id	sid	tid	token	lemma	pos
ejpam-5629	1	1	european	european	PROPN
ejpam-5629	1	2	journal	journal	PROPN
ejpam-5629	1	3	of	of	ADP
ejpam-5629	1	4	pure	pure	ADJ
ejpam-5629	1	5	and	and	CCONJ
ejpam-5629	1	6	applied	applied	ADJ
ejpam-5629	1	7	mathematics	mathematic	NOUN
ejpam-5629	1	8	2025	2025	NUM
ejpam-5629	1	9	,	,	PUNCT
ejpam-5629	1	10	vol	vol	NOUN
ejpam-5629	1	11	.	.	PROPN
ejpam-5629	1	12	18	18	NUM
ejpam-5629	1	13	,	,	PUNCT
ejpam-5629	1	14	issue	issue	NOUN
ejpam-5629	1	15	1	1	NUM
ejpam-5629	1	16	,	,	PUNCT
ejpam-5629	1	17	article	article	NOUN
ejpam-5629	1	18	number	number	NOUN
ejpam-5629	1	19	5629	5629	NUM
ejpam-5629	1	20	issn	issn	PROPN
ejpam-5629	1	21	1307	1307	NUM
ejpam-5629	1	22	-	-	SYM
ejpam-5629	1	23	5543	5543	NUM
ejpam-5629	1	24	–	–	PUNCT
ejpam-5629	2	1	ejpam.com	ejpam.com	X
ejpam-5629	2	2	published	publish	VERB
ejpam-5629	2	3	by	by	ADP
ejpam-5629	2	4	new	new	PROPN
ejpam-5629	2	5	york	york	PROPN
ejpam-5629	2	6	business	business	PROPN
ejpam-5629	2	7	global	global	ADJ
ejpam-5629	2	8	existence	existence	NOUN
ejpam-5629	2	9	of	of	ADP
ejpam-5629	2	10	solutions	solution	NOUN
ejpam-5629	2	11	to	to	ADP
ejpam-5629	2	12	a	a	DET
ejpam-5629	2	13	system	system	NOUN
ejpam-5629	2	14	of	of	ADP
ejpam-5629	2	15	fractional	fractional	ADJ
ejpam-5629	2	16	differential	differential	ADJ
ejpam-5629	2	17	equations	equation	NOUN
ejpam-5629	2	18	with	with	ADP
ejpam-5629	2	19	applications	application	NOUN
ejpam-5629	2	20	to	to	PART
ejpam-5629	2	21	beam	beam	VERB
ejpam-5629	2	22	deflections	deflection	NOUN
ejpam-5629	2	23	hasanen	hasanen	PROPN
ejpam-5629	2	24	a.	a.	PROPN
ejpam-5629	2	25	hammad1,2,∗	hammad1,2,∗	PROPN
ejpam-5629	2	26	,	,	PUNCT
ejpam-5629	2	27	manal	manal	ADJ
ejpam-5629	2	28	elzain	elzain	NOUN
ejpam-5629	2	29	mohamed	mohamed	PROPN
ejpam-5629	2	30	abdalla3	abdalla3	PROPN
ejpam-5629	2	31	1	1	NUM
ejpam-5629	2	32	department	department	NOUN
ejpam-5629	2	33	of	of	ADP
ejpam-5629	2	34	mathematics	mathematic	NOUN
ejpam-5629	2	35	,	,	PUNCT
ejpam-5629	2	36	college	college	NOUN
ejpam-5629	2	37	of	of	ADP
ejpam-5629	2	38	science	science	NOUN
ejpam-5629	2	39	,	,	PUNCT
ejpam-5629	2	40	qassim	qassim	PROPN
ejpam-5629	2	41	university	university	PROPN
ejpam-5629	2	42	,	,	PUNCT
ejpam-5629	2	43	buraydah	buraydah	NOUN
ejpam-5629	2	44	51452	51452	NUM
ejpam-5629	2	45	,	,	PUNCT
ejpam-5629	2	46	saudi	saudi	PROPN
ejpam-5629	2	47	arabia	arabia	PROPN
ejpam-5629	2	48	2	2	NUM
ejpam-5629	2	49	department	department	NOUN
ejpam-5629	2	50	of	of	ADP
ejpam-5629	2	51	mathematics	mathematic	NOUN
ejpam-5629	2	52	,	,	PUNCT
ejpam-5629	2	53	faculty	faculty	NOUN
ejpam-5629	2	54	of	of	ADP
ejpam-5629	2	55	science	science	NOUN
ejpam-5629	2	56	,	,	PUNCT
ejpam-5629	2	57	sohag	sohag	NOUN
ejpam-5629	2	58	university	university	NOUN
ejpam-5629	2	59	,	,	PUNCT
ejpam-5629	2	60	sohag	sohag	NOUN
ejpam-5629	2	61	82524	82524	NUM
ejpam-5629	2	62	,	,	PUNCT
ejpam-5629	2	63	egypt	egypt	PROPN
ejpam-5629	2	64	3	3	NUM
ejpam-5629	2	65	department	department	NOUN
ejpam-5629	2	66	of	of	ADP
ejpam-5629	2	67	mathematics	mathematics	PROPN
ejpam-5629	2	68	,	,	PUNCT
ejpam-5629	2	69	college	college	NOUN
ejpam-5629	2	70	of	of	ADP
ejpam-5629	2	71	science	science	NOUN
ejpam-5629	2	72	and	and	CCONJ
ejpam-5629	2	73	arts	art	NOUN
ejpam-5629	2	74	,	,	PUNCT
ejpam-5629	2	75	king	king	PROPN
ejpam-5629	2	76	khalid	khalid	PROPN
ejpam-5629	2	77	university	university	PROPN
ejpam-5629	2	78	,	,	PUNCT
ejpam-5629	2	79	mahayil	mahayil	NOUN
ejpam-5629	2	80	,	,	PUNCT
ejpam-5629	2	81	saudi	saudi	PROPN
ejpam-5629	2	82	arabia	arabia	PROPN
ejpam-5629	2	83	abstract	abstract	NOUN
ejpam-5629	2	84	.	.	PUNCT
ejpam-5629	3	1	in	in	ADP
ejpam-5629	3	2	this	this	DET
ejpam-5629	3	3	manuscript	manuscript	NOUN
ejpam-5629	3	4	,	,	PUNCT
ejpam-5629	3	5	we	we	PRON
ejpam-5629	3	6	introduce	introduce	VERB
ejpam-5629	3	7	a	a	DET
ejpam-5629	3	8	novel	novel	ADJ
ejpam-5629	3	9	system	system	NOUN
ejpam-5629	3	10	of	of	ADP
ejpam-5629	3	11	fractional	fractional	ADJ
ejpam-5629	3	12	differential	differential	ADJ
ejpam-5629	3	13	equations	equation	NOUN
ejpam-5629	3	14	incorporating	incorporate	VERB
ejpam-5629	3	15	both	both	DET
ejpam-5629	3	16	caputo	caputo	NOUN
ejpam-5629	3	17	and	and	CCONJ
ejpam-5629	3	18	conformable	conformable	ADJ
ejpam-5629	3	19	derivatives	derivative	NOUN
ejpam-5629	3	20	.	.	PUNCT
ejpam-5629	4	1	we	we	PRON
ejpam-5629	4	2	delve	delve	VERB
ejpam-5629	4	3	into	into	ADP
ejpam-5629	4	4	the	the	DET
ejpam-5629	4	5	existence	existence	NOUN
ejpam-5629	4	6	and	and	CCONJ
ejpam-5629	4	7	uniqueness	uniqueness	NOUN
ejpam-5629	4	8	of	of	ADP
ejpam-5629	4	9	solutions	solution	NOUN
ejpam-5629	4	10	for	for	ADP
ejpam-5629	4	11	this	this	DET
ejpam-5629	4	12	system	system	NOUN
ejpam-5629	4	13	,	,	PUNCT
ejpam-5629	4	14	employing	employ	VERB
ejpam-5629	4	15	fixed	fix	VERB
ejpam-5629	4	16	-	-	PUNCT
ejpam-5629	4	17	point	point	NOUN
ejpam-5629	4	18	techniques	technique	NOUN
ejpam-5629	4	19	under	under	ADP
ejpam-5629	4	20	appropriate	appropriate	ADJ
ejpam-5629	4	21	conditions	condition	NOUN
ejpam-5629	4	22	.	.	PUNCT
ejpam-5629	5	1	to	to	PART
ejpam-5629	5	2	illustrate	illustrate	VERB
ejpam-5629	5	3	the	the	DET
ejpam-5629	5	4	practical	practical	ADJ
ejpam-5629	5	5	applications	application	NOUN
ejpam-5629	5	6	of	of	ADP
ejpam-5629	5	7	our	our	PRON
ejpam-5629	5	8	theoretical	theoretical	ADJ
ejpam-5629	5	9	findings	finding	NOUN
ejpam-5629	5	10	,	,	PUNCT
ejpam-5629	5	11	we	we	PRON
ejpam-5629	5	12	investigate	investigate	VERB
ejpam-5629	5	13	the	the	DET
ejpam-5629	5	14	traveling	travel	VERB
ejpam-5629	5	15	wave	wave	NOUN
ejpam-5629	5	16	solutions	solution	NOUN
ejpam-5629	5	17	of	of	ADP
ejpam-5629	5	18	a	a	DET
ejpam-5629	5	19	tripled	triple	VERB
ejpam-5629	5	20	system	system	NOUN
ejpam-5629	5	21	of	of	ADP
ejpam-5629	5	22	conformable	conformable	ADJ
ejpam-5629	5	23	fractional	fractional	ADJ
ejpam-5629	5	24	differential	differential	ADJ
ejpam-5629	5	25	equations	equation	NOUN
ejpam-5629	5	26	.	.	PUNCT
ejpam-5629	6	1	our	our	PRON
ejpam-5629	6	2	analysis	analysis	NOUN
ejpam-5629	6	3	provides	provide	VERB
ejpam-5629	6	4	valuable	valuable	ADJ
ejpam-5629	6	5	insights	insight	NOUN
ejpam-5629	6	6	into	into	ADP
ejpam-5629	6	7	the	the	DET
ejpam-5629	6	8	dynamics	dynamic	NOUN
ejpam-5629	6	9	and	and	CCONJ
ejpam-5629	6	10	behavior	behavior	NOUN
ejpam-5629	6	11	of	of	ADP
ejpam-5629	6	12	complex	complex	ADJ
ejpam-5629	6	13	systems	system	NOUN
ejpam-5629	6	14	modeled	model	VERB
ejpam-5629	6	15	by	by	ADP
ejpam-5629	6	16	fractional	fractional	ADJ
ejpam-5629	6	17	differential	differential	ADJ
ejpam-5629	6	18	equations	equation	NOUN
ejpam-5629	6	19	.	.	PUNCT
ejpam-5629	7	1	2020	2020	NUM
ejpam-5629	7	2	mathematics	mathematic	NOUN
ejpam-5629	7	3	subject	subject	NOUN
ejpam-5629	7	4	classifications	classification	NOUN
ejpam-5629	7	5	:	:	PUNCT
ejpam-5629	7	6	47h10	47h10	NUM
ejpam-5629	7	7	,	,	PUNCT
ejpam-5629	7	8	30c45	30c45	NUM
ejpam-5629	7	9	,	,	PUNCT
ejpam-5629	7	10	39b72	39b72	NUM
ejpam-5629	7	11	,	,	PUNCT
ejpam-5629	7	12	39b82	39b82	NUM
ejpam-5629	7	13	key	key	ADJ
ejpam-5629	7	14	words	word	NOUN
ejpam-5629	7	15	and	and	CCONJ
ejpam-5629	7	16	phrases	phrase	NOUN
ejpam-5629	7	17	:	:	PUNCT
ejpam-5629	7	18	nonlinear	nonlinear	ADJ
ejpam-5629	7	19	system	system	NOUN
ejpam-5629	7	20	,	,	PUNCT
ejpam-5629	7	21	fractional	fractional	ADJ
ejpam-5629	7	22	derivative	derivative	NOUN
ejpam-5629	7	23	,	,	PUNCT
ejpam-5629	7	24	tanh	tanh	PROPN
ejpam-5629	7	25	’s	’s	PART
ejpam-5629	7	26	method	method	NOUN
ejpam-5629	7	27	,	,	PUNCT
ejpam-5629	7	28	traveling	travel	VERB
ejpam-5629	7	29	wave	wave	NOUN
ejpam-5629	7	30	solution	solution	NOUN
ejpam-5629	7	31	,	,	PUNCT
ejpam-5629	7	32	evaluation	evaluation	NOUN
ejpam-5629	7	33	metrics	metric	NOUN
ejpam-5629	7	34	1	1	NUM
ejpam-5629	7	35	.	.	PUNCT
ejpam-5629	7	36	background	background	NOUN
ejpam-5629	7	37	materials	material	NOUN
ejpam-5629	7	38	fractional	fractional	ADJ
ejpam-5629	7	39	differential	differential	ADJ
ejpam-5629	7	40	equations	equation	NOUN
ejpam-5629	7	41	(	(	PUNCT
ejpam-5629	7	42	des	des	PROPN
ejpam-5629	7	43	)	)	PUNCT
ejpam-5629	7	44	have	have	AUX
ejpam-5629	7	45	gained	gain	VERB
ejpam-5629	7	46	significant	significant	ADJ
ejpam-5629	7	47	attention	attention	NOUN
ejpam-5629	7	48	due	due	ADP
ejpam-5629	7	49	to	to	ADP
ejpam-5629	7	50	their	their	PRON
ejpam-5629	7	51	ability	ability	NOUN
ejpam-5629	7	52	to	to	PART
ejpam-5629	7	53	model	model	VERB
ejpam-5629	7	54	complex	complex	ADJ
ejpam-5629	7	55	phenomena	phenomenon	NOUN
ejpam-5629	7	56	more	more	ADV
ejpam-5629	7	57	accurately	accurately	ADV
ejpam-5629	7	58	than	than	ADP
ejpam-5629	7	59	classical	classical	ADJ
ejpam-5629	7	60	integer	integer	NOUN
ejpam-5629	7	61	-	-	PUNCT
ejpam-5629	7	62	order	order	NOUN
ejpam-5629	7	63	des	des	PROPN
ejpam-5629	7	64	.	.	PUNCT
ejpam-5629	8	1	several	several	ADJ
ejpam-5629	8	2	analytical	analytical	ADJ
ejpam-5629	8	3	techniques	technique	NOUN
ejpam-5629	8	4	have	have	AUX
ejpam-5629	8	5	been	be	AUX
ejpam-5629	8	6	developed	develop	VERB
ejpam-5629	8	7	to	to	PART
ejpam-5629	8	8	solve	solve	VERB
ejpam-5629	8	9	fractional	fractional	ADJ
ejpam-5629	8	10	des	des	PROPN
ejpam-5629	8	11	,	,	PUNCT
ejpam-5629	8	12	including	include	VERB
ejpam-5629	8	13	the	the	DET
ejpam-5629	8	14	laplace	laplace	NOUN
ejpam-5629	8	15	transform	transform	NOUN
ejpam-5629	8	16	,	,	PUNCT
ejpam-5629	8	17	fourier	fourier	NOUN
ejpam-5629	8	18	transform	transform	NOUN
ejpam-5629	8	19	,	,	PUNCT
ejpam-5629	8	20	mellin	mellin	NOUN
ejpam-5629	8	21	transform	transform	NOUN
ejpam-5629	8	22	,	,	PUNCT
ejpam-5629	8	23	and	and	CCONJ
ejpam-5629	8	24	operational	operational	ADJ
ejpam-5629	8	25	calculus	calculus	NOUN
ejpam-5629	8	26	.	.	PUNCT
ejpam-5629	9	1	these	these	DET
ejpam-5629	9	2	methods	method	NOUN
ejpam-5629	9	3	often	often	ADV
ejpam-5629	9	4	involve	involve	VERB
ejpam-5629	9	5	transforming	transform	VERB
ejpam-5629	9	6	the	the	DET
ejpam-5629	9	7	fractional	fractional	NOUN
ejpam-5629	9	8	de	de	NOUN
ejpam-5629	9	9	into	into	ADP
ejpam-5629	9	10	an	an	DET
ejpam-5629	9	11	algebraic	algebraic	ADJ
ejpam-5629	9	12	equation	equation	NOUN
ejpam-5629	9	13	,	,	PUNCT
ejpam-5629	9	14	solving	solve	VERB
ejpam-5629	9	15	the	the	DET
ejpam-5629	9	16	transformed	transform	VERB
ejpam-5629	9	17	equation	equation	NOUN
ejpam-5629	9	18	,	,	PUNCT
ejpam-5629	9	19	and	and	CCONJ
ejpam-5629	9	20	then	then	ADV
ejpam-5629	9	21	inverting	invert	VERB
ejpam-5629	9	22	the	the	DET
ejpam-5629	9	23	transform	transform	NOUN
ejpam-5629	9	24	to	to	PART
ejpam-5629	9	25	obtain	obtain	VERB
ejpam-5629	9	26	the	the	DET
ejpam-5629	9	27	solution	solution	NOUN
ejpam-5629	9	28	.	.	PUNCT
ejpam-5629	10	1	additionally	additionally	ADV
ejpam-5629	10	2	,	,	PUNCT
ejpam-5629	10	3	various	various	ADJ
ejpam-5629	10	4	iterative	iterative	NOUN
ejpam-5629	10	5	methods	method	NOUN
ejpam-5629	10	6	like	like	ADP
ejpam-5629	10	7	the	the	DET
ejpam-5629	10	8	adomian	adomian	NOUN
ejpam-5629	10	9	decomposition	decomposition	NOUN
ejpam-5629	10	10	method	method	NOUN
ejpam-5629	10	11	,	,	PUNCT
ejpam-5629	10	12	variational	variational	ADJ
ejpam-5629	10	13	iteration	iteration	NOUN
ejpam-5629	10	14	method	method	NOUN
ejpam-5629	10	15	,	,	PUNCT
ejpam-5629	10	16	and	and	CCONJ
ejpam-5629	10	17	homotopy	homotopy	VERB
ejpam-5629	10	18	perturbation	perturbation	NOUN
ejpam-5629	10	19	method	method	NOUN
ejpam-5629	10	20	have	have	AUX
ejpam-5629	10	21	been	be	AUX
ejpam-5629	10	22	employed	employ	VERB
ejpam-5629	10	23	to	to	PART
ejpam-5629	10	24	find	find	VERB
ejpam-5629	10	25	approximate	approximate	ADJ
ejpam-5629	10	26	solutions	solution	NOUN
ejpam-5629	10	27	to	to	PART
ejpam-5629	10	28	nonlinear	nonlinear	VERB
ejpam-5629	10	29	fractional	fractional	PROPN
ejpam-5629	10	30	des	des	PROPN
ejpam-5629	10	31	.	.	PUNCT
ejpam-5629	11	1	these	these	DET
ejpam-5629	11	2	methods	method	NOUN
ejpam-5629	11	3	provide	provide	VERB
ejpam-5629	11	4	a	a	DET
ejpam-5629	11	5	powerful	powerful	ADJ
ejpam-5629	11	6	tool	tool	NOUN
ejpam-5629	11	7	∗corresponding	∗corresponde	VERB
ejpam-5629	11	8	author	author	NOUN
ejpam-5629	11	9	.	.	PUNCT
ejpam-5629	12	1	doi	doi	NOUN
ejpam-5629	12	2	:	:	PUNCT
ejpam-5629	12	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5629	https://doi.org/10.29020/nybg.ejpam.v18i1.5629	NOUN
ejpam-5629	12	4	email	email	NOUN
ejpam-5629	12	5	addresses	address	NOUN
ejpam-5629	12	6	:	:	PUNCT
ejpam-5629	12	7	h.abdelwareth@qu.edu.sa	h.abdelwareth@qu.edu.sa	PROPN
ejpam-5629	12	8	(	(	PUNCT
ejpam-5629	12	9	h.a	h.a	PROPN
ejpam-5629	12	10	.	.	PROPN
ejpam-5629	12	11	hammad	hammad	PROPN
ejpam-5629	12	12	)	)	PUNCT
ejpam-5629	12	13	,	,	PUNCT
ejpam-5629	12	14	mabdalla@kku.edu.sa	mabdalla@kku.edu.sa	NOUN
ejpam-5629	12	15	(	(	PUNCT
ejpam-5629	12	16	m.e.m	m.e.m	NOUN
ejpam-5629	12	17	.	.	PUNCT
ejpam-5629	12	18	abdalla	abdalla	PROPN
ejpam-5629	12	19	)	)	PUNCT
ejpam-5629	12	20	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5629	13	1	1	1	NUM
ejpam-5629	13	2	copyright	copyright	NOUN
ejpam-5629	13	3	:	:	PUNCT
ejpam-5629	13	4	©	©	PROPN
ejpam-5629	13	5	2025	2025	NUM
ejpam-5629	13	6	the	the	DET
ejpam-5629	13	7	author(s	author(s	NOUN
ejpam-5629	13	8	)	)	PUNCT
ejpam-5629	13	9	.	.	PUNCT
ejpam-5629	14	1	(	(	PUNCT
ejpam-5629	14	2	cc	cc	NOUN
ejpam-5629	14	3	by	by	ADP
ejpam-5629	14	4	-	-	PUNCT
ejpam-5629	14	5	nc	nc	PROPN
ejpam-5629	14	6	4.0	4.0	NUM
ejpam-5629	14	7	)	)	PUNCT
ejpam-5629	14	8	h.a	h.a	PROPN
ejpam-5629	14	9	.	.	PROPN
ejpam-5629	14	10	hammad	hammad	PROPN
ejpam-5629	14	11	,	,	PUNCT
ejpam-5629	14	12	m.e.m	m.e.m	NOUN
ejpam-5629	14	13	.	.	PUNCT
ejpam-5629	14	14	abdalla	abdalla	PROPN
ejpam-5629	14	15	/	/	SYM
ejpam-5629	14	16	eur	eur	PROPN
ejpam-5629	14	17	.	.	PUNCT
ejpam-5629	15	1	j.	j.	PROPN
ejpam-5629	15	2	pure	pure	PROPN
ejpam-5629	15	3	appl	appl	PROPN
ejpam-5629	15	4	.	.	PROPN
ejpam-5629	15	5	math	math	PROPN
ejpam-5629	15	6	,	,	PUNCT
ejpam-5629	15	7	18	18	NUM
ejpam-5629	15	8	(	(	PUNCT
ejpam-5629	15	9	1	1	NUM
ejpam-5629	15	10	)	)	PUNCT
ejpam-5629	15	11	(	(	PUNCT
ejpam-5629	15	12	2025	2025	NUM
ejpam-5629	15	13	)	)	PUNCT
ejpam-5629	15	14	,	,	PUNCT
ejpam-5629	15	15	5629	5629	NUM
ejpam-5629	15	16	2	2	NUM
ejpam-5629	15	17	of	of	ADP
ejpam-5629	15	18	20	20	NUM
ejpam-5629	15	19	for	for	ADP
ejpam-5629	15	20	investigating	investigate	VERB
ejpam-5629	15	21	the	the	DET
ejpam-5629	15	22	behavior	behavior	NOUN
ejpam-5629	15	23	of	of	ADP
ejpam-5629	15	24	systems	system	NOUN
ejpam-5629	15	25	described	describe	VERB
ejpam-5629	15	26	by	by	ADP
ejpam-5629	15	27	fractional	fractional	PROPN
ejpam-5629	15	28	des	des	PROPN
ejpam-5629	15	29	,	,	PUNCT
ejpam-5629	15	30	for	for	ADP
ejpam-5629	15	31	more	more	ADJ
ejpam-5629	15	32	details	detail	NOUN
ejpam-5629	15	33	;	;	PUNCT
ejpam-5629	15	34	see[1	see[1	NUM
ejpam-5629	15	35	,	,	PUNCT
ejpam-5629	15	36	3	3	NUM
ejpam-5629	15	37	,	,	PUNCT
ejpam-5629	15	38	26	26	NUM
ejpam-5629	15	39	,	,	PUNCT
ejpam-5629	15	40	30	30	NUM
ejpam-5629	15	41	,	,	PUNCT
ejpam-5629	15	42	31	31	NUM
ejpam-5629	15	43	]	]	PUNCT
ejpam-5629	15	44	.	.	PUNCT
ejpam-5629	16	1	the	the	DET
ejpam-5629	16	2	classical	classical	ADJ
ejpam-5629	16	3	des	des	PROPN
ejpam-5629	16	4	can	can	AUX
ejpam-5629	16	5	be	be	AUX
ejpam-5629	16	6	extended	extend	VERB
ejpam-5629	16	7	to	to	ADP
ejpam-5629	16	8	fractional	fractional	ADJ
ejpam-5629	16	9	des	des	PROPN
ejpam-5629	16	10	,	,	PUNCT
ejpam-5629	16	11	where	where	SCONJ
ejpam-5629	16	12	the	the	DET
ejpam-5629	16	13	order	order	NOUN
ejpam-5629	16	14	of	of	ADP
ejpam-5629	16	15	differentiation	differentiation	NOUN
ejpam-5629	16	16	might	might	AUX
ejpam-5629	16	17	be	be	AUX
ejpam-5629	16	18	non	non	ADJ
ejpam-5629	16	19	-	-	ADJ
ejpam-5629	16	20	integer	integer	ADJ
ejpam-5629	16	21	or	or	CCONJ
ejpam-5629	16	22	fractional	fractional	ADJ
ejpam-5629	16	23	.	.	PUNCT
ejpam-5629	17	1	since	since	SCONJ
ejpam-5629	17	2	integer	integer	NOUN
ejpam-5629	17	3	-	-	PUNCT
ejpam-5629	17	4	order	order	NOUN
ejpam-5629	17	5	des	de	NOUN
ejpam-5629	17	6	and	and	CCONJ
ejpam-5629	17	7	systems	system	NOUN
ejpam-5629	17	8	are	be	AUX
ejpam-5629	17	9	unable	unable	ADJ
ejpam-5629	17	10	to	to	PART
ejpam-5629	17	11	sufficiently	sufficiently	ADV
ejpam-5629	17	12	represent	represent	VERB
ejpam-5629	17	13	complex	complex	ADJ
ejpam-5629	17	14	systems	system	NOUN
ejpam-5629	17	15	with	with	ADP
ejpam-5629	17	16	memory	memory	NOUN
ejpam-5629	17	17	and	and	CCONJ
ejpam-5629	17	18	hereditary	hereditary	ADJ
ejpam-5629	17	19	qualities	quality	NOUN
ejpam-5629	17	20	,	,	PUNCT
ejpam-5629	17	21	these	these	DET
ejpam-5629	17	22	equations	equation	NOUN
ejpam-5629	17	23	and	and	CCONJ
ejpam-5629	17	24	systems	system	NOUN
ejpam-5629	17	25	have	have	AUX
ejpam-5629	17	26	drawn	draw	VERB
ejpam-5629	17	27	a	a	DET
ejpam-5629	17	28	great	great	ADJ
ejpam-5629	17	29	deal	deal	NOUN
ejpam-5629	17	30	of	of	ADP
ejpam-5629	17	31	attention	attention	NOUN
ejpam-5629	17	32	[	[	X
ejpam-5629	17	33	2	2	NUM
ejpam-5629	17	34	,	,	PUNCT
ejpam-5629	17	35	7	7	NUM
ejpam-5629	17	36	,	,	PUNCT
ejpam-5629	17	37	10	10	NUM
ejpam-5629	17	38	,	,	PUNCT
ejpam-5629	17	39	13	13	NUM
ejpam-5629	17	40	,	,	PUNCT
ejpam-5629	17	41	14	14	NUM
ejpam-5629	17	42	,	,	PUNCT
ejpam-5629	17	43	17	17	NUM
ejpam-5629	17	44	,	,	PUNCT
ejpam-5629	17	45	28	28	NUM
ejpam-5629	17	46	,	,	PUNCT
ejpam-5629	17	47	29	29	NUM
ejpam-5629	17	48	,	,	PUNCT
ejpam-5629	17	49	37	37	NUM
ejpam-5629	17	50	,	,	PUNCT
ejpam-5629	17	51	41	41	NUM
ejpam-5629	17	52	,	,	PUNCT
ejpam-5629	17	53	46	46	NUM
ejpam-5629	17	54	]	]	PUNCT
ejpam-5629	17	55	.	.	PUNCT
ejpam-5629	18	1	one	one	NUM
ejpam-5629	18	2	of	of	ADP
ejpam-5629	18	3	the	the	DET
ejpam-5629	18	4	formulations	formulation	NOUN
ejpam-5629	18	5	of	of	ADP
ejpam-5629	18	6	fractional	fractional	ADJ
ejpam-5629	18	7	calculus	calculus	NOUN
ejpam-5629	18	8	(	(	PUNCT
ejpam-5629	18	9	fc	fc	INTJ
ejpam-5629	18	10	)	)	PUNCT
ejpam-5629	18	11	that	that	PRON
ejpam-5629	18	12	is	be	AUX
ejpam-5629	18	13	frequently	frequently	ADV
ejpam-5629	18	14	employed	employ	VERB
ejpam-5629	18	15	,	,	PUNCT
ejpam-5629	18	16	the	the	DET
ejpam-5629	18	17	caputo	caputo	PROPN
ejpam-5629	18	18	fractional	fractional	PROPN
ejpam-5629	18	19	derivative	derivative	PROPN
ejpam-5629	18	20	(	(	PUNCT
ejpam-5629	18	21	cfd	cfd	NOUN
ejpam-5629	18	22	)	)	PUNCT
ejpam-5629	19	1	[	[	X
ejpam-5629	19	2	12	12	NUM
ejpam-5629	19	3	,	,	PUNCT
ejpam-5629	19	4	28	28	NUM
ejpam-5629	19	5	]	]	PUNCT
ejpam-5629	19	6	,	,	PUNCT
ejpam-5629	19	7	is	be	AUX
ejpam-5629	19	8	very	very	ADV
ejpam-5629	19	9	helpful	helpful	ADJ
ejpam-5629	19	10	for	for	ADP
ejpam-5629	19	11	initial	initial	ADJ
ejpam-5629	19	12	value	value	NOUN
ejpam-5629	19	13	problems	problem	NOUN
ejpam-5629	19	14	,	,	PUNCT
ejpam-5629	19	15	which	which	PRON
ejpam-5629	19	16	makes	make	VERB
ejpam-5629	19	17	it	it	PRON
ejpam-5629	19	18	appropriate	appropriate	ADJ
ejpam-5629	19	19	for	for	ADP
ejpam-5629	19	20	physical	physical	ADJ
ejpam-5629	19	21	applications	application	NOUN
ejpam-5629	19	22	.	.	PUNCT
ejpam-5629	20	1	fixed	fix	VERB
ejpam-5629	20	2	point	point	NOUN
ejpam-5629	20	3	(	(	PUNCT
ejpam-5629	20	4	fp	fp	X
ejpam-5629	20	5	)	)	PUNCT
ejpam-5629	20	6	theorems	theorem	NOUN
ejpam-5629	20	7	are	be	AUX
ejpam-5629	20	8	a	a	DET
ejpam-5629	20	9	powerful	powerful	ADJ
ejpam-5629	20	10	tool	tool	NOUN
ejpam-5629	20	11	in	in	ADP
ejpam-5629	20	12	the	the	DET
ejpam-5629	20	13	study	study	NOUN
ejpam-5629	20	14	of	of	ADP
ejpam-5629	20	15	fractional	fractional	ADJ
ejpam-5629	20	16	differential	differential	ADJ
ejpam-5629	20	17	equations	equation	NOUN
ejpam-5629	20	18	.	.	PUNCT
ejpam-5629	21	1	by	by	ADP
ejpam-5629	21	2	transforming	transform	VERB
ejpam-5629	21	3	fractional	fractional	ADJ
ejpam-5629	21	4	des	de	NOUN
ejpam-5629	21	5	into	into	ADP
ejpam-5629	21	6	equivalent	equivalent	ADJ
ejpam-5629	21	7	integral	integral	ADJ
ejpam-5629	21	8	equations	equation	NOUN
ejpam-5629	21	9	,	,	PUNCT
ejpam-5629	21	10	fp	fp	PROPN
ejpam-5629	21	11	techniques	technique	NOUN
ejpam-5629	21	12	,	,	PUNCT
ejpam-5629	21	13	such	such	ADJ
ejpam-5629	21	14	as	as	ADP
ejpam-5629	21	15	the	the	DET
ejpam-5629	21	16	banach	banach	NOUN
ejpam-5629	21	17	contraction	contraction	NOUN
ejpam-5629	21	18	mapping	mapping	NOUN
ejpam-5629	21	19	principle	principle	NOUN
ejpam-5629	21	20	or	or	CCONJ
ejpam-5629	21	21	the	the	DET
ejpam-5629	21	22	schauder	schauder	NOUN
ejpam-5629	21	23	fp	fp	PROPN
ejpam-5629	21	24	theorem	theorem	PROPN
ejpam-5629	21	25	,	,	PUNCT
ejpam-5629	21	26	can	can	AUX
ejpam-5629	21	27	be	be	AUX
ejpam-5629	21	28	applied	apply	VERB
ejpam-5629	21	29	to	to	PART
ejpam-5629	21	30	establish	establish	VERB
ejpam-5629	21	31	the	the	DET
ejpam-5629	21	32	existence	existence	NOUN
ejpam-5629	21	33	and	and	CCONJ
ejpam-5629	21	34	uniqueness	uniqueness	NOUN
ejpam-5629	21	35	of	of	ADP
ejpam-5629	21	36	solutions	solution	NOUN
ejpam-5629	21	37	.	.	PUNCT
ejpam-5629	22	1	these	these	DET
ejpam-5629	22	2	techniques	technique	NOUN
ejpam-5629	22	3	are	be	AUX
ejpam-5629	22	4	particularly	particularly	ADV
ejpam-5629	22	5	useful	useful	ADJ
ejpam-5629	22	6	for	for	ADP
ejpam-5629	22	7	nonlinear	nonlinear	ADJ
ejpam-5629	22	8	fractional	fractional	ADJ
ejpam-5629	22	9	des	des	PROPN
ejpam-5629	22	10	,	,	PUNCT
ejpam-5629	22	11	where	where	SCONJ
ejpam-5629	22	12	analytical	analytical	ADJ
ejpam-5629	22	13	solutions	solution	NOUN
ejpam-5629	22	14	may	may	AUX
ejpam-5629	22	15	be	be	AUX
ejpam-5629	22	16	difficult	difficult	ADJ
ejpam-5629	22	17	to	to	PART
ejpam-5629	22	18	obtain	obtain	VERB
ejpam-5629	22	19	.	.	PUNCT
ejpam-5629	23	1	by	by	ADP
ejpam-5629	23	2	employing	employ	VERB
ejpam-5629	23	3	fp	fp	ADJ
ejpam-5629	23	4	methods	method	NOUN
ejpam-5629	23	5	,	,	PUNCT
ejpam-5629	23	6	researchers	researcher	NOUN
ejpam-5629	23	7	can	can	AUX
ejpam-5629	23	8	gain	gain	VERB
ejpam-5629	23	9	insights	insight	NOUN
ejpam-5629	23	10	into	into	ADP
ejpam-5629	23	11	the	the	DET
ejpam-5629	23	12	qualitative	qualitative	ADJ
ejpam-5629	23	13	behavior	behavior	NOUN
ejpam-5629	23	14	of	of	ADP
ejpam-5629	23	15	solutions	solution	NOUN
ejpam-5629	23	16	,	,	PUNCT
ejpam-5629	23	17	including	include	VERB
ejpam-5629	23	18	their	their	PRON
ejpam-5629	23	19	stability	stability	NOUN
ejpam-5629	23	20	,	,	PUNCT
ejpam-5629	23	21	boundedness	boundedness	NOUN
ejpam-5629	23	22	,	,	PUNCT
ejpam-5629	23	23	and	and	CCONJ
ejpam-5629	23	24	asymptotic	asymptotic	ADJ
ejpam-5629	23	25	properties	property	NOUN
ejpam-5629	23	26	.	.	PUNCT
ejpam-5629	24	1	see	see	VERB
ejpam-5629	24	2	[	[	X
ejpam-5629	24	3	4	4	NUM
ejpam-5629	24	4	,	,	PUNCT
ejpam-5629	24	5	8	8	NUM
ejpam-5629	24	6	,	,	PUNCT
ejpam-5629	24	7	9	9	NUM
ejpam-5629	24	8	,	,	PUNCT
ejpam-5629	24	9	18–25	18–25	NUM
ejpam-5629	24	10	,	,	PUNCT
ejpam-5629	24	11	32	32	NUM
ejpam-5629	24	12	,	,	PUNCT
ejpam-5629	24	13	34	34	NUM
ejpam-5629	24	14	,	,	PUNCT
ejpam-5629	24	15	38	38	NUM
ejpam-5629	24	16	]	]	PUNCT
ejpam-5629	24	17	for	for	ADP
ejpam-5629	24	18	more	more	ADJ
ejpam-5629	24	19	information	information	NOUN
ejpam-5629	24	20	.	.	PUNCT
ejpam-5629	25	1	beam	beam	NOUN
ejpam-5629	25	2	deflection	deflection	NOUN
ejpam-5629	25	3	equations	equation	NOUN
ejpam-5629	25	4	and	and	CCONJ
ejpam-5629	25	5	systems	system	NOUN
ejpam-5629	25	6	are	be	AUX
ejpam-5629	25	7	a	a	DET
ejpam-5629	25	8	significant	significant	ADJ
ejpam-5629	25	9	area	area	NOUN
ejpam-5629	25	10	of	of	ADP
ejpam-5629	25	11	study	study	NOUN
ejpam-5629	25	12	for	for	ADP
ejpam-5629	25	13	fractional	fractional	PROPN
ejpam-5629	25	14	des	des	PROPN
ejpam-5629	25	15	.	.	PUNCT
ejpam-5629	26	1	the	the	DET
ejpam-5629	26	2	ability	ability	NOUN
ejpam-5629	26	3	of	of	ADP
ejpam-5629	26	4	beams	beam	NOUN
ejpam-5629	26	5	to	to	PART
ejpam-5629	26	6	sustain	sustain	VERB
ejpam-5629	26	7	loads	load	NOUN
ejpam-5629	26	8	applied	apply	VERB
ejpam-5629	26	9	laterally	laterally	ADV
ejpam-5629	26	10	to	to	ADP
ejpam-5629	26	11	their	their	PRON
ejpam-5629	26	12	axis	axis	NOUN
ejpam-5629	26	13	makes	make	VERB
ejpam-5629	26	14	them	they	PRON
ejpam-5629	26	15	structural	structural	ADJ
ejpam-5629	26	16	components	component	NOUN
ejpam-5629	26	17	.	.	PUNCT
ejpam-5629	27	1	the	the	DET
ejpam-5629	27	2	bending	bending	NOUN
ejpam-5629	27	3	and	and	CCONJ
ejpam-5629	27	4	deflection	deflection	NOUN
ejpam-5629	27	5	of	of	ADP
ejpam-5629	27	6	beams	beam	NOUN
ejpam-5629	27	7	under	under	ADP
ejpam-5629	27	8	varied	varied	ADJ
ejpam-5629	27	9	stresses	stress	NOUN
ejpam-5629	27	10	are	be	AUX
ejpam-5629	27	11	described	describe	VERB
ejpam-5629	27	12	by	by	ADP
ejpam-5629	27	13	the	the	DET
ejpam-5629	27	14	classical	classical	ADJ
ejpam-5629	27	15	beam	beam	NOUN
ejpam-5629	27	16	theory	theory	NOUN
ejpam-5629	27	17	,	,	PUNCT
ejpam-5629	27	18	which	which	PRON
ejpam-5629	27	19	is	be	AUX
ejpam-5629	27	20	frequently	frequently	ADV
ejpam-5629	27	21	represented	represent	VERB
ejpam-5629	27	22	by	by	ADP
ejpam-5629	27	23	fourth	fourth	ADJ
ejpam-5629	27	24	-	-	PUNCT
ejpam-5629	27	25	order	order	NOUN
ejpam-5629	27	26	ordinary	ordinary	ADJ
ejpam-5629	27	27	des	de	NOUN
ejpam-5629	27	28	[	[	X
ejpam-5629	27	29	5	5	NUM
ejpam-5629	27	30	,	,	PUNCT
ejpam-5629	27	31	6	6	NUM
ejpam-5629	27	32	,	,	PUNCT
ejpam-5629	27	33	12	12	NUM
ejpam-5629	27	34	,	,	PUNCT
ejpam-5629	27	35	29	29	NUM
ejpam-5629	27	36	,	,	PUNCT
ejpam-5629	27	37	36	36	NUM
ejpam-5629	27	38	,	,	PUNCT
ejpam-5629	27	39	43	43	NUM
ejpam-5629	27	40	,	,	PUNCT
ejpam-5629	27	41	45	45	NUM
ejpam-5629	27	42	]	]	PUNCT
ejpam-5629	27	43	.	.	PUNCT
ejpam-5629	28	1	fractional	fractional	ADJ
ejpam-5629	28	2	derivatives	derivative	NOUN
ejpam-5629	28	3	(	(	PUNCT
ejpam-5629	28	4	fds	fds	NOUN
ejpam-5629	28	5	)	)	PUNCT
ejpam-5629	28	6	,	,	PUNCT
ejpam-5629	28	7	on	on	ADP
ejpam-5629	28	8	the	the	DET
ejpam-5629	28	9	other	other	ADJ
ejpam-5629	28	10	hand	hand	NOUN
ejpam-5629	28	11	,	,	PUNCT
ejpam-5629	28	12	can	can	AUX
ejpam-5629	28	13	give	give	VERB
ejpam-5629	28	14	these	these	DET
ejpam-5629	28	15	models	model	NOUN
ejpam-5629	28	16	a	a	DET
ejpam-5629	28	17	more	more	ADV
ejpam-5629	28	18	realistic	realistic	ADJ
ejpam-5629	28	19	depiction	depiction	NOUN
ejpam-5629	28	20	of	of	ADP
ejpam-5629	28	21	materials	material	NOUN
ejpam-5629	28	22	with	with	ADP
ejpam-5629	28	23	non	non	ADJ
ejpam-5629	28	24	-	-	ADJ
ejpam-5629	28	25	local	local	ADJ
ejpam-5629	28	26	behavior	behavior	NOUN
ejpam-5629	28	27	and	and	CCONJ
ejpam-5629	28	28	viscoelastic	viscoelastic	NOUN
ejpam-5629	28	29	characteristics	characteristic	NOUN
ejpam-5629	28	30	,	,	PUNCT
ejpam-5629	28	31	which	which	PRON
ejpam-5629	28	32	are	be	AUX
ejpam-5629	28	33	typical	typical	ADJ
ejpam-5629	28	34	of	of	ADP
ejpam-5629	28	35	sophisticated	sophisticated	ADJ
ejpam-5629	28	36	engineering	engineering	NOUN
ejpam-5629	28	37	materials	material	NOUN
ejpam-5629	28	38	and	and	CCONJ
ejpam-5629	28	39	intricate	intricate	ADJ
ejpam-5629	28	40	structures	structure	NOUN
ejpam-5629	28	41	.	.	PUNCT
ejpam-5629	29	1	nevertheless	nevertheless	ADV
ejpam-5629	29	2	,	,	PUNCT
ejpam-5629	29	3	the	the	DET
ejpam-5629	29	4	inclusion	inclusion	NOUN
ejpam-5629	29	5	of	of	ADP
ejpam-5629	29	6	fds	fds	NOUN
ejpam-5629	29	7	in	in	ADP
ejpam-5629	29	8	these	these	DET
ejpam-5629	29	9	models	model	NOUN
ejpam-5629	29	10	can	can	AUX
ejpam-5629	29	11	yield	yield	VERB
ejpam-5629	29	12	a	a	DET
ejpam-5629	29	13	more	more	ADV
ejpam-5629	29	14	precise	precise	ADJ
ejpam-5629	29	15	portrayal	portrayal	NOUN
ejpam-5629	29	16	of	of	ADP
ejpam-5629	29	17	materials	material	NOUN
ejpam-5629	29	18	possessing	possess	VERB
ejpam-5629	29	19	viscoelastic	viscoelastic	ADJ
ejpam-5629	29	20	characteristics	characteristic	NOUN
ejpam-5629	29	21	and	and	CCONJ
ejpam-5629	29	22	non	non	ADJ
ejpam-5629	29	23	-	-	ADJ
ejpam-5629	29	24	local	local	ADJ
ejpam-5629	29	25	behavior	behavior	NOUN
ejpam-5629	29	26	,	,	PUNCT
ejpam-5629	29	27	which	which	PRON
ejpam-5629	29	28	are	be	AUX
ejpam-5629	29	29	prevalent	prevalent	ADJ
ejpam-5629	29	30	in	in	ADP
ejpam-5629	29	31	sophisticated	sophisticated	ADJ
ejpam-5629	29	32	engineering	engineering	NOUN
ejpam-5629	29	33	materials	material	NOUN
ejpam-5629	29	34	and	and	CCONJ
ejpam-5629	29	35	intricate	intricate	ADJ
ejpam-5629	29	36	structures	structure	NOUN
ejpam-5629	29	37	.	.	PUNCT
ejpam-5629	30	1	these	these	DET
ejpam-5629	30	2	results	result	NOUN
ejpam-5629	30	3	in	in	ADP
ejpam-5629	30	4	fd	fd	PROPN
ejpam-5629	30	5	models	model	NOUN
ejpam-5629	30	6	that	that	PRON
ejpam-5629	30	7	provide	provide	VERB
ejpam-5629	30	8	deeper	deep	ADJ
ejpam-5629	30	9	insights	insight	NOUN
ejpam-5629	30	10	and	and	CCONJ
ejpam-5629	30	11	enhanced	enhance	VERB
ejpam-5629	30	12	design	design	NOUN
ejpam-5629	30	13	skills	skill	NOUN
ejpam-5629	30	14	in	in	ADP
ejpam-5629	30	15	applied	applied	ADJ
ejpam-5629	30	16	physics	physics	NOUN
ejpam-5629	30	17	and	and	CCONJ
ejpam-5629	30	18	engineering	engineering	NOUN
ejpam-5629	30	19	by	by	ADP
ejpam-5629	30	20	more	more	ADV
ejpam-5629	30	21	accurately	accurately	ADV
ejpam-5629	30	22	predicting	predict	VERB
ejpam-5629	30	23	the	the	DET
ejpam-5629	30	24	deflection	deflection	NOUN
ejpam-5629	30	25	and	and	CCONJ
ejpam-5629	30	26	dynamic	dynamic	ADJ
ejpam-5629	30	27	response	response	NOUN
ejpam-5629	30	28	of	of	ADP
ejpam-5629	30	29	beams	beam	NOUN
ejpam-5629	30	30	.	.	PUNCT
ejpam-5629	31	1	wang	wang	PROPN
ejpam-5629	31	2	and	and	CCONJ
ejpam-5629	31	3	yang	yang	PROPN
ejpam-5629	31	4	investigated	investigate	VERB
ejpam-5629	31	5	in	in	ADP
ejpam-5629	31	6	[	[	X
ejpam-5629	31	7	43	43	NUM
ejpam-5629	31	8	]	]	PUNCT
ejpam-5629	31	9	whether	whether	SCONJ
ejpam-5629	31	10	positive	positive	ADJ
ejpam-5629	31	11	solutions	solution	NOUN
ejpam-5629	31	12	exist	exist	VERB
ejpam-5629	31	13	for	for	ADP
ejpam-5629	31	14	the	the	DET
ejpam-5629	31	15	nonlinear	nonlinear	ADJ
ejpam-5629	31	16	fourth	fourth	ADJ
ejpam-5629	31	17	-	-	PUNCT
ejpam-5629	31	18	order	order	NOUN
ejpam-5629	31	19	system	system	NOUN
ejpam-5629	31	20	that	that	PRON
ejpam-5629	31	21	describes	describe	VERB
ejpam-5629	31	22	the	the	DET
ejpam-5629	31	23	deformation	deformation	NOUN
ejpam-5629	31	24	of	of	ADP
ejpam-5629	31	25	an	an	DET
ejpam-5629	31	26	elastic	elastic	ADJ
ejpam-5629	31	27	beam	beam	NOUN
ejpam-5629	31	28	as	as	SCONJ
ejpam-5629	31	29	follows	follow	VERB
ejpam-5629	31	30	:	:	PUNCT
ejpam-5629	31	31	{	{	PUNCT
ejpam-5629	31	32	φ(4)(s	φ(4)(s	NOUN
ejpam-5629	31	33	)	)	PUNCT
ejpam-5629	32	1	+	+	CCONJ
ejpam-5629	32	2	γ1φ	γ1φ	VERB
ejpam-5629	32	3	′′(s)−	′′(s)−	PROPN
ejpam-5629	32	4	η1φ(ζ	η1φ(ζ	PROPN
ejpam-5629	32	5	)	)	PUNCT
ejpam-5629	33	1	=	=	SYM
ejpam-5629	33	2	ℓ1	ℓ1	NOUN
ejpam-5629	33	3	(	(	PUNCT
ejpam-5629	33	4	s	s	PROPN
ejpam-5629	33	5	,	,	PUNCT
ejpam-5629	33	6	φ(s	φ(s	NOUN
ejpam-5629	33	7	)	)	PUNCT
ejpam-5629	33	8	,	,	PUNCT
ejpam-5629	33	9	ϕ(s	ϕ(s	PROPN
ejpam-5629	33	10	)	)	PUNCT
ejpam-5629	33	11	)	)	PUNCT
ejpam-5629	33	12	,	,	PUNCT
ejpam-5629	33	13	s	s	VERB
ejpam-5629	33	14	∈	∈	NOUN
ejpam-5629	33	15	v	v	NOUN
ejpam-5629	33	16	=	=	SYM
ejpam-5629	34	1	[	[	X
ejpam-5629	34	2	0	0	NUM
ejpam-5629	34	3	,	,	PUNCT
ejpam-5629	34	4	1	1	NUM
ejpam-5629	34	5	]	]	PUNCT
ejpam-5629	34	6	,	,	PUNCT
ejpam-5629	34	7	ϕ(4)(s	ϕ(4)(s	PROPN
ejpam-5629	34	8	)	)	PUNCT
ejpam-5629	34	9	+	+	NUM
ejpam-5629	34	10	γ2ϕ	γ2ϕ	NOUN
ejpam-5629	34	11	′′(s)−	′′(s)−	PROPN
ejpam-5629	34	12	η2ϕ(ζ	η2ϕ(ζ	PROPN
ejpam-5629	34	13	)	)	PUNCT
ejpam-5629	35	1	=	=	SYM
ejpam-5629	35	2	ℓ2	ℓ2	PROPN
ejpam-5629	35	3	(	(	PUNCT
ejpam-5629	35	4	s	s	PROPN
ejpam-5629	35	5	,	,	PUNCT
ejpam-5629	35	6	φ(s	φ(s	NOUN
ejpam-5629	35	7	)	)	PUNCT
ejpam-5629	35	8	,	,	PUNCT
ejpam-5629	35	9	ϕ(s	ϕ(s	PROPN
ejpam-5629	35	10	)	)	PUNCT
ejpam-5629	35	11	)	)	PUNCT
ejpam-5629	35	12	,	,	PUNCT
ejpam-5629	35	13	s	s	VERB
ejpam-5629	35	14	∈	∈	PROPN
ejpam-5629	35	15	v	v	NOUN
ejpam-5629	35	16	,	,	PUNCT
ejpam-5629	35	17	via	via	ADP
ejpam-5629	35	18	the	the	DET
ejpam-5629	35	19	stipulations	stipulation	NOUN
ejpam-5629	35	20	{	{	PUNCT
ejpam-5629	35	21	φ(0	φ(0	PROPN
ejpam-5629	35	22	)	)	PUNCT
ejpam-5629	35	23	=	=	SYM
ejpam-5629	35	24	φ(1	φ(1	PROPN
ejpam-5629	35	25	)	)	PUNCT
ejpam-5629	35	26	=	=	PUNCT
ejpam-5629	35	27	φ′′(0	φ′′(0	ADJ
ejpam-5629	35	28	)	)	PUNCT
ejpam-5629	35	29	=	=	SYM
ejpam-5629	35	30	φ′′(1	φ′′(1	NOUN
ejpam-5629	35	31	)	)	PUNCT
ejpam-5629	35	32	=	=	SYM
ejpam-5629	36	1	0	0	NUM
ejpam-5629	36	2	,	,	PUNCT
ejpam-5629	36	3	ϕ(0	ϕ(0	PROPN
ejpam-5629	36	4	)	)	PUNCT
ejpam-5629	36	5	=	=	SYM
ejpam-5629	37	1	ϕ(1	ϕ(1	PROPN
ejpam-5629	37	2	)	)	PUNCT
ejpam-5629	37	3	=	=	SYM
ejpam-5629	38	1	ϕ′′(0	ϕ′′(0	ADJ
ejpam-5629	38	2	)	)	PUNCT
ejpam-5629	38	3	=	=	SYM
ejpam-5629	38	4	ϕ′′(1	ϕ′′(1	ADJ
ejpam-5629	38	5	)	)	PUNCT
ejpam-5629	38	6	=	=	SYM
ejpam-5629	39	1	0	0	NUM
ejpam-5629	39	2	,	,	PUNCT
ejpam-5629	39	3	where	where	SCONJ
ejpam-5629	39	4	ℓi	ℓi	NOUN
ejpam-5629	39	5	:	:	PUNCT
ejpam-5629	39	6	v	v	NOUN
ejpam-5629	39	7	×r+×r+	×r+×r+	NOUN
ejpam-5629	39	8	→	→	PUNCT
ejpam-5629	39	9	r+	r+	NOUN
ejpam-5629	39	10	are	be	AUX
ejpam-5629	39	11	continuous	continuous	ADJ
ejpam-5629	39	12	functions	function	NOUN
ejpam-5629	39	13	,	,	PUNCT
ejpam-5629	39	14	and	and	CCONJ
ejpam-5629	39	15	γi	γi	INTJ
ejpam-5629	39	16	,	,	PUNCT
ejpam-5629	39	17	ηi	ηi	PROPN
ejpam-5629	39	18	∈	∈	PROPN
ejpam-5629	39	19	r	r	NOUN
ejpam-5629	39	20	such	such	ADJ
ejpam-5629	39	21	that	that	SCONJ
ejpam-5629	39	22	γi	γi	ADJ
ejpam-5629	39	23	≤	≤	ADV
ejpam-5629	39	24	2π2	2π2	NUM
ejpam-5629	39	25	,	,	PUNCT
ejpam-5629	39	26	−γ2	−γ2	PROPN
ejpam-5629	39	27	i	i	NOUN
ejpam-5629	39	28	4	4	NUM
ejpam-5629	39	29	≤	≤	NUM
ejpam-5629	39	30	ηi	ηi	NOUN
ejpam-5629	39	31	,	,	PUNCT
ejpam-5629	39	32	ηi	ηi	NOUN
ejpam-5629	39	33	π4	π4	NOUN
ejpam-5629	39	34	+	+	CCONJ
ejpam-5629	39	35	γi	γi	X
ejpam-5629	39	36	π4	π4	ADP
ejpam-5629	39	37	<	<	X
ejpam-5629	39	38	1	1	NUM
ejpam-5629	39	39	,	,	PUNCT
ejpam-5629	39	40	i	i	PRON
ejpam-5629	39	41	=	=	NOUN
ejpam-5629	39	42	1	1	NUM
ejpam-5629	39	43	,	,	PUNCT
ejpam-5629	39	44	2	2	NUM
ejpam-5629	39	45	.	.	PUNCT
ejpam-5629	40	1	the	the	DET
ejpam-5629	40	2	authors	author	NOUN
ejpam-5629	40	3	demonstrated	demonstrate	VERB
ejpam-5629	40	4	the	the	DET
ejpam-5629	40	5	existence	existence	NOUN
ejpam-5629	40	6	of	of	ADP
ejpam-5629	40	7	positive	positive	ADJ
ejpam-5629	40	8	solution	solution	NOUN
ejpam-5629	40	9	results	result	NOUN
ejpam-5629	40	10	by	by	ADP
ejpam-5629	40	11	providing	provide	VERB
ejpam-5629	40	12	a	a	DET
ejpam-5629	40	13	cone	cone	NOUN
ejpam-5629	40	14	q	q	NOUN
ejpam-5629	40	15	in	in	ADP
ejpam-5629	40	16	c(v	c(v	PROPN
ejpam-5629	40	17	)	)	PUNCT
ejpam-5629	40	18	×	×	PROPN
ejpam-5629	40	19	c(v	c(v	PROPN
ejpam-5629	40	20	)	)	PUNCT
ejpam-5629	40	21	.	.	PUNCT
ejpam-5629	41	1	they	they	PRON
ejpam-5629	41	2	built	build	VERB
ejpam-5629	41	3	another	another	DET
ejpam-5629	41	4	successful	successful	ADJ
ejpam-5629	41	5	solution	solution	NOUN
ejpam-5629	41	6	outcome	outcome	NOUN
ejpam-5629	41	7	by	by	ADP
ejpam-5629	41	8	building	build	VERB
ejpam-5629	41	9	over	over	ADP
ejpam-5629	41	10	a	a	DET
ejpam-5629	41	11	product	product	NOUN
ejpam-5629	41	12	cone	cone	NOUN
ejpam-5629	41	13	.	.	PUNCT
ejpam-5629	42	1	h.a	h.a	PROPN
ejpam-5629	42	2	.	.	PROPN
ejpam-5629	42	3	hammad	hammad	PROPN
ejpam-5629	42	4	,	,	PUNCT
ejpam-5629	42	5	m.e.m	m.e.m	NOUN
ejpam-5629	42	6	.	.	PUNCT
ejpam-5629	43	1	abdalla	abdalla	PROPN
ejpam-5629	43	2	/	/	SYM
ejpam-5629	43	3	eur	eur	PROPN
ejpam-5629	43	4	.	.	PUNCT
ejpam-5629	44	1	j.	j.	PROPN
ejpam-5629	44	2	pure	pure	PROPN
ejpam-5629	44	3	appl	appl	PROPN
ejpam-5629	44	4	.	.	PROPN
ejpam-5629	44	5	math	math	PROPN
ejpam-5629	44	6	,	,	PUNCT
ejpam-5629	44	7	18	18	NUM
ejpam-5629	44	8	(	(	PUNCT
ejpam-5629	44	9	1	1	NUM
ejpam-5629	44	10	)	)	PUNCT
ejpam-5629	44	11	(	(	PUNCT
ejpam-5629	44	12	2025	2025	NUM
ejpam-5629	44	13	)	)	PUNCT
ejpam-5629	44	14	,	,	PUNCT
ejpam-5629	44	15	5629	5629	NUM
ejpam-5629	44	16	3	3	NUM
ejpam-5629	44	17	of	of	ADP
ejpam-5629	44	18	20	20	NUM
ejpam-5629	44	19	the	the	DET
ejpam-5629	44	20	authors	author	NOUN
ejpam-5629	44	21	of	of	ADP
ejpam-5629	44	22	[	[	X
ejpam-5629	44	23	42	42	NUM
ejpam-5629	44	24	]	]	PUNCT
ejpam-5629	44	25	discussed	discuss	VERB
ejpam-5629	44	26	the	the	DET
ejpam-5629	44	27	existence	existence	NOUN
ejpam-5629	44	28	and	and	CCONJ
ejpam-5629	44	29	uniqueness	uniqueness	NOUN
ejpam-5629	44	30	of	of	ADP
ejpam-5629	44	31	solutions	solution	NOUN
ejpam-5629	44	32	for	for	ADP
ejpam-5629	44	33	the	the	DET
ejpam-5629	44	34	system	system	NOUN
ejpam-5629	44	35	that	that	PRON
ejpam-5629	44	36	has	have	VERB
ejpam-5629	44	37	caputo	caputo	PROPN
ejpam-5629	44	38	sequential	sequential	ADJ
ejpam-5629	44	39	derivatives	derivative	NOUN
ejpam-5629	44	40	(	(	PUNCT
ejpam-5629	44	41	csds	csds	NOUN
ejpam-5629	44	42	)	)	PUNCT
ejpam-5629	44	43	as	as	ADP
ejpam-5629	44	44	the	the	DET
ejpam-5629	44	45	following	following	NOUN
ejpam-5629	44	46	:	:	PUNCT
ejpam-5629	44	47	{	{	PUNCT
ejpam-5629	44	48	(	(	PUNCT
ejpam-5629	44	49	cdη	cdη	NOUN
ejpam-5629	44	50	+	+	CCONJ
ejpam-5629	44	51	ϑ	ϑ	X
ejpam-5629	44	52	cdη−1	cdη−1	NOUN
ejpam-5629	44	53	)	)	PUNCT
ejpam-5629	44	54	ζ	ζ	NOUN
ejpam-5629	44	55	(	(	PUNCT
ejpam-5629	44	56	s	s	NOUN
ejpam-5629	44	57	)	)	PUNCT
ejpam-5629	44	58	=	=	SYM
ejpam-5629	44	59	ℓ1	ℓ1	NOUN
ejpam-5629	44	60	(	(	PUNCT
ejpam-5629	44	61	s	s	PROPN
ejpam-5629	44	62	,	,	PUNCT
ejpam-5629	44	63	ζ(s	ζ(s	PROPN
ejpam-5629	44	64	)	)	PUNCT
ejpam-5629	44	65	,	,	PUNCT
ejpam-5629	44	66	ω(s	ω(s	PROPN
ejpam-5629	44	67	)	)	PUNCT
ejpam-5629	44	68	,	,	PUNCT
ejpam-5629	44	69	ir1	ir1	VERB
ejpam-5629	44	70	0	0	NUM
ejpam-5629	44	71	+	+	NUM
ejpam-5629	44	72	ζ(s	ζ(s	NOUN
ejpam-5629	44	73	)	)	PUNCT
ejpam-5629	44	74	,	,	PUNCT
ejpam-5629	44	75	ir2	ir2	NOUN
ejpam-5629	44	76	0	0	NUM
ejpam-5629	44	77	+	+	NUM
ejpam-5629	44	78	ω(s	ω(	NOUN
ejpam-5629	44	79	)	)	PUNCT
ejpam-5629	44	80	)	)	PUNCT
ejpam-5629	44	81	,	,	PUNCT
ejpam-5629	44	82	s	s	VERB
ejpam-5629	44	83	∈	∈	PROPN
ejpam-5629	44	84	v	v	NOUN
ejpam-5629	44	85	,	,	PUNCT
ejpam-5629	44	86	(	(	PUNCT
ejpam-5629	44	87	cdγ	cdγ	X
ejpam-5629	45	1	+	+	CCONJ
ejpam-5629	46	1	θ	θ	PROPN
ejpam-5629	46	2	cdγ−1	cdγ−1	NOUN
ejpam-5629	46	3	)	)	PUNCT
ejpam-5629	46	4	ω	ω	PROPN
ejpam-5629	46	5	(	(	PUNCT
ejpam-5629	46	6	s	s	NOUN
ejpam-5629	46	7	)	)	PUNCT
ejpam-5629	46	8	=	=	SYM
ejpam-5629	46	9	ℓ2	ℓ2	NOUN
ejpam-5629	46	10	(	(	PUNCT
ejpam-5629	46	11	s	s	PROPN
ejpam-5629	46	12	,	,	PUNCT
ejpam-5629	46	13	ζ(s	ζ(s	PROPN
ejpam-5629	46	14	)	)	PUNCT
ejpam-5629	46	15	,	,	PUNCT
ejpam-5629	46	16	ω(s	ω(s	PROPN
ejpam-5629	46	17	)	)	PUNCT
ejpam-5629	46	18	,	,	PUNCT
ejpam-5629	46	19	iz1	iz1	PROPN
ejpam-5629	46	20	0	0	NUM
ejpam-5629	46	21	+	+	NUM
ejpam-5629	46	22	ζ(s	ζ(s	NOUN
ejpam-5629	46	23	)	)	PUNCT
ejpam-5629	46	24	,	,	PUNCT
ejpam-5629	46	25	iz2	iz2	VERB
ejpam-5629	46	26	0	0	NUM
ejpam-5629	46	27	+	+	ADJ
ejpam-5629	46	28	ω(s	ω(	NOUN
ejpam-5629	46	29	)	)	PUNCT
ejpam-5629	46	30	)	)	PUNCT
ejpam-5629	46	31	,	,	PUNCT
ejpam-5629	46	32	s	s	VERB
ejpam-5629	46	33	∈	∈	PROPN
ejpam-5629	46	34	v	v	NOUN
ejpam-5629	46	35	,	,	PUNCT
ejpam-5629	46	36	under	under	ADP
ejpam-5629	46	37	the	the	DET
ejpam-5629	46	38	constraints	constraint	NOUN
ejpam-5629	46	39	{	{	PUNCT
ejpam-5629	46	40	ζ	ζ	NOUN
ejpam-5629	46	41	(	(	PUNCT
ejpam-5629	46	42	0	0	NUM
ejpam-5629	46	43	)	)	PUNCT
ejpam-5629	46	44	=	=	SYM
ejpam-5629	46	45	ζ	ζ	NOUN
ejpam-5629	46	46	′	′	NUM
ejpam-5629	46	47	(	(	PUNCT
ejpam-5629	46	48	0	0	NUM
ejpam-5629	46	49	)	)	PUNCT
ejpam-5629	46	50	=	=	SYM
ejpam-5629	46	51	0	0	NUM
ejpam-5629	46	52	,	,	PUNCT
ejpam-5629	46	53	ζ	ζ	NOUN
ejpam-5629	46	54	′	′	NUM
ejpam-5629	46	55	(	(	PUNCT
ejpam-5629	46	56	1	1	NUM
ejpam-5629	46	57	)	)	PUNCT
ejpam-5629	46	58	=	=	SYM
ejpam-5629	46	59	1	1	NUM
ejpam-5629	46	60	,	,	PUNCT
ejpam-5629	46	61	ζ	ζ	NOUN
ejpam-5629	46	62	(	(	PUNCT
ejpam-5629	46	63	1	1	NUM
ejpam-5629	46	64	)	)	PUNCT
ejpam-5629	46	65	=	=	SYM
ejpam-5629	47	1	∫	∫	PROPN
ejpam-5629	47	2	1	1	NUM
ejpam-5629	47	3	0	0	NUM
ejpam-5629	47	4	ζ	ζ	NOUN
ejpam-5629	47	5	(	(	PUNCT
ejpam-5629	47	6	t	t	NOUN
ejpam-5629	47	7	)	)	PUNCT
ejpam-5629	47	8	dr1(t	dr1(t	PROPN
ejpam-5629	47	9	)	)	PUNCT
ejpam-5629	48	1	+	+	CCONJ
ejpam-5629	48	2	∫	∫	PROPN
ejpam-5629	48	3	1	1	NUM
ejpam-5629	48	4	0	0	NUM
ejpam-5629	48	5	ω	ω	NUM
ejpam-5629	48	6	(	(	PUNCT
ejpam-5629	48	7	t	t	PROPN
ejpam-5629	48	8	)	)	PUNCT
ejpam-5629	48	9	dr2(t	dr2(t	PROPN
ejpam-5629	48	10	)	)	PUNCT
ejpam-5629	48	11	,	,	PUNCT
ejpam-5629	48	12	ω	ω	PROPN
ejpam-5629	48	13	(	(	PUNCT
ejpam-5629	48	14	0	0	NUM
ejpam-5629	48	15	)	)	PUNCT
ejpam-5629	48	16	=	=	SYM
ejpam-5629	48	17	ω′	ω′	PROPN
ejpam-5629	48	18	(	(	PUNCT
ejpam-5629	48	19	0	0	NUM
ejpam-5629	48	20	)	)	PUNCT
ejpam-5629	48	21	=	=	SYM
ejpam-5629	48	22	0	0	NUM
ejpam-5629	48	23	,	,	PUNCT
ejpam-5629	48	24	ω′	ω′	PUNCT
ejpam-5629	48	25	(	(	PUNCT
ejpam-5629	48	26	1	1	NUM
ejpam-5629	48	27	)	)	PUNCT
ejpam-5629	48	28	=	=	SYM
ejpam-5629	48	29	1	1	NUM
ejpam-5629	48	30	,	,	PUNCT
ejpam-5629	48	31	ω	ω	PROPN
ejpam-5629	48	32	(	(	PUNCT
ejpam-5629	48	33	1	1	NUM
ejpam-5629	48	34	)	)	PUNCT
ejpam-5629	48	35	=	=	SYM
ejpam-5629	49	1	∫	∫	PROPN
ejpam-5629	49	2	1	1	NUM
ejpam-5629	49	3	0	0	NUM
ejpam-5629	49	4	ζ	ζ	NOUN
ejpam-5629	49	5	(	(	PUNCT
ejpam-5629	49	6	t	t	PROPN
ejpam-5629	49	7	)	)	PUNCT
ejpam-5629	49	8	dm1(t	dm1(t	PROPN
ejpam-5629	49	9	)	)	PUNCT
ejpam-5629	50	1	+	+	NUM
ejpam-5629	50	2	∫	∫	PROPN
ejpam-5629	50	3	1	1	NUM
ejpam-5629	50	4	0	0	NUM
ejpam-5629	50	5	ω	ω	NUM
ejpam-5629	50	6	(	(	PUNCT
ejpam-5629	50	7	t	t	PROPN
ejpam-5629	50	8	)	)	PUNCT
ejpam-5629	50	9	dm2(t	dm2(t	PROPN
ejpam-5629	50	10	)	)	PUNCT
ejpam-5629	50	11	,	,	PUNCT
ejpam-5629	50	12	where	where	SCONJ
ejpam-5629	50	13	η	η	PROPN
ejpam-5629	50	14	,	,	PUNCT
ejpam-5629	50	15	γ	γ	PROPN
ejpam-5629	50	16	∈	∈	PROPN
ejpam-5629	50	17	(	(	PUNCT
ejpam-5629	50	18	3	3	NUM
ejpam-5629	50	19	,	,	PUNCT
ejpam-5629	50	20	4	4	NUM
ejpam-5629	50	21	]	]	PUNCT
ejpam-5629	50	22	,	,	PUNCT
ejpam-5629	50	23	ϑ	ϑ	X
ejpam-5629	50	24	,	,	PUNCT
ejpam-5629	50	25	θ	θ	PROPN
ejpam-5629	50	26	>	>	X
ejpam-5629	50	27	0	0	PROPN
ejpam-5629	50	28	,	,	PUNCT
ejpam-5629	50	29	r1	r1	NOUN
ejpam-5629	50	30	,	,	PUNCT
ejpam-5629	50	31	r2	r2	PROPN
ejpam-5629	50	32	,	,	PUNCT
ejpam-5629	50	33	z1	z1	NOUN
ejpam-5629	50	34	,	,	PUNCT
ejpam-5629	50	35	z2	z2	PROPN
ejpam-5629	50	36	>	>	X
ejpam-5629	50	37	0	0	NUM
ejpam-5629	50	38	,	,	PUNCT
ejpam-5629	50	39	ℓ1	ℓ1	NOUN
ejpam-5629	50	40	,	,	PUNCT
ejpam-5629	50	41	ℓ2	ℓ2	NOUN
ejpam-5629	50	42	:	:	PUNCT
ejpam-5629	50	43	v	v	NUM
ejpam-5629	50	44	×	×	NOUN
ejpam-5629	50	45	r4	r4	NOUN
ejpam-5629	50	46	→	→	PUNCT
ejpam-5629	50	47	r	r	NOUN
ejpam-5629	50	48	are	be	AUX
ejpam-5629	50	49	continuous	continuous	ADJ
ejpam-5629	50	50	functions	function	NOUN
ejpam-5629	50	51	,	,	PUNCT
ejpam-5629	50	52	ir1	ir1	X
ejpam-5629	50	53	0	0	NUM
ejpam-5629	51	1	+	+	NUM
ejpam-5629	51	2	,	,	PUNCT
ejpam-5629	51	3	ir2	ir2	PROPN
ejpam-5629	51	4	0	0	NUM
ejpam-5629	52	1	+	+	NUM
ejpam-5629	52	2	,	,	PUNCT
ejpam-5629	52	3	iz1	iz1	PROPN
ejpam-5629	52	4	0	0	NUM
ejpam-5629	52	5	+	+	CCONJ
ejpam-5629	52	6	,	,	PUNCT
ejpam-5629	52	7	iz2	iz2	VERB
ejpam-5629	52	8	0	0	NUM
ejpam-5629	52	9	+	+	NUM
ejpam-5629	52	10	are	be	AUX
ejpam-5629	52	11	riemann	riemann	NOUN
ejpam-5629	52	12	-	-	PUNCT
ejpam-5629	52	13	liouville	liouville	NOUN
ejpam-5629	52	14	(	(	PUNCT
ejpam-5629	52	15	rl	rl	NOUN
ejpam-5629	52	16	)	)	PUNCT
ejpam-5629	52	17	integrals	integral	NOUN
ejpam-5629	52	18	of	of	ADP
ejpam-5629	52	19	orders	order	NOUN
ejpam-5629	52	20	r1	r1	PROPN
ejpam-5629	52	21	,	,	PUNCT
ejpam-5629	52	22	r2	r2	PROPN
ejpam-5629	52	23	,	,	PUNCT
ejpam-5629	52	24	z1	z1	NOUN
ejpam-5629	52	25	,	,	PUNCT
ejpam-5629	52	26	z2	z2	NOUN
ejpam-5629	52	27	,	,	PUNCT
ejpam-5629	52	28	and	and	CCONJ
ejpam-5629	52	29	r1	r1	NOUN
ejpam-5629	52	30	,	,	PUNCT
ejpam-5629	52	31	r2,m1,m2	r2,m1,m2	PROPN
ejpam-5629	52	32	are	be	AUX
ejpam-5629	52	33	riemann	riemann	ADJ
ejpam-5629	52	34	-	-	PUNCT
ejpam-5629	52	35	stieltjes	stieltjes	PROPN
ejpam-5629	52	36	integrals	integral	NOUN
ejpam-5629	52	37	.	.	PUNCT
ejpam-5629	53	1	these	these	DET
ejpam-5629	53	2	systems	system	NOUN
ejpam-5629	53	3	have	have	VERB
ejpam-5629	53	4	applications	application	NOUN
ejpam-5629	53	5	in	in	ADP
ejpam-5629	53	6	biosciences	bioscience	NOUN
ejpam-5629	53	7	(	(	PUNCT
ejpam-5629	53	8	see	see	VERB
ejpam-5629	53	9	to	to	ADP
ejpam-5629	53	10	[	[	X
ejpam-5629	53	11	7	7	NUM
ejpam-5629	53	12	]	]	NUM
ejpam-5629	53	13	)	)	PUNCT
ejpam-5629	53	14	.	.	PUNCT
ejpam-5629	54	1	the	the	DET
ejpam-5629	54	2	authors	author	NOUN
ejpam-5629	54	3	discovered	discover	VERB
ejpam-5629	54	4	that	that	SCONJ
ejpam-5629	54	5	the	the	DET
ejpam-5629	54	6	system	system	NOUN
ejpam-5629	54	7	’s	’s	PART
ejpam-5629	54	8	solutions	solution	NOUN
ejpam-5629	54	9	exist	exist	VERB
ejpam-5629	54	10	and	and	CCONJ
ejpam-5629	54	11	are	be	AUX
ejpam-5629	54	12	unique	unique	ADJ
ejpam-5629	54	13	.	.	PUNCT
ejpam-5629	55	1	the	the	DET
ejpam-5629	55	2	existence	existence	NOUN
ejpam-5629	55	3	,	,	PUNCT
ejpam-5629	55	4	uniqueness	uniqueness	NOUN
ejpam-5629	55	5	,	,	PUNCT
ejpam-5629	55	6	and	and	CCONJ
ejpam-5629	55	7	stability	stability	NOUN
ejpam-5629	55	8	of	of	ADP
ejpam-5629	55	9	the	the	DET
ejpam-5629	55	10	system	system	NOUN
ejpam-5629	55	11	in	in	ADP
ejpam-5629	55	12	the	the	DET
ejpam-5629	55	13	ulam	ulam	NOUN
ejpam-5629	55	14	-	-	PUNCT
ejpam-5629	55	15	hyers	hyer	NOUN
ejpam-5629	55	16	sense	sense	NOUN
ejpam-5629	55	17	were	be	AUX
ejpam-5629	55	18	examined	examine	VERB
ejpam-5629	55	19	by	by	ADP
ejpam-5629	55	20	bensassa	bensassa	PROPN
ejpam-5629	55	21	et	et	PROPN
ejpam-5629	55	22	al	al	PROPN
ejpam-5629	55	23	.	.	PUNCT
ejpam-5629	56	1	in	in	ADP
ejpam-5629	56	2	[	[	X
ejpam-5629	56	3	11	11	NUM
ejpam-5629	56	4	]	]	SYM
ejpam-5629	56	5	:	:	PUNCT
ejpam-5629	56	6	{	{	PUNCT
ejpam-5629	56	7	dη1dη2φ(ζ	dη1dη2φ(ζ	PROPN
ejpam-5629	56	8	)	)	PUNCT
ejpam-5629	56	9	=	=	SYM
ejpam-5629	56	10	ℓ1	ℓ1	NOUN
ejpam-5629	56	11	(	(	PUNCT
ejpam-5629	56	12	ζ	ζ	NOUN
ejpam-5629	56	13	,	,	PUNCT
ejpam-5629	56	14	φ(ζ	φ(ζ	NOUN
ejpam-5629	56	15	)	)	PUNCT
ejpam-5629	56	16	,	,	PUNCT
ejpam-5629	56	17	ω(ζ	ω(ζ	NOUN
ejpam-5629	56	18	)	)	PUNCT
ejpam-5629	56	19	)	)	PUNCT
ejpam-5629	57	1	+	+	CCONJ
ejpam-5629	57	2	b1ℏ1	b1ℏ1	CCONJ
ejpam-5629	57	3	(	(	PUNCT
ejpam-5629	57	4	ζ	ζ	NOUN
ejpam-5629	57	5	,	,	PUNCT
ejpam-5629	57	6	φ(ζ	φ(ζ	NOUN
ejpam-5629	57	7	)	)	PUNCT
ejpam-5629	57	8	)	)	PUNCT
ejpam-5629	58	1	+	+	CCONJ
ejpam-5629	58	2	c1ϖ1	c1ϖ1	X
ejpam-5629	58	3	(	(	PUNCT
ejpam-5629	58	4	ζ	ζ	NOUN
ejpam-5629	58	5	,	,	PUNCT
ejpam-5629	58	6	d	d	NOUN
ejpam-5629	58	7	ρφ(ζ	ρφ(ζ	NOUN
ejpam-5629	58	8	)	)	PUNCT
ejpam-5629	58	9	)	)	PUNCT
ejpam-5629	58	10	,	,	PUNCT
ejpam-5629	58	11	dγ1dγ2ω(ζ	dγ1dγ2ω(ζ	X
ejpam-5629	58	12	)	)	PUNCT
ejpam-5629	58	13	=	=	SYM
ejpam-5629	58	14	ℓ2	ℓ2	NOUN
ejpam-5629	58	15	(	(	PUNCT
ejpam-5629	58	16	ζ	ζ	NOUN
ejpam-5629	58	17	,	,	PUNCT
ejpam-5629	58	18	φ(ζ	φ(ζ	NOUN
ejpam-5629	58	19	)	)	PUNCT
ejpam-5629	58	20	,	,	PUNCT
ejpam-5629	58	21	ω(ζ	ω(ζ	NOUN
ejpam-5629	58	22	)	)	PUNCT
ejpam-5629	58	23	)	)	PUNCT
ejpam-5629	59	1	+	+	CCONJ
ejpam-5629	59	2	b2ℏ2	b2ℏ2	X
ejpam-5629	59	3	(	(	PUNCT
ejpam-5629	59	4	ζ	ζ	NOUN
ejpam-5629	59	5	,	,	PUNCT
ejpam-5629	59	6	ω(ζ	ω(ζ	NOUN
ejpam-5629	59	7	)	)	PUNCT
ejpam-5629	59	8	)	)	PUNCT
ejpam-5629	60	1	+	+	CCONJ
ejpam-5629	60	2	c2ϖ2	c2ϖ2	NOUN
ejpam-5629	60	3	(	(	PUNCT
ejpam-5629	60	4	ζ	ζ	NOUN
ejpam-5629	60	5	,	,	PUNCT
ejpam-5629	60	6	d	d	NOUN
ejpam-5629	60	7	ρω(ζ	ρω(ζ	NOUN
ejpam-5629	60	8	)	)	PUNCT
ejpam-5629	60	9	)	)	PUNCT
ejpam-5629	60	10	,	,	PUNCT
ejpam-5629	60	11	under	under	ADP
ejpam-5629	60	12	the	the	DET
ejpam-5629	60	13	stipulations	stipulation	NOUN
ejpam-5629	60	14	{	{	PUNCT
ejpam-5629	60	15	φ(0	φ(0	PROPN
ejpam-5629	60	16	)	)	PUNCT
ejpam-5629	60	17	=	=	SYM
ejpam-5629	60	18	φ(1	φ(1	PROPN
ejpam-5629	60	19	)	)	PUNCT
ejpam-5629	60	20	=	=	SYM
ejpam-5629	60	21	b	b	PROPN
ejpam-5629	60	22	,	,	PUNCT
ejpam-5629	60	23	φ′(0	φ′(0	X
ejpam-5629	60	24	)	)	PUNCT
ejpam-5629	60	25	=	=	SYM
ejpam-5629	60	26	φ′(1	φ′(1	PROPN
ejpam-5629	60	27	)	)	PUNCT
ejpam-5629	60	28	=	=	SYM
ejpam-5629	60	29	0	0	NUM
ejpam-5629	60	30	,	,	PUNCT
ejpam-5629	60	31	ω(0	ω(0	PROPN
ejpam-5629	60	32	)	)	PUNCT
ejpam-5629	60	33	=	=	PUNCT
ejpam-5629	61	1	ω(1	ω(1	NOUN
ejpam-5629	61	2	)	)	PUNCT
ejpam-5629	61	3	=	=	SYM
ejpam-5629	61	4	c	c	X
ejpam-5629	61	5	,	,	PUNCT
ejpam-5629	61	6	ω′(0	ω′(0	ADJ
ejpam-5629	61	7	)	)	PUNCT
ejpam-5629	61	8	=	=	SYM
ejpam-5629	61	9	ω′(1	ω′(1	PROPN
ejpam-5629	61	10	)	)	PUNCT
ejpam-5629	61	11	=	=	SYM
ejpam-5629	61	12	0	0	NUM
ejpam-5629	61	13	,	,	PUNCT
ejpam-5629	61	14	where	where	SCONJ
ejpam-5629	61	15	dηi	dηi	NOUN
ejpam-5629	61	16	,	,	PUNCT
ejpam-5629	61	17	dγi	dγi	PROPN
ejpam-5629	61	18	,	,	PUNCT
ejpam-5629	61	19	dρ	dρ	PROPN
ejpam-5629	61	20	are	be	AUX
ejpam-5629	61	21	cfds	cfds	NOUN
ejpam-5629	61	22	,	,	PUNCT
ejpam-5629	61	23	ρ	ρ	PROPN
ejpam-5629	61	24	∈	∈	PROPN
ejpam-5629	61	25	(	(	PUNCT
ejpam-5629	61	26	0	0	NUM
ejpam-5629	61	27	,	,	PUNCT
ejpam-5629	61	28	1	1	NUM
ejpam-5629	61	29	]	]	PUNCT
ejpam-5629	61	30	,	,	PUNCT
ejpam-5629	61	31	ℓ1	ℓ1	NOUN
ejpam-5629	61	32	,	,	PUNCT
ejpam-5629	61	33	ℓ2	ℓ2	PROPN
ejpam-5629	61	34	∈	∈	PROPN
ejpam-5629	61	35	c	c	NOUN
ejpam-5629	61	36	(	(	PUNCT
ejpam-5629	61	37	[	[	X
ejpam-5629	61	38	0	0	NUM
ejpam-5629	61	39	,	,	PUNCT
ejpam-5629	61	40	1]×	1]×	NUM
ejpam-5629	61	41	r×	r×	NOUN
ejpam-5629	61	42	r;r	r;r	NOUN
ejpam-5629	61	43	)	)	PUNCT
ejpam-5629	61	44	,	,	PUNCT
ejpam-5629	61	45	b1	b1	NOUN
ejpam-5629	61	46	,	,	PUNCT
ejpam-5629	61	47	b2	b2	NOUN
ejpam-5629	61	48	,	,	PUNCT
ejpam-5629	61	49	c1	c1	NOUN
ejpam-5629	61	50	,	,	PUNCT
ejpam-5629	61	51	c2	c2	PROPN
ejpam-5629	61	52	∈	∈	PROPN
ejpam-5629	61	53	r	r	NOUN
ejpam-5629	61	54	,	,	PUNCT
ejpam-5629	61	55	and	and	CCONJ
ejpam-5629	61	56	ℏ1	ℏ1	ADJ
ejpam-5629	61	57	,	,	PUNCT
ejpam-5629	61	58	ℏ2	ℏ2	NOUN
ejpam-5629	61	59	,	,	PUNCT
ejpam-5629	61	60	ϖ1	ϖ1	VERB
ejpam-5629	61	61	,	,	PUNCT
ejpam-5629	61	62	ϖ2	ϖ2	NOUN
ejpam-5629	61	63	∈	∈	PROPN
ejpam-5629	61	64	c	c	NOUN
ejpam-5629	61	65	(	(	PUNCT
ejpam-5629	61	66	[	[	X
ejpam-5629	61	67	0	0	NUM
ejpam-5629	61	68	,	,	PUNCT
ejpam-5629	61	69	1]×	1]×	NUM
ejpam-5629	61	70	r;r	r;r	NOUN
ejpam-5629	61	71	)	)	PUNCT
ejpam-5629	61	72	.	.	PUNCT
ejpam-5629	62	1	drawing	draw	VERB
ejpam-5629	62	2	on	on	ADP
ejpam-5629	62	3	the	the	DET
ejpam-5629	62	4	previously	previously	ADV
ejpam-5629	62	5	mentioned	mention	VERB
ejpam-5629	62	6	research	research	NOUN
ejpam-5629	62	7	and	and	CCONJ
ejpam-5629	62	8	specifically	specifically	ADV
ejpam-5629	62	9	from	from	ADP
ejpam-5629	62	10	paper	paper	NOUN
ejpam-5629	62	11	[	[	X
ejpam-5629	62	12	43	43	NUM
ejpam-5629	62	13	]	]	PUNCT
ejpam-5629	62	14	,	,	PUNCT
ejpam-5629	62	15	the	the	DET
ejpam-5629	62	16	current	current	ADJ
ejpam-5629	62	17	study	study	NOUN
ejpam-5629	62	18	will	will	AUX
ejpam-5629	62	19	address	address	VERB
ejpam-5629	62	20	the	the	DET
ejpam-5629	62	21	following	follow	VERB
ejpam-5629	62	22	csds	csds	NOUN
ejpam-5629	62	23	problem	problem	NOUN
ejpam-5629	62	24	:	:	PUNCT
ejpam-5629	62	25	{	{	PUNCT
ejpam-5629	62	26	dη1dγ1φ1(ζ	dη1dγ1φ1(ζ	NOUN
ejpam-5629	62	27	)	)	PUNCT
ejpam-5629	62	28	=	=	SYM
ejpam-5629	63	1	⅁1z1	⅁1z1	NOUN
ejpam-5629	63	2	(	(	PUNCT
ejpam-5629	63	3	ζ	ζ	NOUN
ejpam-5629	63	4	,	,	PUNCT
ejpam-5629	63	5	φ1(ζ	φ1(ζ	NOUN
ejpam-5629	63	6	)	)	PUNCT
ejpam-5629	63	7	,	,	PUNCT
ejpam-5629	63	8	φ2(ζ	φ2(ζ	X
ejpam-5629	63	9	)	)	PUNCT
ejpam-5629	63	10	,	,	PUNCT
ejpam-5629	63	11	d	d	PROPN
ejpam-5629	63	12	ρ−1φ1(ζ	ρ−1φ1(ζ	PROPN
ejpam-5629	63	13	)	)	PUNCT
ejpam-5629	63	14	,	,	PUNCT
ejpam-5629	63	15	d	d	PROPN
ejpam-5629	63	16	ρφ1(ζ	ρφ1(ζ	PROPN
ejpam-5629	63	17	)	)	PUNCT
ejpam-5629	63	18	)	)	PUNCT
ejpam-5629	63	19	dη2dγ2φ2(ζ	dη2dγ2φ2(ζ	NOUN
ejpam-5629	63	20	)	)	PUNCT
ejpam-5629	64	1	=	=	SYM
ejpam-5629	65	1	⅁2z2	⅁2z2	ADJ
ejpam-5629	65	2	(	(	PUNCT
ejpam-5629	65	3	ζ	ζ	NOUN
ejpam-5629	65	4	,	,	PUNCT
ejpam-5629	65	5	φ1(ζ	φ1(ζ	NOUN
ejpam-5629	65	6	)	)	PUNCT
ejpam-5629	65	7	,	,	PUNCT
ejpam-5629	65	8	φ2(ζ	φ2(ζ	X
ejpam-5629	65	9	)	)	PUNCT
ejpam-5629	65	10	,	,	PUNCT
ejpam-5629	65	11	d	d	PROPN
ejpam-5629	65	12	ρ−1φ2(ζ	ρ−1φ2(ζ	PROPN
ejpam-5629	65	13	)	)	PUNCT
ejpam-5629	65	14	,	,	PUNCT
ejpam-5629	65	15	d	d	PROPN
ejpam-5629	65	16	ρφ2(ζ	ρφ2(ζ	PROPN
ejpam-5629	65	17	)	)	PUNCT
ejpam-5629	65	18	)	)	PUNCT
ejpam-5629	66	1	(	(	PUNCT
ejpam-5629	66	2	1	1	X
ejpam-5629	66	3	)	)	PUNCT
ejpam-5629	66	4	with	with	ADP
ejpam-5629	66	5	the	the	DET
ejpam-5629	66	6	conditions	condition	NOUN
ejpam-5629	66	7	{	{	PUNCT
ejpam-5629	66	8	φj(0	φj(0	NOUN
ejpam-5629	66	9	)	)	PUNCT
ejpam-5629	66	10	=	=	PUNCT
ejpam-5629	66	11	φj(1	φj(1	NUM
ejpam-5629	66	12	)	)	PUNCT
ejpam-5629	66	13	=	=	PUNCT
ejpam-5629	66	14	bj	bj	ADP
ejpam-5629	66	15	∈	∈	NOUN
ejpam-5629	66	16	r	r	NOUN
ejpam-5629	66	17	,	,	PUNCT
ejpam-5629	66	18	dγjφj(0	dγjφj(0	PROPN
ejpam-5629	66	19	)	)	PUNCT
ejpam-5629	66	20	=	=	SYM
ejpam-5629	66	21	dγjφj(1	dγjφj(1	PROPN
ejpam-5629	66	22	)	)	PUNCT
ejpam-5629	66	23	=	=	SYM
ejpam-5629	67	1	0	0	NUM
ejpam-5629	67	2	,	,	PUNCT
ejpam-5629	67	3	j	j	PROPN
ejpam-5629	67	4	=	=	SYM
ejpam-5629	67	5	1	1	NUM
ejpam-5629	67	6	,	,	PUNCT
ejpam-5629	67	7	2	2	NUM
ejpam-5629	67	8	,	,	PUNCT
ejpam-5629	67	9	(	(	PUNCT
ejpam-5629	67	10	2	2	X
ejpam-5629	67	11	)	)	PUNCT
ejpam-5629	67	12	where	where	SCONJ
ejpam-5629	67	13	dη1	dη1	NOUN
ejpam-5629	67	14	,	,	PUNCT
ejpam-5629	67	15	dγ1	dγ1	NOUN
ejpam-5629	67	16	,	,	PUNCT
ejpam-5629	67	17	and	and	CCONJ
ejpam-5629	67	18	dρ	dρ	PROPN
ejpam-5629	67	19	are	be	AUX
ejpam-5629	67	20	cfds	cfds	NOUN
ejpam-5629	67	21	.	.	PUNCT
ejpam-5629	68	1	in	in	ADP
ejpam-5629	68	2	order	order	NOUN
ejpam-5629	68	3	to	to	PART
ejpam-5629	68	4	ensure	ensure	VERB
ejpam-5629	68	5	that	that	SCONJ
ejpam-5629	68	6	there	there	PRON
ejpam-5629	68	7	are	be	VERB
ejpam-5629	68	8	no	no	DET
ejpam-5629	68	9	semi	semi	NOUN
ejpam-5629	68	10	-	-	NOUN
ejpam-5629	68	11	group	group	NOUN
ejpam-5629	68	12	and	and	CCONJ
ejpam-5629	68	13	commutativity	commutativity	NOUN
ejpam-5629	68	14	properties	property	NOUN
ejpam-5629	68	15	on	on	ADP
ejpam-5629	68	16	the	the	DET
ejpam-5629	68	17	cfd	cfd	NOUN
ejpam-5629	68	18	and	and	CCONJ
ejpam-5629	68	19	to	to	PART
ejpam-5629	68	20	derive	derive	VERB
ejpam-5629	68	21	,	,	PUNCT
ejpam-5629	68	22	as	as	ADP
ejpam-5629	68	23	a	a	DET
ejpam-5629	68	24	specific	specific	ADJ
ejpam-5629	68	25	case	case	NOUN
ejpam-5629	68	26	,	,	PUNCT
ejpam-5629	68	27	the	the	DET
ejpam-5629	68	28	aforementioned	aforementioned	ADJ
ejpam-5629	68	29	wang	wang	PROPN
ejpam-5629	68	30	and	and	CCONJ
ejpam-5629	68	31	yang	yang	PROPN
ejpam-5629	68	32	fourth	fourth	ADJ
ejpam-5629	68	33	-	-	PUNCT
ejpam-5629	68	34	order	order	NOUN
ejpam-5629	68	35	system	system	NOUN
ejpam-5629	68	36	under	under	ADP
ejpam-5629	68	37	various	various	ADJ
ejpam-5629	68	38	circumstances	circumstance	NOUN
ejpam-5629	68	39	,	,	PUNCT
ejpam-5629	68	40	we	we	PRON
ejpam-5629	68	41	also	also	ADV
ejpam-5629	68	42	assume	assume	VERB
ejpam-5629	68	43	that	that	SCONJ
ejpam-5629	68	44	ηj	ηj	ADP
ejpam-5629	68	45	∈	∈	PROPN
ejpam-5629	68	46	(	(	PUNCT
ejpam-5629	68	47	2	2	NUM
ejpam-5629	68	48	,	,	PUNCT
ejpam-5629	68	49	3	3	NUM
ejpam-5629	68	50	]	]	PUNCT
ejpam-5629	68	51	,	,	PUNCT
ejpam-5629	68	52	γj	γj	ADP
ejpam-5629	68	53	∈	∈	PROPN
ejpam-5629	68	54	(	(	PUNCT
ejpam-5629	68	55	0	0	NUM
ejpam-5629	68	56	,	,	PUNCT
ejpam-5629	68	57	1	1	NUM
ejpam-5629	68	58	]	]	PUNCT
ejpam-5629	68	59	,	,	PUNCT
ejpam-5629	68	60	and	and	CCONJ
ejpam-5629	68	61	⅁j	⅁j	NOUN
ejpam-5629	68	62	>	>	X
ejpam-5629	68	63	0	0	PUNCT
ejpam-5629	69	1	j	j	NOUN
ejpam-5629	69	2	=	=	SYM
ejpam-5629	69	3	1	1	NUM
ejpam-5629	69	4	,	,	PUNCT
ejpam-5629	69	5	2	2	NUM
ejpam-5629	69	6	.	.	PUNCT
ejpam-5629	70	1	it	it	PRON
ejpam-5629	70	2	is	be	AUX
ejpam-5629	70	3	also	also	ADV
ejpam-5629	70	4	assumed	assume	VERB
ejpam-5629	70	5	that	that	SCONJ
ejpam-5629	70	6	ρ	ρ	PROPN
ejpam-5629	70	7	∈	∈	PROPN
ejpam-5629	70	8	(	(	PUNCT
ejpam-5629	70	9	1	1	NUM
ejpam-5629	70	10	,	,	PUNCT
ejpam-5629	70	11	2	2	NUM
ejpam-5629	70	12	]	]	PUNCT
ejpam-5629	70	13	.	.	PUNCT
ejpam-5629	71	1	as	as	ADP
ejpam-5629	71	2	a	a	DET
ejpam-5629	71	3	limiting	limit	VERB
ejpam-5629	71	4	case	case	NOUN
ejpam-5629	71	5	of	of	ADP
ejpam-5629	71	6	(	(	PUNCT
ejpam-5629	71	7	1	1	NUM
ejpam-5629	71	8	)	)	PUNCT
ejpam-5629	71	9	,	,	PUNCT
ejpam-5629	71	10	we	we	PRON
ejpam-5629	71	11	can	can	AUX
ejpam-5629	71	12	achieve	achieve	VERB
ejpam-5629	71	13	the	the	DET
ejpam-5629	71	14	aforesaid	aforesaid	NOUN
ejpam-5629	71	15	wang	wang	PROPN
ejpam-5629	71	16	and	and	CCONJ
ejpam-5629	71	17	yang	yang	PROPN
ejpam-5629	72	1	[	[	X
ejpam-5629	72	2	43	43	NUM
ejpam-5629	72	3	]	]	X
ejpam-5629	72	4	problem	problem	NOUN
ejpam-5629	72	5	,	,	PUNCT
ejpam-5629	72	6	where	where	SCONJ
ejpam-5629	72	7	zi	zi	NOUN
ejpam-5629	72	8	:	:	PUNCT
ejpam-5629	73	1	[	[	X
ejpam-5629	73	2	0	0	NUM
ejpam-5629	73	3	,	,	PUNCT
ejpam-5629	73	4	1]×	1]×	NUM
ejpam-5629	73	5	r4	r4	NOUN
ejpam-5629	73	6	→	→	SYM
ejpam-5629	73	7	r	r	NOUN
ejpam-5629	73	8	and	and	CCONJ
ejpam-5629	73	9	j	j	NOUN
ejpam-5629	73	10	=	=	SYM
ejpam-5629	73	11	1	1	NUM
ejpam-5629	73	12	,	,	PUNCT
ejpam-5629	73	13	2	2	NUM
ejpam-5629	73	14	are	be	AUX
ejpam-5629	73	15	some	some	DET
ejpam-5629	73	16	continuous	continuous	ADJ
ejpam-5629	73	17	functions	function	NOUN
ejpam-5629	73	18	.	.	PUNCT
ejpam-5629	74	1	h.a	h.a	PROPN
ejpam-5629	74	2	.	.	PROPN
ejpam-5629	74	3	hammad	hammad	PROPN
ejpam-5629	74	4	,	,	PUNCT
ejpam-5629	74	5	m.e.m	m.e.m	NOUN
ejpam-5629	74	6	.	.	PUNCT
ejpam-5629	75	1	abdalla	abdalla	PROPN
ejpam-5629	75	2	/	/	SYM
ejpam-5629	75	3	eur	eur	PROPN
ejpam-5629	75	4	.	.	PUNCT
ejpam-5629	76	1	j.	j.	PROPN
ejpam-5629	76	2	pure	pure	PROPN
ejpam-5629	76	3	appl	appl	PROPN
ejpam-5629	76	4	.	.	PROPN
ejpam-5629	76	5	math	math	PROPN
ejpam-5629	76	6	,	,	PUNCT
ejpam-5629	76	7	18	18	NUM
ejpam-5629	76	8	(	(	PUNCT
ejpam-5629	76	9	1	1	NUM
ejpam-5629	76	10	)	)	PUNCT
ejpam-5629	76	11	(	(	PUNCT
ejpam-5629	76	12	2025	2025	NUM
ejpam-5629	76	13	)	)	PUNCT
ejpam-5629	76	14	,	,	PUNCT
ejpam-5629	76	15	5629	5629	NUM
ejpam-5629	76	16	4	4	NUM
ejpam-5629	76	17	of	of	ADP
ejpam-5629	76	18	20	20	NUM
ejpam-5629	76	19	it	it	PRON
ejpam-5629	76	20	is	be	AUX
ejpam-5629	76	21	noteworthy	noteworthy	ADJ
ejpam-5629	76	22	that	that	SCONJ
ejpam-5629	76	23	our	our	PRON
ejpam-5629	76	24	problem	problem	NOUN
ejpam-5629	76	25	is	be	AUX
ejpam-5629	76	26	more	more	ADV
ejpam-5629	76	27	substantial	substantial	ADJ
ejpam-5629	76	28	than	than	ADP
ejpam-5629	76	29	the	the	DET
ejpam-5629	76	30	studies	study	NOUN
ejpam-5629	76	31	cited	cite	VERB
ejpam-5629	76	32	above	above	ADV
ejpam-5629	76	33	,	,	PUNCT
ejpam-5629	76	34	and	and	CCONJ
ejpam-5629	76	35	that	that	SCONJ
ejpam-5629	76	36	most	most	ADJ
ejpam-5629	76	37	of	of	ADP
ejpam-5629	76	38	them	they	PRON
ejpam-5629	76	39	are	be	AUX
ejpam-5629	76	40	not	not	PART
ejpam-5629	76	41	the	the	DET
ejpam-5629	76	42	same	same	ADJ
ejpam-5629	76	43	because	because	SCONJ
ejpam-5629	76	44	we	we	PRON
ejpam-5629	76	45	include	include	VERB
ejpam-5629	76	46	cfd	cfd	NOUN
ejpam-5629	76	47	in	in	ADP
ejpam-5629	76	48	the	the	DET
ejpam-5629	76	49	beginning	beginning	ADJ
ejpam-5629	76	50	circumstances	circumstance	NOUN
ejpam-5629	76	51	.	.	PUNCT
ejpam-5629	77	1	this	this	DET
ejpam-5629	77	2	inclusion	inclusion	NOUN
ejpam-5629	77	3	strengthens	strengthen	VERB
ejpam-5629	77	4	our	our	PRON
ejpam-5629	77	5	problem	problem	NOUN
ejpam-5629	77	6	’s	’s	PART
ejpam-5629	77	7	relevance	relevance	NOUN
ejpam-5629	77	8	and	and	CCONJ
ejpam-5629	77	9	applicability	applicability	NOUN
ejpam-5629	77	10	in	in	ADP
ejpam-5629	77	11	physical	physical	ADJ
ejpam-5629	77	12	environments	environment	NOUN
ejpam-5629	77	13	by	by	ADP
ejpam-5629	77	14	adding	add	VERB
ejpam-5629	77	15	a	a	DET
ejpam-5629	77	16	layer	layer	NOUN
ejpam-5629	77	17	of	of	ADP
ejpam-5629	77	18	complexity	complexity	NOUN
ejpam-5629	77	19	and	and	CCONJ
ejpam-5629	77	20	realism	realism	NOUN
ejpam-5629	77	21	.	.	PUNCT
ejpam-5629	78	1	these	these	DET
ejpam-5629	78	2	constraints	constraint	NOUN
ejpam-5629	78	3	are	be	AUX
ejpam-5629	78	4	compatible	compatible	ADJ
ejpam-5629	78	5	with	with	ADP
ejpam-5629	78	6	observable	observable	ADJ
ejpam-5629	78	7	initial	initial	ADJ
ejpam-5629	78	8	circumstances	circumstance	NOUN
ejpam-5629	78	9	and	and	CCONJ
ejpam-5629	78	10	effective	effective	ADJ
ejpam-5629	78	11	numerical	numerical	ADJ
ejpam-5629	78	12	techniques	technique	NOUN
ejpam-5629	78	13	,	,	PUNCT
ejpam-5629	78	14	enabling	enable	VERB
ejpam-5629	78	15	improved	improved	ADJ
ejpam-5629	78	16	capturing	capturing	NOUN
ejpam-5629	78	17	of	of	ADP
ejpam-5629	78	18	memory	memory	NOUN
ejpam-5629	78	19	effects	effect	NOUN
ejpam-5629	78	20	and	and	CCONJ
ejpam-5629	78	21	non	non	ADJ
ejpam-5629	78	22	-	-	ADJ
ejpam-5629	78	23	local	local	ADJ
ejpam-5629	78	24	behaviors	behavior	NOUN
ejpam-5629	78	25	of	of	ADP
ejpam-5629	78	26	the	the	DET
ejpam-5629	78	27	system	system	NOUN
ejpam-5629	78	28	.	.	PUNCT
ejpam-5629	79	1	in	in	ADP
ejpam-5629	79	2	addition	addition	NOUN
ejpam-5629	79	3	,	,	PUNCT
ejpam-5629	79	4	our	our	PRON
ejpam-5629	79	5	system	system	NOUN
ejpam-5629	79	6	has	have	VERB
ejpam-5629	79	7	three	three	NUM
ejpam-5629	79	8	generic	generic	ADJ
ejpam-5629	79	9	functions	function	NOUN
ejpam-5629	79	10	,	,	PUNCT
ejpam-5629	79	11	z1	z1	NOUN
ejpam-5629	79	12	,	,	PUNCT
ejpam-5629	79	13	z2	z2	PROPN
ejpam-5629	79	14	and	and	CCONJ
ejpam-5629	79	15	z3	z3	PROPN
ejpam-5629	79	16	,	,	PUNCT
ejpam-5629	79	17	which	which	PRON
ejpam-5629	79	18	broaden	broaden	VERB
ejpam-5629	79	19	the	the	DET
ejpam-5629	79	20	system	system	NOUN
ejpam-5629	79	21	’s	’s	PART
ejpam-5629	79	22	applicability	applicability	NOUN
ejpam-5629	79	23	beyond	beyond	ADP
ejpam-5629	79	24	issues	issue	NOUN
ejpam-5629	79	25	that	that	PRON
ejpam-5629	79	26	have	have	AUX
ejpam-5629	79	27	already	already	ADV
ejpam-5629	79	28	been	be	AUX
ejpam-5629	79	29	researched	research	VERB
ejpam-5629	79	30	and	and	CCONJ
ejpam-5629	79	31	offer	offer	VERB
ejpam-5629	79	32	a	a	DET
ejpam-5629	79	33	more	more	ADV
ejpam-5629	79	34	thorough	thorough	ADJ
ejpam-5629	79	35	framework	framework	NOUN
ejpam-5629	79	36	for	for	ADP
ejpam-5629	79	37	comprehending	comprehend	VERB
ejpam-5629	79	38	the	the	DET
ejpam-5629	79	39	dynamics	dynamic	NOUN
ejpam-5629	79	40	of	of	ADP
ejpam-5629	79	41	beam	beam	NOUN
ejpam-5629	79	42	deflection	deflection	NOUN
ejpam-5629	79	43	.	.	PUNCT
ejpam-5629	80	1	in	in	ADP
ejpam-5629	80	2	engineering	engineering	NOUN
ejpam-5629	80	3	and	and	CCONJ
ejpam-5629	80	4	applied	applied	ADJ
ejpam-5629	80	5	physics	physic	NOUN
ejpam-5629	80	6	,	,	PUNCT
ejpam-5629	80	7	this	this	DET
ejpam-5629	80	8	more	more	ADV
ejpam-5629	80	9	comprehensive	comprehensive	ADJ
ejpam-5629	80	10	approach	approach	NOUN
ejpam-5629	80	11	enables	enable	VERB
ejpam-5629	80	12	the	the	DET
ejpam-5629	80	13	modeling	modeling	NOUN
ejpam-5629	80	14	of	of	ADP
ejpam-5629	80	15	more	more	ADV
ejpam-5629	80	16	complicated	complicated	ADJ
ejpam-5629	80	17	situations	situation	NOUN
ejpam-5629	80	18	,	,	PUNCT
ejpam-5629	80	19	leading	lead	VERB
ejpam-5629	80	20	to	to	ADP
ejpam-5629	80	21	deeper	deep	ADJ
ejpam-5629	80	22	insights	insight	NOUN
ejpam-5629	80	23	and	and	CCONJ
ejpam-5629	80	24	enhanced	enhanced	ADJ
ejpam-5629	80	25	forecasting	forecasting	NOUN
ejpam-5629	80	26	skills	skill	NOUN
ejpam-5629	80	27	.	.	PUNCT
ejpam-5629	81	1	furthermore	furthermore	ADV
ejpam-5629	81	2	,	,	PUNCT
ejpam-5629	81	3	the	the	DET
ejpam-5629	81	4	problem	problem	NOUN
ejpam-5629	81	5	(	(	PUNCT
ejpam-5629	81	6	1	1	X
ejpam-5629	81	7	)	)	PUNCT
ejpam-5629	81	8	fills	fill	VERB
ejpam-5629	81	9	the	the	DET
ejpam-5629	81	10	gap	gap	NOUN
ejpam-5629	81	11	that	that	PRON
ejpam-5629	81	12	exists	exist	VERB
ejpam-5629	81	13	between	between	ADP
ejpam-5629	81	14	contemporary	contemporary	ADJ
ejpam-5629	81	15	viscoelastic	viscoelastic	NOUN
ejpam-5629	81	16	models	model	NOUN
ejpam-5629	81	17	and	and	CCONJ
ejpam-5629	81	18	traditional	traditional	ADJ
ejpam-5629	81	19	beam	beam	NOUN
ejpam-5629	81	20	deflection	deflection	NOUN
ejpam-5629	81	21	theories	theory	NOUN
ejpam-5629	81	22	.	.	PUNCT
ejpam-5629	82	1	in	in	ADP
ejpam-5629	82	2	particular	particular	ADJ
ejpam-5629	82	3	,	,	PUNCT
ejpam-5629	82	4	our	our	PRON
ejpam-5629	82	5	problem	problem	NOUN
ejpam-5629	82	6	(	(	PUNCT
ejpam-5629	82	7	1	1	X
ejpam-5629	82	8	)	)	PUNCT
ejpam-5629	82	9	may	may	AUX
ejpam-5629	82	10	be	be	AUX
ejpam-5629	82	11	reduced	reduce	VERB
ejpam-5629	82	12	to	to	ADP
ejpam-5629	82	13	the	the	DET
ejpam-5629	82	14	above	above	ADJ
ejpam-5629	82	15	fourth	fourth	ADJ
ejpam-5629	82	16	-	-	PUNCT
ejpam-5629	82	17	order	order	NOUN
ejpam-5629	82	18	odes	ode	VERB
ejpam-5629	82	19	that	that	PRON
ejpam-5629	82	20	describe	describe	VERB
ejpam-5629	82	21	the	the	DET
ejpam-5629	82	22	deformation	deformation	NOUN
ejpam-5629	82	23	of	of	ADP
ejpam-5629	82	24	an	an	DET
ejpam-5629	82	25	elastic	elastic	ADJ
ejpam-5629	82	26	beam	beam	NOUN
ejpam-5629	83	1	[	[	X
ejpam-5629	83	2	43	43	NUM
ejpam-5629	83	3	]	]	PUNCT
ejpam-5629	83	4	if	if	SCONJ
ejpam-5629	83	5	we	we	PRON
ejpam-5629	83	6	consider	consider	VERB
ejpam-5629	83	7	the	the	DET
ejpam-5629	83	8	specific	specific	ADJ
ejpam-5629	83	9	situation	situation	NOUN
ejpam-5629	83	10	:	:	PUNCT
ejpam-5629	83	11	zj	zj	PROPN
ejpam-5629	83	12	(	(	PUNCT
ejpam-5629	83	13	ζ	ζ	NOUN
ejpam-5629	83	14	,	,	PUNCT
ejpam-5629	83	15	φ1(ζ	φ1(ζ	NOUN
ejpam-5629	83	16	)	)	PUNCT
ejpam-5629	83	17	,	,	PUNCT
ejpam-5629	83	18	φ2(ζ	φ2(ζ	X
ejpam-5629	83	19	)	)	PUNCT
ejpam-5629	83	20	,	,	PUNCT
ejpam-5629	83	21	d	d	PROPN
ejpam-5629	83	22	ρ−1φ1(ζ	ρ−1φ1(ζ	PROPN
ejpam-5629	83	23	)	)	PUNCT
ejpam-5629	83	24	,	,	PUNCT
ejpam-5629	83	25	d	d	PROPN
ejpam-5629	83	26	ρφ1(ζ	ρφ1(ζ	PROPN
ejpam-5629	83	27	)	)	PUNCT
ejpam-5629	83	28	)	)	PUNCT
ejpam-5629	84	1	=	=	PUNCT
ejpam-5629	84	2	ℓj	ℓj	NOUN
ejpam-5629	84	3	(	(	PUNCT
ejpam-5629	84	4	ζ	ζ	NOUN
ejpam-5629	84	5	,	,	PUNCT
ejpam-5629	84	6	φ1(ζ	φ1(ζ	NOUN
ejpam-5629	84	7	)	)	PUNCT
ejpam-5629	84	8	,	,	PUNCT
ejpam-5629	84	9	φ2(ζ))−	φ2(ζ))−	NUM
ejpam-5629	84	10	bjφ	bjφ	NOUN
ejpam-5629	84	11	′′	′′	PROPN
ejpam-5629	84	12	j	j	PROPN
ejpam-5629	85	1	+	+	CCONJ
ejpam-5629	85	2	ajφ	ajφ	PROPN
ejpam-5629	85	3	′	′	NUM
ejpam-5629	85	4	j	j	PROPN
ejpam-5629	85	5	,	,	PUNCT
ejpam-5629	86	1	where	where	SCONJ
ejpam-5629	86	2	ρ	ρ	NOUN
ejpam-5629	86	3	=	=	SYM
ejpam-5629	86	4	2	2	NUM
ejpam-5629	86	5	,	,	PUNCT
ejpam-5629	86	6	ηj	ηj	ADP
ejpam-5629	86	7	=	=	SYM
ejpam-5629	86	8	3	3	NUM
ejpam-5629	86	9	,	,	PUNCT
ejpam-5629	86	10	γj	γj	ADP
ejpam-5629	86	11	=	=	SYM
ejpam-5629	86	12	1	1	NUM
ejpam-5629	86	13	,	,	PUNCT
ejpam-5629	86	14	for	for	ADP
ejpam-5629	86	15	j	j	PROPN
ejpam-5629	86	16	=	=	SYM
ejpam-5629	86	17	1	1	NUM
ejpam-5629	86	18	,	,	PUNCT
ejpam-5629	86	19	2	2	NUM
ejpam-5629	86	20	.	.	PUNCT
ejpam-5629	86	21	furthermore	furthermore	ADV
ejpam-5629	86	22	,	,	PUNCT
ejpam-5629	86	23	(	(	PUNCT
ejpam-5629	86	24	1	1	X
ejpam-5629	86	25	)	)	PUNCT
ejpam-5629	86	26	offers	offer	VERB
ejpam-5629	86	27	a	a	DET
ejpam-5629	86	28	powerful	powerful	ADJ
ejpam-5629	86	29	tool	tool	NOUN
ejpam-5629	86	30	for	for	ADP
ejpam-5629	86	31	more	more	ADJ
ejpam-5629	86	32	in	in	ADP
ejpam-5629	86	33	-	-	PUNCT
ejpam-5629	86	34	depth	depth	NOUN
ejpam-5629	86	35	and	and	CCONJ
ejpam-5629	86	36	accurate	accurate	ADJ
ejpam-5629	86	37	research	research	NOUN
ejpam-5629	86	38	on	on	ADP
ejpam-5629	86	39	a	a	DET
ejpam-5629	86	40	variety	variety	NOUN
ejpam-5629	86	41	of	of	ADP
ejpam-5629	86	42	physical	physical	ADJ
ejpam-5629	86	43	phenomena	phenomenon	NOUN
ejpam-5629	86	44	.	.	PUNCT
ejpam-5629	87	1	because	because	SCONJ
ejpam-5629	87	2	of	of	ADP
ejpam-5629	87	3	this	this	PRON
ejpam-5629	87	4	,	,	PUNCT
ejpam-5629	87	5	our	our	PRON
ejpam-5629	87	6	work	work	NOUN
ejpam-5629	87	7	is	be	AUX
ejpam-5629	87	8	conceptually	conceptually	ADV
ejpam-5629	87	9	stimulating	stimulate	VERB
ejpam-5629	87	10	as	as	ADV
ejpam-5629	87	11	well	well	ADV
ejpam-5629	87	12	as	as	ADP
ejpam-5629	87	13	practically	practically	ADV
ejpam-5629	87	14	important	important	ADJ
ejpam-5629	87	15	.	.	PUNCT
ejpam-5629	88	1	the	the	DET
ejpam-5629	88	2	tanh	tanh	PROPN
ejpam-5629	88	3	approach	approach	NOUN
ejpam-5629	88	4	[	[	X
ejpam-5629	88	5	15	15	NUM
ejpam-5629	88	6	,	,	PUNCT
ejpam-5629	88	7	16	16	NUM
ejpam-5629	88	8	]	]	PUNCT
ejpam-5629	88	9	will	will	AUX
ejpam-5629	88	10	be	be	AUX
ejpam-5629	88	11	applied	apply	VERB
ejpam-5629	88	12	in	in	ADP
ejpam-5629	88	13	the	the	DET
ejpam-5629	88	14	second	second	ADJ
ejpam-5629	88	15	section	section	NOUN
ejpam-5629	88	16	of	of	ADP
ejpam-5629	88	17	our	our	PRON
ejpam-5629	88	18	study	study	NOUN
ejpam-5629	88	19	to	to	PART
ejpam-5629	88	20	get	get	VERB
ejpam-5629	88	21	new	new	ADJ
ejpam-5629	88	22	traveling	travel	VERB
ejpam-5629	88	23	wave	wave	NOUN
ejpam-5629	88	24	solutions	solution	NOUN
ejpam-5629	88	25	for	for	ADP
ejpam-5629	88	26	the	the	DET
ejpam-5629	88	27	tripled	triple	VERB
ejpam-5629	88	28	beam	beam	NOUN
ejpam-5629	88	29	issue	issue	NOUN
ejpam-5629	88	30	with	with	ADP
ejpam-5629	88	31	generalized	generalized	ADJ
ejpam-5629	88	32	conformable	conformable	ADJ
ejpam-5629	88	33	fds	fds	NOUN
ejpam-5629	89	1	[	[	X
ejpam-5629	89	2	27	27	NUM
ejpam-5629	89	3	]	]	PUNCT
ejpam-5629	89	4	as	as	SCONJ
ejpam-5629	89	5	follows	follow	VERB
ejpam-5629	89	6	:	:	PUNCT
ejpam-5629	89	7	{	{	PUNCT
ejpam-5629	89	8	ℑ2η	ℑ2η	PROPN
ejpam-5629	89	9	s	s	PART
ejpam-5629	89	10	φ+	φ+	NOUN
ejpam-5629	89	11	ℑ4γ	ℑ4γ	PROPN
ejpam-5629	89	12	ζ	ζ	NOUN
ejpam-5629	89	13	φ+	φ+	PUNCT
ejpam-5629	89	14	⅁1k	⅁1k	NOUN
ejpam-5629	89	15	(	(	PUNCT
ejpam-5629	89	16	φ	φ	PROPN
ejpam-5629	89	17	,	,	PUNCT
ejpam-5629	89	18	ω	ω	PROPN
ejpam-5629	89	19	,	,	PUNCT
ejpam-5629	89	20	·	·	PUNCT
ejpam-5629	89	21	·	·	PUNCT
ejpam-5629	89	22	·	·	PUNCT
ejpam-5629	89	23	)	)	PUNCT
ejpam-5629	90	1	=	=	PUNCT
ejpam-5629	90	2	0	0	NUM
ejpam-5629	90	3	,	,	PUNCT
ejpam-5629	90	4	ℑ2η	ℑ2η	PROPN
ejpam-5629	90	5	s	s	PART
ejpam-5629	90	6	ω	ω	PROPN
ejpam-5629	90	7	+	+	PROPN
ejpam-5629	90	8	ℑ4γ	ℑ4γ	PROPN
ejpam-5629	90	9	ζ	ζ	PROPN
ejpam-5629	90	10	ω	ω	PROPN
ejpam-5629	90	11	+	+	CCONJ
ejpam-5629	90	12	⅁2n	⅁2n	PROPN
ejpam-5629	90	13	(	(	PUNCT
ejpam-5629	90	14	φ	φ	PROPN
ejpam-5629	90	15	,	,	PUNCT
ejpam-5629	90	16	ω	ω	PROPN
ejpam-5629	90	17	,	,	PUNCT
ejpam-5629	90	18	·	·	PUNCT
ejpam-5629	90	19	·	·	PUNCT
ejpam-5629	90	20	·	·	PUNCT
ejpam-5629	90	21	)	)	PUNCT
ejpam-5629	91	1	=	=	PUNCT
ejpam-5629	91	2	0	0	X
ejpam-5629	91	3	.	.	PUNCT
ejpam-5629	92	1	the	the	DET
ejpam-5629	92	2	relationship	relationship	NOUN
ejpam-5629	92	3	and	and	CCONJ
ejpam-5629	92	4	utility	utility	NOUN
ejpam-5629	92	5	of	of	ADP
ejpam-5629	92	6	fds	fds	NOUN
ejpam-5629	92	7	-	-	PUNCT
ejpam-5629	92	8	both	both	CCONJ
ejpam-5629	92	9	caputo	caputo	NOUN
ejpam-5629	92	10	and	and	CCONJ
ejpam-5629	92	11	conformable	conformable	NOUN
ejpam-5629	92	12	-	-	PUNCT
ejpam-5629	92	13	in	in	ADP
ejpam-5629	92	14	tackling	tackle	VERB
ejpam-5629	92	15	and	and	CCONJ
ejpam-5629	92	16	resolving	resolve	VERB
ejpam-5629	92	17	complex	complex	ADJ
ejpam-5629	92	18	mathematical	mathematical	ADJ
ejpam-5629	92	19	issues	issue	NOUN
ejpam-5629	92	20	are	be	AUX
ejpam-5629	92	21	illustrated	illustrate	VERB
ejpam-5629	92	22	via	via	ADP
ejpam-5629	92	23	the	the	DET
ejpam-5629	92	24	application	application	NOUN
ejpam-5629	92	25	of	of	ADP
ejpam-5629	92	26	fractional	fractional	ADJ
ejpam-5629	92	27	calculus	calculus	NOUN
ejpam-5629	92	28	to	to	PART
ejpam-5629	92	29	expand	expand	VERB
ejpam-5629	92	30	and	and	CCONJ
ejpam-5629	92	31	improve	improve	VERB
ejpam-5629	92	32	classical	classical	ADJ
ejpam-5629	92	33	models	model	NOUN
ejpam-5629	92	34	.	.	PUNCT
ejpam-5629	93	1	a	a	DET
ejpam-5629	93	2	range	range	NOUN
ejpam-5629	93	3	of	of	ADP
ejpam-5629	93	4	complex	complex	ADJ
ejpam-5629	93	5	systems	system	NOUN
ejpam-5629	93	6	can	can	AUX
ejpam-5629	93	7	be	be	AUX
ejpam-5629	93	8	studied	study	VERB
ejpam-5629	93	9	and	and	CCONJ
ejpam-5629	93	10	solved	solve	VERB
ejpam-5629	93	11	with	with	ADP
ejpam-5629	93	12	the	the	DET
ejpam-5629	93	13	help	help	NOUN
ejpam-5629	93	14	of	of	ADP
ejpam-5629	93	15	different	different	ADJ
ejpam-5629	93	16	fds	fds	NOUN
ejpam-5629	93	17	,	,	PUNCT
ejpam-5629	93	18	as	as	SCONJ
ejpam-5629	93	19	demonstrated	demonstrate	VERB
ejpam-5629	93	20	by	by	ADP
ejpam-5629	93	21	this	this	DET
ejpam-5629	93	22	cohesive	cohesive	ADJ
ejpam-5629	93	23	method	method	NOUN
ejpam-5629	93	24	.	.	PUNCT
ejpam-5629	94	1	the	the	DET
ejpam-5629	94	2	tanh	tanh	PROPN
ejpam-5629	94	3	method	method	NOUN
ejpam-5629	94	4	was	be	AUX
ejpam-5629	94	5	chosen	choose	VERB
ejpam-5629	94	6	because	because	SCONJ
ejpam-5629	94	7	it	it	PRON
ejpam-5629	94	8	is	be	AUX
ejpam-5629	94	9	generally	generally	ADV
ejpam-5629	94	10	less	less	ADV
ejpam-5629	94	11	computationally	computationally	ADV
ejpam-5629	94	12	demanding	demanding	ADJ
ejpam-5629	94	13	than	than	ADP
ejpam-5629	94	14	other	other	ADJ
ejpam-5629	94	15	approaches	approach	NOUN
ejpam-5629	94	16	,	,	PUNCT
ejpam-5629	94	17	and	and	CCONJ
ejpam-5629	94	18	it	it	PRON
ejpam-5629	94	19	is	be	AUX
ejpam-5629	94	20	also	also	ADV
ejpam-5629	94	21	very	very	ADV
ejpam-5629	94	22	simple	simple	ADJ
ejpam-5629	94	23	to	to	PART
ejpam-5629	94	24	apply	apply	VERB
ejpam-5629	94	25	.	.	PUNCT
ejpam-5629	95	1	because	because	SCONJ
ejpam-5629	95	2	of	of	ADP
ejpam-5629	95	3	this	this	PRON
ejpam-5629	95	4	,	,	PUNCT
ejpam-5629	95	5	it	it	PRON
ejpam-5629	95	6	’s	’	VERB
ejpam-5629	95	7	a	a	DET
ejpam-5629	95	8	useful	useful	ADJ
ejpam-5629	95	9	tool	tool	NOUN
ejpam-5629	95	10	for	for	ADP
ejpam-5629	95	11	problem	problem	NOUN
ejpam-5629	95	12	solving	solving	NOUN
ejpam-5629	95	13	.	.	PUNCT
ejpam-5629	96	1	it	it	PRON
ejpam-5629	96	2	also	also	ADV
ejpam-5629	96	3	offers	offer	VERB
ejpam-5629	96	4	explicit	explicit	ADJ
ejpam-5629	96	5	analytical	analytical	ADJ
ejpam-5629	96	6	solutions	solution	NOUN
ejpam-5629	96	7	,	,	PUNCT
ejpam-5629	96	8	which	which	PRON
ejpam-5629	96	9	are	be	AUX
ejpam-5629	96	10	helpful	helpful	ADJ
ejpam-5629	96	11	for	for	ADP
ejpam-5629	96	12	verifying	verify	VERB
ejpam-5629	96	13	numerical	numerical	ADJ
ejpam-5629	96	14	simulations	simulation	NOUN
ejpam-5629	96	15	and	and	CCONJ
ejpam-5629	96	16	comprehending	comprehend	VERB
ejpam-5629	96	17	the	the	DET
ejpam-5629	96	18	qualitative	qualitative	ADJ
ejpam-5629	96	19	behavior	behavior	NOUN
ejpam-5629	96	20	of	of	ADP
ejpam-5629	96	21	the	the	DET
ejpam-5629	96	22	solutions	solution	NOUN
ejpam-5629	96	23	.	.	PUNCT
ejpam-5629	97	1	the	the	DET
ejpam-5629	97	2	tanh	tanh	PROPN
ejpam-5629	97	3	technique	technique	NOUN
ejpam-5629	97	4	aids	aid	NOUN
ejpam-5629	97	5	in	in	ADP
ejpam-5629	97	6	understanding	understand	VERB
ejpam-5629	97	7	the	the	DET
ejpam-5629	97	8	physical	physical	ADJ
ejpam-5629	97	9	processes	process	NOUN
ejpam-5629	97	10	,	,	PUNCT
ejpam-5629	97	11	such	such	ADJ
ejpam-5629	97	12	as	as	ADP
ejpam-5629	97	13	wave	wave	NOUN
ejpam-5629	97	14	propagation	propagation	NOUN
ejpam-5629	97	15	,	,	PUNCT
ejpam-5629	97	16	solitons	soliton	NOUN
ejpam-5629	97	17	,	,	PUNCT
ejpam-5629	97	18	and	and	CCONJ
ejpam-5629	97	19	other	other	ADJ
ejpam-5629	97	20	localized	localized	ADJ
ejpam-5629	97	21	structures	structure	NOUN
ejpam-5629	97	22	,	,	PUNCT
ejpam-5629	97	23	represented	represent	VERB
ejpam-5629	97	24	by	by	ADP
ejpam-5629	97	25	the	the	DET
ejpam-5629	97	26	equations	equation	NOUN
ejpam-5629	97	27	by	by	ADP
ejpam-5629	97	28	providing	provide	VERB
ejpam-5629	97	29	correct	correct	ADJ
ejpam-5629	97	30	traveling	travel	VERB
ejpam-5629	97	31	wave	wave	NOUN
ejpam-5629	97	32	solutions	solution	NOUN
ejpam-5629	97	33	.	.	PUNCT
ejpam-5629	98	1	the	the	DET
ejpam-5629	98	2	tanh	tanh	PROPN
ejpam-5629	98	3	technique	technique	NOUN
ejpam-5629	98	4	is	be	AUX
ejpam-5629	98	5	a	a	DET
ejpam-5629	98	6	useful	useful	ADJ
ejpam-5629	98	7	tool	tool	NOUN
ejpam-5629	98	8	for	for	ADP
ejpam-5629	98	9	studying	study	VERB
ejpam-5629	98	10	traveling	travel	VERB
ejpam-5629	98	11	waves	wave	NOUN
ejpam-5629	98	12	in	in	ADP
ejpam-5629	98	13	nonlinear	nonlinear	ADJ
ejpam-5629	98	14	equations	equation	NOUN
ejpam-5629	98	15	because	because	SCONJ
ejpam-5629	98	16	of	of	ADP
ejpam-5629	98	17	these	these	DET
ejpam-5629	98	18	benefits	benefit	NOUN
ejpam-5629	98	19	.	.	PUNCT
ejpam-5629	99	1	to	to	PART
ejpam-5629	99	2	obtain	obtain	VERB
ejpam-5629	99	3	additional	additional	ADJ
ejpam-5629	99	4	information	information	NOUN
ejpam-5629	99	5	about	about	ADP
ejpam-5629	99	6	this	this	DET
ejpam-5629	99	7	approach	approach	NOUN
ejpam-5629	99	8	and	and	CCONJ
ejpam-5629	99	9	other	other	ADJ
ejpam-5629	99	10	significant	significant	ADJ
ejpam-5629	99	11	related	relate	VERB
ejpam-5629	99	12	methods	method	NOUN
ejpam-5629	99	13	,	,	PUNCT
ejpam-5629	99	14	see	see	VERB
ejpam-5629	99	15	articles	article	NOUN
ejpam-5629	99	16	[	[	X
ejpam-5629	99	17	33	33	NUM
ejpam-5629	99	18	,	,	PUNCT
ejpam-5629	99	19	35	35	NUM
ejpam-5629	99	20	,	,	PUNCT
ejpam-5629	99	21	44	44	NUM
ejpam-5629	99	22	]	]	PUNCT
ejpam-5629	99	23	.	.	PUNCT
ejpam-5629	100	1	the	the	DET
ejpam-5629	100	2	results	result	NOUN
ejpam-5629	100	3	of	of	ADP
ejpam-5629	100	4	this	this	DET
ejpam-5629	100	5	study	study	NOUN
ejpam-5629	100	6	have	have	VERB
ejpam-5629	100	7	significant	significant	ADJ
ejpam-5629	100	8	implications	implication	NOUN
ejpam-5629	100	9	for	for	ADP
ejpam-5629	100	10	engineering	engineering	NOUN
ejpam-5629	100	11	and	and	CCONJ
ejpam-5629	100	12	applied	applied	ADJ
ejpam-5629	100	13	physics	physic	NOUN
ejpam-5629	100	14	,	,	PUNCT
ejpam-5629	100	15	particularly	particularly	ADV
ejpam-5629	100	16	in	in	ADP
ejpam-5629	100	17	areas	area	NOUN
ejpam-5629	100	18	where	where	SCONJ
ejpam-5629	100	19	beam	beam	NOUN
ejpam-5629	100	20	deflection	deflection	NOUN
ejpam-5629	100	21	models	model	NOUN
ejpam-5629	100	22	with	with	ADP
ejpam-5629	100	23	fractional	fractional	ADJ
ejpam-5629	100	24	derivatives	derivative	NOUN
ejpam-5629	100	25	h.a	h.a	PROPN
ejpam-5629	100	26	.	.	PROPN
ejpam-5629	100	27	hammad	hammad	PROPN
ejpam-5629	100	28	,	,	PUNCT
ejpam-5629	100	29	m.e.m	m.e.m	NOUN
ejpam-5629	100	30	.	.	PUNCT
ejpam-5629	100	31	abdalla	abdalla	PROPN
ejpam-5629	100	32	/	/	SYM
ejpam-5629	100	33	eur	eur	PROPN
ejpam-5629	100	34	.	.	PUNCT
ejpam-5629	101	1	j.	j.	PROPN
ejpam-5629	101	2	pure	pure	PROPN
ejpam-5629	101	3	appl	appl	PROPN
ejpam-5629	101	4	.	.	PROPN
ejpam-5629	101	5	math	math	PROPN
ejpam-5629	101	6	,	,	PUNCT
ejpam-5629	101	7	18	18	NUM
ejpam-5629	101	8	(	(	PUNCT
ejpam-5629	101	9	1	1	NUM
ejpam-5629	101	10	)	)	PUNCT
ejpam-5629	101	11	(	(	PUNCT
ejpam-5629	101	12	2025	2025	NUM
ejpam-5629	101	13	)	)	PUNCT
ejpam-5629	101	14	,	,	PUNCT
ejpam-5629	101	15	5629	5629	NUM
ejpam-5629	101	16	5	5	NUM
ejpam-5629	101	17	of	of	ADP
ejpam-5629	101	18	20	20	NUM
ejpam-5629	101	19	could	could	AUX
ejpam-5629	101	20	offer	offer	VERB
ejpam-5629	101	21	a	a	DET
ejpam-5629	101	22	more	more	ADV
ejpam-5629	101	23	accurate	accurate	ADJ
ejpam-5629	101	24	and	and	CCONJ
ejpam-5629	101	25	comprehensive	comprehensive	ADJ
ejpam-5629	101	26	representation	representation	NOUN
ejpam-5629	101	27	of	of	ADP
ejpam-5629	101	28	real	real	ADJ
ejpam-5629	101	29	-	-	PUNCT
ejpam-5629	101	30	world	world	NOUN
ejpam-5629	101	31	phenomena	phenomenon	NOUN
ejpam-5629	101	32	.	.	PUNCT
ejpam-5629	102	1	by	by	ADP
ejpam-5629	102	2	considering	consider	VERB
ejpam-5629	102	3	the	the	DET
ejpam-5629	102	4	memory	memory	NOUN
ejpam-5629	102	5	and	and	CCONJ
ejpam-5629	102	6	hereditary	hereditary	ADJ
ejpam-5629	102	7	effects	effect	NOUN
ejpam-5629	102	8	inherent	inherent	ADJ
ejpam-5629	102	9	in	in	ADP
ejpam-5629	102	10	materials	material	NOUN
ejpam-5629	102	11	,	,	PUNCT
ejpam-5629	102	12	these	these	DET
ejpam-5629	102	13	models	model	NOUN
ejpam-5629	102	14	can	can	AUX
ejpam-5629	102	15	provide	provide	VERB
ejpam-5629	102	16	valuable	valuable	ADJ
ejpam-5629	102	17	insights	insight	NOUN
ejpam-5629	102	18	into	into	ADP
ejpam-5629	102	19	the	the	DET
ejpam-5629	102	20	long	long	ADJ
ejpam-5629	102	21	-	-	PUNCT
ejpam-5629	102	22	term	term	NOUN
ejpam-5629	102	23	behavior	behavior	NOUN
ejpam-5629	102	24	of	of	ADP
ejpam-5629	102	25	structures	structure	NOUN
ejpam-5629	102	26	and	and	CCONJ
ejpam-5629	102	27	systems	system	NOUN
ejpam-5629	102	28	.	.	PUNCT
ejpam-5629	103	1	this	this	PRON
ejpam-5629	103	2	could	could	AUX
ejpam-5629	103	3	lead	lead	VERB
ejpam-5629	103	4	to	to	ADP
ejpam-5629	103	5	improved	improved	ADJ
ejpam-5629	103	6	design	design	NOUN
ejpam-5629	103	7	and	and	CCONJ
ejpam-5629	103	8	analysis	analysis	NOUN
ejpam-5629	103	9	techniques	technique	NOUN
ejpam-5629	103	10	,	,	PUNCT
ejpam-5629	103	11	enabling	enable	VERB
ejpam-5629	103	12	engineers	engineer	NOUN
ejpam-5629	103	13	to	to	PART
ejpam-5629	103	14	develop	develop	VERB
ejpam-5629	103	15	more	more	ADV
ejpam-5629	103	16	reliable	reliable	ADJ
ejpam-5629	103	17	and	and	CCONJ
ejpam-5629	103	18	efficient	efficient	ADJ
ejpam-5629	103	19	structures	structure	NOUN
ejpam-5629	103	20	.	.	PUNCT
ejpam-5629	104	1	additionally	additionally	ADV
ejpam-5629	104	2	,	,	PUNCT
ejpam-5629	104	3	the	the	DET
ejpam-5629	104	4	application	application	NOUN
ejpam-5629	104	5	of	of	ADP
ejpam-5629	104	6	fractional	fractional	ADJ
ejpam-5629	104	7	calculus	calculus	NOUN
ejpam-5629	104	8	to	to	PART
ejpam-5629	104	9	beam	beam	VERB
ejpam-5629	104	10	deflection	deflection	NOUN
ejpam-5629	104	11	problems	problem	NOUN
ejpam-5629	104	12	can	can	AUX
ejpam-5629	104	13	contribute	contribute	VERB
ejpam-5629	104	14	to	to	ADP
ejpam-5629	104	15	advancements	advancement	NOUN
ejpam-5629	104	16	in	in	ADP
ejpam-5629	104	17	fields	field	NOUN
ejpam-5629	104	18	such	such	ADJ
ejpam-5629	104	19	as	as	ADP
ejpam-5629	104	20	vibration	vibration	NOUN
ejpam-5629	104	21	analysis	analysis	NOUN
ejpam-5629	104	22	,	,	PUNCT
ejpam-5629	104	23	control	control	NOUN
ejpam-5629	104	24	systems	system	NOUN
ejpam-5629	104	25	,	,	PUNCT
ejpam-5629	104	26	and	and	CCONJ
ejpam-5629	104	27	materials	material	NOUN
ejpam-5629	104	28	science	science	NOUN
ejpam-5629	104	29	,	,	PUNCT
ejpam-5629	104	30	ultimately	ultimately	ADV
ejpam-5629	104	31	leading	lead	VERB
ejpam-5629	104	32	to	to	ADP
ejpam-5629	104	33	innovative	innovative	ADJ
ejpam-5629	104	34	solutions	solution	NOUN
ejpam-5629	104	35	and	and	CCONJ
ejpam-5629	104	36	technological	technological	ADJ
ejpam-5629	104	37	breakthroughs	breakthrough	NOUN
ejpam-5629	104	38	.	.	PUNCT
ejpam-5629	105	1	2	2	X
ejpam-5629	105	2	.	.	X
ejpam-5629	105	3	basic	basic	ADJ
ejpam-5629	105	4	facts	fact	NOUN
ejpam-5629	105	5	this	this	DET
ejpam-5629	105	6	section	section	NOUN
ejpam-5629	105	7	is	be	AUX
ejpam-5629	105	8	devoted	devote	VERB
ejpam-5629	105	9	to	to	ADP
ejpam-5629	105	10	presenting	present	VERB
ejpam-5629	105	11	some	some	DET
ejpam-5629	105	12	definitions	definition	NOUN
ejpam-5629	105	13	and	and	CCONJ
ejpam-5629	105	14	lemmas	lemmas	PROPN
ejpam-5629	105	15	concerning	concern	VERB
ejpam-5629	105	16	the	the	DET
ejpam-5629	105	17	fc	fc	INTJ
ejpam-5629	105	18	.	.	PUNCT
ejpam-5629	106	1	we	we	PRON
ejpam-5629	106	2	can	can	AUX
ejpam-5629	106	3	find	find	VERB
ejpam-5629	106	4	these	these	DET
ejpam-5629	106	5	results	result	NOUN
ejpam-5629	106	6	in	in	ADP
ejpam-5629	106	7	[	[	X
ejpam-5629	106	8	12	12	NUM
ejpam-5629	106	9	,	,	PUNCT
ejpam-5629	106	10	28	28	NUM
ejpam-5629	106	11	]	]	PUNCT
ejpam-5629	106	12	.	.	PUNCT
ejpam-5629	107	1	definition	definition	NOUN
ejpam-5629	107	2	1	1	NUM
ejpam-5629	107	3	.	.	PUNCT
ejpam-5629	108	1	for	for	ADP
ejpam-5629	108	2	any	any	DET
ejpam-5629	108	3	function	function	NOUN
ejpam-5629	108	4	ϖ	ϖ	X
ejpam-5629	108	5	∈	∈	PROPN
ejpam-5629	108	6	c(v	c(v	PROPN
ejpam-5629	108	7	)	)	PUNCT
ejpam-5629	108	8	,	,	PUNCT
ejpam-5629	108	9	v	v	X
ejpam-5629	108	10	=	=	PUNCT
ejpam-5629	109	1	[	[	X
ejpam-5629	109	2	0	0	NUM
ejpam-5629	109	3	,	,	PUNCT
ejpam-5629	109	4	1	1	NUM
ejpam-5629	109	5	]	]	PUNCT
ejpam-5629	109	6	,	,	PUNCT
ejpam-5629	109	7	the	the	DET
ejpam-5629	109	8	fractional	fractional	ADJ
ejpam-5629	109	9	integral	integral	NOUN
ejpam-5629	109	10	of	of	ADP
ejpam-5629	109	11	order	order	NOUN
ejpam-5629	109	12	η	η	PROPN
ejpam-5629	109	13	is	be	AUX
ejpam-5629	109	14	described	describe	VERB
ejpam-5629	109	15	as	as	ADP
ejpam-5629	109	16	iηϖ	iηϖ	PROPN
ejpam-5629	109	17	(	(	PUNCT
ejpam-5629	109	18	s	s	X
ejpam-5629	109	19	)	)	PUNCT
ejpam-5629	109	20	=	=	SYM
ejpam-5629	109	21	1	1	NUM
ejpam-5629	109	22	γ	γ	X
ejpam-5629	109	23	(	(	PUNCT
ejpam-5629	109	24	η	η	PROPN
ejpam-5629	109	25	)	)	PUNCT
ejpam-5629	109	26	∫	∫	PROPN
ejpam-5629	109	27	s	s	PART
ejpam-5629	109	28	0	0	NUM
ejpam-5629	109	29	(	(	PUNCT
ejpam-5629	109	30	s−	s−	PROPN
ejpam-5629	109	31	r)η−1ϖ	r)η−1ϖ	PROPN
ejpam-5629	109	32	(	(	PUNCT
ejpam-5629	109	33	r	r	NOUN
ejpam-5629	109	34	)	)	PUNCT
ejpam-5629	109	35	dr	dr	PROPN
ejpam-5629	109	36	,	,	PUNCT
ejpam-5629	109	37	where	where	SCONJ
ejpam-5629	109	38	γ	γ	X
ejpam-5629	109	39	(	(	PUNCT
ejpam-5629	109	40	.	.	PUNCT
ejpam-5629	109	41	)	)	PUNCT
ejpam-5629	109	42	is	be	AUX
ejpam-5629	109	43	the	the	DET
ejpam-5629	109	44	euler	euler	PROPN
ejpam-5629	109	45	gamma	gamma	PROPN
ejpam-5629	109	46	function	function	PROPN
ejpam-5629	109	47	.	.	PUNCT
ejpam-5629	110	1	definition	definition	NOUN
ejpam-5629	110	2	2	2	NUM
ejpam-5629	110	3	.	.	PUNCT
ejpam-5629	110	4	for	for	ADP
ejpam-5629	110	5	the	the	DET
ejpam-5629	110	6	function	function	NOUN
ejpam-5629	110	7	ϖ	ϖ	X
ejpam-5629	110	8	∈	∈	PROPN
ejpam-5629	110	9	cm(v	cm(v	PUNCT
ejpam-5629	110	10	)	)	PUNCT
ejpam-5629	110	11	,	,	PUNCT
ejpam-5629	110	12	the	the	DET
ejpam-5629	110	13	cfd	cfd	NOUN
ejpam-5629	110	14	of	of	ADP
ejpam-5629	110	15	order	order	NOUN
ejpam-5629	110	16	η	η	PROPN
ejpam-5629	110	17	is	be	AUX
ejpam-5629	110	18	given	give	VERB
ejpam-5629	110	19	by	by	ADP
ejpam-5629	110	20	dηϖ	dηϖ	ADJ
ejpam-5629	110	21	(	(	PUNCT
ejpam-5629	110	22	s	s	NOUN
ejpam-5629	110	23	)	)	PUNCT
ejpam-5629	110	24	=	=	SYM
ejpam-5629	110	25	1	1	NUM
ejpam-5629	110	26	γ	γ	X
ejpam-5629	110	27	(	(	PUNCT
ejpam-5629	110	28	m−	m−	PROPN
ejpam-5629	110	29	η	η	PROPN
ejpam-5629	110	30	)	)	PUNCT
ejpam-5629	110	31	∫	∫	PROPN
ejpam-5629	110	32	s	s	PART
ejpam-5629	110	33	0	0	NUM
ejpam-5629	110	34	(	(	PUNCT
ejpam-5629	110	35	s−	s−	PROPN
ejpam-5629	110	36	r)m−η−1ϖ(m	r)m−η−1ϖ(m	PROPN
ejpam-5629	110	37	)	)	PUNCT
ejpam-5629	110	38	(	(	PUNCT
ejpam-5629	110	39	r	r	NOUN
ejpam-5629	110	40	)	)	PUNCT
ejpam-5629	110	41	dr	dr	PROPN
ejpam-5629	110	42	,	,	PUNCT
ejpam-5629	110	43	m	m	VERB
ejpam-5629	110	44	=	=	PUNCT
ejpam-5629	111	1	[	[	X
ejpam-5629	111	2	η	η	X
ejpam-5629	111	3	]	]	X
ejpam-5629	111	4	+	+	NOUN
ejpam-5629	111	5	1	1	NUM
ejpam-5629	111	6	,	,	PUNCT
ejpam-5629	111	7	where	where	SCONJ
ejpam-5629	111	8	[	[	X
ejpam-5629	111	9	η	η	X
ejpam-5629	111	10	]	]	X
ejpam-5629	111	11	represents	represent	VERB
ejpam-5629	111	12	the	the	DET
ejpam-5629	111	13	integer	integer	NOUN
ejpam-5629	111	14	part	part	NOUN
ejpam-5629	111	15	of	of	ADP
ejpam-5629	111	16	η	η	PROPN
ejpam-5629	111	17	.	.	PROPN
ejpam-5629	111	18	lemma	lemma	PROPN
ejpam-5629	111	19	1	1	NUM
ejpam-5629	111	20	.	.	PUNCT
ejpam-5629	112	1	[	[	X
ejpam-5629	112	2	28	28	NUM
ejpam-5629	112	3	]	]	PUNCT
ejpam-5629	112	4	assume	assume	VERB
ejpam-5629	112	5	that	that	SCONJ
ejpam-5629	112	6	η	η	PROPN
ejpam-5629	112	7	>	>	X
ejpam-5629	112	8	0	0	PROPN
ejpam-5629	112	9	,	,	PUNCT
ejpam-5629	112	10	the	the	DET
ejpam-5629	112	11	solution	solution	NOUN
ejpam-5629	112	12	of	of	ADP
ejpam-5629	112	13	the	the	DET
ejpam-5629	112	14	equation	equation	NOUN
ejpam-5629	112	15	dηϖ	dηϖ	ADJ
ejpam-5629	112	16	(	(	PUNCT
ejpam-5629	112	17	s	s	NOUN
ejpam-5629	112	18	)	)	PUNCT
ejpam-5629	112	19	=	=	SYM
ejpam-5629	112	20	0	0	NUM
ejpam-5629	112	21	,	,	PUNCT
ejpam-5629	112	22	s	s	VERB
ejpam-5629	112	23	∈	∈	NOUN
ejpam-5629	112	24	v	v	NOUN
ejpam-5629	112	25	is	be	AUX
ejpam-5629	112	26	written	write	VERB
ejpam-5629	112	27	as	as	ADP
ejpam-5629	112	28	ϖ	ϖ	PROPN
ejpam-5629	112	29	(	(	PUNCT
ejpam-5629	112	30	s	s	NOUN
ejpam-5629	112	31	)	)	PUNCT
ejpam-5629	113	1	=	=	SYM
ejpam-5629	113	2	k0	k0	PROPN
ejpam-5629	113	3	+	+	CCONJ
ejpam-5629	113	4	k1s+	k1s+	PROPN
ejpam-5629	113	5	k2s	k2s	NOUN
ejpam-5629	113	6	2	2	NUM
ejpam-5629	113	7	+	+	CCONJ
ejpam-5629	113	8	·	·	PUNCT
ejpam-5629	113	9	·	·	PUNCT
ejpam-5629	113	10	·	·	PUNCT
ejpam-5629	113	11	+	+	NUM
ejpam-5629	113	12	km−1s	km−1s	X
ejpam-5629	114	1	m−1	m−1	PROPN
ejpam-5629	114	2	,	,	PUNCT
ejpam-5629	114	3	where	where	SCONJ
ejpam-5629	114	4	kv	kv	PROPN
ejpam-5629	114	5	∈	∈	PROPN
ejpam-5629	114	6	r	r	PROPN
ejpam-5629	114	7	,	,	PUNCT
ejpam-5629	114	8	v	v	NOUN
ejpam-5629	114	9	=	=	SYM
ejpam-5629	114	10	0	0	NUM
ejpam-5629	114	11	,	,	PUNCT
ejpam-5629	114	12	1	1	NUM
ejpam-5629	114	13	,	,	PUNCT
ejpam-5629	114	14	2	2	NUM
ejpam-5629	114	15	,	,	PUNCT
ejpam-5629	114	16	·	·	PUNCT
ejpam-5629	114	17	·	·	PUNCT
ejpam-5629	114	18	·	·	PUNCT
ejpam-5629	114	19	,	,	PUNCT
ejpam-5629	114	20	m−	m−	PROPN
ejpam-5629	114	21	1	1	NUM
ejpam-5629	114	22	,	,	PUNCT
ejpam-5629	114	23	m	m	VERB
ejpam-5629	114	24	=	=	PUNCT
ejpam-5629	115	1	[	[	X
ejpam-5629	115	2	η	η	X
ejpam-5629	115	3	]	]	X
ejpam-5629	115	4	+	+	PROPN
ejpam-5629	115	5	1	1	X
ejpam-5629	115	6	.	.	X
ejpam-5629	116	1	lemma	lemma	PROPN
ejpam-5629	116	2	2	2	NUM
ejpam-5629	116	3	.	.	PUNCT
ejpam-5629	117	1	[	[	X
ejpam-5629	117	2	28	28	NUM
ejpam-5629	117	3	]	]	PUNCT
ejpam-5629	117	4	for	for	ADP
ejpam-5629	117	5	any	any	DET
ejpam-5629	117	6	η	η	PROPN
ejpam-5629	117	7	>	>	X
ejpam-5629	117	8	0	0	PROPN
ejpam-5629	117	9	,	,	PUNCT
ejpam-5629	117	10	we	we	PRON
ejpam-5629	117	11	have	have	VERB
ejpam-5629	117	12	iη	iη	VERB
ejpam-5629	117	13	0	0	NUM
ejpam-5629	117	14	+	+	NOUN
ejpam-5629	117	15	dηϖ	dηϖ	ADJ
ejpam-5629	117	16	(	(	PUNCT
ejpam-5629	117	17	s	s	NOUN
ejpam-5629	117	18	)	)	PUNCT
ejpam-5629	117	19	=	=	SYM
ejpam-5629	117	20	ϖ	ϖ	X
ejpam-5629	117	21	(	(	PUNCT
ejpam-5629	117	22	s	s	NOUN
ejpam-5629	117	23	)	)	PUNCT
ejpam-5629	117	24	+	+	CCONJ
ejpam-5629	117	25	k0	k0	PROPN
ejpam-5629	117	26	+	+	CCONJ
ejpam-5629	117	27	k1s+	k1s+	PROPN
ejpam-5629	117	28	k2s	k2s	NOUN
ejpam-5629	117	29	2	2	NUM
ejpam-5629	117	30	+	+	CCONJ
ejpam-5629	117	31	·	·	PUNCT
ejpam-5629	117	32	·	·	PUNCT
ejpam-5629	117	33	·	·	PUNCT
ejpam-5629	118	1	+	+	NUM
ejpam-5629	119	1	km−1s	km−1s	X
ejpam-5629	120	1	m−1	m−1	PROPN
ejpam-5629	120	2	,	,	PUNCT
ejpam-5629	120	3	where	where	SCONJ
ejpam-5629	120	4	kv	kv	PROPN
ejpam-5629	120	5	∈	∈	PROPN
ejpam-5629	120	6	r	r	PROPN
ejpam-5629	120	7	,	,	PUNCT
ejpam-5629	120	8	v	v	NOUN
ejpam-5629	120	9	=	=	SYM
ejpam-5629	120	10	0	0	NUM
ejpam-5629	120	11	,	,	PUNCT
ejpam-5629	120	12	1	1	NUM
ejpam-5629	120	13	,	,	PUNCT
ejpam-5629	120	14	2	2	NUM
ejpam-5629	120	15	,	,	PUNCT
ejpam-5629	120	16	·	·	PUNCT
ejpam-5629	120	17	·	·	PUNCT
ejpam-5629	120	18	·	·	PUNCT
ejpam-5629	120	19	,	,	PUNCT
ejpam-5629	120	20	m−	m−	PROPN
ejpam-5629	120	21	1	1	NUM
ejpam-5629	120	22	,	,	PUNCT
ejpam-5629	120	23	m	m	VERB
ejpam-5629	120	24	=	=	PUNCT
ejpam-5629	120	25	[	[	X
ejpam-5629	120	26	η	η	X
ejpam-5629	120	27	]	]	X
ejpam-5629	120	28	+	+	NOUN
ejpam-5629	120	29	1	1	X
ejpam-5629	120	30	.	.	X
ejpam-5629	120	31	remark	remark	NOUN
ejpam-5629	120	32	1	1	NUM
ejpam-5629	120	33	.	.	PUNCT
ejpam-5629	120	34	for	for	ADP
ejpam-5629	120	35	the	the	DET
ejpam-5629	120	36	function	function	NOUN
ejpam-5629	120	37	ϖ	ϖ	X
ejpam-5629	120	38	∈	∈	PROPN
ejpam-5629	120	39	c(v	c(v	PROPN
ejpam-5629	120	40	)	)	PUNCT
ejpam-5629	120	41	,	,	PUNCT
ejpam-5629	120	42	we	we	PRON
ejpam-5629	120	43	have	have	VERB
ejpam-5629	120	44	the	the	DET
ejpam-5629	120	45	following	follow	VERB
ejpam-5629	120	46	results	result	NOUN
ejpam-5629	120	47	:	:	PUNCT
ejpam-5629	120	48	(	(	PUNCT
ejpam-5629	120	49	i	i	NOUN
ejpam-5629	120	50	)	)	PUNCT
ejpam-5629	120	51	for	for	ADP
ejpam-5629	120	52	each	each	DET
ejpam-5629	120	53	η	η	PROPN
ejpam-5629	120	54	,	,	PUNCT
ejpam-5629	120	55	γ	γ	X
ejpam-5629	120	56	>	>	X
ejpam-5629	120	57	0	0	PUNCT
ejpam-5629	120	58	and	and	CCONJ
ejpam-5629	120	59	for	for	ADP
ejpam-5629	120	60	all	all	DET
ejpam-5629	120	61	s	s	PART
ejpam-5629	120	62	∈	∈	PROPN
ejpam-5629	120	63	v	v	NOUN
ejpam-5629	120	64	,	,	PUNCT
ejpam-5629	120	65	iηiγϖ	iηiγϖ	X
ejpam-5629	120	66	(	(	PUNCT
ejpam-5629	120	67	s	s	X
ejpam-5629	120	68	)	)	PUNCT
ejpam-5629	120	69	=	=	SYM
ejpam-5629	120	70	iη+γϖ	iη+γϖ	X
ejpam-5629	120	71	(	(	PUNCT
ejpam-5629	120	72	s	s	NOUN
ejpam-5629	120	73	)	)	PUNCT
ejpam-5629	120	74	;	;	PUNCT
ejpam-5629	120	75	(	(	PUNCT
ejpam-5629	120	76	ii	ii	NOUN
ejpam-5629	120	77	)	)	PUNCT
ejpam-5629	120	78	according	accord	VERB
ejpam-5629	120	79	to	to	ADP
ejpam-5629	120	80	definition	definition	NOUN
ejpam-5629	120	81	2	2	NUM
ejpam-5629	120	82	and	and	CCONJ
ejpam-5629	120	83	the	the	DET
ejpam-5629	120	84	property	property	NOUN
ejpam-5629	120	85	(	(	PUNCT
ejpam-5629	120	86	i	i	NOUN
ejpam-5629	120	87	)	)	PUNCT
ejpam-5629	120	88	,	,	PUNCT
ejpam-5629	120	89	if	if	SCONJ
ejpam-5629	120	90	0	0	NUM
ejpam-5629	120	91	<	<	X
ejpam-5629	120	92	η	η	PROPN
ejpam-5629	120	93	≤	≤	PROPN
ejpam-5629	120	94	γ	γ	X
ejpam-5629	120	95	,	,	PUNCT
ejpam-5629	120	96	we	we	PRON
ejpam-5629	120	97	get	get	AUX
ejpam-5629	120	98	dηiγϖ	dηiγϖ	NOUN
ejpam-5629	120	99	(	(	PUNCT
ejpam-5629	120	100	s	s	NOUN
ejpam-5629	120	101	)	)	PUNCT
ejpam-5629	120	102	=	=	SYM
ejpam-5629	120	103	iη−γϖ	iη−γϖ	X
ejpam-5629	120	104	(	(	PUNCT
ejpam-5629	120	105	s	s	NOUN
ejpam-5629	120	106	)	)	PUNCT
ejpam-5629	120	107	;	;	PUNCT
ejpam-5629	120	108	h.a	h.a	PROPN
ejpam-5629	120	109	.	.	PROPN
ejpam-5629	120	110	hammad	hammad	PROPN
ejpam-5629	120	111	,	,	PUNCT
ejpam-5629	120	112	m.e.m	m.e.m	NOUN
ejpam-5629	120	113	.	.	PUNCT
ejpam-5629	121	1	abdalla	abdalla	PROPN
ejpam-5629	121	2	/	/	SYM
ejpam-5629	121	3	eur	eur	PROPN
ejpam-5629	121	4	.	.	PUNCT
ejpam-5629	122	1	j.	j.	PROPN
ejpam-5629	122	2	pure	pure	PROPN
ejpam-5629	122	3	appl	appl	PROPN
ejpam-5629	122	4	.	.	PROPN
ejpam-5629	122	5	math	math	PROPN
ejpam-5629	122	6	,	,	PUNCT
ejpam-5629	122	7	18	18	NUM
ejpam-5629	122	8	(	(	PUNCT
ejpam-5629	122	9	1	1	NUM
ejpam-5629	122	10	)	)	PUNCT
ejpam-5629	122	11	(	(	PUNCT
ejpam-5629	122	12	2025	2025	NUM
ejpam-5629	122	13	)	)	PUNCT
ejpam-5629	122	14	,	,	PUNCT
ejpam-5629	122	15	5629	5629	NUM
ejpam-5629	122	16	6	6	NUM
ejpam-5629	122	17	of	of	ADP
ejpam-5629	122	18	20	20	NUM
ejpam-5629	122	19	(	(	PUNCT
ejpam-5629	122	20	iii	iii	NOUN
ejpam-5629	122	21	)	)	PUNCT
ejpam-5629	122	22	if	if	SCONJ
ejpam-5629	122	23	η	η	PROPN
ejpam-5629	122	24	=	=	PROPN
ejpam-5629	122	25	γ	γ	X
ejpam-5629	122	26	in	in	ADP
ejpam-5629	122	27	(	(	PUNCT
ejpam-5629	122	28	ii	ii	NOUN
ejpam-5629	122	29	)	)	PUNCT
ejpam-5629	122	30	,	,	PUNCT
ejpam-5629	122	31	we	we	PRON
ejpam-5629	122	32	have	have	AUX
ejpam-5629	122	33	dηiγϖ	dηiγϖ	NOUN
ejpam-5629	122	34	(	(	PUNCT
ejpam-5629	122	35	s	s	NOUN
ejpam-5629	122	36	)	)	PUNCT
ejpam-5629	122	37	=	=	SYM
ejpam-5629	123	1	ϖ	ϖ	X
ejpam-5629	123	2	(	(	PUNCT
ejpam-5629	123	3	s	s	NOUN
ejpam-5629	123	4	)	)	PUNCT
ejpam-5629	123	5	.	.	PUNCT
ejpam-5629	124	1	it	it	PRON
ejpam-5629	124	2	is	be	AUX
ejpam-5629	124	3	very	very	ADV
ejpam-5629	124	4	important	important	ADJ
ejpam-5629	124	5	to	to	PART
ejpam-5629	124	6	present	present	VERB
ejpam-5629	124	7	the	the	DET
ejpam-5629	124	8	equivalent	equivalent	ADJ
ejpam-5629	124	9	integral	integral	ADJ
ejpam-5629	124	10	eqution	eqution	NOUN
ejpam-5629	124	11	to	to	ADP
ejpam-5629	124	12	the	the	DET
ejpam-5629	124	13	problem	problem	NOUN
ejpam-5629	124	14	(	(	PUNCT
ejpam-5629	124	15	1	1	NUM
ejpam-5629	124	16	)	)	PUNCT
ejpam-5629	124	17	.	.	PUNCT
ejpam-5629	125	1	lemma	lemma	PROPN
ejpam-5629	125	2	3	3	X
ejpam-5629	125	3	.	.	PROPN
ejpam-5629	125	4	assume	assume	VERB
ejpam-5629	125	5	that	that	SCONJ
ejpam-5629	125	6	r1	r1	NOUN
ejpam-5629	125	7	,	,	PUNCT
ejpam-5629	125	8	r2	r2	PROPN
ejpam-5629	125	9	∈	∈	PROPN
ejpam-5629	125	10	c(v	c(v	PROPN
ejpam-5629	125	11	,	,	PUNCT
ejpam-5629	125	12	r	r	NOUN
ejpam-5629	125	13	)	)	PUNCT
ejpam-5629	125	14	,	,	PUNCT
ejpam-5629	125	15	ηj	ηj	ADP
ejpam-5629	125	16	∈	∈	PROPN
ejpam-5629	125	17	(	(	PUNCT
ejpam-5629	125	18	2	2	NUM
ejpam-5629	125	19	,	,	PUNCT
ejpam-5629	125	20	3	3	NUM
ejpam-5629	125	21	]	]	PUNCT
ejpam-5629	125	22	,	,	PUNCT
ejpam-5629	125	23	γj	γj	ADP
ejpam-5629	125	24	∈	∈	PROPN
ejpam-5629	125	25	(	(	PUNCT
ejpam-5629	125	26	0	0	NUM
ejpam-5629	125	27	,	,	PUNCT
ejpam-5629	125	28	1	1	NUM
ejpam-5629	125	29	]	]	PUNCT
ejpam-5629	125	30	,	,	PUNCT
ejpam-5629	125	31	and	and	CCONJ
ejpam-5629	125	32	⅁j	⅁j	NOUN
ejpam-5629	125	33	>	>	X
ejpam-5629	125	34	0	0	PROPN
ejpam-5629	125	35	,	,	PUNCT
ejpam-5629	125	36	j	j	X
ejpam-5629	125	37	=	=	NOUN
ejpam-5629	125	38	1.2	1.2	NUM
ejpam-5629	125	39	.	.	PUNCT
ejpam-5629	126	1	the	the	DET
ejpam-5629	126	2	problem	problem	NOUN
ejpam-5629	126	3	{	{	PUNCT
ejpam-5629	126	4	dη1dγ1φ1(ζ	dη1dγ1φ1(ζ	NOUN
ejpam-5629	126	5	)	)	PUNCT
ejpam-5629	126	6	=	=	SYM
ejpam-5629	127	1	⅁1r1	⅁1r1	ADJ
ejpam-5629	127	2	(	(	PUNCT
ejpam-5629	127	3	ζ	ζ	NOUN
ejpam-5629	127	4	)	)	PUNCT
ejpam-5629	127	5	,	,	PUNCT
ejpam-5629	127	6	dη2dγ2φ2(ζ	dη2dγ2φ2(ζ	NOUN
ejpam-5629	127	7	)	)	PUNCT
ejpam-5629	128	1	=	=	VERB
ejpam-5629	128	2	⅁2r2	⅁2r2	ADJ
ejpam-5629	128	3	(	(	PUNCT
ejpam-5629	128	4	ζ	ζ	NOUN
ejpam-5629	128	5	)	)	PUNCT
ejpam-5629	128	6	,	,	PUNCT
ejpam-5629	128	7	(	(	PUNCT
ejpam-5629	128	8	3	3	X
ejpam-5629	128	9	)	)	PUNCT
ejpam-5629	128	10	via	via	ADP
ejpam-5629	128	11	the	the	DET
ejpam-5629	128	12	conditions	condition	NOUN
ejpam-5629	128	13	{	{	PUNCT
ejpam-5629	128	14	φj(0	φj(0	NOUN
ejpam-5629	128	15	)	)	PUNCT
ejpam-5629	128	16	=	=	PUNCT
ejpam-5629	128	17	φj(1	φj(1	NUM
ejpam-5629	128	18	)	)	PUNCT
ejpam-5629	128	19	=	=	PUNCT
ejpam-5629	128	20	bj	bj	ADP
ejpam-5629	128	21	∈	∈	NOUN
ejpam-5629	128	22	r	r	NOUN
ejpam-5629	128	23	,	,	PUNCT
ejpam-5629	128	24	dλjφj(0	dλjφj(0	PROPN
ejpam-5629	128	25	)	)	PUNCT
ejpam-5629	128	26	=	=	SYM
ejpam-5629	128	27	dλjφj(1	dλjφj(1	NOUN
ejpam-5629	128	28	)	)	PUNCT
ejpam-5629	128	29	=	=	SYM
ejpam-5629	128	30	0	0	NUM
ejpam-5629	128	31	,	,	PUNCT
ejpam-5629	128	32	is	be	AUX
ejpam-5629	128	33	equivalent	equivalent	ADJ
ejpam-5629	128	34	to	to	PUNCT
ejpam-5629	129	1	φ1(ζ	φ1(ζ	NOUN
ejpam-5629	129	2	)	)	PUNCT
ejpam-5629	129	3	=	=	SYM
ejpam-5629	129	4	b1	b1	NOUN
ejpam-5629	129	5	+	+	CCONJ
ejpam-5629	129	6	⅁1i	⅁1i	ADJ
ejpam-5629	129	7	η1+γ1r1	η1+γ1r1	NOUN
ejpam-5629	129	8	(	(	PUNCT
ejpam-5629	129	9	ζ	ζ	NOUN
ejpam-5629	129	10	)	)	PUNCT
ejpam-5629	129	11	+	+	CCONJ
ejpam-5629	129	12	(	(	PUNCT
ejpam-5629	129	13	2⅁1	2⅁1	NOUN
ejpam-5629	129	14	γ1γ(η1	γ1γ(η1	PROPN
ejpam-5629	129	15	)	)	PUNCT
ejpam-5629	129	16	∫	∫	PROPN
ejpam-5629	130	1	1	1	NUM
ejpam-5629	130	2	0	0	NUM
ejpam-5629	130	3	(	(	PUNCT
ejpam-5629	130	4	1−	1−	NUM
ejpam-5629	130	5	r)η1−1r1	r)η1−1r1	NOUN
ejpam-5629	130	6	(	(	PUNCT
ejpam-5629	130	7	r	r	NOUN
ejpam-5629	130	8	)	)	PUNCT
ejpam-5629	130	9	dr	dr	NOUN
ejpam-5629	130	10	−	−	PROPN
ejpam-5629	130	11	⅁1γ(γ1	⅁1γ(γ1	VERB
ejpam-5629	130	12	+	+	NOUN
ejpam-5629	130	13	3	3	NUM
ejpam-5629	130	14	)	)	PUNCT
ejpam-5629	130	15	γ1γ(η1+γ1	γ1γ(η1+γ1	NUM
ejpam-5629	130	16	)	)	PUNCT
ejpam-5629	130	17	∫	∫	PROPN
ejpam-5629	131	1	1	1	NUM
ejpam-5629	131	2	0	0	NUM
ejpam-5629	131	3	(	(	PUNCT
ejpam-5629	131	4	1−	1−	NUM
ejpam-5629	131	5	r)η1+γ1−1r1	r)η1+γ1−1r1	NOUN
ejpam-5629	131	6	(	(	PUNCT
ejpam-5629	131	7	r	r	NOUN
ejpam-5629	131	8	)	)	PUNCT
ejpam-5629	131	9	dr	dr	PROPN
ejpam-5629	131	10	)	)	PUNCT
ejpam-5629	131	11	ζγ1	ζγ1	PROPN
ejpam-5629	131	12	+	+	PROPN
ejpam-5629	131	13	1	1	NUM
ejpam-5629	131	14	+	+	CCONJ
ejpam-5629	131	15	(	(	PUNCT
ejpam-5629	131	16	⅁1γ(γ1	⅁1γ(γ1	VERB
ejpam-5629	131	17	+	+	NOUN
ejpam-5629	131	18	3	3	NUM
ejpam-5629	131	19	)	)	PUNCT
ejpam-5629	131	20	γ1γ(η1+γ1	γ1γ(η1+γ1	NUM
ejpam-5629	131	21	)	)	PUNCT
ejpam-5629	131	22	∫	∫	PROPN
ejpam-5629	132	1	1	1	NUM
ejpam-5629	132	2	0	0	NUM
ejpam-5629	132	3	(	(	PUNCT
ejpam-5629	132	4	1−	1−	NUM
ejpam-5629	132	5	r)η1+γ1−1r1	r)η1+γ1−1r1	NOUN
ejpam-5629	132	6	(	(	PUNCT
ejpam-5629	132	7	r	r	NOUN
ejpam-5629	132	8	)	)	PUNCT
ejpam-5629	132	9	dr	dr	PROPN
ejpam-5629	132	10	−	−	PROPN
ejpam-5629	132	11	⅁1(γ1	⅁1(γ1	NOUN
ejpam-5629	132	12	+	+	ADJ
ejpam-5629	132	13	2	2	NUM
ejpam-5629	132	14	)	)	PUNCT
ejpam-5629	132	15	γ1γ(η1	γ1γ(η1	PROPN
ejpam-5629	132	16	)	)	PUNCT
ejpam-5629	132	17	∫	∫	PROPN
ejpam-5629	133	1	1	1	NUM
ejpam-5629	133	2	0	0	NUM
ejpam-5629	133	3	(	(	PUNCT
ejpam-5629	133	4	1−	1−	NUM
ejpam-5629	133	5	r)η1−1r1	r)η1−1r1	NOUN
ejpam-5629	133	6	(	(	PUNCT
ejpam-5629	133	7	r	r	NOUN
ejpam-5629	133	8	)	)	PUNCT
ejpam-5629	133	9	dr	dr	PROPN
ejpam-5629	133	10	)	)	PUNCT
ejpam-5629	133	11	ζγ1	ζγ1	PROPN
ejpam-5629	133	12	+	+	PROPN
ejpam-5629	133	13	2	2	NUM
ejpam-5629	133	14	,	,	PUNCT
ejpam-5629	133	15	φ2(ζ	φ2(ζ	PRON
ejpam-5629	133	16	)	)	PUNCT
ejpam-5629	133	17	=	=	SYM
ejpam-5629	133	18	b2	b2	NOUN
ejpam-5629	133	19	+	+	CCONJ
ejpam-5629	133	20	⅁2i	⅁2i	NOUN
ejpam-5629	133	21	η2+γ2r2	η2+γ2r2	ADP
ejpam-5629	133	22	(	(	PUNCT
ejpam-5629	133	23	ζ	ζ	NOUN
ejpam-5629	133	24	)	)	PUNCT
ejpam-5629	133	25	+	+	CCONJ
ejpam-5629	133	26	(	(	PUNCT
ejpam-5629	133	27	2⅁2	2⅁2	NUM
ejpam-5629	133	28	γ2γ(η2	γ2γ(η2	PROPN
ejpam-5629	133	29	)	)	PUNCT
ejpam-5629	133	30	∫	∫	PROPN
ejpam-5629	134	1	1	1	NUM
ejpam-5629	134	2	0	0	NUM
ejpam-5629	134	3	(	(	PUNCT
ejpam-5629	134	4	1−	1−	NUM
ejpam-5629	134	5	r)η2−1r2	r)η2−1r2	NOUN
ejpam-5629	134	6	(	(	PUNCT
ejpam-5629	134	7	r	r	NOUN
ejpam-5629	134	8	)	)	PUNCT
ejpam-5629	134	9	dr	dr	PROPN
ejpam-5629	134	10	−	−	PROPN
ejpam-5629	134	11	⅁2γ(γ2	⅁2γ(γ2	NOUN
ejpam-5629	134	12	+	+	NOUN
ejpam-5629	134	13	3	3	NUM
ejpam-5629	134	14	)	)	PUNCT
ejpam-5629	134	15	γ2γ(η2+γ2	γ2γ(η2+γ2	PROPN
ejpam-5629	134	16	)	)	PUNCT
ejpam-5629	134	17	∫	∫	PROPN
ejpam-5629	135	1	1	1	NUM
ejpam-5629	135	2	0	0	NUM
ejpam-5629	135	3	(	(	PUNCT
ejpam-5629	135	4	1−	1−	NUM
ejpam-5629	135	5	r)η2+γ2−1r2	r)η2+γ2−1r2	ADJ
ejpam-5629	135	6	(	(	PUNCT
ejpam-5629	135	7	r	r	NOUN
ejpam-5629	135	8	)	)	PUNCT
ejpam-5629	135	9	dr	dr	PROPN
ejpam-5629	135	10	)	)	PUNCT
ejpam-5629	135	11	ζγ2	ζγ2	PROPN
ejpam-5629	136	1	+	+	PROPN
ejpam-5629	136	2	1	1	NUM
ejpam-5629	136	3	+	+	CCONJ
ejpam-5629	136	4	(	(	PUNCT
ejpam-5629	136	5	⅁2γ(γ2	⅁2γ(γ2	NOUN
ejpam-5629	136	6	+	+	NOUN
ejpam-5629	136	7	3	3	NUM
ejpam-5629	136	8	)	)	PUNCT
ejpam-5629	136	9	γ2γ(η2+γ2	γ2γ(η2+γ2	PROPN
ejpam-5629	136	10	)	)	PUNCT
ejpam-5629	136	11	∫	∫	PROPN
ejpam-5629	136	12	1	1	NUM
ejpam-5629	136	13	0	0	NUM
ejpam-5629	136	14	(	(	PUNCT
ejpam-5629	136	15	1−	1−	NUM
ejpam-5629	136	16	r)η2+γ2−1r2	r)η2+γ2−1r2	ADJ
ejpam-5629	136	17	(	(	PUNCT
ejpam-5629	136	18	r	r	NOUN
ejpam-5629	136	19	)	)	PUNCT
ejpam-5629	136	20	dr	dr	PROPN
ejpam-5629	136	21	−	−	PROPN
ejpam-5629	136	22	⅁2(γ2	⅁2(γ2	PROPN
ejpam-5629	136	23	+	+	PROPN
ejpam-5629	136	24	2	2	NUM
ejpam-5629	136	25	)	)	PUNCT
ejpam-5629	136	26	γ2γ(η2	γ2γ(η2	PROPN
ejpam-5629	136	27	)	)	PUNCT
ejpam-5629	136	28	∫	∫	PROPN
ejpam-5629	137	1	1	1	NUM
ejpam-5629	137	2	0	0	NUM
ejpam-5629	137	3	(	(	PUNCT
ejpam-5629	137	4	1−	1−	NUM
ejpam-5629	137	5	r)η2−1r2	r)η2−1r2	NOUN
ejpam-5629	137	6	(	(	PUNCT
ejpam-5629	137	7	r	r	NOUN
ejpam-5629	137	8	)	)	PUNCT
ejpam-5629	137	9	dr	dr	PROPN
ejpam-5629	137	10	)	)	PUNCT
ejpam-5629	137	11	ζγ2	ζγ2	PROPN
ejpam-5629	137	12	+	+	PROPN
ejpam-5629	137	13	2	2	NUM
ejpam-5629	137	14	.	.	PUNCT
ejpam-5629	137	15	(	(	PUNCT
ejpam-5629	137	16	4	4	X
ejpam-5629	137	17	)	)	PUNCT
ejpam-5629	137	18	proof	proof	NOUN
ejpam-5629	137	19	.	.	PUNCT
ejpam-5629	138	1	applying	apply	VERB
ejpam-5629	138	2	iηj+γj	iηj+γj	NOUN
ejpam-5629	138	3	,	,	PUNCT
ejpam-5629	138	4	(	(	PUNCT
ejpam-5629	138	5	j	j	NOUN
ejpam-5629	138	6	=	=	SYM
ejpam-5629	138	7	1	1	NUM
ejpam-5629	138	8	,	,	PUNCT
ejpam-5629	138	9	2	2	NUM
ejpam-5629	138	10	)	)	PUNCT
ejpam-5629	138	11	on	on	ADP
ejpam-5629	138	12	(	(	PUNCT
ejpam-5629	138	13	3	3	NUM
ejpam-5629	138	14	)	)	PUNCT
ejpam-5629	138	15	and	and	CCONJ
ejpam-5629	138	16	using	use	VERB
ejpam-5629	138	17	lemma	lemma	PROPN
ejpam-5629	138	18	2	2	NUM
ejpam-5629	138	19	,	,	PUNCT
ejpam-5629	138	20	we	we	PRON
ejpam-5629	138	21	have	have	VERB
ejpam-5629	138	22	{	{	PUNCT
ejpam-5629	138	23	φ1(ζ	φ1(ζ	NOUN
ejpam-5629	138	24	)	)	PUNCT
ejpam-5629	138	25	=	=	SYM
ejpam-5629	138	26	⅁1i	⅁1i	ADJ
ejpam-5629	138	27	η1+γ1r1	η1+γ1r1	PROPN
ejpam-5629	138	28	(	(	PUNCT
ejpam-5629	138	29	ζ	ζ	NOUN
ejpam-5629	138	30	)	)	PUNCT
ejpam-5629	138	31	+	+	CCONJ
ejpam-5629	138	32	k0ζγ1	k0ζγ1	PROPN
ejpam-5629	138	33	γ(γ1	γ(γ1	NOUN
ejpam-5629	138	34	+	+	NOUN
ejpam-5629	138	35	1	1	NUM
ejpam-5629	138	36	)	)	PUNCT
ejpam-5629	138	37	+	+	CCONJ
ejpam-5629	139	1	k1ζγ1	k1ζγ1	NOUN
ejpam-5629	139	2	+	+	ADJ
ejpam-5629	139	3	1	1	NUM
ejpam-5629	139	4	γ(γ1	γ(γ1	NOUN
ejpam-5629	139	5	+	+	NOUN
ejpam-5629	139	6	2	2	NUM
ejpam-5629	139	7	)	)	PUNCT
ejpam-5629	139	8	+	+	CCONJ
ejpam-5629	139	9	k2ζγ1	k2ζγ1	ADJ
ejpam-5629	139	10	+	+	ADJ
ejpam-5629	139	11	2	2	NUM
ejpam-5629	139	12	γ(γ1	γ(γ1	NOUN
ejpam-5629	139	13	+	+	NOUN
ejpam-5629	139	14	3	3	NUM
ejpam-5629	139	15	)	)	PUNCT
ejpam-5629	139	16	+	+	CCONJ
ejpam-5629	139	17	k3	k3	ADJ
ejpam-5629	139	18	,	,	PUNCT
ejpam-5629	139	19	φ2(ζ	φ2(ζ	X
ejpam-5629	139	20	)	)	PUNCT
ejpam-5629	139	21	=	=	VERB
ejpam-5629	140	1	⅁2i	⅁2i	NOUN
ejpam-5629	140	2	η2+γ2r2	η2+γ2r2	ADP
ejpam-5629	140	3	(	(	PUNCT
ejpam-5629	140	4	ζ	ζ	NOUN
ejpam-5629	140	5	)	)	PUNCT
ejpam-5629	140	6	+	+	CCONJ
ejpam-5629	140	7	c0ζγ2	c0ζγ2	ADJ
ejpam-5629	140	8	γ(γ2	γ(γ2	NOUN
ejpam-5629	140	9	+	+	PROPN
ejpam-5629	140	10	1	1	NUM
ejpam-5629	140	11	)	)	PUNCT
ejpam-5629	140	12	+	+	CCONJ
ejpam-5629	140	13	c1ζγ2	c1ζγ2	ADJ
ejpam-5629	140	14	+	+	NOUN
ejpam-5629	140	15	1	1	NUM
ejpam-5629	140	16	γ(γ2	γ(γ2	NOUN
ejpam-5629	140	17	+	+	ADJ
ejpam-5629	140	18	2	2	NUM
ejpam-5629	140	19	)	)	PUNCT
ejpam-5629	140	20	+	+	NUM
ejpam-5629	140	21	c2ζγ2	c2ζγ2	ADJ
ejpam-5629	140	22	+	+	ADJ
ejpam-5629	140	23	2	2	NUM
ejpam-5629	140	24	γ(γ2	γ(γ2	NOUN
ejpam-5629	140	25	+	+	NOUN
ejpam-5629	140	26	3	3	NUM
ejpam-5629	140	27	)	)	PUNCT
ejpam-5629	140	28	+	+	CCONJ
ejpam-5629	140	29	c3	c3	PROPN
ejpam-5629	140	30	.	.	PUNCT
ejpam-5629	141	1	(	(	PUNCT
ejpam-5629	141	2	5	5	NUM
ejpam-5629	141	3	)	)	PUNCT
ejpam-5629	141	4	because	because	SCONJ
ejpam-5629	141	5	φj(0	φj(0	PROPN
ejpam-5629	141	6	)	)	PUNCT
ejpam-5629	141	7	=	=	PUNCT
ejpam-5629	141	8	bj	bj	NOUN
ejpam-5629	141	9	(	(	PUNCT
ejpam-5629	141	10	j	j	NOUN
ejpam-5629	141	11	=	=	SYM
ejpam-5629	141	12	1	1	NUM
ejpam-5629	141	13	,	,	PUNCT
ejpam-5629	141	14	2	2	NUM
ejpam-5629	141	15	)	)	PUNCT
ejpam-5629	141	16	,	,	PUNCT
ejpam-5629	141	17	we	we	PRON
ejpam-5629	141	18	conclude	conclude	VERB
ejpam-5629	141	19	that	that	SCONJ
ejpam-5629	141	20	k3	k3	PROPN
ejpam-5629	141	21	=	=	PUNCT
ejpam-5629	141	22	b1	b1	NOUN
ejpam-5629	141	23	,	,	PUNCT
ejpam-5629	141	24	and	and	CCONJ
ejpam-5629	141	25	c3	c3	PROPN
ejpam-5629	141	26	=	=	PROPN
ejpam-5629	141	27	b2	b2	PROPN
ejpam-5629	141	28	.	.	PUNCT
ejpam-5629	142	1	applying	apply	VERB
ejpam-5629	142	2	dγj	dγj	NOUN
ejpam-5629	142	3	(	(	PUNCT
ejpam-5629	142	4	j	j	NOUN
ejpam-5629	142	5	=	=	SYM
ejpam-5629	142	6	1	1	NUM
ejpam-5629	142	7	,	,	PUNCT
ejpam-5629	142	8	2	2	NUM
ejpam-5629	142	9	)	)	PUNCT
ejpam-5629	142	10	on	on	ADP
ejpam-5629	142	11	(	(	PUNCT
ejpam-5629	142	12	5	5	NUM
ejpam-5629	142	13	)	)	PUNCT
ejpam-5629	142	14	,	,	PUNCT
ejpam-5629	142	15	we	we	PRON
ejpam-5629	142	16	get	get	VERB
ejpam-5629	142	17	{	{	PUNCT
ejpam-5629	142	18	dγ1φ1(ζ	dγ1φ1(ζ	NOUN
ejpam-5629	142	19	)	)	PUNCT
ejpam-5629	142	20	=	=	SYM
ejpam-5629	142	21	⅁1	⅁1	PROPN
ejpam-5629	142	22	γ(η1	γ(η1	ADV
ejpam-5629	142	23	)	)	PUNCT
ejpam-5629	143	1	∫	∫	PROPN
ejpam-5629	144	1	ζ	ζ	NOUN
ejpam-5629	144	2	0	0	NUM
ejpam-5629	145	1	(	(	PUNCT
ejpam-5629	145	2	ζ	ζ	NOUN
ejpam-5629	145	3	−	−	PROPN
ejpam-5629	145	4	r)η1−1r1	r)η1−1r1	NOUN
ejpam-5629	145	5	(	(	PUNCT
ejpam-5629	145	6	r	r	NOUN
ejpam-5629	145	7	)	)	PUNCT
ejpam-5629	145	8	dr	dr	PROPN
ejpam-5629	145	9	+	+	PROPN
ejpam-5629	145	10	k0	k0	PROPN
ejpam-5629	145	11	+	+	CCONJ
ejpam-5629	145	12	k1ζ	k1ζ	NOUN
ejpam-5629	145	13	+	+	CCONJ
ejpam-5629	145	14	k2ζ	k2ζ	PROPN
ejpam-5629	145	15	2	2	NUM
ejpam-5629	145	16	,	,	PUNCT
ejpam-5629	145	17	dγ2φ2(ζ	dγ2φ2(ζ	NOUN
ejpam-5629	145	18	)	)	PUNCT
ejpam-5629	145	19	=	=	SYM
ejpam-5629	145	20	⅁2	⅁2	PROPN
ejpam-5629	145	21	γ(η2	γ(η2	NOUN
ejpam-5629	145	22	)	)	PUNCT
ejpam-5629	145	23	∫	∫	PROPN
ejpam-5629	146	1	ζ	ζ	NOUN
ejpam-5629	146	2	0	0	NUM
ejpam-5629	146	3	(	(	PUNCT
ejpam-5629	146	4	ζ	ζ	NOUN
ejpam-5629	146	5	−	−	PROPN
ejpam-5629	146	6	r)η2−1r2	r)η2−1r2	NOUN
ejpam-5629	146	7	(	(	PUNCT
ejpam-5629	146	8	r	r	NOUN
ejpam-5629	146	9	)	)	PUNCT
ejpam-5629	146	10	dr	dr	PROPN
ejpam-5629	146	11	+	+	PROPN
ejpam-5629	146	12	c0	c0	PROPN
ejpam-5629	146	13	+	+	CCONJ
ejpam-5629	146	14	c1ζ	c1ζ	PROPN
ejpam-5629	147	1	+	+	CCONJ
ejpam-5629	147	2	c2ζ	c2ζ	NOUN
ejpam-5629	147	3	2	2	X
ejpam-5629	147	4	.	.	PUNCT
ejpam-5629	147	5	(	(	PUNCT
ejpam-5629	147	6	6	6	X
ejpam-5629	147	7	)	)	PUNCT
ejpam-5629	147	8	letting	let	VERB
ejpam-5629	147	9	ζ	ζ	NOUN
ejpam-5629	147	10	=	=	SYM
ejpam-5629	147	11	0	0	NUM
ejpam-5629	147	12	in	in	ADP
ejpam-5629	147	13	(	(	PUNCT
ejpam-5629	147	14	5	5	NUM
ejpam-5629	147	15	)	)	PUNCT
ejpam-5629	147	16	,	,	PUNCT
ejpam-5629	147	17	we	we	PRON
ejpam-5629	147	18	have	have	VERB
ejpam-5629	147	19	k0	k0	PROPN
ejpam-5629	147	20	=	=	PROPN
ejpam-5629	147	21	c0	c0	PROPN
ejpam-5629	147	22	=	=	SYM
ejpam-5629	147	23	0	0	X
ejpam-5629	147	24	.	.	PUNCT
ejpam-5629	148	1	taking	take	VERB
ejpam-5629	148	2	ζ	ζ	NOUN
ejpam-5629	148	3	=	=	SYM
ejpam-5629	148	4	1	1	NUM
ejpam-5629	148	5	in	in	ADP
ejpam-5629	148	6	(	(	PUNCT
ejpam-5629	148	7	5	5	NUM
ejpam-5629	148	8	)	)	PUNCT
ejpam-5629	148	9	and	and	CCONJ
ejpam-5629	148	10	(	(	PUNCT
ejpam-5629	148	11	6	6	NUM
ejpam-5629	148	12	)	)	PUNCT
ejpam-5629	148	13	,	,	PUNCT
ejpam-5629	148	14	we	we	PRON
ejpam-5629	148	15	obtain	obtain	VERB
ejpam-5629	148	16	that	that	PROPN
ejpam-5629	148	17	⅁1	⅁1	PROPN
ejpam-5629	148	18	γ(η1+γ1	γ(η1+γ1	VERB
ejpam-5629	148	19	)	)	PUNCT
ejpam-5629	148	20	∫	∫	PROPN
ejpam-5629	149	1	1	1	NUM
ejpam-5629	149	2	0	0	NUM
ejpam-5629	149	3	(	(	PUNCT
ejpam-5629	149	4	1−	1−	NUM
ejpam-5629	149	5	r)η1+γ1−1r1	r)η1+γ1−1r1	NOUN
ejpam-5629	149	6	(	(	PUNCT
ejpam-5629	149	7	r	r	NOUN
ejpam-5629	149	8	)	)	PUNCT
ejpam-5629	149	9	dr	dr	PROPN
ejpam-5629	149	10	+	+	PROPN
ejpam-5629	149	11	k1	k1	NOUN
ejpam-5629	149	12	γ(γ1	γ(γ1	NOUN
ejpam-5629	149	13	+	+	NOUN
ejpam-5629	149	14	2	2	NUM
ejpam-5629	149	15	)	)	PUNCT
ejpam-5629	149	16	+	+	NUM
ejpam-5629	149	17	2k2	2k2	NUM
ejpam-5629	149	18	γ(γ1	γ(γ1	NOUN
ejpam-5629	149	19	+	+	NOUN
ejpam-5629	149	20	3	3	NUM
ejpam-5629	149	21	)	)	PUNCT
ejpam-5629	149	22	=	=	SYM
ejpam-5629	149	23	0	0	NUM
ejpam-5629	149	24	,	,	PUNCT
ejpam-5629	149	25	⅁1	⅁1	PROPN
ejpam-5629	149	26	γ(η1	γ(η1	ADV
ejpam-5629	149	27	)	)	PUNCT
ejpam-5629	149	28	∫	∫	PROPN
ejpam-5629	150	1	1	1	NUM
ejpam-5629	150	2	0	0	NUM
ejpam-5629	150	3	(	(	PUNCT
ejpam-5629	150	4	1−	1−	NUM
ejpam-5629	150	5	r)η1−1r1	r)η1−1r1	NOUN
ejpam-5629	150	6	(	(	PUNCT
ejpam-5629	150	7	r	r	NOUN
ejpam-5629	150	8	)	)	PUNCT
ejpam-5629	150	9	dr	dr	PROPN
ejpam-5629	150	10	+	+	PROPN
ejpam-5629	150	11	k1	k1	PROPN
ejpam-5629	150	12	+	+	CCONJ
ejpam-5629	150	13	k2	k2	NOUN
ejpam-5629	150	14	=	=	SYM
ejpam-5629	150	15	0	0	NUM
ejpam-5629	150	16	,	,	PUNCT
ejpam-5629	150	17	⅁2	⅁2	VERB
ejpam-5629	150	18	γ(η2+γ2	γ(η2+γ2	PROPN
ejpam-5629	150	19	)	)	PUNCT
ejpam-5629	150	20	∫	∫	PROPN
ejpam-5629	150	21	1	1	NUM
ejpam-5629	150	22	0	0	NUM
ejpam-5629	150	23	(	(	PUNCT
ejpam-5629	150	24	1−	1−	NUM
ejpam-5629	150	25	r)η2+γ2−1r2	r)η2+γ2−1r2	ADJ
ejpam-5629	150	26	(	(	PUNCT
ejpam-5629	150	27	r	r	NOUN
ejpam-5629	150	28	)	)	PUNCT
ejpam-5629	150	29	dr	dr	PROPN
ejpam-5629	150	30	+	+	PROPN
ejpam-5629	150	31	c1	c1	PROPN
ejpam-5629	150	32	γ(γ2	γ(γ2	NOUN
ejpam-5629	150	33	+	+	PROPN
ejpam-5629	150	34	2	2	NUM
ejpam-5629	150	35	)	)	PUNCT
ejpam-5629	150	36	+	+	NUM
ejpam-5629	150	37	2c2	2c2	NUM
ejpam-5629	150	38	γ(γ2	γ(γ2	NOUN
ejpam-5629	150	39	+	+	NOUN
ejpam-5629	150	40	3	3	NUM
ejpam-5629	150	41	)	)	PUNCT
ejpam-5629	150	42	=	=	SYM
ejpam-5629	150	43	0	0	NUM
ejpam-5629	150	44	,	,	PUNCT
ejpam-5629	150	45	⅁2	⅁2	ADP
ejpam-5629	150	46	γ(η2	γ(η2	NOUN
ejpam-5629	150	47	)	)	PUNCT
ejpam-5629	150	48	∫	∫	PROPN
ejpam-5629	151	1	1	1	NUM
ejpam-5629	151	2	0	0	NUM
ejpam-5629	151	3	(	(	PUNCT
ejpam-5629	151	4	1−	1−	NUM
ejpam-5629	151	5	r)η2−1r2	r)η2−1r2	NOUN
ejpam-5629	151	6	(	(	PUNCT
ejpam-5629	151	7	r	r	NOUN
ejpam-5629	151	8	)	)	PUNCT
ejpam-5629	151	9	dr	dr	PROPN
ejpam-5629	151	10	+	+	PROPN
ejpam-5629	151	11	c1	c1	PROPN
ejpam-5629	151	12	+	+	CCONJ
ejpam-5629	151	13	c2	c2	PROPN
ejpam-5629	151	14	=	=	PUNCT
ejpam-5629	151	15	0	0	PROPN
ejpam-5629	151	16	.	.	PUNCT
ejpam-5629	152	1	after	after	ADP
ejpam-5629	152	2	solving	solve	VERB
ejpam-5629	152	3	the	the	DET
ejpam-5629	152	4	above	above	ADJ
ejpam-5629	152	5	equations	equation	NOUN
ejpam-5629	152	6	,	,	PUNCT
ejpam-5629	152	7	we	we	PRON
ejpam-5629	152	8	have	have	PROPN
ejpam-5629	152	9	k1	k1	NOUN
ejpam-5629	152	10	=	=	SYM
ejpam-5629	152	11	−	−	NOUN
ejpam-5629	152	12	⅁1γ(γ1	⅁1γ(γ1	VERB
ejpam-5629	152	13	+	+	NOUN
ejpam-5629	152	14	3	3	NUM
ejpam-5629	152	15	)	)	PUNCT
ejpam-5629	152	16	γ1γ(η1+γ1	γ1γ(η1+γ1	NUM
ejpam-5629	152	17	)	)	PUNCT
ejpam-5629	152	18	∫	∫	PROPN
ejpam-5629	153	1	1	1	NUM
ejpam-5629	153	2	0	0	NUM
ejpam-5629	153	3	(	(	PUNCT
ejpam-5629	153	4	1−	1−	NUM
ejpam-5629	153	5	r)η1+γ1−1r1	r)η1+γ1−1r1	NOUN
ejpam-5629	153	6	(	(	PUNCT
ejpam-5629	153	7	r	r	NOUN
ejpam-5629	153	8	)	)	PUNCT
ejpam-5629	153	9	dr	dr	PROPN
ejpam-5629	153	10	+	+	PROPN
ejpam-5629	153	11	2⅁1	2⅁1	PROPN
ejpam-5629	153	12	γ1γ(η1	γ1γ(η1	PUNCT
ejpam-5629	153	13	)	)	PUNCT
ejpam-5629	153	14	∫	∫	PROPN
ejpam-5629	154	1	1	1	NUM
ejpam-5629	154	2	0	0	NUM
ejpam-5629	154	3	(	(	PUNCT
ejpam-5629	154	4	1−	1−	NUM
ejpam-5629	154	5	r)η1−1r1	r)η1−1r1	NOUN
ejpam-5629	154	6	(	(	PUNCT
ejpam-5629	154	7	r	r	NOUN
ejpam-5629	154	8	)	)	PUNCT
ejpam-5629	154	9	dr	dr	PROPN
ejpam-5629	154	10	,	,	PUNCT
ejpam-5629	154	11	k2	k2	PROPN
ejpam-5629	154	12	=	=	PUNCT
ejpam-5629	154	13	⅁1γ(γ1	⅁1γ(γ1	VERB
ejpam-5629	154	14	+	+	NOUN
ejpam-5629	154	15	3	3	NUM
ejpam-5629	154	16	)	)	PUNCT
ejpam-5629	154	17	γ1γ(η1+γ1	γ1γ(η1+γ1	NUM
ejpam-5629	154	18	)	)	PUNCT
ejpam-5629	154	19	∫	∫	PROPN
ejpam-5629	155	1	1	1	NUM
ejpam-5629	155	2	0	0	NUM
ejpam-5629	155	3	(	(	PUNCT
ejpam-5629	155	4	1−	1−	NUM
ejpam-5629	155	5	r)η1+γ1−1r1	r)η1+γ1−1r1	NOUN
ejpam-5629	155	6	(	(	PUNCT
ejpam-5629	155	7	r	r	NOUN
ejpam-5629	155	8	)	)	PUNCT
ejpam-5629	155	9	dr	dr	PROPN
ejpam-5629	155	10	−	−	PROPN
ejpam-5629	155	11	⅁1(γ1	⅁1(γ1	NOUN
ejpam-5629	155	12	+	+	ADJ
ejpam-5629	155	13	2	2	NUM
ejpam-5629	155	14	)	)	PUNCT
ejpam-5629	155	15	γ1γ(η1	γ1γ(η1	PROPN
ejpam-5629	155	16	)	)	PUNCT
ejpam-5629	155	17	∫	∫	PROPN
ejpam-5629	156	1	1	1	NUM
ejpam-5629	156	2	0	0	NUM
ejpam-5629	156	3	(	(	PUNCT
ejpam-5629	156	4	1−	1−	NUM
ejpam-5629	156	5	r)η1−1r1	r)η1−1r1	NOUN
ejpam-5629	156	6	(	(	PUNCT
ejpam-5629	156	7	r	r	NOUN
ejpam-5629	156	8	)	)	PUNCT
ejpam-5629	156	9	dr	dr	PROPN
ejpam-5629	156	10	,	,	PUNCT
ejpam-5629	156	11	c1	c1	NOUN
ejpam-5629	156	12	=	=	PUNCT
ejpam-5629	156	13	−	−	PROPN
ejpam-5629	156	14	⅁2γ(γ2	⅁2γ(γ2	NOUN
ejpam-5629	156	15	+	+	NOUN
ejpam-5629	156	16	3	3	NUM
ejpam-5629	156	17	)	)	PUNCT
ejpam-5629	156	18	γ2γ(η2+γ2	γ2γ(η2+γ2	PROPN
ejpam-5629	156	19	)	)	PUNCT
ejpam-5629	156	20	∫	∫	PROPN
ejpam-5629	157	1	1	1	NUM
ejpam-5629	157	2	0	0	NUM
ejpam-5629	157	3	(	(	PUNCT
ejpam-5629	157	4	1−	1−	NUM
ejpam-5629	157	5	r)η2+γ2−1r2	r)η2+γ2−1r2	ADJ
ejpam-5629	157	6	(	(	PUNCT
ejpam-5629	157	7	r	r	NOUN
ejpam-5629	157	8	)	)	PUNCT
ejpam-5629	157	9	dr	dr	PROPN
ejpam-5629	157	10	+	+	PROPN
ejpam-5629	157	11	2⅁2	2⅁2	NUM
ejpam-5629	157	12	γ2γ(η2	γ2γ(η2	NUM
ejpam-5629	157	13	)	)	PUNCT
ejpam-5629	157	14	∫	∫	PROPN
ejpam-5629	158	1	1	1	NUM
ejpam-5629	158	2	0	0	NUM
ejpam-5629	158	3	(	(	PUNCT
ejpam-5629	158	4	1−	1−	NUM
ejpam-5629	158	5	r)η2−1r2	r)η2−1r2	NOUN
ejpam-5629	158	6	(	(	PUNCT
ejpam-5629	158	7	r	r	NOUN
ejpam-5629	158	8	)	)	PUNCT
ejpam-5629	158	9	dr	dr	PROPN
ejpam-5629	158	10	,	,	PUNCT
ejpam-5629	158	11	c2	c2	PROPN
ejpam-5629	158	12	=	=	PUNCT
ejpam-5629	158	13	⅁2γ(γ2	⅁2γ(γ2	PROPN
ejpam-5629	158	14	+	+	NOUN
ejpam-5629	158	15	3	3	NUM
ejpam-5629	158	16	)	)	PUNCT
ejpam-5629	158	17	γ2γ(η2+γ2	γ2γ(η2+γ2	PROPN
ejpam-5629	158	18	)	)	PUNCT
ejpam-5629	158	19	∫	∫	PROPN
ejpam-5629	159	1	1	1	NUM
ejpam-5629	159	2	0	0	NUM
ejpam-5629	159	3	(	(	PUNCT
ejpam-5629	159	4	1−	1−	NUM
ejpam-5629	159	5	r)η2+γ2−1r2	r)η2+γ2−1r2	ADJ
ejpam-5629	159	6	(	(	PUNCT
ejpam-5629	159	7	r	r	NOUN
ejpam-5629	159	8	)	)	PUNCT
ejpam-5629	159	9	dr	dr	PROPN
ejpam-5629	159	10	−	−	PROPN
ejpam-5629	159	11	⅁2(γ2	⅁2(γ2	PROPN
ejpam-5629	159	12	+	+	PROPN
ejpam-5629	159	13	2	2	NUM
ejpam-5629	159	14	)	)	PUNCT
ejpam-5629	159	15	γ2γ(η2	γ2γ(η2	PROPN
ejpam-5629	159	16	)	)	PUNCT
ejpam-5629	159	17	∫	∫	PROPN
ejpam-5629	159	18	1	1	NUM
ejpam-5629	159	19	0	0	NUM
ejpam-5629	159	20	(	(	PUNCT
ejpam-5629	159	21	1−	1−	NUM
ejpam-5629	159	22	r)η2−1r2	r)η2−1r2	NOUN
ejpam-5629	159	23	(	(	PUNCT
ejpam-5629	159	24	r	r	NOUN
ejpam-5629	159	25	)	)	PUNCT
ejpam-5629	159	26	dr	dr	PROPN
ejpam-5629	159	27	.	.	PROPN
ejpam-5629	159	28	h.a	h.a	PROPN
ejpam-5629	159	29	.	.	PROPN
ejpam-5629	159	30	hammad	hammad	PROPN
ejpam-5629	159	31	,	,	PUNCT
ejpam-5629	159	32	m.e.m	m.e.m	NOUN
ejpam-5629	159	33	.	.	PUNCT
ejpam-5629	160	1	abdalla	abdalla	PROPN
ejpam-5629	160	2	/	/	SYM
ejpam-5629	160	3	eur	eur	PROPN
ejpam-5629	160	4	.	.	PUNCT
ejpam-5629	161	1	j.	j.	PROPN
ejpam-5629	161	2	pure	pure	PROPN
ejpam-5629	161	3	appl	appl	PROPN
ejpam-5629	161	4	.	.	PROPN
ejpam-5629	161	5	math	math	PROPN
ejpam-5629	161	6	,	,	PUNCT
ejpam-5629	161	7	18	18	NUM
ejpam-5629	161	8	(	(	PUNCT
ejpam-5629	161	9	1	1	NUM
ejpam-5629	161	10	)	)	PUNCT
ejpam-5629	161	11	(	(	PUNCT
ejpam-5629	161	12	2025	2025	NUM
ejpam-5629	161	13	)	)	PUNCT
ejpam-5629	161	14	,	,	PUNCT
ejpam-5629	161	15	5629	5629	NUM
ejpam-5629	161	16	7	7	NUM
ejpam-5629	161	17	of	of	ADP
ejpam-5629	161	18	20	20	NUM
ejpam-5629	161	19	substituting	substitute	VERB
ejpam-5629	161	20	from	from	ADP
ejpam-5629	161	21	the	the	DET
ejpam-5629	161	22	values	value	NOUN
ejpam-5629	161	23	of	of	ADP
ejpam-5629	161	24	kj	kj	PROPN
ejpam-5629	161	25	and	and	CCONJ
ejpam-5629	161	26	cj	cj	PROPN
ejpam-5629	162	1	(	(	PUNCT
ejpam-5629	162	2	j	j	NOUN
ejpam-5629	162	3	=	=	SYM
ejpam-5629	162	4	1	1	NUM
ejpam-5629	162	5	,	,	PUNCT
ejpam-5629	162	6	2	2	NUM
ejpam-5629	162	7	)	)	PUNCT
ejpam-5629	162	8	in	in	ADP
ejpam-5629	162	9	(	(	PUNCT
ejpam-5629	162	10	5	5	NUM
ejpam-5629	162	11	)	)	PUNCT
ejpam-5629	162	12	,	,	PUNCT
ejpam-5629	162	13	we	we	PRON
ejpam-5629	162	14	get	get	VERB
ejpam-5629	162	15	(	(	PUNCT
ejpam-5629	162	16	4	4	NUM
ejpam-5629	162	17	)	)	PUNCT
ejpam-5629	162	18	.	.	PUNCT
ejpam-5629	163	1	3	3	X
ejpam-5629	163	2	.	.	X
ejpam-5629	163	3	fixed	fix	VERB
ejpam-5629	163	4	point	point	NOUN
ejpam-5629	163	5	approaches	approach	NOUN
ejpam-5629	163	6	in	in	ADP
ejpam-5629	163	7	this	this	DET
ejpam-5629	163	8	section	section	NOUN
ejpam-5629	163	9	,	,	PUNCT
ejpam-5629	163	10	we	we	PRON
ejpam-5629	163	11	illustrate	illustrate	VERB
ejpam-5629	163	12	that	that	SCONJ
ejpam-5629	163	13	the	the	DET
ejpam-5629	163	14	mechanism	mechanism	NOUN
ejpam-5629	163	15	of	of	ADP
ejpam-5629	163	16	the	the	DET
ejpam-5629	163	17	fp	fp	NOUN
ejpam-5629	163	18	for	for	ADP
ejpam-5629	163	19	discussing	discuss	VERB
ejpam-5629	163	20	the	the	DET
ejpam-5629	163	21	existence	existence	NOUN
ejpam-5629	163	22	of	of	ADP
ejpam-5629	163	23	the	the	DET
ejpam-5629	163	24	solution	solution	NOUN
ejpam-5629	163	25	of	of	ADP
ejpam-5629	163	26	our	our	PRON
ejpam-5629	163	27	problem	problem	NOUN
ejpam-5629	163	28	.	.	PUNCT
ejpam-5629	164	1	we	we	PRON
ejpam-5629	164	2	define	define	VERB
ejpam-5629	164	3	the	the	DET
ejpam-5629	164	4	banach	banach	NOUN
ejpam-5629	164	5	space	space	NOUN
ejpam-5629	164	6	(	(	PUNCT
ejpam-5629	164	7	bs	bs	NOUN
ejpam-5629	164	8	)	)	PUNCT
ejpam-5629	164	9	ξ	ξ	NOUN
ejpam-5629	164	10	=	=	SYM
ejpam-5629	164	11	{	{	PUNCT
ejpam-5629	164	12	φ	φ	PROPN
ejpam-5629	164	13	∈	∈	PROPN
ejpam-5629	164	14	c	c	X
ejpam-5629	164	15	(	(	PUNCT
ejpam-5629	164	16	v	v	NOUN
ejpam-5629	164	17	,	,	PUNCT
ejpam-5629	164	18	r	r	NOUN
ejpam-5629	164	19	)	)	PUNCT
ejpam-5629	164	20	,	,	PUNCT
ejpam-5629	164	21	dρ−1φ	dρ−1φ	PROPN
ejpam-5629	164	22	∈	∈	PROPN
ejpam-5629	164	23	c	c	X
ejpam-5629	164	24	(	(	PUNCT
ejpam-5629	164	25	v	v	NOUN
ejpam-5629	164	26	,	,	PUNCT
ejpam-5629	164	27	r	r	NOUN
ejpam-5629	164	28	)	)	PUNCT
ejpam-5629	164	29	,	,	PUNCT
ejpam-5629	164	30	and	and	CCONJ
ejpam-5629	164	31	dρφ	dρφ	PROPN
ejpam-5629	164	32	∈	∈	PROPN
ejpam-5629	164	33	c	c	X
ejpam-5629	164	34	(	(	PUNCT
ejpam-5629	164	35	v	v	NOUN
ejpam-5629	164	36	,	,	PUNCT
ejpam-5629	164	37	r	r	NOUN
ejpam-5629	164	38	)	)	PUNCT
ejpam-5629	164	39	}	}	PUNCT
ejpam-5629	164	40	under	under	ADP
ejpam-5629	164	41	the	the	DET
ejpam-5629	164	42	norm	norm	NOUN
ejpam-5629	164	43	∥φ∥ξ	∥φ∥ξ	NOUN
ejpam-5629	164	44	=	=	PUNCT
ejpam-5629	164	45	∥φ∥∞	∥φ∥∞	PRON
ejpam-5629	164	46	+	+	NUM
ejpam-5629	164	47	∥∥dρ−1φ	∥∥dρ−1φ	X
ejpam-5629	164	48	∥∥	∥∥	X
ejpam-5629	164	49	∞	∞	NUM
ejpam-5629	164	50	+	+	CCONJ
ejpam-5629	164	51	∥dρφ∥∞	∥dρφ∥∞	PUNCT
ejpam-5629	164	52	,	,	PUNCT
ejpam-5629	164	53	where	where	SCONJ
ejpam-5629	164	54	∥φ∥∞	∥φ∥∞	ADV
ejpam-5629	164	55	=	=	SYM
ejpam-5629	164	56	sup	sup	NOUN
ejpam-5629	164	57	ζ∈v	ζ∈v	ADJ
ejpam-5629	164	58	|φ(ζ)|	|φ(ζ)|	PROPN
ejpam-5629	164	59	,	,	PUNCT
ejpam-5629	164	60	∥∥dρ−1φ	∥∥dρ−1φ	X
ejpam-5629	164	61	∥∥	∥∥	X
ejpam-5629	164	62	∞	∞	NUM
ejpam-5629	164	63	=	=	SYM
ejpam-5629	164	64	sup	sup	NOUN
ejpam-5629	164	65	ζ∈v	ζ∈v	PROPN
ejpam-5629	164	66	∣∣dρ−1φ(ζ	∣∣dρ−1φ(ζ	NUM
ejpam-5629	164	67	)	)	PUNCT
ejpam-5629	164	68	∣∣	∣∣	NUM
ejpam-5629	164	69	,	,	PUNCT
ejpam-5629	164	70	and	and	CCONJ
ejpam-5629	164	71	∥dρφ∥∞	∥dρφ∥∞	X
ejpam-5629	164	72	=	=	SYM
ejpam-5629	164	73	sup	sup	NUM
ejpam-5629	164	74	ζ∈v	ζ∈v	PROPN
ejpam-5629	164	75	|dρφ(ζ)|	|dρφ(ζ)|	NOUN
ejpam-5629	164	76	,	,	PUNCT
ejpam-5629	164	77	v	v	NOUN
ejpam-5629	164	78	=	=	PUNCT
ejpam-5629	165	1	[	[	X
ejpam-5629	165	2	0	0	NUM
ejpam-5629	165	3	,	,	PUNCT
ejpam-5629	165	4	1	1	NUM
ejpam-5629	165	5	]	]	PUNCT
ejpam-5629	165	6	.	.	PUNCT
ejpam-5629	166	1	consider	consider	VERB
ejpam-5629	166	2	the	the	DET
ejpam-5629	166	3	product	product	NOUN
ejpam-5629	166	4	space	space	NOUN
ejpam-5629	166	5	ξ×	ξ×	PROPN
ejpam-5629	166	6	ξ	ξ	PROPN
ejpam-5629	166	7	defined	define	VERB
ejpam-5629	166	8	on	on	ADP
ejpam-5629	166	9	the	the	DET
ejpam-5629	166	10	norm	norm	NOUN
ejpam-5629	166	11	∥(φ	∥(φ	NOUN
ejpam-5629	166	12	,	,	PUNCT
ejpam-5629	166	13	ω)∥ξ×ξ	ω)∥ξ×ξ	ADV
ejpam-5629	166	14	=	=	PUNCT
ejpam-5629	166	15	∥φ∥ξ	∥φ∥ξ	NOUN
ejpam-5629	166	16	+	+	CCONJ
ejpam-5629	166	17	∥ω∥ξ	∥ω∥ξ	ADJ
ejpam-5629	166	18	.	.	PUNCT
ejpam-5629	167	1	clearly	clearly	ADV
ejpam-5629	167	2	,	,	PUNCT
ejpam-5629	167	3	the	the	DET
ejpam-5629	167	4	pair	pair	NOUN
ejpam-5629	167	5	(	(	PUNCT
ejpam-5629	167	6	ξ×	ξ×	PROPN
ejpam-5629	167	7	ξ	ξ	PROPN
ejpam-5629	167	8	,	,	PUNCT
ejpam-5629	167	9	∥.∥	∥.∥	NUM
ejpam-5629	167	10	)	)	PUNCT
ejpam-5629	167	11	is	be	AUX
ejpam-5629	167	12	a	a	DET
ejpam-5629	167	13	bs	bs	NOUN
ejpam-5629	167	14	.	.	PUNCT
ejpam-5629	168	1	now	now	ADV
ejpam-5629	168	2	,	,	PUNCT
ejpam-5629	168	3	in	in	ADP
ejpam-5629	168	4	order	order	NOUN
ejpam-5629	168	5	to	to	PART
ejpam-5629	168	6	apply	apply	VERB
ejpam-5629	168	7	the	the	DET
ejpam-5629	168	8	technique	technique	NOUN
ejpam-5629	168	9	of	of	ADP
ejpam-5629	168	10	the	the	DET
ejpam-5629	168	11	fp	fp	NOUN
ejpam-5629	168	12	,	,	PUNCT
ejpam-5629	168	13	we	we	PRON
ejpam-5629	168	14	consider	consider	VERB
ejpam-5629	168	15	the	the	DET
ejpam-5629	168	16	operator	operator	NOUN
ejpam-5629	168	17	℧	℧	PROPN
ejpam-5629	168	18	=	=	SYM
ejpam-5629	168	19	(	(	PUNCT
ejpam-5629	168	20	℧	℧	PROPN
ejpam-5629	168	21	1,	1,	NUM
ejpam-5629	168	22	℧	℧	SYM
ejpam-5629	168	23	2	2	NUM
ejpam-5629	168	24	)	)	PUNCT
ejpam-5629	168	25	such	such	ADJ
ejpam-5629	168	26	that	that	PRON
ejpam-5629	168	27	℧	℧	PROPN
ejpam-5629	168	28	:	:	PUNCT
ejpam-5629	168	29	ξ×	ξ×	PROPN
ejpam-5629	168	30	ξ	ξ	PROPN
ejpam-5629	168	31	→	→	SYM
ejpam-5629	168	32	ξ×	ξ×	PROPN
ejpam-5629	168	33	ξ	ξ	PROPN
ejpam-5629	168	34	.	.	PUNCT
ejpam-5629	169	1	this	this	DET
ejpam-5629	169	2	operator	operator	NOUN
ejpam-5629	169	3	can	can	AUX
ejpam-5629	169	4	be	be	AUX
ejpam-5629	169	5	written	write	VERB
ejpam-5629	169	6	as	as	ADP
ejpam-5629	169	7	℧	℧	PROPN
ejpam-5629	169	8	(	(	PUNCT
ejpam-5629	169	9	φ(ζ	φ(ζ	NOUN
ejpam-5629	169	10	)	)	PUNCT
ejpam-5629	169	11	,	,	PUNCT
ejpam-5629	169	12	ω(ζ	ω(ζ	NOUN
ejpam-5629	169	13	)	)	PUNCT
ejpam-5629	169	14	)	)	PUNCT
ejpam-5629	170	1	=	=	PUNCT
ejpam-5629	170	2	℧	℧	PROPN
ejpam-5629	170	3	1	1	NUM
ejpam-5629	170	4	(	(	PUNCT
ejpam-5629	170	5	φ(ζ	φ(ζ	NOUN
ejpam-5629	170	6	)	)	PUNCT
ejpam-5629	170	7	,	,	PUNCT
ejpam-5629	170	8	ω(ζ	ω(ζ	NOUN
ejpam-5629	170	9	)	)	PUNCT
ejpam-5629	170	10	)	)	PUNCT
ejpam-5629	171	1	+	+	CCONJ
ejpam-5629	171	2	℧	℧	SYM
ejpam-5629	171	3	2	2	NUM
ejpam-5629	171	4	(	(	PUNCT
ejpam-5629	171	5	φ(ζ	φ(ζ	NOUN
ejpam-5629	171	6	)	)	PUNCT
ejpam-5629	171	7	,	,	PUNCT
ejpam-5629	171	8	ω(ζ	ω(ζ	NOUN
ejpam-5629	171	9	)	)	PUNCT
ejpam-5629	171	10	)	)	PUNCT
ejpam-5629	171	11	,	,	PUNCT
ejpam-5629	171	12	where	where	SCONJ
ejpam-5629	171	13	℧	℧	PROPN
ejpam-5629	171	14	j	j	PROPN
ejpam-5629	171	15	(	(	PUNCT
ejpam-5629	171	16	φ(ζ	φ(ζ	NOUN
ejpam-5629	171	17	)	)	PUNCT
ejpam-5629	171	18	,	,	PUNCT
ejpam-5629	171	19	ω(ζ	ω(ζ	NOUN
ejpam-5629	171	20	)	)	PUNCT
ejpam-5629	171	21	)	)	PUNCT
ejpam-5629	171	22	=	=	PUNCT
ejpam-5629	171	23	bj	bj	ADP
ejpam-5629	171	24	+	+	CCONJ
ejpam-5629	171	25	⅁ji	⅁ji	X
ejpam-5629	171	26	ηj+γjzj	ηj+γjzj	PROPN
ejpam-5629	171	27	(	(	PUNCT
ejpam-5629	171	28	ζ	ζ	NOUN
ejpam-5629	171	29	,	,	PUNCT
ejpam-5629	171	30	φ(ζ	φ(ζ	NOUN
ejpam-5629	171	31	)	)	PUNCT
ejpam-5629	171	32	,	,	PUNCT
ejpam-5629	171	33	ω(ζ	ω(ζ	NOUN
ejpam-5629	171	34	)	)	PUNCT
ejpam-5629	171	35	,	,	PUNCT
ejpam-5629	171	36	dρ−1φ(ζ	dρ−1φ(ζ	NOUN
ejpam-5629	171	37	)	)	PUNCT
ejpam-5629	171	38	,	,	PUNCT
ejpam-5629	171	39	dρω(ζ	dρω(ζ	PROPN
ejpam-5629	171	40	)	)	PUNCT
ejpam-5629	171	41	)	)	PUNCT
ejpam-5629	172	1	+	+	CCONJ
ejpam-5629	172	2	(	(	PUNCT
ejpam-5629	172	3	2⅁j	2⅁j	NUM
ejpam-5629	172	4	γjγ	γjγ	NOUN
ejpam-5629	172	5	(	(	PUNCT
ejpam-5629	172	6	ηj	ηj	NOUN
ejpam-5629	172	7	)	)	PUNCT
ejpam-5629	172	8	∫	∫	PROPN
ejpam-5629	172	9	1	1	NUM
ejpam-5629	172	10	0	0	NUM
ejpam-5629	172	11	(	(	PUNCT
ejpam-5629	172	12	1−	1−	NUM
ejpam-5629	172	13	r)ηj−1	r)ηj−1	NOUN
ejpam-5629	172	14	zj	zj	NOUN
ejpam-5629	172	15	(	(	PUNCT
ejpam-5629	172	16	r	r	NOUN
ejpam-5629	172	17	,	,	PUNCT
ejpam-5629	172	18	φ(r	φ(r	ADJ
ejpam-5629	172	19	)	)	PUNCT
ejpam-5629	172	20	,	,	PUNCT
ejpam-5629	172	21	ω(r	ω(r	NUM
ejpam-5629	172	22	)	)	PUNCT
ejpam-5629	172	23	,	,	PUNCT
ejpam-5629	172	24	dρ−1φ(r	dρ−1φ(r	NOUN
ejpam-5629	172	25	)	)	PUNCT
ejpam-5629	172	26	,	,	PUNCT
ejpam-5629	172	27	dρω(r	dρω(r	PROPN
ejpam-5629	172	28	)	)	PUNCT
ejpam-5629	172	29	)	)	PUNCT
ejpam-5629	173	1	dr	dr	PROPN
ejpam-5629	173	2	−	−	PROPN
ejpam-5629	173	3	⅁jγ	⅁jγ	PUNCT
ejpam-5629	173	4	(	(	PUNCT
ejpam-5629	173	5	γj	γj	ADP
ejpam-5629	173	6	+	+	CCONJ
ejpam-5629	173	7	3	3	X
ejpam-5629	173	8	)	)	PUNCT
ejpam-5629	173	9	γjγ	γjγ	NOUN
ejpam-5629	173	10	(	(	PUNCT
ejpam-5629	173	11	ηj	ηj	ADP
ejpam-5629	173	12	+	+	NOUN
ejpam-5629	173	13	γj	γj	PROPN
ejpam-5629	173	14	)	)	PUNCT
ejpam-5629	173	15	∫	∫	PROPN
ejpam-5629	174	1	1	1	NUM
ejpam-5629	174	2	0	0	NUM
ejpam-5629	174	3	(	(	PUNCT
ejpam-5629	174	4	1−	1−	NUM
ejpam-5629	174	5	r)ηj+γj−1	r)ηj+γj−1	PROPN
ejpam-5629	174	6	zj	zj	PROPN
ejpam-5629	174	7	(	(	PUNCT
ejpam-5629	174	8	r	r	NOUN
ejpam-5629	174	9	,	,	PUNCT
ejpam-5629	174	10	φ(r	φ(r	ADJ
ejpam-5629	174	11	)	)	PUNCT
ejpam-5629	174	12	,	,	PUNCT
ejpam-5629	174	13	ω(r	ω(r	NUM
ejpam-5629	174	14	)	)	PUNCT
ejpam-5629	174	15	,	,	PUNCT
ejpam-5629	174	16	dρ−1φ(r	dρ−1φ(r	NOUN
ejpam-5629	174	17	)	)	PUNCT
ejpam-5629	174	18	,	,	PUNCT
ejpam-5629	174	19	dρω(r	dρω(r	PROPN
ejpam-5629	174	20	)	)	PUNCT
ejpam-5629	174	21	)	)	PUNCT
ejpam-5629	174	22	dr	dr	PROPN
ejpam-5629	174	23	)	)	PUNCT
ejpam-5629	174	24	ζγj+1	ζγj+1	NOUN
ejpam-5629	174	25	+	+	CCONJ
ejpam-5629	174	26	(	(	PUNCT
ejpam-5629	174	27	⅁jγ	⅁jγ	PUNCT
ejpam-5629	174	28	(	(	PUNCT
ejpam-5629	174	29	γj	γj	ADP
ejpam-5629	174	30	+	+	CCONJ
ejpam-5629	174	31	3	3	X
ejpam-5629	174	32	)	)	PUNCT
ejpam-5629	174	33	γjγ	γjγ	NOUN
ejpam-5629	174	34	(	(	PUNCT
ejpam-5629	174	35	ηj	ηj	ADP
ejpam-5629	174	36	+	+	NOUN
ejpam-5629	174	37	γj	γj	PROPN
ejpam-5629	174	38	)	)	PUNCT
ejpam-5629	174	39	∫	∫	PROPN
ejpam-5629	175	1	1	1	NUM
ejpam-5629	175	2	0	0	NUM
ejpam-5629	175	3	(	(	PUNCT
ejpam-5629	175	4	1−	1−	NUM
ejpam-5629	175	5	r)ηj+γj−1	r)ηj+γj−1	PROPN
ejpam-5629	175	6	zj	zj	PROPN
ejpam-5629	175	7	(	(	PUNCT
ejpam-5629	175	8	r	r	NOUN
ejpam-5629	175	9	,	,	PUNCT
ejpam-5629	175	10	φ(r	φ(r	ADJ
ejpam-5629	175	11	)	)	PUNCT
ejpam-5629	175	12	,	,	PUNCT
ejpam-5629	175	13	ω(r	ω(r	NUM
ejpam-5629	175	14	)	)	PUNCT
ejpam-5629	175	15	,	,	PUNCT
ejpam-5629	175	16	dρ−1φ(r	dρ−1φ(r	NOUN
ejpam-5629	175	17	)	)	PUNCT
ejpam-5629	175	18	,	,	PUNCT
ejpam-5629	175	19	dρω(r	dρω(r	PROPN
ejpam-5629	175	20	)	)	PUNCT
ejpam-5629	175	21	)	)	PUNCT
ejpam-5629	176	1	dr	dr	PROPN
ejpam-5629	176	2	−	−	PROPN
ejpam-5629	176	3	⅁j	⅁j	PROPN
ejpam-5629	176	4	(	(	PUNCT
ejpam-5629	176	5	γj	γj	ADP
ejpam-5629	176	6	+	+	CCONJ
ejpam-5629	176	7	2	2	X
ejpam-5629	176	8	)	)	PUNCT
ejpam-5629	176	9	γjγ	γjγ	NOUN
ejpam-5629	176	10	(	(	PUNCT
ejpam-5629	176	11	ηj	ηj	NOUN
ejpam-5629	176	12	)	)	PUNCT
ejpam-5629	176	13	∫	∫	PROPN
ejpam-5629	176	14	1	1	NUM
ejpam-5629	176	15	0	0	NUM
ejpam-5629	176	16	(	(	PUNCT
ejpam-5629	176	17	1−	1−	NUM
ejpam-5629	176	18	r)ηj−1	r)ηj−1	NOUN
ejpam-5629	176	19	zj	zj	NOUN
ejpam-5629	176	20	(	(	PUNCT
ejpam-5629	176	21	r	r	NOUN
ejpam-5629	176	22	,	,	PUNCT
ejpam-5629	176	23	φ(r	φ(r	ADJ
ejpam-5629	176	24	)	)	PUNCT
ejpam-5629	176	25	,	,	PUNCT
ejpam-5629	176	26	ω(r	ω(r	NUM
ejpam-5629	176	27	)	)	PUNCT
ejpam-5629	176	28	,	,	PUNCT
ejpam-5629	176	29	dρ−1φ(r	dρ−1φ(r	NOUN
ejpam-5629	176	30	)	)	PUNCT
ejpam-5629	176	31	,	,	PUNCT
ejpam-5629	176	32	dρω(r	dρω(r	PROPN
ejpam-5629	176	33	)	)	PUNCT
ejpam-5629	176	34	)	)	PUNCT
ejpam-5629	177	1	dr	dr	PROPN
ejpam-5629	177	2	)	)	PUNCT
ejpam-5629	177	3	ζγj+2	ζγj+2	VERB
ejpam-5629	177	4	therefore	therefore	ADV
ejpam-5629	177	5	,	,	PUNCT
ejpam-5629	177	6	the	the	DET
ejpam-5629	177	7	fp	fp	NOUN
ejpam-5629	177	8	of	of	ADP
ejpam-5629	177	9	the	the	DET
ejpam-5629	177	10	operator	operator	NOUN
ejpam-5629	177	11	℧	℧	PROPN
ejpam-5629	177	12	is	be	AUX
ejpam-5629	177	13	equivalent	equivalent	ADJ
ejpam-5629	177	14	to	to	ADP
ejpam-5629	177	15	the	the	DET
ejpam-5629	177	16	solution	solution	NOUN
ejpam-5629	177	17	of	of	ADP
ejpam-5629	177	18	the	the	DET
ejpam-5629	177	19	system	system	NOUN
ejpam-5629	177	20	(	(	PUNCT
ejpam-5629	177	21	1	1	NUM
ejpam-5629	177	22	)	)	PUNCT
ejpam-5629	177	23	.	.	PUNCT
ejpam-5629	178	1	h.a	h.a	PROPN
ejpam-5629	178	2	.	.	PROPN
ejpam-5629	178	3	hammad	hammad	PROPN
ejpam-5629	178	4	,	,	PUNCT
ejpam-5629	178	5	m.e.m	m.e.m	NOUN
ejpam-5629	178	6	.	.	PUNCT
ejpam-5629	179	1	abdalla	abdalla	PROPN
ejpam-5629	179	2	/	/	SYM
ejpam-5629	179	3	eur	eur	PROPN
ejpam-5629	179	4	.	.	PUNCT
ejpam-5629	180	1	j.	j.	PROPN
ejpam-5629	180	2	pure	pure	PROPN
ejpam-5629	180	3	appl	appl	PROPN
ejpam-5629	180	4	.	.	PROPN
ejpam-5629	180	5	math	math	PROPN
ejpam-5629	180	6	,	,	PUNCT
ejpam-5629	180	7	18	18	NUM
ejpam-5629	180	8	(	(	PUNCT
ejpam-5629	180	9	1	1	NUM
ejpam-5629	180	10	)	)	PUNCT
ejpam-5629	180	11	(	(	PUNCT
ejpam-5629	180	12	2025	2025	NUM
ejpam-5629	180	13	)	)	PUNCT
ejpam-5629	180	14	,	,	PUNCT
ejpam-5629	180	15	5629	5629	NUM
ejpam-5629	180	16	8	8	NUM
ejpam-5629	180	17	of	of	ADP
ejpam-5629	180	18	20	20	NUM
ejpam-5629	180	19	4	4	NUM
ejpam-5629	180	20	.	.	PUNCT
ejpam-5629	181	1	existence	existence	NOUN
ejpam-5629	181	2	and	and	CCONJ
ejpam-5629	181	3	uniqueness	uniqueness	NOUN
ejpam-5629	181	4	results	result	NOUN
ejpam-5629	181	5	we	we	PRON
ejpam-5629	181	6	begin	begin	VERB
ejpam-5629	181	7	this	this	DET
ejpam-5629	181	8	part	part	NOUN
ejpam-5629	181	9	with	with	ADP
ejpam-5629	181	10	the	the	DET
ejpam-5629	181	11	following	follow	VERB
ejpam-5629	181	12	assertion	assertion	NOUN
ejpam-5629	181	13	:	:	PUNCT
ejpam-5629	181	14	(	(	PUNCT
ejpam-5629	181	15	a1	a1	NOUN
ejpam-5629	181	16	)	)	PUNCT
ejpam-5629	181	17	for	for	ADP
ejpam-5629	181	18	all	all	DET
ejpam-5629	181	19	ζ	ζ	PROPN
ejpam-5629	181	20	∈	∈	PROPN
ejpam-5629	181	21	v	v	NOUN
ejpam-5629	181	22	and	and	CCONJ
ejpam-5629	181	23	(	(	PUNCT
ejpam-5629	181	24	φ	φ	PROPN
ejpam-5629	181	25	,	,	PUNCT
ejpam-5629	181	26	ω	ω	PROPN
ejpam-5629	181	27	,	,	PUNCT
ejpam-5629	181	28	δ	δ	PROPN
ejpam-5629	181	29	,	,	PUNCT
ejpam-5629	181	30	ϱ	ϱ	NOUN
ejpam-5629	181	31	)	)	PUNCT
ejpam-5629	181	32	,	,	PUNCT
ejpam-5629	181	33	(	(	PUNCT
ejpam-5629	181	34	φ̃	φ̃	PROPN
ejpam-5629	181	35	,	,	PUNCT
ejpam-5629	181	36	ω̃	ω̃	PROPN
ejpam-5629	181	37	,	,	PUNCT
ejpam-5629	181	38	δ̃	δ̃	PROPN
ejpam-5629	181	39	,	,	PUNCT
ejpam-5629	181	40	ϱ̃	ϱ̃	PROPN
ejpam-5629	181	41	)	)	PUNCT
ejpam-5629	181	42	∈	∈	PROPN
ejpam-5629	181	43	r4	r4	NOUN
ejpam-5629	181	44	,	,	PUNCT
ejpam-5629	181	45	there	there	PRON
ejpam-5629	181	46	exists	exist	VERB
ejpam-5629	181	47	a	a	DET
ejpam-5629	181	48	matrix	matrix	NOUN
ejpam-5629	181	49	of	of	ADP
ejpam-5629	181	50	positive	positive	ADJ
ejpam-5629	181	51	functions	function	NOUN
ejpam-5629	181	52	mlj	mlj	ADV
ejpam-5629	181	53	,	,	PUNCT
ejpam-5629	182	1	l	l	NOUN
ejpam-5629	182	2	=	=	SYM
ejpam-5629	182	3	1	1	NUM
ejpam-5629	182	4	,	,	PUNCT
ejpam-5629	182	5	2	2	NUM
ejpam-5629	182	6	,	,	PUNCT
ejpam-5629	182	7	3	3	NUM
ejpam-5629	182	8	,	,	PUNCT
ejpam-5629	182	9	4	4	NUM
ejpam-5629	182	10	,	,	PUNCT
ejpam-5629	182	11	j	j	PROPN
ejpam-5629	182	12	=	=	SYM
ejpam-5629	182	13	1	1	NUM
ejpam-5629	182	14	,	,	PUNCT
ejpam-5629	182	15	2	2	NUM
ejpam-5629	182	16	such	such	ADJ
ejpam-5629	182	17	that∣∣∣zj	that∣∣∣zj	ADJ
ejpam-5629	182	18	(	(	PUNCT
ejpam-5629	182	19	ζ	ζ	PROPN
ejpam-5629	182	20	,	,	PUNCT
ejpam-5629	182	21	φ	φ	PROPN
ejpam-5629	182	22	,	,	PUNCT
ejpam-5629	182	23	ω	ω	PROPN
ejpam-5629	182	24	,	,	PUNCT
ejpam-5629	182	25	δ	δ	PROPN
ejpam-5629	182	26	,	,	PUNCT
ejpam-5629	182	27	ϱ)−	ϱ)−	PROPN
ejpam-5629	182	28	zj	zj	PROPN
ejpam-5629	182	29	(	(	PUNCT
ejpam-5629	182	30	ζ	ζ	NOUN
ejpam-5629	182	31	,	,	PUNCT
ejpam-5629	182	32	φ̃	φ̃	PROPN
ejpam-5629	182	33	,	,	PUNCT
ejpam-5629	182	34	ω̃	ω̃	PROPN
ejpam-5629	182	35	,	,	PUNCT
ejpam-5629	182	36	δ̃	δ̃	PROPN
ejpam-5629	182	37	,	,	PUNCT
ejpam-5629	182	38	ϱ̃	ϱ̃	PROPN
ejpam-5629	182	39	)	)	PUNCT
ejpam-5629	182	40	∣∣∣	∣∣∣	ADJ
ejpam-5629	182	41	≤	≤	NUM
ejpam-5629	182	42	m1j(ζ	m1j(ζ	NOUN
ejpam-5629	182	43	)	)	PUNCT
ejpam-5629	182	44	|φ−	|φ−	ADP
ejpam-5629	182	45	φ̃|+m2j(ζ	φ̃|+m2j(ζ	NOUN
ejpam-5629	182	46	)	)	PUNCT
ejpam-5629	182	47	|ω	|ω	PROPN
ejpam-5629	183	1	−	−	PROPN
ejpam-5629	183	2	ω̃|	ω̃|	PROPN
ejpam-5629	183	3	+	+	SYM
ejpam-5629	183	4	m3j(ζ	m3j(ζ	X
ejpam-5629	183	5	)	)	PUNCT
ejpam-5629	183	6	∣∣∣δ	∣∣∣δ	PROPN
ejpam-5629	183	7	−	−	PUNCT
ejpam-5629	184	1	δ̃	δ̃	PROPN
ejpam-5629	184	2	∣∣∣+m1j(ζ	∣∣∣+m1j(ζ	NOUN
ejpam-5629	184	3	)	)	PUNCT
ejpam-5629	184	4	|ϱ−	|ϱ−	NOUN
ejpam-5629	184	5	ϱ̃|	ϱ̃|	ADJ
ejpam-5629	184	6	,	,	PUNCT
ejpam-5629	184	7	with	with	ADP
ejpam-5629	184	8	mlj	mlj	NOUN
ejpam-5629	184	9	=	=	SYM
ejpam-5629	184	10	supζ∈v	supζ∈v	NOUN
ejpam-5629	184	11	{	{	PUNCT
ejpam-5629	184	12	mlj	mlj	NOUN
ejpam-5629	184	13	}	}	PUNCT
ejpam-5629	184	14	.	.	PUNCT
ejpam-5629	185	1	the	the	DET
ejpam-5629	185	2	first	first	ADJ
ejpam-5629	185	3	main	main	ADJ
ejpam-5629	185	4	result	result	NOUN
ejpam-5629	185	5	of	of	ADP
ejpam-5629	185	6	this	this	DET
ejpam-5629	185	7	part	part	NOUN
ejpam-5629	185	8	is	be	AUX
ejpam-5629	185	9	as	as	SCONJ
ejpam-5629	185	10	follows	follow	VERB
ejpam-5629	185	11	:	:	PUNCT
ejpam-5629	185	12	theorem	theorem	NOUN
ejpam-5629	185	13	1	1	NUM
ejpam-5629	185	14	.	.	PUNCT
ejpam-5629	185	15	assume	assume	VERB
ejpam-5629	185	16	that	that	SCONJ
ejpam-5629	185	17	the	the	DET
ejpam-5629	185	18	assertion	assertion	NOUN
ejpam-5629	185	19	(	(	PUNCT
ejpam-5629	185	20	a1	a1	NOUN
ejpam-5629	185	21	)	)	PUNCT
ejpam-5629	185	22	is	be	AUX
ejpam-5629	185	23	true	true	ADJ
ejpam-5629	185	24	.	.	PUNCT
ejpam-5629	186	1	the	the	DET
ejpam-5629	186	2	system	system	NOUN
ejpam-5629	186	3	(	(	PUNCT
ejpam-5629	186	4	1	1	NUM
ejpam-5629	186	5	)	)	PUNCT
ejpam-5629	186	6	under	under	ADP
ejpam-5629	186	7	conditions	condition	NOUN
ejpam-5629	186	8	(	(	PUNCT
ejpam-5629	186	9	3	3	X
ejpam-5629	186	10	)	)	PUNCT
ejpam-5629	186	11	admits	admit	VERB
ejpam-5629	186	12	a	a	DET
ejpam-5629	186	13	unique	unique	ADJ
ejpam-5629	186	14	solution	solution	NOUN
ejpam-5629	186	15	,	,	PUNCT
ejpam-5629	186	16	provided	provide	VERB
ejpam-5629	186	17	that	that	DET
ejpam-5629	186	18	ω1	ω1	PROPN
ejpam-5629	186	19	+	+	PROPN
ejpam-5629	186	20	ω2	ω2	ADJ
ejpam-5629	186	21	<	<	X
ejpam-5629	186	22	1	1	NUM
ejpam-5629	186	23	,	,	PUNCT
ejpam-5629	186	24	where	where	SCONJ
ejpam-5629	186	25	ωj	ωj	ADP
ejpam-5629	186	26	=	=	VERB
ejpam-5629	186	27	bj	bj	ADP
ejpam-5629	186	28	max	max	PROPN
ejpam-5629	186	29	{	{	PUNCT
ejpam-5629	186	30	(	(	PUNCT
ejpam-5629	186	31	m1j	m1j	PROPN
ejpam-5629	186	32	+	+	NOUN
ejpam-5629	186	33	m3j	m3j	NOUN
ejpam-5629	186	34	)	)	PUNCT
ejpam-5629	186	35	,	,	PUNCT
ejpam-5629	186	36	(	(	PUNCT
ejpam-5629	186	37	m2j	m2j	PROPN
ejpam-5629	186	38	+	+	NOUN
ejpam-5629	186	39	m4j	m4j	NOUN
ejpam-5629	186	40	)	)	PUNCT
ejpam-5629	186	41	}	}	PUNCT
ejpam-5629	186	42	,	,	PUNCT
ejpam-5629	186	43	j	j	PROPN
ejpam-5629	186	44	=	=	SYM
ejpam-5629	186	45	1	1	NUM
ejpam-5629	186	46	,	,	PUNCT
ejpam-5629	186	47	2	2	NUM
ejpam-5629	186	48	,	,	PUNCT
ejpam-5629	186	49	and	and	CCONJ
ejpam-5629	186	50	bj	bj	VERB
ejpam-5629	186	51	=	=	VERB
ejpam-5629	186	52	⅁j	⅁j	NOUN
ejpam-5629	186	53	{	{	PUNCT
ejpam-5629	186	54	(	(	PUNCT
ejpam-5629	186	55	γj	γj	ADP
ejpam-5629	186	56	+	+	CCONJ
ejpam-5629	186	57	2γ	2γ	NOUN
ejpam-5629	186	58	(	(	PUNCT
ejpam-5629	186	59	γj	γj	NOUN
ejpam-5629	186	60	+	+	CCONJ
ejpam-5629	186	61	3	3	X
ejpam-5629	186	62	)	)	PUNCT
ejpam-5629	186	63	γjγ	γjγ	NOUN
ejpam-5629	186	64	(	(	PUNCT
ejpam-5629	186	65	ηj	ηj	NOUN
ejpam-5629	186	66	+	+	NOUN
ejpam-5629	186	67	γj	γj	NOUN
ejpam-5629	186	68	)	)	PUNCT
ejpam-5629	187	1	+	+	NOUN
ejpam-5629	187	2	γj	γj	ADP
ejpam-5629	187	3	+	+	CCONJ
ejpam-5629	187	4	4	4	NUM
ejpam-5629	187	5	γjγ	γjγ	NOUN
ejpam-5629	187	6	(	(	PUNCT
ejpam-5629	187	7	ηj	ηj	NOUN
ejpam-5629	187	8	)	)	PUNCT
ejpam-5629	187	9	)	)	PUNCT
ejpam-5629	188	1	+	+	CCONJ
ejpam-5629	188	2	1	1	NUM
ejpam-5629	188	3	γ	γ	X
ejpam-5629	188	4	(	(	PUNCT
ejpam-5629	188	5	ηj	ηj	ADP
ejpam-5629	188	6	+	+	NOUN
ejpam-5629	188	7	γj	γj	ADP
ejpam-5629	188	8	−	−	NOUN
ejpam-5629	188	9	ρ+	ρ+	NOUN
ejpam-5629	188	10	2	2	NUM
ejpam-5629	188	11	)	)	PUNCT
ejpam-5629	188	12	+	+	CCONJ
ejpam-5629	188	13	γ	γ	X
ejpam-5629	188	14	(	(	PUNCT
ejpam-5629	188	15	γj	γj	ADP
ejpam-5629	188	16	+	+	CCONJ
ejpam-5629	188	17	2	2	X
ejpam-5629	188	18	)	)	PUNCT
ejpam-5629	188	19	γjγ	γjγ	NOUN
ejpam-5629	188	20	(	(	PUNCT
ejpam-5629	188	21	ηj	ηj	ADP
ejpam-5629	188	22	+	+	X
ejpam-5629	188	23	1)γ	1)γ	PROPN
ejpam-5629	188	24	(	(	PUNCT
ejpam-5629	188	25	γj	γj	ADP
ejpam-5629	188	26	−	−	PROPN
ejpam-5629	188	27	ρ+	ρ+	NOUN
ejpam-5629	188	28	4	4	NUM
ejpam-5629	188	29	)	)	PUNCT
ejpam-5629	188	30	[	[	PUNCT
ejpam-5629	188	31	2	2	NUM
ejpam-5629	188	32	(	(	PUNCT
ejpam-5629	188	33	γj	γj	NOUN
ejpam-5629	188	34	−	−	NOUN
ejpam-5629	188	35	ρ+	ρ+	NOUN
ejpam-5629	188	36	3	3	NUM
ejpam-5629	188	37	)	)	PUNCT
ejpam-5629	188	38	+	+	CCONJ
ejpam-5629	188	39	(	(	PUNCT
ejpam-5629	188	40	γj	γj	ADP
ejpam-5629	188	41	+	+	CCONJ
ejpam-5629	188	42	2)2	2)2	NUM
ejpam-5629	188	43	]	]	PUNCT
ejpam-5629	189	1	+	+	CCONJ
ejpam-5629	189	2	γ	γ	X
ejpam-5629	189	3	(	(	PUNCT
ejpam-5629	189	4	γj	γj	ADP
ejpam-5629	189	5	+	+	NOUN
ejpam-5629	189	6	2)γ	2)γ	NUM
ejpam-5629	189	7	(	(	PUNCT
ejpam-5629	189	8	γj	γj	ADP
ejpam-5629	189	9	+	+	CCONJ
ejpam-5629	189	10	3	3	X
ejpam-5629	189	11	)	)	PUNCT
ejpam-5629	189	12	γjγ	γjγ	NOUN
ejpam-5629	189	13	(	(	PUNCT
ejpam-5629	189	14	γj	γj	ADP
ejpam-5629	189	15	+	+	CCONJ
ejpam-5629	189	16	ηj	ηj	ADP
ejpam-5629	189	17	+	+	ADJ
ejpam-5629	189	18	1)γ	1)γ	PROPN
ejpam-5629	189	19	(	(	PUNCT
ejpam-5629	189	20	γj	γj	ADP
ejpam-5629	189	21	−	−	PROPN
ejpam-5629	189	22	ρ+	ρ+	NOUN
ejpam-5629	189	23	4	4	NUM
ejpam-5629	189	24	)	)	PUNCT
ejpam-5629	189	25	[	[	X
ejpam-5629	189	26	2γj	2γj	ADJ
ejpam-5629	189	27	−	−	ADP
ejpam-5629	189	28	ρ+	ρ+	NOUN
ejpam-5629	189	29	5	5	NUM
ejpam-5629	189	30	]	]	PUNCT
ejpam-5629	189	31	+	+	CCONJ
ejpam-5629	189	32	1	1	NUM
ejpam-5629	189	33	γ	γ	X
ejpam-5629	189	34	(	(	PUNCT
ejpam-5629	189	35	ηj	ηj	ADP
ejpam-5629	189	36	+	+	NOUN
ejpam-5629	189	37	γj	γj	ADP
ejpam-5629	189	38	−	−	NOUN
ejpam-5629	189	39	ρ+	ρ+	NOUN
ejpam-5629	189	40	1	1	NUM
ejpam-5629	189	41	)	)	PUNCT
ejpam-5629	189	42	+	+	CCONJ
ejpam-5629	189	43	γ	γ	X
ejpam-5629	189	44	(	(	PUNCT
ejpam-5629	189	45	γj	γj	ADP
ejpam-5629	189	46	+	+	CCONJ
ejpam-5629	189	47	2	2	X
ejpam-5629	189	48	)	)	PUNCT
ejpam-5629	189	49	γjγ	γjγ	NOUN
ejpam-5629	189	50	(	(	PUNCT
ejpam-5629	189	51	ηj	ηj	ADP
ejpam-5629	189	52	+	+	X
ejpam-5629	189	53	1)γ	1)γ	PROPN
ejpam-5629	189	54	(	(	PUNCT
ejpam-5629	189	55	γj	γj	ADP
ejpam-5629	189	56	−	−	PROPN
ejpam-5629	189	57	ρ+	ρ+	NOUN
ejpam-5629	189	58	3	3	X
ejpam-5629	189	59	)	)	PUNCT
ejpam-5629	189	60	[	[	PUNCT
ejpam-5629	189	61	2	2	NUM
ejpam-5629	189	62	(	(	PUNCT
ejpam-5629	189	63	γj	γj	NOUN
ejpam-5629	189	64	−	−	NOUN
ejpam-5629	189	65	ρ+	ρ+	NOUN
ejpam-5629	189	66	2	2	NUM
ejpam-5629	189	67	)	)	PUNCT
ejpam-5629	189	68	+	+	CCONJ
ejpam-5629	189	69	(	(	PUNCT
ejpam-5629	189	70	γj	γj	ADP
ejpam-5629	189	71	+	+	CCONJ
ejpam-5629	189	72	2)2	2)2	NUM
ejpam-5629	189	73	]	]	PUNCT
ejpam-5629	190	1	+	+	CCONJ
ejpam-5629	190	2	γ	γ	X
ejpam-5629	190	3	(	(	PUNCT
ejpam-5629	190	4	γj	γj	ADP
ejpam-5629	190	5	+	+	NOUN
ejpam-5629	190	6	2)γ	2)γ	NUM
ejpam-5629	190	7	(	(	PUNCT
ejpam-5629	190	8	γj	γj	ADP
ejpam-5629	190	9	+	+	CCONJ
ejpam-5629	190	10	3	3	X
ejpam-5629	190	11	)	)	PUNCT
ejpam-5629	190	12	γjγ	γjγ	NOUN
ejpam-5629	190	13	(	(	PUNCT
ejpam-5629	190	14	γj	γj	ADP
ejpam-5629	190	15	+	+	CCONJ
ejpam-5629	190	16	ηj	ηj	ADP
ejpam-5629	190	17	+	+	ADJ
ejpam-5629	190	18	1)γ	1)γ	PROPN
ejpam-5629	190	19	(	(	PUNCT
ejpam-5629	190	20	γj	γj	ADP
ejpam-5629	190	21	−	−	PROPN
ejpam-5629	190	22	ρ+	ρ+	NOUN
ejpam-5629	190	23	3	3	X
ejpam-5629	190	24	)	)	PUNCT
ejpam-5629	190	25	[	[	X
ejpam-5629	190	26	2γj	2γj	ADJ
ejpam-5629	190	27	−	−	ADP
ejpam-5629	190	28	ρ+	ρ+	NOUN
ejpam-5629	190	29	4	4	NUM
ejpam-5629	190	30	]	]	PUNCT
ejpam-5629	190	31	}	}	PUNCT
ejpam-5629	190	32	for	for	ADP
ejpam-5629	190	33	j	j	PROPN
ejpam-5629	190	34	=	=	SYM
ejpam-5629	190	35	1	1	NUM
ejpam-5629	190	36	,	,	PUNCT
ejpam-5629	190	37	2	2	NUM
ejpam-5629	190	38	.	.	PUNCT
ejpam-5629	190	39	proof	proof	NOUN
ejpam-5629	190	40	.	.	PUNCT
ejpam-5629	191	1	it	it	PRON
ejpam-5629	191	2	is	be	AUX
ejpam-5629	191	3	enough	enough	ADJ
ejpam-5629	191	4	to	to	PART
ejpam-5629	191	5	prove	prove	VERB
ejpam-5629	191	6	that	that	SCONJ
ejpam-5629	191	7	the	the	DET
ejpam-5629	191	8	mapping	mapping	NOUN
ejpam-5629	191	9	℧	℧	PROPN
ejpam-5629	191	10	is	be	AUX
ejpam-5629	191	11	a	a	DET
ejpam-5629	191	12	banach	banach	NOUN
ejpam-5629	191	13	contraction	contraction	NOUN
ejpam-5629	191	14	principle	principle	NOUN
ejpam-5629	191	15	to	to	PART
ejpam-5629	191	16	finish	finish	VERB
ejpam-5629	191	17	the	the	DET
ejpam-5629	191	18	proof	proof	NOUN
ejpam-5629	191	19	.	.	PUNCT
ejpam-5629	192	1	assume	assume	VERB
ejpam-5629	192	2	that	that	SCONJ
ejpam-5629	192	3	(	(	PUNCT
ejpam-5629	192	4	φ1	φ1	PROPN
ejpam-5629	192	5	,	,	PUNCT
ejpam-5629	192	6	ω1	ω1	PROPN
ejpam-5629	192	7	)	)	PUNCT
ejpam-5629	192	8	and	and	CCONJ
ejpam-5629	192	9	(	(	PUNCT
ejpam-5629	192	10	φ2	φ2	PROPN
ejpam-5629	192	11	,	,	PUNCT
ejpam-5629	192	12	ω2	ω2	NUM
ejpam-5629	192	13	)	)	PUNCT
ejpam-5629	192	14	be	be	AUX
ejpam-5629	192	15	arbitrary	arbitrary	ADJ
ejpam-5629	192	16	elements	element	NOUN
ejpam-5629	192	17	in	in	ADP
ejpam-5629	192	18	ξ×ξ	ξ×ξ	PROPN
ejpam-5629	192	19	.	.	PUNCT
ejpam-5629	193	1	then	then	ADV
ejpam-5629	193	2	for	for	ADP
ejpam-5629	193	3	each	each	DET
ejpam-5629	193	4	ζ	ζ	PROPN
ejpam-5629	193	5	∈	∈	PROPN
ejpam-5629	193	6	v	v	NOUN
ejpam-5629	193	7	and	and	CCONJ
ejpam-5629	193	8	for	for	ADP
ejpam-5629	193	9	j	j	PROPN
ejpam-5629	193	10	=	=	SYM
ejpam-5629	193	11	1	1	NUM
ejpam-5629	193	12	,	,	PUNCT
ejpam-5629	193	13	2	2	NUM
ejpam-5629	193	14	,	,	PUNCT
ejpam-5629	193	15	we	we	PRON
ejpam-5629	193	16	have	have	VERB
ejpam-5629	193	17	|	|	ADV
ejpam-5629	193	18	℧	℧	PROPN
ejpam-5629	193	19	j	j	PROPN
ejpam-5629	193	20	(	(	PUNCT
ejpam-5629	193	21	φ1(ζ	φ1(ζ	NOUN
ejpam-5629	193	22	)	)	PUNCT
ejpam-5629	193	23	,	,	PUNCT
ejpam-5629	193	24	ω1(ζ))−	ω1(ζ))−	NUM
ejpam-5629	193	25	℧	℧	PROPN
ejpam-5629	193	26	j	j	PROPN
ejpam-5629	193	27	(	(	PUNCT
ejpam-5629	193	28	φ2(ζ	φ2(ζ	PROPN
ejpam-5629	193	29	)	)	PUNCT
ejpam-5629	193	30	,	,	PUNCT
ejpam-5629	193	31	ω2(ζ))|	ω2(ζ))|	NUM
ejpam-5629	193	32	≤	≤	NUM
ejpam-5629	193	33	⅁j	⅁j	PROPN
ejpam-5629	193	34	γ	γ	X
ejpam-5629	193	35	(	(	PUNCT
ejpam-5629	193	36	ηj	ηj	ADP
ejpam-5629	193	37	+	+	NOUN
ejpam-5629	193	38	γj	γj	NOUN
ejpam-5629	193	39	)	)	PUNCT
ejpam-5629	193	40	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-5629	193	41	ζ	ζ	NOUN
ejpam-5629	193	42	0	0	NUM
ejpam-5629	193	43	(	(	PUNCT
ejpam-5629	193	44	ζ	ζ	NOUN
ejpam-5629	193	45	−	−	PROPN
ejpam-5629	193	46	r)ηj+γj−1	r)ηj+γj−1	NOUN
ejpam-5629	193	47	[	[	X
ejpam-5629	193	48	zj	zj	X
ejpam-5629	193	49	(	(	PUNCT
ejpam-5629	193	50	r	r	NOUN
ejpam-5629	193	51	,	,	PUNCT
ejpam-5629	193	52	φ1(r	φ1(r	ADJ
ejpam-5629	193	53	)	)	PUNCT
ejpam-5629	193	54	,	,	PUNCT
ejpam-5629	193	55	ω1(r	ω1(r	PROPN
ejpam-5629	193	56	)	)	PUNCT
ejpam-5629	193	57	,	,	PUNCT
ejpam-5629	193	58	d	d	PROPN
ejpam-5629	193	59	ρ−1φ1(r	ρ−1φ1(r	PROPN
ejpam-5629	193	60	)	)	PUNCT
ejpam-5629	193	61	,	,	PUNCT
ejpam-5629	193	62	d	d	NOUN
ejpam-5629	193	63	ρω1(r	ρω1(r	NOUN
ejpam-5629	193	64	)	)	PUNCT
ejpam-5629	193	65	)	)	PUNCT
ejpam-5629	194	1	−	−	PROPN
ejpam-5629	194	2	zj	zj	INTJ
ejpam-5629	194	3	(	(	PUNCT
ejpam-5629	194	4	r	r	PROPN
ejpam-5629	194	5	,	,	PUNCT
ejpam-5629	194	6	φ2(r	φ2(r	NUM
ejpam-5629	194	7	)	)	PUNCT
ejpam-5629	194	8	,	,	PUNCT
ejpam-5629	194	9	ω2(r	ω2(r	PROPN
ejpam-5629	194	10	)	)	PUNCT
ejpam-5629	194	11	,	,	PUNCT
ejpam-5629	194	12	d	d	X
ejpam-5629	194	13	ρ−1φ2(r	ρ−1φ2(r	NOUN
ejpam-5629	194	14	)	)	PUNCT
ejpam-5629	194	15	,	,	PUNCT
ejpam-5629	194	16	d	d	PROPN
ejpam-5629	194	17	ρω2(r	ρω2(r	PROPN
ejpam-5629	194	18	)	)	PUNCT
ejpam-5629	194	19	)	)	PUNCT
ejpam-5629	194	20	]	]	PUNCT
ejpam-5629	195	1	dr	dr	PROPN
ejpam-5629	195	2	∣∣	∣∣	PROPN
ejpam-5629	195	3	h.a	h.a	PROPN
ejpam-5629	195	4	.	.	PROPN
ejpam-5629	195	5	hammad	hammad	PROPN
ejpam-5629	195	6	,	,	PUNCT
ejpam-5629	195	7	m.e.m	m.e.m	NOUN
ejpam-5629	195	8	.	.	PUNCT
ejpam-5629	196	1	abdalla	abdalla	PROPN
ejpam-5629	196	2	/	/	SYM
ejpam-5629	196	3	eur	eur	PROPN
ejpam-5629	196	4	.	.	PUNCT
ejpam-5629	197	1	j.	j.	PROPN
ejpam-5629	197	2	pure	pure	PROPN
ejpam-5629	197	3	appl	appl	PROPN
ejpam-5629	197	4	.	.	PROPN
ejpam-5629	197	5	math	math	PROPN
ejpam-5629	197	6	,	,	PUNCT
ejpam-5629	197	7	18	18	NUM
ejpam-5629	197	8	(	(	PUNCT
ejpam-5629	197	9	1	1	NUM
ejpam-5629	197	10	)	)	PUNCT
ejpam-5629	197	11	(	(	PUNCT
ejpam-5629	197	12	2025	2025	NUM
ejpam-5629	197	13	)	)	PUNCT
ejpam-5629	197	14	,	,	PUNCT
ejpam-5629	197	15	5629	5629	NUM
ejpam-5629	197	16	9	9	NUM
ejpam-5629	197	17	of	of	ADP
ejpam-5629	197	18	20	20	NUM
ejpam-5629	197	19	+	+	NUM
ejpam-5629	197	20	2⅁j	2⅁j	NUM
ejpam-5629	197	21	γjγ	γjγ	NOUN
ejpam-5629	197	22	(	(	PUNCT
ejpam-5629	197	23	ηj	ηj	NOUN
ejpam-5629	197	24	)	)	PUNCT
ejpam-5629	197	25	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-5629	198	1	1	1	NUM
ejpam-5629	198	2	0	0	NUM
ejpam-5629	198	3	(	(	PUNCT
ejpam-5629	198	4	1−	1−	NUM
ejpam-5629	198	5	r)ηj−1	r)ηj−1	NOUN
ejpam-5629	198	6	[	[	X
ejpam-5629	198	7	zj	zj	X
ejpam-5629	198	8	(	(	PUNCT
ejpam-5629	198	9	r	r	NOUN
ejpam-5629	198	10	,	,	PUNCT
ejpam-5629	198	11	φ1(r	φ1(r	ADJ
ejpam-5629	198	12	)	)	PUNCT
ejpam-5629	198	13	,	,	PUNCT
ejpam-5629	198	14	ω1(r	ω1(r	PROPN
ejpam-5629	198	15	)	)	PUNCT
ejpam-5629	198	16	,	,	PUNCT
ejpam-5629	198	17	d	d	PROPN
ejpam-5629	198	18	ρ−1φ1(r	ρ−1φ1(r	PROPN
ejpam-5629	198	19	)	)	PUNCT
ejpam-5629	198	20	,	,	PUNCT
ejpam-5629	199	1	d	d	NOUN
ejpam-5629	199	2	ρω1(r	ρω1(r	NOUN
ejpam-5629	199	3	)	)	PUNCT
ejpam-5629	199	4	)	)	PUNCT
ejpam-5629	200	1	−	−	PROPN
ejpam-5629	200	2	zj	zj	INTJ
ejpam-5629	200	3	(	(	PUNCT
ejpam-5629	200	4	r	r	PROPN
ejpam-5629	200	5	,	,	PUNCT
ejpam-5629	200	6	φ2(r	φ2(r	NUM
ejpam-5629	200	7	)	)	PUNCT
ejpam-5629	200	8	,	,	PUNCT
ejpam-5629	200	9	ω2(r	ω2(r	PROPN
ejpam-5629	200	10	)	)	PUNCT
ejpam-5629	200	11	,	,	PUNCT
ejpam-5629	200	12	d	d	X
ejpam-5629	200	13	ρ−1φ2(r	ρ−1φ2(r	NOUN
ejpam-5629	200	14	)	)	PUNCT
ejpam-5629	200	15	,	,	PUNCT
ejpam-5629	200	16	d	d	PROPN
ejpam-5629	200	17	ρω2(r	ρω2(r	PROPN
ejpam-5629	200	18	)	)	PUNCT
ejpam-5629	200	19	)	)	PUNCT
ejpam-5629	200	20	]	]	PUNCT
ejpam-5629	201	1	dr	dr	PROPN
ejpam-5629	201	2	∣∣	∣∣	PROPN
ejpam-5629	201	3	+	+	CCONJ
ejpam-5629	201	4	⅁jγ	⅁jγ	PUNCT
ejpam-5629	201	5	(	(	PUNCT
ejpam-5629	201	6	γj	γj	ADP
ejpam-5629	201	7	+	+	CCONJ
ejpam-5629	201	8	3	3	X
ejpam-5629	201	9	)	)	PUNCT
ejpam-5629	201	10	γjγ	γjγ	NOUN
ejpam-5629	201	11	(	(	PUNCT
ejpam-5629	201	12	ηj	ηj	ADP
ejpam-5629	201	13	+	+	NOUN
ejpam-5629	201	14	γj	γj	PROPN
ejpam-5629	201	15	)	)	PUNCT
ejpam-5629	201	16	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-5629	202	1	1	1	NUM
ejpam-5629	202	2	0	0	NUM
ejpam-5629	202	3	(	(	PUNCT
ejpam-5629	202	4	1−	1−	NUM
ejpam-5629	202	5	r)ηj+γj−1	r)ηj+γj−1	NOUN
ejpam-5629	202	6	[	[	X
ejpam-5629	202	7	zj	zj	X
ejpam-5629	202	8	(	(	PUNCT
ejpam-5629	202	9	r	r	NOUN
ejpam-5629	202	10	,	,	PUNCT
ejpam-5629	202	11	φ1(r	φ1(r	ADJ
ejpam-5629	202	12	)	)	PUNCT
ejpam-5629	202	13	,	,	PUNCT
ejpam-5629	202	14	ω1(r	ω1(r	PROPN
ejpam-5629	202	15	)	)	PUNCT
ejpam-5629	202	16	,	,	PUNCT
ejpam-5629	202	17	d	d	PROPN
ejpam-5629	202	18	ρ−1φ1(r	ρ−1φ1(r	PROPN
ejpam-5629	202	19	)	)	PUNCT
ejpam-5629	202	20	,	,	PUNCT
ejpam-5629	202	21	d	d	NOUN
ejpam-5629	202	22	ρω1(r	ρω1(r	NOUN
ejpam-5629	202	23	)	)	PUNCT
ejpam-5629	202	24	)	)	PUNCT
ejpam-5629	203	1	−	−	PROPN
ejpam-5629	203	2	zj	zj	INTJ
ejpam-5629	203	3	(	(	PUNCT
ejpam-5629	203	4	r	r	PROPN
ejpam-5629	203	5	,	,	PUNCT
ejpam-5629	203	6	φ2(r	φ2(r	NUM
ejpam-5629	203	7	)	)	PUNCT
ejpam-5629	203	8	,	,	PUNCT
ejpam-5629	203	9	ω2(r	ω2(r	PROPN
ejpam-5629	203	10	)	)	PUNCT
ejpam-5629	203	11	,	,	PUNCT
ejpam-5629	203	12	d	d	X
ejpam-5629	203	13	ρ−1φ2(r	ρ−1φ2(r	NOUN
ejpam-5629	203	14	)	)	PUNCT
ejpam-5629	203	15	,	,	PUNCT
ejpam-5629	203	16	d	d	PROPN
ejpam-5629	203	17	ρω2(r	ρω2(r	PROPN
ejpam-5629	203	18	)	)	PUNCT
ejpam-5629	203	19	)	)	PUNCT
ejpam-5629	203	20	]	]	PUNCT
ejpam-5629	204	1	dr	dr	PROPN
ejpam-5629	204	2	∣∣	∣∣	PROPN
ejpam-5629	204	3	+	+	CCONJ
ejpam-5629	204	4	⅁jγ	⅁jγ	PUNCT
ejpam-5629	204	5	(	(	PUNCT
ejpam-5629	204	6	γj	γj	ADP
ejpam-5629	204	7	+	+	CCONJ
ejpam-5629	204	8	3	3	X
ejpam-5629	204	9	)	)	PUNCT
ejpam-5629	204	10	γjγ	γjγ	NOUN
ejpam-5629	204	11	(	(	PUNCT
ejpam-5629	204	12	ηj	ηj	ADP
ejpam-5629	204	13	+	+	NOUN
ejpam-5629	204	14	γj	γj	PROPN
ejpam-5629	204	15	)	)	PUNCT
ejpam-5629	204	16	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-5629	205	1	1	1	NUM
ejpam-5629	205	2	0	0	NUM
ejpam-5629	205	3	(	(	PUNCT
ejpam-5629	205	4	1−	1−	NUM
ejpam-5629	205	5	r)ηj+γj−1	r)ηj+γj−1	NOUN
ejpam-5629	205	6	[	[	X
ejpam-5629	205	7	zj	zj	X
ejpam-5629	205	8	(	(	PUNCT
ejpam-5629	205	9	r	r	NOUN
ejpam-5629	205	10	,	,	PUNCT
ejpam-5629	205	11	φ1(r	φ1(r	ADJ
ejpam-5629	205	12	)	)	PUNCT
ejpam-5629	205	13	,	,	PUNCT
ejpam-5629	205	14	ω1(r	ω1(r	PROPN
ejpam-5629	205	15	)	)	PUNCT
ejpam-5629	205	16	,	,	PUNCT
ejpam-5629	205	17	d	d	PROPN
ejpam-5629	205	18	ρ−1φ1(r	ρ−1φ1(r	PROPN
ejpam-5629	205	19	)	)	PUNCT
ejpam-5629	205	20	,	,	PUNCT
ejpam-5629	205	21	d	d	NOUN
ejpam-5629	205	22	ρω1(r	ρω1(r	NOUN
ejpam-5629	205	23	)	)	PUNCT
ejpam-5629	205	24	)	)	PUNCT
ejpam-5629	206	1	−	−	PROPN
ejpam-5629	206	2	zj	zj	INTJ
ejpam-5629	206	3	(	(	PUNCT
ejpam-5629	206	4	r	r	PROPN
ejpam-5629	206	5	,	,	PUNCT
ejpam-5629	206	6	φ2(r	φ2(r	NUM
ejpam-5629	206	7	)	)	PUNCT
ejpam-5629	206	8	,	,	PUNCT
ejpam-5629	206	9	ω2(r	ω2(r	PROPN
ejpam-5629	206	10	)	)	PUNCT
ejpam-5629	206	11	,	,	PUNCT
ejpam-5629	206	12	d	d	X
ejpam-5629	206	13	ρ−1φ2(r	ρ−1φ2(r	NOUN
ejpam-5629	206	14	)	)	PUNCT
ejpam-5629	206	15	,	,	PUNCT
ejpam-5629	206	16	d	d	PROPN
ejpam-5629	206	17	ρω2(r	ρω2(r	PROPN
ejpam-5629	206	18	)	)	PUNCT
ejpam-5629	206	19	)	)	PUNCT
ejpam-5629	206	20	]	]	PUNCT
ejpam-5629	207	1	dr	dr	PROPN
ejpam-5629	207	2	∣∣	∣∣	PROPN
ejpam-5629	207	3	+	+	CCONJ
ejpam-5629	207	4	⅁j	⅁j	NOUN
ejpam-5629	207	5	(	(	PUNCT
ejpam-5629	207	6	γj	γj	ADP
ejpam-5629	207	7	+	+	CCONJ
ejpam-5629	207	8	2	2	X
ejpam-5629	207	9	)	)	PUNCT
ejpam-5629	207	10	γjγ	γjγ	NOUN
ejpam-5629	207	11	(	(	PUNCT
ejpam-5629	207	12	ηj	ηj	NOUN
ejpam-5629	207	13	)	)	PUNCT
ejpam-5629	207	14	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-5629	207	15	1	1	NUM
ejpam-5629	207	16	0	0	NUM
ejpam-5629	207	17	(	(	PUNCT
ejpam-5629	207	18	1−	1−	NUM
ejpam-5629	207	19	r)ηj−1	r)ηj−1	NOUN
ejpam-5629	207	20	[	[	X
ejpam-5629	207	21	zj	zj	X
ejpam-5629	207	22	(	(	PUNCT
ejpam-5629	207	23	r	r	NOUN
ejpam-5629	207	24	,	,	PUNCT
ejpam-5629	207	25	φ1(r	φ1(r	ADJ
ejpam-5629	207	26	)	)	PUNCT
ejpam-5629	207	27	,	,	PUNCT
ejpam-5629	207	28	ω1(r	ω1(r	PROPN
ejpam-5629	207	29	)	)	PUNCT
ejpam-5629	207	30	,	,	PUNCT
ejpam-5629	207	31	d	d	PROPN
ejpam-5629	207	32	ρ−1φ1(r	ρ−1φ1(r	PROPN
ejpam-5629	207	33	)	)	PUNCT
ejpam-5629	207	34	,	,	PUNCT
ejpam-5629	207	35	d	d	NOUN
ejpam-5629	207	36	ρω1(r	ρω1(r	NOUN
ejpam-5629	207	37	)	)	PUNCT
ejpam-5629	207	38	)	)	PUNCT
ejpam-5629	208	1	−	−	PROPN
ejpam-5629	208	2	zj	zj	INTJ
ejpam-5629	208	3	(	(	PUNCT
ejpam-5629	208	4	r	r	PROPN
ejpam-5629	208	5	,	,	PUNCT
ejpam-5629	208	6	φ2(r	φ2(r	NUM
ejpam-5629	208	7	)	)	PUNCT
ejpam-5629	208	8	,	,	PUNCT
ejpam-5629	208	9	ω2(r	ω2(r	PROPN
ejpam-5629	208	10	)	)	PUNCT
ejpam-5629	208	11	,	,	PUNCT
ejpam-5629	208	12	d	d	X
ejpam-5629	208	13	ρ−1φ2(r	ρ−1φ2(r	NOUN
ejpam-5629	208	14	)	)	PUNCT
ejpam-5629	208	15	,	,	PUNCT
ejpam-5629	208	16	d	d	PROPN
ejpam-5629	208	17	ρω2(r	ρω2(r	PROPN
ejpam-5629	208	18	)	)	PUNCT
ejpam-5629	208	19	)	)	PUNCT
ejpam-5629	208	20	]	]	PUNCT
ejpam-5629	209	1	dr	dr	PROPN
ejpam-5629	209	2	∣∣	∣∣	PROPN
ejpam-5629	209	3	=	=	PUNCT
ejpam-5629	209	4	⅁jγj	⅁jγj	PROPN
ejpam-5629	209	5	+	+	CCONJ
ejpam-5629	209	6	2⅁jγ	2⅁jγ	NUM
ejpam-5629	209	7	(	(	PUNCT
ejpam-5629	209	8	γj	γj	NOUN
ejpam-5629	209	9	+	+	CCONJ
ejpam-5629	209	10	3	3	X
ejpam-5629	209	11	)	)	PUNCT
ejpam-5629	209	12	γjγ	γjγ	NOUN
ejpam-5629	209	13	(	(	PUNCT
ejpam-5629	209	14	ηj	ηj	ADP
ejpam-5629	209	15	+	+	NOUN
ejpam-5629	209	16	γj	γj	NOUN
ejpam-5629	209	17	)	)	PUNCT
ejpam-5629	209	18	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-5629	209	19	ζ	ζ	NOUN
ejpam-5629	209	20	0	0	NUM
ejpam-5629	210	1	(	(	PUNCT
ejpam-5629	210	2	ζ	ζ	NOUN
ejpam-5629	210	3	−	−	PROPN
ejpam-5629	210	4	r)ηj+γj−1	r)ηj+γj−1	NOUN
ejpam-5629	210	5	[	[	X
ejpam-5629	210	6	zj	zj	X
ejpam-5629	210	7	(	(	PUNCT
ejpam-5629	210	8	r	r	NOUN
ejpam-5629	210	9	,	,	PUNCT
ejpam-5629	210	10	φ1(r	φ1(r	ADJ
ejpam-5629	210	11	)	)	PUNCT
ejpam-5629	210	12	,	,	PUNCT
ejpam-5629	210	13	ω1(r	ω1(r	PROPN
ejpam-5629	210	14	)	)	PUNCT
ejpam-5629	210	15	,	,	PUNCT
ejpam-5629	210	16	d	d	PROPN
ejpam-5629	210	17	ρ−1φ1(r	ρ−1φ1(r	PROPN
ejpam-5629	210	18	)	)	PUNCT
ejpam-5629	210	19	,	,	PUNCT
ejpam-5629	210	20	d	d	NOUN
ejpam-5629	210	21	ρω1(r	ρω1(r	NOUN
ejpam-5629	210	22	)	)	PUNCT
ejpam-5629	210	23	)	)	PUNCT
ejpam-5629	211	1	−	−	PROPN
ejpam-5629	211	2	zj	zj	INTJ
ejpam-5629	211	3	(	(	PUNCT
ejpam-5629	211	4	r	r	PROPN
ejpam-5629	211	5	,	,	PUNCT
ejpam-5629	211	6	φ2(r	φ2(r	NUM
ejpam-5629	211	7	)	)	PUNCT
ejpam-5629	211	8	,	,	PUNCT
ejpam-5629	211	9	ω2(r	ω2(r	PROPN
ejpam-5629	211	10	)	)	PUNCT
ejpam-5629	211	11	,	,	PUNCT
ejpam-5629	211	12	d	d	X
ejpam-5629	211	13	ρ−1φ2(r	ρ−1φ2(r	NOUN
ejpam-5629	211	14	)	)	PUNCT
ejpam-5629	211	15	,	,	PUNCT
ejpam-5629	211	16	d	d	PROPN
ejpam-5629	211	17	ρω2(r	ρω2(r	PROPN
ejpam-5629	211	18	)	)	PUNCT
ejpam-5629	211	19	)	)	PUNCT
ejpam-5629	211	20	]	]	PUNCT
ejpam-5629	212	1	dr	dr	PROPN
ejpam-5629	212	2	∣∣	∣∣	PROPN
ejpam-5629	212	3	+	+	CCONJ
ejpam-5629	212	4	⅁j	⅁j	NOUN
ejpam-5629	212	5	(	(	PUNCT
ejpam-5629	212	6	γj	γj	ADP
ejpam-5629	212	7	+	+	CCONJ
ejpam-5629	212	8	4	4	X
ejpam-5629	212	9	)	)	PUNCT
ejpam-5629	212	10	γjγ	γjγ	NOUN
ejpam-5629	212	11	(	(	PUNCT
ejpam-5629	212	12	ηj	ηj	NOUN
ejpam-5629	212	13	)	)	PUNCT
ejpam-5629	212	14	∣∣∣∣∫	∣∣∣∣∫	NOUN
ejpam-5629	212	15	1	1	NUM
ejpam-5629	212	16	0	0	NUM
ejpam-5629	212	17	(	(	PUNCT
ejpam-5629	212	18	1−	1−	NUM
ejpam-5629	212	19	r)ηj−1	r)ηj−1	NOUN
ejpam-5629	212	20	[	[	X
ejpam-5629	212	21	zj	zj	X
ejpam-5629	212	22	(	(	PUNCT
ejpam-5629	212	23	r	r	NOUN
ejpam-5629	212	24	,	,	PUNCT
ejpam-5629	212	25	φ1(r	φ1(r	ADJ
ejpam-5629	212	26	)	)	PUNCT
ejpam-5629	212	27	,	,	PUNCT
ejpam-5629	212	28	ω1(r	ω1(r	PROPN
ejpam-5629	212	29	)	)	PUNCT
ejpam-5629	212	30	,	,	PUNCT
ejpam-5629	212	31	d	d	PROPN
ejpam-5629	212	32	ρ−1φ1(r	ρ−1φ1(r	PROPN
ejpam-5629	212	33	)	)	PUNCT
ejpam-5629	212	34	,	,	PUNCT
ejpam-5629	212	35	d	d	NOUN
ejpam-5629	212	36	ρω1(r	ρω1(r	NOUN
ejpam-5629	212	37	)	)	PUNCT
ejpam-5629	212	38	)	)	PUNCT
ejpam-5629	213	1	−	−	PROPN
ejpam-5629	213	2	zj	zj	INTJ
ejpam-5629	213	3	(	(	PUNCT
ejpam-5629	213	4	r	r	PROPN
ejpam-5629	213	5	,	,	PUNCT
ejpam-5629	213	6	φ2(r	φ2(r	NUM
ejpam-5629	213	7	)	)	PUNCT
ejpam-5629	213	8	,	,	PUNCT
ejpam-5629	213	9	ω2(r	ω2(r	PROPN
ejpam-5629	213	10	)	)	PUNCT
ejpam-5629	213	11	,	,	PUNCT
ejpam-5629	213	12	d	d	X
ejpam-5629	213	13	ρ−1φ2(r	ρ−1φ2(r	NOUN
ejpam-5629	213	14	)	)	PUNCT
ejpam-5629	213	15	,	,	PUNCT
ejpam-5629	213	16	d	d	PROPN
ejpam-5629	213	17	ρω2(r	ρω2(r	PROPN
ejpam-5629	213	18	)	)	PUNCT
ejpam-5629	213	19	)	)	PUNCT
ejpam-5629	213	20	]	]	PUNCT
ejpam-5629	214	1	dr	dr	PROPN
ejpam-5629	214	2	∣∣	∣∣	PROPN
ejpam-5629	214	3	.	.	PUNCT
ejpam-5629	215	1	applying	apply	VERB
ejpam-5629	215	2	the	the	DET
ejpam-5629	215	3	hypothesis	hypothesis	NOUN
ejpam-5629	215	4	(	(	PUNCT
ejpam-5629	215	5	a1	a1	NOUN
ejpam-5629	215	6	)	)	PUNCT
ejpam-5629	215	7	,	,	PUNCT
ejpam-5629	215	8	we	we	PRON
ejpam-5629	215	9	have	have	VERB
ejpam-5629	215	10	∥	∥	NUM
ejpam-5629	215	11	℧	℧	PROPN
ejpam-5629	215	12	j	j	PROPN
ejpam-5629	215	13	(	(	PUNCT
ejpam-5629	215	14	φ1	φ1	PROPN
ejpam-5629	215	15	,	,	PUNCT
ejpam-5629	215	16	ω1)−	ω1)−	PROPN
ejpam-5629	215	17	℧	℧	PROPN
ejpam-5629	215	18	j	j	PROPN
ejpam-5629	215	19	(	(	PUNCT
ejpam-5629	215	20	φ2	φ2	PROPN
ejpam-5629	215	21	,	,	PUNCT
ejpam-5629	215	22	ω2)∥∞	ω2)∥∞	PROPN
ejpam-5629	215	23	≤	≤	NUM
ejpam-5629	215	24	(	(	PUNCT
ejpam-5629	215	25	⅁jγj	⅁jγj	NUM
ejpam-5629	215	26	+	+	CCONJ
ejpam-5629	215	27	2⅁jγ	2⅁jγ	NUM
ejpam-5629	215	28	(	(	PUNCT
ejpam-5629	215	29	γj	γj	NOUN
ejpam-5629	215	30	+	+	CCONJ
ejpam-5629	215	31	3	3	X
ejpam-5629	215	32	)	)	PUNCT
ejpam-5629	215	33	γjγ	γjγ	NOUN
ejpam-5629	215	34	(	(	PUNCT
ejpam-5629	215	35	ηj	ηj	NOUN
ejpam-5629	215	36	+	+	NOUN
ejpam-5629	215	37	γj	γj	NOUN
ejpam-5629	215	38	)	)	PUNCT
ejpam-5629	216	1	+	+	NUM
ejpam-5629	216	2	⅁j	⅁j	NOUN
ejpam-5629	216	3	(	(	PUNCT
ejpam-5629	216	4	γj	γj	ADP
ejpam-5629	216	5	+	+	CCONJ
ejpam-5629	216	6	4	4	X
ejpam-5629	216	7	)	)	PUNCT
ejpam-5629	216	8	γjγ	γjγ	NOUN
ejpam-5629	216	9	(	(	PUNCT
ejpam-5629	216	10	ηj	ηj	NOUN
ejpam-5629	216	11	)	)	PUNCT
ejpam-5629	216	12	)	)	PUNCT
ejpam-5629	217	1	(	(	PUNCT
ejpam-5629	217	2	m1j	m1j	PUNCT
ejpam-5629	217	3	∥φ1	∥φ1	NUM
ejpam-5629	217	4	−	−	PROPN
ejpam-5629	217	5	φ2∥∞	φ2∥∞	PROPN
ejpam-5629	218	1	+	+	PROPN
ejpam-5629	218	2	m2j	m2j	PROPN
ejpam-5629	218	3	∥ω1	∥ω1	PUNCT
ejpam-5629	218	4	−	−	NOUN
ejpam-5629	218	5	ω2∥∞	ω2∥∞	PROPN
ejpam-5629	219	1	+	+	ADJ
ejpam-5629	219	2	m3j	m3j	PROPN
ejpam-5629	219	3	∥∥dρ−1φ1	∥∥dρ−1φ1	PROPN
ejpam-5629	219	4	−dρ−1φ2	−dρ−1φ2	PROPN
ejpam-5629	219	5	∥∥	∥∥	PUNCT
ejpam-5629	219	6	∞	∞	NUM
ejpam-5629	219	7	+	+	PROPN
ejpam-5629	219	8	m4j	m4j	NOUN
ejpam-5629	219	9	∥dρω1	∥dρω1	PROPN
ejpam-5629	219	10	−dρω2∥∞	−dρω2∥∞	PROPN
ejpam-5629	219	11	)	)	PUNCT
ejpam-5629	219	12	.	.	PUNCT
ejpam-5629	220	1	(	(	PUNCT
ejpam-5629	220	2	7	7	X
ejpam-5629	220	3	)	)	PUNCT
ejpam-5629	220	4	using	use	VERB
ejpam-5629	220	5	the	the	DET
ejpam-5629	220	6	cfd	cfd	NOUN
ejpam-5629	220	7	,	,	PUNCT
ejpam-5629	220	8	we	we	PRON
ejpam-5629	220	9	get	get	VERB
ejpam-5629	220	10	dρ−1	dρ−1	PROPN
ejpam-5629	220	11	(	(	PUNCT
ejpam-5629	220	12	℧	℧	PROPN
ejpam-5629	220	13	j	j	X
ejpam-5629	220	14	(	(	PUNCT
ejpam-5629	220	15	φ(ζ	φ(ζ	NOUN
ejpam-5629	220	16	)	)	PUNCT
ejpam-5629	220	17	,	,	PUNCT
ejpam-5629	220	18	ω(ζ	ω(ζ	NOUN
ejpam-5629	220	19	)	)	PUNCT
ejpam-5629	220	20	)	)	PUNCT
ejpam-5629	220	21	)	)	PUNCT
ejpam-5629	221	1	=	=	PRON
ejpam-5629	221	2	⅁ji	⅁ji	NUM
ejpam-5629	221	3	ηj+γj−ρ+1zj	ηj+γj−ρ+1zj	X
ejpam-5629	221	4	(	(	PUNCT
ejpam-5629	221	5	ζ	ζ	NOUN
ejpam-5629	221	6	,	,	PUNCT
ejpam-5629	221	7	φ(ζ	φ(ζ	NOUN
ejpam-5629	221	8	)	)	PUNCT
ejpam-5629	221	9	,	,	PUNCT
ejpam-5629	221	10	ω(ζ	ω(ζ	NOUN
ejpam-5629	221	11	)	)	PUNCT
ejpam-5629	221	12	,	,	PUNCT
ejpam-5629	221	13	dρ−1φ(ζ	dρ−1φ(ζ	NOUN
ejpam-5629	221	14	)	)	PUNCT
ejpam-5629	221	15	,	,	PUNCT
ejpam-5629	221	16	dρω(ζ	dρω(ζ	PROPN
ejpam-5629	221	17	)	)	PUNCT
ejpam-5629	221	18	)	)	PUNCT
ejpam-5629	222	1	+	+	CCONJ
ejpam-5629	222	2	⅁j	⅁j	NOUN
ejpam-5629	222	3	(	(	PUNCT
ejpam-5629	222	4	γj	γj	ADP
ejpam-5629	222	5	+	+	CCONJ
ejpam-5629	222	6	2	2	X
ejpam-5629	222	7	)	)	PUNCT
ejpam-5629	222	8	γ	γ	NOUN
ejpam-5629	222	9	(	(	PUNCT
ejpam-5629	222	10	γj	γj	PROPN
ejpam-5629	222	11	−	−	PROPN
ejpam-5629	222	12	ρ+	ρ+	NOUN
ejpam-5629	222	13	3	3	X
ejpam-5629	222	14	)	)	PUNCT
ejpam-5629	222	15	ζγj−ρ+2	ζγj−ρ+2	NOUN
ejpam-5629	222	16	(	(	PUNCT
ejpam-5629	222	17	2	2	NUM
ejpam-5629	222	18	γjγ	γjγ	NOUN
ejpam-5629	222	19	(	(	PUNCT
ejpam-5629	222	20	ηj	ηj	NOUN
ejpam-5629	222	21	)	)	PUNCT
ejpam-5629	222	22	∫	∫	PROPN
ejpam-5629	222	23	1	1	NUM
ejpam-5629	222	24	0	0	NUM
ejpam-5629	222	25	(	(	PUNCT
ejpam-5629	222	26	1−	1−	NUM
ejpam-5629	222	27	r)ηj−1	r)ηj−1	NOUN
ejpam-5629	222	28	zj	zj	NOUN
ejpam-5629	222	29	(	(	PUNCT
ejpam-5629	222	30	r	r	NOUN
ejpam-5629	222	31	,	,	PUNCT
ejpam-5629	222	32	φ(r	φ(r	ADJ
ejpam-5629	222	33	)	)	PUNCT
ejpam-5629	222	34	,	,	PUNCT
ejpam-5629	222	35	ω(r	ω(r	NUM
ejpam-5629	222	36	)	)	PUNCT
ejpam-5629	222	37	,	,	PUNCT
ejpam-5629	222	38	dρ−1φ(r	dρ−1φ(r	NOUN
ejpam-5629	222	39	)	)	PUNCT
ejpam-5629	222	40	,	,	PUNCT
ejpam-5629	222	41	dρω(r	dρω(r	PROPN
ejpam-5629	222	42	)	)	PUNCT
ejpam-5629	222	43	)	)	PUNCT
ejpam-5629	223	1	dr	dr	PROPN
ejpam-5629	223	2	−	−	PROPN
ejpam-5629	223	3	γ	γ	X
ejpam-5629	223	4	(	(	PUNCT
ejpam-5629	223	5	γj	γj	PROPN
ejpam-5629	223	6	+	+	CCONJ
ejpam-5629	223	7	3	3	X
ejpam-5629	223	8	)	)	PUNCT
ejpam-5629	223	9	γjγ	γjγ	NOUN
ejpam-5629	223	10	(	(	PUNCT
ejpam-5629	223	11	ηj	ηj	ADP
ejpam-5629	223	12	+	+	NOUN
ejpam-5629	223	13	γj	γj	PROPN
ejpam-5629	223	14	)	)	PUNCT
ejpam-5629	223	15	∫	∫	PROPN
ejpam-5629	223	16	1	1	NUM
ejpam-5629	223	17	0	0	NUM
ejpam-5629	223	18	(	(	PUNCT
ejpam-5629	223	19	1−	1−	NUM
ejpam-5629	223	20	r)ηj+γj−1	r)ηj+γj−1	PROPN
ejpam-5629	223	21	zj	zj	PROPN
ejpam-5629	223	22	(	(	PUNCT
ejpam-5629	223	23	r	r	NOUN
ejpam-5629	223	24	,	,	PUNCT
ejpam-5629	223	25	φ(r	φ(r	ADJ
ejpam-5629	223	26	)	)	PUNCT
ejpam-5629	223	27	,	,	PUNCT
ejpam-5629	223	28	ω(r	ω(r	NUM
ejpam-5629	223	29	)	)	PUNCT
ejpam-5629	223	30	,	,	PUNCT
ejpam-5629	223	31	dρ−1φ(r	dρ−1φ(r	NOUN
ejpam-5629	223	32	)	)	PUNCT
ejpam-5629	223	33	,	,	PUNCT
ejpam-5629	223	34	dρω(r	dρω(r	PROPN
ejpam-5629	223	35	)	)	PUNCT
ejpam-5629	223	36	)	)	PUNCT
ejpam-5629	224	1	dr	dr	PROPN
ejpam-5629	224	2	)	)	PUNCT
ejpam-5629	225	1	+	+	NUM
ejpam-5629	225	2	⅁j	⅁j	NOUN
ejpam-5629	225	3	(	(	PUNCT
ejpam-5629	225	4	γj	γj	ADP
ejpam-5629	225	5	+	+	CCONJ
ejpam-5629	225	6	3	3	X
ejpam-5629	225	7	)	)	PUNCT
ejpam-5629	225	8	γ	γ	NOUN
ejpam-5629	225	9	(	(	PUNCT
ejpam-5629	225	10	γj	γj	ADP
ejpam-5629	225	11	−	−	PROPN
ejpam-5629	225	12	ρ+	ρ+	NOUN
ejpam-5629	225	13	4	4	NUM
ejpam-5629	225	14	)	)	PUNCT
ejpam-5629	225	15	ζγj−ρ+3	ζγj−ρ+3	NOUN
ejpam-5629	225	16	(	(	PUNCT
ejpam-5629	225	17	γ	γ	X
ejpam-5629	225	18	(	(	PUNCT
ejpam-5629	225	19	γj	γj	PROPN
ejpam-5629	225	20	+	+	CCONJ
ejpam-5629	225	21	3	3	X
ejpam-5629	225	22	)	)	PUNCT
ejpam-5629	225	23	γjγ	γjγ	NOUN
ejpam-5629	225	24	(	(	PUNCT
ejpam-5629	225	25	ηj	ηj	ADP
ejpam-5629	225	26	+	+	NOUN
ejpam-5629	225	27	γj	γj	PROPN
ejpam-5629	225	28	)	)	PUNCT
ejpam-5629	225	29	∫	∫	PROPN
ejpam-5629	225	30	1	1	NUM
ejpam-5629	225	31	0	0	NUM
ejpam-5629	225	32	(	(	PUNCT
ejpam-5629	225	33	1−	1−	NUM
ejpam-5629	225	34	r)ηj+γj−1	r)ηj+γj−1	PROPN
ejpam-5629	225	35	zj	zj	PROPN
ejpam-5629	225	36	(	(	PUNCT
ejpam-5629	225	37	r	r	NOUN
ejpam-5629	225	38	,	,	PUNCT
ejpam-5629	225	39	φ(r	φ(r	ADJ
ejpam-5629	225	40	)	)	PUNCT
ejpam-5629	225	41	,	,	PUNCT
ejpam-5629	225	42	ω(r	ω(r	NUM
ejpam-5629	225	43	)	)	PUNCT
ejpam-5629	225	44	,	,	PUNCT
ejpam-5629	225	45	dρ−1φ(r	dρ−1φ(r	NOUN
ejpam-5629	225	46	)	)	PUNCT
ejpam-5629	225	47	,	,	PUNCT
ejpam-5629	225	48	dρω(r	dρω(r	PROPN
ejpam-5629	225	49	)	)	PUNCT
ejpam-5629	225	50	)	)	PUNCT
ejpam-5629	226	1	dr	dr	PROPN
ejpam-5629	226	2	−	−	PROPN
ejpam-5629	226	3	γj	γj	PROPN
ejpam-5629	226	4	+	+	CCONJ
ejpam-5629	226	5	2	2	NUM
ejpam-5629	226	6	γjγ	γjγ	NOUN
ejpam-5629	226	7	(	(	PUNCT
ejpam-5629	226	8	ηj	ηj	NOUN
ejpam-5629	226	9	)	)	PUNCT
ejpam-5629	226	10	∫	∫	PROPN
ejpam-5629	226	11	1	1	NUM
ejpam-5629	226	12	0	0	NUM
ejpam-5629	226	13	(	(	PUNCT
ejpam-5629	226	14	1−	1−	NUM
ejpam-5629	226	15	r)ηj−1	r)ηj−1	NOUN
ejpam-5629	226	16	zj	zj	NOUN
ejpam-5629	226	17	(	(	PUNCT
ejpam-5629	226	18	r	r	NOUN
ejpam-5629	226	19	,	,	PUNCT
ejpam-5629	226	20	φ(r	φ(r	ADJ
ejpam-5629	226	21	)	)	PUNCT
ejpam-5629	226	22	,	,	PUNCT
ejpam-5629	226	23	ω(r	ω(r	NUM
ejpam-5629	226	24	)	)	PUNCT
ejpam-5629	226	25	,	,	PUNCT
ejpam-5629	226	26	dρ−1φ(r	dρ−1φ(r	NOUN
ejpam-5629	226	27	)	)	PUNCT
ejpam-5629	226	28	,	,	PUNCT
ejpam-5629	226	29	dρω(r	dρω(r	PROPN
ejpam-5629	226	30	)	)	PUNCT
ejpam-5629	226	31	)	)	PUNCT
ejpam-5629	227	1	dr	dr	PROPN
ejpam-5629	227	2	)	)	PUNCT
ejpam-5629	227	3	,	,	PUNCT
ejpam-5629	227	4	h.a	h.a	PROPN
ejpam-5629	227	5	.	.	PROPN
ejpam-5629	227	6	hammad	hammad	PROPN
ejpam-5629	227	7	,	,	PUNCT
ejpam-5629	227	8	m.e.m	m.e.m	NOUN
ejpam-5629	227	9	.	.	PUNCT
ejpam-5629	228	1	abdalla	abdalla	PROPN
ejpam-5629	228	2	/	/	SYM
ejpam-5629	228	3	eur	eur	PROPN
ejpam-5629	228	4	.	.	PUNCT
ejpam-5629	229	1	j.	j.	PROPN
ejpam-5629	229	2	pure	pure	PROPN
ejpam-5629	229	3	appl	appl	PROPN
ejpam-5629	229	4	.	.	PROPN
ejpam-5629	229	5	math	math	PROPN
ejpam-5629	229	6	,	,	PUNCT
ejpam-5629	229	7	18	18	NUM
ejpam-5629	229	8	(	(	PUNCT
ejpam-5629	229	9	1	1	NUM
ejpam-5629	229	10	)	)	PUNCT
ejpam-5629	229	11	(	(	PUNCT
ejpam-5629	229	12	2025	2025	NUM
ejpam-5629	229	13	)	)	PUNCT
ejpam-5629	229	14	,	,	PUNCT
ejpam-5629	229	15	5629	5629	NUM
ejpam-5629	229	16	10	10	NUM
ejpam-5629	229	17	of	of	ADP
ejpam-5629	229	18	20	20	NUM
ejpam-5629	229	19	and	and	CCONJ
ejpam-5629	229	20	dρ	dρ	PROPN
ejpam-5629	229	21	(	(	PUNCT
ejpam-5629	229	22	℧	℧	PROPN
ejpam-5629	229	23	j	j	X
ejpam-5629	229	24	(	(	PUNCT
ejpam-5629	229	25	φ(ζ	φ(ζ	NOUN
ejpam-5629	229	26	)	)	PUNCT
ejpam-5629	229	27	,	,	PUNCT
ejpam-5629	229	28	ω(ζ	ω(ζ	NOUN
ejpam-5629	229	29	)	)	PUNCT
ejpam-5629	229	30	)	)	PUNCT
ejpam-5629	229	31	)	)	PUNCT
ejpam-5629	230	1	=	=	PUNCT
ejpam-5629	230	2	⅁ji	⅁ji	NUM
ejpam-5629	230	3	ηj+γj−ρzj	ηj+γj−ρzj	NOUN
ejpam-5629	230	4	(	(	PUNCT
ejpam-5629	230	5	ζ	ζ	NOUN
ejpam-5629	230	6	,	,	PUNCT
ejpam-5629	230	7	φ(ζ	φ(ζ	NOUN
ejpam-5629	230	8	)	)	PUNCT
ejpam-5629	230	9	,	,	PUNCT
ejpam-5629	230	10	ω(ζ	ω(ζ	NOUN
ejpam-5629	230	11	)	)	PUNCT
ejpam-5629	230	12	,	,	PUNCT
ejpam-5629	230	13	dρ−1φ(ζ	dρ−1φ(ζ	NOUN
ejpam-5629	230	14	)	)	PUNCT
ejpam-5629	230	15	,	,	PUNCT
ejpam-5629	230	16	dρω(ζ	dρω(ζ	PROPN
ejpam-5629	230	17	)	)	PUNCT
ejpam-5629	230	18	)	)	PUNCT
ejpam-5629	231	1	+	+	CCONJ
ejpam-5629	231	2	⅁j	⅁j	NOUN
ejpam-5629	231	3	(	(	PUNCT
ejpam-5629	231	4	γj	γj	ADP
ejpam-5629	231	5	+	+	CCONJ
ejpam-5629	231	6	2	2	X
ejpam-5629	231	7	)	)	PUNCT
ejpam-5629	231	8	γ	γ	NOUN
ejpam-5629	231	9	(	(	PUNCT
ejpam-5629	231	10	γj	γj	ADP
ejpam-5629	231	11	−	−	PROPN
ejpam-5629	231	12	ρ+	ρ+	NOUN
ejpam-5629	231	13	2	2	NUM
ejpam-5629	231	14	)	)	PUNCT
ejpam-5629	231	15	ζγj−ρ+1	ζγj−ρ+1	NOUN
ejpam-5629	231	16	(	(	PUNCT
ejpam-5629	231	17	2	2	NUM
ejpam-5629	231	18	γjγ	γjγ	NOUN
ejpam-5629	231	19	(	(	PUNCT
ejpam-5629	231	20	ηj	ηj	NOUN
ejpam-5629	231	21	)	)	PUNCT
ejpam-5629	231	22	∫	∫	PROPN
ejpam-5629	231	23	1	1	NUM
ejpam-5629	231	24	0	0	NUM
ejpam-5629	231	25	(	(	PUNCT
ejpam-5629	231	26	1−	1−	NUM
ejpam-5629	231	27	r)ηj−1	r)ηj−1	NOUN
ejpam-5629	231	28	zj	zj	NOUN
ejpam-5629	231	29	(	(	PUNCT
ejpam-5629	231	30	r	r	NOUN
ejpam-5629	231	31	,	,	PUNCT
ejpam-5629	231	32	φ(r	φ(r	ADJ
ejpam-5629	231	33	)	)	PUNCT
ejpam-5629	231	34	,	,	PUNCT
ejpam-5629	231	35	ω(r	ω(r	NUM
ejpam-5629	231	36	)	)	PUNCT
ejpam-5629	231	37	,	,	PUNCT
ejpam-5629	231	38	dρ−1φ(r	dρ−1φ(r	NOUN
ejpam-5629	231	39	)	)	PUNCT
ejpam-5629	231	40	,	,	PUNCT
ejpam-5629	231	41	dρω(r	dρω(r	PROPN
ejpam-5629	231	42	)	)	PUNCT
ejpam-5629	231	43	)	)	PUNCT
ejpam-5629	232	1	dr	dr	PROPN
ejpam-5629	232	2	−	−	PROPN
ejpam-5629	232	3	γ	γ	X
ejpam-5629	232	4	(	(	PUNCT
ejpam-5629	232	5	γj	γj	PROPN
ejpam-5629	232	6	+	+	CCONJ
ejpam-5629	232	7	3	3	X
ejpam-5629	232	8	)	)	PUNCT
ejpam-5629	232	9	γjγ	γjγ	NOUN
ejpam-5629	232	10	(	(	PUNCT
ejpam-5629	232	11	ηj	ηj	ADP
ejpam-5629	232	12	+	+	NOUN
ejpam-5629	232	13	γj	γj	PROPN
ejpam-5629	232	14	)	)	PUNCT
ejpam-5629	232	15	∫	∫	PROPN
ejpam-5629	232	16	1	1	NUM
ejpam-5629	232	17	0	0	NUM
ejpam-5629	232	18	(	(	PUNCT
ejpam-5629	232	19	1−	1−	NUM
ejpam-5629	232	20	r)ηj+γj−1	r)ηj+γj−1	PROPN
ejpam-5629	232	21	zj	zj	PROPN
ejpam-5629	232	22	(	(	PUNCT
ejpam-5629	232	23	r	r	NOUN
ejpam-5629	232	24	,	,	PUNCT
ejpam-5629	232	25	φ(r	φ(r	ADJ
ejpam-5629	232	26	)	)	PUNCT
ejpam-5629	232	27	,	,	PUNCT
ejpam-5629	232	28	ω(r	ω(r	NUM
ejpam-5629	232	29	)	)	PUNCT
ejpam-5629	232	30	,	,	PUNCT
ejpam-5629	232	31	dρ−1φ(r	dρ−1φ(r	NOUN
ejpam-5629	232	32	)	)	PUNCT
ejpam-5629	232	33	,	,	PUNCT
ejpam-5629	232	34	dρω(r	dρω(r	PROPN
ejpam-5629	232	35	)	)	PUNCT
ejpam-5629	232	36	)	)	PUNCT
ejpam-5629	233	1	dr	dr	PROPN
ejpam-5629	233	2	)	)	PUNCT
ejpam-5629	234	1	+	+	NUM
ejpam-5629	234	2	⅁j	⅁j	NOUN
ejpam-5629	234	3	(	(	PUNCT
ejpam-5629	234	4	γj	γj	ADP
ejpam-5629	234	5	+	+	CCONJ
ejpam-5629	234	6	3	3	X
ejpam-5629	234	7	)	)	PUNCT
ejpam-5629	234	8	γ	γ	NOUN
ejpam-5629	234	9	(	(	PUNCT
ejpam-5629	234	10	γj	γj	PROPN
ejpam-5629	234	11	−	−	PROPN
ejpam-5629	234	12	ρ+	ρ+	NOUN
ejpam-5629	234	13	3	3	X
ejpam-5629	234	14	)	)	PUNCT
ejpam-5629	234	15	ζγj−ρ+2	ζγj−ρ+2	NOUN
ejpam-5629	234	16	(	(	PUNCT
ejpam-5629	234	17	γ	γ	X
ejpam-5629	234	18	(	(	PUNCT
ejpam-5629	234	19	γj	γj	PROPN
ejpam-5629	234	20	+	+	CCONJ
ejpam-5629	234	21	3	3	X
ejpam-5629	234	22	)	)	PUNCT
ejpam-5629	234	23	γjγ	γjγ	NOUN
ejpam-5629	234	24	(	(	PUNCT
ejpam-5629	234	25	ηj	ηj	ADP
ejpam-5629	234	26	+	+	NOUN
ejpam-5629	234	27	γj	γj	PROPN
ejpam-5629	234	28	)	)	PUNCT
ejpam-5629	234	29	∫	∫	PROPN
ejpam-5629	234	30	1	1	NUM
ejpam-5629	234	31	0	0	NUM
ejpam-5629	234	32	(	(	PUNCT
ejpam-5629	234	33	1−	1−	NUM
ejpam-5629	234	34	r)ηj+γj−1	r)ηj+γj−1	PROPN
ejpam-5629	234	35	zj	zj	PROPN
ejpam-5629	234	36	(	(	PUNCT
ejpam-5629	234	37	r	r	NOUN
ejpam-5629	234	38	,	,	PUNCT
ejpam-5629	234	39	φ(r	φ(r	ADJ
ejpam-5629	234	40	)	)	PUNCT
ejpam-5629	234	41	,	,	PUNCT
ejpam-5629	234	42	ω(r	ω(r	NUM
ejpam-5629	234	43	)	)	PUNCT
ejpam-5629	234	44	,	,	PUNCT
ejpam-5629	234	45	dρ−1φ(r	dρ−1φ(r	NOUN
ejpam-5629	234	46	)	)	PUNCT
ejpam-5629	234	47	,	,	PUNCT
ejpam-5629	234	48	dρω(r	dρω(r	PROPN
ejpam-5629	234	49	)	)	PUNCT
ejpam-5629	234	50	)	)	PUNCT
ejpam-5629	235	1	dr	dr	PROPN
ejpam-5629	235	2	−	−	PROPN
ejpam-5629	235	3	γj	γj	PROPN
ejpam-5629	235	4	+	+	CCONJ
ejpam-5629	235	5	2	2	NUM
ejpam-5629	235	6	γjγ	γjγ	NOUN
ejpam-5629	235	7	(	(	PUNCT
ejpam-5629	235	8	ηj	ηj	NOUN
ejpam-5629	235	9	)	)	PUNCT
ejpam-5629	235	10	∫	∫	PROPN
ejpam-5629	235	11	1	1	NUM
ejpam-5629	235	12	0	0	NUM
ejpam-5629	235	13	(	(	PUNCT
ejpam-5629	235	14	1−	1−	NUM
ejpam-5629	235	15	r)ηj−1	r)ηj−1	NOUN
ejpam-5629	235	16	zj	zj	NOUN
ejpam-5629	235	17	(	(	PUNCT
ejpam-5629	235	18	r	r	NOUN
ejpam-5629	235	19	,	,	PUNCT
ejpam-5629	235	20	φ(r	φ(r	ADJ
ejpam-5629	235	21	)	)	PUNCT
ejpam-5629	235	22	,	,	PUNCT
ejpam-5629	235	23	ω(r	ω(r	NUM
ejpam-5629	235	24	)	)	PUNCT
ejpam-5629	235	25	,	,	PUNCT
ejpam-5629	235	26	dρ−1φ(r	dρ−1φ(r	NOUN
ejpam-5629	235	27	)	)	PUNCT
ejpam-5629	235	28	,	,	PUNCT
ejpam-5629	235	29	dρω(r	dρω(r	PROPN
ejpam-5629	235	30	)	)	PUNCT
ejpam-5629	235	31	)	)	PUNCT
ejpam-5629	235	32	dr	dr	PROPN
ejpam-5629	235	33	)	)	PUNCT
ejpam-5629	235	34	.	.	PUNCT
ejpam-5629	236	1	by	by	ADP
ejpam-5629	236	2	using	use	VERB
ejpam-5629	236	3	the	the	DET
ejpam-5629	236	4	hypothesis	hypothesis	NOUN
ejpam-5629	236	5	(	(	PUNCT
ejpam-5629	236	6	a1	a1	NOUN
ejpam-5629	236	7	)	)	PUNCT
ejpam-5629	236	8	,	,	PUNCT
ejpam-5629	236	9	and	and	CCONJ
ejpam-5629	236	10	similar	similar	ADJ
ejpam-5629	236	11	to	to	ADP
ejpam-5629	236	12	(	(	PUNCT
ejpam-5629	236	13	7	7	NUM
ejpam-5629	236	14	)	)	PUNCT
ejpam-5629	236	15	,	,	PUNCT
ejpam-5629	236	16	we	we	PRON
ejpam-5629	236	17	get∥∥dρ−1	get∥∥dρ−1	PROPN
ejpam-5629	236	18	℧	℧	PROPN
ejpam-5629	236	19	j	j	PROPN
ejpam-5629	236	20	(	(	PUNCT
ejpam-5629	236	21	φ1	φ1	PROPN
ejpam-5629	236	22	,	,	PUNCT
ejpam-5629	236	23	ω1)−dρ−1	ω1)−dρ−1	PROPN
ejpam-5629	236	24	℧	℧	PROPN
ejpam-5629	236	25	j	j	PROPN
ejpam-5629	236	26	(	(	PUNCT
ejpam-5629	236	27	φ2	φ2	PROPN
ejpam-5629	236	28	,	,	PUNCT
ejpam-5629	236	29	ω2	ω2	ADJ
ejpam-5629	236	30	)	)	PUNCT
ejpam-5629	236	31	∥∥	∥∥	PROPN
ejpam-5629	236	32	∞	∞	NUM
ejpam-5629	236	33	≤	≤	NUM
ejpam-5629	236	34	(	(	PUNCT
ejpam-5629	236	35	⅁j	⅁j	PROPN
ejpam-5629	236	36	γ	γ	X
ejpam-5629	236	37	(	(	PUNCT
ejpam-5629	236	38	ηj	ηj	ADP
ejpam-5629	236	39	+	+	NOUN
ejpam-5629	236	40	γj	γj	ADP
ejpam-5629	236	41	−	−	NOUN
ejpam-5629	236	42	ρ+	ρ+	NOUN
ejpam-5629	236	43	2	2	NUM
ejpam-5629	236	44	)	)	PUNCT
ejpam-5629	236	45	+	+	NUM
ejpam-5629	236	46	⅁jγ	⅁jγ	PUNCT
ejpam-5629	236	47	(	(	PUNCT
ejpam-5629	236	48	γj	γj	ADP
ejpam-5629	236	49	+	+	CCONJ
ejpam-5629	236	50	2	2	X
ejpam-5629	236	51	)	)	PUNCT
ejpam-5629	236	52	γjγ	γjγ	NOUN
ejpam-5629	236	53	(	(	PUNCT
ejpam-5629	236	54	ηj	ηj	ADP
ejpam-5629	236	55	+	+	X
ejpam-5629	236	56	1)γ	1)γ	PROPN
ejpam-5629	236	57	(	(	PUNCT
ejpam-5629	236	58	γj	γj	ADP
ejpam-5629	236	59	−	−	PROPN
ejpam-5629	236	60	ρ+	ρ+	NOUN
ejpam-5629	236	61	4	4	NUM
ejpam-5629	236	62	)	)	PUNCT
ejpam-5629	236	63	[	[	PUNCT
ejpam-5629	236	64	2	2	NUM
ejpam-5629	236	65	(	(	PUNCT
ejpam-5629	236	66	γj	γj	NOUN
ejpam-5629	236	67	−	−	NOUN
ejpam-5629	236	68	ρ+	ρ+	NOUN
ejpam-5629	236	69	3	3	NUM
ejpam-5629	236	70	)	)	PUNCT
ejpam-5629	236	71	+	+	CCONJ
ejpam-5629	236	72	(	(	PUNCT
ejpam-5629	236	73	γj	γj	ADP
ejpam-5629	236	74	+	+	CCONJ
ejpam-5629	236	75	2)2	2)2	NUM
ejpam-5629	236	76	]	]	PUNCT
ejpam-5629	236	77	+	+	CCONJ
ejpam-5629	236	78	⅁jγ	⅁jγ	PUNCT
ejpam-5629	236	79	(	(	PUNCT
ejpam-5629	236	80	γj	γj	ADP
ejpam-5629	236	81	+	+	VERB
ejpam-5629	236	82	2)γ	2)γ	NUM
ejpam-5629	236	83	(	(	PUNCT
ejpam-5629	236	84	γj	γj	ADP
ejpam-5629	236	85	+	+	CCONJ
ejpam-5629	236	86	3	3	X
ejpam-5629	236	87	)	)	PUNCT
ejpam-5629	236	88	γjγ	γjγ	NOUN
ejpam-5629	236	89	(	(	PUNCT
ejpam-5629	236	90	γj	γj	ADP
ejpam-5629	236	91	+	+	CCONJ
ejpam-5629	236	92	ηj	ηj	ADP
ejpam-5629	236	93	+	+	ADJ
ejpam-5629	236	94	1)γ	1)γ	PROPN
ejpam-5629	236	95	(	(	PUNCT
ejpam-5629	236	96	γj	γj	ADP
ejpam-5629	236	97	−	−	PROPN
ejpam-5629	236	98	ρ+	ρ+	NOUN
ejpam-5629	236	99	4	4	NUM
ejpam-5629	236	100	)	)	PUNCT
ejpam-5629	237	1	[	[	X
ejpam-5629	237	2	2γj	2γj	ADJ
ejpam-5629	237	3	−	−	ADP
ejpam-5629	237	4	ρ+	ρ+	NOUN
ejpam-5629	237	5	5	5	NUM
ejpam-5629	237	6	]	]	PUNCT
ejpam-5629	237	7	)	)	PUNCT
ejpam-5629	238	1	[	[	X
ejpam-5629	238	2	m1j	m1j	PUNCT
ejpam-5629	238	3	∥φ1	∥φ1	NUM
ejpam-5629	238	4	−	−	PUNCT
ejpam-5629	238	5	φ2∥∞	φ2∥∞	PROPN
ejpam-5629	239	1	+	+	PROPN
ejpam-5629	239	2	m2j	m2j	PROPN
ejpam-5629	239	3	∥ω1	∥ω1	PUNCT
ejpam-5629	239	4	−	−	NOUN
ejpam-5629	239	5	ω2∥∞	ω2∥∞	PROPN
ejpam-5629	240	1	+	+	ADJ
ejpam-5629	240	2	m3j	m3j	PROPN
ejpam-5629	240	3	∥∥dρ−1φ1	∥∥dρ−1φ1	PROPN
ejpam-5629	240	4	−dρ−1φ2	−dρ−1φ2	PROPN
ejpam-5629	240	5	∥∥	∥∥	PUNCT
ejpam-5629	240	6	∞	∞	NUM
ejpam-5629	240	7	+	+	PROPN
ejpam-5629	240	8	m4j	m4j	NOUN
ejpam-5629	240	9	∥dρω1	∥dρω1	NOUN
ejpam-5629	240	10	−dρω2∥∞	−dρω2∥∞	PROPN
ejpam-5629	240	11	]	]	PUNCT
ejpam-5629	240	12	(	(	PUNCT
ejpam-5629	240	13	8)	8)	NUM
ejpam-5629	240	14	replacing	replace	VERB
ejpam-5629	240	15	ρ−	ρ−	NOUN
ejpam-5629	240	16	1	1	NUM
ejpam-5629	240	17	with	with	ADP
ejpam-5629	240	18	ρ	ρ	PROPN
ejpam-5629	240	19	in	in	ADP
ejpam-5629	240	20	(	(	PUNCT
ejpam-5629	240	21	8)	8)	NUM
ejpam-5629	240	22	except	except	SCONJ
ejpam-5629	240	23	in	in	ADP
ejpam-5629	240	24	the	the	DET
ejpam-5629	240	25	term	term	NOUN
ejpam-5629	240	26	within	within	ADP
ejpam-5629	240	27	the	the	DET
ejpam-5629	240	28	large	large	ADJ
ejpam-5629	240	29	parentheses	parenthesis	NOUN
ejpam-5629	240	30	,	,	PUNCT
ejpam-5629	240	31	one	one	PRON
ejpam-5629	240	32	has	have	VERB
ejpam-5629	240	33	∥dρ	∥dρ	PROPN
ejpam-5629	240	34	℧	℧	PROPN
ejpam-5629	240	35	j	j	PROPN
ejpam-5629	240	36	(	(	PUNCT
ejpam-5629	240	37	φ1	φ1	PROPN
ejpam-5629	240	38	,	,	PUNCT
ejpam-5629	240	39	ω1)−dρ	ω1)−dρ	PROPN
ejpam-5629	240	40	℧	℧	PROPN
ejpam-5629	240	41	j	j	PROPN
ejpam-5629	240	42	(	(	PUNCT
ejpam-5629	240	43	φ2	φ2	PROPN
ejpam-5629	240	44	,	,	PUNCT
ejpam-5629	240	45	ω2)∥∞	ω2)∥∞	PROPN
ejpam-5629	240	46	≤	≤	NUM
ejpam-5629	240	47	(	(	PUNCT
ejpam-5629	240	48	⅁j	⅁j	PROPN
ejpam-5629	240	49	γ	γ	X
ejpam-5629	240	50	(	(	PUNCT
ejpam-5629	240	51	ηj	ηj	ADP
ejpam-5629	240	52	+	+	NOUN
ejpam-5629	240	53	γj	γj	ADP
ejpam-5629	240	54	−	−	NOUN
ejpam-5629	240	55	ρ+	ρ+	NOUN
ejpam-5629	240	56	1	1	NUM
ejpam-5629	240	57	)	)	PUNCT
ejpam-5629	240	58	+	+	CCONJ
ejpam-5629	240	59	⅁jγ	⅁jγ	PUNCT
ejpam-5629	240	60	(	(	PUNCT
ejpam-5629	240	61	γj	γj	ADP
ejpam-5629	240	62	+	+	CCONJ
ejpam-5629	240	63	2	2	X
ejpam-5629	240	64	)	)	PUNCT
ejpam-5629	240	65	γjγ	γjγ	NOUN
ejpam-5629	240	66	(	(	PUNCT
ejpam-5629	240	67	ηj	ηj	ADP
ejpam-5629	240	68	+	+	X
ejpam-5629	240	69	1)γ	1)γ	PROPN
ejpam-5629	240	70	(	(	PUNCT
ejpam-5629	240	71	γj	γj	ADP
ejpam-5629	240	72	−	−	PROPN
ejpam-5629	240	73	ρ+	ρ+	NOUN
ejpam-5629	240	74	3	3	X
ejpam-5629	240	75	)	)	PUNCT
ejpam-5629	240	76	[	[	PUNCT
ejpam-5629	240	77	2	2	NUM
ejpam-5629	240	78	(	(	PUNCT
ejpam-5629	240	79	γj	γj	NOUN
ejpam-5629	240	80	−	−	NOUN
ejpam-5629	240	81	ρ+	ρ+	NOUN
ejpam-5629	240	82	2	2	NUM
ejpam-5629	240	83	)	)	PUNCT
ejpam-5629	240	84	+	+	CCONJ
ejpam-5629	240	85	(	(	PUNCT
ejpam-5629	240	86	γj	γj	ADP
ejpam-5629	240	87	+	+	CCONJ
ejpam-5629	240	88	2)2	2)2	NUM
ejpam-5629	240	89	]	]	PUNCT
ejpam-5629	240	90	+	+	CCONJ
ejpam-5629	240	91	⅁jγ	⅁jγ	PUNCT
ejpam-5629	240	92	(	(	PUNCT
ejpam-5629	240	93	γj	γj	ADP
ejpam-5629	240	94	+	+	VERB
ejpam-5629	240	95	2)γ	2)γ	NUM
ejpam-5629	240	96	(	(	PUNCT
ejpam-5629	240	97	γj	γj	ADP
ejpam-5629	240	98	+	+	CCONJ
ejpam-5629	240	99	3	3	X
ejpam-5629	240	100	)	)	PUNCT
ejpam-5629	240	101	γjγ	γjγ	NOUN
ejpam-5629	240	102	(	(	PUNCT
ejpam-5629	240	103	γj	γj	ADP
ejpam-5629	240	104	+	+	CCONJ
ejpam-5629	240	105	ηj	ηj	ADP
ejpam-5629	240	106	+	+	ADJ
ejpam-5629	240	107	1)γ	1)γ	PROPN
ejpam-5629	240	108	(	(	PUNCT
ejpam-5629	240	109	γj	γj	ADP
ejpam-5629	240	110	−	−	PROPN
ejpam-5629	240	111	ρ+	ρ+	NOUN
ejpam-5629	240	112	3	3	X
ejpam-5629	240	113	)	)	PUNCT
ejpam-5629	241	1	[	[	X
ejpam-5629	241	2	2γj	2γj	ADJ
ejpam-5629	241	3	−	−	ADP
ejpam-5629	241	4	ρ+	ρ+	NOUN
ejpam-5629	241	5	4	4	NUM
ejpam-5629	241	6	]	]	PUNCT
ejpam-5629	241	7	)	)	PUNCT
ejpam-5629	242	1	[	[	X
ejpam-5629	242	2	m1j	m1j	PUNCT
ejpam-5629	242	3	∥φ1	∥φ1	NUM
ejpam-5629	242	4	−	−	PUNCT
ejpam-5629	242	5	φ2∥∞	φ2∥∞	PROPN
ejpam-5629	243	1	+	+	PROPN
ejpam-5629	243	2	m2j	m2j	PROPN
ejpam-5629	243	3	∥ω1	∥ω1	PUNCT
ejpam-5629	243	4	−	−	NOUN
ejpam-5629	243	5	ω2∥∞	ω2∥∞	PRON
ejpam-5629	244	1	+	+	ADJ
ejpam-5629	244	2	m1j	m1j	NOUN
ejpam-5629	244	3	∥∥dρ−1φ1	∥∥dρ−1φ1	ADJ
ejpam-5629	244	4	−dρ−1φ2	−dρ−1φ2	PROPN
ejpam-5629	244	5	∥∥	∥∥	PUNCT
ejpam-5629	244	6	∞	∞	NUM
ejpam-5629	244	7	+	+	NOUN
ejpam-5629	244	8	m2j	m2j	PROPN
ejpam-5629	244	9	∥dρω1	∥dρω1	ADP
ejpam-5629	244	10	−dρω2∥∞	−dρω2∥∞	PRON
ejpam-5629	244	11	]	]	PUNCT
ejpam-5629	244	12	(	(	PUNCT
ejpam-5629	244	13	9	9	X
ejpam-5629	244	14	)	)	PUNCT
ejpam-5629	244	15	it	it	PRON
ejpam-5629	244	16	follows	follow	VERB
ejpam-5629	244	17	from	from	ADP
ejpam-5629	244	18	(	(	PUNCT
ejpam-5629	244	19	7)-(9	7)-(9	NOUN
ejpam-5629	244	20	)	)	PUNCT
ejpam-5629	244	21	and	and	CCONJ
ejpam-5629	244	22	the	the	DET
ejpam-5629	244	23	definition	definition	NOUN
ejpam-5629	244	24	of	of	ADP
ejpam-5629	244	25	the	the	DET
ejpam-5629	244	26	norm	norm	NOUN
ejpam-5629	244	27	on	on	ADP
ejpam-5629	244	28	ξ	ξ	PROPN
ejpam-5629	244	29	that	that	SCONJ
ejpam-5629	244	30	∥	∥	PUNCT
ejpam-5629	244	31	℧	℧	PROPN
ejpam-5629	244	32	j	j	PROPN
ejpam-5629	244	33	(	(	PUNCT
ejpam-5629	244	34	φ1	φ1	PROPN
ejpam-5629	244	35	,	,	PUNCT
ejpam-5629	244	36	ω1)−	ω1)−	PROPN
ejpam-5629	244	37	℧	℧	PROPN
ejpam-5629	244	38	j	j	PROPN
ejpam-5629	244	39	(	(	PUNCT
ejpam-5629	244	40	φ2	φ2	PROPN
ejpam-5629	244	41	,	,	PUNCT
ejpam-5629	244	42	ω2)∥ξ	ω2)∥ξ	VERB
ejpam-5629	244	43	≤	≤	ADJ
ejpam-5629	244	44	⅁j	⅁j	NOUN
ejpam-5629	244	45	{	{	PUNCT
ejpam-5629	244	46	(	(	PUNCT
ejpam-5629	244	47	γj	γj	ADP
ejpam-5629	244	48	+	+	CCONJ
ejpam-5629	244	49	2γ	2γ	NOUN
ejpam-5629	244	50	(	(	PUNCT
ejpam-5629	244	51	γj	γj	NOUN
ejpam-5629	244	52	+	+	CCONJ
ejpam-5629	244	53	3	3	X
ejpam-5629	244	54	)	)	PUNCT
ejpam-5629	244	55	γjγ	γjγ	NOUN
ejpam-5629	244	56	(	(	PUNCT
ejpam-5629	244	57	ηj	ηj	NOUN
ejpam-5629	244	58	+	+	NOUN
ejpam-5629	244	59	γj	γj	NOUN
ejpam-5629	244	60	)	)	PUNCT
ejpam-5629	245	1	+	+	NOUN
ejpam-5629	245	2	γj	γj	ADP
ejpam-5629	245	3	+	+	CCONJ
ejpam-5629	245	4	4	4	NUM
ejpam-5629	245	5	γjγ	γjγ	NOUN
ejpam-5629	245	6	(	(	PUNCT
ejpam-5629	245	7	ηj	ηj	NOUN
ejpam-5629	245	8	)	)	PUNCT
ejpam-5629	245	9	)	)	PUNCT
ejpam-5629	246	1	+	+	CCONJ
ejpam-5629	246	2	1	1	NUM
ejpam-5629	246	3	γ	γ	X
ejpam-5629	246	4	(	(	PUNCT
ejpam-5629	246	5	ηj	ηj	ADP
ejpam-5629	246	6	+	+	NOUN
ejpam-5629	246	7	γj	γj	ADP
ejpam-5629	246	8	−	−	NOUN
ejpam-5629	246	9	ρ+	ρ+	NOUN
ejpam-5629	246	10	2	2	NUM
ejpam-5629	246	11	)	)	PUNCT
ejpam-5629	246	12	+	+	CCONJ
ejpam-5629	246	13	γ	γ	X
ejpam-5629	246	14	(	(	PUNCT
ejpam-5629	246	15	γj	γj	ADP
ejpam-5629	246	16	+	+	CCONJ
ejpam-5629	246	17	2	2	X
ejpam-5629	246	18	)	)	PUNCT
ejpam-5629	246	19	γjγ	γjγ	NOUN
ejpam-5629	246	20	(	(	PUNCT
ejpam-5629	246	21	ηj	ηj	ADP
ejpam-5629	246	22	+	+	X
ejpam-5629	246	23	1)γ	1)γ	PROPN
ejpam-5629	246	24	(	(	PUNCT
ejpam-5629	246	25	γj	γj	ADP
ejpam-5629	246	26	−	−	PROPN
ejpam-5629	246	27	ρ+	ρ+	NOUN
ejpam-5629	246	28	4	4	NUM
ejpam-5629	246	29	)	)	PUNCT
ejpam-5629	246	30	[	[	PUNCT
ejpam-5629	246	31	2	2	NUM
ejpam-5629	246	32	(	(	PUNCT
ejpam-5629	246	33	γj	γj	NOUN
ejpam-5629	246	34	−	−	NOUN
ejpam-5629	246	35	ρ+	ρ+	NOUN
ejpam-5629	246	36	3	3	NUM
ejpam-5629	246	37	)	)	PUNCT
ejpam-5629	246	38	+	+	CCONJ
ejpam-5629	246	39	(	(	PUNCT
ejpam-5629	246	40	γj	γj	ADP
ejpam-5629	246	41	+	+	CCONJ
ejpam-5629	246	42	2)2	2)2	NUM
ejpam-5629	246	43	]	]	PUNCT
ejpam-5629	247	1	+	+	CCONJ
ejpam-5629	247	2	γ	γ	X
ejpam-5629	247	3	(	(	PUNCT
ejpam-5629	247	4	γj	γj	ADP
ejpam-5629	247	5	+	+	NOUN
ejpam-5629	247	6	2)γ	2)γ	NUM
ejpam-5629	247	7	(	(	PUNCT
ejpam-5629	247	8	γj	γj	ADP
ejpam-5629	247	9	+	+	CCONJ
ejpam-5629	247	10	3	3	X
ejpam-5629	247	11	)	)	PUNCT
ejpam-5629	247	12	γjγ	γjγ	NOUN
ejpam-5629	247	13	(	(	PUNCT
ejpam-5629	247	14	γj	γj	ADP
ejpam-5629	247	15	+	+	CCONJ
ejpam-5629	247	16	ηj	ηj	ADP
ejpam-5629	247	17	+	+	ADJ
ejpam-5629	247	18	1)γ	1)γ	PROPN
ejpam-5629	247	19	(	(	PUNCT
ejpam-5629	247	20	γj	γj	ADP
ejpam-5629	247	21	−	−	PROPN
ejpam-5629	247	22	ρ+	ρ+	NOUN
ejpam-5629	247	23	4	4	NUM
ejpam-5629	247	24	)	)	PUNCT
ejpam-5629	247	25	[	[	X
ejpam-5629	247	26	2γj	2γj	ADJ
ejpam-5629	247	27	−	−	ADP
ejpam-5629	247	28	ρ+	ρ+	NOUN
ejpam-5629	247	29	5	5	NUM
ejpam-5629	247	30	]	]	PUNCT
ejpam-5629	247	31	+	+	CCONJ
ejpam-5629	247	32	1	1	NUM
ejpam-5629	247	33	γ	γ	X
ejpam-5629	247	34	(	(	PUNCT
ejpam-5629	247	35	ηj	ηj	ADP
ejpam-5629	247	36	+	+	NOUN
ejpam-5629	247	37	γj	γj	ADP
ejpam-5629	247	38	−	−	NOUN
ejpam-5629	247	39	ρ+	ρ+	NOUN
ejpam-5629	247	40	1	1	NUM
ejpam-5629	247	41	)	)	PUNCT
ejpam-5629	247	42	+	+	CCONJ
ejpam-5629	247	43	γ	γ	X
ejpam-5629	247	44	(	(	PUNCT
ejpam-5629	247	45	γj	γj	ADP
ejpam-5629	247	46	+	+	CCONJ
ejpam-5629	247	47	2	2	X
ejpam-5629	247	48	)	)	PUNCT
ejpam-5629	247	49	γjγ	γjγ	NOUN
ejpam-5629	247	50	(	(	PUNCT
ejpam-5629	247	51	ηj	ηj	ADP
ejpam-5629	247	52	+	+	X
ejpam-5629	247	53	1)γ	1)γ	PROPN
ejpam-5629	247	54	(	(	PUNCT
ejpam-5629	247	55	γj	γj	ADP
ejpam-5629	247	56	−	−	PROPN
ejpam-5629	247	57	ρ+	ρ+	NOUN
ejpam-5629	247	58	3	3	X
ejpam-5629	247	59	)	)	PUNCT
ejpam-5629	247	60	[	[	PUNCT
ejpam-5629	247	61	2	2	NUM
ejpam-5629	247	62	(	(	PUNCT
ejpam-5629	247	63	γj	γj	NOUN
ejpam-5629	247	64	−	−	NOUN
ejpam-5629	247	65	ρ+	ρ+	NOUN
ejpam-5629	247	66	2	2	NUM
ejpam-5629	247	67	)	)	PUNCT
ejpam-5629	247	68	+	+	CCONJ
ejpam-5629	247	69	(	(	PUNCT
ejpam-5629	247	70	γj	γj	ADP
ejpam-5629	247	71	+	+	CCONJ
ejpam-5629	247	72	2)2	2)2	NUM
ejpam-5629	247	73	]	]	PUNCT
ejpam-5629	247	74	h.a	h.a	PROPN
ejpam-5629	247	75	.	.	PROPN
ejpam-5629	247	76	hammad	hammad	PROPN
ejpam-5629	247	77	,	,	PUNCT
ejpam-5629	247	78	m.e.m	m.e.m	NOUN
ejpam-5629	247	79	.	.	PUNCT
ejpam-5629	248	1	abdalla	abdalla	PROPN
ejpam-5629	248	2	/	/	SYM
ejpam-5629	248	3	eur	eur	PROPN
ejpam-5629	248	4	.	.	PUNCT
ejpam-5629	249	1	j.	j.	PROPN
ejpam-5629	249	2	pure	pure	PROPN
ejpam-5629	249	3	appl	appl	PROPN
ejpam-5629	249	4	.	.	PROPN
ejpam-5629	249	5	math	math	PROPN
ejpam-5629	249	6	,	,	PUNCT
ejpam-5629	249	7	18	18	NUM
ejpam-5629	249	8	(	(	PUNCT
ejpam-5629	249	9	1	1	NUM
ejpam-5629	249	10	)	)	PUNCT
ejpam-5629	249	11	(	(	PUNCT
ejpam-5629	249	12	2025	2025	NUM
ejpam-5629	249	13	)	)	PUNCT
ejpam-5629	249	14	,	,	PUNCT
ejpam-5629	249	15	5629	5629	NUM
ejpam-5629	249	16	11	11	NUM
ejpam-5629	249	17	of	of	ADP
ejpam-5629	249	18	20	20	NUM
ejpam-5629	249	19	+	+	CCONJ
ejpam-5629	249	20	γ	γ	X
ejpam-5629	249	21	(	(	PUNCT
ejpam-5629	249	22	γj	γj	ADP
ejpam-5629	249	23	+	+	NOUN
ejpam-5629	249	24	2)γ	2)γ	NUM
ejpam-5629	249	25	(	(	PUNCT
ejpam-5629	249	26	γj	γj	ADP
ejpam-5629	249	27	+	+	CCONJ
ejpam-5629	249	28	3	3	X
ejpam-5629	249	29	)	)	PUNCT
ejpam-5629	249	30	γjγ	γjγ	NOUN
ejpam-5629	249	31	(	(	PUNCT
ejpam-5629	249	32	γj	γj	ADP
ejpam-5629	249	33	+	+	CCONJ
ejpam-5629	249	34	ηj	ηj	ADP
ejpam-5629	249	35	+	+	ADJ
ejpam-5629	249	36	1)γ	1)γ	PROPN
ejpam-5629	249	37	(	(	PUNCT
ejpam-5629	249	38	γj	γj	ADP
ejpam-5629	249	39	−	−	PROPN
ejpam-5629	249	40	ρ+	ρ+	NOUN
ejpam-5629	249	41	3	3	X
ejpam-5629	249	42	)	)	PUNCT
ejpam-5629	250	1	[	[	X
ejpam-5629	250	2	2γj	2γj	ADJ
ejpam-5629	250	3	−	−	ADP
ejpam-5629	250	4	ρ+	ρ+	NOUN
ejpam-5629	250	5	4	4	NUM
ejpam-5629	250	6	]	]	PUNCT
ejpam-5629	250	7	}	}	PUNCT
ejpam-5629	250	8	×	×	NOUN
ejpam-5629	251	1	[	[	X
ejpam-5629	251	2	(	(	PUNCT
ejpam-5629	251	3	m1j	m1j	INTJ
ejpam-5629	251	4	+	+	NOUN
ejpam-5629	251	5	m3j	m3j	X
ejpam-5629	251	6	)	)	PUNCT
ejpam-5629	251	7	∥φ1	∥φ1	VERB
ejpam-5629	251	8	−	−	PROPN
ejpam-5629	251	9	φ2∥∞	φ2∥∞	PROPN
ejpam-5629	252	1	+	+	CCONJ
ejpam-5629	252	2	(	(	PUNCT
ejpam-5629	252	3	m2j	m2j	PROPN
ejpam-5629	252	4	+	+	NOUN
ejpam-5629	252	5	m4j	m4j	NOUN
ejpam-5629	252	6	)	)	PUNCT
ejpam-5629	252	7	∥ω1	∥ω1	NOUN
ejpam-5629	252	8	−	−	NOUN
ejpam-5629	252	9	ω2∥∞	ω2∥∞	PRON
ejpam-5629	252	10	]	]	PUNCT
ejpam-5629	252	11	≤	≤	NOUN
ejpam-5629	252	12	bj	bj	ADP
ejpam-5629	252	13	[	[	X
ejpam-5629	252	14	(	(	PUNCT
ejpam-5629	252	15	m1j	m1j	INTJ
ejpam-5629	252	16	+	+	NOUN
ejpam-5629	252	17	m3j	m3j	X
ejpam-5629	252	18	)	)	PUNCT
ejpam-5629	252	19	∥φ1	∥φ1	VERB
ejpam-5629	252	20	−	−	PROPN
ejpam-5629	252	21	φ2∥∞	φ2∥∞	PROPN
ejpam-5629	253	1	+	+	CCONJ
ejpam-5629	253	2	(	(	PUNCT
ejpam-5629	253	3	m2j	m2j	PROPN
ejpam-5629	253	4	+	+	NOUN
ejpam-5629	253	5	m4j	m4j	NOUN
ejpam-5629	253	6	)	)	PUNCT
ejpam-5629	253	7	∥ω1	∥ω1	NOUN
ejpam-5629	253	8	−	−	PROPN
ejpam-5629	253	9	ω2∥∞	ω2∥∞	PRON
ejpam-5629	253	10	]	]	PUNCT
ejpam-5629	253	11	.	.	PUNCT
ejpam-5629	254	1	by	by	ADP
ejpam-5629	254	2	the	the	DET
ejpam-5629	254	3	definition	definition	NOUN
ejpam-5629	254	4	of	of	ADP
ejpam-5629	254	5	the	the	DET
ejpam-5629	254	6	norm	norm	NOUN
ejpam-5629	254	7	on	on	ADP
ejpam-5629	254	8	ξ×	ξ×	PROPN
ejpam-5629	254	9	ξ	ξ	PROPN
ejpam-5629	254	10	and	and	CCONJ
ejpam-5629	254	11	ω1	ω1	PROPN
ejpam-5629	254	12	,	,	PUNCT
ejpam-5629	254	13	ω2	ω2	ADJ
ejpam-5629	254	14	,	,	PUNCT
ejpam-5629	254	15	we	we	PRON
ejpam-5629	254	16	have	have	VERB
ejpam-5629	254	17	∥	∥	NUM
ejpam-5629	254	18	℧	℧	X
ejpam-5629	254	19	(	(	PUNCT
ejpam-5629	254	20	φ1	φ1	PROPN
ejpam-5629	254	21	,	,	PUNCT
ejpam-5629	254	22	ω1)−	ω1)−	PROPN
ejpam-5629	254	23	℧	℧	PROPN
ejpam-5629	254	24	(	(	PUNCT
ejpam-5629	254	25	φ2	φ2	PROPN
ejpam-5629	254	26	,	,	PUNCT
ejpam-5629	254	27	ω2)∥ξ×ξ	ω2)∥ξ×ξ	ADJ
ejpam-5629	254	28	≤	≤	X
ejpam-5629	254	29	(	(	PUNCT
ejpam-5629	254	30	ω1	ω1	PROPN
ejpam-5629	254	31	+	+	NOUN
ejpam-5629	254	32	ω2	ω2	ADJ
ejpam-5629	254	33	)	)	PUNCT
ejpam-5629	254	34	∥(φ1	∥(φ1	NUM
ejpam-5629	254	35	,	,	PUNCT
ejpam-5629	254	36	ω1)−	ω1)−	PROPN
ejpam-5629	254	37	(	(	PUNCT
ejpam-5629	254	38	φ2	φ2	PROPN
ejpam-5629	254	39	,	,	PUNCT
ejpam-5629	254	40	ω2)∥	ω2)∥	PROPN
ejpam-5629	254	41	.	.	PUNCT
ejpam-5629	255	1	since	since	SCONJ
ejpam-5629	255	2	ω1	ω1	PROPN
ejpam-5629	255	3	+	+	CCONJ
ejpam-5629	255	4	ω2	ω2	ADJ
ejpam-5629	255	5	<	<	X
ejpam-5629	255	6	1	1	NUM
ejpam-5629	255	7	,	,	PUNCT
ejpam-5629	255	8	we	we	PRON
ejpam-5629	255	9	conclude	conclude	VERB
ejpam-5629	255	10	that	that	SCONJ
ejpam-5629	255	11	℧	℧	PROPN
ejpam-5629	255	12	is	be	AUX
ejpam-5629	255	13	a	a	DET
ejpam-5629	255	14	contraction	contraction	NOUN
ejpam-5629	255	15	mapping	mapping	NOUN
ejpam-5629	255	16	.	.	PUNCT
ejpam-5629	256	1	this	this	PRON
ejpam-5629	256	2	completes	complete	VERB
ejpam-5629	256	3	the	the	DET
ejpam-5629	256	4	proof	proof	NOUN
ejpam-5629	256	5	.	.	PUNCT
ejpam-5629	257	1	the	the	DET
ejpam-5629	257	2	example	example	NOUN
ejpam-5629	257	3	below	below	ADP
ejpam-5629	257	4	support	support	NOUN
ejpam-5629	257	5	the	the	DET
ejpam-5629	257	6	above	above	ADJ
ejpam-5629	257	7	theorem	theorem	PROPN
ejpam-5629	257	8	.	.	PROPN
ejpam-5629	257	9	example	example	NOUN
ejpam-5629	257	10	1	1	NUM
ejpam-5629	257	11	.	.	X
ejpam-5629	258	1	consider	consider	VERB
ejpam-5629	258	2	the	the	DET
ejpam-5629	258	3	following	follow	VERB
ejpam-5629	258	4	problem:	problem:	PROPN
ejpam-5629	258	5	dη1dγ1φ1(ζ	dη1dγ1φ1(ζ	NOUN
ejpam-5629	258	6	)	)	PUNCT
ejpam-5629	259	1	=	=	SYM
ejpam-5629	259	2	⅁1z1	⅁1z1	NOUN
ejpam-5629	259	3	(	(	PUNCT
ejpam-5629	259	4	ζ	ζ	NOUN
ejpam-5629	259	5	,	,	PUNCT
ejpam-5629	259	6	φ1(ζ	φ1(ζ	NOUN
ejpam-5629	259	7	)	)	PUNCT
ejpam-5629	259	8	,	,	PUNCT
ejpam-5629	259	9	φ2(ζ	φ2(ζ	X
ejpam-5629	259	10	)	)	PUNCT
ejpam-5629	259	11	,	,	PUNCT
ejpam-5629	259	12	d	d	PROPN
ejpam-5629	259	13	ρ−1φ1(ζ	ρ−1φ1(ζ	PROPN
ejpam-5629	259	14	)	)	PUNCT
ejpam-5629	259	15	,	,	PUNCT
ejpam-5629	259	16	d	d	PROPN
ejpam-5629	259	17	ρφ1(ζ	ρφ1(ζ	PROPN
ejpam-5629	259	18	)	)	PUNCT
ejpam-5629	259	19	)	)	PUNCT
ejpam-5629	259	20	dη2dγ2φ2(ζ	dη2dγ2φ2(ζ	NOUN
ejpam-5629	259	21	)	)	PUNCT
ejpam-5629	260	1	=	=	SYM
ejpam-5629	261	1	⅁2z2	⅁2z2	ADJ
ejpam-5629	261	2	(	(	PUNCT
ejpam-5629	261	3	ζ	ζ	NOUN
ejpam-5629	261	4	,	,	PUNCT
ejpam-5629	261	5	φ1(ζ	φ1(ζ	NOUN
ejpam-5629	261	6	)	)	PUNCT
ejpam-5629	261	7	,	,	PUNCT
ejpam-5629	261	8	φ2(ζ	φ2(ζ	X
ejpam-5629	261	9	)	)	PUNCT
ejpam-5629	261	10	,	,	PUNCT
ejpam-5629	261	11	d	d	PROPN
ejpam-5629	261	12	ρ−1φ2(ζ	ρ−1φ2(ζ	PROPN
ejpam-5629	261	13	)	)	PUNCT
ejpam-5629	261	14	,	,	PUNCT
ejpam-5629	261	15	d	d	PROPN
ejpam-5629	261	16	ρφ2(ζ	ρφ2(ζ	PROPN
ejpam-5629	261	17	)	)	PUNCT
ejpam-5629	261	18	)	)	PUNCT
ejpam-5629	262	1	φ1(0	φ1(0	PROPN
ejpam-5629	262	2	)	)	PUNCT
ejpam-5629	262	3	=	=	SYM
ejpam-5629	262	4	φ1(1	φ1(1	PROPN
ejpam-5629	262	5	)	)	PUNCT
ejpam-5629	262	6	=	=	PUNCT
ejpam-5629	262	7	φ2(0	φ2(0	ADV
ejpam-5629	262	8	)	)	PUNCT
ejpam-5629	262	9	=	=	SYM
ejpam-5629	262	10	φ2(1	φ2(1	NOUN
ejpam-5629	262	11	)	)	PUNCT
ejpam-5629	262	12	=	=	SYM
ejpam-5629	262	13	0	0	NUM
ejpam-5629	262	14	,	,	PUNCT
ejpam-5629	262	15	dγ1φ1(0	dγ1φ1(0	PROPN
ejpam-5629	262	16	)	)	PUNCT
ejpam-5629	262	17	=	=	SYM
ejpam-5629	262	18	dγ1φ1(1	dγ1φ1(1	PROPN
ejpam-5629	262	19	)	)	PUNCT
ejpam-5629	262	20	=	=	SYM
ejpam-5629	262	21	dγ2φ1(0	dγ2φ1(0	PROPN
ejpam-5629	262	22	)	)	PUNCT
ejpam-5629	262	23	=	=	SYM
ejpam-5629	262	24	dγ2φ1(1	dγ2φ1(1	PROPN
ejpam-5629	262	25	)	)	PUNCT
ejpam-5629	262	26	=	=	SYM
ejpam-5629	263	1	0	0	X
ejpam-5629	263	2	.	.	PUNCT
ejpam-5629	264	1	we	we	PRON
ejpam-5629	264	2	consider	consider	VERB
ejpam-5629	264	3	that	that	SCONJ
ejpam-5629	264	4	η1	η1	NOUN
ejpam-5629	264	5	=	=	SYM
ejpam-5629	264	6	7	7	NUM
ejpam-5629	264	7	3	3	NUM
ejpam-5629	264	8	,	,	PUNCT
ejpam-5629	264	9	γ1	γ1	NOUN
ejpam-5629	264	10	=	=	SYM
ejpam-5629	264	11	2	2	NUM
ejpam-5629	264	12	3	3	NUM
ejpam-5629	264	13	,	,	PUNCT
ejpam-5629	264	14	η2	η2	ADJ
ejpam-5629	264	15	=	=	SYM
ejpam-5629	264	16	5	5	NUM
ejpam-5629	264	17	2	2	NUM
ejpam-5629	264	18	,	,	PUNCT
ejpam-5629	264	19	γ2	γ2	NOUN
ejpam-5629	264	20	=	=	SYM
ejpam-5629	264	21	1	1	NUM
ejpam-5629	264	22	2	2	NUM
ejpam-5629	264	23	,	,	PUNCT
ejpam-5629	264	24	⅁1	⅁1	PROPN
ejpam-5629	264	25	=	=	PUNCT
ejpam-5629	264	26	⅁2	⅁2	NOUN
ejpam-5629	264	27	=	=	SYM
ejpam-5629	264	28	1	1	NUM
ejpam-5629	264	29	,	,	PUNCT
ejpam-5629	264	30	and	and	CCONJ
ejpam-5629	264	31	ρ	ρ	NUM
ejpam-5629	264	32	=	=	SYM
ejpam-5629	264	33	3	3	NUM
ejpam-5629	264	34	2	2	NUM
ejpam-5629	264	35	.	.	PUNCT
ejpam-5629	265	1	moreover	moreover	ADV
ejpam-5629	265	2	,	,	PUNCT
ejpam-5629	265	3	z1	z1	PROPN
ejpam-5629	265	4	(	(	PUNCT
ejpam-5629	265	5	ζ	ζ	NOUN
ejpam-5629	265	6	,	,	PUNCT
ejpam-5629	265	7	φ1(ζ	φ1(ζ	NOUN
ejpam-5629	265	8	)	)	PUNCT
ejpam-5629	265	9	,	,	PUNCT
ejpam-5629	265	10	φ2(ζ	φ2(ζ	X
ejpam-5629	265	11	)	)	PUNCT
ejpam-5629	265	12	,	,	PUNCT
ejpam-5629	265	13	d	d	PROPN
ejpam-5629	265	14	ρ−1φ1(ζ	ρ−1φ1(ζ	PROPN
ejpam-5629	265	15	)	)	PUNCT
ejpam-5629	265	16	,	,	PUNCT
ejpam-5629	265	17	d	d	PROPN
ejpam-5629	265	18	ρφ1(ζ	ρφ1(ζ	PROPN
ejpam-5629	265	19	)	)	PUNCT
ejpam-5629	265	20	)	)	PUNCT
ejpam-5629	266	1	=	=	SYM
ejpam-5629	266	2	1	1	NUM
ejpam-5629	266	3	205eζ	205eζ	NOUN
ejpam-5629	266	4	φ1(ζ	φ1(ζ	NUM
ejpam-5629	266	5	)	)	PUNCT
ejpam-5629	267	1	+	+	CCONJ
ejpam-5629	267	2	(	(	PUNCT
ejpam-5629	267	3	cos	cos	X
ejpam-5629	267	4	(	(	PUNCT
ejpam-5629	267	5	2	2	NUM
ejpam-5629	267	6	+	+	CCONJ
ejpam-5629	267	7	ζ2	ζ2	NOUN
ejpam-5629	267	8	)	)	PUNCT
ejpam-5629	267	9	40	40	NUM
ejpam-5629	267	10	(	(	PUNCT
ejpam-5629	267	11	5	5	NUM
ejpam-5629	267	12	+	+	CCONJ
ejpam-5629	267	13	ζ2	ζ2	NOUN
ejpam-5629	267	14	)	)	PUNCT
ejpam-5629	267	15	)	)	PUNCT
ejpam-5629	268	1	φ2(ζ	φ2(ζ	X
ejpam-5629	268	2	)	)	PUNCT
ejpam-5629	269	1	+	+	CCONJ
ejpam-5629	269	2	(	(	PUNCT
ejpam-5629	269	3	sin	sin	NOUN
ejpam-5629	269	4	(	(	PUNCT
ejpam-5629	269	5	ζ	ζ	NOUN
ejpam-5629	269	6	)	)	PUNCT
ejpam-5629	269	7	25	25	NUM
ejpam-5629	269	8	(	(	PUNCT
ejpam-5629	269	9	ζ2	ζ2	NOUN
ejpam-5629	269	10	+	+	CCONJ
ejpam-5629	269	11	10	10	NUM
ejpam-5629	269	12	)	)	PUNCT
ejpam-5629	269	13	)	)	PUNCT
ejpam-5629	270	1	d	d	ADP
ejpam-5629	270	2	1	1	NUM
ejpam-5629	270	3	2φ1(ζ	2φ1(ζ	NUM
ejpam-5629	270	4	)	)	PUNCT
ejpam-5629	271	1	+	+	CCONJ
ejpam-5629	271	2	1	1	NUM
ejpam-5629	271	3	450eζ	450eζ	NOUN
ejpam-5629	271	4	d	d	PROPN
ejpam-5629	271	5	3	3	NUM
ejpam-5629	271	6	2φ1(ζ	2φ1(ζ	NUM
ejpam-5629	271	7	)	)	PUNCT
ejpam-5629	271	8	,	,	PUNCT
ejpam-5629	271	9	z2	z2	PROPN
ejpam-5629	271	10	(	(	PUNCT
ejpam-5629	271	11	ζ	ζ	NOUN
ejpam-5629	271	12	,	,	PUNCT
ejpam-5629	271	13	φ1(ζ	φ1(ζ	NOUN
ejpam-5629	271	14	)	)	PUNCT
ejpam-5629	271	15	,	,	PUNCT
ejpam-5629	271	16	φ2(ζ	φ2(ζ	X
ejpam-5629	271	17	)	)	PUNCT
ejpam-5629	271	18	,	,	PUNCT
ejpam-5629	271	19	d	d	PROPN
ejpam-5629	271	20	ρ−1φ1(ζ	ρ−1φ1(ζ	PROPN
ejpam-5629	271	21	)	)	PUNCT
ejpam-5629	271	22	,	,	PUNCT
ejpam-5629	271	23	d	d	PROPN
ejpam-5629	271	24	ρφ1(ζ	ρφ1(ζ	PROPN
ejpam-5629	271	25	)	)	PUNCT
ejpam-5629	271	26	)	)	PUNCT
ejpam-5629	272	1	=	=	SYM
ejpam-5629	273	1	1	1	NUM
ejpam-5629	273	2	30	30	NUM
ejpam-5629	273	3	(	(	PUNCT
ejpam-5629	273	4	1	1	NUM
ejpam-5629	273	5	10π	10π	NOUN
ejpam-5629	273	6	ln	ln	X
ejpam-5629	273	7	(	(	PUNCT
ejpam-5629	273	8	1	1	NUM
ejpam-5629	273	9	+	+	CCONJ
ejpam-5629	273	10	ζ	ζ	NOUN
ejpam-5629	273	11	)	)	PUNCT
ejpam-5629	273	12	)	)	PUNCT
ejpam-5629	274	1	φ1(ζ	φ1(ζ	VERB
ejpam-5629	274	2	)	)	PUNCT
ejpam-5629	274	3	+	+	CCONJ
ejpam-5629	274	4	(	(	PUNCT
ejpam-5629	274	5	sin	sin	NOUN
ejpam-5629	274	6	(	(	PUNCT
ejpam-5629	274	7	1	1	NUM
ejpam-5629	274	8	+	+	CCONJ
ejpam-5629	274	9	ζ	ζ	NOUN
ejpam-5629	274	10	)	)	PUNCT
ejpam-5629	274	11	250eζ	250eζ	NOUN
ejpam-5629	274	12	)	)	PUNCT
ejpam-5629	274	13	φ2(ζ	φ2(ζ	X
ejpam-5629	274	14	)	)	PUNCT
ejpam-5629	275	1	+	+	CCONJ
ejpam-5629	275	2	(	(	PUNCT
ejpam-5629	275	3	cos	cos	X
ejpam-5629	275	4	(	(	PUNCT
ejpam-5629	275	5	ζ	ζ	NOUN
ejpam-5629	275	6	)	)	PUNCT
ejpam-5629	275	7	16	16	NUM
ejpam-5629	275	8	(	(	PUNCT
ejpam-5629	275	9	eζ	eζ	ADP
ejpam-5629	275	10	+	+	X
ejpam-5629	275	11	10	10	NUM
ejpam-5629	275	12	)	)	PUNCT
ejpam-5629	275	13	)	)	PUNCT
ejpam-5629	276	1	d	d	ADP
ejpam-5629	276	2	1	1	NUM
ejpam-5629	276	3	2φ1(ζ	2φ1(ζ	NUM
ejpam-5629	276	4	)	)	PUNCT
ejpam-5629	276	5	+	+	CCONJ
ejpam-5629	276	6	1	1	NUM
ejpam-5629	276	7	180πe4ζ	180πe4ζ	NUM
ejpam-5629	276	8	d	d	PROPN
ejpam-5629	276	9	3	3	NUM
ejpam-5629	276	10	2φ1(ζ	2φ1(ζ	NUM
ejpam-5629	276	11	)	)	PUNCT
ejpam-5629	276	12	,	,	PUNCT
ejpam-5629	276	13	clearly	clearly	ADV
ejpam-5629	276	14	,	,	PUNCT
ejpam-5629	276	15	for	for	ADP
ejpam-5629	276	16	all	all	DET
ejpam-5629	276	17	ζ	ζ	NOUN
ejpam-5629	276	18	∈	∈	NOUN
ejpam-5629	277	1	[	[	X
ejpam-5629	277	2	0	0	NUM
ejpam-5629	277	3	,	,	PUNCT
ejpam-5629	277	4	1	1	NUM
ejpam-5629	277	5	]	]	PUNCT
ejpam-5629	277	6	and	and	CCONJ
ejpam-5629	277	7	φ	φ	NUM
ejpam-5629	277	8	,	,	PUNCT
ejpam-5629	277	9	ω	ω	PROPN
ejpam-5629	277	10	,	,	PUNCT
ejpam-5629	277	11	δ	δ	PROPN
ejpam-5629	277	12	,	,	PUNCT
ejpam-5629	277	13	ϱ	ϱ	ADP
ejpam-5629	277	14	,	,	PUNCT
ejpam-5629	277	15	φ̃	φ̃	PROPN
ejpam-5629	277	16	,	,	PUNCT
ejpam-5629	277	17	ω̃	ω̃	PROPN
ejpam-5629	277	18	,	,	PUNCT
ejpam-5629	277	19	δ̃	δ̃	PROPN
ejpam-5629	277	20	,	,	PUNCT
ejpam-5629	277	21	ϱ̃	ϱ̃	PROPN
ejpam-5629	277	22	∈	∈	NOUN
ejpam-5629	277	23	r	r	NOUN
ejpam-5629	277	24	,	,	PUNCT
ejpam-5629	277	25	we	we	PRON
ejpam-5629	277	26	get∣∣∣z1	get∣∣∣z1	VERB
ejpam-5629	277	27	(	(	PUNCT
ejpam-5629	277	28	ζ	ζ	PROPN
ejpam-5629	277	29	,	,	PUNCT
ejpam-5629	277	30	φ	φ	PROPN
ejpam-5629	277	31	,	,	PUNCT
ejpam-5629	277	32	ω	ω	PROPN
ejpam-5629	277	33	,	,	PUNCT
ejpam-5629	277	34	δ	δ	PROPN
ejpam-5629	277	35	,	,	PUNCT
ejpam-5629	277	36	ϱ)−	ϱ)−	PROPN
ejpam-5629	277	37	z1	z1	PROPN
ejpam-5629	277	38	(	(	PUNCT
ejpam-5629	277	39	ζ	ζ	NOUN
ejpam-5629	277	40	,	,	PUNCT
ejpam-5629	277	41	φ̃	φ̃	PROPN
ejpam-5629	277	42	,	,	PUNCT
ejpam-5629	277	43	ω̃	ω̃	PROPN
ejpam-5629	277	44	,	,	PUNCT
ejpam-5629	277	45	δ̃	δ̃	PROPN
ejpam-5629	277	46	,	,	PUNCT
ejpam-5629	277	47	ϱ̃	ϱ̃	PROPN
ejpam-5629	277	48	)	)	PUNCT
ejpam-5629	277	49	∣∣∣	∣∣∣	ADJ
ejpam-5629	277	50	≤	≤	NUM
ejpam-5629	277	51	m11(ζ	m11(ζ	NOUN
ejpam-5629	277	52	)	)	PUNCT
ejpam-5629	277	53	|φ−	|φ−	ADP
ejpam-5629	277	54	φ̃|+m21(ζ	φ̃|+m21(ζ	ADJ
ejpam-5629	277	55	)	)	PUNCT
ejpam-5629	277	56	|ω	|ω	NOUN
ejpam-5629	277	57	−	−	PROPN
ejpam-5629	277	58	ω̃|	ω̃|	PROPN
ejpam-5629	277	59	+	+	SYM
ejpam-5629	277	60	m31(ζ	m31(ζ	NOUN
ejpam-5629	277	61	)	)	PUNCT
ejpam-5629	277	62	∣∣∣δ	∣∣∣δ	PROPN
ejpam-5629	277	63	−	−	PROPN
ejpam-5629	277	64	δ̃	δ̃	PROPN
ejpam-5629	277	65	∣∣∣+m41(ζ	∣∣∣+m41(ζ	NOUN
ejpam-5629	277	66	)	)	PUNCT
ejpam-5629	277	67	|ϱ−	|ϱ−	NOUN
ejpam-5629	277	68	ϱ̃|	ϱ̃|	ADJ
ejpam-5629	277	69	,	,	PUNCT
ejpam-5629	277	70	and	and	CCONJ
ejpam-5629	277	71	∣∣∣z2	∣∣∣z2	PROPN
ejpam-5629	277	72	(	(	PUNCT
ejpam-5629	277	73	ζ	ζ	PROPN
ejpam-5629	277	74	,	,	PUNCT
ejpam-5629	277	75	φ	φ	PROPN
ejpam-5629	277	76	,	,	PUNCT
ejpam-5629	277	77	ω	ω	PROPN
ejpam-5629	277	78	,	,	PUNCT
ejpam-5629	277	79	δ	δ	PROPN
ejpam-5629	277	80	,	,	PUNCT
ejpam-5629	277	81	ϱ)−	ϱ)−	PROPN
ejpam-5629	277	82	z2	z2	PROPN
ejpam-5629	277	83	(	(	PUNCT
ejpam-5629	277	84	ζ	ζ	NOUN
ejpam-5629	277	85	,	,	PUNCT
ejpam-5629	277	86	φ̃	φ̃	PROPN
ejpam-5629	277	87	,	,	PUNCT
ejpam-5629	277	88	ω̃	ω̃	PROPN
ejpam-5629	277	89	,	,	PUNCT
ejpam-5629	277	90	δ̃	δ̃	PROPN
ejpam-5629	277	91	,	,	PUNCT
ejpam-5629	277	92	ϱ̃	ϱ̃	PROPN
ejpam-5629	277	93	)	)	PUNCT
ejpam-5629	277	94	∣∣∣	∣∣∣	ADJ
ejpam-5629	277	95	≤	≤	NUM
ejpam-5629	277	96	m12(ζ	m12(ζ	NOUN
ejpam-5629	277	97	)	)	PUNCT
ejpam-5629	277	98	|φ−	|φ−	ADP
ejpam-5629	277	99	φ̃|+m22(ζ	φ̃|+m22(ζ	NOUN
ejpam-5629	277	100	)	)	PUNCT
ejpam-5629	277	101	|ω	|ω	NOUN
ejpam-5629	277	102	−	−	PROPN
ejpam-5629	277	103	ω̃|	ω̃|	PROPN
ejpam-5629	277	104	h.a	h.a	PROPN
ejpam-5629	277	105	.	.	PROPN
ejpam-5629	277	106	hammad	hammad	PROPN
ejpam-5629	277	107	,	,	PUNCT
ejpam-5629	277	108	m.e.m	m.e.m	NOUN
ejpam-5629	277	109	.	.	PUNCT
ejpam-5629	277	110	abdalla	abdalla	PROPN
ejpam-5629	277	111	/	/	SYM
ejpam-5629	277	112	eur	eur	PROPN
ejpam-5629	277	113	.	.	PUNCT
ejpam-5629	278	1	j.	j.	PROPN
ejpam-5629	278	2	pure	pure	PROPN
ejpam-5629	278	3	appl	appl	PROPN
ejpam-5629	278	4	.	.	PROPN
ejpam-5629	278	5	math	math	PROPN
ejpam-5629	278	6	,	,	PUNCT
ejpam-5629	278	7	18	18	NUM
ejpam-5629	278	8	(	(	PUNCT
ejpam-5629	278	9	1	1	NUM
ejpam-5629	278	10	)	)	PUNCT
ejpam-5629	278	11	(	(	PUNCT
ejpam-5629	278	12	2025	2025	NUM
ejpam-5629	278	13	)	)	PUNCT
ejpam-5629	278	14	,	,	PUNCT
ejpam-5629	278	15	5629	5629	NUM
ejpam-5629	278	16	12	12	NUM
ejpam-5629	278	17	of	of	ADP
ejpam-5629	278	18	20	20	NUM
ejpam-5629	278	19	+	+	NOUN
ejpam-5629	278	20	m32(ζ	m32(ζ	NOUN
ejpam-5629	278	21	)	)	PUNCT
ejpam-5629	279	1	∣∣∣δ	∣∣∣δ	PROPN
ejpam-5629	279	2	−	−	PROPN
ejpam-5629	280	1	δ̃	δ̃	PROPN
ejpam-5629	280	2	∣∣∣+m42(ζ	∣∣∣+m42(ζ	PRON
ejpam-5629	280	3	)	)	PUNCT
ejpam-5629	280	4	|ϱ−	|ϱ−	NOUN
ejpam-5629	280	5	ϱ̃|	ϱ̃|	ADJ
ejpam-5629	280	6	,	,	PUNCT
ejpam-5629	280	7	with	with	PROPN
ejpam-5629	280	8	m11(ζ	m11(ζ	NOUN
ejpam-5629	280	9	)	)	PUNCT
ejpam-5629	280	10	=	=	SYM
ejpam-5629	280	11	1	1	NUM
ejpam-5629	280	12	205eζ	205eζ	NOUN
ejpam-5629	280	13	,	,	PUNCT
ejpam-5629	280	14	m21(ζ	m21(ζ	NOUN
ejpam-5629	280	15	)	)	PUNCT
ejpam-5629	280	16	=	=	SYM
ejpam-5629	280	17	(	(	PUNCT
ejpam-5629	280	18	cos(2+ζ2	cos(2+ζ2	PROPN
ejpam-5629	280	19	)	)	PUNCT
ejpam-5629	280	20	40(5+ζ2	40(5+ζ2	NUM
ejpam-5629	280	21	)	)	PUNCT
ejpam-5629	280	22	)	)	PUNCT
ejpam-5629	280	23	,	,	PUNCT
ejpam-5629	280	24	m31(ζ	m31(ζ	NOUN
ejpam-5629	280	25	)	)	PUNCT
ejpam-5629	280	26	=	=	SYM
ejpam-5629	280	27	(	(	PUNCT
ejpam-5629	280	28	sin(ζ	sin(ζ	PROPN
ejpam-5629	280	29	)	)	PUNCT
ejpam-5629	280	30	25(ζ2	25(ζ2	X
ejpam-5629	280	31	+	+	PROPN
ejpam-5629	280	32	10	10	NUM
ejpam-5629	280	33	)	)	PUNCT
ejpam-5629	280	34	)	)	PUNCT
ejpam-5629	280	35	,	,	PUNCT
ejpam-5629	280	36	m41(ζ	m41(ζ	NOUN
ejpam-5629	280	37	)	)	PUNCT
ejpam-5629	280	38	=	=	SYM
ejpam-5629	280	39	1	1	NUM
ejpam-5629	280	40	450eζ	450eζ	NOUN
ejpam-5629	280	41	,	,	PUNCT
ejpam-5629	280	42	m12(ζ	m12(ζ	NOUN
ejpam-5629	280	43	)	)	PUNCT
ejpam-5629	280	44	=	=	SYM
ejpam-5629	280	45	1	1	NUM
ejpam-5629	280	46	30	30	NUM
ejpam-5629	280	47	(	(	PUNCT
ejpam-5629	280	48	1	1	NUM
ejpam-5629	280	49	10π	10π	NOUN
ejpam-5629	280	50	ln	ln	X
ejpam-5629	280	51	(	(	PUNCT
ejpam-5629	280	52	1	1	NUM
ejpam-5629	280	53	+	+	CCONJ
ejpam-5629	280	54	ζ	ζ	NOUN
ejpam-5629	280	55	)	)	PUNCT
ejpam-5629	280	56	)	)	PUNCT
ejpam-5629	280	57	,	,	PUNCT
ejpam-5629	280	58	m22(ζ	m22(ζ	NOUN
ejpam-5629	280	59	)	)	PUNCT
ejpam-5629	280	60	=	=	SYM
ejpam-5629	280	61	(	(	PUNCT
ejpam-5629	280	62	sin(1+ζ	sin(1+ζ	NOUN
ejpam-5629	280	63	)	)	PUNCT
ejpam-5629	280	64	250eζ	250eζ	NOUN
ejpam-5629	280	65	)	)	PUNCT
ejpam-5629	280	66	,	,	PUNCT
ejpam-5629	280	67	m32(ζ	m32(ζ	NOUN
ejpam-5629	280	68	)	)	PUNCT
ejpam-5629	280	69	=	=	PUNCT
ejpam-5629	280	70	(	(	PUNCT
ejpam-5629	280	71	cos(ζ	cos(ζ	PROPN
ejpam-5629	280	72	)	)	PUNCT
ejpam-5629	280	73	16(eζ+10	16(eζ+10	NOUN
ejpam-5629	280	74	)	)	PUNCT
ejpam-5629	280	75	)	)	PUNCT
ejpam-5629	280	76	,	,	PUNCT
ejpam-5629	280	77	m42(ζ	m42(ζ	NOUN
ejpam-5629	280	78	)	)	PUNCT
ejpam-5629	280	79	=	=	SYM
ejpam-5629	280	80	1	1	NUM
ejpam-5629	280	81	180πe4ζ	180πe4ζ	NUM
ejpam-5629	280	82	.	.	PUNCT
ejpam-5629	281	1	since	since	SCONJ
ejpam-5629	281	2	mlj	mlj	NOUN
ejpam-5629	281	3	=	=	SYM
ejpam-5629	281	4	supζ∈v	supζ∈v	NOUN
ejpam-5629	281	5	{	{	PUNCT
ejpam-5629	281	6	mlj	mlj	PROPN
ejpam-5629	281	7	}	}	PUNCT
ejpam-5629	281	8	,	,	PUNCT
ejpam-5629	281	9	we	we	PRON
ejpam-5629	281	10	have	have	VERB
ejpam-5629	281	11	{	{	PUNCT
ejpam-5629	281	12	m11	m11	NOUN
ejpam-5629	281	13	=	=	SYM
ejpam-5629	281	14	1	1	NUM
ejpam-5629	281	15	205	205	NUM
ejpam-5629	281	16	,	,	PUNCT
ejpam-5629	281	17	m21	m21	NOUN
ejpam-5629	281	18	=	=	SYM
ejpam-5629	281	19	1	1	NUM
ejpam-5629	281	20	240	240	NUM
ejpam-5629	281	21	,	,	PUNCT
ejpam-5629	281	22	m31	m31	NOUN
ejpam-5629	281	23	=	=	SYM
ejpam-5629	281	24	1	1	NUM
ejpam-5629	281	25	250	250	NUM
ejpam-5629	281	26	,	,	PUNCT
ejpam-5629	281	27	m41	m41	NOUN
ejpam-5629	281	28	=	=	NOUN
ejpam-5629	281	29	1	1	NUM
ejpam-5629	281	30	450	450	NUM
ejpam-5629	281	31	,	,	PUNCT
ejpam-5629	281	32	m12	m12	NOUN
ejpam-5629	281	33	=	=	NOUN
ejpam-5629	281	34	1	1	NUM
ejpam-5629	281	35	300π	300π	NUM
ejpam-5629	281	36	,	,	PUNCT
ejpam-5629	281	37	m22(ζ	m22(ζ	NOUN
ejpam-5629	281	38	)	)	PUNCT
ejpam-5629	281	39	=	=	SYM
ejpam-5629	281	40	1	1	NUM
ejpam-5629	281	41	250	250	NUM
ejpam-5629	281	42	,	,	PUNCT
ejpam-5629	281	43	m32(ζ	m32(ζ	NOUN
ejpam-5629	281	44	)	)	PUNCT
ejpam-5629	281	45	=	=	SYM
ejpam-5629	281	46	1	1	NUM
ejpam-5629	281	47	160	160	NUM
ejpam-5629	281	48	,	,	PUNCT
ejpam-5629	281	49	m42(ζ	m42(ζ	NOUN
ejpam-5629	281	50	)	)	PUNCT
ejpam-5629	281	51	=	=	SYM
ejpam-5629	281	52	1	1	NUM
ejpam-5629	281	53	180π	180π	PROPN
ejpam-5629	281	54	.	.	PUNCT
ejpam-5629	282	1	by	by	ADP
ejpam-5629	282	2	simple	simple	ADJ
ejpam-5629	282	3	calculations	calculation	NOUN
ejpam-5629	282	4	,	,	PUNCT
ejpam-5629	282	5	and	and	CCONJ
ejpam-5629	282	6	the	the	DET
ejpam-5629	282	7	definition	definition	NOUN
ejpam-5629	282	8	of	of	ADP
ejpam-5629	282	9	bj	bj	NOUN
ejpam-5629	282	10	(	(	PUNCT
ejpam-5629	282	11	j	j	NOUN
ejpam-5629	282	12	=	=	SYM
ejpam-5629	282	13	1	1	NUM
ejpam-5629	282	14	,	,	PUNCT
ejpam-5629	282	15	2	2	NUM
ejpam-5629	282	16	)	)	PUNCT
ejpam-5629	282	17	,	,	PUNCT
ejpam-5629	282	18	we	we	PRON
ejpam-5629	282	19	can	can	AUX
ejpam-5629	282	20	write	write	VERB
ejpam-5629	282	21	b1	b1	NOUN
ejpam-5629	282	22	=	=	SYM
ejpam-5629	282	23	25.0783	25.0783	NUM
ejpam-5629	282	24	and	and	CCONJ
ejpam-5629	282	25	b2	b2	NOUN
ejpam-5629	282	26	=	=	SYM
ejpam-5629	282	27	29.5855	29.5855	NUM
ejpam-5629	282	28	.	.	PUNCT
ejpam-5629	283	1	further	far	ADV
ejpam-5629	283	2	,	,	PUNCT
ejpam-5629	283	3	ω1	ω1	PROPN
ejpam-5629	283	4	=	=	SYM
ejpam-5629	283	5	25.0783max	25.0783max	NUM
ejpam-5629	283	6	{	{	PUNCT
ejpam-5629	283	7	(	(	PUNCT
ejpam-5629	283	8	1	1	NUM
ejpam-5629	283	9	205	205	NUM
ejpam-5629	283	10	+	+	CCONJ
ejpam-5629	283	11	1	1	NUM
ejpam-5629	283	12	250	250	NUM
ejpam-5629	283	13	)	)	PUNCT
ejpam-5629	283	14	,	,	PUNCT
ejpam-5629	283	15	(	(	PUNCT
ejpam-5629	283	16	1	1	NUM
ejpam-5629	283	17	240	240	NUM
ejpam-5629	283	18	+	+	NUM
ejpam-5629	283	19	1	1	NUM
ejpam-5629	283	20	450	450	NUM
ejpam-5629	283	21	)	)	PUNCT
ejpam-5629	283	22	}	}	PUNCT
ejpam-5629	283	23	≈	≈	PROPN
ejpam-5629	283	24	0.22265	0.22265	NUM
ejpam-5629	283	25	,	,	PUNCT
ejpam-5629	283	26	ω2	ω2	NOUN
ejpam-5629	283	27	=	=	SYM
ejpam-5629	283	28	29.5855max	29.5855max	NUM
ejpam-5629	283	29	{	{	PUNCT
ejpam-5629	283	30	(	(	PUNCT
ejpam-5629	283	31	1	1	NUM
ejpam-5629	283	32	300π	300π	NUM
ejpam-5629	283	33	+	+	CCONJ
ejpam-5629	283	34	1	1	NUM
ejpam-5629	283	35	160	160	NUM
ejpam-5629	283	36	)	)	PUNCT
ejpam-5629	283	37	,	,	PUNCT
ejpam-5629	283	38	(	(	PUNCT
ejpam-5629	283	39	1	1	NUM
ejpam-5629	283	40	250	250	NUM
ejpam-5629	283	41	+	+	SYM
ejpam-5629	283	42	1	1	NUM
ejpam-5629	283	43	180π	180π	NOUN
ejpam-5629	283	44	)	)	PUNCT
ejpam-5629	283	45	}	}	PUNCT
ejpam-5629	283	46	≈	≈	NUM
ejpam-5629	283	47	0.634706	0.634706	NUM
ejpam-5629	283	48	,	,	PUNCT
ejpam-5629	283	49	hence	hence	ADV
ejpam-5629	283	50	,	,	PUNCT
ejpam-5629	283	51	ω1+ω2	ω1+ω2	PROPN
ejpam-5629	283	52	<	<	X
ejpam-5629	283	53	1	1	NUM
ejpam-5629	283	54	.	.	PUNCT
ejpam-5629	284	1	therefore	therefore	ADV
ejpam-5629	284	2	,	,	PUNCT
ejpam-5629	284	3	all	all	DET
ejpam-5629	284	4	requirements	requirement	NOUN
ejpam-5629	284	5	of	of	ADP
ejpam-5629	284	6	theorem	theorem	ADJ
ejpam-5629	284	7	1	1	NUM
ejpam-5629	284	8	are	be	AUX
ejpam-5629	284	9	fulfilled	fulfil	VERB
ejpam-5629	284	10	.	.	PUNCT
ejpam-5629	285	1	so	so	ADV
ejpam-5629	285	2	,	,	PUNCT
ejpam-5629	285	3	the	the	DET
ejpam-5629	285	4	problem	problem	NOUN
ejpam-5629	285	5	has	have	VERB
ejpam-5629	285	6	at	at	ADV
ejpam-5629	285	7	least	least	ADJ
ejpam-5629	285	8	one	one	NUM
ejpam-5629	285	9	solution	solution	NOUN
ejpam-5629	285	10	.	.	PUNCT
ejpam-5629	286	1	5	5	X
ejpam-5629	286	2	.	.	X
ejpam-5629	286	3	applications	application	NOUN
ejpam-5629	286	4	to	to	PART
ejpam-5629	286	5	beam	beam	VERB
ejpam-5629	286	6	systems	system	NOUN
ejpam-5629	286	7	the	the	DET
ejpam-5629	286	8	technique	technique	NOUN
ejpam-5629	286	9	of	of	ADP
ejpam-5629	286	10	tanh	tanh	PROPN
ejpam-5629	286	11	[	[	X
ejpam-5629	286	12	15	15	NUM
ejpam-5629	286	13	,	,	PUNCT
ejpam-5629	286	14	33	33	NUM
ejpam-5629	286	15	,	,	PUNCT
ejpam-5629	286	16	39	39	NUM
ejpam-5629	286	17	]	]	PUNCT
ejpam-5629	286	18	will	will	AUX
ejpam-5629	286	19	be	be	AUX
ejpam-5629	286	20	applied	apply	VERB
ejpam-5629	286	21	in	in	ADP
ejpam-5629	286	22	this	this	DET
ejpam-5629	286	23	section	section	NOUN
ejpam-5629	286	24	to	to	PART
ejpam-5629	286	25	discuss	discuss	VERB
ejpam-5629	286	26	the	the	DET
ejpam-5629	286	27	traveling	travel	VERB
ejpam-5629	286	28	wave	wave	NOUN
ejpam-5629	286	29	solutions	solution	NOUN
ejpam-5629	286	30	for	for	ADP
ejpam-5629	286	31	a	a	DET
ejpam-5629	286	32	tripled	triple	VERB
ejpam-5629	286	33	system	system	NOUN
ejpam-5629	286	34	of	of	ADP
ejpam-5629	286	35	conformable	conformable	ADJ
ejpam-5629	286	36	fds	fds	NOUN
ejpam-5629	286	37	in	in	ADP
ejpam-5629	286	38	the	the	DET
ejpam-5629	286	39	form	form	NOUN
ejpam-5629	286	40	of	of	VERB
ejpam-5629	286	41	ℵ2η	ℵ2η	PROPN
ejpam-5629	286	42	s	s	PART
ejpam-5629	286	43	φ	φ	PROPN
ejpam-5629	286	44	(	(	PUNCT
ejpam-5629	286	45	s	s	PROPN
ejpam-5629	286	46	,	,	PUNCT
ejpam-5629	286	47	ζ	ζ	NOUN
ejpam-5629	286	48	)	)	PUNCT
ejpam-5629	286	49	+	+	CCONJ
ejpam-5629	286	50	ℵ4γ	ℵ4γ	PROPN
ejpam-5629	286	51	ζ	ζ	PROPN
ejpam-5629	286	52	φ	φ	X
ejpam-5629	286	53	(	(	PUNCT
ejpam-5629	286	54	s	s	PROPN
ejpam-5629	286	55	,	,	PUNCT
ejpam-5629	286	56	ζ	ζ	NOUN
ejpam-5629	286	57	)	)	PUNCT
ejpam-5629	287	1	+	+	NUM
ejpam-5629	287	2	⅁1k	⅁1k	NOUN
ejpam-5629	287	3	(	(	PUNCT
ejpam-5629	287	4	φ	φ	PROPN
ejpam-5629	287	5	,	,	PUNCT
ejpam-5629	287	6	ω,ℵ2γ	ω,ℵ2γ	VERB
ejpam-5629	287	7	ζ	ζ	X
ejpam-5629	287	8	(	(	PUNCT
ejpam-5629	287	9	φ	φ	PROPN
ejpam-5629	287	10	,	,	PUNCT
ejpam-5629	287	11	ω	ω	NOUN
ejpam-5629	287	12	)	)	PUNCT
ejpam-5629	287	13	)	)	PUNCT
ejpam-5629	287	14	(	(	PUNCT
ejpam-5629	287	15	s	s	X
ejpam-5629	287	16	,	,	PUNCT
ejpam-5629	287	17	ζ	ζ	NOUN
ejpam-5629	287	18	)	)	PUNCT
ejpam-5629	287	19	=	=	SYM
ejpam-5629	287	20	0	0	NUM
ejpam-5629	287	21	,	,	PUNCT
ejpam-5629	287	22	ℵ2η	ℵ2η	PROPN
ejpam-5629	287	23	s	s	PROPN
ejpam-5629	287	24	ω	ω	X
ejpam-5629	287	25	(	(	PUNCT
ejpam-5629	287	26	s	s	PROPN
ejpam-5629	287	27	,	,	PUNCT
ejpam-5629	287	28	ζ	ζ	NOUN
ejpam-5629	287	29	)	)	PUNCT
ejpam-5629	287	30	+	+	CCONJ
ejpam-5629	287	31	ℵ4γ	ℵ4γ	PROPN
ejpam-5629	287	32	ζ	ζ	PROPN
ejpam-5629	287	33	ω	ω	PROPN
ejpam-5629	287	34	(	(	PUNCT
ejpam-5629	287	35	s	s	PROPN
ejpam-5629	287	36	,	,	PUNCT
ejpam-5629	287	37	ζ	ζ	NOUN
ejpam-5629	287	38	)	)	PUNCT
ejpam-5629	287	39	+	+	NUM
ejpam-5629	287	40	⅁2n	⅁2n	NOUN
ejpam-5629	287	41	(	(	PUNCT
ejpam-5629	287	42	φ	φ	NOUN
ejpam-5629	287	43	,	,	PUNCT
ejpam-5629	287	44	ω,ℵ2γ	ω,ℵ2γ	VERB
ejpam-5629	287	45	ζ	ζ	PROPN
ejpam-5629	287	46	φ	φ	PROPN
ejpam-5629	287	47	(	(	PUNCT
ejpam-5629	287	48	φ	φ	PROPN
ejpam-5629	287	49	,	,	PUNCT
ejpam-5629	287	50	ω	ω	NOUN
ejpam-5629	287	51	)	)	PUNCT
ejpam-5629	287	52	)	)	PUNCT
ejpam-5629	287	53	(	(	PUNCT
ejpam-5629	287	54	s	s	X
ejpam-5629	287	55	,	,	PUNCT
ejpam-5629	287	56	ζ	ζ	NOUN
ejpam-5629	287	57	)	)	PUNCT
ejpam-5629	287	58	=	=	SYM
ejpam-5629	287	59	0	0	NUM
ejpam-5629	287	60	,	,	PUNCT
ejpam-5629	287	61	(	(	PUNCT
ejpam-5629	287	62	10	10	NUM
ejpam-5629	287	63	)	)	PUNCT
ejpam-5629	287	64	where	where	SCONJ
ejpam-5629	287	65	η	η	PROPN
ejpam-5629	287	66	,	,	PUNCT
ejpam-5629	287	67	γ	γ	PROPN
ejpam-5629	287	68	∈	∈	PROPN
ejpam-5629	287	69	(	(	PUNCT
ejpam-5629	287	70	0	0	NUM
ejpam-5629	287	71	,	,	PUNCT
ejpam-5629	287	72	1	1	NUM
ejpam-5629	287	73	]	]	PUNCT
ejpam-5629	287	74	,	,	PUNCT
ejpam-5629	287	75	k	k	PROPN
ejpam-5629	287	76	,	,	PUNCT
ejpam-5629	287	77	n	n	PRON
ejpam-5629	287	78	are	be	AUX
ejpam-5629	287	79	given	give	VERB
ejpam-5629	287	80	function	function	NOUN
ejpam-5629	287	81	,	,	PUNCT
ejpam-5629	287	82	and	and	CCONJ
ejpam-5629	287	83	ℵη	ℵη	ADV
ejpam-5629	287	84	sφ	sφ	PROPN
ejpam-5629	287	85	(	(	PUNCT
ejpam-5629	287	86	s	s	PROPN
ejpam-5629	287	87	,	,	PUNCT
ejpam-5629	287	88	ζ	ζ	NOUN
ejpam-5629	287	89	)	)	PUNCT
ejpam-5629	287	90	refers	refer	VERB
ejpam-5629	287	91	to	to	ADP
ejpam-5629	287	92	the	the	DET
ejpam-5629	287	93	conformable	conformable	ADJ
ejpam-5629	287	94	fd	fd	NOUN
ejpam-5629	287	95	.	.	PUNCT
ejpam-5629	288	1	ℵη	ℵη	ADV
ejpam-5629	288	2	sφ	sφ	PROPN
ejpam-5629	288	3	(	(	PUNCT
ejpam-5629	288	4	s	s	PROPN
ejpam-5629	288	5	,	,	PUNCT
ejpam-5629	288	6	ζ	ζ	NOUN
ejpam-5629	288	7	)	)	PUNCT
ejpam-5629	288	8	is	be	AUX
ejpam-5629	288	9	defined	define	VERB
ejpam-5629	288	10	by	by	ADP
ejpam-5629	288	11	khalil	khalil	PROPN
ejpam-5629	288	12	as	as	SCONJ
ejpam-5629	288	13	follows	follow	VERB
ejpam-5629	288	14	:	:	PUNCT
ejpam-5629	288	15	ℑη	ℑη	PROPN
ejpam-5629	288	16	sφ	sφ	PROPN
ejpam-5629	288	17	(	(	PUNCT
ejpam-5629	288	18	s	s	PROPN
ejpam-5629	288	19	,	,	PUNCT
ejpam-5629	288	20	ζ	ζ	NOUN
ejpam-5629	288	21	)	)	PUNCT
ejpam-5629	289	1	=	=	SYM
ejpam-5629	289	2	∂ηφ	∂ηφ	PROPN
ejpam-5629	289	3	(	(	PUNCT
ejpam-5629	289	4	s	s	PROPN
ejpam-5629	289	5	,	,	PUNCT
ejpam-5629	289	6	ζ	ζ	NOUN
ejpam-5629	289	7	)	)	PUNCT
ejpam-5629	289	8	∂sη	∂sη	PROPN
ejpam-5629	290	1	=	=	SYM
ejpam-5629	290	2	lim	lim	PROPN
ejpam-5629	290	3	ε→0	ε→0	NOUN
ejpam-5629	290	4	(	(	PUNCT
ejpam-5629	290	5	φ	φ	PROPN
ejpam-5629	290	6	(	(	PUNCT
ejpam-5629	290	7	s+	s+	ADV
ejpam-5629	290	8	εs1−η	εs1−η	NUM
ejpam-5629	290	9	,	,	PUNCT
ejpam-5629	290	10	ζ	ζ	NOUN
ejpam-5629	290	11	)	)	PUNCT
ejpam-5629	290	12	−	−	PROPN
ejpam-5629	291	1	φ	φ	PROPN
ejpam-5629	291	2	(	(	PUNCT
ejpam-5629	291	3	s	s	PROPN
ejpam-5629	291	4	,	,	PUNCT
ejpam-5629	291	5	ζ	ζ	NOUN
ejpam-5629	291	6	)	)	PUNCT
ejpam-5629	291	7	ε	ε	PROPN
ejpam-5629	291	8	)	)	PUNCT
ejpam-5629	291	9	,	,	PUNCT
ejpam-5629	291	10	η	η	PROPN
ejpam-5629	291	11	∈	∈	PROPN
ejpam-5629	291	12	(	(	PUNCT
ejpam-5629	291	13	0	0	NUM
ejpam-5629	291	14	,	,	PUNCT
ejpam-5629	291	15	1	1	NUM
ejpam-5629	291	16	]	]	PUNCT
ejpam-5629	291	17	,	,	PUNCT
ejpam-5629	291	18	(	(	PUNCT
ejpam-5629	291	19	11	11	NUM
ejpam-5629	291	20	)	)	PUNCT
ejpam-5629	291	21	where	where	SCONJ
ejpam-5629	291	22	φ	φ	PROPN
ejpam-5629	291	23	(	(	PUNCT
ejpam-5629	291	24	s	s	PROPN
ejpam-5629	291	25	,	,	PUNCT
ejpam-5629	291	26	ζ	ζ	NOUN
ejpam-5629	291	27	)	)	PUNCT
ejpam-5629	291	28	is	be	AUX
ejpam-5629	291	29	unknown	unknown	ADJ
ejpam-5629	291	30	function	function	NOUN
ejpam-5629	291	31	.	.	PUNCT
ejpam-5629	292	1	also	also	ADV
ejpam-5629	292	2	,	,	PUNCT
ejpam-5629	292	3	by	by	ADP
ejpam-5629	292	4	using	use	VERB
ejpam-5629	292	5	(	(	PUNCT
ejpam-5629	292	6	11	11	NUM
ejpam-5629	292	7	)	)	PUNCT
ejpam-5629	292	8	,	,	PUNCT
ejpam-5629	292	9	we	we	PRON
ejpam-5629	292	10	can	can	AUX
ejpam-5629	292	11	present	present	VERB
ejpam-5629	292	12	ℵγ	ℵγ	ADP
ejpam-5629	292	13	ζ	ζ	NOUN
ejpam-5629	292	14	.	.	PUNCT
ejpam-5629	293	1	clearly	clearly	ADV
ejpam-5629	293	2	,	,	PUNCT
ejpam-5629	293	3	the	the	DET
ejpam-5629	293	4	classical	classical	ADJ
ejpam-5629	293	5	coupled	couple	VERB
ejpam-5629	293	6	beam	beam	NOUN
ejpam-5629	293	7	equations	equation	NOUN
ejpam-5629	293	8	[	[	X
ejpam-5629	293	9	40	40	NUM
ejpam-5629	293	10	,	,	PUNCT
ejpam-5629	293	11	47	47	NUM
ejpam-5629	293	12	]	]	PUNCT
ejpam-5629	293	13	can	can	AUX
ejpam-5629	293	14	be	be	AUX
ejpam-5629	293	15	obtained	obtain	VERB
ejpam-5629	293	16	if	if	SCONJ
ejpam-5629	293	17	we	we	PRON
ejpam-5629	293	18	put	put	VERB
ejpam-5629	293	19	η	η	NOUN
ejpam-5629	293	20	=	=	PROPN
ejpam-5629	293	21	γ	γ	X
ejpam-5629	293	22	=	=	SYM
ejpam-5629	293	23	1	1	NUM
ejpam-5629	293	24	and	and	CCONJ
ejpam-5629	293	25	⅁1	⅁1	PROPN
ejpam-5629	293	26	=	=	PUNCT
ejpam-5629	293	27	⅁2	⅁2	NOUN
ejpam-5629	293	28	=	=	SYM
ejpam-5629	293	29	1	1	NUM
ejpam-5629	293	30	in	in	ADP
ejpam-5629	293	31	(	(	PUNCT
ejpam-5629	293	32	10	10	NUM
ejpam-5629	293	33	)	)	PUNCT
ejpam-5629	293	34	.	.	PUNCT
ejpam-5629	294	1	it	it	PRON
ejpam-5629	294	2	takes	take	VERB
ejpam-5629	294	3	the	the	DET
ejpam-5629	294	4	shape	shape	PUNCT
ejpam-5629	294	5	φss	φss	ADV
ejpam-5629	294	6	+	+	CCONJ
ejpam-5629	294	7	φζζζζ	φζζζζ	NOUN
ejpam-5629	294	8	+	+	NUM
ejpam-5629	294	9	⅁1k	⅁1k	NOUN
ejpam-5629	294	10	(	(	PUNCT
ejpam-5629	294	11	φ	φ	PROPN
ejpam-5629	294	12	,	,	PUNCT
ejpam-5629	294	13	ω	ω	PROPN
ejpam-5629	294	14	,	,	PUNCT
ejpam-5629	294	15	(	(	PUNCT
ejpam-5629	294	16	φ	φ	PROPN
ejpam-5629	294	17	,	,	PUNCT
ejpam-5629	294	18	ω)ζζ	ω)ζζ	PROPN
ejpam-5629	294	19	)	)	PUNCT
ejpam-5629	294	20	=	=	SYM
ejpam-5629	294	21	0	0	NUM
ejpam-5629	294	22	,	,	PUNCT
ejpam-5629	294	23	ωss	ωs	NOUN
ejpam-5629	294	24	+	+	CCONJ
ejpam-5629	294	25	ωζζζζ	ωζζζζ	VERB
ejpam-5629	294	26	+	+	CCONJ
ejpam-5629	294	27	⅁1k	⅁1k	NOUN
ejpam-5629	294	28	(	(	PUNCT
ejpam-5629	294	29	φ	φ	PROPN
ejpam-5629	294	30	,	,	PUNCT
ejpam-5629	294	31	ω	ω	PROPN
ejpam-5629	294	32	,	,	PUNCT
ejpam-5629	294	33	(	(	PUNCT
ejpam-5629	294	34	φ	φ	PROPN
ejpam-5629	294	35	,	,	PUNCT
ejpam-5629	294	36	ω)ζζ	ω)ζζ	PROPN
ejpam-5629	294	37	)	)	PUNCT
ejpam-5629	294	38	=	=	SYM
ejpam-5629	295	1	0	0	X
ejpam-5629	295	2	.	.	PUNCT
ejpam-5629	295	3	h.a	h.a	PROPN
ejpam-5629	295	4	.	.	PROPN
ejpam-5629	295	5	hammad	hammad	PROPN
ejpam-5629	295	6	,	,	PUNCT
ejpam-5629	295	7	m.e.m	m.e.m	NOUN
ejpam-5629	295	8	.	.	PUNCT
ejpam-5629	295	9	abdalla	abdalla	PROPN
ejpam-5629	295	10	/	/	SYM
ejpam-5629	295	11	eur	eur	PROPN
ejpam-5629	295	12	.	.	PUNCT
ejpam-5629	296	1	j.	j.	PROPN
ejpam-5629	296	2	pure	pure	PROPN
ejpam-5629	296	3	appl	appl	PROPN
ejpam-5629	296	4	.	.	PROPN
ejpam-5629	296	5	math	math	PROPN
ejpam-5629	296	6	,	,	PUNCT
ejpam-5629	296	7	18	18	NUM
ejpam-5629	296	8	(	(	PUNCT
ejpam-5629	296	9	1	1	NUM
ejpam-5629	296	10	)	)	PUNCT
ejpam-5629	296	11	(	(	PUNCT
ejpam-5629	296	12	2025	2025	NUM
ejpam-5629	296	13	)	)	PUNCT
ejpam-5629	296	14	,	,	PUNCT
ejpam-5629	296	15	5629	5629	NUM
ejpam-5629	296	16	13	13	NUM
ejpam-5629	296	17	of	of	ADP
ejpam-5629	296	18	20	20	NUM
ejpam-5629	296	19	5.1	5.1	NUM
ejpam-5629	296	20	.	.	PUNCT
ejpam-5629	297	1	steps	step	NOUN
ejpam-5629	297	2	of	of	ADP
ejpam-5629	297	3	the	the	DET
ejpam-5629	297	4	tanh	tanh	NOUN
ejpam-5629	297	5	method	method	NOUN
ejpam-5629	297	6	in	in	ADP
ejpam-5629	297	7	this	this	DET
ejpam-5629	297	8	part	part	NOUN
ejpam-5629	297	9	,	,	PUNCT
ejpam-5629	297	10	we	we	PRON
ejpam-5629	297	11	summarize	summarize	VERB
ejpam-5629	297	12	the	the	DET
ejpam-5629	297	13	important	important	ADJ
ejpam-5629	297	14	steps	step	NOUN
ejpam-5629	297	15	of	of	ADP
ejpam-5629	297	16	the	the	DET
ejpam-5629	297	17	tanh	tanh	NOUN
ejpam-5629	297	18	technique	technique	NOUN
ejpam-5629	297	19	involving	involve	VERB
ejpam-5629	297	20	conformable	conformable	ADJ
ejpam-5629	297	21	fds	fds	NOUN
ejpam-5629	297	22	as	as	SCONJ
ejpam-5629	297	23	follows	follow	VERB
ejpam-5629	297	24	:	:	PUNCT
ejpam-5629	297	25	(	(	PUNCT
ejpam-5629	297	26	i	i	NOUN
ejpam-5629	297	27	)	)	PUNCT
ejpam-5629	297	28	we	we	PRON
ejpam-5629	297	29	begin	begin	VERB
ejpam-5629	297	30	with	with	ADP
ejpam-5629	297	31	the	the	DET
ejpam-5629	297	32	following	follow	VERB
ejpam-5629	297	33	coupled	couple	VERB
ejpam-5629	297	34	system:	system:	NOUN
ejpam-5629	297	35	φ1	φ1	PROPN
ejpam-5629	297	36	(	(	PUNCT
ejpam-5629	297	37	φ	φ	PROPN
ejpam-5629	297	38	,	,	PUNCT
ejpam-5629	297	39	ω,ℵη	ω,ℵη	NUM
ejpam-5629	297	40	sφ,ℵγ	sφ,ℵγ	ADJ
ejpam-5629	297	41	ζφ,ℵ	ζφ,ℵ	PUNCT
ejpam-5629	297	42	η	η	PROPN
ejpam-5629	297	43	sω,ℵγ	sω,ℵγ	PROPN
ejpam-5629	297	44	ζω,ℵ	ζω,ℵ	X
ejpam-5629	297	45	2η	2η	PROPN
ejpam-5629	297	46	s	s	PROPN
ejpam-5629	297	47	φ,ℵη	φ,ℵη	NUM
ejpam-5629	297	48	s	s	PART
ejpam-5629	297	49	(	(	PUNCT
ejpam-5629	297	50	ℵγ	ℵγ	ADP
ejpam-5629	297	51	ζφ	ζφ	PROPN
ejpam-5629	297	52	)	)	PUNCT
ejpam-5629	297	53	,	,	PUNCT
ejpam-5629	297	54	ℵ2γ	ℵ2γ	NOUN
ejpam-5629	297	55	ζ	ζ	NOUN
ejpam-5629	297	56	φ,ℵ	φ,ℵ	NOUN
ejpam-5629	297	57	2η	2η	PROPN
ejpam-5629	297	58	s	s	PROPN
ejpam-5629	297	59	ω,ℵη	ω,ℵη	NUM
ejpam-5629	297	60	s	s	PART
ejpam-5629	297	61	(	(	PUNCT
ejpam-5629	297	62	ℵγ	ℵγ	ADP
ejpam-5629	297	63	ζω	ζω	NOUN
ejpam-5629	297	64	)	)	PUNCT
ejpam-5629	297	65	,	,	PUNCT
ejpam-5629	297	66	ℵ2γ	ℵ2γ	X
ejpam-5629	297	67	ζ	ζ	NOUN
ejpam-5629	297	68	ω	ω	PROPN
ejpam-5629	297	69	,	,	PUNCT
ejpam-5629	297	70	·	·	PUNCT
ejpam-5629	297	71	·	·	PUNCT
ejpam-5629	297	72	·	·	PUNCT
ejpam-5629	297	73	)	)	PUNCT
ejpam-5629	298	1	=	=	SYM
ejpam-5629	298	2	0	0	NUM
ejpam-5629	298	3	,	,	PUNCT
ejpam-5629	298	4	φ2	φ2	PROPN
ejpam-5629	298	5	(	(	PUNCT
ejpam-5629	298	6	φ	φ	PROPN
ejpam-5629	298	7	,	,	PUNCT
ejpam-5629	298	8	ω,ℵη	ω,ℵη	NUM
ejpam-5629	298	9	sφ,ℵγ	sφ,ℵγ	ADJ
ejpam-5629	298	10	ζφ,ℵ	ζφ,ℵ	PUNCT
ejpam-5629	298	11	η	η	PROPN
ejpam-5629	298	12	sω,ℵγ	sω,ℵγ	PROPN
ejpam-5629	298	13	ζω,ℵ	ζω,ℵ	X
ejpam-5629	298	14	2η	2η	PROPN
ejpam-5629	298	15	s	s	PROPN
ejpam-5629	298	16	φ,ℵη	φ,ℵη	NUM
ejpam-5629	298	17	s	s	PART
ejpam-5629	298	18	(	(	PUNCT
ejpam-5629	298	19	ℵγ	ℵγ	ADP
ejpam-5629	298	20	ζφ	ζφ	PROPN
ejpam-5629	298	21	)	)	PUNCT
ejpam-5629	298	22	,	,	PUNCT
ejpam-5629	298	23	ℵ2γ	ℵ2γ	NOUN
ejpam-5629	298	24	ζ	ζ	NOUN
ejpam-5629	298	25	φ,ℵ	φ,ℵ	NOUN
ejpam-5629	298	26	2η	2η	PROPN
ejpam-5629	298	27	s	s	PROPN
ejpam-5629	298	28	ω,ℵη	ω,ℵη	NUM
ejpam-5629	298	29	s	s	PART
ejpam-5629	298	30	(	(	PUNCT
ejpam-5629	298	31	ℵγ	ℵγ	ADP
ejpam-5629	298	32	ζω	ζω	NOUN
ejpam-5629	298	33	)	)	PUNCT
ejpam-5629	298	34	,	,	PUNCT
ejpam-5629	298	35	ℵ2γ	ℵ2γ	X
ejpam-5629	298	36	ζ	ζ	NOUN
ejpam-5629	298	37	ω	ω	PROPN
ejpam-5629	298	38	,	,	PUNCT
ejpam-5629	298	39	·	·	PUNCT
ejpam-5629	298	40	·	·	PUNCT
ejpam-5629	298	41	·	·	PUNCT
ejpam-5629	298	42	)	)	PUNCT
ejpam-5629	298	43	=	=	PUNCT
ejpam-5629	299	1	0	0	X
ejpam-5629	299	2	.	.	PUNCT
ejpam-5629	300	1	(	(	PUNCT
ejpam-5629	300	2	12	12	NUM
ejpam-5629	300	3	)	)	PUNCT
ejpam-5629	300	4	(	(	PUNCT
ejpam-5629	300	5	ii	ii	NOUN
ejpam-5629	300	6	)	)	PUNCT
ejpam-5629	300	7	we	we	PRON
ejpam-5629	300	8	use	use	VERB
ejpam-5629	300	9	the	the	DET
ejpam-5629	300	10	relation	relation	NOUN
ejpam-5629	300	11	ϕ	ϕ	NOUN
ejpam-5629	301	1	=	=	SYM
ejpam-5629	301	2	k̃	k̃	PROPN
ejpam-5629	301	3	η	η	PROPN
ejpam-5629	301	4	sη	sη	PROPN
ejpam-5629	301	5	+	+	CCONJ
ejpam-5629	301	6	ν	ν	X
ejpam-5629	301	7	γ	γ	X
ejpam-5629	301	8	sγ	sγ	INTJ
ejpam-5629	301	9	,	,	PUNCT
ejpam-5629	301	10	(	(	PUNCT
ejpam-5629	301	11	13	13	NUM
ejpam-5629	301	12	)	)	PUNCT
ejpam-5629	301	13	for	for	ADP
ejpam-5629	301	14	simplicity	simplicity	NOUN
ejpam-5629	301	15	,	,	PUNCT
ejpam-5629	301	16	the	the	DET
ejpam-5629	301	17	model	model	NOUN
ejpam-5629	301	18	(	(	PUNCT
ejpam-5629	301	19	12	12	NUM
ejpam-5629	301	20	)	)	PUNCT
ejpam-5629	301	21	can	can	AUX
ejpam-5629	301	22	be	be	AUX
ejpam-5629	301	23	written	write	VERB
ejpam-5629	301	24	as	as	ADP
ejpam-5629	301	25	{	{	PUNCT
ejpam-5629	301	26	ψ1	ψ1	NOUN
ejpam-5629	301	27	(	(	PUNCT
ejpam-5629	301	28	w	w	PROPN
ejpam-5629	301	29	,	,	PUNCT
ejpam-5629	301	30	e	e	NOUN
ejpam-5629	301	31	,	,	PUNCT
ejpam-5629	301	32	w	w	PROPN
ejpam-5629	301	33	′	′	NOUN
ejpam-5629	301	34	,	,	PUNCT
ejpam-5629	301	35	e′,w	e′,w	PROPN
ejpam-5629	301	36	′′	′′	PROPN
ejpam-5629	301	37	,	,	PUNCT
ejpam-5629	301	38	e′′,w	e′′,w	PROPN
ejpam-5629	301	39	′′′	′′′	PROPN
ejpam-5629	301	40	,	,	PUNCT
ejpam-5629	301	41	e′′′	e′′′	PROPN
ejpam-5629	301	42	,	,	PUNCT
ejpam-5629	301	43	·	·	PUNCT
ejpam-5629	301	44	·	·	PUNCT
ejpam-5629	301	45	·	·	PUNCT
ejpam-5629	301	46	)	)	PUNCT
ejpam-5629	302	1	=	=	SYM
ejpam-5629	302	2	0	0	NUM
ejpam-5629	302	3	,	,	PUNCT
ejpam-5629	302	4	ψ2	ψ2	NOUN
ejpam-5629	302	5	(	(	PUNCT
ejpam-5629	302	6	w	w	NOUN
ejpam-5629	302	7	,	,	PUNCT
ejpam-5629	302	8	e	e	NOUN
ejpam-5629	302	9	,	,	PUNCT
ejpam-5629	302	10	w	w	PROPN
ejpam-5629	302	11	′	′	NOUN
ejpam-5629	302	12	,	,	PUNCT
ejpam-5629	302	13	e′,w	e′,w	PROPN
ejpam-5629	302	14	′′	′′	PROPN
ejpam-5629	302	15	,	,	PUNCT
ejpam-5629	302	16	e′′,w	e′′,w	PROPN
ejpam-5629	302	17	′′′	′′′	PROPN
ejpam-5629	302	18	,	,	PUNCT
ejpam-5629	302	19	e′′′	e′′′	PROPN
ejpam-5629	302	20	,	,	PUNCT
ejpam-5629	302	21	·	·	PUNCT
ejpam-5629	302	22	·	·	PUNCT
ejpam-5629	302	23	·	·	PUNCT
ejpam-5629	302	24	)	)	PUNCT
ejpam-5629	303	1	=	=	PUNCT
ejpam-5629	303	2	0	0	X
ejpam-5629	303	3	.	.	PUNCT
ejpam-5629	303	4	(	(	PUNCT
ejpam-5629	303	5	iii	iii	X
ejpam-5629	303	6	)	)	PUNCT
ejpam-5629	303	7	we	we	PRON
ejpam-5629	303	8	apply	apply	VERB
ejpam-5629	303	9	the	the	DET
ejpam-5629	303	10	transformation	transformation	NOUN
ejpam-5629	303	11	ℜ	ℜ	NOUN
ejpam-5629	303	12	=	=	PUNCT
ejpam-5629	303	13	tanh	tanh	PROPN
ejpam-5629	303	14	(	(	PUNCT
ejpam-5629	303	15	ϕ	ϕ	NOUN
ejpam-5629	303	16	)	)	PUNCT
ejpam-5629	303	17	,	,	PUNCT
ejpam-5629	304	1	d	d	NOUN
ejpam-5629	304	2	dϕ	dϕ	NOUN
ejpam-5629	304	3	=	=	PUNCT
ejpam-5629	304	4	(	(	PUNCT
ejpam-5629	304	5	1−ℜ2	1−ℜ2	NUM
ejpam-5629	304	6	)	)	PUNCT
ejpam-5629	305	1	d	d	PROPN
ejpam-5629	305	2	dℜ	dℜ	PROPN
ejpam-5629	305	3	,	,	PUNCT
ejpam-5629	305	4	d2	d2	PROPN
ejpam-5629	305	5	dϕ2	dϕ2	PROPN
ejpam-5629	305	6	=	=	SYM
ejpam-5629	305	7	−2ℜ	−2ℜ	PROPN
ejpam-5629	305	8	(	(	PUNCT
ejpam-5629	305	9	1−ℜ2	1−ℜ2	NUM
ejpam-5629	305	10	)	)	PUNCT
ejpam-5629	305	11	d	d	PROPN
ejpam-5629	305	12	dℜ	dℜ	PROPN
ejpam-5629	305	13	+	+	CCONJ
ejpam-5629	305	14	(	(	PUNCT
ejpam-5629	305	15	1−ℜ2	1−ℜ2	NUM
ejpam-5629	305	16	)	)	PUNCT
ejpam-5629	305	17	2	2	NUM
ejpam-5629	305	18	d2	d2	PROPN
ejpam-5629	305	19	dℜ2	dℜ2	PROPN
ejpam-5629	305	20	,	,	PUNCT
ejpam-5629	305	21	d3	d3	VERB
ejpam-5629	305	22	dϕ3	dϕ3	NOUN
ejpam-5629	305	23	=	=	PUNCT
ejpam-5629	305	24	−2	−2	NOUN
ejpam-5629	305	25	(	(	PUNCT
ejpam-5629	305	26	1−ℜ2	1−ℜ2	NUM
ejpam-5629	305	27	)	)	PUNCT
ejpam-5629	305	28	(	(	PUNCT
ejpam-5629	305	29	3ℜ2	3ℜ2	NUM
ejpam-5629	305	30	−	−	NOUN
ejpam-5629	305	31	1	1	NUM
ejpam-5629	305	32	)	)	PUNCT
ejpam-5629	305	33	d	d	NOUN
ejpam-5629	305	34	dℜ	dℜ	NOUN
ejpam-5629	305	35	−	−	PROPN
ejpam-5629	305	36	6ℜ	6ℜ	NOUN
ejpam-5629	305	37	(	(	PUNCT
ejpam-5629	305	38	1−ℜ2	1−ℜ2	NUM
ejpam-5629	305	39	)	)	PUNCT
ejpam-5629	305	40	2	2	NUM
ejpam-5629	305	41	d2	d2	PROPN
ejpam-5629	305	42	dℜ2	dℜ2	PROPN
ejpam-5629	305	43	+	+	CCONJ
ejpam-5629	305	44	(	(	PUNCT
ejpam-5629	305	45	1−ℜ2	1−ℜ2	NUM
ejpam-5629	305	46	)	)	PUNCT
ejpam-5629	305	47	3	3	NUM
ejpam-5629	305	48	d3	d3	PROPN
ejpam-5629	305	49	dℜ3	dℜ3	PROPN
ejpam-5629	305	50	,	,	PUNCT
ejpam-5629	305	51	d4	d4	PROPN
ejpam-5629	305	52	dϕ4	dϕ4	PROPN
ejpam-5629	305	53	=	=	SYM
ejpam-5629	305	54	−8ℜ	−8ℜ	PROPN
ejpam-5629	305	55	(	(	PUNCT
ejpam-5629	305	56	1−ℜ2	1−ℜ2	NUM
ejpam-5629	305	57	)	)	PUNCT
ejpam-5629	305	58	(	(	PUNCT
ejpam-5629	305	59	3ℜ2	3ℜ2	NUM
ejpam-5629	305	60	−	−	NOUN
ejpam-5629	305	61	2	2	NUM
ejpam-5629	305	62	)	)	PUNCT
ejpam-5629	305	63	d	d	NOUN
ejpam-5629	305	64	dℜ	dℜ	PROPN
ejpam-5629	306	1	+	+	CCONJ
ejpam-5629	306	2	4	4	NUM
ejpam-5629	306	3	(	(	PUNCT
ejpam-5629	306	4	1−ℜ2	1−ℜ2	NUM
ejpam-5629	306	5	)	)	PUNCT
ejpam-5629	306	6	2	2	NUM
ejpam-5629	306	7	(	(	PUNCT
ejpam-5629	306	8	9ℜ2	9ℜ2	NOUN
ejpam-5629	306	9	−	−	NOUN
ejpam-5629	306	10	2	2	NUM
ejpam-5629	306	11	)	)	PUNCT
ejpam-5629	306	12	d2	d2	NOUN
ejpam-5629	306	13	dϱ2	dϱ2	NOUN
ejpam-5629	306	14	−12ℜ	−12ℜ	PROPN
ejpam-5629	306	15	(	(	PUNCT
ejpam-5629	306	16	1−ℜ2	1−ℜ2	NUM
ejpam-5629	306	17	)	)	PUNCT
ejpam-5629	306	18	3	3	NUM
ejpam-5629	307	1	d3	d3	PROPN
ejpam-5629	307	2	dℜ3	dℜ3	PROPN
ejpam-5629	307	3	+	+	CCONJ
ejpam-5629	307	4	(	(	PUNCT
ejpam-5629	307	5	1−ℜ2	1−ℜ2	NUM
ejpam-5629	307	6	)	)	PUNCT
ejpam-5629	307	7	4	4	NUM
ejpam-5629	307	8	d4	d4	PROPN
ejpam-5629	307	9	dℜ4	dℜ4	PROPN
ejpam-5629	307	10	.	.	PUNCT
ejpam-5629	308	1	(	(	PUNCT
ejpam-5629	308	2	14	14	NUM
ejpam-5629	308	3	)	)	PUNCT
ejpam-5629	308	4	(	(	PUNCT
ejpam-5629	308	5	iv	iv	X
ejpam-5629	308	6	)	)	PUNCT
ejpam-5629	308	7	we	we	PRON
ejpam-5629	308	8	consider	consider	VERB
ejpam-5629	308	9	that	that	SCONJ
ejpam-5629	308	10	{	{	PUNCT
ejpam-5629	308	11	φ	φ	X
ejpam-5629	308	12	(	(	PUNCT
ejpam-5629	308	13	ζ	ζ	PROPN
ejpam-5629	308	14	,	,	PUNCT
ejpam-5629	308	15	s	s	PART
ejpam-5629	308	16	)	)	PUNCT
ejpam-5629	309	1	=	=	NOUN
ejpam-5629	309	2	w	w	PROPN
ejpam-5629	309	3	(	(	PUNCT
ejpam-5629	309	4	ϕ	ϕ	NOUN
ejpam-5629	309	5	)	)	PUNCT
ejpam-5629	309	6	=	=	SYM
ejpam-5629	309	7	q	q	X
ejpam-5629	309	8	(	(	PUNCT
ejpam-5629	309	9	ℜ	ℜ	PROPN
ejpam-5629	309	10	)	)	PUNCT
ejpam-5629	309	11	=	=	SYM
ejpam-5629	309	12	∑m	∑m	PROPN
ejpam-5629	309	13	j=0	j=0	PROPN
ejpam-5629	309	14	bjℜj	bjℜj	PROPN
ejpam-5629	309	15	,	,	PUNCT
ejpam-5629	309	16	ω	ω	PROPN
ejpam-5629	309	17	(	(	PUNCT
ejpam-5629	309	18	ζ	ζ	PROPN
ejpam-5629	309	19	,	,	PUNCT
ejpam-5629	309	20	s	s	NOUN
ejpam-5629	309	21	)	)	PUNCT
ejpam-5629	309	22	=	=	SYM
ejpam-5629	309	23	e	e	X
ejpam-5629	309	24	(	(	PUNCT
ejpam-5629	309	25	ϕ	ϕ	NOUN
ejpam-5629	309	26	)	)	PUNCT
ejpam-5629	309	27	=	=	SYM
ejpam-5629	309	28	℧	℧	PROPN
ejpam-5629	309	29	(	(	PUNCT
ejpam-5629	309	30	ℜ	ℜ	PROPN
ejpam-5629	309	31	)	)	PUNCT
ejpam-5629	309	32	=	=	SYM
ejpam-5629	310	1	∑n	∑n	PROPN
ejpam-5629	310	2	j=0	j=0	PROPN
ejpam-5629	310	3	cjℜj	cjℜj	PROPN
ejpam-5629	310	4	.	.	PUNCT
ejpam-5629	311	1	(	(	PUNCT
ejpam-5629	311	2	15	15	NUM
ejpam-5629	311	3	)	)	PUNCT
ejpam-5629	311	4	(	(	PUNCT
ejpam-5629	311	5	v	v	NOUN
ejpam-5629	311	6	)	)	PUNCT
ejpam-5629	311	7	lastly	lastly	ADV
ejpam-5629	311	8	,	,	PUNCT
ejpam-5629	311	9	we	we	PRON
ejpam-5629	311	10	obtain	obtain	VERB
ejpam-5629	311	11	the	the	DET
ejpam-5629	311	12	required	require	VERB
ejpam-5629	311	13	solutions	solution	NOUN
ejpam-5629	311	14	for	for	ADP
ejpam-5629	311	15	the	the	DET
ejpam-5629	311	16	constants	constant	NOUN
ejpam-5629	311	17	bj	bj	VERB
ejpam-5629	311	18	and	and	CCONJ
ejpam-5629	311	19	cj	cj	NOUN
ejpam-5629	311	20	by	by	ADP
ejpam-5629	311	21	using	use	VERB
ejpam-5629	311	22	wazwaz	wazwaz	ADJ
ejpam-5629	311	23	term	term	NOUN
ejpam-5629	311	24	-	-	PUNCT
ejpam-5629	311	25	balancing	balancing	NOUN
ejpam-5629	311	26	[	[	X
ejpam-5629	311	27	44	44	NUM
ejpam-5629	311	28	]	]	PUNCT
ejpam-5629	311	29	.	.	PUNCT
ejpam-5629	312	1	h.a	h.a	PROPN
ejpam-5629	312	2	.	.	PROPN
ejpam-5629	312	3	hammad	hammad	PROPN
ejpam-5629	312	4	,	,	PUNCT
ejpam-5629	312	5	m.e.m	m.e.m	NOUN
ejpam-5629	312	6	.	.	PUNCT
ejpam-5629	313	1	abdalla	abdalla	PROPN
ejpam-5629	313	2	/	/	SYM
ejpam-5629	313	3	eur	eur	PROPN
ejpam-5629	313	4	.	.	PUNCT
ejpam-5629	314	1	j.	j.	PROPN
ejpam-5629	314	2	pure	pure	PROPN
ejpam-5629	314	3	appl	appl	PROPN
ejpam-5629	314	4	.	.	PROPN
ejpam-5629	314	5	math	math	PROPN
ejpam-5629	314	6	,	,	PUNCT
ejpam-5629	314	7	18	18	NUM
ejpam-5629	314	8	(	(	PUNCT
ejpam-5629	314	9	1	1	NUM
ejpam-5629	314	10	)	)	PUNCT
ejpam-5629	314	11	(	(	PUNCT
ejpam-5629	314	12	2025	2025	NUM
ejpam-5629	314	13	)	)	PUNCT
ejpam-5629	314	14	,	,	PUNCT
ejpam-5629	314	15	5629	5629	NUM
ejpam-5629	314	16	14	14	NUM
ejpam-5629	314	17	of	of	ADP
ejpam-5629	314	18	20	20	NUM
ejpam-5629	314	19	5.2	5.2	NUM
ejpam-5629	314	20	.	.	PUNCT
ejpam-5629	315	1	traveling	travel	VERB
ejpam-5629	315	2	wave	wave	NOUN
ejpam-5629	315	3	solutions	solution	NOUN
ejpam-5629	315	4	in	in	ADP
ejpam-5629	315	5	this	this	DET
ejpam-5629	315	6	part	part	NOUN
ejpam-5629	315	7	,	,	PUNCT
ejpam-5629	315	8	as	as	ADP
ejpam-5629	315	9	a	a	DET
ejpam-5629	315	10	practical	practical	ADJ
ejpam-5629	315	11	application	application	NOUN
ejpam-5629	315	12	,	,	PUNCT
ejpam-5629	315	13	we	we	PRON
ejpam-5629	315	14	suggest	suggest	VERB
ejpam-5629	315	15	identifying	identify	VERB
ejpam-5629	315	16	traveling	travel	VERB
ejpam-5629	315	17	wave	wave	NOUN
ejpam-5629	315	18	solutions	solution	NOUN
ejpam-5629	315	19	for	for	ADP
ejpam-5629	315	20	the	the	DET
ejpam-5629	315	21	coupled	couple	VERB
ejpam-5629	315	22	problem	problem	NOUN
ejpam-5629	315	23	{	{	PUNCT
ejpam-5629	315	24	ℵ4γ	ℵ4γ	PROPN
ejpam-5629	315	25	ζ	ζ	X
ejpam-5629	315	26	(	(	PUNCT
ejpam-5629	315	27	φ	φ	NOUN
ejpam-5629	315	28	)	)	PUNCT
ejpam-5629	315	29	+	+	NUM
ejpam-5629	315	30	ℵ2η	ℵ2η	PROPN
ejpam-5629	315	31	s	s	X
ejpam-5629	315	32	(	(	PUNCT
ejpam-5629	315	33	φ	φ	NOUN
ejpam-5629	315	34	)	)	PUNCT
ejpam-5629	315	35	+	+	CCONJ
ejpam-5629	315	36	ℵ2γ	ℵ2γ	ADJ
ejpam-5629	315	37	ζ	ζ	NOUN
ejpam-5629	315	38	(	(	PUNCT
ejpam-5629	315	39	φ	φ	NOUN
ejpam-5629	315	40	)	)	PUNCT
ejpam-5629	315	41	+	+	CCONJ
ejpam-5629	315	42	2⅁1cℵγ	2⅁1cℵγ	NUM
ejpam-5629	315	43	ζ	ζ	NOUN
ejpam-5629	315	44	(	(	PUNCT
ejpam-5629	315	45	(	(	PUNCT
ejpam-5629	315	46	ℵγ	ℵγ	INTJ
ejpam-5629	315	47	ζω	ζω	NOUN
ejpam-5629	315	48	)	)	PUNCT
ejpam-5629	315	49	ω	ω	PROPN
ejpam-5629	315	50	)	)	PUNCT
ejpam-5629	316	1	=	=	SYM
ejpam-5629	316	2	0	0	NUM
ejpam-5629	316	3	,	,	PUNCT
ejpam-5629	316	4	ℵ4γ	ℵ4γ	PROPN
ejpam-5629	316	5	ζ	ζ	X
ejpam-5629	316	6	(	(	PUNCT
ejpam-5629	316	7	ω	ω	NOUN
ejpam-5629	316	8	)	)	PUNCT
ejpam-5629	316	9	+	+	NUM
ejpam-5629	316	10	ℵ2η	ℵ2η	PROPN
ejpam-5629	316	11	s	s	X
ejpam-5629	316	12	(	(	PUNCT
ejpam-5629	316	13	ω	ω	NOUN
ejpam-5629	316	14	)	)	PUNCT
ejpam-5629	316	15	+	+	CCONJ
ejpam-5629	316	16	⅁2hℵ2γ	⅁2hℵ2γ	ADV
ejpam-5629	316	17	ζ	ζ	NOUN
ejpam-5629	316	18	(	(	PUNCT
ejpam-5629	316	19	φ	φ	NOUN
ejpam-5629	316	20	)	)	PUNCT
ejpam-5629	316	21	(	(	PUNCT
ejpam-5629	316	22	φω	φω	X
ejpam-5629	316	23	+	+	NUM
ejpam-5629	316	24	eω	eω	PROPN
ejpam-5629	316	25	)	)	PUNCT
ejpam-5629	316	26	=	=	SYM
ejpam-5629	316	27	0	0	NUM
ejpam-5629	316	28	,	,	PUNCT
ejpam-5629	316	29	(	(	PUNCT
ejpam-5629	316	30	16	16	NUM
ejpam-5629	316	31	)	)	PUNCT
ejpam-5629	316	32	where	where	SCONJ
ejpam-5629	316	33	⅁1,⅁2	⅁1,⅁2	PROPN
ejpam-5629	316	34	are	be	AUX
ejpam-5629	316	35	positive	positive	ADJ
ejpam-5629	316	36	real	real	ADJ
ejpam-5629	316	37	constants	constant	NOUN
ejpam-5629	316	38	and	and	CCONJ
ejpam-5629	316	39	h	h	NOUN
ejpam-5629	316	40	,	,	PUNCT
ejpam-5629	316	41	c	c	PROPN
ejpam-5629	316	42	∈	∈	PROPN
ejpam-5629	316	43	r.	r.	NOUN
ejpam-5629	316	44	we	we	PRON
ejpam-5629	316	45	apply	apply	VERB
ejpam-5629	316	46	the	the	DET
ejpam-5629	316	47	relation	relation	NOUN
ejpam-5629	316	48	(	(	PUNCT
ejpam-5629	316	49	13	13	NUM
ejpam-5629	316	50	)	)	PUNCT
ejpam-5629	316	51	to	to	PART
ejpam-5629	316	52	convert	convert	VERB
ejpam-5629	316	53	the	the	DET
ejpam-5629	316	54	problem	problem	NOUN
ejpam-5629	316	55	(	(	PUNCT
ejpam-5629	316	56	16	16	NUM
ejpam-5629	316	57	)	)	PUNCT
ejpam-5629	316	58	to	to	ADP
ejpam-5629	316	59	the	the	DET
ejpam-5629	316	60	following	follow	VERB
ejpam-5629	316	61	integral	integral	ADJ
ejpam-5629	316	62	equation	equation	NOUN
ejpam-5629	316	63	:	:	PUNCT
ejpam-5629	316	64	{	{	PUNCT
ejpam-5629	316	65	ν4wϕϕϕϕ	ν4wϕϕϕϕ	NOUN
ejpam-5629	316	66	+	+	CCONJ
ejpam-5629	316	67	k̃2wϕϕ	k̃2wϕϕ	PROPN
ejpam-5629	317	1	+	+	CCONJ
ejpam-5629	317	2	ν2wϕϕ	ν2wϕϕ	NUM
ejpam-5629	317	3	+	+	SYM
ejpam-5629	317	4	2c⅁1ν	2c⅁1ν	NUM
ejpam-5629	317	5	2	2	NUM
ejpam-5629	317	6	(	(	PUNCT
ejpam-5629	317	7	eϕe)ϕ	eϕe)ϕ	PROPN
ejpam-5629	317	8	=	=	SYM
ejpam-5629	317	9	0	0	NUM
ejpam-5629	317	10	,	,	PUNCT
ejpam-5629	317	11	ν4eϕϕϕϕ	ν4eϕϕϕϕ	NOUN
ejpam-5629	317	12	+	+	CCONJ
ejpam-5629	317	13	k̃2vϕϕ	k̃2vϕϕ	NOUN
ejpam-5629	317	14	+	+	CCONJ
ejpam-5629	317	15	⅁2hν	⅁2hν	NOUN
ejpam-5629	317	16	2	2	NUM
ejpam-5629	317	17	(	(	PUNCT
ejpam-5629	317	18	we)ϕϕ	we)ϕϕ	X
ejpam-5629	317	19	+	+	PUNCT
ejpam-5629	317	20	eν2vϕϕ	eν2vϕϕ	NOUN
ejpam-5629	317	21	=	=	NOUN
ejpam-5629	317	22	0	0	X
ejpam-5629	317	23	.	.	PUNCT
ejpam-5629	317	24	(	(	PUNCT
ejpam-5629	317	25	17	17	NUM
ejpam-5629	317	26	)	)	PUNCT
ejpam-5629	317	27	integrating	integrating	NOUN
ejpam-5629	317	28	(	(	PUNCT
ejpam-5629	317	29	17	17	NUM
ejpam-5629	317	30	)	)	PUNCT
ejpam-5629	317	31	,	,	PUNCT
ejpam-5629	317	32	one	one	PRON
ejpam-5629	317	33	has	have	VERB
ejpam-5629	317	34	{	{	PUNCT
ejpam-5629	317	35	ν4wϕϕ	ν4wϕϕ	NUM
ejpam-5629	318	1	+	+	CCONJ
ejpam-5629	318	2	k̃2w	k̃2w	PROPN
ejpam-5629	318	3	+	+	CCONJ
ejpam-5629	318	4	ν2w	ν2w	PROPN
ejpam-5629	318	5	+	+	CCONJ
ejpam-5629	318	6	c⅁1ν	c⅁1ν	ADJ
ejpam-5629	318	7	2e2	2e2	PROPN
ejpam-5629	318	8	=	=	SYM
ejpam-5629	318	9	0	0	NUM
ejpam-5629	318	10	,	,	PUNCT
ejpam-5629	318	11	ν4eϕϕ	ν4eϕϕ	X
ejpam-5629	318	12	+	+	CCONJ
ejpam-5629	318	13	k̃2v	k̃2v	NOUN
ejpam-5629	318	14	+	+	CCONJ
ejpam-5629	318	15	⅁2hν	⅁2hν	NOUN
ejpam-5629	318	16	2	2	NUM
ejpam-5629	318	17	(	(	PUNCT
ejpam-5629	318	18	we	we	PRON
ejpam-5629	318	19	)	)	PUNCT
ejpam-5629	319	1	+	+	PUNCT
ejpam-5629	319	2	eν2v	eν2v	PROPN
ejpam-5629	319	3	=	=	SYM
ejpam-5629	319	4	0	0	NUM
ejpam-5629	319	5	.	.	PUNCT
ejpam-5629	320	1	(	(	PUNCT
ejpam-5629	320	2	18	18	NUM
ejpam-5629	320	3	)	)	PUNCT
ejpam-5629	320	4	the	the	DET
ejpam-5629	320	5	first	first	ADJ
ejpam-5629	320	6	equation	equation	NOUN
ejpam-5629	320	7	of	of	ADP
ejpam-5629	320	8	(	(	PUNCT
ejpam-5629	320	9	18	18	NUM
ejpam-5629	320	10	)	)	PUNCT
ejpam-5629	320	11	becomes	become	VERB
ejpam-5629	320	12	the	the	DET
ejpam-5629	320	13	following	follow	VERB
ejpam-5629	320	14	equation	equation	NOUN
ejpam-5629	320	15	when	when	SCONJ
ejpam-5629	320	16	(	(	PUNCT
ejpam-5629	320	17	14	14	NUM
ejpam-5629	320	18	)	)	PUNCT
ejpam-5629	320	19	and	and	CCONJ
ejpam-5629	320	20	(	(	PUNCT
ejpam-5629	320	21	15	15	NUM
ejpam-5629	320	22	)	)	PUNCT
ejpam-5629	320	23	are	be	AUX
ejpam-5629	320	24	substituted	substitute	VERB
ejpam-5629	320	25	into	into	ADP
ejpam-5629	320	26	(	(	PUNCT
ejpam-5629	320	27	18	18	NUM
ejpam-5629	320	28	):	):	PUNCT
ejpam-5629	320	29	ν4	ν4	PROPN
ejpam-5629	320	30	[	[	PUNCT
ejpam-5629	320	31	−2ℜ	−2ℜ	PROPN
ejpam-5629	320	32	(	(	PUNCT
ejpam-5629	320	33	1−ℜ2	1−ℜ2	NUM
ejpam-5629	320	34	)	)	PUNCT
ejpam-5629	320	35	dq	dq	ADP
ejpam-5629	320	36	dℜ	dℜ	PROPN
ejpam-5629	321	1	+	+	CCONJ
ejpam-5629	321	2	(	(	PUNCT
ejpam-5629	321	3	1−ℜ2	1−ℜ2	NUM
ejpam-5629	321	4	)	)	SYM
ejpam-5629	321	5	2	2	NUM
ejpam-5629	321	6	d2q	d2q	NOUN
ejpam-5629	321	7	dℜ2	dℜ2	PROPN
ejpam-5629	321	8	]	]	PUNCT
ejpam-5629	322	1	+	+	CCONJ
ejpam-5629	322	2	k̃2q+	k̃2q+	X
ejpam-5629	322	3	c⅁1ν	c⅁1ν	ADJ
ejpam-5629	322	4	2	2	NUM
ejpam-5629	322	5	℧	℧	SYM
ejpam-5629	322	6	2	2	NUM
ejpam-5629	322	7	+	+	CCONJ
ejpam-5629	322	8	eν2q	eν2q	ADJ
ejpam-5629	322	9	=	=	SYM
ejpam-5629	322	10	0	0	X
ejpam-5629	322	11	.	.	PUNCT
ejpam-5629	323	1	(	(	PUNCT
ejpam-5629	323	2	19	19	NUM
ejpam-5629	323	3	)	)	PUNCT
ejpam-5629	323	4	it	it	PRON
ejpam-5629	323	5	is	be	AUX
ejpam-5629	323	6	possible	possible	ADJ
ejpam-5629	323	7	to	to	PART
ejpam-5629	323	8	convert	convert	VERB
ejpam-5629	323	9	the	the	DET
ejpam-5629	323	10	second	second	ADJ
ejpam-5629	323	11	equation	equation	NOUN
ejpam-5629	323	12	of	of	ADP
ejpam-5629	323	13	(	(	PUNCT
ejpam-5629	323	14	18	18	NUM
ejpam-5629	323	15	)	)	PUNCT
ejpam-5629	323	16	into	into	ADP
ejpam-5629	323	17	ν4	ν4	PROPN
ejpam-5629	323	18	[	[	PUNCT
ejpam-5629	323	19	−2ℜ	−2ℜ	PROPN
ejpam-5629	323	20	(	(	PUNCT
ejpam-5629	323	21	1−ℜ2	1−ℜ2	NUM
ejpam-5629	323	22	)	)	PUNCT
ejpam-5629	324	1	d	d	X
ejpam-5629	324	2	℧	℧	PROPN
ejpam-5629	324	3	dℜ	dℜ	PROPN
ejpam-5629	324	4	+	+	PROPN
ejpam-5629	324	5	(	(	PUNCT
ejpam-5629	324	6	1−ℜ2	1−ℜ2	NUM
ejpam-5629	324	7	)	)	SYM
ejpam-5629	324	8	2	2	NUM
ejpam-5629	324	9	d2	d2	PROPN
ejpam-5629	324	10	℧	℧	PROPN
ejpam-5629	324	11	dℜ2	dℜ2	PROPN
ejpam-5629	324	12	]	]	PUNCT
ejpam-5629	325	1	+	+	CCONJ
ejpam-5629	325	2	k̃2	k̃2	PROPN
ejpam-5629	325	3	℧	℧	PROPN
ejpam-5629	325	4	+	+	ADJ
ejpam-5629	325	5	h⅁2ν	h⅁2ν	NOUN
ejpam-5629	325	6	2	2	NUM
ejpam-5629	325	7	(	(	PUNCT
ejpam-5629	325	8	q	q	NOUN
ejpam-5629	325	9	℧	℧	PROPN
ejpam-5629	325	10	)	)	PUNCT
ejpam-5629	325	11	+	+	CCONJ
ejpam-5629	325	12	eν2	eν2	PROPN
ejpam-5629	325	13	℧	℧	PROPN
ejpam-5629	325	14	=	=	SYM
ejpam-5629	325	15	0	0	PROPN
ejpam-5629	325	16	.	.	PUNCT
ejpam-5629	326	1	(	(	PUNCT
ejpam-5629	326	2	20	20	NUM
ejpam-5629	326	3	)	)	PUNCT
ejpam-5629	326	4	we	we	PRON
ejpam-5629	326	5	balance	balance	VERB
ejpam-5629	326	6	ℜ4	ℜ4	PROPN
ejpam-5629	326	7	d2q	d2q	PROPN
ejpam-5629	326	8	dℜ2	dℜ2	PROPN
ejpam-5629	326	9	with	with	ADP
ejpam-5629	326	10	℧	℧	NOUN
ejpam-5629	326	11	2	2	NUM
ejpam-5629	326	12	in	in	ADP
ejpam-5629	326	13	(	(	PUNCT
ejpam-5629	326	14	19	19	NUM
ejpam-5629	326	15	)	)	PUNCT
ejpam-5629	326	16	to	to	ADP
ejpam-5629	326	17	2	2	NUM
ejpam-5629	326	18	+	+	NOUN
ejpam-5629	326	19	m	m	NOUN
ejpam-5629	326	20	=	=	ADJ
ejpam-5629	326	21	2n	2n	NUM
ejpam-5629	326	22	.	.	PUNCT
ejpam-5629	327	1	moreover	moreover	ADV
ejpam-5629	327	2	,	,	PUNCT
ejpam-5629	327	3	with	with	ADP
ejpam-5629	327	4	(	(	PUNCT
ejpam-5629	327	5	20	20	NUM
ejpam-5629	327	6	)	)	PUNCT
ejpam-5629	327	7	,	,	PUNCT
ejpam-5629	327	8	we	we	PRON
ejpam-5629	327	9	can	can	AUX
ejpam-5629	327	10	apply	apply	VERB
ejpam-5629	327	11	the	the	DET
ejpam-5629	327	12	same	same	ADJ
ejpam-5629	327	13	method	method	NOUN
ejpam-5629	327	14	to	to	PART
ejpam-5629	327	15	get	get	VERB
ejpam-5629	327	16	2	2	NUM
ejpam-5629	327	17	+	+	CCONJ
ejpam-5629	327	18	n	n	PROPN
ejpam-5629	327	19	=	=	SYM
ejpam-5629	327	20	n+m	n+m	PROPN
ejpam-5629	327	21	.	.	PUNCT
ejpam-5629	328	1	consequently	consequently	ADV
ejpam-5629	328	2	,	,	PUNCT
ejpam-5629	328	3	we	we	PRON
ejpam-5629	328	4	are	be	AUX
ejpam-5629	328	5	able	able	ADJ
ejpam-5629	328	6	to	to	PART
ejpam-5629	328	7	write	write	VERB
ejpam-5629	328	8	{	{	PUNCT
ejpam-5629	328	9	q	q	PROPN
ejpam-5629	328	10	(	(	PUNCT
ejpam-5629	328	11	ℜ	ℜ	ADJ
ejpam-5629	328	12	)	)	PUNCT
ejpam-5629	328	13	=	=	SYM
ejpam-5629	328	14	b0	b0	NOUN
ejpam-5629	328	15	+	+	CCONJ
ejpam-5629	328	16	b1ℜ+	b1ℜ+	PROPN
ejpam-5629	328	17	b2ℜ2	b2ℜ2	NUM
ejpam-5629	328	18	,	,	PUNCT
ejpam-5629	328	19	℧	℧	PROPN
ejpam-5629	328	20	(	(	PUNCT
ejpam-5629	328	21	ℜ	ℜ	PROPN
ejpam-5629	328	22	)	)	PUNCT
ejpam-5629	328	23	=	=	SYM
ejpam-5629	328	24	c0	c0	NOUN
ejpam-5629	328	25	+	+	CCONJ
ejpam-5629	328	26	c1ℜ+	c1ℜ+	PROPN
ejpam-5629	328	27	c2ℜ2	c2ℜ2	PROPN
ejpam-5629	328	28	.	.	PUNCT
ejpam-5629	329	1	(	(	PUNCT
ejpam-5629	329	2	21	21	NUM
ejpam-5629	329	3	)	)	PUNCT
ejpam-5629	329	4	we	we	PRON
ejpam-5629	329	5	note	note	VERB
ejpam-5629	329	6	that	that	SCONJ
ejpam-5629	329	7	when	when	SCONJ
ejpam-5629	329	8	we	we	PRON
ejpam-5629	329	9	substitute	substitute	VERB
ejpam-5629	329	10	(	(	PUNCT
ejpam-5629	329	11	21	21	NUM
ejpam-5629	329	12	)	)	PUNCT
ejpam-5629	329	13	for	for	ADP
ejpam-5629	329	14	(	(	PUNCT
ejpam-5629	329	15	19	19	NUM
ejpam-5629	329	16	)	)	PUNCT
ejpam-5629	329	17	,	,	PUNCT
ejpam-5629	329	18	−2ν4ℜ	−2ν4ℜ	NOUN
ejpam-5629	329	19	(	(	PUNCT
ejpam-5629	329	20	1−ℜ2	1−ℜ2	NUM
ejpam-5629	329	21	)	)	PUNCT
ejpam-5629	329	22	(	(	PUNCT
ejpam-5629	329	23	b1	b1	NOUN
ejpam-5629	329	24	+	+	CCONJ
ejpam-5629	329	25	2b2ℜ	2b2ℜ	NUM
ejpam-5629	329	26	)	)	PUNCT
ejpam-5629	330	1	+	+	CCONJ
ejpam-5629	330	2	2b2ν	2b2ν	NUM
ejpam-5629	330	3	4	4	NUM
ejpam-5629	330	4	(	(	PUNCT
ejpam-5629	330	5	1−ℜ2	1−ℜ2	NUM
ejpam-5629	330	6	)	)	PUNCT
ejpam-5629	330	7	2	2	NUM
ejpam-5629	331	1	+	+	CCONJ
ejpam-5629	331	2	k̃2	k̃2	PROPN
ejpam-5629	331	3	(	(	PUNCT
ejpam-5629	331	4	b0	b0	NOUN
ejpam-5629	331	5	+	+	CCONJ
ejpam-5629	331	6	b1ℜ+	b1ℜ+	PROPN
ejpam-5629	331	7	b2ℜ2	b2ℜ2	NUM
ejpam-5629	331	8	)	)	PUNCT
ejpam-5629	332	1	+	+	ADV
ejpam-5629	332	2	c⅁1ν	c⅁1ν	ADJ
ejpam-5629	332	3	2	2	NUM
ejpam-5629	332	4	(	(	PUNCT
ejpam-5629	332	5	c0	c0	NOUN
ejpam-5629	332	6	+	+	CCONJ
ejpam-5629	332	7	c1ℜ+	c1ℜ+	PROPN
ejpam-5629	332	8	c2ℜ2	c2ℜ2	NUM
ejpam-5629	332	9	)	)	PUNCT
ejpam-5629	332	10	2	2	NUM
ejpam-5629	332	11	+	+	CCONJ
ejpam-5629	332	12	eν2	eν2	PROPN
ejpam-5629	332	13	(	(	PUNCT
ejpam-5629	332	14	b0	b0	NOUN
ejpam-5629	332	15	+	+	CCONJ
ejpam-5629	332	16	b1ℜ+	b1ℜ+	PROPN
ejpam-5629	332	17	b2ℜ2	b2ℜ2	X
ejpam-5629	332	18	)	)	PUNCT
ejpam-5629	332	19	=	=	PUNCT
ejpam-5629	333	1	0	0	X
ejpam-5629	333	2	.	.	PUNCT
ejpam-5629	334	1	moreover	moreover	ADV
ejpam-5629	334	2	,	,	PUNCT
ejpam-5629	334	3	when	when	SCONJ
ejpam-5629	334	4	we	we	PRON
ejpam-5629	334	5	change	change	VERB
ejpam-5629	334	6	(	(	PUNCT
ejpam-5629	334	7	21	21	NUM
ejpam-5629	334	8	)	)	PUNCT
ejpam-5629	334	9	into	into	ADP
ejpam-5629	334	10	(	(	PUNCT
ejpam-5629	334	11	20	20	NUM
ejpam-5629	334	12	)	)	PUNCT
ejpam-5629	334	13	,	,	PUNCT
ejpam-5629	334	14	we	we	PRON
ejpam-5629	334	15	obtain	obtain	VERB
ejpam-5629	334	16	−2ν4ℜ	−2ν4ℜ	NOUN
ejpam-5629	334	17	(	(	PUNCT
ejpam-5629	334	18	1−ℜ2	1−ℜ2	NUM
ejpam-5629	334	19	)	)	PUNCT
ejpam-5629	334	20	(	(	PUNCT
ejpam-5629	334	21	c1	c1	NOUN
ejpam-5629	334	22	+	+	CCONJ
ejpam-5629	334	23	2c2ℜ	2c2ℜ	NUM
ejpam-5629	334	24	)	)	PUNCT
ejpam-5629	335	1	+	+	NUM
ejpam-5629	335	2	2c2ν	2c2ν	NUM
ejpam-5629	335	3	4	4	NUM
ejpam-5629	335	4	(	(	PUNCT
ejpam-5629	335	5	1−ℜ2	1−ℜ2	NUM
ejpam-5629	335	6	)	)	PUNCT
ejpam-5629	335	7	2	2	NUM
ejpam-5629	336	1	+	+	CCONJ
ejpam-5629	336	2	k̃2	k̃2	PROPN
ejpam-5629	336	3	(	(	PUNCT
ejpam-5629	336	4	c0	c0	NOUN
ejpam-5629	336	5	+	+	CCONJ
ejpam-5629	336	6	c1ℜ+	c1ℜ+	PROPN
ejpam-5629	336	7	c2ℜ2	c2ℜ2	NUM
ejpam-5629	336	8	)	)	PUNCT
ejpam-5629	337	1	+	+	ADV
ejpam-5629	337	2	h⅁2ν	h⅁2ν	NOUN
ejpam-5629	337	3	2	2	NUM
ejpam-5629	337	4	(	(	PUNCT
ejpam-5629	337	5	c0	c0	NOUN
ejpam-5629	337	6	+	+	CCONJ
ejpam-5629	337	7	c1ℜ+	c1ℜ+	PROPN
ejpam-5629	337	8	c2ℜ2	c2ℜ2	NUM
ejpam-5629	337	9	)	)	PUNCT
ejpam-5629	337	10	(	(	PUNCT
ejpam-5629	337	11	b0	b0	VERB
ejpam-5629	337	12	+	+	CCONJ
ejpam-5629	337	13	b1ℜ+	b1ℜ+	PROPN
ejpam-5629	337	14	b2ℜ2	b2ℜ2	PROPN
ejpam-5629	337	15	)	)	PUNCT
ejpam-5629	338	1	+	+	CCONJ
ejpam-5629	338	2	eν2	eν2	PROPN
ejpam-5629	339	1	(	(	PUNCT
ejpam-5629	339	2	c0	c0	NOUN
ejpam-5629	339	3	+	+	CCONJ
ejpam-5629	339	4	c1ℜ+	c1ℜ+	PROPN
ejpam-5629	339	5	c2ℜ2	c2ℜ2	NUM
ejpam-5629	339	6	)	)	PUNCT
ejpam-5629	340	1	=	=	PUNCT
ejpam-5629	340	2	0	0	X
ejpam-5629	340	3	.	.	PUNCT
ejpam-5629	341	1	as	as	ADP
ejpam-5629	341	2	a	a	DET
ejpam-5629	341	3	result	result	NOUN
ejpam-5629	341	4	,	,	PUNCT
ejpam-5629	341	5	we	we	PRON
ejpam-5629	341	6	have	have	VERB
ejpam-5629	341	7	the	the	DET
ejpam-5629	341	8	following	follow	VERB
ejpam-5629	341	9	two	two	NUM
ejpam-5629	341	10	sets	set	NOUN
ejpam-5629	341	11	:	:	PUNCT
ejpam-5629	341	12	h.a	h.a	PROPN
ejpam-5629	341	13	.	.	PROPN
ejpam-5629	341	14	hammad	hammad	PROPN
ejpam-5629	341	15	,	,	PUNCT
ejpam-5629	341	16	m.e.m	m.e.m	NOUN
ejpam-5629	341	17	.	.	PUNCT
ejpam-5629	342	1	abdalla	abdalla	PROPN
ejpam-5629	342	2	/	/	SYM
ejpam-5629	342	3	eur	eur	PROPN
ejpam-5629	342	4	.	.	PUNCT
ejpam-5629	343	1	j.	j.	PROPN
ejpam-5629	343	2	pure	pure	PROPN
ejpam-5629	343	3	appl	appl	PROPN
ejpam-5629	343	4	.	.	PROPN
ejpam-5629	343	5	math	math	PROPN
ejpam-5629	343	6	,	,	PUNCT
ejpam-5629	343	7	18	18	NUM
ejpam-5629	343	8	(	(	PUNCT
ejpam-5629	343	9	1	1	NUM
ejpam-5629	343	10	)	)	PUNCT
ejpam-5629	343	11	(	(	PUNCT
ejpam-5629	343	12	2025	2025	NUM
ejpam-5629	343	13	)	)	PUNCT
ejpam-5629	343	14	,	,	PUNCT
ejpam-5629	343	15	5629	5629	NUM
ejpam-5629	343	16	15	15	NUM
ejpam-5629	343	17	of	of	ADP
ejpam-5629	343	18	20	20	NUM
ejpam-5629	343	19	set	set	VERB
ejpam-5629	343	20	1	1	NUM
ejpam-5629	343	21	:	:	PUNCT
ejpam-5629	343	22			NUM
ejpam-5629	343	23	ℜ0	ℜ0	PROPN
ejpam-5629	343	24	:	:	PUNCT
ejpam-5629	343	25	c⅁1ν	c⅁1ν	ADJ
ejpam-5629	343	26	2c20	2c20	NUM
ejpam-5629	343	27	−	−	NUM
ejpam-5629	343	28	2ν2b1	2ν2b1	NUM
ejpam-5629	343	29	+	+	CCONJ
ejpam-5629	343	30	2ν4b2	2ν4b2	NUM
ejpam-5629	344	1	+	+	CCONJ
ejpam-5629	344	2	k̃2b0	k̃2b0	PROPN
ejpam-5629	344	3	+	+	PROPN
ejpam-5629	344	4	eν2b0	eν2b0	X
ejpam-5629	344	5	=	=	SYM
ejpam-5629	344	6	0	0	PROPN
ejpam-5629	344	7	,	,	PUNCT
ejpam-5629	344	8	ℜ1	ℜ1	NOUN
ejpam-5629	344	9	:	:	PUNCT
ejpam-5629	344	10	2cν2c0c1	2cν2c0c1	NUM
ejpam-5629	344	11	−	−	NUM
ejpam-5629	344	12	4ν2b2	4ν2b2	NUM
ejpam-5629	345	1	+	+	NUM
ejpam-5629	345	2	k̃2b1	k̃2b1	NOUN
ejpam-5629	345	3	+	+	CCONJ
ejpam-5629	345	4	ν2b1	ν2b1	NOUN
ejpam-5629	345	5	=	=	SYM
ejpam-5629	345	6	0	0	NUM
ejpam-5629	345	7	,	,	PUNCT
ejpam-5629	345	8	ℜ2	ℜ2	ADV
ejpam-5629	345	9	:	:	PUNCT
ejpam-5629	345	10	2cν2c0c2	2cν2c0c2	NUM
ejpam-5629	345	11	+	+	CCONJ
ejpam-5629	345	12	c⅁1ν	c⅁1ν	ADJ
ejpam-5629	345	13	2c21	2c21	NUM
ejpam-5629	346	1	+	+	CCONJ
ejpam-5629	346	2	2ν2b1	2ν2b1	NUM
ejpam-5629	346	3	−	−	NOUN
ejpam-5629	346	4	4ν2b2	4ν2b2	NOUN
ejpam-5629	347	1	+	+	CCONJ
ejpam-5629	347	2	k̃2b2	k̃2b2	PROPN
ejpam-5629	348	1	+	+	CCONJ
ejpam-5629	348	2	ν2b2	ν2b2	PROPN
ejpam-5629	348	3	=	=	SYM
ejpam-5629	348	4	0	0	NUM
ejpam-5629	348	5	,	,	PUNCT
ejpam-5629	348	6	ℜ3	ℜ3	PROPN
ejpam-5629	348	7	:	:	PUNCT
ejpam-5629	349	1	2cν2c1c2	2cν2c1c2	NUM
ejpam-5629	349	2	+	+	CCONJ
ejpam-5629	349	3	4ν2b2	4ν2b2	NUM
ejpam-5629	349	4	=	=	SYM
ejpam-5629	349	5	0	0	NUM
ejpam-5629	349	6	,	,	PUNCT
ejpam-5629	349	7	ℜ4	ℜ4	PROPN
ejpam-5629	349	8	:	:	PUNCT
ejpam-5629	349	9	c⅁1ν	c⅁1ν	ADJ
ejpam-5629	349	10	2c22	2c22	NOUN
ejpam-5629	349	11	+	+	CCONJ
ejpam-5629	349	12	2ν2b2	2ν2b2	NUM
ejpam-5629	349	13	=	=	SYM
ejpam-5629	349	14	0	0	NUM
ejpam-5629	349	15	,	,	PUNCT
ejpam-5629	349	16	(	(	PUNCT
ejpam-5629	349	17	22	22	NUM
ejpam-5629	349	18	)	)	PUNCT
ejpam-5629	349	19	set	set	VERB
ejpam-5629	349	20	2	2	NUM
ejpam-5629	349	21	:	:	PUNCT
ejpam-5629	349	22			NUM
ejpam-5629	349	23	ℜ0	ℜ0	NOUN
ejpam-5629	350	1	:	:	PUNCT
ejpam-5629	350	2	hν2⅁2c0b0	hν2⅁2c0b0	ADJ
ejpam-5629	350	3	−	−	NUM
ejpam-5629	350	4	2ν4c1	2ν4c1	NUM
ejpam-5629	351	1	+	+	CCONJ
ejpam-5629	351	2	2ν4c2	2ν4c2	NUM
ejpam-5629	352	1	+	+	CCONJ
ejpam-5629	352	2	eν2c0	eν2c0	PROPN
ejpam-5629	352	3	+	+	CCONJ
ejpam-5629	352	4	k̃2c0	k̃2c0	PROPN
ejpam-5629	352	5	=	=	SYM
ejpam-5629	352	6	0	0	PROPN
ejpam-5629	352	7	,	,	PUNCT
ejpam-5629	352	8	ℜ1	ℜ1	NOUN
ejpam-5629	352	9	:	:	PUNCT
ejpam-5629	353	1	hν2⅁2c0b1	hν2⅁2c0b1	X
ejpam-5629	353	2	+	+	CCONJ
ejpam-5629	353	3	hν2⅁2c1b0	hν2⅁2c1b0	VERB
ejpam-5629	353	4	−	−	X
ejpam-5629	353	5	4ν2c2	4ν2c2	NOUN
ejpam-5629	354	1	+	+	CCONJ
ejpam-5629	354	2	eν2b1	eν2b1	PROPN
ejpam-5629	354	3	+	+	CCONJ
ejpam-5629	354	4	k̃2c1	k̃2c1	PROPN
ejpam-5629	354	5	=	=	SYM
ejpam-5629	354	6	0	0	PROPN
ejpam-5629	354	7	,	,	PUNCT
ejpam-5629	354	8	ℜ2	ℜ2	ADV
ejpam-5629	354	9	:	:	PUNCT
ejpam-5629	354	10	hν2⅁2c0b2	hν2⅁2c0b2	NOUN
ejpam-5629	354	11	+	+	CCONJ
ejpam-5629	354	12	hν2⅁2c1b1	hν2⅁2c1b1	PROPN
ejpam-5629	355	1	+	+	CCONJ
ejpam-5629	355	2	hν2⅁2c2b0	hν2⅁2c2b0	PROPN
ejpam-5629	355	3	+	+	PROPN
ejpam-5629	355	4	2ν2c1	2ν2c1	NOUN
ejpam-5629	355	5	−	−	NOUN
ejpam-5629	355	6	4ν4c2	4ν4c2	NUM
ejpam-5629	355	7	+	+	NUM
ejpam-5629	356	1	eν2c2	eν2c2	PROPN
ejpam-5629	356	2	+	+	CCONJ
ejpam-5629	356	3	k̃2c2	k̃2c2	PROPN
ejpam-5629	356	4	=	=	SYM
ejpam-5629	356	5	0	0	NUM
ejpam-5629	356	6	,	,	PUNCT
ejpam-5629	356	7	ℜ3	ℜ3	X
ejpam-5629	356	8	:	:	PUNCT
ejpam-5629	356	9	hν2⅁2c1b2	hν2⅁2c1b2	NOUN
ejpam-5629	356	10	+	+	CCONJ
ejpam-5629	356	11	hν2⅁2c2b1	hν2⅁2c2b1	ADJ
ejpam-5629	356	12	+	+	CCONJ
ejpam-5629	356	13	4ν4c2	4ν4c2	NUM
ejpam-5629	356	14	=	=	SYM
ejpam-5629	356	15	0	0	NUM
ejpam-5629	356	16	,	,	PUNCT
ejpam-5629	356	17	ℜ4	ℜ4	PROPN
ejpam-5629	356	18	:	:	PUNCT
ejpam-5629	356	19	hν2⅁2c2b2	hν2⅁2c2b2	ADJ
ejpam-5629	356	20	+	+	NOUN
ejpam-5629	356	21	2ν4b2	2ν4b2	NUM
ejpam-5629	356	22	=	=	SYM
ejpam-5629	356	23	0	0	NUM
ejpam-5629	356	24	.	.	PUNCT
ejpam-5629	357	1	(	(	PUNCT
ejpam-5629	357	2	23	23	NUM
ejpam-5629	357	3	)	)	PUNCT
ejpam-5629	357	4	with	with	ADP
ejpam-5629	357	5	the	the	DET
ejpam-5629	357	6	aid	aid	NOUN
ejpam-5629	357	7	of	of	ADP
ejpam-5629	357	8	maple	maple	NOUN
ejpam-5629	357	9	,	,	PUNCT
ejpam-5629	357	10	for	for	ADP
ejpam-5629	357	11	⅁1	⅁1	PROPN
ejpam-5629	357	12	=	=	PUNCT
ejpam-5629	357	13	⅁1	⅁1	PROPN
ejpam-5629	357	14	=	=	SYM
ejpam-5629	357	15	1	1	NUM
ejpam-5629	357	16	,	,	PUNCT
ejpam-5629	357	17	the	the	DET
ejpam-5629	357	18	constants	constant	NOUN
ejpam-5629	357	19	of	of	ADP
ejpam-5629	357	20	(	(	PUNCT
ejpam-5629	357	21	22	22	NUM
ejpam-5629	357	22	)	)	PUNCT
ejpam-5629	357	23	and	and	CCONJ
ejpam-5629	357	24	(	(	PUNCT
ejpam-5629	357	25	23	23	NUM
ejpam-5629	357	26	)	)	PUNCT
ejpam-5629	357	27	can	can	AUX
ejpam-5629	357	28	be	be	AUX
ejpam-5629	357	29	obtained	obtain	VERB
ejpam-5629	357	30	as	as	ADP
ejpam-5629	357	31	follows	follow	VERB
ejpam-5629	357	32	:	:	PUNCT
ejpam-5629	357	33	case	case	NOUN
ejpam-5629	357	34	1	1	NUM
ejpam-5629	357	35	:	:	PUNCT
ejpam-5629	357	36	for	for	ADP
ejpam-5629	357	37	the	the	DET
ejpam-5629	357	38	set	set	NOUN
ejpam-5629	357	39	1	1	NUM
ejpam-5629	357	40	,	,	PUNCT
ejpam-5629	357	41	we	we	PRON
ejpam-5629	357	42	have	have	VERB
ejpam-5629	357	43	ν	ν	NOUN
ejpam-5629	357	44	=	=	SYM
ejpam-5629	357	45	e	e	PROPN
ejpam-5629	357	46	,	,	PUNCT
ejpam-5629	357	47	k̃	k̃	PROPN
ejpam-5629	357	48	=	=	SYM
ejpam-5629	357	49	±e	±e	PROPN
ejpam-5629	357	50	√	√	NUM
ejpam-5629	357	51	4e2	4e2	NUM
ejpam-5629	357	52	−	−	NOUN
ejpam-5629	357	53	1	1	NUM
ejpam-5629	357	54	,	,	PUNCT
ejpam-5629	357	55	b0	b0	NOUN
ejpam-5629	357	56	=	=	SYM
ejpam-5629	357	57	c0	c0	PROPN
ejpam-5629	357	58	=	=	SYM
ejpam-5629	357	59	0	0	NUM
ejpam-5629	357	60	,	,	PUNCT
ejpam-5629	357	61	b1	b1	NOUN
ejpam-5629	357	62	=	=	SYM
ejpam-5629	357	63	b2	b2	PROPN
ejpam-5629	357	64	=	=	SYM
ejpam-5629	357	65	−2e2	−2e2	PROPN
ejpam-5629	357	66	h	h	NOUN
ejpam-5629	357	67	,	,	PUNCT
ejpam-5629	357	68	and	and	CCONJ
ejpam-5629	357	69	c1	c1	PROPN
ejpam-5629	357	70	=	=	PROPN
ejpam-5629	357	71	c2	c2	PROPN
ejpam-5629	357	72	=	=	SYM
ejpam-5629	357	73	±	±	PROPN
ejpam-5629	357	74	√	√	ADV
ejpam-5629	357	75	1	1	NUM
ejpam-5629	357	76	ch	ch	NOUN
ejpam-5629	357	77	.	.	PUNCT
ejpam-5629	358	1	(	(	PUNCT
ejpam-5629	358	2	24	24	NUM
ejpam-5629	358	3	)	)	PUNCT
ejpam-5629	358	4	from	from	ADP
ejpam-5629	358	5	(	(	PUNCT
ejpam-5629	358	6	24	24	NUM
ejpam-5629	358	7	)	)	PUNCT
ejpam-5629	358	8	in	in	ADP
ejpam-5629	358	9	(	(	PUNCT
ejpam-5629	358	10	21	21	NUM
ejpam-5629	358	11	)	)	PUNCT
ejpam-5629	358	12	,	,	PUNCT
ejpam-5629	358	13	the	the	DET
ejpam-5629	358	14	solution	solution	NOUN
ejpam-5629	358	15	of	of	ADP
ejpam-5629	358	16	(	(	PUNCT
ejpam-5629	358	17	16	16	NUM
ejpam-5629	358	18	)	)	PUNCT
ejpam-5629	358	19	can	can	AUX
ejpam-5629	358	20	be	be	AUX
ejpam-5629	358	21	written	write	VERB
ejpam-5629	358	22	as	as	ADP
ejpam-5629	358	23	{	{	PUNCT
ejpam-5629	358	24	φ	φ	PROPN
ejpam-5629	358	25	(	(	PUNCT
ejpam-5629	358	26	ζ	ζ	PROPN
ejpam-5629	358	27	,	,	PUNCT
ejpam-5629	358	28	s	s	NOUN
ejpam-5629	358	29	)	)	PUNCT
ejpam-5629	358	30	=	=	SYM
ejpam-5629	358	31	−2e2	−2e2	PROPN
ejpam-5629	358	32	h	h	NOUN
ejpam-5629	358	33	tanh	tanh	PROPN
ejpam-5629	358	34	(	(	PUNCT
ejpam-5629	358	35	ϕ)−	ϕ)−	PROPN
ejpam-5629	358	36	2e2	2e2	PROPN
ejpam-5629	358	37	h	h	PROPN
ejpam-5629	358	38	tanh2	tanh2	NOUN
ejpam-5629	358	39	(	(	PUNCT
ejpam-5629	358	40	ϕ	ϕ	NOUN
ejpam-5629	358	41	)	)	PUNCT
ejpam-5629	358	42	,	,	PUNCT
ejpam-5629	359	1	ω	ω	PROPN
ejpam-5629	359	2	(	(	PUNCT
ejpam-5629	359	3	ζ	ζ	PROPN
ejpam-5629	359	4	,	,	PUNCT
ejpam-5629	359	5	s	s	NOUN
ejpam-5629	359	6	)	)	PUNCT
ejpam-5629	359	7	=	=	SYM
ejpam-5629	359	8	±	±	NOUN
ejpam-5629	359	9	√	√	NUM
ejpam-5629	359	10	1	1	NUM
ejpam-5629	359	11	ch	ch	NOUN
ejpam-5629	359	12	tanh	tanh	PROPN
ejpam-5629	359	13	(	(	PUNCT
ejpam-5629	359	14	ϕ)±	ϕ)±	PROPN
ejpam-5629	359	15	√	√	NUM
ejpam-5629	359	16	1	1	NUM
ejpam-5629	359	17	ch	ch	NOUN
ejpam-5629	359	18	tanh2	tanh2	NOUN
ejpam-5629	359	19	(	(	PUNCT
ejpam-5629	359	20	ϕ	ϕ	NOUN
ejpam-5629	359	21	)	)	PUNCT
ejpam-5629	359	22	.	.	PUNCT
ejpam-5629	360	1	(	(	PUNCT
ejpam-5629	360	2	25	25	NUM
ejpam-5629	360	3	)	)	PUNCT
ejpam-5629	360	4	under	under	ADP
ejpam-5629	360	5	particular	particular	ADJ
ejpam-5629	360	6	conditions	condition	NOUN
ejpam-5629	360	7	,	,	PUNCT
ejpam-5629	360	8	we	we	PRON
ejpam-5629	360	9	now	now	ADV
ejpam-5629	360	10	trace	trace	VERB
ejpam-5629	360	11	the	the	DET
ejpam-5629	360	12	two	two	NUM
ejpam-5629	360	13	parts	part	NOUN
ejpam-5629	360	14	of	of	ADP
ejpam-5629	360	15	this	this	DET
ejpam-5629	360	16	traveling	travel	VERB
ejpam-5629	360	17	wave	wave	NOUN
ejpam-5629	360	18	solution	solution	NOUN
ejpam-5629	360	19	in	in	ADP
ejpam-5629	360	20	figure	figure	NOUN
ejpam-5629	360	21	1	1	NUM
ejpam-5629	360	22	.	.	PUNCT
ejpam-5629	360	23	figure	figure	NOUN
ejpam-5629	360	24	1	1	NUM
ejpam-5629	360	25	:	:	PUNCT
ejpam-5629	360	26	3d	3d	NUM
ejpam-5629	360	27	shapes	shape	NOUN
ejpam-5629	360	28	for	for	ADP
ejpam-5629	360	29	the	the	DET
ejpam-5629	360	30	solutions	solution	NOUN
ejpam-5629	360	31	of	of	ADP
ejpam-5629	360	32	(	(	PUNCT
ejpam-5629	360	33	25	25	NUM
ejpam-5629	360	34	)	)	PUNCT
ejpam-5629	360	35	with	with	ADP
ejpam-5629	360	36	−10	−10	PRON
ejpam-5629	360	37	≤	≤	NUM
ejpam-5629	360	38	ζ	ζ	NOUN
ejpam-5629	360	39	≤	≤	NUM
ejpam-5629	360	40	10	10	NUM
ejpam-5629	360	41	,	,	PUNCT
ejpam-5629	360	42	0	0	NUM
ejpam-5629	360	43	≤	≤	NUM
ejpam-5629	360	44	s	s	PART
ejpam-5629	360	45	≤	≤	NUM
ejpam-5629	360	46	10	10	NUM
ejpam-5629	360	47	,	,	PUNCT
ejpam-5629	360	48	ν	ν	X
ejpam-5629	360	49	=	=	SYM
ejpam-5629	360	50	e	e	NOUN
ejpam-5629	360	51	=	=	SYM
ejpam-5629	360	52	2	2	NUM
ejpam-5629	360	53	,	,	PUNCT
ejpam-5629	360	54	h	h	NOUN
ejpam-5629	360	55	=	=	SYM
ejpam-5629	360	56	1	1	NUM
ejpam-5629	360	57	,	,	PUNCT
ejpam-5629	360	58	η	η	NOUN
ejpam-5629	360	59	=	=	SYM
ejpam-5629	360	60	2	2	NUM
ejpam-5629	360	61	5	5	NUM
ejpam-5629	360	62	,	,	PUNCT
ejpam-5629	360	63	and	and	CCONJ
ejpam-5629	360	64	γ	γ	X
ejpam-5629	360	65	=	=	SYM
ejpam-5629	360	66	1	1	NUM
ejpam-5629	360	67	5	5	NUM
ejpam-5629	360	68	.	.	PUNCT
ejpam-5629	361	1	h.a	h.a	PROPN
ejpam-5629	361	2	.	.	PROPN
ejpam-5629	361	3	hammad	hammad	PROPN
ejpam-5629	361	4	,	,	PUNCT
ejpam-5629	361	5	m.e.m	m.e.m	NOUN
ejpam-5629	361	6	.	.	PUNCT
ejpam-5629	362	1	abdalla	abdalla	PROPN
ejpam-5629	362	2	/	/	SYM
ejpam-5629	362	3	eur	eur	PROPN
ejpam-5629	362	4	.	.	PUNCT
ejpam-5629	363	1	j.	j.	PROPN
ejpam-5629	363	2	pure	pure	PROPN
ejpam-5629	363	3	appl	appl	PROPN
ejpam-5629	363	4	.	.	PROPN
ejpam-5629	363	5	math	math	PROPN
ejpam-5629	363	6	,	,	PUNCT
ejpam-5629	363	7	18	18	NUM
ejpam-5629	363	8	(	(	PUNCT
ejpam-5629	363	9	1	1	NUM
ejpam-5629	363	10	)	)	PUNCT
ejpam-5629	363	11	(	(	PUNCT
ejpam-5629	363	12	2025	2025	NUM
ejpam-5629	363	13	)	)	PUNCT
ejpam-5629	363	14	,	,	PUNCT
ejpam-5629	363	15	5629	5629	NUM
ejpam-5629	363	16	16	16	NUM
ejpam-5629	363	17	of	of	ADP
ejpam-5629	363	18	20	20	NUM
ejpam-5629	363	19	case	case	NOUN
ejpam-5629	363	20	2	2	NUM
ejpam-5629	363	21	:	:	PUNCT
ejpam-5629	363	22	for	for	ADP
ejpam-5629	363	23	the	the	DET
ejpam-5629	363	24	set	set	NOUN
ejpam-5629	363	25	2	2	NUM
ejpam-5629	363	26	,	,	PUNCT
ejpam-5629	363	27	we	we	PRON
ejpam-5629	363	28	have	have	VERB
ejpam-5629	363	29	ν	ν	NOUN
ejpam-5629	363	30	=	=	SYM
ejpam-5629	363	31	e	e	PROPN
ejpam-5629	363	32	,	,	PUNCT
ejpam-5629	363	33	k̃	k̃	PROPN
ejpam-5629	363	34	=	=	SYM
ejpam-5629	363	35	k̃	k̃	PROPN
ejpam-5629	363	36	,	,	PUNCT
ejpam-5629	363	37	b0	b0	NOUN
ejpam-5629	363	38	=	=	SYM
ejpam-5629	363	39	4e2	4e2	NUM
ejpam-5629	363	40	h	h	NOUN
ejpam-5629	363	41	,	,	PUNCT
ejpam-5629	363	42	b1	b1	NOUN
ejpam-5629	363	43	=	=	SYM
ejpam-5629	363	44	b2	b2	PROPN
ejpam-5629	363	45	=	=	SYM
ejpam-5629	363	46	−2e2	−2e2	PROPN
ejpam-5629	363	47	h	h	NOUN
ejpam-5629	363	48	,	,	PUNCT
ejpam-5629	363	49	c0	c0	PROPN
ejpam-5629	363	50	=	=	PUNCT
ejpam-5629	363	51	±4e2	±4e2	PROPN
ejpam-5629	364	1	√	√	ADV
ejpam-5629	364	2	1	1	NUM
ejpam-5629	364	3	ch	ch	NOUN
ejpam-5629	364	4	and	and	CCONJ
ejpam-5629	364	5	c1	c1	PROPN
ejpam-5629	364	6	=	=	PROPN
ejpam-5629	364	7	c2	c2	PROPN
ejpam-5629	364	8	=	=	PUNCT
ejpam-5629	364	9	±2e2	±2e2	PROPN
ejpam-5629	364	10	√	√	PROPN
ejpam-5629	364	11	1	1	NUM
ejpam-5629	364	12	ch	ch	NOUN
ejpam-5629	364	13	.	.	PUNCT
ejpam-5629	365	1	(	(	PUNCT
ejpam-5629	365	2	26	26	NUM
ejpam-5629	365	3	)	)	PUNCT
ejpam-5629	365	4	from	from	ADP
ejpam-5629	365	5	(	(	PUNCT
ejpam-5629	365	6	26	26	NUM
ejpam-5629	365	7	)	)	PUNCT
ejpam-5629	365	8	in	in	ADP
ejpam-5629	365	9	(	(	PUNCT
ejpam-5629	365	10	21	21	NUM
ejpam-5629	365	11	)	)	PUNCT
ejpam-5629	365	12	,	,	PUNCT
ejpam-5629	365	13	the	the	DET
ejpam-5629	365	14	solution	solution	NOUN
ejpam-5629	365	15	of	of	ADP
ejpam-5629	365	16	(	(	PUNCT
ejpam-5629	365	17	16	16	NUM
ejpam-5629	365	18	)	)	PUNCT
ejpam-5629	365	19	takes	take	VERB
ejpam-5629	365	20	the	the	DET
ejpam-5629	365	21	form	form	NOUN
ejpam-5629	365	22	{	{	PUNCT
ejpam-5629	365	23	φ	φ	PROPN
ejpam-5629	365	24	(	(	PUNCT
ejpam-5629	365	25	ζ	ζ	PROPN
ejpam-5629	365	26	,	,	PUNCT
ejpam-5629	365	27	s	s	NOUN
ejpam-5629	365	28	)	)	PUNCT
ejpam-5629	365	29	=	=	SYM
ejpam-5629	365	30	4e2	4e2	NUM
ejpam-5629	365	31	h	h	NOUN
ejpam-5629	365	32	−	−	PROPN
ejpam-5629	365	33	2e2	2e2	NUM
ejpam-5629	365	34	h	h	PROPN
ejpam-5629	365	35	tanh	tanh	PROPN
ejpam-5629	365	36	(	(	PUNCT
ejpam-5629	365	37	ϕ)−	ϕ)−	PROPN
ejpam-5629	365	38	2e2	2e2	PROPN
ejpam-5629	365	39	h	h	PROPN
ejpam-5629	365	40	tanh2	tanh2	NOUN
ejpam-5629	365	41	(	(	PUNCT
ejpam-5629	365	42	ϕ	ϕ	NOUN
ejpam-5629	365	43	)	)	PUNCT
ejpam-5629	365	44	,	,	PUNCT
ejpam-5629	365	45	ω	ω	PROPN
ejpam-5629	365	46	(	(	PUNCT
ejpam-5629	365	47	ζ	ζ	PROPN
ejpam-5629	365	48	,	,	PUNCT
ejpam-5629	365	49	s	s	NOUN
ejpam-5629	365	50	)	)	PUNCT
ejpam-5629	365	51	=	=	SYM
ejpam-5629	365	52	±4e2	±4e2	NOUN
ejpam-5629	365	53	√	√	ADP
ejpam-5629	365	54	1	1	NUM
ejpam-5629	365	55	ch	ch	PROPN
ejpam-5629	365	56	±	±	NUM
ejpam-5629	365	57	2e2	2e2	NUM
ejpam-5629	365	58	√	√	PROPN
ejpam-5629	365	59	1	1	NUM
ejpam-5629	365	60	ch	ch	NOUN
ejpam-5629	365	61	tanh	tanh	PROPN
ejpam-5629	365	62	(	(	PUNCT
ejpam-5629	365	63	ϕ)±	ϕ)±	PROPN
ejpam-5629	365	64	2e2	2e2	NUM
ejpam-5629	365	65	√	√	PROPN
ejpam-5629	365	66	1	1	NUM
ejpam-5629	365	67	ch	ch	NOUN
ejpam-5629	365	68	tanh2	tanh2	NOUN
ejpam-5629	365	69	(	(	PUNCT
ejpam-5629	365	70	ϕ	ϕ	NOUN
ejpam-5629	365	71	)	)	PUNCT
ejpam-5629	365	72	.	.	PUNCT
ejpam-5629	366	1	(	(	PUNCT
ejpam-5629	366	2	27	27	NUM
ejpam-5629	366	3	)	)	PUNCT
ejpam-5629	366	4	as	as	SCONJ
ejpam-5629	366	5	previously	previously	ADV
ejpam-5629	366	6	mentioned	mention	VERB
ejpam-5629	366	7	,	,	PUNCT
ejpam-5629	366	8	figure	figure	NOUN
ejpam-5629	366	9	2	2	NUM
ejpam-5629	366	10	shows	show	VERB
ejpam-5629	366	11	the	the	DET
ejpam-5629	366	12	two	two	NUM
ejpam-5629	366	13	parts	part	NOUN
ejpam-5629	366	14	of	of	ADP
ejpam-5629	366	15	this	this	DET
ejpam-5629	366	16	traveling	travel	VERB
ejpam-5629	366	17	wave	wave	NOUN
ejpam-5629	366	18	solution	solution	NOUN
ejpam-5629	366	19	for	for	ADP
ejpam-5629	366	20	a	a	DET
ejpam-5629	366	21	given	give	VERB
ejpam-5629	366	22	set	set	NOUN
ejpam-5629	366	23	of	of	ADP
ejpam-5629	366	24	parameters	parameter	NOUN
ejpam-5629	366	25	.	.	PUNCT
ejpam-5629	367	1	figure	figure	VERB
ejpam-5629	367	2	2	2	NUM
ejpam-5629	367	3	:	:	PUNCT
ejpam-5629	367	4	3d	3d	NUM
ejpam-5629	367	5	shapes	shape	NOUN
ejpam-5629	367	6	for	for	ADP
ejpam-5629	367	7	the	the	DET
ejpam-5629	367	8	solutions	solution	NOUN
ejpam-5629	367	9	of	of	ADP
ejpam-5629	367	10	(	(	PUNCT
ejpam-5629	367	11	27	27	NUM
ejpam-5629	367	12	)	)	PUNCT
ejpam-5629	367	13	with	with	ADP
ejpam-5629	367	14	−10	−10	PRON
ejpam-5629	367	15	≤	≤	NUM
ejpam-5629	367	16	ζ	ζ	NOUN
ejpam-5629	367	17	≤	≤	NUM
ejpam-5629	367	18	10	10	NUM
ejpam-5629	367	19	,	,	PUNCT
ejpam-5629	367	20	0	0	NUM
ejpam-5629	368	1	≤	≤	NUM
ejpam-5629	368	2	s	s	PART
ejpam-5629	368	3	≤	≤	NUM
ejpam-5629	368	4	10	10	NUM
ejpam-5629	368	5	,	,	PUNCT
ejpam-5629	368	6	ν	ν	X
ejpam-5629	368	7	=	=	SYM
ejpam-5629	368	8	e	e	NOUN
ejpam-5629	368	9	=	=	SYM
ejpam-5629	368	10	3	3	NUM
ejpam-5629	368	11	7	7	NUM
ejpam-5629	368	12	,	,	PUNCT
ejpam-5629	368	13	h	h	NOUN
ejpam-5629	368	14	=	=	SYM
ejpam-5629	368	15	3	3	NUM
ejpam-5629	368	16	,	,	PUNCT
ejpam-5629	368	17	c	c	NOUN
ejpam-5629	368	18	=	=	SYM
ejpam-5629	368	19	3	3	NUM
ejpam-5629	368	20	2	2	NUM
ejpam-5629	368	21	,	,	PUNCT
ejpam-5629	368	22	η	η	NOUN
ejpam-5629	368	23	=	=	PROPN
ejpam-5629	368	24	7	7	NUM
ejpam-5629	368	25	9	9	NUM
ejpam-5629	368	26	,	,	PUNCT
ejpam-5629	368	27	and	and	CCONJ
ejpam-5629	368	28	γ	γ	X
ejpam-5629	368	29	=	=	SYM
ejpam-5629	368	30	4	4	NUM
ejpam-5629	368	31	15	15	NUM
ejpam-5629	368	32	.	.	PUNCT
ejpam-5629	369	1	6	6	NUM
ejpam-5629	369	2	.	.	X
ejpam-5629	369	3	abbreviations	abbreviation	NOUN
ejpam-5629	369	4	de→differential	de→differential	ADJ
ejpam-5629	369	5	equation	equation	NOUN
ejpam-5629	369	6	fc→fractional	fc→fractional	ADJ
ejpam-5629	369	7	calculus	calculus	NOUN
ejpam-5629	369	8	cfd→caputo	cfd→caputo	NOUN
ejpam-5629	369	9	fractional	fractional	ADJ
ejpam-5629	369	10	derivative	derivative	ADJ
ejpam-5629	369	11	fd→fractional	fd→fractional	ADJ
ejpam-5629	369	12	derivative	derivative	ADJ
ejpam-5629	369	13	csd→caputo	csd→caputo	NOUN
ejpam-5629	369	14	sequential	sequential	ADJ
ejpam-5629	369	15	derivative	derivative	ADJ
ejpam-5629	369	16	rl→riemann	rl→riemann	NOUN
ejpam-5629	369	17	-	-	PUNCT
ejpam-5629	369	18	liouville	liouville	NOUN
ejpam-5629	369	19	fp→fixed	fp→fixe	VERB
ejpam-5629	369	20	point	point	NOUN
ejpam-5629	369	21	bs→banach	bs→banach	NOUN
ejpam-5629	369	22	space	space	NOUN
ejpam-5629	369	23	7	7	NUM
ejpam-5629	369	24	.	.	PUNCT
ejpam-5629	369	25	conclusion	conclusion	NOUN
ejpam-5629	369	26	in	in	ADP
ejpam-5629	369	27	this	this	DET
ejpam-5629	369	28	work	work	NOUN
ejpam-5629	369	29	,	,	PUNCT
ejpam-5629	369	30	we	we	PRON
ejpam-5629	369	31	explored	explore	VERB
ejpam-5629	369	32	two	two	NUM
ejpam-5629	369	33	interconnected	interconnected	ADJ
ejpam-5629	369	34	mathematical	mathematical	ADJ
ejpam-5629	369	35	problems	problem	NOUN
ejpam-5629	369	36	.	.	PUNCT
ejpam-5629	370	1	firstly	firstly	ADV
ejpam-5629	370	2	,	,	PUNCT
ejpam-5629	370	3	we	we	PRON
ejpam-5629	370	4	analyzed	analyze	VERB
ejpam-5629	370	5	a	a	DET
ejpam-5629	370	6	fractional	fractional	ADJ
ejpam-5629	370	7	system	system	NOUN
ejpam-5629	370	8	involving	involve	VERB
ejpam-5629	370	9	caputo	caputo	PROPN
ejpam-5629	370	10	derivatives	derivative	NOUN
ejpam-5629	370	11	,	,	PUNCT
ejpam-5629	370	12	which	which	PRON
ejpam-5629	370	13	generalizes	generalize	VERB
ejpam-5629	370	14	a	a	DET
ejpam-5629	370	15	beam	beam	NOUN
ejpam-5629	370	16	detectiontype	detectiontype	NOUN
ejpam-5629	370	17	system	system	NOUN
ejpam-5629	370	18	.	.	PUNCT
ejpam-5629	371	1	our	our	PRON
ejpam-5629	371	2	primary	primary	ADJ
ejpam-5629	371	3	objective	objective	NOUN
ejpam-5629	371	4	was	be	AUX
ejpam-5629	371	5	to	to	PART
ejpam-5629	371	6	establish	establish	VERB
ejpam-5629	371	7	the	the	DET
ejpam-5629	371	8	existence	existence	NOUN
ejpam-5629	371	9	and	and	CCONJ
ejpam-5629	371	10	uniqueness	uniqueness	NOUN
ejpam-5629	371	11	of	of	ADP
ejpam-5629	371	12	solutions	solution	NOUN
ejpam-5629	371	13	for	for	ADP
ejpam-5629	371	14	this	this	DET
ejpam-5629	371	15	system	system	NOUN
ejpam-5629	371	16	.	.	PUNCT
ejpam-5629	372	1	secondly	secondly	ADV
ejpam-5629	372	2	,	,	PUNCT
ejpam-5629	372	3	we	we	PRON
ejpam-5629	372	4	investigated	investigate	VERB
ejpam-5629	372	5	a	a	DET
ejpam-5629	372	6	system	system	NOUN
ejpam-5629	372	7	composed	compose	VERB
ejpam-5629	372	8	of	of	ADP
ejpam-5629	372	9	two	two	NUM
ejpam-5629	372	10	tripled	triple	VERB
ejpam-5629	372	11	evolution	evolution	NOUN
ejpam-5629	372	12	h.a	h.a	PROPN
ejpam-5629	372	13	.	.	PROPN
ejpam-5629	372	14	hammad	hammad	PROPN
ejpam-5629	372	15	,	,	PUNCT
ejpam-5629	372	16	m.e.m	m.e.m	NOUN
ejpam-5629	372	17	.	.	PUNCT
ejpam-5629	373	1	abdalla	abdalla	PROPN
ejpam-5629	373	2	/	/	SYM
ejpam-5629	373	3	eur	eur	PROPN
ejpam-5629	373	4	.	.	PUNCT
ejpam-5629	374	1	j.	j.	PROPN
ejpam-5629	374	2	pure	pure	PROPN
ejpam-5629	374	3	appl	appl	PROPN
ejpam-5629	374	4	.	.	PROPN
ejpam-5629	374	5	math	math	PROPN
ejpam-5629	374	6	,	,	PUNCT
ejpam-5629	374	7	18	18	NUM
ejpam-5629	374	8	(	(	PUNCT
ejpam-5629	374	9	1	1	NUM
ejpam-5629	374	10	)	)	PUNCT
ejpam-5629	374	11	(	(	PUNCT
ejpam-5629	374	12	2025	2025	NUM
ejpam-5629	374	13	)	)	PUNCT
ejpam-5629	374	14	,	,	PUNCT
ejpam-5629	374	15	5629	5629	NUM
ejpam-5629	374	16	17	17	NUM
ejpam-5629	374	17	of	of	ADP
ejpam-5629	374	18	20	20	NUM
ejpam-5629	374	19	equations	equation	NOUN
ejpam-5629	374	20	utilizing	utilize	VERB
ejpam-5629	374	21	conformable	conformable	ADJ
ejpam-5629	374	22	fds	fds	NOUN
ejpam-5629	374	23	as	as	SCONJ
ejpam-5629	374	24	defined	define	VERB
ejpam-5629	374	25	by	by	ADP
ejpam-5629	374	26	khalil	khalil	PROPN
ejpam-5629	374	27	.	.	PUNCT
ejpam-5629	375	1	we	we	PRON
ejpam-5629	375	2	obtained	obtain	VERB
ejpam-5629	375	3	an	an	DET
ejpam-5629	375	4	ordinary	ordinary	ADJ
ejpam-5629	375	5	differential	differential	NOUN
ejpam-5629	375	6	system	system	NOUN
ejpam-5629	375	7	with	with	ADP
ejpam-5629	375	8	moving	move	VERB
ejpam-5629	375	9	waves	wave	NOUN
ejpam-5629	375	10	by	by	ADP
ejpam-5629	375	11	changing	change	VERB
ejpam-5629	375	12	this	this	DET
ejpam-5629	375	13	conformable	conformable	ADJ
ejpam-5629	375	14	fractional	fractional	ADJ
ejpam-5629	375	15	system	system	NOUN
ejpam-5629	375	16	.	.	PUNCT
ejpam-5629	376	1	the	the	DET
ejpam-5629	376	2	application	application	NOUN
ejpam-5629	376	3	of	of	ADP
ejpam-5629	376	4	fc	fc	PROPN
ejpam-5629	376	5	to	to	PART
ejpam-5629	376	6	expand	expand	VERB
ejpam-5629	376	7	and	and	CCONJ
ejpam-5629	376	8	improve	improve	VERB
ejpam-5629	376	9	classical	classical	ADJ
ejpam-5629	376	10	models	model	NOUN
ejpam-5629	376	11	is	be	AUX
ejpam-5629	376	12	what	what	PRON
ejpam-5629	376	13	connects	connect	VERB
ejpam-5629	376	14	these	these	DET
ejpam-5629	376	15	two	two	NUM
ejpam-5629	376	16	sections	section	NOUN
ejpam-5629	376	17	,	,	PUNCT
ejpam-5629	376	18	showcasing	showcase	VERB
ejpam-5629	376	19	the	the	DET
ejpam-5629	376	20	adaptability	adaptability	NOUN
ejpam-5629	376	21	and	and	CCONJ
ejpam-5629	376	22	strength	strength	NOUN
ejpam-5629	376	23	of	of	ADP
ejpam-5629	376	24	fds	fds	NOUN
ejpam-5629	376	25	both	both	CCONJ
ejpam-5629	376	26	caputo	caputo	PROPN
ejpam-5629	376	27	and	and	CCONJ
ejpam-5629	376	28	conformable	conformable	ADJ
ejpam-5629	376	29	in	in	ADP
ejpam-5629	376	30	tackling	tackle	VERB
ejpam-5629	376	31	and	and	CCONJ
ejpam-5629	376	32	resolving	resolve	VERB
ejpam-5629	376	33	complex	complex	ADJ
ejpam-5629	376	34	mathematical	mathematical	ADJ
ejpam-5629	376	35	problems	problem	NOUN
ejpam-5629	376	36	.	.	PUNCT
ejpam-5629	377	1	this	this	DET
ejpam-5629	377	2	integrated	integrate	VERB
ejpam-5629	377	3	method	method	NOUN
ejpam-5629	377	4	enhances	enhance	VERB
ejpam-5629	377	5	our	our	PRON
ejpam-5629	377	6	knowledge	knowledge	NOUN
ejpam-5629	377	7	and	and	CCONJ
ejpam-5629	377	8	proficiency	proficiency	NOUN
ejpam-5629	377	9	in	in	ADP
ejpam-5629	377	10	mathematical	mathematical	ADJ
ejpam-5629	377	11	modeling	modeling	NOUN
ejpam-5629	377	12	and	and	CCONJ
ejpam-5629	377	13	analysis	analysis	NOUN
ejpam-5629	377	14	by	by	ADP
ejpam-5629	377	15	demonstrating	demonstrate	VERB
ejpam-5629	377	16	how	how	SCONJ
ejpam-5629	377	17	various	various	ADJ
ejpam-5629	377	18	fds	fds	NOUN
ejpam-5629	377	19	can	can	AUX
ejpam-5629	377	20	be	be	AUX
ejpam-5629	377	21	used	use	VERB
ejpam-5629	377	22	to	to	PART
ejpam-5629	377	23	investigate	investigate	VERB
ejpam-5629	377	24	and	and	CCONJ
ejpam-5629	377	25	resolve	resolve	VERB
ejpam-5629	377	26	a	a	DET
ejpam-5629	377	27	range	range	NOUN
ejpam-5629	377	28	of	of	ADP
ejpam-5629	377	29	complicated	complicated	ADJ
ejpam-5629	377	30	problems	problem	NOUN
ejpam-5629	377	31	.	.	PUNCT
ejpam-5629	378	1	while	while	SCONJ
ejpam-5629	378	2	this	this	DET
ejpam-5629	378	3	study	study	NOUN
ejpam-5629	378	4	offers	offer	VERB
ejpam-5629	378	5	a	a	DET
ejpam-5629	378	6	solid	solid	ADJ
ejpam-5629	378	7	theoretical	theoretical	ADJ
ejpam-5629	378	8	framework	framework	NOUN
ejpam-5629	378	9	for	for	ADP
ejpam-5629	378	10	understanding	understand	VERB
ejpam-5629	378	11	fractional	fractional	ADJ
ejpam-5629	378	12	differential	differential	ADJ
ejpam-5629	378	13	equations	equation	NOUN
ejpam-5629	378	14	and	and	CCONJ
ejpam-5629	378	15	their	their	PRON
ejpam-5629	378	16	applications	application	NOUN
ejpam-5629	378	17	,	,	PUNCT
ejpam-5629	378	18	it	it	PRON
ejpam-5629	378	19	’s	’	VERB
ejpam-5629	378	20	essential	essential	ADJ
ejpam-5629	378	21	to	to	PART
ejpam-5629	378	22	acknowledge	acknowledge	VERB
ejpam-5629	378	23	certain	certain	ADJ
ejpam-5629	378	24	limitations	limitation	NOUN
ejpam-5629	378	25	and	and	CCONJ
ejpam-5629	378	26	assumptions	assumption	NOUN
ejpam-5629	378	27	.	.	PUNCT
ejpam-5629	379	1	one	one	NUM
ejpam-5629	379	2	significant	significant	ADJ
ejpam-5629	379	3	limitation	limitation	NOUN
ejpam-5629	379	4	lies	lie	VERB
ejpam-5629	379	5	in	in	ADP
ejpam-5629	379	6	the	the	DET
ejpam-5629	379	7	analytical	analytical	ADJ
ejpam-5629	379	8	nature	nature	NOUN
ejpam-5629	379	9	of	of	ADP
ejpam-5629	379	10	the	the	DET
ejpam-5629	379	11	solutions	solution	NOUN
ejpam-5629	379	12	,	,	PUNCT
ejpam-5629	379	13	which	which	PRON
ejpam-5629	379	14	might	might	AUX
ejpam-5629	379	15	not	not	PART
ejpam-5629	379	16	always	always	ADV
ejpam-5629	379	17	be	be	AUX
ejpam-5629	379	18	practical	practical	ADJ
ejpam-5629	379	19	for	for	ADP
ejpam-5629	379	20	complex	complex	ADJ
ejpam-5629	379	21	systems	system	NOUN
ejpam-5629	379	22	.	.	PUNCT
ejpam-5629	380	1	additionally	additionally	ADV
ejpam-5629	380	2	,	,	PUNCT
ejpam-5629	380	3	the	the	DET
ejpam-5629	380	4	choice	choice	NOUN
ejpam-5629	380	5	of	of	ADP
ejpam-5629	380	6	fractional	fractional	ADJ
ejpam-5629	380	7	derivative	derivative	NOUN
ejpam-5629	380	8	,	,	PUNCT
ejpam-5629	380	9	such	such	ADJ
ejpam-5629	380	10	as	as	ADP
ejpam-5629	380	11	the	the	DET
ejpam-5629	380	12	caputo	caputo	PROPN
ejpam-5629	380	13	or	or	CCONJ
ejpam-5629	380	14	conformable	conformable	ADJ
ejpam-5629	380	15	derivative	derivative	NOUN
ejpam-5629	380	16	,	,	PUNCT
ejpam-5629	380	17	can	can	AUX
ejpam-5629	380	18	significantly	significantly	ADV
ejpam-5629	380	19	influence	influence	VERB
ejpam-5629	380	20	the	the	DET
ejpam-5629	380	21	system	system	NOUN
ejpam-5629	380	22	’s	’s	PART
ejpam-5629	380	23	behavior	behavior	NOUN
ejpam-5629	380	24	.	.	PUNCT
ejpam-5629	381	1	future	future	ADJ
ejpam-5629	381	2	research	research	NOUN
ejpam-5629	381	3	could	could	AUX
ejpam-5629	381	4	concentrate	concentrate	VERB
ejpam-5629	381	5	on	on	ADP
ejpam-5629	381	6	numerical	numerical	ADJ
ejpam-5629	381	7	implementations	implementation	NOUN
ejpam-5629	381	8	of	of	ADP
ejpam-5629	381	9	the	the	DET
ejpam-5629	381	10	proposed	propose	VERB
ejpam-5629	381	11	fractional	fractional	ADJ
ejpam-5629	381	12	systems	system	NOUN
ejpam-5629	381	13	,	,	PUNCT
ejpam-5629	381	14	enabling	enable	VERB
ejpam-5629	381	15	the	the	DET
ejpam-5629	381	16	exploration	exploration	NOUN
ejpam-5629	381	17	of	of	ADP
ejpam-5629	381	18	a	a	DET
ejpam-5629	381	19	wider	wide	ADJ
ejpam-5629	381	20	range	range	NOUN
ejpam-5629	381	21	of	of	ADP
ejpam-5629	381	22	parameter	parameter	NOUN
ejpam-5629	381	23	values	value	NOUN
ejpam-5629	381	24	and	and	CCONJ
ejpam-5629	381	25	initial	initial	ADJ
ejpam-5629	381	26	conditions	condition	NOUN
ejpam-5629	381	27	.	.	PUNCT
ejpam-5629	382	1	furthermore	furthermore	ADV
ejpam-5629	382	2	,	,	PUNCT
ejpam-5629	382	3	empirical	empirical	ADJ
ejpam-5629	382	4	validation	validation	NOUN
ejpam-5629	382	5	of	of	ADP
ejpam-5629	382	6	the	the	DET
ejpam-5629	382	7	traveling	travel	VERB
ejpam-5629	382	8	wave	wave	NOUN
ejpam-5629	382	9	solutions	solution	NOUN
ejpam-5629	382	10	through	through	ADP
ejpam-5629	382	11	experiments	experiment	NOUN
ejpam-5629	382	12	or	or	CCONJ
ejpam-5629	382	13	simulations	simulation	NOUN
ejpam-5629	382	14	would	would	AUX
ejpam-5629	382	15	allow	allow	VERB
ejpam-5629	382	16	for	for	ADP
ejpam-5629	382	17	a	a	DET
ejpam-5629	382	18	direct	direct	ADJ
ejpam-5629	382	19	comparison	comparison	NOUN
ejpam-5629	382	20	between	between	ADP
ejpam-5629	382	21	theoretical	theoretical	ADJ
ejpam-5629	382	22	predictions	prediction	NOUN
ejpam-5629	382	23	and	and	CCONJ
ejpam-5629	382	24	real	real	ADJ
ejpam-5629	382	25	-	-	PUNCT
ejpam-5629	382	26	world	world	NOUN
ejpam-5629	382	27	observations	observation	NOUN
ejpam-5629	382	28	.	.	PUNCT
ejpam-5629	383	1	this	this	PRON
ejpam-5629	383	2	could	could	AUX
ejpam-5629	383	3	lead	lead	VERB
ejpam-5629	383	4	to	to	ADP
ejpam-5629	383	5	refinements	refinement	NOUN
ejpam-5629	383	6	in	in	ADP
ejpam-5629	383	7	the	the	DET
ejpam-5629	383	8	model	model	NOUN
ejpam-5629	383	9	and	and	CCONJ
ejpam-5629	383	10	its	its	PRON
ejpam-5629	383	11	parameters	parameter	NOUN
ejpam-5629	383	12	.	.	PUNCT
ejpam-5629	384	1	another	another	DET
ejpam-5629	384	2	potential	potential	ADJ
ejpam-5629	384	3	area	area	NOUN
ejpam-5629	384	4	for	for	ADP
ejpam-5629	384	5	future	future	ADJ
ejpam-5629	384	6	research	research	NOUN
ejpam-5629	384	7	is	be	AUX
ejpam-5629	384	8	the	the	DET
ejpam-5629	384	9	investigation	investigation	NOUN
ejpam-5629	384	10	of	of	ADP
ejpam-5629	384	11	fractional	fractional	ADJ
ejpam-5629	384	12	systems	system	NOUN
ejpam-5629	384	13	with	with	ADP
ejpam-5629	384	14	more	more	ADV
ejpam-5629	384	15	intricate	intricate	ADJ
ejpam-5629	384	16	boundary	boundary	ADJ
ejpam-5629	384	17	conditions	condition	NOUN
ejpam-5629	384	18	and	and	CCONJ
ejpam-5629	384	19	external	external	ADJ
ejpam-5629	384	20	forcing	force	VERB
ejpam-5629	384	21	terms	term	NOUN
ejpam-5629	384	22	.	.	PUNCT
ejpam-5629	385	1	these	these	DET
ejpam-5629	385	2	extensions	extension	NOUN
ejpam-5629	385	3	could	could	AUX
ejpam-5629	385	4	have	have	VERB
ejpam-5629	385	5	significant	significant	ADJ
ejpam-5629	385	6	implications	implication	NOUN
ejpam-5629	385	7	for	for	ADP
ejpam-5629	385	8	diverse	diverse	ADJ
ejpam-5629	385	9	physical	physical	ADJ
ejpam-5629	385	10	and	and	CCONJ
ejpam-5629	385	11	engineering	engineering	NOUN
ejpam-5629	385	12	applications	application	NOUN
ejpam-5629	385	13	.	.	PUNCT
ejpam-5629	386	1	additionally	additionally	ADV
ejpam-5629	386	2	,	,	PUNCT
ejpam-5629	386	3	exploring	explore	VERB
ejpam-5629	386	4	the	the	DET
ejpam-5629	386	5	stability	stability	NOUN
ejpam-5629	386	6	analysis	analysis	NOUN
ejpam-5629	386	7	of	of	ADP
ejpam-5629	386	8	fractional	fractional	ADJ
ejpam-5629	386	9	systems	system	NOUN
ejpam-5629	386	10	would	would	AUX
ejpam-5629	386	11	provide	provide	VERB
ejpam-5629	386	12	valuable	valuable	ADJ
ejpam-5629	386	13	insights	insight	NOUN
ejpam-5629	386	14	into	into	ADP
ejpam-5629	386	15	their	their	PRON
ejpam-5629	386	16	long	long	ADJ
ejpam-5629	386	17	-	-	PUNCT
ejpam-5629	386	18	term	term	NOUN
ejpam-5629	386	19	behavior	behavior	NOUN
ejpam-5629	386	20	.	.	PUNCT
ejpam-5629	387	1	acknowledgements	acknowledgement	VERB
ejpam-5629	387	2	the	the	DET
ejpam-5629	387	3	authors	author	NOUN
ejpam-5629	387	4	extend	extend	VERB
ejpam-5629	387	5	their	their	PRON
ejpam-5629	387	6	appreciation	appreciation	NOUN
ejpam-5629	387	7	to	to	ADP
ejpam-5629	387	8	the	the	DET
ejpam-5629	387	9	deanship	deanship	NOUN
ejpam-5629	387	10	of	of	ADP
ejpam-5629	387	11	research	research	NOUN
ejpam-5629	387	12	and	and	CCONJ
ejpam-5629	387	13	graduate	graduate	NOUN
ejpam-5629	387	14	studies	study	NOUN
ejpam-5629	387	15	at	at	ADP
ejpam-5629	387	16	king	king	PROPN
ejpam-5629	387	17	khalid	khalid	PROPN
ejpam-5629	387	18	university	university	PROPN
ejpam-5629	387	19	for	for	ADP
ejpam-5629	387	20	funding	fund	VERB
ejpam-5629	387	21	this	this	DET
ejpam-5629	387	22	work	work	NOUN
ejpam-5629	387	23	through	through	ADP
ejpam-5629	387	24	large	large	ADJ
ejpam-5629	387	25	research	research	NOUN
ejpam-5629	387	26	project	project	NOUN
ejpam-5629	387	27	under	under	ADP
ejpam-5629	387	28	grant	grant	NOUN
ejpam-5629	387	29	number	number	NOUN
ejpam-5629	387	30	r.	r.	PROPN
ejpam-5629	387	31	g.	g.	PROPN
ejpam-5629	388	1	p.	p.	NOUN
ejpam-5629	388	2	2/217/45	2/217/45	NUM
ejpam-5629	388	3	.	.	PUNCT
ejpam-5629	389	1	funding	fund	VERB
ejpam-5629	389	2	this	this	DET
ejpam-5629	389	3	work	work	NOUN
ejpam-5629	389	4	was	be	AUX
ejpam-5629	389	5	supported	support	VERB
ejpam-5629	389	6	by	by	ADP
ejpam-5629	389	7	the	the	DET
ejpam-5629	389	8	deanship	deanship	NOUN
ejpam-5629	389	9	of	of	ADP
ejpam-5629	389	10	research	research	NOUN
ejpam-5629	389	11	and	and	CCONJ
ejpam-5629	389	12	graduate	graduate	NOUN
ejpam-5629	389	13	studies	study	NOUN
ejpam-5629	389	14	at	at	ADP
ejpam-5629	389	15	king	king	PROPN
ejpam-5629	389	16	khalid	khalid	PROPN
ejpam-5629	389	17	university	university	PROPN
ejpam-5629	389	18	under	under	ADP
ejpam-5629	389	19	grant	grant	PROPN
ejpam-5629	389	20	r.	r.	PROPN
ejpam-5629	389	21	g.	g.	PROPN
ejpam-5629	390	1	p.	p.	NOUN
ejpam-5629	390	2	2/217/45	2/217/45	NUM
ejpam-5629	390	3	.	.	PUNCT
ejpam-5629	391	1	data	datum	NOUN
ejpam-5629	391	2	availability	availability	NOUN
ejpam-5629	391	3	no	no	DET
ejpam-5629	391	4	data	data	NOUN
ejpam-5629	391	5	is	be	AUX
ejpam-5629	391	6	associated	associate	VERB
ejpam-5629	391	7	with	with	ADP
ejpam-5629	391	8	this	this	DET
ejpam-5629	391	9	study	study	NOUN
ejpam-5629	391	10	.	.	PUNCT
ejpam-5629	392	1	conflicts	conflict	NOUN
ejpam-5629	392	2	of	of	ADP
ejpam-5629	392	3	interest	interest	NOUN
ejpam-5629	392	4	the	the	DET
ejpam-5629	392	5	authors	author	NOUN
ejpam-5629	392	6	declare	declare	VERB
ejpam-5629	392	7	that	that	SCONJ
ejpam-5629	392	8	they	they	PRON
ejpam-5629	392	9	have	have	VERB
ejpam-5629	392	10	no	no	DET
ejpam-5629	392	11	conflicts	conflict	NOUN
ejpam-5629	392	12	of	of	ADP
ejpam-5629	392	13	interest	interest	NOUN
ejpam-5629	392	14	.	.	PUNCT
ejpam-5629	393	1	h.a	h.a	PROPN
ejpam-5629	393	2	.	.	PROPN
ejpam-5629	393	3	hammad	hammad	PROPN
ejpam-5629	393	4	,	,	PUNCT
ejpam-5629	393	5	m.e.m	m.e.m	NOUN
ejpam-5629	393	6	.	.	PUNCT
ejpam-5629	394	1	abdalla	abdalla	PROPN
ejpam-5629	394	2	/	/	SYM
ejpam-5629	394	3	eur	eur	PROPN
ejpam-5629	394	4	.	.	PUNCT
ejpam-5629	395	1	j.	j.	PROPN
ejpam-5629	395	2	pure	pure	PROPN
ejpam-5629	395	3	appl	appl	PROPN
ejpam-5629	395	4	.	.	PROPN
ejpam-5629	395	5	math	math	PROPN
ejpam-5629	395	6	,	,	PUNCT
ejpam-5629	395	7	18	18	NUM
ejpam-5629	395	8	(	(	PUNCT
ejpam-5629	395	9	1	1	NUM
ejpam-5629	395	10	)	)	PUNCT
ejpam-5629	395	11	(	(	PUNCT
ejpam-5629	395	12	2025	2025	NUM
ejpam-5629	395	13	)	)	PUNCT
ejpam-5629	395	14	,	,	PUNCT
ejpam-5629	395	15	5629	5629	NUM
ejpam-5629	395	16	18	18	NUM
ejpam-5629	395	17	of	of	ADP
ejpam-5629	395	18	20	20	NUM
ejpam-5629	395	19	authors	author	NOUN
ejpam-5629	395	20	contributions	contribution	NOUN
ejpam-5629	395	21	all	all	DET
ejpam-5629	395	22	authors	author	NOUN
ejpam-5629	395	23	contributed	contribute	VERB
ejpam-5629	395	24	equally	equally	ADV
ejpam-5629	395	25	and	and	CCONJ
ejpam-5629	395	26	significantly	significantly	ADV
ejpam-5629	395	27	in	in	ADP
ejpam-5629	395	28	writing	write	VERB
ejpam-5629	395	29	this	this	DET
ejpam-5629	395	30	article	article	NOUN
ejpam-5629	395	31	.	.	PUNCT
ejpam-5629	396	1	references	reference	NOUN
ejpam-5629	396	2	[	[	X
ejpam-5629	396	3	1	1	NUM
ejpam-5629	396	4	]	]	X
ejpam-5629	396	5	s	s	PART
ejpam-5629	396	6	abbasbandy	abbasbandy	NOUN
ejpam-5629	396	7	.	.	PUNCT
ejpam-5629	397	1	a	a	DET
ejpam-5629	397	2	new	new	ADJ
ejpam-5629	397	3	application	application	NOUN
ejpam-5629	397	4	of	of	ADP
ejpam-5629	397	5	he	he	PRON
ejpam-5629	397	6	’s	’	VERB
ejpam-5629	397	7	variational	variational	ADJ
ejpam-5629	397	8	iteration	iteration	NOUN
ejpam-5629	397	9	method	method	NOUN
ejpam-5629	397	10	for	for	ADP
ejpam-5629	397	11	quadratic	quadratic	ADJ
ejpam-5629	397	12	riccati	riccati	NOUN
ejpam-5629	397	13	differential	differential	NOUN
ejpam-5629	397	14	equation	equation	NOUN
ejpam-5629	397	15	by	by	ADP
ejpam-5629	397	16	using	use	VERB
ejpam-5629	397	17	adomian	adomian	NOUN
ejpam-5629	397	18	’s	’s	PART
ejpam-5629	397	19	polynomials	polynomial	NOUN
ejpam-5629	397	20	.	.	PUNCT
ejpam-5629	398	1	j.	j.	PROPN
ejpam-5629	398	2	comput	comput	PROPN
ejpam-5629	398	3	.	.	PUNCT
ejpam-5629	399	1	appl	appl	PROPN
ejpam-5629	399	2	.	.	PROPN
ejpam-5629	399	3	math	math	PROPN
ejpam-5629	399	4	.	.	PUNCT
ejpam-5629	399	5	,	,	PUNCT
ejpam-5629	399	6	207(1):59–63	207(1):59–63	NUM
ejpam-5629	399	7	,	,	PUNCT
ejpam-5629	399	8	2007	2007	NUM
ejpam-5629	399	9	.	.	PUNCT
ejpam-5629	400	1	[	[	X
ejpam-5629	400	2	2	2	NUM
ejpam-5629	400	3	]	]	PUNCT
ejpam-5629	400	4	t	t	NOUN
ejpam-5629	400	5	abdeljawad	abdeljawad	NOUN
ejpam-5629	400	6	.	.	PUNCT
ejpam-5629	401	1	on	on	ADP
ejpam-5629	401	2	conformable	conformable	ADJ
ejpam-5629	401	3	fractional	fractional	ADJ
ejpam-5629	401	4	calculus	calculus	NOUN
ejpam-5629	401	5	.	.	PUNCT
ejpam-5629	402	1	j.	j.	PROPN
ejpam-5629	402	2	comput	comput	PROPN
ejpam-5629	402	3	.	.	PUNCT
ejpam-5629	403	1	appl	appl	PROPN
ejpam-5629	403	2	.	.	PROPN
ejpam-5629	403	3	math	math	PROPN
ejpam-5629	403	4	.	.	PUNCT
ejpam-5629	403	5	,	,	PUNCT
ejpam-5629	403	6	279:57	279:57	NUM
ejpam-5629	403	7	–	–	PUNCT
ejpam-5629	403	8	66	66	NUM
ejpam-5629	403	9	,	,	PUNCT
ejpam-5629	403	10	2015	2015	NUM
ejpam-5629	403	11	.	.	PUNCT
ejpam-5629	404	1	[	[	X
ejpam-5629	404	2	3	3	NUM
ejpam-5629	404	3	]	]	X
ejpam-5629	404	4	m	m	VERB
ejpam-5629	404	5	adel	adel	PROPN
ejpam-5629	404	6	,	,	PUNCT
ejpam-5629	404	7	m	m	VERB
ejpam-5629	404	8	m	m	NOUN
ejpam-5629	404	9	khader	khader	NOUN
ejpam-5629	404	10	,	,	PUNCT
ejpam-5629	404	11	and	and	CCONJ
ejpam-5629	404	12	t	t	X
ejpam-5629	404	13	a	a	DET
ejpam-5629	404	14	assiri	assiri	NOUN
ejpam-5629	404	15	.	.	PUNCT
ejpam-5629	405	1	comparative	comparative	ADJ
ejpam-5629	405	2	analysis	analysis	NOUN
ejpam-5629	405	3	of	of	ADP
ejpam-5629	405	4	modified	modified	ADJ
ejpam-5629	405	5	admoian	admoian	ADJ
ejpam-5629	405	6	decomposition	decomposition	NOUN
ejpam-5629	405	7	method	method	NOUN
ejpam-5629	405	8	and	and	CCONJ
ejpam-5629	405	9	homotopy	homotopy	VERB
ejpam-5629	405	10	perturbation	perturbation	NOUN
ejpam-5629	405	11	mohand	mohand	NOUN
ejpam-5629	405	12	transform	transform	VERB
ejpam-5629	405	13	method	method	NOUN
ejpam-5629	405	14	for	for	ADP
ejpam-5629	405	15	solving	solve	VERB
ejpam-5629	405	16	burger	burger	NOUN
ejpam-5629	405	17	’s	’s	PART
ejpam-5629	405	18	equations	equation	NOUN
ejpam-5629	405	19	.	.	PUNCT
ejpam-5629	406	1	european	european	PROPN
ejpam-5629	406	2	j.	j.	PROPN
ejpam-5629	406	3	pure	pure	PROPN
ejpam-5629	406	4	appl	appl	PROPN
ejpam-5629	406	5	.	.	PUNCT
ejpam-5629	406	6	math	math	PROPN
ejpam-5629	406	7	.	.	PUNCT
ejpam-5629	406	8	,	,	PUNCT
ejpam-5629	406	9	17(4):2812–2827	17(4):2812–2827	NUM
ejpam-5629	406	10	,	,	PUNCT
ejpam-5629	406	11	2024	2024	NUM
ejpam-5629	406	12	.	.	PUNCT
ejpam-5629	407	1	[	[	X
ejpam-5629	407	2	4	4	NUM
ejpam-5629	407	3	]	]	X
ejpam-5629	407	4	h	h	NOUN
ejpam-5629	407	5	afshari	afshari	NOUN
ejpam-5629	407	6	,	,	PUNCT
ejpam-5629	407	7	h	h	PROPN
ejpam-5629	407	8	hosseinpour	hosseinpour	NOUN
ejpam-5629	407	9	,	,	PUNCT
ejpam-5629	407	10	and	and	CCONJ
ejpam-5629	407	11	h	h	NOUN
ejpam-5629	407	12	r	r	NOUN
ejpam-5629	407	13	marasi	marasi	NOUN
ejpam-5629	407	14	.	.	PUNCT
ejpam-5629	408	1	application	application	NOUN
ejpam-5629	408	2	of	of	ADP
ejpam-5629	408	3	some	some	DET
ejpam-5629	408	4	new	new	ADJ
ejpam-5629	408	5	contractions	contraction	NOUN
ejpam-5629	408	6	for	for	ADP
ejpam-5629	408	7	existenceand	existenceand	ADJ
ejpam-5629	408	8	uniqueness	uniqueness	NOUN
ejpam-5629	408	9	of	of	ADP
ejpam-5629	408	10	differential	differential	ADJ
ejpam-5629	408	11	equations	equation	NOUN
ejpam-5629	408	12	involving	involve	VERB
ejpam-5629	408	13	caputofabrizio	caputofabrizio	PROPN
ejpam-5629	408	14	derivative	derivative	NOUN
ejpam-5629	408	15	.	.	PUNCT
ejpam-5629	409	1	adv	adv	PROPN
ejpam-5629	409	2	.	.	PROPN
ejpam-5629	409	3	differ	differ	VERB
ejpam-5629	409	4	.	.	PUNCT
ejpam-5629	410	1	equ	equ	PROPN
ejpam-5629	410	2	.	.	PROPN
ejpam-5629	410	3	,	,	PUNCT
ejpam-5629	410	4	2021:321	2021:321	NUM
ejpam-5629	410	5	,	,	PUNCT
ejpam-5629	410	6	2021	2021	NUM
ejpam-5629	410	7	.	.	PUNCT
ejpam-5629	411	1	[	[	X
ejpam-5629	411	2	5	5	NUM
ejpam-5629	411	3	]	]	PUNCT
ejpam-5629	411	4	ar	ar	NOUN
ejpam-5629	411	5	aftabizadeh	aftabizadeh	PROPN
ejpam-5629	411	6	.	.	PUNCT
ejpam-5629	412	1	existence	existence	NOUN
ejpam-5629	412	2	and	and	CCONJ
ejpam-5629	412	3	uniqueness	uniqueness	ADJ
ejpam-5629	412	4	theorems	theorem	NOUN
ejpam-5629	412	5	for	for	ADP
ejpam-5629	412	6	fourth	fourth	ADJ
ejpam-5629	412	7	-	-	PUNCT
ejpam-5629	412	8	order	order	NOUN
ejpam-5629	412	9	boundary	boundary	ADJ
ejpam-5629	412	10	value	value	NOUN
ejpam-5629	412	11	problems	problem	NOUN
ejpam-5629	412	12	.	.	PUNCT
ejpam-5629	413	1	j.	j.	PROPN
ejpam-5629	413	2	math	math	PROPN
ejpam-5629	413	3	.	.	PUNCT
ejpam-5629	414	1	anal	anal	PROPN
ejpam-5629	414	2	.	.	PUNCT
ejpam-5629	415	1	appl	appl	PROPN
ejpam-5629	415	2	.	.	PROPN
ejpam-5629	415	3	,	,	PUNCT
ejpam-5629	415	4	116:415–426	116:415–426	NUM
ejpam-5629	415	5	,	,	PUNCT
ejpam-5629	415	6	1986	1986	NUM
ejpam-5629	415	7	.	.	PUNCT
ejpam-5629	416	1	[	[	X
ejpam-5629	416	2	6	6	NUM
ejpam-5629	416	3	]	]	X
ejpam-5629	416	4	r	r	NOUN
ejpam-5629	416	5	agarwal	agarwal	NOUN
ejpam-5629	416	6	.	.	PUNCT
ejpam-5629	417	1	on	on	ADP
ejpam-5629	417	2	fourth	fourth	ADJ
ejpam-5629	417	3	-	-	PUNCT
ejpam-5629	417	4	order	order	NOUN
ejpam-5629	417	5	boundary	boundary	ADJ
ejpam-5629	417	6	value	value	NOUN
ejpam-5629	417	7	problems	problem	NOUN
ejpam-5629	417	8	arising	arise	VERB
ejpam-5629	417	9	in	in	ADP
ejpam-5629	417	10	beam	beam	ADJ
ejpam-5629	417	11	analysis	analysis	NOUN
ejpam-5629	417	12	.	.	PUNCT
ejpam-5629	418	1	differ	differ	VERB
ejpam-5629	418	2	.	.	PUNCT
ejpam-5629	419	1	integr	integr	PROPN
ejpam-5629	419	2	.	.	PUNCT
ejpam-5629	420	1	equ	equ	PROPN
ejpam-5629	420	2	.	.	PROPN
ejpam-5629	420	3	,	,	PUNCT
ejpam-5629	420	4	2:91–110	2:91–110	NUM
ejpam-5629	420	5	,	,	PUNCT
ejpam-5629	420	6	1989	1989	NUM
ejpam-5629	420	7	.	.	PUNCT
ejpam-5629	421	1	[	[	X
ejpam-5629	421	2	7	7	NUM
ejpam-5629	421	3	]	]	SYM
ejpam-5629	421	4	b	b	X
ejpam-5629	421	5	ahmad	ahmad	PROPN
ejpam-5629	421	6	and	and	CCONJ
ejpam-5629	421	7	s	s	NOUN
ejpam-5629	421	8	k	k	PROPN
ejpam-5629	421	9	ntouyas	ntouyas	NOUN
ejpam-5629	421	10	.	.	PUNCT
ejpam-5629	422	1	existence	existence	NOUN
ejpam-5629	422	2	results	result	VERB
ejpam-5629	422	3	for	for	ADP
ejpam-5629	422	4	a	a	DET
ejpam-5629	422	5	coupled	couple	VERB
ejpam-5629	422	6	system	system	NOUN
ejpam-5629	422	7	of	of	ADP
ejpam-5629	422	8	caputo	caputo	PROPN
ejpam-5629	422	9	type	type	NOUN
ejpam-5629	422	10	sequential	sequential	ADJ
ejpam-5629	422	11	fractional	fractional	ADJ
ejpam-5629	422	12	differential	differential	ADJ
ejpam-5629	422	13	equations	equation	NOUN
ejpam-5629	422	14	with	with	ADP
ejpam-5629	422	15	nonlocal	nonlocal	ADJ
ejpam-5629	422	16	integral	integral	ADJ
ejpam-5629	422	17	boundary	boundary	ADJ
ejpam-5629	422	18	conditions	condition	NOUN
ejpam-5629	422	19	.	.	PUNCT
ejpam-5629	423	1	appl	appl	PROPN
ejpam-5629	423	2	.	.	PROPN
ejpam-5629	423	3	math	math	PROPN
ejpam-5629	423	4	.	.	PUNCT
ejpam-5629	424	1	comput	comput	NOUN
ejpam-5629	424	2	.	.	PUNCT
ejpam-5629	424	3	,	,	PUNCT
ejpam-5629	424	4	266:615–622	266:615–622	NUM
ejpam-5629	424	5	,	,	PUNCT
ejpam-5629	424	6	2015	2015	NUM
ejpam-5629	424	7	.	.	PUNCT
ejpam-5629	425	1	[	[	X
ejpam-5629	425	2	8	8	NUM
ejpam-5629	425	3	]	]	X
ejpam-5629	425	4	s	s	VERB
ejpam-5629	425	5	a	a	DET
ejpam-5629	425	6	al	al	PROPN
ejpam-5629	425	7	-	-	PROPN
ejpam-5629	425	8	mezel	mezel	PROPN
ejpam-5629	425	9	an	an	DET
ejpam-5629	425	10	j	j	PROPN
ejpam-5629	425	11	ahmad	ahmad	PROPN
ejpam-5629	425	12	.	.	PUNCT
ejpam-5629	426	1	smigroups	smigroups	PROPN
ejpam-5629	426	2	without	without	ADP
ejpam-5629	426	3	convexity	convexity	NOUN
ejpam-5629	426	4	.	.	PUNCT
ejpam-5629	427	1	proc	proc	PROPN
ejpam-5629	427	2	.	.	PUNCT
ejpam-5629	428	1	amer	amer	PROPN
ejpam-5629	428	2	.	.	PUNCT
ejpam-5629	428	3	math	math	PROPN
ejpam-5629	428	4	.	.	PUNCT
ejpam-5629	428	5	,	,	PUNCT
ejpam-5629	428	6	122:1175	122:1175	NUM
ejpam-5629	428	7	–	–	PUNCT
ejpam-5629	428	8	1179	1179	NUM
ejpam-5629	428	9	,	,	PUNCT
ejpam-5629	428	10	1994	1994	NUM
ejpam-5629	428	11	.	.	PUNCT
ejpam-5629	429	1	[	[	X
ejpam-5629	429	2	9	9	NUM
ejpam-5629	429	3	]	]	SYM
ejpam-5629	429	4	h	h	NOUN
ejpam-5629	429	5	a	a	DET
ejpam-5629	429	6	hammad	hammad	PROPN
ejpam-5629	429	7	an	an	DET
ejpam-5629	429	8	r	r	NOUN
ejpam-5629	429	9	a	a	DET
ejpam-5629	429	10	rashwan	rashwan	NOUN
ejpam-5629	429	11	,	,	PUNCT
ejpam-5629	429	12	a	a	DET
ejpam-5629	429	13	nafea	nafea	ADJ
ejpam-5629	429	14	,	,	PUNCT
ejpam-5629	429	15	m	m	PROPN
ejpam-5629	429	16	e	e	NOUN
ejpam-5629	429	17	samei	samei	NOUN
ejpam-5629	429	18	,	,	PUNCT
ejpam-5629	429	19	and	and	CCONJ
ejpam-5629	429	20	de	de	PROPN
ejpam-5629	429	21	la	la	X
ejpam-5629	429	22	sen	sen	PROPN
ejpam-5629	429	23	.	.	PROPN
ejpam-5629	429	24	stability	stability	NOUN
ejpam-5629	429	25	and	and	CCONJ
ejpam-5629	429	26	existence	existence	NOUN
ejpam-5629	429	27	of	of	ADP
ejpam-5629	429	28	solutions	solution	NOUN
ejpam-5629	429	29	for	for	ADP
ejpam-5629	429	30	a	a	DET
ejpam-5629	429	31	tripled	triple	VERB
ejpam-5629	429	32	problem	problem	NOUN
ejpam-5629	429	33	of	of	ADP
ejpam-5629	429	34	fractional	fractional	ADJ
ejpam-5629	429	35	hybrid	hybrid	ADJ
ejpam-5629	429	36	delay	delay	NOUN
ejpam-5629	429	37	differential	differential	ADJ
ejpam-5629	429	38	equations	equation	NOUN
ejpam-5629	429	39	.	.	PUNCT
ejpam-5629	430	1	symmetry	symmetry	PROPN
ejpam-5629	430	2	.	.	PUNCT
ejpam-5629	430	3	,	,	PUNCT
ejpam-5629	430	4	14:2579	14:2579	NUM
ejpam-5629	430	5	,	,	PUNCT
ejpam-5629	430	6	2022	2022	NUM
ejpam-5629	430	7	.	.	PUNCT
ejpam-5629	431	1	[	[	X
ejpam-5629	431	2	10	10	NUM
ejpam-5629	431	3	]	]	X
ejpam-5629	431	4	i	i	PRON
ejpam-5629	431	5	m	m	AUX
ejpam-5629	431	6	batiha	batiha	VERB
ejpam-5629	431	7	,	,	PUNCT
ejpam-5629	431	8	s	s	VERB
ejpam-5629	431	9	a	a	DET
ejpam-5629	431	10	njadat	njadat	NOUN
ejpam-5629	431	11	,	,	PUNCT
ejpam-5629	431	12	r	r	NOUN
ejpam-5629	431	13	m	m	NOUN
ejpam-5629	431	14	batyha	batyha	NOUN
ejpam-5629	431	15	,	,	PUNCT
ejpam-5629	431	16	a	a	DET
ejpam-5629	431	17	zraiqat	zraiqat	NOUN
ejpam-5629	431	18	,	,	PUNCT
ejpam-5629	431	19	a	a	DET
ejpam-5629	431	20	dababneh	dababneh	NOUN
ejpam-5629	431	21	,	,	PUNCT
ejpam-5629	431	22	and	and	CCONJ
ejpam-5629	431	23	s	s	NOUN
ejpam-5629	431	24	momani	momani	NOUN
ejpam-5629	431	25	.	.	PUNCT
ejpam-5629	432	1	design	design	VERB
ejpam-5629	432	2	frac	frac	ADJ
ejpam-5629	432	3	-	-	PUNCT
ejpam-5629	432	4	tionalorder	tionalorder	NOUN
ejpam-5629	432	5	pid	pid	NOUN
ejpam-5629	432	6	controllers	controller	NOUN
ejpam-5629	432	7	for	for	ADP
ejpam-5629	432	8	single	single	ADJ
ejpam-5629	432	9	-	-	PUNCT
ejpam-5629	432	10	joint	joint	ADJ
ejpam-5629	432	11	robot	robot	NOUN
ejpam-5629	432	12	arm	arm	NOUN
ejpam-5629	432	13	model	model	PROPN
ejpam-5629	432	14	.	.	PUNCT
ejpam-5629	433	1	int	int	NOUN
ejpam-5629	433	2	.	.	PUNCT
ejpam-5629	434	1	j.	j.	PROPN
ejpam-5629	434	2	adv	adv	PROPN
ejpam-5629	434	3	.	.	PUNCT
ejpam-5629	434	4	soft	soft	ADJ
ejpam-5629	434	5	comput	comput	NOUN
ejpam-5629	434	6	.	.	PUNCT
ejpam-5629	435	1	appl	appl	PROPN
ejpam-5629	435	2	.	.	PROPN
ejpam-5629	435	3	,	,	PUNCT
ejpam-5629	435	4	14:96–114	14:96–114	NUM
ejpam-5629	435	5	,	,	PUNCT
ejpam-5629	435	6	2022	2022	NUM
ejpam-5629	435	7	.	.	PUNCT
ejpam-5629	436	1	[	[	X
ejpam-5629	436	2	11	11	NUM
ejpam-5629	436	3	]	]	X
ejpam-5629	436	4	k	k	NOUN
ejpam-5629	436	5	bensaassa	bensaassa	NOUN
ejpam-5629	436	6	,	,	PUNCT
ejpam-5629	436	7	z	z	PROPN
ejpam-5629	436	8	dahmani	dahmani	PROPN
ejpam-5629	436	9	,	,	PUNCT
ejpam-5629	436	10	m	m	PROPN
ejpam-5629	436	11	rakah	rakah	PROPN
ejpam-5629	436	12	,	,	PUNCT
ejpam-5629	436	13	and	and	CCONJ
ejpam-5629	436	14	m	m	PROPN
ejpam-5629	436	15	z	z	PROPN
ejpam-5629	436	16	sarikaya	sarikaya	PROPN
ejpam-5629	436	17	.	.	PUNCT
ejpam-5629	437	1	beam	beam	NOUN
ejpam-5629	437	2	deflection	deflection	NOUN
ejpam-5629	437	3	coupled	couple	VERB
ejpam-5629	437	4	systems	system	NOUN
ejpam-5629	437	5	of	of	ADP
ejpam-5629	437	6	fractional	fractional	ADJ
ejpam-5629	437	7	differential	differential	ADJ
ejpam-5629	437	8	equations	equation	NOUN
ejpam-5629	437	9	:	:	PUNCT
ejpam-5629	437	10	existence	existence	NOUN
ejpam-5629	437	11	of	of	ADP
ejpam-5629	437	12	solutions	solution	NOUN
ejpam-5629	437	13	,	,	PUNCT
ejpam-5629	437	14	ulam	ulam	NOUN
ejpam-5629	437	15	-	-	PUNCT
ejpam-5629	437	16	hyers	hyer	NOUN
ejpam-5629	437	17	stability	stability	NOUN
ejpam-5629	437	18	and	and	CCONJ
ejpam-5629	437	19	travelling	travel	VERB
ejpam-5629	437	20	waves	wave	NOUN
ejpam-5629	437	21	.	.	PUNCT
ejpam-5629	438	1	anal	anal	PROPN
ejpam-5629	438	2	.	.	PUNCT
ejpam-5629	438	3	math	math	NOUN
ejpam-5629	438	4	.	.	PUNCT
ejpam-5629	439	1	phys	phy	NOUN
ejpam-5629	439	2	.	.	PUNCT
ejpam-5629	439	3	,	,	PUNCT
ejpam-5629	439	4	14:29	14:29	NUM
ejpam-5629	439	5	,	,	PUNCT
ejpam-5629	439	6	2024	2024	NUM
ejpam-5629	439	7	.	.	PUNCT
ejpam-5629	440	1	[	[	X
ejpam-5629	440	2	12	12	NUM
ejpam-5629	440	3	]	]	PUNCT
ejpam-5629	440	4	a	a	DET
ejpam-5629	440	5	carpinteri	carpinteri	NOUN
ejpam-5629	440	6	and	and	CCONJ
ejpam-5629	440	7	f	f	PROPN
ejpam-5629	440	8	mainardi	mainardi	PROPN
ejpam-5629	440	9	.	.	PUNCT
ejpam-5629	441	1	fractional	fractional	ADJ
ejpam-5629	441	2	calculus	calculus	NOUN
ejpam-5629	441	3	in	in	ADP
ejpam-5629	441	4	continuum	continuum	ADJ
ejpam-5629	441	5	mechanics	mechanic	NOUN
ejpam-5629	441	6	,	,	PUNCT
ejpam-5629	441	7	2	2	NUM
ejpam-5629	441	8	eds	ed	NOUN
ejpam-5629	441	9	.	.	PUNCT
ejpam-5629	442	1	new	new	PROPN
ejpam-5629	442	2	york	york	PROPN
ejpam-5629	442	3	:	:	PUNCT
ejpam-5629	442	4	academic	academic	ADJ
ejpam-5629	442	5	press	press	NOUN
ejpam-5629	442	6	.	.	PUNCT
ejpam-5629	442	7	,	,	PUNCT
ejpam-5629	442	8	1997	1997	NUM
ejpam-5629	442	9	.	.	PUNCT
ejpam-5629	443	1	[	[	X
ejpam-5629	443	2	13	13	NUM
ejpam-5629	443	3	]	]	SYM
ejpam-5629	443	4	y	y	PROPN
ejpam-5629	443	5	chatibi	chatibi	NOUN
ejpam-5629	443	6	,	,	PUNCT
ejpam-5629	443	7	el	el	PROPN
ejpam-5629	443	8	-	-	PROPN
ejpam-5629	443	9	h	h	PROPN
ejpam-5629	443	10	el	el	PROPN
ejpam-5629	443	11	kinani	kinani	PROPN
ejpam-5629	443	12	,	,	PUNCT
ejpam-5629	443	13	and	and	CCONJ
ejpam-5629	443	14	a	a	DET
ejpam-5629	443	15	ouhadan	ouhadan	PROPN
ejpam-5629	443	16	.	.	PROPN
ejpam-5629	444	1	lie	lie	PROPN
ejpam-5629	444	2	symmetry	symmetry	NOUN
ejpam-5629	444	3	analysis	analysis	NOUN
ejpam-5629	444	4	and	and	CCONJ
ejpam-5629	444	5	conservation	conservation	NOUN
ejpam-5629	444	6	laws	law	NOUN
ejpam-5629	444	7	for	for	ADP
ejpam-5629	444	8	the	the	DET
ejpam-5629	444	9	time	time	NOUN
ejpam-5629	444	10	-	-	PUNCT
ejpam-5629	444	11	fractional	fractional	ADJ
ejpam-5629	444	12	black	black	ADJ
ejpam-5629	444	13	-	-	PUNCT
ejpam-5629	444	14	scholes	schole	NOUN
ejpam-5629	444	15	equation	equation	NOUN
ejpam-5629	444	16	.	.	PUNCT
ejpam-5629	445	1	int	int	NOUN
ejpam-5629	445	2	.	.	PUNCT
ejpam-5629	446	1	j.	j.	PROPN
ejpam-5629	446	2	geometric	geometric	ADJ
ejpam-5629	446	3	methods	method	NOUN
ejpam-5629	446	4	modern	modern	ADJ
ejpam-5629	446	5	phy	phy	PROPN
ejpam-5629	446	6	.	.	PROPN
ejpam-5629	446	7	,	,	PUNCT
ejpam-5629	446	8	17(01):2050010	17(01):2050010	NUM
ejpam-5629	446	9	,	,	PUNCT
ejpam-5629	446	10	2020	2020	NUM
ejpam-5629	446	11	.	.	PUNCT
ejpam-5629	447	1	[	[	X
ejpam-5629	447	2	14	14	NUM
ejpam-5629	447	3	]	]	X
ejpam-5629	447	4	y	y	PROPN
ejpam-5629	447	5	chatibi	chatibi	NOUN
ejpam-5629	447	6	,	,	PUNCT
ejpam-5629	447	7	el	el	PROPN
ejpam-5629	447	8	-	-	PROPN
ejpam-5629	447	9	h	h	PROPN
ejpam-5629	447	10	el	el	PROPN
ejpam-5629	447	11	kinani	kinani	PROPN
ejpam-5629	447	12	,	,	PUNCT
ejpam-5629	447	13	and	and	CCONJ
ejpam-5629	447	14	a	a	DET
ejpam-5629	447	15	ouhadan	ouhadan	NOUN
ejpam-5629	447	16	.	.	PUNCT
ejpam-5629	448	1	continuous	continuous	ADJ
ejpam-5629	448	2	and	and	CCONJ
ejpam-5629	448	3	discrete	discrete	ADJ
ejpam-5629	448	4	symmetry	symmetry	NOUN
ejpam-5629	448	5	methods	method	NOUN
ejpam-5629	448	6	for	for	ADP
ejpam-5629	448	7	fractional	fractional	ADJ
ejpam-5629	448	8	differential	differential	ADJ
ejpam-5629	448	9	equations	equation	NOUN
ejpam-5629	448	10	,	,	PUNCT
ejpam-5629	448	11	fractional	fractional	ADJ
ejpam-5629	448	12	-	-	PUNCT
ejpam-5629	448	13	order	order	NOUN
ejpam-5629	448	14	model	model	NOUN
ejpam-5629	448	15	.	.	PUNCT
ejpam-5629	449	1	dynamic	dynamic	ADJ
ejpam-5629	449	2	sys	sys	PROPN
ejpam-5629	449	3	.	.	PUNCT
ejpam-5629	449	4	appl	appl	PROPN
ejpam-5629	449	5	.	.	PUNCT
ejpam-5629	450	1	opti	opti	PROPN
ejpam-5629	450	2	.	.	PROPN
ejpam-5629	450	3	,	,	PUNCT
ejpam-5629	450	4	signal	signal	ADJ
ejpam-5629	450	5	proc	proc	NOUN
ejpam-5629	450	6	.	.	PROPN
ejpam-5629	450	7	,	,	PUNCT
ejpam-5629	450	8	2:1	2:1	NUM
ejpam-5629	450	9	–	–	PUNCT
ejpam-5629	450	10	35	35	NUM
ejpam-5629	450	11	,	,	PUNCT
ejpam-5629	450	12	2022	2022	NUM
ejpam-5629	450	13	.	.	PUNCT
ejpam-5629	451	1	h.a	h.a	PROPN
ejpam-5629	451	2	.	.	PROPN
ejpam-5629	451	3	hammad	hammad	PROPN
ejpam-5629	451	4	,	,	PUNCT
ejpam-5629	451	5	m.e.m	m.e.m	NOUN
ejpam-5629	451	6	.	.	PUNCT
ejpam-5629	452	1	abdalla	abdalla	PROPN
ejpam-5629	452	2	/	/	SYM
ejpam-5629	452	3	eur	eur	PROPN
ejpam-5629	452	4	.	.	PUNCT
ejpam-5629	453	1	j.	j.	PROPN
ejpam-5629	453	2	pure	pure	PROPN
ejpam-5629	453	3	appl	appl	PROPN
ejpam-5629	453	4	.	.	PROPN
ejpam-5629	453	5	math	math	PROPN
ejpam-5629	453	6	,	,	PUNCT
ejpam-5629	453	7	18	18	NUM
ejpam-5629	453	8	(	(	PUNCT
ejpam-5629	453	9	1	1	NUM
ejpam-5629	453	10	)	)	PUNCT
ejpam-5629	453	11	(	(	PUNCT
ejpam-5629	453	12	2025	2025	NUM
ejpam-5629	453	13	)	)	PUNCT
ejpam-5629	453	14	,	,	PUNCT
ejpam-5629	453	15	5629	5629	NUM
ejpam-5629	453	16	19	19	NUM
ejpam-5629	453	17	of	of	ADP
ejpam-5629	453	18	20	20	NUM
ejpam-5629	453	19	[	[	SYM
ejpam-5629	453	20	15	15	NUM
ejpam-5629	453	21	]	]	X
ejpam-5629	453	22	z	z	NOUN
ejpam-5629	453	23	dahmani	dahmani	PROPN
ejpam-5629	453	24	,	,	PUNCT
ejpam-5629	453	25	a	a	DET
ejpam-5629	453	26	anber	anber	ADJ
ejpam-5629	453	27	an	an	DET
ejpam-5629	453	28	y	y	PROPN
ejpam-5629	453	29	gouari	gouari	NOUN
ejpam-5629	453	30	,	,	PUNCT
ejpam-5629	453	31	m	m	PROPN
ejpam-5629	453	32	kaid	kaid	ADJ
ejpam-5629	453	33	,	,	PUNCT
ejpam-5629	453	34	and	and	CCONJ
ejpam-5629	453	35	i	i	PRON
ejpam-5629	453	36	jebril	jebril	VERB
ejpam-5629	453	37	.	.	PUNCT
ejpam-5629	454	1	extension	extension	NOUN
ejpam-5629	454	2	of	of	ADP
ejpam-5629	454	3	a	a	DET
ejpam-5629	454	4	method	method	NOUN
ejpam-5629	454	5	for	for	ADP
ejpam-5629	454	6	solving	solve	VERB
ejpam-5629	454	7	nonlinear	nonlinear	ADJ
ejpam-5629	454	8	evolution	evolution	NOUN
ejpam-5629	454	9	equations	equation	NOUN
ejpam-5629	454	10	via	via	ADP
ejpam-5629	454	11	conformable	conformable	ADJ
ejpam-5629	454	12	fractional	fractional	ADJ
ejpam-5629	454	13	approach	approach	NOUN
ejpam-5629	454	14	.	.	PUNCT
ejpam-5629	455	1	int	int	NOUN
ejpam-5629	455	2	.	.	PUNCT
ejpam-5629	455	3	conf	conf	PROPN
ejpam-5629	455	4	.	.	PUNCT
ejpam-5629	456	1	infor	infor	PROPN
ejpam-5629	456	2	.	.	PUNCT
ejpam-5629	457	1	tech	tech	PROPN
ejpam-5629	457	2	.	.	PUNCT
ejpam-5629	457	3	,	,	PUNCT
ejpam-5629	457	4	pages	page	NOUN
ejpam-5629	457	5	38–42	38–42	NUM
ejpam-5629	457	6	,	,	PUNCT
ejpam-5629	457	7	2021	2021	NUM
ejpam-5629	457	8	.	.	PUNCT
ejpam-5629	458	1	[	[	X
ejpam-5629	458	2	16	16	NUM
ejpam-5629	458	3	]	]	X
ejpam-5629	458	4	z	z	NOUN
ejpam-5629	458	5	dahmani	dahmani	PROPN
ejpam-5629	458	6	,	,	PUNCT
ejpam-5629	458	7	a	a	DET
ejpam-5629	458	8	anber	anber	NOUN
ejpam-5629	458	9	,	,	PUNCT
ejpam-5629	458	10	and	and	CCONJ
ejpam-5629	458	11	i	i	PRON
ejpam-5629	458	12	jebril	jebril	VERB
ejpam-5629	458	13	.	.	PUNCT
ejpam-5629	459	1	solving	solve	VERB
ejpam-5629	459	2	conformable	conformable	ADJ
ejpam-5629	459	3	evolution	evolution	NOUN
ejpam-5629	459	4	equations	equation	NOUN
ejpam-5629	459	5	by	by	ADP
ejpam-5629	459	6	an	an	DET
ejpam-5629	459	7	extended	extended	ADJ
ejpam-5629	459	8	numerical	numerical	ADJ
ejpam-5629	459	9	method	method	NOUN
ejpam-5629	459	10	.	.	PUNCT
ejpam-5629	460	1	jordan	jordan	PROPN
ejpam-5629	460	2	j.	j.	PROPN
ejpam-5629	460	3	math	math	PROPN
ejpam-5629	460	4	.	.	PUNCT
ejpam-5629	461	1	stat	stat	PROPN
ejpam-5629	461	2	.	.	PUNCT
ejpam-5629	461	3	,	,	PUNCT
ejpam-5629	461	4	15:363–380	15:363–380	PROPN
ejpam-5629	461	5	,	,	PUNCT
ejpam-5629	461	6	2022	2022	NUM
ejpam-5629	461	7	.	.	PUNCT
ejpam-5629	462	1	[	[	X
ejpam-5629	462	2	17	17	NUM
ejpam-5629	462	3	]	]	X
ejpam-5629	462	4	y	y	PROPN
ejpam-5629	462	5	gouari	gouari	PROPN
ejpam-5629	462	6	,	,	PUNCT
ejpam-5629	462	7	z	z	NOUN
ejpam-5629	462	8	dahmani	dahmani	NOUN
ejpam-5629	462	9	,	,	PUNCT
ejpam-5629	462	10	and	and	CCONJ
ejpam-5629	462	11	i	i	PRON
ejpam-5629	462	12	jebril	jebril	VERB
ejpam-5629	462	13	.	.	PUNCT
ejpam-5629	463	1	application	application	NOUN
ejpam-5629	463	2	of	of	ADP
ejpam-5629	463	3	fractional	fractional	ADJ
ejpam-5629	463	4	calculus	calculus	NOUN
ejpam-5629	463	5	on	on	ADP
ejpam-5629	463	6	a	a	DET
ejpam-5629	463	7	new	new	ADJ
ejpam-5629	463	8	differential	differential	ADJ
ejpam-5629	463	9	problem	problem	NOUN
ejpam-5629	463	10	of	of	ADP
ejpam-5629	463	11	duffing	duffing	NOUN
ejpam-5629	463	12	type	type	NOUN
ejpam-5629	463	13	.	.	PUNCT
ejpam-5629	464	1	adv	adv	PROPN
ejpam-5629	464	2	.	.	PUNCT
ejpam-5629	464	3	math	math	PROPN
ejpam-5629	464	4	.	.	PUNCT
ejpam-5629	465	1	sci	sci	PROPN
ejpam-5629	465	2	.	.	PUNCT
ejpam-5629	466	1	j.	j.	PROPN
ejpam-5629	466	2	,	,	PUNCT
ejpam-5629	466	3	9:10989–11002	9:10989–11002	NUM
ejpam-5629	466	4	,	,	PUNCT
ejpam-5629	466	5	2020	2020	NUM
ejpam-5629	466	6	.	.	PUNCT
ejpam-5629	467	1	[	[	X
ejpam-5629	467	2	18	18	NUM
ejpam-5629	467	3	]	]	X
ejpam-5629	467	4	h	h	NOUN
ejpam-5629	467	5	a	a	DET
ejpam-5629	467	6	hammad	hammad	PROPN
ejpam-5629	467	7	,	,	PUNCT
ejpam-5629	467	8	h	h	NOUN
ejpam-5629	467	9	aydi	aydi	ADJ
ejpam-5629	467	10	,	,	PUNCT
ejpam-5629	467	11	h	h	NOUN
ejpam-5629	467	12	isik	isik	NOUN
ejpam-5629	467	13	,	,	PUNCT
ejpam-5629	467	14	and	and	CCONJ
ejpam-5629	467	15	m	m	PROPN
ejpam-5629	467	16	de	de	X
ejpam-5629	467	17	la	la	X
ejpam-5629	467	18	sen	sen	PROPN
ejpam-5629	467	19	.	.	PROPN
ejpam-5629	467	20	stability	stability	PROPN
ejpam-5629	467	21	and	and	CCONJ
ejpam-5629	467	22	controllability	controllability	NOUN
ejpam-5629	467	23	study	study	NOUN
ejpam-5629	467	24	for	for	ADP
ejpam-5629	467	25	mixed	mixed	ADJ
ejpam-5629	467	26	integral	integral	ADJ
ejpam-5629	467	27	fractional	fractional	ADJ
ejpam-5629	467	28	delay	delay	NOUN
ejpam-5629	467	29	dynamic	dynamic	ADJ
ejpam-5629	467	30	systems	system	NOUN
ejpam-5629	467	31	endowed	endow	VERB
ejpam-5629	467	32	with	with	ADP
ejpam-5629	467	33	impulsive	impulsive	ADJ
ejpam-5629	467	34	effects	effect	NOUN
ejpam-5629	467	35	on	on	ADP
ejpam-5629	467	36	time	time	NOUN
ejpam-5629	467	37	scales	scale	NOUN
ejpam-5629	467	38	.	.	PUNCT
ejpam-5629	468	1	aims	aim	VERB
ejpam-5629	468	2	math	math	NOUN
ejpam-5629	468	3	.	.	PUNCT
ejpam-5629	468	4	,	,	PUNCT
ejpam-5629	468	5	8(3):6913–6941	8(3):6913–6941	PROPN
ejpam-5629	468	6	,	,	PUNCT
ejpam-5629	468	7	2023	2023	NUM
ejpam-5629	468	8	.	.	PUNCT
ejpam-5629	469	1	[	[	X
ejpam-5629	469	2	19	19	NUM
ejpam-5629	469	3	]	]	X
ejpam-5629	469	4	h	h	NOUN
ejpam-5629	469	5	a	a	DET
ejpam-5629	469	6	hammad	hammad	PROPN
ejpam-5629	469	7	,	,	PUNCT
ejpam-5629	469	8	h	h	NOUN
ejpam-5629	469	9	aydi	aydi	ADJ
ejpam-5629	469	10	,	,	PUNCT
ejpam-5629	469	11	and	and	CCONJ
ejpam-5629	469	12	m	m	AUX
ejpam-5629	469	13	zayed	zayed	ADJ
ejpam-5629	469	14	.	.	PUNCT
ejpam-5629	470	1	on	on	ADP
ejpam-5629	470	2	the	the	DET
ejpam-5629	470	3	qualitative	qualitative	ADJ
ejpam-5629	470	4	evaluation	evaluation	NOUN
ejpam-5629	470	5	of	of	ADP
ejpam-5629	470	6	the	the	DET
ejpam-5629	470	7	variable	variable	ADJ
ejpam-5629	470	8	order	order	NOUN
ejpam-5629	470	9	coupled	couple	VERB
ejpam-5629	470	10	boundary	boundary	ADJ
ejpam-5629	470	11	value	value	NOUN
ejpam-5629	470	12	problems	problem	NOUN
ejpam-5629	470	13	with	with	ADP
ejpam-5629	470	14	a	a	DET
ejpam-5629	470	15	fractional	fractional	ADJ
ejpam-5629	470	16	delay	delay	NOUN
ejpam-5629	470	17	.	.	PUNCT
ejpam-5629	471	1	j.	j.	PROPN
ejpam-5629	471	2	inequal	inequal	PROPN
ejpam-5629	471	3	.	.	PUNCT
ejpam-5629	472	1	appl	appl	PROPN
ejpam-5629	472	2	.	.	PROPN
ejpam-5629	472	3	,	,	PUNCT
ejpam-5629	472	4	2023:105	2023:105	NOUN
ejpam-5629	472	5	,	,	PUNCT
ejpam-5629	472	6	2023	2023	NUM
ejpam-5629	472	7	.	.	PUNCT
ejpam-5629	473	1	[	[	X
ejpam-5629	473	2	20	20	NUM
ejpam-5629	473	3	]	]	X
ejpam-5629	473	4	h	h	NOUN
ejpam-5629	473	5	a	a	DET
ejpam-5629	473	6	hammad	hammad	PROPN
ejpam-5629	473	7	and	and	CCONJ
ejpam-5629	473	8	m	m	PROPN
ejpam-5629	473	9	de	de	X
ejpam-5629	473	10	la	la	X
ejpam-5629	473	11	sen	sen	PROPN
ejpam-5629	473	12	.	.	PROPN
ejpam-5629	473	13	analytical	analytical	ADJ
ejpam-5629	473	14	solution	solution	NOUN
ejpam-5629	473	15	of	of	ADP
ejpam-5629	473	16	urysohn	urysohn	PROPN
ejpam-5629	473	17	integral	integral	ADJ
ejpam-5629	473	18	equations	equation	NOUN
ejpam-5629	473	19	by	by	ADP
ejpam-5629	473	20	fixed	fix	VERB
ejpam-5629	473	21	point	point	NOUN
ejpam-5629	473	22	technique	technique	NOUN
ejpam-5629	473	23	in	in	ADP
ejpam-5629	473	24	complex	complex	ADJ
ejpam-5629	473	25	valued	value	VERB
ejpam-5629	473	26	metric	metric	ADJ
ejpam-5629	473	27	spaces	space	NOUN
ejpam-5629	473	28	.	.	PUNCT
ejpam-5629	474	1	mathematics	mathematic	NOUN
ejpam-5629	474	2	.	.	PUNCT
ejpam-5629	474	3	,	,	PUNCT
ejpam-5629	474	4	7:852	7:852	NUM
ejpam-5629	474	5	,	,	PUNCT
ejpam-5629	474	6	2019	2019	NUM
ejpam-5629	474	7	.	.	PUNCT
ejpam-5629	475	1	[	[	X
ejpam-5629	475	2	21	21	NUM
ejpam-5629	475	3	]	]	X
ejpam-5629	475	4	h	h	NOUN
ejpam-5629	475	5	a	a	DET
ejpam-5629	475	6	hammad	hammad	PROPN
ejpam-5629	475	7	and	and	CCONJ
ejpam-5629	475	8	m	m	PROPN
ejpam-5629	475	9	de	de	X
ejpam-5629	475	10	la	la	PROPN
ejpam-5629	475	11	sen	sen	PROPN
ejpam-5629	475	12	.	.	PROPN
ejpam-5629	475	13	solutions	solution	NOUN
ejpam-5629	475	14	of	of	ADP
ejpam-5629	475	15	fractional	fractional	ADJ
ejpam-5629	475	16	differential	differential	ADJ
ejpam-5629	475	17	type	type	NOUN
ejpam-5629	475	18	equations	equation	NOUN
ejpam-5629	475	19	by	by	ADP
ejpam-5629	475	20	fixed	fix	VERB
ejpam-5629	475	21	point	point	NOUN
ejpam-5629	475	22	techniques	technique	NOUN
ejpam-5629	475	23	for	for	ADP
ejpam-5629	475	24	multivalued	multivalued	ADJ
ejpam-5629	475	25	contractions	contraction	NOUN
ejpam-5629	475	26	.	.	PUNCT
ejpam-5629	476	1	complexity	complexity	NOUN
ejpam-5629	476	2	.	.	PUNCT
ejpam-5629	476	3	,	,	PUNCT
ejpam-5629	476	4	2021:5730853	2021:5730853	NOUN
ejpam-5629	476	5	,	,	PUNCT
ejpam-5629	476	6	2021	2021	NUM
ejpam-5629	476	7	.	.	PUNCT
ejpam-5629	477	1	[	[	X
ejpam-5629	477	2	22	22	NUM
ejpam-5629	477	3	]	]	X
ejpam-5629	477	4	h	h	NOUN
ejpam-5629	477	5	a	a	DET
ejpam-5629	477	6	hammad	hammad	PROPN
ejpam-5629	477	7	and	and	CCONJ
ejpam-5629	477	8	m	m	PROPN
ejpam-5629	477	9	de	de	X
ejpam-5629	477	10	la	la	PROPN
ejpam-5629	477	11	sen	sen	PROPN
ejpam-5629	477	12	.	.	PROPN
ejpam-5629	477	13	stability	stability	PROPN
ejpam-5629	477	14	and	and	CCONJ
ejpam-5629	477	15	controllability	controllability	NOUN
ejpam-5629	477	16	study	study	NOUN
ejpam-5629	477	17	for	for	ADP
ejpam-5629	477	18	mixed	mixed	ADJ
ejpam-5629	477	19	integral	integral	ADJ
ejpam-5629	477	20	fractional	fractional	ADJ
ejpam-5629	477	21	delay	delay	NOUN
ejpam-5629	477	22	dynamic	dynamic	ADJ
ejpam-5629	477	23	systems	system	NOUN
ejpam-5629	477	24	endowed	endow	VERB
ejpam-5629	477	25	with	with	ADP
ejpam-5629	477	26	impulsive	impulsive	ADJ
ejpam-5629	477	27	effects	effect	NOUN
ejpam-5629	477	28	on	on	ADP
ejpam-5629	477	29	time	time	NOUN
ejpam-5629	477	30	scales	scale	NOUN
ejpam-5629	477	31	.	.	PUNCT
ejpam-5629	478	1	fractal	fractal	ADJ
ejpam-5629	478	2	fract	fract	PROPN
ejpam-5629	478	3	.	.	PUNCT
ejpam-5629	478	4	,	,	PUNCT
ejpam-5629	478	5	7:92	7:92	NUM
ejpam-5629	478	6	,	,	PUNCT
ejpam-5629	478	7	2023	2023	NUM
ejpam-5629	478	8	.	.	PUNCT
ejpam-5629	479	1	[	[	X
ejpam-5629	479	2	23	23	NUM
ejpam-5629	479	3	]	]	X
ejpam-5629	479	4	h	h	NOUN
ejpam-5629	479	5	a	a	DET
ejpam-5629	479	6	hammad	hammad	PROPN
ejpam-5629	479	7	,	,	PUNCT
ejpam-5629	479	8	mde	mde	PROPN
ejpam-5629	479	9	la	la	PROPN
ejpam-5629	479	10	sen	sen	PROPN
ejpam-5629	479	11	,	,	PUNCT
ejpam-5629	479	12	and	and	CCONJ
ejpam-5629	479	13	h	h	NOUN
ejpam-5629	479	14	aydi	aydi	VERB
ejpam-5629	479	15	.	.	PUNCT
ejpam-5629	480	1	generalized	generalize	VERB
ejpam-5629	480	2	dynamic	dynamic	ADJ
ejpam-5629	480	3	process	process	NOUN
ejpam-5629	480	4	for	for	ADP
ejpam-5629	480	5	an	an	DET
ejpam-5629	480	6	extended	extended	ADJ
ejpam-5629	480	7	multivaluedf	multivaluedf	NOUN
ejpam-5629	480	8	-	-	PUNCT
ejpam-5629	480	9	contraction	contraction	NOUN
ejpam-5629	480	10	in	in	ADP
ejpam-5629	480	11	metric	metric	ADJ
ejpam-5629	480	12	-	-	PUNCT
ejpam-5629	480	13	like	like	ADJ
ejpam-5629	480	14	spaces	space	NOUN
ejpam-5629	480	15	with	with	ADP
ejpam-5629	480	16	applications	application	NOUN
ejpam-5629	480	17	.	.	PUNCT
ejpam-5629	481	1	alex	alex	PROPN
ejpam-5629	481	2	.	.	PUNCT
ejpam-5629	482	1	eng	eng	PROPN
ejpam-5629	482	2	.	.	PUNCT
ejpam-5629	483	1	j.	j.	PROPN
ejpam-5629	483	2	,	,	PUNCT
ejpam-5629	483	3	59(5):5730853	59(5):5730853	NOUN
ejpam-5629	483	4	,	,	PUNCT
ejpam-5629	483	5	2020	2020	NUM
ejpam-5629	483	6	.	.	PUNCT
ejpam-5629	484	1	[	[	X
ejpam-5629	484	2	24	24	NUM
ejpam-5629	484	3	]	]	X
ejpam-5629	484	4	h	h	NOUN
ejpam-5629	484	5	a	a	DET
ejpam-5629	484	6	hammad	hammad	PROPN
ejpam-5629	484	7	,	,	PUNCT
ejpam-5629	484	8	r	r	NOUN
ejpam-5629	484	9	a	a	DET
ejpam-5629	484	10	rashwan	rashwan	NOUN
ejpam-5629	484	11	,	,	PUNCT
ejpam-5629	484	12	a	a	DET
ejpam-5629	484	13	nafea	nafea	ADJ
ejpam-5629	484	14	,	,	PUNCT
ejpam-5629	484	15	m	m	PROPN
ejpam-5629	484	16	e	e	NOUN
ejpam-5629	484	17	samei	samei	NOUN
ejpam-5629	484	18	,	,	PUNCT
ejpam-5629	484	19	and	and	CCONJ
ejpam-5629	484	20	s	s	VERB
ejpam-5629	484	21	noeiaghdam	noeiaghdam	NOUN
ejpam-5629	484	22	.	.	PUNCT
ejpam-5629	485	1	stability	stability	NOUN
ejpam-5629	485	2	analysis	analysis	NOUN
ejpam-5629	485	3	for	for	ADP
ejpam-5629	485	4	a	a	DET
ejpam-5629	485	5	tripled	triple	VERB
ejpam-5629	485	6	system	system	NOUN
ejpam-5629	485	7	of	of	ADP
ejpam-5629	485	8	fractional	fractional	ADJ
ejpam-5629	485	9	pantograph	pantograph	NOUN
ejpam-5629	485	10	differential	differential	NOUN
ejpam-5629	485	11	equations	equation	NOUN
ejpam-5629	485	12	with	with	ADP
ejpam-5629	485	13	nonlocal	nonlocal	ADJ
ejpam-5629	485	14	conditions	condition	NOUN
ejpam-5629	485	15	.	.	PUNCT
ejpam-5629	486	1	j.	j.	PROPN
ejpam-5629	486	2	vib	vib	PROPN
ejpam-5629	486	3	.	.	PUNCT
ejpam-5629	486	4	control	control	PROPN
ejpam-5629	486	5	.	.	PUNCT
ejpam-5629	486	6	,	,	PUNCT
ejpam-5629	486	7	30(3	30(3	X
ejpam-5629	486	8	-	-	SYM
ejpam-5629	486	9	4):632–647	4):632–647	NUM
ejpam-5629	486	10	,	,	PUNCT
ejpam-5629	486	11	2024	2024	NUM
ejpam-5629	486	12	.	.	PUNCT
ejpam-5629	487	1	[	[	X
ejpam-5629	487	2	25	25	NUM
ejpam-5629	487	3	]	]	X
ejpam-5629	487	4	m	m	VERB
ejpam-5629	487	5	q	q	NOUN
ejpam-5629	487	6	iqbal	iqbal	PROPN
ejpam-5629	487	7	and	and	CCONJ
ejpam-5629	487	8	a	a	DET
ejpam-5629	487	9	hussain	hussain	NOUN
ejpam-5629	487	10	.	.	PUNCT
ejpam-5629	488	1	existence	existence	NOUN
ejpam-5629	488	2	criteria	criterion	NOUN
ejpam-5629	488	3	via	via	ADP
ejpam-5629	488	4	α	α	PRON
ejpam-5629	488	5	−	−	PROPN
ejpam-5629	488	6	ψcontractive	ψcontractive	ADJ
ejpam-5629	488	7	mappings	mapping	NOUN
ejpam-5629	488	8	of	of	ADP
ejpam-5629	488	9	ϕ−-fractional	ϕ−-fractional	NOUN
ejpam-5629	488	10	differential	differential	ADJ
ejpam-5629	488	11	nonlocal	nonlocal	ADJ
ejpam-5629	488	12	boundary	boundary	ADJ
ejpam-5629	488	13	value	value	NOUN
ejpam-5629	488	14	problems	problem	NOUN
ejpam-5629	488	15	.	.	PUNCT
ejpam-5629	489	1	aims	aim	VERB
ejpam-5629	489	2	math	math	NOUN
ejpam-5629	489	3	.	.	PUNCT
ejpam-5629	489	4	,	,	PUNCT
ejpam-5629	489	5	2021:350	2021:350	NUM
ejpam-5629	489	6	,	,	PUNCT
ejpam-5629	489	7	2021	2021	NUM
ejpam-5629	489	8	.	.	PUNCT
ejpam-5629	490	1	[	[	X
ejpam-5629	490	2	26	26	NUM
ejpam-5629	490	3	]	]	PUNCT
ejpam-5629	490	4	l	l	NOUN
ejpam-5629	490	5	kexue	kexue	NOUN
ejpam-5629	490	6	and	and	CCONJ
ejpam-5629	490	7	p	p	NOUN
ejpam-5629	490	8	jigen	jigen	PROPN
ejpam-5629	490	9	.	.	PUNCT
ejpam-5629	491	1	laplace	laplace	PROPN
ejpam-5629	491	2	transform	transform	NOUN
ejpam-5629	491	3	and	and	CCONJ
ejpam-5629	491	4	fractional	fractional	ADJ
ejpam-5629	491	5	differential	differential	ADJ
ejpam-5629	491	6	equations	equation	NOUN
ejpam-5629	491	7	.	.	PUNCT
ejpam-5629	492	1	appl	appl	PROPN
ejpam-5629	492	2	.	.	PROPN
ejpam-5629	492	3	math	math	PROPN
ejpam-5629	492	4	.	.	PUNCT
ejpam-5629	493	1	lett	lett	PROPN
ejpam-5629	493	2	.	.	PROPN
ejpam-5629	493	3	,	,	PUNCT
ejpam-5629	493	4	24(12):2019–2023	24(12):2019–2023	NUM
ejpam-5629	493	5	,	,	PUNCT
ejpam-5629	493	6	2011	2011	NUM
ejpam-5629	493	7	.	.	PUNCT
ejpam-5629	494	1	[	[	X
ejpam-5629	494	2	27	27	NUM
ejpam-5629	494	3	]	]	X
ejpam-5629	494	4	r	r	NOUN
ejpam-5629	494	5	khalil	khalil	PROPN
ejpam-5629	494	6	,	,	PUNCT
ejpam-5629	494	7	m	m	PROPN
ejpam-5629	494	8	al	al	PROPN
ejpam-5629	494	9	horani	horani	PROPN
ejpam-5629	494	10	,	,	PUNCT
ejpam-5629	494	11	a	a	DET
ejpam-5629	494	12	yousef	yousef	PROPN
ejpam-5629	494	13	,	,	PUNCT
ejpam-5629	494	14	and	and	CCONJ
ejpam-5629	494	15	m	m	PROPN
ejpam-5629	494	16	sababheh	sababheh	ADJ
ejpam-5629	494	17	.	.	PUNCT
ejpam-5629	495	1	a	a	DET
ejpam-5629	495	2	new	new	ADJ
ejpam-5629	495	3	definition	definition	NOUN
ejpam-5629	495	4	of	of	ADP
ejpam-5629	495	5	fractional	fractional	ADJ
ejpam-5629	495	6	derivative	derivative	NOUN
ejpam-5629	495	7	.	.	PUNCT
ejpam-5629	496	1	j.	j.	PROPN
ejpam-5629	496	2	comput	comput	PROPN
ejpam-5629	496	3	.	.	PUNCT
ejpam-5629	497	1	appl	appl	PROPN
ejpam-5629	497	2	.	.	PROPN
ejpam-5629	497	3	math	math	PROPN
ejpam-5629	497	4	.	.	PUNCT
ejpam-5629	497	5	,	,	PUNCT
ejpam-5629	497	6	264:65–70	264:65–70	NUM
ejpam-5629	497	7	,	,	PUNCT
ejpam-5629	497	8	2014	2014	NUM
ejpam-5629	497	9	.	.	PUNCT
ejpam-5629	498	1	[	[	X
ejpam-5629	498	2	28	28	NUM
ejpam-5629	498	3	]	]	X
ejpam-5629	498	4	a	a	DET
ejpam-5629	498	5	a	a	DET
ejpam-5629	498	6	kilbas	kilbas	NOUN
ejpam-5629	498	7	,	,	PUNCT
ejpam-5629	498	8	h	h	PROPN
ejpam-5629	498	9	m	m	PROPN
ejpam-5629	498	10	srivastava	srivastava	PROPN
ejpam-5629	498	11	,	,	PUNCT
ejpam-5629	498	12	and	and	CCONJ
ejpam-5629	498	13	j	j	PROPN
ejpam-5629	498	14	j	j	PROPN
ejpam-5629	498	15	trujillo	trujillo	PROPN
ejpam-5629	498	16	.	.	PUNCT
ejpam-5629	498	17	theory	theory	NOUN
ejpam-5629	498	18	and	and	CCONJ
ejpam-5629	498	19	applications	application	NOUN
ejpam-5629	498	20	of	of	ADP
ejpam-5629	498	21	fractional	fractional	ADJ
ejpam-5629	498	22	differential	differential	ADJ
ejpam-5629	498	23	equations	equation	NOUN
ejpam-5629	498	24	.	.	PUNCT
ejpam-5629	499	1	amsterdam	amsterdam	PROPN
ejpam-5629	499	2	:	:	PUNCT
ejpam-5629	499	3	elsevier	elsevier	PROPN
ejpam-5629	499	4	b.v	b.v	PROPN
ejpam-5629	499	5	,	,	PUNCT
ejpam-5629	499	6	2006	2006	NUM
ejpam-5629	499	7	.	.	PUNCT
ejpam-5629	500	1	[	[	X
ejpam-5629	500	2	29	29	NUM
ejpam-5629	500	3	]	]	X
ejpam-5629	500	4	p	p	X
ejpam-5629	500	5	li	li	PROPN
ejpam-5629	500	6	,	,	PUNCT
ejpam-5629	500	7	y	y	PROPN
ejpam-5629	500	8	lu	lu	PROPN
ejpam-5629	500	9	,	,	PUNCT
ejpam-5629	500	10	c	c	PROPN
ejpam-5629	500	11	xu	xu	PROPN
ejpam-5629	500	12	,	,	PUNCT
ejpam-5629	500	13	and	and	CCONJ
ejpam-5629	500	14	j	j	PROPN
ejpam-5629	500	15	ren	ren	PROPN
ejpam-5629	500	16	.	.	PUNCT
ejpam-5629	501	1	dynamic	dynamic	ADJ
ejpam-5629	501	2	exploration	exploration	NOUN
ejpam-5629	501	3	and	and	CCONJ
ejpam-5629	501	4	control	control	NOUN
ejpam-5629	501	5	of	of	ADP
ejpam-5629	501	6	bifurcation	bifurcation	NOUN
ejpam-5629	501	7	in	in	ADP
ejpam-5629	501	8	a	a	DET
ejpam-5629	501	9	fractional	fractional	ADJ
ejpam-5629	501	10	-	-	PUNCT
ejpam-5629	501	11	order	order	NOUN
ejpam-5629	501	12	lengyel	lengyel	PROPN
ejpam-5629	501	13	-	-	PUNCT
ejpam-5629	501	14	epstein	epstein	PROPN
ejpam-5629	501	15	model	model	NOUN
ejpam-5629	501	16	owing	owe	VERB
ejpam-5629	501	17	time	time	NOUN
ejpam-5629	501	18	delay	delay	NOUN
ejpam-5629	501	19	.	.	PUNCT
ejpam-5629	502	1	match	match	PROPN
ejpam-5629	502	2	commun	commun	PROPN
ejpam-5629	502	3	.	.	PUNCT
ejpam-5629	502	4	math	math	PROPN
ejpam-5629	502	5	.	.	PUNCT
ejpam-5629	503	1	comput	comput	NOUN
ejpam-5629	503	2	.	.	PUNCT
ejpam-5629	504	1	chem	chem	NOUN
ejpam-5629	504	2	.	.	PUNCT
ejpam-5629	504	3	,	,	PUNCT
ejpam-5629	504	4	92:472–482	92:472–482	NUM
ejpam-5629	504	5	,	,	PUNCT
ejpam-5629	504	6	2024	2024	NUM
ejpam-5629	504	7	.	.	PUNCT
ejpam-5629	505	1	[	[	X
ejpam-5629	505	2	30	30	NUM
ejpam-5629	505	3	]	]	PUNCT
ejpam-5629	505	4	a	a	DET
ejpam-5629	505	5	kılıçman	kılıçman	PROPN
ejpam-5629	505	6	and	and	CCONJ
ejpam-5629	505	7	m	m	PROPN
ejpam-5629	505	8	omran	omran	ADJ
ejpam-5629	505	9	.	.	PUNCT
ejpam-5629	506	1	note	note	NOUN
ejpam-5629	506	2	on	on	ADP
ejpam-5629	506	3	fractional	fractional	ADJ
ejpam-5629	506	4	mellin	mellin	PROPN
ejpam-5629	506	5	transform	transform	NOUN
ejpam-5629	506	6	and	and	CCONJ
ejpam-5629	506	7	applications	application	NOUN
ejpam-5629	506	8	.	.	PUNCT
ejpam-5629	507	1	springerplus	springerplus	PROPN
ejpam-5629	507	2	.	.	PROPN
ejpam-5629	507	3	,	,	PUNCT
ejpam-5629	507	4	5:100	5:100	NUM
ejpam-5629	507	5	,	,	PUNCT
ejpam-5629	507	6	2016	2016	NUM
ejpam-5629	507	7	.	.	PUNCT
ejpam-5629	508	1	[	[	X
ejpam-5629	508	2	31	31	NUM
ejpam-5629	508	3	]	]	X
ejpam-5629	508	4	y	y	PROPN
ejpam-5629	508	5	f	f	PROPN
ejpam-5629	508	6	luchko	luchko	VERB
ejpam-5629	508	7	,	,	PUNCT
ejpam-5629	508	8	h	h	PROPN
ejpam-5629	508	9	matŕınez	matŕınez	PROPN
ejpam-5629	508	10	,	,	PUNCT
ejpam-5629	508	11	and	and	CCONJ
ejpam-5629	508	12	j	j	PROPN
ejpam-5629	508	13	j	j	PROPN
ejpam-5629	508	14	trujillo	trujillo	PROPN
ejpam-5629	508	15	.	.	PUNCT
ejpam-5629	509	1	fractional	fractional	ADJ
ejpam-5629	509	2	fourier	fourier	NOUN
ejpam-5629	509	3	transform	transform	NOUN
ejpam-5629	509	4	and	and	CCONJ
ejpam-5629	509	5	some	some	PRON
ejpam-5629	509	6	of	of	ADP
ejpam-5629	509	7	its	its	PRON
ejpam-5629	509	8	applications	application	NOUN
ejpam-5629	509	9	.	.	PUNCT
ejpam-5629	510	1	fract	fract	PROPN
ejpam-5629	510	2	.	.	PUNCT
ejpam-5629	511	1	calc	calc	PROPN
ejpam-5629	511	2	.	.	PUNCT
ejpam-5629	512	1	appl	appl	PROPN
ejpam-5629	512	2	.	.	PUNCT
ejpam-5629	513	1	anal	anal	PROPN
ejpam-5629	513	2	.	.	PROPN
ejpam-5629	513	3	,	,	PUNCT
ejpam-5629	513	4	11(4):1–15	11(4):1–15	NUM
ejpam-5629	513	5	,	,	PUNCT
ejpam-5629	513	6	2008	2008	NUM
ejpam-5629	513	7	.	.	PUNCT
ejpam-5629	514	1	[	[	X
ejpam-5629	514	2	32	32	NUM
ejpam-5629	514	3	]	]	X
ejpam-5629	514	4	z	z	PROPN
ejpam-5629	514	5	ma	ma	PROPN
ejpam-5629	514	6	,	,	PUNCT
ejpam-5629	514	7	h	h	PROPN
ejpam-5629	514	8	zahed	zahe	VERB
ejpam-5629	514	9	,	,	PUNCT
ejpam-5629	514	10	and	and	CCONJ
ejpam-5629	514	11	j	j	PROPN
ejpam-5629	514	12	ahmad	ahmad	PROPN
ejpam-5629	514	13	.	.	PUNCT
ejpam-5629	515	1	fixed	fix	VERB
ejpam-5629	515	2	point	point	NOUN
ejpam-5629	515	3	results	result	NOUN
ejpam-5629	515	4	with	with	ADP
ejpam-5629	515	5	applications	application	NOUN
ejpam-5629	515	6	to	to	ADP
ejpam-5629	515	7	fractional	fractional	ADJ
ejpam-5629	515	8	h.a	h.a	PROPN
ejpam-5629	515	9	.	.	PROPN
ejpam-5629	515	10	hammad	hammad	PROPN
ejpam-5629	515	11	,	,	PUNCT
ejpam-5629	515	12	m.e.m	m.e.m	NOUN
ejpam-5629	515	13	.	.	PUNCT
ejpam-5629	516	1	abdalla	abdalla	PROPN
ejpam-5629	516	2	/	/	SYM
ejpam-5629	516	3	eur	eur	PROPN
ejpam-5629	516	4	.	.	PUNCT
ejpam-5629	517	1	j.	j.	PROPN
ejpam-5629	517	2	pure	pure	PROPN
ejpam-5629	517	3	appl	appl	PROPN
ejpam-5629	517	4	.	.	PROPN
ejpam-5629	517	5	math	math	PROPN
ejpam-5629	517	6	,	,	PUNCT
ejpam-5629	517	7	18	18	NUM
ejpam-5629	517	8	(	(	PUNCT
ejpam-5629	517	9	1	1	NUM
ejpam-5629	517	10	)	)	PUNCT
ejpam-5629	517	11	(	(	PUNCT
ejpam-5629	517	12	2025	2025	NUM
ejpam-5629	517	13	)	)	PUNCT
ejpam-5629	517	14	,	,	PUNCT
ejpam-5629	517	15	5629	5629	NUM
ejpam-5629	517	16	20	20	NUM
ejpam-5629	517	17	of	of	ADP
ejpam-5629	517	18	20	20	NUM
ejpam-5629	517	19	differential	differential	ADJ
ejpam-5629	517	20	equations	equation	NOUN
ejpam-5629	517	21	of	of	ADP
ejpam-5629	517	22	anomalous	anomalous	ADJ
ejpam-5629	517	23	diffusionential	diffusionential	ADJ
ejpam-5629	517	24	equations	equation	NOUN
ejpam-5629	517	25	.	.	PUNCT
ejpam-5629	518	1	fractal	fractal	ADJ
ejpam-5629	518	2	fract	fract	PROPN
ejpam-5629	518	3	.	.	PUNCT
ejpam-5629	518	4	,	,	PUNCT
ejpam-5629	518	5	8:318	8:318	NUM
ejpam-5629	518	6	,	,	PUNCT
ejpam-5629	518	7	2024	2024	NUM
ejpam-5629	518	8	.	.	PUNCT
ejpam-5629	519	1	[	[	X
ejpam-5629	519	2	33	33	NUM
ejpam-5629	519	3	]	]	X
ejpam-5629	519	4	wmaliet	wmaliet	PROPN
ejpam-5629	519	5	and	and	CCONJ
ejpam-5629	519	6	w	w	NOUN
ejpam-5629	519	7	hereman	hereman	NOUN
ejpam-5629	519	8	.	.	PUNCT
ejpam-5629	520	1	the	the	DET
ejpam-5629	520	2	tanh	tanh	PROPN
ejpam-5629	520	3	method	method	NOUN
ejpam-5629	520	4	:	:	PUNCT
ejpam-5629	520	5	i.	i.	PROPN
ejpam-5629	520	6	exact	exact	PROPN
ejpam-5629	520	7	solutions	solution	NOUN
ejpam-5629	520	8	of	of	ADP
ejpam-5629	520	9	nonlinear	nonlinear	ADJ
ejpam-5629	520	10	evolution	evolution	NOUN
ejpam-5629	520	11	and	and	CCONJ
ejpam-5629	520	12	wave	wave	NOUN
ejpam-5629	520	13	equations	equation	NOUN
ejpam-5629	520	14	.	.	PUNCT
ejpam-5629	521	1	phys	phy	NOUN
ejpam-5629	521	2	.	.	PUNCT
ejpam-5629	522	1	scripta	scripta	PROPN
ejpam-5629	522	2	.	.	PROPN
ejpam-5629	522	3	,	,	PUNCT
ejpam-5629	522	4	54:563–568	54:563–568	NUM
ejpam-5629	522	5	,	,	PUNCT
ejpam-5629	522	6	1996	1996	NUM
ejpam-5629	522	7	.	.	PUNCT
ejpam-5629	523	1	[	[	X
ejpam-5629	523	2	34	34	NUM
ejpam-5629	523	3	]	]	X
ejpam-5629	523	4	m	m	VERB
ejpam-5629	523	5	manigandan	manigandan	ADJ
ejpam-5629	523	6	,	,	PUNCT
ejpam-5629	523	7	k	k	PROPN
ejpam-5629	523	8	manikandan	manikandan	PROPN
ejpam-5629	523	9	,	,	PUNCT
ejpam-5629	523	10	h	h	PROPN
ejpam-5629	523	11	a	a	DET
ejpam-5629	523	12	hammad	hammad	PROPN
ejpam-5629	523	13	,	,	PUNCT
ejpam-5629	523	14	and	and	CCONJ
ejpam-5629	523	15	m	m	PROPN
ejpam-5629	523	16	de	de	X
ejpam-5629	523	17	la	la	X
ejpam-5629	523	18	sen	sen	PROPN
ejpam-5629	523	19	.	.	PROPN
ejpam-5629	523	20	applying	apply	VERB
ejpam-5629	523	21	fixed	fix	VERB
ejpam-5629	523	22	point	point	NOUN
ejpam-5629	523	23	techniques	technique	NOUN
ejpam-5629	523	24	to	to	PART
ejpam-5629	523	25	solve	solve	VERB
ejpam-5629	523	26	fractional	fractional	ADJ
ejpam-5629	523	27	differential	differential	ADJ
ejpam-5629	523	28	inclusions	inclusion	NOUN
ejpam-5629	523	29	under	under	ADP
ejpam-5629	523	30	new	new	ADJ
ejpam-5629	523	31	boundary	boundary	ADJ
ejpam-5629	523	32	conditions	condition	NOUN
ejpam-5629	523	33	.	.	PUNCT
ejpam-5629	524	1	aims	aim	VERB
ejpam-5629	524	2	math	math	NOUN
ejpam-5629	524	3	.	.	PUNCT
ejpam-5629	524	4	,	,	PUNCT
ejpam-5629	524	5	9(6):15505–15542	9(6):15505–15542	NUM
ejpam-5629	524	6	,	,	PUNCT
ejpam-5629	524	7	2024	2024	NUM
ejpam-5629	524	8	.	.	PUNCT
ejpam-5629	525	1	[	[	X
ejpam-5629	525	2	35	35	NUM
ejpam-5629	525	3	]	]	SYM
ejpam-5629	525	4	m	m	VERB
ejpam-5629	525	5	marin	marin	NOUN
ejpam-5629	525	6	,	,	PUNCT
ejpam-5629	525	7	a	a	DET
ejpam-5629	525	8	hobiny	hobiny	NOUN
ejpam-5629	525	9	,	,	PUNCT
ejpam-5629	525	10	and	and	CCONJ
ejpam-5629	525	11	i	i	PROPN
ejpam-5629	525	12	abbas	abbas	PROPN
ejpam-5629	525	13	.	.	PUNCT
ejpam-5629	526	1	finite	finite	PROPN
ejpam-5629	526	2	element	element	NOUN
ejpam-5629	526	3	analysis	analysis	NOUN
ejpam-5629	526	4	of	of	ADP
ejpam-5629	526	5	nonlinear	nonlinear	ADJ
ejpam-5629	526	6	bioheat	bioheat	ADJ
ejpam-5629	526	7	model	model	NOUN
ejpam-5629	526	8	in	in	ADP
ejpam-5629	526	9	skintissue	skintissue	NOUN
ejpam-5629	526	10	due	due	ADP
ejpam-5629	526	11	to	to	ADP
ejpam-5629	526	12	external	external	ADJ
ejpam-5629	526	13	thermal	thermal	ADJ
ejpam-5629	526	14	sources	source	NOUN
ejpam-5629	526	15	.	.	PUNCT
ejpam-5629	527	1	mathematics	mathematic	NOUN
ejpam-5629	527	2	.	.	PUNCT
ejpam-5629	527	3	,	,	PUNCT
ejpam-5629	527	4	page	page	NOUN
ejpam-5629	527	5	1459	1459	NUM
ejpam-5629	527	6	,	,	PUNCT
ejpam-5629	527	7	2021	2021	NUM
ejpam-5629	527	8	.	.	PUNCT
ejpam-5629	528	1	[	[	X
ejpam-5629	528	2	36	36	NUM
ejpam-5629	528	3	]	]	X
ejpam-5629	528	4	m	m	AUX
ejpam-5629	528	5	marin	marin	NOUN
ejpam-5629	528	6	,	,	PUNCT
ejpam-5629	528	7	a	a	DET
ejpam-5629	528	8	öchsner	öchsner	NOUN
ejpam-5629	528	9	,	,	PUNCT
ejpam-5629	528	10	and	and	CCONJ
ejpam-5629	528	11	m	m	NOUN
ejpam-5629	528	12	m	m	VERB
ejpam-5629	528	13	bhatti	bhatti	ADJ
ejpam-5629	528	14	.	.	PUNCT
ejpam-5629	529	1	some	some	DET
ejpam-5629	529	2	results	result	NOUN
ejpam-5629	529	3	in	in	ADP
ejpam-5629	529	4	moore	moore	PROPN
ejpam-5629	529	5	-	-	PUNCT
ejpam-5629	529	6	gibson	gibson	PROPN
ejpam-5629	529	7	-	-	PUNCT
ejpam-5629	529	8	thompson	thompson	PROPN
ejpam-5629	529	9	thermoelasticity	thermoelasticity	NOUN
ejpam-5629	529	10	of	of	ADP
ejpam-5629	529	11	dipolar	dipolar	ADJ
ejpam-5629	529	12	bodies	body	NOUN
ejpam-5629	529	13	.	.	PUNCT
ejpam-5629	530	1	zamm	zamm	PROPN
ejpam-5629	530	2	j.	j.	PROPN
ejpam-5629	530	3	appl	appl	PROPN
ejpam-5629	530	4	.	.	PROPN
ejpam-5629	530	5	math	math	PROPN
ejpam-5629	530	6	.	.	PUNCT
ejpam-5629	531	1	mech	mech	PROPN
ejpam-5629	531	2	.	.	PUNCT
ejpam-5629	531	3	,	,	PUNCT
ejpam-5629	531	4	100:202000090	100:202000090	NUM
ejpam-5629	531	5	,	,	PUNCT
ejpam-5629	531	6	2020	2020	NUM
ejpam-5629	531	7	.	.	PUNCT
ejpam-5629	532	1	[	[	X
ejpam-5629	532	2	37	37	NUM
ejpam-5629	532	3	]	]	X
ejpam-5629	532	4	m	m	VERB
ejpam-5629	532	5	a	a	DET
ejpam-5629	532	6	noor	noor	NOUN
ejpam-5629	532	7	,	,	PUNCT
ejpam-5629	532	8	k	k	PROPN
ejpam-5629	532	9	i	i	PRON
ejpam-5629	532	10	noor	noor	PROPN
ejpam-5629	532	11	,	,	PUNCT
ejpam-5629	532	12	s	s	VERB
ejpam-5629	532	13	iftikhar	iftikhar	NOUN
ejpam-5629	532	14	,	,	PUNCT
ejpam-5629	532	15	and	and	CCONJ
ejpam-5629	532	16	m	m	VERB
ejpam-5629	532	17	u	u	PROPN
ejpam-5629	532	18	awan	awan	PROPN
ejpam-5629	532	19	.	.	PUNCT
ejpam-5629	533	1	fractal	fractal	ADJ
ejpam-5629	533	2	integral	integral	ADJ
ejpam-5629	533	3	inequalities	inequality	NOUN
ejpam-5629	533	4	for	for	ADP
ejpam-5629	533	5	harmonic	harmonic	ADJ
ejpam-5629	533	6	convex	convex	NOUN
ejpam-5629	533	7	functions	function	NOUN
ejpam-5629	533	8	..	..	PUNCT
ejpam-5629	534	1	appl	appl	PROPN
ejpam-5629	534	2	.	.	PUNCT
ejpam-5629	535	1	math	math	PROPN
ejpam-5629	535	2	.	.	PUNCT
ejpam-5629	536	1	inf	inf	PROPN
ejpam-5629	536	2	.	.	PUNCT
ejpam-5629	537	1	sci	sci	PROPN
ejpam-5629	537	2	.	.	PROPN
ejpam-5629	537	3	,	,	PUNCT
ejpam-5629	537	4	12(4):831	12(4):831	PROPN
ejpam-5629	537	5	–	–	PUNCT
ejpam-5629	537	6	839	839	NUM
ejpam-5629	537	7	,	,	PUNCT
ejpam-5629	537	8	2018	2018	NUM
ejpam-5629	537	9	.	.	PUNCT
ejpam-5629	538	1	[	[	X
ejpam-5629	538	2	38	38	NUM
ejpam-5629	538	3	]	]	SYM
ejpam-5629	538	4	s	s	PART
ejpam-5629	538	5	k	k	NOUN
ejpam-5629	538	6	panda	panda	NOUN
ejpam-5629	538	7	,	,	PUNCT
ejpam-5629	538	8	t	t	NOUN
ejpam-5629	538	9	abdeljawad	abdeljawad	NOUN
ejpam-5629	538	10	,	,	PUNCT
ejpam-5629	538	11	and	and	CCONJ
ejpam-5629	538	12	f	f	PROPN
ejpam-5629	538	13	jarad	jarad	PROPN
ejpam-5629	538	14	.	.	PUNCT
ejpam-5629	539	1	chaotic	chaotic	ADJ
ejpam-5629	539	2	attractors	attractor	NOUN
ejpam-5629	539	3	and	and	CCONJ
ejpam-5629	539	4	fixed	fix	VERB
ejpam-5629	539	5	point	point	NOUN
ejpam-5629	539	6	methods	method	NOUN
ejpam-5629	539	7	in	in	ADP
ejpam-5629	539	8	piece	piece	NOUN
ejpam-5629	539	9	wise	wise	ADJ
ejpam-5629	539	10	fractional	fractional	ADJ
ejpam-5629	539	11	derivatives	derivative	NOUN
ejpam-5629	539	12	and	and	CCONJ
ejpam-5629	539	13	multi	multi	ADJ
ejpam-5629	539	14	-	-	ADJ
ejpam-5629	539	15	term	term	ADJ
ejpam-5629	539	16	fractional	fractional	ADJ
ejpam-5629	539	17	delay	delay	NOUN
ejpam-5629	539	18	differential	differential	ADJ
ejpam-5629	539	19	equations	equation	NOUN
ejpam-5629	539	20	.	.	PUNCT
ejpam-5629	540	1	results	result	VERB
ejpam-5629	540	2	phy	phy	PROPN
ejpam-5629	540	3	.	.	PROPN
ejpam-5629	540	4	,	,	PUNCT
ejpam-5629	540	5	46:106313	46:106313	NUM
ejpam-5629	540	6	,	,	PUNCT
ejpam-5629	540	7	2023	2023	NUM
ejpam-5629	540	8	.	.	PUNCT
ejpam-5629	541	1	[	[	X
ejpam-5629	541	2	39	39	NUM
ejpam-5629	541	3	]	]	PUNCT
ejpam-5629	541	4	m	m	VERB
ejpam-5629	541	5	rakah	rakah	PROPN
ejpam-5629	541	6	,	,	PUNCT
ejpam-5629	541	7	z	z	NOUN
ejpam-5629	541	8	dahmani	dahmani	NOUN
ejpam-5629	541	9	,	,	PUNCT
ejpam-5629	541	10	and	and	CCONJ
ejpam-5629	541	11	a	a	DET
ejpam-5629	541	12	senouci	senouci	ADJ
ejpam-5629	541	13	.	.	PUNCT
ejpam-5629	542	1	new	new	ADJ
ejpam-5629	542	2	uniqueness	uniqueness	NOUN
ejpam-5629	542	3	results	result	NOUN
ejpam-5629	542	4	for	for	ADP
ejpam-5629	542	5	fractional	fractional	ADJ
ejpam-5629	542	6	differential	differential	ADJ
ejpam-5629	542	7	equations	equation	NOUN
ejpam-5629	542	8	with	with	ADP
ejpam-5629	542	9	a	a	DET
ejpam-5629	542	10	caputo	caputo	PROPN
ejpam-5629	542	11	and	and	CCONJ
ejpam-5629	542	12	khalil	khalil	PROPN
ejpam-5629	542	13	derivatives	derivative	NOUN
ejpam-5629	542	14	.	.	PUNCT
ejpam-5629	543	1	appl	appl	PROPN
ejpam-5629	543	2	.	.	PROPN
ejpam-5629	544	1	math	math	PROPN
ejpam-5629	544	2	.	.	PUNCT
ejpam-5629	545	1	inf	inf	PROPN
ejpam-5629	545	2	.	.	PUNCT
ejpam-5629	546	1	sci	sci	PROPN
ejpam-5629	546	2	.	.	PROPN
ejpam-5629	546	3	,	,	PUNCT
ejpam-5629	546	4	16:943–952	16:943–952	NUM
ejpam-5629	546	5	,	,	PUNCT
ejpam-5629	546	6	2022	2022	NUM
ejpam-5629	546	7	.	.	PUNCT
ejpam-5629	547	1	[	[	X
ejpam-5629	547	2	40	40	NUM
ejpam-5629	547	3	]	]	PUNCT
ejpam-5629	547	4	u	u	PROPN
ejpam-5629	547	5	sadiya	sadiya	PROPN
ejpam-5629	547	6	,	,	PUNCT
ejpam-5629	547	7	m	m	PROPN
ejpam-5629	547	8	inc	inc	PROPN
ejpam-5629	547	9	,	,	PUNCT
ejpam-5629	547	10	m	m	VERB
ejpam-5629	547	11	a	a	DET
ejpam-5629	547	12	aren	aren	NOUN
ejpam-5629	547	13	,	,	PUNCT
ejpam-5629	547	14	and	and	CCONJ
ejpam-5629	547	15	m	m	NOUN
ejpam-5629	547	16	h	h	NOUN
ejpam-5629	547	17	uddin	uddin	ADJ
ejpam-5629	547	18	.	.	PUNCT
ejpam-5629	548	1	consistent	consistent	ADJ
ejpam-5629	548	2	travelling	travel	VERB
ejpam-5629	548	3	waves	wave	NOUN
ejpam-5629	548	4	solutions	solution	NOUN
ejpam-5629	548	5	to	to	ADP
ejpam-5629	548	6	the	the	DET
ejpam-5629	548	7	non	non	ADJ
ejpam-5629	548	8	-	-	ADJ
ejpam-5629	548	9	linear	linear	ADJ
ejpam-5629	548	10	time	time	NOUN
ejpam-5629	548	11	fractional	fractional	PROPN
ejpam-5629	548	12	klein	klein	PROPN
ejpam-5629	548	13	-	-	PUNCT
ejpam-5629	548	14	gordon	gordon	PROPN
ejpam-5629	548	15	and	and	CCONJ
ejpam-5629	548	16	sine	sine	ADJ
ejpam-5629	548	17	-	-	PUNCT
ejpam-5629	548	18	gordon	gordon	PROPN
ejpam-5629	548	19	equations	equation	NOUN
ejpam-5629	548	20	through	through	ADP
ejpam-5629	548	21	extended	extended	ADJ
ejpam-5629	548	22	tanh	tanh	PROPN
ejpam-5629	548	23	function	function	NOUN
ejpam-5629	548	24	approach	approach	NOUN
ejpam-5629	548	25	.	.	PUNCT
ejpam-5629	549	1	j.	j.	PROPN
ejpam-5629	549	2	taibah	taibah	PROPN
ejpam-5629	549	3	univ	univ	PROPN
ejpam-5629	549	4	.	.	PUNCT
ejpam-5629	550	1	sci	sci	PROPN
ejpam-5629	550	2	.	.	PROPN
ejpam-5629	550	3	,	,	PUNCT
ejpam-5629	550	4	16:594–607	16:594–607	PROPN
ejpam-5629	550	5	,	,	PUNCT
ejpam-5629	550	6	2022	2022	NUM
ejpam-5629	550	7	.	.	PUNCT
ejpam-5629	551	1	[	[	X
ejpam-5629	551	2	41	41	NUM
ejpam-5629	551	3	]	]	X
ejpam-5629	551	4	a	a	DET
ejpam-5629	551	5	b	b	X
ejpam-5629	551	6	shaalan	shaalan	NOUN
ejpam-5629	551	7	,	,	PUNCT
ejpam-5629	551	8	n	n	PROPN
ejpam-5629	551	9	f	f	PROPN
ejpam-5629	551	10	habubi	habubi	NOUN
ejpam-5629	551	11	,	,	PUNCT
ejpam-5629	551	12	s	s	NOUN
ejpam-5629	551	13	s	s	NOUN
ejpam-5629	551	14	chiad	chiad	NOUN
ejpam-5629	551	15	,	,	PUNCT
ejpam-5629	551	16	and	and	CCONJ
ejpam-5629	551	17	z	z	X
ejpam-5629	551	18	a	a	DET
ejpam-5629	551	19	toma	toma	PROPN
ejpam-5629	551	20	.	.	PUNCT
ejpam-5629	552	1	new	new	ADJ
ejpam-5629	552	2	design	design	NOUN
ejpam-5629	552	3	of	of	ADP
ejpam-5629	552	4	hairpin	hairpin	NOUN
ejpam-5629	552	5	-	-	PUNCT
ejpam-5629	552	6	koch	koch	NOUN
ejpam-5629	552	7	fractal	fractal	ADJ
ejpam-5629	552	8	filter	filter	NOUN
ejpam-5629	552	9	for	for	ADP
ejpam-5629	552	10	suppression	suppression	NOUN
ejpam-5629	552	11	of	of	ADP
ejpam-5629	552	12	spurious	spurious	ADJ
ejpam-5629	552	13	band	band	NOUN
ejpam-5629	552	14	.	.	PUNCT
ejpam-5629	553	1	int	int	NOUN
ejpam-5629	553	2	.	.	PUNCT
ejpam-5629	554	1	j.	j.	PROPN
ejpam-5629	554	2	thin	thin	PROPN
ejpam-5629	554	3	film	film	PROPN
ejpam-5629	554	4	sci	sci	PROPN
ejpam-5629	554	5	.	.	PUNCT
ejpam-5629	554	6	tech	tech	PROPN
ejpam-5629	554	7	.	.	PUNCT
ejpam-5629	554	8	,	,	PUNCT
ejpam-5629	554	9	2(3):217	2(3):217	NUM
ejpam-5629	554	10	–	–	PUNCT
ejpam-5629	554	11	221	221	NUM
ejpam-5629	554	12	,	,	PUNCT
ejpam-5629	554	13	2013	2013	NUM
ejpam-5629	554	14	.	.	PUNCT
ejpam-5629	555	1	[	[	X
ejpam-5629	555	2	42	42	NUM
ejpam-5629	555	3	]	]	X
ejpam-5629	555	4	a	a	DET
ejpam-5629	555	5	tudorache	tudorache	NOUN
ejpam-5629	555	6	and	and	CCONJ
ejpam-5629	555	7	r	r	PROPN
ejpam-5629	555	8	luca	luca	PROPN
ejpam-5629	555	9	.	.	PUNCT
ejpam-5629	556	1	on	on	ADP
ejpam-5629	556	2	a	a	DET
ejpam-5629	556	3	system	system	NOUN
ejpam-5629	556	4	of	of	ADP
ejpam-5629	556	5	sequential	sequential	ADJ
ejpam-5629	556	6	caputo	caputo	PROPN
ejpam-5629	556	7	fractional	fractional	PROPN
ejpam-5629	556	8	differential	differential	ADJ
ejpam-5629	556	9	equations	equation	NOUN
ejpam-5629	556	10	with	with	ADP
ejpam-5629	556	11	nonlocal	nonlocal	ADJ
ejpam-5629	556	12	boundary	boundary	ADJ
ejpam-5629	556	13	conditions	condition	NOUN
ejpam-5629	556	14	.	.	PUNCT
ejpam-5629	557	1	frac	frac	PROPN
ejpam-5629	557	2	.	.	PUNCT
ejpam-5629	557	3	fract	fract	PROPN
ejpam-5629	557	4	.	.	PUNCT
ejpam-5629	558	1	,	,	PUNCT
ejpam-5629	558	2	7:1–23	7:1–23	NUM
ejpam-5629	558	3	,	,	PUNCT
ejpam-5629	558	4	2023	2023	NUM
ejpam-5629	558	5	.	.	PUNCT
ejpam-5629	559	1	[	[	X
ejpam-5629	559	2	43	43	NUM
ejpam-5629	559	3	]	]	X
ejpam-5629	559	4	q	q	PROPN
ejpam-5629	559	5	wang	wang	PROPN
ejpam-5629	559	6	and	and	CCONJ
ejpam-5629	559	7	l	l	PROPN
ejpam-5629	559	8	yang	yang	PROPN
ejpam-5629	559	9	.	.	PUNCT
ejpam-5629	560	1	positive	positive	ADJ
ejpam-5629	560	2	solution	solution	NOUN
ejpam-5629	560	3	for	for	ADP
ejpam-5629	560	4	a	a	DET
ejpam-5629	560	5	nonlinear	nonlinear	ADJ
ejpam-5629	560	6	system	system	NOUN
ejpam-5629	560	7	of	of	ADP
ejpam-5629	560	8	fourth	fourth	ADJ
ejpam-5629	560	9	-	-	PUNCT
ejpam-5629	560	10	order	order	NOUN
ejpam-5629	560	11	ordinary	ordinary	ADJ
ejpam-5629	560	12	differential	differential	ADJ
ejpam-5629	560	13	equations	equation	NOUN
ejpam-5629	560	14	.	.	PUNCT
ejpam-5629	561	1	electr	electr	PROPN
ejpam-5629	561	2	.	.	PUNCT
ejpam-5629	562	1	j.	j.	PROPN
ejpam-5629	562	2	differ	differ	VERB
ejpam-5629	562	3	.	.	PUNCT
ejpam-5629	563	1	equ	equ	PROPN
ejpam-5629	563	2	.	.	PROPN
ejpam-5629	563	3	,	,	PUNCT
ejpam-5629	563	4	220:1–15	220:1–15	NUM
ejpam-5629	563	5	,	,	PUNCT
ejpam-5629	563	6	2020	2020	NUM
ejpam-5629	563	7	.	.	PUNCT
ejpam-5629	564	1	[	[	X
ejpam-5629	564	2	44	44	NUM
ejpam-5629	564	3	]	]	PUNCT
ejpam-5629	564	4	a	a	DET
ejpam-5629	564	5	m	m	NOUN
ejpam-5629	564	6	wazwaz	wazwaz	NOUN
ejpam-5629	564	7	.	.	PUNCT
ejpam-5629	565	1	the	the	DET
ejpam-5629	565	2	tanh	tanh	PROPN
ejpam-5629	565	3	method	method	NOUN
ejpam-5629	565	4	for	for	ADP
ejpam-5629	565	5	compact	compact	ADJ
ejpam-5629	565	6	and	and	CCONJ
ejpam-5629	565	7	non	non	ADJ
ejpam-5629	565	8	compact	compact	ADJ
ejpam-5629	565	9	solutions	solution	NOUN
ejpam-5629	565	10	for	for	ADP
ejpam-5629	565	11	variants	variant	NOUN
ejpam-5629	565	12	of	of	ADP
ejpam-5629	565	13	the	the	DET
ejpam-5629	565	14	kdv	kdv	NOUN
ejpam-5629	565	15	-	-	PUNCT
ejpam-5629	565	16	burger	burger	NOUN
ejpam-5629	565	17	and	and	CCONJ
ejpam-5629	565	18	thek(n	thek(n	NOUN
ejpam-5629	565	19	,	,	PUNCT
ejpam-5629	565	20	n)−burger	n)−burger	NOUN
ejpam-5629	565	21	equations	equation	NOUN
ejpam-5629	565	22	.	.	PUNCT
ejpam-5629	566	1	phys	phy	NOUN
ejpam-5629	566	2	.	.	PUNCT
ejpam-5629	567	1	nonlinear	nonlinear	ADJ
ejpam-5629	567	2	phen	phen	PROPN
ejpam-5629	567	3	.	.	PUNCT
ejpam-5629	568	1	,	,	PUNCT
ejpam-5629	568	2	213:147	213:147	NUM
ejpam-5629	568	3	–	–	PUNCT
ejpam-5629	568	4	157	157	NUM
ejpam-5629	568	5	,	,	PUNCT
ejpam-5629	568	6	2006	2006	NUM
ejpam-5629	568	7	.	.	PUNCT
ejpam-5629	569	1	[	[	X
ejpam-5629	569	2	45	45	NUM
ejpam-5629	569	3	]	]	X
ejpam-5629	569	4	m	m	VERB
ejpam-5629	569	5	xia	xia	PROPN
ejpam-5629	569	6	,	,	PUNCT
ejpam-5629	569	7	x	x	PROPN
ejpam-5629	569	8	zhang	zhang	PROPN
ejpam-5629	569	9	,	,	PUNCT
ejpam-5629	569	10	d	d	PROPN
ejpam-5629	569	11	kang	kang	PROPN
ejpam-5629	569	12	,	,	PUNCT
ejpam-5629	569	13	and	and	CCONJ
ejpam-5629	569	14	c	c	PROPN
ejpam-5629	569	15	liu	liu	PROPN
ejpam-5629	569	16	.	.	PUNCT
ejpam-5629	570	1	existence	existence	NOUN
ejpam-5629	570	2	and	and	CCONJ
ejpam-5629	570	3	concentration	concentration	NOUN
ejpam-5629	570	4	of	of	ADP
ejpam-5629	570	5	nontrivial	nontrivial	ADJ
ejpam-5629	570	6	solutions	solution	NOUN
ejpam-5629	570	7	for	for	ADP
ejpam-5629	570	8	an	an	DET
ejpam-5629	570	9	elastic	elastic	ADJ
ejpam-5629	570	10	beam	beam	NOUN
ejpam-5629	570	11	equation	equation	NOUN
ejpam-5629	570	12	with	with	ADP
ejpam-5629	570	13	local	local	ADJ
ejpam-5629	570	14	nonlinearity	nonlinearity	NOUN
ejpam-5629	570	15	.	.	PUNCT
ejpam-5629	571	1	aims	aim	VERB
ejpam-5629	571	2	math	math	NOUN
ejpam-5629	571	3	.	.	PUNCT
ejpam-5629	572	1	,	,	PUNCT
ejpam-5629	572	2	7:579	7:579	NUM
ejpam-5629	572	3	–	–	PUNCT
ejpam-5629	572	4	605	605	NUM
ejpam-5629	572	5	,	,	PUNCT
ejpam-5629	572	6	2021	2021	NUM
ejpam-5629	572	7	.	.	PUNCT
ejpam-5629	573	1	[	[	X
ejpam-5629	573	2	46	46	NUM
ejpam-5629	573	3	]	]	PUNCT
ejpam-5629	573	4	x	x	PROPN
ejpam-5629	573	5	j	j	PROPN
ejpam-5629	573	6	yang	yang	PROPN
ejpam-5629	573	7	,	,	PUNCT
ejpam-5629	573	8	m	m	PROPN
ejpam-5629	573	9	abdel	abdel	PROPN
ejpam-5629	573	10	-	-	PUNCT
ejpam-5629	573	11	aty	aty	PROPN
ejpam-5629	573	12	,	,	PUNCT
ejpam-5629	573	13	and	and	CCONJ
ejpam-5629	573	14	c	c	PROPN
ejpam-5629	573	15	cattani	cattani	PROPN
ejpam-5629	573	16	.	.	PUNCT
ejpam-5629	574	1	a	a	DET
ejpam-5629	574	2	new	new	ADJ
ejpam-5629	574	3	general	general	ADJ
ejpam-5629	574	4	fractional	fractional	ADJ
ejpam-5629	574	5	-	-	PUNCT
ejpam-5629	574	6	order	order	NOUN
ejpam-5629	574	7	derivative	derivative	NOUN
ejpam-5629	574	8	with	with	ADP
ejpam-5629	574	9	rabotnov	rabotnov	NOUN
ejpam-5629	574	10	fractional	fractional	ADJ
ejpam-5629	574	11	-	-	PUNCT
ejpam-5629	574	12	exponential	exponential	ADJ
ejpam-5629	574	13	kernel	kernel	NOUN
ejpam-5629	574	14	applied	apply	VERB
ejpam-5629	574	15	to	to	PART
ejpam-5629	574	16	model	model	VERB
ejpam-5629	574	17	the	the	DET
ejpam-5629	574	18	anomalous	anomalous	ADJ
ejpam-5629	574	19	heat	heat	NOUN
ejpam-5629	574	20	transfer	transfer	NOUN
ejpam-5629	574	21	.	.	PUNCT
ejpam-5629	575	1	thermal	thermal	ADJ
ejpam-5629	575	2	sci	sci	PROPN
ejpam-5629	575	3	.	.	PROPN
ejpam-5629	575	4	,	,	PUNCT
ejpam-5629	575	5	23(3):1677–1681	23(3):1677–1681	NUM
ejpam-5629	575	6	,	,	PUNCT
ejpam-5629	575	7	2019	2019	NUM
ejpam-5629	575	8	.	.	PUNCT
ejpam-5629	576	1	[	[	X
ejpam-5629	576	2	47	47	NUM
ejpam-5629	576	3	]	]	X
ejpam-5629	576	4	m	m	VERB
ejpam-5629	576	5	younis	younis	PROPN
ejpam-5629	576	6	.	.	PUNCT
ejpam-5629	577	1	soliton	soliton	NOUN
ejpam-5629	577	2	solutions	solution	NOUN
ejpam-5629	577	3	of	of	ADP
ejpam-5629	577	4	fractional	fractional	ADJ
ejpam-5629	577	5	order	order	NOUN
ejpam-5629	577	6	kdv	kdv	NOUN
ejpam-5629	577	7	-	-	PUNCT
ejpam-5629	577	8	burger	burger	NOUN
ejpam-5629	577	9	’s	’s	PART
ejpam-5629	577	10	equation	equation	NOUN
ejpam-5629	577	11	.	.	PUNCT
ejpam-5629	578	1	j.	j.	PROPN
ejpam-5629	578	2	adv	adv	PROPN
ejpam-5629	578	3	.	.	PUNCT
ejpam-5629	579	1	phys	phy	NOUN
ejpam-5629	579	2	.	.	PUNCT
ejpam-5629	579	3	,	,	PUNCT
ejpam-5629	579	4	3:325–328	3:325–328	NUM
ejpam-5629	579	5	,	,	PUNCT
ejpam-5629	579	6	2014	2014	NUM
ejpam-5629	579	7	.	.	PUNCT