id	sid	tid	token	lemma	pos
ejpam-5751	1	1	european	european	PROPN
ejpam-5751	1	2	journal	journal	PROPN
ejpam-5751	1	3	of	of	ADP
ejpam-5751	1	4	pure	pure	ADJ
ejpam-5751	1	5	and	and	CCONJ
ejpam-5751	1	6	applied	applied	ADJ
ejpam-5751	1	7	mathematics	mathematic	NOUN
ejpam-5751	1	8	2025	2025	NUM
ejpam-5751	1	9	,	,	PUNCT
ejpam-5751	1	10	vol	vol	NOUN
ejpam-5751	1	11	.	.	PROPN
ejpam-5751	1	12	18	18	NUM
ejpam-5751	1	13	,	,	PUNCT
ejpam-5751	1	14	issue	issue	NOUN
ejpam-5751	1	15	1	1	NUM
ejpam-5751	1	16	,	,	PUNCT
ejpam-5751	1	17	article	article	NOUN
ejpam-5751	1	18	number	number	NOUN
ejpam-5751	1	19	5751	5751	NUM
ejpam-5751	1	20	issn	issn	PROPN
ejpam-5751	1	21	1307	1307	NUM
ejpam-5751	1	22	-	-	SYM
ejpam-5751	1	23	5543	5543	NUM
ejpam-5751	1	24	–	–	PUNCT
ejpam-5751	1	25	ejpam.com	ejpam.com	X
ejpam-5751	1	26	published	publish	VERB
ejpam-5751	1	27	by	by	ADP
ejpam-5751	1	28	new	new	PROPN
ejpam-5751	1	29	york	york	PROPN
ejpam-5751	1	30	business	business	PROPN
ejpam-5751	1	31	global	global	ADJ
ejpam-5751	1	32	new	new	ADJ
ejpam-5751	1	33	abundant	abundant	ADJ
ejpam-5751	1	34	optical	optical	ADJ
ejpam-5751	1	35	solutions	solution	NOUN
ejpam-5751	1	36	for	for	ADP
ejpam-5751	1	37	the	the	DET
ejpam-5751	1	38	stochastic	stochastic	ADJ
ejpam-5751	1	39	heisenberg	heisenberg	PROPN
ejpam-5751	1	40	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	1	41	equation	equation	NOUN
ejpam-5751	1	42	used	use	VERB
ejpam-5751	1	43	in	in	ADP
ejpam-5751	1	44	a	a	DET
ejpam-5751	1	45	ferromagnet	ferromagnet	NOUN
ejpam-5751	1	46	via	via	ADP
ejpam-5751	1	47	two	two	NUM
ejpam-5751	1	48	different	different	ADJ
ejpam-5751	1	49	methods	method	NOUN
ejpam-5751	1	50	wael	wael	PROPN
ejpam-5751	1	51	w.	w.	PROPN
ejpam-5751	1	52	mohammed1,∗	mohammed1,∗	PROPN
ejpam-5751	1	53	,	,	PUNCT
ejpam-5751	1	54	naveed	naveed	PROPN
ejpam-5751	1	55	iqbal1	iqbal1	PROPN
ejpam-5751	1	56	,	,	PUNCT
ejpam-5751	1	57	hijeh	hijeh	PROPN
ejpam-5751	1	58	m.	m.	NOUN
ejpam-5751	1	59	alshammari1	alshammari1	PROPN
ejpam-5751	1	60	,	,	PUNCT
ejpam-5751	1	61	mohamed	mohamed	PROPN
ejpam-5751	1	62	s.	s.	PROPN
ejpam-5751	1	63	algolam1	algolam1	PROPN
ejpam-5751	2	1	1	1	NUM
ejpam-5751	2	2	department	department	NOUN
ejpam-5751	2	3	of	of	ADP
ejpam-5751	2	4	mathematics	mathematic	NOUN
ejpam-5751	2	5	,	,	PUNCT
ejpam-5751	2	6	college	college	NOUN
ejpam-5751	2	7	of	of	ADP
ejpam-5751	2	8	science	science	NOUN
ejpam-5751	2	9	,	,	PUNCT
ejpam-5751	2	10	university	university	NOUN
ejpam-5751	2	11	of	of	ADP
ejpam-5751	2	12	ha’il	ha’il	PROPN
ejpam-5751	2	13	,	,	PUNCT
ejpam-5751	2	14	ha’il	ha’il	PROPN
ejpam-5751	2	15	2440	2440	NUM
ejpam-5751	2	16	,	,	PUNCT
ejpam-5751	2	17	saudi	saudi	PROPN
ejpam-5751	2	18	arabia	arabia	PROPN
ejpam-5751	2	19	abstract	abstract	NOUN
ejpam-5751	2	20	.	.	PUNCT
ejpam-5751	3	1	in	in	ADP
ejpam-5751	3	2	this	this	DET
ejpam-5751	3	3	study	study	NOUN
ejpam-5751	3	4	,	,	PUNCT
ejpam-5751	3	5	we	we	PRON
ejpam-5751	3	6	look	look	VERB
ejpam-5751	3	7	at	at	ADP
ejpam-5751	3	8	the	the	DET
ejpam-5751	3	9	stochastic	stochastic	ADJ
ejpam-5751	3	10	heisenberg	heisenberg	PROPN
ejpam-5751	3	11	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	3	12	equation	equation	NOUN
ejpam-5751	3	13	(	(	PUNCT
ejpam-5751	3	14	shfe	shfe	PROPN
ejpam-5751	3	15	)	)	PUNCT
ejpam-5751	3	16	perturbed	perturb	VERB
ejpam-5751	3	17	in	in	ADP
ejpam-5751	3	18	the	the	DET
ejpam-5751	3	19	itô	itô	PROPN
ejpam-5751	3	20	sense	sense	NOUN
ejpam-5751	3	21	by	by	ADP
ejpam-5751	3	22	multiplicative	multiplicative	ADJ
ejpam-5751	3	23	brownian	brownian	ADJ
ejpam-5751	3	24	motion	motion	NOUN
ejpam-5751	3	25	.	.	PUNCT
ejpam-5751	4	1	the	the	DET
ejpam-5751	4	2	shfe	shfe	PROPN
ejpam-5751	4	3	is	be	AUX
ejpam-5751	4	4	transformed	transform	VERB
ejpam-5751	4	5	into	into	ADP
ejpam-5751	4	6	a	a	DET
ejpam-5751	4	7	different	different	ADJ
ejpam-5751	4	8	heisenberg	heisenberg	PROPN
ejpam-5751	4	9	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	4	10	equation	equation	NOUN
ejpam-5751	4	11	with	with	ADP
ejpam-5751	4	12	random	random	ADJ
ejpam-5751	4	13	variable	variable	ADJ
ejpam-5751	4	14	coefficients	coefficient	NOUN
ejpam-5751	4	15	(	(	PUNCT
ejpam-5751	4	16	hfe	hfe	PROPN
ejpam-5751	4	17	-	-	PUNCT
ejpam-5751	4	18	rvcs	rvcs	NOUN
ejpam-5751	4	19	)	)	PUNCT
ejpam-5751	4	20	utilizing	utilize	VERB
ejpam-5751	4	21	the	the	DET
ejpam-5751	4	22	proper	proper	ADJ
ejpam-5751	4	23	transformation	transformation	NOUN
ejpam-5751	4	24	.	.	PUNCT
ejpam-5751	5	1	to	to	PART
ejpam-5751	5	2	provide	provide	VERB
ejpam-5751	5	3	novel	novel	ADJ
ejpam-5751	5	4	solutions	solution	NOUN
ejpam-5751	5	5	for	for	ADP
ejpam-5751	5	6	trigonometric	trigonometric	ADJ
ejpam-5751	5	7	functions	function	NOUN
ejpam-5751	5	8	,	,	PUNCT
ejpam-5751	5	9	hyperbolic	hyperbolic	ADJ
ejpam-5751	5	10	functions	function	NOUN
ejpam-5751	5	11	,	,	PUNCT
ejpam-5751	5	12	and	and	CCONJ
ejpam-5751	5	13	rational	rational	ADJ
ejpam-5751	5	14	functions	function	NOUN
ejpam-5751	5	15	for	for	ADP
ejpam-5751	5	16	hfe	hfe	PROPN
ejpam-5751	5	17	-	-	PUNCT
ejpam-5751	5	18	rvcs	rvcs	PROPN
ejpam-5751	5	19	,	,	PUNCT
ejpam-5751	5	20	we	we	PRON
ejpam-5751	5	21	employ	employ	VERB
ejpam-5751	5	22	the	the	DET
ejpam-5751	5	23	generalizing	generalize	VERB
ejpam-5751	5	24	riccati	riccati	NOUN
ejpam-5751	5	25	equation	equation	NOUN
ejpam-5751	5	26	mapping	mapping	NOUN
ejpam-5751	5	27	technique	technique	NOUN
ejpam-5751	5	28	(	(	PUNCT
ejpam-5751	5	29	grem	grem	NOUN
ejpam-5751	5	30	-	-	NOUN
ejpam-5751	5	31	method	method	NOUN
ejpam-5751	5	32	)	)	PUNCT
ejpam-5751	5	33	and	and	CCONJ
ejpam-5751	5	34	jacobi	jacobi	PROPN
ejpam-5751	5	35	elliptic	elliptic	ADJ
ejpam-5751	5	36	functions	function	NOUN
ejpam-5751	5	37	(	(	PUNCT
ejpam-5751	5	38	jef	jef	NOUN
ejpam-5751	5	39	-	-	PUNCT
ejpam-5751	5	40	method	method	NOUN
ejpam-5751	5	41	)	)	PUNCT
ejpam-5751	5	42	.	.	PUNCT
ejpam-5751	6	1	the	the	DET
ejpam-5751	6	2	solutions	solution	NOUN
ejpam-5751	6	3	of	of	ADP
ejpam-5751	6	4	shfe	shfe	PROPN
ejpam-5751	6	5	can	can	AUX
ejpam-5751	6	6	then	then	ADV
ejpam-5751	6	7	be	be	AUX
ejpam-5751	6	8	obtained	obtain	VERB
ejpam-5751	6	9	.	.	PUNCT
ejpam-5751	7	1	for	for	ADP
ejpam-5751	7	2	the	the	DET
ejpam-5751	7	3	first	first	ADJ
ejpam-5751	7	4	time	time	NOUN
ejpam-5751	7	5	,	,	PUNCT
ejpam-5751	7	6	we	we	PRON
ejpam-5751	7	7	postulate	postulate	VERB
ejpam-5751	7	8	that	that	SCONJ
ejpam-5751	7	9	the	the	DET
ejpam-5751	7	10	solution	solution	NOUN
ejpam-5751	7	11	to	to	ADP
ejpam-5751	7	12	the	the	DET
ejpam-5751	7	13	heisenberg	heisenberg	PROPN
ejpam-5751	7	14	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	7	15	equation	equation	NOUN
ejpam-5751	7	16	is	be	AUX
ejpam-5751	7	17	stochastic	stochastic	ADJ
ejpam-5751	7	18	,	,	PUNCT
ejpam-5751	7	19	in	in	ADP
ejpam-5751	7	20	contrast	contrast	NOUN
ejpam-5751	7	21	to	to	ADP
ejpam-5751	7	22	earlier	early	ADJ
ejpam-5751	7	23	research	research	NOUN
ejpam-5751	7	24	that	that	PRON
ejpam-5751	7	25	suggested	suggest	VERB
ejpam-5751	7	26	it	it	PRON
ejpam-5751	7	27	was	be	AUX
ejpam-5751	7	28	deterministic	deterministic	ADJ
ejpam-5751	7	29	.	.	PUNCT
ejpam-5751	8	1	additionally	additionally	ADV
ejpam-5751	8	2	,	,	PUNCT
ejpam-5751	8	3	we	we	PRON
ejpam-5751	8	4	investigate	investigate	VERB
ejpam-5751	8	5	the	the	DET
ejpam-5751	8	6	impact	impact	NOUN
ejpam-5751	8	7	of	of	ADP
ejpam-5751	8	8	multiplicative	multiplicative	ADJ
ejpam-5751	8	9	brownian	brownian	ADJ
ejpam-5751	8	10	motion	motion	NOUN
ejpam-5751	8	11	on	on	ADP
ejpam-5751	8	12	the	the	DET
ejpam-5751	8	13	exact	exact	ADJ
ejpam-5751	8	14	solutions	solution	NOUN
ejpam-5751	8	15	of	of	ADP
ejpam-5751	8	16	the	the	DET
ejpam-5751	8	17	shfe	shfe	NOUN
ejpam-5751	8	18	by	by	ADP
ejpam-5751	8	19	offering	offer	VERB
ejpam-5751	8	20	several	several	ADJ
ejpam-5751	8	21	graphical	graphical	ADJ
ejpam-5751	8	22	representations	representation	NOUN
ejpam-5751	8	23	.	.	PUNCT
ejpam-5751	9	1	2020	2020	NUM
ejpam-5751	9	2	mathematics	mathematic	NOUN
ejpam-5751	9	3	subject	subject	NOUN
ejpam-5751	9	4	classifications	classification	NOUN
ejpam-5751	9	5	:	:	PUNCT
ejpam-5751	9	6	35a20	35a20	NUM
ejpam-5751	9	7	,	,	PUNCT
ejpam-5751	9	8	60h15	60h15	NUM
ejpam-5751	9	9	,	,	PUNCT
ejpam-5751	9	10	60h10	60h10	NUM
ejpam-5751	9	11	,	,	PUNCT
ejpam-5751	9	12	83c15	83c15	NUM
ejpam-5751	9	13	,	,	PUNCT
ejpam-5751	9	14	35q51	35q51	NUM
ejpam-5751	9	15	key	key	ADJ
ejpam-5751	9	16	words	word	NOUN
ejpam-5751	9	17	and	and	CCONJ
ejpam-5751	9	18	phrases	phrase	NOUN
ejpam-5751	9	19	:	:	PUNCT
ejpam-5751	9	20	white	white	ADJ
ejpam-5751	9	21	noise	noise	NOUN
ejpam-5751	9	22	,	,	PUNCT
ejpam-5751	9	23	stochastic	stochastic	ADJ
ejpam-5751	9	24	solutions	solution	NOUN
ejpam-5751	9	25	,	,	PUNCT
ejpam-5751	9	26	jacobi	jacobi	PROPN
ejpam-5751	9	27	elliptic	elliptic	ADJ
ejpam-5751	9	28	functions	function	NOUN
ejpam-5751	9	29	method	method	NOUN
ejpam-5751	9	30	,	,	PUNCT
ejpam-5751	9	31	random	random	ADJ
ejpam-5751	9	32	variable	variable	ADJ
ejpam-5751	9	33	coefficients	coefficient	NOUN
ejpam-5751	9	34	1	1	NUM
ejpam-5751	9	35	.	.	PUNCT
ejpam-5751	10	1	introduction	introduction	NOUN
ejpam-5751	10	2	the	the	DET
ejpam-5751	10	3	heisenberg	heisenberg	PROPN
ejpam-5751	10	4	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	10	5	equation	equation	NOUN
ejpam-5751	10	6	has	have	VERB
ejpam-5751	10	7	important	important	ADJ
ejpam-5751	10	8	implications	implication	NOUN
ejpam-5751	10	9	for	for	ADP
ejpam-5751	10	10	the	the	DET
ejpam-5751	10	11	behavior	behavior	NOUN
ejpam-5751	10	12	of	of	ADP
ejpam-5751	10	13	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	10	14	materials	material	NOUN
ejpam-5751	10	15	.	.	PUNCT
ejpam-5751	11	1	it	it	PRON
ejpam-5751	11	2	predicts	predict	VERB
ejpam-5751	11	3	phenomena	phenomena	NOUN
ejpam-5751	11	4	such	such	ADJ
ejpam-5751	11	5	as	as	ADP
ejpam-5751	11	6	spontaneous	spontaneous	ADJ
ejpam-5751	11	7	magnetization	magnetization	NOUN
ejpam-5751	11	8	,	,	PUNCT
ejpam-5751	11	9	where	where	SCONJ
ejpam-5751	11	10	the	the	DET
ejpam-5751	11	11	atoms	atom	NOUN
ejpam-5751	11	12	’	'	PUNCT
ejpam-5751	11	13	magnetic	magnetic	ADJ
ejpam-5751	11	14	moments	moment	NOUN
ejpam-5751	11	15	align	align	VERB
ejpam-5751	11	16	parallel	parallel	NOUN
ejpam-5751	11	17	to	to	ADP
ejpam-5751	11	18	each	each	DET
ejpam-5751	11	19	other	other	ADJ
ejpam-5751	11	20	even	even	ADV
ejpam-5751	11	21	in	in	ADP
ejpam-5751	11	22	the	the	DET
ejpam-5751	11	23	absence	absence	NOUN
ejpam-5751	11	24	of	of	ADP
ejpam-5751	11	25	an	an	DET
ejpam-5751	11	26	external	external	ADJ
ejpam-5751	11	27	magnetic	magnetic	ADJ
ejpam-5751	11	28	field	field	NOUN
ejpam-5751	11	29	.	.	PUNCT
ejpam-5751	12	1	it	it	PRON
ejpam-5751	12	2	also	also	ADV
ejpam-5751	12	3	explains	explain	VERB
ejpam-5751	12	4	the	the	DET
ejpam-5751	12	5	existence	existence	NOUN
ejpam-5751	12	6	of	of	ADP
ejpam-5751	12	7	magnetic	magnetic	ADJ
ejpam-5751	12	8	domains	domain	NOUN
ejpam-5751	12	9	and	and	CCONJ
ejpam-5751	12	10	how	how	SCONJ
ejpam-5751	12	11	they	they	PRON
ejpam-5751	12	12	can	can	AUX
ejpam-5751	12	13	change	change	VERB
ejpam-5751	12	14	their	their	PRON
ejpam-5751	12	15	alignment	alignment	NOUN
ejpam-5751	12	16	under	under	ADP
ejpam-5751	12	17	the	the	DET
ejpam-5751	12	18	influence	influence	NOUN
ejpam-5751	12	19	of	of	ADP
ejpam-5751	12	20	an	an	DET
ejpam-5751	12	21	external	external	ADJ
ejpam-5751	12	22	field	field	NOUN
ejpam-5751	12	23	.	.	PUNCT
ejpam-5751	13	1	additionally	additionally	ADV
ejpam-5751	13	2	,	,	PUNCT
ejpam-5751	13	3	the	the	DET
ejpam-5751	13	4	heisenberg	heisenberg	PROPN
ejpam-5751	13	5	equation	equation	NOUN
ejpam-5751	13	6	helps	help	VERB
ejpam-5751	13	7	scientists	scientist	NOUN
ejpam-5751	13	8	understand	understand	VERB
ejpam-5751	13	9	the	the	DET
ejpam-5751	13	10	temperature	temperature	NOUN
ejpam-5751	13	11	dependence	dependence	NOUN
ejpam-5751	13	12	of	of	ADP
ejpam-5751	13	13	magnetism	magnetism	NOUN
ejpam-5751	13	14	and	and	CCONJ
ejpam-5751	13	15	phenomena	phenomenon	NOUN
ejpam-5751	13	16	such	such	ADJ
ejpam-5751	13	17	as	as	ADP
ejpam-5751	13	18	the	the	DET
ejpam-5751	13	19	curie	curie	PROPN
ejpam-5751	13	20	temperature	temperature	NOUN
ejpam-5751	13	21	,	,	PUNCT
ejpam-5751	13	22	which	which	PRON
ejpam-5751	13	23	represents	represent	VERB
ejpam-5751	13	24	the	the	DET
ejpam-5751	13	25	transition	transition	NOUN
ejpam-5751	13	26	from	from	ADP
ejpam-5751	13	27	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	13	28	to	to	ADP
ejpam-5751	13	29	paramagnetic	paramagnetic	ADJ
ejpam-5751	13	30	behavior	behavior	NOUN
ejpam-5751	13	31	[	[	X
ejpam-5751	13	32	3	3	NUM
ejpam-5751	13	33	,	,	PUNCT
ejpam-5751	13	34	4	4	NUM
ejpam-5751	13	35	]	]	PUNCT
ejpam-5751	13	36	.	.	PUNCT
ejpam-5751	14	1	∗corresponding	∗corresponde	VERB
ejpam-5751	14	2	author	author	NOUN
ejpam-5751	14	3	.	.	PUNCT
ejpam-5751	15	1	doi	doi	NOUN
ejpam-5751	15	2	:	:	PUNCT
ejpam-5751	15	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5751	https://doi.org/10.29020/nybg.ejpam.v18i1.5751	ADJ
ejpam-5751	15	4	email	email	NOUN
ejpam-5751	15	5	addresses	address	VERB
ejpam-5751	15	6	:	:	PUNCT
ejpam-5751	15	7	w.mohammed@uoh.edu.sa	w.mohammed@uoh.edu.sa	PROPN
ejpam-5751	15	8	(	(	PUNCT
ejpam-5751	15	9	w.	w.	PROPN
ejpam-5751	15	10	w.	w.	PROPN
ejpam-5751	15	11	mohammed	mohammed	PROPN
ejpam-5751	15	12	)	)	PUNCT
ejpam-5751	15	13	,	,	PUNCT
ejpam-5751	15	14	n.iqbal@uoh.edu.sa	n.iqbal@uoh.edu.sa	PROPN
ejpam-5751	16	1	(	(	PUNCT
ejpam-5751	16	2	n.	n.	PROPN
ejpam-5751	16	3	iqbal	iqbal	PROPN
ejpam-5751	16	4	)	)	PUNCT
ejpam-5751	16	5	,	,	PUNCT
ejpam-5751	16	6	wwelhadad@gmail.com	wwelhadad@gmail.com	X
ejpam-5751	17	1	(	(	PUNCT
ejpam-5751	17	2	h.	h.	PROPN
ejpam-5751	17	3	m.	m.	PROPN
ejpam-5751	17	4	alshammari	alshammari	PROPN
ejpam-5751	17	5	)	)	PUNCT
ejpam-5751	17	6	,	,	PUNCT
ejpam-5751	17	7	moh.algolam@uoh.edu.sa	moh.algolam@uoh.edu.sa	NOUN
ejpam-5751	17	8	(	(	PUNCT
ejpam-5751	17	9	m.	m.	PROPN
ejpam-5751	17	10	s.	s.	PROPN
ejpam-5751	17	11	algolam	algolam	PROPN
ejpam-5751	17	12	)	)	PUNCT
ejpam-5751	17	13	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5751	17	14	1	1	NUM
ejpam-5751	17	15	copyright	copyright	NOUN
ejpam-5751	17	16	:	:	PUNCT
ejpam-5751	17	17	©	©	PROPN
ejpam-5751	17	18	2025	2025	NUM
ejpam-5751	17	19	the	the	DET
ejpam-5751	17	20	author(s	author(s	NOUN
ejpam-5751	17	21	)	)	PUNCT
ejpam-5751	17	22	.	.	PUNCT
ejpam-5751	18	1	(	(	PUNCT
ejpam-5751	18	2	cc	cc	NOUN
ejpam-5751	18	3	by	by	ADP
ejpam-5751	18	4	-	-	PUNCT
ejpam-5751	18	5	nc	nc	PROPN
ejpam-5751	18	6	4.0	4.0	NUM
ejpam-5751	18	7	)	)	PUNCT
ejpam-5751	18	8	w.	w.	PROPN
ejpam-5751	18	9	w.	w.	PROPN
ejpam-5751	18	10	mohammed	mohammed	PROPN
ejpam-5751	18	11	et	et	PROPN
ejpam-5751	18	12	al	al	PROPN
ejpam-5751	18	13	.	.	PUNCT
ejpam-5751	18	14	/	/	SYM
ejpam-5751	18	15	eur	eur	PROPN
ejpam-5751	18	16	.	.	PUNCT
ejpam-5751	19	1	j.	j.	PROPN
ejpam-5751	19	2	pure	pure	PROPN
ejpam-5751	19	3	appl	appl	PROPN
ejpam-5751	19	4	.	.	PROPN
ejpam-5751	19	5	math	math	PROPN
ejpam-5751	19	6	,	,	PUNCT
ejpam-5751	19	7	18	18	NUM
ejpam-5751	19	8	(	(	PUNCT
ejpam-5751	19	9	1	1	NUM
ejpam-5751	19	10	)	)	PUNCT
ejpam-5751	19	11	(	(	PUNCT
ejpam-5751	19	12	2025	2025	NUM
ejpam-5751	19	13	)	)	PUNCT
ejpam-5751	19	14	,	,	PUNCT
ejpam-5751	19	15	5751	5751	NUM
ejpam-5751	19	16	2	2	NUM
ejpam-5751	19	17	of	of	ADP
ejpam-5751	19	18	15	15	NUM
ejpam-5751	19	19	on	on	ADP
ejpam-5751	19	20	the	the	DET
ejpam-5751	19	21	other	other	ADJ
ejpam-5751	19	22	side	side	NOUN
ejpam-5751	19	23	,	,	PUNCT
ejpam-5751	19	24	random	random	ADJ
ejpam-5751	19	25	fluctuations	fluctuation	NOUN
ejpam-5751	19	26	play	play	VERB
ejpam-5751	19	27	a	a	DET
ejpam-5751	19	28	crucial	crucial	ADJ
ejpam-5751	19	29	role	role	NOUN
ejpam-5751	19	30	in	in	ADP
ejpam-5751	19	31	the	the	DET
ejpam-5751	19	32	behavior	behavior	NOUN
ejpam-5751	19	33	of	of	ADP
ejpam-5751	19	34	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	19	35	materials	material	NOUN
ejpam-5751	19	36	as	as	SCONJ
ejpam-5751	19	37	described	describe	VERB
ejpam-5751	19	38	by	by	ADP
ejpam-5751	19	39	the	the	DET
ejpam-5751	19	40	heisenberg	heisenberg	PROPN
ejpam-5751	19	41	ferromagnetic	ferromagnetic	PROPN
ejpam-5751	19	42	equation	equation	NOUN
ejpam-5751	19	43	.	.	PUNCT
ejpam-5751	20	1	these	these	DET
ejpam-5751	20	2	fluctuations	fluctuation	NOUN
ejpam-5751	20	3	arise	arise	VERB
ejpam-5751	20	4	from	from	ADP
ejpam-5751	20	5	the	the	DET
ejpam-5751	20	6	probabilistic	probabilistic	ADJ
ejpam-5751	20	7	nature	nature	NOUN
ejpam-5751	20	8	of	of	ADP
ejpam-5751	20	9	quantum	quantum	ADJ
ejpam-5751	20	10	mechanics	mechanic	NOUN
ejpam-5751	20	11	and	and	CCONJ
ejpam-5751	20	12	lead	lead	VERB
ejpam-5751	20	13	to	to	ADP
ejpam-5751	20	14	variations	variation	NOUN
ejpam-5751	20	15	in	in	ADP
ejpam-5751	20	16	the	the	DET
ejpam-5751	20	17	alignment	alignment	NOUN
ejpam-5751	20	18	of	of	ADP
ejpam-5751	20	19	atomic	atomic	ADJ
ejpam-5751	20	20	magnetic	magnetic	ADJ
ejpam-5751	20	21	moments	moment	NOUN
ejpam-5751	20	22	,	,	PUNCT
ejpam-5751	20	23	both	both	PRON
ejpam-5751	20	24	in	in	ADP
ejpam-5751	20	25	the	the	DET
ejpam-5751	20	26	absence	absence	NOUN
ejpam-5751	20	27	and	and	CCONJ
ejpam-5751	20	28	presence	presence	NOUN
ejpam-5751	20	29	of	of	ADP
ejpam-5751	20	30	an	an	DET
ejpam-5751	20	31	external	external	ADJ
ejpam-5751	20	32	magnetic	magnetic	ADJ
ejpam-5751	20	33	field	field	NOUN
ejpam-5751	20	34	.	.	PUNCT
ejpam-5751	21	1	this	this	PRON
ejpam-5751	21	2	means	mean	VERB
ejpam-5751	21	3	that	that	SCONJ
ejpam-5751	21	4	even	even	ADV
ejpam-5751	21	5	when	when	SCONJ
ejpam-5751	21	6	the	the	DET
ejpam-5751	21	7	system	system	NOUN
ejpam-5751	21	8	is	be	AUX
ejpam-5751	21	9	in	in	ADP
ejpam-5751	21	10	its	its	PRON
ejpam-5751	21	11	lowest	low	ADJ
ejpam-5751	21	12	energy	energy	NOUN
ejpam-5751	21	13	state	state	NOUN
ejpam-5751	21	14	,	,	PUNCT
ejpam-5751	21	15	there	there	PRON
ejpam-5751	21	16	will	will	AUX
ejpam-5751	21	17	still	still	ADV
ejpam-5751	21	18	be	be	AUX
ejpam-5751	21	19	some	some	DET
ejpam-5751	21	20	degree	degree	NOUN
ejpam-5751	21	21	of	of	ADP
ejpam-5751	21	22	variation	variation	NOUN
ejpam-5751	21	23	in	in	ADP
ejpam-5751	21	24	the	the	DET
ejpam-5751	21	25	magnetic	magnetic	ADJ
ejpam-5751	21	26	moments	moment	NOUN
ejpam-5751	21	27	’	'	PUNCT
ejpam-5751	21	28	orientation	orientation	NOUN
ejpam-5751	21	29	.	.	PUNCT
ejpam-5751	22	1	these	these	DET
ejpam-5751	22	2	fluctuations	fluctuation	NOUN
ejpam-5751	22	3	can	can	AUX
ejpam-5751	22	4	give	give	VERB
ejpam-5751	22	5	rise	rise	NOUN
ejpam-5751	22	6	to	to	ADP
ejpam-5751	22	7	interesting	interesting	ADJ
ejpam-5751	22	8	phenomena	phenomenon	NOUN
ejpam-5751	22	9	,	,	PUNCT
ejpam-5751	22	10	such	such	ADJ
ejpam-5751	22	11	as	as	ADP
ejpam-5751	22	12	spontaneous	spontaneous	ADJ
ejpam-5751	22	13	magnetization	magnetization	NOUN
ejpam-5751	22	14	and	and	CCONJ
ejpam-5751	22	15	the	the	DET
ejpam-5751	22	16	formation	formation	NOUN
ejpam-5751	22	17	of	of	ADP
ejpam-5751	22	18	magnetic	magnetic	ADJ
ejpam-5751	22	19	domains	domain	NOUN
ejpam-5751	22	20	.	.	PUNCT
ejpam-5751	23	1	it	it	PRON
ejpam-5751	23	2	seems	seem	VERB
ejpam-5751	23	3	more	more	ADV
ejpam-5751	23	4	relevant	relevant	ADJ
ejpam-5751	23	5	here	here	ADV
ejpam-5751	23	6	the	the	DET
ejpam-5751	23	7	stochastic	stochastic	ADJ
ejpam-5751	23	8	heisenberg	heisenberg	PROPN
ejpam-5751	23	9	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	23	10	equation	equation	NOUN
ejpam-5751	23	11	(	(	PUNCT
ejpam-5751	23	12	shfe	shfe	PROPN
ejpam-5751	23	13	)	)	PUNCT
ejpam-5751	23	14	is	be	AUX
ejpam-5751	23	15	taken	take	VERB
ejpam-5751	23	16	into	into	ADP
ejpam-5751	23	17	consideration	consideration	NOUN
ejpam-5751	23	18	as	as	SCONJ
ejpam-5751	23	19	follows	follow	VERB
ejpam-5751	23	20	:	:	PUNCT
ejpam-5751	23	21	idu	idu	VERB
ejpam-5751	24	1	+	+	CCONJ
ejpam-5751	25	1	[	[	X
ejpam-5751	25	2	ρ1uxx	ρ1uxx	PROPN
ejpam-5751	25	3	+	+	CCONJ
ejpam-5751	25	4	ρ2uyy	ρ2uyy	ADJ
ejpam-5751	25	5	+	+	CCONJ
ejpam-5751	25	6	ρ3uxy	ρ3uxy	NUM
ejpam-5751	25	7	−	−	VERB
ejpam-5751	25	8	ρ4	ρ4	ADV
ejpam-5751	25	9	|u|2	|u|2	PROPN
ejpam-5751	25	10	u	u	X
ejpam-5751	25	11	]	]	X
ejpam-5751	25	12	dt	dt	X
ejpam-5751	25	13	=	=	SYM
ejpam-5751	25	14	iνudβ	iνudβ	PROPN
ejpam-5751	25	15	,	,	PUNCT
ejpam-5751	25	16	(	(	PUNCT
ejpam-5751	25	17	1	1	X
ejpam-5751	25	18	)	)	PUNCT
ejpam-5751	25	19	where	where	SCONJ
ejpam-5751	25	20	u	u	NOUN
ejpam-5751	25	21	is	be	AUX
ejpam-5751	25	22	a	a	DET
ejpam-5751	25	23	stochastic	stochastic	ADJ
ejpam-5751	25	24	complex	complex	ADJ
ejpam-5751	25	25	function	function	NOUN
ejpam-5751	25	26	of	of	ADP
ejpam-5751	25	27	the	the	DET
ejpam-5751	25	28	variables	variable	NOUN
ejpam-5751	25	29	t	t	PROPN
ejpam-5751	25	30	,	,	PUNCT
ejpam-5751	25	31	x	x	X
ejpam-5751	25	32	and	and	CCONJ
ejpam-5751	25	33	y	y	PROPN
ejpam-5751	25	34	;	;	PUNCT
ejpam-5751	25	35	ν	ν	NOUN
ejpam-5751	25	36	is	be	AUX
ejpam-5751	25	37	the	the	DET
ejpam-5751	25	38	amplitude	amplitude	NOUN
ejpam-5751	25	39	of	of	ADP
ejpam-5751	25	40	noise	noise	NOUN
ejpam-5751	25	41	and	and	CCONJ
ejpam-5751	25	42	β(t	β(t	NOUN
ejpam-5751	25	43	)	)	PUNCT
ejpam-5751	25	44	is	be	AUX
ejpam-5751	25	45	brownian	brownian	ADJ
ejpam-5751	25	46	motion	motion	NOUN
ejpam-5751	25	47	in	in	ADP
ejpam-5751	25	48	one	one	NUM
ejpam-5751	25	49	variable	variable	ADJ
ejpam-5751	25	50	t	t	NOUN
ejpam-5751	25	51	;	;	PUNCT
ejpam-5751	25	52	ρ2	ρ2	NOUN
ejpam-5751	25	53	,	,	PUNCT
ejpam-5751	25	54	ρ2	ρ2	NOUN
ejpam-5751	25	55	,	,	PUNCT
ejpam-5751	25	56	ρ3	ρ3	NOUN
ejpam-5751	25	57	and	and	CCONJ
ejpam-5751	25	58	ρ4	ρ4	ADV
ejpam-5751	25	59	are	be	AUX
ejpam-5751	25	60	real	real	ADJ
ejpam-5751	25	61	functions	function	NOUN
ejpam-5751	25	62	of	of	ADP
ejpam-5751	25	63	the	the	DET
ejpam-5751	25	64	variable	variable	ADJ
ejpam-5751	25	65	t	t	NOUN
ejpam-5751	25	66	and	and	CCONJ
ejpam-5751	25	67	they	they	PRON
ejpam-5751	25	68	are	be	AUX
ejpam-5751	25	69	defined	define	VERB
ejpam-5751	25	70	as	as	ADP
ejpam-5751	25	71	ρ1	ρ1	NOUN
ejpam-5751	25	72	=	=	SYM
ejpam-5751	25	73	λ4(θ	λ4(θ	SYM
ejpam-5751	25	74	+	+	NUM
ejpam-5751	25	75	θ2	θ2	PROPN
ejpam-5751	25	76	)	)	PUNCT
ejpam-5751	25	77	,	,	PUNCT
ejpam-5751	25	78	ρ2	ρ2	NOUN
ejpam-5751	25	79	=	=	SYM
ejpam-5751	25	80	λ4(θ1	λ4(θ1	X
ejpam-5751	25	81	+	+	NUM
ejpam-5751	25	82	θ2	θ2	PROPN
ejpam-5751	25	83	)	)	PUNCT
ejpam-5751	25	84	,	,	PUNCT
ejpam-5751	25	85	ρ3	ρ3	NOUN
ejpam-5751	25	86	=	=	SYM
ejpam-5751	25	87	2λ4θ2	2λ4θ2	NUM
ejpam-5751	25	88	,	,	PUNCT
ejpam-5751	25	89	ρ4	ρ4	ADV
ejpam-5751	25	90	=	=	SYM
ejpam-5751	25	91	2λ4k	2λ4k	NUM
ejpam-5751	25	92	,	,	PUNCT
ejpam-5751	25	93	where	where	SCONJ
ejpam-5751	25	94	λ	λ	PROPN
ejpam-5751	25	95	is	be	AUX
ejpam-5751	25	96	the	the	DET
ejpam-5751	25	97	lattice	lattice	PROPN
ejpam-5751	25	98	parameter	parameter	NOUN
ejpam-5751	25	99	with	with	ADP
ejpam-5751	25	100	the	the	DET
ejpam-5751	25	101	interaction	interaction	NOUN
ejpam-5751	25	102	coefficients	coefficient	NOUN
ejpam-5751	25	103	θ	θ	PROPN
ejpam-5751	25	104	,	,	PUNCT
ejpam-5751	25	105	θ1	θ1	NOUN
ejpam-5751	25	106	,	,	PUNCT
ejpam-5751	25	107	θ2	θ2	PROPN
ejpam-5751	25	108	,	,	PUNCT
ejpam-5751	25	109	while	while	SCONJ
ejpam-5751	25	110	k	k	PROPN
ejpam-5751	25	111	is	be	AUX
ejpam-5751	25	112	the	the	DET
ejpam-5751	25	113	anisotropic	anisotropic	NOUN
ejpam-5751	25	114	parameter	parameter	NOUN
ejpam-5751	25	115	.	.	PUNCT
ejpam-5751	26	1	because	because	SCONJ
ejpam-5751	26	2	of	of	ADP
ejpam-5751	26	3	the	the	DET
ejpam-5751	26	4	relevance	relevance	NOUN
ejpam-5751	26	5	of	of	ADP
ejpam-5751	26	6	heisenberg	heisenberg	PROPN
ejpam-5751	26	7	ferromagnetic	ferromagnetic	PROPN
ejpam-5751	26	8	equation	equation	NOUN
ejpam-5751	26	9	,	,	PUNCT
ejpam-5751	26	10	many	many	ADJ
ejpam-5751	26	11	researchers	researcher	NOUN
ejpam-5751	26	12	have	have	AUX
ejpam-5751	26	13	acquired	acquire	VERB
ejpam-5751	26	14	the	the	DET
ejpam-5751	26	15	exact	exact	ADJ
ejpam-5751	26	16	solutions	solution	NOUN
ejpam-5751	26	17	for	for	ADP
ejpam-5751	26	18	this	this	DET
ejpam-5751	26	19	equation	equation	NOUN
ejpam-5751	26	20	without	without	ADP
ejpam-5751	26	21	stochastic	stochastic	ADJ
ejpam-5751	26	22	term	term	NOUN
ejpam-5751	26	23	by	by	ADP
ejpam-5751	26	24	employing	employ	VERB
ejpam-5751	26	25	different	different	ADJ
ejpam-5751	26	26	methods	method	NOUN
ejpam-5751	26	27	such	such	ADJ
ejpam-5751	26	28	as	as	ADP
ejpam-5751	26	29	f	f	NOUN
ejpam-5751	26	30	-	-	PUNCT
ejpam-5751	26	31	expansion	expansion	NOUN
ejpam-5751	26	32	method	method	NOUN
ejpam-5751	26	33	[	[	X
ejpam-5751	26	34	6	6	NUM
ejpam-5751	26	35	]	]	PUNCT
ejpam-5751	26	36	,	,	PUNCT
ejpam-5751	26	37	generalized	generalize	VERB
ejpam-5751	26	38	riccati	riccati	NOUN
ejpam-5751	26	39	mapping	mapping	NOUN
ejpam-5751	27	1	[	[	X
ejpam-5751	27	2	9	9	NUM
ejpam-5751	27	3	]	]	PUNCT
ejpam-5751	27	4	,	,	PUNCT
ejpam-5751	27	5	modified	modify	VERB
ejpam-5751	27	6	exp	exp	NOUN
ejpam-5751	27	7	-	-	PUNCT
ejpam-5751	27	8	function	function	NOUN
ejpam-5751	27	9	expansion	expansion	NOUN
ejpam-5751	28	1	[	[	X
ejpam-5751	28	2	2	2	NUM
ejpam-5751	28	3	]	]	PUNCT
ejpam-5751	28	4	,	,	PUNCT
ejpam-5751	28	5	jacobi	jacobi	PROPN
ejpam-5751	28	6	elliptic	elliptic	ADJ
ejpam-5751	28	7	functions	function	NOUN
ejpam-5751	28	8	[	[	X
ejpam-5751	28	9	12	12	NUM
ejpam-5751	28	10	]	]	PUNCT
ejpam-5751	28	11	,	,	PUNCT
ejpam-5751	28	12	auxiliary	auxiliary	ADJ
ejpam-5751	28	13	ordinary	ordinary	ADJ
ejpam-5751	28	14	differential	differential	ADJ
ejpam-5751	28	15	equation	equation	NOUN
ejpam-5751	28	16	[	[	X
ejpam-5751	28	17	13	13	NUM
ejpam-5751	28	18	]	]	PUNCT
ejpam-5751	28	19	,	,	PUNCT
ejpam-5751	28	20	sub	sub	ADJ
ejpam-5751	28	21	-	-	ADJ
ejpam-5751	28	22	ode	ode	ADJ
ejpam-5751	28	23	[	[	X
ejpam-5751	28	24	11	11	NUM
ejpam-5751	28	25	]	]	PUNCT
ejpam-5751	28	26	,	,	PUNCT
ejpam-5751	28	27	hirota	hirota	PROPN
ejpam-5751	28	28	bilinear	bilinear	NOUN
ejpam-5751	28	29	[	[	X
ejpam-5751	28	30	5	5	NUM
ejpam-5751	28	31	,	,	PUNCT
ejpam-5751	28	32	14	14	NUM
ejpam-5751	28	33	]	]	PUNCT
ejpam-5751	28	34	,	,	PUNCT
ejpam-5751	28	35	and	and	CCONJ
ejpam-5751	28	36	sine	sine	ADJ
ejpam-5751	28	37	-	-	PUNCT
ejpam-5751	28	38	gordon	gordon	NOUN
ejpam-5751	28	39	expansion	expansion	NOUN
ejpam-5751	28	40	and	and	CCONJ
ejpam-5751	28	41	the	the	DET
ejpam-5751	28	42	modified	modify	VERB
ejpam-5751	28	43	exp(−φ(ξ))-expansion	exp(−φ(ξ))-expansion	NOUN
ejpam-5751	28	44	function	function	NOUN
ejpam-5751	28	45	methods	method	NOUN
ejpam-5751	28	46	[	[	X
ejpam-5751	28	47	10	10	NUM
ejpam-5751	28	48	]	]	PUNCT
ejpam-5751	28	49	.	.	PUNCT
ejpam-5751	29	1	however	however	ADV
ejpam-5751	29	2	,	,	PUNCT
ejpam-5751	29	3	many	many	ADJ
ejpam-5751	29	4	authors	author	NOUN
ejpam-5751	29	5	have	have	AUX
ejpam-5751	29	6	studied	study	VERB
ejpam-5751	29	7	the	the	DET
ejpam-5751	29	8	shfe	shfe	NOUN
ejpam-5751	29	9	(	(	PUNCT
ejpam-5751	29	10	1	1	NUM
ejpam-5751	29	11	)	)	PUNCT
ejpam-5751	29	12	by	by	ADP
ejpam-5751	29	13	utilizing	utilize	VERB
ejpam-5751	29	14	different	different	ADJ
ejpam-5751	29	15	methods	method	NOUN
ejpam-5751	29	16	including	include	VERB
ejpam-5751	29	17	(	(	PUNCT
ejpam-5751	29	18	g′/g)-expansion	g′/g)-expansion	PROPN
ejpam-5751	29	19	method	method	NOUN
ejpam-5751	29	20	[	[	X
ejpam-5751	29	21	1	1	NUM
ejpam-5751	29	22	]	]	PUNCT
ejpam-5751	29	23	,	,	PUNCT
ejpam-5751	29	24	jacobi	jacobi	PROPN
ejpam-5751	29	25	elliptic	elliptic	ADJ
ejpam-5751	29	26	function	function	NOUN
ejpam-5751	29	27	method	method	NOUN
ejpam-5751	29	28	[	[	X
ejpam-5751	29	29	7	7	NUM
ejpam-5751	29	30	]	]	PUNCT
ejpam-5751	29	31	and	and	CCONJ
ejpam-5751	29	32	mapping	mapping	NOUN
ejpam-5751	29	33	method	method	NOUN
ejpam-5751	29	34	[	[	X
ejpam-5751	29	35	8	8	NUM
ejpam-5751	29	36	]	]	PUNCT
ejpam-5751	29	37	.	.	PUNCT
ejpam-5751	30	1	this	this	DET
ejpam-5751	30	2	work	work	NOUN
ejpam-5751	30	3	aims	aim	VERB
ejpam-5751	30	4	to	to	PART
ejpam-5751	30	5	obtain	obtain	VERB
ejpam-5751	30	6	accurate	accurate	ADJ
ejpam-5751	30	7	solutions	solution	NOUN
ejpam-5751	30	8	to	to	ADP
ejpam-5751	30	9	the	the	DET
ejpam-5751	30	10	shfe	shfe	PROPN
ejpam-5751	30	11	(	(	PUNCT
ejpam-5751	30	12	1	1	NUM
ejpam-5751	30	13	)	)	PUNCT
ejpam-5751	30	14	.	.	PUNCT
ejpam-5751	31	1	in	in	ADP
ejpam-5751	31	2	order	order	NOUN
ejpam-5751	31	3	to	to	PART
ejpam-5751	31	4	do	do	AUX
ejpam-5751	31	5	this	this	PRON
ejpam-5751	31	6	,	,	PUNCT
ejpam-5751	31	7	we	we	PRON
ejpam-5751	31	8	apply	apply	VERB
ejpam-5751	31	9	an	an	DET
ejpam-5751	31	10	appropriate	appropriate	ADJ
ejpam-5751	31	11	transformation	transformation	NOUN
ejpam-5751	31	12	to	to	PART
ejpam-5751	31	13	change	change	VERB
ejpam-5751	31	14	the	the	DET
ejpam-5751	31	15	shfe	shfe	NOUN
ejpam-5751	31	16	into	into	ADP
ejpam-5751	31	17	another	another	DET
ejpam-5751	31	18	hfe	hfe	PROPN
ejpam-5751	31	19	-	-	PUNCT
ejpam-5751	31	20	rvcs	rvcs	PROPN
ejpam-5751	31	21	.	.	PUNCT
ejpam-5751	32	1	following	follow	VERB
ejpam-5751	32	2	that	that	PRON
ejpam-5751	32	3	,	,	PUNCT
ejpam-5751	32	4	we	we	PRON
ejpam-5751	32	5	use	use	VERB
ejpam-5751	32	6	the	the	DET
ejpam-5751	32	7	jef	jef	PROPN
ejpam-5751	32	8	and	and	CCONJ
ejpam-5751	32	9	gremmethods	gremmethod	NOUN
ejpam-5751	32	10	to	to	PART
ejpam-5751	32	11	obtain	obtain	VERB
ejpam-5751	32	12	the	the	DET
ejpam-5751	32	13	solutions	solution	NOUN
ejpam-5751	32	14	for	for	ADP
ejpam-5751	32	15	hfe	hfe	PROPN
ejpam-5751	32	16	-	-	PUNCT
ejpam-5751	32	17	rvcs	rvcs	PROPN
ejpam-5751	32	18	.	.	PUNCT
ejpam-5751	33	1	finally	finally	ADV
ejpam-5751	33	2	,	,	PUNCT
ejpam-5751	33	3	we	we	PRON
ejpam-5751	33	4	may	may	AUX
ejpam-5751	33	5	obtain	obtain	VERB
ejpam-5751	33	6	the	the	DET
ejpam-5751	33	7	stochastic	stochastic	ADJ
ejpam-5751	33	8	solutions	solution	NOUN
ejpam-5751	33	9	of	of	ADP
ejpam-5751	33	10	shfe	shfe	NOUN
ejpam-5751	33	11	by	by	ADP
ejpam-5751	33	12	applying	apply	VERB
ejpam-5751	33	13	the	the	DET
ejpam-5751	33	14	transformation	transformation	NOUN
ejpam-5751	33	15	that	that	PRON
ejpam-5751	33	16	was	be	AUX
ejpam-5751	33	17	applied	apply	VERB
ejpam-5751	33	18	.	.	PUNCT
ejpam-5751	34	1	because	because	SCONJ
ejpam-5751	34	2	of	of	ADP
ejpam-5751	34	3	the	the	DET
ejpam-5751	34	4	significance	significance	NOUN
ejpam-5751	34	5	of	of	ADP
ejpam-5751	34	6	the	the	DET
ejpam-5751	34	7	heisenberg	heisenberg	PROPN
ejpam-5751	34	8	ferromagnetic	ferromagnetic	PROPN
ejpam-5751	34	9	equation	equation	NOUN
ejpam-5751	34	10	(	(	PUNCT
ejpam-5751	34	11	1	1	NUM
ejpam-5751	34	12	)	)	PUNCT
ejpam-5751	34	13	in	in	ADP
ejpam-5751	34	14	the	the	DET
ejpam-5751	34	15	behavior	behavior	NOUN
ejpam-5751	34	16	of	of	ADP
ejpam-5751	34	17	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	34	18	materials	material	NOUN
ejpam-5751	34	19	,	,	PUNCT
ejpam-5751	34	20	these	these	PRON
ejpam-5751	34	21	obtained	obtain	VERB
ejpam-5751	34	22	solutions	solution	NOUN
ejpam-5751	34	23	are	be	AUX
ejpam-5751	34	24	essential	essential	ADJ
ejpam-5751	34	25	for	for	ADP
ejpam-5751	34	26	comprehending	comprehend	VERB
ejpam-5751	34	27	a	a	DET
ejpam-5751	34	28	number	number	NOUN
ejpam-5751	34	29	of	of	ADP
ejpam-5751	34	30	challenging	challenge	VERB
ejpam-5751	34	31	physical	physical	ADJ
ejpam-5751	34	32	processes	process	NOUN
ejpam-5751	34	33	.	.	PUNCT
ejpam-5751	35	1	using	use	VERB
ejpam-5751	35	2	matlab	matlab	PROPN
ejpam-5751	35	3	tools	tool	NOUN
ejpam-5751	35	4	,	,	PUNCT
ejpam-5751	35	5	we	we	PRON
ejpam-5751	35	6	present	present	VERB
ejpam-5751	35	7	some	some	DET
ejpam-5751	35	8	graphics	graphic	NOUN
ejpam-5751	35	9	to	to	PART
ejpam-5751	35	10	illustrate	illustrate	VERB
ejpam-5751	35	11	the	the	DET
ejpam-5751	35	12	impact	impact	NOUN
ejpam-5751	35	13	of	of	ADP
ejpam-5751	35	14	the	the	DET
ejpam-5751	35	15	stochastic	stochastic	ADJ
ejpam-5751	35	16	term	term	NOUN
ejpam-5751	35	17	.	.	PUNCT
ejpam-5751	36	1	the	the	DET
ejpam-5751	36	2	rest	rest	NOUN
ejpam-5751	36	3	of	of	ADP
ejpam-5751	36	4	this	this	DET
ejpam-5751	36	5	paper	paper	NOUN
ejpam-5751	36	6	is	be	AUX
ejpam-5751	36	7	organized	organize	VERB
ejpam-5751	36	8	as	as	SCONJ
ejpam-5751	36	9	follows	follow	VERB
ejpam-5751	36	10	:	:	PUNCT
ejpam-5751	36	11	in	in	ADP
ejpam-5751	36	12	section	section	NOUN
ejpam-5751	36	13	2	2	NUM
ejpam-5751	36	14	,	,	PUNCT
ejpam-5751	36	15	we	we	PRON
ejpam-5751	36	16	derive	derive	VERB
ejpam-5751	36	17	hfe	hfe	PROPN
ejpam-5751	36	18	-	-	PUNCT
ejpam-5751	36	19	rvcs	rvcs	PROPN
ejpam-5751	36	20	from	from	ADP
ejpam-5751	36	21	shfe	shfe	PROPN
ejpam-5751	36	22	(	(	PUNCT
ejpam-5751	36	23	1	1	NUM
ejpam-5751	36	24	)	)	PUNCT
ejpam-5751	36	25	and	and	CCONJ
ejpam-5751	36	26	determine	determine	VERB
ejpam-5751	36	27	the	the	DET
ejpam-5751	36	28	solutions	solution	NOUN
ejpam-5751	36	29	of	of	ADP
ejpam-5751	36	30	hfe	hfe	PROPN
ejpam-5751	36	31	-	-	PUNCT
ejpam-5751	36	32	rvcs	rvcs	PROPN
ejpam-5751	36	33	.	.	PUNCT
ejpam-5751	37	1	in	in	ADP
ejpam-5751	37	2	section	section	NOUN
ejpam-5751	37	3	3	3	NUM
ejpam-5751	37	4	,	,	PUNCT
ejpam-5751	37	5	we	we	PRON
ejpam-5751	37	6	obtain	obtain	VERB
ejpam-5751	37	7	the	the	DET
ejpam-5751	37	8	solutions	solution	NOUN
ejpam-5751	37	9	to	to	PART
ejpam-5751	37	10	shfe	shfe	VERB
ejpam-5751	37	11	(	(	PUNCT
ejpam-5751	37	12	1	1	NUM
ejpam-5751	37	13	)	)	PUNCT
ejpam-5751	37	14	.	.	PUNCT
ejpam-5751	38	1	we	we	PRON
ejpam-5751	38	2	discuss	discuss	VERB
ejpam-5751	38	3	how	how	SCONJ
ejpam-5751	38	4	brownian	brownian	ADJ
ejpam-5751	38	5	motion	motion	NOUN
ejpam-5751	38	6	affects	affect	VERB
ejpam-5751	38	7	the	the	DET
ejpam-5751	38	8	solutions	solution	NOUN
ejpam-5751	38	9	in	in	ADP
ejpam-5751	38	10	section	section	NOUN
ejpam-5751	38	11	4	4	NUM
ejpam-5751	38	12	.	.	PUNCT
ejpam-5751	39	1	lastly	lastly	ADV
ejpam-5751	39	2	,	,	PUNCT
ejpam-5751	39	3	we	we	PRON
ejpam-5751	39	4	present	present	VERB
ejpam-5751	39	5	the	the	DET
ejpam-5751	39	6	conclusions	conclusion	NOUN
ejpam-5751	39	7	.	.	PUNCT
ejpam-5751	40	1	w.	w.	PROPN
ejpam-5751	40	2	w.	w.	PROPN
ejpam-5751	40	3	mohammed	mohammed	PROPN
ejpam-5751	40	4	et	et	PROPN
ejpam-5751	40	5	al	al	PROPN
ejpam-5751	40	6	.	.	PUNCT
ejpam-5751	40	7	/	/	SYM
ejpam-5751	40	8	eur	eur	PROPN
ejpam-5751	40	9	.	.	PUNCT
ejpam-5751	41	1	j.	j.	PROPN
ejpam-5751	41	2	pure	pure	PROPN
ejpam-5751	41	3	appl	appl	PROPN
ejpam-5751	41	4	.	.	PROPN
ejpam-5751	41	5	math	math	PROPN
ejpam-5751	41	6	,	,	PUNCT
ejpam-5751	41	7	18	18	NUM
ejpam-5751	41	8	(	(	PUNCT
ejpam-5751	41	9	1	1	NUM
ejpam-5751	41	10	)	)	PUNCT
ejpam-5751	41	11	(	(	PUNCT
ejpam-5751	41	12	2025	2025	NUM
ejpam-5751	41	13	)	)	PUNCT
ejpam-5751	41	14	,	,	PUNCT
ejpam-5751	41	15	5751	5751	NUM
ejpam-5751	41	16	3	3	NUM
ejpam-5751	41	17	of	of	ADP
ejpam-5751	41	18	15	15	NUM
ejpam-5751	41	19	2	2	NUM
ejpam-5751	41	20	.	.	PUNCT
ejpam-5751	42	1	hfe	hfe	PROPN
ejpam-5751	42	2	-	-	PUNCT
ejpam-5751	42	3	rvcs	rvcs	PROPN
ejpam-5751	42	4	and	and	CCONJ
ejpam-5751	42	5	its	its	PRON
ejpam-5751	42	6	solutions	solution	NOUN
ejpam-5751	42	7	in	in	ADP
ejpam-5751	42	8	this	this	DET
ejpam-5751	42	9	section	section	NOUN
ejpam-5751	42	10	,	,	PUNCT
ejpam-5751	42	11	we	we	PRON
ejpam-5751	42	12	derive	derive	VERB
ejpam-5751	42	13	the	the	DET
ejpam-5751	42	14	hfe	hfe	PROPN
ejpam-5751	42	15	-	-	PUNCT
ejpam-5751	42	16	rvcs	rvcs	PROPN
ejpam-5751	42	17	.	.	PUNCT
ejpam-5751	43	1	by	by	ADP
ejpam-5751	43	2	applying	apply	VERB
ejpam-5751	43	3	the	the	DET
ejpam-5751	43	4	transformation	transformation	NOUN
ejpam-5751	43	5	u(t	u(t	NOUN
ejpam-5751	43	6	,	,	PUNCT
ejpam-5751	43	7	x	x	NOUN
ejpam-5751	43	8	,	,	PUNCT
ejpam-5751	43	9	y	y	PROPN
ejpam-5751	43	10	)	)	PUNCT
ejpam-5751	43	11	=	=	SYM
ejpam-5751	43	12	w(t	w(t	PROPN
ejpam-5751	43	13	,	,	PUNCT
ejpam-5751	43	14	x	x	NOUN
ejpam-5751	43	15	,	,	PUNCT
ejpam-5751	43	16	y	y	NOUN
ejpam-5751	43	17	)	)	PUNCT
ejpam-5751	43	18	exp[iφ(t	exp[iφ(t	ADJ
ejpam-5751	43	19	,	,	PUNCT
ejpam-5751	43	20	x	x	NOUN
ejpam-5751	43	21	,	,	PUNCT
ejpam-5751	43	22	y	y	PROPN
ejpam-5751	43	23	)	)	PUNCT
ejpam-5751	44	1	+	+	CCONJ
ejpam-5751	44	2	νβ(t)−	νβ(t)−	NOUN
ejpam-5751	44	3	1	1	NUM
ejpam-5751	44	4	2	2	NUM
ejpam-5751	44	5	ν2	ν2	NOUN
ejpam-5751	44	6	t	t	NOUN
ejpam-5751	44	7	]	]	PUNCT
ejpam-5751	44	8	,	,	PUNCT
ejpam-5751	44	9	(	(	PUNCT
ejpam-5751	44	10	2	2	X
ejpam-5751	44	11	)	)	PUNCT
ejpam-5751	44	12	we	we	PRON
ejpam-5751	44	13	get	get	VERB
ejpam-5751	44	14	hfe	hfe	PROPN
ejpam-5751	44	15	-	-	PUNCT
ejpam-5751	44	16	rvcs	rvcs	PROPN
ejpam-5751	44	17	as	as	SCONJ
ejpam-5751	44	18	follows	follow	VERB
ejpam-5751	44	19	iwt	iwt	PROPN
ejpam-5751	44	20	−wφt	−wφt	PUNCT
ejpam-5751	45	1	+	+	PUNCT
ejpam-5751	45	2	ρ1[wxx	ρ1[wxx	VERB
ejpam-5751	45	3	+	+	CCONJ
ejpam-5751	45	4	2iφxwx	2iφxwx	NUM
ejpam-5751	45	5	+	+	NUM
ejpam-5751	45	6	iφxxw	iφxxw	NOUN
ejpam-5751	45	7	−	−	PROPN
ejpam-5751	45	8	φ2	φ2	PROPN
ejpam-5751	45	9	xw	xw	PROPN
ejpam-5751	45	10	]	]	X
ejpam-5751	46	1	+	+	ADJ
ejpam-5751	46	2	ρ2[wyy	ρ2[wyy	PROPN
ejpam-5751	46	3	+	+	X
ejpam-5751	46	4	2iφywy	2iφywy	NUM
ejpam-5751	46	5	+	+	CCONJ
ejpam-5751	46	6	iφyyw	iφyyw	NOUN
ejpam-5751	46	7	−	−	PROPN
ejpam-5751	46	8	φ2	φ2	PROPN
ejpam-5751	46	9	yw	yw	PROPN
ejpam-5751	46	10	]	]	X
ejpam-5751	46	11	+	+	CCONJ
ejpam-5751	46	12	ρ3[wxy	ρ3[wxy	PROPN
ejpam-5751	46	13	+	+	CCONJ
ejpam-5751	46	14	iφxyw	iφxyw	ADJ
ejpam-5751	46	15	+	+	NOUN
ejpam-5751	46	16	iφxwy	iφxwy	NOUN
ejpam-5751	46	17	+	+	CCONJ
ejpam-5751	46	18	iφywx	iφywx	NOUN
ejpam-5751	46	19	−	−	PROPN
ejpam-5751	46	20	φxφyw]−a(t)w3	φxφyw]−a(t)w3	PROPN
ejpam-5751	46	21	=	=	SYM
ejpam-5751	46	22	0	0	NUM
ejpam-5751	46	23	,	,	PUNCT
ejpam-5751	46	24	(	(	PUNCT
ejpam-5751	46	25	3	3	X
ejpam-5751	46	26	)	)	PUNCT
ejpam-5751	46	27	where	where	SCONJ
ejpam-5751	46	28	we	we	PRON
ejpam-5751	46	29	applied	apply	VERB
ejpam-5751	46	30	the	the	DET
ejpam-5751	46	31	itô	itô	PROPN
ejpam-5751	46	32	derivatives	derivative	NOUN
ejpam-5751	46	33	,	,	PUNCT
ejpam-5751	46	34	a(t	a(t	NOUN
ejpam-5751	46	35	)	)	PUNCT
ejpam-5751	46	36	=	=	PUNCT
ejpam-5751	47	1	ρ4e	ρ4e	NOUN
ejpam-5751	47	2	2νβ(t)−ν2	2νβ(t)−ν2	NUM
ejpam-5751	47	3	t	t	PROPN
ejpam-5751	47	4	and	and	CCONJ
ejpam-5751	47	5	w	w	PROPN
ejpam-5751	47	6	is	be	AUX
ejpam-5751	47	7	a	a	DET
ejpam-5751	47	8	stochastic	stochastic	ADJ
ejpam-5751	47	9	real	real	ADJ
ejpam-5751	47	10	function	function	NOUN
ejpam-5751	47	11	.	.	PUNCT
ejpam-5751	48	1	2.1	2.1	NUM
ejpam-5751	48	2	.	.	PUNCT
ejpam-5751	48	3	grem	grem	NOUN
ejpam-5751	48	4	-	-	NOUN
ejpam-5751	48	5	method	method	VERB
ejpam-5751	48	6	the	the	DET
ejpam-5751	48	7	grem	grem	NOUN
ejpam-5751	48	8	-	-	PROPN
ejpam-5751	48	9	method	method	NOUN
ejpam-5751	48	10	described	describe	VERB
ejpam-5751	48	11	in	in	ADP
ejpam-5751	48	12	[	[	X
ejpam-5751	48	13	15	15	NUM
ejpam-5751	48	14	]	]	PUNCT
ejpam-5751	48	15	is	be	AUX
ejpam-5751	48	16	used	use	VERB
ejpam-5751	48	17	here	here	ADV
ejpam-5751	48	18	.	.	PUNCT
ejpam-5751	49	1	to	to	PART
ejpam-5751	49	2	attain	attain	VERB
ejpam-5751	49	3	the	the	DET
ejpam-5751	49	4	solutions	solution	NOUN
ejpam-5751	49	5	of	of	ADP
ejpam-5751	49	6	the	the	DET
ejpam-5751	49	7	hfe	hfe	PROPN
ejpam-5751	49	8	-	-	PUNCT
ejpam-5751	49	9	rvcs	rvcs	PROPN
ejpam-5751	49	10	(	(	PUNCT
ejpam-5751	49	11	3	3	NUM
ejpam-5751	49	12	)	)	PUNCT
ejpam-5751	49	13	,	,	PUNCT
ejpam-5751	49	14	we	we	PRON
ejpam-5751	49	15	suppose	suppose	VERB
ejpam-5751	49	16	the	the	DET
ejpam-5751	49	17	solutions	solution	NOUN
ejpam-5751	49	18	of	of	ADP
ejpam-5751	49	19	eq	eq	PROPN
ejpam-5751	49	20	.	.	PUNCT
ejpam-5751	50	1	(	(	PUNCT
ejpam-5751	50	2	3	3	X
ejpam-5751	50	3	)	)	PUNCT
ejpam-5751	50	4	in	in	ADP
ejpam-5751	50	5	the	the	DET
ejpam-5751	50	6	special	special	ADJ
ejpam-5751	50	7	forms	form	NOUN
ejpam-5751	50	8	:	:	PUNCT
ejpam-5751	50	9	w(t	w(t	PROPN
ejpam-5751	50	10	,	,	PUNCT
ejpam-5751	50	11	x	x	X
ejpam-5751	50	12	,	,	PUNCT
ejpam-5751	50	13	y	y	NOUN
ejpam-5751	50	14	)	)	PUNCT
ejpam-5751	50	15	=	=	SYM
ejpam-5751	50	16	n∑	n∑	PROPN
ejpam-5751	50	17	k=0	k=0	PROPN
ejpam-5751	50	18	αk(t)fk(µ	αk(t)fk(µ	PROPN
ejpam-5751	50	19	)	)	PUNCT
ejpam-5751	50	20	,	,	PUNCT
ejpam-5751	50	21	µ	µ	X
ejpam-5751	50	22	=	=	SYM
ejpam-5751	50	23	k1x+	k1x+	NOUN
ejpam-5751	50	24	k2y	k2y	PROPN
ejpam-5751	50	25	+	+	CCONJ
ejpam-5751	50	26	∫	∫	PROPN
ejpam-5751	50	27	t	t	PROPN
ejpam-5751	50	28	0	0	NUM
ejpam-5751	50	29	λ(τ)dτ	λ(τ)dτ	PROPN
ejpam-5751	50	30	,	,	PUNCT
ejpam-5751	50	31	(	(	PUNCT
ejpam-5751	50	32	4	4	NUM
ejpam-5751	50	33	)	)	PUNCT
ejpam-5751	50	34	and	and	CCONJ
ejpam-5751	50	35	φ(t	φ(t	PROPN
ejpam-5751	50	36	,	,	PUNCT
ejpam-5751	50	37	x	x	X
ejpam-5751	50	38	,	,	PUNCT
ejpam-5751	50	39	y	y	NOUN
ejpam-5751	50	40	)	)	PUNCT
ejpam-5751	50	41	=	=	PUNCT
ejpam-5751	51	1	ψ0(t	ψ0(t	NOUN
ejpam-5751	51	2	)	)	PUNCT
ejpam-5751	51	3	+	+	NUM
ejpam-5751	51	4	ψ1(t)x+	ψ1(t)x+	NOUN
ejpam-5751	51	5	ψ2(t)y	ψ2(t)y	NOUN
ejpam-5751	51	6	.	.	PUNCT
ejpam-5751	52	1	(	(	PUNCT
ejpam-5751	52	2	5	5	NUM
ejpam-5751	52	3	)	)	PUNCT
ejpam-5751	52	4	where	where	SCONJ
ejpam-5751	52	5	α0	α0	ADJ
ejpam-5751	52	6	,	,	PUNCT
ejpam-5751	52	7	α1	α1	PROPN
ejpam-5751	52	8	,	,	PUNCT
ejpam-5751	52	9	.....	.....	PUNCT
ejpam-5751	52	10	,	,	PUNCT
ejpam-5751	52	11	αm−1	αm−1	PROPN
ejpam-5751	52	12	,	,	PUNCT
ejpam-5751	52	13	αm	αm	NOUN
ejpam-5751	52	14	,	,	PUNCT
ejpam-5751	52	15	λ	λ	PROPN
ejpam-5751	52	16	,	,	PUNCT
ejpam-5751	52	17	ψ0	ψ0	ADJ
ejpam-5751	52	18	,	,	PUNCT
ejpam-5751	52	19	ψ1	ψ1	ADJ
ejpam-5751	52	20	,	,	PUNCT
ejpam-5751	52	21	and	and	CCONJ
ejpam-5751	52	22	ψ2	ψ2	NOUN
ejpam-5751	52	23	,	,	PUNCT
ejpam-5751	52	24	are	be	AUX
ejpam-5751	52	25	functions	function	NOUN
ejpam-5751	52	26	of	of	ADP
ejpam-5751	52	27	t	t	PROPN
ejpam-5751	52	28	and	and	CCONJ
ejpam-5751	52	29	αm	αm	NOUN
ejpam-5751	52	30	̸=	̸=	PROPN
ejpam-5751	52	31	0	0	NUM
ejpam-5751	52	32	,	,	PUNCT
ejpam-5751	52	33	and	and	CCONJ
ejpam-5751	52	34	f	f	PROPN
ejpam-5751	52	35	fulfills	fulfill	VERB
ejpam-5751	52	36	f	f	PROPN
ejpam-5751	52	37	′	′	NUM
ejpam-5751	52	38	=	=	PUNCT
ejpam-5751	52	39	sf2	sf2	PROPN
ejpam-5751	52	40	+	+	PROPN
ejpam-5751	52	41	rf	rf	PROPN
ejpam-5751	52	42	+	+	CCONJ
ejpam-5751	52	43	p	p	X
ejpam-5751	52	44	,	,	PUNCT
ejpam-5751	52	45	(	(	PUNCT
ejpam-5751	52	46	6	6	NUM
ejpam-5751	52	47	)	)	PUNCT
ejpam-5751	52	48	with	with	ADP
ejpam-5751	52	49	s	s	PROPN
ejpam-5751	52	50	,	,	PUNCT
ejpam-5751	52	51	r	r	NOUN
ejpam-5751	52	52	,	,	PUNCT
ejpam-5751	52	53	and	and	CCONJ
ejpam-5751	52	54	p	p	NOUN
ejpam-5751	52	55	are	be	AUX
ejpam-5751	52	56	constants	constant	NOUN
ejpam-5751	52	57	.	.	PUNCT
ejpam-5751	53	1	first	first	ADV
ejpam-5751	53	2	,	,	PUNCT
ejpam-5751	53	3	let	let	VERB
ejpam-5751	53	4	us	we	PRON
ejpam-5751	53	5	balance	balance	NOUN
ejpam-5751	53	6	wxx	wxx	VERB
ejpam-5751	53	7	with	with	ADP
ejpam-5751	53	8	w3	w3	PROPN
ejpam-5751	53	9	in	in	ADP
ejpam-5751	53	10	eq	eq	PROPN
ejpam-5751	53	11	.	.	PUNCT
ejpam-5751	54	1	(	(	PUNCT
ejpam-5751	54	2	3	3	X
ejpam-5751	54	3	)	)	PUNCT
ejpam-5751	54	4	in	in	ADP
ejpam-5751	54	5	order	order	NOUN
ejpam-5751	54	6	to	to	PART
ejpam-5751	54	7	determine	determine	VERB
ejpam-5751	54	8	the	the	DET
ejpam-5751	54	9	value	value	NOUN
ejpam-5751	54	10	of	of	ADP
ejpam-5751	54	11	n	n	PRON
ejpam-5751	54	12	as	as	SCONJ
ejpam-5751	54	13	follows	follow	VERB
ejpam-5751	54	14	n	n	X
ejpam-5751	54	15	+	+	CCONJ
ejpam-5751	54	16	2	2	NUM
ejpam-5751	54	17	=	=	SYM
ejpam-5751	54	18	3n	3n	NUM
ejpam-5751	54	19	=	=	NOUN
ejpam-5751	54	20	⇒	⇒	NOUN
ejpam-5751	54	21	n	n	NOUN
ejpam-5751	54	22	=	=	SYM
ejpam-5751	54	23	1	1	X
ejpam-5751	54	24	.	.	X
ejpam-5751	54	25	rewriting	rewrite	VERB
ejpam-5751	54	26	eq	eq	ADP
ejpam-5751	54	27	.	.	PUNCT
ejpam-5751	55	1	(	(	PUNCT
ejpam-5751	55	2	4	4	NUM
ejpam-5751	55	3	)	)	PUNCT
ejpam-5751	55	4	as	as	ADP
ejpam-5751	55	5	w(t	w(t	PROPN
ejpam-5751	55	6	,	,	PUNCT
ejpam-5751	55	7	x	x	NOUN
ejpam-5751	55	8	,	,	PUNCT
ejpam-5751	55	9	y	y	PROPN
ejpam-5751	55	10	)	)	PUNCT
ejpam-5751	56	1	=	=	SYM
ejpam-5751	56	2	α0(t	α0(t	PROPN
ejpam-5751	56	3	)	)	PUNCT
ejpam-5751	57	1	+	+	CCONJ
ejpam-5751	57	2	α1(t)f(µ	α1(t)f(µ	NOUN
ejpam-5751	57	3	)	)	PUNCT
ejpam-5751	57	4	.	.	PUNCT
ejpam-5751	58	1	(	(	PUNCT
ejpam-5751	58	2	7	7	X
ejpam-5751	58	3	)	)	PUNCT
ejpam-5751	58	4	we	we	PRON
ejpam-5751	58	5	differentiate	differentiate	VERB
ejpam-5751	58	6	eqs	eqs	PROPN
ejpam-5751	58	7	.	.	PUNCT
ejpam-5751	59	1	(	(	PUNCT
ejpam-5751	59	2	7	7	NUM
ejpam-5751	59	3	)	)	PUNCT
ejpam-5751	59	4	and	and	CCONJ
ejpam-5751	59	5	(	(	PUNCT
ejpam-5751	59	6	5	5	NUM
ejpam-5751	59	7	)	)	PUNCT
ejpam-5751	59	8	with	with	ADP
ejpam-5751	59	9	regards	regard	NOUN
ejpam-5751	59	10	to	to	ADP
ejpam-5751	59	11	t	t	PROPN
ejpam-5751	59	12	,	,	PUNCT
ejpam-5751	59	13	x	x	X
ejpam-5751	59	14	and	and	CCONJ
ejpam-5751	59	15	y	y	PROPN
ejpam-5751	59	16	as	as	SCONJ
ejpam-5751	59	17	follows	follow	VERB
ejpam-5751	59	18	wt	wt	NOUN
ejpam-5751	59	19	=	=	SYM
ejpam-5751	59	20	(	(	PUNCT
ejpam-5751	59	21	·	·	PUNCT
ejpam-5751	59	22	α0	α0	ADJ
ejpam-5751	59	23	+	+	CCONJ
ejpam-5751	59	24	pα1λ	pα1λ	PROPN
ejpam-5751	59	25	)	)	PUNCT
ejpam-5751	60	1	+	+	CCONJ
ejpam-5751	60	2	(	(	PUNCT
ejpam-5751	60	3	·	·	PUNCT
ejpam-5751	60	4	α1	α1	PROPN
ejpam-5751	60	5	+	+	CCONJ
ejpam-5751	60	6	α1rλ)f	α1rλ)f	PROPN
ejpam-5751	60	7	+	+	PROPN
ejpam-5751	60	8	sλα1f2	sλα1f2	NOUN
ejpam-5751	60	9	,	,	PUNCT
ejpam-5751	60	10	wx	wx	X
ejpam-5751	60	11	=	=	PUNCT
ejpam-5751	60	12	k1α1[sf2	k1α1[sf2	PROPN
ejpam-5751	61	1	+	+	CCONJ
ejpam-5751	61	2	rf	rf	ADJ
ejpam-5751	61	3	+	+	CCONJ
ejpam-5751	62	1	p	p	X
ejpam-5751	62	2	]	]	X
ejpam-5751	62	3	,	,	PUNCT
ejpam-5751	62	4	wy	wy	PROPN
ejpam-5751	62	5	=	=	PROPN
ejpam-5751	62	6	k2α1[sf2	k2α1[sf2	PROPN
ejpam-5751	63	1	+	+	PUNCT
ejpam-5751	63	2	rf	rf	ADJ
ejpam-5751	63	3	+	+	CCONJ
ejpam-5751	63	4	p	p	X
ejpam-5751	63	5	]	]	X
ejpam-5751	63	6	,	,	PUNCT
ejpam-5751	63	7	wxx	wxx	VERB
ejpam-5751	63	8	=	=	SYM
ejpam-5751	63	9	k21α1[2s	k21α1[2s	NOUN
ejpam-5751	63	10	2f3	2f3	NUM
ejpam-5751	64	1	+	+	CCONJ
ejpam-5751	64	2	3srf2	3srf2	NUM
ejpam-5751	64	3	+	+	NUM
ejpam-5751	64	4	(	(	PUNCT
ejpam-5751	64	5	2sp+	2sp+	PROPN
ejpam-5751	64	6	r2)f	r2)f	NOUN
ejpam-5751	64	7	+	+	CCONJ
ejpam-5751	64	8	rp	rp	NOUN
ejpam-5751	64	9	]	]	X
ejpam-5751	64	10	,	,	PUNCT
ejpam-5751	64	11	wyy	wyy	NOUN
ejpam-5751	64	12	=	=	SYM
ejpam-5751	64	13	k22α1[2s	k22α1[2s	ADJ
ejpam-5751	64	14	2f3	2f3	NUM
ejpam-5751	64	15	+	+	CCONJ
ejpam-5751	64	16	3srf2	3srf2	NUM
ejpam-5751	64	17	+	+	NUM
ejpam-5751	64	18	(	(	PUNCT
ejpam-5751	64	19	2sp+	2sp+	PROPN
ejpam-5751	64	20	r2)f	r2)f	NOUN
ejpam-5751	64	21	+	+	CCONJ
ejpam-5751	64	22	rp	rp	NOUN
ejpam-5751	64	23	]	]	X
ejpam-5751	64	24	,	,	PUNCT
ejpam-5751	64	25	wxy	wxy	PROPN
ejpam-5751	64	26	=	=	SYM
ejpam-5751	64	27	k1k2α1[2s	k1k2α1[2s	X
ejpam-5751	64	28	2f3	2f3	NUM
ejpam-5751	64	29	+	+	CCONJ
ejpam-5751	64	30	3srf2	3srf2	NUM
ejpam-5751	64	31	+	+	NUM
ejpam-5751	64	32	(	(	PUNCT
ejpam-5751	64	33	2sp+	2sp+	PROPN
ejpam-5751	64	34	r2)f	r2)f	NOUN
ejpam-5751	64	35	+	+	CCONJ
ejpam-5751	64	36	rp	rp	NOUN
ejpam-5751	64	37	]	]	X
ejpam-5751	64	38	,	,	PUNCT
ejpam-5751	64	39	w.	w.	PROPN
ejpam-5751	64	40	w.	w.	PROPN
ejpam-5751	64	41	mohammed	mohammed	PROPN
ejpam-5751	64	42	et	et	PROPN
ejpam-5751	64	43	al	al	PROPN
ejpam-5751	64	44	.	.	PUNCT
ejpam-5751	64	45	/	/	SYM
ejpam-5751	64	46	eur	eur	PROPN
ejpam-5751	64	47	.	.	PUNCT
ejpam-5751	65	1	j.	j.	PROPN
ejpam-5751	65	2	pure	pure	PROPN
ejpam-5751	65	3	appl	appl	PROPN
ejpam-5751	65	4	.	.	PROPN
ejpam-5751	65	5	math	math	PROPN
ejpam-5751	65	6	,	,	PUNCT
ejpam-5751	65	7	18	18	NUM
ejpam-5751	65	8	(	(	PUNCT
ejpam-5751	65	9	1	1	NUM
ejpam-5751	65	10	)	)	PUNCT
ejpam-5751	65	11	(	(	PUNCT
ejpam-5751	65	12	2025	2025	NUM
ejpam-5751	65	13	)	)	PUNCT
ejpam-5751	65	14	,	,	PUNCT
ejpam-5751	65	15	5751	5751	NUM
ejpam-5751	65	16	4	4	NUM
ejpam-5751	65	17	of	of	ADP
ejpam-5751	65	18	15	15	NUM
ejpam-5751	65	19	w3	w3	NOUN
ejpam-5751	65	20	=	=	SYM
ejpam-5751	65	21	α3	α3	PROPN
ejpam-5751	65	22	1f3	1f3	NUM
ejpam-5751	66	1	+	+	NUM
ejpam-5751	66	2	3α0α	3α0α	NUM
ejpam-5751	66	3	2	2	NUM
ejpam-5751	66	4	1f2	1f2	NUM
ejpam-5751	66	5	+	+	CCONJ
ejpam-5751	66	6	3α2	3α2	NUM
ejpam-5751	66	7	0α1f	0α1f	NOUN
ejpam-5751	67	1	+	+	CCONJ
ejpam-5751	67	2	α3	α3	NOUN
ejpam-5751	67	3	0	0	NUM
ejpam-5751	67	4	,	,	PUNCT
ejpam-5751	67	5	(	(	PUNCT
ejpam-5751	67	6	8)	8)	NUM
ejpam-5751	67	7	and	and	CCONJ
ejpam-5751	67	8	φt	φt	NOUN
ejpam-5751	67	9	=	=	SYM
ejpam-5751	67	10	·	·	PUNCT
ejpam-5751	67	11	ψ0	ψ0	ADJ
ejpam-5751	67	12	+	+	CCONJ
ejpam-5751	67	13	·	·	PUNCT
ejpam-5751	67	14	ψ1x+	ψ1x+	NOUN
ejpam-5751	67	15	·	·	PUNCT
ejpam-5751	67	16	ψ2y	ψ2y	ADP
ejpam-5751	67	17	,	,	PUNCT
ejpam-5751	67	18	φx	φx	ADJ
ejpam-5751	67	19	=	=	SYM
ejpam-5751	67	20	ψ1	ψ1	NOUN
ejpam-5751	67	21	,	,	PUNCT
ejpam-5751	67	22	φy	φy	NOUN
ejpam-5751	67	23	=	=	PUNCT
ejpam-5751	67	24	ψ2	ψ2	NOUN
ejpam-5751	67	25	,	,	PUNCT
ejpam-5751	67	26	φxx	φxx	PROPN
ejpam-5751	67	27	=	=	SYM
ejpam-5751	67	28	φyy	φyy	PROPN
ejpam-5751	67	29	=	=	PUNCT
ejpam-5751	67	30	φxy	φxy	NOUN
ejpam-5751	67	31	=	=	SYM
ejpam-5751	67	32	0	0	X
ejpam-5751	67	33	.	.	PUNCT
ejpam-5751	68	1	(	(	PUNCT
ejpam-5751	68	2	9	9	X
ejpam-5751	68	3	)	)	PUNCT
ejpam-5751	68	4	substituting	substitute	VERB
ejpam-5751	68	5	eqs	eqs	PROPN
ejpam-5751	68	6	.	.	PUNCT
ejpam-5751	69	1	(	(	PUNCT
ejpam-5751	69	2	5	5	NUM
ejpam-5751	69	3	)	)	PUNCT
ejpam-5751	69	4	,	,	PUNCT
ejpam-5751	69	5	(	(	PUNCT
ejpam-5751	69	6	7	7	NUM
ejpam-5751	69	7	)	)	PUNCT
ejpam-5751	69	8	,	,	PUNCT
ejpam-5751	69	9	(	(	PUNCT
ejpam-5751	69	10	8)	8)	NUM
ejpam-5751	69	11	and	and	CCONJ
ejpam-5751	69	12	(	(	PUNCT
ejpam-5751	69	13	9	9	NUM
ejpam-5751	69	14	)	)	PUNCT
ejpam-5751	69	15	into	into	ADP
ejpam-5751	69	16	eq	eq	NOUN
ejpam-5751	69	17	.	.	PUNCT
ejpam-5751	70	1	(	(	PUNCT
ejpam-5751	70	2	3	3	NUM
ejpam-5751	70	3	)	)	PUNCT
ejpam-5751	70	4	.	.	PUNCT
ejpam-5751	71	1	then	then	ADV
ejpam-5751	71	2	,	,	PUNCT
ejpam-5751	71	3	by	by	ADP
ejpam-5751	71	4	setting	set	VERB
ejpam-5751	71	5	each	each	PRON
ejpam-5751	71	6	of	of	ADP
ejpam-5751	71	7	fk	fk	INTJ
ejpam-5751	71	8	’s	’s	PART
ejpam-5751	71	9	coefficients	coefficient	NOUN
ejpam-5751	71	10	to	to	ADP
ejpam-5751	71	11	zero	zero	NUM
ejpam-5751	71	12	,	,	PUNCT
ejpam-5751	71	13	we	we	PRON
ejpam-5751	71	14	gain	gain	VERB
ejpam-5751	71	15	f0	f0	PROPN
ejpam-5751	71	16	:	:	PUNCT
ejpam-5751	71	17	·	·	PUNCT
ejpam-5751	72	1	α0	α0	ADJ
ejpam-5751	72	2	+	+	CCONJ
ejpam-5751	72	3	pλα1	pλα1	NOUN
ejpam-5751	72	4	+	+	CCONJ
ejpam-5751	72	5	2pk1ρ1ψ1α1	2pk1ρ1ψ1α1	NUM
ejpam-5751	72	6	+	+	NUM
ejpam-5751	72	7	2pk2ρ1ψ2α1	2pk2ρ1ψ2α1	NUM
ejpam-5751	72	8	+	+	CCONJ
ejpam-5751	72	9	pk2ρ3ψ1α1	pk2ρ3ψ1α1	NOUN
ejpam-5751	72	10	+	+	CCONJ
ejpam-5751	72	11	pk1ρ3ψ2α1	pk1ρ3ψ2α1	NOUN
ejpam-5751	72	12	=	=	SYM
ejpam-5751	72	13	0	0	NUM
ejpam-5751	72	14	,	,	PUNCT
ejpam-5751	72	15	f1	f1	NOUN
ejpam-5751	72	16	:	:	PUNCT
ejpam-5751	72	17	·	·	PUNCT
ejpam-5751	72	18	α1	α1	PROPN
ejpam-5751	72	19	+	+	CCONJ
ejpam-5751	72	20	rλα1	rλα1	NOUN
ejpam-5751	72	21	+	+	CCONJ
ejpam-5751	72	22	2rk1ρ1ψ1α1	2rk1ρ1ψ1α1	NUM
ejpam-5751	72	23	+	+	NUM
ejpam-5751	72	24	2rk2ρ1ψ2α1	2rk2ρ1ψ2α1	NUM
ejpam-5751	72	25	+	+	CCONJ
ejpam-5751	72	26	rk2ρ3ψ1α1	rk2ρ3ψ1α1	NOUN
ejpam-5751	72	27	+	+	CCONJ
ejpam-5751	72	28	rk1ρ3ψ2α1	rk1ρ3ψ2α1	NOUN
ejpam-5751	72	29	=	=	SYM
ejpam-5751	72	30	0	0	NUM
ejpam-5751	72	31	,	,	PUNCT
ejpam-5751	72	32	f2	f2	PROPN
ejpam-5751	72	33	:	:	PUNCT
ejpam-5751	72	34	sλα1	sλα1	NOUN
ejpam-5751	72	35	+	+	CCONJ
ejpam-5751	72	36	2sk1ρ1ψ1α1	2sk1ρ1ψ1α1	NUM
ejpam-5751	72	37	+	+	CCONJ
ejpam-5751	72	38	2sk2ρ1ψ2α1	2sk2ρ1ψ2α1	NUM
ejpam-5751	72	39	+	+	NUM
ejpam-5751	72	40	sk2ρ3ψ1α1	sk2ρ3ψ1α1	NOUN
ejpam-5751	72	41	+	+	CCONJ
ejpam-5751	72	42	sk1ρ3ψ2α1	sk1ρ3ψ2α1	NOUN
ejpam-5751	72	43	=	=	SYM
ejpam-5751	72	44	0	0	NUM
ejpam-5751	72	45	,	,	PUNCT
ejpam-5751	72	46	xf0	xf0	NUM
ejpam-5751	72	47	:	:	PUNCT
ejpam-5751	73	1	α0	α0	ADJ
ejpam-5751	73	2	·	·	PUNCT
ejpam-5751	73	3	ψ1	ψ1	NOUN
ejpam-5751	73	4	=	=	SYM
ejpam-5751	73	5	0	0	NUM
ejpam-5751	73	6	,	,	PUNCT
ejpam-5751	73	7	yf0	yf0	INTJ
ejpam-5751	73	8	:	:	PUNCT
ejpam-5751	73	9	α0	α0	ADJ
ejpam-5751	73	10	·	·	PUNCT
ejpam-5751	73	11	ψ2	ψ2	NOUN
ejpam-5751	73	12	=	=	SYM
ejpam-5751	73	13	0	0	NUM
ejpam-5751	73	14	,	,	PUNCT
ejpam-5751	73	15	xf1	xf1	VERB
ejpam-5751	73	16	:	:	PUNCT
ejpam-5751	73	17	α1	α1	PROPN
ejpam-5751	73	18	·	·	PUNCT
ejpam-5751	73	19	ψ1	ψ1	NOUN
ejpam-5751	73	20	=	=	SYM
ejpam-5751	73	21	0	0	NUM
ejpam-5751	73	22	,	,	PUNCT
ejpam-5751	73	23	yf1	yf1	NOUN
ejpam-5751	73	24	:	:	PUNCT
ejpam-5751	73	25	α1	α1	PROPN
ejpam-5751	73	26	·	·	PUNCT
ejpam-5751	73	27	ψ2	ψ2	NOUN
ejpam-5751	73	28	=	=	SYM
ejpam-5751	73	29	0	0	NUM
ejpam-5751	73	30	,	,	PUNCT
ejpam-5751	73	31	f0	f0	PROPN
ejpam-5751	73	32	:	:	PUNCT
ejpam-5751	73	33	−α0	−α0	NOUN
ejpam-5751	73	34	·	·	PUNCT
ejpam-5751	74	1	ψ0	ψ0	ADV
ejpam-5751	74	2	+	+	ADJ
ejpam-5751	74	3	prα1(k	prα1(k	VERB
ejpam-5751	74	4	2	2	NUM
ejpam-5751	74	5	1ρ1	1ρ1	NUM
ejpam-5751	74	6	+	+	CCONJ
ejpam-5751	74	7	k22ρ2	k22ρ2	ADJ
ejpam-5751	74	8	+	+	CCONJ
ejpam-5751	74	9	k1k2ρ3)−	k1k2ρ3)−	ADJ
ejpam-5751	74	10	ψ2	ψ2	NOUN
ejpam-5751	74	11	1ρ1α0	1ρ1α0	NUM
ejpam-5751	74	12	−	−	NOUN
ejpam-5751	74	13	ψ2	ψ2	NOUN
ejpam-5751	74	14	2ρ2α0	2ρ2α0	NUM
ejpam-5751	74	15	−	−	NOUN
ejpam-5751	74	16	ψ1ψ2ρ3α0	ψ1ψ2ρ3α0	NOUN
ejpam-5751	74	17	−aα3	−aα3	NOUN
ejpam-5751	74	18	0	0	PUNCT
ejpam-5751	75	1	=	=	SYM
ejpam-5751	75	2	0	0	NUM
ejpam-5751	75	3	,	,	PUNCT
ejpam-5751	75	4	f1	f1	NOUN
ejpam-5751	75	5	:	:	PUNCT
ejpam-5751	75	6	α1	α1	PROPN
ejpam-5751	75	7	[	[	PUNCT
ejpam-5751	75	8	·	·	PUNCT
ejpam-5751	76	1	ψ0	ψ0	PROPN
ejpam-5751	76	2	+	+	CCONJ
ejpam-5751	76	3	(	(	PUNCT
ejpam-5751	76	4	2sp+	2sp+	NUM
ejpam-5751	76	5	r2)(k21ρ1	r2)(k21ρ1	VERB
ejpam-5751	76	6	+	+	CCONJ
ejpam-5751	76	7	k22ρ2	k22ρ2	VERB
ejpam-5751	76	8	+	+	CCONJ
ejpam-5751	76	9	k1k2ρ3)−	k1k2ρ3)−	ADJ
ejpam-5751	76	10	ψ2	ψ2	NOUN
ejpam-5751	76	11	1ρ1	1ρ1	NUM
ejpam-5751	76	12	−	−	NOUN
ejpam-5751	76	13	ψ2	ψ2	NOUN
ejpam-5751	76	14	2ρ2	2ρ2	NUM
ejpam-5751	76	15	−	−	NOUN
ejpam-5751	76	16	ψ1ψ2ρ3	ψ1ψ2ρ3	PROPN
ejpam-5751	76	17	−	−	PROPN
ejpam-5751	76	18	3aα2	3aα2	NUM
ejpam-5751	76	19	0	0	NUM
ejpam-5751	76	20	]	]	X
ejpam-5751	76	21	=	=	SYM
ejpam-5751	76	22	0	0	NUM
ejpam-5751	76	23	,	,	PUNCT
ejpam-5751	76	24	f2	f2	INTJ
ejpam-5751	76	25	:	:	PUNCT
ejpam-5751	76	26	3srα1(k	3srα1(k	NUM
ejpam-5751	76	27	2	2	NUM
ejpam-5751	76	28	1ρ1	1ρ1	NUM
ejpam-5751	76	29	+	+	CCONJ
ejpam-5751	76	30	k22ρ2	k22ρ2	VERB
ejpam-5751	76	31	+	+	CCONJ
ejpam-5751	76	32	k1k2ρ3)−	k1k2ρ3)−	PROPN
ejpam-5751	76	33	3aα0α	3aα0α	NUM
ejpam-5751	76	34	2	2	NUM
ejpam-5751	76	35	1	1	NUM
ejpam-5751	76	36	=	=	SYM
ejpam-5751	76	37	0	0	NUM
ejpam-5751	76	38	,	,	PUNCT
ejpam-5751	76	39	and	and	CCONJ
ejpam-5751	76	40	f3	f3	ADJ
ejpam-5751	76	41	:	:	PUNCT
ejpam-5751	76	42	2s2α1(k	2s2α1(k	NUM
ejpam-5751	76	43	2	2	NUM
ejpam-5751	76	44	1ρ1	1ρ1	NUM
ejpam-5751	76	45	+	+	CCONJ
ejpam-5751	76	46	k22ρ2	k22ρ2	ADJ
ejpam-5751	77	1	+	+	CCONJ
ejpam-5751	77	2	k1k2ρ3)−aα3	k1k2ρ3)−aα3	PROPN
ejpam-5751	77	3	1	1	NUM
ejpam-5751	77	4	=	=	SYM
ejpam-5751	77	5	0	0	NUM
ejpam-5751	77	6	.	.	PUNCT
ejpam-5751	78	1	by	by	ADP
ejpam-5751	78	2	solving	solve	VERB
ejpam-5751	78	3	these	these	DET
ejpam-5751	78	4	equations	equation	NOUN
ejpam-5751	78	5	,	,	PUNCT
ejpam-5751	78	6	we	we	PRON
ejpam-5751	78	7	have	have	VERB
ejpam-5751	78	8	α0(t	α0(t	NUM
ejpam-5751	78	9	)	)	PUNCT
ejpam-5751	78	10	=	=	SYM
ejpam-5751	78	11	r	r	NOUN
ejpam-5751	78	12	=	=	SYM
ejpam-5751	78	13	0	0	NUM
ejpam-5751	78	14	,	,	PUNCT
ejpam-5751	78	15	α1	α1	PROPN
ejpam-5751	78	16	=	=	SYM
ejpam-5751	78	17	ℓ	ℓ	PROPN
ejpam-5751	78	18	,	,	PUNCT
ejpam-5751	78	19	k21ρ1	k21ρ1	PROPN
ejpam-5751	78	20	+	+	CCONJ
ejpam-5751	78	21	k22ρ2	k22ρ2	VERB
ejpam-5751	78	22	+	+	CCONJ
ejpam-5751	78	23	k1k2ρ3	k1k2ρ3	PROPN
ejpam-5751	78	24	=	=	SYM
ejpam-5751	78	25	ℓ2a(t	ℓ2a(t	PROPN
ejpam-5751	78	26	)	)	PUNCT
ejpam-5751	78	27	2s2	2s2	NUM
ejpam-5751	78	28	,	,	PUNCT
ejpam-5751	78	29	(	(	PUNCT
ejpam-5751	78	30	10	10	NUM
ejpam-5751	78	31	)	)	PUNCT
ejpam-5751	78	32	λ(t	λ(t	NOUN
ejpam-5751	78	33	)	)	PUNCT
ejpam-5751	79	1	=	=	PUNCT
ejpam-5751	80	1	−2k1ρ1ψ1	−2k1ρ1ψ1	NOUN
ejpam-5751	80	2	−	−	PROPN
ejpam-5751	81	1	2k2ρ2ψ2	2k2ρ2ψ2	NUM
ejpam-5751	81	2	−	−	NOUN
ejpam-5751	81	3	k2ρ3ψ1	k2ρ3ψ1	PROPN
ejpam-5751	81	4	−	−	PROPN
ejpam-5751	81	5	k1ρ3ψ2	k1ρ3ψ2	PROPN
ejpam-5751	81	6	,	,	PUNCT
ejpam-5751	81	7	(	(	PUNCT
ejpam-5751	81	8	11	11	NUM
ejpam-5751	81	9	)	)	PUNCT
ejpam-5751	81	10	and	and	CCONJ
ejpam-5751	81	11	ψ1	ψ1	NOUN
ejpam-5751	81	12	=	=	SYM
ejpam-5751	81	13	ℏ1	ℏ1	ADJ
ejpam-5751	81	14	,	,	PUNCT
ejpam-5751	81	15	ψ2	ψ2	NOUN
ejpam-5751	81	16	=	=	SYM
ejpam-5751	81	17	ℏ2	ℏ2	NOUN
ejpam-5751	81	18	,	,	PUNCT
ejpam-5751	81	19	ψ0(t	ψ0(t	NOUN
ejpam-5751	81	20	)	)	PUNCT
ejpam-5751	81	21	=	=	SYM
ejpam-5751	81	22	−pℓ	−pℓ	NOUN
ejpam-5751	81	23	2	2	NUM
ejpam-5751	81	24	s	s	PART
ejpam-5751	81	25	∫	∫	PROPN
ejpam-5751	81	26	t	t	PROPN
ejpam-5751	81	27	0	0	NUM
ejpam-5751	81	28	a(τ)dτ	a(τ)dτ	PROPN
ejpam-5751	82	1	+	+	CCONJ
ejpam-5751	82	2	∫	∫	PROPN
ejpam-5751	82	3	t	t	PROPN
ejpam-5751	82	4	0	0	NUM
ejpam-5751	83	1	(	(	PUNCT
ejpam-5751	83	2	ℏ21ρ1	ℏ21ρ1	NOUN
ejpam-5751	83	3	+	+	CCONJ
ejpam-5751	83	4	ℏ22ρ2	ℏ22ρ2	NOUN
ejpam-5751	83	5	+	+	CCONJ
ejpam-5751	83	6	ℏ1ℏ2ρ3)dτ	ℏ1ℏ2ρ3)dτ	PROPN
ejpam-5751	83	7	,	,	PUNCT
ejpam-5751	83	8	(	(	PUNCT
ejpam-5751	83	9	12	12	NUM
ejpam-5751	83	10	)	)	PUNCT
ejpam-5751	83	11	where	where	SCONJ
ejpam-5751	83	12	ℏ1	ℏ1	ADJ
ejpam-5751	83	13	,	,	PUNCT
ejpam-5751	83	14	ℏ2	ℏ2	NOUN
ejpam-5751	83	15	and	and	CCONJ
ejpam-5751	83	16	ℓ	ℓ	PROPN
ejpam-5751	83	17	are	be	AUX
ejpam-5751	83	18	constants	constant	NOUN
ejpam-5751	83	19	.	.	PUNCT
ejpam-5751	84	1	for	for	ADP
ejpam-5751	84	2	simplicity	simplicity	NOUN
ejpam-5751	84	3	,	,	PUNCT
ejpam-5751	84	4	let	let	VERB
ejpam-5751	84	5	ℏ1	ℏ1	ADJ
ejpam-5751	84	6	=	=	SYM
ejpam-5751	84	7	k1	k1	NOUN
ejpam-5751	84	8	and	and	CCONJ
ejpam-5751	84	9	ℏ2	ℏ2	NOUN
ejpam-5751	84	10	=	=	SYM
ejpam-5751	84	11	k2	k2	ADJ
ejpam-5751	84	12	in	in	ADP
ejpam-5751	84	13	order	order	NOUN
ejpam-5751	84	14	to	to	PART
ejpam-5751	84	15	obtain	obtain	VERB
ejpam-5751	84	16	λ(t	λ(t	PRON
ejpam-5751	84	17	)	)	PUNCT
ejpam-5751	85	1	=	=	PUNCT
ejpam-5751	85	2	−ℓ	−ℓ	NOUN
ejpam-5751	85	3	2a(t	2a(t	NOUN
ejpam-5751	85	4	)	)	PUNCT
ejpam-5751	85	5	s2	s2	NOUN
ejpam-5751	85	6	,	,	PUNCT
ejpam-5751	85	7	ψ0(t	ψ0(t	NOUN
ejpam-5751	85	8	)	)	PUNCT
ejpam-5751	85	9	=	=	SYM
ejpam-5751	85	10	(	(	PUNCT
ejpam-5751	85	11	ℓ2	ℓ2	PROPN
ejpam-5751	85	12	2s2	2s2	NUM
ejpam-5751	85	13	−	−	PROPN
ejpam-5751	85	14	pℓ2	pℓ2	PROPN
ejpam-5751	85	15	s	s	PART
ejpam-5751	85	16	)	)	PUNCT
ejpam-5751	85	17	∫	∫	PROPN
ejpam-5751	85	18	t	t	PROPN
ejpam-5751	85	19	0	0	NUM
ejpam-5751	85	20	a(τ)dτ	a(τ)dτ	PROPN
ejpam-5751	85	21	,	,	PUNCT
ejpam-5751	85	22	w.	w.	PROPN
ejpam-5751	85	23	w.	w.	PROPN
ejpam-5751	85	24	mohammed	mohammed	PROPN
ejpam-5751	85	25	et	et	PROPN
ejpam-5751	85	26	al	al	PROPN
ejpam-5751	85	27	.	.	PUNCT
ejpam-5751	85	28	/	/	SYM
ejpam-5751	85	29	eur	eur	PROPN
ejpam-5751	85	30	.	.	PUNCT
ejpam-5751	86	1	j.	j.	PROPN
ejpam-5751	86	2	pure	pure	PROPN
ejpam-5751	86	3	appl	appl	PROPN
ejpam-5751	86	4	.	.	PROPN
ejpam-5751	86	5	math	math	PROPN
ejpam-5751	86	6	,	,	PUNCT
ejpam-5751	86	7	18	18	NUM
ejpam-5751	86	8	(	(	PUNCT
ejpam-5751	86	9	1	1	NUM
ejpam-5751	86	10	)	)	PUNCT
ejpam-5751	86	11	(	(	PUNCT
ejpam-5751	86	12	2025	2025	NUM
ejpam-5751	86	13	)	)	PUNCT
ejpam-5751	86	14	,	,	PUNCT
ejpam-5751	86	15	5751	5751	NUM
ejpam-5751	86	16	5	5	NUM
ejpam-5751	86	17	of	of	ADP
ejpam-5751	86	18	15	15	NUM
ejpam-5751	86	19	and	and	CCONJ
ejpam-5751	86	20	α0(t	α0(t	NUM
ejpam-5751	86	21	)	)	PUNCT
ejpam-5751	86	22	=	=	SYM
ejpam-5751	86	23	0	0	NUM
ejpam-5751	86	24	,	,	PUNCT
ejpam-5751	86	25	α1	α1	PROPN
ejpam-5751	86	26	=	=	SYM
ejpam-5751	86	27	ℓ	ℓ	PROPN
ejpam-5751	86	28	,	,	PUNCT
ejpam-5751	86	29	ψ1	ψ1	NOUN
ejpam-5751	86	30	=	=	SYM
ejpam-5751	86	31	k1	k1	NOUN
ejpam-5751	86	32	,	,	PUNCT
ejpam-5751	86	33	ψ2	ψ2	NOUN
ejpam-5751	86	34	=	=	SYM
ejpam-5751	86	35	k2	k2	NOUN
ejpam-5751	86	36	,	,	PUNCT
ejpam-5751	86	37	r	r	NOUN
ejpam-5751	86	38	=	=	SYM
ejpam-5751	86	39	0	0	NUM
ejpam-5751	86	40	.	.	PUNCT
ejpam-5751	87	1	hence	hence	ADV
ejpam-5751	87	2	,	,	PUNCT
ejpam-5751	87	3	by	by	ADP
ejpam-5751	87	4	utilizing	utilize	VERB
ejpam-5751	87	5	eqs	eq	NOUN
ejpam-5751	87	6	(	(	PUNCT
ejpam-5751	87	7	7	7	NUM
ejpam-5751	87	8	)	)	PUNCT
ejpam-5751	87	9	and	and	CCONJ
ejpam-5751	87	10	(	(	PUNCT
ejpam-5751	87	11	10	10	NUM
ejpam-5751	87	12	)	)	PUNCT
ejpam-5751	87	13	,	,	PUNCT
ejpam-5751	87	14	the	the	DET
ejpam-5751	87	15	solution	solution	NOUN
ejpam-5751	87	16	of	of	ADP
ejpam-5751	87	17	the	the	DET
ejpam-5751	87	18	hfe	hfe	PROPN
ejpam-5751	87	19	-	-	PUNCT
ejpam-5751	87	20	rvcs	rvcs	PROPN
ejpam-5751	87	21	(	(	PUNCT
ejpam-5751	87	22	3	3	X
ejpam-5751	87	23	)	)	PUNCT
ejpam-5751	87	24	is	be	AUX
ejpam-5751	87	25	w(t	w(t	PROPN
ejpam-5751	87	26	,	,	PUNCT
ejpam-5751	87	27	x	x	X
ejpam-5751	87	28	,	,	PUNCT
ejpam-5751	87	29	y	y	PROPN
ejpam-5751	87	30	)	)	PUNCT
ejpam-5751	87	31	=	=	SYM
ejpam-5751	87	32	ℓf(µ	ℓf(µ	NOUN
ejpam-5751	87	33	)	)	PUNCT
ejpam-5751	87	34	,	,	PUNCT
ejpam-5751	87	35	µ	µ	X
ejpam-5751	87	36	=	=	SYM
ejpam-5751	87	37	k1x+	k1x+	NOUN
ejpam-5751	87	38	k2y	k2y	NOUN
ejpam-5751	87	39	−	−	PROPN
ejpam-5751	87	40	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	87	41	s2	s2	NOUN
ejpam-5751	87	42	∫	∫	PROPN
ejpam-5751	87	43	t	t	PROPN
ejpam-5751	87	44	0	0	NUM
ejpam-5751	87	45	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	87	46	.	.	PUNCT
ejpam-5751	88	1	(	(	PUNCT
ejpam-5751	88	2	13	13	NUM
ejpam-5751	88	3	)	)	PUNCT
ejpam-5751	88	4	depending	depend	VERB
ejpam-5751	88	5	on	on	ADP
ejpam-5751	88	6	p	p	PROPN
ejpam-5751	88	7	and	and	CCONJ
ejpam-5751	88	8	s	s	PART
ejpam-5751	88	9	,	,	PUNCT
ejpam-5751	88	10	there	there	PRON
ejpam-5751	88	11	exist	exist	VERB
ejpam-5751	88	12	many	many	ADJ
ejpam-5751	88	13	sets	set	NOUN
ejpam-5751	88	14	to	to	PART
ejpam-5751	88	15	find	find	VERB
ejpam-5751	88	16	the	the	DET
ejpam-5751	88	17	solution	solution	NOUN
ejpam-5751	88	18	f	f	X
ejpam-5751	88	19	of	of	ADP
ejpam-5751	88	20	eq	eq	PROPN
ejpam-5751	88	21	.	.	PUNCT
ejpam-5751	89	1	(	(	PUNCT
ejpam-5751	89	2	6	6	NUM
ejpam-5751	89	3	)	)	PUNCT
ejpam-5751	89	4	as	as	SCONJ
ejpam-5751	89	5	follows	follow	VERB
ejpam-5751	89	6	:	:	PUNCT
ejpam-5751	89	7	set	set	VERB
ejpam-5751	90	1	i	i	PRON
ejpam-5751	90	2	:	:	PUNCT
ejpam-5751	90	3	if	if	SCONJ
ejpam-5751	90	4	ps	ps	PROPN
ejpam-5751	90	5	<	<	X
ejpam-5751	90	6	0	0	PROPN
ejpam-5751	90	7	,	,	PUNCT
ejpam-5751	90	8	hence	hence	ADV
ejpam-5751	90	9	eq	eq	NOUN
ejpam-5751	90	10	.	.	PUNCT
ejpam-5751	91	1	(	(	PUNCT
ejpam-5751	91	2	6	6	NUM
ejpam-5751	91	3	)	)	PUNCT
ejpam-5751	91	4	possess	possess	VERB
ejpam-5751	91	5	the	the	DET
ejpam-5751	91	6	solutions	solution	NOUN
ejpam-5751	91	7	:	:	PUNCT
ejpam-5751	91	8	f1(µ	f1(µ	X
ejpam-5751	91	9	)	)	PUNCT
ejpam-5751	91	10	=	=	SYM
ejpam-5751	92	1	−	−	PROPN
ejpam-5751	92	2	√	√	NUM
ejpam-5751	93	1	−p	−p	NOUN
ejpam-5751	93	2	s	s	NOUN
ejpam-5751	93	3	tanh	tanh	NOUN
ejpam-5751	93	4	(	(	PUNCT
ejpam-5751	93	5	√	√	ADP
ejpam-5751	93	6	−psµ	−psµ	NOUN
ejpam-5751	93	7	)	)	PUNCT
ejpam-5751	93	8	,	,	PUNCT
ejpam-5751	93	9	f2(µ	f2(µ	NOUN
ejpam-5751	93	10	)	)	PUNCT
ejpam-5751	93	11	=	=	SYM
ejpam-5751	94	1	−	−	PROPN
ejpam-5751	94	2	√	√	NUM
ejpam-5751	94	3	−p	−p	NOUN
ejpam-5751	94	4	s	s	PART
ejpam-5751	94	5	coth	coth	NOUN
ejpam-5751	94	6	(	(	PUNCT
ejpam-5751	94	7	√	√	ADP
ejpam-5751	94	8	−psµ	−psµ	NOUN
ejpam-5751	94	9	)	)	PUNCT
ejpam-5751	94	10	,	,	PUNCT
ejpam-5751	94	11	f3(µ	f3(µ	PROPN
ejpam-5751	94	12	)	)	PUNCT
ejpam-5751	94	13	=	=	SYM
ejpam-5751	94	14	−	−	PROPN
ejpam-5751	95	1	√	√	NUM
ejpam-5751	95	2	−p	−p	NOUN
ejpam-5751	95	3	s	s	X
ejpam-5751	95	4	(	(	PUNCT
ejpam-5751	95	5	coth	coth	PROPN
ejpam-5751	95	6	(	(	PUNCT
ejpam-5751	95	7	√	√	NUM
ejpam-5751	95	8	−4psµ)±	−4psµ)±	NUM
ejpam-5751	95	9	csch	csch	NOUN
ejpam-5751	95	10	(	(	PUNCT
ejpam-5751	95	11	√	√	NUM
ejpam-5751	95	12	−4psµ	−4psµ	NOUN
ejpam-5751	95	13	)	)	PUNCT
ejpam-5751	95	14	)	)	PUNCT
ejpam-5751	95	15	,	,	PUNCT
ejpam-5751	95	16	f4(µ	f4(µ	PROPN
ejpam-5751	95	17	)	)	PUNCT
ejpam-5751	95	18	=	=	SYM
ejpam-5751	95	19	−1	−1	NOUN
ejpam-5751	95	20	2	2	NUM
ejpam-5751	95	21	√	√	NOUN
ejpam-5751	95	22	−p	−p	NOUN
ejpam-5751	95	23	s	s	X
ejpam-5751	95	24	(	(	PUNCT
ejpam-5751	95	25	tanh	tanh	NOUN
ejpam-5751	95	26	(	(	PUNCT
ejpam-5751	95	27	1	1	NUM
ejpam-5751	95	28	2	2	NUM
ejpam-5751	95	29	√	√	NUM
ejpam-5751	95	30	−psµ	−psµ	NOUN
ejpam-5751	95	31	)	)	PUNCT
ejpam-5751	95	32	+	+	NUM
ejpam-5751	95	33	coth	coth	X
ejpam-5751	95	34	(	(	PUNCT
ejpam-5751	95	35	1	1	NUM
ejpam-5751	95	36	2	2	NUM
ejpam-5751	95	37	√	√	NUM
ejpam-5751	95	38	−psµ	−psµ	NOUN
ejpam-5751	95	39	)	)	PUNCT
ejpam-5751	95	40	)	)	PUNCT
ejpam-5751	95	41	.	.	PUNCT
ejpam-5751	96	1	consequently	consequently	ADV
ejpam-5751	96	2	,	,	PUNCT
ejpam-5751	96	3	hfe	hfe	PROPN
ejpam-5751	96	4	-	-	PUNCT
ejpam-5751	96	5	rvcs	rvcs	PROPN
ejpam-5751	96	6	(	(	PUNCT
ejpam-5751	96	7	3	3	X
ejpam-5751	96	8	)	)	PUNCT
ejpam-5751	96	9	has	have	VERB
ejpam-5751	96	10	the	the	DET
ejpam-5751	96	11	hyperbolic	hyperbolic	ADJ
ejpam-5751	96	12	function	function	NOUN
ejpam-5751	96	13	solutions	solution	NOUN
ejpam-5751	96	14	:	:	PUNCT
ejpam-5751	96	15	w1(t	w1(t	ADJ
ejpam-5751	96	16	,	,	PUNCT
ejpam-5751	96	17	x	x	NOUN
ejpam-5751	96	18	,	,	PUNCT
ejpam-5751	96	19	y	y	NOUN
ejpam-5751	96	20	)	)	PUNCT
ejpam-5751	97	1	=	=	NOUN
ejpam-5751	97	2	−ℓ	−ℓ	NOUN
ejpam-5751	97	3	√	√	PRON
ejpam-5751	97	4	−p	−p	NOUN
ejpam-5751	97	5	s	s	NOUN
ejpam-5751	97	6	tanh	tanh	NOUN
ejpam-5751	97	7	(	(	PUNCT
ejpam-5751	97	8	√	√	ADP
ejpam-5751	97	9	−psµ	−psµ	NOUN
ejpam-5751	97	10	)	)	PUNCT
ejpam-5751	97	11	,	,	PUNCT
ejpam-5751	97	12	(	(	PUNCT
ejpam-5751	97	13	14	14	X
ejpam-5751	97	14	)	)	PUNCT
ejpam-5751	97	15	w2(t	w2(t	PROPN
ejpam-5751	97	16	,	,	PUNCT
ejpam-5751	97	17	x	x	NOUN
ejpam-5751	97	18	,	,	PUNCT
ejpam-5751	97	19	y	y	NOUN
ejpam-5751	97	20	)	)	PUNCT
ejpam-5751	97	21	=	=	NOUN
ejpam-5751	97	22	−ℓ	−ℓ	NOUN
ejpam-5751	97	23	√	√	PRON
ejpam-5751	97	24	−p	−p	NOUN
ejpam-5751	97	25	s	s	PART
ejpam-5751	97	26	coth	coth	NOUN
ejpam-5751	97	27	(	(	PUNCT
ejpam-5751	97	28	√	√	ADP
ejpam-5751	97	29	−psµ	−psµ	NOUN
ejpam-5751	97	30	)	)	PUNCT
ejpam-5751	97	31	,	,	PUNCT
ejpam-5751	97	32	(	(	PUNCT
ejpam-5751	97	33	15	15	X
ejpam-5751	97	34	)	)	PUNCT
ejpam-5751	97	35	w3(t	w3(t	NUM
ejpam-5751	97	36	,	,	PUNCT
ejpam-5751	97	37	x	x	PRON
ejpam-5751	97	38	,	,	PUNCT
ejpam-5751	97	39	y	y	NOUN
ejpam-5751	97	40	)	)	PUNCT
ejpam-5751	97	41	=	=	NOUN
ejpam-5751	98	1	−ℓ	−ℓ	NOUN
ejpam-5751	98	2	√	√	VERB
ejpam-5751	98	3	−p	−p	NOUN
ejpam-5751	98	4	s	s	X
ejpam-5751	98	5	(	(	PUNCT
ejpam-5751	98	6	coth	coth	PROPN
ejpam-5751	98	7	(	(	PUNCT
ejpam-5751	98	8	√	√	NUM
ejpam-5751	98	9	−4psµ)±	−4psµ)±	NUM
ejpam-5751	98	10	csch	csch	NOUN
ejpam-5751	98	11	(	(	PUNCT
ejpam-5751	98	12	√	√	NUM
ejpam-5751	98	13	−4psµ	−4psµ	NOUN
ejpam-5751	98	14	)	)	PUNCT
ejpam-5751	98	15	)	)	PUNCT
ejpam-5751	98	16	,	,	PUNCT
ejpam-5751	98	17	(	(	PUNCT
ejpam-5751	98	18	16	16	NUM
ejpam-5751	98	19	)	)	PUNCT
ejpam-5751	98	20	w4(t	w4(t	PROPN
ejpam-5751	98	21	,	,	PUNCT
ejpam-5751	98	22	x	x	NOUN
ejpam-5751	98	23	,	,	PUNCT
ejpam-5751	98	24	y	y	NOUN
ejpam-5751	98	25	)	)	PUNCT
ejpam-5751	98	26	=	=	SYM
ejpam-5751	98	27	−1	−1	NOUN
ejpam-5751	98	28	2	2	NUM
ejpam-5751	98	29	ℓ	ℓ	NOUN
ejpam-5751	98	30	√	√	NOUN
ejpam-5751	98	31	−p	−p	NOUN
ejpam-5751	98	32	s	s	X
ejpam-5751	98	33	(	(	PUNCT
ejpam-5751	98	34	tanh	tanh	NOUN
ejpam-5751	98	35	(	(	PUNCT
ejpam-5751	98	36	1	1	NUM
ejpam-5751	98	37	2	2	NUM
ejpam-5751	98	38	√	√	NUM
ejpam-5751	98	39	−psµ	−psµ	NOUN
ejpam-5751	98	40	)	)	PUNCT
ejpam-5751	98	41	+	+	NUM
ejpam-5751	98	42	coth	coth	X
ejpam-5751	98	43	(	(	PUNCT
ejpam-5751	98	44	1	1	NUM
ejpam-5751	98	45	2	2	NUM
ejpam-5751	98	46	√	√	NUM
ejpam-5751	98	47	−psµ	−psµ	NOUN
ejpam-5751	98	48	)	)	PUNCT
ejpam-5751	98	49	)	)	PUNCT
ejpam-5751	98	50	.	.	PUNCT
ejpam-5751	99	1	(	(	PUNCT
ejpam-5751	99	2	17	17	NUM
ejpam-5751	99	3	)	)	PUNCT
ejpam-5751	99	4	set	set	NOUN
ejpam-5751	99	5	ii	ii	NOUN
ejpam-5751	99	6	:	:	PUNCT
ejpam-5751	99	7	if	if	SCONJ
ejpam-5751	99	8	ps	ps	PROPN
ejpam-5751	99	9	>	>	X
ejpam-5751	99	10	0	0	PROPN
ejpam-5751	99	11	,	,	PUNCT
ejpam-5751	99	12	hence	hence	ADV
ejpam-5751	99	13	eq	eq	NOUN
ejpam-5751	99	14	.	.	PUNCT
ejpam-5751	100	1	(	(	PUNCT
ejpam-5751	100	2	6	6	NUM
ejpam-5751	100	3	)	)	PUNCT
ejpam-5751	100	4	possess	possess	VERB
ejpam-5751	100	5	the	the	DET
ejpam-5751	100	6	solutions	solution	NOUN
ejpam-5751	100	7	:	:	PUNCT
ejpam-5751	100	8	f5(µ	f5(µ	X
ejpam-5751	100	9	)	)	PUNCT
ejpam-5751	100	10	=	=	PUNCT
ejpam-5751	101	1	√	√	PROPN
ejpam-5751	102	1	p	p	NOUN
ejpam-5751	102	2	s	s	PROPN
ejpam-5751	102	3	tan	tan	PROPN
ejpam-5751	102	4	(	(	PUNCT
ejpam-5751	102	5	√	√	NUM
ejpam-5751	102	6	psµ	psµ	NOUN
ejpam-5751	102	7	)	)	PUNCT
ejpam-5751	102	8	,	,	PUNCT
ejpam-5751	102	9	f6(µ	f6(µ	NUM
ejpam-5751	102	10	)	)	PUNCT
ejpam-5751	102	11	=	=	SYM
ejpam-5751	103	1	−	−	PROPN
ejpam-5751	103	2	√	√	NUM
ejpam-5751	103	3	p	p	NOUN
ejpam-5751	103	4	s	s	X
ejpam-5751	103	5	cot	cot	NOUN
ejpam-5751	103	6	(	(	PUNCT
ejpam-5751	103	7	√	√	NUM
ejpam-5751	103	8	psµ	psµ	NOUN
ejpam-5751	103	9	)	)	PUNCT
ejpam-5751	103	10	,	,	PUNCT
ejpam-5751	103	11	f7(µ	f7(µ	NUM
ejpam-5751	103	12	)	)	PUNCT
ejpam-5751	103	13	=	=	PUNCT
ejpam-5751	104	1	√	√	PROPN
ejpam-5751	104	2	p	p	NOUN
ejpam-5751	104	3	s	s	X
ejpam-5751	104	4	(	(	PUNCT
ejpam-5751	104	5	tan	tan	PROPN
ejpam-5751	104	6	(	(	PUNCT
ejpam-5751	104	7	√	√	PROPN
ejpam-5751	104	8	4psµ)±	4psµ)±	NUM
ejpam-5751	104	9	sec	sec	PROPN
ejpam-5751	104	10	(	(	PUNCT
ejpam-5751	104	11	√	√	NOUN
ejpam-5751	104	12	4psµ	4psµ	NUM
ejpam-5751	104	13	)	)	PUNCT
ejpam-5751	104	14	)	)	PUNCT
ejpam-5751	104	15	,	,	PUNCT
ejpam-5751	104	16	w.	w.	PROPN
ejpam-5751	104	17	w.	w.	PROPN
ejpam-5751	104	18	mohammed	mohammed	PROPN
ejpam-5751	104	19	et	et	PROPN
ejpam-5751	104	20	al	al	PROPN
ejpam-5751	104	21	.	.	PUNCT
ejpam-5751	104	22	/	/	SYM
ejpam-5751	104	23	eur	eur	PROPN
ejpam-5751	104	24	.	.	PUNCT
ejpam-5751	105	1	j.	j.	PROPN
ejpam-5751	105	2	pure	pure	PROPN
ejpam-5751	105	3	appl	appl	PROPN
ejpam-5751	105	4	.	.	PROPN
ejpam-5751	105	5	math	math	PROPN
ejpam-5751	105	6	,	,	PUNCT
ejpam-5751	105	7	18	18	NUM
ejpam-5751	105	8	(	(	PUNCT
ejpam-5751	105	9	1	1	NUM
ejpam-5751	105	10	)	)	PUNCT
ejpam-5751	105	11	(	(	PUNCT
ejpam-5751	105	12	2025	2025	NUM
ejpam-5751	105	13	)	)	PUNCT
ejpam-5751	105	14	,	,	PUNCT
ejpam-5751	105	15	5751	5751	NUM
ejpam-5751	105	16	6	6	NUM
ejpam-5751	105	17	of	of	ADP
ejpam-5751	105	18	15	15	NUM
ejpam-5751	105	19	f8(µ	f8(µ	PROPN
ejpam-5751	105	20	)	)	PUNCT
ejpam-5751	105	21	=	=	SYM
ejpam-5751	106	1	−	−	PROPN
ejpam-5751	106	2	√	√	PROPN
ejpam-5751	106	3	p	p	NOUN
ejpam-5751	106	4	s	s	X
ejpam-5751	106	5	(	(	PUNCT
ejpam-5751	106	6	cot	cot	NOUN
ejpam-5751	106	7	(	(	PUNCT
ejpam-5751	106	8	√	√	PROPN
ejpam-5751	106	9	4psµ)±	4psµ)±	NUM
ejpam-5751	106	10	csc	csc	PROPN
ejpam-5751	106	11	(	(	PUNCT
ejpam-5751	106	12	√	√	PROPN
ejpam-5751	106	13	4psµ	4psµ	NUM
ejpam-5751	106	14	)	)	PUNCT
ejpam-5751	106	15	)	)	PUNCT
ejpam-5751	106	16	,	,	PUNCT
ejpam-5751	106	17	f9(µ	f9(µ	NUM
ejpam-5751	106	18	)	)	PUNCT
ejpam-5751	106	19	=	=	SYM
ejpam-5751	106	20	1	1	NUM
ejpam-5751	106	21	2	2	NUM
ejpam-5751	106	22	√	√	PROPN
ejpam-5751	107	1	p	p	NOUN
ejpam-5751	107	2	s	s	X
ejpam-5751	107	3	(	(	PUNCT
ejpam-5751	107	4	tan	tan	PROPN
ejpam-5751	107	5	(	(	PUNCT
ejpam-5751	107	6	1	1	NUM
ejpam-5751	107	7	2	2	NUM
ejpam-5751	107	8	√	√	PROPN
ejpam-5751	107	9	psµ)−	psµ)−	NOUN
ejpam-5751	107	10	cot	cot	NOUN
ejpam-5751	107	11	(	(	PUNCT
ejpam-5751	107	12	1	1	NUM
ejpam-5751	107	13	2	2	NUM
ejpam-5751	107	14	√	√	NUM
ejpam-5751	107	15	psµ	psµ	NOUN
ejpam-5751	107	16	)	)	PUNCT
ejpam-5751	107	17	)	)	PUNCT
ejpam-5751	107	18	,	,	PUNCT
ejpam-5751	107	19	consequently	consequently	ADV
ejpam-5751	107	20	,	,	PUNCT
ejpam-5751	107	21	hfe	hfe	PROPN
ejpam-5751	107	22	-	-	PUNCT
ejpam-5751	107	23	rvcs	rvcs	PROPN
ejpam-5751	107	24	(	(	PUNCT
ejpam-5751	107	25	3	3	X
ejpam-5751	107	26	)	)	PUNCT
ejpam-5751	107	27	has	have	VERB
ejpam-5751	107	28	the	the	DET
ejpam-5751	107	29	trigonometric	trigonometric	ADJ
ejpam-5751	107	30	function	function	NOUN
ejpam-5751	107	31	solutions	solution	NOUN
ejpam-5751	107	32	:	:	PUNCT
ejpam-5751	107	33	w5(t	w5(t	NUM
ejpam-5751	107	34	,	,	PUNCT
ejpam-5751	107	35	x	x	PROPN
ejpam-5751	107	36	,	,	PUNCT
ejpam-5751	107	37	y	y	NOUN
ejpam-5751	107	38	)	)	PUNCT
ejpam-5751	108	1	=	=	SYM
ejpam-5751	108	2	ℓ	ℓ	NOUN
ejpam-5751	108	3	√	√	PROPN
ejpam-5751	108	4	p	p	X
ejpam-5751	108	5	s	s	PROPN
ejpam-5751	108	6	tan	tan	PROPN
ejpam-5751	108	7	(	(	PUNCT
ejpam-5751	108	8	√	√	NUM
ejpam-5751	108	9	psµ	psµ	NOUN
ejpam-5751	108	10	)	)	PUNCT
ejpam-5751	108	11	,	,	PUNCT
ejpam-5751	108	12	(	(	PUNCT
ejpam-5751	108	13	18	18	NUM
ejpam-5751	108	14	)	)	PUNCT
ejpam-5751	108	15	w6(t	w6(t	NOUN
ejpam-5751	108	16	,	,	PUNCT
ejpam-5751	108	17	x	x	NOUN
ejpam-5751	108	18	,	,	PUNCT
ejpam-5751	108	19	y	y	NOUN
ejpam-5751	108	20	)	)	PUNCT
ejpam-5751	108	21	=	=	NOUN
ejpam-5751	108	22	−ℓ	−ℓ	VERB
ejpam-5751	108	23	√	√	ADP
ejpam-5751	108	24	p	p	NOUN
ejpam-5751	108	25	s	s	X
ejpam-5751	108	26	cot	cot	NOUN
ejpam-5751	108	27	(	(	PUNCT
ejpam-5751	108	28	√	√	NUM
ejpam-5751	108	29	psµ	psµ	NOUN
ejpam-5751	108	30	)	)	PUNCT
ejpam-5751	108	31	,	,	PUNCT
ejpam-5751	108	32	(	(	PUNCT
ejpam-5751	108	33	19	19	NUM
ejpam-5751	108	34	)	)	PUNCT
ejpam-5751	108	35	w7(t	w7(t	PROPN
ejpam-5751	108	36	,	,	PUNCT
ejpam-5751	108	37	x	x	NOUN
ejpam-5751	108	38	,	,	PUNCT
ejpam-5751	108	39	y	y	NOUN
ejpam-5751	108	40	)	)	PUNCT
ejpam-5751	108	41	=	=	SYM
ejpam-5751	108	42	ℓ	ℓ	NOUN
ejpam-5751	108	43	√	√	PROPN
ejpam-5751	109	1	p	p	NOUN
ejpam-5751	109	2	s	s	X
ejpam-5751	109	3	(	(	PUNCT
ejpam-5751	109	4	tan	tan	PROPN
ejpam-5751	109	5	(	(	PUNCT
ejpam-5751	109	6	√	√	PROPN
ejpam-5751	109	7	4psµ)±	4psµ)±	NUM
ejpam-5751	109	8	sec	sec	PROPN
ejpam-5751	109	9	(	(	PUNCT
ejpam-5751	109	10	√	√	NOUN
ejpam-5751	109	11	4psµ	4psµ	NUM
ejpam-5751	109	12	)	)	PUNCT
ejpam-5751	109	13	)	)	PUNCT
ejpam-5751	109	14	,	,	PUNCT
ejpam-5751	109	15	(	(	PUNCT
ejpam-5751	109	16	20	20	NUM
ejpam-5751	109	17	)	)	PUNCT
ejpam-5751	109	18	w8(t	w8(t	PROPN
ejpam-5751	109	19	,	,	PUNCT
ejpam-5751	109	20	x	x	NOUN
ejpam-5751	109	21	,	,	PUNCT
ejpam-5751	109	22	y	y	NOUN
ejpam-5751	109	23	)	)	PUNCT
ejpam-5751	109	24	=	=	VERB
ejpam-5751	109	25	ℓ1	ℓ1	VERB
ejpam-5751	109	26	√	√	PROPN
ejpam-5751	109	27	p	p	X
ejpam-5751	109	28	s	s	X
ejpam-5751	109	29	(	(	PUNCT
ejpam-5751	109	30	cot	cot	NOUN
ejpam-5751	109	31	(	(	PUNCT
ejpam-5751	109	32	√	√	PROPN
ejpam-5751	109	33	4psµ)±	4psµ)±	NUM
ejpam-5751	109	34	csc	csc	PROPN
ejpam-5751	109	35	(	(	PUNCT
ejpam-5751	109	36	√	√	PROPN
ejpam-5751	109	37	4psµ	4psµ	NUM
ejpam-5751	109	38	)	)	PUNCT
ejpam-5751	109	39	)	)	PUNCT
ejpam-5751	109	40	,	,	PUNCT
ejpam-5751	109	41	(	(	PUNCT
ejpam-5751	109	42	21	21	NUM
ejpam-5751	109	43	)	)	PUNCT
ejpam-5751	109	44	w9(t	w9(t	PROPN
ejpam-5751	109	45	,	,	PUNCT
ejpam-5751	109	46	x	x	NOUN
ejpam-5751	109	47	,	,	PUNCT
ejpam-5751	109	48	y	y	PROPN
ejpam-5751	109	49	)	)	PUNCT
ejpam-5751	109	50	=	=	SYM
ejpam-5751	109	51	1	1	NUM
ejpam-5751	109	52	2	2	NUM
ejpam-5751	109	53	ℓ1	ℓ1	NOUN
ejpam-5751	109	54	√	√	ADP
ejpam-5751	109	55	p	p	X
ejpam-5751	109	56	s	s	X
ejpam-5751	109	57	(	(	PUNCT
ejpam-5751	109	58	tan	tan	PROPN
ejpam-5751	109	59	(	(	PUNCT
ejpam-5751	109	60	1	1	NUM
ejpam-5751	109	61	2	2	NUM
ejpam-5751	109	62	√	√	PROPN
ejpam-5751	109	63	psµ)−	psµ)−	NOUN
ejpam-5751	109	64	cot	cot	NOUN
ejpam-5751	109	65	(	(	PUNCT
ejpam-5751	109	66	1	1	NUM
ejpam-5751	109	67	2	2	NUM
ejpam-5751	109	68	√	√	NUM
ejpam-5751	109	69	psµ	psµ	NOUN
ejpam-5751	109	70	)	)	PUNCT
ejpam-5751	109	71	)	)	PUNCT
ejpam-5751	109	72	.	.	PUNCT
ejpam-5751	110	1	(	(	PUNCT
ejpam-5751	110	2	22	22	X
ejpam-5751	110	3	)	)	PUNCT
ejpam-5751	110	4	set	set	NOUN
ejpam-5751	110	5	iii	iii	NOUN
ejpam-5751	110	6	:	:	PUNCT
ejpam-5751	110	7	if	if	SCONJ
ejpam-5751	110	8	p	p	X
ejpam-5751	110	9	=	=	NOUN
ejpam-5751	110	10	0	0	NUM
ejpam-5751	110	11	and	and	CCONJ
ejpam-5751	110	12	s	s	X
ejpam-5751	110	13	̸=	̸=	PROPN
ejpam-5751	110	14	0	0	NUM
ejpam-5751	110	15	,	,	PUNCT
ejpam-5751	110	16	hence	hence	ADV
ejpam-5751	110	17	eq	eq	NOUN
ejpam-5751	110	18	.	.	PUNCT
ejpam-5751	111	1	(	(	PUNCT
ejpam-5751	111	2	6	6	NUM
ejpam-5751	111	3	)	)	PUNCT
ejpam-5751	111	4	possess	possess	VERB
ejpam-5751	111	5	the	the	DET
ejpam-5751	111	6	the	the	DET
ejpam-5751	111	7	rational	rational	ADJ
ejpam-5751	111	8	function	function	NOUN
ejpam-5751	111	9	solution	solution	NOUN
ejpam-5751	111	10	f10(µ	f10(µ	NOUN
ejpam-5751	111	11	)	)	PUNCT
ejpam-5751	111	12	=	=	SYM
ejpam-5751	111	13	−1	−1	NOUN
ejpam-5751	111	14	sµ	sµ	NOUN
ejpam-5751	111	15	.	.	PUNCT
ejpam-5751	112	1	consequently	consequently	ADV
ejpam-5751	112	2	,	,	PUNCT
ejpam-5751	112	3	the	the	DET
ejpam-5751	112	4	hfe	hfe	PROPN
ejpam-5751	112	5	-	-	PUNCT
ejpam-5751	112	6	rvcs	rvcs	PROPN
ejpam-5751	112	7	(	(	PUNCT
ejpam-5751	112	8	3	3	X
ejpam-5751	112	9	)	)	PUNCT
ejpam-5751	112	10	has	have	VERB
ejpam-5751	112	11	the	the	DET
ejpam-5751	112	12	solution	solution	NOUN
ejpam-5751	112	13	w10(t	w10(t	PROPN
ejpam-5751	112	14	,	,	PUNCT
ejpam-5751	112	15	x	x	NOUN
ejpam-5751	112	16	,	,	PUNCT
ejpam-5751	112	17	y	y	PROPN
ejpam-5751	112	18	)	)	PUNCT
ejpam-5751	112	19	=	=	SYM
ejpam-5751	112	20	−	−	PROPN
ejpam-5751	112	21	ℓ	ℓ	NOUN
ejpam-5751	112	22	sµ	sµ	NOUN
ejpam-5751	112	23	,	,	PUNCT
ejpam-5751	112	24	(	(	PUNCT
ejpam-5751	112	25	23	23	NUM
ejpam-5751	112	26	)	)	PUNCT
ejpam-5751	112	27	where	where	SCONJ
ejpam-5751	112	28	µ	µ	X
ejpam-5751	112	29	=	=	SYM
ejpam-5751	112	30	k1x+	k1x+	NOUN
ejpam-5751	112	31	k2y	k2y	NOUN
ejpam-5751	112	32	−	−	PROPN
ejpam-5751	112	33	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	112	34	s2	s2	NOUN
ejpam-5751	112	35	∫	∫	PROPN
ejpam-5751	112	36	t	t	PROPN
ejpam-5751	112	37	0	0	NUM
ejpam-5751	112	38	e	e	X
ejpam-5751	112	39	2νβ(τ)−ν2τdτ	2νβ(τ)−ν2τdτ	NUM
ejpam-5751	112	40	.	.	PUNCT
ejpam-5751	113	1	2.2	2.2	NUM
ejpam-5751	113	2	.	.	PUNCT
ejpam-5751	114	1	jef	jef	PROPN
ejpam-5751	114	2	-	-	PUNCT
ejpam-5751	114	3	method	method	NOUN
ejpam-5751	114	4	assuming	assume	VERB
ejpam-5751	114	5	that	that	SCONJ
ejpam-5751	114	6	the	the	DET
ejpam-5751	114	7	solutions	solution	NOUN
ejpam-5751	114	8	to	to	ADP
ejpam-5751	114	9	eq	eq	PROPN
ejpam-5751	114	10	.	.	PUNCT
ejpam-5751	115	1	(	(	PUNCT
ejpam-5751	115	2	3	3	X
ejpam-5751	115	3	)	)	PUNCT
ejpam-5751	115	4	with	with	ADP
ejpam-5751	115	5	n	n	NOUN
ejpam-5751	115	6	=	=	SYM
ejpam-5751	115	7	1	1	NUM
ejpam-5751	115	8	have	have	VERB
ejpam-5751	115	9	the	the	DET
ejpam-5751	115	10	following	follow	VERB
ejpam-5751	115	11	type	type	NOUN
ejpam-5751	115	12	w(t	w(t	PROPN
ejpam-5751	115	13	,	,	PUNCT
ejpam-5751	115	14	x	x	NOUN
ejpam-5751	115	15	,	,	PUNCT
ejpam-5751	115	16	y	y	NOUN
ejpam-5751	115	17	)	)	PUNCT
ejpam-5751	115	18	=	=	PUNCT
ejpam-5751	116	1	a0(t	a0(t	PROPN
ejpam-5751	116	2	)	)	PUNCT
ejpam-5751	116	3	+	+	CCONJ
ejpam-5751	116	4	a1(t)j(µ	a1(t)j(µ	NOUN
ejpam-5751	116	5	)	)	PUNCT
ejpam-5751	116	6	,	,	PUNCT
ejpam-5751	116	7	(	(	PUNCT
ejpam-5751	116	8	24	24	NUM
ejpam-5751	116	9	)	)	PUNCT
ejpam-5751	116	10	where	where	SCONJ
ejpam-5751	116	11	j(µ	j(µ	PROPN
ejpam-5751	116	12	)	)	PUNCT
ejpam-5751	116	13	can	can	AUX
ejpam-5751	116	14	be	be	AUX
ejpam-5751	116	15	any	any	PRON
ejpam-5751	116	16	of	of	ADP
ejpam-5751	116	17	the	the	DET
ejpam-5751	116	18	elliptic	elliptic	ADJ
ejpam-5751	116	19	functions	function	NOUN
ejpam-5751	116	20	cn(ωµ	cn(ωµ	PROPN
ejpam-5751	116	21	,	,	PUNCT
ejpam-5751	116	22	ň	ň	NOUN
ejpam-5751	116	23	)	)	PUNCT
ejpam-5751	116	24	,	,	PUNCT
ejpam-5751	116	25	sn(ωµ	sn(ωµ	PROPN
ejpam-5751	116	26	,	,	PUNCT
ejpam-5751	116	27	ň	ň	NOUN
ejpam-5751	116	28	)	)	PUNCT
ejpam-5751	116	29	or	or	CCONJ
ejpam-5751	116	30	dn(ωµ	dn(ωµ	NOUN
ejpam-5751	116	31	,	,	PUNCT
ejpam-5751	116	32	ň	ň	NOUN
ejpam-5751	116	33	)	)	PUNCT
ejpam-5751	116	34	.	.	PUNCT
ejpam-5751	117	1	we	we	PRON
ejpam-5751	117	2	differentiate	differentiate	VERB
ejpam-5751	117	3	eq	eq	ADP
ejpam-5751	117	4	.	.	PUNCT
ejpam-5751	118	1	(	(	PUNCT
ejpam-5751	118	2	24	24	NUM
ejpam-5751	118	3	)	)	PUNCT
ejpam-5751	118	4	with	with	ADP
ejpam-5751	118	5	regards	regard	NOUN
ejpam-5751	118	6	to	to	ADP
ejpam-5751	118	7	t	t	PROPN
ejpam-5751	118	8	,	,	PUNCT
ejpam-5751	118	9	x	x	X
ejpam-5751	118	10	and	and	CCONJ
ejpam-5751	118	11	y	y	PROPN
ejpam-5751	118	12	to	to	PART
ejpam-5751	118	13	get	get	VERB
ejpam-5751	118	14	wt	wt	PROPN
ejpam-5751	118	15	=	=	SYM
ejpam-5751	118	16	·	·	PUNCT
ejpam-5751	118	17	a0	a0	PROPN
ejpam-5751	118	18	+	+	CCONJ
ejpam-5751	118	19	·	·	PUNCT
ejpam-5751	118	20	α1j	α1j	PROPN
ejpam-5751	118	21	+	+	NUM
ejpam-5751	118	22	ωλa1j	ωλa1j	PROPN
ejpam-5751	118	23	′	′	NOUN
ejpam-5751	118	24	,	,	PUNCT
ejpam-5751	118	25	wx	wx	X
ejpam-5751	118	26	=	=	SYM
ejpam-5751	118	27	ωk1a1j	ωk1a1j	PROPN
ejpam-5751	118	28	′	′	NUM
ejpam-5751	118	29	,	,	PUNCT
ejpam-5751	118	30	wy	wy	PROPN
ejpam-5751	118	31	=	=	SYM
ejpam-5751	118	32	ωk2a1j	ωk2a1j	PROPN
ejpam-5751	118	33	′	′	NUM
ejpam-5751	118	34	,	,	PUNCT
ejpam-5751	118	35	wxx	wxx	NOUN
ejpam-5751	118	36	=	=	SYM
ejpam-5751	118	37	a1k	a1k	NUM
ejpam-5751	118	38	2	2	NUM
ejpam-5751	118	39	1ω	1ω	NOUN
ejpam-5751	118	40	2j	2j	NUM
ejpam-5751	118	41	′′	′′	PROPN
ejpam-5751	118	42	=	=	PUNCT
ejpam-5751	118	43	k21a1b1j	k21a1b1j	VERB
ejpam-5751	118	44	+	+	CCONJ
ejpam-5751	118	45	k21a1b2j	k21a1b2j	ADJ
ejpam-5751	118	46	3	3	NUM
ejpam-5751	118	47	,	,	PUNCT
ejpam-5751	118	48	wyy	wyy	NOUN
ejpam-5751	118	49	=	=	NOUN
ejpam-5751	118	50	k22a1b1j	k22a1b1j	NOUN
ejpam-5751	118	51	+	+	CCONJ
ejpam-5751	118	52	k22a1b2j	k22a1b2j	NOUN
ejpam-5751	118	53	3	3	NUM
ejpam-5751	118	54	,	,	PUNCT
ejpam-5751	118	55	wxy	wxy	PROPN
ejpam-5751	118	56	=	=	SYM
ejpam-5751	118	57	k1k2a1b1j	k1k2a1b1j	PROPN
ejpam-5751	118	58	+	+	CCONJ
ejpam-5751	118	59	k1k2a1b2j	k1k2a1b2j	PROPN
ejpam-5751	118	60	3	3	NUM
ejpam-5751	118	61	,	,	PUNCT
ejpam-5751	118	62	w.	w.	PROPN
ejpam-5751	118	63	w.	w.	PROPN
ejpam-5751	118	64	mohammed	mohammed	PROPN
ejpam-5751	118	65	et	et	PROPN
ejpam-5751	118	66	al	al	PROPN
ejpam-5751	118	67	.	.	PUNCT
ejpam-5751	118	68	/	/	SYM
ejpam-5751	118	69	eur	eur	PROPN
ejpam-5751	118	70	.	.	PUNCT
ejpam-5751	119	1	j.	j.	PROPN
ejpam-5751	119	2	pure	pure	PROPN
ejpam-5751	119	3	appl	appl	PROPN
ejpam-5751	119	4	.	.	PROPN
ejpam-5751	119	5	math	math	PROPN
ejpam-5751	119	6	,	,	PUNCT
ejpam-5751	119	7	18	18	NUM
ejpam-5751	119	8	(	(	PUNCT
ejpam-5751	119	9	1	1	NUM
ejpam-5751	119	10	)	)	PUNCT
ejpam-5751	119	11	(	(	PUNCT
ejpam-5751	119	12	2025	2025	NUM
ejpam-5751	119	13	)	)	PUNCT
ejpam-5751	119	14	,	,	PUNCT
ejpam-5751	119	15	5751	5751	NUM
ejpam-5751	119	16	7	7	NUM
ejpam-5751	119	17	of	of	ADP
ejpam-5751	119	18	15	15	NUM
ejpam-5751	119	19	w3	w3	NOUN
ejpam-5751	119	20	=	=	PUNCT
ejpam-5751	119	21	a31j	a31j	PART
ejpam-5751	119	22	3	3	NUM
ejpam-5751	119	23	+	+	NUM
ejpam-5751	119	24	3a0a	3a0a	NUM
ejpam-5751	119	25	2	2	NUM
ejpam-5751	119	26	1j	1j	NUM
ejpam-5751	119	27	2	2	NUM
ejpam-5751	119	28	+	+	CCONJ
ejpam-5751	119	29	3a20a1j	3a20a1j	ADJ
ejpam-5751	119	30	+	+	CCONJ
ejpam-5751	119	31	a30	a30	NOUN
ejpam-5751	119	32	,	,	PUNCT
ejpam-5751	119	33	(	(	PUNCT
ejpam-5751	119	34	25	25	NUM
ejpam-5751	119	35	)	)	PUNCT
ejpam-5751	119	36	where	where	SCONJ
ejpam-5751	119	37	b1	b1	NOUN
ejpam-5751	119	38	and	and	CCONJ
ejpam-5751	119	39	b2	b2	NOUN
ejpam-5751	119	40	are	be	AUX
ejpam-5751	119	41	constants	constant	NOUN
ejpam-5751	119	42	that	that	PRON
ejpam-5751	119	43	will	will	AUX
ejpam-5751	119	44	be	be	AUX
ejpam-5751	119	45	determined	determine	VERB
ejpam-5751	119	46	later	later	ADV
ejpam-5751	119	47	and	and	CCONJ
ejpam-5751	119	48	rely	rely	VERB
ejpam-5751	119	49	on	on	ADP
ejpam-5751	119	50	ω	ω	NUM
ejpam-5751	119	51	,	,	PUNCT
ejpam-5751	119	52	and	and	CCONJ
ejpam-5751	119	53	ň.	ň.	NOUN
ejpam-5751	119	54	plugging	plug	VERB
ejpam-5751	119	55	eqs	eq	NOUN
ejpam-5751	119	56	.	.	PUNCT
ejpam-5751	120	1	(	(	PUNCT
ejpam-5751	120	2	25	25	NUM
ejpam-5751	120	3	)	)	PUNCT
ejpam-5751	120	4	and	and	CCONJ
ejpam-5751	120	5	(	(	PUNCT
ejpam-5751	120	6	9	9	NUM
ejpam-5751	120	7	)	)	PUNCT
ejpam-5751	120	8	into	into	ADP
ejpam-5751	120	9	eq	eq	NOUN
ejpam-5751	120	10	.	.	PUNCT
ejpam-5751	121	1	(	(	PUNCT
ejpam-5751	121	2	3	3	NUM
ejpam-5751	121	3	)	)	PUNCT
ejpam-5751	121	4	.	.	PUNCT
ejpam-5751	122	1	then	then	ADV
ejpam-5751	122	2	,	,	PUNCT
ejpam-5751	122	3	by	by	ADP
ejpam-5751	122	4	setting	set	VERB
ejpam-5751	122	5	each	each	PRON
ejpam-5751	122	6	of	of	ADP
ejpam-5751	122	7	jk	jk	PROPN
ejpam-5751	122	8	’s	’s	PART
ejpam-5751	122	9	coefficients	coefficient	NOUN
ejpam-5751	122	10	to	to	ADP
ejpam-5751	122	11	zero	zero	NUM
ejpam-5751	122	12	,	,	PUNCT
ejpam-5751	122	13	we	we	PRON
ejpam-5751	122	14	gain	gain	VERB
ejpam-5751	122	15	j0	j0	PROPN
ejpam-5751	122	16	:	:	PUNCT
ejpam-5751	122	17	·	·	PUNCT
ejpam-5751	122	18	a0	a0	PROPN
ejpam-5751	122	19	=	=	SYM
ejpam-5751	122	20	0	0	PROPN
ejpam-5751	122	21	,	,	PUNCT
ejpam-5751	122	22	j1	j1	PROPN
ejpam-5751	122	23	:	:	PUNCT
ejpam-5751	122	24	·	·	PUNCT
ejpam-5751	122	25	a1	a1	NOUN
ejpam-5751	122	26	=	=	SYM
ejpam-5751	122	27	0	0	PROPN
ejpam-5751	122	28	,	,	PUNCT
ejpam-5751	122	29	j	j	PROPN
ejpam-5751	122	30	′	′	NUM
ejpam-5751	122	31	:	:	PUNCT
ejpam-5751	122	32	ωa1[λ+	ωa1[λ+	NOUN
ejpam-5751	122	33	2ρ1ψ1k1	2ρ1ψ1k1	NUM
ejpam-5751	122	34	+	+	CCONJ
ejpam-5751	122	35	2ρ2ψ2k2	2ρ2ψ2k2	NUM
ejpam-5751	122	36	+	+	CCONJ
ejpam-5751	122	37	ρ3ψ1k2	ρ3ψ1k2	PROPN
ejpam-5751	122	38	+	+	CCONJ
ejpam-5751	122	39	ρ3ψ2k1	ρ3ψ2k1	X
ejpam-5751	122	40	]	]	X
ejpam-5751	122	41	=	=	SYM
ejpam-5751	122	42	0	0	NUM
ejpam-5751	122	43	,	,	PUNCT
ejpam-5751	122	44	xj0	xj0	PROPN
ejpam-5751	122	45	:	:	PUNCT
ejpam-5751	123	1	a0	a0	PROPN
ejpam-5751	123	2	·	·	PUNCT
ejpam-5751	123	3	φ1	φ1	PROPN
ejpam-5751	123	4	=	=	SYM
ejpam-5751	123	5	0	0	NUM
ejpam-5751	123	6	,	,	PUNCT
ejpam-5751	123	7	yj0	yj0	NOUN
ejpam-5751	123	8	:	:	PUNCT
ejpam-5751	123	9	a0	a0	PROPN
ejpam-5751	123	10	·	·	PUNCT
ejpam-5751	123	11	φ2	φ2	PROPN
ejpam-5751	123	12	=	=	PUNCT
ejpam-5751	123	13	0	0	NUM
ejpam-5751	123	14	,	,	PUNCT
ejpam-5751	123	15	xj1	xj1	PROPN
ejpam-5751	123	16	:	:	PUNCT
ejpam-5751	123	17	a1	a1	NOUN
ejpam-5751	123	18	·	·	PUNCT
ejpam-5751	123	19	φ1	φ1	NOUN
ejpam-5751	123	20	=	=	SYM
ejpam-5751	123	21	0	0	NUM
ejpam-5751	123	22	,	,	PUNCT
ejpam-5751	123	23	yj1	yj1	NOUN
ejpam-5751	123	24	:	:	PUNCT
ejpam-5751	123	25	a1	a1	NOUN
ejpam-5751	123	26	·	·	PUNCT
ejpam-5751	123	27	φ2	φ2	NOUN
ejpam-5751	123	28	=	=	SYM
ejpam-5751	123	29	0	0	NUM
ejpam-5751	123	30	,	,	PUNCT
ejpam-5751	123	31	j0	j0	NUM
ejpam-5751	123	32	:	:	PUNCT
ejpam-5751	123	33	−a0	−a0	PROPN
ejpam-5751	123	34	·	·	PUNCT
ejpam-5751	123	35	φ0	φ0	ADJ
ejpam-5751	123	36	−	−	PROPN
ejpam-5751	123	37	φ2	φ2	PROPN
ejpam-5751	123	38	1ρ1a0	1ρ1a0	PROPN
ejpam-5751	123	39	−	−	PROPN
ejpam-5751	124	1	φ2	φ2	PROPN
ejpam-5751	124	2	2ρ2a0	2ρ2a0	NUM
ejpam-5751	125	1	−	−	PROPN
ejpam-5751	125	2	φ1φ2ρ3a0	φ1φ2ρ3a0	PROPN
ejpam-5751	125	3	−aa30	−aa30	PROPN
ejpam-5751	125	4	=	=	SYM
ejpam-5751	125	5	0	0	PROPN
ejpam-5751	125	6	,	,	PUNCT
ejpam-5751	125	7	j1	j1	NOUN
ejpam-5751	125	8	:	:	PUNCT
ejpam-5751	125	9	−a1	−a1	PROPN
ejpam-5751	125	10	·	·	PUNCT
ejpam-5751	125	11	φ0	φ0	PROPN
ejpam-5751	125	12	+	+	CCONJ
ejpam-5751	125	13	ρ1a1k	ρ1a1k	NUM
ejpam-5751	125	14	2	2	NUM
ejpam-5751	125	15	1b1	1b1	NUM
ejpam-5751	125	16	+	+	NOUN
ejpam-5751	125	17	ρ2a1k	ρ2a1k	NUM
ejpam-5751	125	18	2	2	NUM
ejpam-5751	125	19	2b1	2b1	NUM
ejpam-5751	125	20	+	+	CCONJ
ejpam-5751	125	21	ρ3a1k1k2b1	ρ3a1k1k2b1	NUM
ejpam-5751	125	22	−ρ1a1φ2	−ρ1a1φ2	NOUN
ejpam-5751	125	23	1	1	NUM
ejpam-5751	125	24	−	−	NOUN
ejpam-5751	125	25	ρ2a1φ	ρ2a1φ	NUM
ejpam-5751	125	26	2	2	NUM
ejpam-5751	125	27	2	2	NUM
ejpam-5751	125	28	−	−	NOUN
ejpam-5751	125	29	ρ3a1φ1φ2	ρ3a1φ1φ2	PROPN
ejpam-5751	125	30	−	−	PROPN
ejpam-5751	125	31	3aa20a1	3aa20a1	NUM
ejpam-5751	125	32	=	=	SYM
ejpam-5751	125	33	0	0	NUM
ejpam-5751	125	34	,	,	PUNCT
ejpam-5751	125	35	j2	j2	NOUN
ejpam-5751	125	36	:	:	PUNCT
ejpam-5751	125	37	3aa0a	3aa0a	NUM
ejpam-5751	125	38	2	2	NUM
ejpam-5751	125	39	1	1	NUM
ejpam-5751	125	40	=	=	SYM
ejpam-5751	125	41	0	0	NUM
ejpam-5751	125	42	,	,	PUNCT
ejpam-5751	125	43	and	and	CCONJ
ejpam-5751	125	44	j3	j3	PROPN
ejpam-5751	125	45	:	:	PUNCT
ejpam-5751	125	46	ρ1a1k	ρ1a1k	NUM
ejpam-5751	125	47	2	2	NUM
ejpam-5751	125	48	1b2	1b2	NUM
ejpam-5751	125	49	+	+	SYM
ejpam-5751	125	50	ρ2a1k	ρ2a1k	NUM
ejpam-5751	125	51	2	2	NUM
ejpam-5751	125	52	2b2	2b2	NUM
ejpam-5751	125	53	+	+	CCONJ
ejpam-5751	125	54	ρ3a1k1k2b2	ρ3a1k1k2b2	NUM
ejpam-5751	125	55	−aa31	−aa31	ADP
ejpam-5751	125	56	=	=	NOUN
ejpam-5751	125	57	0	0	PROPN
ejpam-5751	125	58	.	.	PUNCT
ejpam-5751	126	1	solving	solve	VERB
ejpam-5751	126	2	these	these	DET
ejpam-5751	126	3	equations	equation	NOUN
ejpam-5751	126	4	,	,	PUNCT
ejpam-5751	126	5	yields	yield	NOUN
ejpam-5751	126	6	a0(t	a0(t	PROPN
ejpam-5751	126	7	)	)	PUNCT
ejpam-5751	126	8	=	=	SYM
ejpam-5751	126	9	0	0	NUM
ejpam-5751	126	10	,	,	PUNCT
ejpam-5751	126	11	a1	a1	NOUN
ejpam-5751	126	12	=	=	SYM
ejpam-5751	126	13	ℏ	ℏ	PROPN
ejpam-5751	126	14	,	,	PUNCT
ejpam-5751	126	15	ρ1k21	ρ1k21	NOUN
ejpam-5751	126	16	+	+	PUNCT
ejpam-5751	126	17	ρ2k	ρ2k	PROPN
ejpam-5751	126	18	2	2	NUM
ejpam-5751	126	19	2	2	NUM
ejpam-5751	126	20	+	+	CCONJ
ejpam-5751	126	21	ρ3k1k2	ρ3k1k2	NOUN
ejpam-5751	126	22	=	=	SYM
ejpam-5751	126	23	ℏ2a(t	ℏ2a(t	PROPN
ejpam-5751	126	24	)	)	PUNCT
ejpam-5751	126	25	b2	b2	NOUN
ejpam-5751	126	26	,	,	PUNCT
ejpam-5751	126	27	φ1	φ1	PROPN
ejpam-5751	126	28	=	=	SYM
ejpam-5751	126	29	k1	k1	PROPN
ejpam-5751	126	30	,	,	PUNCT
ejpam-5751	126	31	φ2	φ2	NOUN
ejpam-5751	126	32	=	=	SYM
ejpam-5751	126	33	k2	k2	PROPN
ejpam-5751	126	34	,	,	PUNCT
ejpam-5751	126	35	(	(	PUNCT
ejpam-5751	126	36	26	26	NUM
ejpam-5751	126	37	)	)	PUNCT
ejpam-5751	126	38	and	and	CCONJ
ejpam-5751	126	39	φ0	φ0	PROPN
ejpam-5751	126	40	=	=	PROPN
ejpam-5751	127	1	ℏ2(b1	ℏ2(b1	AUX
ejpam-5751	127	2	−	−	NOUN
ejpam-5751	127	3	1	1	NUM
ejpam-5751	127	4	)	)	PUNCT
ejpam-5751	127	5	b2	b2	NOUN
ejpam-5751	127	6	∫	∫	PROPN
ejpam-5751	127	7	t	t	PROPN
ejpam-5751	127	8	0	0	NUM
ejpam-5751	127	9	a(τ)dτ	a(τ)dτ	PROPN
ejpam-5751	127	10	,	,	PUNCT
ejpam-5751	127	11	λ(t	λ(t	X
ejpam-5751	127	12	)	)	PUNCT
ejpam-5751	127	13	=	=	SYM
ejpam-5751	127	14	−2ℏ2	−2ℏ2	PUNCT
ejpam-5751	127	15	b2	b2	NOUN
ejpam-5751	127	16	a(t	a(t	NOUN
ejpam-5751	127	17	)	)	PUNCT
ejpam-5751	127	18	,	,	PUNCT
ejpam-5751	127	19	where	where	SCONJ
ejpam-5751	127	20	ℏ	ℏ	PROPN
ejpam-5751	127	21	is	be	AUX
ejpam-5751	127	22	a	a	DET
ejpam-5751	127	23	constant	constant	ADJ
ejpam-5751	127	24	.	.	PUNCT
ejpam-5751	128	1	therefore	therefore	ADV
ejpam-5751	128	2	,	,	PUNCT
ejpam-5751	128	3	the	the	DET
ejpam-5751	128	4	solutions	solution	NOUN
ejpam-5751	128	5	of	of	ADP
ejpam-5751	128	6	the	the	DET
ejpam-5751	128	7	hfe	hfe	PROPN
ejpam-5751	128	8	-	-	PUNCT
ejpam-5751	128	9	rvcs	rvcs	PROPN
ejpam-5751	128	10	(	(	PUNCT
ejpam-5751	128	11	3	3	NUM
ejpam-5751	128	12	)	)	PUNCT
ejpam-5751	128	13	,	,	PUNCT
ejpam-5751	128	14	using	use	VERB
ejpam-5751	128	15	eqs	eqs	PROPN
ejpam-5751	128	16	(	(	PUNCT
ejpam-5751	128	17	24	24	NUM
ejpam-5751	128	18	)	)	PUNCT
ejpam-5751	128	19	and	and	CCONJ
ejpam-5751	128	20	(	(	PUNCT
ejpam-5751	128	21	26	26	NUM
ejpam-5751	128	22	)	)	PUNCT
ejpam-5751	128	23	,	,	PUNCT
ejpam-5751	128	24	are	be	AUX
ejpam-5751	128	25	w(t	w(t	PROPN
ejpam-5751	128	26	,	,	PUNCT
ejpam-5751	128	27	x	x	X
ejpam-5751	128	28	,	,	PUNCT
ejpam-5751	128	29	y	y	PROPN
ejpam-5751	128	30	)	)	PUNCT
ejpam-5751	128	31	=	=	PUNCT
ejpam-5751	128	32	ℏj(µ	ℏj(µ	NOUN
ejpam-5751	128	33	)	)	PUNCT
ejpam-5751	128	34	,	,	PUNCT
ejpam-5751	128	35	µ	µ	X
ejpam-5751	128	36	=	=	SYM
ejpam-5751	128	37	k1x+	k1x+	NOUN
ejpam-5751	128	38	k2y	k2y	NOUN
ejpam-5751	128	39	−	−	PROPN
ejpam-5751	128	40	2ℏ2ρ4	2ℏ2ρ4	NUM
ejpam-5751	128	41	b2	b2	NOUN
ejpam-5751	128	42	∫	∫	PROPN
ejpam-5751	128	43	t	t	PROPN
ejpam-5751	128	44	0	0	NUM
ejpam-5751	128	45	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	128	46	.	.	PUNCT
ejpam-5751	129	1	(	(	PUNCT
ejpam-5751	129	2	27	27	NUM
ejpam-5751	129	3	)	)	PUNCT
ejpam-5751	129	4	in	in	ADP
ejpam-5751	129	5	the	the	DET
ejpam-5751	129	6	following	following	NOUN
ejpam-5751	129	7	,	,	PUNCT
ejpam-5751	129	8	we	we	PRON
ejpam-5751	129	9	define	define	VERB
ejpam-5751	129	10	j(µ	j(µ	PROPN
ejpam-5751	129	11	)	)	PUNCT
ejpam-5751	129	12	as	as	ADP
ejpam-5751	129	13	:	:	PUNCT
ejpam-5751	129	14	set	set	NOUN
ejpam-5751	129	15	1	1	NUM
ejpam-5751	129	16	:	:	PUNCT
ejpam-5751	129	17	when	when	SCONJ
ejpam-5751	129	18	j(µ	j(µ	PROPN
ejpam-5751	129	19	)	)	PUNCT
ejpam-5751	129	20	=	=	SYM
ejpam-5751	129	21	sn(ωµ	sn(ωµ	PROPN
ejpam-5751	129	22	,	,	PUNCT
ejpam-5751	129	23	ň	ň	NOUN
ejpam-5751	129	24	)	)	PUNCT
ejpam-5751	129	25	,	,	PUNCT
ejpam-5751	129	26	eq	eq	NOUN
ejpam-5751	129	27	.	.	PUNCT
ejpam-5751	130	1	(	(	PUNCT
ejpam-5751	130	2	27	27	NUM
ejpam-5751	130	3	)	)	PUNCT
ejpam-5751	130	4	has	have	VERB
ejpam-5751	130	5	the	the	DET
ejpam-5751	130	6	form	form	NOUN
ejpam-5751	130	7	w(t	w(t	PROPN
ejpam-5751	130	8	,	,	PUNCT
ejpam-5751	130	9	x	x	NOUN
ejpam-5751	130	10	,	,	PUNCT
ejpam-5751	130	11	y	y	NOUN
ejpam-5751	130	12	)	)	PUNCT
ejpam-5751	130	13	=	=	NOUN
ejpam-5751	130	14	ℏ[sn(k1ωx+	ℏ[sn(k1ωx+	NOUN
ejpam-5751	130	15	ωk2y	ωk2y	ADJ
ejpam-5751	130	16	−	−	ADP
ejpam-5751	130	17	2ωℏ2ρ4	2ωℏ2ρ4	NUM
ejpam-5751	130	18	b2	b2	NOUN
ejpam-5751	130	19	∫	∫	PROPN
ejpam-5751	130	20	t	t	PROPN
ejpam-5751	130	21	0	0	NUM
ejpam-5751	130	22	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	130	23	,	,	PUNCT
ejpam-5751	130	24	ň	ň	NOUN
ejpam-5751	130	25	)	)	PUNCT
ejpam-5751	130	26	]	]	PUNCT
ejpam-5751	130	27	,	,	PUNCT
ejpam-5751	130	28	(	(	PUNCT
ejpam-5751	130	29	28	28	NUM
ejpam-5751	130	30	)	)	PUNCT
ejpam-5751	130	31	where	where	SCONJ
ejpam-5751	130	32	b1	b1	NOUN
ejpam-5751	130	33	=	=	SYM
ejpam-5751	130	34	−ω2(1	−ω2(1	PROPN
ejpam-5751	130	35	+	+	NUM
ejpam-5751	130	36	ň2	ň2	NUM
ejpam-5751	130	37	)	)	PUNCT
ejpam-5751	130	38	and	and	CCONJ
ejpam-5751	130	39	b2	b2	NOUN
ejpam-5751	130	40	=	=	SYM
ejpam-5751	130	41	2ω2ň2	2ω2ň2	NUM
ejpam-5751	130	42	.	.	PUNCT
ejpam-5751	131	1	w.	w.	PROPN
ejpam-5751	131	2	w.	w.	PROPN
ejpam-5751	131	3	mohammed	mohammed	PROPN
ejpam-5751	131	4	et	et	PROPN
ejpam-5751	131	5	al	al	PROPN
ejpam-5751	131	6	.	.	PUNCT
ejpam-5751	131	7	/	/	SYM
ejpam-5751	131	8	eur	eur	PROPN
ejpam-5751	131	9	.	.	PUNCT
ejpam-5751	132	1	j.	j.	PROPN
ejpam-5751	132	2	pure	pure	PROPN
ejpam-5751	132	3	appl	appl	PROPN
ejpam-5751	132	4	.	.	PROPN
ejpam-5751	132	5	math	math	PROPN
ejpam-5751	132	6	,	,	PUNCT
ejpam-5751	132	7	18	18	NUM
ejpam-5751	132	8	(	(	PUNCT
ejpam-5751	132	9	1	1	NUM
ejpam-5751	132	10	)	)	PUNCT
ejpam-5751	132	11	(	(	PUNCT
ejpam-5751	132	12	2025	2025	NUM
ejpam-5751	132	13	)	)	PUNCT
ejpam-5751	132	14	,	,	PUNCT
ejpam-5751	132	15	5751	5751	NUM
ejpam-5751	132	16	8	8	NUM
ejpam-5751	132	17	of	of	ADP
ejpam-5751	132	18	15	15	NUM
ejpam-5751	132	19	set	set	VERB
ejpam-5751	132	20	2	2	NUM
ejpam-5751	132	21	:	:	PUNCT
ejpam-5751	132	22	when	when	SCONJ
ejpam-5751	132	23	j(µ	j(µ	PROPN
ejpam-5751	132	24	)	)	PUNCT
ejpam-5751	132	25	=	=	SYM
ejpam-5751	133	1	cn(ωµ	cn(ωµ	PROPN
ejpam-5751	133	2	,	,	PUNCT
ejpam-5751	133	3	ň	ň	NOUN
ejpam-5751	133	4	)	)	PUNCT
ejpam-5751	133	5	,	,	PUNCT
ejpam-5751	133	6	eq	eq	NOUN
ejpam-5751	133	7	.	.	PUNCT
ejpam-5751	134	1	(	(	PUNCT
ejpam-5751	134	2	27	27	NUM
ejpam-5751	134	3	)	)	PUNCT
ejpam-5751	134	4	has	have	VERB
ejpam-5751	134	5	the	the	DET
ejpam-5751	134	6	form	form	NOUN
ejpam-5751	134	7	w(t	w(t	PROPN
ejpam-5751	134	8	,	,	PUNCT
ejpam-5751	134	9	x	x	NOUN
ejpam-5751	134	10	,	,	PUNCT
ejpam-5751	134	11	y	y	NOUN
ejpam-5751	134	12	)	)	PUNCT
ejpam-5751	135	1	=	=	NOUN
ejpam-5751	135	2	ℏ[cn(k1ωx+	ℏ[cn(k1ωx+	NOUN
ejpam-5751	135	3	ωk2y	ωk2y	ADJ
ejpam-5751	135	4	−	−	PROPN
ejpam-5751	135	5	2ωℏ2ρ4	2ωℏ2ρ4	NUM
ejpam-5751	135	6	b2	b2	NOUN
ejpam-5751	135	7	∫	∫	PROPN
ejpam-5751	135	8	t	t	PROPN
ejpam-5751	135	9	0	0	NUM
ejpam-5751	135	10	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	135	11	,	,	PUNCT
ejpam-5751	135	12	ň	ň	NOUN
ejpam-5751	135	13	)	)	PUNCT
ejpam-5751	135	14	]	]	PUNCT
ejpam-5751	135	15	,	,	PUNCT
ejpam-5751	135	16	(	(	PUNCT
ejpam-5751	135	17	29	29	NUM
ejpam-5751	135	18	)	)	PUNCT
ejpam-5751	135	19	where	where	SCONJ
ejpam-5751	135	20	b1	b1	NOUN
ejpam-5751	135	21	=	=	SYM
ejpam-5751	135	22	ω2(1−	ω2(1−	NOUN
ejpam-5751	135	23	2ň2	2ň2	NUM
ejpam-5751	135	24	)	)	PUNCT
ejpam-5751	135	25	and	and	CCONJ
ejpam-5751	135	26	b2	b2	NOUN
ejpam-5751	135	27	=	=	SYM
ejpam-5751	135	28	−2ω2ň2	−2ω2ň2	NOUN
ejpam-5751	135	29	.	.	PUNCT
ejpam-5751	136	1	set	set	VERB
ejpam-5751	136	2	3	3	NUM
ejpam-5751	136	3	:	:	PUNCT
ejpam-5751	136	4	when	when	SCONJ
ejpam-5751	136	5	j(µ	j(µ	PROPN
ejpam-5751	136	6	)	)	PUNCT
ejpam-5751	136	7	=	=	SYM
ejpam-5751	136	8	dn(ωµ	dn(ωµ	PROPN
ejpam-5751	136	9	,	,	PUNCT
ejpam-5751	136	10	ň	ň	NOUN
ejpam-5751	136	11	)	)	PUNCT
ejpam-5751	136	12	,	,	PUNCT
ejpam-5751	136	13	eq	eq	NOUN
ejpam-5751	136	14	.	.	PUNCT
ejpam-5751	137	1	(	(	PUNCT
ejpam-5751	137	2	27	27	NUM
ejpam-5751	137	3	)	)	PUNCT
ejpam-5751	137	4	has	have	VERB
ejpam-5751	137	5	the	the	DET
ejpam-5751	137	6	form	form	NOUN
ejpam-5751	137	7	w(t	w(t	PROPN
ejpam-5751	137	8	,	,	PUNCT
ejpam-5751	137	9	x	x	NOUN
ejpam-5751	137	10	,	,	PUNCT
ejpam-5751	137	11	y	y	NOUN
ejpam-5751	137	12	)	)	PUNCT
ejpam-5751	137	13	=	=	NOUN
ejpam-5751	137	14	ℏ[dn(k1ωx+	ℏ[dn(k1ωx+	ADJ
ejpam-5751	137	15	ωk2y	ωk2y	PROPN
ejpam-5751	137	16	−	−	PROPN
ejpam-5751	137	17	2ωℏ2ρ4	2ωℏ2ρ4	NUM
ejpam-5751	137	18	b2	b2	NOUN
ejpam-5751	137	19	∫	∫	PROPN
ejpam-5751	137	20	t	t	PROPN
ejpam-5751	137	21	0	0	NUM
ejpam-5751	137	22	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	137	23	,	,	PUNCT
ejpam-5751	137	24	ň	ň	NOUN
ejpam-5751	137	25	)	)	PUNCT
ejpam-5751	137	26	]	]	PUNCT
ejpam-5751	137	27	,	,	PUNCT
ejpam-5751	137	28	(	(	PUNCT
ejpam-5751	137	29	30	30	NUM
ejpam-5751	137	30	)	)	PUNCT
ejpam-5751	137	31	where	where	SCONJ
ejpam-5751	137	32	b1	b1	NOUN
ejpam-5751	137	33	=	=	SYM
ejpam-5751	137	34	ω2(2−	ω2(2−	NOUN
ejpam-5751	137	35	ň2	ň2	NUM
ejpam-5751	137	36	)	)	PUNCT
ejpam-5751	137	37	and	and	CCONJ
ejpam-5751	137	38	b2	b2	NOUN
ejpam-5751	137	39	=	=	PUNCT
ejpam-5751	137	40	−2ω2	−2ω2	NUM
ejpam-5751	137	41	.	.	NOUN
ejpam-5751	138	1	3	3	X
ejpam-5751	138	2	.	.	NOUN
ejpam-5751	138	3	exact	exact	ADJ
ejpam-5751	138	4	solutions	solution	NOUN
ejpam-5751	138	5	of	of	ADP
ejpam-5751	138	6	shfe	shfe	PROPN
ejpam-5751	138	7	the	the	DET
ejpam-5751	138	8	solution	solution	NOUN
ejpam-5751	138	9	of	of	ADP
ejpam-5751	138	10	shfe	shfe	PROPN
ejpam-5751	138	11	(	(	PUNCT
ejpam-5751	138	12	1	1	X
ejpam-5751	138	13	)	)	PUNCT
ejpam-5751	138	14	is	be	AUX
ejpam-5751	138	15	obtained	obtain	VERB
ejpam-5751	138	16	by	by	ADP
ejpam-5751	138	17	putting	put	VERB
ejpam-5751	138	18	eq	eq	NOUN
ejpam-5751	138	19	.	.	PUNCT
ejpam-5751	139	1	(	(	PUNCT
ejpam-5751	139	2	13	13	NUM
ejpam-5751	139	3	)	)	PUNCT
ejpam-5751	139	4	into	into	ADP
ejpam-5751	139	5	eq	eq	NOUN
ejpam-5751	139	6	.	.	PUNCT
ejpam-5751	140	1	(	(	PUNCT
ejpam-5751	140	2	2	2	NUM
ejpam-5751	140	3	)	)	PUNCT
ejpam-5751	140	4	as	as	ADP
ejpam-5751	140	5	u(t	u(t	NOUN
ejpam-5751	140	6	,	,	PUNCT
ejpam-5751	140	7	x	x	NOUN
ejpam-5751	140	8	,	,	PUNCT
ejpam-5751	140	9	y	y	PROPN
ejpam-5751	140	10	)	)	PUNCT
ejpam-5751	140	11	=	=	SYM
ejpam-5751	140	12	w(t	w(t	PROPN
ejpam-5751	140	13	,	,	PUNCT
ejpam-5751	140	14	x	x	NOUN
ejpam-5751	140	15	,	,	PUNCT
ejpam-5751	140	16	y	y	NOUN
ejpam-5751	140	17	)	)	PUNCT
ejpam-5751	140	18	exp[iφ(t	exp[iφ(t	ADJ
ejpam-5751	140	19	,	,	PUNCT
ejpam-5751	140	20	x	x	NOUN
ejpam-5751	140	21	,	,	PUNCT
ejpam-5751	140	22	y	y	PROPN
ejpam-5751	140	23	)	)	PUNCT
ejpam-5751	140	24	+	+	CCONJ
ejpam-5751	140	25	νβ(t)−	νβ(t)−	NOUN
ejpam-5751	140	26	1	1	NUM
ejpam-5751	140	27	2	2	NUM
ejpam-5751	140	28	ν2	ν2	NOUN
ejpam-5751	140	29	t	t	NOUN
ejpam-5751	140	30	]	]	PUNCT
ejpam-5751	140	31	,	,	PUNCT
ejpam-5751	140	32	(	(	PUNCT
ejpam-5751	140	33	31	31	NUM
ejpam-5751	140	34	)	)	PUNCT
ejpam-5751	140	35	where	where	SCONJ
ejpam-5751	140	36	φ(t	φ(t	PROPN
ejpam-5751	140	37	,	,	PUNCT
ejpam-5751	140	38	x	x	NOUN
ejpam-5751	140	39	,	,	PUNCT
ejpam-5751	140	40	y	y	NOUN
ejpam-5751	140	41	)	)	PUNCT
ejpam-5751	140	42	=	=	SYM
ejpam-5751	141	1	k1x+	k1x+	NOUN
ejpam-5751	141	2	k2y	k2y	PROPN
ejpam-5751	141	3	+	+	CCONJ
ejpam-5751	141	4	(	(	PUNCT
ejpam-5751	141	5	ρ4ℓ	ρ4ℓ	NUM
ejpam-5751	141	6	2	2	NUM
ejpam-5751	141	7	2s2	2s2	NUM
ejpam-5751	141	8	−	−	PROPN
ejpam-5751	141	9	pρ4ℓ	pρ4ℓ	NOUN
ejpam-5751	141	10	2	2	NUM
ejpam-5751	141	11	s	s	PART
ejpam-5751	141	12	)	)	PUNCT
ejpam-5751	141	13	∫	∫	PROPN
ejpam-5751	141	14	t	t	PROPN
ejpam-5751	141	15	0	0	NUM
ejpam-5751	141	16	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	141	17	.	.	PUNCT
ejpam-5751	142	1	3.1	3.1	NUM
ejpam-5751	142	2	.	.	PUNCT
ejpam-5751	142	3	grem	grem	NOUN
ejpam-5751	142	4	-	-	NOUN
ejpam-5751	142	5	method	method	NOUN
ejpam-5751	142	6	substituting	substitute	VERB
ejpam-5751	142	7	eqs	eq	NOUN
ejpam-5751	142	8	(	(	PUNCT
ejpam-5751	142	9	18)-(23	18)-(23	NOUN
ejpam-5751	142	10	)	)	PUNCT
ejpam-5751	142	11	into	into	ADP
ejpam-5751	142	12	(	(	PUNCT
ejpam-5751	142	13	31	31	NUM
ejpam-5751	142	14	)	)	PUNCT
ejpam-5751	142	15	,	,	PUNCT
ejpam-5751	142	16	we	we	PRON
ejpam-5751	142	17	get	get	VERB
ejpam-5751	142	18	the	the	DET
ejpam-5751	142	19	solutions	solution	NOUN
ejpam-5751	142	20	of	of	ADP
ejpam-5751	142	21	the	the	DET
ejpam-5751	142	22	shfe	shfe	PROPN
ejpam-5751	142	23	(	(	PUNCT
ejpam-5751	142	24	1	1	NUM
ejpam-5751	142	25	)	)	PUNCT
ejpam-5751	142	26	as	as	ADP
ejpam-5751	142	27	:	:	PUNCT
ejpam-5751	142	28	u1(t	u1(t	ADP
ejpam-5751	142	29	,	,	PUNCT
ejpam-5751	142	30	x	x	NOUN
ejpam-5751	142	31	,	,	PUNCT
ejpam-5751	142	32	y	y	NOUN
ejpam-5751	142	33	)	)	PUNCT
ejpam-5751	143	1	=	=	SYM
ejpam-5751	143	2	ℓ	ℓ	NOUN
ejpam-5751	143	3	√	√	NOUN
ejpam-5751	143	4	−p	−p	NOUN
ejpam-5751	143	5	s	s	X
ejpam-5751	143	6	(	(	PUNCT
ejpam-5751	143	7	tanh	tanh	PROPN
ejpam-5751	143	8	[	[	PUNCT
ejpam-5751	143	9	√	√	NUM
ejpam-5751	143	10	−ps(k1x+	−ps(k1x+	INTJ
ejpam-5751	143	11	k2y	k2y	PROPN
ejpam-5751	143	12	−	−	NOUN
ejpam-5751	143	13	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	143	14	s2	s2	NOUN
ejpam-5751	143	15	∫	∫	PROPN
ejpam-5751	143	16	t	t	PROPN
ejpam-5751	143	17	0	0	NUM
ejpam-5751	143	18	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	143	19	)	)	PUNCT
ejpam-5751	143	20	]	]	PUNCT
ejpam-5751	143	21	)	)	PUNCT
ejpam-5751	143	22	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	143	23	1	1	NUM
ejpam-5751	143	24	2	2	NUM
ejpam-5751	143	25	ν2	ν2	NOUN
ejpam-5751	143	26	t	t	NOUN
ejpam-5751	143	27	]	]	PUNCT
ejpam-5751	143	28	,	,	PUNCT
ejpam-5751	143	29	(	(	PUNCT
ejpam-5751	143	30	32	32	NUM
ejpam-5751	143	31	)	)	PUNCT
ejpam-5751	143	32	u2(t	u2(t	PROPN
ejpam-5751	143	33	,	,	PUNCT
ejpam-5751	143	34	x	x	NOUN
ejpam-5751	143	35	,	,	PUNCT
ejpam-5751	143	36	y	y	NOUN
ejpam-5751	143	37	)	)	PUNCT
ejpam-5751	143	38	=	=	SYM
ejpam-5751	144	1	ℓ	ℓ	NOUN
ejpam-5751	144	2	√	√	NOUN
ejpam-5751	144	3	−p	−p	NOUN
ejpam-5751	144	4	s	s	X
ejpam-5751	144	5	(	(	PUNCT
ejpam-5751	144	6	coth	coth	PROPN
ejpam-5751	144	7	[	[	PUNCT
ejpam-5751	144	8	√	√	NOUN
ejpam-5751	144	9	−ps(k1x+	−ps(k1x+	NOUN
ejpam-5751	144	10	k2y	k2y	PROPN
ejpam-5751	144	11	−	−	NOUN
ejpam-5751	144	12	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	144	13	s2	s2	NOUN
ejpam-5751	144	14	∫	∫	PROPN
ejpam-5751	144	15	t	t	PROPN
ejpam-5751	144	16	0	0	NUM
ejpam-5751	144	17	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	144	18	)	)	PUNCT
ejpam-5751	144	19	]	]	PUNCT
ejpam-5751	144	20	)	)	PUNCT
ejpam-5751	145	1	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	145	2	1	1	NUM
ejpam-5751	145	3	2	2	NUM
ejpam-5751	145	4	ν2	ν2	NOUN
ejpam-5751	145	5	t	t	NOUN
ejpam-5751	145	6	]	]	PUNCT
ejpam-5751	145	7	,	,	PUNCT
ejpam-5751	145	8	(	(	PUNCT
ejpam-5751	145	9	33	33	NUM
ejpam-5751	145	10	)	)	PUNCT
ejpam-5751	145	11	u3(t	u3(t	PROPN
ejpam-5751	145	12	,	,	PUNCT
ejpam-5751	145	13	x	x	NOUN
ejpam-5751	145	14	,	,	PUNCT
ejpam-5751	145	15	y	y	NOUN
ejpam-5751	145	16	)	)	PUNCT
ejpam-5751	146	1	=	=	SYM
ejpam-5751	146	2	ℓ	ℓ	NOUN
ejpam-5751	146	3	√	√	NOUN
ejpam-5751	146	4	−p	−p	NOUN
ejpam-5751	146	5	s	s	X
ejpam-5751	146	6	(	(	PUNCT
ejpam-5751	146	7	coth	coth	PROPN
ejpam-5751	146	8	[	[	PUNCT
ejpam-5751	146	9	√	√	ADP
ejpam-5751	146	10	−4ps(k1x+	−4ps(k1x+	NUM
ejpam-5751	146	11	k2y	k2y	NOUN
ejpam-5751	146	12	−	−	NOUN
ejpam-5751	146	13	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	146	14	s2	s2	VERB
ejpam-5751	146	15	∫	∫	PROPN
ejpam-5751	146	16	t	t	PROPN
ejpam-5751	146	17	0	0	NUM
ejpam-5751	146	18	e	e	X
ejpam-5751	146	19	2νβ(τ)−ν2τdτ	2νβ(τ)−ν2τdτ	NUM
ejpam-5751	146	20	)	)	PUNCT
ejpam-5751	146	21	]	]	PUNCT
ejpam-5751	147	1	+	+	NOUN
ejpam-5751	147	2	csch	csch	NOUN
ejpam-5751	147	3	[	[	PUNCT
ejpam-5751	147	4	√	√	ADP
ejpam-5751	147	5	−4ps(k1x+	−4ps(k1x+	NUM
ejpam-5751	147	6	k2y	k2y	NOUN
ejpam-5751	147	7	−	−	NOUN
ejpam-5751	147	8	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	147	9	s2	s2	VERB
ejpam-5751	147	10	∫	∫	PROPN
ejpam-5751	147	11	t	t	PROPN
ejpam-5751	147	12	0	0	NUM
ejpam-5751	147	13	e	e	X
ejpam-5751	147	14	2νβ(τ)−ν2τdτ	2νβ(τ)−ν2τdτ	NUM
ejpam-5751	147	15	)	)	PUNCT
ejpam-5751	147	16	]	]	PUNCT
ejpam-5751	147	17	)	)	PUNCT
ejpam-5751	147	18	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	147	19	1	1	NUM
ejpam-5751	147	20	2	2	NUM
ejpam-5751	147	21	ν2	ν2	NOUN
ejpam-5751	147	22	t	t	NOUN
ejpam-5751	147	23	]	]	PUNCT
ejpam-5751	147	24	,	,	PUNCT
ejpam-5751	147	25	(	(	PUNCT
ejpam-5751	147	26	34	34	NUM
ejpam-5751	147	27	)	)	PUNCT
ejpam-5751	147	28	u4(t	u4(t	PROPN
ejpam-5751	147	29	,	,	PUNCT
ejpam-5751	147	30	x	x	NOUN
ejpam-5751	147	31	,	,	PUNCT
ejpam-5751	147	32	y	y	NOUN
ejpam-5751	147	33	)	)	PUNCT
ejpam-5751	147	34	=	=	SYM
ejpam-5751	147	35	−1	−1	NOUN
ejpam-5751	147	36	2ℓ	2ℓ	NOUN
ejpam-5751	148	1	√	√	ADP
ejpam-5751	148	2	−p	−p	NOUN
ejpam-5751	148	3	s	s	X
ejpam-5751	148	4	(	(	PUNCT
ejpam-5751	148	5	tanh[12	tanh[12	NOUN
ejpam-5751	148	6	√	√	PROPN
ejpam-5751	149	1	−ps(k1x+	−ps(k1x+	INTJ
ejpam-5751	149	2	k2y	k2y	PROPN
ejpam-5751	149	3	−	−	NOUN
ejpam-5751	149	4	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	149	5	s2	s2	NOUN
ejpam-5751	149	6	∫	∫	PROPN
ejpam-5751	149	7	t	t	PROPN
ejpam-5751	149	8	0	0	NUM
ejpam-5751	149	9	e	e	X
ejpam-5751	149	10	2νβ(τ)−ν2τdτ	2νβ(τ)−ν2τdτ	NUM
ejpam-5751	149	11	)	)	PUNCT
ejpam-5751	149	12	]	]	PUNCT
ejpam-5751	150	1	+	+	PUNCT
ejpam-5751	150	2	coth[12	coth[12	X
ejpam-5751	150	3	√	√	NUM
ejpam-5751	150	4	−ps(k1x+	−ps(k1x+	INTJ
ejpam-5751	151	1	k2y	k2y	PROPN
ejpam-5751	151	2	−	−	NOUN
ejpam-5751	151	3	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	151	4	s2	s2	NOUN
ejpam-5751	151	5	∫	∫	PROPN
ejpam-5751	151	6	t	t	PROPN
ejpam-5751	151	7	0	0	NUM
ejpam-5751	151	8	e	e	X
ejpam-5751	151	9	2νβ(τ)−ν2τdτ	2νβ(τ)−ν2τdτ	NUM
ejpam-5751	151	10	)	)	PUNCT
ejpam-5751	151	11	]	]	PUNCT
ejpam-5751	151	12	)	)	PUNCT
ejpam-5751	152	1	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	152	2	1	1	NUM
ejpam-5751	152	3	2	2	NUM
ejpam-5751	152	4	ν2	ν2	NOUN
ejpam-5751	152	5	t	t	NOUN
ejpam-5751	152	6	]	]	PUNCT
ejpam-5751	152	7	,	,	PUNCT
ejpam-5751	152	8	(	(	PUNCT
ejpam-5751	152	9	35	35	NUM
ejpam-5751	152	10	)	)	PUNCT
ejpam-5751	152	11	for	for	ADP
ejpam-5751	152	12	ps	ps	PROPN
ejpam-5751	152	13	<	<	X
ejpam-5751	152	14	0	0	PROPN
ejpam-5751	152	15	,	,	PUNCT
ejpam-5751	152	16	u5(t	u5(t	PROPN
ejpam-5751	152	17	,	,	PUNCT
ejpam-5751	152	18	x	x	NOUN
ejpam-5751	152	19	,	,	PUNCT
ejpam-5751	152	20	y	y	NOUN
ejpam-5751	152	21	)	)	PUNCT
ejpam-5751	152	22	=	=	SYM
ejpam-5751	152	23	ℓ	ℓ	NOUN
ejpam-5751	152	24	√	√	PROPN
ejpam-5751	152	25	p	p	X
ejpam-5751	152	26	s	s	PROPN
ejpam-5751	152	27	tan	tan	PROPN
ejpam-5751	152	28	[	[	PUNCT
ejpam-5751	152	29	√	√	NUM
ejpam-5751	152	30	ps(k1x+	ps(k1x+	NUM
ejpam-5751	152	31	k2y	k2y	PROPN
ejpam-5751	152	32	−	−	PROPN
ejpam-5751	152	33	ℓ2ρ4	ℓ2ρ4	NOUN
ejpam-5751	152	34	s2	s2	VERB
ejpam-5751	152	35	e2νβ(τ)−ν2τdτ)]e[iφ+νβ(t)−	e2νβ(τ)−ν2τdτ)]e[iφ+νβ(t)−	NOUN
ejpam-5751	152	36	1	1	NUM
ejpam-5751	152	37	2	2	NUM
ejpam-5751	152	38	ν2	ν2	NOUN
ejpam-5751	152	39	t	t	NOUN
ejpam-5751	152	40	]	]	PUNCT
ejpam-5751	152	41	,	,	PUNCT
ejpam-5751	152	42	(	(	PUNCT
ejpam-5751	152	43	36	36	NUM
ejpam-5751	152	44	)	)	PUNCT
ejpam-5751	152	45	w.	w.	PROPN
ejpam-5751	152	46	w.	w.	PROPN
ejpam-5751	152	47	mohammed	mohammed	PROPN
ejpam-5751	152	48	et	et	PROPN
ejpam-5751	152	49	al	al	PROPN
ejpam-5751	152	50	.	.	PUNCT
ejpam-5751	152	51	/	/	SYM
ejpam-5751	152	52	eur	eur	PROPN
ejpam-5751	152	53	.	.	PUNCT
ejpam-5751	153	1	j.	j.	PROPN
ejpam-5751	153	2	pure	pure	PROPN
ejpam-5751	153	3	appl	appl	PROPN
ejpam-5751	153	4	.	.	PROPN
ejpam-5751	153	5	math	math	PROPN
ejpam-5751	153	6	,	,	PUNCT
ejpam-5751	153	7	18	18	NUM
ejpam-5751	153	8	(	(	PUNCT
ejpam-5751	153	9	1	1	NUM
ejpam-5751	153	10	)	)	PUNCT
ejpam-5751	153	11	(	(	PUNCT
ejpam-5751	153	12	2025	2025	NUM
ejpam-5751	153	13	)	)	PUNCT
ejpam-5751	153	14	,	,	PUNCT
ejpam-5751	153	15	5751	5751	NUM
ejpam-5751	153	16	9	9	NUM
ejpam-5751	153	17	of	of	ADP
ejpam-5751	153	18	15	15	NUM
ejpam-5751	153	19	u6(t	u6(t	NUM
ejpam-5751	153	20	,	,	PUNCT
ejpam-5751	153	21	x	x	NOUN
ejpam-5751	153	22	,	,	PUNCT
ejpam-5751	153	23	y	y	NOUN
ejpam-5751	153	24	)	)	PUNCT
ejpam-5751	153	25	=	=	NOUN
ejpam-5751	153	26	−ℓ	−ℓ	VERB
ejpam-5751	153	27	√	√	ADP
ejpam-5751	154	1	p	p	X
ejpam-5751	154	2	s	s	X
ejpam-5751	154	3	cot	cot	NOUN
ejpam-5751	154	4	[	[	PUNCT
ejpam-5751	154	5	√	√	ADP
ejpam-5751	154	6	ps(k1x+	ps(k1x+	NUM
ejpam-5751	154	7	k2y	k2y	PROPN
ejpam-5751	154	8	−	−	NOUN
ejpam-5751	154	9	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	154	10	s2	s2	NOUN
ejpam-5751	154	11	∫	∫	PROPN
ejpam-5751	154	12	t	t	PROPN
ejpam-5751	154	13	0	0	NUM
ejpam-5751	154	14	e2νβ(τ)−ν2τdτ)]e[iφ+νβ(t)−	e2νβ(τ)−ν2τdτ)]e[iφ+νβ(t)−	PROPN
ejpam-5751	154	15	1	1	NUM
ejpam-5751	154	16	2	2	NUM
ejpam-5751	154	17	ν2	ν2	NOUN
ejpam-5751	154	18	t	t	NOUN
ejpam-5751	154	19	]	]	PUNCT
ejpam-5751	154	20	,	,	PUNCT
ejpam-5751	154	21	(	(	PUNCT
ejpam-5751	154	22	37	37	NUM
ejpam-5751	154	23	)	)	PUNCT
ejpam-5751	154	24	u7(t	u7(t	PROPN
ejpam-5751	154	25	,	,	PUNCT
ejpam-5751	154	26	x	x	NOUN
ejpam-5751	154	27	,	,	PUNCT
ejpam-5751	154	28	y	y	NOUN
ejpam-5751	154	29	)	)	PUNCT
ejpam-5751	154	30	=	=	SYM
ejpam-5751	154	31	ℓ	ℓ	NOUN
ejpam-5751	154	32	√	√	PROPN
ejpam-5751	154	33	p	p	NOUN
ejpam-5751	154	34	s	s	X
ejpam-5751	154	35	(	(	PUNCT
ejpam-5751	154	36	tan	tan	PROPN
ejpam-5751	154	37	[	[	PUNCT
ejpam-5751	154	38	√	√	NUM
ejpam-5751	154	39	4ps(k1x+	4ps(k1x+	NOUN
ejpam-5751	154	40	k2y	k2y	NOUN
ejpam-5751	154	41	−	−	NOUN
ejpam-5751	154	42	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	154	43	s2	s2	VERB
ejpam-5751	154	44	∫	∫	PROPN
ejpam-5751	154	45	t	t	PROPN
ejpam-5751	154	46	0	0	NUM
ejpam-5751	154	47	e	e	X
ejpam-5751	154	48	2νβ(τ)−ν2τdτ	2νβ(τ)−ν2τdτ	NUM
ejpam-5751	154	49	)	)	PUNCT
ejpam-5751	154	50	]	]	PUNCT
ejpam-5751	154	51	−	−	PROPN
ejpam-5751	154	52	sec	sec	PROPN
ejpam-5751	154	53	[	[	PUNCT
ejpam-5751	154	54	√	√	ADP
ejpam-5751	154	55	ps(k1x+	ps(k1x+	NUM
ejpam-5751	154	56	k2y	k2y	PROPN
ejpam-5751	154	57	−	−	NOUN
ejpam-5751	154	58	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	154	59	s2	s2	NOUN
ejpam-5751	154	60	∫	∫	PROPN
ejpam-5751	154	61	t	t	PROPN
ejpam-5751	154	62	0	0	NUM
ejpam-5751	154	63	e	e	X
ejpam-5751	154	64	2νβ(τ)−ν2τdτ	2νβ(τ)−ν2τdτ	NUM
ejpam-5751	154	65	)	)	PUNCT
ejpam-5751	154	66	]	]	PUNCT
ejpam-5751	154	67	)	)	PUNCT
ejpam-5751	154	68	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	154	69	1	1	NUM
ejpam-5751	154	70	2	2	NUM
ejpam-5751	154	71	ν2	ν2	NOUN
ejpam-5751	154	72	t	t	NOUN
ejpam-5751	154	73	]	]	PUNCT
ejpam-5751	154	74	,	,	PUNCT
ejpam-5751	154	75	(	(	PUNCT
ejpam-5751	154	76	38	38	NUM
ejpam-5751	154	77	)	)	PUNCT
ejpam-5751	154	78	u8(t	u8(t	PROPN
ejpam-5751	154	79	,	,	PUNCT
ejpam-5751	154	80	x	x	NOUN
ejpam-5751	154	81	,	,	PUNCT
ejpam-5751	154	82	y	y	NOUN
ejpam-5751	154	83	)	)	PUNCT
ejpam-5751	154	84	=	=	SYM
ejpam-5751	154	85	ℓ	ℓ	NOUN
ejpam-5751	154	86	√	√	PROPN
ejpam-5751	154	87	p	p	NOUN
ejpam-5751	154	88	s	s	X
ejpam-5751	154	89	(	(	PUNCT
ejpam-5751	154	90	cot	cot	NOUN
ejpam-5751	154	91	[	[	PUNCT
ejpam-5751	154	92	√	√	NUM
ejpam-5751	154	93	4ps(k1x+	4ps(k1x+	NOUN
ejpam-5751	154	94	k2y	k2y	NOUN
ejpam-5751	154	95	−	−	NOUN
ejpam-5751	154	96	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	154	97	s2	s2	VERB
ejpam-5751	154	98	∫	∫	PROPN
ejpam-5751	154	99	t	t	PROPN
ejpam-5751	154	100	0	0	NUM
ejpam-5751	154	101	e	e	X
ejpam-5751	154	102	2νβ(τ)−ν2τdτ	2νβ(τ)−ν2τdτ	NUM
ejpam-5751	154	103	)	)	PUNCT
ejpam-5751	154	104	]	]	PUNCT
ejpam-5751	155	1	+	+	CCONJ
ejpam-5751	155	2	csc	csc	PROPN
ejpam-5751	155	3	[	[	PUNCT
ejpam-5751	155	4	√	√	NUM
ejpam-5751	155	5	4ps(k1x+	4ps(k1x+	NOUN
ejpam-5751	155	6	k2y	k2y	NOUN
ejpam-5751	155	7	−	−	NOUN
ejpam-5751	155	8	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	155	9	s2	s2	VERB
ejpam-5751	155	10	∫	∫	PROPN
ejpam-5751	155	11	t	t	PROPN
ejpam-5751	155	12	0	0	NUM
ejpam-5751	155	13	e	e	X
ejpam-5751	155	14	2νβ(τ)−ν2τdτ	2νβ(τ)−ν2τdτ	NUM
ejpam-5751	155	15	)	)	PUNCT
ejpam-5751	155	16	]	]	PUNCT
ejpam-5751	155	17	)	)	PUNCT
ejpam-5751	155	18	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	156	1	1	1	NUM
ejpam-5751	156	2	2	2	NUM
ejpam-5751	156	3	ν2	ν2	NOUN
ejpam-5751	156	4	t	t	NOUN
ejpam-5751	156	5	]	]	PUNCT
ejpam-5751	156	6	(	(	PUNCT
ejpam-5751	156	7	39	39	NUM
ejpam-5751	156	8	)	)	PUNCT
ejpam-5751	156	9	u9(t	u9(t	PROPN
ejpam-5751	156	10	,	,	PUNCT
ejpam-5751	156	11	x	x	NOUN
ejpam-5751	156	12	,	,	PUNCT
ejpam-5751	156	13	y	y	NOUN
ejpam-5751	156	14	)	)	PUNCT
ejpam-5751	156	15	=	=	SYM
ejpam-5751	156	16	1	1	NUM
ejpam-5751	156	17	2ℓ	2ℓ	NUM
ejpam-5751	157	1	√	√	ADP
ejpam-5751	157	2	p	p	NOUN
ejpam-5751	157	3	s	s	X
ejpam-5751	157	4	(	(	PUNCT
ejpam-5751	157	5	tan	tan	PROPN
ejpam-5751	157	6	[	[	PUNCT
ejpam-5751	157	7	√	√	NUM
ejpam-5751	157	8	ps	ps	PROPN
ejpam-5751	157	9	2	2	NUM
ejpam-5751	157	10	(	(	PUNCT
ejpam-5751	157	11	k1x+	k1x+	NOUN
ejpam-5751	157	12	k2y	k2y	PROPN
ejpam-5751	157	13	−	−	PROPN
ejpam-5751	157	14	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	157	15	s2	s2	NOUN
ejpam-5751	157	16	∫	∫	PROPN
ejpam-5751	157	17	t	t	PROPN
ejpam-5751	157	18	0	0	NUM
ejpam-5751	157	19	e	e	X
ejpam-5751	157	20	2νβ(τ)−ν2τdτ	2νβ(τ)−ν2τdτ	NUM
ejpam-5751	157	21	)	)	PUNCT
ejpam-5751	157	22	]	]	PUNCT
ejpam-5751	157	23	−	−	PRON
ejpam-5751	157	24	cot	cot	NOUN
ejpam-5751	157	25	[	[	PUNCT
ejpam-5751	157	26	√	√	NUM
ejpam-5751	157	27	ps	ps	PROPN
ejpam-5751	157	28	2	2	NUM
ejpam-5751	157	29	(	(	PUNCT
ejpam-5751	157	30	k1x+	k1x+	NOUN
ejpam-5751	157	31	k2y	k2y	PROPN
ejpam-5751	157	32	−	−	PROPN
ejpam-5751	157	33	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	157	34	s2	s2	NOUN
ejpam-5751	157	35	∫	∫	PROPN
ejpam-5751	157	36	t	t	PROPN
ejpam-5751	157	37	0	0	NUM
ejpam-5751	157	38	e	e	X
ejpam-5751	157	39	2νβ(τ)−ν2τdτ	2νβ(τ)−ν2τdτ	NUM
ejpam-5751	157	40	)	)	PUNCT
ejpam-5751	157	41	]	]	PUNCT
ejpam-5751	157	42	)	)	PUNCT
ejpam-5751	158	1	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	158	2	1	1	NUM
ejpam-5751	158	3	2	2	NUM
ejpam-5751	158	4	ν2	ν2	NOUN
ejpam-5751	158	5	t	t	NOUN
ejpam-5751	158	6	]	]	PUNCT
ejpam-5751	158	7	,	,	PUNCT
ejpam-5751	158	8	(	(	PUNCT
ejpam-5751	158	9	40	40	NUM
ejpam-5751	158	10	)	)	PUNCT
ejpam-5751	158	11	for	for	ADP
ejpam-5751	158	12	ps	ps	PROPN
ejpam-5751	158	13	>	>	X
ejpam-5751	158	14	0	0	NUM
ejpam-5751	158	15	,	,	PUNCT
ejpam-5751	158	16	and	and	CCONJ
ejpam-5751	158	17	u10(t	u10(t	PROPN
ejpam-5751	158	18	,	,	PUNCT
ejpam-5751	158	19	x	x	NOUN
ejpam-5751	158	20	,	,	PUNCT
ejpam-5751	158	21	y	y	PROPN
ejpam-5751	158	22	)	)	PUNCT
ejpam-5751	159	1	=	=	PRON
ejpam-5751	159	2	(	(	PUNCT
ejpam-5751	159	3	−1	−1	NOUN
ejpam-5751	159	4	s(k1x+	s(k1x+	NOUN
ejpam-5751	160	1	k2y	k2y	NOUN
ejpam-5751	160	2	−	−	NOUN
ejpam-5751	160	3	ℓ2ρ4	ℓ2ρ4	PUNCT
ejpam-5751	160	4	s2	s2	VERB
ejpam-5751	160	5	∫	∫	PROPN
ejpam-5751	160	6	t	t	PROPN
ejpam-5751	160	7	0	0	NUM
ejpam-5751	160	8	e	e	NOUN
ejpam-5751	160	9	2νβ(τ)−ν2τdτ	2νβ(τ)−ν2τdτ	NUM
ejpam-5751	160	10	)	)	PUNCT
ejpam-5751	160	11	)	)	PUNCT
ejpam-5751	161	1	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	161	2	1	1	NUM
ejpam-5751	161	3	2	2	NUM
ejpam-5751	161	4	ν2	ν2	NOUN
ejpam-5751	161	5	t	t	NOUN
ejpam-5751	161	6	]	]	PUNCT
ejpam-5751	161	7	for	for	ADP
ejpam-5751	161	8	s	s	PROPN
ejpam-5751	161	9	̸=	̸=	PROPN
ejpam-5751	161	10	0	0	NUM
ejpam-5751	161	11	.	.	PUNCT
ejpam-5751	162	1	(	(	PUNCT
ejpam-5751	162	2	41	41	NUM
ejpam-5751	162	3	)	)	PUNCT
ejpam-5751	162	4	remark	remark	NOUN
ejpam-5751	162	5	1	1	NUM
ejpam-5751	162	6	.	.	PUNCT
ejpam-5751	163	1	eqs	eqs	X
ejpam-5751	163	2	(	(	PUNCT
ejpam-5751	163	3	32	32	NUM
ejpam-5751	163	4	)	)	PUNCT
ejpam-5751	163	5	and	and	CCONJ
ejpam-5751	163	6	(	(	PUNCT
ejpam-5751	163	7	33	33	NUM
ejpam-5751	163	8	)	)	PUNCT
ejpam-5751	163	9	,	,	PUNCT
ejpam-5751	163	10	with	with	ADP
ejpam-5751	163	11	ν	ν	X
ejpam-5751	163	12	=	=	SYM
ejpam-5751	163	13	0	0	NUM
ejpam-5751	163	14	coincide	coincide	NOUN
ejpam-5751	163	15	with	with	ADP
ejpam-5751	163	16	the	the	DET
ejpam-5751	163	17	solutions	solution	NOUN
ejpam-5751	163	18	(	(	PUNCT
ejpam-5751	163	19	45	45	NUM
ejpam-5751	163	20	)	)	PUNCT
ejpam-5751	163	21	and	and	CCONJ
ejpam-5751	163	22	(	(	PUNCT
ejpam-5751	163	23	46	46	NUM
ejpam-5751	163	24	)	)	PUNCT
ejpam-5751	163	25	that	that	PRON
ejpam-5751	163	26	reported	report	VERB
ejpam-5751	163	27	in	in	ADP
ejpam-5751	163	28	[	[	X
ejpam-5751	163	29	6	6	NUM
ejpam-5751	163	30	]	]	PUNCT
ejpam-5751	163	31	.	.	PUNCT
ejpam-5751	164	1	3.2	3.2	NUM
ejpam-5751	164	2	.	.	X
ejpam-5751	165	1	jef	jef	PROPN
ejpam-5751	165	2	-	-	PUNCT
ejpam-5751	165	3	method	method	VERB
ejpam-5751	165	4	the	the	DET
ejpam-5751	165	5	solutions	solution	NOUN
ejpam-5751	165	6	of	of	ADP
ejpam-5751	165	7	the	the	DET
ejpam-5751	165	8	shfe	shfe	PROPN
ejpam-5751	165	9	(	(	PUNCT
ejpam-5751	165	10	1	1	X
ejpam-5751	165	11	)	)	PUNCT
ejpam-5751	165	12	are	be	AUX
ejpam-5751	165	13	obtained	obtain	VERB
ejpam-5751	165	14	by	by	ADP
ejpam-5751	165	15	substituting	substitute	VERB
ejpam-5751	165	16	eqs	eqs	X
ejpam-5751	165	17	(	(	PUNCT
ejpam-5751	165	18	28)-(30	28)-(30	NUM
ejpam-5751	165	19	)	)	PUNCT
ejpam-5751	165	20	into	into	ADP
ejpam-5751	165	21	(	(	PUNCT
ejpam-5751	165	22	31	31	NUM
ejpam-5751	165	23	)	)	PUNCT
ejpam-5751	165	24	as	as	ADP
ejpam-5751	165	25	:	:	PUNCT
ejpam-5751	165	26	u(t	u(t	NOUN
ejpam-5751	165	27	,	,	PUNCT
ejpam-5751	165	28	x	x	NOUN
ejpam-5751	165	29	,	,	PUNCT
ejpam-5751	165	30	y	y	NOUN
ejpam-5751	165	31	)	)	PUNCT
ejpam-5751	165	32	=	=	SYM
ejpam-5751	165	33	ℏ	ℏ	PROPN
ejpam-5751	165	34	(	(	PUNCT
ejpam-5751	165	35	sn(k1ωx+	sn(k1ωx+	NOUN
ejpam-5751	165	36	ωk2y	ωk2y	PROPN
ejpam-5751	165	37	−	−	PROPN
ejpam-5751	165	38	ℏ2ρ4	ℏ2ρ4	NOUN
ejpam-5751	165	39	ωň2	ωň2	ADP
ejpam-5751	165	40	∫	∫	PROPN
ejpam-5751	165	41	t	t	PROPN
ejpam-5751	165	42	0	0	NUM
ejpam-5751	165	43	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	165	44	,	,	PUNCT
ejpam-5751	165	45	ň	ň	NOUN
ejpam-5751	165	46	)	)	PUNCT
ejpam-5751	165	47	)	)	PUNCT
ejpam-5751	166	1	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	166	2	1	1	NUM
ejpam-5751	166	3	2	2	NUM
ejpam-5751	166	4	ν2	ν2	NOUN
ejpam-5751	166	5	t	t	NOUN
ejpam-5751	166	6	]	]	PUNCT
ejpam-5751	166	7	,	,	PUNCT
ejpam-5751	166	8	(	(	PUNCT
ejpam-5751	166	9	42	42	NUM
ejpam-5751	166	10	)	)	PUNCT
ejpam-5751	166	11	u(t	u(t	NOUN
ejpam-5751	166	12	,	,	PUNCT
ejpam-5751	166	13	x	x	NOUN
ejpam-5751	166	14	,	,	PUNCT
ejpam-5751	166	15	y	y	NOUN
ejpam-5751	166	16	)	)	PUNCT
ejpam-5751	166	17	=	=	SYM
ejpam-5751	166	18	ℏ	ℏ	PROPN
ejpam-5751	166	19	(	(	PUNCT
ejpam-5751	166	20	cn(k1ωx+	cn(k1ωx+	PROPN
ejpam-5751	166	21	ωk2y	ωk2y	PROPN
ejpam-5751	166	22	+	+	CCONJ
ejpam-5751	166	23	ℏ2ρ4	ℏ2ρ4	X
ejpam-5751	166	24	ωň2	ωň2	ADP
ejpam-5751	166	25	∫	∫	PROPN
ejpam-5751	166	26	t	t	PROPN
ejpam-5751	166	27	0	0	NUM
ejpam-5751	166	28	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	166	29	,	,	PUNCT
ejpam-5751	166	30	ň	ň	NOUN
ejpam-5751	166	31	)	)	PUNCT
ejpam-5751	166	32	)	)	PUNCT
ejpam-5751	167	1	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	167	2	1	1	NUM
ejpam-5751	167	3	2	2	NUM
ejpam-5751	167	4	ν2	ν2	NOUN
ejpam-5751	167	5	t	t	NOUN
ejpam-5751	167	6	]	]	PUNCT
ejpam-5751	167	7	,	,	PUNCT
ejpam-5751	167	8	(	(	PUNCT
ejpam-5751	167	9	43	43	NUM
ejpam-5751	167	10	)	)	PUNCT
ejpam-5751	167	11	and	and	CCONJ
ejpam-5751	167	12	u(t	u(t	NOUN
ejpam-5751	167	13	,	,	PUNCT
ejpam-5751	167	14	x	x	NOUN
ejpam-5751	167	15	,	,	PUNCT
ejpam-5751	167	16	y	y	NOUN
ejpam-5751	167	17	)	)	PUNCT
ejpam-5751	168	1	=	=	SYM
ejpam-5751	168	2	ℏ	ℏ	PROPN
ejpam-5751	168	3	(	(	PUNCT
ejpam-5751	168	4	dn(k1ωx+	dn(k1ωx+	NOUN
ejpam-5751	168	5	ωk2y	ωk2y	PROPN
ejpam-5751	168	6	+	+	CCONJ
ejpam-5751	168	7	ℏ2ρ4	ℏ2ρ4	PROPN
ejpam-5751	168	8	ω	ω	NUM
ejpam-5751	168	9	∫	∫	PROPN
ejpam-5751	168	10	t	t	PROPN
ejpam-5751	168	11	0	0	NUM
ejpam-5751	168	12	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	168	13	,	,	PUNCT
ejpam-5751	168	14	ň	ň	NOUN
ejpam-5751	168	15	)	)	PUNCT
ejpam-5751	168	16	)	)	PUNCT
ejpam-5751	168	17	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	168	18	1	1	NUM
ejpam-5751	168	19	2	2	NUM
ejpam-5751	168	20	ν2	ν2	NOUN
ejpam-5751	168	21	t	t	NOUN
ejpam-5751	168	22	]	]	PUNCT
ejpam-5751	168	23	,	,	PUNCT
ejpam-5751	168	24	(	(	PUNCT
ejpam-5751	168	25	44	44	NUM
ejpam-5751	168	26	)	)	PUNCT
ejpam-5751	168	27	where	where	SCONJ
ejpam-5751	168	28	φ0	φ0	PROPN
ejpam-5751	168	29	=	=	NOUN
ejpam-5751	168	30	k1x+	k1x+	NOUN
ejpam-5751	169	1	k2y	k2y	PROPN
ejpam-5751	169	2	+	+	CCONJ
ejpam-5751	169	3	ℏ2(b1	ℏ2(b1	VERB
ejpam-5751	169	4	−	−	NOUN
ejpam-5751	169	5	1	1	NUM
ejpam-5751	169	6	)	)	PUNCT
ejpam-5751	169	7	b2	b2	NOUN
ejpam-5751	169	8	∫	∫	PROPN
ejpam-5751	169	9	t	t	PROPN
ejpam-5751	169	10	0	0	NUM
ejpam-5751	169	11	a(τ)dτ	a(τ)dτ	PROPN
ejpam-5751	169	12	.	.	PUNCT
ejpam-5751	170	1	if	if	SCONJ
ejpam-5751	170	2	ň→	ň→	NOUN
ejpam-5751	170	3	1	1	NUM
ejpam-5751	170	4	,	,	PUNCT
ejpam-5751	170	5	then	then	ADV
ejpam-5751	170	6	the	the	DET
ejpam-5751	170	7	eqs	eqs	X
ejpam-5751	170	8	(	(	PUNCT
ejpam-5751	170	9	42)-(44	42)-(44	PROPN
ejpam-5751	170	10	)	)	PUNCT
ejpam-5751	170	11	become	become	VERB
ejpam-5751	170	12	u(t	u(t	NOUN
ejpam-5751	170	13	,	,	PUNCT
ejpam-5751	170	14	x	x	NOUN
ejpam-5751	170	15	,	,	PUNCT
ejpam-5751	170	16	y	y	NOUN
ejpam-5751	170	17	)	)	PUNCT
ejpam-5751	170	18	=	=	SYM
ejpam-5751	170	19	ℏ	ℏ	PROPN
ejpam-5751	170	20	(	(	PUNCT
ejpam-5751	170	21	tanh(k1ωx+	tanh(k1ωx+	PROPN
ejpam-5751	170	22	ωk2y	ωk2y	PROPN
ejpam-5751	170	23	−	−	PROPN
ejpam-5751	170	24	ℏ2ρ4	ℏ2ρ4	PROPN
ejpam-5751	170	25	ω	ω	NUM
ejpam-5751	170	26	∫	∫	PROPN
ejpam-5751	170	27	t	t	PROPN
ejpam-5751	170	28	0	0	NUM
ejpam-5751	170	29	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	170	30	)	)	PUNCT
ejpam-5751	170	31	)	)	PUNCT
ejpam-5751	171	1	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	171	2	1	1	NUM
ejpam-5751	171	3	2	2	NUM
ejpam-5751	171	4	ν2	ν2	NOUN
ejpam-5751	171	5	t	t	NOUN
ejpam-5751	171	6	]	]	PUNCT
ejpam-5751	171	7	,	,	PUNCT
ejpam-5751	171	8	(	(	PUNCT
ejpam-5751	171	9	45	45	NUM
ejpam-5751	171	10	)	)	PUNCT
ejpam-5751	171	11	and	and	CCONJ
ejpam-5751	171	12	u(t	u(t	NOUN
ejpam-5751	171	13	,	,	PUNCT
ejpam-5751	171	14	x	x	NOUN
ejpam-5751	171	15	,	,	PUNCT
ejpam-5751	171	16	y	y	NOUN
ejpam-5751	171	17	)	)	PUNCT
ejpam-5751	172	1	=	=	SYM
ejpam-5751	172	2	ℏ	ℏ	PROPN
ejpam-5751	172	3	(	(	PUNCT
ejpam-5751	172	4	sech(k1ωx+	sech(k1ωx+	PROPN
ejpam-5751	172	5	ωk2y	ωk2y	PROPN
ejpam-5751	172	6	+	+	CCONJ
ejpam-5751	172	7	ℏ2ρ4	ℏ2ρ4	PROPN
ejpam-5751	172	8	ω	ω	NUM
ejpam-5751	172	9	∫	∫	PROPN
ejpam-5751	172	10	t	t	PROPN
ejpam-5751	172	11	0	0	NUM
ejpam-5751	172	12	e2νβ(τ)−ν2τdτ	e2νβ(τ)−ν2τdτ	NOUN
ejpam-5751	172	13	)	)	PUNCT
ejpam-5751	172	14	)	)	PUNCT
ejpam-5751	172	15	e[iφ+νβ(t)−	e[iφ+νβ(t)−	PROPN
ejpam-5751	172	16	1	1	NUM
ejpam-5751	172	17	2	2	NUM
ejpam-5751	172	18	ν2	ν2	NOUN
ejpam-5751	172	19	t	t	NOUN
ejpam-5751	172	20	]	]	PUNCT
ejpam-5751	172	21	.	.	PUNCT
ejpam-5751	173	1	(	(	PUNCT
ejpam-5751	173	2	46	46	NUM
ejpam-5751	173	3	)	)	PUNCT
ejpam-5751	173	4	remark	remark	NOUN
ejpam-5751	173	5	2	2	NUM
ejpam-5751	173	6	.	.	PUNCT
ejpam-5751	174	1	if	if	SCONJ
ejpam-5751	174	2	we	we	PRON
ejpam-5751	174	3	put	put	VERB
ejpam-5751	174	4	ν	ν	NOUN
ejpam-5751	174	5	=	=	SYM
ejpam-5751	174	6	0	0	NUM
ejpam-5751	174	7	in	in	ADP
ejpam-5751	174	8	eqs	eqs	X
ejpam-5751	174	9	(	(	PUNCT
ejpam-5751	174	10	42)-(46	42)-(46	NOUN
ejpam-5751	174	11	)	)	PUNCT
ejpam-5751	174	12	,	,	PUNCT
ejpam-5751	174	13	we	we	PRON
ejpam-5751	174	14	have	have	VERB
ejpam-5751	174	15	the	the	DET
ejpam-5751	174	16	same	same	ADJ
ejpam-5751	174	17	solutions	solution	NOUN
ejpam-5751	174	18	that	that	PRON
ejpam-5751	174	19	stated	state	VERB
ejpam-5751	174	20	in	in	ADP
ejpam-5751	174	21	[	[	X
ejpam-5751	174	22	12	12	NUM
ejpam-5751	174	23	]	]	PUNCT
ejpam-5751	174	24	.	.	PUNCT
ejpam-5751	175	1	w.	w.	PROPN
ejpam-5751	175	2	w.	w.	PROPN
ejpam-5751	175	3	mohammed	mohammed	PROPN
ejpam-5751	175	4	et	et	PROPN
ejpam-5751	175	5	al	al	PROPN
ejpam-5751	175	6	.	.	PUNCT
ejpam-5751	175	7	/	/	SYM
ejpam-5751	175	8	eur	eur	PROPN
ejpam-5751	175	9	.	.	PUNCT
ejpam-5751	176	1	j.	j.	PROPN
ejpam-5751	176	2	pure	pure	PROPN
ejpam-5751	176	3	appl	appl	PROPN
ejpam-5751	176	4	.	.	PROPN
ejpam-5751	176	5	math	math	PROPN
ejpam-5751	176	6	,	,	PUNCT
ejpam-5751	176	7	18	18	NUM
ejpam-5751	176	8	(	(	PUNCT
ejpam-5751	176	9	1	1	NUM
ejpam-5751	176	10	)	)	PUNCT
ejpam-5751	176	11	(	(	PUNCT
ejpam-5751	176	12	2025	2025	NUM
ejpam-5751	176	13	)	)	PUNCT
ejpam-5751	176	14	,	,	PUNCT
ejpam-5751	176	15	5751	5751	NUM
ejpam-5751	176	16	10	10	NUM
ejpam-5751	176	17	of	of	ADP
ejpam-5751	176	18	15	15	NUM
ejpam-5751	176	19	4	4	NUM
ejpam-5751	176	20	.	.	PUNCT
ejpam-5751	176	21	discussion	discussion	NOUN
ejpam-5751	176	22	and	and	CCONJ
ejpam-5751	176	23	impacts	impact	NOUN
ejpam-5751	176	24	of	of	ADP
ejpam-5751	176	25	noise	noise	NOUN
ejpam-5751	176	26	discussion	discussion	NOUN
ejpam-5751	176	27	:	:	PUNCT
ejpam-5751	176	28	in	in	ADP
ejpam-5751	176	29	this	this	DET
ejpam-5751	176	30	paper	paper	NOUN
ejpam-5751	176	31	,	,	PUNCT
ejpam-5751	176	32	the	the	DET
ejpam-5751	176	33	exact	exact	ADJ
ejpam-5751	176	34	solutions	solution	NOUN
ejpam-5751	176	35	of	of	ADP
ejpam-5751	176	36	the	the	DET
ejpam-5751	176	37	shfe	shfe	PROPN
ejpam-5751	176	38	(	(	PUNCT
ejpam-5751	176	39	1	1	X
ejpam-5751	176	40	)	)	PUNCT
ejpam-5751	176	41	were	be	AUX
ejpam-5751	176	42	acquired	acquire	VERB
ejpam-5751	176	43	.	.	PUNCT
ejpam-5751	177	1	we	we	PRON
ejpam-5751	177	2	applied	apply	VERB
ejpam-5751	177	3	two	two	NUM
ejpam-5751	177	4	methods	method	NOUN
ejpam-5751	177	5	such	such	ADJ
ejpam-5751	177	6	as	as	ADP
ejpam-5751	177	7	the	the	DET
ejpam-5751	177	8	grem	grem	NOUN
ejpam-5751	177	9	-	-	NOUN
ejpam-5751	177	10	method	method	NOUN
ejpam-5751	177	11	and	and	CCONJ
ejpam-5751	177	12	jef	jef	PROPN
ejpam-5751	177	13	-	-	PUNCT
ejpam-5751	177	14	method	method	NOUN
ejpam-5751	177	15	which	which	PRON
ejpam-5751	177	16	they	they	PRON
ejpam-5751	177	17	provided	provide	VERB
ejpam-5751	177	18	many	many	ADJ
ejpam-5751	177	19	types	type	NOUN
ejpam-5751	177	20	of	of	ADP
ejpam-5751	177	21	solutions	solution	NOUN
ejpam-5751	177	22	such	such	ADJ
ejpam-5751	177	23	as	as	ADP
ejpam-5751	177	24	optical	optical	ADJ
ejpam-5751	177	25	kink	kink	NOUN
ejpam-5751	177	26	solution	solution	NOUN
ejpam-5751	177	27	(	(	PUNCT
ejpam-5751	177	28	32	32	NUM
ejpam-5751	177	29	)	)	PUNCT
ejpam-5751	177	30	,	,	PUNCT
ejpam-5751	177	31	optical	optical	ADJ
ejpam-5751	177	32	singular	singular	ADJ
ejpam-5751	177	33	solution	solution	NOUN
ejpam-5751	177	34	(	(	PUNCT
ejpam-5751	177	35	33	33	NUM
ejpam-5751	177	36	)	)	PUNCT
ejpam-5751	177	37	,	,	PUNCT
ejpam-5751	177	38	optical	optical	ADJ
ejpam-5751	177	39	singular	singular	ADJ
ejpam-5751	177	40	periodic	periodic	NOUN
ejpam-5751	177	41	(	(	PUNCT
ejpam-5751	177	42	36	36	NUM
ejpam-5751	177	43	)	)	PUNCT
ejpam-5751	177	44	and	and	CCONJ
ejpam-5751	177	45	(	(	PUNCT
ejpam-5751	177	46	37	37	NUM
ejpam-5751	177	47	)	)	PUNCT
ejpam-5751	177	48	,	,	PUNCT
ejpam-5751	177	49	elliptic	elliptic	ADJ
ejpam-5751	177	50	solutions	solution	NOUN
ejpam-5751	177	51	(	(	PUNCT
ejpam-5751	177	52	42)-(44	42)-(44	NUM
ejpam-5751	177	53	)	)	PUNCT
ejpam-5751	177	54	and	and	CCONJ
ejpam-5751	177	55	etc	etc	X
ejpam-5751	177	56	.	.	X
ejpam-5751	177	57	one	one	NUM
ejpam-5751	177	58	of	of	ADP
ejpam-5751	177	59	the	the	DET
ejpam-5751	177	60	key	key	ADJ
ejpam-5751	177	61	features	feature	NOUN
ejpam-5751	177	62	of	of	ADP
ejpam-5751	177	63	singular	singular	ADJ
ejpam-5751	177	64	solitons	soliton	NOUN
ejpam-5751	177	65	in	in	ADP
ejpam-5751	177	66	the	the	DET
ejpam-5751	177	67	heisenberg	heisenberg	PROPN
ejpam-5751	177	68	ferromagnet	ferromagnet	NOUN
ejpam-5751	177	69	equation	equation	NOUN
ejpam-5751	177	70	is	be	AUX
ejpam-5751	177	71	their	their	PRON
ejpam-5751	177	72	ability	ability	NOUN
ejpam-5751	177	73	to	to	PART
ejpam-5751	177	74	maintain	maintain	VERB
ejpam-5751	177	75	their	their	PRON
ejpam-5751	177	76	shape	shape	NOUN
ejpam-5751	177	77	and	and	CCONJ
ejpam-5751	177	78	energy	energy	NOUN
ejpam-5751	177	79	despite	despite	SCONJ
ejpam-5751	177	80	interacting	interact	VERB
ejpam-5751	177	81	with	with	ADP
ejpam-5751	177	82	other	other	ADJ
ejpam-5751	177	83	solitons	soliton	NOUN
ejpam-5751	177	84	or	or	CCONJ
ejpam-5751	177	85	external	external	ADJ
ejpam-5751	177	86	perturbations	perturbation	NOUN
ejpam-5751	177	87	.	.	PUNCT
ejpam-5751	178	1	this	this	DET
ejpam-5751	178	2	stability	stability	NOUN
ejpam-5751	178	3	arises	arise	VERB
ejpam-5751	178	4	from	from	ADP
ejpam-5751	178	5	the	the	DET
ejpam-5751	178	6	non	non	ADJ
ejpam-5751	178	7	-	-	ADJ
ejpam-5751	178	8	linear	linear	ADJ
ejpam-5751	178	9	nature	nature	NOUN
ejpam-5751	178	10	of	of	ADP
ejpam-5751	178	11	the	the	DET
ejpam-5751	178	12	equation	equation	NOUN
ejpam-5751	178	13	,	,	PUNCT
ejpam-5751	178	14	which	which	PRON
ejpam-5751	178	15	allows	allow	VERB
ejpam-5751	178	16	solitons	soliton	NOUN
ejpam-5751	178	17	to	to	PART
ejpam-5751	178	18	balance	balance	VERB
ejpam-5751	178	19	the	the	DET
ejpam-5751	178	20	competing	compete	VERB
ejpam-5751	178	21	effects	effect	NOUN
ejpam-5751	178	22	of	of	ADP
ejpam-5751	178	23	dispersion	dispersion	NOUN
ejpam-5751	178	24	and	and	CCONJ
ejpam-5751	178	25	nonlinearity	nonlinearity	NOUN
ejpam-5751	178	26	.	.	PUNCT
ejpam-5751	179	1	solitons	soliton	NOUN
ejpam-5751	179	2	in	in	ADP
ejpam-5751	179	3	the	the	DET
ejpam-5751	179	4	heisenberg	heisenberg	PROPN
ejpam-5751	179	5	ferromagnet	ferromagnet	NOUN
ejpam-5751	179	6	equation	equation	NOUN
ejpam-5751	179	7	often	often	ADV
ejpam-5751	179	8	exhibit	exhibit	VERB
ejpam-5751	179	9	complex	complex	ADJ
ejpam-5751	179	10	and	and	CCONJ
ejpam-5751	179	11	interesting	interesting	ADJ
ejpam-5751	179	12	dynamics	dynamic	NOUN
ejpam-5751	179	13	,	,	PUNCT
ejpam-5751	179	14	such	such	ADJ
ejpam-5751	179	15	as	as	ADP
ejpam-5751	179	16	the	the	DET
ejpam-5751	179	17	formation	formation	NOUN
ejpam-5751	179	18	of	of	ADP
ejpam-5751	179	19	bound	bind	VERB
ejpam-5751	179	20	states	state	NOUN
ejpam-5751	179	21	or	or	CCONJ
ejpam-5751	179	22	the	the	DET
ejpam-5751	179	23	reflection	reflection	NOUN
ejpam-5751	179	24	and	and	CCONJ
ejpam-5751	179	25	transmission	transmission	NOUN
ejpam-5751	179	26	of	of	ADP
ejpam-5751	179	27	solitons	soliton	NOUN
ejpam-5751	179	28	at	at	ADP
ejpam-5751	179	29	interfaces	interface	NOUN
ejpam-5751	179	30	between	between	ADP
ejpam-5751	179	31	different	different	ADJ
ejpam-5751	179	32	regions	region	NOUN
ejpam-5751	179	33	of	of	ADP
ejpam-5751	179	34	the	the	DET
ejpam-5751	179	35	material	material	NOUN
ejpam-5751	179	36	.	.	PUNCT
ejpam-5751	180	1	impacts	impact	NOUN
ejpam-5751	180	2	of	of	ADP
ejpam-5751	180	3	brownian	brownian	ADJ
ejpam-5751	180	4	motion	motion	NOUN
ejpam-5751	180	5	:	:	PUNCT
ejpam-5751	180	6	the	the	DET
ejpam-5751	180	7	impacts	impact	NOUN
ejpam-5751	180	8	of	of	ADP
ejpam-5751	180	9	noise	noise	NOUN
ejpam-5751	180	10	on	on	ADP
ejpam-5751	180	11	the	the	DET
ejpam-5751	180	12	solutions	solution	NOUN
ejpam-5751	180	13	to	to	ADP
ejpam-5751	180	14	the	the	DET
ejpam-5751	180	15	heisenberg	heisenberg	PROPN
ejpam-5751	180	16	ferromagnet	ferromagnet	NOUN
ejpam-5751	180	17	equation	equation	NOUN
ejpam-5751	180	18	can	can	AUX
ejpam-5751	180	19	have	have	VERB
ejpam-5751	180	20	significant	significant	ADJ
ejpam-5751	180	21	implications	implication	NOUN
ejpam-5751	180	22	for	for	ADP
ejpam-5751	180	23	the	the	DET
ejpam-5751	180	24	design	design	NOUN
ejpam-5751	180	25	and	and	CCONJ
ejpam-5751	180	26	performance	performance	NOUN
ejpam-5751	180	27	of	of	ADP
ejpam-5751	180	28	magnetic	magnetic	ADJ
ejpam-5751	180	29	devices	device	NOUN
ejpam-5751	180	30	.	.	PUNCT
ejpam-5751	181	1	by	by	ADP
ejpam-5751	181	2	understanding	understand	VERB
ejpam-5751	181	3	the	the	DET
ejpam-5751	181	4	impacts	impact	NOUN
ejpam-5751	181	5	of	of	ADP
ejpam-5751	181	6	noise	noise	NOUN
ejpam-5751	181	7	on	on	ADP
ejpam-5751	181	8	the	the	DET
ejpam-5751	181	9	solutions	solution	NOUN
ejpam-5751	181	10	to	to	ADP
ejpam-5751	181	11	the	the	DET
ejpam-5751	181	12	heisenberg	heisenberg	PROPN
ejpam-5751	181	13	ferromagnet	ferromagnet	NOUN
ejpam-5751	181	14	equation	equation	NOUN
ejpam-5751	181	15	,	,	PUNCT
ejpam-5751	181	16	scientists	scientist	NOUN
ejpam-5751	181	17	and	and	CCONJ
ejpam-5751	181	18	engineers	engineer	NOUN
ejpam-5751	181	19	can	can	AUX
ejpam-5751	181	20	work	work	VERB
ejpam-5751	181	21	towards	towards	ADP
ejpam-5751	181	22	developing	develop	VERB
ejpam-5751	181	23	better	well	ADJ
ejpam-5751	181	24	strategies	strategy	NOUN
ejpam-5751	181	25	for	for	ADP
ejpam-5751	181	26	mitigating	mitigate	VERB
ejpam-5751	181	27	the	the	DET
ejpam-5751	181	28	effects	effect	NOUN
ejpam-5751	181	29	of	of	ADP
ejpam-5751	181	30	noise	noise	NOUN
ejpam-5751	181	31	and	and	CCONJ
ejpam-5751	181	32	improving	improve	VERB
ejpam-5751	181	33	the	the	DET
ejpam-5751	181	34	performance	performance	NOUN
ejpam-5751	181	35	of	of	ADP
ejpam-5751	181	36	magnetic	magnetic	ADJ
ejpam-5751	181	37	devices	device	NOUN
ejpam-5751	181	38	based	base	VERB
ejpam-5751	181	39	on	on	ADP
ejpam-5751	181	40	these	these	DET
ejpam-5751	181	41	solutions	solution	NOUN
ejpam-5751	181	42	.	.	PUNCT
ejpam-5751	182	1	ultimately	ultimately	ADV
ejpam-5751	182	2	,	,	PUNCT
ejpam-5751	182	3	addressing	address	VERB
ejpam-5751	182	4	the	the	DET
ejpam-5751	182	5	challenges	challenge	NOUN
ejpam-5751	182	6	posed	pose	VERB
ejpam-5751	182	7	by	by	ADP
ejpam-5751	182	8	noise	noise	NOUN
ejpam-5751	182	9	will	will	AUX
ejpam-5751	182	10	be	be	AUX
ejpam-5751	182	11	crucial	crucial	ADJ
ejpam-5751	182	12	in	in	ADP
ejpam-5751	182	13	unlocking	unlock	VERB
ejpam-5751	182	14	the	the	DET
ejpam-5751	182	15	full	full	ADJ
ejpam-5751	182	16	potential	potential	NOUN
ejpam-5751	182	17	of	of	ADP
ejpam-5751	182	18	the	the	DET
ejpam-5751	182	19	heisenberg	heisenberg	PROPN
ejpam-5751	182	20	ferromagnet	ferromagnet	NOUN
ejpam-5751	182	21	equation	equation	NOUN
ejpam-5751	182	22	and	and	CCONJ
ejpam-5751	182	23	advancing	advance	VERB
ejpam-5751	182	24	the	the	DET
ejpam-5751	182	25	field	field	NOUN
ejpam-5751	182	26	of	of	ADP
ejpam-5751	182	27	magnetic	magnetic	ADJ
ejpam-5751	182	28	materials	material	NOUN
ejpam-5751	182	29	and	and	CCONJ
ejpam-5751	182	30	technology	technology	NOUN
ejpam-5751	182	31	.	.	PUNCT
ejpam-5751	183	1	now	now	ADV
ejpam-5751	183	2	,	,	PUNCT
ejpam-5751	183	3	the	the	DET
ejpam-5751	183	4	effect	effect	NOUN
ejpam-5751	183	5	of	of	ADP
ejpam-5751	183	6	noise	noise	NOUN
ejpam-5751	183	7	on	on	ADP
ejpam-5751	183	8	the	the	DET
ejpam-5751	183	9	exact	exact	ADJ
ejpam-5751	183	10	solutions	solution	NOUN
ejpam-5751	183	11	of	of	ADP
ejpam-5751	183	12	the	the	DET
ejpam-5751	183	13	shfe	shfe	PROPN
ejpam-5751	183	14	(	(	PUNCT
ejpam-5751	183	15	1	1	X
ejpam-5751	183	16	)	)	PUNCT
ejpam-5751	183	17	will	will	AUX
ejpam-5751	183	18	be	be	AUX
ejpam-5751	183	19	examined	examine	VERB
ejpam-5751	183	20	.	.	PUNCT
ejpam-5751	184	1	we	we	PRON
ejpam-5751	184	2	provide	provide	VERB
ejpam-5751	184	3	some	some	DET
ejpam-5751	184	4	figures	figure	NOUN
ejpam-5751	184	5	for	for	ADP
ejpam-5751	184	6	different	different	ADJ
ejpam-5751	184	7	solutions	solution	NOUN
ejpam-5751	184	8	with	with	ADP
ejpam-5751	184	9	varying	vary	VERB
ejpam-5751	184	10	noise	noise	NOUN
ejpam-5751	184	11	intensity	intensity	NOUN
ejpam-5751	184	12	ν	ν	NOUN
ejpam-5751	184	13	.	.	PUNCT
ejpam-5751	184	14	graphs	graphs	PROPN
ejpam-5751	184	15	1	1	NUM
ejpam-5751	184	16	,	,	PUNCT
ejpam-5751	184	17	2	2	NUM
ejpam-5751	184	18	and	and	CCONJ
ejpam-5751	184	19	3	3	NUM
ejpam-5751	184	20	show	show	VERB
ejpam-5751	184	21	the	the	DET
ejpam-5751	184	22	solutions	solution	NOUN
ejpam-5751	184	23	u(t	u(t	NOUN
ejpam-5751	184	24	,	,	PUNCT
ejpam-5751	184	25	x	x	NOUN
ejpam-5751	184	26	,	,	PUNCT
ejpam-5751	184	27	y	y	NOUN
ejpam-5751	184	28	)	)	PUNCT
ejpam-5751	184	29	presented	present	VERB
ejpam-5751	184	30	in	in	ADP
ejpam-5751	184	31	eqs	eqs	X
ejpam-5751	184	32	(	(	PUNCT
ejpam-5751	184	33	43	43	NUM
ejpam-5751	184	34	)	)	PUNCT
ejpam-5751	184	35	,	,	PUNCT
ejpam-5751	184	36	(	(	PUNCT
ejpam-5751	184	37	45	45	NUM
ejpam-5751	184	38	)	)	PUNCT
ejpam-5751	184	39	and	and	CCONJ
ejpam-5751	184	40	(	(	PUNCT
ejpam-5751	184	41	46	46	NUM
ejpam-5751	184	42	)	)	PUNCT
ejpam-5751	184	43	for	for	ADP
ejpam-5751	184	44	distinct	distinct	ADJ
ejpam-5751	184	45	value	value	NOUN
ejpam-5751	184	46	of	of	ADP
ejpam-5751	184	47	ν	ν	NOUN
ejpam-5751	184	48	as	as	SCONJ
ejpam-5751	184	49	follows	follow	VERB
ejpam-5751	184	50	:	:	PUNCT
ejpam-5751	184	51	w.	w.	PROPN
ejpam-5751	184	52	w.	w.	PROPN
ejpam-5751	184	53	mohammed	mohammed	PROPN
ejpam-5751	184	54	et	et	PROPN
ejpam-5751	184	55	al	al	PROPN
ejpam-5751	184	56	.	.	PUNCT
ejpam-5751	184	57	/	/	SYM
ejpam-5751	184	58	eur	eur	PROPN
ejpam-5751	184	59	.	.	PUNCT
ejpam-5751	185	1	j.	j.	PROPN
ejpam-5751	185	2	pure	pure	PROPN
ejpam-5751	185	3	appl	appl	PROPN
ejpam-5751	185	4	.	.	PROPN
ejpam-5751	185	5	math	math	PROPN
ejpam-5751	185	6	,	,	PUNCT
ejpam-5751	185	7	18	18	NUM
ejpam-5751	185	8	(	(	PUNCT
ejpam-5751	185	9	1	1	NUM
ejpam-5751	185	10	)	)	PUNCT
ejpam-5751	185	11	(	(	PUNCT
ejpam-5751	185	12	2025	2025	NUM
ejpam-5751	185	13	)	)	PUNCT
ejpam-5751	185	14	,	,	PUNCT
ejpam-5751	185	15	5751	5751	NUM
ejpam-5751	185	16	11	11	NUM
ejpam-5751	185	17	of	of	ADP
ejpam-5751	185	18	15	15	NUM
ejpam-5751	185	19	(	(	PUNCT
ejpam-5751	185	20	a	a	NOUN
ejpam-5751	185	21	)	)	PUNCT
ejpam-5751	185	22	ν	ν	NOUN
ejpam-5751	185	23	=	=	SYM
ejpam-5751	185	24	0	0	PUNCT
ejpam-5751	185	25	(	(	PUNCT
ejpam-5751	185	26	b	b	NOUN
ejpam-5751	185	27	)	)	PUNCT
ejpam-5751	185	28	ν	ν	NOUN
ejpam-5751	185	29	=	=	SYM
ejpam-5751	185	30	0.1	0.1	NUM
ejpam-5751	185	31	(	(	PUNCT
ejpam-5751	185	32	c	c	NOUN
ejpam-5751	185	33	)	)	PUNCT
ejpam-5751	185	34	ν	ν	NOUN
ejpam-5751	185	35	=	=	SYM
ejpam-5751	185	36	0.4	0.4	NUM
ejpam-5751	185	37	(	(	PUNCT
ejpam-5751	185	38	d	d	NOUN
ejpam-5751	185	39	)	)	PUNCT
ejpam-5751	185	40	ν	ν	NOUN
ejpam-5751	185	41	=	=	SYM
ejpam-5751	185	42	1	1	NUM
ejpam-5751	185	43	0	0	NUM
ejpam-5751	185	44	0.5	0.5	NUM
ejpam-5751	185	45	1	1	NUM
ejpam-5751	185	46	1.5	1.5	NUM
ejpam-5751	185	47	2	2	NUM
ejpam-5751	185	48	2.5	2.5	NUM
ejpam-5751	185	49	3	3	NUM
ejpam-5751	185	50	3.5	3.5	NUM
ejpam-5751	185	51	4	4	NUM
ejpam-5751	185	52	4.5	4.5	NUM
ejpam-5751	185	53	5	5	NUM
ejpam-5751	185	54	time	time	NOUN
ejpam-5751	185	55	"	"	PUNCT
ejpam-5751	185	56	t	t	PROPN
ejpam-5751	185	57	"	"	PUNCT
ejpam-5751	185	58	0	0	NUM
ejpam-5751	185	59	0.2	0.2	NUM
ejpam-5751	185	60	0.4	0.4	NUM
ejpam-5751	185	61	0.6	0.6	NUM
ejpam-5751	185	62	0.8	0.8	NUM
ejpam-5751	185	63	1	1	NUM
ejpam-5751	185	64	1.2	1.2	NUM
ejpam-5751	185	65	s	s	NOUN
ejpam-5751	185	66	o	o	NOUN
ejpam-5751	185	67	lu	lu	NOUN
ejpam-5751	185	68	ti	ti	NOUN
ejpam-5751	185	69	o	o	NOUN
ejpam-5751	185	70	n	n	PROPN
ejpam-5751	185	71	=	=	NOUN
ejpam-5751	185	72	0	0	NUM
ejpam-5751	185	73	=	=	SYM
ejpam-5751	185	74	0.1	0.1	NUM
ejpam-5751	185	75	=	=	SYM
ejpam-5751	185	76	0.4	0.4	NUM
ejpam-5751	185	77	=	=	SYM
ejpam-5751	185	78	1	1	NUM
ejpam-5751	185	79	=	=	SYM
ejpam-5751	185	80	2	2	NUM
ejpam-5751	185	81	(	(	PUNCT
ejpam-5751	185	82	e	e	NOUN
ejpam-5751	185	83	)	)	PUNCT
ejpam-5751	185	84	ν	ν	NOUN
ejpam-5751	185	85	=	=	SYM
ejpam-5751	185	86	2	2	NUM
ejpam-5751	185	87	(	(	PUNCT
ejpam-5751	185	88	f	f	X
ejpam-5751	185	89	)	)	PUNCT
ejpam-5751	185	90	ν	ν	NOUN
ejpam-5751	185	91	=	=	SYM
ejpam-5751	185	92	0	0	NUM
ejpam-5751	185	93	,	,	PUNCT
ejpam-5751	185	94	0.1	0.1	NUM
ejpam-5751	185	95	,	,	PUNCT
ejpam-5751	185	96	0.4	0.4	NUM
ejpam-5751	185	97	,	,	PUNCT
ejpam-5751	185	98	1	1	NUM
ejpam-5751	185	99	,	,	PUNCT
ejpam-5751	185	100	2	2	NUM
ejpam-5751	185	101	figure	figure	NOUN
ejpam-5751	185	102	1	1	NUM
ejpam-5751	185	103	:	:	PUNCT
ejpam-5751	185	104	(	(	PUNCT
ejpam-5751	185	105	a	a	X
ejpam-5751	185	106	-	-	PUNCT
ejpam-5751	185	107	e	e	NOUN
ejpam-5751	185	108	)	)	PUNCT
ejpam-5751	185	109	display	display	NOUN
ejpam-5751	185	110	3d	3d	NUM
ejpam-5751	185	111	-	-	PUNCT
ejpam-5751	185	112	shape	shape	NOUN
ejpam-5751	185	113	of	of	ADP
ejpam-5751	185	114	|u(x	|u(x	PROPN
ejpam-5751	185	115	,	,	PUNCT
ejpam-5751	185	116	y	y	PROPN
ejpam-5751	185	117	,	,	PUNCT
ejpam-5751	185	118	t)|	t)|	ADV
ejpam-5751	185	119	described	describe	VERB
ejpam-5751	185	120	in	in	ADP
ejpam-5751	185	121	eq	eq	ADP
ejpam-5751	185	122	.	.	PUNCT
ejpam-5751	186	1	(	(	PUNCT
ejpam-5751	186	2	43	43	NUM
ejpam-5751	186	3	)	)	PUNCT
ejpam-5751	186	4	with	with	ADP
ejpam-5751	186	5	k1	k1	NOUN
ejpam-5751	186	6	=	=	SYM
ejpam-5751	186	7	k2	k2	NOUN
ejpam-5751	186	8	=	=	SYM
ejpam-5751	186	9	1	1	NUM
ejpam-5751	186	10	,	,	PUNCT
ejpam-5751	186	11	p	p	NOUN
ejpam-5751	186	12	=	=	X
ejpam-5751	186	13	s	s	PART
ejpam-5751	186	14	=	=	SYM
ejpam-5751	186	15	0.5	0.5	NUM
ejpam-5751	186	16	,	,	PUNCT
ejpam-5751	186	17	ℓ	ℓ	NOUN
ejpam-5751	186	18	=	=	SYM
ejpam-5751	186	19	1	1	NUM
ejpam-5751	186	20	,	,	PUNCT
ejpam-5751	186	21	ρ4	ρ4	ADV
ejpam-5751	186	22	=	=	SYM
ejpam-5751	186	23	1	1	NUM
ejpam-5751	186	24	,	,	PUNCT
ejpam-5751	186	25	x	x	SYM
ejpam-5751	186	26	∈	∈	PROPN
ejpam-5751	187	1	[	[	X
ejpam-5751	187	2	−4	−4	X
ejpam-5751	187	3	,	,	PUNCT
ejpam-5751	187	4	4	4	NUM
ejpam-5751	187	5	]	]	PUNCT
ejpam-5751	187	6	,	,	PUNCT
ejpam-5751	187	7	y	y	PROPN
ejpam-5751	187	8	=	=	SYM
ejpam-5751	187	9	0	0	NUM
ejpam-5751	187	10	and	and	CCONJ
ejpam-5751	187	11	t	t	PROPN
ejpam-5751	187	12	∈	∈	PROPN
ejpam-5751	188	1	[	[	X
ejpam-5751	188	2	0	0	NUM
ejpam-5751	188	3	,	,	PUNCT
ejpam-5751	188	4	3	3	NUM
ejpam-5751	188	5	]	]	PUNCT
ejpam-5751	188	6	(	(	PUNCT
ejpam-5751	188	7	f	f	X
ejpam-5751	188	8	)	)	PUNCT
ejpam-5751	188	9	exhibits	exhibit	VERB
ejpam-5751	188	10	2d	2d	NOUN
ejpam-5751	188	11	-	-	PUNCT
ejpam-5751	188	12	shape	shape	NOUN
ejpam-5751	188	13	of	of	ADP
ejpam-5751	188	14	eq	eq	NOUN
ejpam-5751	188	15	.	.	PUNCT
ejpam-5751	189	1	(	(	PUNCT
ejpam-5751	189	2	43	43	NUM
ejpam-5751	189	3	)	)	PUNCT
ejpam-5751	189	4	with	with	ADP
ejpam-5751	189	5	distinct	distinct	ADJ
ejpam-5751	189	6	ν	ν	PROPN
ejpam-5751	189	7	w.	w.	PROPN
ejpam-5751	189	8	w.	w.	PROPN
ejpam-5751	189	9	mohammed	mohammed	PROPN
ejpam-5751	189	10	et	et	PROPN
ejpam-5751	189	11	al	al	PROPN
ejpam-5751	189	12	.	.	PUNCT
ejpam-5751	189	13	/	/	SYM
ejpam-5751	189	14	eur	eur	PROPN
ejpam-5751	189	15	.	.	PUNCT
ejpam-5751	190	1	j.	j.	PROPN
ejpam-5751	190	2	pure	pure	PROPN
ejpam-5751	190	3	appl	appl	PROPN
ejpam-5751	190	4	.	.	PROPN
ejpam-5751	190	5	math	math	PROPN
ejpam-5751	190	6	,	,	PUNCT
ejpam-5751	190	7	18	18	NUM
ejpam-5751	190	8	(	(	PUNCT
ejpam-5751	190	9	1	1	NUM
ejpam-5751	190	10	)	)	PUNCT
ejpam-5751	190	11	(	(	PUNCT
ejpam-5751	190	12	2025	2025	NUM
ejpam-5751	190	13	)	)	PUNCT
ejpam-5751	190	14	,	,	PUNCT
ejpam-5751	190	15	5751	5751	NUM
ejpam-5751	190	16	12	12	NUM
ejpam-5751	190	17	of	of	ADP
ejpam-5751	190	18	15	15	NUM
ejpam-5751	190	19	(	(	PUNCT
ejpam-5751	190	20	a	a	NOUN
ejpam-5751	190	21	)	)	PUNCT
ejpam-5751	190	22	ν	ν	NOUN
ejpam-5751	190	23	=	=	SYM
ejpam-5751	190	24	0	0	PUNCT
ejpam-5751	190	25	(	(	PUNCT
ejpam-5751	190	26	b	b	NOUN
ejpam-5751	190	27	)	)	PUNCT
ejpam-5751	190	28	ν	ν	NOUN
ejpam-5751	190	29	=	=	SYM
ejpam-5751	190	30	0.1	0.1	NUM
ejpam-5751	190	31	(	(	PUNCT
ejpam-5751	190	32	c	c	NOUN
ejpam-5751	190	33	)	)	PUNCT
ejpam-5751	190	34	ν	ν	NOUN
ejpam-5751	190	35	=	=	SYM
ejpam-5751	190	36	0.4	0.4	NUM
ejpam-5751	190	37	(	(	PUNCT
ejpam-5751	190	38	d	d	NOUN
ejpam-5751	190	39	)	)	PUNCT
ejpam-5751	190	40	ν	ν	NOUN
ejpam-5751	190	41	=	=	SYM
ejpam-5751	190	42	1	1	NUM
ejpam-5751	190	43	0	0	NUM
ejpam-5751	190	44	0.5	0.5	NUM
ejpam-5751	190	45	1	1	NUM
ejpam-5751	190	46	1.5	1.5	NUM
ejpam-5751	190	47	2	2	NUM
ejpam-5751	190	48	2.5	2.5	NUM
ejpam-5751	190	49	3	3	NUM
ejpam-5751	190	50	3.5	3.5	NUM
ejpam-5751	190	51	4	4	NUM
ejpam-5751	190	52	4.5	4.5	NUM
ejpam-5751	190	53	5	5	NUM
ejpam-5751	190	54	time	time	NOUN
ejpam-5751	190	55	"	"	PUNCT
ejpam-5751	190	56	t	t	PROPN
ejpam-5751	190	57	"	"	PUNCT
ejpam-5751	190	58	0	0	NUM
ejpam-5751	190	59	0.1	0.1	NUM
ejpam-5751	190	60	0.2	0.2	NUM
ejpam-5751	190	61	0.3	0.3	NUM
ejpam-5751	190	62	0.4	0.4	NUM
ejpam-5751	190	63	0.5	0.5	NUM
ejpam-5751	190	64	0.6	0.6	NUM
ejpam-5751	190	65	0.7	0.7	NUM
ejpam-5751	190	66	0.8	0.8	NUM
ejpam-5751	190	67	0.9	0.9	NUM
ejpam-5751	190	68	1	1	NUM
ejpam-5751	190	69	s	s	NOUN
ejpam-5751	190	70	o	o	NOUN
ejpam-5751	190	71	lu	lu	NOUN
ejpam-5751	190	72	ti	ti	NOUN
ejpam-5751	190	73	o	o	NOUN
ejpam-5751	190	74	n	n	PROPN
ejpam-5751	190	75	=	=	NOUN
ejpam-5751	190	76	0	0	NUM
ejpam-5751	190	77	=	=	SYM
ejpam-5751	190	78	0.1	0.1	NUM
ejpam-5751	190	79	=	=	SYM
ejpam-5751	190	80	0.4	0.4	NUM
ejpam-5751	190	81	=	=	SYM
ejpam-5751	190	82	1	1	NUM
ejpam-5751	190	83	=	=	SYM
ejpam-5751	190	84	2	2	NUM
ejpam-5751	190	85	(	(	PUNCT
ejpam-5751	190	86	e	e	NOUN
ejpam-5751	190	87	)	)	PUNCT
ejpam-5751	190	88	ν	ν	NOUN
ejpam-5751	190	89	=	=	SYM
ejpam-5751	190	90	2	2	NUM
ejpam-5751	190	91	(	(	PUNCT
ejpam-5751	190	92	f	f	X
ejpam-5751	190	93	)	)	PUNCT
ejpam-5751	190	94	ν	ν	NOUN
ejpam-5751	190	95	=	=	SYM
ejpam-5751	190	96	0	0	NUM
ejpam-5751	190	97	,	,	PUNCT
ejpam-5751	190	98	0.1	0.1	NUM
ejpam-5751	190	99	,	,	PUNCT
ejpam-5751	190	100	0.4	0.4	NUM
ejpam-5751	190	101	,	,	PUNCT
ejpam-5751	190	102	1	1	NUM
ejpam-5751	190	103	,	,	PUNCT
ejpam-5751	190	104	2	2	NUM
ejpam-5751	190	105	figure	figure	NOUN
ejpam-5751	190	106	2	2	NUM
ejpam-5751	190	107	:	:	PUNCT
ejpam-5751	190	108	(	(	PUNCT
ejpam-5751	190	109	a	a	X
ejpam-5751	190	110	-	-	PUNCT
ejpam-5751	190	111	e	e	NOUN
ejpam-5751	190	112	)	)	PUNCT
ejpam-5751	190	113	display	display	NOUN
ejpam-5751	190	114	3d	3d	NUM
ejpam-5751	190	115	-	-	PUNCT
ejpam-5751	190	116	shape	shape	NOUN
ejpam-5751	190	117	of	of	ADP
ejpam-5751	190	118	|u(x	|u(x	PROPN
ejpam-5751	190	119	,	,	PUNCT
ejpam-5751	190	120	y	y	PROPN
ejpam-5751	190	121	,	,	PUNCT
ejpam-5751	190	122	t)|	t)|	NOUN
ejpam-5751	190	123	presented	present	VERB
ejpam-5751	190	124	in	in	ADP
ejpam-5751	190	125	eq	eq	ADP
ejpam-5751	190	126	.	.	PUNCT
ejpam-5751	191	1	(	(	PUNCT
ejpam-5751	191	2	43	43	NUM
ejpam-5751	191	3	)	)	PUNCT
ejpam-5751	191	4	with	with	ADP
ejpam-5751	191	5	ň	ň	NOUN
ejpam-5751	191	6	=	=	SYM
ejpam-5751	191	7	ℏ	ℏ	NOUN
ejpam-5751	191	8	=	=	SYM
ejpam-5751	191	9	0.5	0.5	NUM
ejpam-5751	191	10	,	,	PUNCT
ejpam-5751	191	11	k1	k1	NOUN
ejpam-5751	191	12	=	=	SYM
ejpam-5751	191	13	k2	k2	NOUN
ejpam-5751	191	14	=	=	SYM
ejpam-5751	191	15	1	1	NUM
ejpam-5751	191	16	,	,	PUNCT
ejpam-5751	191	17	ρ4	ρ4	ADV
ejpam-5751	191	18	=	=	SYM
ejpam-5751	191	19	2	2	NUM
ejpam-5751	191	20	,	,	PUNCT
ejpam-5751	191	21	ω	ω	NOUN
ejpam-5751	191	22	=	=	SYM
ejpam-5751	191	23	1	1	NUM
ejpam-5751	191	24	,	,	PUNCT
ejpam-5751	191	25	x	x	SYM
ejpam-5751	191	26	∈	∈	PROPN
ejpam-5751	192	1	[	[	X
ejpam-5751	192	2	−4	−4	X
ejpam-5751	192	3	,	,	PUNCT
ejpam-5751	192	4	4	4	NUM
ejpam-5751	192	5	]	]	PUNCT
ejpam-5751	192	6	,	,	PUNCT
ejpam-5751	192	7	y	y	PROPN
ejpam-5751	192	8	=	=	SYM
ejpam-5751	192	9	0	0	NUM
ejpam-5751	192	10	,	,	PUNCT
ejpam-5751	192	11	and	and	CCONJ
ejpam-5751	192	12	t	t	PROPN
ejpam-5751	192	13	∈	∈	PROPN
ejpam-5751	193	1	[	[	X
ejpam-5751	193	2	0	0	NUM
ejpam-5751	193	3	,	,	PUNCT
ejpam-5751	193	4	4	4	NUM
ejpam-5751	193	5	]	]	PUNCT
ejpam-5751	193	6	(	(	PUNCT
ejpam-5751	193	7	f	f	X
ejpam-5751	193	8	)	)	PUNCT
ejpam-5751	193	9	exhibits	exhibit	VERB
ejpam-5751	193	10	2d	2d	NOUN
ejpam-5751	193	11	-	-	PUNCT
ejpam-5751	193	12	shape	shape	NOUN
ejpam-5751	193	13	of	of	ADP
ejpam-5751	193	14	eq	eq	NOUN
ejpam-5751	193	15	.	.	PUNCT
ejpam-5751	194	1	(	(	PUNCT
ejpam-5751	194	2	43	43	NUM
ejpam-5751	194	3	)	)	PUNCT
ejpam-5751	194	4	with	with	ADP
ejpam-5751	194	5	different	different	ADJ
ejpam-5751	194	6	ν	ν	X
ejpam-5751	194	7	w.	w.	PROPN
ejpam-5751	194	8	w.	w.	PROPN
ejpam-5751	194	9	mohammed	mohammed	PROPN
ejpam-5751	194	10	et	et	PROPN
ejpam-5751	194	11	al	al	PROPN
ejpam-5751	194	12	.	.	PUNCT
ejpam-5751	194	13	/	/	SYM
ejpam-5751	194	14	eur	eur	PROPN
ejpam-5751	194	15	.	.	PUNCT
ejpam-5751	195	1	j.	j.	PROPN
ejpam-5751	195	2	pure	pure	PROPN
ejpam-5751	195	3	appl	appl	PROPN
ejpam-5751	195	4	.	.	PROPN
ejpam-5751	195	5	math	math	PROPN
ejpam-5751	195	6	,	,	PUNCT
ejpam-5751	195	7	18	18	NUM
ejpam-5751	195	8	(	(	PUNCT
ejpam-5751	195	9	1	1	NUM
ejpam-5751	195	10	)	)	PUNCT
ejpam-5751	195	11	(	(	PUNCT
ejpam-5751	195	12	2025	2025	NUM
ejpam-5751	195	13	)	)	PUNCT
ejpam-5751	195	14	,	,	PUNCT
ejpam-5751	195	15	5751	5751	NUM
ejpam-5751	195	16	13	13	NUM
ejpam-5751	195	17	of	of	ADP
ejpam-5751	195	18	15	15	NUM
ejpam-5751	195	19	(	(	PUNCT
ejpam-5751	195	20	a	a	NOUN
ejpam-5751	195	21	)	)	PUNCT
ejpam-5751	195	22	ν	ν	NOUN
ejpam-5751	195	23	=	=	SYM
ejpam-5751	195	24	0	0	PUNCT
ejpam-5751	195	25	(	(	PUNCT
ejpam-5751	195	26	b	b	NOUN
ejpam-5751	195	27	)	)	PUNCT
ejpam-5751	195	28	ν	ν	NOUN
ejpam-5751	195	29	=	=	SYM
ejpam-5751	195	30	0.1	0.1	NUM
ejpam-5751	195	31	(	(	PUNCT
ejpam-5751	195	32	c	c	NOUN
ejpam-5751	195	33	)	)	PUNCT
ejpam-5751	195	34	ν	ν	NOUN
ejpam-5751	195	35	=	=	SYM
ejpam-5751	195	36	0.4	0.4	NUM
ejpam-5751	195	37	(	(	PUNCT
ejpam-5751	195	38	d	d	NOUN
ejpam-5751	195	39	)	)	PUNCT
ejpam-5751	195	40	ν	ν	NOUN
ejpam-5751	195	41	=	=	SYM
ejpam-5751	195	42	1	1	NUM
ejpam-5751	195	43	0	0	NUM
ejpam-5751	195	44	0.5	0.5	NUM
ejpam-5751	195	45	1	1	NUM
ejpam-5751	195	46	1.5	1.5	NUM
ejpam-5751	195	47	2	2	NUM
ejpam-5751	195	48	2.5	2.5	NUM
ejpam-5751	195	49	3	3	NUM
ejpam-5751	195	50	3.5	3.5	NUM
ejpam-5751	195	51	4	4	NUM
ejpam-5751	195	52	4.5	4.5	NUM
ejpam-5751	195	53	5	5	NUM
ejpam-5751	195	54	time	time	NOUN
ejpam-5751	195	55	"	"	PUNCT
ejpam-5751	195	56	t	t	PROPN
ejpam-5751	195	57	"	"	PUNCT
ejpam-5751	195	58	0	0	NUM
ejpam-5751	195	59	0.1	0.1	NUM
ejpam-5751	195	60	0.2	0.2	NUM
ejpam-5751	195	61	0.3	0.3	NUM
ejpam-5751	195	62	0.4	0.4	NUM
ejpam-5751	195	63	0.5	0.5	NUM
ejpam-5751	195	64	0.6	0.6	NUM
ejpam-5751	195	65	0.7	0.7	NUM
ejpam-5751	195	66	0.8	0.8	NUM
ejpam-5751	195	67	0.9	0.9	NUM
ejpam-5751	195	68	1	1	NUM
ejpam-5751	195	69	s	s	NOUN
ejpam-5751	195	70	o	o	NOUN
ejpam-5751	195	71	lu	lu	NOUN
ejpam-5751	195	72	ti	ti	NOUN
ejpam-5751	195	73	o	o	NOUN
ejpam-5751	195	74	n	n	PROPN
ejpam-5751	195	75	=	=	NOUN
ejpam-5751	195	76	0	0	NUM
ejpam-5751	195	77	=	=	SYM
ejpam-5751	195	78	0.1	0.1	NUM
ejpam-5751	195	79	=	=	SYM
ejpam-5751	195	80	0.4	0.4	NUM
ejpam-5751	195	81	=	=	SYM
ejpam-5751	195	82	1	1	NUM
ejpam-5751	195	83	=	=	SYM
ejpam-5751	195	84	2	2	NUM
ejpam-5751	195	85	(	(	PUNCT
ejpam-5751	195	86	e	e	NOUN
ejpam-5751	195	87	)	)	PUNCT
ejpam-5751	195	88	ν	ν	NOUN
ejpam-5751	195	89	=	=	SYM
ejpam-5751	195	90	2	2	NUM
ejpam-5751	195	91	(	(	PUNCT
ejpam-5751	195	92	f	f	X
ejpam-5751	195	93	)	)	PUNCT
ejpam-5751	195	94	ν	ν	NOUN
ejpam-5751	195	95	=	=	SYM
ejpam-5751	195	96	0	0	NUM
ejpam-5751	195	97	,	,	PUNCT
ejpam-5751	195	98	0.1	0.1	NUM
ejpam-5751	195	99	,	,	PUNCT
ejpam-5751	195	100	0.4	0.4	NUM
ejpam-5751	195	101	,	,	PUNCT
ejpam-5751	195	102	1	1	NUM
ejpam-5751	195	103	,	,	PUNCT
ejpam-5751	195	104	2	2	NUM
ejpam-5751	195	105	figure	figure	NOUN
ejpam-5751	195	106	3	3	NUM
ejpam-5751	195	107	:	:	PUNCT
ejpam-5751	195	108	(	(	PUNCT
ejpam-5751	195	109	a	a	X
ejpam-5751	195	110	-	-	PUNCT
ejpam-5751	195	111	e	e	NOUN
ejpam-5751	195	112	)	)	PUNCT
ejpam-5751	195	113	display	display	NOUN
ejpam-5751	195	114	3d	3d	NUM
ejpam-5751	195	115	-	-	PUNCT
ejpam-5751	195	116	shape	shape	NOUN
ejpam-5751	195	117	of	of	ADP
ejpam-5751	195	118	|u(x	|u(x	PROPN
ejpam-5751	195	119	,	,	PUNCT
ejpam-5751	195	120	y	y	PROPN
ejpam-5751	195	121	,	,	PUNCT
ejpam-5751	195	122	t)|	t)|	NOUN
ejpam-5751	195	123	presented	present	VERB
ejpam-5751	195	124	in	in	ADP
ejpam-5751	195	125	eq	eq	PROPN
ejpam-5751	195	126	(	(	PUNCT
ejpam-5751	195	127	46	46	NUM
ejpam-5751	195	128	)	)	PUNCT
ejpam-5751	195	129	with	with	ADP
ejpam-5751	195	130	k1	k1	NOUN
ejpam-5751	195	131	=	=	SYM
ejpam-5751	195	132	k2	k2	NOUN
ejpam-5751	195	133	=	=	SYM
ejpam-5751	195	134	1	1	NUM
ejpam-5751	195	135	,	,	PUNCT
ejpam-5751	195	136	ω	ω	NOUN
ejpam-5751	195	137	=	=	SYM
ejpam-5751	195	138	2	2	NUM
ejpam-5751	195	139	,	,	PUNCT
ejpam-5751	195	140	ρ4	ρ4	ADV
ejpam-5751	195	141	=	=	SYM
ejpam-5751	195	142	1	1	NUM
ejpam-5751	195	143	,	,	PUNCT
ejpam-5751	195	144	x	x	SYM
ejpam-5751	195	145	∈	∈	PROPN
ejpam-5751	196	1	[	[	X
ejpam-5751	196	2	−4	−4	X
ejpam-5751	196	3	,	,	PUNCT
ejpam-5751	196	4	4	4	NUM
ejpam-5751	196	5	]	]	PUNCT
ejpam-5751	196	6	,	,	PUNCT
ejpam-5751	196	7	y	y	PROPN
ejpam-5751	196	8	=	=	SYM
ejpam-5751	196	9	0	0	NUM
ejpam-5751	196	10	and	and	CCONJ
ejpam-5751	196	11	t	t	PROPN
ejpam-5751	196	12	∈	∈	PROPN
ejpam-5751	197	1	[	[	X
ejpam-5751	197	2	0	0	NUM
ejpam-5751	197	3	,	,	PUNCT
ejpam-5751	197	4	3	3	NUM
ejpam-5751	197	5	]	]	PUNCT
ejpam-5751	197	6	(	(	PUNCT
ejpam-5751	197	7	f	f	X
ejpam-5751	197	8	)	)	PUNCT
ejpam-5751	197	9	shows	show	VERB
ejpam-5751	197	10	2d	2d	NOUN
ejpam-5751	197	11	-	-	PUNCT
ejpam-5751	197	12	shape	shape	NOUN
ejpam-5751	197	13	of	of	ADP
ejpam-5751	197	14	eq	eq	NOUN
ejpam-5751	197	15	.	.	PUNCT
ejpam-5751	198	1	(	(	PUNCT
ejpam-5751	198	2	46	46	NUM
ejpam-5751	198	3	)	)	PUNCT
ejpam-5751	198	4	as	as	SCONJ
ejpam-5751	198	5	seen	see	VERB
ejpam-5751	198	6	in	in	ADP
ejpam-5751	198	7	figures	figure	NOUN
ejpam-5751	198	8	1	1	NUM
ejpam-5751	198	9	-	-	SYM
ejpam-5751	198	10	3	3	NUM
ejpam-5751	198	11	,	,	PUNCT
ejpam-5751	198	12	a	a	DET
ejpam-5751	198	13	wide	wide	ADJ
ejpam-5751	198	14	variety	variety	NOUN
ejpam-5751	198	15	of	of	ADP
ejpam-5751	198	16	solutions	solution	NOUN
ejpam-5751	198	17	,	,	PUNCT
ejpam-5751	198	18	such	such	ADJ
ejpam-5751	198	19	as	as	ADP
ejpam-5751	198	20	optical	optical	ADJ
ejpam-5751	198	21	kink	kink	NOUN
ejpam-5751	198	22	solutions	solution	NOUN
ejpam-5751	198	23	,	,	PUNCT
ejpam-5751	198	24	optical	optical	ADJ
ejpam-5751	198	25	singular	singular	ADJ
ejpam-5751	198	26	solutions	solution	NOUN
ejpam-5751	198	27	,	,	PUNCT
ejpam-5751	198	28	optical	optical	ADJ
ejpam-5751	198	29	periodic	periodic	ADJ
ejpam-5751	198	30	solutions	solution	NOUN
ejpam-5751	198	31	,	,	PUNCT
ejpam-5751	198	32	and	and	CCONJ
ejpam-5751	198	33	others	other	NOUN
ejpam-5751	198	34	,	,	PUNCT
ejpam-5751	198	35	arise	arise	VERB
ejpam-5751	198	36	when	when	SCONJ
ejpam-5751	198	37	noise	noise	NOUN
ejpam-5751	198	38	is	be	AUX
ejpam-5751	198	39	disregarded	disregard	VERB
ejpam-5751	198	40	(	(	PUNCT
ejpam-5751	198	41	i.e.	i.e.	X
ejpam-5751	198	42	,	,	PUNCT
ejpam-5751	198	43	ν	ν	X
ejpam-5751	198	44	=	=	NOUN
ejpam-5751	198	45	0	0	NUM
ejpam-5751	198	46	)	)	PUNCT
ejpam-5751	198	47	.	.	PUNCT
ejpam-5751	199	1	after	after	ADP
ejpam-5751	199	2	a	a	DET
ejpam-5751	199	3	few	few	ADJ
ejpam-5751	199	4	transit	transit	NOUN
ejpam-5751	199	5	patterns	pattern	NOUN
ejpam-5751	199	6	,	,	PUNCT
ejpam-5751	199	7	the	the	DET
ejpam-5751	199	8	surface	surface	NOUN
ejpam-5751	199	9	flattens	flatten	VERB
ejpam-5751	199	10	when	when	SCONJ
ejpam-5751	199	11	noise	noise	NOUN
ejpam-5751	199	12	is	be	AUX
ejpam-5751	199	13	added	add	VERB
ejpam-5751	199	14	at	at	ADP
ejpam-5751	199	15	ν	ν	X
ejpam-5751	199	16	=	=	SYM
ejpam-5751	199	17	0.1	0.1	NUM
ejpam-5751	199	18	,	,	PUNCT
ejpam-5751	199	19	0.4	0.4	NUM
ejpam-5751	199	20	,	,	PUNCT
ejpam-5751	199	21	1	1	NUM
ejpam-5751	199	22	,	,	PUNCT
ejpam-5751	199	23	2	2	NUM
ejpam-5751	199	24	.	.	PUNCT
ejpam-5751	200	1	this	this	DET
ejpam-5751	200	2	finding	finding	NOUN
ejpam-5751	200	3	demonstrates	demonstrate	VERB
ejpam-5751	200	4	the	the	DET
ejpam-5751	200	5	stabilization	stabilization	NOUN
ejpam-5751	200	6	of	of	ADP
ejpam-5751	200	7	the	the	DET
ejpam-5751	200	8	shfe	shfe	PROPN
ejpam-5751	200	9	eq	eq	PROPN
ejpam-5751	200	10	.	.	PUNCT
ejpam-5751	201	1	(	(	PUNCT
ejpam-5751	201	2	1	1	X
ejpam-5751	201	3	)	)	PUNCT
ejpam-5751	201	4	solutions	solution	NOUN
ejpam-5751	201	5	around	around	ADP
ejpam-5751	201	6	zero	zero	NUM
ejpam-5751	201	7	due	due	ADP
ejpam-5751	201	8	to	to	ADP
ejpam-5751	201	9	multiplicative	multiplicative	ADJ
ejpam-5751	201	10	brownian	brownian	ADJ
ejpam-5751	201	11	motion	motion	NOUN
ejpam-5751	201	12	.	.	PUNCT
ejpam-5751	202	1	w.	w.	PROPN
ejpam-5751	202	2	w.	w.	PROPN
ejpam-5751	202	3	mohammed	mohammed	PROPN
ejpam-5751	202	4	et	et	PROPN
ejpam-5751	202	5	al	al	PROPN
ejpam-5751	202	6	.	.	PUNCT
ejpam-5751	202	7	/	/	SYM
ejpam-5751	202	8	eur	eur	PROPN
ejpam-5751	202	9	.	.	PUNCT
ejpam-5751	203	1	j.	j.	PROPN
ejpam-5751	203	2	pure	pure	PROPN
ejpam-5751	203	3	appl	appl	PROPN
ejpam-5751	203	4	.	.	PROPN
ejpam-5751	203	5	math	math	PROPN
ejpam-5751	203	6	,	,	PUNCT
ejpam-5751	203	7	18	18	NUM
ejpam-5751	203	8	(	(	PUNCT
ejpam-5751	203	9	1	1	NUM
ejpam-5751	203	10	)	)	PUNCT
ejpam-5751	203	11	(	(	PUNCT
ejpam-5751	203	12	2025	2025	NUM
ejpam-5751	203	13	)	)	PUNCT
ejpam-5751	203	14	,	,	PUNCT
ejpam-5751	203	15	5751	5751	NUM
ejpam-5751	203	16	14	14	NUM
ejpam-5751	203	17	of	of	ADP
ejpam-5751	203	18	15	15	NUM
ejpam-5751	203	19	5	5	NUM
ejpam-5751	203	20	.	.	PUNCT
ejpam-5751	203	21	conclusions	conclusion	NOUN
ejpam-5751	203	22	the	the	DET
ejpam-5751	203	23	stochastic	stochastic	ADJ
ejpam-5751	203	24	heisenberg	heisenberg	PROPN
ejpam-5751	203	25	ferromagnet	ferromagnet	NOUN
ejpam-5751	203	26	equation	equation	NOUN
ejpam-5751	203	27	(	(	PUNCT
ejpam-5751	203	28	shfe	shfe	PROPN
ejpam-5751	203	29	)	)	PUNCT
ejpam-5751	203	30	(	(	PUNCT
ejpam-5751	203	31	1	1	X
ejpam-5751	203	32	)	)	PUNCT
ejpam-5751	203	33	driven	drive	VERB
ejpam-5751	203	34	by	by	ADP
ejpam-5751	203	35	multiplicative	multiplicative	ADJ
ejpam-5751	203	36	noise	noise	NOUN
ejpam-5751	203	37	in	in	ADP
ejpam-5751	203	38	the	the	DET
ejpam-5751	203	39	itô	itô	PROPN
ejpam-5751	203	40	sense	sense	NOUN
ejpam-5751	203	41	was	be	AUX
ejpam-5751	203	42	examined	examine	VERB
ejpam-5751	203	43	in	in	ADP
ejpam-5751	203	44	this	this	DET
ejpam-5751	203	45	study	study	NOUN
ejpam-5751	203	46	.	.	PUNCT
ejpam-5751	204	1	we	we	PRON
ejpam-5751	204	2	transformed	transform	VERB
ejpam-5751	204	3	the	the	DET
ejpam-5751	204	4	shfe	shfe	NOUN
ejpam-5751	204	5	into	into	ADP
ejpam-5751	204	6	another	another	DET
ejpam-5751	204	7	heisenberg	heisenberg	PROPN
ejpam-5751	204	8	ferromagnet	ferromagnet	NOUN
ejpam-5751	204	9	equation	equation	NOUN
ejpam-5751	204	10	with	with	ADP
ejpam-5751	204	11	random	random	ADJ
ejpam-5751	204	12	variable	variable	ADJ
ejpam-5751	204	13	coefficients	coefficient	NOUN
ejpam-5751	204	14	(	(	PUNCT
ejpam-5751	204	15	3	3	NUM
ejpam-5751	204	16	)	)	PUNCT
ejpam-5751	204	17	(	(	PUNCT
ejpam-5751	204	18	hfe	hfe	PROPN
ejpam-5751	204	19	-	-	PUNCT
ejpam-5751	204	20	rvcs	rvcs	PROPN
ejpam-5751	204	21	)	)	PUNCT
ejpam-5751	204	22	by	by	ADP
ejpam-5751	204	23	applying	apply	VERB
ejpam-5751	204	24	the	the	DET
ejpam-5751	204	25	proper	proper	ADJ
ejpam-5751	204	26	transformation	transformation	NOUN
ejpam-5751	204	27	.	.	PUNCT
ejpam-5751	205	1	we	we	PRON
ejpam-5751	205	2	found	find	VERB
ejpam-5751	205	3	novel	novel	ADJ
ejpam-5751	205	4	stochastic	stochastic	ADJ
ejpam-5751	205	5	exact	exact	ADJ
ejpam-5751	205	6	solutions	solution	NOUN
ejpam-5751	205	7	for	for	ADP
ejpam-5751	205	8	hfervcs	hfervcs	NOUN
ejpam-5751	205	9	in	in	ADP
ejpam-5751	205	10	the	the	DET
ejpam-5751	205	11	form	form	NOUN
ejpam-5751	205	12	of	of	ADP
ejpam-5751	205	13	hyperbolic	hyperbolic	ADJ
ejpam-5751	205	14	,	,	PUNCT
ejpam-5751	205	15	trigonometric	trigonometric	ADJ
ejpam-5751	205	16	,	,	PUNCT
ejpam-5751	205	17	rational	rational	ADJ
ejpam-5751	205	18	,	,	PUNCT
ejpam-5751	205	19	and	and	CCONJ
ejpam-5751	205	20	elliptic	elliptic	ADJ
ejpam-5751	205	21	functions	function	NOUN
ejpam-5751	205	22	utilizing	utilize	VERB
ejpam-5751	205	23	two	two	NUM
ejpam-5751	205	24	various	various	ADJ
ejpam-5751	205	25	methods	method	NOUN
ejpam-5751	205	26	including	include	VERB
ejpam-5751	205	27	the	the	DET
ejpam-5751	205	28	jef	jef	PROPN
ejpam-5751	205	29	-	-	PUNCT
ejpam-5751	205	30	method	method	NOUN
ejpam-5751	205	31	and	and	CCONJ
ejpam-5751	205	32	grem	grem	NOUN
ejpam-5751	205	33	-	-	NOUN
ejpam-5751	205	34	method	method	NOUN
ejpam-5751	205	35	,	,	PUNCT
ejpam-5751	205	36	and	and	CCONJ
ejpam-5751	205	37	then	then	ADV
ejpam-5751	205	38	we	we	PRON
ejpam-5751	205	39	acquired	acquire	VERB
ejpam-5751	205	40	the	the	DET
ejpam-5751	205	41	solutions	solution	NOUN
ejpam-5751	205	42	of	of	ADP
ejpam-5751	205	43	shfe	shfe	PROPN
ejpam-5751	205	44	(	(	PUNCT
ejpam-5751	205	45	1	1	NUM
ejpam-5751	205	46	)	)	PUNCT
ejpam-5751	205	47	.	.	PUNCT
ejpam-5751	206	1	additionally	additionally	ADV
ejpam-5751	206	2	,	,	PUNCT
ejpam-5751	206	3	we	we	PRON
ejpam-5751	206	4	generated	generate	VERB
ejpam-5751	206	5	a	a	DET
ejpam-5751	206	6	few	few	ADJ
ejpam-5751	206	7	earlier	early	ADJ
ejpam-5751	206	8	solutions	solution	NOUN
ejpam-5751	206	9	,	,	PUNCT
ejpam-5751	206	10	such	such	DET
ejpam-5751	206	11	the	the	DET
ejpam-5751	206	12	solutions	solution	NOUN
ejpam-5751	206	13	documented	document	VERB
ejpam-5751	206	14	in	in	ADP
ejpam-5751	206	15	[	[	X
ejpam-5751	206	16	6	6	NUM
ejpam-5751	206	17	,	,	PUNCT
ejpam-5751	206	18	12	12	NUM
ejpam-5751	206	19	]	]	PUNCT
ejpam-5751	206	20	.	.	PUNCT
ejpam-5751	207	1	the	the	DET
ejpam-5751	207	2	obtained	obtain	VERB
ejpam-5751	207	3	solutions	solution	NOUN
ejpam-5751	207	4	are	be	AUX
ejpam-5751	207	5	essential	essential	ADJ
ejpam-5751	207	6	for	for	ADP
ejpam-5751	207	7	comprehending	comprehend	VERB
ejpam-5751	207	8	a	a	DET
ejpam-5751	207	9	number	number	NOUN
ejpam-5751	207	10	of	of	ADP
ejpam-5751	207	11	challenging	challenge	VERB
ejpam-5751	207	12	physical	physical	ADJ
ejpam-5751	207	13	processes	process	NOUN
ejpam-5751	207	14	due	due	ADP
ejpam-5751	207	15	to	to	ADP
ejpam-5751	207	16	the	the	DET
ejpam-5751	207	17	significance	significance	NOUN
ejpam-5751	207	18	of	of	ADP
ejpam-5751	207	19	the	the	DET
ejpam-5751	207	20	heisenberg	heisenberg	PROPN
ejpam-5751	207	21	ferromagnet	ferromagnet	NOUN
ejpam-5751	207	22	equation	equation	NOUN
ejpam-5751	207	23	in	in	ADP
ejpam-5751	207	24	the	the	DET
ejpam-5751	207	25	behavior	behavior	NOUN
ejpam-5751	207	26	of	of	ADP
ejpam-5751	207	27	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	207	28	materials	material	NOUN
ejpam-5751	207	29	.	.	PUNCT
ejpam-5751	208	1	the	the	DET
ejpam-5751	208	2	impact	impact	NOUN
ejpam-5751	208	3	of	of	ADP
ejpam-5751	208	4	the	the	DET
ejpam-5751	208	5	stochastic	stochastic	ADJ
ejpam-5751	208	6	term	term	NOUN
ejpam-5751	208	7	on	on	ADP
ejpam-5751	208	8	the	the	DET
ejpam-5751	208	9	stochastic	stochastic	ADJ
ejpam-5751	208	10	exact	exact	ADJ
ejpam-5751	208	11	solutions	solution	NOUN
ejpam-5751	208	12	of	of	ADP
ejpam-5751	208	13	shfe	shfe	PROPN
ejpam-5751	208	14	was	be	AUX
ejpam-5751	208	15	finally	finally	ADV
ejpam-5751	208	16	illustrated	illustrate	VERB
ejpam-5751	208	17	using	use	VERB
ejpam-5751	208	18	a	a	DET
ejpam-5751	208	19	few	few	ADJ
ejpam-5751	208	20	graphics	graphic	NOUN
ejpam-5751	208	21	.	.	PUNCT
ejpam-5751	209	1	in	in	ADP
ejpam-5751	209	2	future	future	ADJ
ejpam-5751	209	3	work	work	NOUN
ejpam-5751	209	4	,	,	PUNCT
ejpam-5751	209	5	we	we	PRON
ejpam-5751	209	6	can	can	AUX
ejpam-5751	209	7	study	study	VERB
ejpam-5751	209	8	shfe	shfe	PROPN
ejpam-5751	209	9	(	(	PUNCT
ejpam-5751	209	10	1	1	NUM
ejpam-5751	209	11	)	)	PUNCT
ejpam-5751	209	12	with	with	ADP
ejpam-5751	209	13	additive	additive	ADJ
ejpam-5751	209	14	noise	noise	NOUN
ejpam-5751	209	15	.	.	PUNCT
ejpam-5751	210	1	acknowledgements	acknowledgement	NOUN
ejpam-5751	210	2	this	this	DET
ejpam-5751	210	3	research	research	NOUN
ejpam-5751	210	4	has	have	AUX
ejpam-5751	210	5	been	be	AUX
ejpam-5751	210	6	funded	fund	VERB
ejpam-5751	210	7	by	by	ADP
ejpam-5751	210	8	scientific	scientific	ADJ
ejpam-5751	210	9	research	research	NOUN
ejpam-5751	210	10	deanship	deanship	NOUN
ejpam-5751	210	11	at	at	ADP
ejpam-5751	210	12	the	the	DET
ejpam-5751	210	13	university	university	NOUN
ejpam-5751	210	14	of	of	ADP
ejpam-5751	210	15	ha’il	ha’il	PROPN
ejpam-5751	210	16	-	-	PUNCT
ejpam-5751	210	17	saudi	saudi	PROPN
ejpam-5751	210	18	arabia	arabia	PROPN
ejpam-5751	210	19	through	through	ADP
ejpam-5751	210	20	project	project	NOUN
ejpam-5751	210	21	number	number	NOUN
ejpam-5751	210	22	rg-24097	rg-24097	NOUN
ejpam-5751	210	23	.	.	PUNCT
ejpam-5751	211	1	references	reference	NOUN
ejpam-5751	211	2	[	[	X
ejpam-5751	211	3	1	1	NUM
ejpam-5751	211	4	]	]	PUNCT
ejpam-5751	211	5	f.	f.	PROPN
ejpam-5751	211	6	m.	m.	PROPN
ejpam-5751	211	7	al	al	PROPN
ejpam-5751	211	8	-	-	PUNCT
ejpam-5751	211	9	askar	askar	PROPN
ejpam-5751	211	10	.	.	PUNCT
ejpam-5751	212	1	the	the	DET
ejpam-5751	212	2	solitary	solitary	ADJ
ejpam-5751	212	3	wave	wave	NOUN
ejpam-5751	212	4	solutions	solution	NOUN
ejpam-5751	212	5	of	of	ADP
ejpam-5751	212	6	the	the	DET
ejpam-5751	212	7	stochastic	stochastic	ADJ
ejpam-5751	212	8	heisenberg	heisenberg	PROPN
ejpam-5751	212	9	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	212	10	spin	spin	NOUN
ejpam-5751	212	11	chain	chain	NOUN
ejpam-5751	212	12	equation	equation	NOUN
ejpam-5751	212	13	using	use	VERB
ejpam-5751	212	14	two	two	NUM
ejpam-5751	212	15	different	different	ADJ
ejpam-5751	212	16	analytical	analytical	ADJ
ejpam-5751	212	17	methods	method	NOUN
ejpam-5751	212	18	.	.	PUNCT
ejpam-5751	213	1	frontiers	frontier	NOUN
ejpam-5751	213	2	in	in	ADP
ejpam-5751	213	3	physics	physics	PROPN
ejpam-5751	213	4	,	,	PUNCT
ejpam-5751	213	5	11:1267673	11:1267673	NUM
ejpam-5751	213	6	,	,	PUNCT
ejpam-5751	213	7	2023	2023	NUM
ejpam-5751	213	8	.	.	PUNCT
ejpam-5751	214	1	[	[	X
ejpam-5751	214	2	2	2	NUM
ejpam-5751	214	3	]	]	PUNCT
ejpam-5751	214	4	h.	h.	PROPN
ejpam-5751	214	5	bulut	bulut	PROPN
ejpam-5751	214	6	,	,	PUNCT
ejpam-5751	214	7	t.	t.	PROPN
ejpam-5751	214	8	a.	a.	NOUN
ejpam-5751	214	9	sulaiman	sulaiman	PROPN
ejpam-5751	214	10	,	,	PUNCT
ejpam-5751	214	11	and	and	CCONJ
ejpam-5751	214	12	h.	h.	PROPN
ejpam-5751	214	13	m.	m.	PROPN
ejpam-5751	214	14	baskonus	baskonus	PROPN
ejpam-5751	214	15	.	.	PUNCT
ejpam-5751	215	1	dark	dark	ADJ
ejpam-5751	215	2	,	,	PUNCT
ejpam-5751	215	3	bright	bright	ADJ
ejpam-5751	215	4	and	and	CCONJ
ejpam-5751	215	5	other	other	ADJ
ejpam-5751	215	6	soliton	soliton	NOUN
ejpam-5751	215	7	solutions	solution	NOUN
ejpam-5751	215	8	to	to	ADP
ejpam-5751	215	9	the	the	DET
ejpam-5751	215	10	heisenberg	heisenberg	PROPN
ejpam-5751	215	11	ferromagnetic	ferromagnetic	PROPN
ejpam-5751	215	12	spin	spin	NOUN
ejpam-5751	215	13	chain	chain	NOUN
ejpam-5751	215	14	equation	equation	NOUN
ejpam-5751	215	15	.	.	PUNCT
ejpam-5751	216	1	physica	physica	PROPN
ejpam-5751	216	2	a	a	PRON
ejpam-5751	216	3	,	,	PUNCT
ejpam-5751	216	4	12:123	12:123	NUM
ejpam-5751	216	5	,	,	PUNCT
ejpam-5751	216	6	2018	2018	NUM
ejpam-5751	216	7	.	.	PUNCT
ejpam-5751	217	1	[	[	X
ejpam-5751	217	2	3	3	X
ejpam-5751	217	3	]	]	PUNCT
ejpam-5751	217	4	m.	m.	NOUN
ejpam-5751	217	5	daniel	daniel	PROPN
ejpam-5751	217	6	,	,	PUNCT
ejpam-5751	217	7	l.	l.	PROPN
ejpam-5751	217	8	kavitha	kavitha	PROPN
ejpam-5751	217	9	,	,	PUNCT
ejpam-5751	217	10	and	and	CCONJ
ejpam-5751	217	11	r.	r.	PROPN
ejpam-5751	217	12	amuda	amuda	PROPN
ejpam-5751	217	13	.	.	PUNCT
ejpam-5751	218	1	soliton	soliton	NOUN
ejpam-5751	218	2	spin	spin	NOUN
ejpam-5751	218	3	excitations	excitation	NOUN
ejpam-5751	218	4	in	in	ADP
ejpam-5751	218	5	an	an	DET
ejpam-5751	218	6	anisotropic	anisotropic	NOUN
ejpam-5751	218	7	heisenberg	heisenberg	PROPN
ejpam-5751	218	8	ferromagnet	ferromagnet	NOUN
ejpam-5751	218	9	with	with	ADP
ejpam-5751	218	10	octupole	octupole	ADJ
ejpam-5751	218	11	-	-	PUNCT
ejpam-5751	218	12	dipole	dipole	NOUN
ejpam-5751	218	13	interaction	interaction	NOUN
ejpam-5751	218	14	.	.	PUNCT
ejpam-5751	219	1	physical	physical	ADJ
ejpam-5751	219	2	review	review	PROPN
ejpam-5751	219	3	,	,	PUNCT
ejpam-5751	219	4	59:13774	59:13774	NUM
ejpam-5751	219	5	,	,	PUNCT
ejpam-5751	219	6	1999	1999	NUM
ejpam-5751	219	7	.	.	PUNCT
ejpam-5751	220	1	[	[	X
ejpam-5751	220	2	4	4	NUM
ejpam-5751	220	3	]	]	PUNCT
ejpam-5751	220	4	x.	x.	NOUN
ejpam-5751	220	5	y.	y.	PROPN
ejpam-5751	220	6	gao	gao	PROPN
ejpam-5751	220	7	.	.	PUNCT
ejpam-5751	220	8	variety	variety	NOUN
ejpam-5751	220	9	of	of	ADP
ejpam-5751	220	10	the	the	DET
ejpam-5751	220	11	cosmic	cosmic	ADJ
ejpam-5751	220	12	plasmas	plasma	NOUN
ejpam-5751	220	13	:	:	PUNCT
ejpam-5751	220	14	general	general	ADJ
ejpam-5751	220	15	variable	variable	ADJ
ejpam-5751	220	16	-	-	PUNCT
ejpam-5751	220	17	coefficient	coefficient	NOUN
ejpam-5751	220	18	korteweg	korteweg	NOUN
ejpam-5751	220	19	-	-	PUNCT
ejpam-5751	220	20	de	de	NOUN
ejpam-5751	220	21	vries	vrie	NOUN
ejpam-5751	220	22	-	-	PUNCT
ejpam-5751	220	23	burgers	burger	NOUN
ejpam-5751	220	24	equation	equation	NOUN
ejpam-5751	220	25	with	with	ADP
ejpam-5751	220	26	experimental	experimental	ADJ
ejpam-5751	220	27	/	/	SYM
ejpam-5751	220	28	observational	observational	ADJ
ejpam-5751	220	29	support	support	NOUN
ejpam-5751	220	30	.	.	PUNCT
ejpam-5751	221	1	epl	epl	PROPN
ejpam-5751	221	2	,	,	PUNCT
ejpam-5751	221	3	110:15002	110:15002	NUM
ejpam-5751	221	4	,	,	PUNCT
ejpam-5751	221	5	2015	2015	NUM
ejpam-5751	221	6	.	.	PUNCT
ejpam-5751	222	1	[	[	X
ejpam-5751	222	2	5	5	X
ejpam-5751	222	3	]	]	PUNCT
ejpam-5751	222	4	d.	d.	PROPN
ejpam-5751	222	5	y.	y.	PROPN
ejpam-5751	222	6	liu	liu	PROPN
ejpam-5751	222	7	,	,	PUNCT
ejpam-5751	222	8	b.	b.	PROPN
ejpam-5751	222	9	tian	tian	PROPN
ejpam-5751	222	10	,	,	PUNCT
ejpam-5751	222	11	y.	y.	PROPN
ejpam-5751	222	12	jiang	jiang	PROPN
ejpam-5751	222	13	,	,	PUNCT
ejpam-5751	222	14	x.	x.	PROPN
ejpam-5751	222	15	y.	y.	PROPN
ejpam-5751	222	16	xie	xie	PROPN
ejpam-5751	222	17	,	,	PUNCT
ejpam-5751	222	18	and	and	CCONJ
ejpam-5751	222	19	x.	x.	PROPN
ejpam-5751	222	20	y.	y.	PROPN
ejpam-5751	222	21	wu	wu	PROPN
ejpam-5751	222	22	.	.	PUNCT
ejpam-5751	223	1	analytic	analytic	ADJ
ejpam-5751	223	2	study	study	NOUN
ejpam-5751	223	3	on	on	ADP
ejpam-5751	223	4	a	a	DET
ejpam-5751	223	5	(	(	PUNCT
ejpam-5751	223	6	2	2	NUM
ejpam-5751	223	7	+	+	NOUN
ejpam-5751	223	8	1)dimensional	1)dimensional	NUM
ejpam-5751	223	9	nonlinear	nonlinear	ADJ
ejpam-5751	223	10	schrödinger	schrödinger	NOUN
ejpam-5751	223	11	equation	equation	NOUN
ejpam-5751	223	12	in	in	ADP
ejpam-5751	223	13	the	the	DET
ejpam-5751	223	14	heisenberg	heisenberg	PROPN
ejpam-5751	223	15	ferromagnetism	ferromagnetism	PROPN
ejpam-5751	223	16	.	.	PUNCT
ejpam-5751	224	1	computational	computational	ADJ
ejpam-5751	224	2	and	and	CCONJ
ejpam-5751	224	3	applied	applied	ADJ
ejpam-5751	224	4	mathematics	mathematic	NOUN
ejpam-5751	224	5	,	,	PUNCT
ejpam-5751	224	6	71:2001–2007	71:2001–2007	NUM
ejpam-5751	224	7	,	,	PUNCT
ejpam-5751	224	8	2016	2016	NUM
ejpam-5751	224	9	.	.	PUNCT
ejpam-5751	225	1	[	[	X
ejpam-5751	225	2	6	6	NUM
ejpam-5751	225	3	]	]	X
ejpam-5751	225	4	y.	y.	PROPN
ejpam-5751	225	5	l.	l.	PROPN
ejpam-5751	225	6	ma	ma	PROPN
ejpam-5751	225	7	,	,	PUNCT
ejpam-5751	225	8	b.	b.	PROPN
ejpam-5751	225	9	q.	q.	PROPN
ejpam-5751	225	10	li	li	PROPN
ejpam-5751	225	11	,	,	PUNCT
ejpam-5751	225	12	and	and	CCONJ
ejpam-5751	225	13	y.	y.	PROPN
ejpam-5751	225	14	y.	y.	PROPN
ejpam-5751	225	15	fu	fu	PROPN
ejpam-5751	225	16	.	.	PUNCT
ejpam-5751	226	1	a	a	DET
ejpam-5751	226	2	series	series	NOUN
ejpam-5751	226	3	of	of	ADP
ejpam-5751	226	4	the	the	DET
ejpam-5751	226	5	solutions	solution	NOUN
ejpam-5751	226	6	for	for	ADP
ejpam-5751	226	7	the	the	DET
ejpam-5751	226	8	heisenberg	heisenberg	PROPN
ejpam-5751	226	9	ferromagnetic	ferromagnetic	PROPN
ejpam-5751	226	10	spin	spin	NOUN
ejpam-5751	226	11	chain	chain	NOUN
ejpam-5751	226	12	equation	equation	NOUN
ejpam-5751	226	13	.	.	PUNCT
ejpam-5751	227	1	mathematical	mathematical	ADJ
ejpam-5751	227	2	methods	method	NOUN
ejpam-5751	227	3	in	in	ADP
ejpam-5751	227	4	the	the	DET
ejpam-5751	227	5	applied	apply	VERB
ejpam-5751	227	6	sciences	science	NOUN
ejpam-5751	227	7	,	,	PUNCT
ejpam-5751	227	8	41:3316–3322	41:3316–3322	NUM
ejpam-5751	227	9	,	,	PUNCT
ejpam-5751	227	10	2018	2018	NUM
ejpam-5751	227	11	.	.	PUNCT
ejpam-5751	228	1	[	[	X
ejpam-5751	228	2	7	7	X
ejpam-5751	228	3	]	]	X
ejpam-5751	228	4	w.	w.	PROPN
ejpam-5751	228	5	w.	w.	PROPN
ejpam-5751	228	6	mohammed	mohammed	PROPN
ejpam-5751	228	7	,	,	PUNCT
ejpam-5751	228	8	f.	f.	PROPN
ejpam-5751	228	9	m.	m.	PROPN
ejpam-5751	228	10	al	al	PROPN
ejpam-5751	228	11	-	-	PUNCT
ejpam-5751	228	12	askar	askar	PROPN
ejpam-5751	228	13	,	,	PUNCT
ejpam-5751	228	14	c.	c.	PROPN
ejpam-5751	228	15	cesarano	cesarano	PROPN
ejpam-5751	228	16	,	,	PUNCT
ejpam-5751	228	17	t.	t.	NOUN
ejpam-5751	228	18	botmart	botmart	NOUN
ejpam-5751	228	19	,	,	PUNCT
ejpam-5751	228	20	and	and	CCONJ
ejpam-5751	228	21	m.	m.	PROPN
ejpam-5751	228	22	el	el	PROPN
ejpam-5751	228	23	-	-	PUNCT
ejpam-5751	228	24	morshedy	morshedy	PROPN
ejpam-5751	228	25	.	.	PUNCT
ejpam-5751	229	1	wiener	wiener	NOUN
ejpam-5751	229	2	process	process	NOUN
ejpam-5751	229	3	effects	effect	NOUN
ejpam-5751	229	4	on	on	ADP
ejpam-5751	229	5	the	the	DET
ejpam-5751	229	6	solutions	solution	NOUN
ejpam-5751	229	7	of	of	ADP
ejpam-5751	229	8	the	the	DET
ejpam-5751	229	9	fractional	fractional	ADJ
ejpam-5751	229	10	(	(	PUNCT
ejpam-5751	229	11	2	2	NUM
ejpam-5751	229	12	+	+	PROPN
ejpam-5751	229	13	1)-dimensional	1)-dimensional	PROPN
ejpam-5751	229	14	heisenberg	heisenberg	PROPN
ejpam-5751	229	15	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	229	16	spin	spin	NOUN
ejpam-5751	229	17	chain	chain	NOUN
ejpam-5751	229	18	equation	equation	NOUN
ejpam-5751	229	19	.	.	PUNCT
ejpam-5751	230	1	mathematics	mathematic	NOUN
ejpam-5751	230	2	,	,	PUNCT
ejpam-5751	230	3	10:2043	10:2043	NUM
ejpam-5751	230	4	,	,	PUNCT
ejpam-5751	230	5	2022	2022	NUM
ejpam-5751	230	6	.	.	PUNCT
ejpam-5751	231	1	w.	w.	PROPN
ejpam-5751	231	2	w.	w.	PROPN
ejpam-5751	231	3	mohammed	mohammed	PROPN
ejpam-5751	231	4	et	et	PROPN
ejpam-5751	231	5	al	al	PROPN
ejpam-5751	231	6	.	.	PUNCT
ejpam-5751	231	7	/	/	SYM
ejpam-5751	231	8	eur	eur	PROPN
ejpam-5751	231	9	.	.	PUNCT
ejpam-5751	232	1	j.	j.	PROPN
ejpam-5751	232	2	pure	pure	PROPN
ejpam-5751	232	3	appl	appl	PROPN
ejpam-5751	232	4	.	.	PROPN
ejpam-5751	232	5	math	math	PROPN
ejpam-5751	232	6	,	,	PUNCT
ejpam-5751	232	7	18	18	NUM
ejpam-5751	232	8	(	(	PUNCT
ejpam-5751	232	9	1	1	NUM
ejpam-5751	232	10	)	)	PUNCT
ejpam-5751	232	11	(	(	PUNCT
ejpam-5751	232	12	2025	2025	NUM
ejpam-5751	232	13	)	)	PUNCT
ejpam-5751	232	14	,	,	PUNCT
ejpam-5751	232	15	5751	5751	NUM
ejpam-5751	232	16	15	15	NUM
ejpam-5751	232	17	of	of	ADP
ejpam-5751	232	18	15	15	NUM
ejpam-5751	233	1	[	[	SYM
ejpam-5751	233	2	8	8	NUM
ejpam-5751	233	3	]	]	X
ejpam-5751	233	4	w.	w.	PROPN
ejpam-5751	233	5	w.	w.	PROPN
ejpam-5751	233	6	mohammed	mohammed	PROPN
ejpam-5751	233	7	,	,	PUNCT
ejpam-5751	233	8	f.	f.	PROPN
ejpam-5751	233	9	gassem	gassem	PROPN
ejpam-5751	233	10	,	,	PUNCT
ejpam-5751	233	11	and	and	CCONJ
ejpam-5751	233	12	r.	r.	PROPN
ejpam-5751	233	13	sidaoui	sidaoui	PROPN
ejpam-5751	233	14	.	.	PUNCT
ejpam-5751	234	1	random	random	ADJ
ejpam-5751	234	2	traveling	travel	VERB
ejpam-5751	234	3	wave	wave	NOUN
ejpam-5751	234	4	equations	equation	NOUN
ejpam-5751	234	5	for	for	ADP
ejpam-5751	234	6	the	the	DET
ejpam-5751	234	7	heisenberg	heisenberg	PROPN
ejpam-5751	234	8	ferromagnetic	ferromagnetic	PROPN
ejpam-5751	234	9	spin	spin	NOUN
ejpam-5751	234	10	chain	chain	NOUN
ejpam-5751	234	11	model	model	NOUN
ejpam-5751	234	12	and	and	CCONJ
ejpam-5751	234	13	their	their	PRON
ejpam-5751	234	14	optical	optical	ADJ
ejpam-5751	234	15	stochastic	stochastic	ADJ
ejpam-5751	234	16	solutions	solution	NOUN
ejpam-5751	234	17	in	in	ADP
ejpam-5751	234	18	a	a	DET
ejpam-5751	234	19	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	234	20	materials	material	NOUN
ejpam-5751	234	21	.	.	PUNCT
ejpam-5751	235	1	axioms	axiom	NOUN
ejpam-5751	235	2	,	,	PUNCT
ejpam-5751	235	3	13:864	13:864	NUM
ejpam-5751	235	4	,	,	PUNCT
ejpam-5751	235	5	2024	2024	NUM
ejpam-5751	235	6	.	.	PUNCT
ejpam-5751	236	1	[	[	X
ejpam-5751	236	2	9	9	NUM
ejpam-5751	236	3	]	]	PUNCT
ejpam-5751	236	4	a.	a.	PROPN
ejpam-5751	236	5	r.	r.	PROPN
ejpam-5751	236	6	seadawy	seadawy	PROPN
ejpam-5751	236	7	,	,	PUNCT
ejpam-5751	236	8	n.	n.	PROPN
ejpam-5751	236	9	nasreen	nasreen	PROPN
ejpam-5751	236	10	,	,	PUNCT
ejpam-5751	236	11	d.	d.	PROPN
ejpam-5751	236	12	lu	lu	PROPN
ejpam-5751	236	13	,	,	PUNCT
ejpam-5751	236	14	and	and	CCONJ
ejpam-5751	236	15	m.	m.	PROPN
ejpam-5751	236	16	arshad	arshad	PROPN
ejpam-5751	236	17	.	.	PUNCT
ejpam-5751	236	18	arising	arise	VERB
ejpam-5751	236	19	wave	wave	NOUN
ejpam-5751	236	20	propagation	propagation	NOUN
ejpam-5751	236	21	in	in	ADP
ejpam-5751	236	22	nonlinear	nonlinear	ADJ
ejpam-5751	236	23	media	medium	NOUN
ejpam-5751	236	24	for	for	ADP
ejpam-5751	236	25	the	the	DET
ejpam-5751	236	26	(	(	PUNCT
ejpam-5751	236	27	2	2	NUM
ejpam-5751	236	28	+	+	PROPN
ejpam-5751	236	29	1)-dimensional	1)-dimensional	PROPN
ejpam-5751	236	30	heisenberg	heisenberg	PROPN
ejpam-5751	236	31	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	236	32	spin	spin	NOUN
ejpam-5751	236	33	chain	chain	NOUN
ejpam-5751	236	34	dynamical	dynamical	ADJ
ejpam-5751	236	35	model	model	NOUN
ejpam-5751	236	36	.	.	PUNCT
ejpam-5751	237	1	physica	physica	PROPN
ejpam-5751	237	2	a	a	DET
ejpam-5751	237	3	,	,	PUNCT
ejpam-5751	237	4	538:122846	538:122846	NUM
ejpam-5751	237	5	,	,	PUNCT
ejpam-5751	237	6	2020	2020	NUM
ejpam-5751	237	7	.	.	PUNCT
ejpam-5751	238	1	[	[	X
ejpam-5751	238	2	10	10	NUM
ejpam-5751	238	3	]	]	PUNCT
ejpam-5751	238	4	t.	t.	PROPN
ejpam-5751	238	5	a.	a.	PROPN
ejpam-5751	238	6	sulaiman	sulaiman	PROPN
ejpam-5751	238	7	,	,	PUNCT
ejpam-5751	238	8	t.	t.	PROPN
ejpam-5751	238	9	akturk	akturk	PROPN
ejpam-5751	238	10	,	,	PUNCT
ejpam-5751	238	11	h.	h.	PROPN
ejpam-5751	238	12	bulut	bulut	PROPN
ejpam-5751	238	13	,	,	PUNCT
ejpam-5751	238	14	and	and	CCONJ
ejpam-5751	238	15	h.	h.	PROPN
ejpam-5751	238	16	m.	m.	PROPN
ejpam-5751	238	17	baskonus	baskonus	PROPN
ejpam-5751	238	18	.	.	PUNCT
ejpam-5751	239	1	investigation	investigation	NOUN
ejpam-5751	239	2	of	of	ADP
ejpam-5751	239	3	various	various	ADJ
ejpam-5751	239	4	soliton	soliton	NOUN
ejpam-5751	239	5	solutions	solution	NOUN
ejpam-5751	239	6	to	to	ADP
ejpam-5751	239	7	the	the	DET
ejpam-5751	239	8	heisenberg	heisenberg	PROPN
ejpam-5751	239	9	ferromagnetic	ferromagnetic	PROPN
ejpam-5751	239	10	spin	spin	NOUN
ejpam-5751	239	11	chain	chain	NOUN
ejpam-5751	239	12	equation	equation	NOUN
ejpam-5751	239	13	.	.	PUNCT
ejpam-5751	240	1	journal	journal	PROPN
ejpam-5751	240	2	of	of	ADP
ejpam-5751	240	3	electromagnetic	electromagnetic	ADJ
ejpam-5751	240	4	waves	wave	NOUN
ejpam-5751	240	5	and	and	CCONJ
ejpam-5751	240	6	applications	application	NOUN
ejpam-5751	240	7	,	,	PUNCT
ejpam-5751	240	8	32:1093	32:1093	NUM
ejpam-5751	240	9	,	,	PUNCT
ejpam-5751	240	10	2018	2018	NUM
ejpam-5751	240	11	.	.	PUNCT
ejpam-5751	241	1	[	[	X
ejpam-5751	241	2	11	11	NUM
ejpam-5751	241	3	]	]	X
ejpam-5751	241	4	g.	g.	PROPN
ejpam-5751	241	5	s.	s.	PROPN
ejpam-5751	241	6	tang	tang	PROPN
ejpam-5751	241	7	,	,	PUNCT
ejpam-5751	241	8	s.	s.	PROPN
ejpam-5751	241	9	h.	h.	PROPN
ejpam-5751	241	10	wang	wang	PROPN
ejpam-5751	241	11	,	,	PUNCT
ejpam-5751	241	12	and	and	CCONJ
ejpam-5751	241	13	g.	g.	PROPN
ejpam-5751	241	14	w.	w.	PROPN
ejpam-5751	241	15	wang	wang	PROPN
ejpam-5751	241	16	.	.	PUNCT
ejpam-5751	242	1	solitons	soliton	NOUN
ejpam-5751	242	2	and	and	CCONJ
ejpam-5751	242	3	complexitons	complexiton	NOUN
ejpam-5751	242	4	solutions	solution	NOUN
ejpam-5751	242	5	of	of	ADP
ejpam-5751	242	6	an	an	DET
ejpam-5751	242	7	integrable	integrable	ADJ
ejpam-5751	242	8	model	model	NOUN
ejpam-5751	242	9	of	of	ADP
ejpam-5751	242	10	(	(	PUNCT
ejpam-5751	242	11	2	2	NUM
ejpam-5751	242	12	+	+	PROPN
ejpam-5751	242	13	1)-dimensional	1)-dimensional	PROPN
ejpam-5751	242	14	heisenberg	heisenberg	PROPN
ejpam-5751	242	15	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	242	16	spin	spin	NOUN
ejpam-5751	242	17	chain	chain	NOUN
ejpam-5751	242	18	.	.	PUNCT
ejpam-5751	243	1	nonlinear	nonlinear	ADJ
ejpam-5751	243	2	dynamics	dynamic	NOUN
ejpam-5751	243	3	,	,	PUNCT
ejpam-5751	243	4	88:2319–2327	88:2319–2327	NOUN
ejpam-5751	243	5	,	,	PUNCT
ejpam-5751	243	6	2017	2017	NUM
ejpam-5751	243	7	.	.	PUNCT
ejpam-5751	244	1	[	[	X
ejpam-5751	244	2	12	12	NUM
ejpam-5751	244	3	]	]	X
ejpam-5751	244	4	h.	h.	PROPN
ejpam-5751	244	5	triki	triki	PROPN
ejpam-5751	244	6	and	and	CCONJ
ejpam-5751	244	7	a.	a.	NOUN
ejpam-5751	244	8	m.	m.	NOUN
ejpam-5751	244	9	wazwaz	wazwaz	PROPN
ejpam-5751	244	10	.	.	PUNCT
ejpam-5751	245	1	new	new	ADJ
ejpam-5751	245	2	solitons	soliton	NOUN
ejpam-5751	245	3	and	and	CCONJ
ejpam-5751	245	4	periodic	periodic	ADJ
ejpam-5751	245	5	wave	wave	NOUN
ejpam-5751	245	6	solutions	solution	NOUN
ejpam-5751	245	7	for	for	ADP
ejpam-5751	245	8	the	the	DET
ejpam-5751	245	9	(	(	PUNCT
ejpam-5751	245	10	2	2	NUM
ejpam-5751	245	11	+	+	PROPN
ejpam-5751	245	12	1)dimensional	1)dimensional	PROPN
ejpam-5751	245	13	heisenberg	heisenberg	PROPN
ejpam-5751	245	14	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	245	15	spin	spin	NOUN
ejpam-5751	245	16	chain	chain	NOUN
ejpam-5751	245	17	equation	equation	NOUN
ejpam-5751	245	18	.	.	PUNCT
ejpam-5751	246	1	journal	journal	PROPN
ejpam-5751	246	2	of	of	ADP
ejpam-5751	246	3	electromagnetic	electromagnetic	ADJ
ejpam-5751	246	4	waves	wave	NOUN
ejpam-5751	246	5	and	and	CCONJ
ejpam-5751	246	6	applications	application	NOUN
ejpam-5751	246	7	,	,	PUNCT
ejpam-5751	246	8	30:788–794	30:788–794	PROPN
ejpam-5751	246	9	,	,	PUNCT
ejpam-5751	246	10	2016	2016	NUM
ejpam-5751	246	11	.	.	PUNCT
ejpam-5751	247	1	[	[	X
ejpam-5751	247	2	13	13	NUM
ejpam-5751	247	3	]	]	PUNCT
ejpam-5751	247	4	q.	q.	PROPN
ejpam-5751	247	5	m.	m.	PROPN
ejpam-5751	247	6	wang	wang	PROPN
ejpam-5751	247	7	,	,	PUNCT
ejpam-5751	247	8	y.	y.	PROPN
ejpam-5751	247	9	t.	t.	PROPN
ejpam-5751	247	10	gao	gao	PROPN
ejpam-5751	247	11	,	,	PUNCT
ejpam-5751	247	12	c.	c.	PROPN
ejpam-5751	247	13	q.	q.	PROPN
ejpam-5751	247	14	su	su	PROPN
ejpam-5751	247	15	,	,	PUNCT
ejpam-5751	247	16	b.	b.	PROPN
ejpam-5751	247	17	q.	q.	PROPN
ejpam-5751	247	18	mao	mao	PROPN
ejpam-5751	247	19	,	,	PUNCT
ejpam-5751	247	20	z.	z.	PROPN
ejpam-5751	247	21	gao	gao	PROPN
ejpam-5751	247	22	,	,	PUNCT
ejpam-5751	247	23	and	and	CCONJ
ejpam-5751	247	24	j.	j.	PROPN
ejpam-5751	247	25	w.	w.	PROPN
ejpam-5751	247	26	yang	yang	PROPN
ejpam-5751	247	27	.	.	PUNCT
ejpam-5751	247	28	dark	dark	ADJ
ejpam-5751	247	29	solitonic	solitonic	NOUN
ejpam-5751	247	30	interaction	interaction	NOUN
ejpam-5751	247	31	and	and	CCONJ
ejpam-5751	247	32	conservation	conservation	NOUN
ejpam-5751	247	33	laws	law	NOUN
ejpam-5751	247	34	for	for	ADP
ejpam-5751	247	35	a	a	DET
ejpam-5751	247	36	higher	high	ADJ
ejpam-5751	247	37	-	-	PUNCT
ejpam-5751	247	38	order	order	NOUN
ejpam-5751	247	39	(	(	PUNCT
ejpam-5751	247	40	2	2	NUM
ejpam-5751	247	41	+	+	NOUN
ejpam-5751	247	42	1)-dimensional	1)-dimensional	ADJ
ejpam-5751	247	43	nonlinear	nonlinear	ADJ
ejpam-5751	247	44	schrödinger	schrödinger	NOUN
ejpam-5751	247	45	-	-	PUNCT
ejpam-5751	247	46	type	type	NOUN
ejpam-5751	247	47	equation	equation	NOUN
ejpam-5751	247	48	in	in	ADP
ejpam-5751	247	49	a	a	DET
ejpam-5751	247	50	heisenberg	heisenberg	PROPN
ejpam-5751	247	51	ferromagnetic	ferromagnetic	ADJ
ejpam-5751	247	52	spin	spin	NOUN
ejpam-5751	247	53	chain	chain	NOUN
ejpam-5751	247	54	with	with	ADP
ejpam-5751	247	55	bilinear	bilinear	NOUN
ejpam-5751	247	56	and	and	CCONJ
ejpam-5751	247	57	biquadratic	biquadratic	ADJ
ejpam-5751	247	58	interaction	interaction	NOUN
ejpam-5751	247	59	.	.	PUNCT
ejpam-5751	248	1	annals	annal	NOUN
ejpam-5751	248	2	of	of	ADP
ejpam-5751	248	3	physics	physics	NOUN
ejpam-5751	248	4	,	,	PUNCT
ejpam-5751	248	5	363:440–456	363:440–456	NUM
ejpam-5751	248	6	,	,	PUNCT
ejpam-5751	248	7	2015	2015	NUM
ejpam-5751	248	8	.	.	PUNCT
ejpam-5751	249	1	[	[	X
ejpam-5751	249	2	14	14	NUM
ejpam-5751	249	3	]	]	PUNCT
ejpam-5751	249	4	x.	x.	PROPN
ejpam-5751	249	5	h.	h.	PROPN
ejpam-5751	249	6	zhao	zhao	PROPN
ejpam-5751	249	7	,	,	PUNCT
ejpam-5751	249	8	b.	b.	PROPN
ejpam-5751	249	9	tian	tian	PROPN
ejpam-5751	249	10	,	,	PUNCT
ejpam-5751	249	11	d.	d.	PROPN
ejpam-5751	249	12	y.	y.	PROPN
ejpam-5751	249	13	liu	liu	PROPN
ejpam-5751	249	14	,	,	PUNCT
ejpam-5751	249	15	x.	x.	PROPN
ejpam-5751	249	16	y.	y.	PROPN
ejpam-5751	249	17	wu	wu	PROPN
ejpam-5751	249	18	,	,	PUNCT
ejpam-5751	249	19	j.	j.	PROPN
ejpam-5751	249	20	chai	chai	PROPN
ejpam-5751	249	21	,	,	PUNCT
ejpam-5751	249	22	and	and	CCONJ
ejpam-5751	249	23	y.	y.	PROPN
ejpam-5751	249	24	j.	j.	PROPN
ejpam-5751	249	25	guo	guo	PROPN
ejpam-5751	249	26	.	.	PUNCT
ejpam-5751	250	1	dark	dark	ADJ
ejpam-5751	250	2	solitons	soliton	NOUN
ejpam-5751	250	3	interaction	interaction	NOUN
ejpam-5751	250	4	for	for	ADP
ejpam-5751	250	5	a	a	DET
ejpam-5751	250	6	(	(	PUNCT
ejpam-5751	250	7	2	2	NUM
ejpam-5751	250	8	+	+	NOUN
ejpam-5751	250	9	1)-dimensional	1)-dimensional	ADJ
ejpam-5751	250	10	nonlinear	nonlinear	ADJ
ejpam-5751	250	11	schrödinger	schrödinger	NOUN
ejpam-5751	250	12	equation	equation	NOUN
ejpam-5751	250	13	in	in	ADP
ejpam-5751	250	14	the	the	DET
ejpam-5751	250	15	heisenberg	heisenberg	PROPN
ejpam-5751	250	16	ferromagnetic	ferromagnetic	PROPN
ejpam-5751	250	17	spin	spin	NOUN
ejpam-5751	250	18	chain	chain	NOUN
ejpam-5751	250	19	.	.	PUNCT
ejpam-5751	251	1	superlattices	superlattice	NOUN
ejpam-5751	251	2	and	and	CCONJ
ejpam-5751	251	3	microstructures	microstructure	NOUN
ejpam-5751	251	4	,	,	PUNCT
ejpam-5751	251	5	100:587–595	100:587–595	NUM
ejpam-5751	251	6	,	,	PUNCT
ejpam-5751	251	7	2016	2016	NUM
ejpam-5751	251	8	.	.	PUNCT
ejpam-5751	252	1	[	[	X
ejpam-5751	252	2	15	15	NUM
ejpam-5751	252	3	]	]	X
ejpam-5751	252	4	s.	s.	PROPN
ejpam-5751	252	5	d.	d.	PROPN
ejpam-5751	252	6	zhu	zhu	PROPN
ejpam-5751	252	7	.	.	PUNCT
ejpam-5751	253	1	the	the	DET
ejpam-5751	253	2	generalizing	generalize	VERB
ejpam-5751	253	3	riccati	riccati	NOUN
ejpam-5751	253	4	equation	equation	NOUN
ejpam-5751	253	5	mapping	mapping	NOUN
ejpam-5751	253	6	method	method	NOUN
ejpam-5751	253	7	in	in	ADP
ejpam-5751	253	8	nonlinear	nonlinear	ADJ
ejpam-5751	253	9	evolution	evolution	NOUN
ejpam-5751	253	10	equation	equation	NOUN
ejpam-5751	253	11	:	:	PUNCT
ejpam-5751	253	12	application	application	NOUN
ejpam-5751	253	13	to	to	ADP
ejpam-5751	253	14	(	(	PUNCT
ejpam-5751	253	15	2	2	NUM
ejpam-5751	253	16	+	+	NOUN
ejpam-5751	253	17	1)-dimensional	1)-dimensional	PROPN
ejpam-5751	253	18	boiti	boiti	PROPN
ejpam-5751	253	19	-	-	PUNCT
ejpam-5751	253	20	leon	leon	PROPN
ejpam-5751	253	21	-	-	PUNCT
ejpam-5751	253	22	pempinelle	pempinelle	NOUN
ejpam-5751	253	23	equation	equation	NOUN
ejpam-5751	253	24	.	.	PUNCT
ejpam-5751	254	1	chaos	chaos	NOUN
ejpam-5751	254	2	,	,	PUNCT
ejpam-5751	254	3	solitons	soliton	NOUN
ejpam-5751	254	4	and	and	CCONJ
ejpam-5751	254	5	fractals	fractal	NOUN
ejpam-5751	254	6	,	,	PUNCT
ejpam-5751	254	7	37:1335–1342	37:1335–1342	NUM
ejpam-5751	254	8	,	,	PUNCT
ejpam-5751	254	9	2008	2008	NUM
ejpam-5751	254	10	.	.	PUNCT