id	sid	tid	token	lemma	pos
ejpam-5871	1	1	european	european	PROPN
ejpam-5871	1	2	journal	journal	PROPN
ejpam-5871	1	3	of	of	ADP
ejpam-5871	1	4	pure	pure	ADJ
ejpam-5871	1	5	and	and	CCONJ
ejpam-5871	1	6	applied	applied	ADJ
ejpam-5871	1	7	mathematics	mathematic	NOUN
ejpam-5871	1	8	2025	2025	NUM
ejpam-5871	1	9	,	,	PUNCT
ejpam-5871	1	10	vol	vol	NOUN
ejpam-5871	1	11	.	.	PROPN
ejpam-5871	1	12	18	18	NUM
ejpam-5871	1	13	,	,	PUNCT
ejpam-5871	1	14	issue	issue	NOUN
ejpam-5871	1	15	2	2	NUM
ejpam-5871	1	16	,	,	PUNCT
ejpam-5871	1	17	article	article	NOUN
ejpam-5871	1	18	number	number	NOUN
ejpam-5871	1	19	5871	5871	NUM
ejpam-5871	1	20	issn	issn	VERB
ejpam-5871	1	21	1307	1307	NUM
ejpam-5871	1	22	-	-	SYM
ejpam-5871	1	23	5543	5543	NUM
ejpam-5871	1	24	–	–	PUNCT
ejpam-5871	1	25	ejpam.com	ejpam.com	X
ejpam-5871	1	26	published	publish	VERB
ejpam-5871	1	27	by	by	ADP
ejpam-5871	1	28	new	new	PROPN
ejpam-5871	1	29	york	york	PROPN
ejpam-5871	1	30	business	business	PROPN
ejpam-5871	1	31	global	global	ADJ
ejpam-5871	1	32	computational	computational	ADJ
ejpam-5871	1	33	illustration	illustration	NOUN
ejpam-5871	1	34	of	of	ADP
ejpam-5871	1	35	fractional	fractional	ADJ
ejpam-5871	1	36	inequalities	inequality	NOUN
ejpam-5871	1	37	via	via	ADP
ejpam-5871	1	38	2d	2d	NUM
ejpam-5871	1	39	graphs	graph	NOUN
ejpam-5871	1	40	with	with	ADP
ejpam-5871	1	41	application	application	NOUN
ejpam-5871	1	42	ahsan	ahsan	PROPN
ejpam-5871	1	43	mehmood1,∗	mehmood1,∗	PROPN
ejpam-5871	1	44	,	,	PUNCT
ejpam-5871	1	45	muhammad	muhammad	PROPN
ejpam-5871	1	46	younis1	younis1	PROPN
ejpam-5871	1	47	,	,	PUNCT
ejpam-5871	1	48	ahmad	ahmad	PROPN
ejpam-5871	1	49	aloqaily2	aloqaily2	PROPN
ejpam-5871	1	50	,	,	PUNCT
ejpam-5871	1	51	dania	dania	PROPN
ejpam-5871	1	52	santina2	santina2	PROPN
ejpam-5871	1	53	,	,	PUNCT
ejpam-5871	1	54	muhammad	muhammad	PROPN
ejpam-5871	1	55	samraiz3	samraiz3	PROPN
ejpam-5871	1	56	,	,	PUNCT
ejpam-5871	1	57	gauhar	gauhar	PROPN
ejpam-5871	1	58	rahman4	rahman4	PROPN
ejpam-5871	1	59	,	,	PUNCT
ejpam-5871	1	60	nabil	nabil	NOUN
ejpam-5871	1	61	mlaiki2	mlaiki2	PROPN
ejpam-5871	1	62	1	1	NUM
ejpam-5871	1	63	school	school	NOUN
ejpam-5871	1	64	of	of	ADP
ejpam-5871	1	65	mathematical	mathematical	ADJ
ejpam-5871	1	66	sciences	sciences	PROPN
ejpam-5871	1	67	and	and	CCONJ
ejpam-5871	1	68	shanghai	shanghai	PROPN
ejpam-5871	1	69	key	key	PROPN
ejpam-5871	1	70	laboratory	laboratory	NOUN
ejpam-5871	1	71	of	of	ADP
ejpam-5871	1	72	pmmp	pmmp	PROPN
ejpam-5871	1	73	,	,	PUNCT
ejpam-5871	1	74	east	east	PROPN
ejpam-5871	1	75	china	china	PROPN
ejpam-5871	1	76	normal	normal	ADJ
ejpam-5871	1	77	university	university	NOUN
ejpam-5871	1	78	,	,	PUNCT
ejpam-5871	1	79	500	500	NUM
ejpam-5871	1	80	dongchuan	dongchuan	PROPN
ejpam-5871	1	81	road	road	NOUN
ejpam-5871	1	82	,	,	PUNCT
ejpam-5871	1	83	shanghai	shanghai	PROPN
ejpam-5871	1	84	200241	200241	NUM
ejpam-5871	1	85	,	,	PUNCT
ejpam-5871	1	86	peoples	people	NOUN
ejpam-5871	1	87	republic	republic	NOUN
ejpam-5871	1	88	of	of	ADP
ejpam-5871	1	89	china	china	PROPN
ejpam-5871	1	90	2	2	PROPN
ejpam-5871	1	91	department	department	NOUN
ejpam-5871	1	92	of	of	ADP
ejpam-5871	1	93	mathematics	mathematic	NOUN
ejpam-5871	1	94	and	and	CCONJ
ejpam-5871	1	95	sciences	science	NOUN
ejpam-5871	1	96	,	,	PUNCT
ejpam-5871	1	97	prince	prince	PROPN
ejpam-5871	1	98	sultan	sultan	PROPN
ejpam-5871	1	99	university	university	PROPN
ejpam-5871	1	100	,	,	PUNCT
ejpam-5871	1	101	riyadh	riyadh	PROPN
ejpam-5871	1	102	11586	11586	NUM
ejpam-5871	1	103	,	,	PUNCT
ejpam-5871	1	104	saudi	saudi	PROPN
ejpam-5871	1	105	arabia	arabia	PROPN
ejpam-5871	1	106	3	3	NUM
ejpam-5871	1	107	department	department	NOUN
ejpam-5871	1	108	of	of	ADP
ejpam-5871	1	109	mathematics	mathematics	PROPN
ejpam-5871	1	110	,	,	PUNCT
ejpam-5871	1	111	university	university	PROPN
ejpam-5871	1	112	of	of	ADP
ejpam-5871	1	113	sargodha	sargodha	PROPN
ejpam-5871	1	114	p.o	p.o	PROPN
ejpam-5871	1	115	.	.	PROPN
ejpam-5871	1	116	box	box	PROPN
ejpam-5871	1	117	40100	40100	PROPN
ejpam-5871	1	118	,	,	PUNCT
ejpam-5871	1	119	sargodha	sargodha	PROPN
ejpam-5871	1	120	,	,	PUNCT
ejpam-5871	1	121	pakistan	pakistan	PROPN
ejpam-5871	1	122	4	4	NUM
ejpam-5871	1	123	department	department	NOUN
ejpam-5871	1	124	of	of	ADP
ejpam-5871	1	125	mathematics	mathematic	NOUN
ejpam-5871	1	126	and	and	CCONJ
ejpam-5871	1	127	statistics	statistic	NOUN
ejpam-5871	1	128	,	,	PUNCT
ejpam-5871	1	129	hazara	hazara	PROPN
ejpam-5871	1	130	university	university	PROPN
ejpam-5871	1	131	,	,	PUNCT
ejpam-5871	1	132	mansehra	mansehra	PROPN
ejpam-5871	1	133	21300	21300	NUM
ejpam-5871	1	134	,	,	PUNCT
ejpam-5871	1	135	pakistan	pakistan	PROPN
ejpam-5871	1	136	abstract	abstract	NOUN
ejpam-5871	1	137	.	.	PUNCT
ejpam-5871	2	1	in	in	ADP
ejpam-5871	2	2	this	this	DET
ejpam-5871	2	3	article	article	NOUN
ejpam-5871	2	4	,	,	PUNCT
ejpam-5871	2	5	we	we	PRON
ejpam-5871	2	6	use	use	VERB
ejpam-5871	2	7	generalized	generalized	ADJ
ejpam-5871	2	8	(	(	PUNCT
ejpam-5871	2	9	k	k	NOUN
ejpam-5871	2	10	,	,	PUNCT
ejpam-5871	2	11	s)-riemann	s)-riemann	NOUN
ejpam-5871	2	12	-	-	PUNCT
ejpam-5871	2	13	liouville	liouville	VERB
ejpam-5871	2	14	fractional	fractional	ADJ
ejpam-5871	2	15	integral	integral	ADJ
ejpam-5871	2	16	operator	operator	NOUN
ejpam-5871	2	17	(	(	PUNCT
ejpam-5871	2	18	grlfio	grlfio	NOUN
ejpam-5871	2	19	)	)	PUNCT
ejpam-5871	2	20	to	to	PART
ejpam-5871	2	21	explore	explore	VERB
ejpam-5871	2	22	the	the	DET
ejpam-5871	2	23	reverse	reverse	ADJ
ejpam-5871	2	24	forms	form	NOUN
ejpam-5871	2	25	of	of	ADP
ejpam-5871	2	26	minkowskis	minkowskis	PROPN
ejpam-5871	2	27	,	,	PUNCT
ejpam-5871	2	28	holder	holder	NOUN
ejpam-5871	2	29	and	and	CCONJ
ejpam-5871	2	30	hermite	hermite	PROPN
ejpam-5871	2	31	-	-	PUNCT
ejpam-5871	2	32	hadamard	hadamard	ADV
ejpam-5871	2	33	-	-	PUNCT
ejpam-5871	2	34	fejer	fejer	ADJ
ejpam-5871	2	35	type	type	NOUN
ejpam-5871	2	36	inequalities	inequality	NOUN
ejpam-5871	2	37	within	within	ADP
ejpam-5871	2	38	an	an	DET
ejpam-5871	2	39	interval	interval	NOUN
ejpam-5871	2	40	-	-	PUNCT
ejpam-5871	2	41	valued	value	VERB
ejpam-5871	2	42	(	(	PUNCT
ejpam-5871	2	43	ı.υ	ı.υ	PROPN
ejpam-5871	2	44	)	)	PUNCT
ejpam-5871	2	45	(	(	PUNCT
ejpam-5871	2	46	⋋s+1	⋋s+1	PROPN
ejpam-5871	2	47	,	,	PUNCT
ejpam-5871	2	48	℧	℧	NOUN
ejpam-5871	2	49	)	)	PUNCT
ejpam-5871	2	50	class	class	NOUN
ejpam-5871	2	51	of	of	ADP
ejpam-5871	2	52	convexity	convexity	NOUN
ejpam-5871	2	53	.	.	PUNCT
ejpam-5871	3	1	we	we	PRON
ejpam-5871	3	2	comprise	comprise	VERB
ejpam-5871	3	3	various	various	ADJ
ejpam-5871	3	4	existing	exist	VERB
ejpam-5871	3	5	definitions	definition	NOUN
ejpam-5871	3	6	and	and	CCONJ
ejpam-5871	3	7	propose	propose	VERB
ejpam-5871	3	8	the	the	DET
ejpam-5871	3	9	novel	novel	ADJ
ejpam-5871	3	10	concept	concept	NOUN
ejpam-5871	3	11	of	of	ADP
ejpam-5871	3	12	an	an	DET
ejpam-5871	3	13	ı.υ	ı.υ	PROPN
ejpam-5871	3	14	(	(	PUNCT
ejpam-5871	3	15	⋋s+1	⋋s+1	PROPN
ejpam-5871	3	16	,	,	PUNCT
ejpam-5871	3	17	℧	℧	NOUN
ejpam-5871	3	18	)	)	PUNCT
ejpam-5871	3	19	convexity	convexity	NOUN
ejpam-5871	3	20	.	.	PUNCT
ejpam-5871	4	1	our	our	PRON
ejpam-5871	4	2	findings	finding	NOUN
ejpam-5871	4	3	show	show	VERB
ejpam-5871	4	4	the	the	DET
ejpam-5871	4	5	remarkable	remarkable	ADJ
ejpam-5871	4	6	adaptability	adaptability	NOUN
ejpam-5871	4	7	by	by	ADP
ejpam-5871	4	8	adjusting	adjust	VERB
ejpam-5871	4	9	parameter	parameter	NOUN
ejpam-5871	4	10	bounds	bound	NOUN
ejpam-5871	4	11	for	for	ADP
ejpam-5871	4	12	(	(	PUNCT
ejpam-5871	4	13	k	k	NOUN
ejpam-5871	4	14	,	,	PUNCT
ejpam-5871	4	15	s)-grlfio	s)-grlfio	NOUN
ejpam-5871	4	16	within	within	ADP
ejpam-5871	4	17	structure	structure	NOUN
ejpam-5871	4	18	of	of	ADP
ejpam-5871	4	19	an	an	DET
ejpam-5871	4	20	ı.υ	ı.υ	PROPN
ejpam-5871	4	21	(	(	PUNCT
ejpam-5871	4	22	⋋s+1	⋋s+1	PROPN
ejpam-5871	4	23	,	,	PUNCT
ejpam-5871	4	24	℧	℧	NOUN
ejpam-5871	4	25	)	)	PUNCT
ejpam-5871	4	26	convexity	convexity	NOUN
ejpam-5871	4	27	presenting	present	VERB
ejpam-5871	4	28	broader	broad	ADJ
ejpam-5871	4	29	generalization	generalization	NOUN
ejpam-5871	4	30	and	and	CCONJ
ejpam-5871	4	31	new	new	ADJ
ejpam-5871	4	32	perspective	perspective	NOUN
ejpam-5871	4	33	advancements	advancement	NOUN
ejpam-5871	4	34	to	to	ADP
ejpam-5871	4	35	hermite	hermite	VERB
ejpam-5871	4	36	-	-	PUNCT
ejpam-5871	4	37	hadamard	hadamard	ADV
ejpam-5871	4	38	-	-	PUNCT
ejpam-5871	4	39	fejer	fejer	ADJ
ejpam-5871	4	40	and	and	CCONJ
ejpam-5871	4	41	pachpatte	pachpatte	NOUN
ejpam-5871	4	42	-	-	PUNCT
ejpam-5871	4	43	type	type	NOUN
ejpam-5871	4	44	inequalities	inequality	NOUN
ejpam-5871	4	45	.	.	PUNCT
ejpam-5871	5	1	in	in	ADP
ejpam-5871	5	2	order	order	NOUN
ejpam-5871	5	3	to	to	PART
ejpam-5871	5	4	facilitate	facilitate	VERB
ejpam-5871	5	5	their	their	PRON
ejpam-5871	5	6	applications	application	NOUN
ejpam-5871	5	7	,	,	PUNCT
ejpam-5871	5	8	we	we	PRON
ejpam-5871	5	9	examine	examine	VERB
ejpam-5871	5	10	the	the	DET
ejpam-5871	5	11	further	further	ADJ
ejpam-5871	5	12	consequences	consequence	NOUN
ejpam-5871	5	13	,	,	PUNCT
ejpam-5871	5	14	constructed	construct	VERB
ejpam-5871	5	15	specific	specific	ADJ
ejpam-5871	5	16	inequalities	inequality	NOUN
ejpam-5871	5	17	and	and	CCONJ
ejpam-5871	5	18	illustrate	illustrate	VERB
ejpam-5871	5	19	them	they	PRON
ejpam-5871	5	20	through	through	ADP
ejpam-5871	5	21	graphical	graphical	ADJ
ejpam-5871	5	22	representations	representation	NOUN
ejpam-5871	5	23	.	.	PUNCT
ejpam-5871	6	1	additionally	additionally	ADV
ejpam-5871	6	2	,	,	PUNCT
ejpam-5871	6	3	we	we	PRON
ejpam-5871	6	4	validate	validate	VERB
ejpam-5871	6	5	the	the	DET
ejpam-5871	6	6	results	result	NOUN
ejpam-5871	6	7	using	use	VERB
ejpam-5871	6	8	tables	table	NOUN
ejpam-5871	6	9	for	for	ADP
ejpam-5871	6	10	various	various	ADJ
ejpam-5871	6	11	fractional	fractional	ADJ
ejpam-5871	6	12	orders	order	NOUN
ejpam-5871	6	13	.	.	PUNCT
ejpam-5871	7	1	this	this	DET
ejpam-5871	7	2	study	study	NOUN
ejpam-5871	7	3	establishes	establish	VERB
ejpam-5871	7	4	the	the	DET
ejpam-5871	7	5	foundation	foundation	NOUN
ejpam-5871	7	6	for	for	ADP
ejpam-5871	7	7	future	future	ADJ
ejpam-5871	7	8	research	research	NOUN
ejpam-5871	7	9	into	into	ADP
ejpam-5871	7	10	the	the	DET
ejpam-5871	7	11	mathematical	mathematical	ADJ
ejpam-5871	7	12	inequalities	inequality	NOUN
ejpam-5871	7	13	by	by	ADP
ejpam-5871	7	14	emphasizing	emphasize	VERB
ejpam-5871	7	15	the	the	DET
ejpam-5871	7	16	importance	importance	NOUN
ejpam-5871	7	17	of	of	ADP
ejpam-5871	7	18	fractional	fractional	ADJ
ejpam-5871	7	19	integral	integral	ADJ
ejpam-5871	7	20	operators	operator	NOUN
ejpam-5871	7	21	and	and	CCONJ
ejpam-5871	7	22	the	the	DET
ejpam-5871	7	23	expanded	expand	VERB
ejpam-5871	7	24	concept	concept	NOUN
ejpam-5871	7	25	of	of	ADP
ejpam-5871	7	26	convexity	convexity	NOUN
ejpam-5871	7	27	.	.	PUNCT
ejpam-5871	8	1	2020	2020	NUM
ejpam-5871	8	2	mathematics	mathematics	PROPN
ejpam-5871	8	3	subject	subject	NOUN
ejpam-5871	8	4	classifications	classification	NOUN
ejpam-5871	8	5	:	:	PUNCT
ejpam-5871	8	6	26a33	26a33	NUM
ejpam-5871	8	7	,	,	PUNCT
ejpam-5871	8	8	26a51	26a51	NUM
ejpam-5871	8	9	,	,	PUNCT
ejpam-5871	8	10	26d15	26d15	NUM
ejpam-5871	8	11	,	,	PUNCT
ejpam-5871	8	12	26d20	26d20	NUM
ejpam-5871	8	13	key	key	ADJ
ejpam-5871	8	14	words	word	NOUN
ejpam-5871	8	15	and	and	CCONJ
ejpam-5871	8	16	phrases	phrase	NOUN
ejpam-5871	8	17	:	:	PUNCT
ejpam-5871	8	18	hermite	hermite	ADJ
ejpam-5871	8	19	-	-	PUNCT
ejpam-5871	8	20	hadamard	hadamard	NOUN
ejpam-5871	8	21	-	-	PUNCT
ejpam-5871	8	22	inequality	inequality	NOUN
ejpam-5871	8	23	,	,	PUNCT
ejpam-5871	8	24	fractional	fractional	ADJ
ejpam-5871	8	25	calculus	calculus	NOUN
ejpam-5871	8	26	,	,	PUNCT
ejpam-5871	8	27	interval	interval	NOUN
ejpam-5871	8	28	-	-	PUNCT
ejpam-5871	8	29	valued	value	VERB
ejpam-5871	8	30	,	,	PUNCT
ejpam-5871	8	31	(	(	PUNCT
ejpam-5871	8	32	k	k	NOUN
ejpam-5871	8	33	,	,	PUNCT
ejpam-5871	8	34	s)-riemann	s)-riemann	NOUN
ejpam-5871	8	35	-	-	PUNCT
ejpam-5871	8	36	liouville	liouville	VERB
ejpam-5871	8	37	fractional	fractional	ADJ
ejpam-5871	8	38	integral	integral	ADJ
ejpam-5871	8	39	operator	operator	NOUN
ejpam-5871	8	40	1	1	NUM
ejpam-5871	8	41	.	.	PUNCT
ejpam-5871	9	1	introduction	introduction	NOUN
ejpam-5871	9	2	abel	abel	PROPN
ejpam-5871	9	3	was	be	AUX
ejpam-5871	9	4	the	the	DET
ejpam-5871	9	5	first	first	ADJ
ejpam-5871	9	6	scientist	scientist	NOUN
ejpam-5871	9	7	in	in	ADP
ejpam-5871	9	8	the	the	DET
ejpam-5871	9	9	history	history	NOUN
ejpam-5871	9	10	of	of	ADP
ejpam-5871	9	11	fractional	fractional	ADJ
ejpam-5871	9	12	calculus	calculus	NOUN
ejpam-5871	9	13	to	to	PART
ejpam-5871	9	14	use	use	VERB
ejpam-5871	9	15	it	it	PRON
ejpam-5871	9	16	to	to	PART
ejpam-5871	9	17	solve	solve	VERB
ejpam-5871	9	18	the	the	DET
ejpam-5871	9	19	tautochrone	tautochrone	NOUN
ejpam-5871	9	20	problem	problem	NOUN
ejpam-5871	9	21	[	[	X
ejpam-5871	9	22	1	1	NUM
ejpam-5871	9	23	]	]	PUNCT
ejpam-5871	9	24	.	.	PUNCT
ejpam-5871	10	1	to	to	PART
ejpam-5871	10	2	further	far	ADV
ejpam-5871	10	3	improve	improve	VERB
ejpam-5871	10	4	the	the	DET
ejpam-5871	10	5	field	field	NOUN
ejpam-5871	10	6	,	,	PUNCT
ejpam-5871	10	7	researchers	researcher	NOUN
ejpam-5871	10	8	have	have	AUX
ejpam-5871	10	9	published	publish	VERB
ejpam-5871	10	10	their	their	PRON
ejpam-5871	10	11	∗corresponding	∗corresponding	NOUN
ejpam-5871	10	12	author	author	NOUN
ejpam-5871	10	13	.	.	PUNCT
ejpam-5871	11	1	doi	doi	NOUN
ejpam-5871	11	2	:	:	PUNCT
ejpam-5871	11	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5871	https://doi.org/10.29020/nybg.ejpam.v18i2.5871	PROPN
ejpam-5871	11	4	email	email	NOUN
ejpam-5871	11	5	addresses	address	VERB
ejpam-5871	11	6	:	:	PUNCT
ejpam-5871	11	7	mehmoodahsan154@gmail.com	mehmoodahsan154@gmail.com	X
ejpam-5871	11	8	(	(	PUNCT
ejpam-5871	11	9	a.	a.	PROPN
ejpam-5871	11	10	mehmood	mehmood	PROPN
ejpam-5871	11	11	)	)	PUNCT
ejpam-5871	11	12	,	,	PUNCT
ejpam-5871	11	13	younismuhammad303@gmail.com	younismuhammad303@gmail.com	X
ejpam-5871	11	14	(	(	PUNCT
ejpam-5871	11	15	m.	m.	NOUN
ejpam-5871	11	16	younis	younis	PROPN
ejpam-5871	11	17	)	)	PUNCT
ejpam-5871	11	18	,	,	PUNCT
ejpam-5871	11	19	maloqaily@psu.edu.sa	maloqaily@psu.edu.sa	PROPN
ejpam-5871	11	20	(	(	PUNCT
ejpam-5871	11	21	a.	a.	NOUN
ejpam-5871	11	22	aloqaily	aloqaily	ADV
ejpam-5871	11	23	)	)	PUNCT
ejpam-5871	11	24	,	,	PUNCT
ejpam-5871	12	1	dsantina@psu.edu.sa	dsantina@psu.edu.sa	PROPN
ejpam-5871	12	2	(	(	PUNCT
ejpam-5871	12	3	d.	d.	PROPN
ejpam-5871	12	4	santina	santina	PROPN
ejpam-5871	12	5	)	)	PUNCT
ejpam-5871	12	6	,	,	PUNCT
ejpam-5871	12	7	muhammad.samraiz@uos.edu.pk	muhammad.samraiz@uos.edu.pk	PROPN
ejpam-5871	12	8	(	(	PUNCT
ejpam-5871	12	9	m.	m.	NOUN
ejpam-5871	12	10	samraiz	samraiz	PROPN
ejpam-5871	12	11	)	)	PUNCT
ejpam-5871	12	12	,	,	PUNCT
ejpam-5871	12	13	gauhar55uom@gmail.com	gauhar55uom@gmail.com	X
ejpam-5871	12	14	(	(	PUNCT
ejpam-5871	12	15	g.	g.	PROPN
ejpam-5871	12	16	rehman	rehman	PROPN
ejpam-5871	12	17	)	)	PUNCT
ejpam-5871	12	18	,	,	PUNCT
ejpam-5871	12	19	nmlaiki@psu.edu.sa	nmlaiki@psu.edu.sa	NOUN
ejpam-5871	12	20	(	(	PUNCT
ejpam-5871	12	21	n.	n.	PROPN
ejpam-5871	12	22	mlaiki	mlaiki	PROPN
ejpam-5871	12	23	)	)	PUNCT
ejpam-5871	12	24	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-5871	12	25	1	1	NUM
ejpam-5871	12	26	copyright	copyright	NOUN
ejpam-5871	12	27	:	:	PUNCT
ejpam-5871	12	28	©	©	PROPN
ejpam-5871	12	29	2025	2025	NUM
ejpam-5871	12	30	the	the	DET
ejpam-5871	12	31	author(s	author(s	NOUN
ejpam-5871	12	32	)	)	PUNCT
ejpam-5871	12	33	.	.	PUNCT
ejpam-5871	13	1	(	(	PUNCT
ejpam-5871	13	2	cc	cc	NOUN
ejpam-5871	13	3	by	by	ADP
ejpam-5871	13	4	-	-	PUNCT
ejpam-5871	13	5	nc	nc	PROPN
ejpam-5871	13	6	4.0	4.0	NUM
ejpam-5871	13	7	)	)	PUNCT
ejpam-5871	13	8	a.	a.	NOUN
ejpam-5871	13	9	mehmood	mehmood	PROPN
ejpam-5871	13	10	et	et	PROPN
ejpam-5871	13	11	al	al	PROPN
ejpam-5871	13	12	.	.	PUNCT
ejpam-5871	13	13	/	/	SYM
ejpam-5871	13	14	eur	eur	PROPN
ejpam-5871	13	15	.	.	PUNCT
ejpam-5871	14	1	j.	j.	PROPN
ejpam-5871	14	2	pure	pure	PROPN
ejpam-5871	14	3	appl	appl	PROPN
ejpam-5871	14	4	.	.	PROPN
ejpam-5871	14	5	math	math	PROPN
ejpam-5871	14	6	,	,	PUNCT
ejpam-5871	14	7	18	18	NUM
ejpam-5871	14	8	(	(	PUNCT
ejpam-5871	14	9	2	2	NUM
ejpam-5871	14	10	)	)	PUNCT
ejpam-5871	14	11	(	(	PUNCT
ejpam-5871	14	12	2025	2025	NUM
ejpam-5871	14	13	)	)	PUNCT
ejpam-5871	14	14	,	,	PUNCT
ejpam-5871	14	15	5871	5871	NUM
ejpam-5871	14	16	2	2	NUM
ejpam-5871	14	17	of	of	ADP
ejpam-5871	14	18	26	26	NUM
ejpam-5871	14	19	work	work	NOUN
ejpam-5871	14	20	[	[	X
ejpam-5871	14	21	2	2	NUM
ejpam-5871	14	22	,	,	PUNCT
ejpam-5871	14	23	3	3	NUM
ejpam-5871	14	24	]	]	PUNCT
ejpam-5871	14	25	.	.	PUNCT
ejpam-5871	15	1	these	these	DET
ejpam-5871	15	2	studies	study	NOUN
ejpam-5871	15	3	have	have	AUX
ejpam-5871	15	4	made	make	VERB
ejpam-5871	15	5	a	a	DET
ejpam-5871	15	6	significant	significant	ADJ
ejpam-5871	15	7	impact	impact	NOUN
ejpam-5871	15	8	on	on	ADP
ejpam-5871	15	9	the	the	DET
ejpam-5871	15	10	applications	application	NOUN
ejpam-5871	15	11	and	and	CCONJ
ejpam-5871	15	12	accomplishments	accomplishment	NOUN
ejpam-5871	15	13	of	of	ADP
ejpam-5871	15	14	fractional	fractional	ADJ
ejpam-5871	15	15	calculus	calculus	NOUN
ejpam-5871	15	16	in	in	ADP
ejpam-5871	15	17	mathematical	mathematical	ADJ
ejpam-5871	15	18	modeling	modeling	NOUN
ejpam-5871	15	19	and	and	CCONJ
ejpam-5871	15	20	applied	apply	VERB
ejpam-5871	15	21	analysis	analysis	NOUN
ejpam-5871	15	22	[	[	X
ejpam-5871	15	23	4	4	NUM
ejpam-5871	15	24	,	,	PUNCT
ejpam-5871	15	25	5	5	NUM
ejpam-5871	15	26	]	]	PUNCT
ejpam-5871	15	27	.	.	PUNCT
ejpam-5871	16	1	without	without	ADP
ejpam-5871	16	2	a	a	DET
ejpam-5871	16	3	non	non	ADJ
ejpam-5871	16	4	-	-	ADJ
ejpam-5871	16	5	singular	singular	ADJ
ejpam-5871	16	6	kernel	kernel	NOUN
ejpam-5871	16	7	,	,	PUNCT
ejpam-5871	16	8	caputo	caputo	PROPN
ejpam-5871	16	9	et	et	PROPN
ejpam-5871	16	10	al	al	PROPN
ejpam-5871	16	11	.	.	PROPN
ejpam-5871	16	12	introduced	introduce	VERB
ejpam-5871	16	13	the	the	DET
ejpam-5871	16	14	well	well	ADV
ejpam-5871	16	15	-	-	PUNCT
ejpam-5871	16	16	known	know	VERB
ejpam-5871	16	17	caputo	caputo	PROPN
ejpam-5871	16	18	derivative	derivative	NOUN
ejpam-5871	16	19	in	in	ADP
ejpam-5871	16	20	[	[	X
ejpam-5871	16	21	6	6	NUM
ejpam-5871	16	22	]	]	PUNCT
ejpam-5871	16	23	.	.	PUNCT
ejpam-5871	17	1	still	still	ADV
ejpam-5871	17	2	,	,	PUNCT
ejpam-5871	17	3	there	there	PRON
ejpam-5871	17	4	are	be	VERB
ejpam-5871	17	5	a	a	DET
ejpam-5871	17	6	number	number	NOUN
ejpam-5871	17	7	of	of	ADP
ejpam-5871	17	8	important	important	ADJ
ejpam-5871	17	9	research	research	NOUN
ejpam-5871	17	10	gaps	gap	NOUN
ejpam-5871	17	11	in	in	ADP
ejpam-5871	17	12	the	the	DET
ejpam-5871	17	13	idea	idea	NOUN
ejpam-5871	17	14	.	.	PUNCT
ejpam-5871	18	1	several	several	ADJ
ejpam-5871	18	2	academics	academic	NOUN
ejpam-5871	18	3	have	have	AUX
ejpam-5871	18	4	created	create	VERB
ejpam-5871	18	5	their	their	PRON
ejpam-5871	18	6	own	own	ADJ
ejpam-5871	18	7	fractional	fractional	ADJ
ejpam-5871	18	8	operators	operator	NOUN
ejpam-5871	18	9	with	with	ADP
ejpam-5871	18	10	non	non	ADJ
ejpam-5871	18	11	-	-	ADJ
ejpam-5871	18	12	singular	singular	ADJ
ejpam-5871	18	13	kernels	kernel	NOUN
ejpam-5871	18	14	to	to	PART
ejpam-5871	18	15	fill	fill	VERB
ejpam-5871	18	16	in	in	ADP
ejpam-5871	18	17	these	these	DET
ejpam-5871	18	18	gaps	gap	NOUN
ejpam-5871	19	1	[	[	X
ejpam-5871	19	2	7–10	7–10	X
ejpam-5871	19	3	]	]	PUNCT
ejpam-5871	19	4	.	.	PUNCT
ejpam-5871	20	1	non	non	ADJ
ejpam-5871	20	2	-	-	ADJ
ejpam-5871	20	3	linear	linear	ADJ
ejpam-5871	20	4	and	and	CCONJ
ejpam-5871	20	5	non	non	ADJ
ejpam-5871	20	6	-	-	ADJ
ejpam-5871	20	7	singular	singular	ADJ
ejpam-5871	20	8	extensions	extension	NOUN
ejpam-5871	20	9	of	of	ADP
ejpam-5871	20	10	fractional	fractional	ADJ
ejpam-5871	20	11	operators	operator	NOUN
ejpam-5871	20	12	and	and	CCONJ
ejpam-5871	20	13	their	their	PRON
ejpam-5871	20	14	symmetric	symmetric	ADJ
ejpam-5871	20	15	features	feature	NOUN
ejpam-5871	20	16	were	be	AUX
ejpam-5871	20	17	established	establish	VERB
ejpam-5871	20	18	by	by	ADP
ejpam-5871	20	19	wu	wu	PROPN
ejpam-5871	20	20	et	et	PROPN
ejpam-5871	20	21	al	al	PROPN
ejpam-5871	20	22	.	.	PUNCT
ejpam-5871	21	1	in	in	ADP
ejpam-5871	21	2	[	[	X
ejpam-5871	21	3	11	11	NUM
ejpam-5871	21	4	]	]	PUNCT
ejpam-5871	21	5	.	.	PUNCT
ejpam-5871	22	1	a	a	DET
ejpam-5871	22	2	non	non	ADJ
ejpam-5871	22	3	-	-	ADJ
ejpam-5871	22	4	linear	linear	ADJ
ejpam-5871	22	5	and	and	CCONJ
ejpam-5871	22	6	non	non	ADJ
ejpam-5871	22	7	-	-	ADJ
ejpam-5871	22	8	singular	singular	ADJ
ejpam-5871	22	9	fractional	fractional	ADJ
ejpam-5871	22	10	derivative	derivative	NOUN
ejpam-5871	22	11	was	be	AUX
ejpam-5871	22	12	also	also	ADV
ejpam-5871	22	13	introduced	introduce	VERB
ejpam-5871	22	14	by	by	ADP
ejpam-5871	22	15	samraiz	samraiz	PROPN
ejpam-5871	22	16	et	et	PROPN
ejpam-5871	22	17	al	al	PROPN
ejpam-5871	22	18	.	.	PUNCT
ejpam-5871	23	1	in	in	ADP
ejpam-5871	23	2	[	[	X
ejpam-5871	23	3	12	12	NUM
ejpam-5871	23	4	]	]	PUNCT
ejpam-5871	23	5	,	,	PUNCT
ejpam-5871	23	6	who	who	PRON
ejpam-5871	23	7	also	also	ADV
ejpam-5871	23	8	examined	examine	VERB
ejpam-5871	23	9	its	its	PRON
ejpam-5871	23	10	uses	use	NOUN
ejpam-5871	23	11	in	in	ADP
ejpam-5871	23	12	applied	applied	ADJ
ejpam-5871	23	13	analysis	analysis	NOUN
ejpam-5871	23	14	.	.	PUNCT
ejpam-5871	24	1	in	in	ADP
ejpam-5871	24	2	[	[	X
ejpam-5871	24	3	13	13	NUM
ejpam-5871	24	4	,	,	PUNCT
ejpam-5871	24	5	14	14	NUM
ejpam-5871	24	6	]	]	PUNCT
ejpam-5871	24	7	,	,	PUNCT
ejpam-5871	24	8	additional	additional	ADJ
ejpam-5871	24	9	advancements	advancement	NOUN
ejpam-5871	24	10	in	in	ADP
ejpam-5871	24	11	fractional	fractional	ADJ
ejpam-5871	24	12	operators	operator	NOUN
ejpam-5871	24	13	using	use	VERB
ejpam-5871	24	14	different	different	ADJ
ejpam-5871	24	15	kinds	kind	NOUN
ejpam-5871	24	16	of	of	ADP
ejpam-5871	24	17	kernel	kernel	NOUN
ejpam-5871	24	18	functions	function	NOUN
ejpam-5871	24	19	were	be	AUX
ejpam-5871	24	20	introduced	introduce	VERB
ejpam-5871	24	21	.	.	PUNCT
ejpam-5871	25	1	the	the	DET
ejpam-5871	25	2	reader	reader	NOUN
ejpam-5871	25	3	is	be	AUX
ejpam-5871	25	4	referred	refer	VERB
ejpam-5871	25	5	to	to	ADP
ejpam-5871	25	6	[	[	X
ejpam-5871	25	7	15	15	NUM
ejpam-5871	25	8	]	]	PUNCT
ejpam-5871	25	9	for	for	ADP
ejpam-5871	25	10	further	further	ADJ
ejpam-5871	25	11	information	information	NOUN
ejpam-5871	25	12	and	and	CCONJ
ejpam-5871	25	13	applications	application	NOUN
ejpam-5871	25	14	concerning	concern	VERB
ejpam-5871	25	15	fractional	fractional	ADJ
ejpam-5871	25	16	operators	operator	NOUN
ejpam-5871	25	17	.	.	PUNCT
ejpam-5871	26	1	convex	convex	NOUN
ejpam-5871	26	2	analysis	analysis	NOUN
ejpam-5871	26	3	is	be	AUX
ejpam-5871	26	4	based	base	VERB
ejpam-5871	26	5	on	on	ADP
ejpam-5871	26	6	the	the	DET
ejpam-5871	26	7	idea	idea	NOUN
ejpam-5871	26	8	of	of	ADP
ejpam-5871	26	9	convex	convex	NOUN
ejpam-5871	26	10	functions	function	NOUN
ejpam-5871	26	11	(	(	PUNCT
ejpam-5871	26	12	cf	cf	NOUN
ejpam-5871	26	13	)	)	PUNCT
ejpam-5871	26	14	and	and	CCONJ
ejpam-5871	26	15	sets	set	NOUN
ejpam-5871	26	16	with	with	ADP
ejpam-5871	26	17	convex	convex	NOUN
ejpam-5871	26	18	epigraphs	epigraph	NOUN
ejpam-5871	26	19	.	.	PUNCT
ejpam-5871	27	1	convexity	convexity	NOUN
ejpam-5871	27	2	is	be	AUX
ejpam-5871	27	3	important	important	ADJ
ejpam-5871	27	4	in	in	ADP
ejpam-5871	27	5	many	many	ADJ
ejpam-5871	27	6	areas	area	NOUN
ejpam-5871	27	7	of	of	ADP
ejpam-5871	27	8	mathematics	mathematic	NOUN
ejpam-5871	27	9	such	such	ADJ
ejpam-5871	27	10	as	as	ADP
ejpam-5871	27	11	optimization	optimization	NOUN
ejpam-5871	27	12	,	,	PUNCT
ejpam-5871	27	13	fixed	fix	VERB
ejpam-5871	27	14	point	point	NOUN
ejpam-5871	27	15	theory	theory	NOUN
ejpam-5871	27	16	,	,	PUNCT
ejpam-5871	27	17	topological	topological	ADJ
ejpam-5871	27	18	spaces	space	NOUN
ejpam-5871	27	19	and	and	CCONJ
ejpam-5871	27	20	advanced	advanced	ADJ
ejpam-5871	27	21	analysis	analysis	NOUN
ejpam-5871	27	22	.	.	PUNCT
ejpam-5871	28	1	a	a	DET
ejpam-5871	28	2	positive	positive	ADJ
ejpam-5871	28	3	second	second	ADJ
ejpam-5871	28	4	-	-	PUNCT
ejpam-5871	28	5	order	order	NOUN
ejpam-5871	28	6	derivative	derivative	NOUN
ejpam-5871	28	7	indicates	indicate	VERB
ejpam-5871	28	8	concavity	concavity	NOUN
ejpam-5871	28	9	,	,	PUNCT
ejpam-5871	28	10	and	and	CCONJ
ejpam-5871	28	11	derivatives	derivative	NOUN
ejpam-5871	28	12	can	can	AUX
ejpam-5871	28	13	be	be	AUX
ejpam-5871	28	14	used	use	VERB
ejpam-5871	28	15	to	to	PART
ejpam-5871	28	16	assess	assess	VERB
ejpam-5871	28	17	the	the	DET
ejpam-5871	28	18	convexity	convexity	NOUN
ejpam-5871	28	19	of	of	ADP
ejpam-5871	28	20	functions	function	NOUN
ejpam-5871	28	21	.	.	PUNCT
ejpam-5871	29	1	known	know	VERB
ejpam-5871	29	2	for	for	ADP
ejpam-5871	29	3	its	its	PRON
ejpam-5871	29	4	real	real	ADJ
ejpam-5871	29	5	-	-	PUNCT
ejpam-5871	29	6	world	world	NOUN
ejpam-5871	29	7	applications	application	NOUN
ejpam-5871	29	8	,	,	PUNCT
ejpam-5871	29	9	the	the	DET
ejpam-5871	29	10	theory	theory	NOUN
ejpam-5871	29	11	of	of	ADP
ejpam-5871	29	12	inequalities	inequality	NOUN
ejpam-5871	29	13	encompasses	encompass	VERB
ejpam-5871	29	14	several	several	ADJ
ejpam-5871	29	15	branches	branch	NOUN
ejpam-5871	29	16	of	of	ADP
ejpam-5871	29	17	mathematical	mathematical	ADJ
ejpam-5871	29	18	analysis	analysis	NOUN
ejpam-5871	29	19	.	.	PUNCT
ejpam-5871	30	1	error	error	NOUN
ejpam-5871	30	2	limitations	limitation	NOUN
ejpam-5871	30	3	for	for	ADP
ejpam-5871	30	4	numerical	numerical	ADJ
ejpam-5871	30	5	quadrature	quadrature	NOUN
ejpam-5871	30	6	methods	method	NOUN
ejpam-5871	30	7	,	,	PUNCT
ejpam-5871	30	8	including	include	VERB
ejpam-5871	30	9	the	the	DET
ejpam-5871	30	10	trapezoidal	trapezoidal	ADJ
ejpam-5871	30	11	rule	rule	NOUN
ejpam-5871	30	12	,	,	PUNCT
ejpam-5871	30	13	midpoint	midpoint	NOUN
ejpam-5871	30	14	rule	rule	NOUN
ejpam-5871	30	15	,	,	PUNCT
ejpam-5871	30	16	ostrowski	ostrowski	NOUN
ejpam-5871	30	17	’s	’s	PART
ejpam-5871	30	18	rule	rule	NOUN
ejpam-5871	30	19	,	,	PUNCT
ejpam-5871	30	20	and	and	CCONJ
ejpam-5871	30	21	simpson	simpson	PROPN
ejpam-5871	30	22	’s	’s	PART
ejpam-5871	30	23	rules	rule	NOUN
ejpam-5871	30	24	,	,	PUNCT
ejpam-5871	30	25	are	be	AUX
ejpam-5871	30	26	notably	notably	ADV
ejpam-5871	30	27	refined	refine	VERB
ejpam-5871	30	28	by	by	ADP
ejpam-5871	30	29	integral	integral	ADJ
ejpam-5871	30	30	inequalities	inequality	NOUN
ejpam-5871	30	31	,	,	PUNCT
ejpam-5871	30	32	especially	especially	ADV
ejpam-5871	30	33	when	when	SCONJ
ejpam-5871	30	34	cf	cf	NOUN
ejpam-5871	30	35	and	and	CCONJ
ejpam-5871	30	36	their	their	PRON
ejpam-5871	30	37	generalizations	generalization	NOUN
ejpam-5871	30	38	are	be	AUX
ejpam-5871	30	39	applied	apply	VERB
ejpam-5871	30	40	.	.	PUNCT
ejpam-5871	31	1	additionally	additionally	ADV
ejpam-5871	31	2	,	,	PUNCT
ejpam-5871	31	3	these	these	DET
ejpam-5871	31	4	bounds	bound	NOUN
ejpam-5871	31	5	show	show	VERB
ejpam-5871	31	6	links	link	NOUN
ejpam-5871	31	7	between	between	ADP
ejpam-5871	31	8	special	special	ADJ
ejpam-5871	31	9	functions	function	NOUN
ejpam-5871	31	10	,	,	PUNCT
ejpam-5871	31	11	probability	probability	NOUN
ejpam-5871	31	12	theory	theory	NOUN
ejpam-5871	31	13	,	,	PUNCT
ejpam-5871	31	14	information	information	NOUN
ejpam-5871	31	15	theory	theory	NOUN
ejpam-5871	31	16	,	,	PUNCT
ejpam-5871	31	17	and	and	CCONJ
ejpam-5871	31	18	other	other	ADJ
ejpam-5871	31	19	fields	field	NOUN
ejpam-5871	31	20	.	.	PUNCT
ejpam-5871	32	1	the	the	DET
ejpam-5871	32	2	notion	notion	NOUN
ejpam-5871	32	3	of	of	ADP
ejpam-5871	32	4	convexity	convexity	NOUN
ejpam-5871	32	5	can	can	AUX
ejpam-5871	32	6	be	be	AUX
ejpam-5871	32	7	used	use	VERB
ejpam-5871	32	8	to	to	PART
ejpam-5871	32	9	generate	generate	VERB
ejpam-5871	32	10	a	a	DET
ejpam-5871	32	11	number	number	NOUN
ejpam-5871	32	12	of	of	ADP
ejpam-5871	32	13	basic	basic	ADJ
ejpam-5871	32	14	and	and	CCONJ
ejpam-5871	32	15	hermite	hermite	ADJ
ejpam-5871	32	16	-	-	PUNCT
ejpam-5871	32	17	hadamard	hadamard	ADV
ejpam-5871	32	18	-	-	PUNCT
ejpam-5871	32	19	fejer	fejer	NOUN
ejpam-5871	32	20	inequality	inequality	NOUN
ejpam-5871	32	21	.	.	PUNCT
ejpam-5871	33	1	let	let	VERB
ejpam-5871	33	2	a	a	DET
ejpam-5871	33	3	function	function	NOUN
ejpam-5871	33	4	∅	∅	NOUN
ejpam-5871	33	5	:	:	PUNCT
ejpam-5871	34	1	[	[	X
ejpam-5871	34	2	r1	r1	NOUN
ejpam-5871	34	3	,	,	PUNCT
ejpam-5871	34	4	r2	r2	PROPN
ejpam-5871	34	5	]	]	PUNCT
ejpam-5871	34	6	⊂	⊂	X
ejpam-5871	34	7	r	r	NOUN
ejpam-5871	34	8	→	→	SYM
ejpam-5871	34	9	r	r	NOUN
ejpam-5871	34	10	be	be	AUX
ejpam-5871	34	11	continuous	continuous	ADJ
ejpam-5871	34	12	,	,	PUNCT
ejpam-5871	34	13	so	so	ADV
ejpam-5871	34	14	∅	∅	NOUN
ejpam-5871	34	15	(	(	PUNCT
ejpam-5871	34	16	r1	r1	NOUN
ejpam-5871	34	17	+	+	CCONJ
ejpam-5871	34	18	r2	r2	PROPN
ejpam-5871	34	19	2	2	NUM
ejpam-5871	34	20	)	)	PUNCT
ejpam-5871	34	21	≤	≤	NOUN
ejpam-5871	34	22	1	1	NUM
ejpam-5871	34	23	r2	r2	NOUN
ejpam-5871	34	24	−	−	PROPN
ejpam-5871	34	25	r1	r1	PROPN
ejpam-5871	34	26	∫	∫	PROPN
ejpam-5871	34	27	r2	r2	PROPN
ejpam-5871	34	28	r1	r1	PROPN
ejpam-5871	34	29	∅(x)dx	∅(x)dx	VERB
ejpam-5871	34	30	≤	≤	NUM
ejpam-5871	34	31	∅(r1	∅(r1	NOUN
ejpam-5871	34	32	)	)	PUNCT
ejpam-5871	35	1	+	+	VERB
ejpam-5871	35	2	∅(r2	∅(r2	NOUN
ejpam-5871	35	3	)	)	PUNCT
ejpam-5871	35	4	2	2	NUM
ejpam-5871	35	5	.	.	PUNCT
ejpam-5871	36	1	one	one	PRON
ejpam-5871	36	2	could	could	AUX
ejpam-5871	36	3	consider	consider	VERB
ejpam-5871	36	4	this	this	DET
ejpam-5871	36	5	inequality	inequality	NOUN
ejpam-5871	36	6	to	to	PART
ejpam-5871	36	7	be	be	AUX
ejpam-5871	36	8	an	an	DET
ejpam-5871	36	9	extra	extra	ADJ
ejpam-5871	36	10	standard	standard	NOUN
ejpam-5871	36	11	for	for	ADP
ejpam-5871	36	12	cf	cf	NOUN
ejpam-5871	36	13	.	.	PUNCT
ejpam-5871	37	1	additional	additional	ADJ
ejpam-5871	37	2	information	information	NOUN
ejpam-5871	37	3	can	can	AUX
ejpam-5871	37	4	be	be	AUX
ejpam-5871	37	5	found	find	VERB
ejpam-5871	37	6	in	in	ADP
ejpam-5871	37	7	[	[	X
ejpam-5871	37	8	16	16	NUM
ejpam-5871	37	9	,	,	PUNCT
ejpam-5871	37	10	17	17	NUM
ejpam-5871	37	11	]	]	PUNCT
ejpam-5871	37	12	.	.	PUNCT
ejpam-5871	38	1	wu	wu	PROPN
ejpam-5871	38	2	redpresented	redpresente	VERB
ejpam-5871	38	3	the	the	DET
ejpam-5871	38	4	unified	unified	ADJ
ejpam-5871	38	5	form	form	NOUN
ejpam-5871	38	6	of	of	ADP
ejpam-5871	38	7	convexity	convexity	NOUN
ejpam-5871	38	8	,	,	PUNCT
ejpam-5871	38	9	explained	explain	VERB
ejpam-5871	38	10	as	as	SCONJ
ejpam-5871	38	11	follows	follow	VERB
ejpam-5871	38	12	.	.	PUNCT
ejpam-5871	39	1	definition	definition	NOUN
ejpam-5871	39	2	1	1	NUM
ejpam-5871	39	3	.	.	PUNCT
ejpam-5871	40	1	[	[	X
ejpam-5871	40	2	18	18	NUM
ejpam-5871	40	3	]	]	X
ejpam-5871	40	4	if	if	SCONJ
ejpam-5871	40	5	a	a	DET
ejpam-5871	40	6	function	function	NOUN
ejpam-5871	40	7	⋋	⋋	PUNCT
ejpam-5871	40	8	:	:	PUNCT
ejpam-5871	40	9	®	®	NOUN
ejpam-5871	40	10	→	→	SYM
ejpam-5871	40	11	r	r	NOUN
ejpam-5871	40	12	be	be	AUX
ejpam-5871	40	13	monotonic	monotonic	ADJ
ejpam-5871	40	14	continuous-(mc	continuous-(mc	ADJ
ejpam-5871	40	15	)	)	PUNCT
ejpam-5871	40	16	function	function	NOUN
ejpam-5871	40	17	,	,	PUNCT
ejpam-5871	40	18	then	then	ADV
ejpam-5871	40	19	®	®	NOUN
ejpam-5871	40	20	⊂	⊂	PROPN
ejpam-5871	40	21	r	r	NOUN
ejpam-5871	40	22	is	be	AUX
ejpam-5871	40	23	considered	consider	VERB
ejpam-5871	40	24	to	to	PART
ejpam-5871	40	25	be	be	AUX
ejpam-5871	40	26	⋋-convex	⋋-convex	PROPN
ejpam-5871	40	27	set	set	NOUN
ejpam-5871	40	28	based	base	VERB
ejpam-5871	40	29	on	on	ADP
ejpam-5871	40	30	⋋	⋋	NUM
ejpam-5871	40	31	if	if	SCONJ
ejpam-5871	40	32	:	:	PUNCT
ejpam-5871	40	33	⋋−1	⋋−1	ADJ
ejpam-5871	40	34	(	(	PUNCT
ejpam-5871	40	35	(	(	PUNCT
ejpam-5871	40	36	1−	1−	NUM
ejpam-5871	40	37	θ)⋋	θ)⋋	NUM
ejpam-5871	40	38	(	(	PUNCT
ejpam-5871	40	39	x	x	X
ejpam-5871	40	40	)	)	PUNCT
ejpam-5871	41	1	+	+	NUM
ejpam-5871	41	2	θ	θ	NOUN
ejpam-5871	41	3	⋋	⋋	NUM
ejpam-5871	41	4	(	(	PUNCT
ejpam-5871	41	5	y	y	NOUN
ejpam-5871	41	6	)	)	PUNCT
ejpam-5871	41	7	)	)	PUNCT
ejpam-5871	42	1	∈	∈	PROPN
ejpam-5871	42	2	®	®	NOUN
ejpam-5871	42	3	,	,	PUNCT
ejpam-5871	42	4	for	for	ADP
ejpam-5871	42	5	all	all	DET
ejpam-5871	42	6	x	x	NOUN
ejpam-5871	42	7	,	,	PUNCT
ejpam-5871	42	8	y	y	PROPN
ejpam-5871	42	9	∈	∈	PROPN
ejpam-5871	42	10	®	®	NOUN
ejpam-5871	42	11	and	and	CCONJ
ejpam-5871	42	12	θ	θ	PROPN
ejpam-5871	42	13	∈	∈	PROPN
ejpam-5871	43	1	[	[	X
ejpam-5871	43	2	0	0	NUM
ejpam-5871	43	3	,	,	PUNCT
ejpam-5871	43	4	1	1	NUM
ejpam-5871	43	5	]	]	PUNCT
ejpam-5871	43	6	.	.	PUNCT
ejpam-5871	44	1	we	we	PRON
ejpam-5871	44	2	,	,	PUNCT
ejpam-5871	44	3	now	now	ADV
ejpam-5871	44	4	resume	resume	VERB
ejpam-5871	44	5	the	the	DET
ejpam-5871	44	6	class	class	NOUN
ejpam-5871	44	7	⋋-cf	⋋-cf	PROPN
ejpam-5871	44	8	.	.	PUNCT
ejpam-5871	45	1	definition	definition	NOUN
ejpam-5871	45	2	2	2	NUM
ejpam-5871	45	3	.	.	PUNCT
ejpam-5871	46	1	a	a	DET
ejpam-5871	46	2	function	function	NOUN
ejpam-5871	46	3	∅	∅	NOUN
ejpam-5871	46	4	:	:	PUNCT
ejpam-5871	46	5	®	®	NOUN
ejpam-5871	46	6	→	→	SYM
ejpam-5871	46	7	r	r	NOUN
ejpam-5871	46	8	is	be	AUX
ejpam-5871	46	9	stated	state	VERB
ejpam-5871	46	10	to	to	PART
ejpam-5871	46	11	be	be	AUX
ejpam-5871	46	12	⋋-cf	⋋-cf	ADJ
ejpam-5871	46	13	with	with	ADP
ejpam-5871	46	14	respect	respect	NOUN
ejpam-5871	46	15	to	to	ADP
ejpam-5871	46	16	(	(	PUNCT
ejpam-5871	46	17	w.r.t	w.r.t	PROPN
ejpam-5871	46	18	)	)	PUNCT
ejpam-5871	46	19	strictly	strictly	ADV
ejpam-5871	46	20	mc	mc	PROPN
ejpam-5871	46	21	function	function	VERB
ejpam-5871	46	22	⋋	⋋	PUNCT
ejpam-5871	46	23	if	if	SCONJ
ejpam-5871	46	24	:	:	PUNCT
ejpam-5871	46	25	∅(⋋−1((1−	∅(⋋−1((1−	PROPN
ejpam-5871	46	26	θ)⋋	θ)⋋	PUNCT
ejpam-5871	46	27	(	(	PUNCT
ejpam-5871	46	28	x	x	X
ejpam-5871	46	29	)	)	PUNCT
ejpam-5871	47	1	+	+	NUM
ejpam-5871	47	2	θ	θ	NOUN
ejpam-5871	47	3	⋋	⋋	NUM
ejpam-5871	47	4	(	(	PUNCT
ejpam-5871	47	5	y	y	NOUN
ejpam-5871	47	6	)	)	PUNCT
ejpam-5871	47	7	)	)	PUNCT
ejpam-5871	47	8	)	)	PUNCT
ejpam-5871	48	1	≤	≤	NOUN
ejpam-5871	48	2	(	(	PUNCT
ejpam-5871	48	3	1−	1−	NUM
ejpam-5871	48	4	θ)∅(x	θ)∅(x	NUM
ejpam-5871	48	5	)	)	PUNCT
ejpam-5871	48	6	+	+	NUM
ejpam-5871	48	7	θ∅(y	θ∅(y	PROPN
ejpam-5871	48	8	)	)	PUNCT
ejpam-5871	48	9	,	,	PUNCT
ejpam-5871	48	10	for	for	ADP
ejpam-5871	48	11	all	all	DET
ejpam-5871	48	12	x	x	NOUN
ejpam-5871	48	13	,	,	PUNCT
ejpam-5871	48	14	y	y	PROPN
ejpam-5871	48	15	∈	∈	PROPN
ejpam-5871	48	16	®	®	NOUN
ejpam-5871	48	17	and	and	CCONJ
ejpam-5871	48	18	θ	θ	PROPN
ejpam-5871	48	19	∈	∈	PROPN
ejpam-5871	49	1	[	[	X
ejpam-5871	49	2	0	0	NUM
ejpam-5871	49	3	,	,	PUNCT
ejpam-5871	49	4	1	1	NUM
ejpam-5871	49	5	]	]	PUNCT
ejpam-5871	49	6	.	.	PUNCT
ejpam-5871	50	1	a.	a.	PROPN
ejpam-5871	50	2	mehmood	mehmood	PROPN
ejpam-5871	50	3	et	et	PROPN
ejpam-5871	50	4	al	al	PROPN
ejpam-5871	50	5	.	.	PUNCT
ejpam-5871	50	6	/	/	SYM
ejpam-5871	50	7	eur	eur	PROPN
ejpam-5871	50	8	.	.	PUNCT
ejpam-5871	51	1	j.	j.	PROPN
ejpam-5871	51	2	pure	pure	PROPN
ejpam-5871	51	3	appl	appl	PROPN
ejpam-5871	51	4	.	.	PROPN
ejpam-5871	51	5	math	math	PROPN
ejpam-5871	51	6	,	,	PUNCT
ejpam-5871	51	7	18	18	NUM
ejpam-5871	51	8	(	(	PUNCT
ejpam-5871	51	9	2	2	NUM
ejpam-5871	51	10	)	)	PUNCT
ejpam-5871	51	11	(	(	PUNCT
ejpam-5871	51	12	2025	2025	NUM
ejpam-5871	51	13	)	)	PUNCT
ejpam-5871	51	14	,	,	PUNCT
ejpam-5871	51	15	5871	5871	NUM
ejpam-5871	51	16	3	3	NUM
ejpam-5871	51	17	of	of	ADP
ejpam-5871	51	18	26	26	NUM
ejpam-5871	51	19	in	in	ADP
ejpam-5871	51	20	order	order	NOUN
ejpam-5871	51	21	to	to	PART
ejpam-5871	51	22	investigate	investigate	VERB
ejpam-5871	51	23	the	the	DET
ejpam-5871	51	24	several	several	ADJ
ejpam-5871	51	25	relevant	relevant	ADJ
ejpam-5871	51	26	scientific	scientific	ADJ
ejpam-5871	51	27	domains	domain	NOUN
ejpam-5871	51	28	,	,	PUNCT
ejpam-5871	51	29	numerous	numerous	ADJ
ejpam-5871	51	30	authors	author	NOUN
ejpam-5871	51	31	have	have	AUX
ejpam-5871	51	32	combined	combine	VERB
ejpam-5871	51	33	fractional	fractional	ADJ
ejpam-5871	51	34	calculus	calculus	NOUN
ejpam-5871	51	35	with	with	ADP
ejpam-5871	51	36	ı.υ	ı.υ	PROPN
ejpam-5871	51	37	concepts	concept	NOUN
ejpam-5871	51	38	.	.	PUNCT
ejpam-5871	52	1	working	work	VERB
ejpam-5871	52	2	along	along	ADP
ejpam-5871	52	3	these	these	DET
ejpam-5871	52	4	lines	line	NOUN
ejpam-5871	52	5	,	,	PUNCT
ejpam-5871	52	6	breckner	breckner	NOUN
ejpam-5871	52	7	developed	develop	VERB
ejpam-5871	52	8	the	the	DET
ejpam-5871	52	9	idea	idea	NOUN
ejpam-5871	52	10	of	of	ADP
ejpam-5871	52	11	set	set	NOUN
ejpam-5871	52	12	-	-	PUNCT
ejpam-5871	52	13	valued	value	VERB
ejpam-5871	52	14	cf	cf	NOUN
ejpam-5871	52	15	,	,	PUNCT
ejpam-5871	52	16	as	as	SCONJ
ejpam-5871	52	17	seen	see	VERB
ejpam-5871	52	18	below	below	ADV
ejpam-5871	52	19	.	.	PUNCT
ejpam-5871	53	1	definition	definition	NOUN
ejpam-5871	53	2	3	3	NUM
ejpam-5871	53	3	.	.	PUNCT
ejpam-5871	54	1	[	[	X
ejpam-5871	54	2	19	19	NUM
ejpam-5871	54	3	]	]	PUNCT
ejpam-5871	54	4	a	a	DET
ejpam-5871	54	5	function	function	NOUN
ejpam-5871	54	6	∅	∅	NOUN
ejpam-5871	54	7	:	:	PUNCT
ejpam-5871	55	1	[	[	X
ejpam-5871	55	2	r1	r1	NOUN
ejpam-5871	55	3	,	,	PUNCT
ejpam-5871	55	4	r2	r2	PROPN
ejpam-5871	55	5	]	]	PUNCT
ejpam-5871	55	6	→	→	SYM
ejpam-5871	55	7	r+	r+	NOUN
ejpam-5871	55	8	i	i	PRON
ejpam-5871	55	9	is	be	AUX
ejpam-5871	55	10	stated	state	VERB
ejpam-5871	55	11	to	to	PART
ejpam-5871	55	12	be	be	AUX
ejpam-5871	55	13	ı.υ	ı.υ	ADP
ejpam-5871	55	14	cf	cf	NOUN
ejpam-5871	55	15	,	,	PUNCT
ejpam-5871	55	16	if	if	SCONJ
ejpam-5871	55	17	:	:	PUNCT
ejpam-5871	55	18	∅((1−	∅((1−	PROPN
ejpam-5871	55	19	θ)r1	θ)r1	PROPN
ejpam-5871	55	20	+	+	CCONJ
ejpam-5871	55	21	θr2	θr2	NOUN
ejpam-5871	55	22	)	)	PUNCT
ejpam-5871	55	23	⊇	⊇	NOUN
ejpam-5871	55	24	(	(	PUNCT
ejpam-5871	55	25	1−	1−	NUM
ejpam-5871	55	26	θ)∅(r1	θ)∅(r1	NOUN
ejpam-5871	55	27	)	)	PUNCT
ejpam-5871	55	28	+	+	CCONJ
ejpam-5871	55	29	θ∅(r2	θ∅(r2	NOUN
ejpam-5871	55	30	)	)	PUNCT
ejpam-5871	55	31	,	,	PUNCT
ejpam-5871	55	32	θ	θ	PROPN
ejpam-5871	55	33	∈	∈	PROPN
ejpam-5871	56	1	[	[	X
ejpam-5871	56	2	0	0	NUM
ejpam-5871	56	3	,	,	PUNCT
ejpam-5871	56	4	1	1	NUM
ejpam-5871	56	5	]	]	PUNCT
ejpam-5871	56	6	.	.	PUNCT
ejpam-5871	57	1	the	the	DET
ejpam-5871	57	2	first	first	ADJ
ejpam-5871	57	3	person	person	NOUN
ejpam-5871	57	4	to	to	PART
ejpam-5871	57	5	apply	apply	VERB
ejpam-5871	57	6	inequalities	inequality	NOUN
ejpam-5871	57	7	to	to	PART
ejpam-5871	57	8	set	set	VERB
ejpam-5871	57	9	-	-	PUNCT
ejpam-5871	57	10	valued	value	VERB
ejpam-5871	57	11	functions	function	NOUN
ejpam-5871	57	12	was	be	AUX
ejpam-5871	57	13	sadowska	sadowska	NOUN
ejpam-5871	57	14	[	[	X
ejpam-5871	57	15	20	20	NUM
ejpam-5871	57	16	]	]	PUNCT
ejpam-5871	57	17	.	.	PUNCT
ejpam-5871	58	1	he	he	PRON
ejpam-5871	58	2	investigated	investigate	VERB
ejpam-5871	58	3	the	the	DET
ejpam-5871	58	4	hermite	hermite	PROPN
ejpam-5871	58	5	-	-	PUNCT
ejpam-5871	58	6	hadamard	hadamard	ADV
ejpam-5871	58	7	-	-	PUNCT
ejpam-5871	58	8	fejer	fejer	NOUN
ejpam-5871	58	9	inequality	inequality	NOUN
ejpam-5871	58	10	in	in	ADP
ejpam-5871	58	11	the	the	DET
ejpam-5871	58	12	context	context	NOUN
ejpam-5871	58	13	of	of	ADP
ejpam-5871	58	14	set	set	NOUN
ejpam-5871	58	15	-	-	PUNCT
ejpam-5871	58	16	valued	value	VERB
ejpam-5871	58	17	cf	cf	NOUN
ejpam-5871	58	18	.	.	PUNCT
ejpam-5871	59	1	if	if	SCONJ
ejpam-5871	59	2	function	function	NOUN
ejpam-5871	59	3	∅	∅	NOUN
ejpam-5871	59	4	:	:	PUNCT
ejpam-5871	60	1	[	[	X
ejpam-5871	60	2	r1	r1	NOUN
ejpam-5871	60	3	,	,	PUNCT
ejpam-5871	60	4	r2	r2	PROPN
ejpam-5871	60	5	]	]	PUNCT
ejpam-5871	60	6	→	→	PUNCT
ejpam-5871	60	7	r	r	NOUN
ejpam-5871	60	8	be	be	AUX
ejpam-5871	60	9	an	an	DET
ejpam-5871	60	10	ı.υ	ı.υ	PROPN
ejpam-5871	60	11	cf	cf	NOUN
ejpam-5871	60	12	,	,	PUNCT
ejpam-5871	60	13	so	so	ADV
ejpam-5871	60	14	∅	∅	NOUN
ejpam-5871	60	15	(	(	PUNCT
ejpam-5871	60	16	r1	r1	NOUN
ejpam-5871	60	17	+	+	CCONJ
ejpam-5871	60	18	r2	r2	PROPN
ejpam-5871	60	19	2	2	NUM
ejpam-5871	60	20	)	)	PUNCT
ejpam-5871	60	21	⊇	⊇	NOUN
ejpam-5871	60	22	1	1	NUM
ejpam-5871	60	23	r2	r2	PROPN
ejpam-5871	60	24	−	−	PROPN
ejpam-5871	60	25	r1	r1	PROPN
ejpam-5871	60	26	∫	∫	PROPN
ejpam-5871	60	27	r2	r2	PROPN
ejpam-5871	60	28	r1	r1	PROPN
ejpam-5871	60	29	∅(θ)dθ	∅(θ)dθ	NOUN
ejpam-5871	60	30	⊇	⊇	NOUN
ejpam-5871	60	31	∅(r1	∅(r1	NOUN
ejpam-5871	60	32	)	)	PUNCT
ejpam-5871	61	1	+	+	NOUN
ejpam-5871	61	2	∅(r2	∅(r2	NOUN
ejpam-5871	61	3	)	)	PUNCT
ejpam-5871	61	4	2	2	NUM
ejpam-5871	61	5	.	.	PUNCT
ejpam-5871	62	1	if	if	SCONJ
ejpam-5871	62	2	b([r1	b([r1	NOUN
ejpam-5871	62	3	,	,	PUNCT
ejpam-5871	62	4	r2	r2	PROPN
ejpam-5871	62	5	]	]	PUNCT
ejpam-5871	62	6	)	)	PUNCT
ejpam-5871	62	7	is	be	AUX
ejpam-5871	62	8	a	a	DET
ejpam-5871	62	9	collection	collection	NOUN
ejpam-5871	62	10	of	of	ADP
ejpam-5871	62	11	all	all	DET
ejpam-5871	62	12	divisions	division	NOUN
ejpam-5871	62	13	of	of	ADP
ejpam-5871	62	14	[	[	X
ejpam-5871	62	15	r1	r1	NOUN
ejpam-5871	62	16	,	,	PUNCT
ejpam-5871	62	17	r2	r2	PROPN
ejpam-5871	62	18	]	]	PUNCT
ejpam-5871	62	19	and	and	CCONJ
ejpam-5871	62	20	b(ρ1	b(ρ1	PROPN
ejpam-5871	62	21	,	,	PUNCT
ejpam-5871	62	22	[	[	X
ejpam-5871	62	23	r1	r1	NOUN
ejpam-5871	62	24	,	,	PUNCT
ejpam-5871	62	25	r2	r2	PROPN
ejpam-5871	62	26	]	]	PUNCT
ejpam-5871	62	27	)	)	PUNCT
ejpam-5871	62	28	be	be	VERB
ejpam-5871	62	29	the	the	DET
ejpam-5871	62	30	family	family	NOUN
ejpam-5871	62	31	of	of	ADP
ejpam-5871	62	32	all	all	DET
ejpam-5871	62	33	divisions	division	NOUN
ejpam-5871	62	34	p	p	NOUN
ejpam-5871	62	35	in	in	ADP
ejpam-5871	62	36	a	a	DET
ejpam-5871	62	37	way	way	NOUN
ejpam-5871	62	38	that	that	PRON
ejpam-5871	62	39	meshp	meshp	NOUN
ejpam-5871	62	40	<	<	X
ejpam-5871	62	41	ρ1	ρ1	PROPN
ejpam-5871	62	42	,	,	PUNCT
ejpam-5871	62	43	then	then	ADV
ejpam-5871	62	44	∅	∅	NOUN
ejpam-5871	62	45	:	:	PUNCT
ejpam-5871	63	1	[	[	X
ejpam-5871	63	2	r1	r1	NOUN
ejpam-5871	63	3	,	,	PUNCT
ejpam-5871	63	4	r2	r2	PROPN
ejpam-5871	63	5	]	]	PUNCT
ejpam-5871	63	6	→	→	SYM
ejpam-5871	63	7	r	r	NOUN
ejpam-5871	63	8	is	be	AUX
ejpam-5871	63	9	referred	refer	VERB
ejpam-5871	63	10	to	to	ADP
ejpam-5871	63	11	as	as	SCONJ
ejpam-5871	63	12	ı.υ	ı.υ	PROPN
ejpam-5871	63	13	riemann	riemann	PROPN
ejpam-5871	63	14	integrable	integrable	VERB
ejpam-5871	63	15	on	on	ADP
ejpam-5871	63	16	[	[	X
ejpam-5871	63	17	r1	r1	NOUN
ejpam-5871	63	18	,	,	PUNCT
ejpam-5871	63	19	r2	r2	PROPN
ejpam-5871	63	20	]	]	PUNCT
ejpam-5871	63	21	,	,	PUNCT
ejpam-5871	63	22	if	if	SCONJ
ejpam-5871	63	23	there	there	PRON
ejpam-5871	63	24	exist	exist	VERB
ejpam-5871	63	25	→∈	→∈	NOUN
ejpam-5871	63	26	r	r	NOUN
ejpam-5871	63	27	,	,	PUNCT
ejpam-5871	63	28	and	and	CCONJ
ejpam-5871	63	29	for	for	ADP
ejpam-5871	63	30	each	each	PRON
ejpam-5871	63	31	ϵ	ϵ	X
ejpam-5871	63	32	>	>	X
ejpam-5871	63	33	0	0	PUNCT
ejpam-5871	63	34	there	there	PRON
ejpam-5871	63	35	exist	exist	VERB
ejpam-5871	63	36	ρ	ρ	PROPN
ejpam-5871	63	37	>	>	X
ejpam-5871	63	38	0	0	NUM
ejpam-5871	63	39	such	such	ADJ
ejpam-5871	63	40	that	that	SCONJ
ejpam-5871	63	41	:	:	PUNCT
ejpam-5871	63	42	d(s(∅	d(s(∅	PROPN
ejpam-5871	63	43	,	,	PUNCT
ejpam-5871	63	44	p	p	X
ejpam-5871	63	45	,	,	PUNCT
ejpam-5871	63	46	ρ	ρ	PROPN
ejpam-5871	63	47	)	)	PUNCT
ejpam-5871	63	48	,	,	PUNCT
ejpam-5871	63	49	®	®	NOUN
ejpam-5871	63	50	)	)	PUNCT
ejpam-5871	63	51	<	<	X
ejpam-5871	64	1	ϵ	ϵ	X
ejpam-5871	64	2	,	,	PUNCT
ejpam-5871	64	3	where	where	SCONJ
ejpam-5871	64	4	s(∅	s(∅	NOUN
ejpam-5871	64	5	,	,	PUNCT
ejpam-5871	64	6	p	p	X
ejpam-5871	64	7	,	,	PUNCT
ejpam-5871	64	8	ρ	ρ	NOUN
ejpam-5871	64	9	)	)	PUNCT
ejpam-5871	64	10	specifies	specifie	NOUN
ejpam-5871	64	11	the	the	DET
ejpam-5871	64	12	riemann	riemann	PROPN
ejpam-5871	64	13	sum	sum	NOUN
ejpam-5871	64	14	of	of	ADP
ejpam-5871	64	15	phi	phi	NOUN
ejpam-5871	64	16	for	for	ADP
ejpam-5871	64	17	any	any	DET
ejpam-5871	64	18	p	p	PROPN
ejpam-5871	64	19	∈	∈	PROPN
ejpam-5871	64	20	b(ρ	b(ρ	NOUN
ejpam-5871	64	21	,	,	PUNCT
ejpam-5871	64	22	[	[	X
ejpam-5871	64	23	r1	r1	NOUN
ejpam-5871	64	24	,	,	PUNCT
ejpam-5871	64	25	r2	r2	PROPN
ejpam-5871	64	26	]	]	PUNCT
ejpam-5871	64	27	)	)	PUNCT
ejpam-5871	64	28	.	.	PUNCT
ejpam-5871	65	1	the	the	DET
ejpam-5871	65	2	above	above	ADJ
ejpam-5871	65	3	expression	expression	NOUN
ejpam-5871	65	4	represents	represent	VERB
ejpam-5871	65	5	that	that	SCONJ
ejpam-5871	65	6	®	®	NOUN
ejpam-5871	65	7	is	be	AUX
ejpam-5871	65	8	the	the	DET
ejpam-5871	65	9	(	(	PUNCT
ejpam-5871	65	10	ir)-integral	ir)-integral	ADJ
ejpam-5871	65	11	of	of	ADP
ejpam-5871	65	12	∅	∅	NOUN
ejpam-5871	65	13	such	such	ADJ
ejpam-5871	65	14	that	that	PRON
ejpam-5871	65	15	:	:	PUNCT
ejpam-5871	65	16	®	®	NOUN
ejpam-5871	65	17	=	=	SYM
ejpam-5871	65	18	(	(	PUNCT
ejpam-5871	65	19	ir	ir	PROPN
ejpam-5871	65	20	)	)	PUNCT
ejpam-5871	65	21	∫	∫	PROPN
ejpam-5871	65	22	r2	r2	PROPN
ejpam-5871	65	23	r1	r1	PROPN
ejpam-5871	65	24	∅(θ)dθ	∅(θ)dθ	NOUN
ejpam-5871	65	25	for	for	ADP
ejpam-5871	65	26	the	the	DET
ejpam-5871	65	27	sake	sake	NOUN
ejpam-5871	65	28	of	of	ADP
ejpam-5871	65	29	brevity	brevity	NOUN
ejpam-5871	65	30	,	,	PUNCT
ejpam-5871	65	31	we	we	PRON
ejpam-5871	65	32	specify	specify	VERB
ejpam-5871	65	33	the	the	DET
ejpam-5871	65	34	space	space	NOUN
ejpam-5871	65	35	of	of	ADP
ejpam-5871	65	36	riemann	riemann	PROPN
ejpam-5871	65	37	integrable	integrable	ADJ
ejpam-5871	65	38	functions	function	NOUN
ejpam-5871	65	39	and	and	CCONJ
ejpam-5871	65	40	ı.υ	ı.υ	PROPN
ejpam-5871	65	41	riemann	riemann	PROPN
ejpam-5871	65	42	integration	integration	NOUN
ejpam-5871	65	43	on[r1	on[r1	PROPN
ejpam-5871	65	44	,	,	PUNCT
ejpam-5871	65	45	r2	r2	PROPN
ejpam-5871	65	46	]	]	PUNCT
ejpam-5871	65	47	and	and	CCONJ
ejpam-5871	65	48	by	by	ADP
ejpam-5871	65	49	r[r1,r2	r[r1,r2	NOUN
ejpam-5871	65	50	]	]	PUNCT
ejpam-5871	65	51	and	and	CCONJ
ejpam-5871	65	52	ir[r1,r2	ir[r1,r2	X
ejpam-5871	65	53	]	]	PUNCT
ejpam-5871	65	54	respectively	respectively	ADV
ejpam-5871	65	55	.	.	PUNCT
ejpam-5871	66	1	theorem	theorem	VERB
ejpam-5871	66	2	1	1	NUM
ejpam-5871	66	3	.	.	PUNCT
ejpam-5871	67	1	[	[	X
ejpam-5871	67	2	21	21	NUM
ejpam-5871	67	3	]	]	X
ejpam-5871	67	4	if	if	SCONJ
ejpam-5871	67	5	a	a	DET
ejpam-5871	67	6	function	function	NOUN
ejpam-5871	67	7	∅(θ	∅(θ	NOUN
ejpam-5871	67	8	)	)	PUNCT
ejpam-5871	67	9	:	:	PUNCT
ejpam-5871	68	1	[	[	X
ejpam-5871	68	2	r1	r1	NOUN
ejpam-5871	68	3	,	,	PUNCT
ejpam-5871	68	4	r2	r2	PROPN
ejpam-5871	68	5	]	]	PUNCT
ejpam-5871	68	6	→	→	PUNCT
ejpam-5871	68	7	r	r	NOUN
ejpam-5871	68	8	be	be	AUX
ejpam-5871	68	9	an	an	DET
ejpam-5871	68	10	ı.υ	ı.υ	PROPN
ejpam-5871	68	11	continuous	continuous	ADJ
ejpam-5871	68	12	,	,	PUNCT
ejpam-5871	68	13	then	then	ADV
ejpam-5871	68	14	∅(θ	∅(θ	NOUN
ejpam-5871	68	15	)	)	PUNCT
ejpam-5871	68	16	=	=	PUNCT
ejpam-5871	69	1	[	[	X
ejpam-5871	69	2	∅∗(θ),∅∗(θ)],∅(θ	∅∗(θ),∅∗(θ)],∅(θ	NOUN
ejpam-5871	69	3	)	)	PUNCT
ejpam-5871	69	4	∈	∈	PROPN
ejpam-5871	69	5	ir[r1,r2	ir[r1,r2	NOUN
ejpam-5871	69	6	]	]	X
ejpam-5871	69	7	⇔	⇔	X
ejpam-5871	69	8	∅∗(θ),∅∗(θ	∅∗(θ),∅∗(θ	PROPN
ejpam-5871	69	9	)	)	PUNCT
ejpam-5871	69	10	∈	∈	PROPN
ejpam-5871	69	11	ir[r1,r2	ir[r1,r2	NOUN
ejpam-5871	69	12	]	]	X
ejpam-5871	69	13	,	,	PUNCT
ejpam-5871	69	14	and	and	CCONJ
ejpam-5871	69	15	(	(	PUNCT
ejpam-5871	69	16	ir	ir	NOUN
ejpam-5871	69	17	)	)	PUNCT
ejpam-5871	69	18	∫	∫	PROPN
ejpam-5871	69	19	r2	r2	PROPN
ejpam-5871	69	20	r1	r1	PROPN
ejpam-5871	69	21	∅(θ)dθ	∅(θ)dθ	NOUN
ejpam-5871	69	22	=	=	X
ejpam-5871	69	23	[	[	PUNCT
ejpam-5871	69	24	(	(	PUNCT
ejpam-5871	69	25	r	r	NOUN
ejpam-5871	69	26	)	)	PUNCT
ejpam-5871	69	27	∫	∫	PROPN
ejpam-5871	69	28	r2	r2	PROPN
ejpam-5871	69	29	r1	r1	PROPN
ejpam-5871	69	30	∅∗(θ)dθ	∅∗(θ)dθ	PROPN
ejpam-5871	69	31	,	,	PUNCT
ejpam-5871	69	32	(	(	PUNCT
ejpam-5871	69	33	r	r	NOUN
ejpam-5871	69	34	)	)	PUNCT
ejpam-5871	69	35	∫	∫	PROPN
ejpam-5871	69	36	r2	r2	PROPN
ejpam-5871	69	37	r1	r1	PROPN
ejpam-5871	69	38	∅∗(θ)dθ	∅∗(θ)dθ	PROPN
ejpam-5871	69	39	]	]	PUNCT
ejpam-5871	69	40	.	.	PUNCT
ejpam-5871	70	1	the	the	DET
ejpam-5871	70	2	lebesgue	lebesgue	NOUN
ejpam-5871	70	3	integrable	integrable	ADJ
ejpam-5871	70	4	function	function	NOUN
ejpam-5871	70	5	(	(	PUNCT
ejpam-5871	70	6	li∅	li∅	X
ejpam-5871	70	7	)	)	PUNCT
ejpam-5871	70	8	space	space	NOUN
ejpam-5871	70	9	is	be	AUX
ejpam-5871	70	10	defined	define	VERB
ejpam-5871	70	11	by	by	ADP
ejpam-5871	70	12	l[r1	l[r1	ADJ
ejpam-5871	70	13	,	,	PUNCT
ejpam-5871	70	14	r2	r2	PROPN
ejpam-5871	70	15	]	]	PUNCT
ejpam-5871	70	16	.	.	PUNCT
ejpam-5871	71	1	now	now	ADV
ejpam-5871	71	2	,	,	PUNCT
ejpam-5871	71	3	we	we	PRON
ejpam-5871	71	4	retrieve	retrieve	VERB
ejpam-5871	71	5	the	the	DET
ejpam-5871	71	6	riemann	riemann	PROPN
ejpam-5871	71	7	-	-	PUNCT
ejpam-5871	71	8	liouville	liouville	VERB
ejpam-5871	71	9	fractional	fractional	ADJ
ejpam-5871	71	10	operator	operator	NOUN
ejpam-5871	71	11	,	,	PUNCT
ejpam-5871	71	12	which	which	PRON
ejpam-5871	71	13	are	be	AUX
ejpam-5871	71	14	provided	provide	VERB
ejpam-5871	71	15	below	below	ADP
ejpam-5871	71	16	.	.	PUNCT
ejpam-5871	72	1	definition	definition	NOUN
ejpam-5871	72	2	4	4	NUM
ejpam-5871	72	3	.	.	PUNCT
ejpam-5871	73	1	[	[	X
ejpam-5871	73	2	22	22	NUM
ejpam-5871	73	3	]	]	PUNCT
ejpam-5871	73	4	let	let	VERB
ejpam-5871	73	5	∅(θ	∅(θ	NOUN
ejpam-5871	73	6	)	)	PUNCT
ejpam-5871	73	7	∈	∈	PROPN
ejpam-5871	74	1	[	[	X
ejpam-5871	74	2	r1	r1	NOUN
ejpam-5871	74	3	,	,	PUNCT
ejpam-5871	74	4	r2	r2	PROPN
ejpam-5871	74	5	]	]	PUNCT
ejpam-5871	74	6	,	,	PUNCT
ejpam-5871	74	7	then	then	ADV
ejpam-5871	74	8	zβ	zβ	PROPN
ejpam-5871	74	9	r+1	r+1	PROPN
ejpam-5871	74	10	∅(r2	∅(r2	PROPN
ejpam-5871	74	11	)	)	PUNCT
ejpam-5871	74	12	=	=	PUNCT
ejpam-5871	74	13	1	1	NUM
ejpam-5871	74	14	γ(β	γ(β	PROPN
ejpam-5871	74	15	)	)	PUNCT
ejpam-5871	74	16	∫	∫	PROPN
ejpam-5871	74	17	r2	r2	PROPN
ejpam-5871	74	18	r1	r1	PROPN
ejpam-5871	74	19	∅(θ)(r2	∅(θ)(r2	NUM
ejpam-5871	74	20	−	−	PROPN
ejpam-5871	74	21	θ)β−1dθ	θ)β−1dθ	PROPN
ejpam-5871	74	22	,	,	PUNCT
ejpam-5871	74	23	r1	r1	NOUN
ejpam-5871	74	24	<	<	X
ejpam-5871	74	25	r2	r2	PROPN
ejpam-5871	74	26	,	,	PUNCT
ejpam-5871	74	27	β	β	X
ejpam-5871	74	28	>	>	X
ejpam-5871	74	29	0	0	X
ejpam-5871	74	30	.	.	PUNCT
ejpam-5871	75	1	similarly	similarly	ADV
ejpam-5871	75	2	,	,	PUNCT
ejpam-5871	75	3	the	the	DET
ejpam-5871	75	4	right	right	ADJ
ejpam-5871	75	5	side	side	NOUN
ejpam-5871	75	6	of	of	ADP
ejpam-5871	75	7	the	the	DET
ejpam-5871	75	8	riemann	riemann	PROPN
ejpam-5871	75	9	-	-	PUNCT
ejpam-5871	75	10	liouville	liouville	VERB
ejpam-5871	75	11	fractional	fractional	ADJ
ejpam-5871	75	12	operator	operator	NOUN
ejpam-5871	75	13	is	be	AUX
ejpam-5871	75	14	given	give	VERB
ejpam-5871	75	15	below	below	ADP
ejpam-5871	75	16	zβ	zβ	PROPN
ejpam-5871	75	17	r−2	r−2	PROPN
ejpam-5871	75	18	∅(r1	∅(r1	NOUN
ejpam-5871	75	19	)	)	PUNCT
ejpam-5871	76	1	=	=	SYM
ejpam-5871	76	2	1	1	NUM
ejpam-5871	76	3	γ(β	γ(β	PROPN
ejpam-5871	76	4	)	)	PUNCT
ejpam-5871	76	5	∫	∫	PROPN
ejpam-5871	76	6	r2	r2	PROPN
ejpam-5871	76	7	r1	r1	PROPN
ejpam-5871	76	8	∅(θ)(θ	∅(θ)(θ	PROPN
ejpam-5871	77	1	−	−	PROPN
ejpam-5871	77	2	r1	r1	PROPN
ejpam-5871	77	3	)	)	PUNCT
ejpam-5871	77	4	β−1dθ	β−1dθ	NOUN
ejpam-5871	77	5	,	,	PUNCT
ejpam-5871	77	6	r1	r1	NOUN
ejpam-5871	77	7	<	<	X
ejpam-5871	77	8	r2	r2	PROPN
ejpam-5871	77	9	,	,	PUNCT
ejpam-5871	77	10	β	β	X
ejpam-5871	77	11	>	>	X
ejpam-5871	77	12	0	0	X
ejpam-5871	77	13	.	.	PUNCT
ejpam-5871	77	14	a.	a.	PROPN
ejpam-5871	77	15	mehmood	mehmood	PROPN
ejpam-5871	77	16	et	et	PROPN
ejpam-5871	77	17	al	al	PROPN
ejpam-5871	77	18	.	.	PUNCT
ejpam-5871	77	19	/	/	SYM
ejpam-5871	77	20	eur	eur	PROPN
ejpam-5871	77	21	.	.	PUNCT
ejpam-5871	78	1	j.	j.	PROPN
ejpam-5871	78	2	pure	pure	PROPN
ejpam-5871	78	3	appl	appl	PROPN
ejpam-5871	78	4	.	.	PROPN
ejpam-5871	78	5	math	math	PROPN
ejpam-5871	78	6	,	,	PUNCT
ejpam-5871	78	7	18	18	NUM
ejpam-5871	78	8	(	(	PUNCT
ejpam-5871	78	9	2	2	NUM
ejpam-5871	78	10	)	)	PUNCT
ejpam-5871	78	11	(	(	PUNCT
ejpam-5871	78	12	2025	2025	NUM
ejpam-5871	78	13	)	)	PUNCT
ejpam-5871	78	14	,	,	PUNCT
ejpam-5871	78	15	5871	5871	NUM
ejpam-5871	78	16	4	4	NUM
ejpam-5871	78	17	of	of	ADP
ejpam-5871	78	18	26	26	NUM
ejpam-5871	78	19	we	we	PRON
ejpam-5871	78	20	,	,	PUNCT
ejpam-5871	78	21	now	now	ADV
ejpam-5871	78	22	replicated	replicate	VERB
ejpam-5871	78	23	the	the	DET
ejpam-5871	78	24	ı.υ	ı.υ	PROPN
ejpam-5871	78	25	riemann	riemann	PROPN
ejpam-5871	78	26	-	-	PUNCT
ejpam-5871	78	27	liouville	liouville	VERB
ejpam-5871	78	28	fractional	fractional	ADJ
ejpam-5871	78	29	integral	integral	ADJ
ejpam-5871	78	30	operator	operator	NOUN
ejpam-5871	78	31	.	.	PUNCT
ejpam-5871	79	1	definition	definition	NOUN
ejpam-5871	79	2	5	5	NUM
ejpam-5871	79	3	.	.	PUNCT
ejpam-5871	80	1	[	[	X
ejpam-5871	80	2	23	23	NUM
ejpam-5871	80	3	]	]	PUNCT
ejpam-5871	80	4	let	let	AUX
ejpam-5871	80	5	∅(x	∅(x	PROPN
ejpam-5871	80	6	)	)	PUNCT
ejpam-5871	80	7	be	be	VERB
ejpam-5871	80	8	ı.υ	ı.υ	PROPN
ejpam-5871	80	9	function	function	NOUN
ejpam-5871	80	10	such	such	ADJ
ejpam-5871	80	11	that	that	DET
ejpam-5871	80	12	∅1(x),∅2(x	∅1(x),∅2(x	PROPN
ejpam-5871	80	13	)	)	PUNCT
ejpam-5871	80	14	∈	∈	PROPN
ejpam-5871	80	15	l[r1	l[r1	X
ejpam-5871	80	16	,	,	PUNCT
ejpam-5871	80	17	r2	r2	PROPN
ejpam-5871	80	18	]	]	PUNCT
ejpam-5871	80	19	,	,	PUNCT
ejpam-5871	80	20	then	then	ADV
ejpam-5871	80	21	zβ	zβ	PROPN
ejpam-5871	80	22	x+∅(r2	x+∅(r2	NOUN
ejpam-5871	80	23	)	)	PUNCT
ejpam-5871	81	1	=	=	SYM
ejpam-5871	81	2	1	1	NUM
ejpam-5871	81	3	γ(β	γ(β	PROPN
ejpam-5871	81	4	)	)	PUNCT
ejpam-5871	81	5	∫	∫	PROPN
ejpam-5871	81	6	r2	r2	PROPN
ejpam-5871	81	7	x	x	PUNCT
ejpam-5871	81	8	∅(θ)(r2	∅(θ)(r2	NUM
ejpam-5871	81	9	−	−	PROPN
ejpam-5871	81	10	θ)β−1dθ	θ)β−1dθ	PROPN
ejpam-5871	81	11	,	,	PUNCT
ejpam-5871	81	12	x	x	X
ejpam-5871	81	13	<	<	X
ejpam-5871	81	14	r2	r2	NOUN
ejpam-5871	81	15	,	,	PUNCT
ejpam-5871	81	16	and	and	CCONJ
ejpam-5871	81	17	zβ	zβ	PROPN
ejpam-5871	81	18	y−∅(r1	y−∅(r1	PROPN
ejpam-5871	81	19	)	)	PUNCT
ejpam-5871	81	20	=	=	SYM
ejpam-5871	81	21	1	1	NUM
ejpam-5871	81	22	γ(β	γ(β	PROPN
ejpam-5871	81	23	)	)	PUNCT
ejpam-5871	81	24	∫	∫	PROPN
ejpam-5871	82	1	y	y	PROPN
ejpam-5871	82	2	r1	r1	PROPN
ejpam-5871	82	3	∅(θ)(θ	∅(θ)(θ	PROPN
ejpam-5871	82	4	−	−	PROPN
ejpam-5871	82	5	r1	r1	PROPN
ejpam-5871	82	6	)	)	PUNCT
ejpam-5871	82	7	β−1dθ	β−1dθ	NOUN
ejpam-5871	82	8	,	,	PUNCT
ejpam-5871	82	9	r1	r1	PROPN
ejpam-5871	82	10	<	<	X
ejpam-5871	82	11	y	y	PROPN
ejpam-5871	82	12	,	,	PUNCT
ejpam-5871	82	13	with	with	ADP
ejpam-5871	82	14	β	β	X
ejpam-5871	82	15	>	>	X
ejpam-5871	82	16	0	0	PROPN
ejpam-5871	82	17	,	,	PUNCT
ejpam-5871	82	18	obviously	obviously	ADV
ejpam-5871	82	19	zβ	zβ	PROPN
ejpam-5871	82	20	x+∅(r2	x+∅(r2	NOUN
ejpam-5871	82	21	)	)	PUNCT
ejpam-5871	83	1	=	=	PUNCT
ejpam-5871	83	2	[	[	PUNCT
ejpam-5871	83	3	zβ	zβ	NUM
ejpam-5871	83	4	x+∅1(r2),z	x+∅1(r2),z	PROPN
ejpam-5871	83	5	β	β	PROPN
ejpam-5871	83	6	x+∅2(r2	x+∅2(r2	PROPN
ejpam-5871	83	7	)	)	PUNCT
ejpam-5871	83	8	]	]	PUNCT
ejpam-5871	83	9	,	,	PUNCT
ejpam-5871	83	10	and	and	CCONJ
ejpam-5871	83	11	zβ	zβ	PROPN
ejpam-5871	83	12	y−∅(r1	y−∅(r1	PROPN
ejpam-5871	83	13	)	)	PUNCT
ejpam-5871	84	1	=	=	PUNCT
ejpam-5871	85	1	[	[	PUNCT
ejpam-5871	85	2	zβ	zβ	X
ejpam-5871	85	3	y−∅1(r1),z	y−∅1(r1),z	ADV
ejpam-5871	85	4	β	β	PROPN
ejpam-5871	85	5	y−∅2(r1	y−∅2(r1	PROPN
ejpam-5871	85	6	)	)	PUNCT
ejpam-5871	85	7	]	]	PUNCT
ejpam-5871	85	8	.	.	PUNCT
ejpam-5871	86	1	in	in	ADP
ejpam-5871	86	2	recent	recent	ADJ
ejpam-5871	86	3	years	year	NOUN
ejpam-5871	86	4	,	,	PUNCT
ejpam-5871	86	5	ı.υ	ı.υ	PROPN
ejpam-5871	86	6	functions	function	NOUN
ejpam-5871	86	7	based	base	VERB
ejpam-5871	86	8	on	on	ADP
ejpam-5871	86	9	different	different	ADJ
ejpam-5871	86	10	partial	partial	ADJ
ejpam-5871	86	11	and	and	CCONJ
ejpam-5871	86	12	total	total	ADJ
ejpam-5871	86	13	ordered	order	VERB
ejpam-5871	86	14	relations	relation	NOUN
ejpam-5871	86	15	have	have	AUX
ejpam-5871	86	16	been	be	AUX
ejpam-5871	86	17	used	use	VERB
ejpam-5871	86	18	to	to	PART
ejpam-5871	86	19	refine	refine	VERB
ejpam-5871	86	20	and	and	CCONJ
ejpam-5871	86	21	generalize	generalize	VERB
ejpam-5871	86	22	a	a	DET
ejpam-5871	86	23	number	number	NOUN
ejpam-5871	86	24	of	of	ADP
ejpam-5871	86	25	integral	integral	ADJ
ejpam-5871	86	26	inequalities	inequality	NOUN
ejpam-5871	86	27	.	.	PUNCT
ejpam-5871	87	1	these	these	DET
ejpam-5871	87	2	works	work	NOUN
ejpam-5871	87	3	provided	provide	VERB
ejpam-5871	87	4	the	the	DET
ejpam-5871	87	5	groundwork	groundwork	NOUN
ejpam-5871	87	6	for	for	ADP
ejpam-5871	87	7	subsequent	subsequent	ADJ
ejpam-5871	87	8	developments	development	NOUN
ejpam-5871	87	9	especially	especially	ADV
ejpam-5871	87	10	in	in	ADP
ejpam-5871	87	11	mathematical	mathematical	ADJ
ejpam-5871	87	12	inequalities	inequality	NOUN
ejpam-5871	87	13	pertaining	pertain	VERB
ejpam-5871	87	14	to	to	PART
ejpam-5871	87	15	set	set	VERB
ejpam-5871	87	16	-	-	PUNCT
ejpam-5871	87	17	valued	value	VERB
ejpam-5871	87	18	functions	function	NOUN
ejpam-5871	87	19	and	and	CCONJ
ejpam-5871	87	20	represented	represent	VERB
ejpam-5871	87	21	the	the	DET
ejpam-5871	87	22	first	first	ADJ
ejpam-5871	87	23	attempts	attempt	NOUN
ejpam-5871	87	24	to	to	PART
ejpam-5871	87	25	improve	improve	VERB
ejpam-5871	87	26	the	the	DET
ejpam-5871	87	27	practical	practical	ADJ
ejpam-5871	87	28	applications	application	NOUN
ejpam-5871	87	29	of	of	ADP
ejpam-5871	87	30	inequalities	inequality	NOUN
ejpam-5871	87	31	.	.	PUNCT
ejpam-5871	88	1	we	we	PRON
ejpam-5871	88	2	will	will	AUX
ejpam-5871	88	3	derive	derive	VERB
ejpam-5871	88	4	several	several	ADJ
ejpam-5871	88	5	fractional	fractional	ADJ
ejpam-5871	88	6	variations	variation	NOUN
ejpam-5871	88	7	of	of	ADP
ejpam-5871	88	8	reverse	reverse	ADJ
ejpam-5871	88	9	minkowski	minkowski	ADJ
ejpam-5871	88	10	inequality	inequality	NOUN
ejpam-5871	88	11	,	,	PUNCT
ejpam-5871	88	12	holders	holder	NOUN
ejpam-5871	88	13	inequality	inequality	NOUN
ejpam-5871	88	14	,	,	PUNCT
ejpam-5871	88	15	hermite	hermite	PROPN
ejpam-5871	88	16	-	-	PUNCT
ejpam-5871	88	17	hadamard	hadamard	ADJ
ejpam-5871	88	18	inequality	inequality	NOUN
ejpam-5871	88	19	,	,	PUNCT
ejpam-5871	88	20	its	its	PRON
ejpam-5871	88	21	weighted	weight	VERB
ejpam-5871	88	22	form	form	NOUN
ejpam-5871	88	23	known	know	VERB
ejpam-5871	88	24	as	as	ADP
ejpam-5871	88	25	fejer	fejer	NOUN
ejpam-5871	88	26	-	-	PUNCT
ejpam-5871	88	27	hermite	hermite	ADJ
ejpam-5871	88	28	-	-	PUNCT
ejpam-5871	88	29	hadamard	hadamard	ADJ
ejpam-5871	88	30	inequality	inequality	NOUN
ejpam-5871	88	31	and	and	CCONJ
ejpam-5871	88	32	some	some	DET
ejpam-5871	88	33	inequalities	inequality	NOUN
ejpam-5871	88	34	for	for	ADP
ejpam-5871	88	35	the	the	DET
ejpam-5871	88	36	product	product	NOUN
ejpam-5871	88	37	of	of	ADP
ejpam-5871	88	38	functions	function	NOUN
ejpam-5871	88	39	that	that	PRON
ejpam-5871	88	40	are	be	AUX
ejpam-5871	88	41	known	know	VERB
ejpam-5871	88	42	to	to	PART
ejpam-5871	88	43	be	be	AUX
ejpam-5871	88	44	pachpatee	pachpatee	NOUN
ejpam-5871	88	45	’s	’s	PART
ejpam-5871	88	46	type	type	NOUN
ejpam-5871	88	47	inclusions	inclusion	NOUN
ejpam-5871	88	48	as	as	ADP
ejpam-5871	88	49	applications	application	NOUN
ejpam-5871	88	50	of	of	ADP
ejpam-5871	88	51	this	this	DET
ejpam-5871	88	52	class	class	NOUN
ejpam-5871	88	53	.	.	PUNCT
ejpam-5871	89	1	since	since	SCONJ
ejpam-5871	89	2	the	the	DET
ejpam-5871	89	3	generic	generic	ADJ
ejpam-5871	89	4	class	class	NOUN
ejpam-5871	89	5	of	of	ADP
ejpam-5871	89	6	convexity	convexity	NOUN
ejpam-5871	89	7	and	and	CCONJ
ejpam-5871	89	8	its	its	PRON
ejpam-5871	89	9	implications	implication	NOUN
ejpam-5871	89	10	in	in	ADP
ejpam-5871	89	11	inequalities	inequality	NOUN
ejpam-5871	89	12	is	be	AUX
ejpam-5871	89	13	a	a	DET
ejpam-5871	89	14	broader	broad	ADJ
ejpam-5871	89	15	space	space	NOUN
ejpam-5871	89	16	of	of	ADP
ejpam-5871	89	17	functions	function	NOUN
ejpam-5871	89	18	that	that	PRON
ejpam-5871	89	19	contains	contain	VERB
ejpam-5871	89	20	redcf	redcf	ADJ
ejpam-5871	89	21	and	and	CCONJ
ejpam-5871	89	22	non	non	ADJ
ejpam-5871	89	23	-	-	ADJ
ejpam-5871	89	24	redcf	redcf	ADJ
ejpam-5871	89	25	classes	class	NOUN
ejpam-5871	89	26	,	,	PUNCT
ejpam-5871	89	27	it	it	PRON
ejpam-5871	89	28	is	be	AUX
ejpam-5871	89	29	the	the	DET
ejpam-5871	89	30	novel	novel	ADJ
ejpam-5871	89	31	aspect	aspect	NOUN
ejpam-5871	89	32	of	of	ADP
ejpam-5871	89	33	the	the	DET
ejpam-5871	89	34	current	current	ADJ
ejpam-5871	89	35	proceeding	proceeding	NOUN
ejpam-5871	89	36	.	.	PUNCT
ejpam-5871	90	1	our	our	PRON
ejpam-5871	90	2	developed	develop	VERB
ejpam-5871	90	3	results	result	NOUN
ejpam-5871	90	4	allow	allow	VERB
ejpam-5871	90	5	for	for	ADP
ejpam-5871	90	6	the	the	DET
ejpam-5871	90	7	characterization	characterization	NOUN
ejpam-5871	90	8	of	of	ADP
ejpam-5871	90	9	large	large	ADJ
ejpam-5871	90	10	classes	class	NOUN
ejpam-5871	90	11	of	of	ADP
ejpam-5871	90	12	functions	function	NOUN
ejpam-5871	90	13	.	.	PUNCT
ejpam-5871	91	1	our	our	PRON
ejpam-5871	91	2	findings	finding	NOUN
ejpam-5871	91	3	will	will	AUX
ejpam-5871	91	4	also	also	ADV
ejpam-5871	91	5	be	be	AUX
ejpam-5871	91	6	useful	useful	ADJ
ejpam-5871	91	7	tools	tool	NOUN
ejpam-5871	91	8	for	for	ADP
ejpam-5871	91	9	calculating	calculate	VERB
ejpam-5871	91	10	different	different	ADJ
ejpam-5871	91	11	bounds	bound	NOUN
ejpam-5871	91	12	for	for	ADP
ejpam-5871	91	13	the	the	DET
ejpam-5871	91	14	ı.υ	ı.υ	PROPN
ejpam-5871	91	15	fractional	fractional	ADJ
ejpam-5871	91	16	operators	operator	NOUN
ejpam-5871	91	17	.	.	PUNCT
ejpam-5871	92	1	there	there	PRON
ejpam-5871	92	2	are	be	VERB
ejpam-5871	92	3	a	a	DET
ejpam-5871	92	4	few	few	ADJ
ejpam-5871	92	5	simulations	simulation	NOUN
ejpam-5871	92	6	for	for	ADP
ejpam-5871	92	7	numerical	numerical	ADJ
ejpam-5871	92	8	examples	example	NOUN
ejpam-5871	92	9	provided	provide	VERB
ejpam-5871	92	10	to	to	PART
ejpam-5871	92	11	verify	verify	VERB
ejpam-5871	92	12	the	the	DET
ejpam-5871	92	13	accuracy	accuracy	NOUN
ejpam-5871	92	14	of	of	ADP
ejpam-5871	92	15	the	the	DET
ejpam-5871	92	16	suggested	suggest	VERB
ejpam-5871	92	17	findings	finding	NOUN
ejpam-5871	92	18	.	.	PUNCT
ejpam-5871	93	1	with	with	ADP
ejpam-5871	93	2	this	this	DET
ejpam-5871	93	3	work	work	NOUN
ejpam-5871	93	4	,	,	PUNCT
ejpam-5871	93	5	we	we	PRON
ejpam-5871	93	6	intend	intend	VERB
ejpam-5871	93	7	to	to	PART
ejpam-5871	93	8	demonstrate	demonstrate	VERB
ejpam-5871	93	9	further	further	ADJ
ejpam-5871	93	10	inequalities	inequality	NOUN
ejpam-5871	93	11	and	and	CCONJ
ejpam-5871	93	12	related	related	ADJ
ejpam-5871	93	13	optimization	optimization	NOUN
ejpam-5871	93	14	issues	issue	NOUN
ejpam-5871	93	15	to	to	ADP
ejpam-5871	93	16	interested	interested	ADJ
ejpam-5871	93	17	readers	reader	NOUN
ejpam-5871	93	18	.	.	PUNCT
ejpam-5871	94	1	now	now	ADV
ejpam-5871	94	2	,	,	PUNCT
ejpam-5871	94	3	we	we	PRON
ejpam-5871	94	4	introduce	introduce	VERB
ejpam-5871	94	5	the	the	DET
ejpam-5871	94	6	idea	idea	NOUN
ejpam-5871	94	7	of	of	ADP
ejpam-5871	94	8	ı.υ-(⋋s+1	ı.υ-(⋋s+1	PROPN
ejpam-5871	94	9	,	,	PUNCT
ejpam-5871	94	10	℧	℧	PROPN
ejpam-5871	94	11	)	)	PUNCT
ejpam-5871	94	12	redcf	redcf	ADJ
ejpam-5871	94	13	,	,	PUNCT
ejpam-5871	94	14	it	it	PRON
ejpam-5871	94	15	indicates	indicate	VERB
ejpam-5871	94	16	how	how	SCONJ
ejpam-5871	94	17	several	several	ADJ
ejpam-5871	94	18	new	new	ADJ
ejpam-5871	94	19	generalizations	generalization	NOUN
ejpam-5871	94	20	of	of	ADP
ejpam-5871	94	21	convexity	convexity	NOUN
ejpam-5871	94	22	and	and	CCONJ
ejpam-5871	94	23	the	the	DET
ejpam-5871	94	24	numerous	numerous	ADJ
ejpam-5871	94	25	classes	class	NOUN
ejpam-5871	94	26	of	of	ADP
ejpam-5871	94	27	convexity	convexity	NOUN
ejpam-5871	94	28	that	that	PRON
ejpam-5871	94	29	now	now	ADV
ejpam-5871	94	30	exist	exist	VERB
ejpam-5871	94	31	can	can	AUX
ejpam-5871	94	32	be	be	AUX
ejpam-5871	94	33	produced	produce	VERB
ejpam-5871	94	34	as	as	ADP
ejpam-5871	94	35	special	special	ADJ
ejpam-5871	94	36	instances	instance	NOUN
ejpam-5871	94	37	.	.	PUNCT
ejpam-5871	95	1	for	for	ADP
ejpam-5871	95	2	our	our	PRON
ejpam-5871	95	3	convenient	convenient	ADJ
ejpam-5871	95	4	the	the	DET
ejpam-5871	95	5	family	family	NOUN
ejpam-5871	95	6	of	of	ADP
ejpam-5871	95	7	ı.υ-(⋋s+1	ı.υ-(⋋s+1	PROPN
ejpam-5871	95	8	,	,	PUNCT
ejpam-5871	95	9	℧	℧	PROPN
ejpam-5871	95	10	)	)	PUNCT
ejpam-5871	95	11	redcf	redcf	ADJ
ejpam-5871	95	12	,	,	PUNCT
ejpam-5871	95	13	ı.υ-(⋋s+1	ı.υ-(⋋s+1	PROPN
ejpam-5871	95	14	,	,	PUNCT
ejpam-5871	95	15	℧	℧	PROPN
ejpam-5871	95	16	)	)	PUNCT
ejpam-5871	95	17	concave	concave	NOUN
ejpam-5871	95	18	function	function	NOUN
ejpam-5871	95	19	,	,	PUNCT
ejpam-5871	95	20	(	(	PUNCT
ejpam-5871	95	21	⋋s+1	⋋s+1	PROPN
ejpam-5871	95	22	,	,	PUNCT
ejpam-5871	95	23	℧	℧	NOUN
ejpam-5871	95	24	)	)	PUNCT
ejpam-5871	95	25	redcf	redcf	ADJ
ejpam-5871	95	26	and	and	CCONJ
ejpam-5871	95	27	(	(	PUNCT
ejpam-5871	95	28	⋋s+1	⋋s+1	PROPN
ejpam-5871	95	29	,	,	PUNCT
ejpam-5871	95	30	℧	℧	NOUN
ejpam-5871	95	31	)	)	PUNCT
ejpam-5871	95	32	concave	concave	NOUN
ejpam-5871	95	33	functions	function	NOUN
ejpam-5871	95	34	are	be	AUX
ejpam-5871	95	35	represented	represent	VERB
ejpam-5871	95	36	as	as	ADP
ejpam-5871	95	37	sigx([r1	sigx([r1	NOUN
ejpam-5871	95	38	,	,	PUNCT
ejpam-5871	95	39	r2	r2	PROPN
ejpam-5871	95	40	]	]	PUNCT
ejpam-5871	95	41	,	,	PUNCT
ejpam-5871	96	1	r	r	NOUN
ejpam-5871	96	2	+	+	PROPN
ejpam-5871	96	3	i	i	NOUN
ejpam-5871	96	4	)	)	PUNCT
ejpam-5871	96	5	,	,	PUNCT
ejpam-5871	96	6	sigv	sigv	NOUN
ejpam-5871	96	7	(	(	PUNCT
ejpam-5871	96	8	[	[	X
ejpam-5871	96	9	r1	r1	NOUN
ejpam-5871	96	10	,	,	PUNCT
ejpam-5871	96	11	r2	r2	PROPN
ejpam-5871	96	12	]	]	PUNCT
ejpam-5871	96	13	,	,	PUNCT
ejpam-5871	96	14	r	r	NOUN
ejpam-5871	97	1	+	+	PROPN
ejpam-5871	97	2	i	i	NOUN
ejpam-5871	97	3	)	)	PUNCT
ejpam-5871	97	4	,	,	PUNCT
ejpam-5871	97	5	sgx([r1	sgx([r1	PROPN
ejpam-5871	97	6	,	,	PUNCT
ejpam-5871	97	7	r2	r2	PROPN
ejpam-5871	97	8	]	]	PUNCT
ejpam-5871	97	9	,	,	PUNCT
ejpam-5871	97	10	r	r	NOUN
ejpam-5871	97	11	)	)	PUNCT
ejpam-5871	97	12	and	and	CCONJ
ejpam-5871	97	13	sgv	sgv	NOUN
ejpam-5871	97	14	(	(	PUNCT
ejpam-5871	97	15	[	[	X
ejpam-5871	97	16	r1	r1	NOUN
ejpam-5871	97	17	,	,	PUNCT
ejpam-5871	97	18	r2	r2	PROPN
ejpam-5871	97	19	]	]	PUNCT
ejpam-5871	97	20	,	,	PUNCT
ejpam-5871	97	21	r	r	NOUN
ejpam-5871	97	22	)	)	PUNCT
ejpam-5871	97	23	respectively	respectively	ADV
ejpam-5871	97	24	.	.	PUNCT
ejpam-5871	98	1	definition	definition	NOUN
ejpam-5871	98	2	6	6	NUM
ejpam-5871	98	3	.	.	PUNCT
ejpam-5871	99	1	let	let	VERB
ejpam-5871	99	2	s	s	PRON
ejpam-5871	99	3	∈	∈	VERB
ejpam-5871	99	4	r/{−1	r/{−1	PROPN
ejpam-5871	99	5	}	}	PUNCT
ejpam-5871	99	6	,	,	PUNCT
ejpam-5871	99	7	⋋	⋋	PRON
ejpam-5871	99	8	be	be	AUX
ejpam-5871	99	9	an	an	DET
ejpam-5871	99	10	increasing	increase	VERB
ejpam-5871	99	11	function	function	NOUN
ejpam-5871	99	12	and	and	CCONJ
ejpam-5871	99	13	∅	∅	NOUN
ejpam-5871	99	14	:	:	PUNCT
ejpam-5871	100	1	[	[	X
ejpam-5871	100	2	r1	r1	NOUN
ejpam-5871	100	3	,	,	PUNCT
ejpam-5871	100	4	r2	r2	PROPN
ejpam-5871	100	5	]	]	PUNCT
ejpam-5871	100	6	→	→	SYM
ejpam-5871	100	7	r+	r+	PUNCT
ejpam-5871	100	8	i	i	PRON
ejpam-5871	100	9	be	be	VERB
ejpam-5871	100	10	an	an	DET
ejpam-5871	100	11	ı.υ-(⋋s+1	ı.υ-(⋋s+1	PROPN
ejpam-5871	100	12	,	,	PUNCT
ejpam-5871	100	13	℧	℧	NOUN
ejpam-5871	100	14	)	)	PUNCT
ejpam-5871	100	15	function	function	NOUN
ejpam-5871	100	16	fulfill	fulfill	VERB
ejpam-5871	100	17	the	the	DET
ejpam-5871	100	18	condition	condition	NOUN
ejpam-5871	100	19	∅(x	∅(x	PROPN
ejpam-5871	100	20	)	)	PUNCT
ejpam-5871	100	21	=	=	PUNCT
ejpam-5871	101	1	[	[	X
ejpam-5871	101	2	∅∗(x),∅∗(x	∅∗(x),∅∗(x	NOUN
ejpam-5871	101	3	)	)	PUNCT
ejpam-5871	101	4	]	]	PUNCT
ejpam-5871	101	5	and	and	CCONJ
ejpam-5871	101	6	℧	℧	ADP
ejpam-5871	101	7	:	:	PUNCT
ejpam-5871	102	1	[	[	X
ejpam-5871	102	2	0	0	NUM
ejpam-5871	102	3	,	,	PUNCT
ejpam-5871	102	4	1	1	NUM
ejpam-5871	102	5	]	]	PUNCT
ejpam-5871	102	6	→	→	PUNCT
ejpam-5871	102	7	r	r	NOUN
ejpam-5871	102	8	be	be	AUX
ejpam-5871	102	9	a	a	DET
ejpam-5871	102	10	positive	positive	ADJ
ejpam-5871	102	11	function	function	NOUN
ejpam-5871	102	12	,	,	PUNCT
ejpam-5871	102	13	so	so	ADV
ejpam-5871	102	14	∅	∅	NOUN
ejpam-5871	102	15	(	(	PUNCT
ejpam-5871	102	16	⋋−1	⋋−1	X
ejpam-5871	102	17	(	(	PUNCT
ejpam-5871	102	18	(	(	PUNCT
ejpam-5871	102	19	1−	1−	NUM
ejpam-5871	102	20	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	102	21	(	(	PUNCT
ejpam-5871	102	22	r1	r1	PROPN
ejpam-5871	102	23	)	)	PUNCT
ejpam-5871	102	24	+	+	NUM
ejpam-5871	102	25	θ	θ	PUNCT
ejpam-5871	102	26	⋋s+1	⋋s+1	VERB
ejpam-5871	102	27	(	(	PUNCT
ejpam-5871	102	28	r2	r2	PROPN
ejpam-5871	102	29	)	)	PUNCT
ejpam-5871	102	30	)	)	PUNCT
ejpam-5871	102	31	1	1	NUM
ejpam-5871	102	32	s+1	s+1	PROPN
ejpam-5871	102	33	)	)	PUNCT
ejpam-5871	102	34	⊇	⊇	PROPN
ejpam-5871	102	35	℧	℧	PROPN
ejpam-5871	102	36	(	(	PUNCT
ejpam-5871	102	37	1−	1−	NUM
ejpam-5871	102	38	θ)∅(r1	θ)∅(r1	NOUN
ejpam-5871	102	39	)	)	PUNCT
ejpam-5871	102	40	+	+	CCONJ
ejpam-5871	102	41	℧	℧	PROPN
ejpam-5871	102	42	(	(	PUNCT
ejpam-5871	102	43	θ)∅(r2	θ)∅(r2	NOUN
ejpam-5871	102	44	)	)	PUNCT
ejpam-5871	102	45	,	,	PUNCT
ejpam-5871	102	46	for	for	ADP
ejpam-5871	102	47	all	all	DET
ejpam-5871	102	48	x	x	SYM
ejpam-5871	102	49	∈	∈	PROPN
ejpam-5871	102	50	[	[	X
ejpam-5871	102	51	r1	r1	NOUN
ejpam-5871	102	52	,	,	PUNCT
ejpam-5871	102	53	r2	r2	PROPN
ejpam-5871	102	54	]	]	PUNCT
ejpam-5871	102	55	and	and	CCONJ
ejpam-5871	102	56	θ	θ	PROPN
ejpam-5871	102	57	∈	∈	PROPN
ejpam-5871	103	1	[	[	X
ejpam-5871	103	2	0	0	NUM
ejpam-5871	103	3	,	,	PUNCT
ejpam-5871	103	4	1	1	NUM
ejpam-5871	103	5	]	]	PUNCT
ejpam-5871	103	6	.	.	PUNCT
ejpam-5871	104	1	a.	a.	PROPN
ejpam-5871	104	2	mehmood	mehmood	PROPN
ejpam-5871	104	3	et	et	PROPN
ejpam-5871	104	4	al	al	PROPN
ejpam-5871	104	5	.	.	PUNCT
ejpam-5871	104	6	/	/	SYM
ejpam-5871	104	7	eur	eur	PROPN
ejpam-5871	104	8	.	.	PUNCT
ejpam-5871	105	1	j.	j.	PROPN
ejpam-5871	105	2	pure	pure	PROPN
ejpam-5871	105	3	appl	appl	PROPN
ejpam-5871	105	4	.	.	PROPN
ejpam-5871	105	5	math	math	PROPN
ejpam-5871	105	6	,	,	PUNCT
ejpam-5871	105	7	18	18	NUM
ejpam-5871	105	8	(	(	PUNCT
ejpam-5871	105	9	2	2	NUM
ejpam-5871	105	10	)	)	PUNCT
ejpam-5871	105	11	(	(	PUNCT
ejpam-5871	105	12	2025	2025	NUM
ejpam-5871	105	13	)	)	PUNCT
ejpam-5871	105	14	,	,	PUNCT
ejpam-5871	105	15	5871	5871	NUM
ejpam-5871	105	16	5	5	NUM
ejpam-5871	105	17	of	of	ADP
ejpam-5871	105	18	26	26	NUM
ejpam-5871	105	19	remark	remark	NOUN
ejpam-5871	105	20	1	1	NUM
ejpam-5871	105	21	.	.	PUNCT
ejpam-5871	106	1	(	(	PUNCT
ejpam-5871	106	2	i	i	NOUN
ejpam-5871	106	3	)	)	PUNCT
ejpam-5871	106	4	if	if	SCONJ
ejpam-5871	106	5	we	we	PRON
ejpam-5871	106	6	choose	choose	VERB
ejpam-5871	106	7	s	s	NOUN
ejpam-5871	106	8	=	=	SYM
ejpam-5871	106	9	0	0	NUM
ejpam-5871	106	10	and	and	CCONJ
ejpam-5871	106	11	⋋(θ	⋋(θ	NUM
ejpam-5871	106	12	)	)	PUNCT
ejpam-5871	106	13	=	=	SYM
ejpam-5871	106	14	θ	θ	NOUN
ejpam-5871	106	15	in	in	ADP
ejpam-5871	106	16	(	(	PUNCT
ejpam-5871	106	17	6	6	NUM
ejpam-5871	106	18	)	)	PUNCT
ejpam-5871	106	19	,	,	PUNCT
ejpam-5871	106	20	then	then	ADV
ejpam-5871	106	21	we	we	PRON
ejpam-5871	106	22	obtain	obtain	VERB
ejpam-5871	106	23	the	the	DET
ejpam-5871	106	24	following	follow	VERB
ejpam-5871	106	25	definition	definition	NOUN
ejpam-5871	106	26	presented	present	VERB
ejpam-5871	106	27	in	in	ADP
ejpam-5871	106	28	[	[	X
ejpam-5871	106	29	24	24	NUM
ejpam-5871	106	30	]	]	PUNCT
ejpam-5871	106	31	.	.	PUNCT
ejpam-5871	107	1	∅	∅	NOUN
ejpam-5871	107	2	(	(	PUNCT
ejpam-5871	107	3	⋋−1	⋋−1	ADJ
ejpam-5871	107	4	(	(	PUNCT
ejpam-5871	107	5	(	(	PUNCT
ejpam-5871	107	6	1−	1−	NUM
ejpam-5871	107	7	θ)⋋	θ)⋋	NUM
ejpam-5871	107	8	(	(	PUNCT
ejpam-5871	107	9	r1	r1	PROPN
ejpam-5871	107	10	)	)	PUNCT
ejpam-5871	107	11	+	+	NUM
ejpam-5871	107	12	θ	θ	NOUN
ejpam-5871	107	13	⋋	⋋	ADP
ejpam-5871	107	14	(	(	PUNCT
ejpam-5871	107	15	r2	r2	PROPN
ejpam-5871	107	16	)	)	PUNCT
ejpam-5871	107	17	)	)	PUNCT
ejpam-5871	107	18	)	)	PUNCT
ejpam-5871	108	1	⊇	⊇	PROPN
ejpam-5871	108	2	℧	℧	PROPN
ejpam-5871	108	3	(	(	PUNCT
ejpam-5871	108	4	1−	1−	NUM
ejpam-5871	108	5	θ)∅(r1	θ)∅(r1	NOUN
ejpam-5871	108	6	)	)	PUNCT
ejpam-5871	108	7	+	+	CCONJ
ejpam-5871	108	8	℧	℧	PROPN
ejpam-5871	108	9	(	(	PUNCT
ejpam-5871	108	10	θ)∅(r2	θ)∅(r2	NOUN
ejpam-5871	108	11	)	)	PUNCT
ejpam-5871	108	12	,	,	PUNCT
ejpam-5871	108	13	(	(	PUNCT
ejpam-5871	108	14	ii	ii	NOUN
ejpam-5871	108	15	)	)	PUNCT
ejpam-5871	108	16	for	for	ADP
ejpam-5871	108	17	the	the	DET
ejpam-5871	108	18	choice	choice	NOUN
ejpam-5871	108	19	of	of	ADP
ejpam-5871	108	20	s	s	NOUN
ejpam-5871	108	21	=	=	SYM
ejpam-5871	108	22	0	0	NUM
ejpam-5871	108	23	,	,	PUNCT
ejpam-5871	108	24	and	and	CCONJ
ejpam-5871	108	25	⋋(θ	⋋(θ	NUM
ejpam-5871	108	26	)	)	PUNCT
ejpam-5871	108	27	=	=	SYM
ejpam-5871	108	28	℧	℧	PROPN
ejpam-5871	108	29	(	(	PUNCT
ejpam-5871	108	30	θ	θ	NOUN
ejpam-5871	108	31	)	)	PUNCT
ejpam-5871	108	32	=	=	SYM
ejpam-5871	108	33	θ	θ	PROPN
ejpam-5871	108	34	in	in	ADP
ejpam-5871	108	35	(	(	PUNCT
ejpam-5871	108	36	6	6	NUM
ejpam-5871	108	37	)	)	PUNCT
ejpam-5871	108	38	we	we	PRON
ejpam-5871	108	39	acquire	acquire	VERB
ejpam-5871	108	40	⋋-ı.υ	⋋-ı.υ	ADJ
ejpam-5871	108	41	cf	cf	NOUN
ejpam-5871	108	42	:	:	PUNCT
ejpam-5871	108	43	∅	∅	NOUN
ejpam-5871	108	44	(	(	PUNCT
ejpam-5871	108	45	⋋−1	⋋−1	X
ejpam-5871	108	46	(	(	PUNCT
ejpam-5871	108	47	(	(	PUNCT
ejpam-5871	108	48	1−	1−	NUM
ejpam-5871	108	49	θ)⋋	θ)⋋	NUM
ejpam-5871	108	50	(	(	PUNCT
ejpam-5871	108	51	r1	r1	PROPN
ejpam-5871	108	52	)	)	PUNCT
ejpam-5871	108	53	+	+	NUM
ejpam-5871	108	54	θ	θ	NOUN
ejpam-5871	108	55	⋋	⋋	ADP
ejpam-5871	108	56	(	(	PUNCT
ejpam-5871	108	57	r2	r2	PROPN
ejpam-5871	108	58	)	)	PUNCT
ejpam-5871	108	59	)	)	PUNCT
ejpam-5871	108	60	)	)	PUNCT
ejpam-5871	109	1	⊇	⊇	NOUN
ejpam-5871	109	2	(	(	PUNCT
ejpam-5871	109	3	1−	1−	NUM
ejpam-5871	109	4	θ)∅(r1	θ)∅(r1	NOUN
ejpam-5871	109	5	)	)	PUNCT
ejpam-5871	109	6	+	+	CCONJ
ejpam-5871	109	7	θ∅(r2	θ∅(r2	NOUN
ejpam-5871	109	8	)	)	PUNCT
ejpam-5871	109	9	.	.	PUNCT
ejpam-5871	110	1	(	(	PUNCT
ejpam-5871	110	2	iii	iii	X
ejpam-5871	110	3	)	)	PUNCT
ejpam-5871	110	4	if	if	SCONJ
ejpam-5871	110	5	we	we	PRON
ejpam-5871	110	6	choose	choose	VERB
ejpam-5871	110	7	s	s	NOUN
ejpam-5871	110	8	=	=	NOUN
ejpam-5871	110	9	0	0	NUM
ejpam-5871	110	10	,	,	PUNCT
ejpam-5871	110	11	⋋(θ	⋋(θ	NUM
ejpam-5871	110	12	)	)	PUNCT
ejpam-5871	110	13	=	=	SYM
ejpam-5871	110	14	℧	℧	PROPN
ejpam-5871	110	15	(	(	PUNCT
ejpam-5871	110	16	θ	θ	NOUN
ejpam-5871	110	17	)	)	PUNCT
ejpam-5871	110	18	=	=	SYM
ejpam-5871	110	19	θ	θ	NOUN
ejpam-5871	110	20	and	and	CCONJ
ejpam-5871	110	21	⋋(x	⋋(x	NOUN
ejpam-5871	110	22	)	)	PUNCT
ejpam-5871	111	1	=	=	SYM
ejpam-5871	111	2	1	1	NUM
ejpam-5871	111	3	x	x	X
ejpam-5871	111	4	in	in	ADP
ejpam-5871	111	5	(	(	PUNCT
ejpam-5871	111	6	6	6	NUM
ejpam-5871	111	7	)	)	PUNCT
ejpam-5871	111	8	,	,	PUNCT
ejpam-5871	111	9	then	then	ADV
ejpam-5871	111	10	we	we	PRON
ejpam-5871	111	11	acquire	acquire	VERB
ejpam-5871	111	12	the	the	DET
ejpam-5871	111	13	ı.υ	ı.υ	PROPN
ejpam-5871	111	14	hc	hc	NOUN
ejpam-5871	111	15	function	function	NOUN
ejpam-5871	111	16	define	define	VERB
ejpam-5871	111	17	in	in	ADP
ejpam-5871	111	18	[	[	X
ejpam-5871	111	19	25	25	NUM
ejpam-5871	111	20	]	]	PUNCT
ejpam-5871	111	21	.	.	PUNCT
ejpam-5871	112	1	∅	∅	NOUN
ejpam-5871	112	2	(	(	PUNCT
ejpam-5871	112	3	r1r2	r1r2	VERB
ejpam-5871	112	4	θr1	θr1	X
ejpam-5871	112	5	+	+	CCONJ
ejpam-5871	112	6	(	(	PUNCT
ejpam-5871	112	7	1−	1−	NUM
ejpam-5871	112	8	θ)r2	θ)r2	ADJ
ejpam-5871	112	9	)	)	PUNCT
ejpam-5871	112	10	⊇	⊇	NOUN
ejpam-5871	112	11	(	(	PUNCT
ejpam-5871	112	12	1−	1−	NUM
ejpam-5871	112	13	θ)∅(r1	θ)∅(r1	NOUN
ejpam-5871	112	14	)	)	PUNCT
ejpam-5871	112	15	+	+	CCONJ
ejpam-5871	112	16	θ∅(r2	θ∅(r2	NOUN
ejpam-5871	112	17	)	)	PUNCT
ejpam-5871	112	18	.	.	PUNCT
ejpam-5871	113	1	(	(	PUNCT
ejpam-5871	113	2	iv	iv	X
ejpam-5871	113	3	)	)	PUNCT
ejpam-5871	113	4	if	if	SCONJ
ejpam-5871	113	5	we	we	PRON
ejpam-5871	113	6	choose	choose	VERB
ejpam-5871	113	7	s	s	NOUN
ejpam-5871	113	8	=	=	NOUN
ejpam-5871	113	9	0	0	NUM
ejpam-5871	113	10	,	,	PUNCT
ejpam-5871	113	11	⋋(θ	⋋(θ	NUM
ejpam-5871	113	12	)	)	PUNCT
ejpam-5871	113	13	=	=	SYM
ejpam-5871	113	14	℧	℧	PROPN
ejpam-5871	113	15	(	(	PUNCT
ejpam-5871	113	16	θ	θ	NOUN
ejpam-5871	113	17	)	)	PUNCT
ejpam-5871	113	18	=	=	SYM
ejpam-5871	113	19	θ	θ	NOUN
ejpam-5871	113	20	and	and	CCONJ
ejpam-5871	113	21	⋋(x	⋋(x	NOUN
ejpam-5871	113	22	)	)	PUNCT
ejpam-5871	114	1	=	=	PRON
ejpam-5871	114	2	xp	xp	INTJ
ejpam-5871	114	3	in	in	ADP
ejpam-5871	114	4	(	(	PUNCT
ejpam-5871	114	5	6	6	NUM
ejpam-5871	114	6	)	)	PUNCT
ejpam-5871	114	7	then	then	ADV
ejpam-5871	114	8	we	we	PRON
ejpam-5871	114	9	obtain	obtain	VERB
ejpam-5871	114	10	the	the	DET
ejpam-5871	114	11	ı.υ	ı.υ	PROPN
ejpam-5871	114	12	-	-	ADJ
ejpam-5871	114	13	p	p	NOUN
ejpam-5871	114	14	cf	cf	NOUN
ejpam-5871	114	15	define	define	NOUN
ejpam-5871	114	16	in	in	ADP
ejpam-5871	114	17	[	[	X
ejpam-5871	114	18	26	26	NUM
ejpam-5871	114	19	]	]	PUNCT
ejpam-5871	114	20	.	.	PUNCT
ejpam-5871	115	1	∅	∅	NOUN
ejpam-5871	115	2	(	(	PUNCT
ejpam-5871	115	3	(	(	PUNCT
ejpam-5871	115	4	(	(	PUNCT
ejpam-5871	115	5	1−	1−	NUM
ejpam-5871	115	6	θ)rp1	θ)rp1	NOUN
ejpam-5871	115	7	+	+	CCONJ
ejpam-5871	115	8	θrp2	θrp2	NOUN
ejpam-5871	115	9	)	)	PUNCT
ejpam-5871	115	10	1	1	NUM
ejpam-5871	115	11	p	p	NOUN
ejpam-5871	115	12	)	)	PUNCT
ejpam-5871	115	13	⊇	⊇	NOUN
ejpam-5871	115	14	(	(	PUNCT
ejpam-5871	115	15	1−	1−	NUM
ejpam-5871	115	16	θ)∅(r1	θ)∅(r1	NOUN
ejpam-5871	115	17	)	)	PUNCT
ejpam-5871	115	18	+	+	CCONJ
ejpam-5871	115	19	θ∅(r2	θ∅(r2	NOUN
ejpam-5871	115	20	)	)	PUNCT
ejpam-5871	115	21	.	.	PUNCT
ejpam-5871	116	1	(	(	PUNCT
ejpam-5871	116	2	v	v	NOUN
ejpam-5871	116	3	)	)	PUNCT
ejpam-5871	116	4	by	by	ADP
ejpam-5871	116	5	selecting	select	VERB
ejpam-5871	116	6	s	s	PART
ejpam-5871	116	7	=	=	NOUN
ejpam-5871	116	8	0	0	NUM
ejpam-5871	116	9	,	,	PUNCT
ejpam-5871	116	10	⋋(θ	⋋(θ	NUM
ejpam-5871	116	11	)	)	PUNCT
ejpam-5871	116	12	=	=	SYM
ejpam-5871	116	13	θ	θ	NOUN
ejpam-5871	116	14	and	and	CCONJ
ejpam-5871	116	15	⋋(x	⋋(x	NOUN
ejpam-5871	116	16	)	)	PUNCT
ejpam-5871	117	1	=	=	SYM
ejpam-5871	117	2	x	x	X
ejpam-5871	117	3	in	in	ADP
ejpam-5871	117	4	(	(	PUNCT
ejpam-5871	117	5	6	6	NUM
ejpam-5871	117	6	)	)	PUNCT
ejpam-5871	117	7	,	,	PUNCT
ejpam-5871	117	8	we	we	PRON
ejpam-5871	117	9	retrieve	retrieve	VERB
ejpam-5871	117	10	the	the	DET
ejpam-5871	117	11	definition	definition	NOUN
ejpam-5871	117	12	of	of	ADP
ejpam-5871	117	13	ı.υ	ı.υ	PROPN
ejpam-5871	117	14	cf	cf	NOUN
ejpam-5871	117	15	presented	present	VERB
ejpam-5871	117	16	in	in	ADP
ejpam-5871	117	17	[	[	X
ejpam-5871	117	18	24	24	NUM
ejpam-5871	117	19	]	]	PUNCT
ejpam-5871	117	20	.	.	PUNCT
ejpam-5871	118	1	definition	definition	NOUN
ejpam-5871	118	2	7	7	NUM
ejpam-5871	118	3	.	.	PUNCT
ejpam-5871	119	1	if	if	SCONJ
ejpam-5871	119	2	we	we	PRON
ejpam-5871	119	3	fix	fix	VERB
ejpam-5871	119	4	s	s	NOUN
ejpam-5871	119	5	=	=	NOUN
ejpam-5871	119	6	0	0	NUM
ejpam-5871	119	7	,	,	PUNCT
ejpam-5871	119	8	⋋(θ	⋋(θ	NUM
ejpam-5871	119	9	)	)	PUNCT
ejpam-5871	119	10	=	=	SYM
ejpam-5871	119	11	θ	θ	PROPN
ejpam-5871	119	12	and	and	CCONJ
ejpam-5871	119	13	℧	℧	PROPN
ejpam-5871	119	14	(	(	PUNCT
ejpam-5871	119	15	θ	θ	NOUN
ejpam-5871	119	16	)	)	PUNCT
ejpam-5871	120	1	=	=	SYM
ejpam-5871	120	2	θs	θs	PRON
ejpam-5871	120	3	in	in	ADP
ejpam-5871	120	4	(	(	PUNCT
ejpam-5871	120	5	6	6	NUM
ejpam-5871	120	6	)	)	PUNCT
ejpam-5871	120	7	,	,	PUNCT
ejpam-5871	120	8	we	we	PRON
ejpam-5871	120	9	retrieve	retrieve	VERB
ejpam-5871	120	10	the	the	DET
ejpam-5871	120	11	(	(	PUNCT
ejpam-5871	120	12	⋋	⋋	ADP
ejpam-5871	120	13	,	,	PUNCT
ejpam-5871	120	14	s)-ı.υ	s)-ı.υ	X
ejpam-5871	120	15	cf	cf	NOUN
ejpam-5871	120	16	∅	∅	NOUN
ejpam-5871	120	17	(	(	PUNCT
ejpam-5871	120	18	⋋−1	⋋−1	X
ejpam-5871	120	19	(	(	PUNCT
ejpam-5871	120	20	θ	θ	X
ejpam-5871	120	21	⋋	⋋	NUM
ejpam-5871	120	22	(	(	PUNCT
ejpam-5871	120	23	r1	r1	PROPN
ejpam-5871	120	24	)	)	PUNCT
ejpam-5871	120	25	+	+	CCONJ
ejpam-5871	120	26	(	(	PUNCT
ejpam-5871	120	27	1−	1−	NUM
ejpam-5871	120	28	θ)⋋	θ)⋋	NUM
ejpam-5871	120	29	(	(	PUNCT
ejpam-5871	120	30	r2	r2	PROPN
ejpam-5871	120	31	)	)	PUNCT
ejpam-5871	120	32	)	)	PUNCT
ejpam-5871	120	33	)	)	PUNCT
ejpam-5871	121	1	⊇	⊇	NOUN
ejpam-5871	121	2	(	(	PUNCT
ejpam-5871	121	3	1−	1−	NUM
ejpam-5871	121	4	θ)s∅(r1	θ)s∅(r1	PROPN
ejpam-5871	121	5	)	)	PUNCT
ejpam-5871	121	6	+	+	NUM
ejpam-5871	121	7	θs∅(r2	θs∅(r2	NUM
ejpam-5871	121	8	)	)	PUNCT
ejpam-5871	121	9	.	.	PUNCT
ejpam-5871	122	1	remark	remark	NOUN
ejpam-5871	122	2	2	2	NUM
ejpam-5871	122	3	.	.	PUNCT
ejpam-5871	123	1	the	the	DET
ejpam-5871	123	2	main	main	ADJ
ejpam-5871	123	3	definitional	definitional	ADJ
ejpam-5871	123	4	deductions	deduction	NOUN
ejpam-5871	123	5	will	will	AUX
ejpam-5871	123	6	now	now	ADV
ejpam-5871	123	7	be	be	AUX
ejpam-5871	123	8	presented	present	VERB
ejpam-5871	123	9	for	for	ADP
ejpam-5871	123	10	definition	definition	NOUN
ejpam-5871	123	11	7	7	NUM
ejpam-5871	123	12	,	,	PUNCT
ejpam-5871	123	13	presented	present	VERB
ejpam-5871	123	14	in	in	ADP
ejpam-5871	123	15	[	[	X
ejpam-5871	123	16	24	24	NUM
ejpam-5871	123	17	]	]	PUNCT
ejpam-5871	123	18	.	.	PUNCT
ejpam-5871	124	1	(	(	PUNCT
ejpam-5871	124	2	i	i	NOUN
ejpam-5871	124	3	)	)	PUNCT
ejpam-5871	124	4	choosing	choose	VERB
ejpam-5871	124	5	⋋(x	⋋(x	NOUN
ejpam-5871	124	6	)	)	PUNCT
ejpam-5871	125	1	=	=	SYM
ejpam-5871	125	2	1	1	NUM
ejpam-5871	125	3	x	x	X
ejpam-5871	125	4	,	,	PUNCT
ejpam-5871	125	5	we	we	PRON
ejpam-5871	125	6	retrieve	retrieve	VERB
ejpam-5871	125	7	the	the	DET
ejpam-5871	125	8	ı.υ	ı.υ	PROPN
ejpam-5871	125	9	harmonically	harmonically	ADV
ejpam-5871	125	10	s−	s−	PROPN
ejpam-5871	125	11	cf	cf	NOUN
ejpam-5871	125	12	,	,	PUNCT
ejpam-5871	125	13	that	that	ADV
ejpam-5871	125	14	is	is	ADV
ejpam-5871	125	15	∅	∅	NOUN
ejpam-5871	125	16	(	(	PUNCT
ejpam-5871	125	17	r1r2	r1r2	VERB
ejpam-5871	125	18	θr1	θr1	X
ejpam-5871	125	19	+	+	CCONJ
ejpam-5871	125	20	(	(	PUNCT
ejpam-5871	125	21	1−	1−	NUM
ejpam-5871	125	22	θ)r2	θ)r2	ADJ
ejpam-5871	125	23	)	)	PUNCT
ejpam-5871	125	24	⊇	⊇	NOUN
ejpam-5871	125	25	(	(	PUNCT
ejpam-5871	125	26	1−	1−	NUM
ejpam-5871	125	27	θ)s∅(r1	θ)s∅(r1	PROPN
ejpam-5871	125	28	)	)	PUNCT
ejpam-5871	126	1	+	+	NUM
ejpam-5871	126	2	θs∅(r2	θs∅(r2	NUM
ejpam-5871	126	3	)	)	PUNCT
ejpam-5871	126	4	.	.	PUNCT
ejpam-5871	127	1	(	(	PUNCT
ejpam-5871	127	2	ii	ii	NOUN
ejpam-5871	127	3	)	)	PUNCT
ejpam-5871	127	4	choosing	choose	VERB
ejpam-5871	127	5	⋋(x	⋋(x	NOUN
ejpam-5871	127	6	)	)	PUNCT
ejpam-5871	128	1	=	=	SYM
ejpam-5871	128	2	xp	xp	PROPN
ejpam-5871	128	3	,	,	PUNCT
ejpam-5871	128	4	p	p	PRON
ejpam-5871	128	5	≥	≥	NOUN
ejpam-5871	128	6	−1	−1	NOUN
ejpam-5871	128	7	,	,	PUNCT
ejpam-5871	128	8	we	we	PRON
ejpam-5871	128	9	retrieve	retrieve	VERB
ejpam-5871	128	10	the	the	DET
ejpam-5871	128	11	ı.υ	ı.υ	PROPN
ejpam-5871	128	12	-	-	PUNCT
ejpam-5871	128	13	p	p	PROPN
ejpam-5871	128	14	,	,	PUNCT
ejpam-5871	128	15	s−	s−	PROPN
ejpam-5871	128	16	cf	cf	NOUN
ejpam-5871	128	17	,	,	PUNCT
ejpam-5871	128	18	which	which	PRON
ejpam-5871	128	19	are	be	AUX
ejpam-5871	128	20	as	as	SCONJ
ejpam-5871	128	21	follows	follow	VERB
ejpam-5871	128	22	:	:	PUNCT
ejpam-5871	128	23	∅	∅	NOUN
ejpam-5871	128	24	(	(	PUNCT
ejpam-5871	128	25	(	(	PUNCT
ejpam-5871	128	26	(	(	PUNCT
ejpam-5871	128	27	1−	1−	NUM
ejpam-5871	128	28	θ)rp1	θ)rp1	NOUN
ejpam-5871	128	29	+	+	CCONJ
ejpam-5871	128	30	θrp2	θrp2	NOUN
ejpam-5871	128	31	)	)	PUNCT
ejpam-5871	128	32	1	1	NUM
ejpam-5871	128	33	p	p	NOUN
ejpam-5871	128	34	)	)	PUNCT
ejpam-5871	128	35	⊇	⊇	NOUN
ejpam-5871	128	36	(	(	PUNCT
ejpam-5871	128	37	1−	1−	NUM
ejpam-5871	128	38	θ)s∅(r1	θ)s∅(r1	PROPN
ejpam-5871	128	39	)	)	PUNCT
ejpam-5871	128	40	+	+	NUM
ejpam-5871	128	41	θs∅(r2	θs∅(r2	NUM
ejpam-5871	128	42	)	)	PUNCT
ejpam-5871	128	43	.	.	PUNCT
ejpam-5871	129	1	the	the	DET
ejpam-5871	129	2	authors	author	NOUN
ejpam-5871	129	3	in	in	ADP
ejpam-5871	129	4	[	[	X
ejpam-5871	129	5	27	27	NUM
ejpam-5871	129	6	]	]	PUNCT
ejpam-5871	129	7	used	use	VERB
ejpam-5871	129	8	ı.υ	ı.υ	PROPN
ejpam-5871	129	9	cf	cf	NOUN
ejpam-5871	129	10	and	and	CCONJ
ejpam-5871	129	11	postquantum	postquantum	NOUN
ejpam-5871	129	12	calculus	calculus	NOUN
ejpam-5871	129	13	to	to	PART
ejpam-5871	129	14	investigate	investigate	VERB
ejpam-5871	129	15	novel	novel	ADJ
ejpam-5871	129	16	representations	representation	NOUN
ejpam-5871	129	17	of	of	ADP
ejpam-5871	129	18	well	well	ADV
ejpam-5871	129	19	-	-	PUNCT
ejpam-5871	129	20	known	know	VERB
ejpam-5871	129	21	results	result	NOUN
ejpam-5871	129	22	.	.	PUNCT
ejpam-5871	130	1	in	in	ADP
ejpam-5871	130	2	[	[	X
ejpam-5871	130	3	28	28	NUM
ejpam-5871	130	4	]	]	PUNCT
ejpam-5871	130	5	,	,	PUNCT
ejpam-5871	130	6	different	different	ADJ
ejpam-5871	130	7	forms	form	NOUN
ejpam-5871	130	8	of	of	ADP
ejpam-5871	130	9	trapezoid	trapezoid	ADJ
ejpam-5871	130	10	-	-	PUNCT
ejpam-5871	130	11	type	type	NOUN
ejpam-5871	130	12	inequalities	inequality	NOUN
ejpam-5871	130	13	for	for	ADP
ejpam-5871	130	14	non	non	ADJ
ejpam-5871	130	15	-	-	ADJ
ejpam-5871	130	16	cf	cf	ADJ
ejpam-5871	130	17	linked	link	VERB
ejpam-5871	130	18	sets	set	NOUN
ejpam-5871	130	19	on	on	ADP
ejpam-5871	130	20	fuzzy	fuzzy	ADJ
ejpam-5871	130	21	domains	domain	NOUN
ejpam-5871	130	22	were	be	AUX
ejpam-5871	130	23	introduced	introduce	VERB
ejpam-5871	130	24	.	.	PUNCT
ejpam-5871	131	1	a	a	DET
ejpam-5871	131	2	generic	generic	ADJ
ejpam-5871	131	3	convexity	convexity	NOUN
ejpam-5871	131	4	framework	framework	NOUN
ejpam-5871	131	5	was	be	AUX
ejpam-5871	131	6	used	use	VERB
ejpam-5871	131	7	by	by	ADP
ejpam-5871	131	8	cortez	cortez	PROPN
ejpam-5871	131	9	et	et	PROPN
ejpam-5871	131	10	al	al	PROPN
ejpam-5871	131	11	.	.	PUNCT
ejpam-5871	132	1	[	[	X
ejpam-5871	132	2	29	29	NUM
ejpam-5871	132	3	]	]	PUNCT
ejpam-5871	132	4	to	to	PART
ejpam-5871	132	5	expand	expand	VERB
ejpam-5871	132	6	jensen	jensen	PROPN
ejpam-5871	132	7	’s	’s	PART
ejpam-5871	132	8	and	and	CCONJ
ejpam-5871	132	9	hermite	hermite	ADJ
ejpam-5871	132	10	-	-	PUNCT
ejpam-5871	132	11	hadamard	hadamard	ADJ
ejpam-5871	132	12	inequalities	inequality	NOUN
ejpam-5871	132	13	.	.	PUNCT
ejpam-5871	133	1	inspired	inspire	VERB
ejpam-5871	133	2	by	by	ADP
ejpam-5871	133	3	these	these	DET
ejpam-5871	133	4	investigations	investigation	NOUN
ejpam-5871	133	5	,	,	PUNCT
ejpam-5871	133	6	we	we	PRON
ejpam-5871	133	7	provide	provide	VERB
ejpam-5871	133	8	ı.υ	ı.υ	PROPN
ejpam-5871	133	9	(	(	PUNCT
ejpam-5871	133	10	⋋s+1,	⋋s+1,	NOUN
ejpam-5871	133	11	℧	℧	SYM
ejpam-5871	133	12	)-cf	)-cf	NUM
ejpam-5871	133	13	,	,	PUNCT
ejpam-5871	133	14	defined	define	VERB
ejpam-5871	133	15	by	by	ADP
ejpam-5871	133	16	weighted	weight	VERB
ejpam-5871	133	17	arithmetic	arithmetic	ADJ
ejpam-5871	133	18	means	mean	NOUN
ejpam-5871	133	19	,	,	PUNCT
ejpam-5871	133	20	which	which	PRON
ejpam-5871	133	21	have	have	VERB
ejpam-5871	133	22	a	a	DET
ejpam-5871	133	23	strictly	strictly	ADV
ejpam-5871	133	24	monotone	monotone	ADJ
ejpam-5871	133	25	function	function	NOUN
ejpam-5871	133	26	⋋	⋋	PUNCT
ejpam-5871	133	27	and	and	CCONJ
ejpam-5871	133	28	a	a	DET
ejpam-5871	133	29	non	non	ADJ
ejpam-5871	133	30	-	-	ADJ
ejpam-5871	133	31	negative	negative	ADJ
ejpam-5871	133	32	function	function	NOUN
ejpam-5871	133	33	℧	℧	PROPN
ejpam-5871	133	34	.	.	PUNCT
ejpam-5871	134	1	using	use	VERB
ejpam-5871	134	2	a.	a.	PROPN
ejpam-5871	134	3	mehmood	mehmood	PROPN
ejpam-5871	134	4	et	et	PROPN
ejpam-5871	134	5	al	al	PROPN
ejpam-5871	134	6	.	.	PUNCT
ejpam-5871	134	7	/	/	SYM
ejpam-5871	134	8	eur	eur	PROPN
ejpam-5871	134	9	.	.	PUNCT
ejpam-5871	135	1	j.	j.	PROPN
ejpam-5871	135	2	pure	pure	PROPN
ejpam-5871	135	3	appl	appl	PROPN
ejpam-5871	135	4	.	.	PROPN
ejpam-5871	135	5	math	math	PROPN
ejpam-5871	135	6	,	,	PUNCT
ejpam-5871	135	7	18	18	NUM
ejpam-5871	135	8	(	(	PUNCT
ejpam-5871	135	9	2	2	NUM
ejpam-5871	135	10	)	)	PUNCT
ejpam-5871	135	11	(	(	PUNCT
ejpam-5871	135	12	2025	2025	NUM
ejpam-5871	135	13	)	)	PUNCT
ejpam-5871	135	14	,	,	PUNCT
ejpam-5871	135	15	5871	5871	NUM
ejpam-5871	135	16	6	6	NUM
ejpam-5871	135	17	of	of	ADP
ejpam-5871	135	18	26	26	NUM
ejpam-5871	135	19	suitable	suitable	ADJ
ejpam-5871	135	20	replacements	replacement	NOUN
ejpam-5871	135	21	for	for	ADP
ejpam-5871	135	22	⋋	⋋	PRON
ejpam-5871	135	23	and	and	CCONJ
ejpam-5871	135	24	℧	℧	ADP
ejpam-5871	136	1	,	,	PUNCT
ejpam-5871	136	2	this	this	DET
ejpam-5871	136	3	framework	framework	NOUN
ejpam-5871	136	4	creates	create	VERB
ejpam-5871	136	5	new	new	ADJ
ejpam-5871	136	6	classes	class	NOUN
ejpam-5871	136	7	and	and	CCONJ
ejpam-5871	136	8	unifies	unify	VERB
ejpam-5871	136	9	current	current	ADJ
ejpam-5871	136	10	convexity	convexity	NOUN
ejpam-5871	136	11	notions	notion	NOUN
ejpam-5871	136	12	.	.	PUNCT
ejpam-5871	137	1	in	in	ADP
ejpam-5871	137	2	addition	addition	NOUN
ejpam-5871	137	3	to	to	ADP
ejpam-5871	137	4	inequalities	inequality	NOUN
ejpam-5871	137	5	for	for	ADP
ejpam-5871	137	6	function	function	NOUN
ejpam-5871	137	7	products	product	NOUN
ejpam-5871	137	8	of	of	ADP
ejpam-5871	137	9	the	the	DET
ejpam-5871	137	10	pachpatte	pachpatte	NOUN
ejpam-5871	137	11	type	type	NOUN
ejpam-5871	137	12	,	,	PUNCT
ejpam-5871	137	13	we	we	PRON
ejpam-5871	137	14	derive	derive	VERB
ejpam-5871	137	15	several	several	ADJ
ejpam-5871	137	16	inequalities	inequality	NOUN
ejpam-5871	137	17	,	,	PUNCT
ejpam-5871	137	18	such	such	ADJ
ejpam-5871	137	19	as	as	ADP
ejpam-5871	137	20	minkowski	minkowski	ADJ
ejpam-5871	137	21	,	,	PUNCT
ejpam-5871	137	22	holder	holder	NOUN
ejpam-5871	137	23	’s	’s	PART
ejpam-5871	137	24	,	,	PUNCT
ejpam-5871	137	25	hermite	hermite	PROPN
ejpam-5871	137	26	-	-	PUNCT
ejpam-5871	137	27	hadamard	hadamard	ADJ
ejpam-5871	137	28	,	,	PUNCT
ejpam-5871	137	29	and	and	CCONJ
ejpam-5871	137	30	hermite	hermite	ADJ
ejpam-5871	137	31	-	-	PUNCT
ejpam-5871	137	32	hadamard	hadamard	NOUN
ejpam-5871	137	33	-	-	PUNCT
ejpam-5871	137	34	fejer	fejer	NOUN
ejpam-5871	137	35	.	.	PUNCT
ejpam-5871	138	1	the	the	DET
ejpam-5871	138	2	scope	scope	NOUN
ejpam-5871	138	3	of	of	ADP
ejpam-5871	138	4	convex	convex	PROPN
ejpam-5871	138	5	and	and	CCONJ
ejpam-5871	138	6	non	non	ADJ
ejpam-5871	138	7	-	-	ADJ
ejpam-5871	138	8	cf	cf	ADJ
ejpam-5871	138	9	analysis	analysis	NOUN
ejpam-5871	138	10	is	be	AUX
ejpam-5871	138	11	expanded	expand	VERB
ejpam-5871	138	12	by	by	ADP
ejpam-5871	138	13	this	this	DET
ejpam-5871	138	14	generalized	generalize	VERB
ejpam-5871	138	15	convexity	convexity	NOUN
ejpam-5871	138	16	framework	framework	NOUN
ejpam-5871	138	17	,	,	PUNCT
ejpam-5871	138	18	which	which	PRON
ejpam-5871	138	19	offers	offer	VERB
ejpam-5871	138	20	methods	method	NOUN
ejpam-5871	138	21	for	for	ADP
ejpam-5871	138	22	bounding	bound	VERB
ejpam-5871	138	23	ı.υ	ı.υ	PROPN
ejpam-5871	138	24	riemann	riemann	PROPN
ejpam-5871	138	25	-	-	PUNCT
ejpam-5871	138	26	liouville	liouville	VERB
ejpam-5871	138	27	fractional	fractional	ADJ
ejpam-5871	138	28	operators	operator	NOUN
ejpam-5871	138	29	.	.	PUNCT
ejpam-5871	139	1	our	our	PRON
ejpam-5871	139	2	results	result	NOUN
ejpam-5871	139	3	are	be	AUX
ejpam-5871	139	4	supported	support	VERB
ejpam-5871	139	5	by	by	ADP
ejpam-5871	139	6	numerical	numerical	ADJ
ejpam-5871	139	7	examples	example	NOUN
ejpam-5871	139	8	and	and	CCONJ
ejpam-5871	139	9	simulations	simulation	NOUN
ejpam-5871	139	10	,	,	PUNCT
ejpam-5871	139	11	providing	provide	VERB
ejpam-5871	139	12	a	a	DET
ejpam-5871	139	13	basis	basis	NOUN
ejpam-5871	139	14	for	for	ADP
ejpam-5871	139	15	more	more	ADJ
ejpam-5871	139	16	inequality	inequality	NOUN
ejpam-5871	139	17	proofs	proof	NOUN
ejpam-5871	139	18	and	and	CCONJ
ejpam-5871	139	19	optimization	optimization	NOUN
ejpam-5871	139	20	problems	problem	NOUN
ejpam-5871	139	21	.	.	PUNCT
ejpam-5871	140	1	theorem	theorem	NOUN
ejpam-5871	140	2	2	2	NUM
ejpam-5871	140	3	.	.	PUNCT
ejpam-5871	141	1	[	[	X
ejpam-5871	141	2	24	24	NUM
ejpam-5871	141	3	]	]	PUNCT
ejpam-5871	141	4	let	let	VERB
ejpam-5871	141	5	∅	∅	NOUN
ejpam-5871	141	6	:	:	PUNCT
ejpam-5871	142	1	[	[	X
ejpam-5871	142	2	r1	r1	NOUN
ejpam-5871	142	3	,	,	PUNCT
ejpam-5871	142	4	r2	r2	PROPN
ejpam-5871	142	5	]	]	PUNCT
ejpam-5871	142	6	→	→	SYM
ejpam-5871	142	7	r+	r+	PUNCT
ejpam-5871	142	8	i	i	PRON
ejpam-5871	142	9	be	be	VERB
ejpam-5871	142	10	ı.υ	ı.υ	PROPN
ejpam-5871	142	11	function	function	NOUN
ejpam-5871	142	12	such	such	ADJ
ejpam-5871	142	13	that	that	DET
ejpam-5871	142	14	∅(r1	∅(r1	NOUN
ejpam-5871	142	15	)	)	PUNCT
ejpam-5871	142	16	=	=	PUNCT
ejpam-5871	143	1	[	[	X
ejpam-5871	143	2	∅∗,∅∗	∅∗,∅∗	X
ejpam-5871	143	3	]	]	PUNCT
ejpam-5871	143	4	with	with	ADP
ejpam-5871	143	5	∅∗	∅∗	PROPN
ejpam-5871	143	6	≤	≤	PROPN
ejpam-5871	143	7	∅∗	∅∗	PROPN
ejpam-5871	143	8	then	then	ADV
ejpam-5871	143	9	,	,	PUNCT
ejpam-5871	143	10	∅	∅	NOUN
ejpam-5871	143	11	∈	∈	PROPN
ejpam-5871	143	12	sigx([r1	sigx([r1	NOUN
ejpam-5871	143	13	,	,	PUNCT
ejpam-5871	143	14	r2	r2	PROPN
ejpam-5871	143	15	]	]	PUNCT
ejpam-5871	143	16	,	,	PUNCT
ejpam-5871	143	17	r	r	NOUN
ejpam-5871	144	1	+	+	PROPN
ejpam-5871	144	2	i	i	NOUN
ejpam-5871	144	3	)	)	PUNCT
ejpam-5871	144	4	,	,	PUNCT
ejpam-5871	144	5	this	this	PRON
ejpam-5871	144	6	implies	imply	VERB
ejpam-5871	144	7	∅∗	∅∗	PROPN
ejpam-5871	144	8	∈	∈	PROPN
ejpam-5871	144	9	sgx([r1	sgx([r1	NOUN
ejpam-5871	144	10	,	,	PUNCT
ejpam-5871	144	11	r2	r2	PROPN
ejpam-5871	144	12	]	]	PUNCT
ejpam-5871	144	13	,	,	PUNCT
ejpam-5871	144	14	r	r	NOUN
ejpam-5871	144	15	)	)	PUNCT
ejpam-5871	144	16	and	and	CCONJ
ejpam-5871	144	17	∅∗	∅∗	PROPN
ejpam-5871	144	18	∈	∈	PROPN
ejpam-5871	144	19	sgv	sgv	NOUN
ejpam-5871	144	20	(	(	PUNCT
ejpam-5871	144	21	[	[	X
ejpam-5871	144	22	r1	r1	NOUN
ejpam-5871	144	23	,	,	PUNCT
ejpam-5871	144	24	r2	r2	PROPN
ejpam-5871	144	25	]	]	PUNCT
ejpam-5871	144	26	,	,	PUNCT
ejpam-5871	144	27	r	r	NOUN
ejpam-5871	144	28	)	)	PUNCT
ejpam-5871	144	29	.	.	PUNCT
ejpam-5871	145	1	theorem	theorem	NOUN
ejpam-5871	145	2	3	3	NUM
ejpam-5871	145	3	.	.	PUNCT
ejpam-5871	146	1	[	[	X
ejpam-5871	146	2	24	24	NUM
ejpam-5871	146	3	]	]	PUNCT
ejpam-5871	146	4	let	let	VERB
ejpam-5871	146	5	∅	∅	NOUN
ejpam-5871	146	6	∈	∈	PROPN
ejpam-5871	146	7	sigx([r1	sigx([r1	PROPN
ejpam-5871	146	8	,	,	PUNCT
ejpam-5871	146	9	r2	r2	PROPN
ejpam-5871	146	10	]	]	PUNCT
ejpam-5871	146	11	,	,	PUNCT
ejpam-5871	146	12	r	r	NOUN
ejpam-5871	146	13	+	+	PROPN
ejpam-5871	146	14	i	i	NOUN
ejpam-5871	146	15	)	)	PUNCT
ejpam-5871	146	16	,	,	PUNCT
ejpam-5871	146	17	then	then	ADV
ejpam-5871	146	18	∅	∅	NOUN
ejpam-5871	146	19	(	(	PUNCT
ejpam-5871	146	20	⋋−1	⋋−1	ADJ
ejpam-5871	146	21	(	(	PUNCT
ejpam-5871	146	22	1	1	NUM
ejpam-5871	146	23	wn	wn	PROPN
ejpam-5871	146	24	n∑	n∑	PROPN
ejpam-5871	146	25	i=1	i=1	PROPN
ejpam-5871	146	26	θi	θi	ADP
ejpam-5871	146	27	⋋	⋋	NUM
ejpam-5871	146	28	(	(	PUNCT
ejpam-5871	146	29	xi	xi	NOUN
ejpam-5871	146	30	)	)	PUNCT
ejpam-5871	146	31	)	)	PUNCT
ejpam-5871	146	32	)	)	PUNCT
ejpam-5871	146	33	⊇	⊇	PROPN
ejpam-5871	146	34	n∑	n∑	PROPN
ejpam-5871	146	35	i=1	i=1	PROPN
ejpam-5871	147	1	℧	℧	PROPN
ejpam-5871	147	2	(	(	PUNCT
ejpam-5871	147	3	θi	θi	PROPN
ejpam-5871	147	4	wn	wn	PROPN
ejpam-5871	147	5	)	)	PUNCT
ejpam-5871	147	6	∅(xi	∅(xi	PROPN
ejpam-5871	147	7	)	)	PUNCT
ejpam-5871	147	8	for	for	ADP
ejpam-5871	147	9	xi	xi	PROPN
ejpam-5871	147	10	∈	∈	PROPN
ejpam-5871	148	1	[	[	X
ejpam-5871	148	2	r1	r1	NOUN
ejpam-5871	148	3	,	,	PUNCT
ejpam-5871	148	4	r2	r2	PROPN
ejpam-5871	148	5	]	]	PUNCT
ejpam-5871	148	6	and	and	CCONJ
ejpam-5871	148	7	wn	wn	X
ejpam-5871	148	8	=	=	SYM
ejpam-5871	148	9	∑n	∑n	PROPN
ejpam-5871	148	10	i=1	i=1	NOUN
ejpam-5871	148	11	θixi	θixi	ADJ
ejpam-5871	148	12	.	.	PUNCT
ejpam-5871	149	1	definition	definition	NOUN
ejpam-5871	149	2	8	8	NUM
ejpam-5871	149	3	.	.	PUNCT
ejpam-5871	150	1	[	[	X
ejpam-5871	150	2	30	30	NUM
ejpam-5871	150	3	]	]	X
ejpam-5871	150	4	if	if	SCONJ
ejpam-5871	150	5	a	a	DET
ejpam-5871	150	6	function	function	NOUN
ejpam-5871	150	7	∅	∅	NOUN
ejpam-5871	150	8	is	be	AUX
ejpam-5871	150	9	continuous	continuous	ADJ
ejpam-5871	150	10	on	on	ADP
ejpam-5871	150	11	[	[	X
ejpam-5871	150	12	a	a	X
ejpam-5871	150	13	,	,	PUNCT
ejpam-5871	150	14	b	b	NOUN
ejpam-5871	150	15	]	]	PUNCT
ejpam-5871	150	16	,	,	PUNCT
ejpam-5871	150	17	s	s	PROPN
ejpam-5871	150	18	∈	∈	PROPN
ejpam-5871	150	19	r/{−1	r/{−1	PROPN
ejpam-5871	150	20	}	}	PUNCT
ejpam-5871	150	21	and	and	CCONJ
ejpam-5871	150	22	k	k	PROPN
ejpam-5871	150	23	≥	≥	PROPN
ejpam-5871	150	24	0	0	NUM
ejpam-5871	150	25	,	,	PUNCT
ejpam-5871	150	26	then	then	ADV
ejpam-5871	150	27	the	the	DET
ejpam-5871	150	28	(	(	PUNCT
ejpam-5871	150	29	k	k	NOUN
ejpam-5871	150	30	,	,	PUNCT
ejpam-5871	150	31	s)-riemann	s)-riemann	NOUN
ejpam-5871	150	32	-	-	PUNCT
ejpam-5871	150	33	liouville	liouville	VERB
ejpam-5871	150	34	fractional	fractional	ADJ
ejpam-5871	150	35	integral	integral	ADJ
ejpam-5871	150	36	operator	operator	NOUN
ejpam-5871	150	37	for	for	ADP
ejpam-5871	150	38	order	order	NOUN
ejpam-5871	150	39	β	β	X
ejpam-5871	150	40	>	>	X
ejpam-5871	150	41	0	0	NUM
ejpam-5871	150	42	can	can	AUX
ejpam-5871	150	43	be	be	AUX
ejpam-5871	150	44	stated	state	VERB
ejpam-5871	150	45	as	as	ADP
ejpam-5871	150	46	s	s	PROPN
ejpam-5871	150	47	kz	kz	PROPN
ejpam-5871	150	48	β	β	X
ejpam-5871	150	49	α+∅(m1	α+∅(m1	NOUN
ejpam-5871	150	50	)	)	PUNCT
ejpam-5871	150	51	=	=	SYM
ejpam-5871	151	1	(	(	PUNCT
ejpam-5871	151	2	s+	s+	NUM
ejpam-5871	151	3	1)1−	1)1−	PROPN
ejpam-5871	151	4	β	β	X
ejpam-5871	151	5	k	k	PROPN
ejpam-5871	151	6	kγk(β	kγk(β	PROPN
ejpam-5871	151	7	)	)	PUNCT
ejpam-5871	151	8	∫	∫	PROPN
ejpam-5871	151	9	m1	m1	PROPN
ejpam-5871	151	10	α+	α+	PRON
ejpam-5871	151	11	(	(	PUNCT
ejpam-5871	151	12	ms+1	ms+1	NOUN
ejpam-5871	151	13	1	1	NUM
ejpam-5871	151	14	−	−	NOUN
ejpam-5871	151	15	ns+1	ns+1	PROPN
ejpam-5871	151	16	1	1	NUM
ejpam-5871	151	17	)	)	PUNCT
ejpam-5871	151	18	β	β	X
ejpam-5871	151	19	k	k	X
ejpam-5871	151	20	−1ns	−1ns	PROPN
ejpam-5871	151	21	1∅(n1)dn1	1∅(n1)dn1	NUM
ejpam-5871	151	22	.	.	PUNCT
ejpam-5871	152	1	(	(	PUNCT
ejpam-5871	152	2	1	1	X
ejpam-5871	152	3	)	)	PUNCT
ejpam-5871	152	4	now	now	ADV
ejpam-5871	152	5	we	we	PRON
ejpam-5871	152	6	are	be	AUX
ejpam-5871	152	7	going	go	VERB
ejpam-5871	152	8	to	to	PART
ejpam-5871	152	9	present	present	VERB
ejpam-5871	152	10	generalized	generalized	ADJ
ejpam-5871	152	11	form	form	NOUN
ejpam-5871	152	12	of	of	ADP
ejpam-5871	152	13	fractional	fractional	ADJ
ejpam-5871	152	14	operator	operator	NOUN
ejpam-5871	152	15	(	(	PUNCT
ejpam-5871	152	16	1	1	NUM
ejpam-5871	152	17	)	)	PUNCT
ejpam-5871	152	18	.	.	PUNCT
ejpam-5871	153	1	definition	definition	NOUN
ejpam-5871	153	2	9	9	NUM
ejpam-5871	153	3	.	.	PUNCT
ejpam-5871	154	1	if	if	SCONJ
ejpam-5871	154	2	a	a	DET
ejpam-5871	154	3	function	function	NOUN
ejpam-5871	154	4	∅	∅	NOUN
ejpam-5871	154	5	is	be	AUX
ejpam-5871	154	6	continuous	continuous	ADJ
ejpam-5871	154	7	on	on	ADP
ejpam-5871	154	8	[	[	X
ejpam-5871	154	9	a	a	X
ejpam-5871	154	10	,	,	PUNCT
ejpam-5871	154	11	b	b	NOUN
ejpam-5871	154	12	]	]	PUNCT
ejpam-5871	154	13	,	,	PUNCT
ejpam-5871	154	14	s	s	PROPN
ejpam-5871	154	15	∈	∈	PROPN
ejpam-5871	154	16	r/{−1	r/{−1	PROPN
ejpam-5871	154	17	}	}	PUNCT
ejpam-5871	154	18	,	,	PUNCT
ejpam-5871	154	19	k	k	X
ejpam-5871	154	20	≥	≥	X
ejpam-5871	154	21	0	0	NUM
ejpam-5871	154	22	and	and	CCONJ
ejpam-5871	154	23	⋋	⋋	PROPN
ejpam-5871	154	24	be	be	AUX
ejpam-5871	154	25	an	an	DET
ejpam-5871	154	26	increasing	increase	VERB
ejpam-5871	154	27	function	function	NOUN
ejpam-5871	154	28	then	then	ADV
ejpam-5871	154	29	the	the	DET
ejpam-5871	154	30	(	(	PUNCT
ejpam-5871	154	31	k	k	NOUN
ejpam-5871	154	32	,	,	PUNCT
ejpam-5871	154	33	s)-grlfio	s)-grlfio	NOUN
ejpam-5871	154	34	for	for	ADP
ejpam-5871	154	35	order	order	NOUN
ejpam-5871	154	36	β	β	X
ejpam-5871	154	37	>	>	X
ejpam-5871	154	38	0	0	NUM
ejpam-5871	154	39	can	can	AUX
ejpam-5871	154	40	be	be	AUX
ejpam-5871	154	41	stated	state	VERB
ejpam-5871	154	42	as	as	ADP
ejpam-5871	154	43	s	s	PROPN
ejpam-5871	154	44	kz	kz	PROPN
ejpam-5871	154	45	β	β	PROPN
ejpam-5871	154	46	α∅(m1	α∅(m1	NOUN
ejpam-5871	154	47	)	)	PUNCT
ejpam-5871	154	48	=	=	SYM
ejpam-5871	155	1	(	(	PUNCT
ejpam-5871	155	2	s+	s+	NUM
ejpam-5871	155	3	1)1−	1)1−	PROPN
ejpam-5871	155	4	β	β	X
ejpam-5871	155	5	k	k	PROPN
ejpam-5871	155	6	kγk(β	kγk(β	PROPN
ejpam-5871	155	7	)	)	PUNCT
ejpam-5871	155	8	∫	∫	PROPN
ejpam-5871	155	9	m1	m1	PROPN
ejpam-5871	155	10	α	α	PROPN
ejpam-5871	155	11	(	(	PUNCT
ejpam-5871	155	12	⋋s+1(m1)−⋋s+1(n1	⋋s+1(m1)−⋋s+1(n1	NOUN
ejpam-5871	155	13	)	)	PUNCT
ejpam-5871	155	14	)	)	PUNCT
ejpam-5871	156	1	β	β	X
ejpam-5871	156	2	k	k	X
ejpam-5871	156	3	−1	−1	ADV
ejpam-5871	156	4	⋋s	⋋s	PROPN
ejpam-5871	156	5	(	(	PUNCT
ejpam-5871	156	6	n1)⋋	n1)⋋	NOUN
ejpam-5871	156	7	′	′	NUM
ejpam-5871	156	8	(	(	PUNCT
ejpam-5871	156	9	n1)∅(n1)dn1	n1)∅(n1)dn1	PROPN
ejpam-5871	156	10	.	.	PUNCT
ejpam-5871	157	1	(	(	PUNCT
ejpam-5871	157	2	2	2	X
ejpam-5871	157	3	)	)	PUNCT
ejpam-5871	157	4	definition	definition	NOUN
ejpam-5871	157	5	10	10	NUM
ejpam-5871	157	6	.	.	PUNCT
ejpam-5871	158	1	[	[	X
ejpam-5871	158	2	31	31	NUM
ejpam-5871	158	3	]	]	PUNCT
ejpam-5871	158	4	if	if	SCONJ
ejpam-5871	158	5	a	a	DET
ejpam-5871	158	6	function	function	NOUN
ejpam-5871	158	7	∅	∅	NOUN
ejpam-5871	158	8	is	be	AUX
ejpam-5871	158	9	continuous	continuous	ADJ
ejpam-5871	158	10	on	on	ADP
ejpam-5871	158	11	[	[	X
ejpam-5871	158	12	a	a	X
ejpam-5871	158	13	,	,	PUNCT
ejpam-5871	158	14	b	b	NOUN
ejpam-5871	158	15	]	]	PUNCT
ejpam-5871	158	16	,	,	PUNCT
ejpam-5871	158	17	s	s	PROPN
ejpam-5871	158	18	∈	∈	PROPN
ejpam-5871	158	19	r/{−1	r/{−1	PROPN
ejpam-5871	158	20	}	}	PUNCT
ejpam-5871	158	21	,	,	PUNCT
ejpam-5871	158	22	k	k	X
ejpam-5871	158	23	≥	≥	X
ejpam-5871	158	24	0	0	NUM
ejpam-5871	158	25	and	and	CCONJ
ejpam-5871	158	26	⋋	⋋	PROPN
ejpam-5871	158	27	be	be	AUX
ejpam-5871	158	28	an	an	DET
ejpam-5871	158	29	increasing	increase	VERB
ejpam-5871	158	30	function	function	NOUN
ejpam-5871	158	31	then	then	ADV
ejpam-5871	158	32	left	leave	VERB
ejpam-5871	158	33	and	and	CCONJ
ejpam-5871	158	34	right	right	ADV
ejpam-5871	158	35	sided	sided	ADJ
ejpam-5871	158	36	(	(	PUNCT
ejpam-5871	158	37	k	k	NOUN
ejpam-5871	158	38	,	,	PUNCT
ejpam-5871	158	39	s)-grlfio	s)-grlfio	NOUN
ejpam-5871	158	40	for	for	ADP
ejpam-5871	158	41	order	order	NOUN
ejpam-5871	158	42	β	β	X
ejpam-5871	158	43	>	>	X
ejpam-5871	158	44	0	0	NUM
ejpam-5871	158	45	can	can	AUX
ejpam-5871	158	46	be	be	AUX
ejpam-5871	158	47	stated	state	VERB
ejpam-5871	158	48	as	as	ADP
ejpam-5871	158	49	s	s	PROPN
ejpam-5871	158	50	kz	kz	PROPN
ejpam-5871	158	51	β	β	X
ejpam-5871	158	52	α+∅(m1	α+∅(m1	NOUN
ejpam-5871	158	53	)	)	PUNCT
ejpam-5871	158	54	=	=	SYM
ejpam-5871	159	1	(	(	PUNCT
ejpam-5871	159	2	s+	s+	NUM
ejpam-5871	159	3	1)1−	1)1−	PROPN
ejpam-5871	159	4	β	β	X
ejpam-5871	159	5	k	k	PROPN
ejpam-5871	159	6	kγk(β	kγk(β	PROPN
ejpam-5871	159	7	)	)	PUNCT
ejpam-5871	159	8	∫	∫	PROPN
ejpam-5871	159	9	m1	m1	PROPN
ejpam-5871	159	10	α+	α+	PRON
ejpam-5871	159	11	(	(	PUNCT
ejpam-5871	159	12	⋋s+1(m1)−⋋s+1(n1	⋋s+1(m1)−⋋s+1(n1	NOUN
ejpam-5871	159	13	)	)	PUNCT
ejpam-5871	159	14	)	)	PUNCT
ejpam-5871	160	1	β	β	X
ejpam-5871	160	2	k	k	X
ejpam-5871	160	3	−1	−1	ADV
ejpam-5871	160	4	⋋s	⋋s	PROPN
ejpam-5871	160	5	(	(	PUNCT
ejpam-5871	160	6	n1)⋋	n1)⋋	NOUN
ejpam-5871	160	7	′	′	NUM
ejpam-5871	160	8	(	(	PUNCT
ejpam-5871	160	9	n1)∅(n1)dn1	n1)∅(n1)dn1	PROPN
ejpam-5871	160	10	,	,	PUNCT
ejpam-5871	160	11	m1	m1	PROPN
ejpam-5871	160	12	>	>	X
ejpam-5871	160	13	α+	α+	X
ejpam-5871	160	14	(	(	PUNCT
ejpam-5871	160	15	3	3	NUM
ejpam-5871	160	16	)	)	PUNCT
ejpam-5871	160	17	and	and	CCONJ
ejpam-5871	160	18	s	s	PROPN
ejpam-5871	160	19	kz	kz	PROPN
ejpam-5871	160	20	β	β	PROPN
ejpam-5871	160	21	ζ−∅(m1	ζ−∅(m1	PROPN
ejpam-5871	160	22	)	)	PUNCT
ejpam-5871	160	23	=	=	SYM
ejpam-5871	161	1	(	(	PUNCT
ejpam-5871	161	2	s+	s+	NUM
ejpam-5871	161	3	1)1−	1)1−	PROPN
ejpam-5871	161	4	β	β	X
ejpam-5871	161	5	k	k	PROPN
ejpam-5871	161	6	kγk(β	kγk(β	PROPN
ejpam-5871	161	7	)	)	PUNCT
ejpam-5871	161	8	∫	∫	PROPN
ejpam-5871	161	9	ζ	ζ	PROPN
ejpam-5871	161	10	m1	m1	PROPN
ejpam-5871	161	11	(	(	PUNCT
ejpam-5871	161	12	⋋s+1(n1)−⋋s+1(m1	⋋s+1(n1)−⋋s+1(m1	NOUN
ejpam-5871	161	13	)	)	PUNCT
ejpam-5871	161	14	)	)	PUNCT
ejpam-5871	161	15	β	β	X
ejpam-5871	161	16	k	k	X
ejpam-5871	161	17	−1	−1	ADV
ejpam-5871	161	18	⋋s	⋋s	PROPN
ejpam-5871	161	19	(	(	PUNCT
ejpam-5871	161	20	n1)⋋	n1)⋋	NOUN
ejpam-5871	161	21	′	′	NUM
ejpam-5871	161	22	(	(	PUNCT
ejpam-5871	161	23	n1)∅(n1)dn1	n1)∅(n1)dn1	PROPN
ejpam-5871	161	24	,	,	PUNCT
ejpam-5871	161	25	m1	m1	PROPN
ejpam-5871	161	26	<	<	X
ejpam-5871	161	27	ζ	ζ	X
ejpam-5871	161	28	.	.	PUNCT
ejpam-5871	162	1	(	(	PUNCT
ejpam-5871	162	2	4	4	X
ejpam-5871	162	3	)	)	PUNCT
ejpam-5871	162	4	a.	a.	NOUN
ejpam-5871	162	5	mehmood	mehmood	PROPN
ejpam-5871	162	6	et	et	PROPN
ejpam-5871	162	7	al	al	PROPN
ejpam-5871	162	8	.	.	PUNCT
ejpam-5871	162	9	/	/	SYM
ejpam-5871	162	10	eur	eur	PROPN
ejpam-5871	162	11	.	.	PUNCT
ejpam-5871	163	1	j.	j.	PROPN
ejpam-5871	163	2	pure	pure	PROPN
ejpam-5871	163	3	appl	appl	PROPN
ejpam-5871	163	4	.	.	PROPN
ejpam-5871	163	5	math	math	PROPN
ejpam-5871	163	6	,	,	PUNCT
ejpam-5871	163	7	18	18	NUM
ejpam-5871	163	8	(	(	PUNCT
ejpam-5871	163	9	2	2	NUM
ejpam-5871	163	10	)	)	PUNCT
ejpam-5871	163	11	(	(	PUNCT
ejpam-5871	163	12	2025	2025	NUM
ejpam-5871	163	13	)	)	PUNCT
ejpam-5871	163	14	,	,	PUNCT
ejpam-5871	163	15	5871	5871	NUM
ejpam-5871	163	16	7	7	NUM
ejpam-5871	163	17	of	of	ADP
ejpam-5871	163	18	26	26	NUM
ejpam-5871	163	19	now	now	ADV
ejpam-5871	163	20	we	we	PRON
ejpam-5871	163	21	discuss	discuss	VERB
ejpam-5871	163	22	some	some	DET
ejpam-5871	163	23	applications	application	NOUN
ejpam-5871	163	24	of	of	ADP
ejpam-5871	163	25	defined	define	VERB
ejpam-5871	163	26	operators	operator	NOUN
ejpam-5871	163	27	which	which	PRON
ejpam-5871	163	28	we	we	PRON
ejpam-5871	163	29	used	use	VERB
ejpam-5871	163	30	later	later	ADV
ejpam-5871	163	31	.	.	PUNCT
ejpam-5871	164	1	proposition	proposition	NOUN
ejpam-5871	164	2	1	1	NUM
ejpam-5871	164	3	.	.	PUNCT
ejpam-5871	165	1	if	if	SCONJ
ejpam-5871	165	2	a	a	DET
ejpam-5871	165	3	function	function	NOUN
ejpam-5871	165	4	∅	∅	NOUN
ejpam-5871	165	5	is	be	AUX
ejpam-5871	165	6	continuous	continuous	ADJ
ejpam-5871	165	7	on	on	ADP
ejpam-5871	165	8	[	[	X
ejpam-5871	165	9	a	a	X
ejpam-5871	165	10	,	,	PUNCT
ejpam-5871	165	11	b	b	NOUN
ejpam-5871	165	12	]	]	PUNCT
ejpam-5871	165	13	,	,	PUNCT
ejpam-5871	165	14	s	s	PROPN
ejpam-5871	165	15	∈	∈	PROPN
ejpam-5871	165	16	r/{−1	r/{−1	PROPN
ejpam-5871	165	17	}	}	PUNCT
ejpam-5871	165	18	,	,	PUNCT
ejpam-5871	165	19	k	k	X
ejpam-5871	165	20	≥	≥	PROPN
ejpam-5871	165	21	0	0	NUM
ejpam-5871	165	22	,	,	PUNCT
ejpam-5871	165	23	⋋	⋋	PRON
ejpam-5871	165	24	be	be	AUX
ejpam-5871	165	25	an	an	DET
ejpam-5871	165	26	increasing	increase	VERB
ejpam-5871	165	27	function	function	NOUN
ejpam-5871	165	28	and	and	CCONJ
ejpam-5871	165	29	c	c	NOUN
ejpam-5871	165	30	be	be	AUX
ejpam-5871	165	31	a	a	DET
ejpam-5871	165	32	constant	constant	ADJ
ejpam-5871	165	33	function	function	NOUN
ejpam-5871	165	34	then	then	ADV
ejpam-5871	165	35	for	for	ADP
ejpam-5871	165	36	left	left	ADJ
ejpam-5871	165	37	and	and	CCONJ
ejpam-5871	165	38	right	right	ADV
ejpam-5871	165	39	sided	sided	ADJ
ejpam-5871	165	40	(	(	PUNCT
ejpam-5871	165	41	k	k	NOUN
ejpam-5871	165	42	,	,	PUNCT
ejpam-5871	165	43	s)-grlfio	s)-grlfio	NOUN
ejpam-5871	165	44	of	of	ADP
ejpam-5871	165	45	order	order	NOUN
ejpam-5871	165	46	β	β	X
ejpam-5871	165	47	>	>	X
ejpam-5871	165	48	0	0	NUM
ejpam-5871	165	49	,	,	PUNCT
ejpam-5871	165	50	we	we	PRON
ejpam-5871	165	51	have	have	VERB
ejpam-5871	165	52	the	the	DET
ejpam-5871	165	53	following	follow	VERB
ejpam-5871	165	54	results	result	NOUN
ejpam-5871	165	55	holds	hold	VERB
ejpam-5871	165	56	:	:	PUNCT
ejpam-5871	165	57	s	s	VERB
ejpam-5871	165	58	kz	kz	PROPN
ejpam-5871	165	59	β	β	PROPN
ejpam-5871	165	60	r+1	r+1	PROPN
ejpam-5871	165	61	⋋s+1	⋋s+1	PROPN
ejpam-5871	165	62	(	(	PUNCT
ejpam-5871	165	63	r2	r2	PROPN
ejpam-5871	165	64	)	)	PUNCT
ejpam-5871	165	65	=	=	SYM
ejpam-5871	166	1	(	(	PUNCT
ejpam-5871	166	2	s+	s+	NUM
ejpam-5871	166	3	1)1−	1)1−	PROPN
ejpam-5871	166	4	β	β	X
ejpam-5871	166	5	k	k	PROPN
ejpam-5871	166	6	kγk(β	kγk(β	PROPN
ejpam-5871	166	7	)	)	PUNCT
ejpam-5871	166	8	(	(	PUNCT
ejpam-5871	166	9	⋋s+1(r1)(⋋s+1(r2)−⋋s+1(r1	⋋s+1(r1)(⋋s+1(r2)−⋋s+1(r1	PROPN
ejpam-5871	166	10	)	)	PUNCT
ejpam-5871	166	11	)	)	PUNCT
ejpam-5871	166	12	β	β	X
ejpam-5871	166	13	k	k	X
ejpam-5871	166	14	β	β	X
ejpam-5871	166	15	k	k	X
ejpam-5871	166	16	(	(	PUNCT
ejpam-5871	166	17	s+	s+	NOUN
ejpam-5871	166	18	1	1	NUM
ejpam-5871	166	19	)	)	PUNCT
ejpam-5871	166	20	)	)	PUNCT
ejpam-5871	167	1	+	+	CCONJ
ejpam-5871	167	2	(	(	PUNCT
ejpam-5871	167	3	⋋s+1(r2)−⋋s+1(r1	⋋s+1(r2)−⋋s+1(r1	NOUN
ejpam-5871	167	4	)	)	PUNCT
ejpam-5871	167	5	)	)	PUNCT
ejpam-5871	168	1	β	β	X
ejpam-5871	168	2	k	k	NOUN
ejpam-5871	169	1	+1	+1	INTJ
ejpam-5871	169	2	β	β	X
ejpam-5871	169	3	k	k	X
ejpam-5871	169	4	(	(	PUNCT
ejpam-5871	169	5	s+	s+	NUM
ejpam-5871	169	6	1)(βk	1)(βk	NUM
ejpam-5871	169	7	+	+	SYM
ejpam-5871	169	8	1	1	NUM
ejpam-5871	169	9	)	)	PUNCT
ejpam-5871	169	10	s	s	PART
ejpam-5871	170	1	kz	kz	PROPN
ejpam-5871	170	2	β	β	PROPN
ejpam-5871	170	3	r−2	r−2	PROPN
ejpam-5871	170	4	⋋s+1	⋋s+1	PROPN
ejpam-5871	170	5	(	(	PUNCT
ejpam-5871	170	6	r1	r1	PROPN
ejpam-5871	170	7	)	)	PUNCT
ejpam-5871	170	8	=	=	PUNCT
ejpam-5871	170	9	(	(	PUNCT
ejpam-5871	170	10	s+	s+	NUM
ejpam-5871	170	11	1)−	1)−	PROPN
ejpam-5871	170	12	β	β	X
ejpam-5871	170	13	k	k	PROPN
ejpam-5871	170	14	βγk(β	βγk(β	PROPN
ejpam-5871	170	15	)	)	PUNCT
ejpam-5871	170	16	(	(	PUNCT
ejpam-5871	170	17	⋋s+1	⋋s+1	PROPN
ejpam-5871	170	18	(	(	PUNCT
ejpam-5871	170	19	r2)(⋋	r2)(⋋	NOUN
ejpam-5871	170	20	s+1(r2)−⋋s+1(r1	s+1(r2)−⋋s+1(r1	PROPN
ejpam-5871	170	21	)	)	PUNCT
ejpam-5871	170	22	)	)	PUNCT
ejpam-5871	171	1	β	β	PROPN
ejpam-5871	171	2	k	k	PROPN
ejpam-5871	171	3	)	)	PUNCT
ejpam-5871	172	1	−	−	PROPN
ejpam-5871	172	2	(	(	PUNCT
ejpam-5871	172	3	⋋s+1(r2)−⋋s+1(r1	⋋s+1(r2)−⋋s+1(r1	NOUN
ejpam-5871	172	4	)	)	PUNCT
ejpam-5871	172	5	)	)	PUNCT
ejpam-5871	173	1	β	β	X
ejpam-5871	174	1	k	k	PROPN
ejpam-5871	174	2	+1	+1	PROPN
ejpam-5871	174	3	(	(	PUNCT
ejpam-5871	174	4	βk	βk	ADP
ejpam-5871	174	5	+	+	NOUN
ejpam-5871	174	6	1	1	NUM
ejpam-5871	174	7	)	)	PUNCT
ejpam-5871	174	8	s	s	PART
ejpam-5871	174	9	kz	kz	PROPN
ejpam-5871	174	10	β	β	PROPN
ejpam-5871	174	11	r+1	r+1	PROPN
ejpam-5871	174	12	c	c	NOUN
ejpam-5871	174	13	=	=	PUNCT
ejpam-5871	174	14	c(s+	c(s+	NOUN
ejpam-5871	175	1	1)−	1)−	PROPN
ejpam-5871	175	2	β	β	X
ejpam-5871	175	3	k	k	PROPN
ejpam-5871	175	4	βγk(β	βγk(β	PROPN
ejpam-5871	175	5	)	)	PUNCT
ejpam-5871	175	6	(	(	PUNCT
ejpam-5871	175	7	⋋s+1	⋋s+1	PROPN
ejpam-5871	175	8	(	(	PUNCT
ejpam-5871	175	9	r2)−⋋s+1(r1	r2)−⋋s+1(r1	NOUN
ejpam-5871	175	10	)	)	PUNCT
ejpam-5871	175	11	β	β	PROPN
ejpam-5871	175	12	k	k	PROPN
ejpam-5871	175	13	)	)	PUNCT
ejpam-5871	175	14	s	s	PROPN
ejpam-5871	175	15	kz	kz	PROPN
ejpam-5871	175	16	β	β	X
ejpam-5871	175	17	r−2	r−2	PROPN
ejpam-5871	175	18	c	c	NOUN
ejpam-5871	176	1	=	=	PRON
ejpam-5871	176	2	c(s+	c(s+	NOUN
ejpam-5871	177	1	1)−	1)−	PROPN
ejpam-5871	177	2	β	β	X
ejpam-5871	177	3	k	k	PROPN
ejpam-5871	177	4	βγk(β	βγk(β	PROPN
ejpam-5871	177	5	)	)	PUNCT
ejpam-5871	177	6	(	(	PUNCT
ejpam-5871	177	7	⋋s+1	⋋s+1	PROPN
ejpam-5871	177	8	(	(	PUNCT
ejpam-5871	177	9	r2)−⋋s+1(r1	r2)−⋋s+1(r1	NOUN
ejpam-5871	177	10	)	)	PUNCT
ejpam-5871	177	11	β	β	PROPN
ejpam-5871	177	12	k	k	PROPN
ejpam-5871	177	13	)	)	PUNCT
ejpam-5871	177	14	.	.	PUNCT
ejpam-5871	178	1	2	2	X
ejpam-5871	178	2	.	.	X
ejpam-5871	178	3	a	a	DET
ejpam-5871	178	4	class	class	NOUN
ejpam-5871	178	5	of	of	ADP
ejpam-5871	178	6	some	some	DET
ejpam-5871	178	7	results	result	NOUN
ejpam-5871	178	8	in	in	ADP
ejpam-5871	178	9	this	this	DET
ejpam-5871	178	10	session	session	NOUN
ejpam-5871	178	11	,	,	PUNCT
ejpam-5871	178	12	we	we	PRON
ejpam-5871	178	13	will	will	AUX
ejpam-5871	178	14	examine	examine	VERB
ejpam-5871	178	15	the	the	DET
ejpam-5871	178	16	reverse	reverse	ADJ
ejpam-5871	178	17	forms	form	NOUN
ejpam-5871	178	18	of	of	ADP
ejpam-5871	178	19	minkowski	minkowski	ADJ
ejpam-5871	178	20	,	,	PUNCT
ejpam-5871	178	21	holder	holder	NOUN
ejpam-5871	178	22	and	and	CCONJ
ejpam-5871	178	23	hermitehadamard	hermitehadamard	NOUN
ejpam-5871	178	24	-	-	PUNCT
ejpam-5871	178	25	fejer	fejer	NOUN
ejpam-5871	178	26	type	type	NOUN
ejpam-5871	178	27	inequalities	inequality	NOUN
ejpam-5871	178	28	via	via	ADP
ejpam-5871	178	29	an	an	DET
ejpam-5871	178	30	ı.υ	ı.υ	PROPN
ejpam-5871	178	31	cf	cf	NOUN
ejpam-5871	178	32	involving	involve	VERB
ejpam-5871	178	33	(	(	PUNCT
ejpam-5871	178	34	k	k	NOUN
ejpam-5871	178	35	,	,	PUNCT
ejpam-5871	178	36	s)-grlfio	s)-grlfio	NOUN
ejpam-5871	178	37	under	under	ADP
ejpam-5871	178	38	the	the	DET
ejpam-5871	178	39	framework	framework	NOUN
ejpam-5871	178	40	of	of	ADP
ejpam-5871	178	41	convexity	convexity	NOUN
ejpam-5871	178	42	.	.	PUNCT
ejpam-5871	179	1	in	in	ADP
ejpam-5871	179	2	this	this	DET
ejpam-5871	179	3	result	result	NOUN
ejpam-5871	179	4	,	,	PUNCT
ejpam-5871	179	5	we	we	PRON
ejpam-5871	179	6	want	want	VERB
ejpam-5871	179	7	to	to	PART
ejpam-5871	179	8	explore	explore	VERB
ejpam-5871	179	9	the	the	DET
ejpam-5871	179	10	minkowski	minkowski	PROPN
ejpam-5871	179	11	’s	’s	PART
ejpam-5871	179	12	inequality	inequality	NOUN
ejpam-5871	179	13	.	.	PUNCT
ejpam-5871	180	1	theorem	theorem	VERB
ejpam-5871	180	2	4	4	NUM
ejpam-5871	180	3	.	.	PUNCT
ejpam-5871	181	1	let	let	VERB
ejpam-5871	181	2	s	s	PRON
ejpam-5871	181	3	∈	∈	VERB
ejpam-5871	181	4	r/{−1	r/{−1	PROPN
ejpam-5871	181	5	}	}	PUNCT
ejpam-5871	181	6	,	,	PUNCT
ejpam-5871	181	7	k	k	X
ejpam-5871	181	8	≥	≥	NOUN
ejpam-5871	181	9	0	0	NUM
ejpam-5871	181	10	,	,	PUNCT
ejpam-5871	181	11	also	also	ADV
ejpam-5871	181	12	∅	∅	NOUN
ejpam-5871	181	13	,	,	PUNCT
ejpam-5871	181	14	ϕ	ϕ	X
ejpam-5871	181	15	:	:	PUNCT
ejpam-5871	182	1	[	[	X
ejpam-5871	182	2	r1	r1	NOUN
ejpam-5871	182	3	,	,	PUNCT
ejpam-5871	182	4	r2	r2	PROPN
ejpam-5871	182	5	]	]	PUNCT
ejpam-5871	182	6	→	→	SYM
ejpam-5871	182	7	r+	r+	PUNCT
ejpam-5871	182	8	i	i	PRON
ejpam-5871	182	9	be	be	VERB
ejpam-5871	182	10	ı.υ	ı.υ	PROPN
ejpam-5871	182	11	functions	function	NOUN
ejpam-5871	182	12	such	such	ADJ
ejpam-5871	182	13	that	that	DET
ejpam-5871	182	14	∅(χ	∅(χ	NOUN
ejpam-5871	182	15	)	)	PUNCT
ejpam-5871	182	16	=	=	PUNCT
ejpam-5871	183	1	[	[	X
ejpam-5871	183	2	∅∗,∅∗	∅∗,∅∗	X
ejpam-5871	183	3	]	]	PUNCT
ejpam-5871	183	4	and	and	CCONJ
ejpam-5871	183	5	ϕ(χ	ϕ(χ	NUM
ejpam-5871	183	6	)	)	PUNCT
ejpam-5871	184	1	=	=	PUNCT
ejpam-5871	185	1	[	[	X
ejpam-5871	185	2	ϕ∗	ϕ∗	PROPN
ejpam-5871	185	3	,	,	PUNCT
ejpam-5871	185	4	ϕ	ϕ	NOUN
ejpam-5871	185	5	∗	∗	NOUN
ejpam-5871	185	6	]	]	PUNCT
ejpam-5871	185	7	,	,	PUNCT
ejpam-5871	185	8	(	(	PUNCT
ejpam-5871	185	9	s	s	AUX
ejpam-5871	185	10	kz	kz	PROPN
ejpam-5871	185	11	β	β	PROPN
ejpam-5871	185	12	r+1	r+1	PROPN
ejpam-5871	185	13	∅p(χ	∅p(χ	PROPN
ejpam-5871	185	14	)	)	PUNCT
ejpam-5871	185	15	)	)	PUNCT
ejpam-5871	186	1	<	<	X
ejpam-5871	186	2	∞	∞	PROPN
ejpam-5871	186	3	and	and	CCONJ
ejpam-5871	186	4	(	(	PUNCT
ejpam-5871	186	5	s	s	AUX
ejpam-5871	186	6	kz	kz	PROPN
ejpam-5871	186	7	β	β	PROPN
ejpam-5871	186	8	r+1	r+1	PROPN
ejpam-5871	186	9	ϕp(χ	ϕp(χ	PUNCT
ejpam-5871	186	10	)	)	PUNCT
ejpam-5871	186	11	)	)	PUNCT
ejpam-5871	187	1	<	<	X
ejpam-5871	187	2	∞	∞	PROPN
ejpam-5871	187	3	,	,	PUNCT
ejpam-5871	187	4	then	then	ADV
ejpam-5871	187	5	the	the	DET
ejpam-5871	187	6	expression	expression	NOUN
ejpam-5871	187	7	(	(	PUNCT
ejpam-5871	187	8	5	5	NUM
ejpam-5871	187	9	)	)	PUNCT
ejpam-5871	187	10	holds	hold	VERB
ejpam-5871	187	11	.	.	PUNCT
ejpam-5871	188	1	[	[	PUNCT
ejpam-5871	188	2	1	1	NUM
ejpam-5871	188	3	+	+	X
ejpam-5871	188	4	ϑ(2	ϑ(2	PROPN
ejpam-5871	188	5	+	+	NUM
ejpam-5871	188	6	µ	µ	X
ejpam-5871	188	7	)	)	PUNCT
ejpam-5871	188	8	(	(	PUNCT
ejpam-5871	188	9	1	1	NUM
ejpam-5871	188	10	+	+	CCONJ
ejpam-5871	188	11	ϑ)(1	ϑ)(1	X
ejpam-5871	188	12	+	+	ADJ
ejpam-5871	188	13	µ	µ	X
ejpam-5871	188	14	)	)	PUNCT
ejpam-5871	188	15	,	,	PUNCT
ejpam-5871	188	16	1	1	NUM
ejpam-5871	188	17	+	+	CCONJ
ejpam-5871	188	18	µ(2	µ(2	PROPN
ejpam-5871	188	19	+	+	CCONJ
ejpam-5871	188	20	ϑ	ϑ	X
ejpam-5871	188	21	)	)	PUNCT
ejpam-5871	188	22	(	(	PUNCT
ejpam-5871	188	23	1	1	NUM
ejpam-5871	188	24	+	+	CCONJ
ejpam-5871	188	25	ϑ)(1	ϑ)(1	X
ejpam-5871	188	26	+	+	ADJ
ejpam-5871	188	27	µ	µ	X
ejpam-5871	188	28	)	)	PUNCT
ejpam-5871	188	29	]	]	PUNCT
ejpam-5871	189	1	[	[	X
ejpam-5871	189	2	[	[	X
ejpam-5871	189	3	s	s	X
ejpam-5871	189	4	kz	kz	PROPN
ejpam-5871	189	5	β	β	PROPN
ejpam-5871	189	6	r+1	r+1	PROPN
ejpam-5871	189	7	(	(	PUNCT
ejpam-5871	189	8	∅(χ	∅(χ	NOUN
ejpam-5871	189	9	)	)	PUNCT
ejpam-5871	189	10	+	+	CCONJ
ejpam-5871	189	11	ϕ(χ))p	ϕ(χ))p	X
ejpam-5871	189	12	]	]	PUNCT
ejpam-5871	189	13	1	1	NUM
ejpam-5871	189	14	p	p	X
ejpam-5871	189	15	]	]	X
ejpam-5871	189	16	⊇	⊇	X
ejpam-5871	189	17	[	[	PUNCT
ejpam-5871	189	18	s	s	X
ejpam-5871	189	19	kz	kz	PROPN
ejpam-5871	189	20	β	β	PROPN
ejpam-5871	189	21	r+1	r+1	PROPN
ejpam-5871	189	22	∅p(χ	∅p(χ	PROPN
ejpam-5871	189	23	)	)	PUNCT
ejpam-5871	189	24	]	]	PUNCT
ejpam-5871	189	25	1	1	NUM
ejpam-5871	189	26	p	p	NOUN
ejpam-5871	190	1	+	+	X
ejpam-5871	190	2	[	[	PUNCT
ejpam-5871	190	3	s	s	X
ejpam-5871	190	4	kz	kz	PROPN
ejpam-5871	190	5	β	β	PROPN
ejpam-5871	190	6	r+1	r+1	PROPN
ejpam-5871	190	7	ϕp(χ	ϕp(χ	PUNCT
ejpam-5871	190	8	)	)	PUNCT
ejpam-5871	190	9	]	]	PUNCT
ejpam-5871	191	1	1	1	NUM
ejpam-5871	191	2	p	p	NOUN
ejpam-5871	191	3	,	,	PUNCT
ejpam-5871	191	4	(	(	PUNCT
ejpam-5871	191	5	5	5	NUM
ejpam-5871	191	6	)	)	PUNCT
ejpam-5871	191	7	where	where	SCONJ
ejpam-5871	191	8	,	,	PUNCT
ejpam-5871	191	9	0	0	PUNCT
ejpam-5871	191	10	<	<	X
ejpam-5871	191	11	ϑ	ϑ	X
ejpam-5871	191	12	≤	≤	ADJ
ejpam-5871	191	13	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	191	14	)	)	PUNCT
ejpam-5871	191	15	ϕ∗(χ	ϕ∗(χ	PROPN
ejpam-5871	191	16	)	)	PUNCT
ejpam-5871	191	17	≤	≤	NOUN
ejpam-5871	191	18	µ	µ	ADP
ejpam-5871	191	19	and	and	CCONJ
ejpam-5871	191	20	0	0	NUM
ejpam-5871	191	21	<	<	X
ejpam-5871	191	22	ϑ	ϑ	X
ejpam-5871	191	23	≤	≤	ADJ
ejpam-5871	191	24	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	191	25	)	)	PUNCT
ejpam-5871	191	26	ϕ∗(χ	ϕ∗(χ	PROPN
ejpam-5871	191	27	)	)	PUNCT
ejpam-5871	191	28	≤	≤	NOUN
ejpam-5871	191	29	µ	µ	X
ejpam-5871	191	30	for	for	ADP
ejpam-5871	191	31	χ	χ	PROPN
ejpam-5871	191	32	∈	∈	PROPN
ejpam-5871	191	33	[	[	X
ejpam-5871	191	34	r1	r1	NOUN
ejpam-5871	191	35	,	,	PUNCT
ejpam-5871	191	36	r2	r2	PROPN
ejpam-5871	191	37	]	]	PUNCT
ejpam-5871	191	38	,	,	PUNCT
ejpam-5871	191	39	p	p	NOUN
ejpam-5871	191	40	≥	≥	NUM
ejpam-5871	191	41	1	1	NUM
ejpam-5871	191	42	with	with	ADP
ejpam-5871	191	43	β	β	X
ejpam-5871	191	44	>	>	X
ejpam-5871	191	45	0	0	X
ejpam-5871	191	46	.	.	PUNCT
ejpam-5871	191	47	proof	proof	NOUN
ejpam-5871	191	48	.	.	PUNCT
ejpam-5871	192	1	since	since	SCONJ
ejpam-5871	192	2	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	192	3	)	)	PUNCT
ejpam-5871	192	4	ϕ∗(χ	ϕ∗(χ	PROPN
ejpam-5871	192	5	)	)	PUNCT
ejpam-5871	192	6	≤	≤	NOUN
ejpam-5871	192	7	µ	µ	NUM
ejpam-5871	192	8	,	,	PUNCT
ejpam-5871	192	9	this	this	PRON
ejpam-5871	192	10	implies	imply	VERB
ejpam-5871	192	11	(	(	PUNCT
ejpam-5871	192	12	µ+	µ+	X
ejpam-5871	192	13	1)p∅∗p(χ	1)p∅∗p(χ	NUM
ejpam-5871	192	14	)	)	PUNCT
ejpam-5871	192	15	≤	≤	NUM
ejpam-5871	192	16	µp(∅∗(χ	µp(∅∗(χ	NOUN
ejpam-5871	192	17	)	)	PUNCT
ejpam-5871	192	18	+	+	PROPN
ejpam-5871	192	19	ϕ∗(χ))p	ϕ∗(χ))p	PROPN
ejpam-5871	192	20	.	.	PUNCT
ejpam-5871	193	1	after	after	ADP
ejpam-5871	193	2	multiplying	multiply	VERB
ejpam-5871	193	3	by	by	ADP
ejpam-5871	193	4	(	(	PUNCT
ejpam-5871	193	5	s+1)1−	s+1)1−	PROPN
ejpam-5871	193	6	β	β	X
ejpam-5871	193	7	k	k	PROPN
ejpam-5871	193	8	kγk(β	kγk(β	PROPN
ejpam-5871	193	9	)	)	PUNCT
ejpam-5871	193	10	(	(	PUNCT
ejpam-5871	193	11	⋋s+1	⋋s+1	PROPN
ejpam-5871	193	12	(	(	PUNCT
ejpam-5871	193	13	r2	r2	PROPN
ejpam-5871	193	14	)	)	PUNCT
ejpam-5871	193	15	−	−	NOUN
ejpam-5871	193	16	⋋s+1(χ	⋋s+1(χ	NUM
ejpam-5871	193	17	)	)	PUNCT
ejpam-5871	193	18	)	)	PUNCT
ejpam-5871	193	19	β	β	X
ejpam-5871	193	20	k	k	X
ejpam-5871	193	21	−1	−1	ADV
ejpam-5871	193	22	⋋s	⋋s	PROPN
ejpam-5871	193	23	(	(	PUNCT
ejpam-5871	193	24	χ	χ	NOUN
ejpam-5871	193	25	)	)	PUNCT
ejpam-5871	193	26	⋋	⋋	NUM
ejpam-5871	193	27	′	′	NUM
ejpam-5871	193	28	(	(	PUNCT
ejpam-5871	193	29	χ	χ	X
ejpam-5871	193	30	)	)	PUNCT
ejpam-5871	193	31	and	and	CCONJ
ejpam-5871	193	32	applying	apply	VERB
ejpam-5871	193	33	the	the	DET
ejpam-5871	193	34	integration	integration	NOUN
ejpam-5871	193	35	w.r.t	w.r.t	VERB
ejpam-5871	193	36	”	"	PUNCT
ejpam-5871	193	37	χ	χ	NOUN
ejpam-5871	193	38	”	"	PUNCT
ejpam-5871	193	39	over	over	ADP
ejpam-5871	193	40	[	[	X
ejpam-5871	193	41	r1	r1	NOUN
ejpam-5871	193	42	,	,	PUNCT
ejpam-5871	193	43	r2	r2	PROPN
ejpam-5871	193	44	]	]	PUNCT
ejpam-5871	193	45	,	,	PUNCT
ejpam-5871	193	46	we	we	PRON
ejpam-5871	193	47	obtain	obtain	VERB
ejpam-5871	193	48	the	the	DET
ejpam-5871	193	49	following	follow	VERB
ejpam-5871	193	50	expression	expression	NOUN
ejpam-5871	193	51	.	.	PUNCT
ejpam-5871	194	1	(	(	PUNCT
ejpam-5871	194	2	µ+	µ+	PROPN
ejpam-5871	194	3	1)p	1)p	NUM
ejpam-5871	194	4	(	(	PUNCT
ejpam-5871	194	5	s+	s+	NUM
ejpam-5871	194	6	1)1−	1)1−	PROPN
ejpam-5871	194	7	β	β	X
ejpam-5871	194	8	k	k	PROPN
ejpam-5871	194	9	kγk(β	kγk(β	PROPN
ejpam-5871	194	10	)	)	PUNCT
ejpam-5871	194	11	∫	∫	PROPN
ejpam-5871	194	12	r2	r2	PROPN
ejpam-5871	194	13	r1	r1	PROPN
ejpam-5871	194	14	(	(	PUNCT
ejpam-5871	194	15	⋋s+1	⋋s+1	PROPN
ejpam-5871	194	16	(	(	PUNCT
ejpam-5871	194	17	r2)−⋋s+1(χ	r2)−⋋s+1(χ	NOUN
ejpam-5871	194	18	)	)	PUNCT
ejpam-5871	194	19	)	)	PUNCT
ejpam-5871	194	20	β	β	X
ejpam-5871	194	21	k	k	X
ejpam-5871	194	22	−1	−1	ADV
ejpam-5871	194	23	⋋s	⋋s	PROPN
ejpam-5871	194	24	(	(	PUNCT
ejpam-5871	194	25	χ)⋋	χ)⋋	NOUN
ejpam-5871	194	26	′	′	NUM
ejpam-5871	194	27	(	(	PUNCT
ejpam-5871	194	28	χ)∅∗p(χ)dχ	χ)∅∗p(χ)dχ	NOUN
ejpam-5871	194	29	a.	a.	NOUN
ejpam-5871	194	30	mehmood	mehmood	PROPN
ejpam-5871	194	31	et	et	PROPN
ejpam-5871	195	1	al	al	PROPN
ejpam-5871	195	2	.	.	PUNCT
ejpam-5871	195	3	/	/	SYM
ejpam-5871	195	4	eur	eur	PROPN
ejpam-5871	195	5	.	.	PUNCT
ejpam-5871	196	1	j.	j.	PROPN
ejpam-5871	196	2	pure	pure	PROPN
ejpam-5871	196	3	appl	appl	PROPN
ejpam-5871	196	4	.	.	PROPN
ejpam-5871	196	5	math	math	PROPN
ejpam-5871	196	6	,	,	PUNCT
ejpam-5871	196	7	18	18	NUM
ejpam-5871	196	8	(	(	PUNCT
ejpam-5871	196	9	2	2	NUM
ejpam-5871	196	10	)	)	PUNCT
ejpam-5871	196	11	(	(	PUNCT
ejpam-5871	196	12	2025	2025	NUM
ejpam-5871	196	13	)	)	PUNCT
ejpam-5871	196	14	,	,	PUNCT
ejpam-5871	196	15	5871	5871	NUM
ejpam-5871	196	16	8	8	NUM
ejpam-5871	196	17	of	of	ADP
ejpam-5871	196	18	26	26	NUM
ejpam-5871	196	19	≤	≤	NUM
ejpam-5871	196	20	µp	µp	NOUN
ejpam-5871	196	21	(	(	PUNCT
ejpam-5871	196	22	s+	s+	NUM
ejpam-5871	196	23	1)1−	1)1−	PROPN
ejpam-5871	196	24	β	β	X
ejpam-5871	196	25	k	k	PROPN
ejpam-5871	196	26	kγk(β	kγk(β	PROPN
ejpam-5871	196	27	)	)	PUNCT
ejpam-5871	196	28	∫	∫	PROPN
ejpam-5871	196	29	r2	r2	PROPN
ejpam-5871	196	30	r1	r1	PROPN
ejpam-5871	196	31	(	(	PUNCT
ejpam-5871	196	32	⋋s+1	⋋s+1	PROPN
ejpam-5871	196	33	(	(	PUNCT
ejpam-5871	196	34	r2)−⋋s+1(χ	r2)−⋋s+1(χ	NOUN
ejpam-5871	196	35	)	)	PUNCT
ejpam-5871	196	36	)	)	PUNCT
ejpam-5871	197	1	β	β	X
ejpam-5871	197	2	k	k	X
ejpam-5871	197	3	−1	−1	ADV
ejpam-5871	197	4	⋋s	⋋s	PROPN
ejpam-5871	197	5	(	(	PUNCT
ejpam-5871	197	6	χ)⋋	χ)⋋	NOUN
ejpam-5871	197	7	′	′	NUM
ejpam-5871	197	8	(	(	PUNCT
ejpam-5871	197	9	χ)[∅∗(χ	χ)[∅∗(χ	NOUN
ejpam-5871	197	10	)	)	PUNCT
ejpam-5871	197	11	+	+	CCONJ
ejpam-5871	197	12	ϕ∗(χ)]pdχ	ϕ∗(χ)]pdχ	NOUN
ejpam-5871	197	13	.	.	PUNCT
ejpam-5871	198	1	(	(	PUNCT
ejpam-5871	198	2	6	6	NUM
ejpam-5871	198	3	)	)	PUNCT
ejpam-5871	198	4	by	by	ADP
ejpam-5871	198	5	comparing	compare	VERB
ejpam-5871	198	6	the	the	DET
ejpam-5871	198	7	expressions	expression	NOUN
ejpam-5871	198	8	(	(	PUNCT
ejpam-5871	198	9	3	3	NUM
ejpam-5871	198	10	)	)	PUNCT
ejpam-5871	198	11	and	and	CCONJ
ejpam-5871	198	12	(	(	PUNCT
ejpam-5871	198	13	6	6	NUM
ejpam-5871	198	14	)	)	PUNCT
ejpam-5871	198	15	,	,	PUNCT
ejpam-5871	198	16	we	we	PRON
ejpam-5871	198	17	have[s	have[	VERB
ejpam-5871	198	18	k	k	PROPN
ejpam-5871	199	1	zβ	zβ	PROPN
ejpam-5871	199	2	r+1	r+1	PROPN
ejpam-5871	199	3	∅∗p(χ	∅∗p(χ	PROPN
ejpam-5871	199	4	)	)	PUNCT
ejpam-5871	199	5	]	]	PUNCT
ejpam-5871	200	1	1	1	NUM
ejpam-5871	200	2	p	p	NOUN
ejpam-5871	200	3	≤	≤	NUM
ejpam-5871	200	4	µ	µ	X
ejpam-5871	200	5	µ+	µ+	X
ejpam-5871	200	6	1	1	NUM
ejpam-5871	200	7	[	[	X
ejpam-5871	200	8	s	s	X
ejpam-5871	200	9	k	k	X
ejpam-5871	200	10	zβ	zβ	PROPN
ejpam-5871	201	1	r+1	r+1	PROPN
ejpam-5871	202	1	[	[	X
ejpam-5871	202	2	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	202	3	)	)	PUNCT
ejpam-5871	202	4	+	+	NUM
ejpam-5871	202	5	ϕ∗(χ)]p	ϕ∗(χ)]p	NOUN
ejpam-5871	202	6	]	]	X
ejpam-5871	202	7	1	1	NUM
ejpam-5871	202	8	p	p	NOUN
ejpam-5871	202	9	.	.	PUNCT
ejpam-5871	203	1	(	(	PUNCT
ejpam-5871	203	2	7	7	NUM
ejpam-5871	203	3	)	)	PUNCT
ejpam-5871	203	4	for	for	ADP
ejpam-5871	203	5	ϑ	ϑ	PRON
ejpam-5871	203	6	≤	≤	ADJ
ejpam-5871	203	7	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	203	8	)	)	PUNCT
ejpam-5871	203	9	ϕ∗(χ	ϕ∗(χ	PROPN
ejpam-5871	203	10	)	)	PUNCT
ejpam-5871	203	11	,	,	PUNCT
ejpam-5871	203	12	we	we	PRON
ejpam-5871	203	13	can	can	AUX
ejpam-5871	203	14	write	write	VERB
ejpam-5871	203	15	ϑp[∅∗(χ	ϑp[∅∗(χ	NOUN
ejpam-5871	203	16	)	)	PUNCT
ejpam-5871	203	17	+	+	NOUN
ejpam-5871	203	18	ϕ∗(χ	ϕ∗(χ	NOUN
ejpam-5871	203	19	)	)	PUNCT
ejpam-5871	203	20	]	]	PUNCT
ejpam-5871	204	1	p	p	X
ejpam-5871	204	2	≤	≤	NOUN
ejpam-5871	204	3	(	(	PUNCT
ejpam-5871	204	4	1	1	NUM
ejpam-5871	204	5	+	+	CCONJ
ejpam-5871	204	6	ϑ)p(∅∗(χ	ϑ)p(∅∗(χ	NOUN
ejpam-5871	204	7	)	)	PUNCT
ejpam-5871	204	8	)	)	PUNCT
ejpam-5871	205	1	p.	p.	NOUN
ejpam-5871	205	2	again	again	ADV
ejpam-5871	205	3	multiplying	multiply	VERB
ejpam-5871	205	4	by	by	ADP
ejpam-5871	205	5	(	(	PUNCT
ejpam-5871	205	6	s+1)1−	s+1)1−	PROPN
ejpam-5871	205	7	β	β	X
ejpam-5871	205	8	k	k	PROPN
ejpam-5871	205	9	kγk(β	kγk(β	PROPN
ejpam-5871	205	10	)	)	PUNCT
ejpam-5871	205	11	(	(	PUNCT
ejpam-5871	205	12	⋋s+1	⋋s+1	PROPN
ejpam-5871	205	13	(	(	PUNCT
ejpam-5871	205	14	r2	r2	PROPN
ejpam-5871	205	15	)	)	PUNCT
ejpam-5871	205	16	−	−	NOUN
ejpam-5871	205	17	⋋s+1(χ	⋋s+1(χ	NUM
ejpam-5871	205	18	)	)	PUNCT
ejpam-5871	205	19	)	)	PUNCT
ejpam-5871	206	1	β	β	X
ejpam-5871	206	2	k	k	X
ejpam-5871	206	3	−1	−1	ADV
ejpam-5871	206	4	⋋s	⋋s	PROPN
ejpam-5871	206	5	(	(	PUNCT
ejpam-5871	206	6	χ	χ	NOUN
ejpam-5871	206	7	)	)	PUNCT
ejpam-5871	206	8	⋋	⋋	NUM
ejpam-5871	206	9	′	′	NUM
ejpam-5871	206	10	(	(	PUNCT
ejpam-5871	206	11	χ	χ	X
ejpam-5871	206	12	)	)	PUNCT
ejpam-5871	206	13	and	and	CCONJ
ejpam-5871	206	14	applying	apply	VERB
ejpam-5871	206	15	the	the	DET
ejpam-5871	206	16	integration	integration	NOUN
ejpam-5871	206	17	over	over	ADP
ejpam-5871	206	18	[	[	X
ejpam-5871	206	19	r1	r1	NOUN
ejpam-5871	206	20	,	,	PUNCT
ejpam-5871	206	21	r2	r2	PROPN
ejpam-5871	206	22	]	]	PUNCT
ejpam-5871	206	23	w.r.t	w.r.t	NOUN
ejpam-5871	206	24	”	"	PUNCT
ejpam-5871	206	25	χ	χ	NOUN
ejpam-5871	206	26	”	"	PUNCT
ejpam-5871	206	27	,	,	PUNCT
ejpam-5871	206	28	we	we	PRON
ejpam-5871	206	29	have	have	VERB
ejpam-5871	206	30	ϑp	ϑp	NOUN
ejpam-5871	206	31	(	(	PUNCT
ejpam-5871	206	32	s+	s+	NUM
ejpam-5871	206	33	1)1−	1)1−	PROPN
ejpam-5871	206	34	β	β	X
ejpam-5871	206	35	k	k	PROPN
ejpam-5871	206	36	kγk(β	kγk(β	PROPN
ejpam-5871	206	37	)	)	PUNCT
ejpam-5871	206	38	∫	∫	PROPN
ejpam-5871	206	39	r2	r2	PROPN
ejpam-5871	206	40	r1	r1	PROPN
ejpam-5871	206	41	(	(	PUNCT
ejpam-5871	206	42	⋋s+1	⋋s+1	PROPN
ejpam-5871	206	43	(	(	PUNCT
ejpam-5871	206	44	r2)−⋋s+1(χ	r2)−⋋s+1(χ	NOUN
ejpam-5871	206	45	)	)	PUNCT
ejpam-5871	206	46	)	)	PUNCT
ejpam-5871	207	1	β	β	X
ejpam-5871	207	2	k	k	X
ejpam-5871	207	3	−1	−1	ADV
ejpam-5871	207	4	⋋s	⋋s	PROPN
ejpam-5871	207	5	(	(	PUNCT
ejpam-5871	207	6	χ)⋋	χ)⋋	NOUN
ejpam-5871	207	7	′	′	NUM
ejpam-5871	207	8	(	(	PUNCT
ejpam-5871	207	9	χ)[∅∗(χ	χ)[∅∗(χ	NOUN
ejpam-5871	207	10	)	)	PUNCT
ejpam-5871	207	11	+	+	NOUN
ejpam-5871	207	12	ϕ∗(χ	ϕ∗(χ	PROPN
ejpam-5871	207	13	)	)	PUNCT
ejpam-5871	207	14	]	]	PUNCT
ejpam-5871	207	15	pdχ	pdχ	PROPN
ejpam-5871	207	16	≤	≤	NUM
ejpam-5871	207	17	(	(	PUNCT
ejpam-5871	207	18	ϑ+	ϑ+	PROPN
ejpam-5871	207	19	1)p	1)p	NUM
ejpam-5871	207	20	(	(	PUNCT
ejpam-5871	207	21	s+	s+	NUM
ejpam-5871	207	22	1)1−	1)1−	PROPN
ejpam-5871	207	23	β	β	X
ejpam-5871	207	24	k	k	PROPN
ejpam-5871	207	25	kγk(β	kγk(β	PROPN
ejpam-5871	207	26	)	)	PUNCT
ejpam-5871	207	27	∫	∫	PROPN
ejpam-5871	207	28	r2	r2	PROPN
ejpam-5871	207	29	r1	r1	PROPN
ejpam-5871	207	30	(	(	PUNCT
ejpam-5871	207	31	⋋s+1	⋋s+1	PROPN
ejpam-5871	207	32	(	(	PUNCT
ejpam-5871	207	33	r2)−⋋s+1(χ	r2)−⋋s+1(χ	NOUN
ejpam-5871	207	34	)	)	PUNCT
ejpam-5871	207	35	)	)	PUNCT
ejpam-5871	207	36	β	β	X
ejpam-5871	207	37	k	k	X
ejpam-5871	207	38	−1	−1	ADV
ejpam-5871	207	39	⋋s	⋋s	PROPN
ejpam-5871	207	40	(	(	PUNCT
ejpam-5871	207	41	χ)⋋	χ)⋋	NOUN
ejpam-5871	207	42	′	′	NUM
ejpam-5871	207	43	(	(	PUNCT
ejpam-5871	207	44	χ)∅p	χ)∅p	NOUN
ejpam-5871	207	45	∗(χ)dχ	∗(χ)dχ	NOUN
ejpam-5871	207	46	.	.	PUNCT
ejpam-5871	207	47	(	(	PUNCT
ejpam-5871	207	48	8)	8)	NUM
ejpam-5871	207	49	again	again	ADV
ejpam-5871	207	50	by	by	ADP
ejpam-5871	207	51	comparing	compare	VERB
ejpam-5871	207	52	the	the	DET
ejpam-5871	207	53	expressions	expression	NOUN
ejpam-5871	207	54	(	(	PUNCT
ejpam-5871	207	55	3	3	NUM
ejpam-5871	207	56	)	)	PUNCT
ejpam-5871	207	57	and	and	CCONJ
ejpam-5871	207	58	(	(	PUNCT
ejpam-5871	207	59	8)	8)	NUM
ejpam-5871	207	60	,	,	PUNCT
ejpam-5871	207	61	we	we	PRON
ejpam-5871	207	62	have	have	VERB
ejpam-5871	207	63	ϑ	ϑ	X
ejpam-5871	207	64	ϑ+	ϑ+	X
ejpam-5871	207	65	1	1	NUM
ejpam-5871	207	66	[	[	X
ejpam-5871	207	67	s	s	X
ejpam-5871	207	68	k	k	X
ejpam-5871	207	69	zβ	zβ	PROPN
ejpam-5871	208	1	r+1	r+1	PROPN
ejpam-5871	209	1	[	[	X
ejpam-5871	209	2	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	209	3	)	)	PUNCT
ejpam-5871	209	4	+	+	NOUN
ejpam-5871	209	5	ϕ∗(χ	ϕ∗(χ	NOUN
ejpam-5871	209	6	)	)	PUNCT
ejpam-5871	209	7	]	]	PUNCT
ejpam-5871	210	1	p	p	X
ejpam-5871	210	2	]	]	PUNCT
ejpam-5871	210	3	1	1	NUM
ejpam-5871	210	4	p	p	NOUN
ejpam-5871	210	5	≤	≤	NOUN
ejpam-5871	211	1	[	[	X
ejpam-5871	211	2	s	s	X
ejpam-5871	211	3	k	k	X
ejpam-5871	211	4	zβ	zβ	PROPN
ejpam-5871	211	5	r+1	r+1	PROPN
ejpam-5871	211	6	∅p	∅p	VERB
ejpam-5871	211	7	∗(χ	∗(χ	NOUN
ejpam-5871	211	8	)	)	PUNCT
ejpam-5871	211	9	]	]	PUNCT
ejpam-5871	211	10	1	1	NUM
ejpam-5871	211	11	p	p	NOUN
ejpam-5871	211	12	.	.	PUNCT
ejpam-5871	212	1	(	(	PUNCT
ejpam-5871	212	2	9	9	NUM
ejpam-5871	212	3	)	)	PUNCT
ejpam-5871	212	4	from	from	ADP
ejpam-5871	212	5	the	the	DET
ejpam-5871	212	6	expressions	expression	NOUN
ejpam-5871	212	7	(	(	PUNCT
ejpam-5871	212	8	7	7	NUM
ejpam-5871	212	9	)	)	PUNCT
ejpam-5871	212	10	and	and	CCONJ
ejpam-5871	212	11	(	(	PUNCT
ejpam-5871	212	12	9)red	9)red	NUM
ejpam-5871	212	13	,	,	PUNCT
ejpam-5871	212	14	we	we	PRON
ejpam-5871	212	15	have	have	VERB
ejpam-5871	212	16	[	[	X
ejpam-5871	212	17	s	s	X
ejpam-5871	212	18	k	k	X
ejpam-5871	212	19	zβ	zβ	PROPN
ejpam-5871	212	20	r+1	r+1	PROPN
ejpam-5871	212	21	∅p(χ	∅p(χ	PROPN
ejpam-5871	212	22	)	)	PUNCT
ejpam-5871	212	23	]	]	PUNCT
ejpam-5871	213	1	1	1	NUM
ejpam-5871	213	2	p	p	NOUN
ejpam-5871	213	3	=	=	PUNCT
ejpam-5871	214	1	[	[	X
ejpam-5871	214	2	[	[	X
ejpam-5871	214	3	s	s	X
ejpam-5871	214	4	k	k	X
ejpam-5871	214	5	zβ	zβ	PROPN
ejpam-5871	214	6	r+1	r+1	PROPN
ejpam-5871	214	7	∅p	∅p	VERB
ejpam-5871	214	8	∗(χ	∗(χ	NOUN
ejpam-5871	214	9	)	)	PUNCT
ejpam-5871	214	10	]	]	PUNCT
ejpam-5871	214	11	1	1	NUM
ejpam-5871	214	12	p	p	NOUN
ejpam-5871	214	13	,	,	PUNCT
ejpam-5871	215	1	[	[	X
ejpam-5871	215	2	s	s	X
ejpam-5871	215	3	k	k	X
ejpam-5871	215	4	zβ	zβ	PROPN
ejpam-5871	215	5	r+1	r+1	PROPN
ejpam-5871	215	6	∅∗p(χ	∅∗p(χ	PROPN
ejpam-5871	215	7	)	)	PUNCT
ejpam-5871	215	8	]	]	PUNCT
ejpam-5871	215	9	1	1	NUM
ejpam-5871	215	10	p	p	X
ejpam-5871	215	11	]	]	X
ejpam-5871	215	12	⊇	⊇	X
ejpam-5871	215	13	[	[	PUNCT
ejpam-5871	215	14	ϑ	ϑ	X
ejpam-5871	215	15	ϑ+	ϑ+	X
ejpam-5871	215	16	1	1	NUM
ejpam-5871	215	17	[	[	X
ejpam-5871	215	18	s	s	X
ejpam-5871	215	19	k	k	X
ejpam-5871	216	1	zβ	zβ	PROPN
ejpam-5871	216	2	r+1	r+1	PROPN
ejpam-5871	217	1	[	[	X
ejpam-5871	217	2	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	217	3	)	)	PUNCT
ejpam-5871	217	4	+	+	NOUN
ejpam-5871	217	5	ϕ∗(χ	ϕ∗(χ	NOUN
ejpam-5871	217	6	)	)	PUNCT
ejpam-5871	217	7	]	]	PUNCT
ejpam-5871	218	1	p	p	X
ejpam-5871	218	2	]	]	PUNCT
ejpam-5871	218	3	1	1	NUM
ejpam-5871	218	4	p	p	NOUN
ejpam-5871	218	5	,	,	PUNCT
ejpam-5871	218	6	µ	µ	X
ejpam-5871	218	7	µ+	µ+	X
ejpam-5871	218	8	1	1	NUM
ejpam-5871	219	1	[	[	X
ejpam-5871	219	2	s	s	X
ejpam-5871	219	3	k	k	X
ejpam-5871	219	4	zβ	zβ	PROPN
ejpam-5871	220	1	r+1	r+1	PROPN
ejpam-5871	221	1	[	[	X
ejpam-5871	221	2	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	221	3	)	)	PUNCT
ejpam-5871	221	4	+	+	NUM
ejpam-5871	221	5	ϕ∗(χ)]p	ϕ∗(χ)]p	NOUN
ejpam-5871	221	6	]	]	X
ejpam-5871	221	7	1	1	NUM
ejpam-5871	221	8	p	p	NOUN
ejpam-5871	221	9	]	]	X
ejpam-5871	221	10	=	=	PUNCT
ejpam-5871	221	11	[	[	PUNCT
ejpam-5871	221	12	ϑ	ϑ	X
ejpam-5871	221	13	ϑ+	ϑ+	X
ejpam-5871	221	14	1	1	NUM
ejpam-5871	221	15	,	,	PUNCT
ejpam-5871	221	16	µ	µ	X
ejpam-5871	221	17	µ+	µ+	X
ejpam-5871	221	18	1	1	NUM
ejpam-5871	221	19	]	]	PUNCT
ejpam-5871	222	1	[	[	X
ejpam-5871	222	2	s	s	X
ejpam-5871	222	3	k	k	X
ejpam-5871	222	4	zβ	zβ	PROPN
ejpam-5871	222	5	r+1	r+1	PROPN
ejpam-5871	223	1	[	[	X
ejpam-5871	223	2	∅(χ	∅(χ	X
ejpam-5871	223	3	)	)	PUNCT
ejpam-5871	223	4	+	+	CCONJ
ejpam-5871	223	5	ϕ(χ)]p	ϕ(χ)]p	X
ejpam-5871	223	6	]	]	PUNCT
ejpam-5871	223	7	1	1	NUM
ejpam-5871	223	8	p	p	NOUN
ejpam-5871	223	9	.	.	PUNCT
ejpam-5871	224	1	(	(	PUNCT
ejpam-5871	224	2	10	10	NUM
ejpam-5871	224	3	)	)	PUNCT
ejpam-5871	224	4	continuing	continue	VERB
ejpam-5871	224	5	the	the	DET
ejpam-5871	224	6	same	same	ADJ
ejpam-5871	224	7	procedure	procedure	NOUN
ejpam-5871	224	8	for	for	ADP
ejpam-5871	224	9	ϑ	ϑ	PRON
ejpam-5871	224	10	≤	≤	ADJ
ejpam-5871	224	11	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	224	12	)	)	PUNCT
ejpam-5871	224	13	ϕ∗(χ	ϕ∗(χ	PROPN
ejpam-5871	224	14	)	)	PUNCT
ejpam-5871	224	15	,	,	PUNCT
ejpam-5871	224	16	then	then	ADV
ejpam-5871	224	17	we	we	PRON
ejpam-5871	224	18	have	have	VERB
ejpam-5871	224	19	[	[	X
ejpam-5871	224	20	s	s	X
ejpam-5871	224	21	k	k	X
ejpam-5871	224	22	zβ	zβ	PROPN
ejpam-5871	224	23	r+1	r+1	PROPN
ejpam-5871	224	24	ϕ∗p(χ	ϕ∗p(χ	PROPN
ejpam-5871	224	25	)	)	PUNCT
ejpam-5871	224	26	]	]	PUNCT
ejpam-5871	225	1	1	1	NUM
ejpam-5871	225	2	p	p	NOUN
ejpam-5871	225	3	≤	≤	NUM
ejpam-5871	225	4	1	1	NUM
ejpam-5871	225	5	ϑ+	ϑ+	SYM
ejpam-5871	225	6	1	1	NUM
ejpam-5871	226	1	[	[	X
ejpam-5871	226	2	s	s	X
ejpam-5871	226	3	k	k	X
ejpam-5871	226	4	zβ	zβ	PROPN
ejpam-5871	227	1	r+1	r+1	PROPN
ejpam-5871	228	1	[	[	X
ejpam-5871	228	2	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	228	3	)	)	PUNCT
ejpam-5871	228	4	+	+	NUM
ejpam-5871	228	5	ϕ∗(χ)]p	ϕ∗(χ)]p	NOUN
ejpam-5871	228	6	]	]	X
ejpam-5871	228	7	1	1	NUM
ejpam-5871	228	8	p	p	NOUN
ejpam-5871	228	9	.	.	PUNCT
ejpam-5871	229	1	(	(	PUNCT
ejpam-5871	229	2	11	11	NUM
ejpam-5871	229	3	)	)	PUNCT
ejpam-5871	229	4	also	also	ADV
ejpam-5871	229	5	for	for	ADP
ejpam-5871	229	6	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	229	7	)	)	PUNCT
ejpam-5871	229	8	ϕ∗(χ	ϕ∗(χ	PROPN
ejpam-5871	229	9	)	)	PUNCT
ejpam-5871	229	10	≤	≤	NOUN
ejpam-5871	229	11	µ	µ	NUM
ejpam-5871	229	12	,	,	PUNCT
ejpam-5871	229	13	we	we	PRON
ejpam-5871	229	14	have	have	VERB
ejpam-5871	229	15	1	1	NUM
ejpam-5871	229	16	µ+	µ+	SYM
ejpam-5871	229	17	1	1	NUM
ejpam-5871	230	1	[	[	X
ejpam-5871	230	2	s	s	X
ejpam-5871	230	3	k	k	X
ejpam-5871	230	4	zβ	zβ	PROPN
ejpam-5871	231	1	r+1	r+1	PROPN
ejpam-5871	232	1	[	[	X
ejpam-5871	232	2	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	232	3	)	)	PUNCT
ejpam-5871	232	4	+	+	NOUN
ejpam-5871	232	5	ϕ∗(χ	ϕ∗(χ	NOUN
ejpam-5871	232	6	)	)	PUNCT
ejpam-5871	232	7	]	]	PUNCT
ejpam-5871	233	1	p	p	X
ejpam-5871	233	2	]	]	PUNCT
ejpam-5871	233	3	1	1	NUM
ejpam-5871	233	4	p	p	NOUN
ejpam-5871	233	5	≤	≤	NOUN
ejpam-5871	234	1	[	[	X
ejpam-5871	234	2	s	s	X
ejpam-5871	234	3	k	k	X
ejpam-5871	234	4	zβ	zβ	PROPN
ejpam-5871	234	5	r+1	r+1	PROPN
ejpam-5871	234	6	ϕp	ϕp	PROPN
ejpam-5871	234	7	∗(χ	∗(χ	PROPN
ejpam-5871	234	8	)	)	PUNCT
ejpam-5871	234	9	]	]	PUNCT
ejpam-5871	234	10	1	1	NUM
ejpam-5871	234	11	p	p	NOUN
ejpam-5871	234	12	.	.	PUNCT
ejpam-5871	235	1	(	(	PUNCT
ejpam-5871	235	2	12	12	NUM
ejpam-5871	235	3	)	)	PUNCT
ejpam-5871	235	4	a.	a.	NOUN
ejpam-5871	235	5	mehmood	mehmood	PROPN
ejpam-5871	235	6	et	et	PROPN
ejpam-5871	235	7	al	al	PROPN
ejpam-5871	235	8	.	.	PUNCT
ejpam-5871	235	9	/	/	SYM
ejpam-5871	235	10	eur	eur	PROPN
ejpam-5871	235	11	.	.	PUNCT
ejpam-5871	236	1	j.	j.	PROPN
ejpam-5871	236	2	pure	pure	PROPN
ejpam-5871	236	3	appl	appl	PROPN
ejpam-5871	236	4	.	.	PROPN
ejpam-5871	236	5	math	math	PROPN
ejpam-5871	236	6	,	,	PUNCT
ejpam-5871	236	7	18	18	NUM
ejpam-5871	236	8	(	(	PUNCT
ejpam-5871	236	9	2	2	NUM
ejpam-5871	236	10	)	)	PUNCT
ejpam-5871	236	11	(	(	PUNCT
ejpam-5871	236	12	2025	2025	NUM
ejpam-5871	236	13	)	)	PUNCT
ejpam-5871	236	14	,	,	PUNCT
ejpam-5871	236	15	5871	5871	NUM
ejpam-5871	236	16	9	9	NUM
ejpam-5871	236	17	of	of	ADP
ejpam-5871	236	18	26	26	NUM
ejpam-5871	236	19	from	from	ADP
ejpam-5871	236	20	the	the	DET
ejpam-5871	236	21	expressions	expression	NOUN
ejpam-5871	236	22	(	(	PUNCT
ejpam-5871	236	23	11	11	NUM
ejpam-5871	236	24	)	)	PUNCT
ejpam-5871	236	25	and	and	CCONJ
ejpam-5871	236	26	(	(	PUNCT
ejpam-5871	236	27	12	12	NUM
ejpam-5871	236	28	)	)	PUNCT
ejpam-5871	236	29	,	,	PUNCT
ejpam-5871	236	30	we	we	PRON
ejpam-5871	236	31	have	have	VERB
ejpam-5871	236	32	[	[	X
ejpam-5871	236	33	s	s	X
ejpam-5871	236	34	k	k	X
ejpam-5871	236	35	zβ	zβ	PROPN
ejpam-5871	236	36	r+1	r+1	PROPN
ejpam-5871	236	37	ϕp(χ	ϕp(χ	PUNCT
ejpam-5871	236	38	)	)	PUNCT
ejpam-5871	236	39	]	]	PUNCT
ejpam-5871	237	1	1	1	NUM
ejpam-5871	237	2	p	p	NOUN
ejpam-5871	237	3	=	=	PUNCT
ejpam-5871	238	1	[	[	X
ejpam-5871	238	2	[	[	X
ejpam-5871	238	3	s	s	X
ejpam-5871	238	4	k	k	X
ejpam-5871	238	5	zβ	zβ	PROPN
ejpam-5871	238	6	r+1	r+1	PROPN
ejpam-5871	238	7	ϕp	ϕp	PROPN
ejpam-5871	238	8	∗(χ	∗(χ	PROPN
ejpam-5871	238	9	)	)	PUNCT
ejpam-5871	238	10	]	]	PUNCT
ejpam-5871	238	11	1	1	NUM
ejpam-5871	238	12	p	p	NOUN
ejpam-5871	238	13	,	,	PUNCT
ejpam-5871	239	1	[	[	X
ejpam-5871	239	2	s	s	X
ejpam-5871	239	3	k	k	X
ejpam-5871	239	4	zβ	zβ	PROPN
ejpam-5871	239	5	r+1	r+1	PROPN
ejpam-5871	239	6	ϕ∗p(χ	ϕ∗p(χ	PROPN
ejpam-5871	239	7	)	)	PUNCT
ejpam-5871	239	8	]	]	PUNCT
ejpam-5871	240	1	1	1	NUM
ejpam-5871	240	2	p	p	X
ejpam-5871	240	3	]	]	X
ejpam-5871	240	4	⊇	⊇	X
ejpam-5871	240	5	[	[	PUNCT
ejpam-5871	240	6	1	1	NUM
ejpam-5871	240	7	µ+	µ+	SYM
ejpam-5871	240	8	1	1	NUM
ejpam-5871	240	9	[	[	X
ejpam-5871	240	10	s	s	X
ejpam-5871	240	11	k	k	X
ejpam-5871	240	12	zβ	zβ	PROPN
ejpam-5871	241	1	r+1	r+1	PROPN
ejpam-5871	242	1	[	[	X
ejpam-5871	242	2	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	242	3	)	)	PUNCT
ejpam-5871	242	4	+	+	NOUN
ejpam-5871	242	5	ϕ∗(χ	ϕ∗(χ	NOUN
ejpam-5871	242	6	)	)	PUNCT
ejpam-5871	242	7	]	]	PUNCT
ejpam-5871	243	1	p	p	X
ejpam-5871	243	2	]	]	PUNCT
ejpam-5871	243	3	1	1	NUM
ejpam-5871	243	4	p	p	NOUN
ejpam-5871	243	5	,	,	PUNCT
ejpam-5871	243	6	1	1	NUM
ejpam-5871	243	7	ϑ+	ϑ+	SYM
ejpam-5871	243	8	1	1	NUM
ejpam-5871	244	1	[	[	X
ejpam-5871	244	2	s	s	X
ejpam-5871	244	3	k	k	X
ejpam-5871	244	4	zβ	zβ	PROPN
ejpam-5871	245	1	r+1	r+1	PROPN
ejpam-5871	246	1	[	[	X
ejpam-5871	246	2	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	246	3	)	)	PUNCT
ejpam-5871	246	4	+	+	NUM
ejpam-5871	246	5	ϕ∗(χ)]p	ϕ∗(χ)]p	NOUN
ejpam-5871	246	6	]	]	X
ejpam-5871	246	7	1	1	NUM
ejpam-5871	246	8	p	p	NOUN
ejpam-5871	246	9	]	]	X
ejpam-5871	246	10	=	=	PUNCT
ejpam-5871	246	11	[	[	PUNCT
ejpam-5871	246	12	1	1	NUM
ejpam-5871	246	13	µ+	µ+	SYM
ejpam-5871	246	14	1	1	NUM
ejpam-5871	246	15	,	,	PUNCT
ejpam-5871	246	16	1	1	NUM
ejpam-5871	246	17	ϑ+	ϑ+	SYM
ejpam-5871	246	18	1	1	NUM
ejpam-5871	246	19	]	]	PUNCT
ejpam-5871	246	20	[	[	X
ejpam-5871	246	21	s	s	X
ejpam-5871	246	22	k	k	X
ejpam-5871	246	23	zβ	zβ	PROPN
ejpam-5871	246	24	r+1	r+1	PROPN
ejpam-5871	247	1	[	[	X
ejpam-5871	247	2	∅(χ	∅(χ	X
ejpam-5871	247	3	)	)	PUNCT
ejpam-5871	247	4	+	+	CCONJ
ejpam-5871	247	5	ϕ(χ)]p	ϕ(χ)]p	X
ejpam-5871	247	6	]	]	PUNCT
ejpam-5871	247	7	1	1	NUM
ejpam-5871	247	8	p	p	NOUN
ejpam-5871	247	9	(	(	PUNCT
ejpam-5871	247	10	13	13	NUM
ejpam-5871	247	11	)	)	PUNCT
ejpam-5871	247	12	hence	hence	ADV
ejpam-5871	247	13	by	by	ADP
ejpam-5871	247	14	adding	add	VERB
ejpam-5871	247	15	(	(	PUNCT
ejpam-5871	247	16	10	10	NUM
ejpam-5871	247	17	)	)	PUNCT
ejpam-5871	247	18	and	and	CCONJ
ejpam-5871	247	19	(	(	PUNCT
ejpam-5871	247	20	13	13	X
ejpam-5871	247	21	)	)	PUNCT
ejpam-5871	247	22	we	we	PRON
ejpam-5871	247	23	get	get	VERB
ejpam-5871	247	24	the	the	DET
ejpam-5871	247	25	required	require	VERB
ejpam-5871	247	26	result	result	NOUN
ejpam-5871	247	27	(	(	PUNCT
ejpam-5871	247	28	5	5	NUM
ejpam-5871	247	29	)	)	PUNCT
ejpam-5871	247	30	.	.	PUNCT
ejpam-5871	248	1	in	in	ADP
ejpam-5871	248	2	this	this	DET
ejpam-5871	248	3	result	result	NOUN
ejpam-5871	248	4	,	,	PUNCT
ejpam-5871	248	5	redwe	redwe	NOUN
ejpam-5871	248	6	are	be	AUX
ejpam-5871	248	7	going	go	VERB
ejpam-5871	248	8	to	to	PART
ejpam-5871	248	9	present	present	VERB
ejpam-5871	248	10	the	the	DET
ejpam-5871	248	11	fractional	fractional	ADJ
ejpam-5871	248	12	reverse	reverse	NOUN
ejpam-5871	248	13	holder	holder	NOUN
ejpam-5871	248	14	’s	’s	PART
ejpam-5871	248	15	inequality	inequality	NOUN
ejpam-5871	248	16	involving	involve	VERB
ejpam-5871	248	17	(	(	PUNCT
ejpam-5871	248	18	k	k	NOUN
ejpam-5871	248	19	,	,	PUNCT
ejpam-5871	248	20	s)-grlfio	s)-grlfio	PROPN
ejpam-5871	248	21	.	.	PUNCT
ejpam-5871	249	1	theorem	theorem	NOUN
ejpam-5871	249	2	5	5	NUM
ejpam-5871	249	3	.	.	PUNCT
ejpam-5871	250	1	let	let	VERB
ejpam-5871	250	2	s	s	PRON
ejpam-5871	250	3	∈	∈	VERB
ejpam-5871	250	4	r/{−1	r/{−1	PROPN
ejpam-5871	250	5	}	}	PUNCT
ejpam-5871	250	6	,	,	PUNCT
ejpam-5871	250	7	k	k	X
ejpam-5871	250	8	≥	≥	NOUN
ejpam-5871	250	9	0	0	NUM
ejpam-5871	250	10	,	,	PUNCT
ejpam-5871	250	11	also	also	ADV
ejpam-5871	250	12	∅	∅	NOUN
ejpam-5871	250	13	,	,	PUNCT
ejpam-5871	250	14	ϕ	ϕ	X
ejpam-5871	250	15	:	:	PUNCT
ejpam-5871	251	1	[	[	X
ejpam-5871	251	2	r1	r1	NOUN
ejpam-5871	251	3	,	,	PUNCT
ejpam-5871	251	4	r2	r2	PROPN
ejpam-5871	251	5	]	]	PUNCT
ejpam-5871	251	6	→	→	SYM
ejpam-5871	251	7	r+	r+	PUNCT
ejpam-5871	251	8	i	i	PRON
ejpam-5871	251	9	be	be	VERB
ejpam-5871	251	10	ı.υ	ı.υ	PROPN
ejpam-5871	251	11	functions	function	NOUN
ejpam-5871	251	12	such	such	ADJ
ejpam-5871	251	13	that	that	DET
ejpam-5871	251	14	∅(χ	∅(χ	NOUN
ejpam-5871	251	15	)	)	PUNCT
ejpam-5871	251	16	=	=	PUNCT
ejpam-5871	252	1	[	[	X
ejpam-5871	252	2	∅∗,∅∗	∅∗,∅∗	X
ejpam-5871	252	3	]	]	PUNCT
ejpam-5871	252	4	and	and	CCONJ
ejpam-5871	252	5	ϕ(χ	ϕ(χ	NUM
ejpam-5871	252	6	)	)	PUNCT
ejpam-5871	253	1	=	=	PUNCT
ejpam-5871	254	1	[	[	X
ejpam-5871	254	2	ϕ∗	ϕ∗	PROPN
ejpam-5871	254	3	,	,	PUNCT
ejpam-5871	254	4	ϕ	ϕ	NOUN
ejpam-5871	254	5	∗	∗	NOUN
ejpam-5871	254	6	]	]	PUNCT
ejpam-5871	254	7	,	,	PUNCT
ejpam-5871	254	8	(	(	PUNCT
ejpam-5871	254	9	s	s	AUX
ejpam-5871	254	10	kz	kz	PROPN
ejpam-5871	254	11	β	β	PROPN
ejpam-5871	254	12	r+1	r+1	PROPN
ejpam-5871	254	13	∅p(χ	∅p(χ	PROPN
ejpam-5871	254	14	)	)	PUNCT
ejpam-5871	254	15	)	)	PUNCT
ejpam-5871	255	1	<	<	X
ejpam-5871	255	2	∞	∞	PROPN
ejpam-5871	255	3	and	and	CCONJ
ejpam-5871	255	4	(	(	PUNCT
ejpam-5871	255	5	s	s	AUX
ejpam-5871	255	6	kz	kz	PROPN
ejpam-5871	255	7	β	β	PROPN
ejpam-5871	255	8	r+1	r+1	PROPN
ejpam-5871	255	9	ϕp(χ	ϕp(χ	PUNCT
ejpam-5871	255	10	)	)	PUNCT
ejpam-5871	255	11	)	)	PUNCT
ejpam-5871	256	1	<	<	X
ejpam-5871	256	2	∞	∞	PROPN
ejpam-5871	256	3	,	,	PUNCT
ejpam-5871	256	4	then	then	ADV
ejpam-5871	256	5	the	the	DET
ejpam-5871	256	6	expression	expression	NOUN
ejpam-5871	256	7	(	(	PUNCT
ejpam-5871	256	8	14	14	NUM
ejpam-5871	256	9	)	)	PUNCT
ejpam-5871	256	10	holds	hold	VERB
ejpam-5871	256	11	.	.	PUNCT
ejpam-5871	257	1	[	[	X
ejpam-5871	257	2	(	(	PUNCT
ejpam-5871	257	3	ϑ	ϑ	X
ejpam-5871	257	4	µ	µ	X
ejpam-5871	257	5	)	)	PUNCT
ejpam-5871	257	6	1	1	NUM
ejpam-5871	257	7	pq	pq	INTJ
ejpam-5871	257	8	,	,	PUNCT
ejpam-5871	257	9	(	(	PUNCT
ejpam-5871	257	10	µ	µ	X
ejpam-5871	257	11	ϑ	ϑ	X
ejpam-5871	257	12	)	)	PUNCT
ejpam-5871	257	13	1	1	NUM
ejpam-5871	257	14	pq	pq	NOUN
ejpam-5871	257	15	]	]	PUNCT
ejpam-5871	258	1	[	[	X
ejpam-5871	258	2	skz	skz	X
ejpam-5871	258	3	β	β	X
ejpam-5871	258	4	r+1	r+1	X
ejpam-5871	259	1	[	[	X
ejpam-5871	259	2	∅	∅	NOUN
ejpam-5871	259	3	1	1	NUM
ejpam-5871	259	4	p	p	NOUN
ejpam-5871	259	5	(	(	PUNCT
ejpam-5871	259	6	χ)ϕ	χ)ϕ	NOUN
ejpam-5871	259	7	1	1	NUM
ejpam-5871	259	8	q	q	NOUN
ejpam-5871	259	9	(	(	PUNCT
ejpam-5871	259	10	χ	χ	NOUN
ejpam-5871	259	11	)	)	PUNCT
ejpam-5871	259	12	]	]	X
ejpam-5871	259	13	]	]	X
ejpam-5871	259	14	⊇	⊇	NOUN
ejpam-5871	259	15	[	[	X
ejpam-5871	259	16	skz	skz	X
ejpam-5871	259	17	β	β	X
ejpam-5871	259	18	r+1	r+1	X
ejpam-5871	259	19	∅(χ	∅(χ	PROPN
ejpam-5871	259	20	)	)	PUNCT
ejpam-5871	259	21	]	]	PUNCT
ejpam-5871	260	1	1	1	NUM
ejpam-5871	260	2	p	p	NOUN
ejpam-5871	260	3	[	[	X
ejpam-5871	260	4	skz	skz	X
ejpam-5871	260	5	β	β	X
ejpam-5871	260	6	r+1	r+1	PROPN
ejpam-5871	260	7	ϕ(χ	ϕ(χ	PROPN
ejpam-5871	260	8	)	)	PUNCT
ejpam-5871	260	9	]	]	PUNCT
ejpam-5871	260	10	1	1	NUM
ejpam-5871	260	11	q	q	NOUN
ejpam-5871	260	12	,	,	PUNCT
ejpam-5871	260	13	(	(	PUNCT
ejpam-5871	260	14	14	14	NUM
ejpam-5871	260	15	)	)	PUNCT
ejpam-5871	260	16	where	where	SCONJ
ejpam-5871	260	17	,	,	PUNCT
ejpam-5871	260	18	0	0	PUNCT
ejpam-5871	260	19	<	<	X
ejpam-5871	260	20	ϑ	ϑ	X
ejpam-5871	260	21	≤	≤	ADJ
ejpam-5871	260	22	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	260	23	)	)	PUNCT
ejpam-5871	260	24	ϕ∗(χ	ϕ∗(χ	PROPN
ejpam-5871	260	25	)	)	PUNCT
ejpam-5871	260	26	≤	≤	NOUN
ejpam-5871	260	27	µ	µ	ADP
ejpam-5871	260	28	and	and	CCONJ
ejpam-5871	260	29	0	0	NUM
ejpam-5871	260	30	<	<	X
ejpam-5871	260	31	ϑ	ϑ	X
ejpam-5871	260	32	≤	≤	ADJ
ejpam-5871	260	33	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	260	34	)	)	PUNCT
ejpam-5871	260	35	ϕ∗(χ	ϕ∗(χ	PROPN
ejpam-5871	260	36	)	)	PUNCT
ejpam-5871	260	37	≤	≤	NOUN
ejpam-5871	260	38	µ	µ	X
ejpam-5871	260	39	for	for	ADP
ejpam-5871	260	40	χ	χ	PROPN
ejpam-5871	260	41	∈	∈	PROPN
ejpam-5871	260	42	[	[	X
ejpam-5871	260	43	r1	r1	NOUN
ejpam-5871	260	44	,	,	PUNCT
ejpam-5871	260	45	r2	r2	PROPN
ejpam-5871	260	46	]	]	PUNCT
ejpam-5871	260	47	,	,	PUNCT
ejpam-5871	260	48	p	p	X
ejpam-5871	260	49	>	>	X
ejpam-5871	260	50	1	1	NUM
ejpam-5871	260	51	and	and	CCONJ
ejpam-5871	260	52	1	1	NUM
ejpam-5871	260	53	p	p	NOUN
ejpam-5871	260	54	+	+	NOUN
ejpam-5871	260	55	1	1	NUM
ejpam-5871	260	56	q	q	NOUN
ejpam-5871	260	57	=	=	NOUN
ejpam-5871	260	58	1	1	NUM
ejpam-5871	260	59	with	with	ADP
ejpam-5871	260	60	β	β	X
ejpam-5871	260	61	>	>	X
ejpam-5871	260	62	0	0	X
ejpam-5871	260	63	.	.	PUNCT
ejpam-5871	260	64	proof	proof	NOUN
ejpam-5871	260	65	.	.	PUNCT
ejpam-5871	261	1	since	since	SCONJ
ejpam-5871	261	2	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	261	3	)	)	PUNCT
ejpam-5871	261	4	ϕ∗(χ	ϕ∗(χ	PROPN
ejpam-5871	261	5	)	)	PUNCT
ejpam-5871	261	6	≤	≤	NOUN
ejpam-5871	261	7	µ	µ	NUM
ejpam-5871	261	8	,	,	PUNCT
ejpam-5871	261	9	implies	imply	VERB
ejpam-5871	261	10	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	261	11	)	)	PUNCT
ejpam-5871	261	12	≤	≤	NOUN
ejpam-5871	261	13	µ	µ	PRON
ejpam-5871	261	14	1	1	NUM
ejpam-5871	261	15	q∅∗	q∅∗	PROPN
ejpam-5871	261	16	1	1	NUM
ejpam-5871	261	17	p	p	NOUN
ejpam-5871	261	18	(	(	PUNCT
ejpam-5871	261	19	χ)ϕ	χ)ϕ	NOUN
ejpam-5871	261	20	∗	∗	NOUN
ejpam-5871	261	21	1	1	NUM
ejpam-5871	261	22	q	q	NOUN
ejpam-5871	261	23	(	(	PUNCT
ejpam-5871	261	24	χ	χ	NOUN
ejpam-5871	261	25	)	)	PUNCT
ejpam-5871	261	26	.	.	PUNCT
ejpam-5871	262	1	multiplying	multiply	VERB
ejpam-5871	262	2	by	by	ADP
ejpam-5871	262	3	(	(	PUNCT
ejpam-5871	262	4	s+1)1−	s+1)1−	PROPN
ejpam-5871	262	5	β	β	X
ejpam-5871	262	6	k	k	PROPN
ejpam-5871	262	7	kγk(β	kγk(β	PROPN
ejpam-5871	262	8	)	)	PUNCT
ejpam-5871	262	9	(	(	PUNCT
ejpam-5871	262	10	⋋s+1(r2)−⋋s+1(χ	⋋s+1(r2)−⋋s+1(χ	PROPN
ejpam-5871	262	11	)	)	PUNCT
ejpam-5871	262	12	)	)	PUNCT
ejpam-5871	263	1	β	β	X
ejpam-5871	263	2	k	k	X
ejpam-5871	263	3	−1	−1	NOUN
ejpam-5871	263	4	⋋s(χ)⋋	⋋s(χ)⋋	AUX
ejpam-5871	263	5	′	′	NUM
ejpam-5871	263	6	(	(	PUNCT
ejpam-5871	263	7	χ	χ	NOUN
ejpam-5871	263	8	)	)	PUNCT
ejpam-5871	263	9	and	and	CCONJ
ejpam-5871	263	10	applying	apply	VERB
ejpam-5871	263	11	the	the	DET
ejpam-5871	263	12	integration	integration	NOUN
ejpam-5871	263	13	over	over	ADP
ejpam-5871	263	14	[	[	X
ejpam-5871	263	15	r1	r1	NOUN
ejpam-5871	263	16	,	,	PUNCT
ejpam-5871	263	17	r2	r2	PROPN
ejpam-5871	263	18	]	]	PUNCT
ejpam-5871	263	19	w.r.t	w.r.t	NOUN
ejpam-5871	263	20	”	"	PUNCT
ejpam-5871	263	21	χ”red	χ”re	VERB
ejpam-5871	263	22	,	,	PUNCT
ejpam-5871	263	23	so	so	ADV
ejpam-5871	263	24	we	we	PRON
ejpam-5871	263	25	have	have	VERB
ejpam-5871	263	26	[	[	X
ejpam-5871	263	27	skz	skz	X
ejpam-5871	263	28	β	β	X
ejpam-5871	263	29	r+1	r+1	PROPN
ejpam-5871	263	30	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	263	31	)	)	PUNCT
ejpam-5871	263	32	]	]	PUNCT
ejpam-5871	263	33	1	1	NUM
ejpam-5871	263	34	p	p	NOUN
ejpam-5871	263	35	≤	≤	NUM
ejpam-5871	263	36	µ	µ	PRON
ejpam-5871	263	37	1	1	NUM
ejpam-5871	263	38	pq	pq	NOUN
ejpam-5871	264	1	[	[	X
ejpam-5871	264	2	skz	skz	X
ejpam-5871	264	3	β	β	X
ejpam-5871	264	4	r+1	r+1	NOUN
ejpam-5871	264	5	]	]	X
ejpam-5871	265	1	[	[	PUNCT
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ejpam-5871	265	5	(	(	PUNCT
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ejpam-5871	265	8	1	1	NUM
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ejpam-5871	265	13	]	]	PUNCT
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ejpam-5871	266	2	15	15	NUM
ejpam-5871	266	3	)	)	PUNCT
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ejpam-5871	266	6	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	266	7	)	)	PUNCT
ejpam-5871	266	8	ϕ∗(χ	ϕ∗(χ	PROPN
ejpam-5871	266	9	)	)	PUNCT
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ejpam-5871	266	11	ϑ	ϑ	NOUN
ejpam-5871	266	12	,	,	PUNCT
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ejpam-5871	266	14	have	have	VERB
ejpam-5871	266	15	[	[	X
ejpam-5871	266	16	skz	skz	X
ejpam-5871	266	17	β	β	X
ejpam-5871	266	18	r+1	r+1	PROPN
ejpam-5871	266	19	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	266	20	)	)	PUNCT
ejpam-5871	266	21	]	]	PUNCT
ejpam-5871	267	1	1	1	NUM
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ejpam-5871	267	3	≥	≥	NOUN
ejpam-5871	267	4	ϑ	ϑ	PROPN
ejpam-5871	267	5	1	1	NUM
ejpam-5871	267	6	pq	pq	NOUN
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ejpam-5871	267	8	skz	skz	X
ejpam-5871	267	9	β	β	X
ejpam-5871	267	10	r+1	r+1	NOUN
ejpam-5871	267	11	]	]	X
ejpam-5871	267	12	[	[	PUNCT
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ejpam-5871	267	14	1	1	NUM
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ejpam-5871	267	17	(	(	PUNCT
ejpam-5871	267	18	χ)ϕ	χ)ϕ	NOUN
ejpam-5871	267	19	1	1	NUM
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ejpam-5871	267	21	∗	∗	NOUN
ejpam-5871	267	22	(	(	PUNCT
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ejpam-5871	267	27	p	p	NOUN
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ejpam-5871	268	2	16	16	NUM
ejpam-5871	268	3	)	)	PUNCT
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ejpam-5871	268	5	the	the	DET
ejpam-5871	268	6	expressions	expression	NOUN
ejpam-5871	268	7	(	(	PUNCT
ejpam-5871	268	8	15	15	NUM
ejpam-5871	268	9	)	)	PUNCT
ejpam-5871	268	10	and	and	CCONJ
ejpam-5871	268	11	(	(	PUNCT
ejpam-5871	268	12	16	16	NUM
ejpam-5871	268	13	)	)	PUNCT
ejpam-5871	268	14	,	,	PUNCT
ejpam-5871	268	15	we	we	PRON
ejpam-5871	268	16	can	can	AUX
ejpam-5871	268	17	write	write	VERB
ejpam-5871	268	18	[	[	X
ejpam-5871	268	19	s	s	X
ejpam-5871	268	20	k	k	X
ejpam-5871	268	21	zβ	zβ	PROPN
ejpam-5871	268	22	r+1	r+1	PROPN
ejpam-5871	268	23	∅(χ	∅(χ	PROPN
ejpam-5871	268	24	)	)	PUNCT
ejpam-5871	268	25	]	]	PUNCT
ejpam-5871	269	1	1	1	NUM
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ejpam-5871	270	1	[	[	X
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ejpam-5871	270	3	s	s	X
ejpam-5871	270	4	k	k	X
ejpam-5871	270	5	zβ	zβ	PROPN
ejpam-5871	270	6	r+1	r+1	PROPN
ejpam-5871	270	7	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	270	8	)	)	PUNCT
ejpam-5871	270	9	]	]	PUNCT
ejpam-5871	270	10	1	1	NUM
ejpam-5871	270	11	p	p	NOUN
ejpam-5871	270	12	,	,	PUNCT
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ejpam-5871	271	2	s	s	X
ejpam-5871	271	3	k	k	X
ejpam-5871	271	4	zβ	zβ	PROPN
ejpam-5871	271	5	r+1	r+1	PROPN
ejpam-5871	271	6	∅∗(χ	∅∗(χ	NOUN
ejpam-5871	271	7	)	)	PUNCT
ejpam-5871	271	8	]	]	PUNCT
ejpam-5871	272	1	1	1	NUM
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ejpam-5871	272	3	]	]	X
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ejpam-5871	272	5	[	[	PUNCT
ejpam-5871	272	6	ϑ	ϑ	PROPN
ejpam-5871	272	7	1	1	NUM
ejpam-5871	272	8	pq	pq	NOUN
ejpam-5871	273	1	[	[	X
ejpam-5871	273	2	skz	skz	X
ejpam-5871	273	3	β	β	X
ejpam-5871	273	4	r+1	r+1	NOUN
ejpam-5871	273	5	]	]	X
ejpam-5871	273	6	[	[	PUNCT
ejpam-5871	273	7	∅	∅	NOUN
ejpam-5871	273	8	1	1	NUM
ejpam-5871	273	9	p	p	NOUN
ejpam-5871	273	10	∗	∗	NOUN
ejpam-5871	273	11	(	(	PUNCT
ejpam-5871	273	12	χ)ϕ	χ)ϕ	NOUN
ejpam-5871	273	13	1	1	NUM
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ejpam-5871	273	15	∗	∗	NOUN
ejpam-5871	273	16	(	(	PUNCT
ejpam-5871	273	17	χ	χ	NOUN
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ejpam-5871	273	22	,	,	PUNCT
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ejpam-5871	273	25	pq	pq	NOUN
ejpam-5871	274	1	[	[	X
ejpam-5871	274	2	skz	skz	X
ejpam-5871	274	3	β	β	X
ejpam-5871	274	4	r+1	r+1	NOUN
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ejpam-5871	275	1	[	[	PUNCT
ejpam-5871	275	2	∅∗	∅∗	ADP
ejpam-5871	275	3	1	1	NUM
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ejpam-5871	275	5	(	(	PUNCT
ejpam-5871	275	6	χ)ϕ	χ)ϕ	NOUN
ejpam-5871	275	7	∗	∗	NOUN
ejpam-5871	275	8	1	1	NUM
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ejpam-5871	275	10	(	(	PUNCT
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ejpam-5871	275	17	a.	a.	PROPN
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ejpam-5871	276	5	math	math	PROPN
ejpam-5871	276	6	,	,	PUNCT
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ejpam-5871	276	10	)	)	PUNCT
ejpam-5871	276	11	(	(	PUNCT
ejpam-5871	276	12	2025	2025	NUM
ejpam-5871	276	13	)	)	PUNCT
ejpam-5871	276	14	,	,	PUNCT
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ejpam-5871	276	17	of	of	ADP
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ejpam-5871	276	19	=	=	SYM
ejpam-5871	276	20	[	[	PUNCT
ejpam-5871	276	21	ϑ	ϑ	X
ejpam-5871	276	22	1	1	NUM
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ejpam-5871	276	24	,	,	PUNCT
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ejpam-5871	276	26	1	1	NUM
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ejpam-5871	277	1	[	[	X
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ejpam-5871	277	3	k	k	X
ejpam-5871	277	4	zβ	zβ	PROPN
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ejpam-5871	278	3	1	1	NUM
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ejpam-5871	278	5	(	(	PUNCT
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ejpam-5871	279	8	following	follow	VERB
ejpam-5871	279	9	confinement	confinement	NOUN
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ejpam-5871	279	11	[	[	X
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ejpam-5871	279	13	k	k	X
ejpam-5871	279	14	zβ	zβ	PROPN
ejpam-5871	279	15	r+1	r+1	PROPN
ejpam-5871	279	16	ϕ(χ	ϕ(χ	PROPN
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ejpam-5871	280	1	1	1	NUM
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ejpam-5871	281	4	zβ	zβ	PROPN
ejpam-5871	281	5	r+1	r+1	PROPN
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ejpam-5871	281	11	=	=	PUNCT
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ejpam-5871	282	5	zβ	zβ	PROPN
ejpam-5871	282	6	r+1	r+1	PROPN
ejpam-5871	282	7	ϕ∗(χ	ϕ∗(χ	PROPN
ejpam-5871	282	8	)	)	PUNCT
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ejpam-5871	283	1	1	1	NUM
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ejpam-5871	283	3	,	,	PUNCT
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ejpam-5871	283	5	s	s	X
ejpam-5871	283	6	k	k	X
ejpam-5871	283	7	zβ	zβ	PROPN
ejpam-5871	283	8	r+1	r+1	PROPN
ejpam-5871	283	9	ϕ∗(χ	ϕ∗(χ	PROPN
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ejpam-5871	283	11	]	]	PUNCT
ejpam-5871	283	12	1	1	NUM
ejpam-5871	283	13	q	q	X
ejpam-5871	283	14	]	]	PUNCT
ejpam-5871	283	15	⊇	⊇	X
ejpam-5871	283	16	[	[	PUNCT
ejpam-5871	283	17	1	1	NUM
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ejpam-5871	283	19	1	1	NUM
ejpam-5871	283	20	pq	pq	NOUN
ejpam-5871	284	1	[	[	X
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ejpam-5871	284	4	r+1	r+1	NOUN
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ejpam-5871	284	6	[	[	PUNCT
ejpam-5871	284	7	∅	∅	NOUN
ejpam-5871	284	8	1	1	NUM
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ejpam-5871	284	11	(	(	PUNCT
ejpam-5871	284	12	χ)ϕ	χ)ϕ	NOUN
ejpam-5871	284	13	1	1	NUM
ejpam-5871	284	14	q	q	NOUN
ejpam-5871	284	15	∗	∗	NOUN
ejpam-5871	284	16	(	(	PUNCT
ejpam-5871	284	17	χ	χ	NOUN
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ejpam-5871	284	20	1	1	NUM
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ejpam-5871	284	22	,	,	PUNCT
ejpam-5871	284	23	1	1	NUM
ejpam-5871	284	24	ϑ	ϑ	SYM
ejpam-5871	284	25	1	1	NUM
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ejpam-5871	285	1	[	[	X
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ejpam-5871	285	4	r+1	r+1	NOUN
ejpam-5871	285	5	]	]	X
ejpam-5871	286	1	[	[	PUNCT
ejpam-5871	286	2	∅∗	∅∗	ADP
ejpam-5871	286	3	1	1	NUM
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ejpam-5871	286	5	(	(	PUNCT
ejpam-5871	286	6	χ)ϕ	χ)ϕ	NOUN
ejpam-5871	286	7	∗	∗	NOUN
ejpam-5871	286	8	1	1	NUM
ejpam-5871	286	9	q	q	NOUN
ejpam-5871	286	10	(	(	PUNCT
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ejpam-5871	286	13	]	]	PUNCT
ejpam-5871	286	14	1	1	NUM
ejpam-5871	286	15	q	q	NOUN
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ejpam-5871	286	17	=	=	PUNCT
ejpam-5871	286	18	[	[	PUNCT
ejpam-5871	286	19	1	1	NUM
ejpam-5871	286	20	µ	µ	NUM
ejpam-5871	286	21	1	1	NUM
ejpam-5871	286	22	pq	pq	NOUN
ejpam-5871	286	23	,	,	PUNCT
ejpam-5871	286	24	1	1	NUM
ejpam-5871	286	25	ϑ	ϑ	SYM
ejpam-5871	286	26	1	1	NUM
ejpam-5871	286	27	pq	pq	NOUN
ejpam-5871	286	28	]	]	PUNCT
ejpam-5871	287	1	[	[	X
ejpam-5871	287	2	s	s	X
ejpam-5871	287	3	k	k	X
ejpam-5871	287	4	zβ	zβ	PROPN
ejpam-5871	287	5	r+1	r+1	X
ejpam-5871	288	1	[	[	X
ejpam-5871	288	2	∅	∅	NOUN
ejpam-5871	288	3	1	1	NUM
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ejpam-5871	288	5	(	(	PUNCT
ejpam-5871	288	6	χ)ϕ	χ)ϕ	NOUN
ejpam-5871	288	7	1	1	NUM
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ejpam-5871	288	10	χ	χ	NOUN
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ejpam-5871	288	12	]	]	PUNCT
ejpam-5871	288	13	1	1	NUM
ejpam-5871	288	14	q	q	NOUN
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ejpam-5871	288	16	.	.	PUNCT
ejpam-5871	289	1	(	(	PUNCT
ejpam-5871	289	2	18	18	NUM
ejpam-5871	289	3	)	)	PUNCT
ejpam-5871	289	4	adding	add	VERB
ejpam-5871	289	5	expressions	expression	NOUN
ejpam-5871	289	6	(	(	PUNCT
ejpam-5871	289	7	17	17	NUM
ejpam-5871	289	8	)	)	PUNCT
ejpam-5871	289	9	and	and	CCONJ
ejpam-5871	289	10	(	(	PUNCT
ejpam-5871	289	11	18	18	NUM
ejpam-5871	289	12	)	)	PUNCT
ejpam-5871	289	13	we	we	PRON
ejpam-5871	289	14	get	get	VERB
ejpam-5871	289	15	our	our	PRON
ejpam-5871	289	16	required	require	VERB
ejpam-5871	289	17	relation	relation	NOUN
ejpam-5871	289	18	(	(	PUNCT
ejpam-5871	289	19	14	14	NUM
ejpam-5871	289	20	)	)	PUNCT
ejpam-5871	289	21	.	.	PUNCT
ejpam-5871	290	1	theorem	theorem	VERB
ejpam-5871	290	2	6	6	NUM
ejpam-5871	290	3	.	.	PUNCT
ejpam-5871	291	1	let	let	VERB
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ejpam-5871	291	4	r/{−1	r/{−1	PROPN
ejpam-5871	291	5	}	}	PUNCT
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ejpam-5871	291	9	0	0	NUM
ejpam-5871	291	10	and	and	CCONJ
ejpam-5871	291	11	∅	∅	NOUN
ejpam-5871	291	12	∈	∈	PROPN
ejpam-5871	291	13	sigx([r1	sigx([r1	NOUN
ejpam-5871	291	14	,	,	PUNCT
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ejpam-5871	292	1	r	r	NOUN
ejpam-5871	292	2	+	+	PROPN
ejpam-5871	292	3	i	i	NOUN
ejpam-5871	292	4	)	)	PUNCT
ejpam-5871	292	5	,	,	PUNCT
ejpam-5871	292	6	then	then	ADV
ejpam-5871	292	7	for	for	ADP
ejpam-5871	292	8	β	β	X
ejpam-5871	292	9	>	>	X
ejpam-5871	292	10	0	0	PUNCT
ejpam-5871	293	1	the	the	DET
ejpam-5871	293	2	following	follow	VERB
ejpam-5871	293	3	redinequality	redinequality	NOUN
ejpam-5871	293	4	hold	hold	NOUN
ejpam-5871	293	5	(	(	PUNCT
ejpam-5871	293	6	s+	s+	NUM
ejpam-5871	293	7	1)−	1)−	PROPN
ejpam-5871	293	8	β	β	NOUN
ejpam-5871	293	9	k	k	X
ejpam-5871	293	10	℧	℧	PROPN
ejpam-5871	293	11	(	(	PUNCT
ejpam-5871	293	12	12)βγk(β	12)βγk(β	NOUN
ejpam-5871	293	13	)	)	PUNCT
ejpam-5871	293	14	∅	∅	NOUN
ejpam-5871	293	15	(	(	PUNCT
ejpam-5871	293	16	⋋−1	⋋−1	X
ejpam-5871	293	17	(	(	PUNCT
ejpam-5871	293	18	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	293	19	)	)	PUNCT
ejpam-5871	293	20	+	+	NOUN
ejpam-5871	293	21	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	293	22	)	)	PUNCT
ejpam-5871	293	23	2	2	NUM
ejpam-5871	293	24	)	)	PUNCT
ejpam-5871	293	25	1	1	NUM
ejpam-5871	293	26	s+1	s+1	PROPN
ejpam-5871	293	27	)	)	PUNCT
ejpam-5871	293	28	⊇	⊇	PROPN
ejpam-5871	293	29	1	1	NUM
ejpam-5871	293	30	(	(	PUNCT
ejpam-5871	293	31	⋋s+1	⋋s+1	PROPN
ejpam-5871	293	32	(	(	PUNCT
ejpam-5871	293	33	r2)−⋋s+1(r1	r2)−⋋s+1(r1	NOUN
ejpam-5871	293	34	)	)	PUNCT
ejpam-5871	293	35	)	)	PUNCT
ejpam-5871	294	1	β	β	X
ejpam-5871	294	2	k	k	X
ejpam-5871	295	1	[	[	PUNCT
ejpam-5871	295	2	s	s	X
ejpam-5871	295	3	kz	kz	PROPN
ejpam-5871	295	4	β	β	PROPN
ejpam-5871	295	5	r+1	r+1	PROPN
ejpam-5871	295	6	∅(r2	∅(r2	PROPN
ejpam-5871	295	7	)	)	PUNCT
ejpam-5871	296	1	+	+	NUM
ejpam-5871	296	2	s	s	VERB
ejpam-5871	296	3	kz	kz	PROPN
ejpam-5871	296	4	β	β	PROPN
ejpam-5871	296	5	r−2	r−2	PROPN
ejpam-5871	296	6	∅	∅	NOUN
ejpam-5871	296	7	(	(	PUNCT
ejpam-5871	296	8	r1	r1	PROPN
ejpam-5871	296	9	)	)	PUNCT
ejpam-5871	296	10	]	]	PUNCT
ejpam-5871	297	1	⊇	⊇	PROPN
ejpam-5871	297	2	[	[	PUNCT
ejpam-5871	297	3	∅(r1	∅(r1	PROPN
ejpam-5871	297	4	)	)	PUNCT
ejpam-5871	298	1	+	+	NOUN
ejpam-5871	298	2	∅(r2	∅(r2	NOUN
ejpam-5871	298	3	)	)	PUNCT
ejpam-5871	298	4	]	]	PUNCT
ejpam-5871	298	5	(	(	PUNCT
ejpam-5871	298	6	s+	s+	NUM
ejpam-5871	298	7	1)−	1)−	PROPN
ejpam-5871	298	8	β	β	X
ejpam-5871	298	9	k	k	PROPN
ejpam-5871	298	10	kγk(β	kγk(β	PROPN
ejpam-5871	298	11	)	)	PUNCT
ejpam-5871	298	12	∫	∫	PROPN
ejpam-5871	299	1	1	1	NUM
ejpam-5871	299	2	0	0	NUM
ejpam-5871	299	3	θ	θ	PROPN
ejpam-5871	299	4	β	β	X
ejpam-5871	299	5	k	k	X
ejpam-5871	299	6	−1[	−1[	X
ejpam-5871	299	7	℧	℧	PROPN
ejpam-5871	299	8	(θ	(θ	NOUN
ejpam-5871	299	9	)	)	PUNCT
ejpam-5871	299	10	+	+	CCONJ
ejpam-5871	299	11	℧	℧	PROPN
ejpam-5871	299	12	(	(	PUNCT
ejpam-5871	299	13	1−	1−	NUM
ejpam-5871	299	14	θ)]dθ,∀x	θ)]dθ,∀x	NOUN
ejpam-5871	299	15	,	,	PUNCT
ejpam-5871	299	16	y	y	PROPN
ejpam-5871	299	17	∈	∈	PROPN
ejpam-5871	300	1	[	[	X
ejpam-5871	300	2	r1	r1	NOUN
ejpam-5871	300	3	,	,	PUNCT
ejpam-5871	300	4	r2	r2	PROPN
ejpam-5871	300	5	]	]	PUNCT
ejpam-5871	300	6	.	.	PUNCT
ejpam-5871	301	1	proof	proof	NOUN
ejpam-5871	301	2	.	.	PUNCT
ejpam-5871	302	1	since	since	SCONJ
ejpam-5871	302	2	∅	∅	NOUN
ejpam-5871	302	3	is	be	AUX
ejpam-5871	302	4	ı.υ-(⋋s+1	ı.υ-(⋋s+1	PROPN
ejpam-5871	302	5	,	,	PUNCT
ejpam-5871	302	6	℧	℧	NOUN
ejpam-5871	302	7	)	)	PUNCT
ejpam-5871	302	8	cf	cf	NOUN
ejpam-5871	302	9	and	and	CCONJ
ejpam-5871	302	10	for	for	ADP
ejpam-5871	302	11	θ	θ	PROPN
ejpam-5871	302	12	=	=	SYM
ejpam-5871	302	13	1	1	NUM
ejpam-5871	302	14	2	2	NUM
ejpam-5871	302	15	,	,	PUNCT
ejpam-5871	302	16	we	we	PRON
ejpam-5871	302	17	have	have	VERB
ejpam-5871	302	18	∅	∅	NOUN
ejpam-5871	302	19	(	(	PUNCT
ejpam-5871	302	20	⋋−1	⋋−1	X
ejpam-5871	302	21	(	(	PUNCT
ejpam-5871	302	22	⋋s+1(x	⋋s+1(x	NUM
ejpam-5871	302	23	)	)	PUNCT
ejpam-5871	302	24	+	+	ADJ
ejpam-5871	302	25	⋋s+1(y	⋋s+1(y	NUM
ejpam-5871	302	26	)	)	PUNCT
ejpam-5871	302	27	2	2	NUM
ejpam-5871	302	28	)	)	PUNCT
ejpam-5871	302	29	1	1	NUM
ejpam-5871	302	30	s+1	s+1	PROPN
ejpam-5871	302	31	)	)	PUNCT
ejpam-5871	302	32	⊇	⊇	PROPN
ejpam-5871	302	33	℧	℧	PROPN
ejpam-5871	302	34	(	(	PUNCT
ejpam-5871	302	35	1	1	NUM
ejpam-5871	302	36	2	2	NUM
ejpam-5871	302	37	)	)	PUNCT
ejpam-5871	302	38	[	[	PUNCT
ejpam-5871	302	39	∅(x	∅(x	NOUN
ejpam-5871	302	40	)	)	PUNCT
ejpam-5871	302	41	+	+	NOUN
ejpam-5871	302	42	∅(y	∅(y	NOUN
ejpam-5871	302	43	)	)	PUNCT
ejpam-5871	302	44	]	]	PUNCT
ejpam-5871	302	45	.	.	PUNCT
ejpam-5871	303	1	(	(	PUNCT
ejpam-5871	303	2	19	19	NUM
ejpam-5871	303	3	)	)	PUNCT
ejpam-5871	303	4	by	by	ADP
ejpam-5871	303	5	substituting	substitute	VERB
ejpam-5871	303	6	x	x	X
ejpam-5871	303	7	=	=	SYM
ejpam-5871	303	8	⋋−1(θ⋋s+1	⋋−1(θ⋋s+1	PROPN
ejpam-5871	303	9	(	(	PUNCT
ejpam-5871	303	10	r1)+(1−θ)⋋s+1	r1)+(1−θ)⋋s+1	X
ejpam-5871	303	11	(	(	PUNCT
ejpam-5871	303	12	r2	r2	PROPN
ejpam-5871	303	13	)	)	PUNCT
ejpam-5871	303	14	)	)	PUNCT
ejpam-5871	304	1	1	1	NUM
ejpam-5871	304	2	s+1	s+1	NOUN
ejpam-5871	304	3	and	and	CCONJ
ejpam-5871	304	4	y	y	PROPN
ejpam-5871	304	5	=	=	PUNCT
ejpam-5871	304	6	⋋−1((1−θ)⋋s+1	⋋−1((1−θ)⋋s+1	NOUN
ejpam-5871	304	7	(	(	PUNCT
ejpam-5871	304	8	r1)+	r1)+	VERB
ejpam-5871	304	9	θ⋋s+1	θ⋋s+1	PROPN
ejpam-5871	304	10	(	(	PUNCT
ejpam-5871	304	11	r2	r2	PROPN
ejpam-5871	304	12	)	)	PUNCT
ejpam-5871	304	13	)	)	PUNCT
ejpam-5871	305	1	1	1	NUM
ejpam-5871	305	2	s+1	s+1	NOUN
ejpam-5871	305	3	in	in	ADP
ejpam-5871	305	4	above	above	ADP
ejpam-5871	305	5	inequality	inequality	NOUN
ejpam-5871	305	6	19red	19re	VERB
ejpam-5871	305	7	.	.	PUNCT
ejpam-5871	306	1	also	also	ADV
ejpam-5871	306	2	by	by	ADP
ejpam-5871	306	3	multiplying	multiply	VERB
ejpam-5871	306	4	both	both	DET
ejpam-5871	306	5	sides	side	NOUN
ejpam-5871	306	6	by	by	ADP
ejpam-5871	306	7	(	(	PUNCT
ejpam-5871	306	8	s+1)−	s+1)−	PROPN
ejpam-5871	306	9	β	β	PROPN
ejpam-5871	306	10	k	k	PROPN
ejpam-5871	306	11	kγk(β	kγk(β	PROPN
ejpam-5871	306	12	)	)	PUNCT
ejpam-5871	306	13	θ	θ	PROPN
ejpam-5871	306	14	β	β	X
ejpam-5871	306	15	k	k	X
ejpam-5871	306	16	−1	−1	NOUN
ejpam-5871	306	17	also	also	ADV
ejpam-5871	306	18	taking	take	VERB
ejpam-5871	306	19	the	the	DET
ejpam-5871	306	20	integration	integration	NOUN
ejpam-5871	306	21	over	over	ADP
ejpam-5871	306	22	[	[	X
ejpam-5871	306	23	0	0	NUM
ejpam-5871	306	24	,	,	PUNCT
ejpam-5871	306	25	1	1	NUM
ejpam-5871	306	26	]	]	PUNCT
ejpam-5871	306	27	w.r.t	w.r.t	NOUN
ejpam-5871	306	28	”	"	PUNCT
ejpam-5871	306	29	θ”red	θ”re	VERB
ejpam-5871	306	30	,	,	PUNCT
ejpam-5871	306	31	we	we	PRON
ejpam-5871	306	32	have	have	VERB
ejpam-5871	306	33	1	1	NUM
ejpam-5871	306	34	℧	℧	NOUN
ejpam-5871	306	35	(	(	PUNCT
ejpam-5871	306	36	12	12	NUM
ejpam-5871	306	37	)	)	PUNCT
ejpam-5871	306	38	(	(	PUNCT
ejpam-5871	306	39	s+	s+	NUM
ejpam-5871	306	40	1)−	1)−	PROPN
ejpam-5871	306	41	β	β	X
ejpam-5871	306	42	k	k	PROPN
ejpam-5871	306	43	kγk(β	kγk(β	PROPN
ejpam-5871	306	44	)	)	PUNCT
ejpam-5871	306	45	∫	∫	PROPN
ejpam-5871	307	1	1	1	NUM
ejpam-5871	307	2	0	0	NUM
ejpam-5871	307	3	θ	θ	PROPN
ejpam-5871	307	4	β	β	X
ejpam-5871	307	5	k	k	X
ejpam-5871	307	6	−1∅	−1∅	PROPN
ejpam-5871	307	7	(	(	PUNCT
ejpam-5871	307	8	⋋−1	⋋−1	ADJ
ejpam-5871	307	9	(	(	PUNCT
ejpam-5871	307	10	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	307	11	)	)	PUNCT
ejpam-5871	307	12	+	+	NOUN
ejpam-5871	307	13	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	307	14	)	)	PUNCT
ejpam-5871	307	15	2	2	NUM
ejpam-5871	307	16	)	)	PUNCT
ejpam-5871	307	17	1	1	NUM
ejpam-5871	307	18	s+1	s+1	PROPN
ejpam-5871	307	19	)	)	PUNCT
ejpam-5871	307	20	dθ	dθ	PROPN
ejpam-5871	307	21	⊇	⊇	PROPN
ejpam-5871	307	22	(	(	PUNCT
ejpam-5871	307	23	s+	s+	NUM
ejpam-5871	307	24	1)−	1)−	PROPN
ejpam-5871	307	25	β	β	X
ejpam-5871	307	26	k	k	PROPN
ejpam-5871	307	27	kγk(β	kγk(β	PROPN
ejpam-5871	307	28	)	)	PUNCT
ejpam-5871	307	29	∫	∫	PROPN
ejpam-5871	307	30	1	1	NUM
ejpam-5871	307	31	0	0	NUM
ejpam-5871	307	32	θ	θ	PROPN
ejpam-5871	307	33	β	β	X
ejpam-5871	307	34	k	k	X
ejpam-5871	307	35	−1∅	−1∅	PROPN
ejpam-5871	307	36	(	(	PUNCT
ejpam-5871	307	37	⋋−1	⋋−1	ADJ
ejpam-5871	307	38	(	(	PUNCT
ejpam-5871	307	39	θ	θ	PROPN
ejpam-5871	307	40	⋋s+1	⋋s+1	PROPN
ejpam-5871	307	41	(	(	PUNCT
ejpam-5871	307	42	r1	r1	PROPN
ejpam-5871	307	43	)	)	PUNCT
ejpam-5871	307	44	+	+	CCONJ
ejpam-5871	307	45	(	(	PUNCT
ejpam-5871	307	46	1−	1−	NUM
ejpam-5871	307	47	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	307	48	(	(	PUNCT
ejpam-5871	307	49	r2	r2	PROPN
ejpam-5871	307	50	)	)	PUNCT
ejpam-5871	307	51	)	)	PUNCT
ejpam-5871	307	52	1	1	NUM
ejpam-5871	307	53	s+1	s+1	NOUN
ejpam-5871	307	54	)	)	PUNCT
ejpam-5871	307	55	dθ	dθ	PROPN
ejpam-5871	307	56	+	+	X
ejpam-5871	307	57	(	(	PUNCT
ejpam-5871	307	58	s+	s+	X
ejpam-5871	307	59	1)−	1)−	PROPN
ejpam-5871	307	60	β	β	X
ejpam-5871	307	61	k	k	PROPN
ejpam-5871	307	62	kγk(β	kγk(β	PROPN
ejpam-5871	307	63	)	)	PUNCT
ejpam-5871	307	64	∫	∫	PROPN
ejpam-5871	307	65	1	1	NUM
ejpam-5871	307	66	0	0	NUM
ejpam-5871	307	67	θ	θ	PROPN
ejpam-5871	307	68	β	β	X
ejpam-5871	307	69	k	k	X
ejpam-5871	307	70	−1∅	−1∅	PROPN
ejpam-5871	307	71	(	(	PUNCT
ejpam-5871	307	72	⋋−1	⋋−1	ADJ
ejpam-5871	307	73	(	(	PUNCT
ejpam-5871	307	74	(	(	PUNCT
ejpam-5871	307	75	1−	1−	NUM
ejpam-5871	307	76	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	307	77	(	(	PUNCT
ejpam-5871	307	78	r1	r1	PROPN
ejpam-5871	307	79	)	)	PUNCT
ejpam-5871	307	80	+	+	NUM
ejpam-5871	307	81	θ	θ	PUNCT
ejpam-5871	307	82	⋋s+1	⋋s+1	VERB
ejpam-5871	307	83	(	(	PUNCT
ejpam-5871	307	84	r2	r2	PROPN
ejpam-5871	307	85	)	)	PUNCT
ejpam-5871	307	86	)	)	PUNCT
ejpam-5871	307	87	1	1	NUM
ejpam-5871	307	88	s+1	s+1	PROPN
ejpam-5871	307	89	)	)	PUNCT
ejpam-5871	307	90	dθ	dθ	PROPN
ejpam-5871	307	91	.	.	PUNCT
ejpam-5871	308	1	(	(	PUNCT
ejpam-5871	308	2	20	20	NUM
ejpam-5871	308	3	)	)	PUNCT
ejpam-5871	308	4	a.	a.	NOUN
ejpam-5871	308	5	mehmood	mehmood	PROPN
ejpam-5871	308	6	et	et	PROPN
ejpam-5871	308	7	al	al	PROPN
ejpam-5871	308	8	.	.	PUNCT
ejpam-5871	308	9	/	/	SYM
ejpam-5871	308	10	eur	eur	PROPN
ejpam-5871	308	11	.	.	PUNCT
ejpam-5871	309	1	j.	j.	PROPN
ejpam-5871	309	2	pure	pure	PROPN
ejpam-5871	309	3	appl	appl	PROPN
ejpam-5871	309	4	.	.	PROPN
ejpam-5871	309	5	math	math	PROPN
ejpam-5871	309	6	,	,	PUNCT
ejpam-5871	309	7	18	18	NUM
ejpam-5871	309	8	(	(	PUNCT
ejpam-5871	309	9	2	2	NUM
ejpam-5871	309	10	)	)	PUNCT
ejpam-5871	309	11	(	(	PUNCT
ejpam-5871	309	12	2025	2025	NUM
ejpam-5871	309	13	)	)	PUNCT
ejpam-5871	309	14	,	,	PUNCT
ejpam-5871	309	15	5871	5871	NUM
ejpam-5871	309	16	11	11	NUM
ejpam-5871	309	17	of	of	ADP
ejpam-5871	309	18	26	26	NUM
ejpam-5871	309	19	now	now	ADV
ejpam-5871	309	20	we	we	PRON
ejpam-5871	309	21	are	be	AUX
ejpam-5871	309	22	proceeding	proceed	VERB
ejpam-5871	309	23	with	with	ADP
ejpam-5871	309	24	the	the	DET
ejpam-5871	309	25	left	left	ADJ
ejpam-5871	309	26	part	part	NOUN
ejpam-5871	309	27	of	of	ADP
ejpam-5871	309	28	the	the	DET
ejpam-5871	309	29	inclusion	inclusion	NOUN
ejpam-5871	309	30	(	(	PUNCT
ejpam-5871	309	31	20	20	NUM
ejpam-5871	309	32	)	)	PUNCT
ejpam-5871	309	33	.	.	PUNCT
ejpam-5871	310	1	(	(	PUNCT
ejpam-5871	310	2	s+	s+	PROPN
ejpam-5871	310	3	1)−	1)−	NUM
ejpam-5871	310	4	β	β	X
ejpam-5871	310	5	k	k	PROPN
ejpam-5871	310	6	kγk(β	kγk(β	PROPN
ejpam-5871	310	7	)	)	PUNCT
ejpam-5871	310	8	∫	∫	PROPN
ejpam-5871	310	9	1	1	NUM
ejpam-5871	310	10	0	0	NUM
ejpam-5871	310	11	θ	θ	PROPN
ejpam-5871	310	12	β	β	X
ejpam-5871	311	1	k	k	X
ejpam-5871	311	2	−1∅	−1∅	PROPN
ejpam-5871	311	3	(	(	PUNCT
ejpam-5871	311	4	⋋−1	⋋−1	ADJ
ejpam-5871	311	5	(	(	PUNCT
ejpam-5871	311	6	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	311	7	)	)	PUNCT
ejpam-5871	311	8	+	+	NOUN
ejpam-5871	311	9	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	311	10	)	)	PUNCT
ejpam-5871	311	11	2	2	NUM
ejpam-5871	311	12	)	)	PUNCT
ejpam-5871	311	13	1	1	NUM
ejpam-5871	311	14	s+1	s+1	PROPN
ejpam-5871	311	15	)	)	PUNCT
ejpam-5871	311	16	dθ	dθ	PROPN
ejpam-5871	311	17	=	=	PUNCT
ejpam-5871	312	1	[	[	PUNCT
ejpam-5871	312	2	(	(	PUNCT
ejpam-5871	312	3	s+	s+	NUM
ejpam-5871	312	4	1)1−	1)1−	NUM
ejpam-5871	312	5	β	β	X
ejpam-5871	312	6	k	k	PROPN
ejpam-5871	312	7	kγk(β	kγk(β	PROPN
ejpam-5871	312	8	)	)	PUNCT
ejpam-5871	312	9	∫	∫	PROPN
ejpam-5871	312	10	1	1	NUM
ejpam-5871	312	11	0	0	NUM
ejpam-5871	312	12	θ	θ	PROPN
ejpam-5871	312	13	β	β	X
ejpam-5871	312	14	k	k	X
ejpam-5871	313	1	−1∅∗	−1∅∗	PROPN
ejpam-5871	313	2	(	(	PUNCT
ejpam-5871	313	3	⋋−1	⋋−1	X
ejpam-5871	313	4	(	(	PUNCT
ejpam-5871	313	5	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	313	6	)	)	PUNCT
ejpam-5871	313	7	+	+	NOUN
ejpam-5871	313	8	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	313	9	)	)	PUNCT
ejpam-5871	313	10	2	2	NUM
ejpam-5871	313	11	)	)	PUNCT
ejpam-5871	313	12	1	1	NUM
ejpam-5871	313	13	s+1	s+1	PROPN
ejpam-5871	313	14	)	)	PUNCT
ejpam-5871	313	15	dθ	dθ	PROPN
ejpam-5871	313	16	,	,	PUNCT
ejpam-5871	313	17	(	(	PUNCT
ejpam-5871	313	18	s+	s+	NUM
ejpam-5871	313	19	1)−	1)−	PROPN
ejpam-5871	313	20	β	β	X
ejpam-5871	313	21	k	k	PROPN
ejpam-5871	313	22	kγk(β	kγk(β	PROPN
ejpam-5871	313	23	)	)	PUNCT
ejpam-5871	313	24	∫	∫	PROPN
ejpam-5871	313	25	1	1	NUM
ejpam-5871	313	26	0	0	NUM
ejpam-5871	313	27	θ	θ	PROPN
ejpam-5871	313	28	β	β	X
ejpam-5871	313	29	k	k	X
ejpam-5871	313	30	−1∅∗	−1∅∗	PROPN
ejpam-5871	313	31	(	(	PUNCT
ejpam-5871	313	32	⋋−1	⋋−1	X
ejpam-5871	313	33	(	(	PUNCT
ejpam-5871	313	34	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	313	35	)	)	PUNCT
ejpam-5871	313	36	+	+	NOUN
ejpam-5871	313	37	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	313	38	)	)	PUNCT
ejpam-5871	313	39	2	2	NUM
ejpam-5871	313	40	)	)	PUNCT
ejpam-5871	313	41	1	1	NUM
ejpam-5871	313	42	s+1	s+1	PROPN
ejpam-5871	313	43	)	)	PUNCT
ejpam-5871	313	44	dθ	dθ	NOUN
ejpam-5871	313	45	]	]	X
ejpam-5871	314	1	=	=	PUNCT
ejpam-5871	314	2	[	[	PUNCT
ejpam-5871	314	3	(	(	PUNCT
ejpam-5871	314	4	s+	s+	NUM
ejpam-5871	314	5	1)−	1)−	PROPN
ejpam-5871	314	6	β	β	X
ejpam-5871	314	7	k	k	PROPN
ejpam-5871	314	8	βγk(β	βγk(β	PROPN
ejpam-5871	314	9	)	)	PUNCT
ejpam-5871	314	10	∅∗	∅∗	PROPN
ejpam-5871	315	1	(	(	PUNCT
ejpam-5871	315	2	⋋−1	⋋−1	ADJ
ejpam-5871	315	3	(	(	PUNCT
ejpam-5871	315	4	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	315	5	)	)	PUNCT
ejpam-5871	315	6	+	+	NOUN
ejpam-5871	315	7	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	315	8	)	)	PUNCT
ejpam-5871	315	9	2	2	NUM
ejpam-5871	315	10	)	)	PUNCT
ejpam-5871	315	11	1	1	NUM
ejpam-5871	315	12	s+1	s+1	PROPN
ejpam-5871	315	13	)	)	PUNCT
ejpam-5871	315	14	+	+	CCONJ
ejpam-5871	315	15	(	(	PUNCT
ejpam-5871	315	16	s+	s+	X
ejpam-5871	315	17	1)−	1)−	PROPN
ejpam-5871	315	18	β	β	X
ejpam-5871	315	19	k	k	PROPN
ejpam-5871	315	20	βγk(β	βγk(β	PROPN
ejpam-5871	315	21	)	)	PUNCT
ejpam-5871	315	22	∅∗	∅∗	PROPN
ejpam-5871	316	1	(	(	PUNCT
ejpam-5871	316	2	⋋−1	⋋−1	ADJ
ejpam-5871	316	3	(	(	PUNCT
ejpam-5871	316	4	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	316	5	)	)	PUNCT
ejpam-5871	316	6	+	+	NOUN
ejpam-5871	316	7	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	316	8	)	)	PUNCT
ejpam-5871	316	9	2	2	NUM
ejpam-5871	316	10	)	)	PUNCT
ejpam-5871	316	11	1	1	NUM
ejpam-5871	316	12	s+1	s+1	NOUN
ejpam-5871	316	13	)	)	PUNCT
ejpam-5871	316	14	]	]	PUNCT
ejpam-5871	317	1	=	=	PUNCT
ejpam-5871	317	2	(	(	PUNCT
ejpam-5871	317	3	s+	s+	NUM
ejpam-5871	317	4	1)−	1)−	PROPN
ejpam-5871	317	5	β	β	X
ejpam-5871	317	6	k	k	X
ejpam-5871	317	7	βγk(β	βγk(β	PROPN
ejpam-5871	317	8	)	)	PUNCT
ejpam-5871	317	9	∅	∅	NOUN
ejpam-5871	317	10	(	(	PUNCT
ejpam-5871	317	11	⋋−1	⋋−1	X
ejpam-5871	317	12	(	(	PUNCT
ejpam-5871	317	13	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	317	14	)	)	PUNCT
ejpam-5871	317	15	+	+	NOUN
ejpam-5871	317	16	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	317	17	)	)	PUNCT
ejpam-5871	317	18	2	2	NUM
ejpam-5871	317	19	)	)	PUNCT
ejpam-5871	317	20	1	1	NUM
ejpam-5871	317	21	s+1	s+1	PROPN
ejpam-5871	317	22	)	)	PUNCT
ejpam-5871	317	23	.	.	PUNCT
ejpam-5871	318	1	(	(	PUNCT
ejpam-5871	318	2	21	21	NUM
ejpam-5871	318	3	)	)	PUNCT
ejpam-5871	318	4	for	for	ADP
ejpam-5871	318	5	the	the	DET
ejpam-5871	318	6	right	right	ADJ
ejpam-5871	318	7	part	part	NOUN
ejpam-5871	318	8	of	of	ADP
ejpam-5871	318	9	the	the	DET
ejpam-5871	318	10	inclusion	inclusion	NOUN
ejpam-5871	318	11	(	(	PUNCT
ejpam-5871	318	12	20	20	NUM
ejpam-5871	318	13	)	)	PUNCT
ejpam-5871	318	14	.	.	PUNCT
ejpam-5871	319	1	(	(	PUNCT
ejpam-5871	319	2	s+	s+	PROPN
ejpam-5871	319	3	1)−	1)−	NUM
ejpam-5871	319	4	β	β	X
ejpam-5871	319	5	k	k	PROPN
ejpam-5871	319	6	kγk(β	kγk(β	PROPN
ejpam-5871	319	7	)	)	PUNCT
ejpam-5871	319	8	∫	∫	PROPN
ejpam-5871	319	9	1	1	NUM
ejpam-5871	319	10	0	0	NUM
ejpam-5871	319	11	θ	θ	PROPN
ejpam-5871	319	12	β	β	X
ejpam-5871	320	1	k	k	X
ejpam-5871	320	2	−1∅	−1∅	PROPN
ejpam-5871	320	3	(	(	PUNCT
ejpam-5871	320	4	⋋−1	⋋−1	ADJ
ejpam-5871	320	5	(	(	PUNCT
ejpam-5871	320	6	θ	θ	PROPN
ejpam-5871	320	7	⋋s+1	⋋s+1	PROPN
ejpam-5871	320	8	(	(	PUNCT
ejpam-5871	320	9	r1	r1	PROPN
ejpam-5871	320	10	)	)	PUNCT
ejpam-5871	320	11	+	+	CCONJ
ejpam-5871	320	12	(	(	PUNCT
ejpam-5871	320	13	1−	1−	NUM
ejpam-5871	320	14	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	320	15	(	(	PUNCT
ejpam-5871	320	16	r2	r2	PROPN
ejpam-5871	320	17	)	)	PUNCT
ejpam-5871	320	18	)	)	PUNCT
ejpam-5871	320	19	1	1	NUM
ejpam-5871	320	20	s+1	s+1	NOUN
ejpam-5871	320	21	)	)	PUNCT
ejpam-5871	320	22	dθ	dθ	PROPN
ejpam-5871	320	23	+	+	X
ejpam-5871	320	24	(	(	PUNCT
ejpam-5871	320	25	s+	s+	X
ejpam-5871	320	26	1)−	1)−	PROPN
ejpam-5871	320	27	β	β	X
ejpam-5871	320	28	k	k	PROPN
ejpam-5871	320	29	kγk(β	kγk(β	PROPN
ejpam-5871	320	30	)	)	PUNCT
ejpam-5871	320	31	∫	∫	PROPN
ejpam-5871	321	1	1	1	NUM
ejpam-5871	321	2	0	0	NUM
ejpam-5871	321	3	θ	θ	PROPN
ejpam-5871	321	4	β	β	X
ejpam-5871	321	5	k	k	X
ejpam-5871	321	6	−1∅	−1∅	PROPN
ejpam-5871	321	7	(	(	PUNCT
ejpam-5871	321	8	⋋−1	⋋−1	ADJ
ejpam-5871	321	9	(	(	PUNCT
ejpam-5871	321	10	(	(	PUNCT
ejpam-5871	321	11	1−	1−	NUM
ejpam-5871	321	12	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	321	13	(	(	PUNCT
ejpam-5871	321	14	r1	r1	PROPN
ejpam-5871	321	15	)	)	PUNCT
ejpam-5871	321	16	+	+	NUM
ejpam-5871	321	17	θ	θ	PUNCT
ejpam-5871	321	18	⋋s+1	⋋s+1	VERB
ejpam-5871	321	19	(	(	PUNCT
ejpam-5871	321	20	r2	r2	PROPN
ejpam-5871	321	21	)	)	PUNCT
ejpam-5871	321	22	)	)	PUNCT
ejpam-5871	321	23	1	1	NUM
ejpam-5871	321	24	s+1	s+1	NOUN
ejpam-5871	321	25	)	)	PUNCT
ejpam-5871	321	26	dθ	dθ	PROPN
ejpam-5871	321	27	=	=	PUNCT
ejpam-5871	322	1	[	[	PUNCT
ejpam-5871	322	2	(	(	PUNCT
ejpam-5871	322	3	s+	s+	NUM
ejpam-5871	322	4	1)1−	1)1−	NUM
ejpam-5871	322	5	β	β	X
ejpam-5871	322	6	k	k	PROPN
ejpam-5871	322	7	kγk(β	kγk(β	PROPN
ejpam-5871	322	8	)	)	PUNCT
ejpam-5871	322	9	∫	∫	PROPN
ejpam-5871	322	10	1	1	NUM
ejpam-5871	322	11	0	0	NUM
ejpam-5871	322	12	θ	θ	PROPN
ejpam-5871	322	13	β	β	X
ejpam-5871	322	14	k	k	X
ejpam-5871	323	1	−1∅∗	−1∅∗	PROPN
ejpam-5871	323	2	(	(	PUNCT
ejpam-5871	323	3	⋋−1	⋋−1	ADJ
ejpam-5871	323	4	(	(	PUNCT
ejpam-5871	323	5	θ	θ	PROPN
ejpam-5871	323	6	⋋s+1	⋋s+1	PROPN
ejpam-5871	323	7	(	(	PUNCT
ejpam-5871	323	8	r1	r1	PROPN
ejpam-5871	323	9	)	)	PUNCT
ejpam-5871	323	10	+	+	CCONJ
ejpam-5871	323	11	(	(	PUNCT
ejpam-5871	323	12	1−	1−	NUM
ejpam-5871	323	13	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	323	14	(	(	PUNCT
ejpam-5871	323	15	r2	r2	PROPN
ejpam-5871	323	16	)	)	PUNCT
ejpam-5871	323	17	)	)	PUNCT
ejpam-5871	323	18	1	1	NUM
ejpam-5871	323	19	s+1	s+1	NOUN
ejpam-5871	323	20	)	)	PUNCT
ejpam-5871	323	21	dθ	dθ	PROPN
ejpam-5871	323	22	+	+	X
ejpam-5871	323	23	(	(	PUNCT
ejpam-5871	323	24	s+	s+	X
ejpam-5871	323	25	1)−	1)−	PROPN
ejpam-5871	323	26	β	β	X
ejpam-5871	323	27	k	k	PROPN
ejpam-5871	323	28	kγk(β	kγk(β	PROPN
ejpam-5871	323	29	)	)	PUNCT
ejpam-5871	323	30	∫	∫	PROPN
ejpam-5871	324	1	1	1	NUM
ejpam-5871	324	2	0	0	NUM
ejpam-5871	324	3	θ	θ	PROPN
ejpam-5871	324	4	β	β	X
ejpam-5871	324	5	k	k	X
ejpam-5871	325	1	−1∅∗	−1∅∗	PROPN
ejpam-5871	325	2	(	(	PUNCT
ejpam-5871	325	3	⋋−1	⋋−1	ADJ
ejpam-5871	325	4	(	(	PUNCT
ejpam-5871	325	5	(	(	PUNCT
ejpam-5871	325	6	1−	1−	NUM
ejpam-5871	325	7	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	325	8	(	(	PUNCT
ejpam-5871	325	9	r1	r1	PROPN
ejpam-5871	325	10	)	)	PUNCT
ejpam-5871	325	11	+	+	NUM
ejpam-5871	325	12	θ	θ	PUNCT
ejpam-5871	325	13	⋋s+1	⋋s+1	VERB
ejpam-5871	325	14	(	(	PUNCT
ejpam-5871	325	15	r2	r2	PROPN
ejpam-5871	325	16	)	)	PUNCT
ejpam-5871	325	17	)	)	PUNCT
ejpam-5871	325	18	1	1	NUM
ejpam-5871	325	19	s+1	s+1	PROPN
ejpam-5871	325	20	)	)	PUNCT
ejpam-5871	325	21	dθ	dθ	PROPN
ejpam-5871	325	22	,	,	PUNCT
ejpam-5871	325	23	(	(	PUNCT
ejpam-5871	325	24	s+	s+	NUM
ejpam-5871	325	25	1)−	1)−	PROPN
ejpam-5871	325	26	β	β	X
ejpam-5871	325	27	k	k	PROPN
ejpam-5871	325	28	kγk(β	kγk(β	PROPN
ejpam-5871	325	29	)	)	PUNCT
ejpam-5871	325	30	∫	∫	PROPN
ejpam-5871	325	31	1	1	NUM
ejpam-5871	325	32	0	0	NUM
ejpam-5871	325	33	θ	θ	PROPN
ejpam-5871	325	34	β	β	X
ejpam-5871	325	35	k	k	X
ejpam-5871	325	36	−1∅∗	−1∅∗	PROPN
ejpam-5871	325	37	(	(	PUNCT
ejpam-5871	325	38	⋋−1	⋋−1	ADJ
ejpam-5871	325	39	(	(	PUNCT
ejpam-5871	325	40	θ	θ	PROPN
ejpam-5871	325	41	⋋s+1	⋋s+1	PROPN
ejpam-5871	325	42	(	(	PUNCT
ejpam-5871	325	43	r1	r1	PROPN
ejpam-5871	325	44	)	)	PUNCT
ejpam-5871	325	45	+	+	CCONJ
ejpam-5871	325	46	(	(	PUNCT
ejpam-5871	325	47	1−	1−	NUM
ejpam-5871	325	48	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	325	49	(	(	PUNCT
ejpam-5871	325	50	r2	r2	PROPN
ejpam-5871	325	51	)	)	PUNCT
ejpam-5871	325	52	)	)	PUNCT
ejpam-5871	325	53	1	1	NUM
ejpam-5871	325	54	s+1	s+1	NOUN
ejpam-5871	325	55	)	)	PUNCT
ejpam-5871	325	56	dθ	dθ	PROPN
ejpam-5871	325	57	+	+	X
ejpam-5871	325	58	(	(	PUNCT
ejpam-5871	325	59	s+	s+	X
ejpam-5871	325	60	1)−	1)−	PROPN
ejpam-5871	325	61	β	β	X
ejpam-5871	325	62	k	k	PROPN
ejpam-5871	325	63	kγk(β	kγk(β	PROPN
ejpam-5871	325	64	)	)	PUNCT
ejpam-5871	325	65	∫	∫	PROPN
ejpam-5871	326	1	1	1	NUM
ejpam-5871	326	2	0	0	NUM
ejpam-5871	326	3	θ	θ	PROPN
ejpam-5871	326	4	β	β	X
ejpam-5871	326	5	k	k	X
ejpam-5871	327	1	−1∅∗	−1∅∗	PROPN
ejpam-5871	327	2	(	(	PUNCT
ejpam-5871	327	3	⋋−1	⋋−1	ADJ
ejpam-5871	327	4	(	(	PUNCT
ejpam-5871	327	5	(	(	PUNCT
ejpam-5871	327	6	1−	1−	NUM
ejpam-5871	327	7	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	327	8	(	(	PUNCT
ejpam-5871	327	9	r1	r1	PROPN
ejpam-5871	327	10	)	)	PUNCT
ejpam-5871	327	11	+	+	NUM
ejpam-5871	327	12	θ	θ	PUNCT
ejpam-5871	327	13	⋋s+1	⋋s+1	VERB
ejpam-5871	327	14	(	(	PUNCT
ejpam-5871	327	15	r2	r2	PROPN
ejpam-5871	327	16	)	)	PUNCT
ejpam-5871	327	17	)	)	PUNCT
ejpam-5871	327	18	1	1	NUM
ejpam-5871	327	19	s+1	s+1	PROPN
ejpam-5871	327	20	)	)	PUNCT
ejpam-5871	327	21	dθ	dθ	PROPN
ejpam-5871	327	22	]	]	PUNCT
ejpam-5871	327	23	.	.	PUNCT
ejpam-5871	328	1	by	by	ADP
ejpam-5871	328	2	substituting	substitute	VERB
ejpam-5871	328	3	⋋s+1(χ	⋋s+1(χ	PRON
ejpam-5871	328	4	)	)	PUNCT
ejpam-5871	328	5	=	=	SYM
ejpam-5871	328	6	θ	θ	X
ejpam-5871	328	7	⋋s+1	⋋s+1	PUNCT
ejpam-5871	328	8	(	(	PUNCT
ejpam-5871	328	9	r1	r1	PROPN
ejpam-5871	328	10	)	)	PUNCT
ejpam-5871	328	11	+	+	CCONJ
ejpam-5871	328	12	(	(	PUNCT
ejpam-5871	328	13	1−	1−	NUM
ejpam-5871	328	14	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	328	15	(	(	PUNCT
ejpam-5871	328	16	r2)red	r2)re	VERB
ejpam-5871	328	17	,	,	PUNCT
ejpam-5871	328	18	we	we	PRON
ejpam-5871	328	19	have	have	VERB
ejpam-5871	328	20	=	=	SYM
ejpam-5871	328	21	1	1	NUM
ejpam-5871	328	22	(	(	PUNCT
ejpam-5871	328	23	⋋s+1	⋋s+1	PROPN
ejpam-5871	328	24	(	(	PUNCT
ejpam-5871	328	25	r2)−⋋s+1(r1	r2)−⋋s+1(r1	NOUN
ejpam-5871	328	26	)	)	PUNCT
ejpam-5871	328	27	)	)	PUNCT
ejpam-5871	329	1	β	β	X
ejpam-5871	329	2	k	k	NOUN
ejpam-5871	329	3	×	×	PROPN
ejpam-5871	329	4	[	[	PUNCT
ejpam-5871	329	5	(	(	PUNCT
ejpam-5871	329	6	s+	s+	NUM
ejpam-5871	329	7	1)1−	1)1−	NUM
ejpam-5871	329	8	β	β	X
ejpam-5871	329	9	k	k	PROPN
ejpam-5871	329	10	kγk(β	kγk(β	PROPN
ejpam-5871	329	11	)	)	PUNCT
ejpam-5871	329	12	∫	∫	PROPN
ejpam-5871	329	13	r2	r2	PROPN
ejpam-5871	329	14	r1	r1	PROPN
ejpam-5871	329	15	(	(	PUNCT
ejpam-5871	329	16	⋋s+1	⋋s+1	PROPN
ejpam-5871	329	17	(	(	PUNCT
ejpam-5871	329	18	r2)−⋋s+1(χ	r2)−⋋s+1(χ	NOUN
ejpam-5871	329	19	)	)	PUNCT
ejpam-5871	329	20	)	)	PUNCT
ejpam-5871	330	1	β	β	X
ejpam-5871	330	2	k	k	X
ejpam-5871	330	3	−1	−1	ADV
ejpam-5871	330	4	⋋s	⋋s	PROPN
ejpam-5871	330	5	(	(	PUNCT
ejpam-5871	330	6	χ)⋋	χ)⋋	NOUN
ejpam-5871	330	7	′	′	NUM
ejpam-5871	330	8	(	(	PUNCT
ejpam-5871	330	9	χ)∅(χ)dχ	χ)∅(χ)dχ	VERB
ejpam-5871	330	10	+	+	PUNCT
ejpam-5871	330	11	(	(	PUNCT
ejpam-5871	330	12	s+	s+	NUM
ejpam-5871	330	13	1)1−	1)1−	NUM
ejpam-5871	330	14	β	β	X
ejpam-5871	330	15	k	k	PROPN
ejpam-5871	330	16	kγk(β	kγk(β	PROPN
ejpam-5871	330	17	)	)	PUNCT
ejpam-5871	330	18	∫	∫	PROPN
ejpam-5871	330	19	r2	r2	PROPN
ejpam-5871	330	20	r1	r1	PROPN
ejpam-5871	330	21	(	(	PUNCT
ejpam-5871	330	22	⋋s+1(χ)−⋋s+1(r1	⋋s+1(χ)−⋋s+1(r1	PROPN
ejpam-5871	330	23	)	)	PUNCT
ejpam-5871	330	24	)	)	PUNCT
ejpam-5871	331	1	β	β	X
ejpam-5871	331	2	k	k	X
ejpam-5871	331	3	−1	−1	ADV
ejpam-5871	331	4	⋋s	⋋s	PROPN
ejpam-5871	331	5	(	(	PUNCT
ejpam-5871	331	6	χ)⋋	χ)⋋	NOUN
ejpam-5871	331	7	′	′	NUM
ejpam-5871	331	8	(	(	PUNCT
ejpam-5871	331	9	χ)∅(χ)dχ	χ)∅(χ)dχ	NOUN
ejpam-5871	331	10	]	]	PUNCT
ejpam-5871	331	11	.	.	PUNCT
ejpam-5871	332	1	a.	a.	PROPN
ejpam-5871	332	2	mehmood	mehmood	PROPN
ejpam-5871	332	3	et	et	PROPN
ejpam-5871	332	4	al	al	PROPN
ejpam-5871	332	5	.	.	PUNCT
ejpam-5871	332	6	/	/	SYM
ejpam-5871	332	7	eur	eur	PROPN
ejpam-5871	332	8	.	.	PUNCT
ejpam-5871	333	1	j.	j.	PROPN
ejpam-5871	333	2	pure	pure	PROPN
ejpam-5871	333	3	appl	appl	PROPN
ejpam-5871	333	4	.	.	PROPN
ejpam-5871	333	5	math	math	PROPN
ejpam-5871	333	6	,	,	PUNCT
ejpam-5871	333	7	18	18	NUM
ejpam-5871	333	8	(	(	PUNCT
ejpam-5871	333	9	2	2	NUM
ejpam-5871	333	10	)	)	PUNCT
ejpam-5871	333	11	(	(	PUNCT
ejpam-5871	333	12	2025	2025	NUM
ejpam-5871	333	13	)	)	PUNCT
ejpam-5871	333	14	,	,	PUNCT
ejpam-5871	333	15	5871	5871	NUM
ejpam-5871	333	16	12	12	NUM
ejpam-5871	333	17	of	of	ADP
ejpam-5871	333	18	26	26	NUM
ejpam-5871	333	19	this	this	PRON
ejpam-5871	333	20	implies	imply	VERB
ejpam-5871	333	21	=	=	SYM
ejpam-5871	333	22	1	1	NUM
ejpam-5871	333	23	(	(	PUNCT
ejpam-5871	333	24	⋋s+1	⋋s+1	PROPN
ejpam-5871	333	25	(	(	PUNCT
ejpam-5871	333	26	r2)−⋋s+1(r1	r2)−⋋s+1(r1	NOUN
ejpam-5871	333	27	)	)	PUNCT
ejpam-5871	333	28	)	)	PUNCT
ejpam-5871	334	1	β	β	X
ejpam-5871	334	2	k	k	X
ejpam-5871	335	1	[	[	PUNCT
ejpam-5871	335	2	s	s	X
ejpam-5871	335	3	kz	kz	PROPN
ejpam-5871	335	4	β	β	PROPN
ejpam-5871	335	5	r+1	r+1	PROPN
ejpam-5871	335	6	∅(r2	∅(r2	PROPN
ejpam-5871	335	7	)	)	PUNCT
ejpam-5871	336	1	+	+	NUM
ejpam-5871	336	2	s	s	AUX
ejpam-5871	336	3	kz	kz	PROPN
ejpam-5871	336	4	β	β	PROPN
ejpam-5871	336	5	r−2	r−2	PROPN
ejpam-5871	336	6	∅(r1	∅(r1	PROPN
ejpam-5871	336	7	)	)	PUNCT
ejpam-5871	336	8	]	]	PUNCT
ejpam-5871	336	9	.	.	PUNCT
ejpam-5871	337	1	(	(	PUNCT
ejpam-5871	337	2	22	22	X
ejpam-5871	337	3	)	)	PUNCT
ejpam-5871	337	4	we	we	PRON
ejpam-5871	337	5	get	get	VERB
ejpam-5871	337	6	first	first	ADJ
ejpam-5871	337	7	half	half	NOUN
ejpam-5871	337	8	of	of	ADP
ejpam-5871	337	9	our	our	PRON
ejpam-5871	337	10	relation	relation	NOUN
ejpam-5871	337	11	from	from	ADP
ejpam-5871	337	12	the	the	DET
ejpam-5871	337	13	inclusions	inclusion	NOUN
ejpam-5871	337	14	(	(	PUNCT
ejpam-5871	337	15	21	21	NUM
ejpam-5871	337	16	)	)	PUNCT
ejpam-5871	337	17	and	and	CCONJ
ejpam-5871	337	18	(	(	PUNCT
ejpam-5871	337	19	22	22	NUM
ejpam-5871	337	20	)	)	PUNCT
ejpam-5871	337	21	for	for	ADP
ejpam-5871	337	22	the	the	DET
ejpam-5871	337	23	second	second	ADJ
ejpam-5871	337	24	half	half	NOUN
ejpam-5871	337	25	employing	employ	VERB
ejpam-5871	337	26	ı.υ-(⋋s+1	ı.υ-(⋋s+1	PROPN
ejpam-5871	337	27	,	,	PUNCT
ejpam-5871	337	28	℧	℧	NOUN
ejpam-5871	337	29	)	)	PUNCT
ejpam-5871	337	30	convexity	convexity	NOUN
ejpam-5871	337	31	of	of	ADP
ejpam-5871	337	32	function	function	NOUN
ejpam-5871	337	33	∅	∅	NOUN
ejpam-5871	337	34	,	,	PUNCT
ejpam-5871	337	35	we	we	PRON
ejpam-5871	337	36	have	have	VERB
ejpam-5871	337	37	∅	∅	NOUN
ejpam-5871	337	38	(	(	PUNCT
ejpam-5871	337	39	⋋−1	⋋−1	X
ejpam-5871	337	40	(	(	PUNCT
ejpam-5871	337	41	θ	θ	PROPN
ejpam-5871	337	42	⋋s+1	⋋s+1	PROPN
ejpam-5871	337	43	(	(	PUNCT
ejpam-5871	337	44	r1	r1	PROPN
ejpam-5871	337	45	)	)	PUNCT
ejpam-5871	337	46	+	+	CCONJ
ejpam-5871	337	47	(	(	PUNCT
ejpam-5871	337	48	1−	1−	NUM
ejpam-5871	337	49	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	337	50	(	(	PUNCT
ejpam-5871	337	51	r2	r2	PROPN
ejpam-5871	337	52	)	)	PUNCT
ejpam-5871	337	53	)	)	PUNCT
ejpam-5871	337	54	1	1	NUM
ejpam-5871	337	55	s+1	s+1	PROPN
ejpam-5871	337	56	)	)	PUNCT
ejpam-5871	337	57	⊇	⊇	PROPN
ejpam-5871	337	58	℧	℧	PROPN
ejpam-5871	337	59	(	(	PUNCT
ejpam-5871	337	60	θ)∅(r1	θ)∅(r1	NOUN
ejpam-5871	337	61	)	)	PUNCT
ejpam-5871	337	62	+	+	CCONJ
ejpam-5871	338	1	℧	℧	PROPN
ejpam-5871	338	2	(	(	PUNCT
ejpam-5871	338	3	1−	1−	NUM
ejpam-5871	338	4	θ)∅(r2	θ)∅(r2	NOUN
ejpam-5871	338	5	)	)	PUNCT
ejpam-5871	338	6	,	,	PUNCT
ejpam-5871	338	7	(	(	PUNCT
ejpam-5871	338	8	23	23	NUM
ejpam-5871	338	9	)	)	PUNCT
ejpam-5871	338	10	and	and	CCONJ
ejpam-5871	338	11	∅	∅	NOUN
ejpam-5871	338	12	(	(	PUNCT
ejpam-5871	338	13	⋋−1	⋋−1	X
ejpam-5871	338	14	(	(	PUNCT
ejpam-5871	338	15	(	(	PUNCT
ejpam-5871	338	16	1−	1−	NUM
ejpam-5871	338	17	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	338	18	(	(	PUNCT
ejpam-5871	338	19	r1	r1	PROPN
ejpam-5871	338	20	)	)	PUNCT
ejpam-5871	338	21	+	+	NUM
ejpam-5871	338	22	θ	θ	PUNCT
ejpam-5871	338	23	⋋s+1	⋋s+1	VERB
ejpam-5871	338	24	(	(	PUNCT
ejpam-5871	338	25	r2	r2	PROPN
ejpam-5871	338	26	)	)	PUNCT
ejpam-5871	338	27	)	)	PUNCT
ejpam-5871	338	28	1	1	NUM
ejpam-5871	338	29	s+1	s+1	PROPN
ejpam-5871	338	30	)	)	PUNCT
ejpam-5871	338	31	⊇	⊇	PROPN
ejpam-5871	338	32	℧	℧	PROPN
ejpam-5871	338	33	(	(	PUNCT
ejpam-5871	338	34	1−	1−	NUM
ejpam-5871	338	35	θ)∅(r1	θ)∅(r1	NOUN
ejpam-5871	338	36	)	)	PUNCT
ejpam-5871	338	37	+	+	CCONJ
ejpam-5871	338	38	℧	℧	PROPN
ejpam-5871	338	39	(	(	PUNCT
ejpam-5871	338	40	θ)∅(r2	θ)∅(r2	NOUN
ejpam-5871	338	41	)	)	PUNCT
ejpam-5871	338	42	.	.	PUNCT
ejpam-5871	339	1	(	(	PUNCT
ejpam-5871	339	2	24	24	NUM
ejpam-5871	339	3	)	)	PUNCT
ejpam-5871	339	4	adding	add	VERB
ejpam-5871	339	5	(	(	PUNCT
ejpam-5871	339	6	23	23	NUM
ejpam-5871	339	7	)	)	PUNCT
ejpam-5871	339	8	and	and	CCONJ
ejpam-5871	339	9	(	(	PUNCT
ejpam-5871	339	10	24	24	NUM
ejpam-5871	339	11	)	)	PUNCT
ejpam-5871	339	12	inclusions	inclusion	NOUN
ejpam-5871	339	13	and	and	CCONJ
ejpam-5871	339	14	multiplying	multiply	VERB
ejpam-5871	339	15	both	both	DET
ejpam-5871	339	16	sides	side	NOUN
ejpam-5871	339	17	by	by	ADP
ejpam-5871	339	18	(	(	PUNCT
ejpam-5871	339	19	s+1)−	s+1)−	PROPN
ejpam-5871	339	20	β	β	PROPN
ejpam-5871	339	21	k	k	PROPN
ejpam-5871	339	22	kγk(β	kγk(β	PROPN
ejpam-5871	339	23	)	)	PUNCT
ejpam-5871	339	24	θ	θ	PROPN
ejpam-5871	339	25	β	β	X
ejpam-5871	339	26	k	k	X
ejpam-5871	339	27	−1	−1	NOUN
ejpam-5871	339	28	also	also	ADV
ejpam-5871	339	29	taking	take	VERB
ejpam-5871	339	30	the	the	DET
ejpam-5871	339	31	integration	integration	NOUN
ejpam-5871	339	32	over	over	ADP
ejpam-5871	339	33	[	[	X
ejpam-5871	339	34	0	0	NUM
ejpam-5871	339	35	,	,	PUNCT
ejpam-5871	339	36	1	1	NUM
ejpam-5871	339	37	]	]	PUNCT
ejpam-5871	339	38	w.r.t	w.r.t	NOUN
ejpam-5871	339	39	”	"	PUNCT
ejpam-5871	339	40	θ”red	θ”re	VERB
ejpam-5871	339	41	,	,	PUNCT
ejpam-5871	339	42	then	then	ADV
ejpam-5871	339	43	we	we	PRON
ejpam-5871	339	44	acquired	acquire	VERB
ejpam-5871	339	45	our	our	PRON
ejpam-5871	339	46	required	required	ADJ
ejpam-5871	339	47	relation	relation	NOUN
ejpam-5871	339	48	.	.	PUNCT
ejpam-5871	340	1	corollary	corollary	ADJ
ejpam-5871	340	2	1	1	NUM
ejpam-5871	340	3	.	.	PUNCT
ejpam-5871	341	1	if	if	SCONJ
ejpam-5871	341	2	we	we	PRON
ejpam-5871	341	3	fix	fix	VERB
ejpam-5871	341	4	℧	℧	PROPN
ejpam-5871	341	5	(	(	PUNCT
ejpam-5871	341	6	θ	θ	NOUN
ejpam-5871	341	7	)	)	PUNCT
ejpam-5871	341	8	=	=	SYM
ejpam-5871	341	9	θ	θ	PROPN
ejpam-5871	341	10	in	in	ADP
ejpam-5871	341	11	theorem	theorem	NOUN
ejpam-5871	341	12	6	6	NUM
ejpam-5871	341	13	,	,	PUNCT
ejpam-5871	341	14	we	we	PRON
ejpam-5871	341	15	possess	possess	VERB
ejpam-5871	341	16	2(s+	2(s+	NUM
ejpam-5871	341	17	1)−	1)−	NUM
ejpam-5871	341	18	β	β	X
ejpam-5871	341	19	k	k	X
ejpam-5871	341	20	βγk(β	βγk(β	PROPN
ejpam-5871	341	21	)	)	PUNCT
ejpam-5871	341	22	∅	∅	NOUN
ejpam-5871	341	23	(	(	PUNCT
ejpam-5871	341	24	⋋−1	⋋−1	X
ejpam-5871	341	25	(	(	PUNCT
ejpam-5871	341	26	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	341	27	)	)	PUNCT
ejpam-5871	341	28	+	+	NOUN
ejpam-5871	341	29	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	341	30	)	)	PUNCT
ejpam-5871	341	31	2	2	NUM
ejpam-5871	341	32	)	)	PUNCT
ejpam-5871	341	33	1	1	NUM
ejpam-5871	341	34	s+1	s+1	PROPN
ejpam-5871	341	35	)	)	PUNCT
ejpam-5871	341	36	⊇	⊇	PROPN
ejpam-5871	341	37	1	1	NUM
ejpam-5871	341	38	(	(	PUNCT
ejpam-5871	341	39	⋋s+1	⋋s+1	PROPN
ejpam-5871	341	40	(	(	PUNCT
ejpam-5871	341	41	r2)−⋋s+1(r1	r2)−⋋s+1(r1	NOUN
ejpam-5871	341	42	)	)	PUNCT
ejpam-5871	341	43	)	)	PUNCT
ejpam-5871	342	1	β	β	X
ejpam-5871	342	2	k	k	X
ejpam-5871	343	1	[	[	PUNCT
ejpam-5871	343	2	s	s	X
ejpam-5871	343	3	kz	kz	PROPN
ejpam-5871	343	4	β	β	PROPN
ejpam-5871	343	5	r+1	r+1	PROPN
ejpam-5871	343	6	∅(r2	∅(r2	PROPN
ejpam-5871	343	7	)	)	PUNCT
ejpam-5871	344	1	+	+	NUM
ejpam-5871	344	2	s	s	AUX
ejpam-5871	344	3	kz	kz	PROPN
ejpam-5871	344	4	β	β	PROPN
ejpam-5871	344	5	r−2	r−2	PROPN
ejpam-5871	344	6	∅(r1	∅(r1	PROPN
ejpam-5871	344	7	)	)	PUNCT
ejpam-5871	344	8	]	]	PUNCT
ejpam-5871	345	1	⊇	⊇	X
ejpam-5871	345	2	(	(	PUNCT
ejpam-5871	345	3	s+	s+	PROPN
ejpam-5871	345	4	1)−	1)−	PROPN
ejpam-5871	345	5	β	β	X
ejpam-5871	345	6	k	k	PROPN
ejpam-5871	345	7	βγk(β	βγk(β	PROPN
ejpam-5871	345	8	)	)	PUNCT
ejpam-5871	345	9	[	[	PUNCT
ejpam-5871	345	10	∅(r1	∅(r1	NOUN
ejpam-5871	345	11	)	)	PUNCT
ejpam-5871	346	1	+	+	NOUN
ejpam-5871	346	2	∅(r2	∅(r2	NOUN
ejpam-5871	346	3	)	)	PUNCT
ejpam-5871	346	4	]	]	PUNCT
ejpam-5871	346	5	.	.	PUNCT
ejpam-5871	347	1	(	(	PUNCT
ejpam-5871	347	2	25	25	NUM
ejpam-5871	347	3	)	)	PUNCT
ejpam-5871	347	4	example	example	NOUN
ejpam-5871	348	1	1	1	NUM
ejpam-5871	348	2	.	.	PUNCT
ejpam-5871	349	1	if	if	SCONJ
ejpam-5871	349	2	we	we	PRON
ejpam-5871	349	3	choose	choose	VERB
ejpam-5871	349	4	∅(r	∅(r	PROPN
ejpam-5871	349	5	)	)	PUNCT
ejpam-5871	349	6	=	=	PUNCT
ejpam-5871	350	1	[	[	X
ejpam-5871	350	2	4	4	NUM
ejpam-5871	350	3	−	−	NOUN
ejpam-5871	350	4	⋋s+1(r	⋋s+1(r	NUM
ejpam-5871	350	5	)	)	PUNCT
ejpam-5871	350	6	,	,	PUNCT
ejpam-5871	350	7	8	8	NUM
ejpam-5871	350	8	+	+	NOUN
ejpam-5871	350	9	⋋s+1(r	⋋s+1(r	NUM
ejpam-5871	350	10	)	)	PUNCT
ejpam-5871	350	11	]	]	PUNCT
ejpam-5871	350	12	and	and	CCONJ
ejpam-5871	350	13	⋋(r	⋋(r	NUM
ejpam-5871	350	14	)	)	PUNCT
ejpam-5871	351	1	=	=	SYM
ejpam-5871	351	2	r	r	NOUN
ejpam-5871	351	3	in	in	ADP
ejpam-5871	351	4	(	(	PUNCT
ejpam-5871	351	5	25	25	NUM
ejpam-5871	351	6	)	)	PUNCT
ejpam-5871	351	7	and	and	CCONJ
ejpam-5871	351	8	using	use	VERB
ejpam-5871	351	9	proposition	proposition	NOUN
ejpam-5871	351	10	1	1	NUM
ejpam-5871	351	11	,	,	PUNCT
ejpam-5871	351	12	we	we	PRON
ejpam-5871	351	13	have	have	VERB
ejpam-5871	351	14	2(s+	2(s+	NUM
ejpam-5871	351	15	1)−	1)−	PROPN
ejpam-5871	351	16	β	β	X
ejpam-5871	351	17	k	k	PROPN
ejpam-5871	351	18	βγk(β	βγk(β	PROPN
ejpam-5871	351	19	)	)	PUNCT
ejpam-5871	351	20	(	(	PUNCT
ejpam-5871	351	21	4−	4−	NOUN
ejpam-5871	351	22	rs+1	rs+1	NOUN
ejpam-5871	351	23	1	1	NUM
ejpam-5871	352	1	+	+	CCONJ
ejpam-5871	352	2	rs+1	rs+1	NUM
ejpam-5871	352	3	2	2	NUM
ejpam-5871	352	4	2	2	NUM
ejpam-5871	352	5	,	,	PUNCT
ejpam-5871	352	6	8	8	NUM
ejpam-5871	352	7	+	+	CCONJ
ejpam-5871	352	8	rs+1	rs+1	PROPN
ejpam-5871	352	9	1	1	NUM
ejpam-5871	352	10	+	+	CCONJ
ejpam-5871	352	11	rs+1	rs+1	NUM
ejpam-5871	352	12	2	2	NUM
ejpam-5871	352	13	2	2	NUM
ejpam-5871	352	14	)	)	PUNCT
ejpam-5871	352	15	⊇	⊇	NOUN
ejpam-5871	352	16	(	(	PUNCT
ejpam-5871	352	17	s+	s+	NOUN
ejpam-5871	352	18	1	1	X
ejpam-5871	352	19	)	)	PUNCT
ejpam-5871	352	20	−β	−β	NOUN
ejpam-5871	352	21	k	k	PROPN
ejpam-5871	352	22	βγk(β	βγk(β	PROPN
ejpam-5871	352	23	)	)	PUNCT
ejpam-5871	352	24	(	(	PUNCT
ejpam-5871	352	25	8−	8−	NUM
ejpam-5871	352	26	(	(	PUNCT
ejpam-5871	352	27	rs+1	rs+1	NOUN
ejpam-5871	352	28	1	1	NUM
ejpam-5871	352	29	+	+	CCONJ
ejpam-5871	352	30	rs+1	rs+1	PROPN
ejpam-5871	352	31	2	2	NUM
ejpam-5871	352	32	)	)	PUNCT
ejpam-5871	352	33	,	,	PUNCT
ejpam-5871	352	34	16	16	NUM
ejpam-5871	353	1	+	+	CCONJ
ejpam-5871	353	2	(	(	PUNCT
ejpam-5871	353	3	rs+1	rs+1	PROPN
ejpam-5871	353	4	1	1	NUM
ejpam-5871	353	5	+	+	CCONJ
ejpam-5871	353	6	rs+1	rs+1	PROPN
ejpam-5871	353	7	2	2	NUM
ejpam-5871	353	8	)	)	PUNCT
ejpam-5871	353	9	)	)	PUNCT
ejpam-5871	354	1	⊇	⊇	NOUN
ejpam-5871	354	2	(	(	PUNCT
ejpam-5871	354	3	s+	s+	NUM
ejpam-5871	354	4	1)−	1)−	PROPN
ejpam-5871	354	5	β	β	X
ejpam-5871	354	6	k	k	PROPN
ejpam-5871	354	7	βγk(β	βγk(β	PROPN
ejpam-5871	354	8	)	)	PUNCT
ejpam-5871	354	9	(	(	PUNCT
ejpam-5871	354	10	8−	8−	NUM
ejpam-5871	354	11	(	(	PUNCT
ejpam-5871	354	12	rs+1	rs+1	NOUN
ejpam-5871	354	13	1	1	NUM
ejpam-5871	354	14	+	+	CCONJ
ejpam-5871	354	15	rs+1	rs+1	PROPN
ejpam-5871	354	16	2	2	NUM
ejpam-5871	354	17	)	)	PUNCT
ejpam-5871	354	18	,	,	PUNCT
ejpam-5871	354	19	16	16	NUM
ejpam-5871	354	20	+	+	CCONJ
ejpam-5871	354	21	(	(	PUNCT
ejpam-5871	354	22	rs+1	rs+1	PROPN
ejpam-5871	354	23	1	1	NUM
ejpam-5871	354	24	+	+	CCONJ
ejpam-5871	354	25	rs+1	rs+1	PROPN
ejpam-5871	354	26	2	2	NUM
ejpam-5871	354	27	)	)	PUNCT
ejpam-5871	354	28	)	)	PUNCT
ejpam-5871	354	29	.	.	PUNCT
ejpam-5871	355	1	example	example	NOUN
ejpam-5871	356	1	2	2	NUM
ejpam-5871	356	2	.	.	X
ejpam-5871	356	3	for	for	ADP
ejpam-5871	356	4	graphical	graphical	ADJ
ejpam-5871	356	5	representation	representation	NOUN
ejpam-5871	356	6	if	if	SCONJ
ejpam-5871	356	7	we	we	PRON
ejpam-5871	356	8	choose	choose	VERB
ejpam-5871	356	9	∅(r	∅(r	PROPN
ejpam-5871	356	10	)	)	PUNCT
ejpam-5871	356	11	=	=	PUNCT
ejpam-5871	357	1	[	[	X
ejpam-5871	357	2	4−⋋s+1(r	4−⋋s+1(r	NUM
ejpam-5871	357	3	)	)	PUNCT
ejpam-5871	357	4	,	,	PUNCT
ejpam-5871	357	5	8+⋋s+1(r	8+⋋s+1(r	NOUN
ejpam-5871	357	6	)	)	PUNCT
ejpam-5871	357	7	]	]	PUNCT
ejpam-5871	357	8	,	,	PUNCT
ejpam-5871	357	9	℧	℧	PROPN
ejpam-5871	357	10	(	(	PUNCT
ejpam-5871	357	11	r	r	NOUN
ejpam-5871	357	12	)	)	PUNCT
ejpam-5871	357	13	=	=	SYM
ejpam-5871	357	14	1	1	NUM
ejpam-5871	357	15	8	8	NUM
ejpam-5871	357	16	and	and	CCONJ
ejpam-5871	357	17	⋋(r	⋋(r	NUM
ejpam-5871	357	18	)	)	PUNCT
ejpam-5871	358	1	=	=	PUNCT
ejpam-5871	358	2	sin	sin	NOUN
ejpam-5871	358	3	r	r	NOUN
ejpam-5871	358	4	in	in	ADP
ejpam-5871	358	5	(	(	PUNCT
ejpam-5871	358	6	25	25	NUM
ejpam-5871	358	7	)	)	PUNCT
ejpam-5871	358	8	and	and	CCONJ
ejpam-5871	358	9	using	use	VERB
ejpam-5871	358	10	the	the	DET
ejpam-5871	358	11	proposition	proposition	NOUN
ejpam-5871	358	12	1	1	NUM
ejpam-5871	358	13	,	,	PUNCT
ejpam-5871	358	14	we	we	PRON
ejpam-5871	358	15	have	have	VERB
ejpam-5871	358	16	8(s+	8(s+	NUM
ejpam-5871	359	1	1)−	1)−	NUM
ejpam-5871	359	2	β	β	SYM
ejpam-5871	359	3	k	k	X
ejpam-5871	359	4	(	(	PUNCT
ejpam-5871	359	5	β)γk(β	β)γk(β	NUM
ejpam-5871	359	6	)	)	PUNCT
ejpam-5871	359	7	(	(	PUNCT
ejpam-5871	359	8	4−	4−	NOUN
ejpam-5871	359	9	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	359	10	)	)	PUNCT
ejpam-5871	360	1	+	+	SYM
ejpam-5871	360	2	sins+1(r2	sins+1(r2	X
ejpam-5871	360	3	)	)	PUNCT
ejpam-5871	360	4	2	2	NUM
ejpam-5871	360	5	,	,	PUNCT
ejpam-5871	360	6	8	8	NUM
ejpam-5871	360	7	+	+	SYM
ejpam-5871	360	8	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	360	9	)	)	PUNCT
ejpam-5871	361	1	+	+	SYM
ejpam-5871	361	2	sins+1(r2	sins+1(r2	X
ejpam-5871	361	3	)	)	PUNCT
ejpam-5871	361	4	2	2	NUM
ejpam-5871	361	5	)	)	PUNCT
ejpam-5871	362	1	a.	a.	NOUN
ejpam-5871	362	2	mehmood	mehmood	PROPN
ejpam-5871	362	3	et	et	PROPN
ejpam-5871	362	4	al	al	PROPN
ejpam-5871	362	5	.	.	PUNCT
ejpam-5871	362	6	/	/	SYM
ejpam-5871	362	7	eur	eur	PROPN
ejpam-5871	362	8	.	.	PUNCT
ejpam-5871	363	1	j.	j.	PROPN
ejpam-5871	363	2	pure	pure	PROPN
ejpam-5871	363	3	appl	appl	PROPN
ejpam-5871	363	4	.	.	PROPN
ejpam-5871	363	5	math	math	PROPN
ejpam-5871	363	6	,	,	PUNCT
ejpam-5871	363	7	18	18	NUM
ejpam-5871	363	8	(	(	PUNCT
ejpam-5871	363	9	2	2	NUM
ejpam-5871	363	10	)	)	PUNCT
ejpam-5871	363	11	(	(	PUNCT
ejpam-5871	363	12	2025	2025	NUM
ejpam-5871	363	13	)	)	PUNCT
ejpam-5871	363	14	,	,	PUNCT
ejpam-5871	363	15	5871	5871	NUM
ejpam-5871	363	16	13	13	NUM
ejpam-5871	363	17	of	of	ADP
ejpam-5871	363	18	26	26	NUM
ejpam-5871	363	19	⊇	⊇	NOUN
ejpam-5871	363	20	(	(	PUNCT
ejpam-5871	363	21	s+	s+	NOUN
ejpam-5871	363	22	1	1	X
ejpam-5871	363	23	)	)	PUNCT
ejpam-5871	363	24	−β	−β	NOUN
ejpam-5871	363	25	k	k	PROPN
ejpam-5871	363	26	βγk(β	βγk(β	PROPN
ejpam-5871	363	27	)	)	PUNCT
ejpam-5871	363	28	(	(	PUNCT
ejpam-5871	363	29	8−	8−	NUM
ejpam-5871	363	30	(	(	PUNCT
ejpam-5871	363	31	sins+1(r1	sins+1(r1	X
ejpam-5871	363	32	)	)	PUNCT
ejpam-5871	363	33	+	+	SYM
ejpam-5871	363	34	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	363	35	)	)	PUNCT
ejpam-5871	363	36	)	)	PUNCT
ejpam-5871	363	37	,	,	PUNCT
ejpam-5871	363	38	16	16	NUM
ejpam-5871	363	39	+	+	CCONJ
ejpam-5871	363	40	(	(	PUNCT
ejpam-5871	363	41	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	363	42	)	)	PUNCT
ejpam-5871	363	43	+	+	SYM
ejpam-5871	363	44	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	363	45	)	)	PUNCT
ejpam-5871	363	46	)	)	PUNCT
ejpam-5871	363	47	)	)	PUNCT
ejpam-5871	364	1	⊇	⊇	NOUN
ejpam-5871	364	2	(	(	PUNCT
ejpam-5871	364	3	s+	s+	NUM
ejpam-5871	364	4	1)−	1)−	PROPN
ejpam-5871	364	5	β	β	X
ejpam-5871	364	6	k	k	PROPN
ejpam-5871	364	7	4βγk(β	4βγk(β	PROPN
ejpam-5871	364	8	)	)	PUNCT
ejpam-5871	364	9	(	(	PUNCT
ejpam-5871	364	10	8−	8−	NUM
ejpam-5871	364	11	(	(	PUNCT
ejpam-5871	364	12	sins+1(r1	sins+1(r1	X
ejpam-5871	364	13	)	)	PUNCT
ejpam-5871	364	14	+	+	SYM
ejpam-5871	364	15	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	364	16	)	)	PUNCT
ejpam-5871	364	17	)	)	PUNCT
ejpam-5871	364	18	,	,	PUNCT
ejpam-5871	364	19	16	16	NUM
ejpam-5871	364	20	+	+	CCONJ
ejpam-5871	364	21	(	(	PUNCT
ejpam-5871	364	22	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	364	23	)	)	PUNCT
ejpam-5871	364	24	+	+	SYM
ejpam-5871	364	25	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	364	26	)	)	PUNCT
ejpam-5871	364	27	)	)	PUNCT
ejpam-5871	364	28	)	)	PUNCT
ejpam-5871	364	29	.	.	PUNCT
ejpam-5871	365	1	figure	figure	VERB
ejpam-5871	365	2	1	1	NUM
ejpam-5871	365	3	:	:	PUNCT
ejpam-5871	365	4	graphical	graphical	ADJ
ejpam-5871	365	5	representation	representation	NOUN
ejpam-5871	365	6	of	of	ADP
ejpam-5871	365	7	theorem	theorem	NOUN
ejpam-5871	365	8	6	6	NUM
ejpam-5871	365	9	corresponding	correspond	VERB
ejpam-5871	365	10	to	to	ADP
ejpam-5871	365	11	the	the	DET
ejpam-5871	365	12	choice	choice	NOUN
ejpam-5871	365	13	of	of	ADP
ejpam-5871	365	14	parameters	parameter	NOUN
ejpam-5871	365	15	r1	r1	NOUN
ejpam-5871	365	16	=	=	SYM
ejpam-5871	365	17	0.6	0.6	NUM
ejpam-5871	365	18	,	,	PUNCT
ejpam-5871	365	19	r1	r1	NOUN
ejpam-5871	365	20	<	<	X
ejpam-5871	365	21	r2	r2	PROPN
ejpam-5871	365	22	≤	≤	PROPN
ejpam-5871	365	23	π	π	PROPN
ejpam-5871	365	24	2	2	NUM
ejpam-5871	365	25	,	,	PUNCT
ejpam-5871	365	26	k	k	NOUN
ejpam-5871	365	27	=	=	SYM
ejpam-5871	365	28	1	1	NUM
ejpam-5871	365	29	,	,	PUNCT
ejpam-5871	365	30	s	s	PART
ejpam-5871	365	31	=	=	SYM
ejpam-5871	365	32	3	3	NUM
ejpam-5871	365	33	and	and	CCONJ
ejpam-5871	365	34	β	β	X
ejpam-5871	365	35	=	=	NOUN
ejpam-5871	365	36	0.8	0.8	NUM
ejpam-5871	365	37	.	.	PUNCT
ejpam-5871	366	1	also	also	ADV
ejpam-5871	366	2	for	for	ADP
ejpam-5871	366	3	tabular	tabular	NOUN
ejpam-5871	366	4	form	form	NOUN
ejpam-5871	366	5	we	we	PRON
ejpam-5871	366	6	have	have	VERB
ejpam-5871	366	7	r2	r2	PROPN
ejpam-5871	366	8	(	(	PUNCT
ejpam-5871	366	9	a1	a1	NOUN
ejpam-5871	366	10	,	,	PUNCT
ejpam-5871	366	11	b1	b1	NOUN
ejpam-5871	366	12	)	)	PUNCT
ejpam-5871	366	13	(	(	PUNCT
ejpam-5871	366	14	a2	a2	PROPN
ejpam-5871	366	15	,	,	PUNCT
ejpam-5871	366	16	b2	b2	NOUN
ejpam-5871	366	17	)	)	PUNCT
ejpam-5871	366	18	(	(	PUNCT
ejpam-5871	366	19	a3	a3	NOUN
ejpam-5871	366	20	,	,	PUNCT
ejpam-5871	366	21	b3	b3	PROPN
ejpam-5871	366	22	)	)	PUNCT
ejpam-5871	366	23	0.610000	0.610000	NUM
ejpam-5871	366	24	(	(	PUNCT
ejpam-5871	366	25	11.037156	11.037156	NUM
ejpam-5871	366	26	,	,	PUNCT
ejpam-5871	366	27	22.964070	22.964070	NUM
ejpam-5871	366	28	)	)	PUNCT
ejpam-5871	366	29	(	(	PUNCT
ejpam-5871	366	30	2.759289	2.759289	NUM
ejpam-5871	366	31	,	,	PUNCT
ejpam-5871	366	32	5.741017	5.741017	NUM
ejpam-5871	366	33	)	)	PUNCT
ejpam-5871	366	34	(	(	PUNCT
ejpam-5871	366	35	0.6898221.435254	0.6898221.435254	NUM
ejpam-5871	366	36	)	)	PUNCT
ejpam-5871	366	37	0.802159	0.802159	NUM
ejpam-5871	366	38	(	(	PUNCT
ejpam-5871	366	39	10.811418	10.811418	NUM
ejpam-5871	366	40	,	,	PUNCT
ejpam-5871	366	41	23.189807	23.189807	NUM
ejpam-5871	366	42	)	)	PUNCT
ejpam-5871	366	43	(	(	PUNCT
ejpam-5871	366	44	2.702855	2.702855	NUM
ejpam-5871	366	45	,	,	PUNCT
ejpam-5871	366	46	5.797452	5.797452	NUM
ejpam-5871	366	47	)	)	PUNCT
ejpam-5871	366	48	(	(	PUNCT
ejpam-5871	366	49	0.675714	0.675714	NUM
ejpam-5871	366	50	,	,	PUNCT
ejpam-5871	366	51	1.449363	1.449363	NUM
ejpam-5871	366	52	)	)	PUNCT
ejpam-5871	367	1	0.994319	0.994319	NUM
ejpam-5871	367	2	(	(	PUNCT
ejpam-5871	367	3	10.489794	10.489794	NUM
ejpam-5871	367	4	,	,	PUNCT
ejpam-5871	367	5	23.511432	23.511432	NUM
ejpam-5871	367	6	)	)	PUNCT
ejpam-5871	367	7	(	(	PUNCT
ejpam-5871	367	8	2.622448	2.622448	NUM
ejpam-5871	367	9	,	,	PUNCT
ejpam-5871	367	10	5.877858	5.877858	NUM
ejpam-5871	367	11	)	)	PUNCT
ejpam-5871	367	12	(	(	PUNCT
ejpam-5871	367	13	0.655612	0.655612	NUM
ejpam-5871	367	14	,	,	PUNCT
ejpam-5871	367	15	1.469465	1.469465	NUM
ejpam-5871	367	16	)	)	PUNCT
ejpam-5871	367	17	1.186478	1.186478	NUM
ejpam-5871	367	18	(	(	PUNCT
ejpam-5871	367	19	10.143322	10.143322	NUM
ejpam-5871	367	20	,	,	PUNCT
ejpam-5871	367	21	23.857903	23.857903	NUM
ejpam-5871	367	22	)	)	PUNCT
ejpam-5871	367	23	(	(	PUNCT
ejpam-5871	367	24	2.535831	2.535831	NUM
ejpam-5871	367	25	,	,	PUNCT
ejpam-5871	367	26	5.964476	5.964476	NUM
ejpam-5871	367	27	)	)	PUNCT
ejpam-5871	367	28	(	(	PUNCT
ejpam-5871	367	29	0.633958	0.633958	NUM
ejpam-5871	367	30	,	,	PUNCT
ejpam-5871	367	31	1.491119	1.491119	NUM
ejpam-5871	367	32	)	)	PUNCT
ejpam-5871	367	33	1.378637	1.378637	NUM
ejpam-5871	367	34	(	(	PUNCT
ejpam-5871	367	35	9.874478	9.874478	NUM
ejpam-5871	367	36	,	,	PUNCT
ejpam-5871	367	37	24.126747	24.126747	NUM
ejpam-5871	367	38	)	)	PUNCT
ejpam-5871	367	39	(	(	PUNCT
ejpam-5871	367	40	2.468620	2.468620	NUM
ejpam-5871	367	41	,	,	PUNCT
ejpam-5871	367	42	6.031687	6.031687	NUM
ejpam-5871	367	43	)	)	PUNCT
ejpam-5871	367	44	(	(	PUNCT
ejpam-5871	367	45	0.617155	0.617155	NUM
ejpam-5871	367	46	,	,	PUNCT
ejpam-5871	367	47	1.507922	1.507922	NUM
ejpam-5871	367	48	)	)	PUNCT
ejpam-5871	367	49	1.570796	1.570796	NUM
ejpam-5871	367	50	(	(	PUNCT
ejpam-5871	367	51	9.773019	9.773019	NUM
ejpam-5871	367	52	,	,	PUNCT
ejpam-5871	367	53	24.228207	24.228207	NUM
ejpam-5871	367	54	)	)	PUNCT
ejpam-5871	367	55	(	(	PUNCT
ejpam-5871	367	56	2.443255	2.443255	NUM
ejpam-5871	367	57	,	,	PUNCT
ejpam-5871	367	58	6.057052	6.057052	NUM
ejpam-5871	367	59	)	)	PUNCT
ejpam-5871	367	60	(	(	PUNCT
ejpam-5871	367	61	0.610814	0.610814	NUM
ejpam-5871	367	62	,	,	PUNCT
ejpam-5871	367	63	1.514263	1.514263	NUM
ejpam-5871	367	64	)	)	PUNCT
ejpam-5871	367	65	table	table	NOUN
ejpam-5871	367	66	1	1	NUM
ejpam-5871	367	67	:	:	PUNCT
ejpam-5871	367	68	interval	interval	NOUN
ejpam-5871	367	69	bounds	bound	NOUN
ejpam-5871	367	70	of	of	ADP
ejpam-5871	367	71	theorem	theorem	NOUN
ejpam-5871	367	72	6	6	NUM
ejpam-5871	367	73	corresponding	correspond	VERB
ejpam-5871	367	74	to	to	ADP
ejpam-5871	367	75	the	the	DET
ejpam-5871	367	76	choice	choice	NOUN
ejpam-5871	367	77	of	of	ADP
ejpam-5871	367	78	parameters	parameter	NOUN
ejpam-5871	367	79	r1	r1	NOUN
ejpam-5871	367	80	=	=	SYM
ejpam-5871	367	81	0.6	0.6	NUM
ejpam-5871	367	82	,	,	PUNCT
ejpam-5871	367	83	r1	r1	NOUN
ejpam-5871	367	84	<	<	X
ejpam-5871	367	85	r2	r2	PROPN
ejpam-5871	367	86	≤	≤	PROPN
ejpam-5871	367	87	π	π	PROPN
ejpam-5871	367	88	2	2	NUM
ejpam-5871	367	89	,	,	PUNCT
ejpam-5871	367	90	k	k	NOUN
ejpam-5871	367	91	=	=	SYM
ejpam-5871	367	92	1	1	NUM
ejpam-5871	367	93	,	,	PUNCT
ejpam-5871	367	94	s	s	PART
ejpam-5871	367	95	=	=	SYM
ejpam-5871	367	96	3	3	NUM
ejpam-5871	367	97	and	and	CCONJ
ejpam-5871	367	98	β	β	X
ejpam-5871	367	99	=	=	SYM
ejpam-5871	367	100	0.8	0.8	NUM
ejpam-5871	367	101	corollary	corollary	NOUN
ejpam-5871	367	102	2	2	NUM
ejpam-5871	367	103	.	.	PUNCT
ejpam-5871	368	1	if	if	SCONJ
ejpam-5871	368	2	we	we	PRON
ejpam-5871	368	3	fix	fix	VERB
ejpam-5871	368	4	s	s	NOUN
ejpam-5871	368	5	=	=	NOUN
ejpam-5871	368	6	0	0	NUM
ejpam-5871	368	7	,	,	PUNCT
ejpam-5871	368	8	k	k	NOUN
ejpam-5871	368	9	=	=	SYM
ejpam-5871	368	10	1	1	NUM
ejpam-5871	368	11	,	,	PUNCT
ejpam-5871	368	12	⋋(r	⋋(r	X
ejpam-5871	368	13	)	)	PUNCT
ejpam-5871	369	1	=	=	SYM
ejpam-5871	369	2	r	r	NOUN
ejpam-5871	369	3	and	and	CCONJ
ejpam-5871	369	4	℧	℧	PROPN
ejpam-5871	369	5	(	(	PUNCT
ejpam-5871	369	6	θ	θ	NOUN
ejpam-5871	369	7	)	)	PUNCT
ejpam-5871	369	8	=	=	SYM
ejpam-5871	369	9	θ	θ	PROPN
ejpam-5871	369	10	in	in	ADP
ejpam-5871	369	11	theorem	theorem	NOUN
ejpam-5871	369	12	6	6	NUM
ejpam-5871	369	13	,	,	PUNCT
ejpam-5871	369	14	we	we	PRON
ejpam-5871	369	15	possess	possess	VERB
ejpam-5871	369	16	hermite	hermite	ADJ
ejpam-5871	369	17	-	-	PUNCT
ejpam-5871	369	18	hadamard	hadamard	ADV
ejpam-5871	369	19	-	-	PUNCT
ejpam-5871	369	20	fejer	fejer	NOUN
ejpam-5871	369	21	inequality	inequality	NOUN
ejpam-5871	369	22	for	for	ADP
ejpam-5871	369	23	ı.υ-(⋋s+1	ı.υ-(⋋s+1	PROPN
ejpam-5871	369	24	,	,	PUNCT
ejpam-5871	369	25	℧	℧	PROPN
ejpam-5871	369	26	)	)	PUNCT
ejpam-5871	369	27	cf	cf	NOUN
ejpam-5871	369	28	that	that	PRON
ejpam-5871	369	29	is	be	AUX
ejpam-5871	369	30	provided	provide	VERB
ejpam-5871	369	31	in	in	ADP
ejpam-5871	369	32	[	[	NOUN
ejpam-5871	369	33	23	23	NUM
ejpam-5871	369	34	]	]	SYM
ejpam-5871	369	35	.	.	PROPN
ejpam-5871	370	1	1	1	NUM
ejpam-5871	370	2	βγ(β	βγ(β	NUM
ejpam-5871	370	3	)	)	PUNCT
ejpam-5871	370	4	∅	∅	NOUN
ejpam-5871	370	5	(	(	PUNCT
ejpam-5871	370	6	r1	r1	NOUN
ejpam-5871	370	7	+	+	CCONJ
ejpam-5871	370	8	r2	r2	PROPN
ejpam-5871	370	9	2	2	NUM
ejpam-5871	370	10	)	)	PUNCT
ejpam-5871	370	11	⊇	⊇	NOUN
ejpam-5871	370	12	1	1	NUM
ejpam-5871	370	13	(	(	PUNCT
ejpam-5871	370	14	r2	r2	PROPN
ejpam-5871	370	15	−	−	PROPN
ejpam-5871	370	16	r1	r1	PROPN
ejpam-5871	370	17	)	)	PUNCT
ejpam-5871	371	1	β	β	X
ejpam-5871	372	1	[	[	X
ejpam-5871	372	2	zβ	zβ	X
ejpam-5871	372	3	r+1	r+1	PROPN
ejpam-5871	372	4	∅(r2	∅(r2	PROPN
ejpam-5871	372	5	)	)	PUNCT
ejpam-5871	373	1	+	+	CCONJ
ejpam-5871	373	2	zβ	zβ	PROPN
ejpam-5871	373	3	r−2	r−2	PROPN
ejpam-5871	373	4	∅(r1	∅(r1	NOUN
ejpam-5871	373	5	)	)	PUNCT
ejpam-5871	373	6	]	]	PUNCT
ejpam-5871	374	1	⊇	⊇	PROPN
ejpam-5871	374	2	1	1	NUM
ejpam-5871	374	3	βγ(β	βγ(β	NUM
ejpam-5871	374	4	)	)	PUNCT
ejpam-5871	374	5	[	[	PUNCT
ejpam-5871	374	6	∅(r1	∅(r1	NOUN
ejpam-5871	374	7	)	)	PUNCT
ejpam-5871	375	1	+	+	NOUN
ejpam-5871	375	2	∅(r2	∅(r2	NOUN
ejpam-5871	375	3	)	)	PUNCT
ejpam-5871	375	4	]	]	PUNCT
ejpam-5871	375	5	.	.	PUNCT
ejpam-5871	376	1	a.	a.	PROPN
ejpam-5871	376	2	mehmood	mehmood	PROPN
ejpam-5871	376	3	et	et	PROPN
ejpam-5871	376	4	al	al	PROPN
ejpam-5871	376	5	.	.	PUNCT
ejpam-5871	376	6	/	/	SYM
ejpam-5871	376	7	eur	eur	PROPN
ejpam-5871	376	8	.	.	PUNCT
ejpam-5871	377	1	j.	j.	PROPN
ejpam-5871	377	2	pure	pure	PROPN
ejpam-5871	377	3	appl	appl	PROPN
ejpam-5871	377	4	.	.	PROPN
ejpam-5871	377	5	math	math	PROPN
ejpam-5871	377	6	,	,	PUNCT
ejpam-5871	377	7	18	18	NUM
ejpam-5871	377	8	(	(	PUNCT
ejpam-5871	377	9	2	2	NUM
ejpam-5871	377	10	)	)	PUNCT
ejpam-5871	377	11	(	(	PUNCT
ejpam-5871	377	12	2025	2025	NUM
ejpam-5871	377	13	)	)	PUNCT
ejpam-5871	377	14	,	,	PUNCT
ejpam-5871	377	15	5871	5871	NUM
ejpam-5871	377	16	14	14	NUM
ejpam-5871	377	17	of	of	ADP
ejpam-5871	377	18	26	26	NUM
ejpam-5871	377	19	theorem	theorem	NOUN
ejpam-5871	377	20	7	7	NUM
ejpam-5871	377	21	.	.	PUNCT
ejpam-5871	378	1	let	let	VERB
ejpam-5871	378	2	s	s	PRON
ejpam-5871	378	3	∈	∈	VERB
ejpam-5871	378	4	r/{−1	r/{−1	PROPN
ejpam-5871	378	5	}	}	PUNCT
ejpam-5871	378	6	,	,	PUNCT
ejpam-5871	378	7	k	k	X
ejpam-5871	378	8	≥	≥	PROPN
ejpam-5871	378	9	0	0	NUM
ejpam-5871	378	10	,	,	PUNCT
ejpam-5871	378	11	∅	∅	NOUN
ejpam-5871	378	12	∈	∈	PROPN
ejpam-5871	378	13	sigx([r1	sigx([r1	NOUN
ejpam-5871	378	14	,	,	PUNCT
ejpam-5871	378	15	r2	r2	PROPN
ejpam-5871	378	16	]	]	PUNCT
ejpam-5871	378	17	,	,	PUNCT
ejpam-5871	379	1	r	r	NOUN
ejpam-5871	379	2	+	+	PROPN
ejpam-5871	379	3	i	i	NOUN
ejpam-5871	379	4	)	)	PUNCT
ejpam-5871	379	5	,	,	PUNCT
ejpam-5871	379	6	and	and	CCONJ
ejpam-5871	379	7	⅁	⅁	VERB
ejpam-5871	379	8	:	:	PUNCT
ejpam-5871	380	1	[	[	X
ejpam-5871	380	2	r1	r1	NOUN
ejpam-5871	380	3	,	,	PUNCT
ejpam-5871	380	4	r2	r2	PROPN
ejpam-5871	380	5	]	]	PUNCT
ejpam-5871	380	6	→	→	PUNCT
ejpam-5871	380	7	r	r	NOUN
ejpam-5871	380	8	be	be	VERB
ejpam-5871	380	9	symmetric	symmetric	ADJ
ejpam-5871	380	10	w.r.t	w.r.t	NOUN
ejpam-5871	380	11	r1+r2	r1+r2	PROPN
ejpam-5871	380	12	2	2	NUM
ejpam-5871	380	13	,	,	PUNCT
ejpam-5871	380	14	then	then	ADV
ejpam-5871	380	15	for	for	ADP
ejpam-5871	380	16	β	β	X
ejpam-5871	380	17	>	>	X
ejpam-5871	380	18	0	0	PUNCT
ejpam-5871	381	1	the	the	DET
ejpam-5871	381	2	following	follow	VERB
ejpam-5871	381	3	inclusions	inclusion	NOUN
ejpam-5871	381	4	holds	hold	VERB
ejpam-5871	381	5	.	.	PUNCT
ejpam-5871	381	6	1	1	NUM
ejpam-5871	381	7	2	2	NUM
ejpam-5871	381	8	℧	℧	NOUN
ejpam-5871	381	9	(12	(12	NUM
ejpam-5871	381	10	)	)	PUNCT
ejpam-5871	381	11	∅	∅	NOUN
ejpam-5871	381	12	(	(	PUNCT
ejpam-5871	381	13	⋋−1	⋋−1	X
ejpam-5871	381	14	(	(	PUNCT
ejpam-5871	381	15	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	381	16	)	)	PUNCT
ejpam-5871	381	17	+	+	NOUN
ejpam-5871	381	18	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	381	19	)	)	PUNCT
ejpam-5871	381	20	2	2	NUM
ejpam-5871	381	21	)	)	PUNCT
ejpam-5871	381	22	1	1	NUM
ejpam-5871	381	23	s+1	s+1	NOUN
ejpam-5871	381	24	)	)	PUNCT
ejpam-5871	382	1	[	[	PUNCT
ejpam-5871	382	2	s	s	X
ejpam-5871	382	3	kz	kz	PROPN
ejpam-5871	382	4	β	β	PROPN
ejpam-5871	382	5	r+1	r+1	PROPN
ejpam-5871	382	6	⅁(r2	⅁(r2	NOUN
ejpam-5871	382	7	)	)	PUNCT
ejpam-5871	383	1	+	+	SYM
ejpam-5871	383	2	s	s	VERB
ejpam-5871	383	3	kz	kz	PROPN
ejpam-5871	383	4	β	β	PROPN
ejpam-5871	383	5	r−2	r−2	PROPN
ejpam-5871	383	6	⅁(r1	⅁(r1	NUM
ejpam-5871	383	7	)	)	PUNCT
ejpam-5871	383	8	]	]	PUNCT
ejpam-5871	384	1	⊇	⊇	PROPN
ejpam-5871	384	2	[	[	PUNCT
ejpam-5871	384	3	s	s	X
ejpam-5871	384	4	kz	kz	PROPN
ejpam-5871	384	5	β	β	PROPN
ejpam-5871	384	6	r+1	r+1	PROPN
ejpam-5871	384	7	⅁∅(r2	⅁∅(r2	NOUN
ejpam-5871	384	8	)	)	PUNCT
ejpam-5871	384	9	+	+	SYM
ejpam-5871	384	10	s	s	VERB
ejpam-5871	384	11	kz	kz	PROPN
ejpam-5871	384	12	β	β	PROPN
ejpam-5871	384	13	r−2	r−2	PROPN
ejpam-5871	384	14	⅁∅(r1	⅁∅(r1	NOUN
ejpam-5871	384	15	)	)	PUNCT
ejpam-5871	384	16	]	]	PUNCT
ejpam-5871	384	17	⊇	⊇	X
ejpam-5871	384	18	(	(	PUNCT
ejpam-5871	384	19	s+	s+	NUM
ejpam-5871	384	20	1)−	1)−	PROPN
ejpam-5871	384	21	β	β	X
ejpam-5871	384	22	k	k	PROPN
ejpam-5871	384	23	kγk(β	kγk(β	PROPN
ejpam-5871	384	24	)	)	PUNCT
ejpam-5871	384	25	(	(	PUNCT
ejpam-5871	384	26	∫	∫	PROPN
ejpam-5871	384	27	1	1	NUM
ejpam-5871	384	28	0	0	NUM
ejpam-5871	384	29	θ	θ	PROPN
ejpam-5871	384	30	β	β	X
ejpam-5871	384	31	k	k	X
ejpam-5871	384	32	−1[	−1[	X
ejpam-5871	384	33	℧	℧	PROPN
ejpam-5871	384	34	(θ	(θ	NOUN
ejpam-5871	384	35	)	)	PUNCT
ejpam-5871	384	36	+	+	CCONJ
ejpam-5871	384	37	℧	℧	PROPN
ejpam-5871	384	38	(	(	PUNCT
ejpam-5871	384	39	1−	1−	NUM
ejpam-5871	384	40	θ	θ	NOUN
ejpam-5871	384	41	)	)	PUNCT
ejpam-5871	384	42	]	]	PUNCT
ejpam-5871	385	1	[	[	PUNCT
ejpam-5871	385	2	⅁(⋋−1(θ	⅁(⋋−1(θ	PROPN
ejpam-5871	385	3	⋋s+1	⋋s+1	PROPN
ejpam-5871	385	4	(	(	PUNCT
ejpam-5871	385	5	r1	r1	PROPN
ejpam-5871	385	6	)	)	PUNCT
ejpam-5871	385	7	+	+	CCONJ
ejpam-5871	385	8	(	(	PUNCT
ejpam-5871	385	9	1−	1−	NUM
ejpam-5871	385	10	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	385	11	(	(	PUNCT
ejpam-5871	385	12	r2	r2	PROPN
ejpam-5871	385	13	)	)	PUNCT
ejpam-5871	385	14	)	)	PUNCT
ejpam-5871	385	15	1	1	NUM
ejpam-5871	385	16	s+1	s+1	NOUN
ejpam-5871	385	17	)	)	PUNCT
ejpam-5871	385	18	]	]	PUNCT
ejpam-5871	386	1	×	×	NOUN
ejpam-5871	387	1	[	[	X
ejpam-5871	387	2	∅(r1	∅(r1	NOUN
ejpam-5871	387	3	)	)	PUNCT
ejpam-5871	388	1	+	+	NUM
ejpam-5871	388	2	∅(r2)]dθ	∅(r2)]dθ	NOUN
ejpam-5871	388	3	)	)	PUNCT
ejpam-5871	388	4	.	.	PUNCT
ejpam-5871	389	1	proof	proof	NOUN
ejpam-5871	389	2	.	.	PUNCT
ejpam-5871	390	1	since	since	SCONJ
ejpam-5871	390	2	∅	∅	NOUN
ejpam-5871	390	3	is	be	AUX
ejpam-5871	390	4	ı.υ-(⋋s+1	ı.υ-(⋋s+1	PROPN
ejpam-5871	390	5	,	,	PUNCT
ejpam-5871	390	6	℧	℧	NOUN
ejpam-5871	390	7	)	)	PUNCT
ejpam-5871	390	8	cf	cf	NOUN
ejpam-5871	390	9	and	and	CCONJ
ejpam-5871	390	10	for	for	ADP
ejpam-5871	390	11	θ	θ	PROPN
ejpam-5871	390	12	=	=	SYM
ejpam-5871	390	13	1	1	NUM
ejpam-5871	390	14	2	2	NUM
ejpam-5871	390	15	,	,	PUNCT
ejpam-5871	390	16	we	we	PRON
ejpam-5871	390	17	have	have	VERB
ejpam-5871	390	18	∅	∅	NOUN
ejpam-5871	390	19	(	(	PUNCT
ejpam-5871	390	20	⋋−1	⋋−1	X
ejpam-5871	390	21	(	(	PUNCT
ejpam-5871	390	22	⋋s+1(x	⋋s+1(x	NUM
ejpam-5871	390	23	)	)	PUNCT
ejpam-5871	390	24	+	+	ADJ
ejpam-5871	390	25	⋋s+1(y	⋋s+1(y	NUM
ejpam-5871	390	26	)	)	PUNCT
ejpam-5871	390	27	2	2	NUM
ejpam-5871	390	28	)	)	PUNCT
ejpam-5871	390	29	1	1	NUM
ejpam-5871	390	30	s+1	s+1	PROPN
ejpam-5871	390	31	)	)	PUNCT
ejpam-5871	390	32	⊇	⊇	PROPN
ejpam-5871	390	33	℧	℧	PROPN
ejpam-5871	390	34	(	(	PUNCT
ejpam-5871	390	35	1	1	NUM
ejpam-5871	390	36	2	2	NUM
ejpam-5871	390	37	)	)	PUNCT
ejpam-5871	390	38	[	[	PUNCT
ejpam-5871	390	39	∅(x	∅(x	NOUN
ejpam-5871	390	40	)	)	PUNCT
ejpam-5871	390	41	+	+	NOUN
ejpam-5871	390	42	∅(y	∅(y	NOUN
ejpam-5871	390	43	)	)	PUNCT
ejpam-5871	390	44	]	]	PUNCT
ejpam-5871	390	45	.	.	PUNCT
ejpam-5871	391	1	by	by	ADP
ejpam-5871	391	2	substituting	substitute	VERB
ejpam-5871	391	3	x	x	X
ejpam-5871	391	4	=	=	SYM
ejpam-5871	391	5	⋋−1(θ⋋s+1	⋋−1(θ⋋s+1	PROPN
ejpam-5871	391	6	(	(	PUNCT
ejpam-5871	391	7	r1)+(1−θ)⋋s+1	r1)+(1−θ)⋋s+1	X
ejpam-5871	391	8	(	(	PUNCT
ejpam-5871	391	9	r2	r2	PROPN
ejpam-5871	391	10	)	)	PUNCT
ejpam-5871	391	11	)	)	PUNCT
ejpam-5871	391	12	1	1	NUM
ejpam-5871	391	13	s+1	s+1	NOUN
ejpam-5871	391	14	and	and	CCONJ
ejpam-5871	391	15	y	y	PROPN
ejpam-5871	391	16	=	=	PUNCT
ejpam-5871	391	17	⋋−1((1−θ)⋋s+1	⋋−1((1−θ)⋋s+1	NOUN
ejpam-5871	391	18	(	(	PUNCT
ejpam-5871	391	19	r1)+	r1)+	VERB
ejpam-5871	391	20	θ⋋s+1	θ⋋s+1	PROPN
ejpam-5871	391	21	(	(	PUNCT
ejpam-5871	391	22	r2	r2	PROPN
ejpam-5871	391	23	)	)	PUNCT
ejpam-5871	391	24	)	)	PUNCT
ejpam-5871	391	25	1	1	NUM
ejpam-5871	391	26	s+1	s+1	NOUN
ejpam-5871	391	27	in	in	ADP
ejpam-5871	391	28	above	above	ADP
ejpam-5871	391	29	expression	expression	NOUN
ejpam-5871	391	30	.	.	PUNCT
ejpam-5871	392	1	multiplying	multiply	VERB
ejpam-5871	392	2	both	both	DET
ejpam-5871	392	3	sides	side	NOUN
ejpam-5871	392	4	by	by	ADP
ejpam-5871	392	5	(	(	PUNCT
ejpam-5871	392	6	s+1)−	s+1)−	PROPN
ejpam-5871	392	7	β	β	PROPN
ejpam-5871	392	8	k	k	PROPN
ejpam-5871	392	9	kγk(β	kγk(β	PROPN
ejpam-5871	392	10	)	)	PUNCT
ejpam-5871	392	11	θ	θ	PROPN
ejpam-5871	392	12	β	β	X
ejpam-5871	392	13	k	k	X
ejpam-5871	392	14	−1	−1	NOUN
ejpam-5871	392	15	[	[	PUNCT
ejpam-5871	392	16	⅁(⋋−1(θ⋋s+1	⅁(⋋−1(θ⋋s+1	PROPN
ejpam-5871	392	17	(	(	PUNCT
ejpam-5871	392	18	r1	r1	PROPN
ejpam-5871	392	19	)	)	PUNCT
ejpam-5871	392	20	+	+	CCONJ
ejpam-5871	392	21	(	(	PUNCT
ejpam-5871	392	22	1−	1−	NUM
ejpam-5871	392	23	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	392	24	(	(	PUNCT
ejpam-5871	392	25	r2	r2	PROPN
ejpam-5871	392	26	)	)	PUNCT
ejpam-5871	392	27	)	)	PUNCT
ejpam-5871	392	28	1	1	NUM
ejpam-5871	392	29	s+1	s+1	NOUN
ejpam-5871	392	30	)	)	PUNCT
ejpam-5871	392	31	]	]	PUNCT
ejpam-5871	392	32	and	and	CCONJ
ejpam-5871	392	33	taking	take	VERB
ejpam-5871	392	34	the	the	DET
ejpam-5871	392	35	integration	integration	NOUN
ejpam-5871	392	36	over	over	ADP
ejpam-5871	392	37	[	[	X
ejpam-5871	392	38	0	0	NUM
ejpam-5871	392	39	,	,	PUNCT
ejpam-5871	392	40	1	1	NUM
ejpam-5871	392	41	]	]	PUNCT
ejpam-5871	392	42	w.r.t	w.r.t	ADJ
ejpam-5871	392	43	”	"	PUNCT
ejpam-5871	392	44	θ	θ	PROPN
ejpam-5871	392	45	”	"	PUNCT
ejpam-5871	392	46	,	,	PUNCT
ejpam-5871	392	47	we	we	PRON
ejpam-5871	392	48	have	have	VERB
ejpam-5871	392	49	1	1	NUM
ejpam-5871	392	50	℧	℧	NOUN
ejpam-5871	392	51	(	(	PUNCT
ejpam-5871	392	52	12	12	NUM
ejpam-5871	392	53	)	)	PUNCT
ejpam-5871	392	54	(	(	PUNCT
ejpam-5871	392	55	s+	s+	NUM
ejpam-5871	392	56	1)−	1)−	PROPN
ejpam-5871	392	57	β	β	X
ejpam-5871	392	58	k	k	PROPN
ejpam-5871	392	59	kγk(β	kγk(β	PROPN
ejpam-5871	392	60	)	)	PUNCT
ejpam-5871	392	61	∫	∫	PROPN
ejpam-5871	393	1	1	1	NUM
ejpam-5871	393	2	0	0	NUM
ejpam-5871	393	3	θ	θ	PROPN
ejpam-5871	393	4	β	β	X
ejpam-5871	393	5	k	k	X
ejpam-5871	393	6	−1	−1	NOUN
ejpam-5871	393	7	[	[	PUNCT
ejpam-5871	393	8	⅁(⋋−1(θ	⅁(⋋−1(θ	PROPN
ejpam-5871	393	9	⋋s+1	⋋s+1	PROPN
ejpam-5871	393	10	(	(	PUNCT
ejpam-5871	393	11	r1	r1	PROPN
ejpam-5871	393	12	)	)	PUNCT
ejpam-5871	393	13	+	+	CCONJ
ejpam-5871	393	14	(	(	PUNCT
ejpam-5871	393	15	1−	1−	NUM
ejpam-5871	393	16	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	393	17	(	(	PUNCT
ejpam-5871	393	18	r2	r2	PROPN
ejpam-5871	393	19	)	)	PUNCT
ejpam-5871	393	20	)	)	PUNCT
ejpam-5871	393	21	1	1	NUM
ejpam-5871	393	22	s+1	s+1	NOUN
ejpam-5871	393	23	)	)	PUNCT
ejpam-5871	393	24	]	]	PUNCT
ejpam-5871	394	1	×∅	×∅	PROPN
ejpam-5871	394	2	(	(	PUNCT
ejpam-5871	394	3	⋋−1	⋋−1	X
ejpam-5871	394	4	(	(	PUNCT
ejpam-5871	394	5	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	394	6	)	)	PUNCT
ejpam-5871	394	7	+	+	NOUN
ejpam-5871	394	8	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	394	9	)	)	PUNCT
ejpam-5871	394	10	2	2	NUM
ejpam-5871	394	11	)	)	PUNCT
ejpam-5871	394	12	1	1	NUM
ejpam-5871	394	13	s+1	s+1	PROPN
ejpam-5871	394	14	)	)	PUNCT
ejpam-5871	394	15	dθ	dθ	PROPN
ejpam-5871	394	16	⊇	⊇	PROPN
ejpam-5871	394	17	(	(	PUNCT
ejpam-5871	394	18	s+	s+	NUM
ejpam-5871	394	19	1)−	1)−	PROPN
ejpam-5871	394	20	β	β	X
ejpam-5871	394	21	k	k	PROPN
ejpam-5871	394	22	kγk(β	kγk(β	PROPN
ejpam-5871	394	23	)	)	PUNCT
ejpam-5871	394	24	∫	∫	PROPN
ejpam-5871	394	25	1	1	NUM
ejpam-5871	394	26	0	0	NUM
ejpam-5871	394	27	θ	θ	PROPN
ejpam-5871	394	28	β	β	X
ejpam-5871	394	29	k	k	X
ejpam-5871	394	30	−1	−1	NOUN
ejpam-5871	394	31	[	[	PUNCT
ejpam-5871	394	32	⅁(⋋−1(θ	⅁(⋋−1(θ	PROPN
ejpam-5871	394	33	⋋s+1	⋋s+1	PROPN
ejpam-5871	394	34	(	(	PUNCT
ejpam-5871	394	35	r1	r1	PROPN
ejpam-5871	394	36	)	)	PUNCT
ejpam-5871	394	37	+	+	CCONJ
ejpam-5871	394	38	(	(	PUNCT
ejpam-5871	394	39	1−	1−	NUM
ejpam-5871	394	40	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	394	41	(	(	PUNCT
ejpam-5871	394	42	r2	r2	PROPN
ejpam-5871	394	43	)	)	PUNCT
ejpam-5871	394	44	)	)	PUNCT
ejpam-5871	394	45	1	1	NUM
ejpam-5871	394	46	s+1	s+1	NOUN
ejpam-5871	394	47	)	)	PUNCT
ejpam-5871	394	48	]	]	PUNCT
ejpam-5871	394	49	×∅	×∅	PROPN
ejpam-5871	395	1	(	(	PUNCT
ejpam-5871	395	2	⋋−1	⋋−1	X
ejpam-5871	395	3	(	(	PUNCT
ejpam-5871	395	4	θ	θ	PROPN
ejpam-5871	395	5	⋋s+1	⋋s+1	PROPN
ejpam-5871	395	6	(	(	PUNCT
ejpam-5871	395	7	r1	r1	PROPN
ejpam-5871	395	8	)	)	PUNCT
ejpam-5871	395	9	+	+	CCONJ
ejpam-5871	395	10	(	(	PUNCT
ejpam-5871	395	11	1−	1−	NUM
ejpam-5871	395	12	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	395	13	(	(	PUNCT
ejpam-5871	395	14	r2	r2	PROPN
ejpam-5871	395	15	)	)	PUNCT
ejpam-5871	395	16	)	)	PUNCT
ejpam-5871	395	17	1	1	NUM
ejpam-5871	395	18	s+1	s+1	NOUN
ejpam-5871	395	19	)	)	PUNCT
ejpam-5871	395	20	dθ	dθ	PROPN
ejpam-5871	395	21	+	+	X
ejpam-5871	395	22	(	(	PUNCT
ejpam-5871	395	23	s+	s+	X
ejpam-5871	395	24	1)−	1)−	PROPN
ejpam-5871	395	25	β	β	X
ejpam-5871	395	26	k	k	PROPN
ejpam-5871	395	27	kγk(β	kγk(β	PROPN
ejpam-5871	395	28	)	)	PUNCT
ejpam-5871	395	29	∫	∫	PROPN
ejpam-5871	395	30	1	1	NUM
ejpam-5871	395	31	0	0	NUM
ejpam-5871	395	32	θ	θ	PROPN
ejpam-5871	395	33	β	β	X
ejpam-5871	395	34	k	k	X
ejpam-5871	395	35	−1	−1	NOUN
ejpam-5871	395	36	[	[	PUNCT
ejpam-5871	395	37	⅁(⋋−1(θ	⅁(⋋−1(θ	PROPN
ejpam-5871	395	38	⋋s+1	⋋s+1	PROPN
ejpam-5871	395	39	(	(	PUNCT
ejpam-5871	395	40	r1	r1	PROPN
ejpam-5871	395	41	)	)	PUNCT
ejpam-5871	395	42	+	+	CCONJ
ejpam-5871	395	43	(	(	PUNCT
ejpam-5871	395	44	1−	1−	NUM
ejpam-5871	395	45	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	395	46	(	(	PUNCT
ejpam-5871	395	47	r2	r2	PROPN
ejpam-5871	395	48	)	)	PUNCT
ejpam-5871	395	49	)	)	PUNCT
ejpam-5871	395	50	1	1	NUM
ejpam-5871	395	51	s+1	s+1	NOUN
ejpam-5871	395	52	)	)	PUNCT
ejpam-5871	395	53	]	]	PUNCT
ejpam-5871	396	1	×∅	×∅	PROPN
ejpam-5871	396	2	(	(	PUNCT
ejpam-5871	396	3	⋋−1	⋋−1	ADJ
ejpam-5871	396	4	(	(	PUNCT
ejpam-5871	396	5	(	(	PUNCT
ejpam-5871	396	6	1−	1−	NUM
ejpam-5871	396	7	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	396	8	(	(	PUNCT
ejpam-5871	396	9	r1	r1	PROPN
ejpam-5871	396	10	)	)	PUNCT
ejpam-5871	396	11	+	+	NUM
ejpam-5871	396	12	θ	θ	PUNCT
ejpam-5871	396	13	⋋s+1	⋋s+1	VERB
ejpam-5871	396	14	(	(	PUNCT
ejpam-5871	396	15	r2	r2	PROPN
ejpam-5871	396	16	)	)	PUNCT
ejpam-5871	396	17	)	)	PUNCT
ejpam-5871	396	18	1	1	NUM
ejpam-5871	396	19	s+1	s+1	PROPN
ejpam-5871	396	20	)	)	PUNCT
ejpam-5871	396	21	dθ	dθ	PROPN
ejpam-5871	396	22	.	.	PUNCT
ejpam-5871	397	1	(	(	PUNCT
ejpam-5871	397	2	26	26	NUM
ejpam-5871	397	3	)	)	PUNCT
ejpam-5871	397	4	taking	take	VERB
ejpam-5871	397	5	benefit	benefit	NOUN
ejpam-5871	397	6	of	of	ADP
ejpam-5871	397	7	the	the	DET
ejpam-5871	397	8	fact	fact	NOUN
ejpam-5871	397	9	⅁(⋋−1(θ⋋s+1	⅁(⋋−1(θ⋋s+1	PROPN
ejpam-5871	397	10	(	(	PUNCT
ejpam-5871	397	11	r1)+	r1)+	PROPN
ejpam-5871	397	12	(	(	PUNCT
ejpam-5871	397	13	1−	1−	NUM
ejpam-5871	397	14	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	397	15	(	(	PUNCT
ejpam-5871	397	16	r2	r2	PROPN
ejpam-5871	397	17	)	)	PUNCT
ejpam-5871	397	18	)	)	PUNCT
ejpam-5871	397	19	1	1	NUM
ejpam-5871	397	20	s+1	s+1	NOUN
ejpam-5871	397	21	)	)	PUNCT
ejpam-5871	398	1	=	=	SYM
ejpam-5871	398	2	⅁(⋋−1((1−	⅁(⋋−1((1−	PROPN
ejpam-5871	398	3	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	398	4	(	(	PUNCT
ejpam-5871	398	5	r1	r1	PROPN
ejpam-5871	398	6	)	)	PUNCT
ejpam-5871	398	7	+	+	NUM
ejpam-5871	398	8	θ	θ	PUNCT
ejpam-5871	398	9	⋋s+1	⋋s+1	VERB
ejpam-5871	398	10	(	(	PUNCT
ejpam-5871	398	11	r2	r2	PROPN
ejpam-5871	398	12	)	)	PUNCT
ejpam-5871	398	13	)	)	PUNCT
ejpam-5871	398	14	1	1	NUM
ejpam-5871	398	15	s+1	s+1	NOUN
ejpam-5871	398	16	)	)	PUNCT
ejpam-5871	398	17	for	for	ADP
ejpam-5871	398	18	the	the	DET
ejpam-5871	398	19	left	left	ADJ
ejpam-5871	398	20	part	part	NOUN
ejpam-5871	398	21	of	of	ADP
ejpam-5871	398	22	(	(	PUNCT
ejpam-5871	398	23	26	26	NUM
ejpam-5871	398	24	)	)	PUNCT
ejpam-5871	398	25	.	.	PUNCT
ejpam-5871	399	1	(	(	PUNCT
ejpam-5871	399	2	s+	s+	PROPN
ejpam-5871	399	3	1)−	1)−	NUM
ejpam-5871	399	4	β	β	X
ejpam-5871	399	5	k	k	PROPN
ejpam-5871	399	6	kγk(β	kγk(β	PROPN
ejpam-5871	399	7	)	)	PUNCT
ejpam-5871	399	8	∫	∫	PROPN
ejpam-5871	399	9	1	1	NUM
ejpam-5871	399	10	0	0	NUM
ejpam-5871	399	11	θ	θ	PROPN
ejpam-5871	399	12	β	β	X
ejpam-5871	399	13	k	k	X
ejpam-5871	399	14	−1	−1	NOUN
ejpam-5871	399	15	[	[	PUNCT
ejpam-5871	399	16	⅁(⋋−1(θ	⅁(⋋−1(θ	PROPN
ejpam-5871	399	17	⋋s+1	⋋s+1	PROPN
ejpam-5871	399	18	(	(	PUNCT
ejpam-5871	399	19	r1	r1	PROPN
ejpam-5871	399	20	)	)	PUNCT
ejpam-5871	399	21	+	+	CCONJ
ejpam-5871	399	22	(	(	PUNCT
ejpam-5871	399	23	1−	1−	NUM
ejpam-5871	399	24	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	399	25	(	(	PUNCT
ejpam-5871	399	26	r2	r2	PROPN
ejpam-5871	399	27	)	)	PUNCT
ejpam-5871	399	28	)	)	PUNCT
ejpam-5871	399	29	1	1	NUM
ejpam-5871	399	30	s+1	s+1	NOUN
ejpam-5871	399	31	)	)	PUNCT
ejpam-5871	399	32	]	]	PUNCT
ejpam-5871	400	1	a.	a.	PROPN
ejpam-5871	400	2	mehmood	mehmood	PROPN
ejpam-5871	400	3	et	et	PROPN
ejpam-5871	400	4	al	al	PROPN
ejpam-5871	400	5	.	.	PUNCT
ejpam-5871	400	6	/	/	SYM
ejpam-5871	400	7	eur	eur	PROPN
ejpam-5871	400	8	.	.	PUNCT
ejpam-5871	401	1	j.	j.	PROPN
ejpam-5871	401	2	pure	pure	PROPN
ejpam-5871	401	3	appl	appl	PROPN
ejpam-5871	401	4	.	.	PROPN
ejpam-5871	401	5	math	math	PROPN
ejpam-5871	401	6	,	,	PUNCT
ejpam-5871	401	7	18	18	NUM
ejpam-5871	401	8	(	(	PUNCT
ejpam-5871	401	9	2	2	NUM
ejpam-5871	401	10	)	)	PUNCT
ejpam-5871	401	11	(	(	PUNCT
ejpam-5871	401	12	2025	2025	NUM
ejpam-5871	401	13	)	)	PUNCT
ejpam-5871	401	14	,	,	PUNCT
ejpam-5871	401	15	5871	5871	NUM
ejpam-5871	401	16	15	15	NUM
ejpam-5871	401	17	of	of	ADP
ejpam-5871	401	18	26	26	NUM
ejpam-5871	401	19	×∅	×∅	PUNCT
ejpam-5871	401	20	(	(	PUNCT
ejpam-5871	401	21	⋋−1	⋋−1	ADJ
ejpam-5871	401	22	(	(	PUNCT
ejpam-5871	401	23	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	401	24	)	)	PUNCT
ejpam-5871	402	1	+	+	NOUN
ejpam-5871	402	2	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	402	3	)	)	PUNCT
ejpam-5871	402	4	2	2	NUM
ejpam-5871	402	5	)	)	PUNCT
ejpam-5871	402	6	1	1	NUM
ejpam-5871	402	7	s+1	s+1	PROPN
ejpam-5871	402	8	)	)	PUNCT
ejpam-5871	403	1	dθ	dθ	PROPN
ejpam-5871	403	2	=	=	NOUN
ejpam-5871	403	3	1	1	NUM
ejpam-5871	403	4	2	2	NUM
ejpam-5871	403	5	[	[	PUNCT
ejpam-5871	403	6	(	(	PUNCT
ejpam-5871	403	7	s+	s+	NUM
ejpam-5871	403	8	1)−	1)−	PROPN
ejpam-5871	403	9	β	β	X
ejpam-5871	403	10	k	k	PROPN
ejpam-5871	403	11	kγk(β	kγk(β	PROPN
ejpam-5871	403	12	)	)	PUNCT
ejpam-5871	403	13	∫	∫	PROPN
ejpam-5871	404	1	1	1	NUM
ejpam-5871	404	2	0	0	NUM
ejpam-5871	404	3	θ	θ	PROPN
ejpam-5871	404	4	β	β	X
ejpam-5871	404	5	k	k	X
ejpam-5871	404	6	−1	−1	NOUN
ejpam-5871	404	7	[	[	PUNCT
ejpam-5871	404	8	⅁(⋋−1(θ	⅁(⋋−1(θ	PROPN
ejpam-5871	404	9	⋋s+1	⋋s+1	PROPN
ejpam-5871	404	10	(	(	PUNCT
ejpam-5871	404	11	r1	r1	PROPN
ejpam-5871	404	12	)	)	PUNCT
ejpam-5871	404	13	+	+	CCONJ
ejpam-5871	404	14	(	(	PUNCT
ejpam-5871	404	15	1−	1−	NUM
ejpam-5871	404	16	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	404	17	(	(	PUNCT
ejpam-5871	404	18	r2	r2	PROPN
ejpam-5871	404	19	)	)	PUNCT
ejpam-5871	404	20	)	)	PUNCT
ejpam-5871	404	21	1	1	NUM
ejpam-5871	404	22	s+1	s+1	NOUN
ejpam-5871	404	23	)	)	PUNCT
ejpam-5871	404	24	]	]	PUNCT
ejpam-5871	405	1	×∅	×∅	PROPN
ejpam-5871	405	2	(	(	PUNCT
ejpam-5871	405	3	⋋−1	⋋−1	X
ejpam-5871	405	4	(	(	PUNCT
ejpam-5871	405	5	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	405	6	)	)	PUNCT
ejpam-5871	405	7	+	+	NOUN
ejpam-5871	405	8	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	405	9	)	)	PUNCT
ejpam-5871	405	10	2	2	NUM
ejpam-5871	405	11	)	)	PUNCT
ejpam-5871	405	12	1	1	NUM
ejpam-5871	405	13	s+1	s+1	PROPN
ejpam-5871	405	14	)	)	PUNCT
ejpam-5871	405	15	dθ	dθ	PROPN
ejpam-5871	405	16	+	+	X
ejpam-5871	405	17	(	(	PUNCT
ejpam-5871	405	18	s+	s+	X
ejpam-5871	405	19	1)−	1)−	PROPN
ejpam-5871	405	20	β	β	X
ejpam-5871	405	21	k	k	PROPN
ejpam-5871	405	22	kγk(β	kγk(β	PROPN
ejpam-5871	405	23	)	)	PUNCT
ejpam-5871	405	24	∫	∫	PROPN
ejpam-5871	405	25	1	1	NUM
ejpam-5871	405	26	0	0	NUM
ejpam-5871	405	27	θ	θ	PROPN
ejpam-5871	405	28	β	β	X
ejpam-5871	405	29	k	k	X
ejpam-5871	405	30	−1	−1	NOUN
ejpam-5871	405	31	[	[	PUNCT
ejpam-5871	405	32	⅁(⋋−1((1−	⅁(⋋−1((1−	PROPN
ejpam-5871	405	33	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	405	34	(	(	PUNCT
ejpam-5871	405	35	r1	r1	PROPN
ejpam-5871	405	36	)	)	PUNCT
ejpam-5871	405	37	+	+	NUM
ejpam-5871	405	38	θ	θ	PUNCT
ejpam-5871	405	39	⋋s+1	⋋s+1	VERB
ejpam-5871	405	40	(	(	PUNCT
ejpam-5871	405	41	r2	r2	PROPN
ejpam-5871	405	42	)	)	PUNCT
ejpam-5871	405	43	)	)	PUNCT
ejpam-5871	405	44	1	1	NUM
ejpam-5871	405	45	s+1	s+1	NOUN
ejpam-5871	405	46	)	)	PUNCT
ejpam-5871	405	47	]	]	PUNCT
ejpam-5871	405	48	×∅	×∅	PROPN
ejpam-5871	405	49	(	(	PUNCT
ejpam-5871	405	50	⋋−1	⋋−1	X
ejpam-5871	405	51	(	(	PUNCT
ejpam-5871	405	52	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	405	53	)	)	PUNCT
ejpam-5871	405	54	+	+	NOUN
ejpam-5871	405	55	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	405	56	)	)	PUNCT
ejpam-5871	405	57	2	2	NUM
ejpam-5871	405	58	)	)	PUNCT
ejpam-5871	405	59	1	1	NUM
ejpam-5871	405	60	s+1	s+1	PROPN
ejpam-5871	405	61	)	)	PUNCT
ejpam-5871	405	62	dθ	dθ	PROPN
ejpam-5871	405	63	]	]	PUNCT
ejpam-5871	405	64	.	.	PUNCT
ejpam-5871	406	1	by	by	ADP
ejpam-5871	406	2	substituting	substitute	VERB
ejpam-5871	406	3	⋋s+1(χ	⋋s+1(χ	PRON
ejpam-5871	406	4	)	)	PUNCT
ejpam-5871	406	5	=	=	SYM
ejpam-5871	406	6	θ	θ	X
ejpam-5871	406	7	⋋s+1	⋋s+1	PUNCT
ejpam-5871	406	8	(	(	PUNCT
ejpam-5871	406	9	r1	r1	PROPN
ejpam-5871	406	10	)	)	PUNCT
ejpam-5871	406	11	+	+	CCONJ
ejpam-5871	406	12	(	(	PUNCT
ejpam-5871	406	13	1−	1−	NUM
ejpam-5871	406	14	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	406	15	(	(	PUNCT
ejpam-5871	406	16	r2)red	r2)re	VERB
ejpam-5871	406	17	,	,	PUNCT
ejpam-5871	406	18	we	we	PRON
ejpam-5871	406	19	have	have	VERB
ejpam-5871	406	20	=	=	NOUN
ejpam-5871	406	21	1	1	NUM
ejpam-5871	406	22	2(⋋s+1(r2)−⋋s+1(r1	2(⋋s+1(r2)−⋋s+1(r1	NUM
ejpam-5871	406	23	)	)	PUNCT
ejpam-5871	406	24	)	)	PUNCT
ejpam-5871	407	1	β	β	PROPN
ejpam-5871	407	2	k	k	NOUN
ejpam-5871	407	3	∅	∅	NOUN
ejpam-5871	407	4	(	(	PUNCT
ejpam-5871	407	5	⋋−1	⋋−1	X
ejpam-5871	407	6	(	(	PUNCT
ejpam-5871	407	7	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	407	8	)	)	PUNCT
ejpam-5871	407	9	+	+	NOUN
ejpam-5871	407	10	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	407	11	)	)	PUNCT
ejpam-5871	407	12	2	2	NUM
ejpam-5871	407	13	)	)	PUNCT
ejpam-5871	407	14	1	1	NUM
ejpam-5871	407	15	s+1	s+1	PROPN
ejpam-5871	407	16	)	)	PUNCT
ejpam-5871	407	17	×	×	NOUN
ejpam-5871	407	18	[	[	PUNCT
ejpam-5871	407	19	(	(	PUNCT
ejpam-5871	407	20	s+	s+	NUM
ejpam-5871	407	21	1)1−	1)1−	NUM
ejpam-5871	407	22	β	β	X
ejpam-5871	407	23	k	k	PROPN
ejpam-5871	407	24	kγk(β	kγk(β	PROPN
ejpam-5871	407	25	)	)	PUNCT
ejpam-5871	407	26	∫	∫	PROPN
ejpam-5871	407	27	r2	r2	PROPN
ejpam-5871	407	28	r1	r1	PROPN
ejpam-5871	407	29	(	(	PUNCT
ejpam-5871	407	30	⋋s+1	⋋s+1	PROPN
ejpam-5871	407	31	(	(	PUNCT
ejpam-5871	407	32	r2)−⋋s+1(χ	r2)−⋋s+1(χ	NOUN
ejpam-5871	407	33	)	)	PUNCT
ejpam-5871	407	34	)	)	PUNCT
ejpam-5871	407	35	β	β	X
ejpam-5871	407	36	k	k	X
ejpam-5871	407	37	−1	−1	ADV
ejpam-5871	407	38	⋋s	⋋s	PROPN
ejpam-5871	407	39	(	(	PUNCT
ejpam-5871	407	40	χ)⋋	χ)⋋	NOUN
ejpam-5871	407	41	′	′	NUM
ejpam-5871	407	42	(	(	PUNCT
ejpam-5871	407	43	χ)⅁(χ)dχ	χ)⅁(χ)dχ	NOUN
ejpam-5871	407	44	+	+	CCONJ
ejpam-5871	407	45	(	(	PUNCT
ejpam-5871	407	46	s+	s+	NUM
ejpam-5871	407	47	1)1−	1)1−	PROPN
ejpam-5871	407	48	β	β	X
ejpam-5871	407	49	k	k	PROPN
ejpam-5871	407	50	kγk(β	kγk(β	PROPN
ejpam-5871	407	51	)	)	PUNCT
ejpam-5871	407	52	∫	∫	PROPN
ejpam-5871	407	53	r2	r2	PROPN
ejpam-5871	407	54	r1	r1	PROPN
ejpam-5871	407	55	(	(	PUNCT
ejpam-5871	407	56	⋋s+1(χ)−⋋s+1(r1	⋋s+1(χ)−⋋s+1(r1	PROPN
ejpam-5871	407	57	)	)	PUNCT
ejpam-5871	407	58	)	)	PUNCT
ejpam-5871	407	59	β	β	X
ejpam-5871	407	60	k	k	X
ejpam-5871	407	61	−1	−1	ADV
ejpam-5871	407	62	⋋s	⋋s	PROPN
ejpam-5871	407	63	(	(	PUNCT
ejpam-5871	407	64	χ)⋋	χ)⋋	NOUN
ejpam-5871	407	65	′	′	NUM
ejpam-5871	407	66	(	(	PUNCT
ejpam-5871	407	67	χ)⅁(χ)dχ	χ)⅁(χ)dχ	NOUN
ejpam-5871	407	68	]	]	PUNCT
ejpam-5871	407	69	=	=	SYM
ejpam-5871	407	70	1	1	NUM
ejpam-5871	407	71	2(⋋s+1(r2)−⋋s+1(r1	2(⋋s+1(r2)−⋋s+1(r1	NUM
ejpam-5871	407	72	)	)	PUNCT
ejpam-5871	407	73	)	)	PUNCT
ejpam-5871	408	1	β	β	PROPN
ejpam-5871	408	2	k	k	NOUN
ejpam-5871	408	3	∅	∅	NOUN
ejpam-5871	408	4	(	(	PUNCT
ejpam-5871	408	5	⋋−1	⋋−1	X
ejpam-5871	408	6	(	(	PUNCT
ejpam-5871	408	7	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	408	8	)	)	PUNCT
ejpam-5871	408	9	+	+	NOUN
ejpam-5871	408	10	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	408	11	)	)	PUNCT
ejpam-5871	408	12	2	2	NUM
ejpam-5871	408	13	)	)	PUNCT
ejpam-5871	408	14	1	1	NUM
ejpam-5871	408	15	s+1	s+1	PROPN
ejpam-5871	408	16	)	)	PUNCT
ejpam-5871	408	17	×	×	NOUN
ejpam-5871	408	18	[	[	PUNCT
ejpam-5871	408	19	s	s	NOUN
ejpam-5871	408	20	kz	kz	PROPN
ejpam-5871	408	21	β	β	PROPN
ejpam-5871	408	22	r+1	r+1	PROPN
ejpam-5871	408	23	⅁(r2	⅁(r2	NOUN
ejpam-5871	408	24	)	)	PUNCT
ejpam-5871	408	25	+	+	SYM
ejpam-5871	408	26	s	s	VERB
ejpam-5871	408	27	kz	kz	PROPN
ejpam-5871	408	28	β	β	PROPN
ejpam-5871	408	29	r−2	r−2	PROPN
ejpam-5871	408	30	⅁(r1	⅁(r1	NUM
ejpam-5871	408	31	)	)	PUNCT
ejpam-5871	408	32	]	]	PUNCT
ejpam-5871	408	33	.	.	PUNCT
ejpam-5871	409	1	(	(	PUNCT
ejpam-5871	409	2	27	27	NUM
ejpam-5871	409	3	)	)	PUNCT
ejpam-5871	409	4	for	for	ADP
ejpam-5871	409	5	the	the	DET
ejpam-5871	409	6	right	right	ADJ
ejpam-5871	409	7	part	part	NOUN
ejpam-5871	409	8	of	of	ADP
ejpam-5871	409	9	(	(	PUNCT
ejpam-5871	409	10	26)red	26)red	NUM
ejpam-5871	409	11	,	,	PUNCT
ejpam-5871	409	12	we	we	PRON
ejpam-5871	409	13	have	have	VERB
ejpam-5871	409	14	(	(	PUNCT
ejpam-5871	409	15	s+	s+	NUM
ejpam-5871	409	16	1)−	1)−	PROPN
ejpam-5871	409	17	β	β	X
ejpam-5871	409	18	k	k	PROPN
ejpam-5871	409	19	kγk(β	kγk(β	PROPN
ejpam-5871	409	20	)	)	PUNCT
ejpam-5871	409	21	∫	∫	PROPN
ejpam-5871	410	1	1	1	NUM
ejpam-5871	410	2	0	0	NUM
ejpam-5871	410	3	θ	θ	PROPN
ejpam-5871	410	4	β	β	X
ejpam-5871	410	5	k	k	X
ejpam-5871	410	6	−1	−1	NOUN
ejpam-5871	410	7	[	[	PUNCT
ejpam-5871	410	8	⅁(⋋−1(θ	⅁(⋋−1(θ	PROPN
ejpam-5871	410	9	⋋s+1	⋋s+1	PROPN
ejpam-5871	410	10	(	(	PUNCT
ejpam-5871	410	11	r1	r1	PROPN
ejpam-5871	410	12	)	)	PUNCT
ejpam-5871	410	13	+	+	CCONJ
ejpam-5871	410	14	(	(	PUNCT
ejpam-5871	410	15	1−	1−	NUM
ejpam-5871	410	16	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	410	17	(	(	PUNCT
ejpam-5871	410	18	r2	r2	PROPN
ejpam-5871	410	19	)	)	PUNCT
ejpam-5871	410	20	)	)	PUNCT
ejpam-5871	410	21	1	1	NUM
ejpam-5871	410	22	s+1	s+1	NOUN
ejpam-5871	410	23	)	)	PUNCT
ejpam-5871	410	24	]	]	PUNCT
ejpam-5871	411	1	×∅	×∅	PROPN
ejpam-5871	411	2	(	(	PUNCT
ejpam-5871	411	3	⋋−1	⋋−1	X
ejpam-5871	411	4	(	(	PUNCT
ejpam-5871	411	5	θ	θ	PROPN
ejpam-5871	411	6	⋋s+1	⋋s+1	PROPN
ejpam-5871	411	7	(	(	PUNCT
ejpam-5871	411	8	r1	r1	PROPN
ejpam-5871	411	9	)	)	PUNCT
ejpam-5871	411	10	+	+	CCONJ
ejpam-5871	411	11	(	(	PUNCT
ejpam-5871	411	12	1−	1−	NUM
ejpam-5871	411	13	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	411	14	(	(	PUNCT
ejpam-5871	411	15	r2	r2	PROPN
ejpam-5871	411	16	)	)	PUNCT
ejpam-5871	411	17	)	)	PUNCT
ejpam-5871	411	18	1	1	NUM
ejpam-5871	411	19	s+1	s+1	NOUN
ejpam-5871	411	20	)	)	PUNCT
ejpam-5871	411	21	dθ	dθ	PROPN
ejpam-5871	411	22	+	+	X
ejpam-5871	411	23	(	(	PUNCT
ejpam-5871	411	24	s+	s+	X
ejpam-5871	411	25	1)−	1)−	PROPN
ejpam-5871	411	26	β	β	X
ejpam-5871	411	27	k	k	PROPN
ejpam-5871	411	28	kγk(β	kγk(β	PROPN
ejpam-5871	411	29	)	)	PUNCT
ejpam-5871	411	30	∫	∫	PROPN
ejpam-5871	411	31	1	1	NUM
ejpam-5871	411	32	0	0	NUM
ejpam-5871	411	33	θ	θ	PROPN
ejpam-5871	411	34	β	β	X
ejpam-5871	411	35	k	k	X
ejpam-5871	411	36	−1	−1	NOUN
ejpam-5871	411	37	[	[	PUNCT
ejpam-5871	411	38	⅁(⋋−1(θ	⅁(⋋−1(θ	PROPN
ejpam-5871	411	39	⋋s+1	⋋s+1	PROPN
ejpam-5871	411	40	(	(	PUNCT
ejpam-5871	411	41	r1	r1	PROPN
ejpam-5871	411	42	)	)	PUNCT
ejpam-5871	411	43	+	+	CCONJ
ejpam-5871	411	44	(	(	PUNCT
ejpam-5871	411	45	1−	1−	NUM
ejpam-5871	411	46	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	411	47	(	(	PUNCT
ejpam-5871	411	48	r2	r2	PROPN
ejpam-5871	411	49	)	)	PUNCT
ejpam-5871	411	50	)	)	PUNCT
ejpam-5871	411	51	1	1	NUM
ejpam-5871	411	52	s+1	s+1	NOUN
ejpam-5871	411	53	)	)	PUNCT
ejpam-5871	411	54	]	]	PUNCT
ejpam-5871	412	1	×∅	×∅	PROPN
ejpam-5871	412	2	(	(	PUNCT
ejpam-5871	412	3	⋋−1	⋋−1	ADJ
ejpam-5871	412	4	(	(	PUNCT
ejpam-5871	412	5	(	(	PUNCT
ejpam-5871	412	6	1−	1−	NUM
ejpam-5871	412	7	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	412	8	(	(	PUNCT
ejpam-5871	412	9	r1	r1	PROPN
ejpam-5871	412	10	)	)	PUNCT
ejpam-5871	412	11	+	+	NUM
ejpam-5871	412	12	θ	θ	PUNCT
ejpam-5871	412	13	⋋s+1	⋋s+1	VERB
ejpam-5871	412	14	(	(	PUNCT
ejpam-5871	412	15	r2	r2	PROPN
ejpam-5871	412	16	)	)	PUNCT
ejpam-5871	412	17	)	)	PUNCT
ejpam-5871	412	18	1	1	NUM
ejpam-5871	412	19	s+1	s+1	PROPN
ejpam-5871	412	20	)	)	PUNCT
ejpam-5871	412	21	dθ	dθ	PROPN
ejpam-5871	412	22	.	.	PUNCT
ejpam-5871	413	1	substituting	substitute	VERB
ejpam-5871	413	2	⋋s+1(χ	⋋s+1(χ	PRON
ejpam-5871	413	3	)	)	PUNCT
ejpam-5871	413	4	=	=	SYM
ejpam-5871	414	1	θ	θ	X
ejpam-5871	414	2	⋋s+1	⋋s+1	PUNCT
ejpam-5871	414	3	(	(	PUNCT
ejpam-5871	414	4	r1	r1	PROPN
ejpam-5871	414	5	)	)	PUNCT
ejpam-5871	414	6	+	+	CCONJ
ejpam-5871	414	7	(	(	PUNCT
ejpam-5871	414	8	1−	1−	NUM
ejpam-5871	414	9	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	414	10	(	(	PUNCT
ejpam-5871	414	11	r2)red	r2)re	VERB
ejpam-5871	414	12	,	,	PUNCT
ejpam-5871	414	13	we	we	PRON
ejpam-5871	414	14	have	have	AUX
ejpam-5871	414	15	=	=	SYM
ejpam-5871	414	16	1	1	NUM
ejpam-5871	414	17	(	(	PUNCT
ejpam-5871	414	18	⋋s+1(r2)−⋋s+1(r1	⋋s+1(r2)−⋋s+1(r1	NOUN
ejpam-5871	414	19	)	)	PUNCT
ejpam-5871	414	20	)	)	PUNCT
ejpam-5871	415	1	β	β	X
ejpam-5871	415	2	k	k	X
ejpam-5871	416	1	[	[	PUNCT
ejpam-5871	416	2	s	s	X
ejpam-5871	416	3	kz	kz	PROPN
ejpam-5871	416	4	β	β	PROPN
ejpam-5871	416	5	r+1	r+1	PROPN
ejpam-5871	416	6	⅁∅(r2	⅁∅(r2	NOUN
ejpam-5871	416	7	)	)	PUNCT
ejpam-5871	417	1	+	+	SYM
ejpam-5871	417	2	s	s	VERB
ejpam-5871	417	3	kz	kz	PROPN
ejpam-5871	417	4	β	β	PROPN
ejpam-5871	417	5	r−2	r−2	PROPN
ejpam-5871	417	6	⅁∅(r1	⅁∅(r1	NOUN
ejpam-5871	417	7	)	)	PUNCT
ejpam-5871	417	8	]	]	PUNCT
ejpam-5871	417	9	.	.	PUNCT
ejpam-5871	418	1	(	(	PUNCT
ejpam-5871	418	2	28	28	NUM
ejpam-5871	418	3	)	)	PUNCT
ejpam-5871	418	4	a.	a.	NOUN
ejpam-5871	418	5	mehmood	mehmood	PROPN
ejpam-5871	418	6	et	et	PROPN
ejpam-5871	418	7	al	al	PROPN
ejpam-5871	418	8	.	.	PUNCT
ejpam-5871	418	9	/	/	SYM
ejpam-5871	418	10	eur	eur	PROPN
ejpam-5871	418	11	.	.	PUNCT
ejpam-5871	419	1	j.	j.	PROPN
ejpam-5871	419	2	pure	pure	PROPN
ejpam-5871	419	3	appl	appl	PROPN
ejpam-5871	419	4	.	.	PROPN
ejpam-5871	419	5	math	math	PROPN
ejpam-5871	419	6	,	,	PUNCT
ejpam-5871	419	7	18	18	NUM
ejpam-5871	419	8	(	(	PUNCT
ejpam-5871	419	9	2	2	NUM
ejpam-5871	419	10	)	)	PUNCT
ejpam-5871	419	11	(	(	PUNCT
ejpam-5871	419	12	2025	2025	NUM
ejpam-5871	419	13	)	)	PUNCT
ejpam-5871	419	14	,	,	PUNCT
ejpam-5871	419	15	5871	5871	NUM
ejpam-5871	419	16	16	16	NUM
ejpam-5871	419	17	of	of	ADP
ejpam-5871	419	18	26	26	NUM
ejpam-5871	419	19	we	we	PRON
ejpam-5871	419	20	achieve	achieve	VERB
ejpam-5871	419	21	our	our	PRON
ejpam-5871	419	22	first	first	ADV
ejpam-5871	419	23	desired	desire	VERB
ejpam-5871	419	24	inclusion	inclusion	NOUN
ejpam-5871	419	25	from	from	ADP
ejpam-5871	419	26	(	(	PUNCT
ejpam-5871	419	27	27	27	NUM
ejpam-5871	419	28	)	)	PUNCT
ejpam-5871	419	29	and	and	CCONJ
ejpam-5871	419	30	(	(	PUNCT
ejpam-5871	419	31	28	28	NUM
ejpam-5871	419	32	)	)	PUNCT
ejpam-5871	419	33	.	.	PUNCT
ejpam-5871	420	1	in	in	ADP
ejpam-5871	420	2	this	this	DET
ejpam-5871	420	3	way	way	NOUN
ejpam-5871	420	4	for	for	ADP
ejpam-5871	420	5	the	the	DET
ejpam-5871	420	6	other	other	ADJ
ejpam-5871	420	7	inclusion	inclusion	NOUN
ejpam-5871	420	8	employing	employ	VERB
ejpam-5871	420	9	ı.υ-(⋋s+1	ı.υ-(⋋s+1	PROPN
ejpam-5871	420	10	,	,	PUNCT
ejpam-5871	420	11	℧	℧	NOUN
ejpam-5871	420	12	)	)	PUNCT
ejpam-5871	420	13	convexity	convexity	NOUN
ejpam-5871	420	14	of	of	ADP
ejpam-5871	420	15	function	function	NOUN
ejpam-5871	420	16	∅	∅	NOUN
ejpam-5871	420	17	,	,	PUNCT
ejpam-5871	420	18	we	we	PRON
ejpam-5871	420	19	have	have	VERB
ejpam-5871	420	20	∅	∅	NOUN
ejpam-5871	420	21	(	(	PUNCT
ejpam-5871	420	22	⋋−1	⋋−1	X
ejpam-5871	420	23	(	(	PUNCT
ejpam-5871	420	24	θ	θ	PROPN
ejpam-5871	420	25	⋋s+1	⋋s+1	PROPN
ejpam-5871	420	26	(	(	PUNCT
ejpam-5871	420	27	r1	r1	PROPN
ejpam-5871	420	28	)	)	PUNCT
ejpam-5871	420	29	+	+	CCONJ
ejpam-5871	420	30	(	(	PUNCT
ejpam-5871	420	31	1−	1−	NUM
ejpam-5871	420	32	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	420	33	(	(	PUNCT
ejpam-5871	420	34	r2	r2	PROPN
ejpam-5871	420	35	)	)	PUNCT
ejpam-5871	420	36	)	)	PUNCT
ejpam-5871	421	1	⊇	⊇	PROPN
ejpam-5871	421	2	℧	℧	PROPN
ejpam-5871	421	3	(	(	PUNCT
ejpam-5871	421	4	θ)∅(r1	θ)∅(r1	NOUN
ejpam-5871	421	5	)	)	PUNCT
ejpam-5871	421	6	+	+	CCONJ
ejpam-5871	421	7	℧	℧	PROPN
ejpam-5871	421	8	(	(	PUNCT
ejpam-5871	421	9	1−	1−	NUM
ejpam-5871	421	10	θ)∅(r2	θ)∅(r2	NOUN
ejpam-5871	421	11	)	)	PUNCT
ejpam-5871	421	12	,	,	PUNCT
ejpam-5871	421	13	(	(	PUNCT
ejpam-5871	421	14	29	29	NUM
ejpam-5871	421	15	)	)	PUNCT
ejpam-5871	421	16	and	and	CCONJ
ejpam-5871	421	17	∅	∅	NOUN
ejpam-5871	421	18	(	(	PUNCT
ejpam-5871	421	19	⋋−1	⋋−1	X
ejpam-5871	421	20	(	(	PUNCT
ejpam-5871	421	21	(	(	PUNCT
ejpam-5871	421	22	1−	1−	NUM
ejpam-5871	421	23	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	421	24	(	(	PUNCT
ejpam-5871	421	25	r1	r1	PROPN
ejpam-5871	421	26	)	)	PUNCT
ejpam-5871	421	27	+	+	NUM
ejpam-5871	421	28	θ	θ	PUNCT
ejpam-5871	421	29	⋋s+1	⋋s+1	VERB
ejpam-5871	421	30	(	(	PUNCT
ejpam-5871	421	31	r2	r2	PROPN
ejpam-5871	421	32	)	)	PUNCT
ejpam-5871	421	33	)	)	PUNCT
ejpam-5871	421	34	⊇	⊇	PROPN
ejpam-5871	421	35	℧	℧	PROPN
ejpam-5871	421	36	(	(	PUNCT
ejpam-5871	421	37	1−	1−	NUM
ejpam-5871	421	38	θ)∅(r1	θ)∅(r1	NOUN
ejpam-5871	421	39	)	)	PUNCT
ejpam-5871	421	40	+	+	CCONJ
ejpam-5871	421	41	℧	℧	PROPN
ejpam-5871	421	42	(	(	PUNCT
ejpam-5871	421	43	θ)∅(r2	θ)∅(r2	NOUN
ejpam-5871	421	44	)	)	PUNCT
ejpam-5871	421	45	.	.	PUNCT
ejpam-5871	422	1	(	(	PUNCT
ejpam-5871	422	2	30	30	X
ejpam-5871	422	3	)	)	PUNCT
ejpam-5871	422	4	adding	add	VERB
ejpam-5871	422	5	(	(	PUNCT
ejpam-5871	422	6	29	29	NUM
ejpam-5871	422	7	)	)	PUNCT
ejpam-5871	422	8	and	and	CCONJ
ejpam-5871	422	9	(	(	PUNCT
ejpam-5871	422	10	30	30	NUM
ejpam-5871	422	11	)	)	PUNCT
ejpam-5871	422	12	inclusions	inclusion	NOUN
ejpam-5871	422	13	and	and	CCONJ
ejpam-5871	422	14	multiplying	multiply	VERB
ejpam-5871	422	15	both	both	DET
ejpam-5871	422	16	sides	side	NOUN
ejpam-5871	422	17	by	by	ADP
ejpam-5871	422	18	(	(	PUNCT
ejpam-5871	422	19	s+1)−	s+1)−	PROPN
ejpam-5871	422	20	β	β	PROPN
ejpam-5871	422	21	k	k	PROPN
ejpam-5871	422	22	kγk(β	kγk(β	PROPN
ejpam-5871	422	23	)	)	PUNCT
ejpam-5871	422	24	θ	θ	PROPN
ejpam-5871	422	25	β	β	X
ejpam-5871	422	26	k	k	X
ejpam-5871	422	27	−1	−1	NOUN
ejpam-5871	422	28	[	[	PUNCT
ejpam-5871	422	29	⅁(⋋−1(θ⋋s+1	⅁(⋋−1(θ⋋s+1	PROPN
ejpam-5871	422	30	(	(	PUNCT
ejpam-5871	422	31	r1	r1	PROPN
ejpam-5871	422	32	)	)	PUNCT
ejpam-5871	422	33	+	+	CCONJ
ejpam-5871	422	34	(	(	PUNCT
ejpam-5871	422	35	1	1	NUM
ejpam-5871	422	36	−	−	NUM
ejpam-5871	422	37	θ	θ	NOUN
ejpam-5871	422	38	)	)	PUNCT
ejpam-5871	422	39	⋋s+1	⋋s+1	PROPN
ejpam-5871	422	40	(	(	PUNCT
ejpam-5871	422	41	r2	r2	PROPN
ejpam-5871	422	42	)	)	PUNCT
ejpam-5871	422	43	)	)	PUNCT
ejpam-5871	422	44	1	1	NUM
ejpam-5871	422	45	s+1	s+1	NOUN
ejpam-5871	422	46	)	)	PUNCT
ejpam-5871	422	47	]	]	PUNCT
ejpam-5871	422	48	also	also	ADV
ejpam-5871	422	49	taking	take	VERB
ejpam-5871	422	50	the	the	DET
ejpam-5871	422	51	integration	integration	NOUN
ejpam-5871	422	52	over	over	ADP
ejpam-5871	422	53	[	[	X
ejpam-5871	422	54	0	0	NUM
ejpam-5871	422	55	,	,	PUNCT
ejpam-5871	422	56	1	1	NUM
ejpam-5871	422	57	]	]	PUNCT
ejpam-5871	422	58	w.r.t	w.r.t	NOUN
ejpam-5871	422	59	”	"	PUNCT
ejpam-5871	422	60	θ”red	θ”re	VERB
ejpam-5871	422	61	,	,	PUNCT
ejpam-5871	422	62	then	then	ADV
ejpam-5871	422	63	we	we	PRON
ejpam-5871	422	64	acquired	acquire	VERB
ejpam-5871	422	65	our	our	PRON
ejpam-5871	422	66	required	required	ADJ
ejpam-5871	422	67	relation	relation	NOUN
ejpam-5871	422	68	.	.	PUNCT
ejpam-5871	423	1	corollary	corollary	ADJ
ejpam-5871	423	2	3	3	NUM
ejpam-5871	423	3	.	.	PUNCT
ejpam-5871	424	1	if	if	SCONJ
ejpam-5871	424	2	we	we	PRON
ejpam-5871	424	3	fix	fix	VERB
ejpam-5871	424	4	℧	℧	PROPN
ejpam-5871	424	5	(	(	PUNCT
ejpam-5871	424	6	θ	θ	NOUN
ejpam-5871	424	7	)	)	PUNCT
ejpam-5871	424	8	=	=	SYM
ejpam-5871	424	9	θ	θ	PROPN
ejpam-5871	424	10	in	in	ADP
ejpam-5871	424	11	theorem	theorem	NOUN
ejpam-5871	424	12	7	7	NUM
ejpam-5871	424	13	,	,	PUNCT
ejpam-5871	424	14	we	we	PRON
ejpam-5871	424	15	possess	possess	VERB
ejpam-5871	424	16	∅	∅	NOUN
ejpam-5871	424	17	(	(	PUNCT
ejpam-5871	424	18	⋋−1	⋋−1	X
ejpam-5871	424	19	(	(	PUNCT
ejpam-5871	424	20	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	424	21	)	)	PUNCT
ejpam-5871	424	22	+	+	NOUN
ejpam-5871	424	23	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	424	24	)	)	PUNCT
ejpam-5871	424	25	2	2	NUM
ejpam-5871	424	26	)	)	PUNCT
ejpam-5871	424	27	1	1	NUM
ejpam-5871	424	28	s+1	s+1	NOUN
ejpam-5871	424	29	)	)	PUNCT
ejpam-5871	425	1	[	[	PUNCT
ejpam-5871	425	2	s	s	X
ejpam-5871	425	3	kz	kz	PROPN
ejpam-5871	425	4	β	β	PROPN
ejpam-5871	425	5	r+1	r+1	PROPN
ejpam-5871	425	6	⅁(r2	⅁(r2	NOUN
ejpam-5871	425	7	)	)	PUNCT
ejpam-5871	426	1	+	+	SYM
ejpam-5871	426	2	s	s	VERB
ejpam-5871	426	3	kz	kz	PROPN
ejpam-5871	426	4	β	β	PROPN
ejpam-5871	426	5	r−2	r−2	PROPN
ejpam-5871	426	6	⅁(r1	⅁(r1	NUM
ejpam-5871	426	7	)	)	PUNCT
ejpam-5871	426	8	]	]	PUNCT
ejpam-5871	427	1	⊇	⊇	PROPN
ejpam-5871	427	2	[	[	PUNCT
ejpam-5871	427	3	s	s	X
ejpam-5871	427	4	kz	kz	PROPN
ejpam-5871	427	5	β	β	PROPN
ejpam-5871	427	6	r+1	r+1	PROPN
ejpam-5871	427	7	⅁∅(r2	⅁∅(r2	NOUN
ejpam-5871	427	8	)	)	PUNCT
ejpam-5871	427	9	+	+	SYM
ejpam-5871	427	10	s	s	VERB
ejpam-5871	427	11	kz	kz	PROPN
ejpam-5871	427	12	β	β	PROPN
ejpam-5871	427	13	r−2	r−2	PROPN
ejpam-5871	427	14	⅁∅(r1	⅁∅(r1	NOUN
ejpam-5871	427	15	)	)	PUNCT
ejpam-5871	427	16	]	]	PUNCT
ejpam-5871	428	1	⊇	⊇	PROPN
ejpam-5871	429	1	[	[	X
ejpam-5871	429	2	∅(r1	∅(r1	X
ejpam-5871	429	3	)	)	PUNCT
ejpam-5871	430	1	+	+	NOUN
ejpam-5871	430	2	∅(r2	∅(r2	NOUN
ejpam-5871	430	3	)	)	PUNCT
ejpam-5871	430	4	]	]	PUNCT
ejpam-5871	431	1	[	[	PUNCT
ejpam-5871	431	2	s	s	X
ejpam-5871	431	3	kz	kz	PROPN
ejpam-5871	431	4	β	β	PROPN
ejpam-5871	431	5	r+1	r+1	PROPN
ejpam-5871	431	6	⅁(r2	⅁(r2	NOUN
ejpam-5871	431	7	)	)	PUNCT
ejpam-5871	432	1	+	+	SYM
ejpam-5871	432	2	s	s	VERB
ejpam-5871	432	3	kz	kz	PROPN
ejpam-5871	432	4	β	β	PROPN
ejpam-5871	432	5	r−2	r−2	PROPN
ejpam-5871	432	6	⅁(r1	⅁(r1	NUM
ejpam-5871	432	7	)	)	PUNCT
ejpam-5871	432	8	]	]	PUNCT
ejpam-5871	432	9	.	.	PUNCT
ejpam-5871	433	1	(	(	PUNCT
ejpam-5871	433	2	31	31	NUM
ejpam-5871	433	3	)	)	PUNCT
ejpam-5871	433	4	example	example	NOUN
ejpam-5871	434	1	3	3	NUM
ejpam-5871	434	2	.	.	PUNCT
ejpam-5871	435	1	if	if	SCONJ
ejpam-5871	435	2	we	we	PRON
ejpam-5871	435	3	choose	choose	VERB
ejpam-5871	435	4	∅(r	∅(r	PROPN
ejpam-5871	435	5	)	)	PUNCT
ejpam-5871	435	6	=	=	PUNCT
ejpam-5871	436	1	[	[	X
ejpam-5871	436	2	4−⋋s+1(r	4−⋋s+1(r	NUM
ejpam-5871	436	3	)	)	PUNCT
ejpam-5871	436	4	,	,	PUNCT
ejpam-5871	436	5	8	8	NUM
ejpam-5871	436	6	+	+	NOUN
ejpam-5871	436	7	⋋s+1(r	⋋s+1(r	NUM
ejpam-5871	436	8	)	)	PUNCT
ejpam-5871	436	9	]	]	PUNCT
ejpam-5871	436	10	and	and	CCONJ
ejpam-5871	436	11	⋋(r	⋋(r	NUM
ejpam-5871	436	12	)	)	PUNCT
ejpam-5871	436	13	=	=	SYM
ejpam-5871	436	14	r	r	NOUN
ejpam-5871	436	15	and	and	CCONJ
ejpam-5871	436	16	⅁(r	⅁(r	NOUN
ejpam-5871	436	17	)	)	PUNCT
ejpam-5871	436	18	=	=	SYM
ejpam-5871	436	19	1	1	NUM
ejpam-5871	436	20	in	in	ADP
ejpam-5871	436	21	(	(	PUNCT
ejpam-5871	436	22	31	31	NUM
ejpam-5871	436	23	)	)	PUNCT
ejpam-5871	436	24	and	and	CCONJ
ejpam-5871	436	25	utilizing	utilize	VERB
ejpam-5871	436	26	proposition	proposition	NOUN
ejpam-5871	436	27	1	1	NUM
ejpam-5871	436	28	,	,	PUNCT
ejpam-5871	436	29	we	we	PRON
ejpam-5871	436	30	have	have	VERB
ejpam-5871	436	31	8(s+	8(s+	NUM
ejpam-5871	437	1	1)−	1)−	NUM
ejpam-5871	437	2	β	β	X
ejpam-5871	437	3	k	k	PROPN
ejpam-5871	437	4	βγk(β	βγk(β	PROPN
ejpam-5871	437	5	)	)	PUNCT
ejpam-5871	437	6	(	(	PUNCT
ejpam-5871	437	7	4−	4−	NOUN
ejpam-5871	437	8	rs+1	rs+1	NOUN
ejpam-5871	437	9	1	1	NUM
ejpam-5871	438	1	+	+	CCONJ
ejpam-5871	438	2	rs+1	rs+1	NUM
ejpam-5871	438	3	2	2	NUM
ejpam-5871	438	4	2	2	NUM
ejpam-5871	438	5	,	,	PUNCT
ejpam-5871	438	6	8	8	NUM
ejpam-5871	438	7	+	+	CCONJ
ejpam-5871	438	8	rs+1	rs+1	PROPN
ejpam-5871	438	9	1	1	NUM
ejpam-5871	438	10	+	+	CCONJ
ejpam-5871	438	11	rs+1	rs+1	NUM
ejpam-5871	438	12	2	2	NUM
ejpam-5871	438	13	2	2	NUM
ejpam-5871	438	14	)	)	PUNCT
ejpam-5871	438	15	(	(	PUNCT
ejpam-5871	438	16	rs+1	rs+1	NOUN
ejpam-5871	438	17	2	2	NUM
ejpam-5871	438	18	−	−	NOUN
ejpam-5871	438	19	rs+1	rs+1	NOUN
ejpam-5871	438	20	1	1	NUM
ejpam-5871	438	21	)	)	PUNCT
ejpam-5871	438	22	β	β	PROPN
ejpam-5871	438	23	k	k	PROPN
ejpam-5871	438	24	⊇	⊇	PROPN
ejpam-5871	438	25	(	(	PUNCT
ejpam-5871	438	26	s+	s+	PROPN
ejpam-5871	438	27	1	1	X
ejpam-5871	438	28	)	)	PUNCT
ejpam-5871	438	29	−β	−β	NOUN
ejpam-5871	438	30	k	k	PROPN
ejpam-5871	438	31	βγk(β	βγk(β	PROPN
ejpam-5871	438	32	)	)	PUNCT
ejpam-5871	438	33	(	(	PUNCT
ejpam-5871	438	34	rs+1	rs+1	NOUN
ejpam-5871	438	35	2	2	NUM
ejpam-5871	438	36	−	−	NOUN
ejpam-5871	438	37	rs+1	rs+1	NOUN
ejpam-5871	438	38	1	1	NUM
ejpam-5871	438	39	)	)	PUNCT
ejpam-5871	438	40	β	β	X
ejpam-5871	438	41	k	k	X
ejpam-5871	438	42	(	(	PUNCT
ejpam-5871	438	43	8−	8−	NUM
ejpam-5871	438	44	(	(	PUNCT
ejpam-5871	438	45	rs+1	rs+1	NOUN
ejpam-5871	438	46	1	1	NUM
ejpam-5871	438	47	+	+	CCONJ
ejpam-5871	438	48	rs+1	rs+1	PROPN
ejpam-5871	438	49	2	2	NUM
ejpam-5871	438	50	)	)	PUNCT
ejpam-5871	438	51	,	,	PUNCT
ejpam-5871	438	52	16	16	NUM
ejpam-5871	439	1	+	+	CCONJ
ejpam-5871	439	2	(	(	PUNCT
ejpam-5871	439	3	rs+1	rs+1	PROPN
ejpam-5871	439	4	1	1	NUM
ejpam-5871	439	5	+	+	CCONJ
ejpam-5871	439	6	rs+1	rs+1	PROPN
ejpam-5871	439	7	2	2	NUM
ejpam-5871	439	8	)	)	PUNCT
ejpam-5871	439	9	)	)	PUNCT
ejpam-5871	440	1	⊇	⊇	NOUN
ejpam-5871	440	2	(	(	PUNCT
ejpam-5871	440	3	s+	s+	NUM
ejpam-5871	440	4	1)−	1)−	PROPN
ejpam-5871	440	5	β	β	X
ejpam-5871	440	6	k	k	PROPN
ejpam-5871	440	7	2δγk(β	2δγk(β	PROPN
ejpam-5871	440	8	)	)	PUNCT
ejpam-5871	440	9	(	(	PUNCT
ejpam-5871	440	10	8−	8−	NUM
ejpam-5871	440	11	(	(	PUNCT
ejpam-5871	440	12	rs+1	rs+1	NOUN
ejpam-5871	440	13	1	1	NUM
ejpam-5871	440	14	+	+	CCONJ
ejpam-5871	440	15	rs+1	rs+1	PROPN
ejpam-5871	440	16	2	2	NUM
ejpam-5871	440	17	)	)	PUNCT
ejpam-5871	440	18	,	,	PUNCT
ejpam-5871	440	19	16	16	NUM
ejpam-5871	440	20	+	+	CCONJ
ejpam-5871	440	21	(	(	PUNCT
ejpam-5871	440	22	rs+1	rs+1	PROPN
ejpam-5871	440	23	1	1	NUM
ejpam-5871	440	24	+	+	CCONJ
ejpam-5871	440	25	rs+1	rs+1	PROPN
ejpam-5871	440	26	2	2	NUM
ejpam-5871	440	27	)	)	PUNCT
ejpam-5871	440	28	)	)	PUNCT
ejpam-5871	441	1	(	(	PUNCT
ejpam-5871	441	2	rs+1	rs+1	NOUN
ejpam-5871	441	3	2	2	NUM
ejpam-5871	441	4	−	−	NOUN
ejpam-5871	441	5	rs+1	rs+1	NOUN
ejpam-5871	441	6	1	1	NUM
ejpam-5871	441	7	)	)	PUNCT
ejpam-5871	441	8	β	β	PROPN
ejpam-5871	441	9	k	k	X
ejpam-5871	441	10	.	.	PUNCT
ejpam-5871	442	1	example	example	NOUN
ejpam-5871	443	1	4	4	NUM
ejpam-5871	443	2	.	.	X
ejpam-5871	443	3	for	for	ADP
ejpam-5871	443	4	graphical	graphical	ADJ
ejpam-5871	443	5	representation	representation	NOUN
ejpam-5871	443	6	if	if	SCONJ
ejpam-5871	443	7	we	we	PRON
ejpam-5871	443	8	choose	choose	VERB
ejpam-5871	443	9	∅(r	∅(r	PROPN
ejpam-5871	443	10	)	)	PUNCT
ejpam-5871	443	11	=	=	PUNCT
ejpam-5871	444	1	[	[	X
ejpam-5871	444	2	4−⋋s+1(r	4−⋋s+1(r	NUM
ejpam-5871	444	3	)	)	PUNCT
ejpam-5871	444	4	,	,	PUNCT
ejpam-5871	444	5	8+⋋s+1(r	8+⋋s+1(r	NOUN
ejpam-5871	444	6	)	)	PUNCT
ejpam-5871	444	7	]	]	PUNCT
ejpam-5871	444	8	,	,	PUNCT
ejpam-5871	444	9	℧	℧	PROPN
ejpam-5871	444	10	(	(	PUNCT
ejpam-5871	444	11	r	r	NOUN
ejpam-5871	444	12	)	)	PUNCT
ejpam-5871	444	13	=	=	SYM
ejpam-5871	444	14	1	1	NUM
ejpam-5871	444	15	8	8	NUM
ejpam-5871	444	16	and	and	CCONJ
ejpam-5871	444	17	⋋(r	⋋(r	NUM
ejpam-5871	444	18	)	)	PUNCT
ejpam-5871	445	1	=	=	PUNCT
ejpam-5871	445	2	sin	sin	NOUN
ejpam-5871	445	3	r	r	NOUN
ejpam-5871	445	4	and	and	CCONJ
ejpam-5871	445	5	⅁(r	⅁(r	NOUN
ejpam-5871	445	6	)	)	PUNCT
ejpam-5871	445	7	=	=	SYM
ejpam-5871	445	8	1	1	NUM
ejpam-5871	445	9	in	in	ADP
ejpam-5871	445	10	(	(	PUNCT
ejpam-5871	445	11	31	31	NUM
ejpam-5871	445	12	)	)	PUNCT
ejpam-5871	446	1	and	and	CCONJ
ejpam-5871	446	2	utilizing	utilize	VERB
ejpam-5871	446	3	proposition	proposition	NOUN
ejpam-5871	446	4	1	1	NUM
ejpam-5871	446	5	,	,	PUNCT
ejpam-5871	446	6	we	we	PRON
ejpam-5871	446	7	have	have	VERB
ejpam-5871	446	8	4(s+	4(s+	NUM
ejpam-5871	447	1	1)−	1)−	PROPN
ejpam-5871	447	2	β	β	X
ejpam-5871	447	3	k	k	PROPN
ejpam-5871	447	4	βγk(β	βγk(β	PROPN
ejpam-5871	447	5	)	)	PUNCT
ejpam-5871	447	6	(	(	PUNCT
ejpam-5871	447	7	4−	4−	NOUN
ejpam-5871	447	8	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	447	9	)	)	PUNCT
ejpam-5871	448	1	+	+	SYM
ejpam-5871	448	2	sins+1(r2	sins+1(r2	X
ejpam-5871	448	3	)	)	PUNCT
ejpam-5871	448	4	2	2	NUM
ejpam-5871	448	5	,	,	PUNCT
ejpam-5871	448	6	8	8	NUM
ejpam-5871	448	7	+	+	SYM
ejpam-5871	448	8	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	448	9	)	)	PUNCT
ejpam-5871	449	1	+	+	SYM
ejpam-5871	449	2	sins+1(r2	sins+1(r2	X
ejpam-5871	449	3	)	)	PUNCT
ejpam-5871	449	4	2	2	NUM
ejpam-5871	449	5	)	)	PUNCT
ejpam-5871	449	6	(	(	PUNCT
ejpam-5871	449	7	sins+1(r2)−	sins+1(r2)−	ADJ
ejpam-5871	449	8	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	449	9	)	)	PUNCT
ejpam-5871	449	10	)	)	PUNCT
ejpam-5871	450	1	β	β	X
ejpam-5871	450	2	k	k	PROPN
ejpam-5871	450	3	⊇	⊇	PROPN
ejpam-5871	450	4	(	(	PUNCT
ejpam-5871	450	5	s+	s+	PROPN
ejpam-5871	450	6	1	1	X
ejpam-5871	450	7	)	)	PUNCT
ejpam-5871	450	8	−β	−β	NOUN
ejpam-5871	450	9	k	k	PROPN
ejpam-5871	450	10	βγk(β	βγk(β	PROPN
ejpam-5871	450	11	)	)	PUNCT
ejpam-5871	450	12	(	(	PUNCT
ejpam-5871	450	13	sins+1(r2)−	sins+1(r2)−	ADJ
ejpam-5871	450	14	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	450	15	)	)	PUNCT
ejpam-5871	450	16	)	)	PUNCT
ejpam-5871	451	1	β	β	X
ejpam-5871	451	2	k	k	X
ejpam-5871	451	3	(	(	PUNCT
ejpam-5871	451	4	8−	8−	PROPN
ejpam-5871	451	5	(	(	PUNCT
ejpam-5871	451	6	sins+1(r1	sins+1(r1	X
ejpam-5871	451	7	)	)	PUNCT
ejpam-5871	451	8	+	+	SYM
ejpam-5871	451	9	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	451	10	)	)	PUNCT
ejpam-5871	451	11	)	)	PUNCT
ejpam-5871	451	12	,	,	PUNCT
ejpam-5871	451	13	16	16	NUM
ejpam-5871	451	14	+	+	CCONJ
ejpam-5871	451	15	(	(	PUNCT
ejpam-5871	451	16	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	451	17	)	)	PUNCT
ejpam-5871	451	18	+	+	SYM
ejpam-5871	451	19	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	451	20	)	)	PUNCT
ejpam-5871	451	21	)	)	PUNCT
ejpam-5871	451	22	)	)	PUNCT
ejpam-5871	452	1	⊇	⊇	NOUN
ejpam-5871	452	2	(	(	PUNCT
ejpam-5871	452	3	s+	s+	NUM
ejpam-5871	452	4	1)−	1)−	PROPN
ejpam-5871	452	5	β	β	X
ejpam-5871	452	6	k	k	PROPN
ejpam-5871	452	7	4δγk(β	4δγk(β	PROPN
ejpam-5871	452	8	)	)	PUNCT
ejpam-5871	452	9	(	(	PUNCT
ejpam-5871	452	10	8−	8−	NUM
ejpam-5871	452	11	(	(	PUNCT
ejpam-5871	452	12	sins+1(r1	sins+1(r1	X
ejpam-5871	452	13	)	)	PUNCT
ejpam-5871	452	14	+	+	SYM
ejpam-5871	452	15	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	452	16	)	)	PUNCT
ejpam-5871	452	17	)	)	PUNCT
ejpam-5871	452	18	,	,	PUNCT
ejpam-5871	452	19	16	16	NUM
ejpam-5871	452	20	+	+	CCONJ
ejpam-5871	452	21	(	(	PUNCT
ejpam-5871	452	22	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	452	23	)	)	PUNCT
ejpam-5871	452	24	+	+	SYM
ejpam-5871	452	25	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	452	26	)	)	PUNCT
ejpam-5871	452	27	)	)	PUNCT
ejpam-5871	452	28	)	)	PUNCT
ejpam-5871	452	29	(	(	PUNCT
ejpam-5871	452	30	sins+1(r2)−	sins+1(r2)−	ADJ
ejpam-5871	452	31	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	452	32	)	)	PUNCT
ejpam-5871	452	33	)	)	PUNCT
ejpam-5871	453	1	β	β	PROPN
ejpam-5871	453	2	k	k	X
ejpam-5871	453	3	.	.	PUNCT
ejpam-5871	454	1	a.	a.	PROPN
ejpam-5871	454	2	mehmood	mehmood	PROPN
ejpam-5871	454	3	et	et	PROPN
ejpam-5871	454	4	al	al	PROPN
ejpam-5871	454	5	.	.	PUNCT
ejpam-5871	454	6	/	/	SYM
ejpam-5871	454	7	eur	eur	PROPN
ejpam-5871	454	8	.	.	PUNCT
ejpam-5871	455	1	j.	j.	PROPN
ejpam-5871	455	2	pure	pure	PROPN
ejpam-5871	455	3	appl	appl	PROPN
ejpam-5871	455	4	.	.	PROPN
ejpam-5871	455	5	math	math	PROPN
ejpam-5871	455	6	,	,	PUNCT
ejpam-5871	455	7	18	18	NUM
ejpam-5871	455	8	(	(	PUNCT
ejpam-5871	455	9	2	2	NUM
ejpam-5871	455	10	)	)	PUNCT
ejpam-5871	455	11	(	(	PUNCT
ejpam-5871	455	12	2025	2025	NUM
ejpam-5871	455	13	)	)	PUNCT
ejpam-5871	455	14	,	,	PUNCT
ejpam-5871	455	15	5871	5871	NUM
ejpam-5871	455	16	17	17	NUM
ejpam-5871	455	17	of	of	ADP
ejpam-5871	455	18	26	26	NUM
ejpam-5871	455	19	figure	figure	NOUN
ejpam-5871	455	20	2	2	NUM
ejpam-5871	455	21	:	:	PUNCT
ejpam-5871	455	22	graphical	graphical	ADJ
ejpam-5871	455	23	representation	representation	NOUN
ejpam-5871	455	24	of	of	ADP
ejpam-5871	455	25	theorem	theorem	NOUN
ejpam-5871	455	26	7	7	NUM
ejpam-5871	455	27	corresponding	correspond	VERB
ejpam-5871	455	28	to	to	ADP
ejpam-5871	455	29	the	the	DET
ejpam-5871	455	30	choice	choice	NOUN
ejpam-5871	455	31	of	of	ADP
ejpam-5871	455	32	parameters	parameter	NOUN
ejpam-5871	455	33	r1	r1	NOUN
ejpam-5871	455	34	=	=	SYM
ejpam-5871	455	35	0.6	0.6	NUM
ejpam-5871	455	36	,	,	PUNCT
ejpam-5871	455	37	r1	r1	NOUN
ejpam-5871	455	38	<	<	X
ejpam-5871	455	39	r2	r2	PROPN
ejpam-5871	455	40	≤	≤	PROPN
ejpam-5871	456	1	π	π	PROPN
ejpam-5871	456	2	2	2	NUM
ejpam-5871	456	3	,	,	PUNCT
ejpam-5871	456	4	k	k	NOUN
ejpam-5871	456	5	=	=	SYM
ejpam-5871	456	6	1	1	NUM
ejpam-5871	456	7	,	,	PUNCT
ejpam-5871	456	8	s	s	PART
ejpam-5871	456	9	=	=	SYM
ejpam-5871	456	10	3	3	NUM
ejpam-5871	456	11	and	and	CCONJ
ejpam-5871	456	12	β	β	X
ejpam-5871	456	13	=	=	NOUN
ejpam-5871	456	14	0.8	0.8	NUM
ejpam-5871	456	15	.	.	PUNCT
ejpam-5871	457	1	r2	r2	PROPN
ejpam-5871	457	2	(	(	PUNCT
ejpam-5871	457	3	a1	a1	PROPN
ejpam-5871	457	4	,	,	PUNCT
ejpam-5871	457	5	b1	b1	NOUN
ejpam-5871	457	6	)	)	PUNCT
ejpam-5871	457	7	(	(	PUNCT
ejpam-5871	457	8	a2	a2	PROPN
ejpam-5871	457	9	,	,	PUNCT
ejpam-5871	457	10	b2	b2	NOUN
ejpam-5871	457	11	)	)	PUNCT
ejpam-5871	457	12	(	(	PUNCT
ejpam-5871	457	13	a3	a3	NOUN
ejpam-5871	457	14	,	,	PUNCT
ejpam-5871	457	15	b3	b3	PROPN
ejpam-5871	457	16	)	)	PUNCT
ejpam-5871	457	17	0.6100	0.6100	NUM
ejpam-5871	457	18	(	(	PUNCT
ejpam-5871	457	19	0.0928	0.0928	NUM
ejpam-5871	457	20	,	,	PUNCT
ejpam-5871	457	21	0.1930	0.1930	NUM
ejpam-5871	457	22	)	)	PUNCT
ejpam-5871	457	23	(	(	PUNCT
ejpam-5871	457	24	0.0464	0.0464	NUM
ejpam-5871	457	25	,	,	PUNCT
ejpam-5871	457	26	0.0965	0.0965	NUM
ejpam-5871	457	27	)	)	PUNCT
ejpam-5871	457	28	(	(	PUNCT
ejpam-5871	457	29	0.0116	0.0116	NUM
ejpam-5871	457	30	,	,	PUNCT
ejpam-5871	457	31	0.0241	0.0241	NUM
ejpam-5871	457	32	)	)	PUNCT
ejpam-5871	457	33	0.8022	0.8022	PROPN
ejpam-5871	457	34	(	(	PUNCT
ejpam-5871	457	35	1.2813	1.2813	NUM
ejpam-5871	457	36	,	,	PUNCT
ejpam-5871	457	37	2.7484	2.7484	NUM
ejpam-5871	457	38	)	)	PUNCT
ejpam-5871	457	39	(	(	PUNCT
ejpam-5871	457	40	0.6407	0.6407	NUM
ejpam-5871	457	41	,	,	PUNCT
ejpam-5871	457	42	1.3742	1.3742	NUM
ejpam-5871	457	43	)	)	PUNCT
ejpam-5871	457	44	(	(	PUNCT
ejpam-5871	457	45	0.1602	0.1602	NUM
ejpam-5871	457	46	,	,	PUNCT
ejpam-5871	457	47	0.3435	0.3435	NUM
ejpam-5871	457	48	)	)	PUNCT
ejpam-5871	457	49	0.9943	0.9943	NUM
ejpam-5871	457	50	(	(	PUNCT
ejpam-5871	457	51	2.4816	2.4816	NUM
ejpam-5871	457	52	,	,	PUNCT
ejpam-5871	457	53	5.5622	5.5622	NUM
ejpam-5871	457	54	)	)	PUNCT
ejpam-5871	457	55	(	(	PUNCT
ejpam-5871	457	56	1.2408	1.2408	NUM
ejpam-5871	457	57	,	,	PUNCT
ejpam-5871	457	58	2.7811	2.7811	NUM
ejpam-5871	457	59	)	)	PUNCT
ejpam-5871	457	60	(	(	PUNCT
ejpam-5871	457	61	0.3102	0.3102	NUM
ejpam-5871	457	62	,	,	PUNCT
ejpam-5871	457	63	0.6953	0.6953	NUM
ejpam-5871	457	64	)	)	PUNCT
ejpam-5871	457	65	1.1865	1.1865	NUM
ejpam-5871	457	66	(	(	PUNCT
ejpam-5871	457	67	3.5355	3.5355	NUM
ejpam-5871	457	68	,	,	PUNCT
ejpam-5871	457	69	8.3157	8.3157	NUM
ejpam-5871	457	70	)	)	PUNCT
ejpam-5871	457	71	(	(	PUNCT
ejpam-5871	457	72	1.7677	1.7677	NUM
ejpam-5871	457	73	,	,	PUNCT
ejpam-5871	457	74	4.1578	4.1578	NUM
ejpam-5871	457	75	)	)	PUNCT
ejpam-5871	457	76	(	(	PUNCT
ejpam-5871	457	77	0.4419	0.4419	NUM
ejpam-5871	457	78	,	,	PUNCT
ejpam-5871	457	79	1.0395	1.0395	NUM
ejpam-5871	457	80	)	)	PUNCT
ejpam-5871	457	81	1.3786	1.3786	NUM
ejpam-5871	457	82	(	(	PUNCT
ejpam-5871	457	83	4.2401	4.2401	NUM
ejpam-5871	457	84	,	,	PUNCT
ejpam-5871	457	85	10.3601	10.3601	NUM
ejpam-5871	457	86	)	)	PUNCT
ejpam-5871	457	87	(	(	PUNCT
ejpam-5871	457	88	2.1201	2.1201	NUM
ejpam-5871	457	89	,	,	PUNCT
ejpam-5871	457	90	5.1800	5.1800	NUM
ejpam-5871	457	91	)	)	PUNCT
ejpam-5871	457	92	(	(	PUNCT
ejpam-5871	457	93	0.5300	0.5300	NUM
ejpam-5871	457	94	,	,	PUNCT
ejpam-5871	457	95	1.2950	1.2950	NUM
ejpam-5871	457	96	)	)	PUNCT
ejpam-5871	457	97	1.5708	1.5708	NUM
ejpam-5871	457	98	(	(	PUNCT
ejpam-5871	457	99	4.4849	4.4849	NUM
ejpam-5871	457	100	,	,	PUNCT
ejpam-5871	457	101	11.1186	11.1186	NUM
ejpam-5871	457	102	)	)	PUNCT
ejpam-5871	457	103	(	(	PUNCT
ejpam-5871	457	104	2.2425	2.2425	NUM
ejpam-5871	457	105	,	,	PUNCT
ejpam-5871	457	106	5.5593	5.5593	NUM
ejpam-5871	457	107	)	)	PUNCT
ejpam-5871	457	108	(	(	PUNCT
ejpam-5871	457	109	0.5606	0.5606	NUM
ejpam-5871	457	110	,	,	PUNCT
ejpam-5871	457	111	1.3898	1.3898	NUM
ejpam-5871	457	112	)	)	PUNCT
ejpam-5871	457	113	table	table	NOUN
ejpam-5871	457	114	2	2	NUM
ejpam-5871	457	115	:	:	PUNCT
ejpam-5871	457	116	interval	interval	NOUN
ejpam-5871	457	117	bounds	bound	NOUN
ejpam-5871	457	118	of	of	ADP
ejpam-5871	457	119	theorem	theorem	ADJ
ejpam-5871	457	120	7	7	NUM
ejpam-5871	457	121	corresponding	correspond	VERB
ejpam-5871	457	122	to	to	ADP
ejpam-5871	457	123	the	the	DET
ejpam-5871	457	124	choice	choice	NOUN
ejpam-5871	457	125	of	of	ADP
ejpam-5871	457	126	parameters	parameter	NOUN
ejpam-5871	457	127	r1	r1	NOUN
ejpam-5871	457	128	=	=	SYM
ejpam-5871	457	129	0.6	0.6	NUM
ejpam-5871	457	130	,	,	PUNCT
ejpam-5871	457	131	r1	r1	NOUN
ejpam-5871	457	132	<	<	X
ejpam-5871	457	133	r2	r2	PROPN
ejpam-5871	457	134	≤	≤	PROPN
ejpam-5871	457	135	π	π	PROPN
ejpam-5871	457	136	2	2	NUM
ejpam-5871	457	137	,	,	PUNCT
ejpam-5871	457	138	k	k	NOUN
ejpam-5871	457	139	=	=	SYM
ejpam-5871	457	140	1	1	NUM
ejpam-5871	457	141	,	,	PUNCT
ejpam-5871	457	142	s	s	PART
ejpam-5871	457	143	=	=	SYM
ejpam-5871	457	144	3	3	NUM
ejpam-5871	457	145	and	and	CCONJ
ejpam-5871	457	146	β	β	X
ejpam-5871	457	147	=	=	NOUN
ejpam-5871	457	148	0.8	0.8	NUM
ejpam-5871	457	149	.	.	PUNCT
ejpam-5871	458	1	for	for	ADP
ejpam-5871	458	2	tabular	tabular	NOUN
ejpam-5871	458	3	form	form	NOUN
ejpam-5871	458	4	we	we	PRON
ejpam-5871	458	5	have	have	VERB
ejpam-5871	458	6	corollary	corollary	ADJ
ejpam-5871	458	7	4	4	NUM
ejpam-5871	458	8	.	.	PUNCT
ejpam-5871	459	1	if	if	SCONJ
ejpam-5871	459	2	we	we	PRON
ejpam-5871	459	3	fix	fix	VERB
ejpam-5871	459	4	s	s	NOUN
ejpam-5871	459	5	=	=	NOUN
ejpam-5871	459	6	0	0	NUM
ejpam-5871	459	7	,	,	PUNCT
ejpam-5871	459	8	k	k	NOUN
ejpam-5871	459	9	=	=	SYM
ejpam-5871	459	10	1	1	NUM
ejpam-5871	459	11	,	,	PUNCT
ejpam-5871	459	12	⋋(r	⋋(r	X
ejpam-5871	459	13	)	)	PUNCT
ejpam-5871	460	1	=	=	SYM
ejpam-5871	460	2	r	r	NOUN
ejpam-5871	460	3	and	and	CCONJ
ejpam-5871	460	4	℧	℧	PROPN
ejpam-5871	460	5	(	(	PUNCT
ejpam-5871	460	6	θ	θ	NOUN
ejpam-5871	460	7	)	)	PUNCT
ejpam-5871	460	8	=	=	SYM
ejpam-5871	460	9	θ	θ	PROPN
ejpam-5871	460	10	in	in	ADP
ejpam-5871	460	11	theorem	theorem	NOUN
ejpam-5871	460	12	7	7	NUM
ejpam-5871	460	13	,	,	PUNCT
ejpam-5871	460	14	we	we	PRON
ejpam-5871	460	15	possess	possess	VERB
ejpam-5871	460	16	∅	∅	NOUN
ejpam-5871	460	17	(	(	PUNCT
ejpam-5871	460	18	r1	r1	NOUN
ejpam-5871	460	19	+	+	CCONJ
ejpam-5871	460	20	r2	r2	PROPN
ejpam-5871	460	21	2	2	NUM
ejpam-5871	460	22	)	)	PUNCT
ejpam-5871	460	23	[	[	PUNCT
ejpam-5871	460	24	zβ	zβ	PROPN
ejpam-5871	460	25	r+1	r+1	PROPN
ejpam-5871	460	26	⅁(r2	⅁(r2	NOUN
ejpam-5871	460	27	)	)	PUNCT
ejpam-5871	461	1	+	+	CCONJ
ejpam-5871	461	2	zβ	zβ	PROPN
ejpam-5871	461	3	r−2	r−2	PROPN
ejpam-5871	461	4	⅁(r1	⅁(r1	NUM
ejpam-5871	461	5	)	)	PUNCT
ejpam-5871	461	6	]	]	PUNCT
ejpam-5871	462	1	⊇	⊇	NOUN
ejpam-5871	462	2	[	[	PUNCT
ejpam-5871	462	3	zβ	zβ	PROPN
ejpam-5871	462	4	r+1	r+1	PROPN
ejpam-5871	462	5	⅁∅(r2	⅁∅(r2	NOUN
ejpam-5871	462	6	)	)	PUNCT
ejpam-5871	462	7	+	+	CCONJ
ejpam-5871	462	8	zβ	zβ	PROPN
ejpam-5871	462	9	r−2	r−2	PROPN
ejpam-5871	462	10	⅁∅(r1	⅁∅(r1	NOUN
ejpam-5871	462	11	)	)	PUNCT
ejpam-5871	462	12	]	]	PUNCT
ejpam-5871	462	13	⊇	⊇	PROPN
ejpam-5871	463	1	[	[	X
ejpam-5871	463	2	∅(r1	∅(r1	X
ejpam-5871	463	3	)	)	PUNCT
ejpam-5871	464	1	+	+	NOUN
ejpam-5871	464	2	∅(r2	∅(r2	NOUN
ejpam-5871	464	3	)	)	PUNCT
ejpam-5871	464	4	]	]	PUNCT
ejpam-5871	465	1	[	[	PUNCT
ejpam-5871	465	2	zβ	zβ	NOUN
ejpam-5871	465	3	r+1	r+1	PROPN
ejpam-5871	465	4	⅁(r2	⅁(r2	NOUN
ejpam-5871	465	5	)	)	PUNCT
ejpam-5871	466	1	+	+	CCONJ
ejpam-5871	466	2	zβ	zβ	PROPN
ejpam-5871	466	3	r−2	r−2	PROPN
ejpam-5871	466	4	⅁(r1	⅁(r1	NUM
ejpam-5871	466	5	)	)	PUNCT
ejpam-5871	466	6	]	]	PUNCT
ejpam-5871	466	7	.	.	PUNCT
ejpam-5871	467	1	theorem	theorem	ADJ
ejpam-5871	467	2	8	8	NUM
ejpam-5871	467	3	.	.	PUNCT
ejpam-5871	468	1	let	let	VERB
ejpam-5871	468	2	s	s	PRON
ejpam-5871	468	3	∈	∈	VERB
ejpam-5871	468	4	r/{−1	r/{−1	PROPN
ejpam-5871	468	5	}	}	PUNCT
ejpam-5871	468	6	,	,	PUNCT
ejpam-5871	468	7	∅,⅁	∅,⅁	NOUN
ejpam-5871	468	8	∈	∈	PROPN
ejpam-5871	468	9	sigx([r1	sigx([r1	NOUN
ejpam-5871	468	10	,	,	PUNCT
ejpam-5871	468	11	r2	r2	PROPN
ejpam-5871	468	12	]	]	PUNCT
ejpam-5871	468	13	,	,	PUNCT
ejpam-5871	469	1	r	r	NOUN
ejpam-5871	469	2	+	+	NUM
ejpam-5871	469	3	i	i	NOUN
ejpam-5871	469	4	)	)	PUNCT
ejpam-5871	469	5	and	and	CCONJ
ejpam-5871	469	6	k	k	X
ejpam-5871	469	7	≥	≥	PROPN
ejpam-5871	469	8	0	0	NUM
ejpam-5871	469	9	,	,	PUNCT
ejpam-5871	469	10	then	then	ADV
ejpam-5871	469	11	for	for	ADP
ejpam-5871	469	12	β	β	X
ejpam-5871	469	13	>	>	X
ejpam-5871	469	14	0	0	PUNCT
ejpam-5871	470	1	the	the	DET
ejpam-5871	470	2	following	follow	VERB
ejpam-5871	470	3	redinequality	redinequality	NOUN
ejpam-5871	470	4	fulfilled	fulfil	VERB
ejpam-5871	470	5	1	1	NUM
ejpam-5871	470	6	(	(	PUNCT
ejpam-5871	470	7	⋋s+1(r2)−⋋s+1(r1	⋋s+1(r2)−⋋s+1(r1	NOUN
ejpam-5871	470	8	)	)	PUNCT
ejpam-5871	470	9	)	)	PUNCT
ejpam-5871	471	1	β	β	X
ejpam-5871	471	2	k	k	X
ejpam-5871	472	1	[	[	PUNCT
ejpam-5871	472	2	s	s	X
ejpam-5871	472	3	kz	kz	PROPN
ejpam-5871	472	4	β	β	PROPN
ejpam-5871	472	5	r+1	r+1	PROPN
ejpam-5871	472	6	∅⅁(r2	∅⅁(r2	NOUN
ejpam-5871	472	7	)	)	PUNCT
ejpam-5871	473	1	+	+	SYM
ejpam-5871	473	2	s	s	VERB
ejpam-5871	473	3	kz	kz	PROPN
ejpam-5871	473	4	β	β	PROPN
ejpam-5871	473	5	r−2	r−2	PROPN
ejpam-5871	473	6	∅⅁(r1	∅⅁(r1	PROPN
ejpam-5871	473	7	)	)	PUNCT
ejpam-5871	473	8	]	]	PUNCT
ejpam-5871	474	1	⊇	⊇	PROPN
ejpam-5871	474	2	p	p	X
ejpam-5871	474	3	(	(	PUNCT
ejpam-5871	474	4	r1	r1	PROPN
ejpam-5871	474	5	,	,	PUNCT
ejpam-5871	474	6	r2	r2	PROPN
ejpam-5871	474	7	)	)	PUNCT
ejpam-5871	474	8	(	(	PUNCT
ejpam-5871	474	9	s+	s+	NUM
ejpam-5871	474	10	1)−	1)−	PROPN
ejpam-5871	474	11	β	β	X
ejpam-5871	474	12	k	k	PROPN
ejpam-5871	474	13	kγk(β	kγk(β	PROPN
ejpam-5871	474	14	)	)	PUNCT
ejpam-5871	474	15	∫	∫	PROPN
ejpam-5871	474	16	1	1	NUM
ejpam-5871	474	17	0	0	NUM
ejpam-5871	474	18	θ	θ	PROPN
ejpam-5871	474	19	β	β	X
ejpam-5871	474	20	k	k	X
ejpam-5871	474	21	−1[	−1[	X
ejpam-5871	474	22	℧	℧	PROPN
ejpam-5871	474	23	1(θ)	1(θ)	NUM
ejpam-5871	474	24	℧	℧	NOUN
ejpam-5871	474	25	2(θ	2(θ	NUM
ejpam-5871	474	26	)	)	PUNCT
ejpam-5871	475	1	+	+	CCONJ
ejpam-5871	475	2	℧	℧	PROPN
ejpam-5871	475	3	1(1−	1(1−	NUM
ejpam-5871	475	4	θ)	θ)	PROPN
ejpam-5871	475	5	℧	℧	NOUN
ejpam-5871	475	6	2(1−	2(1−	NUM
ejpam-5871	475	7	θ)]dθ	θ)]dθ	NOUN
ejpam-5871	475	8	+	+	NOUN
ejpam-5871	475	9	q(r1	q(r1	ADJ
ejpam-5871	475	10	,	,	PUNCT
ejpam-5871	475	11	r2	r2	PROPN
ejpam-5871	475	12	)	)	PUNCT
ejpam-5871	475	13	(	(	PUNCT
ejpam-5871	475	14	s+	s+	NUM
ejpam-5871	475	15	1)−	1)−	PROPN
ejpam-5871	475	16	β	β	X
ejpam-5871	475	17	k	k	PROPN
ejpam-5871	475	18	kγk(β	kγk(β	PROPN
ejpam-5871	475	19	)	)	PUNCT
ejpam-5871	475	20	∫	∫	PROPN
ejpam-5871	475	21	1	1	NUM
ejpam-5871	475	22	0	0	NUM
ejpam-5871	475	23	θ	θ	PROPN
ejpam-5871	475	24	β	β	X
ejpam-5871	475	25	k	k	X
ejpam-5871	475	26	−1[	−1[	X
ejpam-5871	475	27	℧	℧	PROPN
ejpam-5871	475	28	1(θ)	1(θ)	NUM
ejpam-5871	475	29	℧	℧	SYM
ejpam-5871	475	30	2(1−	2(1−	NUM
ejpam-5871	475	31	θ	θ	NOUN
ejpam-5871	475	32	)	)	PUNCT
ejpam-5871	475	33	+	+	CCONJ
ejpam-5871	475	34	℧	℧	PROPN
ejpam-5871	475	35	1(1−	1(1−	NUM
ejpam-5871	475	36	θ)	θ)	NOUN
ejpam-5871	475	37	℧	℧	NOUN
ejpam-5871	475	38	2(θ)]dθ	2(θ)]dθ	NOUN
ejpam-5871	475	39	,	,	PUNCT
ejpam-5871	475	40	where	where	SCONJ
ejpam-5871	475	41	,	,	PUNCT
ejpam-5871	475	42	p	p	X
ejpam-5871	475	43	(	(	PUNCT
ejpam-5871	475	44	r1	r1	PROPN
ejpam-5871	475	45	,	,	PUNCT
ejpam-5871	475	46	r2	r2	PROPN
ejpam-5871	475	47	)	)	PUNCT
ejpam-5871	475	48	=	=	SYM
ejpam-5871	475	49	∅(r1)⅁(r1	∅(r1)⅁(r1	NOUN
ejpam-5871	475	50	)	)	PUNCT
ejpam-5871	476	1	+	+	NUM
ejpam-5871	476	2	∅(r2)⅁(r2	∅(r2)⅁(r2	NOUN
ejpam-5871	476	3	)	)	PUNCT
ejpam-5871	476	4	,	,	PUNCT
ejpam-5871	476	5	q(r1	q(r1	PROPN
ejpam-5871	476	6	,	,	PUNCT
ejpam-5871	476	7	r2	r2	PROPN
ejpam-5871	476	8	)	)	PUNCT
ejpam-5871	476	9	=	=	SYM
ejpam-5871	476	10	∅(r1)⅁(r2	∅(r1)⅁(r2	NOUN
ejpam-5871	476	11	)	)	PUNCT
ejpam-5871	477	1	+	+	NOUN
ejpam-5871	477	2	∅(r2)⅁(r1	∅(r2)⅁(r1	ADJ
ejpam-5871	477	3	)	)	PUNCT
ejpam-5871	477	4	.	.	PUNCT
ejpam-5871	478	1	a.	a.	PROPN
ejpam-5871	478	2	mehmood	mehmood	PROPN
ejpam-5871	478	3	et	et	PROPN
ejpam-5871	478	4	al	al	PROPN
ejpam-5871	478	5	.	.	PUNCT
ejpam-5871	478	6	/	/	SYM
ejpam-5871	478	7	eur	eur	PROPN
ejpam-5871	478	8	.	.	PUNCT
ejpam-5871	479	1	j.	j.	PROPN
ejpam-5871	479	2	pure	pure	PROPN
ejpam-5871	479	3	appl	appl	PROPN
ejpam-5871	479	4	.	.	PROPN
ejpam-5871	479	5	math	math	PROPN
ejpam-5871	479	6	,	,	PUNCT
ejpam-5871	479	7	18	18	NUM
ejpam-5871	479	8	(	(	PUNCT
ejpam-5871	479	9	2	2	NUM
ejpam-5871	479	10	)	)	PUNCT
ejpam-5871	479	11	(	(	PUNCT
ejpam-5871	479	12	2025	2025	NUM
ejpam-5871	479	13	)	)	PUNCT
ejpam-5871	479	14	,	,	PUNCT
ejpam-5871	479	15	5871	5871	NUM
ejpam-5871	479	16	18	18	NUM
ejpam-5871	479	17	of	of	ADP
ejpam-5871	479	18	26	26	NUM
ejpam-5871	479	19	proof	proof	NOUN
ejpam-5871	479	20	.	.	PUNCT
ejpam-5871	480	1	since	since	SCONJ
ejpam-5871	480	2	∅,⅁	∅,⅁	PROPN
ejpam-5871	480	3	∈	∈	PROPN
ejpam-5871	480	4	sigx([r1	sigx([r1	PROPN
ejpam-5871	480	5	,	,	PUNCT
ejpam-5871	480	6	r2	r2	PROPN
ejpam-5871	480	7	]	]	PUNCT
ejpam-5871	480	8	,	,	PUNCT
ejpam-5871	480	9	r	r	NOUN
ejpam-5871	480	10	+	+	NOUN
ejpam-5871	480	11	)	)	PUNCT
ejpam-5871	480	12	,	,	PUNCT
ejpam-5871	480	13	then	then	ADV
ejpam-5871	480	14	∅	∅	NOUN
ejpam-5871	480	15	(	(	PUNCT
ejpam-5871	480	16	⋋−1	⋋−1	X
ejpam-5871	480	17	(	(	PUNCT
ejpam-5871	480	18	θ	θ	PROPN
ejpam-5871	480	19	⋋s+1	⋋s+1	PROPN
ejpam-5871	480	20	(	(	PUNCT
ejpam-5871	480	21	r1	r1	PROPN
ejpam-5871	480	22	)	)	PUNCT
ejpam-5871	480	23	+	+	CCONJ
ejpam-5871	480	24	(	(	PUNCT
ejpam-5871	480	25	1−	1−	NUM
ejpam-5871	480	26	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	480	27	(	(	PUNCT
ejpam-5871	480	28	r2	r2	PROPN
ejpam-5871	480	29	)	)	PUNCT
ejpam-5871	480	30	)	)	PUNCT
ejpam-5871	480	31	1	1	NUM
ejpam-5871	480	32	s+1	s+1	PROPN
ejpam-5871	480	33	)	)	PUNCT
ejpam-5871	480	34	⊇	⊇	PROPN
ejpam-5871	480	35	℧	℧	PROPN
ejpam-5871	480	36	1(θ)∅(r1	1(θ)∅(r1	NUM
ejpam-5871	480	37	)	)	PUNCT
ejpam-5871	480	38	+	+	CCONJ
ejpam-5871	480	39	℧	℧	PROPN
ejpam-5871	480	40	1(1−	1(1−	NUM
ejpam-5871	480	41	θ)∅(r2	θ)∅(r2	NOUN
ejpam-5871	480	42	)	)	PUNCT
ejpam-5871	480	43	⅁	⅁	NOUN
ejpam-5871	480	44	(	(	PUNCT
ejpam-5871	480	45	⋋−1	⋋−1	X
ejpam-5871	480	46	(	(	PUNCT
ejpam-5871	480	47	θ	θ	PROPN
ejpam-5871	480	48	⋋s+1	⋋s+1	PROPN
ejpam-5871	480	49	(	(	PUNCT
ejpam-5871	480	50	r1	r1	PROPN
ejpam-5871	480	51	)	)	PUNCT
ejpam-5871	480	52	+	+	CCONJ
ejpam-5871	480	53	(	(	PUNCT
ejpam-5871	480	54	1−	1−	NUM
ejpam-5871	480	55	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	480	56	(	(	PUNCT
ejpam-5871	480	57	r2	r2	PROPN
ejpam-5871	480	58	)	)	PUNCT
ejpam-5871	480	59	)	)	PUNCT
ejpam-5871	480	60	1	1	NUM
ejpam-5871	481	1	s+1	s+1	NOUN
ejpam-5871	481	2	⊇	⊇	NOUN
ejpam-5871	481	3	℧	℧	NOUN
ejpam-5871	481	4	2(θ)⅁(r1	2(θ)⅁(r1	NUM
ejpam-5871	481	5	)	)	PUNCT
ejpam-5871	481	6	+	+	CCONJ
ejpam-5871	481	7	℧	℧	NOUN
ejpam-5871	481	8	2(1−	2(1−	NUM
ejpam-5871	481	9	θ)⅁(r2	θ)⅁(r2	NOUN
ejpam-5871	481	10	)	)	PUNCT
ejpam-5871	481	11	.	.	PUNCT
ejpam-5871	482	1	by	by	ADP
ejpam-5871	482	2	multiplying	multiply	VERB
ejpam-5871	482	3	,	,	PUNCT
ejpam-5871	482	4	we	we	PRON
ejpam-5871	482	5	have	have	VERB
ejpam-5871	482	6	∅	∅	NOUN
ejpam-5871	482	7	(	(	PUNCT
ejpam-5871	482	8	⋋−1	⋋−1	X
ejpam-5871	482	9	(	(	PUNCT
ejpam-5871	482	10	θ	θ	PROPN
ejpam-5871	482	11	⋋s+1	⋋s+1	PROPN
ejpam-5871	482	12	(	(	PUNCT
ejpam-5871	482	13	r1	r1	PROPN
ejpam-5871	482	14	)	)	PUNCT
ejpam-5871	482	15	+	+	CCONJ
ejpam-5871	482	16	(	(	PUNCT
ejpam-5871	482	17	1−	1−	NUM
ejpam-5871	482	18	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	482	19	(	(	PUNCT
ejpam-5871	482	20	r2	r2	PROPN
ejpam-5871	482	21	)	)	PUNCT
ejpam-5871	482	22	)	)	PUNCT
ejpam-5871	482	23	1	1	NUM
ejpam-5871	482	24	s+1	s+1	NOUN
ejpam-5871	482	25	)	)	PUNCT
ejpam-5871	482	26	⅁	⅁	PROPN
ejpam-5871	482	27	(	(	PUNCT
ejpam-5871	482	28	⋋−1	⋋−1	X
ejpam-5871	482	29	(	(	PUNCT
ejpam-5871	482	30	θ	θ	PROPN
ejpam-5871	482	31	⋋s+1	⋋s+1	PROPN
ejpam-5871	482	32	(	(	PUNCT
ejpam-5871	482	33	r1	r1	PROPN
ejpam-5871	482	34	)	)	PUNCT
ejpam-5871	482	35	+	+	CCONJ
ejpam-5871	482	36	(	(	PUNCT
ejpam-5871	482	37	1−	1−	NUM
ejpam-5871	482	38	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	482	39	(	(	PUNCT
ejpam-5871	482	40	r2	r2	PROPN
ejpam-5871	482	41	)	)	PUNCT
ejpam-5871	482	42	)	)	PUNCT
ejpam-5871	482	43	1	1	NUM
ejpam-5871	482	44	s+1	s+1	PROPN
ejpam-5871	482	45	)	)	PUNCT
ejpam-5871	482	46	⊇	⊇	PROPN
ejpam-5871	482	47	℧	℧	PROPN
ejpam-5871	482	48	1(θ)	1(θ)	NUM
ejpam-5871	482	49	℧	℧	ADP
ejpam-5871	482	50	2(θ)∅(r1)⅁(r1	2(θ)∅(r1)⅁(r1	NUM
ejpam-5871	482	51	)	)	PUNCT
ejpam-5871	483	1	+	+	CCONJ
ejpam-5871	483	2	℧	℧	NOUN
ejpam-5871	483	3	1(θ)	1(θ)	NUM
ejpam-5871	483	4	℧	℧	NOUN
ejpam-5871	483	5	2(1−	2(1−	NUM
ejpam-5871	483	6	θ)∅(r1)⅁(r2	θ)∅(r1)⅁(r2	NUM
ejpam-5871	483	7	)	)	PUNCT
ejpam-5871	484	1	+	+	CCONJ
ejpam-5871	484	2	℧	℧	PROPN
ejpam-5871	484	3	1(1−	1(1−	NUM
ejpam-5871	484	4	θ)	θ)	PROPN
ejpam-5871	484	5	℧	℧	NOUN
ejpam-5871	484	6	2(θ)∅(r2)⅁(r1	2(θ)∅(r2)⅁(r1	NUM
ejpam-5871	484	7	)	)	PUNCT
ejpam-5871	484	8	+	+	CCONJ
ejpam-5871	484	9	℧	℧	PROPN
ejpam-5871	484	10	1(1−	1(1−	NUM
ejpam-5871	484	11	θ)	θ)	PROPN
ejpam-5871	484	12	℧	℧	PROPN
ejpam-5871	484	13	2(1−	2(1−	PROPN
ejpam-5871	484	14	θ)∅(r2)⅁(r2	θ)∅(r2)⅁(r2	PROPN
ejpam-5871	484	15	)	)	PUNCT
ejpam-5871	484	16	.	.	PUNCT
ejpam-5871	485	1	(	(	PUNCT
ejpam-5871	485	2	32	32	NUM
ejpam-5871	485	3	)	)	PUNCT
ejpam-5871	485	4	similarly	similarly	ADV
ejpam-5871	485	5	,	,	PUNCT
ejpam-5871	485	6	∅	∅	NOUN
ejpam-5871	485	7	(	(	PUNCT
ejpam-5871	485	8	⋋−1	⋋−1	X
ejpam-5871	485	9	(	(	PUNCT
ejpam-5871	485	10	(	(	PUNCT
ejpam-5871	485	11	1−	1−	NUM
ejpam-5871	485	12	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	485	13	(	(	PUNCT
ejpam-5871	485	14	r1	r1	PROPN
ejpam-5871	485	15	)	)	PUNCT
ejpam-5871	485	16	+	+	NUM
ejpam-5871	485	17	θ	θ	PUNCT
ejpam-5871	485	18	⋋s+1	⋋s+1	VERB
ejpam-5871	485	19	(	(	PUNCT
ejpam-5871	485	20	r2	r2	PROPN
ejpam-5871	485	21	)	)	PUNCT
ejpam-5871	485	22	)	)	PUNCT
ejpam-5871	485	23	1	1	NUM
ejpam-5871	485	24	s+1	s+1	NOUN
ejpam-5871	485	25	)	)	PUNCT
ejpam-5871	485	26	⅁	⅁	PROPN
ejpam-5871	485	27	(	(	PUNCT
ejpam-5871	485	28	⋋−1	⋋−1	X
ejpam-5871	485	29	(	(	PUNCT
ejpam-5871	485	30	(	(	PUNCT
ejpam-5871	485	31	1−	1−	NUM
ejpam-5871	485	32	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	485	33	(	(	PUNCT
ejpam-5871	485	34	r1	r1	PROPN
ejpam-5871	485	35	)	)	PUNCT
ejpam-5871	485	36	+	+	NUM
ejpam-5871	485	37	θ	θ	PUNCT
ejpam-5871	485	38	⋋s+1	⋋s+1	VERB
ejpam-5871	485	39	(	(	PUNCT
ejpam-5871	485	40	r2	r2	PROPN
ejpam-5871	485	41	)	)	PUNCT
ejpam-5871	485	42	)	)	PUNCT
ejpam-5871	485	43	1	1	NUM
ejpam-5871	485	44	s+1	s+1	PROPN
ejpam-5871	485	45	)	)	PUNCT
ejpam-5871	485	46	⊇	⊇	PROPN
ejpam-5871	485	47	℧	℧	PROPN
ejpam-5871	485	48	1(1−	1(1−	NUM
ejpam-5871	485	49	θ)	θ)	PROPN
ejpam-5871	485	50	℧	℧	PROPN
ejpam-5871	485	51	2(1−	2(1−	PROPN
ejpam-5871	485	52	θ)∅(r1)⅁(r1	θ)∅(r1)⅁(r1	PROPN
ejpam-5871	485	53	)	)	PUNCT
ejpam-5871	486	1	+	+	CCONJ
ejpam-5871	486	2	℧	℧	PROPN
ejpam-5871	486	3	1(1−	1(1−	NUM
ejpam-5871	486	4	θ)	θ)	PROPN
ejpam-5871	486	5	℧	℧	NOUN
ejpam-5871	486	6	2(θ)∅(r1)⅁(r2	2(θ)∅(r1)⅁(r2	NUM
ejpam-5871	486	7	)	)	PUNCT
ejpam-5871	486	8	+	+	CCONJ
ejpam-5871	486	9	℧	℧	NOUN
ejpam-5871	486	10	1(θ)	1(θ)	NUM
ejpam-5871	486	11	℧	℧	SYM
ejpam-5871	486	12	2(1−	2(1−	NUM
ejpam-5871	486	13	θ)∅(r2)⅁(r1	θ)∅(r2)⅁(r1	NOUN
ejpam-5871	486	14	)	)	PUNCT
ejpam-5871	487	1	+	+	CCONJ
ejpam-5871	487	2	℧	℧	NOUN
ejpam-5871	487	3	1(θ)	1(θ)	NUM
ejpam-5871	487	4	℧	℧	NOUN
ejpam-5871	487	5	2(θ)∅(r2)⅁(r2	2(θ)∅(r2)⅁(r2	NUM
ejpam-5871	487	6	)	)	PUNCT
ejpam-5871	487	7	.	.	PUNCT
ejpam-5871	488	1	(	(	PUNCT
ejpam-5871	488	2	33	33	NUM
ejpam-5871	488	3	)	)	PUNCT
ejpam-5871	488	4	adding	add	VERB
ejpam-5871	488	5	(	(	PUNCT
ejpam-5871	488	6	32	32	NUM
ejpam-5871	488	7	)	)	PUNCT
ejpam-5871	488	8	and	and	CCONJ
ejpam-5871	488	9	(	(	PUNCT
ejpam-5871	488	10	33	33	NUM
ejpam-5871	488	11	)	)	PUNCT
ejpam-5871	488	12	inclusions	inclusion	NOUN
ejpam-5871	488	13	and	and	CCONJ
ejpam-5871	488	14	multiplying	multiply	VERB
ejpam-5871	488	15	both	both	DET
ejpam-5871	488	16	sides	side	NOUN
ejpam-5871	488	17	by	by	ADP
ejpam-5871	488	18	(	(	PUNCT
ejpam-5871	488	19	s+1)−	s+1)−	PROPN
ejpam-5871	488	20	β	β	PROPN
ejpam-5871	488	21	k	k	PROPN
ejpam-5871	488	22	kγk(β	kγk(β	PROPN
ejpam-5871	488	23	)	)	PUNCT
ejpam-5871	488	24	θ	θ	PROPN
ejpam-5871	488	25	β	β	X
ejpam-5871	488	26	k	k	X
ejpam-5871	488	27	−1	−1	NOUN
ejpam-5871	488	28	also	also	ADV
ejpam-5871	488	29	taking	take	VERB
ejpam-5871	488	30	the	the	DET
ejpam-5871	488	31	integration	integration	NOUN
ejpam-5871	488	32	over	over	ADP
ejpam-5871	488	33	[	[	X
ejpam-5871	488	34	0	0	NUM
ejpam-5871	488	35	,	,	PUNCT
ejpam-5871	488	36	1	1	NUM
ejpam-5871	488	37	]	]	PUNCT
ejpam-5871	488	38	w.r.t	w.r.t	NOUN
ejpam-5871	488	39	”	"	PUNCT
ejpam-5871	488	40	θ”red	θ”re	VERB
ejpam-5871	488	41	,	,	PUNCT
ejpam-5871	488	42	then	then	ADV
ejpam-5871	488	43	we	we	PRON
ejpam-5871	488	44	have	have	VERB
ejpam-5871	488	45	(	(	PUNCT
ejpam-5871	488	46	s+	s+	NUM
ejpam-5871	488	47	1)−	1)−	PROPN
ejpam-5871	488	48	β	β	X
ejpam-5871	488	49	k	k	PROPN
ejpam-5871	488	50	kγk(β	kγk(β	PROPN
ejpam-5871	488	51	)	)	PUNCT
ejpam-5871	488	52	∫	∫	PROPN
ejpam-5871	489	1	1	1	NUM
ejpam-5871	489	2	0	0	NUM
ejpam-5871	489	3	θ	θ	PROPN
ejpam-5871	489	4	β	β	X
ejpam-5871	489	5	k	k	X
ejpam-5871	489	6	−1∅	−1∅	PROPN
ejpam-5871	489	7	(	(	PUNCT
ejpam-5871	489	8	⋋−1	⋋−1	ADJ
ejpam-5871	489	9	(	(	PUNCT
ejpam-5871	489	10	θ	θ	PROPN
ejpam-5871	489	11	⋋s+1	⋋s+1	PROPN
ejpam-5871	489	12	(	(	PUNCT
ejpam-5871	489	13	r1	r1	PROPN
ejpam-5871	489	14	)	)	PUNCT
ejpam-5871	489	15	+	+	CCONJ
ejpam-5871	489	16	(	(	PUNCT
ejpam-5871	489	17	1−	1−	NUM
ejpam-5871	489	18	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	489	19	(	(	PUNCT
ejpam-5871	489	20	r2	r2	PROPN
ejpam-5871	489	21	)	)	PUNCT
ejpam-5871	489	22	)	)	PUNCT
ejpam-5871	489	23	1	1	NUM
ejpam-5871	489	24	s+1	s+1	NOUN
ejpam-5871	489	25	)	)	PUNCT
ejpam-5871	489	26	×	×	NOUN
ejpam-5871	489	27	⅁	⅁	NOUN
ejpam-5871	489	28	(	(	PUNCT
ejpam-5871	489	29	⋋−1	⋋−1	X
ejpam-5871	489	30	(	(	PUNCT
ejpam-5871	489	31	θ	θ	PROPN
ejpam-5871	489	32	⋋s+1	⋋s+1	PROPN
ejpam-5871	489	33	(	(	PUNCT
ejpam-5871	489	34	r1	r1	PROPN
ejpam-5871	489	35	)	)	PUNCT
ejpam-5871	489	36	+	+	CCONJ
ejpam-5871	489	37	(	(	PUNCT
ejpam-5871	489	38	1−	1−	NUM
ejpam-5871	489	39	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	489	40	(	(	PUNCT
ejpam-5871	489	41	r2	r2	PROPN
ejpam-5871	489	42	)	)	PUNCT
ejpam-5871	489	43	)	)	PUNCT
ejpam-5871	489	44	1	1	NUM
ejpam-5871	489	45	s+1	s+1	NOUN
ejpam-5871	489	46	)	)	PUNCT
ejpam-5871	489	47	dθ	dθ	PROPN
ejpam-5871	489	48	+	+	X
ejpam-5871	489	49	(	(	PUNCT
ejpam-5871	489	50	s+	s+	X
ejpam-5871	489	51	1)−	1)−	PROPN
ejpam-5871	489	52	β	β	X
ejpam-5871	489	53	k	k	PROPN
ejpam-5871	489	54	kγk(β	kγk(β	PROPN
ejpam-5871	489	55	)	)	PUNCT
ejpam-5871	489	56	∫	∫	PROPN
ejpam-5871	490	1	1	1	NUM
ejpam-5871	490	2	0	0	NUM
ejpam-5871	490	3	θ	θ	PROPN
ejpam-5871	490	4	β	β	X
ejpam-5871	490	5	k	k	X
ejpam-5871	490	6	−1∅	−1∅	PROPN
ejpam-5871	490	7	(	(	PUNCT
ejpam-5871	490	8	⋋−1	⋋−1	ADJ
ejpam-5871	490	9	(	(	PUNCT
ejpam-5871	490	10	(	(	PUNCT
ejpam-5871	490	11	1−	1−	NUM
ejpam-5871	490	12	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	490	13	(	(	PUNCT
ejpam-5871	490	14	r1	r1	PROPN
ejpam-5871	490	15	)	)	PUNCT
ejpam-5871	490	16	+	+	NUM
ejpam-5871	490	17	θ	θ	PUNCT
ejpam-5871	490	18	⋋s+1	⋋s+1	VERB
ejpam-5871	490	19	(	(	PUNCT
ejpam-5871	490	20	r2	r2	PROPN
ejpam-5871	490	21	)	)	PUNCT
ejpam-5871	490	22	)	)	PUNCT
ejpam-5871	490	23	1	1	NUM
ejpam-5871	490	24	s+1	s+1	NOUN
ejpam-5871	490	25	)	)	PUNCT
ejpam-5871	490	26	×	×	NOUN
ejpam-5871	490	27	⅁	⅁	NOUN
ejpam-5871	490	28	(	(	PUNCT
ejpam-5871	490	29	⋋−1	⋋−1	X
ejpam-5871	490	30	(	(	PUNCT
ejpam-5871	490	31	(	(	PUNCT
ejpam-5871	490	32	1−	1−	NUM
ejpam-5871	490	33	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	490	34	(	(	PUNCT
ejpam-5871	490	35	r1	r1	PROPN
ejpam-5871	490	36	)	)	PUNCT
ejpam-5871	490	37	+	+	NUM
ejpam-5871	490	38	θ	θ	PUNCT
ejpam-5871	490	39	⋋s+1	⋋s+1	VERB
ejpam-5871	490	40	(	(	PUNCT
ejpam-5871	490	41	r2	r2	PROPN
ejpam-5871	490	42	)	)	PUNCT
ejpam-5871	490	43	)	)	PUNCT
ejpam-5871	490	44	1	1	NUM
ejpam-5871	490	45	s+1	s+1	NOUN
ejpam-5871	490	46	)	)	PUNCT
ejpam-5871	490	47	dθ	dθ	PROPN
ejpam-5871	490	48	⊇	⊇	PROPN
ejpam-5871	490	49	(	(	PUNCT
ejpam-5871	490	50	s+	s+	NUM
ejpam-5871	490	51	1)−	1)−	PROPN
ejpam-5871	490	52	β	β	X
ejpam-5871	490	53	k	k	PROPN
ejpam-5871	490	54	kγk(β	kγk(β	PROPN
ejpam-5871	490	55	)	)	PUNCT
ejpam-5871	490	56	∫	∫	PROPN
ejpam-5871	490	57	1	1	NUM
ejpam-5871	490	58	0	0	NUM
ejpam-5871	490	59	θ	θ	PROPN
ejpam-5871	490	60	β	β	X
ejpam-5871	490	61	k	k	X
ejpam-5871	490	62	−1[	−1[	X
ejpam-5871	490	63	℧	℧	PROPN
ejpam-5871	490	64	1(θ)	1(θ)	NUM
ejpam-5871	490	65	℧	℧	NOUN
ejpam-5871	490	66	2(θ	2(θ	NUM
ejpam-5871	490	67	)	)	PUNCT
ejpam-5871	491	1	+	+	CCONJ
ejpam-5871	491	2	℧	℧	PROPN
ejpam-5871	491	3	1(1−	1(1−	NUM
ejpam-5871	491	4	θ)	θ)	PROPN
ejpam-5871	491	5	℧	℧	NOUN
ejpam-5871	491	6	2(1−	2(1−	NOUN
ejpam-5871	491	7	θ)][∅(r1)⅁(r1	θ)][∅(r1)⅁(r1	NUM
ejpam-5871	491	8	)	)	PUNCT
ejpam-5871	492	1	+	+	NOUN
ejpam-5871	492	2	∅(r2)⅁(r2)]dθ	∅(r2)⅁(r2)]dθ	NOUN
ejpam-5871	492	3	+	+	CCONJ
ejpam-5871	492	4	(	(	PUNCT
ejpam-5871	492	5	s+	s+	X
ejpam-5871	492	6	1)−	1)−	PROPN
ejpam-5871	492	7	β	β	X
ejpam-5871	492	8	k	k	PROPN
ejpam-5871	492	9	kγk(β	kγk(β	PROPN
ejpam-5871	492	10	)	)	PUNCT
ejpam-5871	492	11	∫	∫	PROPN
ejpam-5871	492	12	1	1	NUM
ejpam-5871	492	13	0	0	NUM
ejpam-5871	492	14	θ	θ	PROPN
ejpam-5871	492	15	β	β	X
ejpam-5871	492	16	k	k	X
ejpam-5871	492	17	−1[	−1[	X
ejpam-5871	492	18	℧	℧	PROPN
ejpam-5871	492	19	1(θ)	1(θ)	NUM
ejpam-5871	492	20	℧	℧	SYM
ejpam-5871	492	21	2(1−	2(1−	NUM
ejpam-5871	492	22	θ	θ	NOUN
ejpam-5871	492	23	)	)	PUNCT
ejpam-5871	492	24	+	+	CCONJ
ejpam-5871	492	25	℧	℧	PROPN
ejpam-5871	492	26	1(1−	1(1−	NUM
ejpam-5871	492	27	θ)	θ)	PROPN
ejpam-5871	492	28	℧	℧	NOUN
ejpam-5871	492	29	2(θ)][∅(r1)⅁(r2	2(θ)][∅(r1)⅁(r2	NUM
ejpam-5871	492	30	)	)	PUNCT
ejpam-5871	493	1	+	+	NOUN
ejpam-5871	493	2	∅(r2)⅁(r1)]dθ	∅(r2)⅁(r1)]dθ	NOUN
ejpam-5871	493	3	.	.	PUNCT
ejpam-5871	494	1	substituting	substitute	VERB
ejpam-5871	494	2	⋋s+1(χ	⋋s+1(χ	PRON
ejpam-5871	494	3	)	)	PUNCT
ejpam-5871	494	4	=	=	SYM
ejpam-5871	495	1	θ	θ	X
ejpam-5871	495	2	⋋s+1	⋋s+1	PUNCT
ejpam-5871	495	3	(	(	PUNCT
ejpam-5871	495	4	r1	r1	PROPN
ejpam-5871	495	5	)	)	PUNCT
ejpam-5871	495	6	+	+	CCONJ
ejpam-5871	495	7	(	(	PUNCT
ejpam-5871	495	8	1−	1−	NUM
ejpam-5871	495	9	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	495	10	(	(	PUNCT
ejpam-5871	495	11	r2)red	r2)re	VERB
ejpam-5871	495	12	,	,	PUNCT
ejpam-5871	495	13	then	then	ADV
ejpam-5871	495	14	we	we	PRON
ejpam-5871	495	15	have	have	VERB
ejpam-5871	495	16	=	=	SYM
ejpam-5871	495	17	1	1	NUM
ejpam-5871	495	18	(	(	PUNCT
ejpam-5871	495	19	⋋s+1(r2)−⋋s+1(r1	⋋s+1(r2)−⋋s+1(r1	NOUN
ejpam-5871	495	20	)	)	PUNCT
ejpam-5871	495	21	)	)	PUNCT
ejpam-5871	496	1	β	β	X
ejpam-5871	496	2	k	k	X
ejpam-5871	497	1	[	[	PUNCT
ejpam-5871	497	2	s	s	X
ejpam-5871	497	3	kz	kz	PROPN
ejpam-5871	497	4	β	β	PROPN
ejpam-5871	497	5	r+1	r+1	PROPN
ejpam-5871	497	6	∅⅁(r2	∅⅁(r2	NOUN
ejpam-5871	497	7	)	)	PUNCT
ejpam-5871	498	1	+	+	SYM
ejpam-5871	498	2	s	s	VERB
ejpam-5871	498	3	kz	kz	PROPN
ejpam-5871	498	4	β	β	PROPN
ejpam-5871	498	5	r−2	r−2	PROPN
ejpam-5871	498	6	∅⅁(r1	∅⅁(r1	PROPN
ejpam-5871	498	7	)	)	PUNCT
ejpam-5871	498	8	]	]	PUNCT
ejpam-5871	499	1	⊇	⊇	PROPN
ejpam-5871	499	2	p	p	X
ejpam-5871	499	3	(	(	PUNCT
ejpam-5871	499	4	r1	r1	PROPN
ejpam-5871	499	5	,	,	PUNCT
ejpam-5871	499	6	r2	r2	PROPN
ejpam-5871	499	7	)	)	PUNCT
ejpam-5871	499	8	(	(	PUNCT
ejpam-5871	499	9	s+	s+	NUM
ejpam-5871	499	10	1)−	1)−	PROPN
ejpam-5871	499	11	β	β	X
ejpam-5871	499	12	k	k	PROPN
ejpam-5871	499	13	kγk(β	kγk(β	PROPN
ejpam-5871	499	14	)	)	PUNCT
ejpam-5871	499	15	∫	∫	PROPN
ejpam-5871	499	16	1	1	NUM
ejpam-5871	499	17	0	0	NUM
ejpam-5871	499	18	θ	θ	PROPN
ejpam-5871	499	19	β	β	X
ejpam-5871	499	20	k	k	X
ejpam-5871	499	21	−1[	−1[	X
ejpam-5871	499	22	℧	℧	PROPN
ejpam-5871	499	23	1(θ)	1(θ)	NUM
ejpam-5871	499	24	℧	℧	NOUN
ejpam-5871	499	25	2(θ	2(θ	NUM
ejpam-5871	499	26	)	)	PUNCT
ejpam-5871	500	1	+	+	CCONJ
ejpam-5871	500	2	℧	℧	PROPN
ejpam-5871	500	3	1(1−	1(1−	NUM
ejpam-5871	500	4	θ)	θ)	PROPN
ejpam-5871	500	5	℧	℧	NOUN
ejpam-5871	500	6	2(1−	2(1−	NUM
ejpam-5871	500	7	θ)]dθ	θ)]dθ	NOUN
ejpam-5871	500	8	+	+	NOUN
ejpam-5871	500	9	q(r1	q(r1	ADJ
ejpam-5871	500	10	,	,	PUNCT
ejpam-5871	500	11	r2	r2	PROPN
ejpam-5871	500	12	)	)	PUNCT
ejpam-5871	500	13	(	(	PUNCT
ejpam-5871	500	14	s+	s+	NUM
ejpam-5871	500	15	1)−	1)−	PROPN
ejpam-5871	500	16	β	β	X
ejpam-5871	500	17	k	k	PROPN
ejpam-5871	500	18	kγk(β	kγk(β	PROPN
ejpam-5871	500	19	)	)	PUNCT
ejpam-5871	500	20	∫	∫	PROPN
ejpam-5871	500	21	1	1	NUM
ejpam-5871	500	22	0	0	NUM
ejpam-5871	500	23	θ	θ	PROPN
ejpam-5871	500	24	β	β	X
ejpam-5871	500	25	k	k	X
ejpam-5871	500	26	−1[	−1[	X
ejpam-5871	500	27	℧	℧	PROPN
ejpam-5871	500	28	1(θ)	1(θ)	NUM
ejpam-5871	500	29	℧	℧	SYM
ejpam-5871	500	30	2(1−	2(1−	NUM
ejpam-5871	500	31	θ	θ	NOUN
ejpam-5871	500	32	)	)	PUNCT
ejpam-5871	500	33	+	+	CCONJ
ejpam-5871	500	34	℧	℧	PROPN
ejpam-5871	500	35	1(1−	1(1−	NUM
ejpam-5871	500	36	θ)	θ)	NOUN
ejpam-5871	500	37	℧	℧	NOUN
ejpam-5871	500	38	2(θ)]dθ	2(θ)]dθ	NOUN
ejpam-5871	500	39	.	.	PUNCT
ejpam-5871	501	1	this	this	PRON
ejpam-5871	501	2	complete	complete	VERB
ejpam-5871	501	3	our	our	PRON
ejpam-5871	501	4	required	required	ADJ
ejpam-5871	501	5	relation	relation	NOUN
ejpam-5871	501	6	.	.	PUNCT
ejpam-5871	502	1	a.	a.	PROPN
ejpam-5871	502	2	mehmood	mehmood	PROPN
ejpam-5871	502	3	et	et	PROPN
ejpam-5871	502	4	al	al	PROPN
ejpam-5871	502	5	.	.	PUNCT
ejpam-5871	502	6	/	/	SYM
ejpam-5871	502	7	eur	eur	PROPN
ejpam-5871	502	8	.	.	PUNCT
ejpam-5871	503	1	j.	j.	PROPN
ejpam-5871	503	2	pure	pure	PROPN
ejpam-5871	503	3	appl	appl	PROPN
ejpam-5871	503	4	.	.	PROPN
ejpam-5871	503	5	math	math	PROPN
ejpam-5871	503	6	,	,	PUNCT
ejpam-5871	503	7	18	18	NUM
ejpam-5871	503	8	(	(	PUNCT
ejpam-5871	503	9	2	2	NUM
ejpam-5871	503	10	)	)	PUNCT
ejpam-5871	503	11	(	(	PUNCT
ejpam-5871	503	12	2025	2025	NUM
ejpam-5871	503	13	)	)	PUNCT
ejpam-5871	503	14	,	,	PUNCT
ejpam-5871	503	15	5871	5871	NUM
ejpam-5871	503	16	19	19	NUM
ejpam-5871	503	17	of	of	ADP
ejpam-5871	503	18	26	26	NUM
ejpam-5871	503	19	corollary	corollary	ADJ
ejpam-5871	503	20	5	5	NUM
ejpam-5871	503	21	.	.	PUNCT
ejpam-5871	504	1	if	if	SCONJ
ejpam-5871	504	2	we	we	PRON
ejpam-5871	504	3	fix	fix	VERB
ejpam-5871	504	4	℧	℧	PROPN
ejpam-5871	504	5	(	(	PUNCT
ejpam-5871	504	6	θ	θ	NOUN
ejpam-5871	504	7	)	)	PUNCT
ejpam-5871	504	8	=	=	SYM
ejpam-5871	504	9	θ	θ	PROPN
ejpam-5871	504	10	in	in	ADP
ejpam-5871	504	11	theorem	theorem	NOUN
ejpam-5871	504	12	8	8	NUM
ejpam-5871	504	13	,	,	PUNCT
ejpam-5871	504	14	we	we	PRON
ejpam-5871	504	15	possess	possess	VERB
ejpam-5871	504	16	1	1	NUM
ejpam-5871	504	17	(	(	PUNCT
ejpam-5871	504	18	⋋s+1(r2)−⋋s+1(r1	⋋s+1(r2)−⋋s+1(r1	NOUN
ejpam-5871	504	19	)	)	PUNCT
ejpam-5871	504	20	)	)	PUNCT
ejpam-5871	505	1	β	β	X
ejpam-5871	505	2	k	k	X
ejpam-5871	506	1	[	[	PUNCT
ejpam-5871	506	2	s	s	X
ejpam-5871	506	3	kz	kz	PROPN
ejpam-5871	506	4	β	β	PROPN
ejpam-5871	506	5	r+1	r+1	PROPN
ejpam-5871	506	6	∅⅁(r2	∅⅁(r2	NOUN
ejpam-5871	506	7	)	)	PUNCT
ejpam-5871	507	1	+	+	SYM
ejpam-5871	507	2	s	s	VERB
ejpam-5871	507	3	kz	kz	PROPN
ejpam-5871	507	4	β	β	PROPN
ejpam-5871	507	5	r−2	r−2	PROPN
ejpam-5871	507	6	∅⅁(r1	∅⅁(r1	PROPN
ejpam-5871	507	7	)	)	PUNCT
ejpam-5871	507	8	]	]	PUNCT
ejpam-5871	508	1	⊇	⊇	X
ejpam-5871	508	2	(	(	PUNCT
ejpam-5871	508	3	s+	s+	NUM
ejpam-5871	508	4	1)−	1)−	PROPN
ejpam-5871	508	5	β	β	X
ejpam-5871	508	6	k	k	PROPN
ejpam-5871	508	7	kγk(β	kγk(β	PROPN
ejpam-5871	508	8	)	)	PUNCT
ejpam-5871	508	9	[	[	PUNCT
ejpam-5871	508	10	p	p	X
ejpam-5871	508	11	(	(	PUNCT
ejpam-5871	508	12	r1	r1	PROPN
ejpam-5871	508	13	,	,	PUNCT
ejpam-5871	508	14	r2	r2	PROPN
ejpam-5871	508	15	)	)	PUNCT
ejpam-5871	508	16	β2	β2	NOUN
ejpam-5871	508	17	k2	k2	NOUN
ejpam-5871	508	18	+	+	CCONJ
ejpam-5871	508	19	β	β	X
ejpam-5871	508	20	k	k	X
ejpam-5871	509	1	+	+	CCONJ
ejpam-5871	509	2	1	1	NUM
ejpam-5871	509	3	(	(	PUNCT
ejpam-5871	509	4	βk	βk	ADP
ejpam-5871	509	5	+	+	NOUN
ejpam-5871	509	6	2)(βk	2)(βk	NUM
ejpam-5871	509	7	+	+	CCONJ
ejpam-5871	509	8	1)(βk	1)(βk	NUM
ejpam-5871	509	9	)	)	PUNCT
ejpam-5871	510	1	+	+	VERB
ejpam-5871	510	2	q(r1	q(r1	ADJ
ejpam-5871	510	3	,	,	PUNCT
ejpam-5871	510	4	r2	r2	PROPN
ejpam-5871	510	5	)	)	PUNCT
ejpam-5871	510	6	2	2	NUM
ejpam-5871	510	7	(	(	PUNCT
ejpam-5871	510	8	βk	βk	ADP
ejpam-5871	510	9	+	+	NOUN
ejpam-5871	510	10	2)(βk	2)(βk	NUM
ejpam-5871	510	11	+	+	CCONJ
ejpam-5871	510	12	1	1	NUM
ejpam-5871	510	13	)	)	PUNCT
ejpam-5871	510	14	]	]	PUNCT
ejpam-5871	510	15	,	,	PUNCT
ejpam-5871	510	16	where	where	SCONJ
ejpam-5871	510	17	,	,	PUNCT
ejpam-5871	510	18	p	p	X
ejpam-5871	510	19	(	(	PUNCT
ejpam-5871	510	20	r1	r1	PROPN
ejpam-5871	510	21	,	,	PUNCT
ejpam-5871	510	22	r2	r2	PROPN
ejpam-5871	510	23	)	)	PUNCT
ejpam-5871	510	24	=	=	SYM
ejpam-5871	510	25	∅(r1)⅁(r1	∅(r1)⅁(r1	NOUN
ejpam-5871	510	26	)	)	PUNCT
ejpam-5871	511	1	+	+	NUM
ejpam-5871	511	2	∅(r2)⅁(r2	∅(r2)⅁(r2	NOUN
ejpam-5871	511	3	)	)	PUNCT
ejpam-5871	511	4	,	,	PUNCT
ejpam-5871	511	5	q(r1	q(r1	PROPN
ejpam-5871	511	6	,	,	PUNCT
ejpam-5871	511	7	r2	r2	PROPN
ejpam-5871	511	8	)	)	PUNCT
ejpam-5871	511	9	=	=	SYM
ejpam-5871	511	10	∅(r1)⅁(r2	∅(r1)⅁(r2	NOUN
ejpam-5871	511	11	)	)	PUNCT
ejpam-5871	512	1	+	+	NOUN
ejpam-5871	512	2	∅(r2)⅁(r1	∅(r2)⅁(r1	ADJ
ejpam-5871	512	3	)	)	PUNCT
ejpam-5871	512	4	.	.	PUNCT
ejpam-5871	513	1	example	example	NOUN
ejpam-5871	514	1	5	5	NUM
ejpam-5871	514	2	.	.	PUNCT
ejpam-5871	515	1	if	if	SCONJ
ejpam-5871	515	2	we	we	PRON
ejpam-5871	515	3	choose	choose	VERB
ejpam-5871	515	4	∅(r	∅(r	PROPN
ejpam-5871	515	5	)	)	PUNCT
ejpam-5871	515	6	=	=	PUNCT
ejpam-5871	516	1	[	[	X
ejpam-5871	516	2	4	4	NUM
ejpam-5871	516	3	−	−	NOUN
ejpam-5871	516	4	⋋s+1(r	⋋s+1(r	NUM
ejpam-5871	516	5	)	)	PUNCT
ejpam-5871	516	6	,	,	PUNCT
ejpam-5871	516	7	8	8	NUM
ejpam-5871	516	8	+	+	NOUN
ejpam-5871	516	9	⋋s+1(r	⋋s+1(r	NUM
ejpam-5871	516	10	)	)	PUNCT
ejpam-5871	516	11	]	]	PUNCT
ejpam-5871	516	12	and	and	CCONJ
ejpam-5871	516	13	⋋(r	⋋(r	NUM
ejpam-5871	516	14	)	)	PUNCT
ejpam-5871	516	15	=	=	SYM
ejpam-5871	517	1	r	r	X
ejpam-5871	517	2	,	,	PUNCT
ejpam-5871	517	3	⅁(r	⅁(r	NOUN
ejpam-5871	517	4	)	)	PUNCT
ejpam-5871	517	5	=	=	SYM
ejpam-5871	517	6	1	1	NUM
ejpam-5871	517	7	,	,	PUNCT
ejpam-5871	517	8	℧	℧	NOUN
ejpam-5871	517	9	(	(	PUNCT
ejpam-5871	517	10	θ	θ	NOUN
ejpam-5871	517	11	)	)	PUNCT
ejpam-5871	517	12	=	=	SYM
ejpam-5871	517	13	1	1	NUM
ejpam-5871	517	14	4	4	NUM
ejpam-5871	517	15	in	in	ADP
ejpam-5871	517	16	theorem	theorem	ADJ
ejpam-5871	517	17	8	8	NUM
ejpam-5871	517	18	and	and	CCONJ
ejpam-5871	517	19	utilizing	utilize	VERB
ejpam-5871	517	20	proposition	proposition	NOUN
ejpam-5871	517	21	1	1	NUM
ejpam-5871	517	22	,	,	PUNCT
ejpam-5871	517	23	we	we	PRON
ejpam-5871	517	24	have	have	VERB
ejpam-5871	517	25	(	(	PUNCT
ejpam-5871	517	26	s+	s+	X
ejpam-5871	517	27	1	1	X
ejpam-5871	517	28	)	)	PUNCT
ejpam-5871	517	29	−β	−β	NOUN
ejpam-5871	517	30	k	k	PROPN
ejpam-5871	517	31	βγk(β	βγk(β	PROPN
ejpam-5871	517	32	)	)	PUNCT
ejpam-5871	517	33	(	(	PUNCT
ejpam-5871	517	34	8−	8−	NUM
ejpam-5871	517	35	(	(	PUNCT
ejpam-5871	517	36	rs+1	rs+1	NOUN
ejpam-5871	517	37	1	1	NUM
ejpam-5871	517	38	+	+	CCONJ
ejpam-5871	517	39	rs+1	rs+1	PROPN
ejpam-5871	517	40	2	2	NUM
ejpam-5871	517	41	)	)	PUNCT
ejpam-5871	517	42	,	,	PUNCT
ejpam-5871	517	43	16	16	NUM
ejpam-5871	518	1	+	+	CCONJ
ejpam-5871	518	2	(	(	PUNCT
ejpam-5871	518	3	rs+1	rs+1	PROPN
ejpam-5871	518	4	1	1	NUM
ejpam-5871	518	5	+	+	CCONJ
ejpam-5871	518	6	rs+1	rs+1	PROPN
ejpam-5871	518	7	2	2	NUM
ejpam-5871	518	8	)	)	PUNCT
ejpam-5871	518	9	)	)	PUNCT
ejpam-5871	519	1	⊇	⊇	NOUN
ejpam-5871	519	2	(	(	PUNCT
ejpam-5871	519	3	s+	s+	NUM
ejpam-5871	519	4	1)−	1)−	PROPN
ejpam-5871	519	5	β	β	X
ejpam-5871	519	6	k	k	PROPN
ejpam-5871	519	7	8βγk(β	8βγk(β	NUM
ejpam-5871	519	8	)	)	PUNCT
ejpam-5871	519	9	(	(	PUNCT
ejpam-5871	519	10	8−	8−	NUM
ejpam-5871	519	11	(	(	PUNCT
ejpam-5871	519	12	rs+1	rs+1	NOUN
ejpam-5871	519	13	1	1	NUM
ejpam-5871	519	14	+	+	CCONJ
ejpam-5871	519	15	rs+1	rs+1	PROPN
ejpam-5871	519	16	2	2	NUM
ejpam-5871	519	17	)	)	PUNCT
ejpam-5871	519	18	,	,	PUNCT
ejpam-5871	519	19	16	16	NUM
ejpam-5871	519	20	+	+	CCONJ
ejpam-5871	519	21	(	(	PUNCT
ejpam-5871	519	22	rs+1	rs+1	PROPN
ejpam-5871	519	23	1	1	NUM
ejpam-5871	519	24	+	+	CCONJ
ejpam-5871	519	25	rs+1	rs+1	PROPN
ejpam-5871	519	26	2	2	NUM
ejpam-5871	519	27	)	)	PUNCT
ejpam-5871	519	28	)	)	PUNCT
ejpam-5871	519	29	.	.	PUNCT
ejpam-5871	520	1	example	example	NOUN
ejpam-5871	521	1	6	6	NUM
ejpam-5871	521	2	.	.	X
ejpam-5871	522	1	for	for	ADP
ejpam-5871	522	2	graphical	graphical	ADJ
ejpam-5871	522	3	representation	representation	NOUN
ejpam-5871	522	4	if	if	SCONJ
ejpam-5871	522	5	we	we	PRON
ejpam-5871	522	6	choose	choose	VERB
ejpam-5871	522	7	∅(r	∅(r	PROPN
ejpam-5871	522	8	)	)	PUNCT
ejpam-5871	522	9	=	=	PUNCT
ejpam-5871	523	1	[	[	X
ejpam-5871	523	2	4−⋋s+1(r	4−⋋s+1(r	NUM
ejpam-5871	523	3	)	)	PUNCT
ejpam-5871	523	4	,	,	PUNCT
ejpam-5871	523	5	8	8	NUM
ejpam-5871	523	6	+	+	NOUN
ejpam-5871	523	7	⋋s+1(r	⋋s+1(r	NUM
ejpam-5871	523	8	)	)	PUNCT
ejpam-5871	523	9	]	]	PUNCT
ejpam-5871	523	10	and	and	CCONJ
ejpam-5871	523	11	⋋(r	⋋(r	NUM
ejpam-5871	523	12	)	)	PUNCT
ejpam-5871	524	1	=	=	PUNCT
ejpam-5871	524	2	sin	sin	NOUN
ejpam-5871	524	3	r	r	NOUN
ejpam-5871	524	4	,	,	PUNCT
ejpam-5871	524	5	⅁(r	⅁(r	NOUN
ejpam-5871	524	6	)	)	PUNCT
ejpam-5871	524	7	=	=	SYM
ejpam-5871	524	8	1	1	NUM
ejpam-5871	524	9	,	,	PUNCT
ejpam-5871	524	10	℧	℧	NOUN
ejpam-5871	524	11	(	(	PUNCT
ejpam-5871	524	12	θ	θ	NOUN
ejpam-5871	524	13	)	)	PUNCT
ejpam-5871	524	14	=	=	SYM
ejpam-5871	524	15	1	1	NUM
ejpam-5871	524	16	8	8	NUM
ejpam-5871	524	17	in	in	ADP
ejpam-5871	524	18	theorem	theorem	ADJ
ejpam-5871	524	19	8	8	NUM
ejpam-5871	524	20	and	and	CCONJ
ejpam-5871	524	21	utilizing	utilize	VERB
ejpam-5871	524	22	proposition	proposition	NOUN
ejpam-5871	524	23	1	1	NUM
ejpam-5871	524	24	,	,	PUNCT
ejpam-5871	524	25	we	we	PRON
ejpam-5871	524	26	have	have	VERB
ejpam-5871	524	27	(	(	PUNCT
ejpam-5871	524	28	s+	s+	X
ejpam-5871	524	29	1	1	X
ejpam-5871	524	30	)	)	PUNCT
ejpam-5871	524	31	−β	−β	NOUN
ejpam-5871	524	32	k	k	PROPN
ejpam-5871	524	33	βγk(β	βγk(β	PROPN
ejpam-5871	524	34	)	)	PUNCT
ejpam-5871	524	35	(	(	PUNCT
ejpam-5871	524	36	8−	8−	NUM
ejpam-5871	524	37	(	(	PUNCT
ejpam-5871	524	38	sins+1(r1	sins+1(r1	X
ejpam-5871	524	39	)	)	PUNCT
ejpam-5871	524	40	+	+	SYM
ejpam-5871	524	41	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	524	42	)	)	PUNCT
ejpam-5871	524	43	)	)	PUNCT
ejpam-5871	524	44	,	,	PUNCT
ejpam-5871	524	45	16	16	NUM
ejpam-5871	524	46	+	+	CCONJ
ejpam-5871	524	47	(	(	PUNCT
ejpam-5871	524	48	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	524	49	)	)	PUNCT
ejpam-5871	524	50	+	+	SYM
ejpam-5871	524	51	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	524	52	)	)	PUNCT
ejpam-5871	524	53	)	)	PUNCT
ejpam-5871	524	54	)	)	PUNCT
ejpam-5871	525	1	⊇	⊇	NOUN
ejpam-5871	525	2	(	(	PUNCT
ejpam-5871	525	3	s+	s+	NUM
ejpam-5871	525	4	1)−	1)−	PROPN
ejpam-5871	525	5	β	β	X
ejpam-5871	525	6	k	k	PROPN
ejpam-5871	525	7	32βγk(β	32βγk(β	NUM
ejpam-5871	525	8	)	)	PUNCT
ejpam-5871	525	9	(	(	PUNCT
ejpam-5871	525	10	8−	8−	NUM
ejpam-5871	525	11	(	(	PUNCT
ejpam-5871	525	12	sins+1(r1	sins+1(r1	X
ejpam-5871	525	13	)	)	PUNCT
ejpam-5871	525	14	+	+	SYM
ejpam-5871	525	15	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	525	16	)	)	PUNCT
ejpam-5871	525	17	)	)	PUNCT
ejpam-5871	525	18	,	,	PUNCT
ejpam-5871	525	19	16	16	NUM
ejpam-5871	525	20	+	+	CCONJ
ejpam-5871	525	21	(	(	PUNCT
ejpam-5871	525	22	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	525	23	)	)	PUNCT
ejpam-5871	525	24	+	+	SYM
ejpam-5871	525	25	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	525	26	)	)	PUNCT
ejpam-5871	525	27	)	)	PUNCT
ejpam-5871	525	28	)	)	PUNCT
ejpam-5871	525	29	.	.	PUNCT
ejpam-5871	526	1	figure	figure	VERB
ejpam-5871	526	2	3	3	NUM
ejpam-5871	526	3	:	:	PUNCT
ejpam-5871	526	4	graphical	graphical	ADJ
ejpam-5871	526	5	representation	representation	NOUN
ejpam-5871	526	6	of	of	ADP
ejpam-5871	526	7	theorem	theorem	ADJ
ejpam-5871	526	8	8	8	NUM
ejpam-5871	526	9	corresponding	correspond	VERB
ejpam-5871	526	10	to	to	ADP
ejpam-5871	526	11	the	the	DET
ejpam-5871	526	12	choice	choice	NOUN
ejpam-5871	526	13	of	of	ADP
ejpam-5871	526	14	parameters	parameter	NOUN
ejpam-5871	526	15	r1	r1	NOUN
ejpam-5871	526	16	=	=	SYM
ejpam-5871	526	17	0.6	0.6	NUM
ejpam-5871	526	18	,	,	PUNCT
ejpam-5871	526	19	r1	r1	NOUN
ejpam-5871	526	20	<	<	X
ejpam-5871	526	21	r2	r2	PROPN
ejpam-5871	526	22	≤	≤	PROPN
ejpam-5871	526	23	π	π	PROPN
ejpam-5871	526	24	2	2	NUM
ejpam-5871	526	25	,	,	PUNCT
ejpam-5871	526	26	k	k	NOUN
ejpam-5871	526	27	=	=	SYM
ejpam-5871	526	28	1	1	NUM
ejpam-5871	526	29	,	,	PUNCT
ejpam-5871	526	30	s	s	PART
ejpam-5871	526	31	=	=	SYM
ejpam-5871	526	32	3	3	NUM
ejpam-5871	526	33	and	and	CCONJ
ejpam-5871	526	34	β	β	X
ejpam-5871	526	35	=	=	NOUN
ejpam-5871	526	36	0.8	0.8	NUM
ejpam-5871	526	37	.	.	PUNCT
ejpam-5871	527	1	for	for	ADP
ejpam-5871	527	2	tabular	tabular	NOUN
ejpam-5871	527	3	form	form	NOUN
ejpam-5871	527	4	we	we	PRON
ejpam-5871	527	5	have	have	VERB
ejpam-5871	527	6	corollary	corollary	ADJ
ejpam-5871	527	7	6	6	NUM
ejpam-5871	527	8	.	.	PUNCT
ejpam-5871	528	1	if	if	SCONJ
ejpam-5871	528	2	we	we	PRON
ejpam-5871	528	3	fix	fix	VERB
ejpam-5871	528	4	s	s	NOUN
ejpam-5871	528	5	=	=	NOUN
ejpam-5871	528	6	0	0	NUM
ejpam-5871	528	7	,	,	PUNCT
ejpam-5871	528	8	k	k	NOUN
ejpam-5871	528	9	=	=	SYM
ejpam-5871	528	10	1	1	NUM
ejpam-5871	528	11	,	,	PUNCT
ejpam-5871	528	12	⋋(θ	⋋(θ	NUM
ejpam-5871	528	13	)	)	PUNCT
ejpam-5871	528	14	=	=	SYM
ejpam-5871	528	15	θ	θ	NOUN
ejpam-5871	528	16	,	,	PUNCT
ejpam-5871	528	17	and	and	CCONJ
ejpam-5871	528	18	℧	℧	PROPN
ejpam-5871	528	19	(	(	PUNCT
ejpam-5871	528	20	θ	θ	NOUN
ejpam-5871	528	21	)	)	PUNCT
ejpam-5871	528	22	=	=	SYM
ejpam-5871	528	23	θ	θ	PROPN
ejpam-5871	528	24	in	in	ADP
ejpam-5871	528	25	theorem	theorem	NOUN
ejpam-5871	528	26	8	8	NUM
ejpam-5871	528	27	,	,	PUNCT
ejpam-5871	528	28	we	we	PRON
ejpam-5871	528	29	possess	possess	VERB
ejpam-5871	528	30	1	1	NUM
ejpam-5871	528	31	(	(	PUNCT
ejpam-5871	528	32	r2	r2	PROPN
ejpam-5871	528	33	−	−	PROPN
ejpam-5871	528	34	r1)β	r1)β	PROPN
ejpam-5871	528	35	[	[	PUNCT
ejpam-5871	528	36	zβ	zβ	NOUN
ejpam-5871	528	37	r+1	r+1	PROPN
ejpam-5871	528	38	∅⅁(r2	∅⅁(r2	NOUN
ejpam-5871	528	39	)	)	PUNCT
ejpam-5871	529	1	+	+	CCONJ
ejpam-5871	529	2	zβ	zβ	PROPN
ejpam-5871	529	3	r−2	r−2	PROPN
ejpam-5871	529	4	∅⅁(r1	∅⅁(r1	NOUN
ejpam-5871	529	5	)	)	PUNCT
ejpam-5871	529	6	]	]	PUNCT
ejpam-5871	529	7	⊇	⊇	PROPN
ejpam-5871	529	8	1	1	NUM
ejpam-5871	529	9	γ(β	γ(β	PROPN
ejpam-5871	529	10	)	)	PUNCT
ejpam-5871	530	1	[	[	PUNCT
ejpam-5871	530	2	p	p	X
ejpam-5871	530	3	(	(	PUNCT
ejpam-5871	530	4	r1	r1	PROPN
ejpam-5871	530	5	,	,	PUNCT
ejpam-5871	530	6	r2	r2	PROPN
ejpam-5871	530	7	)	)	PUNCT
ejpam-5871	530	8	β2	β2	NOUN
ejpam-5871	530	9	+	+	NOUN
ejpam-5871	530	10	β	β	X
ejpam-5871	531	1	+	+	CCONJ
ejpam-5871	531	2	1	1	NUM
ejpam-5871	531	3	(	(	PUNCT
ejpam-5871	531	4	β	β	X
ejpam-5871	531	5	+	+	ADJ
ejpam-5871	531	6	2)(β	2)(β	NUM
ejpam-5871	531	7	+	+	CCONJ
ejpam-5871	531	8	1)(β	1)(β	NOUN
ejpam-5871	531	9	)	)	PUNCT
ejpam-5871	532	1	+	+	ADJ
ejpam-5871	532	2	q(r1	q(r1	ADJ
ejpam-5871	532	3	,	,	PUNCT
ejpam-5871	532	4	r2	r2	PROPN
ejpam-5871	532	5	)	)	PUNCT
ejpam-5871	532	6	2	2	NUM
ejpam-5871	532	7	(	(	PUNCT
ejpam-5871	532	8	β	β	X
ejpam-5871	532	9	+	+	ADJ
ejpam-5871	532	10	2)(β	2)(β	NUM
ejpam-5871	532	11	+	+	CCONJ
ejpam-5871	532	12	1	1	NUM
ejpam-5871	532	13	)	)	PUNCT
ejpam-5871	532	14	]	]	PUNCT
ejpam-5871	532	15	.	.	PUNCT
ejpam-5871	533	1	a.	a.	PROPN
ejpam-5871	533	2	mehmood	mehmood	PROPN
ejpam-5871	533	3	et	et	PROPN
ejpam-5871	533	4	al	al	PROPN
ejpam-5871	533	5	.	.	PUNCT
ejpam-5871	533	6	/	/	SYM
ejpam-5871	533	7	eur	eur	PROPN
ejpam-5871	533	8	.	.	PUNCT
ejpam-5871	534	1	j.	j.	PROPN
ejpam-5871	534	2	pure	pure	PROPN
ejpam-5871	534	3	appl	appl	PROPN
ejpam-5871	534	4	.	.	PROPN
ejpam-5871	534	5	math	math	PROPN
ejpam-5871	534	6	,	,	PUNCT
ejpam-5871	534	7	18	18	NUM
ejpam-5871	534	8	(	(	PUNCT
ejpam-5871	534	9	2	2	NUM
ejpam-5871	534	10	)	)	PUNCT
ejpam-5871	534	11	(	(	PUNCT
ejpam-5871	534	12	2025	2025	NUM
ejpam-5871	534	13	)	)	PUNCT
ejpam-5871	534	14	,	,	PUNCT
ejpam-5871	534	15	5871	5871	NUM
ejpam-5871	534	16	20	20	NUM
ejpam-5871	534	17	of	of	ADP
ejpam-5871	534	18	26	26	NUM
ejpam-5871	534	19	r2	r2	NOUN
ejpam-5871	534	20	(	(	PUNCT
ejpam-5871	534	21	a1	a1	NOUN
ejpam-5871	534	22	,	,	PUNCT
ejpam-5871	534	23	b1	b1	NOUN
ejpam-5871	534	24	)	)	PUNCT
ejpam-5871	534	25	(	(	PUNCT
ejpam-5871	534	26	a2	a2	PROPN
ejpam-5871	534	27	,	,	PUNCT
ejpam-5871	534	28	b2	b2	NOUN
ejpam-5871	534	29	)	)	PUNCT
ejpam-5871	534	30	0.6100	0.6100	NUM
ejpam-5871	534	31	(	(	PUNCT
ejpam-5871	534	32	2.7593	2.7593	NUM
ejpam-5871	534	33	,	,	PUNCT
ejpam-5871	534	34	5.7410	5.7410	NUM
ejpam-5871	534	35	)	)	PUNCT
ejpam-5871	534	36	(	(	PUNCT
ejpam-5871	534	37	0.0862	0.0862	NUM
ejpam-5871	534	38	,	,	PUNCT
ejpam-5871	534	39	0.1794	0.1794	NUM
ejpam-5871	534	40	)	)	PUNCT
ejpam-5871	534	41	0.8022	0.8022	PROPN
ejpam-5871	534	42	(	(	PUNCT
ejpam-5871	534	43	2.7029	2.7029	NUM
ejpam-5871	534	44	,	,	PUNCT
ejpam-5871	534	45	5.7975	5.7975	NUM
ejpam-5871	534	46	)	)	PUNCT
ejpam-5871	534	47	(	(	PUNCT
ejpam-5871	534	48	0.0845	0.0845	NUM
ejpam-5871	534	49	,	,	PUNCT
ejpam-5871	534	50	0.1812	0.1812	NUM
ejpam-5871	534	51	)	)	PUNCT
ejpam-5871	534	52	0.9943	0.9943	NUM
ejpam-5871	534	53	(	(	PUNCT
ejpam-5871	534	54	2.6224	2.6224	NUM
ejpam-5871	534	55	,	,	PUNCT
ejpam-5871	534	56	5.8779	5.8779	NUM
ejpam-5871	534	57	)	)	PUNCT
ejpam-5871	534	58	(	(	PUNCT
ejpam-5871	534	59	0.0820	0.0820	NUM
ejpam-5871	534	60	,	,	PUNCT
ejpam-5871	534	61	0.1837	0.1837	NUM
ejpam-5871	534	62	)	)	PUNCT
ejpam-5871	534	63	1.1865	1.1865	NUM
ejpam-5871	534	64	(	(	PUNCT
ejpam-5871	534	65	2.5358	2.5358	NUM
ejpam-5871	534	66	,	,	PUNCT
ejpam-5871	534	67	5.9645	5.9645	NUM
ejpam-5871	534	68	)	)	PUNCT
ejpam-5871	534	69	(	(	PUNCT
ejpam-5871	534	70	0.0792	0.0792	NUM
ejpam-5871	534	71	,	,	PUNCT
ejpam-5871	534	72	0.1864	0.1864	NUM
ejpam-5871	534	73	)	)	PUNCT
ejpam-5871	534	74	1.3786	1.3786	NUM
ejpam-5871	534	75	(	(	PUNCT
ejpam-5871	534	76	2.4686	2.4686	NUM
ejpam-5871	534	77	,	,	PUNCT
ejpam-5871	534	78	6.0317	6.0317	NUM
ejpam-5871	534	79	)	)	PUNCT
ejpam-5871	534	80	(	(	PUNCT
ejpam-5871	534	81	0.0771	0.0771	NUM
ejpam-5871	534	82	,	,	PUNCT
ejpam-5871	534	83	0.1885	0.1885	NUM
ejpam-5871	534	84	)	)	PUNCT
ejpam-5871	534	85	1.5708	1.5708	NUM
ejpam-5871	534	86	(	(	PUNCT
ejpam-5871	534	87	2.4433	2.4433	NUM
ejpam-5871	534	88	,	,	PUNCT
ejpam-5871	534	89	6.0571	6.0571	NUM
ejpam-5871	534	90	)	)	PUNCT
ejpam-5871	534	91	(	(	PUNCT
ejpam-5871	534	92	0.0764	0.0764	NUM
ejpam-5871	534	93	,	,	PUNCT
ejpam-5871	534	94	0.1893	0.1893	NUM
ejpam-5871	534	95	)	)	PUNCT
ejpam-5871	534	96	table	table	NOUN
ejpam-5871	534	97	3	3	NUM
ejpam-5871	534	98	:	:	PUNCT
ejpam-5871	534	99	interval	interval	NOUN
ejpam-5871	534	100	bounds	bound	NOUN
ejpam-5871	534	101	of	of	ADP
ejpam-5871	534	102	theorem	theorem	ADJ
ejpam-5871	534	103	8	8	NUM
ejpam-5871	534	104	corresponding	correspond	VERB
ejpam-5871	534	105	to	to	ADP
ejpam-5871	534	106	the	the	DET
ejpam-5871	534	107	choice	choice	NOUN
ejpam-5871	534	108	of	of	ADP
ejpam-5871	534	109	parameters	parameter	NOUN
ejpam-5871	534	110	r1	r1	NOUN
ejpam-5871	534	111	=	=	SYM
ejpam-5871	534	112	0.6	0.6	NUM
ejpam-5871	534	113	,	,	PUNCT
ejpam-5871	534	114	r1	r1	NOUN
ejpam-5871	534	115	<	<	X
ejpam-5871	534	116	r2	r2	PROPN
ejpam-5871	534	117	≤	≤	PROPN
ejpam-5871	535	1	π	π	PROPN
ejpam-5871	535	2	2	2	NUM
ejpam-5871	535	3	,	,	PUNCT
ejpam-5871	535	4	k	k	NOUN
ejpam-5871	535	5	=	=	SYM
ejpam-5871	535	6	1	1	NUM
ejpam-5871	535	7	,	,	PUNCT
ejpam-5871	535	8	s	s	PART
ejpam-5871	535	9	=	=	SYM
ejpam-5871	535	10	3	3	NUM
ejpam-5871	535	11	and	and	CCONJ
ejpam-5871	535	12	β	β	X
ejpam-5871	535	13	=	=	NOUN
ejpam-5871	535	14	0.8	0.8	NUM
ejpam-5871	535	15	.	.	PUNCT
ejpam-5871	536	1	corollary	corollary	ADJ
ejpam-5871	536	2	7	7	NUM
ejpam-5871	536	3	.	.	PUNCT
ejpam-5871	537	1	if	if	SCONJ
ejpam-5871	537	2	we	we	PRON
ejpam-5871	537	3	fix	fix	VERB
ejpam-5871	537	4	⋋(θ	⋋(θ	NOUN
ejpam-5871	537	5	)	)	PUNCT
ejpam-5871	537	6	=	=	SYM
ejpam-5871	537	7	θ	θ	PROPN
ejpam-5871	537	8	and	and	CCONJ
ejpam-5871	537	9	s+	s+	NUM
ejpam-5871	537	10	1	1	NUM
ejpam-5871	537	11	≥	≥	NOUN
ejpam-5871	537	12	0	0	NUM
ejpam-5871	537	13	in	in	ADP
ejpam-5871	537	14	theorem	theorem	NOUN
ejpam-5871	537	15	8	8	NUM
ejpam-5871	537	16	,	,	PUNCT
ejpam-5871	537	17	we	we	PRON
ejpam-5871	537	18	possess	possess	VERB
ejpam-5871	537	19	1	1	NUM
ejpam-5871	537	20	(	(	PUNCT
ejpam-5871	537	21	rs+1	rs+1	PROPN
ejpam-5871	537	22	2	2	NUM
ejpam-5871	537	23	−	−	NOUN
ejpam-5871	537	24	rs+1	rs+1	NOUN
ejpam-5871	537	25	1	1	NUM
ejpam-5871	537	26	)	)	PUNCT
ejpam-5871	537	27	β	β	X
ejpam-5871	537	28	k	k	X
ejpam-5871	538	1	[	[	PUNCT
ejpam-5871	538	2	s	s	X
ejpam-5871	538	3	kz	kz	PROPN
ejpam-5871	538	4	β	β	X
ejpam-5871	538	5	(	(	PUNCT
ejpam-5871	538	6	rs+1	rs+1	PROPN
ejpam-5871	538	7	1	1	NUM
ejpam-5871	538	8	)	)	PUNCT
ejpam-5871	538	9	+	+	CCONJ
ejpam-5871	538	10	∅⅁(rs+1	∅⅁(rs+1	PROPN
ejpam-5871	538	11	2	2	NUM
ejpam-5871	538	12	)	)	PUNCT
ejpam-5871	539	1	+	+	NUM
ejpam-5871	539	2	s	s	VERB
ejpam-5871	539	3	kz	kz	PROPN
ejpam-5871	539	4	β	β	X
ejpam-5871	539	5	(	(	PUNCT
ejpam-5871	539	6	rs+1	rs+1	PROPN
ejpam-5871	539	7	2	2	NUM
ejpam-5871	539	8	)	)	PUNCT
ejpam-5871	539	9	−	−	NOUN
ejpam-5871	539	10	∅⅁(rs+1	∅⅁(rs+1	PROPN
ejpam-5871	539	11	2	2	NUM
ejpam-5871	539	12	)	)	PUNCT
ejpam-5871	539	13	]	]	PUNCT
ejpam-5871	540	1	⊇	⊇	PROPN
ejpam-5871	540	2	p	p	X
ejpam-5871	540	3	(	(	PUNCT
ejpam-5871	540	4	r1	r1	PROPN
ejpam-5871	540	5	,	,	PUNCT
ejpam-5871	540	6	r2	r2	PROPN
ejpam-5871	540	7	)	)	PUNCT
ejpam-5871	540	8	(	(	PUNCT
ejpam-5871	540	9	s+	s+	NUM
ejpam-5871	540	10	1)−	1)−	PROPN
ejpam-5871	540	11	β	β	X
ejpam-5871	540	12	k	k	PROPN
ejpam-5871	540	13	kγk(β	kγk(β	PROPN
ejpam-5871	540	14	)	)	PUNCT
ejpam-5871	540	15	∫	∫	PROPN
ejpam-5871	540	16	1	1	NUM
ejpam-5871	540	17	0	0	NUM
ejpam-5871	540	18	θ	θ	PROPN
ejpam-5871	540	19	β	β	X
ejpam-5871	540	20	k	k	X
ejpam-5871	540	21	−1[	−1[	X
ejpam-5871	540	22	℧	℧	PROPN
ejpam-5871	540	23	1(θ)	1(θ)	NUM
ejpam-5871	540	24	℧	℧	NOUN
ejpam-5871	540	25	2(θ	2(θ	NUM
ejpam-5871	540	26	)	)	PUNCT
ejpam-5871	541	1	+	+	CCONJ
ejpam-5871	541	2	℧	℧	PROPN
ejpam-5871	541	3	1(1−	1(1−	NUM
ejpam-5871	541	4	θ)	θ)	PROPN
ejpam-5871	541	5	℧	℧	NOUN
ejpam-5871	541	6	2(1−	2(1−	NUM
ejpam-5871	541	7	θ)]dθ	θ)]dθ	NOUN
ejpam-5871	541	8	+	+	NOUN
ejpam-5871	541	9	q(r1	q(r1	ADJ
ejpam-5871	541	10	,	,	PUNCT
ejpam-5871	541	11	r2	r2	PROPN
ejpam-5871	541	12	)	)	PUNCT
ejpam-5871	541	13	(	(	PUNCT
ejpam-5871	541	14	s+	s+	NUM
ejpam-5871	541	15	1)−	1)−	PROPN
ejpam-5871	541	16	β	β	X
ejpam-5871	541	17	k	k	PROPN
ejpam-5871	541	18	kγk(β	kγk(β	PROPN
ejpam-5871	541	19	)	)	PUNCT
ejpam-5871	541	20	∫	∫	PROPN
ejpam-5871	541	21	1	1	NUM
ejpam-5871	541	22	0	0	NUM
ejpam-5871	541	23	θ	θ	PROPN
ejpam-5871	541	24	β	β	X
ejpam-5871	541	25	k	k	X
ejpam-5871	541	26	−1[	−1[	X
ejpam-5871	541	27	℧	℧	PROPN
ejpam-5871	541	28	1(θ)	1(θ)	NUM
ejpam-5871	541	29	℧	℧	SYM
ejpam-5871	541	30	2(1−	2(1−	NUM
ejpam-5871	541	31	θ	θ	NOUN
ejpam-5871	541	32	)	)	PUNCT
ejpam-5871	541	33	+	+	CCONJ
ejpam-5871	541	34	℧	℧	PROPN
ejpam-5871	541	35	1(1−	1(1−	NUM
ejpam-5871	541	36	θ)	θ)	NOUN
ejpam-5871	541	37	℧	℧	PROPN
ejpam-5871	541	38	2(θ)]dθ	2(θ)]dθ	NOUN
ejpam-5871	541	39	corollary	corollary	ADJ
ejpam-5871	541	40	8	8	NUM
ejpam-5871	541	41	.	.	PUNCT
ejpam-5871	542	1	if	if	SCONJ
ejpam-5871	542	2	we	we	PRON
ejpam-5871	542	3	fix	fix	VERB
ejpam-5871	542	4	⋋(θ	⋋(θ	NOUN
ejpam-5871	542	5	)	)	PUNCT
ejpam-5871	543	1	=	=	SYM
ejpam-5871	543	2	θ	θ	NOUN
ejpam-5871	543	3	,	,	PUNCT
ejpam-5871	543	4	s+	s+	NUM
ejpam-5871	543	5	1	1	NUM
ejpam-5871	543	6	≥	≥	NOUN
ejpam-5871	543	7	0	0	NUM
ejpam-5871	543	8	and	and	CCONJ
ejpam-5871	543	9	℧	℧	PROPN
ejpam-5871	543	10	(	(	PUNCT
ejpam-5871	543	11	θ	θ	NOUN
ejpam-5871	543	12	)	)	PUNCT
ejpam-5871	543	13	=	=	SYM
ejpam-5871	543	14	θ	θ	PROPN
ejpam-5871	543	15	in	in	ADP
ejpam-5871	543	16	theorem	theorem	NOUN
ejpam-5871	543	17	8	8	NUM
ejpam-5871	543	18	,	,	PUNCT
ejpam-5871	543	19	we	we	PRON
ejpam-5871	543	20	possess	possess	VERB
ejpam-5871	543	21	1	1	NUM
ejpam-5871	543	22	(	(	PUNCT
ejpam-5871	543	23	rs+1	rs+1	PROPN
ejpam-5871	543	24	2	2	NUM
ejpam-5871	543	25	−	−	NOUN
ejpam-5871	543	26	rs+1	rs+1	NOUN
ejpam-5871	543	27	1	1	NUM
ejpam-5871	543	28	)	)	PUNCT
ejpam-5871	543	29	β	β	X
ejpam-5871	544	1	k	k	X
ejpam-5871	545	1	[	[	PUNCT
ejpam-5871	545	2	s	s	X
ejpam-5871	545	3	kz	kz	PROPN
ejpam-5871	545	4	β	β	X
ejpam-5871	545	5	(	(	PUNCT
ejpam-5871	545	6	rs+1	rs+1	PROPN
ejpam-5871	545	7	1	1	NUM
ejpam-5871	545	8	)	)	PUNCT
ejpam-5871	545	9	+	+	CCONJ
ejpam-5871	545	10	∅⅁(rs+1	∅⅁(rs+1	PROPN
ejpam-5871	545	11	2	2	NUM
ejpam-5871	545	12	)	)	PUNCT
ejpam-5871	546	1	+	+	NUM
ejpam-5871	546	2	s	s	VERB
ejpam-5871	546	3	kz	kz	PROPN
ejpam-5871	546	4	β	β	X
ejpam-5871	546	5	(	(	PUNCT
ejpam-5871	546	6	rs+1	rs+1	PROPN
ejpam-5871	546	7	2	2	NUM
ejpam-5871	546	8	)	)	PUNCT
ejpam-5871	546	9	−	−	NOUN
ejpam-5871	546	10	∅⅁(rs+1	∅⅁(rs+1	PROPN
ejpam-5871	546	11	2	2	NUM
ejpam-5871	546	12	)	)	PUNCT
ejpam-5871	546	13	]	]	PUNCT
ejpam-5871	547	1	⊇	⊇	X
ejpam-5871	547	2	(	(	PUNCT
ejpam-5871	547	3	s+	s+	NUM
ejpam-5871	547	4	1)−	1)−	PROPN
ejpam-5871	547	5	β	β	X
ejpam-5871	547	6	k	k	PROPN
ejpam-5871	547	7	kγk(β	kγk(β	PROPN
ejpam-5871	547	8	)	)	PUNCT
ejpam-5871	547	9	[	[	PUNCT
ejpam-5871	547	10	p	p	X
ejpam-5871	547	11	(	(	PUNCT
ejpam-5871	547	12	r1	r1	PROPN
ejpam-5871	547	13	,	,	PUNCT
ejpam-5871	547	14	r2	r2	PROPN
ejpam-5871	547	15	)	)	PUNCT
ejpam-5871	547	16	β2	β2	NOUN
ejpam-5871	547	17	k2	k2	NOUN
ejpam-5871	547	18	+	+	CCONJ
ejpam-5871	547	19	β	β	X
ejpam-5871	547	20	k	k	X
ejpam-5871	548	1	+	+	CCONJ
ejpam-5871	548	2	1	1	NUM
ejpam-5871	548	3	(	(	PUNCT
ejpam-5871	548	4	βk	βk	ADP
ejpam-5871	548	5	+	+	NOUN
ejpam-5871	548	6	2)(βk	2)(βk	NUM
ejpam-5871	548	7	+	+	CCONJ
ejpam-5871	548	8	1)(βk	1)(βk	NUM
ejpam-5871	548	9	)	)	PUNCT
ejpam-5871	549	1	+	+	VERB
ejpam-5871	549	2	q(r1	q(r1	ADJ
ejpam-5871	549	3	,	,	PUNCT
ejpam-5871	549	4	r2	r2	PROPN
ejpam-5871	549	5	)	)	PUNCT
ejpam-5871	549	6	2	2	NUM
ejpam-5871	549	7	(	(	PUNCT
ejpam-5871	549	8	βk	βk	ADP
ejpam-5871	549	9	+	+	NOUN
ejpam-5871	549	10	2)(βk	2)(βk	NUM
ejpam-5871	549	11	+	+	CCONJ
ejpam-5871	549	12	1	1	NUM
ejpam-5871	549	13	)	)	PUNCT
ejpam-5871	549	14	]	]	PUNCT
ejpam-5871	549	15	.	.	PUNCT
ejpam-5871	550	1	theorem	theorem	ADJ
ejpam-5871	550	2	9	9	NUM
ejpam-5871	550	3	.	.	PUNCT
ejpam-5871	551	1	let	let	VERB
ejpam-5871	551	2	s	s	PRON
ejpam-5871	551	3	∈	∈	VERB
ejpam-5871	551	4	r/{−1	r/{−1	PROPN
ejpam-5871	551	5	}	}	PUNCT
ejpam-5871	551	6	,	,	PUNCT
ejpam-5871	551	7	∅,⅁	∅,⅁	NOUN
ejpam-5871	551	8	∈	∈	PROPN
ejpam-5871	551	9	sigx([r1	sigx([r1	NOUN
ejpam-5871	551	10	,	,	PUNCT
ejpam-5871	551	11	r2	r2	PROPN
ejpam-5871	551	12	]	]	PUNCT
ejpam-5871	551	13	,	,	PUNCT
ejpam-5871	552	1	r	r	NOUN
ejpam-5871	552	2	+	+	NUM
ejpam-5871	552	3	i	i	NOUN
ejpam-5871	552	4	)	)	PUNCT
ejpam-5871	552	5	and	and	CCONJ
ejpam-5871	552	6	k	k	X
ejpam-5871	552	7	≥	≥	PROPN
ejpam-5871	552	8	0	0	NUM
ejpam-5871	552	9	,	,	PUNCT
ejpam-5871	552	10	then	then	ADV
ejpam-5871	552	11	for	for	ADP
ejpam-5871	552	12	β	β	X
ejpam-5871	552	13	>	>	X
ejpam-5871	552	14	0	0	PUNCT
ejpam-5871	553	1	the	the	DET
ejpam-5871	553	2	following	follow	VERB
ejpam-5871	553	3	redinequality	redinequality	NOUN
ejpam-5871	553	4	fulfill	fulfill	NOUN
ejpam-5871	553	5	(	(	PUNCT
ejpam-5871	553	6	s+	s+	NUM
ejpam-5871	553	7	1)−	1)−	PROPN
ejpam-5871	553	8	β	β	X
ejpam-5871	553	9	k	k	X
ejpam-5871	553	10	βγk(β	βγk(β	PROPN
ejpam-5871	553	11	)	)	PUNCT
ejpam-5871	553	12	∅	∅	NOUN
ejpam-5871	553	13	(	(	PUNCT
ejpam-5871	553	14	⋋−1	⋋−1	X
ejpam-5871	553	15	(	(	PUNCT
ejpam-5871	553	16	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	553	17	)	)	PUNCT
ejpam-5871	553	18	+	+	NOUN
ejpam-5871	553	19	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	553	20	)	)	PUNCT
ejpam-5871	553	21	2	2	NUM
ejpam-5871	553	22	)	)	PUNCT
ejpam-5871	553	23	1	1	NUM
ejpam-5871	553	24	s+1	s+1	NOUN
ejpam-5871	553	25	)	)	PUNCT
ejpam-5871	553	26	⅁	⅁	PROPN
ejpam-5871	553	27	(	(	PUNCT
ejpam-5871	553	28	⋋−1	⋋−1	X
ejpam-5871	553	29	(	(	PUNCT
ejpam-5871	553	30	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	553	31	)	)	PUNCT
ejpam-5871	553	32	+	+	NOUN
ejpam-5871	553	33	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	553	34	)	)	PUNCT
ejpam-5871	553	35	2	2	NUM
ejpam-5871	553	36	)	)	PUNCT
ejpam-5871	553	37	1	1	NUM
ejpam-5871	553	38	s+1	s+1	PROPN
ejpam-5871	553	39	)	)	PUNCT
ejpam-5871	553	40	⊇	⊇	PROPN
ejpam-5871	553	41	℧	℧	PROPN
ejpam-5871	553	42	1	1	NUM
ejpam-5871	553	43	(	(	PUNCT
ejpam-5871	553	44	1	1	NUM
ejpam-5871	553	45	2)	2)	NUM
ejpam-5871	553	46	℧	℧	PROPN
ejpam-5871	553	47	2	2	NUM
ejpam-5871	553	48	(	(	PUNCT
ejpam-5871	553	49	1	1	NUM
ejpam-5871	553	50	2	2	NUM
ejpam-5871	553	51	)	)	PUNCT
ejpam-5871	553	52	(	(	PUNCT
ejpam-5871	553	53	⋋s+1(r2)−⋋s+1(r1	⋋s+1(r2)−⋋s+1(r1	NOUN
ejpam-5871	553	54	)	)	PUNCT
ejpam-5871	553	55	)	)	PUNCT
ejpam-5871	554	1	β	β	X
ejpam-5871	554	2	k	k	X
ejpam-5871	555	1	[	[	PUNCT
ejpam-5871	555	2	s	s	X
ejpam-5871	555	3	kz	kz	PROPN
ejpam-5871	555	4	β	β	PROPN
ejpam-5871	555	5	r+1	r+1	PROPN
ejpam-5871	555	6	∅⅁(r2	∅⅁(r2	NOUN
ejpam-5871	555	7	)	)	PUNCT
ejpam-5871	556	1	+	+	SYM
ejpam-5871	556	2	s	s	VERB
ejpam-5871	556	3	kz	kz	PROPN
ejpam-5871	556	4	β	β	PROPN
ejpam-5871	556	5	r−2	r−2	PROPN
ejpam-5871	556	6	∅⅁(r1	∅⅁(r1	PROPN
ejpam-5871	556	7	)	)	PUNCT
ejpam-5871	556	8	]	]	PUNCT
ejpam-5871	557	1	+	+	CCONJ
ejpam-5871	557	2	℧	℧	PROPN
ejpam-5871	557	3	1	1	NUM
ejpam-5871	557	4	(	(	PUNCT
ejpam-5871	557	5	1	1	NUM
ejpam-5871	557	6	2	2	NUM
ejpam-5871	557	7	)	)	PUNCT
ejpam-5871	557	8	℧	℧	SYM
ejpam-5871	557	9	2	2	NUM
ejpam-5871	557	10	(	(	PUNCT
ejpam-5871	557	11	1	1	NUM
ejpam-5871	557	12	2	2	NUM
ejpam-5871	557	13	)	)	PUNCT
ejpam-5871	557	14	(	(	PUNCT
ejpam-5871	557	15	p	p	X
ejpam-5871	557	16	(	(	PUNCT
ejpam-5871	557	17	r1	r1	PROPN
ejpam-5871	557	18	,	,	PUNCT
ejpam-5871	557	19	r2	r2	PROPN
ejpam-5871	557	20	)	)	PUNCT
ejpam-5871	557	21	(	(	PUNCT
ejpam-5871	557	22	s+	s+	NUM
ejpam-5871	557	23	1)−	1)−	PROPN
ejpam-5871	557	24	β	β	X
ejpam-5871	557	25	k	k	PROPN
ejpam-5871	557	26	kγk(β	kγk(β	PROPN
ejpam-5871	557	27	)	)	PUNCT
ejpam-5871	557	28	∫	∫	PROPN
ejpam-5871	557	29	1	1	NUM
ejpam-5871	557	30	0	0	NUM
ejpam-5871	557	31	θ	θ	PROPN
ejpam-5871	557	32	β	β	X
ejpam-5871	557	33	k	k	X
ejpam-5871	557	34	−1[	−1[	X
ejpam-5871	557	35	℧	℧	PROPN
ejpam-5871	557	36	1(θ)	1(θ)	NUM
ejpam-5871	557	37	℧	℧	SYM
ejpam-5871	557	38	2(1−	2(1−	NUM
ejpam-5871	557	39	θ	θ	NOUN
ejpam-5871	557	40	)	)	PUNCT
ejpam-5871	558	1	+	+	CCONJ
ejpam-5871	558	2	℧	℧	PROPN
ejpam-5871	558	3	1(1−	1(1−	NUM
ejpam-5871	558	4	θ)	θ)	PROPN
ejpam-5871	558	5	℧	℧	PROPN
ejpam-5871	558	6	2(θ)]dθ	2(θ)]dθ	NOUN
ejpam-5871	558	7	+	+	ADJ
ejpam-5871	558	8	q(r1	q(r1	ADJ
ejpam-5871	558	9	,	,	PUNCT
ejpam-5871	558	10	r2	r2	PROPN
ejpam-5871	558	11	)	)	PUNCT
ejpam-5871	558	12	(	(	PUNCT
ejpam-5871	558	13	s+	s+	NUM
ejpam-5871	558	14	1)−	1)−	PROPN
ejpam-5871	558	15	β	β	X
ejpam-5871	558	16	k	k	PROPN
ejpam-5871	558	17	kγk(β	kγk(β	PROPN
ejpam-5871	558	18	)	)	PUNCT
ejpam-5871	558	19	∫	∫	PROPN
ejpam-5871	558	20	1	1	NUM
ejpam-5871	558	21	0	0	NUM
ejpam-5871	558	22	θ	θ	PROPN
ejpam-5871	558	23	β	β	X
ejpam-5871	558	24	k	k	X
ejpam-5871	558	25	−1[	−1[	X
ejpam-5871	558	26	℧	℧	PROPN
ejpam-5871	558	27	1(θ)	1(θ)	NUM
ejpam-5871	558	28	℧	℧	NOUN
ejpam-5871	558	29	2(θ	2(θ	NUM
ejpam-5871	558	30	)	)	PUNCT
ejpam-5871	558	31	+	+	CCONJ
ejpam-5871	558	32	℧	℧	PROPN
ejpam-5871	558	33	1(1−	1(1−	NUM
ejpam-5871	558	34	θ)	θ)	PROPN
ejpam-5871	558	35	℧	℧	NOUN
ejpam-5871	558	36	2(1−	2(1−	NUM
ejpam-5871	558	37	θ)]dθ	θ)]dθ	NOUN
ejpam-5871	558	38	)	)	PUNCT
ejpam-5871	558	39	,	,	PUNCT
ejpam-5871	558	40	where	where	SCONJ
ejpam-5871	558	41	,	,	PUNCT
ejpam-5871	558	42	p	p	X
ejpam-5871	558	43	(	(	PUNCT
ejpam-5871	558	44	r1	r1	PROPN
ejpam-5871	558	45	,	,	PUNCT
ejpam-5871	558	46	r2	r2	PROPN
ejpam-5871	558	47	)	)	PUNCT
ejpam-5871	559	1	=	=	SYM
ejpam-5871	559	2	∅(r1)⅁(r1	∅(r1)⅁(r1	NOUN
ejpam-5871	559	3	)	)	PUNCT
ejpam-5871	560	1	+	+	NUM
ejpam-5871	560	2	∅(r2)⅁(r2	∅(r2)⅁(r2	NOUN
ejpam-5871	560	3	)	)	PUNCT
ejpam-5871	560	4	,	,	PUNCT
ejpam-5871	560	5	q(r1	q(r1	PROPN
ejpam-5871	560	6	,	,	PUNCT
ejpam-5871	560	7	r2	r2	PROPN
ejpam-5871	560	8	)	)	PUNCT
ejpam-5871	560	9	=	=	SYM
ejpam-5871	560	10	∅(r1)⅁(r2	∅(r1)⅁(r2	NOUN
ejpam-5871	560	11	)	)	PUNCT
ejpam-5871	561	1	+	+	NOUN
ejpam-5871	561	2	∅(r2)⅁(r1	∅(r2)⅁(r1	ADJ
ejpam-5871	561	3	)	)	PUNCT
ejpam-5871	561	4	.	.	PUNCT
ejpam-5871	562	1	proof	proof	NOUN
ejpam-5871	562	2	.	.	PUNCT
ejpam-5871	563	1	since	since	SCONJ
ejpam-5871	563	2	∅,⅁	∅,⅁	PROPN
ejpam-5871	563	3	∈	∈	PROPN
ejpam-5871	563	4	sigx([r1	sigx([r1	PROPN
ejpam-5871	563	5	,	,	PUNCT
ejpam-5871	563	6	r2	r2	PROPN
ejpam-5871	563	7	]	]	PUNCT
ejpam-5871	563	8	,	,	PUNCT
ejpam-5871	563	9	r	r	NOUN
ejpam-5871	563	10	+	+	NOUN
ejpam-5871	563	11	)	)	PUNCT
ejpam-5871	563	12	,	,	PUNCT
ejpam-5871	563	13	then	then	ADV
ejpam-5871	563	14	∅	∅	NOUN
ejpam-5871	563	15	(	(	PUNCT
ejpam-5871	563	16	⋋−1	⋋−1	X
ejpam-5871	563	17	(	(	PUNCT
ejpam-5871	563	18	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	563	19	)	)	PUNCT
ejpam-5871	563	20	+	+	NOUN
ejpam-5871	563	21	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	563	22	)	)	PUNCT
ejpam-5871	563	23	2	2	NUM
ejpam-5871	563	24	)	)	PUNCT
ejpam-5871	563	25	1	1	NUM
ejpam-5871	563	26	s+1	s+1	NOUN
ejpam-5871	563	27	)	)	PUNCT
ejpam-5871	563	28	⅁	⅁	PROPN
ejpam-5871	563	29	(	(	PUNCT
ejpam-5871	563	30	⋋−1	⋋−1	X
ejpam-5871	563	31	(	(	PUNCT
ejpam-5871	563	32	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	563	33	)	)	PUNCT
ejpam-5871	563	34	+	+	NOUN
ejpam-5871	563	35	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	563	36	)	)	PUNCT
ejpam-5871	563	37	2	2	NUM
ejpam-5871	563	38	)	)	PUNCT
ejpam-5871	563	39	1	1	NUM
ejpam-5871	563	40	s+1	s+1	PROPN
ejpam-5871	563	41	)	)	PUNCT
ejpam-5871	563	42	a.	a.	NOUN
ejpam-5871	563	43	mehmood	mehmood	PROPN
ejpam-5871	563	44	et	et	PROPN
ejpam-5871	563	45	al	al	PROPN
ejpam-5871	563	46	.	.	PUNCT
ejpam-5871	563	47	/	/	SYM
ejpam-5871	563	48	eur	eur	PROPN
ejpam-5871	563	49	.	.	PUNCT
ejpam-5871	564	1	j.	j.	PROPN
ejpam-5871	564	2	pure	pure	PROPN
ejpam-5871	564	3	appl	appl	PROPN
ejpam-5871	564	4	.	.	PROPN
ejpam-5871	564	5	math	math	PROPN
ejpam-5871	564	6	,	,	PUNCT
ejpam-5871	564	7	18	18	NUM
ejpam-5871	564	8	(	(	PUNCT
ejpam-5871	564	9	2	2	NUM
ejpam-5871	564	10	)	)	PUNCT
ejpam-5871	564	11	(	(	PUNCT
ejpam-5871	564	12	2025	2025	NUM
ejpam-5871	564	13	)	)	PUNCT
ejpam-5871	564	14	,	,	PUNCT
ejpam-5871	564	15	5871	5871	NUM
ejpam-5871	564	16	21	21	NUM
ejpam-5871	564	17	of	of	ADP
ejpam-5871	564	18	26	26	NUM
ejpam-5871	564	19	⊇	⊇	NOUN
ejpam-5871	564	20	℧	℧	PROPN
ejpam-5871	564	21	1	1	NUM
ejpam-5871	564	22	(	(	PUNCT
ejpam-5871	564	23	1	1	NUM
ejpam-5871	564	24	2	2	NUM
ejpam-5871	564	25	)	)	PUNCT
ejpam-5871	564	26	℧	℧	SYM
ejpam-5871	564	27	2	2	NUM
ejpam-5871	564	28	(	(	PUNCT
ejpam-5871	564	29	1	1	NUM
ejpam-5871	564	30	2	2	NUM
ejpam-5871	564	31	)	)	PUNCT
ejpam-5871	564	32	[	[	PUNCT
ejpam-5871	564	33	∅	∅	NOUN
ejpam-5871	564	34	(	(	PUNCT
ejpam-5871	564	35	⋋−1	⋋−1	X
ejpam-5871	564	36	(	(	PUNCT
ejpam-5871	564	37	θ	θ	PROPN
ejpam-5871	564	38	⋋s+1	⋋s+1	PROPN
ejpam-5871	564	39	(	(	PUNCT
ejpam-5871	564	40	r1	r1	PROPN
ejpam-5871	564	41	)	)	PUNCT
ejpam-5871	564	42	+	+	CCONJ
ejpam-5871	564	43	(	(	PUNCT
ejpam-5871	564	44	1−	1−	NUM
ejpam-5871	564	45	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	564	46	(	(	PUNCT
ejpam-5871	564	47	r2	r2	PROPN
ejpam-5871	564	48	)	)	PUNCT
ejpam-5871	564	49	)	)	PUNCT
ejpam-5871	564	50	1	1	NUM
ejpam-5871	564	51	s+1	s+1	NOUN
ejpam-5871	564	52	)	)	PUNCT
ejpam-5871	564	53	⅁	⅁	PROPN
ejpam-5871	564	54	(	(	PUNCT
ejpam-5871	564	55	⋋−1	⋋−1	X
ejpam-5871	564	56	(	(	PUNCT
ejpam-5871	564	57	θ	θ	PROPN
ejpam-5871	564	58	⋋s+1	⋋s+1	PROPN
ejpam-5871	564	59	(	(	PUNCT
ejpam-5871	564	60	r1	r1	PROPN
ejpam-5871	564	61	)	)	PUNCT
ejpam-5871	564	62	+	+	CCONJ
ejpam-5871	564	63	(	(	PUNCT
ejpam-5871	564	64	(	(	PUNCT
ejpam-5871	564	65	1−	1−	NUM
ejpam-5871	564	66	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	564	67	(	(	PUNCT
ejpam-5871	564	68	r2	r2	PROPN
ejpam-5871	564	69	)	)	PUNCT
ejpam-5871	564	70	)	)	PUNCT
ejpam-5871	564	71	1	1	NUM
ejpam-5871	564	72	s+1	s+1	NOUN
ejpam-5871	564	73	)	)	PUNCT
ejpam-5871	565	1	+	+	NOUN
ejpam-5871	565	2	∅	∅	NOUN
ejpam-5871	565	3	(	(	PUNCT
ejpam-5871	565	4	⋋−1	⋋−1	X
ejpam-5871	565	5	(	(	PUNCT
ejpam-5871	565	6	θ	θ	PROPN
ejpam-5871	565	7	⋋s+1	⋋s+1	PROPN
ejpam-5871	565	8	(	(	PUNCT
ejpam-5871	565	9	r1	r1	PROPN
ejpam-5871	565	10	)	)	PUNCT
ejpam-5871	565	11	+	+	CCONJ
ejpam-5871	565	12	(	(	PUNCT
ejpam-5871	565	13	1−	1−	NUM
ejpam-5871	565	14	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	565	15	(	(	PUNCT
ejpam-5871	565	16	r2	r2	PROPN
ejpam-5871	565	17	)	)	PUNCT
ejpam-5871	565	18	)	)	PUNCT
ejpam-5871	565	19	1	1	NUM
ejpam-5871	565	20	s+1	s+1	NOUN
ejpam-5871	565	21	)	)	PUNCT
ejpam-5871	565	22	⅁	⅁	PROPN
ejpam-5871	565	23	(	(	PUNCT
ejpam-5871	565	24	⋋−1	⋋−1	X
ejpam-5871	565	25	(	(	PUNCT
ejpam-5871	565	26	(	(	PUNCT
ejpam-5871	565	27	1−	1−	NUM
ejpam-5871	565	28	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	565	29	(	(	PUNCT
ejpam-5871	565	30	r1	r1	PROPN
ejpam-5871	565	31	)	)	PUNCT
ejpam-5871	565	32	+	+	NUM
ejpam-5871	565	33	θ	θ	PUNCT
ejpam-5871	565	34	⋋s+1	⋋s+1	VERB
ejpam-5871	565	35	(	(	PUNCT
ejpam-5871	565	36	r2	r2	PROPN
ejpam-5871	565	37	)	)	PUNCT
ejpam-5871	565	38	)	)	PUNCT
ejpam-5871	565	39	1	1	NUM
ejpam-5871	565	40	s+1	s+1	NOUN
ejpam-5871	565	41	)	)	PUNCT
ejpam-5871	566	1	+	+	NOUN
ejpam-5871	566	2	∅	∅	NOUN
ejpam-5871	566	3	(	(	PUNCT
ejpam-5871	566	4	⋋−1	⋋−1	X
ejpam-5871	566	5	(	(	PUNCT
ejpam-5871	566	6	(	(	PUNCT
ejpam-5871	566	7	1−	1−	NUM
ejpam-5871	566	8	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	566	9	(	(	PUNCT
ejpam-5871	566	10	r1	r1	PROPN
ejpam-5871	566	11	)	)	PUNCT
ejpam-5871	566	12	+	+	NUM
ejpam-5871	566	13	θ	θ	PUNCT
ejpam-5871	566	14	⋋s+1	⋋s+1	VERB
ejpam-5871	566	15	(	(	PUNCT
ejpam-5871	566	16	r2	r2	PROPN
ejpam-5871	566	17	)	)	PUNCT
ejpam-5871	566	18	)	)	PUNCT
ejpam-5871	566	19	1	1	NUM
ejpam-5871	566	20	s+1	s+1	NOUN
ejpam-5871	566	21	)	)	PUNCT
ejpam-5871	566	22	⅁	⅁	PROPN
ejpam-5871	566	23	(	(	PUNCT
ejpam-5871	566	24	⋋−1	⋋−1	X
ejpam-5871	566	25	(	(	PUNCT
ejpam-5871	566	26	θ(r1	θ(r1	NOUN
ejpam-5871	566	27	)	)	PUNCT
ejpam-5871	566	28	+	+	CCONJ
ejpam-5871	566	29	(	(	PUNCT
ejpam-5871	566	30	1−	1−	NUM
ejpam-5871	566	31	θ)r2	θ)r2	ADJ
ejpam-5871	566	32	)	)	PUNCT
ejpam-5871	566	33	1	1	NUM
ejpam-5871	566	34	s+1	s+1	NOUN
ejpam-5871	566	35	)	)	PUNCT
ejpam-5871	567	1	+	+	NOUN
ejpam-5871	567	2	∅	∅	NOUN
ejpam-5871	567	3	(	(	PUNCT
ejpam-5871	567	4	⋋−1	⋋−1	X
ejpam-5871	567	5	(	(	PUNCT
ejpam-5871	567	6	(	(	PUNCT
ejpam-5871	567	7	1−	1−	NUM
ejpam-5871	567	8	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	567	9	(	(	PUNCT
ejpam-5871	567	10	r1	r1	PROPN
ejpam-5871	567	11	)	)	PUNCT
ejpam-5871	567	12	+	+	NUM
ejpam-5871	567	13	θ	θ	PUNCT
ejpam-5871	567	14	⋋s+1	⋋s+1	VERB
ejpam-5871	567	15	(	(	PUNCT
ejpam-5871	567	16	r2	r2	PROPN
ejpam-5871	567	17	)	)	PUNCT
ejpam-5871	567	18	)	)	PUNCT
ejpam-5871	567	19	1	1	NUM
ejpam-5871	567	20	s+1	s+1	NOUN
ejpam-5871	567	21	)	)	PUNCT
ejpam-5871	567	22	⅁	⅁	PROPN
ejpam-5871	567	23	(	(	PUNCT
ejpam-5871	567	24	⋋−1	⋋−1	X
ejpam-5871	567	25	(	(	PUNCT
ejpam-5871	567	26	(	(	PUNCT
ejpam-5871	567	27	1−	1−	NUM
ejpam-5871	567	28	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	567	29	(	(	PUNCT
ejpam-5871	567	30	r1	r1	PROPN
ejpam-5871	567	31	)	)	PUNCT
ejpam-5871	567	32	+	+	NUM
ejpam-5871	567	33	θ	θ	PUNCT
ejpam-5871	567	34	⋋s+1	⋋s+1	VERB
ejpam-5871	567	35	(	(	PUNCT
ejpam-5871	567	36	r2	r2	PROPN
ejpam-5871	567	37	)	)	PUNCT
ejpam-5871	567	38	)	)	PUNCT
ejpam-5871	567	39	1	1	NUM
ejpam-5871	567	40	s+1	s+1	NOUN
ejpam-5871	567	41	)	)	PUNCT
ejpam-5871	567	42	]	]	PUNCT
ejpam-5871	567	43	.	.	PUNCT
ejpam-5871	568	1	multiplying	multiply	VERB
ejpam-5871	568	2	preceding	precede	VERB
ejpam-5871	568	3	inclusion	inclusion	NOUN
ejpam-5871	568	4	by	by	ADP
ejpam-5871	568	5	(	(	PUNCT
ejpam-5871	568	6	s+1)−	s+1)−	PROPN
ejpam-5871	568	7	β	β	PROPN
ejpam-5871	568	8	k	k	PROPN
ejpam-5871	568	9	kγk(β	kγk(β	PROPN
ejpam-5871	568	10	)	)	PUNCT
ejpam-5871	568	11	θ	θ	PROPN
ejpam-5871	568	12	β	β	X
ejpam-5871	568	13	k	k	X
ejpam-5871	568	14	−1	−1	NOUN
ejpam-5871	568	15	and	and	CCONJ
ejpam-5871	568	16	taking	take	VERB
ejpam-5871	568	17	the	the	DET
ejpam-5871	568	18	integration	integration	NOUN
ejpam-5871	568	19	on	on	ADP
ejpam-5871	568	20	[	[	X
ejpam-5871	568	21	0	0	NUM
ejpam-5871	568	22	,	,	PUNCT
ejpam-5871	568	23	1	1	NUM
ejpam-5871	568	24	]	]	PUNCT
ejpam-5871	568	25	w.r.t	w.r.t	NOUN
ejpam-5871	568	26	”	"	PUNCT
ejpam-5871	568	27	θ”red	θ”re	VERB
ejpam-5871	568	28	,	,	PUNCT
ejpam-5871	568	29	we	we	PRON
ejpam-5871	568	30	have	have	VERB
ejpam-5871	568	31	(	(	PUNCT
ejpam-5871	568	32	s+	s+	NUM
ejpam-5871	568	33	1)−	1)−	PROPN
ejpam-5871	568	34	β	β	X
ejpam-5871	568	35	k	k	PROPN
ejpam-5871	568	36	kγk(β	kγk(β	PROPN
ejpam-5871	568	37	)	)	PUNCT
ejpam-5871	568	38	∫	∫	PROPN
ejpam-5871	569	1	1	1	NUM
ejpam-5871	569	2	0	0	NUM
ejpam-5871	569	3	θ	θ	PROPN
ejpam-5871	569	4	β	β	X
ejpam-5871	569	5	k	k	X
ejpam-5871	569	6	−1∅	−1∅	PROPN
ejpam-5871	569	7	(	(	PUNCT
ejpam-5871	569	8	⋋−1	⋋−1	ADJ
ejpam-5871	569	9	(	(	PUNCT
ejpam-5871	569	10	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	569	11	)	)	PUNCT
ejpam-5871	569	12	+	+	NOUN
ejpam-5871	569	13	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	569	14	)	)	PUNCT
ejpam-5871	569	15	2	2	NUM
ejpam-5871	569	16	)	)	PUNCT
ejpam-5871	569	17	1	1	NUM
ejpam-5871	569	18	s+1	s+1	NOUN
ejpam-5871	569	19	)	)	PUNCT
ejpam-5871	569	20	⅁	⅁	PROPN
ejpam-5871	569	21	(	(	PUNCT
ejpam-5871	569	22	⋋−1	⋋−1	X
ejpam-5871	569	23	(	(	PUNCT
ejpam-5871	569	24	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	569	25	)	)	PUNCT
ejpam-5871	569	26	+	+	NOUN
ejpam-5871	569	27	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	569	28	)	)	PUNCT
ejpam-5871	569	29	2	2	NUM
ejpam-5871	569	30	)	)	PUNCT
ejpam-5871	569	31	1	1	NUM
ejpam-5871	569	32	s+1	s+1	PROPN
ejpam-5871	569	33	)	)	PUNCT
ejpam-5871	569	34	dθ	dθ	PROPN
ejpam-5871	569	35	⊇	⊇	PROPN
ejpam-5871	569	36	℧	℧	PROPN
ejpam-5871	569	37	1	1	NUM
ejpam-5871	569	38	(	(	PUNCT
ejpam-5871	569	39	1	1	NUM
ejpam-5871	569	40	2	2	NUM
ejpam-5871	569	41	)	)	PUNCT
ejpam-5871	569	42	℧	℧	SYM
ejpam-5871	569	43	2	2	NUM
ejpam-5871	569	44	(	(	PUNCT
ejpam-5871	569	45	1	1	NUM
ejpam-5871	569	46	2	2	NUM
ejpam-5871	569	47	)	)	PUNCT
ejpam-5871	569	48	[	[	PUNCT
ejpam-5871	569	49	(	(	PUNCT
ejpam-5871	569	50	s+	s+	NUM
ejpam-5871	569	51	1)−	1)−	PROPN
ejpam-5871	569	52	β	β	X
ejpam-5871	569	53	k	k	PROPN
ejpam-5871	569	54	kγk(β	kγk(β	PROPN
ejpam-5871	569	55	)	)	PUNCT
ejpam-5871	569	56	∫	∫	PROPN
ejpam-5871	570	1	1	1	NUM
ejpam-5871	570	2	0	0	NUM
ejpam-5871	570	3	θ	θ	PROPN
ejpam-5871	570	4	β	β	X
ejpam-5871	570	5	k	k	X
ejpam-5871	570	6	−1∅	−1∅	PROPN
ejpam-5871	570	7	(	(	PUNCT
ejpam-5871	570	8	⋋−1	⋋−1	ADJ
ejpam-5871	570	9	(	(	PUNCT
ejpam-5871	570	10	θ	θ	PROPN
ejpam-5871	570	11	⋋s+1	⋋s+1	PROPN
ejpam-5871	570	12	(	(	PUNCT
ejpam-5871	570	13	r1	r1	PROPN
ejpam-5871	570	14	)	)	PUNCT
ejpam-5871	570	15	+	+	CCONJ
ejpam-5871	570	16	(	(	PUNCT
ejpam-5871	570	17	1−	1−	NUM
ejpam-5871	570	18	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	570	19	(	(	PUNCT
ejpam-5871	570	20	r2	r2	PROPN
ejpam-5871	570	21	)	)	PUNCT
ejpam-5871	570	22	)	)	PUNCT
ejpam-5871	570	23	1	1	NUM
ejpam-5871	570	24	s+1	s+1	NOUN
ejpam-5871	570	25	)	)	PUNCT
ejpam-5871	570	26	×	×	NOUN
ejpam-5871	570	27	⅁	⅁	NOUN
ejpam-5871	570	28	(	(	PUNCT
ejpam-5871	570	29	⋋−1	⋋−1	X
ejpam-5871	570	30	(	(	PUNCT
ejpam-5871	570	31	θ	θ	PROPN
ejpam-5871	570	32	⋋s+1	⋋s+1	PROPN
ejpam-5871	570	33	(	(	PUNCT
ejpam-5871	570	34	r1	r1	PROPN
ejpam-5871	570	35	)	)	PUNCT
ejpam-5871	570	36	+	+	CCONJ
ejpam-5871	570	37	(	(	PUNCT
ejpam-5871	570	38	1−	1−	NUM
ejpam-5871	570	39	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	570	40	(	(	PUNCT
ejpam-5871	570	41	r2	r2	PROPN
ejpam-5871	570	42	)	)	PUNCT
ejpam-5871	570	43	)	)	PUNCT
ejpam-5871	570	44	1	1	NUM
ejpam-5871	570	45	s+1	s+1	NOUN
ejpam-5871	570	46	)	)	PUNCT
ejpam-5871	570	47	dθ	dθ	PROPN
ejpam-5871	570	48	+	+	X
ejpam-5871	570	49	(	(	PUNCT
ejpam-5871	570	50	s+	s+	X
ejpam-5871	570	51	1)−	1)−	PROPN
ejpam-5871	570	52	β	β	X
ejpam-5871	570	53	k	k	PROPN
ejpam-5871	570	54	kγk(β	kγk(β	PROPN
ejpam-5871	570	55	)	)	PUNCT
ejpam-5871	570	56	∫	∫	PROPN
ejpam-5871	571	1	1	1	NUM
ejpam-5871	571	2	0	0	NUM
ejpam-5871	571	3	θ	θ	PROPN
ejpam-5871	571	4	β	β	X
ejpam-5871	571	5	k	k	X
ejpam-5871	571	6	−1∅	−1∅	PROPN
ejpam-5871	571	7	(	(	PUNCT
ejpam-5871	571	8	⋋−1	⋋−1	ADJ
ejpam-5871	571	9	(	(	PUNCT
ejpam-5871	571	10	θ	θ	PROPN
ejpam-5871	571	11	⋋s+1	⋋s+1	PROPN
ejpam-5871	571	12	(	(	PUNCT
ejpam-5871	571	13	r1	r1	PROPN
ejpam-5871	571	14	)	)	PUNCT
ejpam-5871	571	15	+	+	CCONJ
ejpam-5871	571	16	(	(	PUNCT
ejpam-5871	571	17	1−	1−	NUM
ejpam-5871	571	18	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	571	19	(	(	PUNCT
ejpam-5871	571	20	r2	r2	PROPN
ejpam-5871	571	21	)	)	PUNCT
ejpam-5871	571	22	)	)	PUNCT
ejpam-5871	571	23	1	1	NUM
ejpam-5871	571	24	s+1	s+1	NOUN
ejpam-5871	571	25	)	)	PUNCT
ejpam-5871	571	26	×	×	NOUN
ejpam-5871	571	27	⅁	⅁	NOUN
ejpam-5871	571	28	(	(	PUNCT
ejpam-5871	571	29	⋋−1	⋋−1	X
ejpam-5871	571	30	(	(	PUNCT
ejpam-5871	571	31	(	(	PUNCT
ejpam-5871	571	32	1−	1−	NUM
ejpam-5871	571	33	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	571	34	(	(	PUNCT
ejpam-5871	571	35	r1	r1	PROPN
ejpam-5871	571	36	)	)	PUNCT
ejpam-5871	571	37	+	+	NUM
ejpam-5871	571	38	θ	θ	PROPN
ejpam-5871	571	39	⋋s+1	⋋s+1	ADJ
ejpam-5871	571	40	r2	r2	NOUN
ejpam-5871	571	41	)	)	PUNCT
ejpam-5871	571	42	1	1	NUM
ejpam-5871	571	43	s+1	s+1	PROPN
ejpam-5871	571	44	)	)	PUNCT
ejpam-5871	571	45	dθ	dθ	PROPN
ejpam-5871	571	46	+	+	X
ejpam-5871	571	47	(	(	PUNCT
ejpam-5871	571	48	s+	s+	X
ejpam-5871	571	49	1)−	1)−	PROPN
ejpam-5871	571	50	β	β	X
ejpam-5871	571	51	k	k	PROPN
ejpam-5871	571	52	kγk(β	kγk(β	PROPN
ejpam-5871	571	53	)	)	PUNCT
ejpam-5871	571	54	∫	∫	PROPN
ejpam-5871	571	55	1	1	NUM
ejpam-5871	571	56	0	0	NUM
ejpam-5871	571	57	θ	θ	PROPN
ejpam-5871	571	58	β	β	X
ejpam-5871	571	59	k	k	X
ejpam-5871	571	60	−1∅	−1∅	PROPN
ejpam-5871	571	61	(	(	PUNCT
ejpam-5871	571	62	⋋−1	⋋−1	ADJ
ejpam-5871	571	63	(	(	PUNCT
ejpam-5871	571	64	(	(	PUNCT
ejpam-5871	571	65	1−	1−	NUM
ejpam-5871	571	66	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	571	67	(	(	PUNCT
ejpam-5871	571	68	r1	r1	PROPN
ejpam-5871	571	69	)	)	PUNCT
ejpam-5871	571	70	+	+	NUM
ejpam-5871	571	71	θ	θ	PUNCT
ejpam-5871	571	72	⋋s+1	⋋s+1	VERB
ejpam-5871	571	73	(	(	PUNCT
ejpam-5871	571	74	r2	r2	PROPN
ejpam-5871	571	75	)	)	PUNCT
ejpam-5871	571	76	)	)	PUNCT
ejpam-5871	571	77	1	1	NUM
ejpam-5871	571	78	s+1	s+1	NOUN
ejpam-5871	571	79	)	)	PUNCT
ejpam-5871	571	80	×	×	NOUN
ejpam-5871	571	81	⅁	⅁	NOUN
ejpam-5871	571	82	(	(	PUNCT
ejpam-5871	571	83	⋋−1	⋋−1	X
ejpam-5871	571	84	(	(	PUNCT
ejpam-5871	571	85	θ	θ	PROPN
ejpam-5871	571	86	⋋s+1	⋋s+1	PROPN
ejpam-5871	571	87	(	(	PUNCT
ejpam-5871	571	88	r1	r1	PROPN
ejpam-5871	571	89	)	)	PUNCT
ejpam-5871	571	90	+	+	CCONJ
ejpam-5871	571	91	(	(	PUNCT
ejpam-5871	571	92	1−	1−	NUM
ejpam-5871	571	93	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	571	94	(	(	PUNCT
ejpam-5871	571	95	r2	r2	PROPN
ejpam-5871	571	96	)	)	PUNCT
ejpam-5871	571	97	)	)	PUNCT
ejpam-5871	571	98	1	1	NUM
ejpam-5871	571	99	s+1	s+1	NOUN
ejpam-5871	571	100	)	)	PUNCT
ejpam-5871	571	101	dθ	dθ	PROPN
ejpam-5871	571	102	+	+	X
ejpam-5871	571	103	(	(	PUNCT
ejpam-5871	571	104	s+	s+	X
ejpam-5871	571	105	1)−	1)−	PROPN
ejpam-5871	571	106	β	β	X
ejpam-5871	571	107	k	k	PROPN
ejpam-5871	571	108	kγk(β	kγk(β	PROPN
ejpam-5871	571	109	)	)	PUNCT
ejpam-5871	571	110	∫	∫	PROPN
ejpam-5871	571	111	1	1	NUM
ejpam-5871	571	112	0	0	NUM
ejpam-5871	571	113	θ	θ	PROPN
ejpam-5871	571	114	β	β	X
ejpam-5871	571	115	k	k	X
ejpam-5871	571	116	−1∅	−1∅	PROPN
ejpam-5871	571	117	(	(	PUNCT
ejpam-5871	571	118	⋋−1	⋋−1	ADJ
ejpam-5871	571	119	(	(	PUNCT
ejpam-5871	571	120	(	(	PUNCT
ejpam-5871	571	121	1−	1−	NUM
ejpam-5871	571	122	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	571	123	(	(	PUNCT
ejpam-5871	571	124	r1	r1	PROPN
ejpam-5871	571	125	)	)	PUNCT
ejpam-5871	571	126	+	+	NUM
ejpam-5871	571	127	θ	θ	PUNCT
ejpam-5871	571	128	⋋s+1	⋋s+1	VERB
ejpam-5871	571	129	(	(	PUNCT
ejpam-5871	571	130	r2	r2	PROPN
ejpam-5871	571	131	)	)	PUNCT
ejpam-5871	571	132	)	)	PUNCT
ejpam-5871	571	133	1	1	NUM
ejpam-5871	571	134	s+1	s+1	NOUN
ejpam-5871	571	135	)	)	PUNCT
ejpam-5871	571	136	×	×	NOUN
ejpam-5871	571	137	⅁	⅁	NOUN
ejpam-5871	571	138	(	(	PUNCT
ejpam-5871	571	139	⋋−1	⋋−1	X
ejpam-5871	571	140	(	(	PUNCT
ejpam-5871	571	141	(	(	PUNCT
ejpam-5871	571	142	1−	1−	NUM
ejpam-5871	571	143	θ)⋋s+1	θ)⋋s+1	X
ejpam-5871	571	144	(	(	PUNCT
ejpam-5871	571	145	r1	r1	PROPN
ejpam-5871	571	146	)	)	PUNCT
ejpam-5871	571	147	+	+	NUM
ejpam-5871	571	148	θ	θ	PUNCT
ejpam-5871	571	149	⋋s+1	⋋s+1	VERB
ejpam-5871	571	150	(	(	PUNCT
ejpam-5871	571	151	r2	r2	PROPN
ejpam-5871	571	152	)	)	PUNCT
ejpam-5871	571	153	)	)	PUNCT
ejpam-5871	571	154	1	1	NUM
ejpam-5871	571	155	s+1	s+1	PROPN
ejpam-5871	571	156	)	)	PUNCT
ejpam-5871	571	157	dθ	dθ	PROPN
ejpam-5871	571	158	]	]	PUNCT
ejpam-5871	571	159	.	.	PUNCT
ejpam-5871	572	1	by	by	ADP
ejpam-5871	572	2	definition	definition	NOUN
ejpam-5871	572	3	of	of	ADP
ejpam-5871	572	4	ı.υ-(⋋s+1	ı.υ-(⋋s+1	PROPN
ejpam-5871	572	5	,	,	PUNCT
ejpam-5871	572	6	℧	℧	PROPN
ejpam-5871	572	7	)	)	PUNCT
ejpam-5871	572	8	and	and	CCONJ
ejpam-5871	572	9	substituting	substitute	VERB
ejpam-5871	572	10	⋋s+1(χ	⋋s+1(χ	PRON
ejpam-5871	572	11	)	)	PUNCT
ejpam-5871	573	1	=	=	SYM
ejpam-5871	573	2	θ⋋s+1	θ⋋s+1	ADJ
ejpam-5871	573	3	(	(	PUNCT
ejpam-5871	573	4	r1)+(1−θ)⋋s+1	r1)+(1−θ)⋋s+1	PROPN
ejpam-5871	573	5	(	(	PUNCT
ejpam-5871	573	6	r2)red	r2)re	VERB
ejpam-5871	573	7	,	,	PUNCT
ejpam-5871	573	8	we	we	PRON
ejpam-5871	573	9	have	have	VERB
ejpam-5871	573	10	(	(	PUNCT
ejpam-5871	573	11	s+	s+	NUM
ejpam-5871	573	12	1)−	1)−	PROPN
ejpam-5871	573	13	β	β	X
ejpam-5871	573	14	k	k	X
ejpam-5871	573	15	βγk(β	βγk(β	PROPN
ejpam-5871	573	16	)	)	PUNCT
ejpam-5871	573	17	∅	∅	NOUN
ejpam-5871	573	18	(	(	PUNCT
ejpam-5871	573	19	⋋−1	⋋−1	X
ejpam-5871	573	20	(	(	PUNCT
ejpam-5871	573	21	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	573	22	)	)	PUNCT
ejpam-5871	573	23	+	+	NOUN
ejpam-5871	573	24	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	573	25	)	)	PUNCT
ejpam-5871	573	26	2	2	NUM
ejpam-5871	573	27	)	)	PUNCT
ejpam-5871	573	28	1	1	NUM
ejpam-5871	573	29	s+1	s+1	NOUN
ejpam-5871	573	30	)	)	PUNCT
ejpam-5871	573	31	⅁	⅁	PROPN
ejpam-5871	573	32	(	(	PUNCT
ejpam-5871	573	33	⋋−1	⋋−1	X
ejpam-5871	573	34	(	(	PUNCT
ejpam-5871	573	35	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	573	36	)	)	PUNCT
ejpam-5871	573	37	+	+	NOUN
ejpam-5871	573	38	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	573	39	)	)	PUNCT
ejpam-5871	573	40	2	2	NUM
ejpam-5871	573	41	)	)	PUNCT
ejpam-5871	573	42	1	1	NUM
ejpam-5871	573	43	s+1	s+1	PROPN
ejpam-5871	573	44	)	)	PUNCT
ejpam-5871	573	45	⊇	⊇	PROPN
ejpam-5871	573	46	℧	℧	PROPN
ejpam-5871	573	47	1	1	NUM
ejpam-5871	573	48	(	(	PUNCT
ejpam-5871	573	49	1	1	NUM
ejpam-5871	573	50	2)	2)	NUM
ejpam-5871	573	51	℧	℧	PROPN
ejpam-5871	573	52	2	2	NUM
ejpam-5871	573	53	(	(	PUNCT
ejpam-5871	573	54	1	1	NUM
ejpam-5871	573	55	2	2	NUM
ejpam-5871	573	56	)	)	PUNCT
ejpam-5871	573	57	(	(	PUNCT
ejpam-5871	573	58	⋋s+1(r2)−⋋s+1(r1	⋋s+1(r2)−⋋s+1(r1	NOUN
ejpam-5871	573	59	)	)	PUNCT
ejpam-5871	573	60	)	)	PUNCT
ejpam-5871	574	1	β	β	X
ejpam-5871	574	2	k	k	X
ejpam-5871	575	1	[	[	PUNCT
ejpam-5871	575	2	s	s	X
ejpam-5871	575	3	kz	kz	PROPN
ejpam-5871	575	4	β	β	PROPN
ejpam-5871	575	5	r+1	r+1	PROPN
ejpam-5871	575	6	∅⅁(r2	∅⅁(r2	NOUN
ejpam-5871	575	7	)	)	PUNCT
ejpam-5871	576	1	+	+	SYM
ejpam-5871	576	2	s	s	VERB
ejpam-5871	576	3	kz	kz	PROPN
ejpam-5871	576	4	β	β	PROPN
ejpam-5871	576	5	r−2	r−2	PROPN
ejpam-5871	576	6	∅⅁(r1	∅⅁(r1	PROPN
ejpam-5871	576	7	)	)	PUNCT
ejpam-5871	576	8	]	]	PUNCT
ejpam-5871	577	1	+	+	CCONJ
ejpam-5871	577	2	℧	℧	PROPN
ejpam-5871	577	3	1	1	NUM
ejpam-5871	577	4	(	(	PUNCT
ejpam-5871	577	5	1	1	NUM
ejpam-5871	577	6	2	2	NUM
ejpam-5871	577	7	)	)	PUNCT
ejpam-5871	577	8	℧	℧	SYM
ejpam-5871	577	9	2	2	NUM
ejpam-5871	577	10	(	(	PUNCT
ejpam-5871	577	11	1	1	NUM
ejpam-5871	577	12	2	2	NUM
ejpam-5871	577	13	)	)	PUNCT
ejpam-5871	577	14	(	(	PUNCT
ejpam-5871	577	15	p	p	X
ejpam-5871	577	16	(	(	PUNCT
ejpam-5871	577	17	r1	r1	PROPN
ejpam-5871	577	18	,	,	PUNCT
ejpam-5871	577	19	r2	r2	PROPN
ejpam-5871	577	20	)	)	PUNCT
ejpam-5871	577	21	(	(	PUNCT
ejpam-5871	577	22	s+	s+	NUM
ejpam-5871	577	23	1)−	1)−	PROPN
ejpam-5871	577	24	β	β	X
ejpam-5871	577	25	k	k	PROPN
ejpam-5871	577	26	kγk(β	kγk(β	PROPN
ejpam-5871	577	27	)	)	PUNCT
ejpam-5871	577	28	∫	∫	PROPN
ejpam-5871	577	29	1	1	NUM
ejpam-5871	577	30	0	0	NUM
ejpam-5871	577	31	θ	θ	PROPN
ejpam-5871	577	32	β	β	X
ejpam-5871	577	33	k	k	X
ejpam-5871	577	34	−1[	−1[	X
ejpam-5871	577	35	℧	℧	PROPN
ejpam-5871	577	36	1(θ)	1(θ)	NUM
ejpam-5871	577	37	℧	℧	SYM
ejpam-5871	577	38	2(1−	2(1−	NUM
ejpam-5871	577	39	θ	θ	NOUN
ejpam-5871	577	40	)	)	PUNCT
ejpam-5871	577	41	+	+	CCONJ
ejpam-5871	578	1	℧	℧	PROPN
ejpam-5871	578	2	1(1−	1(1−	NUM
ejpam-5871	578	3	θ)	θ)	PROPN
ejpam-5871	578	4	℧	℧	PROPN
ejpam-5871	578	5	2(θ)]dθ	2(θ)]dθ	NUM
ejpam-5871	578	6	a.	a.	NOUN
ejpam-5871	578	7	mehmood	mehmood	PROPN
ejpam-5871	578	8	et	et	PROPN
ejpam-5871	578	9	al	al	PROPN
ejpam-5871	578	10	.	.	PUNCT
ejpam-5871	578	11	/	/	SYM
ejpam-5871	578	12	eur	eur	PROPN
ejpam-5871	578	13	.	.	PUNCT
ejpam-5871	579	1	j.	j.	PROPN
ejpam-5871	579	2	pure	pure	PROPN
ejpam-5871	579	3	appl	appl	PROPN
ejpam-5871	579	4	.	.	PROPN
ejpam-5871	579	5	math	math	PROPN
ejpam-5871	579	6	,	,	PUNCT
ejpam-5871	579	7	18	18	NUM
ejpam-5871	579	8	(	(	PUNCT
ejpam-5871	579	9	2	2	NUM
ejpam-5871	579	10	)	)	PUNCT
ejpam-5871	579	11	(	(	PUNCT
ejpam-5871	579	12	2025	2025	NUM
ejpam-5871	579	13	)	)	PUNCT
ejpam-5871	579	14	,	,	PUNCT
ejpam-5871	579	15	5871	5871	NUM
ejpam-5871	579	16	22	22	NUM
ejpam-5871	579	17	of	of	ADP
ejpam-5871	579	18	26	26	NUM
ejpam-5871	580	1	+	+	NOUN
ejpam-5871	580	2	q(r1	q(r1	ADJ
ejpam-5871	580	3	,	,	PUNCT
ejpam-5871	580	4	r2	r2	PROPN
ejpam-5871	580	5	)	)	PUNCT
ejpam-5871	580	6	(	(	PUNCT
ejpam-5871	580	7	s+	s+	NUM
ejpam-5871	580	8	1)−	1)−	PROPN
ejpam-5871	580	9	β	β	X
ejpam-5871	580	10	k	k	PROPN
ejpam-5871	580	11	kγk(β	kγk(β	PROPN
ejpam-5871	580	12	)	)	PUNCT
ejpam-5871	580	13	∫	∫	PROPN
ejpam-5871	581	1	1	1	NUM
ejpam-5871	581	2	0	0	NUM
ejpam-5871	581	3	θ	θ	PROPN
ejpam-5871	581	4	β	β	X
ejpam-5871	581	5	k	k	X
ejpam-5871	581	6	−1[	−1[	X
ejpam-5871	581	7	℧	℧	PROPN
ejpam-5871	581	8	1(θ)	1(θ)	NUM
ejpam-5871	581	9	℧	℧	NOUN
ejpam-5871	581	10	2(θ	2(θ	NUM
ejpam-5871	581	11	)	)	PUNCT
ejpam-5871	581	12	+	+	CCONJ
ejpam-5871	581	13	℧	℧	PROPN
ejpam-5871	581	14	1(1−	1(1−	NUM
ejpam-5871	581	15	θ)	θ)	PROPN
ejpam-5871	581	16	℧	℧	NOUN
ejpam-5871	581	17	2(1−	2(1−	NUM
ejpam-5871	581	18	θ)]dθ	θ)]dθ	NOUN
ejpam-5871	581	19	)	)	PUNCT
ejpam-5871	581	20	.	.	PUNCT
ejpam-5871	582	1	hence	hence	ADV
ejpam-5871	582	2	we	we	PRON
ejpam-5871	582	3	have	have	AUX
ejpam-5871	582	4	proved	prove	VERB
ejpam-5871	582	5	our	our	PRON
ejpam-5871	582	6	result	result	NOUN
ejpam-5871	582	7	.	.	PUNCT
ejpam-5871	583	1	corollary	corollary	ADJ
ejpam-5871	583	2	9	9	NUM
ejpam-5871	583	3	.	.	PUNCT
ejpam-5871	584	1	if	if	SCONJ
ejpam-5871	584	2	we	we	PRON
ejpam-5871	584	3	fix	fix	VERB
ejpam-5871	584	4	℧	℧	PROPN
ejpam-5871	584	5	(	(	PUNCT
ejpam-5871	584	6	θ	θ	NOUN
ejpam-5871	584	7	)	)	PUNCT
ejpam-5871	584	8	=	=	SYM
ejpam-5871	584	9	θ	θ	PROPN
ejpam-5871	584	10	in	in	ADP
ejpam-5871	584	11	theorem	theorem	NOUN
ejpam-5871	584	12	9	9	NUM
ejpam-5871	584	13	,	,	PUNCT
ejpam-5871	584	14	we	we	PRON
ejpam-5871	584	15	possess	possess	VERB
ejpam-5871	584	16	(	(	PUNCT
ejpam-5871	584	17	s+	s+	NUM
ejpam-5871	584	18	1)−	1)−	PROPN
ejpam-5871	584	19	β	β	X
ejpam-5871	584	20	k	k	X
ejpam-5871	584	21	βγk(β	βγk(β	PROPN
ejpam-5871	584	22	)	)	PUNCT
ejpam-5871	584	23	∅	∅	NOUN
ejpam-5871	584	24	(	(	PUNCT
ejpam-5871	584	25	⋋−1	⋋−1	X
ejpam-5871	584	26	(	(	PUNCT
ejpam-5871	584	27	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	584	28	)	)	PUNCT
ejpam-5871	584	29	+	+	NOUN
ejpam-5871	584	30	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	584	31	)	)	PUNCT
ejpam-5871	584	32	2	2	NUM
ejpam-5871	584	33	)	)	PUNCT
ejpam-5871	584	34	1	1	NUM
ejpam-5871	584	35	s+1	s+1	NOUN
ejpam-5871	584	36	)	)	PUNCT
ejpam-5871	584	37	⅁	⅁	PROPN
ejpam-5871	584	38	(	(	PUNCT
ejpam-5871	584	39	⋋−1	⋋−1	X
ejpam-5871	584	40	(	(	PUNCT
ejpam-5871	584	41	⋋s+1(r1	⋋s+1(r1	NOUN
ejpam-5871	584	42	)	)	PUNCT
ejpam-5871	584	43	+	+	NOUN
ejpam-5871	584	44	⋋s+1(r2	⋋s+1(r2	NOUN
ejpam-5871	584	45	)	)	PUNCT
ejpam-5871	584	46	2	2	NUM
ejpam-5871	584	47	)	)	PUNCT
ejpam-5871	584	48	1	1	NUM
ejpam-5871	584	49	s+1	s+1	PROPN
ejpam-5871	584	50	)	)	PUNCT
ejpam-5871	584	51	⊇	⊇	PROPN
ejpam-5871	584	52	1	1	NUM
ejpam-5871	584	53	(	(	PUNCT
ejpam-5871	584	54	⋋s+1(r2)−⋋s+1(r1	⋋s+1(r2)−⋋s+1(r1	NOUN
ejpam-5871	584	55	)	)	PUNCT
ejpam-5871	584	56	)	)	PUNCT
ejpam-5871	585	1	β	β	X
ejpam-5871	585	2	k	k	X
ejpam-5871	586	1	[	[	PUNCT
ejpam-5871	586	2	s	s	X
ejpam-5871	586	3	kz	kz	PROPN
ejpam-5871	586	4	β	β	PROPN
ejpam-5871	586	5	r+1	r+1	PROPN
ejpam-5871	586	6	∅⅁(r2	∅⅁(r2	NOUN
ejpam-5871	586	7	)	)	PUNCT
ejpam-5871	587	1	+	+	SYM
ejpam-5871	587	2	s	s	VERB
ejpam-5871	587	3	kz	kz	PROPN
ejpam-5871	587	4	β	β	PROPN
ejpam-5871	587	5	r−2	r−2	PROPN
ejpam-5871	587	6	∅⅁(r1	∅⅁(r1	PROPN
ejpam-5871	587	7	)	)	PUNCT
ejpam-5871	587	8	]	]	PUNCT
ejpam-5871	588	1	+	+	CCONJ
ejpam-5871	588	2	(	(	PUNCT
ejpam-5871	588	3	s+	s+	X
ejpam-5871	588	4	1)−	1)−	PROPN
ejpam-5871	588	5	β	β	X
ejpam-5871	588	6	k	k	PROPN
ejpam-5871	588	7	kγk(β	kγk(β	PROPN
ejpam-5871	588	8	)	)	PUNCT
ejpam-5871	588	9	[	[	PUNCT
ejpam-5871	588	10	p	p	X
ejpam-5871	588	11	(	(	PUNCT
ejpam-5871	588	12	r1	r1	PROPN
ejpam-5871	588	13	,	,	PUNCT
ejpam-5871	588	14	r2	r2	PROPN
ejpam-5871	588	15	)	)	PUNCT
ejpam-5871	588	16	2	2	NUM
ejpam-5871	588	17	(	(	PUNCT
ejpam-5871	588	18	β	β	X
ejpam-5871	588	19	+	+	ADJ
ejpam-5871	588	20	2)(β	2)(β	NUM
ejpam-5871	588	21	+	+	CCONJ
ejpam-5871	588	22	1	1	NUM
ejpam-5871	588	23	)	)	PUNCT
ejpam-5871	589	1	+	+	ADJ
ejpam-5871	589	2	q(r1	q(r1	ADJ
ejpam-5871	589	3	,	,	PUNCT
ejpam-5871	589	4	r2	r2	PROPN
ejpam-5871	589	5	)	)	PUNCT
ejpam-5871	589	6	β2	β2	NOUN
ejpam-5871	589	7	+	+	NOUN
ejpam-5871	589	8	β	β	X
ejpam-5871	590	1	+	+	CCONJ
ejpam-5871	590	2	1	1	NUM
ejpam-5871	590	3	(	(	PUNCT
ejpam-5871	590	4	β	β	X
ejpam-5871	590	5	+	+	ADJ
ejpam-5871	590	6	2)(β	2)(β	NUM
ejpam-5871	590	7	+	+	CCONJ
ejpam-5871	590	8	1)(β	1)(β	NOUN
ejpam-5871	590	9	)	)	PUNCT
ejpam-5871	590	10	]	]	PUNCT
ejpam-5871	590	11	.	.	PUNCT
ejpam-5871	591	1	example	example	NOUN
ejpam-5871	592	1	7	7	NUM
ejpam-5871	592	2	.	.	PUNCT
ejpam-5871	593	1	if	if	SCONJ
ejpam-5871	593	2	we	we	PRON
ejpam-5871	593	3	choose	choose	VERB
ejpam-5871	593	4	∅(r	∅(r	PROPN
ejpam-5871	593	5	)	)	PUNCT
ejpam-5871	593	6	=	=	PUNCT
ejpam-5871	594	1	[	[	X
ejpam-5871	594	2	4	4	NUM
ejpam-5871	594	3	−	−	NOUN
ejpam-5871	594	4	⋋s+1(r	⋋s+1(r	NUM
ejpam-5871	594	5	)	)	PUNCT
ejpam-5871	594	6	,	,	PUNCT
ejpam-5871	594	7	8	8	NUM
ejpam-5871	594	8	+	+	NOUN
ejpam-5871	594	9	⋋s+1(r	⋋s+1(r	NUM
ejpam-5871	594	10	)	)	PUNCT
ejpam-5871	594	11	]	]	PUNCT
ejpam-5871	594	12	and	and	CCONJ
ejpam-5871	594	13	⋋(r	⋋(r	NUM
ejpam-5871	594	14	)	)	PUNCT
ejpam-5871	594	15	=	=	SYM
ejpam-5871	595	1	r	r	X
ejpam-5871	595	2	,	,	PUNCT
ejpam-5871	595	3	⅁(r	⅁(r	NOUN
ejpam-5871	595	4	)	)	PUNCT
ejpam-5871	595	5	=	=	SYM
ejpam-5871	595	6	1	1	NUM
ejpam-5871	595	7	,	,	PUNCT
ejpam-5871	595	8	℧	℧	NOUN
ejpam-5871	595	9	1(r	1(r	NUM
ejpam-5871	595	10	)	)	PUNCT
ejpam-5871	595	11	=	=	SYM
ejpam-5871	595	12	℧	℧	NOUN
ejpam-5871	595	13	2(r	2(r	NUM
ejpam-5871	595	14	)	)	PUNCT
ejpam-5871	595	15	=	=	SYM
ejpam-5871	595	16	1	1	NUM
ejpam-5871	595	17	4	4	NUM
ejpam-5871	595	18	in	in	ADP
ejpam-5871	595	19	theorem	theorem	ADJ
ejpam-5871	595	20	9	9	NUM
ejpam-5871	595	21	and	and	CCONJ
ejpam-5871	595	22	utilizing	utilize	VERB
ejpam-5871	595	23	proposition	proposition	NOUN
ejpam-5871	595	24	1	1	NUM
ejpam-5871	595	25	,	,	PUNCT
ejpam-5871	595	26	we	we	PRON
ejpam-5871	595	27	have	have	VERB
ejpam-5871	595	28	(	(	PUNCT
ejpam-5871	595	29	s+	s+	X
ejpam-5871	595	30	1	1	X
ejpam-5871	595	31	)	)	PUNCT
ejpam-5871	595	32	−β	−β	NOUN
ejpam-5871	595	33	k	k	PROPN
ejpam-5871	595	34	βγk(β	βγk(β	PROPN
ejpam-5871	595	35	)	)	PUNCT
ejpam-5871	595	36	(	(	PUNCT
ejpam-5871	595	37	4−	4−	NOUN
ejpam-5871	595	38	rs+1	rs+1	NOUN
ejpam-5871	595	39	1	1	NUM
ejpam-5871	595	40	+	+	CCONJ
ejpam-5871	595	41	rs+1	rs+1	NUM
ejpam-5871	595	42	2	2	NUM
ejpam-5871	595	43	2	2	NUM
ejpam-5871	595	44	,	,	PUNCT
ejpam-5871	595	45	8	8	NUM
ejpam-5871	595	46	+	+	CCONJ
ejpam-5871	595	47	rs+1	rs+1	PROPN
ejpam-5871	595	48	1	1	NUM
ejpam-5871	595	49	+	+	CCONJ
ejpam-5871	595	50	rs+1	rs+1	NUM
ejpam-5871	595	51	2	2	NUM
ejpam-5871	595	52	2	2	NUM
ejpam-5871	595	53	)	)	PUNCT
ejpam-5871	595	54	⊇	⊇	NOUN
ejpam-5871	595	55	(	(	PUNCT
ejpam-5871	595	56	s+	s+	NUM
ejpam-5871	595	57	1)−	1)−	PROPN
ejpam-5871	595	58	β	β	X
ejpam-5871	595	59	k	k	PROPN
ejpam-5871	595	60	δγk(β	δγk(β	PROPN
ejpam-5871	595	61	)	)	PUNCT
ejpam-5871	595	62	(	(	PUNCT
ejpam-5871	595	63	1	1	NUM
ejpam-5871	595	64	64	64	NUM
ejpam-5871	595	65	(	(	PUNCT
ejpam-5871	595	66	rs+1	rs+1	PROPN
ejpam-5871	595	67	2	2	NUM
ejpam-5871	595	68	−	−	NOUN
ejpam-5871	595	69	rs+1	rs+1	NOUN
ejpam-5871	595	70	1	1	NUM
ejpam-5871	595	71	)	)	PUNCT
ejpam-5871	595	72	β	β	PROPN
ejpam-5871	595	73	k	k	X
ejpam-5871	595	74	−1	−1	NOUN
ejpam-5871	595	75	(	(	PUNCT
ejpam-5871	595	76	8−	8−	NUM
ejpam-5871	595	77	(	(	PUNCT
ejpam-5871	595	78	rs+1	rs+1	NOUN
ejpam-5871	595	79	1	1	NUM
ejpam-5871	595	80	+	+	CCONJ
ejpam-5871	595	81	rs+1	rs+1	PROPN
ejpam-5871	595	82	2	2	NUM
ejpam-5871	595	83	)	)	PUNCT
ejpam-5871	595	84	,	,	PUNCT
ejpam-5871	595	85	16	16	NUM
ejpam-5871	596	1	+	+	CCONJ
ejpam-5871	596	2	(	(	PUNCT
ejpam-5871	596	3	rs+1	rs+1	PROPN
ejpam-5871	596	4	1	1	NUM
ejpam-5871	596	5	+	+	CCONJ
ejpam-5871	596	6	rs+1	rs+1	PROPN
ejpam-5871	596	7	2	2	NUM
ejpam-5871	596	8	)	)	PUNCT
ejpam-5871	596	9	)	)	PUNCT
ejpam-5871	597	1	+	+	CCONJ
ejpam-5871	597	2	1	1	NUM
ejpam-5871	597	3	8	8	NUM
ejpam-5871	597	4	(	(	PUNCT
ejpam-5871	597	5	8−	8−	NUM
ejpam-5871	597	6	(	(	PUNCT
ejpam-5871	597	7	rs+1	rs+1	NOUN
ejpam-5871	597	8	1	1	NUM
ejpam-5871	597	9	+	+	CCONJ
ejpam-5871	597	10	rs+1	rs+1	PROPN
ejpam-5871	597	11	2	2	NUM
ejpam-5871	597	12	)	)	PUNCT
ejpam-5871	597	13	,	,	PUNCT
ejpam-5871	597	14	16	16	NUM
ejpam-5871	597	15	+	+	CCONJ
ejpam-5871	597	16	(	(	PUNCT
ejpam-5871	597	17	rs+1	rs+1	PROPN
ejpam-5871	597	18	1	1	NUM
ejpam-5871	597	19	+	+	CCONJ
ejpam-5871	597	20	rs+1	rs+1	PROPN
ejpam-5871	597	21	2	2	NUM
ejpam-5871	597	22	)	)	PUNCT
ejpam-5871	597	23	)	)	PUNCT
ejpam-5871	597	24	)	)	PUNCT
ejpam-5871	597	25	.	.	PUNCT
ejpam-5871	598	1	example	example	NOUN
ejpam-5871	599	1	8	8	NUM
ejpam-5871	599	2	.	.	PUNCT
ejpam-5871	600	1	for	for	ADP
ejpam-5871	600	2	graphical	graphical	ADJ
ejpam-5871	600	3	representation	representation	NOUN
ejpam-5871	600	4	if	if	SCONJ
ejpam-5871	600	5	we	we	PRON
ejpam-5871	600	6	choose	choose	VERB
ejpam-5871	600	7	∅(r	∅(r	PROPN
ejpam-5871	600	8	)	)	PUNCT
ejpam-5871	600	9	=	=	PUNCT
ejpam-5871	601	1	[	[	X
ejpam-5871	601	2	4−⋋s+1(r	4−⋋s+1(r	NUM
ejpam-5871	601	3	)	)	PUNCT
ejpam-5871	601	4	,	,	PUNCT
ejpam-5871	601	5	8+⋋s+1(r	8+⋋s+1(r	NOUN
ejpam-5871	601	6	)	)	PUNCT
ejpam-5871	601	7	]	]	PUNCT
ejpam-5871	601	8	,	,	PUNCT
ejpam-5871	601	9	⋋(r	⋋(r	X
ejpam-5871	601	10	)	)	PUNCT
ejpam-5871	601	11	=	=	PUNCT
ejpam-5871	601	12	sin	sin	NOUN
ejpam-5871	601	13	r	r	NOUN
ejpam-5871	601	14	,	,	PUNCT
ejpam-5871	601	15	⅁(r	⅁(r	NOUN
ejpam-5871	601	16	)	)	PUNCT
ejpam-5871	601	17	=	=	SYM
ejpam-5871	601	18	1	1	NUM
ejpam-5871	601	19	and	and	CCONJ
ejpam-5871	601	20	℧	℧	NOUN
ejpam-5871	601	21	1(r	1(r	NUM
ejpam-5871	601	22	)	)	PUNCT
ejpam-5871	601	23	=	=	SYM
ejpam-5871	601	24	℧	℧	NOUN
ejpam-5871	601	25	2(r	2(r	NUM
ejpam-5871	601	26	)	)	PUNCT
ejpam-5871	601	27	=	=	SYM
ejpam-5871	601	28	1	1	NUM
ejpam-5871	601	29	4	4	NUM
ejpam-5871	601	30	in	in	ADP
ejpam-5871	601	31	theorem	theorem	ADJ
ejpam-5871	601	32	9	9	NUM
ejpam-5871	601	33	and	and	CCONJ
ejpam-5871	601	34	utilizing	utilize	VERB
ejpam-5871	601	35	proposition	proposition	NOUN
ejpam-5871	601	36	1	1	NUM
ejpam-5871	601	37	,	,	PUNCT
ejpam-5871	601	38	we	we	PRON
ejpam-5871	601	39	have	have	AUX
ejpam-5871	601	40	(	(	PUNCT
ejpam-5871	601	41	s+	s+	X
ejpam-5871	601	42	1	1	X
ejpam-5871	601	43	)	)	PUNCT
ejpam-5871	601	44	−β	−β	NOUN
ejpam-5871	601	45	k	k	PROPN
ejpam-5871	601	46	βγk(β	βγk(β	PROPN
ejpam-5871	601	47	)	)	PUNCT
ejpam-5871	601	48	(	(	PUNCT
ejpam-5871	601	49	4−	4−	NOUN
ejpam-5871	601	50	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	601	51	)	)	PUNCT
ejpam-5871	601	52	+	+	SYM
ejpam-5871	601	53	sins+1(r2	sins+1(r2	X
ejpam-5871	601	54	)	)	PUNCT
ejpam-5871	601	55	2	2	NUM
ejpam-5871	601	56	,	,	PUNCT
ejpam-5871	601	57	8	8	NUM
ejpam-5871	601	58	+	+	SYM
ejpam-5871	601	59	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	601	60	)	)	PUNCT
ejpam-5871	601	61	+	+	SYM
ejpam-5871	601	62	sins+1(r2	sins+1(r2	X
ejpam-5871	601	63	)	)	PUNCT
ejpam-5871	601	64	2	2	NUM
ejpam-5871	601	65	)	)	PUNCT
ejpam-5871	601	66	⊇	⊇	NOUN
ejpam-5871	601	67	(	(	PUNCT
ejpam-5871	601	68	s+	s+	NUM
ejpam-5871	601	69	1)−	1)−	PROPN
ejpam-5871	601	70	β	β	PROPN
ejpam-5871	601	71	k	k	PROPN
ejpam-5871	601	72	2048βγk(β	2048βγk(β	PROPN
ejpam-5871	601	73	)	)	PUNCT
ejpam-5871	601	74	(	(	PUNCT
ejpam-5871	601	75	(	(	PUNCT
ejpam-5871	601	76	8−	8−	NUM
ejpam-5871	601	77	(	(	PUNCT
ejpam-5871	601	78	sins+1(r1	sins+1(r1	X
ejpam-5871	601	79	)	)	PUNCT
ejpam-5871	601	80	+	+	SYM
ejpam-5871	601	81	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	601	82	)	)	PUNCT
ejpam-5871	601	83	)	)	PUNCT
ejpam-5871	601	84	,	,	PUNCT
ejpam-5871	601	85	16	16	NUM
ejpam-5871	601	86	+	+	CCONJ
ejpam-5871	601	87	(	(	PUNCT
ejpam-5871	601	88	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	601	89	)	)	PUNCT
ejpam-5871	601	90	+	+	SYM
ejpam-5871	601	91	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	601	92	)	)	PUNCT
ejpam-5871	601	93	)	)	PUNCT
ejpam-5871	601	94	)	)	PUNCT
ejpam-5871	602	1	+	+	CCONJ
ejpam-5871	602	2	(	(	PUNCT
ejpam-5871	602	3	8−	8−	NUM
ejpam-5871	602	4	(	(	PUNCT
ejpam-5871	602	5	sins+1(r1	sins+1(r1	X
ejpam-5871	602	6	)	)	PUNCT
ejpam-5871	602	7	+	+	SYM
ejpam-5871	602	8	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	602	9	)	)	PUNCT
ejpam-5871	602	10	)	)	PUNCT
ejpam-5871	602	11	,	,	PUNCT
ejpam-5871	602	12	16	16	NUM
ejpam-5871	602	13	+	+	CCONJ
ejpam-5871	602	14	(	(	PUNCT
ejpam-5871	602	15	sins+1(r1	sins+1(r1	NOUN
ejpam-5871	602	16	)	)	PUNCT
ejpam-5871	602	17	+	+	SYM
ejpam-5871	602	18	sins+1(r2	sins+1(r2	NOUN
ejpam-5871	602	19	)	)	PUNCT
ejpam-5871	602	20	)	)	PUNCT
ejpam-5871	602	21	)	)	PUNCT
ejpam-5871	602	22	)	)	PUNCT
ejpam-5871	602	23	.	.	PUNCT
ejpam-5871	603	1	for	for	ADP
ejpam-5871	603	2	tabular	tabular	NOUN
ejpam-5871	603	3	value	value	NOUN
ejpam-5871	603	4	corollary	corollary	ADJ
ejpam-5871	603	5	10	10	NUM
ejpam-5871	603	6	.	.	PUNCT
ejpam-5871	604	1	if	if	SCONJ
ejpam-5871	604	2	we	we	PRON
ejpam-5871	604	3	fix	fix	VERB
ejpam-5871	604	4	s	s	NOUN
ejpam-5871	604	5	=	=	NOUN
ejpam-5871	604	6	0	0	NUM
ejpam-5871	604	7	,	,	PUNCT
ejpam-5871	604	8	k	k	NOUN
ejpam-5871	604	9	=	=	SYM
ejpam-5871	604	10	1	1	NUM
ejpam-5871	604	11	,	,	PUNCT
ejpam-5871	604	12	⋋(r	⋋(r	X
ejpam-5871	604	13	)	)	PUNCT
ejpam-5871	605	1	=	=	SYM
ejpam-5871	605	2	r	r	NOUN
ejpam-5871	605	3	and	and	CCONJ
ejpam-5871	605	4	℧	℧	PROPN
ejpam-5871	605	5	(	(	PUNCT
ejpam-5871	605	6	θ	θ	NOUN
ejpam-5871	605	7	)	)	PUNCT
ejpam-5871	605	8	=	=	SYM
ejpam-5871	605	9	θ	θ	PROPN
ejpam-5871	605	10	in	in	ADP
ejpam-5871	605	11	theorem	theorem	NOUN
ejpam-5871	605	12	9	9	NUM
ejpam-5871	605	13	,	,	PUNCT
ejpam-5871	605	14	we	we	PRON
ejpam-5871	605	15	possess	possess	VERB
ejpam-5871	605	16	1	1	NUM
ejpam-5871	605	17	βγ(β	βγ(β	NUM
ejpam-5871	605	18	)	)	PUNCT
ejpam-5871	605	19	∅	∅	NOUN
ejpam-5871	605	20	(	(	PUNCT
ejpam-5871	605	21	r1	r1	NOUN
ejpam-5871	605	22	+	+	CCONJ
ejpam-5871	605	23	r2	r2	PROPN
ejpam-5871	605	24	2	2	NUM
ejpam-5871	605	25	)	)	PUNCT
ejpam-5871	605	26	⅁	⅁	NOUN
ejpam-5871	605	27	(	(	PUNCT
ejpam-5871	605	28	r1	r1	NOUN
ejpam-5871	605	29	+	+	CCONJ
ejpam-5871	605	30	r2	r2	PROPN
ejpam-5871	605	31	2	2	NUM
ejpam-5871	605	32	)	)	PUNCT
ejpam-5871	606	1	a.	a.	NOUN
ejpam-5871	606	2	mehmood	mehmood	PROPN
ejpam-5871	606	3	et	et	PROPN
ejpam-5871	606	4	al	al	PROPN
ejpam-5871	606	5	.	.	PUNCT
ejpam-5871	606	6	/	/	SYM
ejpam-5871	606	7	eur	eur	PROPN
ejpam-5871	606	8	.	.	PUNCT
ejpam-5871	607	1	j.	j.	PROPN
ejpam-5871	607	2	pure	pure	PROPN
ejpam-5871	607	3	appl	appl	PROPN
ejpam-5871	607	4	.	.	PROPN
ejpam-5871	607	5	math	math	PROPN
ejpam-5871	607	6	,	,	PUNCT
ejpam-5871	607	7	18	18	NUM
ejpam-5871	607	8	(	(	PUNCT
ejpam-5871	607	9	2	2	NUM
ejpam-5871	607	10	)	)	PUNCT
ejpam-5871	607	11	(	(	PUNCT
ejpam-5871	607	12	2025	2025	NUM
ejpam-5871	607	13	)	)	PUNCT
ejpam-5871	607	14	,	,	PUNCT
ejpam-5871	607	15	5871	5871	NUM
ejpam-5871	607	16	23	23	NUM
ejpam-5871	607	17	of	of	ADP
ejpam-5871	607	18	26	26	NUM
ejpam-5871	607	19	figure	figure	NOUN
ejpam-5871	607	20	4	4	NUM
ejpam-5871	607	21	:	:	PUNCT
ejpam-5871	607	22	graphical	graphical	ADJ
ejpam-5871	607	23	representation	representation	NOUN
ejpam-5871	607	24	of	of	ADP
ejpam-5871	607	25	theorem	theorem	ADJ
ejpam-5871	607	26	9	9	NUM
ejpam-5871	607	27	corresponding	correspond	VERB
ejpam-5871	607	28	to	to	ADP
ejpam-5871	607	29	the	the	DET
ejpam-5871	607	30	choice	choice	NOUN
ejpam-5871	607	31	of	of	ADP
ejpam-5871	607	32	parameters	parameter	NOUN
ejpam-5871	607	33	r1	r1	NOUN
ejpam-5871	607	34	=	=	SYM
ejpam-5871	607	35	0.6	0.6	NUM
ejpam-5871	607	36	,	,	PUNCT
ejpam-5871	607	37	r1	r1	NOUN
ejpam-5871	607	38	<	<	X
ejpam-5871	607	39	r2	r2	PROPN
ejpam-5871	607	40	≤	≤	PROPN
ejpam-5871	608	1	π	π	PROPN
ejpam-5871	608	2	2	2	NUM
ejpam-5871	608	3	,	,	PUNCT
ejpam-5871	608	4	k	k	NOUN
ejpam-5871	608	5	=	=	SYM
ejpam-5871	608	6	1	1	NUM
ejpam-5871	608	7	,	,	PUNCT
ejpam-5871	608	8	s	s	PART
ejpam-5871	608	9	=	=	SYM
ejpam-5871	608	10	3	3	NUM
ejpam-5871	608	11	and	and	CCONJ
ejpam-5871	608	12	β	β	X
ejpam-5871	608	13	=	=	NOUN
ejpam-5871	608	14	0.8	0.8	NUM
ejpam-5871	608	15	.	.	PUNCT
ejpam-5871	609	1	r2	r2	PROPN
ejpam-5871	609	2	(	(	PUNCT
ejpam-5871	609	3	a1	a1	PROPN
ejpam-5871	609	4	,	,	PUNCT
ejpam-5871	609	5	b1	b1	NOUN
ejpam-5871	609	6	)	)	PUNCT
ejpam-5871	609	7	(	(	PUNCT
ejpam-5871	609	8	a2	a2	PROPN
ejpam-5871	609	9	,	,	PUNCT
ejpam-5871	609	10	b2	b2	NOUN
ejpam-5871	609	11	)	)	PUNCT
ejpam-5871	609	12	0.6100	0.6100	NUM
ejpam-5871	609	13	(	(	PUNCT
ejpam-5871	609	14	1.3796e+	1.3796e+	NOUN
ejpam-5871	609	15	00	00	NUM
ejpam-5871	609	16	,	,	PUNCT
ejpam-5871	609	17	2.8705e+	2.8705e+	NUM
ejpam-5871	609	18	00	00	NUM
ejpam-5871	609	19	)	)	PUNCT
ejpam-5871	609	20	(	(	PUNCT
ejpam-5871	609	21	2.6946e−	2.6946e−	NOUN
ejpam-5871	609	22	03	03	NUM
ejpam-5871	609	23	,	,	PUNCT
ejpam-5871	609	24	5.6065e−	5.6065e−	NOUN
ejpam-5871	609	25	03	03	NUM
ejpam-5871	609	26	)	)	PUNCT
ejpam-5871	609	27	0.8022	0.8022	PROPN
ejpam-5871	609	28	(	(	PUNCT
ejpam-5871	609	29	1.3514e+	1.3514e+	NUM
ejpam-5871	609	30	00	00	NUM
ejpam-5871	609	31	,	,	PUNCT
ejpam-5871	609	32	2.8987e+	2.8987e+	NUM
ejpam-5871	609	33	00	00	NUM
ejpam-5871	609	34	)	)	PUNCT
ejpam-5871	609	35	(	(	PUNCT
ejpam-5871	609	36	2.6395e−	2.6395e−	NOUN
ejpam-5871	609	37	03	03	NUM
ejpam-5871	609	38	,	,	PUNCT
ejpam-5871	609	39	5.6616e−	5.6616e−	NUM
ejpam-5871	609	40	03	03	NUM
ejpam-5871	609	41	)	)	PUNCT
ejpam-5871	609	42	0.9943	0.9943	NUM
ejpam-5871	609	43	(	(	PUNCT
ejpam-5871	609	44	1.3112e+	1.3112e+	NUM
ejpam-5871	609	45	00	00	NUM
ejpam-5871	609	46	,	,	PUNCT
ejpam-5871	609	47	2.9389e+	2.9389e+	NUM
ejpam-5871	609	48	00	00	NUM
ejpam-5871	609	49	)	)	PUNCT
ejpam-5871	609	50	(	(	PUNCT
ejpam-5871	609	51	2.5610e−	2.5610e−	PROPN
ejpam-5871	609	52	03	03	NUM
ejpam-5871	609	53	,	,	PUNCT
ejpam-5871	609	54	5.7401e−	5.7401e−	NOUN
ejpam-5871	609	55	03	03	NUM
ejpam-5871	609	56	)	)	PUNCT
ejpam-5871	609	57	1.1865	1.1865	NUM
ejpam-5871	609	58	(	(	PUNCT
ejpam-5871	609	59	1.2679e+	1.2679e+	NUM
ejpam-5871	609	60	00	00	NUM
ejpam-5871	609	61	,	,	PUNCT
ejpam-5871	609	62	2.9822e+	2.9822e+	NUM
ejpam-5871	609	63	00	00	NUM
ejpam-5871	609	64	)	)	PUNCT
ejpam-5871	609	65	(	(	PUNCT
ejpam-5871	609	66	2.4764e−	2.4764e−	NUM
ejpam-5871	609	67	03	03	NUM
ejpam-5871	609	68	,	,	PUNCT
ejpam-5871	609	69	5.8247e−	5.8247e−	NUM
ejpam-5871	609	70	03	03	NUM
ejpam-5871	609	71	)	)	PUNCT
ejpam-5871	609	72	1.3786	1.3786	NUM
ejpam-5871	609	73	(	(	PUNCT
ejpam-5871	609	74	1.2343e+	1.2343e+	NUM
ejpam-5871	609	75	00	00	NUM
ejpam-5871	609	76	,	,	PUNCT
ejpam-5871	609	77	3.0158e+	3.0158e+	NUM
ejpam-5871	609	78	00	00	NUM
ejpam-5871	609	79	)	)	PUNCT
ejpam-5871	609	80	(	(	PUNCT
ejpam-5871	609	81	2.4108e−	2.4108e−	NOUN
ejpam-5871	609	82	03	03	NUM
ejpam-5871	609	83	,	,	PUNCT
ejpam-5871	609	84	5.8903e−	5.8903e−	NUM
ejpam-5871	609	85	03	03	NUM
ejpam-5871	609	86	)	)	PUNCT
ejpam-5871	609	87	1.5708	1.5708	NUM
ejpam-5871	609	88	(	(	PUNCT
ejpam-5871	609	89	1.2216e+	1.2216e+	NOUN
ejpam-5871	609	90	00	00	NUM
ejpam-5871	609	91	,	,	PUNCT
ejpam-5871	609	92	3.0285e+	3.0285e+	NUM
ejpam-5871	609	93	00	00	NUM
ejpam-5871	609	94	)	)	PUNCT
ejpam-5871	609	95	(	(	PUNCT
ejpam-5871	609	96	2.3860e−	2.3860e−	NUM
ejpam-5871	609	97	03	03	NUM
ejpam-5871	609	98	,	,	PUNCT
ejpam-5871	609	99	5.9151e−	5.9151e−	NUM
ejpam-5871	609	100	03	03	NUM
ejpam-5871	609	101	)	)	PUNCT
ejpam-5871	609	102	table	table	NOUN
ejpam-5871	609	103	4	4	NUM
ejpam-5871	609	104	:	:	PUNCT
ejpam-5871	609	105	interval	interval	NOUN
ejpam-5871	609	106	bounds	bound	NOUN
ejpam-5871	609	107	of	of	ADP
ejpam-5871	609	108	theorem	theorem	ADJ
ejpam-5871	609	109	9	9	NUM
ejpam-5871	609	110	corresponding	correspond	VERB
ejpam-5871	609	111	to	to	ADP
ejpam-5871	609	112	the	the	DET
ejpam-5871	609	113	choice	choice	NOUN
ejpam-5871	609	114	of	of	ADP
ejpam-5871	609	115	parameters	parameter	NOUN
ejpam-5871	609	116	r1	r1	NOUN
ejpam-5871	609	117	=	=	SYM
ejpam-5871	609	118	0.6	0.6	NUM
ejpam-5871	609	119	,	,	PUNCT
ejpam-5871	609	120	r1	r1	NOUN
ejpam-5871	609	121	<	<	X
ejpam-5871	609	122	r2	r2	PROPN
ejpam-5871	609	123	≤	≤	PROPN
ejpam-5871	610	1	π	π	PROPN
ejpam-5871	610	2	2	2	NUM
ejpam-5871	610	3	,	,	PUNCT
ejpam-5871	610	4	k	k	NOUN
ejpam-5871	610	5	=	=	SYM
ejpam-5871	610	6	1	1	NUM
ejpam-5871	610	7	,	,	PUNCT
ejpam-5871	610	8	s	s	PART
ejpam-5871	610	9	=	=	SYM
ejpam-5871	610	10	3	3	NUM
ejpam-5871	610	11	and	and	CCONJ
ejpam-5871	610	12	β	β	X
ejpam-5871	610	13	=	=	NOUN
ejpam-5871	610	14	0.8	0.8	NUM
ejpam-5871	610	15	.	.	PUNCT
ejpam-5871	611	1	⊇	⊇	NOUN
ejpam-5871	611	2	1	1	NUM
ejpam-5871	611	3	4(r2	4(r2	NUM
ejpam-5871	611	4	−	−	PROPN
ejpam-5871	611	5	r1)β	r1)β	PROPN
ejpam-5871	611	6	[	[	PUNCT
ejpam-5871	611	7	zβ	zβ	NOUN
ejpam-5871	611	8	r+1	r+1	PROPN
ejpam-5871	611	9	∅⅁(r2	∅⅁(r2	NOUN
ejpam-5871	611	10	)	)	PUNCT
ejpam-5871	611	11	+	+	CCONJ
ejpam-5871	611	12	zβ	zβ	PROPN
ejpam-5871	611	13	r−2	r−2	PROPN
ejpam-5871	611	14	∅⅁(r1	∅⅁(r1	NOUN
ejpam-5871	611	15	)	)	PUNCT
ejpam-5871	611	16	]	]	PUNCT
ejpam-5871	612	1	+	+	CCONJ
ejpam-5871	612	2	1	1	NUM
ejpam-5871	612	3	kγ(β	kγ(β	NOUN
ejpam-5871	612	4	)	)	PUNCT
ejpam-5871	612	5	[	[	PUNCT
ejpam-5871	612	6	p	p	X
ejpam-5871	612	7	(	(	PUNCT
ejpam-5871	612	8	r1	r1	PROPN
ejpam-5871	612	9	,	,	PUNCT
ejpam-5871	612	10	r2	r2	PROPN
ejpam-5871	612	11	)	)	PUNCT
ejpam-5871	612	12	2	2	NUM
ejpam-5871	612	13	(	(	PUNCT
ejpam-5871	612	14	β	β	X
ejpam-5871	612	15	+	+	ADJ
ejpam-5871	612	16	2)(β	2)(β	NUM
ejpam-5871	612	17	+	+	CCONJ
ejpam-5871	612	18	1	1	NUM
ejpam-5871	612	19	)	)	PUNCT
ejpam-5871	612	20	+	+	ADJ
ejpam-5871	612	21	q(r1	q(r1	ADJ
ejpam-5871	612	22	,	,	PUNCT
ejpam-5871	612	23	r2	r2	PROPN
ejpam-5871	612	24	)	)	PUNCT
ejpam-5871	612	25	β2	β2	NOUN
ejpam-5871	612	26	+	+	NOUN
ejpam-5871	612	27	β	β	X
ejpam-5871	613	1	+	+	CCONJ
ejpam-5871	613	2	1	1	NUM
ejpam-5871	613	3	(	(	PUNCT
ejpam-5871	613	4	β	β	X
ejpam-5871	613	5	+	+	ADJ
ejpam-5871	613	6	2)(β	2)(β	NUM
ejpam-5871	613	7	+	+	CCONJ
ejpam-5871	613	8	1)(β	1)(β	NOUN
ejpam-5871	613	9	)	)	PUNCT
ejpam-5871	613	10	]	]	PUNCT
ejpam-5871	613	11	.	.	PUNCT
ejpam-5871	614	1	3	3	X
ejpam-5871	614	2	.	.	X
ejpam-5871	614	3	conclusion	conclusion	NOUN
ejpam-5871	614	4	redfractional	redfractional	ADJ
ejpam-5871	614	5	inequalities	inequality	NOUN
ejpam-5871	614	6	,	,	PUNCT
ejpam-5871	614	7	which	which	PRON
ejpam-5871	614	8	extend	extend	VERB
ejpam-5871	614	9	classical	classical	ADJ
ejpam-5871	614	10	inequalities	inequality	NOUN
ejpam-5871	614	11	to	to	ADP
ejpam-5871	614	12	fractional	fractional	ADJ
ejpam-5871	614	13	-	-	PUNCT
ejpam-5871	614	14	order	order	NOUN
ejpam-5871	614	15	settings	setting	NOUN
ejpam-5871	614	16	,	,	PUNCT
ejpam-5871	614	17	play	play	VERB
ejpam-5871	614	18	a	a	DET
ejpam-5871	614	19	crucial	crucial	ADJ
ejpam-5871	614	20	role	role	NOUN
ejpam-5871	614	21	in	in	ADP
ejpam-5871	614	22	various	various	ADJ
ejpam-5871	614	23	industrial	industrial	ADJ
ejpam-5871	614	24	applications	application	NOUN
ejpam-5871	614	25	by	by	ADP
ejpam-5871	614	26	providing	provide	VERB
ejpam-5871	614	27	precise	precise	ADJ
ejpam-5871	614	28	analytical	analytical	ADJ
ejpam-5871	614	29	tools	tool	NOUN
ejpam-5871	614	30	for	for	ADP
ejpam-5871	614	31	optimization	optimization	NOUN
ejpam-5871	614	32	,	,	PUNCT
ejpam-5871	614	33	stability	stability	NOUN
ejpam-5871	614	34	analysis	analysis	NOUN
ejpam-5871	614	35	,	,	PUNCT
ejpam-5871	614	36	and	and	CCONJ
ejpam-5871	614	37	error	error	NOUN
ejpam-5871	614	38	estimation	estimation	NOUN
ejpam-5871	614	39	.	.	PUNCT
ejpam-5871	615	1	in	in	ADP
ejpam-5871	615	2	control	control	NOUN
ejpam-5871	615	3	systems	system	NOUN
ejpam-5871	615	4	and	and	CCONJ
ejpam-5871	615	5	automation	automation	NOUN
ejpam-5871	615	6	,	,	PUNCT
ejpam-5871	615	7	fractional	fractional	ADJ
ejpam-5871	615	8	inequalities	inequality	NOUN
ejpam-5871	615	9	help	help	AUX
ejpam-5871	615	10	establish	establish	VERB
ejpam-5871	615	11	stability	stability	NOUN
ejpam-5871	615	12	criteria	criterion	NOUN
ejpam-5871	615	13	for	for	ADP
ejpam-5871	615	14	fractional	fractional	ADJ
ejpam-5871	615	15	-	-	PUNCT
ejpam-5871	615	16	order	order	NOUN
ejpam-5871	615	17	controllers	controller	NOUN
ejpam-5871	615	18	,	,	PUNCT
ejpam-5871	615	19	improving	improve	VERB
ejpam-5871	615	20	system	system	NOUN
ejpam-5871	615	21	robustness	robustness	NOUN
ejpam-5871	615	22	in	in	ADP
ejpam-5871	615	23	robotics	robotic	NOUN
ejpam-5871	615	24	,	,	PUNCT
ejpam-5871	615	25	aerospace	aerospace	NOUN
ejpam-5871	615	26	and	and	CCONJ
ejpam-5871	615	27	process	process	NOUN
ejpam-5871	615	28	control	control	NOUN
ejpam-5871	615	29	industries	industry	NOUN
ejpam-5871	615	30	.	.	PUNCT
ejpam-5871	616	1	in	in	ADP
ejpam-5871	616	2	signal	signal	ADJ
ejpam-5871	616	3	processing	processing	NOUN
ejpam-5871	616	4	and	and	CCONJ
ejpam-5871	616	5	telecommunications	telecommunication	NOUN
ejpam-5871	616	6	,	,	PUNCT
ejpam-5871	616	7	they	they	PRON
ejpam-5871	616	8	aid	aid	VERB
ejpam-5871	616	9	in	in	ADP
ejpam-5871	616	10	error	error	NOUN
ejpam-5871	616	11	bounds	bound	NOUN
ejpam-5871	616	12	estimation	estimation	NOUN
ejpam-5871	616	13	and	and	CCONJ
ejpam-5871	616	14	performance	performance	NOUN
ejpam-5871	616	15	analysis	analysis	NOUN
ejpam-5871	616	16	of	of	ADP
ejpam-5871	616	17	fractional	fractional	ADJ
ejpam-5871	616	18	filters	filter	NOUN
ejpam-5871	616	19	,	,	PUNCT
ejpam-5871	616	20	enhancing	enhance	VERB
ejpam-5871	616	21	data	data	NOUN
ejpam-5871	616	22	transmission	transmission	NOUN
ejpam-5871	616	23	and	and	CCONJ
ejpam-5871	616	24	noise	noise	NOUN
ejpam-5871	616	25	reduction	reduction	NOUN
ejpam-5871	616	26	.	.	PUNCT
ejpam-5871	617	1	in	in	ADP
ejpam-5871	617	2	materials	material	NOUN
ejpam-5871	617	3	science	science	NOUN
ejpam-5871	617	4	and	and	CCONJ
ejpam-5871	617	5	mechanical	mechanical	ADJ
ejpam-5871	617	6	engineering	engineering	NOUN
ejpam-5871	617	7	,	,	PUNCT
ejpam-5871	617	8	fractional	fractional	ADJ
ejpam-5871	617	9	inequalities	inequality	NOUN
ejpam-5871	617	10	contribute	contribute	VERB
ejpam-5871	617	11	to	to	ADP
ejpam-5871	617	12	modeling	model	VERB
ejpam-5871	617	13	stress	stress	NOUN
ejpam-5871	617	14	-	-	PUNCT
ejpam-5871	617	15	strain	strain	NOUN
ejpam-5871	617	16	relationships	relationship	NOUN
ejpam-5871	617	17	in	in	ADP
ejpam-5871	617	18	viscoelastic	viscoelastic	ADJ
ejpam-5871	617	19	and	and	CCONJ
ejpam-5871	617	20	complex	complex	ADJ
ejpam-5871	617	21	materials	material	NOUN
ejpam-5871	617	22	,	,	PUNCT
ejpam-5871	617	23	optimizing	optimize	VERB
ejpam-5871	617	24	designs	design	NOUN
ejpam-5871	617	25	in	in	ADP
ejpam-5871	617	26	structural	structural	ADJ
ejpam-5871	617	27	engineering	engineering	NOUN
ejpam-5871	617	28	and	and	CCONJ
ejpam-5871	617	29	manufacturing	manufacturing	NOUN
ejpam-5871	617	30	.	.	PUNCT
ejpam-5871	618	1	the	the	DET
ejpam-5871	618	2	energy	energy	NOUN
ejpam-5871	618	3	sector	sector	NOUN
ejpam-5871	618	4	benefits	benefit	NOUN
ejpam-5871	618	5	from	from	ADP
ejpam-5871	618	6	these	these	DET
ejpam-5871	618	7	inequalities	inequality	NOUN
ejpam-5871	618	8	in	in	ADP
ejpam-5871	618	9	analyzing	analyze	VERB
ejpam-5871	618	10	fractional	fractional	ADJ
ejpam-5871	618	11	diffusion	diffusion	NOUN
ejpam-5871	618	12	processes	process	NOUN
ejpam-5871	618	13	,	,	PUNCT
ejpam-5871	618	14	optimizing	optimize	VERB
ejpam-5871	618	15	heat	heat	NOUN
ejpam-5871	618	16	conduction	conduction	NOUN
ejpam-5871	618	17	models	model	NOUN
ejpam-5871	618	18	,	,	PUNCT
ejpam-5871	618	19	and	and	CCONJ
ejpam-5871	618	20	improving	improve	VERB
ejpam-5871	618	21	energy	energy	NOUN
ejpam-5871	618	22	storage	storage	NOUN
ejpam-5871	618	23	systems	system	NOUN
ejpam-5871	618	24	like	like	ADP
ejpam-5871	618	25	batteries	battery	NOUN
ejpam-5871	618	26	and	and	CCONJ
ejpam-5871	618	27	supercapacitors	supercapacitor	NOUN
ejpam-5871	618	28	.	.	PUNCT
ejpam-5871	619	1	additionally	additionally	ADV
ejpam-5871	619	2	,	,	PUNCT
ejpam-5871	619	3	in	in	ADP
ejpam-5871	619	4	biomedical	biomedical	ADJ
ejpam-5871	619	5	engineering	engineering	NOUN
ejpam-5871	619	6	,	,	PUNCT
ejpam-5871	619	7	they	they	PRON
ejpam-5871	619	8	assist	assist	VERB
ejpam-5871	619	9	in	in	ADP
ejpam-5871	619	10	developing	develop	VERB
ejpam-5871	619	11	fractional	fractional	ADJ
ejpam-5871	619	12	-	-	PUNCT
ejpam-5871	619	13	order	order	NOUN
ejpam-5871	619	14	models	model	NOUN
ejpam-5871	619	15	for	for	ADP
ejpam-5871	619	16	physiological	physiological	ADJ
ejpam-5871	619	17	systems	system	NOUN
ejpam-5871	619	18	,	,	PUNCT
ejpam-5871	619	19	ensuring	ensure	VERB
ejpam-5871	619	20	accurate	accurate	ADJ
ejpam-5871	619	21	predictions	prediction	NOUN
ejpam-5871	619	22	in	in	ADP
ejpam-5871	619	23	drug	drug	NOUN
ejpam-5871	619	24	delivery	delivery	NOUN
ejpam-5871	619	25	and	and	CCONJ
ejpam-5871	619	26	neural	neural	ADJ
ejpam-5871	619	27	activity	activity	NOUN
ejpam-5871	619	28	analysis	analysis	NOUN
ejpam-5871	619	29	.	.	PUNCT
ejpam-5871	620	1	by	by	ADP
ejpam-5871	620	2	a.	a.	PROPN
ejpam-5871	620	3	mehmood	mehmood	PROPN
ejpam-5871	620	4	et	et	PROPN
ejpam-5871	620	5	al	al	PROPN
ejpam-5871	620	6	.	.	PUNCT
ejpam-5871	620	7	/	/	SYM
ejpam-5871	620	8	eur	eur	PROPN
ejpam-5871	620	9	.	.	PUNCT
ejpam-5871	621	1	j.	j.	PROPN
ejpam-5871	621	2	pure	pure	PROPN
ejpam-5871	621	3	appl	appl	PROPN
ejpam-5871	621	4	.	.	PROPN
ejpam-5871	621	5	math	math	PROPN
ejpam-5871	621	6	,	,	PUNCT
ejpam-5871	621	7	18	18	NUM
ejpam-5871	621	8	(	(	PUNCT
ejpam-5871	621	9	2	2	NUM
ejpam-5871	621	10	)	)	PUNCT
ejpam-5871	621	11	(	(	PUNCT
ejpam-5871	621	12	2025	2025	NUM
ejpam-5871	621	13	)	)	PUNCT
ejpam-5871	621	14	,	,	PUNCT
ejpam-5871	621	15	5871	5871	NUM
ejpam-5871	621	16	24	24	NUM
ejpam-5871	621	17	of	of	ADP
ejpam-5871	621	18	26	26	NUM
ejpam-5871	621	19	refining	refining	NOUN
ejpam-5871	621	20	analytical	analytical	ADJ
ejpam-5871	621	21	bounds	bound	NOUN
ejpam-5871	621	22	and	and	CCONJ
ejpam-5871	621	23	improving	improve	VERB
ejpam-5871	621	24	modeling	modeling	NOUN
ejpam-5871	621	25	accuracy	accuracy	NOUN
ejpam-5871	621	26	,	,	PUNCT
ejpam-5871	621	27	fractional	fractional	ADJ
ejpam-5871	621	28	inequalities	inequality	NOUN
ejpam-5871	621	29	significantly	significantly	ADV
ejpam-5871	621	30	contribute	contribute	VERB
ejpam-5871	621	31	to	to	ADP
ejpam-5871	621	32	industrial	industrial	ADJ
ejpam-5871	621	33	advancements	advancement	NOUN
ejpam-5871	621	34	across	across	ADP
ejpam-5871	621	35	multiple	multiple	ADJ
ejpam-5871	621	36	domains	domain	NOUN
ejpam-5871	621	37	.	.	PUNCT
ejpam-5871	622	1	in	in	ADP
ejpam-5871	622	2	this	this	DET
ejpam-5871	622	3	study	study	NOUN
ejpam-5871	622	4	,	,	PUNCT
ejpam-5871	622	5	we	we	PRON
ejpam-5871	622	6	introduce	introduce	VERB
ejpam-5871	622	7	the	the	DET
ejpam-5871	622	8	novel	novel	ADJ
ejpam-5871	622	9	hermite	hermite	ADJ
ejpam-5871	622	10	-	-	PUNCT
ejpam-5871	622	11	hadamard	hadamard	ADV
ejpam-5871	622	12	-	-	PUNCT
ejpam-5871	622	13	fejer	fejer	ADJ
ejpam-5871	622	14	type	type	NOUN
ejpam-5871	622	15	inequalities	inequality	NOUN
ejpam-5871	622	16	within	within	ADP
ejpam-5871	622	17	the	the	DET
ejpam-5871	622	18	structure	structure	NOUN
ejpam-5871	622	19	of	of	ADP
ejpam-5871	622	20	ı.υ	ı.υ	PROPN
ejpam-5871	622	21	(	(	PUNCT
ejpam-5871	622	22	⋋s+1	⋋s+1	PROPN
ejpam-5871	622	23	,	,	PUNCT
ejpam-5871	622	24	℧	℧	NOUN
ejpam-5871	622	25	)	)	PUNCT
ejpam-5871	622	26	class	class	NOUN
ejpam-5871	622	27	of	of	ADP
ejpam-5871	622	28	convexity	convexity	NOUN
ejpam-5871	622	29	.	.	PUNCT
ejpam-5871	623	1	our	our	PRON
ejpam-5871	623	2	analysis	analysis	NOUN
ejpam-5871	623	3	provides	provide	VERB
ejpam-5871	623	4	comprehensive	comprehensive	ADJ
ejpam-5871	623	5	bounds	bound	NOUN
ejpam-5871	623	6	for	for	ADP
ejpam-5871	623	7	several	several	ADJ
ejpam-5871	623	8	wellknown	wellknown	ADJ
ejpam-5871	623	9	fractional	fractional	ADJ
ejpam-5871	623	10	problems	problem	NOUN
ejpam-5871	623	11	.	.	PUNCT
ejpam-5871	624	1	specifically	specifically	ADV
ejpam-5871	624	2	,	,	PUNCT
ejpam-5871	624	3	we	we	PRON
ejpam-5871	624	4	investigate	investigate	VERB
ejpam-5871	624	5	the	the	DET
ejpam-5871	624	6	interplay	interplay	NOUN
ejpam-5871	624	7	between	between	ADP
ejpam-5871	624	8	the	the	DET
ejpam-5871	624	9	classical	classical	ADJ
ejpam-5871	624	10	hermite	hermite	ADJ
ejpam-5871	624	11	-	-	PUNCT
ejpam-5871	624	12	hadamard	hadamard	ADV
ejpam-5871	624	13	-	-	PUNCT
ejpam-5871	624	14	fejer	fejer	NOUN
ejpam-5871	624	15	inequality	inequality	NOUN
ejpam-5871	624	16	and	and	CCONJ
ejpam-5871	624	17	unified	unified	ADJ
ejpam-5871	624	18	forms	form	NOUN
ejpam-5871	624	19	of	of	ADP
ejpam-5871	624	20	minkowskis	minkowskis	PROPN
ejpam-5871	624	21	and	and	CCONJ
ejpam-5871	624	22	holder	holder	NOUN
ejpam-5871	624	23	inequalities	inequality	NOUN
ejpam-5871	624	24	within	within	ADP
ejpam-5871	624	25	the	the	DET
ejpam-5871	624	26	class	class	NOUN
ejpam-5871	624	27	of	of	ADP
ejpam-5871	624	28	convexity	convexity	NOUN
ejpam-5871	624	29	.	.	PUNCT
ejpam-5871	625	1	we	we	PRON
ejpam-5871	625	2	provide	provide	VERB
ejpam-5871	625	3	a	a	DET
ejpam-5871	625	4	versatile	versatile	ADJ
ejpam-5871	625	5	structure	structure	NOUN
ejpam-5871	625	6	for	for	ADP
ejpam-5871	625	7	mathematical	mathematical	ADJ
ejpam-5871	625	8	inequalities	inequality	NOUN
ejpam-5871	625	9	related	relate	VERB
ejpam-5871	625	10	to	to	ADP
ejpam-5871	625	11	generalized	generalize	VERB
ejpam-5871	625	12	fractional	fractional	ADJ
ejpam-5871	625	13	operators	operator	NOUN
ejpam-5871	625	14	by	by	ADP
ejpam-5871	625	15	extending	extend	VERB
ejpam-5871	625	16	and	and	CCONJ
ejpam-5871	625	17	generalizing	generalize	VERB
ejpam-5871	625	18	the	the	DET
ejpam-5871	625	19	reverse	reverse	ADJ
ejpam-5871	625	20	forms	form	NOUN
ejpam-5871	625	21	of	of	ADP
ejpam-5871	625	22	these	these	DET
ejpam-5871	625	23	inequalities	inequality	NOUN
ejpam-5871	625	24	with	with	ADP
ejpam-5871	625	25	in	in	ADP
ejpam-5871	625	26	the	the	DET
ejpam-5871	625	27	unified	unified	ADJ
ejpam-5871	625	28	class	class	NOUN
ejpam-5871	625	29	of	of	ADP
ejpam-5871	625	30	convexity	convexity	NOUN
ejpam-5871	625	31	.	.	PUNCT
ejpam-5871	626	1	to	to	PART
ejpam-5871	626	2	enhance	enhance	VERB
ejpam-5871	626	3	their	their	PRON
ejpam-5871	626	4	practical	practical	ADJ
ejpam-5871	626	5	applications	application	NOUN
ejpam-5871	626	6	,	,	PUNCT
ejpam-5871	626	7	we	we	PRON
ejpam-5871	626	8	investigate	investigate	VERB
ejpam-5871	626	9	the	the	DET
ejpam-5871	626	10	additional	additional	ADJ
ejpam-5871	626	11	implications	implication	NOUN
ejpam-5871	626	12	,	,	PUNCT
ejpam-5871	626	13	derive	derive	VERB
ejpam-5871	626	14	specific	specific	ADJ
ejpam-5871	626	15	inequalities	inequality	NOUN
ejpam-5871	626	16	,	,	PUNCT
ejpam-5871	626	17	and	and	CCONJ
ejpam-5871	626	18	illustrate	illustrate	VERB
ejpam-5871	626	19	them	they	PRON
ejpam-5871	626	20	through	through	ADP
ejpam-5871	626	21	graphical	graphical	ADJ
ejpam-5871	626	22	representations	representation	NOUN
ejpam-5871	626	23	.	.	PUNCT
ejpam-5871	627	1	we	we	PRON
ejpam-5871	627	2	also	also	ADV
ejpam-5871	627	3	check	check	VERB
ejpam-5871	627	4	the	the	DET
ejpam-5871	627	5	results	result	NOUN
ejpam-5871	627	6	by	by	ADP
ejpam-5871	627	7	using	use	VERB
ejpam-5871	627	8	tables	table	NOUN
ejpam-5871	627	9	for	for	ADP
ejpam-5871	627	10	different	different	ADJ
ejpam-5871	627	11	fractional	fractional	ADJ
ejpam-5871	627	12	orders	order	NOUN
ejpam-5871	627	13	.	.	PUNCT
ejpam-5871	628	1	the	the	DET
ejpam-5871	628	2	sharpness	sharpness	NOUN
ejpam-5871	628	3	of	of	ADP
ejpam-5871	628	4	our	our	PRON
ejpam-5871	628	5	inequalities	inequality	NOUN
ejpam-5871	628	6	is	be	AUX
ejpam-5871	628	7	confirmed	confirm	VERB
ejpam-5871	628	8	by	by	ADP
ejpam-5871	628	9	these	these	DET
ejpam-5871	628	10	graphical	graphical	ADJ
ejpam-5871	628	11	comparison	comparison	NOUN
ejpam-5871	628	12	.	.	PUNCT
ejpam-5871	629	1	we	we	PRON
ejpam-5871	629	2	urge	urge	VERB
ejpam-5871	629	3	readers	reader	NOUN
ejpam-5871	629	4	to	to	PART
ejpam-5871	629	5	investigate	investigate	VERB
ejpam-5871	629	6	more	more	ADV
ejpam-5871	629	7	generalized	generalized	ADJ
ejpam-5871	629	8	fractional	fractional	ADJ
ejpam-5871	629	9	operators	operator	NOUN
ejpam-5871	629	10	in	in	ADP
ejpam-5871	629	11	order	order	NOUN
ejpam-5871	629	12	to	to	PART
ejpam-5871	629	13	create	create	VERB
ejpam-5871	629	14	bigger	big	ADJ
ejpam-5871	629	15	classes	class	NOUN
ejpam-5871	629	16	of	of	ADP
ejpam-5871	629	17	inequalities	inequality	NOUN
ejpam-5871	629	18	for	for	ADP
ejpam-5871	629	19	future	future	ADJ
ejpam-5871	629	20	research	research	NOUN
ejpam-5871	629	21	.	.	PUNCT
ejpam-5871	630	1	also	also	ADV
ejpam-5871	630	2	,	,	PUNCT
ejpam-5871	630	3	by	by	ADP
ejpam-5871	630	4	comparing	compare	VERB
ejpam-5871	630	5	recently	recently	ADV
ejpam-5871	630	6	hypothesized	hypothesize	VERB
ejpam-5871	630	7	disparities	disparity	NOUN
ejpam-5871	630	8	with	with	ADP
ejpam-5871	630	9	those	those	PRON
ejpam-5871	630	10	that	that	PRON
ejpam-5871	630	11	already	already	ADV
ejpam-5871	630	12	exist	exist	VERB
ejpam-5871	630	13	,	,	PUNCT
ejpam-5871	630	14	future	future	ADJ
ejpam-5871	630	15	research	research	NOUN
ejpam-5871	630	16	could	could	AUX
ejpam-5871	630	17	evaluate	evaluate	VERB
ejpam-5871	630	18	the	the	DET
ejpam-5871	630	19	adaptability	adaptability	NOUN
ejpam-5871	630	20	of	of	ADP
ejpam-5871	630	21	their	their	PRON
ejpam-5871	630	22	findings	finding	NOUN
ejpam-5871	630	23	by	by	ADP
ejpam-5871	630	24	graphical	graphical	ADJ
ejpam-5871	630	25	analysis	analysis	NOUN
ejpam-5871	630	26	.	.	PUNCT
ejpam-5871	631	1	acknowledgements	acknowledgement	NOUN
ejpam-5871	631	2	the	the	DET
ejpam-5871	631	3	authors	author	NOUN
ejpam-5871	631	4	a.	a.	PROPN
ejpam-5871	631	5	aloqaily	aloqaily	ADV
ejpam-5871	631	6	,	,	PUNCT
ejpam-5871	631	7	d.	d.	PROPN
ejpam-5871	631	8	santina	santina	PROPN
ejpam-5871	631	9	and	and	CCONJ
ejpam-5871	631	10	n.	n.	PROPN
ejpam-5871	631	11	mlaiki	mlaiki	PROPN
ejpam-5871	631	12	would	would	AUX
ejpam-5871	631	13	like	like	VERB
ejpam-5871	631	14	to	to	PART
ejpam-5871	631	15	thank	thank	VERB
ejpam-5871	631	16	prince	prince	PROPN
ejpam-5871	631	17	sultan	sultan	PROPN
ejpam-5871	631	18	university	university	PROPN
ejpam-5871	631	19	for	for	ADP
ejpam-5871	631	20	paying	pay	VERB
ejpam-5871	631	21	the	the	DET
ejpam-5871	631	22	apc	apc	NOUN
ejpam-5871	631	23	and	and	CCONJ
ejpam-5871	631	24	for	for	ADP
ejpam-5871	631	25	the	the	DET
ejpam-5871	631	26	support	support	NOUN
ejpam-5871	631	27	through	through	ADP
ejpam-5871	631	28	the	the	DET
ejpam-5871	631	29	tas	tas	PROPN
ejpam-5871	631	30	research	research	NOUN
ejpam-5871	631	31	lab	lab	NOUN
ejpam-5871	631	32	.	.	PUNCT
ejpam-5871	632	1	declarations	declaration	NOUN
ejpam-5871	632	2	:	:	PUNCT
ejpam-5871	632	3	availability	availability	NOUN
ejpam-5871	632	4	of	of	ADP
ejpam-5871	632	5	data	datum	NOUN
ejpam-5871	632	6	and	and	CCONJ
ejpam-5871	632	7	material	material	NOUN
ejpam-5871	632	8	the	the	DET
ejpam-5871	632	9	data	datum	NOUN
ejpam-5871	632	10	used	use	VERB
ejpam-5871	632	11	to	to	PART
ejpam-5871	632	12	support	support	VERB
ejpam-5871	632	13	the	the	DET
ejpam-5871	632	14	findings	finding	NOUN
ejpam-5871	632	15	of	of	ADP
ejpam-5871	632	16	this	this	DET
ejpam-5871	632	17	study	study	NOUN
ejpam-5871	632	18	are	be	AUX
ejpam-5871	632	19	available	available	ADJ
ejpam-5871	632	20	from	from	ADP
ejpam-5871	632	21	the	the	DET
ejpam-5871	632	22	corresponding	corresponding	ADJ
ejpam-5871	632	23	author	author	NOUN
ejpam-5871	632	24	upon	upon	SCONJ
ejpam-5871	632	25	request	request	NOUN
ejpam-5871	632	26	.	.	PUNCT
ejpam-5871	633	1	authors	author	NOUN
ejpam-5871	633	2	’	'	PUNCT
ejpam-5871	633	3	contributions	contribution	NOUN
ejpam-5871	633	4	all	all	DET
ejpam-5871	633	5	authors	author	NOUN
ejpam-5871	633	6	contributed	contribute	VERB
ejpam-5871	633	7	equally	equally	ADV
ejpam-5871	633	8	and	and	CCONJ
ejpam-5871	633	9	significantly	significantly	ADV
ejpam-5871	633	10	in	in	ADP
ejpam-5871	633	11	writing	write	VERB
ejpam-5871	633	12	this	this	DET
ejpam-5871	633	13	article	article	NOUN
ejpam-5871	633	14	.	.	PUNCT
ejpam-5871	634	1	all	all	DET
ejpam-5871	634	2	authors	author	NOUN
ejpam-5871	634	3	read	read	VERB
ejpam-5871	634	4	and	and	CCONJ
ejpam-5871	634	5	approved	approve	VERB
ejpam-5871	634	6	the	the	DET
ejpam-5871	634	7	final	final	ADJ
ejpam-5871	634	8	version	version	NOUN
ejpam-5871	634	9	.	.	PUNCT
ejpam-5871	635	1	competing	compete	VERB
ejpam-5871	635	2	interests	interest	NOUN
ejpam-5871	635	3	the	the	DET
ejpam-5871	635	4	authors	author	NOUN
ejpam-5871	635	5	declare	declare	VERB
ejpam-5871	635	6	that	that	SCONJ
ejpam-5871	635	7	they	they	PRON
ejpam-5871	635	8	have	have	VERB
ejpam-5871	635	9	no	no	DET
ejpam-5871	635	10	conflicts	conflict	NOUN
ejpam-5871	635	11	of	of	ADP
ejpam-5871	635	12	interest	interest	NOUN
ejpam-5871	635	13	.	.	PUNCT
ejpam-5871	636	1	references	reference	NOUN
ejpam-5871	636	2	[	[	X
ejpam-5871	636	3	1	1	NUM
ejpam-5871	636	4	]	]	PUNCT
ejpam-5871	636	5	n.	n.	PROPN
ejpam-5871	636	6	abel	abel	PROPN
ejpam-5871	636	7	.	.	PUNCT
ejpam-5871	637	1	solution	solution	NOUN
ejpam-5871	637	2	de	de	X
ejpam-5871	637	3	quelques	quelques	X
ejpam-5871	637	4	problèmes	problème	NOUN
ejpam-5871	637	5	à	à	PROPN
ejpam-5871	637	6	l’aide	l’aide	ADV
ejpam-5871	637	7	d’intégrales	d’intégrales	PROPN
ejpam-5871	637	8	définies	définies	PROPN
ejpam-5871	637	9	.	.	PROPN
ejpam-5871	637	10	magasin	magasin	PROPN
ejpam-5871	637	11	for	for	ADP
ejpam-5871	637	12	naturvidenskaberne	naturvidenskaberne	NOUN
ejpam-5871	637	13	,	,	PUNCT
ejpam-5871	637	14	1:11–17	1:11–17	NUM
ejpam-5871	637	15	,	,	PUNCT
ejpam-5871	637	16	1823	1823	NUM
ejpam-5871	637	17	.	.	PUNCT
ejpam-5871	638	1	[	[	X
ejpam-5871	638	2	2	2	NUM
ejpam-5871	638	3	]	]	PUNCT
ejpam-5871	638	4	a.	a.	NOUN
ejpam-5871	638	5	a.	a.	NOUN
ejpam-5871	638	6	kilbas	kilbas	PROPN
ejpam-5871	638	7	,	,	PUNCT
ejpam-5871	638	8	h.	h.	PROPN
ejpam-5871	638	9	m.	m.	PROPN
ejpam-5871	638	10	srivastava	srivastava	PROPN
ejpam-5871	638	11	,	,	PUNCT
ejpam-5871	638	12	and	and	CCONJ
ejpam-5871	638	13	j.	j.	PROPN
ejpam-5871	638	14	j.	j.	PROPN
ejpam-5871	638	15	trujillo	trujillo	PROPN
ejpam-5871	638	16	.	.	PUNCT
ejpam-5871	638	17	theory	theory	NOUN
ejpam-5871	638	18	and	and	CCONJ
ejpam-5871	638	19	applications	application	NOUN
ejpam-5871	638	20	of	of	ADP
ejpam-5871	638	21	fractional	fractional	ADJ
ejpam-5871	638	22	differential	differential	ADJ
ejpam-5871	638	23	equations	equation	NOUN
ejpam-5871	638	24	.	.	PUNCT
ejpam-5871	639	1	north	north	NOUN
ejpam-5871	639	2	-	-	PUNCT
ejpam-5871	639	3	holland	holland	PROPN
ejpam-5871	639	4	mathematics	mathematics	PROPN
ejpam-5871	639	5	studies	study	NOUN
ejpam-5871	639	6	,	,	PUNCT
ejpam-5871	639	7	204	204	NUM
ejpam-5871	639	8	,	,	PUNCT
ejpam-5871	639	9	2006	2006	NUM
ejpam-5871	639	10	.	.	PUNCT
ejpam-5871	640	1	a.	a.	PROPN
ejpam-5871	640	2	mehmood	mehmood	PROPN
ejpam-5871	640	3	et	et	PROPN
ejpam-5871	640	4	al	al	PROPN
ejpam-5871	640	5	.	.	PUNCT
ejpam-5871	640	6	/	/	SYM
ejpam-5871	640	7	eur	eur	PROPN
ejpam-5871	640	8	.	.	PUNCT
ejpam-5871	641	1	j.	j.	PROPN
ejpam-5871	641	2	pure	pure	PROPN
ejpam-5871	641	3	appl	appl	PROPN
ejpam-5871	641	4	.	.	PROPN
ejpam-5871	641	5	math	math	PROPN
ejpam-5871	641	6	,	,	PUNCT
ejpam-5871	641	7	18	18	NUM
ejpam-5871	641	8	(	(	PUNCT
ejpam-5871	641	9	2	2	NUM
ejpam-5871	641	10	)	)	PUNCT
ejpam-5871	641	11	(	(	PUNCT
ejpam-5871	641	12	2025	2025	NUM
ejpam-5871	641	13	)	)	PUNCT
ejpam-5871	641	14	,	,	PUNCT
ejpam-5871	641	15	5871	5871	NUM
ejpam-5871	641	16	25	25	NUM
ejpam-5871	641	17	of	of	ADP
ejpam-5871	641	18	26	26	NUM
ejpam-5871	641	19	[	[	X
ejpam-5871	641	20	3	3	NUM
ejpam-5871	641	21	]	]	PUNCT
ejpam-5871	641	22	k.	k.	PROPN
ejpam-5871	641	23	b.	b.	PROPN
ejpam-5871	641	24	oldham	oldham	PROPN
ejpam-5871	641	25	and	and	CCONJ
ejpam-5871	641	26	j.	j.	PROPN
ejpam-5871	641	27	spanier	spanier	PROPN
ejpam-5871	641	28	.	.	PUNCT
ejpam-5871	642	1	the	the	DET
ejpam-5871	642	2	fractional	fractional	ADJ
ejpam-5871	642	3	calculus	calculus	NOUN
ejpam-5871	642	4	.	.	PUNCT
ejpam-5871	643	1	academic	academic	ADJ
ejpam-5871	643	2	press	press	NOUN
ejpam-5871	643	3	,	,	PUNCT
ejpam-5871	643	4	new	new	PROPN
ejpam-5871	643	5	york	york	PROPN
ejpam-5871	643	6	,	,	PUNCT
ejpam-5871	643	7	1974	1974	NUM
ejpam-5871	643	8	.	.	PUNCT
ejpam-5871	644	1	[	[	X
ejpam-5871	644	2	4	4	X
ejpam-5871	644	3	]	]	PUNCT
ejpam-5871	644	4	t.	t.	NOUN
ejpam-5871	644	5	abdeljawad	abdeljawad	PROPN
ejpam-5871	644	6	and	and	CCONJ
ejpam-5871	644	7	d.	d.	PROPN
ejpam-5871	644	8	baleanu	baleanu	PROPN
ejpam-5871	644	9	.	.	PUNCT
ejpam-5871	645	1	discrete	discrete	ADJ
ejpam-5871	645	2	fractional	fractional	ADJ
ejpam-5871	645	3	differences	difference	NOUN
ejpam-5871	645	4	with	with	ADP
ejpam-5871	645	5	nonsingular	nonsingular	ADJ
ejpam-5871	645	6	discrete	discrete	ADJ
ejpam-5871	645	7	mittag	mittag	ADJ
ejpam-5871	645	8	-	-	PUNCT
ejpam-5871	645	9	leffler	leffler	NOUN
ejpam-5871	645	10	kernels	kernel	NOUN
ejpam-5871	645	11	.	.	PUNCT
ejpam-5871	646	1	advances	advance	NOUN
ejpam-5871	646	2	in	in	ADP
ejpam-5871	646	3	difference	difference	NOUN
ejpam-5871	646	4	equations	equation	NOUN
ejpam-5871	646	5	,	,	PUNCT
ejpam-5871	646	6	2016:232	2016:232	PROPN
ejpam-5871	646	7	,	,	PUNCT
ejpam-5871	646	8	2016	2016	NUM
ejpam-5871	646	9	.	.	PUNCT
ejpam-5871	647	1	[	[	X
ejpam-5871	647	2	5	5	X
ejpam-5871	647	3	]	]	PUNCT
ejpam-5871	647	4	t.	t.	NOUN
ejpam-5871	647	5	abdeljawad	abdeljawad	PROPN
ejpam-5871	647	6	and	and	CCONJ
ejpam-5871	647	7	d.	d.	PROPN
ejpam-5871	647	8	baleanu	baleanu	PROPN
ejpam-5871	647	9	.	.	PUNCT
ejpam-5871	648	1	on	on	ADP
ejpam-5871	648	2	fractional	fractional	ADJ
ejpam-5871	648	3	derivatives	derivative	NOUN
ejpam-5871	648	4	with	with	ADP
ejpam-5871	648	5	exponential	exponential	ADJ
ejpam-5871	648	6	kernel	kernel	NOUN
ejpam-5871	648	7	and	and	CCONJ
ejpam-5871	648	8	their	their	PRON
ejpam-5871	648	9	discrete	discrete	ADJ
ejpam-5871	648	10	versions	version	NOUN
ejpam-5871	648	11	.	.	PUNCT
ejpam-5871	649	1	reports	report	NOUN
ejpam-5871	649	2	on	on	ADP
ejpam-5871	649	3	mathematical	mathematical	ADJ
ejpam-5871	649	4	physics	physics	NOUN
ejpam-5871	649	5	,	,	PUNCT
ejpam-5871	649	6	80(1):11–27	80(1):11–27	NUM
ejpam-5871	649	7	,	,	PUNCT
ejpam-5871	649	8	2017	2017	NUM
ejpam-5871	649	9	.	.	PUNCT
ejpam-5871	650	1	[	[	X
ejpam-5871	650	2	6	6	NUM
ejpam-5871	650	3	]	]	PUNCT
ejpam-5871	650	4	m.	m.	NOUN
ejpam-5871	650	5	caputo	caputo	PROPN
ejpam-5871	650	6	and	and	CCONJ
ejpam-5871	650	7	m.	m.	PROPN
ejpam-5871	650	8	fabrizio	fabrizio	PROPN
ejpam-5871	650	9	.	.	PUNCT
ejpam-5871	651	1	a	a	DET
ejpam-5871	651	2	new	new	ADJ
ejpam-5871	651	3	definition	definition	NOUN
ejpam-5871	651	4	of	of	ADP
ejpam-5871	651	5	fractional	fractional	ADJ
ejpam-5871	651	6	derivative	derivative	NOUN
ejpam-5871	651	7	without	without	ADP
ejpam-5871	651	8	singular	singular	ADJ
ejpam-5871	651	9	kernel	kernel	PROPN
ejpam-5871	651	10	.	.	PUNCT
ejpam-5871	652	1	progress	progress	NOUN
ejpam-5871	652	2	in	in	ADP
ejpam-5871	652	3	fractional	fractional	ADJ
ejpam-5871	652	4	differentiation	differentiation	NOUN
ejpam-5871	652	5	and	and	CCONJ
ejpam-5871	652	6	applications	application	NOUN
ejpam-5871	652	7	,	,	PUNCT
ejpam-5871	652	8	1(2):73–85	1(2):73–85	NUM
ejpam-5871	652	9	,	,	PUNCT
ejpam-5871	652	10	2015	2015	NUM
ejpam-5871	652	11	.	.	PUNCT
ejpam-5871	653	1	[	[	X
ejpam-5871	653	2	7	7	X
ejpam-5871	653	3	]	]	X
ejpam-5871	653	4	j.	j.	PROPN
ejpam-5871	653	5	losada	losada	PROPN
ejpam-5871	653	6	and	and	CCONJ
ejpam-5871	653	7	j.	j.	PROPN
ejpam-5871	653	8	j.	j.	PROPN
ejpam-5871	653	9	nieto	nieto	PROPN
ejpam-5871	653	10	.	.	PUNCT
ejpam-5871	654	1	properties	property	NOUN
ejpam-5871	654	2	of	of	ADP
ejpam-5871	654	3	a	a	DET
ejpam-5871	654	4	new	new	ADJ
ejpam-5871	654	5	fractional	fractional	ADJ
ejpam-5871	654	6	derivative	derivative	NOUN
ejpam-5871	654	7	without	without	ADP
ejpam-5871	654	8	singular	singular	ADJ
ejpam-5871	654	9	kernel	kernel	PROPN
ejpam-5871	654	10	.	.	PUNCT
ejpam-5871	655	1	progress	progress	NOUN
ejpam-5871	655	2	in	in	ADP
ejpam-5871	655	3	fractional	fractional	ADJ
ejpam-5871	655	4	differentiation	differentiation	NOUN
ejpam-5871	655	5	and	and	CCONJ
ejpam-5871	655	6	applications	application	NOUN
ejpam-5871	655	7	,	,	PUNCT
ejpam-5871	655	8	1(2):87–92	1(2):87–92	NUM
ejpam-5871	655	9	,	,	PUNCT
ejpam-5871	655	10	2015	2015	NUM
ejpam-5871	655	11	.	.	PUNCT
ejpam-5871	656	1	[	[	X
ejpam-5871	656	2	8	8	NUM
ejpam-5871	656	3	]	]	PUNCT
ejpam-5871	656	4	x.	x.	NOUN
ejpam-5871	656	5	j.	j.	PROPN
ejpam-5871	656	6	yang	yang	PROPN
ejpam-5871	656	7	,	,	PUNCT
ejpam-5871	656	8	h.	h.	PROPN
ejpam-5871	656	9	m.	m.	PROPN
ejpam-5871	656	10	srivastava	srivastava	PROPN
ejpam-5871	656	11	,	,	PUNCT
ejpam-5871	656	12	and	and	CCONJ
ejpam-5871	656	13	j.	j.	PROPN
ejpam-5871	656	14	a.	a.	PROPN
ejpam-5871	656	15	t.	t.	PROPN
ejpam-5871	656	16	machado	machado	PROPN
ejpam-5871	656	17	.	.	PUNCT
ejpam-5871	657	1	a	a	DET
ejpam-5871	657	2	new	new	ADJ
ejpam-5871	657	3	fractional	fractional	ADJ
ejpam-5871	657	4	derivative	derivative	NOUN
ejpam-5871	657	5	without	without	ADP
ejpam-5871	657	6	a	a	DET
ejpam-5871	657	7	singular	singular	ADJ
ejpam-5871	657	8	kernel	kernel	NOUN
ejpam-5871	657	9	:	:	PUNCT
ejpam-5871	657	10	application	application	NOUN
ejpam-5871	657	11	to	to	ADP
ejpam-5871	657	12	the	the	DET
ejpam-5871	657	13	modeling	modeling	NOUN
ejpam-5871	657	14	of	of	ADP
ejpam-5871	657	15	the	the	DET
ejpam-5871	657	16	steady	steady	ADJ
ejpam-5871	657	17	heat	heat	NOUN
ejpam-5871	657	18	flow	flow	NOUN
ejpam-5871	657	19	.	.	PUNCT
ejpam-5871	658	1	thermal	thermal	ADJ
ejpam-5871	658	2	science	science	NOUN
ejpam-5871	658	3	,	,	PUNCT
ejpam-5871	658	4	20(2):753–756	20(2):753–756	PROPN
ejpam-5871	658	5	,	,	PUNCT
ejpam-5871	658	6	2016	2016	NUM
ejpam-5871	658	7	.	.	PUNCT
ejpam-5871	659	1	[	[	X
ejpam-5871	659	2	9	9	NUM
ejpam-5871	659	3	]	]	SYM
ejpam-5871	659	4	a.	a.	NOUN
ejpam-5871	659	5	m.	m.	NOUN
ejpam-5871	659	6	fernandez	fernandez	PROPN
ejpam-5871	659	7	,	,	PUNCT
ejpam-5871	659	8	a.	a.	NOUN
ejpam-5871	659	9	ozarslan	ozarslan	NOUN
ejpam-5871	659	10	,	,	PUNCT
ejpam-5871	659	11	and	and	CCONJ
ejpam-5871	659	12	d.	d.	PROPN
ejpam-5871	659	13	baleanu	baleanu	PROPN
ejpam-5871	659	14	.	.	PUNCT
ejpam-5871	660	1	on	on	ADP
ejpam-5871	660	2	fractional	fractional	ADJ
ejpam-5871	660	3	calculus	calculus	NOUN
ejpam-5871	660	4	with	with	ADP
ejpam-5871	660	5	general	general	ADJ
ejpam-5871	660	6	analytic	analytic	ADJ
ejpam-5871	660	7	kernels	kernel	NOUN
ejpam-5871	660	8	.	.	PUNCT
ejpam-5871	661	1	applied	apply	VERB
ejpam-5871	661	2	mathematics	mathematic	NOUN
ejpam-5871	661	3	and	and	CCONJ
ejpam-5871	661	4	computation	computation	NOUN
ejpam-5871	661	5	,	,	PUNCT
ejpam-5871	661	6	354:248–265	354:248–265	NUM
ejpam-5871	661	7	,	,	PUNCT
ejpam-5871	661	8	2019	2019	NUM
ejpam-5871	661	9	.	.	PUNCT
ejpam-5871	662	1	[	[	X
ejpam-5871	662	2	10	10	NUM
ejpam-5871	662	3	]	]	X
ejpam-5871	662	4	g.	g.	PROPN
ejpam-5871	662	5	s.	s.	PROPN
ejpam-5871	662	6	teodoro	teodoro	PROPN
ejpam-5871	662	7	,	,	PUNCT
ejpam-5871	662	8	j.	j.	PROPN
ejpam-5871	662	9	a.	a.	PROPN
ejpam-5871	662	10	t.	t.	PROPN
ejpam-5871	662	11	machado	machado	PROPN
ejpam-5871	662	12	,	,	PUNCT
ejpam-5871	662	13	and	and	CCONJ
ejpam-5871	662	14	e.	e.	PROPN
ejpam-5871	662	15	c.	c.	PROPN
ejpam-5871	662	16	de	de	PROPN
ejpam-5871	662	17	oliveira	oliveira	PROPN
ejpam-5871	662	18	.	.	PUNCT
ejpam-5871	663	1	a	a	DET
ejpam-5871	663	2	review	review	NOUN
ejpam-5871	663	3	of	of	ADP
ejpam-5871	663	4	definitions	definition	NOUN
ejpam-5871	663	5	of	of	ADP
ejpam-5871	663	6	fractional	fractional	ADJ
ejpam-5871	663	7	derivatives	derivative	NOUN
ejpam-5871	663	8	and	and	CCONJ
ejpam-5871	663	9	other	other	ADJ
ejpam-5871	663	10	operators	operator	NOUN
ejpam-5871	663	11	.	.	PUNCT
ejpam-5871	664	1	journal	journal	NOUN
ejpam-5871	664	2	of	of	ADP
ejpam-5871	664	3	computational	computational	ADJ
ejpam-5871	664	4	physics	physics	NOUN
ejpam-5871	664	5	,	,	PUNCT
ejpam-5871	664	6	388:195–208	388:195–208	NUM
ejpam-5871	664	7	,	,	PUNCT
ejpam-5871	664	8	2019	2019	NUM
ejpam-5871	664	9	.	.	PUNCT
ejpam-5871	665	1	[	[	X
ejpam-5871	665	2	11	11	NUM
ejpam-5871	665	3	]	]	PUNCT
ejpam-5871	665	4	s.	s.	PROPN
ejpam-5871	665	5	wu	wu	PROPN
ejpam-5871	665	6	,	,	PUNCT
ejpam-5871	665	7	m.	m.	NOUN
ejpam-5871	665	8	samraiz	samraiz	PROPN
ejpam-5871	665	9	,	,	PUNCT
ejpam-5871	665	10	a.	a.	PROPN
ejpam-5871	665	11	mehmood	mehmood	PROPN
ejpam-5871	665	12	,	,	PUNCT
ejpam-5871	665	13	f.	f.	PROPN
ejpam-5871	665	14	jarad	jarad	PROPN
ejpam-5871	665	15	,	,	PUNCT
ejpam-5871	665	16	and	and	CCONJ
ejpam-5871	665	17	s.	s.	PROPN
ejpam-5871	665	18	naheed	naheed	PROPN
ejpam-5871	665	19	.	.	PUNCT
ejpam-5871	666	1	some	some	DET
ejpam-5871	666	2	symmetric	symmetric	ADJ
ejpam-5871	666	3	properties	property	NOUN
ejpam-5871	666	4	and	and	CCONJ
ejpam-5871	666	5	applications	application	NOUN
ejpam-5871	666	6	of	of	ADP
ejpam-5871	666	7	weighted	weight	VERB
ejpam-5871	666	8	fractional	fractional	ADJ
ejpam-5871	666	9	integral	integral	ADJ
ejpam-5871	666	10	operator	operator	NOUN
ejpam-5871	666	11	.	.	PUNCT
ejpam-5871	667	1	fractals	fractal	NOUN
ejpam-5871	667	2	,	,	PUNCT
ejpam-5871	667	3	31(4):2340011	31(4):2340011	NUM
ejpam-5871	667	4	,	,	PUNCT
ejpam-5871	667	5	2023	2023	NUM
ejpam-5871	667	6	.	.	PUNCT
ejpam-5871	668	1	[	[	X
ejpam-5871	668	2	12	12	NUM
ejpam-5871	668	3	]	]	PUNCT
ejpam-5871	668	4	m.	m.	NOUN
ejpam-5871	668	5	samraiz	samraiz	PROPN
ejpam-5871	668	6	,	,	PUNCT
ejpam-5871	668	7	a.	a.	PROPN
ejpam-5871	668	8	mehmood	mehmood	PROPN
ejpam-5871	668	9	,	,	PUNCT
ejpam-5871	668	10	s.	s.	PROPN
ejpam-5871	668	11	iqbal	iqbal	PROPN
ejpam-5871	668	12	,	,	PUNCT
ejpam-5871	668	13	s.	s.	PROPN
ejpam-5871	668	14	naheed	naheed	PROPN
ejpam-5871	668	15	,	,	PUNCT
ejpam-5871	668	16	g.	g.	PROPN
ejpam-5871	668	17	rehman	rehman	PROPN
ejpam-5871	668	18	,	,	PUNCT
ejpam-5871	668	19	and	and	CCONJ
ejpam-5871	668	20	y.	y.	PROPN
ejpam-5871	668	21	m.	m.	PROPN
ejpam-5871	668	22	chu	chu	PROPN
ejpam-5871	668	23	.	.	PROPN
ejpam-5871	669	1	generalized	generalize	VERB
ejpam-5871	669	2	fractional	fractional	ADJ
ejpam-5871	669	3	operator	operator	NOUN
ejpam-5871	669	4	with	with	ADP
ejpam-5871	669	5	applications	application	NOUN
ejpam-5871	669	6	in	in	ADP
ejpam-5871	669	7	mathematical	mathematical	ADJ
ejpam-5871	669	8	physics	physics	NOUN
ejpam-5871	669	9	.	.	PUNCT
ejpam-5871	670	1	chaos	chaos	NOUN
ejpam-5871	670	2	,	,	PUNCT
ejpam-5871	670	3	solitons	soliton	NOUN
ejpam-5871	670	4	&	&	CCONJ
ejpam-5871	670	5	fractals	fractal	NOUN
ejpam-5871	670	6	,	,	PUNCT
ejpam-5871	670	7	165:112830	165:112830	NUM
ejpam-5871	670	8	,	,	PUNCT
ejpam-5871	670	9	2022	2022	NUM
ejpam-5871	670	10	.	.	PUNCT
ejpam-5871	671	1	[	[	X
ejpam-5871	671	2	13	13	NUM
ejpam-5871	671	3	]	]	PUNCT
ejpam-5871	671	4	m.	m.	NOUN
ejpam-5871	671	5	samraiz	samraiz	PROPN
ejpam-5871	671	6	,	,	PUNCT
ejpam-5871	671	7	a.	a.	PROPN
ejpam-5871	671	8	mehmood	mehmood	PROPN
ejpam-5871	671	9	,	,	PUNCT
ejpam-5871	671	10	s.	s.	PROPN
ejpam-5871	671	11	naheed	naheed	PROPN
ejpam-5871	671	12	,	,	PUNCT
ejpam-5871	671	13	g.	g.	PROPN
ejpam-5871	671	14	rehman	rehman	PROPN
ejpam-5871	671	15	,	,	PUNCT
ejpam-5871	671	16	a.	a.	NOUN
ejpam-5871	671	17	kashuri	kashuri	PROPN
ejpam-5871	671	18	,	,	PUNCT
ejpam-5871	671	19	and	and	CCONJ
ejpam-5871	671	20	k.	k.	X
ejpam-5871	671	21	nonlaopon	nonlaopon	NOUN
ejpam-5871	671	22	.	.	PUNCT
ejpam-5871	672	1	on	on	ADP
ejpam-5871	672	2	novel	novel	ADJ
ejpam-5871	672	3	fractional	fractional	ADJ
ejpam-5871	672	4	operators	operator	NOUN
ejpam-5871	672	5	involving	involve	VERB
ejpam-5871	672	6	the	the	DET
ejpam-5871	672	7	multivariate	multivariate	NOUN
ejpam-5871	672	8	mittag	mittag	ADJ
ejpam-5871	672	9	-	-	PUNCT
ejpam-5871	672	10	leffler	leffler	NOUN
ejpam-5871	672	11	function	function	NOUN
ejpam-5871	672	12	.	.	PUNCT
ejpam-5871	673	1	mathematics	mathematic	NOUN
ejpam-5871	673	2	,	,	PUNCT
ejpam-5871	673	3	10(21):3991	10(21):3991	NUM
ejpam-5871	673	4	,	,	PUNCT
ejpam-5871	673	5	2022	2022	NUM
ejpam-5871	673	6	.	.	PUNCT
ejpam-5871	674	1	[	[	X
ejpam-5871	674	2	14	14	NUM
ejpam-5871	674	3	]	]	X
ejpam-5871	674	4	w.	w.	PROPN
ejpam-5871	674	5	h.	h.	PROPN
ejpam-5871	674	6	huang	huang	PROPN
ejpam-5871	674	7	,	,	PUNCT
ejpam-5871	674	8	m.	m.	PROPN
ejpam-5871	674	9	samraiz	samraiz	PROPN
ejpam-5871	674	10	,	,	PUNCT
ejpam-5871	674	11	a.	a.	PROPN
ejpam-5871	674	12	mehmood	mehmood	PROPN
ejpam-5871	674	13	,	,	PUNCT
ejpam-5871	674	14	d.	d.	PROPN
ejpam-5871	674	15	baleanu	baleanu	PROPN
ejpam-5871	674	16	,	,	PUNCT
ejpam-5871	674	17	g.	g.	PROPN
ejpam-5871	674	18	rehman	rehman	PROPN
ejpam-5871	674	19	,	,	PUNCT
ejpam-5871	674	20	and	and	CCONJ
ejpam-5871	674	21	s.	s.	PROPN
ejpam-5871	674	22	naheed	naheed	PROPN
ejpam-5871	674	23	.	.	PUNCT
ejpam-5871	675	1	modified	modify	VERB
ejpam-5871	675	2	atangana	atangana	PROPN
ejpam-5871	675	3	-	-	PUNCT
ejpam-5871	675	4	baleanu	baleanu	ADJ
ejpam-5871	675	5	fractional	fractional	ADJ
ejpam-5871	675	6	operators	operator	NOUN
ejpam-5871	675	7	involving	involve	VERB
ejpam-5871	675	8	generalized	generalize	VERB
ejpam-5871	675	9	mittag	mittag	ADJ
ejpam-5871	675	10	-	-	PUNCT
ejpam-5871	675	11	leffler	leffler	NOUN
ejpam-5871	675	12	function	function	NOUN
ejpam-5871	675	13	.	.	PUNCT
ejpam-5871	676	1	alexandria	alexandria	PROPN
ejpam-5871	676	2	engineering	engineering	PROPN
ejpam-5871	676	3	journal	journal	PROPN
ejpam-5871	676	4	,	,	PUNCT
ejpam-5871	676	5	75:639–648	75:639–648	PROPN
ejpam-5871	676	6	,	,	PUNCT
ejpam-5871	676	7	2023	2023	NUM
ejpam-5871	676	8	.	.	PUNCT
ejpam-5871	677	1	[	[	X
ejpam-5871	677	2	15	15	NUM
ejpam-5871	677	3	]	]	X
ejpam-5871	677	4	m.	m.	NOUN
ejpam-5871	677	5	samraiz	samraiz	PROPN
ejpam-5871	677	6	,	,	PUNCT
ejpam-5871	677	7	m.	m.	NOUN
ejpam-5871	677	8	umer	umer	PROPN
ejpam-5871	677	9	,	,	PUNCT
ejpam-5871	677	10	t.	t.	PROPN
ejpam-5871	677	11	abdeljawad	abdeljawad	PROPN
ejpam-5871	677	12	,	,	PUNCT
ejpam-5871	677	13	s.	s.	PROPN
ejpam-5871	677	14	naheed	naheed	PROPN
ejpam-5871	677	15	,	,	PUNCT
ejpam-5871	677	16	g.	g.	PROPN
ejpam-5871	677	17	rahman	rahman	PROPN
ejpam-5871	677	18	,	,	PUNCT
ejpam-5871	677	19	and	and	CCONJ
ejpam-5871	677	20	k.	k.	PROPN
ejpam-5871	677	21	shah	shah	PROPN
ejpam-5871	677	22	.	.	PUNCT
ejpam-5871	678	1	on	on	ADP
ejpam-5871	678	2	riemann	riemann	PROPN
ejpam-5871	678	3	-	-	PUNCT
ejpam-5871	678	4	type	type	NOUN
ejpam-5871	678	5	weighted	weight	VERB
ejpam-5871	678	6	fractional	fractional	ADJ
ejpam-5871	678	7	operator	operator	NOUN
ejpam-5871	678	8	and	and	CCONJ
ejpam-5871	678	9	solution	solution	NOUN
ejpam-5871	678	10	to	to	ADP
ejpam-5871	678	11	cauchy	cauchy	PROPN
ejpam-5871	678	12	problems	problem	NOUN
ejpam-5871	678	13	.	.	PUNCT
ejpam-5871	679	1	computer	computer	NOUN
ejpam-5871	679	2	modeling	modeling	NOUN
ejpam-5871	679	3	in	in	ADP
ejpam-5871	679	4	engineering	engineering	NOUN
ejpam-5871	679	5	&	&	CCONJ
ejpam-5871	679	6	sciences	sciences	PROPN
ejpam-5871	679	7	,	,	PUNCT
ejpam-5871	679	8	132(3):881–897	132(3):881–897	NUM
ejpam-5871	679	9	,	,	PUNCT
ejpam-5871	679	10	2022	2022	NUM
ejpam-5871	679	11	.	.	PUNCT
ejpam-5871	680	1	[	[	X
ejpam-5871	680	2	16	16	NUM
ejpam-5871	680	3	]	]	PUNCT
ejpam-5871	680	4	s.	s.	PROPN
ejpam-5871	680	5	s.	s.	PROPN
ejpam-5871	680	6	dragomir	dragomir	PROPN
ejpam-5871	680	7	and	and	CCONJ
ejpam-5871	680	8	c.	c.	PROPN
ejpam-5871	680	9	e.	e.	PROPN
ejpam-5871	680	10	m.	m.	PROPN
ejpam-5871	680	11	pearce	pearce	PROPN
ejpam-5871	680	12	.	.	PUNCT
ejpam-5871	681	1	selected	select	VERB
ejpam-5871	681	2	topics	topic	NOUN
ejpam-5871	681	3	on	on	ADP
ejpam-5871	681	4	hermite	hermite	ADJ
ejpam-5871	681	5	–	–	PUNCT
ejpam-5871	681	6	hadamard	hadamard	ADJ
ejpam-5871	681	7	inequalities	inequality	NOUN
ejpam-5871	681	8	and	and	CCONJ
ejpam-5871	681	9	applications	application	NOUN
ejpam-5871	681	10	.	.	PUNCT
ejpam-5871	682	1	rgmia	rgmia	NOUN
ejpam-5871	682	2	monographs	monograph	NOUN
ejpam-5871	682	3	,	,	PUNCT
ejpam-5871	682	4	victoria	victoria	PROPN
ejpam-5871	682	5	university	university	PROPN
ejpam-5871	682	6	,	,	PUNCT
ejpam-5871	682	7	sydney	sydney	PROPN
ejpam-5871	682	8	,	,	PUNCT
ejpam-5871	682	9	australia	australia	PROPN
ejpam-5871	682	10	,	,	PUNCT
ejpam-5871	682	11	2000	2000	NUM
ejpam-5871	682	12	.	.	PUNCT
ejpam-5871	683	1	available	available	ADJ
ejpam-5871	683	2	at	at	ADP
ejpam-5871	683	3	https://rgmia.org/papers/monographs/master.pdf	https://rgmia.org/papers/monographs/master.pdf	NOUN
ejpam-5871	683	4	.	.	PUNCT
ejpam-5871	684	1	[	[	X
ejpam-5871	684	2	17	17	NUM
ejpam-5871	684	3	]	]	PUNCT
ejpam-5871	684	4	j.	j.	PROPN
ejpam-5871	684	5	e.	e.	PROPN
ejpam-5871	684	6	pečarić	pečarić	PROPN
ejpam-5871	684	7	and	and	CCONJ
ejpam-5871	684	8	y.	y.	PROPN
ejpam-5871	684	9	l.	l.	PROPN
ejpam-5871	684	10	tong	tong	PROPN
ejpam-5871	684	11	.	.	PUNCT
ejpam-5871	685	1	convex	convex	PROPN
ejpam-5871	685	2	functions	function	NOUN
ejpam-5871	685	3	,	,	PUNCT
ejpam-5871	685	4	partial	partial	ADJ
ejpam-5871	685	5	orderings	ordering	NOUN
ejpam-5871	685	6	,	,	PUNCT
ejpam-5871	685	7	and	and	CCONJ
ejpam-5871	685	8	statistical	statistical	ADJ
ejpam-5871	685	9	applications	application	NOUN
ejpam-5871	685	10	.	.	PUNCT
ejpam-5871	686	1	academic	academic	ADJ
ejpam-5871	686	2	press	press	PROPN
ejpam-5871	686	3	,	,	PUNCT
ejpam-5871	686	4	cambridge	cambridge	PROPN
ejpam-5871	686	5	,	,	PUNCT
ejpam-5871	686	6	ma	ma	PROPN
ejpam-5871	686	7	,	,	PUNCT
ejpam-5871	686	8	usa	usa	PROPN
ejpam-5871	686	9	,	,	PUNCT
ejpam-5871	686	10	1992	1992	NUM
ejpam-5871	686	11	.	.	PUNCT
ejpam-5871	687	1	[	[	X
ejpam-5871	687	2	18	18	NUM
ejpam-5871	687	3	]	]	X
ejpam-5871	687	4	s.	s.	PROPN
ejpam-5871	687	5	wu	wu	PROPN
ejpam-5871	687	6	,	,	PUNCT
ejpam-5871	687	7	m.	m.	NOUN
ejpam-5871	687	8	u.	u.	PROPN
ejpam-5871	687	9	awan	awan	PROPN
ejpam-5871	687	10	,	,	PUNCT
ejpam-5871	687	11	m.	m.	NOUN
ejpam-5871	687	12	a.	a.	PROPN
ejpam-5871	687	13	noor	noor	PROPN
ejpam-5871	687	14	,	,	PUNCT
ejpam-5871	687	15	k.	k.	PROPN
ejpam-5871	687	16	i.	i.	PROPN
ejpam-5871	687	17	noor	noor	PROPN
ejpam-5871	687	18	,	,	PUNCT
ejpam-5871	687	19	and	and	CCONJ
ejpam-5871	687	20	s.	s.	PROPN
ejpam-5871	687	21	iftikhar	iftikhar	PROPN
ejpam-5871	687	22	.	.	PUNCT
ejpam-5871	688	1	on	on	ADP
ejpam-5871	688	2	a	a	DET
ejpam-5871	688	3	new	new	ADJ
ejpam-5871	688	4	class	class	NOUN
ejpam-5871	688	5	of	of	ADP
ejpam-5871	688	6	convex	convex	NOUN
ejpam-5871	688	7	functions	function	NOUN
ejpam-5871	688	8	and	and	CCONJ
ejpam-5871	688	9	integral	integral	ADJ
ejpam-5871	688	10	inequalities	inequality	NOUN
ejpam-5871	688	11	.	.	PUNCT
ejpam-5871	689	1	journal	journal	PROPN
ejpam-5871	689	2	of	of	ADP
ejpam-5871	689	3	inequalities	inequality	NOUN
ejpam-5871	689	4	and	and	CCONJ
ejpam-5871	689	5	applications	application	NOUN
ejpam-5871	689	6	,	,	PUNCT
ejpam-5871	689	7	2019:131	2019:131	NUM
ejpam-5871	689	8	,	,	PUNCT
ejpam-5871	689	9	2019	2019	NUM
ejpam-5871	689	10	.	.	PUNCT
ejpam-5871	690	1	[	[	X
ejpam-5871	690	2	19	19	NUM
ejpam-5871	690	3	]	]	PUNCT
ejpam-5871	690	4	w.	w.	PROPN
ejpam-5871	690	5	w.	w.	PROPN
ejpam-5871	690	6	breckner	breckner	PROPN
ejpam-5871	690	7	.	.	PUNCT
ejpam-5871	691	1	continuity	continuity	NOUN
ejpam-5871	691	2	of	of	ADP
ejpam-5871	691	3	generalized	generalized	ADJ
ejpam-5871	691	4	convex	convex	NOUN
ejpam-5871	691	5	and	and	CCONJ
ejpam-5871	691	6	generalized	generalize	VERB
ejpam-5871	691	7	concave	concave	NOUN
ejpam-5871	691	8	set	set	NOUN
ejpam-5871	691	9	-	-	PUNCT
ejpam-5871	691	10	valued	value	VERB
ejpam-5871	691	11	functions	function	NOUN
ejpam-5871	691	12	.	.	PUNCT
ejpam-5871	692	1	revue	revue	NOUN
ejpam-5871	692	2	d’analyse	d’analyse	PROPN
ejpam-5871	692	3	numérique	numérique	NOUN
ejpam-5871	692	4	et	et	PROPN
ejpam-5871	692	5	de	de	X
ejpam-5871	692	6	théorie	théorie	PROPN
ejpam-5871	692	7	de	de	X
ejpam-5871	692	8	l’approximation	l’approximation	PROPN
ejpam-5871	692	9	,	,	PUNCT
ejpam-5871	692	10	22(1):39	22(1):39	NUM
ejpam-5871	692	11	–	–	PUNCT
ejpam-5871	692	12	a.	a.	NOUN
ejpam-5871	692	13	mehmood	mehmood	PROPN
ejpam-5871	692	14	et	et	PROPN
ejpam-5871	692	15	al	al	PROPN
ejpam-5871	692	16	.	.	PUNCT
ejpam-5871	692	17	/	/	SYM
ejpam-5871	692	18	eur	eur	PROPN
ejpam-5871	692	19	.	.	PUNCT
ejpam-5871	693	1	j.	j.	PROPN
ejpam-5871	693	2	pure	pure	PROPN
ejpam-5871	693	3	appl	appl	PROPN
ejpam-5871	693	4	.	.	PROPN
ejpam-5871	693	5	math	math	PROPN
ejpam-5871	693	6	,	,	PUNCT
ejpam-5871	693	7	18	18	NUM
ejpam-5871	693	8	(	(	PUNCT
ejpam-5871	693	9	2	2	NUM
ejpam-5871	693	10	)	)	PUNCT
ejpam-5871	693	11	(	(	PUNCT
ejpam-5871	693	12	2025	2025	NUM
ejpam-5871	693	13	)	)	PUNCT
ejpam-5871	693	14	,	,	PUNCT
ejpam-5871	693	15	5871	5871	NUM
ejpam-5871	693	16	26	26	NUM
ejpam-5871	693	17	of	of	ADP
ejpam-5871	693	18	26	26	NUM
ejpam-5871	693	19	51	51	NUM
ejpam-5871	693	20	,	,	PUNCT
ejpam-5871	693	21	1993	1993	NUM
ejpam-5871	693	22	.	.	PUNCT
ejpam-5871	694	1	[	[	X
ejpam-5871	694	2	20	20	NUM
ejpam-5871	694	3	]	]	X
ejpam-5871	694	4	e.	e.	PROPN
ejpam-5871	694	5	sadowska	sadowska	PROPN
ejpam-5871	694	6	.	.	PUNCT
ejpam-5871	695	1	hadamard	hadamard	ADJ
ejpam-5871	695	2	inequality	inequality	NOUN
ejpam-5871	695	3	and	and	CCONJ
ejpam-5871	695	4	a	a	DET
ejpam-5871	695	5	refinement	refinement	NOUN
ejpam-5871	695	6	of	of	ADP
ejpam-5871	695	7	jensen	jensen	PROPN
ejpam-5871	695	8	inequality	inequality	NOUN
ejpam-5871	695	9	for	for	ADP
ejpam-5871	695	10	setvalued	setvalue	VERB
ejpam-5871	695	11	functions	function	NOUN
ejpam-5871	695	12	.	.	PUNCT
ejpam-5871	696	1	results	result	NOUN
ejpam-5871	696	2	in	in	ADP
ejpam-5871	696	3	mathematics	mathematic	NOUN
ejpam-5871	696	4	,	,	PUNCT
ejpam-5871	696	5	32(3	32(3	PROPN
ejpam-5871	696	6	-	-	SYM
ejpam-5871	696	7	4):332–337	4):332–337	NUM
ejpam-5871	696	8	,	,	PUNCT
ejpam-5871	696	9	1997	1997	NUM
ejpam-5871	696	10	.	.	PUNCT
ejpam-5871	697	1	[	[	X
ejpam-5871	697	2	21	21	NUM
ejpam-5871	697	3	]	]	X
ejpam-5871	697	4	r.	r.	PROPN
ejpam-5871	697	5	e.	e.	PROPN
ejpam-5871	697	6	moore	moore	PROPN
ejpam-5871	697	7	.	.	PUNCT
ejpam-5871	698	1	interval	interval	NOUN
ejpam-5871	698	2	analysis	analysis	NOUN
ejpam-5871	698	3	.	.	PUNCT
ejpam-5871	699	1	prentice	prentice	NOUN
ejpam-5871	699	2	-	-	PUNCT
ejpam-5871	699	3	hall	hall	PROPN
ejpam-5871	699	4	,	,	PUNCT
ejpam-5871	699	5	englewood	englewood	PROPN
ejpam-5871	699	6	cliffs	cliffs	PROPN
ejpam-5871	699	7	,	,	PUNCT
ejpam-5871	699	8	nj	nj	PROPN
ejpam-5871	699	9	,	,	PUNCT
ejpam-5871	699	10	usa	usa	PROPN
ejpam-5871	699	11	,	,	PUNCT
ejpam-5871	699	12	1966	1966	NUM
ejpam-5871	699	13	.	.	PUNCT
ejpam-5871	700	1	[	[	X
ejpam-5871	700	2	22	22	NUM
ejpam-5871	700	3	]	]	PUNCT
ejpam-5871	700	4	a.	a.	NOUN
ejpam-5871	700	5	a.	a.	NOUN
ejpam-5871	700	6	kilbas	kilbas	PROPN
ejpam-5871	700	7	,	,	PUNCT
ejpam-5871	700	8	h.	h.	PROPN
ejpam-5871	700	9	m.	m.	PROPN
ejpam-5871	700	10	srivastava	srivastava	PROPN
ejpam-5871	700	11	,	,	PUNCT
ejpam-5871	700	12	and	and	CCONJ
ejpam-5871	700	13	j.	j.	PROPN
ejpam-5871	700	14	j.	j.	PROPN
ejpam-5871	700	15	trujillo	trujillo	PROPN
ejpam-5871	700	16	.	.	PUNCT
ejpam-5871	700	17	theory	theory	NOUN
ejpam-5871	700	18	and	and	CCONJ
ejpam-5871	700	19	applications	application	NOUN
ejpam-5871	700	20	of	of	ADP
ejpam-5871	700	21	fractional	fractional	ADJ
ejpam-5871	700	22	differential	differential	ADJ
ejpam-5871	700	23	equations	equation	NOUN
ejpam-5871	700	24	.	.	PUNCT
ejpam-5871	701	1	elsevier	elsevier	PROPN
ejpam-5871	701	2	,	,	PUNCT
ejpam-5871	701	3	amsterdam	amsterdam	PROPN
ejpam-5871	701	4	,	,	PUNCT
ejpam-5871	701	5	the	the	DET
ejpam-5871	701	6	netherlands	netherlands	PROPN
ejpam-5871	701	7	,	,	PUNCT
ejpam-5871	701	8	2006	2006	NUM
ejpam-5871	701	9	.	.	PUNCT
ejpam-5871	702	1	[	[	X
ejpam-5871	702	2	23	23	NUM
ejpam-5871	702	3	]	]	X
ejpam-5871	702	4	h.	h.	PROPN
ejpam-5871	702	5	budak	budak	PROPN
ejpam-5871	702	6	,	,	PUNCT
ejpam-5871	702	7	t.	t.	PROPN
ejpam-5871	702	8	tunç	tunç	PROPN
ejpam-5871	702	9	,	,	PUNCT
ejpam-5871	702	10	and	and	CCONJ
ejpam-5871	702	11	m.	m.	PROPN
ejpam-5871	702	12	z.	z.	PROPN
ejpam-5871	702	13	sarıkaya	sarıkaya	PROPN
ejpam-5871	702	14	.	.	PUNCT
ejpam-5871	703	1	fractional	fractional	ADJ
ejpam-5871	703	2	hermite	hermite	PROPN
ejpam-5871	703	3	-	-	PUNCT
ejpam-5871	703	4	hadamard	hadamard	ADJ
ejpam-5871	703	5	-	-	PUNCT
ejpam-5871	703	6	type	type	NOUN
ejpam-5871	703	7	inequalities	inequality	NOUN
ejpam-5871	703	8	for	for	ADP
ejpam-5871	703	9	interval	interval	NOUN
ejpam-5871	703	10	-	-	PUNCT
ejpam-5871	703	11	valued	value	VERB
ejpam-5871	703	12	functions	function	NOUN
ejpam-5871	703	13	.	.	PUNCT
ejpam-5871	704	1	proceedings	proceeding	NOUN
ejpam-5871	704	2	of	of	ADP
ejpam-5871	704	3	the	the	DET
ejpam-5871	704	4	american	american	PROPN
ejpam-5871	704	5	mathematical	mathematical	PROPN
ejpam-5871	704	6	society	society	NOUN
ejpam-5871	704	7	,	,	PUNCT
ejpam-5871	704	8	148(2):705–718	148(2):705–718	NUM
ejpam-5871	704	9	,	,	PUNCT
ejpam-5871	704	10	2020	2020	NUM
ejpam-5871	704	11	.	.	PUNCT
ejpam-5871	705	1	[	[	X
ejpam-5871	705	2	24	24	NUM
ejpam-5871	705	3	]	]	X
ejpam-5871	705	4	b.	b.	PROPN
ejpam-5871	705	5	bin	bin	PROPN
ejpam-5871	705	6	-	-	PUNCT
ejpam-5871	705	7	mohsin	mohsin	PROPN
ejpam-5871	705	8	,	,	PUNCT
ejpam-5871	705	9	m.	m.	NOUN
ejpam-5871	705	10	z.	z.	PROPN
ejpam-5871	705	11	javed	javed	PROPN
ejpam-5871	705	12	,	,	PUNCT
ejpam-5871	705	13	m.	m.	NOUN
ejpam-5871	705	14	u.	u.	PROPN
ejpam-5871	705	15	awan	awan	PROPN
ejpam-5871	705	16	,	,	PUNCT
ejpam-5871	705	17	b.	b.	PROPN
ejpam-5871	705	18	meftah	meftah	PROPN
ejpam-5871	705	19	,	,	PUNCT
ejpam-5871	705	20	and	and	CCONJ
ejpam-5871	705	21	a.	a.	NOUN
ejpam-5871	705	22	kashuri	kashuri	PROPN
ejpam-5871	705	23	.	.	PUNCT
ejpam-5871	706	1	fractional	fractional	ADJ
ejpam-5871	706	2	reverse	reverse	ADJ
ejpam-5871	706	3	inequalities	inequality	NOUN
ejpam-5871	706	4	involving	involve	VERB
ejpam-5871	706	5	generic	generic	ADJ
ejpam-5871	706	6	interval	interval	NOUN
ejpam-5871	706	7	-	-	PUNCT
ejpam-5871	706	8	valued	value	VERB
ejpam-5871	706	9	convex	convex	NOUN
ejpam-5871	706	10	functions	function	NOUN
ejpam-5871	706	11	and	and	CCONJ
ejpam-5871	706	12	applications	application	NOUN
ejpam-5871	706	13	.	.	PUNCT
ejpam-5871	707	1	fractal	fractal	ADJ
ejpam-5871	707	2	and	and	CCONJ
ejpam-5871	707	3	fractional	fractional	ADJ
ejpam-5871	707	4	,	,	PUNCT
ejpam-5871	707	5	8(10):587	8(10):587	NUM
ejpam-5871	707	6	,	,	PUNCT
ejpam-5871	707	7	2024	2024	NUM
ejpam-5871	707	8	.	.	PUNCT
ejpam-5871	708	1	[	[	X
ejpam-5871	708	2	25	25	NUM
ejpam-5871	708	3	]	]	X
ejpam-5871	708	4	h.	h.	PROPN
ejpam-5871	708	5	budak	budak	PROPN
ejpam-5871	708	6	,	,	PUNCT
ejpam-5871	708	7	c.	c.	PROPN
ejpam-5871	708	8	c.	c.	PROPN
ejpam-5871	708	9	bilisik	bilisik	PROPN
ejpam-5871	708	10	,	,	PUNCT
ejpam-5871	708	11	a.	a.	NOUN
ejpam-5871	708	12	kashuri	kashuri	PROPN
ejpam-5871	708	13	,	,	PUNCT
ejpam-5871	708	14	and	and	CCONJ
ejpam-5871	708	15	m.	m.	PROPN
ejpam-5871	708	16	a.	a.	PROPN
ejpam-5871	708	17	ali	ali	PROPN
ejpam-5871	708	18	.	.	PUNCT
ejpam-5871	709	1	hermite	hermite	PROPN
ejpam-5871	709	2	-	-	PUNCT
ejpam-5871	709	3	hadamard	hadamard	ADJ
ejpam-5871	709	4	type	type	NOUN
ejpam-5871	709	5	inequalities	inequality	NOUN
ejpam-5871	709	6	for	for	ADP
ejpam-5871	709	7	the	the	DET
ejpam-5871	709	8	interval	interval	NOUN
ejpam-5871	709	9	-	-	PUNCT
ejpam-5871	709	10	valued	value	VERB
ejpam-5871	709	11	harmonically	harmonically	ADV
ejpam-5871	709	12	h	h	ADJ
ejpam-5871	709	13	-	-	PUNCT
ejpam-5871	709	14	convex	convex	NOUN
ejpam-5871	709	15	functions	function	NOUN
ejpam-5871	709	16	via	via	ADP
ejpam-5871	709	17	fractional	fractional	ADJ
ejpam-5871	709	18	integrals	integral	NOUN
ejpam-5871	709	19	.	.	PUNCT
ejpam-5871	710	1	applied	apply	VERB
ejpam-5871	710	2	mathematics	mathematic	NOUN
ejpam-5871	710	3	e	e	NOUN
ejpam-5871	711	1	-	-	NOUN
ejpam-5871	711	2	notes	note	NOUN
ejpam-5871	711	3	,	,	PUNCT
ejpam-5871	711	4	21:12–32	21:12–32	PROPN
ejpam-5871	711	5	,	,	PUNCT
ejpam-5871	711	6	2021	2021	NUM
ejpam-5871	711	7	.	.	PUNCT
ejpam-5871	712	1	[	[	X
ejpam-5871	712	2	26	26	NUM
ejpam-5871	712	3	]	]	PUNCT
ejpam-5871	712	4	t.	t.	NOUN
ejpam-5871	712	5	abdeljawad	abdeljawad	PROPN
ejpam-5871	712	6	,	,	PUNCT
ejpam-5871	712	7	s.	s.	PROPN
ejpam-5871	712	8	rashid	rashid	PROPN
ejpam-5871	712	9	,	,	PUNCT
ejpam-5871	712	10	h.	h.	PROPN
ejpam-5871	712	11	khan	khan	PROPN
ejpam-5871	712	12	,	,	PUNCT
ejpam-5871	712	13	and	and	CCONJ
ejpam-5871	712	14	y.	y.	PROPN
ejpam-5871	712	15	m.	m.	PROPN
ejpam-5871	712	16	chu	chu	PROPN
ejpam-5871	712	17	.	.	PUNCT
ejpam-5871	713	1	on	on	ADP
ejpam-5871	713	2	new	new	ADJ
ejpam-5871	713	3	fractional	fractional	ADJ
ejpam-5871	713	4	integral	integral	ADJ
ejpam-5871	713	5	inequalities	inequality	NOUN
ejpam-5871	713	6	for	for	ADP
ejpam-5871	713	7	p	p	NOUN
ejpam-5871	713	8	-	-	PUNCT
ejpam-5871	713	9	convexity	convexity	NOUN
ejpam-5871	713	10	within	within	ADP
ejpam-5871	713	11	interval	interval	NOUN
ejpam-5871	713	12	-	-	PUNCT
ejpam-5871	713	13	valued	value	VERB
ejpam-5871	713	14	functions	function	NOUN
ejpam-5871	713	15	.	.	PUNCT
ejpam-5871	714	1	advances	advance	NOUN
ejpam-5871	714	2	in	in	ADP
ejpam-5871	714	3	difference	difference	NOUN
ejpam-5871	714	4	equations	equation	NOUN
ejpam-5871	714	5	,	,	PUNCT
ejpam-5871	714	6	2020:330	2020:330	NUM
ejpam-5871	714	7	,	,	PUNCT
ejpam-5871	714	8	2020	2020	NUM
ejpam-5871	714	9	.	.	PUNCT
ejpam-5871	715	1	[	[	X
ejpam-5871	715	2	27	27	NUM
ejpam-5871	715	3	]	]	X
ejpam-5871	715	4	h.	h.	PROPN
ejpam-5871	715	5	kalsoom	kalsoom	PROPN
ejpam-5871	715	6	,	,	PUNCT
ejpam-5871	715	7	m.	m.	NOUN
ejpam-5871	715	8	a.	a.	PROPN
ejpam-5871	715	9	ali	ali	PROPN
ejpam-5871	715	10	,	,	PUNCT
ejpam-5871	715	11	m.	m.	NOUN
ejpam-5871	715	12	idrees	idree	NOUN
ejpam-5871	715	13	,	,	PUNCT
ejpam-5871	715	14	p.	p.	NOUN
ejpam-5871	715	15	agarwal	agarwal	PROPN
ejpam-5871	715	16	,	,	PUNCT
ejpam-5871	715	17	and	and	CCONJ
ejpam-5871	715	18	m.	m.	PROPN
ejpam-5871	715	19	arif	arif	PROPN
ejpam-5871	715	20	.	.	PUNCT
ejpam-5871	716	1	new	new	ADJ
ejpam-5871	716	2	post	post	ADJ
ejpam-5871	716	3	-	-	ADJ
ejpam-5871	716	4	quantum	quantum	ADJ
ejpam-5871	716	5	analogues	analogue	NOUN
ejpam-5871	716	6	of	of	ADP
ejpam-5871	716	7	hermite	hermite	ADJ
ejpam-5871	716	8	-	-	PUNCT
ejpam-5871	716	9	hadamard	hadamard	ADJ
ejpam-5871	716	10	type	type	NOUN
ejpam-5871	716	11	inequalities	inequality	NOUN
ejpam-5871	716	12	for	for	ADP
ejpam-5871	716	13	interval	interval	NOUN
ejpam-5871	716	14	-	-	PUNCT
ejpam-5871	716	15	valued	value	VERB
ejpam-5871	716	16	convex	convex	NOUN
ejpam-5871	716	17	functions	function	NOUN
ejpam-5871	716	18	.	.	PUNCT
ejpam-5871	717	1	mathematical	mathematical	ADJ
ejpam-5871	717	2	problems	problem	NOUN
ejpam-5871	717	3	in	in	ADP
ejpam-5871	717	4	engineering	engineering	NOUN
ejpam-5871	717	5	,	,	PUNCT
ejpam-5871	717	6	2021:5529650	2021:5529650	NUM
ejpam-5871	717	7	,	,	PUNCT
ejpam-5871	717	8	2021	2021	NUM
ejpam-5871	717	9	.	.	PUNCT
ejpam-5871	718	1	[	[	X
ejpam-5871	718	2	28	28	NUM
ejpam-5871	718	3	]	]	X
ejpam-5871	718	4	b.	b.	PROPN
ejpam-5871	718	5	bin	bin	PROPN
ejpam-5871	718	6	-	-	PUNCT
ejpam-5871	718	7	mohsin	mohsin	PROPN
ejpam-5871	718	8	,	,	PUNCT
ejpam-5871	718	9	s.	s.	PROPN
ejpam-5871	718	10	rafique	rafique	PROPN
ejpam-5871	718	11	,	,	PUNCT
ejpam-5871	718	12	c.	c.	PROPN
ejpam-5871	718	13	cesarano	cesarano	PROPN
ejpam-5871	718	14	,	,	PUNCT
ejpam-5871	718	15	m.	m.	PROPN
ejpam-5871	718	16	z.	z.	PROPN
ejpam-5871	718	17	javed	javed	PROPN
ejpam-5871	718	18	,	,	PUNCT
ejpam-5871	718	19	m.	m.	NOUN
ejpam-5871	718	20	u.	u.	PROPN
ejpam-5871	718	21	awan	awan	PROPN
ejpam-5871	718	22	,	,	PUNCT
ejpam-5871	718	23	a.	a.	NOUN
ejpam-5871	718	24	kashuri	kashuri	PROPN
ejpam-5871	718	25	,	,	PUNCT
ejpam-5871	718	26	and	and	CCONJ
ejpam-5871	718	27	m.	m.	NOUN
ejpam-5871	718	28	a.	a.	PROPN
ejpam-5871	718	29	noor	noor	PROPN
ejpam-5871	718	30	.	.	PUNCT
ejpam-5871	719	1	some	some	DET
ejpam-5871	719	2	general	general	ADJ
ejpam-5871	719	3	fractional	fractional	ADJ
ejpam-5871	719	4	integral	integral	ADJ
ejpam-5871	719	5	inequalities	inequality	NOUN
ejpam-5871	719	6	involving	involve	VERB
ejpam-5871	719	7	lr	lr	NOUN
ejpam-5871	719	8	-	-	PUNCT
ejpam-5871	719	9	bi	bi	ADJ
ejpam-5871	719	10	-	-	ADJ
ejpam-5871	719	11	convex	convex	ADJ
ejpam-5871	719	12	fuzzy	fuzzy	ADJ
ejpam-5871	719	13	interval	interval	NOUN
ejpam-5871	719	14	-	-	PUNCT
ejpam-5871	719	15	valued	value	VERB
ejpam-5871	719	16	functions	function	NOUN
ejpam-5871	719	17	.	.	PUNCT
ejpam-5871	720	1	fractal	fractal	ADJ
ejpam-5871	720	2	and	and	CCONJ
ejpam-5871	720	3	fractional	fractional	ADJ
ejpam-5871	720	4	,	,	PUNCT
ejpam-5871	720	5	6(10):565	6(10):565	NUM
ejpam-5871	720	6	,	,	PUNCT
ejpam-5871	720	7	2022	2022	NUM
ejpam-5871	720	8	.	.	PUNCT
ejpam-5871	721	1	[	[	X
ejpam-5871	721	2	29	29	NUM
ejpam-5871	721	3	]	]	PUNCT
ejpam-5871	721	4	m.	m.	NOUN
ejpam-5871	721	5	vivas	vivas	PROPN
ejpam-5871	721	6	-	-	PROPN
ejpam-5871	721	7	cortez	cortez	PROPN
ejpam-5871	721	8	,	,	PUNCT
ejpam-5871	721	9	s.	s.	PROPN
ejpam-5871	721	10	ramzan	ramzan	PROPN
ejpam-5871	721	11	,	,	PUNCT
ejpam-5871	721	12	m.	m.	PROPN
ejpam-5871	721	13	u.	u.	PROPN
ejpam-5871	721	14	awan	awan	PROPN
ejpam-5871	721	15	,	,	PUNCT
ejpam-5871	721	16	m.	m.	PROPN
ejpam-5871	721	17	z.	z.	PROPN
ejpam-5871	721	18	javed	javed	PROPN
ejpam-5871	721	19	,	,	PUNCT
ejpam-5871	721	20	a.	a.	PROPN
ejpam-5871	721	21	g.	g.	PROPN
ejpam-5871	721	22	khan	khan	PROPN
ejpam-5871	721	23	,	,	PUNCT
ejpam-5871	721	24	and	and	CCONJ
ejpam-5871	721	25	m.	m.	NOUN
ejpam-5871	721	26	a.	a.	PROPN
ejpam-5871	721	27	noor	noor	PROPN
ejpam-5871	721	28	.	.	PUNCT
ejpam-5871	722	1	i.v	i.v	PROPN
ejpam-5871	722	2	-	-	PUNCT
ejpam-5871	722	3	cr	cr	NOUN
ejpam-5871	722	4	-	-	PUNCT
ejpam-5871	722	5	convex	convex	NOUN
ejpam-5871	722	6	functions	function	NOUN
ejpam-5871	722	7	and	and	CCONJ
ejpam-5871	722	8	their	their	PRON
ejpam-5871	722	9	application	application	NOUN
ejpam-5871	722	10	in	in	ADP
ejpam-5871	722	11	fractional	fractional	ADJ
ejpam-5871	722	12	hermite	hermite	PROPN
ejpam-5871	722	13	-	-	PUNCT
ejpam-5871	722	14	hadamard	hadamard	ADJ
ejpam-5871	722	15	inequalities	inequality	NOUN
ejpam-5871	722	16	.	.	PUNCT
ejpam-5871	723	1	symmetry	symmetry	NOUN
ejpam-5871	723	2	,	,	PUNCT
ejpam-5871	723	3	15(7):1405	15(7):1405	NUM
ejpam-5871	723	4	,	,	PUNCT
ejpam-5871	723	5	2023	2023	NUM
ejpam-5871	723	6	.	.	PUNCT
ejpam-5871	724	1	[	[	X
ejpam-5871	724	2	30	30	NUM
ejpam-5871	724	3	]	]	X
ejpam-5871	724	4	m.	m.	NOUN
ejpam-5871	724	5	a.	a.	PROPN
ejpam-5871	724	6	alqudah	alqudah	PROPN
ejpam-5871	724	7	,	,	PUNCT
ejpam-5871	724	8	p.	p.	PROPN
ejpam-5871	724	9	o.	o.	PROPN
ejpam-5871	724	10	mohammed	mohammed	PROPN
ejpam-5871	724	11	,	,	PUNCT
ejpam-5871	724	12	and	and	CCONJ
ejpam-5871	724	13	t.	t.	PROPN
ejpam-5871	724	14	abdeljawad	abdeljawad	NOUN
ejpam-5871	724	15	.	.	PUNCT
ejpam-5871	725	1	solution	solution	NOUN
ejpam-5871	725	2	of	of	ADP
ejpam-5871	725	3	singular	singular	ADJ
ejpam-5871	725	4	integral	integral	ADJ
ejpam-5871	725	5	equation	equation	NOUN
ejpam-5871	725	6	via	via	ADP
ejpam-5871	725	7	riemann	riemann	PROPN
ejpam-5871	725	8	-	-	PUNCT
ejpam-5871	725	9	liouville	liouville	VERB
ejpam-5871	725	10	fractional	fractional	ADJ
ejpam-5871	725	11	integral	integral	ADJ
ejpam-5871	725	12	.	.	PUNCT
ejpam-5871	726	1	mathematical	mathematical	ADJ
ejpam-5871	726	2	problems	problem	NOUN
ejpam-5871	726	3	in	in	ADP
ejpam-5871	726	4	engineering	engineering	NOUN
ejpam-5871	726	5	,	,	PUNCT
ejpam-5871	726	6	2020:1250970	2020:1250970	NUM
ejpam-5871	726	7	,	,	PUNCT
ejpam-5871	726	8	2020	2020	NUM
ejpam-5871	726	9	.	.	PUNCT
ejpam-5871	727	1	[	[	X
ejpam-5871	727	2	31	31	NUM
ejpam-5871	727	3	]	]	X
ejpam-5871	727	4	d.	d.	PROPN
ejpam-5871	727	5	baleanu	baleanu	PROPN
ejpam-5871	727	6	,	,	PUNCT
ejpam-5871	727	7	m.	m.	NOUN
ejpam-5871	727	8	samraiz	samraiz	PROPN
ejpam-5871	727	9	,	,	PUNCT
ejpam-5871	727	10	z.	z.	PROPN
ejpam-5871	727	11	perveen	perveen	PROPN
ejpam-5871	727	12	,	,	PUNCT
ejpam-5871	727	13	s.	s.	PROPN
ejpam-5871	727	14	iqbal	iqbal	PROPN
ejpam-5871	727	15	,	,	PUNCT
ejpam-5871	727	16	k.	k.	PROPN
ejpam-5871	727	17	s.	s.	PROPN
ejpam-5871	727	18	nisar	nisar	PROPN
ejpam-5871	727	19	,	,	PUNCT
ejpam-5871	727	20	and	and	CCONJ
ejpam-5871	727	21	g.	g.	PROPN
ejpam-5871	727	22	rahman	rahman	PROPN
ejpam-5871	727	23	.	.	PUNCT
ejpam-5871	728	1	hermitehadamard	hermitehadamard	NOUN
ejpam-5871	728	2	-	-	PUNCT
ejpam-5871	728	3	fejer	fejer	NOUN
ejpam-5871	728	4	type	type	NOUN
ejpam-5871	728	5	inequalities	inequality	NOUN
ejpam-5871	728	6	via	via	ADP
ejpam-5871	728	7	fractional	fractional	ADJ
ejpam-5871	728	8	integral	integral	ADJ
ejpam-5871	728	9	of	of	ADP
ejpam-5871	728	10	a	a	DET
ejpam-5871	728	11	function	function	NOUN
ejpam-5871	728	12	concerning	concern	VERB
ejpam-5871	728	13	another	another	DET
ejpam-5871	728	14	function	function	NOUN
ejpam-5871	728	15	.	.	PUNCT
ejpam-5871	729	1	aims	aim	VERB
ejpam-5871	729	2	mathematics	mathematic	NOUN
ejpam-5871	729	3	,	,	PUNCT
ejpam-5871	729	4	5(5):4280–4295	5(5):4280–4295	NUM
ejpam-5871	729	5	,	,	PUNCT
ejpam-5871	729	6	2020	2020	NUM
ejpam-5871	729	7	.	.	PUNCT