9	0.9	NUM
iajs-3671	275	26	1	1	NUM
iajs-3671	275	27	t	t	NOUN
iajs-3671	275	28	-1	-1	PUNCT
iajs-3671	275	29	-0.5	-0.5	X
iajs-3671	275	30	0	0	NUM
iajs-3671	275	31	0.5	0.5	NUM
iajs-3671	275	32	1	1	NUM
iajs-3671	275	33	1.5	1.5	NUM
iajs-3671	275	34	p	p	NOUN
iajs-3671	275	35	(	(	PUNCT
iajs-3671	275	36	t	t	NOUN
iajs-3671	275	37	)	)	PUNCT
iajs-3671	275	38	exact	exact	PROPN
iajs-3671	275	39	numerical	numerical	ADJ
iajs-3671	275	40	ihjpas	ihjpas	PROPN
iajs-3671	275	41	.	.	PUNCT
iajs-3671	276	1	2025	2025	NUM
iajs-3671	276	2	,	,	PUNCT
iajs-3671	276	3	38	38	NUM
iajs-3671	276	4	(	(	PUNCT
iajs-3671	276	5	1	1	NUM
iajs-3671	276	6	)	)	PUNCT
iajs-3671	276	7	485	485	NUM
iajs-3671	276	8	figure	figure	NOUN
iajs-3671	276	9	12	12	NUM
iajs-3671	276	10	.	.	PUNCT
iajs-3671	277	1	the	the	DET
iajs-3671	277	2	unregularized	unregularized	ADJ
iajs-3671	277	3	objective	objective	ADJ
iajs-3671	277	4	function	function	NOUN
iajs-3671	277	5	equation	equation	NOUN
iajs-3671	277	6	(	(	PUNCT
iajs-3671	277	7	60	60	NUM
iajs-3671	277	8	)	)	PUNCT
iajs-3671	277	9	,	,	PUNCT
iajs-3671	277	10	with	with	ADP
iajs-3671	277	11	q	q	PROPN
iajs-3671	277	12	=	=	PUNCT
iajs-3671	277	13	{	{	PUNCT
iajs-3671	277	14	0	0	NUM
iajs-3671	277	15	,	,	PUNCT
iajs-3671	277	16	1	1	NUM
iajs-3671	277	17	%	%	NOUN
iajs-3671	277	18	,	,	PUNCT
iajs-3671	277	19	3	3	NUM
iajs-3671	277	20	%	%	NOUN
iajs-3671	277	21	}	}	PUNCT
iajs-3671	277	22	noise	noise	NOUN
iajs-3671	277	23	data	datum	NOUN
iajs-3671	277	24	included	include	VERB
iajs-3671	277	25	in	in	ADP
iajs-3671	277	26	measurements	measurement	NOUN
iajs-3671	277	27	equation	equation	NOUN
iajs-3671	277	28	(	(	PUNCT
iajs-3671	277	29	7	7	NUM
iajs-3671	277	30	)	)	PUNCT
iajs-3671	277	31	,	,	PUNCT
iajs-3671	277	32	for	for	ADP
iajs-3671	277	33	example	example	NOUN
iajs-3671	277	34	,	,	PUNCT
iajs-3671	277	35	in	in	ADP
iajs-3671	277	36	ip	ip	NOUN
iajs-3671	277	37	-	-	PUNCT
iajs-3671	277	38	ii	ii	NOUN
iajs-3671	277	39	.	.	PUNCT
iajs-3671	277	40	figure	figure	NOUN
iajs-3671	277	41	13	13	NUM
iajs-3671	277	42	.	.	PUNCT
iajs-3671	278	1	numerical	numerical	ADJ
iajs-3671	278	2	reconstructions	reconstruction	NOUN
iajs-3671	278	3	and	and	CCONJ
iajs-3671	278	4	exact	exact	ADJ
iajs-3671	278	5	solution	solution	NOUN
iajs-3671	278	6	for	for	ADP
iajs-3671	278	7	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	278	8	)	)	PUNCT
iajs-3671	278	9	,	,	PUNCT
iajs-3671	278	10	with	with	ADP
iajs-3671	278	11	noise	noise	NOUN
iajs-3671	278	12	level	level	NOUN
iajs-3671	278	13	𝑞	𝑞	X
iajs-3671	278	14	=	=	X
iajs-3671	278	15	{	{	PUNCT
iajs-3671	278	16	0	0	NUM
iajs-3671	278	17	,	,	PUNCT
iajs-3671	278	18	1	1	NUM
iajs-3671	278	19	%	%	NOUN
iajs-3671	278	20	,	,	PUNCT
iajs-3671	278	21	3	3	NUM
iajs-3671	278	22	%	%	NOUN
iajs-3671	278	23	}	}	PUNCT
iajs-3671	278	24	,	,	PUNCT
iajs-3671	278	25	without	without	SCONJ
iajs-3671	278	26	regularization	regularization	NOUN
iajs-3671	278	27	applied	apply	VERB
iajs-3671	278	28	for	for	ADP
iajs-3671	278	29	ipii	ipii	NOUN
iajs-3671	278	30	.	.	PUNCT
iajs-3671	279	1	for	for	ADP
iajs-3671	279	2	the	the	DET
iajs-3671	279	3	cases	case	NOUN
iajs-3671	279	4	plotted	plot	VERB
iajs-3671	279	5	in	in	ADP
iajs-3671	279	6	figure	figure	NOUN
iajs-3671	279	7	13	13	NUM
iajs-3671	279	8	.	.	PUNCT
iajs-3671	279	9	,	,	PUNCT
iajs-3671	279	10	the	the	DET
iajs-3671	279	11	results	result	NOUN
iajs-3671	279	12	obtained	obtain	VERB
iajs-3671	279	13	were	be	AUX
iajs-3671	279	14	inaccurate	inaccurate	ADJ
iajs-3671	279	15	and	and	CCONJ
iajs-3671	279	16	unstable	unstable	ADJ
iajs-3671	279	17	when	when	SCONJ
iajs-3671	279	18	the	the	DET
iajs-3671	279	19	regularization	regularization	NOUN
iajs-3671	279	20	parameter	parameter	NOUN
iajs-3671	279	21	was	be	AUX
iajs-3671	279	22	set	set	VERB
iajs-3671	279	23	𝛽	𝛽	NOUN
iajs-3671	279	24	=	=	SYM
iajs-3671	279	25	0	0	NUM
iajs-3671	279	26	and	and	CCONJ
iajs-3671	279	27	q	q	PROPN
iajs-3671	279	28	∈	∈	PROPN
iajs-3671	279	29	{	{	PUNCT
iajs-3671	279	30	1	1	NUM
iajs-3671	279	31	%	%	NOUN
iajs-3671	279	32	,	,	PUNCT
iajs-3671	279	33	3%}—the	3%}—the	DET
iajs-3671	279	34	tikhonov	tikhonov	NOUN
iajs-3671	279	35	regularization	regularization	NOUN
iajs-3671	279	36	method	method	NOUN
iajs-3671	279	37	employed	employ	VERB
iajs-3671	279	38	to	to	PART
iajs-3671	279	39	obtain	obtain	VERB
iajs-3671	279	40	stable	stable	ADJ
iajs-3671	279	41	reconstructions	reconstruction	NOUN
iajs-3671	279	42	for	for	ADP
iajs-3671	279	43	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	279	44	)	)	PUNCT
iajs-3671	279	45	.	.	PUNCT
iajs-3671	280	1	regularization	regularization	NOUN
iajs-3671	280	2	parameters	parameter	NOUN
iajs-3671	280	3	𝛽	𝛽	NOUN
iajs-3671	280	4	=	=	SYM
iajs-3671	280	5	{	{	PUNCT
iajs-3671	280	6	10−5	10−5	NUM
iajs-3671	280	7	,	,	PUNCT
iajs-3671	280	8	10−4	10−4	NUM
iajs-3671	280	9	,	,	PUNCT
iajs-3671	280	10	10−3	10−3	NUM
iajs-3671	280	11	}	}	PUNCT
iajs-3671	280	12	were	be	AUX
iajs-3671	280	13	chosen	choose	VERB
iajs-3671	280	14	by	by	ADP
iajs-3671	280	15	trial	trial	NOUN
iajs-3671	280	16	and	and	CCONJ
iajs-3671	280	17	error	error	NOUN
iajs-3671	280	18	strategy	strategy	NOUN
iajs-3671	280	19	,	,	PUNCT
iajs-3671	280	20	which	which	PRON
iajs-3671	280	21	is	be	AUX
iajs-3671	280	22	based	base	VERB
iajs-3671	280	23	on	on	ADP
iajs-3671	280	24	starting	start	VERB
iajs-3671	280	25	from	from	ADP
iajs-3671	280	26	a	a	DET
iajs-3671	280	27	small	small	ADJ
iajs-3671	280	28	value	value	NOUN
iajs-3671	280	29	for	for	ADP
iajs-3671	280	30	𝛽	𝛽	NOUN
iajs-3671	280	31	and	and	CCONJ
iajs-3671	280	32	gradually	gradually	ADV
iajs-3671	280	33	increasing	increase	VERB
iajs-3671	280	34	it	it	PRON
iajs-3671	280	35	until	until	SCONJ
iajs-3671	280	36	the	the	DET
iajs-3671	280	37	oscillatory	oscillatory	ADJ
iajs-3671	280	38	behaviour	behaviour	NOUN
iajs-3671	280	39	starts	start	VERB
iajs-3671	280	40	to	to	PART
iajs-3671	280	41	disappear	disappear	VERB
iajs-3671	280	42	as	as	SCONJ
iajs-3671	280	43	applied	apply	VERB
iajs-3671	280	44	in	in	ADP
iajs-3671	280	45	)	)	PUNCT
iajs-3671	280	46	40	40	NUM
iajs-3671	280	47	(	(	PUNCT
iajs-3671	280	48	,	,	PUNCT
iajs-3671	280	49	for	for	ADP
iajs-3671	280	50	noise	noise	NOUN
iajs-3671	280	51	data	datum	NOUN
iajs-3671	280	52	𝑞	𝑞	X
iajs-3671	280	53	=	=	SYM
iajs-3671	280	54	1	1	NUM
iajs-3671	280	55	%	%	NOUN
iajs-3671	280	56	.	.	PUNCT
iajs-3671	281	1	figure	figure	NOUN
iajs-3671	281	2	15	15	NUM
iajs-3671	281	3	.	.	PUNCT
iajs-3671	282	1	shows	show	VERB
iajs-3671	282	2	the	the	DET
iajs-3671	282	3	objective	objective	ADJ
iajs-3671	282	4	function	function	NOUN
iajs-3671	282	5	equation	equation	NOUN
iajs-3671	282	6	(	(	PUNCT
iajs-3671	282	7	60	60	NUM
iajs-3671	282	8	)	)	PUNCT
iajs-3671	282	9	decreases	decrease	VERB
iajs-3671	282	10	steadily	steadily	ADV
iajs-3671	282	11	in	in	ADP
iajs-3671	282	12	just	just	ADV
iajs-3671	282	13	below	below	ADP
iajs-3671	282	14	50	50	NUM
iajs-3671	282	15	iterations	iteration	NOUN
iajs-3671	282	16	.	.	PUNCT
iajs-3671	283	1	tikhonov	tikhonov	NOUN
iajs-3671	283	2	's	's	PART
iajs-3671	283	3	approach	approach	NOUN
iajs-3671	283	4	with	with	ADP
iajs-3671	283	5	the	the	DET
iajs-3671	283	6	selected	select	VERB
iajs-3671	283	7	parameters	parameter	NOUN
iajs-3671	283	8	gives	give	VERB
iajs-3671	283	9	a	a	DET
iajs-3671	283	10	reasonable	reasonable	ADJ
iajs-3671	283	11	and	and	CCONJ
iajs-3671	283	12	stable	stable	ADJ
iajs-3671	283	13	approximate	approximate	ADJ
iajs-3671	283	14	solution	solution	NOUN
iajs-3671	283	15	of	of	ADP
iajs-3671	283	16	the	the	DET
iajs-3671	283	17	potential	potential	ADJ
iajs-3671	283	18	term	term	NOUN
iajs-3671	283	19	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	283	20	)	)	PUNCT
iajs-3671	283	21	(	(	PUNCT
iajs-3671	283	22	see	see	VERB
iajs-3671	283	23	figure	figure	NOUN
iajs-3671	283	24	14	14	NUM
iajs-3671	283	25	.	.	PUNCT
iajs-3671	283	26	)	)	PUNCT
iajs-3671	283	27	.	.	PUNCT
iajs-3671	284	1	when	when	SCONJ
iajs-3671	284	2	𝑞	𝑞	X
iajs-3671	284	3	=	=	PROPN
iajs-3671	284	4	3	3	NUM
iajs-3671	284	5	%	%	NOUN
iajs-3671	284	6	,	,	PUNCT
iajs-3671	284	7	we	we	PRON
iajs-3671	284	8	deduce	deduce	VERB
iajs-3671	284	9	that	that	SCONJ
iajs-3671	284	10	the	the	DET
iajs-3671	284	11	regularization	regularization	NOUN
iajs-3671	284	12	parameters	parameter	NOUN
iajs-3671	284	13	𝛽	𝛽	NOUN
iajs-3671	284	14	=	=	SYM
iajs-3671	284	15	{	{	PUNCT
iajs-3671	284	16	10−4	10−4	NUM
iajs-3671	284	17	and	and	CCONJ
iajs-3671	284	18	10−3	10−3	NUM
iajs-3671	284	19	}	}	PUNCT
iajs-3671	284	20	give	give	VERB
iajs-3671	284	21	the	the	DET
iajs-3671	284	22	stable	stable	ADJ
iajs-3671	284	23	and	and	CCONJ
iajs-3671	284	24	accurate	accurate	ADJ
iajs-3671	284	25	approximate	approximate	ADJ
iajs-3671	284	26	solution	solution	NOUN
iajs-3671	284	27	for	for	ADP
iajs-3671	284	28	𝑝(𝑡)(see	𝑝(𝑡)(see	PROPN
iajs-3671	284	29	figures	figure	NOUN
iajs-3671	284	30	16	16	NUM
iajs-3671	284	31	.	.	PUNCT
iajs-3671	284	32	and	and	CCONJ
iajs-3671	284	33	17	17	NUM
iajs-3671	284	34	)	)	PUNCT
iajs-3671	284	35	.	.	PUNCT
iajs-3671	285	1	the	the	DET
iajs-3671	285	2	3d	3d	NUM
iajs-3671	285	3	graphs	graph	NOUN
iajs-3671	285	4	of	of	ADP
iajs-3671	285	5	the	the	DET
iajs-3671	285	6	exact	exact	ADJ
iajs-3671	285	7	and	and	CCONJ
iajs-3671	285	8	numerical	numerical	ADJ
iajs-3671	285	9	solutions	solution	NOUN
iajs-3671	285	10	for	for	ADP
iajs-3671	285	11	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	285	12	,	,	PUNCT
iajs-3671	285	13	𝑡	𝑡	NOUN
iajs-3671	285	14	)	)	PUNCT
iajs-3671	285	15	,	,	PUNCT
iajs-3671	285	16	and	and	CCONJ
iajs-3671	285	17	the	the	DET
iajs-3671	285	18	absolute	absolute	ADJ
iajs-3671	285	19	error	error	NOUN
iajs-3671	285	20	between	between	ADP
iajs-3671	285	21	are	be	AUX
iajs-3671	285	22	plotted	plot	VERB
iajs-3671	285	23	in	in	ADP
iajs-3671	285	24	figure	figure	NOUN
iajs-3671	285	25	0	0	NUM
iajs-3671	285	26	5	5	NUM
iajs-3671	285	27	10	10	NUM
iajs-3671	285	28	15	15	NUM
iajs-3671	285	29	20	20	NUM
iajs-3671	285	30	25	25	NUM
iajs-3671	285	31	30	30	NUM
iajs-3671	285	32	35	35	NUM
iajs-3671	285	33	number	number	NOUN
iajs-3671	285	34	of	of	ADP
iajs-3671	285	35	iterations	iteration	NOUN
iajs-3671	285	36	10	10	NUM
iajs-3671	285	37	-9	-9	NUM
iajs-3671	285	38	10	10	NUM
iajs-3671	285	39	-8	-8	SYM
iajs-3671	285	40	10	10	NUM
iajs-3671	285	41	-7	-7	NUM
iajs-3671	285	42	10	10	NUM
iajs-3671	286	1	-6	-6	NOUN
iajs-3671	286	2	10	10	NUM
iajs-3671	286	3	-5	-5	NUM
iajs-3671	286	4	10	10	NUM
iajs-3671	286	5	-4	-4	SYM
iajs-3671	286	6	10	10	NUM
iajs-3671	286	7	-3	-3	SYM
iajs-3671	286	8	10	10	NUM
iajs-3671	286	9	-2	-2	NOUN
iajs-3671	286	10	10	10	NUM
iajs-3671	286	11	-1	-1	SYM
iajs-3671	287	1	10	10	NUM
iajs-3671	287	2	0	0	NUM
iajs-3671	287	3	o	o	PROPN
iajs-3671	287	4	b	b	X
iajs-3671	287	5	je	je	X
iajs-3671	287	6	ct	ct	NUM
iajs-3671	287	7	iv	iv	NUM
iajs-3671	287	8	e	e	X
iajs-3671	287	9	f	f	PROPN
iajs-3671	287	10	u	u	PROPN
iajs-3671	287	11	n	n	PROPN
iajs-3671	287	12	ct	ct	PROPN
iajs-3671	287	13	io	io	PROPN
iajs-3671	287	14	n	n	PROPN
iajs-3671	287	15	q=0	q=0	ADV
iajs-3671	287	16	%	%	NOUN
iajs-3671	287	17	q=1	q=1	NOUN
iajs-3671	287	18	%	%	NOUN
iajs-3671	287	19	q=3	q=3	NOUN
iajs-3671	287	20	%	%	NOUN
iajs-3671	287	21	0	0	NUM
iajs-3671	287	22	0.1	0.1	NUM
iajs-3671	287	23	0.2	0.2	NUM
iajs-3671	287	24	0.3	0.3	NUM
iajs-3671	287	25	0.4	0.4	NUM
iajs-3671	287	26	0.5	0.5	NUM
iajs-3671	287	27	0.6	0.6	NUM
iajs-3671	287	28	0.7	0.7	NUM
iajs-3671	287	29	0.8	0.8	NUM
iajs-3671	287	30	0.9	0.9	NUM
iajs-3671	287	31	1	1	NUM
iajs-3671	287	32	t	t	NOUN
iajs-3671	287	33	-8	-8	NOUN
iajs-3671	288	1	-6	-6	INTJ
iajs-3671	288	2	-4	-4	INTJ
iajs-3671	289	1	-2	-2	NOUN
iajs-3671	289	2	0	0	NUM
iajs-3671	289	3	2	2	NUM
iajs-3671	289	4	4	4	NUM
iajs-3671	289	5	6	6	NUM
iajs-3671	289	6	8	8	NUM
iajs-3671	289	7	10	10	NUM
iajs-3671	289	8	12	12	NUM
iajs-3671	289	9	p	p	NOUN
iajs-3671	289	10	(	(	PUNCT
iajs-3671	289	11	t	t	PROPN
iajs-3671	289	12	)	)	PUNCT
iajs-3671	289	13	exact	exact	ADJ
iajs-3671	289	14	q=0	q=0	ADV
iajs-3671	289	15	%	%	NOUN
iajs-3671	289	16	q=1	q=1	NOUN
iajs-3671	289	17	%	%	NOUN
iajs-3671	289	18	q=3	q=3	NOUN
iajs-3671	289	19	%	%	NOUN
iajs-3671	289	20	ihjpas	ihjpa	NOUN
iajs-3671	289	21	.	.	PUNCT
iajs-3671	290	1	2025	2025	NUM
iajs-3671	290	2	,	,	PUNCT
iajs-3671	290	3	38	38	NUM
iajs-3671	290	4	(	(	PUNCT
iajs-3671	290	5	1	1	NUM
iajs-3671	290	6	)	)	PUNCT
iajs-3671	290	7	486	486	NUM
iajs-3671	290	8	18	18	NUM
iajs-3671	290	9	.	.	PUNCT
iajs-3671	291	1	with	with	ADP
iajs-3671	291	2	(	(	PUNCT
iajs-3671	291	3	i	i	NOUN
iajs-3671	291	4	)	)	PUNCT
iajs-3671	291	5	𝑞	𝑞	NOUN
iajs-3671	291	6	=	=	SYM
iajs-3671	291	7	1	1	NUM
iajs-3671	291	8	%	%	NOUN
iajs-3671	291	9	and	and	CCONJ
iajs-3671	291	10	𝛽	𝛽	NOUN
iajs-3671	291	11	=	=	SYM
iajs-3671	291	12	10−4	10−4	PROPN
iajs-3671	291	13	,	,	PUNCT
iajs-3671	291	14	(	(	PUNCT
iajs-3671	291	15	ii	ii	NOUN
iajs-3671	291	16	)	)	PUNCT
iajs-3671	291	17	𝑞	𝑞	NOUN
iajs-3671	291	18	=	=	PUNCT
iajs-3671	291	19	3	3	NUM
iajs-3671	291	20	%	%	NOUN
iajs-3671	291	21	and	and	CCONJ
iajs-3671	291	22	𝛽	𝛽	NOUN
iajs-3671	291	23	=	=	SYM
iajs-3671	291	24	10−3	10−3	NUM
iajs-3671	291	25	.	.	PUNCT
iajs-3671	291	26	other	other	ADJ
iajs-3671	291	27	information	information	NOUN
iajs-3671	291	28	about	about	ADP
iajs-3671	291	29	the	the	DET
iajs-3671	291	30	number	number	NOUN
iajs-3671	291	31	of	of	ADP
iajs-3671	291	32	iterations	iteration	NOUN
iajs-3671	291	33	,	,	PUNCT
iajs-3671	291	34	the	the	DET
iajs-3671	291	35	value	value	NOUN
iajs-3671	291	36	of	of	ADP
iajs-3671	291	37	the	the	DET
iajs-3671	291	38	objective	objective	ADJ
iajs-3671	291	39	function	function	NOUN
iajs-3671	291	40	equation	equation	NOUN
iajs-3671	291	41	(	(	PUNCT
iajs-3671	291	42	60	60	NUM
iajs-3671	291	43	)	)	PUNCT
iajs-3671	291	44	at	at	ADP
iajs-3671	291	45	the	the	DET
iajs-3671	291	46	final	final	ADJ
iajs-3671	291	47	iteration	iteration	NOUN
iajs-3671	291	48	and	and	CCONJ
iajs-3671	291	49	the	the	DET
iajs-3671	291	50	rmse	rmse	NOUN
iajs-3671	291	51	of	of	ADP
iajs-3671	291	52	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	291	53	)	)	PUNCT
iajs-3671	291	54	are	be	AUX
iajs-3671	291	55	given	give	VERB
iajs-3671	291	56	in	in	ADP
iajs-3671	291	57	table	table	NOUN
iajs-3671	291	58	2	2	NUM
iajs-3671	291	59	.	.	PUNCT
iajs-3671	291	60	from	from	ADP
iajs-3671	291	61	figures	figure	NOUN
iajs-3671	291	62	14	14	NUM
iajs-3671	291	63	,	,	PUNCT
iajs-3671	291	64	16	16	NUM
iajs-3671	291	65	.	.	PUNCT
iajs-3671	292	1	and	and	CCONJ
iajs-3671	292	2	18	18	NUM
iajs-3671	292	3	.	.	PUNCT
iajs-3671	293	1	and	and	CCONJ
iajs-3671	293	2	table	table	NOUN
iajs-3671	293	3	2	2	NUM
iajs-3671	293	4	.	.	NUM
iajs-3671	293	5	,	,	PUNCT
iajs-3671	293	6	it	it	PRON
iajs-3671	293	7	can	can	AUX
iajs-3671	293	8	be	be	AUX
iajs-3671	293	9	seen	see	VERB
iajs-3671	293	10	that	that	SCONJ
iajs-3671	293	11	there	there	PRON
iajs-3671	293	12	is	be	VERB
iajs-3671	293	13	an	an	DET
iajs-3671	293	14	adequate	adequate	ADJ
iajs-3671	293	15	agreement	agreement	NOUN
iajs-3671	293	16	between	between	ADP
iajs-3671	293	17	the	the	DET
iajs-3671	293	18	numerical	numerical	ADJ
iajs-3671	293	19	results	result	NOUN
iajs-3671	293	20	of	of	ADP
iajs-3671	293	21	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	293	22	)	)	PUNCT
iajs-3671	293	23	and	and	CCONJ
iajs-3671	293	24	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	293	25	,	,	PUNCT
iajs-3671	293	26	𝑡	𝑡	PROPN
iajs-3671	293	27	)	)	PUNCT
iajs-3671	293	28	for	for	ADP
iajs-3671	293	29	their	their	PRON
iajs-3671	293	30	analytical	analytical	ADJ
iajs-3671	293	31	solutions	solution	NOUN
iajs-3671	293	32	.	.	PUNCT
iajs-3671	294	1	figure	figure	NOUN
iajs-3671	294	2	14	14	NUM
iajs-3671	294	3	.	.	PUNCT
iajs-3671	295	1	numerical	numerical	ADJ
iajs-3671	295	2	reconstructions	reconstruction	NOUN
iajs-3671	295	3	and	and	CCONJ
iajs-3671	295	4	exact	exact	ADJ
iajs-3671	295	5	solution	solution	NOUN
iajs-3671	295	6	for	for	ADP
iajs-3671	295	7	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	295	8	)	)	PUNCT
iajs-3671	295	9	,	,	PUNCT
iajs-3671	295	10	with	with	ADP
iajs-3671	295	11	regularization	regularization	NOUN
iajs-3671	295	12	parameter	parameter	NOUN
iajs-3671	295	13	𝛽	𝛽	PROPN
iajs-3671	295	14	=	=	PUNCT
iajs-3671	295	15	{	{	PUNCT
iajs-3671	295	16	10−5	10−5	NUM
iajs-3671	295	17	,	,	PUNCT
iajs-3671	295	18	10−4	10−4	NUM
iajs-3671	295	19	,	,	PUNCT
iajs-3671	295	20	10−3	10−3	NUM
iajs-3671	295	21	}	}	PUNCT
iajs-3671	295	22	and	and	CCONJ
iajs-3671	295	23	𝑞	𝑞	X
iajs-3671	295	24	=	=	SYM
iajs-3671	295	25	1	1	NUM
iajs-3671	295	26	%	%	NOUN
iajs-3671	295	27	noise	noise	NOUN
iajs-3671	295	28	.	.	PUNCT
iajs-3671	296	1	figure	figure	NOUN
iajs-3671	296	2	15	15	NUM
iajs-3671	296	3	.	.	PUNCT
iajs-3671	297	1	the	the	DET
iajs-3671	297	2	regularized	regularize	VERB
iajs-3671	297	3	objective	objective	ADJ
iajs-3671	297	4	function	function	NOUN
iajs-3671	297	5	equation	equation	NOUN
iajs-3671	297	6	(	(	PUNCT
iajs-3671	297	7	60	60	NUM
iajs-3671	297	8	)	)	PUNCT
iajs-3671	297	9	,	,	PUNCT
iajs-3671	297	10	with	with	ADP
iajs-3671	297	11	regularization	regularization	NOUN
iajs-3671	297	12	parameter	parameter	NOUN
iajs-3671	297	13	𝛽	𝛽	PROPN
iajs-3671	297	14	=	=	PUNCT
iajs-3671	297	15	{	{	PUNCT
iajs-3671	297	16	10−5	10−5	NUM
iajs-3671	297	17	,	,	PUNCT
iajs-3671	297	18	10−4	10−4	NUM
iajs-3671	297	19	,	,	PUNCT
iajs-3671	297	20	10−3	10−3	NUM
iajs-3671	297	21	}	}	PUNCT
iajs-3671	297	22	and	and	CCONJ
iajs-3671	297	23	𝑞	𝑞	X
iajs-3671	297	24	=	=	SYM
iajs-3671	297	25	1	1	NUM
iajs-3671	297	26	%	%	NOUN
iajs-3671	297	27	noise	noise	NOUN
iajs-3671	297	28	.	.	PUNCT
iajs-3671	298	1	0	0	NUM
iajs-3671	298	2	0.1	0.1	NUM
iajs-3671	298	3	0.2	0.2	NUM
iajs-3671	298	4	0.3	0.3	NUM
iajs-3671	298	5	0.4	0.4	NUM
iajs-3671	298	6	0.5	0.5	NUM
iajs-3671	298	7	0.6	0.6	NUM
iajs-3671	298	8	0.7	0.7	NUM
iajs-3671	298	9	0.8	0.8	NUM
iajs-3671	298	10	0.9	0.9	NUM
iajs-3671	298	11	1	1	NUM
iajs-3671	298	12	t	t	NOUN
iajs-3671	298	13	-2	-2	NOUN
iajs-3671	298	14	-1.5	-1.5	NUM
iajs-3671	298	15	-1	-1	PROPN
iajs-3671	299	1	-0.5	-0.5	X
iajs-3671	299	2	0	0	NUM
iajs-3671	299	3	0.5	0.5	NUM
iajs-3671	299	4	1	1	NUM
iajs-3671	299	5	1.5	1.5	NUM
iajs-3671	299	6	2	2	NUM
iajs-3671	299	7	2.5	2.5	NUM
iajs-3671	299	8	p	p	NOUN
iajs-3671	299	9	(	(	PUNCT
iajs-3671	299	10	t	t	NOUN
iajs-3671	299	11	)	)	PUNCT
iajs-3671	299	12	exact	exact	ADJ
iajs-3671	299	13	1	1	NUM
iajs-3671	299	14	=	=	SYM
iajs-3671	299	15	10	10	NUM
iajs-3671	299	16	-3	-3	SYM
iajs-3671	299	17	2	2	NUM
iajs-3671	299	18	=	=	SYM
iajs-3671	299	19	10	10	NUM
iajs-3671	299	20	-4	-4	SYM
iajs-3671	299	21	2	2	NUM
iajs-3671	299	22	=	=	SYM
iajs-3671	299	23	10	10	NUM
iajs-3671	299	24	-5	-5	NOUN
iajs-3671	299	25	0	0	NUM
iajs-3671	299	26	5	5	NUM
iajs-3671	299	27	10	10	NUM
iajs-3671	299	28	15	15	NUM
iajs-3671	299	29	20	20	NUM
iajs-3671	299	30	25	25	NUM
iajs-3671	299	31	30	30	NUM
iajs-3671	299	32	35	35	NUM
iajs-3671	299	33	40	40	NUM
iajs-3671	299	34	45	45	NUM
iajs-3671	299	35	number	number	NOUN
iajs-3671	299	36	of	of	ADP
iajs-3671	299	37	iterations	iteration	NOUN
iajs-3671	299	38	10	10	NUM
iajs-3671	299	39	-3	-3	SYM
iajs-3671	299	40	10	10	NUM
iajs-3671	299	41	-2	-2	NOUN
iajs-3671	299	42	10	10	NUM
iajs-3671	299	43	-1	-1	NOUN
iajs-3671	299	44	r	r	NOUN
iajs-3671	299	45	e	e	NOUN
iajs-3671	299	46	g	g	NOUN
iajs-3671	299	47	u	u	PROPN
iajs-3671	299	48	la	la	X
iajs-3671	299	49	ri	ri	PROPN
iajs-3671	299	50	z	z	PROPN
iajs-3671	299	51	e	e	PROPN
iajs-3671	300	1	d	d	X
iajs-3671	300	2	o	o	X
iajs-3671	300	3	b	b	X
iajs-3671	300	4	je	je	X
iajs-3671	300	5	c	c	X
iajs-3671	300	6	ti	ti	X
iajs-3671	300	7	v	v	ADP
iajs-3671	300	8	e	e	X
iajs-3671	300	9	f	f	PROPN
iajs-3671	300	10	u	u	PROPN
iajs-3671	300	11	n	n	ADV
iajs-3671	300	12	c	c	NOUN
iajs-3671	300	13	ti	ti	NOUN
iajs-3671	300	14	o	o	NOUN
iajs-3671	300	15	n	n	CCONJ
iajs-3671	300	16	1	1	NUM
iajs-3671	300	17	=	=	SYM
iajs-3671	300	18	10	10	NUM
iajs-3671	300	19	-3	-3	SYM
iajs-3671	300	20	2	2	NUM
iajs-3671	300	21	=	=	SYM
iajs-3671	300	22	10	10	NUM
iajs-3671	300	23	-4	-4	SYM
iajs-3671	300	24	2	2	NUM
iajs-3671	300	25	=	=	SYM
iajs-3671	300	26	10	10	NUM
iajs-3671	300	27	-5	-5	NUM
iajs-3671	300	28	ihjpas	ihjpas	PROPN
iajs-3671	300	29	.	.	PUNCT
iajs-3671	301	1	2025	2025	NUM
iajs-3671	301	2	,	,	PUNCT
iajs-3671	301	3	38	38	NUM
iajs-3671	301	4	(	(	PUNCT
iajs-3671	301	5	1	1	NUM
iajs-3671	301	6	)	)	PUNCT
iajs-3671	301	7	487	487	NUM
iajs-3671	301	8	figure	figure	NOUN
iajs-3671	301	9	16	16	NUM
iajs-3671	301	10	.	.	PUNCT
iajs-3671	302	1	numerical	numerical	ADJ
iajs-3671	302	2	reconstructions	reconstruction	NOUN
iajs-3671	302	3	and	and	CCONJ
iajs-3671	302	4	exact	exact	ADJ
iajs-3671	302	5	solution	solution	NOUN
iajs-3671	302	6	for	for	ADP
iajs-3671	302	7	𝑝(𝑡	𝑝(𝑡	PROPN
iajs-3671	302	8	)	)	PUNCT
iajs-3671	302	9	,	,	PUNCT
iajs-3671	302	10	with	with	ADP
iajs-3671	302	11	regularization	regularization	NOUN
iajs-3671	302	12	parameter	parameter	NOUN
iajs-3671	302	13	𝛽	𝛽	PROPN
iajs-3671	302	14	=	=	PUNCT
iajs-3671	302	15	{	{	PUNCT
iajs-3671	302	16	10−4	10−4	PROPN
iajs-3671	302	17	,	,	PUNCT
iajs-3671	302	18	10−3	10−3	NUM
iajs-3671	302	19	}	}	PUNCT
iajs-3671	302	20	and	and	CCONJ
iajs-3671	302	21	q	q	NOUN
iajs-3671	302	22	=	=	SYM
iajs-3671	302	23	3	3	NUM
iajs-3671	302	24	%	%	NOUN
iajs-3671	302	25	noise	noise	NOUN
iajs-3671	302	26	.	.	PUNCT
iajs-3671	303	1	figure	figure	NOUN
iajs-3671	303	2	17	17	NUM
iajs-3671	303	3	.	.	PUNCT
iajs-3671	304	1	the	the	DET
iajs-3671	304	2	regularized	regularize	VERB
iajs-3671	304	3	objective	objective	ADJ
iajs-3671	304	4	function	function	NOUN
iajs-3671	304	5	equation	equation	NOUN
iajs-3671	304	6	(	(	PUNCT
iajs-3671	304	7	60	60	NUM
iajs-3671	304	8	)	)	PUNCT
iajs-3671	304	9	,	,	PUNCT
iajs-3671	304	10	with	with	ADP
iajs-3671	304	11	regularization	regularization	NOUN
iajs-3671	304	12	parameter	parameter	NOUN
iajs-3671	304	13	𝛽	𝛽	PROPN
iajs-3671	304	14	=	=	PUNCT
iajs-3671	304	15	{	{	PUNCT
iajs-3671	304	16	10−4	10−4	PROPN
iajs-3671	304	17	,	,	PUNCT
iajs-3671	304	18	10−3	10−3	NUM
iajs-3671	304	19	}	}	PUNCT
iajs-3671	304	20	and	and	CCONJ
iajs-3671	304	21	𝑞	𝑞	X
iajs-3671	304	22	=	=	SYM
iajs-3671	304	23	3	3	NUM
iajs-3671	304	24	%	%	NOUN
iajs-3671	304	25	noise	noise	NOUN
iajs-3671	304	26	.	.	PUNCT
iajs-3671	305	1	0	0	NUM
iajs-3671	305	2	0.1	0.1	NUM
iajs-3671	305	3	0.2	0.2	NUM
iajs-3671	305	4	0.3	0.3	NUM
iajs-3671	305	5	0.4	0.4	NUM
iajs-3671	305	6	0.5	0.5	NUM
iajs-3671	305	7	0.6	0.6	NUM
iajs-3671	305	8	0.7	0.7	NUM
iajs-3671	305	9	0.8	0.8	NUM
iajs-3671	305	10	0.9	0.9	NUM
iajs-3671	305	11	1	1	NUM
iajs-3671	305	12	t	t	NOUN
iajs-3671	305	13	-2	-2	NOUN
iajs-3671	305	14	-1.5	-1.5	NUM
iajs-3671	305	15	-1	-1	PROPN
iajs-3671	306	1	-0.5	-0.5	X
iajs-3671	306	2	0	0	NUM
iajs-3671	306	3	0.5	0.5	NUM
iajs-3671	306	4	1	1	NUM
iajs-3671	306	5	1.5	1.5	NUM
iajs-3671	306	6	2	2	NUM
iajs-3671	306	7	2.5	2.5	NUM
iajs-3671	306	8	p	p	NOUN
iajs-3671	306	9	(	(	PUNCT
iajs-3671	306	10	t	t	PROPN
iajs-3671	306	11	)	)	PUNCT
iajs-3671	306	12	exact	exact	ADJ
iajs-3671	306	13	1	1	NUM
iajs-3671	306	14	=	=	SYM
iajs-3671	306	15	10	10	NUM
iajs-3671	306	16	-3	-3	SYM
iajs-3671	306	17	2	2	NUM
iajs-3671	306	18	=	=	SYM
iajs-3671	306	19	10	10	NUM
iajs-3671	306	20	-4	-4	SYM
iajs-3671	306	21	0	0	NUM
iajs-3671	306	22	5	5	NUM
iajs-3671	306	23	10	10	NUM
iajs-3671	306	24	15	15	NUM
iajs-3671	306	25	20	20	NUM
iajs-3671	306	26	25	25	NUM
iajs-3671	306	27	30	30	NUM
iajs-3671	306	28	35	35	NUM
iajs-3671	306	29	40	40	NUM
iajs-3671	306	30	45	45	NUM
iajs-3671	306	31	50	50	NUM
iajs-3671	306	32	number	number	NOUN
iajs-3671	306	33	of	of	ADP
iajs-3671	306	34	iterations	iteration	NOUN
iajs-3671	306	35	10	10	NUM
iajs-3671	306	36	-2	-2	NOUN
iajs-3671	306	37	10	10	NUM
iajs-3671	306	38	-1	-1	NOUN
iajs-3671	306	39	r	r	NOUN
iajs-3671	306	40	e	e	NOUN
iajs-3671	306	41	g	g	NOUN
iajs-3671	306	42	u	u	X
iajs-3671	306	43	la	la	X
iajs-3671	306	44	ri	ri	PROPN
iajs-3671	306	45	ze	ze	PROPN
iajs-3671	306	46	d	d	PROPN
iajs-3671	306	47	o	o	PROPN
iajs-3671	306	48	b	b	X
iajs-3671	306	49	je	je	X
iajs-3671	306	50	ct	ct	NUM
iajs-3671	306	51	iv	iv	NUM
iajs-3671	306	52	e	e	X
iajs-3671	306	53	f	f	PROPN
iajs-3671	306	54	u	u	PROPN
iajs-3671	306	55	n	n	PROPN
iajs-3671	306	56	ct	ct	PROPN
iajs-3671	306	57	io	io	PROPN
iajs-3671	306	58	n	n	PROPN
iajs-3671	306	59	1	1	NUM
iajs-3671	306	60	=	=	SYM
iajs-3671	306	61	10	10	NUM
iajs-3671	306	62	-3	-3	SYM
iajs-3671	306	63	2	2	NUM
iajs-3671	306	64	=	=	SYM
iajs-3671	306	65	10	10	NUM
iajs-3671	306	66	-4	-4	NUM
iajs-3671	306	67	ihjpas	ihjpas	PROPN
iajs-3671	306	68	.	.	PUNCT
iajs-3671	307	1	2025	2025	NUM
iajs-3671	307	2	,	,	PUNCT
iajs-3671	307	3	38	38	NUM
iajs-3671	307	4	(	(	PUNCT
iajs-3671	307	5	1	1	NUM
iajs-3671	307	6	)	)	PUNCT
iajs-3671	307	7	488	488	NUM
iajs-3671	307	8	(	(	PUNCT
iajs-3671	307	9	a	a	NOUN
iajs-3671	307	10	)	)	PUNCT
iajs-3671	307	11	(	(	PUNCT
iajs-3671	307	12	b	b	X
iajs-3671	307	13	)	)	PUNCT
iajs-3671	307	14	figure	figure	NOUN
iajs-3671	308	1	18	18	NUM
iajs-3671	308	2	.	.	PUNCT
iajs-3671	309	1	exact	exact	ADJ
iajs-3671	309	2	and	and	CCONJ
iajs-3671	309	3	numerical	numerical	ADJ
iajs-3671	309	4	temperature	temperature	NOUN
iajs-3671	309	5	𝑢(𝑥	𝑢(𝑥	PROPN
iajs-3671	309	6	,	,	PUNCT
iajs-3671	309	7	𝑡	𝑡	PROPN
iajs-3671	309	8	)	)	PUNCT
iajs-3671	309	9	with	with	ADP
iajs-3671	309	10	(	(	PUNCT
iajs-3671	309	11	a	a	X
iajs-3671	309	12	)	)	PUNCT
iajs-3671	309	13	𝑞	𝑞	NOUN
iajs-3671	309	14	=	=	SYM
iajs-3671	309	15	1	1	NUM
iajs-3671	309	16	%	%	NOUN
iajs-3671	309	17	and	and	CCONJ
iajs-3671	309	18	𝛽	𝛽	NOUN
iajs-3671	309	19	=	=	SYM
iajs-3671	309	20	10−4	10−4	PROPN
iajs-3671	309	21	,	,	PUNCT
iajs-3671	309	22	(	(	PUNCT
iajs-3671	309	23	b	b	X
iajs-3671	309	24	)	)	PUNCT
iajs-3671	309	25	𝑞	𝑞	NOUN
iajs-3671	309	26	=	=	SYM
iajs-3671	309	27	3	3	NUM
iajs-3671	309	28	%	%	NOUN
iajs-3671	309	29	noise	noise	NOUN
iajs-3671	309	30	and	and	CCONJ
iajs-3671	309	31	𝛽	𝛽	NOUN
iajs-3671	309	32	=	=	SYM
iajs-3671	309	33	10−3	10−3	PROPN
iajs-3671	309	34	.	.	PUNCT
iajs-3671	309	35	table	table	NOUN
iajs-3671	309	36	2	2	NUM
iajs-3671	309	37	.	.	PUNCT
iajs-3671	309	38	numerical	numerical	ADJ
iajs-3671	309	39	information	information	NOUN
iajs-3671	309	40	for	for	ADP
iajs-3671	309	41	inverse	inverse	NOUN
iajs-3671	309	42	problem	problem	NOUN
iajs-3671	309	43	ii	ii	PROPN
iajs-3671	309	44	with	with	ADP
iajs-3671	309	45	noisy	noisy	ADJ
iajs-3671	309	46	data	datum	NOUN
iajs-3671	309	47	and	and	CCONJ
iajs-3671	309	48	regularization	regularization	NOUN
iajs-3671	309	49	.	.	PUNCT
iajs-3671	310	1	𝑞	𝑞	X
iajs-3671	310	2	=	=	SYM
iajs-3671	310	3	1	1	NUM
iajs-3671	310	4	%	%	NOUN
iajs-3671	310	5	𝛽	𝛽	NOUN
iajs-3671	310	6	=	=	SYM
iajs-3671	310	7	10−3	10−3	PROPN
iajs-3671	310	8	𝛽	𝛽	NOUN
iajs-3671	310	9	=	=	SYM
iajs-3671	310	10	10−4	10−4	NUM
iajs-3671	310	11	𝛽	𝛽	NOUN
iajs-3671	310	12	=	=	SYM
iajs-3671	310	13	10−5	10−5	NUM
iajs-3671	310	14	no	no	NOUN
iajs-3671	310	15	.	.	PUNCT
iajs-3671	310	16	of	of	ADP
iajs-3671	310	17	iterations	iteration	NOUN
iajs-3671	310	18	36	36	NUM
iajs-3671	310	19	45	45	NUM
iajs-3671	310	20	44	44	NUM
iajs-3671	310	21	objective	objective	ADJ
iajs-3671	310	22	function	function	NOUN
iajs-3671	310	23	(	(	PUNCT
iajs-3671	310	24	60	60	NUM
iajs-3671	310	25	)	)	PUNCT
iajs-3671	310	26	at	at	ADP
iajs-3671	310	27	final	final	ADJ
iajs-3671	310	28	iteration	iteration	NOUN
iajs-3671	310	29	0.0141	0.0141	NUM
iajs-3671	310	30	0.0028	0.0028	NUM
iajs-3671	310	31	5.9268e-04	5.9268e-04	NUM
iajs-3671	310	32	𝑟𝑚𝑠𝑒(𝑝	𝑟𝑚𝑠𝑒(𝑝	NOUN
iajs-3671	310	33	)	)	PUNCT
iajs-3671	310	34	0.3054	0.3054	NUM
iajs-3671	311	1	0.1684	0.1684	NUM
iajs-3671	312	1	0.6502	0.6502	NUM
iajs-3671	312	2	q	q	NOUN
iajs-3671	312	3	=	=	PUNCT
iajs-3671	312	4	3	3	NUM
iajs-3671	312	5	%	%	NOUN
iajs-3671	312	6	𝛽	𝛽	NOUN
iajs-3671	312	7	=	=	SYM
iajs-3671	312	8	10−3	10−3	PROPN
iajs-3671	312	9	𝛽	𝛽	NOUN
iajs-3671	312	10	=	=	SYM
iajs-3671	312	11	10−4	10−4	NUM
iajs-3671	312	12	𝛽	𝛽	NOUN
iajs-3671	312	13	=	=	SYM
iajs-3671	312	14	10−5	10−5	NUM
iajs-3671	312	15	no	no	NOUN
iajs-3671	312	16	.	.	PUNCT
iajs-3671	312	17	of	of	ADP
iajs-3671	312	18	iterations	iteration	NOUN
iajs-3671	312	19	43	43	NUM
iajs-3671	312	20	49	49	NUM
iajs-3671	312	21	52	52	NUM
iajs-3671	312	22	objective	objective	ADJ
iajs-3671	312	23	function	function	NOUN
iajs-3671	312	24	(	(	PUNCT
iajs-3671	312	25	60	60	NUM
iajs-3671	312	26	)	)	PUNCT
iajs-3671	312	27	at	at	ADP
iajs-3671	312	28	final	final	ADJ
iajs-3671	312	29	iteration	iteration	NOUN
iajs-3671	312	30	0.0237	0.0237	NUM
iajs-3671	312	31	0.0089	0.0089	NUM
iajs-3671	312	32	0.0036	0.0036	NUM
iajs-3671	312	33	𝑟𝑚𝑠𝑒(𝑝	𝑟𝑚𝑠𝑒(𝑝	NOUN
iajs-3671	312	34	)	)	PUNCT
iajs-3671	312	35	0.2919	0.2919	NUM
iajs-3671	312	36	0.4942	0.4942	NUM
iajs-3671	312	37	1.9405	1.9405	NUM
iajs-3671	312	38	4	4	NUM
iajs-3671	312	39	.	.	PUNCT
iajs-3671	313	1	conclusions	conclusion	NOUN
iajs-3671	313	2	in	in	ADP
iajs-3671	313	3	this	this	DET
iajs-3671	313	4	work	work	NOUN
iajs-3671	313	5	,	,	PUNCT
iajs-3671	313	6	an	an	DET
iajs-3671	313	7	investigation	investigation	NOUN
iajs-3671	313	8	was	be	AUX
iajs-3671	313	9	conducted	conduct	VERB
iajs-3671	313	10	by	by	ADP
iajs-3671	313	11	considering	consider	VERB
iajs-3671	313	12	the	the	DET
iajs-3671	313	13	pseudo	pseudo	NOUN
iajs-3671	313	14	-	-	ADJ
iajs-3671	313	15	parabolic	parabolic	ADJ
iajs-3671	313	16	equations	equation	NOUN
iajs-3671	313	17	of	of	ADP
iajs-3671	313	18	the	the	DET
iajs-3671	313	19	third	third	ADJ
iajs-3671	313	20	-	-	PUNCT
iajs-3671	313	21	order	order	NOUN
iajs-3671	313	22	with	with	ADP
iajs-3671	313	23	initial	initial	ADJ
iajs-3671	313	24	and	and	CCONJ
iajs-3671	313	25	various	various	ADJ
iajs-3671	313	26	boundary	boundary	ADJ
iajs-3671	313	27	conditions	condition	NOUN
iajs-3671	313	28	and	and	CCONJ
iajs-3671	313	29	overdetermination	overdetermination	NOUN
iajs-3671	313	30	data	datum	NOUN
iajs-3671	313	31	to	to	ADP
iajs-3671	313	32	ihjpas	ihjpas	PROPN
iajs-3671	313	33	.	.	PUNCT
iajs-3671	314	1	2025	2025	NUM
iajs-3671	314	2	,	,	PUNCT
iajs-3671	314	3	38	38	NUM
iajs-3671	314	4	(	(	PUNCT
iajs-3671	314	5	1	1	NUM
iajs-3671	314	6	)	)	PUNCT
iajs-3671	314	7	489	489	NUM
iajs-3671	314	8	recover	recover	VERB
iajs-3671	314	9	the	the	DET
iajs-3671	314	10	time	time	NOUN
iajs-3671	314	11	–	–	PUNCT
iajs-3671	314	12	dependent	dependent	ADJ
iajs-3671	314	13	potential	potential	ADJ
iajs-3671	314	14	terms	term	NOUN
iajs-3671	314	15	.	.	PUNCT
iajs-3671	315	1	the	the	DET
iajs-3671	315	2	direct	direct	ADJ
iajs-3671	315	3	problems	problem	NOUN
iajs-3671	315	4	were	be	AUX
iajs-3671	315	5	solved	solve	VERB
iajs-3671	315	6	by	by	ADP
iajs-3671	315	7	the	the	DET
iajs-3671	315	8	fdm	fdm	NOUN
iajs-3671	315	9	.	.	PUNCT
iajs-3671	316	1	von	von	PROPN
iajs-3671	316	2	neumann	neumann	PROPN
iajs-3671	316	3	technique	technique	NOUN
iajs-3671	316	4	was	be	AUX
iajs-3671	316	5	employed	employ	VERB
iajs-3671	316	6	to	to	PART
iajs-3671	316	7	study	study	VERB
iajs-3671	316	8	the	the	DET
iajs-3671	316	9	stability	stability	NOUN
iajs-3671	316	10	of	of	ADP
iajs-3671	316	11	the	the	DET
iajs-3671	316	12	proposed	propose	VERB
iajs-3671	316	13	numerical	numerical	ADJ
iajs-3671	316	14	direct	direct	ADJ
iajs-3671	316	15	algorithm	algorithm	NOUN
iajs-3671	316	16	.	.	PUNCT
iajs-3671	317	1	the	the	DET
iajs-3671	317	2	inverse	inverse	NOUN
iajs-3671	317	3	problems	problem	NOUN
iajs-3671	317	4	were	be	AUX
iajs-3671	317	5	reformulated	reformulate	VERB
iajs-3671	317	6	as	as	ADP
iajs-3671	317	7	a	a	DET
iajs-3671	317	8	nonlinear	nonlinear	ADJ
iajs-3671	317	9	optimization	optimization	NOUN
iajs-3671	317	10	problem	problem	NOUN
iajs-3671	317	11	and	and	CCONJ
iajs-3671	317	12	solved	solve	VERB
iajs-3671	317	13	numerically	numerically	ADV
iajs-3671	317	14	by	by	ADP
iajs-3671	317	15	lsqnonlin	lsqnonlin	PROPN
iajs-3671	317	16	iterative	iterative	PROPN
iajs-3671	317	17	routine	routine	NOUN
iajs-3671	317	18	from	from	ADP
iajs-3671	317	19	matlab	matlab	PROPN
iajs-3671	317	20	.	.	PUNCT
iajs-3671	318	1	to	to	PART
iajs-3671	318	2	stabilize	stabilize	VERB
iajs-3671	318	3	the	the	DET
iajs-3671	318	4	ill	ill	ADV
iajs-3671	318	5	-	-	PUNCT
iajs-3671	318	6	posed	pose	VERB
iajs-3671	318	7	problem	problem	NOUN
iajs-3671	318	8	under	under	ADP
iajs-3671	318	9	investigation	investigation	NOUN
iajs-3671	318	10	,	,	PUNCT
iajs-3671	318	11	tikhonov	tikhonov	NOUN
iajs-3671	318	12	's	's	PART
iajs-3671	318	13	regularization	regularization	NOUN
iajs-3671	318	14	method	method	NOUN
iajs-3671	318	15	was	be	AUX
iajs-3671	318	16	applied	apply	VERB
iajs-3671	318	17	.	.	PUNCT
iajs-3671	319	1	the	the	DET
iajs-3671	319	2	numerical	numerical	PROPN
iajs-3671	319	3	test	test	NOUN
iajs-3671	319	4	examples	example	NOUN
iajs-3671	319	5	for	for	ADP
iajs-3671	319	6	each	each	DET
iajs-3671	319	7	problem	problem	NOUN
iajs-3671	319	8	confirmed	confirm	VERB
iajs-3671	319	9	the	the	DET
iajs-3671	319	10	applicability	applicability	NOUN
iajs-3671	319	11	of	of	ADP
iajs-3671	319	12	the	the	DET
iajs-3671	319	13	proposed	propose	VERB
iajs-3671	319	14	algorithm	algorithm	NOUN
iajs-3671	319	15	to	to	PART
iajs-3671	319	16	obtain	obtain	VERB
iajs-3671	319	17	an	an	DET
iajs-3671	319	18	accurate	accurate	ADJ
iajs-3671	319	19	and	and	CCONJ
iajs-3671	319	20	stable	stable	ADJ
iajs-3671	319	21	solution	solution	NOUN
iajs-3671	319	22	.	.	PUNCT
iajs-3671	320	1	as	as	ADP
iajs-3671	320	2	a	a	DET
iajs-3671	320	3	future	future	ADJ
iajs-3671	320	4	work	work	NOUN
iajs-3671	320	5	,	,	PUNCT
iajs-3671	320	6	it	it	PRON
iajs-3671	320	7	can	can	AUX
iajs-3671	320	8	apply	apply	VERB
iajs-3671	320	9	this	this	DET
iajs-3671	320	10	process	process	NOUN
iajs-3671	320	11	to	to	PART
iajs-3671	320	12	solve	solve	VERB
iajs-3671	320	13	the	the	DET
iajs-3671	320	14	other	other	ADJ
iajs-3671	320	15	different	different	ADJ
iajs-3671	320	16	inverse	inverse	NOUN
iajs-3671	320	17	problems	problem	NOUN
iajs-3671	320	18	of	of	ADP
iajs-3671	320	19	higher	high	ADJ
iajs-3671	320	20	dimensions	dimension	NOUN
iajs-3671	320	21	.	.	PUNCT
iajs-3671	321	1	acknowledgements	acknowledgement	NOUN
iajs-3671	321	2	we	we	PRON
iajs-3671	321	3	would	would	AUX
iajs-3671	321	4	like	like	VERB
iajs-3671	321	5	to	to	PART
iajs-3671	321	6	express	express	VERB
iajs-3671	321	7	our	our	PRON
iajs-3671	321	8	gratitude	gratitude	NOUN
iajs-3671	321	9	other	other	ADJ
iajs-3671	321	10	referees	referee	NOUN
iajs-3671	321	11	for	for	ADP
iajs-3671	321	12	their	their	PRON
iajs-3671	321	13	valuable	valuable	ADJ
iajs-3671	321	14	comments	comment	NOUN
iajs-3671	321	15	and	and	CCONJ
iajs-3671	321	16	suggestions	suggestion	NOUN
iajs-3671	321	17	that	that	PRON
iajs-3671	321	18	led	lead	VERB
iajs-3671	321	19	to	to	ADP
iajs-3671	321	20	a	a	DET
iajs-3671	321	21	truly	truly	ADV
iajs-3671	321	22	significant	significant	ADJ
iajs-3671	321	23	improvement	improvement	NOUN
iajs-3671	321	24	of	of	ADP
iajs-3671	321	25	the	the	DET
iajs-3671	321	26	paper	paper	NOUN
iajs-3671	321	27	.	.	PUNCT
iajs-3671	322	1	conflict	conflict	NOUN
iajs-3671	322	2	of	of	ADP
iajs-3671	322	3	interest	interest	NOUN
iajs-3671	322	4	the	the	DET
iajs-3671	322	5	authors	author	NOUN
iajs-3671	322	6	declare	declare	VERB
iajs-3671	322	7	that	that	SCONJ
iajs-3671	322	8	there	there	PRON
iajs-3671	322	9	are	be	VERB
iajs-3671	322	10	no	no	DET
iajs-3671	322	11	competing	compete	VERB
iajs-3671	322	12	interests	interest	NOUN
iajs-3671	322	13	regarding	regard	VERB
iajs-3671	322	14	the	the	DET
iajs-3671	322	15	publication	publication	NOUN
iajs-3671	322	16	of	of	ADP
iajs-3671	322	17	this	this	DET
iajs-3671	322	18	paper	paper	NOUN
iajs-3671	322	19	.	.	PUNCT
iajs-3671	323	1	funding	fund	VERB
iajs-3671	323	2	this	this	DET
iajs-3671	323	3	work	work	NOUN
iajs-3671	323	4	is	be	AUX
iajs-3671	323	5	not	not	PART
iajs-3671	323	6	supported	support	VERB
iajs-3671	323	7	by	by	ADP
iajs-3671	323	8	any	any	DET
iajs-3671	323	9	the	the	DET
iajs-3671	323	10	foundation	foundation	NOUN
iajs-3671	323	11	.	.	PUNCT
iajs-3671	324	1	ethical	ethical	ADJ
iajs-3671	324	2	clearance	clearance	NOUN
iajs-3671	324	3	ethics	ethic	NOUN
iajs-3671	324	4	of	of	ADP
iajs-3671	324	5	scientific	scientific	ADJ
iajs-3671	324	6	research	research	NOUN
iajs-3671	324	7	were	be	AUX
iajs-3671	324	8	carried	carry	VERB
iajs-3671	324	9	out	out	ADP
iajs-3671	324	10	in	in	ADP
iajs-3671	324	11	accordance	accordance	NOUN
iajs-3671	324	12	with	with	ADP
iajs-3671	324	13	international	international	ADJ
iajs-3671	324	14	conditions	condition	NOUN
iajs-3671	324	15	.	.	PUNCT
iajs-3671	325	1	references	reference	NOUN
iajs-3671	325	2	1	1	NUM
iajs-3671	325	3	.	.	PUNCT
iajs-3671	325	4	hussein	hussein	PROPN
iajs-3671	325	5	m.s	m.s	PROPN
iajs-3671	325	6	.	.	PROPN
iajs-3671	325	7	;	;	PUNCT
iajs-3671	325	8	lesnic	lesnic	PROPN
iajs-3671	325	9	d.	d.	PROPN
iajs-3671	325	10	;	;	PUNCT
iajs-3671	325	11	ivanchov	ivanchov	PROPN
iajs-3671	325	12	m.i	m.i	PROPN
iajs-3671	325	13	.	.	PROPN
iajs-3671	325	14	;	;	PUNCT
iajs-3671	325	15	snitkoh	snitkoh	NOUN
iajs-3671	325	16	a.	a.	NOUN
iajs-3671	325	17	multiple	multiple	ADJ
iajs-3671	325	18	time	time	NOUN
iajs-3671	325	19	-	-	PUNCT
iajs-3671	325	20	dependent	dependent	ADJ
iajs-3671	325	21	coefficient	coefficient	NOUN
iajs-3671	325	22	identification	identification	NOUN
iajs-3671	325	23	thermal	thermal	ADJ
iajs-3671	325	24	problems	problem	NOUN
iajs-3671	325	25	with	with	ADP
iajs-3671	325	26	a	a	DET
iajs-3671	325	27	free	free	ADJ
iajs-3671	325	28	boundary	boundary	NOUN
iajs-3671	325	29	.	.	PUNCT
iajs-3671	326	1	applied	apply	VERB
iajs-3671	326	2	numerical	numerical	ADJ
iajs-3671	326	3	mathematics	mathematic	NOUN
iajs-3671	326	4	.	.	PUNCT
iajs-3671	327	1	2016	2016	NUM
iajs-3671	327	2	;	;	PUNCT
iajs-3671	327	3	99	99	NUM
iajs-3671	327	4	:	:	SYM
iajs-3671	327	5	24	24	NUM
iajs-3671	327	6	-	-	SYM
iajs-3671	327	7	50	50	NUM
iajs-3671	327	8	.	.	PUNCT
iajs-3671	328	1	https://doi.org/10.1016/j.apnum.2015.09.001	https://doi.org/10.1016/j.apnum.2015.09.001	NUM
iajs-3671	328	2	2	2	NUM
iajs-3671	328	3	.	.	PUNCT
iajs-3671	328	4	hussein	hussein	PROPN
iajs-3671	328	5	m.s	m.s	PROPN
iajs-3671	328	6	.	.	PROPN
iajs-3671	328	7	;	;	PUNCT
iajs-3671	328	8	lesnic	lesnic	PROPN
iajs-3671	328	9	d.	d.	PROPN
iajs-3671	328	10	identification	identification	NOUN
iajs-3671	328	11	of	of	ADP
iajs-3671	328	12	the	the	DET
iajs-3671	328	13	time	time	NOUN
iajs-3671	328	14	-	-	PUNCT
iajs-3671	328	15	dependent	dependent	ADJ
iajs-3671	328	16	conductivity	conductivity	NOUN
iajs-3671	328	17	of	of	ADP
iajs-3671	328	18	an	an	DET
iajs-3671	328	19	inhomogeneous	inhomogeneous	ADJ
iajs-3671	328	20	diffusive	diffusive	ADJ
iajs-3671	328	21	material	material	NOUN
iajs-3671	328	22	.	.	PUNCT
iajs-3671	329	1	applied	apply	VERB
iajs-3671	329	2	mathematics	mathematic	NOUN
iajs-3671	329	3	and	and	CCONJ
iajs-3671	329	4	computation	computation	NOUN
iajs-3671	329	5	.	.	PUNCT
iajs-3671	330	1	2015	2015	NUM
iajs-3671	330	2	;	;	PUNCT
iajs-3671	330	3	269	269	NUM
iajs-3671	330	4	:	:	SYM
iajs-3671	330	5	35	35	NUM
iajs-3671	330	6	-	-	SYM
iajs-3671	330	7	58	58	NUM
iajs-3671	330	8	.	.	PUNCT
iajs-3671	331	1	https://doi.org/10.1016/j.amc.2015.07.039	https://doi.org/10.1016/j.amc.2015.07.039	NOUN
iajs-3671	331	2	3	3	NUM
iajs-3671	331	3	.	.	PUNCT
iajs-3671	331	4	hussein	hussein	PROPN
iajs-3671	331	5	m.	m.	PROPN
iajs-3671	331	6	s.	s.	PROPN
iajs-3671	331	7	;	;	PUNCT
iajs-3671	331	8	lesnic	lesnic	PROPN
iajs-3671	331	9	d.	d.	PROPN
iajs-3671	331	10	simultaneous	simultaneous	ADJ
iajs-3671	331	11	determination	determination	NOUN
iajs-3671	331	12	of	of	ADP
iajs-3671	331	13	time	time	NOUN
iajs-3671	331	14	and	and	CCONJ
iajs-3671	331	15	space	space	NOUN
iajs-3671	331	16	-	-	PUNCT
iajs-3671	331	17	dependent	dependent	ADJ
iajs-3671	331	18	coefficients	coefficient	NOUN
iajs-3671	331	19	in	in	ADP
iajs-3671	331	20	a	a	DET
iajs-3671	331	21	parabolic	parabolic	ADJ
iajs-3671	331	22	equation	equation	NOUN
iajs-3671	331	23	.	.	PUNCT
iajs-3671	332	1	communications	communication	NOUN
iajs-3671	332	2	in	in	ADP
iajs-3671	332	3	nonlinear	nonlinear	ADJ
iajs-3671	332	4	science	science	NOUN
iajs-3671	332	5	and	and	CCONJ
iajs-3671	332	6	numerical	numerical	PROPN
iajs-3671	332	7	simulation	simulation	PROPN
iajs-3671	332	8	.	.	PUNCT
iajs-3671	333	1	2016	2016	NUM
iajs-3671	333	2	;	;	PUNCT
iajs-3671	333	3	33	33	NUM
iajs-3671	333	4	:	:	SYM
iajs-3671	333	5	194217	194217	NUM
iajs-3671	333	6	.	.	PUNCT
iajs-3671	334	1	https://doi.org/10.1016/j.cnsns.2015.09.008	https://doi.org/10.1016/j.cnsns.2015.09.008	NOUN
iajs-3671	334	2	4	4	NUM
iajs-3671	334	3	.	.	PUNCT
iajs-3671	334	4	huntul	huntul	PROPN
iajs-3671	334	5	m.j	m.j	PROPN
iajs-3671	334	6	.	.	PROPN
iajs-3671	334	7	;	;	PUNCT
iajs-3671	334	8	hussein	hussein	PROPN
iajs-3671	334	9	m.	m.	PROPN
iajs-3671	334	10	s.	s.	PROPN
iajs-3671	334	11	simultaneous	simultaneous	ADJ
iajs-3671	334	12	identification	identification	NOUN
iajs-3671	334	13	of	of	ADP
iajs-3671	334	14	thermal	thermal	ADJ
iajs-3671	334	15	conductivity	conductivity	NOUN
iajs-3671	334	16	and	and	CCONJ
iajs-3671	334	17	heat	heat	NOUN
iajs-3671	334	18	source	source	NOUN
iajs-3671	334	19	in	in	ADP
iajs-3671	334	20	the	the	DET
iajs-3671	334	21	heat	heat	NOUN
iajs-3671	334	22	equation	equation	NOUN
iajs-3671	334	23	.	.	PUNCT
iajs-3671	335	1	iraqi	iraqi	ADJ
iajs-3671	335	2	journal	journal	PROPN
iajs-3671	335	3	of	of	ADP
iajs-3671	335	4	science	science	NOUN
iajs-3671	335	5	.	.	PUNCT
iajs-3671	336	1	2021	2021	NUM
iajs-3671	336	2	;	;	PUNCT
iajs-3671	336	3	1968	1968	NUM
iajs-3671	336	4	-	-	SYM
iajs-3671	336	5	1978	1978	NUM
iajs-3671	336	6	.	.	PUNCT
iajs-3671	337	1	doi	doi	NOUN
iajs-3671	337	2	:	:	PUNCT
iajs-3671	337	3	10.24996	10.24996	NUM
iajs-3671	337	4	/	/	SYM
iajs-3671	337	5	ijs.2021.62.6.22	ijs.2021.62.6.22	VERB
iajs-3671	337	6	5	5	NUM
iajs-3671	337	7	.	.	PUNCT
iajs-3671	338	1	hazanee	hazanee	NOUN
iajs-3671	338	2	a.	a.	NOUN
iajs-3671	338	3	;	;	PUNCT
iajs-3671	338	4	lesnic	lesnic	PROPN
iajs-3671	338	5	d.	d.	PROPN
iajs-3671	338	6	;	;	PUNCT
iajs-3671	338	7	ismailov	ismailov	PROPN
iajs-3671	338	8	m.i	m.i	PROPN
iajs-3671	338	9	.	.	PROPN
iajs-3671	338	10	;	;	PUNCT
iajs-3671	338	11	kerimov	kerimov	PROPN
iajs-3671	338	12	n.	n.	PROPN
iajs-3671	338	13	b.	b.	PROPN
iajs-3671	338	14	inverse	inverse	PROPN
iajs-3671	338	15	time	time	NOUN
iajs-3671	338	16	-	-	PUNCT
iajs-3671	338	17	dependent	dependent	ADJ
iajs-3671	338	18	source	source	NOUN
iajs-3671	338	19	problems	problem	NOUN
iajs-3671	338	20	for	for	ADP
iajs-3671	338	21	the	the	DET
iajs-3671	338	22	heat	heat	NOUN
iajs-3671	338	23	equation	equation	NOUN
iajs-3671	338	24	with	with	ADP
iajs-3671	338	25	nonlocal	nonlocal	ADJ
iajs-3671	338	26	boundary	boundary	ADJ
iajs-3671	338	27	conditions	condition	NOUN
iajs-3671	338	28	.	.	PUNCT
iajs-3671	339	1	applied	apply	VERB
iajs-3671	339	2	mathematics	mathematic	NOUN
iajs-3671	339	3	and	and	CCONJ
iajs-3671	339	4	computation	computation	NOUN
iajs-3671	339	5	.	.	PUNCT
iajs-3671	340	1	2019	2019	NUM
iajs-3671	340	2	;	;	PUNCT
iajs-3671	340	3	346	346	NUM
iajs-3671	340	4	,	,	PUNCT
iajs-3671	340	5	800	800	NUM
iajs-3671	340	6	-	-	SYM
iajs-3671	340	7	815	815	NUM
iajs-3671	340	8	.	.	PUNCT
iajs-3671	340	9	https://doi.org/10.1016/j.amc.2018.10.059	https://doi.org/10.1016/j.amc.2018.10.059	PROPN
iajs-3671	340	10	6	6	NUM
iajs-3671	340	11	.	.	PUNCT
iajs-3671	341	1	hussein	hussein	PROPN
iajs-3671	341	2	m.s	m.s	PROPN
iajs-3671	341	3	.	.	PROPN
iajs-3671	341	4	;	;	PUNCT
iajs-3671	341	5	adil	adil	PROPN
iajs-3671	341	6	z.	z.	PROPN
iajs-3671	341	7	numerical	numerical	PROPN
iajs-3671	341	8	solution	solution	NOUN
iajs-3671	341	9	for	for	ADP
iajs-3671	341	10	two	two	NUM
iajs-3671	341	11	-	-	PUNCT
iajs-3671	341	12	sided	sided	ADJ
iajs-3671	341	13	stefan	stefan	PROPN
iajs-3671	341	14	problem	problem	PROPN
iajs-3671	341	15	.	.	PUNCT
iajs-3671	342	1	iraqi	iraqi	ADJ
iajs-3671	342	2	journal	journal	PROPN
iajs-3671	342	3	of	of	ADP
iajs-3671	342	4	science	science	NOUN
iajs-3671	342	5	.	.	PUNCT
iajs-3671	343	1	2020	2020	NUM
iajs-3671	343	2	;	;	PUNCT
iajs-3671	343	3	61.2	61.2	NUM
iajs-3671	343	4	:	:	SYM
iajs-3671	343	5	444	444	NUM
iajs-3671	343	6	-	-	SYM
iajs-3671	343	7	452	452	NUM
iajs-3671	343	8	.	.	PUNCT
iajs-3671	344	1	https://doi.org/	https://doi.org/	NOUN
iajs-3671	344	2	10.24996	10.24996	NUM
iajs-3671	344	3	/	/	SYM
iajs-3671	344	4	ijs.2020.61.2.24	ijs.2020.61.2.24	PROPN
iajs-3671	344	5	7	7	NUM
iajs-3671	344	6	.	.	PUNCT
iajs-3671	344	7	hazanee	hazanee	NOUN
iajs-3671	344	8	a.	a.	NOUN
iajs-3671	344	9	;	;	PUNCT
iajs-3671	344	10	lesnic	lesnic	PROPN
iajs-3671	344	11	d.	d.	PROPN
iajs-3671	344	12	reconstruction	reconstruction	NOUN
iajs-3671	344	13	of	of	ADP
iajs-3671	344	14	multiplicative	multiplicative	ADJ
iajs-3671	344	15	space	space	NOUN
iajs-3671	344	16	-	-	PUNCT
iajs-3671	344	17	and	and	CCONJ
iajs-3671	344	18	time	time	NOUN
iajs-3671	344	19	-	-	PUNCT
iajs-3671	344	20	dependent	dependent	ADJ
iajs-3671	344	21	sources	source	NOUN
iajs-3671	344	22	.	.	PUNCT
iajs-3671	345	1	inverse	inverse	NOUN
iajs-3671	345	2	problems	problem	NOUN
iajs-3671	345	3	in	in	ADP
iajs-3671	345	4	science	science	NOUN
iajs-3671	345	5	and	and	CCONJ
iajs-3671	345	6	engineering	engineering	NOUN
iajs-3671	345	7	.	.	PUNCT
iajs-3671	346	1	2016	2016	NUM
iajs-3671	346	2	;	;	PUNCT
iajs-3671	346	3	24(9	24(9	NUM
iajs-3671	346	4	)	)	PUNCT
iajs-3671	346	5	,	,	PUNCT
iajs-3671	346	6	1528	1528	NUM
iajs-3671	346	7	-	-	SYM
iajs-3671	346	8	1549	1549	NUM
iajs-3671	346	9	.	.	PUNCT
iajs-3671	347	1	https://doi.org/10.1080/17415977.2015.1130041	https://doi.org/10.1080/17415977.2015.1130041	NOUN
iajs-3671	347	2	8	8	NUM
iajs-3671	347	3	.	.	PUNCT
iajs-3671	348	1	qassim	qassim	ADJ
iajs-3671	348	2	m.	m.	NOUN
iajs-3671	348	3	;	;	PUNCT
iajs-3671	348	4	hussein	hussein	PROPN
iajs-3671	348	5	m.s	m.s	PROPN
iajs-3671	348	6	.	.	PROPN
iajs-3671	348	7	numerical	numerical	PROPN
iajs-3671	348	8	solution	solution	NOUN
iajs-3671	348	9	to	to	PART
iajs-3671	348	10	recover	recover	VERB
iajs-3671	348	11	time	time	NOUN
iajs-3671	348	12	-	-	PUNCT
iajs-3671	348	13	dependent	dependent	ADJ
iajs-3671	348	14	coefficient	coefficient	NOUN
iajs-3671	348	15	and	and	CCONJ
iajs-3671	348	16	free	free	ADJ
iajs-3671	348	17	https://doi.org/10.1016/j.apnum.2015.09.001	https://doi.org/10.1016/j.apnum.2015.09.001	NOUN
iajs-3671	348	18	https://doi.org/10.1016/j.apnum.2015.09.001	https://doi.org/10.1016/j.apnum.2015.09.001	NOUN
iajs-3671	348	19	https://doi.org/10.1016/j.amc.2015.07.039	https://doi.org/10.1016/j.amc.2015.07.039	NOUN
iajs-3671	348	20	https://doi.org/10.1016/j.amc.2015.07.039	https://doi.org/10.1016/j.amc.2015.07.039	NOUN
iajs-3671	348	21	https://doi.org/10.1016/j.cnsns.2015.09.008	https://doi.org/10.1016/j.cnsns.2015.09.008	NOUN
iajs-3671	348	22	https://doi.org/10.1016/j.cnsns.2015.09.008	https://doi.org/10.1016/j.cnsns.2015.09.008	NOUN
iajs-3671	348	23	https://doi.org/10.1016/j.amc.2018.10.059	https://doi.org/10.1016/j.amc.2018.10.059	NOUN
iajs-3671	348	24	https://doi.org/10.1016/j.amc.2018.10.059	https://doi.org/10.1016/j.amc.2018.10.059	PROPN
iajs-3671	348	25	https://doi.org/%2010.24996/ijs.2020.61.2.24	https://doi.org/%2010.24996/ijs.2020.61.2.24	PROPN
iajs-3671	348	26	https://doi.org/10.1080/17415977.2015.1130041	https://doi.org/10.1080/17415977.2015.1130041	PROPN
iajs-3671	348	27	ihjpas	ihjpas	PROPN
iajs-3671	348	28	.	.	PUNCT
iajs-3671	349	1	2025	2025	NUM
iajs-3671	349	2	,	,	PUNCT
iajs-3671	349	3	38	38	NUM
iajs-3671	349	4	(	(	PUNCT
iajs-3671	349	5	1	1	NUM
iajs-3671	349	6	)	)	PUNCT
iajs-3671	349	7	490	490	NUM
iajs-3671	349	8	boundary	boundary	NOUN
iajs-3671	349	9	from	from	ADP
iajs-3671	349	10	nonlocal	nonlocal	ADJ
iajs-3671	349	11	and	and	CCONJ
iajs-3671	349	12	stefan	stefan	PROPN
iajs-3671	349	13	type	type	PROPN
iajs-3671	349	14	overdetermination	overdetermination	NOUN
iajs-3671	349	15	conditions	condition	NOUN
iajs-3671	349	16	in	in	ADP
iajs-3671	349	17	heat	heat	NOUN
iajs-3671	349	18	equation	equation	NOUN
iajs-3671	349	19	.	.	PUNCT
iajs-3671	350	1	iraqi	iraqi	ADJ
iajs-3671	350	2	journal	journal	PROPN
iajs-3671	350	3	of	of	ADP
iajs-3671	350	4	science	science	NOUN
iajs-3671	350	5	.	.	PUNCT
iajs-3671	351	1	2021	2021	NUM
iajs-3671	351	2	;	;	PUNCT
iajs-3671	351	3	950	950	NUM
iajs-3671	351	4	-	-	SYM
iajs-3671	351	5	960	960	NUM
iajs-3671	351	6	.	.	PUNCT
iajs-3671	352	1	https://doi.org/10.24996/ijs.2021.62.3.25	https://doi.org/10.24996/ijs.2021.62.3.25	PROPN
iajs-3671	352	2	9	9	NUM
iajs-3671	352	3	.	.	PUNCT
iajs-3671	352	4	asanov	asanov	PROPN
iajs-3671	352	5	a.	a.	PROPN
iajs-3671	352	6	;	;	PUNCT
iajs-3671	352	7	atamanov	atamanov	PROPN
iajs-3671	352	8	e	e	NOUN
iajs-3671	352	9	;	;	PUNCT
iajs-3671	352	10	.	.	PUNCT
iajs-3671	353	1	nonclassical	nonclassical	ADJ
iajs-3671	353	2	and	and	CCONJ
iajs-3671	353	3	inverse	inverse	NOUN
iajs-3671	353	4	problems	problem	NOUN
iajs-3671	353	5	for	for	ADP
iajs-3671	353	6	pseudo	pseudo	NOUN
iajs-3671	353	7	-	-	NOUN
iajs-3671	353	8	parabolic	parabolic	NOUN
iajs-3671	353	9	equations,1997	equations,1997	NOUN
iajs-3671	353	10	,	,	PUNCT
iajs-3671	353	11	vol	vol	NOUN
iajs-3671	353	12	.	.	PUNCT
iajs-3671	354	1	7	7	NUM
iajs-3671	354	2	.	.	X
iajs-3671	354	3	vsp	vsp	NOUN
iajs-3671	354	4	.	.	PUNCT
iajs-3671	355	1	10	10	NUM
iajs-3671	355	2	.	.	PUNCT
iajs-3671	355	3	colton	colton	PROPN
iajs-3671	355	4	d.	d.	PROPN
iajs-3671	355	5	pseudoparabolic	pseudoparabolic	PROPN
iajs-3671	355	6	equations	equation	NOUN
iajs-3671	355	7	in	in	ADP
iajs-3671	355	8	one	one	NUM
iajs-3671	355	9	space	space	NOUN
iajs-3671	355	10	variable	variable	NOUN
iajs-3671	355	11	.	.	PUNCT
iajs-3671	356	1	journal	journal	PROPN
iajs-3671	356	2	of	of	ADP
iajs-3671	356	3	differential	differential	ADJ
iajs-3671	356	4	equations	equation	NOUN
iajs-3671	356	5	.	.	PUNCT
iajs-3671	357	1	1972	1972	NUM
iajs-3671	357	2	;	;	PUNCT
iajs-3671	357	3	12(3):559–565	12(3):559–565	NUM
iajs-3671	357	4	.	.	PUNCT
iajs-3671	357	5	https://core.ac.uk/reader/82773480	https://core.ac.uk/reader/82773480	PROPN
iajs-3671	357	6	11	11	NUM
iajs-3671	357	7	.	.	PUNCT
iajs-3671	357	8	khompysh	khompysh	PROPN
iajs-3671	357	9	,	,	PUNCT
iajs-3671	357	10	k.	k.	PROPN
iajs-3671	357	11	inverse	inverse	PROPN
iajs-3671	357	12	problem	problem	NOUN
iajs-3671	357	13	for	for	ADP
iajs-3671	357	14	1d	1d	NUM
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iajs-3671	401	7	i.	i.	PROPN
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iajs-3671	401	9	heat	heat	NOUN
iajs-3671	401	10	propagation	propagation	NOUN
iajs-3671	401	11	in	in	ADP
iajs-3671	401	12	heterogeneous	heterogeneous	ADJ
iajs-3671	401	13	media	medium	NOUN
iajs-3671	401	14	.	.	PUNCT
iajs-3671	402	1	izvestiya	izvestiya	PROPN
iajs-3671	402	2	rossiiskoi	rossiiskoi	PROPN
iajs-3671	402	3	akademii	akademii	PROPN
iajs-3671	402	4	nauk	nauk	PROPN
iajs-3671	402	5	.	.	PUNCT
iajs-3671	402	6	seriya	seriya	PROPN
iajs-3671	402	7	geograficheskaya	geograficheskaya	PROPN
iajs-3671	402	8	.	.	PUNCT
iajs-3671	403	1	1948	1948	NUM
iajs-3671	403	2	;	;	PUNCT
iajs-3671	403	3	12	12	NUM
iajs-3671	403	4	,	,	PUNCT
iajs-3671	403	5	27–45	27–45	NUM
iajs-3671	403	6	.	.	PROPN
iajs-3671	403	7	23	23	NUM
iajs-3671	403	8	.	.	PUNCT
iajs-3671	404	1	ting	ting	PROPN
iajs-3671	404	2	t.w	t.w	PROPN
iajs-3671	404	3	.	.	PROPN
iajs-3671	405	1	a	a	DET
iajs-3671	405	2	cooling	cool	VERB
iajs-3671	405	3	process	process	NOUN
iajs-3671	405	4	according	accord	VERB
iajs-3671	405	5	to	to	ADP
iajs-3671	405	6	the	the	DET
iajs-3671	405	7	two	two	NUM
iajs-3671	405	8	-	-	PUNCT
iajs-3671	405	9	temperature	temperature	NOUN
iajs-3671	405	10	theory	theory	NOUN
iajs-3671	405	11	of	of	ADP
iajs-3671	405	12	heat	heat	NOUN
iajs-3671	405	13	conduction	conduction	NOUN
iajs-3671	405	14	.	.	PUNCT
iajs-3671	406	1	j.	j.	PROPN
iajs-3671	406	2	math	math	PROPN
iajs-3671	406	3	.	.	PUNCT
iajs-3671	407	1	anal	anal	PROPN
iajs-3671	407	2	.	.	PUNCT
iajs-3671	407	3	appl	appl	PROPN
iajs-3671	407	4	.	.	PROPN
iajs-3671	408	1	1974	1974	NUM
iajs-3671	408	2	;	;	PUNCT
iajs-3671	408	3	45	45	NUM
iajs-3671	408	4	,	,	PUNCT
iajs-3671	408	5	23–31	23–31	NUM
iajs-3671	408	6	.	.	PUNCT
iajs-3671	409	1	https://doi.org/10.1016/0022-247x(74)90116-4	https://doi.org/10.1016/0022-247x(74)90116-4	PROPN
iajs-3671	409	2	https://doi.org/10.24996/ijs.2021.62.3.25	https://doi.org/10.24996/ijs.2021.62.3.25	INTJ
iajs-3671	409	3	https://core.ac.uk/reader/82773480	https://core.ac.uk/reader/82773480	PROPN
iajs-3671	409	4	https://doi.org/10.100	https://doi.org/10.100	ADP
iajs-3671	409	5	https://doi.org/10.1007/978-0-387-34149-1	https://doi.org/10.1007/978-0-387-34149-1	PROPN
iajs-3671	409	6	https://doi.org/10.1007/978-0-387-34149-1	https://doi.org/10.1007/978-0-387-34149-1	PROPN
iajs-3671	409	7	https://doi.org/10.1080/00036811.2011.630667	https://doi.org/10.1080/00036811.2011.630667	PROPN
iajs-3671	409	8	http://dx.doi.org/10.12988/ams.2014.4167	http://dx.doi.org/10.12988/ams.2014.4167	NOUN
iajs-3671	409	9	http://dx.doi.org/10.12988/ams.2015.57464	http://dx.doi.org/10.12988/ams.2015.57464	NOUN
iajs-3671	409	10	http://dx.doi.org/10.3934/eect.2021005	http://dx.doi.org/10.3934/eect.2021005	VERB
iajs-3671	409	11	https://doi.org/10.1134/s0012266114040089	https://doi.org/10.1134/s0012266114040089	PROPN
iajs-3671	409	12	https://doi.org/10.1080/00036811.2010.530258	https://doi.org/10.1080/00036811.2010.530258	PROPN
iajs-3671	410	1	https://doi.org/10.1016/s0096-3003(03)00691-x	https://doi.org/10.1016/s0096-3003(03)00691-x	PROPN
iajs-3671	410	2	https://doi.org/10.1016/s0096-3003(03)00691-x	https://doi.org/10.1016/s0096-3003(03)00691-x	PROPN
iajs-3671	410	3	https://doi.org/10.1016/0022-247x(74)90116-4	https://doi.org/10.1016/0022-247x(74)90116-4	PROPN
iajs-3671	410	4	ihjpas	ihjpa	VERB
iajs-3671	410	5	.	.	PUNCT
iajs-3671	411	1	2025	2025	NUM
iajs-3671	411	2	,	,	PUNCT
iajs-3671	411	3	38	38	NUM
iajs-3671	411	4	(	(	PUNCT
iajs-3671	411	5	1	1	NUM
iajs-3671	411	6	)	)	PUNCT
iajs-3671	411	7	491	491	NUM
iajs-3671	411	8	24	24	NUM
iajs-3671	411	9	.	.	PUNCT
iajs-3671	412	1	huntul	huntul	PROPN
iajs-3671	412	2	m.	m.	PROPN
iajs-3671	412	3	j.	j.	PROPN
iajs-3671	412	4	;	;	PUNCT
iajs-3671	412	5	dhiman	dhiman	NOUN
iajs-3671	412	6	n.	n.	NOUN
iajs-3671	412	7	;	;	PUNCT
iajs-3671	412	8	tamsir	tamsir	NOUN
iajs-3671	412	9	,	,	PUNCT
iajs-3671	412	10	m.	m.	NOUN
iajs-3671	412	11	reconstructing	reconstruct	VERB
iajs-3671	412	12	an	an	DET
iajs-3671	412	13	unknown	unknown	ADJ
iajs-3671	412	14	potential	potential	ADJ
iajs-3671	412	15	term	term	NOUN
iajs-3671	412	16	in	in	ADP
iajs-3671	412	17	the	the	DET
iajs-3671	412	18	third	third	ADJ
iajs-3671	412	19	-	-	PUNCT
iajs-3671	412	20	order	order	NOUN
iajs-3671	412	21	pseudo	pseudo	NOUN
iajs-3671	412	22	-	-	ADJ
iajs-3671	412	23	parabolic	parabolic	ADJ
iajs-3671	412	24	problem	problem	NOUN
iajs-3671	412	25	.	.	PUNCT
iajs-3671	413	1	comput	comput	NOUN
iajs-3671	413	2	.	.	PUNCT
iajs-3671	414	1	appl	appl	PROPN
iajs-3671	414	2	.	.	PROPN
iajs-3671	414	3	math	math	PROPN
iajs-3671	414	4	.	.	PUNCT
iajs-3671	415	1	2021	2021	NUM
iajs-3671	415	2	;	;	PUNCT
iajs-3671	415	3	40	40	NUM
iajs-3671	415	4	:	:	SYM
iajs-3671	415	5	140	140	NUM
iajs-3671	415	6	.	.	X
iajs-3671	415	7	25	25	NUM
iajs-3671	415	8	.	.	PUNCT
iajs-3671	416	1	huntul	huntul	PROPN
iajs-3671	416	2	m.	m.	PROPN
iajs-3671	416	3	j.	j.	PROPN
iajs-3671	416	4	;	;	PUNCT
iajs-3671	416	5	tamsir	tamsir	NOUN
iajs-3671	416	6	m.	m.	NOUN
iajs-3671	416	7	;	;	PUNCT
iajs-3671	416	8	dhiman	dhiman	NOUN
iajs-3671	416	9	n.	n.	NOUN
iajs-3671	416	10	an	an	DET
iajs-3671	416	11	inverse	inverse	NOUN
iajs-3671	416	12	problem	problem	NOUN
iajs-3671	416	13	of	of	ADP
iajs-3671	416	14	identifying	identify	VERB
iajs-3671	416	15	the	the	DET
iajs-3671	416	16	time	time	NOUN
iajs-3671	416	17	dependent	dependent	ADJ
iajs-3671	416	18	potential	potential	NOUN
iajs-3671	416	19	in	in	ADP
iajs-3671	416	20	a	a	DET
iajs-3671	416	21	fourth	fourth	ADJ
iajs-3671	416	22	-	-	PUNCT
iajs-3671	416	23	order	order	NOUN
iajs-3671	416	24	pseudo	pseudo	NOUN
iajs-3671	416	25	-	-	ADJ
iajs-3671	416	26	parabolic	parabolic	ADJ
iajs-3671	416	27	equation	equation	NOUN
iajs-3671	416	28	from	from	ADP
iajs-3671	416	29	additional	additional	ADJ
iajs-3671	416	30	condition	condition	NOUN
iajs-3671	416	31	.	.	PUNCT
iajs-3671	417	1	num	num	ADJ
iajs-3671	417	2	.	.	PUNCT
iajs-3671	417	3	meth	meth	NOUN
iajs-3671	417	4	.	.	PUNCT
iajs-3671	418	1	part	part	NOUN
iajs-3671	418	2	.	.	PUNCT
iajs-3671	419	1	differential	differential	ADJ
iajs-3671	419	2	equations	equation	NOUN
iajs-3671	419	3	.	.	PUNCT
iajs-3671	420	1	2021	2021	NUM
iajs-3671	420	2	.	.	PUNCT
iajs-3671	421	1	https://doi.org/10.1002/num.22778	https://doi.org/10.1002/num.22778	PROPN
iajs-3671	421	2	.	.	PUNCT
iajs-3671	422	1	26	26	NUM
iajs-3671	422	2	.	.	PUNCT
iajs-3671	422	3	huntul	huntul	PROPN
iajs-3671	422	4	m.	m.	PROPN
iajs-3671	422	5	j.	j.	PROPN
iajs-3671	422	6	determination	determination	NOUN
iajs-3671	422	7	of	of	ADP
iajs-3671	422	8	a	a	DET
iajs-3671	422	9	time	time	NOUN
iajs-3671	422	10	-	-	PUNCT
iajs-3671	422	11	dependent	dependent	ADJ
iajs-3671	422	12	potential	potential	NOUN
iajs-3671	422	13	in	in	ADP
iajs-3671	422	14	the	the	DET
iajs-3671	422	15	higher	high	ADJ
iajs-3671	422	16	-	-	PUNCT
iajs-3671	422	17	order	order	NOUN
iajs-3671	422	18	pseudo	pseudo	NOUN
iajs-3671	422	19	-	-	ADJ
iajs-3671	422	20	hyperbolic	hyperbolic	ADJ
iajs-3671	422	21	problem	problem	NOUN
iajs-3671	422	22	.	.	PUNCT
iajs-3671	423	1	inverse	inverse	PROPN
iajs-3671	423	2	prob	prob	PROPN
iajs-3671	423	3	.	.	PUNCT
iajs-3671	424	1	sci	sci	PROPN
iajs-3671	424	2	.	.	PUNCT
iajs-3671	425	1	eng	eng	PROPN
iajs-3671	425	2	.	.	PROPN
iajs-3671	425	3	2021	2021	NUM
iajs-3671	425	4	.	.	PUNCT
iajs-3671	426	1	https://doi.org/10.1080/17415977.2021.1964496	https://doi.org/10.1080/17415977.2021.1964496	NOUN
iajs-3671	426	2	.	.	PUNCT
iajs-3671	427	1	27	27	NUM
iajs-3671	427	2	.	.	PUNCT
iajs-3671	428	1	ramazanova	ramazanova	PROPN
iajs-3671	428	2	a.	a.	PROPN
iajs-3671	428	3	t.	t.	PROPN
iajs-3671	428	4	;	;	PUNCT
iajs-3671	428	5	mehraliyev	mehraliyev	PROPN
iajs-3671	428	6	y.	y.	PROPN
iajs-3671	428	7	t.	t.	PROPN
iajs-3671	428	8	;	;	PUNCT
iajs-3671	428	9	allahverdieva	allahverdieva	PROPN
iajs-3671	428	10	s.	s.	PROPN
iajs-3671	428	11	i.	i.	PROPN
iajs-3671	428	12	on	on	ADP
iajs-3671	428	13	an	an	DET
iajs-3671	428	14	inverse	inverse	NOUN
iajs-3671	428	15	boundary	boundary	NOUN
iajs-3671	428	16	value	value	NOUN
iajs-3671	428	17	problem	problem	NOUN
iajs-3671	428	18	with	with	ADP
iajs-3671	428	19	non	non	ADJ
iajs-3671	428	20	-	-	ADJ
iajs-3671	428	21	local	local	ADJ
iajs-3671	428	22	integral	integral	ADJ
iajs-3671	428	23	terms	term	NOUN
iajs-3671	428	24	condition	condition	NOUN
iajs-3671	428	25	for	for	ADP
iajs-3671	428	26	the	the	DET
iajs-3671	428	27	pseudo	pseudo	NOUN
iajs-3671	428	28	-	-	ADJ
iajs-3671	428	29	parabolic	parabolic	ADJ
iajs-3671	428	30	equation	equation	NOUN
iajs-3671	428	31	of	of	ADP
iajs-3671	428	32	the	the	DET
iajs-3671	428	33	fourth	fourth	ADJ
iajs-3671	428	34	order	order	NOUN
iajs-3671	428	35	.	.	PUNCT
iajs-3671	429	1	differential	differential	ADJ
iajs-3671	429	2	equations	equation	NOUN
iajs-3671	429	3	and	and	CCONJ
iajs-3671	429	4	their	their	PRON
iajs-3671	429	5	applications	application	NOUN
iajs-3671	429	6	in	in	ADP
iajs-3671	429	7	mathematical	mathematical	ADJ
iajs-3671	429	8	modelling	modelling	NOUN
iajs-3671	429	9	.	.	PUNCT
iajs-3671	430	1	2019	2019	NUM
iajs-3671	430	2	;	;	PUNCT
iajs-3671	430	3	101–103	101–103	NUM
iajs-3671	430	4	.	.	PUNCT
iajs-3671	431	1	https://conf.svmo.ru/files/2019/papers/paper32	https://conf.svmo.ru/files/2019/papers/paper32	NOUN
iajs-3671	431	2	.	.	PUNCT
iajs-3671	432	1	28	28	NUM
iajs-3671	432	2	.	.	PUNCT
iajs-3671	433	1	mehraliyev	mehraliyev	PROPN
iajs-3671	433	2	y.	y.	PROPN
iajs-3671	433	3	;	;	PUNCT
iajs-3671	433	4	shafiyeva	shafiyeva	PROPN
iajs-3671	433	5	t.	t.	PROPN
iajs-3671	433	6	;	;	PUNCT
iajs-3671	433	7	gulshan	gulshan	PROPN
iajs-3671	433	8	kh	kh	PROPN
iajs-3671	433	9	.	.	PUNCT
iajs-3671	433	10	determination	determination	NOUN
iajs-3671	433	11	of	of	ADP
iajs-3671	433	12	an	an	DET
iajs-3671	433	13	unknown	unknown	ADJ
iajs-3671	433	14	coefficient	coefficient	NOUN
iajs-3671	433	15	in	in	ADP
iajs-3671	433	16	the	the	DET
iajs-3671	433	17	third	third	ADJ
iajs-3671	433	18	-	-	PUNCT
iajs-3671	433	19	order	order	NOUN
iajs-3671	433	20	pseudo	pseudo	NOUN
iajs-3671	433	21	-	-	ADJ
iajs-3671	433	22	parabolic	parabolic	ADJ
iajs-3671	433	23	equation	equation	NOUN
iajs-3671	433	24	with	with	ADP
iajs-3671	433	25	non	non	ADJ
iajs-3671	433	26	-	-	ADJ
iajs-3671	433	27	self	self	NOUN
iajs-3671	433	28	-	-	PUNCT
iajs-3671	433	29	adjoint	adjoint	NOUN
iajs-3671	433	30	boundary	boundary	ADJ
iajs-3671	433	31	conditions	condition	NOUN
iajs-3671	433	32	.	.	PUNCT
iajs-3671	434	1	journal	journal	NOUN
iajs-3671	434	2	of	of	ADP
iajs-3671	434	3	applied	apply	VERB
iajs-3671	434	4	mathematics	mathematic	NOUN
iajs-3671	434	5	.	.	PUNCT
iajs-3671	435	1	2014	2014	NUM
iajs-3671	435	2	.	.	PUNCT
iajs-3671	436	1	https://doi.org/10.1155/2014/358696	https://doi.org/10.1155/2014/358696	NOUN
iajs-3671	436	2	29	29	NUM
iajs-3671	436	3	.	.	PUNCT
iajs-3671	437	1	mehraliyev	mehraliyev	PROPN
iajs-3671	437	2	y.	y.	PROPN
iajs-3671	437	3	t.	t.	PROPN
iajs-3671	437	4	;	;	PUNCT
iajs-3671	437	5	shafiyeva	shafiyeva	PROPN
iajs-3671	437	6	g.	g.	PROPN
iajs-3671	437	7	inverse	inverse	PROPN
iajs-3671	437	8	boundary	boundary	PROPN
iajs-3671	437	9	value	value	NOUN
iajs-3671	437	10	problem	problem	NOUN
iajs-3671	437	11	for	for	ADP
iajs-3671	437	12	the	the	DET
iajs-3671	437	13	pseudo	pseudo	NOUN
iajs-3671	437	14	-	-	ADJ
iajs-3671	437	15	parabolic	parabolic	ADJ
iajs-3671	437	16	equation	equation	NOUN
iajs-3671	437	17	of	of	ADP
iajs-3671	437	18	the	the	DET
iajs-3671	437	19	third	third	ADJ
iajs-3671	437	20	order	order	NOUN
iajs-3671	437	21	with	with	ADP
iajs-3671	437	22	periodic	periodic	ADJ
iajs-3671	437	23	and	and	CCONJ
iajs-3671	437	24	integral	integral	ADJ
iajs-3671	437	25	conditions	condition	NOUN
iajs-3671	437	26	.	.	PUNCT
iajs-3671	438	1	applied	apply	VERB
iajs-3671	438	2	mathematical	mathematical	ADJ
iajs-3671	438	3	sciences	science	NOUN
iajs-3671	438	4	.	.	PUNCT
iajs-3671	438	5	2014	2014	NUM
iajs-3671	438	6	;	;	PUNCT
iajs-3671	438	7	8(23	8(23	NUM
iajs-3671	438	8	)	)	PUNCT
iajs-3671	438	9	,	,	PUNCT
iajs-3671	438	10	1145	1145	NUM
iajs-3671	438	11	-	-	SYM
iajs-3671	438	12	1155	1155	NUM
iajs-3671	438	13	.	.	PUNCT
iajs-3671	439	1	http://dx.doi.org/10.12988/ams.2014.4167	http://dx.doi.org/10.12988/ams.2014.4167	ADJ
iajs-3671	439	2	30	30	NUM
iajs-3671	439	3	.	.	PUNCT
iajs-3671	439	4	dhiman	dhiman	NOUN
iajs-3671	439	5	n.	n.	PROPN
iajs-3671	439	6	;	;	PUNCT
iajs-3671	439	7	tamsir	tamsir	NOUN
iajs-3671	439	8	,	,	PUNCT
iajs-3671	439	9	m.	m.	NOUN
iajs-3671	439	10	a	a	DET
iajs-3671	439	11	collocation	collocation	NOUN
iajs-3671	439	12	technique	technique	NOUN
iajs-3671	439	13	based	base	VERB
iajs-3671	439	14	on	on	ADP
iajs-3671	439	15	a	a	DET
iajs-3671	439	16	modified	modify	VERB
iajs-3671	439	17	form	form	NOUN
iajs-3671	439	18	of	of	ADP
iajs-3671	439	19	trigonometric	trigonometric	ADJ
iajs-3671	439	20	cubic	cubic	ADJ
iajs-3671	439	21	bspline	bspline	NOUN
iajs-3671	439	22	basis	basis	NOUN
iajs-3671	439	23	functions	function	NOUN
iajs-3671	439	24	for	for	ADP
iajs-3671	439	25	fisher	fisher	NOUN
iajs-3671	439	26	's	's	PART
iajs-3671	439	27	reaction	reaction	NOUN
iajs-3671	439	28	-	-	PUNCT
iajs-3671	439	29	diffusion	diffusion	NOUN
iajs-3671	439	30	equation	equation	NOUN
iajs-3671	439	31	.	.	PUNCT
iajs-3671	440	1	multidiscipline	multidiscipline	VERB
iajs-3671	440	2	modeling	modeling	NOUN
iajs-3671	440	3	in	in	ADP
iajs-3671	440	4	materials	material	NOUN
iajs-3671	440	5	and	and	CCONJ
iajs-3671	440	6	structures	structure	NOUN
iajs-3671	440	7	.	.	PUNCT
iajs-3671	441	1	2018	2018	NUM
iajs-3671	441	2	;	;	PUNCT
iajs-3671	441	3	14:923–939	14:923–939	NUM
iajs-3671	441	4	,	,	PUNCT
iajs-3671	441	5	10	10	NUM
iajs-3671	441	6	.	.	PUNCT
iajs-3671	441	7	https://doi.org/10.1108/mmms-12-2017-0150	https://doi.org/10.1108/mmms-12-2017-0150	PROPN
iajs-3671	441	8	31	31	NUM
iajs-3671	441	9	.	.	PUNCT
iajs-3671	442	1	sousa	sousa	PROPN
iajs-3671	442	2	e.	e.	PROPN
iajs-3671	442	3	on	on	ADP
iajs-3671	442	4	the	the	DET
iajs-3671	442	5	edge	edge	NOUN
iajs-3671	442	6	of	of	ADP
iajs-3671	442	7	stability	stability	NOUN
iajs-3671	442	8	analysis	analysis	NOUN
iajs-3671	442	9	.	.	PUNCT
iajs-3671	443	1	applied	apply	VERB
iajs-3671	443	2	numerical	numerical	ADJ
iajs-3671	443	3	mathematics	mathematic	NOUN
iajs-3671	443	4	.	.	PUNCT
iajs-3671	444	1	2009	2009	NUM
iajs-3671	444	2	;	;	PUNCT
iajs-3671	444	3	59(6	59(6	NUM
iajs-3671	444	4	):	):	PUNCT
iajs-3671	444	5	1322	1322	NUM
iajs-3671	444	6	-	-	SYM
iajs-3671	444	7	1336	1336	NUM
iajs-3671	444	8	.	.	PUNCT
iajs-3671	445	1	https://doi.org/10.1016/j.apnum.2008.08.001	https://doi.org/10.1016/j.apnum.2008.08.001	PROPN
iajs-3671	445	2	32	32	NUM
iajs-3671	445	3	.	.	PUNCT
iajs-3671	446	1	strikwerda	strikwerda	PROPN
iajs-3671	446	2	j.	j.	PROPN
iajs-3671	446	3	c.	c.	PROPN
iajs-3671	446	4	finite	finite	PROPN
iajs-3671	446	5	difference	difference	NOUN
iajs-3671	446	6	schemes	scheme	NOUN
iajs-3671	446	7	and	and	CCONJ
iajs-3671	446	8	partial	partial	ADJ
iajs-3671	446	9	differential	differential	ADJ
iajs-3671	446	10	equations	equation	NOUN
iajs-3671	446	11	.	.	PUNCT
iajs-3671	447	1	pacific	pacific	PROPN
iajs-3671	447	2	grove	grove	PROPN
iajs-3671	447	3	,	,	PUNCT
iajs-3671	447	4	ca	can	AUX
iajs-3671	447	5	:	:	PUNCT
iajs-3671	447	6	wadsworth	wadsworth	PROPN
iajs-3671	447	7	and	and	CCONJ
iajs-3671	447	8	brooks	brooks	PROPN
iajs-3671	447	9	,	,	PUNCT
iajs-3671	447	10	1989	1989	NUM
iajs-3671	447	11	.	.	PUNCT
iajs-3671	448	1	33	33	NUM
iajs-3671	448	2	.	.	PUNCT
iajs-3671	449	1	alosaimi	alosaimi	PROPN
iajs-3671	449	2	m.	m.	PROPN
iajs-3671	449	3	;	;	PUNCT
iajs-3671	449	4	lesnic	lesnic	PROPN
iajs-3671	449	5	d.	d.	PROPN
iajs-3671	449	6	;	;	PUNCT
iajs-3671	449	7	niesen	niesen	PROPN
iajs-3671	449	8	j.	j.	PROPN
iajs-3671	449	9	identification	identification	NOUN
iajs-3671	449	10	of	of	ADP
iajs-3671	449	11	the	the	DET
iajs-3671	449	12	thermo	thermo	NOUN
iajs-3671	449	13	-	-	PUNCT
iajs-3671	449	14	physical	physical	ADJ
iajs-3671	449	15	properties	property	NOUN
iajs-3671	449	16	of	of	ADP
iajs-3671	449	17	a	a	DET
iajs-3671	449	18	stratified	stratified	ADJ
iajs-3671	449	19	tissue	tissue	NOUN
iajs-3671	449	20	.	.	PUNCT
iajs-3671	450	1	adiabatic	adiabatic	ADJ
iajs-3671	450	2	hypodermic	hypodermic	ADJ
iajs-3671	450	3	wall	wall	NOUN
iajs-3671	450	4	.	.	PUNCT
iajs-3671	451	1	international	international	ADJ
iajs-3671	451	2	communications	communication	NOUN
iajs-3671	451	3	in	in	ADP
iajs-3671	451	4	heat	heat	NOUN
iajs-3671	451	5	and	and	CCONJ
iajs-3671	451	6	mass	mass	NOUN
iajs-3671	451	7	transfer	transfer	NOUN
iajs-3671	451	8	.	.	PUNCT
iajs-3671	452	1	2021	2021	NUM
iajs-3671	452	2	;	;	PUNCT
iajs-3671	452	3	126	126	NUM
iajs-3671	452	4	,	,	PUNCT
iajs-3671	452	5	105376	105376	NUM
iajs-3671	452	6	.	.	PUNCT
iajs-3671	453	1	https://doi.org/10.1016/j.icheatmasstransfer.2021.105376	https://doi.org/10.1016/j.icheatmasstransfer.2021.105376	NOUN
iajs-3671	453	2	34	34	NUM
iajs-3671	453	3	.	.	PUNCT
iajs-3671	454	1	cao	cao	PROPN
iajs-3671	454	2	kai	kai	PROPN
iajs-3671	454	3	.	.	PROPN
iajs-3671	454	4	;	;	PUNCT
iajs-3671	454	5	lesnic	lesnic	PROPN
iajs-3671	454	6	d.	d.	PROPN
iajs-3671	454	7	;	;	PUNCT
iajs-3671	454	8	ismailov	ismailov	ADJ
iajs-3671	454	9	m.	m.	NOUN
iajs-3671	454	10	i.	i.	PROPN
iajs-3671	454	11	determination	determination	NOUN
iajs-3671	454	12	of	of	ADP
iajs-3671	454	13	the	the	DET
iajs-3671	454	14	time	time	NOUN
iajs-3671	454	15	-	-	PUNCT
iajs-3671	454	16	dependent	dependent	ADJ
iajs-3671	454	17	thermal	thermal	ADJ
iajs-3671	454	18	grooving	grooving	NOUN
iajs-3671	454	19	coefficient	coefficient	NOUN
iajs-3671	454	20	.	.	PUNCT
iajs-3671	455	1	journal	journal	PROPN
iajs-3671	455	2	of	of	ADP
iajs-3671	455	3	applied	apply	VERB
iajs-3671	455	4	mathematics	mathematic	NOUN
iajs-3671	455	5	and	and	CCONJ
iajs-3671	455	6	computing	computing	NOUN
iajs-3671	455	7	.	.	PUNCT
iajs-3671	456	1	2021	2021	NUM
iajs-3671	456	2	;	;	PUNCT
iajs-3671	456	3	65	65	NUM
iajs-3671	456	4	:	:	SYM
iajs-3671	456	5	199	199	NUM
iajs-3671	456	6	-	-	SYM
iajs-3671	456	7	221	221	NUM
iajs-3671	456	8	.	.	PUNCT
iajs-3671	457	1	https://doi.org/10.1007/s12190020-01388-7	https://doi.org/10.1007/s12190020-01388-7	PROPN
iajs-3671	457	2	35	35	NUM
iajs-3671	457	3	.	.	PUNCT
iajs-3671	458	1	hussein	hussein	PROPN
iajs-3671	458	2	m.	m.	PROPN
iajs-3671	458	3	s.	s.	PROPN
iajs-3671	458	4	;	;	PUNCT
iajs-3671	458	5	lesnic	lesnic	PROPN
iajs-3671	458	6	d.	d.	PROPN
iajs-3671	458	7	;	;	PUNCT
iajs-3671	458	8	kamynin	kamynin	PROPN
iajs-3671	458	9	v.	v.	PROPN
iajs-3671	458	10	l.	l.	PROPN
iajs-3671	458	11	;	;	PUNCT
iajs-3671	458	12	kostin	kostin	X
iajs-3671	458	13	,	,	PUNCT
iajs-3671	458	14	a.	a.	PROPN
iajs-3671	458	15	b.	b.	PROPN
iajs-3671	458	16	direct	direct	ADJ
iajs-3671	458	17	and	and	CCONJ
iajs-3671	458	18	inverse	inverse	ADJ
iajs-3671	458	19	source	source	NOUN
iajs-3671	458	20	problems	problem	NOUN
iajs-3671	458	21	for	for	ADP
iajs-3671	458	22	degenerate	degenerate	ADJ
iajs-3671	458	23	parabolic	parabolic	NOUN
iajs-3671	458	24	equations	equation	NOUN
iajs-3671	458	25	.	.	PUNCT
iajs-3671	459	1	journal	journal	PROPN
iajs-3671	459	2	of	of	ADP
iajs-3671	459	3	inverse	inverse	NOUN
iajs-3671	459	4	and	and	CCONJ
iajs-3671	459	5	ill	ill	ADV
iajs-3671	459	6	-	-	PUNCT
iajs-3671	459	7	posed	pose	VERB
iajs-3671	459	8	problems	problem	NOUN
iajs-3671	459	9	.	.	PUNCT
iajs-3671	460	1	2020	2020	NUM
iajs-3671	460	2	;	;	PUNCT
iajs-3671	460	3	28.3	28.3	NUM
iajs-3671	460	4	:	:	SYM
iajs-3671	460	5	425	425	NUM
iajs-3671	460	6	-	-	SYM
iajs-3671	460	7	448	448	NUM
iajs-3671	460	8	.	.	PUNCT
iajs-3671	461	1	https://doi.org/10.1515/jiip-2019-0046	https://doi.org/10.1515/jiip-2019-0046	PROPN
iajs-3671	461	2	36	36	NUM
iajs-3671	461	3	.	.	PUNCT
iajs-3671	462	1	alosaimi	alosaimi	PROPN
iajs-3671	462	2	m.	m.	PROPN
iajs-3671	462	3	;	;	PUNCT
iajs-3671	462	4	lesnic	lesnic	PROPN
iajs-3671	462	5	d.	d.	PROPN
iajs-3671	462	6	;	;	PUNCT
iajs-3671	462	7	b.	b.	PROPN
iajs-3671	462	8	t.	t.	PROPN
iajs-3671	462	9	johansson	johansson	PROPN
iajs-3671	462	10	b.	b.	PROPN
iajs-3671	463	1	t.	t.	PROPN
iajs-3671	463	2	solution	solution	NOUN
iajs-3671	463	3	of	of	ADP
iajs-3671	463	4	the	the	DET
iajs-3671	463	5	cauchy	cauchy	ADJ
iajs-3671	463	6	problem	problem	NOUN
iajs-3671	463	7	for	for	ADP
iajs-3671	463	8	the	the	DET
iajs-3671	463	9	wave	wave	NOUN
iajs-3671	463	10	equation	equation	NOUN
iajs-3671	463	11	using	use	VERB
iajs-3671	463	12	iterative	iterative	ADJ
iajs-3671	463	13	regularization	regularization	NOUN
iajs-3671	463	14	.	.	PUNCT
iajs-3671	464	1	inverse	inverse	NOUN
iajs-3671	464	2	problems	problem	NOUN
iajs-3671	464	3	in	in	ADP
iajs-3671	464	4	science	science	NOUN
iajs-3671	464	5	and	and	CCONJ
iajs-3671	464	6	engineering	engineering	NOUN
iajs-3671	464	7	.	.	PUNCT
iajs-3671	465	1	2021;29(13	2021;29(13	NUM
iajs-3671	465	2	):	):	PUNCT
iajs-3671	465	3	2757	2757	NUM
iajs-3671	465	4	-	-	SYM
iajs-3671	465	5	2771	2771	NUM
iajs-3671	465	6	.	.	PUNCT
iajs-3671	466	1	https://doi.org/10.1080/17415977.2021.1949590	https://doi.org/10.1080/17415977.2021.1949590	NOUN
iajs-3671	467	1	1	1	NUM
iajs-3671	467	2	.	.	X
iajs-3671	468	1	37.anwer	37.anwer	X
iajs-3671	469	1	f.	f.	PROPN
iajs-3671	469	2	;	;	PUNCT
iajs-3671	469	3	hussein	hussein	PROPN
iajs-3671	469	4	m.	m.	PROPN
iajs-3671	469	5	s.	s.	PROPN
iajs-3671	469	6	retrieval	retrieval	PROPN
iajs-3671	469	7	of	of	ADP
iajs-3671	469	8	timewise	timewise	ADJ
iajs-3671	469	9	coefficients	coefficient	NOUN
iajs-3671	469	10	in	in	ADP
iajs-3671	469	11	the	the	DET
iajs-3671	469	12	heat	heat	NOUN
iajs-3671	469	13	equation	equation	NOUN
iajs-3671	469	14	from	from	ADP
iajs-3671	469	15	nonlocal	nonlocal	ADJ
iajs-3671	469	16	overdetermination	overdetermination	NOUN
iajs-3671	469	17	conditions	condition	NOUN
iajs-3671	469	18	.	.	PUNCT
iajs-3671	470	1	iraqi	iraqi	ADJ
iajs-3671	470	2	journal	journal	PROPN
iajs-3671	470	3	of	of	ADP
iajs-3671	470	4	science	science	NOUN
iajs-3671	470	5	.	.	PUNCT
iajs-3671	471	1	2022	2022	NUM
iajs-3671	471	2	;	;	PUNCT
iajs-3671	471	3	1184–1199.https://doi.org/	1184–1199.https://doi.org/	NUM
iajs-3671	471	4	10.24996	10.24996	NUM
iajs-3671	471	5	/	/	SYM
iajs-3671	471	6	ijs.2022.63.3.24	ijs.2022.63.3.24	NOUN
iajs-3671	471	7	37	37	NUM
iajs-3671	471	8	.	.	PUNCT
iajs-3671	472	1	hussein	hussein	PROPN
iajs-3671	472	2	m.	m.	PROPN
iajs-3671	472	3	s.	s.	PROPN
iajs-3671	472	4	;	;	PUNCT
iajs-3671	472	5	lesnic	lesnic	PROPN
iajs-3671	472	6	d.	d.	PROPN
iajs-3671	472	7	;	;	PUNCT
iajs-3671	472	8	johansson	johansson	PROPN
iajs-3671	472	9	b.	b.	PROPN
iajs-3671	472	10	t.	t.	PROPN
iajs-3671	472	11	;	;	PUNCT
iajs-3671	472	12	hazanee	hazanee	PROPN
iajs-3671	472	13	a.	a.	NOUN
iajs-3671	472	14	a.	a.	NOUN
iajs-3671	472	15	identification	identification	NOUN
iajs-3671	472	16	of	of	ADP
iajs-3671	472	17	a	a	DET
iajs-3671	472	18	multidimensional	multidimensional	ADJ
iajs-3671	472	19	spacedependent	spacedependent	NOUN
iajs-3671	472	20	heat	heat	NOUN
iajs-3671	472	21	source	source	NOUN
iajs-3671	472	22	from	from	ADP
iajs-3671	472	23	boundary	boundary	ADJ
iajs-3671	472	24	data	datum	NOUN
iajs-3671	472	25	.	.	PUNCT
iajs-3671	473	1	applied	apply	VERB
iajs-3671	473	2	mathematical	mathematical	ADJ
iajs-3671	473	3	modelling	modelling	NOUN
iajs-3671	473	4	.	.	PUNCT
iajs-3671	474	1	2018	2018	NUM
iajs-3671	474	2	;	;	PUNCT
iajs-3671	475	1	54:202–220	54:202–220	NUM
iajs-3671	475	2	.	.	PUNCT
iajs-3671	475	3	https://doi.org/10.1016/j.apm.2017.09.029	https://doi.org/10.1016/j.apm.2017.09.029	NOUN
iajs-3671	475	4	38	38	NUM
iajs-3671	475	5	.	.	PUNCT
iajs-3671	476	1	hussein	hussein	PROPN
iajs-3671	476	2	m.	m.	PROPN
iajs-3671	476	3	s.	s.	PROPN
iajs-3671	476	4	;	;	PUNCT
iajs-3671	476	5	kinash	kinash	PROPN
iajs-3671	476	6	n.	n.	PROPN
iajs-3671	476	7	s.	s.	PROPN
iajs-3671	476	8	e.	e.	PROPN
iajs-3671	476	9	p.	p.	PROPN
iajs-3671	476	10	;	;	PUNCT
iajs-3671	476	11	lesnic	lesnic	PROPN
iajs-3671	476	12	d.	d.	PROPN
iajs-3671	476	13	;	;	PUNCT
iajs-3671	476	14	ivanchov	ivanchov	NOUN
iajs-3671	476	15	,	,	PUNCT
iajs-3671	476	16	m.	m.	NOUN
iajs-3671	476	17	retrieving	retrieve	VERB
iajs-3671	476	18	the	the	DET
iajs-3671	476	19	time	time	NOUN
iajs-3671	476	20	-	-	PUNCT
iajs-3671	476	21	dependent	dependent	ADJ
iajs-3671	476	22	thermal	thermal	ADJ
iajs-3671	476	23	conductivity	conductivity	NOUN
iajs-3671	476	24	of	of	ADP
iajs-3671	476	25	an	an	DET
iajs-3671	476	26	orthotropic	orthotropic	ADJ
iajs-3671	476	27	rectangular	rectangular	ADJ
iajs-3671	476	28	conductor	conductor	NOUN
iajs-3671	476	29	.	.	PUNCT
iajs-3671	477	1	applicable	applicable	ADJ
iajs-3671	477	2	analysis	analysis	NOUN
iajs-3671	477	3	.	.	PUNCT
iajs-3671	478	1	2017	2017	NUM
iajs-3671	478	2	;	;	PUNCT
iajs-3671	478	3	96.15	96.15	NUM
iajs-3671	478	4	:	:	PUNCT
iajs-3671	478	5	2604	2604	NUM
iajs-3671	478	6	-	-	SYM
iajs-3671	478	7	2618	2618	NUM
iajs-3671	478	8	.	.	PUNCT
iajs-3671	479	1	https://doi.org/10.1080/00036811.2016.1232401	https://doi.org/10.1080/00036811.2016.1232401	PROPN
iajs-3671	479	2	https://doi.org/10.1080/17415977.2021.1964496	https://doi.org/10.1080/17415977.2021.1964496	PROPN
iajs-3671	479	3	.	.	PUNCT
iajs-3671	480	1	https://conf.svmo.ru/files/2019/papers/paper32	https://conf.svmo.ru/files/2019/papers/paper32	NOUN
iajs-3671	480	2	.	.	PUNCT
iajs-3671	481	1	https://doi.org/10.1155/2014/358696	https://doi.org/10.1155/2014/358696	ADJ
iajs-3671	481	2	https://doi.org/10.1155/2014/358696	https://doi.org/10.1155/2014/358696	NOUN
iajs-3671	481	3	http://dx.doi.org/10.12988/ams.2014.4167	http://dx.doi.org/10.12988/ams.2014.4167	PROPN
iajs-3671	482	1	https://doi.org/10.1108/mmms-12-2017-0150	https://doi.org/10.1108/mmms-12-2017-0150	PROPN
iajs-3671	482	2	https://doi.org/10.1108/mmms-12-2017-0150	https://doi.org/10.1108/mmms-12-2017-0150	PROPN
iajs-3671	482	3	https://doi.org/10.1016/j.apnum.2008.08.001	https://doi.org/10.1016/j.apnum.2008.08.001	PROPN
iajs-3671	482	4	https://doi.org/10.1016/j.apnum.2008.08.001	https://doi.org/10.1016/j.apnum.2008.08.001	PROPN
iajs-3671	482	5	https://doi.org/10.1016/j.icheatmasstransfer.2021.105376	https://doi.org/10.1016/j.icheatmasstransfer.2021.105376	PROPN
iajs-3671	482	6	https://doi.org/10.1016/j.icheatmasstransfer.2021.105376	https://doi.org/10.1016/j.icheatmasstransfer.2021.105376	PROPN
iajs-3671	482	7	https://doi.org/10.1007/s12190-020-01388-7	https://doi.org/10.1007/s12190-020-01388-7	PROPN
iajs-3671	482	8	https://doi.org/10.1007/s12190-020-01388-7	https://doi.org/10.1007/s12190-020-01388-7	PROPN
iajs-3671	482	9	https://doi.org/10.1515/jiip-2019-0046	https://doi.org/10.1515/jiip-2019-0046	PROPN
iajs-3671	482	10	https://doi.org/10.1515/jiip-2019-0046	https://doi.org/10.1515/jiip-2019-0046	PROPN
iajs-3671	482	11	https://doi.org/10.1080/17415977.2021.1949590	https://doi.org/10.1080/17415977.2021.1949590	PROPN
iajs-3671	482	12	https://doi.org/%2010.24996/ijs.2022.63.3.24	https://doi.org/%2010.24996/ijs.2022.63.3.24	PROPN
iajs-3671	482	13	https://doi.org/%2010.24996/ijs.2022.63.3.24	https://doi.org/%2010.24996/ijs.2022.63.3.24	PROPN
iajs-3671	482	14	https://doi.org/10.1016/j.apm.2017.09.029	https://doi.org/10.1016/j.apm.2017.09.029	PROPN
iajs-3671	482	15	https://doi.org/10.1016/j.apm.2017.09.029	https://doi.org/10.1016/j.apm.2017.09.029	PROPN
iajs-3671	482	16	https://doi.org/10.1080/00036811.2016.1232401	https://doi.org/10.1080/00036811.2016.1232401	PROPN
iajs-3671	482	17	ihjpas	ihjpas	PROPN
iajs-3671	482	18	.	.	PUNCT
iajs-3671	483	1	2025	2025	NUM
iajs-3671	483	2	,	,	PUNCT
iajs-3671	483	3	38	38	NUM
iajs-3671	483	4	(	(	PUNCT
iajs-3671	483	5	1	1	NUM
iajs-3671	483	6	)	)	PUNCT
iajs-3671	483	7	492	492	NUM
iajs-3671	483	8	39	39	NUM
iajs-3671	483	9	.	.	PUNCT
iajs-3671	484	1	ibraheem	ibraheem	PROPN
iajs-3671	484	2	q.	q.	PROPN
iajs-3671	484	3	w.	w.	PROPN
iajs-3671	484	4	;	;	PUNCT
iajs-3671	484	5	hussein	hussein	PROPN
iajs-3671	484	6	m.	m.	PROPN
iajs-3671	484	7	s.	s.	PROPN
iajs-3671	484	8	determination	determination	NOUN
iajs-3671	484	9	of	of	ADP
iajs-3671	484	10	time	time	NOUN
iajs-3671	484	11	-	-	PUNCT
iajs-3671	484	12	dependent	dependent	ADJ
iajs-3671	484	13	coefficient	coefficient	NOUN
iajs-3671	484	14	in	in	ADP
iajs-3671	484	15	time	time	NOUN
iajs-3671	484	16	-	-	PUNCT
iajs-3671	484	17	fractional	fractional	ADJ
iajs-3671	484	18	heat	heat	NOUN
iajs-3671	484	19	equation	equation	NOUN
iajs-3671	484	20	.	.	PUNCT
iajs-3671	485	1	partial	partial	ADJ
iajs-3671	485	2	differential	differential	ADJ
iajs-3671	485	3	equations	equation	NOUN
iajs-3671	485	4	in	in	ADP
iajs-3671	485	5	applied	applied	ADJ
iajs-3671	485	6	mathematics	mathematic	NOUN
iajs-3671	485	7	.	.	PUNCT
iajs-3671	486	1	2023	2023	NUM
iajs-3671	486	2	;	;	PUNCT
iajs-3671	486	3	100492	100492	NUM
iajs-3671	486	4	.	.	PUNCT
iajs-3671	487	1	https://doi.org/10.1016/j.padiff.2023.100492	https://doi.org/10.1016/j.padiff.2023.100492	PROPN
iajs-3671	487	2	40	40	NUM
iajs-3671	487	3	.	.	PUNCT
iajs-3671	488	1	hansen	hansen	PROPN
iajs-3671	488	2	,	,	PUNCT
iajs-3671	488	3	p.	p.	PROPN
iajs-3671	488	4	c.	c.	NOUN
iajs-3671	488	5	analysis	analysis	NOUN
iajs-3671	488	6	of	of	ADP
iajs-3671	488	7	discrete	discrete	ADJ
iajs-3671	488	8	ill	ill	ADV
iajs-3671	488	9	-	-	PUNCT
iajs-3671	488	10	posed	pose	VERB
iajs-3671	488	11	problems	problem	NOUN
iajs-3671	488	12	by	by	ADP
iajs-3671	488	13	means	mean	NOUN
iajs-3671	488	14	of	of	ADP
iajs-3671	488	15	the	the	DET
iajs-3671	488	16	l	l	NOUN
iajs-3671	488	17	-	-	NOUN
iajs-3671	488	18	curve	curve	NOUN
iajs-3671	488	19	.	.	PUNCT
iajs-3671	489	1	siam	siam	PROPN
iajs-3671	489	2	review	review	PROPN
iajs-3671	489	3	.	.	PUNCT
iajs-3671	490	1	1992	1992	NUM
iajs-3671	490	2	;	;	PUNCT
iajs-3671	491	1	34(4):561–580	34(4):561–580	PROPN
iajs-3671	491	2	.	.	PUNCT
iajs-3671	491	3	https://doi.org/10.1137/1034115	https://doi.org/10.1137/1034115	X
iajs-3671	492	1	41	41	NUM
iajs-3671	492	2	.	.	PUNCT
iajs-3671	493	1	morozov	morozov	PROPN
iajs-3671	493	2	v.	v.	ADP
iajs-3671	493	3	a.	a.	NOUN
iajs-3671	493	4	on	on	ADP
iajs-3671	493	5	the	the	DET
iajs-3671	493	6	solution	solution	NOUN
iajs-3671	493	7	of	of	ADP
iajs-3671	493	8	functional	functional	ADJ
iajs-3671	493	9	equations	equation	NOUN
iajs-3671	493	10	by	by	ADP
iajs-3671	493	11	the	the	DET
iajs-3671	493	12	method	method	NOUN
iajs-3671	493	13	of	of	ADP
iajs-3671	493	14	regularization	regularization	NOUN
iajs-3671	493	15	.	.	PUNCT
iajs-3671	494	1	in	in	ADP
iajs-3671	494	2	doklady	doklady	PROPN
iajs-3671	494	3	akademii	akademii	NOUN
iajs-3671	494	4	nauk	nauk	PROPN
iajs-3671	494	5	.	.	PUNCT
iajs-3671	495	1	russian	russian	PROPN
iajs-3671	495	2	academy	academy	PROPN
iajs-3671	495	3	of	of	ADP
iajs-3671	495	4	sciences	sciences	PROPN
iajs-3671	495	5	.	.	PUNCT
iajs-3671	496	1	1966	1966	NUM
iajs-3671	496	2	;	;	PUNCT
iajs-3671	497	1	167	167	NUM
iajs-3671	497	2	:	:	PUNCT
iajs-3671	497	3	510–512	510–512	NUM
iajs-3671	497	4	.	.	PUNCT
iajs-3671	497	5	http://www.mathnet.ru/eng/agreement	http://www.mathnet.ru/eng/agreement	NUM
iajs-3671	498	1	42	42	NUM
iajs-3671	498	2	.	.	PUNCT
iajs-3671	499	1	hussein	hussein	PROPN
iajs-3671	499	2	s.	s.	PROPN
iajs-3671	499	3	o.	o.	PROPN
iajs-3671	499	4	determination	determination	NOUN
iajs-3671	499	5	force	force	PROPN
iajs-3671	499	6	/	/	SYM
iajs-3671	499	7	source	source	NOUN
iajs-3671	499	8	function	function	NOUN
iajs-3671	499	9	dependent	dependent	ADJ
iajs-3671	499	10	on	on	ADP
iajs-3671	499	11	space	space	NOUN
iajs-3671	499	12	under	under	ADP
iajs-3671	499	13	the	the	DET
iajs-3671	499	14	non	non	ADJ
iajs-3671	499	15	-	-	ADJ
iajs-3671	499	16	classical	classical	ADJ
iajs-3671	499	17	condition	condition	NOUN
iajs-3671	499	18	data	datum	NOUN
iajs-3671	499	19	.	.	PUNCT
iajs-3671	500	1	journal	journal	PROPN
iajs-3671	500	2	of	of	ADP
iajs-3671	500	3	university	university	PROPN
iajs-3671	500	4	of	of	ADP
iajs-3671	500	5	babylon	babylon	PROPN
iajs-3671	500	6	for	for	ADP
iajs-3671	500	7	pure	pure	ADJ
iajs-3671	500	8	and	and	CCONJ
iajs-3671	500	9	applied	applied	ADJ
iajs-3671	500	10	sciences	science	NOUN
iajs-3671	500	11	.	.	PUNCT
iajs-3671	501	1	2020	2020	NUM
iajs-3671	501	2	;	;	PUNCT
iajs-3671	501	3	28(3	28(3	NUM
iajs-3671	501	4	):	):	PUNCT
iajs-3671	501	5	68	68	NUM
iajs-3671	501	6	-	-	SYM
iajs-3671	501	7	75	75	NUM
iajs-3671	501	8	.	.	PUNCT
iajs-3671	502	1	https://www.journalofbabylon.com/index.php/jubpas/article/view/3333/2546	https://www.journalofbabylon.com/index.php/jubpas/article/view/3333/2546	PROPN
iajs-3671	502	2	43	43	NUM
iajs-3671	502	3	.	.	PUNCT
iajs-3671	503	1	hussein	hussein	PROPN
iajs-3671	503	2	s.	s.	PROPN
iajs-3671	503	3	o.	o.	PROPN
iajs-3671	503	4	splitting	split	VERB
iajs-3671	503	5	the	the	DET
iajs-3671	503	6	one	one	NUM
iajs-3671	503	7	-	-	PUNCT
iajs-3671	503	8	dimensional	dimensional	ADJ
iajs-3671	503	9	wave	wave	NOUN
iajs-3671	503	10	equation	equation	NOUN
iajs-3671	503	11	.	.	PUNCT
iajs-3671	504	1	part	part	NOUN
iajs-3671	505	1	i	i	PRON
iajs-3671	505	2	:	:	PUNCT
iajs-3671	505	3	solving	solve	VERB
iajs-3671	505	4	by	by	ADP
iajs-3671	505	5	finite	finite	ADJ
iajs-3671	505	6	-	-	PUNCT
iajs-3671	505	7	difference	difference	NOUN
iajs-3671	505	8	method	method	NOUN
iajs-3671	505	9	and	and	CCONJ
iajs-3671	505	10	separation	separation	NOUN
iajs-3671	505	11	variables	variable	NOUN
iajs-3671	505	12	.	.	PUNCT
iajs-3671	506	1	baghdad	baghdad	PROPN
iajs-3671	506	2	science	science	PROPN
iajs-3671	506	3	journal	journal	PROPN
iajs-3671	506	4	.	.	PUNCT
iajs-3671	507	1	2020	2020	NUM
iajs-3671	507	2	;	;	PUNCT
iajs-3671	507	3	17(2	17(2	NUM
iajs-3671	507	4	(	(	PUNCT
iajs-3671	507	5	si	si	NOUN
iajs-3671	507	6	)	)	PUNCT
iajs-3671	507	7	):	):	PUNCT
iajs-3671	507	8	0675	0675	NUM
iajs-3671	507	9	-	-	PUNCT
iajs-3671	507	10	0675	0675	NUM
iajs-3671	507	11	.	.	PUNCT
iajs-3671	508	1	http://dx.doi.org/10.21123/bsj.2020.17.2(si).0675	http://dx.doi.org/10.21123/bsj.2020.17.2(si).0675	PROPN
iajs-3671	508	2	44	44	NUM
iajs-3671	508	3	.	.	PUNCT
iajs-3671	509	1	alosaimi	alosaimi	PROPN
iajs-3671	509	2	m.	m.	PROPN
iajs-3671	509	3	a.	a.	PROPN
iajs-3671	509	4	;	;	PUNCT
iajs-3671	509	5	lesnic	lesnic	PROPN
iajs-3671	509	6	d.	d.	PROPN
iajs-3671	509	7	determination	determination	NOUN
iajs-3671	509	8	of	of	ADP
iajs-3671	509	9	the	the	DET
iajs-3671	509	10	space	space	NOUN
iajs-3671	509	11	-	-	PUNCT
iajs-3671	509	12	dependent	dependent	ADJ
iajs-3671	509	13	blood	blood	NOUN
iajs-3671	509	14	perfusion	perfusion	NOUN
iajs-3671	509	15	coefficient	coefficient	NOUN
iajs-3671	509	16	in	in	ADP
iajs-3671	509	17	the	the	DET
iajs-3671	509	18	thermal	thermal	ADJ
iajs-3671	509	19	-	-	PUNCT
iajs-3671	509	20	wave	wave	NOUN
iajs-3671	509	21	model	model	NOUN
iajs-3671	509	22	of	of	ADP
iajs-3671	509	23	bio	bio	ADJ
iajs-3671	509	24	-	-	ADJ
iajs-3671	509	25	heat	heat	NOUN
iajs-3671	509	26	transfer	transfer	NOUN
iajs-3671	509	27	.	.	PUNCT
iajs-3671	510	1	engineering	engineering	NOUN
iajs-3671	510	2	computations	computation	NOUN
iajs-3671	510	3	.	.	PUNCT
iajs-3671	511	1	2023	2023	NUM
iajs-3671	511	2	;	;	PUNCT
iajs-3671	511	3	129	129	NUM
iajs-3671	511	4	:	:	SYM
iajs-3671	511	5	34	34	NUM
iajs-3671	511	6	-	-	SYM
iajs-3671	511	7	49	49	NUM
iajs-3671	511	8	.	.	PUNCT
iajs-3671	511	9	https://doi.org/10.1108/ec-07-2022-0467	https://doi.org/10.1108/ec-07-2022-0467	PROPN
iajs-3671	511	10	45	45	NUM
iajs-3671	511	11	.	.	PUNCT
iajs-3671	511	12	alosaimi	alosaimi	PROPN
iajs-3671	511	13	m.	m.	PROPN
iajs-3671	511	14	;	;	PUNCT
iajs-3671	511	15	lesnic	lesnic	PROPN
iajs-3671	511	16	d.	d.	PROPN
iajs-3671	511	17	determination	determination	NOUN
iajs-3671	511	18	of	of	ADP
iajs-3671	511	19	a	a	DET
iajs-3671	511	20	space	space	NOUN
iajs-3671	511	21	-	-	PUNCT
iajs-3671	511	22	dependent	dependent	ADJ
iajs-3671	511	23	source	source	NOUN
iajs-3671	511	24	in	in	ADP
iajs-3671	511	25	the	the	DET
iajs-3671	511	26	thermal	thermal	ADJ
iajs-3671	511	27	-	-	PUNCT
iajs-3671	511	28	wave	wave	NOUN
iajs-3671	511	29	model	model	NOUN
iajs-3671	511	30	of	of	ADP
iajs-3671	511	31	bioheat	bioheat	ADJ
iajs-3671	511	32	transfer	transfer	NOUN
iajs-3671	511	33	.	.	PUNCT
iajs-3671	512	1	computers	computer	NOUN
iajs-3671	512	2	&	&	CCONJ
iajs-3671	512	3	mathematics	mathematics	PROPN
iajs-3671	512	4	with	with	ADP
iajs-3671	512	5	applications	application	NOUN
iajs-3671	512	6	.	.	PUNCT
iajs-3671	513	1	2023	2023	NUM
iajs-3671	513	2	;	;	PUNCT
iajs-3671	513	3	129	129	NUM
iajs-3671	513	4	:	:	SYM
iajs-3671	513	5	34	34	NUM
iajs-3671	513	6	-	-	SYM
iajs-3671	513	7	49	49	NUM
iajs-3671	513	8	.	.	PUNCT
iajs-3671	513	9	https://doi.org/10.1016/j.camwa.2022.10.026	https://doi.org/10.1016/j.camwa.2022.10.026	PROPN
iajs-3671	513	10	46	46	NUM
iajs-3671	513	11	.	.	PUNCT
iajs-3671	514	1	hussein	hussein	PROPN
iajs-3671	514	2	s.	s.	PROPN
iajs-3671	514	3	o	o	PROPN
iajs-3671	514	4	,	,	PUNCT
iajs-3671	514	5	placement	placement	NOUN
iajs-3671	514	6	inverse	inverse	NOUN
iajs-3671	514	7	source	source	NOUN
iajs-3671	514	8	problem	problem	NOUN
iajs-3671	514	9	under	under	ADP
iajs-3671	514	10	partition	partition	NOUN
iajs-3671	514	11	hyperbolic	hyperbolic	ADJ
iajs-3671	514	12	equation	equation	NOUN
iajs-3671	514	13	.	.	PUNCT
iajs-3671	515	1	iraqi	iraqi	ADJ
iajs-3671	515	2	journal	journal	PROPN
iajs-3671	515	3	of	of	ADP
iajs-3671	515	4	science	science	NOUN
iajs-3671	515	5	.	.	PUNCT
iajs-3671	516	1	2021	2021	NUM
iajs-3671	516	2	;	;	PUNCT
iajs-3671	516	3	1994	1994	NUM
iajs-3671	516	4	-	-	SYM
iajs-3671	516	5	1999	1999	NUM
iajs-3671	516	6	.	.	PUNCT
iajs-3671	517	1	https://doi.org/10.24996/ijs.2021.62.6.25	https://doi.org/10.24996/ijs.2021.62.6.25	PROPN
iajs-3671	517	2	47	47	NUM
iajs-3671	517	3	.	.	PUNCT
iajs-3671	518	1	hussein	hussein	PROPN
iajs-3671	518	2	s.	s.	PROPN
iajs-3671	518	3	o	o	PROPN
iajs-3671	518	4	;	;	PUNCT
iajs-3671	518	5	t.	t.	PROPN
iajs-3671	518	6	e.	e.	PROPN
iajs-3671	518	7	dyhoum	dyhoum	PROPN
iajs-3671	518	8	.	.	PUNCT
iajs-3671	519	1	solutions	solution	NOUN
iajs-3671	519	2	for	for	ADP
iajs-3671	519	3	non	non	ADJ
iajs-3671	519	4	-	-	ADJ
iajs-3671	519	5	homogeneous	homogeneous	ADJ
iajs-3671	519	6	wave	wave	NOUN
iajs-3671	519	7	equations	equation	NOUN
iajs-3671	519	8	subject	subject	ADJ
iajs-3671	519	9	to	to	ADP
iajs-3671	519	10	unusual	unusual	ADJ
iajs-3671	519	11	and	and	CCONJ
iajs-3671	519	12	neumann	neumann	PROPN
iajs-3671	519	13	boundary	boundary	ADJ
iajs-3671	519	14	conditions	condition	NOUN
iajs-3671	519	15	.	.	PUNCT
iajs-3671	520	1	applied	apply	VERB
iajs-3671	520	2	mathematics	mathematic	NOUN
iajs-3671	520	3	and	and	CCONJ
iajs-3671	520	4	computation	computation	NOUN
iajs-3671	520	5	.	.	PUNCT
iajs-3671	521	1	2022	2022	NUM
iajs-3671	521	2	;	;	PUNCT
iajs-3671	521	3	430	430	NUM
iajs-3671	521	4	,	,	PUNCT
iajs-3671	521	5	127285	127285	NUM
iajs-3671	521	6	.	.	PUNCT
iajs-3671	522	1	https://doi.org/10.1016/j.amc.2022.127285	https://doi.org/10.1016/j.amc.2022.127285	PROPN
iajs-3671	522	2	48	48	NUM
iajs-3671	522	3	.	.	PUNCT
iajs-3671	522	4	karami	karami	PROPN
iajs-3671	522	5	a.	a.	PROPN
iajs-3671	522	6	;	;	PUNCT
iajs-3671	522	7	abbasbandy	abbasbandy	PROPN
iajs-3671	522	8	s.	s.	PROPN
iajs-3671	522	9	;	;	PUNCT
iajs-3671	522	10	shivanian	shivanian	PROPN
iajs-3671	522	11	e.	e.	PROPN
iajs-3671	522	12	inverse	inverse	PROPN
iajs-3671	522	13	problem	problem	NOUN
iajs-3671	522	14	of	of	ADP
iajs-3671	522	15	identifying	identify	VERB
iajs-3671	522	16	a	a	DET
iajs-3671	522	17	time	time	NOUN
iajs-3671	522	18	-	-	PUNCT
iajs-3671	522	19	dependent	dependent	ADJ
iajs-3671	522	20	coefficient	coefficient	NOUN
iajs-3671	522	21	and	and	CCONJ
iajs-3671	522	22	free	free	ADJ
iajs-3671	522	23	boundary	boundary	NOUN
iajs-3671	522	24	in	in	ADP
iajs-3671	522	25	heat	heat	NOUN
iajs-3671	522	26	conduction	conduction	NOUN
iajs-3671	522	27	equation	equation	NOUN
iajs-3671	522	28	by	by	ADP
iajs-3671	522	29	using	use	VERB
iajs-3671	522	30	the	the	DET
iajs-3671	522	31	meshless	meshless	ADJ
iajs-3671	522	32	local	local	ADJ
iajs-3671	522	33	petrov	petrov	PROPN
iajs-3671	522	34	-	-	PUNCT
iajs-3671	522	35	galerkin	galerkin	PROPN
iajs-3671	522	36	(	(	PUNCT
iajs-3671	522	37	mlpg	mlpg	NOUN
iajs-3671	522	38	)	)	PUNCT
iajs-3671	522	39	method	method	NOUN
iajs-3671	522	40	via	via	ADP
iajs-3671	522	41	moving	move	VERB
iajs-3671	522	42	least	least	ADJ
iajs-3671	522	43	squares	square	NOUN
iajs-3671	522	44	approximation	approximation	NOUN
iajs-3671	522	45	.	.	PUNCT
iajs-3671	523	1	filomat	filomat	PROPN
iajs-3671	523	2	.	.	PUNCT
iajs-3671	524	1	2020	2020	NUM
iajs-3671	524	2	;	;	PUNCT
iajs-3671	524	3	34(10	34(10	NUM
iajs-3671	524	4	):	):	PUNCT
iajs-3671	524	5	3319	3319	NUM
iajs-3671	524	6	-	-	SYM
iajs-3671	524	7	3337	3337	NUM
iajs-3671	524	8	.	.	PUNCT
iajs-3671	525	1	https://doi.org/10.2298/fil2010319k	https://doi.org/10.2298/fil2010319k	NOUN
iajs-3671	525	2	49	49	NUM
iajs-3671	525	3	.	.	PUNCT
iajs-3671	526	1	karami	karami	PROPN
iajs-3671	526	2	a.	a.	PROPN
iajs-3671	526	3	;	;	PUNCT
iajs-3671	526	4	abbasbandy	abbasbandy	PROPN
iajs-3671	526	5	s.	s.	PROPN
iajs-3671	526	6	;	;	PUNCT
iajs-3671	527	1	shivanian	shivanian	PROPN
iajs-3671	527	2	e.	e.	PROPN
iajs-3671	527	3	meshless	meshless	PROPN
iajs-3671	527	4	local	local	ADJ
iajs-3671	527	5	petrov	petrov	PROPN
iajs-3671	527	6	–	–	PUNCT
iajs-3671	527	7	galerkin	galerkin	ADJ
iajs-3671	527	8	formulation	formulation	NOUN
iajs-3671	527	9	of	of	ADP
iajs-3671	527	10	inverse	inverse	NOUN
iajs-3671	527	11	stefan	stefan	PROPN
iajs-3671	527	12	problem	problem	PROPN
iajs-3671	527	13	via	via	ADP
iajs-3671	527	14	moving	move	VERB
iajs-3671	527	15	least	least	ADJ
iajs-3671	527	16	squares	square	NOUN
iajs-3671	527	17	approximation	approximation	NOUN
iajs-3671	527	18	.	.	PUNCT
iajs-3671	528	1	mathematical	mathematical	ADJ
iajs-3671	528	2	and	and	CCONJ
iajs-3671	528	3	computational	computational	ADJ
iajs-3671	528	4	applications	application	NOUN
iajs-3671	528	5	.	.	PUNCT
iajs-3671	529	1	2019	2019	NUM
iajs-3671	529	2	;	;	PUNCT
iajs-3671	529	3	24(4	24(4	NOUN
iajs-3671	529	4	):	):	PUNCT
iajs-3671	529	5	101	101	NUM
iajs-3671	529	6	.	.	PUNCT
iajs-3671	530	1	https://doi.org/10.3390/mca24040101	https://doi.org/10.3390/mca24040101	NOUN
iajs-3671	530	2	50	50	NUM
iajs-3671	530	3	.	.	PUNCT
iajs-3671	531	1	huntul	huntul	PROPN
iajs-3671	531	2	m.	m.	PROPN
iajs-3671	531	3	j.	j.	PROPN
iajs-3671	531	4	;	;	PUNCT
iajs-3671	531	5	tamsir	tamsir	PROPN
iajs-3671	531	6	m.	m.	NOUN
iajs-3671	531	7	reconstruction	reconstruction	NOUN
iajs-3671	531	8	of	of	ADP
iajs-3671	531	9	a	a	DET
iajs-3671	531	10	potential	potential	ADJ
iajs-3671	531	11	coefficient	coefficient	NOUN
iajs-3671	531	12	in	in	ADP
iajs-3671	531	13	the	the	DET
iajs-3671	531	14	rayleigh	rayleigh	PROPN
iajs-3671	531	15	–	–	PUNCT
iajs-3671	531	16	love	love	NOUN
iajs-3671	531	17	equation	equation	NOUN
iajs-3671	531	18	with	with	ADP
iajs-3671	531	19	non	non	ADJ
iajs-3671	531	20	-	-	ADJ
iajs-3671	531	21	classical	classical	ADJ
iajs-3671	531	22	boundary	boundary	ADJ
iajs-3671	531	23	condition	condition	NOUN
iajs-3671	531	24	.	.	PUNCT
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