id	sid	tid	token	lemma	pos
ejpam-6927	1	1	european	european	PROPN
ejpam-6927	1	2	journal	journal	PROPN
ejpam-6927	1	3	of	of	ADP
ejpam-6927	1	4	pure	pure	ADJ
ejpam-6927	1	5	and	and	CCONJ
ejpam-6927	1	6	applied	applied	ADJ
ejpam-6927	1	7	mathematics	mathematic	NOUN
ejpam-6927	1	8	2025	2025	NUM
ejpam-6927	1	9	,	,	PUNCT
ejpam-6927	1	10	vol	vol	NOUN
ejpam-6927	1	11	.	.	PROPN
ejpam-6927	1	12	18	18	NUM
ejpam-6927	1	13	,	,	PUNCT
ejpam-6927	1	14	issue	issue	NOUN
ejpam-6927	1	15	4	4	NUM
ejpam-6927	1	16	,	,	PUNCT
ejpam-6927	1	17	article	article	NOUN
ejpam-6927	1	18	number	number	NOUN
ejpam-6927	1	19	6927	6927	NUM
ejpam-6927	1	20	issn	issn	PROPN
ejpam-6927	1	21	1307	1307	NUM
ejpam-6927	1	22	-	-	SYM
ejpam-6927	1	23	5543	5543	NUM
ejpam-6927	1	24	–	–	PUNCT
ejpam-6927	1	25	ejpam.com	ejpam.com	X
ejpam-6927	1	26	published	publish	VERB
ejpam-6927	1	27	by	by	ADP
ejpam-6927	1	28	new	new	PROPN
ejpam-6927	1	29	york	york	PROPN
ejpam-6927	1	30	business	business	PROPN
ejpam-6927	1	31	global	global	PROPN
ejpam-6927	1	32	development	development	NOUN
ejpam-6927	1	33	of	of	ADP
ejpam-6927	1	34	quantum	quantum	ADJ
ejpam-6927	1	35	hermite	hermite	PROPN
ejpam-6927	1	36	-	-	PUNCT
ejpam-6927	1	37	hadamard	hadamard	ADJ
ejpam-6927	1	38	type	type	NOUN
ejpam-6927	1	39	inequalities	inequality	NOUN
ejpam-6927	1	40	using	use	VERB
ejpam-6927	1	41	green	green	PROPN
ejpam-6927	1	42	’s	’s	PART
ejpam-6927	1	43	function	function	NOUN
ejpam-6927	1	44	techniques	technique	NOUN
ejpam-6927	1	45	muhammad	muhammad	PROPN
ejpam-6927	1	46	adil	adil	PROPN
ejpam-6927	1	47	khan1	khan1	PROPN
ejpam-6927	1	48	,	,	PUNCT
ejpam-6927	1	49	tareq	tareq	PROPN
ejpam-6927	1	50	saeed2,∗	saeed2,∗	PROPN
ejpam-6927	1	51	,	,	PUNCT
ejpam-6927	1	52	sajjad	sajjad	PROPN
ejpam-6927	1	53	ali1	ali1	PROPN
ejpam-6927	1	54	,	,	PUNCT
ejpam-6927	1	55	çetin	çetin	PROPN
ejpam-6927	1	56	yildiz3	yildiz3	PROPN
ejpam-6927	1	57	,	,	PUNCT
ejpam-6927	1	58	mohammed	mohammed	PROPN
ejpam-6927	1	59	kbiri	kbiri	PROPN
ejpam-6927	1	60	alaoui4	alaoui4	PROPN
ejpam-6927	1	61	1	1	NUM
ejpam-6927	1	62	department	department	NOUN
ejpam-6927	1	63	of	of	ADP
ejpam-6927	1	64	mathematics	mathematic	NOUN
ejpam-6927	1	65	,	,	PUNCT
ejpam-6927	1	66	university	university	NOUN
ejpam-6927	1	67	of	of	ADP
ejpam-6927	1	68	peshawar	peshawar	PROPN
ejpam-6927	1	69	,	,	PUNCT
ejpam-6927	1	70	peshawar	peshawar	NOUN
ejpam-6927	1	71	25000	25000	NUM
ejpam-6927	1	72	,	,	PUNCT
ejpam-6927	1	73	pakistan	pakistan	PROPN
ejpam-6927	1	74	2	2	NUM
ejpam-6927	1	75	financial	financial	ADJ
ejpam-6927	1	76	mathematics	mathematic	NOUN
ejpam-6927	1	77	and	and	CCONJ
ejpam-6927	1	78	actuarial	actuarial	ADJ
ejpam-6927	1	79	science	science	NOUN
ejpam-6927	1	80	(	(	PUNCT
ejpam-6927	1	81	fmas)-research	fmas)-research	PROPN
ejpam-6927	1	82	group	group	NOUN
ejpam-6927	1	83	,	,	PUNCT
ejpam-6927	1	84	department	department	NOUN
ejpam-6927	1	85	of	of	ADP
ejpam-6927	1	86	mathematics	mathematic	NOUN
ejpam-6927	1	87	,	,	PUNCT
ejpam-6927	1	88	faculty	faculty	NOUN
ejpam-6927	1	89	of	of	ADP
ejpam-6927	1	90	science	science	NOUN
ejpam-6927	1	91	,	,	PUNCT
ejpam-6927	1	92	king	king	PROPN
ejpam-6927	1	93	abdulaziz	abdulaziz	PROPN
ejpam-6927	1	94	university	university	PROPN
ejpam-6927	1	95	,	,	PUNCT
ejpam-6927	1	96	p.o	p.o	PROPN
ejpam-6927	1	97	.	.	PROPN
ejpam-6927	1	98	box	box	PROPN
ejpam-6927	1	99	80203	80203	NUM
ejpam-6927	1	100	,	,	PUNCT
ejpam-6927	1	101	jeddah	jeddah	PROPN
ejpam-6927	1	102	21589	21589	NUM
ejpam-6927	1	103	,	,	PUNCT
ejpam-6927	1	104	saudi	saudi	PROPN
ejpam-6927	1	105	arabia	arabia	PROPN
ejpam-6927	1	106	3	3	NUM
ejpam-6927	1	107	department	department	NOUN
ejpam-6927	1	108	of	of	ADP
ejpam-6927	1	109	mathematics	mathematics	PROPN
ejpam-6927	1	110	,	,	PUNCT
ejpam-6927	1	111	k.k	k.k	PROPN
ejpam-6927	1	112	.	.	PROPN
ejpam-6927	1	113	education	education	PROPN
ejpam-6927	1	114	faculty	faculty	PROPN
ejpam-6927	1	115	,	,	PUNCT
ejpam-6927	1	116	ataturk	ataturk	PROPN
ejpam-6927	1	117	university	university	PROPN
ejpam-6927	1	118	,	,	PUNCT
ejpam-6927	1	119	25240	25240	NUM
ejpam-6927	1	120	campus	campus	NOUN
ejpam-6927	1	121	,	,	PUNCT
ejpam-6927	1	122	erzurum	erzurum	PROPN
ejpam-6927	1	123	,	,	PUNCT
ejpam-6927	1	124	turkey	turkey	PROPN
ejpam-6927	1	125	4	4	NUM
ejpam-6927	1	126	department	department	NOUN
ejpam-6927	1	127	of	of	ADP
ejpam-6927	1	128	mathematics	mathematic	NOUN
ejpam-6927	1	129	,	,	PUNCT
ejpam-6927	1	130	college	college	NOUN
ejpam-6927	1	131	of	of	ADP
ejpam-6927	1	132	science	science	NOUN
ejpam-6927	1	133	,	,	PUNCT
ejpam-6927	1	134	king	king	PROPN
ejpam-6927	1	135	khalid	khalid	PROPN
ejpam-6927	1	136	university	university	PROPN
ejpam-6927	1	137	,	,	PUNCT
ejpam-6927	1	138	p.o	p.o	PROPN
ejpam-6927	1	139	.	.	PROPN
ejpam-6927	1	140	box	box	PROPN
ejpam-6927	1	141	9004	9004	NUM
ejpam-6927	1	142	,	,	PUNCT
ejpam-6927	1	143	61413	61413	NUM
ejpam-6927	1	144	abha	abha	NOUN
ejpam-6927	1	145	,	,	PUNCT
ejpam-6927	1	146	saudi	saudi	PROPN
ejpam-6927	1	147	arabia	arabia	PROPN
ejpam-6927	1	148	abstract	abstract	NOUN
ejpam-6927	1	149	.	.	PUNCT
ejpam-6927	2	1	in	in	ADP
ejpam-6927	2	2	this	this	DET
ejpam-6927	2	3	paper	paper	NOUN
ejpam-6927	2	4	,	,	PUNCT
ejpam-6927	2	5	we	we	PRON
ejpam-6927	2	6	investigate	investigate	VERB
ejpam-6927	2	7	the	the	DET
ejpam-6927	2	8	quantum	quantum	ADJ
ejpam-6927	2	9	hermite	hermite	ADJ
ejpam-6927	2	10	-	-	PUNCT
ejpam-6927	2	11	hadamard	hadamard	ADJ
ejpam-6927	2	12	inequality	inequality	NOUN
ejpam-6927	2	13	using	use	VERB
ejpam-6927	2	14	the	the	DET
ejpam-6927	2	15	green	green	NOUN
ejpam-6927	2	16	’s	’s	PART
ejpam-6927	2	17	function	function	NOUN
ejpam-6927	2	18	.	.	PUNCT
ejpam-6927	3	1	this	this	DET
ejpam-6927	3	2	process	process	NOUN
ejpam-6927	3	3	leads	lead	VERB
ejpam-6927	3	4	to	to	ADP
ejpam-6927	3	5	the	the	DET
ejpam-6927	3	6	derivation	derivation	NOUN
ejpam-6927	3	7	of	of	ADP
ejpam-6927	3	8	novel	novel	ADJ
ejpam-6927	3	9	quantum	quantum	ADJ
ejpam-6927	3	10	identities	identity	NOUN
ejpam-6927	3	11	,	,	PUNCT
ejpam-6927	3	12	which	which	PRON
ejpam-6927	3	13	are	be	AUX
ejpam-6927	3	14	then	then	ADV
ejpam-6927	3	15	employed	employ	VERB
ejpam-6927	3	16	to	to	PART
ejpam-6927	3	17	establish	establish	VERB
ejpam-6927	3	18	novel	novel	ADJ
ejpam-6927	3	19	inequalities	inequality	NOUN
ejpam-6927	3	20	.	.	PUNCT
ejpam-6927	4	1	utilizing	utilize	VERB
ejpam-6927	4	2	these	these	DET
ejpam-6927	4	3	identities	identity	NOUN
ejpam-6927	4	4	,	,	PUNCT
ejpam-6927	4	5	we	we	PRON
ejpam-6927	4	6	establish	establish	VERB
ejpam-6927	4	7	novel	novel	ADJ
ejpam-6927	4	8	inequalities	inequality	NOUN
ejpam-6927	4	9	.	.	PUNCT
ejpam-6927	5	1	the	the	DET
ejpam-6927	5	2	main	main	ADJ
ejpam-6927	5	3	results	result	NOUN
ejpam-6927	5	4	of	of	ADP
ejpam-6927	5	5	the	the	DET
ejpam-6927	5	6	paper	paper	NOUN
ejpam-6927	5	7	are	be	AUX
ejpam-6927	5	8	derived	derive	VERB
ejpam-6927	5	9	using	use	VERB
ejpam-6927	5	10	various	various	ADJ
ejpam-6927	5	11	techniques	technique	NOUN
ejpam-6927	5	12	such	such	ADJ
ejpam-6927	5	13	as	as	ADP
ejpam-6927	5	14	q	q	NOUN
ejpam-6927	5	15	-	-	NOUN
ejpam-6927	5	16	identities	identity	NOUN
ejpam-6927	5	17	,	,	PUNCT
ejpam-6927	5	18	convexity	convexity	NOUN
ejpam-6927	5	19	and	and	CCONJ
ejpam-6927	5	20	jensen	jensen	PROPN
ejpam-6927	5	21	inequality	inequality	NOUN
ejpam-6927	5	22	.	.	PUNCT
ejpam-6927	6	1	furthermore	furthermore	ADV
ejpam-6927	6	2	,	,	PUNCT
ejpam-6927	6	3	the	the	DET
ejpam-6927	6	4	study	study	NOUN
ejpam-6927	6	5	provides	provide	VERB
ejpam-6927	6	6	numerical	numerical	ADJ
ejpam-6927	6	7	validation	validation	NOUN
ejpam-6927	6	8	and	and	CCONJ
ejpam-6927	6	9	graphical	graphical	ADJ
ejpam-6927	6	10	representations	representation	NOUN
ejpam-6927	6	11	to	to	PART
ejpam-6927	6	12	support	support	VERB
ejpam-6927	6	13	the	the	DET
ejpam-6927	6	14	main	main	ADJ
ejpam-6927	6	15	results	result	NOUN
ejpam-6927	6	16	.	.	PUNCT
ejpam-6927	7	1	2020	2020	NUM
ejpam-6927	7	2	mathematics	mathematic	NOUN
ejpam-6927	7	3	subject	subject	NOUN
ejpam-6927	7	4	classifications	classification	NOUN
ejpam-6927	7	5	:	:	PUNCT
ejpam-6927	7	6	26a51	26a51	NUM
ejpam-6927	7	7	,	,	PUNCT
ejpam-6927	7	8	26d15	26d15	NUM
ejpam-6927	7	9	,	,	PUNCT
ejpam-6927	7	10	68p30	68p30	NUM
ejpam-6927	7	11	key	key	ADJ
ejpam-6927	7	12	words	word	NOUN
ejpam-6927	7	13	and	and	CCONJ
ejpam-6927	7	14	phrases	phrase	NOUN
ejpam-6927	7	15	:	:	PUNCT
ejpam-6927	7	16	quantum	quantum	PROPN
ejpam-6927	7	17	integral	integral	ADJ
ejpam-6927	7	18	,	,	PUNCT
ejpam-6927	7	19	green	green	ADJ
ejpam-6927	7	20	function	function	NOUN
ejpam-6927	7	21	,	,	PUNCT
ejpam-6927	7	22	h	h	NOUN
ejpam-6927	7	23	-	-	PUNCT
ejpam-6927	7	24	h	h	NOUN
ejpam-6927	7	25	-	-	PUNCT
ejpam-6927	7	26	inequality	inequality	NOUN
ejpam-6927	7	27	1	1	NUM
ejpam-6927	7	28	.	.	PUNCT
ejpam-6927	8	1	introduction	introduction	NOUN
ejpam-6927	8	2	scientists	scientist	NOUN
ejpam-6927	8	3	are	be	AUX
ejpam-6927	8	4	very	very	ADV
ejpam-6927	8	5	interested	interested	ADJ
ejpam-6927	8	6	in	in	ADP
ejpam-6927	8	7	the	the	DET
ejpam-6927	8	8	theory	theory	NOUN
ejpam-6927	8	9	of	of	ADP
ejpam-6927	8	10	convexity	convexity	NOUN
ejpam-6927	8	11	because	because	SCONJ
ejpam-6927	8	12	of	of	ADP
ejpam-6927	8	13	its	its	PRON
ejpam-6927	8	14	many	many	ADJ
ejpam-6927	8	15	uses	use	NOUN
ejpam-6927	8	16	.	.	PUNCT
ejpam-6927	9	1	convexity	convexity	NOUN
ejpam-6927	9	2	is	be	AUX
ejpam-6927	9	3	an	an	DET
ejpam-6927	9	4	important	important	ADJ
ejpam-6927	9	5	term	term	NOUN
ejpam-6927	9	6	in	in	ADP
ejpam-6927	9	7	the	the	DET
ejpam-6927	9	8	extension	extension	NOUN
ejpam-6927	9	9	and	and	CCONJ
ejpam-6927	9	10	generalization	generalization	NOUN
ejpam-6927	9	11	of	of	ADP
ejpam-6927	9	12	inequalities	inequality	NOUN
ejpam-6927	9	13	.	.	PUNCT
ejpam-6927	10	1	as	as	ADP
ejpam-6927	10	2	a	a	DET
ejpam-6927	10	3	result	result	NOUN
ejpam-6927	10	4	,	,	PUNCT
ejpam-6927	10	5	convexity	convexity	NOUN
ejpam-6927	10	6	and	and	CCONJ
ejpam-6927	10	7	inequality	inequality	NOUN
ejpam-6927	10	8	theory	theory	NOUN
ejpam-6927	10	9	are	be	AUX
ejpam-6927	10	10	closely	closely	ADV
ejpam-6927	10	11	related	relate	VERB
ejpam-6927	10	12	.	.	PUNCT
ejpam-6927	11	1	many	many	ADJ
ejpam-6927	11	2	inequalities	inequality	NOUN
ejpam-6927	11	3	have	have	AUX
ejpam-6927	11	4	been	be	AUX
ejpam-6927	11	5	motivated	motivate	VERB
ejpam-6927	11	6	by	by	ADP
ejpam-6927	11	7	convex	convex	NOUN
ejpam-6927	11	8	functions	function	NOUN
ejpam-6927	11	9	,	,	PUNCT
ejpam-6927	11	10	which	which	PRON
ejpam-6927	11	11	are	be	AUX
ejpam-6927	11	12	essential	essential	ADJ
ejpam-6927	11	13	to	to	ADP
ejpam-6927	11	14	inequality	inequality	NOUN
ejpam-6927	11	15	theory	theory	NOUN
ejpam-6927	11	16	.	.	PUNCT
ejpam-6927	12	1	therefore	therefore	ADV
ejpam-6927	12	2	,	,	PUNCT
ejpam-6927	12	3	it	it	PRON
ejpam-6927	12	4	is	be	AUX
ejpam-6927	12	5	evident	evident	ADJ
ejpam-6927	12	6	that	that	SCONJ
ejpam-6927	12	7	the	the	DET
ejpam-6927	12	8	hermite	hermite	PROPN
ejpam-6927	12	9	-	-	PUNCT
ejpam-6927	12	10	hadamard	hadamard	ADJ
ejpam-6927	12	11	(	(	PUNCT
ejpam-6927	12	12	h−h	h−h	NOUN
ejpam-6927	12	13	)	)	PUNCT
ejpam-6927	12	14	inequality	inequality	NOUN
ejpam-6927	12	15	assumes	assume	VERB
ejpam-6927	12	16	particular	particular	ADJ
ejpam-6927	12	17	significance	significance	NOUN
ejpam-6927	12	18	in	in	ADP
ejpam-6927	12	19	the	the	DET
ejpam-6927	12	20	context	context	NOUN
ejpam-6927	12	21	of	of	ADP
ejpam-6927	12	22	convex	convex	NOUN
ejpam-6927	12	23	functions	function	NOUN
ejpam-6927	12	24	.	.	PUNCT
ejpam-6927	13	1	the	the	DET
ejpam-6927	13	2	integral	integral	ADJ
ejpam-6927	13	3	mean	mean	NOUN
ejpam-6927	13	4	of	of	ADP
ejpam-6927	13	5	any	any	DET
ejpam-6927	13	6	convex	convex	NOUN
ejpam-6927	13	7	function	function	NOUN
ejpam-6927	13	8	defined	define	VERB
ejpam-6927	13	9	within	within	ADP
ejpam-6927	13	10	a	a	DET
ejpam-6927	13	11	closed	closed	ADJ
ejpam-6927	13	12	and	and	CCONJ
ejpam-6927	13	13	bounded	bounded	ADJ
ejpam-6927	13	14	area	area	NOUN
ejpam-6927	13	15	,	,	PUNCT
ejpam-6927	13	16	inclusive	inclusive	ADJ
ejpam-6927	13	17	of	of	ADP
ejpam-6927	13	18	the	the	DET
ejpam-6927	13	19	endpoints	endpoint	NOUN
ejpam-6927	13	20	and	and	CCONJ
ejpam-6927	13	21	midpoints	midpoint	NOUN
ejpam-6927	13	22	of	of	ADP
ejpam-6927	13	23	the	the	DET
ejpam-6927	13	24	function	function	NOUN
ejpam-6927	13	25	’s	’s	PART
ejpam-6927	13	26	domain	domain	NOUN
ejpam-6927	13	27	,	,	PUNCT
ejpam-6927	13	28	can	can	AUX
ejpam-6927	13	29	∗corresponding	∗corresponde	VERB
ejpam-6927	13	30	author	author	NOUN
ejpam-6927	13	31	.	.	PUNCT
ejpam-6927	14	1	doi	doi	NOUN
ejpam-6927	14	2	:	:	PUNCT
ejpam-6927	14	3	https://doi.org/10.29020/nybg.ejpam.v18i4.6927	https://doi.org/10.29020/nybg.ejpam.v18i4.6927	PRON
ejpam-6927	14	4	email	email	NOUN
ejpam-6927	14	5	addresses	address	NOUN
ejpam-6927	14	6	:	:	PUNCT
ejpam-6927	14	7	madilkhan@uop.edu.pk	madilkhan@uop.edu.pk	PROPN
ejpam-6927	14	8	(	(	PUNCT
ejpam-6927	14	9	m.	m.	PROPN
ejpam-6927	14	10	adil	adil	PROPN
ejpam-6927	14	11	khan	khan	PROPN
ejpam-6927	14	12	)	)	PUNCT
ejpam-6927	14	13	,	,	PUNCT
ejpam-6927	14	14	tsalmalki@kau.edu.sa	tsalmalki@kau.edu.sa	PROPN
ejpam-6927	14	15	(	(	PUNCT
ejpam-6927	14	16	t.	t.	PROPN
ejpam-6927	14	17	saeed	saeed	PROPN
ejpam-6927	14	18	)	)	PUNCT
ejpam-6927	14	19	,	,	PUNCT
ejpam-6927	14	20	sajjadbtk15302@gmail.com	sajjadbtk15302@gmail.com	X
ejpam-6927	15	1	(	(	PUNCT
ejpam-6927	15	2	s.	s.	PROPN
ejpam-6927	15	3	ali	ali	PROPN
ejpam-6927	15	4	)	)	PUNCT
ejpam-6927	15	5	,	,	PUNCT
ejpam-6927	15	6	cetin@atauni.edu.tr	cetin@atauni.edu.tr	NOUN
ejpam-6927	15	7	(	(	PUNCT
ejpam-6927	15	8	ç.	ç.	ADP
ejpam-6927	15	9	yildiz	yildiz	NOUN
ejpam-6927	15	10	)	)	PUNCT
ejpam-6927	15	11	,	,	PUNCT
ejpam-6927	15	12	mka	mka	PROPN
ejpam-6927	15	13	la@yahoo.fr	la@yahoo.fr	PROPN
ejpam-6927	15	14	(	(	PUNCT
ejpam-6927	15	15	m.	m.	PROPN
ejpam-6927	15	16	k.	k.	PROPN
ejpam-6927	15	17	alaoui	alaoui	PROPN
ejpam-6927	15	18	)	)	PUNCT
ejpam-6927	15	19	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6927	16	1	1	1	NUM
ejpam-6927	16	2	copyright	copyright	NOUN
ejpam-6927	16	3	:	:	PUNCT
ejpam-6927	16	4	©	©	PROPN
ejpam-6927	16	5	2025	2025	NUM
ejpam-6927	16	6	the	the	DET
ejpam-6927	16	7	author(s	author(s	NOUN
ejpam-6927	16	8	)	)	PUNCT
ejpam-6927	16	9	.	.	PUNCT
ejpam-6927	17	1	(	(	PUNCT
ejpam-6927	17	2	cc	cc	NOUN
ejpam-6927	17	3	by	by	ADP
ejpam-6927	17	4	-	-	PUNCT
ejpam-6927	17	5	nc	nc	PROPN
ejpam-6927	17	6	4.0	4.0	NUM
ejpam-6927	17	7	)	)	PUNCT
ejpam-6927	17	8	m.	m.	NOUN
ejpam-6927	17	9	adil	adil	PROPN
ejpam-6927	17	10	khan	khan	PROPN
ejpam-6927	17	11	et	et	PROPN
ejpam-6927	17	12	al	al	PROPN
ejpam-6927	17	13	.	.	PUNCT
ejpam-6927	17	14	/	/	SYM
ejpam-6927	17	15	eur	eur	PROPN
ejpam-6927	17	16	.	.	PUNCT
ejpam-6927	18	1	j.	j.	PROPN
ejpam-6927	18	2	pure	pure	PROPN
ejpam-6927	18	3	appl	appl	PROPN
ejpam-6927	18	4	.	.	PROPN
ejpam-6927	18	5	math	math	PROPN
ejpam-6927	18	6	,	,	PUNCT
ejpam-6927	18	7	18	18	NUM
ejpam-6927	18	8	(	(	PUNCT
ejpam-6927	18	9	4	4	NUM
ejpam-6927	18	10	)	)	PUNCT
ejpam-6927	18	11	(	(	PUNCT
ejpam-6927	18	12	2025	2025	NUM
ejpam-6927	18	13	)	)	PUNCT
ejpam-6927	18	14	,	,	PUNCT
ejpam-6927	18	15	6927	6927	NUM
ejpam-6927	18	16	2	2	NUM
ejpam-6927	18	17	of	of	ADP
ejpam-6927	18	18	18	18	NUM
ejpam-6927	18	19	be	be	AUX
ejpam-6927	18	20	estimated	estimate	VERB
ejpam-6927	18	21	through	through	ADP
ejpam-6927	18	22	the	the	DET
ejpam-6927	18	23	utilization	utilization	NOUN
ejpam-6927	18	24	of	of	ADP
ejpam-6927	18	25	upper	upper	ADJ
ejpam-6927	18	26	and	and	CCONJ
ejpam-6927	18	27	lower	low	ADJ
ejpam-6927	18	28	bounds	bound	NOUN
ejpam-6927	18	29	.	.	PUNCT
ejpam-6927	19	1	this	this	DET
ejpam-6927	19	2	estimation	estimation	NOUN
ejpam-6927	19	3	is	be	AUX
ejpam-6927	19	4	facilitated	facilitate	VERB
ejpam-6927	19	5	by	by	ADP
ejpam-6927	19	6	the	the	DET
ejpam-6927	19	7	h−h	h−h	NOUN
ejpam-6927	19	8	inequality	inequality	NOUN
ejpam-6927	19	9	,	,	PUNCT
ejpam-6927	19	10	a	a	DET
ejpam-6927	19	11	geometric	geometric	ADJ
ejpam-6927	19	12	-	-	PUNCT
ejpam-6927	19	13	based	base	VERB
ejpam-6927	19	14	principle	principle	NOUN
ejpam-6927	19	15	.	.	PUNCT
ejpam-6927	20	1	the	the	DET
ejpam-6927	20	2	aforementioned	aforementioned	ADJ
ejpam-6927	20	3	double	double	ADJ
ejpam-6927	20	4	inequality	inequality	NOUN
ejpam-6927	20	5	can	can	AUX
ejpam-6927	20	6	be	be	AUX
ejpam-6927	20	7	articulated	articulate	VERB
ejpam-6927	20	8	as	as	SCONJ
ejpam-6927	20	9	follows	follow	VERB
ejpam-6927	20	10	:	:	PUNCT
ejpam-6927	20	11	let	let	VERB
ejpam-6927	20	12	φ	φ	PROPN
ejpam-6927	20	13	be	be	AUX
ejpam-6927	20	14	a	a	DET
ejpam-6927	20	15	convex	convex	NOUN
ejpam-6927	20	16	mapping	mapping	NOUN
ejpam-6927	20	17	on	on	ADP
ejpam-6927	20	18	[	[	X
ejpam-6927	20	19	ω1	ω1	PROPN
ejpam-6927	20	20	,	,	PUNCT
ejpam-6927	20	21	ω2	ω2	PROPN
ejpam-6927	20	22	]	]	X
ejpam-6927	20	23	⊂	⊂	PROPN
ejpam-6927	20	24	r	r	NOUN
ejpam-6927	20	25	,	,	PUNCT
ejpam-6927	20	26	where	where	SCONJ
ejpam-6927	20	27	ω1	ω1	PROPN
ejpam-6927	20	28	̸=	̸=	PROPN
ejpam-6927	20	29	ω2	ω2	NOUN
ejpam-6927	20	30	.	.	PUNCT
ejpam-6927	21	1	then	then	ADV
ejpam-6927	21	2	φ	φ	PROPN
ejpam-6927	21	3	(	(	PUNCT
ejpam-6927	21	4	ω1	ω1	PROPN
ejpam-6927	21	5	+	+	CCONJ
ejpam-6927	21	6	ω2	ω2	ADJ
ejpam-6927	21	7	2	2	NUM
ejpam-6927	21	8	)	)	PUNCT
ejpam-6927	21	9	≤	≤	NOUN
ejpam-6927	21	10	1	1	NUM
ejpam-6927	21	11	ω2	ω2	NUM
ejpam-6927	21	12	−	−	PROPN
ejpam-6927	21	13	ω1	ω1	PROPN
ejpam-6927	21	14	∫	∫	PROPN
ejpam-6927	21	15	ω2	ω2	PROPN
ejpam-6927	21	16	ω1	ω1	PROPN
ejpam-6927	21	17	φ(κ)dκ	φ(κ)dκ	PART
ejpam-6927	21	18	≤	≤	NUM
ejpam-6927	21	19	φ(ω1	φ(ω1	NOUN
ejpam-6927	21	20	)	)	PUNCT
ejpam-6927	21	21	+	+	CCONJ
ejpam-6927	21	22	φ(ω2	φ(ω2	NOUN
ejpam-6927	21	23	)	)	PUNCT
ejpam-6927	21	24	2	2	NUM
ejpam-6927	21	25	.	.	PUNCT
ejpam-6927	21	26	one	one	NUM
ejpam-6927	21	27	important	important	ADJ
ejpam-6927	21	28	finding	finding	NOUN
ejpam-6927	21	29	in	in	ADP
ejpam-6927	21	30	convexity	convexity	NOUN
ejpam-6927	21	31	theory	theory	NOUN
ejpam-6927	21	32	is	be	AUX
ejpam-6927	21	33	the	the	DET
ejpam-6927	21	34	h−h	h−h	NOUN
ejpam-6927	21	35	inequality	inequality	NOUN
ejpam-6927	21	36	.	.	PUNCT
ejpam-6927	22	1	the	the	DET
ejpam-6927	22	2	field	field	NOUN
ejpam-6927	22	3	has	have	AUX
ejpam-6927	22	4	advanced	advance	VERB
ejpam-6927	22	5	significantly	significantly	ADV
ejpam-6927	22	6	as	as	ADP
ejpam-6927	22	7	a	a	DET
ejpam-6927	22	8	result	result	NOUN
ejpam-6927	22	9	of	of	ADP
ejpam-6927	22	10	the	the	DET
ejpam-6927	22	11	efforts	effort	NOUN
ejpam-6927	22	12	of	of	ADP
ejpam-6927	22	13	several	several	ADJ
ejpam-6927	22	14	mathematicians	mathematician	NOUN
ejpam-6927	22	15	who	who	PRON
ejpam-6927	22	16	have	have	AUX
ejpam-6927	22	17	concentrated	concentrate	VERB
ejpam-6927	22	18	on	on	ADP
ejpam-6927	22	19	enhancing	enhance	VERB
ejpam-6927	22	20	and	and	CCONJ
ejpam-6927	22	21	generalizing	generalize	VERB
ejpam-6927	22	22	the	the	DET
ejpam-6927	22	23	inequality	inequality	NOUN
ejpam-6927	22	24	.	.	PUNCT
ejpam-6927	23	1	we	we	PRON
ejpam-6927	23	2	encourage	encourage	VERB
ejpam-6927	23	3	interested	interested	ADJ
ejpam-6927	23	4	readers	reader	NOUN
ejpam-6927	23	5	to	to	PART
ejpam-6927	23	6	review	review	VERB
ejpam-6927	23	7	some	some	PRON
ejpam-6927	23	8	of	of	ADP
ejpam-6927	23	9	the	the	DET
ejpam-6927	23	10	references	reference	NOUN
ejpam-6927	23	11	and	and	CCONJ
ejpam-6927	23	12	the	the	DET
ejpam-6927	23	13	papers	paper	NOUN
ejpam-6927	24	1	[	[	X
ejpam-6927	24	2	1–4	1–4	X
ejpam-6927	24	3	]	]	PUNCT
ejpam-6927	24	4	as	as	SCONJ
ejpam-6927	24	5	it	it	PRON
ejpam-6927	24	6	has	have	AUX
ejpam-6927	24	7	been	be	AUX
ejpam-6927	24	8	widely	widely	ADV
ejpam-6927	24	9	researched	research	VERB
ejpam-6927	24	10	and	and	CCONJ
ejpam-6927	24	11	used	use	VERB
ejpam-6927	24	12	in	in	ADP
ejpam-6927	24	13	a	a	DET
ejpam-6927	24	14	variety	variety	NOUN
ejpam-6927	24	15	of	of	ADP
ejpam-6927	24	16	settings	setting	NOUN
ejpam-6927	24	17	.	.	PUNCT
ejpam-6927	25	1	definition	definition	NOUN
ejpam-6927	25	2	1	1	NUM
ejpam-6927	25	3	.	.	PUNCT
ejpam-6927	26	1	a	a	DET
ejpam-6927	26	2	function	function	NOUN
ejpam-6927	26	3	φ	φ	NOUN
ejpam-6927	26	4	:	:	PUNCT
ejpam-6927	26	5	i	i	PRON
ejpam-6927	26	6	⊆	⊆	NUM
ejpam-6927	26	7	r	r	NOUN
ejpam-6927	26	8	→	→	SYM
ejpam-6927	26	9	r	r	NOUN
ejpam-6927	26	10	is	be	AUX
ejpam-6927	26	11	said	say	VERB
ejpam-6927	26	12	to	to	PART
ejpam-6927	26	13	be	be	AUX
ejpam-6927	26	14	convex	convex	ADJ
ejpam-6927	26	15	if	if	SCONJ
ejpam-6927	26	16	φ	φ	PROPN
ejpam-6927	26	17	(	(	PUNCT
ejpam-6927	26	18	σω1	σω1	NOUN
ejpam-6927	26	19	+	+	CCONJ
ejpam-6927	26	20	(	(	PUNCT
ejpam-6927	26	21	1−	1−	NUM
ejpam-6927	26	22	σ)ω2	σ)ω2	PROPN
ejpam-6927	26	23	)	)	PUNCT
ejpam-6927	26	24	≤	≤	NOUN
ejpam-6927	26	25	σφ	σφ	NOUN
ejpam-6927	26	26	(	(	PUNCT
ejpam-6927	26	27	ω1	ω1	PROPN
ejpam-6927	26	28	)	)	PUNCT
ejpam-6927	26	29	+	+	CCONJ
ejpam-6927	26	30	(	(	PUNCT
ejpam-6927	26	31	1−	1−	NUM
ejpam-6927	26	32	σ)φ	σ)φ	NOUN
ejpam-6927	26	33	(	(	PUNCT
ejpam-6927	26	34	ω2	ω2	ADJ
ejpam-6927	26	35	)	)	PUNCT
ejpam-6927	26	36	holds	hold	VERB
ejpam-6927	26	37	for	for	ADP
ejpam-6927	26	38	all	all	DET
ejpam-6927	26	39	ω1	ω1	PROPN
ejpam-6927	26	40	,	,	PUNCT
ejpam-6927	26	41	ω2	ω2	NOUN
ejpam-6927	26	42	∈	∈	PROPN
ejpam-6927	27	1	i	i	PRON
ejpam-6927	27	2	and	and	CCONJ
ejpam-6927	27	3	σ	σ	PROPN
ejpam-6927	27	4	∈	∈	PROPN
ejpam-6927	28	1	[	[	X
ejpam-6927	28	2	0	0	NUM
ejpam-6927	28	3	,	,	PUNCT
ejpam-6927	28	4	1	1	NUM
ejpam-6927	28	5	]	]	PUNCT
ejpam-6927	28	6	.	.	PUNCT
ejpam-6927	29	1	if	if	SCONJ
ejpam-6927	29	2	−φ	−φ	NOUN
ejpam-6927	29	3	is	be	AUX
ejpam-6927	29	4	convex	convex	PROPN
ejpam-6927	29	5	,	,	PUNCT
ejpam-6927	29	6	then	then	ADV
ejpam-6927	29	7	φ	φ	PROPN
ejpam-6927	29	8	is	be	AUX
ejpam-6927	29	9	said	say	VERB
ejpam-6927	29	10	to	to	PART
ejpam-6927	29	11	be	be	AUX
ejpam-6927	29	12	concave	concave	VERB
ejpam-6927	29	13	.	.	PUNCT
ejpam-6927	30	1	convex	convex	PROPN
ejpam-6927	30	2	function	function	NOUN
ejpam-6927	30	3	theory	theory	NOUN
ejpam-6927	30	4	plays	play	VERB
ejpam-6927	30	5	a	a	DET
ejpam-6927	30	6	crucial	crucial	ADJ
ejpam-6927	30	7	role	role	NOUN
ejpam-6927	30	8	in	in	ADP
ejpam-6927	30	9	both	both	CCONJ
ejpam-6927	30	10	pure	pure	ADJ
ejpam-6927	30	11	and	and	CCONJ
ejpam-6927	30	12	applied	applied	ADJ
ejpam-6927	30	13	mathematics	mathematic	NOUN
ejpam-6927	30	14	.	.	PUNCT
ejpam-6927	31	1	noteworthy	noteworthy	ADJ
ejpam-6927	31	2	inequalities	inequality	NOUN
ejpam-6927	31	3	have	have	AUX
ejpam-6927	31	4	been	be	AUX
ejpam-6927	31	5	derived	derive	VERB
ejpam-6927	31	6	using	use	VERB
ejpam-6927	31	7	various	various	ADJ
ejpam-6927	31	8	types	type	NOUN
ejpam-6927	31	9	of	of	ADP
ejpam-6927	31	10	convexity	convexity	NOUN
ejpam-6927	31	11	[	[	X
ejpam-6927	31	12	5–9	5–9	X
ejpam-6927	31	13	]	]	PUNCT
ejpam-6927	31	14	.	.	PUNCT
ejpam-6927	32	1	the	the	DET
ejpam-6927	32	2	study	study	NOUN
ejpam-6927	32	3	of	of	ADP
ejpam-6927	32	4	integrals	integral	NOUN
ejpam-6927	32	5	and	and	CCONJ
ejpam-6927	32	6	derivatives	derivative	NOUN
ejpam-6927	32	7	requires	require	VERB
ejpam-6927	32	8	a	a	DET
ejpam-6927	32	9	solid	solid	ADJ
ejpam-6927	32	10	understanding	understanding	NOUN
ejpam-6927	32	11	of	of	ADP
ejpam-6927	32	12	calculus	calculus	NOUN
ejpam-6927	32	13	,	,	PUNCT
ejpam-6927	32	14	a	a	DET
ejpam-6927	32	15	fundamental	fundamental	ADJ
ejpam-6927	32	16	branch	branch	NOUN
ejpam-6927	32	17	of	of	ADP
ejpam-6927	32	18	mathematics	mathematic	NOUN
ejpam-6927	32	19	.	.	PUNCT
ejpam-6927	33	1	a	a	DET
ejpam-6927	33	2	new	new	ADJ
ejpam-6927	33	3	mathematical	mathematical	ADJ
ejpam-6927	33	4	framework	framework	NOUN
ejpam-6927	33	5	called	call	VERB
ejpam-6927	33	6	quantum	quantum	NOUN
ejpam-6927	33	7	calculus	calculus	NOUN
ejpam-6927	33	8	,	,	PUNCT
ejpam-6927	33	9	or	or	CCONJ
ejpam-6927	33	10	q	q	NOUN
ejpam-6927	33	11	-	-	NOUN
ejpam-6927	33	12	calculus	calculus	NOUN
ejpam-6927	33	13	,	,	PUNCT
ejpam-6927	33	14	has	have	AUX
ejpam-6927	33	15	emerged	emerge	VERB
ejpam-6927	33	16	as	as	ADP
ejpam-6927	33	17	a	a	DET
ejpam-6927	33	18	result	result	NOUN
ejpam-6927	33	19	of	of	ADP
ejpam-6927	33	20	the	the	DET
ejpam-6927	33	21	evolution	evolution	NOUN
ejpam-6927	33	22	and	and	CCONJ
ejpam-6927	33	23	adaptation	adaptation	NOUN
ejpam-6927	33	24	of	of	ADP
ejpam-6927	33	25	the	the	DET
ejpam-6927	33	26	classical	classical	ADJ
ejpam-6927	33	27	calculus	calculus	NOUN
ejpam-6927	33	28	concepts	concept	NOUN
ejpam-6927	33	29	.	.	PUNCT
ejpam-6927	34	1	quantum	quantum	NOUN
ejpam-6927	34	2	calculus	calculus	NOUN
ejpam-6927	34	3	,	,	PUNCT
ejpam-6927	34	4	which	which	PRON
ejpam-6927	34	5	includes	include	VERB
ejpam-6927	34	6	q	q	ADJ
ejpam-6927	34	7	-	-	ADJ
ejpam-6927	34	8	integral	integral	ADJ
ejpam-6927	34	9	calculus	calculus	NOUN
ejpam-6927	34	10	,	,	PUNCT
ejpam-6927	34	11	q	q	ADJ
ejpam-6927	34	12	-	-	PUNCT
ejpam-6927	34	13	fractional	fractional	ADJ
ejpam-6927	34	14	calculus	calculus	NOUN
ejpam-6927	34	15	,	,	PUNCT
ejpam-6927	34	16	and	and	CCONJ
ejpam-6927	34	17	q	q	ADJ
ejpam-6927	34	18	-	-	PUNCT
ejpam-6927	34	19	transform	transform	NOUN
ejpam-6927	34	20	analysis	analysis	NOUN
ejpam-6927	34	21	,	,	PUNCT
ejpam-6927	34	22	is	be	AUX
ejpam-6927	34	23	the	the	DET
ejpam-6927	34	24	study	study	NOUN
ejpam-6927	34	25	of	of	ADP
ejpam-6927	34	26	calculus	calculus	NOUN
ejpam-6927	34	27	without	without	ADP
ejpam-6927	34	28	limits	limit	NOUN
ejpam-6927	34	29	.	.	PUNCT
ejpam-6927	35	1	numerous	numerous	ADJ
ejpam-6927	35	2	mathematical	mathematical	ADJ
ejpam-6927	35	3	and	and	CCONJ
ejpam-6927	35	4	physical	physical	ADJ
ejpam-6927	35	5	areas	area	NOUN
ejpam-6927	35	6	have	have	AUX
ejpam-6927	35	7	shown	show	VERB
ejpam-6927	35	8	how	how	SCONJ
ejpam-6927	35	9	effective	effective	ADJ
ejpam-6927	35	10	these	these	DET
ejpam-6927	35	11	techniques	technique	NOUN
ejpam-6927	35	12	are	be	AUX
ejpam-6927	35	13	.	.	PUNCT
ejpam-6927	36	1	in	in	ADP
ejpam-6927	36	2	the	the	DET
ejpam-6927	36	3	early	early	ADJ
ejpam-6927	36	4	20th	20th	ADJ
ejpam-6927	36	5	century	century	NOUN
ejpam-6927	36	6	,	,	PUNCT
ejpam-6927	36	7	the	the	DET
ejpam-6927	36	8	first	first	ADJ
ejpam-6927	36	9	description	description	NOUN
ejpam-6927	36	10	of	of	ADP
ejpam-6927	36	11	quantum	quantum	NOUN
ejpam-6927	36	12	calculus	calculus	NOUN
ejpam-6927	36	13	was	be	AUX
ejpam-6927	36	14	provided	provide	VERB
ejpam-6927	36	15	by	by	ADP
ejpam-6927	36	16	jackson	jackson	PROPN
ejpam-6927	36	17	.	.	PUNCT
ejpam-6927	37	1	the	the	DET
ejpam-6927	37	2	book	book	NOUN
ejpam-6927	37	3	[	[	X
ejpam-6927	37	4	10	10	NUM
ejpam-6927	37	5	]	]	PUNCT
ejpam-6927	37	6	is	be	AUX
ejpam-6927	37	7	recommended	recommend	VERB
ejpam-6927	37	8	for	for	ADP
ejpam-6927	37	9	those	those	PRON
ejpam-6927	37	10	who	who	PRON
ejpam-6927	37	11	wish	wish	VERB
ejpam-6927	37	12	to	to	PART
ejpam-6927	37	13	investigate	investigate	VERB
ejpam-6927	37	14	deeper	deeply	ADV
ejpam-6927	37	15	into	into	ADP
ejpam-6927	37	16	this	this	DET
ejpam-6927	37	17	topic	topic	NOUN
ejpam-6927	37	18	.	.	PUNCT
ejpam-6927	38	1	q	q	X
ejpam-6927	38	2	-	-	PUNCT
ejpam-6927	38	3	deformation	deformation	NOUN
ejpam-6927	38	4	is	be	AUX
ejpam-6927	38	5	a	a	DET
ejpam-6927	38	6	key	key	ADJ
ejpam-6927	38	7	idea	idea	NOUN
ejpam-6927	38	8	in	in	ADP
ejpam-6927	38	9	the	the	DET
ejpam-6927	38	10	field	field	NOUN
ejpam-6927	38	11	of	of	ADP
ejpam-6927	38	12	quantum	quantum	NOUN
ejpam-6927	38	13	calculus	calculus	NOUN
ejpam-6927	38	14	.	.	PUNCT
ejpam-6927	39	1	this	this	DET
ejpam-6927	39	2	procedure	procedure	NOUN
ejpam-6927	39	3	includes	include	VERB
ejpam-6927	39	4	changing	change	VERB
ejpam-6927	39	5	the	the	DET
ejpam-6927	39	6	characteristics	characteristic	NOUN
ejpam-6927	39	7	of	of	ADP
ejpam-6927	39	8	calculus	calculus	NOUN
ejpam-6927	39	9	operations	operation	NOUN
ejpam-6927	39	10	,	,	PUNCT
ejpam-6927	39	11	such	such	ADJ
ejpam-6927	39	12	as	as	ADP
ejpam-6927	39	13	differentiation	differentiation	NOUN
ejpam-6927	39	14	and	and	CCONJ
ejpam-6927	39	15	integration	integration	NOUN
ejpam-6927	39	16	,	,	PUNCT
ejpam-6927	39	17	by	by	ADP
ejpam-6927	39	18	adding	add	VERB
ejpam-6927	39	19	a	a	DET
ejpam-6927	39	20	parameter	parameter	NOUN
ejpam-6927	39	21	q.	q.	NOUN
ejpam-6927	39	22	similar	similar	ADJ
ejpam-6927	39	23	to	to	ADP
ejpam-6927	39	24	ordinary	ordinary	ADJ
ejpam-6927	39	25	differential	differential	ADJ
ejpam-6927	39	26	equations	equation	NOUN
ejpam-6927	39	27	in	in	ADP
ejpam-6927	39	28	classical	classical	ADJ
ejpam-6927	39	29	calculus	calculus	NOUN
ejpam-6927	39	30	,	,	PUNCT
ejpam-6927	39	31	q	q	ADJ
ejpam-6927	39	32	-	-	PUNCT
ejpam-6927	39	33	difference	difference	NOUN
ejpam-6927	39	34	equations	equation	NOUN
ejpam-6927	39	35	are	be	AUX
ejpam-6927	39	36	used	use	VERB
ejpam-6927	39	37	in	in	ADP
ejpam-6927	39	38	q	q	NOUN
ejpam-6927	39	39	-	-	NOUN
ejpam-6927	39	40	calculus	calculus	NOUN
ejpam-6927	39	41	to	to	PART
ejpam-6927	39	42	define	define	VERB
ejpam-6927	39	43	functions	function	NOUN
ejpam-6927	39	44	and	and	CCONJ
ejpam-6927	39	45	their	their	PRON
ejpam-6927	39	46	derivatives	derivative	NOUN
ejpam-6927	39	47	.	.	PUNCT
ejpam-6927	40	1	q	q	X
ejpam-6927	40	2	-	-	PUNCT
ejpam-6927	40	3	integrals	integral	NOUN
ejpam-6927	40	4	and	and	CCONJ
ejpam-6927	40	5	q	q	NOUN
ejpam-6927	40	6	-	-	PUNCT
ejpam-6927	40	7	derivatives	derivative	NOUN
ejpam-6927	40	8	,	,	PUNCT
ejpam-6927	40	9	which	which	PRON
ejpam-6927	40	10	are	be	AUX
ejpam-6927	40	11	extensions	extension	NOUN
ejpam-6927	40	12	of	of	ADP
ejpam-6927	40	13	their	their	PRON
ejpam-6927	40	14	classical	classical	ADJ
ejpam-6927	40	15	counterparts	counterpart	NOUN
ejpam-6927	40	16	,	,	PUNCT
ejpam-6927	40	17	are	be	AUX
ejpam-6927	40	18	introduced	introduce	VERB
ejpam-6927	40	19	in	in	ADP
ejpam-6927	40	20	quantum	quantum	NOUN
ejpam-6927	40	21	calculus	calculus	NOUN
ejpam-6927	40	22	.	.	PUNCT
ejpam-6927	41	1	it	it	PRON
ejpam-6927	41	2	is	be	AUX
ejpam-6927	41	3	clear	clear	ADJ
ejpam-6927	41	4	that	that	SCONJ
ejpam-6927	41	5	these	these	DET
ejpam-6927	41	6	operators	operator	NOUN
ejpam-6927	41	7	meet	meet	VERB
ejpam-6927	41	8	several	several	ADJ
ejpam-6927	41	9	q	q	NOUN
ejpam-6927	41	10	-	-	PUNCT
ejpam-6927	41	11	analogues	analogue	NOUN
ejpam-6927	41	12	of	of	ADP
ejpam-6927	41	13	the	the	DET
ejpam-6927	41	14	basic	basic	ADJ
ejpam-6927	41	15	theorem	theorem	NOUN
ejpam-6927	41	16	of	of	ADP
ejpam-6927	41	17	calculus	calculus	NOUN
ejpam-6927	41	18	and	and	CCONJ
ejpam-6927	41	19	the	the	DET
ejpam-6927	41	20	leibniz	leibniz	PROPN
ejpam-6927	41	21	rule	rule	NOUN
ejpam-6927	41	22	,	,	PUNCT
ejpam-6927	41	23	which	which	PRON
ejpam-6927	41	24	are	be	AUX
ejpam-6927	41	25	characteristics	characteristic	NOUN
ejpam-6927	41	26	of	of	ADP
ejpam-6927	41	27	ordinary	ordinary	ADJ
ejpam-6927	41	28	derivatives	derivative	NOUN
ejpam-6927	41	29	and	and	CCONJ
ejpam-6927	41	30	integrals	integral	NOUN
ejpam-6927	41	31	.	.	PUNCT
ejpam-6927	42	1	this	this	DET
ejpam-6927	42	2	research	research	NOUN
ejpam-6927	42	3	paper	paper	NOUN
ejpam-6927	42	4	’s	’s	PART
ejpam-6927	42	5	main	main	ADJ
ejpam-6927	42	6	goal	goal	NOUN
ejpam-6927	42	7	is	be	AUX
ejpam-6927	42	8	to	to	PART
ejpam-6927	42	9	investigate	investigate	VERB
ejpam-6927	42	10	the	the	DET
ejpam-6927	42	11	h−h	h−h	NOUN
ejpam-6927	42	12	inequality	inequality	NOUN
ejpam-6927	42	13	related	relate	VERB
ejpam-6927	42	14	to	to	ADP
ejpam-6927	42	15	the	the	DET
ejpam-6927	42	16	quantum	quantum	ADJ
ejpam-6927	42	17	integral	integral	ADJ
ejpam-6927	42	18	operator	operator	NOUN
ejpam-6927	42	19	.	.	PUNCT
ejpam-6927	43	1	several	several	ADJ
ejpam-6927	43	2	features	feature	NOUN
ejpam-6927	43	3	of	of	ADP
ejpam-6927	43	4	the	the	DET
ejpam-6927	43	5	q	q	NOUN
ejpam-6927	43	6	-	-	NOUN
ejpam-6927	43	7	integral	integral	ADJ
ejpam-6927	43	8	for	for	ADP
ejpam-6927	43	9	a	a	DET
ejpam-6927	43	10	continuous	continuous	ADJ
ejpam-6927	43	11	function	function	NOUN
ejpam-6927	43	12	were	be	AUX
ejpam-6927	43	13	defined	define	VERB
ejpam-6927	43	14	and	and	CCONJ
ejpam-6927	43	15	shown	show	VERB
ejpam-6927	43	16	by	by	ADP
ejpam-6927	43	17	tariboon	tariboon	NOUN
ejpam-6927	43	18	and	and	CCONJ
ejpam-6927	43	19	ntouyas	ntouyas	NOUN
ejpam-6927	43	20	in	in	ADP
ejpam-6927	43	21	[	[	X
ejpam-6927	43	22	11	11	NUM
ejpam-6927	43	23	]	]	PUNCT
ejpam-6927	43	24	in	in	ADP
ejpam-6927	43	25	2013	2013	NUM
ejpam-6927	43	26	.	.	PUNCT
ejpam-6927	44	1	however	however	ADV
ejpam-6927	44	2	,	,	PUNCT
ejpam-6927	44	3	kunt	kunt	PROPN
ejpam-6927	44	4	and	and	CCONJ
ejpam-6927	44	5	iscan	iscan	PROPN
ejpam-6927	44	6	showed	show	VERB
ejpam-6927	44	7	in	in	ADP
ejpam-6927	44	8	[	[	X
ejpam-6927	44	9	12	12	NUM
ejpam-6927	44	10	]	]	PUNCT
ejpam-6927	44	11	that	that	SCONJ
ejpam-6927	44	12	the	the	DET
ejpam-6927	44	13	h−h	h−h	NOUN
ejpam-6927	44	14	inequality	inequality	NOUN
ejpam-6927	44	15	derived	derive	VERB
ejpam-6927	44	16	in	in	ADP
ejpam-6927	44	17	[	[	X
ejpam-6927	44	18	11	11	NUM
ejpam-6927	44	19	]	]	PUNCT
ejpam-6927	44	20	is	be	AUX
ejpam-6927	44	21	incorrect	incorrect	ADJ
ejpam-6927	44	22	on	on	ADP
ejpam-6927	44	23	the	the	DET
ejpam-6927	44	24	left	left	NOUN
ejpam-6927	44	25	.	.	PUNCT
ejpam-6927	45	1	the	the	DET
ejpam-6927	45	2	following	follow	VERB
ejpam-6927	45	3	variation	variation	NOUN
ejpam-6927	45	4	of	of	ADP
ejpam-6927	45	5	the	the	DET
ejpam-6927	45	6	h−h	h−h	NOUN
ejpam-6927	45	7	inequality	inequality	NOUN
ejpam-6927	45	8	for	for	ADP
ejpam-6927	45	9	the	the	DET
ejpam-6927	45	10	q	q	ADJ
ejpam-6927	45	11	-	-	ADJ
ejpam-6927	45	12	integral	integral	ADJ
ejpam-6927	45	13	was	be	AUX
ejpam-6927	45	14	then	then	ADV
ejpam-6927	45	15	established	establish	VERB
ejpam-6927	45	16	by	by	ADP
ejpam-6927	45	17	alp	alp	PROPN
ejpam-6927	45	18	et	et	PROPN
ejpam-6927	45	19	al	al	PROPN
ejpam-6927	45	20	.	.	PUNCT
ejpam-6927	46	1	in	in	ADP
ejpam-6927	46	2	[	[	X
ejpam-6927	46	3	13	13	NUM
ejpam-6927	46	4	]	]	SYM
ejpam-6927	46	5	:	:	PUNCT
ejpam-6927	46	6	φ	φ	PROPN
ejpam-6927	46	7	(	(	PUNCT
ejpam-6927	46	8	qω1	qω1	PROPN
ejpam-6927	46	9	+	+	CCONJ
ejpam-6927	46	10	ω2	ω2	PROPN
ejpam-6927	46	11	q	q	X
ejpam-6927	47	1	+	+	NUM
ejpam-6927	47	2	1	1	NUM
ejpam-6927	47	3	)	)	PUNCT
ejpam-6927	47	4	≤	≤	NUM
ejpam-6927	47	5	1	1	NUM
ejpam-6927	47	6	ω2	ω2	NUM
ejpam-6927	47	7	−	−	PROPN
ejpam-6927	47	8	ω1	ω1	PROPN
ejpam-6927	47	9	∫	∫	PROPN
ejpam-6927	47	10	ω2	ω2	PROPN
ejpam-6927	47	11	ω1	ω1	PROPN
ejpam-6927	47	12	φ(κ1)ω1dqκ1	φ(κ1)ω1dqκ1	NOUN
ejpam-6927	47	13	≤	≤	NUM
ejpam-6927	47	14	qφ(ω1	qφ(ω1	ADV
ejpam-6927	47	15	)	)	PUNCT
ejpam-6927	47	16	+	+	CCONJ
ejpam-6927	47	17	φ(ω2	φ(ω2	NOUN
ejpam-6927	47	18	)	)	PUNCT
ejpam-6927	47	19	q	q	NOUN
ejpam-6927	48	1	+	+	NUM
ejpam-6927	48	2	1	1	NUM
ejpam-6927	48	3	,	,	PUNCT
ejpam-6927	48	4	(	(	PUNCT
ejpam-6927	48	5	1	1	X
ejpam-6927	48	6	)	)	PUNCT
ejpam-6927	48	7	m.	m.	NOUN
ejpam-6927	48	8	adil	adil	PROPN
ejpam-6927	48	9	khan	khan	PROPN
ejpam-6927	48	10	et	et	PROPN
ejpam-6927	48	11	al	al	PROPN
ejpam-6927	48	12	.	.	PUNCT
ejpam-6927	48	13	/	/	SYM
ejpam-6927	48	14	eur	eur	PROPN
ejpam-6927	48	15	.	.	PUNCT
ejpam-6927	49	1	j.	j.	PROPN
ejpam-6927	49	2	pure	pure	PROPN
ejpam-6927	49	3	appl	appl	PROPN
ejpam-6927	49	4	.	.	PROPN
ejpam-6927	49	5	math	math	PROPN
ejpam-6927	49	6	,	,	PUNCT
ejpam-6927	49	7	18	18	NUM
ejpam-6927	49	8	(	(	PUNCT
ejpam-6927	49	9	4	4	NUM
ejpam-6927	49	10	)	)	PUNCT
ejpam-6927	49	11	(	(	PUNCT
ejpam-6927	49	12	2025	2025	NUM
ejpam-6927	49	13	)	)	PUNCT
ejpam-6927	49	14	,	,	PUNCT
ejpam-6927	49	15	6927	6927	NUM
ejpam-6927	49	16	3	3	NUM
ejpam-6927	49	17	of	of	ADP
ejpam-6927	49	18	18	18	NUM
ejpam-6927	49	19	where	where	SCONJ
ejpam-6927	49	20	q	q	PROPN
ejpam-6927	49	21	∈	∈	PROPN
ejpam-6927	49	22	(	(	PUNCT
ejpam-6927	49	23	0	0	NUM
ejpam-6927	49	24	,	,	PUNCT
ejpam-6927	49	25	1	1	NUM
ejpam-6927	49	26	)	)	PUNCT
ejpam-6927	49	27	and	and	CCONJ
ejpam-6927	49	28	φ	φ	NUM
ejpam-6927	49	29	:	:	PUNCT
ejpam-6927	50	1	[	[	X
ejpam-6927	50	2	ω1	ω1	PROPN
ejpam-6927	50	3	,	,	PUNCT
ejpam-6927	50	4	ω2	ω2	PROPN
ejpam-6927	50	5	]	]	PUNCT
ejpam-6927	50	6	→	→	SYM
ejpam-6927	50	7	r	r	NOUN
ejpam-6927	50	8	is	be	AUX
ejpam-6927	50	9	a	a	DET
ejpam-6927	50	10	convex	convex	ADJ
ejpam-6927	50	11	function	function	NOUN
ejpam-6927	50	12	.	.	PUNCT
ejpam-6927	51	1	the	the	DET
ejpam-6927	51	2	aforementioned	aforementioned	ADJ
ejpam-6927	51	3	inequality	inequality	NOUN
ejpam-6927	51	4	(	(	PUNCT
ejpam-6927	51	5	1	1	NUM
ejpam-6927	51	6	)	)	PUNCT
ejpam-6927	51	7	is	be	AUX
ejpam-6927	51	8	referred	refer	VERB
ejpam-6927	51	9	to	to	ADP
ejpam-6927	51	10	as	as	ADP
ejpam-6927	51	11	the	the	DET
ejpam-6927	51	12	quantum	quantum	ADJ
ejpam-6927	51	13	h−h	h−h	NOUN
ejpam-6927	51	14	inequality	inequality	NOUN
ejpam-6927	51	15	.	.	PUNCT
ejpam-6927	52	1	in	in	ADP
ejpam-6927	52	2	recent	recent	ADJ
ejpam-6927	52	3	years	year	NOUN
ejpam-6927	52	4	,	,	PUNCT
ejpam-6927	52	5	this	this	DET
ejpam-6927	52	6	inequality	inequality	NOUN
ejpam-6927	52	7	has	have	AUX
ejpam-6927	52	8	been	be	AUX
ejpam-6927	52	9	the	the	DET
ejpam-6927	52	10	focus	focus	NOUN
ejpam-6927	52	11	of	of	ADP
ejpam-6927	52	12	research	research	NOUN
ejpam-6927	52	13	by	by	ADP
ejpam-6927	52	14	numerous	numerous	ADJ
ejpam-6927	52	15	mathematicians	mathematician	NOUN
ejpam-6927	52	16	.	.	PUNCT
ejpam-6927	53	1	in	in	ADP
ejpam-6927	53	2	[	[	X
ejpam-6927	53	3	14	14	NUM
ejpam-6927	53	4	]	]	X
ejpam-6927	53	5	,	,	PUNCT
ejpam-6927	53	6	ali	ali	PROPN
ejpam-6927	53	7	et	et	PROPN
ejpam-6927	53	8	al	al	PROPN
ejpam-6927	53	9	.	.	PROPN
ejpam-6927	53	10	established	establish	VERB
ejpam-6927	53	11	an	an	DET
ejpam-6927	53	12	identity	identity	NOUN
ejpam-6927	53	13	related	relate	VERB
ejpam-6927	53	14	to	to	ADP
ejpam-6927	53	15	the	the	DET
ejpam-6927	53	16	quantum	quantum	ADJ
ejpam-6927	53	17	h−h	h−h	NOUN
ejpam-6927	53	18	inequality	inequality	NOUN
ejpam-6927	53	19	and	and	CCONJ
ejpam-6927	53	20	the	the	DET
ejpam-6927	53	21	q	q	NOUN
ejpam-6927	53	22	-	-	NOUN
ejpam-6927	53	23	integral	integral	ADJ
ejpam-6927	53	24	.	.	PUNCT
ejpam-6927	54	1	since	since	SCONJ
ejpam-6927	54	2	integral	integral	ADJ
ejpam-6927	54	3	identity	identity	NOUN
ejpam-6927	54	4	and	and	CCONJ
ejpam-6927	54	5	applications	application	NOUN
ejpam-6927	54	6	of	of	ADP
ejpam-6927	54	7	power	power	NOUN
ejpam-6927	54	8	-	-	PUNCT
ejpam-6927	54	9	mean	mean	NOUN
ejpam-6927	54	10	inequality	inequality	NOUN
ejpam-6927	54	11	and	and	CCONJ
ejpam-6927	54	12	hölder	hölder	NOUN
ejpam-6927	54	13	inequality	inequality	NOUN
ejpam-6927	54	14	result	result	NOUN
ejpam-6927	54	15	in	in	ADP
ejpam-6927	54	16	the	the	DET
ejpam-6927	54	17	q	q	ADJ
ejpam-6927	54	18	-	-	ADJ
ejpam-6927	54	19	integral	integral	ADJ
ejpam-6927	54	20	form	form	NOUN
ejpam-6927	54	21	of	of	ADP
ejpam-6927	54	22	the	the	DET
ejpam-6927	54	23	h−h	h−h	NOUN
ejpam-6927	54	24	inequality	inequality	NOUN
ejpam-6927	54	25	,	,	PUNCT
ejpam-6927	54	26	it	it	PRON
ejpam-6927	54	27	is	be	AUX
ejpam-6927	54	28	clear	clear	ADJ
ejpam-6927	54	29	that	that	SCONJ
ejpam-6927	54	30	certain	certain	ADJ
ejpam-6927	54	31	conclusions	conclusion	NOUN
ejpam-6927	54	32	have	have	AUX
ejpam-6927	54	33	been	be	AUX
ejpam-6927	54	34	established	establish	VERB
ejpam-6927	54	35	.	.	PUNCT
ejpam-6927	55	1	previously	previously	ADV
ejpam-6927	55	2	,	,	PUNCT
ejpam-6927	55	3	the	the	DET
ejpam-6927	55	4	findings	finding	NOUN
ejpam-6927	55	5	were	be	AUX
ejpam-6927	55	6	deduced	deduce	VERB
ejpam-6927	55	7	for	for	ADP
ejpam-6927	55	8	a	a	DET
ejpam-6927	55	9	certain	certain	ADJ
ejpam-6927	55	10	value	value	NOUN
ejpam-6927	55	11	of	of	ADP
ejpam-6927	55	12	q.	q.	PROPN
ejpam-6927	55	13	noor	noor	PROPN
ejpam-6927	55	14	et	et	PROPN
ejpam-6927	55	15	al	al	PROPN
ejpam-6927	55	16	.	.	PROPN
ejpam-6927	55	17	,	,	PUNCT
ejpam-6927	55	18	in	in	ADP
ejpam-6927	55	19	[	[	X
ejpam-6927	55	20	15	15	NUM
ejpam-6927	55	21	]	]	PUNCT
ejpam-6927	55	22	,	,	PUNCT
ejpam-6927	55	23	established	establish	VERB
ejpam-6927	55	24	some	some	DET
ejpam-6927	55	25	novel	novel	ADJ
ejpam-6927	55	26	quantum	quantum	NOUN
ejpam-6927	55	27	estimates	estimate	NOUN
ejpam-6927	55	28	for	for	ADP
ejpam-6927	55	29	h−h	h−h	NOUN
ejpam-6927	55	30	inequalities	inequality	NOUN
ejpam-6927	55	31	via	via	ADP
ejpam-6927	55	32	q	q	ADJ
ejpam-6927	55	33	-	-	PUNCT
ejpam-6927	55	34	differentiable	differentiable	ADJ
ejpam-6927	55	35	convex	convex	NOUN
ejpam-6927	55	36	functions	function	NOUN
ejpam-6927	55	37	and	and	CCONJ
ejpam-6927	55	38	q	q	ADJ
ejpam-6927	55	39	-	-	PUNCT
ejpam-6927	55	40	differentiable	differentiable	ADJ
ejpam-6927	55	41	quasi	quasi	ADJ
ejpam-6927	55	42	-	-	ADJ
ejpam-6927	55	43	convex	convex	ADJ
ejpam-6927	55	44	functions	function	NOUN
ejpam-6927	55	45	.	.	PUNCT
ejpam-6927	56	1	in	in	ADP
ejpam-6927	56	2	the	the	DET
ejpam-6927	56	3	present	present	ADJ
ejpam-6927	56	4	study	study	NOUN
ejpam-6927	56	5	[	[	X
ejpam-6927	56	6	16	16	NUM
ejpam-6927	56	7	]	]	PUNCT
ejpam-6927	56	8	,	,	PUNCT
ejpam-6927	56	9	the	the	DET
ejpam-6927	56	10	authors	author	NOUN
ejpam-6927	56	11	propose	propose	VERB
ejpam-6927	56	12	a	a	DET
ejpam-6927	56	13	novel	novel	ADJ
ejpam-6927	56	14	definition	definition	NOUN
ejpam-6927	56	15	of	of	ADP
ejpam-6927	56	16	convexity	convexity	NOUN
ejpam-6927	56	17	(	(	PUNCT
ejpam-6927	56	18	k	k	NOUN
ejpam-6927	56	19	-	-	ADJ
ejpam-6927	56	20	harmonically	harmonically	ADV
ejpam-6927	56	21	γ−convex	γ−convex	NOUN
ejpam-6927	56	22	function	function	NOUN
ejpam-6927	56	23	)	)	PUNCT
ejpam-6927	56	24	and	and	CCONJ
ejpam-6927	56	25	employ	employ	VERB
ejpam-6927	56	26	this	this	DET
ejpam-6927	56	27	definition	definition	NOUN
ejpam-6927	56	28	to	to	PART
ejpam-6927	56	29	derive	derive	VERB
ejpam-6927	56	30	new	new	ADJ
ejpam-6927	56	31	h−h	h−h	NOUN
ejpam-6927	56	32	-	-	PUNCT
ejpam-6927	56	33	type	type	NOUN
ejpam-6927	56	34	integral	integral	ADJ
ejpam-6927	56	35	inequalities	inequality	NOUN
ejpam-6927	56	36	for	for	ADP
ejpam-6927	56	37	quantum	quantum	NOUN
ejpam-6927	56	38	integrals	integral	NOUN
ejpam-6927	56	39	.	.	PUNCT
ejpam-6927	57	1	a	a	DET
ejpam-6927	57	2	number	number	NOUN
ejpam-6927	57	3	of	of	ADP
ejpam-6927	57	4	authors	author	NOUN
ejpam-6927	57	5	engaged	engage	VERB
ejpam-6927	57	6	in	in	ADP
ejpam-6927	57	7	research	research	NOUN
ejpam-6927	57	8	within	within	ADP
ejpam-6927	57	9	this	this	DET
ejpam-6927	57	10	field	field	NOUN
ejpam-6927	57	11	have	have	AUX
ejpam-6927	57	12	also	also	ADV
ejpam-6927	57	13	studied	study	VERB
ejpam-6927	57	14	the	the	DET
ejpam-6927	57	15	symmetric	symmetric	ADJ
ejpam-6927	57	16	quantum	quantum	ADJ
ejpam-6927	57	17	calculus	calculus	NOUN
ejpam-6927	57	18	of	of	ADP
ejpam-6927	57	19	the	the	DET
ejpam-6927	57	20	h−h	h−h	NOUN
ejpam-6927	57	21	inequality	inequality	NOUN
ejpam-6927	57	22	.	.	PUNCT
ejpam-6927	58	1	researchers	researcher	NOUN
ejpam-6927	58	2	interested	interested	ADJ
ejpam-6927	58	3	in	in	ADP
ejpam-6927	58	4	further	further	ADJ
ejpam-6927	58	5	works	work	NOUN
ejpam-6927	58	6	may	may	AUX
ejpam-6927	58	7	refer	refer	VERB
ejpam-6927	58	8	to	to	ADP
ejpam-6927	58	9	studies	study	NOUN
ejpam-6927	58	10	[	[	X
ejpam-6927	58	11	17	17	NUM
ejpam-6927	58	12	]	]	PUNCT
ejpam-6927	58	13	and	and	CCONJ
ejpam-6927	58	14	[	[	X
ejpam-6927	58	15	18	18	NUM
ejpam-6927	58	16	]	]	PUNCT
ejpam-6927	58	17	.	.	PUNCT
ejpam-6927	59	1	in	in	ADP
ejpam-6927	59	2	[	[	X
ejpam-6927	59	3	19	19	NUM
ejpam-6927	59	4	]	]	PUNCT
ejpam-6927	59	5	,	,	PUNCT
ejpam-6927	59	6	budak	budak	PROPN
ejpam-6927	59	7	and	and	CCONJ
ejpam-6927	59	8	colleagues	colleague	NOUN
ejpam-6927	59	9	took	take	VERB
ejpam-6927	59	10	into	into	ADP
ejpam-6927	59	11	account	account	NOUN
ejpam-6927	59	12	the	the	DET
ejpam-6927	59	13	class	class	NOUN
ejpam-6927	59	14	of	of	ADP
ejpam-6927	59	15	coordinated	coordinate	VERB
ejpam-6927	59	16	convex	convex	NOUN
ejpam-6927	59	17	functions	function	NOUN
ejpam-6927	59	18	in	in	ADP
ejpam-6927	59	19	order	order	NOUN
ejpam-6927	59	20	to	to	PART
ejpam-6927	59	21	derive	derive	VERB
ejpam-6927	59	22	the	the	DET
ejpam-6927	59	23	extended	extended	ADJ
ejpam-6927	59	24	form	form	NOUN
ejpam-6927	59	25	of	of	ADP
ejpam-6927	59	26	the	the	DET
ejpam-6927	59	27	quantum	quantum	ADJ
ejpam-6927	59	28	h−h	h−h	NOUN
ejpam-6927	59	29	inequality	inequality	NOUN
ejpam-6927	59	30	.	.	PUNCT
ejpam-6927	60	1	in	in	ADP
ejpam-6927	60	2	order	order	NOUN
ejpam-6927	60	3	to	to	PART
ejpam-6927	60	4	further	far	ADV
ejpam-6927	60	5	generalize	generalize	VERB
ejpam-6927	60	6	the	the	DET
ejpam-6927	60	7	quantum	quantum	NOUN
ejpam-6927	60	8	h−h	h−h	NOUN
ejpam-6927	60	9	inequality	inequality	NOUN
ejpam-6927	60	10	,	,	PUNCT
ejpam-6927	60	11	the	the	DET
ejpam-6927	60	12	double	double	ADJ
ejpam-6927	60	13	integral	integral	ADJ
ejpam-6927	60	14	identity	identity	NOUN
ejpam-6927	60	15	has	have	AUX
ejpam-6927	60	16	been	be	AUX
ejpam-6927	60	17	developed	develop	VERB
ejpam-6927	60	18	.	.	PUNCT
ejpam-6927	61	1	furthermore	furthermore	ADV
ejpam-6927	61	2	,	,	PUNCT
ejpam-6927	61	3	as	as	SCONJ
ejpam-6927	61	4	mentioned	mention	VERB
ejpam-6927	61	5	in	in	ADP
ejpam-6927	61	6	[	[	X
ejpam-6927	61	7	20	20	NUM
ejpam-6927	61	8	]	]	PUNCT
ejpam-6927	61	9	and	and	CCONJ
ejpam-6927	61	10	[	[	X
ejpam-6927	61	11	21	21	NUM
ejpam-6927	61	12	]	]	PUNCT
ejpam-6927	61	13	,	,	PUNCT
ejpam-6927	61	14	it	it	PRON
ejpam-6927	61	15	has	have	AUX
ejpam-6927	61	16	been	be	AUX
ejpam-6927	61	17	shown	show	VERB
ejpam-6927	61	18	that	that	SCONJ
ejpam-6927	61	19	the	the	DET
ejpam-6927	61	20	above	above	ADJ
ejpam-6927	61	21	inequality	inequality	NOUN
ejpam-6927	61	22	holds	hold	VERB
ejpam-6927	61	23	for	for	ADP
ejpam-6927	61	24	the	the	DET
ejpam-6927	61	25	class	class	NOUN
ejpam-6927	61	26	of	of	ADP
ejpam-6927	61	27	s	s	NOUN
ejpam-6927	61	28	-	-	NOUN
ejpam-6927	61	29	convex	convex	ADJ
ejpam-6927	61	30	and	and	CCONJ
ejpam-6927	61	31	r	r	NOUN
ejpam-6927	61	32	-	-	PUNCT
ejpam-6927	61	33	convex	convex	NOUN
ejpam-6927	61	34	functions	function	NOUN
ejpam-6927	61	35	,	,	PUNCT
ejpam-6927	61	36	respectively	respectively	ADV
ejpam-6927	61	37	.	.	PUNCT
ejpam-6927	62	1	this	this	DET
ejpam-6927	62	2	study	study	NOUN
ejpam-6927	62	3	’s	’s	PART
ejpam-6927	62	4	main	main	ADJ
ejpam-6927	62	5	goal	goal	NOUN
ejpam-6927	62	6	is	be	AUX
ejpam-6927	62	7	to	to	PART
ejpam-6927	62	8	analyze	analyze	VERB
ejpam-6927	62	9	the	the	DET
ejpam-6927	62	10	quantum	quantum	NOUN
ejpam-6927	62	11	h−h	h−h	NOUN
ejpam-6927	62	12	inequality	inequality	NOUN
ejpam-6927	62	13	using	use	VERB
ejpam-6927	62	14	a	a	DET
ejpam-6927	62	15	green	green	ADJ
ejpam-6927	62	16	function	function	NOUN
ejpam-6927	62	17	method	method	NOUN
ejpam-6927	62	18	.	.	PUNCT
ejpam-6927	63	1	several	several	ADJ
ejpam-6927	63	2	novel	novel	ADJ
ejpam-6927	63	3	quantum	quantum	NOUN
ejpam-6927	63	4	identities	identity	NOUN
ejpam-6927	63	5	were	be	AUX
ejpam-6927	63	6	inferred	infer	VERB
ejpam-6927	63	7	throughout	throughout	ADP
ejpam-6927	63	8	this	this	DET
ejpam-6927	63	9	particular	particular	ADJ
ejpam-6927	63	10	technique	technique	NOUN
ejpam-6927	63	11	.	.	PUNCT
ejpam-6927	64	1	new	new	ADJ
ejpam-6927	64	2	inequalities	inequality	NOUN
ejpam-6927	64	3	have	have	AUX
ejpam-6927	64	4	been	be	AUX
ejpam-6927	64	5	made	make	VERB
ejpam-6927	64	6	possible	possible	ADJ
ejpam-6927	64	7	by	by	ADP
ejpam-6927	64	8	the	the	DET
ejpam-6927	64	9	use	use	NOUN
ejpam-6927	64	10	of	of	ADP
ejpam-6927	64	11	these	these	DET
ejpam-6927	64	12	identities	identity	NOUN
ejpam-6927	64	13	.	.	PUNCT
ejpam-6927	65	1	convexity	convexity	PROPN
ejpam-6927	65	2	,	,	PUNCT
ejpam-6927	65	3	jensen	jensen	PROPN
ejpam-6927	65	4	’s	’s	PART
ejpam-6927	65	5	inequality	inequality	NOUN
ejpam-6927	65	6	for	for	ADP
ejpam-6927	65	7	convex	convex	NOUN
ejpam-6927	65	8	mappings	mapping	NOUN
ejpam-6927	65	9	,	,	PUNCT
ejpam-6927	65	10	and	and	CCONJ
ejpam-6927	65	11	q	q	NOUN
ejpam-6927	65	12	-	-	PUNCT
ejpam-6927	65	13	identities	identity	NOUN
ejpam-6927	65	14	are	be	AUX
ejpam-6927	65	15	among	among	ADP
ejpam-6927	65	16	the	the	DET
ejpam-6927	65	17	methods	method	NOUN
ejpam-6927	65	18	used	use	VERB
ejpam-6927	65	19	in	in	ADP
ejpam-6927	65	20	the	the	DET
ejpam-6927	65	21	study	study	NOUN
ejpam-6927	65	22	to	to	PART
ejpam-6927	65	23	arrive	arrive	VERB
ejpam-6927	65	24	at	at	ADP
ejpam-6927	65	25	the	the	DET
ejpam-6927	65	26	main	main	ADJ
ejpam-6927	65	27	results	result	NOUN
ejpam-6927	65	28	of	of	ADP
ejpam-6927	65	29	the	the	DET
ejpam-6927	65	30	work	work	NOUN
ejpam-6927	65	31	.	.	PUNCT
ejpam-6927	66	1	to	to	PART
ejpam-6927	66	2	support	support	VERB
ejpam-6927	66	3	the	the	DET
ejpam-6927	66	4	primary	primary	ADJ
ejpam-6927	66	5	findings	finding	NOUN
ejpam-6927	66	6	,	,	PUNCT
ejpam-6927	66	7	the	the	DET
ejpam-6927	66	8	study	study	NOUN
ejpam-6927	66	9	offers	offer	VERB
ejpam-6927	66	10	graphical	graphical	ADJ
ejpam-6927	66	11	representations	representation	NOUN
ejpam-6927	66	12	and	and	CCONJ
ejpam-6927	66	13	numerical	numerical	ADJ
ejpam-6927	66	14	confirmation	confirmation	NOUN
ejpam-6927	66	15	.	.	PUNCT
ejpam-6927	67	1	2	2	X
ejpam-6927	67	2	.	.	NUM
ejpam-6927	67	3	preliminaries	preliminary	NOUN
ejpam-6927	67	4	and	and	CCONJ
ejpam-6927	67	5	definitions	definition	NOUN
ejpam-6927	67	6	of	of	ADP
ejpam-6927	67	7	q	q	NOUN
ejpam-6927	67	8	-	-	NOUN
ejpam-6927	67	9	calculus	calculus	NOUN
ejpam-6927	67	10	the	the	DET
ejpam-6927	67	11	following	follow	VERB
ejpam-6927	67	12	discussion	discussion	NOUN
ejpam-6927	67	13	will	will	AUX
ejpam-6927	67	14	commence	commence	VERB
ejpam-6927	67	15	with	with	ADP
ejpam-6927	67	16	a	a	DET
ejpam-6927	67	17	presentation	presentation	NOUN
ejpam-6927	67	18	of	of	ADP
ejpam-6927	67	19	these	these	DET
ejpam-6927	67	20	fundamental	fundamental	ADJ
ejpam-6927	67	21	definitions	definition	NOUN
ejpam-6927	67	22	.	.	PUNCT
ejpam-6927	68	1	definition	definition	NOUN
ejpam-6927	68	2	2	2	NUM
ejpam-6927	68	3	.	.	PUNCT
ejpam-6927	69	1	[	[	X
ejpam-6927	69	2	11	11	NUM
ejpam-6927	69	3	]	]	PUNCT
ejpam-6927	69	4	let	let	VERB
ejpam-6927	69	5	φ	φ	NOUN
ejpam-6927	69	6	:	:	PUNCT
ejpam-6927	70	1	[	[	X
ejpam-6927	70	2	ω1	ω1	PROPN
ejpam-6927	70	3	,	,	PUNCT
ejpam-6927	70	4	ω2	ω2	PROPN
ejpam-6927	70	5	]	]	PUNCT
ejpam-6927	70	6	→	→	SYM
ejpam-6927	70	7	r	r	NOUN
ejpam-6927	70	8	be	be	AUX
ejpam-6927	70	9	a	a	DET
ejpam-6927	70	10	continuous	continuous	ADJ
ejpam-6927	70	11	function	function	NOUN
ejpam-6927	70	12	,	,	PUNCT
ejpam-6927	70	13	and	and	CCONJ
ejpam-6927	70	14	let	let	VERB
ejpam-6927	70	15	c	c	PROPN
ejpam-6927	70	16	∈	∈	PROPN
ejpam-6927	70	17	[	[	X
ejpam-6927	70	18	ω1	ω1	PROPN
ejpam-6927	70	19	,	,	PUNCT
ejpam-6927	70	20	ω2	ω2	ADJ
ejpam-6927	70	21	]	]	PUNCT
ejpam-6927	70	22	.	.	PUNCT
ejpam-6927	71	1	then	then	ADV
ejpam-6927	71	2	the	the	DET
ejpam-6927	71	3	expression	expression	NOUN
ejpam-6927	71	4	ω1dqφ(c	ω1dqφ(c	NUM
ejpam-6927	71	5	)	)	PUNCT
ejpam-6927	71	6	=	=	SYM
ejpam-6927	71	7	φ(c)−	φ(c)−	ADJ
ejpam-6927	71	8	φ(qc+	φ(qc+	X
ejpam-6927	71	9	(	(	PUNCT
ejpam-6927	71	10	1−	1−	NUM
ejpam-6927	71	11	q)ω1	q)ω1	PROPN
ejpam-6927	71	12	)	)	PUNCT
ejpam-6927	71	13	(	(	PUNCT
ejpam-6927	71	14	1−	1−	NUM
ejpam-6927	71	15	q)(c−	q)(c−	NOUN
ejpam-6927	71	16	ω1	ω1	PROPN
ejpam-6927	71	17	)	)	PUNCT
ejpam-6927	71	18	,	,	PUNCT
ejpam-6927	71	19	c	c	PROPN
ejpam-6927	71	20	̸=	̸=	PROPN
ejpam-6927	71	21	ω1,ω1	ω1,ω1	PROPN
ejpam-6927	71	22	dqφ(ω1	dqφ(ω1	NOUN
ejpam-6927	71	23	)	)	PUNCT
ejpam-6927	71	24	=	=	VERB
ejpam-6927	72	1	lim	lim	PROPN
ejpam-6927	72	2	c→b1	c→b1	NOUN
ejpam-6927	72	3	ω1dqφ(c	ω1dqφ(c	NUM
ejpam-6927	72	4	)	)	PUNCT
ejpam-6927	72	5	is	be	AUX
ejpam-6927	72	6	called	call	VERB
ejpam-6927	72	7	the	the	DET
ejpam-6927	72	8	q	q	NOUN
ejpam-6927	72	9	-	-	NOUN
ejpam-6927	72	10	derivative	derivative	NOUN
ejpam-6927	72	11	on	on	ADP
ejpam-6927	72	12	[	[	X
ejpam-6927	72	13	ω1	ω1	PROPN
ejpam-6927	72	14	,	,	PUNCT
ejpam-6927	72	15	ω2	ω2	NUM
ejpam-6927	72	16	]	]	PUNCT
ejpam-6927	72	17	of	of	ADP
ejpam-6927	72	18	the	the	DET
ejpam-6927	72	19	function	function	NOUN
ejpam-6927	72	20	at	at	ADP
ejpam-6927	72	21	c.	c.	NOUN
ejpam-6927	72	22	we	we	PRON
ejpam-6927	72	23	call	call	VERB
ejpam-6927	72	24	φ	φ	NUM
ejpam-6927	72	25	q	q	ADJ
ejpam-6927	72	26	-	-	PUNCT
ejpam-6927	72	27	differentiable	differentiable	ADJ
ejpam-6927	72	28	on	on	ADP
ejpam-6927	72	29	[	[	X
ejpam-6927	72	30	ω1	ω1	PROPN
ejpam-6927	72	31	,	,	PUNCT
ejpam-6927	72	32	ω2	ω2	ADJ
ejpam-6927	72	33	]	]	PUNCT
ejpam-6927	72	34	if	if	SCONJ
ejpam-6927	72	35	ω1dqφ(c	ω1dqφ(c	NUM
ejpam-6927	72	36	)	)	PUNCT
ejpam-6927	72	37	exists	exist	VERB
ejpam-6927	72	38	for	for	ADP
ejpam-6927	72	39	all	all	DET
ejpam-6927	72	40	c	c	NOUN
ejpam-6927	72	41	∈	∈	PROPN
ejpam-6927	72	42	[	[	X
ejpam-6927	72	43	ω1	ω1	PROPN
ejpam-6927	72	44	,	,	PUNCT
ejpam-6927	72	45	ω2	ω2	PROPN
ejpam-6927	72	46	]	]	PUNCT
ejpam-6927	72	47	.	.	PUNCT
ejpam-6927	73	1	the	the	DET
ejpam-6927	73	2	q	q	PROPN
ejpam-6927	73	3	-	-	PUNCT
ejpam-6927	73	4	jackson	jackson	PROPN
ejpam-6927	73	5	integral	integral	ADJ
ejpam-6927	73	6	,	,	PUNCT
ejpam-6927	73	7	or	or	CCONJ
ejpam-6927	73	8	q	q	ADJ
ejpam-6927	73	9	-	-	ADJ
ejpam-6927	73	10	integral	integral	ADJ
ejpam-6927	73	11	(	(	PUNCT
ejpam-6927	73	12	[	[	X
ejpam-6927	73	13	22	22	NUM
ejpam-6927	73	14	]	]	PUNCT
ejpam-6927	73	15	)	)	PUNCT
ejpam-6927	73	16	,	,	PUNCT
ejpam-6927	73	17	was	be	AUX
ejpam-6927	73	18	found	find	VERB
ejpam-6927	73	19	by	by	ADP
ejpam-6927	73	20	jackson	jackson	PROPN
ejpam-6927	73	21	in	in	ADP
ejpam-6927	73	22	1910	1910	NUM
ejpam-6927	73	23	.	.	PUNCT
ejpam-6927	74	1	definition	definition	NOUN
ejpam-6927	74	2	3	3	NUM
ejpam-6927	74	3	.	.	PUNCT
ejpam-6927	75	1	[	[	X
ejpam-6927	75	2	11	11	NUM
ejpam-6927	75	3	]	]	X
ejpam-6927	75	4	if	if	SCONJ
ejpam-6927	75	5	φ	φ	PROPN
ejpam-6927	75	6	:	:	PUNCT
ejpam-6927	76	1	[	[	X
ejpam-6927	76	2	ω1	ω1	PROPN
ejpam-6927	76	3	,	,	PUNCT
ejpam-6927	76	4	ω2	ω2	PROPN
ejpam-6927	76	5	]	]	PUNCT
ejpam-6927	76	6	→	→	SYM
ejpam-6927	76	7	r	r	NOUN
ejpam-6927	76	8	is	be	AUX
ejpam-6927	76	9	a	a	DET
ejpam-6927	76	10	continuous	continuous	ADJ
ejpam-6927	76	11	function	function	NOUN
ejpam-6927	76	12	,	,	PUNCT
ejpam-6927	76	13	then	then	ADV
ejpam-6927	76	14	the	the	DET
ejpam-6927	76	15	q	q	NOUN
ejpam-6927	76	16	-	-	ADJ
ejpam-6927	76	17	integral	integral	ADJ
ejpam-6927	76	18	of	of	ADP
ejpam-6927	76	19	φ	φ	PROPN
ejpam-6927	76	20	on	on	ADP
ejpam-6927	76	21	[	[	X
ejpam-6927	76	22	ω1	ω1	PROPN
ejpam-6927	76	23	,	,	PUNCT
ejpam-6927	76	24	ω2	ω2	PROPN
ejpam-6927	76	25	]	]	PUNCT
ejpam-6927	76	26	is	be	AUX
ejpam-6927	76	27	defined	define	VERB
ejpam-6927	76	28	as:∫	as:∫	PROPN
ejpam-6927	76	29	c	c	PROPN
ejpam-6927	76	30	ω1	ω1	PROPN
ejpam-6927	76	31	φ(κ	φ(κ	PROPN
ejpam-6927	76	32	)	)	PUNCT
ejpam-6927	76	33	ω1dqκ	ω1dqκ	NOUN
ejpam-6927	76	34	=	=	SYM
ejpam-6927	76	35	(	(	PUNCT
ejpam-6927	76	36	c−	c−	X
ejpam-6927	76	37	ω1)(1−	ω1)(1−	ADJ
ejpam-6927	76	38	q	q	X
ejpam-6927	76	39	)	)	PUNCT
ejpam-6927	77	1	∞∑	∞∑	PROPN
ejpam-6927	77	2	k=0	k=0	PROPN
ejpam-6927	77	3	qkφ	qkφ	PROPN
ejpam-6927	77	4	(	(	PUNCT
ejpam-6927	77	5	qkc+	qkc+	PROPN
ejpam-6927	77	6	(	(	PUNCT
ejpam-6927	77	7	1−	1−	NUM
ejpam-6927	77	8	qk)ω1	qk)ω1	PROPN
ejpam-6927	77	9	)	)	PUNCT
ejpam-6927	77	10	,	,	PUNCT
ejpam-6927	77	11	m.	m.	NOUN
ejpam-6927	77	12	adil	adil	PROPN
ejpam-6927	77	13	khan	khan	PROPN
ejpam-6927	77	14	et	et	PROPN
ejpam-6927	77	15	al	al	PROPN
ejpam-6927	77	16	.	.	PUNCT
ejpam-6927	77	17	/	/	SYM
ejpam-6927	77	18	eur	eur	PROPN
ejpam-6927	77	19	.	.	PUNCT
ejpam-6927	78	1	j.	j.	PROPN
ejpam-6927	78	2	pure	pure	PROPN
ejpam-6927	78	3	appl	appl	PROPN
ejpam-6927	78	4	.	.	PROPN
ejpam-6927	78	5	math	math	PROPN
ejpam-6927	78	6	,	,	PUNCT
ejpam-6927	78	7	18	18	NUM
ejpam-6927	78	8	(	(	PUNCT
ejpam-6927	78	9	4	4	NUM
ejpam-6927	78	10	)	)	PUNCT
ejpam-6927	78	11	(	(	PUNCT
ejpam-6927	78	12	2025	2025	NUM
ejpam-6927	78	13	)	)	PUNCT
ejpam-6927	78	14	,	,	PUNCT
ejpam-6927	78	15	6927	6927	NUM
ejpam-6927	78	16	4	4	NUM
ejpam-6927	78	17	of	of	ADP
ejpam-6927	78	18	18	18	NUM
ejpam-6927	79	1	where	where	SCONJ
ejpam-6927	79	2	0	0	NUM
ejpam-6927	79	3	<	<	X
ejpam-6927	79	4	q	q	X
ejpam-6927	79	5	<	<	X
ejpam-6927	79	6	1	1	NUM
ejpam-6927	79	7	and	and	CCONJ
ejpam-6927	79	8	c	c	NOUN
ejpam-6927	79	9	∈	∈	PROPN
ejpam-6927	80	1	[	[	X
ejpam-6927	80	2	ω1	ω1	PROPN
ejpam-6927	80	3	,	,	PUNCT
ejpam-6927	80	4	ω2	ω2	ADJ
ejpam-6927	80	5	]	]	PUNCT
ejpam-6927	80	6	.	.	PUNCT
ejpam-6927	81	1	there	there	PRON
ejpam-6927	81	2	are	be	VERB
ejpam-6927	81	3	several	several	ADJ
ejpam-6927	81	4	important	important	ADJ
ejpam-6927	81	5	properties	property	NOUN
ejpam-6927	81	6	of	of	ADP
ejpam-6927	81	7	q	q	NOUN
ejpam-6927	81	8	-	-	ADJ
ejpam-6927	81	9	integral	integral	ADJ
ejpam-6927	81	10	,	,	PUNCT
ejpam-6927	81	11	for	for	ADP
ejpam-6927	81	12	example	example	NOUN
ejpam-6927	81	13	interval	interval	NOUN
ejpam-6927	81	14	addition	addition	NOUN
ejpam-6927	81	15	,	,	PUNCT
ejpam-6927	81	16	linearity	linearity	NOUN
ejpam-6927	81	17	,	,	PUNCT
ejpam-6927	81	18	triangular	triangular	NOUN
ejpam-6927	81	19	,	,	PUNCT
ejpam-6927	81	20	and	and	CCONJ
ejpam-6927	81	21	monotonicity	monotonicity	NOUN
ejpam-6927	81	22	property	property	NOUN
ejpam-6927	81	23	.	.	PUNCT
ejpam-6927	82	1	theorem	theorem	NOUN
ejpam-6927	82	2	1	1	NUM
ejpam-6927	82	3	.	.	PUNCT
ejpam-6927	83	1	[	[	X
ejpam-6927	83	2	11	11	NUM
ejpam-6927	83	3	]	]	X
ejpam-6927	83	4	if	if	SCONJ
ejpam-6927	83	5	φ	φ	PROPN
ejpam-6927	83	6	:	:	PUNCT
ejpam-6927	84	1	[	[	X
ejpam-6927	84	2	ω1	ω1	PROPN
ejpam-6927	84	3	,	,	PUNCT
ejpam-6927	84	4	ω2	ω2	PROPN
ejpam-6927	84	5	]	]	PUNCT
ejpam-6927	84	6	→	→	SYM
ejpam-6927	84	7	r	r	NOUN
ejpam-6927	84	8	is	be	AUX
ejpam-6927	84	9	a	a	DET
ejpam-6927	84	10	continuous	continuous	ADJ
ejpam-6927	84	11	function	function	NOUN
ejpam-6927	84	12	.	.	PUNCT
ejpam-6927	85	1	then∫	then∫	NOUN
ejpam-6927	86	1	c	c	PUNCT
ejpam-6927	86	2	ξ	ξ	X
ejpam-6927	86	3	ω1dqφ(c)ω1dqκ	ω1dqφ(c)ω1dqκ	PROPN
ejpam-6927	86	4	=	=	SYM
ejpam-6927	86	5	φ(c)−	φ(c)−	PROPN
ejpam-6927	86	6	φ(ξ	φ(ξ	PROPN
ejpam-6927	86	7	)	)	PUNCT
ejpam-6927	86	8	where	where	SCONJ
ejpam-6927	86	9	ξ	ξ	PROPN
ejpam-6927	86	10	∈	∈	PROPN
ejpam-6927	86	11	(	(	PUNCT
ejpam-6927	86	12	ω1	ω1	PROPN
ejpam-6927	86	13	,	,	PUNCT
ejpam-6927	86	14	c	c	NOUN
ejpam-6927	86	15	)	)	PUNCT
ejpam-6927	86	16	.	.	PUNCT
ejpam-6927	87	1	theorem	theorem	NOUN
ejpam-6927	87	2	2	2	NUM
ejpam-6927	87	3	.	.	PUNCT
ejpam-6927	88	1	[	[	X
ejpam-6927	88	2	23	23	NUM
ejpam-6927	88	3	]	]	X
ejpam-6927	88	4	if	if	SCONJ
ejpam-6927	88	5	φ	φ	PROPN
ejpam-6927	88	6	,	,	PUNCT
ejpam-6927	88	7	ω	ω	NOUN
ejpam-6927	88	8	:	:	PUNCT
ejpam-6927	89	1	[	[	X
ejpam-6927	89	2	ω1	ω1	PROPN
ejpam-6927	89	3	,	,	PUNCT
ejpam-6927	89	4	ω2	ω2	ADJ
ejpam-6927	89	5	]	]	PUNCT
ejpam-6927	89	6	→	→	SYM
ejpam-6927	89	7	r	r	NOUN
ejpam-6927	89	8	are	be	AUX
ejpam-6927	89	9	two	two	NUM
ejpam-6927	89	10	continuous	continuous	ADJ
ejpam-6927	89	11	functions	function	NOUN
ejpam-6927	89	12	and	and	CCONJ
ejpam-6927	89	13	suppose	suppose	VERB
ejpam-6927	89	14	φ(κ	φ(κ	NOUN
ejpam-6927	89	15	)	)	PUNCT
ejpam-6927	89	16	≤	≤	NOUN
ejpam-6927	89	17	ω(κ	ω(κ	NUM
ejpam-6927	89	18	)	)	PUNCT
ejpam-6927	89	19	,	,	PUNCT
ejpam-6927	89	20	∀κ	∀κ	X
ejpam-6927	89	21	∈	∈	X
ejpam-6927	90	1	[	[	X
ejpam-6927	90	2	ω1	ω1	PROPN
ejpam-6927	90	3	,	,	PUNCT
ejpam-6927	90	4	ω2	ω2	ADJ
ejpam-6927	90	5	]	]	PUNCT
ejpam-6927	90	6	.	.	PUNCT
ejpam-6927	91	1	then	then	ADV
ejpam-6927	91	2	we	we	PRON
ejpam-6927	91	3	have∫	have∫	VERB
ejpam-6927	91	4	c	c	PROPN
ejpam-6927	91	5	ω1	ω1	PROPN
ejpam-6927	91	6	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	91	7	≤	≤	NUM
ejpam-6927	91	8	∫	∫	PROPN
ejpam-6927	91	9	c	c	PROPN
ejpam-6927	91	10	ω1	ω1	PROPN
ejpam-6927	91	11	ω(κ	ω(κ	PROPN
ejpam-6927	91	12	)	)	PUNCT
ejpam-6927	91	13	ω1dqκ	ω1dqκ	NOUN
ejpam-6927	91	14	.	.	PUNCT
ejpam-6927	91	15	theorem	theorem	VERB
ejpam-6927	91	16	3	3	NUM
ejpam-6927	91	17	.	.	PUNCT
ejpam-6927	92	1	[	[	X
ejpam-6927	92	2	11	11	NUM
ejpam-6927	92	3	]	]	X
ejpam-6927	92	4	if	if	SCONJ
ejpam-6927	92	5	φ	φ	PROPN
ejpam-6927	92	6	:	:	PUNCT
ejpam-6927	93	1	[	[	X
ejpam-6927	93	2	ω1	ω1	PROPN
ejpam-6927	93	3	,	,	PUNCT
ejpam-6927	93	4	ω2	ω2	PROPN
ejpam-6927	93	5	]	]	PUNCT
ejpam-6927	93	6	→	→	SYM
ejpam-6927	93	7	r	r	NOUN
ejpam-6927	93	8	is	be	AUX
ejpam-6927	93	9	a	a	DET
ejpam-6927	93	10	continuous	continuous	ADJ
ejpam-6927	93	11	function	function	NOUN
ejpam-6927	93	12	.	.	PUNCT
ejpam-6927	94	1	then	then	ADV
ejpam-6927	94	2	we	we	PRON
ejpam-6927	94	3	have	have	VERB
ejpam-6927	94	4	ω1dq	ω1dq	NUM
ejpam-6927	94	5	∫	∫	PROPN
ejpam-6927	94	6	c	c	PROPN
ejpam-6927	94	7	ω1	ω1	PROPN
ejpam-6927	94	8	φ(κ)ω1dqκ	φ(κ)ω1dqκ	NOUN
ejpam-6927	94	9	=	=	PUNCT
ejpam-6927	94	10	φ(c);∫	φ(c);∫	NOUN
ejpam-6927	94	11	c	c	NOUN
ejpam-6927	94	12	ξ	ξ	X
ejpam-6927	94	13	ω1dqφ(κ)ω1dqκ	ω1dqφ(κ)ω1dqκ	X
ejpam-6927	94	14	=	=	SYM
ejpam-6927	94	15	φ(c)−	φ(c)−	PROPN
ejpam-6927	94	16	φ(ξ	φ(ξ	PROPN
ejpam-6927	94	17	)	)	PUNCT
ejpam-6927	94	18	where	where	SCONJ
ejpam-6927	94	19	ξ	ξ	PROPN
ejpam-6927	94	20	∈	∈	PROPN
ejpam-6927	94	21	(	(	PUNCT
ejpam-6927	94	22	ω1	ω1	PROPN
ejpam-6927	94	23	,	,	PUNCT
ejpam-6927	94	24	c	c	NOUN
ejpam-6927	94	25	)	)	PUNCT
ejpam-6927	94	26	.	.	PUNCT
ejpam-6927	95	1	theorem	theorem	ADJ
ejpam-6927	95	2	4	4	NUM
ejpam-6927	95	3	.	.	PUNCT
ejpam-6927	96	1	[	[	X
ejpam-6927	96	2	11	11	NUM
ejpam-6927	96	3	]	]	X
ejpam-6927	96	4	if	if	SCONJ
ejpam-6927	96	5	φ	φ	PROPN
ejpam-6927	96	6	,	,	PUNCT
ejpam-6927	96	7	ω	ω	NOUN
ejpam-6927	96	8	:	:	PUNCT
ejpam-6927	96	9	[	[	X
ejpam-6927	96	10	ω1	ω1	PROPN
ejpam-6927	96	11	,	,	PUNCT
ejpam-6927	96	12	ω2	ω2	ADJ
ejpam-6927	96	13	]	]	PUNCT
ejpam-6927	96	14	→	→	SYM
ejpam-6927	96	15	r	r	NOUN
ejpam-6927	96	16	are	be	AUX
ejpam-6927	96	17	two	two	NUM
ejpam-6927	96	18	continuous	continuous	ADJ
ejpam-6927	96	19	functions	function	NOUN
ejpam-6927	96	20	and	and	CCONJ
ejpam-6927	96	21	suppose	suppose	VERB
ejpam-6927	96	22	κ	κ	PROPN
ejpam-6927	96	23	∈	∈	PROPN
ejpam-6927	96	24	r	r	PROPN
ejpam-6927	96	25	,	,	PUNCT
ejpam-6927	96	26	c	c	PROPN
ejpam-6927	96	27	∈	∈	PROPN
ejpam-6927	97	1	[	[	X
ejpam-6927	97	2	ω1	ω1	PROPN
ejpam-6927	97	3	,	,	PUNCT
ejpam-6927	97	4	ω2	ω2	NOUN
ejpam-6927	97	5	]	]	PUNCT
ejpam-6927	97	6	,	,	PUNCT
ejpam-6927	97	7	and	and	CCONJ
ejpam-6927	97	8	ξ	ξ	X
ejpam-6927	97	9	∈	∈	PROPN
ejpam-6927	97	10	(	(	PUNCT
ejpam-6927	97	11	ω1	ω1	PROPN
ejpam-6927	97	12	,	,	PUNCT
ejpam-6927	97	13	c	c	NOUN
ejpam-6927	97	14	)	)	PUNCT
ejpam-6927	97	15	.	.	PUNCT
ejpam-6927	98	1	then	then	ADV
ejpam-6927	98	2	we	we	PRON
ejpam-6927	98	3	have∫	have∫	VERB
ejpam-6927	98	4	c	c	PROPN
ejpam-6927	98	5	ω1	ω1	PROPN
ejpam-6927	98	6	[	[	X
ejpam-6927	98	7	φ(κ	φ(κ	ADV
ejpam-6927	98	8	)	)	PUNCT
ejpam-6927	98	9	+	+	NUM
ejpam-6927	98	10	ω(κ)]ω1dqκ	ω(κ)]ω1dqκ	NOUN
ejpam-6927	98	11	=	=	SYM
ejpam-6927	98	12	∫	∫	PROPN
ejpam-6927	98	13	c	c	PROPN
ejpam-6927	98	14	ω1	ω1	PROPN
ejpam-6927	98	15	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	98	16	+	+	CCONJ
ejpam-6927	98	17	∫	∫	PROPN
ejpam-6927	98	18	c	c	PROPN
ejpam-6927	98	19	ω1	ω1	PROPN
ejpam-6927	98	20	ω(κ)ω1dqκ;∫	ω(κ)ω1dqκ;∫	PROPN
ejpam-6927	98	21	c	c	PROPN
ejpam-6927	98	22	ω1	ω1	PROPN
ejpam-6927	98	23	κφ(κ)ω1dqκ	κφ(κ)ω1dqκ	PROPN
ejpam-6927	98	24	=	=	SYM
ejpam-6927	98	25	κ	κ	PROPN
ejpam-6927	98	26	∫	∫	PROPN
ejpam-6927	98	27	c	c	PROPN
ejpam-6927	98	28	ω1	ω1	PROPN
ejpam-6927	98	29	φ(κ)ω1dqκ;∫	φ(κ)ω1dqκ;∫	PROPN
ejpam-6927	98	30	c	c	PROPN
ejpam-6927	98	31	ξ	ξ	X
ejpam-6927	98	32	φ(κ)ω1dqω(κ)ω1dqκ	φ(κ)ω1dqω(κ)ω1dqκ	PROPN
ejpam-6927	98	33	=	=	SYM
ejpam-6927	98	34	φ(c)ω(c)−	φ(c)ω(c)−	ADJ
ejpam-6927	98	35	φ(ξ)ω(ξ)−	φ(ξ)ω(ξ)−	NOUN
ejpam-6927	98	36	∫	∫	PROPN
ejpam-6927	98	37	c	c	PROPN
ejpam-6927	98	38	ξ	ξ	PROPN
ejpam-6927	98	39	ω(qκ	ω(qκ	PROPN
ejpam-6927	98	40	+	+	CCONJ
ejpam-6927	98	41	(	(	PUNCT
ejpam-6927	98	42	1−	1−	NUM
ejpam-6927	98	43	q)ω1)ω1dqφ(κ)ω1dqκ	q)ω1)ω1dqφ(κ)ω1dqκ	NOUN
ejpam-6927	98	44	.	.	PROPN
ejpam-6927	99	1	3	3	X
ejpam-6927	99	2	.	.	X
ejpam-6927	99	3	main	main	ADJ
ejpam-6927	99	4	results	result	NOUN
ejpam-6927	99	5	the	the	DET
ejpam-6927	99	6	fundamental	fundamental	ADJ
ejpam-6927	99	7	results	result	NOUN
ejpam-6927	99	8	will	will	AUX
ejpam-6927	99	9	be	be	AUX
ejpam-6927	99	10	established	establish	VERB
ejpam-6927	99	11	through	through	ADP
ejpam-6927	99	12	the	the	DET
ejpam-6927	99	13	utilization	utilization	NOUN
ejpam-6927	99	14	of	of	ADP
ejpam-6927	99	15	the	the	DET
ejpam-6927	99	16	following	follow	VERB
ejpam-6927	99	17	lemma	lemma	PROPN
ejpam-6927	99	18	.	.	PUNCT
ejpam-6927	100	1	m.	m.	PROPN
ejpam-6927	100	2	adil	adil	PROPN
ejpam-6927	100	3	khan	khan	PROPN
ejpam-6927	100	4	et	et	PROPN
ejpam-6927	100	5	al	al	PROPN
ejpam-6927	100	6	.	.	PUNCT
ejpam-6927	100	7	/	/	SYM
ejpam-6927	100	8	eur	eur	PROPN
ejpam-6927	100	9	.	.	PUNCT
ejpam-6927	101	1	j.	j.	PROPN
ejpam-6927	101	2	pure	pure	PROPN
ejpam-6927	101	3	appl	appl	PROPN
ejpam-6927	101	4	.	.	PROPN
ejpam-6927	101	5	math	math	PROPN
ejpam-6927	101	6	,	,	PUNCT
ejpam-6927	101	7	18	18	NUM
ejpam-6927	101	8	(	(	PUNCT
ejpam-6927	101	9	4	4	NUM
ejpam-6927	101	10	)	)	PUNCT
ejpam-6927	101	11	(	(	PUNCT
ejpam-6927	101	12	2025	2025	NUM
ejpam-6927	101	13	)	)	PUNCT
ejpam-6927	101	14	,	,	PUNCT
ejpam-6927	101	15	6927	6927	NUM
ejpam-6927	101	16	5	5	NUM
ejpam-6927	101	17	of	of	ADP
ejpam-6927	101	18	18	18	NUM
ejpam-6927	101	19	lemma	lemma	PROPN
ejpam-6927	101	20	1	1	NUM
ejpam-6927	101	21	.	.	PUNCT
ejpam-6927	102	1	[	[	X
ejpam-6927	102	2	24	24	NUM
ejpam-6927	102	3	,	,	PUNCT
ejpam-6927	102	4	25	25	NUM
ejpam-6927	102	5	]	]	PUNCT
ejpam-6927	102	6	let	let	VERB
ejpam-6927	102	7	g	g	NOUN
ejpam-6927	102	8	be	be	AUX
ejpam-6927	102	9	the	the	DET
ejpam-6927	102	10	green	green	ADJ
ejpam-6927	102	11	function	function	NOUN
ejpam-6927	102	12	defined	define	VERB
ejpam-6927	102	13	on	on	ADP
ejpam-6927	102	14	[	[	X
ejpam-6927	102	15	ω1	ω1	PROPN
ejpam-6927	102	16	,	,	PUNCT
ejpam-6927	102	17	ω2]×	ω2]×	PROPN
ejpam-6927	102	18	[	[	X
ejpam-6927	102	19	ω1	ω1	PROPN
ejpam-6927	102	20	,	,	PUNCT
ejpam-6927	102	21	ω2	ω2	NUM
ejpam-6927	102	22	]	]	PUNCT
ejpam-6927	102	23	by	by	ADP
ejpam-6927	102	24	g(κ	g(κ	PROPN
ejpam-6927	102	25	,	,	PUNCT
ejpam-6927	102	26	ℓ	ℓ	NUM
ejpam-6927	102	27	)	)	PUNCT
ejpam-6927	102	28	=	=	SYM
ejpam-6927	102	29	{	{	PUNCT
ejpam-6927	102	30	ω1	ω1	PROPN
ejpam-6927	102	31	−	−	PROPN
ejpam-6927	102	32	ℓ	ℓ	PROPN
ejpam-6927	102	33	,	,	PUNCT
ejpam-6927	102	34	ω1	ω1	PROPN
ejpam-6927	102	35	≤	≤	NUM
ejpam-6927	102	36	ℓ	ℓ	PROPN
ejpam-6927	102	37	≤	≤	NUM
ejpam-6927	102	38	κ	κ	PROPN
ejpam-6927	102	39	,	,	PUNCT
ejpam-6927	102	40	ω1	ω1	PROPN
ejpam-6927	102	41	−	−	PROPN
ejpam-6927	102	42	κ	κ	PROPN
ejpam-6927	102	43	,	,	PUNCT
ejpam-6927	102	44	κ	κ	PROPN
ejpam-6927	102	45	≤	≤	PROPN
ejpam-6927	102	46	ℓ	ℓ	NOUN
ejpam-6927	102	47	≤	≤	NOUN
ejpam-6927	102	48	ω2	ω2	ADJ
ejpam-6927	102	49	.	.	PUNCT
ejpam-6927	103	1	then	then	ADV
ejpam-6927	103	2	any	any	DET
ejpam-6927	103	3	φ	φ	PROPN
ejpam-6927	103	4	∈	∈	PROPN
ejpam-6927	103	5	c2([ω1	c2([ω1	PROPN
ejpam-6927	103	6	,	,	PUNCT
ejpam-6927	103	7	ω2	ω2	PROPN
ejpam-6927	103	8	]	]	PUNCT
ejpam-6927	103	9	)	)	PUNCT
ejpam-6927	103	10	can	can	AUX
ejpam-6927	103	11	be	be	AUX
ejpam-6927	103	12	expressed	express	VERB
ejpam-6927	103	13	as	as	ADP
ejpam-6927	103	14	φ(κ	φ(κ	NOUN
ejpam-6927	103	15	)	)	PUNCT
ejpam-6927	103	16	=	=	SYM
ejpam-6927	103	17	φ(ω1	φ(ω1	X
ejpam-6927	103	18	)	)	PUNCT
ejpam-6927	103	19	+	+	CCONJ
ejpam-6927	103	20	(	(	PUNCT
ejpam-6927	103	21	κ	κ	X
ejpam-6927	103	22	−	−	PROPN
ejpam-6927	103	23	ω1)φ	ω1)φ	NOUN
ejpam-6927	103	24	′(ω2	′(ω2	NUM
ejpam-6927	103	25	)	)	PUNCT
ejpam-6927	104	1	+	+	CCONJ
ejpam-6927	104	2	∫	∫	PROPN
ejpam-6927	104	3	ω2	ω2	PROPN
ejpam-6927	104	4	ω1	ω1	PROPN
ejpam-6927	104	5	g(κ	g(κ	PROPN
ejpam-6927	104	6	,	,	PUNCT
ejpam-6927	104	7	ℓ)φ′′(ℓ)dℓ.	ℓ)φ′′(ℓ)dℓ.	PROPN
ejpam-6927	104	8	(	(	PUNCT
ejpam-6927	104	9	2	2	NUM
ejpam-6927	104	10	)	)	PUNCT
ejpam-6927	104	11	theorem	theorem	NOUN
ejpam-6927	104	12	5	5	NUM
ejpam-6927	104	13	.	.	PUNCT
ejpam-6927	105	1	let	let	VERB
ejpam-6927	105	2	φ	φ	PROPN
ejpam-6927	105	3	∈	∈	PROPN
ejpam-6927	105	4	c2[ω1	c2[ω1	PROPN
ejpam-6927	105	5	,	,	PUNCT
ejpam-6927	105	6	ω2	ω2	NOUN
ejpam-6927	105	7	]	]	PUNCT
ejpam-6927	105	8	such	such	ADJ
ejpam-6927	105	9	that	that	SCONJ
ejpam-6927	105	10	φ′′	φ′′	PROPN
ejpam-6927	105	11	is	be	AUX
ejpam-6927	105	12	convex	convex	ADJ
ejpam-6927	105	13	and	and	CCONJ
ejpam-6927	105	14	0	0	NUM
ejpam-6927	105	15	<	<	X
ejpam-6927	105	16	q	q	X
ejpam-6927	105	17	<	<	X
ejpam-6927	105	18	1	1	NUM
ejpam-6927	105	19	.	.	PUNCT
ejpam-6927	106	1	then	then	ADV
ejpam-6927	106	2	1	1	NUM
ejpam-6927	106	3	ω2	ω2	ADJ
ejpam-6927	106	4	−	−	PROPN
ejpam-6927	106	5	ω1	ω1	PROPN
ejpam-6927	106	6	∫	∫	PROPN
ejpam-6927	106	7	ω2	ω2	PROPN
ejpam-6927	106	8	ω1	ω1	PROPN
ejpam-6927	106	9	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	106	10	−	−	PROPN
ejpam-6927	106	11	φ	φ	PROPN
ejpam-6927	106	12	(	(	PUNCT
ejpam-6927	106	13	qω1	qω1	PROPN
ejpam-6927	106	14	+	+	CCONJ
ejpam-6927	106	15	ω2	ω2	PROPN
ejpam-6927	106	16	q	q	X
ejpam-6927	107	1	+	+	NUM
ejpam-6927	107	2	1	1	NUM
ejpam-6927	107	3	)	)	PUNCT
ejpam-6927	107	4	≤	≤	NUM
ejpam-6927	107	5	1	1	NUM
ejpam-6927	107	6	ω2	ω2	NUM
ejpam-6927	107	7	−	−	PROPN
ejpam-6927	107	8	ω1	ω1	PROPN
ejpam-6927	107	9	[	[	PUNCT
ejpam-6927	107	10	1	1	NUM
ejpam-6927	107	11	6	6	NUM
ejpam-6927	107	12	(	(	PUNCT
ejpam-6927	107	13	φ′′(ω2)−	φ′′(ω2)−	NOUN
ejpam-6927	107	14	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	107	15	)	)	PUNCT
ejpam-6927	107	16	)	)	PUNCT
ejpam-6927	108	1	(	(	PUNCT
ejpam-6927	108	2	(	(	PUNCT
ejpam-6927	108	3	ω2	ω2	ADJ
ejpam-6927	108	4	−	−	PROPN
ejpam-6927	108	5	ω1	ω1	PROPN
ejpam-6927	108	6	)	)	PUNCT
ejpam-6927	108	7	3	3	NUM
ejpam-6927	108	8	(	(	PUNCT
ejpam-6927	108	9	1	1	NUM
ejpam-6927	108	10	+	+	NUM
ejpam-6927	108	11	q)(1	q)(1	X
ejpam-6927	108	12	+	+	X
ejpam-6927	108	13	q2	q2	NOUN
ejpam-6927	108	14	)	)	PUNCT
ejpam-6927	108	15	)	)	PUNCT
ejpam-6927	109	1	−	−	PROPN
ejpam-6927	109	2	(	(	PUNCT
ejpam-6927	109	3	φ′′(ω2	φ′′(ω2	X
ejpam-6927	109	4	)	)	PUNCT
ejpam-6927	109	5	+	+	CCONJ
ejpam-6927	109	6	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	109	7	)	)	PUNCT
ejpam-6927	109	8	2	2	NUM
ejpam-6927	109	9	)	)	PUNCT
ejpam-6927	109	10	(	(	PUNCT
ejpam-6927	109	11	(	(	PUNCT
ejpam-6927	109	12	ω2	ω2	ADJ
ejpam-6927	109	13	−	−	PROPN
ejpam-6927	109	14	ω1	ω1	PROPN
ejpam-6927	109	15	)	)	PUNCT
ejpam-6927	109	16	1	1	NUM
ejpam-6927	110	1	+	+	CCONJ
ejpam-6927	110	2	q	q	X
ejpam-6927	110	3	)	)	PUNCT
ejpam-6927	110	4	ω2	ω2	ADJ
ejpam-6927	110	5	1	1	NUM
ejpam-6927	110	6	−	−	PROPN
ejpam-6927	110	7	(	(	PUNCT
ejpam-6927	110	8	2φ′′(ω2	2φ′′(ω2	NUM
ejpam-6927	110	9	)	)	PUNCT
ejpam-6927	111	1	+	+	PUNCT
ejpam-6927	111	2	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	111	3	)	)	PUNCT
ejpam-6927	111	4	6	6	NUM
ejpam-6927	111	5	)	)	PUNCT
ejpam-6927	111	6	ω3	ω3	NOUN
ejpam-6927	111	7	1	1	NUM
ejpam-6927	111	8	−	−	PROPN
ejpam-6927	111	9	(	(	PUNCT
ejpam-6927	111	10	φ′′(ω2	φ′′(ω2	X
ejpam-6927	111	11	)	)	PUNCT
ejpam-6927	111	12	+	+	CCONJ
ejpam-6927	111	13	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	111	14	)	)	PUNCT
ejpam-6927	111	15	6	6	NUM
ejpam-6927	111	16	)	)	PUNCT
ejpam-6927	111	17	(	(	PUNCT
ejpam-6927	111	18	(	(	PUNCT
ejpam-6927	111	19	qω1	qω1	NOUN
ejpam-6927	111	20	+	+	CCONJ
ejpam-6927	111	21	ω2	ω2	NUM
ejpam-6927	111	22	)	)	PUNCT
ejpam-6927	111	23	(	(	PUNCT
ejpam-6927	111	24	1	1	NUM
ejpam-6927	111	25	+	+	CCONJ
ejpam-6927	111	26	q	q	NOUN
ejpam-6927	111	27	)	)	PUNCT
ejpam-6927	111	28	)	)	PUNCT
ejpam-6927	111	29	3	3	NUM
ejpam-6927	112	1	+	+	CCONJ
ejpam-6927	112	2	(	(	PUNCT
ejpam-6927	112	3	φ′′(ω2)ω1	φ′′(ω2)ω1	NOUN
ejpam-6927	112	4	−	−	PROPN
ejpam-6927	112	5	φ′′(ω1)ω2	φ′′(ω1)ω2	NOUN
ejpam-6927	112	6	2	2	NUM
ejpam-6927	112	7	)	)	PUNCT
ejpam-6927	112	8	(	(	PUNCT
ejpam-6927	112	9	(	(	PUNCT
ejpam-6927	112	10	qω1	qω1	NOUN
ejpam-6927	112	11	+	+	CCONJ
ejpam-6927	112	12	ω2	ω2	NUM
ejpam-6927	112	13	)	)	PUNCT
ejpam-6927	112	14	(	(	PUNCT
ejpam-6927	112	15	1	1	NUM
ejpam-6927	112	16	+	+	CCONJ
ejpam-6927	112	17	q	q	NOUN
ejpam-6927	112	18	)	)	PUNCT
ejpam-6927	112	19	)	)	PUNCT
ejpam-6927	112	20	2	2	NUM
ejpam-6927	112	21	+	+	CCONJ
ejpam-6927	112	22	ω1ω2φ	ω1ω2φ	X
ejpam-6927	112	23	′′(ω1)(ω2	′′(ω1)(ω2	X
ejpam-6927	112	24	−	−	PROPN
ejpam-6927	112	25	ω1	ω1	PROPN
ejpam-6927	112	26	)	)	PUNCT
ejpam-6927	112	27	(	(	PUNCT
ejpam-6927	112	28	1	1	NUM
ejpam-6927	112	29	+	+	CCONJ
ejpam-6927	112	30	q	q	X
ejpam-6927	112	31	)	)	PUNCT
ejpam-6927	113	1	+	+	CCONJ
ejpam-6927	113	2	φ′′(ω1)ω	φ′′(ω1)ω	PROPN
ejpam-6927	113	3	2	2	NUM
ejpam-6927	113	4	1ω2	1ω2	NUM
ejpam-6927	113	5	+	+	CCONJ
ejpam-6927	113	6	1	1	NUM
ejpam-6927	113	7	2	2	NUM
ejpam-6927	113	8	(	(	PUNCT
ejpam-6927	113	9	(	(	PUNCT
ejpam-6927	113	10	ω2	ω2	ADJ
ejpam-6927	113	11	−	−	PROPN
ejpam-6927	113	12	ω1	ω1	PROPN
ejpam-6927	113	13	)	)	PUNCT
ejpam-6927	113	14	3	3	NUM
ejpam-6927	113	15	1	1	NUM
ejpam-6927	113	16	+	+	CCONJ
ejpam-6927	113	17	q	q	ADJ
ejpam-6927	113	18	+	+	NUM
ejpam-6927	113	19	q2	q2	NOUN
ejpam-6927	113	20	)	)	PUNCT
ejpam-6927	113	21	φ′′(ω1	φ′′(ω1	ADV
ejpam-6927	113	22	)	)	PUNCT
ejpam-6927	113	23	]	]	PUNCT
ejpam-6927	113	24	.	.	PUNCT
ejpam-6927	114	1	(	(	PUNCT
ejpam-6927	114	2	3	3	X
ejpam-6927	114	3	)	)	PUNCT
ejpam-6927	114	4	proof	proof	NOUN
ejpam-6927	114	5	.	.	PUNCT
ejpam-6927	115	1	if	if	SCONJ
ejpam-6927	115	2	we	we	PRON
ejpam-6927	115	3	set	set	VERB
ejpam-6927	115	4	κ	κ	NOUN
ejpam-6927	115	5	=	=	SYM
ejpam-6927	115	6	qω1+ω2	qω1+ω2	PROPN
ejpam-6927	115	7	1+q	1+q	NUM
ejpam-6927	115	8	in	in	ADP
ejpam-6927	115	9	(	(	PUNCT
ejpam-6927	115	10	2	2	NUM
ejpam-6927	115	11	)	)	PUNCT
ejpam-6927	115	12	,	,	PUNCT
ejpam-6927	115	13	then	then	ADV
ejpam-6927	115	14	we	we	PRON
ejpam-6927	115	15	get	get	VERB
ejpam-6927	115	16	φ	φ	NUM
ejpam-6927	115	17	(	(	PUNCT
ejpam-6927	115	18	qω1	qω1	PROPN
ejpam-6927	115	19	+	+	PROPN
ejpam-6927	115	20	ω2	ω2	PROPN
ejpam-6927	115	21	q	q	X
ejpam-6927	116	1	+	+	NUM
ejpam-6927	116	2	1	1	X
ejpam-6927	116	3	)	)	PUNCT
ejpam-6927	116	4	=	=	NOUN
ejpam-6927	116	5	φ(ω1	φ(ω1	X
ejpam-6927	116	6	)	)	PUNCT
ejpam-6927	116	7	+	+	CCONJ
ejpam-6927	116	8	(	(	PUNCT
ejpam-6927	116	9	qω1	qω1	PROPN
ejpam-6927	116	10	+	+	CCONJ
ejpam-6927	116	11	ω2	ω2	PROPN
ejpam-6927	116	12	q	q	PROPN
ejpam-6927	117	1	+	+	NUM
ejpam-6927	117	2	1	1	NUM
ejpam-6927	117	3	−	−	PROPN
ejpam-6927	117	4	ω1	ω1	PROPN
ejpam-6927	117	5	)	)	PUNCT
ejpam-6927	117	6	φ	φ	PROPN
ejpam-6927	117	7	′	′	NUM
ejpam-6927	118	1	(	(	PUNCT
ejpam-6927	118	2	ω2	ω2	ADJ
ejpam-6927	118	3	)	)	PUNCT
ejpam-6927	119	1	+	+	NUM
ejpam-6927	119	2	∫	∫	PROPN
ejpam-6927	119	3	ω2	ω2	PROPN
ejpam-6927	119	4	ω1	ω1	PROPN
ejpam-6927	119	5	g	g	PROPN
ejpam-6927	119	6	(	(	PUNCT
ejpam-6927	119	7	qω1	qω1	PROPN
ejpam-6927	119	8	+	+	CCONJ
ejpam-6927	119	9	ω2	ω2	PROPN
ejpam-6927	119	10	q	q	PROPN
ejpam-6927	119	11	+	+	NUM
ejpam-6927	119	12	1	1	NUM
ejpam-6927	119	13	,	,	PUNCT
ejpam-6927	119	14	ℓ	ℓ	PROPN
ejpam-6927	119	15	)	)	PUNCT
ejpam-6927	119	16	φ	φ	PROPN
ejpam-6927	119	17	′′	′′	PROPN
ejpam-6927	119	18	dℓ	dℓ	NOUN
ejpam-6927	119	19	=	=	SYM
ejpam-6927	119	20	φ(ω1	φ(ω1	X
ejpam-6927	119	21	)	)	PUNCT
ejpam-6927	119	22	+	+	CCONJ
ejpam-6927	119	23	ω2	ω2	ADJ
ejpam-6927	119	24	−	−	PROPN
ejpam-6927	119	25	ω1	ω1	PROPN
ejpam-6927	119	26	q	q	PROPN
ejpam-6927	119	27	+	+	PROPN
ejpam-6927	119	28	1	1	NUM
ejpam-6927	119	29	φ′(ω2	φ′(ω2	PROPN
ejpam-6927	119	30	)	)	PUNCT
ejpam-6927	120	1	+	+	CCONJ
ejpam-6927	120	2	∫	∫	PROPN
ejpam-6927	120	3	ω2	ω2	PROPN
ejpam-6927	120	4	ω1	ω1	PROPN
ejpam-6927	120	5	g	g	PROPN
ejpam-6927	120	6	(	(	PUNCT
ejpam-6927	120	7	qω1	qω1	PROPN
ejpam-6927	120	8	+	+	CCONJ
ejpam-6927	120	9	ω2	ω2	PROPN
ejpam-6927	120	10	q	q	PROPN
ejpam-6927	121	1	+	+	NUM
ejpam-6927	121	2	1	1	NUM
ejpam-6927	121	3	,	,	PUNCT
ejpam-6927	121	4	ℓ	ℓ	PROPN
ejpam-6927	121	5	)	)	PUNCT
ejpam-6927	121	6	φ′′(ℓ)dℓ.	φ′′(ℓ)dℓ.	PROPN
ejpam-6927	121	7	(	(	PUNCT
ejpam-6927	121	8	4	4	NUM
ejpam-6927	121	9	)	)	PUNCT
ejpam-6927	121	10	also	also	ADV
ejpam-6927	121	11	from	from	ADP
ejpam-6927	121	12	(	(	PUNCT
ejpam-6927	121	13	2	2	NUM
ejpam-6927	121	14	)	)	PUNCT
ejpam-6927	121	15	,	,	PUNCT
ejpam-6927	121	16	we	we	PRON
ejpam-6927	121	17	obtain	obtain	VERB
ejpam-6927	121	18	that	that	DET
ejpam-6927	121	19	1	1	NUM
ejpam-6927	121	20	ω2	ω2	NUM
ejpam-6927	121	21	−	−	PROPN
ejpam-6927	121	22	ω1	ω1	PROPN
ejpam-6927	121	23	∫	∫	PROPN
ejpam-6927	121	24	ω2	ω2	PROPN
ejpam-6927	121	25	ω1	ω1	PROPN
ejpam-6927	121	26	φ(κ)ω1dqκ	φ(κ)ω1dqκ	NOUN
ejpam-6927	121	27	=	=	SYM
ejpam-6927	121	28	1	1	NUM
ejpam-6927	121	29	ω2	ω2	NUM
ejpam-6927	121	30	−	−	PROPN
ejpam-6927	121	31	ω1	ω1	PROPN
ejpam-6927	121	32	∫	∫	PROPN
ejpam-6927	121	33	ω2	ω2	PROPN
ejpam-6927	121	34	ω1	ω1	PROPN
ejpam-6927	121	35	{	{	PUNCT
ejpam-6927	121	36	φ(ω1	φ(ω1	NOUN
ejpam-6927	121	37	)	)	PUNCT
ejpam-6927	121	38	+	+	CCONJ
ejpam-6927	121	39	(	(	PUNCT
ejpam-6927	121	40	κ	κ	X
ejpam-6927	121	41	−	−	PROPN
ejpam-6927	121	42	ω1)φ	ω1)φ	NOUN
ejpam-6927	121	43	′(ω2	′(ω2	NUM
ejpam-6927	121	44	)	)	PUNCT
ejpam-6927	122	1	+	+	CCONJ
ejpam-6927	122	2	∫	∫	PROPN
ejpam-6927	122	3	ω2	ω2	PROPN
ejpam-6927	122	4	ω1	ω1	PROPN
ejpam-6927	122	5	g(κ	g(κ	PROPN
ejpam-6927	122	6	,	,	PUNCT
ejpam-6927	122	7	ℓ)φ′′(ℓ)dℓ	ℓ)φ′′(ℓ)dℓ	PROPN
ejpam-6927	122	8	}	}	PUNCT
ejpam-6927	122	9	ω1	ω1	PROPN
ejpam-6927	122	10	dqκ	dqκ	NOUN
ejpam-6927	122	11	=	=	SYM
ejpam-6927	122	12	φ(ω1	φ(ω1	NOUN
ejpam-6927	122	13	)	)	PUNCT
ejpam-6927	122	14	+	+	CCONJ
ejpam-6927	123	1	ω2	ω2	ADJ
ejpam-6927	123	2	−	−	PROPN
ejpam-6927	123	3	ω1	ω1	PROPN
ejpam-6927	123	4	q	q	PROPN
ejpam-6927	123	5	+	+	PROPN
ejpam-6927	123	6	1	1	NUM
ejpam-6927	123	7	φ′(ω2	φ′(ω2	PROPN
ejpam-6927	123	8	)	)	PUNCT
ejpam-6927	124	1	+	+	CCONJ
ejpam-6927	124	2	1	1	NUM
ejpam-6927	124	3	ω2	ω2	NUM
ejpam-6927	124	4	−	−	PROPN
ejpam-6927	124	5	ω1	ω1	PROPN
ejpam-6927	124	6	∫	∫	PROPN
ejpam-6927	124	7	ω2	ω2	PROPN
ejpam-6927	124	8	ω1	ω1	PROPN
ejpam-6927	124	9	∫	∫	PROPN
ejpam-6927	124	10	ω2	ω2	PROPN
ejpam-6927	124	11	ω1	ω1	PROPN
ejpam-6927	124	12	g(κ	g(κ	PROPN
ejpam-6927	124	13	,	,	PUNCT
ejpam-6927	124	14	ℓ)φ′′(ℓ)dℓω1dqκ	ℓ)φ′′(ℓ)dℓω1dqκ	PROPN
ejpam-6927	124	15	.	.	PUNCT
ejpam-6927	125	1	(	(	PUNCT
ejpam-6927	125	2	5	5	X
ejpam-6927	125	3	)	)	PUNCT
ejpam-6927	125	4	m.	m.	NOUN
ejpam-6927	125	5	adil	adil	PROPN
ejpam-6927	125	6	khan	khan	PROPN
ejpam-6927	125	7	et	et	PROPN
ejpam-6927	125	8	al	al	PROPN
ejpam-6927	125	9	.	.	PUNCT
ejpam-6927	125	10	/	/	SYM
ejpam-6927	125	11	eur	eur	PROPN
ejpam-6927	125	12	.	.	PUNCT
ejpam-6927	126	1	j.	j.	PROPN
ejpam-6927	126	2	pure	pure	PROPN
ejpam-6927	126	3	appl	appl	PROPN
ejpam-6927	126	4	.	.	PROPN
ejpam-6927	126	5	math	math	PROPN
ejpam-6927	126	6	,	,	PUNCT
ejpam-6927	126	7	18	18	NUM
ejpam-6927	126	8	(	(	PUNCT
ejpam-6927	126	9	4	4	NUM
ejpam-6927	126	10	)	)	PUNCT
ejpam-6927	126	11	(	(	PUNCT
ejpam-6927	126	12	2025	2025	NUM
ejpam-6927	126	13	)	)	PUNCT
ejpam-6927	126	14	,	,	PUNCT
ejpam-6927	126	15	6927	6927	NUM
ejpam-6927	126	16	6	6	NUM
ejpam-6927	126	17	of	of	ADP
ejpam-6927	126	18	18	18	NUM
ejpam-6927	126	19	subtracting	subtract	VERB
ejpam-6927	126	20	(	(	PUNCT
ejpam-6927	126	21	4	4	NUM
ejpam-6927	126	22	)	)	PUNCT
ejpam-6927	126	23	from	from	ADP
ejpam-6927	126	24	(	(	PUNCT
ejpam-6927	126	25	5	5	NUM
ejpam-6927	126	26	)	)	PUNCT
ejpam-6927	126	27	,	,	PUNCT
ejpam-6927	126	28	we	we	PRON
ejpam-6927	126	29	get	get	VERB
ejpam-6927	126	30	:	:	PUNCT
ejpam-6927	126	31	1	1	NUM
ejpam-6927	126	32	ω2	ω2	NUM
ejpam-6927	126	33	−	−	PROPN
ejpam-6927	127	1	ω1	ω1	PROPN
ejpam-6927	127	2	∫	∫	PROPN
ejpam-6927	127	3	ω2	ω2	PROPN
ejpam-6927	127	4	ω1	ω1	PROPN
ejpam-6927	127	5	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	127	6	−	−	PROPN
ejpam-6927	127	7	φ	φ	PROPN
ejpam-6927	127	8	(	(	PUNCT
ejpam-6927	127	9	qω1	qω1	PROPN
ejpam-6927	127	10	+	+	CCONJ
ejpam-6927	127	11	ω2	ω2	PROPN
ejpam-6927	127	12	q	q	X
ejpam-6927	128	1	+	+	NUM
ejpam-6927	128	2	1	1	X
ejpam-6927	128	3	)	)	PUNCT
ejpam-6927	128	4	=	=	NOUN
ejpam-6927	128	5	φ(ω1	φ(ω1	X
ejpam-6927	128	6	)	)	PUNCT
ejpam-6927	128	7	+	+	CCONJ
ejpam-6927	128	8	ω2	ω2	ADJ
ejpam-6927	128	9	−	−	PROPN
ejpam-6927	128	10	ω1	ω1	PROPN
ejpam-6927	128	11	q	q	PROPN
ejpam-6927	128	12	+	+	PROPN
ejpam-6927	128	13	1	1	NUM
ejpam-6927	128	14	φ′(ω2	φ′(ω2	PROPN
ejpam-6927	128	15	)	)	PUNCT
ejpam-6927	129	1	+	+	CCONJ
ejpam-6927	129	2	1	1	NUM
ejpam-6927	129	3	ω2	ω2	NUM
ejpam-6927	129	4	−	−	PROPN
ejpam-6927	129	5	ω1	ω1	PROPN
ejpam-6927	129	6	∫	∫	PROPN
ejpam-6927	129	7	ω2	ω2	PROPN
ejpam-6927	129	8	ω1	ω1	PROPN
ejpam-6927	129	9	∫	∫	PROPN
ejpam-6927	129	10	ω2	ω2	PROPN
ejpam-6927	129	11	ω1	ω1	PROPN
ejpam-6927	129	12	g(κ	g(κ	PROPN
ejpam-6927	129	13	,	,	PUNCT
ejpam-6927	129	14	ℓ)φ′′(ℓ)dℓω1dqκ	ℓ)φ′′(ℓ)dℓω1dqκ	ADJ
ejpam-6927	129	15	−	−	NOUN
ejpam-6927	129	16	φ(ω1)−	φ(ω1)−	PROPN
ejpam-6927	129	17	ω2	ω2	ADJ
ejpam-6927	129	18	−	−	PROPN
ejpam-6927	129	19	ω1	ω1	PROPN
ejpam-6927	129	20	q	q	PROPN
ejpam-6927	130	1	+	+	NUM
ejpam-6927	130	2	1	1	NUM
ejpam-6927	130	3	φ′(ω2)−	φ′(ω2)−	ADJ
ejpam-6927	130	4	∫	∫	PROPN
ejpam-6927	130	5	ω2	ω2	PROPN
ejpam-6927	130	6	ω1	ω1	PROPN
ejpam-6927	130	7	g	g	PROPN
ejpam-6927	130	8	(	(	PUNCT
ejpam-6927	130	9	qω1	qω1	PROPN
ejpam-6927	130	10	+	+	CCONJ
ejpam-6927	130	11	ω2	ω2	PROPN
ejpam-6927	130	12	q	q	PROPN
ejpam-6927	131	1	+	+	NUM
ejpam-6927	131	2	1	1	NUM
ejpam-6927	131	3	,	,	PUNCT
ejpam-6927	131	4	ℓ	ℓ	PROPN
ejpam-6927	131	5	)	)	PUNCT
ejpam-6927	131	6	φ′′(ℓ)dℓ.	φ′′(ℓ)dℓ.	PROPN
ejpam-6927	131	7	=	=	SYM
ejpam-6927	131	8	∫	∫	PROPN
ejpam-6927	131	9	ω2	ω2	PROPN
ejpam-6927	131	10	ω1	ω1	PROPN
ejpam-6927	131	11	{	{	PUNCT
ejpam-6927	131	12	1	1	NUM
ejpam-6927	131	13	ω2	ω2	NUM
ejpam-6927	131	14	−	−	PROPN
ejpam-6927	131	15	ω1	ω1	PROPN
ejpam-6927	131	16	∫	∫	PROPN
ejpam-6927	131	17	ω2	ω2	PROPN
ejpam-6927	131	18	ω1	ω1	PROPN
ejpam-6927	131	19	g(κ	g(κ	PROPN
ejpam-6927	131	20	,	,	PUNCT
ejpam-6927	131	21	ℓ)ω1dqκ	ℓ)ω1dqκ	ADJ
ejpam-6927	131	22	−	−	PROPN
ejpam-6927	131	23	g	g	NOUN
ejpam-6927	131	24	(	(	PUNCT
ejpam-6927	131	25	qω1	qω1	PROPN
ejpam-6927	131	26	+	+	CCONJ
ejpam-6927	131	27	ω2	ω2	PROPN
ejpam-6927	131	28	q	q	PROPN
ejpam-6927	131	29	+	+	NUM
ejpam-6927	131	30	1	1	NUM
ejpam-6927	131	31	,	,	PUNCT
ejpam-6927	131	32	ℓ	ℓ	PROPN
ejpam-6927	131	33	)	)	PUNCT
ejpam-6927	131	34	}	}	PUNCT
ejpam-6927	131	35	φ′′(ℓ)dℓ.	φ′′(ℓ)dℓ.	PROPN
ejpam-6927	131	36	(	(	PUNCT
ejpam-6927	131	37	6	6	NUM
ejpam-6927	131	38	)	)	PUNCT
ejpam-6927	131	39	let	let	VERB
ejpam-6927	131	40	γ(ℓ	γ(ℓ	X
ejpam-6927	131	41	)	)	PUNCT
ejpam-6927	132	1	=	=	SYM
ejpam-6927	132	2	1	1	NUM
ejpam-6927	132	3	ω2	ω2	NUM
ejpam-6927	132	4	−	−	PROPN
ejpam-6927	132	5	ω1	ω1	PROPN
ejpam-6927	132	6	∫	∫	PROPN
ejpam-6927	132	7	ω2	ω2	PROPN
ejpam-6927	132	8	ω1	ω1	PROPN
ejpam-6927	132	9	g(κ	g(κ	PROPN
ejpam-6927	132	10	,	,	PUNCT
ejpam-6927	133	1	ℓ)ω1dqκ	ℓ)ω1dqκ	ADJ
ejpam-6927	133	2	−	−	PROPN
ejpam-6927	133	3	g	g	NOUN
ejpam-6927	133	4	(	(	PUNCT
ejpam-6927	133	5	qω1	qω1	PROPN
ejpam-6927	133	6	+	+	CCONJ
ejpam-6927	133	7	ω2	ω2	PROPN
ejpam-6927	133	8	q	q	PROPN
ejpam-6927	134	1	+	+	NUM
ejpam-6927	134	2	1	1	NUM
ejpam-6927	134	3	,	,	PUNCT
ejpam-6927	134	4	ℓ	ℓ	PROPN
ejpam-6927	134	5	)	)	PUNCT
ejpam-6927	134	6	.	.	PUNCT
ejpam-6927	135	1	clearly	clearly	ADV
ejpam-6927	135	2	γ(ℓ	γ(ℓ	X
ejpam-6927	135	3	)	)	PUNCT
ejpam-6927	135	4	is	be	AUX
ejpam-6927	135	5	the	the	DET
ejpam-6927	135	6	difference	difference	NOUN
ejpam-6927	135	7	of	of	ADP
ejpam-6927	135	8	middle	middle	ADJ
ejpam-6927	135	9	and	and	CCONJ
ejpam-6927	135	10	left	leave	VERB
ejpam-6927	135	11	side	side	NOUN
ejpam-6927	135	12	of	of	ADP
ejpam-6927	135	13	(	(	PUNCT
ejpam-6927	135	14	1	1	NUM
ejpam-6927	135	15	)	)	PUNCT
ejpam-6927	135	16	,	,	PUNCT
ejpam-6927	135	17	for	for	ADP
ejpam-6927	135	18	the	the	DET
ejpam-6927	135	19	green	green	PROPN
ejpam-6927	135	20	function	function	NOUN
ejpam-6927	135	21	therefore	therefore	ADV
ejpam-6927	135	22	γ(ℓ	γ(ℓ	VERB
ejpam-6927	135	23	)	)	PUNCT
ejpam-6927	135	24	is	be	AUX
ejpam-6927	135	25	non	non	ADJ
ejpam-6927	135	26	-	-	ADJ
ejpam-6927	135	27	negative	negative	ADJ
ejpam-6927	135	28	.	.	PUNCT
ejpam-6927	136	1	let	let	VERB
ejpam-6927	136	2	ℓ	ℓ	NOUN
ejpam-6927	136	3	=	=	SYM
ejpam-6927	136	4	ℓ−	ℓ−	PROPN
ejpam-6927	136	5	ω1	ω1	PROPN
ejpam-6927	136	6	ω2	ω2	PROPN
ejpam-6927	136	7	−	−	PROPN
ejpam-6927	136	8	ω1	ω1	PROPN
ejpam-6927	136	9	ω2	ω2	PROPN
ejpam-6927	136	10	+	+	CCONJ
ejpam-6927	136	11	ω2	ω2	ADJ
ejpam-6927	136	12	−	−	PROPN
ejpam-6927	136	13	ℓ	ℓ	PROPN
ejpam-6927	136	14	ω2	ω2	PROPN
ejpam-6927	136	15	−	−	PROPN
ejpam-6927	136	16	ω1	ω1	PROPN
ejpam-6927	136	17	ω1	ω1	PROPN
ejpam-6927	136	18	,	,	PUNCT
ejpam-6927	136	19	then	then	ADV
ejpam-6927	136	20	from	from	ADP
ejpam-6927	136	21	(	(	PUNCT
ejpam-6927	136	22	6	6	NUM
ejpam-6927	136	23	)	)	PUNCT
ejpam-6927	136	24	we	we	PRON
ejpam-6927	136	25	have	have	VERB
ejpam-6927	136	26	1	1	NUM
ejpam-6927	136	27	ω2	ω2	ADJ
ejpam-6927	136	28	−	−	PROPN
ejpam-6927	136	29	ω1	ω1	PROPN
ejpam-6927	136	30	∫	∫	PROPN
ejpam-6927	136	31	ω2	ω2	PROPN
ejpam-6927	136	32	ω1	ω1	PROPN
ejpam-6927	136	33	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	136	34	−	−	PROPN
ejpam-6927	136	35	φ	φ	PROPN
ejpam-6927	136	36	(	(	PUNCT
ejpam-6927	136	37	qω1	qω1	PROPN
ejpam-6927	136	38	+	+	CCONJ
ejpam-6927	136	39	ω2	ω2	PROPN
ejpam-6927	136	40	q	q	X
ejpam-6927	137	1	+	+	NOUN
ejpam-6927	137	2	1	1	NUM
ejpam-6927	137	3	)	)	PUNCT
ejpam-6927	137	4	=	=	SYM
ejpam-6927	138	1	∫	∫	PROPN
ejpam-6927	138	2	ω2	ω2	PROPN
ejpam-6927	138	3	ω1	ω1	PROPN
ejpam-6927	138	4	γ(ℓ)φ′′	γ(ℓ)φ′′	PROPN
ejpam-6927	138	5	(	(	PUNCT
ejpam-6927	138	6	ℓ−	ℓ−	PROPN
ejpam-6927	138	7	ω1	ω1	PROPN
ejpam-6927	138	8	ω2	ω2	PROPN
ejpam-6927	138	9	−	−	PROPN
ejpam-6927	139	1	ω1	ω1	PROPN
ejpam-6927	139	2	ω2	ω2	PROPN
ejpam-6927	139	3	+	+	CCONJ
ejpam-6927	139	4	ω2	ω2	ADJ
ejpam-6927	139	5	−	−	PROPN
ejpam-6927	139	6	ℓ	ℓ	PROPN
ejpam-6927	139	7	ω2	ω2	PROPN
ejpam-6927	139	8	−	−	PROPN
ejpam-6927	139	9	ω1	ω1	PROPN
ejpam-6927	139	10	ω1	ω1	PROPN
ejpam-6927	139	11	)	)	PUNCT
ejpam-6927	139	12	dℓ.	dℓ.	VERB
ejpam-6927	139	13	by	by	ADP
ejpam-6927	139	14	convexity	convexity	NOUN
ejpam-6927	139	15	of	of	ADP
ejpam-6927	139	16	φ′′	φ′′	PROPN
ejpam-6927	139	17	,	,	PUNCT
ejpam-6927	139	18	we	we	PRON
ejpam-6927	139	19	obtain	obtain	VERB
ejpam-6927	139	20	1	1	NUM
ejpam-6927	139	21	ω2	ω2	ADJ
ejpam-6927	139	22	−	−	PROPN
ejpam-6927	139	23	ω1	ω1	PROPN
ejpam-6927	139	24	∫	∫	PROPN
ejpam-6927	139	25	ω2	ω2	PROPN
ejpam-6927	139	26	ω1	ω1	PROPN
ejpam-6927	139	27	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	139	28	−	−	PROPN
ejpam-6927	139	29	φ	φ	PROPN
ejpam-6927	139	30	(	(	PUNCT
ejpam-6927	139	31	qω1	qω1	PROPN
ejpam-6927	139	32	+	+	CCONJ
ejpam-6927	139	33	ω2	ω2	PROPN
ejpam-6927	139	34	q	q	X
ejpam-6927	140	1	+	+	NUM
ejpam-6927	140	2	1	1	NUM
ejpam-6927	140	3	)	)	PUNCT
ejpam-6927	140	4	≤	≤	NUM
ejpam-6927	140	5	∫	∫	PROPN
ejpam-6927	140	6	ω2	ω2	PROPN
ejpam-6927	140	7	ω1	ω1	PROPN
ejpam-6927	140	8	γ(ℓ	γ(ℓ	PROPN
ejpam-6927	140	9	)	)	PUNCT
ejpam-6927	140	10	{	{	PUNCT
ejpam-6927	140	11	ℓ−	ℓ−	PROPN
ejpam-6927	140	12	ω1	ω1	PROPN
ejpam-6927	140	13	ω2	ω2	PROPN
ejpam-6927	140	14	−	−	PROPN
ejpam-6927	140	15	ω1	ω1	PROPN
ejpam-6927	140	16	φ′′(ω2	φ′′(ω2	PROPN
ejpam-6927	140	17	)	)	PUNCT
ejpam-6927	141	1	+	+	CCONJ
ejpam-6927	141	2	(	(	PUNCT
ejpam-6927	141	3	ω2	ω2	ADJ
ejpam-6927	141	4	−	−	PROPN
ejpam-6927	141	5	ℓ	ℓ	PROPN
ejpam-6927	141	6	ω2	ω2	PROPN
ejpam-6927	141	7	−	−	PROPN
ejpam-6927	141	8	ω1	ω1	PROPN
ejpam-6927	141	9	)	)	PUNCT
ejpam-6927	141	10	φ′′(ω1	φ′′(ω1	ADJ
ejpam-6927	141	11	)	)	PUNCT
ejpam-6927	141	12	}	}	PUNCT
ejpam-6927	141	13	dℓ	dℓ	VERB
ejpam-6927	141	14	⇒	⇒	NOUN
ejpam-6927	141	15	1	1	NUM
ejpam-6927	141	16	ω2	ω2	NUM
ejpam-6927	141	17	−	−	PROPN
ejpam-6927	141	18	ω1	ω1	PROPN
ejpam-6927	141	19	∫	∫	PROPN
ejpam-6927	141	20	ω2	ω2	PROPN
ejpam-6927	141	21	ω1	ω1	PROPN
ejpam-6927	141	22	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	141	23	−	−	PROPN
ejpam-6927	141	24	φ	φ	PROPN
ejpam-6927	141	25	(	(	PUNCT
ejpam-6927	141	26	qω1	qω1	PROPN
ejpam-6927	141	27	+	+	CCONJ
ejpam-6927	141	28	ω2	ω2	PROPN
ejpam-6927	141	29	q	q	X
ejpam-6927	142	1	+	+	NUM
ejpam-6927	142	2	1	1	NUM
ejpam-6927	142	3	)	)	PUNCT
ejpam-6927	142	4	≤	≤	NOUN
ejpam-6927	142	5	1	1	NUM
ejpam-6927	142	6	(	(	PUNCT
ejpam-6927	142	7	ω2	ω2	ADJ
ejpam-6927	142	8	−	−	PROPN
ejpam-6927	142	9	ω1	ω1	PROPN
ejpam-6927	142	10	)	)	PUNCT
ejpam-6927	142	11	{	{	PUNCT
ejpam-6927	142	12	φ′′(ω2	φ′′(ω2	NOUN
ejpam-6927	142	13	)	)	PUNCT
ejpam-6927	142	14	∫	∫	PROPN
ejpam-6927	142	15	ω2	ω2	PROPN
ejpam-6927	142	16	ω1	ω1	PROPN
ejpam-6927	142	17	γ(ℓ)(ℓ−	γ(ℓ)(ℓ−	PROPN
ejpam-6927	142	18	ω1)dℓ+	ω1)dℓ+	PROPN
ejpam-6927	142	19	φ′′(ω1)∫	φ′′(ω1)∫	PROPN
ejpam-6927	142	20	ω2	ω2	PROPN
ejpam-6927	142	21	ω1	ω1	PROPN
ejpam-6927	142	22	γ(ℓ)(ω2	γ(ℓ)(ω2	PROPN
ejpam-6927	142	23	−	−	PROPN
ejpam-6927	142	24	ℓ)dℓ	ℓ)dℓ	PROPN
ejpam-6927	142	25	}	}	PUNCT
ejpam-6927	142	26	.	.	PUNCT
ejpam-6927	143	1	(	(	PUNCT
ejpam-6927	143	2	7	7	X
ejpam-6927	143	3	)	)	PUNCT
ejpam-6927	143	4	now	now	ADV
ejpam-6927	143	5	we	we	PRON
ejpam-6927	143	6	find	find	VERB
ejpam-6927	143	7	the	the	DET
ejpam-6927	143	8	integral	integral	ADJ
ejpam-6927	143	9	∫	∫	PROPN
ejpam-6927	143	10	ω2	ω2	PROPN
ejpam-6927	143	11	ω1	ω1	PROPN
ejpam-6927	143	12	γ(ℓ)(ℓ−	γ(ℓ)(ℓ−	CCONJ
ejpam-6927	143	13	ω1)dℓ.	ω1)dℓ.	PUNCT
ejpam-6927	143	14	if	if	SCONJ
ejpam-6927	143	15	φ(ℓ	φ(ℓ	PROPN
ejpam-6927	143	16	)	)	PUNCT
ejpam-6927	143	17	=	=	SYM
ejpam-6927	143	18	1	1	NUM
ejpam-6927	143	19	6ℓ	6ℓ	NOUN
ejpam-6927	143	20	3	3	NUM
ejpam-6927	143	21	−	−	NOUN
ejpam-6927	143	22	1	1	NUM
ejpam-6927	143	23	2ω1ℓ	2ω1ℓ	NUM
ejpam-6927	143	24	2	2	NUM
ejpam-6927	143	25	,	,	PUNCT
ejpam-6927	143	26	then	then	ADV
ejpam-6927	143	27	φ	φ	NUM
ejpam-6927	143	28	′′	′′	PROPN
ejpam-6927	143	29	(	(	PUNCT
ejpam-6927	143	30	ℓ	ℓ	NOUN
ejpam-6927	143	31	)	)	PUNCT
ejpam-6927	143	32	=	=	SYM
ejpam-6927	143	33	ℓ−	ℓ−	PROPN
ejpam-6927	143	34	ω1	ω1	PROPN
ejpam-6927	143	35	,	,	PUNCT
ejpam-6927	143	36	using	use	VERB
ejpam-6927	143	37	these	these	DET
ejpam-6927	143	38	functions	function	NOUN
ejpam-6927	143	39	in	in	ADP
ejpam-6927	143	40	(	(	PUNCT
ejpam-6927	143	41	6	6	NUM
ejpam-6927	143	42	)	)	PUNCT
ejpam-6927	143	43	we	we	PRON
ejpam-6927	143	44	obtain.∫	obtain.∫	NOUN
ejpam-6927	143	45	ω2	ω2	PROPN
ejpam-6927	143	46	ω1	ω1	PROPN
ejpam-6927	143	47	γ(ℓ)(ℓ−	γ(ℓ)(ℓ−	PROPN
ejpam-6927	143	48	ω1)dℓ	ω1)dℓ	PROPN
ejpam-6927	144	1	=	=	SYM
ejpam-6927	144	2	1	1	NUM
ejpam-6927	144	3	ω2	ω2	NUM
ejpam-6927	144	4	−	−	PROPN
ejpam-6927	144	5	ω1	ω1	PROPN
ejpam-6927	144	6	∫	∫	PROPN
ejpam-6927	144	7	ω2	ω2	PROPN
ejpam-6927	144	8	ω1	ω1	PROPN
ejpam-6927	144	9	(	(	PUNCT
ejpam-6927	144	10	κ3	κ3	PROPN
ejpam-6927	144	11	6	6	NUM
ejpam-6927	144	12	−	−	NOUN
ejpam-6927	144	13	b1	b1	NOUN
ejpam-6927	144	14	κ2	κ2	NOUN
ejpam-6927	144	15	2	2	NUM
ejpam-6927	144	16	)	)	PUNCT
ejpam-6927	144	17	dqκ	dqκ	NOUN
ejpam-6927	144	18	−	−	PROPN
ejpam-6927	144	19	1	1	NUM
ejpam-6927	144	20	6	6	NUM
ejpam-6927	144	21	(	(	PUNCT
ejpam-6927	144	22	qω1	qω1	NOUN
ejpam-6927	144	23	+	+	CCONJ
ejpam-6927	144	24	ω2	ω2	ADJ
ejpam-6927	144	25	1	1	NUM
ejpam-6927	144	26	+	+	NOUN
ejpam-6927	144	27	q	q	NOUN
ejpam-6927	144	28	)	)	PUNCT
ejpam-6927	144	29	3	3	NUM
ejpam-6927	144	30	+	+	SYM
ejpam-6927	144	31	ω1	ω1	PROPN
ejpam-6927	144	32	2	2	NUM
ejpam-6927	144	33	(	(	PUNCT
ejpam-6927	144	34	qω1	qω1	NOUN
ejpam-6927	144	35	+	+	CCONJ
ejpam-6927	144	36	ω2	ω2	ADJ
ejpam-6927	144	37	1	1	NUM
ejpam-6927	144	38	+	+	CCONJ
ejpam-6927	144	39	q	q	NOUN
ejpam-6927	144	40	)	)	PUNCT
ejpam-6927	144	41	2	2	NUM
ejpam-6927	144	42	.	.	PUNCT
ejpam-6927	144	43	finding	find	VERB
ejpam-6927	144	44	the	the	DET
ejpam-6927	144	45	above	above	ADJ
ejpam-6927	144	46	integrals	integral	NOUN
ejpam-6927	144	47	,	,	PUNCT
ejpam-6927	144	48	we	we	PRON
ejpam-6927	144	49	deduce.∫	deduce.∫	VERB
ejpam-6927	144	50	ω2	ω2	ADJ
ejpam-6927	144	51	ω1	ω1	PROPN
ejpam-6927	144	52	γ(ℓ)(ℓ−	γ(ℓ)(ℓ−	PROPN
ejpam-6927	144	53	ω1)dℓ	ω1)dℓ	PROPN
ejpam-6927	144	54	=	=	NOUN
ejpam-6927	144	55	1	1	NUM
ejpam-6927	144	56	6	6	NUM
ejpam-6927	144	57	(	(	PUNCT
ejpam-6927	144	58	ω2	ω2	ADJ
ejpam-6927	144	59	−	−	PROPN
ejpam-6927	144	60	ω1	ω1	PROPN
ejpam-6927	144	61	)	)	PUNCT
ejpam-6927	144	62	3	3	NUM
ejpam-6927	144	63	(	(	PUNCT
ejpam-6927	144	64	1	1	NUM
ejpam-6927	144	65	+	+	NUM
ejpam-6927	144	66	q)(1	q)(1	X
ejpam-6927	144	67	+	+	CCONJ
ejpam-6927	144	68	q2	q2	NOUN
ejpam-6927	144	69	)	)	PUNCT
ejpam-6927	145	1	−	−	NOUN
ejpam-6927	145	2	1	1	NUM
ejpam-6927	145	3	2	2	NUM
ejpam-6927	145	4	ω2	ω2	NUM
ejpam-6927	145	5	1(ω2	1(ω2	NUM
ejpam-6927	145	6	−	−	PROPN
ejpam-6927	145	7	ω1	ω1	PROPN
ejpam-6927	145	8	)	)	PUNCT
ejpam-6927	145	9	1	1	NUM
ejpam-6927	146	1	+	+	CCONJ
ejpam-6927	146	2	q	q	ADJ
ejpam-6927	146	3	−	−	NUM
ejpam-6927	146	4	1	1	NUM
ejpam-6927	146	5	3	3	NUM
ejpam-6927	146	6	ω3	ω3	NOUN
ejpam-6927	146	7	1	1	NUM
ejpam-6927	146	8	−	−	NUM
ejpam-6927	146	9	1	1	NUM
ejpam-6927	146	10	6	6	NUM
ejpam-6927	146	11	(	(	PUNCT
ejpam-6927	146	12	qω1	qω1	NOUN
ejpam-6927	146	13	+	+	CCONJ
ejpam-6927	146	14	ω2	ω2	ADJ
ejpam-6927	146	15	1	1	NUM
ejpam-6927	146	16	+	+	NOUN
ejpam-6927	146	17	q	q	NOUN
ejpam-6927	146	18	)	)	PUNCT
ejpam-6927	146	19	3	3	NUM
ejpam-6927	146	20	+	+	SYM
ejpam-6927	146	21	ω1	ω1	PROPN
ejpam-6927	146	22	2	2	NUM
ejpam-6927	146	23	(	(	PUNCT
ejpam-6927	146	24	qω1	qω1	NOUN
ejpam-6927	146	25	+	+	CCONJ
ejpam-6927	146	26	ω2	ω2	ADJ
ejpam-6927	146	27	1	1	NUM
ejpam-6927	146	28	+	+	CCONJ
ejpam-6927	146	29	q	q	NOUN
ejpam-6927	146	30	)	)	PUNCT
ejpam-6927	146	31	2	2	NUM
ejpam-6927	146	32	.	.	PUNCT
ejpam-6927	147	1	(	(	PUNCT
ejpam-6927	147	2	8)	8)	NUM
ejpam-6927	147	3	m.	m.	NOUN
ejpam-6927	147	4	adil	adil	PROPN
ejpam-6927	147	5	khan	khan	PROPN
ejpam-6927	147	6	et	et	PROPN
ejpam-6927	147	7	al	al	PROPN
ejpam-6927	147	8	.	.	PUNCT
ejpam-6927	147	9	/	/	SYM
ejpam-6927	147	10	eur	eur	PROPN
ejpam-6927	147	11	.	.	PUNCT
ejpam-6927	148	1	j.	j.	PROPN
ejpam-6927	148	2	pure	pure	PROPN
ejpam-6927	148	3	appl	appl	PROPN
ejpam-6927	148	4	.	.	PROPN
ejpam-6927	148	5	math	math	PROPN
ejpam-6927	148	6	,	,	PUNCT
ejpam-6927	148	7	18	18	NUM
ejpam-6927	148	8	(	(	PUNCT
ejpam-6927	148	9	4	4	NUM
ejpam-6927	148	10	)	)	PUNCT
ejpam-6927	148	11	(	(	PUNCT
ejpam-6927	148	12	2025	2025	NUM
ejpam-6927	148	13	)	)	PUNCT
ejpam-6927	148	14	,	,	PUNCT
ejpam-6927	148	15	6927	6927	NUM
ejpam-6927	148	16	7	7	NUM
ejpam-6927	148	17	of	of	ADP
ejpam-6927	148	18	18	18	NUM
ejpam-6927	148	19	now	now	ADV
ejpam-6927	148	20	we	we	PRON
ejpam-6927	148	21	find	find	VERB
ejpam-6927	148	22	the	the	DET
ejpam-6927	148	23	integral	integral	ADJ
ejpam-6927	148	24	∫	∫	PROPN
ejpam-6927	148	25	ω2	ω2	PROPN
ejpam-6927	148	26	ω1	ω1	PROPN
ejpam-6927	148	27	γ(ℓ)(ω2	γ(ℓ)(ω2	PROPN
ejpam-6927	148	28	−	−	PROPN
ejpam-6927	148	29	ℓ)dℓ.	ℓ)dℓ.	PROPN
ejpam-6927	148	30	if	if	SCONJ
ejpam-6927	148	31	φ(ℓ	φ(ℓ	X
ejpam-6927	148	32	)	)	PUNCT
ejpam-6927	148	33	=	=	SYM
ejpam-6927	149	1	1	1	NUM
ejpam-6927	149	2	2ω2ℓ	2ω2ℓ	ADJ
ejpam-6927	149	3	2	2	NUM
ejpam-6927	149	4	−	−	NOUN
ejpam-6927	149	5	1	1	NUM
ejpam-6927	149	6	6ℓ	6ℓ	NOUN
ejpam-6927	149	7	3	3	NUM
ejpam-6927	149	8	,	,	PUNCT
ejpam-6927	149	9	then	then	ADV
ejpam-6927	149	10	φ	φ	NUM
ejpam-6927	149	11	′′	′′	PROPN
ejpam-6927	149	12	(	(	PUNCT
ejpam-6927	149	13	ℓ	ℓ	NOUN
ejpam-6927	149	14	)	)	PUNCT
ejpam-6927	149	15	=	=	SYM
ejpam-6927	149	16	ω2	ω2	ADJ
ejpam-6927	149	17	−	−	PROPN
ejpam-6927	149	18	ℓ	ℓ	PROPN
ejpam-6927	149	19	,	,	PUNCT
ejpam-6927	149	20	using	use	VERB
ejpam-6927	149	21	these	these	DET
ejpam-6927	149	22	functions	function	NOUN
ejpam-6927	149	23	in	in	ADP
ejpam-6927	149	24	(	(	PUNCT
ejpam-6927	149	25	6	6	NUM
ejpam-6927	149	26	)	)	PUNCT
ejpam-6927	149	27	we	we	PRON
ejpam-6927	149	28	obtain.∫	obtain.∫	NOUN
ejpam-6927	149	29	ω2	ω2	ADJ
ejpam-6927	149	30	ω1	ω1	PROPN
ejpam-6927	149	31	γ(ℓ)(ω2	γ(ℓ)(ω2	PROPN
ejpam-6927	149	32	−	−	PROPN
ejpam-6927	149	33	ℓ)dℓ	ℓ)dℓ	PROPN
ejpam-6927	149	34	=	=	PROPN
ejpam-6927	149	35	1	1	NUM
ejpam-6927	149	36	ω2	ω2	NUM
ejpam-6927	149	37	−	−	PROPN
ejpam-6927	149	38	ω1	ω1	PROPN
ejpam-6927	149	39	∫	∫	PROPN
ejpam-6927	149	40	ω2	ω2	PROPN
ejpam-6927	149	41	ω1	ω1	PROPN
ejpam-6927	149	42	(	(	PUNCT
ejpam-6927	149	43	ω2	ω2	ADJ
ejpam-6927	149	44	2	2	NUM
ejpam-6927	149	45	κ2	κ2	NOUN
ejpam-6927	149	46	−	−	NOUN
ejpam-6927	149	47	1	1	NUM
ejpam-6927	149	48	6	6	NUM
ejpam-6927	149	49	κ3	κ3	PROPN
ejpam-6927	149	50	)	)	PUNCT
ejpam-6927	149	51	ω1dqκ	ω1dqκ	NOUN
ejpam-6927	149	52	−	−	PROPN
ejpam-6927	149	53	ω2	ω2	ADJ
ejpam-6927	149	54	2	2	NUM
ejpam-6927	149	55	(	(	PUNCT
ejpam-6927	149	56	qω1	qω1	NOUN
ejpam-6927	149	57	+	+	CCONJ
ejpam-6927	149	58	ω2	ω2	ADJ
ejpam-6927	149	59	1	1	NUM
ejpam-6927	149	60	+	+	NOUN
ejpam-6927	149	61	q	q	NOUN
ejpam-6927	149	62	)	)	PUNCT
ejpam-6927	149	63	2	2	NUM
ejpam-6927	149	64	−	−	NOUN
ejpam-6927	149	65	1	1	NUM
ejpam-6927	149	66	6	6	NUM
ejpam-6927	149	67	(	(	PUNCT
ejpam-6927	149	68	qω1	qω1	NOUN
ejpam-6927	149	69	+	+	CCONJ
ejpam-6927	149	70	ω2	ω2	ADJ
ejpam-6927	149	71	1	1	NUM
ejpam-6927	149	72	+	+	CCONJ
ejpam-6927	149	73	q	q	NOUN
ejpam-6927	149	74	)	)	PUNCT
ejpam-6927	149	75	3	3	X
ejpam-6927	149	76	.	.	PUNCT
ejpam-6927	150	1	finding	find	VERB
ejpam-6927	150	2	the	the	DET
ejpam-6927	150	3	above	above	ADJ
ejpam-6927	150	4	integrals	integral	NOUN
ejpam-6927	150	5	,	,	PUNCT
ejpam-6927	150	6	we	we	PRON
ejpam-6927	150	7	deduce.∫	deduce.∫	VERB
ejpam-6927	150	8	ω2	ω2	ADJ
ejpam-6927	150	9	ω1	ω1	PROPN
ejpam-6927	151	1	γ(ℓ)(ω2	γ(ℓ)(ω2	PROPN
ejpam-6927	151	2	−	−	PROPN
ejpam-6927	151	3	ℓ)dℓ	ℓ)dℓ	PROPN
ejpam-6927	151	4	=	=	SYM
ejpam-6927	151	5	ω2	ω2	PROPN
ejpam-6927	151	6	2	2	NUM
ejpam-6927	151	7	(	(	PUNCT
ejpam-6927	151	8	(	(	PUNCT
ejpam-6927	151	9	ω2	ω2	ADJ
ejpam-6927	151	10	−	−	PROPN
ejpam-6927	151	11	ω1	ω1	PROPN
ejpam-6927	151	12	)	)	PUNCT
ejpam-6927	151	13	2	2	NUM
ejpam-6927	151	14	1	1	NUM
ejpam-6927	151	15	+	+	CCONJ
ejpam-6927	151	16	q	q	NOUN
ejpam-6927	151	17	+	+	NUM
ejpam-6927	151	18	q2	q2	NOUN
ejpam-6927	151	19	)	)	PUNCT
ejpam-6927	152	1	+	+	CCONJ
ejpam-6927	152	2	ω1ω2(ω2	ω1ω2(ω2	NUM
ejpam-6927	152	3	−	−	PROPN
ejpam-6927	152	4	ω1	ω1	PROPN
ejpam-6927	152	5	)	)	PUNCT
ejpam-6927	152	6	1	1	NUM
ejpam-6927	153	1	+	+	CCONJ
ejpam-6927	153	2	q	q	ADJ
ejpam-6927	153	3	+	+	NUM
ejpam-6927	153	4	ω1	ω1	ADJ
ejpam-6927	153	5	2ω2	2ω2	NUM
ejpam-6927	153	6	−	−	PROPN
ejpam-6927	153	7	1	1	NUM
ejpam-6927	153	8	6	6	NUM
ejpam-6927	153	9	(	(	PUNCT
ejpam-6927	153	10	ω2	ω2	ADJ
ejpam-6927	153	11	−	−	PROPN
ejpam-6927	153	12	ω1	ω1	PROPN
ejpam-6927	153	13	)	)	PUNCT
ejpam-6927	153	14	3	3	NUM
ejpam-6927	153	15	(	(	PUNCT
ejpam-6927	153	16	1	1	NUM
ejpam-6927	153	17	+	+	NUM
ejpam-6927	153	18	q)(1	q)(1	X
ejpam-6927	153	19	+	+	CCONJ
ejpam-6927	153	20	q2	q2	NOUN
ejpam-6927	153	21	)	)	PUNCT
ejpam-6927	153	22	−	−	NOUN
ejpam-6927	153	23	1	1	NUM
ejpam-6927	153	24	2	2	NUM
ejpam-6927	153	25	ω1(ω2	ω1(ω2	NUM
ejpam-6927	153	26	−	−	NOUN
ejpam-6927	153	27	ω1	ω1	PROPN
ejpam-6927	153	28	)	)	PUNCT
ejpam-6927	153	29	2	2	NUM
ejpam-6927	153	30	1	1	NUM
ejpam-6927	153	31	+	+	CCONJ
ejpam-6927	153	32	q	q	NOUN
ejpam-6927	153	33	+	+	NUM
ejpam-6927	153	34	q2	q2	NOUN
ejpam-6927	153	35	−	−	NOUN
ejpam-6927	153	36	1	1	NUM
ejpam-6927	153	37	2	2	NUM
ejpam-6927	153	38	ω2	ω2	NUM
ejpam-6927	153	39	1(ω2	1(ω2	NUM
ejpam-6927	153	40	−	−	PROPN
ejpam-6927	153	41	ω1	ω1	PROPN
ejpam-6927	153	42	)	)	PUNCT
ejpam-6927	153	43	1	1	NUM
ejpam-6927	153	44	+	+	CCONJ
ejpam-6927	153	45	q	q	ADJ
ejpam-6927	153	46	−	−	NUM
ejpam-6927	153	47	1	1	NUM
ejpam-6927	153	48	6	6	NUM
ejpam-6927	153	49	ω3	ω3	NOUN
ejpam-6927	153	50	1	1	NUM
ejpam-6927	153	51	−	−	NOUN
ejpam-6927	153	52	ω2	ω2	ADJ
ejpam-6927	153	53	2	2	NUM
ejpam-6927	153	54	(	(	PUNCT
ejpam-6927	153	55	qω1	qω1	NOUN
ejpam-6927	153	56	+	+	CCONJ
ejpam-6927	153	57	ω2	ω2	ADJ
ejpam-6927	153	58	1	1	NUM
ejpam-6927	153	59	+	+	NOUN
ejpam-6927	153	60	q	q	NOUN
ejpam-6927	153	61	)	)	PUNCT
ejpam-6927	153	62	2	2	NUM
ejpam-6927	153	63	−	−	NOUN
ejpam-6927	153	64	1	1	NUM
ejpam-6927	153	65	6	6	NUM
ejpam-6927	153	66	(	(	PUNCT
ejpam-6927	153	67	qω1	qω1	NOUN
ejpam-6927	153	68	+	+	CCONJ
ejpam-6927	153	69	ω2	ω2	ADJ
ejpam-6927	153	70	1	1	NUM
ejpam-6927	153	71	+	+	CCONJ
ejpam-6927	153	72	q	q	NOUN
ejpam-6927	153	73	)	)	PUNCT
ejpam-6927	153	74	3	3	NUM
ejpam-6927	153	75	.	.	PUNCT
ejpam-6927	154	1	(	(	PUNCT
ejpam-6927	154	2	9	9	X
ejpam-6927	154	3	)	)	PUNCT
ejpam-6927	154	4	using	use	VERB
ejpam-6927	154	5	(	(	PUNCT
ejpam-6927	154	6	8)	8)	NUM
ejpam-6927	154	7	and	and	CCONJ
ejpam-6927	154	8	(	(	PUNCT
ejpam-6927	154	9	9	9	NUM
ejpam-6927	154	10	)	)	PUNCT
ejpam-6927	154	11	in	in	ADP
ejpam-6927	154	12	(	(	PUNCT
ejpam-6927	154	13	7	7	NUM
ejpam-6927	154	14	)	)	PUNCT
ejpam-6927	154	15	,	,	PUNCT
ejpam-6927	154	16	we	we	PRON
ejpam-6927	154	17	get	get	VERB
ejpam-6927	154	18	≤	≤	NUM
ejpam-6927	154	19	1	1	NUM
ejpam-6927	154	20	(	(	PUNCT
ejpam-6927	154	21	ω2	ω2	ADJ
ejpam-6927	154	22	−	−	PROPN
ejpam-6927	154	23	ω1	ω1	PROPN
ejpam-6927	154	24	)	)	PUNCT
ejpam-6927	154	25	[	[	PUNCT
ejpam-6927	154	26	φ′′(ω2	φ′′(ω2	X
ejpam-6927	154	27	)	)	PUNCT
ejpam-6927	154	28	{	{	PUNCT
ejpam-6927	154	29	1	1	NUM
ejpam-6927	154	30	6	6	NUM
ejpam-6927	154	31	(	(	PUNCT
ejpam-6927	154	32	ω2	ω2	ADJ
ejpam-6927	154	33	−	−	PROPN
ejpam-6927	154	34	ω1	ω1	PROPN
ejpam-6927	154	35	)	)	PUNCT
ejpam-6927	154	36	3	3	NUM
ejpam-6927	154	37	(	(	PUNCT
ejpam-6927	154	38	1	1	NUM
ejpam-6927	154	39	+	+	NUM
ejpam-6927	154	40	q)(1	q)(1	X
ejpam-6927	154	41	+	+	CCONJ
ejpam-6927	154	42	q2	q2	NOUN
ejpam-6927	154	43	)	)	PUNCT
ejpam-6927	154	44	−	−	NOUN
ejpam-6927	155	1	1	1	NUM
ejpam-6927	155	2	2	2	NUM
ejpam-6927	155	3	ω2	ω2	NUM
ejpam-6927	155	4	1(ω2	1(ω2	NUM
ejpam-6927	155	5	−	−	PROPN
ejpam-6927	155	6	ω1	ω1	PROPN
ejpam-6927	155	7	)	)	PUNCT
ejpam-6927	155	8	1	1	NUM
ejpam-6927	156	1	+	+	CCONJ
ejpam-6927	156	2	q	q	ADJ
ejpam-6927	156	3	−	−	NUM
ejpam-6927	156	4	1	1	NUM
ejpam-6927	156	5	3	3	NUM
ejpam-6927	156	6	ω3	ω3	NOUN
ejpam-6927	156	7	1	1	NUM
ejpam-6927	156	8	−	−	NUM
ejpam-6927	156	9	1	1	NUM
ejpam-6927	156	10	6	6	NUM
ejpam-6927	156	11	(	(	PUNCT
ejpam-6927	156	12	qω1	qω1	NOUN
ejpam-6927	156	13	+	+	CCONJ
ejpam-6927	156	14	ω2	ω2	ADJ
ejpam-6927	156	15	1	1	NUM
ejpam-6927	156	16	+	+	NOUN
ejpam-6927	156	17	q	q	NOUN
ejpam-6927	156	18	)	)	PUNCT
ejpam-6927	156	19	3	3	NUM
ejpam-6927	156	20	+	+	SYM
ejpam-6927	156	21	ω1	ω1	PROPN
ejpam-6927	156	22	2	2	NUM
ejpam-6927	156	23	(	(	PUNCT
ejpam-6927	156	24	qω1	qω1	NOUN
ejpam-6927	156	25	+	+	CCONJ
ejpam-6927	156	26	ω2	ω2	ADJ
ejpam-6927	156	27	1	1	NUM
ejpam-6927	156	28	+	+	NOUN
ejpam-6927	156	29	q	q	NOUN
ejpam-6927	156	30	)	)	PUNCT
ejpam-6927	156	31	2	2	NUM
ejpam-6927	156	32	}	}	PUNCT
ejpam-6927	156	33	+	+	CCONJ
ejpam-6927	156	34	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	156	35	)	)	PUNCT
ejpam-6927	156	36	{	{	PUNCT
ejpam-6927	156	37	ω2	ω2	NOUN
ejpam-6927	156	38	2	2	NUM
ejpam-6927	156	39	(	(	PUNCT
ejpam-6927	156	40	(	(	PUNCT
ejpam-6927	156	41	ω2	ω2	ADJ
ejpam-6927	156	42	−	−	PROPN
ejpam-6927	156	43	ω1	ω1	PROPN
ejpam-6927	156	44	)	)	PUNCT
ejpam-6927	156	45	2	2	NUM
ejpam-6927	156	46	1	1	NUM
ejpam-6927	156	47	+	+	CCONJ
ejpam-6927	156	48	q	q	NOUN
ejpam-6927	156	49	+	+	NUM
ejpam-6927	156	50	q2	q2	NOUN
ejpam-6927	156	51	)	)	PUNCT
ejpam-6927	157	1	+	+	CCONJ
ejpam-6927	157	2	ω1ω2(ω2	ω1ω2(ω2	NUM
ejpam-6927	157	3	−	−	PROPN
ejpam-6927	157	4	ω1	ω1	PROPN
ejpam-6927	157	5	)	)	PUNCT
ejpam-6927	157	6	1	1	NUM
ejpam-6927	158	1	+	+	CCONJ
ejpam-6927	158	2	q	q	ADJ
ejpam-6927	158	3	+	+	NUM
ejpam-6927	158	4	ω1	ω1	ADJ
ejpam-6927	158	5	2ω2	2ω2	NUM
ejpam-6927	158	6	−	−	PROPN
ejpam-6927	158	7	1	1	NUM
ejpam-6927	158	8	6	6	NUM
ejpam-6927	158	9	(	(	PUNCT
ejpam-6927	158	10	ω2	ω2	ADJ
ejpam-6927	158	11	−	−	PROPN
ejpam-6927	158	12	ω1	ω1	PROPN
ejpam-6927	158	13	)	)	PUNCT
ejpam-6927	158	14	3	3	NUM
ejpam-6927	158	15	(	(	PUNCT
ejpam-6927	158	16	1	1	NUM
ejpam-6927	158	17	+	+	NUM
ejpam-6927	158	18	q)(1	q)(1	X
ejpam-6927	158	19	+	+	CCONJ
ejpam-6927	158	20	q2	q2	NOUN
ejpam-6927	158	21	)	)	PUNCT
ejpam-6927	158	22	−	−	NOUN
ejpam-6927	158	23	1	1	NUM
ejpam-6927	158	24	2	2	NUM
ejpam-6927	158	25	ω1(ω2	ω1(ω2	NUM
ejpam-6927	158	26	−	−	NOUN
ejpam-6927	158	27	ω1	ω1	PROPN
ejpam-6927	158	28	)	)	PUNCT
ejpam-6927	158	29	2	2	NUM
ejpam-6927	158	30	1	1	NUM
ejpam-6927	158	31	+	+	CCONJ
ejpam-6927	158	32	q	q	NOUN
ejpam-6927	158	33	+	+	NUM
ejpam-6927	158	34	q2	q2	NOUN
ejpam-6927	158	35	−	−	NOUN
ejpam-6927	158	36	1	1	NUM
ejpam-6927	158	37	2	2	NUM
ejpam-6927	158	38	ω2	ω2	NUM
ejpam-6927	158	39	1(ω2	1(ω2	NUM
ejpam-6927	158	40	−	−	PROPN
ejpam-6927	158	41	ω1	ω1	PROPN
ejpam-6927	158	42	)	)	PUNCT
ejpam-6927	158	43	1	1	NUM
ejpam-6927	158	44	+	+	CCONJ
ejpam-6927	158	45	q	q	ADJ
ejpam-6927	158	46	−	−	NUM
ejpam-6927	158	47	1	1	NUM
ejpam-6927	158	48	6	6	NUM
ejpam-6927	158	49	ω3	ω3	NOUN
ejpam-6927	158	50	1	1	NUM
ejpam-6927	158	51	−	−	NOUN
ejpam-6927	158	52	ω2	ω2	ADJ
ejpam-6927	158	53	2	2	NUM
ejpam-6927	158	54	(	(	PUNCT
ejpam-6927	158	55	qω1	qω1	NOUN
ejpam-6927	158	56	+	+	CCONJ
ejpam-6927	158	57	ω2	ω2	ADJ
ejpam-6927	158	58	1	1	NUM
ejpam-6927	158	59	+	+	NOUN
ejpam-6927	158	60	q	q	NOUN
ejpam-6927	158	61	)	)	PUNCT
ejpam-6927	158	62	2	2	NUM
ejpam-6927	158	63	−	−	NOUN
ejpam-6927	158	64	1	1	NUM
ejpam-6927	158	65	6	6	NUM
ejpam-6927	158	66	(	(	PUNCT
ejpam-6927	158	67	qω1	qω1	NOUN
ejpam-6927	158	68	+	+	CCONJ
ejpam-6927	158	69	ω2	ω2	ADJ
ejpam-6927	158	70	1	1	NUM
ejpam-6927	158	71	+	+	NOUN
ejpam-6927	158	72	q	q	NOUN
ejpam-6927	158	73	)	)	PUNCT
ejpam-6927	158	74	3	3	NUM
ejpam-6927	158	75	}	}	PUNCT
ejpam-6927	158	76	]	]	PUNCT
ejpam-6927	158	77	.	.	PUNCT
ejpam-6927	159	1	=	=	SYM
ejpam-6927	159	2	1	1	NUM
ejpam-6927	159	3	ω2	ω2	NUM
ejpam-6927	159	4	−	−	PROPN
ejpam-6927	159	5	ω1	ω1	PROPN
ejpam-6927	159	6	[	[	PUNCT
ejpam-6927	159	7	1	1	NUM
ejpam-6927	159	8	6	6	NUM
ejpam-6927	159	9	(	(	PUNCT
ejpam-6927	159	10	φ′′(ω2)−	φ′′(ω2)−	NOUN
ejpam-6927	159	11	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	159	12	)	)	PUNCT
ejpam-6927	159	13	)	)	PUNCT
ejpam-6927	159	14	(	(	PUNCT
ejpam-6927	159	15	(	(	PUNCT
ejpam-6927	159	16	ω2	ω2	ADJ
ejpam-6927	159	17	−	−	PROPN
ejpam-6927	159	18	ω1	ω1	PROPN
ejpam-6927	159	19	)	)	PUNCT
ejpam-6927	159	20	3	3	NUM
ejpam-6927	159	21	(	(	PUNCT
ejpam-6927	159	22	1	1	NUM
ejpam-6927	159	23	+	+	NUM
ejpam-6927	159	24	q)(1	q)(1	X
ejpam-6927	159	25	+	+	X
ejpam-6927	159	26	q2	q2	NOUN
ejpam-6927	159	27	)	)	PUNCT
ejpam-6927	159	28	)	)	PUNCT
ejpam-6927	160	1	−	−	PROPN
ejpam-6927	160	2	(	(	PUNCT
ejpam-6927	160	3	φ′′(ω2	φ′′(ω2	X
ejpam-6927	160	4	)	)	PUNCT
ejpam-6927	160	5	2	2	NUM
ejpam-6927	160	6	+	+	CCONJ
ejpam-6927	160	7	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	160	8	)	)	PUNCT
ejpam-6927	160	9	2	2	NUM
ejpam-6927	160	10	)	)	PUNCT
ejpam-6927	160	11	(	(	PUNCT
ejpam-6927	160	12	(	(	PUNCT
ejpam-6927	160	13	ω2	ω2	ADJ
ejpam-6927	160	14	−	−	PROPN
ejpam-6927	160	15	ω1	ω1	PROPN
ejpam-6927	160	16	)	)	PUNCT
ejpam-6927	160	17	1	1	NUM
ejpam-6927	161	1	+	+	CCONJ
ejpam-6927	161	2	q	q	X
ejpam-6927	161	3	)	)	PUNCT
ejpam-6927	161	4	ω2	ω2	ADJ
ejpam-6927	161	5	1	1	NUM
ejpam-6927	161	6	−	−	PROPN
ejpam-6927	161	7	(	(	PUNCT
ejpam-6927	161	8	φ′′(ω2	φ′′(ω2	X
ejpam-6927	161	9	)	)	PUNCT
ejpam-6927	161	10	3	3	NUM
ejpam-6927	161	11	+	+	CCONJ
ejpam-6927	161	12	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	161	13	)	)	PUNCT
ejpam-6927	161	14	6	6	NUM
ejpam-6927	161	15	)	)	PUNCT
ejpam-6927	161	16	ω3	ω3	NOUN
ejpam-6927	161	17	1	1	NUM
ejpam-6927	161	18	−	−	PROPN
ejpam-6927	161	19	(	(	PUNCT
ejpam-6927	161	20	φ′′(ω2	φ′′(ω2	X
ejpam-6927	161	21	)	)	PUNCT
ejpam-6927	161	22	6	6	NUM
ejpam-6927	162	1	+	+	CCONJ
ejpam-6927	162	2	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	162	3	)	)	PUNCT
ejpam-6927	162	4	6	6	NUM
ejpam-6927	162	5	)	)	PUNCT
ejpam-6927	162	6	(	(	PUNCT
ejpam-6927	162	7	(	(	PUNCT
ejpam-6927	162	8	qω1	qω1	NOUN
ejpam-6927	162	9	+	+	CCONJ
ejpam-6927	162	10	ω2	ω2	NUM
ejpam-6927	162	11	)	)	PUNCT
ejpam-6927	162	12	(	(	PUNCT
ejpam-6927	162	13	1	1	NUM
ejpam-6927	162	14	+	+	CCONJ
ejpam-6927	162	15	q	q	NOUN
ejpam-6927	162	16	)	)	PUNCT
ejpam-6927	162	17	)	)	PUNCT
ejpam-6927	162	18	3	3	NUM
ejpam-6927	163	1	+	+	CCONJ
ejpam-6927	163	2	(	(	PUNCT
ejpam-6927	163	3	φ′′(ω2)ω1	φ′′(ω2)ω1	NOUN
ejpam-6927	163	4	2	2	NUM
ejpam-6927	163	5	−	−	PROPN
ejpam-6927	163	6	φ′′(ω1)ω2	φ′′(ω1)ω2	NOUN
ejpam-6927	163	7	2	2	NUM
ejpam-6927	163	8	)	)	PUNCT
ejpam-6927	163	9	(	(	PUNCT
ejpam-6927	163	10	(	(	PUNCT
ejpam-6927	163	11	qω1	qω1	PROPN
ejpam-6927	163	12	+	+	CCONJ
ejpam-6927	163	13	ω2	ω2	ADJ
ejpam-6927	163	14	(	(	PUNCT
ejpam-6927	163	15	1	1	NUM
ejpam-6927	163	16	+	+	CCONJ
ejpam-6927	163	17	q	q	NOUN
ejpam-6927	163	18	)	)	PUNCT
ejpam-6927	163	19	)	)	PUNCT
ejpam-6927	163	20	2	2	NUM
ejpam-6927	164	1	+	+	NUM
ejpam-6927	164	2	φ′′(ω1)ω2	φ′′(ω1)ω2	NOUN
ejpam-6927	164	3	2	2	NUM
ejpam-6927	164	4	(	(	PUNCT
ejpam-6927	164	5	(	(	PUNCT
ejpam-6927	164	6	ω2	ω2	ADJ
ejpam-6927	164	7	−	−	PROPN
ejpam-6927	164	8	ω1	ω1	PROPN
ejpam-6927	164	9	)	)	PUNCT
ejpam-6927	164	10	2	2	NUM
ejpam-6927	164	11	(	(	PUNCT
ejpam-6927	164	12	1	1	NUM
ejpam-6927	164	13	+	+	CCONJ
ejpam-6927	164	14	q	q	ADJ
ejpam-6927	164	15	+	+	NUM
ejpam-6927	164	16	q2	q2	NOUN
ejpam-6927	164	17	)	)	PUNCT
ejpam-6927	164	18	)	)	PUNCT
ejpam-6927	165	1	+	+	CCONJ
ejpam-6927	165	2	ω1ω2φ	ω1ω2φ	X
ejpam-6927	165	3	′′(ω1)(ω2	′′(ω1)(ω2	X
ejpam-6927	165	4	−	−	PROPN
ejpam-6927	165	5	ω1	ω1	PROPN
ejpam-6927	165	6	)	)	PUNCT
ejpam-6927	165	7	(	(	PUNCT
ejpam-6927	165	8	1	1	NUM
ejpam-6927	165	9	+	+	CCONJ
ejpam-6927	165	10	q	q	X
ejpam-6927	165	11	)	)	PUNCT
ejpam-6927	166	1	+	+	NUM
ejpam-6927	166	2	φ′′(ω1)ω	φ′′(ω1)ω	PROPN
ejpam-6927	166	3	2	2	NUM
ejpam-6927	166	4	1ω2	1ω2	NUM
ejpam-6927	166	5	−	−	NUM
ejpam-6927	166	6	ω1φ	ω1φ	PUNCT
ejpam-6927	166	7	′′(ω1)(ω2	′′(ω1)(ω2	PUNCT
ejpam-6927	166	8	−	−	PROPN
ejpam-6927	166	9	ω1	ω1	PROPN
ejpam-6927	166	10	)	)	PUNCT
ejpam-6927	166	11	2	2	NUM
ejpam-6927	166	12	2(1	2(1	NUM
ejpam-6927	166	13	+	+	CCONJ
ejpam-6927	166	14	q	q	ADJ
ejpam-6927	166	15	+	+	NUM
ejpam-6927	166	16	q2	q2	NOUN
ejpam-6927	166	17	)	)	PUNCT
ejpam-6927	166	18	]	]	PUNCT
ejpam-6927	166	19	.	.	PUNCT
ejpam-6927	167	1	=	=	SYM
ejpam-6927	167	2	1	1	NUM
ejpam-6927	167	3	ω2	ω2	NUM
ejpam-6927	167	4	−	−	PROPN
ejpam-6927	167	5	ω1	ω1	PROPN
ejpam-6927	167	6	[	[	PUNCT
ejpam-6927	167	7	1	1	NUM
ejpam-6927	167	8	6	6	NUM
ejpam-6927	167	9	(	(	PUNCT
ejpam-6927	167	10	φ′′(ω2)−	φ′′(ω2)−	NOUN
ejpam-6927	167	11	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	167	12	)	)	PUNCT
ejpam-6927	167	13	)	)	PUNCT
ejpam-6927	167	14	(	(	PUNCT
ejpam-6927	167	15	(	(	PUNCT
ejpam-6927	167	16	ω2	ω2	ADJ
ejpam-6927	167	17	−	−	PROPN
ejpam-6927	167	18	ω1	ω1	PROPN
ejpam-6927	167	19	)	)	PUNCT
ejpam-6927	167	20	3	3	NUM
ejpam-6927	167	21	(	(	PUNCT
ejpam-6927	167	22	1	1	NUM
ejpam-6927	167	23	+	+	NUM
ejpam-6927	167	24	q)(1	q)(1	X
ejpam-6927	167	25	+	+	CCONJ
ejpam-6927	167	26	q2	q2	NOUN
ejpam-6927	167	27	)	)	PUNCT
ejpam-6927	167	28	)	)	PUNCT
ejpam-6927	168	1	m.	m.	NOUN
ejpam-6927	168	2	adil	adil	PROPN
ejpam-6927	168	3	khan	khan	PROPN
ejpam-6927	168	4	et	et	PROPN
ejpam-6927	168	5	al	al	PROPN
ejpam-6927	168	6	.	.	PUNCT
ejpam-6927	168	7	/	/	SYM
ejpam-6927	168	8	eur	eur	PROPN
ejpam-6927	168	9	.	.	PUNCT
ejpam-6927	169	1	j.	j.	PROPN
ejpam-6927	169	2	pure	pure	PROPN
ejpam-6927	169	3	appl	appl	PROPN
ejpam-6927	169	4	.	.	PROPN
ejpam-6927	169	5	math	math	PROPN
ejpam-6927	169	6	,	,	PUNCT
ejpam-6927	169	7	18	18	NUM
ejpam-6927	169	8	(	(	PUNCT
ejpam-6927	169	9	4	4	NUM
ejpam-6927	169	10	)	)	PUNCT
ejpam-6927	169	11	(	(	PUNCT
ejpam-6927	169	12	2025	2025	NUM
ejpam-6927	169	13	)	)	PUNCT
ejpam-6927	169	14	,	,	PUNCT
ejpam-6927	169	15	6927	6927	NUM
ejpam-6927	169	16	8	8	NUM
ejpam-6927	169	17	of	of	ADP
ejpam-6927	169	18	18	18	NUM
ejpam-6927	169	19	−	−	NOUN
ejpam-6927	169	20	(	(	PUNCT
ejpam-6927	169	21	φ′′(ω2	φ′′(ω2	X
ejpam-6927	169	22	)	)	PUNCT
ejpam-6927	169	23	+	+	CCONJ
ejpam-6927	169	24	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	169	25	)	)	PUNCT
ejpam-6927	169	26	2	2	NUM
ejpam-6927	169	27	)	)	PUNCT
ejpam-6927	169	28	(	(	PUNCT
ejpam-6927	169	29	(	(	PUNCT
ejpam-6927	169	30	ω2	ω2	ADJ
ejpam-6927	169	31	−	−	PROPN
ejpam-6927	169	32	ω1	ω1	PROPN
ejpam-6927	169	33	)	)	PUNCT
ejpam-6927	169	34	1	1	NUM
ejpam-6927	170	1	+	+	CCONJ
ejpam-6927	170	2	q	q	X
ejpam-6927	170	3	)	)	PUNCT
ejpam-6927	170	4	ω2	ω2	ADJ
ejpam-6927	170	5	1	1	NUM
ejpam-6927	170	6	−	−	PROPN
ejpam-6927	170	7	(	(	PUNCT
ejpam-6927	170	8	2φ′′(ω2	2φ′′(ω2	NUM
ejpam-6927	170	9	)	)	PUNCT
ejpam-6927	171	1	+	+	PUNCT
ejpam-6927	171	2	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	171	3	)	)	PUNCT
ejpam-6927	171	4	6	6	NUM
ejpam-6927	171	5	)	)	PUNCT
ejpam-6927	171	6	ω3	ω3	NOUN
ejpam-6927	171	7	1	1	NUM
ejpam-6927	171	8	−	−	PROPN
ejpam-6927	171	9	(	(	PUNCT
ejpam-6927	171	10	φ′′(ω2	φ′′(ω2	X
ejpam-6927	171	11	)	)	PUNCT
ejpam-6927	171	12	+	+	CCONJ
ejpam-6927	171	13	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	171	14	)	)	PUNCT
ejpam-6927	171	15	6	6	NUM
ejpam-6927	171	16	)	)	PUNCT
ejpam-6927	171	17	(	(	PUNCT
ejpam-6927	171	18	(	(	PUNCT
ejpam-6927	171	19	qω1	qω1	NOUN
ejpam-6927	171	20	+	+	CCONJ
ejpam-6927	171	21	ω2	ω2	NUM
ejpam-6927	171	22	)	)	PUNCT
ejpam-6927	171	23	(	(	PUNCT
ejpam-6927	171	24	1	1	NUM
ejpam-6927	171	25	+	+	CCONJ
ejpam-6927	171	26	q	q	NOUN
ejpam-6927	171	27	)	)	PUNCT
ejpam-6927	171	28	)	)	PUNCT
ejpam-6927	171	29	3	3	NUM
ejpam-6927	172	1	+	+	CCONJ
ejpam-6927	172	2	(	(	PUNCT
ejpam-6927	172	3	φ′′(ω2)ω1	φ′′(ω2)ω1	NOUN
ejpam-6927	172	4	−	−	PROPN
ejpam-6927	172	5	φ′′(ω1)ω2	φ′′(ω1)ω2	NOUN
ejpam-6927	172	6	2	2	NUM
ejpam-6927	172	7	)	)	PUNCT
ejpam-6927	172	8	(	(	PUNCT
ejpam-6927	172	9	(	(	PUNCT
ejpam-6927	172	10	qω1	qω1	NOUN
ejpam-6927	172	11	+	+	CCONJ
ejpam-6927	172	12	ω2	ω2	NUM
ejpam-6927	172	13	)	)	PUNCT
ejpam-6927	172	14	(	(	PUNCT
ejpam-6927	172	15	1	1	NUM
ejpam-6927	172	16	+	+	CCONJ
ejpam-6927	172	17	q	q	NOUN
ejpam-6927	172	18	)	)	PUNCT
ejpam-6927	172	19	)	)	PUNCT
ejpam-6927	172	20	2	2	NUM
ejpam-6927	172	21	+	+	CCONJ
ejpam-6927	172	22	ω1ω2φ	ω1ω2φ	X
ejpam-6927	172	23	′′(ω1)(ω2	′′(ω1)(ω2	X
ejpam-6927	172	24	−	−	PROPN
ejpam-6927	172	25	ω1	ω1	PROPN
ejpam-6927	172	26	)	)	PUNCT
ejpam-6927	172	27	(	(	PUNCT
ejpam-6927	172	28	1	1	NUM
ejpam-6927	172	29	+	+	CCONJ
ejpam-6927	172	30	q	q	X
ejpam-6927	172	31	)	)	PUNCT
ejpam-6927	173	1	+	+	CCONJ
ejpam-6927	173	2	φ′′(ω1)ω	φ′′(ω1)ω	PROPN
ejpam-6927	173	3	2	2	NUM
ejpam-6927	173	4	1ω2	1ω2	NUM
ejpam-6927	173	5	+	+	CCONJ
ejpam-6927	173	6	1	1	NUM
ejpam-6927	173	7	2	2	NUM
ejpam-6927	173	8	(	(	PUNCT
ejpam-6927	173	9	(	(	PUNCT
ejpam-6927	173	10	ω2	ω2	ADJ
ejpam-6927	173	11	−	−	PROPN
ejpam-6927	173	12	ω1	ω1	PROPN
ejpam-6927	173	13	)	)	PUNCT
ejpam-6927	173	14	3	3	NUM
ejpam-6927	173	15	1	1	NUM
ejpam-6927	173	16	+	+	CCONJ
ejpam-6927	173	17	q	q	ADJ
ejpam-6927	173	18	+	+	NUM
ejpam-6927	173	19	q2	q2	NOUN
ejpam-6927	173	20	)	)	PUNCT
ejpam-6927	173	21	φ′′(ω1	φ′′(ω1	ADV
ejpam-6927	173	22	)	)	PUNCT
ejpam-6927	173	23	]	]	PUNCT
ejpam-6927	173	24	.	.	PUNCT
ejpam-6927	174	1	(	(	PUNCT
ejpam-6927	174	2	10	10	NUM
ejpam-6927	174	3	)	)	PUNCT
ejpam-6927	174	4	(	(	PUNCT
ejpam-6927	174	5	10	10	NUM
ejpam-6927	174	6	)	)	PUNCT
ejpam-6927	174	7	is	be	AUX
ejpam-6927	174	8	equivalent	equivalent	ADJ
ejpam-6927	174	9	to	to	ADP
ejpam-6927	174	10	(	(	PUNCT
ejpam-6927	174	11	3	3	NUM
ejpam-6927	174	12	)	)	PUNCT
ejpam-6927	174	13	.	.	PUNCT
ejpam-6927	175	1	remark	remark	PROPN
ejpam-6927	175	2	1	1	NUM
ejpam-6927	175	3	.	.	PUNCT
ejpam-6927	176	1	under	under	ADP
ejpam-6927	176	2	the	the	DET
ejpam-6927	176	3	assumptions	assumption	NOUN
ejpam-6927	176	4	of	of	ADP
ejpam-6927	176	5	theorem	theorem	NOUN
ejpam-6927	176	6	5	5	NUM
ejpam-6927	176	7	with	with	ADP
ejpam-6927	176	8	the	the	DET
ejpam-6927	176	9	limit	limit	NOUN
ejpam-6927	176	10	as	as	ADP
ejpam-6927	176	11	q	q	NOUN
ejpam-6927	176	12	→	→	SYM
ejpam-6927	176	13	1	1	NUM
ejpam-6927	176	14	,	,	PUNCT
ejpam-6927	176	15	we	we	PRON
ejpam-6927	176	16	have	have	VERB
ejpam-6927	176	17	the	the	DET
ejpam-6927	176	18	following	follow	VERB
ejpam-6927	176	19	h−h	h−h	NOUN
ejpam-6927	176	20	inequality	inequality	NOUN
ejpam-6927	176	21	:	:	PUNCT
ejpam-6927	177	1	1	1	NUM
ejpam-6927	177	2	ω2	ω2	NUM
ejpam-6927	177	3	−	−	PROPN
ejpam-6927	177	4	ω1	ω1	PROPN
ejpam-6927	177	5	∫	∫	PROPN
ejpam-6927	177	6	ω2	ω2	PROPN
ejpam-6927	177	7	ω1	ω1	PROPN
ejpam-6927	177	8	φ(κ)dκ	φ(κ)dκ	PART
ejpam-6927	177	9	−	−	PROPN
ejpam-6927	177	10	φ	φ	PROPN
ejpam-6927	177	11	(	(	PUNCT
ejpam-6927	177	12	ω1	ω1	PROPN
ejpam-6927	177	13	+	+	CCONJ
ejpam-6927	177	14	ω2	ω2	ADJ
ejpam-6927	177	15	2	2	NUM
ejpam-6927	177	16	)	)	PUNCT
ejpam-6927	177	17	≤	≤	NOUN
ejpam-6927	177	18	1	1	NUM
ejpam-6927	177	19	ω2	ω2	NUM
ejpam-6927	177	20	−	−	PROPN
ejpam-6927	177	21	ω1	ω1	PROPN
ejpam-6927	177	22	[	[	PUNCT
ejpam-6927	177	23	1	1	NUM
ejpam-6927	177	24	24	24	NUM
ejpam-6927	177	25	(	(	PUNCT
ejpam-6927	177	26	φ′′(ω2)−	φ′′(ω2)−	NOUN
ejpam-6927	177	27	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	177	28	)	)	PUNCT
ejpam-6927	177	29	)	)	PUNCT
ejpam-6927	178	1	(	(	PUNCT
ejpam-6927	178	2	ω2	ω2	NUM
ejpam-6927	178	3	−	−	PROPN
ejpam-6927	178	4	ω1	ω1	PROPN
ejpam-6927	178	5	)	)	PUNCT
ejpam-6927	178	6	3	3	NUM
ejpam-6927	178	7	−	−	NOUN
ejpam-6927	178	8	1	1	NUM
ejpam-6927	178	9	4	4	NUM
ejpam-6927	178	10	(	(	PUNCT
ejpam-6927	178	11	φ′′(ω2	φ′′(ω2	X
ejpam-6927	178	12	)	)	PUNCT
ejpam-6927	178	13	+	+	PUNCT
ejpam-6927	178	14	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	178	15	)	)	PUNCT
ejpam-6927	178	16	)	)	PUNCT
ejpam-6927	179	1	(	(	PUNCT
ejpam-6927	179	2	ω2	ω2	ADV
ejpam-6927	179	3	−	−	NOUN
ejpam-6927	179	4	ω1)ω	ω1)ω	VERB
ejpam-6927	179	5	2	2	NUM
ejpam-6927	179	6	1	1	NUM
ejpam-6927	179	7	−	−	NUM
ejpam-6927	179	8	1	1	NUM
ejpam-6927	179	9	6	6	NUM
ejpam-6927	179	10	(	(	PUNCT
ejpam-6927	179	11	2φ′′(ω2	2φ′′(ω2	NUM
ejpam-6927	179	12	)	)	PUNCT
ejpam-6927	180	1	+	+	PUNCT
ejpam-6927	180	2	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	180	3	)	)	PUNCT
ejpam-6927	181	1	)	)	PUNCT
ejpam-6927	181	2	ω3	ω3	NOUN
ejpam-6927	181	3	1	1	NUM
ejpam-6927	181	4	−	−	PROPN
ejpam-6927	181	5	1	1	NUM
ejpam-6927	181	6	48	48	NUM
ejpam-6927	181	7	(	(	PUNCT
ejpam-6927	181	8	φ′′(ω2	φ′′(ω2	X
ejpam-6927	181	9	)	)	PUNCT
ejpam-6927	181	10	+	+	PUNCT
ejpam-6927	181	11	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	181	12	)	)	PUNCT
ejpam-6927	181	13	)	)	PUNCT
ejpam-6927	182	1	(	(	PUNCT
ejpam-6927	182	2	ω1	ω1	PROPN
ejpam-6927	182	3	+	+	CCONJ
ejpam-6927	182	4	ω2	ω2	NUM
ejpam-6927	182	5	)	)	PUNCT
ejpam-6927	182	6	3	3	NUM
ejpam-6927	183	1	+	+	CCONJ
ejpam-6927	183	2	1	1	NUM
ejpam-6927	183	3	8	8	NUM
ejpam-6927	183	4	(	(	PUNCT
ejpam-6927	183	5	φ′′(ω2)ω1	φ′′(ω2)ω1	NOUN
ejpam-6927	183	6	−	−	PROPN
ejpam-6927	183	7	φ′′(ω1)ω2	φ′′(ω1)ω2	NOUN
ejpam-6927	183	8	)	)	PUNCT
ejpam-6927	183	9	(	(	PUNCT
ejpam-6927	183	10	ω1	ω1	PROPN
ejpam-6927	183	11	+	+	CCONJ
ejpam-6927	183	12	ω2	ω2	NUM
ejpam-6927	183	13	)	)	PUNCT
ejpam-6927	183	14	2	2	NUM
ejpam-6927	184	1	+	+	CCONJ
ejpam-6927	184	2	1	1	NUM
ejpam-6927	184	3	2	2	NUM
ejpam-6927	184	4	(	(	PUNCT
ejpam-6927	184	5	ω1ω2φ	ω1ω2φ	X
ejpam-6927	184	6	′′(ω1)(ω2	′′(ω1)(ω2	X
ejpam-6927	184	7	−	−	PROPN
ejpam-6927	184	8	ω1	ω1	PROPN
ejpam-6927	184	9	)	)	PUNCT
ejpam-6927	184	10	)	)	PUNCT
ejpam-6927	185	1	+	+	CCONJ
ejpam-6927	185	2	φ′′(ω1)ω	φ′′(ω1)ω	PROPN
ejpam-6927	185	3	2	2	NUM
ejpam-6927	185	4	1ω2	1ω2	NUM
ejpam-6927	185	5	+	+	CCONJ
ejpam-6927	185	6	1	1	NUM
ejpam-6927	185	7	6	6	NUM
ejpam-6927	185	8	(	(	PUNCT
ejpam-6927	185	9	ω2	ω2	ADJ
ejpam-6927	185	10	−	−	PROPN
ejpam-6927	185	11	ω1	ω1	PROPN
ejpam-6927	185	12	)	)	PUNCT
ejpam-6927	185	13	3φ′′(ω1	3φ′′(ω1	ADP
ejpam-6927	185	14	)	)	PUNCT
ejpam-6927	185	15	]	]	PUNCT
ejpam-6927	185	16	.	.	PUNCT
ejpam-6927	186	1	theorem	theorem	ADJ
ejpam-6927	186	2	6	6	NUM
ejpam-6927	186	3	.	.	PUNCT
ejpam-6927	187	1	let	let	VERB
ejpam-6927	187	2	φ	φ	PROPN
ejpam-6927	187	3	∈	∈	PROPN
ejpam-6927	187	4	c2[ω1	c2[ω1	PROPN
ejpam-6927	187	5	,	,	PUNCT
ejpam-6927	187	6	ω2	ω2	NOUN
ejpam-6927	187	7	]	]	PUNCT
ejpam-6927	187	8	such	such	ADJ
ejpam-6927	187	9	that	that	SCONJ
ejpam-6927	187	10	φ′′	φ′′	PROPN
ejpam-6927	187	11	is	be	AUX
ejpam-6927	187	12	convex	convex	ADJ
ejpam-6927	187	13	and	and	CCONJ
ejpam-6927	187	14	0	0	NUM
ejpam-6927	187	15	<	<	X
ejpam-6927	187	16	q	q	X
ejpam-6927	187	17	<	<	X
ejpam-6927	187	18	1	1	NUM
ejpam-6927	187	19	.	.	PUNCT
ejpam-6927	188	1	then	then	ADV
ejpam-6927	188	2	qφ(ω1	qφ(ω1	X
ejpam-6927	188	3	)	)	PUNCT
ejpam-6927	188	4	+	+	CCONJ
ejpam-6927	188	5	φ(ω2	φ(ω2	NOUN
ejpam-6927	188	6	)	)	PUNCT
ejpam-6927	188	7	q	q	NOUN
ejpam-6927	189	1	+	+	NUM
ejpam-6927	189	2	1	1	NUM
ejpam-6927	189	3	−	−	NUM
ejpam-6927	189	4	1	1	NUM
ejpam-6927	189	5	ω2	ω2	NUM
ejpam-6927	189	6	−	−	PROPN
ejpam-6927	189	7	ω1	ω1	PROPN
ejpam-6927	189	8	∫	∫	PROPN
ejpam-6927	189	9	ω2	ω2	PROPN
ejpam-6927	189	10	ω1	ω1	PROPN
ejpam-6927	189	11	φ(κ)ω1dqκ	φ(κ)ω1dqκ	NOUN
ejpam-6927	189	12	≤	≤	NUM
ejpam-6927	189	13	1	1	NUM
ejpam-6927	189	14	ω2	ω2	NUM
ejpam-6927	189	15	−	−	PROPN
ejpam-6927	189	16	ω1	ω1	PROPN
ejpam-6927	189	17	[	[	PUNCT
ejpam-6927	189	18	−	−	PROPN
ejpam-6927	189	19	1	1	NUM
ejpam-6927	189	20	6	6	NUM
ejpam-6927	189	21	(	(	PUNCT
ejpam-6927	189	22	φ′′(ω2)−	φ′′(ω2)−	NOUN
ejpam-6927	189	23	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	189	24	)	)	PUNCT
ejpam-6927	189	25	)	)	PUNCT
ejpam-6927	189	26	(	(	PUNCT
ejpam-6927	189	27	(	(	PUNCT
ejpam-6927	189	28	ω2	ω2	ADJ
ejpam-6927	189	29	−	−	PROPN
ejpam-6927	189	30	ω1	ω1	PROPN
ejpam-6927	189	31	)	)	PUNCT
ejpam-6927	189	32	3	3	NUM
ejpam-6927	189	33	(	(	PUNCT
ejpam-6927	189	34	1	1	NUM
ejpam-6927	189	35	+	+	NUM
ejpam-6927	189	36	q)(1	q)(1	X
ejpam-6927	189	37	+	+	X
ejpam-6927	189	38	q2	q2	NOUN
ejpam-6927	189	39	)	)	PUNCT
ejpam-6927	189	40	)	)	PUNCT
ejpam-6927	189	41	−	−	PROPN
ejpam-6927	190	1	(	(	PUNCT
ejpam-6927	190	2	φ′′(ω2)−	φ′′(ω2)−	NOUN
ejpam-6927	190	3	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	190	4	)	)	PUNCT
ejpam-6927	190	5	2	2	NUM
ejpam-6927	190	6	)	)	PUNCT
ejpam-6927	190	7	(	(	PUNCT
ejpam-6927	190	8	(	(	PUNCT
ejpam-6927	190	9	ω2	ω2	ADJ
ejpam-6927	190	10	−	−	PROPN
ejpam-6927	190	11	ω1	ω1	PROPN
ejpam-6927	190	12	)	)	PUNCT
ejpam-6927	190	13	1	1	NUM
ejpam-6927	191	1	+	+	CCONJ
ejpam-6927	191	2	q	q	X
ejpam-6927	191	3	)	)	PUNCT
ejpam-6927	191	4	ω2	ω2	CCONJ
ejpam-6927	191	5	1	1	NUM
ejpam-6927	192	1	+	+	CCONJ
ejpam-6927	192	2	(	(	PUNCT
ejpam-6927	192	3	2φ′′(ω2	2φ′′(ω2	NUM
ejpam-6927	192	4	)	)	PUNCT
ejpam-6927	193	1	+	+	PUNCT
ejpam-6927	193	2	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	193	3	)	)	PUNCT
ejpam-6927	193	4	6	6	NUM
ejpam-6927	193	5	)	)	PUNCT
ejpam-6927	193	6	ω3	ω3	NOUN
ejpam-6927	193	7	1	1	NUM
ejpam-6927	193	8	−	−	NUM
ejpam-6927	193	9	1	1	NUM
ejpam-6927	193	10	2	2	NUM
ejpam-6927	193	11	(	(	PUNCT
ejpam-6927	193	12	(	(	PUNCT
ejpam-6927	193	13	ω2	ω2	ADJ
ejpam-6927	193	14	−	−	PROPN
ejpam-6927	193	15	ω1	ω1	PROPN
ejpam-6927	193	16	)	)	PUNCT
ejpam-6927	193	17	3	3	NUM
ejpam-6927	193	18	1	1	NUM
ejpam-6927	193	19	+	+	CCONJ
ejpam-6927	193	20	q	q	ADJ
ejpam-6927	193	21	+	+	NUM
ejpam-6927	193	22	q2	q2	NOUN
ejpam-6927	193	23	)	)	PUNCT
ejpam-6927	193	24	φ′′(ω1)−	φ′′(ω1)−	NOUN
ejpam-6927	193	25	ω1ω2φ	ω1ω2φ	PUNCT
ejpam-6927	193	26	′′(ω1)(ω2	′′(ω1)(ω2	X
ejpam-6927	193	27	−	−	PROPN
ejpam-6927	193	28	ω1	ω1	PROPN
ejpam-6927	193	29	)	)	PUNCT
ejpam-6927	193	30	(	(	PUNCT
ejpam-6927	193	31	1	1	NUM
ejpam-6927	193	32	+	+	CCONJ
ejpam-6927	193	33	q	q	X
ejpam-6927	193	34	)	)	PUNCT
ejpam-6927	193	35	−	−	NOUN
ejpam-6927	193	36	1	1	NUM
ejpam-6927	193	37	2	2	NUM
ejpam-6927	193	38	φ′′(ω1)ω	φ′′(ω1)ω	NOUN
ejpam-6927	193	39	2	2	NUM
ejpam-6927	193	40	1ω2	1ω2	NUM
ejpam-6927	193	41	−	−	PROPN
ejpam-6927	193	42	(	(	PUNCT
ejpam-6927	193	43	2φ′′(ω2	2φ′′(ω2	NUM
ejpam-6927	193	44	)	)	PUNCT
ejpam-6927	194	1	+	+	PUNCT
ejpam-6927	194	2	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	194	3	)	)	PUNCT
ejpam-6927	194	4	6	6	NUM
ejpam-6927	194	5	)	)	PUNCT
ejpam-6927	194	6	(	(	PUNCT
ejpam-6927	194	7	qω3	qω3	NOUN
ejpam-6927	194	8	1	1	NUM
ejpam-6927	194	9	1	1	NUM
ejpam-6927	194	10	+	+	CCONJ
ejpam-6927	194	11	q	q	PUNCT
ejpam-6927	194	12	)	)	PUNCT
ejpam-6927	194	13	+	+	CCONJ
ejpam-6927	194	14	(	(	PUNCT
ejpam-6927	194	15	φ′′(ω2	φ′′(ω2	X
ejpam-6927	194	16	)	)	PUNCT
ejpam-6927	194	17	+	+	CCONJ
ejpam-6927	194	18	2φ′′(ω1	2φ′′(ω1	X
ejpam-6927	194	19	)	)	PUNCT
ejpam-6927	194	20	6	6	NUM
ejpam-6927	194	21	)	)	PUNCT
ejpam-6927	194	22	(	(	PUNCT
ejpam-6927	194	23	ω3	ω3	NOUN
ejpam-6927	194	24	2	2	NUM
ejpam-6927	194	25	1	1	NUM
ejpam-6927	194	26	+	+	CCONJ
ejpam-6927	194	27	q	q	NOUN
ejpam-6927	194	28	)	)	PUNCT
ejpam-6927	194	29	m.	m.	NOUN
ejpam-6927	194	30	adil	adil	PROPN
ejpam-6927	194	31	khan	khan	PROPN
ejpam-6927	194	32	et	et	PROPN
ejpam-6927	194	33	al	al	PROPN
ejpam-6927	194	34	.	.	PUNCT
ejpam-6927	194	35	/	/	SYM
ejpam-6927	194	36	eur	eur	PROPN
ejpam-6927	194	37	.	.	PUNCT
ejpam-6927	195	1	j.	j.	PROPN
ejpam-6927	195	2	pure	pure	PROPN
ejpam-6927	195	3	appl	appl	PROPN
ejpam-6927	195	4	.	.	PROPN
ejpam-6927	195	5	math	math	PROPN
ejpam-6927	195	6	,	,	PUNCT
ejpam-6927	195	7	18	18	NUM
ejpam-6927	195	8	(	(	PUNCT
ejpam-6927	195	9	4	4	NUM
ejpam-6927	195	10	)	)	PUNCT
ejpam-6927	195	11	(	(	PUNCT
ejpam-6927	195	12	2025	2025	NUM
ejpam-6927	195	13	)	)	PUNCT
ejpam-6927	195	14	,	,	PUNCT
ejpam-6927	195	15	6927	6927	NUM
ejpam-6927	195	16	9	9	NUM
ejpam-6927	195	17	of	of	ADP
ejpam-6927	195	18	18	18	NUM
ejpam-6927	195	19	−	−	NOUN
ejpam-6927	195	20	(	(	PUNCT
ejpam-6927	195	21	ω2φ	ω2φ	PROPN
ejpam-6927	195	22	′′(ω2)−	′′(ω2)−	VERB
ejpam-6927	195	23	qω1φ	qω1φ	PROPN
ejpam-6927	195	24	′′(ω1	′′(ω1	ADP
ejpam-6927	195	25	)	)	PUNCT
ejpam-6927	195	26	2	2	NUM
ejpam-6927	195	27	)	)	PUNCT
ejpam-6927	195	28	(	(	PUNCT
ejpam-6927	195	29	ω1ω2	ω1ω2	X
ejpam-6927	195	30	1	1	NUM
ejpam-6927	195	31	+	+	CCONJ
ejpam-6927	195	32	q	q	NOUN
ejpam-6927	195	33	)	)	PUNCT
ejpam-6927	195	34	]	]	PUNCT
ejpam-6927	195	35	.	.	PUNCT
ejpam-6927	196	1	(	(	PUNCT
ejpam-6927	196	2	11	11	NUM
ejpam-6927	196	3	)	)	PUNCT
ejpam-6927	196	4	proof	proof	NOUN
ejpam-6927	196	5	.	.	PUNCT
ejpam-6927	197	1	if	if	SCONJ
ejpam-6927	197	2	we	we	PRON
ejpam-6927	197	3	set	set	VERB
ejpam-6927	197	4	κ	κ	NOUN
ejpam-6927	197	5	=	=	SYM
ejpam-6927	197	6	ω2	ω2	ADJ
ejpam-6927	197	7	in	in	ADP
ejpam-6927	197	8	(	(	PUNCT
ejpam-6927	197	9	2	2	NUM
ejpam-6927	197	10	)	)	PUNCT
ejpam-6927	197	11	,	,	PUNCT
ejpam-6927	197	12	then	then	ADV
ejpam-6927	197	13	we	we	PRON
ejpam-6927	197	14	get	get	VERB
ejpam-6927	197	15	φ(ω2	φ(ω2	NOUN
ejpam-6927	197	16	)	)	PUNCT
ejpam-6927	197	17	=	=	SYM
ejpam-6927	197	18	φ(ω1	φ(ω1	X
ejpam-6927	197	19	)	)	PUNCT
ejpam-6927	197	20	+	+	CCONJ
ejpam-6927	197	21	(	(	PUNCT
ejpam-6927	197	22	ω2	ω2	ADJ
ejpam-6927	197	23	−	−	PROPN
ejpam-6927	197	24	ω1)φ	ω1)φ	PROPN
ejpam-6927	197	25	′(ω2	′(ω2	NUM
ejpam-6927	197	26	)	)	PUNCT
ejpam-6927	198	1	+	+	CCONJ
ejpam-6927	198	2	∫	∫	PROPN
ejpam-6927	198	3	ω2	ω2	ADJ
ejpam-6927	198	4	ω1	ω1	PROPN
ejpam-6927	198	5	g(ω2	g(ω2	PROPN
ejpam-6927	198	6	,	,	PUNCT
ejpam-6927	198	7	ℓ)φ	ℓ)φ	X
ejpam-6927	198	8	′′(ℓ)dℓ.	′′(ℓ)dℓ.	X
ejpam-6927	198	9	adding	add	VERB
ejpam-6927	198	10	qφ(ω1	qφ(ω1	NOUN
ejpam-6927	198	11	)	)	PUNCT
ejpam-6927	198	12	and	and	CCONJ
ejpam-6927	198	13	divide	divide	VERB
ejpam-6927	198	14	by	by	ADP
ejpam-6927	198	15	(	(	PUNCT
ejpam-6927	198	16	q	q	X
ejpam-6927	198	17	+	+	NUM
ejpam-6927	198	18	1	1	X
ejpam-6927	198	19	)	)	PUNCT
ejpam-6927	198	20	both	both	DET
ejpam-6927	198	21	sides	side	NOUN
ejpam-6927	198	22	we	we	PRON
ejpam-6927	198	23	get	get	VERB
ejpam-6927	198	24	qφ(ω1	qφ(ω1	ADV
ejpam-6927	198	25	)	)	PUNCT
ejpam-6927	198	26	+	+	CCONJ
ejpam-6927	198	27	φ(ω2	φ(ω2	NOUN
ejpam-6927	198	28	)	)	PUNCT
ejpam-6927	198	29	q	q	NOUN
ejpam-6927	199	1	+	+	NUM
ejpam-6927	199	2	1	1	NUM
ejpam-6927	199	3	=	=	SYM
ejpam-6927	199	4	φ(ω1	φ(ω1	X
ejpam-6927	199	5	)	)	PUNCT
ejpam-6927	199	6	+	+	CCONJ
ejpam-6927	199	7	ω2	ω2	ADJ
ejpam-6927	199	8	−	−	PROPN
ejpam-6927	199	9	ω1	ω1	PROPN
ejpam-6927	199	10	q	q	PROPN
ejpam-6927	199	11	+	+	PROPN
ejpam-6927	199	12	1	1	NUM
ejpam-6927	199	13	φ′(ω2	φ′(ω2	PROPN
ejpam-6927	199	14	)	)	PUNCT
ejpam-6927	199	15	+	+	CCONJ
ejpam-6927	199	16	1	1	NUM
ejpam-6927	199	17	q	q	NOUN
ejpam-6927	199	18	+	+	NUM
ejpam-6927	199	19	1	1	NUM
ejpam-6927	199	20	∫	∫	PROPN
ejpam-6927	199	21	ω2	ω2	PROPN
ejpam-6927	199	22	ω1	ω1	PROPN
ejpam-6927	199	23	g(ω2	g(ω2	PROPN
ejpam-6927	199	24	,	,	PUNCT
ejpam-6927	199	25	ℓ)φ	ℓ)φ	X
ejpam-6927	199	26	′′(ℓ)dℓ.	′′(ℓ)dℓ.	X
ejpam-6927	199	27	(	(	PUNCT
ejpam-6927	199	28	12	12	NUM
ejpam-6927	199	29	)	)	PUNCT
ejpam-6927	199	30	subtracting	subtract	VERB
ejpam-6927	199	31	(	(	PUNCT
ejpam-6927	199	32	5	5	NUM
ejpam-6927	199	33	)	)	PUNCT
ejpam-6927	199	34	from	from	ADP
ejpam-6927	199	35	(	(	PUNCT
ejpam-6927	199	36	12	12	NUM
ejpam-6927	199	37	)	)	PUNCT
ejpam-6927	199	38	,	,	PUNCT
ejpam-6927	199	39	we	we	PRON
ejpam-6927	199	40	get	get	VERB
ejpam-6927	199	41	:	:	PUNCT
ejpam-6927	199	42	qφ(ω1	qφ(ω1	X
ejpam-6927	199	43	)	)	PUNCT
ejpam-6927	199	44	+	+	CCONJ
ejpam-6927	199	45	φ(ω2	φ(ω2	NOUN
ejpam-6927	199	46	)	)	PUNCT
ejpam-6927	199	47	q	q	NOUN
ejpam-6927	200	1	+	+	NUM
ejpam-6927	200	2	1	1	NUM
ejpam-6927	200	3	−	−	NUM
ejpam-6927	200	4	1	1	NUM
ejpam-6927	200	5	ω2	ω2	NUM
ejpam-6927	200	6	−	−	PROPN
ejpam-6927	200	7	ω1	ω1	PROPN
ejpam-6927	200	8	∫	∫	PROPN
ejpam-6927	200	9	ω2	ω2	PROPN
ejpam-6927	200	10	ω1	ω1	PROPN
ejpam-6927	200	11	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	200	12	=	=	SYM
ejpam-6927	200	13	∫	∫	PROPN
ejpam-6927	200	14	ω2	ω2	PROPN
ejpam-6927	200	15	ω1	ω1	PROPN
ejpam-6927	200	16	{	{	PUNCT
ejpam-6927	200	17	g(ω2	g(ω2	NOUN
ejpam-6927	200	18	,	,	PUNCT
ejpam-6927	200	19	ℓ	ℓ	NOUN
ejpam-6927	200	20	)	)	PUNCT
ejpam-6927	200	21	q	q	NOUN
ejpam-6927	201	1	+	+	NOUN
ejpam-6927	201	2	1	1	NUM
ejpam-6927	201	3	−	−	NUM
ejpam-6927	201	4	1	1	NUM
ejpam-6927	201	5	ω2	ω2	NUM
ejpam-6927	201	6	−	−	PROPN
ejpam-6927	201	7	ω1	ω1	PROPN
ejpam-6927	201	8	∫	∫	PROPN
ejpam-6927	201	9	ω2	ω2	PROPN
ejpam-6927	201	10	ω1	ω1	PROPN
ejpam-6927	201	11	g(κ	g(κ	PROPN
ejpam-6927	201	12	,	,	PUNCT
ejpam-6927	201	13	ℓ)ω1dqκ	ℓ)ω1dqκ	PROPN
ejpam-6927	201	14	}	}	PUNCT
ejpam-6927	201	15	φ′′(ℓ)dℓ.	φ′′(ℓ)dℓ.	PROPN
ejpam-6927	201	16	(	(	PUNCT
ejpam-6927	201	17	13	13	NUM
ejpam-6927	201	18	)	)	PUNCT
ejpam-6927	201	19	let	let	VERB
ejpam-6927	201	20	γ(ℓ	γ(ℓ	X
ejpam-6927	201	21	)	)	PUNCT
ejpam-6927	202	1	=	=	SYM
ejpam-6927	202	2	g(ω2	g(ω2	NOUN
ejpam-6927	202	3	,	,	PUNCT
ejpam-6927	202	4	ℓ	ℓ	NOUN
ejpam-6927	202	5	)	)	PUNCT
ejpam-6927	202	6	q	q	NOUN
ejpam-6927	203	1	+	+	NOUN
ejpam-6927	203	2	1	1	NUM
ejpam-6927	203	3	−	−	NUM
ejpam-6927	203	4	1	1	NUM
ejpam-6927	203	5	ω2	ω2	NUM
ejpam-6927	203	6	−	−	PROPN
ejpam-6927	203	7	ω1	ω1	PROPN
ejpam-6927	203	8	∫	∫	PROPN
ejpam-6927	203	9	ω2	ω2	PROPN
ejpam-6927	203	10	ω1	ω1	PROPN
ejpam-6927	203	11	g(κ	g(κ	PROPN
ejpam-6927	203	12	,	,	PUNCT
ejpam-6927	203	13	ℓ)ω1dqκ	ℓ)ω1dqκ	PROPN
ejpam-6927	203	14	.	.	PROPN
ejpam-6927	203	15	clearly	clearly	ADV
ejpam-6927	203	16	γ(ℓ	γ(ℓ	X
ejpam-6927	203	17	)	)	PUNCT
ejpam-6927	203	18	is	be	AUX
ejpam-6927	203	19	the	the	DET
ejpam-6927	203	20	difference	difference	NOUN
ejpam-6927	203	21	of	of	ADP
ejpam-6927	203	22	right	right	ADJ
ejpam-6927	203	23	and	and	CCONJ
ejpam-6927	203	24	middle	middle	ADJ
ejpam-6927	203	25	side	side	NOUN
ejpam-6927	203	26	of	of	ADP
ejpam-6927	203	27	(	(	PUNCT
ejpam-6927	203	28	1	1	NUM
ejpam-6927	203	29	)	)	PUNCT
ejpam-6927	203	30	,	,	PUNCT
ejpam-6927	203	31	for	for	ADP
ejpam-6927	203	32	the	the	DET
ejpam-6927	203	33	green	green	ADJ
ejpam-6927	203	34	function	function	NOUN
ejpam-6927	203	35	therefore	therefore	ADV
ejpam-6927	203	36	by	by	ADP
ejpam-6927	203	37	γ(ℓ	γ(ℓ	PROPN
ejpam-6927	203	38	)	)	PUNCT
ejpam-6927	203	39	is	be	AUX
ejpam-6927	203	40	non	non	ADJ
ejpam-6927	203	41	-	-	ADJ
ejpam-6927	203	42	negative	negative	ADJ
ejpam-6927	203	43	.	.	PUNCT
ejpam-6927	204	1	let	let	VERB
ejpam-6927	204	2	ℓ	ℓ	NOUN
ejpam-6927	204	3	=	=	SYM
ejpam-6927	204	4	ℓ−	ℓ−	PROPN
ejpam-6927	204	5	ω1	ω1	PROPN
ejpam-6927	204	6	ω2	ω2	PROPN
ejpam-6927	204	7	−	−	PROPN
ejpam-6927	204	8	ω1	ω1	PROPN
ejpam-6927	204	9	ω2	ω2	PROPN
ejpam-6927	204	10	+	+	CCONJ
ejpam-6927	204	11	ω2	ω2	ADJ
ejpam-6927	204	12	−	−	PROPN
ejpam-6927	204	13	ℓ	ℓ	PROPN
ejpam-6927	204	14	ω2	ω2	PROPN
ejpam-6927	204	15	−	−	PROPN
ejpam-6927	204	16	ω1	ω1	PROPN
ejpam-6927	204	17	ω1	ω1	PROPN
ejpam-6927	204	18	.	.	PUNCT
ejpam-6927	205	1	then	then	ADV
ejpam-6927	205	2	from	from	ADP
ejpam-6927	205	3	(	(	PUNCT
ejpam-6927	205	4	13	13	NUM
ejpam-6927	205	5	)	)	PUNCT
ejpam-6927	205	6	we	we	PRON
ejpam-6927	205	7	have	have	VERB
ejpam-6927	205	8	qφ(ω1	qφ(ω1	NOUN
ejpam-6927	205	9	)	)	PUNCT
ejpam-6927	205	10	+	+	CCONJ
ejpam-6927	205	11	φ(ω2	φ(ω2	NOUN
ejpam-6927	205	12	)	)	PUNCT
ejpam-6927	205	13	q	q	NOUN
ejpam-6927	206	1	+	+	NUM
ejpam-6927	206	2	1	1	NUM
ejpam-6927	206	3	−	−	NUM
ejpam-6927	206	4	1	1	NUM
ejpam-6927	206	5	ω2	ω2	NUM
ejpam-6927	206	6	−	−	PROPN
ejpam-6927	206	7	ω1	ω1	PROPN
ejpam-6927	206	8	∫	∫	PROPN
ejpam-6927	206	9	ω2	ω2	PROPN
ejpam-6927	206	10	ω1	ω1	PROPN
ejpam-6927	206	11	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	206	12	=	=	SYM
ejpam-6927	206	13	∫	∫	PROPN
ejpam-6927	206	14	ω2	ω2	PROPN
ejpam-6927	206	15	ω1	ω1	PROPN
ejpam-6927	206	16	γ(ℓ)φ′′	γ(ℓ)φ′′	PROPN
ejpam-6927	206	17	(	(	PUNCT
ejpam-6927	206	18	ℓ−	ℓ−	PROPN
ejpam-6927	206	19	ω1	ω1	PROPN
ejpam-6927	206	20	ω2	ω2	PROPN
ejpam-6927	206	21	−	−	PROPN
ejpam-6927	206	22	ω1	ω1	PROPN
ejpam-6927	206	23	ω2	ω2	PROPN
ejpam-6927	206	24	+	+	CCONJ
ejpam-6927	206	25	ω2	ω2	ADJ
ejpam-6927	206	26	−	−	PROPN
ejpam-6927	206	27	ℓ	ℓ	PROPN
ejpam-6927	206	28	ω2	ω2	PROPN
ejpam-6927	206	29	−	−	PROPN
ejpam-6927	206	30	ω1	ω1	PROPN
ejpam-6927	206	31	ω1	ω1	PROPN
ejpam-6927	206	32	)	)	PUNCT
ejpam-6927	206	33	dℓ.	dℓ.	VERB
ejpam-6927	206	34	by	by	ADP
ejpam-6927	206	35	convexity	convexity	NOUN
ejpam-6927	206	36	of	of	ADP
ejpam-6927	206	37	φ′′	φ′′	PROPN
ejpam-6927	206	38	,	,	PUNCT
ejpam-6927	206	39	we	we	PRON
ejpam-6927	206	40	obtain	obtain	VERB
ejpam-6927	206	41	qφ(ω1	qφ(ω1	ADV
ejpam-6927	206	42	)	)	PUNCT
ejpam-6927	206	43	+	+	CCONJ
ejpam-6927	206	44	φ(ω2	φ(ω2	NOUN
ejpam-6927	206	45	)	)	PUNCT
ejpam-6927	206	46	q	q	NOUN
ejpam-6927	207	1	+	+	NUM
ejpam-6927	207	2	1	1	NUM
ejpam-6927	207	3	−	−	NUM
ejpam-6927	207	4	1	1	NUM
ejpam-6927	207	5	ω2	ω2	NUM
ejpam-6927	207	6	−	−	PROPN
ejpam-6927	207	7	ω1	ω1	PROPN
ejpam-6927	207	8	∫	∫	PROPN
ejpam-6927	207	9	ω2	ω2	PROPN
ejpam-6927	207	10	ω1	ω1	PROPN
ejpam-6927	207	11	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	207	12	≤	≤	NUM
ejpam-6927	207	13	∫	∫	PROPN
ejpam-6927	207	14	ω2	ω2	PROPN
ejpam-6927	207	15	ω1	ω1	PROPN
ejpam-6927	207	16	γ(ℓ	γ(ℓ	PROPN
ejpam-6927	207	17	)	)	PUNCT
ejpam-6927	207	18	{	{	PUNCT
ejpam-6927	207	19	ℓ−	ℓ−	PROPN
ejpam-6927	207	20	ω1	ω1	PROPN
ejpam-6927	207	21	ω2	ω2	PROPN
ejpam-6927	207	22	−	−	PROPN
ejpam-6927	207	23	ω1	ω1	PROPN
ejpam-6927	207	24	φ′′(ω2	φ′′(ω2	PROPN
ejpam-6927	207	25	)	)	PUNCT
ejpam-6927	207	26	+	+	CCONJ
ejpam-6927	207	27	(	(	PUNCT
ejpam-6927	207	28	ω2	ω2	ADJ
ejpam-6927	207	29	−	−	PROPN
ejpam-6927	207	30	ℓ	ℓ	PROPN
ejpam-6927	207	31	ω2	ω2	PROPN
ejpam-6927	207	32	−	−	PROPN
ejpam-6927	207	33	ω1	ω1	PROPN
ejpam-6927	207	34	)	)	PUNCT
ejpam-6927	207	35	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	207	36	)	)	PUNCT
ejpam-6927	207	37	}	}	PUNCT
ejpam-6927	207	38	dℓ.	dℓ.	VERB
ejpam-6927	207	39	⇒	⇒	NOUN
ejpam-6927	207	40	qφ(ω1	qφ(ω1	ADV
ejpam-6927	207	41	)	)	PUNCT
ejpam-6927	207	42	+	+	CCONJ
ejpam-6927	207	43	φ(ω2	φ(ω2	NOUN
ejpam-6927	207	44	)	)	PUNCT
ejpam-6927	207	45	q	q	NOUN
ejpam-6927	208	1	+	+	NUM
ejpam-6927	208	2	1	1	NUM
ejpam-6927	208	3	−	−	NUM
ejpam-6927	208	4	1	1	NUM
ejpam-6927	208	5	ω2	ω2	NUM
ejpam-6927	208	6	−	−	PROPN
ejpam-6927	208	7	ω1	ω1	PROPN
ejpam-6927	208	8	∫	∫	PROPN
ejpam-6927	208	9	ω2	ω2	PROPN
ejpam-6927	208	10	ω1	ω1	PROPN
ejpam-6927	208	11	φ(κ)ω1dqκ	φ(κ)ω1dqκ	NOUN
ejpam-6927	208	12	≤	≤	ADV
ejpam-6927	208	13	1	1	NUM
ejpam-6927	208	14	(	(	PUNCT
ejpam-6927	208	15	ω2	ω2	ADJ
ejpam-6927	208	16	−	−	PROPN
ejpam-6927	208	17	ω1	ω1	PROPN
ejpam-6927	208	18	)	)	PUNCT
ejpam-6927	208	19	{	{	PUNCT
ejpam-6927	208	20	φ′′(ω2	φ′′(ω2	NOUN
ejpam-6927	208	21	)	)	PUNCT
ejpam-6927	208	22	∫	∫	PROPN
ejpam-6927	208	23	ω2	ω2	PROPN
ejpam-6927	208	24	ω1	ω1	PROPN
ejpam-6927	208	25	γ(ℓ)(ℓ−	γ(ℓ)(ℓ−	PROPN
ejpam-6927	208	26	ω1)dℓ+	ω1)dℓ+	PROPN
ejpam-6927	208	27	φ′′(ω1)∫	φ′′(ω1)∫	PROPN
ejpam-6927	208	28	ω2	ω2	PROPN
ejpam-6927	208	29	ω1	ω1	PROPN
ejpam-6927	208	30	γ(ℓ)(ω2	γ(ℓ)(ω2	PROPN
ejpam-6927	208	31	−	−	PROPN
ejpam-6927	208	32	ℓ)dℓ	ℓ)dℓ	PROPN
ejpam-6927	208	33	}	}	PUNCT
ejpam-6927	208	34	.	.	PUNCT
ejpam-6927	209	1	(	(	PUNCT
ejpam-6927	209	2	14	14	NUM
ejpam-6927	209	3	)	)	PUNCT
ejpam-6927	209	4	now	now	ADV
ejpam-6927	209	5	we	we	PRON
ejpam-6927	209	6	find	find	VERB
ejpam-6927	209	7	the	the	DET
ejpam-6927	209	8	integral	integral	ADJ
ejpam-6927	209	9	∫	∫	PROPN
ejpam-6927	209	10	ω2	ω2	PROPN
ejpam-6927	209	11	ω1	ω1	PROPN
ejpam-6927	209	12	γ(ℓ)(ℓ−	γ(ℓ)(ℓ−	CCONJ
ejpam-6927	209	13	ω1)dℓ.	ω1)dℓ.	PUNCT
ejpam-6927	209	14	if	if	SCONJ
ejpam-6927	209	15	φ(ℓ	φ(ℓ	PROPN
ejpam-6927	209	16	)	)	PUNCT
ejpam-6927	209	17	=	=	SYM
ejpam-6927	209	18	1	1	NUM
ejpam-6927	209	19	6ℓ	6ℓ	NOUN
ejpam-6927	209	20	3	3	NUM
ejpam-6927	209	21	−	−	NOUN
ejpam-6927	209	22	1	1	NUM
ejpam-6927	209	23	2ω1ℓ	2ω1ℓ	NUM
ejpam-6927	209	24	2	2	NUM
ejpam-6927	209	25	,	,	PUNCT
ejpam-6927	209	26	then	then	ADV
ejpam-6927	209	27	φ	φ	NUM
ejpam-6927	209	28	′′	′′	PROPN
ejpam-6927	209	29	(	(	PUNCT
ejpam-6927	209	30	ℓ	ℓ	NOUN
ejpam-6927	209	31	)	)	PUNCT
ejpam-6927	209	32	=	=	SYM
ejpam-6927	209	33	ℓ−	ℓ−	PROPN
ejpam-6927	209	34	ω1	ω1	PROPN
ejpam-6927	209	35	,	,	PUNCT
ejpam-6927	209	36	using	use	VERB
ejpam-6927	209	37	these	these	DET
ejpam-6927	209	38	functions	function	NOUN
ejpam-6927	209	39	in	in	ADP
ejpam-6927	209	40	(	(	PUNCT
ejpam-6927	209	41	13	13	NUM
ejpam-6927	209	42	)	)	PUNCT
ejpam-6927	209	43	we	we	PRON
ejpam-6927	209	44	obtain	obtain	VERB
ejpam-6927	209	45	.	.	PUNCT
ejpam-6927	210	1	∫	∫	PROPN
ejpam-6927	211	1	ω2	ω2	PROPN
ejpam-6927	211	2	ω1	ω1	PROPN
ejpam-6927	211	3	γ(ℓ)(ℓ−	γ(ℓ)(ℓ−	PROPN
ejpam-6927	211	4	ω1)dℓ	ω1)dℓ	PROPN
ejpam-6927	211	5	=	=	SYM
ejpam-6927	211	6	q	q	PROPN
ejpam-6927	212	1	(	(	PUNCT
ejpam-6927	212	2	ω3	ω3	NOUN
ejpam-6927	212	3	1	1	NUM
ejpam-6927	212	4	6	6	NUM
ejpam-6927	212	5	−	−	NOUN
ejpam-6927	212	6	ω1ω2	ω1ω2	SYM
ejpam-6927	212	7	1	1	NUM
ejpam-6927	212	8	2	2	NUM
ejpam-6927	212	9	)	)	PUNCT
ejpam-6927	213	1	+	+	CCONJ
ejpam-6927	213	2	ω3	ω3	ADJ
ejpam-6927	213	3	2	2	NUM
ejpam-6927	213	4	6	6	NUM
ejpam-6927	213	5	−	−	NOUN
ejpam-6927	213	6	ω1ω2	ω1ω2	SYM
ejpam-6927	213	7	2	2	NUM
ejpam-6927	213	8	2	2	NUM
ejpam-6927	213	9	1	1	NUM
ejpam-6927	213	10	+	+	NOUN
ejpam-6927	213	11	q	q	NOUN
ejpam-6927	213	12	−	−	PROPN
ejpam-6927	213	13	1	1	NUM
ejpam-6927	213	14	ω2	ω2	NUM
ejpam-6927	213	15	−	−	PROPN
ejpam-6927	213	16	ω1	ω1	PROPN
ejpam-6927	213	17	∫	∫	PROPN
ejpam-6927	213	18	ω2	ω2	PROPN
ejpam-6927	213	19	ω1	ω1	PROPN
ejpam-6927	213	20	(	(	PUNCT
ejpam-6927	213	21	κ3	κ3	PROPN
ejpam-6927	213	22	6	6	NUM
ejpam-6927	213	23	−	−	NOUN
ejpam-6927	213	24	b1	b1	NOUN
ejpam-6927	213	25	κ2	κ2	NOUN
ejpam-6927	213	26	2	2	NUM
ejpam-6927	213	27	)	)	PUNCT
ejpam-6927	213	28	ω1	ω1	PROPN
ejpam-6927	213	29	dqκ	dqκ	PROPN
ejpam-6927	213	30	.	.	PUNCT
ejpam-6927	214	1	m.	m.	PROPN
ejpam-6927	214	2	adil	adil	PROPN
ejpam-6927	214	3	khan	khan	PROPN
ejpam-6927	214	4	et	et	PROPN
ejpam-6927	214	5	al	al	PROPN
ejpam-6927	214	6	.	.	PUNCT
ejpam-6927	214	7	/	/	SYM
ejpam-6927	214	8	eur	eur	PROPN
ejpam-6927	214	9	.	.	PUNCT
ejpam-6927	215	1	j.	j.	PROPN
ejpam-6927	215	2	pure	pure	PROPN
ejpam-6927	215	3	appl	appl	PROPN
ejpam-6927	215	4	.	.	PROPN
ejpam-6927	215	5	math	math	PROPN
ejpam-6927	215	6	,	,	PUNCT
ejpam-6927	215	7	18	18	NUM
ejpam-6927	215	8	(	(	PUNCT
ejpam-6927	215	9	4	4	NUM
ejpam-6927	215	10	)	)	PUNCT
ejpam-6927	215	11	(	(	PUNCT
ejpam-6927	215	12	2025	2025	NUM
ejpam-6927	215	13	)	)	PUNCT
ejpam-6927	215	14	,	,	PUNCT
ejpam-6927	215	15	6927	6927	NUM
ejpam-6927	215	16	10	10	NUM
ejpam-6927	215	17	of	of	ADP
ejpam-6927	215	18	18	18	NUM
ejpam-6927	215	19	finding	find	VERB
ejpam-6927	215	20	the	the	DET
ejpam-6927	215	21	above	above	ADJ
ejpam-6927	215	22	integrals	integral	NOUN
ejpam-6927	215	23	,	,	PUNCT
ejpam-6927	215	24	we	we	PRON
ejpam-6927	215	25	deduce.∫	deduce.∫	VERB
ejpam-6927	215	26	ω2	ω2	ADJ
ejpam-6927	215	27	ω1	ω1	PROPN
ejpam-6927	215	28	γ(ℓ)(ℓ−	γ(ℓ)(ℓ−	PROPN
ejpam-6927	215	29	ω1)dℓ	ω1)dℓ	PROPN
ejpam-6927	215	30	=	=	SYM
ejpam-6927	215	31	−1	−1	NOUN
ejpam-6927	215	32	6	6	NUM
ejpam-6927	215	33	(	(	PUNCT
ejpam-6927	215	34	ω2	ω2	ADJ
ejpam-6927	215	35	−	−	PROPN
ejpam-6927	215	36	ω1	ω1	PROPN
ejpam-6927	215	37	)	)	PUNCT
ejpam-6927	215	38	3	3	NUM
ejpam-6927	215	39	(	(	PUNCT
ejpam-6927	215	40	1	1	NUM
ejpam-6927	215	41	+	+	NUM
ejpam-6927	215	42	q)(1	q)(1	X
ejpam-6927	215	43	+	+	CCONJ
ejpam-6927	215	44	q2	q2	NOUN
ejpam-6927	215	45	)	)	PUNCT
ejpam-6927	215	46	−	−	NOUN
ejpam-6927	215	47	1	1	NUM
ejpam-6927	215	48	2	2	NUM
ejpam-6927	215	49	ω2	ω2	NUM
ejpam-6927	215	50	1(ω2	1(ω2	NUM
ejpam-6927	215	51	−	−	PROPN
ejpam-6927	215	52	ω1	ω1	PROPN
ejpam-6927	215	53	)	)	PUNCT
ejpam-6927	215	54	1	1	NUM
ejpam-6927	216	1	+	+	CCONJ
ejpam-6927	216	2	q	q	PUNCT
ejpam-6927	217	1	+	+	NUM
ejpam-6927	217	2	1	1	NUM
ejpam-6927	217	3	3	3	NUM
ejpam-6927	217	4	ω3	ω3	NOUN
ejpam-6927	217	5	1	1	NUM
ejpam-6927	217	6	+	+	CCONJ
ejpam-6927	217	7	−	−	PROPN
ejpam-6927	217	8	qω3	qω3	NOUN
ejpam-6927	217	9	1	1	NUM
ejpam-6927	217	10	3	3	NUM
ejpam-6927	217	11	+	+	CCONJ
ejpam-6927	217	12	ω3	ω3	ADJ
ejpam-6927	217	13	2	2	NUM
ejpam-6927	217	14	6	6	NUM
ejpam-6927	217	15	−	−	NOUN
ejpam-6927	217	16	ω1ω2	ω1ω2	SYM
ejpam-6927	217	17	2	2	NUM
ejpam-6927	217	18	2	2	NUM
ejpam-6927	217	19	1	1	NUM
ejpam-6927	217	20	+	+	CCONJ
ejpam-6927	217	21	q	q	NOUN
ejpam-6927	217	22	.	.	PUNCT
ejpam-6927	218	1	(	(	PUNCT
ejpam-6927	218	2	15	15	NUM
ejpam-6927	218	3	)	)	PUNCT
ejpam-6927	218	4	now	now	ADV
ejpam-6927	218	5	we	we	PRON
ejpam-6927	218	6	find	find	VERB
ejpam-6927	218	7	the	the	DET
ejpam-6927	218	8	integral	integral	ADJ
ejpam-6927	218	9	∫	∫	PROPN
ejpam-6927	218	10	ω2	ω2	PROPN
ejpam-6927	218	11	ω1	ω1	PROPN
ejpam-6927	218	12	γ(ℓ)(ω2	γ(ℓ)(ω2	PROPN
ejpam-6927	218	13	−	−	PROPN
ejpam-6927	218	14	ℓ)dℓ.	ℓ)dℓ.	PROPN
ejpam-6927	218	15	if	if	SCONJ
ejpam-6927	218	16	φ(ℓ	φ(ℓ	X
ejpam-6927	218	17	)	)	PUNCT
ejpam-6927	218	18	=	=	SYM
ejpam-6927	219	1	1	1	NUM
ejpam-6927	219	2	2ω2ℓ	2ω2ℓ	ADJ
ejpam-6927	219	3	2	2	NUM
ejpam-6927	219	4	−	−	NOUN
ejpam-6927	219	5	1	1	NUM
ejpam-6927	219	6	6ℓ	6ℓ	NOUN
ejpam-6927	219	7	3	3	NUM
ejpam-6927	219	8	,	,	PUNCT
ejpam-6927	219	9	then	then	ADV
ejpam-6927	219	10	φ	φ	NUM
ejpam-6927	219	11	′′	′′	PROPN
ejpam-6927	219	12	(	(	PUNCT
ejpam-6927	219	13	ℓ	ℓ	NOUN
ejpam-6927	219	14	)	)	PUNCT
ejpam-6927	219	15	=	=	SYM
ejpam-6927	219	16	ω2	ω2	ADJ
ejpam-6927	219	17	−	−	PROPN
ejpam-6927	219	18	ℓ.	ℓ.	NOUN
ejpam-6927	219	19	using	use	VERB
ejpam-6927	219	20	these	these	DET
ejpam-6927	219	21	functions	function	NOUN
ejpam-6927	219	22	in	in	ADP
ejpam-6927	219	23	(	(	PUNCT
ejpam-6927	219	24	13	13	NUM
ejpam-6927	219	25	)	)	PUNCT
ejpam-6927	219	26	we	we	PRON
ejpam-6927	219	27	obtain	obtain	VERB
ejpam-6927	219	28	.	.	PUNCT
ejpam-6927	220	1	∫	∫	PROPN
ejpam-6927	220	2	ω2	ω2	PROPN
ejpam-6927	220	3	ω1	ω1	PROPN
ejpam-6927	221	1	γ(ℓ)(ω2	γ(ℓ)(ω2	PROPN
ejpam-6927	221	2	−	−	PROPN
ejpam-6927	221	3	ℓ)dℓ	ℓ)dℓ	PROPN
ejpam-6927	221	4	=	=	SYM
ejpam-6927	221	5	q	q	PROPN
ejpam-6927	222	1	(	(	PUNCT
ejpam-6927	222	2	ω2ω2	ω2ω2	PROPN
ejpam-6927	222	3	1	1	NUM
ejpam-6927	222	4	2	2	NUM
ejpam-6927	222	5	−	−	NOUN
ejpam-6927	222	6	ω3	ω3	NOUN
ejpam-6927	222	7	1	1	NUM
ejpam-6927	222	8	6	6	NUM
ejpam-6927	222	9	)	)	PUNCT
ejpam-6927	223	1	+	+	CCONJ
ejpam-6927	223	2	ω2ω2	ω2ω2	NUM
ejpam-6927	223	3	2	2	NUM
ejpam-6927	223	4	2	2	NUM
ejpam-6927	223	5	−	−	NOUN
ejpam-6927	223	6	ω3	ω3	NOUN
ejpam-6927	223	7	2	2	NUM
ejpam-6927	223	8	6	6	NUM
ejpam-6927	223	9	1	1	NUM
ejpam-6927	223	10	+	+	CCONJ
ejpam-6927	223	11	q	q	NOUN
ejpam-6927	223	12	−	−	PROPN
ejpam-6927	223	13	1	1	NUM
ejpam-6927	223	14	ω2	ω2	NUM
ejpam-6927	223	15	−	−	PROPN
ejpam-6927	223	16	ω1	ω1	PROPN
ejpam-6927	223	17	∫	∫	PROPN
ejpam-6927	223	18	ω2	ω2	PROPN
ejpam-6927	223	19	ω1	ω1	PROPN
ejpam-6927	223	20	(	(	PUNCT
ejpam-6927	223	21	ω2	ω2	ADJ
ejpam-6927	223	22	2	2	NUM
ejpam-6927	223	23	κ2	κ2	NOUN
ejpam-6927	223	24	−	−	NOUN
ejpam-6927	223	25	1	1	NUM
ejpam-6927	223	26	6	6	NUM
ejpam-6927	223	27	κ3	κ3	PROPN
ejpam-6927	223	28	)	)	PUNCT
ejpam-6927	223	29	ω1dqκ	ω1dqκ	NOUN
ejpam-6927	223	30	.	.	PUNCT
ejpam-6927	224	1	finding	find	VERB
ejpam-6927	224	2	the	the	DET
ejpam-6927	224	3	above	above	ADJ
ejpam-6927	224	4	integrals	integral	NOUN
ejpam-6927	224	5	,	,	PUNCT
ejpam-6927	224	6	we	we	PRON
ejpam-6927	224	7	deduce.∫	deduce.∫	VERB
ejpam-6927	224	8	ω2	ω2	ADJ
ejpam-6927	224	9	ω1	ω1	PROPN
ejpam-6927	225	1	γ(ℓ)(ω2	γ(ℓ)(ω2	PROPN
ejpam-6927	225	2	−	−	PROPN
ejpam-6927	225	3	ℓ)dℓ	ℓ)dℓ	PROPN
ejpam-6927	225	4	=	=	PROPN
ejpam-6927	225	5	−	−	PROPN
ejpam-6927	225	6	ω2	ω2	ADJ
ejpam-6927	225	7	2	2	NUM
ejpam-6927	225	8	(	(	PUNCT
ejpam-6927	225	9	(	(	PUNCT
ejpam-6927	225	10	ω2	ω2	ADJ
ejpam-6927	225	11	−	−	PROPN
ejpam-6927	225	12	ω1	ω1	PROPN
ejpam-6927	225	13	)	)	PUNCT
ejpam-6927	225	14	2	2	NUM
ejpam-6927	225	15	1	1	NUM
ejpam-6927	225	16	+	+	CCONJ
ejpam-6927	225	17	q	q	ADJ
ejpam-6927	225	18	+	+	NUM
ejpam-6927	225	19	q2	q2	NOUN
ejpam-6927	225	20	)	)	PUNCT
ejpam-6927	225	21	−	−	PROPN
ejpam-6927	225	22	ω1ω2(ω2	ω1ω2(ω2	NUM
ejpam-6927	225	23	−	−	PROPN
ejpam-6927	225	24	ω1	ω1	PROPN
ejpam-6927	225	25	)	)	PUNCT
ejpam-6927	225	26	1	1	NUM
ejpam-6927	225	27	+	+	CCONJ
ejpam-6927	225	28	q	q	NOUN
ejpam-6927	225	29	−	−	PROPN
ejpam-6927	225	30	ω1	ω1	PROPN
ejpam-6927	225	31	2ω2	2ω2	NUM
ejpam-6927	225	32	2	2	NUM
ejpam-6927	225	33	+	+	CCONJ
ejpam-6927	225	34	1	1	NUM
ejpam-6927	225	35	6	6	NUM
ejpam-6927	225	36	(	(	PUNCT
ejpam-6927	225	37	ω2	ω2	ADJ
ejpam-6927	225	38	−	−	PROPN
ejpam-6927	225	39	ω1	ω1	PROPN
ejpam-6927	225	40	)	)	PUNCT
ejpam-6927	225	41	3	3	NUM
ejpam-6927	225	42	(	(	PUNCT
ejpam-6927	225	43	1	1	NUM
ejpam-6927	225	44	+	+	NUM
ejpam-6927	225	45	q)(1	q)(1	X
ejpam-6927	225	46	+	+	X
ejpam-6927	225	47	q2	q2	NOUN
ejpam-6927	225	48	)	)	PUNCT
ejpam-6927	226	1	+	+	CCONJ
ejpam-6927	226	2	1	1	NUM
ejpam-6927	226	3	2	2	NUM
ejpam-6927	226	4	ω1(ω2	ω1(ω2	NUM
ejpam-6927	226	5	−	−	NOUN
ejpam-6927	226	6	ω1	ω1	PROPN
ejpam-6927	226	7	)	)	PUNCT
ejpam-6927	226	8	2	2	NUM
ejpam-6927	226	9	1	1	NUM
ejpam-6927	226	10	+	+	CCONJ
ejpam-6927	226	11	q	q	NOUN
ejpam-6927	227	1	+	+	NUM
ejpam-6927	227	2	q2	q2	NOUN
ejpam-6927	227	3	+	+	CCONJ
ejpam-6927	227	4	1	1	NUM
ejpam-6927	227	5	2	2	NUM
ejpam-6927	227	6	ω2	ω2	NUM
ejpam-6927	227	7	1(ω2	1(ω2	NUM
ejpam-6927	227	8	−	−	PROPN
ejpam-6927	227	9	ω1	ω1	PROPN
ejpam-6927	227	10	)	)	PUNCT
ejpam-6927	227	11	1	1	NUM
ejpam-6927	228	1	+	+	CCONJ
ejpam-6927	228	2	q	q	PUNCT
ejpam-6927	229	1	+	+	NUM
ejpam-6927	229	2	1	1	NUM
ejpam-6927	229	3	6	6	NUM
ejpam-6927	229	4	ω3	ω3	NOUN
ejpam-6927	229	5	1	1	NUM
ejpam-6927	229	6	+	+	CCONJ
ejpam-6927	229	7	qω2	qω2	VERB
ejpam-6927	229	8	1ω2	1ω2	NUM
ejpam-6927	229	9	2	2	NUM
ejpam-6927	229	10	−	−	NOUN
ejpam-6927	229	11	qω3	qω3	NOUN
ejpam-6927	229	12	1	1	NUM
ejpam-6927	229	13	6	6	NUM
ejpam-6927	229	14	+	+	CCONJ
ejpam-6927	229	15	ω3	ω3	ADJ
ejpam-6927	229	16	2	2	NUM
ejpam-6927	229	17	3	3	NUM
ejpam-6927	229	18	1	1	NUM
ejpam-6927	229	19	+	+	CCONJ
ejpam-6927	229	20	q	q	NOUN
ejpam-6927	229	21	.	.	PUNCT
ejpam-6927	230	1	(	(	PUNCT
ejpam-6927	230	2	16	16	NUM
ejpam-6927	230	3	)	)	PUNCT
ejpam-6927	230	4	using	use	VERB
ejpam-6927	230	5	(	(	PUNCT
ejpam-6927	230	6	15	15	NUM
ejpam-6927	230	7	)	)	PUNCT
ejpam-6927	230	8	and	and	CCONJ
ejpam-6927	230	9	(	(	PUNCT
ejpam-6927	230	10	16	16	NUM
ejpam-6927	230	11	)	)	PUNCT
ejpam-6927	230	12	in	in	ADP
ejpam-6927	230	13	(	(	PUNCT
ejpam-6927	230	14	14	14	NUM
ejpam-6927	230	15	)	)	PUNCT
ejpam-6927	230	16	,	,	PUNCT
ejpam-6927	230	17	we	we	PRON
ejpam-6927	230	18	get	get	VERB
ejpam-6927	230	19	≤	≤	NUM
ejpam-6927	230	20	1	1	NUM
ejpam-6927	230	21	(	(	PUNCT
ejpam-6927	230	22	ω2	ω2	ADJ
ejpam-6927	230	23	−	−	PROPN
ejpam-6927	230	24	ω1	ω1	PROPN
ejpam-6927	230	25	)	)	PUNCT
ejpam-6927	230	26	[	[	PUNCT
ejpam-6927	230	27	φ′′(ω2	φ′′(ω2	X
ejpam-6927	230	28	)	)	PUNCT
ejpam-6927	230	29	{	{	PUNCT
ejpam-6927	230	30	−	−	PROPN
ejpam-6927	230	31	1	1	NUM
ejpam-6927	230	32	6	6	NUM
ejpam-6927	230	33	(	(	PUNCT
ejpam-6927	230	34	ω2	ω2	ADJ
ejpam-6927	230	35	−	−	PROPN
ejpam-6927	230	36	ω1	ω1	PROPN
ejpam-6927	230	37	)	)	PUNCT
ejpam-6927	230	38	3	3	NUM
ejpam-6927	230	39	(	(	PUNCT
ejpam-6927	230	40	1	1	NUM
ejpam-6927	230	41	+	+	NUM
ejpam-6927	230	42	q)(1	q)(1	X
ejpam-6927	230	43	+	+	CCONJ
ejpam-6927	230	44	q2	q2	NOUN
ejpam-6927	230	45	)	)	PUNCT
ejpam-6927	230	46	−	−	NOUN
ejpam-6927	231	1	1	1	NUM
ejpam-6927	231	2	2	2	NUM
ejpam-6927	231	3	ω2	ω2	NUM
ejpam-6927	231	4	1(ω2	1(ω2	NUM
ejpam-6927	231	5	−	−	PROPN
ejpam-6927	231	6	ω1	ω1	PROPN
ejpam-6927	231	7	)	)	PUNCT
ejpam-6927	231	8	1	1	NUM
ejpam-6927	232	1	+	+	CCONJ
ejpam-6927	232	2	q	q	PUNCT
ejpam-6927	233	1	+	+	NUM
ejpam-6927	233	2	1	1	NUM
ejpam-6927	233	3	3	3	NUM
ejpam-6927	233	4	ω3	ω3	NOUN
ejpam-6927	233	5	1	1	NUM
ejpam-6927	233	6	+	+	CCONJ
ejpam-6927	233	7	−	−	PROPN
ejpam-6927	233	8	qω3	qω3	NOUN
ejpam-6927	233	9	1	1	NUM
ejpam-6927	233	10	3	3	NUM
ejpam-6927	233	11	+	+	CCONJ
ejpam-6927	233	12	ω3	ω3	ADJ
ejpam-6927	233	13	2	2	NUM
ejpam-6927	233	14	6	6	NUM
ejpam-6927	233	15	−	−	NOUN
ejpam-6927	233	16	ω1ω2	ω1ω2	SYM
ejpam-6927	233	17	2	2	NUM
ejpam-6927	233	18	2	2	NUM
ejpam-6927	233	19	1	1	NUM
ejpam-6927	233	20	+	+	CCONJ
ejpam-6927	233	21	q	q	NOUN
ejpam-6927	233	22	}	}	PUNCT
ejpam-6927	233	23	+	+	PUNCT
ejpam-6927	233	24	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	233	25	)	)	PUNCT
ejpam-6927	233	26	{	{	PUNCT
ejpam-6927	234	1	−	−	PROPN
ejpam-6927	234	2	ω2	ω2	ADJ
ejpam-6927	234	3	2	2	NUM
ejpam-6927	234	4	(	(	PUNCT
ejpam-6927	234	5	(	(	PUNCT
ejpam-6927	234	6	ω2	ω2	ADJ
ejpam-6927	234	7	−	−	PROPN
ejpam-6927	234	8	ω1	ω1	PROPN
ejpam-6927	234	9	)	)	PUNCT
ejpam-6927	234	10	2	2	NUM
ejpam-6927	234	11	1	1	NUM
ejpam-6927	234	12	+	+	CCONJ
ejpam-6927	234	13	q	q	ADJ
ejpam-6927	234	14	+	+	NUM
ejpam-6927	234	15	q2	q2	NOUN
ejpam-6927	234	16	)	)	PUNCT
ejpam-6927	235	1	−	−	PROPN
ejpam-6927	235	2	ω1ω2(ω2	ω1ω2(ω2	NUM
ejpam-6927	235	3	−	−	PROPN
ejpam-6927	235	4	ω1	ω1	PROPN
ejpam-6927	235	5	)	)	PUNCT
ejpam-6927	235	6	1	1	NUM
ejpam-6927	236	1	+	+	CCONJ
ejpam-6927	236	2	q	q	NOUN
ejpam-6927	236	3	−	−	PROPN
ejpam-6927	236	4	ω1	ω1	PROPN
ejpam-6927	236	5	2ω2	2ω2	NUM
ejpam-6927	236	6	2	2	NUM
ejpam-6927	236	7	+	+	CCONJ
ejpam-6927	236	8	1	1	NUM
ejpam-6927	236	9	6	6	NUM
ejpam-6927	236	10	(	(	PUNCT
ejpam-6927	236	11	ω2	ω2	ADJ
ejpam-6927	236	12	−	−	PROPN
ejpam-6927	236	13	ω1	ω1	PROPN
ejpam-6927	236	14	)	)	PUNCT
ejpam-6927	236	15	3	3	NUM
ejpam-6927	236	16	(	(	PUNCT
ejpam-6927	236	17	1	1	NUM
ejpam-6927	236	18	+	+	NUM
ejpam-6927	236	19	q)(1	q)(1	X
ejpam-6927	236	20	+	+	X
ejpam-6927	236	21	q2	q2	NOUN
ejpam-6927	236	22	)	)	PUNCT
ejpam-6927	237	1	+	+	CCONJ
ejpam-6927	237	2	1	1	NUM
ejpam-6927	237	3	2	2	NUM
ejpam-6927	237	4	ω1(ω2	ω1(ω2	NUM
ejpam-6927	237	5	−	−	NOUN
ejpam-6927	237	6	ω1	ω1	PROPN
ejpam-6927	237	7	)	)	PUNCT
ejpam-6927	237	8	2	2	NUM
ejpam-6927	237	9	1	1	NUM
ejpam-6927	237	10	+	+	CCONJ
ejpam-6927	237	11	q	q	NOUN
ejpam-6927	238	1	+	+	NUM
ejpam-6927	238	2	q2	q2	NOUN
ejpam-6927	238	3	+	+	CCONJ
ejpam-6927	238	4	1	1	NUM
ejpam-6927	238	5	2	2	NUM
ejpam-6927	238	6	ω2	ω2	NUM
ejpam-6927	238	7	1(ω2	1(ω2	NUM
ejpam-6927	238	8	−	−	PROPN
ejpam-6927	238	9	ω1	ω1	PROPN
ejpam-6927	238	10	)	)	PUNCT
ejpam-6927	238	11	1	1	NUM
ejpam-6927	239	1	+	+	CCONJ
ejpam-6927	239	2	q	q	PUNCT
ejpam-6927	240	1	+	+	NUM
ejpam-6927	240	2	1	1	NUM
ejpam-6927	240	3	6	6	NUM
ejpam-6927	240	4	ω3	ω3	NOUN
ejpam-6927	240	5	1	1	NUM
ejpam-6927	240	6	+	+	CCONJ
ejpam-6927	240	7	qω2	qω2	VERB
ejpam-6927	240	8	1ω2	1ω2	NUM
ejpam-6927	240	9	2	2	NUM
ejpam-6927	240	10	−	−	NOUN
ejpam-6927	240	11	qω3	qω3	NOUN
ejpam-6927	240	12	1	1	NUM
ejpam-6927	240	13	6	6	NUM
ejpam-6927	240	14	+	+	CCONJ
ejpam-6927	240	15	ω3	ω3	ADJ
ejpam-6927	240	16	2	2	NUM
ejpam-6927	240	17	3	3	NUM
ejpam-6927	240	18	1	1	NUM
ejpam-6927	240	19	+	+	CCONJ
ejpam-6927	240	20	q	q	X
ejpam-6927	240	21	}	}	PUNCT
ejpam-6927	240	22	]	]	PUNCT
ejpam-6927	240	23	.	.	PUNCT
ejpam-6927	241	1	=	=	SYM
ejpam-6927	241	2	1	1	NUM
ejpam-6927	241	3	ω2	ω2	NUM
ejpam-6927	241	4	−	−	PROPN
ejpam-6927	241	5	ω1	ω1	PROPN
ejpam-6927	241	6	[	[	PUNCT
ejpam-6927	241	7	−	−	PROPN
ejpam-6927	241	8	1	1	NUM
ejpam-6927	241	9	6	6	NUM
ejpam-6927	241	10	(	(	PUNCT
ejpam-6927	241	11	φ′′(ω2)−	φ′′(ω2)−	NOUN
ejpam-6927	241	12	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	241	13	)	)	PUNCT
ejpam-6927	241	14	)	)	PUNCT
ejpam-6927	241	15	(	(	PUNCT
ejpam-6927	241	16	(	(	PUNCT
ejpam-6927	241	17	ω2	ω2	ADJ
ejpam-6927	241	18	−	−	PROPN
ejpam-6927	241	19	ω1	ω1	PROPN
ejpam-6927	241	20	)	)	PUNCT
ejpam-6927	241	21	3	3	NUM
ejpam-6927	241	22	(	(	PUNCT
ejpam-6927	241	23	1	1	NUM
ejpam-6927	241	24	+	+	NUM
ejpam-6927	241	25	q)(1	q)(1	X
ejpam-6927	241	26	+	+	X
ejpam-6927	241	27	q2	q2	NOUN
ejpam-6927	241	28	)	)	PUNCT
ejpam-6927	241	29	)	)	PUNCT
ejpam-6927	242	1	−	−	PROPN
ejpam-6927	242	2	(	(	PUNCT
ejpam-6927	242	3	φ′′(ω2)−	φ′′(ω2)−	NOUN
ejpam-6927	242	4	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	242	5	)	)	PUNCT
ejpam-6927	242	6	2	2	NUM
ejpam-6927	242	7	)	)	PUNCT
ejpam-6927	242	8	(	(	PUNCT
ejpam-6927	242	9	(	(	PUNCT
ejpam-6927	242	10	ω2	ω2	ADJ
ejpam-6927	242	11	−	−	PROPN
ejpam-6927	242	12	ω1	ω1	PROPN
ejpam-6927	242	13	)	)	PUNCT
ejpam-6927	242	14	1	1	NUM
ejpam-6927	243	1	+	+	CCONJ
ejpam-6927	243	2	q	q	X
ejpam-6927	243	3	)	)	PUNCT
ejpam-6927	243	4	ω2	ω2	CCONJ
ejpam-6927	243	5	1	1	NUM
ejpam-6927	244	1	+	+	CCONJ
ejpam-6927	244	2	(	(	PUNCT
ejpam-6927	244	3	2φ′′(ω2	2φ′′(ω2	NUM
ejpam-6927	244	4	)	)	PUNCT
ejpam-6927	245	1	+	+	PUNCT
ejpam-6927	245	2	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	245	3	)	)	PUNCT
ejpam-6927	245	4	6	6	NUM
ejpam-6927	245	5	)	)	PUNCT
ejpam-6927	245	6	ω3	ω3	NOUN
ejpam-6927	245	7	1	1	NUM
ejpam-6927	245	8	−	−	NUM
ejpam-6927	245	9	1	1	NUM
ejpam-6927	245	10	2	2	NUM
ejpam-6927	245	11	(	(	PUNCT
ejpam-6927	245	12	(	(	PUNCT
ejpam-6927	245	13	ω2	ω2	ADJ
ejpam-6927	245	14	−	−	PROPN
ejpam-6927	245	15	ω1	ω1	PROPN
ejpam-6927	245	16	)	)	PUNCT
ejpam-6927	245	17	3	3	NUM
ejpam-6927	245	18	1	1	NUM
ejpam-6927	245	19	+	+	CCONJ
ejpam-6927	245	20	q	q	ADJ
ejpam-6927	245	21	+	+	NUM
ejpam-6927	245	22	q2	q2	NOUN
ejpam-6927	245	23	)	)	PUNCT
ejpam-6927	245	24	φ′′(ω1)−	φ′′(ω1)−	NOUN
ejpam-6927	245	25	ω1ω2φ	ω1ω2φ	PUNCT
ejpam-6927	245	26	′′(ω1)(ω2	′′(ω1)(ω2	X
ejpam-6927	245	27	−	−	PROPN
ejpam-6927	245	28	ω1	ω1	PROPN
ejpam-6927	245	29	)	)	PUNCT
ejpam-6927	245	30	(	(	PUNCT
ejpam-6927	245	31	1	1	NUM
ejpam-6927	245	32	+	+	CCONJ
ejpam-6927	245	33	q	q	X
ejpam-6927	245	34	)	)	PUNCT
ejpam-6927	245	35	−	−	NOUN
ejpam-6927	245	36	1	1	NUM
ejpam-6927	245	37	2	2	NUM
ejpam-6927	245	38	φ′′(ω1)ω	φ′′(ω1)ω	NOUN
ejpam-6927	245	39	2	2	NUM
ejpam-6927	245	40	1ω2	1ω2	NUM
ejpam-6927	245	41	−	−	PROPN
ejpam-6927	245	42	(	(	PUNCT
ejpam-6927	245	43	2φ′′(ω2	2φ′′(ω2	NUM
ejpam-6927	245	44	)	)	PUNCT
ejpam-6927	246	1	+	+	PUNCT
ejpam-6927	246	2	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	246	3	)	)	PUNCT
ejpam-6927	246	4	6	6	NUM
ejpam-6927	246	5	)	)	PUNCT
ejpam-6927	246	6	(	(	PUNCT
ejpam-6927	246	7	qω3	qω3	NOUN
ejpam-6927	246	8	1	1	NUM
ejpam-6927	246	9	1	1	NUM
ejpam-6927	246	10	+	+	CCONJ
ejpam-6927	246	11	q	q	PUNCT
ejpam-6927	246	12	)	)	PUNCT
ejpam-6927	246	13	+	+	CCONJ
ejpam-6927	246	14	(	(	PUNCT
ejpam-6927	246	15	φ′′(ω2	φ′′(ω2	X
ejpam-6927	246	16	)	)	PUNCT
ejpam-6927	246	17	+	+	CCONJ
ejpam-6927	246	18	2φ′′(ω1	2φ′′(ω1	X
ejpam-6927	246	19	)	)	PUNCT
ejpam-6927	246	20	6	6	NUM
ejpam-6927	246	21	)	)	PUNCT
ejpam-6927	246	22	(	(	PUNCT
ejpam-6927	246	23	ω3	ω3	NOUN
ejpam-6927	246	24	2	2	NUM
ejpam-6927	246	25	1	1	NUM
ejpam-6927	246	26	+	+	CCONJ
ejpam-6927	246	27	q	q	NOUN
ejpam-6927	246	28	)	)	PUNCT
ejpam-6927	246	29	−	−	PROPN
ejpam-6927	246	30	(	(	PUNCT
ejpam-6927	246	31	ω2φ	ω2φ	PROPN
ejpam-6927	246	32	′′(ω2)−	′′(ω2)−	VERB
ejpam-6927	246	33	qω1φ	qω1φ	PROPN
ejpam-6927	246	34	′′(ω1	′′(ω1	ADP
ejpam-6927	246	35	)	)	PUNCT
ejpam-6927	246	36	2	2	NUM
ejpam-6927	246	37	)	)	PUNCT
ejpam-6927	246	38	(	(	PUNCT
ejpam-6927	246	39	ω1ω2	ω1ω2	X
ejpam-6927	246	40	1	1	NUM
ejpam-6927	246	41	+	+	CCONJ
ejpam-6927	246	42	q	q	NOUN
ejpam-6927	246	43	)	)	PUNCT
ejpam-6927	246	44	]	]	PUNCT
ejpam-6927	246	45	.	.	PUNCT
ejpam-6927	247	1	(	(	PUNCT
ejpam-6927	247	2	17	17	NUM
ejpam-6927	247	3	)	)	PUNCT
ejpam-6927	247	4	(	(	PUNCT
ejpam-6927	247	5	17	17	NUM
ejpam-6927	247	6	)	)	PUNCT
ejpam-6927	247	7	is	be	AUX
ejpam-6927	247	8	equivalent	equivalent	ADJ
ejpam-6927	247	9	to	to	ADP
ejpam-6927	247	10	(	(	PUNCT
ejpam-6927	247	11	11	11	NUM
ejpam-6927	247	12	)	)	PUNCT
ejpam-6927	247	13	.	.	PUNCT
ejpam-6927	248	1	m.	m.	PROPN
ejpam-6927	248	2	adil	adil	PROPN
ejpam-6927	248	3	khan	khan	PROPN
ejpam-6927	248	4	et	et	PROPN
ejpam-6927	248	5	al	al	PROPN
ejpam-6927	248	6	.	.	PUNCT
ejpam-6927	248	7	/	/	SYM
ejpam-6927	248	8	eur	eur	PROPN
ejpam-6927	248	9	.	.	PUNCT
ejpam-6927	249	1	j.	j.	PROPN
ejpam-6927	249	2	pure	pure	PROPN
ejpam-6927	249	3	appl	appl	PROPN
ejpam-6927	249	4	.	.	PROPN
ejpam-6927	249	5	math	math	PROPN
ejpam-6927	249	6	,	,	PUNCT
ejpam-6927	249	7	18	18	NUM
ejpam-6927	249	8	(	(	PUNCT
ejpam-6927	249	9	4	4	NUM
ejpam-6927	249	10	)	)	PUNCT
ejpam-6927	249	11	(	(	PUNCT
ejpam-6927	249	12	2025	2025	NUM
ejpam-6927	249	13	)	)	PUNCT
ejpam-6927	249	14	,	,	PUNCT
ejpam-6927	249	15	6927	6927	NUM
ejpam-6927	249	16	11	11	NUM
ejpam-6927	249	17	of	of	ADP
ejpam-6927	249	18	18	18	NUM
ejpam-6927	249	19	remark	remark	NOUN
ejpam-6927	249	20	2	2	NUM
ejpam-6927	249	21	.	.	PUNCT
ejpam-6927	250	1	under	under	ADP
ejpam-6927	250	2	the	the	DET
ejpam-6927	250	3	assumptions	assumption	NOUN
ejpam-6927	250	4	of	of	ADP
ejpam-6927	250	5	theorem	theorem	NOUN
ejpam-6927	250	6	6	6	NUM
ejpam-6927	250	7	with	with	ADP
ejpam-6927	250	8	the	the	DET
ejpam-6927	250	9	limit	limit	NOUN
ejpam-6927	250	10	as	as	ADP
ejpam-6927	250	11	q	q	NOUN
ejpam-6927	250	12	→	→	SYM
ejpam-6927	250	13	1	1	NUM
ejpam-6927	250	14	,	,	PUNCT
ejpam-6927	250	15	we	we	PRON
ejpam-6927	250	16	have	have	VERB
ejpam-6927	250	17	the	the	DET
ejpam-6927	250	18	following	follow	VERB
ejpam-6927	250	19	h−h	h−h	NOUN
ejpam-6927	250	20	inequality	inequality	NOUN
ejpam-6927	250	21	:	:	PUNCT
ejpam-6927	250	22	φ(ω1	φ(ω1	NOUN
ejpam-6927	250	23	)	)	PUNCT
ejpam-6927	250	24	+	+	CCONJ
ejpam-6927	250	25	φ(ω2	φ(ω2	NOUN
ejpam-6927	250	26	)	)	PUNCT
ejpam-6927	250	27	2	2	NUM
ejpam-6927	250	28	−	−	PROPN
ejpam-6927	250	29	1	1	NUM
ejpam-6927	251	1	ω2	ω2	NUM
ejpam-6927	251	2	−	−	PROPN
ejpam-6927	251	3	ω1	ω1	PROPN
ejpam-6927	251	4	∫	∫	PROPN
ejpam-6927	251	5	ω2	ω2	PROPN
ejpam-6927	251	6	ω1	ω1	PROPN
ejpam-6927	251	7	φ(κ)dκ	φ(κ)dκ	PART
ejpam-6927	251	8	≤	≤	NUM
ejpam-6927	251	9	1	1	NUM
ejpam-6927	251	10	ω2	ω2	NUM
ejpam-6927	251	11	−	−	PROPN
ejpam-6927	251	12	ω1	ω1	PROPN
ejpam-6927	251	13	[	[	PUNCT
ejpam-6927	251	14	−	−	PROPN
ejpam-6927	251	15	1	1	NUM
ejpam-6927	251	16	24	24	NUM
ejpam-6927	251	17	(	(	PUNCT
ejpam-6927	251	18	φ′′(ω2)−	φ′′(ω2)−	NOUN
ejpam-6927	251	19	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	251	20	)	)	PUNCT
ejpam-6927	251	21	)	)	PUNCT
ejpam-6927	252	1	(	(	PUNCT
ejpam-6927	252	2	ω2	ω2	NUM
ejpam-6927	252	3	−	−	PROPN
ejpam-6927	252	4	ω1	ω1	PROPN
ejpam-6927	252	5	)	)	PUNCT
ejpam-6927	252	6	3	3	NUM
ejpam-6927	252	7	−	−	NOUN
ejpam-6927	252	8	1	1	NUM
ejpam-6927	252	9	4	4	NUM
ejpam-6927	252	10	(	(	PUNCT
ejpam-6927	252	11	φ′′(ω2)−	φ′′(ω2)−	NOUN
ejpam-6927	252	12	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	252	13	)	)	PUNCT
ejpam-6927	252	14	)	)	PUNCT
ejpam-6927	253	1	(	(	PUNCT
ejpam-6927	253	2	ω2	ω2	ADV
ejpam-6927	253	3	−	−	NOUN
ejpam-6927	253	4	ω1)ω	ω1)ω	VERB
ejpam-6927	253	5	2	2	NUM
ejpam-6927	253	6	1	1	NUM
ejpam-6927	253	7	+	+	CCONJ
ejpam-6927	253	8	1	1	NUM
ejpam-6927	253	9	6	6	NUM
ejpam-6927	253	10	(	(	PUNCT
ejpam-6927	253	11	2φ′′(ω2	2φ′′(ω2	NUM
ejpam-6927	253	12	)	)	PUNCT
ejpam-6927	253	13	+	+	PUNCT
ejpam-6927	253	14	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	253	15	)	)	PUNCT
ejpam-6927	253	16	)	)	PUNCT
ejpam-6927	254	1	ω3	ω3	NOUN
ejpam-6927	254	2	1	1	NUM
ejpam-6927	254	3	−	−	NUM
ejpam-6927	254	4	1	1	NUM
ejpam-6927	254	5	6	6	NUM
ejpam-6927	254	6	(	(	PUNCT
ejpam-6927	254	7	ω2	ω2	ADJ
ejpam-6927	254	8	−	−	PROPN
ejpam-6927	254	9	ω1	ω1	PROPN
ejpam-6927	254	10	)	)	PUNCT
ejpam-6927	254	11	3	3	NUM
ejpam-6927	254	12	φ′′(ω1)−	φ′′(ω1)−	NOUN
ejpam-6927	254	13	1	1	NUM
ejpam-6927	254	14	2	2	NUM
ejpam-6927	254	15	(	(	PUNCT
ejpam-6927	254	16	ω1ω2φ	ω1ω2φ	X
ejpam-6927	254	17	′′(ω1)(ω2	′′(ω1)(ω2	X
ejpam-6927	254	18	−	−	PROPN
ejpam-6927	254	19	ω1	ω1	PROPN
ejpam-6927	254	20	)	)	PUNCT
ejpam-6927	254	21	)	)	PUNCT
ejpam-6927	255	1	−	−	NOUN
ejpam-6927	255	2	1	1	NUM
ejpam-6927	255	3	2	2	NUM
ejpam-6927	255	4	φ′′(ω1)ω	φ′′(ω1)ω	NOUN
ejpam-6927	255	5	2	2	NUM
ejpam-6927	255	6	1ω2	1ω2	NUM
ejpam-6927	255	7	−	−	NOUN
ejpam-6927	255	8	1	1	NUM
ejpam-6927	255	9	12	12	NUM
ejpam-6927	255	10	(	(	PUNCT
ejpam-6927	255	11	2φ′′(ω2	2φ′′(ω2	NUM
ejpam-6927	255	12	)	)	PUNCT
ejpam-6927	255	13	+	+	PUNCT
ejpam-6927	255	14	φ′′(ω1	φ′′(ω1	NOUN
ejpam-6927	255	15	)	)	PUNCT
ejpam-6927	255	16	)	)	PUNCT
ejpam-6927	256	1	ω3	ω3	NOUN
ejpam-6927	256	2	1	1	NUM
ejpam-6927	257	1	+	+	CCONJ
ejpam-6927	257	2	1	1	NUM
ejpam-6927	257	3	12	12	NUM
ejpam-6927	257	4	(	(	PUNCT
ejpam-6927	257	5	φ′′(ω2	φ′′(ω2	X
ejpam-6927	257	6	)	)	PUNCT
ejpam-6927	257	7	+	+	CCONJ
ejpam-6927	257	8	2φ′′(ω1	2φ′′(ω1	X
ejpam-6927	257	9	)	)	PUNCT
ejpam-6927	257	10	)	)	PUNCT
ejpam-6927	257	11	ω3	ω3	NOUN
ejpam-6927	257	12	2	2	NUM
ejpam-6927	257	13	−	−	NOUN
ejpam-6927	257	14	1	1	NUM
ejpam-6927	257	15	4	4	NUM
ejpam-6927	257	16	(	(	PUNCT
ejpam-6927	257	17	ω2φ	ω2φ	NOUN
ejpam-6927	257	18	′′(ω2)−	′′(ω2)−	NOUN
ejpam-6927	257	19	ω1φ	ω1φ	NOUN
ejpam-6927	257	20	′′(ω1	′′(ω1	ADJ
ejpam-6927	257	21	)	)	PUNCT
ejpam-6927	257	22	)	)	PUNCT
ejpam-6927	258	1	ω1ω2	ω1ω2	PUNCT
ejpam-6927	258	2	]	]	PUNCT
ejpam-6927	258	3	.	.	PUNCT
ejpam-6927	259	1	a	a	DET
ejpam-6927	259	2	wide	wide	ADJ
ejpam-6927	259	3	range	range	NOUN
ejpam-6927	259	4	of	of	ADP
ejpam-6927	259	5	inequalities	inequality	NOUN
ejpam-6927	259	6	for	for	ADP
ejpam-6927	259	7	convex	convex	NOUN
ejpam-6927	259	8	functions	function	NOUN
ejpam-6927	259	9	have	have	AUX
ejpam-6927	259	10	been	be	AUX
ejpam-6927	259	11	published	publish	VERB
ejpam-6927	259	12	in	in	ADP
ejpam-6927	259	13	the	the	DET
ejpam-6927	259	14	literature	literature	NOUN
ejpam-6927	259	15	,	,	PUNCT
ejpam-6927	259	16	and	and	CCONJ
ejpam-6927	259	17	jensen	jensen	PROPN
ejpam-6927	259	18	’s	’s	PART
ejpam-6927	259	19	inequality	inequality	NOUN
ejpam-6927	259	20	has	have	VERB
ejpam-6927	259	21	a	a	DET
ejpam-6927	259	22	special	special	ADJ
ejpam-6927	259	23	place	place	NOUN
ejpam-6927	259	24	among	among	ADP
ejpam-6927	259	25	them	they	PRON
ejpam-6927	259	26	.	.	PUNCT
ejpam-6927	260	1	the	the	DET
ejpam-6927	260	2	following	follow	VERB
ejpam-6927	260	3	is	be	AUX
ejpam-6927	260	4	the	the	DET
ejpam-6927	260	5	presentation	presentation	NOUN
ejpam-6927	260	6	of	of	ADP
ejpam-6927	260	7	jensen	jensen	PROPN
ejpam-6927	260	8	’s	’s	PART
ejpam-6927	260	9	inequality	inequality	NOUN
ejpam-6927	260	10	:	:	PUNCT
ejpam-6927	260	11	lemma	lemma	PROPN
ejpam-6927	260	12	2	2	X
ejpam-6927	260	13	.	.	PUNCT
ejpam-6927	261	1	[	[	X
ejpam-6927	261	2	26	26	NUM
ejpam-6927	261	3	]	]	PUNCT
ejpam-6927	261	4	let	let	VERB
ejpam-6927	261	5	p	p	NOUN
ejpam-6927	261	6	:	:	PUNCT
ejpam-6927	261	7	[	[	X
ejpam-6927	261	8	ω1	ω1	PROPN
ejpam-6927	261	9	,	,	PUNCT
ejpam-6927	261	10	ω2	ω2	PROPN
ejpam-6927	261	11	]	]	PUNCT
ejpam-6927	261	12	→	→	X
ejpam-6927	261	13	i	i	PRON
ejpam-6927	261	14	be	be	VERB
ejpam-6927	261	15	integrable	integrable	ADJ
ejpam-6927	261	16	functions	function	NOUN
ejpam-6927	261	17	with	with	ADP
ejpam-6927	261	18	p(κ	p(κ	PROPN
ejpam-6927	261	19	)	)	PUNCT
ejpam-6927	261	20	≥	≥	NOUN
ejpam-6927	261	21	0	0	NUM
ejpam-6927	261	22	,	,	PUNCT
ejpam-6927	261	23	∀	∀	X
ejpam-6927	261	24	κ	κ	X
ejpam-6927	261	25	∈	∈	PROPN
ejpam-6927	261	26	[	[	X
ejpam-6927	261	27	ω1	ω1	PROPN
ejpam-6927	261	28	,	,	PUNCT
ejpam-6927	261	29	ω2	ω2	NOUN
ejpam-6927	261	30	]	]	PUNCT
ejpam-6927	261	31	,	,	PUNCT
ejpam-6927	261	32	and	and	CCONJ
ejpam-6927	261	33	∫	∫	PROPN
ejpam-6927	261	34	ω2	ω2	PROPN
ejpam-6927	261	35	ω1	ω1	PROPN
ejpam-6927	261	36	p(κ)dκ	p(κ)dκ	PROPN
ejpam-6927	261	37	>	>	X
ejpam-6927	261	38	0	0	PROPN
ejpam-6927	261	39	.	.	PUNCT
ejpam-6927	262	1	if	if	SCONJ
ejpam-6927	262	2	φ	φ	PROPN
ejpam-6927	262	3	:	:	PUNCT
ejpam-6927	262	4	i	i	PRON
ejpam-6927	262	5	→	→	PUNCT
ejpam-6927	262	6	r	r	NOUN
ejpam-6927	262	7	is	be	AUX
ejpam-6927	262	8	convex	convex	ADJ
ejpam-6927	262	9	function	function	NOUN
ejpam-6927	262	10	,	,	PUNCT
ejpam-6927	262	11	then	then	ADV
ejpam-6927	262	12	φ	φ	PROPN
ejpam-6927	262	13	(	(	PUNCT
ejpam-6927	262	14	∫	∫	PROPN
ejpam-6927	262	15	ω2	ω2	PROPN
ejpam-6927	262	16	ω1	ω1	PROPN
ejpam-6927	262	17	p(κ)κdκ∫	p(κ)κdκ∫	PROPN
ejpam-6927	262	18	ω2	ω2	PROPN
ejpam-6927	262	19	ω1	ω1	PROPN
ejpam-6927	262	20	p(κ)dκ	p(κ)dκ	PROPN
ejpam-6927	262	21	)	)	PUNCT
ejpam-6927	262	22	≤	≤	PROPN
ejpam-6927	262	23	∫	∫	PROPN
ejpam-6927	262	24	ω2	ω2	PROPN
ejpam-6927	262	25	ω1	ω1	PROPN
ejpam-6927	262	26	p(κ)φ	p(κ)φ	PROPN
ejpam-6927	262	27	(	(	PUNCT
ejpam-6927	262	28	κ	κ	NOUN
ejpam-6927	262	29	)	)	PUNCT
ejpam-6927	262	30	dκ∫	dκ∫	PROPN
ejpam-6927	262	31	ω2	ω2	PROPN
ejpam-6927	262	32	ω1	ω1	PROPN
ejpam-6927	262	33	p(κ)dκ	p(κ)dκ	PROPN
ejpam-6927	262	34	.	.	PUNCT
ejpam-6927	263	1	(	(	PUNCT
ejpam-6927	263	2	18	18	NUM
ejpam-6927	263	3	)	)	PUNCT
ejpam-6927	263	4	theorem	theorem	NOUN
ejpam-6927	263	5	7	7	NUM
ejpam-6927	263	6	.	.	PUNCT
ejpam-6927	264	1	let	let	VERB
ejpam-6927	264	2	φ	φ	PROPN
ejpam-6927	264	3	∈	∈	PROPN
ejpam-6927	264	4	c2[ω1	c2[ω1	PROPN
ejpam-6927	264	5	,	,	PUNCT
ejpam-6927	264	6	ω2	ω2	NOUN
ejpam-6927	264	7	]	]	PUNCT
ejpam-6927	264	8	such	such	ADJ
ejpam-6927	264	9	that	that	SCONJ
ejpam-6927	264	10	φ′′	φ′′	PROPN
ejpam-6927	264	11	is	be	AUX
ejpam-6927	264	12	a	a	DET
ejpam-6927	264	13	convex	convex	NOUN
ejpam-6927	264	14	and	and	CCONJ
ejpam-6927	264	15	0	0	NUM
ejpam-6927	264	16	<	<	X
ejpam-6927	264	17	q	q	X
ejpam-6927	264	18	<	<	X
ejpam-6927	264	19	1	1	NUM
ejpam-6927	264	20	.	.	PUNCT
ejpam-6927	265	1	then	then	ADV
ejpam-6927	265	2	1	1	NUM
ejpam-6927	265	3	ω2	ω2	ADJ
ejpam-6927	265	4	−	−	PROPN
ejpam-6927	265	5	ω1	ω1	PROPN
ejpam-6927	265	6	∫	∫	PROPN
ejpam-6927	265	7	ω2	ω2	PROPN
ejpam-6927	265	8	ω1	ω1	PROPN
ejpam-6927	265	9	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	265	10	−	−	PROPN
ejpam-6927	265	11	φ	φ	PROPN
ejpam-6927	265	12	(	(	PUNCT
ejpam-6927	265	13	qω1	qω1	PROPN
ejpam-6927	265	14	+	+	CCONJ
ejpam-6927	265	15	ω2	ω2	PROPN
ejpam-6927	265	16	q	q	X
ejpam-6927	266	1	+	+	NUM
ejpam-6927	266	2	1	1	NUM
ejpam-6927	266	3	)	)	PUNCT
ejpam-6927	266	4	≥	≥	NOUN
ejpam-6927	266	5	(	(	PUNCT
ejpam-6927	266	6	1	1	NUM
ejpam-6927	266	7	2	2	NUM
ejpam-6927	266	8	(	(	PUNCT
ejpam-6927	266	9	(	(	PUNCT
ejpam-6927	266	10	ω2	ω2	ADJ
ejpam-6927	266	11	−	−	PROPN
ejpam-6927	266	12	ω1	ω1	PROPN
ejpam-6927	266	13	)	)	PUNCT
ejpam-6927	266	14	2	2	NUM
ejpam-6927	266	15	1	1	NUM
ejpam-6927	266	16	+	+	CCONJ
ejpam-6927	266	17	q	q	NOUN
ejpam-6927	266	18	+	+	NUM
ejpam-6927	266	19	q2	q2	NOUN
ejpam-6927	266	20	)	)	PUNCT
ejpam-6927	267	1	+	+	CCONJ
ejpam-6927	267	2	ω1(ω2	ω1(ω2	NUM
ejpam-6927	267	3	−	−	PROPN
ejpam-6927	267	4	ω1	ω1	PROPN
ejpam-6927	267	5	)	)	PUNCT
ejpam-6927	267	6	(	(	PUNCT
ejpam-6927	267	7	1	1	NUM
ejpam-6927	267	8	+	+	CCONJ
ejpam-6927	267	9	q	q	X
ejpam-6927	267	10	)	)	PUNCT
ejpam-6927	268	1	+	+	CCONJ
ejpam-6927	268	2	1	1	NUM
ejpam-6927	268	3	2	2	NUM
ejpam-6927	268	4	ω2	ω2	ADJ
ejpam-6927	268	5	1	1	NUM
ejpam-6927	268	6	−	−	NOUN
ejpam-6927	268	7	1	1	NUM
ejpam-6927	268	8	2	2	NUM
ejpam-6927	268	9	(	(	PUNCT
ejpam-6927	268	10	qω1	qω1	NOUN
ejpam-6927	268	11	+	+	CCONJ
ejpam-6927	268	12	ω2	ω2	ADJ
ejpam-6927	268	13	1	1	NUM
ejpam-6927	268	14	+	+	CCONJ
ejpam-6927	268	15	q	q	NOUN
ejpam-6927	268	16	)	)	PUNCT
ejpam-6927	268	17	2	2	X
ejpam-6927	268	18	)	)	PUNCT
ejpam-6927	268	19	φ′′	φ′′	PROPN
ejpam-6927	268	20			X
ejpam-6927	268	21	1	1	NUM
ejpam-6927	268	22	6	6	NUM
ejpam-6927	268	23	(	(	PUNCT
ejpam-6927	268	24	ω2−ω1)3	ω2−ω1)3	NOUN
ejpam-6927	268	25	(	(	PUNCT
ejpam-6927	268	26	1+q)(1+q2	1+q)(1+q2	NUM
ejpam-6927	268	27	)	)	PUNCT
ejpam-6927	269	1	+	+	CCONJ
ejpam-6927	269	2	1	1	NUM
ejpam-6927	269	3	2	2	NUM
ejpam-6927	269	4	ω1(ω2−ω1)2	ω1(ω2−ω1)2	SYM
ejpam-6927	269	5	1+q+q2	1+q+q2	NUM
ejpam-6927	269	6	+	+	NOUN
ejpam-6927	269	7	1	1	NUM
ejpam-6927	269	8	2	2	NUM
ejpam-6927	269	9	ω2	ω2	NUM
ejpam-6927	269	10	1(ω2−ω1	1(ω2−ω1	NUM
ejpam-6927	269	11	)	)	PUNCT
ejpam-6927	269	12	1+q	1+q	NUM
ejpam-6927	269	13	+	+	CCONJ
ejpam-6927	269	14	1	1	NUM
ejpam-6927	269	15	6ω	6ω	NUM
ejpam-6927	269	16	3	3	NUM
ejpam-6927	269	17	1	1	NUM
ejpam-6927	269	18	−	−	NUM
ejpam-6927	269	19	1	1	NUM
ejpam-6927	269	20	6	6	NUM
ejpam-6927	269	21	(	(	PUNCT
ejpam-6927	269	22	qω1+ω2	qω1+ω2	PROPN
ejpam-6927	269	23	1+q	1+q	NUM
ejpam-6927	269	24	)	)	PUNCT
ejpam-6927	269	25	3	3	NUM
ejpam-6927	269	26	1	1	NUM
ejpam-6927	269	27	2	2	NUM
ejpam-6927	269	28	(	(	PUNCT
ejpam-6927	269	29	ω2−ω1)2	ω2−ω1)2	PROPN
ejpam-6927	269	30	1+q+q2	1+q+q2	NUM
ejpam-6927	269	31	+	+	CCONJ
ejpam-6927	269	32	ω1(ω2−ω1	ω1(ω2−ω1	NUM
ejpam-6927	269	33	)	)	PUNCT
ejpam-6927	270	1	1+q	1+q	NUM
ejpam-6927	271	1	+	+	CCONJ
ejpam-6927	271	2	1	1	NUM
ejpam-6927	271	3	2ω	2ω	NUM
ejpam-6927	271	4	2	2	NUM
ejpam-6927	271	5	1	1	NUM
ejpam-6927	271	6	−	−	NUM
ejpam-6927	271	7	1	1	NUM
ejpam-6927	271	8	2	2	NUM
ejpam-6927	271	9	(	(	PUNCT
ejpam-6927	271	10	qω1+ω2	qω1+ω2	PROPN
ejpam-6927	271	11	1+q	1+q	NUM
ejpam-6927	271	12	)	)	PUNCT
ejpam-6927	271	13	2	2	NUM
ejpam-6927	271	14			PROPN
ejpam-6927	271	15	.	.	PUNCT
ejpam-6927	272	1	(	(	PUNCT
ejpam-6927	272	2	19	19	NUM
ejpam-6927	272	3	)	)	PUNCT
ejpam-6927	272	4	proof	proof	NOUN
ejpam-6927	272	5	.	.	PUNCT
ejpam-6927	273	1	from	from	ADP
ejpam-6927	273	2	(	(	PUNCT
ejpam-6927	273	3	18	18	NUM
ejpam-6927	273	4	)	)	PUNCT
ejpam-6927	273	5	,	,	PUNCT
ejpam-6927	273	6	we	we	PRON
ejpam-6927	273	7	have∫	have∫	VERB
ejpam-6927	273	8	ω2	ω2	PROPN
ejpam-6927	273	9	ω1	ω1	PROPN
ejpam-6927	273	10	p(κ)dκφ	p(κ)dκφ	PROPN
ejpam-6927	273	11	(	(	PUNCT
ejpam-6927	273	12	∫	∫	PROPN
ejpam-6927	273	13	ω2	ω2	PROPN
ejpam-6927	273	14	ω1	ω1	PROPN
ejpam-6927	273	15	p(κ)κdκ∫	p(κ)κdκ∫	PROPN
ejpam-6927	273	16	ω2	ω2	PROPN
ejpam-6927	273	17	ω1	ω1	PROPN
ejpam-6927	273	18	p(κ)dκ	p(κ)dκ	PROPN
ejpam-6927	273	19	)	)	PUNCT
ejpam-6927	273	20	≤	≤	PROPN
ejpam-6927	273	21	∫	∫	PROPN
ejpam-6927	273	22	ω2	ω2	PROPN
ejpam-6927	273	23	ω1	ω1	PROPN
ejpam-6927	273	24	p(κ)φ	p(κ)φ	PROPN
ejpam-6927	273	25	(	(	PUNCT
ejpam-6927	273	26	κ	κ	NOUN
ejpam-6927	273	27	)	)	PUNCT
ejpam-6927	273	28	dκ	dκ	PROPN
ejpam-6927	273	29	.	.	PUNCT
ejpam-6927	274	1	(	(	PUNCT
ejpam-6927	274	2	20	20	NUM
ejpam-6927	274	3	)	)	PUNCT
ejpam-6927	274	4	m.	m.	NOUN
ejpam-6927	274	5	adil	adil	PROPN
ejpam-6927	274	6	khan	khan	PROPN
ejpam-6927	274	7	et	et	PROPN
ejpam-6927	274	8	al	al	PROPN
ejpam-6927	274	9	.	.	PUNCT
ejpam-6927	274	10	/	/	SYM
ejpam-6927	274	11	eur	eur	PROPN
ejpam-6927	274	12	.	.	PUNCT
ejpam-6927	275	1	j.	j.	PROPN
ejpam-6927	275	2	pure	pure	PROPN
ejpam-6927	275	3	appl	appl	PROPN
ejpam-6927	275	4	.	.	PROPN
ejpam-6927	275	5	math	math	PROPN
ejpam-6927	275	6	,	,	PUNCT
ejpam-6927	275	7	18	18	NUM
ejpam-6927	275	8	(	(	PUNCT
ejpam-6927	275	9	4	4	NUM
ejpam-6927	275	10	)	)	PUNCT
ejpam-6927	275	11	(	(	PUNCT
ejpam-6927	275	12	2025	2025	NUM
ejpam-6927	275	13	)	)	PUNCT
ejpam-6927	275	14	,	,	PUNCT
ejpam-6927	275	15	6927	6927	NUM
ejpam-6927	275	16	12	12	NUM
ejpam-6927	275	17	of	of	ADP
ejpam-6927	275	18	18	18	NUM
ejpam-6927	275	19	comparing	compare	VERB
ejpam-6927	275	20	(	(	PUNCT
ejpam-6927	275	21	20	20	NUM
ejpam-6927	275	22	)	)	PUNCT
ejpam-6927	275	23	with	with	ADP
ejpam-6927	275	24	(	(	PUNCT
ejpam-6927	275	25	6	6	NUM
ejpam-6927	275	26	)	)	PUNCT
ejpam-6927	275	27	,	,	PUNCT
ejpam-6927	275	28	we	we	PRON
ejpam-6927	275	29	have	have	AUX
ejpam-6927	275	30	p(κ	p(κ	NOUN
ejpam-6927	275	31	)	)	PUNCT
ejpam-6927	275	32	=	=	PUNCT
ejpam-6927	275	33	γ(ℓ	γ(ℓ	NOUN
ejpam-6927	275	34	)	)	PUNCT
ejpam-6927	275	35	and	and	CCONJ
ejpam-6927	275	36	φ(κ	φ(κ	NOUN
ejpam-6927	275	37	)	)	PUNCT
ejpam-6927	275	38	=	=	SYM
ejpam-6927	275	39	φ′′(ℓ	φ′′(ℓ	NOUN
ejpam-6927	275	40	)	)	PUNCT
ejpam-6927	275	41	.	.	PUNCT
ejpam-6927	276	1	(	(	PUNCT
ejpam-6927	276	2	20	20	NUM
ejpam-6927	276	3	)	)	PUNCT
ejpam-6927	276	4	,	,	PUNCT
ejpam-6927	276	5	becomes	become	VERB
ejpam-6927	276	6	∫	∫	PROPN
ejpam-6927	276	7	ω2	ω2	PROPN
ejpam-6927	276	8	ω1	ω1	PROPN
ejpam-6927	276	9	γ(ℓ)φ′′	γ(ℓ)φ′′	PROPN
ejpam-6927	276	10	(	(	PUNCT
ejpam-6927	276	11	ℓ	ℓ	NOUN
ejpam-6927	276	12	)	)	PUNCT
ejpam-6927	276	13	dℓ	dℓ	PROPN
ejpam-6927	276	14	≥	≥	NUM
ejpam-6927	276	15	∫	∫	PROPN
ejpam-6927	276	16	ω2	ω2	PROPN
ejpam-6927	276	17	ω1	ω1	PROPN
ejpam-6927	276	18	γ(ℓ)dℓ.φ′′	γ(ℓ)dℓ.φ′′	PROPN
ejpam-6927	276	19	(	(	PUNCT
ejpam-6927	276	20	∫	∫	PROPN
ejpam-6927	276	21	ω2	ω2	PROPN
ejpam-6927	276	22	ω1	ω1	PROPN
ejpam-6927	276	23	γ(ℓ)ℓdℓ∫	γ(ℓ)ℓdℓ∫	PROPN
ejpam-6927	276	24	ω2	ω2	PROPN
ejpam-6927	276	25	ω1	ω1	PROPN
ejpam-6927	276	26	γ(ℓ)dℓ	γ(ℓ)dℓ	NUM
ejpam-6927	276	27	)	)	PUNCT
ejpam-6927	276	28	.	.	PUNCT
ejpam-6927	277	1	by	by	ADP
ejpam-6927	277	2	(	(	PUNCT
ejpam-6927	277	3	6	6	NUM
ejpam-6927	277	4	)	)	PUNCT
ejpam-6927	277	5	,	,	PUNCT
ejpam-6927	277	6	we	we	PRON
ejpam-6927	277	7	have	have	VERB
ejpam-6927	277	8	1	1	NUM
ejpam-6927	277	9	ω2	ω2	ADJ
ejpam-6927	277	10	−	−	PROPN
ejpam-6927	277	11	ω1	ω1	PROPN
ejpam-6927	277	12	∫	∫	PROPN
ejpam-6927	277	13	ω2	ω2	PROPN
ejpam-6927	277	14	ω1	ω1	PROPN
ejpam-6927	277	15	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	277	16	−	−	PROPN
ejpam-6927	277	17	φ	φ	PROPN
ejpam-6927	277	18	(	(	PUNCT
ejpam-6927	277	19	qω1	qω1	PROPN
ejpam-6927	277	20	+	+	CCONJ
ejpam-6927	277	21	ω2	ω2	PROPN
ejpam-6927	277	22	q	q	X
ejpam-6927	278	1	+	+	NUM
ejpam-6927	278	2	1	1	NUM
ejpam-6927	278	3	)	)	PUNCT
ejpam-6927	278	4	≥	≥	NOUN
ejpam-6927	278	5	∫	∫	PROPN
ejpam-6927	278	6	ω2	ω2	PROPN
ejpam-6927	278	7	ω1	ω1	PROPN
ejpam-6927	278	8	γ(ℓ)dℓ.φ′′	γ(ℓ)dℓ.φ′′	PROPN
ejpam-6927	278	9	(	(	PUNCT
ejpam-6927	278	10	∫	∫	PROPN
ejpam-6927	278	11	ω2	ω2	PROPN
ejpam-6927	278	12	ω1	ω1	PROPN
ejpam-6927	278	13	γ(ℓ)ℓdℓ∫	γ(ℓ)ℓdℓ∫	PROPN
ejpam-6927	278	14	ω2	ω2	PROPN
ejpam-6927	278	15	ω1	ω1	PROPN
ejpam-6927	278	16	γ(ℓ)dℓ	γ(ℓ)dℓ	NUM
ejpam-6927	278	17	)	)	PUNCT
ejpam-6927	278	18	.	.	PUNCT
ejpam-6927	279	1	(	(	PUNCT
ejpam-6927	279	2	21	21	NUM
ejpam-6927	279	3	)	)	PUNCT
ejpam-6927	279	4	now	now	ADV
ejpam-6927	279	5	we	we	PRON
ejpam-6927	279	6	solve	solve	VERB
ejpam-6927	279	7	the	the	DET
ejpam-6927	279	8	integral	integral	ADJ
ejpam-6927	279	9	,	,	PUNCT
ejpam-6927	279	10	∫	∫	PROPN
ejpam-6927	279	11	ω2	ω2	PROPN
ejpam-6927	279	12	ω1	ω1	PROPN
ejpam-6927	279	13	γ(ℓ)dℓ.	γ(ℓ)dℓ.	PROPN
ejpam-6927	279	14	if	if	SCONJ
ejpam-6927	279	15	φ(ℓ	φ(ℓ	PROPN
ejpam-6927	279	16	)	)	PUNCT
ejpam-6927	279	17	=	=	SYM
ejpam-6927	279	18	1	1	NUM
ejpam-6927	279	19	2ℓ	2ℓ	NUM
ejpam-6927	279	20	2	2	NUM
ejpam-6927	279	21	,	,	PUNCT
ejpam-6927	279	22	then	then	ADV
ejpam-6927	279	23	φ′′(ℓ	φ′′(ℓ	NOUN
ejpam-6927	279	24	)	)	PUNCT
ejpam-6927	279	25	=	=	SYM
ejpam-6927	279	26	1	1	NUM
ejpam-6927	279	27	,	,	PUNCT
ejpam-6927	279	28	using	use	VERB
ejpam-6927	279	29	these	these	DET
ejpam-6927	279	30	functions	function	NOUN
ejpam-6927	279	31	in	in	ADP
ejpam-6927	279	32	(	(	PUNCT
ejpam-6927	279	33	6	6	NUM
ejpam-6927	279	34	)	)	PUNCT
ejpam-6927	279	35	,	,	PUNCT
ejpam-6927	280	1	we	we	PRON
ejpam-6927	280	2	obtain.∫	obtain.∫	NOUN
ejpam-6927	280	3	ω2	ω2	PROPN
ejpam-6927	280	4	ω1	ω1	PROPN
ejpam-6927	280	5	γ(ℓ)dℓ	γ(ℓ)dℓ	PROPN
ejpam-6927	280	6	=	=	SYM
ejpam-6927	280	7	1	1	NUM
ejpam-6927	280	8	ω2	ω2	NUM
ejpam-6927	280	9	−	−	PROPN
ejpam-6927	280	10	ω1	ω1	PROPN
ejpam-6927	280	11	∫	∫	PROPN
ejpam-6927	280	12	ω2	ω2	PROPN
ejpam-6927	280	13	ω1	ω1	PROPN
ejpam-6927	280	14	1	1	NUM
ejpam-6927	280	15	2	2	NUM
ejpam-6927	280	16	(	(	PUNCT
ejpam-6927	280	17	ℓ2)ω1dqℓ−	ℓ2)ω1dqℓ−	NOUN
ejpam-6927	280	18	1	1	NUM
ejpam-6927	280	19	2	2	NUM
ejpam-6927	280	20	(	(	PUNCT
ejpam-6927	280	21	qω1	qω1	NOUN
ejpam-6927	280	22	+	+	CCONJ
ejpam-6927	280	23	ω2	ω2	ADJ
ejpam-6927	280	24	1	1	NUM
ejpam-6927	280	25	+	+	CCONJ
ejpam-6927	280	26	q	q	NOUN
ejpam-6927	280	27	)	)	PUNCT
ejpam-6927	280	28	2	2	NUM
ejpam-6927	280	29	.	.	PUNCT
ejpam-6927	281	1	finding	find	VERB
ejpam-6927	281	2	the	the	DET
ejpam-6927	281	3	above	above	ADJ
ejpam-6927	281	4	integrals	integral	NOUN
ejpam-6927	281	5	,	,	PUNCT
ejpam-6927	281	6	we	we	PRON
ejpam-6927	281	7	get.∫	get.∫	NOUN
ejpam-6927	281	8	ω2	ω2	PROPN
ejpam-6927	281	9	ω1	ω1	PROPN
ejpam-6927	281	10	γ(ℓ)dℓ	γ(ℓ)dℓ	PROPN
ejpam-6927	281	11	=	=	SYM
ejpam-6927	281	12	1	1	NUM
ejpam-6927	281	13	2	2	NUM
ejpam-6927	281	14	(	(	PUNCT
ejpam-6927	281	15	(	(	PUNCT
ejpam-6927	281	16	ω2	ω2	ADJ
ejpam-6927	281	17	−	−	PROPN
ejpam-6927	281	18	ω1	ω1	PROPN
ejpam-6927	281	19	)	)	PUNCT
ejpam-6927	281	20	2	2	NUM
ejpam-6927	281	21	1	1	NUM
ejpam-6927	281	22	+	+	CCONJ
ejpam-6927	281	23	q	q	NOUN
ejpam-6927	281	24	+	+	NUM
ejpam-6927	281	25	q2	q2	NOUN
ejpam-6927	281	26	)	)	PUNCT
ejpam-6927	282	1	+	+	CCONJ
ejpam-6927	282	2	ω1(ω2	ω1(ω2	NUM
ejpam-6927	282	3	−	−	PROPN
ejpam-6927	282	4	ω1	ω1	PROPN
ejpam-6927	282	5	)	)	PUNCT
ejpam-6927	282	6	(	(	PUNCT
ejpam-6927	282	7	1	1	NUM
ejpam-6927	282	8	+	+	CCONJ
ejpam-6927	282	9	q	q	X
ejpam-6927	282	10	)	)	PUNCT
ejpam-6927	283	1	+	+	CCONJ
ejpam-6927	283	2	1	1	NUM
ejpam-6927	283	3	2	2	NUM
ejpam-6927	283	4	ω2	ω2	ADJ
ejpam-6927	283	5	1	1	NUM
ejpam-6927	283	6	−	−	NOUN
ejpam-6927	283	7	1	1	NUM
ejpam-6927	283	8	2	2	NUM
ejpam-6927	283	9	(	(	PUNCT
ejpam-6927	283	10	qω1	qω1	NOUN
ejpam-6927	283	11	+	+	CCONJ
ejpam-6927	283	12	ω2	ω2	ADJ
ejpam-6927	283	13	1	1	NUM
ejpam-6927	283	14	+	+	CCONJ
ejpam-6927	283	15	q	q	NOUN
ejpam-6927	283	16	)	)	PUNCT
ejpam-6927	283	17	2	2	NUM
ejpam-6927	283	18	.	.	PUNCT
ejpam-6927	284	1	(	(	PUNCT
ejpam-6927	284	2	22	22	NUM
ejpam-6927	284	3	)	)	PUNCT
ejpam-6927	284	4	now	now	ADV
ejpam-6927	284	5	we	we	PRON
ejpam-6927	284	6	solve	solve	VERB
ejpam-6927	284	7	the	the	DET
ejpam-6927	284	8	integral	integral	ADJ
ejpam-6927	284	9	,	,	PUNCT
ejpam-6927	284	10	∫	∫	PROPN
ejpam-6927	284	11	ω2	ω2	PROPN
ejpam-6927	284	12	ω1	ω1	PROPN
ejpam-6927	284	13	γ(ℓ)ℓdℓ.	γ(ℓ)ℓdℓ.	PROPN
ejpam-6927	284	14	if	if	SCONJ
ejpam-6927	284	15	φ(ℓ	φ(ℓ	PROPN
ejpam-6927	284	16	)	)	PUNCT
ejpam-6927	284	17	=	=	SYM
ejpam-6927	284	18	1	1	NUM
ejpam-6927	284	19	6ℓ	6ℓ	NOUN
ejpam-6927	284	20	3	3	NUM
ejpam-6927	284	21	,	,	PUNCT
ejpam-6927	284	22	then	then	ADV
ejpam-6927	284	23	φ′′(ℓ	φ′′(ℓ	NOUN
ejpam-6927	284	24	)	)	PUNCT
ejpam-6927	284	25	=	=	SYM
ejpam-6927	284	26	ℓ	ℓ	PROPN
ejpam-6927	284	27	,	,	PUNCT
ejpam-6927	284	28	using	use	VERB
ejpam-6927	284	29	these	these	DET
ejpam-6927	284	30	functions	function	NOUN
ejpam-6927	284	31	in	in	ADP
ejpam-6927	284	32	(	(	PUNCT
ejpam-6927	284	33	6	6	NUM
ejpam-6927	284	34	)	)	PUNCT
ejpam-6927	284	35	,	,	PUNCT
ejpam-6927	284	36	we	we	PRON
ejpam-6927	284	37	obtain.∫	obtain.∫	NOUN
ejpam-6927	284	38	ω2	ω2	ADJ
ejpam-6927	284	39	ω1	ω1	PROPN
ejpam-6927	284	40	γ(ℓ)ℓdℓ	γ(ℓ)ℓdℓ	PROPN
ejpam-6927	284	41	=	=	PUNCT
ejpam-6927	284	42	1	1	NUM
ejpam-6927	284	43	ω2	ω2	NUM
ejpam-6927	284	44	−	−	PROPN
ejpam-6927	284	45	ω1	ω1	PROPN
ejpam-6927	284	46	∫	∫	PROPN
ejpam-6927	284	47	ω2	ω2	PROPN
ejpam-6927	284	48	ω1	ω1	PROPN
ejpam-6927	284	49	1	1	NUM
ejpam-6927	284	50	6	6	NUM
ejpam-6927	284	51	(	(	PUNCT
ejpam-6927	284	52	ℓ3)ω1dqℓ−	ℓ3)ω1dqℓ−	NOUN
ejpam-6927	284	53	1	1	NUM
ejpam-6927	284	54	6	6	NUM
ejpam-6927	284	55	(	(	PUNCT
ejpam-6927	284	56	qω1	qω1	NOUN
ejpam-6927	284	57	+	+	CCONJ
ejpam-6927	284	58	ω2	ω2	ADJ
ejpam-6927	284	59	1	1	NUM
ejpam-6927	284	60	+	+	CCONJ
ejpam-6927	284	61	q	q	NOUN
ejpam-6927	284	62	)	)	PUNCT
ejpam-6927	284	63	3	3	X
ejpam-6927	284	64	.	.	PUNCT
ejpam-6927	285	1	finding	find	VERB
ejpam-6927	285	2	the	the	DET
ejpam-6927	285	3	above	above	ADJ
ejpam-6927	285	4	integrals	integral	NOUN
ejpam-6927	285	5	,	,	PUNCT
ejpam-6927	285	6	we	we	PRON
ejpam-6927	285	7	get.∫	get.∫	NOUN
ejpam-6927	285	8	ω2	ω2	PROPN
ejpam-6927	285	9	ω1	ω1	PROPN
ejpam-6927	285	10	γ(ℓ)ℓdℓ	γ(ℓ)ℓdℓ	PROPN
ejpam-6927	285	11	=	=	PUNCT
ejpam-6927	285	12	1	1	NUM
ejpam-6927	285	13	6	6	NUM
ejpam-6927	285	14	(	(	PUNCT
ejpam-6927	285	15	ω2	ω2	ADJ
ejpam-6927	285	16	−	−	PROPN
ejpam-6927	285	17	ω1	ω1	PROPN
ejpam-6927	285	18	)	)	PUNCT
ejpam-6927	285	19	3	3	NUM
ejpam-6927	285	20	(	(	PUNCT
ejpam-6927	285	21	1	1	NUM
ejpam-6927	285	22	+	+	NUM
ejpam-6927	285	23	q)(1	q)(1	X
ejpam-6927	285	24	+	+	X
ejpam-6927	285	25	q2	q2	NOUN
ejpam-6927	285	26	)	)	PUNCT
ejpam-6927	286	1	+	+	CCONJ
ejpam-6927	286	2	1	1	NUM
ejpam-6927	286	3	2	2	NUM
ejpam-6927	286	4	ω1(ω2	ω1(ω2	NUM
ejpam-6927	286	5	−	−	NOUN
ejpam-6927	286	6	ω1	ω1	PROPN
ejpam-6927	286	7	)	)	PUNCT
ejpam-6927	286	8	2	2	NUM
ejpam-6927	286	9	1	1	NUM
ejpam-6927	286	10	+	+	CCONJ
ejpam-6927	286	11	q	q	NOUN
ejpam-6927	287	1	+	+	NUM
ejpam-6927	287	2	q2	q2	NOUN
ejpam-6927	287	3	+	+	CCONJ
ejpam-6927	287	4	1	1	NUM
ejpam-6927	287	5	2	2	NUM
ejpam-6927	287	6	ω2	ω2	NUM
ejpam-6927	287	7	1(ω2	1(ω2	NUM
ejpam-6927	287	8	−	−	PROPN
ejpam-6927	287	9	ω1	ω1	PROPN
ejpam-6927	287	10	)	)	PUNCT
ejpam-6927	287	11	1	1	NUM
ejpam-6927	288	1	+	+	CCONJ
ejpam-6927	288	2	q	q	PUNCT
ejpam-6927	289	1	+	+	NUM
ejpam-6927	289	2	1	1	NUM
ejpam-6927	289	3	6	6	NUM
ejpam-6927	289	4	ω3	ω3	NOUN
ejpam-6927	289	5	1	1	NUM
ejpam-6927	289	6	−	−	NUM
ejpam-6927	289	7	1	1	NUM
ejpam-6927	289	8	6	6	NUM
ejpam-6927	289	9	(	(	PUNCT
ejpam-6927	289	10	qω1	qω1	NOUN
ejpam-6927	289	11	+	+	CCONJ
ejpam-6927	289	12	ω2	ω2	ADJ
ejpam-6927	289	13	1	1	NUM
ejpam-6927	289	14	+	+	CCONJ
ejpam-6927	289	15	q	q	NOUN
ejpam-6927	289	16	)	)	PUNCT
ejpam-6927	289	17	3	3	NUM
ejpam-6927	289	18	.	.	PUNCT
ejpam-6927	290	1	(	(	PUNCT
ejpam-6927	290	2	23	23	NUM
ejpam-6927	290	3	)	)	PUNCT
ejpam-6927	290	4	using	use	VERB
ejpam-6927	290	5	(	(	PUNCT
ejpam-6927	290	6	22	22	NUM
ejpam-6927	290	7	)	)	PUNCT
ejpam-6927	290	8	and	and	CCONJ
ejpam-6927	290	9	(	(	PUNCT
ejpam-6927	290	10	23	23	NUM
ejpam-6927	290	11	)	)	PUNCT
ejpam-6927	290	12	in	in	ADP
ejpam-6927	290	13	(	(	PUNCT
ejpam-6927	290	14	21	21	NUM
ejpam-6927	290	15	)	)	PUNCT
ejpam-6927	290	16	,	,	PUNCT
ejpam-6927	290	17	we	we	PRON
ejpam-6927	290	18	get	get	VERB
ejpam-6927	290	19	1	1	NUM
ejpam-6927	290	20	ω2	ω2	ADJ
ejpam-6927	290	21	−	−	PROPN
ejpam-6927	290	22	ω1	ω1	PROPN
ejpam-6927	290	23	∫	∫	PROPN
ejpam-6927	290	24	ω2	ω2	PROPN
ejpam-6927	290	25	ω1	ω1	PROPN
ejpam-6927	290	26	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	290	27	−	−	PROPN
ejpam-6927	290	28	φ	φ	PROPN
ejpam-6927	290	29	(	(	PUNCT
ejpam-6927	290	30	qω1	qω1	PROPN
ejpam-6927	290	31	+	+	CCONJ
ejpam-6927	290	32	ω2	ω2	PROPN
ejpam-6927	290	33	q	q	X
ejpam-6927	291	1	+	+	NUM
ejpam-6927	291	2	1	1	NUM
ejpam-6927	291	3	)	)	PUNCT
ejpam-6927	291	4	≥	≥	NOUN
ejpam-6927	291	5	(	(	PUNCT
ejpam-6927	291	6	1	1	NUM
ejpam-6927	291	7	2	2	NUM
ejpam-6927	291	8	(	(	PUNCT
ejpam-6927	291	9	(	(	PUNCT
ejpam-6927	291	10	ω2	ω2	ADJ
ejpam-6927	291	11	−	−	PROPN
ejpam-6927	291	12	ω1	ω1	PROPN
ejpam-6927	291	13	)	)	PUNCT
ejpam-6927	291	14	2	2	NUM
ejpam-6927	291	15	1	1	NUM
ejpam-6927	291	16	+	+	CCONJ
ejpam-6927	291	17	q	q	NOUN
ejpam-6927	291	18	+	+	NUM
ejpam-6927	291	19	q2	q2	NOUN
ejpam-6927	291	20	)	)	PUNCT
ejpam-6927	292	1	+	+	CCONJ
ejpam-6927	292	2	ω1(ω2	ω1(ω2	NUM
ejpam-6927	292	3	−	−	PROPN
ejpam-6927	292	4	ω1	ω1	PROPN
ejpam-6927	292	5	)	)	PUNCT
ejpam-6927	292	6	(	(	PUNCT
ejpam-6927	292	7	1	1	NUM
ejpam-6927	292	8	+	+	CCONJ
ejpam-6927	292	9	q	q	X
ejpam-6927	292	10	)	)	PUNCT
ejpam-6927	293	1	+	+	CCONJ
ejpam-6927	293	2	1	1	NUM
ejpam-6927	293	3	2	2	NUM
ejpam-6927	293	4	ω2	ω2	ADJ
ejpam-6927	293	5	1	1	NUM
ejpam-6927	293	6	−	−	NOUN
ejpam-6927	293	7	1	1	NUM
ejpam-6927	293	8	2	2	NUM
ejpam-6927	293	9	(	(	PUNCT
ejpam-6927	293	10	qω1	qω1	NOUN
ejpam-6927	293	11	+	+	CCONJ
ejpam-6927	293	12	ω2	ω2	ADJ
ejpam-6927	293	13	1	1	NUM
ejpam-6927	293	14	+	+	CCONJ
ejpam-6927	293	15	q	q	NOUN
ejpam-6927	293	16	)	)	PUNCT
ejpam-6927	293	17	2	2	X
ejpam-6927	293	18	)	)	PUNCT
ejpam-6927	293	19	φ′′	φ′′	PROPN
ejpam-6927	293	20			X
ejpam-6927	293	21	1	1	NUM
ejpam-6927	293	22	6	6	NUM
ejpam-6927	293	23	(	(	PUNCT
ejpam-6927	293	24	ω2−ω1)3	ω2−ω1)3	NOUN
ejpam-6927	293	25	(	(	PUNCT
ejpam-6927	293	26	1+q)(1+q2	1+q)(1+q2	NUM
ejpam-6927	293	27	)	)	PUNCT
ejpam-6927	294	1	+	+	CCONJ
ejpam-6927	294	2	1	1	NUM
ejpam-6927	294	3	2	2	NUM
ejpam-6927	294	4	ω1(ω2−ω1)2	ω1(ω2−ω1)2	SYM
ejpam-6927	294	5	1+q+q2	1+q+q2	NUM
ejpam-6927	294	6	+	+	NOUN
ejpam-6927	294	7	1	1	NUM
ejpam-6927	294	8	2	2	NUM
ejpam-6927	294	9	ω2	ω2	NUM
ejpam-6927	294	10	1(ω2−ω1	1(ω2−ω1	NUM
ejpam-6927	294	11	)	)	PUNCT
ejpam-6927	294	12	1+q	1+q	NUM
ejpam-6927	294	13	+	+	CCONJ
ejpam-6927	294	14	1	1	NUM
ejpam-6927	294	15	6ω	6ω	NUM
ejpam-6927	294	16	3	3	NUM
ejpam-6927	294	17	1	1	NUM
ejpam-6927	294	18	−	−	NUM
ejpam-6927	294	19	1	1	NUM
ejpam-6927	294	20	6	6	NUM
ejpam-6927	294	21	(	(	PUNCT
ejpam-6927	294	22	qω1+ω2	qω1+ω2	PROPN
ejpam-6927	294	23	1+q	1+q	NUM
ejpam-6927	294	24	)	)	PUNCT
ejpam-6927	294	25	3	3	NUM
ejpam-6927	294	26	1	1	NUM
ejpam-6927	294	27	2	2	NUM
ejpam-6927	294	28	(	(	PUNCT
ejpam-6927	294	29	ω2−ω1)2	ω2−ω1)2	PROPN
ejpam-6927	294	30	1+q+q2	1+q+q2	NUM
ejpam-6927	294	31	+	+	CCONJ
ejpam-6927	294	32	ω1(ω2−ω1	ω1(ω2−ω1	NUM
ejpam-6927	294	33	)	)	PUNCT
ejpam-6927	295	1	1+q	1+q	NUM
ejpam-6927	296	1	+	+	CCONJ
ejpam-6927	296	2	1	1	NUM
ejpam-6927	296	3	2ω	2ω	NUM
ejpam-6927	296	4	2	2	NUM
ejpam-6927	296	5	1	1	NUM
ejpam-6927	296	6	−	−	NUM
ejpam-6927	296	7	1	1	NUM
ejpam-6927	296	8	2	2	NUM
ejpam-6927	296	9	(	(	PUNCT
ejpam-6927	296	10	qω1+ω2	qω1+ω2	PROPN
ejpam-6927	296	11	1+q	1+q	NUM
ejpam-6927	296	12	)	)	PUNCT
ejpam-6927	296	13	2	2	NUM
ejpam-6927	296	14			PROPN
ejpam-6927	296	15	.	.	PUNCT
ejpam-6927	297	1	(	(	PUNCT
ejpam-6927	297	2	24	24	NUM
ejpam-6927	297	3	)	)	PUNCT
ejpam-6927	297	4	(	(	PUNCT
ejpam-6927	297	5	24	24	NUM
ejpam-6927	297	6	)	)	PUNCT
ejpam-6927	297	7	is	be	AUX
ejpam-6927	297	8	equivalent	equivalent	ADJ
ejpam-6927	297	9	to	to	ADP
ejpam-6927	297	10	(	(	PUNCT
ejpam-6927	297	11	19	19	NUM
ejpam-6927	297	12	)	)	PUNCT
ejpam-6927	297	13	.	.	PUNCT
ejpam-6927	298	1	m.	m.	PROPN
ejpam-6927	298	2	adil	adil	PROPN
ejpam-6927	298	3	khan	khan	PROPN
ejpam-6927	298	4	et	et	PROPN
ejpam-6927	298	5	al	al	PROPN
ejpam-6927	298	6	.	.	PUNCT
ejpam-6927	298	7	/	/	SYM
ejpam-6927	298	8	eur	eur	PROPN
ejpam-6927	298	9	.	.	PUNCT
ejpam-6927	299	1	j.	j.	PROPN
ejpam-6927	299	2	pure	pure	PROPN
ejpam-6927	299	3	appl	appl	PROPN
ejpam-6927	299	4	.	.	PROPN
ejpam-6927	299	5	math	math	PROPN
ejpam-6927	299	6	,	,	PUNCT
ejpam-6927	299	7	18	18	NUM
ejpam-6927	299	8	(	(	PUNCT
ejpam-6927	299	9	4	4	NUM
ejpam-6927	299	10	)	)	PUNCT
ejpam-6927	299	11	(	(	PUNCT
ejpam-6927	299	12	2025	2025	NUM
ejpam-6927	299	13	)	)	PUNCT
ejpam-6927	299	14	,	,	PUNCT
ejpam-6927	299	15	6927	6927	NUM
ejpam-6927	299	16	13	13	NUM
ejpam-6927	299	17	of	of	ADP
ejpam-6927	299	18	18	18	NUM
ejpam-6927	299	19	remark	remark	NOUN
ejpam-6927	299	20	3	3	NUM
ejpam-6927	299	21	.	.	PUNCT
ejpam-6927	300	1	under	under	ADP
ejpam-6927	300	2	the	the	DET
ejpam-6927	300	3	assumptions	assumption	NOUN
ejpam-6927	300	4	of	of	ADP
ejpam-6927	300	5	theorem	theorem	NOUN
ejpam-6927	300	6	7	7	NUM
ejpam-6927	300	7	with	with	ADP
ejpam-6927	300	8	the	the	DET
ejpam-6927	300	9	limit	limit	NOUN
ejpam-6927	300	10	as	as	ADP
ejpam-6927	300	11	q	q	NOUN
ejpam-6927	300	12	→	→	SYM
ejpam-6927	300	13	1	1	NUM
ejpam-6927	300	14	,	,	PUNCT
ejpam-6927	300	15	we	we	PRON
ejpam-6927	300	16	have	have	VERB
ejpam-6927	300	17	the	the	DET
ejpam-6927	300	18	following	follow	VERB
ejpam-6927	300	19	h−h	h−h	NOUN
ejpam-6927	300	20	inequality	inequality	NOUN
ejpam-6927	300	21	:	:	PUNCT
ejpam-6927	301	1	1	1	NUM
ejpam-6927	301	2	ω2	ω2	NUM
ejpam-6927	301	3	−	−	PROPN
ejpam-6927	301	4	ω1	ω1	PROPN
ejpam-6927	301	5	∫	∫	PROPN
ejpam-6927	301	6	ω2	ω2	PROPN
ejpam-6927	301	7	ω1	ω1	PROPN
ejpam-6927	301	8	φ(κ)dκ	φ(κ)dκ	PART
ejpam-6927	301	9	−	−	PROPN
ejpam-6927	301	10	φ	φ	PROPN
ejpam-6927	301	11	(	(	PUNCT
ejpam-6927	301	12	ω1	ω1	PROPN
ejpam-6927	301	13	+	+	CCONJ
ejpam-6927	301	14	ω2	ω2	PROPN
ejpam-6927	301	15	2	2	NUM
ejpam-6927	301	16	)	)	PUNCT
ejpam-6927	301	17	≥	≥	NOUN
ejpam-6927	301	18	(	(	PUNCT
ejpam-6927	301	19	1	1	NUM
ejpam-6927	301	20	6	6	NUM
ejpam-6927	301	21	(	(	PUNCT
ejpam-6927	301	22	ω2	ω2	ADJ
ejpam-6927	301	23	−	−	PROPN
ejpam-6927	301	24	ω1	ω1	PROPN
ejpam-6927	301	25	)	)	PUNCT
ejpam-6927	301	26	2	2	NUM
ejpam-6927	302	1	+	+	CCONJ
ejpam-6927	302	2	1	1	NUM
ejpam-6927	302	3	2	2	NUM
ejpam-6927	302	4	ω1(ω2	ω1(ω2	NUM
ejpam-6927	302	5	−	−	NOUN
ejpam-6927	302	6	ω1	ω1	PROPN
ejpam-6927	302	7	)	)	PUNCT
ejpam-6927	302	8	+	+	CCONJ
ejpam-6927	302	9	1	1	NUM
ejpam-6927	302	10	2	2	NUM
ejpam-6927	302	11	ω2	ω2	ADJ
ejpam-6927	302	12	1	1	NUM
ejpam-6927	302	13	−	−	PROPN
ejpam-6927	302	14	1	1	NUM
ejpam-6927	302	15	8	8	NUM
ejpam-6927	302	16	(	(	PUNCT
ejpam-6927	302	17	ω1	ω1	PROPN
ejpam-6927	302	18	+	+	CCONJ
ejpam-6927	302	19	ω2	ω2	ADJ
ejpam-6927	302	20	)	)	PUNCT
ejpam-6927	302	21	2	2	NUM
ejpam-6927	302	22	)	)	PUNCT
ejpam-6927	302	23	φ′′	φ′′	PROPN
ejpam-6927	302	24	(	(	PUNCT
ejpam-6927	302	25	1	1	NUM
ejpam-6927	302	26	24(ω2	24(ω2	NUM
ejpam-6927	302	27	−	−	PROPN
ejpam-6927	302	28	ω1	ω1	PROPN
ejpam-6927	302	29	)	)	PUNCT
ejpam-6927	302	30	3	3	NUM
ejpam-6927	303	1	+	+	SYM
ejpam-6927	303	2	1	1	NUM
ejpam-6927	303	3	6(ω2	6(ω2	NUM
ejpam-6927	303	4	−	−	PROPN
ejpam-6927	303	5	ω1	ω1	PROPN
ejpam-6927	303	6	)	)	PUNCT
ejpam-6927	303	7	2ω1	2ω1	NUM
ejpam-6927	304	1	+	+	SYM
ejpam-6927	304	2	1	1	NUM
ejpam-6927	304	3	4(ω2	4(ω2	NUM
ejpam-6927	304	4	−	−	NOUN
ejpam-6927	304	5	ω1)ω	ω1)ω	VERB
ejpam-6927	304	6	2	2	NUM
ejpam-6927	304	7	1	1	NUM
ejpam-6927	304	8	+	+	SYM
ejpam-6927	304	9	1	1	NUM
ejpam-6927	304	10	6ω	6ω	NUM
ejpam-6927	304	11	3	3	NUM
ejpam-6927	304	12	1	1	NUM
ejpam-6927	304	13	−	−	NUM
ejpam-6927	304	14	1	1	NUM
ejpam-6927	304	15	48(ω1	48(ω1	NUM
ejpam-6927	304	16	+	+	CCONJ
ejpam-6927	304	17	ω2	ω2	ADJ
ejpam-6927	304	18	)	)	PUNCT
ejpam-6927	304	19	3	3	NUM
ejpam-6927	304	20	1	1	NUM
ejpam-6927	304	21	6(ω2	6(ω2	NUM
ejpam-6927	304	22	−	−	NOUN
ejpam-6927	304	23	ω1)2	ω1)2	NUM
ejpam-6927	305	1	+	+	NUM
ejpam-6927	305	2	1	1	NUM
ejpam-6927	305	3	2(ω2	2(ω2	NUM
ejpam-6927	305	4	−	−	NOUN
ejpam-6927	305	5	ω1)ω1	ω1)ω1	NOUN
ejpam-6927	305	6	+	+	NOUN
ejpam-6927	305	7	1	1	NUM
ejpam-6927	305	8	2ω	2ω	NUM
ejpam-6927	305	9	2	2	NUM
ejpam-6927	305	10	1	1	NUM
ejpam-6927	305	11	−	−	NUM
ejpam-6927	305	12	1	1	NUM
ejpam-6927	305	13	8(ω1	8(ω1	NUM
ejpam-6927	305	14	+	+	CCONJ
ejpam-6927	305	15	ω2)2	ω2)2	NUM
ejpam-6927	305	16	)	)	PUNCT
ejpam-6927	305	17	.	.	PUNCT
ejpam-6927	306	1	theorem	theorem	ADJ
ejpam-6927	306	2	8	8	NUM
ejpam-6927	306	3	.	.	PUNCT
ejpam-6927	307	1	let	let	VERB
ejpam-6927	307	2	φ	φ	PROPN
ejpam-6927	307	3	∈	∈	PROPN
ejpam-6927	307	4	c2[ω1	c2[ω1	PROPN
ejpam-6927	307	5	,	,	PUNCT
ejpam-6927	307	6	ω2	ω2	NOUN
ejpam-6927	307	7	]	]	PUNCT
ejpam-6927	307	8	such	such	ADJ
ejpam-6927	307	9	that	that	SCONJ
ejpam-6927	307	10	φ′′	φ′′	PROPN
ejpam-6927	307	11	is	be	AUX
ejpam-6927	307	12	convex	convex	ADJ
ejpam-6927	307	13	and	and	CCONJ
ejpam-6927	307	14	0	0	NUM
ejpam-6927	307	15	<	<	X
ejpam-6927	307	16	q	q	X
ejpam-6927	307	17	<	<	X
ejpam-6927	307	18	1	1	NUM
ejpam-6927	307	19	.	.	PUNCT
ejpam-6927	308	1	then	then	ADV
ejpam-6927	308	2	qφ(ω1	qφ(ω1	X
ejpam-6927	308	3	)	)	PUNCT
ejpam-6927	308	4	+	+	CCONJ
ejpam-6927	308	5	φ(ω2	φ(ω2	NOUN
ejpam-6927	308	6	)	)	PUNCT
ejpam-6927	308	7	q	q	NOUN
ejpam-6927	309	1	+	+	NUM
ejpam-6927	309	2	1	1	NUM
ejpam-6927	309	3	−	−	NUM
ejpam-6927	309	4	1	1	NUM
ejpam-6927	309	5	ω2	ω2	NUM
ejpam-6927	309	6	−	−	PROPN
ejpam-6927	309	7	ω1	ω1	PROPN
ejpam-6927	309	8	∫	∫	PROPN
ejpam-6927	309	9	ω2	ω2	PROPN
ejpam-6927	309	10	ω1	ω1	PROPN
ejpam-6927	309	11	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	309	12	≥	≥	X
ejpam-6927	309	13	(	(	PUNCT
ejpam-6927	309	14	1	1	NUM
ejpam-6927	309	15	2	2	NUM
ejpam-6927	309	16	(	(	PUNCT
ejpam-6927	309	17	qω2	qω2	NOUN
ejpam-6927	309	18	1	1	NUM
ejpam-6927	309	19	+	+	CCONJ
ejpam-6927	309	20	ω2	ω2	ADJ
ejpam-6927	309	21	2	2	NUM
ejpam-6927	309	22	1	1	NUM
ejpam-6927	309	23	+	+	CCONJ
ejpam-6927	309	24	q	q	NOUN
ejpam-6927	309	25	)	)	PUNCT
ejpam-6927	309	26	−	−	NOUN
ejpam-6927	309	27	1	1	NUM
ejpam-6927	309	28	2	2	NUM
ejpam-6927	309	29	(	(	PUNCT
ejpam-6927	309	30	(	(	PUNCT
ejpam-6927	309	31	ω2	ω2	ADJ
ejpam-6927	309	32	−	−	PROPN
ejpam-6927	309	33	ω1	ω1	PROPN
ejpam-6927	309	34	)	)	PUNCT
ejpam-6927	309	35	2	2	NUM
ejpam-6927	309	36	1	1	NUM
ejpam-6927	309	37	+	+	CCONJ
ejpam-6927	309	38	q	q	ADJ
ejpam-6927	309	39	+	+	NUM
ejpam-6927	309	40	q2	q2	NOUN
ejpam-6927	309	41	)	)	PUNCT
ejpam-6927	310	1	−	−	PROPN
ejpam-6927	310	2	ω1(ω2	ω1(ω2	NUM
ejpam-6927	310	3	−	−	PROPN
ejpam-6927	310	4	ω1	ω1	PROPN
ejpam-6927	310	5	)	)	PUNCT
ejpam-6927	310	6	(	(	PUNCT
ejpam-6927	310	7	1	1	NUM
ejpam-6927	310	8	+	+	CCONJ
ejpam-6927	310	9	q	q	X
ejpam-6927	310	10	)	)	PUNCT
ejpam-6927	310	11	−	−	NOUN
ejpam-6927	310	12	1	1	NUM
ejpam-6927	310	13	2	2	NUM
ejpam-6927	310	14	ω2	ω2	NUM
ejpam-6927	310	15	1	1	NUM
ejpam-6927	310	16	)	)	PUNCT
ejpam-6927	310	17	φ′′	φ′′	PROPN
ejpam-6927	310	18			PROPN
ejpam-6927	310	19	1	1	NUM
ejpam-6927	310	20	6	6	NUM
ejpam-6927	310	21	(	(	PUNCT
ejpam-6927	310	22	qω3	qω3	NOUN
ejpam-6927	310	23	1+ω3	1+ω3	NUM
ejpam-6927	310	24	2	2	NUM
ejpam-6927	310	25	1+q	1+q	NUM
ejpam-6927	310	26	)	)	PUNCT
ejpam-6927	310	27	−	−	ADP
ejpam-6927	310	28	1	1	NUM
ejpam-6927	310	29	6	6	NUM
ejpam-6927	310	30	(	(	PUNCT
ejpam-6927	310	31	ω2−ω1)2	ω2−ω1)2	PROPN
ejpam-6927	310	32	(	(	PUNCT
ejpam-6927	310	33	1+q)(1+q2	1+q)(1+q2	NUM
ejpam-6927	310	34	)	)	PUNCT
ejpam-6927	310	35	−	−	NOUN
ejpam-6927	310	36	1	1	NUM
ejpam-6927	310	37	2	2	NUM
ejpam-6927	310	38	ω1(ω2−ω1)2	ω1(ω2−ω1)2	ADP
ejpam-6927	310	39	1+q+q2	1+q+q2	NUM
ejpam-6927	310	40	−	−	NOUN
ejpam-6927	310	41	1	1	NUM
ejpam-6927	310	42	2	2	NUM
ejpam-6927	310	43	ω2	ω2	NUM
ejpam-6927	310	44	1(ω2−ω1	1(ω2−ω1	NUM
ejpam-6927	310	45	)	)	PUNCT
ejpam-6927	311	1	1+q	1+q	NUM
ejpam-6927	311	2	−	−	NOUN
ejpam-6927	311	3	1	1	NUM
ejpam-6927	311	4	6ω	6ω	NUM
ejpam-6927	311	5	3	3	NUM
ejpam-6927	311	6	1	1	NUM
ejpam-6927	311	7	1	1	NUM
ejpam-6927	311	8	2	2	NUM
ejpam-6927	311	9	(	(	PUNCT
ejpam-6927	311	10	qω2	qω2	NOUN
ejpam-6927	311	11	1+ω2	1+ω2	NUM
ejpam-6927	311	12	2	2	NUM
ejpam-6927	311	13	1+q	1+q	NUM
ejpam-6927	311	14	)	)	PUNCT
ejpam-6927	311	15	−	−	NOUN
ejpam-6927	311	16	1	1	NUM
ejpam-6927	311	17	2	2	NUM
ejpam-6927	311	18	(	(	PUNCT
ejpam-6927	311	19	ω2−ω1)2	ω2−ω1)2	PROPN
ejpam-6927	311	20	1+q+q2	1+q+q2	NUM
ejpam-6927	311	21	−	−	NOUN
ejpam-6927	311	22	ω1(ω2−ω1	ω1(ω2−ω1	NUM
ejpam-6927	311	23	)	)	PUNCT
ejpam-6927	312	1	1+q	1+q	NUM
ejpam-6927	312	2	−	−	NUM
ejpam-6927	312	3	1	1	NUM
ejpam-6927	312	4	2ω	2ω	NUM
ejpam-6927	312	5	2	2	NUM
ejpam-6927	312	6	1	1	NUM
ejpam-6927	312	7			PROPN
ejpam-6927	312	8	.	.	PUNCT
ejpam-6927	313	1	(	(	PUNCT
ejpam-6927	313	2	25	25	NUM
ejpam-6927	313	3	)	)	PUNCT
ejpam-6927	313	4	proof	proof	NOUN
ejpam-6927	313	5	.	.	PUNCT
ejpam-6927	314	1	from	from	ADP
ejpam-6927	314	2	(	(	PUNCT
ejpam-6927	314	3	18	18	NUM
ejpam-6927	314	4	)	)	PUNCT
ejpam-6927	314	5	,	,	PUNCT
ejpam-6927	314	6	we	we	PRON
ejpam-6927	314	7	have∫	have∫	VERB
ejpam-6927	314	8	ω2	ω2	PROPN
ejpam-6927	314	9	ω1	ω1	PROPN
ejpam-6927	314	10	p(κ)dκφ	p(κ)dκφ	PROPN
ejpam-6927	314	11	(	(	PUNCT
ejpam-6927	314	12	∫	∫	PROPN
ejpam-6927	314	13	ω2	ω2	PROPN
ejpam-6927	314	14	ω1	ω1	PROPN
ejpam-6927	314	15	p(κ)κdκ∫	p(κ)κdκ∫	PROPN
ejpam-6927	314	16	ω2	ω2	PROPN
ejpam-6927	314	17	ω1	ω1	PROPN
ejpam-6927	314	18	p(κ)dκ	p(κ)dκ	PROPN
ejpam-6927	314	19	)	)	PUNCT
ejpam-6927	314	20	≤	≤	PROPN
ejpam-6927	314	21	∫	∫	PROPN
ejpam-6927	314	22	ω2	ω2	PROPN
ejpam-6927	314	23	ω1	ω1	PROPN
ejpam-6927	314	24	p(κ)φ	p(κ)φ	PROPN
ejpam-6927	314	25	(	(	PUNCT
ejpam-6927	314	26	κ	κ	NOUN
ejpam-6927	314	27	)	)	PUNCT
ejpam-6927	314	28	dκ	dκ	PROPN
ejpam-6927	314	29	.	.	PUNCT
ejpam-6927	315	1	(	(	PUNCT
ejpam-6927	315	2	26	26	NUM
ejpam-6927	315	3	)	)	PUNCT
ejpam-6927	315	4	comparing	compare	VERB
ejpam-6927	315	5	(	(	PUNCT
ejpam-6927	315	6	26	26	NUM
ejpam-6927	315	7	)	)	PUNCT
ejpam-6927	315	8	with	with	ADP
ejpam-6927	315	9	(	(	PUNCT
ejpam-6927	315	10	13	13	NUM
ejpam-6927	315	11	)	)	PUNCT
ejpam-6927	315	12	,	,	PUNCT
ejpam-6927	315	13	we	we	PRON
ejpam-6927	315	14	have	have	VERB
ejpam-6927	315	15	p(κ	p(κ	NOUN
ejpam-6927	315	16	)	)	PUNCT
ejpam-6927	315	17	=	=	PUNCT
ejpam-6927	315	18	γ(ℓ	γ(ℓ	NOUN
ejpam-6927	315	19	)	)	PUNCT
ejpam-6927	315	20	and	and	CCONJ
ejpam-6927	315	21	φ(κ	φ(κ	NOUN
ejpam-6927	315	22	)	)	PUNCT
ejpam-6927	315	23	=	=	SYM
ejpam-6927	315	24	φ′′(ℓ	φ′′(ℓ	NOUN
ejpam-6927	315	25	)	)	PUNCT
ejpam-6927	315	26	.	.	PUNCT
ejpam-6927	316	1	(	(	PUNCT
ejpam-6927	316	2	26	26	NUM
ejpam-6927	316	3	)	)	PUNCT
ejpam-6927	316	4	,	,	PUNCT
ejpam-6927	316	5	becomes	become	VERB
ejpam-6927	316	6	∫	∫	PROPN
ejpam-6927	316	7	ω2	ω2	PROPN
ejpam-6927	316	8	ω1	ω1	PROPN
ejpam-6927	316	9	γ(ℓ)φ′′	γ(ℓ)φ′′	PROPN
ejpam-6927	316	10	(	(	PUNCT
ejpam-6927	316	11	ℓ	ℓ	NOUN
ejpam-6927	316	12	)	)	PUNCT
ejpam-6927	316	13	dℓ	dℓ	PROPN
ejpam-6927	316	14	≥	≥	NUM
ejpam-6927	316	15	∫	∫	PROPN
ejpam-6927	316	16	ω2	ω2	PROPN
ejpam-6927	316	17	ω1	ω1	PROPN
ejpam-6927	316	18	γ(ℓ)dℓ.φ	γ(ℓ)dℓ.φ	PROPN
ejpam-6927	316	19	(	(	PUNCT
ejpam-6927	316	20	∫	∫	PROPN
ejpam-6927	316	21	ω2	ω2	PROPN
ejpam-6927	316	22	ω1	ω1	PROPN
ejpam-6927	316	23	γ(ℓ)ℓdℓ∫	γ(ℓ)ℓdℓ∫	PROPN
ejpam-6927	316	24	ω2	ω2	PROPN
ejpam-6927	316	25	ω1	ω1	PROPN
ejpam-6927	316	26	γ(ℓ)dℓ	γ(ℓ)dℓ	NUM
ejpam-6927	316	27	)	)	PUNCT
ejpam-6927	316	28	.	.	PUNCT
ejpam-6927	317	1	by	by	ADP
ejpam-6927	317	2	(	(	PUNCT
ejpam-6927	317	3	13	13	NUM
ejpam-6927	317	4	)	)	PUNCT
ejpam-6927	317	5	,	,	PUNCT
ejpam-6927	317	6	we	we	PRON
ejpam-6927	317	7	have	have	VERB
ejpam-6927	317	8	qφ(ω1	qφ(ω1	NOUN
ejpam-6927	317	9	)	)	PUNCT
ejpam-6927	317	10	+	+	CCONJ
ejpam-6927	317	11	φ(ω2	φ(ω2	NOUN
ejpam-6927	317	12	)	)	PUNCT
ejpam-6927	317	13	q	q	NOUN
ejpam-6927	318	1	+	+	NUM
ejpam-6927	318	2	1	1	NUM
ejpam-6927	318	3	−	−	NUM
ejpam-6927	318	4	1	1	NUM
ejpam-6927	318	5	ω2	ω2	NUM
ejpam-6927	318	6	−	−	PROPN
ejpam-6927	318	7	ω1	ω1	PROPN
ejpam-6927	318	8	∫	∫	PROPN
ejpam-6927	318	9	ω2	ω2	PROPN
ejpam-6927	318	10	ω1	ω1	PROPN
ejpam-6927	318	11	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	318	12	≥	≥	NUM
ejpam-6927	318	13	∫	∫	PROPN
ejpam-6927	318	14	ω2	ω2	PROPN
ejpam-6927	318	15	ω1	ω1	PROPN
ejpam-6927	318	16	γ(ℓ)dℓ.φ′′	γ(ℓ)dℓ.φ′′	PROPN
ejpam-6927	318	17	(	(	PUNCT
ejpam-6927	318	18	∫	∫	PROPN
ejpam-6927	318	19	ω2	ω2	PROPN
ejpam-6927	318	20	ω1	ω1	PROPN
ejpam-6927	318	21	γ(ℓ)ℓdℓ∫	γ(ℓ)ℓdℓ∫	PROPN
ejpam-6927	318	22	ω2	ω2	PROPN
ejpam-6927	318	23	ω1	ω1	PROPN
ejpam-6927	318	24	γ(ℓ)dℓ	γ(ℓ)dℓ	NUM
ejpam-6927	318	25	)	)	PUNCT
ejpam-6927	318	26	.	.	PUNCT
ejpam-6927	319	1	(	(	PUNCT
ejpam-6927	319	2	27	27	NUM
ejpam-6927	319	3	)	)	PUNCT
ejpam-6927	319	4	now	now	ADV
ejpam-6927	319	5	we	we	PRON
ejpam-6927	319	6	solve	solve	VERB
ejpam-6927	319	7	the	the	DET
ejpam-6927	319	8	integral	integral	ADJ
ejpam-6927	319	9	,	,	PUNCT
ejpam-6927	319	10	∫	∫	PROPN
ejpam-6927	319	11	ω2	ω2	PROPN
ejpam-6927	319	12	ω1	ω1	PROPN
ejpam-6927	319	13	γ(ℓ)dℓ.	γ(ℓ)dℓ.	PROPN
ejpam-6927	319	14	if	if	SCONJ
ejpam-6927	319	15	φ(ℓ	φ(ℓ	PROPN
ejpam-6927	319	16	)	)	PUNCT
ejpam-6927	319	17	=	=	SYM
ejpam-6927	319	18	1	1	NUM
ejpam-6927	319	19	2ℓ	2ℓ	NUM
ejpam-6927	319	20	2	2	NUM
ejpam-6927	319	21	,	,	PUNCT
ejpam-6927	319	22	then	then	ADV
ejpam-6927	319	23	φ′′(ℓ	φ′′(ℓ	NOUN
ejpam-6927	319	24	)	)	PUNCT
ejpam-6927	319	25	=	=	SYM
ejpam-6927	319	26	1	1	NUM
ejpam-6927	319	27	,	,	PUNCT
ejpam-6927	319	28	using	use	VERB
ejpam-6927	319	29	these	these	DET
ejpam-6927	319	30	functions	function	NOUN
ejpam-6927	319	31	in	in	ADP
ejpam-6927	319	32	(	(	PUNCT
ejpam-6927	319	33	13	13	NUM
ejpam-6927	319	34	)	)	PUNCT
ejpam-6927	319	35	,	,	PUNCT
ejpam-6927	320	1	we	we	PRON
ejpam-6927	320	2	obtain.∫	obtain.∫	NOUN
ejpam-6927	320	3	ω2	ω2	PROPN
ejpam-6927	320	4	ω1	ω1	PROPN
ejpam-6927	320	5	γ(ℓ)dℓ	γ(ℓ)dℓ	PROPN
ejpam-6927	320	6	=	=	SYM
ejpam-6927	320	7	1	1	NUM
ejpam-6927	320	8	2qω	2qω	NOUN
ejpam-6927	320	9	2	2	NUM
ejpam-6927	320	10	1	1	NUM
ejpam-6927	320	11	+	+	SYM
ejpam-6927	320	12	1	1	NUM
ejpam-6927	320	13	2ω	2ω	NUM
ejpam-6927	320	14	2	2	NUM
ejpam-6927	320	15	2	2	NUM
ejpam-6927	320	16	1	1	NUM
ejpam-6927	320	17	+	+	NOUN
ejpam-6927	320	18	q	q	NOUN
ejpam-6927	320	19	−	−	PROPN
ejpam-6927	320	20	1	1	NUM
ejpam-6927	320	21	ω2	ω2	NUM
ejpam-6927	320	22	−	−	PROPN
ejpam-6927	320	23	ω1	ω1	PROPN
ejpam-6927	320	24	∫	∫	PROPN
ejpam-6927	320	25	ω2	ω2	PROPN
ejpam-6927	320	26	ω1	ω1	PROPN
ejpam-6927	320	27	1	1	NUM
ejpam-6927	320	28	2	2	NUM
ejpam-6927	320	29	(	(	PUNCT
ejpam-6927	320	30	ℓ2)ω1dqℓ.	ℓ2)ω1dqℓ.	PROPN
ejpam-6927	320	31	m.	m.	NOUN
ejpam-6927	320	32	adil	adil	PROPN
ejpam-6927	320	33	khan	khan	PROPN
ejpam-6927	320	34	et	et	PROPN
ejpam-6927	320	35	al	al	PROPN
ejpam-6927	320	36	.	.	PUNCT
ejpam-6927	320	37	/	/	SYM
ejpam-6927	320	38	eur	eur	PROPN
ejpam-6927	320	39	.	.	PUNCT
ejpam-6927	321	1	j.	j.	PROPN
ejpam-6927	321	2	pure	pure	PROPN
ejpam-6927	321	3	appl	appl	PROPN
ejpam-6927	321	4	.	.	PROPN
ejpam-6927	321	5	math	math	PROPN
ejpam-6927	321	6	,	,	PUNCT
ejpam-6927	321	7	18	18	NUM
ejpam-6927	321	8	(	(	PUNCT
ejpam-6927	321	9	4	4	NUM
ejpam-6927	321	10	)	)	PUNCT
ejpam-6927	321	11	(	(	PUNCT
ejpam-6927	321	12	2025	2025	NUM
ejpam-6927	321	13	)	)	PUNCT
ejpam-6927	321	14	,	,	PUNCT
ejpam-6927	321	15	6927	6927	NUM
ejpam-6927	321	16	14	14	NUM
ejpam-6927	321	17	of	of	ADP
ejpam-6927	321	18	18	18	NUM
ejpam-6927	321	19	finding	find	VERB
ejpam-6927	321	20	the	the	DET
ejpam-6927	321	21	above	above	ADJ
ejpam-6927	321	22	integrals	integral	NOUN
ejpam-6927	321	23	,	,	PUNCT
ejpam-6927	321	24	we	we	PRON
ejpam-6927	321	25	get.∫	get.∫	NOUN
ejpam-6927	321	26	ω2	ω2	PROPN
ejpam-6927	321	27	ω1	ω1	PROPN
ejpam-6927	321	28	γ(ℓ)dℓ	γ(ℓ)dℓ	PROPN
ejpam-6927	321	29	=	=	SYM
ejpam-6927	321	30	1	1	NUM
ejpam-6927	321	31	2	2	NUM
ejpam-6927	321	32	(	(	PUNCT
ejpam-6927	321	33	qω2	qω2	NOUN
ejpam-6927	321	34	1	1	NUM
ejpam-6927	321	35	+	+	CCONJ
ejpam-6927	321	36	ω2	ω2	ADJ
ejpam-6927	321	37	2	2	NUM
ejpam-6927	321	38	1	1	NUM
ejpam-6927	321	39	+	+	CCONJ
ejpam-6927	321	40	q	q	NOUN
ejpam-6927	321	41	)	)	PUNCT
ejpam-6927	321	42	−	−	NOUN
ejpam-6927	321	43	1	1	NUM
ejpam-6927	321	44	2	2	NUM
ejpam-6927	321	45	(	(	PUNCT
ejpam-6927	321	46	(	(	PUNCT
ejpam-6927	321	47	ω2	ω2	ADJ
ejpam-6927	321	48	−	−	PROPN
ejpam-6927	321	49	ω1	ω1	PROPN
ejpam-6927	321	50	)	)	PUNCT
ejpam-6927	321	51	2	2	NUM
ejpam-6927	321	52	1	1	NUM
ejpam-6927	321	53	+	+	CCONJ
ejpam-6927	321	54	q	q	ADJ
ejpam-6927	321	55	+	+	NUM
ejpam-6927	321	56	q2	q2	NOUN
ejpam-6927	321	57	)	)	PUNCT
ejpam-6927	322	1	−	−	PROPN
ejpam-6927	322	2	ω1(ω2	ω1(ω2	NUM
ejpam-6927	322	3	−	−	PROPN
ejpam-6927	322	4	ω1	ω1	PROPN
ejpam-6927	322	5	)	)	PUNCT
ejpam-6927	322	6	(	(	PUNCT
ejpam-6927	322	7	1	1	NUM
ejpam-6927	322	8	+	+	CCONJ
ejpam-6927	322	9	q	q	X
ejpam-6927	322	10	)	)	PUNCT
ejpam-6927	322	11	−	−	NOUN
ejpam-6927	322	12	1	1	NUM
ejpam-6927	322	13	2	2	NUM
ejpam-6927	322	14	ω2	ω2	NUM
ejpam-6927	322	15	1	1	NUM
ejpam-6927	322	16	.	.	PUNCT
ejpam-6927	323	1	(	(	PUNCT
ejpam-6927	323	2	28	28	NUM
ejpam-6927	323	3	)	)	PUNCT
ejpam-6927	323	4	now	now	ADV
ejpam-6927	323	5	we	we	PRON
ejpam-6927	323	6	solve	solve	VERB
ejpam-6927	323	7	the	the	DET
ejpam-6927	323	8	integral	integral	ADJ
ejpam-6927	323	9	,	,	PUNCT
ejpam-6927	323	10	∫	∫	PROPN
ejpam-6927	323	11	ω2	ω2	PROPN
ejpam-6927	323	12	ω1	ω1	PROPN
ejpam-6927	323	13	γ(ℓ)ℓdℓ.	γ(ℓ)ℓdℓ.	PROPN
ejpam-6927	323	14	if	if	SCONJ
ejpam-6927	323	15	φ(ℓ	φ(ℓ	PROPN
ejpam-6927	323	16	)	)	PUNCT
ejpam-6927	323	17	=	=	SYM
ejpam-6927	323	18	1	1	NUM
ejpam-6927	323	19	6ℓ	6ℓ	NOUN
ejpam-6927	323	20	3	3	NUM
ejpam-6927	323	21	,	,	PUNCT
ejpam-6927	323	22	then	then	ADV
ejpam-6927	323	23	φ′′(ℓ	φ′′(ℓ	NOUN
ejpam-6927	323	24	)	)	PUNCT
ejpam-6927	323	25	=	=	SYM
ejpam-6927	323	26	ℓ	ℓ	PROPN
ejpam-6927	323	27	,	,	PUNCT
ejpam-6927	323	28	using	use	VERB
ejpam-6927	323	29	these	these	DET
ejpam-6927	323	30	functions	function	NOUN
ejpam-6927	323	31	in	in	ADP
ejpam-6927	323	32	(	(	PUNCT
ejpam-6927	323	33	13	13	NUM
ejpam-6927	323	34	)	)	PUNCT
ejpam-6927	323	35	,	,	PUNCT
ejpam-6927	323	36	we	we	PRON
ejpam-6927	323	37	obtain.∫	obtain.∫	NOUN
ejpam-6927	323	38	ω2	ω2	ADJ
ejpam-6927	323	39	ω1	ω1	PROPN
ejpam-6927	323	40	γ(ℓ)ℓdℓ	γ(ℓ)ℓdℓ	PROPN
ejpam-6927	323	41	=	=	NOUN
ejpam-6927	323	42	1	1	NUM
ejpam-6927	323	43	6qω	6qω	NOUN
ejpam-6927	323	44	3	3	NUM
ejpam-6927	323	45	1	1	NUM
ejpam-6927	323	46	+	+	SYM
ejpam-6927	323	47	1	1	NUM
ejpam-6927	323	48	6ω	6ω	NUM
ejpam-6927	323	49	3	3	NUM
ejpam-6927	323	50	2	2	NUM
ejpam-6927	323	51	1	1	NUM
ejpam-6927	323	52	+	+	CCONJ
ejpam-6927	323	53	q	q	NOUN
ejpam-6927	323	54	−	−	PROPN
ejpam-6927	323	55	1	1	NUM
ejpam-6927	323	56	ω2	ω2	NUM
ejpam-6927	323	57	−	−	PROPN
ejpam-6927	323	58	ω1	ω1	PROPN
ejpam-6927	323	59	∫	∫	PROPN
ejpam-6927	323	60	ω2	ω2	PROPN
ejpam-6927	323	61	ω1	ω1	PROPN
ejpam-6927	323	62	1	1	NUM
ejpam-6927	323	63	6	6	NUM
ejpam-6927	323	64	(	(	PUNCT
ejpam-6927	323	65	ℓ3)ω1dqℓ.	ℓ3)ω1dqℓ.	NOUN
ejpam-6927	323	66	finding	find	VERB
ejpam-6927	323	67	the	the	DET
ejpam-6927	323	68	above	above	ADJ
ejpam-6927	323	69	integrals	integral	NOUN
ejpam-6927	323	70	,	,	PUNCT
ejpam-6927	323	71	we	we	PRON
ejpam-6927	323	72	get.∫	get.∫	NOUN
ejpam-6927	323	73	ω2	ω2	PROPN
ejpam-6927	323	74	ω1	ω1	PROPN
ejpam-6927	323	75	γ(ℓ)ℓdℓ	γ(ℓ)ℓdℓ	PROPN
ejpam-6927	323	76	=	=	PUNCT
ejpam-6927	323	77	1	1	NUM
ejpam-6927	323	78	6	6	NUM
ejpam-6927	323	79	(	(	PUNCT
ejpam-6927	323	80	qω3	qω3	NOUN
ejpam-6927	323	81	1	1	NUM
ejpam-6927	323	82	+	+	CCONJ
ejpam-6927	323	83	ω3	ω3	ADJ
ejpam-6927	323	84	2	2	NUM
ejpam-6927	323	85	1	1	NUM
ejpam-6927	323	86	+	+	CCONJ
ejpam-6927	323	87	q	q	NOUN
ejpam-6927	323	88	)	)	PUNCT
ejpam-6927	323	89	−	−	PROPN
ejpam-6927	323	90	1	1	NUM
ejpam-6927	323	91	6	6	NUM
ejpam-6927	323	92	(	(	PUNCT
ejpam-6927	323	93	ω2	ω2	ADJ
ejpam-6927	323	94	−	−	PROPN
ejpam-6927	323	95	ω1	ω1	PROPN
ejpam-6927	323	96	)	)	PUNCT
ejpam-6927	323	97	3	3	NUM
ejpam-6927	323	98	(	(	PUNCT
ejpam-6927	323	99	1	1	NUM
ejpam-6927	323	100	+	+	NUM
ejpam-6927	323	101	q)(1	q)(1	X
ejpam-6927	323	102	+	+	CCONJ
ejpam-6927	323	103	q2	q2	NOUN
ejpam-6927	323	104	)	)	PUNCT
ejpam-6927	324	1	−	−	NOUN
ejpam-6927	324	2	1	1	NUM
ejpam-6927	324	3	2	2	NUM
ejpam-6927	324	4	ω1(ω2	ω1(ω2	NUM
ejpam-6927	324	5	−	−	NOUN
ejpam-6927	324	6	ω1	ω1	PROPN
ejpam-6927	324	7	)	)	PUNCT
ejpam-6927	324	8	2	2	NUM
ejpam-6927	324	9	1	1	NUM
ejpam-6927	324	10	+	+	CCONJ
ejpam-6927	324	11	q	q	NOUN
ejpam-6927	325	1	+	+	NUM
ejpam-6927	325	2	q2	q2	NOUN
ejpam-6927	325	3	−1	−1	NOUN
ejpam-6927	325	4	2	2	NUM
ejpam-6927	325	5	ω2	ω2	NOUN
ejpam-6927	325	6	1(ω2	1(ω2	NUM
ejpam-6927	325	7	−	−	PROPN
ejpam-6927	325	8	ω1	ω1	PROPN
ejpam-6927	325	9	)	)	PUNCT
ejpam-6927	325	10	1	1	NUM
ejpam-6927	326	1	+	+	CCONJ
ejpam-6927	326	2	q	q	ADJ
ejpam-6927	326	3	−	−	NUM
ejpam-6927	326	4	1	1	NUM
ejpam-6927	326	5	6	6	NUM
ejpam-6927	326	6	ω3	ω3	NOUN
ejpam-6927	326	7	1	1	NUM
ejpam-6927	326	8	.	.	PUNCT
ejpam-6927	327	1	(	(	PUNCT
ejpam-6927	327	2	29	29	NUM
ejpam-6927	327	3	)	)	PUNCT
ejpam-6927	327	4	using	use	VERB
ejpam-6927	327	5	(	(	PUNCT
ejpam-6927	327	6	28	28	NUM
ejpam-6927	327	7	)	)	PUNCT
ejpam-6927	327	8	and	and	CCONJ
ejpam-6927	327	9	(	(	PUNCT
ejpam-6927	327	10	29	29	NUM
ejpam-6927	327	11	)	)	PUNCT
ejpam-6927	327	12	in	in	ADP
ejpam-6927	327	13	(	(	PUNCT
ejpam-6927	327	14	27	27	NUM
ejpam-6927	327	15	)	)	PUNCT
ejpam-6927	327	16	,	,	PUNCT
ejpam-6927	327	17	we	we	PRON
ejpam-6927	327	18	get	get	VERB
ejpam-6927	327	19	qφ(ω1	qφ(ω1	ADV
ejpam-6927	327	20	)	)	PUNCT
ejpam-6927	328	1	+	+	CCONJ
ejpam-6927	328	2	φ(ω2	φ(ω2	NOUN
ejpam-6927	328	3	)	)	PUNCT
ejpam-6927	328	4	q	q	NOUN
ejpam-6927	329	1	+	+	NUM
ejpam-6927	329	2	1	1	NUM
ejpam-6927	329	3	−	−	NUM
ejpam-6927	329	4	1	1	NUM
ejpam-6927	329	5	ω2	ω2	NUM
ejpam-6927	329	6	−	−	PROPN
ejpam-6927	329	7	ω1	ω1	PROPN
ejpam-6927	329	8	∫	∫	PROPN
ejpam-6927	329	9	ω2	ω2	PROPN
ejpam-6927	329	10	ω1	ω1	PROPN
ejpam-6927	329	11	φ(κ)ω1dqκ	φ(κ)ω1dqκ	PROPN
ejpam-6927	329	12	≥	≥	X
ejpam-6927	329	13	(	(	PUNCT
ejpam-6927	329	14	1	1	NUM
ejpam-6927	329	15	2	2	NUM
ejpam-6927	329	16	(	(	PUNCT
ejpam-6927	329	17	qω2	qω2	NOUN
ejpam-6927	329	18	1	1	NUM
ejpam-6927	329	19	+	+	CCONJ
ejpam-6927	329	20	ω2	ω2	ADJ
ejpam-6927	329	21	2	2	NUM
ejpam-6927	329	22	1	1	NUM
ejpam-6927	329	23	+	+	CCONJ
ejpam-6927	329	24	q	q	NOUN
ejpam-6927	329	25	)	)	PUNCT
ejpam-6927	329	26	−	−	NOUN
ejpam-6927	329	27	1	1	NUM
ejpam-6927	329	28	2	2	NUM
ejpam-6927	329	29	(	(	PUNCT
ejpam-6927	329	30	(	(	PUNCT
ejpam-6927	329	31	ω2	ω2	ADJ
ejpam-6927	329	32	−	−	PROPN
ejpam-6927	329	33	ω1	ω1	PROPN
ejpam-6927	329	34	)	)	PUNCT
ejpam-6927	329	35	2	2	NUM
ejpam-6927	329	36	1	1	NUM
ejpam-6927	329	37	+	+	CCONJ
ejpam-6927	329	38	q	q	ADJ
ejpam-6927	329	39	+	+	NUM
ejpam-6927	329	40	q2	q2	NOUN
ejpam-6927	329	41	)	)	PUNCT
ejpam-6927	330	1	−	−	PROPN
ejpam-6927	330	2	ω1(ω2	ω1(ω2	NUM
ejpam-6927	330	3	−	−	PROPN
ejpam-6927	330	4	ω1	ω1	PROPN
ejpam-6927	330	5	)	)	PUNCT
ejpam-6927	330	6	(	(	PUNCT
ejpam-6927	330	7	1	1	NUM
ejpam-6927	330	8	+	+	CCONJ
ejpam-6927	330	9	q	q	X
ejpam-6927	330	10	)	)	PUNCT
ejpam-6927	330	11	−	−	NOUN
ejpam-6927	330	12	1	1	NUM
ejpam-6927	330	13	2	2	NUM
ejpam-6927	330	14	ω2	ω2	NUM
ejpam-6927	330	15	1	1	NUM
ejpam-6927	330	16	)	)	PUNCT
ejpam-6927	330	17	φ	φ	PROPN
ejpam-6927	331	1			PROPN
ejpam-6927	331	2	1	1	NUM
ejpam-6927	331	3	6	6	NUM
ejpam-6927	331	4	(	(	PUNCT
ejpam-6927	331	5	qω3	qω3	NOUN
ejpam-6927	331	6	1+ω3	1+ω3	NUM
ejpam-6927	331	7	2	2	NUM
ejpam-6927	331	8	1+q	1+q	NUM
ejpam-6927	331	9	)	)	PUNCT
ejpam-6927	331	10	−	−	ADP
ejpam-6927	331	11	1	1	NUM
ejpam-6927	331	12	6	6	NUM
ejpam-6927	331	13	(	(	PUNCT
ejpam-6927	331	14	ω2−ω1)2	ω2−ω1)2	PROPN
ejpam-6927	331	15	(	(	PUNCT
ejpam-6927	331	16	1+q)(1+q2	1+q)(1+q2	NUM
ejpam-6927	331	17	)	)	PUNCT
ejpam-6927	331	18	−	−	NOUN
ejpam-6927	331	19	1	1	NUM
ejpam-6927	331	20	2	2	NUM
ejpam-6927	331	21	ω1(ω2−ω1)2	ω1(ω2−ω1)2	ADP
ejpam-6927	331	22	1+q+q2	1+q+q2	NUM
ejpam-6927	331	23	−	−	NOUN
ejpam-6927	331	24	1	1	NUM
ejpam-6927	331	25	2	2	NUM
ejpam-6927	331	26	ω2	ω2	NUM
ejpam-6927	331	27	1(ω2−ω1	1(ω2−ω1	NUM
ejpam-6927	331	28	)	)	PUNCT
ejpam-6927	331	29	1+q	1+q	NUM
ejpam-6927	331	30	−	−	NOUN
ejpam-6927	331	31	1	1	NUM
ejpam-6927	331	32	6ω	6ω	NUM
ejpam-6927	331	33	3	3	NUM
ejpam-6927	331	34	1	1	NUM
ejpam-6927	331	35	1	1	NUM
ejpam-6927	331	36	2	2	NUM
ejpam-6927	331	37	(	(	PUNCT
ejpam-6927	331	38	qω2	qω2	NOUN
ejpam-6927	331	39	1+ω2	1+ω2	NUM
ejpam-6927	331	40	2	2	NUM
ejpam-6927	331	41	1+q	1+q	NUM
ejpam-6927	331	42	)	)	PUNCT
ejpam-6927	331	43	−	−	NOUN
ejpam-6927	331	44	1	1	NUM
ejpam-6927	331	45	2	2	NUM
ejpam-6927	331	46	(	(	PUNCT
ejpam-6927	331	47	ω2−ω1)2	ω2−ω1)2	PROPN
ejpam-6927	331	48	1+q+q2	1+q+q2	NUM
ejpam-6927	331	49	−	−	NOUN
ejpam-6927	331	50	ω1(ω2−ω1	ω1(ω2−ω1	NUM
ejpam-6927	331	51	)	)	PUNCT
ejpam-6927	332	1	1+q	1+q	NUM
ejpam-6927	332	2	−	−	NUM
ejpam-6927	332	3	1	1	NUM
ejpam-6927	332	4	2ω	2ω	NUM
ejpam-6927	332	5	2	2	NUM
ejpam-6927	332	6	1	1	NUM
ejpam-6927	332	7			PROPN
ejpam-6927	332	8	.	.	PUNCT
ejpam-6927	333	1	(	(	PUNCT
ejpam-6927	333	2	30	30	NUM
ejpam-6927	333	3	)	)	PUNCT
ejpam-6927	333	4	(	(	PUNCT
ejpam-6927	333	5	30	30	NUM
ejpam-6927	333	6	)	)	PUNCT
ejpam-6927	333	7	is	be	AUX
ejpam-6927	333	8	equivalent	equivalent	ADJ
ejpam-6927	333	9	to	to	ADP
ejpam-6927	333	10	(	(	PUNCT
ejpam-6927	333	11	25	25	NUM
ejpam-6927	333	12	)	)	PUNCT
ejpam-6927	333	13	.	.	PUNCT
ejpam-6927	334	1	remark	remark	PROPN
ejpam-6927	334	2	4	4	NUM
ejpam-6927	334	3	.	.	PUNCT
ejpam-6927	335	1	under	under	ADP
ejpam-6927	335	2	the	the	DET
ejpam-6927	335	3	assumptions	assumption	NOUN
ejpam-6927	335	4	of	of	ADP
ejpam-6927	335	5	theorem	theorem	NOUN
ejpam-6927	335	6	8	8	NUM
ejpam-6927	335	7	with	with	ADP
ejpam-6927	335	8	the	the	DET
ejpam-6927	335	9	limit	limit	NOUN
ejpam-6927	335	10	as	as	ADP
ejpam-6927	335	11	q	q	NOUN
ejpam-6927	335	12	→	→	SYM
ejpam-6927	335	13	1	1	NUM
ejpam-6927	335	14	,	,	PUNCT
ejpam-6927	335	15	we	we	PRON
ejpam-6927	335	16	have	have	VERB
ejpam-6927	335	17	the	the	DET
ejpam-6927	335	18	following	follow	VERB
ejpam-6927	335	19	h−h	h−h	NOUN
ejpam-6927	335	20	inequality	inequality	NOUN
ejpam-6927	335	21	:	:	PUNCT
ejpam-6927	335	22	φ(ω1	φ(ω1	NOUN
ejpam-6927	335	23	)	)	PUNCT
ejpam-6927	335	24	+	+	CCONJ
ejpam-6927	335	25	φ(ω2	φ(ω2	NOUN
ejpam-6927	335	26	)	)	PUNCT
ejpam-6927	335	27	2	2	NUM
ejpam-6927	335	28	−	−	PROPN
ejpam-6927	335	29	1	1	NUM
ejpam-6927	336	1	ω2	ω2	NUM
ejpam-6927	336	2	−	−	PROPN
ejpam-6927	336	3	ω1	ω1	PROPN
ejpam-6927	336	4	∫	∫	PROPN
ejpam-6927	336	5	ω2	ω2	PROPN
ejpam-6927	336	6	ω1	ω1	PROPN
ejpam-6927	336	7	φ(κ)dκ	φ(κ)dκ	PART
ejpam-6927	336	8	≥	≥	NUM
ejpam-6927	336	9	(	(	PUNCT
ejpam-6927	336	10	1	1	NUM
ejpam-6927	336	11	4	4	NUM
ejpam-6927	336	12	(	(	PUNCT
ejpam-6927	336	13	ω2	ω2	NOUN
ejpam-6927	336	14	1	1	NUM
ejpam-6927	336	15	+	+	CCONJ
ejpam-6927	336	16	ω2	ω2	PROPN
ejpam-6927	336	17	2)−	2)−	NUM
ejpam-6927	336	18	1	1	NUM
ejpam-6927	336	19	6	6	NUM
ejpam-6927	336	20	(	(	PUNCT
ejpam-6927	336	21	ω2	ω2	ADJ
ejpam-6927	336	22	−	−	PROPN
ejpam-6927	336	23	ω1	ω1	PROPN
ejpam-6927	336	24	)	)	PUNCT
ejpam-6927	336	25	2	2	NUM
ejpam-6927	336	26	−	−	NOUN
ejpam-6927	336	27	1	1	NUM
ejpam-6927	336	28	2	2	NUM
ejpam-6927	336	29	(	(	PUNCT
ejpam-6927	336	30	ω2	ω2	ADV
ejpam-6927	336	31	−	−	PROPN
ejpam-6927	336	32	ω1)ω1	ω1)ω1	NOUN
ejpam-6927	336	33	−	−	NOUN
ejpam-6927	336	34	1	1	NUM
ejpam-6927	336	35	2	2	NUM
ejpam-6927	336	36	ω2	ω2	NUM
ejpam-6927	336	37	1	1	NUM
ejpam-6927	336	38	)	)	PUNCT
ejpam-6927	336	39	φ′′	φ′′	PROPN
ejpam-6927	336	40	(	(	PUNCT
ejpam-6927	336	41	1	1	NUM
ejpam-6927	336	42	12(ω	12(ω	NUM
ejpam-6927	336	43	3	3	NUM
ejpam-6927	336	44	1	1	NUM
ejpam-6927	336	45	+	+	CCONJ
ejpam-6927	336	46	ω3	ω3	NOUN
ejpam-6927	336	47	2)−	2)−	NUM
ejpam-6927	336	48	1	1	NUM
ejpam-6927	336	49	24(ω2	24(ω2	NUM
ejpam-6927	336	50	−	−	PROPN
ejpam-6927	336	51	ω1	ω1	PROPN
ejpam-6927	336	52	)	)	PUNCT
ejpam-6927	336	53	2	2	NUM
ejpam-6927	336	54	−	−	NUM
ejpam-6927	336	55	1	1	NUM
ejpam-6927	336	56	6(ω2	6(ω2	NUM
ejpam-6927	336	57	−	−	PROPN
ejpam-6927	336	58	ω1	ω1	PROPN
ejpam-6927	336	59	)	)	PUNCT
ejpam-6927	336	60	2ω1	2ω1	NUM
ejpam-6927	336	61	−	−	NOUN
ejpam-6927	336	62	1	1	NUM
ejpam-6927	336	63	4(ω2	4(ω2	NUM
ejpam-6927	336	64	−	−	NOUN
ejpam-6927	336	65	ω1)ω	ω1)ω	VERB
ejpam-6927	336	66	2	2	NUM
ejpam-6927	336	67	1	1	NUM
ejpam-6927	336	68	−	−	NUM
ejpam-6927	336	69	1	1	NUM
ejpam-6927	336	70	6ω	6ω	NUM
ejpam-6927	336	71	3	3	NUM
ejpam-6927	336	72	1	1	NUM
ejpam-6927	336	73	1	1	NUM
ejpam-6927	336	74	4(ω	4(ω	NUM
ejpam-6927	336	75	2	2	NUM
ejpam-6927	336	76	1	1	NUM
ejpam-6927	336	77	+	+	CCONJ
ejpam-6927	336	78	ω2	ω2	ADJ
ejpam-6927	336	79	2)−	2)−	NUM
ejpam-6927	336	80	1	1	NUM
ejpam-6927	336	81	6(ω2	6(ω2	NUM
ejpam-6927	336	82	−	−	NOUN
ejpam-6927	336	83	ω1)2	ω1)2	NUM
ejpam-6927	336	84	−	−	NUM
ejpam-6927	336	85	1	1	NUM
ejpam-6927	336	86	2(ω2	2(ω2	NUM
ejpam-6927	336	87	−	−	NOUN
ejpam-6927	336	88	ω1)ω1	ω1)ω1	NOUN
ejpam-6927	336	89	−	−	NOUN
ejpam-6927	336	90	1	1	NUM
ejpam-6927	336	91	2ω	2ω	NUM
ejpam-6927	336	92	2	2	NUM
ejpam-6927	336	93	1	1	NUM
ejpam-6927	336	94	)	)	PUNCT
ejpam-6927	336	95	.	.	PUNCT
ejpam-6927	337	1	m.	m.	PROPN
ejpam-6927	337	2	adil	adil	PROPN
ejpam-6927	337	3	khan	khan	PROPN
ejpam-6927	337	4	et	et	PROPN
ejpam-6927	337	5	al	al	PROPN
ejpam-6927	337	6	.	.	PUNCT
ejpam-6927	337	7	/	/	SYM
ejpam-6927	337	8	eur	eur	PROPN
ejpam-6927	337	9	.	.	PUNCT
ejpam-6927	338	1	j.	j.	PROPN
ejpam-6927	338	2	pure	pure	PROPN
ejpam-6927	338	3	appl	appl	PROPN
ejpam-6927	338	4	.	.	PROPN
ejpam-6927	338	5	math	math	PROPN
ejpam-6927	338	6	,	,	PUNCT
ejpam-6927	338	7	18	18	NUM
ejpam-6927	338	8	(	(	PUNCT
ejpam-6927	338	9	4	4	NUM
ejpam-6927	338	10	)	)	PUNCT
ejpam-6927	338	11	(	(	PUNCT
ejpam-6927	338	12	2025	2025	NUM
ejpam-6927	338	13	)	)	PUNCT
ejpam-6927	338	14	,	,	PUNCT
ejpam-6927	338	15	6927	6927	NUM
ejpam-6927	338	16	15	15	NUM
ejpam-6927	338	17	of	of	ADP
ejpam-6927	338	18	18	18	NUM
ejpam-6927	338	19	4	4	NUM
ejpam-6927	338	20	.	.	PUNCT
ejpam-6927	338	21	numerical	numerical	ADJ
ejpam-6927	338	22	examples	example	NOUN
ejpam-6927	338	23	and	and	CCONJ
ejpam-6927	338	24	graphical	graphical	ADJ
ejpam-6927	338	25	analysis	analysis	NOUN
ejpam-6927	338	26	in	in	ADP
ejpam-6927	338	27	this	this	DET
ejpam-6927	338	28	section	section	NOUN
ejpam-6927	338	29	,	,	PUNCT
ejpam-6927	338	30	we	we	PRON
ejpam-6927	338	31	present	present	VERB
ejpam-6927	338	32	our	our	PRON
ejpam-6927	338	33	primary	primary	ADJ
ejpam-6927	338	34	results	result	NOUN
ejpam-6927	338	35	through	through	ADP
ejpam-6927	338	36	numerical	numerical	ADJ
ejpam-6927	338	37	examples	example	NOUN
ejpam-6927	338	38	and	and	CCONJ
ejpam-6927	338	39	graphical	graphical	ADJ
ejpam-6927	338	40	representations	representation	NOUN
ejpam-6927	338	41	.	.	PUNCT
ejpam-6927	339	1	under	under	ADP
ejpam-6927	339	2	the	the	DET
ejpam-6927	339	3	assumption	assumption	NOUN
ejpam-6927	339	4	of	of	ADP
ejpam-6927	339	5	theorem	theorem	NOUN
ejpam-6927	339	6	5	5	NUM
ejpam-6927	339	7	,	,	PUNCT
ejpam-6927	339	8	we	we	PRON
ejpam-6927	339	9	take	take	VERB
ejpam-6927	339	10	q	q	NOUN
ejpam-6927	339	11	∈	∈	NOUN
ejpam-6927	339	12	(	(	PUNCT
ejpam-6927	339	13	0	0	NUM
ejpam-6927	339	14	,	,	PUNCT
ejpam-6927	339	15	1	1	NUM
ejpam-6927	339	16	)	)	PUNCT
ejpam-6927	339	17	,	,	PUNCT
ejpam-6927	339	18	φ(κ	φ(κ	PROPN
ejpam-6927	339	19	)	)	PUNCT
ejpam-6927	339	20	=	=	SYM
ejpam-6927	339	21	κ2	κ2	NOUN
ejpam-6927	339	22	,	,	PUNCT
ejpam-6927	339	23	and	and	CCONJ
ejpam-6927	339	24	[	[	X
ejpam-6927	339	25	ω1	ω1	PROPN
ejpam-6927	339	26	,	,	PUNCT
ejpam-6927	339	27	ω2	ω2	ADJ
ejpam-6927	339	28	]	]	X
ejpam-6927	339	29	=	=	PUNCT
ejpam-6927	340	1	[	[	X
ejpam-6927	340	2	6	6	NUM
ejpam-6927	340	3	,	,	PUNCT
ejpam-6927	340	4	8	8	NUM
ejpam-6927	340	5	]	]	PUNCT
ejpam-6927	340	6	,	,	PUNCT
ejpam-6927	340	7	as	as	SCONJ
ejpam-6927	340	8	a	a	DET
ejpam-6927	340	9	variable	variable	NOUN
ejpam-6927	340	10	to	to	PART
ejpam-6927	340	11	illustrate	illustrate	VERB
ejpam-6927	340	12	a	a	DET
ejpam-6927	340	13	figure	figure	NOUN
ejpam-6927	340	14	1	1	NUM
ejpam-6927	340	15	between	between	ADP
ejpam-6927	340	16	the	the	DET
ejpam-6927	340	17	left	left	ADJ
ejpam-6927	340	18	and	and	CCONJ
ejpam-6927	340	19	right	right	ADJ
ejpam-6927	340	20	-	-	PUNCT
ejpam-6927	340	21	hand	hand	NOUN
ejpam-6927	340	22	sides	side	NOUN
ejpam-6927	340	23	of	of	ADP
ejpam-6927	340	24	theorem	theorem	NOUN
ejpam-6927	340	25	5	5	NUM
ejpam-6927	340	26	.	.	PUNCT
ejpam-6927	340	27	figure	figure	NOUN
ejpam-6927	340	28	1	1	NUM
ejpam-6927	340	29	:	:	PUNCT
ejpam-6927	340	30	lhs	lhs	PROPN
ejpam-6927	340	31	vs	vs	ADP
ejpam-6927	340	32	rhs	rhs	PROPN
ejpam-6927	340	33	of	of	ADP
ejpam-6927	340	34	theorem	theorem	NOUN
ejpam-6927	340	35	5	5	NUM
ejpam-6927	340	36	for	for	ADP
ejpam-6927	340	37	q	q	PROPN
ejpam-6927	340	38	∈	∈	PROPN
ejpam-6927	340	39	(	(	PUNCT
ejpam-6927	340	40	0	0	NUM
ejpam-6927	340	41	,	,	PUNCT
ejpam-6927	340	42	1	1	NUM
ejpam-6927	340	43	)	)	PUNCT
ejpam-6927	340	44	,	,	PUNCT
ejpam-6927	340	45	φ(κ	φ(κ	PROPN
ejpam-6927	340	46	)	)	PUNCT
ejpam-6927	340	47	=	=	SYM
ejpam-6927	340	48	κ2	κ2	NOUN
ejpam-6927	340	49	,	,	PUNCT
ejpam-6927	340	50	on	on	ADP
ejpam-6927	340	51	[	[	X
ejpam-6927	340	52	ω1	ω1	PROPN
ejpam-6927	340	53	,	,	PUNCT
ejpam-6927	340	54	ω2	ω2	ADJ
ejpam-6927	340	55	]	]	X
ejpam-6927	340	56	=	=	PUNCT
ejpam-6927	341	1	[	[	X
ejpam-6927	341	2	6	6	NUM
ejpam-6927	341	3	,	,	PUNCT
ejpam-6927	341	4	8	8	NUM
ejpam-6927	341	5	]	]	PUNCT
ejpam-6927	341	6	.	.	PUNCT
ejpam-6927	342	1	under	under	ADP
ejpam-6927	342	2	the	the	DET
ejpam-6927	342	3	assumption	assumption	NOUN
ejpam-6927	342	4	of	of	ADP
ejpam-6927	342	5	theorem	theorem	NOUN
ejpam-6927	342	6	6	6	NUM
ejpam-6927	342	7	,	,	PUNCT
ejpam-6927	342	8	we	we	PRON
ejpam-6927	342	9	take	take	VERB
ejpam-6927	342	10	q	q	NOUN
ejpam-6927	342	11	∈	∈	NOUN
ejpam-6927	342	12	(	(	PUNCT
ejpam-6927	342	13	0	0	NUM
ejpam-6927	342	14	,	,	PUNCT
ejpam-6927	342	15	1	1	NUM
ejpam-6927	342	16	)	)	PUNCT
ejpam-6927	342	17	,	,	PUNCT
ejpam-6927	342	18	φ(κ	φ(κ	PROPN
ejpam-6927	342	19	)	)	PUNCT
ejpam-6927	342	20	=	=	SYM
ejpam-6927	342	21	κ2	κ2	NOUN
ejpam-6927	342	22	,	,	PUNCT
ejpam-6927	342	23	and	and	CCONJ
ejpam-6927	342	24	[	[	X
ejpam-6927	342	25	ω1	ω1	PROPN
ejpam-6927	342	26	,	,	PUNCT
ejpam-6927	342	27	ω2	ω2	ADJ
ejpam-6927	342	28	]	]	X
ejpam-6927	342	29	=	=	PUNCT
ejpam-6927	343	1	[	[	X
ejpam-6927	343	2	2	2	NUM
ejpam-6927	343	3	,	,	PUNCT
ejpam-6927	343	4	2.4	2.4	NUM
ejpam-6927	343	5	]	]	PUNCT
ejpam-6927	343	6	,	,	PUNCT
ejpam-6927	343	7	as	as	SCONJ
ejpam-6927	343	8	a	a	DET
ejpam-6927	343	9	variable	variable	NOUN
ejpam-6927	343	10	to	to	PART
ejpam-6927	343	11	illustrate	illustrate	VERB
ejpam-6927	343	12	a	a	DET
ejpam-6927	343	13	figure	figure	NOUN
ejpam-6927	343	14	2	2	NUM
ejpam-6927	343	15	between	between	ADP
ejpam-6927	343	16	the	the	DET
ejpam-6927	343	17	left	left	ADJ
ejpam-6927	343	18	and	and	CCONJ
ejpam-6927	343	19	right	right	ADJ
ejpam-6927	343	20	-	-	PUNCT
ejpam-6927	343	21	hand	hand	NOUN
ejpam-6927	343	22	sides	side	NOUN
ejpam-6927	343	23	of	of	ADP
ejpam-6927	343	24	theorem	theorem	ADJ
ejpam-6927	343	25	6	6	NUM
ejpam-6927	343	26	.	.	PUNCT
ejpam-6927	343	27	figure	figure	NOUN
ejpam-6927	343	28	2	2	NUM
ejpam-6927	343	29	:	:	PUNCT
ejpam-6927	343	30	lhs	lhs	PROPN
ejpam-6927	343	31	vs	vs	ADP
ejpam-6927	343	32	rhs	rhs	PROPN
ejpam-6927	343	33	of	of	ADP
ejpam-6927	343	34	theorem	theorem	NOUN
ejpam-6927	343	35	6	6	NUM
ejpam-6927	343	36	for	for	ADP
ejpam-6927	343	37	q	q	PROPN
ejpam-6927	343	38	∈	∈	PROPN
ejpam-6927	343	39	(	(	PUNCT
ejpam-6927	343	40	0	0	NUM
ejpam-6927	343	41	,	,	PUNCT
ejpam-6927	343	42	1	1	NUM
ejpam-6927	343	43	)	)	PUNCT
ejpam-6927	343	44	,	,	PUNCT
ejpam-6927	343	45	φ(κ	φ(κ	PROPN
ejpam-6927	343	46	)	)	PUNCT
ejpam-6927	343	47	=	=	SYM
ejpam-6927	343	48	κ2	κ2	NOUN
ejpam-6927	343	49	,	,	PUNCT
ejpam-6927	343	50	on	on	ADP
ejpam-6927	343	51	[	[	X
ejpam-6927	343	52	ω1	ω1	PROPN
ejpam-6927	343	53	,	,	PUNCT
ejpam-6927	343	54	ω2	ω2	ADJ
ejpam-6927	343	55	]	]	X
ejpam-6927	343	56	=	=	PUNCT
ejpam-6927	344	1	[	[	X
ejpam-6927	344	2	2	2	NUM
ejpam-6927	344	3	,	,	PUNCT
ejpam-6927	344	4	2.4	2.4	NUM
ejpam-6927	344	5	]	]	PUNCT
ejpam-6927	344	6	.	.	PUNCT
ejpam-6927	345	1	m.	m.	PROPN
ejpam-6927	345	2	adil	adil	PROPN
ejpam-6927	345	3	khan	khan	PROPN
ejpam-6927	345	4	et	et	PROPN
ejpam-6927	345	5	al	al	PROPN
ejpam-6927	345	6	.	.	PUNCT
ejpam-6927	345	7	/	/	SYM
ejpam-6927	345	8	eur	eur	PROPN
ejpam-6927	345	9	.	.	PUNCT
ejpam-6927	346	1	j.	j.	PROPN
ejpam-6927	346	2	pure	pure	PROPN
ejpam-6927	346	3	appl	appl	PROPN
ejpam-6927	346	4	.	.	PROPN
ejpam-6927	346	5	math	math	PROPN
ejpam-6927	346	6	,	,	PUNCT
ejpam-6927	346	7	18	18	NUM
ejpam-6927	346	8	(	(	PUNCT
ejpam-6927	346	9	4	4	NUM
ejpam-6927	346	10	)	)	PUNCT
ejpam-6927	346	11	(	(	PUNCT
ejpam-6927	346	12	2025	2025	NUM
ejpam-6927	346	13	)	)	PUNCT
ejpam-6927	346	14	,	,	PUNCT
ejpam-6927	346	15	6927	6927	NUM
ejpam-6927	346	16	16	16	NUM
ejpam-6927	346	17	of	of	ADP
ejpam-6927	346	18	18	18	NUM
ejpam-6927	346	19	under	under	ADP
ejpam-6927	346	20	the	the	DET
ejpam-6927	346	21	assumption	assumption	NOUN
ejpam-6927	346	22	of	of	ADP
ejpam-6927	346	23	theorem	theorem	NOUN
ejpam-6927	346	24	7	7	NUM
ejpam-6927	346	25	,	,	PUNCT
ejpam-6927	346	26	we	we	PRON
ejpam-6927	346	27	take	take	VERB
ejpam-6927	346	28	q	q	NOUN
ejpam-6927	346	29	∈	∈	NOUN
ejpam-6927	346	30	(	(	PUNCT
ejpam-6927	346	31	0	0	NUM
ejpam-6927	346	32	,	,	PUNCT
ejpam-6927	346	33	1	1	NUM
ejpam-6927	346	34	)	)	PUNCT
ejpam-6927	346	35	,	,	PUNCT
ejpam-6927	346	36	φ(κ	φ(κ	PROPN
ejpam-6927	346	37	)	)	PUNCT
ejpam-6927	346	38	=	=	SYM
ejpam-6927	346	39	κ2	κ2	NOUN
ejpam-6927	346	40	,	,	PUNCT
ejpam-6927	346	41	and	and	CCONJ
ejpam-6927	346	42	[	[	X
ejpam-6927	346	43	ω1	ω1	PROPN
ejpam-6927	346	44	,	,	PUNCT
ejpam-6927	346	45	ω2	ω2	ADJ
ejpam-6927	346	46	]	]	X
ejpam-6927	346	47	=	=	PUNCT
ejpam-6927	347	1	[	[	X
ejpam-6927	347	2	0	0	NUM
ejpam-6927	347	3	,	,	PUNCT
ejpam-6927	347	4	1	1	NUM
ejpam-6927	347	5	]	]	PUNCT
ejpam-6927	347	6	,	,	PUNCT
ejpam-6927	347	7	as	as	SCONJ
ejpam-6927	347	8	a	a	DET
ejpam-6927	347	9	variable	variable	NOUN
ejpam-6927	347	10	to	to	PART
ejpam-6927	347	11	illustrate	illustrate	VERB
ejpam-6927	347	12	a	a	DET
ejpam-6927	347	13	figure	figure	NOUN
ejpam-6927	347	14	3	3	NUM
ejpam-6927	347	15	between	between	ADP
ejpam-6927	347	16	the	the	DET
ejpam-6927	347	17	left	left	ADJ
ejpam-6927	347	18	and	and	CCONJ
ejpam-6927	347	19	right	right	ADJ
ejpam-6927	347	20	-	-	PUNCT
ejpam-6927	347	21	hand	hand	NOUN
ejpam-6927	347	22	sided	sided	NOUN
ejpam-6927	347	23	of	of	ADP
ejpam-6927	347	24	theorem	theorem	ADJ
ejpam-6927	347	25	7	7	NUM
ejpam-6927	347	26	.	.	PUNCT
ejpam-6927	347	27	figure	figure	NOUN
ejpam-6927	347	28	3	3	NUM
ejpam-6927	347	29	:	:	PUNCT
ejpam-6927	347	30	lhs	lhs	PROPN
ejpam-6927	347	31	vs	vs	ADP
ejpam-6927	347	32	rhs	rhs	PROPN
ejpam-6927	347	33	of	of	ADP
ejpam-6927	347	34	theorem	theorem	NOUN
ejpam-6927	347	35	7	7	NUM
ejpam-6927	347	36	for	for	ADP
ejpam-6927	347	37	q	q	PROPN
ejpam-6927	347	38	∈	∈	PROPN
ejpam-6927	347	39	(	(	PUNCT
ejpam-6927	347	40	0	0	NUM
ejpam-6927	347	41	,	,	PUNCT
ejpam-6927	347	42	1	1	NUM
ejpam-6927	347	43	)	)	PUNCT
ejpam-6927	347	44	,	,	PUNCT
ejpam-6927	347	45	φ(κ	φ(κ	PROPN
ejpam-6927	347	46	)	)	PUNCT
ejpam-6927	347	47	=	=	SYM
ejpam-6927	347	48	κ2	κ2	NOUN
ejpam-6927	347	49	,	,	PUNCT
ejpam-6927	347	50	on	on	ADP
ejpam-6927	347	51	[	[	X
ejpam-6927	347	52	ω1	ω1	PROPN
ejpam-6927	347	53	,	,	PUNCT
ejpam-6927	347	54	ω2	ω2	ADJ
ejpam-6927	347	55	]	]	X
ejpam-6927	347	56	=	=	PUNCT
ejpam-6927	348	1	[	[	X
ejpam-6927	348	2	0	0	NUM
ejpam-6927	348	3	,	,	PUNCT
ejpam-6927	348	4	1	1	NUM
ejpam-6927	348	5	]	]	PUNCT
ejpam-6927	348	6	.	.	PUNCT
ejpam-6927	349	1	under	under	ADP
ejpam-6927	349	2	the	the	DET
ejpam-6927	349	3	assumption	assumption	NOUN
ejpam-6927	349	4	of	of	ADP
ejpam-6927	349	5	theorem	theorem	NOUN
ejpam-6927	349	6	8	8	NUM
ejpam-6927	349	7	,	,	PUNCT
ejpam-6927	349	8	we	we	PRON
ejpam-6927	349	9	take	take	VERB
ejpam-6927	349	10	q	q	NOUN
ejpam-6927	349	11	∈	∈	NOUN
ejpam-6927	349	12	(	(	PUNCT
ejpam-6927	349	13	0	0	NUM
ejpam-6927	349	14	,	,	PUNCT
ejpam-6927	349	15	1	1	NUM
ejpam-6927	349	16	)	)	PUNCT
ejpam-6927	349	17	,	,	PUNCT
ejpam-6927	349	18	φ(κ	φ(κ	PROPN
ejpam-6927	349	19	)	)	PUNCT
ejpam-6927	349	20	=	=	SYM
ejpam-6927	349	21	κ4	κ4	NOUN
ejpam-6927	349	22	,	,	PUNCT
ejpam-6927	349	23	and	and	CCONJ
ejpam-6927	349	24	[	[	X
ejpam-6927	349	25	ω1	ω1	PROPN
ejpam-6927	349	26	,	,	PUNCT
ejpam-6927	349	27	ω2	ω2	ADJ
ejpam-6927	349	28	]	]	X
ejpam-6927	349	29	=	=	PUNCT
ejpam-6927	350	1	[	[	X
ejpam-6927	350	2	7	7	NUM
ejpam-6927	350	3	,	,	PUNCT
ejpam-6927	350	4	8	8	NUM
ejpam-6927	350	5	]	]	PUNCT
ejpam-6927	350	6	as	as	ADP
ejpam-6927	350	7	a	a	DET
ejpam-6927	350	8	variable	variable	NOUN
ejpam-6927	350	9	to	to	PART
ejpam-6927	350	10	illustrate	illustrate	VERB
ejpam-6927	350	11	a	a	DET
ejpam-6927	350	12	figure	figure	NOUN
ejpam-6927	350	13	4	4	NUM
ejpam-6927	350	14	between	between	ADP
ejpam-6927	350	15	the	the	DET
ejpam-6927	350	16	left	left	ADJ
ejpam-6927	350	17	and	and	CCONJ
ejpam-6927	350	18	right	right	ADJ
ejpam-6927	350	19	hand	hand	NOUN
ejpam-6927	350	20	side	side	NOUN
ejpam-6927	350	21	of	of	ADP
ejpam-6927	350	22	theorem	theorem	ADJ
ejpam-6927	350	23	8	8	NUM
ejpam-6927	350	24	.	.	PUNCT
ejpam-6927	350	25	figure	figure	NOUN
ejpam-6927	350	26	4	4	NUM
ejpam-6927	350	27	:	:	PUNCT
ejpam-6927	350	28	lhs	lhs	PROPN
ejpam-6927	350	29	vs	vs	ADP
ejpam-6927	350	30	rhs	rhs	PROPN
ejpam-6927	350	31	of	of	ADP
ejpam-6927	350	32	theorem	theorem	NOUN
ejpam-6927	350	33	8	8	NUM
ejpam-6927	350	34	for	for	ADP
ejpam-6927	350	35	q	q	PROPN
ejpam-6927	350	36	∈	∈	PROPN
ejpam-6927	350	37	(	(	PUNCT
ejpam-6927	350	38	0	0	NUM
ejpam-6927	350	39	,	,	PUNCT
ejpam-6927	350	40	1	1	NUM
ejpam-6927	350	41	)	)	PUNCT
ejpam-6927	350	42	,	,	PUNCT
ejpam-6927	350	43	φ(κ	φ(κ	PROPN
ejpam-6927	350	44	)	)	PUNCT
ejpam-6927	350	45	=	=	SYM
ejpam-6927	350	46	κ4	κ4	NOUN
ejpam-6927	350	47	,	,	PUNCT
ejpam-6927	350	48	on	on	ADP
ejpam-6927	350	49	[	[	X
ejpam-6927	350	50	ω1	ω1	PROPN
ejpam-6927	350	51	,	,	PUNCT
ejpam-6927	350	52	ω2	ω2	ADJ
ejpam-6927	350	53	]	]	X
ejpam-6927	350	54	=	=	PUNCT
ejpam-6927	351	1	[	[	X
ejpam-6927	351	2	7	7	NUM
ejpam-6927	351	3	,	,	PUNCT
ejpam-6927	351	4	8	8	NUM
ejpam-6927	351	5	]	]	PUNCT
ejpam-6927	351	6	.	.	PUNCT
ejpam-6927	352	1	5	5	X
ejpam-6927	352	2	.	.	X
ejpam-6927	352	3	conclusion	conclusion	NOUN
ejpam-6927	352	4	the	the	DET
ejpam-6927	352	5	present	present	ADJ
ejpam-6927	352	6	study	study	NOUN
ejpam-6927	352	7	has	have	AUX
ejpam-6927	352	8	employed	employ	VERB
ejpam-6927	352	9	a	a	DET
ejpam-6927	352	10	green	green	ADJ
ejpam-6927	352	11	function	function	NOUN
ejpam-6927	352	12	technique	technique	NOUN
ejpam-6927	352	13	to	to	PART
ejpam-6927	352	14	analyze	analyze	VERB
ejpam-6927	352	15	the	the	DET
ejpam-6927	352	16	quantum	quantum	ADJ
ejpam-6927	352	17	h−h	h−h	NOUN
ejpam-6927	352	18	inequality	inequality	NOUN
ejpam-6927	352	19	.	.	PUNCT
ejpam-6927	353	1	new	new	ADJ
ejpam-6927	353	2	quantum	quantum	ADJ
ejpam-6927	353	3	identities	identity	NOUN
ejpam-6927	353	4	were	be	AUX
ejpam-6927	353	5	obtained	obtain	VERB
ejpam-6927	353	6	throughout	throughout	ADP
ejpam-6927	353	7	this	this	DET
ejpam-6927	353	8	procedure	procedure	NOUN
ejpam-6927	353	9	and	and	CCONJ
ejpam-6927	353	10	m.	m.	NOUN
ejpam-6927	353	11	adil	adil	PROPN
ejpam-6927	353	12	khan	khan	PROPN
ejpam-6927	353	13	et	et	PROPN
ejpam-6927	353	14	al	al	PROPN
ejpam-6927	353	15	.	.	PUNCT
ejpam-6927	353	16	/	/	SYM
ejpam-6927	353	17	eur	eur	PROPN
ejpam-6927	353	18	.	.	PUNCT
ejpam-6927	354	1	j.	j.	PROPN
ejpam-6927	354	2	pure	pure	PROPN
ejpam-6927	354	3	appl	appl	PROPN
ejpam-6927	354	4	.	.	PROPN
ejpam-6927	354	5	math	math	PROPN
ejpam-6927	354	6	,	,	PUNCT
ejpam-6927	354	7	18	18	NUM
ejpam-6927	354	8	(	(	PUNCT
ejpam-6927	354	9	4	4	NUM
ejpam-6927	354	10	)	)	PUNCT
ejpam-6927	354	11	(	(	PUNCT
ejpam-6927	354	12	2025	2025	NUM
ejpam-6927	354	13	)	)	PUNCT
ejpam-6927	354	14	,	,	PUNCT
ejpam-6927	354	15	6927	6927	NUM
ejpam-6927	354	16	17	17	NUM
ejpam-6927	354	17	of	of	ADP
ejpam-6927	354	18	18	18	NUM
ejpam-6927	354	19	applied	apply	VERB
ejpam-6927	354	20	to	to	PART
ejpam-6927	354	21	create	create	VERB
ejpam-6927	354	22	new	new	ADJ
ejpam-6927	354	23	inequalities	inequality	NOUN
ejpam-6927	354	24	.	.	PUNCT
ejpam-6927	355	1	jensen	jensen	PROPN
ejpam-6927	355	2	’s	’s	PART
ejpam-6927	355	3	inequality	inequality	NOUN
ejpam-6927	355	4	for	for	ADP
ejpam-6927	355	5	convex	convex	NOUN
ejpam-6927	355	6	mappings	mapping	NOUN
ejpam-6927	355	7	,	,	PUNCT
ejpam-6927	355	8	convexity	convexity	NOUN
ejpam-6927	355	9	principles	principle	NOUN
ejpam-6927	355	10	,	,	PUNCT
ejpam-6927	355	11	and	and	CCONJ
ejpam-6927	355	12	q	q	NOUN
ejpam-6927	355	13	-	-	PUNCT
ejpam-6927	355	14	identities	identity	NOUN
ejpam-6927	355	15	are	be	AUX
ejpam-6927	355	16	some	some	PRON
ejpam-6927	355	17	of	of	ADP
ejpam-6927	355	18	the	the	DET
ejpam-6927	355	19	methods	method	NOUN
ejpam-6927	355	20	used	use	VERB
ejpam-6927	355	21	in	in	ADP
ejpam-6927	355	22	this	this	DET
ejpam-6927	355	23	work	work	NOUN
ejpam-6927	355	24	to	to	PART
ejpam-6927	355	25	arrive	arrive	VERB
ejpam-6927	355	26	at	at	ADP
ejpam-6927	355	27	its	its	PRON
ejpam-6927	355	28	main	main	ADJ
ejpam-6927	355	29	conclusions	conclusion	NOUN
ejpam-6927	355	30	.	.	PUNCT
ejpam-6927	356	1	furthermore	furthermore	ADV
ejpam-6927	356	2	,	,	PUNCT
ejpam-6927	356	3	the	the	DET
ejpam-6927	356	4	major	major	ADJ
ejpam-6927	356	5	results	result	NOUN
ejpam-6927	356	6	are	be	AUX
ejpam-6927	356	7	supported	support	VERB
ejpam-6927	356	8	by	by	ADP
ejpam-6927	356	9	graphical	graphical	ADJ
ejpam-6927	356	10	representations	representation	NOUN
ejpam-6927	356	11	and	and	CCONJ
ejpam-6927	356	12	numerical	numerical	ADJ
ejpam-6927	356	13	validations	validation	NOUN
ejpam-6927	356	14	.	.	PUNCT
ejpam-6927	357	1	in	in	ADP
ejpam-6927	357	2	this	this	DET
ejpam-6927	357	3	regard	regard	NOUN
ejpam-6927	357	4	,	,	PUNCT
ejpam-6927	357	5	the	the	DET
ejpam-6927	357	6	presented	present	VERB
ejpam-6927	357	7	consequences	consequence	NOUN
ejpam-6927	357	8	and	and	CCONJ
ejpam-6927	357	9	methods	method	NOUN
ejpam-6927	357	10	in	in	ADP
ejpam-6927	357	11	this	this	DET
ejpam-6927	357	12	paper	paper	NOUN
ejpam-6927	357	13	may	may	AUX
ejpam-6927	357	14	explore	explore	VERB
ejpam-6927	357	15	further	further	ADJ
ejpam-6927	357	16	investigation	investigation	NOUN
ejpam-6927	357	17	in	in	ADP
ejpam-6927	357	18	this	this	DET
ejpam-6927	357	19	area	area	NOUN
ejpam-6927	357	20	by	by	ADP
ejpam-6927	357	21	mathematicians	mathematician	NOUN
ejpam-6927	357	22	.	.	PUNCT
ejpam-6927	358	1	acknowledgements	acknowledgement	NOUN
ejpam-6927	358	2	the	the	DET
ejpam-6927	358	3	authors	author	NOUN
ejpam-6927	358	4	extend	extend	VERB
ejpam-6927	358	5	their	their	PRON
ejpam-6927	358	6	appreciation	appreciation	NOUN
ejpam-6927	358	7	to	to	ADP
ejpam-6927	358	8	the	the	DET
ejpam-6927	358	9	deanship	deanship	NOUN
ejpam-6927	358	10	of	of	ADP
ejpam-6927	358	11	research	research	NOUN
ejpam-6927	358	12	and	and	CCONJ
ejpam-6927	358	13	graduate	graduate	NOUN
ejpam-6927	358	14	studies	study	NOUN
ejpam-6927	358	15	at	at	ADP
ejpam-6927	358	16	king	king	PROPN
ejpam-6927	358	17	khalid	khalid	PROPN
ejpam-6927	358	18	university	university	PROPN
ejpam-6927	358	19	for	for	ADP
ejpam-6927	358	20	funding	fund	VERB
ejpam-6927	358	21	this	this	DET
ejpam-6927	358	22	work	work	NOUN
ejpam-6927	358	23	through	through	ADP
ejpam-6927	358	24	large	large	ADJ
ejpam-6927	358	25	research	research	NOUN
ejpam-6927	358	26	project	project	NOUN
ejpam-6927	358	27	under	under	ADP
ejpam-6927	358	28	grant	grant	NOUN
ejpam-6927	358	29	number	number	NOUN
ejpam-6927	358	30	rgp2/305/46	rgp2/305/46	PROPN
ejpam-6927	358	31	.	.	PUNCT
ejpam-6927	359	1	references	reference	NOUN
ejpam-6927	359	2	[	[	X
ejpam-6927	359	3	1	1	NUM
ejpam-6927	359	4	]	]	PUNCT
ejpam-6927	359	5	s.	s.	PROPN
ejpam-6927	359	6	khan	khan	PROPN
ejpam-6927	359	7	,	,	PUNCT
ejpam-6927	359	8	m.	m.	PROPN
ejpam-6927	359	9	adil	adil	PROPN
ejpam-6927	359	10	khan	khan	PROPN
ejpam-6927	359	11	,	,	PUNCT
ejpam-6927	359	12	and	and	CCONJ
ejpam-6927	359	13	y.-m	y.-m	NOUN
ejpam-6927	359	14	.	.	PUNCT
ejpam-6927	360	1	chu	chu	PROPN
ejpam-6927	360	2	.	.	PUNCT
ejpam-6927	361	1	new	new	ADJ
ejpam-6927	361	2	converses	converse	NOUN
ejpam-6927	361	3	of	of	ADP
ejpam-6927	361	4	jensen	jensen	PROPN
ejpam-6927	361	5	inequality	inequality	NOUN
ejpam-6927	361	6	via	via	ADP
ejpam-6927	361	7	green	green	ADJ
ejpam-6927	361	8	functions	function	NOUN
ejpam-6927	361	9	with	with	ADP
ejpam-6927	361	10	applications	application	NOUN
ejpam-6927	361	11	.	.	PUNCT
ejpam-6927	362	1	revista	revista	PROPN
ejpam-6927	362	2	de	de	X
ejpam-6927	362	3	la	la	PROPN
ejpam-6927	362	4	real	real	PROPN
ejpam-6927	362	5	academia	academia	PROPN
ejpam-6927	362	6	de	de	PROPN
ejpam-6927	362	7	ciencias	ciencias	PROPN
ejpam-6927	362	8	exactas	exacta	NOUN
ejpam-6927	362	9	,	,	PUNCT
ejpam-6927	362	10	f́ısicas	f́ısicas	PROPN
ejpam-6927	362	11	y	y	PROPN
ejpam-6927	362	12	naturales	naturale	NOUN
ejpam-6927	362	13	.	.	PUNCT
ejpam-6927	363	1	serie	serie	PROPN
ejpam-6927	363	2	a.	a.	PROPN
ejpam-6927	363	3	matemáticas	matemáticas	PROPN
ejpam-6927	363	4	,	,	PUNCT
ejpam-6927	363	5	114(3):114	114(3):114	NUM
ejpam-6927	363	6	,	,	PUNCT
ejpam-6927	363	7	2020	2020	NUM
ejpam-6927	363	8	.	.	PUNCT
ejpam-6927	364	1	[	[	X
ejpam-6927	364	2	2	2	NUM
ejpam-6927	364	3	]	]	PUNCT
ejpam-6927	364	4	m.	m.	NOUN
ejpam-6927	364	5	adil	adil	PROPN
ejpam-6927	364	6	khan	khan	PROPN
ejpam-6927	364	7	,	,	PUNCT
ejpam-6927	364	8	z.	z.	PROPN
ejpam-6927	364	9	husain	husain	PROPN
ejpam-6927	364	10	,	,	PUNCT
ejpam-6927	364	11	and	and	CCONJ
ejpam-6927	364	12	y.-m	y.-m	NOUN
ejpam-6927	364	13	.	.	PUNCT
ejpam-6927	365	1	chu	chu	PROPN
ejpam-6927	365	2	.	.	PUNCT
ejpam-6927	366	1	new	new	ADJ
ejpam-6927	366	2	estimates	estimate	NOUN
ejpam-6927	366	3	for	for	ADP
ejpam-6927	366	4	csiszár	csiszár	NOUN
ejpam-6927	366	5	divergence	divergence	NOUN
ejpam-6927	366	6	and	and	CCONJ
ejpam-6927	366	7	zipf	zipf	NOUN
ejpam-6927	366	8	–	–	PUNCT
ejpam-6927	366	9	mandelbrot	mandelbrot	PROPN
ejpam-6927	366	10	entropy	entropy	PROPN
ejpam-6927	366	11	via	via	ADP
ejpam-6927	366	12	jensen	jensen	PROPN
ejpam-6927	366	13	–	–	PUNCT
ejpam-6927	366	14	mercer	mercer	PROPN
ejpam-6927	366	15	’s	’s	PART
ejpam-6927	366	16	inequality	inequality	NOUN
ejpam-6927	366	17	.	.	PUNCT
ejpam-6927	367	1	complexity	complexity	NOUN
ejpam-6927	367	2	,	,	PUNCT
ejpam-6927	367	3	page	page	NOUN
ejpam-6927	367	4	8928691	8928691	NUM
ejpam-6927	367	5	,	,	PUNCT
ejpam-6927	367	6	2020	2020	NUM
ejpam-6927	367	7	.	.	PUNCT
ejpam-6927	368	1	[	[	X
ejpam-6927	368	2	3	3	X
ejpam-6927	368	3	]	]	PUNCT
ejpam-6927	368	4	s.	s.	PROPN
ejpam-6927	368	5	i.	i.	PROPN
ejpam-6927	368	6	bradanović	bradanović	PROPN
ejpam-6927	368	7	,	,	PUNCT
ejpam-6927	368	8	.	.	PUNCT
ejpam-6927	369	1	pečarić	pečarić	PROPN
ejpam-6927	369	2	,	,	PUNCT
ejpam-6927	369	3	and	and	CCONJ
ejpam-6927	369	4	j.	j.	PROPN
ejpam-6927	369	5	pečarić.	pečarić.	PROPN
ejpam-6927	369	6	n	n	CCONJ
ejpam-6927	369	7	-	-	PUNCT
ejpam-6927	369	8	convexity	convexity	NOUN
ejpam-6927	369	9	and	and	CCONJ
ejpam-6927	369	10	weighted	weight	VERB
ejpam-6927	369	11	majorization	majorization	NOUN
ejpam-6927	369	12	with	with	ADP
ejpam-6927	369	13	applications	application	NOUN
ejpam-6927	369	14	to	to	ADP
ejpam-6927	369	15	f	f	NOUN
ejpam-6927	369	16	-	-	PUNCT
ejpam-6927	369	17	divergences	divergence	NOUN
ejpam-6927	369	18	and	and	CCONJ
ejpam-6927	369	19	zipf	zipf	NOUN
ejpam-6927	369	20	–	–	PUNCT
ejpam-6927	369	21	mandelbrot	mandelbrot	PROPN
ejpam-6927	369	22	law	law	NOUN
ejpam-6927	369	23	.	.	PUNCT
ejpam-6927	370	1	periodica	periodica	PROPN
ejpam-6927	370	2	mathematica	mathematica	PROPN
ejpam-6927	370	3	hungarica	hungarica	PROPN
ejpam-6927	370	4	,	,	PUNCT
ejpam-6927	370	5	90:57–77	90:57–77	NUM
ejpam-6927	370	6	,	,	PUNCT
ejpam-6927	370	7	2025	2025	NUM
ejpam-6927	370	8	.	.	PUNCT
ejpam-6927	371	1	[	[	X
ejpam-6927	371	2	4	4	NUM
ejpam-6927	371	3	]	]	PUNCT
ejpam-6927	371	4	ç.	ç.	ADP
ejpam-6927	371	5	yıldız	yıldız	PROPN
ejpam-6927	371	6	.	.	PUNCT
ejpam-6927	372	1	new	new	ADJ
ejpam-6927	372	2	inequalities	inequality	NOUN
ejpam-6927	372	3	of	of	ADP
ejpam-6927	372	4	the	the	DET
ejpam-6927	372	5	hermite	hermite	ADJ
ejpam-6927	372	6	–	–	PUNCT
ejpam-6927	372	7	hadamard	hadamard	ADJ
ejpam-6927	372	8	type	type	NOUN
ejpam-6927	372	9	for	for	ADP
ejpam-6927	372	10	n	n	CCONJ
ejpam-6927	372	11	-	-	PUNCT
ejpam-6927	372	12	times	time	NOUN
ejpam-6927	372	13	differentiable	differentiable	ADJ
ejpam-6927	372	14	functions	function	NOUN
ejpam-6927	372	15	which	which	PRON
ejpam-6927	372	16	are	be	AUX
ejpam-6927	372	17	quasi	quasi	ADJ
ejpam-6927	372	18	-	-	ADJ
ejpam-6927	372	19	convex	convex	ADJ
ejpam-6927	372	20	.	.	PUNCT
ejpam-6927	373	1	journal	journal	PROPN
ejpam-6927	373	2	of	of	ADP
ejpam-6927	373	3	mathematical	mathematical	ADJ
ejpam-6927	373	4	inequalities	inequality	NOUN
ejpam-6927	373	5	,	,	PUNCT
ejpam-6927	373	6	10(3):703	10(3):703	NUM
ejpam-6927	373	7	–	–	PUNCT
ejpam-6927	373	8	711	711	NUM
ejpam-6927	373	9	,	,	PUNCT
ejpam-6927	373	10	2016	2016	NUM
ejpam-6927	373	11	.	.	PUNCT
ejpam-6927	374	1	[	[	X
ejpam-6927	374	2	5	5	X
ejpam-6927	374	3	]	]	PUNCT
ejpam-6927	374	4	s.	s.	PROPN
ejpam-6927	374	5	s.	s.	PROPN
ejpam-6927	374	6	dragomir	dragomir	PROPN
ejpam-6927	374	7	and	and	CCONJ
ejpam-6927	374	8	r.	r.	PROPN
ejpam-6927	374	9	agarwal	agarwal	PROPN
ejpam-6927	374	10	.	.	PUNCT
ejpam-6927	375	1	two	two	NUM
ejpam-6927	375	2	inequalities	inequality	NOUN
ejpam-6927	375	3	for	for	ADP
ejpam-6927	375	4	differentiable	differentiable	ADJ
ejpam-6927	375	5	mappings	mapping	NOUN
ejpam-6927	375	6	and	and	CCONJ
ejpam-6927	375	7	applications	application	NOUN
ejpam-6927	375	8	to	to	ADP
ejpam-6927	375	9	special	special	ADJ
ejpam-6927	375	10	means	mean	NOUN
ejpam-6927	375	11	of	of	ADP
ejpam-6927	375	12	real	real	ADJ
ejpam-6927	375	13	numbers	number	NOUN
ejpam-6927	375	14	and	and	CCONJ
ejpam-6927	375	15	to	to	ADP
ejpam-6927	375	16	trapezoidal	trapezoidal	ADJ
ejpam-6927	375	17	formula	formula	NOUN
ejpam-6927	375	18	.	.	PUNCT
ejpam-6927	376	1	applied	apply	VERB
ejpam-6927	376	2	mathematics	mathematics	NOUN
ejpam-6927	376	3	letters	letter	NOUN
ejpam-6927	376	4	,	,	PUNCT
ejpam-6927	376	5	11(5):91–95	11(5):91–95	NUM
ejpam-6927	376	6	,	,	PUNCT
ejpam-6927	376	7	1998	1998	NUM
ejpam-6927	376	8	.	.	PUNCT
ejpam-6927	377	1	[	[	X
ejpam-6927	377	2	6	6	NUM
ejpam-6927	377	3	]	]	PUNCT
ejpam-6927	377	4	s.	s.	PROPN
ejpam-6927	377	5	s.	s.	PROPN
ejpam-6927	377	6	dragomir	dragomir	PROPN
ejpam-6927	377	7	.	.	PUNCT
ejpam-6927	378	1	on	on	ADP
ejpam-6927	378	2	some	some	DET
ejpam-6927	378	3	new	new	ADJ
ejpam-6927	378	4	inequalities	inequality	NOUN
ejpam-6927	378	5	of	of	ADP
ejpam-6927	378	6	hermite	hermite	ADJ
ejpam-6927	378	7	–	–	PUNCT
ejpam-6927	378	8	hadamard	hadamard	ADJ
ejpam-6927	378	9	type	type	NOUN
ejpam-6927	378	10	for	for	ADP
ejpam-6927	378	11	m	m	NOUN
ejpam-6927	378	12	-	-	ADJ
ejpam-6927	378	13	convex	convex	ADJ
ejpam-6927	378	14	functions	function	NOUN
ejpam-6927	378	15	.	.	PUNCT
ejpam-6927	379	1	tamkang	tamkang	PROPN
ejpam-6927	379	2	journal	journal	PROPN
ejpam-6927	379	3	of	of	ADP
ejpam-6927	379	4	mathematics	mathematic	NOUN
ejpam-6927	379	5	,	,	PUNCT
ejpam-6927	379	6	33(1):45–56	33(1):45–56	NUM
ejpam-6927	379	7	,	,	PUNCT
ejpam-6927	379	8	2002	2002	NUM
ejpam-6927	379	9	.	.	PUNCT
ejpam-6927	380	1	[	[	X
ejpam-6927	380	2	7	7	X
ejpam-6927	380	3	]	]	X
ejpam-6927	380	4	c.	c.	PROPN
ejpam-6927	380	5	p.	p.	PROPN
ejpam-6927	380	6	niculescu	niculescu	PROPN
ejpam-6927	380	7	and	and	CCONJ
ejpam-6927	380	8	l.	l.	PROPN
ejpam-6927	380	9	e.	e.	PROPN
ejpam-6927	380	10	persson	persson	PROPN
ejpam-6927	380	11	.	.	PUNCT
ejpam-6927	381	1	convex	convex	NOUN
ejpam-6927	381	2	functions	function	NOUN
ejpam-6927	381	3	and	and	CCONJ
ejpam-6927	381	4	their	their	PRON
ejpam-6927	381	5	applications	application	NOUN
ejpam-6927	381	6	:	:	PUNCT
ejpam-6927	381	7	a	a	DET
ejpam-6927	381	8	contemporary	contemporary	ADJ
ejpam-6927	381	9	approach	approach	NOUN
ejpam-6927	381	10	.	.	PUNCT
ejpam-6927	382	1	cms	cms	NOUN
ejpam-6927	382	2	books	book	NOUN
ejpam-6927	382	3	in	in	ADP
ejpam-6927	382	4	mathematics	mathematic	NOUN
ejpam-6927	382	5	.	.	PUNCT
ejpam-6927	383	1	springer	springer	NOUN
ejpam-6927	383	2	,	,	PUNCT
ejpam-6927	383	3	2	2	NUM
ejpam-6927	383	4	edition	edition	NOUN
ejpam-6927	383	5	,	,	PUNCT
ejpam-6927	383	6	2017	2017	NUM
ejpam-6927	383	7	.	.	PUNCT
ejpam-6927	384	1	[	[	X
ejpam-6927	384	2	8	8	NUM
ejpam-6927	384	3	]	]	PUNCT
ejpam-6927	384	4	m.	m.	NOUN
ejpam-6927	384	5	a.	a.	PROPN
ejpam-6927	384	6	latif	latif	PROPN
ejpam-6927	384	7	and	and	CCONJ
ejpam-6927	384	8	s.	s.	PROPN
ejpam-6927	384	9	s.	s.	PROPN
ejpam-6927	384	10	dragomir	dragomir	PROPN
ejpam-6927	384	11	.	.	PUNCT
ejpam-6927	385	1	on	on	ADP
ejpam-6927	385	2	some	some	DET
ejpam-6927	385	3	new	new	ADJ
ejpam-6927	385	4	inequalities	inequality	NOUN
ejpam-6927	385	5	for	for	ADP
ejpam-6927	385	6	differentiable	differentiable	ADJ
ejpam-6927	385	7	coordinated	coordinate	VERB
ejpam-6927	385	8	convex	convex	NOUN
ejpam-6927	385	9	functions	function	NOUN
ejpam-6927	385	10	.	.	PUNCT
ejpam-6927	386	1	journal	journal	PROPN
ejpam-6927	386	2	of	of	ADP
ejpam-6927	386	3	inequalities	inequality	NOUN
ejpam-6927	386	4	and	and	CCONJ
ejpam-6927	386	5	applications	application	NOUN
ejpam-6927	386	6	,	,	PUNCT
ejpam-6927	386	7	2012:28	2012:28	NUM
ejpam-6927	386	8	,	,	PUNCT
ejpam-6927	386	9	2012	2012	NUM
ejpam-6927	386	10	.	.	PUNCT
ejpam-6927	387	1	[	[	X
ejpam-6927	387	2	9	9	NUM
ejpam-6927	387	3	]	]	X
ejpam-6927	387	4	g.	g.	PROPN
ejpam-6927	387	5	rahman	rahman	PROPN
ejpam-6927	387	6	,	,	PUNCT
ejpam-6927	387	7	t.	t.	PROPN
ejpam-6927	387	8	abdeljawad	abdeljawad	PROPN
ejpam-6927	387	9	,	,	PUNCT
ejpam-6927	387	10	f.	f.	PROPN
ejpam-6927	387	11	jarad	jarad	PROPN
ejpam-6927	387	12	,	,	PUNCT
ejpam-6927	387	13	and	and	CCONJ
ejpam-6927	387	14	k.	k.	PROPN
ejpam-6927	387	15	s.	s.	PROPN
ejpam-6927	387	16	nisar	nisar	PROPN
ejpam-6927	387	17	.	.	PUNCT
ejpam-6927	388	1	bounds	bound	NOUN
ejpam-6927	388	2	of	of	ADP
ejpam-6927	388	3	generalized	generalized	ADJ
ejpam-6927	388	4	proportional	proportional	ADJ
ejpam-6927	388	5	fractional	fractional	ADJ
ejpam-6927	388	6	integrals	integral	NOUN
ejpam-6927	388	7	in	in	ADP
ejpam-6927	388	8	general	general	ADJ
ejpam-6927	388	9	form	form	NOUN
ejpam-6927	388	10	via	via	ADP
ejpam-6927	388	11	convex	convex	NOUN
ejpam-6927	388	12	functions	function	NOUN
ejpam-6927	388	13	and	and	CCONJ
ejpam-6927	388	14	their	their	PRON
ejpam-6927	388	15	applications	application	NOUN
ejpam-6927	388	16	.	.	PUNCT
ejpam-6927	389	1	mathematics	mathematic	NOUN
ejpam-6927	389	2	,	,	PUNCT
ejpam-6927	389	3	8(1):113	8(1):113	NUM
ejpam-6927	389	4	,	,	PUNCT
ejpam-6927	389	5	2020	2020	NUM
ejpam-6927	389	6	.	.	PUNCT
ejpam-6927	390	1	[	[	X
ejpam-6927	390	2	10	10	NUM
ejpam-6927	390	3	]	]	X
ejpam-6927	390	4	v.	v.	CCONJ
ejpam-6927	390	5	kac	kac	PROPN
ejpam-6927	390	6	and	and	CCONJ
ejpam-6927	390	7	p.	p.	PROPN
ejpam-6927	390	8	cheung	cheung	PROPN
ejpam-6927	390	9	.	.	PUNCT
ejpam-6927	390	10	quantum	quantum	PROPN
ejpam-6927	390	11	calculus	calculus	NOUN
ejpam-6927	390	12	.	.	PUNCT
ejpam-6927	390	13	springer	springer	NOUN
ejpam-6927	390	14	,	,	PUNCT
ejpam-6927	390	15	new	new	PROPN
ejpam-6927	390	16	york	york	PROPN
ejpam-6927	390	17	,	,	PUNCT
ejpam-6927	390	18	2002	2002	NUM
ejpam-6927	390	19	.	.	PUNCT
ejpam-6927	391	1	[	[	X
ejpam-6927	391	2	11	11	NUM
ejpam-6927	391	3	]	]	PUNCT
ejpam-6927	391	4	j.	j.	PROPN
ejpam-6927	391	5	tariboon	tariboon	PROPN
ejpam-6927	391	6	and	and	CCONJ
ejpam-6927	391	7	s.	s.	PROPN
ejpam-6927	391	8	k.	k.	PROPN
ejpam-6927	391	9	ntouyas	ntouyas	PROPN
ejpam-6927	391	10	.	.	PUNCT
ejpam-6927	392	1	quantum	quantum	ADJ
ejpam-6927	392	2	calculus	calculus	NOUN
ejpam-6927	392	3	on	on	ADP
ejpam-6927	392	4	finite	finite	ADJ
ejpam-6927	392	5	intervals	interval	NOUN
ejpam-6927	392	6	and	and	CCONJ
ejpam-6927	392	7	applications	application	NOUN
ejpam-6927	392	8	to	to	ADP
ejpam-6927	392	9	impulsive	impulsive	ADJ
ejpam-6927	392	10	difference	difference	NOUN
ejpam-6927	392	11	equations	equation	NOUN
ejpam-6927	392	12	.	.	PUNCT
ejpam-6927	393	1	advances	advance	NOUN
ejpam-6927	393	2	in	in	ADP
ejpam-6927	393	3	difference	difference	NOUN
ejpam-6927	393	4	equations	equation	NOUN
ejpam-6927	393	5	,	,	PUNCT
ejpam-6927	393	6	2013:28	2013:28	NUM
ejpam-6927	393	7	,	,	PUNCT
ejpam-6927	393	8	2013	2013	NUM
ejpam-6927	393	9	.	.	PUNCT
ejpam-6927	394	1	[	[	X
ejpam-6927	394	2	12	12	NUM
ejpam-6927	394	3	]	]	PUNCT
ejpam-6927	394	4	m.	m.	NOUN
ejpam-6927	394	5	kunt	kunt	PROPN
ejpam-6927	394	6	and	and	CCONJ
ejpam-6927	394	7	i.	i.	PROPN
ejpam-6927	394	8	iscan	iscan	PROPN
ejpam-6927	394	9	.	.	PUNCT
ejpam-6927	395	1	erratum	erratum	PROPN
ejpam-6927	395	2	:	:	PUNCT
ejpam-6927	395	3	quantum	quantum	ADJ
ejpam-6927	395	4	integral	integral	ADJ
ejpam-6927	395	5	inequalities	inequality	NOUN
ejpam-6927	395	6	on	on	ADP
ejpam-6927	395	7	finite	finite	ADJ
ejpam-6927	395	8	intervals	interval	NOUN
ejpam-6927	395	9	,	,	PUNCT
ejpam-6927	395	10	2016	2016	NUM
ejpam-6927	395	11	.	.	PUNCT
ejpam-6927	396	1	available	available	ADJ
ejpam-6927	396	2	at	at	ADP
ejpam-6927	396	3	https://www.researchgate.net/publication/305303595	https://www.researchgate.net/publication/305303595	PROPN
ejpam-6927	396	4	.	.	PUNCT
ejpam-6927	397	1	m.	m.	PROPN
ejpam-6927	397	2	adil	adil	PROPN
ejpam-6927	397	3	khan	khan	PROPN
ejpam-6927	397	4	et	et	PROPN
ejpam-6927	397	5	al	al	PROPN
ejpam-6927	397	6	.	.	PUNCT
ejpam-6927	397	7	/	/	SYM
ejpam-6927	397	8	eur	eur	PROPN
ejpam-6927	397	9	.	.	PUNCT
ejpam-6927	398	1	j.	j.	PROPN
ejpam-6927	398	2	pure	pure	PROPN
ejpam-6927	398	3	appl	appl	PROPN
ejpam-6927	398	4	.	.	PROPN
ejpam-6927	398	5	math	math	PROPN
ejpam-6927	398	6	,	,	PUNCT
ejpam-6927	398	7	18	18	NUM
ejpam-6927	398	8	(	(	PUNCT
ejpam-6927	398	9	4	4	NUM
ejpam-6927	398	10	)	)	PUNCT
ejpam-6927	398	11	(	(	PUNCT
ejpam-6927	398	12	2025	2025	NUM
ejpam-6927	398	13	)	)	PUNCT
ejpam-6927	398	14	,	,	PUNCT
ejpam-6927	398	15	6927	6927	NUM
ejpam-6927	398	16	18	18	NUM
ejpam-6927	398	17	of	of	ADP
ejpam-6927	398	18	18	18	NUM
ejpam-6927	398	19	[	[	SYM
ejpam-6927	398	20	13	13	NUM
ejpam-6927	398	21	]	]	X
ejpam-6927	398	22	n.	n.	PROPN
ejpam-6927	398	23	alp	alp	PROPN
ejpam-6927	398	24	,	,	PUNCT
ejpam-6927	398	25	m.	m.	NOUN
ejpam-6927	398	26	z.	z.	PROPN
ejpam-6927	398	27	sarikaya	sarikaya	PROPN
ejpam-6927	398	28	,	,	PUNCT
ejpam-6927	398	29	m.	m.	NOUN
ejpam-6927	398	30	kunt	kunt	PROPN
ejpam-6927	398	31	,	,	PUNCT
ejpam-6927	398	32	and	and	CCONJ
ejpam-6927	398	33	i.	i.	PROPN
ejpam-6927	398	34	iscan	iscan	PROPN
ejpam-6927	398	35	.	.	PUNCT
ejpam-6927	399	1	q	q	X
ejpam-6927	399	2	-	-	PUNCT
ejpam-6927	399	3	hermite	hermite	ADJ
ejpam-6927	399	4	–	–	PUNCT
ejpam-6927	399	5	hadamard	hadamard	ADJ
ejpam-6927	399	6	inequalities	inequality	NOUN
ejpam-6927	399	7	and	and	CCONJ
ejpam-6927	399	8	quantum	quantum	NOUN
ejpam-6927	399	9	estimates	estimate	NOUN
ejpam-6927	399	10	for	for	ADP
ejpam-6927	399	11	midpoint	midpoint	NOUN
ejpam-6927	399	12	type	type	NOUN
ejpam-6927	399	13	inequalities	inequality	NOUN
ejpam-6927	399	14	via	via	ADP
ejpam-6927	399	15	convex	convex	NOUN
ejpam-6927	399	16	and	and	CCONJ
ejpam-6927	399	17	quasi	quasi	ADJ
ejpam-6927	399	18	-	-	ADJ
ejpam-6927	399	19	convex	convex	ADJ
ejpam-6927	399	20	functions	function	NOUN
ejpam-6927	399	21	.	.	PUNCT
ejpam-6927	400	1	journal	journal	NOUN
ejpam-6927	400	2	of	of	ADP
ejpam-6927	400	3	king	king	PROPN
ejpam-6927	400	4	saud	saud	PROPN
ejpam-6927	400	5	university	university	PROPN
ejpam-6927	400	6	science	science	NOUN
ejpam-6927	400	7	,	,	PUNCT
ejpam-6927	400	8	30:193–203	30:193–203	PROPN
ejpam-6927	400	9	,	,	PUNCT
ejpam-6927	400	10	2018	2018	NUM
ejpam-6927	400	11	.	.	PUNCT
ejpam-6927	401	1	[	[	X
ejpam-6927	401	2	14	14	NUM
ejpam-6927	401	3	]	]	X
ejpam-6927	401	4	m.	m.	PROPN
ejpam-6927	401	5	a.	a.	PROPN
ejpam-6927	401	6	ali	ali	PROPN
ejpam-6927	401	7	,	,	PUNCT
ejpam-6927	401	8	h.	h.	PROPN
ejpam-6927	401	9	budak	budak	PROPN
ejpam-6927	401	10	,	,	PUNCT
ejpam-6927	401	11	m.	m.	NOUN
ejpam-6927	401	12	abass	abass	PROPN
ejpam-6927	401	13	,	,	PUNCT
ejpam-6927	401	14	and	and	CCONJ
ejpam-6927	401	15	y.-m	y.-m	NOUN
ejpam-6927	401	16	.	.	PUNCT
ejpam-6927	402	1	chu	chu	PROPN
ejpam-6927	402	2	.	.	PUNCT
ejpam-6927	402	3	quantum	quantum	PROPN
ejpam-6927	402	4	hermite	hermite	PROPN
ejpam-6927	402	5	–	–	PUNCT
ejpam-6927	402	6	hadamardtype	hadamardtype	NOUN
ejpam-6927	402	7	inequalities	inequality	NOUN
ejpam-6927	402	8	for	for	ADP
ejpam-6927	402	9	functions	function	NOUN
ejpam-6927	402	10	with	with	ADP
ejpam-6927	402	11	convex	convex	ADJ
ejpam-6927	402	12	absolute	absolute	ADJ
ejpam-6927	402	13	values	value	NOUN
ejpam-6927	402	14	of	of	ADP
ejpam-6927	402	15	second	second	ADJ
ejpam-6927	402	16	qω2	qω2	NOUN
ejpam-6927	402	17	-	-	NOUN
ejpam-6927	402	18	derivatives	derivative	NOUN
ejpam-6927	402	19	.	.	PUNCT
ejpam-6927	403	1	advances	advance	NOUN
ejpam-6927	403	2	in	in	ADP
ejpam-6927	403	3	difference	difference	NOUN
ejpam-6927	403	4	equations	equation	NOUN
ejpam-6927	403	5	,	,	PUNCT
ejpam-6927	403	6	2021:7	2021:7	NUM
ejpam-6927	403	7	,	,	PUNCT
ejpam-6927	403	8	2021	2021	NUM
ejpam-6927	403	9	.	.	PUNCT
ejpam-6927	404	1	[	[	X
ejpam-6927	404	2	15	15	NUM
ejpam-6927	404	3	]	]	X
ejpam-6927	404	4	m.	m.	NOUN
ejpam-6927	404	5	a.	a.	PROPN
ejpam-6927	404	6	noor	noor	PROPN
ejpam-6927	404	7	,	,	PUNCT
ejpam-6927	404	8	k.	k.	PROPN
ejpam-6927	404	9	i.	i.	PROPN
ejpam-6927	404	10	noor	noor	PROPN
ejpam-6927	404	11	,	,	PUNCT
ejpam-6927	404	12	and	and	CCONJ
ejpam-6927	404	13	m.	m.	NOUN
ejpam-6927	404	14	u.	u.	PROPN
ejpam-6927	404	15	awan	awan	PROPN
ejpam-6927	404	16	.	.	PUNCT
ejpam-6927	405	1	some	some	DET
ejpam-6927	405	2	quantum	quantum	ADJ
ejpam-6927	405	3	estimates	estimate	NOUN
ejpam-6927	405	4	for	for	ADP
ejpam-6927	405	5	hermite	hermite	ADJ
ejpam-6927	405	6	–	–	PUNCT
ejpam-6927	405	7	hadamard	hadamard	ADJ
ejpam-6927	405	8	inequalities	inequality	NOUN
ejpam-6927	405	9	.	.	PUNCT
ejpam-6927	406	1	applied	apply	VERB
ejpam-6927	406	2	mathematics	mathematic	NOUN
ejpam-6927	406	3	and	and	CCONJ
ejpam-6927	406	4	computation	computation	NOUN
ejpam-6927	406	5	,	,	PUNCT
ejpam-6927	406	6	251:675–679	251:675–679	NUM
ejpam-6927	406	7	,	,	PUNCT
ejpam-6927	406	8	2015	2015	NUM
ejpam-6927	406	9	.	.	PUNCT
ejpam-6927	407	1	[	[	X
ejpam-6927	407	2	16	16	NUM
ejpam-6927	407	3	]	]	PUNCT
ejpam-6927	407	4	a.	a.	PROPN
ejpam-6927	407	5	f.	f.	PROPN
ejpam-6927	407	6	shah	shah	PROPN
ejpam-6927	407	7	,	,	PUNCT
ejpam-6927	407	8	s.	s.	PROPN
ejpam-6927	407	9	m.	m.	PROPN
ejpam-6927	407	10	boulaaras	boulaaras	PROPN
ejpam-6927	407	11	,	,	PUNCT
ejpam-6927	407	12	p.	p.	PROPN
ejpam-6927	407	13	j.	j.	PROPN
ejpam-6927	407	14	wong	wong	PROPN
ejpam-6927	407	15	,	,	PUNCT
ejpam-6927	407	16	m.	m.	PROPN
ejpam-6927	407	17	s.	s.	PROPN
ejpam-6927	407	18	saleem	saleem	PROPN
ejpam-6927	407	19	,	,	PUNCT
ejpam-6927	407	20	and	and	CCONJ
ejpam-6927	407	21	s.	s.	PROPN
ejpam-6927	407	22	m.	m.	PROPN
ejpam-6927	407	23	umair	umair	PROPN
ejpam-6927	407	24	.	.	PUNCT
ejpam-6927	408	1	quantum	quantum	ADJ
ejpam-6927	408	2	integral	integral	ADJ
ejpam-6927	408	3	inequalities	inequality	NOUN
ejpam-6927	408	4	via	via	ADP
ejpam-6927	408	5	different	different	ADJ
ejpam-6927	408	6	variants	variant	NOUN
ejpam-6927	408	7	of	of	ADP
ejpam-6927	408	8	parameterized	parameterized	ADJ
ejpam-6927	408	9	harmonically	harmonically	ADV
ejpam-6927	408	10	convex	convex	NOUN
ejpam-6927	408	11	functions	function	NOUN
ejpam-6927	408	12	on	on	ADP
ejpam-6927	408	13	finite	finite	ADJ
ejpam-6927	408	14	intervals	interval	NOUN
ejpam-6927	408	15	with	with	ADP
ejpam-6927	408	16	related	related	ADJ
ejpam-6927	408	17	applications	application	NOUN
ejpam-6927	408	18	.	.	PUNCT
ejpam-6927	409	1	mathematical	mathematical	ADJ
ejpam-6927	409	2	methods	method	NOUN
ejpam-6927	409	3	in	in	ADP
ejpam-6927	409	4	the	the	DET
ejpam-6927	409	5	applied	apply	VERB
ejpam-6927	409	6	sciences	science	NOUN
ejpam-6927	409	7	,	,	PUNCT
ejpam-6927	409	8	48:9194–9206	48:9194–9206	NUM
ejpam-6927	409	9	,	,	PUNCT
ejpam-6927	409	10	2025	2025	NUM
ejpam-6927	409	11	.	.	PUNCT
ejpam-6927	410	1	[	[	X
ejpam-6927	410	2	17	17	NUM
ejpam-6927	410	3	]	]	PUNCT
ejpam-6927	410	4	s.	s.	PROPN
ejpam-6927	410	5	i.	i.	PROPN
ejpam-6927	410	6	butt	butt	PROPN
ejpam-6927	410	7	,	,	PUNCT
ejpam-6927	410	8	m.	m.	NOUN
ejpam-6927	410	9	n.	n.	PROPN
ejpam-6927	410	10	aftab	aftab	PROPN
ejpam-6927	410	11	,	,	PUNCT
ejpam-6927	410	12	h.	h.	PROPN
ejpam-6927	410	13	a.	a.	PROPN
ejpam-6927	410	14	nabwey	nabwey	PROPN
ejpam-6927	410	15	,	,	PUNCT
ejpam-6927	410	16	and	and	CCONJ
ejpam-6927	410	17	s.	s.	PROPN
ejpam-6927	410	18	etemad	etemad	PROPN
ejpam-6927	410	19	.	.	PUNCT
ejpam-6927	411	1	some	some	DET
ejpam-6927	411	2	hermite	hermite	ADJ
ejpam-6927	411	3	–	–	PUNCT
ejpam-6927	411	4	hadamard	hadamard	ADJ
ejpam-6927	411	5	and	and	CCONJ
ejpam-6927	411	6	midpoint	midpoint	NOUN
ejpam-6927	411	7	type	type	NOUN
ejpam-6927	411	8	inequalities	inequality	NOUN
ejpam-6927	411	9	in	in	ADP
ejpam-6927	411	10	symmetric	symmetric	ADJ
ejpam-6927	411	11	quantum	quantum	NOUN
ejpam-6927	411	12	calculus	calculus	NOUN
ejpam-6927	411	13	.	.	PUNCT
ejpam-6927	412	1	aims	aim	VERB
ejpam-6927	412	2	mathematics	mathematic	NOUN
ejpam-6927	412	3	,	,	PUNCT
ejpam-6927	412	4	9(3):5523–5549	9(3):5523–5549	NOUN
ejpam-6927	412	5	,	,	PUNCT
ejpam-6927	412	6	2024	2024	NUM
ejpam-6927	412	7	.	.	PUNCT
ejpam-6927	413	1	[	[	X
ejpam-6927	413	2	18	18	NUM
ejpam-6927	413	3	]	]	X
ejpam-6927	413	4	s.	s.	PROPN
ejpam-6927	413	5	i.	i.	PROPN
ejpam-6927	413	6	butt	butt	PROPN
ejpam-6927	413	7	,	,	PUNCT
ejpam-6927	413	8	m.	m.	NOUN
ejpam-6927	413	9	n.	n.	PROPN
ejpam-6927	413	10	aftab	aftab	PROPN
ejpam-6927	413	11	,	,	PUNCT
ejpam-6927	413	12	and	and	CCONJ
ejpam-6927	413	13	y.	y.	PROPN
ejpam-6927	413	14	seol	seol	PROPN
ejpam-6927	413	15	.	.	PUNCT
ejpam-6927	414	1	symmetric	symmetric	ADJ
ejpam-6927	414	2	quantum	quantum	ADJ
ejpam-6927	414	3	inequalities	inequality	NOUN
ejpam-6927	414	4	on	on	ADP
ejpam-6927	414	5	finite	finite	ADJ
ejpam-6927	414	6	rectangular	rectangular	ADJ
ejpam-6927	414	7	plane	plane	NOUN
ejpam-6927	414	8	.	.	PUNCT
ejpam-6927	415	1	mathematics	mathematic	NOUN
ejpam-6927	415	2	,	,	PUNCT
ejpam-6927	415	3	12(10	12(10	NUM
ejpam-6927	415	4	)	)	PUNCT
ejpam-6927	415	5	,	,	PUNCT
ejpam-6927	415	6	2024	2024	NUM
ejpam-6927	415	7	.	.	PUNCT
ejpam-6927	416	1	[	[	X
ejpam-6927	416	2	19	19	NUM
ejpam-6927	416	3	]	]	X
ejpam-6927	416	4	h.	h.	PROPN
ejpam-6927	416	5	budak	budak	PROPN
ejpam-6927	416	6	,	,	PUNCT
ejpam-6927	416	7	m.	m.	PROPN
ejpam-6927	416	8	a.	a.	PROPN
ejpam-6927	416	9	ali	ali	PROPN
ejpam-6927	416	10	,	,	PUNCT
ejpam-6927	416	11	and	and	CCONJ
ejpam-6927	416	12	m.	m.	PROPN
ejpam-6927	416	13	tarhanaci	tarhanaci	PROPN
ejpam-6927	416	14	.	.	PUNCT
ejpam-6927	417	1	some	some	DET
ejpam-6927	417	2	new	new	ADJ
ejpam-6927	417	3	quantum	quantum	ADJ
ejpam-6927	417	4	hermite	hermite	NOUN
ejpam-6927	417	5	–	–	PUNCT
ejpam-6927	417	6	hadamard	hadamard	NOUN
ejpam-6927	417	7	-	-	PUNCT
ejpam-6927	417	8	like	like	ADJ
ejpam-6927	417	9	inequalities	inequality	NOUN
ejpam-6927	417	10	for	for	ADP
ejpam-6927	417	11	coordinated	coordinated	ADJ
ejpam-6927	417	12	convex	convex	NOUN
ejpam-6927	417	13	functions	function	NOUN
ejpam-6927	417	14	.	.	PUNCT
ejpam-6927	418	1	journal	journal	NOUN
ejpam-6927	418	2	of	of	ADP
ejpam-6927	418	3	optimization	optimization	NOUN
ejpam-6927	418	4	theory	theory	NOUN
ejpam-6927	418	5	and	and	CCONJ
ejpam-6927	418	6	applications	application	NOUN
ejpam-6927	418	7	,	,	PUNCT
ejpam-6927	418	8	186:899–910	186:899–910	NUM
ejpam-6927	418	9	,	,	PUNCT
ejpam-6927	418	10	2020	2020	NUM
ejpam-6927	418	11	.	.	PUNCT
ejpam-6927	419	1	[	[	X
ejpam-6927	419	2	20	20	NUM
ejpam-6927	419	3	]	]	PUNCT
ejpam-6927	419	4	l.	l.	PROPN
ejpam-6927	419	5	ciurdariu	ciurdariu	PROPN
ejpam-6927	419	6	and	and	CCONJ
ejpam-6927	419	7	e.	e.	PROPN
ejpam-6927	419	8	grecu	grecu	PROPN
ejpam-6927	419	9	.	.	PUNCT
ejpam-6927	420	1	on	on	ADP
ejpam-6927	420	2	q	q	ADJ
ejpam-6927	420	3	-	-	PUNCT
ejpam-6927	420	4	hermite	hermite	ADJ
ejpam-6927	420	5	–	–	PUNCT
ejpam-6927	420	6	hadamard	hadamard	ADJ
ejpam-6927	420	7	type	type	NOUN
ejpam-6927	420	8	inequalities	inequality	NOUN
ejpam-6927	420	9	via	via	ADP
ejpam-6927	420	10	s	s	NOUN
ejpam-6927	420	11	-	-	NOUN
ejpam-6927	420	12	convexity	convexity	NOUN
ejpam-6927	420	13	and	and	CCONJ
ejpam-6927	420	14	(	(	PUNCT
ejpam-6927	420	15	a	a	PRON
ejpam-6927	420	16	,	,	PUNCT
ejpam-6927	420	17	m)-convexity	m)-convexity	NOUN
ejpam-6927	420	18	.	.	PROPN
ejpam-6927	420	19	fractal	fractal	PROPN
ejpam-6927	420	20	and	and	CCONJ
ejpam-6927	420	21	fractional	fractional	ADJ
ejpam-6927	420	22	,	,	PUNCT
ejpam-6927	420	23	8:1–12	8:1–12	NUM
ejpam-6927	420	24	,	,	PUNCT
ejpam-6927	420	25	2023	2023	NUM
ejpam-6927	420	26	.	.	PUNCT
ejpam-6927	421	1	[	[	X
ejpam-6927	421	2	21	21	NUM
ejpam-6927	421	3	]	]	PUNCT
ejpam-6927	421	4	x.	x.	NOUN
ejpam-6927	421	5	you	you	PRON
ejpam-6927	421	6	,	,	PUNCT
ejpam-6927	421	7	h.	h.	PROPN
ejpam-6927	421	8	kara	kara	PROPN
ejpam-6927	421	9	,	,	PUNCT
ejpam-6927	421	10	h.	h.	PROPN
ejpam-6927	421	11	budak	budak	PROPN
ejpam-6927	421	12	,	,	PUNCT
ejpam-6927	421	13	and	and	CCONJ
ejpam-6927	421	14	h.	h.	PROPN
ejpam-6927	421	15	kalsoom	kalsoom	PROPN
ejpam-6927	421	16	.	.	PUNCT
ejpam-6927	422	1	quantum	quantum	ADJ
ejpam-6927	422	2	inequalities	inequality	NOUN
ejpam-6927	422	3	of	of	ADP
ejpam-6927	422	4	hermite	hermite	ADJ
ejpam-6927	422	5	–	–	PUNCT
ejpam-6927	422	6	hadamard	hadamard	ADJ
ejpam-6927	422	7	type	type	NOUN
ejpam-6927	422	8	for	for	ADP
ejpam-6927	422	9	r	r	NOUN
ejpam-6927	422	10	-	-	PUNCT
ejpam-6927	422	11	convex	convex	NOUN
ejpam-6927	422	12	functions	function	NOUN
ejpam-6927	422	13	.	.	PUNCT
ejpam-6927	423	1	journal	journal	NOUN
ejpam-6927	423	2	of	of	ADP
ejpam-6927	423	3	mathematics	mathematic	NOUN
ejpam-6927	423	4	,	,	PUNCT
ejpam-6927	423	5	pages	page	NOUN
ejpam-6927	423	6	1–14	1–14	PROPN
ejpam-6927	423	7	,	,	PUNCT
ejpam-6927	423	8	2021	2021	NUM
ejpam-6927	423	9	.	.	PUNCT
ejpam-6927	424	1	[	[	X
ejpam-6927	424	2	22	22	NUM
ejpam-6927	424	3	]	]	X
ejpam-6927	424	4	f.	f.	PROPN
ejpam-6927	424	5	h.	h.	PROPN
ejpam-6927	424	6	jackson	jackson	PROPN
ejpam-6927	424	7	.	.	PUNCT
ejpam-6927	425	1	on	on	ADP
ejpam-6927	425	2	a	a	DET
ejpam-6927	425	3	q	q	ADJ
ejpam-6927	425	4	-	-	PUNCT
ejpam-6927	425	5	definite	definite	ADJ
ejpam-6927	425	6	integrals	integral	NOUN
ejpam-6927	425	7	.	.	PUNCT
ejpam-6927	426	1	the	the	DET
ejpam-6927	426	2	quarterly	quarterly	ADJ
ejpam-6927	426	3	journal	journal	NOUN
ejpam-6927	426	4	of	of	ADP
ejpam-6927	426	5	pure	pure	ADJ
ejpam-6927	426	6	and	and	CCONJ
ejpam-6927	426	7	applied	applied	ADJ
ejpam-6927	426	8	mathematics	mathematic	NOUN
ejpam-6927	426	9	,	,	PUNCT
ejpam-6927	426	10	41:193–203	41:193–203	NUM
ejpam-6927	426	11	,	,	PUNCT
ejpam-6927	426	12	1910	1910	NUM
ejpam-6927	426	13	.	.	PUNCT
ejpam-6927	427	1	[	[	X
ejpam-6927	427	2	23	23	NUM
ejpam-6927	427	3	]	]	X
ejpam-6927	427	4	f.	f.	PROPN
ejpam-6927	427	5	chen	chen	PROPN
ejpam-6927	427	6	and	and	CCONJ
ejpam-6927	427	7	w.	w.	PROPN
ejpam-6927	427	8	yang	yang	PROPN
ejpam-6927	427	9	.	.	PUNCT
ejpam-6927	428	1	some	some	DET
ejpam-6927	428	2	new	new	ADJ
ejpam-6927	428	3	chebyshev	chebyshev	NOUN
ejpam-6927	428	4	type	type	NOUN
ejpam-6927	428	5	quantum	quantum	ADJ
ejpam-6927	428	6	integral	integral	ADJ
ejpam-6927	428	7	inequalities	inequality	NOUN
ejpam-6927	428	8	on	on	ADP
ejpam-6927	428	9	finite	finite	ADJ
ejpam-6927	428	10	intervals	interval	NOUN
ejpam-6927	428	11	.	.	PUNCT
ejpam-6927	429	1	journal	journal	NOUN
ejpam-6927	429	2	of	of	ADP
ejpam-6927	429	3	applied	apply	VERB
ejpam-6927	429	4	analysis	analysis	NOUN
ejpam-6927	429	5	and	and	CCONJ
ejpam-6927	429	6	computation	computation	NOUN
ejpam-6927	429	7	,	,	PUNCT
ejpam-6927	429	8	21:417–426	21:417–426	PROPN
ejpam-6927	429	9	,	,	PUNCT
ejpam-6927	429	10	2016	2016	NUM
ejpam-6927	429	11	.	.	PUNCT
ejpam-6927	430	1	[	[	X
ejpam-6927	430	2	24	24	NUM
ejpam-6927	430	3	]	]	PUNCT
ejpam-6927	430	4	ç.	ç.	ADP
ejpam-6927	430	5	yıldız	yıldız	PROPN
ejpam-6927	430	6	and	and	CCONJ
ejpam-6927	430	7	l.	l.	PROPN
ejpam-6927	430	8	i.	i.	PROPN
ejpam-6927	430	9	cot̂ırlă.	cot̂ırlă.	NOUN
ejpam-6927	430	10	examining	examine	VERB
ejpam-6927	430	11	the	the	DET
ejpam-6927	430	12	hermite	hermite	ADJ
ejpam-6927	430	13	–	–	PUNCT
ejpam-6927	430	14	hadamard	hadamard	ADJ
ejpam-6927	430	15	inequalities	inequality	NOUN
ejpam-6927	430	16	for	for	ADP
ejpam-6927	430	17	kfractional	kfractional	ADJ
ejpam-6927	430	18	operators	operator	NOUN
ejpam-6927	430	19	using	use	VERB
ejpam-6927	430	20	the	the	DET
ejpam-6927	430	21	green	green	ADJ
ejpam-6927	430	22	function	function	NOUN
ejpam-6927	430	23	.	.	PUNCT
ejpam-6927	431	1	fractal	fractal	ADJ
ejpam-6927	431	2	and	and	CCONJ
ejpam-6927	431	3	fractional	fractional	ADJ
ejpam-6927	431	4	,	,	PUNCT
ejpam-6927	431	5	7:161	7:161	NUM
ejpam-6927	431	6	,	,	PUNCT
ejpam-6927	431	7	2023	2023	NUM
ejpam-6927	431	8	.	.	PUNCT
ejpam-6927	432	1	[	[	X
ejpam-6927	432	2	25	25	NUM
ejpam-6927	432	3	]	]	X
ejpam-6927	432	4	s.	s.	PROPN
ejpam-6927	432	5	i.	i.	PROPN
ejpam-6927	432	6	bradanović	bradanović	PROPN
ejpam-6927	432	7	,	,	PUNCT
ejpam-6927	432	8	n.	n.	PROPN
ejpam-6927	432	9	latif	latif	PROPN
ejpam-6927	432	10	,	,	PUNCT
ejpam-6927	432	11	and	and	CCONJ
ejpam-6927	432	12	j.	j.	PROPN
ejpam-6927	432	13	pečarić.	pečarić.	PROPN
ejpam-6927	432	14	generalizations	generalization	NOUN
ejpam-6927	432	15	of	of	ADP
ejpam-6927	432	16	sherman	sherman	PROPN
ejpam-6927	432	17	’s	’s	PART
ejpam-6927	432	18	inequality	inequality	NOUN
ejpam-6927	432	19	via	via	ADP
ejpam-6927	432	20	fink	fink	PROPN
ejpam-6927	432	21	’s	’s	PART
ejpam-6927	432	22	identity	identity	NOUN
ejpam-6927	432	23	and	and	CCONJ
ejpam-6927	432	24	green	green	PROPN
ejpam-6927	432	25	’s	’s	PART
ejpam-6927	432	26	function	function	NOUN
ejpam-6927	432	27	.	.	PUNCT
ejpam-6927	433	1	ukrainian	ukrainian	ADJ
ejpam-6927	433	2	mathematical	mathematical	ADJ
ejpam-6927	433	3	journal	journal	NOUN
ejpam-6927	433	4	,	,	PUNCT
ejpam-6927	433	5	70(8):1192	70(8):1192	NUM
ejpam-6927	433	6	–	–	PUNCT
ejpam-6927	433	7	1204	1204	NUM
ejpam-6927	433	8	,	,	PUNCT
ejpam-6927	433	9	2019	2019	NUM
ejpam-6927	433	10	.	.	PUNCT
ejpam-6927	434	1	[	[	X
ejpam-6927	434	2	26	26	NUM
ejpam-6927	434	3	]	]	PUNCT
ejpam-6927	434	4	a.	a.	NOUN
ejpam-6927	434	5	basir	basir	PROPN
ejpam-6927	434	6	,	,	PUNCT
ejpam-6927	434	7	m.	m.	PROPN
ejpam-6927	434	8	adil	adil	PROPN
ejpam-6927	434	9	khan	khan	PROPN
ejpam-6927	434	10	,	,	PUNCT
ejpam-6927	434	11	and	and	CCONJ
ejpam-6927	434	12	j.	j.	PROPN
ejpam-6927	434	13	pečarić.	pečarić.	PROPN
ejpam-6927	434	14	majorization	majorization	NOUN
ejpam-6927	434	15	type	type	NOUN
ejpam-6927	434	16	inequalities	inequality	NOUN
ejpam-6927	434	17	via	via	ADP
ejpam-6927	434	18	4	4	NUM
ejpam-6927	434	19	-	-	PUNCT
ejpam-6927	434	20	convex	convex	NOUN
ejpam-6927	434	21	functions	function	NOUN
ejpam-6927	434	22	.	.	PUNCT
ejpam-6927	435	1	journal	journal	NOUN
ejpam-6927	435	2	of	of	ADP
ejpam-6927	435	3	mathematical	mathematical	ADJ
ejpam-6927	435	4	inequalities	inequality	NOUN
ejpam-6927	435	5	,	,	PUNCT
ejpam-6927	435	6	18(1):51–67	18(1):51–67	NUM
ejpam-6927	435	7	,	,	PUNCT
ejpam-6927	435	8	2024	2024	NUM
ejpam-6927	435	9	.	.	PUNCT